LMFDB - Embedded newform 45.4.e.a.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,4,Mod(16,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 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("45.16"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	45.31
Dual form			45.4.e.a.16.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68614 + 2.92048i) q^{2} +(-1.50000 + 4.97494i) q^{3} +(-1.68614 + 2.92048i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-17.0584 + 4.00772i) q^{6} +(-0.813859 - 1.40965i) q^{7} +15.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} -16.8614 q^{10} +(16.4307 + 28.4588i) q^{11} +(-12.0000 - 12.7692i) q^{12} +(16.5109 - 28.5977i) q^{13} +(2.74456 - 4.75372i) q^{14} +(-17.7921 - 18.9325i) q^{15} +(39.8030 + 68.9408i) q^{16} +110.307 q^{17} +(5.64947 - 90.8762i) q^{18} -54.3070 q^{19} +(-8.43070 - 14.6024i) q^{20} +(8.23369 - 1.93443i) q^{21} +(-55.4090 + 95.9711i) q^{22} +(33.7188 - 58.4026i) q^{23} +(-23.4090 + 77.6387i) q^{24} +(-12.5000 - 21.6506i) q^{25} +111.359 q^{26} +(108.000 - 89.5489i) q^{27} +5.48913 q^{28} +(-137.259 - 237.740i) q^{29} +(25.2921 - 83.8844i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-71.8030 + 124.366i) q^{32} +(-166.227 + 39.0535i) q^{33} +(185.993 + 322.150i) q^{34} +8.13859 q^{35} +(81.5258 - 40.5455i) q^{36} -347.723 q^{37} +(-91.5693 - 158.603i) q^{38} +(117.505 + 125.037i) q^{39} +(-39.0149 + 67.5758i) q^{40} +(-145.668 + 252.305i) q^{41} +(19.5326 + 20.7846i) q^{42} +(-100.694 - 174.408i) q^{43} -110.818 q^{44} +(120.876 - 60.1158i) q^{45} +227.418 q^{46} +(241.048 + 417.507i) q^{47} +(-402.681 + 94.6062i) q^{48} +(170.175 - 294.752i) q^{49} +(42.1535 - 73.0120i) q^{50} +(-165.461 + 548.771i) q^{51} +(55.6793 + 96.4394i) q^{52} -175.228 q^{53} +(443.629 + 164.420i) q^{54} -164.307 q^{55} +(-12.7011 - 21.9989i) q^{56} +(81.4605 - 270.174i) q^{57} +(462.878 - 801.728i) q^{58} +(91.6209 - 158.692i) q^{59} +(85.2921 - 20.0386i) q^{60} +(-218.297 - 378.102i) q^{61} +20.2337 q^{62} +(-2.72686 + 43.8637i) q^{63} +152.568 q^{64} +(82.5544 + 142.988i) q^{65} +(-394.337 - 419.613i) q^{66} +(415.750 - 720.100i) q^{67} +(-185.993 + 322.150i) q^{68} +(239.971 + 255.353i) q^{69} +(13.7228 + 23.7686i) q^{70} -118.951 q^{71} +(-351.134 - 232.916i) q^{72} +183.318 q^{73} +(-586.310 - 1015.52i) q^{74} +(126.461 - 29.7108i) q^{75} +(91.5693 - 158.603i) q^{76} +(26.7446 - 46.3229i) q^{77} +(-167.038 + 554.002i) q^{78} +(319.147 + 552.778i) q^{79} -398.030 q^{80} +(283.500 + 671.617i) q^{81} -982.470 q^{82} +(747.322 + 1294.40i) q^{83} +(-8.23369 + 27.3081i) q^{84} +(-275.768 + 477.643i) q^{85} +(339.569 - 588.151i) q^{86} +(1388.63 - 326.247i) q^{87} +(256.417 + 444.127i) q^{88} -1437.27 q^{89} +(379.382 + 251.653i) q^{90} -53.7501 q^{91} +(113.709 + 196.950i) q^{92} +(21.3505 + 22.7190i) q^{93} +(-812.880 + 1407.95i) q^{94} +(135.768 - 235.156i) q^{95} +(-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} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9} - 10 q^{10} + 37 q^{11} - 48 q^{12} + 112 q^{13} - 12 q^{14} + 15 q^{15} + 119 q^{16} + 154 q^{17} + 126 q^{18} + 70 q^{19}+ \cdots - 90 q^{99}+O(q^{100}) $ 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9 - 10 * q^10 + 37 * q^11 - 48 * q^12 + 112 * q^13 - 12 * q^14 + 15 * q^15 + 119 * q^16 + 154 * q^17 + 126 * q^18 + 70 * q^19 - 5 * q^20 - 36 * q^21 - 101 * q^22 + 267 * q^23 + 27 * q^24 - 50 * q^25 - 152 * q^26 + 432 * q^27 - 24 * q^28 - 325 * q^29 + 15 * q^30 + 12 * q^31 - 247 * q^32 - 303 * q^33 + 451 * q^34 + 90 * q^35 + 171 * q^36 - 1276 * q^37 - 395 * q^38 - 564 * q^39 + 45 * q^40 - 238 * q^41 + 216 * q^42 + 97 * q^43 - 202 * q^44 + 225 * q^45 - 492 * q^46 + 901 * q^47 - 525 * q^48 + 629 * q^49 + 25 * q^50 - 231 * q^51 - 76 * q^52 + 448 * q^53 + 999 * q^54 - 370 * q^55 + 156 * q^56 - 105 * q^57 + 806 * q^58 + 85 * q^59 + 255 * q^60 + 247 * q^61 + 12 * q^62 + 351 * q^63 + 1426 * q^64 + 560 * q^65 - 888 * q^66 + 606 * q^67 - 451 * q^68 - 1539 * q^69 - 60 * q^70 + 788 * q^71 + 405 * q^72 - 1622 * q^73 - 484 * q^74 + 75 * q^75 + 395 * q^76 + 84 * q^77 + 228 * q^78 + 840 * q^79 - 1190 * q^80 + 1134 * q^81 - 2218 * q^82 + 387 * q^83 + 36 * q^84 - 385 * q^85 + 1387 * q^86 + 2418 * q^87 + 411 * q^88 - 2130 * q^89 + 225 * q^90 - 1272 * q^91 - 246 * q^92 - 18 * q^93 - 632 * q^94 - 175 * q^95 + 24 * q^96 + 1031 * q^97 + 926 * q^98 - 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.68614	+	2.92048i	0.596141	+	1.03255i	0.993385	+	0.114833i	$0.0366333\pi$
$2$	1.68614	+	2.92048i	0.596141	+	1.03255i	−0.397244	+	0.917713i	$0.630033\pi$
$3$	−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
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−17.0584	+	4.00772i	−1.16068	+	0.272691i
$7$	−0.813859	−	1.40965i	−0.0439443	−	0.0761137i	0.843217	−	0.537574i	$-0.180659\pi$
$7$	−0.813859	−	1.40965i	−0.0439443	−	0.0761137i	−0.887161	+	0.461460i	$0.847326\pi$
$8$	15.6060			0.689693
$9$	−22.5000	−	14.9248i	−0.833333	−	0.552771i
$10$	−16.8614			−0.533204
$11$	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	$0.684626\pi$
$12$	−12.0000	−	12.7692i	−0.288675	−	0.307178i
$13$	16.5109	−	28.5977i	0.352253	−	0.610121i	−0.634391	−	0.773013i	$-0.718749\pi$
$13$	16.5109	−	28.5977i	0.352253	−	0.610121i	0.986644	+	0.162892i	$0.0520822\pi$
$14$	2.74456	−	4.75372i	0.0523939	−	0.0907490i
$15$	−17.7921	−	18.9325i	−0.306260	−	0.325891i
$16$	39.8030	+	68.9408i	0.621922	+	1.07720i
$17$	110.307			1.57373			0.786864	−	0.617126i	$-0.211703\pi$
$17$	110.307			1.57373			0.786864	+	0.617126i	$0.211703\pi$
$18$	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	$0.606329\pi$
$20$	−8.43070	−	14.6024i	−0.0942581	−	0.163260i
$21$	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	$-0.734447\pi$
$23$	33.7188	−	58.4026i	0.305689	−	0.529469i	0.977415	+	0.211331i	$0.0677799\pi$
$24$	−23.4090	+	77.6387i	−0.199097	+	0.660331i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	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	−0.852536	−	0.522668i	$-0.824937\pi$
$29$	−137.259	−	237.740i	−0.878912	−	1.52232i	−0.0263757	−	0.999652i	$-0.508397\pi$
$30$	25.2921	−	83.8844i	0.153923	−	0.510504i
$31$	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	$0.161134\pi$
$32$	−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
$35$	8.13859			0.0393050
$36$	81.5258	−	40.5455i	0.377434	−	0.187711i
$37$	−347.723			−1.54501			−0.772504	−	0.635010i	$-0.780996\pi$
$37$	−347.723			−1.54501			−0.772504	+	0.635010i	$0.780996\pi$
$38$	−91.5693	−	158.603i	−0.390908	−	0.677072i
$39$	117.505	+	125.037i	0.482459	+	0.513383i
$40$	−39.0149	+	67.5758i	−0.154220	+	0.267117i
