LMFDB - Embedded newform 29.4.d.a.16.1

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			16.1
Character	$\chi$	$=$	29.16
Dual form			29.4.d.a.20.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.50314 - 2.16860i) q^{2} +(4.54313 - 5.69691i) q^{3} +(10.5875 + 13.2763i) q^{4} +(-16.6453 - 8.01597i) q^{5} +(-32.8126 + 15.8017i) q^{6} +(-4.27206 + 5.35699i) q^{7} +(-9.98861 - 43.7630i) q^{8} +(-5.80663 - 25.4405i) q^{9} +(57.5728 + 72.1941i) q^{10} +(-0.169748 + 0.743714i) q^{11} +123.735 q^{12} +(15.7909 - 69.1847i) q^{13} +(30.8548 - 14.8589i) q^{14} +(-121.288 + 58.4093i) q^{15} +(-19.6950 + 86.2893i) q^{16} +65.5487 q^{17} +(-29.0222 + 127.154i) q^{18} +(-41.8366 - 52.4614i) q^{19} +(-69.8102 - 305.858i) q^{20} +(11.1098 + 48.6750i) q^{21} +(2.37721 - 2.98093i) q^{22} +(99.5673 - 47.9491i) q^{23} +(-294.693 - 141.917i) q^{24} +(134.875 + 169.128i) q^{25} +(-221.143 + 277.304i) q^{26} +(5.94287 + 2.86194i) q^{27} -116.352 q^{28} +(-148.555 - 48.1699i) q^{29} +672.844 q^{30} +(66.9852 + 32.2584i) q^{31} +(51.9164 - 65.1011i) q^{32} +(3.46568 + 4.34583i) q^{33} +(-295.175 - 142.149i) q^{34} +(114.051 - 54.9242i) q^{35} +(276.279 - 346.443i) q^{36} +(-18.4388 - 80.7856i) q^{37} +(74.6282 + 326.968i) q^{38} +(-322.398 - 404.274i) q^{39} +(-184.539 + 808.517i) q^{40} +148.978 q^{41} +(55.5278 - 243.283i) q^{42} +(76.1651 - 36.6792i) q^{43} +(-11.6710 + 5.62046i) q^{44} +(-107.277 + 470.012i) q^{45} -552.347 q^{46} +(-74.0384 + 324.383i) q^{47} +(402.105 + 504.224i) q^{48} +(65.8778 + 288.629i) q^{49} +(-240.591 - 1054.10i) q^{50} +(297.796 - 373.425i) q^{51} +(1085.71 - 522.849i) q^{52} +(-54.7915 - 26.3862i) q^{53} +(-20.5552 - 25.7754i) q^{54} +(8.78710 - 11.0187i) q^{55} +(277.110 + 133.449i) q^{56} -488.937 q^{57} +(564.504 + 539.072i) q^{58} +402.090 q^{59} +(-2059.60 - 991.853i) q^{60} +(-332.555 + 417.010i) q^{61} +(-231.688 - 290.528i) q^{62} +(161.091 + 77.5773i) q^{63} +(262.982 - 126.645i) q^{64} +(-817.428 + 1025.02i) q^{65} +(-6.18210 - 27.0855i) q^{66} +(-116.564 - 510.702i) q^{67} +(693.999 + 870.247i) q^{68} +(179.186 - 785.064i) q^{69} -632.698 q^{70} +(14.9717 - 65.5952i) q^{71} +(-1055.35 + 508.231i) q^{72} +(210.381 - 101.314i) q^{73} +(-92.1591 + 403.775i) q^{74} +1576.26 q^{75} +(253.550 - 1110.87i) q^{76} +(-3.25890 - 4.08653i) q^{77} +(575.095 + 2519.66i) q^{78} +(-116.401 - 509.988i) q^{79} +(1019.52 - 1278.44i) q^{80} +(678.089 - 326.550i) q^{81} +(-670.870 - 323.074i) q^{82} +(32.3502 + 40.5658i) q^{83} +(-528.602 + 662.845i) q^{84} +(-1091.08 - 525.436i) q^{85} -422.525 q^{86} +(-949.325 + 627.463i) q^{87} +34.2427 q^{88} +(762.029 + 366.974i) q^{89} +(1502.35 - 1883.89i) q^{90} +(303.162 + 380.153i) q^{91} +(1690.76 + 814.227i) q^{92} +(488.096 - 235.054i) q^{93} +(1036.86 - 1300.18i) q^{94} +(275.855 + 1208.60i) q^{95} +(-135.012 - 591.525i) q^{96} +(537.437 + 673.924i) q^{97} +(329.264 - 1442.60i) q^{98} +19.9061 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−4.50314	−	2.16860i	−1.59210	−	0.766715i	−0.592845	−	0.805316i	$-0.701996\pi$
$2$	−4.50314	−	2.16860i	−1.59210	−	0.766715i	−0.999255	+	0.0386012i	$0.987710\pi$
$3$	4.54313	−	5.69691i	0.874326	−	1.09637i	−0.120290	−	0.992739i	$-0.538382\pi$
$3$	4.54313	−	5.69691i	0.874326	−	1.09637i	0.994616	−	0.103631i	$-0.0330462\pi$
$4$	10.5875	+	13.2763i	1.32344	+	1.65954i
$5$	−16.6453	−	8.01597i	−1.48880	−	0.716970i	−0.499977	−	0.866039i	$-0.666658\pi$
$5$	−16.6453	−	8.01597i	−1.48880	−	0.716970i	−0.988827	+	0.149069i	$0.952372\pi$
$6$	−32.8126	+	15.8017i	−2.23262	+	1.07517i
$7$	−4.27206	+	5.35699i	−0.230670	+	0.289250i	−0.883673	−	0.468104i	$-0.844937\pi$
$7$	−4.27206	+	5.35699i	−0.230670	+	0.289250i	0.653004	+	0.757355i	$0.273509\pi$
$8$	−9.98861	−	43.7630i	−0.441438	−	1.93407i
$9$	−5.80663	−	25.4405i	−0.215060	−	0.942241i
$10$	57.5728	+	72.1941i	1.82061	+	2.28298i
$11$	−0.169748	+	0.743714i	−0.00465281	+	0.0203853i	−0.977201	−	0.212316i	$-0.931899\pi$
$11$	−0.169748	+	0.743714i	−0.00465281	+	0.0203853i	0.972548	+	0.232701i	$0.0747565\pi$
$12$	123.735			2.97659
$13$	15.7909	−	69.1847i	0.336894	−	1.47603i	−0.468593	−	0.883414i	$-0.655239\pi$
$13$	15.7909	−	69.1847i	0.336894	−	1.47603i	0.805486	−	0.592614i	$-0.201904\pi$
$14$	30.8548	−	14.8589i	0.589022	−	0.283658i
$15$	−121.288	+	58.4093i	−2.08776	+	1.00541i
$16$	−19.6950	+	86.2893i	−0.307734	+	1.34827i
$17$	65.5487			0.935170			0.467585	−	0.883948i	$-0.345124\pi$
$17$	65.5487			0.935170			0.467585	+	0.883948i	$0.345124\pi$
$18$	−29.0222	+	127.154i	−0.380033	+	1.66503i
$19$	−41.8366	−	52.4614i	−0.505156	−	0.633446i	0.462228	−	0.886761i	$-0.347050\pi$
$19$	−41.8366	−	52.4614i	−0.505156	−	0.633446i	−0.967384	+	0.253316i	$0.918479\pi$
$20$	−69.8102	−	305.858i	−0.780502	−	3.41960i
$21$	11.1098	+	48.6750i	0.115445	+	0.505798i
$22$	2.37721	−	2.98093i	0.0230375	−	0.0288880i
$23$	99.5673	−	47.9491i	0.902661	−	0.434699i	0.0758119	−	0.997122i	$-0.475845\pi$
$23$	99.5673	−	47.9491i	0.902661	−	0.434699i	0.826849	+	0.562423i	$0.190131\pi$
$24$	−294.693	−	141.917i	−2.50641	−	1.20703i
$25$	134.875	+	169.128i	1.07900	+	1.35302i
$26$	−221.143	+	277.304i	−1.66806	+	2.09168i
$27$	5.94287	+	2.86194i	0.0423595	+	0.0203993i
$28$	−116.352			−0.785301
$29$	−148.555	−	48.1699i	−0.951242	−	0.308446i
$29$	−148.555	−	48.1699i	−0.951242	−	0.308446i
$30$	672.844			4.09480
$31$	66.9852	+	32.2584i	0.388094	+	0.186896i	0.617748	−	0.786376i	$-0.288045\pi$
$31$	66.9852	+	32.2584i	0.388094	+	0.186896i	−0.229654	+	0.973272i	$0.573760\pi$
$32$	51.9164	−	65.1011i	0.286800	−	0.359636i
$33$	3.46568	+	4.34583i	0.0182818	+	0.0229246i
$34$	−295.175	−	142.149i	−1.48888	−	0.717009i
$35$	114.051	−	54.9242i	0.550806	−	0.265254i
$36$	276.279	−	346.443i	1.27907	−	1.60390i
$37$	−18.4388	−	80.7856i	−0.0819275	−	0.358948i	0.917302	−	0.398192i	$-0.130362\pi$
$37$	−18.4388	−	80.7856i	−0.0819275	−	0.358948i	−0.999230	+	0.0392439i	$0.987505\pi$
$38$	74.6282	+	326.968i	0.318587	+	1.39582i
$39$	−322.398	−	404.274i	−1.32372	−	1.65989i
$40$	−184.539	+	808.517i	−0.729454	+	3.19595i
$41$	148.978			0.567475			0.283738	−	0.958902i	$-0.408425\pi$
$41$	148.978			0.567475			0.283738	+	0.958902i	$0.408425\pi$
$42$	55.5278	−	243.283i	0.204003	−	0.893795i
$43$	76.1651	−	36.6792i	0.270118	−	0.130082i	−0.293922	−	0.955829i	$-0.594961\pi$
$43$	76.1651	−	36.6792i	0.270118	−	0.130082i	0.564040	+	0.825747i	$0.309246\pi$
$44$	−11.6710	+	5.62046i	−0.0399880	+	0.0192572i
$45$	−107.277	+	470.012i	−0.355376	+	1.55700i
$46$	−552.347			−1.77042
$47$	−74.0384	+	324.383i	−0.229779	+	1.00673i	0.720041	+	0.693931i	$0.244123\pi$
$47$	−74.0384	+	324.383i	−0.229779	+	1.00673i	−0.949820	+	0.312796i	$0.898734\pi$
$48$	402.105	+	504.224i	1.20914	+	1.51622i
$49$	65.8778	+	288.629i	0.192064	+	0.841485i
$50$	−240.591	−	1054.10i	−0.680493	−	2.98144i
$51$	297.796	−	373.425i	0.817644	−	1.02529i
$52$	1085.71	−	522.849i	2.89539	−	1.39435i
$53$	−54.7915	−	26.3862i	−0.142003	−	0.0683853i	0.361533	−	0.932359i	$-0.382254\pi$
$53$	−54.7915	−	26.3862i	−0.142003	−	0.0683853i	−0.503536	+	0.863974i	$0.667968\pi$
$54$	−20.5552	−	25.7754i	−0.0518002	−	0.0649553i
$55$	8.78710	−	11.0187i	0.0215428	−	0.0270138i
$56$	277.110	+	133.449i	0.661256	+	0.318444i
$57$	−488.937			−1.13616
$58$	564.504	+	539.072i	1.27798	+	1.22041i
$59$	402.090			0.887248			0.443624	−	0.896213i	$-0.353693\pi$
$59$	402.090			0.887248			0.443624	+	0.896213i	$0.353693\pi$
$60$	−2059.60	−	991.853i	−4.43156	−	2.13413i
$61$	−332.555	+	417.010i	−0.698021	+	0.875290i	−0.996874	−	0.0790088i	$-0.974824\pi$
$61$	−332.555	+	417.010i	−0.698021	+	0.875290i	0.298853	+	0.954299i	$0.403396\pi$
$62$	−231.688	−	290.528i	−0.474588	−	0.595114i
$63$	161.091	+	77.5773i	0.322152	+	0.155140i
$64$	262.982	−	126.645i	0.513637	−	0.247354i
$65$	−817.428	+	1025.02i	−1.55984	+	1.95597i
$66$	−6.18210	−	27.0855i	−0.0115298	−	0.0505151i
$67$	−116.564	−	510.702i	−0.212546	−	0.931227i	−0.962829	−	0.270110i	$-0.912940\pi$
$67$	−116.564	−	510.702i	−0.212546	−	0.931227i	0.750283	−	0.661117i	$-0.229917\pi$
$68$	693.999	+	870.247i	1.23764	+	1.55195i
$69$	179.186	−	785.064i	0.312629	−	1.36972i
$70$	−632.698			−1.08031
$71$	14.9717	−	65.5952i	0.0250255	−	0.109644i	−0.960873	−	0.276991i	$-0.910663\pi$
$71$	14.9717	−	65.5952i	0.0250255	−	0.109644i	0.985898	+	0.167347i	$0.0535200\pi$
$72$	−1055.35	+	508.231i	−1.72742	+	0.831883i
$73$	210.381	−	101.314i	0.337304	−	0.162437i	−0.257562	−	0.966262i	$-0.582919\pi$
$73$	210.381	−	101.314i	0.337304	−	0.162437i	0.594866	+	0.803825i	$0.297205\pi$
$74$	−92.1591	+	403.775i	−0.144774	+	0.634296i
$75$	1576.26			2.42681
$76$	253.550	−	1110.87i	0.382686	−	1.67666i
$77$	−3.25890	−	4.08653i	−0.00482319	−	0.00604809i
$78$	575.095	+	2519.66i	0.834829	+	3.65763i
$79$	−116.401	−	509.988i	−0.165775	−	0.726306i	−0.987655	−	0.156646i	$-0.949932\pi$
