LMFDB - Embedded newform 29.4.d.a.20.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [29,4,Mod(7,29)] 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("29.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, 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:	$1.71105539017$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			20.2
Character	$\chi$	$=$	29.20
Dual form			29.4.d.a.16.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.77959 + 1.82016i) q^{2} +(-2.29509 - 2.87796i) q^{3} +(5.98444 - 7.50425i) q^{4} +(15.1796 - 7.31010i) q^{5} +(13.9128 + 6.70007i) q^{6} +(-0.697313 - 0.874402i) q^{7} +(-1.49198 + 6.53678i) q^{8} +(2.99289 - 13.1127i) q^{9} +(-44.0671 + 55.2584i) q^{10} +(-11.5503 - 50.6050i) q^{11} -35.3317 q^{12} +(12.0778 + 52.9164i) q^{13} +(4.22711 + 2.03567i) q^{14} +(-55.8767 - 26.9088i) q^{15} +(10.8277 + 47.4391i) q^{16} -17.6876 q^{17} +(12.5553 + 55.0082i) q^{18} +(52.4402 - 65.7579i) q^{19} +(35.9845 - 157.658i) q^{20} +(-0.916094 + 4.01367i) q^{21} +(135.764 + 170.243i) q^{22} +(31.8854 + 15.3552i) q^{23} +(22.2368 - 10.7087i) q^{24} +(99.0460 - 124.200i) q^{25} +(-141.965 - 178.019i) q^{26} +(-134.152 + 64.6044i) q^{27} -10.7348 q^{28} +(154.898 + 19.8874i) q^{29} +260.169 q^{30} +(-292.895 + 141.051i) q^{31} +(-160.714 - 201.529i) q^{32} +(-119.130 + 149.384i) q^{33} +(66.8519 - 32.1942i) q^{34} +(-16.9769 - 8.17564i) q^{35} +(-80.4902 - 100.932i) q^{36} +(-38.8742 + 170.319i) q^{37} +(-78.5129 + 343.987i) q^{38} +(124.571 - 156.207i) q^{39} +(25.1370 + 110.132i) q^{40} +318.857 q^{41} +(-3.84304 - 16.8375i) q^{42} +(258.729 + 124.597i) q^{43} +(-448.874 - 216.166i) q^{44} +(-50.4244 - 220.924i) q^{45} -148.463 q^{46} +(40.5877 + 177.826i) q^{47} +(111.677 - 140.039i) q^{48} +(76.0463 - 333.181i) q^{49} +(-148.291 + 649.704i) q^{50} +(40.5947 + 50.9041i) q^{51} +(469.377 + 226.040i) q^{52} +(-445.738 + 214.656i) q^{53} +(389.451 - 488.357i) q^{54} +(-545.256 - 683.729i) q^{55} +(6.75615 - 3.25359i) q^{56} -309.603 q^{57} +(-621.651 + 206.773i) q^{58} +225.125 q^{59} +(-536.321 + 258.279i) q^{60} +(485.551 + 608.862i) q^{61} +(850.289 - 1066.23i) q^{62} +(-13.5528 + 6.52666i) q^{63} +(623.527 + 300.275i) q^{64} +(570.160 + 714.959i) q^{65} +(178.360 - 781.447i) q^{66} +(67.6078 - 296.209i) q^{67} +(-105.850 + 132.732i) q^{68} +(-28.9884 - 127.007i) q^{69} +79.0467 q^{70} +(-46.8127 - 205.100i) q^{71} +(81.2496 + 39.1277i) q^{72} +(316.380 + 152.361i) q^{73} +(-163.079 - 714.494i) q^{74} -584.761 q^{75} +(-179.639 - 787.048i) q^{76} +(-36.1950 + 45.3871i) q^{77} +(-186.507 + 817.140i) q^{78} +(-109.326 + 478.991i) q^{79} +(511.145 + 640.955i) q^{80} +(166.636 + 80.2476i) q^{81} +(-1205.15 + 580.369i) q^{82} +(-334.768 + 419.785i) q^{83} +(24.6373 + 30.8941i) q^{84} +(-268.490 + 129.298i) q^{85} -1204.68 q^{86} +(-298.271 - 491.434i) q^{87} +348.027 q^{88} +(-838.575 + 403.836i) q^{89} +(592.699 + 743.221i) q^{90} +(37.8482 - 47.4601i) q^{91} +(306.046 - 147.384i) q^{92} +(1078.16 + 519.214i) q^{93} +(-477.077 - 598.235i) q^{94} +(315.323 - 1381.52i) q^{95} +(-211.138 + 925.057i) q^{96} +(916.045 - 1148.68i) q^{97} +(319.017 + 1397.70i) q^{98} -698.137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) $ 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	−3.77959	+	1.82016i	−1.33629	+	0.643522i	−0.959219	−	0.282663i	$-0.908782\pi$
$2$	−3.77959	+	1.82016i	−1.33629	+	0.643522i	−0.377069	+	0.926185i	$0.623068\pi$
$3$	−2.29509	−	2.87796i	−0.441691	−	0.553863i	0.510297	−	0.859998i	$-0.329535\pi$
$3$	−2.29509	−	2.87796i	−0.441691	−	0.553863i	−0.951988	+	0.306135i	$0.900964\pi$
$4$	5.98444	−	7.50425i	0.748055	−	0.938031i
$5$	15.1796	−	7.31010i	1.35770	−	0.653835i	0.393580	−	0.919290i	$-0.371236\pi$
$5$	15.1796	−	7.31010i	1.35770	−	0.653835i	0.964123	+	0.265455i	$0.0855221\pi$
$6$	13.9128	+	6.70007i	0.946649	+	0.455882i
$7$	−0.697313	−	0.874402i	−0.0376513	−	0.0472133i	0.762649	−	0.646812i	$-0.223898\pi$
$7$	−0.697313	−	0.874402i	−0.0376513	−	0.0472133i	−0.800301	+	0.599599i	$0.795327\pi$
$8$	−1.49198	+	6.53678i	−0.0659367	+	0.288888i
$9$	2.99289	−	13.1127i	0.110848	−	0.485656i
$10$	−44.0671	+	55.2584i	−1.39352	+	1.74743i
$11$	−11.5503	−	50.6050i	−0.316594	−	1.38709i	−0.843483	−	0.537155i	$-0.819499\pi$
$11$	−11.5503	−	50.6050i	−0.316594	−	1.38709i	0.526889	−	0.849934i	$-0.323358\pi$
$12$	−35.3317			−0.849949
$13$	12.0778	+	52.9164i	0.257676	+	1.12895i	0.923729	+	0.383047i	$0.125125\pi$
$13$	12.0778	+	52.9164i	0.257676	+	1.12895i	−0.666053	+	0.745904i	$0.732018\pi$
$14$	4.22711	+	2.03567i	0.0806958	+	0.0388611i
$15$	−55.8767	−	26.9088i	−0.961820	−	0.463188i
$16$	10.8277	+	47.4391i	0.169182	+	0.741236i
$17$	−17.6876			−0.252345			−0.126173	−	0.992008i	$-0.540269\pi$
$17$	−17.6876			−0.252345			−0.126173	+	0.992008i	$0.540269\pi$
$18$	12.5553	+	55.0082i	0.164406	+	0.720309i
$19$	52.4402	−	65.7579i	0.633189	−	0.793994i	−0.356944	−	0.934126i	$-0.616181\pi$
$19$	52.4402	−	65.7579i	0.633189	−	0.793994i	0.990133	+	0.140132i	$0.0447526\pi$
$20$	35.9845	−	157.658i	0.402318	−	1.76267i
$21$	−0.916094	+	4.01367i	−0.00951943	+	0.0417074i
$22$	135.764	+	170.243i	1.31568	+	1.64982i
$23$	31.8854	+	15.3552i	0.289068	+	0.139208i	0.572799	−	0.819696i	$-0.305858\pi$
$23$	31.8854	+	15.3552i	0.289068	+	0.139208i	−0.283730	+	0.958904i	$0.591572\pi$
$24$	22.2368	−	10.7087i	0.189128	−	0.0910792i
$25$	99.0460	−	124.200i	0.792368	−	0.993598i
$26$	−141.965	−	178.019i	−1.07083	−	1.34278i
$27$	−134.152	+	64.6044i	−0.956209	+	0.460486i
$28$	−10.7348			−0.0724528
$29$	154.898	+	19.8874i	0.991859	+	0.127345i
$29$	154.898	+	19.8874i	0.991859	+	0.127345i
$30$	260.169			1.58334
$31$	−292.895	+	141.051i	−1.69695	+	0.817208i	−0.702537	+	0.711647i	$0.747949\pi$
$31$	−292.895	+	141.051i	−1.69695	+	0.817208i	−0.994413	+	0.105560i	$0.966336\pi$
$32$	−160.714	−	201.529i	−0.887829	−	1.11330i
$33$	−119.130	+	149.384i	−0.628421	+	0.788014i
$34$	66.8519	−	32.1942i	0.337206	−	0.162390i
$35$	−16.9769	−	8.17564i	−0.0819891	−	0.0394839i
$36$	−80.4902	−	100.932i	−0.372640	−	0.467276i
$37$	−38.8742	+	170.319i	−0.172726	+	0.756764i	0.812142	+	0.583460i	$0.198301\pi$
$37$	−38.8742	+	170.319i	−0.172726	+	0.756764i	−0.984868	+	0.173304i	$0.944556\pi$
$38$	−78.5129	+	343.987i	−0.335170	+	1.46848i
$39$	124.571	−	156.207i	0.511471	−	0.641364i
$40$	25.1370	+	110.132i	0.0993625	+	0.435336i
$41$	318.857			1.21456			0.607282	−	0.794487i	$-0.292260\pi$
$41$	318.857			1.21456			0.607282	+	0.794487i	$0.292260\pi$
$42$	−3.84304	−	16.8375i	−0.0141189	−	0.0618590i
$43$	258.729	+	124.597i	0.917578	+	0.441882i	0.832206	−	0.554467i	$-0.187078\pi$
$43$	258.729	+	124.597i	0.917578	+	0.441882i	0.0853722	+	0.996349i	$0.472792\pi$
$44$	−448.874	−	216.166i	−1.53796	−	0.740644i
$45$	−50.4244	−	220.924i	−0.167041	−	0.731853i
$46$	−148.463			−0.475862
$47$	40.5877	+	177.826i	0.125964	+	0.551886i	0.998044	+	0.0625213i	$0.0199141\pi$
$47$	40.5877	+	177.826i	0.125964	+	0.551886i	−0.872079	+	0.489365i	$0.837229\pi$
$48$	111.677	−	140.039i	0.335817	−	0.421101i
$49$	76.0463	−	333.181i	0.221709	−	0.971373i
$50$	−148.291	+	649.704i	−0.419429	+	1.83764i
$51$	40.5947	+	50.9041i	0.111459	+	0.139765i
$52$	469.377	+	226.040i	1.25175	+	0.602809i
$53$	−445.738	+	214.656i	−1.15522	+	0.556327i	−0.910599	−	0.413291i	$-0.864379\pi$
$53$	−445.738	+	214.656i	−1.15522	+	0.556327i	−0.244625	+	0.969618i	$0.578665\pi$
$54$	389.451	−	488.357i	0.981437	−	1.23068i
$55$	−545.256	−	683.729i	−1.33677	−	1.67626i
$56$	6.75615	−	3.25359i	0.0161219	−	0.00776392i
$57$	−309.603			−0.719438
$58$	−621.651	+	206.773i	−1.40736	+	0.468114i
$59$	225.125			0.496759			0.248379	−	0.968663i	$-0.420102\pi$
$59$	225.125			0.496759			0.248379	+	0.968663i	$0.420102\pi$
$60$	−536.321	+	258.279i	−1.15398	+	0.555727i
$61$	485.551	+	608.862i	1.01916	+	1.27798i	0.960080	+	0.279727i	$0.0902440\pi$
$61$	485.551	+	608.862i	1.01916	+	1.27798i	0.0590759	+	0.998253i	$0.481185\pi$
$62$	850.289	−	1066.23i	1.74172	−	2.18405i
$63$	−13.5528	+	6.52666i	−0.0271030	+	0.0130521i
$64$	623.527	+	300.275i	1.21783	+	0.586474i
$65$	570.160	+	714.959i	1.08800	+	1.36430i
$66$	178.360	−	781.447i	0.332646	−	1.45742i
$67$	67.6078	−	296.209i	0.123278	−	0.540115i	−0.875139	−	0.483871i	$-0.839230\pi$
$67$	67.6078	−	296.209i	0.123278	−	0.540115i	0.998417	−	0.0562440i	$-0.0179125\pi$
$68$	−105.850	+	132.732i	−0.188768	+	0.236708i
$69$	−28.9884	−	127.007i	−0.0505767	−	0.221591i
$70$	79.0467			0.134970
$71$	−46.8127	−	205.100i	−0.0782486	−	0.342829i	0.920616	−	0.390469i	$-0.127687\pi$
$71$	−46.8127	−	205.100i	−0.0782486	−	0.342829i	−0.998865	+	0.0476398i	$0.984830\pi$
$72$	81.2496	+	39.1277i	0.132991	+	0.0640451i
$73$	316.380	+	152.361i	0.507253	+	0.244280i	0.669964	−	0.742394i	$-0.266310\pi$
$73$	316.380	+	152.361i	0.507253	+	0.244280i	−0.162711	+	0.986674i	$0.552024\pi$
$74$	−163.079	−	714.494i	−0.256182	−	1.12241i
$75$	−584.761			−0.900299
$76$	−179.639	−	787.048i	−0.271131	−	1.18790i
$77$	−36.1950	+	45.3871i	−0.0535689	+	0.0671732i
$78$	−186.507	+	817.140i	−0.270740	+	1.18619i
