LMFDB - Embedded newform 39.4.j.c.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(4,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("39.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$-5.36472i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.c.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.23249 + 12.5270i) q^{10} +(57.9240 + 33.4424i) q^{11} -62.3408 q^{12} +(46.8650 - 0.818689i) q^{13} -81.5570 q^{14} +(7.00522 + 4.04447i) q^{15} +(-100.789 + 174.571i) q^{16} +(2.08177 + 3.60573i) q^{17} +48.2825i q^{18} +(-22.5903 + 13.0425i) q^{19} +(48.5235 - 28.0150i) q^{20} +45.6074i q^{21} +(-179.409 - 310.746i) q^{22} +(23.6621 - 40.9839i) q^{23} +(178.131 + 102.844i) q^{24} +117.730 q^{25} +(-219.930 - 121.905i) q^{26} +27.0000 q^{27} +(273.587 + 157.956i) q^{28} +(-128.503 + 222.575i) q^{29} +(-21.6975 - 37.5811i) q^{30} -206.242i q^{31} +(461.511 - 266.453i) q^{32} +(-173.772 + 100.327i) q^{33} -22.3362i q^{34} +(-20.4953 - 35.4989i) q^{35} +(93.5112 - 161.966i) q^{36} +(-152.149 - 87.8430i) q^{37} +139.939 q^{38} +(-68.1705 + 122.987i) q^{39} -184.866 q^{40} +(135.501 + 78.2313i) q^{41} +(122.336 - 211.891i) q^{42} +(25.9922 + 45.0199i) q^{43} +1389.88i q^{44} +(-21.0157 + 12.1334i) q^{45} +(-219.868 + 126.941i) q^{46} -354.222i q^{47} +(-302.366 - 523.714i) q^{48} +(-55.9425 + 96.8953i) q^{49} +(-546.972 - 315.794i) q^{50} -12.4906 q^{51} +(501.667 + 834.888i) q^{52} -10.4723 q^{53} +(-125.442 - 72.4238i) q^{54} +(90.1712 - 156.181i) q^{55} +(-521.160 - 902.676i) q^{56} -78.2550i q^{57} +(1194.05 - 689.386i) q^{58} +(385.480 - 222.557i) q^{59} +168.090i q^{60} +(-59.8481 - 103.660i) q^{61} +(-553.216 + 958.199i) q^{62} +(-118.491 - 68.4111i) q^{63} -1246.28 q^{64} +(-2.20744 - 126.363i) q^{65} +1076.46 q^{66} +(-19.4057 - 11.2039i) q^{67} +(-43.2597 + 74.9281i) q^{68} +(70.9863 + 122.952i) q^{69} +219.903i q^{70} +(-246.997 + 142.604i) q^{71} +(-534.393 + 308.532i) q^{72} +740.989i q^{73} +(471.253 + 816.235i) q^{74} +(-176.595 + 305.871i) q^{75} +(-469.432 - 271.027i) q^{76} +1016.81 q^{77} +(646.615 - 388.538i) q^{78} -547.679 q^{79} +(470.698 + 271.758i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-419.689 - 726.923i) q^{82} -603.056i q^{83} +(-820.762 + 473.867i) q^{84} +(9.72218 - 5.61310i) q^{85} -278.882i q^{86} +(-385.510 - 667.724i) q^{87} +(2292.90 - 3971.42i) q^{88} +(-186.774 - 107.834i) q^{89} +130.185 q^{90} +(610.789 - 367.011i) q^{91} +983.409 q^{92} +(535.833 + 309.363i) q^{93} +(-950.153 + 1645.71i) q^{94} +(35.1666 + 60.9104i) q^{95} +1598.72i q^{96} +(-1253.58 + 723.752i) q^{97} +(519.817 - 300.116i) q^{98} -601.964i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.64599	−	2.68236i	−1.64260	−	0.948358i	−0.979903	−	0.199475i	$-0.936076\pi$
$2$	−4.64599	−	2.68236i	−1.64260	−	0.948358i	−0.662702	−	0.748883i	$-0.730590\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	10.3901	+	17.9962i	1.29877	+	2.24953i
$5$		−	2.69631i		−	0.241165i	−0.992703	−	0.120583i	$-0.961524\pi$
$5$		−	2.69631i		−	0.241165i	0.992703	−	0.120583i	$-0.0384763\pi$
$6$	13.9380	−	8.04709i	0.948358	−	0.547535i
$7$	13.1657	−	7.60123i	0.710882	−	0.410428i	−0.100505	−	0.994937i	$-0.532046\pi$
$7$	13.1657	−	7.60123i	0.710882	−	0.410428i	0.811388	+	0.584509i	$0.198713\pi$
$8$		−	68.5626i		−	3.03007i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−7.23249	+	12.5270i	−0.228711	+	0.396140i
$11$	57.9240	+	33.4424i	1.58770	+	0.916661i	0.993685	+	0.112209i	$0.0357927\pi$
$11$	57.9240	+	33.4424i	1.58770	+	0.916661i	0.594018	+	0.804451i	$0.297541\pi$
$12$	−62.3408			−1.49969
$13$	46.8650	−	0.818689i	0.999847	−	0.0174664i
$13$	46.8650	−	0.818689i	0.999847	−	0.0174664i
$14$	−81.5570			−1.55693
$15$	7.00522	+	4.04447i	0.120583	+	0.0696185i
$16$	−100.789	+	174.571i	−1.57482	+	2.72767i
$17$	2.08177	+	3.60573i	0.0297002	+	0.0514422i	0.880493	−	0.474058i	$-0.157211\pi$
$17$	2.08177	+	3.60573i	0.0297002	+	0.0514422i	−0.850793	+	0.525501i	$0.823878\pi$
$18$			48.2825i			0.632239i
$19$	−22.5903	+	13.0425i	−0.272766	+	0.157482i	−0.630144	−	0.776478i	$-0.717004\pi$
$19$	−22.5903	+	13.0425i	−0.272766	+	0.157482i	0.357378	+	0.933960i	$0.383671\pi$
$20$	48.5235	−	28.0150i	0.542509	−	0.313218i
$21$			45.6074i			0.473921i
$22$	−179.409	−	310.746i	−1.73865	−	3.01142i
$23$	23.6621	−	40.9839i	0.214517	−	0.371554i	−0.738606	−	0.674137i	$-0.764516\pi$
$23$	23.6621	−	40.9839i	0.214517	−	0.371554i	0.953123	+	0.302583i	$0.0978490\pi$
$24$	178.131	+	102.844i	1.51503	+	0.874705i
$25$	117.730			0.941839
$26$	−219.930	−	121.905i	−1.65892	−	0.919523i
$27$	27.0000			0.192450
$28$	273.587	+	157.956i	1.84654	+	1.06610i
$29$	−128.503	+	222.575i	−0.822845	+	1.42521i	0.0807106	+	0.996738i	$0.474281\pi$
$29$	−128.503	+	222.575i	−0.822845	+	1.42521i	−0.903555	+	0.428471i	$0.859052\pi$
$30$	−21.6975	−	37.5811i	−0.132047	−	0.228711i
$31$		−	206.242i		−	1.19491i	−0.801903	−	0.597455i	$-0.796179\pi$
$31$		−	206.242i		−	1.19491i	0.801903	−	0.597455i	$-0.203821\pi$
$32$	461.511	−	266.453i	2.54951	−	1.47196i
$33$	−173.772	+	100.327i	−0.916661	+	0.529234i
$34$		−	22.3362i		−	0.112666i
$35$	−20.4953	−	35.4989i	−0.0989811	−	0.171440i
$36$	93.5112	−	161.966i	0.432922	−	0.749843i
$37$	−152.149	−	87.8430i	−0.676029	−	0.390305i	0.122328	−	0.992490i	$-0.460964\pi$
$37$	−152.149	−	87.8430i	−0.676029	−	0.390305i	−0.798357	+	0.602184i	$0.794297\pi$
$38$	139.939			0.597396
$39$	−68.1705	+	122.987i	−0.279898	+	0.504966i
$40$	−184.866			−0.730748
$41$	135.501	+	78.2313i	0.516137	+	0.297992i	0.735353	−	0.677684i	$-0.237016\pi$
$41$	135.501	+	78.2313i	0.516137	+	0.297992i	−0.219216	+	0.975676i	$0.570350\pi$
$42$	122.336	−	211.891i	0.449447	−	0.778466i
$43$	25.9922	+	45.0199i	0.0921809	+	0.159662i	0.908429	−	0.418040i	$-0.137283\pi$
$43$	25.9922	+	45.0199i	0.0921809	+	0.159662i	−0.816248	+	0.577702i	$0.803950\pi$
$44$			1389.88i			4.76211i
$45$	−21.0157	+	12.1334i	−0.0696185	+	0.0401942i
$46$	−219.868	+	126.941i	−0.704733	+	0.406878i
$47$		−	354.222i		−	1.09933i	−0.835384	−	0.549666i	$-0.814755\pi$
$47$		−	354.222i		−	1.09933i	0.835384	−	0.549666i	$-0.185245\pi$
$48$	−302.366	−	523.714i	−0.909225	−	1.57482i
$49$	−55.9425	+	96.8953i	−0.163098	+	0.282494i
$50$	−546.972	−	315.794i	−1.54707	−	0.893201i
$51$	−12.4906			−0.0342948
$52$	501.667	+	834.888i	1.33786	+	2.22650i
$53$	−10.4723			−0.0271412			−0.0135706	−	0.999908i	$-0.504320\pi$
$53$	−10.4723			−0.0271412			−0.0135706	+	0.999908i	$0.504320\pi$
$54$	−125.442	−	72.4238i	−0.316119	−	0.182512i
$55$	90.1712	−	156.181i	0.221067	−	0.382899i
$56$	−521.160	−	902.676i	−1.24362	−	2.15402i
$57$		−	78.2550i		−	0.181844i
$58$	1194.05	−	689.386i	2.70322	−	1.56070i
$59$	385.480	−	222.557i	0.850597	−	0.491092i	−0.0102552	−	0.999947i	$-0.503264\pi$
$59$	385.480	−	222.557i	0.850597	−	0.491092i	0.860852	+	0.508855i	$0.169931\pi$
$60$			168.090i			0.361673i
$61$	−59.8481	−	103.660i	−0.125619	−	0.217579i	0.796356	−	0.604829i	$-0.206758\pi$
$61$	−59.8481	−	103.660i	−0.125619	−	0.217579i	−0.921975	+	0.387250i	$0.873425\pi$
$62$	−553.216	+	958.199i	−1.13320	+	1.96276i
$63$	−118.491	−	68.4111i	−0.236961	−	0.136809i
$64$	−1246.28			−2.43413
$65$	−2.20744	−	126.363i	−0.00421230	−	0.241129i
$66$	1076.46			2.00761
$67$	−19.4057	−	11.2039i	−0.0353848	−	0.0204294i	0.482203	−	0.876059i	$-0.339837\pi$
$67$	−19.4057	−	11.2039i	−0.0353848	−	0.0204294i	−0.517588	+	0.855630i	$0.673170\pi$
$68$	−43.2597	+	74.9281i	−0.0771473	+	0.133623i
$69$	70.9863	+	122.952i	0.123851	+	0.214517i
$70$			219.903i			0.375478i
$71$	−246.997	+	142.604i	−0.412861	+	0.238365i	−0.692018	−	0.721880i	$-0.743278\pi$
$71$	−246.997	+	142.604i	−0.412861	+	0.238365i	0.279157	+	0.960245i	$0.409945\pi$
$72$	−534.393	+	308.532i	−0.874705	+	0.505011i
$73$			740.989i			1.18803i	0.804454	+	0.594015i	$0.202458\pi$
$73$			740.989i			1.18803i	−0.804454	+	0.594015i	$0.797542\pi$
$74$	471.253	+	816.235i	0.740299	+	1.28223i
$75$	−176.595	+	305.871i	−0.271886	+	0.470920i
$76$	−469.432	−	271.027i	−0.708520	−	0.409064i
$77$	1016.81			1.50489
$78$	646.615	−	388.538i	0.938650	−	0.564016i
$79$	−547.679			−0.779983			−0.389992	−	0.920818i	$-0.627522\pi$
$79$	−547.679			−0.779983			−0.389992	+	0.920818i	$0.627522\pi$
$80$	470.698	+	271.758i	0.657821	+	0.379793i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−419.689	−	726.923i	−0.565206	−	0.978966i
