LMFDB - Embedded newform 546.4.l.b.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(211,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.211"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,3,-4,44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.4.l.b.295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +22.0000 q^{5} +(3.00000 - 5.19615i) q^{6} +(-3.50000 + 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-22.0000 - 38.1051i) q^{10} +(-8.00000 - 13.8564i) q^{11} -12.0000 q^{12} +(45.5000 - 11.2583i) q^{13} +14.0000 q^{14} +(33.0000 + 57.1577i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(49.5000 - 85.7365i) q^{17} +18.0000 q^{18} +(11.0000 - 19.0526i) q^{19} +(-44.0000 + 76.2102i) q^{20} -21.0000 q^{21} +(-16.0000 + 27.7128i) q^{22} +(-76.5000 - 132.502i) q^{23} +(12.0000 + 20.7846i) q^{24} +359.000 q^{25} +(-65.0000 - 67.5500i) q^{26} -27.0000 q^{27} +(-14.0000 - 24.2487i) q^{28} +(-111.000 - 192.258i) q^{29} +(66.0000 - 114.315i) q^{30} +91.0000 q^{31} +(-16.0000 + 27.7128i) q^{32} +(24.0000 - 41.5692i) q^{33} -198.000 q^{34} +(-77.0000 + 133.368i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(133.000 + 230.363i) q^{37} -44.0000 q^{38} +(97.5000 + 101.325i) q^{39} +176.000 q^{40} +(189.000 + 327.358i) q^{41} +(21.0000 + 36.3731i) q^{42} +(-42.5000 + 73.6122i) q^{43} +64.0000 q^{44} +(-99.0000 + 171.473i) q^{45} +(-153.000 + 265.004i) q^{46} -262.000 q^{47} +(24.0000 - 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-359.000 - 621.806i) q^{50} +297.000 q^{51} +(-52.0000 + 180.133i) q^{52} +371.000 q^{53} +(27.0000 + 46.7654i) q^{54} +(-176.000 - 304.841i) q^{55} +(-28.0000 + 48.4974i) q^{56} +66.0000 q^{57} +(-222.000 + 384.515i) q^{58} +(-257.500 + 446.003i) q^{59} -264.000 q^{60} +(-241.500 + 418.290i) q^{61} +(-91.0000 - 157.617i) q^{62} +(-31.5000 - 54.5596i) q^{63} +64.0000 q^{64} +(1001.00 - 247.683i) q^{65} -96.0000 q^{66} +(77.5000 + 134.234i) q^{67} +(198.000 + 342.946i) q^{68} +(229.500 - 397.506i) q^{69} +308.000 q^{70} +(424.500 - 735.256i) q^{71} +(-36.0000 + 62.3538i) q^{72} +284.000 q^{73} +(266.000 - 460.726i) q^{74} +(538.500 + 932.709i) q^{75} +(44.0000 + 76.2102i) q^{76} +112.000 q^{77} +(78.0000 - 270.200i) q^{78} -116.000 q^{79} +(-176.000 - 304.841i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(378.000 - 654.715i) q^{82} +323.000 q^{83} +(42.0000 - 72.7461i) q^{84} +(1089.00 - 1886.20i) q^{85} +170.000 q^{86} +(333.000 - 576.773i) q^{87} +(-64.0000 - 110.851i) q^{88} +(-268.500 - 465.056i) q^{89} +396.000 q^{90} +(-91.0000 + 315.233i) q^{91} +612.000 q^{92} +(136.500 + 236.425i) q^{93} +(262.000 + 453.797i) q^{94} +(242.000 - 419.156i) q^{95} -96.0000 q^{96} +(-446.000 + 772.495i) q^{97} +(-49.0000 + 84.8705i) q^{98} +144.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} + 44 q^{5} + 6 q^{6} - 7 q^{7} + 16 q^{8} - 9 q^{9} - 44 q^{10} - 16 q^{11} - 24 q^{12} + 91 q^{13} + 28 q^{14} + 66 q^{15} - 16 q^{16} + 99 q^{17} + 36 q^{18} + 22 q^{19}+ \cdots + 288 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 + 44 * q^5 + 6 * q^6 - 7 * q^7 + 16 * q^8 - 9 * q^9 - 44 * q^10 - 16 * q^11 - 24 * q^12 + 91 * q^13 + 28 * q^14 + 66 * q^15 - 16 * q^16 + 99 * q^17 + 36 * q^18 + 22 * q^19 - 88 * q^20 - 42 * q^21 - 32 * q^22 - 153 * q^23 + 24 * q^24 + 718 * q^25 - 130 * q^26 - 54 * q^27 - 28 * q^28 - 222 * q^29 + 132 * q^30 + 182 * q^31 - 32 * q^32 + 48 * q^33 - 396 * q^34 - 154 * q^35 - 36 * q^36 + 266 * q^37 - 88 * q^38 + 195 * q^39 + 352 * q^40 + 378 * q^41 + 42 * q^42 - 85 * q^43 + 128 * q^44 - 198 * q^45 - 306 * q^46 - 524 * q^47 + 48 * q^48 - 49 * q^49 - 718 * q^50 + 594 * q^51 - 104 * q^52 + 742 * q^53 + 54 * q^54 - 352 * q^55 - 56 * q^56 + 132 * q^57 - 444 * q^58 - 515 * q^59 - 528 * q^60 - 483 * q^61 - 182 * q^62 - 63 * q^63 + 128 * q^64 + 2002 * q^65 - 192 * q^66 + 155 * q^67 + 396 * q^68 + 459 * q^69 + 616 * q^70 + 849 * q^71 - 72 * q^72 + 568 * q^73 + 532 * q^74 + 1077 * q^75 + 88 * q^76 + 224 * q^77 + 156 * q^78 - 232 * q^79 - 352 * q^80 - 81 * q^81 + 756 * q^82 + 646 * q^83 + 84 * q^84 + 2178 * q^85 + 340 * q^86 + 666 * q^87 - 128 * q^88 - 537 * q^89 + 792 * q^90 - 182 * q^91 + 1224 * q^92 + 273 * q^93 + 524 * q^94 + 484 * q^95 - 192 * q^96 - 892 * q^97 - 98 * q^98 + 288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	22.0000			1.96774			0.983870	−	0.178885i	$-0.0572491\pi$
$5$	22.0000			1.96774			0.983870	+	0.178885i	$0.0572491\pi$
$6$	3.00000	−	5.19615i	0.204124	−	0.353553i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−22.0000	−	38.1051i	−0.695701	−	1.20499i
$11$	−8.00000	−	13.8564i	−0.219281	−	0.379806i	0.735307	−	0.677734i	$-0.237038\pi$
$11$	−8.00000	−	13.8564i	−0.219281	−	0.379806i	−0.954588	+	0.297928i	$0.903704\pi$
$12$	−12.0000			−0.288675
$13$	45.5000	−	11.2583i	0.970725	−	0.240192i
$13$	45.5000	−	11.2583i	0.970725	−	0.240192i
$14$	14.0000			0.267261
$15$	33.0000	+	57.1577i	0.568038	+	0.983870i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	49.5000	−	85.7365i	0.706207	−	1.22319i	−0.260048	−	0.965596i	$-0.583738\pi$
$17$	49.5000	−	85.7365i	0.706207	−	1.22319i	0.966254	−	0.257590i	$-0.0829284\pi$
$18$	18.0000			0.235702
$19$	11.0000	−	19.0526i	0.132820	−	0.230050i	−0.791943	−	0.610595i	$-0.790930\pi$
$19$	11.0000	−	19.0526i	0.132820	−	0.230050i	0.924762	+	0.380545i	$0.124264\pi$
$20$	−44.0000	+	76.2102i	−0.491935	+	0.852056i
$21$	−21.0000			−0.218218
$22$	−16.0000	+	27.7128i	−0.155055	+	0.268563i
$23$	−76.5000	−	132.502i	−0.693537	−	1.20124i	−0.970671	−	0.240410i	$-0.922718\pi$
$23$	−76.5000	−	132.502i	−0.693537	−	1.20124i	0.277134	−	0.960831i	$-0.410615\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	359.000			2.87200
$26$	−65.0000	−	67.5500i	−0.490290	−	0.509525i
$27$	−27.0000			−0.192450
$28$	−14.0000	−	24.2487i	−0.0944911	−	0.163663i
$29$	−111.000	−	192.258i	−0.710765	−	1.23108i	−0.964570	−	0.263826i	$-0.915016\pi$
$29$	−111.000	−	192.258i	−0.710765	−	1.23108i	0.253805	−	0.967255i	$-0.418318\pi$
$30$	66.0000	−	114.315i	0.401663	−	0.695701i
$31$	91.0000			0.527228			0.263614	−	0.964628i	$-0.415085\pi$
$31$	91.0000			0.527228			0.263614	+	0.964628i	$0.415085\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	24.0000	−	41.5692i	0.126602	−	0.219281i
$34$	−198.000			−0.998727
$35$	−77.0000	+	133.368i	−0.371868	+	0.644094i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	133.000	+	230.363i	0.590948	+	1.02355i	0.994105	+	0.108421i	$0.0345794\pi$
$37$	133.000	+	230.363i	0.590948	+	1.02355i	−0.403157	+	0.915131i	$0.632087\pi$
$38$	−44.0000			−0.187835
$39$	97.5000	+	101.325i	0.400320	+	0.416025i
$40$	176.000			0.695701
$41$	189.000	+	327.358i	0.719923	+	1.24694i	0.961030	+	0.276445i	$0.0891562\pi$
$41$	189.000	+	327.358i	0.719923	+	1.24694i	−0.241107	+	0.970499i	$0.577510\pi$
$42$	21.0000	+	36.3731i	0.0771517	+	0.133631i
$43$	−42.5000	+	73.6122i	−0.150725	+	0.261064i	−0.931494	−	0.363756i	$-0.881494\pi$
$43$	−42.5000	+	73.6122i	−0.150725	+	0.261064i	0.780769	+	0.624820i	$0.214828\pi$
$44$	64.0000			0.219281
$45$	−99.0000	+	171.473i	−0.327957	+	0.568038i
$46$	−153.000	+	265.004i	−0.490405	+	0.849406i
$47$	−262.000			−0.813120			−0.406560	−	0.913624i	$-0.633272\pi$
$47$	−262.000			−0.813120			−0.406560	+	0.913624i	$0.633272\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	−359.000	−	621.806i	−1.01541	−	1.75873i
$51$	297.000			0.815457
$52$	−52.0000	+	180.133i	−0.138675	+	0.480384i
$53$	371.000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	371.000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−176.000	−	304.841i	−0.431488	−	0.747359i
$56$	−28.0000	+	48.4974i	−0.0668153	+	0.115728i
$57$	66.0000			0.153367
$58$	−222.000	+	384.515i	−0.502587	+	0.870506i
$59$	−257.500	+	446.003i	−0.568197	+	0.984147i	0.428547	+	0.903520i	$0.359026\pi$
$59$	−257.500	+	446.003i	−0.568197	+	0.984147i	−0.996744	+	0.0806272i	$0.974308\pi$
$60$	−264.000			−0.568038
$61$	−241.500	+	418.290i	−0.506900	+	0.877977i	0.493068	+	0.869991i	$0.335875\pi$
$61$	−241.500	+	418.290i	−0.506900	+	0.877977i	−0.999968	+	0.00798597i	$0.997458\pi$
$62$	−91.0000	−	157.617i	−0.186403	−	0.322860i
$63$	−31.5000	−	54.5596i	−0.0629941	−	0.109109i
$64$	64.0000			0.125000
$65$	1001.00	−	247.683i	1.91013	−	0.472636i
$66$	−96.0000			−0.179042
$67$	77.5000	+	134.234i	0.141315	+	0.244765i	0.927992	−	0.372600i	$-0.121533\pi$
$67$	77.5000	+	134.234i	0.141315	+	0.244765i	−0.786677	+	0.617365i	$0.788200\pi$
$68$	198.000	+	342.946i	0.353103	+	0.611593i
$69$	229.500	−	397.506i	0.400414	−	0.693537i
