LMFDB - Embedded newform 77.4.e.c.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,4,Mod(23,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("77.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.54314707044$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67 x^{18} - 2 x^{17} + 2960 x^{16} - 261 x^{15} + 74338 x^{14} - 19762 x^{13} + \cdots + 649230400 $ x^20 + 67x^18 - 2x^17 + 2960x^16 - 261x^15 + 74338x^14 - 19762x^13 + 1348686x^12 - 533131x^11 + 15140516x^10 - 9917906x^9 + 123558653x^8 - 86301269x^7 + 611013951x^6 - 481586362x^5 + 2045671324x^4 - 970096176x^3 + 1858590384x^2 + 644949760x + 649230400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			23.3
Root			$-1.64894 - 2.85605i$ of defining polynomial
Character	$\chi$	$=$	77.23
Dual form			77.4.e.c.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64894 + 2.85605i) q^{2} +(2.68131 + 4.64416i) q^{3} +(-1.43800 - 2.49069i) q^{4} +(-4.02020 + 6.96320i) q^{5} -17.6853 q^{6} +(15.2781 + 10.4681i) q^{7} -16.8983 q^{8} +(-0.878841 + 1.52220i) q^{9} +O(q^{10})$	\(q+(-1.64894 + 2.85605i) q^{2} +(2.68131 + 4.64416i) q^{3} +(-1.43800 - 2.49069i) q^{4} +(-4.02020 + 6.96320i) q^{5} -17.6853 q^{6} +(15.2781 + 10.4681i) q^{7} -16.8983 q^{8} +(-0.878841 + 1.52220i) q^{9} +(-13.2581 - 22.9638i) q^{10} +(5.50000 + 9.52628i) q^{11} +(7.71145 - 13.3566i) q^{12} +11.3184 q^{13} +(-55.0899 + 26.3737i) q^{14} -43.1176 q^{15} +(39.3683 - 68.1879i) q^{16} +(-65.2098 - 112.947i) q^{17} +(-2.89831 - 5.02002i) q^{18} +(-16.7843 + 29.0713i) q^{19} +23.1242 q^{20} +(-7.65024 + 99.0220i) q^{21} -36.2767 q^{22} +(-47.9330 + 83.0224i) q^{23} +(-45.3096 - 78.4786i) q^{24} +(30.1759 + 52.2663i) q^{25} +(-18.6633 + 32.3258i) q^{26} +135.365 q^{27} +(4.10287 - 53.1061i) q^{28} +162.969 q^{29} +(71.0984 - 123.146i) q^{30} +(100.296 + 173.717i) q^{31} +(62.2386 + 107.801i) q^{32} +(-29.4944 + 51.0858i) q^{33} +430.108 q^{34} +(-134.312 + 64.3004i) q^{35} +5.05510 q^{36} +(24.2728 - 42.0417i) q^{37} +(-55.3527 - 95.8737i) q^{38} +(30.3481 + 52.5644i) q^{39} +(67.9347 - 117.666i) q^{40} +133.331 q^{41} +(-270.197 - 185.131i) q^{42} +120.441 q^{43} +(15.8180 - 27.3976i) q^{44} +(-7.06624 - 12.2391i) q^{45} +(-158.077 - 273.798i) q^{46} +(-307.522 + 532.643i) q^{47} +422.235 q^{48} +(123.839 + 319.864i) q^{49} -199.033 q^{50} +(349.695 - 605.690i) q^{51} +(-16.2758 - 28.1906i) q^{52} +(-248.113 - 429.745i) q^{53} +(-223.209 + 386.609i) q^{54} -88.4445 q^{55} +(-258.174 - 176.893i) q^{56} -180.016 q^{57} +(-268.726 + 465.446i) q^{58} +(-37.6802 - 65.2640i) q^{59} +(62.0032 + 107.393i) q^{60} +(-12.3185 + 21.3363i) q^{61} -661.525 q^{62} +(-29.3615 + 14.0565i) q^{63} +219.382 q^{64} +(-45.5022 + 78.8121i) q^{65} +(-97.2690 - 168.475i) q^{66} +(-32.6620 - 56.5723i) q^{67} +(-187.544 + 324.835i) q^{68} -514.093 q^{69} +(37.8278 - 489.629i) q^{70} +730.333 q^{71} +(14.8509 - 25.7226i) q^{72} +(-508.151 - 880.143i) q^{73} +(80.0488 + 138.649i) q^{74} +(-161.822 + 280.284i) q^{75} +96.5436 q^{76} +(-15.6924 + 203.118i) q^{77} -200.168 q^{78} +(678.129 - 1174.55i) q^{79} +(316.537 + 548.259i) q^{80} +(386.684 + 669.756i) q^{81} +(-219.855 + 380.800i) q^{82} -92.4757 q^{83} +(257.634 - 123.339i) q^{84} +1048.63 q^{85} +(-198.600 + 343.985i) q^{86} +(436.970 + 756.854i) q^{87} +(-92.9408 - 160.978i) q^{88} +(-311.957 + 540.326i) q^{89} +46.6072 q^{90} +(172.923 + 118.482i) q^{91} +275.711 q^{92} +(-537.847 + 931.578i) q^{93} +(-1014.17 - 1756.59i) q^{94} +(-134.953 - 233.745i) q^{95} +(-333.762 + 578.093i) q^{96} -122.988 q^{97} +(-1117.75 - 173.747i) q^{98} -19.3345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9}+O(q^{10}) $ 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9	\( 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9} - 63 q^{10} + 110 q^{11} - 55 q^{12} + 324 q^{13} + 58 q^{14} + 60 q^{15} - 286 q^{16} - 200 q^{17} + 252 q^{18} - 252 q^{19} + 192 q^{20} + 458 q^{21} - 134 q^{23} - 786 q^{24} - 86 q^{25} - 363 q^{26} + 348 q^{27} - 1057 q^{28} + 296 q^{29} + 316 q^{30} - 530 q^{31} + 731 q^{32} + 204 q^{34} - 288 q^{35} + 2574 q^{36} + 902 q^{37} - 66 q^{38} + 208 q^{39} - 2163 q^{40} + 336 q^{41} - 1482 q^{42} + 236 q^{43} + 594 q^{44} - 58 q^{45} + 210 q^{46} - 288 q^{47} - 1700 q^{48} - 1072 q^{49} + 4650 q^{50} + 1022 q^{51} - 1663 q^{52} + 608 q^{53} - 2312 q^{54} - 220 q^{55} - 4905 q^{56} + 1656 q^{57} + 1951 q^{58} + 464 q^{59} + 818 q^{60} - 3484 q^{61} - 1618 q^{62} - 3948 q^{63} + 6090 q^{64} + 1560 q^{65} + 583 q^{66} - 142 q^{67} - 1145 q^{68} + 3432 q^{69} - 4133 q^{70} + 668 q^{71} + 1176 q^{72} - 1466 q^{73} + 3460 q^{74} - 2982 q^{75} + 6774 q^{76} - 330 q^{77} + 10840 q^{78} - 578 q^{79} - 2911 q^{80} - 118 q^{81} + 307 q^{82} + 1092 q^{83} - 6786 q^{84} + 5164 q^{85} - 2597 q^{86} - 1516 q^{87} + 33 q^{88} - 3150 q^{89} - 3672 q^{90} - 3638 q^{91} + 4326 q^{92} + 1484 q^{93} - 5700 q^{94} + 1338 q^{95} - 5429 q^{96} + 3308 q^{97} - 3186 q^{98} - 1672 q^{99}+O(q^{100}) \) 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9 - 63 * q^10 + 110 * q^11 - 55 * q^12 + 324 * q^13 + 58 * q^14 + 60 * q^15 - 286 * q^16 - 200 * q^17 + 252 * q^18 - 252 * q^19 + 192 * q^20 + 458 * q^21 - 134 * q^23 - 786 * q^24 - 86 * q^25 - 363 * q^26 + 348 * q^27 - 1057 * q^28 + 296 * q^29 + 316 * q^30 - 530 * q^31 + 731 * q^32 + 204 * q^34 - 288 * q^35 + 2574 * q^36 + 902 * q^37 - 66 * q^38 + 208 * q^39 - 2163 * q^40 + 336 * q^41 - 1482 * q^42 + 236 * q^43 + 594 * q^44 - 58 * q^45 + 210 * q^46 - 288 * q^47 - 1700 * q^48 - 1072 * q^49 + 4650 * q^50 + 1022 * q^51 - 1663 * q^52 + 608 * q^53 - 2312 * q^54 - 220 * q^55 - 4905 * q^56 + 1656 * q^57 + 1951 * q^58 + 464 * q^59 + 818 * q^60 - 3484 * q^61 - 1618 * q^62 - 3948 * q^63 + 6090 * q^64 + 1560 * q^65 + 583 * q^66 - 142 * q^67 - 1145 * q^68 + 3432 * q^69 - 4133 * q^70 + 668 * q^71 + 1176 * q^72 - 1466 * q^73 + 3460 * q^74 - 2982 * q^75 + 6774 * q^76 - 330 * q^77 + 10840 * q^78 - 578 * q^79 - 2911 * q^80 - 118 * q^81 + 307 * q^82 + 1092 * q^83 - 6786 * q^84 + 5164 * q^85 - 2597 * q^86 - 1516 * q^87 + 33 * q^88 - 3150 * q^89 - 3672 * q^90 - 3638 * q^91 + 4326 * q^92 + 1484 * q^93 - 5700 * q^94 + 1338 * q^95 - 5429 * q^96 + 3308 * q^97 - 3186 * q^98 - 1672 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.64894	+	2.85605i	−0.582988	+	1.00976i	0.412135	+	0.911123i	$0.364783\pi$
$2$	−1.64894	+	2.85605i	−0.582988	+	1.00976i	−0.995123	+	0.0986421i	$0.968550\pi$
$3$	2.68131	+	4.64416i	0.516018	+	0.893770i	0.999827	+	0.0185961i	$0.00591967\pi$
$3$	2.68131	+	4.64416i	0.516018	+	0.893770i	−0.483809	+	0.875174i	$0.660747\pi$
$4$	−1.43800	−	2.49069i	−0.179750	−	0.311336i
$5$	−4.02020	+	6.96320i	−0.359578	+	0.622807i	−0.987890	−	0.155154i	$-0.950413\pi$
$5$	−4.02020	+	6.96320i	−0.359578	+	0.622807i	0.628312	+	0.777961i	$0.283746\pi$
$6$	−17.6853			−1.20333
$7$	15.2781	+	10.4681i	0.824938	+	0.565223i
$7$	15.2781	+	10.4681i	0.824938	+	0.565223i
$8$	−16.8983			−0.746807
$9$	−0.878841	+	1.52220i	−0.0325497	+	0.0563777i
$10$	−13.2581	−	22.9638i	−0.419259	−	0.726178i
$11$	5.50000	+	9.52628i	0.150756	+	0.261116i
$11$	5.50000	+	9.52628i	0.150756	+	0.261116i
$12$	7.71145	−	13.3566i	0.185509	−	0.321311i
$13$	11.3184			0.241473			0.120737	−	0.992685i	$-0.461474\pi$
$13$	11.3184			0.241473			0.120737	+	0.992685i	$0.461474\pi$
$14$	−55.0899	+	26.3737i	−1.05167	+	0.503475i
$15$	−43.1176			−0.742195
$16$	39.3683	−	68.1879i	0.615130	−	1.06544i
$17$	−65.2098	−	112.947i	−0.930335	−	1.61139i	−0.782749	−	0.622338i	$-0.786183\pi$
$17$	−65.2098	−	112.947i	−0.930335	−	1.61139i	−0.147586	−	0.989049i	$-0.547150\pi$
$18$	−2.89831	−	5.02002i	−0.0379521	−	0.0657350i
$19$	−16.7843	+	29.0713i	−0.202663	+	0.351022i	−0.949386	−	0.314113i	$-0.898293\pi$
$19$	−16.7843	+	29.0713i	−0.202663	+	0.351022i	0.746723	+	0.665135i	$0.231626\pi$
$20$	23.1242			0.258537
$21$	−7.65024	+	99.0220i	−0.0794961	+	1.02897i
$22$	−36.2767			−0.351555
$23$	−47.9330	+	83.0224i	−0.434553	+	0.752668i	−0.997259	−	0.0739892i	$-0.976427\pi$
$23$	−47.9330	+	83.0224i	−0.434553	+	0.752668i	0.562706	+	0.826657i	$0.309760\pi$
$24$	−45.3096	−	78.4786i	−0.385366	−	0.667474i
$25$	30.1759	+	52.2663i	0.241407	+	0.418130i
$26$	−18.6633	+	32.3258i	−0.140776	+	0.243831i
$27$	135.365			0.964852
$28$	4.10287	−	53.1061i	0.0276917	−	0.358432i
$29$	162.969			1.04354			0.521768	−	0.853087i	$-0.325273\pi$
$29$	162.969			1.04354			0.521768	+	0.853087i	$0.325273\pi$
$30$	71.0984	−	123.146i	0.432691	−	0.749443i
$31$	100.296	+	173.717i	0.581084	+	1.00647i	0.995351	+	0.0963123i	$0.0307048\pi$
$31$	100.296	+	173.717i	0.581084	+	1.00647i	−0.414267	+	0.910156i	$0.635962\pi$
$32$	62.2386	+	107.801i	0.343823	+	0.595519i
$33$	−29.4944	+	51.0858i	−0.155585	+	0.269482i
$34$	430.108			2.16950
$35$	−134.312	+	64.3004i	−0.648654	+	0.310536i
$36$	5.05510			0.0234032
$37$	24.2728	−	42.0417i	0.107849	−	0.186800i	−0.807049	−	0.590484i	$-0.798937\pi$
$37$	24.2728	−	42.0417i	0.107849	−	0.186800i	0.914899	+	0.403683i	$0.132270\pi$
$38$	−55.3527	−	95.8737i	−0.236300	−	0.409283i
$39$	30.3481	+	52.5644i	0.124605	+	0.215821i
$40$	67.9347	−	117.666i	0.268535	−	0.465117i
