LMFDB - Embedded newform 40.4.k.a.3.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,4,Mod(3,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	40.3
Dual form			40.4.k.a.27.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.583098 + 2.76767i) q^{2} +(6.15076 + 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(11.1441 + 0.899439i) q^{5} +(-20.6098 + 13.4368i) q^{6} +(-16.5614 - 16.5614i) q^{7} +(13.2013 - 18.3773i) q^{8} +48.6638i q^{9} +(-8.98745 + 30.3187i) q^{10} -11.0706 q^{11} +(-25.1711 - 64.8760i) q^{12} +(4.95962 - 4.95962i) q^{13} +(55.4933 - 36.1795i) q^{14} +(63.0125 + 74.0770i) q^{15} +(43.1646 + 47.2527i) q^{16} +(68.6010 - 68.6010i) q^{17} +(-134.685 - 28.3757i) q^{18} -29.4303i q^{19} +(-78.6717 - 42.5531i) q^{20} -203.730i q^{21} +(6.45526 - 30.6398i) q^{22} +(-70.5372 + 70.5372i) q^{23} +(194.233 - 31.8362i) q^{24} +(123.382 + 20.0469i) q^{25} +(10.8346 + 16.6185i) q^{26} +(-133.249 + 133.249i) q^{27} +(67.7750 + 174.683i) q^{28} -39.6115 q^{29} +(-241.763 + 131.204i) q^{30} +167.596i q^{31} +(-155.949 + 91.9125i) q^{32} +(-68.0928 - 68.0928i) q^{33} +(149.864 + 229.866i) q^{34} +(-169.666 - 199.458i) q^{35} +(157.069 - 356.218i) q^{36} +(-38.3756 - 38.3756i) q^{37} +(81.4534 + 17.1608i) q^{38} +61.0109 q^{39} +(163.646 - 192.925i) q^{40} -305.291 q^{41} +(563.858 + 118.795i) q^{42} +(-114.783 - 114.783i) q^{43} +(81.0369 + 35.7320i) q^{44} +(-43.7701 + 542.314i) q^{45} +(-154.094 - 236.354i) q^{46} +(-335.637 - 335.637i) q^{47} +(-25.1446 + 556.135i) q^{48} +205.559i q^{49} +(-127.427 + 329.791i) q^{50} +843.897 q^{51} +(-52.3123 + 20.2965i) q^{52} +(455.381 - 455.381i) q^{53} +(-291.091 - 446.485i) q^{54} +(-123.372 - 9.95735i) q^{55} +(-522.986 + 85.7212i) q^{56} +(181.019 - 181.019i) q^{57} +(23.0974 - 109.632i) q^{58} -170.086i q^{59} +(-222.157 - 745.625i) q^{60} +512.994i q^{61} +(-463.849 - 97.7246i) q^{62} +(805.939 - 805.939i) q^{63} +(-163.450 - 485.209i) q^{64} +(59.7314 - 50.8096i) q^{65} +(228.163 - 148.754i) q^{66} +(-476.312 + 476.312i) q^{67} +(-723.578 + 280.739i) q^{68} -867.716 q^{69} +(650.965 - 353.276i) q^{70} +627.703i q^{71} +(894.308 + 642.426i) q^{72} +(-2.93764 - 2.93764i) q^{73} +(128.588 - 83.8342i) q^{74} +(635.590 + 882.197i) q^{75} +(-94.9906 + 215.430i) q^{76} +(183.345 + 183.345i) q^{77} +(-35.5753 + 168.858i) q^{78} +132.081 q^{79} +(438.530 + 565.413i) q^{80} -325.240 q^{81} +(178.015 - 844.946i) q^{82} +(-111.150 - 111.150i) q^{83} +(-657.569 + 1491.30i) q^{84} +(826.199 - 702.794i) q^{85} +(384.613 - 250.753i) q^{86} +(-243.641 - 243.641i) q^{87} +(-146.147 + 203.448i) q^{88} +836.950i q^{89} +(-1475.42 - 437.363i) q^{90} -164.276 q^{91} +(744.001 - 288.663i) q^{92} +(-1030.84 + 1030.84i) q^{93} +(1124.64 - 733.224i) q^{94} +(26.4708 - 327.975i) q^{95} +(-1524.54 - 393.873i) q^{96} +(-485.063 + 485.063i) q^{97} +(-568.919 - 119.861i) q^{98} -538.738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + 70 q^{10} - 8 q^{11} + 28 q^{12} + 72 q^{16} + 48 q^{17} - 278 q^{18} - 320 q^{20} + 68 q^{22} + 40 q^{25} - 92 q^{26} + 104 q^{27} + 620 q^{28} - 740 q^{30}+ \cdots - 3814 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8 + 70 * q^10 - 8 * q^11 + 28 * q^12 + 72 * q^16 + 48 * q^17 - 278 * q^18 - 320 * q^20 + 68 * q^22 + 40 * q^25 - 92 * q^26 + 104 * q^27 + 620 * q^28 - 740 * q^30 + 288 * q^32 - 112 * q^33 - 460 * q^35 + 476 * q^36 + 636 * q^38 + 540 * q^40 - 8 * q^41 + 1020 * q^42 - 868 * q^43 + 1328 * q^46 - 784 * q^48 + 790 * q^50 + 1480 * q^51 - 1900 * q^52 - 2392 * q^56 + 104 * q^57 - 700 * q^58 - 1100 * q^60 - 2880 * q^62 + 520 * q^65 - 4360 * q^66 - 1852 * q^67 + 1196 * q^68 - 1500 * q^70 + 5596 * q^72 - 744 * q^73 + 3300 * q^75 + 4312 * q^76 + 2240 * q^78 + 1120 * q^80 - 1240 * q^81 + 5828 * q^82 + 2676 * q^83 + 6976 * q^86 - 2864 * q^88 + 4070 * q^90 - 1704 * q^91 - 7500 * q^92 - 10656 * q^96 - 584 * q^97 - 3814 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−0.583098	+	2.76767i	−0.206156	+	0.978519i
$2$	−0.583098	+	2.76767i	−0.206156	+	0.978519i
$3$	6.15076	+	6.15076i	1.18371	+	1.18371i	0.978774	+	0.204940i	$0.0657000\pi$
$3$	6.15076	+	6.15076i	1.18371	+	1.18371i	0.204940	+	0.978774i	$0.434300\pi$
$4$	−7.31999	−	3.22764i	−0.914999	−	0.403456i
$5$	11.1441	+	0.899439i	0.996759	+	0.0804483i
$5$	11.1441	+	0.899439i	0.996759	+	0.0804483i
$6$	−20.6098	+	13.4368i	−1.40232	+	0.914257i
$7$	−16.5614	−	16.5614i	−0.894231	−	0.894231i	0.100687	−	0.994918i	$-0.467896\pi$
$7$	−16.5614	−	16.5614i	−0.894231	−	0.894231i	−0.994918	+	0.100687i	$0.967896\pi$
$8$	13.2013	−	18.3773i	0.583422	−	0.812169i
$9$			48.6638i			1.80236i
$10$	−8.98745	+	30.3187i	−0.284208	+	0.958763i
$11$	−11.0706			−0.303447			−0.151724	−	0.988423i	$-0.548482\pi$
$11$	−11.0706			−0.303447			−0.151724	+	0.988423i	$0.548482\pi$
$12$	−25.1711	−	64.8760i	−0.605522	−	1.56067i
$13$	4.95962	−	4.95962i	0.105812	−	0.105812i	−0.652219	−	0.758031i	$-0.726162\pi$
$13$	4.95962	−	4.95962i	0.105812	−	0.105812i	0.758031	+	0.652219i	$0.226162\pi$
$14$	55.4933	−	36.1795i	1.05937	−	0.690671i
$15$	63.0125	+	74.0770i	1.08465	+	1.27511i
$16$	43.1646	+	47.2527i	0.674447	+	0.738323i
$17$	68.6010	−	68.6010i	0.978717	−	0.978717i	−0.0210615	−	0.999778i	$-0.506705\pi$
$17$	68.6010	−	68.6010i	0.978717	−	0.978717i	0.999778	+	0.0210615i	$0.00670459\pi$
$18$	−134.685	−	28.3757i	−1.76365	−	0.371568i
$19$		−	29.4303i		−	0.355357i	−0.984089	−	0.177678i	$-0.943141\pi$
$19$		−	29.4303i		−	0.355357i	0.984089	−	0.177678i	$-0.0568587\pi$
$20$	−78.6717	−	42.5531i	−0.879576	−	0.475758i
$21$		−	203.730i		−	2.11703i
$22$	6.45526	−	30.6398i	0.0625575	−	0.296929i
$23$	−70.5372	+	70.5372i	−0.639480	+	0.639480i	−0.950427	−	0.310947i	$-0.899354\pi$
$23$	−70.5372	+	70.5372i	−0.639480	+	0.639480i	0.310947	+	0.950427i	$0.399354\pi$
$24$	194.233	−	31.8362i	1.65198	−	0.270772i
$25$	123.382	+	20.0469i	0.987056	+	0.160375i
$26$	10.8346	+	16.6185i	0.0817249	+	0.125352i
$27$	−133.249	+	133.249i	−0.949767	+	0.949767i
$28$	67.7750	+	174.683i	0.457438	+	1.17900i
$29$	−39.6115			−0.253644			−0.126822	−	0.991925i	$-0.540478\pi$
$29$	−39.6115			−0.253644			−0.126822	+	0.991925i	$0.540478\pi$
$30$	−241.763	+	131.204i	−1.47132	+	0.798480i
$31$			167.596i			0.971002i	0.874236	+	0.485501i	$0.161363\pi$
$31$			167.596i			0.971002i	−0.874236	+	0.485501i	$0.838637\pi$
$32$	−155.949	+	91.9125i	−0.861505	+	0.507750i
$33$	−68.0928	−	68.0928i	−0.359195	−	0.359195i
$34$	149.864	+	229.866i	0.755924	+	1.15946i
$35$	−169.666	−	199.458i	−0.819393	−	0.963272i
$36$	157.069	−	356.218i	0.727173	−	1.64916i
$37$	−38.3756	−	38.3756i	−0.170511	−	0.170511i	0.616693	−	0.787204i	$-0.288472\pi$
$37$	−38.3756	−	38.3756i	−0.170511	−	0.170511i	−0.787204	+	0.616693i	$0.788472\pi$
$38$	81.4534	+	17.1608i	0.347723	+	0.0732590i
$39$	61.0109			0.250501
$40$	163.646	−	192.925i	0.646868	−	0.762602i
$41$	−305.291			−1.16289			−0.581445	−	0.813586i	$-0.697512\pi$
$41$	−305.291			−1.16289			−0.581445	+	0.813586i	$0.697512\pi$
$42$	563.858	+	118.795i	2.07155	+	0.436438i
$43$	−114.783	−	114.783i	−0.407077	−	0.407077i	0.473641	−	0.880718i	$-0.342939\pi$
$43$	−114.783	−	114.783i	−0.407077	−	0.407077i	−0.880718	+	0.473641i	$0.842939\pi$
$44$	81.0369	+	35.7320i	0.277654	+	0.122427i
$45$	−43.7701	+	542.314i	−0.144997	+	1.79652i
$46$	−154.094	−	236.354i	−0.493910	−	0.757576i
$47$	−335.637	−	335.637i	−1.04165	−	1.04165i	−0.999094	−	0.0425604i	$-0.986449\pi$
$47$	−335.637	−	335.637i	−1.04165	−	1.04165i	−0.0425604	−	0.999094i	$-0.513551\pi$
$48$	−25.1446	+	556.135i	−0.0756107	+	1.67232i
$49$			205.559i			0.599297i
$50$	−127.427	+	329.791i	−0.360418	+	0.932791i
$51$	843.897			2.31704
$52$	−52.3123	+	20.2965i	−0.139508	+	0.0541272i
$53$	455.381	−	455.381i	1.18022	−	1.18022i	0.200527	−	0.979688i	$-0.435734\pi$
$53$	455.381	−	455.381i	1.18022	−	1.18022i	0.979688	−	0.200527i	$-0.0642655\pi$
$54$	−291.091	−	446.485i	−0.733565	−	1.12517i
$55$	−123.372	−	9.95735i	−0.302464	−	0.0244118i
$56$	−522.986	+	85.7212i	−1.24798	+	0.204553i
$57$	181.019	−	181.019i	0.420641	−	0.420641i
$58$	23.0974	−	109.632i	0.0522903	−	0.248195i
$59$		−	170.086i		−	0.375311i	−0.982235	−	0.187655i	$-0.939911\pi$
$59$		−	170.086i		−	0.375311i	0.982235	−	0.187655i	$-0.0600888\pi$
$60$	−222.157	−	745.625i	−0.478006	−	1.60433i
$61$			512.994i			1.07676i	0.842703	+	0.538378i	$0.180963\pi$
$61$			512.994i			1.07676i	−0.842703	+	0.538378i	$0.819037\pi$
$62$	−463.849	−	97.7246i	−0.950144	−	0.200178i
$63$	805.939	−	805.939i	1.61173	−	1.61173i
$64$	−163.450	−	485.209i	−0.319238	−	0.947674i
$65$	59.7314	−	50.8096i	0.113981	−	0.0969563i
$66$	228.163	−	148.754i	0.425529	−	0.277429i
$67$	−476.312	+	476.312i	−0.868519	+	0.868519i	−0.992308	−	0.123790i	$-0.960495\pi$
$67$	−476.312	+	476.312i	−0.868519	+	0.868519i	0.123790	+	0.992308i	$0.460495\pi$
$68$	−723.578	+	280.739i	−1.29039	+	0.500656i
$69$	−867.716			−1.51392
