LMFDB - Embedded newform 225.4.e.a.151.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,4,Mod(76,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.76"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.a.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68614 + 2.92048i) q^{2} +(1.50000 + 4.97494i) q^{3} +(-1.68614 - 2.92048i) q^{4} +(-17.0584 - 4.00772i) q^{6} +(0.813859 - 1.40965i) q^{7} -15.6060 q^{8} +(-22.5000 + 14.9248i) q^{9} +(16.4307 - 28.4588i) q^{11} +(12.0000 - 12.7692i) q^{12} +(-16.5109 - 28.5977i) q^{13} +(2.74456 + 4.75372i) q^{14} +(39.8030 - 68.9408i) q^{16} -110.307 q^{17} +(-5.64947 - 90.8762i) q^{18} -54.3070 q^{19} +(8.23369 + 1.93443i) q^{21} +(55.4090 + 95.9711i) q^{22} +(-33.7188 - 58.4026i) q^{23} +(-23.4090 - 77.6387i) q^{24} +111.359 q^{26} +(-108.000 - 89.5489i) q^{27} -5.48913 q^{28} +(-137.259 + 237.740i) q^{29} +(3.00000 + 5.19615i) q^{31} +(71.8030 + 124.366i) q^{32} +(166.227 + 39.0535i) q^{33} +(185.993 - 322.150i) q^{34} +(81.5258 + 40.5455i) q^{36} +347.723 q^{37} +(91.5693 - 158.603i) q^{38} +(117.505 - 125.037i) q^{39} +(-145.668 - 252.305i) q^{41} +(-19.5326 + 20.7846i) q^{42} +(100.694 - 174.408i) q^{43} -110.818 q^{44} +227.418 q^{46} +(-241.048 + 417.507i) q^{47} +(402.681 + 94.6062i) q^{48} +(170.175 + 294.752i) q^{49} +(-165.461 - 548.771i) q^{51} +(-55.6793 + 96.4394i) q^{52} +175.228 q^{53} +(443.629 - 164.420i) q^{54} +(-12.7011 + 21.9989i) q^{56} +(-81.4605 - 270.174i) q^{57} +(-462.878 - 801.728i) q^{58} +(91.6209 + 158.692i) q^{59} +(-218.297 + 378.102i) q^{61} -20.2337 q^{62} +(2.72686 + 43.8637i) q^{63} +152.568 q^{64} +(-394.337 + 419.613i) q^{66} +(-415.750 - 720.100i) q^{67} +(185.993 + 322.150i) q^{68} +(239.971 - 255.353i) q^{69} -118.951 q^{71} +(351.134 - 232.916i) q^{72} -183.318 q^{73} +(-586.310 + 1015.52i) q^{74} +(91.5693 + 158.603i) q^{76} +(-26.7446 - 46.3229i) q^{77} +(167.038 + 554.002i) q^{78} +(319.147 - 552.778i) q^{79} +(283.500 - 671.617i) q^{81} +982.470 q^{82} +(-747.322 + 1294.40i) q^{83} +(-8.23369 - 27.3081i) q^{84} +(339.569 + 588.151i) q^{86} +(-1388.63 - 326.247i) q^{87} +(-256.417 + 444.127i) q^{88} -1437.27 q^{89} -53.7501 q^{91} +(-113.709 + 196.950i) q^{92} +(-21.3505 + 22.7190i) q^{93} +(-812.880 - 1407.95i) q^{94} +(-511.011 + 543.765i) q^{96} +(-445.884 + 772.294i) q^{97} -1147.76 q^{98} +(55.0516 + 885.548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 6 q^{3} - q^{4} - 51 q^{6} + 9 q^{7} + 18 q^{8} - 90 q^{9} + 37 q^{11} + 48 q^{12} - 112 q^{13} - 12 q^{14} + 119 q^{16} - 154 q^{17} - 126 q^{18} + 70 q^{19} - 36 q^{21} + 101 q^{22} - 267 q^{23}+ \cdots - 90 q^{99}+O(q^{100}) $ 4 * q - q^2 + 6 * q^3 - q^4 - 51 * q^6 + 9 * q^7 + 18 * q^8 - 90 * q^9 + 37 * q^11 + 48 * q^12 - 112 * q^13 - 12 * q^14 + 119 * q^16 - 154 * q^17 - 126 * q^18 + 70 * q^19 - 36 * q^21 + 101 * q^22 - 267 * q^23 + 27 * q^24 - 152 * q^26 - 432 * q^27 + 24 * q^28 - 325 * q^29 + 12 * q^31 + 247 * q^32 + 303 * q^33 + 451 * q^34 + 171 * q^36 + 1276 * q^37 + 395 * q^38 - 564 * q^39 - 238 * q^41 - 216 * q^42 - 97 * q^43 - 202 * q^44 - 492 * q^46 - 901 * q^47 + 525 * q^48 + 629 * q^49 - 231 * q^51 + 76 * q^52 - 448 * q^53 + 999 * q^54 + 156 * q^56 + 105 * q^57 - 806 * q^58 + 85 * q^59 + 247 * q^61 - 12 * q^62 - 351 * q^63 + 1426 * q^64 - 888 * q^66 - 606 * q^67 + 451 * q^68 - 1539 * q^69 + 788 * q^71 - 405 * q^72 + 1622 * q^73 - 484 * q^74 + 395 * q^76 - 84 * q^77 - 228 * q^78 + 840 * q^79 + 1134 * q^81 + 2218 * q^82 - 387 * q^83 + 36 * q^84 + 1387 * q^86 - 2418 * q^87 - 411 * q^88 - 2130 * q^89 - 1272 * q^91 + 246 * q^92 + 18 * q^93 - 632 * q^94 + 24 * q^96 - 1031 * q^97 - 926 * q^98 - 90 * q^99

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.68614	+	2.92048i	−0.596141	+	1.03255i	0.397244	+	0.917713i	$0.369967\pi$
$2$	−1.68614	+	2.92048i	−0.596141	+	1.03255i	−0.993385	+	0.114833i	$0.963367\pi$
$3$	1.50000	+	4.97494i	0.288675	+	0.957427i
$3$	1.50000	+	4.97494i	0.288675	+	0.957427i
$4$	−1.68614	−	2.92048i	−0.210768	−	0.365060i
$5$		0			0
$5$		0			0
$6$	−17.0584	−	4.00772i	−1.16068	−	0.272691i
$7$	0.813859	−	1.40965i	0.0439443	−	0.0761137i	−0.843217	−	0.537574i	$-0.819341\pi$
$7$	0.813859	−	1.40965i	0.0439443	−	0.0761137i	0.887161	+	0.461460i	$0.152674\pi$
$8$	−15.6060			−0.689693
$9$	−22.5000	+	14.9248i	−0.833333	+	0.552771i
$10$		0			0
$11$	16.4307	−	28.4588i	0.450368	−	0.780060i	−0.548041	−	0.836451i	$-0.684626\pi$
$11$	16.4307	−	28.4588i	0.450368	−	0.780060i	0.998409	+	0.0563918i	$0.0179596\pi$
$12$	12.0000	−	12.7692i	0.288675	−	0.307178i
$13$	−16.5109	−	28.5977i	−0.352253	−	0.610121i	0.634391	−	0.773013i	$-0.281251\pi$
$13$	−16.5109	−	28.5977i	−0.352253	−	0.610121i	−0.986644	+	0.162892i	$0.947918\pi$
$14$	2.74456	+	4.75372i	0.0523939	+	0.0907490i
$15$		0			0
$16$	39.8030	−	68.9408i	0.621922	−	1.07720i
$17$	−110.307			−1.57373			−0.786864	−	0.617126i	$-0.788297\pi$
$17$	−110.307			−1.57373			−0.786864	+	0.617126i	$0.788297\pi$
$18$	−5.64947	−	90.8762i	−0.0739774	−	1.18998i
$19$	−54.3070			−0.655731			−0.327865	−	0.944724i	$-0.606329\pi$
$19$	−54.3070			−0.655731			−0.327865	+	0.944724i	$0.606329\pi$
$20$		0			0
$21$	8.23369	+	1.93443i	0.0855590	+	0.0201013i
$22$	55.4090	+	95.9711i	0.536965	+	0.930051i
$23$	−33.7188	−	58.4026i	−0.305689	−	0.529469i	0.671725	−	0.740800i	$-0.265553\pi$
$23$	−33.7188	−	58.4026i	−0.305689	−	0.529469i	−0.977415	+	0.211331i	$0.932220\pi$
$24$	−23.4090	−	77.6387i	−0.199097	−	0.660331i
$25$		0			0
$26$	111.359			0.839970
$27$	−108.000	−	89.5489i	−0.769800	−	0.638285i
$28$	−5.48913			−0.0370481
$29$	−137.259	+	237.740i	−0.878912	+	1.52232i	−0.0263757	+	0.999652i	$0.508397\pi$
$29$	−137.259	+	237.740i	−0.878912	+	1.52232i	−0.852536	+	0.522668i	$0.824937\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	0.874585	−	0.484872i	$-0.161134\pi$
$31$	3.00000	+	5.19615i	0.0173812	+	0.0301050i	−0.857204	+	0.514977i	$0.827800\pi$
$32$	71.8030	+	124.366i	0.396659	+	0.687034i
$33$	166.227	+	39.0535i	0.876860	+	0.206010i
$34$	185.993	−	322.150i	0.938164	−	1.62495i
$35$		0			0
$36$	81.5258	+	40.5455i	0.377434	+	0.187711i
$37$	347.723			1.54501			0.772504	−	0.635010i	$-0.219004\pi$
$37$	347.723			1.54501			0.772504	+	0.635010i	$0.219004\pi$
$38$	91.5693	−	158.603i	0.390908	−	0.677072i
$39$	117.505	−	125.037i	0.482459	−	0.513383i
$40$		0			0
$41$	−145.668	−	252.305i	−0.554868	−	0.961060i	−0.997914	−	0.0645606i	$-0.979435\pi$
$41$	−145.668	−	252.305i	−0.554868	−	0.961060i	0.443046	−	0.896499i	$-0.353898\pi$
$42$	−19.5326	+	20.7846i	−0.0717607	+	0.0763604i
$43$	100.694	−	174.408i	0.357110	−	0.618533i	−0.630367	−	0.776297i	$-0.717095\pi$
$43$	100.694	−	174.408i	0.357110	−	0.618533i	0.987477	+	0.157765i	$0.0504288\pi$
$44$	−110.818			−0.379692
$45$		0			0
$46$	227.418			0.728935
$47$	−241.048	+	417.507i	−0.748094	+	1.29574i	0.200642	+	0.979665i	$0.435697\pi$
$47$	−241.048	+	417.507i	−0.748094	+	1.29574i	−0.948735	+	0.316071i	$0.897636\pi$
$48$	402.681	+	94.6062i	1.21087	+	0.284484i
$49$	170.175	+	294.752i	0.496138	+	0.859336i
$50$		0			0
$51$	−165.461	−	548.771i	−0.454296	−	1.50673i
$52$	−55.6793	+	96.4394i	−0.148487	+	0.257187i
$53$	175.228			0.454140			0.227070	−	0.973878i	$-0.427085\pi$
$53$	175.228			0.454140			0.227070	+	0.973878i	$0.427085\pi$
$54$	443.629	−	164.420i	1.11797	−	0.414347i
$55$		0			0
$56$	−12.7011	+	21.9989i	−0.0303081	+	0.0524951i
$57$	−81.4605	−	270.174i	−0.189293	−	0.627815i
$58$	−462.878	−	801.728i	−1.04791	−	1.81503i
$59$	91.6209	+	158.692i	0.202170	+	0.350169i	0.949227	−	0.314591i	$-0.101867\pi$
$59$	91.6209	+	158.692i	0.202170	+	0.350169i	−0.747057	+	0.664760i	$0.768534\pi$
$60$		0			0
$61$	−218.297	+	378.102i	−0.458199	+	0.793623i	−0.998866	−	0.0476132i	$-0.984839\pi$
$61$	−218.297	+	378.102i	−0.458199	+	0.793623i	0.540667	+	0.841237i	$0.318172\pi$
$62$	−20.2337			−0.0414465
$63$	2.72686	+	43.8637i	0.00545321	+	0.0877192i