$70$	308.000			0.525901
$71$	424.500	−	735.256i	0.709562	−	1.22900i	−0.255458	−	0.966820i	$-0.582226\pi$
$71$	424.500	−	735.256i	0.709562	−	1.22900i	0.965020	−	0.262177i	$-0.0844404\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	284.000			0.455338			0.227669	−	0.973739i	$-0.426890\pi$
$73$	284.000			0.455338			0.227669	+	0.973739i	$0.426890\pi$
$74$	266.000	−	460.726i	0.417863	−	0.723760i
$75$	538.500	+	932.709i	0.829075	+	1.43600i
$76$	44.0000	+	76.2102i	0.0664098	+	0.115025i
$77$	112.000			0.165761
$78$	78.0000	−	270.200i	0.113228	−	0.392232i
$79$	−116.000			−0.165203			−0.0826014	−	0.996583i	$-0.526323\pi$
$79$	−116.000			−0.165203			−0.0826014	+	0.996583i	$0.526323\pi$
$80$	−176.000	−	304.841i	−0.245967	−	0.426028i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	378.000	−	654.715i	0.509062	−	0.881722i
$83$	323.000			0.427155			0.213577	−	0.976926i	$-0.431488\pi$
$83$	323.000			0.427155			0.213577	+	0.976926i	$0.431488\pi$
$84$	42.0000	−	72.7461i	0.0545545	−	0.0944911i
$85$	1089.00	−	1886.20i	1.38963	−	2.40691i
$86$	170.000			0.213158
$87$	333.000	−	576.773i	0.410360	−	0.710765i
$88$	−64.0000	−	110.851i	−0.0775275	−	0.134282i
$89$	−268.500	−	465.056i	−0.319786	−	0.553885i	0.660657	−	0.750688i	$-0.270278\pi$
$89$	−268.500	−	465.056i	−0.319786	−	0.553885i	−0.980443	+	0.196802i	$0.936944\pi$
$90$	396.000			0.463801
$91$	−91.0000	+	315.233i	−0.104828	+	0.363137i
$92$	612.000			0.693537
$93$	136.500	+	236.425i	0.152198	+	0.263614i
$94$	262.000	+	453.797i	0.287481	+	0.497932i
$95$	242.000	−	419.156i	0.261354	−	0.452679i
$96$	−96.0000			−0.102062
$97$	−446.000	+	772.495i	−0.466850	+	0.808608i	−0.999283	−	0.0378644i	$-0.987944\pi$
$97$	−446.000	+	772.495i	−0.466850	+	0.808608i	0.532433	+	0.846472i	$0.321278\pi$
$98$	−49.0000	+	84.8705i	−0.0505076	+	0.0874818i
$99$	144.000			0.146187
$100$	−718.000	+	1243.61i	−0.718000	+	1.24361i
$101$	230.000	+	398.372i	0.226593	+	0.392470i	0.956796	−	0.290760i	$-0.0939081\pi$
$101$	230.000	+	398.372i	0.226593	+	0.392470i	−0.730203	+	0.683230i	$0.760575\pi$
$102$	−297.000	−	514.419i	−0.288308	−	0.499364i
$103$	1233.00			1.17953			0.589763	−	0.807577i	$-0.299221\pi$
$103$	1233.00			1.17953			0.589763	+	0.807577i	$0.299221\pi$
$104$	364.000	−	90.0666i	0.343203	−	0.0849208i
$105$	−462.000			−0.429396
$106$	−371.000	−	642.591i	−0.339950	−	0.588811i
$107$	−91.0000	−	157.617i	−0.0822178	−	0.142405i	0.821984	−	0.569510i	$-0.192867\pi$
$107$	−91.0000	−	157.617i	−0.0822178	−	0.142405i	−0.904202	+	0.427105i	$0.859534\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−924.000			−0.811955			−0.405978	−	0.913883i	$-0.633069\pi$
$109$	−924.000			−0.811955			−0.405978	+	0.913883i	$0.633069\pi$
$110$	−352.000	+	609.682i	−0.305108	+	0.528463i
$111$	−399.000	+	691.088i	−0.341184	+	0.590948i
$112$	112.000			0.0944911
$113$	118.000	−	204.382i	0.0982346	−	0.170147i	−0.812719	−	0.582655i	$-0.802014\pi$
$113$	118.000	−	204.382i	0.0982346	−	0.170147i	0.910954	+	0.412508i	$0.135347\pi$
$114$	−66.0000	−	114.315i	−0.0542234	−	0.0939177i
$115$	−1683.00	−	2915.04i	−1.36470	−	2.36373i
$116$	888.000			0.710765
$117$	−117.000	+	405.300i	−0.0924500	+	0.320256i
$118$	1030.00			0.803552
$119$	346.500	+	600.156i	0.266921	+	0.462321i
$120$	264.000	+	457.261i	0.200832	+	0.347851i
$121$	537.500	−	930.977i	0.403832	−	0.699457i
$122$	966.000			0.716865
$123$	−567.000	+	982.073i	−0.415648	+	0.719923i
$124$	−182.000	+	315.233i	−0.131807	+	0.228297i
$125$	5148.00			3.68361
$126$	−63.0000	+	109.119i	−0.0445435	+	0.0771517i
$127$	−514.000	−	890.274i	−0.359135	−	0.622040i	0.628682	−	0.777663i	$-0.283595\pi$
$127$	−514.000	−	890.274i	−0.359135	−	0.622040i	−0.987817	+	0.155623i	$0.950262\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−255.000			−0.174043
$130$	−1430.00	−	1486.10i	−0.964764	−	1.00261i
$131$	−445.000			−0.296793			−0.148396	−	0.988928i	$-0.547411\pi$
$131$	−445.000			−0.296793			−0.148396	+	0.988928i	$0.547411\pi$
$132$	96.0000	+	166.277i	0.0633010	+	0.109640i
$133$	77.0000	+	133.368i	0.0502011	+	0.0869509i
$134$	155.000	−	268.468i	0.0999251	−	0.173075i
$135$	−594.000			−0.378692
$136$	396.000	−	685.892i	0.249682	−	0.432462i
$137$	554.000	−	959.556i	0.345485	−	0.598397i	−0.639957	−	0.768411i	$-0.721048\pi$
$137$	554.000	−	959.556i	0.345485	−	0.598397i	0.985442	+	0.170014i	$0.0543812\pi$
$138$	−918.000			−0.566271
$139$	−1482.00	+	2566.90i	−0.904328	+	1.56634i	−0.0825114	+	0.996590i	$0.526294\pi$
$139$	−1482.00	+	2566.90i	−0.904328	+	1.56634i	−0.821817	+	0.569752i	$0.807039\pi$
$140$	−308.000	−	533.472i	−0.185934	−	0.322047i
$141$	−393.000	−	680.696i	−0.234727	−	0.406560i
$142$	−1698.00			−1.00347
$143$	−520.000	−	540.400i	−0.304088	−	0.316018i
$144$	144.000			0.0833333
$145$	−2442.00	−	4229.67i	−1.39860	−	2.42245i
$146$	−284.000	−	491.902i	−0.160986	−	0.278837i
$147$	73.5000	−	127.306i	0.0412393	−	0.0714286i
$148$	−1064.00			−0.590948
$149$	−1074.50	+	1861.09i	−0.590782	+	1.02326i	0.403346	+	0.915048i	$0.367847\pi$
$149$	−1074.50	+	1861.09i	−0.590782	+	1.02326i	−0.994127	+	0.108216i	$0.965486\pi$
$150$	1077.00	−	1865.42i	0.586245	−	1.01541i
$151$	−2300.00			−1.23955			−0.619773	−	0.784781i	$-0.712775\pi$
$151$	−2300.00			−1.23955			−0.619773	+	0.784781i	$0.712775\pi$
$152$	88.0000	−	152.420i	0.0469588	−	0.0813351i
$153$	445.500	+	771.629i	0.235402	+	0.407729i
$154$	−112.000	−	193.990i	−0.0586053	−	0.101507i
$155$	2002.00			1.03745
$156$	−546.000	+	135.100i	−0.280224	+	0.0693375i
$157$	990.000			0.503252			0.251626	−	0.967825i	$-0.419035\pi$
$157$	990.000			0.503252			0.251626	+	0.967825i	$0.419035\pi$
$158$	116.000	+	200.918i	0.0584080	+	0.101166i
$159$	556.500	+	963.886i	0.277568	+	0.480762i
$160$	−352.000	+	609.682i	−0.173925	+	0.301247i
$161$	1071.00			0.524265
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	1406.50	−	2436.13i	0.675862	−	1.17063i	−0.300354	−	0.953828i	$-0.597105\pi$
$163$	1406.50	−	2436.13i	0.675862	−	1.17063i	0.976216	−	0.216800i	$-0.0695620\pi$
$164$	−1512.00			−0.719923
$165$	528.000	−	914.523i	0.249120	−	0.431488i
$166$	−323.000	−	559.452i	−0.151022	−	0.261578i
$167$	1200.00	+	2078.46i	0.556041	+	0.963091i	0.997822	+	0.0659678i	$0.0210135\pi$
$167$	1200.00	+	2078.46i	0.556041	+	0.963091i	−0.441781	+	0.897123i	$0.645653\pi$
$168$	−168.000			−0.0771517
$169$	1943.50	−	1024.51i	0.884615	−	0.466321i
$170$	−4356.00			−1.96523
$171$	99.0000	+	171.473i	0.0442732	+	0.0766835i
$172$	−170.000	−	294.449i	−0.0753627	−	0.130532i
$173$	−1134.00	+	1964.15i	−0.498361	+	0.863186i	−0.999998	−	0.00189172i	$-0.999398\pi$
$173$	−1134.00	+	1964.15i	−0.498361	+	0.863186i	0.501637	+	0.865078i	$0.332731\pi$
$174$	−1332.00			−0.580337
$175$	−1256.50	+	2176.32i	−0.542757	+	0.940083i
$176$	−128.000	+	221.703i	−0.0548202	+	0.0949514i
$177$	−1545.00			−0.656098
$178$	−537.000	+	930.111i	−0.226123	+	0.391656i
$179$	303.000	+	524.811i	0.126521	+	0.219141i	0.922327	−	0.386411i	$-0.126286\pi$
$179$	303.000	+	524.811i	0.126521	+	0.219141i	−0.795805	+	0.605552i	$0.792952\pi$
$180$	−396.000	−	685.892i	−0.163978	−	0.284019i
$181$	1538.00			0.631595			0.315797	−	0.948827i	$-0.397728\pi$
$181$	1538.00			0.631595			0.315797	+	0.948827i	$0.397728\pi$
$182$	637.000	−	157.617i	0.259437	−	0.0641941i
$183$	−1449.00			−0.585318
$184$	−612.000	−	1060.02i	−0.245202	−	0.424703i
$185$	2926.00	+	5067.98i	1.16283	+	2.01408i
$186$	273.000	−	472.850i	0.107620	−	0.186403i
$187$	−1584.00			−0.619431
$188$	524.000	−	907.595i	0.203280	−	0.352091i
$189$	94.5000	−	163.679i	0.0363696	−	0.0629941i
$190$	−968.000			−0.369611
$191$	13.5000	−	23.3827i	0.00511427	−	0.00885818i	−0.863457	−	0.504423i	$-0.831705\pi$
$191$	13.5000	−	23.3827i	0.00511427	−	0.00885818i	0.868571	+	0.495564i	$0.165039\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	1467.00	+	2540.92i	0.547135	+	0.947665i	0.998469	+	0.0553101i	$0.0176147\pi$
$193$	1467.00	+	2540.92i	0.547135	+	0.947665i	−0.451335	+	0.892355i	$0.649052\pi$
$194$	1784.00			0.660225
$195$	2145.00	+	2229.15i	0.787726	+	0.818629i
$196$	196.000			0.0714286
$197$	−2611.50	−	4523.25i	−0.944475	−	1.63588i	−0.756798	−	0.653649i	$-0.773237\pi$
$197$	−2611.50	−	4523.25i	−0.944475	−	1.63588i	−0.187677	−	0.982231i	$-0.560096\pi$
$198$	−144.000	−	249.415i	−0.0516850	−	0.0895211i
$199$	−2327.50	+	4031.35i	−0.829106	+	1.43605i	0.0696343	+	0.997573i	$0.477817\pi$
$199$	−2327.50	+	4031.35i	−0.829106	+	1.43605i	−0.898740	+	0.438481i	$0.855517\pi$
$200$	2872.00			1.01541
$201$	−232.500	+	402.702i	−0.0815885	+	0.141315i
$202$	460.000	−	796.743i	0.160225	−	0.277518i
