LMFDB - Embedded newform 117.4.r.a.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(43,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("117.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	117.49
Dual form			117.4.r.a.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.59109 - 2.07331i) q^{2} +(4.58787 - 2.43956i) q^{3} +(4.59727 + 7.96270i) q^{4} +(4.17848 + 2.41245i) q^{5} +(-21.5334 - 0.751409i) q^{6} -15.5822i q^{7} -4.95329i q^{8} +(15.0971 - 22.3848i) q^{9} +(-10.0035 - 17.3266i) q^{10} +(39.1432 + 22.5993i) q^{11} +(40.5172 + 25.3165i) q^{12} +(21.5929 - 41.6022i) q^{13} +(-32.3068 + 55.9571i) q^{14} +(25.0557 + 0.874318i) q^{15} +(26.5084 - 45.9139i) q^{16} +(-1.85014 + 3.20453i) q^{17} +(-100.626 + 49.0848i) q^{18} +(-10.2746 - 5.93207i) q^{19} +44.3627i q^{20} +(-38.0138 - 71.4891i) q^{21} +(-93.7110 - 162.312i) q^{22} -134.490 q^{23} +(-12.0839 - 22.7251i) q^{24} +(-50.8602 - 88.0924i) q^{25} +(-163.797 + 104.628i) q^{26} +(14.6542 - 139.529i) q^{27} +(124.077 - 71.6356i) q^{28} +(99.7201 - 172.720i) q^{29} +(-88.1643 - 55.0880i) q^{30} +(-37.0698 - 21.4022i) q^{31} +(-224.705 + 129.734i) q^{32} +(234.716 + 8.19043i) q^{33} +(13.2880 - 7.67183i) q^{34} +(37.5913 - 65.1100i) q^{35} +(247.649 + 17.3045i) q^{36} +(-139.181 + 80.3560i) q^{37} +(24.5981 + 42.6052i) q^{38} +(-2.42586 - 243.543i) q^{39} +(11.9496 - 20.6973i) q^{40} +369.833i q^{41} +(-11.7086 + 335.538i) q^{42} +210.696 q^{43} +415.580i q^{44} +(117.085 - 57.1136i) q^{45} +(482.967 + 278.841i) q^{46} +(160.177 - 92.4781i) q^{47} +(9.60716 - 275.316i) q^{48} +100.195 q^{49} +421.797i q^{50} +(-0.670525 + 19.2155i) q^{51} +(430.535 - 19.3187i) q^{52} -437.724 q^{53} +(-341.911 + 470.677i) q^{54} +(109.039 + 188.862i) q^{55} -77.1833 q^{56} +(-61.6104 - 2.14990i) q^{57} +(-716.207 + 413.502i) q^{58} +(401.536 - 231.827i) q^{59} +(108.226 + 203.530i) q^{60} +495.381 q^{61} +(88.7471 + 153.715i) q^{62} +(-348.805 - 235.246i) q^{63} +651.781 q^{64} +(190.589 - 121.742i) q^{65} +(-825.904 - 516.053i) q^{66} -233.027i q^{67} -34.0223 q^{68} +(-617.024 + 328.098i) q^{69} +(-269.987 + 155.877i) q^{70} +(824.189 + 475.846i) q^{71} +(-110.878 - 74.7801i) q^{72} +885.664i q^{73} +666.413 q^{74} +(-448.247 - 280.080i) q^{75} -109.085i q^{76} +(352.147 - 609.937i) q^{77} +(-496.229 + 879.613i) q^{78} +(-221.888 - 384.322i) q^{79} +(221.530 - 127.900i) q^{80} +(-273.158 - 675.889i) q^{81} +(766.781 - 1328.10i) q^{82} +(-604.028 + 348.736i) q^{83} +(394.487 - 631.347i) q^{84} +(-15.4615 + 8.92672i) q^{85} +(-756.628 - 436.839i) q^{86} +(36.1405 - 1035.69i) q^{87} +(111.941 - 193.888i) q^{88} +(322.550 - 186.224i) q^{89} +(-538.877 - 37.6541i) q^{90} +(-648.255 - 336.466i) q^{91} +(-618.289 - 1070.91i) q^{92} +(-222.283 - 7.75658i) q^{93} -766.944 q^{94} +(-28.6216 - 49.5741i) q^{95} +(-714.425 + 1143.38i) q^{96} +135.651i q^{97} +(-359.807 - 207.735i) q^{98} +(1096.83 - 535.028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) $ 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−3.59109	−	2.07331i	−1.26964	−	0.733027i	−0.294721	−	0.955583i	$-0.595227\pi$
$2$	−3.59109	−	2.07331i	−1.26964	−	0.733027i	−0.974920	+	0.222556i	$0.928560\pi$
$3$	4.58787	−	2.43956i	0.882936	−	0.469494i
$3$	4.58787	−	2.43956i	0.882936	−	0.469494i
$4$	4.59727	+	7.96270i	0.574658	+	0.995338i
$5$	4.17848	+	2.41245i	0.373735	+	0.215776i	0.675089	−	0.737736i	$-0.264105\pi$
$5$	4.17848	+	2.41245i	0.373735	+	0.215776i	−0.301354	+	0.953512i	$0.597439\pi$
$6$	−21.5334	−	0.751409i	−1.46516	−	0.0511269i
$7$		−	15.5822i		−	0.841361i	−0.907209	−	0.420680i	$-0.861791\pi$
$7$		−	15.5822i		−	0.841361i	0.907209	−	0.420680i	$-0.138209\pi$
$8$		−	4.95329i		−	0.218907i
$9$	15.0971	−	22.3848i	0.559150	−	0.829066i
$10$	−10.0035	−	17.3266i	−0.316339	−	0.547916i
$11$	39.1432	+	22.5993i	1.07292	+	0.619450i	0.928977	−	0.370136i	$-0.120689\pi$
$11$	39.1432	+	22.5993i	1.07292	+	0.619450i	0.143941	+	0.989586i	$0.454022\pi$
$12$	40.5172	+	25.3165i	0.974692	+	0.609020i
$13$	21.5929	−	41.6022i	0.460677	−	0.887568i
$13$	21.5929	−	41.6022i	0.460677	−	0.887568i
$14$	−32.3068	+	55.9571i	−0.616740	+	1.06823i
$15$	25.0557	+	0.874318i	0.431289	+	0.0150499i
$16$	26.5084	−	45.9139i	0.414194	−	0.717405i
$17$	−1.85014	+	3.20453i	−0.0263955	+	0.0457184i	−0.878921	−	0.476967i	$-0.841736\pi$
$17$	−1.85014	+	3.20453i	−0.0263955	+	0.0457184i	0.852526	+	0.522685i	$0.175070\pi$
$18$	−100.626	+	49.0848i	−1.31765	+	0.642744i
$19$	−10.2746	−	5.93207i	−0.124061	−	0.0716269i	0.436685	−	0.899614i	$-0.356152\pi$
$19$	−10.2746	−	5.93207i	−0.124061	−	0.0716269i	−0.560746	+	0.827988i	$0.689486\pi$
$20$			44.3627i			0.495990i
$21$	−38.0138	−	71.4891i	−0.395014	−	0.742867i
$22$	−93.7110	−	162.312i	−0.908148	−	1.57296i
$23$	−134.490			−1.21927			−0.609635	−	0.792682i	$-0.708684\pi$
$23$	−134.490			−1.21927			−0.609635	+	0.792682i	$0.708684\pi$
$24$	−12.0839	−	22.7251i	−0.102775	−	0.193280i
$25$	−50.8602	−	88.0924i	−0.406881	−	0.704739i
$26$	−163.797	+	104.628i	−1.23551	+	0.789204i
$27$	14.6542	−	139.529i	0.104452	−	0.994530i
$28$	124.077	−	71.6356i	0.837438	−	0.483495i
$29$	99.7201	−	172.720i	0.638536	−	1.10598i	−0.347218	−	0.937785i	$-0.612874\pi$
$29$	99.7201	−	172.720i	0.638536	−	1.10598i	0.985754	−	0.168193i	$-0.0537932\pi$
$30$	−88.1643	−	55.0880i	−0.536551	−	0.335255i
$31$	−37.0698	−	21.4022i	−0.214772	−	0.123999i	0.388755	−	0.921341i	$-0.372905\pi$
$31$	−37.0698	−	21.4022i	−0.214772	−	0.123999i	−0.603527	+	0.797342i	$0.706238\pi$
$32$	−224.705	+	129.734i	−1.24133	+	0.716684i
$33$	234.716	+	8.19043i	1.23815	+	0.0432052i
$34$	13.2880	−	7.67183i	0.0670257	−	0.0386973i
$35$	37.5913	−	65.1100i	0.181545	−	0.314446i
$36$	247.649	+	17.3045i	1.14652	+	0.0801134i
$37$	−139.181	+	80.3560i	−0.618410	+	0.357039i	−0.776250	−	0.630426i	$-0.782880\pi$
$37$	−139.181	+	80.3560i	−0.618410	+	0.357039i	0.157840	+	0.987465i	$0.449547\pi$
$38$	24.5981	+	42.6052i	0.105009	+	0.181881i
$39$	−2.42586	−	243.543i	−0.00996023	−	0.999950i
$40$	11.9496	−	20.6973i	0.0472348	−	0.0818131i
$41$			369.833i			1.40874i	0.709834	+	0.704369i	$0.248770\pi$
$41$			369.833i			1.40874i	−0.709834	+	0.704369i	$0.751230\pi$
$42$	−11.7086	+	335.538i	−0.0430162	+	1.23273i
$43$	210.696			0.747229			0.373614	−	0.927584i	$-0.378118\pi$
$43$	210.696			0.747229			0.373614	+	0.927584i	$0.378118\pi$
$44$			415.580i			1.42389i
$45$	117.085	−	57.1136i	0.387867	−	0.189200i
$46$	482.967	+	278.841i	1.54803	+	0.893758i
$47$	160.177	−	92.4781i	0.497110	−	0.287007i	−0.230409	−	0.973094i	$-0.574006\pi$
$47$	160.177	−	92.4781i	0.497110	−	0.287007i	0.727519	+	0.686087i	$0.240673\pi$
$48$	9.60716	−	275.316i	0.0288890	−	0.827884i
$49$	100.195			0.292112
$50$			421.797i			1.19302i
$51$	−0.670525	+	19.2155i	−0.00184103	+	0.0527590i
$52$	430.535	−	19.3187i	1.14816	−	0.0515196i
$53$	−437.724			−1.13445			−0.567227	−	0.823561i	$-0.691984\pi$
$53$	−437.724			−1.13445			−0.567227	+	0.823561i	$0.691984\pi$
$54$	−341.911	+	470.677i	−0.861634	+	1.18613i
$55$	109.039	+	188.862i	0.267325	+	0.463020i
$56$	−77.1833			−0.184179
$57$	−61.6104	−	2.14990i	−0.143167	−	0.00499580i
$58$	−716.207	+	413.502i	−1.62142	+	0.936129i
$59$	401.536	−	231.827i	0.886026	−	0.511547i	0.0133856	−	0.999910i	$-0.495739\pi$
$59$	401.536	−	231.827i	0.886026	−	0.511547i	0.872641	+	0.488363i	$0.162406\pi$
$60$	108.226	+	203.530i	0.232864	+	0.437927i
$61$	495.381			1.03979			0.519894	−	0.854231i	$-0.325971\pi$
$61$	495.381			1.03979			0.519894	+	0.854231i	$0.325971\pi$
$62$	88.7471	+	153.715i	0.181789	+	0.314867i
$63$	−348.805	−	235.246i	−0.697544	−	0.470447i
$64$	651.781			1.27301
$65$	190.589	−	121.742i	0.363687	−	0.232312i
$66$	−825.904	−	516.053i	−1.54033	−	0.962450i
$67$		−	233.027i		−	0.424907i	−0.977171	−	0.212453i	$-0.931855\pi$
$67$		−	233.027i		−	0.424907i	0.977171	−	0.212453i	$-0.0681453\pi$
$68$	−34.0223			−0.0606737
$69$	−617.024	+	328.098i	−1.07654	+	0.572440i
$70$	−269.987	+	155.877i	−0.460995	+	0.266156i
$71$	824.189	+	475.846i	1.37765	+	0.795388i	0.991876	−	0.127205i	$-0.0406007\pi$
$71$	824.189	+	475.846i	1.37765	+	0.795388i	0.385775	+	0.922593i	$0.373934\pi$
$72$	−110.878	−	74.7801i	−0.181488	−	0.122402i
$73$			885.664i			1.41999i	0.704208	+	0.709994i	$0.251302\pi$
$73$			885.664i			1.41999i	−0.704208	+	0.709994i	$0.748698\pi$
$74$	666.413			1.04688
$75$	−448.247	−	280.080i	−0.690121	−	0.431211i
$76$		−	109.085i		−	0.164644i
$77$	352.147	−	609.937i	0.521181	−	0.902712i
$78$	−496.229	+	879.613i	−0.720345	+	1.27688i
$79$	−221.888	−	384.322i	−0.316005	−	0.547336i	0.663646	−	0.748047i	$-0.269008\pi$
$79$	−221.888	−	384.322i	−0.316005	−	0.547336i	−0.979651	+	0.200711i	$0.935675\pi$