$64$	152.568			0.297984
$65$		0			0
$66$	−394.337	+	419.613i	−0.735447	+	0.782587i
$67$	−415.750	−	720.100i	−0.758089	−	1.31305i	−0.943824	−	0.330448i	$-0.892800\pi$
$67$	−415.750	−	720.100i	−0.758089	−	1.31305i	0.185736	−	0.982600i	$-0.440533\pi$
$68$	185.993	+	322.150i	0.331691	+	0.574506i
$69$	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	$0.531697\pi$
$72$	351.134	−	232.916i	0.574744	−	0.381242i
$73$	−183.318			−0.293914			−0.146957	−	0.989143i	$-0.546948\pi$
$73$	−183.318			−0.293914			−0.146957	+	0.989143i	$0.546948\pi$
$74$	−586.310	+	1015.52i	−0.921042	+	1.59529i
$75$		0			0
$76$	91.5693	+	158.603i	0.138207	+	0.239381i
$77$	−26.7446	−	46.3229i	−0.0395822	−	0.0685583i
$78$	167.038	+	554.002i	0.242478	+	0.804210i
$79$	319.147	−	552.778i	0.454517	−	0.787246i	−0.544144	−	0.838992i	$-0.683145\pi$
$79$	319.147	−	552.778i	0.454517	−	0.787246i	0.998660	+	0.0517463i	$0.0164787\pi$
$80$		0			0
$81$	283.500	−	671.617i	0.388889	−	0.921285i
$82$	982.470			1.32312
$83$	−747.322	+	1294.40i	−0.988304	+	1.71179i	−0.362085	+	0.932145i	$0.617935\pi$
$83$	−747.322	+	1294.40i	−0.988304	+	1.71179i	−0.626219	+	0.779647i	$0.715398\pi$
$84$	−8.23369	−	27.3081i	−0.0106949	−	0.0354709i
$85$		0			0
$86$	339.569	+	588.151i	0.425776	+	0.737465i
$87$	−1388.63	−	326.247i	−1.71123	−	0.402038i
$88$	−256.417	+	444.127i	−0.310615	+	0.538002i
$89$	−1437.27			−1.71180			−0.855900	−	0.517142i	$-0.826996\pi$
$89$	−1437.27			−1.71180			−0.855900	+	0.517142i	$0.826996\pi$
$90$		0			0
$91$	−53.7501			−0.0619181
$92$	−113.709	+	196.950i	−0.128859	+	0.223190i
$93$	−21.3505	+	22.7190i	−0.0238059	+	0.0253318i
$94$	−812.880	−	1407.95i	−0.891938	−	1.54488i
$95$		0			0
$96$	−511.011	+	543.765i	−0.543279	+	0.578102i
$97$	−445.884	+	772.294i	−0.466729	+	0.808398i	−0.999278	−	0.0380011i	$-0.987901\pi$
$97$	−445.884	+	772.294i	−0.466729	+	0.808398i	0.532549	+	0.846399i	$0.321234\pi$
$98$	−1147.76			−1.18307
$99$	55.0516	+	885.548i	0.0558878	+	0.899000i
$100$		0			0
$101$	76.8720	−	133.146i	0.0757332	−	0.131174i	−0.825672	−	0.564151i	$-0.809204\pi$
$101$	76.8720	−	133.146i	0.0757332	−	0.131174i	0.901405	+	0.432977i	$0.142537\pi$
$102$	1881.66	+	442.080i	1.82659	+	0.429142i
$103$	67.6469	+	117.168i	0.0647131	+	0.112086i	0.896567	−	0.442909i	$-0.146053\pi$
$103$	67.6469	+	117.168i	0.0647131	+	0.112086i	−0.831854	+	0.554995i	$0.812720\pi$
$104$	257.668	+	446.294i	0.242947	+	0.420796i
$105$		0			0
$106$	−295.459	+	511.750i	−0.270732	+	0.468921i
$107$	718.783			0.649414			0.324707	−	0.945815i	$-0.394734\pi$
$107$	718.783			0.649414			0.324707	+	0.945815i	$0.394734\pi$
$108$	−79.4226	+	466.404i	−0.0707634	+	0.415553i
$109$	−2010.56			−1.76676			−0.883378	−	0.468661i	$-0.844736\pi$
$109$	−2010.56			−1.76676			−0.883378	+	0.468661i	$0.844736\pi$
$110$		0			0
$111$	521.584	+	1729.90i	0.446005	+	1.47923i
$112$	−64.7881	−	112.216i	−0.0546598	−	0.0946735i
$113$	−113.372	−	196.367i	−0.0943820	−	0.163474i	0.814969	−	0.579505i	$-0.196754\pi$
$113$	−113.372	−	196.367i	−0.0943820	−	0.163474i	−0.909351	+	0.416031i	$0.863421\pi$
$114$	926.392	+	217.647i	0.761093	+	0.178812i
$115$		0			0
$116$	925.755			0.740985
$117$	798.310	+	397.026i	0.630801	+	0.313718i
$118$	−617.943			−0.482087
$119$	−89.7744	+	155.494i	−0.0691564	+	0.119782i
$120$		0			0
$121$	125.564	+	217.483i	0.0943381	+	0.163398i
$122$	−736.160	−	1275.07i	−0.546302	−	0.946223i
$123$	1036.70	−	1103.15i	0.759968	−	0.808680i
$124$	10.1168	−	17.5229i	0.00732677	−	0.0126903i
$125$		0			0
$126$	−132.701	−	65.9967i	−0.0938250	−	0.0466623i
$127$	−1132.24			−0.791100			−0.395550	−	0.918444i	$-0.629446\pi$
$127$	−1132.24			−0.791100			−0.395550	+	0.918444i	$0.629446\pi$
$128$	−831.675	+	1440.50i	−0.574300	+	0.994717i
$129$	1018.71	+	239.336i	0.695289	+	0.163352i
$130$		0			0
$131$	−388.753	−	673.339i	−0.259278	−	0.449083i	0.706770	−	0.707443i	$-0.250151\pi$
$131$	−388.753	−	673.339i	−0.259278	−	0.449083i	−0.966049	+	0.258360i	$0.916818\pi$
$132$	−166.227	−	551.312i	−0.109608	−	0.363527i
$133$	−44.1983	+	76.5537i	−0.0288156	+	0.0499101i
$134$	2804.05			1.80771
$135$		0			0
$136$	1721.45			1.08539
$137$	311.819	−	540.087i	0.194456	−	0.336808i	−0.752266	−	0.658860i	$-0.771039\pi$
$137$	311.819	−	540.087i	0.194456	−	0.336808i	0.946722	+	0.322052i	$0.104372\pi$
$138$	341.127	+	1131.39i	0.210425	+	0.697902i
$139$	−641.341	−	1110.83i	−0.391351	−	0.677840i	0.601277	−	0.799041i	$-0.294659\pi$
$139$	−641.341	−	1110.83i	−0.391351	−	0.677840i	−0.992628	+	0.121201i	$0.961326\pi$
$140$		0			0
$141$	−2438.64	−	572.937i	−1.45653	−	0.342198i
$142$	200.568	−	347.394i	0.118530	−	0.205300i
$143$	−1085.14			−0.634574
$144$	133.361	+	2145.22i	0.0771766	+	1.24145i
$145$		0			0
$146$	309.099	−	535.376i	0.175214	−	0.303480i
$147$	−1211.11	+	1288.74i	−0.679529	+	0.723085i
$148$	−586.310	−	1015.52i	−0.325638	−	0.564021i
$149$	−762.156	−	1320.09i	−0.419049	−	0.725814i	0.576795	−	0.816889i	$-0.304303\pi$
$149$	−762.156	−	1320.09i	−0.419049	−	0.725814i	−0.995844	+	0.0910749i	$0.970970\pi$
$150$		0			0
$151$	−1581.28	+	2738.86i	−0.852203	+	1.47606i	0.0270124	+	0.999635i	$0.491401\pi$
$151$	−1581.28	+	2738.86i	−0.852203	+	1.47606i	−0.879216	+	0.476424i	$0.841933\pi$
$152$	847.514			0.452253
$153$	2481.91	−	1646.31i	1.31144	−	0.869911i
$154$	180.380			0.0943861
$155$		0			0
$156$	−563.299	−	132.342i	−0.289103	−	0.0679220i
$157$	−1194.35	−	2068.67i	−0.607131	−	1.05158i	−0.991711	−	0.128490i	$-0.958987\pi$
$157$	−1194.35	−	2068.67i	−0.607131	−	1.05158i	0.384580	−	0.923092i	$-0.374346\pi$
$158$	1076.25	+	1864.12i	0.541912	+	0.938619i
$159$	262.842	+	871.749i	0.131099	+	0.434806i
$160$		0			0
$161$	−109.769			−0.0537331
$162$	1483.42	+	1960.40i	0.719436	+	0.950761i
$163$	2544.79			1.22284			0.611422	−	0.791305i	$-0.290598\pi$
$163$	2544.79			1.22284			0.611422	+	0.791305i	$0.290598\pi$
$164$	−491.235	+	850.844i	−0.233896	+	0.405120i
$165$		0			0
$166$	−2520.18	−	4365.08i	−1.17834	−	2.04094i
$167$	−687.279	−	1190.40i	−0.318462	−	0.551593i	0.661705	−	0.749764i	$-0.269833\pi$
$167$	−687.279	−	1190.40i	−0.318462	−	0.551593i	−0.980167	+	0.198171i	$0.936500\pi$
$168$	−128.495	−	30.1887i	−0.0590094	−	0.0138637i
$169$	553.282	−	958.313i	0.251835	−	0.436191i
$170$		0			0
$171$	1221.91	−	810.522i	0.546442	−	0.362469i
$172$	−679.139			−0.301069
$173$	1180.23	−	2044.21i	0.518675	−	0.898372i	−0.481089	−	0.876672i	$-0.659759\pi$
$173$	1180.23	−	2044.21i	0.518675	−	0.898372i	0.999765	−	0.0217005i	$-0.00690803\pi$
$174$	3294.23	−	3505.38i	1.43526	−	1.52725i
$175$		0			0
$176$	−1307.98	−	2265.49i	−0.560187	−	0.970272i
$177$	−652.052	+	693.846i	−0.276899	+	0.294648i
$178$	2423.44	−	4197.52i	1.02047	−	1.76751i
$179$	1305.11			0.544963			0.272482	−	0.962161i	$-0.412156\pi$
$179$	1305.11			0.544963			0.272482	+	0.962161i	$0.412156\pi$
$180$		0			0
$181$	3099.43			1.27281			0.636406	−	0.771355i	$-0.280420\pi$
$181$	3099.43			1.27281			0.636406	+	0.771355i	$0.280420\pi$
$182$	90.6303	−	156.976i	0.0369119	−	0.0639332i
$183$	−2208.48	−	518.863i	−0.892107	−	0.209593i
$184$	526.214	+	911.429i	0.210832	+	0.365171i
$185$		0			0
$186$	−30.3505	−	100.661i	−0.0119646	−	0.0396820i
$187$	−1812.42	+	3139.21i	−0.708756	+	1.22760i
$188$	1625.76			0.630696
$189$	−214.129	+	79.3616i	−0.0824105	+	0.0305434i
$190$		0			0
$191$	−190.356	+	329.706i	−0.0721135	+	0.124904i	−0.899827	−	0.436246i	$-0.856308\pi$
$191$	−190.356	+	329.706i	−0.0721135	+	0.124904i	0.827714	+	0.561150i	$0.189641\pi$
$192$	228.852	+	759.016i	0.0860207	+	0.285298i
$193$	773.020	+	1338.91i	0.288307	+	0.499362i	0.973406	−	0.229088i	$-0.0735744\pi$
$193$	773.020	+	1338.91i	0.288307	+	0.499362i	−0.685099	+	0.728450i	$0.740241\pi$
$194$	−1503.65	−	2604.39i	−0.556472	−	0.963838i
$195$		0			0
$196$	573.879	−	993.987i	0.209140	−	0.362240i
$197$	4284.60			1.54957			0.774784	−	0.632226i	$-0.217859\pi$
$197$	4284.60			1.54957			0.774784	+	0.632226i	$0.217859\pi$