$79$	−109.326	+	478.991i	−0.155699	+	0.682160i	0.835468	+	0.549539i	$0.185197\pi$
$79$	−109.326	+	478.991i	−0.155699	+	0.682160i	−0.991167	+	0.132621i	$0.957661\pi$
$80$	511.145	+	640.955i	0.714346	+	0.895762i
$81$	166.636	+	80.2476i	0.228581	+	0.110079i
$82$	−1205.15	+	580.369i	−1.62301	+	0.781599i
$83$	−334.768	+	419.785i	−0.442717	+	0.555150i	−0.952257	−	0.305297i	$-0.901244\pi$
$83$	−334.768	+	419.785i	−0.442717	+	0.555150i	0.509540	+	0.860447i	$0.329816\pi$
$84$	24.6373	+	30.8941i	0.0320017	+	0.0401289i
$85$	−268.490	+	129.298i	−0.342610	+	0.164992i
$86$	−1204.68			−1.51051
$87$	−298.271	−	491.434i	−0.367563	−	0.605601i
$88$	348.027			0.421588
$89$	−838.575	+	403.836i	−0.998750	+	0.480973i	−0.860514	−	0.509427i	$-0.829857\pi$
$89$	−838.575	+	403.836i	−0.998750	+	0.480973i	−0.138236	+	0.990399i	$0.544143\pi$
$90$	592.699	+	743.221i	0.694178	+	0.870471i
$91$	37.8482	−	47.4601i	0.0435996	−	0.0546722i
$92$	306.046	−	147.384i	0.346820	−	0.167020i
$93$	1078.16	+	519.214i	1.20215	+	0.578924i
$94$	−477.077	−	598.235i	−0.523476	−	0.656418i
$95$	315.323	−	1381.52i	0.340542	−	1.49201i
$96$	−211.138	+	925.057i	−0.224471	+	0.983471i
$97$	916.045	−	1148.68i	0.958869	−	1.20238i	−0.0203944	−	0.999792i	$-0.506492\pi$
$97$	916.045	−	1148.68i	0.958869	−	1.20238i	0.979263	−	0.202592i	$-0.0649364\pi$
$98$	319.017	+	1397.70i	0.328832	+	1.44071i
$99$	−698.137			−0.708742
$100$	−339.291	−	1486.53i	−0.339291	−	1.48653i
$101$	−613.753	−	295.568i	−0.604661	−	0.291189i	0.106396	−	0.994324i	$-0.466069\pi$
$101$	−613.753	−	295.568i	−0.604661	−	0.291189i	−0.711057	+	0.703135i	$0.751783\pi$
$102$	−246.085	−	118.508i	−0.238883	−	0.115040i
$103$	−6.91431	−	30.2936i	−0.00661444	−	0.0289798i	0.971513	−	0.236986i	$-0.0761596\pi$
$103$	−6.91431	−	30.2936i	−0.00661444	−	0.0289798i	−0.978127	+	0.208006i	$0.933302\pi$
$104$	−363.923			−0.343130
$105$	15.4344	+	67.6226i	0.0143452	+	0.0628504i
$106$	1294.00	−	1622.63i	1.18570	−	1.48682i
$107$	145.285	−	636.537i	0.131264	−	0.575106i	−0.865924	−	0.500175i	$-0.833269\pi$
$107$	145.285	−	636.537i	0.131264	−	0.575106i	0.997189	−	0.0749314i	$-0.0238738\pi$
$108$	−318.019	+	1393.33i	−0.283346	+	1.24142i
$109$	37.1690	+	46.6085i	0.0326619	+	0.0409567i	0.797894	−	0.602798i	$-0.205947\pi$
$109$	37.1690	+	46.6085i	0.0326619	+	0.0409567i	−0.765232	+	0.643754i	$0.777376\pi$
$110$	3305.34	+	1591.77i	2.86502	+	1.37972i
$111$	579.390	−	279.020i	0.495435	−	0.238589i
$112$	33.9306	−	42.5476i	0.0286263	−	0.0358962i
$113$	−27.9008	−	34.9865i	−0.0232273	−	0.0291262i	0.770082	−	0.637945i	$-0.220215\pi$
$113$	−27.9008	−	34.9865i	−0.0232273	−	0.0291262i	−0.793310	+	0.608819i	$0.791644\pi$
$114$	1170.17	−	563.526i	0.961376	−	0.462974i
$115$	596.256			0.483488
$116$	1076.22	−	1043.38i	0.861418	−	0.835133i
$117$	730.024			0.576844
$118$	−850.880	+	409.762i	−0.663813	+	0.319675i
$119$	12.3338	+	15.4661i	0.00950114	+	0.0119141i
$120$	259.264	−	325.107i	0.197229	−	0.247317i
$121$	−1228.27	+	591.503i	−0.922816	+	0.444405i
$122$	−2943.41	−	1417.47i	−2.18429	−	1.05190i
$123$	−731.806	−	917.656i	−0.536461	−	0.672701i
$124$	−694.331	+	3042.06i	−0.502845	+	2.20311i
$125$	126.933	−	556.130i	0.0908259	−	0.397934i
$126$	39.3444	−	49.3363i	0.0278180	−	0.0348827i
$127$	256.601	+	1124.24i	0.179289	+	0.785516i	0.981959	+	0.189093i	$0.0605547\pi$
$127$	256.601	+	1124.24i	0.179289	+	0.785516i	−0.802670	+	0.596423i	$0.796588\pi$
$128$	−841.098			−0.580807
$129$	−235.222	−	1030.57i	−0.160544	−	0.703388i
$130$	−3456.31	−	1664.47i	−2.33183	−	1.12295i
$131$	524.544	+	252.607i	0.349844	+	0.168476i	0.600550	−	0.799587i	$-0.294948\pi$
$131$	524.544	+	252.607i	0.349844	+	0.168476i	−0.250706	+	0.968063i	$0.580663\pi$
$132$	408.091	+	1787.96i	0.269089	+	1.17896i
$133$	−94.0660			−0.0613275
$134$	283.617	+	1242.61i	0.182842	+	0.801081i
$135$	−1564.11	+	1961.34i	−0.997166	+	1.25041i
$136$	26.3895	−	115.620i	0.0166388	−	0.0728995i
$137$	430.716	−	1887.09i	0.268603	−	1.17683i	−0.643037	−	0.765835i	$-0.722326\pi$
$137$	430.716	−	1887.09i	0.268603	−	1.17683i	0.911640	−	0.410990i	$-0.134817\pi$
$138$	340.736	+	427.269i	0.210184	+	0.263562i
$139$	−1347.86	−	649.094i	−0.822473	−	0.396082i	−0.0251864	−	0.999683i	$-0.508018\pi$
$139$	−1347.86	−	649.094i	−0.822473	−	0.396082i	−0.797287	+	0.603601i	$0.793732\pi$
$140$	−162.949	+	78.4722i	−0.0983694	+	0.0473722i
$141$	418.624	−	524.938i	0.250032	−	0.313530i
$142$	550.247	+	689.988i	0.325181	+	0.407764i
$143$	2538.33	−	1222.40i	1.48438	−	0.714838i
$144$	654.461			0.378739
$145$	2496.67	−	830.440i	1.42991	−	0.475616i
$146$	−1473.11			−0.835036
$147$	−1133.41	+	545.823i	−0.635934	+	0.306250i
$148$	1045.48	+	1310.99i	0.580659	+	0.728124i
$149$	−695.149	+	871.689i	−0.382207	+	0.479272i	−0.935304	−	0.353844i	$-0.884874\pi$
$149$	−695.149	+	871.689i	−0.382207	+	0.479272i	0.553098	+	0.833116i	$0.313446\pi$
$150$	2210.16	−	1064.36i	1.20306	−	0.579362i
$151$	3102.74	+	1494.20i	1.67217	+	0.805274i	0.997758	+	0.0669183i	$0.0213167\pi$
$151$	3102.74	+	1494.20i	1.67217	+	0.805274i	0.674411	+	0.738356i	$0.264398\pi$
$152$	351.605	+	440.899i	0.187625	+	0.235274i
$153$	−52.9370	+	231.932i	−0.0279719	+	0.122553i
$154$	54.1908	−	237.425i	0.0283559	−	0.124236i
$155$	−3414.93	+	4282.18i	−1.76963	+	2.21905i
$156$	−426.730	−	1869.63i	−0.219011	−	0.959551i
$157$	−2146.09			−1.09093			−0.545467	−	0.838132i	$-0.683648\pi$
$157$	−2146.09			−1.09093			−0.545467	+	0.838132i	$0.683648\pi$
$158$	−458.628	−	2009.38i	−0.230927	−	1.01176i
$159$	1640.78	+	790.159i	0.818380	+	0.394111i
$160$	−3912.78	−	1884.29i	−1.93333	−	0.931041i
$161$	−8.80748	−	38.5881i	−0.00431134	−	0.0188892i
$162$	−775.879			−0.376289
$163$	−309.608	−	1356.48i	−0.148775	−	0.651826i	−0.993227	−	0.116194i	$-0.962931\pi$
$163$	−309.608	−	1356.48i	−0.148775	−	0.651826i	0.844451	−	0.535632i	$-0.179927\pi$
$164$	1908.18	−	2392.78i	0.908560	−	1.13930i
$165$	−716.330	+	3138.45i	−0.337977	+	1.48077i
$166$	501.211	−	2195.95i	0.234346	−	1.02674i
$167$	1632.31	+	2046.85i	0.756358	+	0.948443i	0.999769	−	0.0214803i	$-0.00683792\pi$
$167$	1632.31	+	2046.85i	0.756358	+	0.948443i	−0.243411	+	0.969923i	$0.578266\pi$
$168$	−24.8697	−	11.9766i	−0.0114211	−	0.00550009i
$169$	−674.840	+	324.986i	−0.307165	+	0.147923i
$170$	779.441	−	977.388i	0.351650	−	0.440955i
$171$	−705.316	−	884.438i	−0.315420	−	0.395524i
$172$	2483.36	−	1195.92i	1.10090	−	0.530164i
$173$	−651.007			−0.286099			−0.143049	−	0.989716i	$-0.545691\pi$
$173$	−651.007			−0.286099			−0.143049	+	0.989716i	$0.545691\pi$
$174$	2021.83	+	1314.52i	0.880888	+	0.572722i
$175$	−177.667			−0.0767447
$176$	2275.60	−	1095.87i	0.974599	−	0.469342i
$177$	−516.682	−	647.899i	−0.219414	−	0.275136i
$178$	2434.43	−	3052.67i	1.02510	−	1.28544i
$179$	−2520.21	+	1213.67i	−1.05234	+	0.506782i	−0.878377	−	0.477969i	$-0.841373\pi$
$179$	−2520.21	+	1213.67i	−1.05234	+	0.506782i	−0.173967	+	0.984751i	$0.555659\pi$
$180$	−1959.63	−	943.707i	−0.811456	−	0.390777i
$181$	406.393	+	509.600i	0.166889	+	0.209272i	0.858242	−	0.513245i	$-0.171557\pi$
$181$	406.393	+	509.600i	0.166889	+	0.209272i	−0.691353	+	0.722517i	$0.742985\pi$
$182$	−56.6659	+	248.270i	−0.0230789	+	0.101115i
$183$	637.893	−	2794.79i	0.257674	−	1.12894i
$184$	−147.946	+	185.519i	−0.0592757	+	0.0743294i
$185$	654.955	+	2869.55i	0.260288	+	1.14040i
$186$	−5020.05			−1.97897
$187$	204.296	+	895.081i	0.0798910	+	0.350026i
$188$	1577.35	+	759.611i	0.611914	+	0.294682i
$189$	150.036	+	72.2537i	0.0577436	+	0.0278078i
$190$	1322.79	+	5795.52i	0.505080	+	2.21290i
$191$	2252.41			0.853291			0.426646	−	0.904419i	$-0.359695\pi$
$191$	2252.41			0.853291			0.426646	+	0.904419i	$0.359695\pi$
$192$	−566.875	−	2483.64i	−0.213076	−	0.933548i
$193$	−56.8958	+	71.3450i	−0.0212199	+	0.0266090i	−0.792328	−	0.610095i	$-0.791131\pi$
$193$	−56.8958	+	71.3450i	−0.0212199	+	0.0266090i	0.771108	+	0.636704i	$0.219703\pi$
$194$	−1371.49	+	6008.90i	−0.507564	+	2.22378i
$195$	749.048	−	3281.79i	0.275079	−	1.20520i
$196$	−2045.18	−	2564.57i	−0.745327	−	0.934610i
$197$	−3393.29	−	1634.12i	−1.22722	−	0.590997i	−0.295906	−	0.955217i	$-0.595621\pi$
$197$	−3393.29	−	1634.12i	−1.22722	−	0.590997i	−0.931313	+	0.364220i	$0.881336\pi$
$198$	2638.67	−	1270.72i	0.947083	−	0.456091i
$199$	1232.51	−	1545.52i	0.439047	−	0.550547i	−0.512245	−	0.858839i	$-0.671186\pi$
$199$	1232.51	−	1545.52i	0.439047	−	0.550547i	0.951292	+	0.308292i	$0.0997575\pi$
$200$	664.092	+	832.745i	0.234792	+	0.294420i
$201$	−1007.64	+	485.255i	−0.353600	+	0.170285i
$202$	2857.72			0.995387
$203$	−90.6229	−	149.311i	−0.0313324	−	0.0516236i
$204$	624.933			0.214481
$205$	4840.12	−	2330.88i	1.64902	−	0.794124i
$206$	81.2723	+	101.912i	0.0274879	+	0.0344688i
$207$	296.778	−	372.148i	0.0996497	−	0.124957i
$208$	−2379.53	+	1145.92i	−0.793225	+	0.381997i
$209$	−3933.38	−	1894.21i	−1.30181	−	0.626916i
$210$	−181.419	−	227.493i	−0.0596149	−	0.0747547i
$211$	−614.177	+	2690.88i	−0.200387	+	0.877953i	0.770314	+	0.637664i	$0.220099\pi$
$211$	−614.177	+	2690.88i	−0.200387	+	0.877953i	−0.970701	+	0.240289i	$0.922758\pi$
$212$	−1056.66	+	4629.53i	−0.342319	+	1.49980i
$213$	−482.829	+	605.448i	−0.155319	+	0.194764i