$70$	650.965	−	353.276i	1.11150	−	0.603207i
$71$			627.703i			1.04922i	0.851343	+	0.524610i	$0.175789\pi$
$71$			627.703i			1.04922i	−0.851343	+	0.524610i	$0.824211\pi$
$72$	894.308	+	642.426i	1.46382	+	1.05154i
$73$	−2.93764	−	2.93764i	−0.00470992	−	0.00470992i	0.704748	−	0.709458i	$-0.251060\pi$
$73$	−2.93764	−	2.93764i	−0.00470992	−	0.00470992i	−0.709458	+	0.704748i	$0.751060\pi$
$74$	128.588	−	83.8342i	0.202000	−	0.131696i
$75$	635.590	+	882.197i	0.978555	+	1.35823i
$76$	−94.9906	+	215.430i	−0.143371	+	0.325151i
$77$	183.345	+	183.345i	0.271352	+	0.271352i
$78$	−35.5753	+	168.858i	−0.0516424	+	0.245120i
$79$	132.081			0.188105			0.0940523	−	0.995567i	$-0.470018\pi$
$79$	132.081			0.188105			0.0940523	+	0.995567i	$0.470018\pi$
$80$	438.530	+	565.413i	0.612864	+	0.790188i
$81$	−325.240			−0.446145
$82$	178.015	−	844.946i	0.239737	−	1.13791i
$83$	−111.150	−	111.150i	−0.146991	−	0.146991i	0.629781	−	0.776772i	$-0.283145\pi$
$83$	−111.150	−	111.150i	−0.146991	−	0.146991i	−0.776772	+	0.629781i	$0.783145\pi$
$84$	−657.569	+	1491.30i	−0.854127	+	1.93708i
$85$	826.199	−	702.794i	1.05428	−	0.896808i
$86$	384.613	−	250.753i	0.482254	−	0.314411i
$87$	−243.641	−	243.641i	−0.300242	−	0.300242i
$88$	−146.147	+	203.448i	−0.177038	+	0.246451i
$89$			836.950i			0.996815i	0.866943	+	0.498407i	$0.166082\pi$
$89$			836.950i			0.996815i	−0.866943	+	0.498407i	$0.833918\pi$
$90$	−1475.42	−	437.363i	−1.72804	−	0.512246i
$91$	−164.276			−0.189240
$92$	744.001	−	288.663i	0.843125	−	0.327122i
$93$	−1030.84	+	1030.84i	−1.14939	+	1.14939i
$94$	1124.64	−	733.224i	1.23402	−	0.804535i
$95$	26.4708	−	327.975i	0.0285878	−	0.354205i
$96$	−1524.54	−	393.873i	−1.62081	−	0.418745i
$97$	−485.063	+	485.063i	−0.507739	+	0.507739i	−0.913832	−	0.406093i	$-0.866891\pi$
$97$	−485.063	+	485.063i	−0.507739	+	0.507739i	0.406093	+	0.913832i	$0.366891\pi$
$98$	−568.919	−	119.861i	−0.586423	−	0.123549i
$99$		−	538.738i		−	0.546922i
$100$	−838.451	−	544.976i	−0.838451	−	0.544976i
$101$		−	143.353i		−	0.141229i	−0.997504	−	0.0706146i	$-0.977504\pi$
$101$		−	143.353i		−	0.141229i	0.997504	−	0.0706146i	$-0.0224960\pi$
$102$	−492.074	+	2335.63i	−0.477673	+	2.26727i
$103$	97.3092	−	97.3092i	0.0930889	−	0.0930889i	−0.659029	−	0.752118i	$-0.729032\pi$
$103$	97.3092	−	97.3092i	0.0930889	−	0.0930889i	0.752118	+	0.659029i	$0.229032\pi$
$104$	−25.6708	−	156.618i	−0.0242042	−	0.147670i
$105$	183.243	−	2270.39i	0.170311	−	2.11017i
$106$	994.813	+	1525.88i	0.911555	+	1.39817i
$107$	1354.74	−	1354.74i	1.22400	−	1.22400i	0.257804	−	0.966197i	$-0.417001\pi$
$107$	1354.74	−	1354.74i	1.22400	−	1.22400i	0.966197	−	0.257804i	$-0.0829989\pi$
$108$	1405.46	−	545.300i	1.25222	−	0.485847i
$109$	208.105			0.182870			0.0914350	−	0.995811i	$-0.470855\pi$
$109$	208.105			0.182870			0.0914350	+	0.995811i	$0.470855\pi$
$110$	99.4967	−	335.647i	0.0862422	−	0.290934i
$111$		−	472.078i		−	0.403673i
$112$	67.7037	−	1497.44i	0.0571197	−	1.26334i
$113$	821.764	+	821.764i	0.684115	+	0.684115i	0.960925	−	0.276810i	$-0.0892771\pi$
$113$	821.764	+	821.764i	0.684115	+	0.684115i	−0.276810	+	0.960925i	$0.589277\pi$
$114$	395.449	+	606.552i	0.324888	+	0.498323i
$115$	−849.518	+	722.630i	−0.688852	+	0.585962i
$116$	289.956	+	127.852i	0.232084	+	0.102334i
$117$	241.354	+	241.354i	0.190711	+	0.190711i
$118$	470.742	+	99.1769i	0.367249	+	0.0773726i
$119$	−2272.25			−1.75040
$120$	2193.18	−	180.085i	1.66841	−	0.136995i
$121$	−1208.44			−0.907920
$122$	−1419.80	−	299.126i	−1.05363	−	0.221980i
$123$	−1877.77	−	1877.77i	−1.37653	−	1.37653i
$124$	540.939	−	1226.80i	0.391756	−	0.888466i
$125$	1356.95	+	334.379i	0.970955	+	0.239262i
$126$	1760.63	+	2700.51i	1.24484	+	1.90937i
$127$	1732.61	+	1732.61i	1.21059	+	1.21059i	0.970834	+	0.239754i	$0.0770666\pi$
$127$	1732.61	+	1732.61i	1.21059	+	1.21059i	0.239754	+	0.970834i	$0.422933\pi$
$128$	1438.21	−	169.451i	0.993131	−	0.117012i
$129$		−	1412.01i		−	0.963726i
$130$	105.795	+	194.944i	0.0713757	+	0.131521i
$131$	−58.8534			−0.0392523			−0.0196261	−	0.999807i	$-0.506248\pi$
$131$	−58.8534			−0.0392523			−0.0196261	+	0.999807i	$0.506248\pi$
$132$	278.660	+	718.218i	0.183744	+	0.473582i
$133$	−487.407	+	487.407i	−0.317771	+	0.317771i
$134$	−1040.54	−	1596.01i	−0.670812	−	1.02891i
$135$	−1604.79	+	1365.09i	−1.02310	+	0.870281i
$136$	−355.077	−	2166.32i	−0.223879	−	1.36589i
$137$	105.459	−	105.459i	0.0657661	−	0.0657661i	−0.673459	−	0.739225i	$-0.735192\pi$
$137$	105.459	−	105.459i	0.0657661	−	0.0657661i	0.739225	+	0.673459i	$0.235192\pi$
$138$	505.963	−	2401.55i	0.312105	−	1.48140i
$139$			918.385i			0.560406i	0.959941	+	0.280203i	$0.0904017\pi$
$139$			918.385i			0.560406i	−0.959941	+	0.280203i	$0.909598\pi$
$140$	598.174	+	2007.65i	0.361107	+	1.21198i
$141$		−	4128.85i		−	2.46604i
$142$	−1737.27	−	366.012i	−1.02668	−	0.216303i
$143$	−54.9061	+	54.9061i	−0.0321082	+	0.0321082i
$144$	−2299.49	+	2100.55i	−1.33072	+	1.21560i
$145$	−441.435	−	35.6281i	−0.252822	−	0.0204052i
$146$	9.84333	−	6.41748i	0.00557973	−	0.00363777i
$147$	−1264.34	+	1264.34i	−0.709396	+	0.709396i
$148$	157.046	+	404.772i	0.0872238	+	0.224811i
$149$	−414.329			−0.227806			−0.113903	−	0.993492i	$-0.536335\pi$
$149$	−414.329			−0.227806			−0.113903	+	0.993492i	$0.536335\pi$
$150$	−2812.24	+	1244.70i	−1.53079	+	0.677527i
$151$			1749.49i			0.942860i	0.881904	+	0.471430i	$0.156262\pi$
$151$			1749.49i			0.942860i	−0.881904	+	0.471430i	$0.843738\pi$
$152$	−540.850	−	388.519i	−0.288610	−	0.207323i
$153$	3338.38	+	3338.38i	1.76400	+	1.76400i
$154$	−614.346	+	400.530i	−0.321464	+	0.209582i
$155$	−150.742	+	1867.70i	−0.0781154	+	0.967855i
$156$	−446.599	−	196.921i	−0.229209	−	0.101066i
$157$	−1876.43	−	1876.43i	−0.953859	−	0.953859i	0.0451229	−	0.998981i	$-0.485632\pi$
$157$	−1876.43	−	1876.43i	−0.953859	−	0.953859i	−0.998981	+	0.0451229i	$0.985632\pi$
$158$	−77.0161	+	365.556i	−0.0387789	+	0.184064i
$159$	5601.88			2.79408
$160$	−1820.58	+	884.016i	−0.899560	+	0.436797i
$161$	2336.39			1.14368
$162$	189.647	−	900.156i	0.0919756	−	0.436562i
$163$	842.965	+	842.965i	0.405068	+	0.405068i	0.880015	−	0.474947i	$-0.157533\pi$
$163$	842.965	+	842.965i	0.405068	+	0.405068i	−0.474947	+	0.880015i	$0.657533\pi$
$164$	2234.73	+	985.372i	1.06404	+	0.469174i
$165$	−697.588	−	820.078i	−0.329134	−	0.386927i
$166$	372.437	−	242.815i	0.174137	−	0.113531i
$167$	−274.097	−	274.097i	−0.127008	−	0.127008i	0.640746	−	0.767753i	$-0.278625\pi$
$167$	−274.097	−	274.097i	−0.127008	−	0.127008i	−0.767753	+	0.640746i	$0.778625\pi$
$168$	−3744.01	−	2689.51i	−1.71939	−	1.23512i
$169$			2147.80i			0.977608i
$170$	1463.35	+	2696.44i	0.660198	+	1.21652i
$171$	1432.19			0.640481
$172$	469.734	+	1210.69i	0.208238	+	0.536713i
$173$	763.567	−	763.567i	0.335566	−	0.335566i	−0.519130	−	0.854696i	$-0.673744\pi$
$173$	763.567	−	763.567i	0.335566	−	0.335566i	0.854696	+	0.519130i	$0.173744\pi$
$174$	816.384	−	532.251i	0.355689	−	0.231896i
$175$	−1711.37	−	2375.38i	−0.739244	−	1.02607i
$176$	−477.860	−	523.117i	−0.204659	−	0.224042i
$177$	1046.16	−	1046.16i	0.444261	−	0.444261i
$178$	−2316.40	−	488.023i	−0.975402	−	0.205499i
$179$		−	3353.66i		−	1.40036i	−0.713966	−	0.700180i	$-0.753103\pi$
$179$		−	3353.66i		−	1.40036i	0.713966	−	0.700180i	$-0.246897\pi$
$180$	2070.79	−	3828.46i	0.857488	−	1.58531i
$181$			3141.93i			1.29026i	0.764071	+	0.645132i	$0.223198\pi$
$181$			3141.93i			1.29026i	−0.764071	+	0.645132i	$0.776802\pi$
$182$	95.7891	−	454.662i	0.0390130	−	0.185175i
$183$	−3155.30	+	3155.30i	−1.27457	+	1.27457i
$184$	365.099	+	2227.47i	0.146279	+	0.892452i
$185$	−393.145	−	462.178i	−0.156241	−	0.183676i
$186$	−2251.95	−	3454.11i	−0.887746	−	1.36165i
$187$	−759.456	+	759.456i	−0.296989	+	0.296989i
$188$	1373.55	+	3540.18i	0.532852	+	1.37337i
$189$	4413.56			1.69862
$190$	892.290	+	264.504i	0.340703	+	0.100995i
$191$		−	2646.53i		−	1.00260i	−0.865275	−	0.501298i	$-0.832856\pi$
$191$		−	2646.53i		−	1.00260i	0.865275	−	0.501298i	$-0.167144\pi$
$192$	1979.07	−	3989.75i	0.743889	−	1.49966i
$193$	−3524.97	−	3524.97i	−1.31468	−	1.31468i	−0.917925	−	0.396754i	$-0.870137\pi$
$193$	−3524.97	−	3524.97i	−1.31468	−	1.31468i	−0.396754	−	0.917925i	$-0.629863\pi$
$194$	−1059.66	−	1625.33i	−0.392159	−	0.601506i
$195$	679.911	+	54.8755i	0.249690	+	0.0201524i
$196$	663.471	−	1504.69i	0.241790	−	0.548356i
$197$	3725.92	+	3725.92i	1.34752	+	1.34752i	0.888352	+	0.459164i	$0.151851\pi$
$197$	3725.92	+	3725.92i	1.34752	+	1.34752i	0.459164	+	0.888352i	$0.348149\pi$
$198$	1491.05	+	314.137i	0.535173	+	0.112751i
$199$	2702.93			0.962841			0.481420	−	0.876490i	$-0.340121\pi$
$199$	2702.93			0.962841			0.481420	+	0.876490i	$0.340121\pi$
$200$	1997.21	−	2002.78i	0.706122	−	0.708091i
$201$	−5859.36			−2.05616
$202$	396.753	+	83.5887i	0.138195	+	0.0291153i
$203$	656.021	+	656.021i	0.226816	+	0.226816i
$204$	−6177.32	−	2723.80i	−2.12009	−	0.934824i
