LMFDB - Embedded newform 143.4.j.a.23.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,4,Mod(23,143)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("143.23"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.34
Character	$\chi$	$=$	143.23
Dual form			143.4.j.a.56.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.20201 - 2.42603i) q^{2} +(-1.96385 - 3.40149i) q^{3} +(7.77126 - 13.4602i) q^{4} +7.28280i q^{5} +(-16.5043 - 9.52874i) q^{6} +(-29.1148 - 16.8094i) q^{7} -36.5968i q^{8} +(5.78656 - 10.0226i) q^{9} +(17.6683 + 30.6024i) q^{10} +(9.52628 - 5.50000i) q^{11} -61.0464 q^{12} +(-1.52904 - 46.8472i) q^{13} -163.121 q^{14} +(24.7724 - 14.3023i) q^{15} +(-26.6149 - 46.0983i) q^{16} +(9.84298 - 17.0485i) q^{17} -56.1535i q^{18} +(121.650 + 70.2344i) q^{19} +(98.0280 + 56.5965i) q^{20} +132.045i q^{21} +(26.6863 - 46.2221i) q^{22} +(24.7810 + 42.9220i) q^{23} +(-124.484 + 71.8707i) q^{24} +71.9609 q^{25} +(-120.078 - 193.143i) q^{26} -151.504 q^{27} +(-452.518 + 261.261i) q^{28} +(25.5634 + 44.2771i) q^{29} +(69.3959 - 120.197i) q^{30} -28.5019i q^{31} +(29.8781 + 17.2501i) q^{32} +(-37.4164 - 21.6024i) q^{33} -95.5175i q^{34} +(122.420 - 212.037i) q^{35} +(-89.9377 - 155.777i) q^{36} +(136.505 - 78.8110i) q^{37} +681.564 q^{38} +(-156.348 + 97.2021i) q^{39} +266.527 q^{40} +(-219.967 + 126.998i) q^{41} +(320.346 + 554.855i) q^{42} +(-18.6198 + 32.2504i) q^{43} -170.968i q^{44} +(72.9927 + 42.1424i) q^{45} +(208.260 + 120.239i) q^{46} -579.589i q^{47} +(-104.535 + 181.061i) q^{48} +(393.615 + 681.761i) q^{49} +(302.380 - 174.579i) q^{50} -77.3206 q^{51} +(-642.456 - 343.481i) q^{52} +412.349 q^{53} +(-636.621 + 367.553i) q^{54} +(40.0554 + 69.3780i) q^{55} +(-615.172 + 1065.51i) q^{56} -551.720i q^{57} +(214.835 + 124.035i) q^{58} +(-366.526 - 211.614i) q^{59} -444.589i q^{60} +(-124.839 + 216.228i) q^{61} +(-69.1466 - 119.765i) q^{62} +(-336.949 + 194.538i) q^{63} +593.235 q^{64} +(341.179 - 11.1357i) q^{65} -209.632 q^{66} +(550.538 - 317.853i) q^{67} +(-152.985 - 264.977i) q^{68} +(97.3325 - 168.585i) q^{69} -1187.98i q^{70} +(-622.583 - 359.448i) q^{71} +(-366.796 - 211.770i) q^{72} +1151.31i q^{73} +(382.396 - 662.329i) q^{74} +(-141.321 - 244.774i) q^{75} +(1890.74 - 1091.62i) q^{76} -369.808 q^{77} +(-421.159 + 787.749i) q^{78} -388.060 q^{79} +(335.725 - 193.831i) q^{80} +(141.294 + 244.729i) q^{81} +(-616.202 + 1067.29i) q^{82} -616.271i q^{83} +(1777.36 + 1026.16i) q^{84} +(124.161 + 71.6844i) q^{85} +180.689i q^{86} +(100.405 - 173.907i) q^{87} +(-201.282 - 348.631i) q^{88} +(-911.267 + 526.120i) q^{89} +408.955 q^{90} +(-742.958 + 1389.65i) q^{91} +770.319 q^{92} +(-96.9492 + 55.9736i) q^{93} +(-1406.10 - 2435.44i) q^{94} +(-511.503 + 885.949i) q^{95} -135.507i q^{96} +(966.580 + 558.055i) q^{97} +(3307.95 + 1909.84i) q^{98} -127.304i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25}+ \cdots - 8550 q^{98}+O(q^{100}) $ 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Character values

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

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	4.20201	−	2.42603i	1.48563	−	0.857732i	0.485769	−	0.874087i	$-0.338540\pi$
$2$	4.20201	−	2.42603i	1.48563	−	0.857732i	0.999866	+	0.0163557i	$0.00520641\pi$
$3$	−1.96385	−	3.40149i	−0.377944	−	0.654618i	0.612819	−	0.790223i	$-0.290035\pi$
$3$	−1.96385	−	3.40149i	−0.377944	−	0.654618i	−0.990763	+	0.135605i	$0.956702\pi$
$4$	7.77126	−	13.4602i	0.971407	−	1.68253i
$5$			7.28280i			0.651393i	0.945474	+	0.325697i	$0.105599\pi$
$5$			7.28280i			0.651393i	−0.945474	+	0.325697i	$0.894401\pi$
$6$	−16.5043	−	9.52874i	−1.12297	−	0.648349i
$7$	−29.1148	−	16.8094i	−1.57205	−	0.907625i	−0.995917	−	0.0902703i	$-0.971227\pi$
$7$	−29.1148	−	16.8094i	−1.57205	−	0.907625i	−0.576135	−	0.817355i	$-0.695440\pi$
$8$		−	36.5968i		−	1.61736i
$9$	5.78656	−	10.0226i	0.214317	−	0.371208i
$10$	17.6683	+	30.6024i	0.558721	+	0.967732i
$11$	9.52628	−	5.50000i	0.261116	−	0.150756i
$11$	9.52628	−	5.50000i	0.261116	−	0.150756i
$12$	−61.0464			−1.46855
$13$	−1.52904	−	46.8472i	−0.0326215	−	0.999468i
$13$	−1.52904	−	46.8472i	−0.0326215	−	0.999468i
$14$	−163.121			−3.11399
$15$	24.7724	−	14.3023i	0.426414	−	0.246190i
$16$	−26.6149	−	46.0983i	−0.415857	−	0.720286i
$17$	9.84298	−	17.0485i	0.140428	−	0.243228i	−0.787230	−	0.616660i	$-0.788486\pi$
$17$	9.84298	−	17.0485i	0.140428	−	0.243228i	0.927658	+	0.373431i	$0.121819\pi$
$18$		−	56.1535i		−	0.735306i
$19$	121.650	+	70.2344i	1.46886	+	0.848047i	0.999391	−	0.0349025i	$-0.0111121\pi$
$19$	121.650	+	70.2344i	1.46886	+	0.848047i	0.469469	+	0.882949i	$0.344445\pi$
$20$	98.0280	+	56.5965i	1.09599	+	0.632768i
$21$			132.045i			1.37212i
$22$	26.6863	−	46.2221i	0.258616	−	0.447936i
$23$	24.7810	+	42.9220i	0.224661	+	0.389124i	0.956218	−	0.292657i	$-0.0945393\pi$
$23$	24.7810	+	42.9220i	0.224661	+	0.389124i	−0.731557	+	0.681780i	$0.761206\pi$
$24$	−124.484	+	71.8707i	−1.05876	+	0.611273i
$25$	71.9609			0.575687
$26$	−120.078	−	193.143i	−0.905739	−	1.45686i
$27$	−151.504			−1.07989
$28$	−452.518	+	261.261i	−3.05421	+	1.76335i
$29$	25.5634	+	44.2771i	0.163690	+	0.283519i	0.936189	−	0.351497i	$-0.114327\pi$
$29$	25.5634	+	44.2771i	0.163690	+	0.283519i	−0.772500	+	0.635015i	$0.780994\pi$
$30$	69.3959	−	120.197i	0.422330	−	0.731497i
$31$		−	28.5019i		−	0.165132i	−0.996586	−	0.0825661i	$-0.973688\pi$
$31$		−	28.5019i		−	0.165132i	0.996586	−	0.0825661i	$-0.0263116\pi$
$32$	29.8781	+	17.2501i	0.165054	+	0.0952943i
$33$	−37.4164	−	21.6024i	−0.197375	−	0.113954i
$34$		−	95.5175i		−	0.481797i
$35$	122.420	−	212.037i	0.591221	−	1.02402i
$36$	−89.9377	−	155.777i	−0.416378	−	0.721189i
$37$	136.505	−	78.8110i	0.606519	−	0.350174i	−0.165083	−	0.986280i	$-0.552789\pi$
$37$	136.505	−	78.8110i	0.606519	−	0.350174i	0.771602	+	0.636106i	$0.219456\pi$
$38$	681.564			2.90959
$39$	−156.348	+	97.2021i	−0.641940	+	0.399097i
$40$	266.527			1.05354
$41$	−219.967	+	126.998i	−0.837879	+	0.483750i	−0.856543	−	0.516076i	$-0.827392\pi$
$41$	−219.967	+	126.998i	−0.837879	+	0.483750i	0.0186638	+	0.999826i	$0.494059\pi$
$42$	320.346	+	554.855i	1.17691	+	2.03848i
$43$	−18.6198	+	32.2504i	−0.0660346	+	0.114375i	−0.897152	−	0.441721i	$-0.854368\pi$
$43$	−18.6198	+	32.2504i	−0.0660346	+	0.114375i	0.831118	+	0.556096i	$0.187701\pi$
$44$		−	170.968i		−	0.585781i
$45$	72.9927	+	42.1424i	0.241802	+	0.139605i
$46$	208.260	+	120.239i	0.667528	+	0.385397i
$47$		−	579.589i		−	1.79876i	−0.437168	−	0.899380i	$-0.644018\pi$
$47$		−	579.589i		−	1.79876i	0.437168	−	0.899380i	$-0.355982\pi$
$48$	−104.535	+	181.061i	−0.314341	+	0.544455i
$49$	393.615	+	681.761i	1.14757	+	1.98764i
$50$	302.380	−	174.579i	0.855261	−	0.493785i
$51$	−77.3206			−0.212295
$52$	−642.456	−	343.481i	−1.71332	−	0.916004i
$53$	412.349			1.06869			0.534344	−	0.845267i	$-0.320559\pi$
$53$	412.349			1.06869			0.534344	+	0.845267i	$0.320559\pi$
$54$	−636.621	+	367.553i	−1.60432	+	0.926253i
$55$	40.0554	+	69.3780i	0.0982012	+	0.170089i
$56$	−615.172	+	1065.51i	−1.46796	+	2.54258i
$57$		−	551.720i		−	1.28206i
$58$	214.835	+	124.035i	0.486366	+	0.280804i
$59$	−366.526	−	211.614i	−0.808774	−	0.466946i	0.0377561	−	0.999287i	$-0.487979\pi$
$59$	−366.526	−	211.614i	−0.808774	−	0.466946i	−0.846530	+	0.532341i	$0.821312\pi$
$60$		−	444.589i		−	0.956603i
$61$	−124.839	+	216.228i	−0.262034	+	0.453856i	−0.966782	−	0.255602i	$-0.917726\pi$
$61$	−124.839	+	216.228i	−0.262034	+	0.453856i	0.704749	+	0.709457i	$0.251060\pi$
$62$	−69.1466	−	119.765i	−0.141639	−	0.245326i
$63$	−336.949	+	194.538i	−0.673835	+	0.389039i
$64$	593.235			1.15866
$65$	341.179	−	11.1357i	0.651046	−	0.0212494i
$66$	−209.632			−0.390969
$67$	550.538	−	317.853i	1.00386	−	0.579581i	0.0944751	−	0.995527i	$-0.469883\pi$
$67$	550.538	−	317.853i	1.00386	−	0.579581i	0.909389	+	0.415946i	$0.136549\pi$
$68$	−152.985	−	264.977i	−0.272825	−	0.472547i
$69$	97.3325	−	168.585i	0.169818	−	0.294134i
$70$		−	1187.98i		−	2.02843i
$71$	−622.583	−	359.448i	−1.04066	−	0.600826i	−0.120641	−	0.992696i	$-0.538495\pi$
$71$	−622.583	−	359.448i	−1.04066	−	0.600826i	−0.920021	+	0.391870i	$0.871828\pi$
$72$	−366.796	−	211.770i	−0.600379	−	0.346629i
$73$			1151.31i			1.84589i	0.384929	+	0.922946i	$0.374226\pi$
$73$			1151.31i			1.84589i	−0.384929	+	0.922946i	$0.625774\pi$
$74$	382.396	−	662.329i	0.600711	−	1.04046i
$75$	−141.321	−	244.774i	−0.217577	−	0.376855i
$76$	1890.74	−	1091.62i	2.85372	−	1.64760i
$77$	−369.808			−0.547318
$78$	−421.159	+	787.749i	−0.611371	+	1.14353i
