LMFDB - Embedded newform 165.4.p.a.41.40

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			41.40
Character	$\chi$	$=$	165.41
Dual form			165.4.p.a.161.40

$q$-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} +(-4.50184 + 2.59488i) q^{3} +(2.14208 - 6.59266i) q^{4} +(2.93893 - 4.04508i) q^{5} +(-8.17983 + 18.3372i) q^{6} +(16.5110 + 5.36474i) q^{7} +(1.27538 + 3.92522i) q^{8} +(13.5332 - 23.3635i) 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} +(-2.73405 + 25.8365i) q^{15} +(57.7669 + 41.9701i) q^{16} +(5.17123 + 3.75712i) q^{17} +(-10.7586 - 103.777i) 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} +(-15.9271 - 14.3613i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(22.9202 + 7.44721i) q^{26} +(-0.298508 + 140.296i) q^{27} +(70.7358 - 97.3594i) q^{28} +(32.3149 - 99.4551i) q^{29} +(50.1356 + 86.9798i) q^{30} +(-222.925 + 161.965i) q^{31} +242.900 q^{32} +(8.00695 + 189.401i) q^{33} +24.6998 q^{34} +(70.2254 - 51.0217i) q^{35} +(-125.038 - 139.266i) q^{36} +(-82.9044 + 255.153i) q^{37} +(307.982 - 423.901i) q^{38} +(-29.5957 - 13.2020i) q^{39} +(19.6261 + 6.37691i) q^{40} +(105.458 + 324.566i) q^{41} +(-233.431 + 258.882i) 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} +(-368.965 - 39.0444i) q^{48} +(-33.6611 - 24.4562i) q^{49} +(-78.1548 - 56.7828i) q^{50} +(-33.0293 - 3.49521i) 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} +(-471.828 + 523.271i) q^{57} +(-124.871 - 384.313i) q^{58} +(-762.991 - 247.911i) q^{59} +(164.475 + 73.3686i) q^{60} +(366.468 - 504.399i) q^{61} +(-329.035 + 1012.67i) q^{62} +(348.785 - 313.152i) q^{63} +(297.216 - 215.940i) q^{64} +31.1834 q^{65} +(455.221 + 573.919i) q^{66} -438.653 q^{67} +(35.8466 - 26.0441i) q^{68} +(401.732 + 696.962i) q^{69} +(103.652 - 319.007i) q^{70} +(-54.8356 + 75.4748i) q^{71} +(108.967 + 23.3232i) q^{72} +(911.904 + 296.296i) q^{73} +(320.358 + 985.960i) q^{74} +(96.4757 + 86.9911i) 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} +(-362.707 - 632.364i) q^{81} +(1066.87 + 775.129i) q^{82} +(-113.092 - 82.1661i) q^{83} +(-65.8048 + 621.848i) 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} +(-451.405 - 261.473i) q^{90} +(33.4582 + 102.974i) q^{91} +(-1020.66 - 331.631i) q^{92} +(583.295 - 1307.60i) q^{93} +(-158.200 + 217.744i) q^{94} +(209.508 - 644.801i) q^{95} +(-1093.50 + 630.297i) q^{96} +(350.112 - 254.371i) q^{97} -160.779 q^{98} +(-527.521 - 831.878i) 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	0.123363	−	0.992362i	$-0.460632\pi$
$2$	3.12619	−	2.27131i	1.10528	−	0.803030i	0.981913	+	0.189332i	$0.0606322\pi$
$3$	−4.50184	+	2.59488i	−0.866380	+	0.499386i
$3$	−4.50184	+	2.59488i	−0.866380	+	0.499386i
$4$	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
$6$	−8.17983	+	18.3372i	−0.556567	+	1.24769i
$7$	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
$9$	13.5332	−	23.3635i	0.501228	−	0.865315i
$10$		−	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
$15$	−2.73405	+	25.8365i	−0.0470620	+	0.444730i
$16$	57.7669	+	41.9701i	0.902608	+	0.655783i
$17$	5.17123	+	3.75712i	0.0737769	+	0.0536020i	0.624062	−	0.781375i	$-0.285481\pi$
$17$	5.17123	+	3.75712i	0.0737769	+	0.0536020i	−0.550285	+	0.834977i	$0.685481\pi$
$18$	−10.7586	−	103.777i	−0.140879	−	1.35891i
$19$	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	$-0.752392\pi$
$23$		−	154.817i		−	1.40355i	0.712400	−	0.701774i	$-0.247608\pi$
$24$	−15.9271	−	14.3613i	−0.135462	−	0.122145i
$25$	−7.72542	−	23.7764i	−0.0618034	−	0.190211i
$26$	22.9202	+	7.44721i	0.172885	+	0.0561738i
$27$	−0.298508	+	140.296i	−0.00212770	+	0.999998i
$28$	70.7358	−	97.3594i	0.477422	−	0.657114i
$29$	32.3149	−	99.4551i	0.206922	−	0.636839i	−0.792707	−	0.609602i	$-0.791329\pi$
$29$	32.3149	−	99.4551i	0.206922	−	0.636839i	0.999629	−	0.0272370i	$-0.00867087\pi$
$30$	50.1356	+	86.9798i	0.305115	+	0.529342i
$31$	−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
$33$	8.00695	+	189.401i	0.0422373	+	0.999108i
$34$	24.6998			0.124588
$35$	70.2254	−	51.0217i	0.339150	−	0.246407i
$36$	−125.038	−	139.266i	−0.578882	−	0.644750i
$37$	−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
$39$	−29.5957	−	13.2020i	−0.121515	−	0.0542054i
$40$	19.6261	+	6.37691i	0.0775790	+	0.0252070i
$41$	105.458	+	324.566i	0.401702	+	1.23631i	0.923618	+	0.383314i	$0.125217\pi$
$41$	105.458	+	324.566i	0.401702	+	1.23631i	−0.521916	+	0.852997i	$0.674783\pi$
$42$	−233.431	+	258.882i	−0.857600	+	0.951104i
$43$			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	−0.409999	−	0.912086i	$-0.634471\pi$
$47$	−66.2426	+	21.5235i	−0.205585	+	0.0667985i	0.204414	+	0.978884i	$0.434471\pi$
$48$	−368.965	−	39.0444i	−1.10949	−	0.117408i
$49$	−33.6611	−	24.4562i	−0.0981372	−	0.0713009i
$50$	−78.1548	−	56.7828i	−0.221055	−	0.160606i
$51$	−33.0293	−	3.49521i	−0.0906869	−	0.00959661i
$52$	41.1163	−	13.3595i	0.109650	−	0.0356275i
$53$	−55.8988	−	76.9381i	−0.144873	−	0.199401i	0.730413	−	0.683005i	$-0.239327\pi$
$53$	−55.8988	−	76.9381i	−0.144873	−	0.199401i	−0.875287	+	0.483604i	$0.839327\pi$
$54$	317.722	+	439.270i	0.800676	+	1.10698i
$55$	−81.2828	−	163.304i	−0.199276	−	0.400361i
$56$			71.6513i			0.170979i
$57$	−471.828	+	523.271i	−1.09641	+	1.21595i
$58$	−124.871	−	384.313i	−0.282695	−	0.870047i
$59$	−762.991	−	247.911i	−1.68361	−	0.547038i	−0.698003	−	0.716095i	$-0.745928\pi$
$59$	−762.991	−	247.911i	−1.68361	−	0.547038i	−0.985606	+	0.169057i	$0.945928\pi$
$60$	164.475	+	73.3686i	0.353893	+	0.157864i
$61$	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
$63$	348.785	−	313.152i	0.697504	−	0.626246i
$64$	297.216	−	215.940i	0.580500	−	0.421758i
$65$	31.1834			0.0595050
$66$	455.221	+	573.919i	0.848997	+	1.07037i
$67$	−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
$69$	401.732	+	696.962i	0.700911	+	1.21601i
$70$	103.652	−	319.007i	0.176982	−	0.544695i
$71$	−54.8356	+	75.4748i	−0.0916590	+	0.126158i	−0.852384	−	0.522917i	$-0.824844\pi$
$71$	−54.8356	+	75.4748i	−0.0916590	+	0.126158i	0.760725	+	0.649075i	$0.224844\pi$
$72$	108.967	+	23.3232i	0.178359	+	0.0381760i
$73$	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
$75$	96.4757	+	86.9911i	0.148534	+	0.133932i
$76$		−	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
$81$	−362.707	−	632.364i	−0.497541	−	0.867440i