$198$	−2679.05	−	1332.38i	−0.961576	−	0.478224i
$199$	−1402.85			−0.499727			−0.249863	−	0.968281i	$-0.580386\pi$
$199$	−1402.85			−0.499727			−0.249863	+	0.968281i	$0.580386\pi$
$200$		0			0
$201$	2958.83	−	3148.48i	1.03831	−	1.10486i
$202$	259.234	+	449.007i	0.0902953	+	0.156396i
$203$	223.420	+	386.974i	0.0772463	+	0.133795i
$204$	−1323.68	+	1408.53i	−0.454296	+	0.483415i
$205$		0			0
$206$	−456.249			−0.154312
$207$	1630.32	+	810.813i	0.547416	+	0.272248i
$208$	−2628.73			−0.876296
$209$	−892.303	+	1545.51i	−0.295320	+	0.511509i
$210$		0			0
$211$	1075.23	+	1862.35i	0.350814	+	0.607628i	0.986392	−	0.164409i	$-0.0525716\pi$
$211$	1075.23	+	1862.35i	0.350814	+	0.607628i	−0.635578	+	0.772036i	$0.719238\pi$
$212$	−295.459	−	511.750i	−0.0957180	−	0.165789i
$213$	−178.426	−	591.773i	−0.0573971	−	0.190365i
$214$	−1211.97	+	2099.19i	−0.387142	+	0.670550i
$215$		0			0
$216$	1685.44	+	1397.50i	0.530926	+	0.440220i
$217$	9.76631			0.00305521
$218$	3390.08	−	5871.79i	1.05324	−	1.82426i
$219$	−274.977	−	911.994i	−0.0848456	−	0.281401i
$220$		0			0
$221$	1821.27	+	3154.52i	0.554351	+	0.960164i
$222$	−5931.60	−	1393.58i	−1.79326	−	0.421310i
$223$	−1279.07	+	2215.42i	−0.384095	+	0.665272i	−0.991643	−	0.129011i	$-0.958820\pi$
$223$	−1279.07	+	2215.42i	−0.384095	+	0.665272i	0.607548	+	0.794283i	$0.292153\pi$
$224$	233.750			0.0697236
$225$		0			0
$226$	764.646			0.225060
$227$	−2042.27	+	3537.32i	−0.597138	+	1.03427i	0.396104	+	0.918206i	$0.370362\pi$
$227$	−2042.27	+	3537.32i	−0.597138	+	1.03427i	−0.993241	+	0.116067i	$0.962971\pi$
$228$	−651.684	+	693.456i	−0.189293	+	0.201426i
$229$	1370.95	+	2374.56i	0.395612	+	0.685221i	0.993179	−	0.116598i	$-0.0371991\pi$
$229$	1370.95	+	2374.56i	0.395612	+	0.685221i	−0.597567	+	0.801819i	$0.703866\pi$
$230$		0			0
$231$	190.337	−	202.537i	0.0542132	−	0.0576881i
$232$	2142.07	−	3710.17i	0.606179	−	1.04993i
$233$	−5084.70			−1.42966			−0.714828	−	0.699300i	$-0.753495\pi$
$233$	−5084.70			−1.42966			−0.714828	+	0.699300i	$0.753495\pi$
$234$	−2505.57	+	1662.01i	−0.699975	+	0.464311i
$235$		0			0
$236$	308.971	−	535.154i	0.0852217	−	0.147608i
$237$	3228.76	+	758.567i	0.884938	+	0.207908i
$238$	−302.745	−	524.369i	−0.0824538	−	0.142814i
$239$	−738.236	−	1278.66i	−0.199801	−	0.346066i	0.748663	−	0.662951i	$-0.230696\pi$
$239$	−738.236	−	1278.66i	−0.199801	−	0.346066i	−0.948464	+	0.316885i	$0.897363\pi$
$240$		0			0
$241$	−881.728	+	1527.20i	−0.235673	+	0.408197i	−0.959468	−	0.281818i	$-0.909063\pi$
$241$	−881.728	+	1527.20i	−0.235673	+	0.408197i	0.723795	+	0.690015i	$0.242396\pi$
$242$	−846.874			−0.224955
$243$	3766.50	+	402.970i	0.994325	+	0.106381i
$244$	1472.32			0.386294
$245$		0			0
$246$	1473.70	+	4887.73i	0.381951	+	1.26679i
$247$	896.657	+	1553.05i	0.230983	+	0.400075i
$248$	−46.8179	−	81.0910i	−0.0119877	−	0.0207632i
$249$	−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	$0.431220\pi$
$252$	123.505	−	81.9242i	0.0308734	−	0.0204791i
$253$	−2216.09			−0.550690
$254$	1909.11	−	3306.68i	0.471607	−	0.816848i
$255$		0			0
$256$	−2194.37	−	3800.76i	−0.535735	−	0.927920i
$257$	114.298	+	197.970i	0.0277421	+	0.0480507i	0.879563	−	0.475782i	$-0.157835\pi$
$257$	114.298	+	197.970i	0.0277421	+	0.0480507i	−0.851821	+	0.523833i	$0.824502\pi$
$258$	−2416.66	+	2571.56i	−0.583158	+	0.620537i
$259$	282.997	−	490.166i	0.0678942	−	0.117596i
$260$		0			0
$261$	−459.892	−	7397.73i	−0.109068	−	1.75444i
$262$	2621.97			0.618266
$263$	−644.380	+	1116.10i	−0.151081	+	0.261679i	−0.931625	−	0.363421i	$-0.881609\pi$
$263$	−644.380	+	1116.10i	−0.151081	+	0.261679i	0.780544	+	0.625100i	$0.214942\pi$
$264$	−2594.13	−	609.468i	−0.604764	−	0.142084i
$265$		0			0
$266$	−149.049	−	258.161i	−0.0343563	−	0.0595069i
$267$	−2155.90	−	7150.32i	−0.494154	−	1.63892i
$268$	−1402.03	+	2428.38i	−0.319561	+	0.553496i
$269$	973.981			0.220761			0.110380	−	0.993889i	$-0.464793\pi$
$269$	973.981			0.220761			0.110380	+	0.993889i	$0.464793\pi$
$270$		0			0
$271$	−4021.83			−0.901508			−0.450754	−	0.892648i	$-0.648845\pi$
$271$	−4021.83			−0.901508			−0.450754	+	0.892648i	$0.648845\pi$
$272$	−4390.55	+	7604.65i	−0.978736	+	1.69522i
$273$	−80.6252	−	267.403i	−0.0178742	−	0.0592820i
$274$	1051.54	+	1821.32i	0.231847	+	0.401570i
$275$		0			0
$276$	−1150.38	−	270.271i	−0.250886	−	0.0589435i
$277$	−1689.59	+	2926.45i	−0.366489	+	0.634777i	−0.989014	−	0.147823i	$-0.952773\pi$
$277$	−1689.59	+	2926.45i	−0.366489	+	0.634777i	0.622525	+	0.782600i	$0.286107\pi$
$278$	4325.56			0.933201
$279$	−145.052	−	72.1390i	−0.0311255	−	0.0154797i
$280$		0			0
$281$	−366.654	+	635.063i	−0.0778388	+	0.134821i	−0.902317	−	0.431073i	$-0.858135\pi$
$281$	−366.654	+	635.063i	−0.0778388	+	0.134821i	0.824478	+	0.565893i	$0.191469\pi$
$282$	5785.14	−	6155.95i	1.22163	−	1.29993i
$283$	3454.51	+	5983.39i	0.725617	+	1.25680i	0.958720	+	0.284353i	$0.0917787\pi$
$283$	3454.51	+	5983.39i	0.725617	+	1.25680i	−0.233103	+	0.972452i	$0.574888\pi$
$284$	200.568	+	347.394i	0.0419068	+	0.0725847i
$285$		0			0
$286$	1829.70	−	3169.13i	0.378295	−	0.655227i
$287$	−474.214			−0.0975331
$288$	−3471.71	−	1726.60i	−0.710322	−	0.353267i
$289$	7254.64			1.47662
$290$		0			0
$291$	−4510.94	−	1059.81i	−0.908715	−	0.213494i
$292$	309.099	+	535.376i	0.0619475	+	0.107296i
$293$	−2324.74	−	4026.57i	−0.463525	−	0.802850i	0.535608	−	0.844467i	$-0.320082\pi$
$293$	−2324.74	−	4026.57i	−0.463525	−	0.802850i	−0.999134	+	0.0416170i	$0.986749\pi$
$294$	−1721.64	−	5710.02i	−0.341523	−	1.13271i
$295$		0			0
$296$	−5426.55			−1.06558
$297$	−4322.97	+	1602.20i	−0.844593	+	0.313027i
$298$	5140.41			0.999248
$299$	−1113.45	+	1928.56i	−0.215360	+	0.373014i
$300$		0			0
$301$	−163.902	−	283.886i	−0.0313859	−	0.0543619i
$302$	−5332.52	−	9236.19i	−1.01607	−	1.75988i
$303$	777.702	+	182.714i	0.147452	+	0.0346424i
$304$	−2161.58	+	3743.97i	−0.407813	+	0.706353i
$305$		0			0
$306$	623.176	+	10024.3i	0.116420	+	1.87271i
$307$	7361.42			1.36853			0.684264	−	0.729234i	$-0.260123\pi$
$307$	7361.42			1.36853			0.684264	+	0.729234i	$0.260123\pi$
$308$	−90.1902	+	156.214i	−0.0166853	+	0.0288997i
$309$	−481.433	+	512.291i	−0.0886335	+	0.0943146i
$310$		0			0
$311$	1354.60	+	2346.24i	0.246986	+	0.427792i	0.962688	−	0.270614i	$-0.0872266\pi$
$311$	1354.60	+	2346.24i	0.246986	+	0.427792i	−0.715702	+	0.698405i	$0.753893\pi$
$312$	−1833.78	+	1951.32i	−0.332749	+	0.354077i
$313$	−3121.86	+	5407.22i	−0.563763	+	0.976467i	0.433400	+	0.901202i	$0.357314\pi$
$313$	−3121.86	+	5407.22i	−0.563763	+	0.976467i	−0.997164	+	0.0752653i	$0.976020\pi$
$314$	8055.37			1.44774
$315$		0			0
$316$	−2152.50			−0.383189
$317$	1042.02	−	1804.82i	0.184623	−	0.319776i	−0.758827	−	0.651293i	$-0.774227\pi$
$317$	1042.02	−	1804.82i	0.184623	−	0.319776i	0.943449	+	0.331517i	$0.107560\pi$
$318$	−2989.12	−	702.266i	−0.527111	−	0.123840i
$319$	4510.54	+	7812.48i	0.791667	+	1.37121i
$320$		0			0
$321$	1078.17	+	3575.90i	0.187470	+	0.621767i
$322$	185.087	−	320.579i	0.0320325	−	0.0554819i
$323$	5990.45			1.03194
$324$	−2439.46	+	304.483i	−0.418289	+	0.0522091i
$325$		0			0
$326$	−4290.88	+	7432.02i	−0.728987	+	1.26264i
$327$	−3015.83	−	10002.4i	−0.510018	−	1.69154i
$328$	2273.30	+	3937.47i	0.382689	+	0.662836i
$329$	392.358	+	679.583i	0.0657489	+	0.113880i
$330$		0			0
$331$	113.938	−	197.347i	0.0189203	−	0.0327709i	−0.856410	−	0.516296i	$-0.827310\pi$
$331$	113.938	−	197.347i	0.0189203	−	0.0327709i	0.875331	+	0.483525i	$0.160644\pi$
$332$	5040.36			0.833210
$333$	−7823.76	+	5189.70i	−1.28751	+	0.854035i
$334$	4635.39			0.759394
$335$		0			0
$336$	461.087	−	490.641i	0.0748641	−	0.0796627i
$337$	1708.74	+	2959.62i	0.276205	+	0.478400i	0.970438	−	0.241349i	$-0.0775899\pi$
$337$	1708.74	+	2959.62i	0.276205	+	0.478400i	−0.694234	+	0.719750i	$0.744257\pi$
$338$	1865.82	+	3231.70i	0.300259	+	0.520063i
$339$	806.853	−	858.570i	0.129269	−	0.137555i
$340$		0			0
$341$	197.168			0.0313116