$83$		−	603.056i		−	0.797518i	−0.917056	−	0.398759i	$-0.869441\pi$
$83$		−	603.056i		−	0.797518i	0.917056	−	0.398759i	$-0.130559\pi$
$84$	−820.762	+	473.867i	−1.06610	+	0.615513i
$85$	9.72218	−	5.61310i	0.0124061	−	0.00716266i
$86$		−	278.882i		−	0.349682i
$87$	−385.510	−	667.724i	−0.475070	−	0.822845i
$88$	2292.90	−	3971.42i	2.77754	−	4.81085i
$89$	−186.774	−	107.834i	−0.222450	−	0.128431i	0.384634	−	0.923069i	$-0.374328\pi$
$89$	−186.774	−	107.834i	−0.222450	−	0.128431i	−0.607084	+	0.794638i	$0.707661\pi$
$90$	130.185			0.152474
$91$	610.789	−	367.011i	0.703605	−	0.422782i
$92$	983.409			1.11443
$93$	535.833	+	309.363i	0.597455	+	0.344941i
$94$	−950.153	+	1645.71i	−1.04256	+	1.80577i
$95$	35.1666	+	60.9104i	0.0379792	+	0.0657818i
$96$			1598.72i			1.69967i
$97$	−1253.58	+	723.752i	−1.31218	+	0.757586i	−0.982457	−	0.186492i	$-0.940288\pi$
$97$	−1253.58	+	723.752i	−1.31218	+	0.757586i	−0.329722	+	0.944078i	$0.606955\pi$
$98$	519.817	−	300.116i	0.535810	−	0.309350i
$99$		−	601.964i		−	0.611107i
$100$	1223.23	+	2118.70i	1.22323	+	2.11870i
$101$	−441.725	+	765.090i	−0.435181	+	0.753756i	−0.997310	−	0.0732935i	$-0.976649\pi$
$101$	−441.725	+	765.090i	−0.435181	+	0.753756i	0.562129	+	0.827049i	$0.309982\pi$
$102$	58.0313	+	33.5044i	0.0563328	+	0.0325238i
$103$	−1251.74			−1.19745			−0.598726	−	0.800954i	$-0.704326\pi$
$103$	−1251.74			−1.19745			−0.598726	+	0.800954i	$0.704326\pi$
$104$	−56.1315	−	3213.19i	−0.0529244	−	3.02961i
$105$	122.972			0.114293
$106$	48.6543	+	28.0906i	0.0445823	+	0.0257396i
$107$	170.807	−	295.846i	0.154323	−	0.267294i	−0.778490	−	0.627658i	$-0.784014\pi$
$107$	170.807	−	295.846i	0.154323	−	0.267294i	0.932812	+	0.360363i	$0.117347\pi$
$108$	280.534	+	485.899i	0.249948	+	0.432922i
$109$		−	775.177i		−	0.681179i	−0.940212	−	0.340589i	$-0.889373\pi$
$109$		−	775.177i		−	0.681179i	0.940212	−	0.340589i	$-0.110627\pi$
$110$	−837.869	+	483.744i	−0.726251	+	0.419301i
$111$	456.446	−	263.529i	0.390305	−	0.225343i
$112$			3064.47i			2.58541i
$113$	−639.524	−	1107.69i	−0.532402	−	0.922147i	−0.999284	−	0.0378273i	$-0.987956\pi$
$113$	−639.524	−	1107.69i	−0.532402	−	0.922147i	0.466883	−	0.884319i	$-0.345377\pi$
$114$	−209.908	+	363.572i	−0.172454	+	0.298698i
$115$	−110.505	−	63.8004i	−0.0896060	−	0.0517340i
$116$	−5340.67			−4.27473
$117$	−217.274	−	361.593i	−0.171683	−	0.285720i
$118$	−2387.91			−1.86293
$119$	54.8160	+	31.6480i	0.0422267	+	0.0243796i
$120$	277.299	−	480.297i	0.210949	−	0.365374i
$121$	1571.29	+	2721.55i	1.18053	+	2.04474i
$122$			642.137i			0.476528i
$123$	−406.502	+	234.694i	−0.297992	+	0.172046i
$124$	3711.58	−	2142.88i	2.68798	−	1.55191i
$125$		−	654.476i		−	0.468305i
$126$	367.007	+	635.674i	0.259489	+	0.449447i
$127$	−556.910	+	964.597i	−0.389117	+	0.673970i	−0.992331	−	0.123609i	$-0.960553\pi$
$127$	−556.910	+	964.597i	−0.389117	+	0.673970i	0.603214	+	0.797579i	$0.293886\pi$
$128$	2098.10	+	1211.34i	1.44881	+	0.836472i
$129$	−155.953			−0.106441
$130$	−328.695	+	593.001i	−0.221757	+	0.400074i
$131$	2100.12			1.40068			0.700339	−	0.713811i	$-0.253032\pi$
$131$	2100.12			1.40068			0.700339	+	0.713811i	$0.253032\pi$
$132$	−3611.03	−	2084.83i	−2.38106	−	1.37470i
$133$	−198.278	+	343.428i	−0.129270	+	0.223902i
$134$	60.1057	+	104.106i	0.0387488	+	0.0671150i
$135$		−	72.8004i		−	0.0464123i
$136$	247.218	−	142.732i	0.155874	−	0.0899936i
$137$	−1043.58	+	602.509i	−0.650793	+	0.375736i	−0.788760	−	0.614701i	$-0.789277\pi$
$137$	−1043.58	+	602.509i	−0.650793	+	0.375736i	0.137967	+	0.990437i	$0.455943\pi$
$138$		−	761.643i		−	0.469822i
$139$	−161.445	−	279.631i	−0.0985149	−	0.170633i	0.812555	−	0.582884i	$-0.198076\pi$
$139$	−161.445	−	279.631i	−0.0985149	−	0.170633i	−0.911070	+	0.412251i	$0.864743\pi$
$140$	425.898	−	737.677i	0.257107	−	0.445322i
$141$	920.297	+	531.334i	0.549666	+	0.317350i
$142$	1530.06			0.904223
$143$	2741.99	+	1519.86i	1.60347	+	0.888789i
$144$	1814.20			1.04988
$145$	600.131	+	346.486i	0.343711	+	0.198442i
$146$	1987.60	−	3442.63i	1.12668	−	1.95146i
$147$	−167.828	−	290.686i	−0.0941645	−	0.163098i
$148$		−	3650.80i		−	2.02766i
$149$	−977.620	+	564.429i	−0.537515	+	0.310335i	−0.744071	−	0.668100i	$-0.767108\pi$
$149$	−977.620	+	564.429i	−0.537515	+	0.310335i	0.206556	+	0.978435i	$0.433774\pi$
$150$	1640.92	−	947.383i	0.893201	−	0.515690i
$151$		−	2940.44i		−	1.58470i	−0.610066	−	0.792350i	$-0.708857\pi$
$151$		−	2940.44i		−	1.58470i	0.610066	−	0.792350i	$-0.291143\pi$
$152$	894.228	+	1548.85i	0.477181	+	0.826501i
$153$	18.7359	−	32.4516i	0.00990006	−	0.0171474i
$154$	−4724.11	−	2727.46i	−2.47194	−	1.42718i
$155$	−556.093			−0.288171
$156$	−2921.60	+	51.0377i	−1.49946	+	0.0261942i
$157$	629.388			0.319940			0.159970	−	0.987122i	$-0.448860\pi$
$157$	629.388			0.319940			0.159970	+	0.987122i	$0.448860\pi$
$158$	2544.51	+	1469.07i	1.28120	+	0.739703i
$159$	15.7085	−	27.2079i	0.00783500	−	0.0135706i
$160$	−718.441	−	1244.38i	−0.354986	−	0.614854i
$161$		−	719.444i		−	0.352175i
$162$	376.325	−	217.271i	0.182512	−	0.105373i
$163$	−342.004	+	197.456i	−0.164343	+	0.0948832i	−0.579915	−	0.814677i	$-0.696914\pi$
$163$	−342.004	+	197.456i	−0.164343	+	0.0948832i	0.415573	+	0.909560i	$0.363581\pi$
$164$			3251.33i			1.54809i
$165$	270.514	+	468.543i	0.127633	+	0.221067i
$166$	−1617.61	+	2801.79i	−0.756333	+	1.31001i
$167$	131.515	+	75.9299i	0.0609395	+	0.0351834i	0.530160	−	0.847898i	$-0.322132\pi$
$167$	131.515	+	75.9299i	0.0609395	+	0.0351834i	−0.469221	+	0.883081i	$0.655465\pi$
$168$	3126.96			1.43601
$169$	2195.66	−	76.7357i	0.999390	−	0.0349275i
$170$	−60.2255			−0.0271711
$171$	203.312	+	117.382i	0.0909221	+	0.0524939i
$172$	−540.126	+	935.525i	−0.239443	+	0.414728i
$173$	269.407	+	466.626i	0.118397	+	0.205069i	0.919132	−	0.393949i	$-0.128891\pi$
$173$	269.407	+	466.626i	0.118397	+	0.205069i	−0.800736	+	0.599018i	$0.795558\pi$
$174$			4136.31i			1.80214i
$175$	1550.00	−	894.892i	0.669537	−	0.386557i
$176$	−11676.2	+	6741.24i	−5.00070	+	2.88716i
$177$			1335.34i			0.567065i
$178$	578.500	+	1001.99i	0.243598	+	0.421924i
$179$	−1110.40	+	1923.27i	−0.463659	+	0.803081i	−0.999140	−	0.0414660i	$-0.986797\pi$
$179$	−1110.40	+	1923.27i	−0.463659	+	0.803081i	0.535481	+	0.844548i	$0.320130\pi$
$180$	−436.711	−	252.135i	−0.180836	−	0.104406i
$181$	3822.78			1.56986			0.784932	−	0.619582i	$-0.212698\pi$
$181$	3822.78			1.56986			0.784932	+	0.619582i	$0.212698\pi$
$182$	−3822.17	+	66.7698i	−1.55669	+	0.0271940i
$183$	359.089			0.145052
$184$	−2809.97	−	1622.33i	−1.12583	−	0.650001i
$185$	−236.852	+	410.240i	−0.0941282	+	0.163035i
$186$	−1659.65	−	2874.60i	−0.654254	−	1.13320i
$187$			278.478i			0.108900i
$188$	6374.67	−	3680.42i	2.47298	−	1.42778i
$189$	355.474	−	205.233i	0.136809	−	0.0789869i
$190$		−	377.319i		−	0.144071i
$191$	−1732.09	−	3000.08i	−0.656178	−	1.13653i	−0.981597	−	0.190964i	$-0.938839\pi$
$191$	−1732.09	−	3000.08i	−0.656178	−	1.13653i	0.325419	−	0.945570i	$-0.394495\pi$
$192$	1869.42	−	3237.92i	0.702674	−	1.21707i
$193$	−4068.07	−	2348.70i	−1.51723	−	0.875975i	−0.999795	−	0.0202541i	$-0.993552\pi$
$193$	−4068.07	−	2348.70i	−1.51723	−	0.875975i	−0.517438	−	0.855721i	$-0.673114\pi$
$194$	7765.46			2.87385
$195$	331.611	+	183.809i	0.121780	+	0.0675017i
$196$	−2325.00			−0.847304
$197$	−2500.98	−	1443.94i	−0.904506	−	0.522217i	−0.0258469	−	0.999666i	$-0.508228\pi$
$197$	−2500.98	−	1443.94i	−0.904506	−	0.522217i	−0.878660	+	0.477449i	$0.841562\pi$
$198$	−1614.68	+	2796.72i	−0.579549	+	1.00381i
$199$	31.5046	+	54.5676i	0.0112226	+	0.0194382i	0.871582	−	0.490249i	$-0.163094\pi$
$199$	31.5046	+	54.5676i	0.0112226	+	0.0194382i	−0.860360	+	0.509688i	$0.829761\pi$
$200$		−	8071.87i		−	2.85384i
$201$	58.2171	−	33.6117i	0.0204294	−	0.0117949i
$202$	4104.50	−	2369.73i	1.42966	−	0.825415i
$203$			3907.14i			1.35087i
$204$	−129.779	−	224.784i	−0.0445410	−	0.0771473i
$205$	210.936	−	365.352i	0.0718654	−	0.124474i
$206$	5815.57	+	3357.62i	1.96694	+	1.13561i
$207$	−425.918			−0.143011
$208$	−4580.55	+	8263.80i	−1.52694	+	2.75477i
$209$	−1744.69			−0.577429
$210$	−571.325	−	329.855i	−0.187739	−	0.108391i
$211$	524.848	−	909.064i	0.171242	−	0.296600i	−0.767612	−	0.640914i	$-0.778555\pi$
$211$	524.848	−	909.064i	0.171242	−	0.296600i	0.938854	+	0.344315i	$0.111889\pi$
$212$	−108.809	−	188.463i	−0.0352501	−	0.0610550i
$213$		−	855.622i		−	0.275241i
$214$	−1587.13	+	916.331i	−0.506982	+	0.292706i
$215$	121.388	−	70.0832i	0.0385050	−	0.0222309i