$41$	133.331			0.507874			0.253937	−	0.967221i	$-0.418274\pi$
$41$	133.331			0.507874			0.253937	+	0.967221i	$0.418274\pi$
$42$	−270.197	−	185.131i	−0.992673	−	0.680150i
$43$	120.441			0.427141			0.213570	−	0.976928i	$-0.431491\pi$
$43$	120.441			0.427141			0.213570	+	0.976928i	$0.431491\pi$
$44$	15.8180	−	27.3976i	0.0541967	−	0.0938715i
$45$	−7.06624	−	12.2391i	−0.0234083	−	0.0405443i
$46$	−158.077	−	273.798i	−0.506678	−	0.877593i
$47$	−307.522	+	532.643i	−0.954397	+	1.65306i	−0.218656	+	0.975802i	$0.570167\pi$
$47$	−307.522	+	532.643i	−0.954397	+	1.65306i	−0.735742	+	0.677262i	$0.763166\pi$
$48$	422.235			1.26967
$49$	123.839	+	319.864i	0.361046	+	0.932548i
$50$	−199.033			−0.562951
$51$	349.695	−	605.690i	0.960140	−	1.66301i
$52$	−16.2758	−	28.1906i	−0.0434049	−	0.0751794i
$53$	−248.113	−	429.745i	−0.643037	−	1.11377i	−0.984751	−	0.173969i	$-0.944341\pi$
$53$	−248.113	−	429.745i	−0.643037	−	1.11377i	0.341714	−	0.939804i	$-0.388993\pi$
$54$	−223.209	+	386.609i	−0.562497	+	0.974273i
$55$	−88.4445			−0.216834
$56$	−258.174	−	176.893i	−0.616070	−	0.422113i
$57$	−180.016			−0.418311
$58$	−268.726	+	465.446i	−0.608369	+	1.05373i
$59$	−37.6802	−	65.2640i	−0.0831448	−	0.144011i	0.821454	−	0.570274i	$-0.193163\pi$
$59$	−37.6802	−	65.2640i	−0.0831448	−	0.144011i	−0.904599	+	0.426263i	$0.859830\pi$
$60$	62.0032	+	107.393i	0.133410	+	0.231072i
$61$	−12.3185	+	21.3363i	−0.0258561	+	0.0447841i	−0.878664	−	0.477441i	$-0.841564\pi$
$61$	−12.3185	+	21.3363i	−0.0258561	+	0.0447841i	0.852808	+	0.522225i	$0.174898\pi$
$62$	−661.525			−1.35506
$63$	−29.3615	+	14.0565i	−0.0587174	+	0.0281103i
$64$	219.382			0.428481
$65$	−45.5022	+	78.8121i	−0.0868284	+	0.150391i
$66$	−97.2690	−	168.475i	−0.181409	−	0.314209i
$67$	−32.6620	−	56.5723i	−0.0595568	−	0.103155i	0.834710	−	0.550690i	$-0.185635\pi$
$67$	−32.6620	−	56.5723i	−0.0595568	−	0.103155i	−0.894267	+	0.447535i	$0.852302\pi$
$68$	−187.544	+	324.835i	−0.334456	+	0.579294i
$69$	−514.093			−0.896949
$70$	37.8278	−	489.629i	0.0645898	−	0.836027i
$71$	730.333			1.22077			0.610384	−	0.792105i	$-0.291015\pi$
$71$	730.333			1.22077			0.610384	+	0.792105i	$0.291015\pi$
$72$	14.8509	−	25.7226i	0.0243083	−	0.0421033i
$73$	−508.151	−	880.143i	−0.814720	−	1.41114i	−0.909529	−	0.415641i	$-0.863557\pi$
$73$	−508.151	−	880.143i	−0.814720	−	1.41114i	0.0948082	−	0.995496i	$-0.469776\pi$
$74$	80.0488	+	138.649i	0.125750	+	0.217805i
$75$	−161.822	+	280.284i	−0.249141	+	0.431525i
$76$	96.5436			0.145715
$77$	−15.6924	+	203.118i	−0.0232249	+	0.300616i
$78$	−200.168			−0.290572
$79$	678.129	−	1174.55i	0.965765	−	1.67275i	0.258221	−	0.966086i	$-0.416864\pi$
$79$	678.129	−	1174.55i	0.965765	−	1.67275i	0.707544	−	0.706669i	$-0.249803\pi$
$80$	316.537	+	548.259i	0.442374	+	0.766215i
$81$	386.684	+	669.756i	0.530431	+	0.918733i
$82$	−219.855	+	380.800i	−0.296084	+	0.512833i
$83$	−92.4757			−0.122295			−0.0611477	−	0.998129i	$-0.519476\pi$
$83$	−92.4757			−0.122295			−0.0611477	+	0.998129i	$0.519476\pi$
$84$	257.634	−	123.339i	0.334645	−	0.160208i
$85$	1048.63			1.33811
$86$	−198.600	+	343.985i	−0.249018	+	0.431312i
$87$	436.970	+	756.854i	0.538484	+	0.932681i
$88$	−92.9408	−	160.978i	−0.112585	−	0.195004i
$89$	−311.957	+	540.326i	−0.371544	+	0.643533i	−0.989803	−	0.142441i	$-0.954505\pi$
$89$	−311.957	+	540.326i	−0.371544	+	0.643533i	0.618259	+	0.785974i	$0.287838\pi$
$90$	46.6072			0.0545870
$91$	172.923	+	118.482i	0.199200	+	0.136486i
$92$	275.711			0.312444
$93$	−537.847	+	931.578i	−0.599700	+	1.03871i
$94$	−1014.17	−	1756.59i	−1.11280	−	1.92743i
$95$	−134.953	−	233.745i	−0.145746	−	0.252440i
$96$	−333.762	+	578.093i	−0.354838	+	0.614598i
$97$	−122.988			−0.128737			−0.0643687	−	0.997926i	$-0.520503\pi$
$97$	−122.988			−0.128737			−0.0643687	+	0.997926i	$0.520503\pi$
$98$	−1117.75	−	173.747i	−1.15214	−	0.179093i
$99$	−19.3345			−0.0196282
$100$	86.7861	−	150.318i	0.0867861	−	0.150318i
$101$	301.122	+	521.559i	0.296661	+	0.513832i	0.975370	−	0.220575i	$-0.0707935\pi$
$101$	301.122	+	521.559i	0.296661	+	0.513832i	−0.678709	+	0.734407i	$0.737460\pi$
$102$	1153.25	+	1997.49i	1.11950	+	1.93903i
$103$	210.229	−	364.128i	0.201112	−	0.348336i	−0.747775	−	0.663952i	$-0.768878\pi$
$103$	210.229	−	364.128i	0.201112	−	0.348336i	0.948887	+	0.315616i	$0.102211\pi$
$104$	−191.261			−0.180334
$105$	−658.754	−	451.359i	−0.612265	−	0.419506i
$106$	1636.49			1.49953
$107$	227.420	−	393.904i	0.205472	−	0.355889i	−0.744811	−	0.667276i	$-0.767460\pi$
$107$	227.420	−	393.904i	0.205472	−	0.355889i	0.950283	+	0.311387i	$0.100794\pi$
$108$	−194.655	−	337.152i	−0.173432	−	0.300394i
$109$	−536.338	−	928.965i	−0.471301	−	0.816318i	0.528160	−	0.849145i	$-0.322882\pi$
$109$	−536.338	−	928.965i	−0.471301	−	0.816318i	−0.999461	+	0.0328271i	$0.989549\pi$
$110$	145.840	−	252.602i	0.126411	−	0.218951i
$111$	260.332			0.222609
$112$	1315.27	−	629.669i	1.10965	−	0.531233i
$113$	1415.49			1.17839			0.589195	−	0.807991i	$-0.299445\pi$
$113$	1415.49			1.17839			0.589195	+	0.807991i	$0.299445\pi$
$114$	296.836	−	514.134i	0.243870	−	0.422395i
$115$	−385.401	−	667.534i	−0.312511	−	0.541285i
$116$	−234.349	−	405.905i	−0.187576	−	0.324891i
$117$	−9.94705	+	17.2288i	−0.00785987	+	0.0136137i
$118$	248.529			0.193890
$119$	186.055	−	2408.23i	0.143324	−	1.85514i
$120$	728.616			0.554277
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	−40.6249	−	70.3644i	−0.0301476	−	0.0522171i
$123$	357.502	+	619.211i	0.262072	+	0.453922i
$124$	288.450	−	499.611i	0.208900	−	0.361826i
$125$	−1490.30			−1.06637
$126$	8.26938	−	107.036i	0.00584679	−	0.0756787i
$127$	−176.653			−0.123429			−0.0617143	−	0.998094i	$-0.519657\pi$
$127$	−176.653			−0.123429			−0.0617143	+	0.998094i	$0.519657\pi$
$128$	−859.657	+	1488.97i	−0.593622	+	1.02818i
$129$	322.939	+	559.347i	0.220412	+	0.381765i
$130$	−150.061	−	259.913i	−0.101240	−	0.175353i
$131$	484.760	−	839.630i	0.323311	−	0.559991i	−0.657858	−	0.753142i	$-0.728537\pi$
$131$	484.760	−	839.630i	0.323311	−	0.559991i	0.981169	+	0.193151i	$0.0618708\pi$
$132$	169.652			0.111866
$133$	−560.753	+	268.454i	−0.365590	+	0.175022i
$134$	215.431			0.138884
$135$	−544.195	+	942.573i	−0.346939	+	0.600916i
$136$	1101.94	+	1908.61i	0.694781	+	1.20340i
$137$	444.587	+	770.048i	0.277253	+	0.480216i	0.970701	−	0.240290i	$-0.0772426\pi$
$137$	444.587	+	770.048i	0.277253	+	0.480216i	−0.693448	+	0.720507i	$0.743909\pi$
$138$	847.708	−	1468.27i	0.522911	−	0.905708i
$139$	−1145.96			−0.699273			−0.349637	−	0.936885i	$-0.613695\pi$
$139$	−1145.96			−0.699273			−0.349637	+	0.936885i	$0.613695\pi$
$140$	353.294	+	242.066i	0.213277	+	0.146131i
$141$	−3298.24			−1.96995
$142$	−1204.27	+	2085.86i	−0.711694	+	1.23269i
$143$	62.2511	+	107.822i	0.0364035	+	0.0630526i
$144$	69.1970	+	119.853i	0.0400445	+	0.0693592i
$145$	−655.168	+	1134.78i	−0.375232	+	0.649922i
$146$	3351.64			1.89989
$147$	−1153.45	+	1432.78i	−0.647177	+	0.803904i
$148$	−139.617			−0.0775437
$149$	1193.54	−	2067.27i	0.656232	−	1.13663i	−0.325352	−	0.945593i	$-0.605483\pi$
$149$	1193.54	−	2067.27i	0.656232	−	1.13663i	0.981583	−	0.191034i	$-0.0611840\pi$
$150$	−533.669	−	924.343i	−0.290493	−	0.503148i
$151$	949.162	+	1644.00i	0.511535	+	0.886004i	0.999911	+	0.0133708i	$0.00425618\pi$
$151$	949.162	+	1644.00i	0.511535	+	0.886004i	−0.488376	+	0.872633i	$0.662410\pi$
$152$	283.627	−	491.257i	0.151350	−	0.262146i
$153$	229.236			0.121128
$154$	−554.237	−	379.747i	−0.290011	−	0.198707i
$155$	−1612.83			−0.835781
$156$	87.2811	−	151.175i	0.0447954	−	0.0775879i
$157$	182.015	+	315.260i	0.0925248	+	0.160258i	0.908573	−	0.417726i	$-0.137173\pi$
$157$	182.015	+	315.260i	0.0925248	+	0.160258i	−0.816048	+	0.577984i	$0.803840\pi$
$158$	2236.39	+	3873.54i	1.12606	+	1.95039i
$159$	1330.54	−	2304.56i	0.663638	−	1.14945i
$160$	−1000.85			−0.494525
$161$	−1601.41	+	766.655i	−0.783905	+	0.375285i
$162$	−2550.47			−1.23694
$163$	1360.69	−	2356.78i	0.653849	−	1.13250i	−0.328332	−	0.944562i	$-0.606486\pi$
$163$	1360.69	−	2356.78i	0.653849	−	1.13250i	0.982181	−	0.187937i	$-0.0601802\pi$
$164$	−191.730	−	332.087i	−0.0912904	−	0.158120i
$165$	−237.147	−	410.751i	−0.111890	−	0.193799i
$166$	152.487	−	264.115i	0.0712968	−	0.123490i
$167$	−1445.20			−0.669660			−0.334830	−	0.942279i	$-0.608679\pi$
$167$	−1445.20			−0.669660			−0.334830	+	0.942279i	$0.608679\pi$
$168$	129.276	−	1673.31i	0.0593683	−	0.768442i
$169$	−2068.89			−0.941691
$170$	−1729.12	+	2994.93i	−0.780103	+	1.35118i
$171$	−29.5015	−	51.0981i	−0.0131932	−	0.0228513i
$172$	−173.194	−	299.981i	−0.0767786	−	0.132984i
$173$	−1580.14	+	2736.88i	−0.694427	+	1.20278i	0.275947	+	0.961173i	$0.411009\pi$
$173$	−1580.14	+	2736.88i	−0.694427	+	1.20278i	−0.970374	+	0.241609i	$0.922325\pi$
$174$	−2882.15			−1.25572
$175$	−86.0972	+	1114.41i	−0.0371905	+	0.481380i
$176$	866.103			0.370937
$177$	202.064	−	349.986i	0.0858084	−	0.148625i
$178$	−1028.80	−	1781.93i	−0.433212	−	0.750344i
$179$	−1729.26	−	2995.16i	−0.722070	−	1.25066i	−0.960169	−	0.279422i	$-0.909857\pi$
$179$	−1729.26	−	2995.16i	−0.722070	−	1.25066i	0.238098	−	0.971241i	$-0.423476\pi$
$180$	−20.3225	+	35.1996i	−0.00841529	+	0.0145757i
