LMFDB - Embedded newform 168.4.ba.c.5.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(5,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.5"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [176,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	168.5
Dual form			168.4.ba.c.101.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.65194 - 0.983470i) q^{2} +(4.15215 - 3.12404i) q^{3} +(6.06558 + 5.21621i) q^{4} +(11.2278 + 6.48238i) q^{5} +(-14.0837 + 4.20125i) q^{6} +(-0.198886 - 18.5192i) q^{7} +(-10.9556 - 19.7984i) q^{8} +(7.48076 - 25.9430i) q^{9} +(-23.4003 - 28.2331i) q^{10} +(11.4142 + 19.7700i) q^{11} +(41.4808 + 2.70939i) q^{12} +3.71397 q^{13} +(-17.6856 + 49.3074i) q^{14} +(66.8709 - 8.16029i) q^{15} +(9.58241 + 63.2786i) q^{16} +(52.8272 + 91.4995i) q^{17} +(-45.3527 + 61.4421i) q^{18} +(58.0142 - 100.484i) q^{19} +(34.2897 + 97.8860i) q^{20} +(-58.6805 - 76.2732i) q^{21} +(-10.8266 - 63.6542i) q^{22} +(-54.0553 - 31.2089i) q^{23} +(-107.340 - 47.9803i) q^{24} +(21.5426 + 37.3129i) q^{25} +(-9.84922 - 3.65257i) q^{26} +(-49.9856 - 131.089i) q^{27} +(95.3935 - 113.367i) q^{28} +57.9724 q^{29} +(-185.363 - 44.1248i) q^{30} +(-10.4280 + 6.02060i) q^{31} +(36.8206 - 177.235i) q^{32} +(109.156 + 46.4295i) q^{33} +(-50.1077 - 294.605i) q^{34} +(117.815 - 209.219i) q^{35} +(180.699 - 118.338i) q^{36} +(-122.443 - 70.6922i) q^{37} +(-252.673 + 209.421i) q^{38} +(15.4210 - 11.6026i) q^{39} +(5.33357 - 293.311i) q^{40} +417.036 q^{41} +(80.6048 + 259.982i) q^{42} -212.999i q^{43} +(-33.8905 + 179.455i) q^{44} +(252.165 - 242.790i) q^{45} +(112.659 + 135.926i) q^{46} +(-88.0065 + 152.432i) q^{47} +(237.472 + 232.807i) q^{48} +(-342.921 + 7.36641i) q^{49} +(-20.4336 - 120.138i) q^{50} +(505.195 + 214.885i) q^{51} +(22.5274 + 19.3728i) q^{52} +(-201.587 - 349.159i) q^{53} +(3.63645 + 396.801i) q^{54} +295.965i q^{55} +(-364.471 + 206.826i) q^{56} +(-73.0307 - 598.462i) q^{57} +(-153.739 - 57.0141i) q^{58} +(-24.0393 + 13.8791i) q^{59} +(448.176 + 299.315i) q^{60} +(-425.644 + 737.237i) q^{61} +(33.5755 - 5.71067i) q^{62} +(-481.931 - 133.378i) q^{63} +(-271.951 + 433.805i) q^{64} +(41.6998 + 24.0754i) q^{65} +(-243.812 - 230.479i) q^{66} +(683.478 - 394.606i) q^{67} +(-156.852 + 830.555i) q^{68} +(-321.944 + 39.2870i) q^{69} +(-518.201 + 438.969i) q^{70} +482.779i q^{71} +(-595.585 + 136.113i) q^{72} +(228.529 - 131.942i) q^{73} +(255.187 + 307.890i) q^{74} +(206.015 + 87.6290i) q^{75} +(876.032 - 306.877i) q^{76} +(363.853 - 215.313i) q^{77} +(-52.3063 + 15.6033i) q^{78} +(-71.1227 + 123.188i) q^{79} +(-302.607 + 772.597i) q^{80} +(-617.077 - 388.146i) q^{81} +(-1105.95 - 410.142i) q^{82} -477.893i q^{83} +(41.9258 - 768.730i) q^{84} +1369.79i q^{85} +(-209.478 + 564.860i) q^{86} +(240.710 - 181.108i) q^{87} +(266.364 - 442.573i) q^{88} +(-677.670 + 1173.76i) q^{89} +(-907.503 + 395.868i) q^{90} +(-0.738656 - 68.7797i) q^{91} +(-165.085 - 471.263i) q^{92} +(-24.4900 + 57.5759i) q^{93} +(383.300 - 317.688i) q^{94} +(1302.75 - 752.141i) q^{95} +(-400.804 - 850.936i) q^{96} +1362.01i q^{97} +(916.650 + 317.717i) q^{98} +(598.278 - 148.224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 30 q^{4} - 76 q^{7} - 110 q^{9} + 330 q^{10} + 162 q^{12} - 332 q^{15} + 374 q^{16} + 18 q^{18} - 212 q^{22} - 84 q^{24} + 1112 q^{25} + 30 q^{28} - 104 q^{30} + 408 q^{31} + 2262 q^{33} + 1372 q^{36}+ \cdots - 1782 q^{96}+O(q^{100}) $ 176 * q + 30 * q^4 - 76 * q^7 - 110 * q^9 + 330 * q^10 + 162 * q^12 - 332 * q^15 + 374 * q^16 + 18 * q^18 - 212 * q^22 - 84 * q^24 + 1112 * q^25 + 30 * q^28 - 104 * q^30 + 408 * q^31 + 2262 * q^33 + 1372 * q^36 - 56 * q^39 - 2274 * q^40 - 1488 * q^42 - 844 * q^46 + 1292 * q^49 - 1632 * q^52 - 480 * q^54 + 100 * q^57 - 574 * q^58 - 524 * q^60 - 3030 * q^63 - 3420 * q^64 + 2376 * q^66 + 2442 * q^70 + 1026 * q^72 - 660 * q^73 - 1316 * q^78 + 3216 * q^79 + 2298 * q^81 - 360 * q^82 - 4164 * q^84 - 6972 * q^87 - 4042 * q^88 + 4476 * q^94 - 1782 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−2.65194	−	0.983470i	−0.937603	−	0.347709i
$2$	−2.65194	−	0.983470i	−0.937603	−	0.347709i
$3$	4.15215	−	3.12404i	0.799082	−	0.601222i
$3$	4.15215	−	3.12404i	0.799082	−	0.601222i
$4$	6.06558	+	5.21621i	0.758197	+	0.652026i
$5$	11.2278	+	6.48238i	1.00425	+	0.579802i	0.909502	−	0.415699i	$-0.136463\pi$
$5$	11.2278	+	6.48238i	1.00425	+	0.579802i	0.0947447	+	0.995502i	$0.469797\pi$
$6$	−14.0837	+	4.20125i	−0.958272	+	0.285859i
$7$	−0.198886	−	18.5192i	−0.0107388	−	0.999942i
$7$	−0.198886	−	18.5192i	−0.0107388	−	0.999942i
$8$	−10.9556	−	19.7984i	−0.484172	−	0.874973i
$9$	7.48076	−	25.9430i	0.277065	−	0.960851i
$10$	−23.4003	−	28.2331i	−0.739982	−	0.892810i
$11$	11.4142	+	19.7700i	0.312864	+	0.541897i	0.978981	−	0.203951i	$-0.0653782\pi$
$11$	11.4142	+	19.7700i	0.312864	+	0.541897i	−0.666117	+	0.745847i	$0.732045\pi$
$12$	41.4808	+	2.70939i	0.997874	+	0.0651778i
$13$	3.71397			0.0792361			0.0396181	−	0.999215i	$-0.487386\pi$
$13$	3.71397			0.0792361			0.0396181	+	0.999215i	$0.487386\pi$
$14$	−17.6856	+	49.3074i	−0.337620	+	0.941282i
$15$	66.8709	−	8.16029i	1.15107	−	0.140465i
$16$	9.58241	+	63.2786i	0.149725	+	0.988728i
$17$	52.8272	+	91.4995i	0.753676	+	1.30540i	0.946030	+	0.324079i	$0.105054\pi$
$17$	52.8272	+	91.4995i	0.753676	+	1.30540i	−0.192354	+	0.981326i	$0.561612\pi$
$18$	−45.3527	+	61.4421i	−0.593874	+	0.804558i
$19$	58.0142	−	100.484i	0.700493	−	1.21329i	−0.267800	−	0.963474i	$-0.586297\pi$
$19$	58.0142	−	100.484i	0.700493	−	1.21329i	0.968293	−	0.249815i	$-0.0803699\pi$
$20$	34.2897	+	97.8860i	0.383371	+	1.09440i
$21$	−58.6805	−	76.2732i	−0.609768	−	0.792580i
$22$	−10.8266	−	63.6542i	−0.104920	−	0.616870i
$23$	−54.0553	−	31.2089i	−0.490057	−	0.282935i	0.234541	−	0.972106i	$-0.424641\pi$
$23$	−54.0553	−	31.2089i	−0.490057	−	0.282935i	−0.724598	+	0.689172i	$0.757975\pi$
$24$	−107.340	−	47.9803i	−0.912946	−	0.408081i
$25$	21.5426	+	37.3129i	0.172341	+	0.298503i
$26$	−9.84922	−	3.65257i	−0.0742920	−	0.0275511i
$27$	−49.9856	−	131.089i	−0.356287	−	0.934377i
$28$	95.3935	−	113.367i	0.643846	−	0.765155i
$29$	57.9724			0.371214			0.185607	−	0.982624i	$-0.440575\pi$
$29$	57.9724			0.371214			0.185607	+	0.982624i	$0.440575\pi$
$30$	−185.363	−	44.1248i	−1.12808	−	0.268535i
$31$	−10.4280	+	6.02060i	−0.0604169	+	0.0348817i	−0.529904	−	0.848058i	$-0.677772\pi$
$31$	−10.4280	+	6.02060i	−0.0604169	+	0.0348817i	0.469487	+	0.882939i	$0.344439\pi$
$32$	36.8206	−	177.235i	0.203407	−	0.979094i
$33$	109.156	+	46.4295i	0.575804	+	0.244919i
$34$	−50.1077	−	294.605i	−0.252747	−	1.48601i
$35$	117.815	−	209.219i	0.568984	−	1.01042i
$36$	180.699	−	118.338i	0.836570	−	0.547861i
$37$	−122.443	−	70.6922i	−0.544039	−	0.314101i	0.202676	−	0.979246i	$-0.435036\pi$
$37$	−122.443	−	70.6922i	−0.544039	−	0.314101i	−0.746714	+	0.665145i	$0.768370\pi$
$38$	−252.673	+	209.421i	−1.07866	+	0.894016i
$39$	15.4210	−	11.6026i	0.0633162	−	0.0476385i
$40$	5.33357	−	293.311i	0.0210828	−	1.15941i
$41$	417.036			1.58854			0.794269	−	0.607566i	$-0.207854\pi$
$41$	417.036			1.58854			0.794269	+	0.607566i	$0.207854\pi$
$42$	80.6048	+	259.982i	0.296133	+	0.955147i
$43$		−	212.999i		−	0.755396i	−0.925929	−	0.377698i	$-0.876716\pi$
$43$		−	212.999i		−	0.755396i	0.925929	−	0.377698i	$-0.123284\pi$
$44$	−33.8905	+	179.455i	−0.116118	+	0.614860i
$45$	252.165	−	242.790i	0.835345	−	0.804289i
$46$	112.659	+	135.926i	0.361100	+	0.435678i
$47$	−88.0065	+	152.432i	−0.273129	+	0.473074i	−0.969661	−	0.244452i	$-0.921392\pi$
$47$	−88.0065	+	152.432i	−0.273129	+	0.473074i	0.696532	+	0.717525i	$0.254725\pi$
$48$	237.472	+	232.807i	0.714087	+	0.700057i
$49$	−342.921	+	7.36641i	−0.999769	+	0.0214764i
$50$	−20.4336	−	120.138i	−0.0577951	−	0.339802i
$51$	505.195	+	214.885i	1.38709	+	0.590000i
$52$	22.5274	+	19.3728i	0.0600766	+	0.0516640i
$53$	−201.587	−	349.159i	−0.522455	−	0.904919i	−0.999659	−	0.0261258i	$-0.991683\pi$
$53$	−201.587	−	349.159i	−0.522455	−	0.904919i	0.477204	−	0.878793i	$-0.341650\pi$
$54$	3.63645	+	396.801i	0.00916405	+	0.999958i
$55$			295.965i			0.725597i
$56$	−364.471	+	206.826i	−0.869723	+	0.493540i
$57$	−73.0307	−	598.462i	−0.169704	−	1.39067i
$58$	−153.739	−	57.0141i	−0.348051	−	0.129074i
$59$	−24.0393	+	13.8791i	−0.0530449	+	0.0306255i	−0.526288	−	0.850306i	$-0.676417\pi$
$59$	−24.0393	+	13.8791i	−0.0530449	+	0.0306255i	0.473243	+	0.880932i	$0.343083\pi$
$60$	448.176	+	299.315i	0.964321	+	0.644024i
$61$	−425.644	+	737.237i	−0.893412	+	1.54743i	−0.0576536	+	0.998337i	$0.518362\pi$
$61$	−425.644	+	737.237i	−0.893412	+	1.54743i	−0.835758	+	0.549098i	$0.814971\pi$
$62$	33.5755	−	5.71067i	0.0687757	−	0.0116977i
$63$	−481.931	−	133.378i	−0.963771	−	0.266731i
$64$	−271.951	+	433.805i	−0.531155	+	0.847275i
$65$	41.6998	+	24.0754i	0.0795726	+	0.0459413i
$66$	−243.812	−	230.479i	−0.454715	−	0.429849i
$67$	683.478	−	394.606i	1.24627	−	0.719535i	0.275908	−	0.961184i	$-0.411022\pi$
$67$	683.478	−	394.606i	1.24627	−	0.719535i	0.970364	+	0.241649i	$0.0776883\pi$
$68$	−156.852	+	830.555i	−0.279723	+	1.48117i
$69$	−321.944	+	39.2870i	−0.561703	+	0.0685449i
$70$	−518.201	+	438.969i	−0.884812	+	0.749527i
