LMFDB - Embedded newform 143.4.e.b.100.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.17
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.55281 - 4.42160i) q^{2} +(-2.28752 + 3.96210i) q^{3} +(-9.03368 - 15.6468i) q^{4} -15.4387 q^{5} +(11.6792 + 20.2290i) q^{6} +(8.38111 + 14.5165i) q^{7} -51.4001 q^{8} +(3.03450 + 5.25591i) q^{9} +O(q^{10})$	\(q+(2.55281 - 4.42160i) q^{2} +(-2.28752 + 3.96210i) q^{3} +(-9.03368 - 15.6468i) q^{4} -15.4387 q^{5} +(11.6792 + 20.2290i) q^{6} +(8.38111 + 14.5165i) q^{7} -51.4001 q^{8} +(3.03450 + 5.25591i) q^{9} +(-39.4122 + 68.2639i) q^{10} +(-5.50000 + 9.52628i) q^{11} +82.6589 q^{12} +(-41.5410 + 21.7106i) q^{13} +85.5815 q^{14} +(35.3164 - 61.1699i) q^{15} +(-58.9453 + 102.096i) q^{16} +(7.01083 + 12.1431i) q^{17} +30.9860 q^{18} +(-37.7325 - 65.3546i) q^{19} +(139.469 + 241.567i) q^{20} -76.6878 q^{21} +(28.0809 + 48.6376i) q^{22} +(-92.5550 + 160.310i) q^{23} +(117.579 - 203.652i) q^{24} +113.355 q^{25} +(-10.0508 + 239.100i) q^{26} -151.292 q^{27} +(151.424 - 262.275i) q^{28} +(66.6645 - 115.466i) q^{29} +(-180.312 - 312.310i) q^{30} -251.441 q^{31} +(95.3518 + 165.154i) q^{32} +(-25.1627 - 43.5831i) q^{33} +71.5893 q^{34} +(-129.394 - 224.117i) q^{35} +(54.8254 - 94.9604i) q^{36} +(37.8807 - 65.6113i) q^{37} -385.296 q^{38} +(9.00632 - 214.253i) q^{39} +793.553 q^{40} +(-83.1930 + 144.094i) q^{41} +(-195.769 + 339.083i) q^{42} +(15.5619 + 26.9540i) q^{43} +198.741 q^{44} +(-46.8489 - 81.1447i) q^{45} +(472.551 + 818.482i) q^{46} +136.902 q^{47} +(-269.677 - 467.094i) q^{48} +(31.0141 - 53.7180i) q^{49} +(289.374 - 501.210i) q^{50} -64.1497 q^{51} +(714.968 + 453.856i) q^{52} +493.058 q^{53} +(-386.220 + 668.952i) q^{54} +(84.9131 - 147.074i) q^{55} +(-430.790 - 746.150i) q^{56} +345.256 q^{57} +(-340.364 - 589.527i) q^{58} +(-48.0816 - 83.2798i) q^{59} -1276.15 q^{60} +(-313.014 - 542.156i) q^{61} +(-641.881 + 1111.77i) q^{62} +(-50.8650 + 88.1007i) q^{63} +30.5359 q^{64} +(641.340 - 335.184i) q^{65} -256.943 q^{66} +(-496.312 + 859.638i) q^{67} +(126.667 - 219.394i) q^{68} +(-423.443 - 733.425i) q^{69} -1321.27 q^{70} +(71.0041 + 122.983i) q^{71} +(-155.974 - 270.154i) q^{72} -997.470 q^{73} +(-193.405 - 334.986i) q^{74} +(-259.302 + 449.124i) q^{75} +(-681.727 + 1180.79i) q^{76} -184.384 q^{77} +(-924.348 - 586.769i) q^{78} +1201.94 q^{79} +(910.041 - 1576.24i) q^{80} +(264.152 - 457.525i) q^{81} +(424.752 + 735.692i) q^{82} +1123.45 q^{83} +(692.773 + 1199.92i) q^{84} +(-108.238 - 187.475i) q^{85} +158.906 q^{86} +(304.993 + 528.263i) q^{87} +(282.701 - 489.652i) q^{88} +(-426.651 + 738.981i) q^{89} -478.385 q^{90} +(-663.321 - 421.071i) q^{91} +3344.45 q^{92} +(575.177 - 996.235i) q^{93} +(349.485 - 605.325i) q^{94} +(582.543 + 1008.99i) q^{95} -872.477 q^{96} +(357.886 + 619.876i) q^{97} +(-158.346 - 274.264i) q^{98} -66.7590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.55281	−	4.42160i	0.902555	−	1.56327i	0.0783883	−	0.996923i	$-0.475023\pi$
$2$	2.55281	−	4.42160i	0.902555	−	1.56327i	0.824166	−	0.566348i	$-0.191644\pi$
$3$	−2.28752	+	3.96210i	−0.440233	+	0.762507i	−0.997707	−	0.0676883i	$-0.978438\pi$
$3$	−2.28752	+	3.96210i	−0.440233	+	0.762507i	0.557473	+	0.830195i	$0.311771\pi$
$4$	−9.03368	−	15.6468i	−1.12921	−	1.95585i
$5$	−15.4387			−1.38088			−0.690442	−	0.723388i	$-0.742584\pi$
$5$	−15.4387			−1.38088			−0.690442	+	0.723388i	$0.742584\pi$
$6$	11.6792	+	20.2290i	0.794670	+	1.37641i
$7$	8.38111	+	14.5165i	0.452537	+	0.783817i	0.998543	−	0.0539641i	$-0.0171856\pi$
$7$	8.38111	+	14.5165i	0.452537	+	0.783817i	−0.546006	+	0.837781i	$0.683852\pi$
$8$	−51.4001			−2.27159
$9$	3.03450	+	5.25591i	0.112389	+	0.194663i
$10$	−39.4122	+	68.2639i	−1.24632	+	2.15869i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	82.6589			1.98846
$13$	−41.5410	+	21.7106i	−0.886261	+	0.463187i
$13$	−41.5410	+	21.7106i	−0.886261	+	0.463187i
$14$	85.5815			1.63376
$15$	35.3164	−	61.1699i	0.607911	−	1.05293i
$16$	−58.9453	+	102.096i	−0.921020	+	1.59525i
$17$	7.01083	+	12.1431i	0.100022	+	0.173243i	0.911694	−	0.410871i	$-0.134775\pi$
$17$	7.01083	+	12.1431i	0.100022	+	0.173243i	−0.811671	+	0.584114i	$0.801442\pi$
$18$	30.9860			0.405749
$19$	−37.7325	−	65.3546i	−0.455602	−	0.789125i	0.543121	−	0.839655i	$-0.317243\pi$
$19$	−37.7325	−	65.3546i	−0.455602	−	0.789125i	−0.998723	+	0.0505291i	$0.983909\pi$
$20$	139.469	+	241.567i	1.55931	+	2.70080i
$21$	−76.6878			−0.796888
$22$	28.0809	+	48.6376i	0.272130	+	0.471344i
$23$	−92.5550	+	160.310i	−0.839089	+	1.45335i	0.0515678	+	0.998669i	$0.483578\pi$
$23$	−92.5550	+	160.310i	−0.839089	+	1.45335i	−0.890657	+	0.454676i	$0.849755\pi$
$24$	117.579	−	203.652i	1.00003	−	1.73210i
$25$	113.355			0.906839
$26$	−10.0508	+	239.100i	−0.0758125	+	1.80352i
$27$	−151.292			−1.07838
$28$	151.424	−	262.275i	1.02202	−	1.77019i
$29$	66.6645	−	115.466i	0.426872	−	0.739364i	−0.569721	−	0.821838i	$-0.692949\pi$
$29$	66.6645	−	115.466i	0.426872	−	0.739364i	0.996593	+	0.0824739i	$0.0262821\pi$
$30$	−180.312	−	312.310i	−1.09735	−	1.90066i
$31$	−251.441			−1.45678			−0.728390	−	0.685163i	$-0.759731\pi$
$31$	−251.441			−1.45678			−0.728390	+	0.685163i	$0.759731\pi$
$32$	95.3518	+	165.154i	0.526749	+	0.912357i
$33$	−25.1627	−	43.5831i	−0.132735	−	0.229904i
$34$	71.5893			0.361102
$35$	−129.394	−	224.117i	−0.624901	−	1.08236i
$36$	54.8254	−	94.9604i	0.253821	−	0.439632i
$37$	37.8807	−	65.6113i	0.168312	−	0.291525i	−0.769514	−	0.638629i	$-0.779502\pi$
$37$	37.8807	−	65.6113i	0.168312	−	0.291525i	0.937827	+	0.347104i	$0.112835\pi$
$38$	−385.296			−1.64482
$39$	9.00632	−	214.253i	0.0369786	−	0.879690i
$40$	793.553			3.13679
$41$	−83.1930	+	144.094i	−0.316892	+	0.548873i	−0.979838	−	0.199795i	$-0.935973\pi$
$41$	−83.1930	+	144.094i	−0.316892	+	0.548873i	0.662946	+	0.748667i	$0.269306\pi$
$42$	−195.769	+	339.083i	−0.719235	+	1.24575i
$43$	15.5619	+	26.9540i	0.0551899	+	0.0955918i	0.892300	−	0.451442i	$-0.149090\pi$
$43$	15.5619	+	26.9540i	0.0551899	+	0.0955918i	−0.837110	+	0.547034i	$0.815757\pi$
$44$	198.741			0.680939
$45$	−46.8489	−	81.1447i	−0.155196	−	0.268807i
$46$	472.551	+	818.482i	1.51465	+	2.62345i
$47$	136.902			0.424876			0.212438	−	0.977175i	$-0.431860\pi$
$47$	136.902			0.424876			0.212438	+	0.977175i	$0.431860\pi$
$48$	−269.677	−	467.094i	−0.810928	−	1.40457i
$49$	31.0141	−	53.7180i	0.0904202	−	0.156612i
$50$	289.374	−	501.210i	0.818472	−	1.41764i
$51$	−64.1497			−0.176132
$52$	714.968	+	453.856i	1.90670	+	1.21036i
$53$	493.058			1.27786			0.638932	−	0.769263i	$-0.279377\pi$
$53$	493.058			1.27786			0.638932	+	0.769263i	$0.279377\pi$
$54$	−386.220	+	668.952i	−0.973294	+	1.68579i
$55$	84.9131	−	147.074i	0.208176	−	0.360571i
$56$	−430.790	−	746.150i	−1.02798	−	1.78051i
$57$	345.256			0.802285
$58$	−340.364	−	589.527i	−0.770551	−	1.33463i
$59$	−48.0816	−	83.2798i	−0.106097	−	0.183765i	0.808089	−	0.589060i	$-0.200502\pi$
$59$	−48.0816	−	83.2798i	−0.106097	−	0.183765i	−0.914186	+	0.405296i	$0.867169\pi$
$60$	−1276.15			−2.74584
$61$	−313.014	−	542.156i	−0.657005	−	1.13797i	−0.981387	−	0.192040i	$-0.938490\pi$
$61$	−313.014	−	542.156i	−0.657005	−	1.13797i	0.324382	−	0.945926i	$-0.394844\pi$
$62$	−641.881	+	1111.77i	−1.31482	+	2.27734i
$63$	−50.8650	+	88.1007i	−0.101720	+	0.176185i
$64$	30.5359			0.0596404
$65$	641.340	−	335.184i	1.22382	−	0.639607i
$66$	−256.943			−0.479204
$67$	−496.312	+	859.638i	−0.904988	+	1.56749i	−0.0840555	+	0.996461i	$0.526787\pi$
$67$	−496.312	+	859.638i	−0.904988	+	1.56749i	−0.820933	+	0.571025i	$0.806546\pi$
$68$	126.667	−	219.394i	0.225892	−	0.391256i
$69$	−423.443	−	733.425i	−0.738790	−	1.27962i
$70$	−1321.27			−2.25603
$71$	71.0041	+	122.983i	0.118685	+	0.205568i	0.919247	−	0.393682i	$-0.128799\pi$
$71$	71.0041	+	122.983i	0.118685	+	0.205568i	−0.800562	+	0.599250i	$0.795465\pi$
$72$	−155.974	−	270.154i	−0.255301	−	0.442195i
$73$	−997.470			−1.59925			−0.799624	−	0.600501i	$-0.794968\pi$
$73$	−997.470			−1.59925			−0.799624	+	0.600501i	$0.794968\pi$
$74$	−193.405	−	334.986i	−0.303822	−	0.526235i
$75$	−259.302	+	449.124i	−0.399221	+	0.691471i
$76$	−681.727	+	1180.79i	−1.02894	+	1.78218i
$77$	−184.384			−0.272890
$78$	−924.348	−	586.769i	−1.34182	−	0.851776i
