LMFDB - Embedded newform 230.4.l.a.33.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.3
Character	$\chi$	$=$	230.33
Dual form			230.4.l.a.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99490 - 0.142678i) q^{2} +(-1.69513 - 7.79240i) q^{3} +(3.95929 + 0.569259i) q^{4} +(-4.22141 + 10.3528i) q^{5} +(2.26982 + 15.7870i) q^{6} +(-6.18513 - 11.3272i) q^{7} +(-7.81717 - 1.70052i) q^{8} +(-33.2880 + 15.2021i) q^{9} +(9.89842 - 20.0505i) q^{10} +(47.3150 + 40.9987i) q^{11} +(-2.27562 - 31.8173i) q^{12} +(2.28569 + 1.24808i) q^{13} +(10.7226 + 23.4792i) q^{14} +(87.8287 + 15.3456i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-25.7244 + 34.3638i) q^{17} +(68.5753 - 25.5773i) q^{18} +(-12.4909 + 86.8764i) q^{19} +(-22.6072 + 38.5865i) q^{20} +(-77.7817 + 67.3982i) q^{21} +(-88.5393 - 88.5393i) q^{22} +(104.287 - 35.9343i) q^{23} +63.7972i q^{24} +(-89.3594 - 87.4065i) q^{25} +(-4.38165 - 2.81592i) q^{26} +(45.8547 + 61.2547i) q^{27} +(-18.0406 - 48.3687i) q^{28} +(166.667 - 23.9631i) q^{29} +(-173.020 - 43.1443i) q^{30} +(67.0723 - 43.1048i) q^{31} +(-29.9824 - 11.1829i) q^{32} +(239.273 - 438.196i) q^{33} +(56.2207 - 64.8822i) q^{34} +(143.378 - 16.2164i) q^{35} +(-140.451 + 41.2400i) q^{36} +(-25.8666 + 69.3509i) q^{37} +(37.3136 - 171.528i) q^{38} +(5.85099 - 19.9266i) q^{39} +(50.6046 - 73.7508i) q^{40} +(67.9144 - 148.712i) q^{41} +(164.783 - 123.355i) q^{42} +(118.510 - 25.7803i) q^{43} +(163.995 + 189.260i) q^{44} +(-16.8617 - 408.797i) q^{45} +(-213.169 + 56.8061i) q^{46} +(70.0685 - 70.0685i) q^{47} +(9.10248 - 127.269i) q^{48} +(95.3896 - 148.429i) q^{49} +(165.792 + 187.117i) q^{50} +(311.383 + 142.204i) q^{51} +(8.33921 + 6.24265i) q^{52} +(121.568 - 66.3809i) q^{53} +(-82.7360 - 128.740i) q^{54} +(-624.186 + 316.769i) q^{55} +(29.0881 + 99.0649i) q^{56} +(698.150 - 49.9326i) q^{57} +(-335.904 + 24.0243i) q^{58} +(69.1230 + 235.411i) q^{59} +(339.003 + 110.755i) q^{60} +(356.042 + 554.011i) q^{61} +(-139.953 + 76.4201i) q^{62} +(378.088 + 283.033i) q^{63} +(58.2164 + 26.5866i) q^{64} +(-22.5699 + 18.3945i) q^{65} +(-539.848 + 840.020i) q^{66} +(-41.7134 + 583.229i) q^{67} +(-121.412 + 121.412i) q^{68} +(-456.795 - 751.731i) q^{69} +(-288.339 + 11.8932i) q^{70} +(-64.6606 - 74.6223i) q^{71} +(286.069 - 62.2306i) q^{72} +(721.886 - 540.397i) q^{73} +(61.4962 - 134.658i) q^{74} +(-529.630 + 844.490i) q^{75} +(-98.9104 + 336.858i) q^{76} +(171.752 - 789.531i) q^{77} +(-14.5153 + 38.9169i) q^{78} +(-86.1370 + 25.2921i) q^{79} +(-111.474 + 139.906i) q^{80} +(-247.453 + 285.576i) q^{81} +(-156.701 + 286.976i) q^{82} +(1207.85 + 450.503i) q^{83} +(-346.327 + 222.571i) q^{84} +(-247.167 - 411.383i) q^{85} +(-240.095 + 34.5204i) q^{86} +(-469.253 - 1258.12i) q^{87} +(-300.151 - 400.954i) q^{88} +(-293.818 - 188.825i) q^{89} +(-24.6890 + 817.916i) q^{90} -33.6100i q^{91} +(433.357 - 82.9081i) q^{92} +(-449.586 - 449.586i) q^{93} +(-149.777 + 129.783i) q^{94} +(-846.682 - 496.057i) q^{95} +(-36.3171 + 252.591i) q^{96} +(-772.785 + 288.234i) q^{97} +(-211.471 + 282.492i) q^{98} +(-2198.29 - 645.476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−1.99490	−	0.142678i	−0.705305	−	0.0504444i
$2$	−1.99490	−	0.142678i	−0.705305	−	0.0504444i
$3$	−1.69513	−	7.79240i	−0.326228	−	1.49965i	−0.789676	−	0.613524i	$-0.789751\pi$
$3$	−1.69513	−	7.79240i	−0.326228	−	1.49965i	0.463448	−	0.886124i	$-0.346612\pi$
$4$	3.95929	+	0.569259i	0.494911	+	0.0711574i
$5$	−4.22141	+	10.3528i	−0.377574	+	0.925979i
$5$	−4.22141	+	10.3528i	−0.377574	+	0.925979i
$6$	2.26982	+	15.7870i	0.154442	+	1.07417i
$7$	−6.18513	−	11.3272i	−0.333966	−	0.611613i	0.655697	−	0.755024i	$-0.272375\pi$
$7$	−6.18513	−	11.3272i	−0.333966	−	0.611613i	−0.989663	+	0.143411i	$0.954193\pi$
$8$	−7.81717	−	1.70052i	−0.345474	−	0.0751532i
$9$	−33.2880	+	15.2021i	−1.23289	+	0.563041i
$10$	9.89842	−	20.0505i	0.313016	−	0.634051i
$11$	47.3150	+	40.9987i	1.29691	+	1.12378i	0.984792	+	0.173737i	$0.0555842\pi$
$11$	47.3150	+	40.9987i	1.29691	+	1.12378i	0.312119	+	0.950043i	$0.398961\pi$
$12$	−2.27562	−	31.8173i	−0.0547429	−	0.765406i
$13$	2.28569	+	1.24808i	0.0487643	+	0.0266273i	0.503446	−	0.864027i	$-0.332065\pi$
$13$	2.28569	+	1.24808i	0.0487643	+	0.0266273i	−0.454682	+	0.890654i	$0.650247\pi$
$14$	10.7226	+	23.4792i	0.204695	+	0.448220i
$15$	87.8287	+	15.3456i	1.51182	+	0.264148i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	−25.7244	+	34.3638i	−0.367005	+	0.490262i	−0.945590	−	0.325361i	$-0.894514\pi$
$17$	−25.7244	+	34.3638i	−0.367005	+	0.490262i	0.578585	+	0.815622i	$0.303605\pi$
$18$	68.5753	−	25.5773i	0.897964	−	0.334923i
$19$	−12.4909	+	86.8764i	−0.150822	+	1.04899i	0.764024	+	0.645188i	$0.223221\pi$
$19$	−12.4909	+	86.8764i	−0.150822	+	1.04899i	−0.914846	+	0.403803i	$0.867688\pi$
$20$	−22.6072	+	38.5865i	−0.252756	+	0.431410i
$21$	−77.7817	+	67.3982i	−0.808255	+	0.700357i
$22$	−88.5393	−	88.5393i	−0.858030	−	0.858030i
$23$	104.287	−	35.9343i	0.945447	−	0.325775i
$23$	104.287	−	35.9343i	0.945447	−	0.325775i
$24$			63.7972i			0.542606i
$25$	−89.3594	−	87.4065i	−0.714875	−	0.699252i
$26$	−4.38165	−	2.81592i	−0.0330505	−	0.0212403i
$27$	45.8547	+	61.2547i	0.326842	+	0.436610i
$28$	−18.0406	−	48.3687i	−0.121762	−	0.326458i
$29$	166.667	−	23.9631i	1.06722	−	0.153443i	0.413745	−	0.910393i	$-0.364220\pi$
$29$	166.667	−	23.9631i	1.06722	−	0.153443i	0.653473	+	0.756950i	$0.273311\pi$
$30$	−173.020	−	43.1443i	−1.05297	−	0.262568i
$31$	67.0723	−	43.1048i	0.388598	−	0.249737i	−0.331724	−	0.943376i	$-0.607630\pi$
$31$	67.0723	−	43.1048i	0.388598	−	0.249737i	0.720322	+	0.693640i	$0.243994\pi$
$32$	−29.9824	−	11.1829i	−0.165631	−	0.0617771i
$33$	239.273	−	438.196i	1.26219	−	2.31152i
$34$	56.2207	−	64.8822i	0.283582	−	0.327271i
$35$	143.378	−	16.2164i	0.692438	−	0.0783162i
$36$	−140.451	+	41.2400i	−0.650234	+	0.190926i
$37$	−25.8666	+	69.3509i	−0.114931	+	0.308141i	−0.981661	−	0.190637i	$-0.938945\pi$
$37$	−25.8666	+	69.3509i	−0.114931	+	0.308141i	0.866730	+	0.498778i	$0.166218\pi$
$38$	37.3136	−	171.528i	0.159291	−	0.732250i
$39$	5.85099	−	19.9266i	0.0240233	−	0.0818158i
$40$	50.6046	−	73.7508i	0.200032	−	0.291525i
$41$	67.9144	−	148.712i	0.258694	−	0.566461i	−0.735067	−	0.677995i	$-0.762849\pi$
$41$	67.9144	−	148.712i	0.258694	−	0.566461i	0.993761	+	0.111534i	$0.0355764\pi$
$42$	164.783	−	123.355i	0.605395	−	0.453193i
$43$	118.510	−	25.7803i	0.420294	−	0.0914293i	0.00255544	−	0.999997i	$-0.499187\pi$
$43$	118.510	−	25.7803i	0.420294	−	0.0914293i	0.417738	+	0.908567i	$0.362823\pi$
$44$	163.995	+	189.260i	0.561890	+	0.648456i
$45$	−16.8617	−	408.797i	−0.0558576	−	1.35422i
$46$	−213.169	+	56.8061i	−0.683262	+	0.182078i
$47$	70.0685	−	70.0685i	0.217458	−	0.217458i	−0.589968	−	0.807427i	$-0.700860\pi$
$47$	70.0685	−	70.0685i	0.217458	−	0.217458i	0.807427	+	0.589968i	$0.200860\pi$
$48$	9.10248	−	127.269i	0.0273714	−	0.382703i
$49$	95.3896	−	148.429i	0.278104	−	0.432738i
$50$	165.792	+	187.117i	0.468932	+	0.529247i
$51$	311.383	+	142.204i	0.854948	+	0.390442i
$52$	8.33921	+	6.24265i	0.0222392	+	0.0166481i
$53$	121.568	−	66.3809i	0.315068	−	0.172040i	−0.313932	−	0.949445i	$-0.601646\pi$
$53$	121.568	−	66.3809i	0.315068	−	0.172040i	0.629000	+	0.777405i	$0.283465\pi$
$54$	−82.7360	−	128.740i	−0.208499	−	0.324431i
$55$	−624.186	+	316.769i	−1.53028	+	0.776602i
$56$	29.0881	+	99.0649i	0.0694117	+	0.236395i
$57$	698.150	−	49.9326i	1.62232	−	0.116031i
$58$	−335.904	+	24.0243i	−0.760455	+	0.0543888i
$59$	69.1230	+	235.411i	0.152526	+	0.519456i	0.999934	−	0.0114860i	$-0.00365620\pi$
$59$	69.1230	+	235.411i	0.152526	+	0.519456i	−0.847408	+	0.530942i	$0.821838\pi$
$60$	339.003	+	110.755i	0.729419	+	0.238307i
$61$	356.042	+	554.011i	0.747319	+	1.16285i	0.981650	+	0.190694i	$0.0610738\pi$
$61$	356.042	+	554.011i	0.747319	+	1.16285i	−0.234331	+	0.972157i	$0.575290\pi$
$62$	−139.953	+	76.4201i	−0.286678	+	0.156538i
$63$	378.088	+	283.033i	0.756105	+	0.566013i
$64$	58.2164	+	26.5866i	0.113704	+	0.0519269i
$65$	−22.5699	+	18.3945i	−0.0430685	+	0.0351009i
$66$	−539.848	+	840.020i	−1.00683	+	1.56666i
$67$	−41.7134	+	583.229i	−0.0760612	+	1.06347i	0.805869	+	0.592094i	$0.201699\pi$
$67$	−41.7134	+	583.229i	−0.0760612	+	1.06347i	−0.881930	+	0.471380i	$0.843756\pi$
$68$	−121.412	+	121.412i	−0.216521	+	0.216521i
$69$	−456.795	−	751.731i	−0.796980	−	1.31156i
$70$	−288.339	+	11.8932i	−0.492331	+	0.0203072i
$71$	−64.6606	−	74.6223i	−0.108082	−	0.124733i	0.699131	−	0.714994i	$-0.253570\pi$
$71$	−64.6606	−	74.6223i	−0.108082	−	0.124733i	−0.807213	+	0.590261i	$0.799025\pi$
$72$	286.069	−	62.2306i	0.468244	−	0.101860i
$73$	721.886	−	540.397i	1.15740	−	0.866420i	0.164620	−	0.986357i	$-0.447360\pi$
$73$	721.886	−	540.397i	1.15740	−	0.866420i	0.992781	+	0.119937i	$0.0382693\pi$
$74$	61.4962	−	134.658i	0.0966052	−	0.211536i
$75$	−529.630	+	844.490i	−0.815419	+	1.30018i
$76$	−98.9104	+	336.858i	−0.149287	+	0.508424i
$77$	171.752	−	789.531i	0.254194	−	1.16851i
$78$	−14.5153	+	38.9169i	−0.0210709	+	0.0564933i
$79$	−86.1370	+	25.2921i	−0.122673	+	0.0360200i	−0.342493	−	0.939520i	$-0.611271\pi$
$79$	−86.1370	+	25.2921i	−0.122673	+	0.0360200i	0.219820	+	0.975540i	$0.429453\pi$
$80$	−111.474	+	139.906i	−0.155790	+	0.195524i
