LMFDB - Embedded newform 165.4.p.a.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	165.41
Dual form			165.4.p.a.161.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.12619 + 2.27131i) q^{2} +(5.16730 - 0.546811i) q^{3} +(2.14208 - 6.59266i) q^{4} +(-2.93893 + 4.04508i) q^{5} +(-14.9120 + 13.4460i) q^{6} +(16.5110 + 5.36474i) q^{7} +(-1.27538 - 3.92522i) q^{8} +(26.4020 - 5.65107i) q^{9} -19.3209i q^{10} +(-16.8677 + 32.3493i) q^{11} +(7.46386 - 35.2376i) q^{12} +(3.66583 + 5.04558i) q^{13} +(-63.8015 + 20.7304i) q^{14} +(-12.9744 + 22.5092i) q^{15} +(57.7669 + 41.9701i) q^{16} +(-5.17123 - 3.75712i) q^{17} +(-69.7024 + 77.6335i) q^{18} +(128.960 - 41.9017i) q^{19} +(20.3724 + 28.0402i) q^{20} +(88.2507 + 18.6928i) q^{21} +(-20.7437 - 139.442i) q^{22} +154.817i q^{23} +(-8.73664 - 19.5854i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(-22.9202 - 7.44721i) q^{26} +(133.337 - 43.6377i) q^{27} +(70.7358 - 97.3594i) q^{28} +(-32.3149 + 99.4551i) q^{29} +(-10.5649 - 99.8370i) q^{30} +(-222.925 + 161.965i) q^{31} -242.900 q^{32} +(-69.4717 + 176.382i) q^{33} +24.6998 q^{34} +(-70.2254 + 51.0217i) q^{35} +(19.2997 - 186.164i) q^{36} +(-82.9044 + 255.153i) q^{37} +(-307.982 + 423.901i) q^{38} +(21.7014 + 24.0675i) q^{39} +(19.6261 + 6.37691i) q^{40} +(-105.458 - 324.566i) q^{41} +(-318.346 + 142.007i) q^{42} +313.704i q^{43} +(177.136 + 180.498i) q^{44} +(-54.7345 + 123.406i) q^{45} +(-351.638 - 483.988i) q^{46} +(66.2426 - 21.5235i) q^{47} +(321.449 + 185.285i) q^{48} +(-33.6611 - 24.4562i) q^{49} +(78.1548 + 56.7828i) q^{50} +(-28.7757 - 16.5865i) q^{51} +(41.1163 - 13.3595i) q^{52} +(55.8988 + 76.9381i) q^{53} +(-317.722 + 439.270i) q^{54} +(-81.2828 - 163.304i) q^{55} -71.6513i q^{56} +(643.463 - 287.035i) q^{57} +(-124.871 - 384.313i) q^{58} +(762.991 + 247.911i) q^{59} +(120.603 + 133.753i) q^{60} +(366.468 - 504.399i) q^{61} +(329.035 - 1012.67i) q^{62} +(466.239 + 48.3352i) q^{63} +(297.216 - 215.940i) q^{64} -31.1834 q^{65} +(-183.437 - 709.196i) q^{66} -438.653 q^{67} +(-35.8466 + 26.0441i) q^{68} +(84.6556 + 799.986i) q^{69} +(103.652 - 319.007i) q^{70} +(54.8356 - 75.4748i) q^{71} +(-55.8544 - 96.4265i) q^{72} +(911.904 + 296.296i) q^{73} +(-320.358 - 985.960i) q^{74} +(-52.9208 - 118.636i) q^{75} -939.947i q^{76} +(-452.048 + 443.628i) q^{77} +(-122.508 - 25.9490i) q^{78} +(-622.548 - 856.864i) q^{79} +(-339.545 + 110.325i) q^{80} +(665.131 - 298.399i) q^{81} +(1066.87 + 775.129i) q^{82} +(113.092 + 82.1661i) q^{83} +(312.276 - 541.765i) q^{84} +(30.3957 - 9.87616i) q^{85} +(-712.519 - 980.698i) q^{86} +(-112.598 + 531.584i) q^{87} +(148.491 + 24.9518i) q^{88} -636.604i q^{89} +(-109.184 - 510.111i) q^{90} +(33.4582 + 102.974i) q^{91} +(1020.66 + 331.631i) q^{92} +(-1063.36 + 958.818i) q^{93} +(-158.200 + 217.744i) q^{94} +(-209.508 + 644.801i) q^{95} +(-1255.14 + 132.820i) q^{96} +(350.112 - 254.371i) q^{97} +160.779 q^{98} +(-262.533 + 949.408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 4 q^{3} - 192 q^{4} - 100 q^{6} + 108 q^{9} + 48 q^{12} - 60 q^{15} - 1248 q^{16} - 460 q^{18} + 900 q^{19} + 888 q^{22} + 1200 q^{24} + 1200 q^{25} + 568 q^{27} - 1680 q^{28} - 576 q^{31} - 1402 q^{33}+ \cdots - 736 q^{99}+O(q^{100}) $ 192 * q + 4 * q^3 - 192 * q^4 - 100 * q^6 + 108 * q^9 + 48 * q^12 - 60 * q^15 - 1248 * q^16 - 460 * q^18 + 900 * q^19 + 888 * q^22 + 1200 * q^24 + 1200 * q^25 + 568 * q^27 - 1680 * q^28 - 576 * q^31 - 1402 * q^33 + 264 * q^34 - 2364 * q^36 + 24 * q^37 + 1220 * q^39 + 4438 * q^42 - 360 * q^46 + 1946 * q^48 + 1848 * q^49 + 930 * q^51 + 840 * q^55 - 4170 * q^57 + 4320 * q^58 - 830 * q^60 - 1560 * q^61 - 7900 * q^63 - 11700 * q^64 - 4214 * q^66 + 168 * q^67 - 4992 * q^69 - 1620 * q^70 + 6720 * q^72 - 360 * q^73 + 150 * q^75 + 13972 * q^78 + 4740 * q^79 + 916 * q^81 + 6420 * q^82 + 6880 * q^84 + 2868 * q^88 + 8736 * q^91 - 5696 * q^93 - 840 * q^94 - 12470 * q^96 - 7356 * q^97 - 736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−3.12619	+	2.27131i	−1.10528	+	0.803030i	−0.981913	−	0.189332i	$-0.939368\pi$
$2$	−3.12619	+	2.27131i	−1.10528	+	0.803030i	−0.123363	+	0.992362i	$0.539368\pi$
$3$	5.16730	−	0.546811i	0.994448	−	0.105234i
$3$	5.16730	−	0.546811i	0.994448	−	0.105234i
$4$	2.14208	−	6.59266i	0.267760	−	0.824082i
$5$	−2.93893	+	4.04508i	−0.262866	+	0.361803i
$5$	−2.93893	+	4.04508i	−0.262866	+	0.361803i
$6$	−14.9120	+	13.4460i	−1.01463	+	0.914883i
$7$	16.5110	+	5.36474i	0.891509	+	0.289669i	0.718728	−	0.695292i	$-0.244725\pi$
$7$	16.5110	+	5.36474i	0.891509	+	0.289669i	0.172781	+	0.984960i	$0.444725\pi$
$8$	−1.27538	−	3.92522i	−0.0563645	−	0.173472i
$9$	26.4020	−	5.65107i	0.977852	−	0.209299i
$10$		−	19.3209i		−	0.610981i
$11$	−16.8677	+	32.3493i	−0.462346	+	0.886699i
$11$	−16.8677	+	32.3493i	−0.462346	+	0.886699i
$12$	7.46386	−	35.2376i	0.179552	−	0.847684i
$13$	3.66583	+	5.04558i	0.0782090	+	0.107646i	0.846329	−	0.532660i	$-0.178808\pi$
$13$	3.66583	+	5.04558i	0.0782090	+	0.107646i	−0.768120	+	0.640306i	$0.778808\pi$
$14$	−63.8015	+	20.7304i	−1.21798	+	0.395744i
$15$	−12.9744	+	22.5092i	−0.223332	+	0.387457i
$16$	57.7669	+	41.9701i	0.902608	+	0.655783i
$17$	−5.17123	−	3.75712i	−0.0737769	−	0.0536020i	0.550285	−	0.834977i	$-0.314519\pi$
$17$	−5.17123	−	3.75712i	−0.0737769	−	0.0536020i	−0.624062	+	0.781375i	$0.714519\pi$
$18$	−69.7024	+	77.6335i	−0.912722	+	1.01658i
$19$	128.960	−	41.9017i	1.55713	−	0.505942i	0.601091	−	0.799181i	$-0.294733\pi$
$19$	128.960	−	41.9017i	1.55713	−	0.505942i	0.956039	+	0.293238i	$0.0947329\pi$
$20$	20.3724	+	28.0402i	0.227771	+	0.313499i
$21$	88.2507	+	18.6928i	0.917042	+	0.194244i
$22$	−20.7437	−	139.442i	−0.201026	−	1.35133i
$23$			154.817i			1.40355i	0.712400	+	0.701774i	$0.247608\pi$
$23$			154.817i			1.40355i	−0.712400	+	0.701774i	$0.752392\pi$
$24$	−8.73664	−	19.5854i	−0.0743066	−	0.166577i
$25$	−7.72542	−	23.7764i	−0.0618034	−	0.190211i
$26$	−22.9202	−	7.44721i	−0.172885	−	0.0561738i
$27$	133.337	−	43.6377i	0.950397	−	0.311040i
$28$	70.7358	−	97.3594i	0.477422	−	0.657114i
$29$	−32.3149	+	99.4551i	−0.206922	+	0.636839i	0.792707	+	0.609602i	$0.208671\pi$
$29$	−32.3149	+	99.4551i	−0.206922	+	0.636839i	−0.999629	+	0.0272370i	$0.991329\pi$
$30$	−10.5649	−	99.8370i	−0.0642959	−	0.607589i
$31$	−222.925	+	161.965i	−1.29157	+	0.938378i	−0.999836	−	0.0181222i	$-0.994231\pi$
$31$	−222.925	+	161.965i	−1.29157	+	0.938378i	−0.291731	+	0.956500i	$0.594231\pi$
$32$	−242.900			−1.34184
$33$	−69.4717	+	176.382i	−0.366469	+	0.930430i
$34$	24.6998			0.124588
$35$	−70.2254	+	51.0217i	−0.339150	+	0.246407i
$36$	19.2997	−	186.164i	0.0893505	−	0.861872i
$37$	−82.9044	+	255.153i	−0.368362	+	1.13370i	0.579487	+	0.814982i	$0.303253\pi$
$37$	−82.9044	+	255.153i	−0.368362	+	1.13370i	−0.947849	+	0.318720i	$0.896747\pi$
$38$	−307.982	+	423.901i	−1.31477	+	1.80963i
$39$	21.7014	+	24.0675i	0.0891027	+	0.0988176i
$40$	19.6261	+	6.37691i	0.0775790	+	0.0252070i
$41$	−105.458	−	324.566i	−0.401702	−	1.23631i	−0.923618	−	0.383314i	$-0.874783\pi$
$41$	−105.458	−	324.566i	−0.401702	−	1.23631i	0.521916	−	0.852997i	$-0.325217\pi$
$42$	−318.346	+	142.007i	−1.16957	+	0.521719i
$43$			313.704i			1.11254i	0.831000	+	0.556272i	$0.187769\pi$
$43$			313.704i			1.11254i	−0.831000	+	0.556272i	$0.812231\pi$
$44$	177.136	+	180.498i	0.606915	+	0.618434i
$45$	−54.7345	+	123.406i	−0.181318	+	0.408808i
$46$	−351.638	−	483.988i	−1.12709	−	1.55131i
$47$	66.2426	−	21.5235i	0.205585	−	0.0667985i	−0.204414	−	0.978884i	$-0.565529\pi$
$47$	66.2426	−	21.5235i	0.205585	−	0.0667985i	0.409999	+	0.912086i	$0.365529\pi$
$48$	321.449	+	185.285i	0.966606	+	0.557157i
$49$	−33.6611	−	24.4562i	−0.0981372	−	0.0713009i
$50$	78.1548	+	56.7828i	0.221055	+	0.160606i
$51$	−28.7757	−	16.5865i	−0.0790080	−	0.0455406i
$52$	41.1163	−	13.3595i	0.109650	−	0.0356275i
$53$	55.8988	+	76.9381i	0.144873	+	0.199401i	0.875287	−	0.483604i	$-0.160673\pi$
$53$	55.8988	+	76.9381i	0.144873	+	0.199401i	−0.730413	+	0.683005i	$0.760673\pi$
$54$	−317.722	+	439.270i	−0.800676	+	1.10698i
$55$	−81.2828	−	163.304i	−0.199276	−	0.400361i
$56$		−	71.6513i		−	0.170979i
$57$	643.463	−	287.035i	1.49524	−	0.666996i
$58$	−124.871	−	384.313i	−0.282695	−	0.870047i
$59$	762.991	+	247.911i	1.68361	+	0.547038i	0.985606	−	0.169057i	$-0.0540721\pi$
$59$	762.991	+	247.911i	1.68361	+	0.547038i	0.698003	+	0.716095i	$0.254072\pi$
$60$	120.603	+	133.753i	0.259497	+	0.287790i
$61$	366.468	−	504.399i	0.769203	−	1.05872i	−0.227189	−	0.973851i	$-0.572954\pi$
$61$	366.468	−	504.399i	0.769203	−	1.05872i	0.996392	−	0.0848663i	$-0.0270463\pi$
$62$	329.035	−	1012.67i	0.673992	−	2.07433i
$63$	466.239	+	48.3352i	0.932391	+	0.0966612i
$64$	297.216	−	215.940i	0.580500	−	0.421758i
$65$	−31.1834			−0.0595050
$66$	−183.437	−	709.196i	−0.342115	−	1.32267i
$67$	−438.653			−0.799850			−0.399925	−	0.916548i	$-0.630964\pi$
$67$	−438.653			−0.799850			−0.399925	+	0.916548i	$0.630964\pi$
$68$	−35.8466	+	26.0441i	−0.0639270	+	0.0464457i
$69$	84.6556	+	799.986i	0.147701	+	1.39575i
$70$	103.652	−	319.007i	0.176982	−	0.544695i
$71$	54.8356	−	75.4748i	0.0916590	−	0.126158i	−0.760725	−	0.649075i	$-0.775156\pi$