$82$	1066.87	+	775.129i	1.43679	+	1.04389i
$83$	−113.092	−	82.1661i	−0.149560	−	0.108661i	0.510489	−	0.859884i	$-0.329464\pi$
$83$	−113.092	−	82.1661i	−0.149560	−	0.108661i	−0.660049	+	0.751223i	$0.729464\pi$
$84$	−65.8048	+	621.848i	−0.0854749	+	0.807728i
$85$	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	$0.123767\pi$
$89$			636.604i			0.758201i	−0.925355	+	0.379101i	$0.876233\pi$
$90$	−451.405	−	261.473i	−0.528692	−	0.306241i
$91$	33.4582	+	102.974i	0.0385425	+	0.118622i
$92$	−1020.66	−	331.631i	−1.15664	−	0.375815i
$93$	583.295	−	1307.60i	0.650375	−	1.45798i
$94$	−158.200	+	217.744i	−0.173587	+	0.238921i
$95$	209.508	−	644.801i	0.226264	−	0.696370i
$96$	−1093.50	+	630.297i	−1.16255	+	0.670098i
$97$	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
$99$	−527.521	−	831.878i	−0.535534	−	0.844514i
$100$	−173.298			−0.173298
$101$	−1317.54	+	957.246i	−1.29802	+	0.943064i	−0.999934	−	0.0114758i	$-0.996347\pi$
$101$	−1317.54	+	957.246i	−1.29802	+	0.943064i	−0.298082	+	0.954540i	$0.596347\pi$
$102$	−111.195	+	64.0932i	−0.107940	+	0.0622174i
$103$	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
$105$	−183.748	+	411.918i	−0.170781	+	0.382849i
$106$	−349.501	−	113.560i	−0.320250	−	0.104056i
$107$	231.097	+	711.242i	0.208794	+	0.642602i	0.999536	+	0.0304524i	$0.00969479\pi$
$107$	231.097	+	711.242i	0.208794	+	0.642602i	−0.790742	+	0.612149i	$0.790305\pi$
$108$	924.283	+	302.493i	0.823510	+	0.269513i
$109$		−	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	−0.613409	−	0.789765i	$-0.710202\pi$
$113$	−775.324	+	251.918i	−0.645455	+	0.209721i	−0.0320458	+	0.999486i	$0.510202\pi$
$114$	−286.513	+	2707.51i	−0.235389	+	2.22440i
$115$	−626.248	−	454.996i	−0.507808	−	0.368944i
$116$	−586.452	−	426.082i	−0.469402	−	0.341041i
$117$	167.493	−	17.3640i	0.132348	−	0.0137205i
$118$	−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
$123$	−1316.97	−	1187.49i	−0.965422	−	0.870511i
$124$	590.253	+	1816.61i	0.427470	+	1.31562i
$125$	−118.882	−	38.6271i	−0.0850651	−	0.0276393i
$126$	379.101	−	1771.17i	0.268040	−	1.25229i
$127$	−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
$129$	−814.025	−	1412.24i	−0.555588	−	0.963885i
$130$	97.4853	−	70.8272i	0.0657694	−	0.0477843i
$131$	115.546			0.0770637			0.0385318	−	0.999257i	$-0.487732\pi$
$131$	115.546			0.0770637			0.0385318	+	0.999257i	$0.487732\pi$
$132$	1265.81	+	352.927i	0.834656	+	0.232715i
$133$	2354.05			1.53475
$134$	−1371.31	+	996.317i	−0.884055	+	0.642303i
$135$	566.631	+	413.526i	0.361243	+	0.263635i
$136$	−8.15223	+	25.0900i	−0.00514006	+	0.0158195i
$137$	1113.39	−	1532.45i	0.694332	−	0.955666i	−0.305662	−	0.952140i	$-0.598878\pi$
$137$	1113.39	−	1532.45i	0.694332	−	0.955666i	0.999994	−	0.00352609i	$-0.00112239\pi$
$138$	2838.91	+	1266.38i	1.75119	+	0.781168i
$139$	−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
$141$	242.363	−	268.787i	0.144756	−	0.160539i
$142$			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
$147$	214.998	+	22.7514i	0.120631	+	0.0127653i
$148$	1504.55	+	1093.12i	0.835631	+	0.607121i
$149$	1227.85	+	892.083i	0.675095	+	0.490485i	0.871727	−	0.489992i	$-0.163000\pi$
$149$	1227.85	+	892.083i	0.675095	+	0.490485i	−0.196632	+	0.980477i	$0.563000\pi$
$150$	499.185	+	52.8245i	0.271722	+	0.0287540i
$151$	−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
$156$	−150.433	+	166.834i	−0.0772067	+	0.0856246i
$157$	−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
$159$	451.293	+	201.312i	0.225094	+	0.100409i
$160$	713.864	−	982.550i	0.352725	−	0.485484i
$161$	830.553	−	2556.18i	0.406564	−	1.25127i
$162$	−2570.19	−	1153.07i	−1.24650	−	0.559220i
$163$	−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
$165$	789.677	+	524.248i	0.372583	+	0.247349i
$166$	−540.172			−0.252563
$167$	−1053.33	+	765.291i	−0.488080	+	0.354611i	−0.804445	−	0.594027i	$-0.797537\pi$
$167$	−1053.33	+	765.291i	−0.488080	+	0.354611i	0.316366	+	0.948637i	$0.397537\pi$
$168$	−185.927	−	322.563i	−0.0853844	−	0.148133i
$169$	666.891	−	2052.48i	0.303546	−	0.934219i
$170$	72.5910	−	99.9129i	0.0327498	−	0.0450763i
$171$	766.267	−	3580.02i	0.342678	−	1.60100i
$172$	2068.14	+	671.980i	0.916827	+	0.297895i
$173$	836.317	+	2573.92i	0.367538	+	1.13116i	0.948377	+	0.317146i	$0.102725\pi$
$173$	836.317	+	2573.92i	0.367538	+	1.13116i	−0.580839	+	0.814018i	$0.697275\pi$
$174$	1559.40	+	1406.09i	0.679411	+	0.612617i
$175$		−	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	−0.704325	−	0.709878i	$-0.748750\pi$
$179$	−2052.11	+	666.770i	−0.856881	+	0.278417i	−0.152555	+	0.988295i	$0.548750\pi$
$180$	−930.822	+	96.4986i	−0.385441	+	0.0399588i
$181$	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
$183$	−340.921	+	3221.67i	−0.137714	+	1.30138i
$184$	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
$189$	−757.579	+	2314.82i	−0.291565	+	0.890890i
$190$	−809.579	−	2491.63i	−0.309121	−	0.951378i
$191$	−2479.80	−	805.737i	−0.939436	−	0.305241i	−0.201021	−	0.979587i	$-0.564426\pi$
$191$	−2479.80	−	805.737i	−0.939436	−	0.305241i	−0.738416	+	0.674346i	$0.764426\pi$
$192$	−777.680	+	1743.37i	−0.292314	+	0.655296i
$193$	−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
$195$	−140.383	+	80.9173i	−0.0515539	+	0.0297159i
$196$	−233.336	+	169.529i	−0.0850350	+	0.0617816i
$197$	2525.92			0.913525			0.456762	−	0.889589i	$-0.349009\pi$
$197$	2525.92			0.913525			0.456762	+	0.889589i	$0.349009\pi$
$198$	−3538.58	−	1402.45i	−1.27008	−	0.503371i
$199$	−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
$201$	1974.74	−	1138.25i	0.692974	−	0.399434i
$202$	−1944.67	+	5985.07i	−0.677357	+	2.08469i
$203$	1067.10	−	1468.74i	0.368945	−	0.507809i
$204$	−93.7943	+	210.264i	−0.0321908	+	0.0721638i
$205$	1622.83	+	527.290i	0.552895	+	0.179646i
$206$	−33.0525	−	101.725i	−0.0111790	−	0.0344054i
$207$	−3617.07	−	2095.16i	−1.21451	−	0.703497i
$208$			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
$213$	51.0130	−	482.068i	0.0164101	−	0.155074i
$214$	2337.90	+	1698.59i	0.746803	+	0.542584i
$215$	1268.96	+	921.952i	0.402522	+	0.292449i
$216$	−551.073	+	177.759i	−0.173592	+	0.0559952i
$217$	−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
$222$	−4000.65	−	3607.35i	−1.20949	−	1.09058i
$223$	−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
$225$	−660.050	−	141.277i	−0.195570	−	0.0418598i