$214$	609.477	+	2670.29i	0.194687	+	0.852979i
$215$	4838.22			1.53472
$216$	−222.152	−	973.313i	−0.0699794	−	0.306600i
$217$	327.574	+	157.751i	0.102475	+	0.0493496i
$218$	−225.318	−	108.508i	−0.0700022	−	0.0337113i
$219$	−287.635	−	1260.21i	−0.0887513	−	0.388845i
$220$	−8393.93			−2.57236
$221$	−213.627	−	935.963i	−0.0650233	−	0.284885i
$222$	−1682.00	+	2109.16i	−0.508507	+	0.637647i
$223$	152.759	−	669.282i	0.0458723	−	0.200980i	−0.946799	−	0.321826i	$-0.895704\pi$
$223$	152.759	−	669.282i	0.0458723	−	0.200980i	0.992671	+	0.120846i	$0.0385607\pi$
$224$	−64.1496	+	281.058i	−0.0191347	+	0.0838347i
$225$	−1332.16	−	1670.48i	−0.394714	−	0.494956i
$226$	169.135	+	81.4510i	0.0497817	+	0.0239736i
$227$	459.822	−	221.438i	0.134447	−	0.0647462i	−0.365451	−	0.930831i	$-0.619085\pi$
$227$	459.822	−	221.438i	0.134447	−	0.0647462i	0.499898	+	0.866084i	$0.333371\pi$
$228$	−1852.80	+	2323.34i	−0.538179	+	0.674855i
$229$	−597.772	−	749.582i	−0.172497	−	0.216305i	0.688066	−	0.725648i	$-0.258460\pi$
$229$	−597.772	−	749.582i	−0.172497	−	0.216305i	−0.860564	+	0.509343i	$0.829888\pi$
$230$	−2253.60	+	1085.28i	−0.646079	+	0.311135i
$231$	213.693			0.0608656
$232$	−361.105	+	982.865i	−0.102188	+	0.278139i
$233$	−4090.22			−1.15004			−0.575020	−	0.818140i	$-0.695006\pi$
$233$	−4090.22			−1.15004			−0.575020	+	0.818140i	$0.695006\pi$
$234$	−2759.19	+	1328.76i	−0.770830	+	0.371212i
$235$	1916.03	+	2402.63i	0.531865	+	0.666938i
$236$	1347.25	−	1689.39i	0.371603	−	0.465975i
$237$	1629.43	−	784.691i	0.446594	−	0.215068i
$238$	−74.7673	−	36.0060i	−0.0203632	−	0.00980641i
$239$	−2712.72	−	3401.65i	−0.734191	−	0.920646i	0.264857	−	0.964288i	$-0.414675\pi$
$239$	−2712.72	−	3401.65i	−0.734191	−	0.920646i	−0.999047	+	0.0436420i	$0.986104\pi$
$240$	671.516	−	2942.10i	0.180609	−	0.791300i
$241$	−954.202	+	4180.63i	−0.255044	+	1.11742i	0.671432	+	0.741066i	$0.265680\pi$
$241$	−954.202	+	4180.63i	−0.255044	+	1.11742i	−0.926476	+	0.376354i	$0.877178\pi$
$242$	3565.73	−	4471.28i	0.947164	−	1.18771i
$243$	743.093	+	3255.70i	0.196170	+	0.859479i
$244$	7474.80			1.96117
$245$	−1281.23	−	5613.45i	−0.334102	−	1.46380i
$246$	4436.21	+	2136.36i	1.14977	+	0.553698i
$247$	4113.03	+	1980.73i	1.05954	+	0.510247i
$248$	−485.025	−	2125.03i	−0.124190	−	0.544112i
$249$	1976.45			0.503021
$250$	532.488	+	2332.98i	0.134710	+	0.590203i
$251$	−357.259	+	447.988i	−0.0898405	+	0.112656i	−0.824720	−	0.565541i	$-0.808667\pi$
$251$	−357.259	+	447.988i	−0.0898405	+	0.112656i	0.734879	+	0.678198i	$0.237239\pi$
$252$	−32.1279	+	140.762i	−0.00803123	+	0.0351871i
$253$	408.766	−	1790.92i	0.101577	−	0.445036i
$254$	−3016.15	−	3782.13i	−0.745078	−	0.934299i
$255$	988.324	+	475.952i	0.242711	+	0.116883i
$256$	−1809.20	+	871.267i	−0.441700	+	0.212712i
$257$	4697.94	−	5891.03i	1.14027	−	1.42985i	0.253687	−	0.967286i	$-0.418357\pi$
$257$	4697.94	−	5891.03i	1.14027	−	1.42985i	0.886584	−	0.462568i	$-0.153072\pi$
$258$	2764.85	+	3467.01i	0.667178	+	0.836615i
$259$	176.035	−	84.7739i	0.0422327	−	0.0203382i
$260$	8777.32			2.09364
$261$	724.371	−	1971.61i	0.171791	−	0.467586i
$262$	−2442.35			−0.575911
$263$	−1198.87	+	577.344i	−0.281085	+	0.135363i	−0.569115	−	0.822258i	$-0.692714\pi$
$263$	−1198.87	+	577.344i	−0.281085	+	0.135363i	0.288030	+	0.957621i	$0.407000\pi$
$264$	−798.754	−	1001.61i	−0.186212	−	0.233502i
$265$	−5196.96	+	6516.79i	−1.20471	+	1.51065i
$266$	355.531	−	171.215i	0.0819512	−	0.0394656i
$267$	3086.83	+	1486.54i	0.707531	+	0.340729i
$268$	−1818.23	−	2279.99i	−0.414426	−	0.519674i
$269$	976.259	−	4277.27i	0.221277	−	0.969479i	−0.735241	−	0.677806i	$-0.762931\pi$
$269$	976.259	−	4277.27i	0.221277	−	0.969479i	0.956518	−	0.291673i	$-0.0942118\pi$
$270$	2341.77	−	10260.0i	0.527836	−	2.31260i
$271$	409.103	−	512.999i	0.0917020	−	0.114991i	−0.733864	−	0.679297i	$-0.762285\pi$
$271$	409.103	−	512.999i	0.0917020	−	0.114991i	0.825566	+	0.564306i	$0.190856\pi$
$272$	−191.515	−	839.084i	−0.0426924	−	0.187048i
$273$	−223.453			−0.0495385
$274$	1806.87	+	7916.41i	0.398383	+	1.74543i
$275$	−7429.14	−	3577.68i	−1.62907	−	0.784518i
$276$	−1126.57	−	542.526i	−0.245693	−	0.118320i
$277$	−247.731	−	1085.38i	−0.0537355	−	0.235431i	0.940927	−	0.338608i	$-0.109956\pi$
$277$	−247.731	−	1085.38i	−0.0537355	−	0.235431i	−0.994663	+	0.103178i	$0.967099\pi$
$278$	6275.81			1.35395
$279$	972.954	+	4262.79i	0.208779	+	0.914719i
$280$	78.7715	−	98.7764i	0.0168125	−	0.0210822i
$281$	174.822	−	765.944i	0.0371138	−	0.162606i	−0.952975	−	0.303049i	$-0.901995\pi$
$281$	174.822	−	765.944i	0.0371138	−	0.162606i	0.990089	+	0.140443i	$0.0448526\pi$
$282$	−626.759	+	2746.01i	−0.132351	+	0.579867i
$283$	346.420	+	434.396i	0.0727651	+	0.0912445i	0.816882	−	0.576805i	$-0.195701\pi$
$283$	346.420	+	434.396i	0.0727651	+	0.0912445i	−0.744117	+	0.668050i	$0.767129\pi$
$284$	−1819.27	−	876.114i	−0.380119	−	0.183056i
$285$	−4699.65	+	2263.23i	−0.976783	+	0.470394i
$286$	−7368.91	+	9240.32i	−1.52354	+	1.91046i
$287$	−222.343	−	278.809i	−0.0457299	−	0.0573435i
$288$	−3123.59	+	1504.24i	−0.639096	+	0.307772i
$289$	−4600.15			−0.936322
$290$	−7924.87	+	7683.06i	−1.60471	+	1.55574i
$291$	−5408.27			−1.08948
$292$	3036.71	−	1462.40i	0.608596	−	0.293084i
$293$	−1982.88	−	2486.45i	−0.395362	−	0.495769i	0.543813	−	0.839206i	$-0.316980\pi$
$293$	−1982.88	−	2486.45i	−0.395362	−	0.495769i	−0.939175	+	0.343438i	$0.888409\pi$
$294$	3290.36	−	4125.98i	0.652713	−	0.818476i
$295$	3417.30	−	1645.69i	0.674451	−	0.324798i
$296$	−1055.34	−	508.224i	−0.207231	−	0.0997971i
$297$	4818.80	+	6042.58i	0.941465	+	1.18056i
$298$	1040.77	−	4559.91i	0.202316	−	0.886404i
$299$	−427.436	+	1872.72i	−0.0826731	+	0.362214i
$300$	−3499.47	+	4388.19i	−0.673473	+	0.844508i
$301$	−71.4669	−	313.117i	−0.0136853	−	0.0599593i
$302$	−14446.8			−2.75271
$303$	557.989	+	2444.71i	0.105794	+	0.463515i
$304$	3687.30	+	1775.71i	0.695662	+	0.335013i
$305$	11821.3	+	5692.84i	2.21930	+	1.06876i
$306$	−222.072	−	972.963i	−0.0414870	−	0.181767i
$307$	−463.514			−0.0861698			−0.0430849	−	0.999071i	$-0.513719\pi$
$307$	−463.514			−0.0861698			−0.0430849	+	0.999071i	$0.513719\pi$
$308$	123.989	+	543.232i	0.0229381	+	0.100498i
$309$	−71.3146	+	89.4256i	−0.0131293	+	0.0164636i
$310$	5112.79	−	22400.6i	0.936732	−	4.10409i
$311$	−1978.61	+	8668.85i	−0.360761	+	1.58060i	0.390508	+	0.920600i	$0.372299\pi$
$311$	−1978.61	+	8668.85i	−0.360761	+	1.58060i	−0.751269	+	0.659997i	$0.770558\pi$
$312$	835.237	+	1047.35i	0.151558	+	0.190047i
$313$	−5348.48	−	2575.69i	−0.965860	−	0.465134i	−0.116641	−	0.993174i	$-0.537213\pi$
$313$	−5348.48	−	2575.69i	−0.965860	−	0.465134i	−0.849219	+	0.528041i	$0.822927\pi$
$314$	8111.35	−	3906.22i	1.45780	−	0.702040i
$315$	−158.015	+	198.144i	−0.0282639	+	0.0354418i
$316$	2940.21	+	3686.90i	0.523416	+	0.656343i
$317$	−6443.79	+	3103.17i	−1.14170	+	0.549814i	−0.906531	−	0.422140i	$-0.861279\pi$
$317$	−6443.79	+	3103.17i	−1.14170	+	0.549814i	−0.235170	+	0.971954i	$0.575565\pi$
$318$	−7639.70			−1.34721
$319$	−782.714	−	8068.34i	−0.137378	−	1.41611i
$320$	11659.9			2.03690
$321$	−2165.37	+	1042.79i	−0.376508	+	0.181317i
$322$	103.525	+	129.816i	0.0179168	+	0.0224670i
$323$	−927.540	+	1163.10i	−0.159782	+	0.200361i
$324$	1599.42	−	770.240i	0.274249	−	0.132071i
$325$	7768.46	+	3741.09i	1.32590	+	0.638518i
$326$	3639.20	+	4563.41i	0.618271	+	0.775287i
$327$	48.8307	−	213.941i	0.00825794	−	0.0361804i
$328$	−475.728	+	2084.30i	−0.0800843	+	0.350872i
$329$	127.189	−	159.491i	0.0213136	−	0.0267264i
$330$	−3005.03	−	13165.9i	−0.501276	−	2.19624i
$331$	9793.82			1.62633			0.813167	−	0.582030i	$-0.197741\pi$
$331$	9793.82			1.62633			0.813167	+	0.582030i	$0.197741\pi$
$332$	1146.78	+	5024.36i	0.189571	+	0.830565i
$333$	2117.00	+	1019.49i	0.348380	+	0.167771i
$334$	−9895.05	−	4765.20i	−1.62106	−	0.780660i
$335$	−1139.06	−	4990.55i	−0.185772	−	0.813919i
$336$	−200.324			−0.0325255
$337$	−1679.66	−	7359.08i	−0.271505	−	1.18954i	−0.908238	−	0.418455i	$-0.862572\pi$
$337$	−1679.66	−	7359.08i	−0.271505	−	1.18954i	0.636733	−	0.771084i	$-0.280285\pi$
$338$	1959.10	−	2456.63i	0.315269	−	0.395334i
$339$	−36.6547	+	160.595i	−0.00587259	+	0.0257295i
$340$	−636.478	+	2788.59i	−0.101523	+	0.444802i
$341$	10520.9	+	13192.8i	1.67078	+	2.09510i
$342$	4275.62	+	2059.03i	0.676021	+	0.325555i
$343$	−689.985	+	332.279i	−0.108617	+	0.0523072i
$344$	−1200.49	+	1505.36i	−0.188156	+	0.235941i
$345$	−1368.46	−	1716.00i	−0.213552	−	0.267786i
$346$	2460.54	−	1184.93i	0.382311	−	0.184111i
$347$	−10252.2			−1.58608			−0.793038	−	0.609173i	$-0.791502\pi$
$347$	−10252.2			−1.58608			−0.793038	+	0.609173i	$0.791502\pi$
$348$	−5472.83	−	702.657i	−0.843030	−	0.108237i
$349$	2889.73			0.443220			0.221610	−	0.975135i	$-0.428869\pi$
$349$	2889.73			0.443220			0.221610	+	0.975135i	$0.428869\pi$
$350$	671.507	−	323.381i	0.102553	−	0.0493869i
$351$	−5038.90	−	6318.58i	−0.766258	−	0.960857i
$352$	−8342.10	+	10460.7i	−1.26317	+	1.58396i
$353$	7400.38	−	3563.83i	1.11581	−	0.537348i	0.217217	−	0.976123i	$-0.430302\pi$
$353$	7400.38	−	3563.83i	1.11581	−	0.537348i	0.898597	+	0.438776i	$0.144588\pi$