$41$	−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	$0.979435\pi$
$42$	19.5326	+	20.7846i	0.0717607	+	0.0763604i
$43$	−100.694	−	174.408i	−0.357110	−	0.618533i	0.630367	−	0.776297i	$-0.282905\pi$
$43$	−100.694	−	174.408i	−0.357110	−	0.618533i	−0.987477	+	0.157765i	$0.949571\pi$
$44$	−110.818			−0.379692
$45$	120.876	−	60.1158i	0.400426	−	0.199145i
$46$	227.418			0.728935
$47$	241.048	+	417.507i	0.748094	+	1.29574i	0.948735	+	0.316071i	$0.102364\pi$
$47$	241.048	+	417.507i	0.748094	+	1.29574i	−0.200642	+	0.979665i	$0.564303\pi$
$48$	−402.681	+	94.6062i	−1.21087	+	0.284484i
$49$	170.175	−	294.752i	0.496138	−	0.859336i
$50$	42.1535	−	73.0120i	0.119228	−	0.206509i
$51$	−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	$-0.572915\pi$
$53$	−175.228			−0.454140			−0.227070	+	0.973878i	$0.572915\pi$
$54$	443.629	+	164.420i	1.11797	+	0.414347i
$55$	−164.307			−0.402821
$56$	−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	−0.747057	−	0.664760i	$-0.768534\pi$
$59$	91.6209	−	158.692i	0.202170	−	0.350169i	0.949227	+	0.314591i	$0.101867\pi$
$60$	85.2921	−	20.0386i	0.183519	−	0.0431162i
$61$	−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	$0.984839\pi$
$62$	20.2337			0.0414465
$63$	−2.72686	+	43.8637i	−0.00545321	+	0.0877192i
$64$	152.568			0.297984
$65$	82.5544	+	142.988i	0.157532	+	0.272854i
$66$	−394.337	−	419.613i	−0.735447	−	0.782587i
$67$	415.750	−	720.100i	0.758089	−	1.31305i	−0.185736	−	0.982600i	$-0.559467\pi$
$67$	415.750	−	720.100i	0.758089	−	1.31305i	0.943824	−	0.330448i	$-0.107200\pi$
$68$	−185.993	+	322.150i	−0.331691	+	0.574506i
$69$	239.971	+	255.353i	0.418683	+	0.445520i
$70$	13.7228	+	23.7686i	0.0234313	+	0.0405842i
$71$	−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	$-0.453052\pi$
$73$	183.318			0.293914			0.146957	+	0.989143i	$0.453052\pi$
$74$	−586.310	−	1015.52i	−0.921042	−	1.59529i
$75$	126.461	−	29.7108i	0.194699	−	0.0457427i
$76$	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	0.998660	−	0.0517463i	$-0.0164787\pi$
$79$	319.147	+	552.778i	0.454517	+	0.787246i	−0.544144	+	0.838992i	$0.683145\pi$
$80$	−398.030			−0.556264
$81$	283.500	+	671.617i	0.388889	+	0.921285i
$82$	−982.470			−1.32312
$83$	747.322	+	1294.40i	0.988304	+	1.71179i	0.626219	+	0.779647i	$0.284602\pi$
$83$	747.322	+	1294.40i	0.988304	+	1.71179i	0.362085	+	0.932145i	$0.382065\pi$
$84$	−8.23369	+	27.3081i	−0.0106949	+	0.0354709i
$85$	−275.768	+	477.643i	−0.351896	+	0.609502i
$86$	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	$0.826996\pi$
$90$	379.382	+	251.653i	0.444337	+	0.294740i
$91$	−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
$95$	135.768	−	235.156i	0.146626	−	0.253964i
$96$	−511.011	−	543.765i	−0.543279	−	0.578102i
$97$	445.884	+	772.294i	0.466729	+	0.808398i	0.999278	−	0.0380011i	$-0.0120990\pi$
$97$	445.884	+	772.294i	0.466729	+	0.808398i	−0.532549	+	0.846399i	$0.678766\pi$
$98$	1147.76			1.18307
$99$	55.0516	−	885.548i	0.0558878	−	0.899000i
$100$	84.3070			0.0843070
$101$	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	$0.809204\pi$
$102$	−1881.66	+	442.080i	−1.82659	+	0.429142i
$103$	−67.6469	+	117.168i	−0.0647131	+	0.112086i	−0.896567	−	0.442909i	$-0.853947\pi$
$103$	−67.6469	+	117.168i	−0.0647131	+	0.112086i	0.831854	+	0.554995i	$0.187280\pi$
$104$	257.668	−	446.294i	0.242947	−	0.420796i
$105$	−12.2079	+	40.4890i	−0.0113464	+	0.0376316i
$106$	−295.459	−	511.750i	−0.270732	−	0.468921i
$107$	−718.783			−0.649414			−0.324707	−	0.945815i	$-0.605266\pi$
$107$	−718.783			−0.649414			−0.324707	+	0.945815i	$0.605266\pi$
$108$	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	$0.844736\pi$
$110$	−277.045	−	479.856i	−0.240138	−	0.415931i
$111$	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	$-0.803246\pi$
$113$	113.372	−	196.367i	0.0943820	−	0.163474i	0.909351	+	0.416031i	$0.136579\pi$
$114$	926.392	−	217.647i	0.761093	−	0.178812i
$115$	168.594	+	292.013i	0.136708	+	0.236786i
$116$	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
$120$	−277.663	−	295.461i	−0.211225	−	0.224764i
$121$	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
$125$	125.000			0.0894427
$126$	−132.701	+	65.9967i	−0.0938250	+	0.0466623i
$127$	1132.24			0.791100			0.395550	−	0.918444i	$-0.370554\pi$
$127$	1132.24			0.791100			0.395550	+	0.918444i	$0.370554\pi$
$128$	831.675	+	1440.50i	0.574300	+	0.994717i
$129$	1018.71	−	239.336i	0.695289	−	0.163352i
$130$	−278.397	+	482.197i	−0.187823	+	0.325319i
$131$	−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	$0.250151\pi$
$132$	166.227	−	551.312i	0.109608	−	0.363527i
$133$	44.1983	+	76.5537i	0.0288156	+	0.0499101i
$134$	2804.05			1.80771
$135$	117.758	+	691.526i	0.0750740	+	0.440867i
$136$	1721.45			1.08539
$137$	−311.819	−	540.087i	−0.194456	−	0.336808i	0.752266	−	0.658860i	$-0.228961\pi$
$137$	−311.819	−	540.087i	−0.194456	−	0.336808i	−0.946722	+	0.322052i	$0.895628\pi$
$138$	−341.127	+	1131.39i	−0.210425	+	0.697902i
$139$	−641.341	+	1110.83i	−0.391351	+	0.677840i	−0.992628	−	0.121201i	$-0.961326\pi$
$139$	−641.341	+	1110.83i	−0.391351	+	0.677840i	0.601277	+	0.799041i	$0.294659\pi$
$140$	−13.7228	+	23.7686i	−0.00828421	+	0.0143487i
$141$	−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
$145$	1372.59			0.786123
$146$	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	−0.995844	−	0.0910749i	$-0.970970\pi$
$149$	−762.156	+	1320.09i	−0.419049	+	0.725814i	0.576795	+	0.816889i	$0.304303\pi$
$150$	300.000	+	319.229i	0.163299	+	0.173766i
$151$	−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	$-0.491401\pi$
$152$	−847.514			−0.452253
$153$	−2481.91	−	1646.31i	−1.31144	−	0.869911i
$154$	180.380			0.0943861
$155$	15.0000	+	25.9808i	0.00777309	+	0.0134634i
$156$	−563.299	+	132.342i	−0.289103	+	0.0679220i
$157$	1194.35	−	2068.67i	0.607131	−	1.05158i	−0.384580	−	0.923092i	$-0.625654\pi$
$157$	1194.35	−	2068.67i	0.607131	−	1.05158i	0.991711	−	0.128490i	$-0.0410129\pi$
$158$	−1076.25	+	1864.12i	−0.541912	+	0.938619i
$159$	262.842	−	871.749i	0.131099	−	0.434806i
$160$	−359.015	−	621.832i	−0.177391	−	0.307251i
$161$	−109.769			−0.0537331
$162$	−1483.42	+	1960.40i	−0.719436	+	0.950761i
$163$	−2544.79			−1.22284			−0.611422	−	0.791305i	$-0.709402\pi$
$163$	−2544.79			−1.22284			−0.611422	+	0.791305i	$0.709402\pi$
$164$	−491.235	−	850.844i	−0.233896	−	0.405120i
$165$	246.461	−	817.417i	0.116284	−	0.385672i
$166$	−2520.18	+	4365.08i	−1.17834	+	2.04094i
$167$	687.279	−	1190.40i	0.318462	−	0.551593i	−0.661705	−	0.749764i	$-0.730167\pi$
$167$	687.279	−	1190.40i	0.318462	−	0.551593i	0.980167	+	0.198171i	$0.0635002\pi$
$168$	128.495	−	30.1887i	0.0590094	−	0.0138637i