$79$	1201.94			1.71176			0.855879	−	0.517176i	$-0.173017\pi$
$79$	1201.94			1.71176			0.855879	+	0.517176i	$0.173017\pi$
$80$	910.041	−	1576.24i	1.27182	−	2.20286i
$81$	264.152	−	457.525i	0.362348	−	0.627606i
$82$	424.752	+	735.692i	0.572024	+	0.990775i
$83$	1123.45			1.48572			0.742862	−	0.669445i	$-0.233468\pi$
$83$	1123.45			1.48572			0.742862	+	0.669445i	$0.233468\pi$
$84$	692.773	+	1199.92i	0.899854	+	1.55859i
$85$	−108.238	−	187.475i	−0.138119	−	0.239229i
$86$	158.906			0.199248
$87$	304.993	+	528.263i	0.375847	+	0.650986i
$88$	282.701	−	489.652i	0.342454	−	0.593148i
$89$	−426.651	+	738.981i	−0.508145	+	0.880133i	0.491810	+	0.870702i	$0.336335\pi$
$89$	−426.651	+	738.981i	−0.508145	+	0.880133i	−0.999956	+	0.00943082i	$0.996998\pi$
$90$	−478.385			−0.560292
$91$	−663.321	−	421.071i	−0.764120	−	0.485057i
$92$	3344.45			3.79003
$93$	575.177	−	996.235i	0.641323	−	1.11080i
$94$	349.485	−	605.325i	0.383474	−	0.664197i
$95$	582.543	+	1008.99i	0.629133	+	1.08969i
$96$	−872.477			−0.927571
$97$	357.886	+	619.876i	0.374616	+	0.648855i	0.990270	−	0.139163i	$-0.0444411\pi$
$97$	357.886	+	619.876i	0.374616	+	0.648855i	−0.615653	+	0.788017i	$0.711108\pi$
$98$	−158.346	−	274.264i	−0.163218	−	0.282702i
$99$	−66.7590			−0.0677731
$100$	−1024.01	−	1773.64i	−1.02401	−	1.77364i
$101$	−10.0145	+	17.3456i	−0.00986611	+	0.0170886i	−0.870916	−	0.491431i	$-0.836474\pi$
$101$	−10.0145	+	17.3456i	−0.00986611	+	0.0170886i	0.861050	+	0.508520i	$0.169807\pi$
$102$	−163.762	+	283.644i	−0.158969	+	0.275343i
$103$	−1645.07			−1.57372			−0.786861	−	0.617130i	$-0.788295\pi$
$103$	−1645.07			−1.57372			−0.786861	+	0.617130i	$0.788295\pi$
$104$	2135.21	−	1115.93i	2.01322	−	1.05217i
$105$	1183.96			1.10041
$106$	1258.68	−	2180.11i	1.15334	−	1.99765i
$107$	246.372	−	426.729i	0.222595	−	0.385546i	−0.733000	−	0.680228i	$-0.761881\pi$
$107$	246.372	−	426.729i	0.222595	−	0.385546i	0.955595	+	0.294683i	$0.0952139\pi$
$108$	1366.72	+	2367.23i	1.21771	+	2.10914i
$109$	1112.05			0.977204			0.488602	−	0.872507i	$-0.337507\pi$
$109$	1112.05			0.977204			0.488602	+	0.872507i	$0.337507\pi$
$110$	−433.534	−	750.903i	−0.375780	−	0.650871i
$111$	173.306	+	300.174i	0.148193	+	0.256678i
$112$	−1976.11			−1.66718
$113$	1015.16	+	1758.31i	0.845116	+	1.46378i	0.885520	+	0.464601i	$0.153802\pi$
$113$	1015.16	+	1758.31i	0.845116	+	1.46378i	−0.0404039	+	0.999183i	$0.512864\pi$
$114$	881.372	−	1526.58i	0.724106	−	1.25419i
$115$	1428.93	−	2474.99i	1.15868	−	2.00690i
$116$	−2408.90			−1.92811
$117$	−240.165	−	152.455i	−0.189771	−	0.120465i
$118$	−490.973			−0.383032
$119$	−117.517	+	203.545i	−0.0905275	+	0.156798i
$120$	−1815.27	+	3144.14i	−1.38092	+	2.39183i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	−3196.26			−2.37193
$123$	−380.611	−	659.238i	−0.279013	−	0.483264i
$124$	2271.44	+	3934.25i	1.64501	+	2.84924i
$125$	179.786			0.128644
$126$	259.697	+	449.809i	0.183616	+	0.318033i
$127$	44.7683	−	77.5410i	0.0312799	−	0.0541783i	−0.849962	−	0.526844i	$-0.823375\pi$
$127$	44.7683	−	77.5410i	0.0312799	−	0.0541783i	0.881242	+	0.472666i	$0.156708\pi$
$128$	−684.862	+	1186.22i	−0.472921	+	0.819123i
$129$	−142.393			−0.0971858
$130$	155.172	−	3691.41i	0.104688	−	2.49045i
$131$	1458.38			0.972666			0.486333	−	0.873774i	$-0.338334\pi$
$131$	1458.38			0.972666			0.486333	+	0.873774i	$0.338334\pi$
$132$	−454.624	+	787.432i	−0.299772	+	0.519221i
$133$	632.481	−	1095.49i	0.412354	−	0.714217i
$134$	2533.98	+	4388.99i	1.63360	+	2.82948i
$135$	2335.76			1.48911
$136$	−360.358	−	624.158i	−0.227209	−	0.393537i
$137$	−305.978	−	529.970i	−0.190814	−	0.330499i	0.754706	−	0.656063i	$-0.227779\pi$
$137$	−305.978	−	529.970i	−0.190814	−	0.330499i	−0.945520	+	0.325564i	$0.894446\pi$
$138$	−4323.88			−2.66719
$139$	322.001	+	557.722i	0.196488	+	0.340327i	0.947387	−	0.320090i	$-0.103713\pi$
$139$	322.001	+	557.722i	0.196488	+	0.340327i	−0.750900	+	0.660416i	$0.770380\pi$
$140$	−2337.80	+	4049.19i	−1.41129	+	2.44442i
$141$	−313.166	+	542.419i	−0.187045	+	0.323971i
$142$	725.040			0.428479
$143$	21.6544	−	515.139i	0.0126631	−	0.301245i
$144$	−715.478			−0.414050
$145$	−1029.22	+	1782.66i	−0.589461	+	1.02098i
$146$	−2546.35	+	4410.41i	−1.44341	+	2.50006i
$147$	141.891	+	245.762i	0.0796120	+	0.137892i
$148$	−1368.81			−0.760239
$149$	−1305.61	−	2261.38i	−0.717851	−	1.24335i	−0.961850	−	0.273578i	$-0.911793\pi$
$149$	−1305.61	−	2261.38i	−0.717851	−	1.24335i	0.243999	−	0.969775i	$-0.421541\pi$
$150$	1323.90	+	2293.05i	0.720638	+	1.24818i
$151$	−2285.24			−1.23159			−0.615795	−	0.787906i	$-0.711165\pi$
$151$	−2285.24			−1.23159			−0.615795	+	0.787906i	$0.711165\pi$
$152$	1939.46	+	3359.24i	1.03494	+	1.79257i
$153$	−42.5488	+	73.6966i	−0.0224828	+	0.0389413i
$154$	−470.698	+	815.273i	−0.246298	+	0.426601i
$155$	3881.94			2.01164
$156$	−3433.73	+	1794.57i	−1.76230	+	0.921030i
$157$	−2923.64			−1.48619			−0.743096	−	0.669185i	$-0.766643\pi$
$157$	−2923.64			−1.48619			−0.743096	+	0.669185i	$0.766643\pi$
$158$	3068.33	−	5314.50i	1.54496	−	2.67594i
$159$	−1127.88	+	1953.55i	−0.562558	+	0.974380i
$160$	−1472.11	−	2549.77i	−0.727380	−	1.25986i
$161$	−3102.85			−1.51888
$162$	−1348.66	−	2335.95i	−0.654079	−	1.13290i
$163$	−1315.76	−	2278.96i	−0.632259	−	1.09511i	−0.987089	−	0.160174i	$-0.948794\pi$
$163$	−1315.76	−	2278.96i	−0.632259	−	1.09511i	0.354829	−	0.934931i	$-0.384539\pi$
$164$	3006.15			1.43135
$165$	388.481	+	672.869i	0.183292	+	0.317471i
$166$	2867.96	−	4967.46i	1.34095	−	2.32259i
$167$	1218.06	−	2109.74i	0.564408	−	0.977583i	−0.432697	−	0.901539i	$-0.642438\pi$
$167$	1218.06	−	2109.74i	0.564408	−	0.977583i	0.997105	−	0.0760433i	$-0.0242287\pi$
$168$	3941.76			1.81020
$169$	1254.30	−	1803.76i	0.570916	−	0.821008i
$170$	−1105.25			−0.498640
$171$	228.999	−	396.638i	0.102409	−	0.177378i
$172$	281.162	−	486.988i	0.124642	−	0.215886i
$173$	−49.5914	−	85.8949i	−0.0217940	−	0.0377484i	0.854923	−	0.518755i	$-0.173604\pi$
$173$	−49.5914	−	85.8949i	−0.0217940	−	0.0377484i	−0.876717	+	0.481007i	$0.840271\pi$
$174$	3114.36			1.35689
$175$	950.040	+	1645.52i	0.410378	+	0.710796i
$176$	−648.398	−	1123.06i	−0.277698	−	0.480987i
$177$	439.951			0.186829
$178$	2178.32	+	3772.96i	0.917257	+	1.58874i
$179$	−1335.55	+	2313.25i	−0.557676	+	0.965922i	0.440014	+	0.897991i	$0.354973\pi$
$179$	−1335.55	+	2313.25i	−0.557676	+	0.965922i	−0.997690	+	0.0679317i	$0.978360\pi$
$180$	−846.436	+	1466.07i	−0.350498	+	0.607080i
$181$	−483.437			−0.198528			−0.0992640	−	0.995061i	$-0.531649\pi$
$181$	−483.437			−0.198528			−0.0992640	+	0.995061i	$0.531649\pi$
$182$	−3555.14	+	1858.02i	−1.44794	+	0.756735i
$183$	2864.10			1.15694
$184$	4757.34	−	8239.95i	1.90606	−	3.30140i
$185$	−584.831	+	1012.96i	−0.232419	+	0.402562i
$186$	−2936.63	−	5086.40i	−1.15766	−	2.00512i
$187$	−154.238			−0.0603156
$188$	−1236.73	−	2142.08i	−0.479775	−	0.830994i
$189$	−1267.99	−	2196.23i	−0.488005	−	0.845250i
$190$	5948.49			2.27131
$191$	977.951	+	1693.86i	0.370482	+	0.641694i	0.989640	−	0.143573i	$-0.0458591\pi$
$191$	977.951	+	1693.86i	0.370482	+	0.641694i	−0.619158	+	0.785267i	$0.712526\pi$
$192$	−69.8515	+	120.986i	−0.0262557	+	0.0454762i
$193$	−914.519	+	1583.99i	−0.341080	+	0.590768i	−0.984634	−	0.174633i	$-0.944126\pi$
$193$	−914.519	+	1583.99i	−0.341080	+	0.590768i	0.643553	+	0.765401i	$0.277459\pi$
$194$	3654.46			1.35245
$195$	−139.046	+	3307.80i	−0.0510631	+	1.21475i
$196$	−1120.69			−0.408413
$197$	−1076.40	+	1864.37i	−0.389290	+	0.674269i	−0.992354	−	0.123423i	$-0.960613\pi$
$197$	−1076.40	+	1864.37i	−0.389290	+	0.674269i	0.603065	+	0.797692i	$0.293946\pi$
$198$	−170.423	+	295.182i	−0.0611689	+	0.105948i
$199$	1532.20	+	2653.85i	0.545802	+	0.945358i	0.998556	+	0.0537219i	$0.0171084\pi$
$199$	1532.20	+	2653.85i	0.545802	+	0.945358i	−0.452753	+	0.891636i	$0.649558\pi$
$200$	−5826.46			−2.05996
$201$	−2270.65	−	3932.88i	−0.796812	−	1.38012i
$202$	51.1301	+	88.5599i	0.0178094	+	0.0308468i
$203$	2234.89			0.772702
$204$	579.508	+	1003.74i	0.198890	+	0.344488i
$205$	1284.40	−	2224.64i	0.437591	−	0.757929i
$206$	−4199.55	+	7273.83i	−1.42037	+	2.46015i
$207$	−1123.43			−0.377217
$208$	232.077	−	5520.91i	0.0773636	−	1.84042i
$209$	830.115			0.274738
$210$	3022.43	−	5235.01i	0.993180	−	1.72024i