$203$	1554.00			0.537288
$204$	−594.000	+	1028.84i	−0.203864	+	0.353103i
$205$	4158.00	+	7201.87i	1.41662	+	2.45366i
$206$	−1233.00	−	2135.62i	−0.417025	−	0.722309i
$207$	1377.00			0.462358
$208$	−520.000	−	540.400i	−0.173344	−	0.180144i
$209$	−352.000			−0.116499
$210$	462.000	+	800.207i	0.151814	+	0.262950i
$211$	−1662.00	−	2878.67i	−0.542260	−	0.939221i	−0.998774	−	0.0495052i	$-0.984236\pi$
$211$	−1662.00	−	2878.67i	−0.542260	−	0.939221i	0.456514	−	0.889716i	$-0.349098\pi$
$212$	−742.000	+	1285.18i	−0.240381	+	0.416352i
$213$	2547.00			0.819331
$214$	−182.000	+	315.233i	−0.0581367	+	0.100696i
$215$	−935.000	+	1619.47i	−0.296588	+	0.513706i
$216$	−216.000			−0.0680414
$217$	−318.500	+	551.658i	−0.0996368	+	0.172576i
$218$	924.000	+	1600.41i	0.287070	+	0.497219i
$219$	426.000	+	737.854i	0.131445	+	0.227669i
$220$	1408.00			0.431488
$221$	1287.00	−	4458.30i	0.391733	−	1.35700i
$222$	1596.00			0.482507
$223$	−1515.50	−	2624.92i	−0.455091	−	0.788241i	0.543602	−	0.839343i	$-0.317060\pi$
$223$	−1515.50	−	2624.92i	−0.455091	−	0.788241i	−0.998693	+	0.0511016i	$0.983727\pi$
$224$	−112.000	−	193.990i	−0.0334077	−	0.0578638i
$225$	−1615.50	+	2798.13i	−0.478667	+	0.829075i
$226$	−472.000			−0.138925
$227$	−2262.00	+	3917.90i	−0.661384	+	1.14555i	0.318868	+	0.947799i	$0.396697\pi$
$227$	−2262.00	+	3917.90i	−0.661384	+	1.14555i	−0.980252	+	0.197752i	$0.936636\pi$
$228$	−132.000	+	228.631i	−0.0383417	+	0.0664098i
$229$	−2553.00			−0.736712			−0.368356	−	0.929685i	$-0.620079\pi$
$229$	−2553.00			−0.736712			−0.368356	+	0.929685i	$0.620079\pi$
$230$	−3366.00	+	5830.08i	−0.964989	+	1.67141i
$231$	168.000	+	290.985i	0.0478510	+	0.0828804i
$232$	−888.000	−	1538.06i	−0.251293	−	0.435253i
$233$	408.000			0.114717			0.0573583	−	0.998354i	$-0.481732\pi$
$233$	408.000			0.114717			0.0573583	+	0.998354i	$0.481732\pi$
$234$	819.000	−	202.650i	0.228802	−	0.0566139i
$235$	−5764.00			−1.60001
$236$	−1030.00	−	1784.01i	−0.284099	−	0.492073i
$237$	−174.000	−	301.377i	−0.0476899	−	0.0826014i
$238$	693.000	−	1200.31i	0.188742	−	0.326910i
$239$	4329.00			1.17163			0.585815	−	0.810445i	$-0.300774\pi$
$239$	4329.00			1.17163			0.585815	+	0.810445i	$0.300774\pi$
$240$	528.000	−	914.523i	0.142009	−	0.245967i
$241$	−2727.00	+	4723.30i	−0.728886	+	1.26247i	0.228468	+	0.973551i	$0.426628\pi$
$241$	−2727.00	+	4723.30i	−0.728886	+	1.26247i	−0.957354	+	0.288916i	$0.906705\pi$
$242$	−2150.00			−0.571104
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−966.000	−	1673.16i	−0.253450	−	0.438988i
$245$	−539.000	−	933.575i	−0.140553	−	0.243445i
$246$	2268.00			0.587815
$247$	286.000	−	990.733i	0.0736751	−	0.255218i
$248$	728.000			0.186403
$249$	484.500	+	839.179i	0.123309	+	0.213577i
$250$	−5148.00	−	8916.60i	−1.30235	−	2.25574i
$251$	3938.50	−	6821.68i	0.990422	−	1.71546i	0.375636	−	0.926767i	$-0.377424\pi$
$251$	3938.50	−	6821.68i	0.990422	−	1.71546i	0.614786	−	0.788694i	$-0.289242\pi$
$252$	252.000			0.0629941
$253$	−1224.00	+	2120.03i	−0.304159	+	0.526819i
$254$	−1028.00	+	1780.55i	−0.253947	+	0.439849i
$255$	6534.00			1.60461
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1060.50	−	1836.84i	−0.257401	−	0.445832i	0.708144	−	0.706068i	$-0.249533\pi$
$257$	−1060.50	−	1836.84i	−0.257401	−	0.445832i	−0.965545	+	0.260236i	$0.916200\pi$
$258$	255.000	+	441.673i	0.0615334	+	0.106579i
$259$	−1862.00			−0.446714
$260$	−1144.00	+	3962.93i	−0.272876	+	0.945272i
$261$	1998.00			0.473843
$262$	445.000	+	770.763i	0.104932	+	0.181748i
$263$	1146.00	+	1984.93i	0.268690	+	0.465384i	0.968524	−	0.248921i	$-0.0800761\pi$
$263$	1146.00	+	1984.93i	0.268690	+	0.465384i	−0.699834	+	0.714305i	$0.746743\pi$
$264$	192.000	−	332.554i	0.0447605	−	0.0775275i
$265$	8162.00			1.89203
$266$	154.000	−	266.736i	0.0354975	−	0.0614835i
$267$	805.500	−	1395.17i	0.184628	−	0.319786i
$268$	−620.000			−0.141315
$269$	−2121.00	+	3673.68i	−0.480742	+	0.832670i	−0.999756	−	0.0220960i	$-0.992966\pi$
$269$	−2121.00	+	3673.68i	−0.480742	+	0.832670i	0.519014	+	0.854766i	$0.326299\pi$
$270$	594.000	+	1028.84i	0.133888	+	0.231900i
$271$	2505.50	+	4339.65i	0.561617	+	0.972750i	0.997356	+	0.0726763i	$0.0231540\pi$
$271$	2505.50	+	4339.65i	0.561617	+	0.972750i	−0.435738	+	0.900073i	$0.643513\pi$
$272$	−1584.00			−0.353103
$273$	−955.500	+	236.425i	−0.211830	+	0.0524142i
$274$	−2216.00			−0.488589
$275$	−2872.00	−	4974.45i	−0.629775	−	1.09080i
$276$	918.000	+	1590.02i	0.200207	+	0.346769i
$277$	−3538.00	+	6128.00i	−0.767429	+	1.32923i	0.171524	+	0.985180i	$0.445131\pi$
$277$	−3538.00	+	6128.00i	−0.767429	+	1.32923i	−0.938953	+	0.344046i	$0.888202\pi$
$278$	5928.00			1.27891
$279$	−409.500	+	709.275i	−0.0878714	+	0.152198i
$280$	−616.000	+	1066.94i	−0.131475	+	0.227722i
$281$	−1126.00			−0.239045			−0.119522	−	0.992832i	$-0.538136\pi$
$281$	−1126.00			−0.239045			−0.119522	+	0.992832i	$0.538136\pi$
$282$	−786.000	+	1361.39i	−0.165977	+	0.287481i
$283$	−4229.00	−	7324.84i	−0.888297	−	1.53857i	−0.841888	−	0.539652i	$-0.818556\pi$
$283$	−4229.00	−	7324.84i	−0.888297	−	1.53857i	−0.0464088	−	0.998923i	$-0.514778\pi$
$284$	1698.00	+	2941.02i	0.354781	+	0.614498i
$285$	1452.00			0.301786
$286$	−416.000	+	1441.07i	−0.0860091	+	0.297944i
$287$	−2646.00			−0.544211
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	−2444.00	−	4233.13i	−0.497456	−	0.861619i
$290$	−4884.00	+	8459.34i	−0.988960	+	1.71293i
$291$	−2676.00			−0.539072
$292$	−568.000	+	983.805i	−0.113835	+	0.197167i
$293$	736.000	−	1274.79i	0.146749	−	0.254177i	−0.783275	−	0.621676i	$-0.786452\pi$
$293$	736.000	−	1274.79i	0.146749	−	0.254177i	0.930024	+	0.367498i	$0.119786\pi$
$294$	−294.000			−0.0583212
$295$	−5665.00	+	9812.07i	−1.11806	+	1.93654i
$296$	1064.00	+	1842.90i	0.208932	+	0.361880i
$297$	216.000	+	374.123i	0.0422006	+	0.0730937i
$298$	4298.00			0.835491
$299$	−4972.50	−	5167.57i	−0.961763	−	0.999493i
$300$	−4308.00			−0.829075
$301$	−297.500	−	515.285i	−0.0569688	−	0.0986729i
$302$	2300.00	+	3983.72i	0.438245	+	0.759063i
$303$	−690.000	+	1195.12i	−0.130823	+	0.226593i
$304$	−352.000			−0.0664098
$305$	−5313.00	+	9202.39i	−0.997448	+	1.72763i
$306$	891.000	−	1543.26i	0.166455	−	0.288308i
$307$	1410.00			0.262127			0.131063	−	0.991374i	$-0.458161\pi$
$307$	1410.00			0.262127			0.131063	+	0.991374i	$0.458161\pi$
$308$	−224.000	+	387.979i	−0.0414402	+	0.0717765i
$309$	1849.50	+	3203.43i	0.340500	+	0.589763i
$310$	−2002.00	−	3467.57i	−0.366793	−	0.635305i
$311$	−10070.0			−1.83607			−0.918034	−	0.396501i	$-0.870224\pi$
$311$	−10070.0			−1.83607			−0.918034	+	0.396501i	$0.870224\pi$
$312$	780.000	+	810.600i	0.141535	+	0.147087i
$313$	−7520.00			−1.35800			−0.679002	−	0.734136i	$-0.737587\pi$
$313$	−7520.00			−1.35800			−0.679002	+	0.734136i	$0.737587\pi$
$314$	−990.000	−	1714.73i	−0.177927	−	0.308178i
$315$	−693.000	−	1200.31i	−0.123956	−	0.214698i
$316$	232.000	−	401.836i	0.0413007	−	0.0715349i
$317$	−10521.0			−1.86410			−0.932048	−	0.362336i	$-0.881979\pi$
$317$	−10521.0			−1.86410			−0.932048	+	0.362336i	$0.881979\pi$
$318$	1113.00	−	1927.77i	0.196270	−	0.339950i
$319$	−1776.00	+	3076.12i	−0.311714	+	0.539905i
$320$	1408.00			0.245967
$321$	273.000	−	472.850i	0.0474685	−	0.0822178i
$322$	−1071.00	−	1855.03i	−0.185356	−	0.321045i
$323$	−1089.00	−	1886.20i	−0.187596	−	0.324926i
$324$	324.000			0.0555556
$325$	16334.5	−	4041.74i	2.78792	−	0.689832i
$326$	−5626.00			−0.955814
$327$	−1386.00	−	2400.62i	−0.234391	−	0.405978i
$328$	1512.00	+	2618.86i	0.254531	+	0.440861i
$329$	917.000	−	1588.29i	0.153665	−	0.266156i
$330$	−2112.00			−0.352308
$331$	−1898.00	+	3287.43i	−0.315177	+	0.545902i	−0.979475	−	0.201565i	$-0.935397\pi$
$331$	−1898.00	+	3287.43i	−0.315177	+	0.545902i	0.664298	+	0.747468i	$0.268730\pi$
$332$	−646.000	+	1118.90i	−0.106789	+	0.184963i
$333$	−2394.00			−0.393965
$334$	2400.00	−	4156.92i	0.393180	−	0.681008i
$335$	1705.00	+	2953.15i	0.278072	+	0.481635i
$336$	168.000	+	290.985i	0.0272772	+	0.0472456i
$337$	−11006.0			−1.77904			−0.889518	−	0.456900i	$-0.848960\pi$
$337$	−11006.0			−1.77904			−0.889518	+	0.456900i	$0.848960\pi$
$338$	−3718.00	−	2341.73i	−0.598321	−	0.376845i
$339$	708.000			0.113432
$340$	4356.00	+	7544.81i	0.694815	+	1.20346i
$341$	−728.000	−	1260.93i	−0.115611	−	0.200244i
$342$	198.000	−	342.946i	0.0313059	−	0.0542234i
$343$	343.000			0.0539949
$344$	−340.000	+	588.897i	−0.0532895	+	0.0923000i
$345$	5049.00	−	8745.12i	0.787910	−	1.36470i
$346$	4536.00			0.704789
$347$	4405.00	−	7629.68i	0.681478	−	1.18035i	−0.293052	−	0.956096i	$-0.594671\pi$