$216$		−	1851.19i		−	0.583137i
$217$	−1567.69	−	2715.33i	−0.490424	−	0.849440i
$218$	−2079.30	+	3601.46i	−0.646001	+	1.11891i
$219$	−1925.15	−	1111.48i	−0.594015	−	0.342955i
$220$	3747.56			1.14846
$221$	100.514	+	167.278i	0.0305942	+	0.0509156i
$222$	−2827.52			−0.854823
$223$	2003.54	+	1156.75i	0.601647	+	0.347361i	0.769689	−	0.638419i	$-0.220411\pi$
$223$	2003.54	+	1156.75i	0.601647	+	0.347361i	−0.168042	+	0.985780i	$0.553745\pi$
$224$	4050.75	−	7016.10i	1.20827	−	2.09278i
$225$	−529.785	−	917.614i	−0.156973	−	0.271886i
$226$			6861.74i			2.01963i
$227$	−3290.43	+	1899.73i	−0.962085	+	0.555460i	−0.896814	−	0.442407i	$-0.854125\pi$
$227$	−3290.43	+	1899.73i	−0.962085	+	0.555460i	−0.0652711	+	0.997868i	$0.520791\pi$
$228$	1408.30	−	813.080i	0.409064	−	0.236173i
$229$		−	4321.07i		−	1.24692i	−0.781856	−	0.623459i	$-0.785727\pi$
$229$		−	4321.07i		−	1.24692i	0.781856	−	0.623459i	$-0.214273\pi$
$230$	342.271	+	592.832i	0.0981248	+	0.169957i
$231$	−1525.22	+	2641.76i	−0.434425	+	0.752446i
$232$	15260.3	+	8810.54i	4.31848	+	2.49328i
$233$	−5279.77			−1.48450			−0.742251	−	0.670122i	$-0.766242\pi$
$233$	−5279.77			−1.48450			−0.742251	+	0.670122i	$0.766242\pi$
$234$	39.5284	+	2262.76i	0.0110429	+	0.632142i
$235$	−955.094			−0.265121
$236$	8010.38	+	4624.79i	2.20945	+	1.27563i
$237$	821.518	−	1422.91i	0.225162	−	0.389992i
$238$	−169.783	−	294.073i	−0.0462412	−	0.0800920i
$239$		−	1547.92i		−	0.418939i	−0.977815	−	0.209469i	$-0.932826\pi$
$239$		−	1547.92i		−	0.418939i	0.977815	−	0.209469i	$-0.0671737\pi$
$240$	−1412.10	+	815.274i	−0.379793	+	0.219274i
$241$	−4259.12	+	2459.00i	−1.13840	+	0.657255i	−0.946033	−	0.324069i	$-0.894949\pi$
$241$	−4259.12	+	2459.00i	−1.13840	+	0.657255i	−0.192365	+	0.981323i	$0.561616\pi$
$242$		−	16859.1i		−	4.47828i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	1243.66	−	2154.08i	0.326300	−	0.565168i
$245$	261.260	+	150.839i	0.0681277	+	0.0393336i
$246$	2518.14			0.652644
$247$	−1048.02	+	629.731i	−0.269974	+	0.162222i
$248$	−14140.5			−3.62066
$249$	1566.78	+	904.584i	0.398759	+	0.230224i
$250$	−1755.54	+	3040.69i	−0.444121	+	0.769239i
$251$	577.890	+	1000.94i	0.145323	+	0.251707i	0.929493	−	0.368839i	$-0.120244\pi$
$251$	577.890	+	1000.94i	0.145323	+	0.251707i	−0.784170	+	0.620546i	$0.786911\pi$
$252$		−	2843.20i		−	0.710734i
$253$	2741.20	−	1582.63i	0.681178	−	0.393278i
$254$	5174.80	−	2987.67i	1.27833	−	0.738044i
$255$			33.6786i			0.00827073i
$256$	−1513.40	−	2621.28i	−0.369482	−	0.639962i
$257$	1175.98	−	2036.85i	0.285429	−	0.494378i	−0.687284	−	0.726389i	$-0.741197\pi$
$257$	1175.98	−	2036.85i	0.285429	−	0.494378i	0.972713	+	0.232011i	$0.0745304\pi$
$258$	724.558	+	418.324i	0.174841	+	0.100945i
$259$	−2670.86			−0.640769
$260$	2251.12	−	1352.65i	0.536956	−	0.322646i
$261$	2313.06			0.548563
$262$	−9757.15	−	5633.29i	−2.30076	−	1.32834i
$263$	−2760.94	+	4782.09i	−0.647326	+	1.12120i	0.336433	+	0.941707i	$0.390779\pi$
$263$	−2760.94	+	4782.09i	−0.647326	+	1.12120i	−0.983759	+	0.179494i	$0.942554\pi$
$264$	6878.70	+	11914.3i	1.60362	+	2.77754i
$265$			28.2367i			0.00654553i
$266$	1842.39	−	1063.71i	0.424678	−	0.245188i
$267$	560.322	−	323.502i	0.128431	−	0.0741499i
$268$		−	465.639i		−	0.106132i
$269$	−1958.48	−	3392.18i	−0.443905	−	0.768866i	0.554070	−	0.832470i	$-0.313074\pi$
$269$	−1958.48	−	3392.18i	−0.443905	−	0.768866i	−0.997975	+	0.0636038i	$0.979741\pi$
$270$	−195.277	+	338.230i	−0.0440155	+	0.0762371i
$271$	2405.41	+	1388.76i	0.539182	+	0.311297i	0.744747	−	0.667347i	$-0.232570\pi$
$271$	2405.41	+	1388.76i	0.539182	+	0.311297i	−0.205566	+	0.978643i	$0.565903\pi$
$272$	−839.276			−0.187090
$273$	37.3383	+	2137.39i	0.00827771	+	0.473849i
$274$	6464.58			1.42533
$275$	6819.38	+	3937.17i	1.49536	+	0.863347i
$276$	−1475.11	+	2554.97i	−0.321708	+	0.557215i
$277$	3291.54	+	5701.12i	0.713969	+	1.23663i	0.963356	+	0.268227i	$0.0864378\pi$
$277$	3291.54	+	5701.12i	0.713969	+	1.23663i	−0.249386	+	0.968404i	$0.580229\pi$
$278$			1732.21i			0.373710i
$279$	−1607.50	+	928.090i	−0.344941	+	0.199152i
$280$	−2433.90	+	1405.21i	−0.519476	+	0.299919i
$281$			2871.66i			0.609640i	0.952410	+	0.304820i	$0.0985963\pi$
$281$			2871.66i			0.609640i	−0.952410	+	0.304820i	$0.901404\pi$
$282$	−2850.46	−	4937.14i	−0.601923	−	1.04256i
$283$	3759.02	−	6510.81i	0.789578	−	1.36759i	−0.136648	−	0.990620i	$-0.543633\pi$
$283$	3759.02	−	6510.81i	0.789578	−	1.36759i	0.926226	−	0.376969i	$-0.123034\pi$
$284$	−5132.66	−	2963.34i	−1.07242	−	0.619162i
$285$	−211.000			−0.0438546
$286$	−8662.43	−	14416.2i	−1.79098	−	2.98060i
$287$	2378.62			0.489217
$288$	−4153.60	−	2398.08i	−0.849837	−	0.490653i
$289$	2447.83	−	4239.77i	0.498236	−	0.862970i
$290$	−1858.80	−	3219.54i	−0.376388	−	0.651923i
$291$		−	4342.51i		−	0.874785i
$292$	−13335.0	+	7698.97i	−2.67251	+	1.54297i
$293$	3902.80	−	2253.28i	0.778171	−	0.449278i	−0.0576104	−	0.998339i	$-0.518348\pi$
$293$	3902.80	−	2253.28i	0.778171	−	0.449278i	0.835782	+	0.549062i	$0.185015\pi$
$294$			1800.70i			0.357207i
$295$	−600.083	−	1039.37i	−0.118435	−	0.205135i
$296$	−6022.75	+	10431.7i	−1.18265	+	2.04841i
$297$	1563.95	+	902.945i	0.305554	+	0.176411i
$298$	6056.02			1.17723
$299$	1075.37	−	1940.08i	0.207994	−	0.375244i
$300$	−7339.38			−1.41246
$301$	684.413	+	395.146i	0.131060	+	0.0756673i
$302$	−7887.33	+	13661.3i	−1.50286	+	2.60304i
$303$	−1325.18	−	2295.27i	−0.251252	−	0.435181i
$304$		−	5258.15i		−	0.992024i
$305$	−279.500	+	161.369i	−0.0524725	+	0.0302950i
$306$	−174.094	+	100.513i	−0.0325238	+	0.0187776i
$307$			9538.89i			1.77333i	0.462409	+	0.886667i	$0.346985\pi$
$307$			9538.89i			1.77333i	−0.462409	+	0.886667i	$0.653015\pi$
$308$	10564.8	+	18298.8i	1.95450	+	3.38530i
$309$	1877.61	−	3252.12i	0.345675	−	0.598726i
$310$	2583.60	+	1491.64i	0.473351	+	0.273289i
$311$	7466.28			1.36133			0.680666	−	0.732594i	$-0.261691\pi$
$311$	7466.28			1.36133			0.680666	+	0.732594i	$0.261691\pi$
$312$	8432.31	+	4673.95i	1.53008	+	0.848110i
$313$	−1821.65			−0.328964			−0.164482	−	0.986380i	$-0.552595\pi$
$313$	−1821.65			−0.328964			−0.164482	+	0.986380i	$0.552595\pi$
$314$	−2924.13	−	1688.25i	−0.525536	−	0.303418i
$315$	−184.458	+	319.490i	−0.0329937	+	0.0571467i
$316$	−5690.46	−	9856.16i	−1.01302	−	1.75460i
$317$		−	3125.14i		−	0.553708i	−0.960912	−	0.276854i	$-0.910708\pi$
$317$		−	3125.14i		−	0.553708i	0.960912	−	0.276854i	$-0.0892918\pi$
$318$	−145.963	+	84.2717i	−0.0257396	+	0.0148608i
$319$	−14886.9	+	8594.93i	−2.61287	+	1.50854i
$320$			3360.35i			0.587029i
$321$	512.420	+	887.538i	0.0890982	+	0.154323i
$322$	−1929.81	+	3342.53i	−0.333988	+	0.578484i
$323$	−94.0554	−	54.3029i	−0.0162024	−	0.00935448i
$324$	−1683.20			−0.288615
$325$	5517.41	−	96.3842i	0.941696	−	0.0164506i
$326$	2118.60			0.359933
$327$	2013.97	+	1162.77i	0.340589	+	0.196639i
$328$	5363.74	−	9290.27i	0.902936	−	1.56393i
$329$	−2692.53	−	4663.59i	−0.451197	−	0.781496i
$330$		−	2902.46i		−	0.484167i
$331$	1345.52	−	776.836i	0.223433	−	0.128999i	−0.384106	−	0.923289i	$-0.625490\pi$
$331$	1345.52	−	776.836i	0.223433	−	0.128999i	0.607539	+	0.794290i	$0.292157\pi$
$332$	10852.7	−	6265.83i	1.79404	−	1.03579i
$333$			1581.17i			0.260204i
$334$	−407.343	−	705.539i	−0.0667330	−	0.115585i
$335$	−30.2092	+	52.3238i	−0.00492688	+	0.00853360i
$336$	−7961.74	−	4596.71i	−1.29270	−	0.746343i
$337$	3190.43			0.515709			0.257855	−	0.966184i	$-0.416984\pi$
$337$	3190.43			0.515709			0.257855	+	0.966184i	$0.416984\pi$
$338$	−10406.8	−	5533.04i	−1.67473	−	0.890408i
$339$	3837.15			0.614764
$340$	202.029	+	116.642i	0.0322252	+	0.0186053i
$341$	6897.24	−	11946.4i	1.09533	−	1.89716i
$342$	−629.724	−	1090.71i	−0.0995661	−	0.172454i
$343$			6915.37i			1.08862i
$344$	3086.68	−	1782.10i	0.483787	−	0.279315i
$345$	331.516	−	191.401i	0.0517340	−	0.0298687i
$346$		−	2890.59i		−	0.449130i
$347$	2859.34	+	4952.53i	0.442356	+	0.766183i	0.997864	−	0.0653283i	$-0.0208095\pi$
$347$	2859.34	+	4952.53i	0.442356	+	0.766183i	−0.555508	+	0.831511i	$0.687476\pi$
$348$	8011.01	−	13875.5i	1.23401	−	2.13737i
$349$	2882.53	+	1664.23i	0.442116	+	0.255256i	0.704495	−	0.709709i	$-0.251174\pi$
$349$	2882.53	+	1664.23i	0.442116	+	0.255256i	−0.262379	+	0.964965i	$0.584507\pi$
$350$	−9601.70			−1.46638
$351$	1265.36	−	22.1046i	0.192421	−	0.00336141i
$352$	35643.4			5.39715
$353$	−10657.7	−	6153.25i	−1.60695	−	0.927774i	−0.990047	−	0.140737i	$-0.955053\pi$