$81$	−247.453	+	285.576i	−0.339442	+	0.391737i
$82$	−156.701	+	286.976i	−0.211033	+	0.386478i
$83$	1207.85	+	450.503i	1.59733	+	0.595773i	0.981391	−	0.192022i	$-0.0615044\pi$
$83$	1207.85	+	450.503i	1.59733	+	0.595773i	0.615938	+	0.787794i	$0.288777\pi$
$84$	−346.327	+	222.571i	−0.449850	+	0.289101i
$85$	−247.167	−	411.383i	−0.315400	−	0.524950i
$86$	−240.095	+	34.5204i	−0.301047	+	0.0432841i
$87$	−469.253	−	1258.12i	−0.578267	−	1.55039i
$88$	−300.151	−	400.954i	−0.363593	−	0.485703i
$89$	−293.818	−	188.825i	−0.349940	−	0.224892i	0.353848	−	0.935303i	$-0.384873\pi$
$89$	−293.818	−	188.825i	−0.349940	−	0.224892i	−0.703788	+	0.710410i	$0.748509\pi$
$90$	−24.6890	+	817.916i	−0.0289161	+	0.957955i
$91$		−	33.6100i		−	0.0387175i
$92$	433.357	−	82.9081i	0.491093	−	0.0939540i
$93$	−449.586	−	449.586i	−0.501289	−	0.501289i
$94$	−149.777	+	129.783i	−0.164344	+	0.142405i
$95$	−846.682	−	496.057i	−0.914397	−	0.535730i
$96$	−36.3171	+	252.591i	−0.0386104	+	0.268542i
$97$	−772.785	+	288.234i	−0.808911	+	0.301708i	−0.719683	−	0.694303i	$-0.755713\pi$
$97$	−772.785	+	288.234i	−0.808911	+	0.301708i	−0.0892284	+	0.996011i	$0.528440\pi$
$98$	−211.471	+	282.492i	−0.217977	+	0.291184i
$99$	−2198.29	−	645.476i	−2.23168	−	0.655280i
$100$	−304.043	−	396.936i	−0.304043	−	0.396936i
$101$	−340.545	−	745.689i	−0.335500	−	0.734642i	0.664419	−	0.747360i	$-0.268679\pi$
$101$	−340.545	−	745.689i	−0.335500	−	0.734642i	−0.999919	+	0.0127180i	$0.995952\pi$
$102$	−600.890	−	328.111i	−0.583303	−	0.318508i
$103$	93.9507	+	1313.60i	0.0898761	+	1.25663i	0.819619	+	0.572910i	$0.194185\pi$
$103$	93.9507	+	1313.60i	0.0898761	+	1.25663i	−0.729743	+	0.683722i	$0.760360\pi$
$104$	−15.7452	−	13.6433i	−0.0148456	−	0.0128638i
$105$	−369.409	−	1089.77i	−0.343340	−	1.01286i
$106$	−251.987	+	115.079i	−0.230897	+	0.105447i
$107$	−1501.93	−	326.726i	−1.35698	−	0.295194i	−0.525525	−	0.850778i	$-0.676131\pi$
$107$	−1501.93	−	326.726i	−1.35698	−	0.295194i	−0.831460	+	0.555584i	$0.812495\pi$
$108$	146.682	+	268.628i	0.130690	+	0.239340i
$109$	235.086	+	1635.06i	0.206579	+	1.43679i	0.784212	+	0.620493i	$0.213068\pi$
$109$	235.086	+	1635.06i	0.206579	+	1.43679i	−0.577633	+	0.816297i	$0.696023\pi$
$110$	1290.39	−	542.866i	1.11849	−	0.470548i
$111$	584.257	+	84.0035i	0.499597	+	0.0718312i
$112$	−43.8935	−	201.775i	−0.0370317	−	0.170232i
$113$	1095.72	+	78.3676i	0.912185	+	0.0652407i	0.519537	−	0.854448i	$-0.326105\pi$
$113$	1095.72	+	78.3676i	0.912185	+	0.0652407i	0.392648	+	0.919689i	$0.371559\pi$
$114$	−1399.87			−1.15008
$115$	−68.2173	+	1231.35i	−0.0553156	+	0.998469i
$116$	673.524			0.539096
$117$	−95.0593	−	6.79878i	−0.0751131	−	0.00537220i
$118$	−104.306	−	479.485i	−0.0813738	−	0.374069i
$119$	548.356	+	78.8417i	0.422418	+	0.0607345i
$120$	−660.477	−	269.314i	−0.502442	−	0.204874i
$121$	368.397	+	2562.26i	0.276782	+	1.92506i
$122$	−631.223	−	1156.00i	−0.468428	−	0.857863i
$123$	−1273.95	−	277.130i	−0.933885	−	0.203154i
$124$	290.096	−	132.483i	0.210092	−	0.0959458i
$125$	1282.12	−	556.138i	0.917411	−	0.397940i
$126$	−713.867	−	618.569i	−0.504733	−	0.437354i
$127$	148.702	+	2079.12i	0.103899	+	1.45270i	0.735564	+	0.677455i	$0.236917\pi$
$127$	148.702	+	2079.12i	0.103899	+	1.45270i	−0.631665	+	0.775241i	$0.717628\pi$
$128$	−112.343	−	61.3439i	−0.0775766	−	0.0423600i
$129$	−401.781	−	879.777i	−0.274223	−	0.600466i
$130$	47.6493	−	33.4751i	0.0321471	−	0.0225843i
$131$	1847.97	+	542.614i	1.23251	+	0.361896i	0.832195	−	0.554483i	$-0.187084\pi$
$131$	1847.97	+	542.614i	1.23251	+	0.361896i	0.400311	+	0.916379i	$0.368902\pi$
$132$	1196.80	−	1598.73i	0.789151	−	1.05418i
$133$	1061.33	−	395.855i	0.691945	−	0.258082i
$134$	166.428	−	1157.53i	0.107293	−	0.746237i
$135$	−827.727	+	216.142i	−0.527699	+	0.137796i
$136$	259.529	−	224.883i	0.163635	−	0.141791i
$137$	1900.47	+	1900.47i	1.18517	+	1.18517i	0.978388	+	0.206779i	$0.0662982\pi$
$137$	1900.47	+	1900.47i	1.18517	+	1.18517i	0.206779	+	0.978388i	$0.433702\pi$
$138$	804.006	+	1564.81i	0.495953	+	0.965254i
$139$		−	3221.90i		−	1.96603i	−0.183521	−	0.983016i	$-0.558749\pi$
$139$		−	3221.90i		−	1.96603i	0.183521	−	0.983016i	$-0.441251\pi$
$140$	576.906	+	17.4141i	0.348268	+	0.0105125i
$141$	−664.778	−	427.227i	−0.397052	−	0.255170i
$142$	118.345	+	158.090i	0.0699385	+	0.0934270i
$143$	56.9777	+	152.763i	0.0333197	+	0.0893335i
$144$	−579.560	+	83.3281i	−0.335394	+	0.0482223i
$145$	−455.486	+	1826.62i	−0.260869	+	1.04616i
$146$	−1517.20	+	975.042i	−0.860027	+	0.552706i
$147$	−1318.32	−	491.707i	−0.739680	−	0.275886i
$148$	−141.892	+	259.855i	−0.0788069	+	0.144324i
$149$	−1978.21	+	2282.98i	−1.08766	+	1.25523i	−0.122810	+	0.992430i	$0.539190\pi$
$149$	−1978.21	+	2282.98i	−1.08766	+	1.25523i	−0.964851	+	0.262797i	$0.915355\pi$
$150$	1177.05	−	1609.11i	0.640706	−	0.875888i
$151$	1073.15	−	315.104i	0.578353	−	0.169820i	0.0205439	−	0.999789i	$-0.493460\pi$
$151$	1073.15	−	315.104i	0.578353	−	0.169820i	0.557809	+	0.829969i	$0.311642\pi$
$152$	245.379	−	657.887i	0.130940	−	0.351064i
$153$	333.912	−	1534.97i	0.176439	−	0.811077i
$154$	−455.278	+	1550.53i	−0.238229	+	0.811335i
$155$	163.114	+	876.347i	0.0845265	+	0.454128i
$156$	34.5092	−	75.5646i	0.0177112	−	0.0387821i
$157$	179.385	−	134.286i	0.0911880	−	0.0682624i	−0.552711	−	0.833373i	$-0.686407\pi$
$157$	179.385	−	134.286i	0.0911880	−	0.0682624i	0.643899	+	0.765111i	$0.277316\pi$
$158$	175.444	−	38.1654i	0.0883389	−	0.0192169i
$159$	−723.340	−	834.779i	−0.360784	−	0.416366i
$160$	242.341	−	263.193i	0.119742	−	0.130045i
$161$	−1052.06	−	959.021i	−0.514995	−	0.469450i
$162$	534.391	−	534.391i	0.259171	−	0.259171i
$163$	−201.295	+	2814.48i	−0.0967280	+	1.35243i	0.684876	+	0.728659i	$0.259856\pi$
$163$	−201.295	+	2814.48i	−0.0967280	+	1.35243i	−0.781604	+	0.623775i	$0.785598\pi$
$164$	353.548	−	550.132i	0.168338	−	0.261940i
$165$	3526.47	+	4326.94i	1.66385	+	2.04153i
$166$	−2345.26	−	1071.04i	−1.09655	−	0.500778i
$167$	1967.03	+	1472.50i	0.911458	+	0.682309i	0.948423	−	0.317008i	$-0.102678\pi$
$167$	1967.03	+	1472.50i	0.911458	+	0.682309i	−0.0369651	+	0.999317i	$0.511769\pi$
$168$	722.645	−	394.594i	0.331865	−	0.181212i
$169$	−1184.12	−	1842.53i	−0.538972	−	0.838657i
$170$	434.379	+	855.934i	0.195973	+	0.386160i
$171$	−904.906	−	3081.83i	−0.404678	−	1.37821i
$172$	483.891	−	34.6086i	0.214514	−	0.0153423i
$173$	−2981.47	+	213.239i	−1.31027	+	0.0937126i	−0.708930	−	0.705279i	$-0.750822\pi$
$173$	−2981.47	+	213.239i	−1.31027	+	0.0937126i	−0.601343	+	0.798991i	$0.705367\pi$
$174$	756.609	+	2576.78i	0.329646	+	1.12267i
$175$	−437.373	+	1552.82i	−0.188927	+	0.670753i
$176$	541.564	+	842.691i	0.231943	+	0.360910i
$177$	1717.25	−	937.687i	0.729244	−	0.398197i
$178$	559.197	+	418.610i	0.235470	+	0.176270i
$179$	862.538	+	393.908i	0.360163	+	0.164481i	0.587274	−	0.809388i	$-0.300201\pi$
$179$	862.538	+	393.908i	0.360163	+	0.164481i	−0.227112	+	0.973869i	$0.572928\pi$
$180$	165.951	−	1628.14i	0.0687182	−	0.674192i
$181$	763.280	−	1187.69i	0.313448	−	0.487735i	−0.648407	−	0.761294i	$-0.724564\pi$
$181$	763.280	−	1187.69i	0.313448	−	0.487735i	0.961855	+	0.273559i	$0.0882008\pi$
$182$	−4.79542	+	67.0488i	−0.00195308	+	0.0273076i
$183$	3713.54	−	3713.54i	1.50007	−	1.50007i
$184$	−876.335	+	103.563i	−0.351110	+	0.0414933i
$185$	−608.780	−	560.549i	−0.241937	−	0.222770i
$186$	832.735	+	961.028i	0.328275	+	0.378849i
$187$	−2626.02	+	571.257i	−1.02692	+	0.223393i
$188$	317.309	−	237.534i	0.123096	−	0.0921487i
$189$	410.229	−	898.275i	0.157882	−	0.345714i
$190$	1618.27	+	1110.39i	0.617904	+	0.423979i
$191$	289.472	−	985.851i	0.109662	−	0.373475i	−0.886315	−	0.463083i	$-0.846743\pi$
$191$	289.472	−	985.851i	0.109662	−	0.373475i	0.995977	+	0.0896080i	$0.0285614\pi$
$192$	108.489	−	498.714i	0.0407786	−	0.187456i
$193$	1086.01	−	2911.72i	0.405042	−	1.08596i	−0.561055	−	0.827779i	$-0.689604\pi$
$193$	1086.01	−	2911.72i	0.405042	−	1.08596i	0.966097	−	0.258180i	$-0.0831229\pi$
$194$	1582.76	−	464.739i	0.585749	−	0.171991i
$195$	181.596	+	144.692i	0.0666892	+	0.0531366i
$196$	462.169	−	533.372i	0.168429	−	0.194377i
$197$	1802.89	−	3301.75i	0.652034	−	1.19411i	−0.317291	−	0.948328i	$-0.602773\pi$
$197$	1802.89	−	3301.75i	0.652034	−	1.19411i	0.969325	−	0.245782i	$-0.0790449\pi$
$198$	4293.28	+	1601.31i	1.54096	+	0.574748i
$199$	−1476.77	+	949.059i	−0.526056	+	0.338076i	−0.776563	−	0.630039i	$-0.783039\pi$
$199$	−1476.77	+	949.059i	−0.526056	+	0.338076i	0.250508	+	0.968115i	$0.419402\pi$
$200$	549.902	+	835.230i	0.194420	+	0.295298i
$201$	4615.46	−	663.604i	1.61965	−	0.232871i
$202$	572.961	+	1536.17i	0.199571	+	0.535071i
$203$	−1302.29	−	1739.66i	−0.450262	−	0.601480i
$204$	1151.90	+	740.283i	0.395340	+	0.254070i
$205$	1252.88	+	1330.88i	0.426855	+	0.453426i
$206$		−	2633.92i		−	0.890843i
$207$	−2925.22	+	2781.56i	−0.982206	+	0.933970i
$208$	29.4636	+	29.4636i	0.00982180	+	0.00982180i
$209$	−4152.83	+	3598.45i	−1.37444	+	1.19096i
$210$	581.450	+	2226.69i	0.191066	+	0.731698i
$211$	−39.2217	+	272.793i	−0.0127968	+	0.0890039i	−0.995219	−	0.0976690i	$-0.968861\pi$
$211$	−39.2217	+	272.793i	−0.0127968	+	0.0890039i	0.982422	+	0.186673i	$0.0597705\pi$
$212$	519.109	−	193.618i	0.168172	−	0.0627250i