$80$	221.530	−	127.900i	0.309597	−	0.178746i
$81$	−273.158	−	675.889i	−0.374702	−	0.927145i
$82$	766.781	−	1328.10i	1.03264	−	1.78859i
$83$	−604.028	+	348.736i	−0.798803	+	0.461189i	−0.843053	−	0.537831i	$-0.819244\pi$
$83$	−604.028	+	348.736i	−0.798803	+	0.461189i	0.0442492	+	0.999021i	$0.485910\pi$
$84$	394.487	−	631.347i	0.512406	−	0.820067i
$85$	−15.4615	+	8.92672i	−0.0197299	+	0.0113910i
$86$	−756.628	−	436.839i	−0.948712	−	0.547739i
$87$	36.1405	−	1035.69i	0.0445364	−	1.27630i
$88$	111.941	−	193.888i	0.135602	−	0.234869i
$89$	322.550	−	186.224i	0.384160	−	0.221795i	−0.295467	−	0.955353i	$-0.595475\pi$
$89$	322.550	−	186.224i	0.384160	−	0.221795i	0.679626	+	0.733558i	$0.262142\pi$
$90$	−538.877	−	37.6541i	−0.631140	−	0.0441010i
$91$	−648.255	−	336.466i	−0.746765	−	0.387595i
$92$	−618.289	−	1070.91i	−0.700664	−	1.21358i
$93$	−222.283	−	7.75658i	−0.247846	−	0.00864860i
$94$	−766.944			−0.841535
$95$	−28.6216	−	49.5741i	−0.0309107	−	0.0535389i
$96$	−714.425	+	1143.38i	−0.759538	+	1.21558i
$97$			135.651i			0.141993i	0.997477	+	0.0709965i	$0.0226179\pi$
$97$			135.651i			0.141993i	−0.997477	+	0.0709965i	$0.977382\pi$
$98$	−359.807	−	207.735i	−0.370878	−	0.214126i
$99$	1096.83	−	535.028i	1.11349	−	0.543155i
$100$	467.636	−	809.969i	0.467636	−	0.809969i
$101$	−383.501	+	664.244i	−0.377820	+	0.654403i	−0.990745	−	0.135738i	$-0.956660\pi$
$101$	−383.501	+	664.244i	−0.377820	+	0.654403i	0.612925	+	0.790141i	$0.289993\pi$
$102$	42.2477	−	67.6143i	0.0410112	−	0.0656354i
$103$	−190.422	+	329.821i	−0.182163	+	0.315516i	−0.942617	−	0.333876i	$-0.891643\pi$
$103$	−190.422	+	329.821i	−0.182163	+	0.315516i	0.760454	+	0.649392i	$0.224977\pi$
$104$	−206.068	−	106.956i	−0.194295	−	0.100845i
$105$	13.6238	−	390.423i	0.0126624	−	0.362870i
$106$	1571.91	+	907.540i	1.44035	+	0.831586i
$107$	−249.465	−	432.086i	−0.225389	−	0.390386i	0.731047	−	0.682327i	$-0.239032\pi$
$107$	−249.465	−	432.086i	−0.225389	−	0.390386i	−0.956436	+	0.291941i	$0.905699\pi$
$108$	1178.39	−	524.764i	1.04992	−	0.467550i
$109$			1867.86i			1.64136i	0.571388	+	0.820680i	$0.306405\pi$
$109$			1867.86i			1.64136i	−0.571388	+	0.820680i	$0.693595\pi$
$110$		−	904.292i		−	0.783826i
$111$	−442.509	+	708.203i	−0.378388	+	0.605582i
$112$	−715.440	−	413.060i	−0.603596	−	0.348486i
$113$	904.664	+	1566.92i	0.753129	+	1.30446i	0.946299	+	0.323293i	$0.104790\pi$
$113$	904.664	+	1566.92i	0.753129	+	1.30446i	−0.193170	+	0.981165i	$0.561877\pi$
$114$	216.791	+	135.458i	0.178108	+	0.111288i
$115$	−561.966	−	324.451i	−0.455684	−	0.263089i
$116$	1833.76			1.46776
$117$	−605.268	−	1111.42i	−0.478265	−	0.878215i
$118$	−1922.60			−1.49991
$119$	49.9337	+	28.8292i	0.0384657	+	0.0222082i
$120$	4.33075	−	124.108i	0.00329452	−	0.0944121i
$121$	355.958	+	616.537i	0.267436	+	0.463214i
$122$	−1778.96	−	1027.08i	−1.32016	−	0.762193i
$123$	902.232	+	1696.75i	0.661394	+	1.24382i
$124$		−	393.567i		−	0.285027i
$125$		−	1093.90i		−	0.782733i
$126$	764.849	+	1567.97i	0.540779	+	1.10862i
$127$	920.407	+	1594.19i	0.643094	+	1.11387i	0.984738	+	0.174042i	$0.0556829\pi$
$127$	920.407	+	1594.19i	0.643094	+	1.11387i	−0.341644	+	0.939829i	$0.610984\pi$
$128$	−542.958	−	313.477i	−0.374931	−	0.216466i
$129$	966.645	−	514.006i	0.659755	−	0.350820i
$130$	−936.832	+	42.0369i	−0.632043	+	0.0283606i
$131$	−1036.68	+	1795.58i	−0.691414	+	1.19756i	0.279961	+	0.960011i	$0.409678\pi$
$131$	−1036.68	+	1795.58i	−0.691414	+	1.19756i	−0.971375	+	0.237552i	$0.923655\pi$
$132$	1013.83	+	1906.63i	0.668507	+	1.25720i
$133$	−92.4348	+	160.102i	−0.0602640	+	0.104380i
$134$	−483.138	+	836.819i	−0.311468	+	0.539479i
$135$	397.838	−	547.666i	0.253633	−	0.349152i
$136$	15.8730	+	9.16427i	0.0100081	+	0.00577816i
$137$		−	1009.61i		−	0.629609i	−0.949157	−	0.314804i	$-0.898061\pi$
$137$		−	1009.61i		−	0.629609i	0.949157	−	0.314804i	$-0.101939\pi$
$138$	2896.04	+	101.057i	1.78643	+	0.0623375i
$139$	938.027	+	1624.71i	0.572391	+	0.991411i	0.996320	+	0.0857152i	$0.0273175\pi$
$139$	938.027	+	1624.71i	0.572391	+	0.991411i	−0.423928	+	0.905696i	$0.639349\pi$
$140$	691.269			0.417306
$141$	509.263	−	815.038i	0.304168	−	0.486799i
$142$	−1973.16	−	3417.61i	−1.16608	−	2.01971i
$143$	1785.40	−	1140.46i	1.04407	−	0.666922i
$144$	−627.574	−	1286.55i	−0.363180	−	0.744531i
$145$	833.357	−	481.139i	0.477287	−	0.275562i
$146$	1836.26	−	3180.50i	1.04089	−	1.80287i
$147$	459.679	−	244.431i	0.257916	−	0.137145i
$148$	−1279.70	−	738.836i	−0.710749	−	0.410351i
$149$	−1970.39	+	1137.61i	−1.08336	+	0.625479i	−0.931801	−	0.362969i	$-0.881763\pi$
$149$	−1970.39	+	1137.61i	−1.08336	+	0.625479i	−0.151561	+	0.988448i	$0.548430\pi$
$150$	1029.00	+	1935.15i	0.560117	+	1.05336i
$151$	124.588	−	71.9311i	0.0671447	−	0.0387660i	−0.466052	−	0.884757i	$-0.654324\pi$
$151$	124.588	−	71.9311i	0.0671447	−	0.0387660i	0.533197	+	0.845991i	$0.320991\pi$
$152$	−29.3833	+	50.8933i	−0.0156796	+	0.0271579i
$153$	43.8011	+	89.7939i	0.0231445	+	0.0474471i
$154$	−2529.18	+	1460.22i	−1.32342	+	0.764080i
$155$	−103.264	−	178.858i	−0.0535118	−	0.0926852i
$156$	1928.11	−	1138.95i	0.989564	−	0.584544i
$157$	1894.28	−	3280.98i	0.962928	−	1.66784i	0.247846	−	0.968799i	$-0.420277\pi$
$157$	1894.28	−	3280.98i	0.962928	−	1.66784i	0.715082	−	0.699041i	$-0.246389\pi$
$158$			1840.18i			0.926560i
$159$	−2008.22	+	1067.86i	−1.00165	+	0.532620i
$160$	−1251.90			−0.618573
$161$			2095.66i			1.02585i
$162$	−420.398	+	2993.52i	−0.203886	+	1.45181i
$163$	−1676.30	−	967.813i	−0.805510	−	0.465061i	0.0398843	−	0.999204i	$-0.487301\pi$
$163$	−1676.30	−	967.813i	−0.805510	−	0.465061i	−0.845394	+	0.534143i	$0.820634\pi$
$164$	−2944.87	+	1700.22i	−1.40217	+	0.809543i
$165$	960.998	+	600.464i	0.453416	+	0.283309i
$166$	2892.16			1.35226
$167$		−	2197.30i		−	1.01816i	−0.860720	−	0.509079i	$-0.829986\pi$
$167$		−	2197.30i		−	1.01816i	0.860720	−	0.509079i	$-0.170014\pi$
$168$	−354.107	+	188.294i	−0.162619	+	0.0864712i
$169$	−1264.49	−	1796.63i	−0.575554	−	0.817764i
$170$	74.0316			0.0333998
$171$	−287.905	+	140.439i	−0.128752	+	0.0628049i
$172$	968.626	+	1677.71i	0.429401	+	0.743745i
$173$	−2935.23			−1.28995			−0.644976	−	0.764203i	$-0.723132\pi$
$173$	−2935.23			−1.28995			−0.644976	+	0.764203i	$0.723132\pi$
$174$	−2277.10	+	3644.33i	−0.992105	+	1.58779i
$175$	−1372.68	+	792.514i	−0.592940	+	0.342334i
$176$	2075.25	−	1198.14i	0.888793	−	0.513145i
$177$	1276.64	−	2043.16i	0.542135	−	0.867648i
$178$	−1544.41			−0.650326
$179$	668.032	+	1157.07i	0.278945	+	0.483146i	0.971123	−	0.238581i	$-0.0766821\pi$
$179$	668.032	+	1157.07i	0.278945	+	0.483146i	−0.692178	+	0.721727i	$0.743349\pi$
$180$	993.049	+	669.746i	0.411209	+	0.277333i
$181$	−4103.79			−1.68526			−0.842630	−	0.538493i	$-0.818994\pi$
$181$	−4103.79			−1.68526			−0.842630	+	0.538493i	$0.818994\pi$
$182$	1630.34	+	2552.31i	0.664005	+	1.03951i
$183$	2272.74	−	1208.51i	0.918066	−	0.488175i
$184$			666.171i			0.266906i
$185$	−775.419			−0.308162
$186$	782.157	+	488.718i	0.308336	+	0.192659i
$187$	−144.840	+	83.6236i	−0.0566405	+	0.0327014i
$188$	1472.75	+	850.293i	0.571337	+	0.329862i
$189$	−2174.17	−	228.345i	−0.836758	−	0.0878816i
$190$			237.367i			0.0906336i
$191$	1791.70			0.678758			0.339379	−	0.940650i	$-0.389783\pi$
$191$	1791.70			0.678758			0.339379	+	0.940650i	$0.389783\pi$
$192$	2990.28	−	1590.06i	1.12398	−	0.597670i
$193$			2660.41i			0.992231i	0.868256	+	0.496116i	$0.165241\pi$
$193$			2660.41i			0.992231i	−0.868256	+	0.496116i	$0.834759\pi$
$194$	281.248	−	487.136i	0.104085	−	0.180280i
$195$	577.398	−	1023.49i	0.212043	−	0.375866i
$196$	460.621	+	797.819i	0.167865	+	0.290750i
$197$	−384.908	+	222.227i	−0.139206	+	0.0803705i	−0.567985	−	0.823039i	$-0.692277\pi$
$197$	−384.908	+	222.227i	−0.139206	+	0.0803705i	0.428780	+	0.903409i	$0.358944\pi$
$198$	−5048.08	−	352.736i	−1.81188	−	0.126605i
$199$	713.480	−	1235.78i	0.254157	−	0.440213i	−0.710509	−	0.703688i	$-0.751535\pi$
$199$	713.480	−	1235.78i	0.254157	−	0.440213i	0.964666	+	0.263475i	$0.0848686\pi$
$200$	−436.348	+	251.925i	−0.154272	+	0.0890691i
$201$	−568.483	−	1069.10i	−0.199491	−	0.375165i
$202$	2754.37	−	1590.24i	0.959391	−	0.553905i
$203$	−2691.36	−	1553.86i	−0.930526	−	0.537239i
$204$	−156.090	+	82.9995i	−0.0535709	+	0.0284859i
$205$	−892.204	+	1545.34i	−0.303972	+	0.526495i
$206$	1367.64	−	789.609i	0.462564	−	0.267062i
$207$	−2030.41	+	3010.54i	−0.681755	+	1.01086i
$208$	−1337.73	−	2094.22i	−0.445936	−	0.698117i
$209$	−268.121	−	464.400i	−0.0887385	−	0.153700i
$210$	−858.393	+	1373.79i	−0.282070	+	0.451433i
$211$	4491.04			1.46529			0.732645	−	0.680611i	$-0.238286\pi$
$211$	4491.04			1.46529			0.732645	+	0.680611i	$0.238286\pi$
$212$	−2012.34	−	3485.47i	−0.651924	−	1.12916i