$354$	3132.13	+	1508.35i	0.470256	+	0.226463i
$355$	−2209.90	−	2771.13i	−0.330392	−	0.414299i
$356$	−1987.91	+	8709.60i	−0.295952	+	1.29665i
$357$	16.2035	−	70.9921i	0.00240218	−	0.0105247i
$358$	7316.31	−	9174.36i	1.08011	−	1.35441i
$359$	−2353.35	−	10310.7i	−0.345975	−	1.51582i	−0.786225	−	0.617941i	$-0.787967\pi$
$359$	−2353.35	−	10310.7i	−0.345975	−	1.51582i	0.440249	−	0.897875i	$-0.354890\pi$
$360$	1519.36			0.222437
$361$	−47.8572	−	209.676i	−0.00697729	−	0.0305695i
$362$	−2463.55	−	1186.38i	−0.357683	−	0.172251i
$363$	4521.31	+	2177.35i	0.653739	+	0.314824i
$364$	−129.652	−	568.044i	−0.0186693	−	0.0817956i
$365$	5916.29			0.848418
$366$	2675.98	+	11724.2i	0.382174	+	1.67441i
$367$	−2471.95	+	3099.73i	−0.351593	+	0.440884i	−0.925907	−	0.377751i	$-0.876697\pi$
$367$	−2471.95	+	3099.73i	−0.351593	+	0.440884i	0.574314	+	0.818635i	$0.305269\pi$
$368$	−383.193	+	1678.88i	−0.0542808	+	0.237820i
$369$	954.303	−	4181.08i	0.134632	−	0.589859i
$370$	−7698.49	−	9653.60i	−1.08169	−	1.35640i
$371$	498.515	+	240.072i	0.0697617	+	0.0335955i
$372$	10348.5	−	4983.56i	1.44232	−	0.694585i
$373$	−7173.67	+	8995.49i	−0.995813	+	1.24871i	−0.0273316	+	0.999626i	$0.508701\pi$
$373$	−7173.67	+	8995.49i	−0.995813	+	1.24871i	−0.968482	+	0.249084i	$0.919870\pi$
$374$	−2401.34	−	3011.19i	−0.332007	−	0.416323i
$375$	−1891.84	+	911.063i	−0.260518	+	0.125459i
$376$	−1222.97			−0.167739
$377$	818.464	+	8436.85i	0.111812	+	1.15257i
$378$	−698.589			−0.0950570
$379$	−1809.80	+	871.552i	−0.245285	+	0.118123i	−0.552488	−	0.833521i	$-0.686321\pi$
$379$	−1809.80	+	871.552i	−0.245285	+	0.118123i	0.307203	+	0.951644i	$0.400607\pi$
$380$	−8480.24	−	10633.9i	−1.14481	−	1.43554i
$381$	2646.60	−	3318.73i	0.355878	−	0.446256i
$382$	−8513.19	+	4099.74i	−1.14024	+	0.549112i
$383$	−4937.63	−	2377.84i	−0.658750	−	0.317237i	0.0744758	−	0.997223i	$-0.476272\pi$
$383$	−4937.63	−	2377.84i	−0.658750	−	0.317237i	−0.733225	+	0.679986i	$0.761986\pi$
$384$	1930.40	+	2420.64i	0.256537	+	0.321687i
$385$	−217.641	+	953.546i	−0.0288104	+	0.126227i
$386$	85.1838	−	373.214i	0.0112325	−	0.0492127i
$387$	2408.16	−	3019.73i	0.316314	−	0.396645i
$388$	−3138.00	−	13748.5i	−0.410587	−	1.79890i
$389$	5943.71			0.774699			0.387350	−	0.921933i	$-0.373391\pi$
$389$	5943.71			0.774699			0.387350	+	0.921933i	$0.373391\pi$
$390$	3142.28	+	13767.2i	0.407988	+	1.78751i
$391$	−563.976	−	271.597i	−0.0729450	−	0.0351285i
$392$	2064.47	+	994.197i	0.265999	+	0.128098i
$393$	−476.885	−	2089.37i	−0.0612104	−	0.268180i
$394$	15799.6			2.02024
$395$	1841.94	+	8070.07i	0.234628	+	1.02797i
$396$	−4177.96	+	5238.99i	−0.530177	+	0.664822i
$397$	187.890	−	823.198i	0.0237529	−	0.104068i	−0.961662	−	0.274238i	$-0.911574\pi$
$397$	187.890	−	823.198i	0.0237529	−	0.104068i	0.985415	+	0.170170i	$0.0544316\pi$
$398$	−1845.30	+	8084.79i	−0.232403	+	1.01823i
$399$	215.890	+	270.718i	0.0270878	+	0.0339670i
$400$	6964.36	+	3353.86i	0.870546	+	0.419233i
$401$	−393.444	+	189.473i	−0.0489967	+	0.0235956i	−0.458222	−	0.888838i	$-0.651513\pi$
$401$	−393.444	+	189.473i	−0.0489967	+	0.0235956i	0.409225	+	0.912434i	$0.365799\pi$
$402$	2925.24	−	3668.13i	0.362930	−	0.455099i
$403$	−11001.4	−	13795.3i	−1.35985	−	1.70520i
$404$	−5890.98	+	2836.95i	−0.725464	+	0.349365i
$405$	3116.08			0.382319
$406$	614.288	+	399.388i	0.0750901	+	0.0488209i
$407$	9068.00			1.10438
$408$	−393.315	+	189.411i	−0.0477255	+	0.0229834i
$409$	1883.98	+	2362.43i	0.227767	+	0.285611i	0.882562	−	0.470196i	$-0.155817\pi$
$409$	1883.98	+	2362.43i	0.227767	+	0.285611i	−0.654795	+	0.755806i	$0.727245\pi$
$410$	−14051.1	+	17619.5i	−1.69252	+	2.12236i
$411$	−6419.50	+	3091.47i	−0.770439	+	0.371024i
$412$	−268.709	−	129.403i	−0.0321319	−	0.0154739i
$413$	−156.982	−	196.850i	−0.0187036	−	0.0234536i
$414$	−444.333	+	1946.75i	−0.0527482	+	0.231105i
$415$	−2012.96	+	8819.35i	−0.238102	+	1.04319i
$416$	8723.12	−	10938.5i	1.02809	−	1.28919i
$417$	1225.39	+	5368.81i	0.143904	+	0.630483i
$418$	18314.3			2.14302
$419$	2049.31	+	8978.59i	0.238938	+	1.04686i	0.941970	+	0.335698i	$0.108972\pi$
$419$	2049.31	+	8978.59i	0.238938	+	1.04686i	−0.703031	+	0.711159i	$0.748171\pi$
$420$	599.823	+	288.859i	0.0696866	+	0.0335593i
$421$	−14678.3	−	7068.70i	−1.69923	−	0.818307i	−0.994006	−	0.109324i	$-0.965132\pi$
$421$	−14678.3	−	7068.70i	−1.69923	−	0.818307i	−0.705225	−	0.708983i	$-0.749154\pi$
$422$	−2576.49	−	11288.3i	−0.297208	−	1.30215i
$423$	2453.26			0.281989
$424$	−738.130	−	3233.96i	−0.0845442	−	0.370412i
$425$	−1751.88	+	2196.79i	−0.199950	+	0.250730i
$426$	722.886	−	3167.17i	0.0822159	−	0.360211i
$427$	193.809	−	849.134i	0.0219651	−	0.0962354i
$428$	−3907.28	−	4899.57i	−0.441275	−	0.553341i
$429$	−9343.71	−	4499.69i	−1.05156	−	0.506404i
$430$	−18286.5	+	8806.32i	−2.05082	+	0.987625i
$431$	5723.35	−	7176.85i	0.639638	−	0.802081i	−0.351320	−	0.936256i	$-0.614267\pi$
$431$	5723.35	−	7176.85i	0.639638	−	0.802081i	0.990958	+	0.134175i	$0.0428384\pi$
$432$	−4517.33	−	5664.56i	−0.503103	−	0.630871i
$433$	438.746	−	211.289i	0.0486947	−	0.0234501i	−0.409378	−	0.912365i	$-0.634254\pi$
$433$	438.746	−	211.289i	0.0486947	−	0.0234501i	0.458073	+	0.888915i	$0.348540\pi$
$434$	−1525.23			−0.168694
$435$	−8120.06	−	5279.37i	−0.895005	−	0.581900i
$436$	572.197			0.0628515
$437$	2681.80	−	1291.49i	0.293565	−	0.141374i
$438$	3380.92	+	4239.54i	0.368828	+	0.462495i
$439$	2811.31	−	3525.27i	0.305641	−	0.383262i	−0.605162	−	0.796102i	$-0.706892\pi$
$439$	2811.31	−	3525.27i	0.305641	−	0.383262i	0.910803	+	0.412840i	$0.135463\pi$
$440$	5282.90	−	2544.11i	0.572392	−	0.275649i
$441$	−4141.30	−	1994.35i	−0.447177	−	0.215349i
$442$	2511.02	+	3148.72i	0.270220	+	0.338845i
$443$	−1894.13	+	8298.74i	−0.203145	+	0.890034i	0.765863	+	0.643004i	$0.222312\pi$
$443$	−1894.13	+	8298.74i	−0.203145	+	0.890034i	−0.969008	+	0.247031i	$0.920545\pi$
$444$	1373.49	−	6017.66i	0.146809	−	0.643211i
$445$	−9777.13	+	12260.1i	−1.04153	+	1.30604i
$446$	640.830	+	2807.66i	0.0680363	+	0.298087i
$447$	4104.11			0.434268
$448$	−172.232	−	754.598i	−0.0181634	−	0.0795791i
$449$	−1382.48	−	665.769i	−0.145308	−	0.0699768i	0.359817	−	0.933023i	$-0.382839\pi$
$449$	−1382.48	−	665.769i	−0.145308	−	0.0699768i	−0.505125	+	0.863046i	$0.668554\pi$
$450$	8075.55	+	3888.98i	0.845967	+	0.407396i
$451$	−3682.88	−	16135.8i	−0.384524	−	1.68471i
$452$	−429.518			−0.0446966
$453$	−2820.84	−	12358.9i	−0.292570	−	1.28183i
$454$	−1334.89	+	1673.89i	−0.137994	+	0.173039i
$455$	227.581	−	997.099i	0.0234487	−	0.102736i
$456$	461.921	−	2023.81i	0.0474374	−	0.207837i
$457$	3763.87	+	4719.74i	0.385265	+	0.483107i	0.936213	−	0.351432i	$-0.114305\pi$
$457$	3763.87	+	4719.74i	0.385265	+	0.483107i	−0.550948	+	0.834540i	$0.685734\pi$
$458$	3623.69	+	1745.08i	0.369703	+	0.178040i
$459$	2372.83	−	1142.70i	0.241295	−	0.116201i
$460$	3568.26	−	4474.45i	0.361676	−	0.453527i
$461$	11503.1	+	14424.5i	1.16216	+	1.45730i	0.864504	+	0.502627i	$0.167633\pi$
$461$	11503.1	+	14424.5i	1.16216	+	1.45730i	0.297655	+	0.954674i	$0.403796\pi$
$462$	−807.672	+	388.954i	−0.0813340	+	0.0391684i
$463$	18203.2			1.82716			0.913581	−	0.406656i	$-0.133305\pi$
$463$	18203.2			1.82716			0.913581	+	0.406656i	$0.133305\pi$
$464$	733.747	+	7563.58i	0.0734124	+	0.756746i
$465$	20161.5			2.01068
$466$	15459.4	−	7444.84i	1.53678	−	0.740076i
$467$	2061.78	+	2585.39i	0.204300	+	0.256184i	0.873417	−	0.486973i	$-0.161899\pi$
$467$	2061.78	+	2585.39i	0.204300	+	0.256184i	−0.669117	+	0.743157i	$0.733328\pi$
$468$	4368.78	−	5478.28i	0.431511	−	0.541098i
$469$	−306.150	+	147.434i	−0.0301422	+	0.0145157i
$470$	−11615.0	−	5593.48i	−1.13991	−	0.548954i
$471$	4925.48	+	6176.35i	0.481856	+	0.604228i
$472$	−335.881	+	1471.59i	−0.0327546	+	0.143507i
$473$	3316.86	−	14532.1i	0.322430	−	1.41266i
$474$	−4730.31	+	5931.63i	−0.458377	+	0.574786i
$475$	−2973.12	−	13026.1i	−0.287192	−	1.25827i
$476$	189.872			0.0182831
$477$	1480.68	+	6487.28i	0.142129	+	0.622709i
$478$	16444.5	+	7919.27i	1.57355	+	0.757780i
$479$	140.455	+	67.6396i	0.0133978	+	0.00645205i	0.440571	−	0.897718i	$-0.354776\pi$
$479$	140.455	+	67.6396i	0.0133978	+	0.00645205i	−0.427173	+	0.904170i	$0.640490\pi$
$480$	3557.27	+	15585.4i	0.338264	+	1.48203i
$481$	−9482.18			−0.898857
$482$	−4002.91	−	17537.9i	−0.378273	−	1.65732i
$483$	−90.8408	+	113.911i	−0.00855776	+	0.0107311i
$484$	−2911.71	+	12757.0i	−0.273452	+	1.19807i
$485$	5508.18	−	24132.9i	0.515699	−	2.25942i
$486$	−8734.47	−	10952.7i	−0.815234	−	1.02227i
$487$	−7416.98	−	3571.83i	−0.690134	−	0.332351i	0.0557330	−	0.998446i	$-0.482250\pi$
$487$	−7416.98	−	3571.83i	−0.690134	−	0.332351i	−0.745867	+	0.666095i	$0.767965\pi$
$488$	−4704.43	+	2265.54i	−0.436393	+	0.210156i
$489$	−3193.31	+	4004.28i	−0.295310	+	0.370307i
$490$	15059.9	+	18884.5i	1.38844	+	1.74105i
$491$	−7114.56	+	3426.19i	−0.653922	+	0.314912i	−0.731266	−	0.682092i	$-0.761070\pi$
$491$	−7114.56	+	3426.19i	−0.653922	+	0.314912i	0.0773442	+	0.997004i	$0.475356\pi$
$492$	−11265.8			−1.03232
$493$	−2739.78	−	351.760i	−0.250291	−	0.0321349i
$494$	−19150.8			−1.74420