$211$	−897.874	+	1555.16i	−0.292949	+	0.507402i	−0.974506	−	0.224363i	$-0.927970\pi$
$211$	−897.874	+	1555.16i	−0.292949	+	0.507402i	0.681557	+	0.731765i	$0.261303\pi$
$212$	−4454.13	−	7714.78i	−1.44298	−	2.49931i
$213$	−649.693			−0.208996
$214$	−1257.88	−	2178.71i	−0.401808	−	0.695952i
$215$	−240.256	−	416.136i	−0.0762109	−	0.132001i
$216$	7776.43			2.44962
$217$	−2107.35	−	3650.05i	−0.659247	−	1.14185i
$218$	2838.86	−	4917.04i	0.881980	−	1.52763i
$219$	2281.73	−	3952.08i	0.704042	−	1.21944i
$220$	−3068.31			−0.940298
$221$	−554.871	−	352.228i	−0.168890	−	0.107210i
$222$	1769.67			0.535010
$223$	−477.498	+	827.051i	−0.143389	+	0.248356i	−0.928771	−	0.370655i	$-0.879133\pi$
$223$	−477.498	+	827.051i	−0.143389	+	0.248356i	0.785382	+	0.619011i	$0.212467\pi$
$224$	−1598.31	+	2768.35i	−0.476747	+	0.825751i
$225$	343.976	+	595.783i	0.101919	+	0.176528i
$226$	10366.0			3.05105
$227$	1255.85	+	2175.19i	0.367196	+	0.636002i	0.989126	−	0.147071i	$-0.0469845\pi$
$227$	1255.85	+	2175.19i	0.367196	+	0.636002i	−0.621930	+	0.783073i	$0.713651\pi$
$228$	−3118.93	−	5402.14i	−0.905948	−	1.56915i
$229$	−4793.13			−1.38314			−0.691570	−	0.722309i	$-0.743081\pi$
$229$	−4793.13			−1.38314			−0.691570	+	0.722309i	$0.743081\pi$
$230$	−7295.59	−	12636.3i	−2.09155	−	3.62267i
$231$	421.783	−	730.549i	0.120135	−	0.208081i
$232$	−3426.56	+	5934.98i	−0.969677	+	1.67953i
$233$	−751.366			−0.211260			−0.105630	−	0.994405i	$-0.533686\pi$
$233$	−751.366			−0.211260			−0.105630	+	0.994405i	$0.533686\pi$
$234$	−1287.19	+	672.724i	−0.359599	+	0.187937i
$235$	−2113.59			−0.586705
$236$	−868.708	+	1504.65i	−0.239610	+	0.415018i
$237$	−2749.46	+	4762.21i	−0.753573	+	1.30523i
$238$	599.997	+	1039.23i	0.163412	+	0.283038i
$239$	−3847.96			−1.04144			−0.520719	−	0.853728i	$-0.674336\pi$
$239$	−3847.96			−1.04144			−0.520719	+	0.853728i	$0.674336\pi$
$240$	4163.48	+	7211.35i	1.11980	+	1.93955i
$241$	3296.19	+	5709.18i	0.881023	+	1.52598i	0.850205	+	0.526452i	$0.176478\pi$
$241$	3296.19	+	5709.18i	0.881023	+	1.52598i	0.0308178	+	0.999525i	$0.490189\pi$
$242$	−617.780			−0.164101
$243$	−833.936	−	1444.42i	−0.220152	−	0.381315i
$244$	−5655.33	+	9795.33i	−1.48379	+	2.57001i
$245$	−478.819	+	829.339i	−0.124860	+	0.216263i
$246$	−3886.51			−1.00730
$247$	2986.33	+	1895.70i	0.769294	+	0.488342i
$248$	12924.1			3.30920
$249$	−2569.92	+	4451.24i	−0.654065	+	1.13287i
$250$	458.958	−	794.939i	0.116108	−	0.201106i
$251$	2175.50	+	3768.07i	0.547077	+	0.947565i	0.998473	+	0.0552411i	$0.0175927\pi$
$251$	2175.50	+	3768.07i	0.547077	+	0.947565i	−0.451396	+	0.892324i	$0.649074\pi$
$252$	1837.99			0.459455
$253$	−1018.11	−	1763.41i	−0.252995	−	0.438200i
$254$	−228.570	−	395.895i	−0.0564636	−	0.0977978i
$255$	990.391			0.243218
$256$	3618.79	+	6267.93i	0.883494	+	1.53026i
$257$	−1162.98	+	2014.34i	−0.282275	+	0.488914i	−0.971945	−	0.235210i	$-0.924422\pi$
$257$	−1162.98	+	2014.34i	−0.282275	+	0.488914i	0.689670	+	0.724124i	$0.257756\pi$
$258$	−363.501	+	629.603i	−0.0877155	+	0.151928i
$259$	1269.93			0.304670
$260$	−11038.2	−	7006.97i	−2.63293	−	1.67136i
$261$	809.175			0.191903
$262$	3722.97	−	6448.37i	0.877884	−	1.52054i
$263$	−1220.94	+	2114.73i	−0.286259	+	0.495816i	−0.972914	−	0.231168i	$-0.925745\pi$
$263$	−1220.94	+	2114.73i	−0.286259	+	0.495816i	0.686654	+	0.726984i	$0.259079\pi$
$264$	1293.37	+	2240.18i	0.301520	+	0.522248i
$265$	−7612.20			−1.76458
$266$	−3229.21	−	5593.15i	−0.744343	−	1.28924i
$267$	−1951.95	−	3380.87i	−0.447405	−	0.774928i
$268$	17934.1			4.08769
$269$	−68.2190	−	118.159i	−0.0154624	−	0.0267817i	0.858191	−	0.513331i	$-0.171589\pi$
$269$	−68.2190	−	118.159i	−0.0154624	−	0.0267817i	−0.873653	+	0.486549i	$0.838255\pi$
$270$	5962.75	−	10327.8i	1.34401	−	2.32789i
$271$	1922.71	−	3330.24i	0.430983	−	0.746485i	−0.565975	−	0.824422i	$-0.691500\pi$
$271$	1922.71	−	3330.24i	0.430983	−	0.746485i	0.996958	+	0.0779375i	$0.0248335\pi$
$272$	−1653.02			−0.368490
$273$	3185.68	−	1664.94i	0.706251	−	0.369108i
$274$	−3124.42			−0.688879
$275$	−623.452	+	1079.85i	−0.136711	+	0.236791i
$276$	−7650.50	+	13251.0i	−1.66850	+	2.88992i
$277$	−1211.91	−	2099.09i	−0.262875	−	0.455313i	0.704129	−	0.710072i	$-0.251337\pi$
$277$	−1211.91	−	2099.09i	−0.262875	−	0.455313i	−0.967005	+	0.254758i	$0.918004\pi$
$278$	3288.03			0.709363
$279$	−762.999	−	1321.55i	−0.163726	−	0.283582i
$280$	6650.85	+	11519.6i	1.41952	+	2.45867i
$281$	−5767.52			−1.22442			−0.612209	−	0.790696i	$-0.709719\pi$
$281$	−5767.52			−1.22442			−0.612209	+	0.790696i	$0.709719\pi$
$282$	1598.91	+	2769.39i	0.337636	+	0.584803i
$283$	−1666.04	+	2885.66i	−0.349949	+	0.606130i	−0.986240	−	0.165320i	$-0.947134\pi$
$283$	−1666.04	+	2885.66i	−0.349949	+	0.606130i	0.636291	+	0.771449i	$0.280468\pi$
$284$	1282.86	−	2221.97i	0.268040	−	0.464260i
$285$	−5330.31			−1.10786
$286$	−2222.46	−	1410.80i	−0.459499	−	0.291686i
$287$	−2789.00			−0.573621
$288$	−578.691	+	1002.32i	−0.118402	+	0.205078i
$289$	2358.20	−	4084.52i	0.479991	−	0.831369i
$290$	5254.79	+	9101.56i	1.06404	+	1.84297i
$291$	−3274.68			−0.659675
$292$	9010.83	+	15607.2i	1.80589	+	3.12789i
$293$	−3153.07	−	5461.27i	−0.628683	−	1.08891i	−0.987816	−	0.155625i	$-0.950261\pi$
$293$	−3153.07	−	5461.27i	−0.628683	−	1.08891i	0.359133	−	0.933286i	$-0.383072\pi$
$294$	1448.88			0.287417
$295$	742.320	+	1285.74i	0.146507	+	0.253757i
$296$	−1947.07	+	3372.43i	−0.382335	+	0.662224i
$297$	832.106	−	1441.25i	0.162571	−	0.281582i
$298$	−13331.9			−2.59160
$299$	364.403	−	8668.85i	0.0704816	−	1.67670i
$300$	9369.79			1.80322
$301$	−260.852	+	451.809i	−0.0499510	+	0.0865177i
$302$	−5833.78	+	10104.4i	−1.11158	+	1.92531i
$303$	−45.8166	−	79.3567i	−0.00868678	−	0.0150460i
$304$	8896.62			1.67847
$305$	4832.54	+	8370.21i	0.907248	+	1.57140i
$306$	217.238	+	376.267i	0.0405839	+	0.0702933i
$307$	322.272			0.0599122			0.0299561	−	0.999551i	$-0.490463\pi$
$307$	322.272			0.0599122			0.0299561	+	0.999551i	$0.490463\pi$
$308$	1665.67	+	2885.02i	0.308150	+	0.533732i
$309$	3763.13	−	6517.93i	0.692805	−	1.19997i
$310$	9909.84	−	17164.4i	1.81562	−	3.14474i
$311$	1110.60			0.202497			0.101248	−	0.994861i	$-0.467716\pi$
$311$	1110.60			0.202497			0.101248	+	0.994861i	$0.467716\pi$
$312$	−462.926	+	11012.6i	−0.0840001	+	1.99829i
$313$	−3338.03			−0.602801			−0.301400	−	0.953498i	$-0.597454\pi$
$313$	−3338.03			−0.602801			−0.301400	+	0.953498i	$0.597454\pi$
$314$	−7463.50	+	12927.2i	−1.34137	+	2.32332i
$315$	785.291	−	1360.16i	0.140464	−	0.243291i
$316$	−10857.9	−	18806.5i	−1.93293	−	3.34794i
$317$	−780.195			−0.138234			−0.0691169	−	0.997609i	$-0.522018\pi$
$317$	−780.195			−0.138234			−0.0691169	+	0.997609i	$0.522018\pi$
$318$	5758.53	+	9974.07i	1.01548	+	1.75886i
$319$	733.310	+	1270.13i	0.128707	+	0.222927i
$320$	−471.436			−0.0823565
$321$	1127.16	+	1952.30i	0.195988	+	0.339460i
$322$	−7921.00	+	13719.6i	−1.37087	+	2.37441i
$323$	529.073	−	916.381i	0.0911405	−	0.157860i
$324$	−9545.06			−1.63667
$325$	−4708.87	+	2461.00i	−0.803696	+	0.420036i
$326$	−13435.5			−2.28259
$327$	−2543.84	+	4406.06i	−0.430198	+	0.745125i
$328$	4276.13	−	7406.47i	0.719847	−	1.24681i
$329$	1147.39	+	1987.34i	0.192272	+	0.333026i
$330$	3966.87			0.661725
$331$	3284.98	+	5689.75i	0.545495	+	0.944825i	0.998576	+	0.0533556i	$0.0169917\pi$
$331$	3284.98	+	5689.75i	0.545495	+	0.944825i	−0.453081	+	0.891470i	$0.649675\pi$
$332$	−10148.9	−	17578.4i	−1.67769	−	2.90585i
$333$	459.796			0.0756657
$334$	−6218.94	−	10771.5i	−1.01882	−	1.76464i
$335$	7662.44	−	13271.7i	1.24968	−	2.16452i
$336$	4520.38	−	7829.54i	0.733950	−	1.27124i
$337$	8378.64			1.35434			0.677172	−	0.735825i	$-0.263205\pi$
$337$	8378.64			1.35434			0.677172	+	0.735825i	$0.263205\pi$
$338$	−4773.48	−	10150.7i	−0.768175	−	1.63350i
$339$	−9288.79			−1.48819
$340$	−1955.58	+	3387.17i	−0.311931	+	0.540280i
$341$	1382.93	−	2395.30i	0.219618	−	0.380389i
$342$	−1169.18	−	2025.08i	−0.184860	−	0.320187i
$343$	6789.17			1.06875
$344$	−799.883	−	1385.44i	−0.125369	−	0.217145i
$345$	6537.43	+	11323.2i	1.02018	+	1.76701i
$346$	−506.390			−0.0786812
$347$	4105.32	+	7110.62i	0.635115	+	1.10005i	0.986491	+	0.163817i	$0.0523807\pi$
$347$	4105.32	+	7110.62i	0.635115	+	1.10005i	−0.351376	+	0.936235i	$0.614286\pi$
$348$	5510.42	−	9544.32i	0.848820	−	1.47020i