$213$	4942.13	+	172.456i	1.58981	+	0.0554764i
$214$			2068.88i			0.660866i
$215$	880.390	+	508.293i	0.279266	+	0.161234i
$216$	−691.126	−	72.5864i	−0.217709	−	0.0228652i
$217$	−333.494	+	577.629i	−0.104327	+	0.180701i
$218$	3872.65	−	6707.63i	1.20316	−	2.08394i
$219$	2160.63	+	4063.31i	0.666676	+	1.25376i
$220$	−1002.57	+	1736.50i	−0.307241	+	0.532157i
$221$	93.3658	+	146.165i	0.0284184	+	0.0444892i
$222$	3057.41	−	1625.76i	0.924325	−	0.491503i
$223$	5100.14	+	2944.57i	1.53153	+	0.884228i	0.999292	+	0.0376324i	$0.0119816\pi$
$223$	5100.14	+	2944.57i	1.53153	+	0.884228i	0.532236	+	0.846596i	$0.321352\pi$
$224$	2021.54	+	3501.41i	0.602990	+	1.04441i
$225$	−2739.77	−	191.442i	−0.811784	−	0.0567235i
$226$		−	7502.61i		−	2.20826i
$227$			441.941i			0.129219i	0.997911	+	0.0646094i	$0.0205801\pi$
$227$			441.941i			0.129219i	−0.997911	+	0.0646094i	$0.979420\pi$
$228$	−266.120	−	500.469i	−0.0772994	−	0.145370i
$229$	−827.880	−	477.977i	−0.238899	−	0.137928i	0.375772	−	0.926712i	$-0.377378\pi$
$229$	−827.880	−	477.977i	−0.238899	−	0.137928i	−0.614671	+	0.788784i	$0.710711\pi$
$230$	1345.38	+	2330.27i	0.385703	+	0.668057i
$231$	127.625	−	3657.40i	0.0363511	−	1.04173i
$232$	−855.534	−	493.943i	−0.242106	−	0.139780i
$233$	−3455.74			−0.971643			−0.485822	−	0.874058i	$-0.661480\pi$
$233$	−3455.74			−0.971643			−0.485822	+	0.874058i	$0.661480\pi$
$234$	−130.763	+	5246.13i	−0.0365310	+	1.46560i
$235$	892.394			0.247717
$236$	3691.94	+	2131.54i	1.01832	+	0.587930i
$237$	−1955.57	−	1221.91i	−0.535983	−	0.334900i
$238$	−119.544	−	207.057i	−0.0325584	−	0.0563928i
$239$	−1556.43	−	898.605i	−0.421243	−	0.243205i	0.274366	−	0.961625i	$-0.411532\pi$
$239$	−1556.43	−	898.605i	−0.421243	−	0.243205i	−0.695609	+	0.718421i	$0.744865\pi$
$240$	704.329	−	1127.23i	0.189434	−	0.303176i
$241$			5699.63i			1.52343i	0.647915	+	0.761713i	$0.275641\pi$
$241$			5699.63i			1.52343i	−0.647915	+	0.761713i	$0.724359\pi$
$242$		−	2952.05i		−	0.784153i
$243$	−2902.09	−	2434.50i	−0.766127	−	0.642689i
$244$	2277.40	+	3944.57i	0.597523	+	1.03494i
$245$	418.661	+	241.714i	0.109173	+	0.0630308i
$246$	277.896	−	7963.77i	0.0720244	−	2.06403i
$247$	−468.647	+	299.358i	−0.120726	+	0.0771161i
$248$	−106.012	+	183.617i	−0.0271441	+	0.0470150i
$249$	−1920.44	+	3073.52i	−0.488766	+	0.782234i
$250$	−2268.00	+	3928.30i	−0.573765	+	0.993790i
$251$	−1524.95	+	2641.30i	−0.383483	+	0.664212i	−0.991557	−	0.129668i	$-0.958609\pi$
$251$	−1524.95	+	2641.30i	−0.383483	+	0.664212i	0.608075	+	0.793880i	$0.291942\pi$
$252$	269.642	−	3858.91i	0.0674042	−	0.964638i
$253$	−5264.38	−	3039.39i	−1.30818	−	0.755277i
$254$		−	7633.18i		−	1.88562i
$255$	−49.1582	+	78.6740i	−0.0120722	+	0.0193206i
$256$	−1307.25	−	2264.22i	−0.319153	−	0.552789i
$257$	−3374.76			−0.819112			−0.409556	−	0.912285i	$-0.634316\pi$
$257$	−3374.76			−0.819112			−0.409556	+	0.912285i	$0.634316\pi$
$258$	−4537.00	−	158.319i	−1.09481	−	0.0382035i
$259$	1252.12	+	2168.74i	0.300399	+	0.520306i
$260$	1845.59	+	957.920i	0.440225	+	0.228491i
$261$	−2360.83	−	4839.78i	−0.559891	−	1.14780i
$262$	7445.62	−	4298.73i	1.75569	−	1.01365i
$263$	2359.38	−	4086.57i	0.553178	−	0.958133i	−0.444865	−	0.895598i	$-0.646748\pi$
$263$	2359.38	−	4086.57i	0.553178	−	0.958133i	0.998043	−	0.0625348i	$-0.0199184\pi$
$264$	40.5696	−	1162.62i	0.00945790	−	0.271039i
$265$	−1829.02	−	1055.99i	−0.423985	−	0.244788i
$266$	663.883	−	383.293i	0.153027	−	0.0883504i
$267$	1025.51	−	1641.25i	0.235057	−	0.376191i
$268$	1855.52	−	1071.29i	0.422925	−	0.244176i
$269$	−318.110	+	550.982i	−0.0721022	+	0.124885i	−0.899822	−	0.436256i	$-0.856304\pi$
$269$	−318.110	+	550.982i	−0.0721022	+	0.124885i	0.827720	+	0.561141i	$0.189637\pi$
$270$	−2564.15	+	1141.87i	−0.577961	+	0.257378i
$271$	1685.24	−	972.975i	0.377753	−	0.218096i	−0.299087	−	0.954226i	$-0.596682\pi$
$271$	1685.24	−	972.975i	0.377753	−	0.218096i	0.676840	+	0.736130i	$0.263349\pi$
$272$	98.0883	+	169.894i	0.0218657	+	0.0378726i
$273$	−3794.94	+	37.8003i	−0.841319	+	0.00838014i
$274$	−2093.23	+	3625.58i	−0.461520	+	0.799377i
$275$		−	4597.62i		−	1.00817i
$276$	−5449.17	−	3404.83i	−1.18841	−	0.742560i
$277$	3079.00			0.667867			0.333933	−	0.942597i	$-0.391624\pi$
$277$	3079.00			0.667867			0.333933	+	0.942597i	$0.391624\pi$
$278$		−	7779.30i		−	1.67831i
$279$	−1038.73	+	506.688i	−0.222893	+	0.108726i
$280$	−322.509	−	186.201i	−0.0688343	−	0.0397415i
$281$	−8038.59	+	4641.08i	−1.70655	+	0.985280i	−0.767803	+	0.640686i	$0.778650\pi$
$281$	−8038.59	+	4641.08i	−1.70655	+	0.985280i	−0.938752	+	0.344594i	$0.888017\pi$
$282$	−3518.64	+	1871.01i	−0.743021	+	0.395096i
$283$	3854.14			0.809557			0.404779	−	0.914415i	$-0.367349\pi$
$283$	3854.14			0.809557			0.404779	+	0.914415i	$0.367349\pi$
$284$			8750.36i			1.82830i
$285$	−252.251	−	157.615i	−0.0524284	−	0.0327590i
$286$	−8776.04	+	393.793i	−1.81447	+	0.0814177i
$287$	5762.82			1.18526
$288$	−488.328	+	6988.58i	−0.0999132	+	1.42988i
$289$	2449.65	+	4242.93i	0.498607	+	0.863612i
$290$	−3990.21			−0.807977
$291$	330.930	+	622.351i	0.0666649	+	0.125371i
$292$	−7052.28	+	4071.63i	−1.41337	+	0.816008i
$293$	6838.83	−	3948.40i	1.36358	−	0.787263i	0.373481	−	0.927638i	$-0.378164\pi$
$293$	6838.83	−	3948.40i	1.36358	−	0.787263i	0.990098	+	0.140375i	$0.0448307\pi$
$294$	−2157.53	−	75.2871i	−0.427992	−	0.0149348i
$295$	2237.08			0.441519
$296$	398.027	+	689.403i	0.0781582	+	0.135374i
$297$	3726.86	−	5130.42i	0.728130	−	1.00235i
$298$	9434.47			1.83397
$299$	−2904.04	+	5595.10i	−0.561689	+	1.08218i
$300$	169.480	−	4856.86i	0.0326165	−	0.934703i
$301$		−	3283.11i		−	0.628689i
$302$	−596.543			−0.113666
$303$	−138.988	+	3983.04i	−0.0263520	+	0.755180i
$304$	−544.729	+	314.499i	−0.102771	+	0.0593348i
$305$	2069.94	+	1195.08i	0.388605	+	0.224361i
$306$	28.8774	−	413.271i	0.00539481	−	0.0772063i
$307$		−	407.325i		−	0.0757241i	−0.999283	−	0.0378620i	$-0.987945\pi$
$307$		−	407.325i		−	0.0757241i	0.999283	−	0.0378620i	$-0.0120547\pi$
$308$	6475.66			1.19800
$309$	−69.0126	+	1977.72i	−0.0127055	+	0.364105i
$310$			856.392i			0.156902i
$311$	−3581.74	+	6203.75i	−0.653060	+	1.13113i	0.329317	+	0.944220i	$0.393182\pi$
$311$	−3581.74	+	6203.75i	−0.653060	+	1.13113i	−0.982376	+	0.186913i	$0.940152\pi$
$312$	−1206.34	+	12.0160i	−0.218896	+	0.00218036i
$313$	3990.28	+	6911.36i	0.720587	+	1.24809i	0.960765	+	0.277364i	$0.0894609\pi$
$313$	3990.28	+	6911.36i	0.720587	+	1.24809i	−0.240178	+	0.970729i	$0.577206\pi$
$314$	−13605.0	+	7854.86i	−2.44515	+	1.41171i
$315$	−889.957	−	1824.44i	−0.159185	−	0.326336i
$316$	2040.16	−	3533.66i	0.363189	−	0.629063i
$317$	−1490.33	+	860.444i	−0.264055	+	0.152452i	−0.626183	−	0.779676i	$-0.715384\pi$
$317$	−1490.33	+	860.444i	−0.264055	+	0.152452i	0.362128	+	0.932128i	$0.382050\pi$
$318$	9425.70	+	328.910i	1.66216	+	0.0580012i
$319$	7806.72	−	4507.21i	1.37020	−	0.791083i
$320$	2723.45	+	1572.39i	0.475768	+	0.274685i
$321$	−2198.61	−	1373.77i	−0.382288	−	0.238867i
$322$	4344.96	−	7525.70i	0.751973	−	1.30246i
$323$	38.0190	−	21.9503i	0.00654933	−	0.00378126i
$324$	4126.12	−	5282.32i	0.707497	−	0.905747i
$325$	−4763.06	+	213.725i	−0.812945	+	0.0364779i
$326$	4013.16	+	6951.00i	0.681805	+	1.18092i
$327$	4556.75	+	8569.48i	0.770609	+	1.44921i
$328$	1831.89			0.308382
$329$	−1441.01	−	2495.91i	−0.241476	−	0.418249i
$330$	−2206.08	−	4148.77i	−0.368002	−	0.692068i
$331$		−	8642.27i		−	1.43511i	−0.696501	−	0.717556i	$-0.745261\pi$
$331$		−	8642.27i		−	1.43511i	0.696501	−	0.717556i	$-0.254739\pi$
$332$	−5553.76	−	3206.46i	−0.918078	−	0.530053i
$333$	−302.466	+	4328.67i	−0.0497750	+	0.712341i
$334$	−4555.70	+	7890.70i	−0.746337	+	1.29269i
$335$	562.165	−	973.698i	0.0916846	−	0.158802i
$336$	−4290.03	−	149.701i	−0.696549	−	0.0243061i
$337$	4315.56	−	7474.77i	0.697577	−	1.20824i	−0.271727	−	0.962374i	$-0.587595\pi$
$337$	4315.56	−	7474.77i	0.697577	−	1.20824i	0.969304	−	0.245864i	$-0.0790718\pi$
$338$	815.926	+	9073.53i	0.131303	+	1.46016i
$339$	7973.09	+	4981.85i	1.27740	+	0.798162i
$340$	−142.162	−	82.0770i	−0.0226759	−	0.0130919i
$341$	−967.352	−	1675.50i	−0.153622	−	0.266081i
$342$	1325.07	+	92.5892i	0.209507	+	0.0146393i
$343$		−	6905.95i		−	1.08713i
$344$		−	1043.64i		−	0.163573i
$345$	−3369.75	−	117.587i	−0.525858	−	0.0183498i
$346$	10540.7	+	6085.66i	1.63777	+	0.945570i
$347$	5717.41	+	9902.84i	0.884514	+	1.53202i	0.846270	+	0.532755i	$0.178843\pi$
$347$	5717.41	+	9902.84i	0.884514	+	1.53202i	0.0382445	+	0.999268i	$0.487823\pi$
$348$	8413.05	−	4473.57i	1.29594	−	0.689105i
$349$	−4032.59	−	2328.21i	−0.618508	−	0.357096i	0.157780	−	0.987474i	$-0.449566\pi$
$349$	−4032.59	−	2328.21i	−0.618508	−	0.357096i	−0.776288	+	0.630378i	$0.782900\pi$