$495$	−10597.4	+	5103.45i	−0.962261	+	0.463400i
$496$	−9862.69	−	12367.4i	−0.892838	−	1.11958i
$497$	−146.697	+	183.952i	−0.0132399	+	0.0166024i
$498$	−7470.16	+	3597.44i	−0.672181	+	0.323705i
$499$	16119.2	+	7762.60i	1.44608	+	0.696396i	0.981910	−	0.189349i	$-0.0606379\pi$
$499$	16119.2	+	7762.60i	1.44608	+	0.696396i	0.464171	+	0.885745i	$0.346352\pi$
$500$	−3413.72	−	4280.66i	−0.305332	−	0.382874i
$501$	2144.44	−	9395.42i	0.191231	−	0.837837i
$502$	534.884	−	2343.48i	0.0475558	−	0.208356i
$503$	−3865.69	+	4847.42i	−0.342669	+	0.429693i	−0.923067	−	0.384640i	$-0.874326\pi$
$503$	−3865.69	+	4847.42i	−0.342669	+	0.429693i	0.580398	+	0.814333i	$0.302897\pi$
$504$	−22.4430	−	98.3291i	−0.00198351	−	0.00869033i
$505$	−11477.1			−1.01134
$506$	1714.78	+	7512.96i	0.150655	+	0.660063i
$507$	2484.12	+	1196.29i	0.217601	+	0.104791i
$508$	9972.22	+	4802.37i	0.870956	+	0.419430i
$509$	780.653	+	3420.26i	0.0679800	+	0.297840i	0.997477	−	0.0709896i	$-0.0226157\pi$
$509$	780.653	+	3420.26i	0.0679800	+	0.297840i	−0.929497	+	0.368830i	$0.879759\pi$
$510$	−4601.77			−0.399549
$511$	−87.3913	−	382.886i	−0.00756549	−	0.0331466i
$512$	9447.54	−	11846.8i	0.815481	−	1.02258i
$513$	−2786.72	+	12209.4i	−0.239838	+	1.05080i
$514$	−7033.71	+	30816.7i	−0.603587	+	2.64449i
$515$	−326.406	−	409.300i	−0.0279284	−	0.0350212i
$516$	−9141.36	−	4402.24i	−0.779895	−	0.375578i
$517$	8530.11	−	4107.88i	0.725636	−	0.349448i
$518$	−511.038	+	640.822i	−0.0433470	+	0.0543554i
$519$	1494.12	+	1873.57i	0.126367	+	0.158460i
$520$	−5524.20	+	2660.31i	−0.465869	+	0.224351i
$521$	−2676.32			−0.225051			−0.112525	−	0.993649i	$-0.535894\pi$
$521$	−2676.32			−0.225051			−0.112525	+	0.993649i	$0.535894\pi$
$522$	850.819	+	8770.37i	0.0713397	+	0.735381i
$523$	−14909.8			−1.24658			−0.623290	−	0.781991i	$-0.714204\pi$
$523$	−14909.8			−1.24658			−0.623290	+	0.781991i	$0.714204\pi$
$524$	5034.73	−	2424.60i	0.419739	−	0.202136i
$525$	407.761	+	511.316i	0.0338974	+	0.0425060i
$526$	3480.38	−	4364.25i	0.288501	−	0.361769i
$527$	5180.60	−	2494.85i	0.428217	−	0.206219i
$528$	−8376.56	−	4033.94i	−0.690423	−	0.332490i
$529$	−6805.10	−	8533.33i	−0.559308	−	0.701350i
$530$	7780.84	−	34090.1i	0.637694	−	2.79392i
$531$	673.774	−	2951.99i	0.0550646	−	0.241254i
$532$	−562.932	+	705.895i	−0.0458763	+	0.0575271i
$533$	3851.10	+	16872.8i	0.312963	+	1.37118i
$534$	−14372.7			−1.16473
$535$	−2447.78	−	10724.4i	−0.197807	−	0.866649i
$536$	1835.39	+	883.875i	0.147904	+	0.0712268i
$537$	9277.01	+	4467.57i	0.745498	+	0.359013i
$538$	4095.44	+	17943.3i	0.328191	+	1.43790i
$539$	−17739.0			−1.41757
$540$	5358.01	+	23475.0i	0.426985	+	1.87074i
$541$	−7008.47	+	8788.34i	−0.556964	+	0.698411i	−0.977993	−	0.208636i	$-0.933098\pi$
$541$	−7008.47	+	8788.34i	−0.556964	+	0.698411i	0.421029	+	0.907047i	$0.361669\pi$
$542$	−612.505	+	2683.56i	−0.0485412	+	0.212673i
$543$	533.898	−	2339.16i	0.0421948	−	0.184867i
$544$	2842.65	+	3564.57i	0.224040	+	0.280937i
$545$	904.923	+	435.788i	0.0711241	+	0.0342516i
$546$	844.562	−	406.720i	0.0661977	−	0.0318791i
$547$	−7099.34	+	8902.29i	−0.554929	+	0.695859i	−0.977611	−	0.210419i	$-0.932517\pi$
$547$	−7099.34	+	8902.29i	−0.554929	+	0.695859i	0.422683	+	0.906278i	$0.361089\pi$
$548$	−11583.6	−	14525.4i	−0.902969	−	1.13229i
$549$	9437.03	−	4544.63i	0.733630	−	0.353297i
$550$	34591.1			2.68176
$551$	9430.65	−	9142.89i	0.729145	−	0.706897i
$552$	873.464			0.0673498
$553$	495.065	−	238.411i	0.0380693	−	0.0183332i
$554$	2911.89	+	3651.39i	0.223311	+	0.280023i
$555$	6755.24	−	8470.81i	0.516656	−	0.647866i
$556$	−12937.1	+	6230.19i	−0.986792	+	0.475214i
$557$	−1441.86	−	694.363i	−0.109683	−	0.0528207i	0.378238	−	0.925709i	$-0.376530\pi$
$557$	−1441.86	−	694.363i	−0.109683	−	0.0528207i	−0.487921	+	0.872888i	$0.662245\pi$
$558$	−11436.3	−	14340.7i	−0.867630	−	1.08797i
$559$	−3468.36	+	15195.9i	−0.262426	+	1.14976i
$560$	204.025	−	893.892i	0.0153958	−	0.0674533i
$561$	2107.12	−	2642.25i	0.158579	−	0.198852i
$562$	733.382	+	3213.16i	0.0550460	+	0.241172i
$563$	8308.99			0.621993			0.310996	−	0.950411i	$-0.399337\pi$
$563$	8308.99			0.621993			0.310996	+	0.950411i	$0.399337\pi$
$564$	−1434.03	−	6282.91i	−0.107063	−	0.469075i
$565$	−679.278	−	327.123i	−0.0505795	−	0.0243578i
$566$	−2099.99	−	1011.30i	−0.155953	−	0.0751030i
$567$	−46.0286	−	201.664i	−0.00340920	−	0.0149367i
$568$	1410.54			0.104199
$569$	628.421	+	2753.29i	0.0463001	+	0.202854i	0.992788	−	0.119886i	$-0.0382530\pi$
$569$	628.421	+	2753.29i	0.0463001	+	0.202854i	−0.946487	+	0.322741i	$0.895396\pi$
$570$	13643.3	−	17108.2i	1.00255	−	1.25716i
$571$	2344.93	−	10273.8i	0.171860	−	0.752970i	−0.813372	−	0.581745i	$-0.802370\pi$
$571$	2344.93	−	10273.8i	0.171860	−	0.752970i	0.985232	−	0.171225i	$-0.0547725\pi$
$572$	6017.32	−	26363.6i	0.439855	−	1.92713i
$573$	−5169.49	−	6482.33i	−0.376891	−	0.472606i
$574$	1347.84	+	649.087i	0.0980102	+	0.0471992i
$575$	5065.24	−	2439.29i	0.367365	−	0.176914i
$576$	5803.56	−	7277.43i	0.419817	−	0.526434i
$577$	10412.5	+	13056.8i	0.751260	+	0.942051i	0.999646	−	0.0266107i	$-0.00847143\pi$
$577$	10412.5	+	13056.8i	0.751260	+	0.942051i	−0.248386	+	0.968661i	$0.579900\pi$
$578$	17386.7	−	8372.99i	1.25120	−	0.602544i
$579$	335.909			0.0241104
$580$	8709.35	−	23705.4i	0.623510	−	1.69709i
$581$	600.499			0.0428793
$582$	20441.1	−	9843.90i	1.45586	−	0.701104i
$583$	16011.1	+	20077.3i	1.13741	+	1.42627i
$584$	−1467.98	+	1840.79i	−0.104016	+	0.130432i
$585$	11081.5	−	5336.55i	0.783183	−	0.377161i
$586$	12020.2	+	5788.63i	0.847356	+	0.408065i
$587$	4186.38	+	5249.55i	0.294362	+	0.369118i	0.906917	−	0.421310i	$-0.138430\pi$
$587$	4186.38	+	5249.55i	0.294362	+	0.369118i	−0.612555	+	0.790428i	$0.709858\pi$
$588$	−2686.85	+	11771.9i	−0.188442	+	0.825618i
$589$	−6084.25	+	26656.9i	−0.425632	+	1.86482i
$590$	−9920.60	+	12440.0i	−0.692245	+	0.868048i
$591$	3084.99	+	13516.2i	0.214720	+	0.940749i
$592$	−8500.70			−0.590163
$593$	−5694.58	−	24949.6i	−0.394348	−	1.72775i	−0.649062	−	0.760735i	$-0.724839\pi$
$593$	−5694.58	−	24949.6i	−0.394348	−	1.72775i	0.254714	−	0.967016i	$-0.418019\pi$
$594$	−29211.6	−	14067.5i	−2.01779	−	0.971714i
$595$	300.280	+	144.607i	0.0206896	+	0.00996357i
$596$	2381.30	+	10433.1i	0.163661	+	0.717044i
$597$	−7276.65			−0.498850
$598$	−1793.11	−	7856.12i	−0.122618	−	0.537225i
$599$	−10997.7	+	13790.7i	−0.750176	+	0.940692i	−0.999616	−	0.0276988i	$-0.991182\pi$
$599$	−10997.7	+	13790.7i	−0.750176	+	0.940692i	0.249440	+	0.968390i	$0.419754\pi$
$600$	872.451	−	3822.46i	0.0593628	−	0.260085i
$601$	3674.80	−	16100.4i	0.249415	−	1.09276i	−0.682730	−	0.730671i	$-0.739207\pi$
$601$	3674.80	−	16100.4i	0.249415	−	1.09276i	0.932145	−	0.362086i	$-0.117935\pi$
$602$	840.037	+	1053.37i	0.0568727	+	0.0713161i
$603$	−3681.76	−	1773.04i	−0.248645	−	0.119741i
$604$	29781.0	−	14341.8i	2.00625	−	0.966157i
$605$	−14320.7	+	17957.5i	−0.962343	+	1.20674i
$606$	−6558.73	−	8224.38i	−0.439654	−	0.551308i
$607$	−10898.3	+	5248.33i	−0.728743	+	0.350944i	−0.761190	−	0.648529i	$-0.775384\pi$
$607$	−10898.3	+	5248.33i	−0.728743	+	0.350944i	0.0324466	+	0.999473i	$0.489670\pi$
$608$	−21680.0			−1.44612
$609$	−221.723	+	603.492i	−0.0147531	+	0.0401555i
$610$	−55041.6			−3.65339
$611$	−8919.72	+	4295.51i	−0.590594	+	0.284415i
$612$	1423.68	+	1785.24i	0.0940339	+	0.117915i
$613$	−12816.8	+	16071.8i	−0.844481	+	1.05895i	0.153015	+	0.988224i	$0.451102\pi$
$613$	−12816.8	+	16071.8i	−0.844481	+	1.05895i	−0.997496	+	0.0707222i	$0.977470\pi$
$614$	1751.89	−	843.668i	0.115148	−	0.0554522i
$615$	−17816.7	−	8580.06i	−1.16819	−	0.562571i
$616$	−242.683	−	304.315i	−0.0158734	−	0.0199046i
$617$	−2240.04	+	9814.26i	−0.146160	+	0.640368i	0.847771	+	0.530362i	$0.177944\pi$
$617$	−2240.04	+	9814.26i	−0.146160	+	0.640368i	−0.993931	+	0.110006i	$0.964913\pi$
$618$	106.771	−	467.796i	0.00694980	−	0.0304491i
$619$	9561.31	−	11989.5i	0.620842	−	0.778511i	−0.367621	−	0.929976i	$-0.619827\pi$
$619$	9561.31	−	11989.5i	0.620842	−	0.778511i	0.988463	+	0.151464i	$0.0483989\pi$
$620$	11698.1	+	51252.9i	0.757756	+	3.31994i
$621$	−5269.52			−0.340513
$622$	−8300.33	−	36366.1i	−0.535069	−	2.34429i
$623$	937.864	+	451.651i	0.0603126	+	0.0290450i
$624$	8759.16	+	4218.19i	0.561934	+	0.270613i
$625$	2280.06	+	9989.60i	0.145924	+	0.639334i
$626$	24903.3			1.58999
$627$	3576.00	+	15667.5i	0.227770	+	0.997925i
$628$	−12843.1	+	16104.8i	−0.816078	+	1.02333i
$629$	687.591	−	3012.53i	0.0435867	−	0.190966i
$630$	236.578	−	1036.52i	0.0149611	−	0.0655488i
$631$	−8312.69	−	10423.8i	−0.524442	−	0.657629i	0.447104	−	0.894482i	$-0.352456\pi$
$631$	−8312.69	−	10423.8i	−0.524442	−	0.657629i	−0.971546	+	0.236853i	$0.923884\pi$
$632$	−2967.95	−	1429.29i	−0.186801	−	0.0899588i
$633$	9153.83	−	4408.25i	0.574775	−	0.276797i
$634$	18706.7	−	23457.4i	1.17182	−	1.46942i
$635$	12113.4	+	15189.8i	0.757019	+	0.949272i
$636$	15748.7	−	7584.18i	0.981882	−	0.472849i
$637$	18549.2			1.15376
$638$	17644.0	+	29070.4i	1.09488	+	1.80393i
$639$	−2829.52			−0.175171
$640$	−12767.5	+	6148.51i	−0.788563	+	0.379752i
$641$	−11358.5	−	14243.2i	−0.699899	−	0.877646i	0.297117	−	0.954841i	$-0.403975\pi$