$71$	54.8356	−	75.4748i	0.0916590	−	0.126158i	0.852384	+	0.522917i	$0.175156\pi$
$72$	−55.8544	−	96.4265i	−0.0914236	−	0.157833i
$73$	911.904	+	296.296i	1.46206	+	0.475052i	0.928698	−	0.370836i	$-0.120929\pi$
$73$	911.904	+	296.296i	1.46206	+	0.475052i	0.533361	+	0.845888i	$0.320929\pi$
$74$	−320.358	−	985.960i	−0.503255	−	1.54886i
$75$	−52.9208	−	118.636i	−0.0814769	−	0.182651i
$76$		−	939.947i		−	1.41867i
$77$	−452.048	+	443.628i	−0.669035	+	0.656573i
$78$	−122.508	−	25.9490i	−0.177837	−	0.0376685i
$79$	−622.548	−	856.864i	−0.886609	−	1.22031i	−0.974546	−	0.224187i	$-0.928027\pi$
$79$	−622.548	−	856.864i	−0.886609	−	1.22031i	0.0879367	−	0.996126i	$-0.471973\pi$
$80$	−339.545	+	110.325i	−0.474529	+	0.154184i
$81$	665.131	−	298.399i	0.912388	−	0.409327i
$82$	1066.87	+	775.129i	1.43679	+	1.04389i
$83$	113.092	+	82.1661i	0.149560	+	0.108661i	0.660049	−	0.751223i	$-0.270536\pi$
$83$	113.092	+	82.1661i	0.149560	+	0.108661i	−0.510489	+	0.859884i	$0.670536\pi$
$84$	312.276	−	541.765i	0.405620	−	0.703707i
$85$	30.3957	−	9.87616i	0.0387868	−	0.0126026i
$86$	−712.519	−	980.698i	−0.893406	−	1.22967i
$87$	−112.598	+	531.584i	−0.138756	+	0.655078i
$88$	148.491	+	24.9518i	0.179877	+	0.0302258i
$89$		−	636.604i		−	0.758201i	−0.925355	−	0.379101i	$-0.876233\pi$
$89$		−	636.604i		−	0.758201i	0.925355	−	0.379101i	$-0.123767\pi$
$90$	−109.184	−	510.111i	−0.127878	−	0.597449i
$91$	33.4582	+	102.974i	0.0385425	+	0.118622i
$92$	1020.66	+	331.631i	1.15664	+	0.375815i
$93$	−1063.36	+	958.818i	−1.18565	+	1.06908i
$94$	−158.200	+	217.744i	−0.173587	+	0.238921i
$95$	−209.508	+	644.801i	−0.226264	+	0.696370i
$96$	−1255.14	+	132.820i	−1.33439	+	0.141207i
$97$	350.112	−	254.371i	0.366479	−	0.266262i	−0.389270	−	0.921124i	$-0.627273\pi$
$97$	350.112	−	254.371i	0.366479	−	0.266262i	0.755749	+	0.654861i	$0.227273\pi$
$98$	160.779			0.165725
$99$	−262.533	+	949.408i	−0.266521	+	0.963829i
$100$	−173.298			−0.173298
$101$	1317.54	−	957.246i	1.29802	−	0.943064i	0.298082	−	0.954540i	$-0.403653\pi$
$101$	1317.54	−	957.246i	1.29802	−	0.943064i	0.999934	+	0.0114758i	$0.00365295\pi$
$102$	127.631	−	13.5061i	0.123896	−	0.0131108i
$103$	8.55354	−	26.3251i	0.00818258	−	0.0251834i	−0.946882	−	0.321582i	$-0.895786\pi$
$103$	8.55354	−	26.3251i	0.00818258	−	0.0251834i	0.955064	+	0.296398i	$0.0957856\pi$
$104$	15.1297	−	20.8242i	0.0142653	−	0.0196345i
$105$	−334.976	+	302.045i	−0.311337	+	0.280729i
$106$	−349.501	−	113.560i	−0.320250	−	0.104056i
$107$	−231.097	−	711.242i	−0.208794	−	0.642602i	−0.999536	−	0.0304524i	$-0.990305\pi$
$107$	−231.097	−	711.242i	−0.208794	−	0.642602i	0.790742	−	0.612149i	$-0.209695\pi$
$108$	−2.06924	−	972.521i	−0.00184363	−	0.866489i
$109$		−	628.108i		−	0.551943i	−0.961166	−	0.275972i	$-0.911000\pi$
$109$		−	628.108i		−	0.551943i	0.961166	−	0.275972i	$-0.0889996\pi$
$110$	625.019	+	325.900i	0.541757	+	0.282485i
$111$	−288.871	+	1363.79i	−0.247013	+	1.16617i
$112$	728.629	+	1002.87i	0.614723	+	0.846093i
$113$	775.324	−	251.918i	0.645455	−	0.209721i	0.0320458	−	0.999486i	$-0.489798\pi$
$113$	775.324	−	251.918i	0.645455	−	0.209721i	0.613409	+	0.789765i	$0.289798\pi$
$114$	−1359.64	+	2358.83i	−1.11704	+	1.93794i
$115$	−626.248	−	454.996i	−0.507808	−	0.368944i
$116$	586.452	+	426.082i	0.469402	+	0.341041i
$117$	125.298	+	112.497i	0.0990069	+	0.0888923i
$118$	−2948.34	+	957.973i	−2.30014	+	0.747361i
$119$	−65.2260	−	89.7759i	−0.0502459	−	0.0691575i
$120$	104.901	+	22.2196i	0.0798009	+	0.0169031i
$121$	−761.960	−	1091.32i	−0.572471	−	0.819925i
$122$			2409.21i			1.78787i
$123$	−722.409	−	1619.47i	−0.529573	−	1.18717i
$124$	590.253	+	1816.61i	0.427470	+	1.31562i
$125$	118.882	+	38.6271i	0.0850651	+	0.0276393i
$126$	−1567.34	+	907.869i	−1.10817	+	0.641900i
$127$	−14.4158	+	19.8416i	−0.0100724	+	0.0138635i	−0.814023	−	0.580832i	$-0.802727\pi$
$127$	−14.4158	+	19.8416i	−0.0100724	+	0.0138635i	0.803951	+	0.594695i	$0.202727\pi$
$128$	161.794	−	497.951i	0.111724	−	0.343852i
$129$	171.537	+	1621.00i	0.117077	+	1.10637i
$130$	97.4853	−	70.8272i	0.0657694	−	0.0477843i
$131$	−115.546			−0.0770637			−0.0385318	−	0.999257i	$-0.512268\pi$
$131$	−115.546			−0.0770637			−0.0385318	+	0.999257i	$0.512268\pi$
$132$	1014.01	+	835.828i	0.668625	+	0.551133i
$133$	2354.05			1.53475
$134$	1371.31	−	996.317i	0.884055	−	0.642303i
$135$	−215.349	+	667.607i	−0.137291	+	0.425618i
$136$	−8.15223	+	25.0900i	−0.00514006	+	0.0158195i
$137$	−1113.39	+	1532.45i	−0.694332	+	0.955666i	0.305662	+	0.952140i	$0.401122\pi$
$137$	−1113.39	+	1532.45i	−0.694332	+	0.955666i	−0.999994	+	0.00352609i	$0.998878\pi$
$138$	−2081.67	−	2308.63i	−1.28408	−	1.42409i
$139$	−651.316	−	211.626i	−0.397438	−	0.129136i	0.103477	−	0.994632i	$-0.467003\pi$
$139$	−651.316	−	211.626i	−0.397438	−	0.129136i	−0.500915	+	0.865496i	$0.667003\pi$
$140$	185.940	+	572.264i	0.112249	+	0.345466i
$141$	330.526	−	147.441i	0.197414	−	0.0880621i
$142$			360.497i			0.213044i
$143$	−225.055	+	33.4796i	−0.131609	+	0.0195784i
$144$	1762.34	+	781.650i	1.01987	+	0.452343i
$145$	−307.333	−	423.008i	−0.176018	−	0.242268i
$146$	−3523.77	+	1144.94i	−1.99746	+	0.649014i
$147$	−187.310	−	107.966i	−0.105096	−	0.0605776i
$148$	1504.55	+	1093.12i	0.835631	+	0.607121i
$149$	−1227.85	−	892.083i	−0.675095	−	0.490485i	0.196632	−	0.980477i	$-0.437000\pi$
$149$	−1227.85	−	892.083i	−0.675095	−	0.490485i	−0.871727	+	0.489992i	$0.837000\pi$
$150$	434.899	+	250.678i	0.236729	+	0.136452i
$151$	−282.201	+	91.6926i	−0.152087	+	0.0494161i	−0.384071	−	0.923303i	$-0.625478\pi$
$151$	−282.201	+	91.6926i	−0.152087	+	0.0494161i	0.231984	+	0.972720i	$0.425478\pi$
$152$	−328.947	−	452.757i	−0.175534	−	0.241601i
$153$	−157.762	−	69.9724i	−0.0833617	−	0.0369734i
$154$	405.572	−	2413.61i	0.212221	−	1.26295i
$155$		−	1377.75i		−	0.713961i
$156$	205.155	−	91.5153i	0.105292	−	0.0469685i
$157$	−126.848	−	390.398i	−0.0644814	−	0.198453i	0.913625	−	0.406557i	$-0.133271\pi$
$157$	−126.848	−	390.398i	−0.0644814	−	0.198453i	−0.978107	+	0.208104i	$0.933271\pi$
$158$	3892.41	+	1264.72i	1.95990	+	0.636809i
$159$	330.917	+	366.996i	0.165053	+	0.183048i
$160$	713.864	−	982.550i	0.352725	−	0.485484i
$161$	−830.553	+	2556.18i	−0.406564	+	1.25127i
$162$	−1401.57	+	2443.57i	−0.679739	+	1.18509i
$163$	−1496.53	+	1087.29i	−0.719125	+	0.522475i	−0.886104	−	0.463486i	$-0.846599\pi$
$163$	−1496.53	+	1087.29i	−0.719125	+	0.522475i	0.166980	+	0.985960i	$0.446599\pi$
$164$	−2365.65			−1.12638
$165$	−509.309	−	799.393i	−0.240301	−	0.377168i
$166$	−540.172			−0.252563
$167$	1053.33	−	765.291i	0.488080	−	0.354611i	−0.316366	−	0.948637i	$-0.602463\pi$
$167$	1053.33	−	765.291i	0.488080	−	0.354611i	0.804445	+	0.594027i	$0.202463\pi$
$168$	−39.1797	−	370.244i	−0.0179927	−	0.170029i
$169$	666.891	−	2052.48i	0.303546	−	0.934219i
$170$	−72.5910	+	99.9129i	−0.0327498	+	0.0450763i
$171$	3168.01	−	1835.05i	1.41675	−	0.820642i
$172$	2068.14	+	671.980i	0.916827	+	0.297895i
$173$	−836.317	−	2573.92i	−0.367538	−	1.13116i	−0.948377	−	0.317146i	$-0.897275\pi$
$173$	−836.317	−	2573.92i	−0.367538	−	1.13116i	0.580839	−	0.814018i	$-0.302725\pi$
$174$	−855.391	−	1917.58i	−0.372684	−	0.835467i
$175$		−	434.017i		−	0.187478i
$176$	−2332.10	+	1160.78i	−0.998800	+	0.497143i
$177$	4078.16	+	863.818i	1.73183	+	0.366828i
$178$	1445.93	+	1990.15i	0.608858	+	0.838022i
$179$	2052.11	−	666.770i	0.856881	−	0.278417i	0.152555	−	0.988295i	$-0.451250\pi$
$179$	2052.11	−	666.770i	0.856881	−	0.278417i	0.704325	+	0.709878i	$0.251250\pi$
$180$	696.330	+	625.192i	0.288341	+	0.258884i
$181$	912.710	+	663.123i	0.374813	+	0.272318i	0.759204	−	0.650853i	$-0.225588\pi$
$181$	912.710	+	663.123i	0.374813	+	0.272318i	−0.384391	+	0.923171i	$0.625588\pi$
$182$	−338.482	−	245.921i	−0.137857	−	0.100159i
$183$	1617.84	−	2806.77i	0.653519	−	1.13378i
$184$	607.692	−	197.451i	0.243476	−	0.0791102i
$185$	−788.468	−	1085.23i	−0.313348	−	0.431286i
$186$	1146.49	−	5412.67i	0.451959	−	2.13374i
$187$	208.767	−	103.912i	0.0816394	−	0.0406352i
$188$		−	482.820i		−	0.187305i
$189$	2435.63	−	5.18230i	0.937386	−	0.00199448i
$190$	−809.579	−	2491.63i	−0.309121	−	0.951378i
$191$	2479.80	+	805.737i	0.939436	+	0.305241i	0.738416	−	0.674346i	$-0.235574\pi$
$191$	2479.80	+	805.737i	0.939436	+	0.305241i	0.201021	+	0.979587i	$0.435574\pi$
$192$	1417.73	−	1278.35i	0.532894	−	0.480504i
$193$	−2940.63	+	4047.44i	−1.09674	+	1.50954i	−0.257112	+	0.966382i	$0.582771\pi$
$193$	−2940.63	+	4047.44i	−1.09674	+	1.50954i	−0.839632	+	0.543156i	$0.817229\pi$
$194$	−516.760	+	1590.43i	−0.191243	+	0.588587i
$195$	−161.134	+	17.0514i	−0.0591746	+	0.00626193i
$196$	−233.336	+	169.529i	−0.0850350	+	0.0617816i
$197$	−2525.92			−0.913525			−0.456762	−	0.889589i	$-0.650991\pi$
$197$	−2525.92			−0.913525			−0.456762	+	0.889589i	$0.650991\pi$
$198$	−1335.67	−	3564.33i	−0.479404	−	1.27932i
$199$	−345.856			−0.123202			−0.0616008	−	0.998101i	$-0.519621\pi$
$199$	−345.856			−0.123202			−0.0616008	+	0.998101i	$0.519621\pi$
$200$	−83.4749	+	60.6480i	−0.0295128	+	0.0214423i
$201$	−2266.65	+	239.860i	−0.795409	+	0.0841713i
$202$	−1944.67	+	5985.07i	−0.677357	+	2.08469i
$203$	−1067.10	+	1468.74i	−0.368945	+	0.507809i