$169$	553.282	+	958.313i	0.251835	+	0.436191i
$170$	−1859.93			−0.839119
$171$	1221.91	+	810.522i	0.546442	+	0.362469i
$172$	679.139			0.301069
$173$	−1180.23	−	2044.21i	−0.518675	−	0.898372i	−0.999765	−	0.0217005i	$-0.993092\pi$
$173$	−1180.23	−	2044.21i	−0.518675	−	0.898372i	0.481089	−	0.876672i	$-0.340241\pi$
$174$	3294.23	+	3505.38i	1.43526	+	1.52725i
$175$	−20.3465	+	35.2411i	−0.00878885	+	0.0152227i
$176$	−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	$0.412156\pi$
$180$	−28.2473	+	454.381i	−0.0116968	+	0.188153i
$181$	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
$185$	869.307	−	1505.68i	0.345474	−	0.598379i
$186$	−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
$190$	915.693			0.349639
$191$	−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	$0.856308\pi$
$192$	−228.852	+	759.016i	−0.0860207	+	0.285298i
$193$	−773.020	+	1338.91i	−0.288307	+	0.499362i	−0.973406	−	0.229088i	$-0.926426\pi$
$193$	−773.020	+	1338.91i	−0.288307	+	0.499362i	0.685099	+	0.728450i	$0.259759\pi$
$194$	−1503.65	+	2604.39i	−0.556472	+	0.963838i
$195$	−835.190	+	196.220i	−0.306714	+	0.0720596i
$196$	573.879	+	993.987i	0.209140	+	0.362240i
$197$	−4284.60			−1.54957			−0.774784	−	0.632226i	$-0.782141\pi$
$197$	−4284.60			−1.54957			−0.774784	+	0.632226i	$0.782141\pi$
$198$	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	$0.580386\pi$
$200$	−195.075	−	337.879i	−0.0689693	−	0.119458i
$201$	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
$205$	−728.342	−	1261.53i	−0.248145	−	0.429799i
$206$	−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
$210$	−138.832	+	32.6172i	−0.0456204	+	0.0107181i
$211$	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	$0.0525716\pi$
$212$	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
$215$	1006.94			0.319409
$216$	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
$220$	277.045	−	479.856i	0.0849016	−	0.147054i
$221$	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	$-0.0411802\pi$
$223$	1279.07	+	2215.42i	0.384095	+	0.665272i	−0.607548	+	0.794283i	$0.707847\pi$
$224$	233.750			0.0697236
$225$	−41.8816	+	673.699i	−0.0124094	+	0.199615i
$226$	764.646			0.225060
$227$	2042.27	+	3537.32i	0.597138	+	1.03427i	0.993241	+	0.116067i	$0.0370287\pi$
$227$	2042.27	+	3537.32i	0.597138	+	1.03427i	−0.396104	+	0.918206i	$0.629638\pi$
$228$	651.684	+	693.456i	0.189293	+	0.201426i
$229$	1370.95	−	2374.56i	0.395612	−	0.685221i	−0.597567	−	0.801819i	$-0.703866\pi$
$229$	1370.95	−	2374.56i	0.395612	−	0.685221i	0.993179	+	0.116598i	$0.0371991\pi$
$230$	−568.546	+	984.750i	−0.162995	+	0.282315i
$231$	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	$-0.246505\pi$
$233$	5084.70			1.42966			0.714828	+	0.699300i	$0.246505\pi$
$234$	−2505.57	−	1662.01i	−0.699975	−	0.464311i
$235$	−2410.48			−0.669115
$236$	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	−0.948464	−	0.316885i	$-0.897363\pi$
$239$	−738.236	+	1278.66i	−0.199801	+	0.346066i	0.748663	+	0.662951i	$0.230696\pi$
$240$	597.045	−	1980.17i	0.160579	−	0.532582i
$241$	−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	$0.909063\pi$
$242$	846.874			0.224955
$243$	−3766.50	+	402.970i	−0.994325	+	0.106381i
$244$	1472.32			0.386294
$245$	850.876	+	1473.76i	0.221880	+	0.384307i
$246$	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
$250$	210.768	+	365.060i	0.0533204	+	0.0923537i
$251$	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
$255$	−1962.59	−	2088.39i	−0.481970	−	0.512863i
$256$	−2194.37	+	3800.76i	−0.535735	+	0.927920i
$257$	−114.298	+	197.970i	−0.0277421	+	0.0480507i	−0.879563	−	0.475782i	$-0.842165\pi$
$257$	−114.298	+	197.970i	−0.0277421	+	0.0480507i	0.851821	+	0.523833i	$0.175498\pi$
$258$	2416.66	+	2571.56i	0.583158	+	0.620537i
$259$	282.997	+	490.166i	0.0678942	+	0.117596i
$260$	−556.793			−0.132811
$261$	−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	$-0.118391\pi$
$263$	644.380	+	1116.10i	0.151081	+	0.261679i	−0.780544	+	0.625100i	$0.785058\pi$
$264$	−2594.13	+	609.468i	−0.604764	+	0.142084i
$265$	438.070	−	758.760i	0.101549	−	0.175888i
$266$	−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	$0.464793\pi$
$270$	−1821.03	+	1509.92i	−0.410461	+	0.340336i
$271$	−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
$275$	410.768	−	711.470i	0.0900735	−	0.156012i
$276$	−1150.38	+	270.271i	−0.250886	+	0.0589435i
$277$	1689.59	+	2926.45i	0.366489	+	0.634777i	0.989014	−	0.147823i	$-0.0472265\pi$
$277$	1689.59	+	2926.45i	0.366489	+	0.634777i	−0.622525	+	0.782600i	$0.713893\pi$
$278$	−4325.56			−0.933201
$279$	−145.052	+	72.1390i	−0.0311255	+	0.0154797i
$280$	127.011			0.0271083
$281$	−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	$0.858135\pi$
$282$	−5785.14	−	6155.95i	−1.22163	−	1.29993i
$283$	−3454.51	+	5983.39i	−0.725617	+	1.25680i	0.233103	+	0.972452i	$0.425112\pi$
$283$	−3454.51	+	5983.39i	−0.725617	+	1.25680i	−0.958720	+	0.284353i	$0.908221\pi$
$284$	200.568	−	347.394i	0.0419068	−	0.0725847i
$285$	966.237	+	1028.17i	0.200824	+	0.213697i
$286$	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
$290$	2314.39	+	4008.64i	0.468640	+	0.811708i
$291$	−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	$-0.679918\pi$
$293$	2324.74	−	4026.57i	0.463525	−	0.802850i	0.999134	+	0.0416170i	$0.0132509\pi$
$294$	−1721.64	+	5710.02i	−0.341523	+	1.13271i
$295$	458.104	+	793.460i	0.0904131	+	0.156600i
$296$	−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
$300$	−126.461	+	419.422i	−0.0243373	+	0.0807178i
$301$	−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
$305$	2182.97			0.409825
$306$	623.176	−	10024.3i	0.116420	−	1.87271i
$307$	−7361.42			−1.36853			−0.684264	−	0.729234i	$-0.739877\pi$
$307$	−7361.42			−1.36853			−0.684264	+	0.729234i	$0.739877\pi$
$308$	90.1902	+	156.214i	0.0166853	+	0.0288997i
$309$	−481.433	−	512.291i	−0.0886335	−	0.0943146i
$310$	−50.5842	+	87.6144i	−0.00926771	+	0.0160521i
$311$	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	$0.0872266\pi$
$312$	1833.78	+	1951.32i	0.332749	+	0.354077i
$313$	3121.86	+	5407.22i	0.563763	+	0.976467i	0.997164	+	0.0752653i	$0.0239804\pi$
$313$	3121.86	+	5407.22i	0.563763	+	0.976467i	−0.433400	+	0.901202i	$0.642686\pi$
$314$	8055.37			1.44774
$315$	−183.118	−	121.467i	−0.0327541	−	0.0217266i
$316$	−2152.50			−0.383189
$317$	−1042.02	−	1804.82i	−0.184623	−	0.319776i	0.758827	−	0.651293i	$-0.225773\pi$
$317$	−1042.02	−	1804.82i	−0.184623	−	0.319776i	−0.943449	+	0.331517i	$0.892440\pi$
$318$	2989.12	−	702.266i	0.527111	−	0.123840i
$319$	4510.54	−	7812.48i	0.791667	−	1.37121i
$320$	−381.420	+	660.639i	−0.0666313	+	0.115409i