$79$	−116.401	−	509.988i	−0.165775	−	0.726306i	0.821880	−	0.569660i	$-0.192925\pi$
$80$	1019.52	−	1278.44i	1.42483	−	1.78667i
$81$	678.089	−	326.550i	0.930163	−	0.447943i
$82$	−670.870	−	323.074i	−0.903478	−	0.435092i
$83$	32.3502	+	40.5658i	0.0427818	+	0.0536467i	0.802762	−	0.596299i	$-0.203363\pi$
$83$	32.3502	+	40.5658i	0.0427818	+	0.0536467i	−0.759980	+	0.649946i	$0.774791\pi$
$84$	−528.602	+	662.845i	−0.686609	+	0.860980i
$85$	−1091.08	−	525.436i	−1.39228	−	0.670489i
$86$	−422.525			−0.529791
$87$	−949.325	+	627.463i	−1.16987	+	0.773231i
$88$	34.2427			0.0414805
$89$	762.029	+	366.974i	0.907583	+	0.437069i	0.828622	−	0.559809i	$-0.189125\pi$
$89$	762.029	+	366.974i	0.907583	+	0.437069i	0.0789612	+	0.996878i	$0.474840\pi$
$90$	1502.35	−	1883.89i	1.75957	−	2.20643i
$91$	303.162	+	380.153i	0.349231	+	0.437921i
$92$	1690.76	+	814.227i	1.91602	+	0.922707i
$93$	488.096	−	235.054i	0.544227	−	0.262086i
$94$	1036.86	−	1300.18i	1.13770	−	1.42664i
$95$	275.855	+	1208.60i	0.297917	+	1.30526i
$96$	−135.012	−	591.525i	−0.143537	−	0.628878i
$97$	537.437	+	673.924i	0.562561	+	0.705429i	0.979029	−	0.203721i	$-0.0653036\pi$
$97$	537.437	+	673.924i	0.562561	+	0.705429i	−0.416468	+	0.909150i	$0.636732\pi$
$98$	329.264	−	1442.60i	0.339395	−	1.48699i
$99$	19.9061			0.0202085
$100$	−817.407	+	3581.30i	−0.817407	+	3.58130i
$101$	−1543.34	+	743.235i	−1.52048	+	0.732225i	−0.993085	−	0.117396i	$-0.962545\pi$
$101$	−1543.34	+	743.235i	−1.52048	+	0.732225i	−0.527395	+	0.849620i	$0.676831\pi$
$102$	−2150.83	+	1035.78i	−2.08788	+	1.00547i
$103$	358.706	−	1571.60i	0.343149	−	1.50344i	−0.449235	−	0.893414i	$-0.648303\pi$
$103$	358.706	−	1571.60i	0.343149	−	1.50344i	0.792384	−	0.610022i	$-0.208839\pi$
$104$	−3185.45			−3.00346
$105$	205.252	−	899.268i	0.190767	−	0.835805i
$106$	189.513	+	237.641i	0.173652	+	0.217752i
$107$	−434.872	−	1905.30i	−0.392903	−	1.72142i	−0.654340	−	0.756200i	$-0.727054\pi$
$107$	−434.872	−	1905.30i	−0.392903	−	1.72142i	0.261437	−	0.965221i	$-0.415804\pi$
$108$	24.9243	+	109.200i	0.0222069	+	0.0972946i
$109$	262.533	−	329.205i	0.230698	−	0.289286i	−0.652986	−	0.757370i	$-0.726484\pi$
$109$	262.533	−	329.205i	0.230698	−	0.289286i	0.883684	+	0.468084i	$0.155055\pi$
$110$	−63.4646	+	30.5629i	−0.0550101	+	0.0264915i
$111$	−543.998	−	261.976i	−0.465171	−	0.224015i
$112$	−378.113	−	474.139i	−0.319003	−	0.400017i
$113$	−599.240	+	751.423i	−0.498865	+	0.625557i	−0.965973	−	0.258644i	$-0.916724\pi$
$113$	−599.240	+	751.423i	−0.498865	+	0.625557i	0.467108	+	0.884200i	$0.345296\pi$
$114$	2201.75	+	1060.31i	1.80888	+	0.871112i
$115$	−2041.69			−1.65555
$116$	−933.312	−	2482.27i	−0.747033	−	1.98684i
$117$	−1851.79			−1.46323
$118$	−1810.67	−	871.971i	−1.41259	−	0.680266i
$119$	−280.028	+	351.144i	−0.215715	+	0.270498i
$120$	3767.66	+	4724.50i	2.86616	+	3.59405i
$121$	1198.67	+	577.247i	0.900575	+	0.433694i
$122$	2401.87	−	1156.68i	1.78242	−	0.858367i
$123$	676.828	−	848.715i	0.496158	−	0.622163i
$124$	280.935	+	1230.86i	0.203457	+	0.891404i
$125$	−375.434	−	1644.88i	−0.268638	−	1.17698i
$126$	−557.181	−	698.683i	−0.393949	−	0.493997i
$127$	−104.158	+	456.347i	−0.0727760	+	0.318853i	−0.998192	−	0.0600993i	$-0.980858\pi$
$127$	−104.158	+	456.347i	−0.0727760	+	0.318853i	0.925416	+	0.378952i	$0.123715\pi$
$128$	−2125.03			−1.46740
$129$	137.070	−	600.544i	0.0935532	−	0.409883i
$130$	5903.85	−	2843.14i	3.98309	−	1.91816i
$131$	1638.11	−	788.872i	1.09254	−	0.526138i	0.201232	−	0.979544i	$-0.435505\pi$
$131$	1638.11	−	788.872i	1.09254	−	0.526138i	0.891304	+	0.453406i	$0.149791\pi$
$132$	−21.0037	+	92.0232i	−0.0138495	+	0.0606787i
$133$	459.764			0.299749
$134$	−582.602	+	2552.54i	−0.375590	+	1.64557i
$135$	−75.9799	−	95.2758i	−0.0484393	−	0.0607410i
$136$	−654.740	−	2868.60i	−0.412820	−	1.80868i
$137$	59.2041	+	259.390i	0.0369208	+	0.161761i	0.990028	−	0.140874i	$-0.0449911\pi$
$137$	59.2041	+	259.390i	0.0369208	+	0.161761i	−0.953107	+	0.302634i	$0.902134\pi$
$138$	−2509.39	+	3146.67i	−1.54792	+	1.94103i
$139$	−2609.42	+	1256.63i	−1.59229	+	0.766805i	−0.999263	−	0.0383787i	$-0.987781\pi$
$139$	−2609.42	+	1256.63i	−1.59229	+	0.766805i	−0.593025	+	0.805184i	$0.702066\pi$
$140$	1936.71	+	932.673i	1.16916	+	0.563037i
$141$	1511.62	+	1895.51i	0.902844	+	1.13213i
$142$	−209.669	+	262.917i	−0.123909	+	0.155377i
$143$	48.7731	+	23.4879i	0.0285218	+	0.0137354i
$144$	2309.61			1.33658
$145$	2086.62	+	1992.62i	1.19507	+	1.14123i
$146$	−1167.08			−0.661565
$147$	1943.59	+	935.982i	1.09051	+	0.525160i
$148$	877.316	−	1100.12i	0.487263	−	0.611009i
$149$	−462.385	−	579.813i	−0.254229	−	0.318793i	0.638296	−	0.769791i	$-0.279640\pi$
$149$	−462.385	−	579.813i	−0.254229	−	0.318793i	−0.892525	+	0.450998i	$0.851068\pi$
$150$	−7098.13	−	3418.28i	−3.86373	−	1.86067i
$151$	−1547.40	+	745.190i	−0.833946	+	0.401607i	−0.801594	−	0.597869i	$-0.796014\pi$
$151$	−1547.40	+	745.190i	−0.833946	+	0.401607i	−0.0323526	+	0.999477i	$0.510300\pi$
$152$	−1877.98	+	2354.91i	−1.00213	+	1.25663i
$153$	−380.617	−	1667.59i	−0.201118	−	0.881156i
$154$	5.81323	+	25.4694i	0.00304184	+	0.0133272i
$155$	−856.409	−	1073.90i	−0.443796	−	0.556503i
$156$	1953.89	−	8560.54i	1.00280	−	4.39353i
$157$	3214.55			1.63407			0.817035	−	0.576587i	$-0.195616\pi$
$157$	3214.55			1.63407			0.817035	+	0.576587i	$0.195616\pi$
$158$	−581.787	+	2548.98i	−0.292940	+	1.28345i
$159$	−399.244	+	192.266i	−0.199133	+	0.0958973i
$160$	−1386.01	+	667.469i	−0.684837	+	0.329800i
$161$	−168.494	+	738.222i	−0.0824796	+	0.361367i
$162$	−3761.69			−1.82436
$163$	−595.440	+	2608.79i	−0.286126	+	1.25360i	0.603668	+	0.797236i	$0.293705\pi$
$163$	−595.440	+	2608.79i	−0.286126	+	1.25360i	−0.889794	+	0.456363i	$0.849152\pi$
$164$	1577.31	+	1977.89i	0.751020	+	0.941750i
$165$	−22.8514	−	100.119i	−0.0107817	−	0.0472377i
$166$	−57.7064	−	252.828i	−0.0269812	−	0.118212i
$167$	2234.81	−	2802.36i	1.03554	−	1.29852i	0.0821998	−	0.996616i	$-0.473805\pi$
$167$	2234.81	−	2802.36i	1.03554	−	1.29852i	0.953337	−	0.301907i	$-0.0976231\pi$
$168$	2019.19	−	972.392i	0.927286	−	0.446557i
$169$	−2557.73	−	1231.74i	−1.16419	−	0.560646i
$170$	3773.82	+	4732.23i	1.70258	+	2.13497i
$171$	−1091.72	+	1368.97i	−0.488220	+	0.612208i
$172$	1293.37	+	622.852i	0.573362	+	0.276117i
$173$	3599.68			1.58196			0.790978	−	0.611844i	$-0.209572\pi$
$173$	3599.68			1.58196			0.790978	+	0.611844i	$0.209572\pi$
$174$	5635.66	−	766.847i	2.45539	−	0.334107i
$175$	−1482.21			−0.640255
$176$	−60.8314	−	29.2949i	−0.0260531	−	0.0125465i
$177$	1826.75	−	2290.67i	0.775744	−	0.972752i
$178$	−2635.70	−	3305.07i	−1.10986	−	1.39172i
$179$	1510.38	+	727.363i	0.630678	+	0.303719i	0.721780	−	0.692123i	$-0.243324\pi$
$179$	1510.38	+	727.363i	0.630678	+	0.303719i	−0.0911013	+	0.995842i	$0.529039\pi$
$180$	−7375.83	+	3552.01i	−3.05423	+	1.47084i
$181$	−846.165	+	1061.06i	−0.347486	+	0.435734i	−0.924606	−	0.380926i	$-0.875605\pi$
$181$	−846.165	+	1061.06i	−0.347486	+	0.435734i	0.577120	+	0.816660i	$0.304177\pi$
$182$	−540.781	−	2369.32i	−0.220249	−	0.964975i
$183$	864.829	+	3789.07i	0.349344	+	1.53058i
$184$	−3092.93	−	3878.41i	−1.23921	−	1.55392i
$185$	−340.655	+	1492.51i	−0.135381	+	0.593143i
$186$	−2707.70			−1.06741
$187$	−11.1268	+	48.7495i	−0.00435117	+	0.0190637i
$188$	−5090.51	+	2451.46i	−1.97481	+	0.951016i
$189$	−40.7197	+	19.6096i	−0.0156715	+	0.00754702i
$190$	1378.75	−	6040.70i	0.526448	−	2.30652i
$191$	702.174			0.266008			0.133004	−	0.991116i	$-0.457538\pi$
$191$	702.174			0.266008			0.133004	+	0.991116i	$0.457538\pi$
$192$	473.274	−	2073.55i	0.177894	−	0.779404i
$193$	−1730.83	−	2170.39i	−0.645534	−	0.809474i	0.346149	−	0.938180i	$-0.387489\pi$
$193$	−1730.83	−	2170.39i	−0.645534	−	0.809474i	−0.991683	+	0.128706i	$0.958918\pi$
$194$	−958.682	−	4200.26i	−0.354790	−	1.55444i
$195$	2125.77	+	9313.62i	0.780665	+	3.42032i
$196$	−3134.46	+	3930.49i	−1.14230	+	1.43239i
$197$	98.9377	−	47.6459i	0.0357818	−	0.0172316i	−0.415907	−	0.909407i	$-0.636536\pi$
$197$	98.9377	−	47.6459i	0.0357818	−	0.0172316i	0.451689	+	0.892175i	$0.350822\pi$
$198$	−89.6401	−	43.1684i	−0.0321740	−	0.0154942i
$199$	−683.419	−	856.981i	−0.243449	−	0.305275i	0.645063	−	0.764130i	$-0.276831\pi$
$199$	−683.419	−	856.981i	−0.243449	−	0.305275i	−0.888511	+	0.458855i	$0.848260\pi$
$200$	6054.33	−	7591.89i	2.14053	−	2.68414i
$201$	−3438.99	−	1656.13i	−1.20680	−	0.581166i
$202$	8561.67			2.98216
$203$	892.683	−	590.024i	0.308641	−	0.203998i
$204$	8110.64			2.78362
$205$	−2479.79	−	1194.21i	−0.844860	−	0.406863i
$206$	−5023.46	+	6299.22i	−1.69904	+	2.13052i
$207$	−1798.00	−	2254.62i	−0.603718	−	0.757038i
$208$	5658.89	+	2725.18i	1.88641	+	0.908448i
$209$	46.1179	−	22.2092i	0.0152634	−	0.00735045i
$210$	−2874.43	+	3604.42i	−0.944545	+	1.18442i
$211$	523.752	+	2294.71i	0.170884	+	0.748693i	0.985636	+	0.168883i	$0.0540161\pi$