$204$	−170.989	+	154.179i	−0.0586844	+	0.0529151i
$205$	1622.83	+	527.290i	0.552895	+	0.179646i
$206$	33.0525	+	101.725i	0.0111790	+	0.0344054i
$207$	874.882	+	4087.48i	0.293761	+	1.37246i
$208$			445.322i			0.148450i
$209$	−819.772	+	4878.56i	−0.271315	+	1.61463i
$210$	361.163	−	1705.08i	0.118679	−	0.560295i
$211$	−119.492	−	164.467i	−0.0389866	−	0.0536604i	0.789079	−	0.614292i	$-0.210558\pi$
$211$	−119.492	−	164.467i	−0.0389866	−	0.0536604i	−0.828065	+	0.560632i	$0.810558\pi$
$212$	626.967	−	203.714i	0.203114	−	0.0659959i
$213$	242.082	−	419.986i	0.0778740	−	0.135103i
$214$	2337.90	+	1698.59i	0.746803	+	0.542584i
$215$	−1268.96	−	921.952i	−0.402522	−	0.292449i
$216$	−341.343	−	467.723i	−0.107525	−	0.147336i
$217$	−4549.61	+	1478.26i	−1.42326	+	0.462446i
$218$	1426.63	+	1963.58i	0.443227	+	0.610049i
$219$	4874.10	+	1032.41i	1.50393	+	0.318556i
$220$	−1250.72	+	186.059i	−0.383289	+	0.0570187i
$221$		−	39.8648i		−	0.0121339i
$222$	−2194.52	−	4919.58i	−0.663453	−	1.48730i
$223$	−570.787	−	1756.70i	−0.171402	−	0.527522i	0.828048	−	0.560657i	$-0.189451\pi$
$223$	−570.787	−	1756.70i	−0.171402	−	0.527522i	−0.999451	+	0.0331340i	$0.989451\pi$
$224$	−4010.51	−	1303.09i	−1.19627	−	0.388690i
$225$	−338.329	−	584.088i	−0.100246	−	0.173063i
$226$	−1851.63	+	2548.55i	−0.544993	+	0.750119i
$227$	1523.91	−	4690.11i	0.445575	−	1.37134i	−0.436278	−	0.899812i	$-0.643704\pi$
$227$	1523.91	−	4690.11i	0.445575	−	1.37134i	0.881852	−	0.471526i	$-0.156296\pi$
$228$	−513.973	−	4856.99i	−0.149292	−	1.41080i
$229$	−1300.37	+	944.774i	−0.375244	+	0.272631i	−0.759382	−	0.650645i	$-0.774499\pi$
$229$	−1300.37	+	944.774i	−0.375244	+	0.272631i	0.384138	+	0.923276i	$0.374499\pi$
$230$	2991.21			0.857541
$231$	−2093.29	+	2539.54i	−0.596227	+	0.723332i
$232$	431.597			0.122137
$233$	1339.67	−	973.327i	0.376673	−	0.273669i	−0.383300	−	0.923624i	$-0.625212\pi$
$233$	1339.67	−	973.327i	0.376673	−	0.273669i	0.759972	+	0.649955i	$0.225212\pi$
$234$	−647.223	−	67.0978i	−0.180813	−	0.0187450i
$235$	−107.618	+	331.213i	−0.0298732	+	0.0919402i
$236$	3268.78	−	4499.09i	0.901608	−	1.24096i
$237$	−3685.44	−	4087.26i	−1.01010	−	1.12024i
$238$	407.818	+	132.508i	0.111071	+	0.0360892i
$239$	1610.22	+	4955.75i	0.435802	+	1.34126i	0.892263	+	0.451516i	$0.149117\pi$
$239$	1610.22	+	4955.75i	0.435802	+	1.34126i	−0.456461	+	0.889743i	$0.650883\pi$
$240$	−1694.21	+	755.749i	−0.455669	+	0.203264i
$241$		−	1620.77i		−	0.433207i	−0.976260	−	0.216603i	$-0.930502\pi$
$241$		−	1620.77i		−	0.433207i	0.976260	−	0.216603i	$-0.0694978\pi$
$242$	4860.76	+	1681.03i	1.29116	+	0.446531i
$243$	3273.76	−	1905.62i	0.864247	−	0.503068i
$244$	−2540.33	−	3496.46i	−0.666507	−	0.917369i
$245$	197.855	−	64.2869i	0.0515938	−	0.0167638i
$246$	5936.70	+	3421.94i	1.53866	+	0.886891i
$247$	684.164	+	497.074i	0.176244	+	0.128049i
$248$	920.063	+	668.465i	0.235581	+	0.171159i
$249$	629.309	+	362.737i	0.160164	+	0.0923194i
$250$	−459.382	+	149.262i	−0.116216	+	0.0377607i
$251$	−4317.89	−	5943.07i	−1.08583	−	1.49451i	−0.852938	−	0.522012i	$-0.825182\pi$
$251$	−4317.89	−	5943.07i	−1.08583	−	1.49451i	−0.232890	−	0.972503i	$-0.574818\pi$
$252$	1317.38	−	2970.22i	0.329314	−	0.742484i
$253$	−5008.23	−	2611.41i	−1.24452	−	0.648925i
$254$		−	94.7715i		−	0.0234114i
$255$	151.663	−	67.6538i	0.0372452	−	0.0166143i
$256$	1533.41	+	4719.36i	0.374368	+	1.15219i
$257$	−7029.84	−	2284.13i	−1.70626	−	0.554398i	−0.716559	−	0.697527i	$-0.754284\pi$
$257$	−7029.84	−	2284.13i	−1.70626	−	0.554398i	−0.989704	+	0.143128i	$0.954284\pi$
$258$	−4218.06	−	4677.95i	−1.01785	−	1.12882i
$259$	−2737.66	+	3768.07i	−0.656796	+	0.904002i
$260$	−66.7974	+	205.581i	−0.0159331	+	0.0490370i
$261$	−291.150	+	2808.43i	−0.0690489	+	0.666043i
$262$	361.220	−	262.442i	0.0851766	−	0.0618844i
$263$	−1846.68			−0.432971			−0.216486	−	0.976286i	$-0.569459\pi$
$263$	−1846.68			−0.432971			−0.216486	+	0.976286i	$0.569459\pi$
$264$	780.943	+	47.7370i	0.182059	+	0.0111288i
$265$	−475.504			−0.110226
$266$	−7359.21	+	5346.78i	−1.69632	+	1.23245i
$267$	−348.102	−	3289.53i	−0.0797884	−	0.753992i
$268$	−939.631	+	2891.89i	−0.214168	+	0.659142i
$269$	3426.66	−	4716.39i	0.776680	−	1.06901i	−0.218960	−	0.975734i	$-0.570267\pi$
$269$	3426.66	−	4716.39i	0.776680	−	1.06901i	0.995640	−	0.0932745i	$-0.0297334\pi$
$270$	−843.121	−	2576.19i	−0.190040	−	0.580675i
$271$	7112.05	+	2310.84i	1.59419	+	0.517984i	0.965662	−	0.259801i	$-0.0836570\pi$
$271$	7112.05	+	2310.84i	1.59419	+	0.517984i	0.628530	+	0.777786i	$0.283657\pi$
$272$	−141.039	−	434.074i	−0.0314403	−	0.0967632i
$273$	229.195	+	513.800i	0.0508115	+	0.113907i
$274$		−	7319.60i		−	1.61384i
$275$	899.462	+	151.142i	0.197235	+	0.0331425i
$276$	5455.37	+	1155.53i	1.18976	+	0.252010i
$277$	337.723	+	464.836i	0.0732556	+	0.100828i	0.844073	−	0.536229i	$-0.180152\pi$
$277$	337.723	+	464.836i	0.0732556	+	0.100828i	−0.770817	+	0.637057i	$0.780152\pi$
$278$	2516.81	−	817.760i	0.542979	−	0.176424i
$279$	−4970.40	+	5535.96i	−1.06656	+	1.18792i
$280$	289.836	+	210.578i	0.0618607	+	0.0449444i
$281$	1379.05	+	1001.94i	0.292765	+	0.212707i	0.724466	−	0.689310i	$-0.242086\pi$
$281$	1379.05	+	1001.94i	0.292765	+	0.212707i	−0.431701	+	0.902017i	$0.642086\pi$
$282$	−698.405	+	1211.66i	−0.147480	+	0.255862i
$283$	7272.53	−	2362.99i	1.52759	−	0.496343i	0.579667	−	0.814853i	$-0.303182\pi$
$283$	7272.53	−	2362.99i	1.52759	−	0.496343i	0.947919	+	0.318510i	$0.103182\pi$
$284$	−380.117	−	523.186i	−0.0794217	−	0.109315i
$285$	−730.009	+	3446.44i	−0.151726	+	0.716314i
$286$	627.523	−	615.834i	0.129742	−	0.127325i
$287$		−	5924.66i		−	1.21854i
$288$	−6413.04	+	1372.64i	−1.31212	+	0.280847i
$289$	−1505.57	−	4633.68i	−0.306447	−	0.943147i
$290$	1921.56	+	624.354i	0.389097	+	0.126425i
$291$	1670.04	−	1505.86i	0.336424	−	0.303350i
$292$	3906.75	−	5377.18i	0.782963	−	1.07766i
$293$	−2222.05	+	6838.78i	−0.443050	+	1.36357i	0.441558	+	0.897233i	$0.354426\pi$
$293$	−2222.05	+	6838.78i	−0.443050	+	1.36357i	−0.884608	+	0.466336i	$0.845574\pi$
$294$	830.791	−	87.9155i	0.164805	−	0.0174399i
$295$	−3245.19	+	2357.77i	−0.640483	+	0.465338i
$296$	1107.27			0.217428
$297$	−837.442	+	5049.43i	−0.163614	+	0.986524i
$298$	5864.68			1.14004
$299$	−781.142	+	567.533i	−0.151086	+	0.109770i
$300$	−895.484	+	94.7613i	−0.172336	+	0.0182368i
$301$	−1682.94	+	5179.55i	−0.322269	+	0.991842i
$302$	673.951	−	927.614i	0.128416	−	0.176749i
$303$	6284.67	−	5666.82i	1.19157	−	1.07442i
$304$	9208.24	+	2991.94i	1.73727	+	0.564472i
$305$	963.317	+	2964.79i	0.180850	+	0.556600i
$306$	652.125	−	139.580i	0.121828	−	0.0260761i
$307$		−	3668.75i		−	0.682041i	−0.940056	−	0.341021i	$-0.889227\pi$
$307$		−	3668.75i		−	0.682041i	0.940056	−	0.341021i	$-0.110773\pi$
$308$	1956.36	+	3930.49i	0.361929	+	0.727144i
$309$	29.8039	−	140.707i	0.00548700	−	0.0259046i
$310$	3129.31	+	4307.12i	0.573332	+	0.789123i
$311$	3015.15	−	979.681i	0.549753	−	0.178626i	−0.0209521	−	0.999780i	$-0.506670\pi$
$311$	3015.15	−	979.681i	0.549753	−	0.178626i	0.570706	+	0.821155i	$0.306670\pi$
$312$	66.7927	−	115.878i	0.0121199	−	0.0210266i
$313$	5233.48	+	3802.34i	0.945092	+	0.686649i	0.949641	−	0.313340i	$-0.101448\pi$
$313$	5233.48	+	3802.34i	0.945092	+	0.686649i	−0.00454930	+	0.999990i	$0.501448\pi$
$314$	1283.27	+	932.348i	0.230634	+	0.167565i
$315$	−1565.76	+	1743.92i	−0.280066	+	0.311933i
$316$	−6982.56	+	2268.77i	−1.24304	+	0.403887i
$317$	−323.457	−	445.200i	−0.0573096	−	0.0788798i	0.779400	−	0.626526i	$-0.215524\pi$
$317$	−323.457	−	445.200i	−0.0573096	−	0.0788798i	−0.836710	+	0.547646i	$0.815524\pi$
$318$	−1868.07	−	395.686i	−0.329422	−	0.0697767i
$319$	−2672.23	−	2722.95i	−0.469016	−	0.477918i
$320$			1836.90i			0.320892i
$321$	−1583.06	−	3548.84i	−0.275258	−	0.617061i
$322$	−3209.41	−	9877.55i	−0.555446	−	1.70949i
$323$	−824.311	−	267.835i	−0.142000	−	0.0461385i
$324$	−542.477	−	5024.17i	−0.0930173	−	0.861484i
$325$	91.6457	−	126.139i	0.0156418	−	0.0215291i
$326$	2208.86	−	6798.17i	0.375268	−	1.15496i
$327$	−343.456	−	3245.62i	−0.0580831	−	0.548878i
$328$	−1139.50	+	827.892i	−0.191824	+	0.139368i
$329$	1209.20			0.202630
$330$	3407.87	+	1342.26i	0.568476	+	0.223905i
$331$	−8288.46			−1.37636			−0.688180	−	0.725540i	$-0.741590\pi$
$331$	−8288.46			−1.37636			−0.688180	+	0.725540i	$0.741590\pi$
$332$	783.945	−	569.570i	0.129592	−	0.0941542i
$333$	−746.951	+	7205.06i	−0.122921	+	1.18569i
$334$	−1554.71	+	4784.89i	−0.254700	+	0.783885i
$335$	1289.17	−	1774.39i	0.210253	−	0.289388i
$336$	4313.42	+	4783.72i	0.700347	+	0.776706i
$337$	1267.42	+	411.810i	0.204869	+	0.0665659i	0.409654	−	0.912241i	$-0.365650\pi$
$337$	1267.42	+	411.810i	0.204869	+	0.0665659i	−0.204785	+	0.978807i	$0.565650\pi$
$338$	2576.99	+	7931.16i	0.414703	+	1.27633i
$339$	3868.58	−	1725.69i	0.619801	−	0.276480i
$340$		−	221.544i		−	0.0353380i
$341$	−1479.21	−	9943.46i	−0.234908	−	1.57909i
$342$	−5735.85	+	12932.3i	−0.906898	+	2.04473i
$343$	−3924.67	−	5401.84i	−0.617819	−	0.850355i
$344$	1231.36	−	400.092i	0.192995	−	0.0627079i
$345$	−3484.81	−	2008.66i	−0.543814	−	0.313457i
$346$	8460.66	+	6147.03i	1.31459	+	0.955105i
$347$	1704.77	+	1238.58i	0.263737	+	0.191616i	0.711793	−	0.702390i	$-0.247884\pi$