$181$	1449.88			0.595407			0.297704	−	0.954658i	$-0.403779\pi$
$181$	1449.88			0.595407			0.297704	+	0.954658i	$0.403779\pi$
$182$	−623.528	+	298.507i	−0.253951	+	0.121576i
$183$	−132.119			−0.0533688
$184$	809.987	−	1402.94i	0.324527	−	0.562098i
$185$	195.163	+	338.033i	0.0775605	+	0.134339i
$186$	−1773.75	−	3072.23i	−0.699236	−	1.21111i
$187$	717.308	−	1242.41i	0.280507	−	0.485852i
$188$	1768.87			0.686212
$189$	2068.11	+	1417.01i	0.795943	+	0.545356i
$190$	890.117			0.339873
$191$	2361.48	−	4090.21i	0.894612	−	1.54951i	0.0603283	−	0.998179i	$-0.480785\pi$
$191$	2361.48	−	4090.21i	0.894612	−	1.54951i	0.834284	−	0.551335i	$-0.185881\pi$
$192$	588.231	+	1018.85i	0.221104	+	0.382963i
$193$	166.142	+	287.766i	0.0619645	+	0.107326i	0.895343	−	0.445376i	$-0.146930\pi$
$193$	166.142	+	287.766i	0.0619645	+	0.107326i	−0.833379	+	0.552702i	$0.813597\pi$
$194$	202.800	−	351.259i	0.0750524	−	0.129995i
$195$	−488.021			−0.179220
$196$	618.602	−	768.409i	0.225438	−	0.280032i
$197$	4379.06			1.58373			0.791865	−	0.610696i	$-0.209110\pi$
$197$	4379.06			1.58373			0.791865	+	0.610696i	$0.209110\pi$
$198$	31.8814	−	55.2202i	0.0114430	−	0.0198199i
$199$	−620.974	−	1075.56i	−0.221204	−	0.383137i	0.733970	−	0.679182i	$-0.237665\pi$
$199$	−620.974	−	1075.56i	−0.221204	−	0.383137i	−0.955174	+	0.296045i	$0.904332\pi$
$200$	−509.923	−	883.212i	−0.180285	−	0.312263i
$201$	175.154	−	303.376i	0.0614648	−	0.106460i
$202$	−1986.13			−0.691799
$203$	2489.85	+	1705.97i	0.860853	+	0.589831i
$204$	−2011.45			−0.690341
$205$	−536.018	+	928.410i	−0.182620	+	0.316307i
$206$	693.311	+	1200.85i	0.234492	+	0.406152i
$207$	−84.2510	−	145.927i	−0.0282891	−	0.0489982i
$208$	445.585	−	771.776i	0.148537	−	0.257274i
$209$	−369.255			−0.122210
$210$	2375.35	−	1137.17i	0.780545	−	0.373677i
$211$	−4792.72			−1.56372			−0.781858	−	0.623456i	$-0.785728\pi$
$211$	−4792.72			−1.56372			−0.781858	+	0.623456i	$0.785728\pi$
$212$	−713.575	+	1235.95i	−0.231172	+	0.400402i
$213$	1958.25	+	3391.79i	0.629939	+	1.09109i
$214$	750.005	+	1299.05i	0.239576	+	0.414958i
$215$	−484.196	+	838.653i	−0.153590	+	0.266026i
$216$	−2287.44			−0.720558
$217$	−286.161	+	3703.96i	−0.0895200	+	1.15872i
$218$	3537.55			1.09905
$219$	2725.02	−	4719.87i	0.840821	−	1.45634i
$220$	127.183	+	220.288i	0.0389759	+	0.0675082i
$221$	−738.069	−	1278.37i	−0.224651	−	0.389107i
$222$	−429.271	+	743.519i	−0.129778	+	0.224783i
$223$	3670.94			1.10235			0.551176	−	0.834389i	$-0.314179\pi$
$223$	3670.94			1.10235			0.551176	+	0.834389i	$0.314179\pi$
$224$	−177.578	+	2298.50i	−0.0529683	+	0.685603i
$225$	−106.079			−0.0314309
$226$	−2334.06	+	4042.71i	−0.686988	+	1.18990i
$227$	−652.807	−	1130.69i	−0.190874	−	0.330603i	0.754666	−	0.656109i	$-0.227799\pi$
$227$	−652.807	−	1130.69i	−0.190874	−	0.330603i	−0.945540	+	0.325506i	$0.894465\pi$
$228$	258.863	+	448.364i	0.0751914	+	0.130235i
$229$	1451.06	−	2513.31i	0.418729	−	0.725259i	−0.577083	−	0.816685i	$-0.695809\pi$
$229$	1451.06	−	2513.31i	0.418729	−	0.725259i	0.995812	+	0.0914259i	$0.0291425\pi$
$230$	2542.01			0.728761
$231$	−985.388	+	471.743i	−0.280666	+	0.134365i
$232$	−2753.90			−0.779320
$233$	−1964.00	+	3401.74i	−0.552213	+	0.956462i	0.445901	+	0.895082i	$0.352883\pi$
$233$	−1964.00	+	3401.74i	−0.552213	+	0.956462i	−0.998115	+	0.0613795i	$0.980450\pi$
$234$	−32.8042	−	56.8185i	−0.00916442	−	0.0158732i
$235$	−2472.60	−	4282.67i	−0.686360	−	1.18881i
$236$	−108.368	+	187.699i	−0.0298906	+	0.0517720i
$237$	7273.09			1.99341
$238$	6571.22	+	4502.40i	1.78970	+	1.22625i
$239$	5381.14			1.45639			0.728195	−	0.685370i	$-0.240360\pi$
$239$	5381.14			1.45639			0.728195	+	0.685370i	$0.240360\pi$
$240$	−1697.47	+	2940.10i	−0.456546	+	0.790761i
$241$	2310.28	+	4001.53i	0.617504	+	1.06955i	0.989940	+	0.141490i	$0.0451894\pi$
$241$	2310.28	+	4001.53i	0.617504	+	1.06955i	−0.372436	+	0.928058i	$0.621477\pi$
$242$	−199.522	−	345.582i	−0.0529989	−	0.0917968i
$243$	−246.212	+	426.452i	−0.0649980	+	0.112580i
$244$	70.8560			0.0185905
$245$	−2725.13	−	423.605i	−0.710622	−	0.110462i
$246$	−2358.00			−0.611140
$247$	−189.971	+	329.040i	−0.0489376	+	0.0847624i
$248$	−1694.83	−	2935.53i	−0.433958	−	0.751637i
$249$	−247.956	−	429.472i	−0.0631067	−	0.109304i
$250$	2457.42	−	4256.38i	0.621684	−	1.07679i
$251$	5040.75			1.26761			0.633804	−	0.773494i	$-0.281493\pi$
$251$	5040.75			1.26761			0.633804	+	0.773494i	$0.281493\pi$
$252$	77.2321	+	52.9172i	0.0193062	+	0.0132280i
$253$	−1054.53			−0.262045
$254$	291.290	−	504.530i	0.0719574	−	0.124634i
$255$	2811.69	+	4869.99i	0.690490	+	1.19596i
$256$	−1957.52	−	3390.52i	−0.477909	−	0.827763i
$257$	213.687	−	370.117i	0.0518655	−	0.0898337i	−0.838927	−	0.544244i	$-0.816817\pi$
$257$	213.687	−	370.117i	0.0518655	−	0.0898337i	0.890793	+	0.454410i	$0.150150\pi$
$258$	−2130.03			−0.513991
$259$	810.938	−	388.227i	0.194553	−	0.0931399i
$260$	261.729			0.0624297
$261$	−143.224	+	248.071i	−0.0339667	+	0.0588321i
$262$	1598.68	+	2769.00i	0.376973	+	0.652936i
$263$	−2418.07	−	4188.22i	−0.566938	−	0.981966i	−0.996866	−	0.0791028i	$-0.974794\pi$
$263$	−2418.07	−	4188.22i	−0.566938	−	0.981966i	0.429928	−	0.902863i	$-0.358539\pi$
$264$	498.406	−	863.264i	0.116192	−	0.201251i
$265$	3989.86			0.924888
$266$	157.931	−	2044.20i	0.0364036	−	0.471196i
$267$	−3345.82			−0.766894
$268$	−93.9361	+	162.702i	−0.0214107	+	0.0370844i
$269$	−2716.90	−	4705.82i	−0.615809	−	1.06661i	−0.990242	−	0.139358i	$-0.955496\pi$
$269$	−2716.90	−	4705.82i	−0.615809	−	1.06661i	0.374433	−	0.927254i	$-0.377837\pi$
$270$	−1794.69	−	3108.49i	−0.404523	−	0.700654i
$271$	−3698.24	+	6405.54i	−0.828975	+	1.43583i	0.0698687	+	0.997556i	$0.477742\pi$
$271$	−3698.24	+	6405.54i	−0.828975	+	1.43583i	−0.898843	+	0.438270i	$0.855591\pi$
$272$	−10268.8			−2.28911
$273$	−86.5883	+	1120.77i	−0.0191962	+	0.248469i
$274$	−2932.39			−0.646541
$275$	−331.935	+	574.929i	−0.0727871	+	0.126071i
$276$	739.266	+	1280.45i	0.161227	+	0.279253i
$277$	−3017.61	−	5226.65i	−0.654551	−	1.13372i	−0.982006	−	0.188848i	$-0.939524\pi$
$277$	−3017.61	−	5226.65i	−0.654551	−	1.13372i	0.327456	−	0.944867i	$-0.393809\pi$
$278$	1889.62	−	3272.91i	0.407668	−	0.706101i
$279$	−352.575			−0.0756564
$280$	2269.65	−	1086.57i	0.484420	−	0.231910i
$281$	−4720.67			−1.00218			−0.501088	−	0.865396i	$-0.667067\pi$
$281$	−4720.67			−1.00218			−0.501088	+	0.865396i	$0.667067\pi$
$282$	5438.61	−	9419.94i	1.14845	−	1.98918i
$283$	−240.530	−	416.611i	−0.0505232	−	0.0875087i	0.839658	−	0.543116i	$-0.182756\pi$
$283$	−240.530	−	416.611i	−0.0505232	−	0.0875087i	−0.890181	+	0.455607i	$0.849422\pi$
$284$	−1050.22	−	1819.03i	−0.219433	−	0.380070i
$285$	723.701	−	1253.49i	0.150415	−	0.260527i
$286$	−410.593			−0.0848911
$287$	2037.04	+	1395.72i	0.418964	+	0.287062i
$288$	−218.791			−0.0447653
$289$	−6048.13	+	10475.7i	−1.23105	+	2.13223i
$290$	−2160.66	−	3742.38i	−0.437512	−	0.757793i
$291$	−329.769	−	571.176i	−0.0664309	−	0.115062i
$292$	−1461.44	+	2531.30i	−0.292892	+	0.507304i
$293$	−4485.11			−0.894276			−0.447138	−	0.894465i	$-0.647557\pi$
$293$	−4485.11			−0.894276			−0.447138	+	0.894465i	$0.647557\pi$
$294$	−2190.12	−	5656.88i	−0.434457	−	1.12216i
$295$	605.928			0.119588
$296$	−410.170	+	710.435i	−0.0805427	+	0.139504i
$297$	744.507	+	1289.52i	0.145457	+	0.251939i
$298$	3936.15	+	6817.61i	0.765151	+	1.32528i
$299$	−542.523	+	939.678i	−0.104933	+	0.181749i
$300$	930.801			0.179133
$301$	1840.10	+	1260.78i	0.352365	+	0.241430i
$302$	−6260.45			−1.19287
$303$	−1614.80	+	2796.92i	−0.306165	+	0.530293i
$304$	1321.54	+	2288.98i	0.249328	+	0.431848i
$305$	−99.0457	−	171.552i	−0.0185946	−	0.0322067i
$306$	−377.996	+	654.709i	−0.0706164	+	0.122311i
$307$	−1946.79			−0.361920			−0.180960	−	0.983490i	$-0.557920\pi$
$307$	−1946.79			−0.361920			−0.180960	+	0.983490i	$0.557920\pi$
$308$	528.469	−	252.998i	0.0977673	−	0.0468049i
$309$	2254.76			0.415110
$310$	2659.47	−	4606.33i	0.487250	−	0.843942i
$311$	−1906.15	−	3301.55i	−0.347550	−	0.601974i	0.638264	−	0.769818i	$-0.279653\pi$
$311$	−1906.15	−	3301.55i	−0.347550	−	0.601974i	−0.985814	+	0.167844i	$0.946320\pi$
$312$	−512.831	−	888.250i	−0.0930556	−	0.161177i
$313$	108.064	−	187.172i	0.0195148	−	0.0338006i	−0.856103	−	0.516805i	$-0.827121\pi$
$313$	108.064	−	187.172i	0.0195148	−	0.0338006i	0.875618	+	0.483005i	$0.160455\pi$
$314$	−1200.53			−0.215763
$315$	20.1612	−	260.959i	0.00360621	−	0.0466775i
$316$	−3900.60			−0.694386
$317$	−1959.85	+	3394.55i	−0.347243	+	0.601442i	−0.985759	−	0.168167i	$-0.946215\pi$
$317$	−1959.85	+	3394.55i	−0.347243	+	0.601442i	0.638516	+	0.769609i	$0.279549\pi$
$318$	4387.95	+	7600.15i	0.773786	+	1.34024i
$319$	896.328	+	1552.49i	0.157319	+	0.272484i
$320$	−881.960	+	1527.60i	−0.154072	+	0.266861i
$321$	2439.14			0.424110
$322$	451.021	−	5837.86i	0.0780573	−	1.01035i
$323$	4378.01			0.754177
$324$	1112.10	−	1926.22i	0.190690	−	0.330285i
$325$	341.543	+	591.569i	0.0582934	+	0.100967i
$326$	4487.39	+	7772.38i	0.762372	+	1.32047i
$327$	2876.18	−	4981.68i	0.486400	−	0.842470i
$328$	−2253.07			−0.379284
$329$	−10274.1	+	4918.60i	−1.72167	+	0.824229i
$330$	1564.16			0.260922