$211$	523.752	+	2294.71i	0.170884	+	0.748693i	−0.814752	+	0.579810i	$0.803127\pi$
$212$	−229.794	−	1006.79i	−0.0744450	−	0.326165i
$213$	−305.671	−	383.300i	−0.0983298	−	0.123302i
$214$	−2173.54	+	9522.88i	−0.694298	+	3.04192i
$215$	−1561.81			−0.495418
$216$	65.8858	−	288.664i	0.0207544	−	0.0909312i
$217$	−458.973	+	221.030i	−0.143581	+	0.0691450i
$218$	−1896.13	+	913.130i	−0.589094	+	0.283693i
$219$	378.611	−	1658.80i	0.116823	−	0.511833i
$220$	239.321			0.0733411
$221$	1035.08	−	4534.96i	0.315053	−	1.38034i
$222$	1881.58	+	2359.43i	0.568844	+	0.713307i
$223$	−552.392	−	2420.19i	−0.165878	−	0.726761i	−0.987615	−	0.156894i	$-0.949852\pi$
$223$	−552.392	−	2420.19i	−0.165878	−	0.726761i	0.821737	−	0.569867i	$-0.193005\pi$
$224$	126.956	+	556.231i	0.0378688	+	0.165914i
$225$	3519.53	−	4413.36i	1.04282	−	1.30766i
$226$	4327.99	−	2084.25i	1.27387	−	0.613462i
$227$	−1038.49	−	500.109i	−0.303642	−	0.146226i	0.275858	−	0.961198i	$-0.411038\pi$
$227$	−1038.49	−	500.109i	−0.303642	−	0.146226i	−0.579500	+	0.814972i	$0.696752\pi$
$228$	−5176.63	−	6491.29i	−1.50364	−	1.88551i
$229$	−92.1586	+	115.563i	−0.0265939	+	0.0333478i	−0.794951	−	0.606674i	$-0.792503\pi$
$229$	−92.1586	+	115.563i	−0.0265939	+	0.0333478i	0.768357	+	0.640022i	$0.221075\pi$
$230$	9194.01	+	4427.60i	2.63580	+	1.26934i
$231$	−38.0862			−0.0108480
$232$	−624.199	+	6982.37i	−0.176641	+	1.97593i
$233$	−3271.17			−0.919749			−0.459874	−	0.887984i	$-0.652106\pi$
$233$	−3271.17			−0.919749			−0.459874	+	0.887984i	$0.652106\pi$
$234$	8338.85	+	4015.78i	2.32960	+	1.12188i
$235$	3832.64	−	4805.98i	1.06389	−	1.33407i
$236$	4257.14	+	5338.28i	1.17422	+	1.47243i
$237$	−3434.18	−	1653.81i	−0.941241	−	0.453278i
$238$	2022.49	−	973.982i	0.550835	−	0.265268i
$239$	215.514	−	270.247i	0.0583283	−	0.0731414i	−0.751812	−	0.659378i	$-0.770820\pi$
$239$	215.514	−	270.247i	0.0583283	−	0.0731414i	0.810140	+	0.586237i	$0.199391\pi$
$240$	−2651.33	−	11616.2i	−0.713095	−	3.12427i
$241$	1118.73	+	4901.47i	0.299019	+	1.31009i	0.871591	+	0.490234i	$0.163089\pi$
$241$	1118.73	+	4901.47i	0.299019	+	1.31009i	−0.572572	+	0.819854i	$0.694054\pi$
$242$	−4145.94	−	5198.85i	−1.10129	−	1.38097i
$243$	1180.69	−	5172.94i	0.311693	−	1.36561i
$244$	−9057.31			−2.37637
$245$	1217.09	−	5332.41i	0.317375	−	1.39051i
$246$	−4888.37	+	2354.12i	−1.26696	+	0.610134i
$247$	−4290.16	+	2066.03i	−1.10517	+	0.532221i
$248$	742.633	−	3253.69i	0.190150	−	0.833102i
$249$	378.071			0.0962219
$250$	−1876.46	+	8221.30i	−0.474710	+	2.07984i
$251$	275.312	+	345.230i	0.0692332	+	0.0868157i	0.815242	−	0.579120i	$-0.196604\pi$
$251$	275.312	+	345.230i	0.0692332	+	0.0868157i	−0.746009	+	0.665936i	$0.768032\pi$
$252$	675.612	+	2960.05i	0.168887	+	0.739943i
$253$	18.7591	+	82.1888i	0.00466155	+	0.0204236i
$254$	1458.67	−	1829.12i	0.360336	−	0.451847i
$255$	−7950.28	+	3828.65i	−1.95241	+	0.940233i
$256$	7465.43	+	3595.16i	1.82262	+	0.877726i
$257$	−2196.36	−	2754.15i	−0.533094	−	0.668478i	0.440238	−	0.897881i	$-0.354894\pi$
$257$	−2196.36	−	2754.15i	−0.533094	−	0.668478i	−0.973332	+	0.229403i	$0.926323\pi$
$258$	−1919.58	+	2407.08i	−0.463210	+	0.580847i
$259$	511.540	+	246.345i	0.122724	+	0.0591008i
$260$	−22263.1			−5.31038
$261$	−362.863	+	4059.03i	−0.0860561	+	0.962634i
$262$	−9087.38			−2.14283
$263$	−970.388	−	467.314i	−0.227516	−	0.109566i	0.316653	−	0.948541i	$-0.397441\pi$
$263$	−970.388	−	467.314i	−0.227516	−	0.109566i	−0.544169	+	0.838975i	$0.683155\pi$
$264$	155.569	−	195.077i	0.0362674	−	0.0454779i
$265$	700.511	+	878.413i	0.162385	+	0.203625i
$266$	−2070.38	−	997.042i	−0.477230	−	0.229822i
$267$	5552.61	−	2674.00i	1.27271	−	0.612906i
$268$	5546.13	−	6954.62i	1.26412	−	1.58515i
$269$	1649.12	+	7225.27i	0.373787	+	1.63767i	0.716040	+	0.698059i	$0.245953\pi$
$269$	1649.12	+	7225.27i	0.373787	+	1.63767i	−0.342253	+	0.939608i	$0.611190\pi$
$270$	135.533	+	593.810i	0.0305492	+	0.133845i
$271$	3901.04	+	4891.74i	0.874432	+	1.09650i	0.994603	+	0.103750i	$0.0330842\pi$
$271$	3901.04	+	4891.74i	0.874432	+	1.09650i	−0.120171	+	0.992753i	$0.538344\pi$
$272$	−1290.98	+	5656.15i	−0.287784	+	1.26086i
$273$	3543.00			0.785465
$274$	295.909	−	1296.46i	0.0652427	−	0.285847i
$275$	−148.678	+	71.5994i	−0.0326022	+	0.0157004i
$276$	12319.9	−	5932.96i	2.68685	−	1.29392i
$277$	−1770.36	+	7756.44i	−0.384009	+	1.68245i	0.300765	+	0.953698i	$0.402758\pi$
$277$	−1770.36	+	7756.44i	−0.384009	+	1.68245i	−0.684774	+	0.728755i	$0.740099\pi$
$278$	14475.7			3.12300
$279$	431.711	−	1891.45i	0.0926376	−	0.405872i
$280$	−3542.86	−	4442.61i	−0.756166	−	0.948202i
$281$	−448.361	−	1964.40i	−0.0951849	−	0.417032i	0.904776	−	0.425888i	$-0.140038\pi$
$281$	−448.361	−	1964.40i	−0.0951849	−	0.417032i	−0.999961	+	0.00885566i	$0.997181\pi$
$282$	−2696.43	−	11813.8i	−0.569396	−	2.49469i
$283$	1753.98	−	2199.43i	0.368422	−	0.461987i	−0.562718	−	0.826649i	$-0.690244\pi$
$283$	1753.98	−	2199.43i	0.368422	−	0.461987i	0.931140	+	0.364662i	$0.118816\pi$
$284$	1029.38	−	495.722i	0.215079	−	0.103576i
$285$	8138.51	+	3919.30i	1.69152	+	0.814594i
$286$	−168.696	−	211.539i	−0.0348784	−	0.0437361i
$287$	−636.444	+	798.075i	−0.130899	+	0.164143i
$288$	−1957.66	−	942.761i	−0.400543	−	0.192891i
$289$	−616.369			−0.125457
$290$	−5075.16	−	13498.1i	−1.02767	−	2.73322i
$291$	6280.93			1.26527
$292$	3572.49	+	1720.42i	0.715973	+	0.344795i
$293$	−2414.68	+	3027.91i	−0.481458	+	0.603729i	−0.961935	−	0.273278i	$-0.911892\pi$
$293$	−2414.68	+	3027.91i	−0.481458	+	0.603729i	0.480477	+	0.877007i	$0.340463\pi$
$294$	−6722.47	−	8429.71i	−1.33355	−	1.67221i
$295$	−6692.92	−	3223.14i	−1.32094	−	0.636130i
$296$	−3351.24	+	1613.87i	−0.658064	+	0.316907i
$297$	−3.13725	+	3.93399i	−0.000612936	+	0.000768597i
$298$	824.805	+	3613.71i	0.160334	+	0.702471i
$299$	−1745.08	−	7645.69i	−0.337527	−	1.47880i
$300$	16688.7	+	20927.0i	3.21174	+	4.02740i
$301$	−128.892	+	564.712i	−0.0246817	+	0.108138i
$302$	8584.19			1.63564
$303$	−2777.47	+	12168.9i	−0.526606	+	2.30721i
$304$	5350.83	−	2576.82i	1.00951	−	0.486154i
$305$	8878.23	−	4275.53i	1.66677	−	0.802676i
$306$	−1902.37	+	8334.81i	−0.355395	+	1.55709i
$307$	−239.611			−0.0445451			−0.0222725	−	0.999752i	$-0.507090\pi$
$307$	−239.611			−0.0445451			−0.0222725	+	0.999752i	$0.507090\pi$
$308$	19.7505	−	86.5325i	0.00365386	−	0.0160086i
$309$	−7323.58	−	9183.48i	−1.34830	−	1.69071i
$310$	1527.67	+	6693.14i	0.279889	+	1.22627i
$311$	2146.22	+	9403.22i	0.391322	+	1.71449i	0.660001	+	0.751265i	$0.270556\pi$
$311$	2146.22	+	9403.22i	0.391322	+	1.71449i	−0.268679	+	0.963230i	$0.586587\pi$
$312$	−14471.9	+	18147.2i	−2.62600	+	3.29290i
$313$	−1661.60	+	800.183i	−0.300061	+	0.144502i	−0.577856	−	0.816139i	$-0.696111\pi$
$313$	−1661.60	+	800.183i	−0.300061	+	0.144502i	0.277795	+	0.960640i	$0.410396\pi$
$314$	−14475.6	−	6971.07i	−2.60160	−	1.25287i
$315$	−2059.55	−	2582.60i	−0.368390	−	0.461946i
$316$	5538.37	−	6944.90i	0.985943	−	1.23633i
$317$	5800.93	+	2793.58i	1.02780	+	0.494963i	0.870282	−	0.492553i	$-0.163936\pi$
$317$	5800.93	+	2793.58i	1.02780	+	0.494963i	0.157518	+	0.987516i	$0.449651\pi$
$318$	2214.80			0.390565
$319$	61.0416	−	102.306i	0.0107137	−	0.0179562i
$320$	−5392.61			−0.942050
$321$	−12830.0	−	6178.59i	−2.23084	−	1.07432i
$322$	2359.66	−	2958.92i	0.408381	−	0.512094i
$323$	−2742.33	−	3438.78i	−0.472407	−	0.592380i
$324$	11514.7	+	5545.18i	1.97440	+	0.950819i
$325$	13830.9	−	6660.60i	2.36061	−	1.13681i
$326$	8338.77	−	10456.5i	1.41669	−	1.77648i
$327$	−682.732	−	2991.25i	−0.115459	−	0.505860i
$328$	−1488.09	−	6519.73i	−0.250505	−	1.09754i
$329$	−1421.42	−	1782.41i	−0.238193	−	0.298685i
$330$	−114.214	+	500.403i	−0.0190523	+	0.0834736i
$331$	−1559.91			−0.259035			−0.129517	−	0.991577i	$-0.541343\pi$
$331$	−1559.91			−0.259035			−0.129517	+	0.991577i	$0.541343\pi$
$332$	−196.057	+	858.984i	−0.0324098	+	0.141997i
$333$	−1948.16	+	938.185i	−0.320596	+	0.154391i
$334$	−16140.9	+	7773.02i	−2.64428	+	1.27342i
$335$	−2153.52	+	9435.18i	−0.351222	+	1.53880i
$336$	−4418.94			−0.717479
$337$	199.558	−	874.320i	0.0322570	−	0.141327i	−0.956235	−	0.292599i	$-0.905480\pi$
$337$	199.558	−	874.320i	0.0322570	−	0.141327i	0.988492	+	0.151272i	$0.0483370\pi$
$338$	8846.68	+	11093.4i	1.42366	+	1.78521i
$339$	1558.36	+	6827.62i	0.249671	+	1.09388i
$340$	−4575.97	−	20048.6i	−0.729902	−	3.19791i
$341$	−35.3616	+	44.3421i	−0.00561566	+	0.00704181i
$342$	7884.89	−	3797.16i	1.24668	−	0.600371i
$343$	−3945.06	−	1899.84i	−0.621030	−	0.299072i
$344$	−2365.97	−	2966.84i	−0.370828	−	0.465003i
$345$	−9275.66	+	11631.3i	−1.44749	+	1.81510i
$346$	−16209.9	−	7806.25i	−2.51863	−	1.21291i
$347$	4707.15			0.728223			0.364111	−	0.931355i	$-0.381373\pi$
$347$	4707.15			0.728223			0.364111	+	0.931355i	$0.381373\pi$
$348$	−18381.4	−	5960.29i	−2.83146	−	0.918118i