$71$			482.779i			0.806976i	0.914985	+	0.403488i	$0.132202\pi$
$71$			482.779i			0.806976i	−0.914985	+	0.403488i	$0.867798\pi$
$72$	−595.585	+	136.113i	−0.974866	+	0.222793i
$73$	228.529	−	131.942i	0.366402	−	0.211542i	−0.305483	−	0.952197i	$-0.598818\pi$
$73$	228.529	−	131.942i	0.366402	−	0.211542i	0.671885	+	0.740655i	$0.265485\pi$
$74$	255.187	+	307.890i	0.400876	+	0.483669i
$75$	206.015	+	87.6290i	0.317181	+	0.134914i
$76$	876.032	−	306.877i	1.32221	−	0.463173i
$77$	363.853	−	215.313i	0.538506	−	0.318666i
$78$	−52.3063	+	15.6033i	−0.0759297	+	0.0226503i
$79$	−71.1227	+	123.188i	−0.101290	+	0.175440i	−0.912216	−	0.409709i	$-0.865630\pi$
$79$	−71.1227	+	123.188i	−0.101290	+	0.175440i	0.810926	+	0.585148i	$0.198964\pi$
$80$	−302.607	+	772.597i	−0.422905	+	1.07974i
$81$	−617.077	−	388.146i	−0.846470	−	0.532437i
$82$	−1105.95	−	410.142i	−1.48942	−	0.552349i
$83$		−	477.893i		−	0.631994i	−0.948760	−	0.315997i	$-0.897661\pi$
$83$		−	477.893i		−	0.631994i	0.948760	−	0.315997i	$-0.102339\pi$
$84$	41.9258	−	768.730i	0.0544581	−	0.998516i
$85$			1369.79i			1.74793i
$86$	−209.478	+	564.860i	−0.262658	+	0.708261i
$87$	240.710	−	181.108i	0.296630	−	0.223182i
$88$	266.364	−	442.573i	0.322665	−	0.536119i
$89$	−677.670	+	1173.76i	−0.807111	+	1.39796i	0.107745	+	0.994179i	$0.465637\pi$
$89$	−677.670	+	1173.76i	−0.807111	+	1.39796i	−0.914857	+	0.403779i	$0.867696\pi$
$90$	−907.503	+	395.868i	−1.06288	+	0.463646i
$91$	−0.738656	−	68.7797i	−0.000850903	−	0.0792315i
$92$	−165.085	−	471.263i	−0.187079	−	0.534050i
$93$	−24.4900	+	57.5759i	−0.0273064	+	0.0641973i
$94$	383.300	−	317.688i	0.420579	−	0.348586i
$95$	1302.75	−	752.141i	1.40694	−	0.812295i
$96$	−400.804	−	850.936i	−0.426114	−	0.904670i
$97$			1362.01i			1.42569i	0.701323	+	0.712844i	$0.252593\pi$
$97$			1362.01i			1.42569i	−0.701323	+	0.712844i	$0.747407\pi$
$98$	916.650	+	317.717i	0.944854	+	0.327492i
$99$	598.278	−	148.224i	0.607366	−	0.150475i
$100$	−63.9634	+	338.695i	−0.0639634	+	0.338695i
$101$	−960.967	+	554.815i	−0.946731	+	0.546595i	−0.892064	−	0.451909i	$-0.850743\pi$
$101$	−960.967	+	554.815i	−0.946731	+	0.546595i	−0.0546669	+	0.998505i	$0.517410\pi$
$102$	−1128.41	−	1066.71i	−1.09539	−	1.03549i
$103$	1462.91	+	844.611i	1.39946	+	0.807981i	0.994336	−	0.106280i	$-0.0338938\pi$
$103$	1462.91	+	844.611i	1.39946	+	0.807981i	0.405127	+	0.914260i	$0.367227\pi$
$104$	−40.6886	−	73.5305i	−0.0383639	−	0.0693294i
$105$	−164.422	−	1236.77i	−0.152818	−	1.14949i
$106$	191.210	+	1124.20i	0.175207	+	1.03012i
$107$	−852.137	+	1475.94i	−0.769899	+	1.33350i	0.167718	+	0.985835i	$0.446360\pi$
$107$	−852.137	+	1475.94i	−0.769899	+	1.33350i	−0.937617	+	0.347669i	$0.886973\pi$
$108$	380.598	−	1055.87i	0.339102	−	0.940750i
$109$	−733.745	+	423.628i	−0.644771	+	0.372259i	−0.786450	−	0.617654i	$-0.788083\pi$
$109$	−733.745	+	423.628i	−0.644771	+	0.372259i	0.141679	+	0.989913i	$0.454750\pi$
$110$	291.072	−	784.881i	0.252297	−	0.680322i
$111$	−729.245	+	88.9903i	−0.623576	+	0.0760953i
$112$	1169.96	−	190.044i	0.987063	−	0.160334i
$113$		−	627.031i		−	0.522001i	−0.965339	−	0.261001i	$-0.915948\pi$
$113$		−	627.031i		−	0.522001i	0.965339	−	0.261001i	$-0.0840525\pi$
$114$	−394.896	+	1658.91i	−0.324433	+	1.36290i
$115$	−404.616	−	700.815i	−0.328092	−	0.568272i
$116$	351.636	+	302.396i	0.281453	+	0.242041i
$117$	27.7833	−	96.3514i	0.0219536	−	0.0761341i
$118$	77.4004	−	13.1646i	0.0603838	−	0.0102703i
$119$	1683.99	−	996.516i	1.29724	−	0.767651i
$120$	−894.169	−	1234.53i	−0.680217	−	0.939142i
$121$	404.933	−	701.364i	0.304232	−	0.526945i
$122$	1853.83	−	1536.50i	1.37572	−	1.14023i
$123$	1731.60	−	1302.84i	1.26937	−	0.955064i
$124$	−94.6565	−	17.8761i	−0.0685516	−	0.0129462i
$125$		−	1062.01i		−	0.759909i
$126$	1146.88	+	827.675i	0.810890	+	0.585199i
$127$	−1710.56			−1.19518			−0.597590	−	0.801802i	$-0.703875\pi$
$127$	−1710.56			−1.19518			−0.597590	+	0.801802i	$0.703875\pi$
$128$	1147.83	−	882.969i	0.792617	−	0.609720i
$129$	−665.417	−	884.404i	−0.454160	−	0.603624i
$130$	−86.9079	−	104.857i	−0.0586333	−	0.0707428i
$131$	719.105	+	415.175i	0.479607	+	0.276901i	0.720253	−	0.693712i	$-0.244026\pi$
$131$	719.105	+	415.175i	0.479607	+	0.276901i	−0.240646	+	0.970613i	$0.577359\pi$
$132$	419.905	+	851.000i	0.276879	+	0.561136i
$133$	−1872.41	−	1054.39i	−1.22074	−	0.687423i
$134$	−2200.63	+	374.293i	−1.41870	+	0.241298i
$135$	288.542	−	1795.87i	0.183954	−	1.14492i
$136$	1232.79	−	2048.32i	0.777285	−	1.29149i
$137$	−1636.51	+	944.837i	−1.02056	+	0.589218i	−0.914265	−	0.405117i	$-0.867231\pi$
$137$	−1636.51	+	944.837i	−1.02056	+	0.589218i	−0.106291	+	0.994335i	$0.533897\pi$
$138$	892.413	+	212.435i	0.550487	+	0.131041i
$139$	2008.82			1.22580			0.612900	−	0.790160i	$-0.290003\pi$
$139$	2008.82			1.22580			0.612900	+	0.790160i	$0.290003\pi$
$140$	1805.95	−	654.486i	1.09022	−	0.395101i
$141$	110.786	+	907.856i	0.0661694	+	0.542236i
$142$	474.798	−	1280.30i	0.280593	−	0.756623i
$143$	42.3919	+	73.4250i	0.0247901	+	0.0429378i
$144$	1713.32	+	224.776i	0.991504	+	0.130078i
$145$	650.903	+	375.799i	0.372790	+	0.215231i
$146$	−735.807	+	125.149i	−0.417095	+	0.0709413i
$147$	−1400.85	+	1101.88i	−0.785986	+	0.618244i
$148$	−373.939	−	1067.47i	−0.207687	−	0.592877i
$149$	−1426.31	+	2470.43i	−0.784211	+	1.35829i	0.145258	+	0.989394i	$0.453599\pi$
$149$	−1426.31	+	2470.43i	−0.784211	+	1.35829i	−0.929469	+	0.368900i	$0.879734\pi$
$150$	−460.160	−	434.997i	−0.250479	−	0.236782i
$151$	1309.78	+	2268.60i	0.705882	+	1.22262i	0.966372	+	0.257147i	$0.0827824\pi$
$151$	1309.78	+	2268.60i	0.705882	+	1.22262i	−0.260491	+	0.965476i	$0.583884\pi$
$152$	−2624.99	−	47.7329i	−1.40075	−	0.0254714i
$153$	2768.96	−	686.011i	1.46312	−	0.362488i
$154$	−1176.67	+	213.160i	−0.615707	+	0.111538i
$155$	−156.111			−0.0808979
$156$	154.058	+	10.0626i	0.0790676	+	0.00516444i
$157$	−1685.32	−	2919.06i	−0.856708	−	1.48386i	−0.875051	−	0.484031i	$-0.839172\pi$
$157$	−1685.32	−	2919.06i	−0.856708	−	1.48386i	0.0183426	−	0.999832i	$-0.494161\pi$
$158$	309.765	−	256.741i	0.155972	−	0.129273i
$159$	−1927.81	−	819.996i	−0.961541	−	0.408993i
$160$	1562.32	−	1751.28i	0.771952	−	0.865317i
$161$	−567.212	+	1007.27i	−0.277656	+	0.493067i
$162$	1254.72	+	1636.22i	0.608519	+	0.793539i
$163$	−795.653	−	459.371i	−0.382334	−	0.220740i	0.296499	−	0.955033i	$-0.404181\pi$
$163$	−795.653	−	459.371i	−0.382334	−	0.220740i	−0.678833	+	0.734293i	$0.737514\pi$
$164$	2529.56	+	2175.35i	1.20443	+	1.03577i
$165$	924.605	+	1228.89i	0.436245	+	0.579812i
$166$	−469.993	+	1267.34i	−0.219750	+	0.592559i
$167$	−3976.72			−1.84268			−0.921340	−	0.388758i	$-0.872904\pi$
$167$	−3976.72			−1.84268			−0.921340	+	0.388758i	$0.872904\pi$
$168$	−867.207	+	1997.39i	−0.398253	+	0.917276i
$169$	−2183.21			−0.993722
$170$	1347.14	−	3632.59i	0.607771	−	1.63886i
$171$	−2172.85	−	2256.75i	−0.971709	−	1.00923i
$172$	1111.05	−	1291.96i	0.492538	−	0.572739i
$173$	891.820	+	514.892i	0.391930	+	0.226281i	0.682996	−	0.730422i	$-0.260677\pi$
$173$	891.820	+	514.892i	0.391930	+	0.226281i	−0.291066	+	0.956703i	$0.594010\pi$
$174$	−816.463	+	243.556i	−0.355724	+	0.106115i
$175$	686.721	−	406.373i	0.296635	−	0.175537i
$176$	−1141.64	+	911.717i	−0.488945	+	0.390473i
$177$	−56.4560	+	132.728i	−0.0239745	+	0.0563640i
$178$	2951.50	−	2446.27i	1.24283	−	1.03009i
$179$	1383.73	+	2396.69i	0.577793	+	1.00077i	0.995732	+	0.0922920i	$0.0294193\pi$
$179$	1383.73	+	2396.69i	0.577793	+	1.00077i	−0.417939	+	0.908475i	$0.637247\pi$
$180$	2795.97	−	157.316i	1.15777	−	0.0651426i
$181$	−482.414			−0.198108			−0.0990540	−	0.995082i	$-0.531582\pi$
$181$	−482.414			−0.198108			−0.0990540	+	0.995082i	$0.531582\pi$
$182$	−65.6839	+	183.126i	−0.0267517	+	0.0745836i
$183$	535.818	+	4390.85i	0.216442	+	1.77367i
$184$	−25.6780	+	1412.12i	−0.0102881	+	0.565776i
$185$	−916.508	−	1587.44i	−0.364233	−	0.630869i
$186$	121.570	−	128.603i	0.0479245	−	0.0506968i
$187$	−1205.96	+	2088.78i	−0.471596	+	0.816829i
$188$	−1328.93	+	465.526i	−0.515542	+	0.180596i
$189$	−2417.73	+	951.765i	−0.930497	+	0.366300i
$190$	−4194.51	+	713.421i	−1.60159	+	0.272405i
$191$	−2001.62	−	1155.64i	−0.758284	−	0.437795i	0.0703955	−	0.997519i	$-0.477574\pi$
$191$	−2001.62	−	1155.64i	−0.758284	−	0.437795i	−0.828679	+	0.559724i	$0.810907\pi$
$192$	226.040	+	2650.81i	0.0849636	+	0.996384i
$193$	2051.69	+	3553.63i	0.765202	+	1.32537i	0.940140	+	0.340789i	$0.110694\pi$
$193$	2051.69	+	3553.63i	0.765202	+	1.32537i	−0.174938	+	0.984579i	$0.555973\pi$
$194$	1339.50	−	3611.98i	0.495724	−	1.33673i
$195$	248.356	−	30.3071i	0.0912059	−	0.0111299i
$196$	−2118.44	−	1744.06i	−0.772025	−	0.635592i
$197$	2402.75			0.868978			0.434489	−	0.900677i	$-0.356929\pi$
$197$	2402.75			0.868978			0.434489	+	0.900677i	$0.356929\pi$
$198$	−1732.37	−	195.308i	−0.621789	−	0.0701006i
$199$	−1916.19	+	1106.31i	−0.682589	+	0.394093i	−0.800830	−	0.598892i	$-0.795608\pi$
$199$	−1916.19	+	1106.31i	−0.682589	+	0.394093i	0.118241	+	0.992985i	$0.462275\pi$
$200$	502.724	−	835.293i	0.177740	−	0.295321i
$201$	1605.14	−	3773.68i	0.563273	−	1.32425i
$202$	3094.07	−	526.253i	1.07771	−	0.183302i
$203$	−11.5299	−	1073.60i	−0.00398640	−	0.371192i
$204$	1943.41	+	3938.60i	0.666990	+	1.35175i