$226$	−1851.63	+	2548.55i	−0.544993	+	0.750119i
$227$	−1523.91	+	4690.11i	−0.445575	+	1.37134i	0.436278	+	0.899812i	$0.356296\pi$
$227$	−1523.91	+	4690.11i	−0.445575	+	1.37134i	−0.881852	+	0.471526i	$0.843704\pi$
$228$	2439.05	+	4231.49i	0.708466	+	1.22911i
$229$	−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
$231$	−883.887	+	3170.16i	−0.251755	+	0.902948i
$232$	431.597			0.122137
$233$	−1339.67	+	973.327i	−0.376673	+	0.273669i	−0.759972	−	0.649955i	$-0.774788\pi$
$233$	−1339.67	+	973.327i	−0.376673	+	0.273669i	0.383300	+	0.923624i	$0.374788\pi$
$234$	484.175	−	434.711i	0.135263	−	0.121444i
$235$	−107.618	+	331.213i	−0.0298732	+	0.0919402i
$236$	−3268.78	+	4499.09i	−0.901608	+	1.24096i
$237$	5026.08	+	2242.03i	1.37755	+	0.614495i
$238$	407.818	+	132.508i	0.111071	+	0.0360892i
$239$	−1610.22	−	4955.75i	−0.435802	−	1.34126i	−0.892263	−	0.451516i	$-0.850883\pi$
$239$	−1610.22	−	4955.75i	−0.435802	−	1.34126i	0.456461	−	0.889743i	$-0.349117\pi$
$240$	−1242.30	+	1377.75i	−0.334125	+	0.370555i
$241$		−	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
$246$	−6814.26	−	721.094i	−1.76610	−	0.186891i
$247$	684.164	+	497.074i	0.176244	+	0.128049i
$248$	−920.063	−	668.465i	−0.235581	−	0.171159i
$249$	722.333	+	76.4383i	0.183839	+	0.0194541i
$250$	−459.382	+	149.262i	−0.116216	+	0.0377607i
$251$	4317.89	+	5943.07i	1.08583	+	1.49451i	0.852938	+	0.522012i	$0.174818\pi$
$251$	4317.89	+	5943.07i	1.08583	+	1.49451i	0.232890	+	0.972503i	$0.425182\pi$
$252$	−1317.38	−	2970.22i	−0.329314	−	0.742484i
$253$	−5008.23	−	2611.41i	−1.24452	−	0.648925i
$254$			94.7715i			0.0234114i
$255$	−111.209	+	123.334i	−0.0273105	+	0.0302882i
$256$	1533.41	+	4719.36i	0.374368	+	1.15219i
$257$	7029.84	+	2284.13i	1.70626	+	0.554398i	0.989704	−	0.143128i	$-0.0457161\pi$
$257$	7029.84	+	2284.13i	1.70626	+	0.554398i	0.716559	+	0.697527i	$0.245716\pi$
$258$	−5752.45	−	2566.04i	−1.38811	−	0.619205i
$259$	−2737.66	+	3768.07i	−0.656796	+	0.904002i
$260$	66.7974	−	205.581i	0.0159331	−	0.0490370i
$261$	−1886.30	−	2100.93i	−0.447352	−	0.498254i
$262$	361.220	−	262.442i	0.0851766	−	0.0618844i
$263$	1846.68			0.432971			0.216486	−	0.976286i	$-0.430541\pi$
$263$	1846.68			0.432971			0.216486	+	0.976286i	$0.430541\pi$
$264$	−733.231	+	272.988i	−0.170937	+	0.0636412i
$265$	−475.504			−0.110226
$266$	7359.21	−	5346.78i	1.69632	−	1.23245i
$267$	−1651.91	−	2865.89i	−0.378635	−	0.656890i
$268$	−939.631	+	2891.89i	−0.214168	+	0.659142i
$269$	−3426.66	+	4716.39i	−0.776680	+	1.06901i	0.218960	+	0.975734i	$0.429733\pi$
$269$	−3426.66	+	4716.39i	−0.776680	+	1.06901i	−0.995640	+	0.0932745i	$0.970267\pi$
$270$	2710.64	+	5.76746i	0.610980	+	0.00129999i
$271$	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
$273$	−417.828	−	376.751i	−0.0926304	−	0.0835238i
$274$		−	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
$279$	767.182	+	7400.21i	0.164624	+	1.58795i
$280$	289.836	+	210.578i	0.0618607	+	0.0449444i
$281$	−1379.05	−	1001.94i	−0.292765	−	0.212707i	0.431701	−	0.902017i	$-0.357914\pi$
$281$	−1379.05	−	1001.94i	−0.292765	−	0.212707i	−0.724466	+	0.689310i	$0.757914\pi$
$282$	147.172	−	1390.76i	0.0310780	−	0.293683i
$283$	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
$288$	3287.20	−	5674.99i	0.672570	−	1.16112i
$289$	−1505.57	−	4633.68i	−0.306447	−	0.943147i
$290$	−1921.56	−	624.354i	−0.389097	−	0.126425i
$291$	−916.084	+	2053.64i	−0.184542	+	0.413699i
$292$	3906.75	−	5377.18i	0.782963	−	1.07766i
$293$	2222.05	−	6838.78i	0.443050	−	1.36357i	−0.441558	−	0.897233i	$-0.645574\pi$
$293$	2222.05	−	6838.78i	0.443050	−	1.36357i	0.884608	−	0.466336i	$-0.154426\pi$
$294$	723.800	−	417.202i	0.143581	−	0.0827609i
$295$	−3245.19	+	2357.77i	−0.640483	+	0.465338i
$296$	−1107.27			−0.217428
$297$	4533.44	+	2376.13i	0.885714	+	0.464232i
$298$	5864.68			1.14004
$299$	781.142	−	567.533i	0.151086	−	0.109770i
$300$	780.161	−	449.689i	0.150142	−	0.0865426i
$301$	−1682.94	+	5179.55i	−0.322269	+	0.991842i
$302$	−673.951	+	927.614i	−0.128416	+	0.176749i
$303$	3447.39	−	7728.22i	0.653623	−	1.46526i
$304$	9208.24	+	2991.94i	1.73727	+	0.564472i
$305$	−963.317	−	2964.79i	−0.180850	−	0.556600i
$306$	334.267	−	577.075i	0.0624469	−	0.107808i
$307$		−	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	−0.570706	−	0.821155i	$-0.693330\pi$
$311$	−3015.15	+	979.681i	−0.549753	+	0.178626i	0.0209521	+	0.999780i	$0.493330\pi$
$312$	14.0750	−	133.007i	0.00255397	−	0.0241348i
$313$	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
$315$	−241.676	−	2331.20i	−0.0432282	−	0.416978i
$316$	−6982.56	+	2268.77i	−1.24304	+	0.403887i
$317$	323.457	+	445.200i	0.0573096	+	0.0788798i	0.836710	−	0.547646i	$-0.184476\pi$
$317$	323.457	+	445.200i	0.0573096	+	0.0788798i	−0.779400	+	0.626526i	$0.784476\pi$
$318$	1868.07	−	395.686i	0.329422	−	0.0697767i
$319$	−2672.23	−	2722.95i	−0.469016	−	0.477918i
$320$		−	1836.90i		−	0.320892i
$321$	−2885.95	−	2602.23i	−0.501801	−	0.452468i
$322$	−3209.41	−	9877.55i	−0.555446	−	1.70949i
$323$	824.311	+	267.835i	0.142000	+	0.0461385i
$324$	−4945.91	+	1036.63i	−0.848064	+	0.177748i
$325$	91.6457	−	126.139i	0.0156418	−	0.0215291i
$326$	−2208.86	+	6798.17i	−0.375268	+	1.15496i
$327$	1629.87	+	2827.64i	0.275632	+	0.478192i
$328$	−1139.50	+	827.892i	−0.191824	+	0.139368i
$329$	−1209.20			−0.202630
$330$	3659.41	−	154.702i	0.610436	−	0.0258062i
$331$	−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
$333$	4839.32	+	5389.97i	0.796376	+	0.886993i
$334$	−1554.71	+	4784.89i	−0.254700	+	0.783885i
$335$	−1289.17	+	1774.39i	−0.210253	+	0.289388i
$336$	−5882.51	−	2624.06i	−0.955110	−	0.426054i
$337$	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
$339$	2836.69	−	3145.97i	0.454477	−	0.504029i
$340$		−	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
$345$	3999.93	+	423.278i	0.624200	+	0.0660537i
$346$	8460.66	+	6147.03i	1.31459	+	0.955105i
$347$	−1704.77	−	1238.58i	−0.263737	−	0.191616i	0.448056	−	0.894005i	$-0.352116\pi$
$347$	−1704.77	−	1238.58i	−0.263737	−	0.191616i	−0.711793	+	0.702390i	$0.752116\pi$
$348$	3745.75	+	396.380i	0.576992	+	0.0610580i
$349$	−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	$0.0696363\pi$
$353$			2878.77i			0.434056i	−0.976165	+	0.217028i	$0.930364\pi$
$354$	10787.1	−	11963.2i	1.61957	−	1.79616i
$355$	144.144	+	443.630i	0.0215503	+	0.0663251i