$349$	10807.7			1.65765			0.828827	−	0.559505i	$-0.189009\pi$
$349$	10807.7			1.65765			0.828827	+	0.559505i	$0.189009\pi$
$350$	6674.61	+	3214.32i	1.01935	+	0.490893i
$351$	291.846	−	365.963i	0.0443806	−	0.0556515i
$352$	39.6039	+	49.6617i	0.00599686	+	0.00751982i
$353$	5525.13	+	2660.76i	0.833068	+	0.401184i	0.801265	−	0.598310i	$-0.204161\pi$
$353$	5525.13	+	2660.76i	0.833068	+	0.401184i	0.0318029	+	0.999494i	$0.489875\pi$
$354$	−13193.6	+	6353.72i	−1.98089	+	0.953944i
$355$	−775.018	+	971.841i	−0.115869	+	0.145296i
$356$	3195.93	+	14002.3i	0.475798	+	2.08461i
$357$	728.230	+	3190.58i	0.107961	+	0.473007i
$358$	−5224.11	−	6550.83i	−0.771237	−	0.967101i
$359$	2288.78	−	10027.8i	0.336482	−	1.47422i	−0.469843	−	0.882750i	$-0.655689\pi$
$359$	2288.78	−	10027.8i	0.336482	−	1.47422i	0.806325	−	0.591473i	$-0.201454\pi$
$360$	21640.6			3.16823
$361$	524.371	−	2297.42i	0.0764501	−	0.334950i
$362$	6111.41	−	2943.10i	0.887316	−	0.427309i
$363$	8734.21	−	4206.18i	1.26289	−	0.608173i
$364$	−1837.31	+	8049.76i	−0.264563	+	1.15913i
$365$	−4313.99			−0.618642
$366$	4322.51	−	18938.2i	0.617326	−	2.70468i
$367$	−6077.08	−	7620.42i	−0.864363	−	1.08388i	−0.995709	−	0.0925402i	$-0.970501\pi$
$367$	−6077.08	−	7620.42i	−0.864363	−	1.08388i	0.131346	−	0.991337i	$-0.458070\pi$
$368$	2176.52	+	9535.95i	0.308312	+	1.35080i
$369$	−865.062	−	3790.08i	−0.122042	−	0.534699i
$370$	4770.67	−	5982.23i	0.670312	−	0.840544i
$371$	375.423	−	180.794i	0.0525363	−	0.0253002i
$372$	8288.39	+	3991.48i	1.15520	+	0.556313i
$373$	229.116	+	287.303i	0.0318048	+	0.0398819i	0.797480	−	0.603346i	$-0.206166\pi$
$373$	229.116	+	287.303i	0.0318048	+	0.0398819i	−0.765675	+	0.643228i	$0.777595\pi$
$374$	155.823	−	195.396i	0.0215439	−	0.0270152i
$375$	−11076.4	−	5334.10i	−1.52528	−	0.734538i
$376$	14935.5			2.04851
$377$	−5678.45	+	9517.09i	−0.775743	+	1.30015i
$378$	225.892			0.0307371
$379$	10342.7	+	4980.79i	1.40177	+	0.675056i	0.973519	−	0.228605i	$-0.0734163\pi$
$379$	10342.7	+	4980.79i	1.40177	+	0.675056i	0.428249	+	0.903661i	$0.359131\pi$
$380$	−13125.1	+	16458.4i	−1.77186	+	2.22184i
$381$	2126.56	+	2666.63i	0.285950	+	0.358571i
$382$	−3161.99	−	1522.73i	−0.423511	−	0.203952i
$383$	−9181.33	+	4421.50i	−1.22492	+	0.589890i	−0.930677	−	0.365841i	$-0.880781\pi$
$383$	−9181.33	+	4421.50i	−1.22492	+	0.589890i	−0.294242	+	0.955731i	$0.595067\pi$
$384$	−9654.27	+	12106.1i	−1.28299	+	1.60882i
$385$	21.4879	+	94.1449i	0.00284449	+	0.0124625i
$386$	3087.46	+	13527.1i	0.407119	+	1.78370i
$387$	−1375.40	−	1724.70i	−0.180660	−	0.226541i
$388$	−3257.12	+	14270.4i	−0.426174	+	1.86719i
$389$	2563.05			0.334066			0.167033	−	0.985951i	$-0.446581\pi$
$389$	2563.05			0.334066			0.167033	+	0.985951i	$0.446581\pi$
$390$	10624.8	−	46550.5i	1.37951	−	6.04404i
$391$	6526.50	−	3143.00i	0.844142	−	0.406517i
$392$	11973.3	−	5766.01i	1.54271	−	0.742928i
$393$	2948.02	−	12916.1i	0.378391	−	1.65784i
$394$	−548.855			−0.0701800
$395$	−2150.51	+	9421.99i	−0.273934	+	1.20018i
$396$	210.757	+	264.281i	0.0267448	+	0.0335369i
$397$	2020.80	+	8853.72i	0.255469	+	1.11928i	0.926036	+	0.377435i	$0.123194\pi$
$397$	2020.80	+	8853.72i	0.255469	+	1.11928i	−0.670567	+	0.741849i	$0.733949\pi$
$398$	1219.09	+	5341.17i	0.153536	+	0.672685i
$399$	2088.77	−	2619.23i	0.262078	−	0.328635i
$400$	−17250.3	+	8307.31i	−2.15629	+	1.03841i
$401$	−10460.2	−	5037.35i	−1.30263	−	0.627315i	−0.351526	−	0.936178i	$-0.614337\pi$
$401$	−10460.2	−	5037.35i	−1.30263	−	0.627315i	−0.951106	+	0.308864i	$0.900051\pi$
$402$	11894.8	+	14915.6i	1.47576	+	1.85055i
$403$	3289.55	−	4124.96i	0.406610	−	0.509873i
$404$	−26207.7	−	12620.9i	−3.22742	−	1.55425i
$405$	−13904.6			−1.70599
$406$	−5299.40	+	721.092i	−0.647795	+	0.0881459i
$407$	63.2114			0.00769845
$408$	−19316.7	−	9302.45i	−2.34392	−	1.12877i
$409$	2980.07	−	3736.88i	0.360281	−	0.451778i	−0.568348	−	0.822788i	$-0.692417\pi$
$409$	2980.07	−	3736.88i	0.360281	−	0.451778i	0.928629	+	0.371011i	$0.120989\pi$
$410$	8577.10	+	10755.3i	1.03315	+	1.29553i
$411$	1746.69	+	841.163i	0.209630	+	0.100953i
$412$	24662.9	−	11877.0i	2.94915	−	1.42024i
$413$	−1717.75	+	2153.99i	−0.204661	+	0.256637i
$414$	3207.28	+	14052.0i	0.380747	+	1.66816i
$415$	−213.305	−	934.550i	−0.0252307	−	0.110543i
$416$	−3684.19	−	4619.82i	−0.434212	−	0.544484i
$417$	−4696.03	+	20574.6i	−0.551476	+	2.41617i
$418$	−255.838			−0.0299365
$419$	1681.20	−	7365.82i	0.196019	−	0.858816i	−0.777258	−	0.629182i	$-0.783390\pi$
$419$	1681.20	−	7365.82i	0.196019	−	0.858816i	0.973277	−	0.229634i	$-0.0737529\pi$
$420$	14112.1	−	6796.03i	1.63952	−	0.789553i
$421$	−5603.53	+	2698.52i	−0.648691	+	0.312393i	−0.729139	−	0.684365i	$-0.760079\pi$
$421$	−5603.53	+	2698.52i	−0.648691	+	0.312393i	0.0804477	+	0.996759i	$0.474365\pi$
$422$	2617.77	−	11469.2i	0.301969	−	1.32301i
$423$	8682.39			0.997996
$424$	−607.447	+	2661.40i	−0.0695760	+	0.304832i
$425$	8840.89	+	11086.1i	1.00905	+	1.26531i
$426$	545.258	+	2388.93i	0.0620137	+	0.271700i
$427$	−813.228	−	3562.99i	−0.0921660	−	0.403806i
$428$	20691.2	−	25945.9i	2.33679	−	2.93024i
$429$	355.391	−	171.147i	0.0399964	−	0.0192612i
$430$	7033.06	+	3386.94i	0.788755	+	0.379844i
$431$	9059.35	+	11360.1i	1.01247	+	1.26959i	0.962625	+	0.270837i	$0.0873005\pi$
$431$	9059.35	+	11360.1i	1.01247	+	1.26959i	0.0498423	+	0.998757i	$0.484128\pi$
$432$	−363.999	+	456.441i	−0.0405392	+	0.0508345i
$433$	1800.08	+	866.874i	0.199784	+	0.0962108i	0.531101	−	0.847309i	$-0.321779\pi$
$433$	1800.08	+	866.874i	0.199784	+	0.0962108i	−0.331317	+	0.943520i	$0.607493\pi$
$434$	2546.14			0.281610
$435$	20831.6	−	2834.56i	2.29608	−	0.312430i
$436$	7150.21			0.785397
$437$	−6681.03	−	3217.41i	−0.731343	−	0.352196i
$438$	−5302.21	+	6648.76i	−0.578423	+	0.725320i
$439$	−7135.37	−	8947.47i	−0.775747	−	0.972755i	0.224252	−	0.974531i	$-0.428006\pi$
$439$	−7135.37	−	8947.47i	−0.775747	−	0.972755i	−0.999998	+	0.00177574i	$0.999435\pi$
$440$	−569.981	−	274.488i	−0.0617563	−	0.0297403i
$441$	6960.36	−	3351.93i	0.751577	−	0.361940i
$442$	−14495.6	+	18176.9i	−1.55992	+	1.95608i
$443$	−1807.99	−	7921.31i	−0.193905	−	0.849555i	−0.974477	−	0.224488i	$-0.927929\pi$
$443$	−1807.99	−	7921.31i	−0.193905	−	0.849555i	0.780571	−	0.625067i	$-0.214928\pi$
$444$	−2281.52	−	9995.98i	−0.243865	−	1.06844i
$445$	−9742.57	−	12216.8i	−1.03785	−	1.30142i
$446$	−2760.91	+	12096.4i	−0.293123	+	1.28426i
$447$	−5403.82			−0.571794
$448$	−445.036	+	1949.83i	−0.0469330	+	0.205627i
$449$	6092.12	−	2933.81i	0.640323	−	0.308363i	−0.0854038	−	0.996346i	$-0.527218\pi$
$449$	6092.12	−	2933.81i	0.640323	−	0.308363i	0.725727	+	0.687983i	$0.241504\pi$
$450$	−25419.7	+	12241.5i	−2.66289	+	1.28238i
$451$	−25.2887	+	110.797i	−0.00264036	+	0.0115682i
$452$	−16320.6			−1.69836
$453$	−2784.78	+	12200.9i	−0.288831	+	1.26545i
$454$	3591.91	+	4504.12i	0.371315	+	0.465614i
$455$	−1998.94	−	8757.91i	−0.205959	−	0.902367i
$456$	4883.80	+	21397.3i	0.501545	+	2.19741i
$457$	−2789.87	+	3498.38i	−0.285568	+	0.358091i	−0.903838	−	0.427875i	$-0.859262\pi$
$457$	−2789.87	+	3498.38i	−0.285568	+	0.358091i	0.618270	+	0.785966i	$0.287834\pi$
$458$	665.613	−	320.542i	0.0679084	−	0.0327030i
$459$	389.548	+	187.596i	0.0396133	+	0.0190768i
$460$	−21616.4	−	27106.2i	−2.19103	−	2.74746i
$461$	−4154.86	+	5210.03i	−0.419764	+	0.526368i	−0.946085	−	0.323918i	$-0.895000\pi$
$461$	−4154.86	+	5210.03i	−0.419764	+	0.526368i	0.526321	+	0.850286i	$0.323571\pi$
$462$	171.507	+	82.5936i	0.0172711	+	0.00831732i
$463$	4726.91			0.474467			0.237234	−	0.971453i	$-0.423759\pi$
$463$	4726.91			0.474467			0.237234	+	0.971453i	$0.423759\pi$
$464$	7082.34	−	11870.0i	0.708598	−	1.18761i
$465$	−10008.7			−0.998156
$466$	14730.5	+	7093.85i	1.46433	+	0.705185i
$467$	−5605.10	+	7028.57i	−0.555403	+	0.696453i	−0.977700	−	0.210004i	$-0.932652\pi$
$467$	−5605.10	+	7028.57i	−0.555403	+	0.696453i	0.422298	+	0.906457i	$0.361224\pi$
$468$	−19605.8	−	24584.9i	−1.93650	−	2.42829i
$469$	3233.80	+	1557.31i	0.318386	+	0.153326i
$470$	−27681.2	+	13330.5i	−2.71667	+	1.30828i
$471$	14604.1	−	18313.0i	1.42871	−	1.79155i
$472$	−4016.32	−	17596.6i	−0.391665	−	1.71600i
$473$	14.3500	+	62.8713i	0.00139495	+	0.00611168i
$474$	11878.1	+	14894.7i	1.15101	+	1.44333i
$475$	3229.98	−	14151.5i	0.312004	−	1.36698i
$476$	−7626.71			−0.734390
$477$	−353.124	+	1547.14i	−0.0338961	+	0.148509i
$478$	−1556.55	+	749.594i	−0.148943	+	0.0717272i
$479$	12231.1	−	5890.20i	1.16671	−	0.561858i	0.252699	−	0.967545i	$-0.418682\pi$
$479$	12231.1	−	5890.20i	1.16671	−	0.561858i	0.914012	+	0.405687i	$0.132968\pi$
$480$	−2494.33	+	10928.4i	−0.237188	+	1.03919i
$481$	−5880.29			−0.557418
$482$	5591.52	−	24498.1i	0.528396	−	2.31505i
$483$	3440.09	+	4313.74i	0.324078	+	0.406381i
$484$	5027.18	+	22025.5i	0.472124	+	2.06851i
$485$	−3543.66	−	15525.8i	−0.331771	−	1.45359i