$205$	4682.41	+	2703.39i	1.59528	+	0.921038i
$206$	−3048.90	−	3678.59i	−1.03120	−	1.24417i
$207$	−1214.03	+	1168.89i	−0.407636	+	0.392481i
$208$	35.5888	+	235.015i	0.0118636	+	0.0783429i
$209$	2648.74			0.876637
$210$	−780.290	+	3441.55i	−0.256405	+	1.13090i
$211$			588.297i			0.191943i	0.995384	+	0.0959717i	$0.0305958\pi$
$211$			588.297i			0.191943i	−0.995384	+	0.0959717i	$0.969404\pi$
$212$	598.544	−	3169.37i	0.193906	−	1.02676i
$213$	1508.22	+	2004.57i	0.485171	+	0.644840i
$214$	3711.36	−	3076.07i	1.18553	−	0.982596i
$215$	1380.74	−	2391.51i	0.437980	−	0.758604i
$216$	−2047.74	+	2425.79i	−0.645050	+	0.764140i
$217$	113.571	+	191.921i	0.0355285	+	0.0600388i
$218$	2362.47	−	401.820i	0.733977	−	0.124838i
$219$	536.699	−	1261.78i	0.165602	−	0.389329i
$220$	−1543.81	+	1795.20i	−0.473108	+	0.550146i
$221$	196.199	+	339.826i	0.0597183	+	0.103435i
$222$	2021.43	+	481.194i	0.611125	+	0.145476i
$223$		−	1897.52i		−	0.569808i	−0.958556	−	0.284904i	$-0.908038\pi$
$223$		−	1897.52i		−	0.569808i	0.958556	−	0.284904i	$-0.0919617\pi$
$224$	−3289.57	−	646.638i	−0.981222	−	0.192881i
$225$	1129.16	−	279.751i	0.334567	−	0.0828892i
$226$	−616.666	+	1662.85i	−0.181505	+	0.489430i
$227$	−443.460	+	256.032i	−0.129663	+	0.0748610i	−0.563428	−	0.826165i	$-0.690518\pi$
$227$	−443.460	+	256.032i	−0.129663	+	0.0748610i	0.433765	+	0.901026i	$0.357185\pi$
$228$	2678.73	−	4010.96i	0.778083	−	1.16505i
$229$	432.514	−	749.136i	0.124809	−	0.216176i	−0.796849	−	0.604178i	$-0.793501\pi$
$229$	432.514	−	749.136i	0.124809	−	0.216176i	0.921658	+	0.388002i	$0.126835\pi$
$230$	383.787	+	2256.45i	0.110027	+	0.646894i
$231$	838.127	−	2030.71i	0.238722	−	0.578401i
$232$	−635.120	−	1147.76i	−0.179731	−	0.324802i
$233$	1853.37	+	1070.05i	0.521109	+	0.300863i	0.737388	−	0.675469i	$-0.236059\pi$
$233$	1853.37	+	1070.05i	0.521109	+	0.300863i	−0.216279	+	0.976332i	$0.569392\pi$
$234$	−168.438	+	228.194i	−0.0470562	+	0.0637501i
$235$	−1976.24	+	1140.98i	−0.548578	+	0.316722i
$236$	−218.208	−	41.2092i	−0.0601871	−	0.0113665i
$237$	89.5322	+	733.686i	0.0245390	+	0.201089i
$238$	−5445.88	+	986.548i	−1.48321	+	0.268691i
$239$		−	1350.91i		−	0.365619i	−0.983148	−	0.182809i	$-0.941481\pi$
$239$		−	1350.91i		−	0.365619i	0.983148	−	0.182809i	$-0.0585191\pi$
$240$	1157.16	+	4153.30i	0.311225	+	1.11706i
$241$	172.940	−	99.8472i	0.0462244	−	0.0266876i	−0.476710	−	0.879061i	$-0.658171\pi$
$241$	172.940	−	99.8472i	0.0462244	−	0.0266876i	0.522934	+	0.852373i	$0.324837\pi$
$242$	−1763.63	+	1461.74i	−0.468472	+	0.388281i
$243$	−3774.78	+	316.128i	−0.996512	+	0.0834552i
$244$	−6427.35	+	2251.52i	−1.68635	+	0.590733i
$245$	−3898.01	−	2140.24i	−1.01647	−	0.558101i
$246$	−5873.39	+	1752.07i	−1.52225	+	0.454098i
$247$	215.463	−	373.193i	0.0555044	−	0.0961364i
$248$	233.443	+	140.498i	0.0597727	+	0.0359744i
$249$	−1492.96	−	1984.28i	−0.379969	−	0.505016i
$250$	−1044.45	+	2816.38i	−0.264227	+	0.712493i
$251$		−	7334.11i		−	1.84432i	−0.386806	−	0.922161i	$-0.626422\pi$
$251$		−	7334.11i		−	1.84432i	0.386806	−	0.922161i	$-0.373578\pi$
$252$	−2227.46	−	3322.86i	−0.556813	−	0.830638i
$253$		−	1424.90i		−	0.354081i
$254$	4536.31	+	1682.29i	1.12060	+	0.415575i
$255$	4279.26	+	5687.56i	1.05089	+	1.39674i
$256$	−3912.35	+	1212.72i	−0.955165	+	0.296075i
$257$	−1732.87	+	3001.42i	−0.420597	+	0.728495i	−0.995998	−	0.0893761i	$-0.971513\pi$
$257$	−1732.87	+	3001.42i	−0.420597	+	0.728495i	0.575401	+	0.817871i	$0.304846\pi$
$258$	894.861	+	2999.80i	0.215937	+	0.723875i
$259$	−1284.81	+	2281.60i	−0.308240	+	0.547380i
$260$	127.351	+	363.545i	0.0303768	+	0.0867159i
$261$	433.677	−	1503.98i	0.102850	−	0.356681i
$262$	−1498.71	−	1808.24i	−0.353399	−	0.426387i
$263$	4397.98	−	2539.17i	1.03114	−	0.595331i	0.113832	−	0.993500i	$-0.463688\pi$
$263$	4397.98	−	2539.17i	1.03114	−	0.595331i	0.917312	+	0.398169i	$0.130354\pi$
$264$	−276.632	−	2669.76i	−0.0644906	−	0.622396i
$265$		−	5227.06i		−	1.21168i
$266$	3928.56	+	4637.64i	0.905548	+	1.06899i
$267$	853.079	+	6990.70i	0.195534	+	1.60234i
$268$	6204.04	+	1171.65i	1.41407	+	0.267052i
$269$	3287.27	−	1897.91i	0.745088	−	0.430177i	−0.0788286	−	0.996888i	$-0.525118\pi$
$269$	3287.27	−	1897.91i	0.745088	−	0.430177i	0.823916	+	0.566712i	$0.191785\pi$
$270$	−2531.39	+	4478.78i	−0.570575	+	1.00952i
$271$	−2657.85	−	1534.51i	−0.595767	−	0.343966i	0.171607	−	0.985165i	$-0.445104\pi$
$271$	−2657.85	−	1534.51i	−0.595767	−	0.343966i	−0.767375	+	0.641199i	$0.778437\pi$
$272$	−5283.74	+	4219.62i	−1.17785	+	0.940632i
$273$	−217.937	−	283.276i	−0.0483157	−	0.0628009i
$274$	5269.13	−	896.198i	1.16175	−	0.197596i
$275$	−491.783	+	851.793i	−0.107839	+	0.186782i
$276$	−2157.70	−	1441.03i	−0.470574	−	0.314274i
$277$	6213.21	−	3587.20i	1.34771	−	0.778100i	0.359784	−	0.933036i	$-0.382850\pi$
$277$	6213.21	−	3587.20i	1.34771	−	0.778100i	0.987925	+	0.154936i	$0.0495170\pi$
$278$	−5327.28	−	1975.62i	−1.14931	−	0.426222i
$279$	78.1831	+	315.572i	0.0167767	+	0.0677161i
$280$	−5432.94	−	40.4380i	−1.15957	−	0.00863084i
$281$			3571.40i			0.758191i	0.925357	+	0.379096i	$0.123765\pi$
$281$			3571.40i			0.758191i	−0.925357	+	0.379096i	$0.876235\pi$
$282$	599.050	−	2516.53i	0.126500	−	0.531409i
$283$	1218.79	+	2111.01i	0.256007	+	0.443416i	0.965168	−	0.261629i	$-0.0842598\pi$
$283$	1218.79	+	2111.01i	0.256007	+	0.443416i	−0.709162	+	0.705046i	$0.750926\pi$
$284$	−2518.27	+	2928.33i	−0.526169	+	0.611847i
$285$	3059.48	−	7192.83i	0.635888	−	1.49497i
$286$	−40.2096	−	236.410i	−0.00831345	−	0.0488783i
$287$	−82.9426	−	7723.17i	−0.0170590	−	1.58845i
$288$	−4322.56	−	2281.09i	−0.884407	−	0.466717i
$289$	−3124.93	+	5412.54i	−0.636054	+	1.10168i
$290$	−1356.57	−	1636.74i	−0.274691	−	0.331423i
$291$	4254.99	+	5655.29i	0.857154	+	1.13924i
$292$	2074.40	+	391.755i	0.415736	+	0.0785128i
$293$		−	7890.50i		−	1.57327i	−0.617418	−	0.786635i	$-0.711821\pi$
$293$		−	7890.50i		−	1.57327i	0.617418	−	0.786635i	$-0.288179\pi$
$294$	4798.63	−	1544.44i	0.951912	−	0.306373i
$295$	−359.879			−0.0710269
$296$	−58.1641	+	3198.64i	−0.0114213	+	0.628098i
$297$	2021.09	−	2484.49i	0.394866	−	0.485404i
$298$	6212.07	−	5148.71i	1.20757	−	1.00086i
$299$	−200.760	−	115.909i	−0.0388302	−	0.0224186i
$300$	792.511	+	1606.14i	0.152519	+	0.309102i
$301$	−3944.57	+	42.3625i	−0.755352	+	0.00811207i
$302$	−1242.35	−	7304.32i	−0.236719	−	1.39178i
$303$	−2256.82	+	5305.77i	−0.427891	+	1.00597i
$304$	6914.37	+	2708.18i	1.30449	+	0.510937i
$305$	−9558.11	+	5518.37i	−1.79441	+	1.03600i
$306$	−8017.78	−	903.925i	−1.49786	−	0.168869i
$307$	−1122.94			−0.208760			−0.104380	−	0.994537i	$-0.533286\pi$
$307$	−1122.94			−0.208760			−0.104380	+	0.994537i	$0.533286\pi$
$308$	3330.10	+	591.934i	0.616072	+	0.109508i
$309$	8712.82	−	1063.23i	1.60406	−	0.195745i
$310$	413.998	+	153.531i	0.0758501	+	0.0281289i
$311$	−1009.16	−	1747.92i	−0.184001	−	0.318700i	0.759238	−	0.650813i	$-0.225572\pi$
$311$	−1009.16	−	1747.92i	−0.184001	−	0.318700i	−0.943240	+	0.332113i	$0.892238\pi$
$312$	−398.658	−	178.197i	−0.0723383	−	0.0323347i
$313$	608.104	+	351.089i	0.109815	+	0.0634016i	0.553901	−	0.832582i	$-0.313138\pi$
$313$	608.104	+	351.089i	0.109815	+	0.0634016i	−0.444087	+	0.895984i	$0.646472\pi$
$314$	1598.56	+	9398.64i	0.287300	+	1.68916i
$315$	−4546.43	−	4621.60i	−0.813213	−	0.826660i
$316$	−1073.97	+	376.216i	−0.191189	+	0.0669741i
$317$	−2217.08	+	3840.09i	−0.392819	+	0.680382i	−0.992820	−	0.119617i	$-0.961833\pi$
$317$	−2217.08	+	3840.09i	−0.392819	+	0.680382i	0.600001	+	0.799999i	$0.295167\pi$
$318$	4305.99	+	4070.52i	0.759333	+	0.717810i
$319$	661.708	+	1146.11i	0.116140	+	0.201160i
$320$	−5865.51	+	3107.79i	−1.02466	+	0.542908i
$321$	1072.70	+	8790.46i	0.186519	+	1.52846i
$322$	2494.83	−	2113.38i	0.431775	−	0.365758i
$323$	12258.9			2.11178
$324$	−1718.27	−	5573.13i	−0.294628	−	0.955612i
$325$	80.0086	+	138.579i	0.0136556	+	0.0236522i
$326$	1658.25	+	2000.72i	0.281724	+	0.339908i
$327$	−1723.19	+	4051.22i	−0.291415	+	0.685116i
$328$	−4568.87	−	8256.64i	−0.769126	−	1.38993i
$329$	2840.42	+	1599.49i	0.475979	+	0.268033i
$330$	−1243.42	−	4168.27i	−0.207418	−	0.695320i
$331$	−9094.20	−	5250.54i	−1.51016	−	0.871890i	−0.999930	−	0.0118508i	$-0.996228\pi$
$331$	−9094.20	−	5250.54i	−1.51016	−	0.871890i	−0.510228	−	0.860039i	$-0.670439\pi$
$332$	2492.79	−	2898.69i	0.412077	−	0.479176i
$333$	−2749.93	+	2647.69i	−0.452538	+	0.435714i
$334$	10546.0	+	3910.98i	1.72770	+	0.640716i
$335$	10232.0			1.66875
$336$	4264.16	−	4444.10i	0.692348	−	0.721564i
$337$	1582.88			0.255861			0.127930	−	0.991783i	$-0.459167\pi$
$337$	1582.88			0.255861			0.127930	+	0.991783i	$0.459167\pi$
$338$	5789.73	+	2147.12i	0.931716	+	0.345526i
$339$	−1958.87	−	2603.53i	−0.313839	−	0.417122i
$340$	−7145.08	+	8308.54i	−1.13970	+	1.32528i
$341$	−238.054	−	137.441i	−0.0378046	−	0.0218265i
$342$	3542.83	+	8121.71i	0.560158	+	1.28413i
$343$	204.622	+	6349.15i	0.0322115	+	0.999481i
$344$	−4217.03	+	2333.52i	−0.660951	+	0.365742i
$345$	−3869.40	−	1645.86i	−0.603830	−	0.256840i
$346$	−1858.67	−	2242.54i	−0.288794	−	0.348439i
$347$	−3447.64	−	5971.49i	−0.533369	−	0.923822i	−0.999240	−	0.0389695i	$-0.987592\pi$
$347$	−3447.64	−	5971.49i	−0.533369	−	0.923822i	0.465872	−	0.884852i	$-0.345741\pi$