$205$	−3402.20	−	274.591i	−1.15912	−	0.0935525i
$206$	212.579	+	326.060i	0.0718984	+	0.110280i
$207$	−3432.61	−	3432.61i	−1.15257	−	1.15257i
$208$	448.435	+	20.2752i	0.149487	+	0.00675879i
$209$			325.812i			0.107832i
$210$	6176.84	+	1831.02i	2.02973	+	0.601677i
$211$	1795.92			0.585952			0.292976	−	0.956120i	$-0.405354\pi$
$211$	1795.92			0.585952			0.292976	+	0.956120i	$0.405354\pi$
$212$	−4803.20	+	1863.58i	−1.55606	+	0.603732i
$213$	−3860.85	+	3860.85i	−1.24198	+	1.24198i
$214$	2959.54	+	4539.44i	0.945373	+	1.45004i
$215$	−1175.92	−	1382.40i	−0.373009	−	0.438506i
$216$	689.691	+	4207.81i	0.217257	+	1.32549i
$217$	2775.61	−	2775.61i	0.868300	−	0.868300i
$218$	−121.345	+	575.966i	−0.0376998	+	0.178942i
$219$		−	36.1374i		−	0.0111504i
$220$	870.945	+	471.089i	0.266905	+	0.144367i
$221$		−	680.469i		−	0.207119i
$222$	1306.56	+	275.268i	0.395002	+	0.0832197i
$223$	3586.69	−	3586.69i	1.07705	−	1.07705i	0.0802797	−	0.996772i	$-0.474419\pi$
$223$	3586.69	−	3586.69i	1.07705	−	1.07705i	0.996772	−	0.0802797i	$-0.0255814\pi$
$224$	4104.93	+	1060.53i	1.22443	+	0.316339i
$225$	−975.556	+	6004.23i	−0.289054	+	1.77903i
$226$	−2753.54	+	1795.20i	−0.810454	+	0.528385i
$227$	2116.05	−	2116.05i	0.618710	−	0.618710i	−0.326491	−	0.945200i	$-0.605866\pi$
$227$	2116.05	−	2116.05i	0.618710	−	0.618710i	0.945200	+	0.326491i	$0.105866\pi$
$228$	−1909.32	+	740.793i	−0.554596	+	0.215176i
$229$	−1547.09			−0.446440			−0.223220	−	0.974768i	$-0.571657\pi$
$229$	−1547.09			−0.446440			−0.223220	+	0.974768i	$0.571657\pi$
$230$	−1504.65	−	2772.55i	−0.431364	−	0.794854i
$231$			2255.42i			0.642406i
$232$	−522.924	+	727.952i	−0.147981	+	0.206002i
$233$	−1819.85	−	1819.85i	−0.511684	−	0.511684i	0.403358	−	0.915042i	$-0.367843\pi$
$233$	−1819.85	−	1819.85i	−0.511684	−	0.511684i	−0.915042	+	0.403358i	$0.867843\pi$
$234$	−808.720	+	527.254i	−0.225930	+	0.147298i
$235$	−3438.49	−	4042.26i	−0.954479	−	1.12208i
$236$	−548.978	+	1245.03i	−0.151421	+	0.343409i
$237$	812.398	+	812.398i	0.222662	+	0.222662i
$238$	1324.95	−	6288.85i	0.360855	−	1.71280i
$239$	−3314.62			−0.897091			−0.448546	−	0.893760i	$-0.648058\pi$
$239$	−3314.62			−0.897091			−0.448546	+	0.893760i	$0.648058\pi$
$240$	−780.424	+	6175.01i	−0.209901	+	1.66081i
$241$	1482.29			0.396193			0.198096	−	0.980183i	$-0.436524\pi$
$241$	1482.29			0.396193			0.198096	+	0.980183i	$0.436524\pi$
$242$	704.639	−	3344.57i	0.187173	−	0.888417i
$243$	1597.24	+	1597.24i	0.421658	+	0.421658i
$244$	1655.76	−	3755.11i	0.434423	−	0.985231i
$245$	−184.888	+	2290.77i	−0.0482124	+	0.597354i
$246$	6291.99	−	4102.13i	1.63074	−	1.06318i
$247$	−145.963	−	145.963i	−0.0376009	−	0.0376009i
$248$	3079.95	+	2212.48i	0.788618	+	0.566504i
$249$		−	1367.31i		−	0.347991i
$250$	−1716.69	+	3560.62i	−0.434291	+	0.900773i
$251$	1272.42			0.319978			0.159989	−	0.987119i	$-0.448854\pi$
$251$	1272.42			0.319978			0.159989	+	0.987119i	$0.448854\pi$
$252$	−8500.75	+	3298.18i	−2.12499	+	0.824469i
$253$	780.892	−	780.892i	0.194048	−	0.194048i
$254$	−5805.59	+	3785.02i	−1.43415	+	0.935013i
$255$	9404.47	+	759.034i	2.30953	+	0.186402i
$256$	−369.630	+	4079.29i	−0.0902418	+	0.995920i
$257$	−3124.86	+	3124.86i	−0.758457	+	0.758457i	−0.976042	−	0.217584i	$-0.930182\pi$
$257$	−3124.86	+	3124.86i	−0.758457	+	0.758457i	0.217584	+	0.976042i	$0.430182\pi$
$258$	3907.98	+	823.341i	0.943025	+	0.198678i
$259$			1271.11i			0.304952i
$260$	−601.229	+	179.134i	−0.143410	+	0.0427286i
$261$		−	1927.64i		−	0.457158i
$262$	34.3173	−	162.887i	0.00809209	−	0.0384091i
$263$	−2331.55	+	2331.55i	−0.546653	+	0.546653i	−0.925471	−	0.378818i	$-0.876331\pi$
$263$	−2331.55	+	2331.55i	−0.546653	+	0.546653i	0.378818	+	0.925471i	$0.376331\pi$
$264$	−2150.28	+	352.446i	−0.501289	+	0.0821650i
$265$	5484.40	−	4665.23i	1.27134	−	1.08144i
$266$	−1064.78	−	1633.19i	−0.245435	−	0.376455i
$267$	−5147.88	+	5147.88i	−1.17994	+	1.17994i
$268$	5023.97	−	1949.24i	1.14510	−	0.444285i
$269$	−5963.79			−1.35174			−0.675871	−	0.737020i	$-0.736232\pi$
$269$	−5963.79			−1.35174			−0.675871	+	0.737020i	$0.736232\pi$
$270$	−2842.36	−	5237.50i	−0.640670	−	1.18053i
$271$			207.168i			0.0464374i	0.999730	+	0.0232187i	$0.00739141\pi$
$271$			207.168i			0.0464374i	−0.999730	+	0.0232187i	$0.992609\pi$
$272$	6202.72	+	280.444i	1.38270	+	0.0625163i
$273$	−1010.42	−	1010.42i	−0.224006	−	0.224006i
$274$	230.382	+	353.368i	0.0507953	+	0.0779114i
$275$	−1365.92	−	221.932i	−0.299519	−	0.0486654i
$276$	6351.67	+	2800.68i	1.38524	+	0.610801i
$277$	−1139.43	−	1139.43i	−0.247154	−	0.247154i	0.572647	−	0.819802i	$-0.305916\pi$
$277$	−1139.43	−	1139.43i	−0.247154	−	0.247154i	−0.819802	+	0.572647i	$0.805916\pi$
$278$	−2541.79	−	535.508i	−0.548368	−	0.115531i
$279$	−8155.83			−1.75010
$280$	−5905.31	+	484.892i	−1.26039	+	0.103492i
$281$	−4385.55			−0.931032			−0.465516	−	0.885039i	$-0.654131\pi$
$281$	−4385.55			−0.931032			−0.465516	+	0.885039i	$0.654131\pi$
$282$	11427.3	+	2407.52i	2.41307	+	0.508390i
$283$	3933.88	+	3933.88i	0.826307	+	0.826307i	0.987004	−	0.160697i	$-0.0513743\pi$
$283$	3933.88	+	3933.88i	0.826307	+	0.826307i	−0.160697	+	0.987004i	$0.551374\pi$
$284$	2026.00	−	4594.78i	0.423314	−	0.960036i
$285$	2180.11	−	1854.48i	0.453118	−	0.385438i
$286$	−119.946	−	183.978i	−0.0247992	−	0.0380378i
$287$	5056.05	+	5056.05i	1.03989	+	1.03989i
$288$	−4472.81	−	7589.06i	−0.915148	−	1.55274i
$289$		−	4499.19i		−	0.915773i
$290$	356.006	−	1200.97i	0.0720877	−	0.243184i
$291$	−5967.02			−1.20204
$292$	12.0218	+	30.9851i	0.00240933	+	0.00620982i
$293$	6361.20	−	6361.20i	1.26835	−	1.26835i	0.321403	−	0.946943i	$-0.395846\pi$
$293$	6361.20	−	6361.20i	1.26835	−	1.26835i	0.946943	−	0.321403i	$-0.104154\pi$
$294$	−2762.05	−	4236.52i	−0.547911	−	0.840404i
$295$	152.982	−	1895.46i	0.0301931	−	0.374094i
$296$	−1211.85	+	198.631i	−0.237964	+	0.0390040i
$297$	1475.15	−	1475.15i	0.288204	−	0.288204i
$298$	241.594	−	1146.73i	0.0469637	−	0.222913i
$299$			699.675i			0.135329i
$300$	−1805.10	−	8509.14i	−0.347391	−	1.63758i
$301$			3801.95i			0.728042i
$302$	−4842.02	−	1020.13i	−0.922606	−	0.194376i
$303$	881.730	−	881.730i	0.167175	−	0.167175i
$304$	1390.66	−	1270.35i	0.262368	−	0.239669i
$305$	−461.407	+	5716.86i	−0.0866232	+	1.07327i
$306$	−11186.1	+	7292.94i	−2.08977	+	1.36245i
$307$	5521.61	−	5521.61i	1.02650	−	1.02650i	0.0268586	−	0.999639i	$-0.491450\pi$
$307$	5521.61	−	5521.61i	1.02650	−	1.02650i	0.999639	−	0.0268586i	$-0.00855039\pi$
$308$	−750.311	−	1933.86i	−0.138808	−	0.357765i
$309$	1197.05			0.220381
$310$	−5081.29	−	1506.26i	−0.930960	−	0.275967i
$311$		−	6319.98i		−	1.15233i	−0.817335	−	0.576163i	$-0.804549\pi$
$311$		−	6319.98i		−	1.15233i	0.817335	−	0.576163i	$-0.195451\pi$
$312$	805.424	−	1121.21i	0.146148	−	0.203450i
$313$	5524.29	+	5524.29i	0.997608	+	0.997608i	0.999997	−	0.00238920i	$-0.000760506\pi$
$313$	5524.29	+	5524.29i	0.997608	+	0.997608i	−0.00238920	+	0.999997i	$0.500761\pi$
$314$	6287.50	−	4099.21i	1.13001	−	0.736725i
$315$	9706.36	−	8256.57i	1.73616	−	1.47684i
$316$	−966.831	−	426.310i	−0.172116	−	0.0758918i
$317$	4123.56	+	4123.56i	0.730606	+	0.730606i	0.970740	−	0.240134i	$-0.0771914\pi$
$317$	4123.56	+	4123.56i	0.730606	+	0.730606i	−0.240134	+	0.970740i	$0.577191\pi$
$318$	−3266.45	+	15504.2i	−0.576016	+	2.73406i
$319$	438.524			0.0769675
$320$	−1385.09	−	5554.24i	−0.241965	−	0.970285i
$321$	16665.4			2.89774
$322$	−1362.34	+	6466.35i	−0.235778	+	1.11912i
$323$	−2018.95	−	2018.95i	−0.347794	−	0.347794i
$324$	2380.75	+	1049.76i	0.408222	+	0.180000i
$325$	711.352	−	512.503i	0.121411	−	0.0874724i
$326$	−2824.58	+	1841.52i	−0.479874	+	0.312860i
$327$	1280.00	+	1280.00i	0.216466	+	0.216466i
$328$	−4030.25	+	5610.43i	−0.678455	+	0.944464i
$329$			11117.2i			1.86296i
$330$	2676.47	−	1452.51i	0.446469	−	0.242297i
$331$	−1756.83			−0.291734			−0.145867	−	0.989304i	$-0.546597\pi$
$331$	−1756.83			−0.291734			−0.145867	+	0.989304i	$0.546597\pi$
$332$	454.864	+	1172.37i	0.0751924	+	0.193801i
$333$	1867.50	−	1867.50i	0.307322	−	0.307322i
$334$	918.437	−	598.786i	0.150463	−	0.0980961i
$335$	−5736.48	+	4879.66i	−0.935575	+	0.795833i
$336$	9626.80	−	8793.94i	1.56305	−	1.42782i
$337$	−5055.88	+	5055.88i	−0.817245	+	0.817245i	−0.985708	−	0.168463i	$-0.946120\pi$
$337$	−5055.88	+	5055.88i	−0.817245	+	0.817245i	0.168463	+	0.985708i	$0.446120\pi$
$338$	−5944.41	−	1252.38i	−0.956608	−	0.201540i
$339$			10108.9i			1.61959i
$340$	−8316.14	+	2477.77i	−1.32649	+	0.395224i
$341$		−	1855.39i		−	0.294648i
$342$	−835.107	+	3963.83i	−0.132039	+	0.626723i
$343$	−2276.22	+	2276.22i	−0.358321	+	0.358321i
$344$	−3624.70	+	594.116i	−0.568113	+	0.0931180i
$345$	−9669.91	−	780.457i	−1.50902	−	0.121792i
$346$	1668.07	+	2558.54i	0.259179	+	0.397537i
$347$	−3049.33	+	3049.33i	−0.471748	+	0.471748i	−0.902480	−	0.430732i	$-0.858255\pi$
$347$	−3049.33	+	3049.33i	−0.471748	+	0.471748i	0.430732	+	0.902480i	$0.358255\pi$