$486$	−16534.8	+	20734.0i	−1.54328	+	1.93522i
$487$	−6945.72	+	3344.88i	−0.646284	+	0.311234i	−0.728159	−	0.685408i	$-0.759624\pi$
$487$	−6945.72	+	3344.88i	−0.646284	+	0.311234i	0.0818744	+	0.996643i	$0.473909\pi$
$488$	21571.4	+	10388.2i	2.00100	+	0.963633i
$489$	12156.9	+	15244.3i	1.12424	+	1.40975i
$490$	−17044.6	+	21373.2i	−1.57142	+	1.97050i
$491$	−4881.62	−	2350.86i	−0.448685	−	0.216075i	0.195875	−	0.980629i	$-0.437245\pi$
$491$	−4881.62	−	2350.86i	−0.448685	−	0.216075i	−0.644560	+	0.764554i	$0.722960\pi$
$492$	18433.8			1.68914
$493$	−9737.60	−	3157.48i	−0.889573	−	0.288450i
$494$	23799.6			2.16760
$495$	−331.344	−	159.567i	−0.0300865	−	0.0144889i
$496$	−4102.83	+	5144.78i	−0.371416	+	0.465741i
$497$	287.433	+	360.430i	0.0259419	+	0.0325301i
$498$	−1702.51	−	819.883i	−0.153195	−	0.0737748i
$499$	−7650.43	+	3684.25i	−0.686333	+	0.330521i	−0.744345	−	0.667795i	$-0.767238\pi$
$499$	−7650.43	+	3684.25i	−0.686333	+	0.330521i	0.0580119	+	0.998316i	$0.481524\pi$
$500$	17863.1	−	22399.6i	1.59772	−	2.00348i
$501$	−5811.76	−	25463.0i	−0.518264	−	2.27066i
$502$	−491.102	−	2151.66i	−0.0436633	−	0.191301i
$503$	−9889.54	−	12401.1i	−0.876646	−	1.09928i	−0.994342	−	0.106229i	$-0.966122\pi$
$503$	−9889.54	−	12401.1i	−0.876646	−	1.09928i	0.117696	−	0.993050i	$-0.462449\pi$
$504$	1785.94	−	7824.70i	0.157841	−	0.691548i
$505$	31647.2			2.78868
$506$	93.7598	−	410.789i	0.00823742	−	0.0360905i
$507$	−18637.2	+	8975.21i	−1.63256	+	0.786200i
$508$	−7161.40	+	3448.75i	−0.625464	+	0.301208i
$509$	−4713.14	+	20649.6i	−0.410425	+	1.79819i	0.171768	+	0.985137i	$0.445052\pi$
$509$	−4713.14	+	20649.6i	−0.410425	+	1.79819i	−0.582192	+	0.813051i	$0.697805\pi$
$510$	44104.0			3.82933
$511$	−356.020	+	1559.83i	−0.0308208	+	0.135035i
$512$	−15222.0	−	19087.7i	−1.31391	−	1.64759i
$513$	−98.4882	−	431.505i	−0.00847634	−	0.0371373i
$514$	3917.87	+	17165.3i	0.336206	+	1.47302i
$515$	−18568.6	+	23284.3i	−1.58880	+	1.99229i
$516$	9424.26	−	4538.49i	0.804031	−	0.387201i
$517$	−228.681	−	110.127i	−0.0194533	−	0.00936822i
$518$	−1769.31	−	2218.65i	−0.150076	−	0.188189i
$519$	16353.8	−	20507.0i	1.38315	−	1.73441i
$520$	53022.9	+	25534.5i	4.47156	+	2.15339i
$521$	−22417.6			−1.88509			−0.942545	−	0.334078i	$-0.891575\pi$
$521$	−22417.6			−1.88509			−0.942545	+	0.334078i	$0.891575\pi$
$522$	10436.4	−	17491.5i	0.875076	−	1.46663i
$523$	466.183			0.0389766			0.0194883	−	0.999810i	$-0.493796\pi$
$523$	466.183			0.0389766			0.0194883	+	0.999810i	$0.493796\pi$
$524$	27816.9	+	13395.9i	2.31906	+	1.11680i
$525$	−6733.88	+	8444.02i	−0.559792	+	0.701957i
$526$	3356.37	+	4208.76i	0.278222	+	0.348880i
$527$	4390.79	+	2114.49i	0.362934	+	0.174780i
$528$	−443.255	+	213.460i	−0.0365345	+	0.0175941i
$529$	28.5263	−	35.7708i	0.00234456	−	0.00293999i
$530$	−1249.57	−	5474.74i	−0.102411	−	0.448694i
$531$	−2334.79	−	10229.4i	−0.190812	−	0.836002i
$532$	4867.76	+	6103.98i	0.396700	+	0.497446i
$533$	2352.51	−	10307.0i	0.191179	−	0.837610i
$534$	−30803.0			−2.49621
$535$	−8034.22	+	35200.2i	−0.649252	+	2.84456i
$536$	−21185.5	+	10202.4i	−1.70723	+	0.822158i
$537$	11005.6	−	5300.01i	0.884406	−	0.425908i
$538$	8242.48	−	36112.7i	0.660518	−	2.89392i
$539$	−225.840			−0.0180476
$540$	460.474	−	2017.47i	0.0366957	−	0.160774i
$541$	−4486.52	−	5625.92i	−0.356544	−	0.447093i	0.570919	−	0.821006i	$-0.306587\pi$
$541$	−4486.52	−	5625.92i	−0.356544	−	0.447093i	−0.927463	+	0.373914i	$0.878016\pi$
$542$	−6958.68	−	30488.0i	−0.551478	−	2.41618i
$543$	2200.51	+	9641.05i	0.173909	+	0.761946i
$544$	3403.05	−	4267.29i	0.268207	−	0.336321i
$545$	−7008.84	+	3375.28i	−0.550873	+	0.265286i
$546$	−15954.6	−	7683.34i	−1.25054	−	0.602228i
$547$	1806.58	+	2265.38i	0.141213	+	0.177076i	0.847409	−	0.530941i	$-0.178161\pi$
$547$	1806.58	+	2265.38i	0.141213	+	0.177076i	−0.706195	+	0.708017i	$0.749590\pi$
$548$	−2816.93	+	3532.32i	−0.219586	+	0.275352i
$549$	12540.0	+	6038.94i	0.974851	+	0.469464i
$550$	824.786			0.0639437
$551$	3687.98	+	9808.68i	0.285142	+	0.758374i
$552$	−36146.5			−2.78714
$553$	3229.28	+	1555.14i	0.248323	+	0.119586i
$554$	24792.8	−	31089.2i	1.90134	−	2.38421i
$555$	6955.04	+	8721.34i	0.531937	+	0.667028i
$556$	−44310.8	−	21338.9i	−3.37985	−	1.62765i
$557$	11859.3	−	5711.12i	0.902142	−	0.434449i	0.0754800	−	0.997147i	$-0.475951\pi$
$557$	11859.3	−	5711.12i	0.902142	−	0.434449i	0.826662	+	0.562699i	$0.190237\pi$
$558$	−6045.85	+	7581.26i	−0.458676	+	0.575162i
$559$	−1334.92	−	5848.66i	−0.101004	−	0.442526i
$560$	2493.14	+	10923.1i	0.188133	+	0.824263i
$561$	227.171	+	284.863i	0.0170965	+	0.0214384i
$562$	−2240.96	+	9818.27i	−0.168201	+	0.736937i
$563$	−13855.8			−1.03722			−0.518608	−	0.855012i	$-0.673550\pi$
$563$	−13855.8			−1.03722			−0.518608	+	0.855012i	$0.673550\pi$
$564$	−9161.11	+	40137.4i	−0.683958	+	2.99662i
$565$	15997.9	−	7704.19i	1.19122	−	0.573660i
$566$	−12668.1	+	6100.64i	−0.940778	+	0.453055i
$567$	−1147.51	+	5027.56i	−0.0849926	+	0.372377i
$568$	−3020.19			−0.223106
$569$	103.674	−	454.227i	0.00763842	−	0.0334661i	−0.970965	−	0.239221i	$-0.923108\pi$
$569$	103.674	−	454.227i	0.00763842	−	0.0334661i	0.978604	+	0.205755i	$0.0659650\pi$
$570$	−28149.5	−	35298.3i	−2.06851	−	2.59383i
$571$	−241.921	−	1059.92i	−0.0177304	−	0.0776821i	0.965289	−	0.261185i	$-0.0841134\pi$
$571$	−241.921	−	1059.92i	−0.0177304	−	0.0776821i	−0.983019	+	0.183503i	$0.941256\pi$
$572$	204.554	+	896.207i	0.0149525	+	0.0655110i
$573$	3190.07	−	4000.22i	0.232578	−	0.291643i
$574$	4596.70	−	2213.65i	0.334255	−	0.160969i
$575$	21538.7	+	10372.5i	1.56213	+	0.752282i
$576$	−4748.97	−	5955.01i	−0.343530	−	0.430774i
$577$	4142.95	−	5195.09i	0.298914	−	0.374826i	−0.609580	−	0.792725i	$-0.708662\pi$
$577$	4142.95	−	5195.09i	0.298914	−	0.374826i	0.908494	+	0.417899i	$0.137233\pi$
$578$	2775.59	+	1336.66i	0.199740	+	0.0961895i
$579$	−20227.9			−1.45189
$580$	−4362.52	+	48799.6i	−0.312317	+	3.49361i
$581$	−355.513			−0.0253858
$582$	−28283.9	−	13620.8i	−2.01444	−	0.970104i
$583$	28.9245	−	36.2702i	0.00205477	−	0.00257660i
$584$	−6535.21	−	8194.89i	−0.463063	−	0.580663i
$585$	30823.6	+	14843.9i	2.17846	+	1.04909i
$586$	17440.0	−	8398.64i	1.22942	−	0.592056i
$587$	−6297.24	+	7896.49i	−0.442785	+	0.555235i	−0.952275	−	0.305242i	$-0.901263\pi$
$587$	−6297.24	+	7896.49i	−0.442785	+	0.555235i	0.509490	+	0.860477i	$0.329834\pi$
$588$	8151.36	+	35713.5i	0.571695	+	2.50476i
$589$	−1110.11	−	4863.72i	−0.0776594	−	0.340248i
$590$	23149.4	+	29028.5i	1.61534	+	2.02557i
$591$	178.053	−	780.100i	0.0123927	−	0.0542962i
$592$	7334.09			0.509171
$593$	776.977	−	3404.16i	0.0538054	−	0.235737i	−0.940874	−	0.338757i	$-0.889993\pi$
$593$	776.977	−	3404.16i	0.0538054	−	0.235737i	0.994679	+	0.103020i	$0.0328506\pi$
$594$	22.6587	−	10.9119i	0.00156515	−	0.000753736i
$595$	7475.92	−	3600.21i	0.515097	−	0.248058i
$596$	2802.28	−	12277.6i	0.192593	−	0.843807i
$597$	−7987.00			−0.547548
$598$	−8722.09	+	38214.0i	−0.596443	+	2.61319i
$599$	9191.41	+	11525.7i	0.626963	+	0.786187i	0.989305	−	0.145858i	$-0.0465944\pi$
$599$	9191.41	+	11525.7i	0.626963	+	0.786187i	−0.362343	+	0.932045i	$0.618023\pi$
$600$	−15744.7	−	68981.9i	−1.07129	−	4.69362i
$601$	−3754.89	−	16451.3i	−0.254851	−	1.11657i	−0.926675	−	0.375864i	$-0.877346\pi$
$601$	−3754.89	−	16451.3i	−0.254851	−	1.11657i	0.671824	−	0.740711i	$-0.265511\pi$
$602$	1805.05	−	2263.46i	0.122207	−	0.153242i
$603$	−12315.7	+	5930.92i	−0.831730	+	0.400540i
$604$	−26276.6	−	12654.1i	−1.77016	−	0.852466i
$605$	−15325.0	−	19216.9i	−1.02983	−	1.29137i
$606$	38896.8	−	48775.0i	2.60738	−	3.26956i
$607$	10125.2	+	4876.04i	0.677050	+	0.326050i	0.740617	−	0.671927i	$-0.234533\pi$
$607$	10125.2	+	4876.04i	0.677050	+	0.326050i	−0.0635670	+	0.997978i	$0.520248\pi$
$608$	−5587.29			−0.372689
$609$	694.261	−	7766.09i	0.0461952	−	0.516745i
$610$	−49251.8			−3.26909
$611$	21273.2	+	10244.6i	1.40855	+	0.678321i
$612$	18109.7	−	22708.9i	1.19615	−	1.49992i
$613$	6250.43	+	7837.79i	0.411831	+	0.516420i	0.943878	−	0.330295i	$-0.107148\pi$
$613$	6250.43	+	7837.79i	0.411831	+	0.516420i	−0.532046	+	0.846715i	$0.678577\pi$
$614$	1079.00	+	519.621i	0.0709203	+	0.0341534i
$615$	−18069.3	+	8701.71i	−1.18475	+	0.570548i
$616$	−146.287	+	183.438i	−0.00956828	+	0.0119982i
$617$	645.574	+	2828.44i	0.0421229	+	0.184552i	0.991613	−	0.129246i	$-0.0412556\pi$
$617$	645.574	+	2828.44i	0.0421229	+	0.184552i	−0.949490	+	0.313798i	$0.898398\pi$
$618$	13063.8	+	57236.4i	0.850331	+	3.72554i
$619$	−3221.39	−	4039.50i	−0.209174	−	0.262296i	0.666166	−	0.745803i	$-0.267934\pi$
$619$	−3221.39	−	4039.50i	−0.209174	−	0.262296i	−0.875340	+	0.483507i	$0.839363\pi$
$620$	5190.25	−	22740.0i	0.336202	−	1.47300i
$621$	728.943			0.0471038
$622$	10727.1	−	46998.3i	0.691505	−	3.02968i
$623$	−5221.31	+	2514.45i	−0.335774	+	0.161700i
$624$	41234.2	−	19857.3i	2.64533	−	1.27393i