$213$	−471.879	+	630.356i	−0.151796	+	0.202776i
$214$	2949.60	+	866.080i	0.942197	+	0.276654i
$215$	−233.382	+	1335.74i	−0.0740304	+	0.423705i
$216$	−254.289	−	556.816i	−0.0801027	−	0.175400i
$217$	−903.109	−	493.135i	−0.282521	−	0.154268i
$218$	−235.686	−	3295.32i	−0.0732233	−	1.02380i
$219$	−5434.68	−	4709.18i	−1.67690	−	1.45304i
$220$	−2651.66	+	898.856i	−0.812612	+	0.275458i
$221$	−101.687	+	46.4388i	−0.0309511	+	0.0141349i
$222$	−1153.55	−	250.940i	−0.348745	−	0.0758648i
$223$	−2216.11	−	4058.51i	−0.665479	−	1.21873i	−0.964398	−	0.264456i	$-0.914808\pi$
$223$	−2216.11	−	4058.51i	−0.665479	−	1.21873i	0.298919	−	0.954279i	$-0.403374\pi$
$224$	58.7744	+	408.785i	0.0175314	+	0.121933i
$225$	4303.36	+	1551.13i	1.27507	+	0.459595i
$226$	−2174.68	−	312.672i	−0.640078	−	0.0920293i
$227$	−917.370	−	4217.08i	−0.268229	−	1.23303i	−0.892221	−	0.451598i	$-0.850854\pi$
$227$	−917.370	−	4217.08i	−0.268229	−	1.23303i	0.623993	−	0.781430i	$-0.285510\pi$
$228$	2792.60	+	199.731i	0.811159	+	0.0580153i
$229$	4338.72			1.25201			0.626006	−	0.779818i	$-0.284688\pi$
$229$	4338.72			1.25201			0.626006	+	0.779818i	$0.284688\pi$
$230$	311.774	−	2446.69i	0.0893816	−	0.701435i
$231$	−6443.48			−1.83528
$232$	−1343.62	−	96.0973i	−0.380227	−	0.0271944i
$233$	3.17067	+	14.5753i	0.000891491	+	0.00409812i	0.977590	−	0.210516i	$-0.0675143\pi$
$233$	3.17067	+	14.5753i	0.000891491	+	0.00409812i	−0.976699	+	0.214614i	$0.931151\pi$
$234$	188.664	+	27.1258i	0.0527067	+	0.00757808i
$235$	429.615	+	1021.19i	0.119255	+	0.283469i
$236$	139.668	+	971.409i	0.0385237	+	0.267938i
$237$	343.100	+	628.340i	0.0940368	+	0.172216i
$238$	−1082.67	−	235.520i	−0.294870	−	0.0641450i
$239$	4334.12	−	1979.32i	1.17302	−	0.535698i	0.268976	−	0.963147i	$-0.413315\pi$
$239$	4334.12	−	1979.32i	1.17302	−	0.535698i	0.904040	+	0.427449i	$0.140588\pi$
$240$	1279.16	+	631.491i	0.344040	+	0.169844i
$241$	−4932.27	−	4273.83i	−1.31832	−	1.14233i	−0.979492	−	0.201483i	$-0.935424\pi$
$241$	−4932.27	−	4273.83i	−1.31832	−	1.14233i	−0.338828	−	0.940848i	$-0.610031\pi$
$242$	−369.338	−	5164.02i	−0.0981073	−	1.37172i
$243$	4458.03	+	2434.27i	1.17688	+	0.642627i
$244$	1094.29	+	2396.17i	0.287111	+	0.628685i
$245$	1133.97	+	1614.13i	0.295702	+	0.420909i
$246$	2501.86	+	734.613i	0.648426	+	0.190395i
$247$	−136.979	+	182.983i	−0.0352865	+	0.0471373i
$248$	−597.617	+	222.900i	−0.153019	+	0.0570731i
$249$	1463.04	−	10175.7i	0.372356	−	2.58979i
$250$	−2637.06	+	926.512i	−0.667129	+	0.234391i
$251$	4415.97	−	3826.46i	1.11049	−	0.962247i	0.110990	−	0.993821i	$-0.464598\pi$
$251$	4415.97	−	3826.46i	1.11049	−	0.962247i	0.999501	+	0.0315748i	$0.0100522\pi$
$252$	1335.84	+	1335.84i	0.333929	+	0.333929i
$253$	6407.59	+	2575.39i	1.59226	+	0.639973i
$254$		−	4168.87i		−	1.02984i
$255$	−2786.68	+	2623.37i	−0.684347	+	0.644243i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	−1286.82	−	1719.00i	−0.312334	−	0.417230i	0.616715	−	0.787187i	$-0.288463\pi$
$257$	−1286.82	−	1719.00i	−0.312334	−	0.417230i	−0.929049	+	0.369957i	$0.879372\pi$
$258$	675.989	+	1812.40i	0.163121	+	0.437345i
$259$	945.542	−	135.948i	0.226846	−	0.0326155i
$260$	−99.8319	+	59.9810i	−0.0238127	+	0.0143072i
$261$	−5183.72	+	3331.38i	−1.22937	+	0.790065i
$262$	−3609.11	−	1346.13i	−0.851037	−	0.317421i
$263$	−1561.63	+	2859.91i	−0.366137	+	0.670530i	−0.994190	−	0.107640i	$-0.965670\pi$
$263$	−1561.63	+	2859.91i	−0.366137	+	0.670530i	0.628053	+	0.778171i	$0.283852\pi$
$264$	−2615.60	+	3018.57i	−0.609770	+	0.703712i
$265$	174.040	+	1538.78i	0.0403440	+	0.356704i
$266$	−2173.73	+	638.263i	−0.501051	+	0.147122i
$267$	−973.341	+	2609.63i	−0.223099	+	0.598153i
$268$	−497.164	+	2285.42i	−0.113318	+	0.520912i
$269$	−444.208	+	1512.83i	−0.100683	+	0.342896i	−0.994393	−	0.105750i	$-0.966276\pi$
$269$	−444.208	+	1512.83i	−0.100683	+	0.342896i	0.893709	+	0.448646i	$0.148094\pi$
$270$	1682.07	−	313.083i	0.379140	−	0.0705690i
$271$	−3168.67	+	6938.41i	−0.710269	+	1.55527i	0.116791	+	0.993157i	$0.462739\pi$
$271$	−3168.67	+	6938.41i	−0.710269	+	1.55527i	−0.827059	+	0.562115i	$0.809988\pi$
$272$	−549.821	+	411.591i	−0.122565	+	0.0917513i
$273$	−261.903	+	56.9735i	−0.0580626	+	0.0126307i
$274$	−3520.09	−	4062.41i	−0.776119	−	0.895689i
$275$	−644.491	−	7799.26i	−0.141325	−	1.71023i
$276$	−1380.65	−	3236.35i	−0.301107	−	0.705817i
$277$	−2437.89	+	2437.89i	−0.528803	+	0.528803i	−0.920215	−	0.391412i	$-0.871987\pi$
$277$	−2437.89	+	2437.89i	−0.528803	+	0.528803i	0.391412	+	0.920215i	$0.371987\pi$
$278$	−459.696	+	6427.39i	−0.0991753	+	1.38665i
$279$	−1577.42	+	2454.51i	−0.338486	+	0.526694i
$280$	−1148.39	−	117.051i	−0.245105	−	0.0249827i
$281$	7251.74	+	3311.76i	1.53951	+	0.703071i	0.991098	−	0.133137i	$-0.0425051\pi$
$281$	7251.74	+	3311.76i	1.53951	+	0.703071i	0.548412	+	0.836208i	$0.315232\pi$
$282$	1265.21	+	947.126i	0.267171	+	0.200002i
$283$	−7296.42	+	3984.15i	−1.53261	+	0.836866i	−0.999955	−	0.00946988i	$-0.996986\pi$
$283$	−7296.42	+	3984.15i	−1.53261	+	0.836866i	−0.532650	+	0.846336i	$0.678804\pi$
$284$	−213.530	−	332.260i	−0.0446151	−	0.0694225i
$285$	−2430.23	+	7438.56i	−0.505104	+	1.54604i
$286$	−91.8691	−	312.877i	−0.0189942	−	0.0646882i
$287$	−2104.55	+	150.521i	−0.432850	+	0.0309580i
$288$	1168.06	−	83.5410i	0.238987	−	0.0170927i
$289$	865.027	+	2946.01i	0.176069	+	0.599636i
$290$	1169.27	−	3578.95i	0.236765	−	0.724701i
$291$	3556.01	+	5533.25i	0.716346	+	1.11466i
$292$	3165.78	−	1728.65i	0.634463	−	0.346443i
$293$	4566.34	+	3418.32i	0.910473	+	0.681571i	0.948185	−	0.317717i	$-0.102916\pi$
$293$	4566.34	+	3418.32i	0.910473	+	0.681571i	−0.0377128	+	0.999289i	$0.512007\pi$
$294$	2559.76	+	1169.00i	0.507783	+	0.231897i
$295$	−2728.95	−	278.153i	−0.538596	−	0.0548973i
$296$	320.136	−	498.142i	0.0628633	−	0.0978172i
$297$	−341.747	+	4778.25i	−0.0667683	+	0.933543i
$298$	4272.08	−	4272.08i	0.830452	−	0.830452i
$299$	283.216	+	48.0235i	0.0547786	+	0.00928853i
$300$	−2577.69	+	3042.08i	−0.496077	+	0.585449i
$301$	−1025.02	−	1182.94i	−0.196283	−	0.226523i
$302$	−2185.78	+	475.488i	−0.416482	+	0.0906001i
$303$	−5233.44	+	3917.70i	−0.992255	+	0.742793i
$304$	−583.374	+	1277.41i	−0.110062	+	0.241002i
$305$	−7238.55	+	1347.31i	−1.35894	+	0.252939i
$306$	−885.128	+	3014.47i	−0.165358	+	0.563156i
$307$	1895.19	−	8712.06i	0.352327	−	1.61962i	−0.370667	−	0.928766i	$-0.620871\pi$
$307$	1895.19	−	8712.06i	0.352327	−	1.61962i	0.722994	−	0.690855i	$-0.242766\pi$
$308$	1129.46	−	3028.21i	0.208952	−	0.560221i
$309$	10076.9	−	2958.83i	1.85519	−	0.544732i
$310$	−200.361	−	1771.50i	−0.0367088	−	0.324563i
$311$	−1986.72	+	2292.80i	−0.362240	+	0.418047i	−0.907389	−	0.420292i	$-0.861928\pi$
$311$	−1986.72	+	2292.80i	−0.362240	+	0.418047i	0.545149	+	0.838339i	$0.316473\pi$
$312$	−79.6239	+	145.820i	−0.0144481	+	0.0264598i
$313$	−9541.82	−	3558.92i	−1.72312	−	0.642690i	−0.724217	−	0.689572i	$-0.757799\pi$
$313$	−9541.82	−	3558.92i	−1.72312	−	0.642690i	−0.998900	+	0.0468825i	$0.985071\pi$
$314$	−377.016	+	242.294i	−0.0677588	+	0.0435459i
$315$	−4526.24	+	2719.46i	−0.809603	+	0.486426i
$316$	−355.439	+	51.1044i	−0.0632753	+	0.00909761i
$317$	−2529.98	−	6783.14i	−0.448258	−	1.20183i	−0.943002	−	0.332788i	$-0.892011\pi$
$317$	−2529.98	−	6783.14i	−0.448258	−	1.20183i	0.494744	−	0.869039i	$-0.335262\pi$
$318$	1323.89	+	1768.51i	0.233459	+	0.311865i
$319$	8868.32	+	5699.32i	1.55652	+	1.00032i
$320$	−521.000	+	490.468i	−0.0910149	+	0.0856813i
$321$			12257.5i			2.13130i
$322$	1961.94	+	2063.26i	0.339548	+	0.357084i
$323$	−2664.08	−	2664.08i	−0.458927	−	0.458927i
$324$	−1142.31	+	989.813i	−0.195869	+	0.169721i
$325$	−95.1574	−	311.311i	−0.0162412	−	0.0531337i
$326$	803.130	−	5585.89i	0.136445	−	0.948999i
$327$	12342.5	−	4603.52i	2.08729	−	0.778518i
$328$	−783.787	+	1047.02i	−0.131943	+	0.176256i
$329$	−1227.07	−	360.299i	−0.205624	−	0.0603767i
$330$	−6417.61	−	9134.99i	−1.07054	−	1.52383i
$331$	−1457.85	−	3192.25i	−0.242087	−	0.530096i	0.749118	−	0.662437i	$-0.230478\pi$
$331$	−1457.85	−	3192.25i	−0.242087	−	0.530096i	−0.991204	+	0.132341i	$0.957751\pi$
$332$	4525.75	+	2471.25i	0.748142	+	0.408516i
$333$	−193.235	−	2701.78i	−0.0317994	−	0.444614i
$334$	−3713.95	−	3218.15i	−0.608437	−	0.527214i
$335$	−5861.94	−	2893.90i	−0.956036	−	0.471972i
$336$	−1497.91	+	684.072i	−0.243207	+	0.111069i
$337$	−2299.24	−	500.168i	−0.371654	−	0.0808484i	0.0228592	−	0.999739i	$-0.492723\pi$
$337$	−2299.24	−	500.168i	−0.371654	−	0.0808484i	−0.394513	+	0.918890i	$0.629087\pi$
$338$	2099.32	+	3844.62i	0.337834	+	0.618697i
$339$	−1246.72	−	8671.15i	−0.199742	−	1.38924i
$340$	−744.422	−	1769.48i	−0.118741	−	0.282246i
$341$	4940.77	+	710.376i	0.784627	+	0.112812i
$342$	1365.49	+	6277.06i	0.215899	+	0.992470i
$343$	−6686.73	−	478.244i	−1.05262	−	0.0752850i
$344$	−970.254			−0.152072
$345$	9710.81	−	1555.72i	1.51540	−	0.242775i
$346$	5978.18			0.928869
$347$	3305.89	+	236.442i	0.511440	+	0.0365789i	0.324675	−	0.945826i	$-0.394745\pi$
$347$	3305.89	+	236.442i	0.511440	+	0.0365789i	0.186765	+	0.982405i	$0.440200\pi$
$348$	−1141.71	−	5248.37i	−0.175869	−	0.808455i
$349$	1411.35	+	202.921i	0.216469	+	0.0311235i	0.249696	−	0.968324i	$-0.419669\pi$
$349$	1411.35	+	202.921i	0.216469	+	0.0311235i	−0.0332271	+	0.999448i	$0.510578\pi$