$348$	997.064	+	2569.84i	0.153587	+	0.395855i
$349$	−1009.65			−0.154858			−0.0774292	−	0.996998i	$-0.524671\pi$
$349$	−1009.65			−0.154858			−0.0774292	+	0.996998i	$0.524671\pi$
$350$	7572.17	−	3351.44i	1.15643	−	0.511834i
$351$			1321.72i			0.200993i
$352$	1726.45	−	1017.53i	0.261421	−	0.154075i
$353$	−8243.95	−	8243.95i	−1.24301	−	1.24301i	−0.958748	−	0.284259i	$-0.908253\pi$
$353$	−8243.95	−	8243.95i	−1.24301	−	1.24301i	−0.284259	−	0.958748i	$-0.591747\pi$
$354$	2285.41	+	3505.44i	0.343131	+	0.526305i
$355$	−564.581	+	6995.19i	−0.0844080	+	1.04582i
$356$	2701.38	−	6126.47i	0.402170	−	0.912085i
$357$	−13976.1	−	13976.1i	−2.07197	−	2.07197i
$358$	9281.83	+	1955.51i	1.37028	+	0.288693i
$359$	1663.12			0.244502			0.122251	−	0.992499i	$-0.460989\pi$
$359$	1663.12			0.244502			0.122251	+	0.992499i	$0.460989\pi$
$360$	9388.44	+	7963.64i	1.37448	+	1.16589i
$361$	5992.86			0.873721
$362$	−8695.83	−	1832.05i	−1.26255	−	0.265996i
$363$	−7432.83	−	7432.83i	−1.07472	−	1.07472i
$364$	1202.50	+	530.225i	0.173154	+	0.0763499i
$365$	−30.0951	−	35.3795i	−0.00431575	−	0.00507356i
$366$	−6892.99	−	10572.7i	−0.984433	−	1.50995i
$367$	−2941.96	−	2941.96i	−0.418445	−	0.418445i	0.466223	−	0.884667i	$-0.345615\pi$
$367$	−2941.96	−	2941.96i	−0.418445	−	0.418445i	−0.884667	+	0.466223i	$0.845615\pi$
$368$	−6377.79	−	288.360i	−0.903438	−	0.0408472i
$369$		−	14856.6i		−	2.09595i
$370$	1508.40	−	818.601i	0.211940	−	0.115019i
$371$	−15083.5			−2.11077
$372$	10872.9	−	4218.56i	1.51542	−	0.587963i
$373$	6831.30	−	6831.30i	0.948288	−	0.948288i	−0.0504396	−	0.998727i	$-0.516062\pi$
$373$	6831.30	−	6831.30i	0.948288	−	0.948288i	0.998727	+	0.0504396i	$0.0160622\pi$
$374$	−1659.09	−	2544.76i	−0.229383	−	0.351835i
$375$	6289.60	+	10403.0i	0.866116	+	1.43255i
$376$	−10599.0	+	1737.25i	−1.45372	+	0.238276i
$377$	−196.458	+	196.458i	−0.0268385	+	0.0268385i
$378$	−2573.54	+	12215.3i	−0.350181	+	1.66213i
$379$		−	1604.62i		−	0.217477i	−0.994070	−	0.108739i	$-0.965319\pi$
$379$		−	1604.62i		−	0.217477i	0.994070	−	0.108739i	$-0.0346812\pi$
$380$	−1252.35	+	2315.33i	−0.169064	+	0.312563i
$381$			21313.8i			2.86598i
$382$	7324.71	+	1543.18i	0.981060	+	0.206691i
$383$	−1085.46	+	1085.46i	−0.144815	+	0.144815i	−0.775797	−	0.630982i	$-0.782652\pi$
$383$	−1085.46	+	1085.46i	−0.144815	+	0.144815i	0.630982	+	0.775797i	$0.282652\pi$
$384$	9888.32	+	7803.81i	1.31409	+	1.03707i
$385$	1878.31	+	2208.12i	0.248643	+	0.292302i
$386$	11811.4	−	7700.56i	1.55747	−	1.01541i
$387$	5585.80	−	5585.80i	0.733700	−	0.733700i
$388$	5116.27	−	1985.05i	0.669431	−	0.259731i
$389$	9833.10			1.28164			0.640820	−	0.767691i	$-0.278594\pi$
$389$	9833.10			1.28164			0.640820	+	0.767691i	$0.278594\pi$
$390$	−548.332	+	1849.77i	−0.0711946	+	0.240171i
$391$			9677.85i			1.25174i
$392$	3777.61	+	2713.65i	0.486730	+	0.349643i
$393$	−361.993	−	361.993i	−0.0464635	−	0.0464635i
$394$	−12484.7	+	8139.53i	−1.59637	+	1.04077i
$395$	1471.92	+	118.799i	0.187495	+	0.0151327i
$396$	−1738.86	+	3943.56i	−0.220659	+	0.500433i
$397$	−9888.55	−	9888.55i	−1.25011	−	1.25011i	−0.955672	−	0.294435i	$-0.904869\pi$
$397$	−9888.55	−	9888.55i	−1.25011	−	1.25011i	−0.294435	−	0.955672i	$-0.595131\pi$
$398$	−1576.07	+	7480.81i	−0.198496	+	0.942158i
$399$	−5995.85			−0.752300
$400$	4378.47	+	6695.45i	0.547309	+	0.836931i
$401$	8106.73			1.00955			0.504777	−	0.863250i	$-0.331575\pi$
$401$	8106.73			1.00955			0.504777	+	0.863250i	$0.331575\pi$
$402$	3416.58	−	16216.8i	0.423890	−	2.01199i
$403$	831.210	+	831.210i	0.102743	+	0.102743i
$404$	−462.692	+	1049.34i	−0.0569797	+	0.129225i
$405$	−3624.51	−	292.533i	−0.444699	−	0.0358916i
$406$	−2198.18	+	1433.13i	−0.268703	+	0.175184i
$407$	424.842	+	424.842i	0.0517411	+	0.0517411i
$408$	11140.6	−	15508.5i	1.35181	−	1.88183i
$409$		−	8464.46i		−	1.02333i	−0.859186	−	0.511663i	$-0.829030\pi$
$409$		−	8464.46i		−	1.02333i	0.859186	−	0.511663i	$-0.170970\pi$
$410$	2743.79	−	9256.05i	0.330503	−	1.11494i
$411$	1297.30			0.155697
$412$	−1026.38	+	398.223i	−0.122734	+	0.0476191i
$413$	−2816.86	+	2816.86i	−0.335614	+	0.335614i
$414$	11501.9	−	7498.78i	1.36543	−	0.890205i
$415$	−1138.69	−	1338.64i	−0.134690	−	0.158340i
$416$	−317.597	+	1229.30i	−0.0374314	+	0.144883i
$417$	−5648.77	+	5648.77i	−0.663360	+	0.663360i
$418$	−901.741	−	189.980i	−0.105516	−	0.0222302i
$419$		−	2455.99i		−	0.286355i	−0.989697	−	0.143178i	$-0.954268\pi$
$419$		−	2455.99i		−	0.286355i	0.989697	−	0.143178i	$-0.0457320\pi$
$420$	−8669.35	+	16027.8i	−1.00719	+	1.86209i
$421$		−	2783.22i		−	0.322199i	−0.986938	−	0.161100i	$-0.948496\pi$
$421$		−	2783.22i		−	0.322199i	0.986938	−	0.161100i	$-0.0515040\pi$
$422$	−1047.19	+	4970.50i	−0.120798	+	0.573366i
$423$	16333.4	−	16333.4i	1.87744	−	1.87744i
$424$	−2357.04	−	14380.3i	−0.269972	−	1.64710i
$425$	9839.36	−	7088.89i	1.12301	−	0.809087i
$426$	−8434.31	−	12936.8i	−0.959258	−	1.47134i
$427$	8495.89	−	8495.89i	0.962869	−	0.962869i
$428$	−14289.4	+	5544.09i	−1.61379	+	0.626130i
$429$	−675.429			−0.0760140
$430$	4511.70	−	2448.48i	0.505985	−	0.274596i
$431$		−	8674.68i		−	0.969477i	−0.874659	−	0.484738i	$-0.838915\pi$
$431$		−	8674.68i		−	0.969477i	0.874659	−	0.484738i	$-0.161085\pi$
$432$	−12048.0	−	544.727i	−1.34180	−	0.0606671i
$433$	−2596.19	−	2596.19i	−0.288141	−	0.288141i	0.548204	−	0.836345i	$-0.315312\pi$
$433$	−2596.19	−	2596.19i	−0.288141	−	0.288141i	−0.836345	+	0.548204i	$0.815312\pi$
$434$	6063.53	+	9300.44i	0.670642	+	1.02865i
$435$	−2496.02	−	2934.30i	−0.275115	−	0.323423i
$436$	−1523.33	−	671.689i	−0.167326	−	0.0737799i
$437$	2075.93	+	2075.93i	0.227243	+	0.227243i
$438$	100.016	+	21.0716i	0.0109109	+	0.00229873i
$439$	−337.310			−0.0366718			−0.0183359	−	0.999832i	$-0.505837\pi$
$439$	−337.310			−0.0366718			−0.0183359	+	0.999832i	$0.505837\pi$
$440$	−1811.67	+	2135.80i	−0.196290	+	0.231409i
$441$	−10003.3			−1.08015
$442$	1883.31	+	396.780i	0.202670	+	0.0426989i
$443$	3963.04	+	3963.04i	0.425033	+	0.425033i	0.886932	−	0.461899i	$-0.152832\pi$
$443$	3963.04	+	3963.04i	0.425033	+	0.425033i	−0.461899	+	0.886932i	$0.652832\pi$
$444$	−1523.70	+	3455.61i	−0.162864	+	0.369360i
$445$	−752.785	+	9327.05i	−0.0801920	+	0.993584i
$446$	7835.39	+	12018.2i	0.831875	+	1.27596i
$447$	−2548.44	−	2548.44i	−0.269658	−	0.269658i
$448$	−5328.78	+	10742.7i	−0.561967	+	1.13291i
$449$			5050.61i			0.530853i	0.964131	+	0.265426i	$0.0855127\pi$
$449$			5050.61i			0.530853i	−0.964131	+	0.265426i	$0.914487\pi$
$450$	−16048.9	−	6201.07i	−1.68123	−	0.649603i
$451$	3379.77			0.352876
$452$	−3362.94	−	8667.66i	−0.349955	−	0.901975i
$453$	−10760.7	+	10760.7i	−1.11608	+	1.11608i
$454$	4622.66	+	7090.39i	0.477869	+	0.732970i
$455$	−1830.71	−	147.756i	−0.188627	−	0.0152240i
$456$	−936.949	−	5716.33i	−0.0962207	−	0.587043i
$457$	−11219.5	+	11219.5i	−1.14842	+	1.14842i	−0.161551	+	0.986864i	$0.551650\pi$
$457$	−11219.5	+	11219.5i	−1.14842	+	1.14842i	−0.986864	+	0.161551i	$0.948350\pi$
$458$	902.106	−	4281.84i	0.0920364	−	0.436850i
$459$			18282.0i			1.85911i
$460$	8550.86	−	2547.71i	0.866709	−	0.258234i
$461$		−	7285.56i		−	0.736057i	−0.929814	−	0.368029i	$-0.880033\pi$
$461$		−	7285.56i		−	0.736057i	0.929814	−	0.368029i	$-0.119967\pi$
$462$	−6242.26	−	1315.13i	−0.628607	−	0.132436i
$463$	−8950.11	+	8950.11i	−0.898373	+	0.898373i	−0.995292	−	0.0969191i	$-0.969101\pi$
$463$	−8950.11	+	8950.11i	−0.898373	+	0.898373i	0.0969191	+	0.995292i	$0.469101\pi$
$464$	−1709.82	−	1871.75i	−0.171069	−	0.187271i
$465$	−12415.0	+	10560.6i	−1.23813	+	1.05320i
$466$	6097.89	−	3975.59i	0.606179	−	0.395205i
$467$	3141.84	−	3141.84i	0.311322	−	0.311322i	−0.534100	−	0.845421i	$-0.679349\pi$
$467$	3141.84	−	3141.84i	0.311322	−	0.311322i	0.845421	+	0.534100i	$0.179349\pi$
$468$	−987.703	−	2545.71i	−0.0975569	−	0.251443i
$469$	15776.8			1.55331
$470$	13192.6	−	7159.58i	1.29475	−	0.702653i
$471$		−	23083.0i		−	2.25819i
$472$	−3125.72	−	2245.36i	−0.304816	−	0.218964i
$473$	1270.73	+	1270.73i	0.123526	+	0.123526i
$474$	−2722.16	+	1774.74i	−0.263782	+	0.171976i
$475$	589.986	−	3631.17i	0.0569904	−	0.350757i
$476$	16632.9	+	7334.03i	1.60161	+	0.706207i
$477$	22160.6	+	22160.6i	2.12717	+	2.12717i
$478$	1932.75	−	9173.77i	0.184941	−	0.877821i
$479$	1511.49			0.144179			0.0720894	−	0.997398i	$-0.477033\pi$
$479$	1511.49			0.144179			0.0720894	+	0.997398i	$0.477033\pi$
$480$	−16635.3	−	5760.59i	−1.58187	−	0.547779i
$481$	−380.656			−0.0360841
$482$	−864.318	+	4102.48i	−0.0816776	+	0.387682i
$483$	14370.6	+	14370.6i	1.35380	+	1.35380i
$484$	8845.78	+	3900.42i	0.830746	+	0.366305i
$485$	−5841.88	+	4969.31i	−0.546941	+	0.465247i
$486$	−5351.98	+	3489.29i	−0.499528	+	0.325673i
$487$	−4174.17	−	4174.17i	−0.388397	−	0.388397i	0.485718	−	0.874115i	$-0.338558\pi$
$487$	−4174.17	−	4174.17i	−0.388397	−	0.388397i	−0.874115	+	0.485718i	$0.838558\pi$
$488$	9427.44	+	6772.20i	0.874509	+	0.628203i