$347$	4405.00	−	7629.68i	0.681478	−	1.18035i	0.974530	−	0.224258i	$-0.0719957\pi$
$348$	1332.00	+	2307.09i	0.205180	+	0.355382i
$349$	−3482.50	−	6031.87i	−0.534137	−	0.925153i	−0.999205	−	0.0398777i	$-0.987303\pi$
$349$	−3482.50	−	6031.87i	−0.534137	−	0.925153i	0.465067	−	0.885275i	$-0.346030\pi$
$350$	5026.00			0.767574
$351$	−1228.50	+	303.975i	−0.186816	+	0.0462250i
$352$	512.000			0.0775275
$353$	−907.500	−	1571.84i	−0.136831	−	0.236998i	0.789464	−	0.613796i	$-0.210358\pi$
$353$	−907.500	−	1571.84i	−0.136831	−	0.236998i	−0.926295	+	0.376798i	$0.877025\pi$
$354$	1545.00	+	2676.02i	0.231966	+	0.401776i
$355$	9339.00	−	16175.6i	1.39623	−	2.41835i
$356$	2148.00			0.319786
$357$	−1039.50	+	1800.47i	−0.154107	+	0.266921i
$358$	606.000	−	1049.62i	0.0894640	−	0.154956i
$359$	5464.00			0.803284			0.401642	−	0.915797i	$-0.368440\pi$
$359$	5464.00			0.803284			0.401642	+	0.915797i	$0.368440\pi$
$360$	−792.000	+	1371.78i	−0.115950	+	0.200832i
$361$	3187.50	+	5520.91i	0.464718	+	0.804915i
$362$	−1538.00	−	2663.89i	−0.223302	−	0.386771i
$363$	3225.00			0.466305
$364$	−910.000	−	945.700i	−0.131036	−	0.136176i
$365$	6248.00			0.895987
$366$	1449.00	+	2509.74i	0.206941	+	0.358433i
$367$	3999.50	+	6927.34i	0.568862	+	0.985297i	0.996679	+	0.0814319i	$0.0259493\pi$
$367$	3999.50	+	6927.34i	0.568862	+	0.985297i	−0.427817	+	0.903865i	$0.640717\pi$
$368$	−1224.00	+	2120.03i	−0.173384	+	0.300310i
$369$	−3402.00			−0.479949
$370$	5852.00	−	10136.0i	0.822246	−	1.42417i
$371$	−1298.50	+	2249.07i	−0.181711	+	0.314733i
$372$	−1092.00			−0.152198
$373$	356.000	−	616.610i	0.0494182	−	0.0855948i	−0.840258	−	0.542186i	$-0.817597\pi$
$373$	356.000	−	616.610i	0.0494182	−	0.0855948i	0.889676	+	0.456592i	$0.150930\pi$
$374$	1584.00	+	2743.57i	0.219002	+	0.379322i
$375$	7722.00	+	13374.9i	1.06337	+	1.84180i
$376$	−2096.00			−0.287481
$377$	−7215.00	−	7498.05i	−0.985654	−	1.02432i
$378$	−378.000			−0.0514344
$379$	2170.00	+	3758.55i	0.294104	+	0.509403i	0.974776	−	0.223185i	$-0.0716455\pi$
$379$	2170.00	+	3758.55i	0.294104	+	0.509403i	−0.680672	+	0.732588i	$0.738312\pi$
$380$	968.000	+	1676.63i	0.130677	+	0.226340i
$381$	1542.00	−	2670.82i	0.207347	−	0.359135i
$382$	−54.0000			−0.00723267
$383$	−1414.00	+	2449.12i	−0.188648	+	0.326747i	−0.944800	−	0.327649i	$-0.893744\pi$
$383$	−1414.00	+	2449.12i	−0.188648	+	0.326747i	0.756152	+	0.654396i	$0.227077\pi$
$384$	192.000	−	332.554i	0.0255155	−	0.0441942i
$385$	2464.00			0.326174
$386$	2934.00	−	5081.84i	0.386883	−	0.670100i
$387$	−382.500	−	662.509i	−0.0502418	−	0.0870213i
$388$	−1784.00	−	3089.98i	−0.233425	−	0.404304i
$389$	6671.00			0.869494			0.434747	−	0.900553i	$-0.356838\pi$
$389$	6671.00			0.869494			0.434747	+	0.900553i	$0.356838\pi$
$390$	1716.00	−	5944.40i	0.222803	−	0.771811i
$391$	−15147.0			−1.95912
$392$	−196.000	−	339.482i	−0.0252538	−	0.0437409i
$393$	−667.500	−	1156.14i	−0.0856766	−	0.148396i
$394$	−5223.00	+	9046.50i	−0.667845	+	1.15674i
$395$	−2552.00			−0.325076
$396$	−288.000	+	498.831i	−0.0365468	+	0.0633010i
$397$	6301.50	−	10914.5i	0.796633	−	1.37981i	−0.125164	−	0.992136i	$-0.539946\pi$
$397$	6301.50	−	10914.5i	0.796633	−	1.37981i	0.921797	−	0.387672i	$-0.126721\pi$
$398$	9310.00			1.17253
$399$	−231.000	+	400.104i	−0.0289836	+	0.0502011i
$400$	−2872.00	−	4974.45i	−0.359000	−	0.621806i
$401$	1284.00	+	2223.95i	0.159900	+	0.276955i	0.934832	−	0.355089i	$-0.115549\pi$
$401$	1284.00	+	2223.95i	0.159900	+	0.276955i	−0.774932	+	0.632044i	$0.782216\pi$
$402$	930.000			0.115384
$403$	4140.50	−	1024.51i	0.511794	−	0.126636i
$404$	−1840.00			−0.226593
$405$	−891.000	−	1543.26i	−0.109319	−	0.189346i
$406$	−1554.00	−	2691.61i	−0.189960	−	0.329020i
$407$	2128.00	−	3685.80i	0.259167	−	0.448891i
$408$	2376.00			0.288308
$409$	4237.00	−	7338.70i	0.512240	−	0.887226i	−0.487659	−	0.873034i	$-0.662149\pi$
$409$	4237.00	−	7338.70i	0.512240	−	0.887226i	0.999899	−	0.0141917i	$-0.00451751\pi$
$410$	8316.00	−	14403.7i	1.00170	−	1.73500i
$411$	3324.00			0.398931
$412$	−2466.00	+	4271.24i	−0.294881	+	0.510749i
$413$	−1802.50	−	3122.02i	−0.214758	−	0.371972i
$414$	−1377.00	−	2385.03i	−0.163468	−	0.283135i
$415$	7106.00			0.840530
$416$	−416.000	+	1441.07i	−0.0490290	+	0.169842i
$417$	−8892.00			−1.04423
$418$	352.000	+	609.682i	0.0411887	+	0.0713409i
$419$	5889.50	+	10200.9i	0.686685	+	1.18937i	0.972904	+	0.231209i	$0.0742680\pi$
$419$	5889.50	+	10200.9i	0.686685	+	1.18937i	−0.286219	+	0.958164i	$0.592399\pi$
$420$	924.000	−	1600.41i	0.107349	−	0.185934i
$421$	2694.00			0.311871			0.155935	−	0.987767i	$-0.450161\pi$
$421$	2694.00			0.311871			0.155935	+	0.987767i	$0.450161\pi$
$422$	−3324.00	+	5757.34i	−0.383436	+	0.664130i
$423$	1179.00	−	2042.09i	0.135520	−	0.234727i
$424$	2968.00			0.339950
$425$	17770.5	−	30779.4i	2.02823	−	3.51299i
$426$	−2547.00	−	4411.53i	−0.289677	−	0.501736i
$427$	−1690.50	−	2928.03i	−0.191590	−	0.331844i
$428$	728.000			0.0822178
$429$	624.000	−	2161.60i	0.0702261	−	0.243270i
$430$	3740.00			0.419439
$431$	1215.50	+	2105.31i	0.135844	+	0.235288i	0.925919	−	0.377721i	$-0.123292\pi$
$431$	1215.50	+	2105.31i	0.135844	+	0.235288i	−0.790076	+	0.613009i	$0.789959\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−1472.00	+	2549.58i	−0.163371	+	0.282968i	−0.936076	−	0.351799i	$-0.885570\pi$
$433$	−1472.00	+	2549.58i	−0.163371	+	0.282968i	0.772704	+	0.634766i	$0.218904\pi$
$434$	1274.00			0.140908
$435$	7326.00	−	12689.0i	0.807482	−	1.39860i
$436$	1848.00	−	3200.83i	0.202989	−	0.351587i
$437$	−3366.00			−0.368461
$438$	852.000	−	1475.71i	0.0929455	−	0.160986i
$439$	−2438.00	−	4222.74i	−0.265056	−	0.459090i	0.702523	−	0.711661i	$-0.252057\pi$
$439$	−2438.00	−	4222.74i	−0.265056	−	0.459090i	−0.967578	+	0.252572i	$0.918724\pi$
$440$	−1408.00	−	2438.73i	−0.152554	−	0.264231i
$441$	441.000			0.0476190
$442$	−9009.00	+	2229.15i	−0.969490	+	0.239886i
$443$	5358.00			0.574642			0.287321	−	0.957834i	$-0.407235\pi$
$443$	5358.00			0.574642			0.287321	+	0.957834i	$0.407235\pi$
$444$	−1596.00	−	2764.35i	−0.170592	−	0.295474i
$445$	−5907.00	−	10231.2i	−0.629255	−	1.08990i
$446$	−3031.00	+	5249.85i	−0.321798	+	0.557371i
$447$	−6447.00			−0.682176
$448$	−224.000	+	387.979i	−0.0236228	+	0.0409159i
$449$	1729.00	−	2994.72i	0.181730	−	0.314765i	−0.760740	−	0.649057i	$-0.775164\pi$
$449$	1729.00	−	2994.72i	0.181730	−	0.314765i	0.942470	+	0.334292i	$0.108497\pi$
$450$	6462.00			0.676937
$451$	3024.00	−	5237.72i	0.315731	−	0.546862i
$452$	472.000	+	817.528i	0.0491173	+	0.0850736i
$453$	−3450.00	−	5975.58i	−0.357826	−	0.619773i
$454$	9048.00			0.935339
$455$	−2002.00	+	6935.13i	−0.206275	+	0.714558i
$456$	528.000			0.0542234
$457$	5828.50	+	10095.3i	0.596599	+	1.03334i	0.993319	+	0.115400i	$0.0368150\pi$
$457$	5828.50	+	10095.3i	0.596599	+	1.03334i	−0.396720	+	0.917940i	$0.629852\pi$
$458$	2553.00	+	4421.93i	0.260467	+	0.451142i
$459$	−1336.50	+	2314.89i	−0.135910	+	0.235402i
$460$	13464.0			1.36470
$461$	−1660.00	+	2875.20i	−0.167709	+	0.290481i	−0.937614	−	0.347678i	$-0.886970\pi$
$461$	−1660.00	+	2875.20i	−0.167709	+	0.290481i	0.769905	+	0.638159i	$0.220304\pi$
$462$	336.000	−	581.969i	0.0338358	−	0.0586053i
$463$	−3594.00			−0.360750			−0.180375	−	0.983598i	$-0.557731\pi$
$463$	−3594.00			−0.360750			−0.180375	+	0.983598i	$0.557731\pi$
$464$	−1776.00	+	3076.12i	−0.177691	+	0.307770i
$465$	3003.00	+	5201.35i	0.299486	+	0.518724i
$466$	−408.000	−	706.677i	−0.0405584	−	0.0702493i
$467$	−3399.00			−0.336803			−0.168401	−	0.985718i	$-0.553860\pi$
$467$	−3399.00			−0.336803			−0.168401	+	0.985718i	$0.553860\pi$
$468$	−1170.00	−	1215.90i	−0.115563	−	0.120096i
$469$	−1085.00			−0.106824
$470$	5764.00	+	9983.54i	0.565688	+	0.979801i
$471$	1485.00	+	2572.10i	0.145276	+	0.251626i
$472$	−2060.00	+	3568.02i	−0.200888	+	0.347948i
$473$	1360.00			0.132205
$474$	−348.000	+	602.754i	−0.0337219	+	0.0584080i
$475$	3949.00	−	6839.87i	0.381458	−	0.660705i
$476$	−2772.00			−0.266921
$477$	−1669.50	+	2891.66i	−0.160254	+	0.277568i
$478$	−4329.00	−	7498.05i	−0.414234	−	0.717474i
$479$	4900.00	+	8487.05i	0.467404	+	0.809568i	0.999306	−	0.0372377i	$-0.0118559\pi$
$479$	4900.00	+	8487.05i	0.467404	+	0.809568i	−0.531902	+	0.846806i	$0.678523\pi$
$480$	−2112.00			−0.200832
$481$	8645.00	+	8984.15i	0.819497	+	0.851646i
$482$	10908.0			1.03080
$483$	1606.50	+	2782.54i	0.151342	+	0.262132i
$484$	2150.00	+	3723.91i	0.201916	+	0.349729i
$485$	−9812.00	+	16994.9i	−0.918639	+	1.59113i
$486$	−486.000			−0.0453609
$487$	62.0000	−	107.387i	0.00576897	−	0.00999215i	−0.863127	−	0.504988i	$-0.831497\pi$