$79$	−388.060			−0.552660			−0.276330	−	0.961063i	$-0.589118\pi$
$79$	−388.060			−0.552660			−0.276330	+	0.961063i	$0.589118\pi$
$80$	335.725	−	193.831i	0.469189	−	0.270887i
$81$	141.294	+	244.729i	0.193819	+	0.335705i
$82$	−616.202	+	1067.29i	−0.829855	+	1.43735i
$83$		−	616.271i		−	0.814994i	−0.913207	−	0.407497i	$-0.866402\pi$
$83$		−	616.271i		−	0.814994i	0.913207	−	0.407497i	$-0.133598\pi$
$84$	1777.36	+	1026.16i	2.30864	+	1.33289i
$85$	124.161	+	71.6844i	0.158437	+	0.0914737i
$86$			180.689i			0.226560i
$87$	100.405	−	173.907i	0.123731	−	0.214308i
$88$	−201.282	−	348.631i	−0.243827	−	0.422320i
$89$	−911.267	+	526.120i	−1.08533	+	0.626614i	−0.932328	−	0.361613i	$-0.882226\pi$
$89$	−911.267	+	526.120i	−1.08533	+	0.626614i	−0.152999	+	0.988226i	$0.548893\pi$
$90$	408.955			0.478974
$91$	−742.958	+	1389.65i	−0.855859	+	1.60082i
$92$	770.319			0.872949
$93$	−96.9492	+	55.9736i	−0.108099	+	0.0624107i
$94$	−1406.10	−	2435.44i	−1.54285	−	2.67230i
$95$	−511.503	+	885.949i	−0.552412	+	0.956805i
$96$		−	135.507i		−	0.144063i
$97$	966.580	+	558.055i	1.01177	+	0.584144i	0.911708	−	0.410838i	$-0.134764\pi$
$97$	966.580	+	558.055i	1.01177	+	0.584144i	0.100058	+	0.994982i	$0.468097\pi$
$98$	3307.95	+	1909.84i	3.40973	+	1.96861i
$99$		−	127.304i		−	0.129238i
$100$	559.227	−	968.609i	0.559227	−	0.968609i
$101$	871.969	+	1510.30i	0.859051	+	1.48792i	0.872835	+	0.488016i	$0.162279\pi$
$101$	871.969	+	1510.30i	0.859051	+	1.48792i	−0.0137834	+	0.999905i	$0.504388\pi$
$102$	−324.902	+	187.582i	−0.315393	+	0.182092i
$103$	−1242.54			−1.18865			−0.594326	−	0.804224i	$-0.702581\pi$
$103$	−1242.54			−1.18865			−0.594326	+	0.804224i	$0.702581\pi$
$104$	−1714.46	+	55.9579i	−1.61650	+	0.0527608i
$105$	−961.658			−0.893792
$106$	1732.69	−	1000.37i	1.58768	−	0.916647i
$107$	582.268	+	1008.52i	0.526075	+	0.911188i	0.999539	+	0.0303747i	$0.00967004\pi$
$107$	582.268	+	1008.52i	0.526075	+	0.911188i	−0.473464	+	0.880813i	$0.656997\pi$
$108$	−1177.38	+	2039.28i	−1.04901	+	1.81694i
$109$		−	1251.73i		−	1.09995i	−0.835182	−	0.549973i	$-0.814638\pi$
$109$		−	1251.73i		−	1.09995i	0.835182	−	0.549973i	$-0.185362\pi$
$110$	336.626	+	194.351i	0.291782	+	0.168461i
$111$	−536.150	−	309.546i	−0.458460	−	0.264692i
$112$			1789.52i			1.50977i
$113$	510.191	−	883.677i	0.424732	−	0.735658i	−0.571663	−	0.820488i	$-0.693702\pi$
$113$	510.191	−	883.677i	0.424732	−	0.735658i	0.996395	+	0.0848305i	$0.0270349\pi$
$114$	−1338.49	−	2318.33i	−1.09966	−	1.90467i
$115$	−312.592	+	180.475i	−0.253473	+	0.146343i
$116$	794.638			0.636037
$117$	−478.380	−	255.759i	−0.378002	−	0.202094i
$118$	−2053.53			−1.60206
$119$	−573.153	+	330.910i	−0.441520	+	0.254912i
$120$	−523.420	−	906.589i	−0.398179	−	0.689666i
$121$	60.5000	−	104.789i	0.0454545	−	0.0787296i
$122$			1211.46i			0.899018i
$123$	863.965	+	498.810i	0.633342	+	0.365660i
$124$	−383.642	−	221.496i	−0.277840	−	0.160411i
$125$			1434.43i			1.02639i
$126$	−943.910	+	1634.90i	−0.667382	+	1.15594i
$127$	317.057	+	549.158i	0.221529	+	0.383700i	0.955273	−	0.295727i	$-0.0955618\pi$
$127$	317.057	+	549.158i	0.221529	+	0.383700i	−0.733743	+	0.679427i	$0.762228\pi$
$128$	2253.75	−	1301.21i	1.55629	−	0.898527i
$129$	146.266			0.0998295
$130$	1406.62	−	874.503i	0.948991	−	0.589992i
$131$	−923.025			−0.615611			−0.307805	−	0.951449i	$-0.599595\pi$
$131$	−923.025			−0.615611			−0.307805	+	0.951449i	$0.599595\pi$
$132$	−581.545	+	335.755i	−0.383462	+	0.221392i
$133$	−2361.20	−	4089.73i	−1.53942	−	2.66635i
$134$	1542.24	−	2671.25i	0.994251	−	1.72209i
$135$		−	1103.37i		−	0.703431i
$136$	−623.921	−	360.221i	−0.393388	−	0.227123i
$137$	247.120	+	142.675i	0.154109	+	0.0889748i	0.575071	−	0.818103i	$-0.304974\pi$
$137$	247.120	+	142.675i	0.154109	+	0.0889748i	−0.420962	+	0.907078i	$0.638308\pi$
$138$		−	944.527i		−	0.582634i
$139$	116.525	−	201.826i	0.0711042	−	0.123156i	−0.828281	−	0.560312i	$-0.810681\pi$
$139$	116.525	−	201.826i	0.0711042	−	0.123156i	0.899385	+	0.437156i	$0.144014\pi$
$140$	−1902.71	−	3295.59i	−1.14863	−	1.98949i
$141$	−1971.47	+	1138.23i	−1.17750	+	0.679830i
$142$	−3488.13			−2.06139
$143$	−272.226	−	437.870i	−0.159193	−	0.256060i
$144$	−616.034			−0.356501
$145$	−322.461	+	186.173i	−0.184682	+	0.106626i
$146$	2793.10	+	4837.80i	1.58328	+	2.74232i
$147$	1546.00	−	2677.76i	0.867430	−	1.50243i
$148$		−	2449.84i		−	1.36065i
$149$	−1337.60	−	772.263i	−0.735438	−	0.424605i	0.0849701	−	0.996384i	$-0.472921\pi$
$149$	−1337.60	−	772.263i	−0.735438	−	0.424605i	−0.820408	+	0.571778i	$0.806254\pi$
$150$	−1187.66	−	685.696i	−0.646481	−	0.373246i
$151$			1010.81i			0.544759i	0.962190	+	0.272380i	$0.0878106\pi$
$151$			1010.81i			0.544759i	−0.962190	+	0.272380i	$0.912189\pi$
$152$	2570.35	−	4451.98i	1.37160	−	2.37568i
$153$	−113.914	−	197.305i	−0.0601922	−	0.104256i
$154$	−1553.94	+	897.166i	−0.813115	+	0.469452i
$155$	207.574			0.107566
$156$	93.3423	+	2859.86i	0.0479062	+	1.46777i
$157$	1076.84			0.547398			0.273699	−	0.961815i	$-0.411753\pi$
$157$	1076.84			0.547398			0.273699	+	0.961815i	$0.411753\pi$
$158$	−1630.63	+	941.446i	−0.821051	+	0.474034i
$159$	−809.792	−	1402.60i	−0.403904	−	0.699582i
$160$	−125.629	+	217.596i	−0.0620740	+	0.107515i
$161$		−	1666.22i		−	0.815631i
$162$	1187.44	+	685.569i	0.575889	+	0.332490i
$163$	281.655	+	162.613i	0.135343	+	0.0781402i	0.566143	−	0.824307i	$-0.308435\pi$
$163$	281.655	+	162.613i	0.135343	+	0.0781402i	−0.430800	+	0.902448i	$0.641768\pi$
$164$			3947.73i			1.87967i
$165$	157.326	−	272.496i	0.0742291	−	0.128569i
$166$	−1495.09	−	2589.57i	−0.699046	−	1.21078i
$167$	−112.508	+	64.9566i	−0.0521326	+	0.0300987i	−0.525840	−	0.850584i	$-0.676249\pi$
$167$	−112.508	+	64.9566i	−0.0521326	+	0.0300987i	0.473707	+	0.880682i	$0.342916\pi$
$168$	4832.43			2.21922
$169$	−2192.32	+	143.262i	−0.997872	+	0.0652082i
$170$	695.635			0.313840
$171$	1407.87	−	812.832i	0.629603	−	0.363502i
$172$	289.398	+	501.252i	0.128293	+	0.222210i
$173$	−2000.75	+	3465.40i	−0.879272	+	1.52294i	−0.0271313	+	0.999632i	$0.508637\pi$
$173$	−2000.75	+	3465.40i	−0.879272	+	1.52294i	−0.852141	+	0.523312i	$0.824696\pi$
$174$		−	974.347i		−	0.424512i
$175$	−2095.13	−	1209.62i	−0.905010	−	0.522508i
$176$	−507.081	−	292.763i	−0.217174	−	0.125386i
$177$			1662.32i			0.705917i
$178$	−2552.77	+	4421.52i	−1.07493	+	1.86184i
$179$	420.633	+	728.559i	0.175640	+	0.304218i	0.940383	−	0.340118i	$-0.110467\pi$
$179$	420.633	+	728.559i	0.175640	+	0.304218i	−0.764742	+	0.644336i	$0.777134\pi$
$180$	1134.49	−	654.998i	0.469777	−	0.271226i
$181$	3876.21			1.59180			0.795902	−	0.605426i	$-0.206997\pi$
$181$	3876.21			1.59180			0.795902	+	0.605426i	$0.206997\pi$
$182$	249.418	+	7641.77i	0.101583	+	3.11234i
$183$	980.665			0.396136
$184$	1570.81	−	906.905i	0.629355	−	0.363358i
$185$	573.964	+	994.135i	0.228101	+	0.395083i
$186$	−271.588	+	470.404i	−0.107063	+	0.185439i
$187$		−	216.545i		−	0.0846811i
$188$	−7801.39	−	4504.13i	−3.02646	−	1.74733i
$189$	4411.01	+	2546.70i	1.69764	+	0.980132i
$190$			4963.69i			1.89528i
$191$	−327.920	+	567.974i	−0.124228	+	0.215168i	−0.921431	−	0.388543i	$-0.872979\pi$
$191$	−327.920	+	567.974i	−0.124228	+	0.215168i	0.797203	+	0.603711i	$0.206312\pi$
$192$	−1165.03	−	2017.88i	−0.437909	−	0.758481i
$193$	487.023	−	281.183i	0.181641	−	0.104870i	−0.406423	−	0.913685i	$-0.633224\pi$
$193$	487.023	−	281.183i	0.181641	−	0.104870i	0.588063	+	0.808815i	$0.299891\pi$
$194$	5415.44			2.00415
$195$	−707.903	−	1138.65i	−0.259969	−	0.418155i
$196$	12235.5			4.45901
$197$	654.788	−	378.042i	0.236811	−	0.136723i	−0.376899	−	0.926254i	$-0.623010\pi$
$197$	654.788	−	378.042i	0.236811	−	0.136723i	0.613710	+	0.789531i	$0.289676\pi$
$198$	−308.844	−	534.934i	−0.110852	−	0.192001i
$199$	1242.82	−	2152.63i	0.442719	−	0.766813i	−0.555171	−	0.831736i	$-0.687347\pi$
$199$	1242.82	−	2152.63i	0.442719	−	0.766813i	0.997890	+	0.0649238i	$0.0206804\pi$
$200$		−	2633.54i		−	0.931095i
$201$	−2162.35	−	1248.43i	−0.758809	−	0.438098i
$202$	7328.05	+	4230.85i	2.55247	+	1.47367i
$203$		−	1718.82i		−	0.594275i
$204$	−600.879	+	1040.75i	−0.206225	+	0.357192i
$205$	−924.900	−	1601.97i	−0.315111	−	0.545789i
$206$	−5221.17	+	3014.44i	−1.76590	+	1.01954i
$207$	573.588			0.192595
$208$	−2118.88	+	1317.32i	−0.706337	+	0.439133i
$209$	1545.16			0.511391
$210$	−4040.90	+	2333.01i	−1.32785	+	0.766634i
$211$	978.791	+	1695.32i	0.319350	+	0.553130i	0.980352	−	0.197254i	$-0.0632023\pi$
$211$	978.791	+	1695.32i	0.319350	+	0.553130i	−0.661003	+	0.750383i	$0.729869\pi$