$342$	306.806	+	4935.21i	0.0485092	+	0.780309i
$343$	1112.30			0.175098
$344$	−1571.43	+	2721.80i	−0.246296	+	0.426598i
$345$		0			0
$346$	3980.05	+	6893.65i	0.618407	+	1.07111i
$347$	1804.80	+	3126.00i	0.279212	+	0.483610i	0.971189	−	0.238310i	$-0.0765933\pi$
$347$	1804.80	+	3126.00i	0.279212	+	0.483610i	−0.691977	+	0.721920i	$0.743260\pi$
$348$	1388.63	+	4605.57i	0.213904	+	0.709439i
$349$	4400.42	−	7621.74i	0.674925	−	1.16900i	−0.301566	−	0.953445i	$-0.597509\pi$
$349$	4400.42	−	7621.74i	0.674925	−	1.16900i	0.976491	−	0.215559i	$-0.0691574\pi$
$350$		0			0
$351$	−777.715	+	4567.08i	−0.118266	+	0.694509i
$352$	4719.09			0.714570
$353$	4255.24	−	7370.30i	0.641597	−	1.11128i	−0.343479	−	0.939160i	$-0.611605\pi$
$353$	4255.24	−	7370.30i	0.641597	−	1.11128i	0.985076	−	0.172119i	$-0.0550612\pi$
$354$	−926.914	−	3074.23i	−0.139166	−	0.461563i
$355$		0			0
$356$	2423.44	+	4197.52i	0.360792	+	0.624910i
$357$	−908.234	−	213.381i	−0.134647	−	0.0316340i
$358$	−2200.60	+	3811.55i	−0.324875	+	0.562700i
$359$	4320.35			0.635152			0.317576	−	0.948233i	$-0.397131\pi$
$359$	4320.35			0.635152			0.317576	+	0.948233i	$0.397131\pi$
$360$		0			0
$361$	−3909.75			−0.570017
$362$	−5226.08	+	9051.83i	−0.758775	+	1.31424i
$363$	−893.619	+	950.898i	−0.129209	+	0.137491i
$364$	90.6303	+	156.976i	0.0130503	+	0.0226038i
$365$		0			0
$366$	5239.14	−	5574.95i	0.748235	−	0.796195i
$367$	3300.19	−	5716.10i	0.469397	−	0.813020i	−0.529991	−	0.848003i	$-0.677805\pi$
$367$	3300.19	−	5716.10i	0.469397	−	0.813020i	0.999388	+	0.0349838i	$0.0111379\pi$
$368$	−5368.43			−0.760459
$369$	7043.15	+	3502.79i	0.993636	+	0.494168i
$370$		0			0
$371$	142.611	−	247.010i	0.0199569	−	0.0345663i
$372$	102.351	+	24.0463i	0.0142651	+	0.00335146i
$373$	−4304.23	−	7455.14i	−0.597492	−	1.03489i	−0.993190	−	0.116506i	$-0.962831\pi$
$373$	−4304.23	−	7455.14i	−0.597492	−	1.03489i	0.395698	−	0.918381i	$-0.370503\pi$
$374$	−6112.00	−	10586.3i	−0.845037	−	1.46365i
$375$		0			0
$376$	3761.78	−	6515.60i	0.515955	−	0.893660i
$377$	9065.10			1.23840
$378$	129.278	−	759.174i	0.0175908	−	0.103301i
$379$	−7129.80			−0.966314			−0.483157	−	0.875534i	$-0.660510\pi$
$379$	−7129.80			−0.966314			−0.483157	+	0.875534i	$0.660510\pi$
$380$		0			0
$381$	−1698.36	−	5632.81i	−0.228371	−	0.757421i
$382$	−641.934	−	1111.86i	−0.0859796	−	0.148921i
$383$	2963.73	+	5133.33i	0.395404	+	0.684859i	0.993153	−	0.116824i	$-0.0372714\pi$
$383$	2963.73	+	5133.33i	0.395404	+	0.684859i	−0.597749	+	0.801683i	$0.703938\pi$
$384$	−8413.93	−	1976.78i	−1.11815	−	0.262700i
$385$		0			0
$386$	−5213.68			−0.687486
$387$	337.379	+	5427.01i	0.0443151	+	0.712844i
$388$	3007.30			0.393485
$389$	−519.432	+	899.683i	−0.0677024	+	0.117264i	−0.897890	−	0.440221i	$-0.854900\pi$
$389$	−519.432	+	899.683i	−0.0677024	+	0.117264i	0.830187	+	0.557485i	$0.188234\pi$
$390$		0			0
$391$	3719.42	+	6442.22i	0.481072	+	0.833240i
$392$	−2655.75	−	4599.89i	−0.342183	−	0.592678i
$393$	2766.69	−	2944.03i	0.355117	−	0.377879i
$394$	−7224.43	+	12513.1i	−0.923761	+	1.60000i
$395$		0			0
$396$	2493.40	−	1653.94i	0.316410	−	0.209882i
$397$	−13441.4			−1.69926			−0.849628	−	0.527382i	$-0.823174\pi$
$397$	−13441.4			−1.69926			−0.849628	+	0.527382i	$0.823174\pi$
$398$	2365.41	−	4097.01i	0.297907	−	0.515991i
$399$	−447.147	−	105.053i	−0.0561037	−	0.0131810i
$400$		0			0
$401$	−6537.70	−	11323.6i	−0.814157	−	1.41016i	−0.909931	−	0.414759i	$-0.863866\pi$
$401$	−6537.70	−	11323.6i	−0.814157	−	1.41016i	0.0957739	−	0.995403i	$-0.469467\pi$
$402$	4206.08	+	13950.0i	0.521841	+	1.73075i
$403$	99.0652	−	171.586i	0.0122451	−	0.0212092i
$404$	−518.468			−0.0638484
$405$		0			0
$406$	−1506.87			−0.184199
$407$	5713.33	−	9895.78i	0.695821	−	1.20520i
$408$	2582.17	+	8564.10i	0.313325	+	1.03918i
$409$	2636.59	+	4566.71i	0.318756	+	0.552101i	0.980229	−	0.197868i	$-0.0634017\pi$
$409$	2636.59	+	4566.71i	0.318756	+	0.552101i	−0.661473	+	0.749969i	$0.730068\pi$
$410$		0			0
$411$	3154.63	+	741.151i	0.378604	+	0.0889496i
$412$	228.124	−	395.123i	0.0272788	−	0.0472484i
$413$	298.266			0.0355368
$414$	−5116.91	+	3394.18i	−0.607446	+	0.402934i
$415$		0			0
$416$	2371.06	−	4106.80i	0.279449	−	0.484020i
$417$	4564.32	−	4856.88i	0.536009	−	0.570366i
$418$	−3009.10	−	5211.91i	−0.352105	−	0.609863i
$419$	−6923.06	−	11991.1i	−0.807192	−	1.39810i	−0.914801	−	0.403905i	$-0.867653\pi$
$419$	−6923.06	−	11991.1i	−0.807192	−	1.39810i	0.107609	−	0.994193i	$-0.465681\pi$
$420$		0			0
$421$	−548.684	+	950.349i	−0.0635184	+	0.110017i	−0.896036	−	0.443982i	$-0.853565\pi$
$421$	−548.684	+	950.349i	−0.0635184	+	0.110017i	0.832517	+	0.553999i	$0.186899\pi$
$422$	−7251.94			−0.836538
$423$	−807.637	−	12991.5i	−0.0928338	−	1.49330i
$424$	−2734.60			−0.313217
$425$		0			0
$426$	2029.12	+	476.722i	0.230777	+	0.0542189i
$427$	355.327	+	615.444i	0.0402704	+	0.0697504i
$428$	−1211.97	−	2099.19i	−0.136875	−	0.237075i
$429$	−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	$0.151258\pi$
$432$	−10472.3	+	3881.29i	−1.16632	+	0.432266i
$433$	−3566.31			−0.395810			−0.197905	−	0.980221i	$-0.563414\pi$
$433$	−3566.31			−0.395810			−0.197905	+	0.980221i	$0.563414\pi$
$434$	−16.4674	+	28.5223i	−0.00182133	+	0.00315464i
$435$		0			0
$436$	3390.08	+	5871.79i	0.372375	+	0.644972i
$437$	1831.17	+	3171.67i	0.200450	+	0.347189i
$438$	3127.11	+	734.686i	0.341140	+	0.0801476i
$439$	290.411	−	503.007i	0.0315730	−	0.0546861i	−0.849807	−	0.527094i	$-0.823282\pi$
$439$	290.411	−	503.007i	0.0315730	−	0.0546861i	0.881380	+	0.472408i	$0.156615\pi$
$440$		0			0
$441$	−8228.06	−	4092.09i	−0.888464	−	0.441863i
$442$	−12283.6			−1.32188
$443$	−5396.39	+	9346.82i	−0.578759	+	1.00244i	0.416863	+	0.908969i	$0.363129\pi$
$443$	−5396.39	+	9346.82i	−0.578759	+	1.00244i	−0.995622	+	0.0934706i	$0.970204\pi$
$444$	4172.67	−	4440.13i	0.446005	−	0.474593i
$445$		0			0
$446$	−4313.40	−	7471.03i	−0.457949	−	0.793191i
$447$	5424.15	−	5771.82i	0.573945	−	0.610733i
$448$	124.169	−	215.067i	0.0130947	−	0.0226807i
$449$	2894.01			0.304180			0.152090	−	0.988367i	$-0.451400\pi$
$449$	2894.01			0.304180			0.152090	+	0.988367i	$0.451400\pi$
$450$		0			0
$451$	−9573.74			−0.999578
$452$	−382.323	+	662.203i	−0.0397853	+	0.0689102i
$453$	−15997.6	−	3758.48i	−1.65923	−	0.389821i
$454$	−6887.11	−	11928.8i	−0.711956	−	1.23314i
$455$		0			0
$456$	1271.27	+	4216.33i	0.130554	+	0.432999i
$457$	1599.96	−	2771.21i	0.163770	−	0.283658i	−0.772448	−	0.635078i	$-0.780968\pi$
$457$	1599.96	−	2771.21i	0.163770	−	0.283658i	0.936218	+	0.351420i	$0.114301\pi$
$458$	−9246.49			−0.943363
$459$	11913.2	+	9877.87i	1.21146	+	1.00449i
$460$		0			0
$461$	−3658.19	+	6336.17i	−0.369585	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$461$	−3658.19	+	6336.17i	−0.369585	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$462$	270.571	+	897.381i	0.0272469	+	0.0903678i
$463$	3505.99	+	6072.55i	0.351916	+	0.609536i	0.986585	−	0.163248i	$-0.0521970\pi$
$463$	3505.99	+	6072.55i	0.351916	+	0.609536i	−0.634669	+	0.772784i	$0.718864\pi$
$464$	10926.7	+	18925.6i	1.09323	+	1.89353i
$465$		0			0
$466$	8573.53	−	14849.8i	0.852277	−	1.47619i
$467$	8002.63			0.792971			0.396485	−	0.918041i	$-0.370230\pi$
$467$	8002.63			0.792971			0.396485	+	0.918041i	$0.370230\pi$
$468$	−186.555	−	3000.89i	−0.0184263	−	0.296402i
$469$	−1353.45			−0.133255
$470$		0			0
$471$	8500.00	−	9044.83i	0.831549	−	0.884849i
$472$	−1429.83	−	2476.54i	−0.139435	−	0.241509i
$473$	−3308.95	−	5731.28i	−0.321661	−	0.557134i
$474$	−7659.52	+	8150.47i	−0.742222	+	0.789797i
$475$		0			0
$476$	605.489			0.0583037
$477$	−3942.63	+	2615.25i	−0.378450	+	0.251035i
$478$	4979.08			0.476439
$479$	1589.42	−	2752.96i	0.151613	−	0.262601i	−0.780208	−	0.625520i	$-0.784887\pi$
$479$	1589.42	−	2752.96i	0.151613	−	0.262601i	0.931820	+	0.362920i	$0.118220\pi$
$480$		0			0
$481$	−5741.21	−	9944.06i	−0.544234	−	0.942641i
$482$	−2973.44	−	5150.14i	−0.280988	−	0.486686i