$321$	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
$325$	−825.544			−0.140901
$326$	−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
$330$	2802.82	−	658.497i	0.467546	−	0.109846i
$331$	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	$0.827310\pi$
$332$	−5040.36			−0.833210
$333$	7823.76	+	5189.70i	1.28751	+	0.854035i
$334$	4635.39			0.759394
$335$	2078.75	+	3600.50i	0.339028	+	0.587213i
$336$	461.087	+	490.641i	0.0748641	+	0.0796627i
$337$	−1708.74	+	2959.62i	−0.276205	+	0.478400i	−0.970438	−	0.241349i	$-0.922410\pi$
$337$	−1708.74	+	2959.62i	−0.276205	+	0.478400i	0.694234	+	0.719750i	$0.255743\pi$
$338$	−1865.82	+	3231.70i	−0.300259	+	0.520063i
$339$	806.853	+	858.570i	0.129269	+	0.137555i
$340$	−929.966	−	1610.75i	−0.148337	−	0.256927i
$341$	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
$345$	−1705.64	+	400.724i	−0.266169	+	0.0625341i
$346$	3980.05	−	6893.65i	0.618407	−	1.07111i
$347$	−1804.80	+	3126.00i	−0.279212	+	0.483610i	−0.971189	−	0.238310i	$-0.923407\pi$
$347$	−1804.80	+	3126.00i	−0.279212	+	0.483610i	0.691977	+	0.721920i	$0.256740\pi$
$348$	−1388.63	+	4605.57i	−0.213904	+	0.709439i
$349$	4400.42	+	7621.74i	0.674925	+	1.16900i	0.976491	+	0.215559i	$0.0691574\pi$
$349$	4400.42	+	7621.74i	0.674925	+	1.16900i	−0.301566	+	0.953445i	$0.597509\pi$
$350$	−137.228			−0.0209576
$351$	−777.715	−	4567.08i	−0.118266	−	0.694509i
$352$	−4719.09			−0.714570
$353$	−4255.24	−	7370.30i	−0.641597	−	1.11128i	−0.985076	−	0.172119i	$-0.944939\pi$
$353$	−4255.24	−	7370.30i	−0.641597	−	1.11128i	0.343479	−	0.939160i	$-0.388395\pi$
$354$	−926.914	+	3074.23i	−0.139166	+	0.461563i
$355$	297.377	−	515.073i	0.0444596	−	0.0770063i
$356$	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	$0.397131\pi$
$360$	1886.39	−	938.166i	0.276171	−	0.137349i
$361$	−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
$365$	−458.294	+	793.789i	−0.0657211	+	0.113832i
$366$	5239.14	+	5574.95i	0.748235	+	0.796195i
$367$	−3300.19	−	5716.10i	−0.469397	−	0.813020i	0.529991	−	0.848003i	$-0.322195\pi$
$367$	−3300.19	−	5716.10i	−0.469397	−	0.813020i	−0.999388	+	0.0349838i	$0.988862\pi$
$368$	5368.43			0.760459
$369$	7043.15	−	3502.79i	0.993636	−	0.494168i
$370$	5863.10			0.823805
$371$	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	−0.395698	−	0.918381i	$-0.629497\pi$
$373$	4304.23	−	7455.14i	0.597492	−	1.03489i	0.993190	−	0.116506i	$-0.0371693\pi$
$374$	−6112.00	+	10586.3i	−0.845037	+	1.46365i
$375$	−187.500	+	621.867i	−0.0258199	+	0.0856349i
$376$	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	$0.660510\pi$
$380$	457.846	+	793.013i	0.0618080	+	0.107055i
$381$	−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	$-0.962729\pi$
$383$	−2963.73	+	5133.33i	−0.395404	+	0.684859i	0.597749	+	0.801683i	$0.296062\pi$
$384$	−8413.93	+	1976.78i	−1.11815	+	0.262700i
$385$	133.723	+	231.615i	0.0177017	+	0.0306602i
$386$	−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	0.830187	−	0.557485i	$-0.188234\pi$
$389$	−519.432	−	899.683i	−0.0677024	−	0.117264i	−0.897890	+	0.440221i	$0.854900\pi$
$390$	−1981.30	−	2108.30i	−0.257249	−	0.273738i
$391$	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
$395$	−3191.47			−0.406532
$396$	2493.40	+	1653.94i	0.316410	+	0.209882i
$397$	13441.4			1.69926			0.849628	−	0.527382i	$-0.176826\pi$
$397$	13441.4			1.69926			0.849628	+	0.527382i	$0.176826\pi$
$398$	−2365.41	−	4097.01i	−0.297907	−	0.515991i
$399$	−447.147	+	105.053i	−0.0561037	+	0.0131810i
$400$	995.075	−	1723.52i	0.124384	−	0.215440i
$401$	−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	$0.863866\pi$
$402$	−4206.08	+	13950.0i	−0.521841	+	1.73075i
$403$	−99.0652	−	171.586i	−0.0122451	−	0.0212092i
$404$	−518.468			−0.0638484
$405$	−3616.93	−	451.450i	−0.443770	−	0.0553895i
$406$	−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	−0.661473	−	0.749969i	$-0.730068\pi$
$409$	2636.59	−	4566.71i	0.318756	−	0.552101i	0.980229	+	0.197868i	$0.0634017\pi$
$410$	2456.17	−	4254.22i	0.295858	−	0.512441i
$411$	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
$415$	−7473.22			−0.883966
$416$	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	0.107609	+	0.994193i	$0.465681\pi$
$419$	−6923.06	+	11991.1i	−0.807192	+	1.39810i	−0.914801	+	0.403905i	$0.867653\pi$
$420$	−97.6631	−	103.923i	−0.0113464	−	0.0120736i
$421$	−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	$0.853565\pi$
$422$	7251.94			0.836538
$423$	807.637	−	12991.5i	0.0928338	−	1.49330i
$424$	−2734.60			−0.313217
$425$	−1378.84	−	2388.22i	−0.157373	−	0.272578i
$426$	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
$430$	1697.85	+	2940.76i	0.190413	+	0.329804i
$431$	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	$-0.436586\pi$
$433$	3566.31			0.395810			0.197905	+	0.980221i	$0.436586\pi$
$434$	−16.4674	−	28.5223i	−0.00182133	−	0.00315464i
$435$	−2058.89	+	6828.57i	−0.226934	+	0.752655i
$436$	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	0.881380	−	0.472408i	$-0.156615\pi$
$439$	290.411	+	503.007i	0.0315730	+	0.0546861i	−0.849807	+	0.527094i	$0.823282\pi$
$440$	−2564.17			−0.277823
$441$	−8228.06	+	4092.09i	−0.888464	+	0.441863i
$442$	12283.6			1.32188
$443$	5396.39	+	9346.82i	0.578759	+	1.00244i	0.995622	+	0.0934706i	$0.0297961\pi$
$443$	5396.39	+	9346.82i	0.578759	+	1.00244i	−0.416863	+	0.908969i	$0.636871\pi$
$444$	4172.67	+	4440.13i	0.446005	+	0.474593i
$445$	3593.17	−	6223.56i	0.382770	−	0.662977i
$446$	−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	$0.451400\pi$
$450$	−2038.14	+	1013.64i	−0.213509	+	0.106185i
$451$	−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
$455$	134.375	−	232.745i	0.0138453	−	0.0239808i
$456$	1271.27	−	4216.33i	0.130554	−	0.432999i
$457$	−1599.96	−	2771.21i	−0.163770	−	0.283658i	0.772448	−	0.635078i	$-0.219032\pi$
$457$	−1599.96	−	2771.21i	−0.163770	−	0.283658i	−0.936218	+	0.351420i	$0.885699\pi$
$458$	9246.49			0.943363
$459$	11913.2	−	9877.87i	1.21146	−	1.00449i
$460$	−1137.09			−0.115255
$461$	−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	$0.953834\pi$
$462$	−270.571	+	897.381i	−0.0272469	+	0.0903678i
$463$	−3505.99	+	6072.55i	−0.351916	+	0.609536i	−0.986585	−	0.163248i	$-0.947803\pi$
$463$	−3505.99	+	6072.55i	−0.351916	+	0.609536i	0.634669	+	0.772784i	$0.281136\pi$
$464$	10926.7	−	18925.6i	1.09323	−	1.89353i
$465$	−151.753	+	35.6529i	−0.0151341	+	0.00355562i
$466$	8573.53	+	14849.8i	0.852277	+	1.47619i
$467$	−8002.63			−0.792971			−0.396485	−	0.918041i	$-0.629770\pi$
$467$	−8002.63			−0.792971			−0.396485	+	0.918041i	$0.629770\pi$
$468$	186.555	−	3000.89i	0.0184263	−	0.296402i
$469$	−1353.45			−0.133255