$212$	3204.47	−	5550.30i	1.03813	−	1.79810i
$213$			2823.62i			0.908314i
$214$	4893.39	+	2825.20i	1.56311	+	0.902462i
$215$	−234.873	−	135.604i	−0.0745033	−	0.0430145i
$216$			5544.55i			1.74657i
$217$	−479.102	+	829.829i	−0.149878	+	0.259597i
$218$	−3036.74	−	5259.79i	−0.943458	−	1.63412i
$219$	3916.16	−	2261.00i	1.20835	−	0.697644i
$220$	1245.12			0.381574
$221$	−813.727	−	435.048i	−0.247680	−	0.132419i
$222$	−3003.88			−0.908140
$223$	2280.21	−	1316.48i	0.684726	−	0.395327i	−0.116907	−	0.993143i	$-0.537298\pi$
$223$	2280.21	−	1316.48i	0.684726	−	0.395327i	0.801633	+	0.597816i	$0.203965\pi$
$224$	−579.929	−	1004.47i	−0.172983	−	0.299615i
$225$	416.406	−	721.236i	0.123380	−	0.213700i
$226$		−	4950.96i		−	1.45723i
$227$	921.469	+	532.011i	0.269428	+	0.155554i	0.628628	−	0.777707i	$-0.283617\pi$
$227$	921.469	+	532.011i	0.269428	+	0.155554i	−0.359200	+	0.933261i	$0.616950\pi$
$228$	−7426.28	−	4287.56i	−2.15709	−	1.24540i
$229$		−	747.625i		−	0.215740i	−0.994165	−	0.107870i	$-0.965597\pi$
$229$		−	747.625i		−	0.215740i	0.994165	−	0.107870i	$-0.0344030\pi$
$230$	−875.677	+	1516.72i	−0.251045	+	0.434823i
$231$	726.248	+	1257.90i	0.206856	+	0.358284i
$232$	1620.40	−	935.537i	0.458553	−	0.264746i
$233$	2448.79			0.688522			0.344261	−	0.938874i	$-0.388129\pi$
$233$	2448.79			0.688522			0.344261	+	0.938874i	$0.388129\pi$
$234$	−2630.64	+	85.8609i	−0.734915	+	0.0239868i
$235$	4221.03			1.17170
$236$	−5696.74	+	3289.01i	−1.57130	+	0.907189i
$237$	762.093	+	1319.98i	0.208874	+	0.361781i
$238$	−1605.60	+	2780.97i	−0.437291	+	0.757411i
$239$			2808.34i			0.760068i	0.924972	+	0.380034i	$0.124088\pi$
$239$			2808.34i			0.760068i	−0.924972	+	0.380034i	$0.875912\pi$
$240$	−1318.63	−	761.310i	−0.354654	−	0.204760i
$241$	10.6106	+	6.12602i	0.00283605	+	0.00163739i	0.501417	−	0.865206i	$-0.332812\pi$
$241$	10.6106	+	6.12602i	0.00283605	+	0.00163739i	−0.498581	+	0.866843i	$0.666145\pi$
$242$		−	587.100i		−	0.155951i
$243$	−1490.34	+	2581.35i	−0.393438	+	0.681454i
$244$	1940.32	+	3360.73i	0.509083	+	0.881757i
$245$	−4965.13	+	2866.62i	−1.29474	+	0.747516i
$246$	4840.52			1.25455
$247$	3104.28	−	5806.34i	0.799679	−	1.49574i
$248$	−1043.08			−0.267079
$249$	−2096.24	+	1210.26i	−0.533509	+	0.308022i
$250$	3479.96	+	6027.47i	0.880369	+	1.52484i
$251$	−3044.91	+	5273.94i	−0.765709	+	1.32625i	0.174162	+	0.984717i	$0.444278\pi$
$251$	−3044.91	+	5273.94i	−0.765709	+	1.32625i	−0.939871	+	0.341529i	$0.889055\pi$
$252$			6047.21i			1.51166i
$253$	472.142	+	272.591i	0.117325	+	0.0677378i
$254$	2664.55	+	1538.38i	0.658223	+	0.380025i
$255$		−	563.111i		−	0.138288i
$256$	3940.59	−	6825.31i	0.962059	−	1.66634i
$257$	2242.89	+	3884.79i	0.544387	+	0.942906i	0.998645	+	0.0520357i	$0.0165710\pi$
$257$	2242.89	+	3884.79i	0.544387	+	0.942906i	−0.454258	+	0.890870i	$0.650096\pi$
$258$	614.611	−	354.846i	0.148310	−	0.0856269i
$259$	−5299.08			−1.27131
$260$	2501.50	−	4678.88i	0.596679	−	1.11605i
$261$	591.696			0.140326
$262$	−3878.56	+	2239.29i	−0.914573	+	0.528029i
$263$	−3832.93	−	6638.83i	−0.898664	−	1.55653i	−0.829204	−	0.558946i	$-0.811206\pi$
$263$	−3832.93	−	6638.83i	−0.898664	−	1.55653i	−0.0694599	−	0.997585i	$-0.522128\pi$
$264$	−790.578	+	1369.32i	−0.184306	+	0.319227i
$265$			3003.05i			0.696136i
$266$	−19843.6	−	11456.7i	−4.57402	−	2.64081i
$267$	3579.19	+	2066.45i	0.820385	+	0.473650i
$268$		−	9880.48i		−	2.25204i
$269$	1990.43	−	3447.53i	0.451148	−	0.781412i	−0.547309	−	0.836930i	$-0.684348\pi$
$269$	1990.43	−	3447.53i	0.451148	−	0.781412i	0.998458	+	0.0555187i	$0.0176812\pi$
$270$	−2676.82	−	4636.38i	−0.603355	−	1.04504i
$271$	488.838	−	282.231i	0.109575	−	0.0632630i	−0.444211	−	0.895922i	$-0.646516\pi$
$271$	488.838	−	282.231i	0.109575	−	0.0632630i	0.553786	+	0.832659i	$0.313183\pi$
$272$	−1047.88			−0.233592
$273$	6185.95	−	201.902i	1.37139	−	0.0447607i
$274$	1384.54			0.305266
$275$	685.519	−	395.785i	0.150321	−	0.0867881i
$276$	−1512.79	−	2620.23i	−0.329925	−	0.571448i
$277$	1683.95	−	2916.69i	0.365267	−	0.632661i	−0.623552	−	0.781782i	$-0.714311\pi$
$277$	1683.95	−	2916.69i	0.365267	−	0.632661i	0.988819	+	0.149121i	$0.0476443\pi$
$278$		−	1130.77i		−	0.243953i
$279$	−285.664	−	164.928i	−0.0612984	−	0.0353907i
$280$	−7759.88	−	4480.17i	−1.65622	−	0.956219i
$281$			2359.54i			0.500918i	0.968127	+	0.250459i	$0.0805816\pi$
$281$			2359.54i			0.500918i	−0.968127	+	0.250459i	$0.919418\pi$
$282$	−5522.75	+	9565.68i	−1.16622	+	2.01996i
$283$	−2822.48	−	4888.68i	−0.592859	−	1.02686i	−0.993845	−	0.110778i	$-0.964666\pi$
$283$	−2822.48	−	4888.68i	−0.592859	−	1.02686i	0.400986	−	0.916084i	$-0.368668\pi$
$284$	−9676.51	+	5586.73i	−2.02181	+	1.16729i
$285$	4018.07			0.835122
$286$	−2206.18	−	1179.51i	−0.456134	−	0.243866i
$287$	8539.05			1.75625
$288$	345.782	−	199.638i	0.0707480	−	0.0408464i
$289$	2262.73	+	3919.17i	0.460560	+	0.797713i
$290$	−903.322	+	1564.60i	−0.182914	+	0.316815i
$291$		−	4383.76i		−	0.883094i
$292$	15496.8	+	8947.10i	3.10576	+	1.79311i
$293$	785.695	+	453.622i	0.156658	+	0.0904466i	0.576280	−	0.817253i	$-0.304504\pi$
$293$	785.695	+	453.622i	0.156658	+	0.0904466i	−0.419622	+	0.907699i	$0.637837\pi$
$294$		−	15002.6i		−	2.97609i
$295$	1541.14	−	2669.34i	0.304165	−	0.526830i
$296$	−2884.23	−	4995.63i	−0.566359	−	0.980963i
$297$	−1443.27	+	833.271i	−0.281976	+	0.162799i
$298$	−7494.13			−1.45679
$299$	1972.88	−	1226.55i	0.381588	−	0.237235i
$300$	−4392.96			−0.845425
$301$	1084.22	−	625.976i	0.207620	−	0.119869i
$302$	2452.26	+	4247.44i	0.467257	+	0.809313i
$303$	3424.84	−	5932.00i	0.649346	−	1.12470i
$304$		−	7477.12i		−	1.41067i
$305$	−1574.75	−	909.180i	−0.295638	−	0.170687i
$306$	−957.335	−	552.718i	−0.178847	−	0.103257i
$307$		−	4548.47i		−	0.845585i	−0.906227	−	0.422793i	$-0.861050\pi$
$307$		−	4548.47i		−	0.845585i	0.906227	−	0.422793i	$-0.138950\pi$
$308$	−2873.87	+	4977.69i	−0.531669	+	0.920878i
$309$	2440.17	+	4226.49i	0.449243	+	0.778112i
$310$	872.228	−	503.581i	0.159804	−	0.0922628i
$311$	−5264.16			−0.959817			−0.479908	−	0.877319i	$-0.659330\pi$
$311$	−5264.16			−0.959817			−0.479908	+	0.877319i	$0.659330\pi$
$312$	3557.28	+	5721.82i	0.645485	+	1.03825i
$313$	3910.77			0.706229			0.353114	−	0.935580i	$-0.385123\pi$
$313$	3910.77			0.706229			0.353114	+	0.935580i	$0.385123\pi$
$314$	4524.91	−	2612.46i	0.813234	−	0.469521i
$315$	−1416.78	−	2453.93i	−0.253417	−	0.438932i
$316$	−3015.71	+	5223.37i	−0.536858	+	0.929866i
$317$		−	8552.60i		−	1.51534i	−0.652640	−	0.757668i	$-0.726338\pi$
$317$		−	8552.60i		−	1.51534i	0.652640	−	0.757668i	$-0.273662\pi$
$318$	−6805.51	−	3929.16i	−1.20011	−	0.692882i
$319$	487.048	+	281.197i	0.0854841	+	0.0493543i
$320$			4320.41i			0.754745i
$321$	2286.98	−	3961.16i	0.397653	−	0.688755i
$322$	−4042.30	−	7001.48i	−0.699593	−	1.21173i
$323$	2394.79	−	1382.63i	0.412537	−	0.238179i
$324$	4392.14			0.753110
$325$	−110.031	−	3371.17i	−0.0187797	−	0.575381i
$326$	1578.02			0.268093
$327$	−4257.76	+	2458.22i	−0.720044	+	0.415718i
$328$	4647.71	+	8050.07i	0.782399	+	1.35516i
$329$	−9742.57	+	16874.6i	−1.63260	+	2.82774i
$330$		−	1526.71i		−	0.254674i
$331$	8895.99	+	5136.10i	1.47724	+	0.852888i	0.999670	−	0.0257031i	$-0.00818246\pi$
$331$	8895.99	+	5136.10i	1.47724	+	0.852888i	0.477575	+	0.878591i	$0.341516\pi$
$332$	−8295.13	−	4789.20i	−1.37125	−	0.791691i
$333$		−	1824.18i		−	0.300193i
$334$	−315.173	+	545.896i	−0.0516333	+	0.0894315i
$335$	2314.86	+	4009.46i	0.377535	+	0.653910i
$336$	6087.06	−	3514.36i	0.988322	−	0.570608i
$337$	−8953.48			−1.44726			−0.723631	−	0.690187i	$-0.757528\pi$
$337$	−8953.48			−1.44726			−0.723631	+	0.690187i	$0.757528\pi$
$338$	−8864.61	+	5920.64i	−1.42654	+	0.952782i
$339$	−4007.76			−0.642100
$340$	1929.78	−	1114.16i	0.307814	−	0.177716i
$341$	−156.761	−	271.518i	−0.0248946	−	0.0431188i
$342$	3943.91	−	6831.05i	0.623574	−	1.08006i
$343$		−	14934.5i		−	2.35099i
$344$	1180.26	+	681.424i	0.184987	+	0.106802i
$345$	1227.77	+	708.853i	0.191597	+	0.110618i
$346$			19415.5i			3.01672i
$347$	−386.824	+	669.999i	−0.0598439	+	0.103653i	−0.894395	−	0.447278i	$-0.852394\pi$
$347$	−386.824	+	669.999i	−0.0598439	+	0.103653i	0.834551	+	0.550930i	$0.185727\pi$
$348$	−1560.55	−	2702.96i	−0.240386	−	0.416361i
$349$	70.1548	−	40.5039i	0.0107602	−	0.00621239i	−0.494610	−	0.869115i	$-0.664689\pi$
$349$	70.1548	−	40.5039i	0.0107602	−	0.00621239i	0.505370	+	0.862902i	$0.331356\pi$
$350$	−11738.3			−1.79269
$351$	231.655	+	7097.54i	0.0352275	+	1.07931i
$352$	379.502			0.0574646