$350$	1094.07	−	3035.31i	0.167087	−	0.463555i
$351$	28.3587	+	197.239i	0.00431247	+	0.0299939i
$352$	−960.135	−	1758.36i	−0.145385	−	0.266252i
$353$	−4888.14	−	1063.35i	−0.737024	−	0.160330i	−0.171642	−	0.985159i	$-0.554907\pi$
$353$	−4888.14	−	1063.35i	−0.737024	−	0.160330i	−0.565381	+	0.824830i	$0.691271\pi$
$354$	−3559.53	+	1625.58i	−0.534426	+	0.244064i
$355$	1045.51	−	354.405i	0.156309	−	0.0529855i
$356$	−1055.82	−	914.871i	−0.157186	−	0.136203i
$357$	−315.170	−	4406.66i	−0.0467243	−	0.653291i
$358$	−1664.48	−	908.875i	−0.245728	−	0.134177i
$359$	1244.00	+	2723.99i	0.182886	+	0.400464i	0.978763	−	0.204994i	$-0.0657174\pi$
$359$	1244.00	+	2723.99i	0.182886	+	0.400464i	−0.795878	+	0.605458i	$0.792990\pi$
$360$	−563.357	+	3224.31i	−0.0824765	+	0.472045i
$361$	−810.325	−	237.933i	−0.118140	−	0.0346891i
$362$	−1692.13	+	2260.42i	−0.245680	+	0.328190i
$363$	19341.7	−	7214.07i	2.79662	−	1.04309i
$364$	19.1328	−	133.072i	0.00275503	−	0.0191617i
$365$	2547.23	+	9754.75i	0.365282	+	1.39887i
$366$	−7938.00	+	6878.32i	−1.13368	+	0.982337i
$367$	−4396.12	−	4396.12i	−0.625274	−	0.625274i	0.321601	−	0.946875i	$-0.395779\pi$
$367$	−4396.12	−	4396.12i	−0.625274	−	0.625274i	−0.946875	+	0.321601i	$0.895779\pi$
$368$	1762.98	−	81.5644i	0.249733	−	0.0115539i
$369$			5982.76i			0.844038i
$370$	1134.48	+	1205.10i	0.159402	+	0.169325i
$371$	−1503.82	−	966.449i	−0.210444	−	0.135244i
$372$	−1524.11	−	2035.97i	−0.212423	−	0.283764i
$373$	−3312.52	−	8881.20i	−0.459827	−	1.23284i	−0.935533	−	0.353240i	$-0.885080\pi$
$373$	−3312.52	−	8881.20i	−0.459827	−	1.23284i	0.475706	−	0.879605i	$-0.342193\pi$
$374$	5320.17	−	764.925i	0.735561	−	0.105758i
$375$	−6507.02	−	9048.07i	−0.896056	−	1.24597i
$376$	−666.891	+	428.585i	−0.0914689	+	0.0587835i
$377$	410.857	+	153.242i	0.0561279	+	0.0209346i
$378$	−946.531	+	1733.44i	−0.128794	+	0.235869i
$379$	−5940.33	+	6855.51i	−0.805104	+	0.929139i	−0.998650	−	0.0519520i	$-0.983456\pi$
$379$	−5940.33	+	6855.51i	−0.805104	+	0.929139i	0.193546	+	0.981091i	$0.438001\pi$
$380$	−3069.87	−	2446.01i	−0.414424	−	0.330205i
$381$	15949.3	−	4683.14i	2.14464	−	0.629723i
$382$	−718.129	+	1925.38i	−0.0961850	+	0.257882i
$383$	−2609.96	+	11997.8i	−0.348206	+	1.60068i	0.386500	+	0.922289i	$0.373684\pi$
$383$	−2609.96	+	11997.8i	−0.348206	+	1.60068i	−0.734705	+	0.678386i	$0.762680\pi$
$384$	−287.580	+	979.407i	−0.0382174	+	0.130157i
$385$	7448.79	+	5111.04i	0.986040	+	0.676578i
$386$	−2581.93	+	5653.65i	−0.340459	+	0.745500i
$387$	−3553.05	+	2659.78i	−0.466696	+	0.349365i
$388$	−3223.76	+	701.285i	−0.421808	+	0.0917586i
$389$	6759.36	+	7800.72i	0.881011	+	1.01674i	0.999716	+	0.0238113i	$0.00758010\pi$
$389$	6759.36	+	7800.72i	0.881011	+	1.01674i	−0.118706	+	0.992930i	$0.537874\pi$
$390$	−341.623	−	314.557i	−0.0443558	−	0.0408416i
$391$	−1447.88	+	4508.08i	−0.187269	+	0.583078i
$392$	−998.084	+	998.084i	−0.128599	+	0.128599i
$393$	1095.71	−	15320.0i	0.140639	−	1.96639i
$394$	−4067.68	+	6329.44i	−0.520119	+	0.809321i
$395$	101.776	−	998.524i	0.0129644	−	0.127193i
$396$	−8336.21	−	3807.02i	−1.05785	−	0.483106i
$397$	9.72471	+	7.27983i	0.00122939	+	0.000920313i	0.599892	−	0.800081i	$-0.295210\pi$
$397$	9.72471	+	7.27983i	0.00122939	+	0.000920313i	−0.598663	+	0.801001i	$0.704301\pi$
$398$	3081.42	−	1682.58i	0.388084	−	0.211910i
$399$	−4883.75	−	7599.26i	−0.612765	−	0.953481i
$400$	−977.832	−	1744.66i	−0.122229	−	0.218083i
$401$	−2317.18	−	7891.60i	−0.288565	−	0.982762i	−0.968401	−	0.249398i	$-0.919767\pi$
$401$	−2317.18	−	7891.60i	−0.288565	−	0.982762i	0.679836	−	0.733364i	$-0.262051\pi$
$402$	−9302.09	+	665.299i	−1.15409	+	0.0825425i
$403$	207.105	−	14.8124i	0.0255995	−	0.00183091i
$404$	−923.824	−	3146.25i	−0.113767	−	0.387456i
$405$	−1911.90	−	3767.36i	−0.234576	−	0.462226i
$406$	2349.74	+	3656.27i	0.287231	+	0.446940i
$407$	−4067.18	+	2220.85i	−0.495338	+	0.270475i
$408$	−2192.31	−	1641.15i	−0.266019	−	0.199139i
$409$	−4395.57	−	2007.39i	−0.531411	−	0.242687i	0.131592	−	0.991304i	$-0.457991\pi$
$409$	−4395.57	−	2007.39i	−0.531411	−	0.242687i	−0.663003	+	0.748617i	$0.730718\pi$
$410$	−2309.50	−	2833.73i	−0.278190	−	0.341336i
$411$	11587.7	−	18030.7i	1.39070	−	2.16397i
$412$	−375.803	+	5254.41i	−0.0449380	+	0.628316i
$413$	2239.02	−	2239.02i	0.266768	−	0.266768i
$414$	6232.39	−	5131.58i	0.739868	−	0.609187i
$415$	−9762.76	+	10602.8i	−1.15478	+	1.25415i
$416$	−54.5733	−	62.9809i	−0.00643191	−	0.00742282i
$417$	−25106.4	+	5461.56i	−2.94836	+	0.641376i
$418$	8797.92	−	6586.04i	1.02947	−	0.770655i
$419$	565.801	−	1238.93i	0.0659695	−	0.144453i	−0.873775	−	0.486330i	$-0.838335\pi$
$419$	565.801	−	1238.93i	0.0659695	−	0.144453i	0.939745	+	0.341877i	$0.111063\pi$
$420$	−842.235	−	4525.00i	−0.0978497	−	0.525708i
$421$	−2875.62	+	9793.47i	−0.332896	+	1.13374i	0.607687	+	0.794177i	$0.292097\pi$
$421$	−2875.62	+	9793.47i	−0.332896	+	1.13374i	−0.940583	+	0.339563i	$0.889721\pi$
$422$	117.165	−	538.599i	0.0135154	−	0.0621294i
$423$	−1267.25	+	3397.63i	−0.145664	+	0.390540i
$424$	−1063.20	+	312.183i	−0.121777	+	0.0357569i
$425$	5302.34	−	822.248i	0.605179	−	0.0938468i
$426$	1031.29	−	1190.17i	0.117292	−	0.135362i
$427$	4073.25	−	7459.60i	0.461635	−	0.845422i
$428$	−5760.59	−	2148.59i	−0.650581	−	0.242654i
$429$	1093.81	−	702.947i	0.123099	−	0.0791110i
$430$	656.156	−	2631.37i	0.0735876	−	0.295107i
$431$	4563.45	−	656.126i	0.510009	−	0.0733282i	0.117494	−	0.993074i	$-0.462514\pi$
$431$	4563.45	−	656.126i	0.510009	−	0.0733282i	0.392515	+	0.919745i	$0.371605\pi$
$432$	427.837	+	1147.08i	0.0476489	+	0.127752i
$433$	−4627.16	−	6181.16i	−0.513550	−	0.686022i	0.466557	−	0.884491i	$-0.345494\pi$
$433$	−4627.16	−	6181.16i	−0.513550	−	0.686022i	−0.980107	+	0.198469i	$0.936403\pi$
$434$	1731.26	+	1112.61i	0.191481	+	0.123058i
$435$	15005.9	+	452.957i	1.65397	+	0.0499256i
$436$			6607.48i			0.725782i
$437$	1819.21	+	9508.91i	0.199141	+	1.04090i
$438$	10169.8	+	10169.8i	1.10943	+	1.10943i
$439$	−8616.85	+	7466.54i	−0.936810	+	0.811751i	−0.982319	−	0.187213i	$-0.940054\pi$
$439$	−8616.85	+	7466.54i	−0.936810	+	0.811751i	0.0455091	+	0.998964i	$0.485509\pi$
$440$	5418.05	−	1414.80i	0.587034	−	0.153290i
$441$	−918.891	+	6391.03i	−0.0992216	+	0.690101i
$442$	209.481	−	78.1324i	0.0225430	−	0.00840810i
$443$	−4680.20	+	6252.02i	−0.501949	+	0.670525i	−0.977931	−	0.208930i	$-0.933002\pi$
$443$	−4680.20	+	6252.02i	−0.501949	+	0.670525i	0.475982	+	0.879455i	$0.342093\pi$
$444$	2265.42	+	665.188i	0.242145	+	0.0711000i
$445$	3195.19	−	2244.72i	0.340374	−	0.239123i
$446$	3841.87	+	8412.53i	0.407888	+	0.893149i
$447$	21143.2	+	11545.1i	2.23723	+	1.22162i
$448$	−58.9245	−	823.872i	−0.00621411	−	0.0868846i
$449$	−9385.22	−	8132.34i	−0.986450	−	0.854764i	0.00294755	−	0.999996i	$-0.499062\pi$
$449$	−9385.22	−	8132.34i	−0.986450	−	0.854764i	−0.989398	+	0.145232i	$0.953607\pi$
$450$	−8363.47	−	3708.36i	−0.876128	−	0.388475i
$451$	9310.37	−	4251.90i	0.972080	−	0.443934i
$452$	4293.67	+	934.030i	0.446808	+	0.0971970i
$453$	−4274.54	−	7828.24i	−0.443345	−	0.811926i
$454$	1228.38	+	8543.56i	0.126984	+	0.883192i
$455$	347.957	+	141.882i	0.0358516	+	0.0146187i
$456$	−5542.47	−	796.887i	−0.569188	−	0.0818369i
$457$	−989.537	−	4548.83i	−0.101288	−	0.465613i	−0.999652	−	0.0263625i	$-0.991608\pi$
$457$	−989.537	−	4548.83i	−0.101288	−	0.465613i	0.898364	−	0.439251i	$-0.144756\pi$
$458$	−8655.34	−	619.042i	−0.883051	−	0.0631571i
$459$	−3284.53			−0.334006
$460$	−971.049	+	4836.43i	−0.0984247	+	0.490217i
$461$	6847.61			0.691812			0.345906	−	0.938269i	$-0.387572\pi$
$461$	6847.61			0.691812			0.345906	+	0.938269i	$0.387572\pi$
$462$	12854.1	+	919.346i	1.29443	+	0.0925797i
$463$	2758.78	+	12681.9i	0.276914	+	1.27295i	0.879884	+	0.475189i	$0.157620\pi$
$463$	2758.78	+	12681.9i	0.276914	+	1.27295i	−0.602969	+	0.797764i	$0.706016\pi$
$464$	2666.68	+	383.410i	0.266804	+	0.0383607i
$465$	6552.35	−	2756.57i	0.653458	−	0.274910i
$466$	−4.24559	−	29.5288i	−0.000422046	−	0.00293539i
$467$	−1241.45	−	2273.55i	−0.123014	−	0.225284i	0.808914	−	0.587928i	$-0.200056\pi$
$467$	−1241.45	−	2273.55i	−0.123014	−	0.225284i	−0.931928	+	0.362644i	$0.881874\pi$
$468$	−372.497	−	81.0317i	−0.0367920	−	0.00800361i
$469$	6864.37	−	3134.85i	0.675836	−	0.308644i
$470$	−711.339	−	2098.48i	−0.0698120	−	0.205948i
$471$	−1350.49	−	1170.21i	−0.132118	−	0.114481i
$472$	−140.024	−	1957.80i	−0.0136550	−	0.190921i
$473$	6664.27	+	3638.97i	0.647830	+	0.353742i
$474$	−594.801	−	1302.43i	−0.0576373	−	0.126208i
$475$	8709.75	−	6671.44i	0.841327	−	0.644435i
$476$	2126.22	+	624.313i	0.204737	+	0.0601163i
$477$	−3037.61	+	4057.77i	−0.291578	+	0.389502i
$478$	−8928.55	+	3330.18i	−0.854357	+	0.318659i
$479$	−478.082	+	3325.13i	−0.0456036	+	0.317180i	0.954232	+	0.299066i	$0.0966752\pi$
$479$	−478.082	+	3325.13i	−0.0456036	+	0.317180i	−0.999836	+	0.0181136i	$0.994234\pi$
$480$	−2461.71	−	1442.27i	−0.234086	−	0.137147i
$481$	−145.678	+	126.231i	−0.0138095	+	0.0119660i
$482$	9229.61	+	9229.61i	0.872194	+	0.872194i
$483$	−5689.69	+	9823.77i	−0.536004	+	0.925460i
$484$			10354.4i			0.972430i
$485$	278.224	−	9217.21i	0.0260484	−	0.862953i
$486$	−8546.03	−	5492.20i	−0.797645	−	0.512616i