$483$	−164.654	−	546.096i	−0.0155114	−	0.0514456i
$484$	423.437	−	733.414i	0.0397668	−	0.0688781i
$485$		0			0
$486$	−7527.71	+	10320.5i	−0.702601	+	0.963269i
$487$	−13060.3			−1.21523			−0.607615	−	0.794232i	$-0.707874\pi$
$487$	−13060.3			−1.21523			−0.607615	+	0.794232i	$0.707874\pi$
$488$	3406.74	−	5900.65i	0.316016	−	0.547356i
$489$	3817.19	+	12660.2i	0.353005	+	1.17078i
$490$		0			0
$491$	2200.81	+	3811.91i	0.202283	+	0.350365i	0.949264	−	0.314481i	$-0.101831\pi$
$491$	2200.81	+	3811.91i	0.202283	+	0.350365i	−0.746981	+	0.664846i	$0.768497\pi$
$492$	−4969.75	−	1167.60i	−0.455393	−	0.106991i
$493$	15140.7	−	26224.4i	1.38317	−	2.39572i
$494$	−6047.56			−0.550794
$495$		0			0
$496$	477.636			0.0432389
$497$	−96.8093	+	167.679i	−0.00873741	+	0.0151336i
$498$	17935.7	−	19085.3i	1.61389	−	1.71734i
$499$	−9362.60	−	16216.5i	−0.839935	−	1.45481i	−0.889948	−	0.456062i	$-0.849260\pi$
$499$	−9362.60	−	16216.5i	−0.839935	−	1.45481i	0.0500129	−	0.998749i	$-0.484074\pi$
$500$		0			0
$501$	4891.26	−	5204.77i	0.436178	−	0.464136i
$502$	−2875.15	+	4979.90i	−0.255626	+	0.442757i
$503$	3811.68			0.337882			0.168941	−	0.985626i	$-0.445965\pi$
$503$	3811.68			0.337882			0.168941	+	0.985626i	$0.445965\pi$
$504$	−42.5553	−	684.536i	−0.00376104	−	0.0604993i
$505$		0			0
$506$	3736.64	−	6472.06i	0.328289	−	0.568613i
$507$	5597.47	+	1315.07i	0.490320	+	0.115196i
$508$	1909.11	+	3306.68i	0.166738	+	0.288799i
$509$	−2247.74	−	3893.20i	−0.195735	−	0.339024i	0.751406	−	0.659840i	$-0.229376\pi$
$509$	−2247.74	−	3893.20i	−0.195735	−	0.339024i	−0.947141	+	0.320816i	$0.896043\pi$
$510$		0			0
$511$	−149.195	+	258.413i	−0.0129158	+	0.0223709i
$512$	1493.27			0.128894
$513$	5865.16	+	4863.13i	0.504782	+	0.418543i
$514$	−770.891			−0.0661528
$515$		0			0
$516$	−1018.71	−	3378.67i	−0.0869111	−	0.288251i
$517$	7921.16	+	13719.9i	0.673834	+	1.16712i
$518$	954.347	+	1652.98i	0.0809490	+	0.140208i
$519$	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	$0.330189\pi$
$522$	22380.4	+	11130.5i	1.87656	+	0.933274i
$523$	−7385.38			−0.617476			−0.308738	−	0.951147i	$-0.599907\pi$
$523$	−7385.38			−0.617476			−0.308738	+	0.951147i	$0.599907\pi$
$524$	−1310.98	+	2270.69i	−0.109295	+	0.189304i
$525$		0			0
$526$	−2173.03	−	3763.80i	−0.180131	−	0.311995i
$527$	−330.921	−	573.172i	−0.0273532	−	0.0473772i
$528$	9308.70	−	9905.37i	0.767253	−	0.816431i
$529$	3809.59	−	6598.40i	0.313108	−	0.542320i
$530$		0			0
$531$	−4429.92	−	2203.15i	−0.362038	−	0.180054i
$532$	298.098			0.0242936
$533$	−4810.23	+	8331.56i	−0.390908	+	0.677073i
$534$	24517.5	+	5760.17i	1.98685	+	0.466792i
$535$		0			0
$536$	6488.18	+	11237.9i	0.522848	+	0.905600i
$537$	1957.66	+	6492.83i	0.157317	+	0.521763i
$538$	−1642.27	+	2844.49i	−0.131605	+	0.227946i
$539$	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	$0.575783\pi$
$542$	6781.37	−	11745.7i	0.537426	−	0.930849i
$543$	4649.15	+	15419.5i	0.367429	+	1.21862i
$544$	−7920.37	−	13718.5i	−0.624234	−	1.08120i
$545$		0			0
$546$	916.892	+	215.416i	0.0718670	+	0.0168845i
$547$	−5078.61	+	8796.41i	−0.396976	+	0.687582i	−0.993351	−	0.115124i	$-0.963274\pi$
$547$	−5078.61	+	8796.41i	−0.396976	+	0.687582i	0.596376	+	0.802705i	$0.296607\pi$
$548$	−2103.08			−0.163940
$549$	−731.413	−	11765.3i	−0.0568596	−	0.914632i
$550$		0			0
$551$	7454.16	−	12911.0i	0.576330	−	0.998232i
$552$	−3744.98	+	3985.03i	−0.288763	+	0.307272i
$553$	−519.481	−	899.768i	−0.0399468	−	0.0691899i
$554$	−5697.76	−	9868.81i	−0.436958	−	0.756833i
$555$		0			0
$556$	−2162.78	+	3746.05i	−0.164968	+	0.285733i
$557$	−5709.62			−0.434334			−0.217167	−	0.976134i	$-0.569682\pi$
$557$	−5709.62			−0.434334			−0.217167	+	0.976134i	$0.569682\pi$
$558$	455.258	−	301.984i	0.0345387	−	0.0229104i
$559$	−6650.20			−0.503173
$560$		0			0
$561$	−18336.0	−	4307.88i	−1.37994	−	0.324204i
$562$	−1236.46	−	2141.61i	−0.0928058	−	0.160744i
$563$	6469.56	+	11205.6i	0.484297	+	0.838828i	0.999837	−	0.0180378i	$-0.00574193\pi$
$563$	6469.56	+	11205.6i	0.484297	+	0.838828i	−0.515540	+	0.856866i	$0.672409\pi$
$564$	2438.64	+	8088.06i	0.182066	+	0.603845i
$565$		0			0
$566$	−23299.2			−1.73028
$567$	−716.012	−	946.236i	−0.0530330	−	0.0700850i
$568$	1856.34			0.137131
$569$	3062.71	−	5304.77i	0.225651	−	0.390839i	−0.730863	−	0.682524i	$-0.760882\pi$
$569$	3062.71	−	5304.77i	0.225651	−	0.390839i	0.956515	+	0.291684i	$0.0942157\pi$
$570$		0			0
$571$	9641.20	+	16699.0i	0.706605	+	1.22388i	0.966109	+	0.258134i	$0.0831076\pi$
$571$	9641.20	+	16699.0i	0.706605	+	1.22388i	−0.259504	+	0.965742i	$0.583559\pi$
$572$	1829.70	+	3169.13i	0.133748	+	0.231658i
$573$	−1925.80	−	452.450i	−0.140404	−	0.0329867i
$574$	799.592	−	1384.93i	0.0581434	−	0.100707i
$575$		0			0
$576$	−3432.78	+	2277.05i	−0.248320	+	0.164717i
$577$	4988.14			0.359894			0.179947	−	0.983676i	$-0.442407\pi$
$577$	4988.14			0.359894			0.179947	+	0.983676i	$0.442407\pi$
$578$	−12232.3	+	21187.0i	−0.880274	+	1.52468i
$579$	−5501.46	+	5854.09i	−0.394876	+	0.420186i
$580$		0			0
$581$	1216.43	+	2106.92i	0.0868606	+	0.150447i
$582$	10701.2	−	11387.1i	0.762165	−	0.811018i
$583$	2879.12	−	4986.78i	0.204530	−	0.354256i
$584$	2860.85			0.202710
$585$		0			0
$586$	15679.4			1.10531
$587$	−7647.00	+	13245.0i	−0.537693	+	0.931311i	0.461335	+	0.887226i	$0.347371\pi$
$587$	−7647.00	+	13245.0i	−0.537693	+	0.931311i	−0.999028	+	0.0440852i	$0.985963\pi$
$588$	5805.84	+	1364.03i	0.407192	+	0.0956661i
$589$	−162.921	−	282.188i	−0.0113974	−	0.0197408i
$590$		0			0
$591$	6426.90	+	21315.6i	0.447322	+	1.48360i
$592$	13840.4	−	23972.3i	0.960874	−	1.66428i
$593$	11090.9			0.768040			0.384020	−	0.923325i	$-0.374539\pi$
$593$	11090.9			0.768040			0.384020	+	0.923325i	$0.374539\pi$
$594$	2609.94	−	15326.7i	0.180281	−	1.05869i
$595$		0			0
$596$	−2570.21	+	4451.73i	−0.176644	+	0.305956i
$597$	−2104.28	−	6979.10i	−0.144259	−	0.478452i
$598$	−3754.88	−	6503.63i	−0.256770	−	0.444738i
$599$	14100.8	+	24423.3i	0.961840	+	1.66596i	0.717875	+	0.696172i	$0.245115\pi$
$599$	14100.8	+	24423.3i	0.961840	+	1.66596i	0.243965	+	0.969784i	$0.421552\pi$
$600$		0			0
$601$	−10572.0	+	18311.3i	−0.717539	+	1.24281i	0.244433	+	0.969666i	$0.421398\pi$
$601$	−10572.0	+	18311.3i	−0.717539	+	1.24281i	−0.961972	+	0.273148i	$0.911935\pi$
$602$	1105.45			0.0748416
$603$	20101.7	+	9997.26i	1.35755	+	0.675157i
$604$	10665.0			0.718467
$605$		0			0
$606$	−1844.93	+	1963.18i	−0.123672	+	0.131599i
$607$	−4399.49	−	7620.14i	−0.294184	−	0.509542i	0.680611	−	0.732645i	$-0.261715\pi$
$607$	−4399.49	−	7620.14i	−0.294184	−	0.509542i	−0.974795	+	0.223103i	$0.928381\pi$
$608$	−3899.41	−	6753.97i	−0.260102	−	0.450509i
$609$	−1590.04	+	1691.96i	−0.105799	+	0.112581i
$610$		0			0
$611$	15919.6			1.05407
$612$	−8992.87	−	4472.45i	−0.593979	−	0.295406i
$613$	−19539.8			−1.28745			−0.643724	−	0.765257i	$-0.722612\pi$
$613$	−19539.8			−1.28745			−0.643724	+	0.765257i	$0.722612\pi$
$614$	−12412.4	+	21498.9i	−0.815836	+	1.41307i
$615$		0			0
$616$	417.375	+	722.914i	0.0272995	+	0.0472842i
$617$	−1636.94	−	2835.26i	−0.106808	−	0.184997i	0.807667	−	0.589638i	$-0.200730\pi$
$617$	−1636.94	−	2835.26i	−0.106808	−	0.184997i	−0.914475	+	0.404641i	$0.867396\pi$
$618$	−684.373	−	2269.81i	−0.0445462	−	0.147743i
$619$	−4693.24	+	8128.92i	−0.304745	+	0.527834i	−0.977205	−	0.212300i	$-0.931905\pi$
$619$	−4693.24	+	8128.92i	−0.304745	+	0.527834i	0.672460	+	0.740134i	$0.265238\pi$
$620$		0			0
$621$	−1588.26	+	9326.96i	−0.102632	+	0.602702i
$622$	−9136.21			−0.588953
$623$	−1169.73	+	2026.04i	−0.0752238	+	0.130291i
$624$	−3943.09	−	13077.8i	−0.252965	−	0.838989i
$625$		0			0
$626$	−10527.8	−	18234.7i	−0.672165	−	1.16422i
$627$	−9027.29	−	2120.88i	−0.574984	−	0.135087i
$628$	−4027.68	+	6976.15i	−0.255927	+	0.443278i
$629$	−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	$0.401573\pi$
$632$	−4980.59	+	8626.64i	−0.313477	+	0.542958i
$633$	−7652.23	+	8142.72i	−0.480488	+	0.511286i