$353$	−9887.58	+	5708.60i	−1.49083	+	0.860731i	−0.999945	−	0.0104940i	$-0.996660\pi$
$353$	−9887.58	+	5708.60i	−1.49083	+	0.860731i	−0.490884	+	0.871225i	$0.663326\pi$
$354$	4032.83	+	6985.07i	0.605487	+	1.04873i
$355$	2617.79	−	4534.15i	0.391374	−	0.677880i
$356$			16354.5i			2.43479i
$357$	2251.18	+	1299.72i	0.333739	+	0.192684i
$358$	3535.01	+	2040.94i	0.521875	+	0.301305i
$359$		−	1673.33i		−	0.246003i	−0.992406	−	0.123002i	$-0.960748\pi$
$359$		−	1673.33i		−	0.246003i	0.992406	−	0.123002i	$-0.0392520\pi$
$360$	1542.27	−	2671.30i	0.225792	−	0.391083i
$361$	6436.25	+	11147.9i	0.938366	+	1.62530i
$362$	16287.9	−	9403.81i	2.36484	−	1.36534i
$363$	−475.252			−0.0687170
$364$	12931.3	+	20799.7i	1.86204	+	2.99506i
$365$	−8384.73			−1.20240
$366$	4120.77	−	2379.13i	0.588513	−	0.339778i
$367$	3221.05	+	5579.03i	0.458141	+	0.793523i	0.998863	−	0.0476785i	$-0.0151823\pi$
$367$	3221.05	+	5579.03i	0.458141	+	0.793523i	−0.540722	+	0.841201i	$0.681849\pi$
$368$	1319.09	−	2284.73i	0.186854	−	0.323640i
$369$			2939.52i			0.414703i
$370$	4823.61	+	2784.91i	0.677750	+	0.391299i
$371$	−12005.5	−	6931.35i	−1.68003	−	0.969968i
$372$			1739.94i			0.242505i
$373$	−3454.21	+	5982.86i	−0.479496	+	0.830512i	−0.999723	−	0.0235162i	$-0.992514\pi$
$373$	−3454.21	+	5982.86i	−0.479496	+	0.830512i	0.520227	+	0.854028i	$0.325847\pi$
$374$	−525.346	−	909.926i	−0.0726337	−	0.125805i
$375$	4879.19	−	2817.00i	0.671894	−	0.387918i
$376$	−21211.1			−2.90925
$377$	2035.17	−	1265.27i	0.278028	−	0.172851i
$378$	24713.5			3.36276
$379$	−12656.2	+	7307.08i	−1.71532	+	0.990341i	−0.788334	+	0.615248i	$0.789056\pi$
$379$	−12656.2	+	7307.08i	−1.71532	+	0.990341i	−0.926987	+	0.375093i	$0.877611\pi$
$380$	7950.05	+	13769.9i	1.07323	+	1.85890i
$381$	1245.31	−	2156.93i	0.167451	−	0.290034i
$382$			3182.18i			0.426216i
$383$	−1718.22	−	992.013i	−0.229234	−	0.132349i	0.380984	−	0.924581i	$-0.375585\pi$
$383$	−1718.22	−	992.013i	−0.229234	−	0.132349i	−0.610219	+	0.792233i	$0.708918\pi$
$384$	−8852.09	−	5110.76i	−1.17638	−	0.679185i
$385$		−	2693.24i		−	0.356519i
$386$	1364.32	−	2363.06i	0.179901	−	0.311598i
$387$	215.489	+	373.238i	0.0283047	+	0.0490252i
$388$	15023.1	−	8673.59i	1.96568	−	1.13488i
$389$	1403.79			0.182969			0.0914844	−	0.995807i	$-0.470839\pi$
$389$	1403.79			0.182969			0.0914844	+	0.995807i	$0.470839\pi$
$390$	−5737.01	−	3067.22i	−0.744884	−	0.398243i
$391$	975.676			0.126194
$392$	24950.3	−	14405.0i	3.21474	−	1.85603i
$393$	1812.68	+	3139.66i	0.232666	+	0.402990i
$394$	1834.28	−	3177.07i	0.234543	−	0.406240i
$395$		−	2826.16i		−	0.359999i
$396$	−1713.54	−	989.315i	−0.217447	−	0.125543i
$397$	−13128.1	−	7579.50i	−1.65965	−	0.958198i	−0.972877	−	0.231323i	$-0.925695\pi$
$397$	−13128.1	−	7579.50i	−1.65965	−	0.958198i	−0.686770	−	0.726875i	$-0.740972\pi$
$398$		−	12060.5i		−	1.51894i
$399$	−9274.12	+	16063.2i	−1.16363	+	2.01546i
$400$	−1915.23	−	3317.27i	−0.239404	−	0.414659i
$401$	9896.35	−	5713.66i	1.23242	−	0.711538i	0.264886	−	0.964280i	$-0.414666\pi$
$401$	9896.35	−	5713.66i	1.23242	−	0.711538i	0.967534	+	0.252742i	$0.0813325\pi$
$402$	−12115.0			−1.50308
$403$	−1335.24	+	43.5806i	−0.165044	+	0.00538686i
$404$	27105.2			3.33796
$405$	−1782.31	+	1029.02i	−0.218676	+	0.126253i
$406$	−4169.92	−	7222.52i	−0.509728	−	0.882876i
$407$	866.921	−	1501.55i	0.105581	−	0.182872i
$408$			2829.69i			0.343359i
$409$	−12791.4	−	7385.11i	−1.54644	−	0.892836i	−0.998410	−	0.0563767i	$-0.982045\pi$
$409$	−12791.4	−	7385.11i	−1.54644	−	0.892836i	−0.548028	−	0.836460i	$-0.684621\pi$
$410$	−7772.88	−	4487.67i	−0.936280	−	0.540562i
$411$		−	1120.77i		−	0.134510i
$412$	−9656.10	+	16724.9i	−1.15466	+	1.99994i
$413$	7114.23	+	12322.2i	0.847623	+	1.46813i
$414$	2410.22	−	1391.54i	0.286125	−	0.165195i
$415$	4488.17			0.530881
$416$	762.435	−	1426.08i	0.0898592	−	0.168075i
$417$	−915.348			−0.107494
$418$	6492.77	−	3748.60i	0.759741	−	0.438637i
$419$	−2520.76	−	4366.09i	−0.293908	−	0.509063i	0.680822	−	0.732449i	$-0.261623\pi$
$419$	−2520.76	−	4366.09i	−0.293908	−	0.509063i	−0.974730	+	0.223385i	$0.928289\pi$
$420$	−7473.29	+	12944.1i	−0.868237	+	1.50383i
$421$		−	12174.1i		−	1.40934i	−0.709537	−	0.704669i	$-0.751096\pi$
$421$		−	12174.1i		−	1.40934i	0.709537	−	0.704669i	$-0.248904\pi$
$422$	8225.78	+	4749.16i	0.948874	+	0.547833i
$423$	−5809.00	−	3353.83i	−0.667714	−	0.385505i
$424$		−	15090.6i		−	1.72846i
$425$	708.309	−	1226.83i	0.0808424	−	0.140023i
$426$	6850.18	+	11864.9i	0.779090	+	1.34942i
$427$	7269.36	−	4196.96i	0.823861	−	0.475657i
$428$	18099.8			2.04413
$429$	−954.801	+	1785.89i	−0.107455	+	0.200987i
$430$	−1315.92			−0.147580
$431$	854.888	−	493.570i	0.0955418	−	0.0551611i	−0.451468	−	0.892287i	$-0.649099\pi$
$431$	854.888	−	493.570i	0.0955418	−	0.0551611i	0.547010	+	0.837126i	$0.315766\pi$
$432$	4032.26	+	6984.07i	0.449079	+	0.777827i
$433$	8002.02	−	13859.9i	0.888112	−	1.53826i	0.0460073	−	0.998941i	$-0.485350\pi$
$433$	8002.02	−	13859.9i	0.888112	−	1.53826i	0.842105	−	0.539314i	$-0.181316\pi$
$434$			4649.27i			0.514221i
$435$	1266.53	+	731.232i	0.139599	+	0.0805975i
$436$	−16848.6	−	9727.53i	−1.85069	−	1.06850i
$437$			6961.92i			0.762091i
$438$	10970.5	−	19001.5i	1.19678	−	2.07289i
$439$	5441.24	+	9424.50i	0.591563	+	1.02462i	0.994022	+	0.109179i	$0.0348223\pi$
$439$	5441.24	+	9424.50i	0.591563	+	1.02462i	−0.402459	+	0.915438i	$0.631844\pi$
$440$	2539.01	−	1465.90i	0.275097	−	0.158827i
$441$	9110.71			0.983772
$442$	−4474.73	+	146.050i	−0.481541	+	0.0157169i
$443$	−14689.4			−1.57542			−0.787712	−	0.616043i	$-0.788735\pi$
$443$	−14689.4			−1.57542			−0.787712	+	0.616043i	$0.788735\pi$
$444$	−8333.12	+	4811.13i	−0.890704	+	0.514248i
$445$	−3831.63	−	6636.57i	−0.408172	−	0.706975i
$446$	6387.63	−	11063.7i	0.678169	−	1.17462i
$447$			6066.44i			0.641908i
$448$	−17271.9	−	9971.95i	−1.82148	−	1.05163i
$449$	−4251.75	−	2454.75i	−0.446887	−	0.258010i	0.259628	−	0.965709i	$-0.416400\pi$
$449$	−4251.75	−	2454.75i	−0.446887	−	0.258010i	−0.706515	+	0.707698i	$0.749734\pi$
$450$		−	4040.86i		−	0.423306i
$451$	−1396.98	+	2419.63i	−0.145856	+	0.252630i
$452$	−7929.66	−	13734.6i	−0.825176	−	1.42925i
$453$	3438.27	−	1985.08i	0.356609	−	0.205888i
$454$	5162.70			0.533695
$455$	−10120.5	−	5410.81i	−1.04277	−	0.557501i
$456$	−20191.2			−2.07355
$457$	−8446.25	+	4876.44i	−0.864549	+	0.499148i	−0.865533	−	0.500852i	$-0.833020\pi$
$457$	−8446.25	+	4876.44i	−0.864549	+	0.499148i	0.000984000		1.00000i	$0.499687\pi$
$458$	−1813.76	−	3141.53i	−0.185047	−	0.320511i
$459$	−1491.25	+	2582.92i	−0.151646	+	0.262659i
$460$			5610.08i			0.568633i
$461$	4997.84	+	2885.51i	0.504930	+	0.291521i	0.730747	−	0.682648i	$-0.239172\pi$
$461$	4997.84	+	2885.51i	0.504930	+	0.291521i	−0.225817	+	0.974170i	$0.572505\pi$
$462$	6103.41	+	3523.80i	0.614624	+	0.354853i
$463$		−	10103.3i		−	1.01413i	−0.861909	−	0.507063i	$-0.830731\pi$
$463$		−	10103.3i		−	1.01413i	0.861909	−	0.507063i	$-0.169269\pi$
$464$	1360.73	−	2356.86i	0.136143	−	0.235807i
$465$	−407.645	−	706.061i	−0.0406539	−	0.0704146i
$466$	10289.8	−	5940.85i	1.02289	−	0.590567i
$467$	11122.1			1.10207			0.551037	−	0.834481i	$-0.314232\pi$
$467$	11122.1			1.10207			0.551037	+	0.834481i	$0.314232\pi$
$468$	−7160.19	+	4451.52i	−0.707222	+	0.439683i
$469$	−21371.7			−2.10417
$470$	17736.8	−	10240.3i	1.74072	−	1.00500i
$471$	−2114.76	−	3662.88i	−0.206886	−	0.358336i
$472$	−7744.39	+	13413.7i	−0.755221	+	1.30808i
$473$			409.635i			0.0398204i
$474$	6404.64	+	3697.72i	0.620622	+	0.358317i
$475$	8754.01	+	5054.13i	0.845603	+	0.488209i
$476$			10286.3i			0.990492i
$477$	2386.08	−	4132.81i	0.229038	−	0.396706i
$478$	6813.12	+	11800.7i	0.651935	+	1.12918i
$479$	−11232.7	+	6485.20i	−1.07147	+	0.618614i	−0.928583	−	0.371125i	$-0.878972\pi$
$479$	−11232.7	+	6485.20i	−1.07147	+	0.618614i	−0.142888	+	0.989739i	$0.545639\pi$
$480$	986.868			0.0938420
$481$	−3900.80	−	6274.36i	−0.369773	−	0.594773i
$482$	59.4477			0.00561778
$483$	−5667.64	+	3272.21i	−0.533926	+	0.308263i
$484$	−940.322	−	1628.69i	−0.0883098	−	0.152957i
$485$	−4064.20	+	7039.41i	−0.380507	+	0.659058i
$486$			14462.5i			1.34986i
$487$	7708.01	+	4450.22i	0.717214	+	0.414084i	0.813726	−	0.581248i	$-0.197435\pi$
$487$	7708.01	+	4450.22i	0.717214	+	0.414084i	−0.0965126	+	0.995332i	$0.530769\pi$
$488$	7913.26	+	4568.72i	0.734050	+	0.423804i
$489$		−	1277.39i		−	0.118130i
$490$	−13909.0	+	24091.1i	−1.28234	+	2.22107i
$491$	2649.02	+	4588.23i	0.243479	+	0.421719i	0.961703	−	0.274094i	$-0.0883778\pi$
$491$	2649.02	+	4588.23i	0.243479	+	0.421719i	−0.718224	+	0.695812i	$0.755044\pi$