$356$	4196.91	+	1363.66i	0.624820	+	0.203016i
$357$	−526.595	−	234.903i	−0.0780683	−	0.0348246i
$358$	−4900.84	+	6745.42i	−0.723512	+	0.995829i
$359$	2240.28	−	6894.87i	0.329352	−	1.01364i	−0.640085	−	0.768304i	$-0.721101\pi$
$359$	2240.28	−	6894.87i	0.329352	−	1.01364i	0.969438	−	0.245338i	$-0.0788990\pi$
$360$	414.590	−	372.235i	0.0606967	−	0.0544959i
$361$	9325.91	−	6775.67i	1.35966	−	0.987851i
$362$	4359.47			0.632952
$363$	6262.07	+	2935.75i	0.905436	+	0.424482i
$364$	750.540			0.108074
$365$	3878.56	−	2817.94i	0.556200	−	0.404103i
$366$	6251.62	+	10845.9i	0.892835	+	1.54897i
$367$	−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
$369$	9010.19	+	1928.54i	1.27114	+	0.272075i
$370$	4929.80	+	1601.79i	0.692671	+	0.225062i
$371$	−510.191	−	1570.21i	−0.0713957	−	0.219733i
$372$	−7371.12	−	6646.46i	−1.02735	−	0.926352i
$373$			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
$378$	2889.34	+	8957.26i	0.393152	+	1.21881i
$379$	−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
$381$	13.4109	−	126.731i	0.00180331	−	0.0170410i
$382$	−9582.42	+	3113.52i	−1.28345	+	0.417020i
$383$	−6844.77	−	9421.02i	−0.913190	−	1.25690i	−0.966066	−	0.258297i	$-0.916839\pi$
$383$	−6844.77	−	9421.02i	−0.913190	−	1.25690i	0.0528760	−	0.998601i	$-0.483161\pi$
$384$	−563.754	−	2661.53i	−0.0749191	−	0.353700i
$385$	−465.976	−	3132.36i	−0.0616840	−	0.414650i
$386$			19332.2i			2.54917i
$387$	7329.22	+	4245.40i	0.962701	+	0.557638i
$388$	−927.012	−	2853.05i	−0.121294	−	0.373303i
$389$	3669.25	+	1192.21i	0.478247	+	0.155392i	0.538214	−	0.842808i	$-0.319099\pi$
$389$	3669.25	+	1192.21i	0.478247	+	0.155392i	−0.0599663	+	0.998200i	$0.519099\pi$
$390$	−255.075	+	571.816i	−0.0331185	+	0.0742436i
$391$	581.666	−	800.594i	0.0752330	−	0.103549i
$392$	53.0653	−	163.318i	0.00683725	−	0.0210429i
$393$	−520.172	+	299.830i	−0.0667664	+	0.0384845i
$394$	7896.51	−	5737.15i	1.00970	−	0.733587i
$395$	−5295.71			−0.674573
$396$	−6614.28	+	1695.81i	−0.839344	+	0.215196i
$397$	−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
$399$	−10597.6	+	6108.48i	−1.32968	+	0.766433i
$400$	551.625	−	1697.73i	0.0689531	−	0.212216i
$401$	4540.17	−	6249.01i	0.565400	−	0.778206i	−0.426601	−	0.904440i	$-0.640289\pi$
$401$	4540.17	−	6249.01i	0.565400	−	0.778206i	0.992001	+	0.126234i	$0.0402890\pi$
$402$	3588.10	−	8043.66i	0.445170	−	0.997963i
$403$	−1634.41	−	531.052i	−0.202024	−	0.0656417i
$404$	3488.52	+	10736.6i	0.429605	+	1.32219i
$405$	−3623.94	−	391.289i	−0.444629	−	0.0480081i
$406$		−	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
$411$	−1035.78	+	9787.98i	−0.124309	+	1.17471i
$412$	−155.230	−	112.781i	−0.0185622	−	0.0134862i
$413$	−11267.7	−	8186.50i	−1.34249	−	0.975378i
$414$	−16066.4	+	1665.61i	−1.90730	+	0.197730i
$415$	−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	$0.0339744\pi$
$419$			1827.38i			0.213062i	−0.994309	+	0.106531i	$0.966026\pi$
$420$	2322.03	+	2093.75i	0.269770	+	0.243249i
$421$	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
$423$	−393.606	+	1838.94i	−0.0452430	+	0.211377i
$424$	230.707	−	317.541i	0.0264248	−	0.0363706i
$425$	49.3808	−	151.979i	0.00563605	−	0.0173460i
$426$	−935.449	−	1622.90i	−0.106391	−	0.184577i
$427$	8756.71	−	6362.12i	0.992428	−	0.721041i
$428$	5184.00			0.585463
$429$	−926.288	+	734.712i	−0.104246	+	0.0826859i
$430$	6061.05			0.679744
$431$	−7824.42	+	5684.78i	−0.874453	+	0.635327i	−0.931778	−	0.363028i	$-0.881743\pi$
$431$	−7824.42	+	5684.78i	−0.874453	+	0.635327i	0.0573252	+	0.998356i	$0.481743\pi$
$432$	−5905.47	+	8091.92i	−0.657702	+	0.901210i
$433$	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
$435$	2481.22	+	1106.82i	0.273484	+	0.121995i
$436$	−4140.90	−	1345.46i	−0.454846	−	0.147789i
$437$	−6487.09	−	19965.2i	−0.710114	−	2.18551i
$438$	−12892.5	+	14298.1i	−1.40645	+	1.55980i
$439$		−	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	−0.729059	−	0.684451i	$-0.760042\pi$
$443$	−8546.16	+	2776.82i	−0.916570	+	0.297812i	−0.187511	+	0.982263i	$0.560042\pi$
$444$	−9609.77	−	1016.92i	−1.02716	−	0.108696i
$445$	2575.12	+	1870.93i	0.274320	+	0.199305i
$446$	−5774.41	−	4195.35i	−0.613063	−	0.445416i
$447$	−7842.43	−	829.896i	−0.829830	−	0.0878137i
$448$	6065.79	−	1970.89i	0.639691	−	0.207848i
$449$	−3886.68	−	5349.55i	−0.408516	−	0.562274i	0.554340	−	0.832290i	$-0.312971\pi$
$449$	−3886.68	−	5349.55i	−0.408516	−	0.562274i	−0.962856	+	0.270017i	$0.912971\pi$
$450$	−2384.33	+	1057.52i	−0.249774	+	0.110782i
$451$	12278.3	+	2063.20i	1.28196	+	0.215415i
$452$			5651.08i			0.588063i
$453$	1032.49	−	1145.06i	0.107088	−	0.118763i
$454$	5888.67	+	18123.5i	0.608742	+	1.87352i
$455$	514.868	+	167.291i	0.0530492	+	0.0172367i
$456$	−2655.72	−	1184.66i	−0.272731	−	0.121660i
$457$	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
$459$	−528.651	+	724.380i	−0.0537589	+	0.0736626i
$460$	−4341.11	+	3154.00i	−0.440011	+	0.319687i
$461$	10284.7			1.03906			0.519530	−	0.854452i	$-0.326107\pi$
$461$	10284.7			1.03906			0.519530	+	0.854452i	$0.326107\pi$
$462$	4437.21	+	11918.1i	0.446835	+	1.20017i
$463$	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
$465$	−3575.11	−	6202.43i	−0.356542	−	0.618561i
$466$	−1977.34	+	6085.62i	−0.196563	+	0.604959i
$467$	−4471.25	+	6154.15i	−0.443051	+	0.609808i	−0.970887	−	0.239539i	$-0.923004\pi$
$467$	−4471.25	+	6154.15i	−0.443051	+	0.609808i	0.527835	+	0.849347i	$0.323004\pi$
$468$	244.308	−	1141.42i	0.0241307	−	0.112739i
$469$	−7242.58	−	2353.26i	−0.713073	−	0.231692i
$470$	415.855	+	1279.87i	0.0408126	+	0.125608i
$471$	1584.09	+	1428.36i	0.154970	+	0.139735i
$472$		−	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
$477$	−2554.03	+	264.777i	−0.245160	+	0.0254158i
$478$	−16289.9	−	11835.3i	−1.55875	−	1.13250i
$479$	9454.11	+	6868.81i	0.901815	+	0.655207i	0.938931	−	0.344104i	$-0.111817\pi$
$479$	9454.11	+	6868.81i	0.901815	+	0.655207i	−0.0371167	+	0.999311i	$0.511817\pi$
$480$	−664.101	+	6275.68i	−0.0631498	+	0.596759i
$481$	−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
$486$	14562.7	−	1478.40i	1.35921	−	0.137987i
$487$	−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
$489$	3915.74	−	8778.14i	0.362119	−	0.811782i
$490$	−472.516	+	650.363i	−0.0435635	+	0.0599600i
$491$	173.951	−	535.368i	0.0159884	−	0.0492073i	−0.942744	−	0.333517i	$-0.891764\pi$