$353$	−10657.7	−	6153.25i	−1.60695	−	0.927774i	−0.616905	−	0.787037i	$-0.711614\pi$
$354$	3581.87	−	6203.98i	0.537781	−	0.931463i
$355$	384.504	+	665.981i	0.0574855	+	0.0995679i
$356$		−	4481.64i		−	0.667210i
$357$	−164.448	+	94.9441i	−0.0243796	+	0.0140756i
$358$	10317.8	−	5956.98i	1.52322	−	0.879430i
$359$			8539.97i			1.25549i	0.778418	+	0.627747i	$0.216023\pi$
$359$			8539.97i			1.25549i	−0.778418	+	0.627747i	$0.783977\pi$
$360$	831.898	+	1440.89i	0.121791	+	0.210949i
$361$	−3089.29	+	5350.80i	−0.450399	+	0.780114i
$362$	−17760.6	−	10254.1i	−2.57866	−	1.48879i
$363$	−9427.74			−1.36316
$364$	12951.0	+	7178.61i	1.86488	+	1.03369i
$365$	1997.94			0.286512
$366$	−1668.32	−	963.206i	−0.238264	−	0.137562i
$367$	−1248.33	+	2162.17i	−0.177553	+	0.307532i	−0.941042	−	0.338290i	$-0.890152\pi$
$367$	−1248.33	+	2162.17i	−0.177553	+	0.307532i	0.763489	+	0.645821i	$0.223485\pi$
$368$	4769.74	+	8261.44i	0.675652	+	1.17026i
$369$		−	1408.16i		−	0.198661i
$370$	2200.82	−	1270.65i	0.309231	−	0.178535i
$371$	−137.876	+	79.6026i	−0.0192942	+	0.0111395i
$372$			12857.3i			1.79199i
$373$	571.454	+	989.787i	0.0793264	+	0.137397i	0.902960	−	0.429726i	$-0.141390\pi$
$373$	571.454	+	989.787i	0.0793264	+	0.137397i	−0.823633	+	0.567123i	$0.808056\pi$
$374$	746.978	−	1293.80i	0.103276	−	0.178880i
$375$	1700.38	+	981.713i	0.234152	+	0.135188i
$376$	−24286.4			−3.33105
$377$	−5840.10	+	10536.2i	−0.797826	+	1.43936i
$378$	−2202.04			−0.299632
$379$	−10549.8	−	6090.91i	−1.42983	−	0.825512i	−0.432723	−	0.901527i	$-0.642447\pi$
$379$	−10549.8	−	6090.91i	−1.42983	−	0.825512i	−0.997107	+	0.0760146i	$0.975780\pi$
$380$	−730.772	+	1265.73i	−0.0986522	+	0.170871i
$381$	−1670.73	−	2893.79i	−0.224657	−	0.389117i
$382$			18584.4i			2.48917i
$383$	8816.66	−	5090.30i	1.17627	−	0.679118i	0.221119	−	0.975247i	$-0.429029\pi$
$383$	8816.66	−	5090.30i	1.17627	−	0.679118i	0.955148	+	0.296129i	$0.0956957\pi$
$384$	−6294.31	+	3634.02i	−0.836472	+	0.482937i
$385$		−	2741.65i		−	0.362928i
$386$	12600.1	+	21824.1i	1.66148	+	2.87776i
$387$	233.930	−	405.179i	0.0307270	−	0.0532207i
$388$	−26049.6	−	15039.8i	−3.40843	−	1.96786i
$389$	−5845.83			−0.761941			−0.380971	−	0.924587i	$-0.624410\pi$
$389$	−5845.83			−0.761941			−0.380971	+	0.924587i	$0.624410\pi$
$390$	−1047.62	−	1743.48i	−0.136021	−	0.226370i
$391$	197.036			0.0254848
$392$	6643.40	+	3835.57i	0.855975	+	0.494197i
$393$	−3150.19	+	5456.28i	−0.404341	+	0.700339i
$394$	7746.36	+	13417.1i	0.990498	+	1.71559i
$395$			1476.71i			0.188105i
$396$	10833.1	−	6254.48i	1.37470	−	0.793686i
$397$	−2165.86	+	1250.46i	−0.273807	+	0.158083i	−0.630617	−	0.776094i	$-0.717198\pi$
$397$	−2165.86	+	1250.46i	−0.273807	+	0.158083i	0.356809	+	0.934177i	$0.383865\pi$
$398$		−	338.027i		−	0.0425723i
$399$	−594.834	−	1030.28i	−0.0746340	−	0.129270i
$400$	−11865.8	+	20552.2i	−1.48323	+	2.56903i
$401$	7958.12	+	4594.62i	0.991046	+	0.572181i	0.905587	−	0.424161i	$-0.139431\pi$
$401$	7958.12	+	4594.62i	0.991046	+	0.572181i	0.0854594	+	0.996342i	$0.472764\pi$
$402$	−360.634			−0.0447433
$403$	−168.848	−	9665.54i	−0.0208708	−	1.19473i
$404$	−18358.3			−2.26080
$405$	189.141	+	109.201i	0.0232062	+	0.0133981i
$406$	10480.4	−	18152.5i	1.28111	−	2.21895i
$407$	−5875.36	−	10176.4i	−0.715555	−	1.23938i
$408$			856.390i			0.103916i
$409$	−7979.89	+	4607.19i	−0.964744	+	0.556995i	−0.897630	−	0.440750i	$-0.854712\pi$
$409$	−7979.89	+	4607.19i	−0.964744	+	0.556995i	−0.0671140	+	0.997745i	$0.521379\pi$
$410$	−1960.01	+	1131.61i	−0.236093	+	0.136308i
$411$		−	3615.05i		−	0.433862i
$412$	−13005.8	−	22526.6i	−1.55521	−	2.69371i
$413$	3383.42	−	5860.25i	0.403116	−	0.698218i
$414$	1978.81	+	1142.47i	0.234911	+	0.135626i
$415$	−1626.03			−0.192334
$416$	21410.6	−	12865.2i	2.52341	−	1.51627i
$417$	968.669			0.113755
$418$	8105.81	+	4679.89i	0.948488	+	0.547610i
$419$	3247.20	−	5624.32i	0.378607	−	0.655767i	−0.612253	−	0.790662i	$-0.709737\pi$
$419$	3247.20	−	5624.32i	0.378607	−	0.655767i	0.990860	+	0.134895i	$0.0430699\pi$
$420$	1277.69	+	2213.03i	0.148441	+	0.257107i
$421$		−	3059.56i		−	0.354190i	−0.984194	−	0.177095i	$-0.943330\pi$
$421$		−	3059.56i		−	0.354190i	0.984194	−	0.177095i	$-0.0566699\pi$
$422$	−4876.88	+	2815.67i	−0.562566	+	0.324797i
$423$	−2760.89	+	1594.00i	−0.317350	+	0.183222i
$424$			718.010i			0.0822398i
$425$	245.087	+	424.502i	0.0279728	+	0.0484503i
$426$	−2295.09	+	3975.21i	−0.261027	+	0.452112i
$427$	−1575.89	−	909.839i	−0.178601	−	0.103115i
$428$	7098.82			0.801716
$429$	−8061.69	+	4844.10i	−0.907277	+	0.545164i
$430$	−751.954			−0.0843313
$431$	6873.69	+	3968.53i	0.768199	+	0.443520i	0.832232	−	0.554428i	$-0.187063\pi$
$431$	6873.69	+	3968.53i	0.768199	+	0.443520i	−0.0640325	+	0.997948i	$0.520396\pi$
$432$	−2721.30	+	4713.42i	−0.303075	+	0.524941i
$433$	3647.19	+	6317.11i	0.404786	+	0.701111i	0.994297	−	0.106650i	$-0.0340125\pi$
$433$	3647.19	+	6317.11i	0.404786	+	0.701111i	−0.589510	+	0.807761i	$0.700679\pi$
$434$			16820.5i			1.86039i
$435$	−1800.39	+	1039.46i	−0.198442	+	0.114570i
$436$	13950.3	−	8054.19i	1.53233	−	0.884692i
$437$			1234.45i			0.135130i
$438$	5962.80	+	10327.9i	0.650488	+	1.12668i
$439$	7607.35	−	13176.3i	0.827059	−	1.43251i	−0.0732765	−	0.997312i	$-0.523346\pi$
$439$	7607.35	−	13176.3i	0.827059	−	1.43251i	0.900335	−	0.435197i	$-0.143321\pi$
$440$	−10708.2	−	6182.37i	−1.16021	−	0.669848i
$441$	1006.97			0.108732
$442$	−18.2864	−	1046.79i	−0.00196787	−	0.112649i
$443$	1517.05			0.162703			0.0813515	−	0.996685i	$-0.474076\pi$
$443$	1517.05			0.162703			0.0813515	+	0.996685i	$0.474076\pi$
$444$	9485.06	+	5476.20i	1.01383	+	0.585336i
$445$	−290.754	+	503.601i	−0.0309732	+	0.0536472i
$446$	−6205.63	−	10748.5i	−0.658845	−	1.14115i
$447$		−	3386.58i		−	0.358343i
$448$	−16408.1	+	9473.24i	−1.73038	+	0.999037i
$449$	−610.761	+	352.623i	−0.0641951	+	0.0370631i	−0.531754	−	0.846899i	$-0.678467\pi$
$449$	−610.761	+	352.623i	−0.0641951	+	0.0370631i	0.467559	+	0.883962i	$0.345134\pi$
$450$			5684.30i			0.595467i
$451$	5232.48	+	9062.93i	0.546315	+	0.946245i
$452$	13289.5	−	23018.1i	1.38293	−	2.39531i
$453$	7639.49	+	4410.66i	0.792350	+	0.457464i
$454$	20383.1			2.10710
$455$	−989.575	−	1646.88i	−0.101960	−	0.169685i
$456$	−5365.37			−0.551001
$457$	−6302.69	−	3638.86i	−0.645137	−	0.372470i	0.141454	−	0.989945i	$-0.454822\pi$
$457$	−6302.69	−	3638.86i	−0.645137	−	0.372470i	−0.786591	+	0.617475i	$0.788156\pi$
$458$	−11590.7	+	20075.6i	−1.18253	+	2.04820i
$459$	56.2078	+	97.3547i	0.00571580	+	0.00990006i
$460$		−	2651.58i		−	0.268762i
$461$	−1699.04	+	980.941i	−0.171653	+	0.0991041i	−0.583365	−	0.812210i	$-0.698264\pi$
$461$	−1699.04	+	980.941i	−0.171653	+	0.0991041i	0.411712	+	0.911314i	$0.364931\pi$
$462$	14172.3	−	8182.39i	1.42718	−	0.823981i
$463$		−	10374.1i		−	1.04131i	−0.853768	−	0.520653i	$-0.825689\pi$
$463$		−	10374.1i		−	1.04131i	0.853768	−	0.520653i	$-0.174311\pi$
$464$	−25903.4	−	44866.0i	−2.59167	−	4.48891i
$465$	834.140	−	1444.77i	0.0831878	−	0.144085i
$466$	24529.7	+	14162.2i	2.43845	+	1.40784i
$467$	−8788.92			−0.870883			−0.435442	−	0.900217i	$-0.643408\pi$
$467$	−8788.92			−0.870883			−0.435442	+	0.900217i	$0.643408\pi$
$468$	4249.80	−	7667.10i	0.419759	−	0.757291i
$469$	−340.653			−0.0335392
$470$	4437.36	+	2561.91i	0.435489	+	0.251430i
$471$	−944.082	+	1635.20i	−0.0923588	+	0.159970i
$472$	−15259.1	−	26429.5i	−1.48804	−	2.57737i
$473$			3476.97i			0.337995i
$474$	−7633.53	+	4407.22i	−0.739703	+	0.427068i
$475$	−2659.55	+	1535.49i	−0.256902	+	0.148322i
$476$			1315.31i			0.126654i
$477$	47.1255	+	81.6237i	0.00452354	+	0.00783500i
$478$	−4152.07	+	7191.60i	−0.397304	+	0.688151i
$479$	9648.96	+	5570.83i	0.920401	+	0.531394i	0.883763	−	0.467935i	$-0.155002\pi$
$479$	9648.96	+	5570.83i	0.920401	+	0.531394i	0.0366382	+	0.999329i	$0.488335\pi$
$480$	4310.65			0.409903
$481$	−7202.36	−	3992.20i	−0.682743	−	0.378438i
$482$	26383.8			2.49325
$483$	1869.17	+	1079.17i	0.176087	+	0.101664i
$484$	−32651.8	+	56554.6i	−3.06648	+	5.31129i
$485$	1951.46	+	3380.03i	0.182704	+	0.316452i
$486$			1303.63i			0.121674i
$487$	17009.1	−	9820.23i	1.58266	−	0.913752i	0.588195	−	0.808719i	$-0.299839\pi$
$487$	17009.1	−	9820.23i	1.58266	−	0.913752i	0.994469	−	0.105033i	$-0.0334948\pi$
$488$	−7107.20	+	4103.34i	−0.659278	+	0.380634i
$489$		−	1184.74i		−	0.109562i
$490$	−809.207	−	1401.59i	−0.0746046	−	0.129219i