$350$	6572.53			1.00376
$351$	−5488.28	−	3622.48i	−0.834594	−	0.550865i
$352$	−11727.6			−1.77580
$353$	−7582.18	−	4377.57i	−1.14323	−	0.660042i	−0.195998	−	0.980604i	$-0.562795\pi$
$353$	−7582.18	−	4377.57i	−1.14323	−	0.660042i	−0.947227	+	0.320563i	$0.896128\pi$
$354$	−8820.64	+	4690.31i	−1.32433	+	0.704201i
$355$	2295.91	+	3976.63i	0.343251	+	0.594528i
$356$	2965.69	+	1712.24i	0.441521	+	0.254912i
$357$	299.420	+	10.4483i	0.0443893	+	0.00154897i
$358$		−	5540.16i		−	0.817896i
$359$			9826.13i			1.44458i	0.691591	+	0.722289i	$0.256910\pi$
$359$			9826.13i			1.44458i	−0.691591	+	0.722289i	$0.743090\pi$
$360$	−282.900	−	579.956i	−0.0414171	−	0.0849066i
$361$	−3359.12	−	5818.17i	−0.489739	−	0.848253i
$362$	14737.0	+	8508.44i	2.13967	+	1.23534i
$363$	3137.17	+	1960.21i	0.453605	+	0.283428i
$364$	−301.028	−	6708.68i	−0.0433465	−	0.966018i
$365$	−2136.62	+	3700.73i	−0.306399	+	0.530699i
$366$	−10667.2	−	372.234i	−1.52346	−	0.0531612i
$367$	−3902.90	+	6760.02i	−0.555122	+	0.961499i	0.442772	+	0.896634i	$0.353995\pi$
$367$	−3902.90	+	6760.02i	−0.555122	+	0.961499i	−0.997894	+	0.0648650i	$0.979338\pi$
$368$	−3565.13	+	6174.98i	−0.505014	+	0.874710i
$369$	8278.64	+	5583.40i	1.16794	+	0.787696i
$370$	2784.60	+	1607.69i	0.391255	+	0.225891i
$371$			6820.72i			0.954485i
$372$	−960.132	−	1805.63i	−0.133819	−	0.251661i
$373$	−1005.60	−	1741.75i	−0.139592	−	0.241781i	0.787750	−	0.615995i	$-0.211246\pi$
$373$	−1005.60	−	1741.75i	−0.139592	−	0.241781i	−0.927342	+	0.374214i	$0.877913\pi$
$374$	693.512			0.0958842
$375$	−2668.64	−	5018.68i	−0.367489	−	0.691103i
$376$	−458.071	−	793.402i	−0.0628277	−	0.108821i
$377$	−5032.30	−	7878.11i	−0.687471	−	1.07624i
$378$	7334.19	+	5327.74i	0.997963	+	0.724945i
$379$	8431.71	−	4868.05i	1.14276	−	0.659775i	0.195651	−	0.980674i	$-0.437318\pi$
$379$	8431.71	−	4868.05i	1.14276	−	0.659775i	0.947114	+	0.320898i	$0.103985\pi$
$380$	263.163	−	455.811i	0.0355262	−	0.0615332i
$381$	8111.84	+	5068.55i	1.09077	+	0.681548i
$382$	−6434.15	−	3714.76i	−0.861779	−	0.497548i
$383$	−1112.25	+	642.160i	−0.148390	+	0.0856733i	−0.572357	−	0.820005i	$-0.693971\pi$
$383$	−1112.25	+	642.160i	−0.148390	+	0.0856733i	0.423966	+	0.905678i	$0.360637\pi$
$384$	−3255.76	−	113.610i	−0.432669	−	0.0150980i
$385$	2942.88	−	1699.08i	0.389567	−	0.224917i
$386$	5515.87	−	9553.77i	0.727333	−	1.25978i
$387$	3180.89	−	4716.39i	0.417813	−	0.619502i
$388$	−1080.15	+	623.626i	−0.141331	+	0.0815974i
$389$	−2696.83	−	4671.05i	−0.351503	−	0.608822i	0.635010	−	0.772504i	$-0.280996\pi$
$389$	−2696.83	−	4671.05i	−0.351503	−	0.608822i	−0.986513	+	0.163682i	$0.947663\pi$
$390$	−4195.51	+	2478.32i	−0.544738	+	0.321781i
$391$	248.826	−	430.979i	0.0321833	−	0.0557431i
$392$		−	496.293i		−	0.0639453i
$393$	−375.713	+	10766.9i	−0.0482245	+	1.38199i
$394$	1842.98			0.235655
$395$		−	2141.17i		−	0.272745i
$396$	9302.68	+	6274.04i	1.18050	+	0.796168i
$397$	8683.28	+	5013.29i	1.09774	+	0.633778i	0.935625	−	0.352994i	$-0.114837\pi$
$397$	8683.28	+	5013.29i	1.09774	+	0.633778i	0.162111	+	0.986773i	$0.448170\pi$
$398$	−5124.34	+	2958.54i	−0.645376	+	0.372608i
$399$	−33.5002	+	960.027i	−0.00420327	+	0.120455i
$400$	−5392.89			−0.674111
$401$		−	3025.48i		−	0.376771i	−0.982095	−	0.188386i	$-0.939675\pi$
$401$		−	3025.48i		−	0.376771i	0.982095	−	0.188386i	$-0.0603254\pi$
$402$	−175.098	+	5017.86i	−0.0217242	+	0.622557i
$403$	−1690.83	+	1080.05i	−0.208998	+	0.133501i
$404$	−7052.23			−0.868470
$405$	489.162	−	3483.17i	0.0600165	−	0.427358i
$406$	6443.28	+	11160.1i	0.787622	+	1.36420i
$407$	−7263.96			−0.884671
$408$	95.1799	+	3.32131i	0.0115493	+	0.000403013i
$409$	−10432.3	+	6023.11i	−1.26124	+	0.728175i	−0.973314	−	0.229479i	$-0.926298\pi$
$409$	−10432.3	+	6023.11i	−1.26124	+	0.728175i	−0.287922	+	0.957654i	$0.592964\pi$
$410$	6407.96	−	3699.64i	0.771870	−	0.445639i
$411$	−2463.00	−	4631.93i	−0.295598	−	0.555904i
$412$	−3501.68			−0.418727
$413$	−3612.38	−	6256.82i	−0.430396	−	0.745468i
$414$	13533.2	−	6601.43i	1.60657	−	0.783678i
$415$	−3365.23			−0.398054
$416$	545.168	+	12149.6i	0.0642525	+	1.43193i
$417$	8267.13	+	5165.58i	0.970846	+	0.606618i
$418$			2223.60i			0.260191i
$419$	555.751			0.0647977			0.0323989	−	0.999475i	$-0.489685\pi$
$419$	555.751			0.0647977			0.0323989	+	0.999475i	$0.489685\pi$
$420$	3171.45	−	1686.39i	0.368455	−	0.195923i
$421$	3191.54	−	1842.64i	0.369469	−	0.213313i	−0.303758	−	0.952749i	$-0.598241\pi$
$421$	3191.54	−	1842.64i	0.369469	−	0.213313i	0.673226	+	0.739437i	$0.264908\pi$
$422$	−16127.7	−	9311.34i	−1.86039	−	1.07410i
$423$	348.095	−	4981.67i	0.0400117	−	0.572617i
$424$			2168.18i			0.248340i
$425$	376.393			0.0429594
$426$	−17390.1	−	10865.9i	−1.97782	−	1.23581i
$427$		−	7719.14i		−	0.874837i
$428$	2293.71	−	3972.83i	0.259044	−	0.448677i
$429$	5408.95	−	9587.86i	0.608733	−	1.07904i
$430$	−2107.70	−	3650.65i	−0.236378	−	0.409419i
$431$	9362.89	−	5405.67i	1.04639	−	0.604134i	0.124754	−	0.992188i	$-0.460186\pi$
$431$	9362.89	−	5405.67i	1.04639	−	0.604134i	0.921637	+	0.388053i	$0.126852\pi$
$432$	−6017.85	−	4371.51i	−0.670217	−	0.486862i
$433$	−2665.15	+	4616.18i	−0.295795	+	0.512331i	−0.975169	−	0.221460i	$-0.928918\pi$
$433$	−2665.15	+	4616.18i	−0.295795	+	0.512331i	0.679375	+	0.733791i	$0.262251\pi$
$434$	2395.21	−	1382.88i	0.264917	−	0.152950i
$435$	2649.56	−	4240.43i	0.292039	−	0.467386i
$436$	−14873.2	+	8587.03i	−1.63371	+	0.943221i
$437$	1381.84	+	797.807i	0.151264	+	0.0873325i
$438$	665.496	−	19071.4i	0.0725996	−	2.08051i
$439$	3198.24	−	5539.51i	0.347707	−	0.602247i	−0.638134	−	0.769925i	$-0.720294\pi$
$439$	3198.24	−	5539.51i	0.347707	−	0.602247i	0.985842	+	0.167678i	$0.0536269\pi$
$440$	935.487	−	540.104i	0.101358	−	0.0585192i
$441$	1512.64	−	2242.83i	0.163335	−	0.242180i
$442$	−32.2386	−	718.468i	−0.00346931	−	0.0773168i
$443$	−3255.46	−	5638.62i	−0.349146	−	0.604738i	0.636952	−	0.770903i	$-0.280195\pi$
$443$	−3255.46	−	5638.62i	−0.349146	−	0.604738i	−0.986098	+	0.166165i	$0.946861\pi$
$444$	−7673.54	−	267.768i	−0.820203	−	0.0286210i
$445$	1797.02			0.191432
$446$	−12210.0	−	21148.4i	−1.29633	−	2.24530i
$447$	−6264.64	+	10026.1i	−0.662880	+	1.06089i
$448$		−	10156.2i		−	1.07106i
$449$	−9428.38	−	5443.48i	−0.990986	−	0.572146i	−0.0854173	−	0.996345i	$-0.527222\pi$
$449$	−9428.38	−	5443.48i	−0.990986	−	0.572146i	−0.905569	+	0.424199i	$0.860556\pi$
$450$	9441.83	+	6367.89i	0.989094	+	0.667078i
$451$	−8357.98	+	14476.4i	−0.872643	+	1.51146i
$452$	−8317.96	+	14407.1i	−0.865584	+	1.49924i
$453$	396.114	−	633.951i	0.0410840	−	0.0657519i
$454$	916.283	−	1587.05i	0.0947209	−	0.164061i
$455$	−1897.02	−	2969.80i	−0.195458	−	0.305992i
$456$	−10.6491	+	305.174i	−0.00109361	+	0.0313401i
$457$	−6900.23	−	3983.85i	−0.706300	−	0.407783i	0.103389	−	0.994641i	$-0.467031\pi$
$457$	−6900.23	−	3983.85i	−0.706300	−	0.407783i	−0.809690	+	0.586858i	$0.800365\pi$
$458$	1981.99	+	3432.91i	0.202210	+	0.350239i
$459$	420.012	+	305.107i	0.0427113	+	0.0310265i
$460$		−	5966.36i		−	0.604745i
$461$		−	16099.7i		−	1.62654i	−0.581885	−	0.813271i	$-0.697685\pi$
$461$		−	16099.7i		−	1.62654i	0.581885	−	0.813271i	$-0.302315\pi$
$462$	−8041.25	+	12869.4i	−0.809768	+	1.29597i
$463$	−14967.4	−	8641.42i	−1.50236	−	0.867388i	−0.999996	−	0.00273207i	$-0.999130\pi$
$463$	−14967.4	−	8641.42i	−1.50236	−	0.867388i	−0.502364	−	0.864656i	$-0.667536\pi$
$464$	−5286.84	−	9157.08i	−0.528956	−	0.916178i
$465$	−910.095	−	568.658i	−0.0907626	−	0.0567115i
$466$	12409.9	+	7164.83i	1.23364	+	0.712241i
$467$	3133.28			0.310473			0.155237	−	0.987877i	$-0.450386\pi$
$467$	3133.28			0.310473			0.155237	+	0.987877i	$0.450386\pi$
$468$	6067.36	−	9929.08i	0.599282	−	0.980709i
$469$	−3631.07			−0.357500
$470$	−3204.66	−	1850.21i	−0.314511	−	0.181583i
$471$	686.522	−	19673.9i	0.0671619	−	1.92468i
$472$	−1148.31	−	1988.93i	−0.111981	−	0.193957i
$473$	8247.31	+	4761.59i	0.801716	+	0.462871i
$474$	4489.23	+	8442.48i	0.435015	+	0.818093i
$475$			1206.82i			0.116575i
$476$			530.143i			0.0510484i
$477$	−6608.35	+	9798.37i	−0.634330	+	0.940538i
$478$	3726.18	+	6453.94i	0.356552	+	0.617565i
$479$	9386.93	+	5419.55i	0.895407	+	0.516964i	0.875707	−	0.482842i	$-0.160396\pi$
$479$	9386.93	+	5419.55i	0.895407	+	0.516964i	0.0196998	+	0.999806i	$0.493729\pi$
$480$	−5743.57	+	3054.10i	−0.546160	+	0.290416i
$481$	337.673	+	7525.35i	0.0320094	+	0.713360i
$482$	11817.1	−	20467.9i	1.11671	−	1.93420i
$483$	5112.50	+	9614.61i	0.481629	+	0.905755i
$484$	−3272.87	+	5668.77i	−0.307369	+	0.532379i
$485$	−327.252	+	566.817i	−0.0306387	+	0.0530677i
$486$	5374.15	+	14759.4i	0.501597	+	1.37758i
$487$	−1248.82	−	721.005i	−0.116200	−	0.0670880i	0.440774	−	0.897618i	$-0.354704\pi$