$348$	2404.74	+	157.070i	0.370425	+	0.0241949i
$349$	6864.13			1.05280			0.526402	−	0.850236i	$-0.323541\pi$
$349$	6864.13			1.05280			0.526402	+	0.850236i	$0.323541\pi$
$350$	−2220.80	+	402.308i	−0.339162	+	0.0614408i
$351$	−185.645	−	486.862i	−0.0282308	−	0.0740364i
$352$	3924.20	−	1295.05i	0.594207	−	0.196098i
$353$	−1843.40	−	3192.86i	−0.277944	−	0.481413i	0.692930	−	0.721005i	$-0.256320\pi$
$353$	−1843.40	−	3192.86i	−0.277944	−	0.481413i	−0.970874	+	0.239592i	$0.922986\pi$
$354$	280.252	−	296.464i	0.0420769	−	0.0445109i
$355$	−3129.56	+	5420.55i	−0.467886	+	0.810403i
$356$	−10233.0	+	3584.66i	−1.52345	+	0.533670i
$357$	3879.03	−	9398.53i	0.575070	−	1.39334i
$358$	−1312.50	−	7716.75i	−0.193765	−	1.13923i
$359$	4274.90	+	2468.11i	0.628469	+	0.362847i	0.780159	−	0.625581i	$-0.215138\pi$
$359$	4274.90	+	2468.11i	0.628469	+	0.362847i	−0.151690	+	0.988428i	$0.548471\pi$
$360$	−7569.46	−	2332.56i	−1.10818	−	0.341490i
$361$	−3301.79	−	5718.88i	−0.481381	−	0.833777i
$362$	1279.33	+	474.439i	0.185747	+	0.0688839i
$363$	−509.746	−	4177.20i	−0.0737045	−	0.603983i
$364$	354.289	−	421.041i	0.0510158	−	0.0606279i
$365$	3421.18			0.490611
$366$	2897.31	−	12171.2i	0.413783	−	1.73825i
$367$	6855.75	−	3958.17i	0.975115	−	0.562983i	0.0743235	−	0.997234i	$-0.476320\pi$
$367$	6855.75	−	3958.17i	0.975115	−	0.562983i	0.900792	+	0.434251i	$0.142987\pi$
$368$	1456.87	−	3719.60i	0.206371	−	0.526896i
$369$	3119.75	−	10819.2i	0.440129	−	1.52635i
$370$	869.328	+	5111.15i	0.122146	+	0.718152i
$371$	−6426.05	+	3802.67i	−0.899256	+	0.532143i
$372$	−448.874	+	221.486i	−0.0625619	+	0.0308697i
$373$	4997.76	+	2885.46i	0.693765	+	0.400545i	0.805021	−	0.593246i	$-0.202154\pi$
$373$	4997.76	+	2885.46i	0.693765	+	0.400545i	−0.111256	+	0.993792i	$0.535487\pi$
$374$	5252.39	−	4353.31i	0.726189	−	0.601883i
$375$	−3317.75	−	4409.61i	−0.456874	−	0.607230i
$376$	3982.06	+	72.4099i	0.546168	+	0.00993153i
$377$	215.308			0.0294135
$378$	7347.70	−	146.262i	0.999802	−	0.0199019i
$379$		−	11588.5i		−	1.57060i	−0.619113	−	0.785302i	$-0.712508\pi$
$379$		−	11588.5i		−	1.57060i	0.619113	−	0.785302i	$-0.287492\pi$
$380$	11825.2	+	2233.22i	1.59637	+	0.301479i
$381$	−7102.52	+	5343.87i	−0.955048	+	0.718568i
$382$	4171.65	+	5033.21i	0.558743	+	0.674140i
$383$	−4577.70	+	7928.81i	−0.610730	+	1.05782i	0.380388	+	0.924827i	$0.375791\pi$
$383$	−4577.70	+	7928.81i	−0.610730	+	1.05782i	−0.991118	+	0.132988i	$0.957543\pi$
$384$	2007.55	−	7252.09i	0.266790	−	0.963755i
$385$	5481.03	−	58.8632i	0.725556	−	0.00779207i
$386$	−1946.07	−	11441.8i	−0.256613	−	1.50874i
$387$	−5525.83	−	1593.39i	−0.725823	−	0.209294i
$388$	−7104.55	+	8261.40i	−0.929585	+	1.08095i
$389$	1178.80	+	2041.75i	0.153644	+	0.266120i	0.932565	−	0.361003i	$-0.117566\pi$
$389$	1178.80	+	2041.75i	0.153644	+	0.266120i	−0.778920	+	0.627123i	$0.784232\pi$
$390$	−688.432	−	163.878i	−0.0893849	−	0.0212777i
$391$		−	6594.71i		−	0.852964i
$392$	3902.73	+	6708.57i	0.502852	+	0.864373i
$393$	4282.86	−	522.640i	0.549724	−	0.0670832i
$394$	−6371.94	−	2363.03i	−0.814756	−	0.302151i
$395$	−1597.11	+	922.089i	−0.203441	+	0.117457i
$396$	4402.07	+	2221.68i	0.558617	+	0.281928i
$397$	6278.72	−	10875.1i	0.793752	−	1.37482i	−0.129876	−	0.991530i	$-0.541458\pi$
$397$	6278.72	−	10875.1i	0.793752	−	1.37482i	0.923628	−	0.383289i	$-0.125209\pi$
$398$	6169.65	−	1049.36i	0.777027	−	0.132160i
$399$	−11068.5	+	1471.49i	−1.38877	+	0.184629i
$400$	−2154.68	+	1720.73i	−0.269335	+	0.215092i
$401$	70.9500	+	40.9630i	0.00883560	+	0.00510124i	0.504411	−	0.863464i	$-0.331710\pi$
$401$	70.9500	+	40.9630i	0.00883560	+	0.00510124i	−0.495576	+	0.868565i	$0.665043\pi$
$402$	−7968.04	+	8428.97i	−0.988581	+	1.04577i
$403$	−38.7292	+	22.3603i	−0.00478720	+	0.00276389i
$404$	−8722.85	−	1647.33i	−1.07420	−	0.202866i
$405$	−4412.31	−	8358.16i	−0.541357	−	1.02548i
$406$	−1025.28	+	2858.47i	−0.125329	+	0.349417i
$407$		−	3227.58i		−	0.393084i
$408$	−1280.31	−	12356.2i	−0.155355	−	1.49932i
$409$	4583.49	−	2646.28i	0.554129	−	0.319927i	−0.196656	−	0.980472i	$-0.563008\pi$
$409$	4583.49	−	2646.28i	0.554129	−	0.319927i	0.750786	+	0.660546i	$0.229675\pi$
$410$	−9758.76	−	11774.2i	−1.17549	−	1.41826i
$411$	−3843.31	+	9035.61i	−0.461257	+	1.08441i
$412$	4467.72	+	12753.9i	0.534245	+	1.52509i
$413$	261.811	+	442.428i	0.0311934	+	0.0527130i
$414$	4369.09	−	1905.87i	0.518669	−	0.226252i
$415$	3097.88	−	5365.69i	0.366432	−	0.634678i
$416$	136.750	−	658.245i	0.0161172	−	0.0775796i
$417$	8340.95	−	6275.65i	0.979516	−	0.736978i
$418$	−7024.30	−	2604.95i	−0.821937	−	0.304815i
$419$			3417.09i			0.398415i	0.979957	+	0.199207i	$0.0638368\pi$
$419$			3417.09i			0.398415i	−0.979957	+	0.199207i	$0.936163\pi$
$420$	5453.94	−	8359.39i	0.633631	−	0.971182i
$421$			12653.4i			1.46482i	0.680864	+	0.732410i	$0.261605\pi$
$421$			12653.4i			1.46482i	−0.680864	+	0.732410i	$0.738395\pi$
$422$	578.573	−	1560.13i	0.0667404	−	0.179967i
$423$	3296.18	+	3423.46i	0.378879	+	0.393509i
$424$	−4704.28	+	7816.33i	−0.538821	+	0.895270i
$425$	−2276.08	+	3942.28i	−0.259778	+	0.449950i
$426$	−2028.27	−	6799.29i	−0.230681	−	0.773302i
$427$	13737.7	+	7735.95i	1.55694	+	0.876743i
$428$	−12867.5	+	4507.53i	−1.45321	+	0.509065i
$429$	405.400	+	172.438i	0.0456245	+	0.0194065i
$430$	−6013.62	+	4984.23i	−0.674425	+	0.558979i
$431$	−1472.56	+	850.186i	−0.164573	+	0.0950163i	−0.580024	−	0.814599i	$-0.696957\pi$
$431$	−1472.56	+	850.186i	−0.164573	+	0.0950163i	0.415451	+	0.909615i	$0.363624\pi$
$432$	7816.17	−	4419.17i	0.870499	−	0.492170i
$433$		−	2777.80i		−	0.308296i	−0.988048	−	0.154148i	$-0.950737\pi$
$433$		−	2777.80i		−	0.308296i	0.988048	−	0.154148i	$-0.0492633\pi$
$434$	−112.435	−	620.655i	−0.0124356	−	0.0686461i
$435$	3876.66	−	473.072i	0.427291	−	0.0521426i
$436$	−6660.32	−	1257.82i	−0.731586	−	0.138162i
$437$	−6271.95	+	3621.11i	−0.686563	+	0.396388i
$438$	−2664.21	+	2818.33i	−0.290642	+	0.307454i
$439$	−11040.7	−	6374.32i	−1.20032	−	0.693006i	−0.239695	−	0.970848i	$-0.577048\pi$
$439$	−11040.7	−	6374.32i	−1.20032	−	0.693006i	−0.960627	+	0.277842i	$0.910381\pi$
$440$	5859.62	−	3242.46i	0.634878	−	0.351314i
$441$	−2374.20	+	8951.50i	−0.256366	+	0.966580i
$442$	−186.099	−	1094.15i	−0.0200267	−	0.117746i
$443$	−6451.54	+	11174.4i	−0.691923	+	1.19845i	0.279284	+	0.960208i	$0.409903\pi$
$443$	−6451.54	+	11174.4i	−0.691923	+	1.19845i	−0.971207	+	0.238237i	$0.923431\pi$
$444$	−4887.49	−	3264.12i	−0.522409	−	0.348892i
$445$	−15217.5	+	8785.84i	−1.62108	+	0.935930i
$446$	−1866.15	+	5032.10i	−0.198127	+	0.534253i
$447$	1795.49	+	14713.5i	0.189986	+	1.55687i
$448$	8087.80	+	4950.04i	0.852930	+	0.522025i
$449$			9435.20i			0.991703i	0.868407	+	0.495852i	$0.165144\pi$
$449$			9435.20i			0.991703i	−0.868407	+	0.495852i	$0.834856\pi$
$450$	−3269.60	−	368.615i	−0.342512	−	0.0386149i
$451$	4760.13	+	8244.78i	0.496997	+	0.860824i
$452$	3270.72	−	3803.31i	0.340358	−	0.395780i
$453$	12525.6	+	5327.78i	1.29913	+	0.552585i
$454$	1427.83	−	242.852i	0.147602	−	0.0251048i
$455$	437.563	−	777.034i	0.0450841	−	0.0800614i
$456$	−11048.5	+	8002.37i	−1.13463	+	0.821810i
$457$	1715.41	−	2971.18i	0.175588	−	0.304127i	−0.764777	−	0.644295i	$-0.777151\pi$
$457$	1715.41	−	2971.18i	0.175588	−	0.304127i	0.940365	+	0.340168i	$0.110484\pi$
$458$	−1883.75	+	1561.30i	−0.192188	+	0.159290i
$459$	9354.01	−	11498.7i	0.951215	−	1.16932i
$460$	1201.37	−	6361.40i	0.121770	−	0.644787i
$461$			3249.61i			0.328307i	0.986435	+	0.164153i	$0.0524892\pi$
$461$			3249.61i			0.328307i	−0.986435	+	0.164153i	$0.947511\pi$
$462$	−4219.80	+	4561.04i	−0.424942	+	0.459305i
$463$	7686.89			0.771577			0.385788	−	0.922587i	$-0.373929\pi$
$463$	7686.89			0.771577			0.385788	+	0.922587i	$0.373929\pi$
$464$	555.515	+	3668.41i	0.0555800	+	0.367029i
$465$	−648.199	+	487.698i	−0.0646441	+	0.0486376i
$466$	−3862.68	−	4660.43i	−0.383981	−	0.463284i
$467$	1514.65	+	874.483i	0.150085	+	0.0866515i	0.573162	−	0.819442i	$-0.305717\pi$
$467$	1514.65	+	874.483i	0.150085	+	0.0866515i	−0.423077	+	0.906094i	$0.639050\pi$
$468$	671.110	−	439.503i	0.0662865	−	0.0434104i
$469$	−7443.73	−	12579.0i	−0.732877	−	1.23847i
$470$	6363.00	−	1082.25i	0.624475	−	0.106214i
$471$	−16117.0	−	6855.38i	−1.57671	−	0.670657i
$472$	538.148	+	323.886i	0.0524793	+	0.0315848i
$473$	4210.98	−	2431.21i	0.409347	−	0.236336i
$474$	484.124	−	2033.74i	0.0469126	−	0.197074i
$475$	4999.11			0.482895
$476$	15412.4	+	2739.59i	1.48409	+	0.263801i
$477$	−10566.3	+	2617.79i	−1.01425	+	0.251280i
$478$	−1328.57	+	3582.52i	−0.127129	+	0.342805i
$479$	−3453.39	−	5981.45i	−0.329415	−	0.570563i	0.652981	−	0.757374i	$-0.273518\pi$
$479$	−3453.39	−	5981.45i	−0.329415	−	0.570563i	−0.982396	+	0.186811i	$0.940185\pi$
$480$	1015.93	−	12152.3i	0.0966059	−	1.15557i
$481$	−454.748	−	262.549i	−0.0431075	−	0.0248881i
$482$	−556.824	+	94.7072i	−0.0526196	+	0.00894978i
$483$	791.593	+	5954.32i	0.0745730	+	0.560934i
$484$	6114.61	−	2141.96i	0.574249	−	0.201161i
$485$	−8829.10	+	15292.5i	−0.826616	+	1.43174i
$486$	10321.4	+	2874.03i	0.963350	+	0.268248i
$487$	−2097.33	−	3632.69i	−0.195152	−	0.338014i	0.751798	−	0.659393i	$-0.229187\pi$