$487$	7463.05	+	9969.46i	0.694421	+	0.927638i	0.999697	−	0.0246263i	$-0.00783959\pi$
$487$	7463.05	+	9969.46i	0.694421	+	0.927638i	−0.305276	+	0.952264i	$0.598749\pi$
$488$	−1841.13	−	4936.26i	−0.170787	−	0.457898i
$489$	22272.7	−	3202.34i	2.05973	−	0.296145i
$490$	−2031.87	−	3381.82i	−0.187327	−	0.311786i
$491$	1393.23	−	895.377i	0.128057	−	0.0822970i	−0.475044	−	0.879962i	$-0.657568\pi$
$491$	1393.23	−	895.377i	0.128057	−	0.0822970i	0.603101	+	0.797665i	$0.293932\pi$
$492$	−4886.16	−	1822.44i	−0.447734	−	0.166996i
$493$	−3463.95	+	6343.76i	−0.316448	+	0.579530i
$494$	299.368	−	345.489i	0.0272656	−	0.0314661i
$495$	15962.3	−	20033.5i	1.44940	−	1.81907i
$496$	1223.99	−	359.396i	0.110804	−	0.0325350i
$497$	−445.330	+	1193.97i	−0.0401927	+	0.107761i
$498$	−4370.48	+	20090.8i	−0.393265	+	1.80781i
$499$	1609.36	−	5480.96i	0.144378	−	0.491707i	−0.855271	−	0.518180i	$-0.826610\pi$
$499$	1609.36	−	5480.96i	0.144378	−	0.491707i	0.999650	+	0.0264736i	$0.00842781\pi$
$500$	5392.87	−	1472.05i	0.482353	−	0.131664i
$501$	8139.94	−	17824.0i	0.725880	−	1.58945i
$502$	−9355.39	+	7003.36i	−0.831776	+	0.622659i
$503$	5269.37	−	1146.28i	0.467096	−	0.101611i	0.0271436	−	0.999632i	$-0.491359\pi$
$503$	5269.37	−	1146.28i	0.467096	−	0.101611i	0.439953	+	0.898021i	$0.354995\pi$
$504$	−2474.28	−	2855.47i	−0.218677	−	0.252366i
$505$	9157.52	−	377.721i	0.806939	−	0.0332839i
$506$	−12415.1	−	6051.88i	−1.09075	−	0.531697i
$507$	−12350.5	+	12350.5i	−1.08186	+	1.08186i
$508$	−594.808	+	8316.50i	−0.0519494	+	0.726348i
$509$	−1047.53	+	1629.98i	−0.0912197	+	0.141941i	−0.883864	−	0.467743i	$-0.845067\pi$
$509$	−1047.53	+	1629.98i	−0.0912197	+	0.141941i	0.792645	+	0.609684i	$0.208704\pi$
$510$	5933.45	−	4835.78i	0.515172	−	0.419867i
$511$	−10586.2	−	4834.54i	−0.916446	−	0.418527i
$512$	−409.877	−	306.830i	−0.0353793	−	0.0264846i
$513$	−5894.36	+	3218.56i	−0.507295	+	0.277004i
$514$	2321.83	+	3612.83i	0.199244	+	0.310030i
$515$	−13996.0	−	4572.60i	−1.19755	−	0.391248i
$516$	−1089.94	−	3712.01i	−0.0929886	−	0.316690i
$517$	6188.02	−	442.576i	0.526400	−	0.0376489i
$518$	−1905.66	+	136.296i	−0.161641	+	0.0115608i
$519$	6715.64	+	22871.4i	0.567984	+	1.93438i
$520$	207.713	−	105.413i	0.0175170	−	0.00888971i
$521$	−1655.27	−	2575.65i	−0.139191	−	0.216586i	0.764659	−	0.644436i	$-0.222908\pi$
$521$	−1655.27	−	2575.65i	−0.139191	−	0.216586i	−0.903850	+	0.427850i	$0.859271\pi$
$522$	10816.3	−	5906.17i	0.906932	−	0.495222i
$523$	−17728.2	−	13271.2i	−1.48222	−	1.10957i	−0.967703	−	0.252093i	$-0.918881\pi$
$523$	−17728.2	−	13271.2i	−1.48222	−	1.10957i	−0.514515	−	0.857481i	$-0.672028\pi$
$524$	7007.77	+	3200.34i	0.584229	+	0.266808i
$525$	12841.6	+	775.959i	1.06753	+	0.0645059i
$526$	3523.35	−	5482.43i	0.292063	−	0.454459i
$527$	−244.153	+	3413.71i	−0.0201812	+	0.282170i
$528$	5648.56	−	5648.56i	0.465572	−	0.465572i
$529$	9584.45	−	7494.95i	0.787741	−	0.616006i
$530$	−127.641	−	3094.55i	−0.0104611	−	0.253620i
$531$	−5879.71	−	6785.55i	−0.480523	−	0.554553i
$532$	4427.44	−	963.131i	0.360816	−	0.0784906i
$533$	340.835	−	255.146i	0.0276983	−	0.0207347i
$534$	2314.06	−	5067.09i	0.187527	−	0.410626i
$535$	9722.79	−	14169.9i	0.785706	−	1.14508i
$536$	1317.87	−	4488.27i	0.106201	−	0.361686i
$537$	1607.37	−	7388.97i	0.129168	−	0.593776i
$538$	1102.00	−	2954.58i	0.0883097	−	0.236767i
$539$	10598.8	−	3112.08i	0.846978	−	0.248695i
$540$	−3400.25	+	384.575i	−0.270969	+	0.0306472i
$541$	8829.70	−	10190.0i	0.701698	−	0.809803i	−0.287283	−	0.957846i	$-0.592752\pi$
$541$	8829.70	−	10190.0i	0.701698	−	0.809803i	0.988981	+	0.148043i	$0.0472975\pi$
$542$	7311.15	−	13389.4i	0.579411	−	1.06111i
$543$	−10548.8	−	3934.50i	−0.833687	−	0.310949i
$544$	1155.57	−	742.637i	0.0910744	−	0.0585299i
$545$	−17919.8	−	4468.46i	−1.40844	−	0.351207i
$546$	530.600	−	76.2888i	0.0415890	−	0.00597959i
$547$	4745.85	+	12724.1i	0.370965	+	0.994595i	0.979567	+	0.201119i	$0.0644579\pi$
$547$	4745.85	+	12724.1i	0.370965	+	0.994595i	−0.608602	+	0.793476i	$0.708269\pi$
$548$	6442.63	+	8606.35i	0.502218	+	0.670885i
$549$	−20274.0	−	13029.3i	−1.57609	−	1.01289i
$550$	172.911	+	15650.7i	0.0134054	+	1.21336i
$551$			14778.8i			1.14264i
$552$	2292.51	+	6653.20i	0.176768	+	0.513005i
$553$	819.258	+	819.258i	0.0629989	+	0.0629989i
$554$	5211.18	−	4515.52i	0.399643	−	0.346292i
$555$	−3336.06	+	5694.06i	−0.255149	+	0.435495i
$556$	1834.10	−	12756.4i	0.139898	−	0.973010i
$557$	5052.26	−	1884.39i	0.384328	−	0.143347i	−0.149871	−	0.988706i	$-0.547886\pi$
$557$	5052.26	−	1884.39i	0.384328	−	0.143347i	0.534199	+	0.845358i	$0.320613\pi$
$558$	3497.00	−	4671.45i	0.265305	−	0.354406i
$559$	303.053	+	88.9844i	0.0229298	+	0.00673280i
$560$	2274.22	+	397.356i	0.171613	+	0.0299846i
$561$	8902.92	+	19494.7i	0.670021	+	1.46714i
$562$	−13994.0	−	7641.30i	−1.05036	−	0.573539i
$563$	1003.26	+	14027.4i	0.0751020	+	1.05006i	0.885638	+	0.464375i	$0.153721\pi$
$563$	1003.26	+	14027.4i	0.0751020	+	1.05006i	−0.810536	+	0.585688i	$0.800824\pi$
$564$	−2388.84	−	2069.94i	−0.178348	−	0.154540i
$565$	−5436.81	+	11012.9i	−0.404829	+	0.820031i
$566$	15124.1	−	6906.95i	1.12317	−	0.512934i
$567$	4765.32	+	1036.63i	0.352954	+	0.0767803i
$568$	378.567	+	693.293i	0.0279653	+	0.0512146i
$569$	−199.558	−	1387.96i	−0.0147029	−	0.102261i	0.981149	−	0.193255i	$-0.0619045\pi$
$569$	−199.558	−	1387.96i	−0.0147029	−	0.102261i	−0.995851	+	0.0909945i	$0.970995\pi$
$570$	5909.41	−	14492.5i	0.434242	−	1.06495i
$571$	10825.0	+	1556.40i	0.793368	+	0.114069i	0.527070	−	0.849822i	$-0.323290\pi$
$571$	10825.0	+	1556.40i	0.793368	+	0.114069i	0.266298	+	0.963891i	$0.414200\pi$
$572$	138.629	+	637.268i	0.0101335	+	0.0465831i
$573$	−8172.84	−	584.533i	−0.595856	−	0.0426165i
$574$	4219.86			0.306853
$575$	−12459.9	−	5904.27i	−0.903676	−	0.428217i
$576$	−2342.08			−0.169421
$577$	18873.9	+	1349.89i	1.36175	+	0.0973944i	0.733009	−	0.680219i	$-0.238115\pi$
$577$	18873.9	+	1349.89i	1.36175	+	0.0973944i	0.628743	+	0.777613i	$0.283570\pi$
$578$	−1305.31	−	6000.43i	−0.0939340	−	0.431808i
$579$	−24530.2	−	3526.91i	−1.76069	−	0.253149i
$580$	−2843.22	+	6972.84i	−0.203549	+	0.499192i
$581$	−2367.74	−	16468.0i	−0.169071	−	1.17591i
$582$	−6304.42	−	11545.7i	−0.449015	−	0.822309i
$583$	8473.51	+	1843.30i	0.601950	+	0.130946i
$584$	−6562.06	+	2996.79i	−0.464966	+	0.212343i
$585$	471.670	−	955.426i	0.0333353	−	0.0675248i
$586$	−8621.69	−	7470.74i	−0.607780	−	0.526644i
$587$	782.674	+	10943.2i	0.0550331	+	0.769463i	0.947784	+	0.318913i	$0.103318\pi$
$587$	782.674	+	10943.2i	0.0550331	+	0.769463i	−0.892751	+	0.450550i	$0.851228\pi$
$588$	−4939.69	−	2697.27i	−0.346444	−	0.189173i
$589$	2906.99	+	6365.42i	0.203362	+	0.445302i
$590$	5404.31	+	944.252i	0.377105	+	0.0658885i
$591$	−28784.7	−	8451.94i	−2.00346	−	0.588268i
$592$	−709.715	+	948.068i	−0.0492721	+	0.0658199i
$593$	−4680.45	+	1745.72i	−0.324120	+	0.120890i	−0.506257	−	0.862383i	$-0.668971\pi$
$593$	−4680.45	+	1745.72i	−0.324120	+	0.120890i	0.182137	+	0.983273i	$0.441699\pi$
$594$	1363.51	−	9483.40i	0.0941841	−	0.655065i
$595$	−3131.06	+	5344.18i	−0.215733	+	0.368218i
$596$	−9131.91	+	7912.85i	−0.627614	+	0.543830i
$597$	9898.76	+	9898.76i	0.678609	+	0.678609i
$598$	−558.136	−	136.211i	−0.0381670	−	0.00931452i
$599$			8338.39i			0.568777i	0.958709	+	0.284388i	$0.0917905\pi$
$599$			8338.39i			0.568777i	−0.958709	+	0.284388i	$0.908209\pi$
$600$	5576.29	−	5700.88i	0.379418	−	0.387896i
$601$	−14328.2	−	9208.19i	−0.972480	−	0.624975i	−0.0450550	−	0.998985i	$-0.514346\pi$
$601$	−14328.2	−	9208.19i	−0.972480	−	0.624975i	−0.927425	+	0.374010i	$0.877983\pi$
$602$	1876.04	+	2506.09i	0.127013	+	0.169669i
$603$	−7477.76	−	20048.6i	−0.505005	−	1.35397i
$604$	4428.27	−	636.688i	0.298317	−	0.0428915i
$605$	−28081.6	−	7002.41i	−1.88707	−	0.470560i
$606$	10999.2	−	7068.75i	0.737312	−	0.473842i
$607$	3902.23	+	1455.45i	0.260933	+	0.0973231i	0.476526	−	0.879160i	$-0.341896\pi$
$607$	3902.23	+	1455.45i	0.260933	+	0.0973231i	−0.215593	+	0.976483i	$0.569168\pi$
$608$	1346.03	−	2465.08i	0.0897844	−	0.164428i
$609$	−11348.6	+	13097.0i	−0.755119	+	0.871454i
$610$	14632.4	−	1654.96i	0.971230	−	0.109848i
$611$	247.606	−	72.7036i	0.0163945	−	0.00481387i
$612$	2195.85	−	5887.29i	0.145036	−	0.388856i
$613$	3729.90	−	17146.1i	0.245757	−	1.12973i	−0.674457	−	0.738314i	$-0.735622\pi$
$613$	3729.90	−	17146.1i	0.245757	−	1.12973i	0.920215	−	0.391414i	$-0.128014\pi$
$614$	−5023.75	+	17109.3i	−0.330199	+	1.12455i
$615$	8246.91	−	12019.0i	0.540728	−	0.788053i
$616$	−2685.23	+	5879.83i	−0.175635	+	0.384586i
$617$	615.689	−	460.899i	0.0401729	−	0.0300731i	−0.579003	−	0.815326i	$-0.696558\pi$
$617$	615.689	−	460.899i	0.0401729	−	0.0300731i	0.619175	+	0.785253i	$0.287467\pi$
$618$	−20524.5	+	4464.84i	−1.33595	+	0.290618i
$619$	−9204.16	−	10622.2i	−0.597652	−	0.689727i	0.373652	−	0.927569i	$-0.378105\pi$
$619$	−9204.16	−	10622.2i	−0.597652	−	0.689727i	−0.971304	+	0.237842i	$0.923560\pi$
$620$	146.945	+	3562.56i	0.00951850	+	0.230768i
$621$	6983.18	+	4740.29i	0.451249	+	0.306315i
$622$	4290.45	−	4290.45i	0.276578	−	0.276578i
$623$	−321.564	+	4496.05i	−0.0206793	+	0.289134i
$624$	179.648	−	279.537i	0.0115251	−	0.0179334i
$625$	345.211	+	15621.2i	0.0220935	+	0.999756i