$331$	−3049.99	+	5282.74i	−0.506473	+	0.877238i	0.493499	+	0.869747i	$0.335718\pi$
$331$	−3049.99	+	5282.74i	−0.506473	+	0.877238i	−0.999972	+	0.00749096i	$0.997616\pi$
$332$	132.980	+	230.328i	0.0219826	+	0.0380750i
$333$	42.6639	+	73.8960i	0.00702092	+	0.0121606i
$334$	2383.05	−	4127.57i	0.390404	−	0.676199i
$335$	525.232			0.0856612
$336$	6450.93	+	4419.98i	1.04740	+	0.717648i
$337$	−3494.81			−0.564909			−0.282454	−	0.959281i	$-0.591149\pi$
$337$	−3494.81			−0.564909			−0.282454	+	0.959281i	$0.591149\pi$
$338$	3411.48	−	5908.86i	0.548994	−	0.950886i
$339$	3795.37	+	6573.77i	0.608071	+	1.05321i
$340$	−1507.93	−	2611.80i	−0.240526	−	0.416603i
$341$	−1103.25	+	1910.89i	−0.175204	+	0.303461i
$342$	194.585			0.0307659
$343$	−1456.34	+	6183.26i	−0.229257	+	0.973366i
$344$	−2035.25			−0.318992
$345$	2066.76	−	3579.73i	0.322523	−	0.558626i
$346$	−5211.11	−	9025.91i	−0.809685	−	1.40242i
$347$	5762.26	+	9980.52i	0.891453	+	1.54404i	0.838134	+	0.545464i	$0.183647\pi$
$347$	5762.26	+	9980.52i	0.891453	+	1.54404i	0.0533187	+	0.998578i	$0.483020\pi$
$348$	1256.73	−	2176.71i	0.193585	−	0.335299i
$349$	−2736.06			−0.419651			−0.209825	−	0.977739i	$-0.567290\pi$
$349$	−2736.06			−0.419651			−0.209825	+	0.977739i	$0.567290\pi$
$350$	−3040.84	−	2083.49i	−0.464400	−	0.318193i
$351$	1532.11			0.232986
$352$	−684.625	+	1185.81i	−0.103667	+	0.179556i
$353$	−5804.24	−	10053.2i	−0.875152	−	1.51581i	−0.856601	−	0.515979i	$-0.827428\pi$
$353$	−5804.24	−	10053.2i	−0.875152	−	1.51581i	−0.0185504	−	0.999828i	$-0.505905\pi$
$354$	666.384	+	1154.21i	0.100051	+	0.173293i
$355$	−2936.09	+	5085.45i	−0.438961	+	0.760303i
$356$	1794.38			0.267141
$357$	11683.1	−	5593.13i	1.73203	−	0.829188i
$358$	11405.7			1.68383
$359$	5509.17	−	9542.16i	0.809924	−	1.40283i	−0.102992	−	0.994682i	$-0.532842\pi$
$359$	5509.17	−	9542.16i	0.809924	−	1.40283i	0.912916	−	0.408147i	$-0.133825\pi$
$360$	119.408	+	206.820i	0.0174815	+	0.0302788i
$361$	2866.07	+	4964.18i	0.417856	+	0.723747i
$362$	−2390.76	+	4140.92i	−0.347115	+	0.601221i
$363$	−648.877			−0.0938215
$364$	46.4378	−	601.074i	0.00668682	−	0.0865518i
$365$	8171.48			1.17182
$366$	217.856	−	377.337i	0.0311134	−	0.0538900i
$367$	207.412	+	359.248i	0.0295009	+	0.0510970i	0.880399	−	0.474234i	$-0.157275\pi$
$367$	207.412	+	359.248i	0.0295009	+	0.0510970i	−0.850898	+	0.525331i	$0.823942\pi$
$368$	3774.08	+	6536.90i	0.534613	+	0.925977i
$369$	−117.177	+	202.956i	−0.0165311	+	0.0286327i
$370$	−1287.25			−0.180867
$371$	707.910	−	9162.94i	0.0990643	−	1.28225i
$372$	3093.70			0.431185
$373$	2317.27	−	4013.63i	0.321672	−	0.557153i	−0.659161	−	0.752002i	$-0.729088\pi$
$373$	2317.27	−	4013.63i	0.321672	−	0.557153i	0.980833	+	0.194849i	$0.0624217\pi$
$374$	2365.59	+	4097.33i	0.327064	+	0.566491i
$375$	−3995.97	−	6921.22i	−0.550269	−	0.953094i
$376$	5196.60	−	9000.78i	0.712751	−	1.23452i
$377$	1844.54			0.251986
$378$	−7457.24	+	3570.07i	−1.01471	+	0.485779i
$379$	−9401.89			−1.27425			−0.637127	−	0.770759i	$-0.719877\pi$
$379$	−9401.89			−1.27425			−0.637127	+	0.770759i	$0.719877\pi$
$380$	−388.125	+	672.252i	−0.0523958	+	0.0907521i
$381$	−473.662	−	820.406i	−0.0636914	−	0.110317i
$382$	7787.88	+	13489.0i	1.04310	+	1.80670i
$383$	1542.65	−	2671.95i	0.205812	−	0.356476i	−0.744579	−	0.667534i	$-0.767350\pi$
$383$	1542.65	−	2671.95i	0.205812	−	0.356476i	0.950391	+	0.311058i	$0.100683\pi$
$384$	−9220.02			−1.22528
$385$	−1351.26	−	925.843i	−0.178874	−	0.122559i
$386$	−1095.83			−0.144498
$387$	−105.848	+	183.335i	−0.0139033	+	0.0240812i
$388$	176.857	+	306.325i	0.0231406	+	0.0400807i
$389$	−2987.88	−	5175.16i	−0.389439	−	0.674527i	0.602936	−	0.797790i	$-0.293998\pi$
$389$	−2987.88	−	5175.16i	−0.389439	−	0.674527i	−0.992374	+	0.123263i	$0.960664\pi$
$390$	804.718	−	1393.81i	0.104483	−	0.180970i
$391$	12502.8			1.61712
$392$	−2092.67	−	5405.16i	−0.269632	−	0.696434i
$393$	5199.17			0.667337
$394$	−7220.80	+	12506.8i	−0.923296	+	1.59920i
$395$	5452.43	+	9443.89i	0.694536	+	1.20297i
$396$	27.8030	+	48.1563i	0.00352817	+	0.00611097i
$397$	4752.52	−	8231.60i	0.600811	−	1.04064i	−0.391887	−	0.920013i	$-0.628178\pi$
$397$	4752.52	−	8231.60i	0.600811	−	1.04064i	0.992698	−	0.120622i	$-0.0384890\pi$
$398$	4095.79			0.515838
$399$	−2750.30	−	1884.42i	−0.345080	−	0.236439i
$400$	4751.90			0.593988
$401$	107.889	−	186.870i	0.0134358	−	0.0232714i	−0.859229	−	0.511591i	$-0.829056\pi$
$401$	107.889	−	186.870i	0.0134358	−	0.0232714i	0.872665	+	0.488319i	$0.162390\pi$
$402$	577.637	+	1000.50i	0.0716664	+	0.124130i
$403$	1135.18	+	1966.19i	0.140316	+	0.243035i
$404$	866.028	−	1500.00i	0.106650	−	0.184723i
$405$	−6218.19			−0.762925
$406$	−8977.94	+	4298.08i	−1.09746	+	0.525395i
$407$	534.002			0.0650356
$408$	−5909.26	+	10235.1i	−0.717039	+	1.24195i
$409$	−8062.33	−	13964.4i	−0.974710	−	1.68825i	−0.680889	−	0.732387i	$-0.738406\pi$
$409$	−8062.33	−	13964.4i	−0.974710	−	1.68825i	−0.293821	−	0.955860i	$-0.594927\pi$
$410$	−1767.72	−	3061.79i	−0.212931	−	0.368807i
$411$	−2384.15	+	4129.47i	−0.286135	+	0.495601i
$412$	−1209.24			−0.144600
$413$	107.508	−	1391.55i	0.0128090	−	0.165795i
$414$	555.699			0.0659689
$415$	371.771	−	643.926i	0.0439747	−	0.0761665i
$416$	704.440	+	1220.13i	0.0830241	+	0.143802i
$417$	−3072.67	−	5322.02i	−0.360838	−	0.624989i
$418$	608.880	−	1054.61i	0.0712471	−	0.123404i
$419$	−5037.11			−0.587300			−0.293650	−	0.955913i	$-0.594870\pi$
$419$	−5037.11			−0.587300			−0.293650	+	0.955913i	$0.594870\pi$
$420$	−176.906	+	2289.81i	−0.0205527	+	0.266027i
$421$	−111.355			−0.0128910			−0.00644549	−	0.999979i	$-0.502052\pi$
$421$	−111.355			−0.0128910			−0.00644549	+	0.999979i	$0.502052\pi$
$422$	7902.90	−	13688.2i	0.911628	−	1.57899i
$423$	−540.526	−	936.218i	−0.0621306	−	0.107613i
$424$	4192.70	+	7261.96i	0.480225	+	0.831774i
$425$	3935.53	−	6816.54i	0.449180	−	0.778002i
$426$	−12916.1			−1.46899
$427$	−411.552	+	197.026i	−0.0466426	+	0.0223296i
$428$	−1308.12			−0.147735
$429$	−333.829	+	578.208i	−0.0375697	+	0.0650726i
$430$	−1596.82	−	2765.78i	−0.179083	−	0.310180i
$431$	6393.96	+	11074.7i	0.714585	+	1.23770i	0.963119	+	0.269075i	$0.0867178\pi$
$431$	6393.96	+	11074.7i	0.714585	+	1.23770i	−0.248534	+	0.968623i	$0.579949\pi$
$432$	5329.09	−	9230.25i	0.593509	−	1.02799i
$433$	−11918.7			−1.32281			−0.661405	−	0.750029i	$-0.730039\pi$
$433$	−11918.7			−1.32281			−0.661405	+	0.750029i	$0.730039\pi$
$434$	−10106.8	−	6924.90i	−1.11784	−	0.765912i
$435$	−7026.83			−0.774507
$436$	−1542.51	+	2671.70i	−0.169433	+	0.293467i
$437$	−1609.05	−	2786.95i	−0.176135	−	0.305075i
$438$	8986.79	+	15565.6i	0.980377	+	1.69806i
$439$	−1198.21	+	2075.37i	−0.130268	+	0.225631i	−0.923780	−	0.382924i	$-0.874917\pi$
$439$	−1198.21	+	2075.37i	−0.130268	+	0.225631i	0.793512	+	0.608555i	$0.208250\pi$
$440$	1494.56			0.161933
$441$	−595.731	−	92.6026i	−0.0643268	−	0.00999920i
$442$	4868.12			0.523875
$443$	−2940.83	+	5093.67i	−0.315402	+	0.546293i	−0.979523	−	0.201333i	$-0.935473\pi$
$443$	−2940.83	+	5093.67i	−0.315402	+	0.546293i	0.664121	+	0.747625i	$0.268806\pi$
$444$	−374.357	−	648.406i	−0.0400140	−	0.0693063i
$445$	−2508.26	−	4344.44i	−0.267198	−	0.462801i
$446$	−6053.16	+	10484.4i	−0.642658	+	1.11312i
$447$	12801.0			1.35451
$448$	3351.73	+	2296.51i	0.353470	+	0.242187i
$449$	10877.6			1.14331			0.571657	−	0.820493i	$-0.306301\pi$
$449$	10877.6			1.14331			0.571657	+	0.820493i	$0.306301\pi$
$450$	174.918	−	302.968i	0.0183239	−	0.0317379i
$451$	733.321	+	1270.15i	0.0765648	+	0.132614i
$452$	−2035.48	−	3525.55i	−0.211816	−	0.366876i
$453$	−5090.00	+	8816.13i	−0.527923	+	0.914389i
$454$	4305.75			0.445108
$455$	−1520.20	+	727.776i	−0.156633	+	0.0749861i
$456$	3041.97			0.312397
$457$	−3646.27	+	6315.53i	−0.373229	+	0.646451i	−0.990060	−	0.140644i	$-0.955083\pi$
$457$	−3646.27	+	6315.53i	−0.373229	+	0.646451i	0.616831	+	0.787095i	$0.288416\pi$
$458$	4785.43	+	8288.60i	0.488228	+	0.845635i
$459$	−8827.12	−	15289.0i	−0.897635	−	1.55475i
$460$	−1108.41	+	1919.83i	−0.112348	+	0.194592i
$461$	19348.0			1.95472			0.977360	−	0.211585i	$-0.0678625\pi$
$461$	19348.0			1.95472			0.977360	+	0.211585i	$0.0678625\pi$
$462$	277.525	−	3592.19i	0.0279473	−	0.361740i
$463$	−1268.32			−0.127309			−0.0636544	−	0.997972i	$-0.520276\pi$
$463$	−1268.32			−0.127309			−0.0636544	+	0.997972i	$0.520276\pi$
$464$	6415.81	−	11112.5i	0.641910	−	1.11182i
$465$	−4324.51	−	7490.27i	−0.431278	−	0.746995i
$466$	−6477.02	−	11218.5i	−0.643868	−	1.11521i
$467$	−7189.85	+	12453.2i	−0.712433	+	1.23397i	0.251508	+	0.967855i	$0.419074\pi$
$467$	−7189.85	+	12453.2i	−0.712433	+	1.23397i	−0.963941	+	0.266116i	$0.914260\pi$
$468$	57.2155			0.00565126
$469$	93.1904	−	1206.22i	0.00917513	−	0.118760i
$470$	16308.7			1.60056
$471$	−976.078	+	1690.62i	−0.0954890	+	0.165392i
$472$	636.732	+	1102.85i	0.0620931	+	0.107548i
$473$	662.424	+	1147.35i	0.0643939	+	0.111533i
$474$	−11992.9	+	20772.3i	−1.16213	+	2.01288i
$475$	−2025.93			−0.195697
$476$	−6265.70	+	2999.63i	−0.603336	+	0.288840i
$477$	872.208			0.0837226
$478$	−8873.18	+	15368.8i	−0.849058	+	1.47061i
$479$	−436.673	−	756.339i	−0.0416536	−	0.0721462i	0.844447	−	0.535639i	$-0.179929\pi$