$491$	173.951	−	535.368i	0.0159884	−	0.0492073i	0.958732	+	0.284310i	$0.0917645\pi$
$492$	−10649.8	+	6138.60i	−0.975874	+	0.562499i
$493$	540.772	−	392.894i	0.0494019	−	0.0358926i
$494$	3267.84			0.297625
$495$	−4915.36	−	310.962i	−0.446321	−	0.0282358i
$496$	−19675.4			−1.78115
$497$	−1310.29	+	951.983i	−0.118259	+	0.0859201i
$498$	2431.77	−	1401.68i	0.218816	−	0.126126i
$499$	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
$501$	2756.09	−	6178.49i	0.245775	−	0.550967i
$502$	26997.1	+	8771.90i	2.40028	+	0.779898i
$503$	−2867.21	−	8824.36i	−0.254160	−	0.782224i	−0.993994	−	0.109434i	$-0.965096\pi$
$503$	−2867.21	−	8824.36i	−0.254160	−	0.782224i	0.739834	−	0.672789i	$-0.234904\pi$
$504$	1674.03	+	969.669i	0.147951	+	0.0856994i
$505$			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	−0.288724	−	0.957412i	$-0.593231\pi$
$509$	464.459	−	150.912i	0.0404455	−	0.0131415i	0.329170	+	0.944271i	$0.393231\pi$
$510$	−67.5307	+	638.157i	−0.00586335	+	0.0554080i
$511$	13466.9	+	9784.26i	1.16583	+	0.847026i
$512$	12124.2	+	8808.76i	1.04652	+	0.760344i
$513$	5840.13	+	18105.1i	0.502628	+	1.55820i
$514$	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
$519$	−10444.0	−	9417.23i	−0.883314	−	0.796475i
$520$	39.7707	+	122.402i	0.00335397	+	0.0103224i
$521$	15933.5	+	5177.11i	1.33985	+	0.435342i	0.889265	−	0.457393i	$-0.151217\pi$
$521$	15933.5	+	5177.11i	1.33985	+	0.435342i	0.450581	+	0.892735i	$0.351217\pi$
$522$	−10668.8	−	2283.54i	−0.894560	−	0.191471i
$523$	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
$525$	1126.22	+	1953.87i	0.0936236	+	0.162427i
$526$	5773.09	−	4194.39i	0.478553	−	0.347689i
$527$	−1761.32			−0.145587
$528$	−7486.66	+	11277.2i	−0.617074	+	0.929501i
$529$	−11801.3			−0.969945
$530$	−1486.52	+	1080.02i	−0.121830	+	0.0885150i
$531$	−16117.7	+	14471.1i	−1.31723	+	1.18266i
$532$	5042.57	−	15519.4i	0.410946	−	1.26476i
$533$	−1251.03	+	1721.90i	−0.101667	+	0.139932i
$534$	−11673.5	−	5207.32i	−0.945999	−	0.421990i
$535$	3556.21	+	1155.48i	0.287380	+	0.0933755i
$536$	−559.450	−	1721.81i	−0.0450831	−	0.138752i
$537$	7508.07	−	8326.67i	0.603346	−	0.669129i
$538$			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
$543$	−5829.60	−	616.897i	−0.460722	−	0.0487543i
$544$	1256.09	+	912.602i	0.0989970	+	0.0719256i
$545$	−2540.75	−	1845.96i	−0.199695	−	0.145087i
$546$	−2161.93	−	228.778i	−0.169454	−	0.0179319i
$547$	−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
$552$	−2223.37	+	2465.78i	−0.171436	+	0.190128i
$553$	−5682.02	−	17487.5i	−0.436933	−	1.34474i
$554$	2111.57	+	686.092i	0.161935	+	0.0526160i
$555$	−6365.61	−	2839.56i	−0.486856	−	0.217176i
$556$	−2790.35	+	3840.59i	−0.212837	+	0.292944i
$557$	4651.78	−	14316.7i	0.353864	−	1.08908i	−0.602801	−	0.797891i	$-0.705949\pi$
$557$	4651.78	−	14316.7i	0.353864	−	1.08908i	0.956665	−	0.291190i	$-0.0940512\pi$
$558$	19206.5	+	21392.0i	1.45713	+	1.62293i
$559$	−1582.82	+	1149.98i	−0.119760	+	0.0870110i
$560$	6198.09			0.467709
$561$	−670.197	+	1009.52i	−0.0504381	+	0.0759750i
$562$	−6586.88			−0.494396
$563$	−16527.0	+	12007.6i	−1.23718	+	0.898862i	−0.997407	−	0.0719675i	$-0.977072\pi$
$563$	−16527.0	+	12007.6i	−1.23718	+	0.898862i	−0.239771	+	0.970830i	$0.577072\pi$
$564$	−1252.86	−	2173.58i	−0.0935372	−	0.162277i
$565$	−1259.59	+	3876.62i	−0.0937901	+	0.288656i
$566$	17368.2	−	23905.3i	1.28983	−	1.77529i
$567$	−2596.18	−	12386.8i	−0.192292	−	0.917453i
$568$	−366.192	−	118.983i	−0.0270512	−	0.00878946i
$569$	−1746.65	−	5375.63i	−0.128688	−	0.396060i	0.865867	−	0.500274i	$-0.166767\pi$
$569$	−1746.65	−	5375.63i	−0.128688	−	0.396060i	−0.994555	+	0.104214i	$0.966767\pi$
$570$	10110.1	+	9116.15i	0.742921	+	0.669884i
$571$		−	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
$576$	−1022.85	−	9866.36i	−0.0739908	−	0.713712i
$577$	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
$579$	2735.64	−	25851.5i	0.196355	−	1.85553i
$580$	−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
$585$	422.010	−	728.554i	0.0298256	−	0.0514906i
$586$	−8586.43	−	26426.3i	−0.605293	−	1.86290i
$587$	−7883.97	−	2561.66i	−0.554355	−	0.180121i	0.0184246	−	0.999830i	$-0.494135\pi$
$587$	−7883.97	−	2561.66i	−0.554355	−	0.180121i	−0.572780	+	0.819709i	$0.694135\pi$
$588$	610.535	−	1368.67i	0.0428198	−	0.0959916i
$589$	−21961.9	+	30227.9i	−1.53637	+	2.11464i
$590$	−4789.87	+	14741.7i	−0.334230	+	1.02865i
$591$	−11371.3	+	6554.47i	−0.791459	+	0.456201i
$592$	−15497.9	+	11259.9i	−1.07595	+	0.781722i
$593$	−4608.61			−0.319145			−0.159573	−	0.987186i	$-0.551012\pi$
$593$	−4608.61			−0.319145			−0.159573	+	0.987186i	$0.551012\pi$
$594$	19569.3	−	2868.62i	1.35175	−	0.198150i
$595$	554.846			0.0382293
$596$	8511.35	−	6183.86i	0.584964	−	0.425001i
$597$	1556.99	−	897.457i	0.106739	−	0.0615251i
$598$	1152.96	−	3548.43i	0.0788426	−	0.242652i
$599$	6305.20	−	8678.36i	0.430089	−	0.591967i	−0.537884	−	0.843019i	$-0.680776\pi$
$599$	6305.20	−	8678.36i	0.430089	−	0.591967i	0.967974	+	0.251051i	$0.0807763\pi$
$600$	−218.416	+	489.635i	−0.0148613	+	0.0333155i
$601$	−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
$603$	−5936.35	+	10248.5i	−0.400907	+	0.692123i
$604$			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
$609$	−992.713	+	9381.03i	−0.0660538	+	0.624201i
$610$	−9745.46	−	7080.49i	−0.646856	−	0.469969i
$611$	−351.433	−	255.331i	−0.0232691	−	0.0169060i
$612$	−123.364	−	1189.96i	−0.00814816	−	0.0785969i
$613$	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	$-0.957824\pi$
$617$		−	4049.47i		−	0.264223i	0.991235	−	0.132111i	$-0.0421757\pi$
$618$	412.762	+	372.183i	0.0268668	+	0.0242255i
$619$	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
$621$	21720.2	+	46.2142i	1.40354	+	0.00298633i
$622$	−7200.77	+	9911.01i	−0.464187	+	0.638899i
$623$	−3415.22	+	10511.0i	−0.219627	+	0.675943i
$624$	−1155.56	−	2004.77i	−0.0741337	−	0.128614i
$625$	−505.636	+	367.366i	−0.0323607	+	0.0235114i
$626$	24997.2			1.59599
$627$	8968.81	+	24089.7i	0.571260	+	1.53437i
$628$	−2845.48			−0.180807
$629$	−1387.36	+	1007.98i	−0.0879453	+	0.0638960i
$630$	−6050.40	−	6738.84i	−0.382625	−	0.426162i
$631$	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
$633$	964.705	+	430.335i	0.0605744	+	0.0270210i
$634$	2022.37	+	657.109i	0.126686	+	0.0411627i