$626$	18527.2	+	8461.11i	1.18290	+	0.540214i
$627$	35080.2	+	26260.7i	2.23440	+	1.67265i
$628$	786.681	−	429.561i	0.0499873	−	0.0272951i
$629$	−1717.76	−	2672.89i	−0.108890	−	0.169436i
$630$	9417.43	−	4779.26i	0.595554	−	0.302239i
$631$	−5734.96	−	19531.5i	−0.361815	−	1.23223i	−0.916455	−	0.400138i	$-0.868962\pi$
$631$	−5734.96	−	19531.5i	−0.361815	−	1.23223i	0.554640	−	0.832090i	$-0.312856\pi$
$632$	716.357	−	51.2349i	0.0450873	−	0.00322471i
$633$	2192.20	−	156.789i	0.137649	−	0.00984487i
$634$	4079.26	+	13892.7i	0.255533	+	0.870267i
$635$	−22152.4	−	7237.36i	−1.38440	−	0.452292i
$636$	−2388.70	−	3716.90i	−0.148928	−	0.231737i
$637$	403.282	−	220.209i	0.0250842	−	0.0136970i
$638$	−16878.3	−	12634.9i	−1.04736	−	0.784046i
$639$	3286.84	+	1501.05i	0.203482	+	0.0929273i
$640$	1109.32	−	904.102i	0.0685154	−	0.0558403i
$641$	−2531.39	+	3938.92i	−0.155981	+	0.242711i	−0.910445	−	0.413630i	$-0.864261\pi$
$641$	−2531.39	+	3938.92i	−0.155981	+	0.242711i	0.754464	+	0.656342i	$0.227897\pi$
$642$	1748.88	−	24452.6i	0.107512	−	1.50322i
$643$	−9477.31	+	9477.31i	−0.581257	+	0.581257i	−0.935249	−	0.353991i	$-0.884824\pi$
$643$	−9477.31	+	9477.31i	−0.581257	+	0.581257i	0.353991	+	0.935249i	$0.384824\pi$
$644$	−3619.49	−	4395.94i	−0.221472	−	0.268982i
$645$	10804.2	−	445.642i	0.659559	−	0.0272049i
$646$	4934.48	+	5694.70i	0.300533	+	0.346834i
$647$	−8278.83	+	1800.95i	−0.503052	+	0.109432i	−0.456928	−	0.889504i	$-0.651050\pi$
$647$	−8278.83	+	1800.95i	−0.503052	+	0.109432i	−0.0461235	+	0.998936i	$0.514687\pi$
$648$	2420.02	−	1811.60i	0.146709	−	0.109825i
$649$	−6381.00	+	13972.4i	−0.385942	+	0.845095i
$650$	145.412	+	634.614i	0.00877469	+	0.0382948i
$651$	−2311.81	+	7873.32i	−0.139181	+	0.474009i
$652$	−2399.15	+	11028.7i	−0.144107	+	0.662451i
$653$	−2891.03	+	7751.16i	−0.173254	+	0.464512i	−0.994334	−	0.106301i	$-0.966099\pi$
$653$	−2891.03	+	7751.16i	−0.173254	+	0.464512i	0.821080	+	0.570813i	$0.193372\pi$
$654$	−25279.0	+	7422.58i	−1.51145	+	0.443801i
$655$	−13418.6	+	16841.1i	−0.800471	+	1.00463i
$656$	1712.97	−	1976.87i	0.101951	−	0.117658i
$657$	−15814.9	+	28962.9i	−0.939116	+	1.71986i
$658$	2396.47	+	893.838i	0.141982	+	0.0529566i
$659$	2914.32	−	1872.92i	0.172270	−	0.110711i	−0.451664	−	0.892188i	$-0.649170\pi$
$659$	2914.32	−	1872.92i	0.172270	−	0.110711i	0.623934	+	0.781477i	$0.285533\pi$
$660$	11499.2	+	19139.1i	0.678188	+	1.12877i
$661$	24584.0	−	3534.65i	1.44661	−	0.207991i	0.626151	−	0.779701i	$-0.284629\pi$
$661$	24584.0	−	3534.65i	1.44661	−	0.207991i	0.820455	+	0.571711i	$0.193720\pi$
$662$	2452.81	+	6576.23i	0.144005	+	0.386091i
$663$	534.242	+	713.664i	0.0312945	+	0.0418045i
$664$	−8675.85	−	5575.63i	−0.507061	−	0.325868i
$665$	−382.107	+	12658.7i	−0.0222819	+	0.738172i
$666$			5417.36i			0.315193i
$667$	16520.1	−	8488.11i	0.959011	−	0.492745i
$668$	6949.80	+	6949.80i	0.402539	+	0.402539i
$669$	−27868.9	+	24148.5i	−1.61057	+	1.39557i
$670$	11281.1	+	6609.42i	0.650489	+	0.381111i
$671$	−5867.64	+	40810.3i	−0.337582	+	2.34794i
$672$	3085.78	−	1150.94i	0.177138	−	0.0660691i
$673$	−5806.15	+	7756.10i	−0.332556	+	0.444243i	−0.935387	−	0.353626i	$-0.884949\pi$
$673$	−5806.15	+	7756.10i	−0.332556	+	0.444243i	0.602831	+	0.797869i	$0.294040\pi$
$674$	4515.39	+	1325.84i	0.258051	+	0.0757706i
$675$	1256.51	−	9481.68i	0.0716490	−	0.540667i
$676$	−3639.40	−	7969.17i	−0.207066	−	0.453412i
$677$	−24441.5	−	13346.1i	−1.38754	−	0.757654i	−0.400223	−	0.916418i	$-0.631067\pi$
$677$	−24441.5	−	13346.1i	−1.38754	−	0.757654i	−0.987317	+	0.158764i	$0.949249\pi$
$678$	1249.91	+	17476.0i	0.0708000	+	0.989914i
$679$	8044.67	+	6970.74i	0.454677	+	0.393980i
$680$	1232.58	+	3636.16i	0.0695109	+	0.205060i
$681$	−31306.1	+	14297.0i	−1.76160	+	0.804498i
$682$	−9755.01	−	2122.07i	−0.547711	−	0.119147i
$683$	−2352.03	−	4307.42i	−0.131768	−	0.241316i	0.803462	−	0.595357i	$-0.202989\pi$
$683$	−2352.03	−	4307.42i	−0.131768	−	0.241316i	−0.935230	+	0.354041i	$0.884807\pi$
$684$	−1828.42	−	12717.0i	−0.102210	−	0.710885i
$685$	−27697.7	+	11652.4i	−1.54493	+	0.649952i
$686$	13271.1	+	1908.10i	0.738622	+	0.106198i
$687$	−7354.71	−	33809.1i	−0.408442	−	1.87758i
$688$	1935.56	+	138.434i	0.107257	+	0.00767116i
$689$	360.714			0.0199450
$690$	−19594.1	+	1718.00i	−1.08106	+	0.0947872i
$691$	27971.2			1.53990			0.769952	−	0.638102i	$-0.220280\pi$
$691$	27971.2			1.53990			0.769952	+	0.638102i	$0.220280\pi$
$692$	−11925.9	−	852.957i	−0.655136	−	0.0468563i
$693$	6285.26	+	28892.9i	0.344527	+	1.58377i
$694$	−6561.20	−	943.358i	−0.358876	−	0.0515986i
$695$	33355.6	+	13601.0i	1.82050	+	0.742323i
$696$	1528.78	+	10632.9i	0.0832590	+	0.579079i
$697$	3363.25	+	6159.33i	0.182772	+	0.334722i
$698$	−2786.55	−	606.176i	−0.151107	−	0.0328712i
$699$	108.202	−	49.4142i	0.00585490	−	0.00267385i
$700$	−2615.64	+	5899.06i	−0.141231	+	0.318519i
$701$	−7360.93	−	6378.28i	−0.396603	−	0.343658i	0.433614	−	0.901099i	$-0.357238\pi$
$701$	−7360.93	−	6378.28i	−0.396603	−	0.343658i	−0.830217	+	0.557440i	$0.811783\pi$
$702$	−28.4312	−	397.520i	−0.00152858	−	0.0213724i
$703$	−5701.86	−	3113.45i	−0.305903	−	0.167036i
$704$	1664.50	+	3644.74i	0.0891096	+	0.195123i
$705$	7229.28	−	5078.79i	0.386199	−	0.271317i
$706$	9599.65	+	2818.71i	0.511739	+	0.150260i
$707$	−6340.28	+	8469.62i	−0.337271	+	0.450541i
$708$	7332.85	−	2735.01i	0.389245	−	0.145181i
$709$	1569.40	−	10915.4i	0.0831315	−	0.578192i	−0.905097	−	0.425206i	$-0.860202\pi$
$709$	1569.40	−	10915.4i	0.0831315	−	0.578192i	0.988228	−	0.152987i	$-0.0488891\pi$
$710$	−2136.25	+	557.832i	−0.112918	+	0.0294860i
$711$	2482.83	−	2151.39i	0.130961	−	0.113479i
$712$	1975.72	+	1975.72i	0.103993	+	0.103993i
$713$	5445.81	−	6905.46i	0.286041	−	0.362709i
$714$			8835.82i			0.463127i
$715$	−1822.05	−	54.9989i	−0.0953017	−	0.00287671i
$716$	3190.80	+	2050.60i	0.166544	+	0.107032i
$717$	−22770.6	−	30418.0i	−1.18603	−	1.58435i
$718$	−2093.01	−	5611.58i	−0.108789	−	0.291675i
$719$	34703.3	−	4989.58i	1.80002	−	0.258804i	0.840776	−	0.541383i	$-0.182099\pi$
$719$	34703.3	−	4989.58i	1.80002	−	0.258804i	0.959244	+	0.282579i	$0.0911898\pi$
$720$	1583.88	−	6351.81i	0.0819831	−	0.328775i
$721$	14298.4	−	9189.01i	0.738556	−	0.474641i
$722$	1582.57	+	590.269i	0.0815751	+	0.0304260i
$723$	−24942.6	+	45678.9i	−1.28302	+	2.34968i
$724$	3698.15	−	4267.89i	0.189835	−	0.219081i
$725$	−16987.8	−	12426.5i	−0.870223	−	0.636562i
$726$	−39614.1	+	11631.7i	−2.02509	+	0.594620i
$727$	3938.83	−	10560.4i	0.200940	−	0.538740i	−0.796923	−	0.604081i	$-0.793541\pi$
$727$	3938.83	−	10560.4i	0.200940	−	0.538740i	0.997863	+	0.0653402i	$0.0208132\pi$
$728$	−57.1546	+	262.736i	−0.00290974	+	0.0133759i
$729$	8537.46	−	29075.9i	0.433748	−	1.47721i
$730$	−3689.68	−	19823.2i	−0.187070	−	1.00506i
$731$	−2162.70	+	4735.64i	−0.109426	+	0.239609i
$732$	16816.9	−	12589.0i	0.849142	−	0.635660i
$733$	9340.80	−	2031.97i	0.470682	−	0.102391i	0.0290331	−	0.999578i	$-0.490757\pi$
$733$	9340.80	−	2031.97i	0.470682	−	0.102391i	0.441649	+	0.897188i	$0.354394\pi$
$734$	8142.61	+	9397.07i	0.409467	+	0.472551i
$735$	10655.7	−	11572.5i	0.534749	−	0.580761i
$736$	−3528.61	−	88.8260i	−0.176721	−	0.00444860i
$737$	−25885.3	+	25885.3i	−1.29376	+	1.29376i
$738$	853.610	−	11935.0i	0.0425770	−	0.595304i
$739$	12388.7	−	19277.2i	0.616680	−	0.959572i	−0.382683	−	0.923880i	$-0.625000\pi$
$739$	12388.7	−	19277.2i	0.616680	−	0.959572i	0.999363	−	0.0356926i	$-0.0113637\pi$
$740$	−2091.24	−	2565.93i	−0.103886	−	0.127467i
$741$	1658.07	+	757.216i	0.0822008	+	0.0375398i
$742$	2862.09	+	2142.54i	0.141605	+	0.106004i
$743$	15028.1	−	8205.97i	0.742029	−	0.405179i	−0.0633091	−	0.997994i	$-0.520165\pi$
$743$	15028.1	−	8205.97i	0.742029	−	0.405179i	0.805338	+	0.592815i	$0.201984\pi$
$744$	2749.96	+	4279.03i	0.135509	+	0.210856i
$745$	−15284.3	−	30117.3i	−0.751642	−	1.48109i
$746$	5341.00	+	18189.8i	0.262128	+	0.892727i
$747$	−47055.3	+	3365.46i	−2.30477	+	0.164841i
$748$	−10722.4	+	766.879i	−0.524130	+	0.0374865i
$749$	5588.76	+	19033.6i	0.272642	+	0.928534i
$750$	11689.9	+	18978.5i	0.569140	+	0.923994i
$751$	−1172.03	−	1823.71i	−0.0569480	−	0.0886127i	0.811612	−	0.584197i	$-0.198590\pi$
$751$	−1172.03	−	1823.71i	−0.0569480	−	0.0886127i	−0.868560	+	0.495584i	$0.834954\pi$
$752$	1391.53	−	759.835i	0.0674787	−	0.0368462i
$753$	−37303.0	−	27924.6i	−1.80531	−	1.35143i
$754$	−797.756	−	364.323i	−0.0385312	−	0.0175966i
$755$	−1267.99	+	12440.2i	−0.0611217	+	0.599663i
$756$	2135.56	−	3323.00i	0.102738	−	0.159863i
$757$	958.765	−	13405.3i	0.0460329	−	0.643624i	−0.921096	−	0.389336i	$-0.872704\pi$
$757$	958.765	−	13405.3i	0.0460329	−	0.643624i	0.967129	−	0.254288i	$-0.0818410\pi$
$758$	12828.5	−	12828.5i	0.614714	−	0.614714i
$759$	9206.73	−	54296.2i	0.440294	−	2.59661i
$760$	5775.10	+	5317.56i	0.275638	+	0.253800i
$761$	−18889.5	−	21799.7i	−0.899797	−	1.03842i	−0.999060	−	0.0433596i	$-0.986194\pi$
$761$	−18889.5	−	21799.7i	−0.899797	−	1.03842i	0.0992627	−	0.995061i	$-0.468352\pi$
$762$	−32485.5	+	7066.79i	−1.54439	+	0.335962i
$763$	17066.6	−	12775.9i	0.809769	−	0.606185i
$764$	1707.31	−	3738.48i	0.0808485	−	0.177033i
$765$	14481.6	+	9936.63i	0.684421	+	0.469620i
$766$	6918.45	−	23562.1i	0.326336	−	1.11140i
$767$	−135.818	+	624.347i	−0.00639390	+	0.0293923i