$349$	509.709	−	882.841i	0.0781779	−	0.135408i	−0.824286	−	0.566174i	$-0.808423\pi$
$349$	509.709	−	882.841i	0.0781779	−	0.135408i	0.902464	+	0.430766i	$0.141756\pi$
$350$	9701.08			1.48156
$351$	6284.82	−	3284.64i	0.955723	−	0.499490i
$352$	−2097.74			−0.317642
$353$	−792.487	+	1372.63i	−0.119490	+	0.206962i	−0.919565	−	0.392937i	$-0.871459\pi$
$353$	−792.487	+	1372.63i	−0.119490	+	0.206962i	0.800076	+	0.599899i	$0.204792\pi$
$354$	1123.11	−	1945.28i	0.168623	−	0.292064i
$355$	−1096.21	−	1898.70i	−0.163890	−	0.283866i
$356$	15416.9			2.29521
$357$	−537.645	−	931.229i	−0.0797065	−	0.138056i
$358$	6818.83	+	11810.6i	1.00667	+	1.74360i
$359$	−12592.1			−1.85122			−0.925610	−	0.378478i	$-0.876447\pi$
$359$	−12592.1			−1.85122			−0.925610	+	0.378478i	$0.876447\pi$
$360$	2408.04	+	4170.85i	0.352541	+	0.610619i
$361$	582.014	−	1008.08i	0.0848540	−	0.146971i
$362$	−1234.12	+	2137.56i	−0.179182	+	0.310353i
$363$	553.580			0.0800425
$364$	−596.181	+	14182.7i	−0.0858473	+	2.04223i
$365$	15399.7			2.20837
$366$	7311.51	−	12663.9i	1.04420	−	1.80861i
$367$	4354.15	−	7541.61i	0.619304	−	1.07267i	−0.370309	−	0.928909i	$-0.620748\pi$
$367$	4354.15	−	7541.61i	0.619304	−	1.07267i	0.989613	−	0.143758i	$-0.0459186\pi$
$368$	−10911.4	−	18899.0i	−1.54564	−	2.67712i
$369$	−1009.80			−0.142461
$370$	2985.92	+	5171.77i	0.419543	+	0.726669i
$371$	4132.37	+	7157.48i	0.578281	+	1.00161i
$372$	−20783.8			−2.89675
$373$	−2256.31	−	3908.05i	−0.313211	−	0.542497i	0.665845	−	0.746090i	$-0.268071\pi$
$373$	−2256.31	−	3908.05i	−0.313211	−	0.542497i	−0.979055	+	0.203594i	$0.934738\pi$
$374$	−393.741	+	681.980i	−0.0544381	+	0.0942896i
$375$	−411.263	+	712.329i	−0.0566334	+	0.0980920i
$376$	−7036.77			−0.965143
$377$	−262.469	+	6243.91i	−0.0358563	+	0.852991i
$378$	−12947.8			−1.76181
$379$	5412.72	−	9375.10i	0.733595	−	1.27062i	−0.221742	−	0.975105i	$-0.571174\pi$
$379$	5412.72	−	9375.10i	0.733595	−	1.27062i	0.955337	−	0.295519i	$-0.0954924\pi$
$380$	10525.0	−	18229.9i	1.42085	−	2.46098i
$381$	204.817	+	354.753i	0.0275409	+	0.0477022i
$382$	9986.10			1.33752
$383$	6216.95	+	10768.1i	0.829429	+	1.43661i	0.898487	+	0.439000i	$0.144667\pi$
$383$	6216.95	+	10768.1i	0.829429	+	1.43661i	−0.0690582	+	0.997613i	$0.521999\pi$
$384$	−3133.27	−	5426.99i	−0.416391	−	0.721211i
$385$	2846.66			0.376830
$386$	4669.19	+	8087.27i	0.615687	+	1.06640i
$387$	−94.4452	+	163.584i	−0.0124055	+	0.0214869i
$388$	6466.05	−	11199.5i	0.846041	−	1.46539i
$389$	−7665.34			−0.999096			−0.499548	−	0.866286i	$-0.666500\pi$
$389$	−7665.34			−0.999096			−0.499548	+	0.866286i	$0.666500\pi$
$390$	14270.8	+	9058.98i	1.85289	+	1.17620i
$391$	−2595.55			−0.335710
$392$	−1594.13	+	2761.11i	−0.205397	+	0.355758i
$393$	−3336.07	+	5778.25i	−0.428200	+	0.741664i
$394$	5495.67	+	9518.78i	0.702710	+	1.21713i
$395$	−18556.5			−2.36374
$396$	603.080	+	1044.56i	0.0765300	+	0.132554i
$397$	3771.01	+	6531.58i	0.476729	+	0.825720i	0.999644	−	0.0266652i	$-0.00848881\pi$
$397$	3771.01	+	6531.58i	0.476729	+	0.825720i	−0.522915	+	0.852385i	$0.675155\pi$
$398$	15645.7			1.97047
$399$	2893.62	+	5011.90i	0.363064	+	0.628845i
$400$	−6681.74	+	11573.1i	−0.835217	+	1.44664i
$401$	4142.06	−	7174.26i	0.515822	−	0.893430i	−0.484009	−	0.875063i	$-0.660820\pi$
$401$	4142.06	−	7174.26i	0.515822	−	0.893430i	0.999831	−	0.0183673i	$-0.00584683\pi$
$402$	−23186.2			−2.87667
$403$	10445.1	−	5458.93i	1.29109	−	0.674761i
$404$	361.870			0.0445636
$405$	−4078.18	+	7063.61i	−0.500361	+	0.866651i
$406$	5705.25	−	9881.78i	0.697406	−	1.20794i
$407$	416.688	+	721.724i	0.0507480	+	0.0878982i
$408$	3297.30			0.400100
$409$	−7268.26	−	12589.0i	−0.878710	−	1.52197i	−0.852758	−	0.522307i	$-0.825072\pi$
$409$	−7268.26	−	12589.0i	−0.878710	−	1.52197i	−0.0259518	−	0.999663i	$-0.508262\pi$
$410$	−6557.63	−	11358.2i	−0.789899	−	1.36814i
$411$	2799.73			0.336010
$412$	14861.0	+	25740.0i	1.77706	+	3.07796i
$413$	805.954	−	1395.95i	0.0960252	−	0.166321i
$414$	−2867.91	+	4967.37i	−0.340459	+	0.589693i
$415$	−17344.7			−2.05161
$416$	−7546.60	−	4790.52i	−0.889429	−	0.564603i
$417$	−2946.34			−0.346002
$418$	2119.13	−	3670.44i	0.247966	−	0.429490i
$419$	−2686.80	+	4653.67i	−0.313267	+	0.542594i	−0.979068	−	0.203536i	$-0.934757\pi$
$419$	−2686.80	+	4653.67i	−0.313267	+	0.542594i	0.665801	+	0.746130i	$0.268090\pi$
$420$	−10695.5	−	18525.2i	−1.24259	−	2.15224i
$421$	−13114.5			−1.51820			−0.759101	−	0.650973i	$-0.774361\pi$
$421$	−13114.5			−1.51820			−0.759101	+	0.650973i	$0.774361\pi$
$422$	4584.20	+	7940.07i	0.528805	+	0.915916i
$423$	415.429	+	719.544i	0.0477514	+	0.0827079i
$424$	−25343.3			−2.90278
$425$	794.712	+	1376.48i	0.0907040	+	0.157104i
$426$	−1658.54	+	2872.68i	−0.188631	+	0.326718i
$427$	5246.81	−	9087.73i	0.594639	−	1.02994i
$428$	−8902.58			−1.00543
$429$	1991.50	+	1264.19i	0.224127	+	0.142274i
$430$	−2453.31			−0.275138
$431$	−5996.09	+	10385.5i	−0.670119	+	1.16068i	0.307751	+	0.951467i	$0.400424\pi$
$431$	−5996.09	+	10385.5i	−0.670119	+	1.16068i	−0.977870	+	0.209213i	$0.932910\pi$
$432$	8917.95	−	15446.3i	0.993207	−	1.72028i
$433$	4605.81	+	7977.50i	0.511181	+	0.885391i	0.999916	+	0.0129587i	$0.00412499\pi$
$433$	4605.81	+	7977.50i	0.511181	+	0.885391i	−0.488735	+	0.872432i	$0.662542\pi$
$434$	−21518.7			−2.38003
$435$	−4708.71	−	8155.72i	−0.519001	−	0.898936i
$436$	−10045.9	−	17400.0i	−1.10347	−	1.91126i
$437$	13969.3			1.52916
$438$	−11649.7	−	20177.8i	−1.27087	−	2.20122i
$439$	−3784.37	+	6554.72i	−0.411431	+	0.712619i	−0.995046	−	0.0994108i	$-0.968304\pi$
$439$	−3784.37	+	6554.72i	−0.411431	+	0.712619i	0.583616	+	0.812030i	$0.301638\pi$
$440$	−4364.54	+	7559.61i	−0.472890	+	0.819069i
$441$	376.450			0.0406489
$442$	−2973.89	+	1554.24i	−0.320030	+	0.167258i
$443$	9427.11			1.01105			0.505525	−	0.862812i	$-0.331299\pi$
$443$	9427.11			1.01105			0.505525	+	0.862812i	$0.331299\pi$
$444$	3131.18	−	5423.36i	0.334683	−	0.579687i
$445$	6586.96	−	11408.9i	0.701689	−	1.21536i
$446$	2437.92	+	4222.61i	0.258832	+	0.448310i
$447$	11946.4			1.26409
$448$	255.925	+	443.274i	0.0269895	+	0.0467472i
$449$	−3555.29	−	6157.94i	−0.373685	−	0.647241i	0.616444	−	0.787398i	$-0.288572\pi$
$449$	−3555.29	−	6157.94i	−0.373685	−	0.647241i	−0.990129	+	0.140157i	$0.955239\pi$
$450$	3512.42			0.367949
$451$	−915.123	−	1585.04i	−0.0955464	−	0.165491i
$452$	18341.2	−	31768.0i	1.90863	−	3.30584i
$453$	5227.53	−	9054.35i	0.542187	−	0.939096i
$454$	12823.8			1.32566
$455$	10240.8	+	6500.81i	1.05516	+	0.669808i
$456$	−17746.2			−1.82246
$457$	1411.31	−	2444.46i	0.144460	−	0.250212i	−0.784711	−	0.619861i	$-0.787189\pi$
$457$	1411.31	−	2444.46i	0.144460	−	0.250212i	0.929171	+	0.369649i	$0.120522\pi$
$458$	−12236.0	+	21193.3i	−1.24836	+	2.16222i
$459$	−1060.68	−	1837.16i	−0.107862	−	0.186822i
$460$	−51634.1			−5.23359
$461$	807.029	+	1397.82i	0.0815339	+	0.141221i	0.903909	−	0.427725i	$-0.140685\pi$
$461$	807.029	+	1397.82i	0.0815339	+	0.141221i	−0.822375	+	0.568946i	$0.807351\pi$
$462$	−2153.46	−	3729.91i	−0.216858	−	0.375608i
$463$	−6426.71			−0.645085			−0.322543	−	0.946555i	$-0.604538\pi$
$463$	−6426.71			−0.645085			−0.322543	+	0.946555i	$0.604538\pi$
$464$	7859.12	+	13612.4i	0.786316	+	1.36194i
$465$	−8880.01	+	15380.6i	−0.885592	+	1.53389i
$466$	−1918.09	+	3322.24i	−0.190674	+	0.330257i
$467$	10217.8			1.01247			0.506234	−	0.862396i	$-0.331037\pi$
$467$	10217.8			1.01247			0.506234	+	0.862396i	$0.331037\pi$
$468$	−215.856	+	5135.04i	−0.0213204	+	0.507195i
$469$	−16638.6			−1.63816
$470$	−5395.60	+	9345.46i	−0.529533	+	0.917178i
$471$	6687.89	−	11583.8i	0.654271	−	1.13323i
$472$	2471.40	+	4280.59i	0.241007	+	0.417437i
$473$	−342.362			−0.0332808
$474$	14037.7	+	24314.0i	1.36028	+	2.35608i
$475$	−4277.17	−	7408.27i	−0.413158	−	0.715610i
$476$	4246.45			0.408898
$477$	1496.19	+	2591.47i	0.143618	+	0.248753i
$478$	−9823.10	+	17014.1i	−0.939954	+	1.62805i
$479$	−343.761	+	595.411i	−0.0327909	+	0.0567955i	−0.881955	−	0.471333i	$-0.843773\pi$
$479$	−343.761	+	595.411i	−0.0327909	+	0.0567955i	0.849164	+	0.528129i	$0.177106\pi$
$480$	13470.0			1.28087
$481$	−149.142	+	3547.97i	−0.0141378	+	0.336327i
$482$	33658.2			3.18069
$483$	7097.84	−	12293.8i	0.668660	−	1.15815i
$484$	−1093.08	+	1893.26i	−0.102655	+	0.177804i
$485$	−5525.31	−	9570.11i	−0.517302	−	0.895993i
