LMFDB - Embedded newform 171.4.y.a.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(53,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

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

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

chi := DirichletCharacter("171.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.y (of order $18$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	171.53
Dual form			171.4.y.a.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.41758 - 1.24390i) q^{2} +(4.00419 + 3.35992i) q^{4} +(8.24027 + 9.82037i) q^{5} +(8.78095 - 15.2090i) q^{7} +(5.04239 + 8.73367i) q^{8} +O(q^{10})$	\(q+(-3.41758 - 1.24390i) q^{2} +(4.00419 + 3.35992i) q^{4} +(8.24027 + 9.82037i) q^{5} +(8.78095 - 15.2090i) q^{7} +(5.04239 + 8.73367i) q^{8} +(-15.9462 - 43.8119i) q^{10} +(-26.1479 + 15.0965i) q^{11} +(-14.9344 - 2.63335i) q^{13} +(-48.9280 + 41.0555i) q^{14} +(-13.6304 - 77.3017i) q^{16} +(-14.7722 + 40.5862i) q^{17} +(15.7637 + 81.3050i) q^{19} +67.0093i q^{20} +(108.141 - 19.0681i) q^{22} +(-38.7796 + 46.2158i) q^{23} +(-6.83160 + 38.7439i) q^{25} +(47.7640 + 27.5766i) q^{26} +(86.2617 - 31.3967i) q^{28} +(169.499 - 61.6927i) q^{29} +(190.151 + 109.784i) q^{31} +(-35.5628 + 201.687i) q^{32} +(100.970 - 120.331i) q^{34} +(221.716 - 39.0945i) q^{35} +328.229i q^{37} +(47.2615 - 297.474i) q^{38} +(-44.2172 + 121.486i) q^{40} +(72.0795 + 408.783i) q^{41} +(15.5396 - 13.0393i) q^{43} +(-155.424 - 27.4054i) q^{44} +(190.020 - 109.708i) q^{46} +(-3.06102 - 8.41010i) q^{47} +(17.2900 + 29.9471i) q^{49} +(71.5409 - 123.913i) q^{50} +(-50.9526 - 60.7229i) q^{52} +(233.838 + 196.214i) q^{53} +(-363.718 - 132.383i) q^{55} +177.108 q^{56} -656.017 q^{58} +(-739.115 - 269.016i) q^{59} +(286.803 + 240.656i) q^{61} +(-513.296 - 611.723i) q^{62} +(58.4391 - 101.220i) q^{64} +(-97.2034 - 168.361i) q^{65} +(0.129481 + 0.355746i) q^{67} +(-195.517 + 112.882i) q^{68} +(-806.360 - 142.183i) q^{70} +(-34.6533 + 29.0775i) q^{71} +(-86.2498 - 489.147i) q^{73} +(408.282 - 1121.75i) q^{74} +(-210.057 + 378.526i) q^{76} +530.245i q^{77} +(235.529 - 41.5301i) q^{79} +(646.813 - 770.842i) q^{80} +(262.147 - 1486.71i) q^{82} +(-196.347 - 113.361i) q^{83} +(-520.298 + 189.373i) q^{85} +(-69.3272 + 25.2330i) q^{86} +(-263.695 - 152.244i) q^{88} +(-115.476 + 654.899i) q^{89} +(-171.189 + 204.015i) q^{91} +(-310.562 + 54.7605i) q^{92} +32.5497i q^{94} +(-668.548 + 824.780i) q^{95} +(-367.982 + 1011.02i) q^{97} +(-21.8387 - 123.854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 36 q^{4}+O(q^{10}) $ 120 * q - 36 * q^4	$ 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) $ 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.41758	−	1.24390i	−1.20830	−	0.439784i	−0.342183	−	0.939633i	$-0.611166\pi$
$2$	−3.41758	−	1.24390i	−1.20830	−	0.439784i	−0.866112	+	0.499850i	$0.833389\pi$
$3$		0			0
$3$		0			0
$4$	4.00419	+	3.35992i	0.500524	+	0.419990i
$5$	8.24027	+	9.82037i	0.737032	+	0.878360i	0.996166	−	0.0874809i	$-0.0278817\pi$