$347$	1704.77	+	1238.58i	0.263737	+	0.191616i	−0.448056	+	0.894005i	$0.647884\pi$
$348$	3263.36	+	1881.02i	0.502685	+	0.289750i
$349$	−7864.16	+	2555.22i	−1.20619	+	0.391914i	−0.842033	−	0.539426i	$-0.818641\pi$
$349$	−7864.16	+	2555.22i	−1.20619	+	0.391914i	−0.364153	+	0.931339i	$0.618641\pi$
$350$	985.787	+	1356.82i	0.150550	+	0.207214i
$351$	708.968	+	512.794i	0.107812	+	0.0779798i
$352$	4097.17	−	7857.64i	0.620397	−	1.18981i
$353$		−	2878.77i		−	0.434056i	−0.976165	−	0.217028i	$-0.930364\pi$
$353$		−	2878.77i		−	0.434056i	0.976165	−	0.217028i	$-0.0696363\pi$
$354$	−14711.1	+	6562.32i	−2.20872	+	0.985264i
$355$	144.144	+	443.630i	0.0215503	+	0.0663251i
$356$	−4196.91	−	1363.66i	−0.624820	−	0.203016i
$357$	−386.133	−	428.233i	−0.0572446	−	0.0634860i
$358$	−4900.84	+	6745.42i	−0.723512	+	0.995829i
$359$	−2240.28	+	6894.87i	−0.329352	+	1.01364i	0.640085	+	0.768304i	$0.278899\pi$
$359$	−2240.28	+	6894.87i	−0.329352	+	1.01364i	−0.969438	+	0.245338i	$0.921101\pi$
$360$	554.205	+	57.4546i	0.0811366	+	0.00841145i
$361$	9325.91	−	6775.67i	1.35966	−	0.987851i
$362$	−4359.47			−0.632952
$363$	−4534.02	−	5222.53i	−0.655577	−	0.755129i
$364$	750.540			0.108074
$365$	−3878.56	+	2817.94i	−0.556200	+	0.404103i
$366$	1317.38	+	12449.1i	0.188144	+	1.77794i
$367$	−918.801	+	2827.78i	−0.130684	+	0.402204i	−0.994894	−	0.100928i	$-0.967819\pi$
$367$	−918.801	+	2827.78i	−0.130684	+	0.402204i	0.864210	+	0.503132i	$0.167819\pi$
$368$	−6497.69	+	8943.30i	−0.920422	+	1.26685i
$369$	−4618.45	−	7973.25i	−0.651563	−	1.12485i
$370$	4929.80	+	1601.79i	0.692671	+	0.225062i
$371$	510.191	+	1570.21i	0.0713957	+	0.219733i
$372$	4043.36	+	9064.22i	0.563544	+	1.26333i
$373$			9021.06i			1.25226i	0.779719	+	0.626130i	$0.215362\pi$
$373$			9021.06i			1.25226i	−0.779719	+	0.626130i	$0.784638\pi$
$374$	−416.630	+	799.023i	−0.0576027	+	0.110472i
$375$	635.421	+	134.592i	0.0875013	+	0.0185341i
$376$	−168.969	−	232.566i	−0.0231753	−	0.0318981i
$377$	−620.269	+	201.538i	−0.0847360	+	0.0275324i
$378$	−7602.47	+	5548.27i	−1.03447	+	0.754953i
$379$	−4021.80	−	2922.01i	−0.545082	−	0.396025i	0.280887	−	0.959741i	$-0.409371\pi$
$379$	−4021.80	−	2922.01i	−0.545082	−	0.396025i	−0.825969	+	0.563716i	$0.809371\pi$
$380$	3802.16	+	2762.43i	0.513281	+	0.372921i
$381$	−63.6411	+	110.410i	−0.00855757	+	0.0148464i
$382$	−9582.42	+	3113.52i	−1.28345	+	0.417020i
$383$	6844.77	+	9421.02i	0.913190	+	1.25690i	0.966066	+	0.258297i	$0.0831612\pi$
$383$	6844.77	+	9421.02i	0.913190	+	1.25690i	−0.0528760	+	0.998601i	$0.516839\pi$
$384$	563.754	−	2661.53i	0.0749191	−	0.353700i
$385$	−465.976	−	3132.36i	−0.0616840	−	0.414650i
$386$		−	19332.2i		−	2.54917i
$387$	1772.76	+	8282.41i	0.232854	+	1.08790i
$388$	−927.012	−	2853.05i	−0.121294	−	0.373303i
$389$	−3669.25	−	1192.21i	−0.478247	−	0.155392i	0.0599663	−	0.998200i	$-0.480901\pi$
$389$	−3669.25	−	1192.21i	−0.478247	−	0.155392i	−0.538214	+	0.842808i	$0.680901\pi$
$390$	465.007	−	419.291i	0.0603757	−	0.0544401i
$391$	581.666	−	800.594i	0.0752330	−	0.103549i
$392$	−53.0653	+	163.318i	−0.00683725	+	0.0210429i
$393$	−597.064	+	63.1821i	−0.0766358	+	0.00810970i
$394$	7896.51	−	5737.15i	1.00970	−	0.733587i
$395$	5295.71			0.674573
$396$	5696.75	+	3764.50i	0.722910	+	0.477711i
$397$	−14198.5			−1.79497			−0.897486	−	0.441042i	$-0.854609\pi$
$397$	−14198.5			−1.79497			−0.897486	+	0.441042i	$0.854609\pi$
$398$	1081.21	−	785.547i	0.136172	−	0.0989345i
$399$	12164.1	−	1287.22i	1.52623	−	0.161508i
$400$	551.625	−	1697.73i	0.0689531	−	0.212216i
$401$	−4540.17	+	6249.01i	−0.565400	+	0.778206i	−0.992001	−	0.126234i	$-0.959711\pi$
$401$	−4540.17	+	6249.01i	−0.565400	+	0.778206i	0.426601	+	0.904440i	$0.359711\pi$
$402$	6541.19	−	5898.12i	0.811554	−	0.731770i
$403$	−1634.41	−	531.052i	−0.202024	−	0.0656417i
$404$	−3488.52	−	10736.6i	−0.429605	−	1.32219i
$405$	−747.720	+	3567.48i	−0.0917396	+	0.437703i
$406$		−	7015.28i		−	0.857543i
$407$	−6855.64	−	6985.76i	−0.834942	−	0.850790i
$408$	−28.4055	+	134.105i	−0.00344677	+	0.0162725i
$409$	−519.564	−	715.118i	−0.0628136	−	0.0864555i	0.776454	−	0.630173i	$-0.217016\pi$
$409$	−519.564	−	715.118i	−0.0628136	−	0.0864555i	−0.839268	+	0.543718i	$0.817016\pi$
$410$	−6270.92	+	2037.55i	−0.755363	+	0.245432i
$411$	−4915.27	+	8527.46i	−0.589909	+	1.02343i
$412$	−155.230	−	112.781i	−0.0185622	−	0.0134862i
$413$	11267.7	+	8186.50i	1.34249	+	0.975378i
$414$	−12019.0	−	10791.1i	−1.42681	−	1.28105i
$415$	−664.738	+	215.986i	−0.0786282	+	0.0255478i
$416$	−890.428	−	1225.57i	−0.104944	−	0.144443i
$417$	−3481.27	−	737.386i	−0.408821	−	0.0865946i
$418$	−8517.96	−	17113.3i	−0.996716	−	2.00248i
$419$		−	1827.38i		−	0.213062i	−0.994309	−	0.106531i	$-0.966026\pi$
$419$		−	1827.38i		−	0.213062i	0.994309	−	0.106531i	$-0.0339744\pi$
$420$	1273.73	+	2855.39i	0.147980	+	0.331735i
$421$	1699.73	+	5231.25i	0.196770	+	0.605595i	0.999951	+	0.00986051i	$0.00313875\pi$
$421$	1699.73	+	5231.25i	0.196770	+	0.605595i	−0.803182	+	0.595734i	$0.796861\pi$
$422$	747.109	+	242.751i	0.0861818	+	0.0280022i
$423$	1627.31	−	942.606i	0.187050	−	0.108348i
$424$	230.707	−	317.541i	0.0264248	−	0.0363706i
$425$	−49.3808	+	151.979i	−0.00563605	+	0.0173460i
$426$	197.124	+	1862.80i	0.0224194	+	0.211861i
$427$	8756.71	−	6362.12i	0.992428	−	0.721041i
$428$	−5184.00			−0.585463
$429$	−1144.62	+	296.062i	−0.128818	+	0.0333194i
$430$	6061.05			0.679744
$431$	7824.42	−	5684.78i	0.874453	−	0.635327i	−0.0573252	−	0.998356i	$-0.518257\pi$
$431$	7824.42	−	5684.78i	0.874453	−	0.635327i	0.931778	+	0.363028i	$0.118257\pi$
$432$	9533.94	+	3075.35i	1.06181	+	0.342507i
$433$	3798.81	−	11691.5i	0.421615	−	1.29760i	−0.484584	−	0.874745i	$-0.661029\pi$
$433$	3798.81	−	11691.5i	0.421615	−	1.29760i	0.906199	−	0.422853i	$-0.138971\pi$
$434$	10865.4	−	14954.9i	1.20174	−	1.65405i
$435$	−1819.39	−	2017.75i	−0.200536	−	0.222400i
$436$	−4140.90	−	1345.46i	−0.454846	−	0.147789i
$437$	6487.09	+	19965.2i	0.710114	+	2.18551i
$438$	−17582.3	+	7843.09i	−1.91807	+	0.855611i
$439$		−	242.496i		−	0.0263638i	−0.999913	−	0.0131819i	$-0.995804\pi$
$439$		−	242.496i		−	0.0263638i	0.999913	−	0.0131819i	$-0.00419606\pi$
$440$	−537.337	+	527.328i	−0.0582194	+	0.0571349i
$441$	−1026.92	−	455.471i	−0.110887	−	0.0491817i
$442$	90.5453	+	124.625i	0.00974389	+	0.0134113i
$443$	8546.16	−	2776.82i	0.916570	−	0.297812i	0.187511	−	0.982263i	$-0.439958\pi$
$443$	8546.16	−	2776.82i	0.916570	−	0.297812i	0.729059	+	0.684451i	$0.239958\pi$
$444$	8372.20	+	4825.78i	0.894881	+	0.515814i
$445$	2575.12	+	1870.93i	0.274320	+	0.199305i
$446$	5774.41	+	4195.35i	0.613063	+	0.445416i
$447$	−6832.46	−	3938.26i	−0.722962	−	0.416719i
$448$	6065.79	−	1970.89i	0.639691	−	0.207848i
$449$	3886.68	+	5349.55i	0.408516	+	0.562274i	0.962856	−	0.270017i	$-0.0870292\pi$
$449$	3886.68	+	5349.55i	0.408516	+	0.562274i	−0.554340	+	0.832290i	$0.687029\pi$
$450$	2384.33	+	1057.52i	0.249774	+	0.110782i
$451$	12278.3	+	2063.20i	1.28196	+	0.215415i
$452$		−	5651.08i		−	0.588063i
$453$	−1408.08	+	628.113i	−0.146042	+	0.0651464i
$454$	5888.67	+	18123.5i	0.608742	+	1.87352i
$455$	−514.868	−	167.291i	−0.0530492	−	0.0172367i
$456$	−1947.34	−	2159.66i	−0.199984	−	0.221788i
$457$	4.86814	−	6.70041i	0.000498297	−	0.000685847i	−0.808768	−	0.588128i	$-0.799865\pi$
$457$	4.86814	−	6.70041i	0.000498297	−	0.000685847i	0.809266	+	0.587442i	$0.199865\pi$
$458$	1919.33	−	5907.09i	0.195817	−	0.602664i
$459$	−853.468	−	275.302i	−0.0867897	−	0.0279957i
$460$	−4341.11	+	3154.00i	−0.440011	+	0.319687i
$461$	−10284.7			−1.03906			−0.519530	−	0.854452i	$-0.673893\pi$
$461$	−10284.7			−1.03906			−0.519530	+	0.854452i	$0.673893\pi$
$462$	775.928	−	12693.6i	0.0781373	−	1.27827i
$463$	10783.3			1.08238			0.541192	−	0.840899i	$-0.317973\pi$
$463$	10783.3			1.08238			0.541192	+	0.840899i	$0.317973\pi$
$464$	−6040.87	+	4388.95i	−0.604397	+	0.439120i
$465$	−753.371	−	7119.27i	−0.0751328	−	0.709996i
$466$	−1977.34	+	6085.62i	−0.196563	+	0.604959i
$467$	4471.25	−	6154.15i	0.443051	−	0.609808i	−0.527835	−	0.849347i	$-0.676996\pi$
$467$	4471.25	−	6154.15i	0.443051	−	0.609808i	0.970887	+	0.239539i	$0.0769962\pi$
$468$	1010.06	−	585.068i	0.0997647	−	0.0577880i
$469$	−7242.58	−	2353.26i	−0.713073	−	0.231692i
$470$	−415.855	−	1279.87i	−0.0408126	−	0.125608i
$471$	−868.936	−	1947.94i	−0.0850074	−	0.190566i
$472$		−	3311.09i		−	0.322893i
$473$	−10148.1	−	5291.47i	−0.986492	−	0.514381i
$474$	20804.8	+	4406.78i	2.01603	+	0.427026i
$475$	−1992.54	−	2742.50i	−0.192472	−	0.264915i
$476$	−731.581	+	237.705i	−0.0704453	+	0.0228891i
$477$	1910.62	+	1715.43i	0.183399	+	0.164663i
$478$	−16289.9	−	11835.3i	−1.55875	−	1.13250i
$479$	−9454.11	−	6868.81i	−0.901815	−	0.655207i	0.0371167	−	0.999311i	$-0.488183\pi$
$479$	−9454.11	−	6868.81i	−0.901815	−	0.655207i	−0.938931	+	0.344104i	$0.888183\pi$
$480$	3151.48	−	5467.48i	0.299677	−	0.519907i
$481$	−1591.31	+	517.048i	−0.150847	+	0.0490132i
$482$	3681.27	+	5066.83i	0.347878	+	0.478813i
$483$	−2893.97	+	13662.7i	−0.272630	+	1.28711i
$484$	−8826.88	+	2685.64i	−0.828970	+	0.252220i
$485$			2163.81i			0.202585i
$486$	−5906.16	+	13393.1i	−0.551253	+	1.25004i