$487$	−2097.33	−	3632.69i	−0.195152	−	0.338014i	−0.946950	+	0.321379i	$0.895854\pi$
$488$	19259.3	+	350.211i	1.78653	+	0.0324863i
$489$	−4738.77	+	578.275i	−0.438230	+	0.0534775i
$490$	8232.42	+	9509.35i	0.758986	+	0.876711i
$491$	−2191.33			−0.201412			−0.100706	−	0.994916i	$-0.532110\pi$
$491$	−2191.33			−0.201412			−0.100706	+	0.994916i	$0.532110\pi$
$492$	17299.0	+	1129.91i	1.58516	+	0.103537i
$493$	3062.52	+	5304.44i	0.279775	+	0.484584i
$494$	−938.418	+	777.783i	−0.0854685	+	0.0708383i
$495$	7678.20	+	2214.04i	0.697191	+	0.201038i
$496$	−480.900	−	602.177i	−0.0435344	−	0.0545132i
$497$	8940.67	−	96.0179i	0.806929	−	0.00866597i
$498$	2007.75	+	6730.48i	0.180661	+	0.605622i
$499$	−7727.56	−	4461.51i	−0.693253	−	0.400250i	0.111577	−	0.993756i	$-0.464410\pi$
$499$	−7727.56	−	4461.51i	−0.693253	−	0.400250i	−0.804829	+	0.593506i	$0.797743\pi$
$500$	5539.64	−	6441.68i	0.495480	−	0.576161i
$501$	−16511.9	+	12423.4i	−1.47245	+	1.10786i
$502$	−7212.87	+	19449.6i	−0.641288	+	1.72924i
$503$	−1042.38			−0.0924001			−0.0462001	−	0.998932i	$-0.514711\pi$
$503$	−1042.38			−0.0924001			−0.0462001	+	0.998932i	$0.514711\pi$
$504$	2639.16	+	11002.7i	0.233249	+	0.972417i
$505$	−14386.1			−1.26767
$506$	−1401.34	+	3778.74i	−0.123117	+	0.331987i
$507$	−9065.01	+	6820.42i	−0.794065	+	0.597447i
$508$	−10375.5	−	8922.65i	−0.906182	−	0.779288i
$509$	291.527	+	168.313i	0.0253865	+	0.0146569i	0.512640	−	0.858604i	$-0.328668\pi$
$509$	291.527	+	168.313i	0.0253865	+	0.0146569i	−0.487253	+	0.873261i	$0.662001\pi$
$510$	−5754.81	−	19291.6i	−0.499661	−	1.67499i
$511$	−2488.90	−	4205.94i	−0.215465	−	0.364109i
$512$	11568.0	+	631.616i	0.998513	+	0.0545190i
$513$	−16072.2	−	2582.31i	−1.38325	−	0.222246i
$514$	7547.27	−	6255.36i	0.647657	−	0.536794i
$515$	10950.2	+	18966.3i	0.936938	+	1.62282i
$516$	577.097	−	8835.37i	0.0492350	−	0.753790i
$517$	−4018.09			−0.341809
$518$	5651.12	−	4787.09i	0.479336	−	0.406047i
$519$	5311.52	−	648.168i	0.449229	−	0.0548197i
$520$	19.8087	−	1089.35i	0.00167052	−	0.0918673i
$521$	1286.50	+	2228.29i	0.108182	+	0.187376i	0.915034	−	0.403377i	$-0.132164\pi$
$521$	1286.50	+	2228.29i	0.108182	+	0.187376i	−0.806852	+	0.590754i	$0.798830\pi$
$522$	−2629.20	+	3561.95i	−0.220454	+	0.298663i
$523$	−133.339	+	230.950i	−0.0111482	+	0.0193093i	−0.871546	−	0.490314i	$-0.836882\pi$
$523$	−133.339	+	230.950i	−0.0111482	+	0.0193093i	0.860397	+	0.509624i	$0.170215\pi$
$524$	2196.14	+	6269.27i	0.183090	+	0.522661i
$525$	1581.84	−	3832.67i	0.131500	−	0.318612i
$526$	−14160.4	+	2408.46i	−1.17380	+	0.199646i
$527$	−1101.76	−	636.104i	−0.0910694	−	0.0525790i
$528$	−1892.02	+	7352.11i	−0.155946	+	0.605984i
$529$	−4135.51	−	7162.92i	−0.339896	−	0.588717i
$530$	−5140.65	+	13861.9i	−0.421313	+	1.13608i
$531$	180.233	+	727.477i	0.0147296	+	0.0594535i
$532$	−5857.34	−	16162.4i	−0.477345	−	1.31716i
$533$	1548.86			0.125870
$534$	4612.82	−	19377.9i	0.373813	−	1.57034i
$535$	−19135.3	+	11047.8i	−1.54634	+	0.892778i
$536$	−15300.5	−	9208.62i	−1.23298	−	0.742075i
$537$	13232.8	+	5628.61i	1.06339	+	0.452314i
$538$	−10584.2	+	1800.21i	−0.848172	+	0.144261i
$539$	−4059.80	−	6695.45i	−0.324430	−	0.535053i
$540$	11117.8	−	9387.92i	0.885991	−	0.748133i
$541$	4708.64	+	2718.54i	0.374197	+	0.216043i	0.675290	−	0.737552i	$-0.264018\pi$
$541$	4708.64	+	2718.54i	0.374197	+	0.216043i	−0.301094	+	0.953595i	$0.597352\pi$
$542$	5539.32	+	6683.34i	0.438993	+	0.529657i
$543$	−2003.06	+	1507.08i	−0.158305	+	0.119107i
$544$	18162.0	−	5993.77i	1.43142	−	0.472391i
$545$	−10984.5			−0.863346
$546$	299.364	+	965.566i	0.0234644	+	0.0756821i
$547$		−	17749.9i		−	1.38744i	−0.720244	−	0.693721i	$-0.755970\pi$
$547$		−	17749.9i		−	1.38744i	0.720244	−	0.693721i	$-0.244030\pi$
$548$	−14854.8	−	2805.37i	−1.15797	−	0.218685i
$549$	15942.0	+	16557.6i	1.23932	+	1.28718i
$550$	2141.89	−	1775.25i	0.166056	−	0.137631i
$551$	3363.22	−	5825.27i	0.260033	−	0.450390i
$552$	4304.89	+	5943.55i	0.331936	+	0.458287i
$553$	2295.49	+	1292.63i	0.176517	+	0.0994004i
$554$	−20004.9	+	3402.53i	−1.53417	+	0.260938i
$555$	−8764.71	−	3728.08i	−0.670344	−	0.285132i
$556$	12184.7	+	10478.4i	0.929398	+	0.799253i
$557$	−3337.54	−	5780.80i	−0.253889	−	0.439749i	0.710704	−	0.703491i	$-0.248377\pi$
$557$	−3337.54	−	5780.80i	−0.253889	−	0.439749i	−0.964593	+	0.263742i	$0.915043\pi$
$558$	103.018	−	913.769i	0.00781562	−	0.0693242i
$559$		−	791.071i		−	0.0598546i
$560$	14368.1	+	5450.37i	1.08422	+	0.411286i
$561$	1518.11	+	12440.4i	0.114251	+	0.936247i
$562$	3512.36	−	9471.14i	0.263630	−	0.710882i
$563$	2223.58	−	1283.79i	0.166453	−	0.0961016i	−0.414459	−	0.910068i	$-0.636029\pi$
$563$	2223.58	−	1283.79i	0.166453	−	0.0961016i	0.580912	+	0.813966i	$0.302696\pi$
$564$	−4063.58	+	6084.55i	−0.303382	+	0.454266i
$565$	4064.66	−	7040.20i	0.302658	−	0.524218i
$566$	−1156.05	−	6796.93i	−0.0858525	−	0.504764i
$567$	−7065.43	+	11505.0i	−0.523316	+	0.852139i
$568$	9558.23	−	5289.11i	0.706082	−	0.390715i
$569$	2544.71	+	1469.19i	0.187486	+	0.108245i	0.590805	−	0.806814i	$-0.298810\pi$
$569$	2544.71	+	1469.19i	0.187486	+	0.108245i	−0.403319	+	0.915059i	$0.632143\pi$
$570$	−15187.5	+	16066.1i	−1.11603	+	1.18058i
$571$	4983.39	−	2877.16i	0.365233	−	0.210868i	−0.306141	−	0.951986i	$-0.599038\pi$
$571$	4983.39	−	2877.16i	0.365233	−	0.210868i	0.671374	+	0.741119i	$0.265704\pi$
$572$	−125.868	+	666.490i	−0.00920073	+	0.0487191i
$573$	−11921.3	+	1454.76i	−0.869143	+	0.106062i
$574$	−7375.54	+	20563.0i	−0.536323	+	1.49526i
$575$		−	2689.28i		−	0.195045i
$576$	9219.79	+	10300.4i	0.666941	+	0.745111i
$577$	−17569.6	+	10143.8i	−1.26764	+	0.731875i	−0.974542	−	0.224206i	$-0.928021\pi$
$577$	−17569.6	+	10143.8i	−1.26764	+	0.731875i	−0.293103	+	0.956081i	$0.594688\pi$
$578$	13610.2	−	11280.5i	0.979429	−	0.811774i
$579$	19620.6	+	8345.67i	1.40830	+	0.599023i
$580$	1987.86	+	5674.68i	0.142313	+	0.406256i
$581$	−8850.18	+	95.0461i	−0.631958	+	0.00678688i
$582$	−5722.16	−	19182.2i	−0.407545	−	1.36620i
$583$	4601.91	−	7970.73i	0.326915	−	0.566233i
$584$	−5115.90	−	3079.02i	−0.362495	−	0.218169i
$585$	936.533	−	901.714i	0.0661895	−	0.0637287i
$586$	−7760.07	+	20925.1i	−0.547040	+	1.47510i
$587$		−	19525.2i		−	1.37290i	−0.727178	−	0.686449i	$-0.759169\pi$
$587$		−	19525.2i		−	1.37290i	0.727178	−	0.686449i	$-0.240831\pi$
$588$	−14244.6	−	623.542i	−0.999043	−	0.0437320i
$589$			1397.12i			0.0977375i
$590$	954.376	+	353.930i	0.0665950	+	0.0246967i
$591$	9976.58	−	7506.28i	0.694385	−	0.522448i
$592$	3300.01	−	8425.39i	0.229104	−	0.584935i
$593$	−3922.80	+	6794.50i	−0.271653	+	0.470517i	−0.969285	−	0.245939i	$-0.920904\pi$
$593$	−3922.80	+	6794.50i	−0.271653	+	0.470517i	0.697632	+	0.716456i	$0.254237\pi$
$594$	−7803.22	+	4601.05i	−0.539007	+	0.317817i
$595$	25367.3	−	272.431i	1.74783	−	0.0187707i
$596$	−21537.6	+	7544.70i	−1.48023	+	0.518528i
$597$	−4500.15	+	10579.8i	−0.308508	+	0.725300i
$598$	418.410	+	504.824i	0.0286122	+	0.0345214i
$599$	−15602.7	+	9008.23i	−1.06429	+	0.614468i	−0.926616	−	0.376009i	$-0.877296\pi$
$599$	−15602.7	+	9008.23i	−1.06429	+	0.614468i	−0.137674	+	0.990478i	$0.543963\pi$
$600$	−522.103	−	5038.79i	−0.0355246	−	0.342846i
$601$		−	15679.3i		−	1.06418i	−0.846687	−	0.532091i	$-0.821406\pi$
$601$		−	15679.3i		−	1.06418i	0.846687	−	0.532091i	$-0.178594\pi$
$602$	10502.4	+	3767.02i	0.711041	+	0.255037i
$603$	−5124.33	−	20683.4i	−0.346068	−	1.39684i
$604$	−3888.93	+	20592.4i	−0.261984	+	1.38724i
$605$	9093.02	−	5249.86i	0.611048	−	0.352789i
$606$	11203.0	−	11851.1i	0.750976	−	0.794418i
$607$	11342.4	+	6548.53i	0.758441	+	0.437886i	0.828736	−	0.559640i	$-0.189061\pi$
$607$	11342.4	+	6548.53i	0.758441	+	0.437886i	−0.0702949	+	0.997526i	$0.522394\pi$
$608$	−15673.1	−	13982.0i	−1.04544	−	0.932640i
$609$	−3401.85	−	4421.74i	−0.226354	−	0.294217i
$610$	30774.7	−	5234.30i	2.04267	−	0.347427i
$611$	−326.853	+	566.127i	−0.0216417	+	0.0374845i
$612$	20373.7	+	10282.4i	1.34568	+	0.679152i
$613$	−18672.8	+	10780.8i	−1.23032	+	0.710328i	−0.967097	−	0.254406i	$-0.918120\pi$
$613$	−18672.8	+	10780.8i	−1.23032	+	0.710328i	−0.263226	+	0.964734i	$0.584787\pi$
$614$	2977.96	+	1104.37i	0.195734	+	0.0725878i
$615$	27887.6	−	3403.14i	1.82851	−	0.223134i
$616$	−8249.08	−	4844.83i	−0.539553	−	0.316889i
$617$		−	9998.31i		−	0.652377i	−0.945305	−	0.326189i	$-0.894236\pi$
$617$		−	9998.31i		−	0.652377i	0.945305	−	0.326189i	$-0.105764\pi$
$618$	−24151.5	−	5749.17i	−1.57203	−	0.374216i
$619$	−3122.99	−	5409.17i	−0.202784	−	0.351233i	0.746640	−	0.665228i	$-0.231666\pi$
$619$	−3122.99	−	5409.17i	−0.202784	−	0.351233i	−0.949425	+	0.313995i	$0.898332\pi$
$620$	−946.906	−	814.310i	−0.0613365	−	0.0527475i
$621$	−1389.16	+	8646.08i	−0.0897667	+	0.558704i
$622$	957.213	+	5627.87i	0.0617054	+	0.362793i
$623$	21871.8	+	12316.5i	1.40654	+	0.792052i
$624$	881.965	+	864.636i	0.0565815	+	0.0554698i
$625$	9577.16	−	16588.1i	0.612938	−	1.06164i
$626$	−1267.37	−	1529.12i	−0.0809173	−	0.0976291i
$627$	10998.0	−	8274.77i	0.700505	−	0.527053i
$628$	5003.98	−	26496.8i	0.317963	−	1.68366i
$629$		−	14937.9i		−	0.946921i
$630$	7511.64	+	16727.5i	0.475033	+	1.05784i
$631$	−1240.36			−0.0782537			−0.0391269	−	0.999234i	$-0.512458\pi$
$631$	−1240.36			−0.0782537			−0.0391269	+	0.999234i	$0.512458\pi$