$492$	13428.2	−	7752.77i	1.23047	−	0.710410i
$493$	1006.48			0.0919463
$494$	−1042.14	−	31929.4i	−0.0949149	−	2.90804i
$495$	927.132			0.0841848
$496$	−1313.89	+	758.575i	−0.118942	+	0.0686715i
$497$	12084.3	+	20930.5i	1.09065	+	1.88906i
$498$	−5872.28	+	10171.1i	−0.528400	+	0.915216i
$499$			16775.9i			1.50499i	0.658597	+	0.752496i	$0.271150\pi$
$499$			16775.9i			1.50499i	−0.658597	+	0.752496i	$0.728850\pi$
$500$	19307.7	+	11147.3i	1.72693	+	0.997044i
$501$	441.899	+	255.130i	0.0394063	+	0.0227513i
$502$			29548.2i			2.62709i
$503$	−318.750	+	552.092i	−0.0282552	+	0.0489395i	−0.879807	−	0.475331i	$-0.842328\pi$
$503$	−318.750	+	552.092i	−0.0282552	+	0.0489395i	0.851552	+	0.524270i	$0.175662\pi$
$504$	7119.46	+	12331.3i	0.629218	+	1.08984i
$505$	−10999.2	+	6350.38i	−0.969221	+	0.559580i
$506$	2645.26			0.232403
$507$	4792.71	+	7175.83i	0.419826	+	0.628579i
$508$	9855.72			0.860781
$509$	−8064.60	+	4656.10i	−0.702273	+	0.405458i	−0.808194	−	0.588917i	$-0.799555\pi$
$509$	−8064.60	+	4656.10i	−0.702273	+	0.405458i	0.105920	+	0.994375i	$0.466221\pi$
$510$	−1366.12	−	2366.20i	−0.118614	−	0.205445i
$511$	19352.8	−	33520.1i	1.67538	−	2.90184i
$512$		−	17420.7i		−	1.50370i
$513$	−18430.4	−	10640.8i	−1.58620	−	0.915794i
$514$	18849.3	+	10882.6i	1.61752	+	0.933876i
$515$		−	9049.17i		−	0.774280i
$516$	1136.67	−	1968.77i	0.0969751	−	0.167966i
$517$	−3187.74	−	5521.32i	−0.271173	−	0.469686i
$518$	−22266.8	+	12855.7i	−1.88870	+	1.09044i
$519$	15716.7			1.32926
$520$	−407.530	−	12486.0i	−0.0343680	−	1.05298i
$521$	2984.82			0.250993			0.125496	−	0.992094i	$-0.459948\pi$
$521$	2984.82			0.250993			0.125496	+	0.992094i	$0.459948\pi$
$522$	2486.31	−	1435.47i	0.208473	−	0.120362i
$523$	−3404.91	−	5897.48i	−0.284677	−	0.493076i	0.687853	−	0.725850i	$-0.258553\pi$
$523$	−3404.91	−	5897.48i	−0.284677	−	0.493076i	−0.972531	+	0.232774i	$0.925220\pi$
$524$	−7173.06	+	12424.1i	−0.598009	+	1.03578i
$525$			9502.08i			0.789914i
$526$	−32212.0	−	18597.6i	−2.67017	−	1.54162i
$527$	−485.917	−	280.544i	−0.0401648	−	0.0231892i
$528$			2299.78i			0.189555i
$529$	4855.30	−	8409.63i	0.399055	−	0.691184i
$530$	7285.50	+	12618.9i	0.597098	+	1.03420i
$531$	−4241.85	+	2449.04i	−0.346668	+	0.200149i
$532$	−73398.1			−5.98160
$533$	6285.83	+	10110.6i	0.510825	+	0.821652i
$534$	20053.1			1.62506
$535$	−7344.83	+	4240.54i	−0.593542	+	0.342681i
$536$	−11632.4	−	20147.9i	−0.937394	−	1.62361i
$537$	1652.12	−	2861.56i	0.132764	−	0.229955i
$538$		−	19315.4i		−	1.54786i
$539$	7499.37	+	4329.77i	0.599297	+	0.346004i
$540$	−14851.6	−	8574.59i	−1.18354	−	0.683318i
$541$			200.402i			0.0159260i	0.999968	+	0.00796301i	$0.00253473\pi$
$541$			200.402i			0.0159260i	−0.999968	+	0.00796301i	$0.997465\pi$
$542$	1369.40	−	2371.87i	0.108525	−	0.187972i
$543$	−7612.31	−	13184.9i	−0.601612	−	1.04202i
$544$	588.178	−	339.585i	0.0463565	−	0.0267639i
$545$	9116.10			0.716497
$546$	25503.6	−	15855.7i	1.99900	−	1.24279i
$547$	−9841.40			−0.769265			−0.384632	−	0.923070i	$-0.625672\pi$
$547$	−9841.40			−0.769265			−0.384632	+	0.923070i	$0.625672\pi$
$548$	3840.87	−	2217.53i	0.299405	−	0.172862i
$549$	1444.78	+	2502.44i	0.112317	+	0.194538i
$550$	1920.37	−	3326.18i	0.148882	−	0.257871i
$551$			7181.71i			0.555266i
$552$	−6169.66	−	3562.06i	−0.475722	−	0.274658i
$553$	11298.3	+	6523.07i	0.868811	+	0.501608i
$554$		−	16341.3i		−	1.25320i
$555$	2254.36	−	3904.67i	0.172419	−	0.298638i
$556$	−1811.08	−	3136.89i	−0.138142	−	0.239269i
$557$	12143.1	−	7010.84i	0.923737	−	0.533320i	0.0389113	−	0.999243i	$-0.487611\pi$
$557$	12143.1	−	7010.84i	0.923737	−	0.533320i	0.884825	+	0.465923i	$0.154278\pi$
$558$	−1600.49			−0.121423
$559$	1539.31	+	822.972i	0.116469	+	0.0622684i
$560$	−13032.7			−0.983453
$561$	−736.578	+	425.264i	−0.0554338	+	0.0320047i
$562$	5724.31	+	9914.79i	0.429654	+	0.744182i
$563$	1069.43	−	1852.31i	0.0800552	−	0.138660i	−0.823218	−	0.567725i	$-0.807824\pi$
$563$	1069.43	−	1852.31i	0.0800552	−	0.138660i	0.903273	+	0.429065i	$0.141157\pi$
$564$			35381.8i			2.64157i
$565$	6435.64	+	3715.62i	0.479203	+	0.276668i
$566$	−23720.2	−	13694.9i	−1.76154	−	1.01703i
$567$		−	9500.31i		−	0.703661i
$568$	−13154.7	+	22784.5i	−0.971755	+	1.68313i
$569$	6519.91	+	11292.8i	0.480367	+	0.832020i	0.999746	−	0.0225236i	$-0.00717009\pi$
$569$	6519.91	+	11292.8i	0.480367	+	0.832020i	−0.519379	+	0.854544i	$0.673837\pi$
$570$	16884.0	−	9747.96i	1.24069	−	0.716311i
$571$	−15518.7			−1.13736			−0.568682	−	0.822557i	$-0.692547\pi$
$571$	−15518.7			−1.13736			−0.568682	+	0.822557i	$0.692547\pi$
$572$	−8009.36	+	261.416i	−0.585469	+	0.0191090i
$573$	2575.95			0.187804
$574$	35881.2	−	20716.0i	2.60915	−	1.50639i
$575$	1783.26	+	3088.70i	0.129334	+	0.224014i
$576$	3432.79	−	5945.77i	0.248321	−	0.430105i
$577$		−	45.4628i		−	0.00328014i	−0.999999	−	0.00164007i	$-0.999478\pi$
$577$		−	45.4628i		−	0.00328014i	0.999999	−	0.00164007i	$-0.000522051\pi$
$578$	19016.0	+	10978.9i	1.36845	+	0.790074i
$579$	−1912.88	−	1104.40i	−0.137300	−	0.0792701i
$580$			5787.19i			0.414310i
$581$	−10359.2	+	17942.6i	−0.739709	+	1.28121i
$582$	−10635.1	−	18420.6i	−0.757458	−	1.31195i
$583$	3928.15	−	2267.92i	0.279052	−	0.161111i
$584$	42134.1			2.98548
$585$	1862.64	−	3483.94i	0.131642	−	0.246228i
$586$	4402.00			0.310316
$587$	−23726.7	+	13698.6i	−1.66833	+	0.963208i	−0.699785	+	0.714353i	$0.746721\pi$
$587$	−23726.7	+	13698.6i	−1.66833	+	0.963208i	−0.968541	+	0.248855i	$0.919946\pi$
$588$	−24028.8	−	41619.1i	−1.68526	−	2.91895i
$589$	2001.82	−	3467.25i	0.140040	−	0.242556i
$590$		−	14955.4i		−	1.04357i
$591$	−2571.82	−	1484.84i	−0.179002	−	0.103347i
$592$	−7266.10	−	4195.09i	−0.504451	−	0.291245i
$593$			11744.6i			0.813310i	0.913582	+	0.406655i	$0.133305\pi$
$593$			11744.6i			0.813310i	−0.913582	+	0.406655i	$0.866695\pi$
$594$	−4043.09	+	7002.83i	−0.279276	+	0.483720i
$595$	−2409.95	−	4174.16i	−0.166048	−	0.287603i
$596$	−20789.6	+	12002.9i	−1.42882	+	0.824930i
$597$	−9762.86			−0.669292
$598$	5314.43	−	9940.26i	0.363417	−	0.679745i
$599$	27018.7			1.84299			0.921497	−	0.388386i	$-0.126967\pi$
$599$	27018.7			1.84299			0.921497	+	0.388386i	$0.126967\pi$
$600$	−8957.95	+	5171.88i	−0.609512	+	0.351902i
$601$	8908.82	+	15430.5i	0.604656	+	1.04730i	0.992106	+	0.125404i	$0.0400228\pi$
$601$	8908.82	+	15430.5i	0.604656	+	1.04730i	−0.387450	+	0.921891i	$0.626644\pi$
$602$	3037.28	−	5260.72i	0.205631	−	0.356164i
$603$		−	7357.11i		−	0.496857i
$604$	13605.7	+	7855.27i	0.916572	+	0.529183i
$605$	763.158	+	440.609i	0.0512839	+	0.0296088i
$606$		−	33235.1i		−	2.22786i
$607$	−944.176	+	1635.36i	−0.0631349	+	0.109353i	−0.895865	−	0.444326i	$-0.853443\pi$
$607$	−944.176	+	1635.36i	−0.0631349	+	0.109353i	0.832730	+	0.553679i	$0.186777\pi$
$608$	2423.10	+	4196.94i	0.161628	+	0.279948i
$609$	−5846.57	+	3375.52i	−0.389023	+	0.224602i
$610$	−8822.80			−0.585614
$611$	−27152.1	+	886.213i	−1.79780	+	0.0586782i
$612$	−3541.02			−0.233884
$613$	−19997.0	+	11545.3i	−1.31757	+	0.760700i	−0.983337	−	0.181790i	$-0.941811\pi$
$613$	−19997.0	+	11545.3i	−1.31757	+	0.760700i	−0.334234	+	0.942490i	$0.608478\pi$
$614$	−11034.7	−	19112.7i	−0.725285	−	1.25623i
$615$	−3632.73	+	6292.08i	−0.238189	+	0.412555i
$616$			13533.8i			0.885213i
$617$	−5907.17	−	3410.51i	−0.385435	−	0.222531i	0.294745	−	0.955576i	$-0.404765\pi$
$617$	−5907.17	−	3410.51i	−0.385435	−	0.222531i	−0.680180	+	0.733045i	$0.738099\pi$
$618$	20507.2	+	11839.8i	1.33482	+	0.770661i
$619$			6426.72i			0.417305i	0.977990	+	0.208652i	$0.0669077\pi$
$619$			6426.72i			0.417305i	−0.977990	+	0.208652i	$0.933092\pi$
$620$	1613.11	−	2793.99i	0.104490	−	0.180983i
$621$	−3754.42	−	6502.85i	−0.242608	−	0.420210i
$622$	−22120.0	+	12771.0i	−1.42594	+	0.823265i
$623$	35375.2			2.27492
$624$	8642.02	+	4620.34i	0.554420	+	0.296413i
$625$	−1451.53			−0.0928976
$626$	16433.1	−	9487.64i	1.04920	−	0.605755i
$627$	−3034.46	−	5255.84i	−0.193277	−	0.334766i
$628$	8368.43	−	14494.6i	0.531747	−	0.921012i
$629$		−	3102.94i		−	0.196697i
$630$	−11906.6	−	6874.30i	−0.752971	−	0.434728i
$631$	21301.5	+	12298.4i	1.34390	+	0.775899i	0.987377	−	0.158389i	$-0.0506301\pi$
$631$	21301.5	+	12298.4i	1.34390	+	0.775899i	0.356519	+	0.934288i	$0.383963\pi$
$632$			14201.7i			0.893853i
$633$	3844.40	−	6658.70i	0.241392	−	0.418104i
$634$	−20748.9	−	35938.1i	−1.29975	−	2.25124i
$635$	−3999.41	+	2309.06i	−0.249940	+	0.144303i
$636$	−25172.4			−1.56942
$637$	31336.8	−	19482.2i	1.94915	−	1.21179i
$638$	2728.77			0.169331