$487$	62.0000	−	107.387i	0.00576897	−	0.00999215i	0.868895	+	0.494996i	$0.164830\pi$
$488$	−1932.00	+	3346.32i	−0.179216	+	0.310412i
$489$	8439.00			0.780419
$490$	−1078.00	+	1867.15i	−0.0993859	+	0.172141i
$491$	−8956.00	−	15512.2i	−0.823174	−	1.42578i	−0.903307	−	0.428996i	$-0.858868\pi$
$491$	−8956.00	−	15512.2i	−0.823174	−	1.42578i	0.0801322	−	0.996784i	$-0.474466\pi$
$492$	−2268.00	−	3928.29i	−0.207824	−	0.359961i
$493$	−21978.0			−2.00779
$494$	−2002.00	+	495.367i	−0.182337	+	0.0451166i
$495$	3168.00			0.287659
$496$	−728.000	−	1260.93i	−0.0659036	−	0.114148i
$497$	2971.50	+	5146.79i	0.268189	+	0.464517i
$498$	969.000	−	1678.36i	0.0871926	−	0.151022i
$499$	−4927.00			−0.442010			−0.221005	−	0.975273i	$-0.570934\pi$
$499$	−4927.00			−0.442010			−0.221005	+	0.975273i	$0.570934\pi$
$500$	−10296.0	+	17833.2i	−0.920902	+	1.59505i
$501$	−3600.00	+	6235.38i	−0.321030	+	0.556041i
$502$	−15754.0			−1.40067
$503$	324.000	−	561.184i	0.0287206	−	0.0497455i	−0.851308	−	0.524666i	$-0.824190\pi$
$503$	324.000	−	561.184i	0.0287206	−	0.0497455i	0.880028	+	0.474921i	$0.157523\pi$
$504$	−252.000	−	436.477i	−0.0222718	−	0.0385758i
$505$	5060.00	+	8764.18i	0.445875	+	0.772279i
$506$	4896.00			0.430146
$507$	5577.00	+	3512.60i	0.488527	+	0.307692i
$508$	4112.00			0.359135
$509$	−8056.00	−	13953.4i	−0.701524	−	1.21508i	−0.967931	−	0.251215i	$-0.919170\pi$
$509$	−8056.00	−	13953.4i	−0.701524	−	1.21508i	0.266407	−	0.963861i	$-0.414164\pi$
$510$	−6534.00	−	11317.2i	−0.567314	−	0.982617i
$511$	−994.000	+	1721.66i	−0.0860508	+	0.149044i
$512$	512.000			0.0441942
$513$	−297.000	+	514.419i	−0.0255612	+	0.0442732i
$514$	−2121.00	+	3673.68i	−0.182010	+	0.315251i
$515$	27126.0			2.32100
$516$	510.000	−	883.346i	0.0435107	−	0.0753627i
$517$	2096.00	+	3630.38i	0.178302	+	0.308828i
$518$	1862.00	+	3225.08i	0.157937	+	0.273556i
$519$	−6804.00			−0.575458
$520$	8008.00	−	1981.47i	0.675335	−	0.167102i
$521$	14978.0			1.25950			0.629749	−	0.776799i	$-0.283158\pi$
$521$	14978.0			1.25950			0.629749	+	0.776799i	$0.283158\pi$
$522$	−1998.00	−	3460.64i	−0.167529	−	0.290169i
$523$	−506.000	−	876.418i	−0.0423056	−	0.0732755i	0.844097	−	0.536190i	$-0.180137\pi$
$523$	−506.000	−	876.418i	−0.0423056	−	0.0732755i	−0.886403	+	0.462915i	$0.846804\pi$
$524$	890.000	−	1541.53i	0.0741981	−	0.128515i
$525$	−7539.00			−0.626722
$526$	2292.00	−	3969.86i	0.189992	−	0.329076i
$527$	4504.50	−	7802.02i	0.372332	−	0.644898i
$528$	−768.000			−0.0633010
$529$	−5621.00	+	9735.86i	−0.461987	+	0.800186i
$530$	−8162.00	−	14137.0i	−0.668933	−	1.15863i
$531$	−2317.50	−	4014.03i	−0.189399	−	0.328049i
$532$	−616.000			−0.0502011
$533$	12285.0	+	12766.9i	0.998354	+	1.03752i
$534$	−3222.00			−0.261104
$535$	−2002.00	−	3467.57i	−0.161783	−	0.280217i
$536$	620.000	+	1073.87i	0.0499625	+	0.0865377i
$537$	−909.000	+	1574.43i	−0.0730470	+	0.126521i
$538$	8484.00			0.679872
$539$	−392.000	+	678.964i	−0.0313259	+	0.0542580i
$540$	1188.00	−	2057.68i	0.0946729	−	0.163978i
$541$	4454.00			0.353960			0.176980	−	0.984214i	$-0.443367\pi$
$541$	4454.00			0.353960			0.176980	+	0.984214i	$0.443367\pi$
$542$	5011.00	−	8679.31i	0.397123	−	0.687838i
$543$	2307.00	+	3995.84i	0.182326	+	0.315797i
$544$	1584.00	+	2743.57i	0.124841	+	0.216231i
$545$	−20328.0			−1.59772
$546$	1365.00	+	1418.55i	0.106990	+	0.111187i
$547$	−13452.0			−1.05149			−0.525746	−	0.850642i	$-0.676214\pi$
$547$	−13452.0			−1.05149			−0.525746	+	0.850642i	$0.676214\pi$
$548$	2216.00	+	3838.22i	0.172742	+	0.299199i
$549$	−2173.50	−	3764.61i	−0.168967	−	0.292659i
$550$	−5744.00	+	9948.90i	−0.445318	+	0.771314i
$551$	−4884.00			−0.377614
$552$	1836.00	−	3180.05i	0.141568	−	0.245202i
$553$	406.000	−	703.213i	0.0312204	−	0.0540753i
$554$	14152.0			1.08531
$555$	−8778.00	+	15203.9i	−0.671361	+	1.16283i
$556$	−5928.00	−	10267.6i	−0.452164	−	0.783171i
$557$	10065.5	+	17434.0i	0.765689	+	1.32621i	0.939881	+	0.341501i	$0.110935\pi$
$557$	10065.5	+	17434.0i	0.765689	+	1.32621i	−0.174192	+	0.984712i	$0.555731\pi$
$558$	1638.00			0.124269
$559$	−1105.00	+	3827.83i	−0.0836074	+	0.289624i
$560$	2464.00			0.185934
$561$	−2376.00	−	4115.35i	−0.178814	−	0.309715i
$562$	1126.00	+	1950.29i	0.0845150	+	0.146384i
$563$	−8820.00	+	15276.7i	−0.660246	+	1.14358i	0.320304	+	0.947315i	$0.396215\pi$
$563$	−8820.00	+	15276.7i	−0.660246	+	1.14358i	−0.980551	+	0.196266i	$0.937119\pi$
$564$	3144.00			0.234727
$565$	2596.00	−	4496.40i	0.193300	−	0.334806i
$566$	−8458.00	+	14649.7i	−0.628121	+	1.08794i
$567$	567.000			0.0419961
$568$	3396.00	−	5882.04i	0.250868	−	0.434516i
$569$	−5207.00	−	9018.79i	−0.383636	−	0.664477i	0.607943	−	0.793981i	$-0.291995\pi$
$569$	−5207.00	−	9018.79i	−0.383636	−	0.664477i	−0.991579	+	0.129504i	$0.958662\pi$
$570$	−1452.00	−	2514.94i	−0.106698	−	0.184806i
$571$	−23927.0			−1.75361			−0.876807	−	0.480842i	$-0.840331\pi$
$571$	−23927.0			−1.75361			−0.876807	+	0.480842i	$0.840331\pi$
$572$	2912.00	−	720.533i	0.212862	−	0.0526696i
$573$	81.0000			0.00590545
$574$	2646.00	+	4583.01i	0.192408	+	0.333260i
$575$	−27463.5	−	47568.2i	−1.99184	−	3.44997i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	13978.0			1.00851			0.504256	−	0.863554i	$-0.331767\pi$
$577$	13978.0			1.00851			0.504256	+	0.863554i	$0.331767\pi$
$578$	−4888.00	+	8466.26i	−0.351754	+	0.609256i
$579$	−4401.00	+	7622.76i	−0.315888	+	0.547135i
$580$	19536.0			1.39860
$581$	−1130.50	+	1958.08i	−0.0807247	+	0.139819i
$582$	2676.00	+	4634.97i	0.190591	+	0.330113i
$583$	−2968.00	−	5140.73i	−0.210844	−	0.365192i
$584$	2272.00			0.160986
$585$	−2574.00	+	8916.60i	−0.181918	+	0.630181i
$586$	−2944.00			−0.207535
$587$	5507.50	+	9539.27i	0.387255	+	0.670746i	0.992079	−	0.125613i	$-0.0400899\pi$
$587$	5507.50	+	9539.27i	0.387255	+	0.670746i	−0.604824	+	0.796359i	$0.706757\pi$
$588$	294.000	+	509.223i	0.0206197	+	0.0357143i
$589$	1001.00	−	1733.78i	0.0700263	−	0.121289i
$590$	22660.0			1.58118
$591$	7834.50	−	13569.8i	0.545293	−	0.944475i
$592$	2128.00	−	3685.80i	0.147737	−	0.255888i
$593$	−10497.0			−0.726914			−0.363457	−	0.931611i	$-0.618404\pi$
$593$	−10497.0			−0.726914			−0.363457	+	0.931611i	$0.618404\pi$
$594$	432.000	−	748.246i	0.0298404	−	0.0516850i
$595$	7623.00	+	13203.4i	0.525231	+	0.909727i
$596$	−4298.00	−	7444.35i	−0.295391	−	0.511632i
$597$	−13965.0			−0.957369
$598$	−3978.00	+	13780.2i	−0.272028	+	0.942331i
$599$	−19049.0			−1.29937			−0.649684	−	0.760205i	$-0.725099\pi$
$599$	−19049.0			−1.29937			−0.649684	+	0.760205i	$0.725099\pi$
$600$	4308.00	+	7461.67i	0.293122	+	0.507703i
$601$	−8839.00	−	15309.6i	−0.599917	−	1.03909i	−0.992833	−	0.119513i	$-0.961867\pi$
$601$	−8839.00	−	15309.6i	−0.599917	−	1.03909i	0.392915	−	0.919575i	$-0.371467\pi$
$602$	−595.000	+	1030.57i	−0.0402830	+	0.0697723i
$603$	−1395.00			−0.0942103
$604$	4600.00	−	7967.43i	0.309886	−	0.536739i
$605$	11825.0	−	20481.5i	0.794636	−	1.37635i
$606$	2760.00			0.185012
$607$	−7025.50	+	12168.5i	−0.469780	+	0.813682i	−0.999403	−	0.0345507i	$-0.989000\pi$
$607$	−7025.50	+	12168.5i	−0.469780	+	0.813682i	0.529623	+	0.848233i	$0.322333\pi$
$608$	352.000	+	609.682i	0.0234794	+	0.0406675i
$609$	2331.00	+	4037.41i	0.155102	+	0.268644i
$610$	21252.0			1.41060
$611$	−11921.0	+	2949.68i	−0.789316	+	0.195305i
$612$	−3564.00			−0.235402
$613$	5511.00	+	9545.33i	0.363111	+	0.628927i	0.988471	−	0.151409i	$-0.0483812\pi$
$613$	5511.00	+	9545.33i	0.363111	+	0.628927i	−0.625360	+	0.780336i	$0.715048\pi$
$614$	−1410.00	−	2442.19i	−0.0926758	−	0.160519i
$615$	−12474.0	+	21605.6i	−0.817887	+	1.41662i
$616$	896.000			0.0586053
$617$	−12300.0	+	21304.2i	−0.802560	+	1.39007i	0.115366	+	0.993323i	$0.463196\pi$
$617$	−12300.0	+	21304.2i	−0.802560	+	1.39007i	−0.917926	+	0.396751i	$0.870138\pi$
$618$	3699.00	−	6406.86i	0.240770	−	0.417025i
$619$	1402.00			0.0910358			0.0455179	−	0.998964i	$-0.485506\pi$
$619$	1402.00			0.0910358			0.0455179	+	0.998964i	$0.485506\pi$
$620$	−4004.00	+	6935.13i	−0.259362	+	0.449228i
$621$	2065.50	+	3577.55i	0.133471	+	0.231179i
$622$	10070.0	+	17441.8i	0.649148	+	1.12436i
$623$	3759.00			0.241735
$624$	624.000	−	2161.60i	0.0400320	−	0.138675i
$625$	68381.0			4.37638
$626$	7520.00	+	13025.0i	0.480127	+	0.831605i
$627$	−528.000	−	914.523i	−0.0336304	−	0.0582496i
$628$	−1980.00	+	3429.46i	−0.125813	+	0.217915i
$629$	26334.0			1.66932
$630$	−1386.00	+	2400.62i	−0.0876501	+	0.151814i
$631$	14020.0	−	24283.4i	0.884512	−	1.53202i	0.0382411	−	0.999269i	$-0.487825\pi$
$631$	14020.0	−	24283.4i	0.884512	−	1.53202i	0.846271	−	0.532752i	$-0.178842\pi$
$632$	−928.000			−0.0584080