$635$	37.8941	+	116.626i	0.00236816	+	0.00728846i
$636$	2293.89	−	2543.99i	0.143017	−	0.158610i
$637$		−	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	0.142548	−	0.989788i	$-0.454471\pi$
$641$	13626.6	−	4427.55i	0.839654	−	0.272820i	0.697106	+	0.716968i	$0.254471\pi$
$642$	−14932.5	−	1580.18i	−0.917974	−	0.0971412i
$643$	−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
$645$	−8105.01	−	857.683i	−0.494782	−	0.0523585i
$646$	3185.29	−	1034.96i	0.193999	−	0.0630342i
$647$	−6968.90	−	9591.86i	−0.423455	−	0.582836i	0.542980	−	0.839745i	$-0.317296\pi$
$647$	−6968.90	−	9591.86i	−0.423455	−	0.582836i	−0.966436	+	0.256909i	$0.917296\pi$
$648$	2019.58	−	2230.21i	0.122433	−	0.135202i
$649$	−20889.7	+	20500.6i	−1.26347	+	1.23993i
$650$		−	602.492i		−	0.0363564i
$651$	16645.7	−	18460.6i	1.00215	−	1.11141i
$652$	3962.45	+	12195.2i	0.238009	+	0.732516i
$653$	11196.4	+	3637.95i	0.670981	+	0.218015i	0.624643	−	0.780911i	$-0.285245\pi$
$653$	11196.4	+	3637.95i	0.670981	+	0.218015i	0.0463388	+	0.998926i	$0.485245\pi$
$654$	11517.7	+	5137.81i	0.688653	+	0.307193i
$655$	339.583	−	467.395i	0.0202574	−	0.0278819i
$656$	−7530.10	+	23175.3i	−0.448172	+	1.37933i
$657$	19263.5	−	17295.5i	1.14389	−	1.02703i
$658$	−3780.19	+	2746.47i	−0.223962	+	0.162718i
$659$	10218.3			0.604016			0.302008	−	0.953305i	$-0.402343\pi$
$659$	10218.3			0.604016			0.302008	+	0.953305i	$0.402343\pi$
$660$	5147.74	−	4083.08i	0.303599	−	0.240809i
$661$	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
$663$	−103.444	−	179.465i	−0.00605950	−	0.0105126i
$664$	178.285	−	548.704i	0.0104199	−	0.0320691i
$665$	6918.37	−	9522.33i	0.403433	−	0.555278i
$666$	27371.0	+	5858.47i	1.59250	+	0.340857i
$667$	−15397.3	−	5002.90i	−0.893834	−	0.290424i
$668$	2788.97	+	8583.57i	0.161540	+	0.497168i
$669$	7128.03	+	6427.27i	0.411937	+	0.371439i
$670$			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
$675$	3338.04	−	1076.75i	0.190342	−	0.0613985i
$676$	−12102.8	−	8793.16i	−0.688595	−	0.500294i
$677$	4823.93	+	3504.79i	0.273853	+	0.198966i	0.716232	−	0.697862i	$-0.245865\pi$
$677$	4823.93	+	3504.79i	0.273853	+	0.198966i	−0.442379	+	0.896828i	$0.645865\pi$
$678$	1722.55	−	16277.9i	0.0975726	−	0.922050i
$679$	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	$-0.872509\pi$
$683$		−	13919.3i		−	0.779803i	0.920857	−	0.389901i	$-0.127491\pi$
$684$	−21960.5	−	12720.4i	−1.22760	−	0.711079i
$685$	−2926.72	−	9007.53i	−0.163247	−	0.502424i
$686$	−24538.5	−	7973.05i	−1.36572	−	0.443750i
$687$	3402.48	−	7627.53i	0.188956	−	0.423593i
$688$	−13166.2	+	18121.7i	−0.729587	+	1.00419i
$689$	183.282	−	564.084i	0.0101342	−	0.0311900i
$690$	13465.9	−	7761.84i	0.742956	−	0.428244i
$691$	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
$693$	−4247.07	−	16565.1i	−0.232804	−	0.908019i
$694$	−8142.63			−0.445375
$695$	−2770.21	+	2012.68i	−0.151195	+	0.109849i
$696$	−1942.98	+	1119.94i	−0.105817	+	0.0609934i
$697$	−674.086	+	2074.62i	−0.0366325	+	0.112743i
$698$	−18781.2	+	25850.1i	−1.01845	+	1.40178i
$699$	3505.31	−	7858.05i	0.189675	−	0.425206i
$700$	−2861.32	−	929.700i	−0.154497	−	0.0501991i
$701$	−3297.00	−	10147.1i	−0.177640	−	0.546721i	0.822104	−	0.569337i	$-0.192800\pi$
$701$	−3297.00	−	10147.1i	−0.177640	−	0.546721i	−0.999744	+	0.0226168i	$0.992800\pi$
$702$	−1051.65	+	3213.38i	−0.0565415	+	0.172765i
$703$			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
$708$	3040.91	−	28736.3i	0.161419	−	1.52539i
$709$	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
$711$	−28444.4	+	2948.84i	−1.50035	+	0.155542i
$712$	−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
$717$	20108.6	+	18131.7i	1.04738	+	0.944407i
$718$	−8656.86	−	26643.1i	−0.449960	−	1.38483i
$719$	−32453.5	−	10544.8i	−1.68333	−	0.546945i	−0.697773	−	0.716319i	$-0.745826\pi$
$719$	−32453.5	−	10544.8i	−1.68333	−	0.546945i	−0.985552	+	0.169373i	$0.945826\pi$
$720$	2017.54	−	9426.01i	0.104430	−	0.487898i
$721$	282.455	−	388.765i	0.0145897	−	0.0200810i
$722$	13764.9	−	42364.1i	0.709526	−	2.18370i
$723$	4205.70	+	7296.44i	0.216337	+	0.375321i
$724$	6326.84	−	4596.72i	0.324773	−	0.235961i
$725$	−2614.33			−0.133922
$726$	26244.4	−	5045.38i	1.34163	−	0.257923i
$727$	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
$729$	−19682.8	−	83.7589i	−0.999991	−	0.00425539i
$730$	5724.71	−	17618.8i	0.290248	−	0.893291i
$731$	−1178.62	+	1622.23i	−0.0596346	+	0.0820800i
$732$	20509.1	+	9148.66i	1.03557	+	0.461946i
$733$	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
$735$	723.894	−	802.820i	0.0363282	−	0.0402891i
$736$		−	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
$741$	−4369.85	−	462.423i	−0.216640	−	0.0229251i
$742$	−5161.38	−	3749.96i	−0.255364	−	0.185533i
$743$	7422.51	+	5392.77i	0.366495	+	0.266274i	0.755756	−	0.654853i	$-0.227270\pi$
$743$	7422.51	+	5392.77i	0.366495	+	0.266274i	−0.389261	+	0.921127i	$0.627270\pi$
$744$	5876.56	+	621.866i	0.289577	+	0.0306434i
$745$	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
$750$	1680.75	−	1864.00i	0.0818297	−	0.0907515i
$751$	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
$753$	−34860.0	−	15550.3i	−1.68708	−	0.752570i
$754$	1481.33	−	2038.87i	0.0715473	−	0.0984765i
$755$	−458.463	+	1411.00i	−0.0220996	+	0.0680155i
$756$	13638.0	+	9952.99i	0.656097	+	0.478819i
$757$	−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
$759$	29322.6	−	1239.61i	1.40229	−	0.0592820i
$760$	2798.19			0.133554
$761$	−18294.0	+	13291.4i	−0.871429	+	0.633130i	−0.930970	−	0.365096i	$-0.881036\pi$
$761$	−18294.0	+	13291.4i	−0.871429	+	0.633130i	0.0595411	+	0.998226i	$0.481036\pi$
$762$	−245.921	−	426.646i	−0.0116913	−	0.0202832i
$763$	3369.63	−	10370.7i	0.159881	−	0.492062i
$764$	−10623.9	+	14622.5i	−0.503088	+	0.692441i
$765$	180.608	−	843.806i	0.00853581	−	0.0398796i
$766$	−42796.2	−	13905.3i	−2.01865	−	0.655900i
$767$	−1546.14	−	4758.53i	−0.0727873	−	0.224016i
$768$	−19149.4	−	17266.8i	−0.899731	−	0.811278i
$769$			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	−0.159487	−	0.987200i	$-0.550984\pi$
$773$	6270.11	−	2037.28i	0.291747	−	0.0947943i	0.451234	+	0.892406i	$0.350984\pi$
$774$	32555.2	−	3375.01i	1.51185	−	0.156734i
$775$	5573.13	+	4049.12i	0.258313	+	0.187676i
$776$	1444.99	+	1049.85i	0.0668455	+	0.0485661i
$777$	2546.82	−	24067.2i	0.117589	−	1.11120i