$489$			10369.8i			0.958970i
$490$	−6232.28	−	1847.45i	−0.574583	−	0.170325i
$491$	7841.60			0.720746			0.360373	−	0.932808i	$-0.382649\pi$
$491$	7841.60			0.720746			0.360373	+	0.932808i	$0.382649\pi$
$492$	7684.51	+	19806.1i	0.704155	+	1.81489i
$493$	−2717.39	+	2717.39i	−0.248245	+	0.248245i
$494$	489.089	−	318.867i	0.0445448	−	0.0290415i
$495$	484.562	−	6003.76i	0.0439989	−	0.545149i
$496$	−7919.34	+	7234.20i	−0.716913	+	0.654890i
$497$	10395.6	−	10395.6i	0.938245	−	0.938245i
$498$	3784.27	+	797.276i	0.340516	+	0.0717406i
$499$		−	11318.0i		−	1.01535i	−0.861548	−	0.507677i	$-0.830504\pi$
$499$		−	11318.0i		−	1.01535i	0.861548	−	0.507677i	$-0.169496\pi$
$500$	−8853.62	−	6827.41i	−0.791891	−	0.610662i
$501$		−	3371.82i		−	0.300682i
$502$	−741.946	+	3521.64i	−0.0659655	+	0.313105i
$503$	−2339.87	+	2339.87i	−0.207415	+	0.207415i	−0.803168	−	0.595753i	$-0.796854\pi$
$503$	−2339.87	+	2339.87i	−0.207415	+	0.207415i	0.595753	+	0.803168i	$0.296854\pi$
$504$	−4171.52	−	25450.4i	−0.368679	−	2.24931i
$505$	128.937	−	1597.54i	0.0113616	−	0.140771i
$506$	1705.91	+	2616.59i	0.149876	+	0.229884i
$507$	−13210.6	+	13210.6i	−1.15721	+	1.15721i
$508$	−7090.46	−	18275.0i	−0.619268	−	1.59610i
$509$	−12201.2			−1.06249			−0.531245	−	0.847218i	$-0.678276\pi$
$509$	−12201.2			−1.06249			−0.531245	+	0.847218i	$0.678276\pi$
$510$	−7584.48	+	25585.9i	−0.658522	+	2.22149i
$511$			97.3026i			0.00842351i
$512$	−11074.6	−	3401.64i	−0.955923	−	0.293618i
$513$	3921.55	+	3921.55i	0.337506	+	0.337506i
$514$	−6826.49	−	10470.7i	−0.585804	−	0.898525i
$515$	1171.95	−	996.900i	0.100276	−	0.0852984i
$516$	−4557.47	+	10335.9i	−0.388821	+	0.881809i
$517$	3715.72	+	3715.72i	0.316087	+	0.316087i
$518$	−3518.00	−	741.179i	−0.298402	−	0.0628678i
$519$	9393.04			0.794429
$520$	−145.210	−	1768.46i	−0.0122459	−	0.149138i
$521$	−1704.22			−0.143307			−0.0716536	−	0.997430i	$-0.522828\pi$
$521$	−1704.22			−0.143307			−0.0716536	+	0.997430i	$0.522828\pi$
$522$	5335.08	+	1124.01i	0.447338	+	0.0942459i
$523$	−7612.08	−	7612.08i	−0.636430	−	0.636430i	0.313243	−	0.949673i	$-0.398585\pi$
$523$	−7612.08	−	7612.08i	−0.636430	−	0.636430i	−0.949673	+	0.313243i	$0.898585\pi$
$524$	430.807	+	189.958i	0.0359158	+	0.0158365i
$525$	4084.16	−	25136.7i	0.339518	−	2.08963i
$526$	−5093.45	−	7812.49i	−0.422214	−	0.647606i
$527$	11497.2	+	11497.2i	0.950336	+	0.950336i
$528$	278.367	−	6156.77i	0.0229439	−	0.507460i
$529$			2215.99i			0.182132i
$530$	9713.87	+	17899.3i	0.796120	+	1.46697i
$531$	8277.03			0.676445
$532$	5140.99	−	1994.64i	0.418967	−	0.162554i
$533$	−1514.13	+	1514.13i	−0.123047	+	0.123047i
$534$	−11245.9	−	17249.3i	−0.911345	−	1.39785i
$535$	16315.9	−	13878.9i	1.31850	−	1.12157i
$536$	2465.38	+	15041.3i	0.198672	+	1.21210i
$537$	20627.6	−	20627.6i	1.65763	−	1.65763i
$538$	3477.47	−	16505.8i	0.278670	−	1.32271i
$539$		−	2275.66i		−	0.181855i
$540$	16153.0	−	4812.75i	1.28725	−	0.383533i
$541$		−	10667.2i		−	0.847723i	−0.905727	−	0.423861i	$-0.860674\pi$
$541$		−	10667.2i		−	0.847723i	0.905727	−	0.423861i	$-0.139326\pi$
$542$	−573.372	−	120.799i	−0.0454399	−	0.00957337i
$543$	−19325.3	+	19325.3i	−1.52731	+	1.52731i
$544$	−4392.97	+	17003.5i	−0.346226	+	1.34011i
$545$	2319.14	+	187.178i	0.182277	+	0.0147116i
$546$	3385.70	−	2207.34i	0.265374	−	0.173014i
$547$	−11723.3	+	11723.3i	−0.916366	+	0.916366i	−0.996763	−	0.0803966i	$-0.974381\pi$
$547$	−11723.3	+	11723.3i	−0.916366	+	0.916366i	0.0803966	+	0.996763i	$0.474381\pi$
$548$	−1112.34	+	431.574i	−0.0867096	+	0.0336422i
$549$	−24964.2			−1.94070
$550$	1410.70	−	3651.00i	0.109368	−	0.283053i
$551$			1165.78i			0.0901341i
$552$	−11455.0	+	15946.3i	−0.883256	+	1.22956i
$553$	−2187.44	−	2187.44i	−0.168209	−	0.168209i
$554$	3817.97	−	2489.17i	0.292798	−	0.190893i
$555$	424.606	−	5260.89i	0.0324748	−	0.402364i
$556$	2964.22	−	6722.57i	0.226099	−	0.512771i
$557$	−13466.7	−	13466.7i	−1.02442	−	1.02442i	−0.999694	−	0.0247247i	$-0.992129\pi$
$557$	−13466.7	−	13466.7i	−1.02442	−	1.02442i	−0.0247247	−	0.999694i	$-0.507871\pi$
$558$	4755.65	−	22572.6i	0.360793	−	1.71250i
$559$	−1138.56			−0.0861469
$560$	2101.35	−	16626.7i	0.158568	−	1.25465i
$561$	−9342.47			−0.703100
$562$	2557.20	−	12137.8i	0.191938	−	0.911033i
$563$	13321.7	+	13321.7i	0.997236	+	0.997236i	0.999996	−	0.00276031i	$-0.000878637\pi$
$563$	13321.7	+	13321.7i	0.997236	+	0.997236i	−0.00276031	+	0.999996i	$0.500879\pi$
$564$	−13326.5	+	30223.2i	−0.994939	+	2.25643i
$565$	8418.69	+	9896.94i	0.626862	+	0.736934i
$566$	−13181.5	+	8593.84i	−0.978905	+	0.638209i
$567$	5386.42	+	5386.42i	0.398957	+	0.398957i
$568$	11535.5	+	8286.51i	0.852145	+	0.612138i
$569$		−	8946.03i		−	0.659117i	−0.944135	−	0.329558i	$-0.893100\pi$
$569$		−	8946.03i		−	0.659117i	0.944135	−	0.329558i	$-0.106900\pi$
$570$	3861.37	+	7115.17i	0.283745	+	0.522845i
$571$	−15237.7			−1.11678			−0.558388	−	0.829580i	$-0.688580\pi$
$571$	−15237.7			−1.11678			−0.558388	+	0.829580i	$0.688580\pi$
$572$	579.129	−	224.695i	0.0423333	−	0.0164248i
$573$	16278.2	−	16278.2i	1.18679	−	1.18679i
$574$	−16941.6	+	11045.3i	−1.23193	+	0.803174i
$575$	−10117.1	+	7288.98i	−0.733759	+	0.528646i
$576$	23612.1	−	7954.09i	1.70805	−	0.575383i
$577$	1665.78	−	1665.78i	0.120186	−	0.120186i	−0.644456	−	0.764642i	$-0.722916\pi$
$577$	1665.78	−	1665.78i	0.120186	−	0.120186i	0.764642	+	0.644456i	$0.222916\pi$
$578$	12452.3	+	2623.47i	0.896101	+	0.188792i
$579$		−	43362.5i		−	3.11241i
$580$	3116.30	+	1685.59i	0.223099	+	0.120673i
$581$			3681.59i			0.262888i
$582$	3479.36	−	16514.7i	0.247807	−	1.17622i
$583$	−5041.36	+	5041.36i	−0.358133	+	0.358133i
$584$	−92.7665	+	15.2051i	−0.00657312	+	0.00107738i
$585$	2472.59	+	2906.75i	0.174750	+	0.205435i
$586$	13896.5	+	21314.9i	0.979623	+	1.50258i
$587$	2011.28	−	2011.28i	0.141421	−	0.141421i	−0.632852	−	0.774273i	$-0.718116\pi$
$587$	2011.28	−	2011.28i	0.141421	−	0.141421i	0.774273	+	0.632852i	$0.218116\pi$
$588$	13335.8	−	5174.13i	0.935307	−	0.362887i
$589$	4932.39			0.345052
$590$	5156.80	+	1528.64i	0.359834	+	0.106666i
$591$			45834.5i			3.19015i
$592$	156.881	−	3469.82i	0.0108915	−	0.240893i
$593$	−2415.44	−	2415.44i	−0.167269	−	0.167269i	0.618509	−	0.785778i	$-0.287737\pi$
$593$	−2415.44	−	2415.44i	−0.167269	−	0.167269i	−0.785778	+	0.618509i	$0.787737\pi$
$594$	3222.56	+	4942.87i	0.222598	+	0.341428i
$595$	−25322.2	−	2043.75i	−1.74472	−	0.140816i
$596$	3032.88	+	1337.31i	0.208443	+	0.0919097i
$597$	16625.1	+	16625.1i	1.13973	+	1.13973i
$598$	−1936.47	−	407.979i	−0.132422	−	0.0278988i
$599$	20522.7			1.39989			0.699944	−	0.714198i	$-0.253208\pi$
$599$	20522.7			1.39989			0.699944	+	0.714198i	$0.253208\pi$
$600$	24603.0	−	34.2521i	1.67402	−	0.00233056i
$601$	−20598.5			−1.39806			−0.699028	−	0.715095i	$-0.746384\pi$
$601$	−20598.5			−1.39806			−0.699028	+	0.715095i	$0.746384\pi$
$602$	−10522.5	−	2216.91i	−0.712403	−	0.150090i
$603$	−23179.1	−	23179.1i	−1.56538	−	1.56538i
$604$	5646.75	−	12806.3i	0.380402	−	0.862716i
$605$	−13467.0	−	1086.92i	−0.904977	−	0.0730406i
$606$	1926.20	+	2954.47i	0.129120	+	0.198048i
$607$	−12526.9	−	12526.9i	−0.837643	−	0.837643i	0.150905	−	0.988548i	$-0.451781\pi$
$607$	−12526.9	−	12526.9i	−0.837643	−	0.837643i	−0.988548	+	0.150905i	$0.951781\pi$
$608$	2705.02	+	4589.63i	0.180432	+	0.306142i
$609$			8070.06i			0.536971i
$610$	−15553.3	−	4610.51i	−1.03235	−	0.306023i
$611$	−3329.27			−0.220438
$612$	−13661.8	−	35212.0i	−0.902364	−	2.32576i
$613$	−7326.67	+	7326.67i	−0.482743	+	0.482743i	−0.906007	−	0.423264i	$-0.860884\pi$
$613$	−7326.67	+	7326.67i	−0.482743	+	0.482743i	0.423264	+	0.906007i	$0.360884\pi$
$614$	12062.4	+	18501.6i	0.792829	+	1.21607i
$615$	−19237.2	−	22615.1i	−1.26133	−	1.48281i
$616$	5789.78	−	948.988i	0.378696	−	0.0620711i
$617$	6314.93	−	6314.93i	0.412042	−	0.412042i	−0.470408	−	0.882449i	$-0.655893\pi$
$617$	6314.93	−	6314.93i	0.412042	−	0.412042i	0.882449	+	0.470408i	$0.155893\pi$
$618$	−697.998	+	3313.04i	−0.0454330	+	0.215647i
$619$			28929.2i			1.87845i	0.343300	+	0.939226i	$0.388455\pi$
$619$			28929.2i			1.87845i	−0.343300	+	0.939226i	$0.611545\pi$
$620$	7131.71	−	13185.0i	0.461962	−	0.854070i
$621$		−	18798.0i		−	1.21471i
$622$	17491.6	+	3685.17i	1.12757	+	0.237559i
$623$	13861.0	−	13861.0i	0.891382	−	0.891382i
$624$	2633.51	+	2882.93i	0.168950	+	0.184951i
$625$	14821.2	+	4946.85i	0.948560	+	0.316598i
$626$	−18510.6	+	12068.2i	−1.18184	+	0.770515i
$627$	−2003.99	+	2003.99i	−0.127642	+	0.127642i
$628$	7679.03	+	19792.0i	0.487940	+	1.25762i
$629$	−5265.21			−0.333764
$630$	17191.7	+	31678.4i	1.08720	+	2.00333i
$631$			8708.83i			0.549434i	0.961525	+	0.274717i	$0.0885842\pi$
$631$			8708.83i			0.549434i	−0.961525	+	0.274717i	$0.911416\pi$
$632$	1743.64	−	2427.29i	0.109744	−	0.152773i
$633$	11046.3	+	11046.3i	0.693601	+	0.693601i
$634$	−13817.1	+	9008.21i	−0.865530	+	0.564293i
$635$	17750.0	+	20866.8i	1.10927	+	1.30405i