$625$	−919.061	+	4026.67i	−0.0588199	+	0.257707i
$626$	9217.68			0.588519
$627$	82.9960	−	363.629i	0.00528635	−	0.0231610i
$628$	34034.2	+	42677.5i	2.16260	+	2.71181i
$629$	−1208.64	−	5295.39i	−0.0766162	−	0.335677i
$630$	3673.84	+	16096.2i	0.232332	+	1.01791i
$631$	12346.3	−	15481.8i	0.778919	−	0.976734i	−0.221079	−	0.975256i	$-0.570958\pi$
$631$	12346.3	−	15481.8i	0.778919	−	0.976734i	0.999999	−	0.00147827i	$-0.000470548\pi$
$632$	−21155.9	+	10188.1i	−1.33155	+	0.641238i
$633$	15452.2	+	7441.40i	0.970254	+	0.467250i
$634$	−20064.3	−	25159.8i	−1.25687	−	1.57606i
$635$	5391.82	−	6761.12i	0.336957	−	0.422531i
$636$	−6779.60	−	3264.88i	−0.422686	−	0.203555i
$637$	21009.0			1.30676
$638$	−496.739	+	328.323i	−0.0308246	+	0.0203737i
$639$	−1755.71			−0.108693
$640$	35371.8	+	17034.1i	2.18468	+	1.05208i
$641$	−3911.59	+	4904.98i	−0.241027	+	0.302239i	−0.887601	−	0.460613i	$-0.847630\pi$
$641$	−3911.59	+	4904.98i	−0.241027	+	0.302239i	0.646574	+	0.762851i	$0.276201\pi$
$642$	44376.3	+	55646.1i	2.72803	+	3.42084i
$643$	−8101.62	−	3901.53i	−0.496884	−	0.239287i	0.168620	−	0.985681i	$-0.446069\pi$
$643$	−8101.62	−	3901.53i	−0.496884	−	0.239287i	−0.665504	+	0.746394i	$0.731783\pi$
$644$	−11584.8	+	5578.96i	−0.708861	+	0.341369i
$645$	−7095.52	+	8897.50i	−0.433156	+	0.543161i
$646$	4891.78	+	21432.3i	0.297933	+	1.30533i
$647$	2103.52	+	9216.12i	0.127817	+	0.560005i	0.997763	+	0.0668563i	$0.0212969\pi$
$647$	2103.52	+	9216.12i	0.127817	+	0.560005i	−0.869945	+	0.493148i	$0.835846\pi$
$648$	−21064.0	−	26413.4i	−1.27696	−	1.60126i
$649$	−68.2539	+	299.040i	−0.00412820	+	0.0180868i
$650$	−76726.5			−4.62994
$651$	−825.988	+	3618.89i	−0.0497282	+	0.217873i
$652$	−40939.5	+	19715.4i	−2.45907	+	1.18423i
$653$	989.045	−	476.299i	0.0592716	−	0.0285437i	−0.404013	−	0.914753i	$-0.632385\pi$
$653$	989.045	−	476.299i	0.0592716	−	0.0285437i	0.463285	+	0.886209i	$0.346671\pi$
$654$	−3412.37	+	14950.6i	−0.204028	+	0.893905i
$655$	−33590.4			−2.00380
$656$	−2934.12	+	12855.2i	−0.174631	+	0.765110i
$657$	−3799.08	−	4763.90i	−0.225596	−	0.282888i
$658$	2535.54	+	11108.9i	0.150221	+	0.658163i
$659$	1496.87	+	6558.21i	0.0884821	+	0.387665i	0.999706	−	0.0242459i	$-0.00771847\pi$
$659$	1496.87	+	6558.21i	0.0884821	+	0.387665i	−0.911224	+	0.411911i	$0.864861\pi$
$660$	1087.27	−	1363.39i	0.0641240	−	0.0804090i
$661$	24178.5	−	11643.8i	1.42275	−	0.685159i	0.445113	−	0.895474i	$-0.353164\pi$
$661$	24178.5	−	11643.8i	1.42275	−	0.685159i	0.977633	+	0.210316i	$0.0674492\pi$
$662$	7024.50	+	3382.82i	0.412409	+	0.198606i
$663$	−21132.8	−	26499.7i	−1.23790	−	1.55228i
$664$	1452.15	−	1820.94i	0.0848709	−	0.106425i
$665$	−7652.92	−	3685.45i	−0.446267	−	0.214911i
$666$	10807.4			0.628795
$667$	−17100.9	+	2326.93i	−0.992730	+	0.135081i
$668$	60866.2			3.52543
$669$	−16297.2	−	7848.30i	−0.941830	−	0.453562i
$670$	30158.7	−	37817.8i	1.73900	−	2.18064i
$671$	−253.686	−	318.112i	−0.0145953	−	0.0183019i
$672$	3745.57	+	1803.77i	0.215013	+	0.103545i
$673$	−14720.0	+	7088.79i	−0.843114	+	0.406022i	−0.805017	−	0.593252i	$-0.797844\pi$
$673$	−14720.0	+	7088.79i	−0.843114	+	0.406022i	−0.0380969	+	0.999274i	$0.512130\pi$
$674$	−2794.68	+	3504.42i	−0.159714	+	0.200275i
$675$	317.512	+	1391.11i	0.0181052	+	0.0793243i
$676$	−10727.1	−	46998.4i	−0.610326	−	2.67401i
$677$	8920.78	+	11186.3i	0.506431	+	0.635044i	0.967666	−	0.252234i	$-0.0811652\pi$
$677$	8920.78	+	11186.3i	0.506431	+	0.635044i	−0.461236	+	0.887278i	$0.652594\pi$
$678$	7788.85	−	34125.2i	0.441193	−	1.93299i
$679$	−5906.17			−0.333811
$680$	−12096.3	+	52997.3i	−0.682163	+	2.98875i
$681$	−7567.05	+	3644.10i	−0.425800	+	0.205055i
$682$	255.398	−	122.993i	0.0143397	−	0.00690566i
$683$	5498.66	−	24091.2i	0.308053	−	1.34967i	−0.549594	−	0.835432i	$-0.685218\pi$
$683$	5498.66	−	24091.2i	0.308053	−	1.34967i	0.857648	−	0.514238i	$-0.171925\pi$
$684$	−29733.5			−1.66212
$685$	1093.79	−	4792.21i	0.0610097	−	0.267301i
$686$	13645.2	+	17110.5i	0.759439	+	0.952307i
$687$	239.664	+	1050.04i	0.0133097	+	0.0583136i
$688$	1664.95	+	7294.63i	0.0922612	+	0.404223i
$689$	−2690.73	+	3374.07i	−0.148779	+	0.186563i
$690$	66993.2	−	32262.2i	3.69621	−	1.78000i
$691$	−20296.1	−	9774.10i	−1.11737	−	0.538096i	−0.218289	−	0.975884i	$-0.570048\pi$
$691$	−20296.1	−	9774.10i	−1.11737	−	0.538096i	−0.899078	+	0.437788i	$0.855762\pi$
$692$	38111.7	+	47790.6i	2.09363	+	2.62532i
$693$	−85.0402	+	106.637i	−0.00466149	+	0.00584532i
$694$	−21197.0	−	10207.9i	−1.15940	−	0.558339i
$695$	53507.8			2.92038
$696$	36942.1	+	35277.8i	2.01190	+	1.92127i
$697$	9765.33			0.530686
$698$	−48668.4	−	23437.5i	−2.63915	−	1.27095i
$699$	−14861.4	+	18635.5i	−0.804160	+	1.00839i
$700$	−15693.0	−	19678.4i	−0.847340	−	1.06253i
$701$	−14184.7	−	6831.01i	−0.764266	−	0.368051i	0.0107915	−	0.999942i	$-0.496565\pi$
$701$	−14184.7	−	6831.01i	−0.764266	−	0.368051i	−0.775058	+	0.631891i	$0.782279\pi$
$702$	−2107.85	+	1015.09i	−0.113327	+	0.0545754i
$703$	−3466.71	+	4347.12i	−0.185988	+	0.233221i
$704$	49.5474	+	217.081i	0.00265254	+	0.0116215i
$705$	−9967.03	−	43668.4i	−0.532454	−	2.33283i
$706$	−19110.3	−	23963.6i	−1.01873	−	1.27745i
$707$	2611.75	−	11442.8i	0.138932	−	0.608701i
$708$	49752.4			2.64097
$709$	−3980.06	+	17437.8i	−0.210824	+	0.923681i	0.753184	+	0.657809i	$0.228517\pi$
$709$	−3980.06	+	17437.8i	−0.210824	+	0.923681i	−0.964009	+	0.265871i	$0.914340\pi$
$710$	5597.54	−	2695.64i	0.295876	−	0.142486i
$711$	−12298.5	+	5922.63i	−0.648704	+	0.312399i
$712$	8448.25	−	37014.2i	0.444679	−	1.94827i
$713$	8216.29			0.431561
$714$	3639.77	−	15946.9i	0.190777	−	0.835850i
$715$	−623.567	−	781.928i	−0.0326155	−	0.0408985i
$716$	6334.52	+	27753.3i	0.330632	+	1.44859i
$717$	−560.459	−	2455.53i	−0.0291921	−	0.127899i
$718$	−32052.9	+	40193.1i	−1.66602	+	2.08913i
$719$	202.552	−	97.5437i	0.0105061	−	0.00505948i	−0.428623	−	0.903483i	$-0.641001\pi$
$719$	202.552	−	97.5437i	0.0105061	−	0.00505948i	0.439129	+	0.898424i	$0.355287\pi$
$720$	−38444.2	−	18513.7i	−1.98990	−	0.958286i
$721$	6886.61	+	8635.54i	0.355715	+	0.446053i
$722$	−7343.50	+	9208.46i	−0.378527	+	0.474658i
$723$	33005.7	+	15894.7i	1.69778	+	0.817608i
$724$	−23045.8			−1.18300
$725$	−11889.5	−	31621.8i	−0.609056	−	1.61987i
$726$	−48452.9			−2.47694
$727$	7802.46	+	3757.47i	0.398043	+	0.191687i	0.622187	−	0.782869i	$-0.286244\pi$
$727$	7802.46	+	3757.47i	0.398043	+	0.191687i	−0.224144	+	0.974556i	$0.571959\pi$
$728$	13608.4	−	17064.5i	0.692806	−	0.868751i
$729$	−11435.9	−	14340.2i	−0.581005	−	0.728557i
$730$	19426.5	+	9355.30i	0.984940	+	0.474322i
$731$	4992.53	−	2404.27i	0.252606	−	0.121649i
$732$	−41148.5	+	51598.6i	−2.07772	+	2.60538i
$733$	−1426.55	−	6250.13i	−0.0718839	−	0.314944i	0.926184	−	0.377071i	$-0.123069\pi$
$733$	−1426.55	−	6250.13i	−0.0718839	−	0.314944i	−0.998068	+	0.0621271i	$0.980212\pi$
$734$	10840.3	+	47494.6i	0.545128	+	2.38836i
$735$	−24848.8	−	31159.5i	−1.24702	−	1.56372i
$736$	2047.63	−	8971.27i	0.102550	−	0.449301i
$737$	399.603			0.0199723
$738$	−4323.67	+	18943.2i	−0.215659	+	0.944865i
$739$	−18254.4	+	8790.87i	−0.908661	+	0.437588i	−0.829009	−	0.559235i	$-0.811095\pi$
$739$	−18254.4	+	8790.87i	−0.908661	+	0.437588i	−0.0796514	+	0.996823i	$0.525381\pi$
$740$	−23421.8	+	11279.3i	−1.16351	+	0.560319i
$741$	−7720.77	+	33826.9i	−0.382766	+	1.67701i
$742$	−2082.65			−0.103041
$743$	−5389.12	+	23611.3i	−0.266093	+	1.16583i	0.648422	+	0.761281i	$0.275429\pi$
$743$	−5389.12	+	23611.3i	−0.266093	+	1.16583i	−0.914516	+	0.404551i	$0.867428\pi$
$744$	−15162.1	−	19012.6i	−0.747135	−	0.936878i
$745$	3048.80	+	13357.6i	0.149932	+	0.656894i
$746$	−408.698	−	1790.62i	−0.0200583	−	0.0878813i
$747$	844.170	−	1058.56i	0.0413475	−	0.0518481i
$748$	−765.020	+	368.414i	−0.0373956	+	0.0180088i
$749$	12064.5	+	5809.94i	0.588552	+	0.283432i
$750$	38311.0	+	48040.4i	1.86522	+	2.33892i
$751$	19644.5	−	24633.4i	0.954510	−	1.19692i	−0.0258430	−	0.999666i	$-0.508227\pi$
$751$	19644.5	−	24633.4i	0.954510	−	1.19692i	0.980353	−	0.197252i	$-0.0632016\pi$
$752$	−26532.6	−	12777.4i	−1.28663	−	0.619608i
$753$	3217.52			0.155714
$754$	46209.6	−	30542.5i	2.23190	−	1.47519i
$755$	31730.5			1.52952
$756$	−691.464	−	332.992i	−0.0332650	−	0.0160196i
$757$	−13969.0	+	17516.5i	−0.670687	+	0.841015i	−0.994460	−	0.105120i	$-0.966477\pi$
$757$	−13969.0	+	17516.5i	−0.670687	+	0.841015i	0.323772	+	0.946135i	$0.395049\pi$
$758$	−35773.4	−	44858.4i	−1.71418	−	2.14951i
$759$	553.447	+	266.526i	0.0264675	+	0.0127461i
$760$	50136.4	−	24144.4i	2.39295	−	1.15238i
$761$	18313.8	−	22964.7i	0.872370	−	1.09392i	−0.122471	−	0.992472i	$-0.539082\pi$
$761$	18313.8	−	22964.7i	0.872370	−	1.09392i	0.994841	−	0.101445i	$-0.0323466\pi$
$762$	−3793.37	−	16619.8i	−0.180340	−	0.790123i
$763$	641.996	+	2812.77i	0.0304611	+	0.133459i
$764$	7434.29	+	9322.30i	0.352046	+	0.441452i