$632$	3218.11	+	58.5183i	0.202547	+	0.00368312i
$633$	1837.86	+	2442.70i	0.115401	+	0.153379i
$634$	9656.18	−	8003.27i	0.604883	−	0.501341i
$635$	−19205.9	−	11088.5i	−1.20026	−	0.692968i
$636$	−7415.99	−	15029.6i	−0.462363	−	0.937047i
$637$	−1273.60	+	27.3586i	−0.0792178	+	0.00170171i
$638$	−627.644	−	3690.19i	−0.0389477	−	0.228991i
$639$	12524.7	+	3611.55i	0.775384	+	0.223585i
$640$	18611.4	−	2473.12i	1.14950	−	0.152748i
$641$	17186.0	−	9922.36i	1.05898	−	0.611404i	0.133832	−	0.991004i	$-0.457272\pi$
$641$	17186.0	−	9922.36i	1.05898	−	0.611404i	0.925151	+	0.379600i	$0.123939\pi$
$642$	5800.40	−	24366.7i	0.356579	−	1.49794i
$643$	16526.5			1.01360			0.506798	−	0.862065i	$-0.330829\pi$
$643$	16526.5			1.01360			0.506798	+	0.862065i	$0.330829\pi$
$644$	−8694.58	+	3150.97i	−0.532010	+	0.192803i
$645$	−1738.13	−	14243.4i	−0.106107	−	0.869510i
$646$	−32509.9	−	12056.3i	−1.98001	−	0.734284i
$647$	−8911.89	−	15435.8i	−0.541518	−	0.937937i	−0.998817	−	0.0486243i	$-0.984516\pi$
$647$	−8911.89	−	15435.8i	−0.541518	−	0.937937i	0.457299	−	0.889313i	$-0.348817\pi$
$648$	−924.245	+	16469.5i	−0.0560305	+	0.998429i
$649$	−548.778	−	316.837i	−0.0331917	−	0.0191632i
$650$	−75.8899	−	446.189i	−0.00457946	−	0.0269246i
$651$	1071.13	+	442.084i	0.0644868	+	0.0266154i
$652$	−2429.92	−	6936.64i	−0.145956	−	0.416656i
$653$	11568.7	−	20037.6i	0.693291	−	1.20082i	−0.277463	−	0.960736i	$-0.589493\pi$
$653$	11568.7	−	20037.6i	0.693291	−	1.20082i	0.970753	−	0.240079i	$-0.0771732\pi$
$654$	8554.05	−	9048.88i	0.511453	−	0.541039i
$655$	5382.65	+	9323.03i	0.321096	+	0.556154i
$656$	3996.21	+	26389.4i	0.237844	+	1.57063i
$657$	−1713.38	−	6915.76i	−0.101743	−	0.410669i
$658$	−5959.56	−	7035.22i	−0.353082	−	0.416811i
$659$	14423.5			0.852597			0.426299	−	0.904583i	$-0.359817\pi$
$659$	14423.5			0.852597			0.426299	+	0.904583i	$0.359817\pi$
$660$	−801.884	+	12276.9i	−0.0472928	+	0.724055i
$661$	−8382.41	−	14518.8i	−0.493250	−	0.854334i	0.506720	−	0.862111i	$-0.330858\pi$
$661$	−8382.41	−	14518.8i	−0.493250	−	0.854334i	−0.999970	+	0.00777707i	$0.997524\pi$
$662$	18953.5	+	22868.0i	1.11276	+	1.34258i
$663$	1876.28	+	798.078i	0.109907	+	0.0467493i
$664$	−9461.50	+	5235.58i	−0.552978	+	0.305994i
$665$	−14188.1	−	23976.2i	−0.827357	−	1.39813i
$666$	9896.58	−	4317.05i	0.575803	−	0.251175i
$667$	−3133.72	−	1809.25i	−0.181916	−	0.105029i
$668$	−24121.1	−	20743.4i	−1.39711	−	1.20147i
$669$	−5927.92	−	7878.78i	−0.342581	−	0.455323i
$670$	−27134.6	−	10062.8i	−1.56463	−	0.580240i
$671$	−19433.5			−1.11807
$672$	−15678.9	+	7591.81i	−0.900041	+	0.435804i
$673$	24785.1			1.41961			0.709803	−	0.704400i	$-0.248784\pi$
$673$	24785.1			1.41961			0.709803	+	0.704400i	$0.248784\pi$
$674$	−4197.71	−	1556.72i	−0.239896	−	0.0889651i
$675$	3814.51	−	4689.12i	0.217512	−	0.267384i
$676$	−13242.4	−	11388.1i	−0.753437	−	0.647932i
$677$	−7591.21	−	4382.79i	−0.430951	−	0.248810i	0.268801	−	0.963196i	$-0.413373\pi$
$677$	−7591.21	−	4382.79i	−0.430951	−	0.248810i	−0.699752	+	0.714386i	$0.746706\pi$
$678$	2634.32	+	8830.90i	0.149219	+	0.500219i
$679$	25223.4	−	270.885i	1.42560	−	0.0153102i
$680$	27119.5	−	15006.8i	1.52939	−	0.846300i
$681$	−1041.46	+	2448.47i	−0.0586034	+	0.137776i
$682$	496.137	+	598.603i	0.0278564	+	0.0336095i
$683$	−8167.07	−	14145.8i	−0.457546	−	0.792493i	0.541284	−	0.840840i	$-0.317938\pi$
$683$	−8167.07	−	14145.8i	−0.457546	−	0.792493i	−0.998831	+	0.0483462i	$0.984605\pi$
$684$	−1407.91	−	25022.6i	−0.0787027	−	1.39877i
$685$	−24499.2			−1.36652
$686$	5701.55	−	17038.8i	0.317327	−	0.948316i
$687$	−544.466	−	4461.72i	−0.0302368	−	0.247780i
$688$	13478.3	−	2041.04i	0.746881	−	0.113102i
$689$	−748.688	−	1296.77i	−0.0413973	−	0.0717022i
$690$	8642.77	+	8170.15i	0.476847	+	0.450771i
$691$	−10589.0	+	18340.8i	−0.582961	+	1.00972i	0.412165	+	0.911109i	$0.364773\pi$
$691$	−10589.0	+	18340.8i	−0.582961	+	1.00972i	−0.995126	+	0.0986094i	$0.968561\pi$
$692$	2723.62	+	7775.03i	0.149619	+	0.427113i
$693$	−2863.97	−	11050.2i	−0.156989	−	0.605715i
$694$	3270.16	+	19226.7i	0.178867	+	1.05163i
$695$	22554.7	+	13022.0i	1.23101	+	0.710722i
$696$	−6222.76	−	2781.53i	−0.338898	−	0.151485i
$697$	22030.9	+	38158.6i	1.19724	+	2.07369i
$698$	−18203.3	−	6750.66i	−0.987111	−	0.366069i
$699$	11038.3	−	1347.02i	0.597294	−	0.0728882i
$700$	6285.08	+	1117.19i	0.339363	+	0.0603226i
$701$	17795.3			0.958802			0.479401	−	0.877596i	$-0.340854\pi$
$701$	17795.3			0.958802			0.479401	+	0.877596i	$0.340854\pi$
$702$	13.5057	+	1473.70i	0.000726123	+	0.0792328i
$703$	−14206.8	+	8202.31i	−0.762191	+	0.440051i
$704$	−11680.4	−	424.934i	−0.625315	−	0.0227490i
$705$	−4641.18	+	10911.4i	−0.247939	+	0.582904i
$706$	1748.50	+	10280.2i	0.0932093	+	0.548018i
$707$	10465.8	+	17686.0i	0.556730	+	0.940806i
$708$	−1034.77	+	510.585i	−0.0549282	+	0.0271030i
$709$	17872.9	+	10318.9i	0.946731	+	0.546596i	0.892064	−	0.451909i	$-0.149257\pi$
$709$	17872.9	+	10318.9i	0.946731	+	0.546596i	0.0546672	+	0.998505i	$0.482590\pi$
$710$	13630.3	−	11297.2i	0.720476	−	0.597148i
$711$	2663.82	+	2766.68i	0.140508	+	0.145933i
$712$	30662.8	+	557.573i	1.61396	+	0.0293482i
$713$	751.585			0.0394770
$714$	−19530.1	+	21109.4i	−1.02366	+	1.10644i
$715$			1099.20i			0.0574935i
$716$	−4108.52	+	21755.2i	−0.214445	+	1.13551i
$717$	−4220.28	−	5609.17i	−0.219818	−	0.292159i
$718$	−8909.46	−	10749.5i	−0.463089	−	0.558731i
$719$	618.753	−	1071.71i	0.0320940	−	0.0555885i	−0.849532	−	0.527537i	$-0.823116\pi$
$719$	618.753	−	1071.71i	0.0320940	−	0.0555885i	0.881626	+	0.471948i	$0.156449\pi$
$720$	17779.7	+	13630.1i	0.920295	+	0.705507i
$721$	15350.6	−	27259.9i	0.792906	−	1.40806i
$722$	3131.82	+	18413.3i	0.161433	+	0.949132i
$723$	406.149	−	954.854i	0.0208919	−	0.0491167i
$724$	−2926.12	−	2516.37i	−0.150205	−	0.129171i
$725$	1248.88	+	2163.12i	0.0639754	+	0.110809i
$726$	−2756.33	+	11579.0i	−0.140905	+	0.591924i
$727$		−	2385.47i		−	0.121695i	−0.998147	−	0.0608475i	$-0.980620\pi$
$727$		−	2385.47i		−	0.121695i	0.998147	−	0.0608475i	$-0.0193803\pi$
$728$	−1353.63	+	768.144i	−0.0689135	+	0.0391062i
$729$	−14685.9	+	13105.2i	−0.746120	+	0.665812i
$730$	−9072.78	−	3364.63i	−0.459998	−	0.170590i
$731$	19489.3	−	11252.1i	0.986097	−	0.569324i
$732$	−19653.5	+	29428.0i	−0.992370	+	1.48591i
$733$	9688.18	−	16780.4i	0.488187	−	0.845565i	−0.511721	−	0.859152i	$-0.670992\pi$
$733$	9688.18	−	16780.4i	0.488187	−	0.845565i	0.999908	+	0.0135872i	$0.00432506\pi$
$734$	−22073.8	+	3754.41i	−1.11002	+	0.188798i
$735$	−22871.3	+	3290.93i	−1.14778	+	0.165154i
$736$	−7521.65	+	8431.37i	−0.376701	+	0.422261i
$737$	15602.7	+	9008.22i	0.779828	+	0.450234i
$738$	−18913.7	+	25623.6i	−0.943391	+	1.27807i
$739$	1587.59	−	916.595i	0.0790263	−	0.0456258i	−0.459966	−	0.887936i	$-0.652138\pi$
$739$	1587.59	−	916.595i	0.0790263	−	0.0456258i	0.538992	+	0.842311i	$0.318805\pi$
$740$	2721.26	−	14409.4i	0.135183	−	0.715812i
$741$	−271.234	−	2222.67i	−0.0134467	−	0.110191i
$742$	20781.3	−	3764.64i	1.02818	−	0.186259i
$743$			24638.6i			1.21656i	0.793722	+	0.608280i	$0.208140\pi$
$743$			24638.6i			1.21656i	−0.793722	+	0.608280i	$0.791860\pi$
$744$	1408.21	−	145.914i	0.0693919	−	0.00719015i
$745$	−32028.6	+	18491.7i	−1.57508	+	0.909375i
$746$	−10416.0	−	12567.2i	−0.511203	−	0.616781i
$747$	−12398.0	−	3575.00i	−0.607252	−	0.175104i
$748$	−18210.4	+	6379.14i	−0.890156	+	0.311824i
$749$	27502.8	+	15487.3i	1.34170	+	0.755534i
$750$	4461.75	+	14956.9i	0.217227	+	0.728200i
$751$	2664.10	−	4614.35i	0.129446	−	0.224208i	−0.794016	−	0.607897i	$-0.792013\pi$
$751$	2664.10	−	4614.35i	0.129446	−	0.224208i	0.923462	+	0.383689i	$0.125347\pi$
$752$	−10489.0	−	4108.26i	−0.508635	−	0.199219i
$753$	−22912.0	−	30452.4i	−1.10885	−	1.47377i
$754$	−570.983	−	211.748i	−0.0275782	−	0.0102274i
$755$			33961.9i			1.63709i
$756$	−19629.5	−	6838.36i	−0.944337	−	0.328980i
$757$			24477.8i			1.17525i	0.809135	+	0.587623i	$0.199936\pi$
$757$			24477.8i			1.17525i	−0.809135	+	0.587623i	$0.800064\pi$
$758$	−11396.9	+	30731.9i	−0.546113	+	1.47260i
$759$	−4451.43	−	5916.38i	−0.212881	−	0.282940i
$760$	−29163.5	−	17552.1i	−1.39194	−	0.837740i
$761$	−11694.8	+	20255.9i	−0.557077	+	0.964885i	0.440662	+	0.897673i	$0.354744\pi$
$761$	−11694.8	+	20255.9i	−0.557077	+	0.964885i	−0.997739	+	0.0672118i	$0.978590\pi$
$762$	24091.0	−	7186.50i	1.14531	−	0.341653i
$763$	7991.18	+	13504.1i	0.379161	+	0.640736i
$764$	−6112.95	−	17450.5i	−0.289475	−	0.826355i
$765$	35536.3	+	10247.0i	1.67950	+	0.484291i
$766$	19937.5	−	16524.7i	0.940434	−	0.779454i
$767$	−89.2812	+	51.5465i	−0.00420307	+	0.00242664i
$768$	−12456.1	+	17257.8i	−0.585249	+	0.810854i
$769$			24022.3i			1.12648i	0.826292	+	0.563242i	$0.190446\pi$
$769$			24022.3i			1.12648i	−0.826292	+	0.563242i	$0.809554\pi$
$770$	−14593.2	−	5234.32i	−0.682992	−	0.244976i
$771$	2181.41	+	17875.9i	0.101896	+	0.835000i
$772$	−6091.79	+	32256.9i	−0.284001	+	1.50382i
$773$	−16368.4	+	9450.27i	−0.761615	+	0.439719i	−0.829875	−	0.557949i	$-0.811589\pi$
$773$	−16368.4	+	9450.27i	−0.761615	+	0.439719i	0.0682601	+	0.997668i	$0.478255\pi$
$774$	13087.1	+	9660.07i	0.607760	+	0.448610i
$775$	−449.293	−	259.399i	−0.0208246	−	0.0120231i