$470$	−4064.40	−	7039.75i	−0.398887	−	0.690892i
$471$	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
$475$	678.838	+	1175.78i	0.0655731	+	0.113576i
$476$	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	0.931820	−	0.362920i	$-0.118220\pi$
$479$	1589.42	+	2752.96i	0.151613	+	0.262601i	−0.780208	+	0.625520i	$0.784887\pi$
$480$	3632.10	−	853.329i	0.345379	−	0.0811436i
$481$	−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
$485$	−4458.84			−0.417455
$486$	−7527.71	−	10320.5i	−0.702601	−	0.963269i
$487$	13060.3			1.21523			0.607615	−	0.794232i	$-0.292126\pi$
$487$	13060.3			1.21523			0.607615	+	0.794232i	$0.292126\pi$
$488$	−3406.74	−	5900.65i	−0.316016	−	0.547356i
$489$	3817.19	−	12660.2i	0.353005	−	1.17078i
$490$	−2869.39	+	4969.94i	−0.264543	+	0.458202i
$491$	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	$0.101831\pi$
$492$	4969.75	−	1167.60i	0.455393	−	0.106991i
$493$	−15140.7	−	26224.4i	−1.38317	−	2.39572i
$494$	−6047.56			−0.550794
$495$	3696.91	+	2452.25i	0.335684	+	0.222668i
$496$	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	0.0500129	+	0.998749i	$0.484074\pi$
$499$	−9362.60	+	16216.5i	−0.839935	+	1.45481i	−0.889948	+	0.456062i	$0.849260\pi$
$500$	−210.768	+	365.060i	−0.0188516	+	0.0326520i
$501$	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	$-0.554035\pi$
$503$	−3811.68			−0.337882			−0.168941	+	0.985626i	$0.554035\pi$
$504$	−42.5553	+	684.536i	−0.00376104	+	0.0604993i
$505$	−768.720			−0.0677378
$506$	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	−0.947141	−	0.320816i	$-0.896043\pi$
$509$	−2247.74	+	3893.20i	−0.195735	+	0.339024i	0.751406	+	0.659840i	$0.229376\pi$
$510$	2789.90	−	9253.04i	0.242233	−	0.803395i
$511$	−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
$515$	−338.235	−	585.840i	−0.0289406	−	0.0501266i
$516$	−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
$520$	1288.34	+	2231.47i	0.108649	+	0.188186i
$521$	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	$-0.400093\pi$
$523$	7385.38			0.617476			0.308738	+	0.951147i	$0.400093\pi$
$524$	−1310.98	−	2270.69i	−0.109295	−	0.189304i
$525$	−144.803	−	154.084i	−0.0120375	−	0.0128091i
$526$	−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
$530$	2954.59			0.242150
$531$	−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
$535$	1796.96	−	3112.42i	0.145213	−	0.251517i
$536$	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
$540$	−2218.14	−	822.100i	−0.176766	−	0.0655140i
$541$	−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
$545$	5026.39	−	8705.96i	0.395059	−	0.684262i
$546$	916.892	−	215.416i	0.0718670	−	0.0168845i
$547$	5078.61	+	8796.41i	0.396976	+	0.687582i	0.993351	−	0.115124i	$-0.0367264\pi$
$547$	5078.61	+	8796.41i	0.396976	+	0.687582i	−0.596376	+	0.802705i	$0.703393\pi$
$548$	2103.08			0.163940
$549$	−731.413	+	11765.3i	−0.0568596	+	0.914632i
$550$	2770.45			0.214786
$551$	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
$555$	6186.72	+	6583.27i	0.473174	+	0.503503i
$556$	−2162.78	−	3746.05i	−0.164968	−	0.285733i
$557$	5709.62			0.434334			0.217167	−	0.976134i	$-0.430318\pi$
$557$	5709.62			0.434334			0.217167	+	0.976134i	$0.430318\pi$
$558$	−455.258	−	301.984i	−0.0345387	−	0.0229104i
$559$	−6650.20			−0.503173
$560$	323.940	+	561.081i	0.0244446	+	0.0423393i
$561$	−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	$-0.994258\pi$
$563$	−6469.56	+	11205.6i	−0.484297	+	0.838828i	0.515540	+	0.856866i	$0.327591\pi$
$564$	2438.64	−	8088.06i	0.182066	−	0.603845i
$565$	566.861	+	981.833i	0.0422089	+	0.0731080i
$566$	−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	0.956515	−	0.291684i	$-0.0942157\pi$
$569$	3062.71	+	5304.77i	0.225651	+	0.390839i	−0.730863	+	0.682524i	$0.760882\pi$
$570$	−1373.54	+	4555.51i	−0.100932	+	0.334754i
$571$	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	$-0.0831076\pi$
$572$	−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
$575$	−1685.94			−0.122276
$576$	−3432.78	−	2277.05i	−0.248320	−	0.164717i
$577$	−4988.14			−0.359894			−0.179947	−	0.983676i	$-0.557593\pi$
$577$	−4988.14			−0.359894			−0.179947	+	0.983676i	$0.557593\pi$
$578$	12232.3	+	21187.0i	0.880274	+	1.52468i
$579$	−5501.46	−	5854.09i	−0.394876	−	0.420186i
$580$	−2314.39	+	4008.64i	−0.165689	+	0.286982i
$581$	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
$585$	276.601	−	4449.35i	0.0195488	−	0.314458i
$586$	15679.4			1.10531
$587$	7647.00	+	13245.0i	0.537693	+	0.931311i	0.999028	+	0.0440852i	$0.0140373\pi$
$587$	7647.00	+	13245.0i	0.537693	+	0.931311i	−0.461335	+	0.887226i	$0.652629\pi$
$588$	−5805.84	+	1364.03i	−0.407192	+	0.0956661i
$589$	−162.921	+	282.188i	−0.0113974	+	0.0197408i
$590$	−1544.86	+	2675.77i	−0.107798	+	0.186711i
$591$	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	$-0.625461\pi$
$593$	−11090.9			−0.768040			−0.384020	+	0.923325i	$0.625461\pi$
$594$	2609.94	+	15326.7i	0.180281	+	1.05869i
$595$	897.744			0.0618553
$596$	−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	0.243965	−	0.969784i	$-0.421552\pi$
$599$	14100.8	−	24423.3i	0.961840	−	1.66596i	0.717875	−	0.696172i	$-0.245115\pi$
$600$	1973.54	−	463.665i	0.134282	−	0.0315484i
$601$	−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	$-0.421398\pi$
$602$	−1105.45			−0.0748416
$603$	−20101.7	+	9997.26i	−1.35755	+	0.675157i
$604$	10665.0			0.718467
$605$	627.820	+	1087.42i	0.0421893	+	0.0730740i
$606$	−1844.93	−	1963.18i	−0.123672	−	0.131599i
$607$	4399.49	−	7620.14i	0.294184	−	0.509542i	−0.680611	−	0.732645i	$-0.738285\pi$
$607$	4399.49	−	7620.14i	0.294184	−	0.509542i	0.974795	+	0.223103i	$0.0716187\pi$
$608$	3899.41	−	6753.97i	0.260102	−	0.450509i
$609$	−1590.04	−	1691.96i	−0.105799	−	0.112581i
$610$	3680.80	+	6375.34i	0.244314	+	0.423164i
$611$	15919.6			1.05407
$612$	8992.87	−	4472.45i	0.593979	−	0.295406i
$613$	19539.8			1.28745			0.643724	−	0.765257i	$-0.277388\pi$
$613$	19539.8			1.28745			0.643724	+	0.765257i	$0.277388\pi$
$614$	−12412.4	−	21498.9i	−0.815836	−	1.41307i
$615$	7368.52	−	1731.17i	0.483134	−	0.113508i
$616$	417.375	−	722.914i	0.0272995	−	0.0472842i
$617$	1636.94	−	2835.26i	0.106808	−	0.184997i	−0.807667	−	0.589638i	$-0.799270\pi$
$617$	1636.94	−	2835.26i	0.106808	−	0.184997i	0.914475	+	0.404641i	$0.132604\pi$
$618$	684.373	−	2269.81i	0.0445462	−	0.147743i
$619$	−4693.24	−	8128.92i	−0.304745	−	0.527834i	0.672460	−	0.740134i	$-0.265238\pi$
$619$	−4693.24	−	8128.92i	−0.304745	−	0.527834i	−0.977205	+	0.212300i	$0.931905\pi$
$620$	−101.168			−0.00655326
$621$	−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
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−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