$479$	−436.673	−	756.339i	−0.0416536	−	0.0721462i	−0.886101	+	0.463493i	$0.846596\pi$
$480$	−2683.58	−	4648.10i	−0.255184	−	0.441991i
$481$	274.729	−	475.844i	0.0260427	−	0.0451073i
$482$	−15238.1			−1.43999
$483$	−7854.34	−	5381.56i	−0.739928	−	0.506976i
$484$	347.996			0.0326819
$485$	494.436	−	856.389i	0.0462911	−	0.0801786i
$486$	−811.978	−	1406.39i	−0.0757862	−	0.131265i
$487$	1292.10	+	2237.98i	0.120227	+	0.208239i	0.919857	−	0.392254i	$-0.128304\pi$
$487$	1292.10	+	2237.98i	0.120227	+	0.208239i	−0.799630	+	0.600493i	$0.794971\pi$
$488$	208.162	−	360.547i	0.0193095	−	0.0334451i
$489$	14593.7			1.34959
$490$	5703.41	−	7084.61i	0.525824	−	0.653163i
$491$	−1300.12			−0.119499			−0.0597493	−	0.998213i	$-0.519030\pi$
$491$	−1300.12			−0.119499			−0.0597493	+	0.998213i	$0.519030\pi$
$492$	1028.18	−	1780.85i	0.0942150	−	0.163185i
$493$	−10627.2	−	18406.8i	−0.970838	−	1.68154i
$494$	−626.503	−	1085.13i	−0.0570601	−	0.0988310i
$495$	77.7286	−	134.630i	0.00705786	−	0.0122246i
$496$	15793.9			1.42977
$497$	11158.1	+	7645.18i	1.00706	+	0.690006i
$498$	1635.46			0.147162
$499$	4664.83	−	8079.73i	0.418490	−	0.724846i	−0.577298	−	0.816534i	$-0.695893\pi$
$499$	4664.83	−	8079.73i	0.418490	−	0.724846i	0.995788	+	0.0916876i	$0.0292261\pi$
$500$	2143.06	+	3711.89i	0.191681	+	0.332001i
$501$	−3875.04	−	6711.76i	−0.345557	−	0.598522i
$502$	−8311.90	+	14396.6i	−0.739000	+	1.27999i
$503$	−13979.5			−1.23919			−0.619597	−	0.784920i	$-0.712704\pi$
$503$	−13979.5			−1.23919			−0.619597	+	0.784920i	$0.712704\pi$
$504$	496.159	−	237.531i	0.0438506	−	0.0209930i
$505$	−4842.29			−0.426691
$506$	1738.85	−	3011.77i	0.152769	−	0.264604i
$507$	−5547.35	−	9608.29i	−0.485930	−	0.841655i
$508$	254.028	+	439.989i	0.0221863	+	0.0384278i
$509$	−8492.22	+	14709.0i	−0.739511	+	1.28087i	0.213205	+	0.977008i	$0.431610\pi$
$509$	−8492.22	+	14709.0i	−0.739511	+	1.28087i	−0.952716	+	0.303863i	$0.901723\pi$
$510$	−18545.2			−1.61019
$511$	1449.84	−	18766.3i	0.125513	−	1.62460i
$512$	−843.211			−0.0727832
$513$	−2272.01	+	3935.24i	−0.195539	+	0.338684i
$514$	704.714	+	1220.60i	0.0604739	+	0.104744i
$515$	1690.33	+	2927.74i	0.144631	+	0.250508i
$516$	928.774	−	1608.68i	0.0792383	−	0.137245i
$517$	−6765.48			−0.575523
$518$	−228.393	+	2956.24i	−0.0193726	+	0.250752i
$519$	−16947.4			−1.43335
$520$	768.910	−	1331.79i	0.0648441	−	0.112313i
$521$	9655.21	+	16723.3i	0.811905	+	1.40626i	0.911529	+	0.411236i	$0.134903\pi$
$521$	9655.21	+	16723.3i	0.811905	+	1.40626i	−0.0996237	+	0.995025i	$0.531764\pi$
$522$	−472.334	−	818.107i	−0.0396044	−	0.0685969i
$523$	−7411.17	+	12836.5i	−0.619632	+	1.07323i	0.369920	+	0.929064i	$0.379385\pi$
$523$	−7411.17	+	12836.5i	−0.619632	+	1.07323i	−0.989553	+	0.144171i	$0.953948\pi$
$524$	−2788.34			−0.232461
$525$	−5406.36	+	2588.23i	−0.449434	+	0.215161i
$526$	15949.0			1.32207
$527$	13080.5	−	22656.1i	1.08121	−	1.87270i
$528$	2322.29	+	4022.32i	0.191410	+	0.331533i
$529$	1488.36	+	2577.91i	0.122327	+	0.211877i
$530$	−6579.04	+	11395.2i	−0.539199	+	0.933920i
$531$	132.460			0.0108253
$532$	1475.00	+	1010.63i	0.120206	+	0.0823613i
$533$	1509.09			0.122638
$534$	5517.05	−	9555.81i	0.447090	−	0.774383i
$535$	1828.55	+	3167.14i	0.147767	+	0.255939i
$536$	551.934	+	955.977i	0.0444774	+	0.0770372i
$537$	9273.34	−	16061.9i	0.745203	−	1.29073i
$538$	17920.0			1.43604
$539$	−2366.00	+	2938.97i	−0.189074	+	0.234862i
$540$	3130.21			0.249450
$541$	−3581.50	+	6203.34i	−0.284622	+	0.492980i	−0.972517	−	0.232830i	$-0.925201\pi$
$541$	−3581.50	+	6203.34i	−0.284622	+	0.492980i	0.687895	+	0.725810i	$0.258535\pi$
$542$	−12196.3	−	21124.7i	−0.966565	−	1.67414i
$543$	3887.57	+	6733.48i	0.307241	+	0.532157i
$544$	8117.14	−	14059.3i	0.639741	−	1.10806i
$545$	8624.75			0.677878
$546$	−3058.19	−	2095.38i	−0.239704	−	0.164238i
$547$	−14261.9			−1.11480			−0.557398	−	0.830246i	$-0.688200\pi$
$547$	−14261.9			−1.11480			−0.557398	+	0.830246i	$0.688200\pi$
$548$	1278.63	−	2214.66i	0.0996726	−	0.172638i
$549$	−21.6520	−	37.5023i	−0.00168321	−	0.00291541i
$550$	−1094.68	−	1896.05i	−0.0848680	−	0.146996i
$551$	−2735.32	+	4737.72i	−0.211486	+	0.366304i
$552$	8687.30			0.669848
$553$	22655.8	−	10846.2i	1.74218	−	0.834046i
$554$	19903.4			1.52638
$555$	−1046.59	+	1812.74i	−0.0800452	+	0.138642i
$556$	1647.89	+	2854.23i	0.125694	+	0.217709i
$557$	7477.81	+	12952.0i	0.568842	+	0.985264i	0.996681	+	0.0814085i	$0.0259418\pi$
$557$	7477.81	+	12952.0i	0.568842	+	0.985264i	−0.427839	+	0.903855i	$0.640725\pi$
$558$	581.376	−	1006.97i	0.0441068	−	0.0763952i
$559$	1363.19			0.103143
$560$	−903.135	+	11689.9i	−0.0681508	+	0.882120i
$561$	7693.29			0.578986
$562$	7784.10	−	13482.5i	0.584257	−	1.01196i
$563$	−6703.05	−	11610.0i	−0.501776	−	0.869101i	−0.999998	−	0.00205162i	$-0.999347\pi$
$563$	−6703.05	−	11610.0i	−0.501776	−	0.869101i	0.498222	−	0.867049i	$-0.333986\pi$
$564$	4742.88	+	8214.91i	0.354098	+	0.613316i
$565$	−5690.56	+	9856.34i	−0.423723	+	0.733910i
$566$	1586.48			0.117818
$567$	−1103.28	+	14280.4i	−0.0817165	+	1.05771i
$568$	−12341.4			−0.911679
$569$	1423.93	−	2466.31i	0.104911	−	0.181710i	−0.808791	−	0.588096i	$-0.799878\pi$
$569$	1423.93	−	2466.31i	0.104911	−	0.181710i	0.913702	+	0.406386i	$0.133211\pi$
$570$	2386.68	+	4133.85i	0.175381	+	0.303768i
$571$	−9573.38	−	16581.6i	−0.701635	−	1.21527i	−0.967892	−	0.251365i	$-0.919120\pi$
$571$	−9573.38	−	16581.6i	−0.701635	−	1.21527i	0.266257	−	0.963902i	$-0.414213\pi$
$572$	179.034	−	310.096i	0.0130871	−	0.0226675i
$573$	25327.5			1.84654
$574$	−7345.20	+	3516.43i	−0.534116	+	0.255702i
$575$	−5785.69			−0.419617
$576$	−192.802	+	333.943i	−0.0139469	+	0.0241567i
$577$	−8595.67	−	14888.1i	−0.620177	−	1.07418i	−0.989452	−	0.144858i	$-0.953727\pi$
$577$	−8595.67	−	14888.1i	−0.620177	−	1.07418i	0.369275	−	0.929320i	$-0.379606\pi$
$578$	−19946.0	−	34547.5i	−1.43537	−	2.48613i
$579$	−890.955	+	1543.18i	−0.0639496	+	0.110764i
$580$	3768.53			0.269792
$581$	−1412.85	−	968.042i	−0.100886	−	0.0691242i
$582$	2175.07			0.154914
$583$	2729.25	−	4727.19i	0.193883	−	0.335815i
$584$	8586.90	+	14872.9i	0.608439	+	1.05385i
$585$	−79.9783	−	138.527i	−0.00565247	−	0.00979037i
$586$	7395.68	−	12809.7i	0.521352	−	0.903009i
$587$	1783.11			0.125378			0.0626891	−	0.998033i	$-0.480032\pi$
$587$	1783.11			0.125378			0.0626891	+	0.998033i	$0.480032\pi$
$588$	5227.28	+	812.548i	0.366615	+	0.0569880i
$589$	−6733.58			−0.471057
$590$	−999.138	+	1730.56i	−0.0697184	+	0.120756i
$591$	11741.6	+	20337.1i	0.817234	+	1.41549i
$592$	−1911.16	−	3310.22i	−0.132683	−	0.229813i
$593$	−2446.22	+	4236.98i	−0.169400	+	0.293410i	−0.938209	−	0.346069i	$-0.887516\pi$
$593$	−2446.22	+	4236.98i	−0.169400	+	0.293410i	0.768809	+	0.639478i	$0.220850\pi$
$594$	−4910.59			−0.339198
$595$	16021.0	+	10977.1i	1.10386	+	0.756331i
$596$	−6865.25			−0.471831
$597$	3330.05	−	5767.81i	0.228291	−	0.395411i
$598$	−1789.18	−	3098.94i	−0.122349	−	0.211915i
$599$	12170.2	+	21079.4i	0.830152	+	1.43787i	0.897917	+	0.440164i	$0.145080\pi$
$599$	12170.2	+	21079.4i	0.830152	+	1.43787i	−0.0677655	+	0.997701i	$0.521587\pi$
$600$	2734.52	−	4736.33i	0.186061	−	0.322266i
$601$	11554.7			0.784239			0.392120	−	0.919914i	$-0.371742\pi$
$601$	11554.7			0.784239			0.392120	+	0.919914i	$0.371742\pi$
$602$	−6635.07	+	3176.46i	−0.449212	+	0.215055i
$603$	114.819			0.00775421
$604$	2729.79	−	4728.14i	0.183897	−	0.318519i
$605$	−486.445	−	842.547i	−0.0326889	−	0.0566188i
$606$	−5325.42	−	9223.90i	−0.356981	−	0.618309i
$607$	−1225.21	+	2122.13i	−0.0819271	+	0.141902i	−0.904078	−	0.427368i	$-0.859441\pi$
$607$	−1225.21	+	2122.13i	−0.0819271	+	0.141902i	0.822151	+	0.569270i	$0.192774\pi$
$608$	−4178.54			−0.278721
$609$	−1246.75	+	16137.5i	−0.0829571	+	1.07377i
$610$	653.281			0.0433616
$611$	−3480.65	+	6028.66i	−0.230461	+	0.399171i
$612$	−329.642	−	570.956i	−0.0217728	−	0.0377117i
$613$	9213.17	+	15957.7i	0.607041	+	1.05143i	0.991725	+	0.128378i	$0.0409772\pi$
$613$	9213.17	+	15957.7i	0.607041	+	1.05143i	−0.384684	+	0.923048i	$0.625690\pi$
$614$	3210.15	−	5560.14i	0.210995	−	0.365454i
$615$	−5748.92			−0.376941
$616$	265.176	−	3432.35i	0.0173446	−	0.224502i
$617$	12132.0			0.791600			0.395800	−	0.918337i	$-0.370467\pi$
$617$	12132.0			0.791600			0.395800	+	0.918337i	$0.370467\pi$
$618$	−3717.96	+	6439.70i	−0.242004	+	0.419163i
$619$	14678.1	+	25423.3i	0.953091	+	1.65080i	0.738677	+	0.674060i	$0.235451\pi$
$619$	14678.1	+	25423.3i	0.953091	+	1.65080i	0.214414	+	0.976743i	$0.431216\pi$
$620$	2319.26	+	4017.07i	0.150232	+	0.260209i
$621$	−6488.45	+	11238.3i	−0.419279	+	0.726213i
$622$	12572.5			0.810470
$623$	−10422.3	+	4989.55i	−0.670241	+	0.320870i
$624$	4779.01			0.306592
$625$	2219.33	−	3844.00i	0.142037	−	0.246016i
$626$	356.381	+	617.270i	0.0227537	+	0.0394106i
$627$	−990.088	−	1714.88i	−0.0630627	−	0.109228i
$628$	523.476	−	906.688i	0.0332627	−	0.0576127i
$629$	−6331.30			−0.401344
$630$	712.068	+	487.888i	0.0450309	+	0.0308538i
$631$	5914.17			0.373121			0.186561	−	0.982443i	$-0.440266\pi$
$631$	5914.17			0.373121			0.186561	+	0.982443i	$0.440266\pi$
$632$	−11459.2	+	19848.0i	−0.721241	+	1.24923i