$5$	8.24027	+	9.82037i	0.737032	+	0.878360i	−0.259134	+	0.965841i	$0.583437\pi$
$6$		0			0
$7$	8.78095	−	15.2090i	0.474126	−	0.821211i	−0.525435	−	0.850834i	$-0.676097\pi$
$7$	8.78095	−	15.2090i	0.474126	−	0.821211i	0.999561	+	0.0296228i	$0.00943060\pi$
$8$	5.04239	+	8.73367i	0.222844	+	0.385977i
$9$		0			0
$10$	−15.9462	−	43.8119i	−0.504264	−	1.38545i
$11$	−26.1479	+	15.0965i	−0.716716	+	0.413796i	−0.813543	−	0.581505i	$-0.802464\pi$
$11$	−26.1479	+	15.0965i	−0.716716	+	0.413796i	0.0968268	+	0.995301i	$0.469131\pi$
$12$		0			0
$13$	−14.9344	−	2.63335i	−0.318621	−	0.0561814i	0.0120507	−	0.999927i	$-0.496164\pi$
$13$	−14.9344	−	2.63335i	−0.318621	−	0.0561814i	−0.330671	+	0.943746i	$0.607275\pi$
$14$	−48.9280	+	41.0555i	−0.934040	+	0.783753i
$15$		0			0
$16$	−13.6304	−	77.3017i	−0.212975	−	1.20784i
$17$	−14.7722	+	40.5862i	−0.210752	+	0.579035i	−0.999357	−	0.0358647i	$-0.988581\pi$
$17$	−14.7722	+	40.5862i	−0.210752	+	0.579035i	0.788605	+	0.614900i	$0.210804\pi$
$18$		0			0
$19$	15.7637	+	81.3050i	0.190339	+	0.981719i
$19$	15.7637	+	81.3050i	0.190339	+	0.981719i
$20$			67.0093i			0.749186i
$21$		0			0
$22$	108.141	−	19.0681i	1.04799	−	0.184788i
$23$	−38.7796	+	46.2158i	−0.351570	+	0.418985i	−0.912628	−	0.408792i	$-0.865950\pi$
$23$	−38.7796	+	46.2158i	−0.351570	+	0.418985i	0.561057	+	0.827777i	$0.310395\pi$
$24$		0			0
$25$	−6.83160	+	38.7439i	−0.0546528	+	0.309951i
$26$	47.7640	+	27.5766i	0.360280	+	0.208008i
$27$		0			0
$28$	86.2617	−	31.3967i	0.582212	−	0.211908i
$29$	169.499	−	61.6927i	1.08535	−	0.395036i	0.263456	−	0.964671i	$-0.415138\pi$
$29$	169.499	−	61.6927i	1.08535	−	0.395036i	0.821898	+	0.569635i	$0.192915\pi$
$30$		0			0
$31$	190.151	+	109.784i	1.10168	+	0.636057i	0.936662	−	0.350234i	$-0.113898\pi$
$31$	190.151	+	109.784i	1.10168	+	0.636057i	0.165020	+	0.986290i	$0.447231\pi$
$32$	−35.5628	+	201.687i	−0.196459	+	1.11417i
$33$		0			0
$34$	100.970	−	120.331i	0.509301	−	0.606961i
$35$	221.716	−	39.0945i	1.07077	−	0.188805i
$36$		0			0
$37$			328.229i			1.45839i	0.684305	+	0.729196i	$0.260106\pi$
$37$			328.229i			1.45839i	−0.684305	+	0.729196i	$0.739894\pi$
$38$	47.2615	−	297.474i	0.201758	−	1.26991i
$39$		0			0
$40$	−44.2172	+	121.486i	−0.174784	+	0.480215i
$41$	72.0795	+	408.783i	0.274559	+	1.55710i	0.740358	+	0.672213i	$0.234656\pi$
$41$	72.0795	+	408.783i	0.274559	+	1.55710i	−0.465799	+	0.884891i	$0.654233\pi$
$42$		0			0
$43$	15.5396	−	13.0393i	0.0551108	−	0.0462435i	−0.614816	−	0.788670i	$-0.710770\pi$
$43$	15.5396	−	13.0393i	0.0551108	−	0.0462435i	0.669927	+	0.742427i	$0.266325\pi$
$44$	−155.424	−	27.4054i	−0.532524	−	0.0938983i
$45$		0			0
$46$	190.020	−	109.708i	0.609064	−	0.351643i
$47$	−3.06102	−	8.41010i	−0.00949992	−	0.0261008i	0.934852	−	0.355038i	$-0.115532\pi$
$47$	−3.06102	−	8.41010i	−0.00949992	−	0.0261008i	−0.944352	+	0.328937i	$0.893310\pi$
$48$		0			0
$49$	17.2900	+	29.9471i	0.0504081	+	0.0873095i
$50$	71.5409	−	123.913i	0.202348	−	0.350478i
$51$		0			0
$52$	−50.9526	−	60.7229i	−0.135882	−	0.161938i