$630$	45.9787	−	739.604i	0.00290768	−	0.0467723i
$631$	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
$635$	−2830.59	+	4902.73i	−0.176895	+	0.306392i
$636$	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
$640$	−8316.75			−0.513669
$641$	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	$0.764103\pi$
$642$	12261.3	−	2880.68i	0.753761	−	0.177089i
$643$	3144.44	−	5446.34i	0.192853	−	0.334032i	−0.753341	−	0.657630i	$-0.771559\pi$
$643$	3144.44	−	5446.34i	0.192853	−	0.334032i	0.946195	+	0.323598i	$0.104892\pi$
$644$	185.087	−	320.579i	0.0113252	−	0.0196158i
$645$	−1510.41	+	5009.48i	−0.0922054	+	0.305811i
$646$	−10100.7	−	17495.0i	−0.615183	−	1.06553i
$647$	−5900.85			−0.358557			−0.179279	−	0.983798i	$-0.557376\pi$
$647$	−5900.85			−0.358557			−0.179279	+	0.983798i	$0.557376\pi$
$648$	4424.29	+	10481.2i	0.268214	+	0.635404i
$649$	6021.58			0.364203
$650$	−1391.98	−	2410.99i	−0.0839970	−	0.145487i
$651$	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	$-0.757408\pi$
$653$	3942.57	−	6828.74i	0.236271	−	0.409233i	0.959641	+	0.281227i	$0.0907414\pi$
$654$	34296.9	−	8057.75i	2.05064	−	0.481778i
$655$	−1943.76	−	3366.70i	−0.115953	−	0.200836i
$656$	−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	−0.881244	−	0.472662i	$-0.843293\pi$
$659$	−14378.9	−	24905.0i	−0.849959	−	1.47217i	0.0312845	−	0.999511i	$-0.490040\pi$
$660$	1971.68	+	2098.06i	0.116284	+	0.123738i
$661$	−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	$0.244808\pi$
$662$	−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
$665$	−441.983			−0.0257735
$666$	−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
$670$	−7010.13	+	12141.9i	−0.404216	+	0.700123i
$671$	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	$-0.174005\pi$
$673$	−402.481	−	697.118i	−0.0230528	−	0.0399285i	−0.877322	+	0.479903i	$0.840672\pi$
$674$	−11524.7			−0.658627
$675$	−3288.79	−	1218.91i	−0.187534	−	0.0695049i
$676$	−3731.65			−0.212315
$677$	−681.636	−	1180.63i	−0.0386963	−	0.0670240i	0.846029	−	0.533137i	$-0.178987\pi$
$677$	−681.636	−	1180.63i	−0.0386963	−	0.0670240i	−0.884725	+	0.466114i	$0.845654\pi$
$678$	−1146.97	+	3804.07i	−0.0649692	+	0.215478i
$679$	725.774	−	1257.08i	0.0410201	−	0.0710489i
$680$	−4303.62	+	7454.09i	−0.242700	+	0.420370i
$681$	−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	$-0.603784\pi$
$683$	−11434.6			−0.640604			−0.320302	+	0.947315i	$0.603784\pi$
$684$	−4427.42	+	2201.91i	−0.247495	+	0.123088i
$685$	3118.19			0.173927
$686$	−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
$690$	−4046.25	−	4305.60i	−0.223244	−	0.237553i
$691$	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	$0.652660\pi$
$692$	7960.10			0.437280
$693$	−1293.11	+	643.109i	−0.0708822	+	0.0352521i
$694$	−12172.6			−0.665799
$695$	−3206.70	−	5554.17i	−0.175018	−	0.303139i
$696$	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
$700$	−68.6141	−	118.843i	−0.00370481	−	0.00641692i
$701$	−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
$705$	3615.71	−	11992.0i	0.193157	−	0.640629i
$706$	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	0.809136	−	0.587621i	$-0.199935\pi$
$709$	−1969.54	−	3411.34i	−0.104327	−	0.180699i	−0.913463	+	0.406922i	$0.866602\pi$
$710$	2005.68			0.106017
$711$	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
$715$	−2712.85	+	4698.80i	−0.141895	+	0.245769i
$716$	−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	$0.706517\pi$
$720$	8955.67	+	5940.52i	0.463553	+	0.307486i
$721$	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
$725$	−3431.49	+	5943.51i	−0.175782	+	0.304464i
$726$	−1270.31	+	4213.15i	−0.0649389	+	0.215378i
$727$	4752.24	+	8231.12i	0.242436	+	0.419911i	0.961408	−	0.275128i	$-0.0887203\pi$
$727$	4752.24	+	8231.12i	0.242436	+	0.419911i	−0.718972	+	0.695039i	$0.755387\pi$
$728$	−838.823			−0.0427044
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$	−3090.99			−0.156716
$731$	−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	$-0.892383\pi$
$733$	−3660.40	+	6340.01i	−0.184448	+	0.319473i	0.758943	+	0.651157i	$0.225716\pi$
$734$	11129.2	−	19276.3i	0.559653	−	0.969348i
$735$	−8608.18	+	2022.41i	−0.431997	+	0.101494i
$736$	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	$0.510099\pi$
$740$	2931.55	+	5077.59i	0.145630	+	0.252238i
$741$	−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	$-0.848594\pi$
$743$	−970.576	+	1681.09i	−0.0479232	+	0.0830055i	0.841069	+	0.540928i	$0.181927\pi$
$744$	333.196	+	354.553i	0.0164187	+	0.0174711i
$745$	−3810.78	−	6600.47i	−0.187404	−	0.324594i
$746$	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
$750$	−2132.30	+	500.965i	−0.103814	+	0.0243902i
$751$	−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	$0.298294\pi$
$752$	−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
$755$	15812.8			0.762234
$756$	592.826	−	491.545i	0.0285197	−	0.0236472i
$757$	21145.7			1.01526			0.507631	−	0.861575i	$-0.330521\pi$
$757$	21145.7			1.01526			0.507631	+	0.861575i	$0.330521\pi$
$758$	−12021.8	−	20822.4i	−0.576059	−	0.997764i
$759$	−3324.14	+	11024.9i	−0.158970	+	0.527245i
$760$	2118.78	−	3669.84i	0.101127	−	0.175157i
$761$	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	$0.00746901\pi$
$762$	−19314.2	+	4537.69i	−0.918213	+	0.215726i
$763$	1636.31	+	2834.17i	0.0776388	+	0.134474i
$764$	1283.87			0.0607968
$765$	13333.5	−	6631.20i	0.630162	−	0.313401i
$766$	−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	−0.890607	−	0.454773i	$-0.849720\pi$
$769$	−1097.36	+	1900.68i	−0.0514587	+	0.0891291i	0.839149	+	0.543902i	$0.183054\pi$
$770$	−450.951	+	781.070i	−0.0211054	+	0.0365556i
$771$	−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	$-0.562063\pi$
$773$	−8327.70			−0.387486			−0.193743	+	0.981052i	$0.562063\pi$
$774$	−16418.4	+	8165.40i	−0.762462	+	0.379198i
$775$	−150.000			−0.00695246
$776$	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
$780$	835.190	−	2770.01i	0.0383392	−	0.127157i
$781$	−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
$785$	5971.75	+	10343.4i	0.271517	+	0.470281i
$786$	3932.95	−	13044.1i	0.178478	−	0.591944i
$787$	9481.64	−	16422.7i	0.429459	−	0.743845i	−0.567366	−	0.823465i	$-0.692038\pi$
$787$	9481.64	−	16422.7i	0.429459	−	0.743845i	0.996825	+	0.0796209i	$0.0253710\pi$
$788$	7224.43	−	12513.1i	0.326599	−	0.565686i
$789$	−6519.10	+	1531.60i	−0.294152	+	0.0691084i
$790$	−5381.26	−	9320.62i	−0.242350	−	0.419763i
$791$	−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
$795$	3117.68	+	3317.51i	0.139085	+	0.148000i
$796$	2365.41	−	4097.01i	0.105326	−	0.182430i