$487$	−4683.45	−	14414.2i	−0.435785	−	1.34121i	−0.892280	−	0.451482i	$-0.850895\pi$
$487$	−4683.45	−	14414.2i	−0.435785	−	1.34121i	0.456495	−	0.889726i	$-0.349105\pi$
$488$	−2447.27	−	795.165i	−0.227013	−	0.0737611i
$489$	−7138.48	+	6436.69i	−0.660150	+	0.595250i
$490$	−472.516	+	650.363i	−0.0435635	+	0.0599600i
$491$	−173.951	+	535.368i	−0.0159884	+	0.0492073i	−0.958732	−	0.284310i	$-0.908236\pi$
$491$	−173.951	+	535.368i	−0.0159884	+	0.0492073i	0.942744	+	0.333517i	$0.108236\pi$
$492$	−12224.0	+	1293.57i	−1.12013	+	0.118533i
$493$	540.772	−	392.894i	0.0494019	−	0.0358926i
$494$	−3267.84			−0.297625
$495$	−3068.87	−	3852.21i	−0.278657	−	0.349786i
$496$	−19675.4			−1.78115
$497$	1310.29	−	951.983i	0.118259	−	0.0859201i
$498$	−2791.23	+	295.372i	−0.251161	+	0.0265782i
$499$	4765.99	−	14668.2i	0.427565	−	1.31591i	−0.472951	−	0.881089i	$-0.656811\pi$
$499$	4765.99	−	14668.2i	0.427565	−	1.31591i	0.900516	−	0.434822i	$-0.143189\pi$
$500$	509.311	−	701.006i	0.0455541	−	0.0626999i
$501$	5024.42	−	4530.46i	0.448053	−	0.404004i
$502$	26997.1	+	8771.90i	2.40028	+	0.779898i
$503$	2867.21	+	8824.36i	0.254160	+	0.782224i	0.993994	+	0.109434i	$0.0349040\pi$
$503$	2867.21	+	8824.36i	0.254160	+	0.782224i	−0.739834	+	0.672789i	$0.765096\pi$
$504$	−404.907	−	1891.74i	−0.0357857	−	0.167192i
$505$			8142.82i			0.717526i
$506$	21588.0	−	3211.47i	1.89665	−	0.282149i
$507$	2323.71	−	10970.4i	0.203549	−	0.960975i
$508$	99.9292	+	137.541i	0.00872764	+	0.0120126i
$509$	−464.459	+	150.912i	−0.0404455	+	0.0131415i	−0.329170	−	0.944271i	$-0.606769\pi$
$509$	−464.459	+	150.912i	−0.0404455	+	0.0131415i	0.288724	+	0.957412i	$0.406769\pi$
$510$	−320.466	+	555.973i	−0.0278244	+	0.0482724i
$511$	13466.9	+	9784.26i	1.16583	+	0.847026i
$512$	−12124.2	−	8808.76i	−1.04652	−	0.760344i
$513$	15366.7	−	11214.6i	1.32252	−	0.965176i
$514$	27164.6	−	8826.32i	2.33109	−	0.757417i
$515$	81.3490	+	111.967i	0.00696052	+	0.00958033i
$516$	11054.2	+	2341.44i	0.943085	+	0.199760i
$517$	−421.090	+	2505.96i	−0.0358212	+	0.213176i
$518$		−	17997.8i		−	1.52660i
$519$	−5728.95	−	12842.9i	−0.484534	−	1.08621i
$520$	39.7707	+	122.402i	0.00335397	+	0.0103224i
$521$	−15933.5	−	5177.11i	−1.33985	−	0.435342i	−0.450581	−	0.892735i	$-0.648783\pi$
$521$	−15933.5	−	5177.11i	−1.33985	−	0.435342i	−0.889265	+	0.457393i	$0.848783\pi$
$522$	−5468.62	−	9440.97i	−0.458534	−	0.791609i
$523$	8568.06	−	11792.9i	0.716358	−	0.985982i	−0.283279	−	0.959037i	$-0.591422\pi$
$523$	8568.06	−	11792.9i	0.716358	−	0.985982i	0.999637	−	0.0269443i	$-0.00857766\pi$
$524$	−247.510	+	761.758i	−0.0206346	+	0.0635068i
$525$	−237.325	−	2242.69i	−0.0197290	−	0.186437i
$526$	5773.09	−	4194.39i	0.478553	−	0.347689i
$527$	1761.32			0.145587
$528$	−11415.9	+	7273.32i	−0.940938	+	0.599490i
$529$	−11801.3			−0.969945
$530$	1486.52	−	1080.02i	0.121830	−	0.0885150i
$531$	21545.4	+	2233.62i	1.76081	+	0.182544i
$532$	5042.57	−	15519.4i	0.410946	−	1.26476i
$533$	1251.03	−	1721.90i	0.101667	−	0.139932i
$534$	8559.77	+	9493.04i	0.693666	+	0.769296i
$535$	3556.21	+	1155.48i	0.287380	+	0.0933755i
$536$	559.450	+	1721.81i	0.0450831	+	0.138752i
$537$	10239.3	−	4567.51i	0.822824	−	0.367044i
$538$			22527.3i			1.80525i
$539$	1358.93	−	676.393i	0.108596	−	0.0540525i
$540$	3940.01	+	2849.80i	0.313983	+	0.227103i
$541$	2539.37	+	3495.15i	0.201804	+	0.277760i	0.897910	−	0.440180i	$-0.145085\pi$
$541$	2539.37	+	3495.15i	0.201804	+	0.277760i	−0.696105	+	0.717940i	$0.745085\pi$
$542$	−27482.3	+	8929.53i	−2.17798	+	0.707668i
$543$	5078.85	+	2927.48i	0.401389	+	0.231363i
$544$	1256.09	+	912.602i	0.0989970	+	0.0719256i
$545$	2540.75	+	1845.96i	0.199695	+	0.145087i
$546$	−1883.51	−	1085.66i	−0.147631	−	0.0850955i
$547$	−17221.7	+	5595.68i	−1.34616	+	0.437393i	−0.891398	−	0.453222i	$-0.850275\pi$
$547$	−17221.7	+	5595.68i	−1.34616	+	0.437393i	−0.454759	+	0.890615i	$0.650275\pi$
$548$	7717.96	+	10622.9i	0.601633	+	0.828076i
$549$	6825.08	−	15388.1i	0.530578	−	1.19626i
$550$	−3155.18	+	1570.46i	−0.244613	+	0.121754i
$551$			14179.8i			1.09633i
$552$	3032.16	−	1352.58i	0.233799	−	0.104293i
$553$	−5682.02	−	17487.5i	−0.436933	−	1.34474i
$554$	−2111.57	−	686.092i	−0.161935	−	0.0526160i
$555$	−4667.67	−	5176.58i	−0.356994	−	0.395916i
$556$	−2790.35	+	3840.59i	−0.212837	+	0.292944i
$557$	−4651.78	+	14316.7i	−0.353864	+	1.08908i	0.602801	+	0.797891i	$0.294051\pi$
$557$	−4651.78	+	14316.7i	−0.353864	+	1.08908i	−0.956665	+	0.291190i	$0.905949\pi$
$558$	2964.53	−	28595.8i	0.224908	−	2.16946i
$559$	−1582.82	+	1149.98i	−0.119760	+	0.0870110i
$560$	−6198.09			−0.467709
$561$	1021.94	−	651.099i	0.0769099	−	0.0490008i
$562$	−6586.88			−0.494396
$563$	16527.0	−	12007.6i	1.23718	−	0.898862i	0.239771	−	0.970830i	$-0.422928\pi$
$563$	16527.0	−	12007.6i	1.23718	−	0.898862i	0.997407	+	0.0719675i	$0.0229278\pi$
$564$	−264.011	−	2494.88i	−0.0197108	−	0.186265i
$565$	−1259.59	+	3876.62i	−0.0937901	+	0.288656i
$566$	−17368.2	+	23905.3i	−1.28983	+	1.77529i
$567$	12582.8	−	1358.61i	0.931971	−	0.100628i
$568$	−366.192	−	118.983i	−0.0270512	−	0.00878946i
$569$	1746.65	+	5375.63i	0.128688	+	0.396060i	0.994555	−	0.104214i	$-0.0332327\pi$
$569$	1746.65	+	5375.63i	0.128688	+	0.396060i	−0.865867	+	0.500274i	$0.833233\pi$
$570$	−5545.79	−	12432.3i	−0.407522	−	0.913565i
$571$		−	17150.3i		−	1.25695i	−0.777831	−	0.628474i	$-0.783680\pi$
$571$		−	17150.3i		−	1.25695i	0.777831	−	0.628474i	$-0.216320\pi$
$572$	−261.368	+	1555.43i	−0.0191055	+	0.113699i
$573$	13254.5	+	2807.50i	0.966342	+	0.204686i
$574$	13456.7	+	18521.6i	0.978526	+	1.34683i
$575$	3680.99	−	1196.03i	0.266971	−	0.0867440i
$576$	6626.80	−	7380.84i	0.479369	−	0.533915i
$577$	20048.2	+	14565.9i	1.44648	+	1.05093i	0.986638	+	0.162929i	$0.0520941\pi$
$577$	20048.2	+	14565.9i	1.44648	+	1.05093i	0.459842	+	0.888001i	$0.347906\pi$
$578$	15231.3	+	11066.2i	1.09608	+	0.796352i
$579$	−12982.0	+	22522.3i	−0.931799	+	1.61657i
$580$	−3447.08	+	1120.02i	−0.246779	+	0.0801835i
$581$	1426.46	+	1963.35i	0.101858	+	0.140195i
$582$	−1800.59	+	8500.77i	−0.128242	+	0.605444i
$583$	−3431.78	+	510.519i	−0.243791	+	0.0362668i
$584$		−	3957.32i		−	0.280402i
$585$	−823.304	+	176.220i	−0.0581870	+	0.0124543i
$586$	−8586.43	−	26426.3i	−0.605293	−	1.86290i
$587$	7883.97	+	2561.66i	0.554355	+	0.180121i	0.572780	−	0.819709i	$-0.305865\pi$
$587$	7883.97	+	2561.66i	0.554355	+	0.180121i	−0.0184246	+	0.999830i	$0.505865\pi$
$588$	−1113.02	+	1003.60i	−0.0780614	+	0.0703871i
$589$	−21961.9	+	30227.9i	−1.53637	+	2.11464i
$590$	4789.87	−	14741.7i	0.334230	−	1.02865i
$591$	−13052.2	+	1381.20i	−0.908452	+	0.0961337i
$592$	−15497.9	+	11259.9i	−1.07595	+	0.781722i
$593$	4608.61			0.319145			0.159573	−	0.987186i	$-0.448988\pi$
$593$	4608.61			0.319145			0.159573	+	0.987186i	$0.448988\pi$
$594$	−8850.83	−	17687.6i	−0.611370	−	1.22177i
$595$	554.846			0.0382293
$596$	−8511.35	+	6183.86i	−0.584964	+	0.425001i
$597$	−1787.14	+	189.118i	−0.122517	+	0.0129650i
$598$	1152.96	−	3548.43i	0.0788426	−	0.242652i
$599$	−6305.20	+	8678.36i	−0.430089	+	0.591967i	−0.967974	−	0.251051i	$-0.919224\pi$
$599$	−6305.20	+	8678.36i	−0.430089	+	0.591967i	0.537884	+	0.843019i	$0.319224\pi$
$600$	−398.177	+	359.032i	−0.0270925	+	0.0244290i
$601$	−21504.7	−	6987.31i	−1.45956	−	0.474240i	−0.531625	−	0.846980i	$-0.678418\pi$
$601$	−21504.7	−	6987.31i	−1.45956	−	0.474240i	−0.927936	+	0.372740i	$0.878418\pi$
$602$	−6503.19	−	20014.8i	−0.440283	−	1.35505i
$603$	−11581.3	+	2478.86i	−0.782135	+	0.167408i
$604$			2056.87i			0.138564i
$605$	6653.82	+	125.117i	0.447135	+	0.00840783i
$606$	−6775.97	+	31990.0i	−0.454216	+	2.14440i
$607$	−6686.61	−	9203.33i	−0.447119	−	0.615406i	0.524657	−	0.851314i	$-0.324194\pi$
$607$	−6686.61	−	9203.33i	−0.447119	−	0.615406i	−0.971775	+	0.235908i	$0.924194\pi$
$608$	−31324.4	+	10177.9i	−2.08943	+	0.678896i
$609$	−4710.91	+	8172.92i	−0.313458	+	0.543815i
$610$	−9745.46	−	7080.49i	−0.646856	−	0.469969i
$611$	351.433	+	255.331i	0.0232691	+	0.0169060i
$612$	−799.244	+	890.187i	−0.0527901	+	0.0587968i
$613$	13872.2	−	4507.34i	0.914016	−	0.296982i	0.186006	−	0.982549i	$-0.440446\pi$
$613$	13872.2	−	4507.34i	0.914016	−	0.296982i	0.728010	+	0.685567i	$0.240446\pi$
$614$	8332.88	+	11469.2i	0.547700	+	0.753844i
$615$	8673.99	+	1837.28i	0.568730	+	0.120466i
$616$	2317.87	+	1208.60i	0.151607	+	0.0790515i
$617$			4049.47i			0.264223i	0.991235	+	0.132111i	$0.0421757\pi$
$617$			4049.47i			0.264223i	−0.991235	+	0.132111i	$0.957824\pi$
$618$	226.416	+	507.570i	0.0147375	+	0.0330380i
$619$	5974.71	+	18388.3i	0.387954	+	1.19400i	0.934314	+	0.356450i	$0.116013\pi$
$619$	5974.71	+	18388.3i	0.387954	+	1.19400i	−0.546360	+	0.837550i	$0.683987\pi$
$620$	−9083.06	−	2951.27i	−0.588362	−	0.191170i
$621$	6755.86	+	20642.8i	0.436559	+	1.33393i
$622$	−7200.77	+	9911.01i	−0.464187	+	0.638899i
$623$	3415.22	−	10511.0i	0.219627	−	0.675943i
$624$	243.507	+	2301.12i	0.0156219	+	0.147626i
$625$	−505.636	+	367.366i	−0.0323607	+	0.0235114i
$626$	−24997.2			−1.59599
$627$	−1568.36	+	25657.2i	−0.0998952	+	1.63421i
$628$	−2845.48			−0.180807
$629$	1387.36	−	1007.98i	0.0879453	−	0.0638960i
$630$	933.880	−	9008.17i	0.0590582	−	0.569673i