$486$	−8515.52			−0.794798
$487$	−7713.75	−	13360.6i	−0.717749	−	1.24318i	−0.961890	−	0.273437i	$-0.911839\pi$
$487$	−7713.75	−	13360.6i	−0.717749	−	1.24318i	0.244141	−	0.969740i	$-0.421494\pi$
$488$	16089.0	+	27866.9i	1.49244	+	2.58499i
$489$	12039.3			1.11337
$490$	2444.67	+	4234.29i	0.225386	+	0.390379i
$491$	−5967.69	+	10336.3i	−0.548509	+	0.950046i	0.449868	+	0.893095i	$0.351471\pi$
$491$	−5967.69	+	10336.3i	−0.548509	+	0.950046i	−0.998377	+	0.0569505i	$0.981862\pi$
$492$	−6876.64	+	11910.7i	−0.630128	+	1.09141i
$493$	1869.50			0.170787
$494$	16005.6	−	8364.99i	1.45774	−	0.761860i
$495$	1030.68			0.0935867
$496$	14821.3	−	25671.2i	1.34172	−	2.32393i
$497$	−1190.19	+	2061.46i	−0.107419	+	0.186055i
$498$	13121.1	+	22726.3i	1.18066	+	2.04496i
$499$	16986.6			1.52390			0.761948	−	0.647638i	$-0.224243\pi$
$499$	16986.6			1.52390			0.761948	+	0.647638i	$0.224243\pi$
$500$	−1624.13	−	2813.07i	−0.145266	−	0.251608i
$501$	5572.66	+	9652.13i	0.496942	+	0.860729i
$502$	22214.5			1.97507
$503$	8448.16	+	14632.6i	0.748877	+	1.29709i	0.948362	+	0.317191i	$0.102740\pi$
$503$	8448.16	+	14632.6i	0.748877	+	1.29709i	−0.199485	+	0.979901i	$0.563927\pi$
$504$	2614.46	−	4528.39i	0.231067	−	0.400219i
$505$	154.611	−	267.794i	0.0136239	−	0.0235974i
$506$	−10396.1			−0.913367
$507$	4277.42	+	9095.80i	0.374688	+	0.796763i
$508$	−1617.69			−0.141286
$509$	4355.74	−	7544.36i	0.379302	−	0.656970i	−0.611659	−	0.791122i	$-0.709498\pi$
$509$	4355.74	−	7544.36i	0.379302	−	0.656970i	0.990961	+	0.134151i	$0.0428308\pi$
$510$	2528.28	−	4379.11i	0.219518	−	0.380216i
$511$	−8359.91	−	14479.8i	−0.723719	−	1.25352i
$512$	25994.5			2.24376
$513$	5708.63	+	9887.64i	0.491310	+	0.850974i
$514$	5937.73	+	10284.4i	0.509537	+	0.882544i
$515$	25397.8			2.17313
$516$	1286.33	+	2227.99i	0.109743	+	0.190081i
$517$	−752.960	+	1304.17i	−0.0640525	+	0.110942i
$518$	3241.89	−	5615.11i	0.274981	−	0.476282i
$519$	453.766			0.0383779
$520$	−32965.0	+	17228.5i	−2.78002	+	1.45292i
$521$	−6558.64			−0.551515			−0.275758	−	0.961227i	$-0.588929\pi$
$521$	−6558.64			−0.551515			−0.275758	+	0.961227i	$0.588929\pi$
$522$	2065.67	−	3577.84i	0.173203	−	0.299996i
$523$	6683.32	−	11575.8i	0.558778	−	0.967832i	−0.438821	−	0.898575i	$-0.644604\pi$
$523$	6683.32	−	11575.8i	0.558778	−	0.967832i	0.997599	−	0.0692576i	$-0.0220630\pi$
$524$	−13174.5	−	22819.0i	−1.09834	−	1.90239i
$525$	−8692.94			−0.722649
$526$	6233.64	+	10797.0i	0.516729	+	0.895002i
$527$	−1762.81	−	3053.28i	−0.145710	−	0.252377i
$528$	5932.90			0.489008
$529$	−11049.4	−	19138.1i	−0.908142	−	1.57295i
$530$	−19432.5	+	33658.1i	−1.59263	+	2.75852i
$531$	291.808	−	505.426i	0.0238482	−	0.0413062i
$532$	−22854.5			−1.86253
$533$	327.544	−	7791.99i	0.0266182	−	0.633224i
$534$	−19931.8			−1.61523
$535$	−3803.67	+	6588.15i	−0.307378	+	0.532394i
$536$	25510.5	−	44185.5i	2.05576	−	3.56068i
$537$	−6110.21	−	10583.2i	−0.491015	−	0.850463i
$538$	−696.601			−0.0558227
$539$	341.155	+	590.898i	0.0272627	+	0.0472204i
$540$	−21100.5	−	36547.1i	−1.68152	−	2.91248i
$541$	−13872.5			−1.10245			−0.551223	−	0.834358i	$-0.685839\pi$
$541$	−13872.5			−1.10245			−0.551223	+	0.834358i	$0.685839\pi$
$542$	−9816.64	−	17002.9i	−0.777972	−	1.34749i
$543$	1105.87	−	1915.43i	0.0873987	−	0.151379i
$544$	−1336.99	+	2315.74i	−0.105373	+	0.182512i
$545$	−17168.7			−1.34940
$546$	770.774	−	18336.1i	0.0604141	−	1.43720i
$547$	10265.2			0.802394			0.401197	−	0.915992i	$-0.368594\pi$
$547$	10265.2			0.802394			0.401197	+	0.915992i	$0.368594\pi$
$548$	−5528.22	+	9575.15i	−0.430937	+	0.746406i
$549$	1899.68	−	3290.35i	0.147680	−	0.255790i
$550$	3183.11	+	5513.31i	0.246779	+	0.427433i
$551$	−10061.7			−0.777935
$552$	21765.0	+	37698.1i	1.67823	+	2.90677i
$553$	10073.6	+	17448.0i	0.774634	+	1.34171i
$554$	−12375.1			−0.949037
$555$	−2675.62	−	4634.32i	−0.204638	−	0.354443i
$556$	5817.71	−	10076.6i	0.443752	−	0.768600i
$557$	3095.52	−	5361.59i	0.235478	−	0.407860i	−0.723933	−	0.689870i	$-0.757668\pi$
$557$	3095.52	−	5361.59i	0.235478	−	0.407860i	0.959411	+	0.282010i	$0.0910011\pi$
$558$	−7791.16			−0.591086
$559$	−1231.64	−	781.837i	−0.0931895	−	0.0591560i
$560$	30508.6			2.30219
$561$	352.823	−	611.108i	0.0265530	−	0.0459911i
$562$	−14723.4	+	25501.6i	−1.10510	+	1.91410i
$563$	3910.94	+	6773.95i	0.292765	+	0.507083i	0.974462	−	0.224551i	$-0.0720915\pi$
$563$	3910.94	+	6773.95i	0.292765	+	0.507083i	−0.681698	+	0.731634i	$0.738758\pi$
$564$	11316.2			0.844851
$565$	−15672.8	−	27146.1i	−1.16701	−	2.02132i
$566$	8506.15	+	14733.1i	0.631696	+	1.09413i
$567$	8855.55			0.655905
$568$	−3649.62	−	6321.32i	−0.269603	−	0.466966i
$569$	8526.71	−	14768.7i	0.628222	−	1.08811i	−0.359687	−	0.933073i	$-0.617116\pi$
$569$	8526.71	−	14768.7i	0.628222	−	1.08811i	0.987908	−	0.155039i	$-0.0495502\pi$
$570$	−13607.3	+	23568.5i	−0.999906	+	1.73189i
$571$	14574.5			1.06817			0.534083	−	0.845432i	$-0.320657\pi$
$571$	14574.5			1.06817			0.534083	+	0.845432i	$0.320657\pi$
$572$	−8255.89	+	4314.78i	−0.603490	+	0.315402i
$573$	−8948.34			−0.652395
$574$	−7119.78	+	12331.8i	−0.517724	+	0.896725i
$575$	−10491.6	+	18171.9i	−0.760919	+	1.31795i
$576$	92.6612	+	160.494i	0.00670292	+	0.0116098i
$577$	14203.7			1.02480			0.512398	−	0.858748i	$-0.328757\pi$
$577$	14203.7			1.02480			0.512398	+	0.858748i	$0.328757\pi$
$578$	−12040.1	−	20854.0i	−0.866437	−	1.50071i
$579$	−4183.96	−	7246.83i	−0.300310	−	0.520152i
$580$	37190.5			2.66250
$581$	9415.78	+	16308.6i	0.672345	+	1.16454i
$582$	−8359.65	+	14479.3i	−0.595393	+	1.03125i
$583$	−2711.82	+	4697.01i	−0.192645	+	0.333671i
$584$	51270.1			3.63283
$585$	3707.85	+	2353.71i	0.262052	+	0.166349i
$586$	−32196.7			−2.26968
$587$	5905.40	−	10228.4i	0.415233	−	0.719205i	−0.580220	−	0.814460i	$-0.697033\pi$
$587$	5905.40	−	10228.4i	0.415233	−	0.719205i	0.995453	+	0.0952552i	$0.0303667\pi$
$588$	2563.59	−	4440.27i	0.179797	−	0.311418i
$589$	9487.51	+	16432.8i	0.663711	+	1.14958i
$590$	7580.01			0.528922
$591$	−4924.56	−	8529.58i	−0.342757	−	0.593672i
$592$	4465.78	+	7734.96i	0.310038	+	0.537001i
$593$	16422.5			1.13725			0.568626	−	0.822596i	$-0.307475\pi$
$593$	16422.5			1.13725			0.568626	+	0.822596i	$0.307475\pi$
$594$	−4248.42	−	7358.48i	−0.293459	−	0.508286i
$595$	1814.32	−	3142.49i	0.125008	−	0.216520i
$596$	−23588.9	+	40857.2i	−1.62121	+	2.80801i
$597$	−14019.7			−0.961122
$598$	−37399.9	−	23741.2i	−2.55752	−	1.62349i
$599$	−14254.2			−0.972306			−0.486153	−	0.873874i	$-0.661600\pi$
$599$	−14254.2			−0.972306			−0.486153	+	0.873874i	$0.661600\pi$
$600$	13328.1	−	23085.0i	0.906865	−	1.57074i
$601$	−5507.55	+	9539.35i	−0.373806	+	0.647451i	−0.990148	−	0.140028i	$-0.955281\pi$
$601$	−5507.55	+	9539.35i	−0.373806	+	0.647451i	0.616341	+	0.787479i	$0.288614\pi$
$602$	1331.81	+	2306.76i	0.0901670	+	0.156174i
$603$	−6024.24			−0.406843
$604$	20644.1	+	35756.7i	1.39072	+	2.40880i
$605$	934.044	+	1617.81i	0.0627674	+	0.108716i
$606$	−467.844			−0.0313612
$607$	11520.3	+	19953.7i	0.770336	+	1.33426i	0.937379	+	0.348311i	$0.113245\pi$
$607$	11520.3	+	19953.7i	0.770336	+	1.33426i	−0.167043	+	0.985950i	$0.553422\pi$
$608$	7195.73	−	12463.4i	0.479976	−	0.831343i
$609$	−5112.36	+	8854.86i	−0.340169	+	0.589191i
$610$	49346.3			3.27536
$611$	−5687.04	+	2972.22i	−0.376551	+	0.196797i
$612$	1537.49			0.101551
$613$	−4980.28	+	8626.09i	−0.328143	+	0.568360i	−0.982143	−	0.188134i	$-0.939756\pi$
$613$	−4980.28	+	8626.09i	−0.328143	+	0.568360i	0.654001	+	0.756494i	$0.273089\pi$
$614$	822.700	−	1424.96i	0.0540741	−	0.0936590i
$615$	5876.16	+	10177.8i	0.385284	+	0.667331i
$616$	9477.38			0.619893
$617$	−11947.7	−	20694.1i	−0.779574	−	1.35026i	−0.932187	−	0.361976i	$-0.882102\pi$
$617$	−11947.7	−	20694.1i	−0.779574	−	1.35026i	0.152613	−	0.988286i	$-0.451231\pi$
$618$	−19213.1	−	33278.1i	−1.25059	−	2.16608i
$619$	−19474.1			−1.26451			−0.632253	−	0.774762i	$-0.717870\pi$
$619$	−19474.1			−1.26451			−0.632253	+	0.774762i	$0.717870\pi$
$620$	−35068.2	−	60739.8i	−2.27157	−	3.93447i
$621$	14002.8	−	24253.6i	0.904854	−	1.56725i
$622$	2835.16	−	4910.63i	0.182764	−	0.316557i
$623$	−14303.2			−0.919818
$624$	21343.5	+	13548.7i	1.36927	+	0.869203i
$625$	−16945.0			−1.08448
$626$	−8521.36	+	14759.4i	−0.544061	+	0.942341i