$636$	−41005.7	−	18080.9i	−2.55658	−	1.12729i
$637$	1019.49	+	1019.49i	0.0634125	+	0.0634125i
$638$	−255.703	+	1213.69i	−0.0158673	+	0.0753142i
$639$	−30546.4			−1.89107
$640$	16179.9	−	594.801i	0.999325	−	0.0367369i
$641$	−14575.4			−0.898118			−0.449059	−	0.893502i	$-0.648241\pi$
$641$	−14575.4			−0.898118			−0.449059	+	0.893502i	$0.648241\pi$
$642$	−9717.57	+	46124.4i	−0.597386	+	2.83549i
$643$	3421.95	+	3421.95i	0.209873	+	0.209873i	0.804214	−	0.594340i	$-0.202587\pi$
$643$	3421.95	+	3421.95i	0.209873	+	0.209873i	−0.594340	+	0.804214i	$0.702587\pi$
$644$	−17102.4	−	7541.03i	−1.04647	−	0.461426i
$645$	1270.02	−	15735.6i	0.0775301	−	0.960603i
$646$	6765.03	−	4410.54i	0.412023	−	0.268623i
$647$	4080.27	+	4080.27i	0.247932	+	0.247932i	0.820122	−	0.572189i	$-0.193906\pi$
$647$	4080.27	+	4080.27i	0.247932	+	0.247932i	−0.572189	+	0.820122i	$0.693906\pi$
$648$	−4293.60	+	5977.03i	−0.260291	+	0.362345i
$649$			1882.96i			0.113887i
$650$	1003.65	+	2267.63i	0.0605637	+	0.136836i
$651$	34144.3			2.05564
$652$	−3449.71	−	8891.29i	−0.207210	−	0.534064i
$653$	−2251.86	+	2251.86i	−0.134950	+	0.134950i	−0.771355	−	0.636405i	$-0.780421\pi$
$653$	−2251.86	+	2251.86i	−0.134950	+	0.134950i	0.636405	+	0.771355i	$0.280421\pi$
$654$	−4289.00	+	2796.26i	−0.256442	+	0.167190i
$655$	−655.868	−	52.9350i	−0.0391250	−	0.00315778i
$656$	−13177.8	−	14425.8i	−0.784308	−	0.858589i
$657$	142.956	−	142.956i	0.00848898	−	0.00848898i
$658$	−30768.9	−	6482.44i	−1.82294	−	0.384060i
$659$		−	1844.63i		−	0.109039i	−0.998513	−	0.0545195i	$-0.982637\pi$
$659$		−	1844.63i		−	0.109039i	0.998513	−	0.0545195i	$-0.0173627\pi$
$660$	2459.42	+	8254.53i	0.145050	+	0.486829i
$661$			11209.4i			0.659597i	0.944051	+	0.329798i	$0.106981\pi$
$661$			11209.4i			0.659597i	−0.944051	+	0.329798i	$0.893019\pi$
$662$	1024.40	−	4862.32i	0.0601428	−	0.285467i
$663$	4185.40	−	4185.40i	0.245170	−	0.245170i
$664$	−3509.96	+	575.308i	−0.205140	+	0.0336239i
$665$	−5870.11	+	4993.32i	−0.342305	+	0.291177i
$666$	4079.69	+	6257.56i	0.237364	+	0.364077i
$667$	2794.09	−	2794.09i	0.162200	−	0.162200i
$668$	1121.70	+	2891.08i	0.0649700	+	0.167454i
$669$	44121.8			2.54984
$670$	−10160.3	−	18722.0i	−0.585863	−	1.07954i
$671$		−	5679.17i		−	0.326739i
$672$	18725.4	+	31771.5i	1.07492	+	1.82383i
$673$	16141.4	+	16141.4i	0.924522	+	0.924522i	0.997345	−	0.0728227i	$-0.0232007\pi$
$673$	16141.4	+	16141.4i	0.924522	+	0.924522i	−0.0728227	+	0.997345i	$0.523201\pi$
$674$	−11044.9	−	16941.1i	−0.631209	−	0.968169i
$675$	−19111.7	+	13769.3i	−1.08979	+	0.785154i
$676$	6932.35	−	15721.9i	0.394421	−	0.894510i
$677$	1696.37	+	1696.37i	0.0963026	+	0.0963026i	0.753617	−	0.657314i	$-0.228308\pi$
$677$	1696.37	+	1696.37i	0.0963026	+	0.0963026i	−0.657314	+	0.753617i	$0.728308\pi$
$678$	−27978.2	−	5894.50i	−1.58480	−	0.333889i
$679$	16066.6			0.908072
$680$	−2008.53	−	24461.1i	−0.113270	−	1.37947i
$681$	26030.6			1.46475
$682$	5135.10	+	1081.87i	0.288319	+	0.0607435i
$683$	−14046.1	−	14046.1i	−0.786911	−	0.786911i	0.194075	−	0.980987i	$-0.437829\pi$
$683$	−14046.1	−	14046.1i	−0.786911	−	0.786911i	−0.980987	+	0.194075i	$0.937829\pi$
$684$	−10483.6	−	4622.60i	−0.586040	−	0.258406i
$685$	1270.10	−	1080.39i	0.0708437	−	0.0602621i
$686$	−4972.56	−	7627.07i	−0.276754	−	0.424494i
$687$	−9515.80	−	9515.80i	−0.528458	−	0.528458i
$688$	469.240	−	10378.4i	0.0260024	−	0.575106i
$689$		−	4517.03i		−	0.249761i
$690$	7798.55	−	26308.0i	0.430269	−	1.45149i
$691$	29252.6			1.61045			0.805225	−	0.592969i	$-0.202044\pi$
$691$	29252.6			1.61045			0.805225	+	0.592969i	$0.202044\pi$
$692$	−8053.83	+	3124.78i	−0.442429	+	0.171657i
$693$	−8922.25	+	8922.25i	−0.489074	+	0.489074i
$694$	−6661.48	−	10217.6i	−0.364361	−	0.558868i
$695$	−826.031	+	10234.6i	−0.0450837	+	0.558589i
$696$	−7693.85	+	1261.08i	−0.419015	+	0.0686797i
$697$	−20943.3	+	20943.3i	−1.13814	+	1.13814i
$698$	588.727	−	2794.39i	0.0319250	−	0.151532i
$699$		−	22386.9i		−	1.21137i
$700$	4860.35	+	22911.5i	0.262434	+	1.23710i
$701$		−	14092.5i		−	0.759294i	−0.925132	−	0.379647i	$-0.876046\pi$
$701$		−	14092.5i		−	0.759294i	0.925132	−	0.379647i	$-0.123954\pi$
$702$	−3658.10	−	770.695i	−0.196675	−	0.0414359i
$703$	−1129.41	+	1129.41i	−0.0605923	+	0.0605923i
$704$	1809.49	+	5371.57i	0.0968720	+	0.287569i
$705$	3713.65	−	46012.4i	0.198389	−	2.45805i
$706$	27623.6	−	18009.5i	1.47256	−	0.960052i
$707$	−2374.12	+	2374.12i	−0.126291	+	0.126291i
$708$	−11034.5	+	4281.25i	−0.585738	+	0.227259i
$709$	10464.5			0.554303			0.277151	−	0.960826i	$-0.410610\pi$
$709$	10464.5			0.554303			0.277151	+	0.960826i	$0.410610\pi$
$710$	−19031.2	−	5641.45i	−1.00595	−	0.298197i
$711$			6427.55i			0.339032i
$712$	15380.9	+	11048.8i	0.809582	+	0.581563i
$713$	−11821.7	−	11821.7i	−0.620936	−	0.620936i
$714$	46830.7	−	30531.8i	2.45461	−	1.60031i
$715$	−661.264	+	562.494i	−0.0345872	+	0.0294211i
$716$	−10824.4	+	24548.8i	−0.564983	+	1.28133i
$717$	−20387.4	−	20387.4i	−1.06190	−	1.06190i
$718$	−969.761	+	4602.97i	−0.0504055	+	0.239250i
$719$	27447.1			1.42365			0.711826	−	0.702356i	$-0.247869\pi$
$719$	27447.1			1.42365			0.711826	+	0.702356i	$0.247869\pi$
$720$	−27515.1	+	21340.5i	−1.42420	+	1.10460i
$721$	−3223.15			−0.166486
$722$	−3494.42	+	16586.2i	−0.180123	+	0.854953i
$723$	9117.19	+	9117.19i	0.468979	+	0.468979i
$724$	10141.0	−	22998.9i	0.520564	−	1.18059i
$725$	−4887.35	−	794.087i	−0.250361	−	0.0406781i
$726$	24905.7	−	16237.6i	1.27319	−	0.830072i
$727$	14500.4	+	14500.4i	0.739740	+	0.739740i	0.972528	−	0.232787i	$-0.0747846\pi$
$727$	14500.4	+	14500.4i	0.739740	+	0.739740i	−0.232787	+	0.972528i	$0.574785\pi$
$728$	−2168.66	+	3018.95i	−0.110407	+	0.153695i
$729$			28430.0i			1.44439i
$730$	115.467	−	62.6635i	0.00585429	−	0.00317710i
$731$	−15748.5			−0.796826
$732$	33281.0	−	12912.6i	1.68047	−	0.652000i
$733$	−22844.9	+	22844.9i	−1.15115	+	1.15115i	−0.164831	+	0.986322i	$0.552708\pi$
$733$	−22844.9	+	22844.9i	−1.15115	+	1.15115i	−0.986322	+	0.164831i	$0.947292\pi$
$734$	9857.83	−	6426.93i	0.495721	−	0.323191i
$735$	−15227.2	+	12952.8i	−0.764167	+	0.650027i
$736$	4516.96	−	17483.5i	0.226219	−	0.875610i
$737$	5273.07	−	5273.07i	0.263550	−	0.263550i
$738$	41118.2	+	8662.86i	2.05093	+	0.432093i
$739$			16174.1i			0.805109i	0.915396	+	0.402554i	$0.131878\pi$
$739$			16174.1i			0.805109i	−0.915396	+	0.402554i	$0.868122\pi$
$740$	1386.07	+	4652.07i	0.0688555	+	0.231099i
$741$		−	1795.57i		−	0.0890174i
$742$	8795.15	−	41746.1i	0.435148	−	2.06543i
$743$	25013.9	−	25013.9i	1.23509	−	1.23509i	0.273106	−	0.961984i	$-0.411949\pi$
$743$	25013.9	−	25013.9i	1.23509	−	1.23509i	0.961984	−	0.273106i	$-0.0880510\pi$
$744$	5335.60	+	32552.5i	0.262920	+	1.60408i
$745$	−4617.32	−	372.663i	−0.227068	−	0.0183266i
$746$	14923.5	+	22890.1i	0.732422	+	1.12341i
$747$	5408.96	−	5408.96i	0.264931	−	0.264931i
$748$	8010.47	−	3107.96i	0.391566	−	0.151923i
$749$	−44872.9			−2.18908
$750$	−32459.4	+	11341.6i	−1.58033	+	0.552181i
$751$		−	23266.8i		−	1.13052i	−0.824914	−	0.565258i	$-0.808777\pi$
$751$		−	23266.8i		−	1.13052i	0.824914	−	0.565258i	$-0.191223\pi$
$752$	1372.10	−	30347.4i	0.0665365	−	1.47162i
$753$	7826.36	+	7826.36i	0.378763	+	0.378763i
$754$	−429.177	−	658.285i	−0.0207290	−	0.0317949i
$755$	−1573.56	+	19496.5i	−0.0758514	+	0.939804i
$756$	−32307.3	−	14245.4i	−1.55424	−	0.685318i
$757$	1070.85	+	1070.85i	0.0514146	+	0.0514146i	0.732347	−	0.680932i	$-0.238425\pi$
$757$	1070.85	+	1070.85i	0.0514146	+	0.0514146i	−0.680932	+	0.732347i	$0.738425\pi$
$758$	4441.07	+	935.652i	0.212806	+	0.0448343i
$759$	9606.16			0.459396
$760$	−5677.84	−	4816.16i	−0.270996	−	0.229869i
$761$	18964.3			0.903358			0.451679	−	0.892181i	$-0.350825\pi$
$761$	18964.3			0.903358			0.451679	+	0.892181i	$0.350825\pi$
$762$	−58989.5	−	12428.0i	−2.80442	−	0.590840i
$763$	−3446.50	−	3446.50i	−0.163528	−	0.163528i
$764$	−8542.05	+	19372.6i	−0.404503	+	0.917375i
$765$	34200.6	+	40205.9i	1.61637	+	1.90019i
$766$	−2371.26	−	3637.11i	−0.111850	−	0.171559i
$767$	−843.562	−	843.562i	−0.0397122	−	0.0397122i
$768$	−27364.2	+	22817.2i	−1.28571	+	1.07206i
$769$		−	2675.93i		−	0.125483i	−0.998030	−	0.0627416i	$-0.980016\pi$
$769$		−	2675.93i		−	0.125483i	0.998030	−	0.0627416i	$-0.0199844\pi$
$770$	−7206.59	+	3910.98i	−0.337282	+	0.183042i
$771$	−38440.6			−1.79559
$772$	14425.4	+	37180.1i	0.672516	+	1.73334i
$773$	17717.3	−	17717.3i	0.824384	−	0.824384i	−0.162349	−	0.986733i	$-0.551907\pi$
$773$	17717.3	−	17717.3i	0.824384	−	0.824384i	0.986733	+	0.162349i	$0.0519072\pi$
$774$	12202.6	+	18716.7i	0.566683	+	0.869196i
$775$	−3359.77	+	20678.3i	−0.155724	+	0.958433i
$776$	2510.67	+	15317.6i	0.116144	+	0.708597i
$777$	−7818.27	+	7818.27i	−0.360977	+	0.360977i
$778$	−5733.66	+	27214.8i	−0.264218	+	1.25411i
$779$			8984.82i			0.413241i
$780$	−4799.83	−	2596.20i	−0.220335	−	0.119178i
$781$		−	6949.07i		−	0.318383i
$782$	−26785.1	−	5643.13i	−1.22485	−	0.258054i