$634$	3513.97	+	6086.37i	0.220122	+	0.381263i
$635$		0			0
$636$	2102.74	−	2237.52i	0.131099	−	0.139502i
$637$	5619.48	−	9733.23i	0.349532	−	0.605408i
$638$	−30421.6			−1.88778
$639$	2676.40	−	1775.32i	0.165691	−	0.109907i
$640$		0			0
$641$	3501.88	−	6065.44i	0.215782	−	0.373745i	−0.737732	−	0.675093i	$-0.764103\pi$
$641$	3501.88	−	6065.44i	0.215782	−	0.373745i	0.953514	+	0.301348i	$0.0974367\pi$
$642$	−12261.3	−	2880.68i	−0.753761	−	0.177089i
$643$	−3144.44	−	5446.34i	−0.192853	−	0.334032i	0.753341	−	0.657630i	$-0.228441\pi$
$643$	−3144.44	−	5446.34i	−0.192853	−	0.334032i	−0.946195	+	0.323598i	$0.895108\pi$
$644$	185.087	+	320.579i	0.0113252	+	0.0196158i
$645$		0			0
$646$	−10100.7	+	17495.0i	−0.615183	+	1.06553i
$647$	5900.85			0.358557			0.179279	−	0.983798i	$-0.442624\pi$
$647$	5900.85			0.358557			0.179279	+	0.983798i	$0.442624\pi$
$648$	−4424.29	+	10481.2i	−0.268214	+	0.635404i
$649$	6021.58			0.364203
$650$		0			0
$651$	14.6495	+	48.5868i	0.000881963	+	0.00292514i
$652$	−4290.88	−	7432.02i	−0.257736	−	0.446412i
$653$	−3942.57	−	6828.74i	−0.236271	−	0.409233i	0.723370	−	0.690460i	$-0.242592\pi$
$653$	−3942.57	−	6828.74i	−0.236271	−	0.409233i	−0.959641	+	0.281227i	$0.909259\pi$
$654$	34296.9	+	8057.75i	2.05064	+	0.481778i
$655$		0			0
$656$	−23192.2			−1.38034
$657$	4124.65	−	2735.98i	0.244928	−	0.162467i
$658$	−2646.28			−0.156782
$659$	−14378.9	+	24905.0i	−0.849959	+	1.47217i	0.0312845	+	0.999511i	$0.490040\pi$
$659$	−14378.9	+	24905.0i	−0.849959	+	1.47217i	−0.881244	+	0.472662i	$0.843293\pi$
$660$		0			0
$661$	−4130.11	−	7153.57i	−0.243030	−	0.420940i	0.718546	−	0.695479i	$-0.244808\pi$
$661$	−4130.11	−	7153.57i	−0.243030	−	0.420940i	−0.961576	+	0.274539i	$0.911475\pi$
$662$	384.232	+	665.509i	0.0225583	+	0.0390721i
$663$	−12961.7	+	13792.5i	−0.759260	+	0.807926i
$664$	11662.7	−	20200.4i	0.681626	−	1.18061i
$665$		0			0
$666$	−1964.45	−	31599.7i	−0.114296	−	1.83853i
$667$	18512.9			1.07470
$668$	−2317.70	+	4014.37i	−0.134243	+	0.232516i
$669$	−12940.2	−	3040.18i	−0.747828	−	0.175695i
$670$		0			0
$671$	7173.56	+	12425.0i	0.412716	+	0.714845i
$672$	350.625	+	1162.89i	0.0201275	+	0.0667553i
$673$	402.481	−	697.118i	0.0230528	−	0.0399285i	−0.854269	−	0.519831i	$-0.825995\pi$
$673$	402.481	−	697.118i	0.0230528	−	0.0399285i	0.877322	+	0.479903i	$0.159328\pi$
$674$	−11524.7			−0.658627
$675$		0			0
$676$	−3731.65			−0.212315
$677$	681.636	−	1180.63i	0.0386963	−	0.0670240i	−0.846029	−	0.533137i	$-0.821013\pi$
$677$	681.636	−	1180.63i	0.0386963	−	0.0670240i	0.884725	+	0.466114i	$0.154346\pi$
$678$	1146.97	+	3804.07i	0.0649692	+	0.215478i
$679$	725.774	+	1257.08i	0.0410201	+	0.0710489i
$680$		0			0
$681$	−20661.3	−	4854.19i	−1.16262	−	0.273147i
$682$	−332.454	+	575.827i	−0.0186661	+	0.0323307i
$683$	11434.6			0.640604			0.320302	−	0.947315i	$-0.396216\pi$
$683$	11434.6			0.640604			0.320302	+	0.947315i	$0.396216\pi$
$684$	−4427.42	−	2201.91i	−0.247495	−	0.123088i
$685$		0			0
$686$	−1875.50	+	3248.46i	−0.104383	+	0.180797i
$687$	−9756.87	+	10382.3i	−0.541845	+	0.576576i
$688$	−8015.86	−	13883.9i	−0.444189	−	0.769358i
$689$	−2893.17	−	5011.12i	−0.159972	−	0.277080i
$690$		0			0
$691$	9765.29	−	16914.0i	0.537611	−	0.931170i	−0.461421	−	0.887181i	$-0.652660\pi$
$691$	9765.29	−	16914.0i	0.537611	−	0.931170i	0.999032	−	0.0439884i	$-0.0140065\pi$
$692$	−7960.10			−0.437280
$693$	1293.11	+	643.109i	0.0708822	+	0.0352521i
$694$	−12172.6			−0.665799
$695$		0			0
$696$	21671.0	+	5091.40i	1.18022	+	0.277283i
$697$	16068.3	+	27831.0i	0.873212	+	1.51245i
$698$	14839.4	+	25702.7i	0.804701	+	1.39378i
$699$	−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	$0.596137\pi$
$702$	−12026.7	−	9972.04i	−0.646609	−	0.536140i
$703$	−18883.8			−1.01311
$704$	2506.80	−	4341.90i	0.134203	−	0.232446i
$705$		0			0
$706$	14349.9	+	24854.7i	0.764964	+	1.32496i
$707$	−125.126	−	216.725i	−0.00665608	−	0.0115287i
$708$	3125.82	+	734.382i	0.165926	+	0.0389827i
$709$	−1969.54	+	3411.34i	−0.104327	+	0.180699i	−0.913463	−	0.406922i	$-0.866602\pi$
$709$	−1969.54	+	3411.34i	−0.104327	+	0.180699i	0.809136	+	0.587621i	$0.199935\pi$
$710$		0			0
$711$	1069.31	+	17200.7i	0.0564027	+	0.907282i
$712$	22430.0			1.18062
$713$	202.313	−	350.416i	0.0106265	−	0.0184056i
$714$	2154.59	−	2292.69i	0.112932	−	0.120170i
$715$		0			0
$716$	−2200.60	−	3811.55i	−0.114861	−	0.198944i
$717$	5253.91	−	5590.67i	0.273655	−	0.291196i
$718$	−7284.72	+	12617.5i	−0.378640	+	0.655824i
$719$	−23298.2			−1.20845			−0.604225	−	0.796814i	$-0.706517\pi$
$719$	−23298.2			−1.20845			−0.604225	+	0.796814i	$0.706517\pi$
$720$		0			0
$721$	220.220			0.0113751
$722$	6592.38	−	11418.3i	0.339810	−	0.588569i
$723$	−8920.31	−	2095.75i	−0.458852	−	0.107803i
$724$	−5226.08	−	9051.83i	−0.268267	−	0.464653i
$725$		0			0
$726$	−1270.31	−	4213.15i	−0.0649389	−	0.215378i
$727$	−4752.24	+	8231.12i	−0.242436	+	0.419911i	−0.961408	−	0.275128i	$-0.911280\pi$
$727$	−4752.24	+	8231.12i	−0.242436	+	0.419911i	0.718972	+	0.695039i	$0.244613\pi$
$728$	838.823			0.0427044
$729$	3645.00	+	19342.6i	0.185185	+	0.982704i
$730$		0			0
$731$	−11107.3	+	19238.4i	−0.561994	+	0.973402i
$732$	2208.48	+	7324.70i	0.111513	+	0.369848i
$733$	3660.40	+	6340.01i	0.184448	+	0.319473i	0.943390	−	0.331685i	$-0.107617\pi$
$733$	3660.40	+	6340.01i	0.184448	+	0.319473i	−0.758943	+	0.651157i	$0.774284\pi$
$734$	11129.2	+	19276.3i	0.559653	+	0.969348i
$735$		0			0
$736$	4842.22	−	8386.96i	0.242509	−	0.420037i
$737$	−27324.3			−1.36567
$738$	−22105.6	+	14663.2i	−1.10260	+	0.731381i
$739$	−1274.52			−0.0634424			−0.0317212	−	0.999497i	$-0.510099\pi$
$739$	−1274.52			−0.0634424			−0.0317212	+	0.999497i	$0.510099\pi$
$740$		0			0
$741$	−6381.37	+	6790.39i	−0.316363	+	0.336641i
$742$	480.925	+	832.986i	0.0237942	+	0.0412128i
$743$	970.576	+	1681.09i	0.0479232	+	0.0830055i	0.888992	−	0.457923i	$-0.151406\pi$
$743$	970.576	+	1681.09i	0.0479232	+	0.0830055i	−0.841069	+	0.540928i	$0.818073\pi$
$744$	333.196	−	354.553i	0.0164187	−	0.0174711i
$745$		0			0
$746$	29030.1			1.42476
$747$	−2503.93	−	40277.6i	−0.122642	−	1.97280i
$748$	12224.0			0.597531
$749$	584.988	−	1013.23i	0.0285380	−	0.0494293i
$750$		0			0
$751$	−8270.01	−	14324.1i	−0.401834	−	0.695996i	0.592114	−	0.805854i	$-0.298294\pi$
$751$	−8270.01	−	14324.1i	−0.401834	−	0.695996i	−0.993947	+	0.109858i	$0.964960\pi$
$752$	19188.8	+	33236.0i	0.930511	+	1.61169i
$753$	2557.75	+	8483.08i	0.123784	+	0.410545i
$754$	−15285.0	+	26474.4i	−0.738260	+	1.27870i
$755$		0			0
$756$	592.826	+	491.545i	0.0285197	+	0.0236472i
$757$	−21145.7			−1.01526			−0.507631	−	0.861575i	$-0.669479\pi$
$757$	−21145.7			−1.01526			−0.507631	+	0.861575i	$0.669479\pi$
$758$	12021.8	−	20822.4i	0.576059	−	0.997764i
$759$	−3324.14	−	11024.9i	−0.158970	−	0.527245i
$760$		0			0
$761$	10067.1	+	17436.7i	0.479543	+	0.830593i	0.999725	−	0.0234624i	$-0.00746901\pi$
$761$	10067.1	+	17436.7i	0.479543	+	0.830593i	−0.520181	+	0.854056i	$0.674136\pi$
$762$	19314.2	+	4537.69i	0.918213	+	0.215726i
$763$	−1636.31	+	2834.17i	−0.0776388	+	0.134474i
$764$	1283.87			0.0607968
$765$		0			0
$766$	−19989.1			−0.942865
$767$	3025.48	−	5240.29i	0.142430	−	0.246696i
$768$	15617.0	−	16618.0i	0.733762	−	0.780795i
$769$	−1097.36	−	1900.68i	−0.0514587	−	0.0891291i	0.839149	−	0.543902i	$-0.183054\pi$
$769$	−1097.36	−	1900.68i	−0.0514587	−	0.0891291i	−0.890607	+	0.454773i	$0.849720\pi$
$770$		0			0
$771$	−813.442	+	865.581i	−0.0379966	+	0.0404321i
$772$	2606.84	−	4515.18i	0.121531	−	0.210499i
$773$	8327.70			0.387486			0.193743	−	0.981052i	$-0.437937\pi$
$773$	8327.70			0.387486			0.193743	+	0.981052i	$0.437937\pi$
$774$	−16418.4	−	8165.40i	−0.762462	−	0.379198i
$775$		0			0
$776$	6958.46	−	12052.4i	0.321900	−	0.557547i
$777$	2863.04	+	672.646i	0.132189	+	0.0310567i
$778$	−1751.67	−	3033.98i	−0.0807204	−	0.139812i
$779$	7910.82	+	13701.9i	0.363844	+	0.630196i