$633$	−12850.8	−	22258.2i	−0.806906	−	1.39760i
$634$	−6463.33	−	11194.8i	−0.404877	−	0.701267i
$635$	710.182	−	1230.07i	0.0443822	−	0.0768722i
$636$	−7653.26			−0.477156
$637$	1401.65	+	3620.34i	0.0871829	+	0.225185i
$638$	−5911.96			−0.366860
$639$	−641.846	+	1111.71i	−0.0397356	+	0.0688241i
$640$	−6911.99	−	11971.9i	−0.426907	−	0.739424i
$641$	−5076.35	−	8792.50i	−0.312799	−	0.541783i	0.666169	−	0.745801i	$-0.267933\pi$
$641$	−5076.35	−	8792.50i	−0.312799	−	0.541783i	−0.978967	+	0.204018i	$0.934600\pi$
$642$	−4021.99	+	6966.29i	−0.247251	+	0.428252i
$643$	−10272.5			−0.630029			−0.315014	−	0.949087i	$-0.602009\pi$
$643$	−10272.5			−0.630029			−0.315014	+	0.949087i	$0.602009\pi$
$644$	4212.33	+	2886.16i	0.257747	+	0.176601i
$645$	−5193.12			−0.317022
$646$	−7219.08	+	12503.8i	−0.439676	+	0.761541i
$647$	6976.97	+	12084.5i	0.423946	+	0.734296i	0.996321	−	0.0856956i	$-0.0273112\pi$
$647$	6976.97	+	12084.5i	0.423946	+	0.734296i	−0.572375	+	0.819992i	$0.693978\pi$
$648$	−6534.31	−	11317.8i	−0.396129	−	0.686116i
$649$	414.482	−	717.904i	0.0250691	−	0.0434209i
$650$	−2252.73			−0.135938
$651$	−17969.1	+	8602.49i	−1.08182	+	0.517908i
$652$	−7826.69			−0.470118
$653$	−11802.2	+	20442.1i	−0.707285	+	1.22505i	0.258575	+	0.965991i	$0.416747\pi$
$653$	−11802.2	+	20442.1i	−0.707285	+	1.22505i	−0.965860	+	0.259063i	$0.916586\pi$
$654$	9485.28	+	16429.0i	0.567131	+	0.982300i
$655$	3897.67	+	6750.96i	0.232511	+	0.402721i
$656$	5249.02	−	9091.57i	0.312408	−	0.541107i
$657$	1786.34			0.106075
$658$	2893.60	−	37453.8i	0.171435	−	2.21900i
$659$	19192.6			1.13450			0.567251	−	0.823545i	$-0.308007\pi$
$659$	19192.6			1.13450			0.567251	+	0.823545i	$0.308007\pi$
$660$	−682.036	+	1181.32i	−0.0402245	+	0.0696709i
$661$	−12094.1	−	20947.6i	−0.711659	−	1.23263i	−0.964234	−	0.265053i	$-0.914611\pi$
$661$	−12094.1	−	20947.6i	−0.711659	−	1.23263i	0.252575	−	0.967577i	$-0.418723\pi$
$662$	−10058.5	−	17421.8i	−0.590536	−	1.02284i
$663$	3957.98	−	6855.42i	0.231848	−	0.401573i
$664$	1562.68			0.0913311
$665$	385.044	−	4983.87i	0.0224532	−	0.290626i
$666$	−281.401			−0.0163724
$667$	−7811.58	+	13530.1i	−0.453472	+	0.785436i
$668$	2078.20	+	3599.55i	0.120371	+	0.208489i
$669$	9842.93	+	17048.4i	0.568833	+	0.985248i
$670$	−866.076	+	1500.09i	−0.0499395	+	0.0864977i
$671$	−271.007			−0.0155918
$672$	−11150.8	+	5338.30i	−0.640104	+	0.306442i
$673$	−13666.8			−0.782790			−0.391395	−	0.920223i	$-0.628007\pi$
$673$	−13666.8			−0.782790			−0.391395	+	0.920223i	$0.628007\pi$
$674$	5762.72	−	9981.33i	0.329335	−	0.570425i
$675$	4084.76	+	7075.02i	0.232922	+	0.403433i
$676$	2975.07	+	5152.98i	0.169269	+	0.293183i
$677$	3824.52	−	6624.27i	0.217117	−	0.376058i	−0.736808	−	0.676102i	$-0.763668\pi$
$677$	3824.52	−	6624.27i	0.217117	−	0.376058i	0.953925	+	0.300044i	$0.0970013\pi$
$678$	−25033.3			−1.41799
$679$	−1879.02	−	1287.45i	−0.106200	−	0.0727654i
$680$	−17720.0			−0.999311
$681$	3500.75	−	6063.48i	0.196988	−	0.341194i
$682$	−3638.39	−	6301.88i	−0.204283	−	0.353829i
$683$	−15349.2	−	26585.6i	−0.859914	−	1.48941i	−0.872010	−	0.489487i	$-0.837184\pi$
$683$	−15349.2	−	26585.6i	−0.859914	−	1.48941i	0.0120967	−	0.999927i	$-0.496149\pi$
$684$	−84.8465	+	146.958i	−0.00474296	+	0.00821505i
$685$	−7149.33			−0.398776
$686$	−15258.2	−	14355.2i	−0.849217	−	0.798957i
$687$	15563.0			0.864287
$688$	4741.55	−	8212.61i	0.262747	−	0.455091i
$689$	−2808.24	−	4864.01i	−0.155276	−	0.268946i
$690$	6815.91	+	11805.5i	0.376054	+	0.651345i
$691$	12376.3	−	21436.4i	0.681357	−	1.18015i	−0.293210	−	0.956048i	$-0.594723\pi$
$691$	12376.3	−	21436.4i	0.681357	−	1.18015i	0.974567	−	0.224097i	$-0.0719432\pi$
$692$	9088.97			0.499293
$693$	−295.394	−	202.395i	−0.0161920	−	0.0110943i
$694$	−38006.4			−2.07883
$695$	4606.99	−	7979.54i	0.251443	−	0.435512i
$696$	−7384.05	−	12789.6i	−0.402143	−	0.696533i
$697$	−8694.49	−	15059.3i	−0.472493	−	0.818381i
$698$	4511.60	−	7814.32i	0.244651	−	0.423749i
$699$	−21064.3			−1.13981
$700$	2899.46	−	1388.08i	0.156556	−	0.0749495i
$701$	−8065.58			−0.434569			−0.217284	−	0.976108i	$-0.569720\pi$
$701$	−8065.58			−0.434569			−0.217284	+	0.976108i	$0.569720\pi$
$702$	−2526.36	+	4375.78i	−0.135828	+	0.235261i
$703$	814.806	+	1411.29i	0.0437141	+	0.0757150i
$704$	1206.60	+	2089.89i	0.0645959	+	0.111883i
$705$	13259.6	−	22966.3i	0.708349	−	1.22690i
$706$	38283.4			2.04081
$707$	−859.153	+	11120.6i	−0.0457027	+	0.591559i
$708$	−1162.28			−0.0616963
$709$	15591.5	−	27005.2i	0.825882	−	1.43047i	−0.0753618	−	0.997156i	$-0.524011\pi$
$709$	15591.5	−	27005.2i	0.825882	−	1.43047i	0.901244	−	0.433313i	$-0.142655\pi$
$710$	−9682.86	−	16771.2i	−0.511818	−	0.886496i
$711$	1191.93	+	2064.49i	0.0628707	+	0.108895i
$712$	5271.56	−	9130.60i	0.277472	−	0.480595i
$713$	−19229.9			−1.01005
$714$	−3290.43	+	42590.1i	−0.172467	+	2.23235i
$715$	−1001.05			−0.0523595
$716$	−4973.34	+	8614.08i	−0.259585	+	0.449614i
$717$	14428.5	+	24990.9i	0.751524	+	1.30168i
$718$	18168.6	+	31468.9i	0.944352	+	1.63567i
$719$	10014.5	−	17345.7i	0.519442	−	0.899700i	−0.480303	−	0.877103i	$-0.659473\pi$
$719$	10014.5	−	17345.7i	0.519442	−	0.899700i	0.999745	−	0.0225970i	$-0.00719345\pi$
$720$	−1112.74			−0.0575965
$721$	7023.62	−	3362.48i	0.362792	−	0.173683i
$722$	−18903.9			−0.974419
$723$	−12389.2	+	21458.7i	−0.637287	+	1.10381i
$724$	−2084.93	−	3611.20i	−0.107025	−	0.185372i
$725$	4917.74	+	8517.77i	0.251917	+	0.436334i
$726$	1069.96	−	1853.22i	0.0546968	−	0.0947377i
$727$	17160.3			0.875433			0.437717	−	0.899113i	$-0.355787\pi$
$727$	17160.3			0.875433			0.437717	+	0.899113i	$0.355787\pi$
$728$	−2922.11	−	2002.14i	−0.148764	−	0.101929i
$729$	18240.3			0.926701
$730$	−13474.3	+	23338.1i	−0.683158	+	1.18326i
$731$	−7853.92	−	13603.4i	−0.397384	−	0.688289i
$732$	189.987	+	329.067i	0.00959306	+	0.0166157i
$733$	10095.7	−	17486.2i	0.508719	−	0.881128i	−0.491230	−	0.871030i	$-0.663452\pi$
$733$	10095.7	−	17486.2i	0.508719	−	0.881128i	0.999949	−	0.0100978i	$-0.00321428\pi$
$734$	−1368.04			−0.0687946
$735$	−5339.63	−	13791.8i	−0.267966	−	0.692133i
$736$	−11933.1			−0.597638
$737$	359.282	−	622.295i	0.0179570	−	0.0311025i
$738$	−386.435	−	669.325i	−0.0192749	−	0.0333851i
$739$	3624.23	+	6277.34i	0.180405	+	0.312471i	0.942019	−	0.335561i	$-0.108926\pi$
$739$	3624.23	+	6277.34i	0.180405	+	0.312471i	−0.761614	+	0.648032i	$0.775592\pi$
$740$	561.290	−	972.183i	0.0278830	−	0.0482948i
$741$	−2037.49			−0.101011
$742$	25002.5	+	17131.0i	1.23702	+	0.847570i
$743$	−28533.2			−1.40886			−0.704428	−	0.709775i	$-0.748797\pi$
$743$	−28533.2			−1.40886			−0.704428	+	0.709775i	$0.748797\pi$
$744$	9088.71	−	15742.1i	0.447861	−	0.775717i
$745$	9596.54	+	16621.7i	0.471933	+	0.817412i
$746$	7642.08	+	13236.5i	0.375062	+	0.649627i
$747$	81.2714	−	140.766i	0.00398068	−	0.00689473i
$748$	−4125.96			−0.201684
$749$	7597.96	−	3637.43i	0.370659	−	0.177448i
$750$	26356.4			1.28320
$751$	−9106.32	+	15772.6i	−0.442469	+	0.766379i	−0.997872	−	0.0652021i	$-0.979231\pi$
$751$	−9106.32	+	15772.6i	−0.442469	+	0.766379i	0.555403	+	0.831581i	$0.312564\pi$
$752$	24213.2	+	41938.6i	1.17416	+	2.03370i
$753$	13515.8	+	23410.1i	0.654109	+	1.13295i
$754$	−3041.54	+	5268.10i	−0.146905	+	0.254447i
$755$	−15263.3			−0.735746
$756$	555.384	−	7188.70i	0.0267184	−	0.345834i
$757$	−24987.1			−1.19970			−0.599848	−	0.800114i	$-0.704772\pi$
$757$	−24987.1			−1.19970			−0.599848	+	0.800114i	$0.704772\pi$
$758$	15503.1	−	26852.2i	0.742875	−	1.28670i
$759$	−2827.51	−	4897.39i	−0.135220	−	0.234208i
$760$	2280.48	+	3949.90i	0.108844	+	0.188524i
$761$	−4508.98	+	7809.78i	−0.214784	+	0.372016i	−0.953206	−	0.302323i	$-0.902238\pi$
$761$	−4508.98	+	7809.78i	−0.214784	+	0.372016i	0.738422	+	0.674339i	$0.235571\pi$
$762$	3124.16			0.148525
$763$	1530.26	−	19807.2i	0.0726072	−	0.939802i
$764$	−13583.3			−0.643227
$765$	−921.576	+	1596.22i	−0.0435551	+	0.0754396i
$766$	5087.48	+	8811.78i	0.239972	+	0.415643i
$767$	−426.478	−	738.682i	−0.0200772	−	0.0347748i
$768$	10497.4	−	18182.0i	0.493220	−	0.854282i
$769$	−26051.7			−1.22165			−0.610824	−	0.791766i	$-0.709162\pi$
$769$	−26051.7			−1.22165			−0.610824	+	0.791766i	$0.709162\pi$
$770$	4872.40	−	2332.60i	0.228038	−	0.109170i
$771$	2291.84			0.107054
$772$	477.824	−	827.616i	0.0222763	−	0.0385836i
$773$	9995.71	+	17313.1i	0.465098	+	0.805573i	0.999206	−	0.0398429i	$-0.0126858\pi$
$773$	9995.71	+	17313.1i	0.465098	+	0.805573i	−0.534108	+	0.845416i	$0.679352\pi$
$774$	−349.075	−	604.615i	−0.0162109	−	0.0280781i
$775$	−6053.03	+	10484.1i	−0.280556	+	0.485938i
$776$	2078.29			0.0961421
$777$	3977.36	+	2725.17i	0.183639	+	0.125824i
$778$	19707.3			0.908152
$779$	−2237.87	+	3876.11i	−0.102927	+	0.178275i
$780$	701.776	+	1215.51i	0.0322149	+	0.0557978i
$781$	4016.83	+	6957.36i	0.184038	+	0.318763i
$782$	−20616.4	+	35708.6i	−0.942761	+	1.63291i
$783$	22060.3			1.00686
$784$	26686.2	+	4148.20i	1.21566	+	0.188967i
$785$	−2926.95			−0.133080
$786$	−8573.12	+	14849.1i	−0.389050	+	0.673854i
$787$	−799.423	−	1384.64i	−0.0362088	−	0.0627155i	0.847353	−	0.531030i	$-0.178195\pi$
$787$	−799.423	−	1384.64i	−0.0362088	−	0.0627155i	−0.883562	+	0.468314i	$0.844861\pi$