$768$	713.434	−	1912.79i	0.0335206	−	0.0898723i
$769$	−34410.1	+	10103.7i	−1.61360	+	0.473796i	−0.959289	−	0.282427i	$-0.908860\pi$
$769$	−34410.1	+	10103.7i	−1.61360	+	0.473796i	−0.654313	+	0.756224i	$0.727042\pi$
$770$	−14130.4	−	11258.8i	−0.661330	−	0.526934i
$771$	−11213.8	+	12941.4i	−0.523805	+	0.604504i
$772$	5957.37	−	10910.1i	0.277734	−	0.508631i
$773$	−35224.9	−	13138.2i	−1.63900	−	0.611317i	−0.650098	−	0.759851i	$-0.725272\pi$
$773$	−35224.9	−	13138.2i	−1.63900	−	0.611317i	−0.988907	+	0.148533i	$0.952545\pi$
$774$	7467.48	−	4799.06i	0.346787	−	0.222866i
$775$	−9761.18	−	2010.74i	−0.452428	−	0.0931973i
$776$	6531.14	−	939.036i	0.302132	−	0.0434400i
$777$	−2662.18	−	7137.59i	−0.122915	−	0.329549i
$778$	−12371.3	−	16526.1i	−0.570093	−	0.761555i
$779$	12071.2	+	7757.71i	0.555195	+	0.356802i
$780$	636.625	+	676.254i	0.0292241	+	0.0310433i
$781$		−	6181.76i		−	0.283228i
$782$	3531.58	−	8786.61i	0.161495	−	0.401801i
$783$	9110.33	+	9110.33i	0.415807	+	0.415807i
$784$	2133.49	−	1848.68i	0.0971887	−	0.0842145i
$785$	632.974	+	2424.01i	0.0287794	+	0.110212i
$786$	−4371.66	+	30405.5i	−0.198386	+	1.37981i
$787$	410.454	−	153.091i	0.0185910	−	0.00693408i	−0.340151	−	0.940371i	$-0.610478\pi$
$787$	410.454	−	153.091i	0.0185910	−	0.00693408i	0.358742	+	0.933437i	$0.383206\pi$
$788$	9017.71	−	12046.2i	0.407668	−	0.544581i
$789$	24932.7	+	7320.91i	1.12500	+	0.330331i
$790$	−345.502	+	1977.44i	−0.0155600	+	0.0890558i
$791$	−5889.50	−	12896.2i	−0.264736	−	0.579692i
$792$	16086.8	+	8784.04i	0.721740	+	0.394100i
$793$	122.349	+	1710.66i	0.00547887	+	0.0766046i
$794$	−18.3612	−	15.9101i	−0.000820673	−	0.000711117i
$795$	11695.8	−	3964.62i	0.521769	−	0.176869i
$796$	−6387.20	+	2916.93i	−0.284407	+	0.129884i
$797$	−23952.9	−	5210.64i	−1.06456	−	0.231581i	−0.354021	−	0.935237i	$-0.615186\pi$
$797$	−23952.9	−	5210.64i	−1.06456	−	0.231581i	−0.710541	+	0.703656i	$0.751550\pi$
$798$	8658.36	+	15856.6i	0.384088	+	0.703405i
$799$	605.349	+	4210.30i	0.0268031	+	0.186420i
$800$	1701.76	+	3619.95i	0.0752077	+	0.159981i
$801$	12651.1	+	1818.96i	0.558060	+	0.0802369i
$802$	3496.60	+	16073.6i	0.153952	+	0.707704i
$803$	56311.6	+	4027.49i	2.47471	+	0.176995i
$804$	18651.7			0.818153
$805$	14369.7	−	6843.35i	0.629150	−	0.299623i
$806$	−415.267			−0.0181478
$807$	12541.6	+	896.992i	0.547069	+	0.0391271i
$808$	1394.04	+	6408.29i	0.0606956	+	0.279013i
$809$	−4833.17	−	694.905i	−0.210043	−	0.0301997i	0.0364898	−	0.999334i	$-0.488382\pi$
$809$	−4833.17	−	694.905i	−0.210043	−	0.0301997i	−0.246533	+	0.969134i	$0.579291\pi$
$810$	3276.54	+	7788.31i	0.142131	+	0.337844i
$811$	−1498.86	−	10424.8i	−0.0648978	−	0.451374i	−0.996198	−	0.0871210i	$-0.972233\pi$
$811$	−1498.86	−	10424.8i	−0.0648978	−	0.451374i	0.931300	−	0.364253i	$-0.118676\pi$
$812$	−4165.84	−	7629.16i	−0.180040	−	0.329718i
$813$	59438.2	+	12930.0i	2.56407	+	0.557779i
$814$	8430.49	−	3850.08i	0.363008	−	0.165780i
$815$	−28287.8	−	13965.0i	−1.21580	−	0.600212i
$816$	4139.30	+	3586.72i	0.177579	+	0.153873i
$817$	759.397	+	10617.8i	0.0325189	+	0.454673i
$818$	8482.33	+	4631.71i	0.362565	+	0.197975i
$819$	510.943	+	1118.81i	0.0217995	+	0.0477343i
$820$	4202.91	+	5982.53i	0.178990	+	0.254779i
$821$	16414.0	+	4819.60i	0.697752	+	0.204878i	0.611325	−	0.791380i	$-0.290637\pi$
$821$	16414.0	+	4819.60i	0.697752	+	0.204878i	0.0864268	+	0.996258i	$0.472455\pi$
$822$	−25688.9	+	34316.3i	−1.09003	+	1.45611i
$823$	−7363.40	+	2746.41i	−0.311874	+	0.116323i	−0.500527	−	0.865721i	$-0.666860\pi$
$823$	−7363.40	+	2746.41i	−0.311874	+	0.116323i	0.188653	+	0.982044i	$0.439588\pi$
$824$	1499.38	−	10428.4i	0.0633901	−	0.440888i
$825$	−59682.5	+	18242.9i	−2.51864	+	0.769863i
$826$	−4786.09	+	4147.17i	−0.201610	+	0.174696i
$827$	1295.11	+	1295.11i	0.0544564	+	0.0544564i	0.733811	−	0.679354i	$-0.237740\pi$
$827$	1295.11	+	1295.11i	0.0544564	+	0.0544564i	−0.679354	+	0.733811i	$0.737740\pi$
$828$	−13165.2	+	9347.78i	−0.552563	+	0.392340i
$829$		−	5818.54i		−	0.243771i	−0.992544	−	0.121886i	$-0.961106\pi$
$829$		−	5818.54i		−	0.243771i	0.992544	−	0.121886i	$-0.0388941\pi$
$830$	20988.6	−	19758.6i	0.877740	−	0.826303i
$831$	23129.5	+	14864.4i	0.965529	+	0.620508i
$832$	99.8824	+	133.427i	0.00416202	+	0.00555981i
$833$	2646.75	+	7096.20i	0.110089	+	0.295161i
$834$	50864.1	−	7313.15i	2.11184	−	0.303637i
$835$	−23548.1	+	14148.2i	−0.975947	+	0.586369i
$836$	−18490.7	+	11883.2i	−0.764969	+	0.491616i
$837$	5715.95	+	2131.94i	0.236048	+	0.0880414i
$838$	−1305.49	+	2390.82i	−0.0538155	+	0.0985557i
$839$	−753.952	+	870.106i	−0.0310242	+	0.0358038i	−0.771050	−	0.636775i	$-0.780268\pi$
$839$	−753.952	+	870.106i	−0.0310242	+	0.0358038i	0.740025	+	0.672579i	$0.234813\pi$
$840$	1034.56	+	9147.12i	0.0424948	+	0.375721i
$841$	3802.65	−	1116.56i	0.155917	−	0.0457812i
$842$	7133.91	−	19126.7i	0.291984	−	0.782840i
$843$	13513.9	−	62122.3i	0.552127	−	2.53809i
$844$	−310.580	+	1057.74i	−0.0126666	+	0.0431384i
$845$	24073.9	−	4480.86i	0.980081	−	0.182422i
$846$	3012.81	−	6597.14i	0.122438	−	0.268102i
$847$	26744.7	−	20020.8i	1.08496	−	0.812189i
$848$	2165.52	−	471.080i	0.0876936	−	0.0190766i
$849$	43414.5	+	50103.0i	1.75498	+	2.02536i
$850$	−10695.0	+	883.777i	−0.431570	+	0.0356627i
$851$	−205.459	+	8161.88i	−0.00827621	+	0.328773i
$852$	−2227.14	+	2227.14i	−0.0895546	+	0.0895546i
$853$	−254.010	+	3551.53i	−0.0101959	+	0.142558i	0.989804	+	0.142436i	$0.0454934\pi$
$853$	−254.010	+	3551.53i	−0.0101959	+	0.142558i	−1.00000		0.000122165i	$0.999961\pi$
$854$	−9190.07	+	14300.0i	−0.368241	+	0.572994i
$855$	35725.4	+	3641.37i	1.42899	+	0.145652i
$856$	11185.3	+	5108.14i	0.446618	+	0.203963i
$857$	−954.952	−	714.868i	−0.0380637	−	0.0284941i	0.580076	−	0.814562i	$-0.303023\pi$
$857$	−954.952	−	714.868i	−0.0380637	−	0.0284941i	−0.618140	+	0.786068i	$0.712114\pi$
$858$	−2282.34	+	1246.25i	−0.0908131	+	0.0495877i
$859$	−10973.2	−	17074.7i	−0.435858	−	0.678208i	0.551952	−	0.833876i	$-0.313883\pi$
$859$	−10973.2	−	17074.7i	−0.435858	−	0.678208i	−0.987809	+	0.155668i	$0.950247\pi$
$860$	−1684.41	+	5155.71i	−0.0667882	+	0.204428i
$861$	4740.41	+	16144.4i	0.187634	+	0.639023i
$862$	−9197.27	+	657.802i	−0.363411	+	0.0259917i
$863$	15458.3	−	1105.60i	0.609741	−	0.0436096i	0.236945	−	0.971523i	$-0.423854\pi$
$863$	15458.3	−	1105.60i	0.609741	−	0.0436096i	0.372796	+	0.927913i	$0.378399\pi$
$864$	−689.831	−	2349.35i	−0.0271626	−	0.0925075i
$865$	10378.4	−	31766.7i	0.407949	−	1.24867i
$866$	8348.82	+	12991.0i	0.327603	+	0.509761i
$867$	21490.2	−	11734.5i	0.841804	−	0.459660i
$868$	−3294.95	−	2466.56i	−0.128845	−	0.0964524i
$869$	−5112.52	−	2334.81i	−0.199575	−	0.0911426i
$870$	−29870.7	−	3044.62i	−1.16404	−	0.118646i
$871$	−823.260	+	1281.02i	−0.0320265	+	0.0498342i
$872$	942.745	−	13181.3i	0.0366117	−	0.511898i
$873$	21342.7	−	21342.7i	0.827423	−	0.827423i
$874$	−2272.43	−	19228.9i	−0.0879474	−	0.744197i
$875$	−14229.6	−	11083.1i	−0.549769	−	0.428202i
$876$	−18836.7	−	21738.7i	−0.726522	−	0.838451i
$877$	−18729.4	+	4074.32i	−0.721147	+	0.156876i	−0.558137	−	0.829749i	$-0.688484\pi$
$877$	−18729.4	+	4074.32i	−0.721147	+	0.156876i	−0.163009	+	0.986625i	$0.552120\pi$
$878$	18255.1	−	13665.6i	0.701685	−	0.525275i
$879$	18896.4	−	41377.3i	0.725095	−	1.58774i
$880$	−11010.3	+	2049.35i	−0.421771	+	0.0785039i
$881$	2189.01	−	7455.08i	0.0837113	−	0.285094i	−0.906989	−	0.421153i	$-0.861625\pi$
$881$	2189.01	−	7455.08i	0.0837113	−	0.285094i	0.990701	+	0.136059i	$0.0434436\pi$
$882$	2744.96	−	12618.4i	0.104793	−	0.481727i
$883$	12995.7	−	34842.7i	0.495288	−	1.32792i	−0.413441	−	0.910531i	$-0.635673\pi$
$883$	12995.7	−	34842.7i	0.495288	−	1.32792i	0.908729	−	0.417387i	$-0.137054\pi$
$884$	−429.043	+	125.978i	−0.0163238	+	0.00479311i
$885$	2458.46	+	21736.6i	0.0933787	+	0.825613i
$886$	10228.6	−	11804.4i	0.387851	−	0.447604i
$887$	−11418.5	+	20911.4i	−0.432238	+	0.791584i	−0.999489	−	0.0319603i	$-0.989825\pi$
$887$	−11418.5	+	20911.4i	−0.432238	+	0.791584i	0.567251	+	0.823545i	$0.308007\pi$
$888$	−4424.39	−	1650.21i	−0.167199	−	0.0623621i
$889$	22631.0	−	14544.0i	0.853789	−	0.548697i
$890$	−6694.37	+	4022.11i	−0.252130	+	0.151485i
$891$	−23416.5	+	3366.79i	−0.880453	+	0.126590i
$892$	−6463.88	−	17330.3i	−0.242631	−	0.650518i
$893$	5212.08	+	6962.53i	0.195314	+	0.260909i
$894$	−40531.5	−	26048.0i	−1.51630	−	0.974469i
$895$	−7719.17	+	7266.81i	−0.288294	+	0.271400i
$896$			1651.95i			0.0615936i
$897$	−105.870	−	2288.34i	−0.00394080	−	0.0851787i
$898$	17562.3	+	17562.3i	0.652630	+	0.652630i
$899$	10145.8	−	8791.41i	0.376399	−	0.326151i
$900$	16155.2	+	8591.11i	0.598341	+	0.318189i
$901$	−846.155	+	5885.14i	−0.0312869	+	0.217605i
$902$	−19180.0	+	7153.75i	−0.708007	+	0.264073i
$903$	−7480.37	+	9992.60i	−0.275671	+	0.368254i
$904$	−8432.19	−	2475.91i	−0.310233	−	0.0910925i
$905$	9073.73	+	12915.8i	0.333283	+	0.474403i
$906$	7410.38	+	16226.5i	0.271737	+	0.595020i
$907$	40478.6	+	22103.0i	1.48188	+	0.809170i	0.997828	−	0.0658677i	$-0.0209815\pi$
$907$	40478.6	+	22103.0i	1.48188	+	0.809170i	0.484055	+	0.875037i	$0.339163\pi$
$908$	−1231.52	−	17218.8i	−0.0450102	−	0.629325i
$909$	22672.1	+	19645.5i	0.827267	+	0.716831i
$910$	−673.897	−	332.686i	−0.0245489	−	0.0121192i