$639$	−7205.23	+	4159.94i	−0.446063	+	0.257535i
$640$	9476.42	+	16413.6i	0.585294	+	1.01376i
$641$	5340.87	−	9250.66i	0.329098	−	0.570014i	−0.653235	−	0.757155i	$-0.726589\pi$
$641$	5340.87	−	9250.66i	0.329098	−	0.570014i	0.982333	+	0.187141i	$0.0599221\pi$
$642$		−	22193.1i		−	1.36432i
$643$	−14317.3	−	8266.07i	−0.878099	−	0.506971i	−0.00806786	−	0.999967i	$-0.502568\pi$
$643$	−14317.3	−	8266.07i	−0.878099	−	0.506971i	−0.870031	+	0.492997i	$0.835901\pi$
$644$	−22427.7	−	12948.6i	−1.37232	−	0.792310i
$645$			1065.23i			0.0650282i
$646$	6708.62	−	11619.7i	0.408587	−	0.707693i
$647$	8342.25	+	14449.2i	0.506905	+	0.877986i	0.999968	+	0.00799184i	$0.00254391\pi$
$647$	8342.25	+	14449.2i	0.506905	+	0.877986i	−0.493063	+	0.869994i	$0.664123\pi$
$648$	8956.28	−	5170.91i	0.542957	−	0.313476i
$649$	−4655.51			−0.281579
$650$	−8640.91	−	13898.7i	−0.521422	−	0.838697i
$651$	3763.54			0.226582
$652$	4377.62	−	2527.42i	0.262946	−	0.151812i
$653$	7159.01	+	12399.8i	0.429026	+	0.743094i	0.996787	−	0.0800989i	$-0.0255236\pi$
$653$	7159.01	+	12399.8i	0.429026	+	0.743094i	−0.567761	+	0.823193i	$0.692190\pi$
$654$	−11927.4	+	20658.9i	−0.713148	+	1.23521i
$655$		−	6722.20i		−	0.401005i
$656$	11708.8	+	6760.06i	0.696876	+	0.402342i
$657$	11539.1	+	6662.10i	0.685210	+	0.395606i
$658$			94543.1i			5.60133i
$659$	−1305.94	+	2261.96i	−0.0771962	+	0.133708i	−0.902039	−	0.431654i	$-0.857930\pi$
$659$	−1305.94	+	2261.96i	−0.0771962	+	0.133708i	0.824843	+	0.565362i	$0.191263\pi$
$660$	−2445.24	−	4235.28i	−0.144213	−	0.249785i
$661$	−19852.9	+	11462.1i	−1.16821	+	0.674466i	−0.953258	−	0.302158i	$-0.902293\pi$
$661$	−19852.9	+	11462.1i	−1.16821	+	0.674466i	−0.214952	+	0.976625i	$0.568960\pi$
$662$	49841.4			2.92620
$663$	118.226	+	3622.26i	0.00692538	+	0.212182i
$664$	−22553.5			−1.31814
$665$	29784.6	−	17196.2i	1.73684	−	1.00277i
$666$	−4425.51	−	7665.22i	−0.257485	−	0.445978i
$667$	−1266.97	+	2194.46i	−0.0735493	+	0.127391i
$668$			2019.18i			0.116953i
$669$	−8955.98	−	5170.74i	−0.517576	−	0.298823i
$670$	19454.1	+	11231.9i	1.12176	+	0.647648i
$671$			2746.47i			0.158012i
$672$	−2277.79	+	3945.25i	−0.130756	+	0.226475i
$673$	6585.65	+	11406.7i	0.377204	+	0.653336i	0.990654	−	0.136397i	$-0.0435523\pi$
$673$	6585.65	+	11406.7i	0.377204	+	0.653336i	−0.613450	+	0.789733i	$0.710219\pi$
$674$	−37622.6	+	21721.4i	−2.15010	+	1.24136i
$675$	−10902.4			−0.621677
$676$	−15108.8	+	30622.5i	−0.859625	+	1.74229i
$677$	−14414.4			−0.818303			−0.409151	−	0.912467i	$-0.634175\pi$
$677$	−14414.4			−0.818303			−0.409151	+	0.912467i	$0.634175\pi$
$678$	−16840.7	+	9722.96i	−0.953926	+	0.550749i
$679$	−18761.2	−	32495.4i	−1.06037	−	1.83661i
$680$	2623.42	−	4543.89i	0.147946	−	0.256251i
$681$		−	4179.16i		−	0.235163i
$682$	−1317.42	−	760.613i	−0.0739687	−	0.0427058i
$683$	2993.81	+	1728.48i	0.167723	+	0.0968350i	0.581512	−	0.813538i	$-0.302461\pi$
$683$	2993.81	+	1728.48i	0.167723	+	0.0968350i	−0.413789	+	0.910373i	$0.635795\pi$
$684$		−	25266.9i		−	1.41243i
$685$	−1039.07	+	1799.73i	−0.0579576	+	0.100385i
$686$	−36231.6	−	62755.0i	−2.01652	−	3.49271i
$687$	−2543.04	+	1468.23i	−0.141227	+	0.0815375i
$688$	1982.25			0.109844
$689$	−630.497	−	19317.4i	−0.0348622	−	1.06812i
$690$	6878.80			0.379524
$691$	14085.7	−	8132.40i	0.775466	−	0.447715i	−0.0593553	−	0.998237i	$-0.518905\pi$
$691$	14085.7	−	8132.40i	0.775466	−	0.447715i	0.834821	+	0.550522i	$0.185571\pi$
$692$	31096.7	+	53861.0i	1.70826	+	2.95880i
$693$	−2139.92	+	3706.44i	−0.117300	+	0.203169i
$694$			3753.79i			0.205320i
$695$	1469.86	+	848.624i	0.0802230	+	0.0463168i
$696$	−6364.44	−	3674.51i	−0.346614	−	0.200118i
$697$			5000.15i			0.271728i
$698$	196.527	−	340.395i	0.0106571	−	0.0184587i
$699$	−4809.07	−	8329.55i	−0.260223	−	0.450719i
$700$	−32563.6	+	18800.6i	−1.75827	+	1.01514i
$701$	9771.57			0.526487			0.263243	−	0.964729i	$-0.415208\pi$
$701$	9771.57			0.526487			0.263243	+	0.964729i	$0.415208\pi$
$702$	18192.3	+	29261.9i	0.978095	+	1.57325i
$703$	22141.0			1.18786
$704$	5651.32	−	3262.79i	0.302546	−	0.174675i
$705$	−8289.48	−	14357.8i	−0.442837	−	0.767015i
$706$	−27698.5	+	47975.2i	−1.47655	+	2.55746i
$707$		−	58629.3i		−	3.11879i
$708$	22375.1	+	12918.3i	1.18772	+	0.685733i
$709$	−5159.07	−	2978.59i	−0.273276	−	0.157776i	0.357099	−	0.934066i	$-0.383766\pi$
$709$	−5159.07	−	2978.59i	−0.273276	−	0.157776i	−0.630376	+	0.776290i	$0.717099\pi$
$710$		−	25403.4i		−	1.34278i
$711$	−2245.53	+	3889.38i	−0.118445	+	0.205152i
$712$	19254.3	+	33349.4i	1.01346	+	1.75537i
$713$	1223.36	−	706.307i	0.0642569	−	0.0370988i
$714$	12612.6			0.661086
$715$	3188.92	−	1982.56i	0.166796	−	0.103698i
$716$	13075.4			0.682473
$717$	9552.54	−	5515.16i	0.497554	−	0.287263i
$718$	−4059.56	−	7031.36i	−0.211005	−	0.365471i
$719$	13184.3	−	22835.8i	0.683852	−	1.18447i	−0.289944	−	0.957044i	$-0.593637\pi$
$719$	13184.3	−	22835.8i	0.683852	−	1.18447i	0.973796	−	0.227423i	$-0.0730301\pi$
$720$		−	4486.45i		−	0.232223i
$721$	36176.3	+	20886.4i	1.86862	+	1.07885i
$722$	54090.4	+	31229.1i	2.78814	+	1.60973i
$723$		−	48.1224i		−	0.00247537i
$724$	30123.0	−	52174.6i	1.54629	−	2.67825i
$725$	1839.56	+	3186.22i	0.0942340	+	0.163218i
$726$	−1997.02	+	1152.98i	−0.102088	+	0.0589408i
$727$	34152.2			1.74228			0.871138	−	0.491038i	$-0.163382\pi$
$727$	34152.2			1.74228			0.871138	+	0.491038i	$0.163382\pi$
$728$	50856.7	+	27189.9i	2.58911	+	1.38424i
$729$	19337.1			0.982428
$730$	−35232.7	+	20341.6i	−1.78633	+	1.03134i
$731$	366.548	+	634.880i	0.0185462	+	0.0321229i
$732$	7621.00	−	13200.0i	0.384809	−	0.666509i
$733$			10731.5i			0.540758i	0.962754	+	0.270379i	$0.0871491\pi$
$733$			10731.5i			0.540758i	−0.962754	+	0.270379i	$0.912851\pi$
$734$	27069.8	+	15628.8i	1.36126	+	0.785923i
$735$	19501.6	+	11259.2i	0.978675	+	0.565038i
$736$			1709.90i			0.0856355i
$737$	3496.39	−	6055.92i	0.174750	−	0.302677i
$738$	7131.38	+	12351.9i	0.355704	+	0.616098i
$739$	6383.54	−	3685.54i	0.317757	−	0.183457i	−0.332636	−	0.943055i	$-0.607938\pi$
$739$	6383.54	−	3685.54i	0.317757	−	0.183457i	0.650392	+	0.759599i	$0.274605\pi$
$740$	17841.7			0.886316
$741$	−25846.6	+	843.602i	−1.28137	+	0.0418225i
$742$	−67262.7			−3.32789
$743$	−23683.3	+	13673.5i	−1.16939	+	0.675146i	−0.953536	−	0.301281i	$-0.902586\pi$
$743$	−23683.3	+	13673.5i	−1.16939	+	0.675146i	−0.215851	+	0.976426i	$0.569253\pi$
$744$	2048.45	+	3548.03i	0.100941	+	0.174835i
$745$	5624.23	−	9741.46i	0.276585	−	0.479059i
$746$			33520.1i			1.64512i
$747$	−6176.64	−	3566.09i	−0.302532	−	0.174667i
$748$	−2914.75	−	1682.83i	−0.142478	−	0.0822599i
$749$		−	39150.4i		−	1.90991i
$750$	13668.3	−	23674.1i	0.665460	−	1.15261i
$751$	−4473.45	−	7748.25i	−0.217362	−	0.376482i	0.736639	−	0.676286i	$-0.236412\pi$
$751$	−4473.45	−	7748.25i	−0.217362	−	0.376482i	−0.954001	+	0.299805i	$0.903078\pi$
$752$	−26718.1	+	15425.7i	−1.29562	+	0.748027i
$753$	23919.0			1.15758
$754$	5482.21	−	10254.1i	0.264788	−	0.495267i
$755$	−7361.53			−0.354852
$756$	68558.2	−	39582.1i	3.29820	−	1.90421i
$757$	6263.50	+	10848.7i	0.300728	+	0.520876i	0.976301	−	0.216417i	$-0.0694371\pi$
$757$	6263.50	+	10848.7i	0.300728	+	0.520876i	−0.675573	+	0.737293i	$0.736104\pi$
$758$	−35454.4	+	61408.8i	−1.69889	+	2.94257i
$759$		−	2141.32i		−	0.102404i
$760$	32422.9	+	18719.4i	1.54750	+	0.893451i
$761$	−30607.1	−	17671.0i	−1.45796	−	0.841753i	−0.459048	−	0.888412i	$-0.651809\pi$
$761$	−30607.1	−	17671.0i	−1.45796	−	0.841753i	−0.998911	+	0.0466590i	$0.985143\pi$
$762$		−	12084.6i		−	0.574513i
$763$	−21040.9	+	36443.9i	−0.998338	+	1.72917i
$764$	5096.70	+	8827.75i	0.241351	+	0.418032i
$765$	1436.93	−	829.612i	0.0679116	−	0.0392088i
$766$	−9626.62			−0.454078
$767$	−9353.10	+	17494.3i	−0.440314	+	0.823576i
$768$	−30955.0			−1.45442
$769$	9227.68	−	5327.60i	0.432716	−	0.249829i	−0.267787	−	0.963478i	$-0.586292\pi$
$769$	9227.68	−	5327.60i	0.432716	−	0.249829i	0.700503	+	0.713649i	$0.252959\pi$
$770$	−6533.87	−	11317.0i	−0.305798	−	0.529658i
$771$	8809.40	−	15258.3i	0.411495	−	0.712731i
$772$		−	8740.57i		−	0.407487i
$773$	−5480.11	−	3163.94i	−0.254988	−	0.147217i	0.367058	−	0.930198i	$-0.380365\pi$
$773$	−5480.11	−	3163.94i	−0.254988	−	0.147217i	−0.622046	+	0.782981i	$0.713698\pi$
$774$	1810.97	+	1045.57i	0.0841009	+	0.0485557i
$775$		−	2051.02i		−	0.0950645i
$776$	20423.0	−	35373.7i	0.944773	−	1.63640i
$777$	10406.6	+	18024.8i	0.480483	+	0.832220i
$778$	5898.73	−	3405.63i	0.271825	−	0.156938i
$779$	−35678.5			−1.64097
$780$	−20827.8	+	679.793i	−0.956094	+	0.0312058i
$781$	−7907.87			−0.362312