$627$	−1898.91	+	3289.00i	−0.120949	+	0.209490i
$628$	26411.3	+	45745.6i	1.67822	+	2.90677i
$629$	1062.30			0.0673398
$630$	−4009.40	−	6944.48i	−0.253553	−	0.439166i
$631$	−379.578	−	657.449i	−0.0239473	−	0.0414780i	0.853803	−	0.520596i	$-0.174290\pi$
$631$	−379.578	−	657.449i	−0.0239473	−	0.0414780i	−0.877751	+	0.479118i	$0.840957\pi$
$632$	−61779.9			−3.88841
$633$	−4107.81	−	7114.93i	−0.257932	−	0.446751i
$634$	−1991.69	+	3449.71i	−0.124764	+	0.216097i
$635$	−691.166	+	1197.14i	−0.0431939	+	0.0748140i
$636$	40755.7			2.54099
$637$	−122.107	+	2904.83i	−0.00759509	+	0.180681i
$638$	7488.00			0.464660
$639$	−430.924	+	746.382i	−0.0266778	+	0.0462072i
$640$	10573.4	−	18313.7i	0.653048	−	1.13111i
$641$	2058.94	+	3566.18i	0.126869	+	0.219744i	0.922462	−	0.386088i	$-0.126174\pi$
$641$	2058.94	+	3566.18i	0.126869	+	0.219744i	−0.795593	+	0.605832i	$0.792841\pi$
$642$	11509.7			0.707558
$643$	−1473.90	−	2552.86i	−0.0903963	−	0.156571i	0.817282	−	0.576238i	$-0.195480\pi$
$643$	−1473.90	−	2552.86i	−0.0903963	−	0.156571i	−0.907678	+	0.419667i	$0.862147\pi$
$644$	28030.2	+	48549.7i	1.71513	+	2.97069i
$645$	2198.36			0.134202
$646$	−2701.24	−	4678.69i	−0.164519	−	0.284955i
$647$	−4661.81	+	8074.50i	−0.283269	+	0.490636i	−0.972188	−	0.234203i	$-0.924752\pi$
$647$	−4661.81	+	8074.50i	−0.283269	+	0.490636i	0.688919	+	0.724838i	$0.258085\pi$
$648$	−13577.4	+	23516.8i	−0.823106	+	1.42566i
$649$	1057.80			0.0639786
$650$	−1139.31	+	27103.2i	−0.0687498	+	1.63550i
$651$	19282.5			1.16089
$652$	−23772.3	+	41174.9i	−1.42791	+	2.47321i
$653$	−6656.20	+	11528.9i	−0.398893	+	0.690903i	−0.993590	−	0.113047i	$-0.963939\pi$
$653$	−6656.20	+	11528.9i	−0.398893	+	0.690903i	0.594696	+	0.803950i	$0.297272\pi$
$654$	12987.9	+	22495.7i	0.776554	+	1.34503i
$655$	−22515.6			−1.34314
$656$	−9807.67	−	16987.4i	−0.583727	−	1.01105i
$657$	−3026.83	−	5242.62i	−0.179738	−	0.311315i
$658$	11716.3			0.694145
$659$	4703.30	+	8146.35i	0.278019	+	0.481543i	0.970892	−	0.239516i	$-0.0769889\pi$
$659$	4703.30	+	8146.35i	0.278019	+	0.481543i	−0.692874	+	0.721059i	$0.743656\pi$
$660$	7018.82	−	12157.0i	0.413951	−	0.716983i
$661$	13991.6	−	24234.2i	0.823315	−	1.42602i	−0.0798858	−	0.996804i	$-0.525456\pi$
$661$	13991.6	−	24234.2i	0.823315	−	1.42602i	0.903200	−	0.429219i	$-0.141211\pi$
$662$	33543.7			1.96936
$663$	2664.84	−	1392.73i	0.156099	−	0.0815822i
$664$	−57745.6			−3.37495
$665$	−9764.71	+	16913.0i	−0.569412	+	0.986251i
$666$	1173.77	−	2033.03i	0.0682924	−	0.118286i
$667$	12340.3	+	21374.0i	0.716368	+	1.24079i
$668$	−44014.1			−2.54934
$669$	−2184.57	−	3783.79i	−0.126249	−	0.218669i
$670$	−39121.5	−	67760.5i	−2.25582	−	3.90719i
$671$	6886.31			0.396189
$672$	−7312.32	−	12665.3i	−0.419760	−	0.727046i
$673$	−1814.34	+	3142.53i	−0.103919	+	0.179994i	−0.913296	−	0.407296i	$-0.866472\pi$
$673$	−1814.34	+	3142.53i	−0.103919	+	0.179994i	0.809377	+	0.587290i	$0.199805\pi$
$674$	21389.1	−	37047.0i	1.22237	−	2.11721i
$675$	−17149.7			−0.977914
$676$	−39554.0	−	3331.26i	−2.25045	−	0.189535i
$677$	−3329.76			−0.189030			−0.0945148	−	0.995523i	$-0.530130\pi$
$677$	−3329.76			−0.189030			−0.0945148	+	0.995523i	$0.530130\pi$
$678$	−23712.5	+	41071.3i	−1.34318	+	2.32645i
$679$	−5998.96	+	10390.5i	−0.339056	+	0.587262i
$680$	5563.47	+	9636.21i	0.313749	+	0.543429i
$681$	−11491.1			−0.646608
$682$	−7060.70	−	12229.5i	−0.396434	−	0.686644i
$683$	190.695	+	330.293i	0.0106834	+	0.0185041i	0.871318	−	0.490719i	$-0.163266\pi$
$683$	190.695	+	330.293i	0.0106834	+	0.0185041i	−0.860634	+	0.509224i	$0.829933\pi$
$684$	−8274.81			−0.462566
$685$	4723.92	+	8182.07i	0.263492	+	0.456381i
$686$	17331.5	−	30019.0i	0.964604	−	1.67074i
$687$	10964.4	−	18990.9i	0.608905	−	1.05465i
$688$	−3669.20			−0.203324
$689$	−20482.1	+	10704.6i	−1.13252	+	0.591889i
$690$	66755.3			3.68309
$691$	2545.40	−	4408.76i	0.140133	−	0.242717i	−0.787414	−	0.616425i	$-0.788580\pi$
$691$	2545.40	−	4408.76i	0.140133	−	0.242717i	0.927546	+	0.373708i	$0.121914\pi$
$692$	−895.986	+	1551.89i	−0.0492201	+	0.0852517i
$693$	−559.515	−	969.108i	−0.0306698	−	0.0531217i
$694$	41920.4			2.29290
$695$	−4971.30	−	8610.54i	−0.271327	−	0.469951i
$696$	−15676.7	−	27152.8i	−0.853768	−	1.47877i
$697$	−2333.01			−0.126785
$698$	−2602.38	−	4507.45i	−0.141120	−	0.244426i
$699$	1718.76	−	2976.99i	0.0930038	−	0.161087i
$700$	17164.7	−	29730.1i	0.926807	−	1.60528i
$701$	1034.50			0.0557381			0.0278691	−	0.999612i	$-0.491128\pi$
$701$	1034.50			0.0557381			0.0278691	+	0.999612i	$0.491128\pi$
$702$	1520.61	−	36174.0i	0.0817544	−	1.94487i
$703$	−5717.34			−0.306733
$704$	−167.947	+	290.893i	−0.00899113	+	0.0155731i
$705$	4834.89	−	8374.27i	0.258287	−	0.447366i
$706$	4046.14	+	7008.11i	0.215692	+	0.373589i
$707$	−335.729			−0.0178591
$708$	−3974.37	−	6883.82i	−0.210969	−	0.365409i
$709$	9715.19	+	16827.2i	0.514614	+	0.891338i	0.999856	+	0.0169581i	$0.00539819\pi$
$709$	9715.19	+	16827.2i	0.514614	+	0.891338i	−0.485242	+	0.874380i	$0.661268\pi$
$710$	−11193.7			−0.591679
$711$	3647.29	+	6317.30i	0.192383	+	0.333217i
$712$	21929.9	−	37983.7i	1.15430	−	1.99930i
$713$	23272.1	−	40308.5i	1.22237	−	2.11720i
$714$	−5490.02			−0.287758
$715$	−334.316	+	7953.10i	−0.0174863	+	0.415985i
$716$	48259.8			2.51893
$717$	8802.28	−	15246.0i	0.458476	−	0.794103i
$718$	−32145.4	+	55677.4i	−1.67083	+	2.89396i
$719$	3290.30	+	5698.96i	0.170664	+	0.295599i	0.938652	−	0.344865i	$-0.112075\pi$
$719$	3290.30	+	5698.96i	0.170664	+	0.295599i	−0.767988	+	0.640464i	$0.778742\pi$
$720$	11046.1			0.571755
$721$	−13787.5	−	23880.6i	−0.712168	−	1.23351i
$722$	−2971.54	−	5146.86i	−0.153171	−	0.265300i
$723$	−30160.4			−1.55142
$724$	4367.21	+	7564.24i	0.224180	+	0.388291i
$725$	7556.75	−	13088.7i	0.387104	−	0.670485i
$726$	1413.18	−	2447.71i	0.0722427	−	0.125128i
$727$	−25169.7			−1.28404			−0.642018	−	0.766690i	$-0.721902\pi$
$727$	−25169.7			−1.28404			−0.642018	+	0.766690i	$0.721902\pi$
$728$	34094.8	+	21643.1i	1.73576	+	1.10185i
$729$	21894.8			1.11237
$730$	39312.5	−	68091.2i	1.99318	−	3.45229i
$731$	−218.204	+	377.940i	−0.0110404	+	0.0191226i
$732$	−25873.4	−	44814.0i	−1.30643	−	2.26281i
$733$	−29052.5			−1.46395			−0.731977	−	0.681329i	$-0.761402\pi$
$733$	−29052.5			−1.46395			−0.731977	+	0.681329i	$0.761402\pi$
$734$	−22230.6	−	38504.6i	−1.11791	−	1.93628i
$735$	−2190.62	−	3794.26i	−0.109935	−	0.190413i
$736$	−35301.2			−1.76796
$737$	−5459.44	−	9456.02i	−0.272864	−	0.472615i
$738$	−2577.82	+	4464.92i	−0.128578	+	0.222704i
$739$	−5026.43	+	8706.03i	−0.250203	+	0.433365i	−0.963582	−	0.267414i	$-0.913831\pi$
$739$	−5026.43	+	8706.03i	−0.250203	+	0.433365i	0.713378	+	0.700779i	$0.247164\pi$
$740$	21132.7			1.04980
$741$	−14342.2	+	7495.70i	−0.711033	+	0.371608i
$742$	42196.7			2.08772
$743$	12967.0	−	22459.5i	0.640261	−	1.10896i	−0.345113	−	0.938561i	$-0.612160\pi$
$743$	12967.0	−	22459.5i	0.640261	−	1.10896i	0.985374	−	0.170404i	$-0.0545071\pi$
$744$	−29564.1	+	51206.6i	−1.45682	+	2.52329i
$745$	20157.0	+	34912.9i	0.991268	+	1.71693i
$746$	−23039.8			−1.13076
$747$	3409.12	+	5904.77i	0.166979	+	0.289216i
$748$	1393.34	+	2413.33i	0.0681090	+	0.117968i
$749$	8259.47			0.402930
$750$	2099.75	+	3636.88i	0.102230	+	0.177067i
$751$	3462.21	−	5996.72i	0.168226	−	0.291376i	−0.769570	−	0.638562i	$-0.779530\pi$
$751$	3462.21	−	5996.72i	0.168226	−	0.291376i	0.937796	+	0.347186i	$0.112863\pi$
$752$	−8069.72	+	13977.2i	−0.391320	+	0.677786i
$753$	−19906.0			−0.963366
$754$	26938.0	+	17100.0i	1.30109	+	0.825924i
$755$	35281.2			1.70068
$756$	−22909.3	+	39680.1i	−1.10212	+	1.90893i
$757$	−12307.6	+	21317.4i	−0.590923	+	1.02351i	0.403186	+	0.915118i	$0.367903\pi$
$757$	−12307.6	+	21317.4i	−0.590923	+	1.02351i	−0.994108	+	0.108390i	$0.965430\pi$
$758$	−27635.3	−	47865.7i	−1.32422	−	2.29362i
$759$	9315.74			0.445507
$760$	−29942.8	−	51862.4i	−1.42913	−	2.47532i
$761$	−2674.45	−	4632.28i	−0.127396	−	0.220657i	0.795271	−	0.606254i	$-0.207329\pi$
$761$	−2674.45	−	4632.28i	−0.127396	−	0.220657i	−0.922667	+	0.385597i	$0.873995\pi$
$762$	2091.43			0.0994287
$763$	9320.22	+	16143.1i	0.442221	+	0.765949i
$764$	17669.0	−	30603.6i	0.836704	−	1.44921i
$765$	656.900	−	1137.78i	0.0310461	−	0.0537734i
$766$	63482.8			2.99442
$767$	3805.41	+	2415.64i	0.179146	+	0.113721i