$788$	−6297.09	−	10906.9i	−0.284676	−	0.493073i
$789$	12967.2	−	22459.9i	0.585101	−	1.01342i
$790$	−35962.9			−1.61962
$791$	21626.0	+	14817.5i	0.972099	+	0.666053i
$792$	326.721			0.0146585
$793$	−139.425	+	241.492i	−0.00624355	+	0.0108141i
$794$	15673.2	+	27146.8i	0.700532	+	1.21336i
$795$	10698.1	+	18529.6i	0.477259	+	0.826637i
$796$	−1785.92	+	3093.31i	−0.0795230	+	0.137738i
$797$	−27692.7			−1.23077			−0.615387	−	0.788225i	$-0.711000\pi$
$797$	−27692.7			−1.23077			−0.615387	+	0.788225i	$0.711000\pi$
$798$	9917.07	−	4747.68i	0.439925	−	0.210609i
$799$	80213.7			3.55164
$800$	−3756.22	+	6505.96i	−0.166003	+	0.287526i
$801$	−548.322	−	949.722i	−0.0241873	−	0.0418936i
$802$	355.806	+	616.274i	0.0156658	+	0.0271339i
$803$	5589.66	−	9681.58i	0.245647	−	0.425474i
$804$	−1007.49			−0.0441932
$805$	1099.61	−	14233.0i	0.0481445	−	0.623166i
$806$	−7487.39			−0.327211
$807$	14569.7	−	25235.5i	0.635537	−	1.10078i
$808$	−5088.46	−	8813.47i	−0.221549	−	0.383733i
$809$	−11453.2	−	19837.5i	−0.497742	−	0.862114i	0.502255	−	0.864720i	$-0.332504\pi$
$809$	−11453.2	−	19837.5i	−0.497742	−	0.862114i	−0.999997	+	0.00260544i	$0.999171\pi$
$810$	10253.4	−	17759.4i	0.444776	−	0.770375i
$811$	−17475.4			−0.756653			−0.378327	−	0.925672i	$-0.623500\pi$
$811$	−17475.4			−0.756653			−0.378327	+	0.925672i	$0.623500\pi$
$812$	668.639	−	8654.63i	0.0288973	−	0.374037i
$813$	−39664.5			−1.71106
$814$	−880.536	+	1525.13i	−0.0379150	+	0.0656707i
$815$	10940.5	+	18949.5i	0.470219	+	0.814444i
$816$	−27533.8	−	47690.0i	−1.18122	−	2.04594i
$817$	−2021.52	+	3501.37i	−0.0865655	+	0.149936i
$818$	53177.1			2.27298
$819$	−332.324	+	159.096i	−0.0141787	+	0.00678788i
$820$	3083.18			0.131304
$821$	−8715.50	+	15095.7i	−0.370491	+	0.641709i	−0.989641	−	0.143564i	$-0.954144\pi$
$821$	−8715.50	+	15095.7i	−0.370491	+	0.641709i	0.619150	+	0.785273i	$0.287477\pi$
$822$	−7862.65	−	13618.5i	−0.333627	−	0.577859i
$823$	574.122	+	994.409i	0.0243167	+	0.0421178i	0.877928	−	0.478793i	$-0.158926\pi$
$823$	574.122	+	994.409i	0.0243167	+	0.0421178i	−0.853611	+	0.520911i	$0.825592\pi$
$824$	−3552.52	+	6153.15i	−0.150192	+	0.260140i
$825$	−3560.09			−0.150238
$826$	3797.05	+	2601.62i	0.159947	+	0.109591i
$827$	−365.741			−0.0153785			−0.00768927	−	0.999970i	$-0.502448\pi$
$827$	−365.741			−0.0153785			−0.00768927	+	0.999970i	$0.502448\pi$
$828$	−242.306	+	419.686i	−0.0101699	+	0.0176149i
$829$	−10576.0	−	18318.2i	−0.443089	−	0.767453i	0.554827	−	0.831965i	$-0.312784\pi$
$829$	−10576.0	−	18318.2i	−0.443089	−	0.767453i	−0.997917	+	0.0645120i	$0.979451\pi$
$830$	1226.06	+	2123.59i	0.0512735	+	0.0888083i
$831$	16182.3	−	28028.5i	0.675520	−	1.17004i
$832$	2483.05			0.103467
$833$	28052.1	−	34845.4i	1.16680	−	1.44937i
$834$	20266.6			0.841456
$835$	5810.01	−	10063.2i	0.240795	−	0.417069i
$836$	530.990	+	919.702i	0.0219673	+	0.0380485i
$837$	13576.5	+	23515.2i	0.560660	+	0.971092i
$838$	8305.89	−	14386.2i	0.342389	−	0.593035i
$839$	−20538.9			−0.845152			−0.422576	−	0.906327i	$-0.638874\pi$
$839$	−20538.9			−0.845152			−0.422576	+	0.906327i	$0.638874\pi$
$840$	11131.8	+	7627.20i	0.457244	+	0.313290i
$841$	2169.83			0.0889675
$842$	183.617	−	318.034i	0.00751528	−	0.0130169i
$843$	−12657.6	−	21923.6i	−0.517141	−	0.895715i
$844$	6891.93	+	11937.2i	0.281078	+	0.486842i
$845$	8317.38	−	14406.1i	0.338611	−	0.586492i
$846$	3565.18			0.144886
$847$	−2021.26	+	967.656i	−0.0819970	+	0.0392551i
$848$	−39071.2			−1.58221
$849$	1289.87	−	2234.13i	0.0521417	−	0.0903121i
$850$	12978.9	+	22480.1i	0.523733	+	0.907132i
$851$	2326.94	+	4030.37i	0.0937325	+	0.162349i
$852$	5631.93	−	9754.79i	0.226463	−	0.392246i
$853$	8572.78			0.344111			0.172055	−	0.985087i	$-0.444959\pi$
$853$	8572.78			0.344111			0.172055	+	0.985087i	$0.444959\pi$
$854$	115.910	−	1500.30i	0.00464444	−	0.0601160i
$855$	474.409			0.0189759
$856$	−3843.02	+	6656.31i	−0.153448	+	0.265780i
$857$	300.058	+	519.716i	0.0119601	+	0.0207155i	0.871944	−	0.489606i	$-0.162860\pi$
$857$	300.058	+	519.716i	0.0119601	+	0.0207155i	−0.859983	+	0.510322i	$0.829526\pi$
$858$	−1100.93	−	1906.86i	−0.0438054	−	0.0758731i
$859$	−14099.8	+	24421.5i	−0.560044	+	0.970025i	0.437448	+	0.899244i	$0.355882\pi$
$859$	−14099.8	+	24421.5i	−0.560044	+	0.970025i	−0.997492	+	0.0707810i	$0.977451\pi$
$860$	2785.10			0.110432
$861$	−1020.01	+	13202.7i	−0.0403740	+	0.522587i
$862$	−42173.0			−1.66638
$863$	−11266.3	+	19513.9i	−0.444392	+	0.769709i	−0.998010	−	0.0630615i	$-0.979914\pi$
$863$	−11266.3	+	19513.9i	−0.444392	+	0.769709i	0.553618	+	0.832771i	$0.313247\pi$
$864$	8424.93	+	14592.4i	0.331738	+	0.574588i
$865$	−12705.0	−	22005.6i	−0.499401	−	0.864988i
$866$	19653.2	−	34040.4i	0.771182	−	1.33573i
$867$	−64867.6			−2.54097
$868$	9636.93	−	4613.57i	0.376842	−	0.180409i
$869$	14918.8			0.582378
$870$	11586.8	−	20069.0i	0.451528	−	0.782070i
$871$	−369.681	−	640.307i	−0.0143814	−	0.0249093i
$872$	9063.21	+	15697.9i	0.351971	+	0.609632i
$873$	108.087	−	187.212i	0.00419036	−	0.00725792i
$874$	10612.9			0.410739
$875$	−22769.0	−	15600.6i	−0.879693	−	0.602740i
$876$	−15674.3			−0.604551
$877$	−12401.5	+	21480.0i	−0.477500	+	0.827054i	−0.999667	−	0.0257887i	$-0.991790\pi$
$877$	−12401.5	+	21480.0i	−0.477500	+	0.827054i	0.522167	+	0.852843i	$0.325124\pi$
$878$	−3951.57	−	6844.31i	−0.151889	−	0.263080i
$879$	−12026.0	−	20829.6i	−0.461463	−	0.799277i
$880$	−3481.91	+	6030.84i	−0.133381	+	0.231022i
$881$	−13875.0			−0.530602			−0.265301	−	0.964166i	$-0.585471\pi$
$881$	−13875.0			−0.530602			−0.265301	+	0.964166i	$0.585471\pi$
$882$	1246.80	−	1548.74i	0.0475986	−	0.0591255i
$883$	10245.8			0.390487			0.195244	−	0.980755i	$-0.437450\pi$
$883$	10245.8			0.390487			0.195244	+	0.980755i	$0.437450\pi$
$884$	−2122.69	+	3676.60i	−0.0807621	+	0.139884i
$885$	1624.68	+	2814.03i	0.0617096	+	0.106884i
$886$	−9698.51	−	16798.3i	−0.367751	−	0.636964i
$887$	13519.6	−	23416.6i	0.511774	−	0.886419i	−0.488133	−	0.872769i	$-0.662322\pi$
$887$	13519.6	−	23416.6i	0.511774	−	0.886419i	0.999907	−	0.0136492i	$-0.00434482\pi$
$888$	−4399.17			−0.166246
$889$	−2698.92	−	1849.22i	−0.101821	−	0.0697647i
$890$	16543.9			0.623093
$891$	−4253.52	+	7367.32i	−0.159931	+	0.277008i
$892$	−5278.82	−	9143.18i	−0.198148	−	0.343202i
$893$	−10323.1	−	17880.1i	−0.386841	−	0.670029i
$894$	−21108.1	+	36560.2i	−0.789664	+	1.36774i
$895$	27807.8			1.03856
$896$	−28720.5	+	13749.6i	−1.07085	+	0.512659i
$897$	−5818.69			−0.216589
$898$	−17936.6	+	31067.1i	−0.666538	+	1.15448i
$899$	16345.1	+	28310.5i	0.606383	+	1.05029i
$900$	152.542	+	264.211i	0.00564972	+	0.00978560i
$901$	−32358.8	+	56047.1i	−1.19648	+	2.07236i
$902$	−4836.81			−0.178546
$903$	−921.401	+	11926.3i	−0.0339560	+	0.439515i
$904$	−23919.4			−0.880030
$905$	−5828.81	+	10095.8i	−0.214095	+	0.370824i
$906$	−16786.2	−	29074.5i	−0.615545	−	1.06616i
$907$	−12775.4	−	22127.7i	−0.467698	−	0.810076i	0.531621	−	0.846982i	$-0.321583\pi$
$907$	−12775.4	−	22127.7i	−0.467698	−	0.810076i	−0.999319	+	0.0369062i	$0.988250\pi$
$908$	−1877.47	+	3251.88i	−0.0686191	+	0.118852i
$909$	−1058.55			−0.0386249
$910$	428.149	−	5541.81i	0.0155967	−	0.201878i
$911$	1147.83			0.0417447			0.0208724	−	0.999782i	$-0.493356\pi$
$911$	1147.83			0.0417447			0.0208724	+	0.999782i	$0.493356\pi$
$912$	−7086.93	+	12274.9i	−0.257315	+	0.445683i
$913$	−508.616	−	880.949i	−0.0184367	−	0.0319334i
$914$	−12025.0	−	20827.9i	−0.435176	−	0.753747i
$915$	531.144	−	919.969i	0.0191903	−	0.0332385i
$916$	−8346.52			−0.301066
$917$	16195.5	−	7753.41i	0.583231	−	0.279215i
$918$	58221.5			2.09324
$919$	8210.15	−	14220.4i	0.294698	−	0.510433i	−0.680216	−	0.733012i	$-0.738114\pi$
$919$	8210.15	−	14220.4i	0.294698	−	0.510433i	0.974915	+	0.222579i	$0.0714475\pi$
$920$	6512.62	+	11280.2i	0.233386	+	0.404236i
$921$	−5219.96	−	9041.23i	−0.186757	−	0.323473i
$922$	−31903.7	+	55258.8i	−1.13958	+	1.97381i
$923$	8266.18			0.294783
$924$	2591.95	+	1775.93i	0.0922825	+	0.0632292i
$925$	2929.82			0.104143
$926$	2091.39	−	3622.39i	0.0742196	−	0.128552i
$927$	369.517	+	640.021i	0.0130923	+	0.0226764i
$928$	10143.0	+	17568.1i	0.358792	+	0.621446i
$929$	11516.8	−	19947.7i	0.406731	−	0.704479i	−0.587790	−	0.809014i	$-0.700002\pi$
$929$	11516.8	−	19947.7i	0.406731	−	0.704479i	0.994521	+	0.104534i	$0.0333352\pi$
$930$	28523.4			1.00572
$931$	−11377.4	−	1768.55i	−0.400516	−	0.0622576i
$932$	11296.9			0.397042
$933$	10222.0	−	17705.0i	0.358684	−	0.621259i
$934$	−23711.2	−	41069.1i	−0.830680	−	1.43878i
$935$	5767.44	+	9989.51i	0.201728	+	0.349403i
$936$	168.088	−	291.138i	0.00586981	−	0.0101668i
$937$	21478.3			0.748841			0.374420	−	0.927259i	$-0.377842\pi$
$937$	21478.3			0.748841			0.374420	+	0.927259i	$0.377842\pi$
$938$	3291.37	+	2255.15i	0.114570	+	0.0785002i
$939$	1159.01			0.0402799
$940$	−7111.21	+	12317.0i	−0.246747	+	0.427378i
$941$	10695.8	+	18525.7i	0.370536	+	0.641787i	0.989648	−	0.143516i	$-0.0458407\pi$
$941$	10695.8	+	18525.7i	0.370536	+	0.641787i	−0.619112	+	0.785303i	$0.712507\pi$
$942$	−3218.99	−	5575.45i	−0.111338	−	0.192843i
$943$	−6390.96	+	11069.5i	−0.220698	+	0.382260i
$944$	−5933.62			−0.204579