$782$	4099.80	−	2367.02i	0.187479	−	0.108241i
$783$	−3872.95	−	6708.15i	−0.176766	−	0.306168i
$784$	20952.0	−	36290.0i	0.954447	−	1.65315i
$785$			7842.44i			0.356571i
$786$	15233.8	+	8795.26i	0.691314	+	0.399131i
$787$	14826.3	+	8559.95i	0.671536	+	0.387712i	0.796659	−	0.604430i	$-0.206599\pi$
$787$	14826.3	+	8559.95i	0.671536	+	0.387712i	−0.125122	+	0.992141i	$0.539932\pi$
$788$		−	11751.5i		−	0.531254i
$789$	−15054.6	+	26075.4i	−0.679289	+	1.17656i
$790$	−6856.36	−	11875.6i	−0.308783	−	0.534827i
$791$	−29708.2	+	17152.1i	−1.33540	+	0.770995i
$792$	−4658.93			−0.209025
$793$	10320.6	+	5517.76i	0.462162	+	0.247089i
$794$	−73552.5			−3.28751
$795$	10214.9	−	5897.55i	0.455703	−	0.263100i
$796$	−19316.6	−	33457.2i	−0.860122	−	1.48977i
$797$	−12476.2	+	21609.3i	−0.554490	+	0.960404i	0.443454	+	0.896297i	$0.353753\pi$
$797$	−12476.2	+	21609.3i	−0.554490	+	0.960404i	−0.997943	+	0.0641067i	$0.979580\pi$
$798$			89997.2i			3.99231i
$799$	−9881.14	−	5704.88i	−0.437509	−	0.252596i
$800$	2150.05	+	1241.33i	0.0950197	+	0.0548597i
$801$			12177.7i			0.537176i
$802$	27723.0	−	48017.7i	1.22062	−	2.11417i
$803$	6332.18	+	10967.7i	0.278279	+	0.481993i
$804$	−33608.4	+	19403.8i	−1.47422	+	0.851144i
$805$	12134.7			0.531296
$806$	−5504.95	+	3422.45i	−0.240575	+	0.149567i
$807$	−15635.7			−0.682035
$808$	55271.9	−	31911.3i	2.40651	−	1.38940i
$809$	−12348.4	−	21388.1i	−0.536647	−	0.929500i	−0.999082	−	0.0428466i	$-0.986357\pi$
$809$	−12348.4	−	21388.1i	−0.536647	−	0.929500i	0.462435	−	0.886653i	$-0.346976\pi$
$810$	−4992.86	+	8647.88i	−0.216582	+	0.375130i
$811$			30317.8i			1.31270i	0.754455	+	0.656352i	$0.227901\pi$
$811$			30317.8i			1.31270i	−0.754455	+	0.656352i	$0.772099\pi$
$812$	−23135.7	−	13357.4i	−0.999884	−	0.577283i
$813$	−1920.01	−	1108.52i	−0.0828262	−	0.0478197i
$814$		−	8412.71i		−	0.362242i
$815$	−1184.28	+	2051.23i	−0.0509000	+	0.0881614i
$816$	2057.88	+	3564.35i	0.0882845	+	0.152913i
$817$	−4530.18	+	2615.50i	−0.193991	+	0.112001i
$818$	−71666.0			−3.06326
$819$	9628.76	+	15487.7i	0.410813	+	0.660786i
$820$	−28750.5			−1.22441
$821$	−18707.5	+	10800.8i	−0.795244	+	0.459135i	−0.841806	−	0.539781i	$-0.818507\pi$
$821$	−18707.5	+	10800.8i	−0.795244	+	0.459135i	0.0465612	+	0.998915i	$0.485174\pi$
$822$	−2719.03	−	4709.49i	−0.115373	−	0.199833i
$823$	4032.42	−	6984.36i	0.170791	−	0.295819i	−0.767905	−	0.640563i	$-0.778701\pi$
$823$	4032.42	−	6984.36i	0.170791	−	0.295819i	0.938697	+	0.344744i	$0.112034\pi$
$824$			45473.0i			1.92248i
$825$	−2692.52	−	1554.53i	−0.113626	−	0.0656020i
$826$	59788.1	+	34518.7i	2.51852	+	1.45407i
$827$			28844.4i			1.21284i	0.795145	+	0.606420i	$0.207395\pi$
$827$			28844.4i			1.21284i	−0.795145	+	0.606420i	$0.792605\pi$
$828$	4457.50	−	7720.61i	0.187088	−	0.324046i
$829$	−18545.5	−	32121.7i	−0.776974	−	1.34576i	−0.933678	−	0.358114i	$-0.883420\pi$
$829$	−18545.5	−	32121.7i	−0.776974	−	1.34576i	0.156704	−	0.987646i	$-0.449913\pi$
$830$	18859.3	−	10888.5i	0.788696	−	0.455354i
$831$	−13228.2			−0.552202
$832$	−907.079	−	27791.4i	−0.0377972	−	1.15805i
$833$	15497.4			0.644600
$834$	−3846.30	+	2220.66i	−0.159696	+	0.0922006i
$835$	−473.066	−	819.374i	−0.0196061	−	0.0339588i
$836$	12007.8	−	20798.2i	0.496769	−	0.860430i
$837$			4318.16i			0.178324i
$838$	−21184.6	−	12230.9i	−0.873280	−	0.504188i
$839$	2380.10	+	1374.15i	0.0979381	+	0.0565446i	0.548169	−	0.836368i	$-0.315325\pi$
$839$	2380.10	+	1374.15i	0.0979381	+	0.0565446i	−0.450231	+	0.892912i	$0.648658\pi$
$840$			35193.6i			1.44559i
$841$	10887.5	−	18857.8i	0.446411	−	0.773207i
$842$	−29534.8	−	51155.8i	−1.20883	−	2.09376i
$843$	8025.94	−	4633.78i	0.327910	−	0.189319i
$844$	30425.8			1.24087
$845$	−1043.35	−	15966.3i	−0.0424762	−	0.650007i
$846$	−32546.0			−1.32264
$847$	−3522.89	+	2033.94i	−0.142914	+	0.0825113i
$848$	−10974.6	−	19008.6i	−0.444422	−	0.769761i
$849$	−11085.9	+	19201.3i	−0.448135	+	0.776192i
$850$		−	6873.52i		−	0.277365i
$851$	6765.45	+	3906.03i	0.272522	+	0.157341i
$852$	38006.5	+	21943.0i	1.52826	+	0.882343i
$853$		−	27636.7i		−	1.10933i	−0.832072	−	0.554667i	$-0.812846\pi$
$853$		−	27636.7i		−	1.10933i	0.832072	−	0.554667i	$-0.187154\pi$
$854$	20363.9	−	35271.4i	0.815971	−	1.41330i
$855$	5919.69	+	10253.2i	0.236783	+	0.410119i
$856$	36908.5	−	21309.1i	1.47372	−	0.850854i
$857$	−8533.01			−0.340119			−0.170060	−	0.985434i	$-0.554396\pi$
$857$	−8533.01			−0.340119			−0.170060	+	0.985434i	$0.554396\pi$
$858$	320.536	+	9820.69i	0.0127540	+	0.390761i
$859$	−785.062			−0.0311828			−0.0155914	−	0.999878i	$-0.504963\pi$
$859$	−785.062			−0.0311828			−0.0155914	+	0.999878i	$0.504963\pi$
$860$	−3650.52	+	2107.63i	−0.144746	+	0.0835692i
$861$	−16769.4	−	29045.5i	−0.663765	−	1.14967i
$862$	2394.83	−	4147.97i	0.0946268	−	0.163899i
$863$			7926.87i			0.312670i	0.987704	+	0.156335i	$0.0499679\pi$
$863$			7926.87i			0.312670i	−0.987704	+	0.156335i	$0.950032\pi$
$864$	−4526.64	−	2613.46i	−0.178240	−	0.102907i
$865$	−25237.8	−	14571.0i	−0.992035	−	0.572752i
$866$		−	77652.6i		−	3.04705i
$867$	8887.35	−	15393.3i	0.348132	−	0.602982i
$868$	7446.45	+	12897.6i	0.291186	+	0.504348i
$869$	−3696.77	+	2134.33i	−0.144309	+	0.0833167i
$870$	7095.97			0.276524
$871$	−15732.3	−	25305.2i	−0.612020	−	0.984423i
$872$	−45809.3			−1.77901
$873$	11186.4	−	6458.44i	0.433678	−	0.250384i
$874$	16889.8	+	29254.1i	0.653670	+	1.13219i
$875$	24111.9	−	41763.1i	0.931579	−	1.61354i
$876$		−	70283.1i		−	2.71078i
$877$	−29880.7	−	17251.6i	−1.15051	−	0.664249i	−0.201500	−	0.979488i	$-0.564582\pi$
$877$	−29880.7	−	17251.6i	−1.15051	−	0.664249i	−0.949012	+	0.315240i	$0.897915\pi$
$878$	45728.3	+	26401.2i	1.75769	+	1.01480i
$879$		−	3563.38i		−	0.136735i
$880$	2132.14	−	3692.97i	0.0816754	−	0.141466i
$881$	8873.02	+	15368.5i	0.339319	+	0.587717i	0.984305	−	0.176477i	$-0.0564702\pi$
$881$	8873.02	+	15368.5i	0.339319	+	0.587717i	−0.644986	+	0.764194i	$0.723137\pi$
$882$	38283.3	−	22102.9i	1.46153	−	0.843812i
$883$	−31839.7			−1.21347			−0.606733	−	0.794906i	$-0.707520\pi$
$883$	−31839.7			−1.21347			−0.606733	+	0.794906i	$0.707520\pi$
$884$	−12179.5	+	7572.07i	−0.463396	+	0.288095i
$885$	−12106.3			−0.459829
$886$	−61724.9	+	35636.9i	−2.34051	+	1.35129i
$887$	14291.3	+	24753.2i	0.540985	+	0.937014i	0.998848	+	0.0479910i	$0.0152819\pi$
$887$	14291.3	+	24753.2i	0.540985	+	0.937014i	−0.457862	+	0.889023i	$0.651385\pi$
$888$	−11328.4	+	19621.4i	−0.428104	+	0.741498i
$889$		−	21318.2i		−	0.804262i
$890$	−32201.1	−	18591.3i	−1.21279	−	0.700204i
$891$	2692.02	+	1554.24i	0.101219	+	0.0584387i
$892$		−	40922.8i		−	1.53609i
$893$	40707.1	−	70506.7i	1.52543	−	2.64213i
$894$	14717.4	+	25491.2i	0.550585	+	0.953641i
$895$	−5305.94	+	3063.39i	−0.198166	+	0.114411i
$896$	−87490.2			−3.26210
$897$	−8046.56	−	4301.99i	−0.299517	−	0.160133i
$898$	−23821.2			−0.885215
$899$	1261.98	−	728.606i	0.0468181	−	0.0270304i
$900$	−6472.00	−	11209.8i	−0.239704	−	0.415179i
$901$	4058.74	−	7029.94i	0.150073	−	0.259935i
$902$			13556.4i			0.500421i
$903$	−4258.51	−	2458.65i	−0.156937	−	0.0906077i
$904$	−32339.7	−	18671.4i	−1.18983	−	0.686947i
$905$			28229.7i			1.03689i
$906$	9631.76	−	16682.7i	0.353194	−	0.611750i
$907$	590.744	+	1023.20i	0.0216266	+	0.0374584i	0.876636	−	0.481154i	$-0.159782\pi$
$907$	590.744	+	1023.20i	0.0216266	+	0.0374584i	−0.855010	+	0.518612i	$0.826449\pi$
$908$	14322.0	−	8268.78i	0.523448	−	0.302213i
$909$	20182.8			0.736438
$910$	−55653.4	+	1816.46i	−2.02736	+	0.0661705i
$911$	5094.51			0.185279			0.0926393	−	0.995700i	$-0.470470\pi$
$911$	5094.51			0.185279			0.0926393	+	0.995700i	$0.470470\pi$
$912$	−25433.4	+	14684.0i	−0.923446	+	0.533152i
$913$	−3389.49	−	5870.77i	−0.122865	−	0.212808i
$914$	−23660.8	+	40981.7i	−0.856269	+	1.48310i
$915$			7141.99i			0.258040i
$916$	−10063.2	−	5809.99i	−0.362988	−	0.209571i
$917$	26873.7	+	15515.5i	0.967773	+	0.558744i
$918$			14471.3i			0.520287i
$919$	8092.63	−	14016.9i	0.290480	−	0.503127i	−0.683443	−	0.730004i	$-0.739518\pi$
$919$	8092.63	−	14016.9i	0.290480	−	0.503127i	0.973923	+	0.226877i	$0.0728516\pi$
$920$	6604.81	+	11439.9i	0.236689	+	0.409958i
$921$	−15471.6	+	8932.52i	−0.553535	+	0.319584i
$922$	28001.3			1.00019
$923$	−15887.2	+	29715.9i	−0.566559	+	1.05971i
$924$	22575.5			0.803764
$925$	9822.99	−	5671.31i	0.349165	−	0.201591i
$926$	−24510.9	−	42454.1i	−0.869847	−	1.50662i
$927$	−7190.04	+	12453.5i	−0.254748	+	0.441237i
$928$			1763.88i			0.0623947i
$929$	22446.8	+	12959.7i	0.792741	+	0.457689i	0.840927	−	0.541149i	$-0.182011\pi$