$768$	−33112.2			−1.55577
$769$	−17457.0	+	30236.5i	−0.818617	+	1.41789i	0.0880841	+	0.996113i	$0.471926\pi$
$769$	−17457.0	+	30236.5i	−0.818617	+	1.41789i	−0.906701	+	0.421773i	$0.861408\pi$
$770$	7266.99	−	12586.8i	0.340109	−	0.589087i
$771$	−5320.68	−	9215.68i	−0.248534	−	0.430473i
$772$	33045.9			1.54061
$773$	−10052.2	−	17410.9i	−0.467727	−	0.810127i	0.531593	−	0.847000i	$-0.321594\pi$
$773$	−10052.2	−	17410.9i	−0.467727	−	0.810127i	−0.999320	+	0.0368731i	$0.988260\pi$
$774$	482.202	+	835.198i	0.0223932	+	0.0387862i
$775$	−28502.1			−1.32106
$776$	−18395.4	−	31861.7i	−0.850973	−	1.47393i
$777$	−2904.99	+	5031.59i	−0.134126	+	0.232313i
$778$	−19568.2	+	33893.0i	−0.901738	+	1.56186i
$779$	12556.3			0.577506
$780$	53012.5	−	27705.9i	2.43353	−	1.27184i
$781$	−1562.09			−0.0715697
$782$	−6625.95	+	11476.5i	−0.302997	+	0.524806i
$783$	−10085.8	+	17469.1i	−0.460329	+	0.797313i
$784$	3656.27	+	6332.85i	0.166558	+	0.288486i
$785$	45137.4			2.05226
$786$	17032.7	+	29501.5i	0.772948	+	1.33878i
$787$	2216.77	+	3839.55i	0.100406	+	0.173908i	0.911852	−	0.410520i	$-0.134653\pi$
$787$	2216.77	+	3839.55i	0.100406	+	0.173908i	−0.811446	+	0.584427i	$0.801319\pi$
$788$	38895.3			1.75836
$789$	−5585.84	−	9674.95i	−0.252042	−	0.436549i
$790$	−47371.1	+	82049.2i	−2.13340	+	3.69516i
$791$	−17016.3	+	29473.1i	−0.764893	+	1.32483i
$792$	3431.42			0.153952
$793$	24773.4	+	15726.0i	1.10937	+	0.704219i
$794$	38506.7			1.72110
$795$	17413.1	−	30160.3i	0.776828	−	1.34550i
$796$	27682.8	−	47948.0i	1.23265	−	2.13501i
$797$	−18189.0	−	31504.3i	−0.808392	−	1.40018i	−0.913977	−	0.405765i	$-0.867005\pi$
$797$	−18189.0	−	31504.3i	−0.808392	−	1.40018i	0.105585	−	0.994410i	$-0.466328\pi$
$798$	29547.5			1.31074
$799$	959.796	+	1662.42i	0.0424970	+	0.0736070i
$800$	10808.6	+	18721.0i	0.477677	+	0.827361i
$801$	−5178.69			−0.228440
$802$	−21147.8	−	36629.1i	−0.931116	−	1.61274i
$803$	5486.09	−	9502.18i	0.241096	−	0.417590i
$804$	−41024.6	+	71056.8i	−1.79954	+	3.11689i
$805$	47904.2			2.09739
$806$	2527.19	−	60119.7i	0.110442	−	2.62733i
$807$	624.210			0.0272283
$808$	514.745	−	891.564i	0.0224117	−	0.0388182i
$809$	−9488.37	+	16434.3i	−0.412353	+	0.714216i	−0.995147	−	0.0984042i	$-0.968626\pi$
$809$	−9488.37	+	16434.3i	−0.412353	+	0.714216i	0.582794	+	0.812620i	$0.301960\pi$
$810$	20821.6	+	36064.1i	0.903206	+	1.56440i
$811$	−26212.5			−1.13495			−0.567476	−	0.823390i	$-0.692080\pi$
$811$	−26212.5			−1.13495			−0.567476	+	0.823390i	$0.692080\pi$
$812$	−20189.3	−	34968.9i	−0.872543	−	1.51129i
$813$	8796.49	+	15236.0i	0.379467	+	0.657255i
$814$	4254.90			0.183211
$815$	20313.7	+	35184.3i	0.873077	+	1.51221i
$816$	3781.32	−	6549.44i	0.162221	−	0.280976i
$817$	1174.38	−	2034.08i	0.0502893	−	0.0871036i
$818$	−74217.9			−3.17233
$819$	200.263	−	4764.09i	0.00854428	−	0.203261i
$820$	−46411.3			−1.97653
$821$	459.650	−	796.137i	0.0195394	−	0.0338433i	−0.856090	−	0.516826i	$-0.827113\pi$
$821$	459.650	−	796.137i	0.0195394	−	0.0338433i	0.875630	+	0.482983i	$0.160447\pi$
$822$	7147.17	−	12379.3i	0.303268	−	0.525275i
$823$	−293.088	−	507.643i	−0.0124136	−	0.0215010i	0.859752	−	0.510712i	$-0.170618\pi$
$823$	−293.088	−	507.643i	−0.0124136	−	0.0215010i	−0.872165	+	0.489211i	$0.837285\pi$
$824$	84556.7			3.57485
$825$	−2852.32	−	4940.36i	−0.120370	−	0.208486i
$826$	−4114.90	−	7127.21i	−0.173336	−	0.300227i
$827$	−10277.1			−0.432126			−0.216063	−	0.976379i	$-0.569322\pi$
$827$	−10277.1			−0.432126			−0.216063	+	0.976379i	$0.569322\pi$
$828$	10148.7	+	17578.1i	0.425958	+	0.737780i
$829$	3334.57	−	5775.64i	0.139704	−	0.241974i	−0.787681	−	0.616084i	$-0.788718\pi$
$829$	3334.57	−	5775.64i	0.139704	−	0.241974i	0.927384	+	0.374110i	$0.122052\pi$
$830$	−44277.8	+	76691.3i	−1.85169	+	3.20722i
$831$	11089.1			0.462906
$832$	−1268.49	+	662.951i	−0.0528570	+	0.0276246i
$833$	869.739			0.0361761
$834$	−7521.44	+	13027.5i	−0.312286	+	0.540894i
$835$	−18805.3	+	32571.7i	−0.779381	+	1.34993i
$836$	−7499.00	−	12988.6i	−0.310237	−	0.537346i
$837$	38041.0			1.57096
$838$	13717.8	+	23759.9i	0.565481	+	0.979442i
$839$	11151.0	+	19314.2i	0.458852	+	0.794755i	0.998901	−	0.0468788i	$-0.0149274\pi$
$839$	11151.0	+	19314.2i	0.458852	+	0.794755i	−0.540048	+	0.841634i	$0.681594\pi$
$840$	−60855.9			−2.49967
$841$	3306.18	+	5726.48i	0.135560	+	0.234797i
$842$	−33478.9	+	57987.1i	−1.37026	+	2.37336i
$843$	13193.3	−	22851.5i	0.539029	−	0.933626i
$844$	32444.4			1.32320
$845$	−19364.9	+	27847.7i	−0.788369	+	1.13372i
$846$	4242.05			0.172393
$847$	1014.11	−	1756.50i	0.0411397	−	0.0712561i
$848$	−29063.5	+	50339.4i	−1.17694	+	2.03852i
$849$	−7622.18	−	13202.0i	−0.308119	−	0.533677i
$850$	8115.00			0.327461
$851$	7012.10	+	12145.3i	0.282458	+	0.489231i
$852$	5869.12	+	10165.6i	0.236001	+	0.408765i
$853$	−30009.1			−1.20456			−0.602281	−	0.798284i	$-0.705741\pi$
$853$	−30009.1			−1.20456			−0.602281	+	0.798284i	$0.705741\pi$
$854$	−26788.2	−	46398.5i	−1.07339	−	1.85916i
$855$	−3535.45	+	6123.59i	−0.141415	+	0.244938i
$856$	−12663.5	+	21933.9i	−0.505644	+	0.875800i
$857$	11017.4			0.439145			0.219572	−	0.975596i	$-0.429534\pi$
$857$	11017.4			0.439145			0.219572	+	0.975596i	$0.429534\pi$
$858$	10673.6	−	5578.37i	0.424699	−	0.221961i
$859$	−43496.1			−1.72767			−0.863835	−	0.503774i	$-0.831944\pi$
$859$	−43496.1			−1.72767			−0.863835	+	0.503774i	$0.831944\pi$
$860$	−4340.80	+	7518.48i	−0.172116	+	0.298114i
$861$	6379.89	−	11050.3i	0.252527	−	0.437390i
$862$	30613.7	+	53024.6i	1.20964	+	2.09515i
$863$	5170.97			0.203965			0.101983	−	0.994786i	$-0.467481\pi$
$863$	5170.97			0.203965			0.101983	+	0.994786i	$0.467481\pi$
$864$	−14426.0	−	24986.5i	−0.568034	−	0.983864i
$865$	765.630	+	1326.11i	0.0300950	+	0.0521261i
$866$	47031.1			1.84547
$867$	10788.8	+	18686.8i	0.422616	+	0.731993i
$868$	−38074.3	+	65946.7i	−1.48886	+	2.57877i
$869$	−6610.68	+	11450.0i	−0.258057	+	0.446968i
$870$	−48081.8			−1.87371
$871$	1954.06	−	46485.4i	0.0760170	−	1.80838i
$872$	−57159.6			−2.21980
$873$	−2172.01	+	3762.03i	−0.0842055	+	0.145848i
$874$	35661.1	−	61766.8i	1.38015	−	2.39049i
$875$	1506.80	+	2609.86i	0.0582162	+	0.100833i
$876$	−82449.8			−3.18005
$877$	5643.44	+	9774.72i	0.217292	+	0.376361i	0.953979	−	0.299873i	$-0.0969442\pi$
$877$	5643.44	+	9774.72i	0.217292	+	0.376361i	−0.736687	+	0.676234i	$0.763611\pi$
$878$	19321.6	+	33465.9i	0.742678	+	1.28636i
$879$	28850.8			1.10707
$880$	10010.5	+	17338.6i	0.383469	+	0.664187i
$881$	9532.78	−	16511.3i	0.364549	−	0.631417i	−0.624155	−	0.781301i	$-0.714557\pi$
$881$	9532.78	−	16511.3i	0.364549	−	0.631417i	0.988704	+	0.149884i	$0.0478899\pi$
$882$	961.005	−	1664.51i	0.0366879	−	0.0635453i
$883$	−1138.17			−0.0433777			−0.0216889	−	0.999765i	$-0.506904\pi$
$883$	−1138.17			−0.0433777			−0.0216889	+	0.999765i	$0.506904\pi$
$884$	−498.708	+	11863.9i	−0.0189744	+	0.451385i
$885$	−6792.29			−0.257989
$886$	24065.6	−	41682.9i	0.912529	−	1.58055i
$887$	−1763.33	+	3054.18i	−0.0667495	+	0.115614i	−0.897469	−	0.441078i	$-0.854596\pi$
$887$	−1763.33	+	3054.18i	−0.0667495	+	0.115614i	0.830719	+	0.556692i	$0.187930\pi$
$888$	−8907.94	−	15429.0i	−0.336634	−	0.583067i
$889$	1500.83			0.0566212
$890$	−33630.5	−	58249.7i	−1.26663	−	2.19386i
$891$	2905.67	+	5032.77i	0.109252	+	0.189230i
$892$	17254.3			0.647663
$893$	−5165.65	−	8947.17i	−0.193574	−	0.335281i
$894$	30497.0	−	52822.3i	1.14091	−	1.97611i
$895$	20619.3	−	35713.6i	0.770085	−	1.33383i
$896$	−22959.6			−0.856057
$897$	33513.3	+	21274.0i	1.24747	+	0.791881i
$898$	−36303.9			−1.34908
$899$	−16762.2	+	29033.0i	−0.621858	+	1.07709i
$900$	6214.73	−	10764.2i	0.230175	−	0.398675i
$901$	3456.75	+	5987.26i	0.127815	+	0.221381i
$902$	−9344.54			−0.344944
$903$	−1193.41	−	2067.04i	−0.0439802	−	0.0761760i
$904$	−52179.3	−	90377.2i	−1.91975	−	3.32511i
$905$	7463.66			0.274144
$906$	−26689.8	−	46228.1i	−0.978707	−	1.69517i
$907$	−14339.2	+	24836.2i	−0.524944	+	0.909230i	0.474634	+	0.880183i	$0.342580\pi$
$907$	−14339.2	+	24836.2i	−0.524944	+	0.909230i	−0.999578	+	0.0290464i	$0.990753\pi$
$908$	22689.8	−	39300.0i	0.829283	−	1.43636i
$909$	−121.556			−0.00443537
$910$	54886.9	−	28685.5i	1.99943	−	1.04496i
$911$	483.164			0.0175718			0.00878591	−	0.999961i	$-0.497203\pi$