$631$	2137.38	−	6578.18i	0.134846	−	0.415013i	−0.860720	−	0.509079i	$-0.829986\pi$
$631$	2137.38	−	6578.18i	0.134846	−	0.415013i	0.995566	+	0.0940654i	$0.0299863\pi$
$632$	−2569.40	+	3536.47i	−0.161717	+	0.222584i
$633$	−707.383	−	784.508i	−0.0444170	−	0.0492597i
$634$	2022.37	+	657.109i	0.126686	+	0.0411627i
$635$	−37.8941	−	116.626i	−0.00236816	−	0.00728846i
$636$	3128.33	−	1395.48i	0.195042	−	0.0870039i
$637$		−	259.492i		−	0.0161404i
$638$	14538.6	+	2443.00i	0.902174	+	0.151597i
$639$	1021.26	−	2302.56i	0.0632242	−	0.142548i
$640$	1538.75	+	2117.91i	0.0950383	+	0.130809i
$641$	−13626.6	+	4427.55i	−0.839654	+	0.272820i	−0.697106	−	0.716968i	$-0.745529\pi$
$641$	−13626.6	+	4427.55i	−0.839654	+	0.272820i	−0.142548	+	0.989788i	$0.545529\pi$
$642$	13009.5	+	7498.72i	0.799755	+	0.460983i
$643$	−4113.66	−	2988.75i	−0.252297	−	0.183305i	0.454447	−	0.890774i	$-0.349837\pi$
$643$	−4113.66	−	2988.75i	−0.252297	−	0.183305i	−0.706744	+	0.707469i	$0.749837\pi$
$644$	15072.9	+	10951.1i	0.922291	+	0.670084i
$645$	−7061.22	−	4070.13i	−0.431063	−	0.248467i
$646$	3185.29	−	1034.96i	0.193999	−	0.0630342i
$647$	6968.90	+	9591.86i	0.423455	+	0.582836i	0.966436	−	0.256909i	$-0.0827042\pi$
$647$	6968.90	+	9591.86i	0.423455	+	0.582836i	−0.542980	+	0.839745i	$0.682704\pi$
$648$	−2019.58	−	2230.21i	−0.122433	−	0.135202i
$649$	−20889.7	+	20500.6i	−1.26347	+	1.23993i
$650$			602.492i			0.0363564i
$651$	−22700.9	+	10126.4i	−1.36669	+	0.609653i
$652$	3962.45	+	12195.2i	0.238009	+	0.732516i
$653$	−11196.4	−	3637.95i	−0.670981	−	0.218015i	−0.0463388	−	0.998926i	$-0.514755\pi$
$653$	−11196.4	−	3637.95i	−0.670981	−	0.218015i	−0.624643	+	0.780911i	$0.714755\pi$
$654$	8445.53	+	9366.34i	0.504964	+	0.560020i
$655$	339.583	−	467.395i	0.0202574	−	0.0278819i
$656$	7530.10	−	23175.3i	0.448172	−	1.37933i
$657$	25750.5	+	2669.56i	1.52911	+	0.158523i
$658$	−3780.19	+	2746.47i	−0.223962	+	0.162718i
$659$	−10218.3			−0.604016			−0.302008	−	0.953305i	$-0.597657\pi$
$659$	−10218.3			−0.604016			−0.302008	+	0.953305i	$0.597657\pi$
$660$	−6361.11	+	1645.33i	−0.375160	+	0.0970371i
$661$	16776.9			0.987208			0.493604	−	0.869687i	$-0.335679\pi$
$661$	16776.9			0.987208			0.493604	+	0.869687i	$0.335679\pi$
$662$	25911.3	−	18825.7i	1.52126	−	1.10526i
$663$	−21.7985	−	205.993i	−0.00127690	−	0.0120665i
$664$	178.285	−	548.704i	0.0104199	−	0.0320691i
$665$	−6918.37	+	9522.33i	−0.403433	+	0.555278i
$666$	−14029.8	−	24221.0i	−0.816283	−	1.40922i
$667$	−15397.3	−	5002.90i	−0.893834	−	0.290424i
$668$	−2788.97	−	8583.57i	−0.161540	−	0.497168i
$669$	−3910.01	−	8765.30i	−0.225964	−	0.506556i
$670$			8475.18i			0.488694i
$671$	10135.5	+	20363.1i	0.583125	+	1.17155i
$672$	−21436.1	−	4540.49i	−1.23053	−	0.260644i
$673$	−1319.34	−	1815.91i	−0.0755671	−	0.104009i	0.769560	−	0.638574i	$-0.220475\pi$
$673$	−1319.34	−	1815.91i	−0.0755671	−	0.104009i	−0.845127	+	0.534565i	$0.820475\pi$
$674$	−4897.55	+	1591.31i	−0.279891	+	0.0909421i
$675$	−2067.63	−	2833.16i	−0.117901	−	0.161553i
$676$	−12102.8	−	8793.16i	−0.688595	−	0.500294i
$677$	−4823.93	−	3504.79i	−0.273853	−	0.198966i	0.442379	−	0.896828i	$-0.354135\pi$
$677$	−4823.93	−	3504.79i	−0.273853	−	0.198966i	−0.716232	+	0.697862i	$0.754135\pi$
$678$	−8174.35	+	14181.6i	−0.463029	+	0.803306i
$679$	7145.32	−	2321.65i	0.403847	−	0.131218i
$680$	−77.5323	−	106.714i	−0.00437239	−	0.00601808i
$681$	5309.90	−	25068.5i	0.298789	−	1.41061i
$682$	27209.0	+	27725.4i	1.52769	+	1.55669i
$683$			13919.3i			0.779803i	0.920857	+	0.389901i	$0.127491\pi$
$683$			13919.3i			0.779803i	−0.920857	+	0.389901i	$0.872509\pi$
$684$	−5311.71	−	24816.5i	−0.296927	−	1.38725i
$685$	−2926.72	−	9007.53i	−0.163247	−	0.502424i
$686$	24538.5	+	7973.05i	1.36572	+	0.443750i
$687$	−6202.79	+	5592.99i	−0.344471	+	0.310605i
$688$	−13166.2	+	18121.7i	−0.729587	+	1.00419i
$689$	−183.282	+	564.084i	−0.0101342	+	0.0311900i
$690$	15456.5	−	1635.63i	0.852780	−	0.0902423i
$691$	19554.4	−	14207.1i	1.07653	−	0.782147i	0.0994573	−	0.995042i	$-0.468289\pi$
$691$	19554.4	−	14207.1i	1.07653	−	0.782147i	0.977075	+	0.212895i	$0.0682893\pi$
$692$	−18760.4			−1.03058
$693$	−9428.01	+	14267.2i	−0.516797	+	0.782059i
$694$	−8142.63			−0.445375
$695$	2770.21	−	2012.68i	0.151195	−	0.109849i
$696$	2230.19	−	236.002i	0.121459	−	0.0128529i
$697$	−674.086	+	2074.62i	−0.0366325	+	0.112743i
$698$	18781.2	−	25850.1i	1.01845	−	1.40178i
$699$	6390.25	−	5762.02i	0.345782	−	0.311788i
$700$	−2861.32	−	929.700i	−0.154497	−	0.0501991i
$701$	3297.00	+	10147.1i	0.177640	+	0.546721i	0.999744	−	0.0226168i	$-0.00719978\pi$
$701$	3297.00	+	10147.1i	0.177640	+	0.546721i	−0.822104	+	0.569337i	$0.807200\pi$
$702$	−3381.08	+	7.19395i	−0.181782	+	0.000386778i
$703$			36378.5i			1.95169i
$704$	1972.16	+	13257.2i	0.105580	+	0.709727i
$705$	−374.982	+	1770.32i	−0.0200321	+	0.0945734i
$706$	6538.59	+	8999.60i	0.348560	+	0.479751i
$707$	26889.2	−	8736.82i	1.43037	−	0.464755i
$708$	14430.6	−	25035.6i	0.766011	−	1.32895i
$709$	23569.3	+	17124.1i	1.24847	+	0.907066i	0.998132	−	0.0610928i	$-0.0194586\pi$
$709$	23569.3	+	17124.1i	1.24847	+	0.907066i	0.250337	+	0.968159i	$0.419459\pi$
$710$	−1458.24	−	1059.48i	−0.0770801	−	0.0560020i
$711$	−21278.7	−	19104.9i	−1.12238	−	1.00772i
$712$	−2498.81	+	811.914i	−0.131527	+	0.0427356i
$713$	−25074.9	−	34512.6i	−1.31706	−	1.81278i
$714$	2179.78	+	461.710i	0.114252	+	0.0242004i
$715$	525.993	−	1008.76i	0.0275119	−	0.0527630i
$716$		−	14957.1i		−	0.780689i
$717$	11030.4	+	24727.4i	0.574528	+	1.28795i
$718$	−8656.86	−	26643.1i	−0.449960	−	1.38483i
$719$	32453.5	+	10544.8i	1.68333	+	0.546945i	0.985552	−	0.169373i	$-0.0541744\pi$
$719$	32453.5	+	10544.8i	1.68333	+	0.546945i	0.697773	+	0.716319i	$0.254174\pi$
$720$	−8341.22	+	4831.59i	−0.431748	+	0.250087i
$721$	282.455	−	388.765i	0.0145897	−	0.0200810i
$722$	−13764.9	+	42364.1i	−0.709526	+	2.18370i
$723$	−886.253	−	8374.99i	−0.0455880	−	0.430801i
$724$	6326.84	−	4596.72i	0.324773	−	0.235961i
$725$	2614.33			0.133922
$726$	26036.2	+	6028.46i	1.33098	+	0.308178i
$727$	23210.3			1.18408			0.592038	−	0.805910i	$-0.298324\pi$
$727$	23210.3			1.18408			0.592038	+	0.805910i	$0.298324\pi$
$728$	361.522	−	262.661i	0.0184051	−	0.0133721i
$729$	15874.5	−	11637.0i	0.806508	−	0.591223i
$730$	5724.71	−	17618.8i	0.290248	−	0.893291i
$731$	1178.62	−	1622.23i	0.0596346	−	0.0820800i
$732$	−15038.5	−	16678.2i	−0.759345	−	0.842136i
$733$	13040.8	+	4237.21i	0.657126	+	0.213513i	0.618553	−	0.785743i	$-0.287719\pi$
$733$	13040.8	+	4237.21i	0.657126	+	0.213513i	0.0385722	+	0.999256i	$0.487719\pi$
$734$	−3550.42	−	10927.1i	−0.178540	−	0.549490i
$735$	987.223	−	440.379i	0.0495432	−	0.0221002i
$736$		−	37605.0i		−	1.88334i
$737$	7399.07	−	14190.1i	0.369808	−	0.709227i
$738$	32547.9	+	14436.0i	1.62345	+	0.720048i
$739$	7250.39	+	9979.30i	0.360906	+	0.496745i	0.950401	−	0.311027i	$-0.100673\pi$
$739$	7250.39	+	9979.30i	0.360906	+	0.496745i	−0.589495	+	0.807772i	$0.700673\pi$
$740$	−8843.53	+	2873.44i	−0.439317	+	0.142743i
$741$	3807.09	+	2194.42i	0.188741	+	0.108791i
$742$	−5161.38	−	3749.96i	−0.255364	−	0.185533i
$743$	−7422.51	−	5392.77i	−0.366495	−	0.266274i	0.389261	−	0.921127i	$-0.372730\pi$
$743$	−7422.51	−	5392.77i	−0.366495	−	0.266274i	−0.755756	+	0.654853i	$0.772730\pi$
$744$	5119.76	+	2951.06i	0.252285	+	0.145418i
$745$	7217.11	−	2344.98i	0.354918	−	0.115320i
$746$	−20489.6	−	28201.6i	−1.00560	−	1.38409i
$747$	3450.18	+	1530.26i	0.168990	+	0.0749521i
$748$	−237.858	−	1598.92i	−0.0116269	−	0.0781580i
$749$		−	12983.1i		−	0.633366i
$750$	−2292.15	+	1022.48i	−0.111597	+	0.0497809i
$751$	9812.71	+	30200.4i	0.476792	+	1.46742i	0.843525	+	0.537089i	$0.180476\pi$
$751$	9812.71	+	30200.4i	0.476792	+	1.46742i	−0.366733	+	0.930326i	$0.619524\pi$
$752$	4729.97	+	1536.86i	0.229368	+	0.0745260i
$753$	−25561.6	−	28348.6i	−1.23707	−	1.37195i
$754$	1481.33	−	2038.87i	0.0715473	−	0.0984765i
$755$	458.463	−	1411.00i	0.0220996	−	0.0680155i
$756$	5183.15	−	16068.4i	0.249351	−	0.773017i
$757$	−2604.95	+	1892.60i	−0.125071	+	0.0908690i	−0.648562	−	0.761162i	$-0.724629\pi$
$757$	−2604.95	+	1892.60i	−0.125071	+	0.0908690i	0.523491	+	0.852031i	$0.324629\pi$
$758$	19209.7			0.920486
$759$	−27307.0	−	10755.4i	−1.30590	−	0.514356i
$760$	2798.19			0.133554
$761$	18294.0	−	13291.4i	0.871429	−	0.633130i	−0.0595411	−	0.998226i	$-0.518964\pi$
$761$	18294.0	−	13291.4i	0.871429	−	0.633130i	0.930970	+	0.365096i	$0.118964\pi$
$762$	−51.8221	−	489.713i	−0.00246367	−	0.0232814i
$763$	3369.63	−	10370.7i	0.159881	−	0.492062i
$764$	10623.9	−	14622.5i	0.503088	−	0.692441i
$765$	746.696	−	432.519i	0.0352900	−	0.0204415i
$766$	−42796.2	−	13905.3i	−2.01865	−	0.655900i
$767$	1546.14	+	4758.53i	0.0727873	+	0.224016i
$768$	10504.2	+	23547.9i	0.493539	+	1.10639i
$769$			716.158i			0.0335830i	0.999859	+	0.0167915i	$0.00534515\pi$
$769$			716.158i			0.0335830i	−0.999859	+	0.0167915i	$0.994655\pi$
$770$	8571.31	+	8733.99i	0.401154	+	0.408768i
$771$	−37574.3	−	7958.82i	−1.75513	−	0.371764i
$772$	20384.3	+	28056.5i	0.950318	+	1.30800i
$773$	−6270.11	+	2037.28i	−0.291747	+	0.0947943i	−0.451234	−	0.892406i	$-0.649016\pi$