$765$	−7031.87	+	30808.6i	−0.332337	+	1.45606i
$766$	50933.3			2.40247
$767$	6349.38	−	27818.4i	0.298908	−	1.30960i
$768$	54397.8	−	26196.6i	2.55587	−	1.23084i
$769$	−6969.69	+	3356.42i	−0.326831	+	0.157394i	−0.590103	−	0.807328i	$-0.700913\pi$
$769$	−6969.69	+	3356.42i	−0.326831	+	0.157394i	0.263271	+	0.964722i	$0.415199\pi$
$770$	107.399	−	470.546i	0.00502649	−	0.0220225i
$771$	−25668.5			−1.19900
$772$	10489.7	−	45958.2i	0.489030	−	2.14258i
$773$	−20050.6	−	25142.6i	−0.932947	−	1.16988i	−0.985228	−	0.171246i	$-0.945221\pi$
$773$	−20050.6	−	25142.6i	−0.932947	−	1.16988i	0.0522809	−	0.998632i	$-0.483351\pi$
$774$	2453.45	+	10749.2i	0.113937	+	0.499191i
$775$	3578.84	+	15679.9i	0.165878	+	0.726761i
$776$	24124.7	−	30251.4i	1.11601	−	1.39943i
$777$	3727.39	−	1795.02i	0.172097	−	0.0828776i
$778$	−11541.8	−	5558.22i	−0.531867	−	0.256134i
$779$	−6232.74	−	7815.61i	−0.286664	−	0.359465i
$780$	−101144.	+	126831.i	−4.64300	+	5.82214i
$781$	46.2427	+	22.2693i	0.00211868	+	0.00102030i
$782$	−36205.7			−1.65564
$783$	−744.986	−	711.424i	−0.0340021	−	0.0324703i
$784$	−26203.1			−1.19365
$785$	−53507.3	−	25767.7i	−2.43281	−	1.17158i
$786$	−41285.2	+	51769.9i	−1.87353	+	2.34933i
$787$	21264.6	+	26665.0i	0.963154	+	1.20776i	0.978157	+	0.207870i	$0.0666530\pi$
$787$	21264.6	+	26665.0i	0.963154	+	1.20776i	−0.0150022	+	0.999887i	$0.504776\pi$
$788$	1680.07	+	809.078i	0.0759517	+	0.0365764i
$789$	−7070.84	+	3405.14i	−0.319048	+	0.153645i
$790$	30116.6	−	37765.0i	1.35633	−	1.70078i
$791$	−1465.38	−	6420.25i	−0.0658696	−	0.288594i
$792$	−198.835	−	871.151i	−0.00892081	−	0.0390846i
$793$	23599.4	+	29592.7i	1.05679	+	1.32518i
$794$	10100.2	−	44251.9i	0.451439	−	1.97788i
$795$	8186.75			0.365225
$796$	4141.85	−	18146.6i	0.184427	−	0.808028i
$797$	12526.2	−	6032.31i	0.556714	−	0.268099i	−0.134300	−	0.990941i	$-0.542879\pi$
$797$	12526.2	−	6032.31i	0.556714	−	0.268099i	0.691014	+	0.722841i	$0.257164\pi$
$798$	−15086.1	+	7265.06i	−0.669224	+	0.322281i
$799$	−4853.12	+	21262.9i	−0.214882	+	0.941461i
$800$	18012.6			0.796054
$801$	4911.18	−	21517.3i	0.216639	−	0.949159i
$802$	36179.6	+	45367.8i	1.59295	+	1.99750i
$803$	39.6370	+	173.661i	0.00174192	+	0.00763183i
$804$	−14423.1	−	63191.5i	−0.632664	−	2.77188i
$805$	8722.21	−	10937.3i	0.381885	−	0.478869i
$806$	−23758.7	+	11441.6i	−1.03829	+	0.500015i
$807$	48653.8	+	23430.5i	2.12230	+	1.02205i
$808$	47942.0	+	60117.4i	2.08737	+	2.61748i
$809$	−4804.90	+	6025.16i	−0.208815	+	0.261846i	−0.875199	−	0.483763i	$-0.839270\pi$
$809$	−4804.90	+	6025.16i	−0.208815	+	0.261846i	0.666384	+	0.745609i	$0.267841\pi$
$810$	62614.5	+	30153.6i	2.71611	+	1.30801i
$811$	20337.3			0.880568			0.440284	−	0.897859i	$-0.354878\pi$
$811$	20337.3			0.880568			0.440284	+	0.897859i	$0.354878\pi$
$812$	17284.7	+	5604.66i	0.747011	+	0.242223i
$813$	45590.7			1.96671
$814$	−284.650	−	137.080i	−0.0122567	−	0.00590252i
$815$	30823.3	−	38651.2i	1.32478	−	1.66122i
$816$	26357.5	+	33051.2i	1.13076	+	1.41792i
$817$	−5110.73	−	2461.20i	−0.218852	−	0.105393i
$818$	−21523.5	+	10365.1i	−0.919988	+	0.443043i
$819$	7910.94	−	9920.00i	0.337522	−	0.423239i
$820$	−10400.2	−	45566.3i	−0.442916	−	1.94054i
$821$	−6401.58	−	28047.1i	−0.272127	−	1.19227i	−0.907497	−	0.420059i	$-0.862009\pi$
$821$	−6401.58	−	28047.1i	−0.272127	−	1.19227i	0.635369	−	0.772209i	$-0.280848\pi$
$822$	−6041.46	−	7575.75i	−0.256350	−	0.321453i
$823$	−6681.80	+	29274.9i	−0.283005	+	1.23992i	0.610914	+	0.791697i	$0.290802\pi$
$823$	−6681.80	+	29274.9i	−0.283005	+	1.23992i	−0.893919	+	0.448228i	$0.852055\pi$
$824$	−72360.6			−3.05923
$825$	−267.567	+	1172.29i	−0.0112915	+	0.0494713i
$826$	12406.4	−	5974.61i	0.522608	−	0.251675i
$827$	−14008.4	+	6746.11i	−0.589022	+	0.283658i	−0.704559	−	0.709645i	$-0.748855\pi$
$827$	−14008.4	+	6746.11i	−0.589022	+	0.283658i	0.115537	+	0.993303i	$0.463141\pi$
$828$	10896.7	−	47741.7i	0.457352	−	2.00379i
$829$	−825.057			−0.0345663			−0.0172831	−	0.999851i	$-0.505502\pi$
$829$	−825.057			−0.0345663			−0.0172831	+	0.999851i	$0.505502\pi$
$830$	−1066.12	+	4670.98i	−0.0445851	+	0.195340i
$831$	36144.8	+	45324.1i	1.50884	+	1.89203i
$832$	−4609.19	−	20194.2i	−0.192061	−	0.841475i
$833$	4318.20	+	18919.3i	0.179612	+	0.786932i
$834$	65765.0	−	82466.7i	2.73052	−	3.42397i
$835$	−59662.8	+	28732.1i	−2.47271	+	1.19080i
$836$	783.133	+	377.137i	0.0323986	+	0.0156023i
$837$	305.763	+	383.415i	0.0126269	+	0.0158336i
$838$	−23544.2	+	29523.5i	−0.970549	+	1.21703i
$839$	−13753.4	−	6623.30i	−0.565937	−	0.272541i	0.128960	−	0.991650i	$-0.458836\pi$
$839$	−13753.4	−	6623.30i	−0.565937	−	0.272541i	−0.694898	+	0.719109i	$0.744550\pi$
$840$	−41404.8			−1.70072
$841$	19748.3	+	14311.8i	0.809722	+	0.586814i
$842$	31085.4			1.27230
$843$	−13227.9	−	6370.24i	−0.540444	−	0.260264i
$844$	−24920.1	+	31248.8i	−1.01633	+	1.27444i
$845$	32700.7	+	41005.4i	1.33129	+	1.66938i
$846$	−39098.0	−	18828.6i	−1.58891	−	0.765179i
$847$	−8213.08	+	3955.21i	−0.333181	+	0.160452i
$848$	3355.96	−	4208.24i	0.135901	−	0.170415i
$849$	−4561.35	−	19984.6i	−0.184387	−	0.807854i
$850$	−15770.4	−	69094.7i	−0.636377	−	2.78815i
$851$	−5709.50	−	7159.48i	−0.229987	−	0.288395i
$852$	1852.51	−	8116.39i	0.0744907	−	0.326365i
$853$	15398.5			0.618096			0.309048	−	0.951046i	$-0.399990\pi$
$853$	15398.5			0.618096			0.309048	+	0.951046i	$0.399990\pi$
$854$	−4064.60	+	17808.2i	−0.162866	+	0.713564i
$855$	29145.6	−	14035.8i	1.16580	−	0.561419i
$856$	−79037.7	+	38062.5i	−3.15590	+	1.51980i
$857$	−7477.68	+	32761.8i	−0.298054	+	1.30586i	0.574966	+	0.818177i	$0.305015\pi$
$857$	−7477.68	+	32761.8i	−0.298054	+	1.30586i	−0.873020	+	0.487684i	$0.837842\pi$
$858$	−1971.52			−0.0784461
$859$	−5021.44	+	22000.4i	−0.199452	+	0.873857i	0.771812	+	0.635851i	$0.219351\pi$
$859$	−5021.44	+	22000.4i	−0.199452	+	0.873857i	−0.971264	+	0.238006i	$0.923506\pi$
$860$	−16535.7	−	20735.2i	−0.655656	−	0.822167i
$861$	1655.11	+	7251.52i	0.0655123	+	0.287028i
$862$	−16160.1	−	70802.0i	−0.638533	−	2.79760i
$863$	−10037.6	+	12586.8i	−0.395927	+	0.496477i	−0.939339	−	0.342989i	$-0.888561\pi$
$863$	−10037.6	+	12586.8i	−0.395927	+	0.496477i	0.543412	+	0.839466i	$0.317132\pi$
$864$	494.847	−	238.306i	0.0194850	−	0.00938349i
$865$	−59917.8	−	28854.9i	−2.35522	−	1.13422i
$866$	−6226.12	−	7807.31i	−0.244310	−	0.306355i
$867$	−2800.24	+	3511.39i	−0.109690	+	0.137547i
$868$	−7793.85	−	3753.32i	−0.304770	−	0.146770i
$869$	399.044			0.0155773
$870$	−99954.4	−	32410.8i	−3.89514	−	1.26302i
$871$	−37173.4			−1.44612
$872$	−17029.3	−	8200.90i	−0.661337	−	0.318483i
$873$	14024.3	−	17585.9i	0.543700	−	0.681778i
$874$	23108.3	+	28976.9i	0.894337	+	1.12146i
$875$	10415.5	+	5015.84i	0.402409	+	0.193790i
$876$	26031.4	−	12536.0i	1.00402	−	0.483509i
$877$	629.036	−	788.786i	0.0242201	−	0.0303711i	−0.769574	−	0.638558i	$-0.779531\pi$
$877$	629.036	−	788.786i	0.0242201	−	0.0303711i	0.793794	+	0.608187i	$0.208103\pi$
$878$	12728.1	+	55765.5i	0.489240	+	2.14350i
$879$	6279.53	+	27512.4i	0.240959	+	1.05571i
$880$	777.732	+	975.245i	0.0297924	+	0.0373585i
$881$	−8270.81	+	36236.8i	−0.316289	+	1.38575i	0.527717	+	0.849420i	$0.323048\pi$
$881$	−8270.81	+	36236.8i	−0.316289	+	1.38575i	−0.844006	+	0.536333i	$0.819809\pi$
$882$	−38612.4			−1.47409
$883$	5248.41	−	22994.8i	0.200026	−	0.876371i	−0.770893	−	0.636964i	$-0.780190\pi$
$883$	5248.41	−	22994.8i	0.200026	−	0.876371i	0.970919	−	0.239407i	$-0.0769530\pi$
$884$	71166.6	−	34272.0i	2.70768	−	1.30395i
$885$	−48768.7	+	23485.8i	−1.85236	+	0.892052i
$886$	−9036.51	+	39591.6i	−0.342650	+	1.50125i
$887$	−5393.67			−0.204173			−0.102087	−	0.994776i	$-0.532552\pi$
$887$	−5393.67			−0.204173			−0.102087	+	0.994776i	$0.532552\pi$
$888$	−6031.04	+	26423.7i	−0.227915	+	0.998561i
$889$	−1999.68	−	2507.52i	−0.0754410	−	0.0946001i
$890$	17378.8	+	76141.7i	0.654539	+	2.86772i
$891$	127.756	+	559.735i	0.00480358	+	0.0210458i
$892$	26282.8	−	32957.5i	0.986560	−	1.23711i
$893$	20115.1	−	9686.93i	0.753781	−	0.363002i
$894$	24334.1	+	11718.7i	0.910353	+	0.438403i
$895$	−19310.3	−	24214.4i	−0.721199	−	0.904355i
$896$	9078.24	−	11383.8i	0.338485	−	0.424447i
$897$	−51484.9	−	24793.8i	−1.91642	−	0.922900i
$898$	−33795.9			−1.25588
$899$	−8397.12	−	8018.83i	−0.311524	−	0.297489i
$900$	95856.4			3.55024
$901$	−3591.51	−	1729.58i	−0.132797	−	0.0639519i
$902$	354.153	−	444.094i	0.0130732	−	0.0163933i
$903$	2631.54	+	3299.84i	0.0969791	+	0.121608i
$904$	38870.0	+	18718.8i	1.43009	+	0.688694i
$905$	22590.1	−	10878.8i	0.829747	−	0.399585i
$906$	38999.1	−	48903.3i	1.43009	−	1.79327i
$907$	−9680.69	−	42413.9i	−0.354401	−	1.55273i	−0.766895	−	0.641773i	$-0.778199\pi$
$907$	−9680.69	−	42413.9i	−0.354401	−	1.55273i	0.412493	−	0.910961i	$-0.364658\pi$
$908$	−4355.39	−	19082.2i	−0.159184	−	0.697429i
$909$	27869.9	+	34947.8i	1.01693	+	1.27519i