$487$	−1248.82	−	721.005i	−0.116200	−	0.0670880i	−0.556973	+	0.830530i	$0.688037\pi$
$488$		−	2453.77i		−	0.227617i
$489$	−10051.7	−	350.754i	−0.929557	−	0.0324369i
$490$	−1002.30	−	1736.03i	−0.0924066	−	0.160053i
$491$	15805.4			1.45273			0.726363	−	0.687311i	$-0.241209\pi$
$491$	15805.4			1.45273			0.726363	+	0.687311i	$0.241209\pi$
$492$	−9362.88	+	14984.6i	−0.857950	+	1.37309i
$493$	368.992	+	639.112i	0.0337090	+	0.0583857i
$494$	2303.61	−	103.366i	0.209807	−	0.00941431i
$495$	5873.80	+	410.433i	0.533349	+	0.0372679i
$496$	−1965.32	+	1134.68i	−0.177914	+	0.102719i
$497$	7414.73	−	12842.7i	0.669208	−	1.15910i
$498$	13268.8	−	7055.60i	1.19396	−	0.634877i
$499$	4054.09	+	2340.63i	0.363700	+	0.209982i	0.670702	−	0.741727i	$-0.265993\pi$
$499$	4054.09	+	2340.63i	0.363700	+	0.209982i	−0.307003	+	0.951709i	$0.599326\pi$
$500$	8710.42	−	5028.96i	0.779083	−	0.449804i
$501$	−5360.46	−	10080.9i	−0.478019	−	0.898967i
$502$	10952.5	−	6323.41i	0.973771	−	0.562207i
$503$	6676.54	−	11564.1i	0.591834	−	1.02509i	−0.402152	−	0.915573i	$-0.631738\pi$
$503$	6676.54	−	11564.1i	0.591834	−	1.02509i	0.993985	−	0.109513i	$-0.0349291\pi$
$504$	−1165.24	+	1727.73i	−0.102984	+	0.152697i
$505$	−3204.91	+	1850.36i	−0.282409	+	0.163049i
$506$	12603.2	+	21829.4i	1.10728	+	1.91786i
$507$	−10184.3	−	5157.88i	−0.892112	−	0.451813i
$508$	−8462.72	+	14657.9i	−0.739119	+	1.28019i
$509$		−	4598.43i		−	0.400436i	−0.979751	−	0.200218i	$-0.935835\pi$
$509$		−	4598.43i		−	0.400436i	0.979751	−	0.200218i	$-0.0641651\pi$
$510$	339.647	−	180.605i	0.0294899	−	0.0156810i
$511$	13800.6			1.19472
$512$			15857.0i			1.36872i
$513$	−978.261	+	1346.68i	−0.0841935	+	0.115901i
$514$	12119.1	+	6996.94i	1.03998	+	0.600431i
$515$	−1591.35	+	918.766i	−0.136162	+	0.0786130i
$516$	8536.81	+	5334.08i	0.728318	+	0.455077i
$517$	8359.76			0.711145
$518$		−	10384.2i		−	0.880802i
$519$	−13466.5	+	7160.68i	−1.13894	+	0.605625i
$520$	−603.026	−	944.043i	−0.0508547	−	0.0796135i
$521$	21107.9			1.77496			0.887482	−	0.460843i	$-0.152453\pi$
$521$	21107.9			1.77496			0.887482	+	0.460843i	$0.152453\pi$
$522$	−1556.46	+	22274.8i	−0.130506	+	1.86770i
$523$	−551.772	−	955.697i	−0.0461325	−	0.0799039i	0.842037	−	0.539420i	$-0.181356\pi$
$523$	−551.772	−	955.697i	−0.0461325	−	0.0799039i	−0.888170	+	0.459516i	$0.848023\pi$
$524$	−19063.6			−1.58931
$525$	−4364.26	+	6984.68i	−0.362804	+	0.580641i
$526$	−16945.5	+	9783.49i	−1.40468	+	0.810989i
$527$	137.168	−	79.1941i	0.0113380	−	0.00654602i
$528$	6598.00	−	10559.6i	0.543828	−	0.870357i
$529$	5920.69			0.486619
$530$	4378.79	+	7584.29i	0.358873	+	0.621586i
$531$	872.615	−	12488.2i	0.0713150	−	1.02061i
$532$	−1699.79			−0.138525
$533$	15385.9	+	7985.78i	1.25035	+	0.648973i
$534$	−7085.53	+	3767.67i	−0.574196	+	0.305324i
$535$		−	2407.28i		−	0.194534i
$536$	−1154.25			−0.0930149
$537$	5887.58	+	3678.76i	0.473124	+	0.295624i
$538$	2284.72	−	1319.08i	0.183088	−	0.105706i
$539$	3921.93	+	2264.33i	0.313413	+	0.180949i
$540$	6189.87	+	650.099i	0.493277	+	0.0518070i
$541$		−	8406.46i		−	0.668063i	−0.942562	−	0.334031i	$-0.891591\pi$
$541$		−	8406.46i		−	0.668063i	0.942562	−	0.334031i	$-0.108409\pi$
$542$	−8069.13			−0.639481
$543$	−18827.6	+	10011.4i	−1.48798	+	0.791220i
$544$		−	960.100i		−	0.0756690i
$545$	−4506.11	+	7804.81i	−0.354166	+	0.613433i
$546$	13706.3	+	7732.36i	1.07432	+	0.606070i
$547$	−6012.48	−	10413.9i	−0.469972	−	0.814016i	0.529438	−	0.848349i	$-0.322403\pi$
$547$	−6012.48	−	10413.9i	−0.469972	−	0.814016i	−0.999410	+	0.0343326i	$0.989069\pi$
$548$	8039.18	−	4641.42i	0.626673	−	0.361810i
$549$	7478.80	−	11089.0i	0.581398	−	0.862053i
$550$	−9532.32	+	16510.5i	−0.739017	+	1.28001i
$551$	−2049.18	+	1183.09i	−0.158435	+	0.0914727i
$552$	1625.17	+	3056.30i	0.125311	+	0.235661i
$553$	−5988.58	+	3457.51i	−0.460507	+	0.265874i
$554$	−11057.0	−	6383.73i	−0.847951	−	0.489565i
$555$	−3557.52	+	1891.68i	−0.272087	+	0.144680i
$556$	−8624.72	+	14938.5i	−0.657859	+	1.13945i
$557$	−8287.38	+	4784.72i	−0.630427	+	0.363977i	−0.780917	−	0.624635i	$-0.785248\pi$
$557$	−8287.38	+	4784.72i	−0.630427	+	0.363977i	0.150491	+	0.988611i	$0.451915\pi$
$558$	4780.69	+	334.051i	0.362693	+	0.0253432i
$559$	4549.54	−	8765.43i	0.344231	−	0.663216i
$560$	−1992.97	−	3451.93i	−0.150390	−	0.260483i
$561$	−460.503	+	737.002i	−0.0346568	+	0.0554656i
$562$	38489.7			2.88895
$563$	−1435.16	−	2485.77i	−0.107433	−	0.186079i	0.807297	−	0.590146i	$-0.200930\pi$
$563$	−1435.16	−	2485.77i	−0.107433	−	0.186079i	−0.914730	+	0.404067i	$0.867596\pi$
$564$	8831.13	+	308.162i	0.659322	+	0.0230071i
$565$			8729.82i			0.650029i
$566$	−13840.5	−	7990.84i	−1.02785	−	0.593428i
$567$	−10531.8	+	4256.40i	−0.780064	+	0.315259i
$568$	2357.00	−	4082.45i	0.174116	−	0.301577i
$569$	−3062.25	+	5303.98i	−0.225617	+	0.390781i	−0.956505	−	0.291718i	$-0.905773\pi$
$569$	−3062.25	+	5303.98i	−0.225617	+	0.390781i	0.730887	+	0.682498i	$0.239107\pi$
$570$	579.071	+	1089.01i	0.0425520	+	0.0800236i
$571$	−6559.23	+	11360.9i	−0.480727	+	0.832644i	−0.999755	−	0.0221130i	$-0.992961\pi$
$571$	−6559.23	+	11360.9i	−0.480727	+	0.832644i	0.519028	+	0.854757i	$0.326294\pi$
$572$	17289.1	+	8973.59i	1.26380	+	0.655952i
$573$	8220.08	−	4370.96i	0.599300	−	0.318673i
$574$	−20694.8	−	11948.1i	−1.50485	−	0.868826i
$575$	6840.21	+	11847.6i	0.496098	+	0.859267i
$576$	9839.97	−	14590.0i	0.711803	−	1.05541i
$577$			19378.4i			1.39815i	0.715049	+	0.699074i	$0.246404\pi$
$577$			19378.4i			1.39815i	−0.715049	+	0.699074i	$0.753596\pi$
$578$		−	20315.6i		−	1.46197i
$579$	6490.24	+	12205.6i	0.465847	+	0.876076i
$580$	7662.33	+	4423.85i	0.548554	+	0.316708i
$581$	5434.07	+	9412.09i	0.388027	+	0.672082i
$582$	101.930	−	2921.04i	0.00725966	−	0.208043i
$583$	−17133.9	−	9892.27i	−1.21718	−	0.702738i
$584$	4386.95			0.310845
$585$	152.152	−	6104.25i	0.0107534	−	0.431418i
$586$	−32745.1			−2.30834
$587$	2312.61	+	1335.18i	0.162609	+	0.0938824i	0.579096	−	0.815259i	$-0.303406\pi$
$587$	2312.61	+	1335.18i	0.162609	+	0.0938824i	−0.416487	+	0.909142i	$0.636739\pi$
$588$	4059.60	+	2536.57i	0.284719	+	0.177902i
$589$	253.919	+	439.801i	0.0177633	+	0.0307669i
$590$	−8033.56	−	4638.18i	−0.560570	−	0.323645i
$591$	−1223.77	+	1958.55i	−0.0851763	+	0.136318i
$592$			8520.44i			0.591533i
$593$		−	723.279i		−	0.0500869i	−0.999686	−	0.0250434i	$-0.992028\pi$
$593$		−	723.279i		−	0.0500869i	0.999686	−	0.0250434i	$-0.00797241\pi$
$594$	−24020.5	+	10696.8i	−1.65921	+	0.738882i
$595$	139.098	+	240.925i	0.00958397	+	0.0165999i
$596$	−18116.9	−	10459.8i	−1.24513	−	0.718874i
$597$	258.579	−	7410.19i	0.0177269	−	0.508005i
$598$	22029.1	−	14071.5i	1.50641	−	0.962252i
$599$	−274.189	+	474.910i	−0.0187030	+	0.0323945i	−0.875225	−	0.483715i	$-0.839287\pi$
$599$	−274.189	+	474.910i	−0.0187030	+	0.0323945i	0.856522	+	0.516110i	$0.172620\pi$
$600$	−1387.32	+	2220.30i	−0.0943950	+	0.151072i
$601$	−10132.4	+	17549.9i	−0.687705	+	1.19114i	0.284874	+	0.958565i	$0.408048\pi$
$601$	−10132.4	+	17549.9i	−0.687705	+	1.19114i	−0.972579	+	0.232575i	$0.925285\pi$
$602$	−6806.92	+	11789.9i	−0.460846	+	0.798209i
$603$	−5216.25	−	3518.02i	−0.352276	−	0.237587i
$604$	1145.53	+	661.373i	0.0771705	+	0.0445544i
$605$			3434.92i			0.230825i
$606$	8757.21	−	14015.3i	0.587026	−	0.939491i
$607$	−11258.1	−	19499.6i	−0.752802	−	1.30389i	−0.946459	−	0.322823i	$-0.895368\pi$
$607$	−11258.1	−	19499.6i	−0.752802	−	1.30389i	0.193657	−	0.981069i	$-0.437965\pi$
$608$	3078.36			0.205335
$609$	−16138.4	−	563.149i	−1.07383	−	0.0374712i
$610$	−4955.56	−	8583.28i	−0.328926	−	0.569716i
$611$	−388.612	−	8660.58i	−0.0257309	−	0.573436i
$612$	−513.636	+	761.582i	−0.0339257	+	0.0503025i
$613$	12284.6	−	7092.50i	0.809411	−	0.467314i	−0.0373402	−	0.999303i	$-0.511889\pi$
$613$	12284.6	−	7092.50i	0.809411	−	0.467314i	0.846751	+	0.531989i	$0.178555\pi$
$614$	−844.514	+	1462.74i	−0.0555078	+	0.0961424i
$615$	−323.352	+	9266.41i	−0.0212013	+	0.607574i
$616$	−3021.20	−	1744.29i	−0.197610	−	0.114090i
$617$	−3808.76	+	2198.99i	−0.248517	+	0.143481i	−0.619085	−	0.785324i	$-0.712496\pi$
$617$	−3808.76	+	2198.99i	−0.248517	+	0.143481i	0.370568	+	0.928805i	$0.379163\pi$
$618$	4348.26	−	6959.08i	0.283031	−	0.452969i
$619$	3542.68	−	2045.37i	0.230036	−	0.132811i	−0.380553	−	0.924759i	$-0.624266\pi$
$619$	3542.68	−	2045.37i	0.230036	−	0.132811i	0.610589	+	0.791948i	$0.290933\pi$
$620$	949.461	−	1644.51i	0.0615020	−	0.106525i
$621$	−1970.85	+	18765.3i	−0.127355	+	1.21260i
$622$	25724.6	−	14852.1i	1.65830	−	0.957421i
$623$	−2901.79	−	5026.04i	−0.186609	−	0.323217i
$624$	−11246.3	−	6344.55i	−0.721495	−	0.407028i
$625$	−3718.54	+	6440.70i	−0.237987	+	0.412205i
$626$		−	33092.4i		−	2.11284i