$776$	26965.7	−	14921.6i	1.24744	−	0.690278i
$777$	1793.06	+	13487.3i	0.0827874	+	0.622723i
$778$	−1118.12	−	6573.91i	−0.0515251	−	0.302938i
$779$	24194.0	−	41905.3i	1.11276	−	1.92736i
$780$	1664.51	+	1111.65i	0.0764091	+	0.0510299i
$781$	−9544.51	+	5510.53i	−0.437298	+	0.252474i
$782$	−6485.70	+	17488.8i	−0.296583	+	0.799741i
$783$	−2897.79	−	7599.57i	−0.132259	−	0.346854i
$784$	−3752.14	−	21629.0i	−0.170925	−	0.985284i
$785$		−	43699.6i		−	1.98689i
$786$	−11871.9	−	2826.05i	−0.538748	−	0.128247i
$787$	−11764.3	−	20376.4i	−0.532849	−	0.922922i	−0.999264	−	0.0383560i	$-0.987788\pi$
$787$	−11764.3	−	20376.4i	−0.532849	−	0.922922i	0.466415	−	0.884566i	$-0.345545\pi$
$788$	14574.0	+	12533.2i	0.658856	+	0.566596i
$789$	10328.6	−	24282.5i	0.466043	−	1.09566i
$790$	5142.28	−	874.621i	0.231587	−	0.0393894i
$791$	−11612.1	+	124.708i	−0.521971	+	0.00560568i
$792$	−9489.07	−	10221.1i	−0.425731	−	0.458573i
$793$	−1580.83	+	2738.07i	−0.0707905	+	0.122613i
$794$	−27346.1	+	22665.1i	−1.22226	+	1.01304i
$795$	−16329.5	−	21703.6i	−0.728489	−	0.968234i
$796$	−17393.6	−	3284.82i	−0.774495	−	0.146265i
$797$			6656.23i			0.295829i	0.989000	+	0.147915i	$0.0472561\pi$
$797$			6656.23i			0.295829i	−0.989000	+	0.147915i	$0.952744\pi$
$798$	30800.2	+	6983.22i	1.36631	+	0.309779i
$799$	−18596.6			−0.823403
$800$	7406.37	−	2444.22i	0.327318	−	0.108020i
$801$	25381.3	+	26361.4i	1.11961	+	1.16284i
$802$	−147.869	−	178.409i	−0.00651053	−	0.00785515i
$803$	5216.96	+	3012.01i	0.229268	+	0.132368i
$804$	29420.4	−	14516.8i	1.29052	−	0.636776i
$805$	−12898.1	+	7632.54i	−0.564716	+	0.334176i
$806$	124.698	−	21.2092i	0.00544952	−	0.000926878i
$807$	7720.12	−	18150.0i	0.336755	−	0.791709i
$808$	21512.4	+	12947.3i	0.936637	+	0.563717i
$809$	−277.317	+	160.109i	−0.0120519	+	0.00695814i	−0.506014	−	0.862525i	$-0.668882\pi$
$809$	−277.317	+	160.109i	−0.0120519	+	0.00695814i	0.493962	+	0.869484i	$0.335548\pi$
$810$	3481.18	+	26504.7i	0.151008	+	1.14973i
$811$	−537.182			−0.0232590			−0.0116295	−	0.999932i	$-0.503702\pi$
$811$	−537.182			−0.0232590			−0.0116295	+	0.999932i	$0.503702\pi$
$812$	5530.19	−	6572.15i	0.239005	−	0.284036i
$813$	−15829.7	+	1931.70i	−0.682867	+	0.0833307i
$814$	−3174.22	+	8559.34i	−0.136679	+	0.368556i
$815$	−5955.64	−	10315.5i	−0.255972	−	0.443356i
$816$	−8756.66	+	34027.1i	−0.375667	+	1.45979i
$817$	−21402.9	−	12357.0i	−0.916514	−	0.529150i
$818$	−14757.7	+	2510.05i	−0.630794	+	0.107288i
$819$	−1789.88	−	495.361i	−0.0763655	−	0.0211347i
$820$	14300.1	+	40822.0i	0.609000	+	1.73849i
$821$	5948.17	−	10302.5i	0.252853	−	0.437955i	−0.711457	−	0.702730i	$-0.751964\pi$
$821$	5948.17	−	10302.5i	0.252853	−	0.437955i	0.964310	+	0.264775i	$0.0852976\pi$
$822$	19078.5	−	20182.1i	0.809536	−	0.856366i
$823$	13650.5	+	23643.4i	0.578162	+	1.00141i	0.995690	+	0.0927425i	$0.0295633\pi$
$823$	13650.5	+	23643.4i	0.578162	+	1.00141i	−0.417528	+	0.908664i	$0.637103\pi$
$824$	694.928	−	38216.4i	0.0293798	−	1.61569i
$825$	619.077	+	5073.13i	0.0261254	+	0.214089i
$826$	−259.192	−	1430.78i	−0.0109182	−	0.0602700i
$827$	−33391.1			−1.40402			−0.702009	−	0.712168i	$-0.747713\pi$
$827$	−33391.1			−1.40402			−0.702009	+	0.712168i	$0.747713\pi$
$828$	−13460.9	+	757.386i	−0.564976	+	0.0317886i
$829$	11314.8	+	19597.8i	0.474040	+	0.821061i	0.999558	−	0.0297213i	$-0.00946196\pi$
$829$	11314.8	+	19597.8i	0.474040	+	0.821061i	−0.525518	+	0.850782i	$0.676129\pi$
$830$	−13492.4	+	11182.8i	−0.564251	+	0.467664i
$831$	14591.6	−	34304.9i	0.609120	−	1.43204i
$832$	−1010.02	+	1611.14i	−0.0420866	+	0.0671348i
$833$	−18789.6	−	30987.9i	−0.781537	−	1.28892i
$834$	−28291.6	+	8439.57i	−1.17465	+	0.350406i
$835$	−44649.8	−	25778.6i	−1.85050	−	1.06839i
$836$	16066.1	+	13816.4i	0.664664	+	0.571590i
$837$	1310.49	+	1066.06i	0.0541184	+	0.0440242i
$838$	3360.61	−	9061.92i	0.138532	−	0.373555i
$839$	−10587.3			−0.435653			−0.217826	−	0.975988i	$-0.569897\pi$
$839$	−10587.3			−0.435653			−0.217826	+	0.975988i	$0.569897\pi$
$840$	−22684.7	+	16804.8i	−0.931783	+	0.690263i
$841$	−21028.2			−0.862200
$842$	12444.2	−	33556.1i	0.509331	−	1.37342i
$843$	11157.2	+	14829.0i	0.455841	+	0.605857i
$844$	−3068.68	+	3568.36i	−0.125152	+	0.145531i
$845$	−24512.6	−	14152.4i	−0.997942	−	0.576162i
$846$	−5374.40	−	12320.5i	−0.218411	−	0.500694i
$847$	−13069.2	−	7359.53i	−0.530182	−	0.298556i
$848$	20162.6	−	16101.9i	0.816493	−	0.652055i
$849$	11655.5	+	4957.69i	0.471162	+	0.200409i
$850$	9913.13	−	8216.23i	0.400020	−	0.331546i
$851$	4412.45	+	7642.58i	0.177740	+	0.307855i
$852$	−1308.04	+	20026.1i	−0.0525969	+	0.805260i
$853$	17268.2			0.693144			0.346572	−	0.938023i	$-0.387346\pi$
$853$	17268.2			0.693144			0.346572	+	0.938023i	$0.387346\pi$
$854$	−28823.4	−	34025.9i	−1.15494	−	1.36340i
$855$	−9767.24	−	39423.7i	−0.390682	−	1.57691i
$856$	38556.9	+	701.120i	1.53954	+	0.0279951i
$857$	11518.4	+	19950.4i	0.459113	+	0.795208i	0.998914	−	0.0465850i	$-0.0148338\pi$
$857$	11518.4	+	19950.4i	0.459113	+	0.795208i	−0.539801	+	0.841793i	$0.681500\pi$
$858$	−905.510	−	855.993i	−0.0360298	−	0.0340596i
$859$	−17934.9	+	31064.2i	−0.712378	+	1.23387i	0.251584	+	0.967835i	$0.419048\pi$
$859$	−17934.9	+	31064.2i	−0.712378	+	1.23387i	−0.963962	+	0.266039i	$0.914285\pi$
$860$	20849.6	−	7303.68i	0.826704	−	0.289597i
$861$	−24471.9	−	31808.7i	−0.968640	−	1.25904i
$862$	4741.29	−	806.419i	0.187342	−	0.0318640i
$863$	−11853.5	−	6843.62i	−0.467553	−	0.269942i	0.247662	−	0.968846i	$-0.420338\pi$
$863$	−11853.5	−	6843.62i	−0.467553	−	0.269942i	−0.715215	+	0.698905i	$0.753671\pi$
$864$	−25074.1	+	4032.41i	−0.987314	+	0.158780i
$865$	6675.46	+	11562.2i	0.262396	+	0.454483i
$866$	−2731.88	+	7366.55i	−0.107197	+	0.289060i
$867$	3933.79	+	32236.1i	0.154093	+	1.26274i
$868$	−312.225	+	1756.52i	−0.0122092	+	0.0686867i
$869$	−3247.23			−0.126760
$870$	−10745.9	−	2558.02i	−0.418760	−	0.0996840i
$871$	2538.42	−	1465.56i	0.0987497	−	0.0570132i
$872$	16425.7	+	9885.88i	0.637897	+	0.383920i
$873$	35334.7	+	10188.9i	1.36987	+	0.395008i
$874$	20194.1	−	3434.70i	0.781551	−	0.132930i
$875$	−19667.5	+	211.218i	−0.759866	+	0.00816054i
$876$	9837.07	−	4853.87i	0.379411	−	0.187211i
$877$	28782.3	+	16617.5i	1.10822	+	0.639831i	0.938368	−	0.345638i	$-0.112338\pi$
$877$	28782.3	+	16617.5i	1.10822	+	0.639831i	0.169852	+	0.985470i	$0.445671\pi$
$878$	23010.2	+	27762.5i	0.884461	+	1.06713i
$879$	−24650.2	−	32762.6i	−0.945884	−	1.25717i
$880$	−18728.2	+	2836.05i	−0.717418	+	0.108640i
$881$	37284.4			1.42582			0.712908	−	0.701257i	$-0.247377\pi$
$881$	37284.4			1.42582			0.712908	+	0.701257i	$0.247377\pi$
$882$	15099.8	−	21403.9i	0.576458	−	0.817127i
$883$			11175.4i			0.425916i	0.977061	+	0.212958i	$0.0683097\pi$
$883$			11175.4i			0.425916i	−0.977061	+	0.212958i	$0.931690\pi$
$884$	−582.545	+	3084.65i	−0.0221641	+	0.117362i
$885$	−1494.27	+	1124.27i	−0.0567563	+	0.0427029i
$886$	28098.8	−	23288.9i	1.06546	−	0.883077i
$887$	7044.36	−	12201.2i	0.266659	−	0.461867i	−0.701338	−	0.712829i	$-0.747414\pi$
$887$	7044.36	−	12201.2i	0.266659	−	0.461867i	0.967997	+	0.250962i	$0.0807469\pi$
$888$	9751.16	+	13462.9i	0.368499	+	0.508769i
$889$	340.207	+	31678.2i	0.0128348	+	1.19511i
$890$	48996.6	−	8333.55i	1.84536	−	0.313867i
$891$	630.208	−	16629.9i	0.0236956	−	0.625280i
$892$	9897.84	−	11509.5i	0.371529	−	0.432026i
$893$	10211.3	+	17686.4i	0.382650	+	0.662770i
$894$	9708.70	−	40785.0i	0.363207	−	1.52579i
$895$			35879.5i			1.34002i
$896$	−16580.2	−	21081.3i	−0.618196	−	0.786024i
$897$	−1195.69	+	145.911i	−0.0445071	+	0.00543123i
$898$	9279.23	−	25021.6i	0.344824	−	0.929823i
$899$	−604.536	+	349.029i	−0.0224276	+	0.0129486i
$900$	8308.27	+	4193.10i	0.307714	+	0.155300i
$901$	21298.6	−	36890.2i	0.787523	−	1.36403i
$902$	−4515.08	−	26546.1i	−0.166669	−	0.979921i
$903$	−16246.1	+	12498.9i	−0.598712	+	0.460616i
$904$	−12414.2	+	6869.48i	−0.456737	+	0.252739i
$905$	−5416.46	−	3127.19i	−0.198949	−	0.114863i
$906$	−27977.4	−	26447.5i	−1.02592	−	0.969823i
$907$	32502.1	−	18765.1i	1.18987	−	0.686973i	0.231594	−	0.972812i	$-0.425606\pi$
$907$	32502.1	−	18765.1i	1.18987	−	0.686973i	0.958277	+	0.285840i	$0.0922725\pi$
$908$	−4025.36	−	760.199i	−0.147121	−	0.0277842i
$909$	7204.78	+	29080.8i	0.262891	+	1.06111i
$910$	−1924.58	+	1630.32i	−0.0701090	+	0.0593896i
$911$			45690.4i			1.66168i	0.556510	+	0.830841i	$0.312140\pi$
$911$			45690.4i			1.66168i	−0.556510	+	0.830841i	$0.687860\pi$
$912$	37170.0	−	10356.0i	1.34958	−	0.376010i
$913$	9447.91	−	5454.76i	0.342476	−	0.197728i
$914$	−7471.24	+	6192.34i	−0.270379	+	0.224097i
$915$	−22447.1	+	52773.0i	−0.811015	+	1.90669i
$916$	6531.09	−	2287.86i	0.235582	−	0.0825251i
$917$	7545.69	−	13399.8i	0.271735	−	0.482553i
$918$	−36114.9	+	21294.6i	−1.29844	+	0.765607i
$919$	−8003.35	+	13862.2i	−0.287276	+	0.497576i	−0.973158	−	0.230136i	$-0.926083\pi$
$919$	−8003.35	+	13862.2i	−0.287276	+	0.497576i	0.685883	+	0.727712i	$0.259416\pi$
$920$	−9442.20	+	15688.6i	−0.338370	+	0.562213i
$921$	−4662.60	+	3508.10i	−0.166817	+	0.125511i
$922$	3195.89	−	8617.78i	0.114155	−	0.307821i
$923$			1793.02i			0.0639416i
$924$	15676.3	−	7945.56i	0.558131	−	0.282889i
$925$		−	6091.59i		−	0.216530i
$926$	−20385.2	−	7559.82i	−0.723432	−	0.268284i