$633$	4986.00	−	8636.01i	0.313074	−	0.542260i
$634$	10521.0	+	18222.9i	0.659057	+	1.14152i
$635$	−11308.0	−	19586.0i	−0.706684	−	1.22401i
$636$	−4452.00			−0.277568
$637$	−1592.50	−	1654.97i	−0.0990536	−	0.102940i
$638$	7104.00			0.440831
$639$	3820.50	+	6617.30i	0.236521	+	0.409666i
$640$	−1408.00	−	2438.73i	−0.0869626	−	0.150624i
$641$	13254.0	−	22956.6i	0.816695	−	1.41456i	−0.0914093	−	0.995813i	$-0.529137\pi$
$641$	13254.0	−	22956.6i	0.816695	−	1.41456i	0.908104	−	0.418744i	$-0.137530\pi$
$642$	−1092.00			−0.0671305
$643$	−1219.00	+	2111.37i	−0.0747631	+	0.129493i	−0.900983	−	0.433854i	$-0.857153\pi$
$643$	−1219.00	+	2111.37i	−0.0747631	+	0.129493i	0.826220	+	0.563347i	$0.190487\pi$
$644$	−2142.00	+	3710.05i	−0.131066	+	0.227013i
$645$	−5610.00			−0.342471
$646$	−2178.00	+	3772.41i	−0.132651	+	0.229758i
$647$	−2111.00	−	3656.36i	−0.128272	−	0.222174i	0.794735	−	0.606956i	$-0.207610\pi$
$647$	−2111.00	−	3656.36i	−0.128272	−	0.222174i	−0.923007	+	0.384783i	$0.874276\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	8240.00			0.498379
$650$	−23335.0	−	24250.4i	−1.40811	−	1.46335i
$651$	−1911.00			−0.115051
$652$	5626.00	+	9744.52i	0.337931	+	0.585314i
$653$	−13409.5	−	23225.9i	−0.803605	−	1.39189i	−0.917229	−	0.398361i	$-0.869579\pi$
$653$	−13409.5	−	23225.9i	−0.803605	−	1.39189i	0.113623	−	0.993524i	$-0.463754\pi$
$654$	−2772.00	+	4801.24i	−0.165740	+	0.287070i
$655$	−9790.00			−0.584011
$656$	3024.00	−	5237.72i	0.179981	−	0.311736i
$657$	−1278.00	+	2213.56i	−0.0758897	+	0.131445i
$658$	−3668.00			−0.217315
$659$	8547.00	−	14803.8i	0.505226	−	0.875077i	−0.494756	−	0.869032i	$-0.664743\pi$
$659$	8547.00	−	14803.8i	0.505226	−	0.875077i	0.999982	−	0.00604487i	$-0.00192415\pi$
$660$	2112.00	+	3658.09i	0.124560	+	0.215744i
$661$	−12087.5	−	20936.2i	−0.711270	−	1.23196i	−0.964381	−	0.264518i	$-0.914787\pi$
$661$	−12087.5	−	20936.2i	−0.711270	−	1.23196i	0.253111	−	0.967437i	$-0.418546\pi$
$662$	7592.00			0.445727
$663$	13513.5	−	3343.72i	0.791585	−	0.195866i
$664$	2584.00			0.151022
$665$	1694.00	+	2934.09i	0.0987827	+	0.171097i
$666$	2394.00	+	4146.53i	0.139288	+	0.241253i
$667$	−16983.0	+	29415.4i	−0.985884	+	1.70760i
$668$	−9600.00			−0.556041
$669$	4546.50	−	7874.77i	0.262747	−	0.455091i
$670$	3410.00	−	5906.29i	0.196627	−	0.340567i
$671$	7728.00			0.444614
$672$	336.000	−	581.969i	0.0192879	−	0.0334077i
$673$	340.500	+	589.763i	0.0195027	+	0.0337797i	0.875612	−	0.483015i	$-0.160458\pi$
$673$	340.500	+	589.763i	0.0195027	+	0.0337797i	−0.856109	+	0.516795i	$0.827125\pi$
$674$	11006.0	+	19063.0i	0.628984	+	1.08943i
$675$	−9693.00			−0.552717
$676$	−338.000	+	8781.50i	−0.0192308	+	0.499630i
$677$	22244.0			1.26279			0.631393	−	0.775463i	$-0.282483\pi$
$677$	22244.0			1.26279			0.631393	+	0.775463i	$0.282483\pi$
$678$	−708.000	−	1226.29i	−0.0401041	−	0.0694623i
$679$	−3122.00	−	5407.46i	−0.176453	−	0.305625i
$680$	8712.00	−	15089.6i	0.491309	−	0.850972i
$681$	−13572.0			−0.763701
$682$	−1456.00	+	2521.87i	−0.0817494	+	0.141594i
$683$	−11877.0	+	20571.6i	−0.665389	+	1.15249i	0.313791	+	0.949492i	$0.398401\pi$
$683$	−11877.0	+	20571.6i	−0.665389	+	1.15249i	−0.979180	+	0.202996i	$0.934932\pi$
$684$	−792.000			−0.0442732
$685$	12188.0	−	21110.2i	0.679824	−	1.17749i
$686$	−343.000	−	594.093i	−0.0190901	−	0.0330650i
$687$	−3829.50	−	6632.89i	−0.212670	−	0.368356i
$688$	1360.00			0.0753627
$689$	16880.5	−	4176.84i	0.933376	−	0.230951i
$690$	−20196.0			−1.11427
$691$	15122.0	+	26192.1i	0.832515	+	1.44196i	0.896038	+	0.443978i	$0.146433\pi$
$691$	15122.0	+	26192.1i	0.832515	+	1.44196i	−0.0635224	+	0.997980i	$0.520233\pi$
$692$	−4536.00	−	7856.58i	−0.249180	−	0.431593i
$693$	−504.000	+	872.954i	−0.0276268	+	0.0478510i
$694$	−17620.0			−0.963755
$695$	−32604.0	+	56471.8i	−1.77948	+	3.08215i
$696$	2664.00	−	4614.18i	0.145084	−	0.251293i
$697$	37422.0			2.03366
$698$	−6965.00	+	12063.7i	−0.377692	+	0.654182i
$699$	612.000	+	1060.02i	0.0331158	+	0.0573583i
$700$	−5026.00	−	8705.29i	−0.271378	−	0.470041i
$701$	−11135.0			−0.599947			−0.299974	−	0.953947i	$-0.596978\pi$
$701$	−11135.0			−0.599947			−0.299974	+	0.953947i	$0.596978\pi$
$702$	1755.00	+	1823.85i	0.0943564	+	0.0980581i
$703$	5852.00			0.313958
$704$	−512.000	−	886.810i	−0.0274101	−	0.0474757i
$705$	−8646.00	−	14975.3i	−0.461883	−	0.800004i
$706$	−1815.00	+	3143.67i	−0.0967541	+	0.167583i
$707$	−3220.00			−0.171288
$708$	3090.00	−	5352.04i	0.164024	−	0.284099i
$709$	6420.00	−	11119.8i	0.340068	−	0.589015i	−0.644377	−	0.764708i	$-0.722883\pi$
$709$	6420.00	−	11119.8i	0.340068	−	0.589015i	0.984445	+	0.175693i	$0.0562166\pi$
$710$	−37356.0			−1.97457
$711$	522.000	−	904.131i	0.0275338	−	0.0476899i
$712$	−2148.00	−	3720.45i	−0.113061	−	0.195828i
$713$	−6961.50	−	12057.7i	−0.365652	−	0.633329i
$714$	4158.00			0.217940
$715$	−11440.0	−	11888.8i	−0.598366	−	0.621840i
$716$	−2424.00			−0.126521
$717$	6493.50	+	11247.1i	0.338221	+	0.585815i
$718$	−5464.00	−	9463.93i	−0.284004	−	0.491909i
$719$	−13810.0	+	23919.6i	−0.716309	+	1.24068i	0.246144	+	0.969233i	$0.420837\pi$
$719$	−13810.0	+	23919.6i	−0.716309	+	1.24068i	−0.962453	+	0.271450i	$0.912497\pi$
$720$	3168.00			0.163978
$721$	−4315.50	+	7474.67i	−0.222909	+	0.386090i
$722$	6375.00	−	11041.8i	0.328605	−	0.569161i
$723$	−16362.0			−0.841645
$724$	−3076.00	+	5327.79i	−0.157899	+	0.273489i
$725$	−39849.0	−	69020.5i	−2.04132	−	3.53566i
$726$	−3225.00	−	5585.86i	−0.164864	−	0.285552i
$727$	−13313.0			−0.679163			−0.339582	−	0.940577i	$-0.610286\pi$
$727$	−13313.0			−0.679163			−0.339582	+	0.940577i	$0.610286\pi$
$728$	−728.000	+	2521.87i	−0.0370625	+	0.128388i
$729$	729.000			0.0370370
$730$	−6248.00	−	10821.9i	−0.316779	−	0.548678i
$731$	4207.50	+	7287.60i	0.212886	+	0.368730i
$732$	2898.00	−	5019.48i	0.146329	−	0.253450i
$733$	14633.0			0.737356			0.368678	−	0.929557i	$-0.379810\pi$
$733$	14633.0			0.737356			0.368678	+	0.929557i	$0.379810\pi$
$734$	7999.00	−	13854.7i	0.402246	−	0.696710i
$735$	1617.00	−	2800.73i	0.0811482	−	0.140553i
$736$	4896.00			0.245202
$737$	1240.00	−	2147.74i	0.0619756	−	0.107345i
$738$	3402.00	+	5892.44i	0.169687	+	0.293907i
$739$	−5535.50	−	9587.77i	−0.275544	−	0.477255i	0.694729	−	0.719272i	$-0.255524\pi$
$739$	−5535.50	−	9587.77i	−0.275544	−	0.477255i	−0.970272	+	0.242017i	$0.922191\pi$
$740$	−23408.0			−1.16283
$741$	3003.00	−	743.050i	0.148877	−	0.0368375i
$742$	5194.00			0.256978
$743$	−2636.50	−	4566.55i	−0.130180	−	0.225479i	0.793566	−	0.608484i	$-0.208222\pi$
$743$	−2636.50	−	4566.55i	−0.130180	−	0.225479i	−0.923746	+	0.383006i	$0.874889\pi$
$744$	1092.00	+	1891.40i	0.0538100	+	0.0932017i
$745$	−23639.0	+	40943.9i	−1.16250	+	2.01352i
$746$	−1424.00			−0.0698879
$747$	−1453.50	+	2517.54i	−0.0711925	+	0.123309i
$748$	3168.00	−	5487.14i	0.154858	−	0.268221i
$749$	1274.00			0.0621508
$750$	15444.0	−	26749.8i	0.751914	−	1.30235i
$751$	9973.00	+	17273.7i	0.484580	+	0.839318i	0.999843	−	0.0177143i	$-0.00563894\pi$
$751$	9973.00	+	17273.7i	0.484580	+	0.839318i	−0.515263	+	0.857032i	$0.672306\pi$
$752$	2096.00	+	3630.38i	0.101640	+	0.176046i
$753$	23631.0			1.14364
$754$	−5772.00	+	19994.8i	−0.278785	+	0.965739i
$755$	−50600.0			−2.43910
$756$	378.000	+	654.715i	0.0181848	+	0.0314970i
$757$	−17519.0	−	30343.8i	−0.841135	−	1.45689i	−0.888936	−	0.458031i	$-0.848555\pi$
$757$	−17519.0	−	30343.8i	−0.841135	−	1.45689i	0.0478016	−	0.998857i	$-0.484778\pi$
$758$	4340.00	−	7517.10i	0.207963	−	0.360202i
$759$	−7344.00			−0.351213
$760$	1936.00	−	3353.25i	0.0924028	−	0.160046i
$761$	13765.0	−	23841.7i	0.655691	−	1.13569i	−0.326029	−	0.945360i	$-0.605711\pi$
$761$	13765.0	−	23841.7i	0.655691	−	1.13569i	0.981720	−	0.190330i	$-0.0609559\pi$
$762$	−6168.00			−0.293232
$763$	3234.00	−	5601.45i	0.153445	−	0.265775i
$764$	54.0000	+	93.5307i	0.00255714	+	0.00442909i
$765$	9801.00	+	16975.8i	0.463210	+	0.802304i
$766$	5656.00			0.266788
$767$	−6695.00	+	23192.2i	−0.315179	+	1.09181i
$768$	−768.000			−0.0360844
$769$	−3608.00	−	6249.24i	−0.169191	−	0.293047i	0.768945	−	0.639315i	$-0.220782\pi$
$769$	−3608.00	−	6249.24i	−0.169191	−	0.293047i	−0.938136	+	0.346268i	$0.887449\pi$
$770$	−2464.00	−	4267.77i	−0.115320	−	0.199740i
$771$	3181.50	−	5510.52i	0.148611	−	0.257401i
$772$	−11736.0			−0.547135
$773$	5865.00	−	10158.5i	0.272897	−	0.472671i	−0.696705	−	0.717357i	$-0.745352\pi$
$773$	5865.00	−	10158.5i	0.272897	−	0.472671i	0.969602	+	0.244686i	$0.0786848\pi$
$774$	−765.000	+	1325.02i	−0.0355263	+	0.0615334i
$775$	32669.0			1.51420
$776$	−3568.00	+	6179.96i	−0.165056	+	0.285886i