$780$		0			0
$781$	−1954.45	+	3385.20i	−0.0895463	+	0.155099i
$782$	−25085.8			−1.14715
$783$	36113.4	−	13384.5i	1.64826	−	0.610887i
$784$	27093.9			1.23424
$785$		0			0
$786$	3932.95	+	13044.1i	0.178478	+	0.591944i
$787$	−9481.64	−	16422.7i	−0.429459	−	0.743845i	0.567366	−	0.823465i	$-0.307962\pi$
$787$	−9481.64	−	16422.7i	−0.429459	−	0.743845i	−0.996825	+	0.0796209i	$0.974629\pi$
$788$	−7224.43	−	12513.1i	−0.326599	−	0.565686i
$789$	−6519.10	−	1531.60i	−0.294152	−	0.0691084i
$790$		0			0
$791$	−369.076			−0.0165902
$792$	−859.134	−	13819.8i	−0.0385454	−	0.620034i
$793$	14417.1			0.645608
$794$	22664.1	−	39255.4i	1.01300	−	1.75456i
$795$		0			0
$796$	2365.41	+	4097.01i	0.105326	+	0.182430i
$797$	17132.6	+	29674.5i	0.761439	+	1.31885i	0.942109	+	0.335307i	$0.108840\pi$
$797$	17132.6	+	29674.5i	0.761439	+	1.31885i	−0.180670	+	0.983544i	$0.557827\pi$
$798$	1060.76	−	1128.75i	0.0470557	−	0.0500718i
$799$	26589.2	−	46053.9i	1.17730	−	2.03914i
$800$		0			0
$801$	32338.5	−	21451.0i	1.42650	−	0.946233i
$802$	44093.9			1.94141
$803$	−3012.04	+	5217.00i	−0.132369	+	0.229270i
$804$	−14184.1	−	3332.42i	−0.622181	−	0.146176i
$805$		0			0
$806$	334.076	+	578.636i	0.0145997	+	0.0252873i
$807$	1460.97	+	4845.49i	0.0637282	+	0.211362i
$808$	−1199.66	+	2077.88i	−0.0522327	+	0.0904696i
$809$	36425.5			1.58300			0.791502	−	0.611166i	$-0.209299\pi$
$809$	36425.5			1.58300			0.791502	+	0.611166i	$0.209299\pi$
$810$		0			0
$811$	45174.0			1.95595			0.977973	−	0.208732i	$-0.0669335\pi$
$811$	45174.0			1.95595			0.977973	+	0.208732i	$0.0669335\pi$
$812$	753.435	−	1304.99i	0.0325620	−	0.0563991i
$813$	−6032.74	−	20008.3i	−0.260243	−	0.863128i
$814$	19267.0	+	33371.3i	0.829615	+	1.43694i
$815$		0			0
$816$	−44418.5	−	10435.7i	−1.90559	−	0.447700i
$817$	−5468.41	+	9471.56i	−0.234168	+	0.405591i
$818$	−17782.7			−0.760093
$819$	1209.38	−	802.210i	0.0515984	−	0.0342265i
$820$		0			0
$821$	3459.65	−	5992.29i	0.147068	−	0.254729i	−0.783075	−	0.621928i	$-0.786350\pi$
$821$	3459.65	−	5992.29i	0.147068	−	0.254729i	0.930143	+	0.367199i	$0.119683\pi$
$822$	−7483.66	+	7963.34i	−0.317546	+	0.337900i
$823$	−5699.26	−	9871.42i	−0.241390	−	0.418100i	0.719721	−	0.694264i	$-0.244270\pi$
$823$	−5699.26	−	9871.42i	−0.241390	−	0.418100i	−0.961110	+	0.276164i	$0.910937\pi$
$824$	−1055.70	−	1828.52i	−0.0446322	−	0.0773052i
$825$		0			0
$826$	−502.919	+	871.080i	−0.0211850	+	0.0366934i
$827$	−34712.0			−1.45956			−0.729779	−	0.683683i	$-0.760377\pi$
$827$	−34712.0			−1.45956			−0.729779	+	0.683683i	$0.760377\pi$
$828$	−380.986	−	6128.46i	−0.0159906	−	0.257221i
$829$	2732.97			0.114500			0.0572498	−	0.998360i	$-0.481767\pi$
$829$	2732.97			0.114500			0.0572498	+	0.998360i	$0.481767\pi$
$830$		0			0
$831$	−17093.3	−	4015.91i	−0.713549	−	0.167642i
$832$	−2519.03	−	4363.09i	−0.104966	−	0.181806i
$833$	−18771.5	−	32513.2i	−0.780786	−	1.35236i
$834$	6488.34	+	21519.4i	0.269392	+	0.893472i
$835$		0			0
$836$	6018.19			0.248975
$837$	141.310	−	829.831i	0.00583557	−	0.0342690i
$838$	46693.0			1.92480
$839$	4787.89	−	8292.87i	0.197016	−	0.341242i	−0.750544	−	0.660821i	$-0.770208\pi$
$839$	4787.89	−	8292.87i	0.197016	−	0.341242i	0.947560	+	0.319579i	$0.103542\pi$
$840$		0			0
$841$	−25485.8	−	44142.8i	−1.04497	−	1.80995i
$842$	−1850.32	−	3204.85i	−0.0757318	−	0.131171i
$843$	−3709.38	−	871.484i	−0.151551	−	0.0356056i
$844$	3625.97	−	6280.37i	0.147880	−	0.256136i
$845$		0			0
$846$	39303.2	+	19546.8i	1.59725	+	0.794364i
$847$	408.766			0.0165825
$848$	6974.60	−	12080.4i	0.282440	−	0.489200i
$849$	−24585.2	+	26161.1i	−0.993832	+	1.05753i
$850$		0			0
$851$	−11724.8	−	20307.9i	−0.472292	−	0.818034i
$852$	−1427.41	+	1518.90i	−0.0573971	+	0.0610761i
$853$	4520.95	−	7830.51i	0.181470	−	0.314316i	−0.760911	−	0.648856i	$-0.775248\pi$
$853$	4520.95	−	7830.51i	0.181470	−	0.314316i	0.942381	+	0.334540i	$0.108581\pi$
$854$	−2396.52			−0.0960274
$855$		0			0
$856$	−11217.3			−0.447896
$857$	−1157.64	+	2005.09i	−0.0461426	+	0.0799213i	−0.888174	−	0.459507i	$-0.848026\pi$
$857$	−1157.64	+	2005.09i	−0.0461426	+	0.0799213i	0.842032	+	0.539428i	$0.181360\pi$
$858$	18510.8	+	4348.94i	0.736536	+	0.173043i
$859$	15701.6	+	27195.9i	0.623667	+	1.08022i	0.988797	+	0.149266i	$0.0476912\pi$
$859$	15701.6	+	27195.9i	0.623667	+	1.08022i	−0.365130	+	0.930957i	$0.618975\pi$
$860$		0			0
$861$	−711.322	−	2359.19i	−0.0281554	−	0.0933808i
$862$	−26831.3	+	46473.2i	−1.06018	+	1.83629i
$863$	40883.5			1.61262			0.806310	−	0.591493i	$-0.201461\pi$
$863$	40883.5			1.61262			0.806310	+	0.591493i	$0.201461\pi$
$864$	3382.15	−	19861.4i	0.133175	−	0.782060i
$865$		0			0
$866$	6013.30	−	10415.3i	0.235959	−	0.408692i
$867$	10882.0	+	36091.4i	0.426264	+	1.41376i
$868$	−16.4674	−	28.5223i	−0.000643939	−	0.00111534i
$869$	−10487.6	−	18165.1i	−0.409399	−	0.709100i
$870$		0			0
$871$	−13728.8	+	23779.0i	−0.534078	+	0.925051i
$872$	31376.7			1.21852
$873$	−1493.95	−	24031.4i	−0.0579182	−	0.931659i
$874$	−12350.4			−0.477985
$875$		0			0
$876$	−2199.81	+	2340.81i	−0.0848456	+	0.0902840i
$877$	−14157.3	−	24521.2i	−0.545107	−	0.944154i	−0.998600	−	0.0528937i	$-0.983156\pi$
$877$	−14157.3	−	24521.2i	−0.545107	−	0.944154i	0.453493	−	0.891260i	$-0.350178\pi$
$878$	979.348	+	1696.28i	0.0376440	+	0.0652013i
$879$	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	$0.460462\pi$
$882$	25824.5	−	17130.1i	0.985893	−	0.653968i
$883$	17769.0			0.677208			0.338604	−	0.940929i	$-0.390045\pi$
$883$	17769.0			0.677208			0.338604	+	0.940929i	$0.390045\pi$
$884$	6141.82	−	10637.9i	0.233678	−	0.404743i
$885$		0			0
$886$	−18198.1	−	31520.1i	−0.690044	−	1.19519i
$887$	−12944.1	−	22419.8i	−0.489988	−	0.848684i	0.509945	−	0.860207i	$-0.329666\pi$
$887$	−12944.1	−	22419.8i	−0.489988	−	0.848684i	−0.999934	+	0.0115224i	$0.996332\pi$
$888$	−8139.83	−	26996.8i	−0.307607	−	1.02022i
$889$	−921.481	+	1596.05i	−0.0347643	+	0.0602136i
$890$		0			0
$891$	−14455.3	−	19103.2i	−0.543514	−	0.718273i
$892$	8626.80			0.323819
$893$	13090.6	−	22673.5i	0.490548	−	0.849654i
$894$	7710.62	+	25573.2i	0.288458	+	0.956707i
$895$		0			0
$896$	1353.73	+	2344.73i	0.0504744	+	0.0874242i
$897$	−11264.6	−	2646.52i	−0.419303	−	0.0985115i
$898$	−4879.71	+	8451.90i	−0.181334	+	0.314080i
$899$	−1647.11			−0.0611060
$900$		0			0
$901$	−19328.9			−0.714694
$902$	16142.7	−	27959.9i	0.595889	−	1.03211i
$903$	1166.46	−	1241.23i	0.0429873	−	0.0457426i
$904$	1769.28	+	3064.49i	0.0650946	+	0.112747i
$905$		0			0
$906$	37950.7	−	40383.2i	1.39164	−	1.48084i
$907$	−22594.1	+	39134.2i	−0.827150	+	1.43267i	0.0731143	+	0.997324i	$0.476706\pi$
$907$	−22594.1	+	39134.2i	−0.827150	+	1.43267i	−0.900265	+	0.435343i	$0.856627\pi$
$908$	13774.2			0.503429
$909$	257.562	+	4143.09i	0.00939802	+	0.151175i
$910$		0			0
$911$	−6587.08	+	11409.2i	−0.239560	+	0.414931i	−0.960588	−	0.277975i	$-0.910337\pi$
$911$	−6587.08	+	11409.2i	−0.239560	+	0.414931i	0.721028	+	0.692906i	$0.243670\pi$
$912$	−21868.4	−	5137.78i	−0.794007	−	0.186545i
$913$	24558.0	+	42535.8i	0.890200	+	1.54187i
$914$	5395.51	+	9345.29i	0.195260	+	0.338200i
$915$		0			0
$916$	4623.24	−	8007.69i	0.166765	−	0.288845i
$917$	−1265.56			−0.0455752
$918$	−48935.4	+	18136.7i	−1.75938	+	0.652069i
$919$	−54078.5			−1.94112			−0.970558	−	0.240867i	$-0.922568\pi$
$919$	−54078.5			−1.94112			−0.970558	+	0.240867i	$0.922568\pi$
$920$		0			0
$921$	11042.1	+	36622.6i	0.395060	+	1.31027i
$922$	−12336.4	−	21367.3i	−0.440650	−	0.763228i
$923$	1963.98	+	3401.72i	0.0700383	+	0.121310i
$924$	−912.440	−	214.370i	−0.0324860	−	0.00763229i
$925$		0			0
$926$	−23646.4			−0.839166
$927$	−3270.76	−	1626.66i	−0.115886	−	0.0576338i
$928$	−39422.6			−1.39451
$929$	22858.9	−	39592.8i	0.807294	−	1.39827i	−0.107438	−	0.994212i	$-0.534265\pi$
$929$	22858.9	−	39592.8i	0.807294	−	1.39827i	0.914732	−	0.404062i	$-0.132402\pi$
$930$		0			0
$931$	−9241.71	−	16007.1i	−0.325333	−	0.563493i