$491$	−1705.16	+	2953.42i	−0.156726	+	0.271458i	−0.933686	−	0.358092i	$-0.883427\pi$
$491$	−1705.16	+	2953.42i	−0.156726	+	0.271458i	0.776960	+	0.629550i	$0.216761\pi$
$492$	−8447.21	−	4877.00i	−0.774044	−	0.446895i
$493$	−1070.06			−0.0977546
$494$	6558.23	−	114.566i	0.597305	−	0.0104344i
$495$	−1623.08			−0.147378
$496$	36003.9	+	20786.9i	3.25932	+	1.88177i
$497$	−2167.93	+	3754.96i	−0.195664	+	0.338899i
$498$	−4852.84	−	8405.37i	−0.436669	−	0.756333i
$499$			5032.44i			0.451469i	0.974189	+	0.225735i	$0.0724782\pi$
$499$			5032.44i			0.451469i	−0.974189	+	0.225735i	$0.927522\pi$
$500$	11778.1	−	6800.09i	1.05347	−	0.608219i
$501$	−394.544	+	227.790i	−0.0351834	+	0.0203132i
$502$		−	6200.44i		−	0.551274i
$503$	−8594.69	−	14886.4i	−0.761866	−	1.31959i	−0.941888	−	0.335927i	$-0.890950\pi$
$503$	−8594.69	−	14886.4i	−0.761866	−	1.31959i	0.180022	−	0.983663i	$-0.442383\pi$
$504$	−4690.44	+	8124.09i	−0.414542	+	0.718007i
$505$	2062.92	+	1191.03i	0.181780	+	0.104951i
$506$	−16980.8			−1.49187
$507$	−3094.12	+	5819.59i	−0.271035	+	0.509778i
$508$	−23145.5			−2.02149
$509$	−805.889	−	465.280i	−0.0701776	−	0.0405170i	0.464501	−	0.885573i	$-0.346234\pi$
$509$	−805.889	−	465.280i	−0.0701776	−	0.0405170i	−0.534678	+	0.845056i	$0.679567\pi$
$510$	90.3382	−	156.470i	0.00784361	−	0.0135855i
$511$	5632.43	+	9755.65i	0.487601	+	0.844549i
$512$		−	3143.50i		−	0.271337i
$513$	−609.937	+	352.147i	−0.0524939	+	0.0303074i
$514$	−10927.1	+	6308.79i	−0.937695	+	0.541379i
$515$			3375.08i			0.288784i
$516$	−1620.38	−	2806.58i	−0.138243	−	0.239443i
$517$	11846.1	−	20518.0i	1.00772	−	1.74541i
$518$	12408.8	+	7164.21i	1.05253	+	0.607679i
$519$	−1616.44			−0.136713
$520$	−8663.76	+	151.348i	−0.730637	+	0.0127636i
$521$	−9869.60			−0.829933			−0.414966	−	0.909837i	$-0.636207\pi$
$521$	−9869.60			−0.829933			−0.414966	+	0.909837i	$0.636207\pi$
$522$	−10746.5	−	6204.47i	−0.901072	−	0.520234i
$523$	10710.3	−	18550.8i	0.895466	−	1.55099i	0.0622398	−	0.998061i	$-0.480176\pi$
$523$	10710.3	−	18550.8i	0.895466	−	1.55099i	0.833226	−	0.552932i	$-0.186491\pi$
$524$	21820.6	+	37794.3i	1.81915	+	3.15087i
$525$			5369.35i			0.446358i
$526$	25654.6	−	14811.7i	2.12660	−	1.22779i
$527$	743.654	−	429.349i	0.0614688	−	0.0354890i
$528$		−	40447.4i		−	3.33380i
$529$	4963.71	+	8597.40i	0.407965	+	0.706616i
$530$	75.7410	−	131.187i	0.00620750	−	0.0107517i
$531$	−3469.32	−	2003.01i	−0.283532	−	0.163697i
$532$	−8240.54			−0.671565
$533$	6414.28	+	3555.38i	0.521263	+	0.288931i
$534$	−3471.00			−0.281283
$535$	−797.693	−	460.548i	−0.0644622	−	0.0372173i
$536$	−768.168	+	1330.51i	−0.0619026	+	0.107218i
$537$	−3331.19	−	5769.80i	−0.267694	−	0.463659i
$538$			21013.4i			1.68392i
$539$	−6480.83	+	3741.71i	−0.517902	+	0.299011i
$540$	1310.13	−	756.406i	0.104406	−	0.0602788i
$541$			7771.50i			0.617602i	0.951127	+	0.308801i	$0.0999277\pi$
$541$			7771.50i			0.617602i	−0.951127	+	0.308801i	$0.900072\pi$
$542$	−7450.34	−	12904.4i	−0.590442	−	1.02267i
$543$	−5734.17	+	9931.88i	−0.453180	+	0.784932i
$544$	1921.52	+	1109.39i	0.151442	+	0.0874350i
$545$	−2090.12			−0.164277
$546$	5559.78	−	10030.4i	0.435782	−	0.786197i
$547$	−15577.5			−1.21763			−0.608817	−	0.793310i	$-0.708356\pi$
$547$	−15577.5			−1.21763			−0.608817	+	0.793310i	$0.708356\pi$
$548$	−21685.8	−	12520.3i	−1.69046	−	0.975986i
$549$	−538.633	+	932.940i	−0.0418730	+	0.0725262i
$550$	−21121.8	−	36584.1i	−1.63752	−	2.83628i
$551$		−	6704.02i		−	0.518332i
$552$	8429.90	−	4867.00i	0.650001	−	0.375278i
$553$	−7210.58	+	4163.03i	−0.554476	+	0.320127i
$554$		−	35316.4i		−	2.70840i
$555$	−710.556	−	1230.72i	−0.0543449	−	0.0941282i
$556$	3354.87	−	5810.80i	0.255896	−	0.443225i
$557$	19749.3	+	11402.3i	1.50234	+	0.867377i	0.999996	+	0.00270962i	$0.000862500\pi$
$557$	19749.3	+	11402.3i	1.50234	+	0.867377i	0.502345	+	0.864667i	$0.332471\pi$
$558$	9957.89			0.755468
$559$	1254.98	+	2088.58i	0.0949556	+	0.158028i
$560$	8262.78			0.623511
$561$	−723.506	−	417.716i	−0.0544500	−	0.0314367i
$562$	7702.83	−	13341.7i	0.578157	−	1.00140i
$563$	−1758.71	−	3046.17i	−0.131653	−	0.228030i	0.792661	−	0.609663i	$-0.208695\pi$
$563$	−1758.71	−	3046.17i	−0.131653	−	0.228030i	−0.924314	+	0.381633i	$0.875362\pi$
$564$			22082.5i			1.64865i
$565$	−2986.67	+	1724.36i	−0.222390	+	0.128397i
$566$	−34928.7	+	20166.1i	−2.59393	+	1.49761i
$567$			1231.40i			0.0912062i
$568$	9777.29	+	16934.8i	0.722264	+	1.25100i
$569$	−3046.72	+	5277.08i	−0.224473	+	0.388799i	−0.956161	−	0.292841i	$-0.905399\pi$
$569$	−3046.72	+	5277.08i	−0.224473	+	0.388799i	0.731688	+	0.681640i	$0.238733\pi$
$570$	980.303	+	565.978i	0.0720357	+	0.0415898i
$571$	−10460.2			−0.766630			−0.383315	−	0.923618i	$-0.625218\pi$
$571$	−10460.2			−0.766630			−0.383315	+	0.923618i	$0.625218\pi$
$572$	1137.88	+	65137.0i	0.0831771	+	4.76139i
$573$	10392.6			0.757689
$574$	−11051.0	−	6380.31i	−0.803590	−	0.463953i
$575$	2785.74	−	4825.03i	0.202040	−	0.349944i
$576$	5608.25	+	9713.77i	0.405689	+	0.702674i
$577$			9648.19i			0.696117i	0.937473	+	0.348058i	$0.113159\pi$
$577$			9648.19i			0.696117i	−0.937473	+	0.348058i	$0.886841\pi$
$578$	−22745.2	+	13131.9i	−1.63681	+	0.945012i
$579$	12204.2	−	7046.10i	0.875975	−	0.505744i
$580$			14400.1i			1.03092i
$581$	−4583.97	−	7939.66i	−0.327324	−	0.566941i
$582$	−11648.2	+	20175.3i	−0.829610	+	1.43693i
$583$	−606.599	−	350.220i	−0.0430922	−	0.0248793i
$584$	50804.1			3.59981
$585$	−974.966	+	585.838i	−0.0689058	+	0.0414041i
$586$	−24176.5			−1.70430
$587$	1879.91	+	1085.37i	0.132184	+	0.0763166i	0.564634	−	0.825341i	$-0.309017\pi$
$587$	1879.91	+	1085.37i	0.132184	+	0.0763166i	−0.432450	+	0.901658i	$0.642351\pi$
$588$	3487.50	−	6040.53i	0.244596	−	0.423652i
$589$	2689.91	+	4659.06i	0.188176	+	0.325931i
$590$			6438.56i			0.449274i
$591$	7502.95	−	4331.83i	0.522217	−	0.301502i
$592$	30669.7	−	17707.2i	2.12925	−	1.22932i
$593$			22885.9i			1.58484i	0.609975	+	0.792421i	$0.291180\pi$
$593$			22885.9i			1.58484i	−0.609975	+	0.792421i	$0.708820\pi$
$594$	−4844.05	−	8390.15i	−0.334602	−	0.579549i
$595$	85.3330	−	147.801i	0.00587951	−	0.0101836i
$596$	−20315.2	−	11729.0i	−1.39621	−	0.806105i
$597$	−189.028			−0.0129588
$598$	−10200.2	+	6129.08i	−0.697518	+	0.419125i
$599$	−23978.7			−1.63563			−0.817815	−	0.575482i	$-0.804815\pi$
$599$	−23978.7			−1.63563			−0.817815	+	0.575482i	$0.804815\pi$
$600$	20971.3	+	12107.8i	1.42692	+	0.823832i
$601$	−6436.62	+	11148.6i	−0.436864	+	0.756671i	−0.997446	−	0.0714284i	$-0.977244\pi$
$601$	−6436.62	+	11148.6i	−0.436864	+	0.756671i	0.560582	+	0.828099i	$0.310578\pi$
$602$	−2119.85	−	3671.69i	−0.143519	−	0.248583i
$603$			201.670i			0.0136196i
$604$	52916.9	−	30551.6i	3.56483	−	2.05816i
$605$	7338.16	−	4236.69i	0.493122	−	0.284704i
$606$			14218.4i			0.953107i
$607$	3558.57	+	6163.63i	0.237954	+	0.412148i	0.960127	−	0.279564i	$-0.0901899\pi$
$607$	3558.57	+	6163.63i	0.237954	+	0.412148i	−0.722173	+	0.691712i	$0.756857\pi$
$608$	−6950.43	+	12038.5i	−0.463614	+	0.803002i
$609$	−10151.0	−	5860.71i	−0.675437	−	0.389964i
$610$	1731.40			0.114922
$611$	−289.998	−	16600.6i	−0.0192014	−	1.09917i
$612$	778.675			0.0514315
$613$	150.079	+	86.6484i	0.00988850	+	0.00570913i	0.504936	−	0.863157i	$-0.331516\pi$
$613$	150.079	+	86.6484i	0.00988850	+	0.00570913i	−0.495048	+	0.868866i	$0.664849\pi$
$614$	25586.8	−	44317.6i	1.68176	−	2.91289i
$615$	632.808	+	1096.06i	0.0414915	+	0.0718654i
$616$		−	69715.5i		−	4.55993i
$617$	5285.14	−	3051.38i	0.344849	−	0.199099i	−0.317565	−	0.948236i	$-0.602865\pi$
$617$	5285.14	−	3051.38i	0.344849	−	0.199099i	0.662414	+	0.749138i	$0.269532\pi$
$618$	−17446.7	+	10072.9i	−1.13561	+	0.655647i
$619$		−	14867.8i		−	0.965409i	−0.875783	−	0.482705i	$-0.839654\pi$
$619$		−	14867.8i		−	0.965409i	0.875783	−	0.482705i	$-0.160346\pi$
$620$	−5777.88	−	10007.6i	−0.374267	−	0.648249i
$621$	638.876	−	1106.57i	0.0412838	−	0.0715056i
$622$	−34688.3	−	20027.3i	−2.23613	−	1.29103i
$623$	−3278.69			−0.210847
$624$	−14599.2	−	24296.3i	−0.936593	−	1.55870i
$625$	12951.6			0.828900
$626$	8463.35	+	4886.32i	0.540357	+	0.311975i
$627$	2617.03	−	4532.84i	0.166689	−	0.288715i
$628$	6539.43	+	11326.6i	0.415528	+	0.719716i
$629$		−	731.475i		−	0.0463686i
$630$	1713.98	−	989.565i	0.108391	−	0.0625797i
$631$	−14904.8	+	8605.29i	−0.940334	+	0.542902i	−0.890065	−	0.455834i	$-0.849341\pi$
$631$	−14904.8	+	8605.29i	−0.940334	+	0.542902i	−0.0502690	+	0.998736i	$0.516008\pi$