$797$	−17132.6	+	29674.5i	−0.761439	+	1.31885i	0.180670	+	0.983544i	$0.442173\pi$
$797$	−17132.6	+	29674.5i	−0.761439	+	1.31885i	−0.942109	+	0.335307i	$0.891160\pi$
$798$	−1060.76	−	1128.75i	−0.0470557	−	0.0500718i
$799$	26589.2	+	46053.9i	1.17730	+	2.03914i
$800$	3590.15			0.158664
$801$	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
$805$	274.423	−	475.315i	0.0120151	−	0.0208108i
$806$	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	$0.209299\pi$
$810$	−4780.21	−	11324.4i	−0.207357	−	0.491233i
$811$	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
$815$	6361.98	−	11019.3i	0.273436	−	0.473605i
$816$	−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
$820$	4912.35			0.209203
$821$	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	$0.786350\pi$
$822$	7483.66	+	7963.34i	0.317546	+	0.337900i
$823$	5699.26	−	9871.42i	0.241390	−	0.418100i	−0.719721	−	0.694264i	$-0.755730\pi$
$823$	5699.26	−	9871.42i	0.241390	−	0.418100i	0.961110	+	0.276164i	$0.0890634\pi$
$824$	−1055.70	+	1828.52i	−0.0446322	+	0.0773052i
$825$	2923.37	+	3110.75i	0.123368	+	0.131276i
$826$	−502.919	−	871.080i	−0.0211850	−	0.0366934i
$827$	34712.0			1.45956			0.729779	−	0.683683i	$-0.239623\pi$
$827$	34712.0			1.45956			0.729779	+	0.683683i	$0.239623\pi$
$828$	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	$0.481767\pi$
$830$	−12600.9	−	21825.4i	−0.526968	−	0.912735i
$831$	−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
$835$	3436.39	+	5952.01i	0.142421	+	0.246680i
$836$	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	0.947560	−	0.319579i	$-0.103542\pi$
$839$	4787.89	+	8292.87i	0.197016	+	0.341242i	−0.750544	+	0.660821i	$0.770208\pi$
$840$	−190.516	+	631.870i	−0.00782551	+	0.0259543i
$841$	−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
$845$	−5532.82			−0.225248
$846$	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
$850$	4649.83	−	8053.74i	0.187633	−	0.324989i
$851$	−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	$-0.224752\pi$
$853$	−4520.95	−	7830.51i	−0.181470	−	0.314316i	−0.942381	+	0.334540i	$0.891419\pi$
$854$	−2396.52			−0.0960274
$855$	−6564.43	+	3264.71i	−0.262572	+	0.130586i
$856$	−11217.3			−0.447896
$857$	1157.64	+	2005.09i	0.0461426	+	0.0799213i	0.888174	−	0.459507i	$-0.151974\pi$
$857$	1157.64	+	2005.09i	0.0461426	+	0.0799213i	−0.842032	+	0.539428i	$0.818640\pi$
$858$	−18510.8	+	4348.94i	−0.736536	+	0.173043i
$859$	15701.6	−	27195.9i	0.623667	−	1.08022i	−0.365130	−	0.930957i	$-0.618975\pi$
$859$	15701.6	−	27195.9i	0.623667	−	1.08022i	0.988797	−	0.149266i	$-0.0476912\pi$
$860$	−1697.85	+	2940.76i	−0.0673210	+	0.116603i
$861$	−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	$-0.798539\pi$
$863$	−40883.5			−1.61262			−0.806310	+	0.591493i	$0.798539\pi$
$864$	3382.15	+	19861.4i	0.133175	+	0.782060i
$865$	11802.3			0.463917
$866$	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
$870$	−23414.3	+	5500.98i	−0.912436	+	0.214369i
$871$	−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
$875$	−101.732	−	176.206i	−0.00393050	−	0.00680782i
$876$	−2199.81	−	2340.81i	−0.0848456	−	0.0902840i
$877$	14157.3	−	24521.2i	0.545107	−	0.944154i	−0.453493	−	0.891260i	$-0.649822\pi$
$877$	14157.3	−	24521.2i	0.545107	−	0.944154i	0.998600	−	0.0528937i	$-0.0168444\pi$
$878$	−979.348	+	1696.28i	−0.0376440	+	0.0652013i
$879$	16544.8	+	17605.3i	0.634862	+	0.675554i
$880$	−6539.91	−	11327.5i	−0.250523	−	0.433919i
$881$	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	$-0.609955\pi$
$883$	−17769.0			−0.677208			−0.338604	+	0.940929i	$0.609955\pi$
$884$	6141.82	+	10637.9i	0.233678	+	0.404743i
$885$	−4634.57	+	1088.85i	−0.176033	+	0.0413574i
$886$	−18198.1	+	31520.1i	−0.690044	+	1.19519i
$887$	12944.1	−	22419.8i	0.489988	−	0.848684i	−0.509945	−	0.860207i	$-0.670334\pi$
$887$	12944.1	−	22419.8i	0.489988	−	0.848684i	0.999934	+	0.0115224i	$0.00366776\pi$
$888$	8139.83	−	26996.8i	0.307607	−	1.02022i
$889$	−921.481	−	1596.05i	−0.0347643	−	0.0602136i
$890$	24234.4			0.912739
$891$	−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
$895$	−3262.77	+	5651.29i	−0.121857	+	0.211063i
$896$	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
$900$	−1896.91	−	1258.27i	−0.0702559	−	0.0466025i
$901$	−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
$905$	−7748.58	+	13420.9i	−0.284609	+	0.492958i
$906$	37950.7	+	40383.2i	1.39164	+	1.48084i
$907$	22594.1	+	39134.2i	0.827150	+	1.43267i	0.900265	+	0.435343i	$0.143373\pi$
$907$	22594.1	+	39134.2i	0.827150	+	1.43267i	−0.0731143	+	0.997324i	$0.523294\pi$
$908$	−13774.2			−0.503429
$909$	257.562	−	4143.09i	0.00939802	−	0.151175i
$910$	906.303			0.0330150
$911$	−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	$0.910337\pi$
$912$	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
$915$	−3274.46	+	10860.2i	−0.118306	+	0.392378i
$916$	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	$0.922568\pi$
$920$	2631.07	+	4557.15i	0.0942868	+	0.163309i
$921$	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
$925$	4346.54	+	7528.42i	0.154501	+	0.267603i
$926$	−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	0.914732	+	0.404062i	$0.132402\pi$
$929$	22858.9	+	39592.8i	0.807294	+	1.39827i	−0.107438	+	0.994212i	$0.534265\pi$
$930$	−360.000	−	383.075i	−0.0126934	−	0.0135070i
$931$	−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
$935$	−18124.2			−0.633931
$936$	−12458.4	+	6195.98i	−0.435059	+	0.216369i
$937$	−5055.54			−0.176262			−0.0881309	−	0.996109i	$-0.528089\pi$
$937$	−5055.54			−0.176262			−0.0881309	+	0.996109i	$0.528089\pi$
$938$	−2282.10	−	3952.72i	−0.0794385	−	0.137592i
$939$	−31583.4	+	7420.23i	−1.09764	+	0.257881i
$940$	4064.40	−	7039.75i	0.141028	−	0.244267i
$941$	−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	$0.328554\pi$
$942$	−12083.1	+	40075.0i	−0.417927	+	1.38611i
$943$	9823.52	+	17014.8i	0.339234	+	0.587571i
$944$	14587.1			0.502935
$945$	878.968	−	728.802i	0.0302570	−	0.0250878i
$946$	22317.4			0.767022
$947$	−15060.2	−	26085.0i	−0.516780	−	0.895090i	−0.999810	−	0.0194859i	$-0.993797\pi$
$947$	−15060.2	−	26085.0i	−0.516780	−	0.895090i	0.483030	−	0.875604i	$-0.339536\pi$
$948$	3228.76	−	10708.6i	0.110617	−	0.366876i
$949$	3026.74	−	5242.46i	0.103532	−	0.179323i
$950$	−2289.23	+	3965.07i	−0.0781816	+	0.135414i
$951$	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	$-0.393262\pi$
$953$	19362.7			0.658154			0.329077	+	0.944303i	$0.393262\pi$
$954$	−989.946	+	15924.1i	−0.0335961	+	0.540420i
$955$	1903.56			0.0645003
$956$	−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
$960$	−2714.51	−	2888.50i	−0.0912608	−	0.0971103i
$961$	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