$53$	233.838	+	196.214i	0.606041	+	0.508528i	0.893381	−	0.449300i	$-0.148327\pi$
$53$	233.838	+	196.214i	0.606041	+	0.508528i	−0.287340	+	0.957829i	$0.592771\pi$
$54$		0			0
$55$	−363.718	−	132.383i	−0.891705	−	0.324554i
$56$	177.108			0.422625
$57$		0			0
$58$	−656.017			−1.48516
$59$	−739.115	−	269.016i	−1.63092	−	0.593608i	−0.645506	−	0.763755i	$-0.723353\pi$
$59$	−739.115	−	269.016i	−1.63092	−	0.593608i	−0.985419	+	0.170148i	$0.945576\pi$
$60$		0			0
$61$	286.803	+	240.656i	0.601989	+	0.505129i	0.892084	−	0.451869i	$-0.149242\pi$
$61$	286.803	+	240.656i	0.601989	+	0.505129i	−0.290095	+	0.956998i	$0.593687\pi$
$62$	−513.296	−	611.723i	−1.05143	−	1.25305i
$63$		0			0
$64$	58.4391	−	101.220i	0.114139	−	0.197694i
$65$	−97.2034	−	168.361i	−0.185486	−	0.321271i
$66$		0			0
$67$	0.129481	+	0.355746i	0.000236099	+	0.000648676i	0.939811	−	0.341696i	$-0.111001\pi$
$67$	0.129481	+	0.355746i	0.000236099	+	0.000648676i	−0.939575	+	0.342344i	$0.888779\pi$
$68$	−195.517	+	112.882i	−0.348675	+	0.201308i
$69$		0			0
$70$	−806.360	−	142.183i	−1.37683	−	0.242773i
$71$	−34.6533	+	29.0775i	−0.0579237	+	0.0486038i	−0.671290	−	0.741195i	$-0.734259\pi$
$71$	−34.6533	+	29.0775i	−0.0579237	+	0.0486038i	0.613366	+	0.789799i	$0.289815\pi$
$72$		0			0
$73$	−86.2498	−	489.147i	−0.138285	−	0.784251i	−0.972516	−	0.232836i	$-0.925199\pi$
$73$	−86.2498	−	489.147i	−0.138285	−	0.784251i	0.834231	−	0.551415i	$-0.185912\pi$
$74$	408.282	−	1121.75i	0.641377	−	1.76217i
$75$		0			0
$76$	−210.057	+	378.526i	−0.317043	+	0.571314i
$77$			530.245i			0.784767i
$78$		0			0
$79$	235.529	−	41.5301i	0.335431	−	0.0591456i	−0.00339593	−	0.999994i	$-0.501081\pi$
$79$	235.529	−	41.5301i	0.335431	−	0.0591456i	0.338827	+	0.940849i	$0.389970\pi$
$80$	646.813	−	770.842i	0.903949	−	1.07728i
$81$		0			0
$82$	262.147	−	1486.71i	0.353040	−	2.00219i
$83$	−196.347	−	113.361i	−0.259661	−	0.149915i	0.364519	−	0.931196i	$-0.381233\pi$
$83$	−196.347	−	113.361i	−0.259661	−	0.149915i	−0.624180	+	0.781281i	$0.714567\pi$
$84$		0			0
$85$	−520.298	+	189.373i	−0.663932	+	0.241652i
$86$	−69.3272	+	25.2330i	−0.0869273	+	0.0316389i
$87$		0			0
$88$	−263.695	−	152.244i	−0.319432	−	0.184424i
$89$	−115.476	+	654.899i	−0.137533	+	0.779991i	0.835529	+	0.549447i	$0.185162\pi$
$89$	−115.476	+	654.899i	−0.137533	+	0.779991i	−0.973062	+	0.230544i	$0.925950\pi$
$90$		0			0
$91$	−171.189	+	204.015i	−0.197203	+	0.235018i
$92$	−310.562	+	54.7605i	−0.351939	+	0.0620563i
$93$		0			0
$94$			32.5497i			0.0357154i
$95$	−668.548	+	824.780i	−0.722017	+	0.890744i
$96$		0			0
$97$	−367.982	+	1011.02i	−0.385184	+	1.05829i	0.583958	+	0.811784i	$0.301503\pi$
$97$	−367.982	+	1011.02i	−0.385184	+	1.05829i	−0.969142	+	0.246502i	$0.920719\pi$
$98$	−21.8387	−	123.854i	−0.0225107	−	0.127664i
$99$		0			0
$100$	−157.531	+	132.185i	−0.157531	+	0.132185i
$101$	−1187.90	−	209.459i	−1.17030	−	0.206356i	−0.445481	−	0.895292i	$-0.646967\pi$
$101$	−1187.90	−	209.459i	−1.17030	−	0.206356i	−0.724823	+	0.688936i	$0.758078\pi$
$102$		0			0
$103$	676.755	−	390.725i	0.647404	−	0.373779i	−0.140057	−	0.990143i	$-0.544729\pi$