$945$	−18181.2	+	8704.02i	−0.625855	+	0.299621i
$946$	−4369.19			−0.150163
$947$	14524.3	−	25156.8i	0.498390	−	0.863238i	−0.501608	−	0.865095i	$-0.667258\pi$
$947$	14524.3	−	25156.8i	0.498390	−	0.863238i	0.999998	+	0.00185753i	$0.000591271\pi$
$948$	−10458.7	−	18115.0i	−0.358316	−	0.620621i
$949$	−5751.44	−	9961.79i	−0.196733	−	0.340752i
$950$	3340.64	−	5786.16i	0.114089	−	0.197608i
$951$	−21019.8			−0.716734
$952$	−3144.01	+	40695.0i	−0.107036	+	1.38543i
$953$	12519.6			0.425551			0.212776	−	0.977101i	$-0.431750\pi$
$953$	12519.6			0.425551			0.212776	+	0.977101i	$0.431750\pi$
$954$	−1438.22	+	2491.07i	−0.0488093	+	0.0845401i
$955$	18987.3	+	32886.9i	0.643366	+	1.11434i
$956$	−7738.09	−	13402.8i	−0.261786	−	0.453427i
$957$	−4806.67	+	8325.39i	−0.162359	+	0.281214i
$958$	2880.19			0.0971343
$959$	−1268.48	+	16418.8i	−0.0427127	+	0.552859i
$960$	−9459.23			−0.318016
$961$	−5222.91	+	9046.34i	−0.175318	+	0.303660i
$962$	906.022	+	1569.28i	0.0303652	+	0.0525941i
$963$	399.733	+	692.357i	0.0133761	+	0.0231681i
$964$	6644.38	−	11508.4i	0.221993	−	0.384503i
$965$	−2671.70			−0.0891243
$966$	28321.3	−	13558.5i	0.943296	−	0.451592i
$967$	−13418.0			−0.446219			−0.223110	−	0.974793i	$-0.571621\pi$
$967$	−13418.0			−0.446219			−0.223110	+	0.974793i	$0.571621\pi$
$968$	1022.35	−	1770.76i	0.0339458	−	0.0587958i
$969$	11738.8	+	20332.2i	0.389169	+	0.674060i
$970$	1630.59	+	2824.27i	0.0539744	+	0.0934863i
$971$	11556.4	−	20016.2i	0.381937	−	0.661535i	−0.609402	−	0.792862i	$-0.708590\pi$
$971$	11556.4	−	20016.2i	0.381937	−	0.661535i	0.991339	+	0.131327i	$0.0419237\pi$
$972$	1416.21			0.0467336
$973$	−17508.0	−	11996.0i	−0.576857	−	0.395245i
$974$	−8522.36			−0.280363
$975$	−1831.56	+	3172.36i	−0.0601610	+	0.104202i
$976$	969.916	+	1679.94i	0.0318097	+	0.0550960i
$977$	7658.42	+	13264.8i	0.250782	+	0.434368i	0.963741	−	0.266838i	$-0.0859788\pi$
$977$	7658.42	+	13264.8i	0.250782	+	0.434368i	−0.712959	+	0.701206i	$0.752645\pi$
$978$	−24064.1	+	41680.3i	−0.786796	+	1.36277i
$979$	−6863.06			−0.224050
$980$	2863.68	+	7396.61i	0.0933436	+	0.241098i
$981$	1885.42			0.0613628
$982$	2143.83	−	3713.22i	0.0696662	−	0.120665i
$983$	6178.02	+	10700.6i	0.200456	+	0.347200i	0.948675	−	0.316251i	$-0.102424\pi$
$983$	6178.02	+	10700.6i	0.200456	+	0.347200i	−0.748219	+	0.663451i	$0.769091\pi$
$984$	−6041.18	−	10463.6i	−0.195717	−	0.338992i
$985$	−17604.7	+	30492.2i	−0.569475	+	0.986359i
$986$	70094.2			2.26395
$987$	−50390.8	−	34526.3i	−1.62508	−	1.11346i
$988$	1092.72			0.0351862
$989$	−5773.09	+	9999.28i	−0.185615	+	0.321495i
$990$	256.340	+	443.993i	0.00822930	+	0.0142536i
$991$	−1952.84	−	3382.42i	−0.0625975	−	0.108422i	0.833028	−	0.553230i	$-0.186605\pi$
$991$	−1952.84	−	3382.42i	−0.0625975	−	0.108422i	−0.895626	+	0.444808i	$0.853272\pi$
$992$	−12484.5	+	21623.8i	−0.399581	+	0.692094i
$993$	−32711.9			−1.04540
$994$	−40234.0	+	19261.5i	−1.28385	+	0.614627i
$995$	9985.76			0.318161
$996$	−713.122	+	1235.16i	−0.0226869	+	0.0392948i
$997$	−28098.7	−	48668.5i	−0.892574	−	1.54598i	−0.836779	−	0.547541i	$-0.815564\pi$
$997$	−28098.7	−	48668.5i	−0.892574	−	1.54598i	−0.0557950	−	0.998442i	$-0.517769\pi$
$998$	15384.1	+	26646.0i	0.487950	+	0.845153i
$999$	3285.69	−	5690.98i	0.104059	−	0.180235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.e.c.23.3	✓	20
7.2	even	3		539.4.a.n.1.8		10
7.4	even	3	inner	77.4.e.c.67.3	yes	20
7.5	odd	6		539.4.a.m.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.e.c.23.3	✓	20	1.1	even	1	trivial
77.4.e.c.67.3	yes	20	7.4	even	3	inner
539.4.a.m.1.8		10	7.5	odd	6
539.4.a.n.1.8		10	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64894 + 2.85605i) q^{2} +(2.68131 + 4.64416i) q^{3} +(-1.43800 - 2.49069i) q^{4} +(-4.02020 + 6.96320i) q^{5} -17.6853 q^{6} +(15.2781 + 10.4681i) q^{7} -16.8983 q^{8} +(-0.878841 + 1.52220i) q^{9} +O(q^{10})\)	\(q+(-1.64894 + 2.85605i) q^{2} +(2.68131 + 4.64416i) q^{3} +(-1.43800 - 2.49069i) q^{4} +(-4.02020 + 6.96320i) q^{5} -17.6853 q^{6} +(15.2781 + 10.4681i) q^{7} -16.8983 q^{8} +(-0.878841 + 1.52220i) q^{9} +(-13.2581 - 22.9638i) q^{10} +(5.50000 + 9.52628i) q^{11} +(7.71145 - 13.3566i) q^{12} +11.3184 q^{13} +(-55.0899 + 26.3737i) q^{14} -43.1176 q^{15} +(39.3683 - 68.1879i) q^{16} +(-65.2098 - 112.947i) q^{17} +(-2.89831 - 5.02002i) q^{18} +(-16.7843 + 29.0713i) q^{19} +23.1242 q^{20} +(-7.65024 + 99.0220i) q^{21} -36.2767 q^{22} +(-47.9330 + 83.0224i) q^{23} +(-45.3096 - 78.4786i) q^{24} +(30.1759 + 52.2663i) q^{25} +(-18.6633 + 32.3258i) q^{26} +135.365 q^{27} +(4.10287 - 53.1061i) q^{28} +162.969 q^{29} +(71.0984 - 123.146i) q^{30} +(100.296 + 173.717i) q^{31} +(62.2386 + 107.801i) q^{32} +(-29.4944 + 51.0858i) q^{33} +430.108 q^{34} +(-134.312 + 64.3004i) q^{35} +5.05510 q^{36} +(24.2728 - 42.0417i) q^{37} +(-55.3527 - 95.8737i) q^{38} +(30.3481 + 52.5644i) q^{39} +(67.9347 - 117.666i) q^{40} +133.331 q^{41} +(-270.197 - 185.131i) q^{42} +120.441 q^{43} +(15.8180 - 27.3976i) q^{44} +(-7.06624 - 12.2391i) q^{45} +(-158.077 - 273.798i) q^{46} +(-307.522 + 532.643i) q^{47} +422.235 q^{48} +(123.839 + 319.864i) q^{49} -199.033 q^{50} +(349.695 - 605.690i) q^{51} +(-16.2758 - 28.1906i) q^{52} +(-248.113 - 429.745i) q^{53} +(-223.209 + 386.609i) q^{54} -88.4445 q^{55} +(-258.174 - 176.893i) q^{56} -180.016 q^{57} +(-268.726 + 465.446i) q^{58} +(-37.6802 - 65.2640i) q^{59} +(62.0032 + 107.393i) q^{60} +(-12.3185 + 21.3363i) q^{61} -661.525 q^{62} +(-29.3615 + 14.0565i) q^{63} +219.382 q^{64} +(-45.5022 + 78.8121i) q^{65} +(-97.2690 - 168.475i) q^{66} +(-32.6620 - 56.5723i) q^{67} +(-187.544 + 324.835i) q^{68} -514.093 q^{69} +(37.8278 - 489.629i) q^{70} +730.333 q^{71} +(14.8509 - 25.7226i) q^{72} +(-508.151 - 880.143i) q^{73} +(80.0488 + 138.649i) q^{74} +(-161.822 + 280.284i) q^{75} +96.5436 q^{76} +(-15.6924 + 203.118i) q^{77} -200.168 q^{78} +(678.129 - 1174.55i) q^{79} +(316.537 + 548.259i) q^{80} +(386.684 + 669.756i) q^{81} +(-219.855 + 380.800i) q^{82} -92.4757 q^{83} +(257.634 - 123.339i) q^{84} +1048.63 q^{85} +(-198.600 + 343.985i) q^{86} +(436.970 + 756.854i) q^{87} +(-92.9408 - 160.978i) q^{88} +(-311.957 + 540.326i) q^{89} +46.6072 q^{90} +(172.923 + 118.482i) q^{91} +275.711 q^{92} +(-537.847 + 931.578i) q^{93} +(-1014.17 - 1756.59i) q^{94} +(-134.953 - 233.745i) q^{95} +(-333.762 + 578.093i) q^{96} -122.988 q^{97} +(-1117.75 - 173.747i) q^{98} -19.3345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9}+O(q^{10}) \) 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9	\( 20 q - 54 q^{4} - 10 q^{5} + 106 q^{6} - 30 q^{7} + 6 q^{8} - 76 q^{9} - 63 q^{10} + 110 q^{11} - 55 q^{12} + 324 q^{13} + 58 q^{14} + 60 q^{15} - 286 q^{16} - 200 q^{17} + 252 q^{18} - 252 q^{19} + 192 q^{20} + 458 q^{21} - 134 q^{23} - 786 q^{24} - 86 q^{25} - 363 q^{26} + 348 q^{27} - 1057 q^{28} + 296 q^{29} + 316 q^{30} - 530 q^{31} + 731 q^{32} + 204 q^{34} - 288 q^{35} + 2574 q^{36} + 902 q^{37} - 66 q^{38} + 208 q^{39} - 2163 q^{40} + 336 q^{41} - 1482 q^{42} + 236 q^{43} + 594 q^{44} - 58 q^{45} + 210 q^{46} - 288 q^{47} - 1700 q^{48} - 1072 q^{49} + 4650 q^{50} + 1022 q^{51} - 1663 q^{52} + 608 q^{53} - 2312 q^{54} - 220 q^{55} - 4905 q^{56} + 1656 q^{57} + 1951 q^{58} + 464 q^{59} + 818 q^{60} - 3484 q^{61} - 1618 q^{62} - 3948 q^{63} + 6090 q^{64} + 1560 q^{65} + 583 q^{66} - 142 q^{67} - 1145 q^{68} + 3432 q^{69} - 4133 q^{70} + 668 q^{71} + 1176 q^{72} - 1466 q^{73} + 3460 q^{74} - 2982 q^{75} + 6774 q^{76} - 330 q^{77} + 10840 q^{78} - 578 q^{79} - 2911 q^{80} - 118 q^{81} + 307 q^{82} + 1092 q^{83} - 6786 q^{84} + 5164 q^{85} - 2597 q^{86} - 1516 q^{87} + 33 q^{88} - 3150 q^{89} - 3672 q^{90} - 3638 q^{91} + 4326 q^{92} + 1484 q^{93} - 5700 q^{94} + 1338 q^{95} - 5429 q^{96} + 3308 q^{97} - 3186 q^{98} - 1672 q^{99}+O(q^{100}) \) 20 * q - 54 * q^4 - 10 * q^5 + 106 * q^6 - 30 * q^7 + 6 * q^8 - 76 * q^9 - 63 * q^10 + 110 * q^11 - 55 * q^12 + 324 * q^13 + 58 * q^14 + 60 * q^15 - 286 * q^16 - 200 * q^17 + 252 * q^18 - 252 * q^19 + 192 * q^20 + 458 * q^21 - 134 * q^23 - 786 * q^24 - 86 * q^25 - 363 * q^26 + 348 * q^27 - 1057 * q^28 + 296 * q^29 + 316 * q^30 - 530 * q^31 + 731 * q^32 + 204 * q^34 - 288 * q^35 + 2574 * q^36 + 902 * q^37 - 66 * q^38 + 208 * q^39 - 2163 * q^40 + 336 * q^41 - 1482 * q^42 + 236 * q^43 + 594 * q^44 - 58 * q^45 + 210 * q^46 - 288 * q^47 - 1700 * q^48 - 1072 * q^49 + 4650 * q^50 + 1022 * q^51 - 1663 * q^52 + 608 * q^53 - 2312 * q^54 - 220 * q^55 - 4905 * q^56 + 1656 * q^57 + 1951 * q^58 + 464 * q^59 + 818 * q^60 - 3484 * q^61 - 1618 * q^62 - 3948 * q^63 + 6090 * q^64 + 1560 * q^65 + 583 * q^66 - 142 * q^67 - 1145 * q^68 + 3432 * q^69 - 4133 * q^70 + 668 * q^71 + 1176 * q^72 - 1466 * q^73 + 3460 * q^74 - 2982 * q^75 + 6774 * q^76 - 330 * q^77 + 10840 * q^78 - 578 * q^79 - 2911 * q^80 - 118 * q^81 + 307 * q^82 + 1092 * q^83 - 6786 * q^84 + 5164 * q^85 - 2597 * q^86 - 1516 * q^87 + 33 * q^88 - 3150 * q^89 - 3672 * q^90 - 3638 * q^91 + 4326 * q^92 + 1484 * q^93 - 5700 * q^94 + 1338 * q^95 - 5429 * q^96 + 3308 * q^97 - 3186 * q^98 - 1672 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more