$632$			37550.3i			2.36340i
$633$	1574.55	+	2727.19i	0.0988666	+	0.171242i
$634$	−8382.76	+	14519.4i	−0.525113	+	0.909523i
$635$	2600.86	+	1501.60i	0.162538	+	0.0938415i
$636$	652.853			0.0407033
$637$	−2542.42	+	4586.80i	−0.158139	+	0.285299i
$638$	92218.9			5.72254
$639$	2222.97	+	1283.43i	0.137620	+	0.0794552i
$640$	3266.15	−	5657.14i	0.201728	−	0.349403i
$641$	−6318.01	−	10943.1i	−0.389308	−	0.674301i	0.603049	−	0.797704i	$-0.293953\pi$
$641$	−6318.01	−	10943.1i	−0.389308	−	0.674301i	−0.992357	+	0.123403i	$0.960619\pi$
$642$		−	5497.99i		−	0.337988i
$643$	8302.04	−	4793.19i	0.509177	−	0.293973i	−0.223318	−	0.974746i	$-0.571689\pi$
$643$	8302.04	−	4793.19i	0.509177	−	0.293973i	0.732495	+	0.680772i	$0.238356\pi$
$644$	12947.3	−	7475.12i	0.792228	−	0.457393i
$645$			420.499i			0.0256700i
$646$	291.320	+	504.581i	0.0177428	+	0.0307314i
$647$	2622.16	−	4541.72i	0.159332	−	0.275971i	−0.775296	−	0.631598i	$-0.782399\pi$
$647$	2622.16	−	4541.72i	0.159332	−	0.275971i	0.934628	+	0.355627i	$0.115733\pi$
$648$	4809.54	+	2776.79i	0.291568	+	0.168337i
$649$	29771.4			1.80066
$650$	−25892.4	−	14351.9i	−1.56243	−	0.866043i
$651$	9406.17			0.566293
$652$	−7106.94	−	4103.19i	−0.426885	−	0.246462i
$653$	−9434.51	+	16341.1i	−0.565392	+	0.979288i	0.431621	+	0.902055i	$0.357942\pi$
$653$	−9434.51	+	16341.1i	−0.565392	+	0.979288i	−0.997013	+	0.0772326i	$0.975392\pi$
$654$	−6237.91	−	10804.4i	−0.372969	−	0.646001i
$655$		−	5662.59i		−	0.337795i
$656$	−27313.8	+	15769.7i	−1.62565	+	0.938570i
$657$	5775.44	−	3334.45i	0.342955	−	0.198005i
$658$			28889.3i			1.71159i
$659$	12149.9	+	21044.2i	0.718197	+	1.24395i	0.961713	+	0.274057i	$0.0883658\pi$
$659$	12149.9	+	21044.2i	0.718197	+	1.24395i	−0.243516	+	0.969897i	$0.578301\pi$
$660$	−5621.35	+	9736.46i	−0.331531	+	0.574229i
$661$	−25907.2	−	14957.5i	−1.52447	−	0.880151i	−0.999580	−	0.0289779i	$-0.990775\pi$
$661$	−25907.2	−	14957.5i	−1.52447	−	0.880151i	−0.524886	−	0.851173i	$-0.675892\pi$
$662$	−8335.03			−0.489350
$663$	−585.373	+	10.2259i	−0.0342896	+	0.000599008i
$664$	−41347.1			−2.41653
$665$	925.988	+	534.620i	0.0539974	+	0.0311754i
$666$	4241.28	−	7346.11i	0.246766	−	0.427412i
$667$	6081.32	+	10533.2i	0.353028	+	0.611462i
$668$			3155.69i			0.182780i
$669$	−6010.63	+	3470.24i	−0.347361	+	0.200549i
$670$	280.703	−	162.064i	0.0161858	−	0.00934489i
$671$		−	8005.86i		−	0.460600i
$672$	12152.2	+	21048.3i	0.697593	+	1.20827i
$673$	7746.84	−	13417.9i	0.443713	−	0.768533i	−0.554249	−	0.832351i	$-0.686994\pi$
$673$	7746.84	−	13417.9i	0.443713	−	0.768533i	0.997962	+	0.0638177i	$0.0203276\pi$
$674$	−14822.7	−	8557.90i	−0.847106	−	0.489077i
$675$	3178.71			0.181257
$676$	24194.2	+	38716.3i	1.37654	+	2.20279i
$677$	11729.7			0.665891			0.332945	−	0.942946i	$-0.391958\pi$
$677$	11729.7			0.665891			0.332945	+	0.942946i	$0.391958\pi$
$678$	−17827.3	−	10292.6i	−1.00981	−	0.583017i
$679$	−11002.8	+	19057.4i	−0.621869	+	1.07711i
$680$	−384.849	−	666.578i	−0.0217034	−	0.0375913i
$681$		−	11398.4i		−	0.641390i
$682$	−64088.9	+	37001.8i	−3.59838	+	2.07752i
$683$	−1011.88	+	584.210i	−0.0566889	+	0.0327294i	−0.528077	−	0.849197i	$-0.677087\pi$
$683$	−1011.88	+	584.210i	−0.0566889	+	0.0327294i	0.471388	+	0.881926i	$0.343753\pi$
$684$			4878.48i			0.272709i
$685$	1624.55	+	2813.81i	0.0906145	+	0.156949i
$686$	18549.5	−	32128.7i	1.03240	−	1.78816i
$687$	11226.5	+	6481.61i	0.623459	+	0.359955i
$688$	−10478.9			−0.580675
$689$	−490.786	+	8.57358i	−0.0271371	+	0.000474060i
$690$	−2053.63			−0.113305
$691$	28572.7	+	16496.4i	1.57302	+	0.908183i	0.995796	+	0.0915952i	$0.0291966\pi$
$691$	28572.7	+	16496.4i	1.57302	+	0.908183i	0.577222	+	0.816587i	$0.304137\pi$
$692$	−5598.34	+	9696.62i	−0.307539	+	0.532673i
$693$	−4575.66	−	7925.28i	−0.250815	−	0.434425i
$694$		−	30679.2i		−	1.67805i
$695$	−753.972	+	435.306i	−0.0411508	+	0.0237584i
$696$	−45780.9	+	26431.6i	−2.49328	+	1.43949i
$697$			651.438i			0.0354017i
$698$	−8928.14	−	15464.0i	−0.484147	−	0.838568i
$699$	7919.65	−	13717.2i	0.428539	−	0.742251i
$700$	32209.4	+	18596.1i	1.73914	+	1.00410i
$701$	14785.8			0.796651			0.398326	−	0.917244i	$-0.369591\pi$
$701$	14785.8			0.796651			0.398326	+	0.917244i	$0.369591\pi$
$702$	−5938.12	−	3291.44i	−0.319259	−	0.176962i
$703$	4582.77			0.245864
$704$	−72189.3	−	41678.5i	−3.86468	−	2.23128i
$705$	1432.64	−	2481.41i	0.0765339	−	0.132561i
$706$	33010.5	+	57175.8i	1.75973	+	3.04793i
$707$			13430.6i			0.714442i
$708$	−24031.1	+	13874.4i	−1.27563	+	0.736485i
$709$	10941.4	−	6317.00i	0.579565	−	0.334612i	−0.181395	−	0.983410i	$-0.558061\pi$
$709$	10941.4	−	6317.00i	0.579565	−	0.334612i	0.760961	+	0.648798i	$0.224728\pi$
$710$		−	4125.52i		−	0.218067i
$711$	2464.55	+	4268.73i	0.129997	+	0.225162i
$712$	−7393.39	+	12805.7i	−0.389156	+	0.674038i
$713$	−8452.62	−	4880.12i	−0.443973	−	0.256328i
$714$	1018.70			0.0533947
$715$	4098.01	−	7393.25i	0.214345	−	0.386702i
$716$	−46148.7			−2.40874
$717$	4021.60	+	2321.87i	0.209469	+	0.120937i
$718$	22907.3	−	39676.6i	1.19066	−	2.06228i
$719$	−13648.3	−	23639.5i	−0.707920	−	1.22615i	−0.965627	−	0.259931i	$-0.916300\pi$
$719$	−13648.3	−	23639.5i	−0.707920	−	1.22615i	0.257707	−	0.966223i	$-0.417033\pi$
$720$		−	4891.64i		−	0.253195i
$721$	−16480.1	+	9514.77i	−0.851248	+	0.491468i
$722$	28705.6	−	16573.2i	1.47966	−	0.854279i
$723$		−	14754.0i		−	0.758932i
$724$	39719.2	+	68795.7i	2.03889	+	3.53145i
$725$	−15128.7	+	26203.7i	−0.774987	+	1.34232i
$726$	43801.2	+	25288.6i	2.23914	+	1.29277i
$727$	−4658.21			−0.237639			−0.118819	−	0.992916i	$-0.537911\pi$
$727$	−4658.21			−0.237639			−0.118819	+	0.992916i	$0.537911\pi$
$728$	−25163.2	−	41877.3i	−1.28106	−	2.13197i
$729$	729.000			0.0370370
$730$	−9282.39	−	5359.19i	−0.470626	−	0.271716i
$731$	−108.220	+	187.442i	−0.00547558	+	0.00948399i
$732$	3730.98	+	6462.25i	0.188389	+	0.326300i
$733$			166.474i			0.00838864i	0.999991	+	0.00419432i	$0.00133510\pi$
$733$			166.474i			0.00838864i	−0.999991	+	0.00419432i	$0.998665\pi$
$734$	11599.4	−	6696.93i	0.583300	−	0.336769i
$735$	−783.780	+	452.516i	−0.0393336	+	0.0227092i
$736$		−	25219.4i		−	1.26304i
$737$	−749.370	−	1297.95i	−0.0374537	−	0.0648718i
$738$	−3777.20	+	6542.31i	−0.188402	+	0.326322i
$739$	−11031.5	−	6369.03i	−0.549120	−	0.317035i	0.199647	−	0.979868i	$-0.436020\pi$
$739$	−11031.5	−	6369.03i	−0.549120	−	0.317035i	−0.748767	+	0.662833i	$0.769354\pi$
$740$	−9843.70			−0.489002
$741$	−64.0665	−	3667.42i	−0.00317617	−	0.181817i
$742$	854.092			0.0422570
$743$	−26608.2	−	15362.2i	−1.31381	−	0.758527i	−0.331083	−	0.943602i	$-0.607414\pi$
$743$	−26608.2	−	15362.2i	−1.31381	−	0.758527i	−0.982725	+	0.185074i	$0.940747\pi$
$744$	21210.8	−	36738.1i	1.04519	−	1.81033i
$745$	1521.88	+	2635.97i	0.0748420	+	0.129630i
$746$		−	6131.38i		−	0.300919i
$747$	−4700.35	+	2713.75i	−0.230224	+	0.132920i
$748$	−5011.55	+	2893.42i	−0.244974	+	0.141436i
$749$		−	5193.37i		−	0.253353i
$750$	−5266.62	−	9122.06i	−0.256413	−	0.444121i
$751$	−19769.3	+	34241.4i	−0.960575	+	1.66376i	−0.239514	+	0.970893i	$0.576988\pi$
$751$	−19769.3	+	34241.4i	−0.960575	+	1.66376i	−0.721061	+	0.692872i	$0.756345\pi$
$752$	61837.0	+	35701.6i	2.99862	+	1.73126i
$753$	−3467.34			−0.167805
$754$	55394.8	−	33285.6i	2.67555	−	1.60768i
$755$	−7928.35			−0.382175
$756$	7386.86	+	4264.80i	0.355367	+	0.205171i
$757$	−11517.6	+	19949.0i	−0.552990	+	0.957807i	0.445067	+	0.895497i	$0.353180\pi$
$757$	−11517.6	+	19949.0i	−0.552990	+	0.957807i	−0.998057	+	0.0623093i	$0.980153\pi$
$758$	32676.1	+	56596.6i	1.56576	+	2.71198i
$759$			9495.81i			0.454119i
$760$	4176.18	−	2411.12i	0.199323	−	0.115079i
$761$	28106.0	−	16227.0i	1.33882	−	0.772968i	0.352187	−	0.935930i	$-0.385438\pi$
$761$	28106.0	−	16227.0i	1.33882	−	0.772968i	0.986632	+	0.162962i	$0.0521047\pi$
$762$			17926.0i			0.852220i
$763$	−5892.30	−	10205.8i	−0.279575	−	0.484238i
$764$	35993.4	−	62342.4i	1.70444	−	2.95218i
$765$	−87.4996	−	50.5179i	−0.00413536	−	0.00238755i
$766$	−54616.1			−2.57619
$767$	17883.3	−	10745.7i	0.841890	−	0.505874i
$768$	9080.40			0.426641
$769$	−27900.1	−	16108.1i	−1.30833	−	0.755362i	−0.326509	−	0.945194i	$-0.605873\pi$
$769$	−27900.1	−	16108.1i	−1.30833	−	0.755362i	−0.981817	+	0.189831i	$0.939206\pi$
$770$	−7354.10	+	12737.7i	−0.344186	+	0.596148i
$771$	3527.93	+	6110.55i	0.164793	+	0.285429i
$772$		−	97613.2i		−	4.55075i