$778$	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
$783$	13943.5	+	4563.33i	0.636398	+	0.208276i
$784$	−918.066	−	2825.52i	−0.0418215	−	0.128713i
$785$	−1951.99	−	634.240i	−0.0887510	−	0.0288370i
$786$	−945.151	+	2118.80i	−0.0428911	+	0.0961514i
$787$	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
$789$	−8313.48	+	4791.93i	−0.375118	+	0.216220i
$790$	−16555.4	+	12028.2i	−0.745589	+	0.541702i
$791$	−14152.8			−0.636178
$792$	2592.52	−	3131.60i	0.116314	−	0.140501i
$793$	3888.39			0.174125
$794$	−44387.4	+	32249.3i	−1.98394	+	1.44142i
$795$	2140.64	−	1233.88i	0.0954978	−	0.0550454i
$796$	−740.853	+	2280.11i	−0.0329885	+	0.101528i
$797$	−23080.2	+	31767.2i	−1.02577	+	1.41186i	−0.117700	+	0.993049i	$0.537552\pi$
$797$	−23080.2	+	31767.2i	−1.02577	+	1.41186i	−0.908074	+	0.418809i	$0.862448\pi$
$798$	−19255.7	+	43166.6i	−0.854192	+	1.91489i
$799$	−423.422	−	137.578i	−0.0187479	−	0.00609157i
$800$	−1876.50	−	5775.28i	−0.0829305	−	0.255234i
$801$	14873.3	+	8615.26i	0.656083	+	0.380032i
$802$		−	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
$807$	3187.78	−	30124.2i	0.139052	−	1.31403i
$808$	−5437.76	−	3950.77i	−0.236757	−	0.172014i
$809$	16043.8	+	11656.5i	0.697244	+	0.506578i	0.879034	−	0.476760i	$-0.158189\pi$
$809$	16043.8	+	11656.5i	0.697244	+	0.506578i	−0.181789	+	0.983338i	$0.558189\pi$
$810$	−12217.9	+	7007.84i	−0.529990	+	0.303988i
$811$	−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
$816$	−1761.31	−	1588.15i	−0.0755614	−	0.0681329i
$817$	13144.7	+	40455.3i	0.562883	+	1.73238i
$818$	−3248.51	−	1055.51i	−0.138853	−	0.0451160i
$819$	2858.62	+	611.858i	0.121964	+	0.0261051i
$820$	6952.48	−	9569.27i	0.296087	−	0.407529i
$821$	−8000.11	+	24621.8i	−0.340080	+	1.04666i	0.624085	+	0.781356i	$0.285472\pi$
$821$	−8000.11	+	24621.8i	−0.340080	+	1.04666i	−0.964165	+	0.265302i	$0.914528\pi$
$822$	18993.5	+	32951.7i	0.805931	+	1.39820i
$823$	−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
$825$	4441.43	−	1653.58i	0.187431	−	0.0697823i
$826$	−53819.2			−2.26708
$827$	−26406.7	+	19185.6i	−1.11034	+	0.806709i	−0.982717	−	0.185114i	$-0.940735\pi$
$827$	−26406.7	+	19185.6i	−1.11034	+	0.806709i	−0.127622	+	0.991823i	$0.540735\pi$
$828$	−21560.8	+	19358.1i	−0.904937	+	0.812488i
$829$	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
$831$	−2726.57	−	1216.27i	−0.113819	−	0.0507723i
$832$	2179.08	+	708.028i	0.0908007	+	0.0295029i
$833$	−82.1842	−	252.937i	−0.00341839	−	0.0105207i
$834$	9208.28	−	10212.3i	0.382322	−	0.424006i
$835$			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	0.659165	−	0.751998i	$-0.270910\pi$
$839$	39720.6	−	12906.0i	1.63445	−	0.531067i	0.975289	+	0.220931i	$0.0709097\pi$
$840$	−1851.22	−	195.899i	−0.0760395	−	0.00804660i
$841$	10884.1	+	7907.73i	0.446269	+	0.324234i
$842$	17195.5	+	12493.2i	0.703795	+	0.511337i
$843$	8808.16	+	932.092i	0.359869	+	0.0380818i
$844$	−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
$849$	−26608.1	+	29509.2i	−1.07560	+	1.19288i
$850$	−190.817	−	587.273i	−0.00769995	−	0.0236980i
$851$	39502.1	+	12835.0i	1.59120	+	0.517014i
$852$	−3068.83	−	1368.94i	−0.123400	−	0.0550459i
$853$	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
$855$	−12229.5	−	13621.0i	−0.489170	−	0.544830i
$856$	−2497.05	+	1814.21i	−0.0997048	+	0.0724398i
$857$	−17159.8			−0.683976			−0.341988	−	0.939704i	$-0.611100\pi$
$857$	−17159.8			−0.683976			−0.341988	+	0.939704i	$0.611100\pi$
$858$	−1226.99	+	4400.74i	−0.0488215	+	0.175103i
$859$	−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
$861$	−15373.8	−	26671.9i	−0.608523	−	1.05572i
$862$	−11548.8	+	35543.4i	−0.456325	+	1.40442i
$863$	26088.4	−	35907.6i	1.02904	−	1.41635i	0.123368	−	0.992361i	$-0.460630\pi$
$863$	26088.4	−	35907.6i	1.02904	−	1.41635i	0.905668	−	0.423987i	$-0.139370\pi$
$864$	−72.5076	+	34077.8i	−0.00285504	+	1.34184i
$865$	12869.6	+	4181.58i	0.505872	+	0.164368i
$866$	−14679.3	−	45178.3i	−0.576009	−	1.77277i
$867$	18801.7	+	16953.3i	0.736494	+	0.664088i
$868$			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
$873$	−1204.89	−	11622.3i	−0.0467116	−	0.450578i
$874$	−65627.1	−	47680.9i	−2.53990	−	1.84534i
$875$	−1755.63	−	1275.54i	−0.0678300	−	0.0492814i
$876$	−3634.41	+	34344.8i	−0.140177	+	1.32466i
$877$	−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	$-0.998580\pi$
$881$		−	233.275i		−	0.00892079i	0.999990	−	0.00446040i	$-0.00141979\pi$
$882$	−2175.84	+	3756.35i	−0.0830662	+	0.143405i
$883$	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
$885$	8491.21	−	19035.2i	0.322518	−	0.723008i
$886$	−20409.9	+	28091.8i	−0.773911	+	1.06520i
$887$	6378.67	−	19631.5i	0.241460	−	0.743137i	−0.754739	−	0.656025i	$-0.772236\pi$
$887$	6378.67	−	19631.5i	0.241460	−	0.743137i	0.996199	−	0.0871114i	$-0.0277636\pi$
$888$	4984.75	−	2873.24i	0.188375	−	0.108580i
$889$	−344.464	+	250.268i	−0.0129954	+	0.00944174i
$890$	12299.8			0.463247
$891$	−26574.6	+	1066.80i	−0.999195	+	0.0401114i
$892$	−12804.0			−0.480617
$893$	−7640.78	+	5551.35i	−0.286326	+	0.208028i
$894$	−26401.9	+	15218.2i	−0.987708	+	0.569320i
$895$	−3333.85	+	10260.5i	−0.124512	+	0.383209i
$896$	−5342.75	+	7353.67i	−0.199206	+	0.274184i
$897$	−2043.89	+	4581.91i	−0.0760799	+	0.170553i
$898$	−24301.0	−	7895.87i	−0.903045	−	0.293417i
$899$	8904.40	+	27404.9i	0.330343	+	1.01669i
$900$	−2345.27	+	4048.86i	−0.0868619	+	0.149958i
$901$		−	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
$906$	626.970	−	5924.80i	0.0229908	−	0.217261i
$907$	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
$909$	4534.21	+	43736.8i	0.165446	+	1.59588i
$910$	1989.55	−	646.443i	0.0724756	−	0.0235488i
$911$	24938.5	+	34324.9i	0.906969	+	1.24834i	0.968191	+	0.250212i	$0.0805003\pi$
$911$	24938.5	+	34324.9i	0.906969	+	1.24834i	−0.0612219	+	0.998124i	$0.519500\pi$
$912$	−49217.8	+	10425.1i	−1.78702	+	0.378519i
$913$	−4565.62	+	2272.49i	−0.165498	+	0.0823752i
$914$		−	32.0038i		−	0.00115820i
$915$	12030.0	+	10847.3i	0.434643	+	0.391913i
$916$	3443.07	+	10596.7i	0.124195	+	0.382232i
$917$	1907.78	+	619.877i	0.0687030	+	0.0223229i
$918$	−7.37310	+	3465.28i	−0.000265086	+	0.124588i
$919$	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
$921$	9519.99	+	16516.1i	0.340602	+	0.590907i
$922$	32152.0	−	23359.8i	1.14845	−	0.834396i
$923$	−581.832			−0.0207489