$627$	−2363.04	−	1476.51i	−0.150511	−	0.0940446i
$628$	34834.0			2.21342
$629$		−	594.678i		−	0.0376969i
$630$	−586.734	+	8396.89i	−0.0371048	+	0.531016i
$631$	−21280.2	−	12286.1i	−1.34255	−	0.775122i	−0.355370	−	0.934726i	$-0.615645\pi$
$631$	−21280.2	−	12286.1i	−1.34255	−	0.775122i	−0.987181	+	0.159603i	$0.948979\pi$
$632$	−1903.66	+	1099.08i	−0.119816	+	0.0691755i
$633$	20604.3	−	10956.2i	1.29376	−	0.687945i
$634$	7135.89			0.447007
$635$			8881.74i			0.555057i
$636$	−17735.4	−	11081.6i	−1.10574	−	0.690905i
$637$	2163.49	−	4168.32i	0.134569	−	0.259270i
$638$	−37379.5			−2.31954
$639$	23094.5	−	11265.4i	1.42974	−	0.697423i
$640$	−1512.49	−	2619.72i	−0.0934165	−	0.161802i
$641$	27091.7			1.66935			0.834677	−	0.550739i	$-0.185654\pi$
$641$	27091.7			1.66935			0.834677	+	0.550739i	$0.185654\pi$
$642$	5047.15	+	9491.73i	0.310273	+	0.583502i
$643$	−10565.8	+	6100.14i	−0.648013	+	0.374131i	−0.787695	−	0.616066i	$-0.788726\pi$
$643$	−10565.8	+	6100.14i	−0.648013	+	0.374131i	0.139681	+	0.990197i	$0.455392\pi$
$644$	−16687.1	+	9634.31i	−1.02106	+	0.589511i
$645$	5279.13	+	184.215i	0.322272	+	0.0112457i
$646$	−182.039			−0.0110871
$647$	−8686.06	−	15044.7i	−0.527796	−	0.914170i	−0.999475	−	0.0323993i	$-0.989685\pi$
$647$	−8686.06	−	15044.7i	−0.527796	−	0.914170i	0.471679	−	0.881770i	$-0.343648\pi$
$648$	−3347.88	+	1353.03i	−0.202958	+	0.0820248i
$649$	20956.5			1.26751
$650$	17547.7	+	9107.82i	1.05889	+	0.549597i
$651$	−120.865	+	3463.67i	−0.00727660	+	0.208528i
$652$		−	17797.2i		−	1.06901i
$653$	−17666.7			−1.05873			−0.529367	−	0.848393i	$-0.677571\pi$
$653$	−17666.7			−1.05873			−0.529367	+	0.848393i	$0.677571\pi$
$654$	1403.52	−	40221.3i	0.0839177	−	2.40486i
$655$	−8663.51	+	5001.88i	−0.516811	+	0.298381i
$656$	16980.5	+	9803.69i	1.01064	+	0.583491i
$657$	19825.4	+	13370.9i	1.17726	+	0.793987i
$658$			11950.7i			0.708034i
$659$	−3389.99			−0.200388			−0.100194	−	0.994968i	$-0.531946\pi$
$659$	−3389.99			−0.200388			−0.100194	+	0.994968i	$0.531946\pi$
$660$	−363.349	+	10412.6i	−0.0214293	+	0.614108i
$661$			4621.97i			0.271973i	0.990711	+	0.135986i	$0.0434203\pi$
$661$			4621.97i			0.271973i	−0.990711	+	0.135986i	$0.956580\pi$
$662$	−17918.1	+	31035.1i	−1.05198	+	1.82208i
$663$	784.929	+	442.814i	0.0459790	+	0.0259389i
$664$	1727.39	+	2991.93i	0.100957	+	0.174863i
$665$	−772.475	+	445.989i	−0.0450455	+	0.0260071i
$666$	10060.9	−	14917.5i	0.585362	−	0.867931i
$667$	−13411.4	+	23229.2i	−0.778548	+	1.34848i
$668$	17496.5	−	10101.6i	1.01341	−	0.585093i
$669$	30582.2	+	1067.17i	1.76738	+	0.0616728i
$670$	−4037.57	+	2331.09i	−0.232813	+	0.134415i
$671$	19390.8	+	11195.3i	1.11561	+	0.644097i
$672$	17816.5	+	11132.3i	1.02275	+	0.639046i
$673$	−7660.42	+	13268.2i	−0.438763	+	0.759959i	−0.997594	−	0.0693218i	$-0.977916\pi$
$673$	−7660.42	+	13268.2i	−0.438763	+	0.759959i	0.558832	+	0.829281i	$0.311250\pi$
$674$	−30995.1	+	17895.0i	−1.77134	+	1.02269i
$675$	−13036.7	+	5805.53i	−0.743384	+	0.331045i
$676$	8492.80	−	18328.3i	0.483204	−	1.04281i
$677$	−4939.85	−	8556.07i	−0.280434	−	0.485726i	0.691058	−	0.722800i	$-0.257145\pi$
$677$	−4939.85	−	8556.07i	−0.280434	−	0.485726i	−0.971492	+	0.237074i	$0.923812\pi$
$678$	−18303.1	−	34421.0i	−1.03676	−	1.94975i
$679$	2113.75			0.119467
$680$	44.2167	+	76.5855i	0.00249358	+	0.00431900i
$681$	1078.14	+	2027.57i	0.0606675	+	0.114092i
$682$			8022.50i			0.450436i
$683$	9566.46	+	5523.20i	0.535945	+	0.309428i	0.743434	−	0.668809i	$-0.233196\pi$
$683$	9566.46	+	5523.20i	0.535945	+	0.309428i	−0.207489	+	0.978237i	$0.566529\pi$
$684$	−2441.85	−	1646.87i	−0.136501	−	0.0920607i
$685$	2435.62	−	4218.62i	0.135854	−	0.235307i
$686$	−14318.2	+	24799.9i	−0.796898	+	1.38027i
$687$	−4964.26	−	173.228i	−0.275689	−	0.00962017i
$688$	5585.22	−	9673.88i	0.309498	−	0.536066i
$689$	−9451.75	+	18210.3i	−0.522617	+	1.00691i
$690$	11857.3	+	7408.81i	0.654200	+	0.408766i
$691$	−15283.1	−	8823.71i	−0.841385	−	0.485774i	0.0163498	−	0.999866i	$-0.494795\pi$
$691$	−15283.1	−	8823.71i	−0.841385	−	0.485774i	−0.857735	+	0.514092i	$0.828129\pi$
$692$	−13494.0	−	23372.4i	−0.741281	−	1.28394i
$693$	−8336.93	−	17091.0i	−0.456989	−	0.936845i
$694$		−	47415.9i		−	2.59349i
$695$			9051.77i			0.494033i
$696$	−5130.08	−	179.014i	−0.279390	−	0.00974932i
$697$	−1185.14	−	684.242i	−0.0644053	−	0.0371844i
$698$	9654.24	+	16721.6i	0.523522	+	0.906767i
$699$	−15854.5	+	8430.49i	−0.857898	+	0.456181i
$700$	−12621.1	−	7286.80i	−0.681476	−	0.393450i
$701$	−10173.6			−0.548149			−0.274075	−	0.961708i	$-0.588372\pi$
$701$	−10173.6			−0.548149			−0.274075	+	0.961708i	$0.588372\pi$
$702$	12198.3	+	24387.6i	0.655836	+	1.31118i
$703$	1906.71			0.102294
$704$	25512.8	+	14729.8i	1.36584	+	0.788565i
$705$	4094.19	−	2177.05i	0.218718	−	0.116301i
$706$	18152.2	+	31440.5i	0.967657	+	1.67603i
$707$	10350.4	+	5975.80i	0.550589	+	0.317883i
$708$	22138.2	+	772.512i	1.17515	+	0.0410067i
$709$			25991.1i			1.37675i	0.725354	+	0.688376i	$0.241676\pi$
$709$			25991.1i			1.37675i	−0.725354	+	0.688376i	$0.758324\pi$
$710$		−	19040.6i		−	1.00645i
$711$	−11952.8	−	835.205i	−0.630472	−	0.0440543i
$712$	−922.423	−	1597.68i	−0.0485523	−	0.0840951i
$713$	4985.53	+	2878.40i	0.261865	+	0.151188i
$714$	−1053.58	−	658.312i	−0.0552230	−	0.0345052i
$715$	10211.5	−	458.206i	0.534112	−	0.0239663i
$716$	−6142.24	+	10638.7i	−0.320596	+	0.555288i
$717$	−9332.90	−	325.672i	−0.486114	−	0.0169630i
$718$	20372.7	−	35286.5i	1.05892	−	1.83409i
$719$	4071.16	−	7051.46i	0.211167	−	0.365751i	−0.740913	−	0.671601i	$-0.765607\pi$
$719$	4071.16	−	7051.46i	0.211167	−	0.365751i	0.952080	+	0.305849i	$0.0989404\pi$
$720$	481.427	−	6889.82i	0.0249191	−	0.356623i
$721$	5139.33	+	2967.20i	0.265463	+	0.153265i
$722$			27858.1i			1.43597i
$723$	13904.6	+	26149.2i	0.715240	+	1.34509i
$724$	−18866.2	−	32677.2i	−0.968449	−	1.67740i
$725$	−20287.1			−1.03923
$726$	−7201.72	−	13543.6i	−0.368155	−	0.692357i
$727$	−18580.0	−	32181.5i	−0.947858	−	1.64174i	−0.749925	−	0.661523i	$-0.769910\pi$
$727$	−18580.0	−	32181.5i	−0.947858	−	1.64174i	−0.197933	−	0.980215i	$-0.563423\pi$
$728$	−1666.61	+	3211.00i	−0.0848472	+	0.163472i
$729$	−19253.5	−	4089.36i	−0.978180	−	0.207761i
$730$	15345.6	−	8859.76i	0.778034	−	0.449198i
$731$	−389.816	+	675.182i	−0.0197235	+	0.0341621i
$732$	20071.4	+	12541.3i	1.01347	+	0.633252i
$733$	−10221.9	−	5901.60i	−0.515079	−	0.297381i	0.219840	−	0.975536i	$-0.429447\pi$
$733$	−10221.9	−	5901.60i	−0.515079	−	0.297381i	−0.734919	+	0.678155i	$0.762780\pi$
$734$	28031.3	−	16183.9i	1.40961	−	0.813839i
$735$	2510.44	+	87.6019i	0.125985	+	0.00439625i
$736$	30220.7	−	17447.9i	1.51352	−	0.873831i
$737$	5266.24	−	9121.40i	0.263208	−	0.455890i
$738$	−18153.2	−	37214.7i	−0.905458	−	1.85622i
$739$	−7857.56	+	4536.57i	−0.391130	+	0.225819i	−0.682650	−	0.730746i	$-0.739172\pi$
$739$	−7857.56	+	4536.57i	−0.391130	+	0.225819i	0.291520	+	0.956565i	$0.405839\pi$
$740$	−3564.81	−	6174.43i	−0.177088	−	0.306725i
$741$	−1419.79	+	2516.71i	−0.0703876	+	0.124769i
$742$	14141.5	−	24493.8i	0.699664	−	1.21185i
$743$			26844.1i			1.32546i	0.748859	+	0.662729i	$0.230602\pi$
$743$			26844.1i			1.32546i	−0.748859	+	0.662729i	$0.769398\pi$
$744$	−38.4206	+	1101.03i	−0.00189324	+	0.0542552i
$745$	−10977.7			−0.539854
$746$			8339.69i			0.409300i
$747$	−1312.67	+	18785.9i	−0.0642946	+	0.920135i
$748$	−1331.74	−	768.880i	−0.0650979	−	0.0375843i
$749$	−6732.85	+	3887.21i	−0.328455	+	0.189634i
$750$	−821.968	+	23555.5i	−0.0400187	+	1.14683i
$751$	6213.29			0.301899			0.150950	−	0.988541i	$-0.451767\pi$
$751$	6213.29			0.301899			0.150950	+	0.988541i	$0.451767\pi$
$752$		−	9805.78i		−	0.475505i
$753$	−552.672	+	15838.1i	−0.0267470	+	0.766499i
$754$	1737.62	+	38724.5i	0.0839263	+	1.87038i
$755$	694.120			0.0334591
$756$	−8176.98	−	18362.0i	−0.393378	−	0.883359i
$757$	−19308.9	−	33444.0i	−0.927073	−	1.60574i	−0.788192	−	0.615429i	$-0.788983\pi$
$757$	−19308.9	−	33444.0i	−0.927073	−	1.60574i	−0.138881	−	0.990309i	$-0.544351\pi$
$758$	−40372.0			−1.93453
$759$	−31567.1	−	1101.53i	−1.50963	−	0.0526787i
$760$	−245.555	+	141.771i	−0.0117200	+	0.00676656i
$761$	9743.29	−	5625.29i	0.464118	−	0.267959i	−0.249656	−	0.968335i	$-0.580318\pi$
$761$	9743.29	−	5625.29i	0.464118	−	0.267959i	0.713774	+	0.700376i	$0.246984\pi$
$762$	−18621.6	−	35020.0i	−0.885289	−	1.66488i
$763$	29105.3			1.38098
$764$	8236.92	+	14266.8i	0.390054	+	0.675593i
$765$	−33.6009	+	480.870i	−0.00158803	+	0.0227267i
$766$	5325.60			0.251203
$767$	−974.185	−	21710.6i	−0.0458615	−	1.02207i
$768$	−11521.2	−	7198.84i	−0.541323	−	0.338237i
$769$		−	8776.63i		−	0.411565i	−0.978598	−	0.205783i	$-0.934026\pi$