$773$	−6270.11	+	2037.28i	−0.291747	+	0.0947943i	0.159487	+	0.987200i	$0.449016\pi$
$774$	−24353.9	−	21865.9i	−1.13099	−	1.01544i
$775$	5573.13	+	4049.12i	0.258313	+	0.187676i
$776$	−1444.99	−	1049.85i	−0.0668455	−	0.0485661i
$777$	−12085.9	+	20967.7i	−0.558018	+	0.968100i
$778$	14178.7	−	4606.92i	0.653380	−	0.212296i
$779$	−27199.7	−	37437.2i	−1.25100	−	1.72186i
$780$	−232.748	+	1098.83i	−0.0106843	+	0.0504414i
$781$	1516.61	+	3046.98i	0.0694858	+	0.139603i
$782$			3823.95i			0.174865i
$783$	31.2160	+	14671.2i	0.00142474	+	0.669611i
$784$	−918.066	−	2825.52i	−0.0418215	−	0.128713i
$785$	1951.99	+	634.240i	0.0887510	+	0.0288370i
$786$	1723.03	−	1553.64i	0.0781914	−	0.0705043i
$787$	5660.51	−	7791.02i	0.256385	−	0.352884i	−0.661349	−	0.750078i	$-0.730016\pi$
$787$	5660.51	−	7791.02i	0.256385	−	0.352884i	0.917735	+	0.397194i	$0.130016\pi$
$788$	−5410.73	+	16652.5i	−0.244606	+	0.752819i
$789$	−9542.37	+	1009.79i	−0.430567	+	0.0455632i
$790$	−16555.4	+	12028.2i	−0.745589	+	0.541702i
$791$	14152.8			0.636178
$792$	4061.47	−	180.356i	0.182220	−	0.00809178i
$793$	3888.39			0.174125
$794$	44387.4	−	32249.3i	1.98394	−	1.44142i
$795$	−2457.07	+	260.011i	−0.109614	+	0.0115995i
$796$	−740.853	+	2280.11i	−0.0329885	+	0.101528i
$797$	23080.2	−	31767.2i	1.02577	−	1.41186i	0.117700	−	0.993049i	$-0.462448\pi$
$797$	23080.2	−	31767.2i	1.02577	−	1.41186i	0.908074	−	0.418809i	$-0.137552\pi$
$798$	−35103.6	+	31652.5i	−1.55721	+	1.40412i
$799$	−423.422	−	137.578i	−0.0187479	−	0.00609157i
$800$	1876.50	+	5775.28i	0.0829305	+	0.255234i
$801$	−3597.50	−	16807.6i	−0.158691	−	0.741409i
$802$		−	29847.7i		−	1.31417i
$803$	−24966.7	+	24501.7i	−1.09721	+	1.07677i
$804$	−3274.04	+	15457.0i	−0.143615	+	0.678020i
$805$	−7899.03	−	10872.1i	−0.345844	−	0.476013i
$806$	6315.67	−	2052.09i	0.276005	−	0.0896794i
$807$	15127.6	−	26244.7i	0.659872	−	1.14481i
$808$	−5437.76	−	3950.77i	−0.236757	−	0.172014i
$809$	−16043.8	−	11656.5i	−0.697244	−	0.506578i	0.181789	−	0.983338i	$-0.441811\pi$
$809$	−16043.8	−	11656.5i	−0.697244	−	0.506578i	−0.879034	+	0.476760i	$0.841811\pi$
$810$	−5765.35	−	12850.9i	−0.250091	−	0.557452i
$811$	−21047.2	+	6838.65i	−0.911303	+	0.296100i	−0.726894	−	0.686749i	$-0.759037\pi$
$811$	−21047.2	+	6838.65i	−0.911303	+	0.296100i	−0.184409	+	0.982850i	$0.559037\pi$
$812$	7397.07	+	10181.2i	0.319687	+	0.440012i
$813$	38013.7	+	8051.88i	1.63985	+	0.347345i
$814$	37298.9	+	6267.54i	1.60605	+	0.269874i
$815$		−	9249.07i		−	0.397522i
$816$	−966.148	−	2165.87i	−0.0414484	−	0.0929173i
$817$	13144.7	+	40455.3i	0.562883	+	1.73238i
$818$	3248.51	+	1055.51i	0.138853	+	0.0451160i
$819$	1465.27	+	2529.63i	0.0625162	+	0.107927i
$820$	6952.48	−	9569.27i	0.296087	−	0.407529i
$821$	8000.11	−	24621.8i	0.340080	−	1.04666i	−0.624085	−	0.781356i	$-0.714528\pi$
$821$	8000.11	−	24621.8i	0.340080	−	1.04666i	0.964165	−	0.265302i	$-0.0854718\pi$
$822$	−4002.44	−	37822.6i	−0.169831	−	1.60488i
$823$	−29596.0	+	21502.8i	−1.25353	+	0.910741i	−0.998421	−	0.0561724i	$-0.982110\pi$
$823$	−29596.0	+	21502.8i	−1.25353	+	0.910741i	−0.255106	+	0.966913i	$0.582110\pi$
$824$	−114.241			−0.00482982
$825$	4730.43	+	289.159i	0.199627	+	0.0122027i
$826$	−53819.2			−2.26708
$827$	26406.7	−	19185.6i	1.11034	−	0.806709i	0.127622	−	0.991823i	$-0.459265\pi$
$827$	26406.7	−	19185.6i	1.11034	−	0.806709i	0.982717	+	0.185114i	$0.0592654\pi$
$828$	28821.4	+	2987.93i	1.20968	+	0.125408i
$829$	9706.58	−	29873.8i	0.406663	−	1.25158i	−0.512836	−	0.858487i	$-0.671405\pi$
$829$	9706.58	−	29873.8i	0.406663	−	1.25158i	0.919499	−	0.393093i	$-0.128595\pi$
$830$	1587.53	−	2185.04i	0.0663901	−	0.0913782i
$831$	1999.29	+	2217.28i	0.0834594	+	0.0925589i
$832$	2179.08	+	708.028i	0.0908007	+	0.0295029i
$833$	82.1842	+	252.937i	0.00341839	+	0.0105207i
$834$	12557.9	−	5601.83i	0.521398	−	0.232585i
$835$			6509.95i			0.269804i
$836$	30406.7	+	15854.8i	1.25794	+	0.655919i
$837$	−22656.4	+	31323.8i	−0.935628	+	1.29356i
$838$	4150.54	+	5712.73i	0.171095	+	0.235493i
$839$	−39720.6	+	12906.0i	−1.63445	+	0.531067i	−0.975289	−	0.220931i	$-0.929090\pi$
$839$	−39720.6	+	12906.0i	−1.63445	+	0.531067i	−0.659165	+	0.751998i	$0.729090\pi$
$840$	1612.82	+	929.635i	0.0662469	+	0.0381851i
$841$	10884.1	+	7907.73i	0.446269	+	0.324234i
$842$	−17195.5	−	12493.2i	−0.703795	−	0.511337i
$843$	7673.82	+	4423.23i	0.313524	+	0.180717i
$844$	−1340.23	+	435.468i	−0.0546596	+	0.0177600i
$845$	6342.51	+	8729.71i	0.258212	+	0.355398i
$846$	−2946.32	+	6642.89i	−0.119736	+	0.269961i
$847$	−6726.05	−	22106.5i	−0.272857	−	0.896797i
$848$			6790.55i			0.274987i
$849$	36287.2	−	16187.0i	1.46687	−	0.654341i
$850$	−190.817	−	587.273i	−0.00769995	−	0.0236980i
$851$	−39502.1	−	12835.0i	−1.59120	−	0.517014i
$852$	−2250.26	−	2495.61i	−0.0904844	−	0.100350i
$853$	4428.09	−	6094.74i	0.177743	−	0.244642i	−0.710845	−	0.703349i	$-0.751687\pi$
$853$	4428.09	−	6094.74i	0.177743	−	0.244642i	0.888588	+	0.458707i	$0.151687\pi$
$854$	−12924.8	+	39778.4i	−0.517889	+	1.59390i
$855$	−1887.63	+	18208.0i	−0.0755034	+	0.728303i
$856$	−2497.05	+	1814.21i	−0.0997048	+	0.0724398i
$857$	17159.8			0.683976			0.341988	−	0.939704i	$-0.388900\pi$
$857$	17159.8			0.683976			0.341988	+	0.939704i	$0.388900\pi$
$858$	2905.86	−	3525.34i	0.115623	−	0.140272i
$859$	−47027.2			−1.86792			−0.933962	−	0.357374i	$-0.883672\pi$
$859$	−47027.2			−1.86792			−0.933962	+	0.357374i	$0.883672\pi$
$860$	−8796.33	+	6390.91i	−0.348782	+	0.253405i
$861$	−3239.67	−	30614.5i	−0.128232	−	1.21178i
$862$	−11548.8	+	35543.4i	−0.456325	+	1.40442i
$863$	−26088.4	+	35907.6i	−1.02904	+	1.41635i	−0.123368	+	0.992361i	$0.539370\pi$
$863$	−26088.4	+	35907.6i	−1.02904	+	1.41635i	−0.905668	+	0.423987i	$0.860630\pi$
$864$	−32387.5	+	10599.6i	−1.27528	+	0.417367i
$865$	12869.6	+	4181.58i	0.505872	+	0.164368i
$866$	14679.3	+	45178.3i	0.576009	+	1.77277i
$867$	−10313.5	−	23120.4i	−0.403997	−	0.905662i
$868$			33160.6i			1.29671i
$869$	38220.0	−	5685.67i	1.49197	−	0.221948i
$870$	10270.7	+	2175.49i	0.400241	+	0.0847771i
$871$	−1608.03	−	2213.26i	−0.0625555	−	0.0861003i
$872$	−2465.46	+	801.077i	−0.0957467	+	0.0311100i
$873$	7806.18	−	8694.41i	0.302634	−	0.337069i
$874$	−65627.1	−	47680.9i	−2.53990	−	1.84534i
$875$	1755.63	+	1275.54i	0.0678300	+	0.0492814i
$876$	17247.1	−	29921.8i	0.665210	−	1.15407i
$877$	−25222.1	+	8195.14i	−0.971138	+	0.315542i	−0.751275	−	0.659989i	$-0.770561\pi$
$877$	−25222.1	+	8195.14i	−0.971138	+	0.315542i	−0.219863	+	0.975531i	$0.570561\pi$
$878$	550.785	+	758.090i	0.0211709	+	0.0291393i
$879$	−7742.50	+	36553.1i	−0.297097	+	1.40262i
$880$	2158.42	−	12845.0i	0.0826821	−	0.492051i
$881$			233.275i			0.00892079i	0.999990	+	0.00446040i	$0.00141979\pi$
$881$			233.275i			0.00892079i	−0.999990	+	0.00446040i	$0.998580\pi$
$882$	4244.88	−	908.571i	0.162055	−	0.0346862i
$883$	4071.17	+	12529.8i	0.155160	+	0.477532i	0.998177	−	0.0603542i	$-0.0192230\pi$
$883$	4071.17	+	12529.8i	0.155160	+	0.477532i	−0.843017	+	0.537886i	$0.819223\pi$
$884$	−262.815	−	85.3937i	−0.00999934	−	0.00324898i
$885$	−15479.6	+	13957.8i	−0.587958	+	0.530155i
$886$	−20409.9	+	28091.8i	−0.773911	+	1.06520i
$887$	−6378.67	+	19631.5i	−0.241460	+	0.743137i	0.754739	+	0.656025i	$0.227764\pi$
$887$	−6378.67	+	19631.5i	−0.241460	+	0.743137i	−0.996199	+	0.0871114i	$0.972236\pi$
$888$	5721.59	−	605.467i	0.216221	−	0.0228808i
$889$	−344.464	+	250.268i	−0.0129954	+	0.00944174i
$890$	−12299.8			−0.463247
$891$	−1566.23	+	26549.9i	−0.0588896	+	0.998264i
$892$	−12804.0			−0.480617
$893$	7640.78	−	5551.35i	0.286326	−	0.208028i
$894$	30304.6	−	3206.87i	1.13371	−	0.119971i
$895$	−3333.85	+	10260.5i	−0.124512	+	0.383209i
$896$	5342.75	−	7353.67i	0.199206	−	0.274184i
$897$	−3726.06	+	3359.75i	−0.138695	+	0.125060i
$898$	−24301.0	−	7895.87i	−0.903045	−	0.293417i
$899$	−8904.40	−	27404.9i	−0.330343	−	1.01669i
$900$	−4575.42	+	979.321i	−0.169460	+	0.0362711i
$901$		−	607.883i		−	0.0224767i
$902$	−43070.6	+	21438.0i	−1.58991	+	0.791360i
$903$	−5864.02	+	27684.6i	−0.216104	+	1.02025i
$904$	−1977.67	−	2722.03i	−0.0727614	−	0.100148i
$905$	−5364.78	+	1743.12i	−0.197051	+	0.0640258i
$906$	2975.28	−	5161.78i	0.109103	−	0.189281i
$907$	2842.76	+	2065.39i	0.104071	+	0.0756120i	0.638604	−	0.769536i	$-0.279512\pi$
$907$	2842.76	+	2065.39i	0.104071	+	0.0756120i	−0.534533	+	0.845148i	$0.679512\pi$
$908$	−27656.0	−	20093.2i	−1.01079	−	0.734380i
$909$	29376.1	−	32718.7i	1.07189	−	1.19385i
$910$	1989.55	−	646.443i	0.0724756	−	0.0235488i
$911$	−24938.5	−	34324.9i	−0.906969	−	1.24834i	−0.968191	−	0.250212i	$-0.919500\pi$
$911$	−24938.5	−	34324.9i	−0.906969	−	1.24834i	0.0612219	−	0.998124i	$-0.480500\pi$
$912$	49217.8	+	10425.1i	1.78702	+	0.378519i
$913$	−4565.62	+	2272.49i	−0.165498	+	0.0823752i
$914$			32.0038i			0.00115820i
$915$	6598.93	+	14793.2i	0.238419	+	0.534478i
$916$	3443.07	+	10596.7i	0.124195	+	0.382232i
$917$	−1907.78	−	619.877i	−0.0687030	−	0.0223229i
$918$	3293.40	−	1077.84i	0.118408	−	0.0387518i
$919$	29618.4	−	40766.2i	1.06313	−	1.46328i	0.186295	−	0.982494i	$-0.440352\pi$
$919$	29618.4	−	40766.2i	1.06313	−	1.46328i	0.876839	−	0.480784i	$-0.159648\pi$
$920$	−987.255	+	3038.46i	−0.0353792	+	0.108886i