$910$	−9990.89	+	43773.0i	−0.363950	+	1.59457i
$911$	21537.9			0.783297			0.391649	−	0.920115i	$-0.371905\pi$
$911$	21537.9			0.783297			0.391649	+	0.920115i	$0.371905\pi$
$912$	9629.59	−	42190.0i	0.349636	−	1.53185i
$913$	−35.6608	+	17.1733i	−0.00129266	+	0.000622512i
$914$	20149.8	−	9703.61i	0.729206	−	0.351167i
$915$	15977.7	−	70002.7i	0.577273	−	2.52920i
$916$	−2509.99			−0.0905375
$917$	−2772.12	+	12145.4i	−0.0998293	+	0.437381i
$918$	−1347.37	−	1689.54i	−0.0484420	−	0.0607443i
$919$	−5188.64	−	22732.9i	−0.186243	−	0.815984i	−0.978574	−	0.205893i	$-0.933990\pi$
$919$	−5188.64	−	22732.9i	−0.186243	−	0.815984i	0.792332	−	0.610091i	$-0.208867\pi$
$920$	20393.6	+	89350.3i	0.730824	+	3.20195i
$921$	−1088.59	+	1365.04i	−0.0389469	+	0.0488379i
$922$	30008.4	−	14451.3i	1.07188	−	0.516190i
$923$	−4301.76	−	2071.62i	−0.153407	−	0.0738767i
$924$	−403.238	−	505.645i	−0.0143567	−	0.0180027i
$925$	11176.2	−	14014.5i	0.397265	−	0.498155i
$926$	−21286.0	−	10250.8i	−0.755399	−	0.363781i
$927$	−42065.1			−1.49040
$928$	−10848.4	+	7170.29i	−0.383744	+	0.253638i
$929$	7830.14			0.276533			0.138266	−	0.990395i	$-0.455847\pi$
$929$	7830.14			0.276533			0.138266	+	0.990395i	$0.455847\pi$
$930$	45070.6	+	21704.8i	1.58916	+	0.765301i
$931$	12385.8	−	15531.3i	0.436013	−	0.546743i
$932$	−34633.6	−	43429.2i	−1.21723	−	1.52636i
$933$	63319.8	+	30493.2i	2.22186	+	1.06999i
$934$	40482.7	−	19495.4i	1.41824	−	0.682987i
$935$	575.983	−	722.260i	0.0201462	−	0.0252625i
$936$	18496.8	+	81039.6i	0.645925	+	2.82998i
$937$	9457.86	+	41437.6i	0.329749	+	1.44472i	0.819609	+	0.572923i	$0.194191\pi$
$937$	9457.86	+	41437.6i	0.329749	+	1.44472i	−0.489860	+	0.871801i	$0.662952\pi$
$938$	−11185.1	−	14025.6i	−0.389344	−	0.488222i
$939$	−2990.29	+	13101.3i	−0.103924	+	0.455319i
$940$	104384.			3.62195
$941$	−1152.87	+	5051.05i	−0.0399388	+	0.174983i	−0.990964	−	0.134131i	$-0.957176\pi$
$941$	−1152.87	+	5051.05i	−0.0399388	+	0.174983i	0.951025	+	0.309115i	$0.100033\pi$
$942$	−105478.	+	50795.5i	−3.64826	+	1.75691i
$943$	14833.4	−	7143.37i	0.512238	−	0.246681i
$944$	−7919.15	+	34696.1i	−0.273036	+	1.19625i
$945$	834.982			0.0287428
$946$	71.7227	−	314.238i	0.00246502	−	0.0107999i
$947$	−25461.9	−	31928.2i	−0.873708	−	1.09559i	−0.994688	−	0.102940i	$-0.967175\pi$
$947$	−25461.9	−	31928.2i	−0.873708	−	1.09559i	0.120980	−	0.992655i	$-0.461396\pi$
$948$	−14402.9	−	63103.2i	−0.493443	−	2.16192i
$949$	−3687.26	−	16155.0i	−0.126126	−	0.552595i
$950$	−45233.9	+	56721.5i	−1.54482	+	1.93715i
$951$	42269.2	−	20355.8i	1.44130	−	0.694091i
$952$	18164.2	+	8747.41i	0.618387	+	0.297800i
$953$	−16979.2	−	21291.2i	−0.577135	−	0.723704i	0.404487	−	0.914544i	$-0.367450\pi$
$953$	−16979.2	−	21291.2i	−0.577135	−	0.723704i	−0.981621	+	0.190840i	$0.938879\pi$
$954$	4945.29	−	6201.19i	0.167830	−	0.210452i
$955$	−11687.9	−	5628.61i	−0.396034	−	0.190720i
$956$	5869.65			0.198575
$957$	−305.507	−	812.537i	−0.0103194	−	0.0274458i
$958$	−67851.9			−2.28831
$959$	−1642.47	−	790.974i	−0.0553058	−	0.0266339i
$960$	−24499.3	+	30721.2i	−0.823659	+	1.03284i
$961$	−15128.0	−	18969.9i	−0.507803	−	0.636765i
$962$	26479.8	+	12752.0i	0.887466	+	0.427381i
$963$	−45946.6	+	22126.7i	−1.53750	+	0.740419i
$964$	−53229.0	+	66747.0i	−1.77841	+	2.23006i
$965$	11412.5	+	50001.2i	0.380705	+	1.66798i
$966$	−6136.45	−	26885.5i	−0.204386	−	0.895474i
$967$	14508.1	+	18192.6i	0.482471	+	0.604999i	0.962175	−	0.272431i	$-0.0878276\pi$
$967$	14508.1	+	18192.6i	0.482471	+	0.604999i	−0.479705	+	0.877430i	$0.659256\pi$
$968$	13289.0	−	58223.0i	0.441245	−	1.93322i
$969$	−32049.2			−1.06250
$970$	−17711.6	+	77599.5i	−0.586272	+	2.56863i
$971$	−11809.3	+	5687.06i	−0.390297	+	0.187957i	−0.618732	−	0.785602i	$-0.712353\pi$
$971$	−11809.3	+	5687.06i	−0.390297	+	0.187957i	0.228435	+	0.973559i	$0.426639\pi$
$972$	81178.3	−	39093.4i	2.67880	−	1.29004i
$973$	4415.83	−	19347.0i	0.145493	−	0.637449i
$974$	38531.2			1.26758
$975$	24890.7	−	109053.i	0.817579	−	3.58205i
$976$	−29433.9	−	36908.9i	−0.965324	−	1.21048i
$977$	131.180	+	574.737i	0.00429562	+	0.0188203i	0.977030	−	0.213100i	$-0.0683561\pi$
$977$	131.180	+	574.737i	0.00429562	+	0.0188203i	−0.972735	+	0.231921i	$0.925499\pi$
$978$	−21685.5	−	95010.4i	−0.709025	−	3.10644i
$979$	−402.276	+	504.439i	−0.0131326	+	0.0164677i
$980$	83680.8	−	40298.6i	2.72764	−	1.31356i
$981$	−9899.59	−	4767.39i	−0.322191	−	0.155159i
$982$	16884.5	+	21172.5i	0.548683	+	0.688027i
$983$	−23827.8	+	29879.2i	−0.773133	+	0.969478i	−0.999990	−	0.00445002i	$-0.998584\pi$
$983$	−23827.8	+	29879.2i	−0.773133	+	0.969478i	0.226857	+	0.973928i	$0.427155\pi$
$984$	−43902.8	−	21142.5i	−1.42233	−	0.684957i
$985$	−2028.78			−0.0656267
$986$	37002.5	+	35335.5i	1.19513	+	1.14129i
$987$	−16611.9			−0.535728
$988$	−72851.6	−	35083.5i	−2.34587	−	1.12971i
$989$	5824.82	−	7304.09i	0.187279	−	0.234840i
$990$	1146.05	+	1437.10i	0.0367919	+	0.0461355i
$991$	15508.5	+	7468.50i	0.497117	+	0.239399i	0.665604	−	0.746305i	$-0.268174\pi$
$991$	15508.5	+	7468.50i	0.497117	+	0.239399i	−0.168487	+	0.985704i	$0.553888\pi$
$992$	5577.68	−	2686.07i	0.178520	−	0.0859706i
$993$	−7086.88	+	8886.67i	−0.226481	+	0.283998i
$994$	−512.724	−	2246.39i	−0.0163608	−	0.0716813i
$995$	4506.21	+	19743.0i	0.143574	+	0.629040i
$996$	4002.84	+	5019.40i	0.127344	+	0.159684i
$997$	3302.78	−	14470.4i	0.104915	−	0.459661i	−0.894993	−	0.446080i	$-0.852820\pi$
$997$	3302.78	−	14470.4i	0.104915	−	0.459661i	0.999908	−	0.0135813i	$-0.00432318\pi$
$998$	42440.6			1.34613
$999$	121.624	−	532.869i	0.00385186	−	0.0168761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.4.d.a.16.1	✓	42
29.7	even	7		841.4.a.h.1.20		21
29.20	even	7	inner	29.4.d.a.20.1	yes	42
29.22	even	14		841.4.a.i.1.2		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.16.1	✓	42	1.1	even	1	trivial
29.4.d.a.20.1	yes	42	29.20	even	7	inner
841.4.a.h.1.20		21	29.7	even	7
841.4.a.i.1.2		21	29.22	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+(-4.50314 - 2.16860i) q^{2} +(4.54313 - 5.69691i) q^{3} +(10.5875 + 13.2763i) q^{4} +(-16.6453 - 8.01597i) q^{5} +(-32.8126 + 15.8017i) q^{6} +(-4.27206 + 5.35699i) q^{7} +(-9.98861 - 43.7630i) q^{8} +(-5.80663 - 25.4405i) q^{9} +(57.5728 + 72.1941i) q^{10} +(-0.169748 + 0.743714i) q^{11} +123.735 q^{12} +(15.7909 - 69.1847i) q^{13} +(30.8548 - 14.8589i) q^{14} +(-121.288 + 58.4093i) q^{15} +(-19.6950 + 86.2893i) q^{16} +65.5487 q^{17} +(-29.0222 + 127.154i) q^{18} +(-41.8366 - 52.4614i) q^{19} +(-69.8102 - 305.858i) q^{20} +(11.1098 + 48.6750i) q^{21} +(2.37721 - 2.98093i) q^{22} +(99.5673 - 47.9491i) q^{23} +(-294.693 - 141.917i) q^{24} +(134.875 + 169.128i) q^{25} +(-221.143 + 277.304i) q^{26} +(5.94287 + 2.86194i) q^{27} -116.352 q^{28} +(-148.555 - 48.1699i) q^{29} +672.844 q^{30} +(66.9852 + 32.2584i) q^{31} +(51.9164 - 65.1011i) q^{32} +(3.46568 + 4.34583i) q^{33} +(-295.175 - 142.149i) q^{34} +(114.051 - 54.9242i) q^{35} +(276.279 - 346.443i) q^{36} +(-18.4388 - 80.7856i) q^{37} +(74.6282 + 326.968i) q^{38} +(-322.398 - 404.274i) q^{39} +(-184.539 + 808.517i) q^{40} +148.978 q^{41} +(55.5278 - 243.283i) q^{42} +(76.1651 - 36.6792i) q^{43} +(-11.6710 + 5.62046i) q^{44} +(-107.277 + 470.012i) q^{45} -552.347 q^{46} +(-74.0384 + 324.383i) q^{47} +(402.105 + 504.224i) q^{48} +(65.8778 + 288.629i) q^{49} +(-240.591 - 1054.10i) q^{50} +(297.796 - 373.425i) q^{51} +(1085.71 - 522.849i) q^{52} +(-54.7915 - 26.3862i) q^{53} +(-20.5552 - 25.7754i) q^{54} +(8.78710 - 11.0187i) q^{55} +(277.110 + 133.449i) q^{56} -488.937 q^{57} +(564.504 + 539.072i) q^{58} +402.090 q^{59} +(-2059.60 - 991.853i) q^{60} +(-332.555 + 417.010i) q^{61} +(-231.688 - 290.528i) q^{62} +(161.091 + 77.5773i) q^{63} +(262.982 - 126.645i) q^{64} +(-817.428 + 1025.02i) q^{65} +(-6.18210 - 27.0855i) q^{66} +(-116.564 - 510.702i) q^{67} +(693.999 + 870.247i) q^{68} +(179.186 - 785.064i) q^{69} -632.698 q^{70} +(14.9717 - 65.5952i) q^{71} +(-1055.35 + 508.231i) q^{72} +(210.381 - 101.314i) q^{73} +(-92.1591 + 403.775i) q^{74} +1576.26 q^{75} +(253.550 - 1110.87i) q^{76} +(-3.25890 - 4.08653i) q^{77} +(575.095 + 2519.66i) q^{78} +(-116.401 - 509.988i) q^{79} +(1019.52 - 1278.44i) q^{80} +(678.089 - 326.550i) q^{81} +(-670.870 - 323.074i) q^{82} +(32.3502 + 40.5658i) q^{83} +(-528.602 + 662.845i) q^{84} +(-1091.08 - 525.436i) q^{85} -422.525 q^{86} +(-949.325 + 627.463i) q^{87} +34.2427 q^{88} +(762.029 + 366.974i) q^{89} +(1502.35 - 1883.89i) q^{90} +(303.162 + 380.153i) q^{91} +(1690.76 + 814.227i) q^{92} +(488.096 - 235.054i) q^{93} +(1036.86 - 1300.18i) q^{94} +(275.855 + 1208.60i) q^{95} +(-135.012 - 591.525i) q^{96} +(537.437 + 673.924i) q^{97} +(329.264 - 1442.60i) q^{98} +19.9061 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

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