$769$		−	8776.63i		−	0.411565i	0.978598	−	0.205783i	$-0.0659739\pi$
$770$	−14090.9			−0.659480
$771$	−15482.9	+	8232.94i	−0.723223	+	0.384568i
$772$	−21184.1	+	12230.6i	−0.987605	+	0.570194i
$773$	−16628.3	−	9600.38i	−0.773712	−	0.446703i	0.0604849	−	0.998169i	$-0.480735\pi$
$773$	−16628.3	−	9600.38i	−0.773712	−	0.446703i	−0.834197	+	0.551466i	$0.814069\pi$
$774$	−21201.4	+	10342.0i	−0.984585	+	0.480277i
$775$			4354.09i			0.201811i
$776$	671.921			0.0310832
$777$	11035.4	+	6895.27i	0.509513	+	0.318361i
$778$			22365.5i			1.03065i
$779$	2193.88	−	3799.91i	0.100904	−	0.174770i
$780$	10804.2	−	107.618i	0.495965	−	0.00494017i
$781$	21507.6	+	37252.2i	0.985406	+	1.70677i
$782$	−1787.11	+	1031.79i	−0.0817224	+	0.0471824i
$783$	−22638.1	−	16444.9i	−1.03323	−	0.750565i
$784$	2656.00	−	4600.32i	0.120991	−	0.209563i
$785$	15830.4	−	9139.69i	0.719760	−	0.415553i
$786$	23672.5	−	37886.1i	1.07426	−	1.71928i
$787$	21294.7	−	12294.5i	0.964517	−	0.556864i	0.0669566	−	0.997756i	$-0.478671\pi$
$787$	21294.7	−	12294.5i	0.964517	−	0.556864i	0.897560	+	0.440892i	$0.145338\pi$
$788$	−3539.05	−	2043.27i	−0.159992	−	0.0923712i
$789$	855.086	−	24504.5i	0.0385829	−	1.10568i
$790$	−4439.33	+	7689.14i	−0.199929	+	0.346288i
$791$	24416.1	−	14096.7i	1.09752	−	0.633653i
$792$	−2650.15	−	5432.91i	−0.118900	−	0.243750i
$793$	10696.7	−	20609.0i	0.479006	−	0.922883i
$794$	−20788.3	−	36006.3i	−0.929154	−	1.60934i
$795$	−10967.5	−	382.710i	−0.489278	−	0.0170734i
$796$	13120.2			0.584214
$797$	12934.6	+	22403.3i	0.574863	+	0.995691i	0.996057	+	0.0887205i	$0.0282778\pi$
$797$	12934.6	+	22403.3i	0.574863	+	0.995691i	−0.421194	+	0.906971i	$0.638389\pi$
$798$	2110.74	−	3378.08i	0.0936333	−	0.149853i
$799$			684.388i			0.0303028i
$800$	22857.1	+	13196.6i	1.01015	+	0.583211i
$801$	700.963	−	10031.6i	0.0309205	−	0.442510i
$802$	−6272.77	+	10864.8i	−0.276183	+	0.478364i
$803$	−20015.4	+	34667.7i	−0.879611	+	1.52353i
$804$	5899.42	−	9441.58i	0.258777	−	0.414153i
$805$	−5055.67	+	8756.68i	−0.221353	+	0.383394i
$806$	8311.18	−	372.934i	0.363212	−	0.0162978i
$807$	−115.289	+	3303.88i	−0.00502896	+	0.144117i
$808$	3290.20	+	1899.60i	0.143253	+	0.0827073i
$809$	6856.33	+	11875.5i	0.297967	+	0.516095i	0.975671	−	0.219241i	$-0.0703580\pi$
$809$	6856.33	+	11875.5i	0.297967	+	0.516095i	−0.677703	+	0.735335i	$0.737025\pi$
$810$	−8978.33	+	11494.2i	−0.389465	+	0.498598i
$811$			13848.1i			0.599595i	0.954003	+	0.299797i	$0.0969190\pi$
$811$			13848.1i			0.599595i	−0.954003	+	0.299797i	$0.903081\pi$
$812$		−	28574.0i		−	1.23492i
$813$	5358.03	−	8575.13i	0.231137	−	0.369918i
$814$	26085.5	+	15060.5i	1.12321	+	0.648488i
$815$	−4669.60	−	8087.98i	−0.200698	−	0.347619i
$816$	864.484	+	540.158i	0.0370870	+	0.0231732i
$817$	−2164.83	−	1249.86i	−0.0927022	−	0.0535217i
$818$	49951.2			2.13509
$819$	−17318.5	+	9431.41i	−0.738896	+	0.402394i
$820$	−16406.8			−0.698720
$821$	16728.7	+	9658.29i	0.711125	+	0.410568i	0.811478	−	0.584384i	$-0.198664\pi$
$821$	16728.7	+	9658.29i	0.711125	+	0.410568i	−0.100352	+	0.994952i	$0.531997\pi$
$822$	−758.627	+	21740.2i	−0.0321900	+	0.922479i
$823$	6071.20	+	10515.6i	0.257143	+	0.445385i	0.965475	−	0.260494i	$-0.0838855\pi$
$823$	6071.20	+	10515.6i	0.257143	+	0.445385i	−0.708332	+	0.705879i	$0.750552\pi$
$824$	1633.70	+	943.216i	0.0690686	+	0.0398768i
$825$	−11216.2	−	21093.3i	−0.473330	−	0.890150i
$826$			29958.4i			1.26197i
$827$			42693.9i			1.79518i	0.440835	+	0.897588i	$0.354683\pi$
$827$			42693.9i			1.79518i	−0.440835	+	0.897588i	$0.645317\pi$
$828$	−33306.4	−	2327.29i	−1.39792	−	0.0976798i
$829$	3307.74	+	5729.18i	0.138580	+	0.240027i	0.926959	−	0.375162i	$-0.122413\pi$
$829$	3307.74	+	5729.18i	0.138580	+	0.240027i	−0.788380	+	0.615189i	$0.789080\pi$
$830$	12084.8	+	6977.18i	0.505386	+	0.291785i
$831$	14126.0	−	7511.41i	0.589683	−	0.313560i
$832$	14073.8	−	27115.5i	0.586446	−	1.12988i
$833$	−185.374	+	321.076i	−0.00771046	+	0.0133549i
$834$	−18978.1	−	35690.4i	−0.787959	−	1.48184i
$835$	5300.88	−	9181.39i	0.219694	−	0.380521i
$836$	2465.25	−	4269.94i	0.101989	−	0.176650i
$837$	−3529.45	+	4858.66i	−0.145754	+	0.200645i
$838$	−1995.75	−	1152.25i	−0.0822698	−	0.0474985i
$839$		−	30267.8i		−	1.24548i	−0.782428	−	0.622741i	$-0.786019\pi$
$839$		−	30267.8i		−	1.24548i	0.782428	−	0.622741i	$-0.213981\pi$
$840$	−1933.88	−	67.4827i	−0.0794347	−	0.00277188i
$841$	−7693.69	−	13325.9i	−0.315457	−	0.546388i
$842$	−15281.5			−0.625457
$843$	−25557.8	+	40903.3i	−1.04419	+	1.67116i
$844$	20646.5	+	35760.8i	0.842041	+	1.45846i
$845$	−949.388	−	10557.7i	−0.0386508	−	0.429818i
$846$	−11578.6	+	17167.9i	−0.470544	+	0.697688i
$847$	9607.02	−	5546.61i	0.389730	−	0.225011i
$848$	−11603.4	+	20097.6i	−0.469884	+	0.813863i
$849$	17682.3	−	9402.41i	0.714787	−	0.380082i
$850$	−1351.66	−	780.381i	−0.0545430	−	0.0314904i
$851$	18718.5	−	10807.1i	0.754008	−	0.435327i
$852$	21347.1	+	40145.5i	0.858379	+	1.61428i
$853$	−32920.6	+	19006.7i	−1.32143	+	0.762928i	−0.983957	−	0.178407i	$-0.942906\pi$
$853$	−32920.6	+	19006.7i	−1.32143	+	0.762928i	−0.337474	+	0.941335i	$0.609572\pi$
$854$	−16004.2	+	27720.1i	−0.641279	+	1.11073i
$855$	−1541.81	−	107.734i	−0.0616711	−	0.00430927i
$856$	−2140.25	+	1235.67i	−0.0854581	+	0.0493392i
$857$	−21594.2	−	37402.2i	−0.860728	−	1.49082i	−0.871228	−	0.490879i	$-0.836676\pi$
$857$	−21594.2	−	37402.2i	−0.860728	−	1.49082i	0.0105002	−	0.999945i	$-0.496658\pi$
$858$	−39302.6	+	23216.4i	−1.56383	+	0.923770i
$859$	−6630.09	+	11483.6i	−0.263348	+	0.456132i	−0.967129	−	0.254285i	$-0.918160\pi$
$859$	−6630.09	+	11483.6i	−0.263348	+	0.456132i	0.703782	+	0.710416i	$0.251493\pi$
$860$			9347.04i			0.370618i
$861$	26439.1	−	14058.8i	1.04651	−	0.556471i
$862$	−44830.6			−1.77139
$863$		−	18526.0i		−	0.730746i	−0.930861	−	0.365373i	$-0.880941\pi$
$863$		−	18526.0i		−	0.730746i	0.930861	−	0.365373i	$-0.119059\pi$
$864$	14808.7	+	33254.0i	0.583104	+	1.30940i
$865$	−12264.8	−	7081.10i	−0.482100	−	0.278340i
$866$	19141.6	−	11051.4i	0.751106	−	0.433651i
$867$	21589.6	+	13489.9i	0.845698	+	0.528421i
$868$	−6132.65			−0.239811
$869$		−	20058.1i		−	0.782996i
$870$	−18306.6	+	9734.38i	−0.713391	+	0.379340i
$871$	−9694.43	−	5031.73i	−0.377133	−	0.195745i
$872$	9252.04			0.359305
$873$	3036.53	+	2047.94i	0.117722	+	0.0793954i
$874$	−3308.21	−	5729.99i	−0.128034	−	0.221762i
$875$	−17045.4			−0.658561
$876$	−22421.9	+	35884.6i	−0.864801	+	1.38405i
$877$	−20484.8	+	11826.9i	−0.788738	+	0.455378i	−0.839518	−	0.543332i	$-0.817163\pi$
$877$	−20484.8	+	11826.9i	−0.788738	+	0.455378i	0.0507799	+	0.998710i	$0.483829\pi$
$878$	−22970.3	+	13261.9i	−0.882927	+	0.509758i
$879$	21743.3	−	34798.5i	0.834337	−	1.33530i
$880$	11561.8			0.442897
$881$	−8034.27	−	13915.8i	−0.307243	−	0.532161i	0.670515	−	0.741896i	$-0.266073\pi$
$881$	−8034.27	−	13915.8i	−0.307243	−	0.532161i	−0.977758	+	0.209735i	$0.932740\pi$
$882$	−10082.1	+	4918.02i	−0.384901	+	0.187753i
$883$	30283.3			1.15415			0.577075	−	0.816691i	$-0.304194\pi$
$883$	30283.3			1.15415			0.577075	+	0.816691i	$0.304194\pi$
$884$	−734.640	+	1415.40i	−0.0279509	+	0.0538520i
$885$	10263.4	−	5457.51i	0.389832	−	0.207290i
$886$			26998.4i			1.02373i
$887$	−15006.7			−0.568067			−0.284034	−	0.958814i	$-0.591673\pi$
$887$	−15006.7			−0.568067			−0.284034	+	0.958814i	$0.591673\pi$
$888$	3507.94	+	2191.88i	0.132566	+	0.0828317i
$889$	24841.0	−	14342.0i	0.937168	−	0.541074i
$890$	−6453.27	−	3725.80i	−0.243050	−	0.140325i
$891$	4582.37	−	32629.6i	0.172295	−	1.22686i
$892$			54147.9i			2.03252i
$893$	−2194.35			−0.0822295
$894$	43284.1	−	23016.0i	1.61928	−	0.861040i
$895$			6446.37i			0.240758i
$896$	−4884.66	+	8460.49i	−0.182126	+	0.315452i
$897$	326.255	+	32754.2i	0.0121442	+	1.21921i
$898$	22572.1	+	39096.0i	0.838798	+	1.45284i
$899$	−7393.20	+	4268.47i	−0.274279	+	0.158355i
$900$	−11071.1	−	22696.1i	−0.410039	−	0.840595i
$901$	809.850	−	1402.70i	0.0299445	−	0.0518654i
$902$	60028.5	−	34657.4i	2.21589	−	1.27934i
$903$	−8009.36	−	15062.5i	−0.295166	−	0.555092i
$904$	7761.43	−	4481.06i	0.285555	−	0.164865i
$905$	−17147.6	−	9900.17i	−0.629840	−	0.363638i
$906$	−2736.86	+	1455.30i	−0.100360	+	0.0533656i
$907$	7142.03	−	12370.4i	0.261463	−	0.452868i	−0.705168	−	0.709041i	$-0.749128\pi$
$907$	7142.03	−	12370.4i	0.261463	−	0.452868i	0.966631	+	0.256173i	$0.0824616\pi$
$908$	−3519.05	+	2031.72i	−0.128616	+	0.0742567i
$909$	9079.22	+	18612.7i	0.331286	+	0.679148i
$910$	655.028	+	14597.9i	0.0238615	+	0.531776i
$911$	7540.95	+	13061.3i	0.274251	+	0.475017i	0.969946	−	0.243320i	$-0.0782366\pi$
$911$	7540.95	+	13061.3i	0.274251	+	0.475017i	−0.695695	+	0.718338i	$0.744903\pi$
$912$	−1731.90	+	2771.78i	−0.0628827	+	0.100639i
$913$	−31524.7			−1.14273