$929$	22446.8	+	12959.7i	0.792741	+	0.457689i	−0.0481857	+	0.998838i	$0.515344\pi$
$930$	−3425.85	−	1977.92i	−0.120794	−	0.0697403i
$931$			110581.i			3.89276i
$932$	19030.2	−	32961.3i	0.668835	−	1.15846i
$933$	10338.0	+	17906.0i	0.362757	+	0.628313i
$934$	46735.1	−	26982.5i	1.63728	−	0.945284i
$935$	1577.06			0.0551607
$936$	−9359.97	+	17507.2i	−0.326859	+	0.611367i
$937$	2913.18			0.101568			0.0507842	−	0.998710i	$-0.483828\pi$
$937$	2913.18			0.101568			0.0507842	+	0.998710i	$0.483828\pi$
$938$	−89804.3	+	51848.5i	−3.12603	+	1.80481i
$939$	−7680.17	−	13302.4i	−0.266915	−	0.462310i
$940$	32802.7	−	56815.9i	1.13820	−	1.97142i
$941$		−	36762.9i		−	1.27358i	−0.771039	−	0.636788i	$-0.780263\pi$
$941$		−	36762.9i		−	1.27358i	0.771039	−	0.636788i	$-0.219737\pi$
$942$	−17772.5	−	10261.0i	−0.614713	−	0.354905i
$943$	−10902.0	−	6294.27i	−0.376477	−	0.217359i
$944$			22528.3i			0.776731i
$945$	−18547.1	+	32124.5i	−0.638451	+	1.10583i
$946$	993.787	+	1721.29i	0.0341552	+	0.0591585i
$947$	8152.48	−	4706.84i	0.279747	−	0.161512i	−0.353562	−	0.935411i	$-0.615030\pi$
$947$	8152.48	−	4706.84i	0.279747	−	0.161512i	0.633309	+	0.773899i	$0.281696\pi$
$948$	23689.7			0.811609
$949$	53935.5	−	1760.39i	1.84491	−	0.0602157i
$950$	49045.9			1.67501
$951$	−29091.6	+	16796.0i	−0.991966	+	0.572712i
$952$	12110.2	+	20975.5i	0.412285	+	0.714098i
$953$	−9047.04	+	15669.9i	−0.307515	+	0.532632i	−0.977818	−	0.209455i	$-0.932831\pi$
$953$	−9047.04	+	15669.9i	−0.307515	+	0.532632i	0.670303	+	0.742088i	$0.266164\pi$
$954$		−	23154.8i		−	0.785813i
$955$	−4136.44	−	2388.18i	−0.140159	−	0.0809210i
$956$	37800.8	+	21824.3i	1.27884	+	0.738336i
$957$		−	2208.92i		−	0.0746125i
$958$	−31466.6	+	54501.7i	−1.06121	+	1.83807i
$959$	−4796.58	−	8307.91i	−0.161511	−	0.279746i
$960$	14695.8	−	8484.65i	0.494069	−	0.285251i
$961$	28978.6			0.972731
$962$	−31613.0	−	16901.5i	−1.05950	−	0.566450i
$963$	13477.3			0.450987
$964$	164.915	−	95.2138i	0.00550992	−	0.00318115i
$965$	2047.80	+	3546.89i	0.0683118	+	0.118319i
$966$	−15877.0	+	27499.7i	−0.528813	+	0.915931i
$967$		−	28961.4i		−	0.963119i	−0.876413	−	0.481559i	$-0.840071\pi$
$967$		−	28961.4i		−	0.963119i	0.876413	−	0.481559i	$-0.159929\pi$
$968$	−3834.94	−	2214.10i	−0.127334	−	0.0735166i
$969$	−9406.03	−	5430.57i	−0.311832	−	0.180036i
$970$			39439.6i			1.30549i
$971$	9860.67	−	17079.2i	0.325895	−	0.564466i	−0.655798	−	0.754936i	$-0.727668\pi$
$971$	9860.67	−	17079.2i	0.325895	−	0.564466i	0.981693	+	0.190470i	$0.0610011\pi$
$972$	23163.6	+	40120.6i	0.764377	+	1.32394i
$973$	−6785.18	+	3917.43i	−0.223559	+	0.129072i
$974$	43185.5			1.42069
$975$	−11250.9	+	6994.75i	−0.369557	+	0.229755i
$976$	13290.3			0.435874
$977$	26097.8	−	15067.6i	0.854600	−	0.493403i	−0.00760057	−	0.999971i	$-0.502419\pi$
$977$	26097.8	−	15067.6i	0.854600	−	0.493403i	0.862200	+	0.506568i	$0.169086\pi$
$978$	−3099.00	−	5367.62i	−0.101324	−	0.175499i
$979$	−5787.32	+	10023.9i	−0.188931	+	0.327238i
$980$			89108.9i			2.90457i
$981$	−12545.6	−	7243.22i	−0.408309	−	0.235737i
$982$	22262.4	+	12853.2i	0.723443	+	0.417680i
$983$		−	25989.9i		−	0.843285i	−0.906762	−	0.421642i	$-0.861454\pi$
$983$		−	25989.9i		−	0.843285i	0.906762	−	0.421642i	$-0.138546\pi$
$984$	18254.8	−	31618.3i	0.591406	−	1.02434i
$985$	2753.20	+	4768.69i	0.0890603	+	0.154257i
$986$	4229.23	−	2441.75i	0.136599	−	0.0788652i
$987$	76531.9			2.46812
$988$	−54030.4	−	86906.8i	−1.73981	−	2.79846i
$989$	−1845.67			−0.0593416
$990$	3895.82	−	2249.25i	0.125068	−	0.0722080i
$991$	8523.03	+	14762.3i	0.273202	+	0.473199i	0.969680	−	0.244379i	$-0.0785840\pi$
$991$	8523.03	+	14762.3i	0.273202	+	0.473199i	−0.696478	+	0.717578i	$0.745251\pi$
$992$	491.662	−	851.583i	0.0157362	−	0.0272558i
$993$		−	40346.2i		−	1.28937i
$994$	101556.	+	58633.6i	3.24062	+	1.87097i
$995$	15677.1	+	9051.20i	0.499496	+	0.288384i
$996$			37621.1i			1.19686i
$997$	19423.4	−	33642.3i	0.616995	−	1.06867i	−0.373036	−	0.927817i	$-0.621683\pi$
$997$	19423.4	−	33642.3i	0.616995	−	1.06867i	0.990031	−	0.140850i	$-0.0449836\pi$
$998$	40698.8	+	70492.3i	1.29088	+	2.23587i
$999$	−20681.0	+	11940.2i	−0.654972	+	0.378148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.j.a.23.34	✓	72
13.2	odd	12		1859.4.a.l.1.34		36
13.4	even	6	inner	143.4.j.a.56.34	yes	72
13.11	odd	12		1859.4.a.m.1.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.j.a.23.34	✓	72	1.1	even	1	trivial
143.4.j.a.56.34	yes	72	13.4	even	6	inner
1859.4.a.l.1.34		36	13.2	odd	12
1859.4.a.m.1.3		36	13.11	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.20201 - 2.42603i) q^{2} +(-1.96385 - 3.40149i) q^{3} +(7.77126 - 13.4602i) q^{4} +7.28280i q^{5} +(-16.5043 - 9.52874i) q^{6} +(-29.1148 - 16.8094i) q^{7} -36.5968i q^{8} +(5.78656 - 10.0226i) q^{9} +(17.6683 + 30.6024i) q^{10} +(9.52628 - 5.50000i) q^{11} -61.0464 q^{12} +(-1.52904 - 46.8472i) q^{13} -163.121 q^{14} +(24.7724 - 14.3023i) q^{15} +(-26.6149 - 46.0983i) q^{16} +(9.84298 - 17.0485i) q^{17} -56.1535i q^{18} +(121.650 + 70.2344i) q^{19} +(98.0280 + 56.5965i) q^{20} +132.045i q^{21} +(26.6863 - 46.2221i) q^{22} +(24.7810 + 42.9220i) q^{23} +(-124.484 + 71.8707i) q^{24} +71.9609 q^{25} +(-120.078 - 193.143i) q^{26} -151.504 q^{27} +(-452.518 + 261.261i) q^{28} +(25.5634 + 44.2771i) q^{29} +(69.3959 - 120.197i) q^{30} -28.5019i q^{31} +(29.8781 + 17.2501i) q^{32} +(-37.4164 - 21.6024i) q^{33} -95.5175i q^{34} +(122.420 - 212.037i) q^{35} +(-89.9377 - 155.777i) q^{36} +(136.505 - 78.8110i) q^{37} +681.564 q^{38} +(-156.348 + 97.2021i) q^{39} +266.527 q^{40} +(-219.967 + 126.998i) q^{41} +(320.346 + 554.855i) q^{42} +(-18.6198 + 32.2504i) q^{43} -170.968i q^{44} +(72.9927 + 42.1424i) q^{45} +(208.260 + 120.239i) q^{46} -579.589i q^{47} +(-104.535 + 181.061i) q^{48} +(393.615 + 681.761i) q^{49} +(302.380 - 174.579i) q^{50} -77.3206 q^{51} +(-642.456 - 343.481i) q^{52} +412.349 q^{53} +(-636.621 + 367.553i) q^{54} +(40.0554 + 69.3780i) q^{55} +(-615.172 + 1065.51i) q^{56} -551.720i q^{57} +(214.835 + 124.035i) q^{58} +(-366.526 - 211.614i) q^{59} -444.589i q^{60} +(-124.839 + 216.228i) q^{61} +(-69.1466 - 119.765i) q^{62} +(-336.949 + 194.538i) q^{63} +593.235 q^{64} +(341.179 - 11.1357i) q^{65} -209.632 q^{66} +(550.538 - 317.853i) q^{67} +(-152.985 - 264.977i) q^{68} +(97.3325 - 168.585i) q^{69} -1187.98i q^{70} +(-622.583 - 359.448i) q^{71} +(-366.796 - 211.770i) q^{72} +1151.31i q^{73} +(382.396 - 662.329i) q^{74} +(-141.321 - 244.774i) q^{75} +(1890.74 - 1091.62i) q^{76} -369.808 q^{77} +(-421.159 + 787.749i) q^{78} -388.060 q^{79} +(335.725 - 193.831i) q^{80} +(141.294 + 244.729i) q^{81} +(-616.202 + 1067.29i) q^{82} -616.271i q^{83} +(1777.36 + 1026.16i) q^{84} +(124.161 + 71.6844i) q^{85} +180.689i q^{86} +(100.405 - 173.907i) q^{87} +(-201.282 - 348.631i) q^{88} +(-911.267 + 526.120i) q^{89} +408.955 q^{90} +(-742.958 + 1389.65i) q^{91} +770.319 q^{92} +(-96.9492 + 55.9736i) q^{93} +(-1406.10 - 2435.44i) q^{94} +(-511.503 + 885.949i) q^{95} -135.507i q^{96} +(966.580 + 558.055i) q^{97} +(3307.95 + 1909.84i) q^{98} -127.304i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{3} + 152 q^{4} + 90 q^{6} - 36 q^{7} - 360 q^{9} - 56 q^{10} - 132 q^{12} - 46 q^{13} + 328 q^{14} - 644 q^{16} + 138 q^{17} + 492 q^{19} + 540 q^{20} - 44 q^{22} + 46 q^{23} + 720 q^{24} - 1636 q^{25}+ \cdots - 8550 q^{98}+O(q^{100}) \) 72 * q - 12 * q^3 + 152 * q^4 + 90 * q^6 - 36 * q^7 - 360 * q^9 - 56 * q^10 - 132 * q^12 - 46 * q^13 + 328 * q^14 - 644 * q^16 + 138 * q^17 + 492 * q^19 + 540 * q^20 - 44 * q^22 + 46 * q^23 + 720 * q^24 - 1636 * q^25 - 902 * q^26 + 48 * q^27 - 714 * q^28 - 262 * q^29 + 104 * q^30 + 144 * q^32 - 68 * q^35 + 1960 * q^36 + 630 * q^37 - 448 * q^38 - 1612 * q^39 + 216 * q^40 + 126 * q^41 - 82 * q^42 + 436 * q^43 - 570 * q^45 - 1590 * q^46 + 1944 * q^48 + 1192 * q^49 + 1290 * q^50 - 1424 * q^51 + 590 * q^52 + 292 * q^53 - 528 * q^54 - 440 * q^55 - 102 * q^56 - 1128 * q^58 + 504 * q^59 + 590 * q^61 + 1776 * q^62 + 1884 * q^63 - 5028 * q^64 + 994 * q^65 + 2156 * q^66 + 3396 * q^67 + 1530 * q^68 + 12 * q^69 - 1014 * q^71 - 1062 * q^72 - 1568 * q^74 + 4688 * q^75 + 7872 * q^76 - 1232 * q^77 - 4964 * q^78 - 2928 * q^79 - 558 * q^80 - 3780 * q^81 - 4072 * q^82 + 696 * q^84 + 4662 * q^85 + 1832 * q^87 + 924 * q^88 + 1014 * q^89 + 6844 * q^90 + 2900 * q^91 - 1336 * q^92 - 4092 * q^93 + 4166 * q^94 - 256 * q^95 - 5070 * q^97 - 8550 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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