$777$	−2793.00	−	4837.62i	−0.128955	−	0.223357i
$778$	−6671.00	−	11554.5i	−0.307413	−	0.532454i
$779$	8316.00			0.382480
$780$	−12012.0	+	2972.20i	−0.551408	+	0.136438i
$781$	−13584.0			−0.622374
$782$	15147.0	+	26235.4i	0.692654	+	1.19971i
$783$	2997.00	+	5190.96i	0.136787	+	0.236922i
$784$	−392.000	+	678.964i	−0.0178571	+	0.0309295i
$785$	21780.0			0.990269
$786$	−1335.00	+	2312.29i	−0.0605825	+	0.104932i
$787$	−4938.00	+	8552.87i	−0.223660	+	0.387391i	−0.955917	−	0.293638i	$-0.905134\pi$
$787$	−4938.00	+	8552.87i	−0.223660	+	0.387391i	0.732256	+	0.681029i	$0.238467\pi$
$788$	20892.0			0.944475
$789$	−3438.00	+	5954.79i	−0.155128	+	0.268690i
$790$	2552.00	+	4420.19i	0.114932	+	0.199068i
$791$	826.000	+	1430.67i	0.0371292	+	0.0643096i
$792$	1152.00			0.0516850
$793$	−6279.00	+	21751.1i	−0.281178	+	0.974028i
$794$	−25206.0			−1.12661
$795$	12243.0	+	21205.5i	0.546182	+	0.946014i
$796$	−9310.00	−	16125.4i	−0.414553	−	0.718027i
$797$	−18570.0	+	32164.2i	−0.825324	+	1.42950i	0.0763476	+	0.997081i	$0.475674\pi$
$797$	−18570.0	+	32164.2i	−0.825324	+	1.42950i	−0.901672	+	0.432422i	$0.857659\pi$
$798$	924.000			0.0409890
$799$	−12969.0	+	22463.0i	−0.574231	+	0.994597i
$800$	−5744.00	+	9948.90i	−0.253851	+	0.439683i
$801$	4833.00			0.213191
$802$	2568.00	−	4447.91i	0.113066	−	0.195837i
$803$	−2272.00	−	3935.22i	−0.0998470	−	0.172940i
$804$	−930.000	−	1610.81i	−0.0407942	−	0.0706577i
$805$	23562.0			1.03162
$806$	−5915.00	−	6147.05i	−0.258495	−	0.268636i
$807$	−12726.0			−0.555113
$808$	1840.00	+	3186.97i	0.0801126	+	0.138759i
$809$	14262.0	+	24702.5i	0.619809	+	1.07354i	0.989520	+	0.144394i	$0.0461231\pi$
$809$	14262.0	+	24702.5i	0.619809	+	1.07354i	−0.369712	+	0.929147i	$0.620544\pi$
$810$	−1782.00	+	3086.51i	−0.0773001	+	0.133888i
$811$	−43144.0			−1.86805			−0.934026	−	0.357204i	$-0.883730\pi$
$811$	−43144.0			−1.86805			−0.934026	+	0.357204i	$0.883730\pi$
$812$	−3108.00	+	5383.21i	−0.134322	+	0.232652i
$813$	−7516.50	+	13019.0i	−0.324250	+	0.561617i
$814$	−8512.00			−0.366518
$815$	30943.0	−	53594.8i	1.32992	−	2.30349i
$816$	−2376.00	−	4115.35i	−0.101932	−	0.176552i
$817$	935.000	+	1619.47i	0.0400386	+	0.0693488i
$818$	−16948.0			−0.724417
$819$	−2047.50	−	2127.82i	−0.0873571	−	0.0907841i
$820$	−33264.0			−1.41662
$821$	−11141.5	−	19297.6i	−0.473619	−	0.820332i	0.525925	−	0.850531i	$-0.323719\pi$
$821$	−11141.5	−	19297.6i	−0.473619	−	0.820332i	−0.999544	+	0.0301991i	$0.990386\pi$
$822$	−3324.00	−	5757.34i	−0.141044	−	0.244295i
$823$	−13660.0	+	23659.8i	−0.578563	+	1.00210i	0.417081	+	0.908869i	$0.363053\pi$
$823$	−13660.0	+	23659.8i	−0.578563	+	1.00210i	−0.995644	+	0.0932319i	$0.970280\pi$
$824$	9864.00			0.417025
$825$	8616.00	−	14923.3i	0.363601	−	0.629775i
$826$	−3605.00	+	6244.04i	−0.151857	+	0.263024i
$827$	9496.00			0.399284			0.199642	−	0.979869i	$-0.436022\pi$
$827$	9496.00			0.399284			0.199642	+	0.979869i	$0.436022\pi$
$828$	−2754.00	+	4770.07i	−0.115590	+	0.200207i
$829$	3961.00	+	6860.65i	0.165948	+	0.287431i	0.936992	−	0.349352i	$-0.113598\pi$
$829$	3961.00	+	6860.65i	0.165948	+	0.287431i	−0.771043	+	0.636783i	$0.780265\pi$
$830$	−7106.00	−	12308.0i	−0.297172	−	0.514717i
$831$	−21228.0			−0.886151
$832$	2912.00	−	720.533i	0.121341	−	0.0300240i
$833$	−4851.00			−0.201773
$834$	8892.00	+	15401.4i	0.369190	+	0.639456i
$835$	26400.0	+	45726.1i	1.09414	+	1.89511i
$836$	704.000	−	1219.36i	0.0291248	−	0.0504457i
$837$	−2457.00			−0.101465
$838$	11779.0	−	20401.8i	0.485559	−	0.841014i
$839$	−22721.0	+	39353.9i	−0.934942	+	1.61937i	−0.160204	+	0.987084i	$0.551215\pi$
$839$	−22721.0	+	39353.9i	−0.934942	+	1.61937i	−0.774738	+	0.632282i	$0.782118\pi$
$840$	−3696.00			−0.151814
$841$	−12447.5	+	21559.7i	−0.510374	+	0.883993i
$842$	−2694.00	−	4666.14i	−0.110263	−	0.190981i
$843$	−1689.00	−	2925.43i	−0.0690062	−	0.119522i
$844$	13296.0			0.542260
$845$	42757.0	−	22539.2i	1.74069	−	0.917599i
$846$	−4716.00			−0.191654
$847$	3762.50	+	6516.84i	0.152634	+	0.264370i
$848$	−2968.00	−	5140.73i	−0.120190	−	0.208176i
$849$	12687.0	−	21974.5i	0.512858	−	0.888297i
$850$	−71082.0			−2.86834
$851$	20349.0	−	35245.5i	0.819688	−	1.41974i
$852$	−5094.00	+	8823.07i	−0.204833	+	0.354781i
$853$	−2863.00			−0.114921			−0.0574603	−	0.998348i	$-0.518300\pi$
$853$	−2863.00			−0.114921			−0.0574603	+	0.998348i	$0.518300\pi$
$854$	−3381.00	+	5856.06i	−0.135475	+	0.234649i
$855$	2178.00	+	3772.41i	0.0871182	+	0.150893i
$856$	−728.000	−	1260.93i	−0.0290684	−	0.0503479i
$857$	12378.0			0.493377			0.246689	−	0.969095i	$-0.420657\pi$
$857$	12378.0			0.493377			0.246689	+	0.969095i	$0.420657\pi$
$858$	−4368.00	+	1080.80i	−0.173801	+	0.0430045i
$859$	−386.000			−0.0153320			−0.00766598	−	0.999971i	$-0.502440\pi$
$859$	−386.000			−0.0153320			−0.00766598	+	0.999971i	$0.502440\pi$
$860$	−3740.00	−	6477.87i	−0.148294	−	0.256853i
$861$	−3969.00	−	6874.51i	−0.157100	−	0.272105i
$862$	2431.00	−	4210.62i	0.0960559	−	0.166374i
$863$	18616.0			0.734294			0.367147	−	0.930163i	$-0.380335\pi$
$863$	18616.0			0.734294			0.367147	+	0.930163i	$0.380335\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−24948.0	+	43211.2i	−0.980644	+	1.69853i
$866$	5888.00			0.231042
$867$	7332.00	−	12699.4i	0.287206	−	0.497456i
$868$	−1274.00	−	2206.63i	−0.0498184	−	0.0862880i
$869$	928.000	+	1607.34i	0.0362258	+	0.0627450i
$870$	−29304.0			−1.14195
$871$	5037.50	+	5235.12i	0.195969	+	0.203657i
$872$	−7392.00			−0.287070
$873$	−4014.00	−	6952.45i	−0.155617	−	0.269536i
$874$	3366.00	+	5830.08i	0.130271	+	0.225636i
$875$	−18018.0	+	31208.1i	−0.696137	+	1.20574i
$876$	−3408.00			−0.131445
$877$	−16719.0	+	28958.2i	−0.643741	+	1.11499i	0.340850	+	0.940118i	$0.389285\pi$
$877$	−16719.0	+	28958.2i	−0.643741	+	1.11499i	−0.984591	+	0.174874i	$0.944048\pi$
$878$	−4876.00	+	8445.48i	−0.187423	+	0.324625i
$879$	4416.00			0.169452
$880$	−2816.00	+	4877.46i	−0.107872	+	0.186840i
$881$	−15721.5	−	27230.4i	−0.601215	−	1.04134i	−0.992637	−	0.121124i	$-0.961350\pi$
$881$	−15721.5	−	27230.4i	−0.601215	−	1.04134i	0.391422	−	0.920211i	$-0.371983\pi$
$882$	−441.000	−	763.834i	−0.0168359	−	0.0291606i
$883$	50031.0			1.90677			0.953385	−	0.301758i	$-0.0975734\pi$
$883$	50031.0			1.90677			0.953385	+	0.301758i	$0.0975734\pi$
$884$	12870.0	+	13374.9i	0.489666	+	0.508876i
$885$	−33990.0			−1.29103
$886$	−5358.00	−	9280.33i	−0.203167	−	0.351895i
$887$	4737.00	+	8204.72i	0.179316	+	0.310584i	0.941646	−	0.336604i	$-0.109278\pi$
$887$	4737.00	+	8204.72i	0.179316	+	0.310584i	−0.762331	+	0.647188i	$0.775945\pi$
$888$	−3192.00	+	5528.71i	−0.120627	+	0.208932i
$889$	7196.00			0.271480
$890$	−11814.0	+	20462.4i	−0.444951	+	0.770677i
$891$	−648.000	+	1122.37i	−0.0243646	+	0.0422006i
$892$	12124.0			0.455091
$893$	−2882.00	+	4991.77i	−0.107998	+	0.187058i
$894$	6447.00	+	11166.5i	0.241186	+	0.417746i
$895$	6666.00	+	11545.9i	0.248961	+	0.431213i
$896$	896.000			0.0334077
$897$	5967.00	−	20670.3i	0.222110	−	0.769410i
$898$	−6916.00			−0.257004
$899$	−10101.0	−	17495.4i	−0.374735	−	0.649061i
$900$	−6462.00	−	11192.5i	−0.239333	−	0.414537i
$901$	18364.5	−	31808.2i	0.679035	−	1.17612i
$902$	−12096.0			−0.446511
$903$	892.500	−	1545.86i	0.0328910	−	0.0569688i
$904$	944.000	−	1635.06i	0.0347312	−	0.0601561i
$905$	33836.0			1.24281
$906$	−6900.00	+	11951.2i	−0.253021	+	0.438245i
$907$	15211.5	+	26347.1i	0.556879	+	0.964543i	0.997755	+	0.0669750i	$0.0213348\pi$
$907$	15211.5	+	26347.1i	0.556879	+	0.964543i	−0.440875	+	0.897568i	$0.645332\pi$
$908$	−9048.00	−	15671.6i	−0.330692	−	0.572776i
$909$	−4140.00			−0.151062
$910$	14014.0	−	3467.57i	0.510505	−	0.126317i
$911$	17176.0			0.624661			0.312331	−	0.949973i	$-0.398890\pi$
$911$	17176.0			0.624661			0.312331	+	0.949973i	$0.398890\pi$
$912$	−528.000	−	914.523i	−0.0191709	−	0.0332049i
$913$	−2584.00	−	4475.62i	−0.0936669	−	0.162236i
$914$	11657.0	−	20190.5i	0.421859	−	0.730682i
$915$	−31878.0			−1.15175
$916$	5106.00	−	8843.85i	0.184178	−	0.319006i
$917$	1557.50	−	2697.67i	0.0560885	−	0.0971482i
$918$	5346.00			0.192205
$919$	17057.0	−	29543.6i	0.612251	−	1.06045i	−0.378609	−	0.925557i	$-0.623598\pi$
$919$	17057.0	−	29543.6i	0.612251	−	1.06045i	0.990860	−	0.134893i	$-0.0430691\pi$
$920$	−13464.0	−	23320.3i	−0.482494	−	0.835705i
$921$	2115.00	+	3663.29i	0.0756695	+	0.131063i
$922$	6640.00			0.237177
$923$	11037.0	−	38233.3i	0.393594	−	1.36345i
$924$	−1344.00			−0.0478510
$925$	47747.0	+	82700.2i	1.69720	+	2.93964i
$926$	3594.00	+	6224.99i	0.127544	+	0.220913i
$927$	−5548.50	+	9610.28i	−0.196588	+	0.340500i
$928$	7104.00			0.251293