$641$	−11358.5	−	14243.2i	−0.699899	−	0.877646i	−0.997016	+	0.0771954i	$0.975403\pi$
$642$	6286.18	−	7882.62i	0.386442	−	0.484583i
$643$	25031.8	−	12054.7i	1.53524	−	0.739332i	0.540459	−	0.841370i	$-0.318251\pi$
$643$	25031.8	−	12054.7i	1.53524	−	0.739332i	0.994781	+	0.102038i	$0.0325363\pi$
$644$	−342.282	−	164.834i	−0.0209438	−	0.0100860i
$645$	−11104.2	−	13924.2i	−0.677870	−	0.850023i
$646$	1388.70	−	6084.31i	0.0845786	−	0.370563i
$647$	−1603.24	+	7024.26i	−0.0974187	+	0.426819i	−0.999993	−	0.00371470i	$-0.998818\pi$
$647$	−1603.24	+	7024.26i	−0.0974187	+	0.426819i	0.902574	+	0.430534i	$0.141675\pi$
$648$	−773.178	+	969.535i	−0.0468724	+	0.0587761i
$649$	−2600.25	−	11392.4i	−0.157271	−	0.689049i
$650$	−36171.0			−2.18268
$651$	−297.812	−	1304.80i	−0.0179296	−	0.0785546i
$652$	−12032.2	−	5794.40i	−0.722725	−	0.348046i
$653$	−10417.8	−	5016.95i	−0.624318	−	0.300656i	0.0948501	−	0.995492i	$-0.469763\pi$
$653$	−10417.8	−	5016.95i	−0.624318	−	0.300656i	−0.719169	+	0.694836i	$0.755477\pi$
$654$	204.847	+	897.491i	0.0122479	+	0.0536616i
$655$	9808.95			0.585141
$656$	3452.48	+	15126.3i	0.205483	+	0.900278i
$657$	2944.75	−	3692.60i	0.174864	−	0.219272i
$658$	−190.427	+	834.314i	−0.0112821	+	0.0494300i
$659$	1174.75	−	5146.93i	0.0694414	−	0.304243i	−0.928266	−	0.371917i	$-0.878701\pi$
$659$	1174.75	−	5146.93i	0.0694414	−	0.304243i	0.997707	+	0.0676742i	$0.0215578\pi$
$660$	19264.8	+	24157.3i	1.13619	+	1.42473i
$661$	9073.34	+	4369.49i	0.533906	+	0.257116i	0.681354	−	0.731954i	$-0.261392\pi$
$661$	9073.34	+	4369.49i	0.533906	+	0.257116i	−0.147448	+	0.989070i	$0.547106\pi$
$662$	−37016.6	+	17826.3i	−2.17325	+	1.04658i
$663$	−2203.37	+	2762.93i	−0.129067	+	0.161845i
$664$	−2244.58	−	2814.61i	−0.131185	−	0.164500i
$665$	−1427.88	+	687.632i	−0.0832646	+	0.0400981i
$666$	−9857.02			−0.573501
$667$	4633.62	+	3012.62i	0.268987	+	0.174886i
$668$	25128.5			1.45547
$669$	−2276.76	+	1096.43i	−0.131577	+	0.0633639i
$670$	13388.8	+	16789.0i	0.772020	+	0.968082i
$671$	25203.2	−	31603.9i	1.45001	−	1.81826i
$672$	956.101	−	460.434i	0.0548845	−	0.0264310i
$673$	−14144.5	−	6811.62i	−0.810148	−	0.390147i	−0.0175158	−	0.999847i	$-0.505576\pi$
$673$	−14144.5	−	6811.62i	−0.810148	−	0.390147i	−0.792632	+	0.609700i	$0.791290\pi$
$674$	19743.1	+	24757.1i	1.12830	+	1.41485i
$675$	−5263.41	+	23060.5i	−0.300131	+	1.31496i
$676$	−1599.77	+	7009.03i	−0.0910199	+	0.398784i
$677$	17685.8	−	22177.2i	1.00402	−	1.25900i	0.0383354	−	0.999265i	$-0.487794\pi$
$677$	17685.8	−	22177.2i	1.00402	−	1.25900i	0.965681	−	0.259732i	$-0.0836341\pi$
$678$	−153.768	−	673.700i	−0.00871004	−	0.0381612i
$679$	−1643.18			−0.0928712
$680$	−444.612	−	1947.97i	−0.0250737	−	0.109855i
$681$	−1692.62	−	815.124i	−0.0952444	−	0.0458673i
$682$	−63777.5	−	30713.6i	−3.58089	−	1.72447i
$683$	5378.86	+	23566.3i	0.301342	+	1.32026i	0.868104	+	0.496383i	$0.165339\pi$
$683$	5378.86	+	23566.3i	0.301342	+	1.32026i	−0.566762	+	0.823882i	$0.691804\pi$
$684$	−10858.0			−0.606966
$685$	−7256.74	−	31793.9i	−0.404768	−	1.77340i
$686$	2003.06	−	2511.76i	0.111483	−	0.139795i
$687$	−785.322	+	3440.72i	−0.0436127	+	0.191080i
$688$	−3109.36	+	13623.0i	−0.172301	+	0.754901i
$689$	−16742.4	−	20994.3i	−0.925738	−	1.16084i
$690$	8295.62	+	3994.96i	0.457694	+	0.220414i
$691$	−3644.90	+	1755.29i	−0.200663	+	0.0966344i	−0.531517	−	0.847048i	$-0.678378\pi$
$691$	−3644.90	+	1755.29i	−0.200663	+	0.0966344i	0.330853	+	0.943682i	$0.392663\pi$
$692$	−3895.91	+	4885.31i	−0.214018	+	0.268370i
$693$	486.820	+	610.453i	0.0266851	+	0.0334620i
$694$	38749.2	−	18660.6i	2.11945	−	1.02067i
$695$	−25204.9			−1.37565
$696$	3657.41	−	1216.52i	0.199187	−	0.0662532i
$697$	−5639.81			−0.306489
$698$	−10922.0	+	5259.76i	−0.592270	+	0.285222i
$699$	9387.43	+	11771.5i	0.507962	+	0.636964i
$700$	−1063.23	+	1333.25i	−0.0574093	+	0.0719889i
$701$	−3815.57	+	1837.48i	−0.205581	+	0.0990026i	−0.533841	−	0.845585i	$-0.679252\pi$
$701$	−3815.57	+	1837.48i	−0.205581	+	0.0990026i	0.328260	+	0.944587i	$0.393538\pi$
$702$	30545.8	+	14710.1i	1.64227	+	0.790877i
$703$	9161.25	+	11487.8i	0.491498	+	0.616319i
$704$	7993.50	−	35021.8i	0.427935	−	1.87491i
$705$	2517.19	−	11028.5i	0.134472	−	0.589160i
$706$	−21483.7	+	26939.7i	−1.14525	+	1.43610i
$707$	169.532	+	742.770i	0.00901828	+	0.0395117i
$708$	−7954.05			−0.422220
$709$	−4891.55	−	21431.3i	−0.259106	−	1.13522i	−0.922210	−	0.386690i	$-0.873618\pi$
$709$	−4891.55	−	21431.3i	−0.259106	−	1.13522i	0.663104	−	0.748527i	$-0.269239\pi$
$710$	13396.4	+	6451.37i	0.708110	+	0.341008i
$711$	5953.66	+	2867.13i	0.314036	+	0.151232i
$712$	−1388.66	−	6084.10i	−0.0730928	−	0.320240i
$713$	−11504.9			−0.604296
$714$	67.9742	+	297.814i	0.00356284	+	0.0156098i
$715$	29595.0	−	37110.9i	1.54796	−	1.94108i
$716$	−5974.37	+	26175.4i	−0.311834	+	1.36623i
$717$	−3563.84	+	15614.2i	−0.185626	+	0.813282i
$718$	27661.8	+	34686.8i	1.43778	+	1.80292i
$719$	−21270.7	−	10243.4i	−1.10329	−	0.531314i	−0.208596	−	0.978002i	$-0.566889\pi$
$719$	−21270.7	−	10243.4i	−1.10329	−	0.531314i	−0.894690	+	0.446688i	$0.852604\pi$
$720$	9934.45	−	4784.18i	0.514215	−	0.247633i
$721$	−21.6673	+	27.1700i	−0.00111919	+	0.00140342i
$722$	562.524	+	705.383i	0.0289958	+	0.0363596i
$723$	14221.7	−	6848.79i	0.731548	−	0.352295i
$724$	6256.20			0.321146
$725$	17812.1	−	17268.6i	0.912446	−	0.884605i
$726$	−21051.8			−1.07618
$727$	15319.6	−	7377.54i	0.781532	−	0.376366i	−0.000184720	−	1.00000i	$-0.500059\pi$
$727$	15319.6	−	7377.54i	0.781532	−	0.376366i	0.781716	+	0.623634i	$0.214345\pi$
$728$	253.768	+	318.215i	0.0129193	+	0.0162003i
$729$	10777.8	−	13515.0i	0.547570	−	0.686631i
$730$	−22361.2	+	10768.6i	−1.13373	+	0.545976i
$731$	−4576.30	−	2203.83i	−0.231547	−	0.111507i
$732$	−17155.4	−	21512.2i	−0.866231	−	1.08622i
$733$	−4803.97	+	21047.6i	−0.242072	+	1.06059i	0.697056	+	0.717017i	$0.254493\pi$
$733$	−4803.97	+	21047.6i	−0.242072	+	1.06059i	−0.939128	+	0.343569i	$0.888364\pi$
$734$	3700.98	−	16215.0i	0.186111	−	0.815406i
$735$	−13214.7	+	16570.7i	−0.663173	+	0.831593i
$736$	−2029.92	−	8893.65i	−0.101663	−	0.445414i
$737$	−15770.6			−0.788217
$738$	4003.33	+	17539.7i	0.199681	+	0.874860i
$739$	8628.05	+	4155.05i	0.429483	+	0.206828i	0.636121	−	0.771589i	$-0.280538\pi$
$739$	8628.05	+	4155.05i	0.429483	+	0.206828i	−0.206638	+	0.978417i	$0.566252\pi$
$740$	25453.3	+	12257.7i	1.26444	+	0.608920i
$741$	−3739.33	−	16383.1i	−0.185382	−	0.812210i
$742$	−2321.15			−0.114841
$743$	−3076.68	−	13479.8i	−0.151914	−	0.665580i	−0.992328	−	0.123634i	$-0.960545\pi$
$743$	−3076.68	−	13479.8i	−0.151914	−	0.665580i	0.840414	−	0.541946i	$-0.182312\pi$
$744$	−5002.57	+	6273.03i	−0.246510	+	0.309114i
$745$	−4179.93	+	18313.5i	−0.205558	+	0.900610i
$746$	10740.3	−	47056.5i	0.527120	−	2.30947i
$747$	4502.60	+	5646.08i	0.220537	+	0.276545i
$748$	7939.50	+	3823.46i	0.388098	+	0.186898i
$749$	−657.899	+	316.827i	−0.0320949	+	0.0154561i
$750$	5492.11	−	6886.89i	0.267392	−	0.335298i
$751$	−21214.5	−	26602.2i	−1.03080	−	1.29258i	−0.955365	−	0.295427i	$-0.904538\pi$
$751$	−21214.5	−	26602.2i	−1.03080	−	1.29258i	−0.0754316	−	0.997151i	$-0.524033\pi$
$752$	−7996.46	+	3850.89i	−0.387767	+	0.186739i
$753$	2109.23			0.102078
$754$	−18449.9	−	30398.1i	−0.891119	−	1.46822i
$755$	58021.1			2.79683
$756$	1440.09	−	693.512i	0.0692800	−	0.0333635i
$757$	1324.32	+	1660.65i	0.0635842	+	0.0797321i	0.812607	−	0.582813i	$-0.198048\pi$
$757$	1324.32	+	1660.65i	0.0635842	+	0.0797321i	−0.749022	+	0.662545i	$0.769476\pi$
$758$	5253.93	−	6588.22i	0.251757	−	0.315693i
$759$	−6092.34	+	2933.92i	−0.291354	+	0.140309i
$760$	8560.24	+	4122.40i	0.408569	+	0.196757i
$761$	20951.7	+	26272.5i	0.998025	+	1.25148i	0.967742	+	0.251942i	$0.0810693\pi$
$761$	20951.7	+	26272.5i	0.998025	+	1.25148i	0.0302826	+	0.999541i	$0.490359\pi$
$762$	−3962.46	+	17360.7i	−0.188379	+	0.825342i
$763$	14.8361	−	65.0013i	0.000703937	−	0.00308415i
$764$	13479.4	−	16902.6i	0.638308	−	0.800413i
$765$	891.886	+	3907.61i	0.0421519	+	0.184680i
$766$	22990.3			1.08443
$767$	2719.02	+	11912.8i	0.128003	+	0.560816i
$768$	6659.76	+	3207.17i	0.312908	+	0.150689i
$769$	9348.09	+	4501.80i	0.438362	+	0.211104i	0.640030	−	0.768350i	$-0.278922\pi$
$769$	9348.09	+	4501.80i	0.438362	+	0.211104i	−0.201668	+	0.979454i	$0.564636\pi$
$770$	−913.010	−	4000.16i	−0.0427306	−	0.187215i
$771$	−27736.3			−1.29559
$772$	194.902	+	853.920i	0.00908635	+	0.0398099i
$773$	−6348.67	+	7960.99i	−0.295402	+	0.370423i	−0.907278	−	0.420531i	$-0.861844\pi$
$773$	−6348.67	+	7960.99i	−0.295402	+	0.370423i	0.611876	+	0.790954i	$0.290415\pi$
$774$	−3605.47	+	15796.6i	−0.167437	+	0.733588i
$775$	−11491.6	+	50347.9i	−0.532632	+	2.33361i
$776$	6141.98	+	7701.80i	0.284129	+	0.356287i
$777$	−647.992	−	312.056i	−0.0299184	−	0.0144079i
$778$	−22464.8	+	10818.5i	−1.03522	+	0.498536i
$779$	16720.9	−	20967.4i	0.769048	−	0.964356i
$780$	−20144.8	−	25260.7i	−0.924741	−	1.15959i
$781$	−9838.39	+	4737.92i	−0.450762	+	0.217076i
$782$	2625.95			0.120082
$783$	−22064.8	+	7339.17i	−1.00706	+	0.334969i
$784$	16629.2			0.757526