$927$	32855.4	−	31633.9i	1.16409	−	1.12081i
$928$	2134.58	−	10274.7i	0.0755074	−	0.363453i
$929$	6989.54	−	12106.2i	0.246845	−	0.427549i	−0.715803	−	0.698302i	$-0.753939\pi$
$929$	6989.54	−	12106.2i	0.246845	−	0.427549i	0.962649	+	0.270753i	$0.0872727\pi$
$930$	2198.62	−	655.863i	0.0775222	−	0.0231254i
$931$	−19154.1	+	34885.3i	−0.674274	+	1.22805i
$932$	5660.20	+	16158.0i	0.198933	+	0.567890i
$933$	−9650.78	−	4104.98i	−0.338641	−	0.144042i
$934$	−3156.73	−	3808.69i	−0.110590	−	0.133431i
$935$	−27080.6	+	15635.0i	−0.947198	+	0.546865i
$936$	−2211.98	+	505.520i	−0.0772446	+	0.0176532i
$937$		−	18184.3i		−	0.633996i	−0.948426	−	0.316998i	$-0.897325\pi$
$937$		−	18184.3i		−	0.633996i	0.948426	−	0.316998i	$-0.102675\pi$
$938$	7369.27	+	40679.4i	0.256519	+	1.41602i
$939$	3621.75	−	441.965i	0.125870	−	0.0153599i
$940$	−17938.7	−	3387.76i	−0.622441	−	0.117550i
$941$	6499.38	−	3752.42i	0.225158	−	0.129995i	−0.383178	−	0.923674i	$-0.625171\pi$
$941$	6499.38	−	3752.42i	0.225158	−	0.129995i	0.608336	+	0.793679i	$0.291837\pi$
$942$	35999.2	+	34030.6i	1.24513	+	1.17705i
$943$	−22543.0	−	13015.2i	−0.778475	−	0.449453i
$944$	−1108.60	−	1388.18i	−0.0382224	−	0.0478616i
$945$	−33315.5	−	4986.40i	−1.14683	−	0.171648i
$946$	−13558.3	+	2306.05i	−0.465981	+	0.0792561i
$947$	−12640.2	+	21893.4i	−0.433739	+	0.751257i	−0.997192	−	0.0748906i	$-0.976139\pi$
$947$	−12640.2	+	21893.4i	−0.433739	+	0.751257i	0.563453	+	0.826148i	$0.309473\pi$
$948$	−3283.99	+	4917.25i	−0.112510	+	0.168465i
$949$	848.751	−	490.027i	0.0290323	−	0.0167618i
$950$	−13257.4	−	4916.48i	−0.452763	−	0.167907i
$951$	2790.95	+	22870.9i	0.0951659	+	0.779852i
$952$	−38178.4	−	22422.9i	−1.29976	−	0.763371i
$953$		−	42226.4i		−	1.43531i	−0.696401	−	0.717653i	$-0.745216\pi$
$953$		−	42226.4i		−	1.43531i	0.696401	−	0.717653i	$-0.254784\pi$
$954$	30595.6	+	3449.35i	1.03833	+	0.117062i
$955$	−14982.6	−	25950.6i	−0.507669	−	0.879309i
$956$	7046.60	−	8194.02i	0.238393	−	0.277211i
$957$	6328.01	+	2691.63i	0.213747	+	0.0909175i
$958$	3275.62	+	19258.8i	0.110470	+	0.649501i
$959$	17823.1	+	30118.8i	0.600144	+	1.01417i
$960$	−14645.6	+	31228.1i	−0.492381	+	1.04988i
$961$	−14823.0	+	25674.2i	−0.497567	+	0.861811i
$962$	947.755	+	1143.49i	0.0317639	+	0.0383240i
$963$	31915.8	+	33148.2i	1.06799	+	1.10923i
$964$	1569.81	+	296.462i	0.0524482	+	0.00990498i
$965$			53199.4i			1.77466i
$966$	3756.64	−	16569.0i	0.125122	−	0.551863i
$967$	39321.9			1.30766			0.653830	−	0.756641i	$-0.273161\pi$
$967$	39321.9			1.30766			0.653830	+	0.756641i	$0.273161\pi$
$968$	−18322.1	−	333.170i	−0.608363	−	0.0110625i
$969$	50900.9	−	38297.3i	1.68749	−	1.26965i
$970$	38453.9	−	31871.5i	1.27287	−	1.05498i
$971$	−36638.2	−	21153.1i	−1.21089	−	0.699109i	−0.247938	−	0.968776i	$-0.579753\pi$
$971$	−36638.2	−	21153.1i	−1.21089	−	0.699109i	−0.962954	+	0.269667i	$0.913086\pi$
$972$	−24545.2	−	17772.5i	−0.809967	−	0.586476i
$973$	−399.527	−	37201.8i	−0.0131637	−	1.22573i
$974$	1989.37	+	11696.3i	0.0654449	+	0.384779i
$975$	765.134	+	325.451i	0.0251322	+	0.0106900i
$976$	−50730.0	−	19869.6i	−1.66376	−	0.651651i
$977$	−1911.51	+	1103.61i	−0.0625941	+	0.0361387i	−0.530970	−	0.847390i	$-0.678172\pi$
$977$	−1911.51	+	1103.61i	−0.0625941	+	0.0361387i	0.468376	+	0.883529i	$0.344839\pi$
$978$	13135.6	+	3126.88i	0.429480	+	0.102236i
$979$	−30940.2			−1.01007
$980$	−12479.7	−	33314.6i	−0.406786	−	1.08591i
$981$	5501.20	+	22204.6i	0.179042	+	0.722669i
$982$	5811.29	+	2155.11i	0.188845	+	0.0700329i
$983$	11382.6	+	19715.3i	0.369328	+	0.639694i	0.989461	−	0.144803i	$-0.0462547\pi$
$983$	11382.6	+	19715.3i	0.369328	+	0.639694i	−0.620133	+	0.784497i	$0.712921\pi$
$984$	−44764.7	−	20009.5i	−1.45025	−	0.648252i
$985$	26977.6	+	15575.5i	0.872668	+	0.503835i
$986$	−2904.87	−	17079.0i	−0.0938233	−	0.551628i
$987$	16790.7	−	2232.23i	0.541494	−	0.0719885i
$988$	3253.56	−	1139.73i	0.104767	−	0.0367000i
$989$	−6647.45	+	11513.7i	−0.213728	+	0.370187i
$990$	−18184.7	−	13422.8i	−0.583786	−	0.430913i
$991$	−7588.23	−	13143.2i	−0.243237	−	0.421299i	0.718397	−	0.695633i	$-0.244876\pi$
$991$	−7588.23	−	13143.2i	−0.243237	−	0.421299i	−0.961635	+	0.274334i	$0.911543\pi$
$992$	683.097	+	2069.89i	0.0218633	+	0.0662490i
$993$	−54163.4	+	6609.59i	−1.73094	+	0.211228i
$994$	−23804.6	−	8538.24i	−0.759592	−	0.272451i
$995$	−28686.2			−0.913984
$996$	1294.80	−	19823.4i	0.0411920	−	0.630651i
$997$	−20870.9	−	36149.4i	−0.662976	−	1.14831i	−0.979830	−	0.199834i	$-0.935960\pi$
$997$	−20870.9	−	36149.4i	−0.662976	−	1.14831i	0.316853	−	0.948475i	$-0.397374\pi$
$998$	16105.3	+	19431.5i	0.510825	+	0.616325i
$999$	−3146.64	+	19584.5i	−0.0996548	+	0.620247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.ba.c.5.13	✓	176
3.2	odd	2	inner	168.4.ba.c.5.76	yes	176
7.3	odd	6	inner	168.4.ba.c.101.70	yes	176
8.5	even	2	inner	168.4.ba.c.5.19	yes	176
21.17	even	6	inner	168.4.ba.c.101.19	yes	176
24.5	odd	2	inner	168.4.ba.c.5.70	yes	176
56.45	odd	6	inner	168.4.ba.c.101.76	yes	176
168.101	even	6	inner	168.4.ba.c.101.13	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.ba.c.5.13	✓	176	1.1	even	1	trivial
168.4.ba.c.5.19	yes	176	8.5	even	2	inner
168.4.ba.c.5.70	yes	176	24.5	odd	2	inner
168.4.ba.c.5.76	yes	176	3.2	odd	2	inner
168.4.ba.c.101.13	yes	176	168.101	even	6	inner
168.4.ba.c.101.19	yes	176	21.17	even	6	inner
168.4.ba.c.101.70	yes	176	7.3	odd	6	inner
168.4.ba.c.101.76	yes	176	56.45	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65194 - 0.983470i) q^{2} +(4.15215 - 3.12404i) q^{3} +(6.06558 + 5.21621i) q^{4} +(11.2278 + 6.48238i) q^{5} +(-14.0837 + 4.20125i) q^{6} +(-0.198886 - 18.5192i) q^{7} +(-10.9556 - 19.7984i) q^{8} +(7.48076 - 25.9430i) q^{9} +(-23.4003 - 28.2331i) q^{10} +(11.4142 + 19.7700i) q^{11} +(41.4808 + 2.70939i) q^{12} +3.71397 q^{13} +(-17.6856 + 49.3074i) q^{14} +(66.8709 - 8.16029i) q^{15} +(9.58241 + 63.2786i) q^{16} +(52.8272 + 91.4995i) q^{17} +(-45.3527 + 61.4421i) q^{18} +(58.0142 - 100.484i) q^{19} +(34.2897 + 97.8860i) q^{20} +(-58.6805 - 76.2732i) q^{21} +(-10.8266 - 63.6542i) q^{22} +(-54.0553 - 31.2089i) q^{23} +(-107.340 - 47.9803i) q^{24} +(21.5426 + 37.3129i) q^{25} +(-9.84922 - 3.65257i) q^{26} +(-49.9856 - 131.089i) q^{27} +(95.3935 - 113.367i) q^{28} +57.9724 q^{29} +(-185.363 - 44.1248i) q^{30} +(-10.4280 + 6.02060i) q^{31} +(36.8206 - 177.235i) q^{32} +(109.156 + 46.4295i) q^{33} +(-50.1077 - 294.605i) q^{34} +(117.815 - 209.219i) q^{35} +(180.699 - 118.338i) q^{36} +(-122.443 - 70.6922i) q^{37} +(-252.673 + 209.421i) q^{38} +(15.4210 - 11.6026i) q^{39} +(5.33357 - 293.311i) q^{40} +417.036 q^{41} +(80.6048 + 259.982i) q^{42} -212.999i q^{43} +(-33.8905 + 179.455i) q^{44} +(252.165 - 242.790i) q^{45} +(112.659 + 135.926i) q^{46} +(-88.0065 + 152.432i) q^{47} +(237.472 + 232.807i) q^{48} +(-342.921 + 7.36641i) q^{49} +(-20.4336 - 120.138i) q^{50} +(505.195 + 214.885i) q^{51} +(22.5274 + 19.3728i) q^{52} +(-201.587 - 349.159i) q^{53} +(3.63645 + 396.801i) q^{54} +295.965i q^{55} +(-364.471 + 206.826i) q^{56} +(-73.0307 - 598.462i) q^{57} +(-153.739 - 57.0141i) q^{58} +(-24.0393 + 13.8791i) q^{59} +(448.176 + 299.315i) q^{60} +(-425.644 + 737.237i) q^{61} +(33.5755 - 5.71067i) q^{62} +(-481.931 - 133.378i) q^{63} +(-271.951 + 433.805i) q^{64} +(41.6998 + 24.0754i) q^{65} +(-243.812 - 230.479i) q^{66} +(683.478 - 394.606i) q^{67} +(-156.852 + 830.555i) q^{68} +(-321.944 + 39.2870i) q^{69} +(-518.201 + 438.969i) q^{70} +482.779i q^{71} +(-595.585 + 136.113i) q^{72} +(228.529 - 131.942i) q^{73} +(255.187 + 307.890i) q^{74} +(206.015 + 87.6290i) q^{75} +(876.032 - 306.877i) q^{76} +(363.853 - 215.313i) q^{77} +(-52.3063 + 15.6033i) q^{78} +(-71.1227 + 123.188i) q^{79} +(-302.607 + 772.597i) q^{80} +(-617.077 - 388.146i) q^{81} +(-1105.95 - 410.142i) q^{82} -477.893i q^{83} +(41.9258 - 768.730i) q^{84} +1369.79i q^{85} +(-209.478 + 564.860i) q^{86} +(240.710 - 181.108i) q^{87} +(266.364 - 442.573i) q^{88} +(-677.670 + 1173.76i) q^{89} +(-907.503 + 395.868i) q^{90} +(-0.738656 - 68.7797i) q^{91} +(-165.085 - 471.263i) q^{92} +(-24.4900 + 57.5759i) q^{93} +(383.300 - 317.688i) q^{94} +(1302.75 - 752.141i) q^{95} +(-400.804 - 850.936i) q^{96} +1362.01i q^{97} +(916.650 + 317.717i) q^{98} +(598.278 - 148.224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 30 q^{4} - 76 q^{7} - 110 q^{9} + 330 q^{10} + 162 q^{12} - 332 q^{15} + 374 q^{16} + 18 q^{18} - 212 q^{22} - 84 q^{24} + 1112 q^{25} + 30 q^{28} - 104 q^{30} + 408 q^{31} + 2262 q^{33} + 1372 q^{36}+ \cdots - 1782 q^{96}+O(q^{100}) \) 176 * q + 30 * q^4 - 76 * q^7 - 110 * q^9 + 330 * q^10 + 162 * q^12 - 332 * q^15 + 374 * q^16 + 18 * q^18 - 212 * q^22 - 84 * q^24 + 1112 * q^25 + 30 * q^28 - 104 * q^30 + 408 * q^31 + 2262 * q^33 + 1372 * q^36 - 56 * q^39 - 2274 * q^40 - 1488 * q^42 - 844 * q^46 + 1292 * q^49 - 1632 * q^52 - 480 * q^54 + 100 * q^57 - 574 * q^58 - 524 * q^60 - 3030 * q^63 - 3420 * q^64 + 2376 * q^66 + 2442 * q^70 + 1026 * q^72 - 660 * q^73 - 1316 * q^78 + 3216 * q^79 + 2298 * q^81 - 360 * q^82 - 4164 * q^84 - 6972 * q^87 - 4042 * q^88 + 4476 * q^94 - 1782 * q^96

Introduction

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