$932$	8573.53	+	14849.8i	0.301325	+	0.521911i
$933$	−9640.50	+	10258.4i	−0.338281	+	0.359963i
$934$	−13493.6	+	23371.5i	−0.472722	+	0.818779i
$935$		0			0
$936$	−12458.4	−	6195.98i	−0.435059	−	0.216369i
$937$	5055.54			0.176262			0.0881309	−	0.996109i	$-0.471911\pi$
$937$	5055.54			0.176262			0.0881309	+	0.996109i	$0.471911\pi$
$938$	2282.10	−	3952.72i	0.0794385	−	0.137592i
$939$	−31583.4	−	7420.23i	−1.09764	−	0.257881i
$940$		0			0
$941$	−14056.0	−	24345.7i	−0.486942	−	0.843407i	0.512946	−	0.858421i	$-0.328554\pi$
$941$	−14056.0	−	24345.7i	−0.486942	−	0.843407i	−0.999887	+	0.0150136i	$0.995221\pi$
$942$	12083.1	+	40075.0i	0.417927	+	1.38611i
$943$	−9823.52	+	17014.8i	−0.339234	+	0.587571i
$944$	14587.1			0.502935
$945$		0			0
$946$	22317.4			0.767022
$947$	15060.2	−	26085.0i	0.516780	−	0.895090i	−0.483030	−	0.875604i	$-0.660464\pi$
$947$	15060.2	−	26085.0i	0.516780	−	0.895090i	0.999810	−	0.0194859i	$-0.00620295\pi$
$948$	−3228.76	−	10708.6i	−0.110617	−	0.366876i
$949$	3026.74	+	5242.46i	0.103532	+	0.179323i
$950$		0			0
$951$	10541.9	+	2476.73i	0.359458	+	0.0844514i
$952$	1401.02	−	2426.63i	0.0476967	−	0.0826130i
$953$	−19362.7			−0.658154			−0.329077	−	0.944303i	$-0.606738\pi$
$953$	−19362.7			−0.658154			−0.329077	+	0.944303i	$0.606738\pi$
$954$	−989.946	−	15924.1i	−0.0335961	−	0.540420i
$955$		0			0
$956$	−2489.54	+	4312.01i	−0.0842233	+	0.145879i
$957$	−32100.8	+	34158.4i	−1.08430	+	1.15380i
$958$	5359.97	+	9283.74i	0.180765	+	0.313094i
$959$	−507.554	−	879.109i	−0.0170905	−	0.0296016i
$960$		0			0
$961$	14877.5	−	25768.6i	0.499396	−	0.864979i
$962$	38721.9			1.29776
$963$	−16172.6	+	10727.7i	−0.541179	+	0.358977i
$964$	5946.87			0.198689
$965$		0			0
$966$	1872.49	+	439.925i	0.0623669	+	0.0146525i
$967$	−15362.3	−	26608.2i	−0.510876	−	0.884863i	−0.999921	−	0.0126043i	$-0.995988\pi$
$967$	−15362.3	−	26608.2i	−0.510876	−	0.884863i	0.489045	−	0.872259i	$-0.337346\pi$
$968$	−1959.55	−	3394.04i	−0.0650643	−	0.112695i
$969$	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	$0.807587\pi$
$972$	−5173.98	−	11679.5i	−0.170736	−	0.385410i
$973$	−2087.84			−0.0687906
$974$	22021.4	−	38142.3i	0.724448	−	1.25478i
$975$		0			0
$976$	17377.8	+	30099.2i	0.569927	+	0.987143i
$977$	−11195.9	−	19391.9i	−0.366622	−	0.635008i	0.622413	−	0.782689i	$-0.286153\pi$
$977$	−11195.9	−	19391.9i	−0.366622	−	0.635008i	−0.989035	+	0.147681i	$0.952819\pi$
$978$	−43410.2	−	10198.8i	−1.41933	−	0.333458i
$979$	−23615.3	+	40903.0i	−0.770939	+	1.33531i
$980$		0			0
$981$	45237.5	−	30007.2i	1.47230	−	0.976611i
$982$	−14843.5			−0.482357
$983$	−12309.7	+	21321.0i	−0.399408	+	0.691794i	−0.993653	−	0.112490i	$-0.964117\pi$
$983$	−12309.7	+	21321.0i	−0.399408	+	0.691794i	0.594245	+	0.804284i	$0.297451\pi$
$984$	−16178.7	+	17215.7i	−0.524144	+	0.557741i
$985$		0			0
$986$	51058.7	+	88436.2i	1.64913	+	2.85637i
$987$	−2792.35	+	2971.33i	−0.0900521	+	0.0958242i
$988$	3023.78	−	5237.34i	0.0973676	−	0.168646i
$989$	−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	$0.371328\pi$
$992$	−430.818	+	746.199i	−0.0137888	+	0.0238829i
$993$	1152.70	+	270.815i	0.0368375	+	0.00865465i
$994$	−326.468	−	565.460i	−0.0104175	−	0.0180436i
$995$		0			0
$996$	7560.54	+	25075.5i	0.240527	+	0.797737i
$997$	22978.0	−	39799.1i	0.729912	−	1.26424i	−0.227008	−	0.973893i	$-0.572895\pi$
$997$	22978.0	−	39799.1i	0.729912	−	1.26424i	0.956920	−	0.290351i	$-0.0937722\pi$
$998$	63146.7			2.00288
$999$	−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.e.a.151.1		4
5.2	odd	4		225.4.k.a.124.1		8
5.3	odd	4		225.4.k.a.124.4		8
5.4	even	2		45.4.e.a.16.2	✓	4
9.2	odd	6		2025.4.a.j.1.1		2
9.4	even	3	inner	225.4.e.a.76.1		4
9.7	even	3		2025.4.a.l.1.2		2
15.14	odd	2		135.4.e.a.46.1		4
45.4	even	6		45.4.e.a.31.2	yes	4
45.13	odd	12		225.4.k.a.49.1		8
45.14	odd	6		135.4.e.a.91.1		4
45.22	odd	12		225.4.k.a.49.4		8
45.29	odd	6		405.4.a.e.1.2		2
45.34	even	6		405.4.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.2	✓	4	5.4	even	2
45.4.e.a.31.2	yes	4	45.4	even	6
135.4.e.a.46.1		4	15.14	odd	2
135.4.e.a.91.1		4	45.14	odd	6
225.4.e.a.76.1		4	9.4	even	3	inner
225.4.e.a.151.1		4	1.1	even	1	trivial
225.4.k.a.49.1		8	45.13	odd	12
225.4.k.a.49.4		8	45.22	odd	12
225.4.k.a.124.1		8	5.2	odd	4
225.4.k.a.124.4		8	5.3	odd	4
405.4.a.d.1.1		2	45.34	even	6
405.4.a.e.1.2		2	45.29	odd	6
2025.4.a.j.1.1		2	9.2	odd	6
2025.4.a.l.1.2		2	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68614 + 2.92048i) q^{2} +(1.50000 + 4.97494i) q^{3} +(-1.68614 - 2.92048i) q^{4} +(-17.0584 - 4.00772i) q^{6} +(0.813859 - 1.40965i) q^{7} -15.6060 q^{8} +(-22.5000 + 14.9248i) q^{9} +(16.4307 - 28.4588i) q^{11} +(12.0000 - 12.7692i) q^{12} +(-16.5109 - 28.5977i) q^{13} +(2.74456 + 4.75372i) q^{14} +(39.8030 - 68.9408i) q^{16} -110.307 q^{17} +(-5.64947 - 90.8762i) q^{18} -54.3070 q^{19} +(8.23369 + 1.93443i) q^{21} +(55.4090 + 95.9711i) q^{22} +(-33.7188 - 58.4026i) q^{23} +(-23.4090 - 77.6387i) q^{24} +111.359 q^{26} +(-108.000 - 89.5489i) q^{27} -5.48913 q^{28} +(-137.259 + 237.740i) q^{29} +(3.00000 + 5.19615i) q^{31} +(71.8030 + 124.366i) q^{32} +(166.227 + 39.0535i) q^{33} +(185.993 - 322.150i) q^{34} +(81.5258 + 40.5455i) q^{36} +347.723 q^{37} +(91.5693 - 158.603i) q^{38} +(117.505 - 125.037i) q^{39} +(-145.668 - 252.305i) q^{41} +(-19.5326 + 20.7846i) q^{42} +(100.694 - 174.408i) q^{43} -110.818 q^{44} +227.418 q^{46} +(-241.048 + 417.507i) q^{47} +(402.681 + 94.6062i) q^{48} +(170.175 + 294.752i) q^{49} +(-165.461 - 548.771i) q^{51} +(-55.6793 + 96.4394i) q^{52} +175.228 q^{53} +(443.629 - 164.420i) q^{54} +(-12.7011 + 21.9989i) q^{56} +(-81.4605 - 270.174i) q^{57} +(-462.878 - 801.728i) q^{58} +(91.6209 + 158.692i) q^{59} +(-218.297 + 378.102i) q^{61} -20.2337 q^{62} +(2.72686 + 43.8637i) q^{63} +152.568 q^{64} +(-394.337 + 419.613i) q^{66} +(-415.750 - 720.100i) q^{67} +(185.993 + 322.150i) q^{68} +(239.971 - 255.353i) q^{69} -118.951 q^{71} +(351.134 - 232.916i) q^{72} -183.318 q^{73} +(-586.310 + 1015.52i) q^{74} +(91.5693 + 158.603i) q^{76} +(-26.7446 - 46.3229i) q^{77} +(167.038 + 554.002i) q^{78} +(319.147 - 552.778i) q^{79} +(283.500 - 671.617i) q^{81} +982.470 q^{82} +(-747.322 + 1294.40i) q^{83} +(-8.23369 - 27.3081i) q^{84} +(339.569 + 588.151i) q^{86} +(-1388.63 - 326.247i) q^{87} +(-256.417 + 444.127i) q^{88} -1437.27 q^{89} -53.7501 q^{91} +(-113.709 + 196.950i) q^{92} +(-21.3505 + 22.7190i) q^{93} +(-812.880 - 1407.95i) q^{94} +(-511.011 + 543.765i) q^{96} +(-445.884 + 772.294i) q^{97} -1147.76 q^{98} +(55.0516 + 885.548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 6 q^{3} - q^{4} - 51 q^{6} + 9 q^{7} + 18 q^{8} - 90 q^{9} + 37 q^{11} + 48 q^{12} - 112 q^{13} - 12 q^{14} + 119 q^{16} - 154 q^{17} - 126 q^{18} + 70 q^{19} - 36 q^{21} + 101 q^{22} - 267 q^{23}+ \cdots - 90 q^{99}+O(q^{100}) \) 4 * q - q^2 + 6 * q^3 - q^4 - 51 * q^6 + 9 * q^7 + 18 * q^8 - 90 * q^9 + 37 * q^11 + 48 * q^12 - 112 * q^13 - 12 * q^14 + 119 * q^16 - 154 * q^17 - 126 * q^18 + 70 * q^19 - 36 * q^21 + 101 * q^22 - 267 * q^23 + 27 * q^24 - 152 * q^26 - 432 * q^27 + 24 * q^28 - 325 * q^29 + 12 * q^31 + 247 * q^32 + 303 * q^33 + 451 * q^34 + 171 * q^36 + 1276 * q^37 + 395 * q^38 - 564 * q^39 - 238 * q^41 - 216 * q^42 - 97 * q^43 - 202 * q^44 - 492 * q^46 - 901 * q^47 + 525 * q^48 + 629 * q^49 - 231 * q^51 + 76 * q^52 - 448 * q^53 + 999 * q^54 + 156 * q^56 + 105 * q^57 - 806 * q^58 + 85 * q^59 + 247 * q^61 - 12 * q^62 - 351 * q^63 + 1426 * q^64 - 888 * q^66 - 606 * q^67 + 451 * q^68 - 1539 * q^69 + 788 * q^71 - 405 * q^72 + 1622 * q^73 - 484 * q^74 + 395 * q^76 - 84 * q^77 - 228 * q^78 + 840 * q^79 + 1134 * q^81 + 2218 * q^82 - 387 * q^83 + 36 * q^84 + 1387 * q^86 - 2418 * q^87 - 411 * q^88 - 2130 * q^89 - 1272 * q^91 + 246 * q^92 + 18 * q^93 - 632 * q^94 + 24 * q^96 - 1031 * q^97 - 926 * q^98 - 90 * q^99

Introduction

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