$785$	−32576.8	+	15688.1i	−1.48116	+	0.713291i
$786$	5605.41	+	7028.97i	0.254375	+	0.318976i
$787$	−1282.53	+	1608.25i	−0.0580907	+	0.0728435i	−0.810028	−	0.586391i	$-0.800548\pi$
$787$	−1282.53	+	1608.25i	−0.0580907	+	0.0728435i	0.751937	+	0.659235i	$0.229120\pi$
$788$	−32569.8	+	15684.8i	−1.47240	+	0.709071i
$789$	4413.08	+	2125.23i	0.199125	+	0.0958937i
$790$	−21650.6	−	27149.0i	−0.975054	−	1.22268i
$791$	−11.1367	+	48.7931i	−0.000500601	+	0.00219328i
$792$	1041.61	−	4563.57i	0.0467321	−	0.204747i
$793$	−26354.4	+	33047.3i	−1.18017	+	1.47988i
$794$	788.203	+	3453.34i	0.0352296	+	0.154351i
$795$	30682.5			1.36880
$796$	−4222.07	−	18498.1i	−0.187999	−	0.823678i
$797$	−11131.6	−	5360.69i	−0.494731	−	0.238250i	0.169844	−	0.985471i	$-0.445673\pi$
$797$	−11131.6	−	5360.69i	−0.494731	−	0.238250i	−0.664576	+	0.747221i	$0.731388\pi$
$798$	−1308.73	−	630.249i	−0.0580556	−	0.0279581i
$799$	−717.899	−	3145.32i	−0.0317865	−	0.139266i
$800$	−40948.0			−1.80966
$801$	2785.62	+	12204.6i	0.122878	+	0.538363i
$802$	1142.19	−	1432.26i	0.0502894	−	0.0630609i
$803$	4055.94	−	17770.2i	0.178245	−	0.780943i
$804$	−2388.70	+	10465.6i	−0.104780	+	0.459070i
$805$	−415.777	−	521.367i	−0.0182040	−	0.0228271i
$806$	66690.6	+	32116.5i	2.91448	+	1.40354i
$807$	−14550.4	+	7007.10i	−0.634694	+	0.305653i
$808$	2847.77	−	3570.99i	0.123990	−	0.155479i
$809$	10002.1	+	12542.2i	0.434678	+	0.545069i	0.950132	−	0.311848i	$-0.100948\pi$
$809$	10002.1	+	12542.2i	0.434678	+	0.545069i	−0.515454	+	0.856917i	$0.672377\pi$
$810$	−11777.5	+	5671.75i	−0.510889	+	0.246031i
$811$	−14698.7			−0.636426			−0.318213	−	0.948019i	$-0.603083\pi$
$811$	−14698.7			−0.636426			−0.318213	+	0.948019i	$0.603083\pi$
$812$	−1662.80	−	213.486i	−0.0718629	−	0.00922649i
$813$	−2415.32			−0.104193
$814$	−34273.4	+	16505.2i	−1.47577	+	0.710696i
$815$	−14615.7	−	18327.5i	−0.628180	−	0.787712i
$816$	−1975.30	+	2476.95i	−0.0847418	+	0.106263i
$817$	21761.1	−	10479.6i	0.931853	−	0.448757i
$818$	−11420.7	−	5499.90i	−0.488159	−	0.235085i
$819$	−509.055	−	638.335i	−0.0217190	−	0.0272347i
$820$	11473.9	−	50270.4i	0.488641	−	2.14088i
$821$	−4169.28	+	18266.8i	−0.177234	+	0.776512i	0.805666	+	0.592370i	$0.201808\pi$
$821$	−4169.28	+	18266.8i	−0.177234	+	0.776512i	−0.982900	+	0.184142i	$0.941049\pi$
$822$	18636.1	−	23369.0i	0.790767	−	0.991590i
$823$	−5757.25	−	25224.1i	−0.243846	−	1.06836i	−0.937482	−	0.348033i	$-0.886850\pi$
$823$	−5757.25	−	25224.1i	−0.243846	−	1.06836i	0.693637	−	0.720325i	$-0.256007\pi$
$824$	208.339			0.00880803
$825$	6754.14	+	29591.8i	0.285029	+	1.24879i
$826$	951.627	+	458.279i	0.0400863	+	0.0193046i
$827$	−16231.8	−	7816.84i	−0.682511	−	0.328680i	0.0603010	−	0.998180i	$-0.480794\pi$
$827$	−16231.8	−	7816.84i	−0.682511	−	0.328680i	−0.742812	+	0.669500i	$0.766508\pi$
$828$	−1016.64	−	4454.19i	−0.0426699	−	0.186949i
$829$	−4424.73			−0.185377			−0.0926884	−	0.995695i	$-0.529546\pi$
$829$	−4424.73			−0.185377			−0.0926884	+	0.995695i	$0.529546\pi$
$830$	−8444.43	−	36997.5i	−0.353145	−	1.54723i
$831$	−2555.11	+	3204.01i	−0.106662	+	0.133750i
$832$	−8358.60	+	36621.4i	−0.348296	+	1.52598i
$833$	−1345.08	+	5893.17i	−0.0559473	+	0.245121i
$834$	−14403.6	−	18061.5i	−0.598027	−	0.749902i
$835$	39740.4	+	19138.0i	1.64704	+	0.793170i
$836$	−37753.7	+	18181.2i	−1.56189	+	0.752166i
$837$	30180.0	−	37844.6i	1.24633	−	1.56284i
$838$	−24088.0	−	30205.4i	−0.992966	−	1.24514i
$839$	−17299.5	+	8331.02i	−0.711855	+	0.342811i	−0.754519	−	0.656278i	$-0.772130\pi$
$839$	−17299.5	+	8331.02i	−0.711855	+	0.342811i	0.0426641	+	0.999089i	$0.486415\pi$
$840$	−465.062			−0.0191026
$841$	23598.0	+	6161.05i	0.967567	+	0.252616i
$842$	68344.1			2.79726
$843$	−2605.58	+	1254.78i	−0.106454	+	0.0512658i
$844$	16517.6	+	20712.4i	0.673646	+	0.844726i
$845$	−7868.12	+	9866.31i	−0.320321	+	0.401670i
$846$	−9272.32	+	4465.31i	−0.376819	+	0.181467i
$847$	1373.70	+	661.538i	0.0557271	+	0.0268368i
$848$	−15009.4	−	18821.2i	−0.607813	−	0.762173i
$849$	455.109	−	1993.96i	0.0183973	−	0.0806037i
$850$	2622.90	−	11491.7i	0.105841	−	0.463720i
$851$	−3854.81	+	4833.77i	−0.155277	+	0.194712i
$852$	1653.97	+	7246.54i	0.0665073	+	0.291388i
$853$	29128.4			1.16921			0.584605	−	0.811318i	$-0.301250\pi$
$853$	29128.4			1.16921			0.584605	+	0.811318i	$0.301250\pi$
$854$	813.037	+	3562.15i	0.0325779	+	0.142733i
$855$	−17171.7	−	8269.47i	−0.686855	−	0.330772i
$856$	3944.14	+	1899.40i	0.157486	+	0.0758413i
$857$	−2345.05	−	10274.3i	−0.0934717	−	0.409526i	0.906446	−	0.422321i	$-0.138784\pi$
$857$	−2345.05	−	10274.3i	−0.0934717	−	0.409526i	−0.999918	+	0.0127946i	$0.995927\pi$
$858$	43505.6			1.73107
$859$	−2919.03	−	12789.1i	−0.115944	−	0.507984i	−0.999233	−	0.0391552i	$-0.987533\pi$
$859$	−2919.03	−	12789.1i	−0.115944	−	0.507984i	0.883289	−	0.468829i	$-0.155324\pi$
$860$	28954.1	−	36307.2i	1.14805	−	1.43961i
$861$	−292.103	+	1279.79i	−0.0115619	+	0.0506562i
$862$	−8568.94	+	37543.0i	−0.338584	+	1.48343i
$863$	2834.76	+	3554.68i	0.111815	+	0.140212i	0.834589	−	0.550872i	$-0.185705\pi$
$863$	2834.76	+	3554.68i	0.111815	+	0.140212i	−0.722774	+	0.691084i	$0.757133\pi$
$864$	34579.9	+	16652.8i	1.36161	+	0.655717i
$865$	−9882.01	+	4758.92i	−0.388437	+	0.187062i
$866$	−1273.70	+	1597.17i	−0.0499794	+	0.0626722i
$867$	10557.8	+	13239.0i	0.413565	+	0.518594i
$868$	3144.15	−	1514.14i	0.122949	−	0.0592090i
$869$	25502.1			0.995510
$870$	40299.8	+	5174.10i	1.57045	+	0.201630i
$871$	16490.9			0.641529
$872$	−360.125	+	173.427i	−0.0139855	+	0.00673507i
$873$	−12320.7	−	15449.7i	−0.477656	−	0.598962i
$874$	−7785.42	+	9762.60i	−0.301311	+	0.377832i
$875$	−574.794	+	276.806i	−0.0222075	+	0.0106946i
$876$	−11178.3	−	5383.16i	−0.431139	−	0.207626i
$877$	−14150.2	−	17743.8i	−0.544834	−	0.683201i	0.430839	−	0.902429i	$-0.358218\pi$
$877$	−14150.2	−	17743.8i	−0.544834	−	0.683201i	−0.975674	+	0.219228i	$0.929646\pi$
$878$	−4209.06	+	18441.1i	−0.161787	+	0.708835i
$879$	−2605.01	+	11413.3i	−0.0999599	+	0.437953i
$880$	26531.7	−	33269.7i	1.01634	−	1.27445i
$881$	−2035.15	−	8916.56i	−0.0778273	−	0.340983i	0.920991	−	0.389584i	$-0.127381\pi$
$881$	−2035.15	−	8916.56i	−0.0778273	−	0.340983i	−0.998818	+	0.0486002i	$0.984524\pi$
$882$	19282.5			0.736139
$883$	−1070.63	−	4690.75i	−0.0408037	−	0.178773i	0.950420	−	0.310970i	$-0.100654\pi$
$883$	−1070.63	−	4690.75i	−0.0408037	−	0.178773i	−0.991223	+	0.132197i	$0.957797\pi$
$884$	−8302.14	−	3998.10i	−0.315872	−	0.152116i
$885$	−12579.2	−	6057.84i	−0.477792	−	0.230093i
$886$	−7945.95	−	34813.5i	−0.301297	−	1.32007i
$887$	5424.84			0.205353			0.102677	−	0.994715i	$-0.467259\pi$
$887$	5424.84			0.205353			0.102677	+	0.994715i	$0.467259\pi$
$888$	959.454	+	4203.64i	0.0362581	+	0.158857i
$889$	804.110	−	1008.32i	0.0303363	−	0.0380405i
$890$	14638.2	−	64134.2i	0.551319	−	2.41549i
$891$	2136.24	−	9359.49i	0.0803219	−	0.351913i
$892$	−4108.28	−	5151.62i	−0.154210	−	0.193373i
$893$	13821.9	+	6656.28i	0.517954	+	0.249433i
$894$	−15511.9	+	7470.13i	−0.580307	+	0.279461i
$895$	−29383.7	+	36846.0i	−1.09742	+	1.37612i
$896$	586.508	+	735.458i	0.0218681	+	0.0274218i
$897$	6370.61	−	3067.92i	0.237133	−	0.114197i
$898$	6437.03			0.239205
$899$	−48174.0	+	16023.6i	−1.78720	+	0.594457i
$900$	−20507.9			−0.759552
$901$	7884.04	−	3796.75i	0.291515	−	0.140386i
$902$	43289.4	+	54283.2i	1.59798	+	2.00381i
$903$	−737.113	+	924.311i	−0.0271646	+	0.0340633i
$904$	270.327	−	130.183i	0.00994573	−	0.00478961i
$905$	9894.10	+	4764.75i	0.363416	+	0.175012i
$906$	33156.7	+	41577.2i	1.21585	+	1.52462i
$907$	−1582.72	+	6934.34i	−0.0579419	+	0.253860i	−0.995601	−	0.0936970i	$-0.970132\pi$
$907$	−1582.72	+	6934.34i	−0.0579419	+	0.253860i	0.937659	+	0.347557i	$0.112989\pi$
$908$	1090.05	−	4775.80i	0.0398397	−	0.174549i
$909$	−5712.59	+	7163.36i	−0.208443	+	0.261379i
$910$	954.711	+	4182.86i	0.0347784	+	0.152374i
$911$	−37771.0			−1.37367			−0.686833	−	0.726815i	$-0.741000\pi$
$911$	−37771.0			−1.37367			−0.686833	+	0.726815i	$0.741000\pi$
$912$	−3352.28	−	14687.3i	−0.121716	−	0.533274i
$913$	25109.9	+	12092.3i	0.910204	+	0.438331i
$914$	−22816.5	−	10987.9i	−0.825716	−	0.397644i
$915$	−10747.3	−	47086.8i	−0.388299	−	1.70125i
$916$	−9202.38			−0.331938
$917$	−144.891	−	634.809i	−0.00521780	−	0.0228607i
$918$	−6888.46	+	8637.85i	−0.247661	+	0.310557i
$919$	6869.35	−	30096.6i	0.246571	−	1.08030i	−0.688332	−	0.725396i	$-0.741657\pi$
$919$	6869.35	−	30096.6i	0.246571	−	1.08030i	0.934903	−	0.354904i	$-0.115486\pi$
$920$	−889.601	+	3897.60i	−0.0318796	+	0.139674i
$921$	1063.81	+	1333.97i	0.0380604	+	0.0477263i
$922$	−69732.0	−	33581.2i	−2.49078	−	1.19950i
$923$	10287.8	−	4954.32i	0.366875	−	0.176678i
$924$	1278.83	−	1603.60i	0.0455308	−	0.0570938i
$925$	17303.2	+	21697.6i	0.615056	+	0.771256i
$926$	−68800.8	+	33132.7i	−2.44162	+	1.17582i
$927$	−417.924			−0.0148074
$928$	−20886.5	−	34412.7i	−0.738828	−	1.21730i
$929$	−8468.48			−0.299076			−0.149538	−	0.988756i	$-0.547779\pi$
$929$	−8468.48			−0.299076			−0.149538	+	0.988756i	$0.547779\pi$
$930$	−76202.3	+	36697.1i	−2.68685	+	1.29392i
$931$	−17921.4	−	22472.7i	−0.630880	−	0.791099i