$911$	14156.3	−	6464.96i	0.514840	−	0.235119i	−0.141014	−	0.990008i	$-0.545036\pi$
$911$	14156.3	−	6464.96i	0.514840	−	0.235119i	0.655853	+	0.754888i	$0.272309\pi$
$912$	10943.0	+	2380.50i	0.397323	+	0.0864324i
$913$	38679.2	+	70835.7i	1.40208	+	2.56771i
$914$	1325.01	+	9215.67i	0.0479513	+	0.333509i
$915$	22769.0	+	54121.8i	0.822646	+	1.95542i
$916$	17178.2	+	2469.86i	0.619635	+	0.0890900i
$917$	−5283.66	−	24288.6i	−0.190274	−	0.874678i
$918$	6552.32	+	468.632i	0.235576	+	0.0168487i
$919$	−3814.77			−0.136929			−0.0684645	−	0.997654i	$-0.521810\pi$
$919$	−3814.77			−0.136929			−0.0684645	+	0.997654i	$0.521810\pi$
$920$	2627.20	−	9509.67i	0.0941482	−	0.340787i
$921$	−71100.5			−2.54380
$922$	−13660.3	−	977.006i	−0.487938	−	0.0348980i
$923$	−54.6593	−	251.265i	−0.00194922	−	0.00896044i
$924$	−25511.6	−	3668.01i	−0.908301	−	0.130594i
$925$	8373.14	−	3936.25i	0.297629	−	0.139917i
$926$	−3694.06	−	25692.8i	−0.131096	−	0.911790i
$927$	−23096.9	−	42298.9i	−0.818342	−	1.49868i
$928$	−5265.06	−	1145.34i	−0.186244	−	0.0405148i
$929$	−37763.5	+	17246.0i	−1.33367	+	0.609067i	−0.949376	−	0.314143i	$-0.898283\pi$
$929$	−37763.5	+	17246.0i	−1.33367	+	0.609067i	−0.384296	+	0.923210i	$0.625556\pi$
$930$	−13464.6	+	4564.22i	−0.474755	+	0.160932i
$931$	11703.5	+	10141.1i	0.411994	+	0.356995i
$932$	4.25644	+	59.5128i	0.000149597	+	0.00209164i
$933$	21234.1	+	11594.7i	0.745096	+	0.406853i
$934$	2152.20	+	4712.65i	0.0753983	+	0.165099i
$935$	5171.44	−	29598.1i	0.180881	−	1.03525i
$936$	731.534	+	214.798i	0.0255459	+	0.00750094i
$937$	10763.1	−	14377.8i	0.375256	−	0.501284i	−0.572664	−	0.819790i	$-0.694090\pi$
$937$	10763.1	−	14377.8i	0.375256	−	0.501284i	0.947921	+	0.318506i	$0.103181\pi$
$938$	−14141.0	+	5274.34i	−0.492240	+	0.183596i
$939$	−11557.8	+	80386.5i	−0.401678	+	2.79373i
$940$	1119.65	+	4287.75i	0.0388498	+	0.148778i
$941$	−4433.13	+	3841.33i	−0.153577	+	0.133075i	−0.728260	−	0.685301i	$-0.759671\pi$
$941$	−4433.13	+	3841.33i	−0.153577	+	0.133075i	0.574683	+	0.818376i	$0.305125\pi$
$942$	2527.14	+	2527.14i	0.0874084	+	0.0874084i
$943$	1738.71	−	17949.1i	0.0600427	−	0.619835i
$944$			3925.59i			0.135347i
$945$	7567.89	+	8038.99i	0.260512	+	0.276728i
$946$	−12775.4	−	8210.24i	−0.439073	−	0.282175i
$947$	10865.2	+	14514.2i	0.372832	+	0.498045i	0.947240	−	0.320524i	$-0.103859\pi$
$947$	10865.2	+	14514.2i	0.372832	+	0.498045i	−0.574409	+	0.818569i	$0.694768\pi$
$948$	1000.74	+	2683.09i	0.0342854	+	0.0919227i
$949$	2324.46	−	334.207i	0.0795103	−	0.0114318i
$950$	−18327.0	+	12066.2i	−0.625901	+	0.412083i
$951$	−48568.3	+	31212.9i	−1.65608	+	1.06430i
$952$	−4152.52	−	1548.81i	−0.141370	−	0.0527282i
$953$	4445.47	−	8141.27i	0.151105	−	0.276728i	−0.791152	−	0.611620i	$-0.790518\pi$
$953$	4445.47	−	8141.27i	0.151105	−	0.276728i	0.942256	+	0.334892i	$0.108700\pi$
$954$	6638.69	−	7661.46i	0.225299	−	0.260009i
$955$	8984.31	+	7158.52i	0.304424	+	0.242559i
$956$	18286.8	−	5369.48i	0.618657	−	0.181654i
$957$	29378.4	−	78766.6i	0.992341	−	2.66057i
$958$	1428.15	−	6565.11i	0.0481644	−	0.221408i
$959$	9772.38	−	33281.7i	0.329058	−	1.12067i
$960$	4705.09	+	3228.43i	0.158183	+	0.108539i
$961$	−9734.95	+	21316.6i	−0.326775	+	0.715537i
$962$	308.625	−	231.034i	0.0103435	−	0.00774306i
$963$	54963.2	−	11956.5i	1.83922	−	0.400097i
$964$	−17095.3	−	19729.1i	−0.571166	−	0.659160i
$965$	25559.8	+	23534.8i	0.852642	+	0.785090i
$966$	12752.0	−	18785.7i	0.424730	−	0.625693i
$967$	−8029.87	+	8029.87i	−0.267035	+	0.267035i	−0.827904	−	0.560869i	$-0.810467\pi$
$967$	−8029.87	+	8029.87i	−0.267035	+	0.267035i	0.560869	+	0.827904i	$0.310467\pi$
$968$	1477.35	−	20656.1i	0.0490537	−	0.685860i
$969$	−16243.6	+	25275.6i	−0.538514	+	0.837945i
$970$	−1870.13	+	18347.8i	−0.0619032	+	0.607331i
$971$	9538.21	+	4355.96i	0.315238	+	0.143964i	0.566750	−	0.823890i	$-0.308201\pi$
$971$	9538.21	+	4355.96i	0.315238	+	0.143964i	−0.251512	+	0.967854i	$0.580928\pi$
$972$	16264.9	+	12175.7i	0.536725	+	0.401787i
$973$	−36495.2	+	19927.9i	−1.20245	+	0.656587i
$974$	−13465.6	−	20952.9i	−0.442984	−	0.689297i
$975$	−2264.56	+	1269.22i	−0.0743835	+	0.0416898i
$976$	2968.58	+	10110.1i	0.0973586	+	0.331573i
$977$	41382.3	−	2959.72i	1.35511	−	0.0969191i	0.625199	−	0.780466i	$-0.285018\pi$
$977$	41382.3	−	2959.72i	1.35511	−	0.0969191i	0.729907	+	0.683547i	$0.239563\pi$
$978$	−44888.9	+	3210.52i	−1.46768	+	0.104970i
$979$	−6160.41	−	20980.4i	−0.201111	−	0.684921i
$980$	3570.87	+	7036.31i	0.116395	+	0.229354i
$981$	−32681.8	−	50853.9i	−1.06366	−	1.65509i
$982$	−2907.12	+	1587.41i	−0.0944704	+	0.0515847i
$983$	−3204.29	−	2398.70i	−0.103968	−	0.0778297i	0.546029	−	0.837766i	$-0.316139\pi$
$983$	−3204.29	−	2398.70i	−0.103968	−	0.0778297i	−0.649997	+	0.759937i	$0.725230\pi$
$984$	9487.40	+	4332.75i	0.307365	+	0.140369i
$985$	26571.5	+	32602.9i	0.859530	+	1.05464i
$986$	7815.37	−	12161.0i	0.252426	−	0.392783i
$987$	−727.555	+	10172.5i	−0.0234633	+	0.328060i
$988$	−646.504	+	646.504i	−0.0208178	+	0.0208178i
$989$	11432.6	−	6947.13i	0.367580	−	0.223363i
$990$	−34701.7	+	37687.5i	−1.11403	+	1.20989i
$991$	26277.2	+	30325.4i	0.842302	+	0.972068i	0.999881	−	0.0154382i	$-0.00491432\pi$
$991$	26277.2	+	30325.4i	0.842302	+	0.972068i	−0.157579	+	0.987506i	$0.550369\pi$
$992$	−2493.02	+	542.324i	−0.0797919	+	0.0173577i
$993$	−22404.0	+	16771.4i	−0.715982	+	0.535977i
$994$	1058.74	−	2318.33i	0.0337840	−	0.0739767i
$995$	−3591.36	−	19295.0i	−0.114426	−	0.614765i
$996$	11585.2	−	39455.6i	0.368565	−	1.25522i
$997$	7401.32	−	34023.3i	0.235108	−	1.08077i	−0.696571	−	0.717488i	$-0.745292\pi$
$997$	7401.32	−	34023.3i	0.235108	−	1.08077i	0.931678	−	0.363284i	$-0.118345\pi$
$998$	−3992.53	+	10704.4i	−0.126634	+	0.339520i
$999$	−5434.17	+	1595.62i	−0.172102	+	0.0505336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.33.3	yes	720
5.2	odd	4	inner	230.4.l.a.217.21	yes	720
23.7	odd	22	inner	230.4.l.a.53.21	yes	720
115.7	even	44	inner	230.4.l.a.7.3	✓	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.3	✓	720	115.7	even	44	inner
230.4.l.a.33.3	yes	720	1.1	even	1	trivial
230.4.l.a.53.21	yes	720	23.7	odd	22	inner
230.4.l.a.217.21	yes	720	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99490 - 0.142678i) q^{2} +(-1.69513 - 7.79240i) q^{3} +(3.95929 + 0.569259i) q^{4} +(-4.22141 + 10.3528i) q^{5} +(2.26982 + 15.7870i) q^{6} +(-6.18513 - 11.3272i) q^{7} +(-7.81717 - 1.70052i) q^{8} +(-33.2880 + 15.2021i) q^{9} +(9.89842 - 20.0505i) q^{10} +(47.3150 + 40.9987i) q^{11} +(-2.27562 - 31.8173i) q^{12} +(2.28569 + 1.24808i) q^{13} +(10.7226 + 23.4792i) q^{14} +(87.8287 + 15.3456i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-25.7244 + 34.3638i) q^{17} +(68.5753 - 25.5773i) q^{18} +(-12.4909 + 86.8764i) q^{19} +(-22.6072 + 38.5865i) q^{20} +(-77.7817 + 67.3982i) q^{21} +(-88.5393 - 88.5393i) q^{22} +(104.287 - 35.9343i) q^{23} +63.7972i q^{24} +(-89.3594 - 87.4065i) q^{25} +(-4.38165 - 2.81592i) q^{26} +(45.8547 + 61.2547i) q^{27} +(-18.0406 - 48.3687i) q^{28} +(166.667 - 23.9631i) q^{29} +(-173.020 - 43.1443i) q^{30} +(67.0723 - 43.1048i) q^{31} +(-29.9824 - 11.1829i) q^{32} +(239.273 - 438.196i) q^{33} +(56.2207 - 64.8822i) q^{34} +(143.378 - 16.2164i) q^{35} +(-140.451 + 41.2400i) q^{36} +(-25.8666 + 69.3509i) q^{37} +(37.3136 - 171.528i) q^{38} +(5.85099 - 19.9266i) q^{39} +(50.6046 - 73.7508i) q^{40} +(67.9144 - 148.712i) q^{41} +(164.783 - 123.355i) q^{42} +(118.510 - 25.7803i) q^{43} +(163.995 + 189.260i) q^{44} +(-16.8617 - 408.797i) q^{45} +(-213.169 + 56.8061i) q^{46} +(70.0685 - 70.0685i) q^{47} +(9.10248 - 127.269i) q^{48} +(95.3896 - 148.429i) q^{49} +(165.792 + 187.117i) q^{50} +(311.383 + 142.204i) q^{51} +(8.33921 + 6.24265i) q^{52} +(121.568 - 66.3809i) q^{53} +(-82.7360 - 128.740i) q^{54} +(-624.186 + 316.769i) q^{55} +(29.0881 + 99.0649i) q^{56} +(698.150 - 49.9326i) q^{57} +(-335.904 + 24.0243i) q^{58} +(69.1230 + 235.411i) q^{59} +(339.003 + 110.755i) q^{60} +(356.042 + 554.011i) q^{61} +(-139.953 + 76.4201i) q^{62} +(378.088 + 283.033i) q^{63} +(58.2164 + 26.5866i) q^{64} +(-22.5699 + 18.3945i) q^{65} +(-539.848 + 840.020i) q^{66} +(-41.7134 + 583.229i) q^{67} +(-121.412 + 121.412i) q^{68} +(-456.795 - 751.731i) q^{69} +(-288.339 + 11.8932i) q^{70} +(-64.6606 - 74.6223i) q^{71} +(286.069 - 62.2306i) q^{72} +(721.886 - 540.397i) q^{73} +(61.4962 - 134.658i) q^{74} +(-529.630 + 844.490i) q^{75} +(-98.9104 + 336.858i) q^{76} +(171.752 - 789.531i) q^{77} +(-14.5153 + 38.9169i) q^{78} +(-86.1370 + 25.2921i) q^{79} +(-111.474 + 139.906i) q^{80} +(-247.453 + 285.576i) q^{81} +(-156.701 + 286.976i) q^{82} +(1207.85 + 450.503i) q^{83} +(-346.327 + 222.571i) q^{84} +(-247.167 - 411.383i) q^{85} +(-240.095 + 34.5204i) q^{86} +(-469.253 - 1258.12i) q^{87} +(-300.151 - 400.954i) q^{88} +(-293.818 - 188.825i) q^{89} +(-24.6890 + 817.916i) q^{90} -33.6100i q^{91} +(433.357 - 82.9081i) q^{92} +(-449.586 - 449.586i) q^{93} +(-149.777 + 129.783i) q^{94} +(-846.682 - 496.057i) q^{95} +(-36.3171 + 252.591i) q^{96} +(-772.785 + 288.234i) q^{97} +(-211.471 + 282.492i) q^{98} +(-2198.29 - 645.476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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