$783$	5278.18	−	5278.18i	0.240903	−	0.240903i
$784$	−9713.20	+	8872.87i	−0.442475	+	0.404194i
$785$	−19223.4	−	22598.9i	−0.874031	−	1.02750i
$786$	1212.96	−	790.800i	0.0550441	−	0.0358867i
$787$	17445.8	−	17445.8i	0.790185	−	0.790185i	−0.191339	−	0.981524i	$-0.561283\pi$
$787$	17445.8	−	17445.8i	0.790185	−	0.790185i	0.981524	+	0.191339i	$0.0612829\pi$
$788$	−15247.8	−	39299.6i	−0.689313	−	1.77664i
$789$	−28681.7			−1.29416
$790$	−1187.07	+	4004.52i	−0.0534608	+	0.180348i
$791$		−	27219.1i		−	1.22351i
$792$	−9900.55	−	7112.06i	−0.444193	−	0.319086i
$793$	2544.25	+	2544.25i	0.113933	+	0.113933i
$794$	33134.2	−	21602.3i	1.48097	−	0.965536i
$795$	62428.0	+	5038.55i	2.78502	+	0.224779i
$796$	−19785.4	−	8724.08i	−0.880999	−	0.388463i
$797$	20145.7	+	20145.7i	0.895353	+	0.895353i	0.995021	−	0.0996680i	$-0.0317781\pi$
$797$	20145.7	+	20145.7i	0.895353	+	0.895353i	−0.0996680	+	0.995021i	$0.531778\pi$
$798$	3496.17	−	16594.5i	0.155091	−	0.736140i
$799$	−46050.1			−2.03897
$800$	−21083.9	+	8214.06i	−0.931784	+	0.363014i
$801$	−40729.1			−1.79662
$802$	−4727.02	+	22436.8i	−0.208126	+	0.987867i
$803$	32.5215	+	32.5215i	0.00142921	+	0.00142921i
$804$	42890.5	+	18911.9i	1.88138	+	0.829568i
$805$	26037.0	+	2101.44i	1.13998	+	0.0920074i
$806$	−2785.19	+	1815.84i	−0.121717	+	0.0793551i
$807$	−36681.9	−	36681.9i	−1.60008	−	1.60008i
$808$	−2634.44	−	1892.45i	−0.114702	−	0.0823962i
$809$		−	25649.3i		−	1.11469i	−0.830282	−	0.557344i	$-0.811820\pi$
$809$		−	25649.3i		−	1.11469i	0.830282	−	0.557344i	$-0.188180\pi$
$810$	2923.08	−	9860.86i	0.126798	−	0.427747i
$811$	27578.5			1.19410			0.597048	−	0.802205i	$-0.296340\pi$
$811$	27578.5			1.19410			0.597048	+	0.802205i	$0.296340\pi$
$812$	−2684.67	−	6919.48i	−0.116026	−	0.299047i
$813$	−1274.24	+	1274.24i	−0.0549687	+	0.0549687i
$814$	−1423.55	+	928.098i	−0.0612964	+	0.0399629i
$815$	8635.89	+	10152.3i	0.371168	+	0.436342i
$816$	36426.5	+	39876.4i	1.56272	+	1.71073i
$817$	−3378.12	+	3378.12i	−0.144658	+	0.144658i
$818$	23426.8	+	4935.61i	1.00134	+	0.210965i
$819$		−	7994.30i		−	0.341079i
$820$	24017.8	+	12991.1i	1.02285	+	0.553254i
$821$			22360.3i			0.950526i	0.879844	+	0.475263i	$0.157647\pi$
$821$			22360.3i			0.950526i	−0.879844	+	0.475263i	$0.842353\pi$
$822$	−756.455	+	3590.51i	−0.0320978	+	0.152352i
$823$	9906.84	−	9906.84i	0.419600	−	0.419600i	−0.465466	−	0.885066i	$-0.654113\pi$
$823$	9906.84	−	9906.84i	0.419600	−	0.419600i	0.885066	+	0.465466i	$0.154113\pi$
$824$	−503.669	−	3072.89i	−0.0212939	−	0.129914i
$825$	−7036.38	−	9766.48i	−0.296940	−	0.412152i
$826$	−6153.64	−	9438.65i	−0.259216	−	0.397594i
$827$	−25335.7	+	25335.7i	−1.06531	+	1.06531i	−0.0675922	+	0.997713i	$0.521532\pi$
$827$	−25335.7	+	25335.7i	−1.06531	+	1.06531i	−0.997713	+	0.0675922i	$0.978468\pi$
$828$	14047.4	+	36205.9i	0.589592	+	1.51962i
$829$	10159.2			0.425625			0.212813	−	0.977093i	$-0.431738\pi$
$829$	10159.2			0.425625			0.212813	+	0.977093i	$0.431738\pi$
$830$	4368.87	−	2370.97i	0.182706	−	0.0991536i
$831$		−	14016.7i		−	0.585120i
$832$	−3217.10	−	1595.80i	−0.134054	−	0.0664958i
$833$	14101.5	+	14101.5i	0.586542	+	0.586542i
$834$	−12340.1	−	18927.7i	−0.512355	−	0.785867i
$835$	−2808.04	−	3301.10i	−0.116379	−	0.136814i
$836$	1051.61	−	2384.94i	0.0435054	−	0.0986663i
$837$	−22331.9	−	22331.9i	−0.922226	−	0.922226i
$838$	6797.36	+	1432.08i	0.280204	+	0.0590339i
$839$	−39775.3			−1.63671			−0.818353	−	0.574716i	$-0.805112\pi$
$839$	−39775.3			−1.63671			−0.818353	+	0.574716i	$0.805112\pi$
$840$	−39304.6	−	33339.7i	−1.61445	−	1.36944i
$841$	−22819.9			−0.935665
$842$	7703.04	+	1622.89i	0.315278	+	0.0664234i
$843$	−26974.5	−	26974.5i	−1.10208	−	1.10208i
$844$	−13146.1	−	5796.58i	−0.536146	−	0.236406i
$845$	−1931.82	+	23935.4i	−0.0786469	+	0.974439i
$846$	35681.4	+	54729.4i	1.45006	+	2.22415i
$847$	20013.5	+	20013.5i	0.811890	+	0.811890i
$848$	41174.3	+	1861.62i	1.66737	+	0.0753872i
$849$			48392.7i			1.95622i
$850$	13882.4	+	31365.6i	0.560191	+	1.26568i
$851$	5413.82			0.218077
$852$	40722.9	−	15800.0i	1.63749	−	0.635326i
$853$	−3720.58	+	3720.58i	−0.149344	+	0.149344i	−0.777825	−	0.628481i	$-0.783677\pi$
$853$	−3720.58	+	3720.58i	−0.149344	+	0.149344i	0.628481	+	0.777825i	$0.283677\pi$
$854$	18559.9	+	28467.8i	0.743684	+	1.14069i
$855$	15960.5	+	1288.17i	0.638406	+	0.0515256i
$856$	−7012.12	−	42781.0i	−0.279987	−	1.70821i
$857$	2905.23	−	2905.23i	0.115800	−	0.115800i	−0.646832	−	0.762632i	$-0.723907\pi$
$857$	2905.23	−	2905.23i	0.115800	−	0.115800i	0.762632	+	0.646832i	$0.223907\pi$
$858$	393.841	−	1869.36i	0.0156708	−	0.0743811i
$859$		−	1978.23i		−	0.0785756i	−0.999228	−	0.0392878i	$-0.987491\pi$
$859$		−	1978.23i		−	0.0785756i	0.999228	−	0.0392878i	$-0.0125089\pi$
$860$	4145.82	+	13914.6i	0.164385	+	0.551726i
$861$			62197.1i			2.46187i
$862$	24008.6	+	5058.19i	0.948652	+	0.199864i
$863$	−10391.5	+	10391.5i	−0.409886	+	0.409886i	−0.881699	−	0.471813i	$-0.843600\pi$
$863$	−10391.5	+	10391.5i	−0.409886	+	0.409886i	0.471813	+	0.881699i	$0.343600\pi$
$864$	8532.77	−	33027.2i	0.335985	−	1.30047i
$865$	9196.05	−	7822.49i	0.361474	−	0.307483i
$866$	8699.25	−	5671.58i	0.341354	−	0.222550i
$867$	27673.5	−	27673.5i	1.08401	−	1.08401i
$868$	−29276.2	+	11358.8i	−1.14481	+	0.444173i
$869$	−1462.22			−0.0570798
$870$	9576.60	−	5197.17i	0.373192	−	0.202530i
$871$			4724.65i			0.183799i
$872$	2747.26	−	3824.41i	0.106690	−	0.148521i
$873$	−23605.0	−	23605.0i	−0.915130	−	0.915130i
$874$	−6955.97	+	4535.03i	−0.269210	+	0.175514i
$875$	−16935.2	−	28010.8i	−0.654302	−	1.08221i
$876$	−116.639	+	264.526i	−0.00449869	+	0.0102026i
$877$	−18807.7	−	18807.7i	−0.724163	−	0.724163i	0.245287	−	0.969450i	$-0.421118\pi$
$877$	−18807.7	−	18807.7i	−0.724163	−	0.724163i	−0.969450	+	0.245287i	$0.921118\pi$
$878$	196.684	−	933.562i	0.00756011	−	0.0358840i
$879$	78252.4			3.00272
$880$	−4854.80	−	6259.47i	−0.185972	−	0.239780i
$881$	−2797.46			−0.106979			−0.0534896	−	0.998568i	$-0.517034\pi$
$881$	−2797.46			−0.106979			−0.0534896	+	0.998568i	$0.517034\pi$
$882$	5832.88	−	27685.7i	0.222679	−	1.05695i
$883$	−24319.6	−	24319.6i	−0.926861	−	0.926861i	0.0706407	−	0.997502i	$-0.477496\pi$
$883$	−24319.6	−	24319.6i	−0.926861	−	0.926861i	−0.997502	+	0.0706407i	$0.977496\pi$
$884$	−2196.31	+	4981.03i	−0.0835633	+	0.189514i
$885$	12599.5	−	10717.6i	0.478561	−	0.407081i
$886$	−13279.2	+	8657.54i	−0.503526	+	0.328280i
$887$	−8358.09	−	8358.09i	−0.316389	−	0.316389i	0.530989	−	0.847379i	$-0.321820\pi$
$887$	−8358.09	−	8358.09i	−0.316389	−	0.316389i	−0.847379	+	0.530989i	$0.821820\pi$
$888$	−8675.52	−	6232.06i	−0.327851	−	0.235511i
$889$		−	57389.0i		−	2.16509i
$890$	−25375.3	−	7522.04i	−0.955708	−	0.283303i
$891$	3600.61			0.135382
$892$	−37831.1	+	14678.0i	−1.42004	+	0.550959i
$893$	−9877.92	+	9877.92i	−0.370159	+	0.370159i
$894$	8539.22	−	5567.25i	0.319457	−	0.208274i
$895$	3016.41	−	37373.5i	0.112657	−	1.39582i
$896$	−26625.0	−	21012.3i	−0.992723	−	0.783452i
$897$	−4303.54	+	4303.54i	−0.160191	+	0.160191i
$898$	−13978.4	−	2945.00i	−0.519450	−	0.109439i
$899$		−	6638.71i		−	0.246289i
$900$	26520.6	−	40802.2i	0.982244	−	1.51119i
$901$		−	62479.2i		−	2.31019i
$902$	−1970.73	+	9354.08i	−0.0727475	+	0.345296i
$903$	−23384.9	+	23384.9i	−0.861794	+	0.861794i
$904$	25950.2	−	4253.42i	0.954745	−	0.156490i
$905$	−2825.98	+	35014.0i	−0.103800	+	1.28608i
$906$	−23507.6	−	36056.7i	−0.862017	−	1.32219i
$907$	−8805.22	+	8805.22i	−0.322351	+	0.322351i	−0.849669	−	0.527317i	$-0.823198\pi$
$907$	−8805.22	+	8805.22i	−0.322351	+	0.322351i	0.527317	+	0.849669i	$0.323198\pi$
$908$	−22319.3	+	8659.61i	−0.815741	+	0.316497i
$909$	6976.09			0.254546
$910$	1476.42	−	4980.65i	0.0537835	−	0.181436i
$911$			50985.2i			1.85424i	0.374762	+	0.927121i	$0.377724\pi$
$911$			50985.2i			1.85424i	−0.374762	+	0.927121i	$0.622276\pi$
$912$	16367.2	+	740.014i	0.594269	+	0.0268688i
$913$	1230.50	+	1230.50i	0.0446041	+	0.0446041i
$914$	−24509.8	−	37593.9i	−0.886993	−	1.36050i
$915$	−38001.0	+	32325.0i	−1.37298	+	1.16790i
$916$	11324.7	+	4993.46i	0.408492	+	0.180119i
$917$	974.694	+	974.694i	0.0351006	+	0.0351006i
$918$	−50598.5	−	10660.2i	−1.81917	−	0.383266i
$919$	−42995.3			−1.54329			−0.771645	−	0.636054i	$-0.780566\pi$
$919$	−42995.3			−1.54329			−0.771645	+	0.636054i	$0.780566\pi$
$920$	2065.22	+	25151.5i	0.0740091	+	0.901327i
$921$	67924.2			2.43016
$922$	20164.0	+	4248.19i	0.720246	+	0.151743i
$923$	3113.17	+	3113.17i	0.111020	+	0.111020i
$924$	7279.70	−	16509.7i	0.259182	−	0.587801i
$925$	−3965.55	−	5504.17i	−0.140958	−	0.195650i
$926$	−19552.2	−	29989.7i	−0.693870	−	1.06428i
$927$	4735.43	+	4735.43i	0.167780	+	0.167780i
$928$	6177.37	−	3640.79i	0.218515	−	0.128788i
$929$			42375.8i			1.49656i	0.663383	+	0.748280i	$0.269120\pi$
$929$			42375.8i			1.49656i	−0.663383	+	0.748280i	$0.730880\pi$
$930$	−21989.2	−	40518.4i	−0.775326	−	1.42866i