$932$	−24477.7	+	30694.0i	−0.860292	+	1.07877i
$933$	29489.7	−	14201.5i	1.03478	−	0.498323i
$934$	−12498.5	−	6018.97i	−0.437863	−	0.210864i
$935$	9644.26	+	12093.5i	0.337327	+	0.422995i
$936$	−1089.18	+	4772.01i	−0.0380352	+	0.166643i
$937$	−3347.23	+	14665.2i	−0.116702	+	0.511303i	0.882461	+	0.470386i	$0.155885\pi$
$937$	−3347.23	+	14665.2i	−0.116702	+	0.511303i	−0.999163	+	0.0409172i	$0.986972\pi$
$938$	888.768	−	1114.48i	0.0309374	−	0.0387943i
$939$	4862.53	+	21304.2i	0.168991	+	0.740399i
$940$	29496.3			1.02347
$941$	−2104.90	−	9222.15i	−0.0729199	−	0.319483i	0.925292	−	0.379255i	$-0.123820\pi$
$941$	−2104.90	−	9222.15i	−0.0729199	−	0.319483i	−0.998212	+	0.0597721i	$0.980963\pi$
$942$	−29858.2	−	14379.0i	−1.03273	−	0.497337i
$943$	10166.9	+	4896.12i	0.351092	+	0.169077i
$944$	2437.58	+	10679.7i	0.0840428	+	0.368216i
$945$	2805.67			0.0965804
$946$	13914.4	+	60962.8i	0.478218	+	2.09521i
$947$	18407.8	−	23082.6i	0.631650	−	0.792064i	−0.358281	−	0.933614i	$-0.616637\pi$
$947$	18407.8	−	23082.6i	0.631650	−	0.792064i	0.989931	+	0.141549i	$0.0452084\pi$
$948$	3862.69	−	16923.6i	0.132336	−	0.579802i
$949$	−4241.19	+	18581.9i	−0.145074	+	0.635609i
$950$	34946.7	+	43821.8i	1.19350	+	1.49660i
$951$	23719.9	+	11422.9i	0.808801	+	0.389498i
$952$	−119.500	+	57.5482i	−0.00406830	+	0.00195919i
$953$	−6328.30	+	7935.44i	−0.215104	+	0.269732i	−0.877663	−	0.479278i	$-0.840899\pi$
$953$	−6328.30	+	7935.44i	−0.215104	+	0.269732i	0.662560	+	0.749009i	$0.269470\pi$
$954$	−17404.2	−	21824.2i	−0.590652	−	0.740655i
$955$	34190.6	−	16465.3i	1.15852	−	0.557912i
$956$	−41760.9			−1.41281
$957$	−21423.9	+	20770.2i	−0.723654	+	0.701573i
$958$	−653.978			−0.0220554
$959$	−1950.42	+	939.273i	−0.0656751	+	0.0316274i
$960$	−26760.6	−	33556.7i	−0.899681	−	1.12816i
$961$	47317.6	−	59334.4i	1.58832	−	1.99169i
$962$	35838.8	−	17259.0i	1.20113	−	0.578435i
$963$	−7911.90	−	3810.17i	−0.264753	−	0.127498i
$964$	25662.1	+	32179.3i	0.857388	+	1.07513i
$965$	−342.115	+	1498.90i	−0.0114125	+	0.0500014i
$966$	136.006	−	595.881i	0.00452994	−	0.0198469i
$967$	−8371.86	+	10498.0i	−0.278408	+	0.349113i	−0.901300	−	0.433195i	$-0.857386\pi$
$967$	−8371.86	+	10498.0i	−0.278408	+	0.349113i	0.622892	+	0.782308i	$0.285958\pi$
$968$	−2033.98	−	8911.44i	−0.0675356	−	0.295893i
$969$	5476.14			0.181547
$970$	23107.0	+	101238.i	0.764867	+	3.35110i
$971$	19715.0	+	9494.23i	0.651579	+	0.313784i	0.730314	−	0.683112i	$-0.239374\pi$
$971$	19715.0	+	9494.23i	0.651579	+	0.313784i	−0.0787349	+	0.996896i	$0.525088\pi$
$972$	28878.6	+	13907.2i	0.952964	+	0.458923i
$973$	372.309	+	1631.19i	0.0122669	+	0.0537447i
$974$	34534.5			1.13609
$975$	−7062.64	−	30943.4i	−0.231985	−	1.01639i
$976$	−23626.5	+	29626.7i	−0.774863	+	0.971647i
$977$	−2845.81	+	12468.3i	−0.0931887	+	0.408287i	−0.999910	−	0.0134447i	$-0.995720\pi$
$977$	−2845.81	+	12468.3i	−0.0931887	+	0.408287i	0.906721	+	0.421731i	$0.138577\pi$
$978$	4780.99	−	20946.9i	0.156318	−	0.684875i
$979$	30121.9	+	37771.7i	0.983350	+	1.23308i
$980$	−49792.2	−	23978.7i	−1.62301	−	0.781602i
$981$	722.406	−	347.892i	0.0235114	−	0.0113225i
$982$	20653.9	−	25899.2i	0.671175	−	0.841627i
$983$	−27041.9	−	33909.5i	−0.877420	−	1.10025i	−0.994249	−	0.107098i	$-0.965844\pi$
$983$	−27041.9	−	33909.5i	−0.877420	−	1.10025i	0.116829	−	0.993152i	$-0.462727\pi$
$984$	7090.36	−	3414.54i	0.229708	−	0.110621i
$985$	−63454.4			−2.05261
$986$	10995.5	−	3657.31i	0.355140	−	0.118126i
$987$	−750.918			−0.0242168
$988$	39478.1	−	19011.6i	1.27122	−	0.612187i
$989$	6336.48	+	7945.69i	0.203729	+	0.255468i
$990$	30764.9	−	38578.0i	0.987649	−	1.23847i
$991$	−42598.3	+	20514.3i	−1.36547	+	0.657575i	−0.965849	−	0.259106i	$-0.916572\pi$
$991$	−42598.3	+	20514.3i	−1.36547	+	0.657575i	−0.399620	+	0.916681i	$0.630858\pi$
$992$	75498.2	+	36358.0i	2.41640	+	1.16368i
$993$	−22477.7	−	28186.2i	−0.718337	−	0.900766i
$994$	219.633	−	962.274i	0.00700838	−	0.0307057i
$995$	7411.09	−	32470.1i	0.236128	−	1.03454i
$996$	11827.9	−	14831.7i	0.376287	−	0.471849i
$997$	−9157.67	−	40122.4i	−0.290899	−	1.27451i	−0.883277	−	0.468852i	$-0.844668\pi$
$997$	−9157.67	−	40122.4i	−0.290899	−	1.27451i	0.592378	−	0.805660i	$-0.298189\pi$
$998$	−75053.2			−2.38053
$999$	−5788.29	−	25360.1i	−0.183317	−	0.803163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.4.d.a.20.2	yes	42
29.4	even	14		841.4.a.i.1.4		21
29.16	even	7	inner	29.4.d.a.16.2	✓	42
29.25	even	7		841.4.a.h.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.16.2	✓	42	29.16	even	7	inner
29.4.d.a.20.2	yes	42	1.1	even	1	trivial
841.4.a.h.1.18		21	29.25	even	7
841.4.a.i.1.4		21	29.4	even	14

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.77959 + 1.82016i) q^{2} +(-2.29509 - 2.87796i) q^{3} +(5.98444 - 7.50425i) q^{4} +(15.1796 - 7.31010i) q^{5} +(13.9128 + 6.70007i) q^{6} +(-0.697313 - 0.874402i) q^{7} +(-1.49198 + 6.53678i) q^{8} +(2.99289 - 13.1127i) q^{9} +(-44.0671 + 55.2584i) q^{10} +(-11.5503 - 50.6050i) q^{11} -35.3317 q^{12} +(12.0778 + 52.9164i) q^{13} +(4.22711 + 2.03567i) q^{14} +(-55.8767 - 26.9088i) q^{15} +(10.8277 + 47.4391i) q^{16} -17.6876 q^{17} +(12.5553 + 55.0082i) q^{18} +(52.4402 - 65.7579i) q^{19} +(35.9845 - 157.658i) q^{20} +(-0.916094 + 4.01367i) q^{21} +(135.764 + 170.243i) q^{22} +(31.8854 + 15.3552i) q^{23} +(22.2368 - 10.7087i) q^{24} +(99.0460 - 124.200i) q^{25} +(-141.965 - 178.019i) q^{26} +(-134.152 + 64.6044i) q^{27} -10.7348 q^{28} +(154.898 + 19.8874i) q^{29} +260.169 q^{30} +(-292.895 + 141.051i) q^{31} +(-160.714 - 201.529i) q^{32} +(-119.130 + 149.384i) q^{33} +(66.8519 - 32.1942i) q^{34} +(-16.9769 - 8.17564i) q^{35} +(-80.4902 - 100.932i) q^{36} +(-38.8742 + 170.319i) q^{37} +(-78.5129 + 343.987i) q^{38} +(124.571 - 156.207i) q^{39} +(25.1370 + 110.132i) q^{40} +318.857 q^{41} +(-3.84304 - 16.8375i) q^{42} +(258.729 + 124.597i) q^{43} +(-448.874 - 216.166i) q^{44} +(-50.4244 - 220.924i) q^{45} -148.463 q^{46} +(40.5877 + 177.826i) q^{47} +(111.677 - 140.039i) q^{48} +(76.0463 - 333.181i) q^{49} +(-148.291 + 649.704i) q^{50} +(40.5947 + 50.9041i) q^{51} +(469.377 + 226.040i) q^{52} +(-445.738 + 214.656i) q^{53} +(389.451 - 488.357i) q^{54} +(-545.256 - 683.729i) q^{55} +(6.75615 - 3.25359i) q^{56} -309.603 q^{57} +(-621.651 + 206.773i) q^{58} +225.125 q^{59} +(-536.321 + 258.279i) q^{60} +(485.551 + 608.862i) q^{61} +(850.289 - 1066.23i) q^{62} +(-13.5528 + 6.52666i) q^{63} +(623.527 + 300.275i) q^{64} +(570.160 + 714.959i) q^{65} +(178.360 - 781.447i) q^{66} +(67.6078 - 296.209i) q^{67} +(-105.850 + 132.732i) q^{68} +(-28.9884 - 127.007i) q^{69} +79.0467 q^{70} +(-46.8127 - 205.100i) q^{71} +(81.2496 + 39.1277i) q^{72} +(316.380 + 152.361i) q^{73} +(-163.079 - 714.494i) q^{74} -584.761 q^{75} +(-179.639 - 787.048i) q^{76} +(-36.1950 + 45.3871i) q^{77} +(-186.507 + 817.140i) q^{78} +(-109.326 + 478.991i) q^{79} +(511.145 + 640.955i) q^{80} +(166.636 + 80.2476i) q^{81} +(-1205.15 + 580.369i) q^{82} +(-334.768 + 419.785i) q^{83} +(24.6373 + 30.8941i) q^{84} +(-268.490 + 129.298i) q^{85} -1204.68 q^{86} +(-298.271 - 491.434i) q^{87} +348.027 q^{88} +(-838.575 + 403.836i) q^{89} +(592.699 + 743.221i) q^{90} +(37.8482 - 47.4601i) q^{91} +(306.046 - 147.384i) q^{92} +(1078.16 + 519.214i) q^{93} +(-477.077 - 598.235i) q^{94} +(315.323 - 1381.52i) q^{95} +(-211.138 + 925.057i) q^{96} +(916.045 - 1148.68i) q^{97} +(319.017 + 1397.70i) q^{98} -698.137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 5 q^{2} - 5 q^{3} - 23 q^{4} - 7 q^{5} - 11 q^{6} - 31 q^{7} + 38 q^{8} - 72 q^{9} + 31 q^{10} - 63 q^{11} + 136 q^{12} + 173 q^{13} + 129 q^{14} - 229 q^{15} - 451 q^{16} - 140 q^{17} + 846 q^{18}+ \cdots - 17404 q^{99}+O(q^{100}) \) 42 * q - 5 * q^2 - 5 * q^3 - 23 * q^4 - 7 * q^5 - 11 * q^6 - 31 * q^7 + 38 * q^8 - 72 * q^9 + 31 * q^10 - 63 * q^11 + 136 * q^12 + 173 * q^13 + 129 * q^14 - 229 * q^15 - 451 * q^16 - 140 * q^17 + 846 * q^18 - q^19 - 395 * q^20 - 961 * q^21 - 396 * q^22 + 57 * q^23 - 83 * q^24 + 1028 * q^25 + 141 * q^26 - 35 * q^27 + 356 * q^28 + 472 * q^29 + 2174 * q^30 + 175 * q^31 + 1356 * q^32 - 173 * q^33 - 1469 * q^34 + 477 * q^35 - 712 * q^36 - 417 * q^37 - 2834 * q^38 - 2273 * q^39 + 507 * q^40 + 1104 * q^41 + 2866 * q^42 - 573 * q^43 - 1644 * q^44 - 81 * q^45 - 5984 * q^46 - 223 * q^47 - 2442 * q^48 + 1400 * q^49 - 1234 * q^50 + 92 * q^51 + 2394 * q^52 - 791 * q^53 + 4228 * q^54 + 1505 * q^55 + 4167 * q^56 + 1718 * q^57 + 3635 * q^58 + 6172 * q^59 - 848 * q^60 + 2591 * q^61 + 1333 * q^62 - 1797 * q^63 + 2426 * q^64 - 3483 * q^65 + 679 * q^66 - 2611 * q^67 - 2796 * q^68 + 3665 * q^69 - 13558 * q^70 - 2169 * q^71 - 12175 * q^72 - 1309 * q^73 + 44 * q^74 - 7468 * q^75 + 1679 * q^76 - 1697 * q^77 + 6185 * q^78 + 933 * q^79 + 4604 * q^80 + 2562 * q^81 - 7016 * q^82 + 2553 * q^83 + 5579 * q^84 + 5294 * q^85 + 6824 * q^86 - 3909 * q^87 + 16298 * q^88 - 2543 * q^89 + 16038 * q^90 + 2781 * q^91 - 290 * q^92 + 6515 * q^93 - 3230 * q^94 + 1737 * q^95 - 15242 * q^96 - 5527 * q^97 - 786 * q^98 - 17404 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more