$773$	−2532.78	+	1462.30i	−0.117849	+	0.0680404i	−0.557766	−	0.829998i	$-0.688341\pi$
$773$	−2532.78	+	1462.30i	−0.117849	+	0.0680404i	0.439917	+	0.898039i	$0.355008\pi$
$774$	−2173.67	+	1254.97i	−0.100945	+	0.0582804i
$775$		−	24280.9i		−	1.12541i
$776$	49622.3	+	85948.4i	2.29554	+	3.97599i
$777$	4006.29	−	6939.10i	0.184974	−	0.320384i
$778$	27159.6	+	15680.6i	1.25157	+	0.722593i
$779$	−4081.32			−0.187713
$780$	137.614	+	7877.55i	0.00631713	+	0.361618i
$781$	−19076.1			−0.874001
$782$	−915.427	−	528.522i	−0.0418614	−	0.0241687i
$783$	−3469.59	+	6009.51i	−0.158357	+	0.274282i
$784$	−11276.8	−	19531.9i	−0.513701	−	0.889755i
$785$		−	1697.03i		−	0.0771586i
$786$	29271.5	−	16899.9i	1.32834	−	0.766920i
$787$	22089.8	−	12753.6i	1.00053	−	0.577656i	0.0921250	−	0.995747i	$-0.470634\pi$
$787$	22089.8	−	12753.6i	1.00053	−	0.577656i	0.908405	+	0.418091i	$0.137301\pi$
$788$		−	60011.1i		−	2.71295i
$789$	−8282.82	−	14346.3i	−0.373734	−	0.647326i
$790$	3961.08	−	6860.79i	0.178391	−	0.308982i
$791$	−16839.6	−	9722.34i	−0.756949	−	0.437025i
$792$	−41272.2			−1.85170
$793$	−2889.65	−	4809.03i	−0.129400	−	0.215351i
$794$	13416.8			0.599677
$795$	−73.3610	−	42.3550i	−0.00327276	−	0.00188953i
$796$	−654.674	+	1133.93i	−0.0291512	+	0.0504913i
$797$	2724.49	+	4718.95i	0.121087	+	0.209729i	0.920197	−	0.391457i	$-0.128029\pi$
$797$	2724.49	+	4718.95i	0.121087	+	0.209729i	−0.799110	+	0.601185i	$0.794695\pi$
$798$			6382.24i			0.283119i
$799$	1277.23	−	737.409i	0.0565521	−	0.0326504i
$800$	54333.6	−	31369.5i	2.40123	−	1.38635i
$801$			1941.01i			0.0856209i
$802$	−24648.9	−	42693.1i	−1.08526	−	1.87973i
$803$	−24780.5	+	42921.0i	−1.08902	+	1.88624i
$804$	1209.77	+	698.459i	0.0530661	+	0.0306378i
$805$	−1939.85			−0.0849324
$806$	−25142.0	+	45358.9i	−1.09875	+	1.98226i
$807$	11750.9			0.512577
$808$	52456.6	+	30285.8i	2.28393	+	1.31863i
$809$	1226.56	−	2124.46i	0.0533048	−	0.0923266i	−0.838142	−	0.545452i	$-0.816358\pi$
$809$	1226.56	−	2124.46i	0.0533048	−	0.0923266i	0.891447	+	0.453126i	$0.149691\pi$
$810$	−585.831	−	1014.69i	−0.0254124	−	0.0440155i
$811$			5133.85i			0.222286i	0.993804	+	0.111143i	$0.0354512\pi$
$811$			5133.85i			0.222286i	−0.993804	+	0.111143i	$0.964549\pi$
$812$	−70313.8	+	40595.7i	−3.03883	+	1.75447i
$813$	−7216.23	+	4166.29i	−0.311297	+	0.179727i
$814$			63039.4i			2.71441i
$815$	532.404	+	922.150i	0.0228826	+	0.0396338i
$816$	1258.91	−	2180.50i	0.0540083	−	0.0935451i
$817$	−1174.34	−	678.007i	−0.0502877	−	0.0290336i
$818$	49432.6			2.11292
$819$	−5609.11	−	3109.08i	−0.239314	−	0.132650i
$820$	8766.61			0.373345
$821$	−20658.1	−	11927.0i	−0.878166	−	0.507009i	−0.00811266	−	0.999967i	$-0.502582\pi$
$821$	−20658.1	−	11927.0i	−0.878166	−	0.507009i	−0.870053	+	0.492958i	$0.835916\pi$
$822$	−9696.88	+	16795.5i	−0.411457	+	0.712664i
$823$	378.578	+	655.716i	0.0160345	+	0.0277726i	0.873931	−	0.486049i	$-0.161563\pi$
$823$	378.578	+	655.716i	0.0160345	+	0.0277726i	−0.857897	+	0.513822i	$0.828229\pi$
$824$			85822.6i			3.62836i
$825$	−20458.1	+	11811.5i	−0.863347	+	0.498454i
$826$	−31438.6	+	18151.1i	−1.32432	+	0.764597i
$827$			28621.2i			1.20345i	0.798702	+	0.601726i	$0.205520\pi$
$827$			28621.2i			1.20345i	−0.798702	+	0.601726i	$0.794480\pi$
$828$	−4425.34	−	7664.92i	−0.185738	−	0.321708i
$829$	13714.6	−	23754.4i	0.574582	−	0.995204i	−0.421505	−	0.906826i	$-0.638498\pi$
$829$	13714.6	−	23754.4i	0.574582	−	0.995204i	0.996087	−	0.0883785i	$-0.0281685\pi$
$830$	7554.50	+	4361.59i	0.315928	+	0.182401i
$831$	−19749.2			−0.824421
$832$	−58406.8	+	1020.31i	−2.43376	+	0.0425156i
$833$	−465.838			−0.0193761
$834$	−4500.43	−	2598.32i	−0.186855	−	0.107881i
$835$	204.731	−	354.604i	0.00848503	−	0.0146965i
$836$	−18127.6	−	31397.9i	−0.749946	−	1.29894i
$837$		−	5568.54i		−	0.229960i
$838$	−30172.9	+	17420.4i	−1.24380	+	0.718110i
$839$	−4012.83	+	2316.81i	−0.165123	+	0.0953339i	−0.580284	−	0.814414i	$-0.697059\pi$
$839$	−4012.83	+	2316.81i	−0.165123	+	0.0953339i	0.415161	+	0.909748i	$0.363725\pi$
$840$		−	8431.27i		−	0.346317i
$841$	−20831.8	−	36081.7i	−0.854147	−	1.47943i
$842$	−8206.85	+	14214.7i	−0.335899	+	0.581794i
$843$	−7460.79	−	4307.49i	−0.304820	−	0.175988i
$844$	21813.0			0.889614
$845$	−206.904	−	5920.18i	−0.00842331	−	0.241018i
$846$	17102.7			0.695041
$847$	41374.3	+	23887.5i	1.67844	+	0.969048i
$848$	1055.49	−	1828.17i	0.0427426	−	0.0740324i
$849$	11277.1	+	19532.4i	0.455863	+	0.789578i
$850$		−	2629.64i		−	0.106113i
$851$	−7200.30	+	4157.10i	−0.290039	+	0.167454i
$852$	15398.0	−	8890.03i	0.619162	−	0.357474i
$853$		−	14854.6i		−	0.596261i	−0.954525	−	0.298131i	$-0.903637\pi$
$853$		−	14854.6i		−	0.596261i	0.954525	−	0.298131i	$-0.0963631\pi$
$854$	4881.03	+	8454.20i	0.195580	+	0.338755i
$855$	316.500	−	548.194i	0.0126597	−	0.0219273i
$856$	−20284.0	−	11711.0i	−0.809921	−	0.467608i
$857$	42799.5			1.70595			0.852977	−	0.521948i	$-0.174794\pi$
$857$	42799.5			1.70595			0.852977	+	0.521948i	$0.174794\pi$
$858$	50448.1	−	881.283i	2.00731	−	0.0350658i
$859$	−8246.47			−0.327551			−0.163775	−	0.986498i	$-0.552367\pi$
$859$	−8246.47			−0.327551			−0.163775	+	0.986498i	$0.552367\pi$
$860$	2522.47	+	1456.35i	0.100018	+	0.0577454i
$861$	−3567.92	+	6179.83i	−0.141225	+	0.244608i
$862$	−21290.1	−	36875.5i	−0.841232	−	1.45706i
$863$		−	17695.4i		−	0.697983i	−0.937126	−	0.348991i	$-0.886524\pi$
$863$		−	17695.4i		−	0.697983i	0.937126	−	0.348991i	$-0.113476\pi$
$864$	12460.8	−	7194.24i	0.490653	−	0.283279i
$865$	1258.17	−	726.405i	0.0494556	−	0.0285532i
$866$		−	39132.3i		−	1.53553i
$867$	7343.50	+	12719.3i	0.287657	+	0.498236i
$868$	32577.1	−	56425.2i	1.27389	−	2.20645i
$869$	−31723.7	−	18315.7i	−1.23838	−	0.714980i
$870$	11152.8			0.434615
$871$	−918.621	−	509.183i	−0.0357363	−	0.0198083i
$872$	−53148.2			−2.06402
$873$	11282.2	+	6513.77i	0.437393	+	0.252529i
$874$	3311.24	−	5735.24i	0.128152	−	0.221965i
$875$	−4974.82	−	8616.64i	−0.192205	−	0.332909i
$876$		−	46193.8i		−	1.78167i
$877$	12424.7	−	7173.38i	0.478393	−	0.276200i	−0.241353	−	0.970437i	$-0.577591\pi$
$877$	12424.7	−	7173.38i	0.478393	−	0.276200i	0.719747	+	0.694237i	$0.244258\pi$
$878$	−70687.3	+	40811.3i	−2.71706	+	1.56870i
$879$			13519.7i			0.518781i
$880$	18176.5	+	31482.6i	0.696283	+	1.20600i
$881$	−1031.76	+	1787.06i	−0.0394560	+	0.0683399i	−0.885079	−	0.465441i	$-0.845896\pi$
$881$	−1031.76	+	1787.06i	−0.0394560	+	0.0683399i	0.845623	+	0.533781i	$0.179229\pi$
$882$	−4678.35	−	2701.05i	−0.178603	−	0.103117i
$883$	34137.1			1.30103			0.650513	−	0.759495i	$-0.274554\pi$
$883$	34137.1			1.30103			0.650513	+	0.759495i	$0.274554\pi$
$884$	−1966.03	+	3546.92i	−0.0748016	+	0.134950i
$885$	3600.50			0.136756
$886$	−7048.22	−	4069.29i	−0.267257	−	0.154301i
$887$	11119.2	−	19259.1i	0.420910	−	0.729038i	−0.575118	−	0.818070i	$-0.695044\pi$
$887$	11119.2	−	19259.1i	0.420910	−	0.729038i	0.996029	+	0.0890320i	$0.0283773\pi$
$888$	−18068.2	−	31295.1i	−0.682805	−	1.18265i
$889$			16932.8i			0.638817i
$890$	2701.68	−	1559.82i	0.101753	−	0.0587474i
$891$	−4691.84	+	2708.84i	−0.176411	+	0.101851i
$892$			48075.0i			1.80456i
$893$	4619.94	+	8001.98i	0.173125	+	0.299861i
$894$	−9084.02	+	15734.0i	−0.339838	+	0.588617i
$895$	5185.72	+	2993.98i	0.193676	+	0.111819i
$896$	36830.7			1.37325
$897$	3427.43	+	5704.02i	0.127579	+	0.212321i
$898$	3783.45			0.140596
$899$	45904.3	+	26502.8i	1.70300	+	0.983225i
$900$	11009.1	−	19068.3i	0.407743	−	0.706232i
$901$	−21.8010	−	37.7604i	−0.000806100	−	0.00139621i
$902$		−	56141.7i		−	2.07241i
$903$	−2053.24	+	1185.44i	−0.0756673	+	0.0436865i
$904$	−75946.0	+	43847.5i	−2.79417	+	1.61321i
$905$		−	10307.4i		−	0.378597i
$906$	−23662.0	−	40983.8i	−0.867679	−	1.50286i
$907$	−22080.2	+	38243.9i	−0.808335	+	1.40008i	0.105682	+	0.994400i	$0.466297\pi$
$907$	−22080.2	+	38243.9i	−0.808335	+	1.40008i	−0.914017	+	0.405677i	$0.867036\pi$
$908$	−68376.0	−	39476.9i	−2.49905	−	1.44283i
$909$	7951.05			0.290121
$910$	180.032	+	10305.8i	0.00655826	+	0.375421i
$911$	11916.3			0.433376			0.216688	−	0.976241i	$-0.430475\pi$
$911$	11916.3			0.433376			0.216688	+	0.976241i	$0.430475\pi$
$912$	13661.1	+	7887.22i	0.496012	+	0.286373i
$913$	20167.6	−	34931.4i	0.731053	−	1.26622i
$914$	19521.5	+	33812.2i	0.706470	+	1.22364i
$915$		−	968.215i		−	0.0349816i
$916$	77763.0	−	44896.5i	2.80498	−	1.61946i
$917$	27649.6	−	15963.5i	0.995716	−	0.574877i
$918$		−	603.078i		−	0.0216825i