$965$	−3865.10	−	6694.55i	−0.128935	−	0.223321i
$966$	1872.49	−	439.925i	0.0623669	−	0.0146525i
$967$	15362.3	−	26608.2i	0.510876	−	0.884863i	−0.489045	−	0.872259i	$-0.662654\pi$
$967$	15362.3	−	26608.2i	0.510876	−	0.884863i	0.999921	−	0.0126043i	$-0.00401218\pi$
$968$	1959.55	−	3394.04i	0.0650643	−	0.112695i
$969$	8985.67	−	29802.1i	0.297896	−	0.988010i
$970$	−7518.24	−	13022.0i	−0.248862	−	0.431042i
$971$	−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
$975$	1238.32	−	4107.03i	0.0406747	−	0.134903i
$976$	17377.8	−	30099.2i	0.569927	−	0.987143i
$977$	11195.9	−	19391.9i	0.366622	−	0.635008i	−0.622413	−	0.782689i	$-0.713847\pi$
$977$	11195.9	−	19391.9i	0.366622	−	0.635008i	0.989035	+	0.147681i	$0.0471808\pi$
$978$	43410.2	−	10198.8i	1.41933	−	0.333458i
$979$	−23615.3	−	40903.0i	−0.770939	−	1.33531i
$980$	−5738.79			−0.187060
$981$	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	$-0.0358825\pi$
$983$	12309.7	+	21321.0i	0.399408	+	0.691794i	−0.594245	+	0.804284i	$0.702549\pi$
$984$	−16178.7	−	17215.7i	−0.524144	−	0.557741i
$985$	10711.5	−	18552.8i	0.346494	−	0.600145i
$986$	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
$990$	−928.247	+	14931.6i	−0.0297996	+	0.479351i
$991$	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
$995$	3507.13	−	6074.53i	0.111742	−	0.193543i
$996$	7560.54	−	25075.5i	0.240527	−	0.797737i
$997$	−22978.0	−	39799.1i	−0.729912	−	1.26424i	−0.956920	−	0.290351i	$-0.906228\pi$
$997$	−22978.0	−	39799.1i	−0.729912	−	1.26424i	0.227008	−	0.973893i	$-0.427105\pi$
$998$	−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	45.4.e.a.31.2	yes	4
3.2	odd	2		135.4.e.a.91.1		4
5.2	odd	4		225.4.k.a.49.1		8
5.3	odd	4		225.4.k.a.49.4		8
5.4	even	2		225.4.e.a.76.1		4
9.2	odd	6		135.4.e.a.46.1		4
9.4	even	3		405.4.a.d.1.1		2
9.5	odd	6		405.4.a.e.1.2		2
9.7	even	3	inner	45.4.e.a.16.2	✓	4
45.4	even	6		2025.4.a.l.1.2		2
45.7	odd	12		225.4.k.a.124.4		8
45.14	odd	6		2025.4.a.j.1.1		2
45.34	even	6		225.4.e.a.151.1		4
45.43	odd	12		225.4.k.a.124.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.2	✓	4	9.7	even	3	inner
45.4.e.a.31.2	yes	4	1.1	even	1	trivial
135.4.e.a.46.1		4	9.2	odd	6
135.4.e.a.91.1		4	3.2	odd	2
225.4.e.a.76.1		4	5.4	even	2
225.4.e.a.151.1		4	45.34	even	6
225.4.k.a.49.1		8	5.2	odd	4
225.4.k.a.49.4		8	5.3	odd	4
225.4.k.a.124.1		8	45.43	odd	12
225.4.k.a.124.4		8	45.7	odd	12
405.4.a.d.1.1		2	9.4	even	3
405.4.a.e.1.2		2	9.5	odd	6
2025.4.a.j.1.1		2	45.14	odd	6
2025.4.a.l.1.2		2	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.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} +(-2.50000 + 4.33013i) q^{5} +(-17.0584 + 4.00772i) q^{6} +(-0.813859 - 1.40965i) q^{7} +15.6060 q^{8} +(-22.5000 - 14.9248i) q^{9} -16.8614 q^{10} +(16.4307 + 28.4588i) q^{11} +(-12.0000 - 12.7692i) q^{12} +(16.5109 - 28.5977i) q^{13} +(2.74456 - 4.75372i) q^{14} +(-17.7921 - 18.9325i) q^{15} +(39.8030 + 68.9408i) q^{16} +110.307 q^{17} +(5.64947 - 90.8762i) q^{18} -54.3070 q^{19} +(-8.43070 - 14.6024i) q^{20} +(8.23369 - 1.93443i) q^{21} +(-55.4090 + 95.9711i) q^{22} +(33.7188 - 58.4026i) q^{23} +(-23.4090 + 77.6387i) q^{24} +(-12.5000 - 21.6506i) q^{25} +111.359 q^{26} +(108.000 - 89.5489i) q^{27} +5.48913 q^{28} +(-137.259 - 237.740i) q^{29} +(25.2921 - 83.8844i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-71.8030 + 124.366i) q^{32} +(-166.227 + 39.0535i) q^{33} +(185.993 + 322.150i) q^{34} +8.13859 q^{35} +(81.5258 - 40.5455i) q^{36} -347.723 q^{37} +(-91.5693 - 158.603i) q^{38} +(117.505 + 125.037i) q^{39} +(-39.0149 + 67.5758i) q^{40} +(-145.668 + 252.305i) q^{41} +(19.5326 + 20.7846i) q^{42} +(-100.694 - 174.408i) q^{43} -110.818 q^{44} +(120.876 - 60.1158i) q^{45} +227.418 q^{46} +(241.048 + 417.507i) q^{47} +(-402.681 + 94.6062i) q^{48} +(170.175 - 294.752i) q^{49} +(42.1535 - 73.0120i) q^{50} +(-165.461 + 548.771i) q^{51} +(55.6793 + 96.4394i) q^{52} -175.228 q^{53} +(443.629 + 164.420i) q^{54} -164.307 q^{55} +(-12.7011 - 21.9989i) q^{56} +(81.4605 - 270.174i) q^{57} +(462.878 - 801.728i) q^{58} +(91.6209 - 158.692i) q^{59} +(85.2921 - 20.0386i) q^{60} +(-218.297 - 378.102i) q^{61} +20.2337 q^{62} +(-2.72686 + 43.8637i) q^{63} +152.568 q^{64} +(82.5544 + 142.988i) q^{65} +(-394.337 - 419.613i) q^{66} +(415.750 - 720.100i) q^{67} +(-185.993 + 322.150i) q^{68} +(239.971 + 255.353i) q^{69} +(13.7228 + 23.7686i) q^{70} -118.951 q^{71} +(-351.134 - 232.916i) q^{72} +183.318 q^{73} +(-586.310 - 1015.52i) q^{74} +(126.461 - 29.7108i) q^{75} +(91.5693 - 158.603i) q^{76} +(26.7446 - 46.3229i) q^{77} +(-167.038 + 554.002i) q^{78} +(319.147 + 552.778i) q^{79} -398.030 q^{80} +(283.500 + 671.617i) q^{81} -982.470 q^{82} +(747.322 + 1294.40i) q^{83} +(-8.23369 + 27.3081i) q^{84} +(-275.768 + 477.643i) q^{85} +(339.569 - 588.151i) q^{86} +(1388.63 - 326.247i) q^{87} +(256.417 + 444.127i) q^{88} -1437.27 q^{89} +(379.382 + 251.653i) q^{90} -53.7501 q^{91} +(113.709 + 196.950i) q^{92} +(21.3505 + 22.7190i) q^{93} +(-812.880 + 1407.95i) q^{94} +(135.768 - 235.156i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 6 q^{3} - q^{4} - 10 q^{5} - 51 q^{6} - 9 q^{7} - 18 q^{8} - 90 q^{9} - 10 q^{10} + 37 q^{11} - 48 q^{12} + 112 q^{13} - 12 q^{14} + 15 q^{15} + 119 q^{16} + 154 q^{17} + 126 q^{18} + 70 q^{19}+ \cdots - 90 q^{99}+O(q^{100}) \) 4 * q + q^2 - 6 * q^3 - q^4 - 10 * q^5 - 51 * q^6 - 9 * q^7 - 18 * q^8 - 90 * q^9 - 10 * q^10 + 37 * q^11 - 48 * q^12 + 112 * q^13 - 12 * q^14 + 15 * q^15 + 119 * q^16 + 154 * q^17 + 126 * q^18 + 70 * q^19 - 5 * q^20 - 36 * q^21 - 101 * q^22 + 267 * q^23 + 27 * q^24 - 50 * q^25 - 152 * q^26 + 432 * q^27 - 24 * q^28 - 325 * q^29 + 15 * q^30 + 12 * q^31 - 247 * q^32 - 303 * q^33 + 451 * q^34 + 90 * q^35 + 171 * q^36 - 1276 * q^37 - 395 * q^38 - 564 * q^39 + 45 * q^40 - 238 * q^41 + 216 * q^42 + 97 * q^43 - 202 * q^44 + 225 * q^45 - 492 * q^46 + 901 * q^47 - 525 * q^48 + 629 * q^49 + 25 * q^50 - 231 * q^51 - 76 * q^52 + 448 * q^53 + 999 * q^54 - 370 * q^55 + 156 * q^56 - 105 * q^57 + 806 * q^58 + 85 * q^59 + 255 * q^60 + 247 * q^61 + 12 * q^62 + 351 * q^63 + 1426 * q^64 + 560 * q^65 - 888 * q^66 + 606 * q^67 - 451 * q^68 - 1539 * q^69 - 60 * q^70 + 788 * q^71 + 405 * q^72 - 1622 * q^73 - 484 * q^74 + 75 * q^75 + 395 * q^76 + 84 * q^77 + 228 * q^78 + 840 * q^79 - 1190 * q^80 + 1134 * q^81 - 2218 * q^82 + 387 * q^83 + 36 * q^84 - 385 * q^85 + 1387 * q^86 + 2418 * q^87 + 411 * q^88 - 2130 * q^89 + 225 * q^90 - 1272 * q^91 - 246 * q^92 - 18 * q^93 - 632 * q^94 - 175 * q^95 + 24 * q^96 + 1031 * q^97 + 926 * q^98 - 90 * q^99

Introduction

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