$921$	−2006.11	−	18957.5i	−0.0717738	−	0.678254i
$922$	32152.0	−	23359.8i	1.14845	−	0.834396i
$923$	581.832			0.0207489
$924$	12258.3	+	19240.3i	0.436439	+	0.685019i
$925$	6707.11			0.238409
$926$	−33710.7	+	24492.3i	−1.19633	+	0.869186i
$927$	77.0656	−	743.372i	0.00273049	−	0.0263382i
$928$	7849.28	−	24157.6i	0.277657	−	0.854539i
$929$	−27705.1	+	38132.8i	−0.978445	+	1.34671i	−0.0407819	+	0.999168i	$0.512985\pi$
$929$	−27705.1	+	38132.8i	−0.978445	+	1.34671i	−0.937663	+	0.347546i	$0.887015\pi$
$930$	18525.3	+	20545.1i	0.653191	+	0.724408i
$931$	−5365.69	−	1743.42i	−0.188887	−	0.0613730i
$932$	−3547.13	−	10916.9i	−0.124667	−	0.383687i
$933$	15044.5	−	6711.02i	0.527904	−	0.235487i
$934$			29394.7i			1.02979i
$935$	−193.219	+	1149.87i	−0.00675823	+	0.0402190i
$936$	281.775	−	635.300i	0.00983985	−	0.0221853i
$937$	−22699.3	−	31242.9i	−0.791413	−	1.08929i	−0.993931	−	0.110008i	$-0.964912\pi$
$937$	−22699.3	−	31242.9i	−0.791413	−	1.08929i	0.202518	−	0.979279i	$-0.435088\pi$
$938$	27986.7	−	9093.42i	0.974198	−	0.316536i
$939$	29122.1	+	16786.1i	1.01210	+	0.583381i
$940$	1953.05	+	1418.97i	0.0677674	+	0.0492359i
$941$	3510.20	+	2550.31i	0.121604	+	0.0883504i	0.646925	−	0.762554i	$-0.276055\pi$
$941$	3510.20	+	2550.31i	0.121604	+	0.0883504i	−0.525321	+	0.850904i	$0.676055\pi$
$942$	7140.85	+	4116.02i	0.246987	+	0.142364i
$943$	50248.4	−	16326.7i	1.73522	−	0.563807i
$944$	33670.8	+	46343.8i	1.16090	+	1.59784i
$945$	−7137.17	+	9867.55i	−0.245685	+	0.339674i
$946$	43743.5	−	6507.37i	1.50341	−	0.223650i
$947$		−	26628.5i		−	0.913737i	−0.889534	−	0.456869i	$-0.848971\pi$
$947$		−	26628.5i		−	0.913737i	0.889534	−	0.456869i	$-0.151029\pi$
$948$	−34840.4	+	15541.6i	−1.19363	+	0.532454i
$949$	1847.90	+	5687.25i	0.0632091	+	0.194537i
$950$	12458.1	+	4047.90i	0.425469	+	0.138243i
$951$	−1914.84	−	2123.61i	−0.0652922	−	0.0724110i
$952$	−269.202	+	370.525i	−0.00916481	+	0.0126143i
$953$	−8328.10	+	25631.3i	−0.283078	+	0.871225i	0.703890	+	0.710309i	$0.251445\pi$
$953$	−8328.10	+	25631.3i	−0.283078	+	0.871225i	−0.986968	+	0.160916i	$0.948555\pi$
$954$	−9869.25	−	1023.15i	−0.334936	−	0.0347229i
$955$	−10547.2	+	7663.02i	−0.357383	+	0.259654i
$956$	36120.8			1.22200
$957$	−15297.1	−	12609.1i	−0.516704	−	0.425908i
$958$	45156.6			1.52290
$959$	−26604.4	+	19329.2i	−0.895830	+	0.650858i
$960$	1004.43	+	9491.79i	0.0337687	+	0.319111i
$961$	14257.2	−	43879.2i	0.478574	−	1.47290i
$962$	3800.36	−	5230.75i	0.127369	−	0.175308i
$963$	−10120.7	−	17472.3i	−0.338665	−	0.584669i
$964$	−10685.2	−	3471.82i	−0.356998	−	0.115996i
$965$	−7729.91	−	23790.2i	−0.257860	−	0.793611i
$966$	−21985.1	−	49285.4i	−0.732257	−	1.64154i
$967$			4679.27i			0.155610i	0.996969	+	0.0778052i	$0.0247912\pi$
$967$			4679.27i			0.155610i	−0.996969	+	0.0778052i	$0.975209\pi$
$968$	−3311.88	+	4382.71i	−0.109967	+	0.145522i
$969$	−4405.92	−	933.242i	−0.146067	−	0.0309392i
$970$	−4914.68	−	6764.48i	−0.162681	−	0.223912i
$971$	12144.2	−	3945.90i	0.401366	−	0.130412i	−0.101376	−	0.994848i	$-0.532325\pi$
$971$	12144.2	−	3945.90i	0.401366	−	0.130412i	0.502742	+	0.864436i	$0.332325\pi$
$972$	−5550.42	−	25664.8i	−0.183158	−	0.846912i
$973$	−9618.55	−	6988.29i	−0.316913	−	0.230251i
$974$	47380.4	+	34423.9i	1.55869	+	1.13246i
$975$	404.586	−	701.913i	0.0132894	−	0.0230556i
$976$	42339.4	−	13756.9i	1.38858	−	0.451176i
$977$	13380.8	+	18417.1i	0.438169	+	0.603088i	0.969804	−	0.243886i	$-0.0784222\pi$
$977$	13380.8	+	18417.1i	0.438169	+	0.603088i	−0.531635	+	0.846974i	$0.678422\pi$
$978$	7696.53	−	36336.0i	0.251644	−	1.18803i
$979$	20593.7	+	10738.1i	0.672297	+	0.350552i
$980$		−	1442.10i		−	0.0470062i
$981$	−3549.48	−	16583.3i	−0.115521	−	0.539719i
$982$	−672.181	−	2068.76i	−0.0218433	−	0.0672268i
$983$	−44775.6	−	14548.5i	−1.45282	−	0.472049i	−0.526949	−	0.849897i	$-0.676664\pi$
$983$	−44775.6	−	14548.5i	−1.45282	−	0.472049i	−0.925868	+	0.377848i	$0.876664\pi$
$984$	−5435.42	+	4901.06i	−0.176092	+	0.158780i
$985$	7423.49	−	10217.6i	0.240134	−	0.330516i
$986$	−798.173	+	2456.52i	−0.0257799	+	0.0793424i
$987$	6248.29	−	661.203i	0.201505	−	0.0213235i
$988$	4742.57	−	3445.68i	0.152714	−	0.110953i
$989$	−48566.7			−1.56151
$990$	18343.4	+	5072.39i	0.588882	+	0.162839i
$991$	58613.8			1.87884			0.939419	−	0.342770i	$-0.111365\pi$
$991$	58613.8			1.87884			0.939419	+	0.342770i	$0.111365\pi$
$992$	54148.5	−	39341.2i	1.73308	−	1.25916i
$993$	−42829.0	+	4532.22i	−1.36872	+	0.144840i
$994$	−1933.97	+	5952.16i	−0.0617122	+	0.189931i
$995$	1016.45	−	1399.02i	0.0323854	−	0.0445747i
$996$	3739.43	−	3371.81i	0.118964	−	0.107269i
$997$	−3153.39	−	1024.60i	−0.100169	−	0.0325470i	0.258504	−	0.966010i	$-0.416771\pi$
$997$	−3153.39	−	1024.60i	−0.100169	−	0.0325470i	−0.358673	+	0.933463i	$0.616771\pi$
$998$	18416.7	+	56680.7i	0.584138	+	1.79779i
$999$	80.0851	+	37639.2i	0.00253632	+	1.19204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.p.a.41.9	✓	192
3.2	odd	2	inner	165.4.p.a.41.40	yes	192
11.7	odd	10	inner	165.4.p.a.161.40	yes	192
33.29	even	10	inner	165.4.p.a.161.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.p.a.41.9	✓	192	1.1	even	1	trivial
165.4.p.a.41.40	yes	192	3.2	odd	2	inner
165.4.p.a.161.9	yes	192	33.29	even	10	inner
165.4.p.a.161.40	yes	192	11.7	odd	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.12619 + 2.27131i) q^{2} +(5.16730 - 0.546811i) q^{3} +(2.14208 - 6.59266i) q^{4} +(-2.93893 + 4.04508i) q^{5} +(-14.9120 + 13.4460i) q^{6} +(16.5110 + 5.36474i) q^{7} +(-1.27538 - 3.92522i) q^{8} +(26.4020 - 5.65107i) q^{9} -19.3209i q^{10} +(-16.8677 + 32.3493i) q^{11} +(7.46386 - 35.2376i) q^{12} +(3.66583 + 5.04558i) q^{13} +(-63.8015 + 20.7304i) q^{14} +(-12.9744 + 22.5092i) q^{15} +(57.7669 + 41.9701i) q^{16} +(-5.17123 - 3.75712i) q^{17} +(-69.7024 + 77.6335i) q^{18} +(128.960 - 41.9017i) q^{19} +(20.3724 + 28.0402i) q^{20} +(88.2507 + 18.6928i) q^{21} +(-20.7437 - 139.442i) q^{22} +154.817i q^{23} +(-8.73664 - 19.5854i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(-22.9202 - 7.44721i) q^{26} +(133.337 - 43.6377i) q^{27} +(70.7358 - 97.3594i) q^{28} +(-32.3149 + 99.4551i) q^{29} +(-10.5649 - 99.8370i) q^{30} +(-222.925 + 161.965i) q^{31} -242.900 q^{32} +(-69.4717 + 176.382i) q^{33} +24.6998 q^{34} +(-70.2254 + 51.0217i) q^{35} +(19.2997 - 186.164i) q^{36} +(-82.9044 + 255.153i) q^{37} +(-307.982 + 423.901i) q^{38} +(21.7014 + 24.0675i) q^{39} +(19.6261 + 6.37691i) q^{40} +(-105.458 - 324.566i) q^{41} +(-318.346 + 142.007i) q^{42} +313.704i q^{43} +(177.136 + 180.498i) q^{44} +(-54.7345 + 123.406i) q^{45} +(-351.638 - 483.988i) q^{46} +(66.2426 - 21.5235i) q^{47} +(321.449 + 185.285i) q^{48} +(-33.6611 - 24.4562i) q^{49} +(78.1548 + 56.7828i) q^{50} +(-28.7757 - 16.5865i) q^{51} +(41.1163 - 13.3595i) q^{52} +(55.8988 + 76.9381i) q^{53} +(-317.722 + 439.270i) q^{54} +(-81.2828 - 163.304i) q^{55} -71.6513i q^{56} +(643.463 - 287.035i) q^{57} +(-124.871 - 384.313i) q^{58} +(762.991 + 247.911i) q^{59} +(120.603 + 133.753i) q^{60} +(366.468 - 504.399i) q^{61} +(329.035 - 1012.67i) q^{62} +(466.239 + 48.3352i) q^{63} +(297.216 - 215.940i) q^{64} -31.1834 q^{65} +(-183.437 - 709.196i) q^{66} -438.653 q^{67} +(-35.8466 + 26.0441i) q^{68} +(84.6556 + 799.986i) q^{69} +(103.652 - 319.007i) q^{70} +(54.8356 - 75.4748i) q^{71} +(-55.8544 - 96.4265i) q^{72} +(911.904 + 296.296i) q^{73} +(-320.358 - 985.960i) q^{74} +(-52.9208 - 118.636i) q^{75} -939.947i q^{76} +(-452.048 + 443.628i) q^{77} +(-122.508 - 25.9490i) q^{78} +(-622.548 - 856.864i) q^{79} +(-339.545 + 110.325i) q^{80} +(665.131 - 298.399i) q^{81} +(1066.87 + 775.129i) q^{82} +(113.092 + 82.1661i) q^{83} +(312.276 - 541.765i) q^{84} +(30.3957 - 9.87616i) q^{85} +(-712.519 - 980.698i) q^{86} +(-112.598 + 531.584i) q^{87} +(148.491 + 24.9518i) q^{88} -636.604i q^{89} +(-109.184 - 510.111i) q^{90} +(33.4582 + 102.974i) q^{91} +(1020.66 + 331.631i) q^{92} +(-1063.36 + 958.818i) q^{93} +(-158.200 + 217.744i) q^{94} +(-209.508 + 644.801i) q^{95} +(-1255.14 + 132.820i) q^{96} +(350.112 - 254.371i) q^{97} +160.779 q^{98} +(-262.533 + 949.408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 4 q^{3} - 192 q^{4} - 100 q^{6} + 108 q^{9} + 48 q^{12} - 60 q^{15} - 1248 q^{16} - 460 q^{18} + 900 q^{19} + 888 q^{22} + 1200 q^{24} + 1200 q^{25} + 568 q^{27} - 1680 q^{28} - 576 q^{31} - 1402 q^{33}+ \cdots - 736 q^{99}+O(q^{100}) \) 192 * q + 4 * q^3 - 192 * q^4 - 100 * q^6 + 108 * q^9 + 48 * q^12 - 60 * q^15 - 1248 * q^16 - 460 * q^18 + 900 * q^19 + 888 * q^22 + 1200 * q^24 + 1200 * q^25 + 568 * q^27 - 1680 * q^28 - 576 * q^31 - 1402 * q^33 + 264 * q^34 - 2364 * q^36 + 24 * q^37 + 1220 * q^39 + 4438 * q^42 - 360 * q^46 + 1946 * q^48 + 1848 * q^49 + 930 * q^51 + 840 * q^55 - 4170 * q^57 + 4320 * q^58 - 830 * q^60 - 1560 * q^61 - 7900 * q^63 - 11700 * q^64 - 4214 * q^66 + 168 * q^67 - 4992 * q^69 - 1620 * q^70 + 6720 * q^72 - 360 * q^73 + 150 * q^75 + 13972 * q^78 + 4740 * q^79 + 916 * q^81 + 6420 * q^82 + 6880 * q^84 + 2868 * q^88 + 8736 * q^91 - 5696 * q^93 - 840 * q^94 - 12470 * q^96 - 7356 * q^97 - 736 * q^99

Introduction

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