$911$	483.164			0.0175718			0.00878591	+	0.999961i	$0.497203\pi$
$912$	−20351.2	+	35249.3i	−0.738920	+	1.27985i
$913$	−6178.99	+	10702.3i	−0.223981	+	0.387947i
$914$	−7205.61	−	12480.5i	−0.260766	−	0.451661i
$915$	−44218.2			−1.59760
$916$	43299.6	+	74997.1i	1.56186	+	2.70521i
$917$	12222.8	+	21170.6i	0.440167	+	0.762392i
$918$	−10830.9			−0.389404
$919$	−2068.56	−	3582.85i	−0.0742497	−	0.128604i	0.826510	−	0.562922i	$-0.190323\pi$
$919$	−2068.56	−	3582.85i	−0.0742497	−	0.128604i	−0.900760	+	0.434318i	$0.856990\pi$
$920$	−73447.3	+	127215.i	−2.63205	+	4.55885i
$921$	−737.204	+	1276.88i	−0.0263754	+	0.0456835i
$922$	8240.77			0.294355
$923$	−5619.60	−	3567.28i	−0.200402	−	0.127214i
$924$	−15241.0			−0.542632
$925$	4293.96	−	7437.36i	0.152632	−	0.264367i
$926$	−16406.2	+	28416.3i	−0.582225	+	1.00844i
$927$	−4991.96	−	8646.33i	−0.176869	−	0.306346i
$928$	25426.3			0.899419
$929$	13440.3	+	23279.3i	0.474663	+	0.822140i	0.999579	−	0.0290136i	$-0.00923660\pi$
$929$	13440.3	+	23279.3i	0.474663	+	0.822140i	−0.524916	+	0.851154i	$0.675903\pi$
$930$	45337.9	+	78527.6i	1.59859	+	2.76884i
$931$	−4680.96			−0.164782
$932$	6787.60	+	11756.5i	0.238557	+	0.413193i
$933$	−2540.52	+	4400.32i	−0.0891458	+	0.154405i
$934$	26084.1	−	45178.9i	0.913808	−	1.58276i
$935$	2381.25			0.0832888
$936$	12344.5	+	7836.20i	0.431082	+	0.273648i
$937$	54046.4			1.88433			0.942165	−	0.335149i	$-0.108787\pi$
$937$	54046.4			1.88433			0.942165	+	0.335149i	$0.108787\pi$
$938$	−42475.2	+	73569.1i	−1.47853	+	2.56089i
$939$	7635.82	−	13225.6i	0.265373	−	0.459640i
$940$	19093.5	+	33071.0i	0.662513	+	1.14751i
$941$	20813.2			0.721030			0.360515	−	0.932753i	$-0.382601\pi$
$941$	20813.2			0.721030			0.360515	+	0.932753i	$0.382601\pi$
$942$	−34145.8	−	59142.3i	−1.18103	−	2.04561i
$943$	−15399.9	−	26673.3i	−0.531801	−	0.921106i
$944$	11336.7			0.390868
$945$	19576.2	+	33907.1i	0.673879	+	1.16719i
$946$	−873.985	+	1513.79i	−0.0300377	+	0.0520269i
$947$	−7254.62	+	12565.4i	−0.248937	+	0.431172i	−0.963231	−	0.268674i	$-0.913415\pi$
$947$	−7254.62	+	12565.4i	−0.248937	+	0.431172i	0.714294	+	0.699846i	$0.246748\pi$
$948$	99351.1			3.40377
$949$	41435.9	−	21655.6i	1.41735	−	0.740750i
$950$	−43675.2			−1.49159
$951$	1784.71	−	3091.21i	0.0608552	−	0.105404i
$952$	6040.39	−	10462.3i	0.205641	−	0.356180i
$953$	3740.54	+	6478.81i	0.127144	+	0.220220i	0.922569	−	0.385832i	$-0.126086\pi$
$953$	3740.54	+	6478.81i	0.127144	+	0.220220i	−0.795425	+	0.606052i	$0.792752\pi$
$954$	15277.9			0.518492
$955$	−15098.3	−	26151.1i	−0.511593	−	0.886104i
$956$	34761.2	+	60208.2i	1.17600	+	2.03689i
$957$	−6709.84			−0.226644
$958$	1755.11	+	3039.94i	0.0591911	+	0.102522i
$959$	5128.87	−	8883.47i	0.172701	−	0.299126i
$960$	1078.42	−	1867.88i	0.0362561	−	0.0627974i
$961$	33431.6			1.12221
$962$	15307.0	+	9716.74i	0.513010	+	0.325655i
$963$	2990.46			0.100069
$964$	59553.5	−	103150.i	1.98972	−	3.44630i
$965$	14119.0	−	24454.9i	0.470992	−	0.815782i
$966$	−36238.9	−	62767.6i	−1.20700	−	2.09059i
$967$	27135.3			0.902392			0.451196	−	0.892425i	$-0.350997\pi$
$967$	27135.3			0.902392			0.451196	+	0.892425i	$0.350997\pi$
$968$	3109.71	+	5386.17i	0.103254	+	0.178841i
$969$	2420.53	+	4192.48i	0.0802462	+	0.138991i
$970$	−56420.2			−1.86757
$971$	−18535.7	−	32104.7i	−0.612603	−	1.06106i	−0.990800	−	0.135335i	$-0.956789\pi$
$971$	−18535.7	−	32104.7i	−0.612603	−	1.06106i	0.378196	−	0.925725i	$-0.376544\pi$
$972$	−15067.0	+	26096.8i	−0.497197	+	0.861170i
$973$	−5397.45	+	9348.66i	−0.177836	+	0.308021i
$974$	−78767.0			−2.59123
$975$	1020.91	−	24286.6i	0.0335337	−	0.797738i
$976$	73802.8			2.42046
$977$	−13433.2	+	23267.0i	−0.439884	+	0.761901i	−0.997680	−	0.0680770i	$-0.978314\pi$
$977$	−13433.2	+	23267.0i	−0.439884	+	0.761901i	0.557796	+	0.829978i	$0.311647\pi$
$978$	30734.1	−	53233.0i	1.00487	−	1.74049i
$979$	−4693.16	−	8128.79i	−0.153212	−	0.265370i
$980$	17302.0			0.563971
$981$	3374.52	+	5844.84i	0.109827	+	0.190226i
$982$	30468.7	+	52773.4i	0.990119	+	1.71494i
$983$	−47014.2			−1.52545			−0.762727	−	0.646721i	$-0.776140\pi$
$983$	−47014.2			−1.52545			−0.762727	+	0.646721i	$0.776140\pi$
$984$	19563.5	+	33884.9i	0.633801	+	1.09778i
$985$	16618.2	−	28783.6i	0.537564	−	0.931087i
$986$	4772.47	−	8266.15i	0.154144	−	0.266986i
$987$	−10498.7			−0.338579
$988$	2684.06	−	63851.7i	0.0864286	−	2.05606i
$989$	−5761.33			−0.185237
$990$	2631.12	−	4557.23i	0.0844672	−	0.146301i
$991$	21455.7	−	37162.3i	0.687751	−	1.19122i	−0.284813	−	0.958583i	$-0.591931\pi$
$991$	21455.7	−	37162.3i	0.687751	−	1.19122i	0.972564	−	0.232637i	$-0.0747353\pi$
$992$	−23975.4	−	41526.6i	−0.767358	−	1.32910i
$993$	−30057.8			−0.960581
$994$	6076.63	+	10525.0i	0.193903	+	0.335849i
$995$	−23655.2	−	40972.1i	−0.753690	−	1.30543i
$996$	92863.4			2.95431
$997$	−11886.4	−	20587.8i	−0.377578	−	0.653985i	0.613131	−	0.789981i	$-0.289910\pi$
$997$	−11886.4	−	20587.8i	−0.377578	−	0.653985i	−0.990709	+	0.135996i	$0.956576\pi$
$998$	43363.6	−	75107.9i	1.37540	−	2.38226i
$999$	−5731.05	+	9926.47i	−0.181504	+	0.314374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.17	✓	34
13.3	even	3	inner	143.4.e.b.133.17	yes	34
13.4	even	6		1859.4.a.h.1.17		17
13.9	even	3		1859.4.a.g.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.17	✓	34	1.1	even	1	trivial
143.4.e.b.133.17	yes	34	13.3	even	3	inner
1859.4.a.g.1.1		17	13.9	even	3
1859.4.a.h.1.17		17	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.55281 - 4.42160i) q^{2} +(-2.28752 + 3.96210i) q^{3} +(-9.03368 - 15.6468i) q^{4} -15.4387 q^{5} +(11.6792 + 20.2290i) q^{6} +(8.38111 + 14.5165i) q^{7} -51.4001 q^{8} +(3.03450 + 5.25591i) q^{9} +O(q^{10})\)	\(q+(2.55281 - 4.42160i) q^{2} +(-2.28752 + 3.96210i) q^{3} +(-9.03368 - 15.6468i) q^{4} -15.4387 q^{5} +(11.6792 + 20.2290i) q^{6} +(8.38111 + 14.5165i) q^{7} -51.4001 q^{8} +(3.03450 + 5.25591i) q^{9} +(-39.4122 + 68.2639i) q^{10} +(-5.50000 + 9.52628i) q^{11} +82.6589 q^{12} +(-41.5410 + 21.7106i) q^{13} +85.5815 q^{14} +(35.3164 - 61.1699i) q^{15} +(-58.9453 + 102.096i) q^{16} +(7.01083 + 12.1431i) q^{17} +30.9860 q^{18} +(-37.7325 - 65.3546i) q^{19} +(139.469 + 241.567i) q^{20} -76.6878 q^{21} +(28.0809 + 48.6376i) q^{22} +(-92.5550 + 160.310i) q^{23} +(117.579 - 203.652i) q^{24} +113.355 q^{25} +(-10.0508 + 239.100i) q^{26} -151.292 q^{27} +(151.424 - 262.275i) q^{28} +(66.6645 - 115.466i) q^{29} +(-180.312 - 312.310i) q^{30} -251.441 q^{31} +(95.3518 + 165.154i) q^{32} +(-25.1627 - 43.5831i) q^{33} +71.5893 q^{34} +(-129.394 - 224.117i) q^{35} +(54.8254 - 94.9604i) q^{36} +(37.8807 - 65.6113i) q^{37} -385.296 q^{38} +(9.00632 - 214.253i) q^{39} +793.553 q^{40} +(-83.1930 + 144.094i) q^{41} +(-195.769 + 339.083i) q^{42} +(15.5619 + 26.9540i) q^{43} +198.741 q^{44} +(-46.8489 - 81.1447i) q^{45} +(472.551 + 818.482i) q^{46} +136.902 q^{47} +(-269.677 - 467.094i) q^{48} +(31.0141 - 53.7180i) q^{49} +(289.374 - 501.210i) q^{50} -64.1497 q^{51} +(714.968 + 453.856i) q^{52} +493.058 q^{53} +(-386.220 + 668.952i) q^{54} +(84.9131 - 147.074i) q^{55} +(-430.790 - 746.150i) q^{56} +345.256 q^{57} +(-340.364 - 589.527i) q^{58} +(-48.0816 - 83.2798i) q^{59} -1276.15 q^{60} +(-313.014 - 542.156i) q^{61} +(-641.881 + 1111.77i) q^{62} +(-50.8650 + 88.1007i) q^{63} +30.5359 q^{64} +(641.340 - 335.184i) q^{65} -256.943 q^{66} +(-496.312 + 859.638i) q^{67} +(126.667 - 219.394i) q^{68} +(-423.443 - 733.425i) q^{69} -1321.27 q^{70} +(71.0041 + 122.983i) q^{71} +(-155.974 - 270.154i) q^{72} -997.470 q^{73} +(-193.405 - 334.986i) q^{74} +(-259.302 + 449.124i) q^{75} +(-681.727 + 1180.79i) q^{76} -184.384 q^{77} +(-924.348 - 586.769i) q^{78} +1201.94 q^{79} +(910.041 - 1576.24i) q^{80} +(264.152 - 457.525i) q^{81} +(424.752 + 735.692i) q^{82} +1123.45 q^{83} +(692.773 + 1199.92i) q^{84} +(-108.238 - 187.475i) q^{85} +158.906 q^{86} +(304.993 + 528.263i) q^{87} +(282.701 - 489.652i) q^{88} +(-426.651 + 738.981i) q^{89} -478.385 q^{90} +(-663.321 - 421.071i) q^{91} +3344.45 q^{92} +(575.177 - 996.235i) q^{93} +(349.485 - 605.325i) q^{94} +(582.543 + 1008.99i) q^{95} -872.477 q^{96} +(357.886 + 619.876i) q^{97} +(-158.346 - 274.264i) q^{98} -66.7590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

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