$924$	19006.4	+	12617.9i	0.676693	+	0.449241i
$925$	6707.11			0.238409
$926$	33710.7	−	24492.3i	1.19633	−	0.869186i
$927$	−499.290	−	556.102i	−0.0176902	−	0.0197031i
$928$	7849.28	−	24157.6i	0.277657	−	0.854539i
$929$	27705.1	−	38132.8i	0.978445	−	1.34671i	0.0407819	−	0.999168i	$-0.487015\pi$
$929$	27705.1	−	38132.8i	0.978445	−	1.34671i	0.937663	−	0.347546i	$-0.112985\pi$
$930$	−25264.1	−	11269.8i	−0.890800	−	0.397367i
$931$	−5365.69	−	1743.42i	−0.188887	−	0.0613730i
$932$	3547.13	+	10916.9i	0.124667	+	0.383687i
$933$	11031.6	−	12234.3i	0.387092	−	0.429297i
$934$			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
$939$	−33426.9	−	3537.28i	−1.16171	−	0.122934i
$940$	1953.05	+	1418.97i	0.0677674	+	0.0492359i
$941$	−3510.20	−	2550.31i	−0.121604	−	0.0883504i	0.525321	−	0.850904i	$-0.323945\pi$
$941$	−3510.20	−	2550.31i	−0.121604	−	0.0883504i	−0.646925	+	0.762554i	$0.723945\pi$
$942$	8196.40	+	867.354i	0.283496	+	0.0299999i
$943$	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	$0.151029\pi$
$947$			26628.5i			0.913737i	−0.889534	+	0.456869i	$0.848971\pi$
$948$	25547.2	−	28332.6i	0.875247	−	0.970675i
$949$	1847.90	+	5687.25i	0.0632091	+	0.194537i
$950$	−12458.1	−	4047.90i	−0.425469	−	0.138243i
$951$	−2611.39	−	1164.89i	−0.0890433	−	0.0397203i
$952$	−269.202	+	370.525i	−0.00916481	+	0.0126143i
$953$	8328.10	−	25631.3i	0.283078	−	0.871225i	−0.703890	−	0.710309i	$-0.748555\pi$
$953$	8328.10	−	25631.3i	0.283078	−	0.871225i	0.986968	−	0.160916i	$-0.0514449\pi$
$954$	−7383.00	+	6628.75i	−0.250559	+	0.224962i
$955$	−10547.2	+	7663.02i	−0.357383	+	0.259654i
$956$	−36120.8			−1.22200
$957$	19095.7	+	5324.16i	0.645011	+	0.179839i
$958$	45156.6			1.52290
$959$	26604.4	−	19329.2i	0.895830	−	0.650858i
$960$	4766.53	+	8269.41i	0.160249	+	0.278015i
$961$	14257.2	−	43879.2i	0.478574	−	1.47290i
$962$	−3800.36	+	5230.75i	−0.127369	+	0.175308i
$963$	19744.6	+	4226.12i	0.660706	+	0.141417i
$964$	−10685.2	−	3471.82i	−0.356998	−	0.115996i
$965$	7729.91	+	23790.2i	0.257860	+	0.793611i
$966$	40079.4	+	36139.1i	1.33492	+	1.20368i
$967$			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	−0.502742	−	0.864436i	$-0.667675\pi$
$971$	−12144.2	+	3945.90i	−0.401366	+	0.130412i	0.101376	+	0.994848i	$0.467675\pi$
$972$	19575.8	−	17500.8i	0.645980	−	0.577509i
$973$	−9618.55	−	6988.29i	−0.316913	−	0.230251i
$974$	−47380.4	−	34423.9i	−1.55869	−	1.13246i
$975$	−85.2571	+	805.670i	−0.00280042	+	0.0264637i
$976$	42339.4	−	13756.9i	1.38858	−	0.451176i
$977$	−13380.8	−	18417.1i	−0.438169	−	0.603088i	0.531635	−	0.846974i	$-0.321578\pi$
$977$	−13380.8	−	18417.1i	−0.438169	−	0.603088i	−0.969804	+	0.243886i	$0.921578\pi$
$978$	−7696.53	−	36336.0i	−0.251644	−	1.18803i
$979$	20593.7	+	10738.1i	0.672297	+	0.350552i
$980$			1442.10i			0.0470062i
$981$	−14674.8	−	8500.28i	−0.477605	−	0.276649i
$982$	−672.181	−	2068.76i	−0.0218433	−	0.0672268i
$983$	44775.6	+	14548.5i	1.45282	+	0.472049i	0.925868	−	0.377848i	$-0.123336\pi$
$983$	44775.6	+	14548.5i	1.45282	+	0.472049i	0.526949	+	0.849897i	$0.323336\pi$
$984$	2981.55	−	6683.90i	0.0965937	−	0.216540i
$985$	7423.49	−	10217.6i	0.240134	−	0.330516i
$986$	798.173	−	2456.52i	0.0257799	−	0.0793424i
$987$	5443.62	−	3137.73i	0.175554	−	0.101190i
$988$	4742.57	−	3445.68i	0.152714	−	0.110953i
$989$	48566.7			1.56151
$990$	−16072.7	+	10192.2i	−0.515982	+	0.327201i
$991$	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
$993$	37313.3	−	21507.6i	1.19245	−	0.687334i
$994$	−1933.97	+	5952.16i	−0.0617122	+	0.189931i
$995$	−1016.45	+	1399.02i	−0.0323854	+	0.0445747i
$996$	2051.23	−	4598.36i	0.0652567	−	0.146290i
$997$	−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
$999$	−35772.2	−	11707.3i	−1.13292	−	0.370773i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.p.a.41.9	✓	192	3.2	odd	2	inner
165.4.p.a.41.40	yes	192	1.1	even	1	trivial
165.4.p.a.161.9	yes	192	11.7	odd	10	inner
165.4.p.a.161.40	yes	192	33.29	even	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} +(-4.50184 + 2.59488i) q^{3} +(2.14208 - 6.59266i) q^{4} +(2.93893 - 4.04508i) q^{5} +(-8.17983 + 18.3372i) q^{6} +(16.5110 + 5.36474i) q^{7} +(1.27538 + 3.92522i) q^{8} +(13.5332 - 23.3635i) 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} +(-2.73405 + 25.8365i) q^{15} +(57.7669 + 41.9701i) q^{16} +(5.17123 + 3.75712i) q^{17} +(-10.7586 - 103.777i) 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} +(-15.9271 - 14.3613i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(22.9202 + 7.44721i) q^{26} +(-0.298508 + 140.296i) q^{27} +(70.7358 - 97.3594i) q^{28} +(32.3149 - 99.4551i) q^{29} +(50.1356 + 86.9798i) q^{30} +(-222.925 + 161.965i) q^{31} +242.900 q^{32} +(8.00695 + 189.401i) q^{33} +24.6998 q^{34} +(70.2254 - 51.0217i) q^{35} +(-125.038 - 139.266i) q^{36} +(-82.9044 + 255.153i) q^{37} +(307.982 - 423.901i) q^{38} +(-29.5957 - 13.2020i) q^{39} +(19.6261 + 6.37691i) q^{40} +(105.458 + 324.566i) q^{41} +(-233.431 + 258.882i) 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} +(-368.965 - 39.0444i) q^{48} +(-33.6611 - 24.4562i) q^{49} +(-78.1548 - 56.7828i) q^{50} +(-33.0293 - 3.49521i) 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} +(-471.828 + 523.271i) q^{57} +(-124.871 - 384.313i) q^{58} +(-762.991 - 247.911i) q^{59} +(164.475 + 73.3686i) q^{60} +(366.468 - 504.399i) q^{61} +(-329.035 + 1012.67i) q^{62} +(348.785 - 313.152i) q^{63} +(297.216 - 215.940i) q^{64} +31.1834 q^{65} +(455.221 + 573.919i) q^{66} -438.653 q^{67} +(35.8466 - 26.0441i) q^{68} +(401.732 + 696.962i) q^{69} +(103.652 - 319.007i) q^{70} +(-54.8356 + 75.4748i) q^{71} +(108.967 + 23.3232i) q^{72} +(911.904 + 296.296i) q^{73} +(320.358 + 985.960i) q^{74} +(96.4757 + 86.9911i) 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} +(-362.707 - 632.364i) q^{81} +(1066.87 + 775.129i) q^{82} +(-113.092 - 82.1661i) q^{83} +(-65.8048 + 621.848i) 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} +(-451.405 - 261.473i) q^{90} +(33.4582 + 102.974i) q^{91} +(-1020.66 - 331.631i) q^{92} +(583.295 - 1307.60i) q^{93} +(-158.200 + 217.744i) q^{94} +(209.508 - 644.801i) q^{95} +(-1093.50 + 630.297i) q^{96} +(350.112 - 254.371i) q^{97} -160.779 q^{98} +(-527.521 - 831.878i) 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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