$931$	6049.66			0.212964
$932$	7447.46	+	19195.1i	0.261749	+	0.674632i
$933$	38872.7	−	38872.7i	1.36403	−	1.36403i
$934$	6863.58	+	10527.6i	0.240453	+	0.368815i
$935$	−9146.54	+	7780.37i	−0.319919	+	0.272134i
$936$	7621.61	−	1249.24i	0.266154	−	0.0436246i
$937$	8563.59	−	8563.59i	0.298570	−	0.298570i	−0.541884	−	0.840454i	$-0.682289\pi$
$937$	8563.59	−	8563.59i	0.298570	−	0.298570i	0.840454	+	0.541884i	$0.182289\pi$
$938$	−9199.40	+	43664.9i	−0.320225	+	1.51995i
$939$			67957.2i			2.36177i
$940$	12122.8	+	40687.6i	0.420639	+	1.41179i
$941$		−	33594.2i		−	1.16380i	−0.813259	−	0.581902i	$-0.802309\pi$
$941$		−	33594.2i		−	1.16380i	0.813259	−	0.581902i	$-0.197691\pi$
$942$	63886.1	+	13459.6i	2.20968	+	0.465540i
$943$	21534.4	−	21534.4i	0.743645	−	0.743645i
$944$	8037.03	−	7341.70i	0.277101	−	0.253127i
$945$	49185.2	+	3969.73i	1.69312	+	0.136651i
$946$	−4257.91	+	2775.99i	−0.146339	+	0.0954072i
$947$	11378.3	−	11378.3i	0.390437	−	0.390437i	−0.484406	−	0.874843i	$-0.660964\pi$
$947$	11378.3	−	11378.3i	0.390437	−	0.390437i	0.874843	+	0.484406i	$0.160964\pi$
$948$	−3324.62	−	8568.88i	−0.113901	−	0.293570i
$949$	−29.1391			−0.000996728
$950$	9705.87	+	3750.22i	0.331474	+	0.128077i
$951$			50726.0i			1.72966i
$952$	−29996.8	+	41757.9i	−1.02122	+	1.42162i
$953$	956.027	+	956.027i	0.0324961	+	0.0324961i	0.723168	−	0.690672i	$-0.242685\pi$
$953$	956.027	+	956.027i	0.0324961	+	0.0324961i	−0.690672	+	0.723168i	$0.742685\pi$
$954$	−74254.9	+	48411.3i	−2.52001	+	1.64295i
$955$	2380.39	−	29493.2i	0.0806571	−	0.999347i
$956$	24263.0	+	10698.4i	0.820838	+	0.361936i
$957$	2697.26	+	2697.26i	0.0911076	+	0.0911076i
$958$	−881.345	+	4183.30i	−0.0297234	+	0.141082i
$959$	−3493.09			−0.117620
$960$	25643.4	−	42682.1i	0.862123	−	1.43496i
$961$	1702.72			0.0571554
$962$	221.960	−	1053.53i	0.00743896	−	0.0353090i
$963$	65927.0	+	65927.0i	2.20609	+	2.20609i
$964$	−10850.3	−	4784.29i	−0.362516	−	0.159846i
$965$	−36112.1	−	42453.1i	−1.20465	−	1.41618i
$966$	−48152.4	+	31393.5i	−1.60381	+	1.04562i
$967$	29318.1	+	29318.1i	0.974981	+	0.974981i	0.999695	−	0.0247134i	$-0.00786732\pi$
$967$	29318.1	+	29318.1i	0.974981	+	0.974981i	−0.0247134	+	0.999695i	$0.507867\pi$
$968$	−15953.0	+	22207.9i	−0.529700	+	0.737385i
$969$		−	24836.2i		−	0.823377i
$970$	−10347.0	−	19066.0i	−0.342498	−	0.631105i
$971$	3662.16			0.121034			0.0605171	−	0.998167i	$-0.480725\pi$
$971$	3662.16			0.121034			0.0605171	+	0.998167i	$0.480725\pi$
$972$	−6536.47	−	16847.1i	−0.215697	−	0.555938i
$973$	15209.7	−	15209.7i	0.501132	−	0.501132i
$974$	13986.7	−	9118.77i	0.460125	−	0.299984i
$975$	7527.64	+	1223.08i	0.247259	+	0.0401742i
$976$	−24240.3	+	22143.2i	−0.794994	+	0.726215i
$977$	25024.4	−	25024.4i	0.819449	−	0.819449i	−0.166579	−	0.986028i	$-0.553272\pi$
$977$	25024.4	−	25024.4i	0.819449	−	0.819449i	0.986028	+	0.166579i	$0.0532721\pi$
$978$	−28700.1	−	6046.58i	−0.938371	−	0.197698i
$979$		−	9265.56i		−	0.302481i
$980$	8747.16	−	16171.7i	0.285120	−	0.527127i
$981$			10127.2i			0.329598i
$982$	−4572.42	+	21702.9i	−0.148586	+	0.705264i
$983$	6252.93	−	6252.93i	0.202886	−	0.202886i	−0.598349	−	0.801236i	$-0.704176\pi$
$983$	6252.93	−	6252.93i	0.202886	−	0.202886i	0.801236	+	0.598349i	$0.204176\pi$
$984$	−59297.5	+	9719.30i	−1.92107	+	0.314878i
$985$	38170.8	+	44873.2i	1.23474	+	1.45155i
$986$	−5936.33	−	9105.34i	−0.191736	−	0.294090i
$987$	−68379.5	+	68379.5i	−2.20521	+	2.20521i
$988$	597.332	+	1539.57i	0.0192345	+	0.0495750i
$989$	16193.0			0.520635
$990$	16333.9	+	4841.88i	0.524368	+	0.155440i
$991$			4516.98i			0.144790i	0.997376	+	0.0723948i	$0.0230642\pi$
$991$			4516.98i			0.144790i	−0.997376	+	0.0723948i	$0.976936\pi$
$992$	−15404.1	−	26136.4i	−0.493026	−	0.836523i
$993$	−10805.8	−	10805.8i	−0.345330	−	0.345330i
$994$	22710.0	+	34833.3i	0.724666	+	1.11152i
$995$	30121.7	+	2431.12i	0.959720	+	0.0774589i
$996$	−4413.19	+	10008.7i	−0.140399	+	0.318412i
$997$	10276.7	+	10276.7i	0.326447	+	0.326447i	0.851234	−	0.524787i	$-0.175855\pi$
$997$	10276.7	+	10276.7i	0.326447	+	0.326447i	−0.524787	+	0.851234i	$0.675855\pi$
$998$	31324.4	+	6599.48i	0.993543	+	0.209321i
$999$	10227.0			0.323891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.k.a.3.8	yes	32
4.3	odd	2		160.4.o.a.143.2		32
5.2	odd	4	inner	40.4.k.a.27.1	yes	32
5.3	odd	4		200.4.k.j.107.16		32
5.4	even	2		200.4.k.j.43.9		32
8.3	odd	2	inner	40.4.k.a.3.1	✓	32
8.5	even	2		160.4.o.a.143.1		32
20.7	even	4		160.4.o.a.47.1		32
40.3	even	4		200.4.k.j.107.9		32
40.19	odd	2		200.4.k.j.43.16		32
40.27	even	4	inner	40.4.k.a.27.8	yes	32
40.37	odd	4		160.4.o.a.47.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.1	✓	32	8.3	odd	2	inner
40.4.k.a.3.8	yes	32	1.1	even	1	trivial
40.4.k.a.27.1	yes	32	5.2	odd	4	inner
40.4.k.a.27.8	yes	32	40.27	even	4	inner
160.4.o.a.47.1		32	20.7	even	4
160.4.o.a.47.2		32	40.37	odd	4
160.4.o.a.143.1		32	8.5	even	2
160.4.o.a.143.2		32	4.3	odd	2
200.4.k.j.43.9		32	5.4	even	2
200.4.k.j.43.16		32	40.19	odd	2
200.4.k.j.107.9		32	40.3	even	4
200.4.k.j.107.16		32	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.583098 + 2.76767i) q^{2} +(6.15076 + 6.15076i) q^{3} +(-7.31999 - 3.22764i) q^{4} +(11.1441 + 0.899439i) q^{5} +(-20.6098 + 13.4368i) q^{6} +(-16.5614 - 16.5614i) q^{7} +(13.2013 - 18.3773i) q^{8} +48.6638i q^{9} +(-8.98745 + 30.3187i) q^{10} -11.0706 q^{11} +(-25.1711 - 64.8760i) q^{12} +(4.95962 - 4.95962i) q^{13} +(55.4933 - 36.1795i) q^{14} +(63.0125 + 74.0770i) q^{15} +(43.1646 + 47.2527i) q^{16} +(68.6010 - 68.6010i) q^{17} +(-134.685 - 28.3757i) q^{18} -29.4303i q^{19} +(-78.6717 - 42.5531i) q^{20} -203.730i q^{21} +(6.45526 - 30.6398i) q^{22} +(-70.5372 + 70.5372i) q^{23} +(194.233 - 31.8362i) q^{24} +(123.382 + 20.0469i) q^{25} +(10.8346 + 16.6185i) q^{26} +(-133.249 + 133.249i) q^{27} +(67.7750 + 174.683i) q^{28} -39.6115 q^{29} +(-241.763 + 131.204i) q^{30} +167.596i q^{31} +(-155.949 + 91.9125i) q^{32} +(-68.0928 - 68.0928i) q^{33} +(149.864 + 229.866i) q^{34} +(-169.666 - 199.458i) q^{35} +(157.069 - 356.218i) q^{36} +(-38.3756 - 38.3756i) q^{37} +(81.4534 + 17.1608i) q^{38} +61.0109 q^{39} +(163.646 - 192.925i) q^{40} -305.291 q^{41} +(563.858 + 118.795i) q^{42} +(-114.783 - 114.783i) q^{43} +(81.0369 + 35.7320i) q^{44} +(-43.7701 + 542.314i) q^{45} +(-154.094 - 236.354i) q^{46} +(-335.637 - 335.637i) q^{47} +(-25.1446 + 556.135i) q^{48} +205.559i q^{49} +(-127.427 + 329.791i) q^{50} +843.897 q^{51} +(-52.3123 + 20.2965i) q^{52} +(455.381 - 455.381i) q^{53} +(-291.091 - 446.485i) q^{54} +(-123.372 - 9.95735i) q^{55} +(-522.986 + 85.7212i) q^{56} +(181.019 - 181.019i) q^{57} +(23.0974 - 109.632i) q^{58} -170.086i q^{59} +(-222.157 - 745.625i) q^{60} +512.994i q^{61} +(-463.849 - 97.7246i) q^{62} +(805.939 - 805.939i) q^{63} +(-163.450 - 485.209i) q^{64} +(59.7314 - 50.8096i) q^{65} +(228.163 - 148.754i) q^{66} +(-476.312 + 476.312i) q^{67} +(-723.578 + 280.739i) q^{68} -867.716 q^{69} +(650.965 - 353.276i) q^{70} +627.703i q^{71} +(894.308 + 642.426i) q^{72} +(-2.93764 - 2.93764i) q^{73} +(128.588 - 83.8342i) q^{74} +(635.590 + 882.197i) q^{75} +(-94.9906 + 215.430i) q^{76} +(183.345 + 183.345i) q^{77} +(-35.5753 + 168.858i) q^{78} +132.081 q^{79} +(438.530 + 565.413i) q^{80} -325.240 q^{81} +(178.015 - 844.946i) q^{82} +(-111.150 - 111.150i) q^{83} +(-657.569 + 1491.30i) q^{84} +(826.199 - 702.794i) q^{85} +(384.613 - 250.753i) q^{86} +(-243.641 - 243.641i) q^{87} +(-146.147 + 203.448i) q^{88} +836.950i q^{89} +(-1475.42 - 437.363i) q^{90} -164.276 q^{91} +(744.001 - 288.663i) q^{92} +(-1030.84 + 1030.84i) q^{93} +(1124.64 - 733.224i) q^{94} +(26.4708 - 327.975i) q^{95} +(-1524.54 - 393.873i) q^{96} +(-485.063 + 485.063i) q^{97} +(-568.919 - 119.861i) q^{98} -538.738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 44 q^{8} + 70 q^{10} - 8 q^{11} + 28 q^{12} + 72 q^{16} + 48 q^{17} - 278 q^{18} - 320 q^{20} + 68 q^{22} + 40 q^{25} - 92 q^{26} + 104 q^{27} + 620 q^{28} - 740 q^{30}+ \cdots - 3814 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 44 * q^8 + 70 * q^10 - 8 * q^11 + 28 * q^12 + 72 * q^16 + 48 * q^17 - 278 * q^18 - 320 * q^20 + 68 * q^22 + 40 * q^25 - 92 * q^26 + 104 * q^27 + 620 * q^28 - 740 * q^30 + 288 * q^32 - 112 * q^33 - 460 * q^35 + 476 * q^36 + 636 * q^38 + 540 * q^40 - 8 * q^41 + 1020 * q^42 - 868 * q^43 + 1328 * q^46 - 784 * q^48 + 790 * q^50 + 1480 * q^51 - 1900 * q^52 - 2392 * q^56 + 104 * q^57 - 700 * q^58 - 1100 * q^60 - 2880 * q^62 + 520 * q^65 - 4360 * q^66 - 1852 * q^67 + 1196 * q^68 - 1500 * q^70 + 5596 * q^72 - 744 * q^73 + 3300 * q^75 + 4312 * q^76 + 2240 * q^78 + 1120 * q^80 - 1240 * q^81 + 5828 * q^82 + 2676 * q^83 + 6976 * q^86 - 2864 * q^88 + 4070 * q^90 - 1704 * q^91 - 7500 * q^92 - 10656 * q^96 - 584 * q^97 - 3814 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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