$919$	10064.5	+	17432.2i	0.361258	+	0.625717i	0.988168	−	0.153375i	$-0.0490141\pi$
$919$	10064.5	+	17432.2i	0.361258	+	0.625717i	−0.626910	+	0.779091i	$0.715681\pi$
$920$	−4374.32	+	7576.55i	−0.156758	+	0.271512i
$921$	−24782.8	−	14308.3i	−0.886667	−	0.511917i
$922$	10525.0			0.375945
$923$	−11458.8	+	6885.34i	−0.408635	+	0.245540i
$924$	−63389.0			−2.25687
$925$	−17912.4	−	10341.7i	−0.636710	−	0.367605i
$926$	−27827.1	+	48197.9i	−0.987531	+	1.71045i
$927$	5632.83	+	9756.35i	0.199575	+	0.345675i
$928$			136961.i			4.84478i
$929$	27217.8	−	15714.2i	0.961234	−	0.554969i	0.0646814	−	0.997906i	$-0.479397\pi$
$929$	27217.8	−	15714.2i	0.961234	−	0.554969i	0.896553	+	0.442937i	$0.146064\pi$
$930$	−7750.81	+	4474.93i	−0.273289	+	0.157784i
$931$		−	2918.52i		−	0.102740i
$932$	−54857.5	−	95016.0i	−1.92802	−	3.33943i
$933$	−11199.4	+	19398.0i	−0.392983	+	0.680666i
$934$	40833.2	+	23575.1i	1.43052	+	0.825909i
$935$	750.863			0.0262629
$936$	−24791.7	+	14896.9i	−0.865751	+	0.520212i
$937$	42473.2			1.48083			0.740416	−	0.672149i	$-0.234629\pi$
$937$	42473.2			1.48083			0.740416	+	0.672149i	$0.234629\pi$
$938$	1582.67	+	913.756i	0.0550917	+	0.0318072i
$939$	2732.47	−	4732.78i	0.0949636	−	0.164482i
$940$	−9923.56	−	17188.1i	−0.344331	−	0.596398i
$941$			42644.0i			1.47732i	0.674079	+	0.738659i	$0.264541\pi$
$941$			42644.0i			1.47732i	−0.674079	+	0.738659i	$0.735459\pi$
$942$	8772.39	−	5064.74i	0.303418	−	0.175179i
$943$	6412.45	−	3702.23i	0.221440	−	0.127849i
$944$			89725.0i			3.09354i
$945$	−553.373	−	958.470i	−0.0190489	−	0.0329937i
$946$	9326.50	−	16154.0i	0.320540	−	0.555191i
$947$	−3709.14	−	2141.47i	−0.127277	−	0.0734831i	0.435010	−	0.900426i	$-0.356745\pi$
$947$	−3709.14	−	2141.47i	−0.127277	−	0.0734831i	−0.562286	+	0.826943i	$0.690078\pi$
$948$	34142.7			1.16973
$949$	606.639	+	34726.5i	0.0207506	+	1.18785i
$950$	16475.0			0.562651
$951$	8119.35	+	4687.71i	0.276854	+	0.159842i
$952$	2169.87	−	3758.33i	0.0738718	−	0.127950i
$953$	20297.0	+	35155.4i	0.689908	+	1.19496i	0.971867	+	0.235530i	$0.0756826\pi$
$953$	20297.0	+	35155.4i	0.689908	+	1.19496i	−0.281959	+	0.959427i	$0.590984\pi$
$954$		−	505.630i		−	0.0171597i
$955$	−8089.14	+	4670.27i	−0.274093	+	0.158247i
$956$	27856.7	−	16083.1i	0.942415	−	0.544104i
$957$		−	51569.6i		−	1.74191i
$958$	−29886.0	−	51764.0i	−1.00790	−	1.74574i
$959$	−9159.61	+	15864.9i	−0.308425	+	0.534207i
$960$	−8730.45	−	5040.53i	−0.293515	−	0.169461i
$961$	−12744.8			−0.427808
$962$	22753.5	+	37867.1i	0.762582	+	1.26911i
$963$	−3074.52			−0.102882
$964$	−88505.6	−	51098.8i	−2.95703	−	1.70724i
$965$	−6332.83	+	10968.8i	−0.211255	+	0.365904i
$966$	−5789.43	−	10027.6i	−0.192828	−	0.333988i
$967$		−	17709.4i		−	0.588931i	−0.955662	−	0.294466i	$-0.904858\pi$
$967$		−	17709.4i		−	0.588931i	0.955662	−	0.294466i	$-0.0951416\pi$
$968$	186597.	−	107732.i	6.19572	−	3.57710i
$969$	282.166	−	162.909i	0.00935448	−	0.00540081i
$970$		−	20938.1i		−	0.693074i
$971$	−2019.49	−	3497.85i	−0.0667440	−	0.115604i	0.830722	−	0.556687i	$-0.187928\pi$
$971$	−2019.49	−	3497.85i	−0.0667440	−	0.115604i	−0.897466	+	0.441083i	$0.854594\pi$
$972$	2524.80	−	4373.09i	0.0833159	−	0.144307i
$973$	−4251.08	−	2454.36i	−0.140065	−	0.0808666i
$974$	−105366.			−3.46626
$975$	−8025.71	+	14479.2i	−0.263619	+	0.475597i
$976$	24128.1			0.791312
$977$	−2393.95	−	1382.15i	−0.0783924	−	0.0452598i	0.460291	−	0.887768i	$-0.347745\pi$
$977$	−2393.95	−	1382.15i	−0.0783924	−	0.0452598i	−0.538684	+	0.842508i	$0.681078\pi$
$978$	−3177.89	+	5504.27i	−0.103904	+	0.179967i
$979$	−7212.46	−	12492.4i	−0.235456	−	0.407822i
$980$			6268.93i			0.204340i
$981$	−6041.91	+	3488.30i	−0.196639	+	0.113530i
$982$	15844.3	−	9147.69i	0.514879	−	0.297265i
$983$		−	17804.5i		−	0.577695i	−0.957375	−	0.288848i	$-0.906728\pi$
$983$		−	17804.5i		−	0.577695i	0.957375	−	0.288848i	$-0.0932721\pi$
$984$	16091.2	+	27870.8i	0.521310	+	0.902936i
$985$	−3893.32	+	6743.43i	−0.125941	+	0.218136i
$986$	4971.48	+	2870.28i	0.160572	+	0.0927064i
$987$	16155.2			0.520997
$988$	−22221.8	−	12317.3i	−0.715557	−	0.396626i
$989$	2460.12			0.0790974
$990$	7540.82	+	4353.69i	0.242084	+	0.139767i
$991$	4064.84	−	7040.52i	0.130297	−	0.225680i	−0.793494	−	0.608578i	$-0.791740\pi$
$991$	4064.84	−	7040.52i	0.130297	−	0.225680i	0.923791	+	0.382897i	$0.125074\pi$
$992$	−54953.9	−	95182.9i	−1.75886	−	3.04643i
$993$			4661.02i			0.148956i
$994$	20144.3	−	11630.3i	0.642796	−	0.371119i
$995$	147.131	−	84.9463i	0.00468781	−	0.00270651i
$996$			37595.0i			1.19603i
$997$	14726.4	+	25507.0i	0.467795	+	0.810244i	0.999323	−	0.0367966i	$-0.0117154\pi$
$997$	14726.4	+	25507.0i	0.467795	+	0.810244i	−0.531528	+	0.847041i	$0.678382\pi$
$998$	13498.8	−	23380.7i	0.428154	−	0.741585i
$999$	−4108.01	−	2371.76i	−0.130102	−	0.0751143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.c.4.1	✓	10
3.2	odd	2		117.4.q.e.82.5		10
4.3	odd	2		624.4.bv.h.433.3		10
13.4	even	6		507.4.b.i.337.1		10
13.6	odd	12		507.4.a.r.1.10		10
13.7	odd	12		507.4.a.r.1.1		10
13.9	even	3		507.4.b.i.337.10		10
13.10	even	6	inner	39.4.j.c.10.1	yes	10
39.20	even	12		1521.4.a.bk.1.10		10
39.23	odd	6		117.4.q.e.10.5		10
39.32	even	12		1521.4.a.bk.1.1		10
52.23	odd	6		624.4.bv.h.49.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.1	✓	10	1.1	even	1	trivial
39.4.j.c.10.1	yes	10	13.10	even	6	inner
117.4.q.e.10.5		10	39.23	odd	6
117.4.q.e.82.5		10	3.2	odd	2
507.4.a.r.1.1		10	13.7	odd	12
507.4.a.r.1.10		10	13.6	odd	12
507.4.b.i.337.1		10	13.4	even	6
507.4.b.i.337.10		10	13.9	even	3
624.4.bv.h.49.3		10	52.23	odd	6
624.4.bv.h.433.3		10	4.3	odd	2
1521.4.a.bk.1.1		10	39.32	even	12
1521.4.a.bk.1.10		10	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-4.64599 - 2.68236i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(10.3901 + 17.9962i) q^{4} -2.69631i q^{5} +(13.9380 - 8.04709i) q^{6} +(13.1657 - 7.60123i) q^{7} -68.5626i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-7.23249 + 12.5270i) q^{10} +(57.9240 + 33.4424i) q^{11} -62.3408 q^{12} +(46.8650 - 0.818689i) q^{13} -81.5570 q^{14} +(7.00522 + 4.04447i) q^{15} +(-100.789 + 174.571i) q^{16} +(2.08177 + 3.60573i) q^{17} +48.2825i q^{18} +(-22.5903 + 13.0425i) q^{19} +(48.5235 - 28.0150i) q^{20} +45.6074i q^{21} +(-179.409 - 310.746i) q^{22} +(23.6621 - 40.9839i) q^{23} +(178.131 + 102.844i) q^{24} +117.730 q^{25} +(-219.930 - 121.905i) q^{26} +27.0000 q^{27} +(273.587 + 157.956i) q^{28} +(-128.503 + 222.575i) q^{29} +(-21.6975 - 37.5811i) q^{30} -206.242i q^{31} +(461.511 - 266.453i) q^{32} +(-173.772 + 100.327i) q^{33} -22.3362i q^{34} +(-20.4953 - 35.4989i) q^{35} +(93.5112 - 161.966i) q^{36} +(-152.149 - 87.8430i) q^{37} +139.939 q^{38} +(-68.1705 + 122.987i) q^{39} -184.866 q^{40} +(135.501 + 78.2313i) q^{41} +(122.336 - 211.891i) q^{42} +(25.9922 + 45.0199i) q^{43} +1389.88i q^{44} +(-21.0157 + 12.1334i) q^{45} +(-219.868 + 126.941i) q^{46} -354.222i q^{47} +(-302.366 - 523.714i) q^{48} +(-55.9425 + 96.8953i) q^{49} +(-546.972 - 315.794i) q^{50} -12.4906 q^{51} +(501.667 + 834.888i) q^{52} -10.4723 q^{53} +(-125.442 - 72.4238i) q^{54} +(90.1712 - 156.181i) q^{55} +(-521.160 - 902.676i) q^{56} -78.2550i q^{57} +(1194.05 - 689.386i) q^{58} +(385.480 - 222.557i) q^{59} +168.090i q^{60} +(-59.8481 - 103.660i) q^{61} +(-553.216 + 958.199i) q^{62} +(-118.491 - 68.4111i) q^{63} -1246.28 q^{64} +(-2.20744 - 126.363i) q^{65} +1076.46 q^{66} +(-19.4057 - 11.2039i) q^{67} +(-43.2597 + 74.9281i) q^{68} +(70.9863 + 122.952i) q^{69} +219.903i q^{70} +(-246.997 + 142.604i) q^{71} +(-534.393 + 308.532i) q^{72} +740.989i q^{73} +(471.253 + 816.235i) q^{74} +(-176.595 + 305.871i) q^{75} +(-469.432 - 271.027i) q^{76} +1016.81 q^{77} +(646.615 - 388.538i) q^{78} -547.679 q^{79} +(470.698 + 271.758i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-419.689 - 726.923i) q^{82} -603.056i q^{83} +(-820.762 + 473.867i) q^{84} +(9.72218 - 5.61310i) q^{85} -278.882i q^{86} +(-385.510 - 667.724i) q^{87} +(2292.90 - 3971.42i) q^{88} +(-186.774 - 107.834i) q^{89} +130.185 q^{90} +(610.789 - 367.011i) q^{91} +983.409 q^{92} +(535.833 + 309.363i) q^{93} +(-950.153 + 1645.71i) q^{94} +(35.1666 + 60.9104i) q^{95} +1598.72i q^{96} +(-1253.58 + 723.752i) q^{97} +(519.817 - 300.116i) q^{98} -601.964i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Introduction

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