$914$	16519.6	+	28612.7i	0.597832	+	1.03548i
$915$	12412.1	+	433.121i	0.448450	+	0.0156487i
$916$		−	8789.54i		−	0.317047i
$917$	27979.2	+	16153.8i	1.00758	+	0.581728i
$918$	−875.716	−	1966.48i	−0.0314847	−	0.0707011i
$919$	12553.0	−	21742.4i	0.450582	−	0.780431i	−0.547840	−	0.836583i	$-0.684550\pi$
$919$	12553.0	−	21742.4i	0.450582	−	0.780431i	0.998422	+	0.0561523i	$0.0178832\pi$
$920$	−1607.10	+	2783.58i	−0.0575920	+	0.0997522i
$921$	−993.696	−	1868.75i	−0.0355520	−	0.0668595i
$922$	−33379.7	+	57815.3i	−1.19230	+	2.06512i
$923$	37592.9	−	24013.2i	1.34061	−	0.856343i
$924$	29709.5	−	15797.8i	1.05776	−	0.562456i
$925$	14157.5	+	8173.84i	0.503239	+	0.290545i
$926$	35832.8	+	62064.2i	1.27164	+	2.20254i
$927$	4508.15	+	9241.87i	0.159727	+	0.327447i
$928$			51748.2i			1.83052i
$929$		−	44786.2i		−	1.58169i	−0.612017	−	0.790844i	$-0.709642\pi$
$929$		−	44786.2i		−	1.58169i	0.612017	−	0.790844i	$-0.290358\pi$
$930$	2089.22	+	3929.01i	0.0736648	+	0.138535i
$931$	−1029.46	−	594.361i	−0.0362399	−	0.0209231i
$932$	−15887.0	−	27517.0i	−0.558363	−	0.967113i
$933$	−1298.09	+	37199.8i	−0.0455494	+	1.30533i
$934$	−11251.9	−	6496.29i	−0.394190	−	0.227586i
$935$	−806.951			−0.0282247
$936$	−5505.21	+	2998.07i	−0.192247	+	0.104695i
$937$	50350.7			1.75548			0.877740	−	0.479138i	$-0.159051\pi$
$937$	50350.7			1.75548			0.877740	+	0.479138i	$0.159051\pi$
$938$	13039.5	+	7528.36i	0.453896	+	0.262057i
$939$	35167.6	+	21973.9i	1.22220	+	0.763674i
$940$	4102.57	+	7105.87i	0.142352	+	0.246562i
$941$	−10299.0	−	5946.14i	−0.356789	−	0.205992i	0.310882	−	0.950448i	$-0.399375\pi$
$941$	−10299.0	−	5946.14i	−0.356789	−	0.205992i	−0.667671	+	0.744456i	$0.732709\pi$
$942$	−43255.6	+	69227.4i	−1.49612	+	2.39443i
$943$		−	49739.1i		−	1.71763i
$944$		−	24581.5i		−	0.847519i
$945$	−8533.85	−	6199.20i	−0.293763	−	0.213397i
$946$	−19744.5	−	34198.5i	−0.678594	−	1.17536i
$947$	−6876.57	−	3970.19i	−0.235965	−	0.136234i	0.377356	−	0.926068i	$-0.376833\pi$
$947$	−6876.57	−	3970.19i	−0.235965	−	0.136234i	−0.613321	+	0.789834i	$0.710167\pi$
$948$	739.393	−	21189.0i	0.0253316	−	0.725937i
$949$	36845.6	+	19124.1i	1.26034	+	0.654155i
$950$	2502.13	−	4333.81i	0.0854524	−	0.148008i
$951$	−4738.34	+	7583.37i	−0.161568	+	0.258578i
$952$	142.800	−	247.336i	0.00486152	−	0.00842039i
$953$	5556.35	−	9623.87i	0.188864	−	0.327123i	−0.756008	−	0.654563i	$-0.772853\pi$
$953$	5556.35	−	9623.87i	0.188864	−	0.327123i	0.944872	+	0.327440i	$0.106186\pi$
$954$	44046.3	−	21485.6i	1.49481	−	0.729164i
$955$	7486.59	+	4322.38i	0.253676	+	0.146460i
$956$		−	16524.5i		−	0.559039i
$957$	24820.6	−	39723.5i	0.838385	−	1.34177i
$958$	−22472.9	−	38924.1i	−0.757897	−	1.31272i
$959$	−15731.9			−0.529728
$960$	16330.8	+	569.863i	0.549035	+	0.0191586i
$961$	−13979.4	−	24213.0i	−0.469249	−	0.812763i
$962$	14389.8	−	27724.3i	0.482272	−	0.929175i
$963$	−13438.3	−	939.005i	−0.449682	−	0.0314216i
$964$	−45384.5	+	26202.7i	−1.51632	+	0.875450i
$965$	−6418.11	+	11116.5i	−0.214100	+	0.370831i
$966$	1574.70	−	45126.7i	0.0524483	−	1.50303i
$967$	23614.5	+	13633.8i	0.785307	+	0.453397i	0.838308	−	0.545197i	$-0.183545\pi$
$967$	23614.5	+	13633.8i	0.785307	+	0.453397i	−0.0530008	+	0.998594i	$0.516879\pi$
$968$	3053.89	−	1763.16i	0.101401	−	0.0585436i
$969$	120.877	−	193.455i	0.00400736	−	0.00641348i
$970$	2350.38	−	1356.99i	0.0778002	−	0.0449179i
$971$	−2589.60	+	4485.33i	−0.0855863	+	0.148240i	−0.905641	−	0.424045i	$-0.860610\pi$
$971$	−2589.60	+	4485.33i	−0.0855863	+	0.148240i	0.820055	+	0.572285i	$0.193943\pi$
$972$	6043.56	−	34300.5i	0.199431	−	1.13188i
$973$	25316.6	−	14616.5i	0.834134	−	0.481588i
$974$	2989.74	+	5178.38i	0.0983547	+	0.170355i
$975$	−21330.9	+	12600.3i	−0.700652	+	0.413881i
$976$	13131.8	−	22744.9i	0.430674	−	0.745949i
$977$			1148.38i			0.0376047i	0.999823	+	0.0188024i	$0.00598533\pi$
$977$			1148.38i			0.0376047i	−0.999823	+	0.0188024i	$0.994015\pi$
$978$	35369.3	+	22099.9i	1.15643	+	0.722574i
$979$	16834.2			0.549563
$980$			4444.90i			0.144885i
$981$	41811.6	+	28199.1i	1.36080	+	0.917767i
$982$	−56758.6	−	32769.6i	−1.84444	−	1.06489i
$983$	−46109.2	+	26621.2i	−1.49609	+	0.863767i	−0.999990	−	0.00449948i	$-0.998568\pi$
$983$	−46109.2	+	26621.2i	−1.49609	+	0.863767i	−0.496098	+	0.868266i	$0.665234\pi$
$984$	8404.48	−	4469.02i	0.272282	−	0.144784i
$985$	−2144.44			−0.0693681
$986$		−	3060.14i		−	0.0988385i
$987$	−12700.1	−	7935.45i	−0.409573	−	0.255915i
$988$	−4538.19	−	2355.47i	−0.146133	−	0.0758476i
$989$	−28336.6			−0.911074
$990$	−20242.4	−	13652.1i	−0.649843	−	0.438276i
$991$	−25165.1	−	43587.2i	−0.806656	−	1.39717i	−0.915168	−	0.403074i	$-0.867942\pi$
$991$	−25165.1	−	43587.2i	−0.806656	−	1.39717i	0.108512	−	0.994095i	$-0.465392\pi$
$992$	11106.4			0.355471
$993$	−21083.4	−	39649.6i	−0.673777	−	1.26711i
$994$	−53253.9	+	30746.2i	−1.69931	+	0.981095i
$995$	5962.53	−	3442.47i	0.189975	−	0.109682i
$996$	−33302.3	−	1162.08i	−1.05946	−	0.0369699i
$997$	11360.4			0.360872			0.180436	−	0.983587i	$-0.442249\pi$
$997$	11360.4			0.360872			0.180436	+	0.983587i	$0.442249\pi$
$998$	−9705.73	−	16810.8i	−0.307845	−	0.533204i
$999$	9172.39	+	20597.2i	0.290492	+	0.652320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.r.a.49.7	yes	80
3.2	odd	2		351.4.r.a.10.34		80
9.2	odd	6		351.4.l.a.127.7		80
9.7	even	3		117.4.l.a.88.34	yes	80
13.4	even	6		117.4.l.a.4.7	✓	80
39.17	odd	6		351.4.l.a.199.34		80
117.43	even	6	inner	117.4.r.a.43.7	yes	80
117.56	odd	6		351.4.r.a.316.34		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.7	✓	80	13.4	even	6
117.4.l.a.88.34	yes	80	9.7	even	3
117.4.r.a.43.7	yes	80	117.43	even	6	inner
117.4.r.a.49.7	yes	80	1.1	even	1	trivial
351.4.l.a.127.7		80	9.2	odd	6
351.4.l.a.199.34		80	39.17	odd	6
351.4.r.a.10.34		80	3.2	odd	2
351.4.r.a.316.34		80	117.56	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.59109 - 2.07331i) q^{2} +(4.58787 - 2.43956i) q^{3} +(4.59727 + 7.96270i) q^{4} +(4.17848 + 2.41245i) q^{5} +(-21.5334 - 0.751409i) q^{6} -15.5822i q^{7} -4.95329i q^{8} +(15.0971 - 22.3848i) q^{9} +(-10.0035 - 17.3266i) q^{10} +(39.1432 + 22.5993i) q^{11} +(40.5172 + 25.3165i) q^{12} +(21.5929 - 41.6022i) q^{13} +(-32.3068 + 55.9571i) q^{14} +(25.0557 + 0.874318i) q^{15} +(26.5084 - 45.9139i) q^{16} +(-1.85014 + 3.20453i) q^{17} +(-100.626 + 49.0848i) q^{18} +(-10.2746 - 5.93207i) q^{19} +44.3627i q^{20} +(-38.0138 - 71.4891i) q^{21} +(-93.7110 - 162.312i) q^{22} -134.490 q^{23} +(-12.0839 - 22.7251i) q^{24} +(-50.8602 - 88.0924i) q^{25} +(-163.797 + 104.628i) q^{26} +(14.6542 - 139.529i) q^{27} +(124.077 - 71.6356i) q^{28} +(99.7201 - 172.720i) q^{29} +(-88.1643 - 55.0880i) q^{30} +(-37.0698 - 21.4022i) q^{31} +(-224.705 + 129.734i) q^{32} +(234.716 + 8.19043i) q^{33} +(13.2880 - 7.67183i) q^{34} +(37.5913 - 65.1100i) q^{35} +(247.649 + 17.3045i) q^{36} +(-139.181 + 80.3560i) q^{37} +(24.5981 + 42.6052i) q^{38} +(-2.42586 - 243.543i) q^{39} +(11.9496 - 20.6973i) q^{40} +369.833i q^{41} +(-11.7086 + 335.538i) q^{42} +210.696 q^{43} +415.580i q^{44} +(117.085 - 57.1136i) q^{45} +(482.967 + 278.841i) q^{46} +(160.177 - 92.4781i) q^{47} +(9.60716 - 275.316i) q^{48} +100.195 q^{49} +421.797i q^{50} +(-0.670525 + 19.2155i) q^{51} +(430.535 - 19.3187i) q^{52} -437.724 q^{53} +(-341.911 + 470.677i) q^{54} +(109.039 + 188.862i) q^{55} -77.1833 q^{56} +(-61.6104 - 2.14990i) q^{57} +(-716.207 + 413.502i) q^{58} +(401.536 - 231.827i) q^{59} +(108.226 + 203.530i) q^{60} +495.381 q^{61} +(88.7471 + 153.715i) q^{62} +(-348.805 - 235.246i) q^{63} +651.781 q^{64} +(190.589 - 121.742i) q^{65} +(-825.904 - 516.053i) q^{66} -233.027i q^{67} -34.0223 q^{68} +(-617.024 + 328.098i) q^{69} +(-269.987 + 155.877i) q^{70} +(824.189 + 475.846i) q^{71} +(-110.878 - 74.7801i) q^{72} +885.664i q^{73} +666.413 q^{74} +(-448.247 - 280.080i) q^{75} -109.085i q^{76} +(352.147 - 609.937i) q^{77} +(-496.229 + 879.613i) q^{78} +(-221.888 - 384.322i) q^{79} +(221.530 - 127.900i) q^{80} +(-273.158 - 675.889i) q^{81} +(766.781 - 1328.10i) q^{82} +(-604.028 + 348.736i) q^{83} +(394.487 - 631.347i) q^{84} +(-15.4615 + 8.92672i) q^{85} +(-756.628 - 436.839i) q^{86} +(36.1405 - 1035.69i) q^{87} +(111.941 - 193.888i) q^{88} +(322.550 - 186.224i) q^{89} +(-538.877 - 37.6541i) q^{90} +(-648.255 - 336.466i) q^{91} +(-618.289 - 1070.91i) q^{92} +(-222.283 - 7.75658i) q^{93} -766.944 q^{94} +(-28.6216 - 49.5741i) q^{95} +(-714.425 + 1143.38i) q^{96} +135.651i q^{97} +(-359.807 - 207.735i) q^{98} +(1096.83 - 535.028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) \) 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Introduction

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