$929$	−8123.50	+	14070.3i	−0.286893	+	0.496913i	−0.973066	−	0.230525i	$-0.925956\pi$
$929$	−8123.50	+	14070.3i	−0.286893	+	0.496913i	0.686174	+	0.727438i	$0.259289\pi$
$930$	6006.00	−	10402.7i	0.211768	−	0.366793i
$931$	−1078.00			−0.0379485
$932$	−816.000	+	1413.35i	−0.0286792	+	0.0496737i
$933$	−15105.0	−	26162.6i	−0.530027	−	0.918034i
$934$	3399.00	+	5887.24i	0.119078	+	0.206249i
$935$	−34848.0			−1.21888
$936$	−936.000	+	3242.40i	−0.0326860	+	0.113228i
$937$	−42994.0			−1.49899			−0.749495	−	0.662011i	$-0.769703\pi$
$937$	−42994.0			−1.49899			−0.749495	+	0.662011i	$0.769703\pi$
$938$	1085.00	+	1879.28i	0.0377681	+	0.0654163i
$939$	−11280.0	−	19537.5i	−0.392022	−	0.679002i
$940$	11528.0	−	19967.1i	0.400002	−	0.692824i
$941$	36432.0			1.26211			0.631057	−	0.775736i	$-0.282621\pi$
$941$	36432.0			1.26211			0.631057	+	0.775736i	$0.282621\pi$
$942$	2970.00	−	5144.19i	0.102726	−	0.177927i
$943$	28917.0	−	50085.7i	0.998587	−	1.72960i
$944$	8240.00			0.284099
$945$	2079.00	−	3600.93i	0.0715660	−	0.123956i
$946$	−1360.00	−	2355.59i	−0.0467415	−	0.0809586i
$947$	−12156.0	−	21054.8i	−0.417125	−	0.722481i	0.578524	−	0.815665i	$-0.303629\pi$
$947$	−12156.0	−	21054.8i	−0.417125	−	0.722481i	−0.995649	+	0.0931842i	$0.970295\pi$
$948$	1392.00			0.0476899
$949$	12922.0	−	3197.37i	0.442008	−	0.109369i
$950$	−15796.0			−0.539463
$951$	−15781.5	−	27334.4i	−0.538118	−	0.932048i
$952$	2772.00	+	4801.24i	0.0943708	+	0.163455i
$953$	−1369.00	+	2371.18i	−0.0465333	+	0.0805981i	−0.888354	−	0.459159i	$-0.848151\pi$
$953$	−1369.00	+	2371.18i	−0.0465333	+	0.0805981i	0.841821	+	0.539757i	$0.181484\pi$
$954$	6678.00			0.226633
$955$	297.000	−	514.419i	0.0100636	−	0.0174306i
$956$	−8658.00	+	14996.1i	−0.292908	+	0.507331i
$957$	−10656.0			−0.359937
$958$	9800.00	−	16974.1i	0.330505	−	0.572451i
$959$	3878.00	+	6716.89i	0.130581	+	0.226173i
$960$	2112.00	+	3658.09i	0.0710047	+	0.122984i
$961$	−21510.0			−0.722030
$962$	6916.00	−	23957.7i	0.231789	−	0.802940i
$963$	1638.00			0.0548119
$964$	−10908.0	−	18893.2i	−0.364443	−	0.631234i
$965$	32274.0	+	55900.2i	1.07662	+	1.86476i
$966$	3213.00	−	5565.08i	0.107015	−	0.185356i
$967$	−4286.00			−0.142532			−0.0712660	−	0.997457i	$-0.522704\pi$
$967$	−4286.00			−0.142532			−0.0712660	+	0.997457i	$0.522704\pi$
$968$	4300.00	−	7447.82i	0.142776	−	0.247295i
$969$	3267.00	−	5658.61i	0.108309	−	0.187596i
$970$	39248.0			1.29915
$971$	−16337.5	+	28297.4i	−0.539954	+	0.935228i	0.458952	+	0.888461i	$0.348225\pi$
$971$	−16337.5	+	28297.4i	−0.539954	+	0.935228i	−0.998906	+	0.0467666i	$0.985108\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	−10374.0	−	17968.3i	−0.341804	−	0.592022i
$974$	−248.000			−0.00815855
$975$	35002.5	+	36375.7i	1.14972	+	1.19482i
$976$	7728.00			0.253450
$977$	6822.00	+	11816.1i	0.223393	+	0.386928i	0.955836	−	0.293900i	$-0.0949533\pi$
$977$	6822.00	+	11816.1i	0.223393	+	0.386928i	−0.732443	+	0.680828i	$0.761620\pi$
$978$	−8439.00	−	14616.8i	−0.275920	−	0.477907i
$979$	−4296.00	+	7440.89i	−0.140246	+	0.242913i
$980$	4312.00			0.140553
$981$	4158.00	−	7201.87i	0.135326	−	0.234391i
$982$	−17912.0	+	31024.5i	−0.582072	+	1.00818i
$983$	8498.00			0.275732			0.137866	−	0.990451i	$-0.455976\pi$
$983$	8498.00			0.275732			0.137866	+	0.990451i	$0.455976\pi$
$984$	−4536.00	+	7856.58i	−0.146954	+	0.254531i
$985$	−57453.0	−	99511.5i	−1.85848	−	3.21899i
$986$	21978.0	+	38067.0i	0.709860	+	1.22951i
$987$	5502.00			0.177437
$988$	2860.00	+	2972.20i	0.0920938	+	0.0957067i
$989$	13005.0			0.418134
$990$	−3168.00	−	5487.14i	−0.101703	−	0.176154i
$991$	16591.0	+	28736.5i	0.531817	+	0.921134i	0.999310	+	0.0371372i	$0.0118239\pi$
$991$	16591.0	+	28736.5i	0.531817	+	0.921134i	−0.467493	+	0.883997i	$0.654843\pi$
$992$	−1456.00	+	2521.87i	−0.0466009	+	0.0807150i
$993$	−11388.0			−0.363935
$994$	5943.00	−	10293.6i	0.189638	−	0.328463i
$995$	−51205.0	+	88689.7i	−1.63146	+	2.82578i
$996$	−3876.00			−0.123309
$997$	1152.50	−	1996.19i	0.0366099	−	0.0634102i	−0.847140	−	0.531370i	$-0.821677\pi$
$997$	1152.50	−	1996.19i	0.0366099	−	0.0634102i	0.883750	+	0.467960i	$0.155011\pi$
$998$	4927.00	+	8533.81i	0.156274	+	0.270675i
$999$	−3591.00	−	6219.79i	−0.113728	−	0.196983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.l.b.211.1	✓	2
13.9	even	3	inner	546.4.l.b.295.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.l.b.211.1	✓	2	1.1	even	1	trivial
546.4.l.b.295.1	yes	2	13.9	even	3	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +22.0000 q^{5} +(3.00000 - 5.19615i) q^{6} +(-3.50000 + 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-22.0000 - 38.1051i) q^{10} +(-8.00000 - 13.8564i) q^{11} -12.0000 q^{12} +(45.5000 - 11.2583i) q^{13} +14.0000 q^{14} +(33.0000 + 57.1577i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(49.5000 - 85.7365i) q^{17} +18.0000 q^{18} +(11.0000 - 19.0526i) q^{19} +(-44.0000 + 76.2102i) q^{20} -21.0000 q^{21} +(-16.0000 + 27.7128i) q^{22} +(-76.5000 - 132.502i) q^{23} +(12.0000 + 20.7846i) q^{24} +359.000 q^{25} +(-65.0000 - 67.5500i) q^{26} -27.0000 q^{27} +(-14.0000 - 24.2487i) q^{28} +(-111.000 - 192.258i) q^{29} +(66.0000 - 114.315i) q^{30} +91.0000 q^{31} +(-16.0000 + 27.7128i) q^{32} +(24.0000 - 41.5692i) q^{33} -198.000 q^{34} +(-77.0000 + 133.368i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(133.000 + 230.363i) q^{37} -44.0000 q^{38} +(97.5000 + 101.325i) q^{39} +176.000 q^{40} +(189.000 + 327.358i) q^{41} +(21.0000 + 36.3731i) q^{42} +(-42.5000 + 73.6122i) q^{43} +64.0000 q^{44} +(-99.0000 + 171.473i) q^{45} +(-153.000 + 265.004i) q^{46} -262.000 q^{47} +(24.0000 - 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-359.000 - 621.806i) q^{50} +297.000 q^{51} +(-52.0000 + 180.133i) q^{52} +371.000 q^{53} +(27.0000 + 46.7654i) q^{54} +(-176.000 - 304.841i) q^{55} +(-28.0000 + 48.4974i) q^{56} +66.0000 q^{57} +(-222.000 + 384.515i) q^{58} +(-257.500 + 446.003i) q^{59} -264.000 q^{60} +(-241.500 + 418.290i) q^{61} +(-91.0000 - 157.617i) q^{62} +(-31.5000 - 54.5596i) q^{63} +64.0000 q^{64} +(1001.00 - 247.683i) q^{65} -96.0000 q^{66} +(77.5000 + 134.234i) q^{67} +(198.000 + 342.946i) q^{68} +(229.500 - 397.506i) q^{69} +308.000 q^{70} +(424.500 - 735.256i) q^{71} +(-36.0000 + 62.3538i) q^{72} +284.000 q^{73} +(266.000 - 460.726i) q^{74} +(538.500 + 932.709i) q^{75} +(44.0000 + 76.2102i) q^{76} +112.000 q^{77} +(78.0000 - 270.200i) q^{78} -116.000 q^{79} +(-176.000 - 304.841i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(378.000 - 654.715i) q^{82} +323.000 q^{83} +(42.0000 - 72.7461i) q^{84} +(1089.00 - 1886.20i) q^{85} +170.000 q^{86} +(333.000 - 576.773i) q^{87} +(-64.0000 - 110.851i) q^{88} +(-268.500 - 465.056i) q^{89} +396.000 q^{90} +(-91.0000 + 315.233i) q^{91} +612.000 q^{92} +(136.500 + 236.425i) q^{93} +(262.000 + 453.797i) q^{94} +(242.000 - 419.156i) q^{95} -96.0000 q^{96} +(-446.000 + 772.495i) q^{97} +(-49.0000 + 84.8705i) q^{98} +144.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} + 44 q^{5} + 6 q^{6} - 7 q^{7} + 16 q^{8} - 9 q^{9} - 44 q^{10} - 16 q^{11} - 24 q^{12} + 91 q^{13} + 28 q^{14} + 66 q^{15} - 16 q^{16} + 99 q^{17} + 36 q^{18} + 22 q^{19}+ \cdots + 288 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 + 44 * q^5 + 6 * q^6 - 7 * q^7 + 16 * q^8 - 9 * q^9 - 44 * q^10 - 16 * q^11 - 24 * q^12 + 91 * q^13 + 28 * q^14 + 66 * q^15 - 16 * q^16 + 99 * q^17 + 36 * q^18 + 22 * q^19 - 88 * q^20 - 42 * q^21 - 32 * q^22 - 153 * q^23 + 24 * q^24 + 718 * q^25 - 130 * q^26 - 54 * q^27 - 28 * q^28 - 222 * q^29 + 132 * q^30 + 182 * q^31 - 32 * q^32 + 48 * q^33 - 396 * q^34 - 154 * q^35 - 36 * q^36 + 266 * q^37 - 88 * q^38 + 195 * q^39 + 352 * q^40 + 378 * q^41 + 42 * q^42 - 85 * q^43 + 128 * q^44 - 198 * q^45 - 306 * q^46 - 524 * q^47 + 48 * q^48 - 49 * q^49 - 718 * q^50 + 594 * q^51 - 104 * q^52 + 742 * q^53 + 54 * q^54 - 352 * q^55 - 56 * q^56 + 132 * q^57 - 444 * q^58 - 515 * q^59 - 528 * q^60 - 483 * q^61 - 182 * q^62 - 63 * q^63 + 128 * q^64 + 2002 * q^65 - 192 * q^66 + 155 * q^67 + 396 * q^68 + 459 * q^69 + 616 * q^70 + 849 * q^71 - 72 * q^72 + 568 * q^73 + 532 * q^74 + 1077 * q^75 + 88 * q^76 + 224 * q^77 + 156 * q^78 - 232 * q^79 - 352 * q^80 - 81 * q^81 + 756 * q^82 + 646 * q^83 + 84 * q^84 + 2178 * q^85 + 340 * q^86 + 666 * q^87 - 128 * q^88 - 537 * q^89 + 792 * q^90 - 182 * q^91 + 1224 * q^92 + 273 * q^93 + 524 * q^94 + 484 * q^95 - 192 * q^96 - 892 * q^97 - 98 * q^98 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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