$103$	676.755	−	390.725i	0.647404	−	0.373779i	0.787461	+	0.616365i	$0.211395\pi$
$104$	−52.3065	−	143.711i	−0.0493180	−	0.135500i
$105$		0			0
$106$	−555.091	−	961.445i	−0.508634	−	0.880979i
$107$	977.241	−	1692.63i	0.882930	−	1.52928i	0.0348618	−	0.999392i	$-0.488901\pi$
$107$	977.241	−	1692.63i	0.882930	−	1.52928i	0.848068	−	0.529887i	$-0.177766\pi$
$108$		0			0
$109$	876.677	+	1044.78i	0.770371	+	0.918092i	0.998456	−	0.0555492i	$-0.0176910\pi$
$109$	876.677	+	1044.78i	0.770371	+	0.918092i	−0.228085	+	0.973641i	$0.573247\pi$
$110$	1078.36	+	904.855i	0.934709	+	0.784314i
$111$		0			0
$112$	−1295.37	−	471.477i	−1.09287	−	0.397771i
$113$	280.971			0.233907			0.116954	−	0.993137i	$-0.462687\pi$
$113$	280.971			0.233907			0.116954	+	0.993137i	$0.462687\pi$
$114$		0			0
$115$	−773.411			−0.627138
$116$	885.991	+	322.474i	0.709157	+	0.258112i
$117$		0			0
$118$	2191.35	+	1838.76i	1.70958	+	1.43451i
$119$	487.564	+	581.056i	0.375587	+	0.447608i
$120$		0			0
$121$	−209.693	+	363.199i	−0.157546	+	0.272877i
$122$	−680.820	−	1179.21i	−0.505234	−	0.875090i
$123$		0			0
$124$	392.537	+	1078.49i	0.284281	+	0.781057i
$125$	950.986	−	549.052i	0.680470	−	0.392870i
$126$		0			0
$127$	2017.43	+	355.727i	1.40959	+	0.248548i	0.826077	−	0.563557i	$-0.190567\pi$
$127$	2017.43	+	355.727i	1.40959	+	0.248548i	0.583511	+	0.812105i	$0.301678\pi$
$128$	929.449	−	779.900i	0.641816	−	0.538548i
$129$		0			0
$130$	122.776	+	696.298i	0.0828322	+	0.469764i
$131$	−737.475	+	2026.19i	−0.491858	+	1.35137i	0.407119	+	0.913375i	$0.366533\pi$
$131$	−737.475	+	2026.19i	−0.491858	+	1.35137i	−0.898977	+	0.437995i	$0.855689\pi$
$132$		0			0
$133$	1374.99	+	474.185i	0.896443	+	0.309151i
$134$		−	1.37685i		−	0.000887625i
$135$		0			0
$136$	−428.953	+	75.6361i	−0.270459	+	0.0476893i
$137$	540.816	−	644.519i	0.337263	−	0.401934i	−0.570582	−	0.821241i	$-0.693282\pi$
$137$	540.816	−	644.519i	0.337263	−	0.401934i	0.907845	+	0.419306i	$0.137727\pi$
$138$		0			0
$139$	468.290	−	2655.80i	0.285754	−	1.62059i	−0.416826	−	0.908987i	$-0.636857\pi$
$139$	468.290	−	2655.80i	0.285754	−	1.62059i	0.702580	−	0.711605i	$-0.252031\pi$
$140$	1019.15	+	588.405i	0.615240	+	0.355209i
$141$		0			0
$142$	154.600	−	56.2696i	0.0913641	−	0.0332538i
$143$	430.258	−	156.601i	0.251608	−	0.0915779i
$144$		0			0
$145$	2002.57	+	1156.18i	1.14692	+	0.662177i
$146$	−313.683	+	1778.98i	−0.177812	+	1.00842i
$147$		0			0
$148$	−1102.82	+	1314.29i	−0.612509	+	0.729960i
$149$	−3381.53	+	596.255i	−1.85923	+	0.327833i	−0.986932	−	0.161137i	$-0.948484\pi$
$149$	−3381.53	+	596.255i	−1.85923	+	0.327833i	−0.872301	+	0.488970i	$0.837373\pi$
$150$		0			0
$151$			955.281i			0.514832i	0.966301	+	0.257416i	$0.0828711\pi$
$151$			955.281i			0.514832i	−0.966301	+	0.257416i	$0.917129\pi$
$152$	−630.605	+	547.646i	−0.336505	+	0.292237i
$153$		0			0
$154$	659.570	−	1812.15i	0.345128	−	0.948230i
$155$	488.779	+	2772.00i	0.253288	+	1.43647i
$156$		0			0
$157$	2095.39	−	1758.24i	1.06516	−	0.893777i	0.0705560	−	0.997508i	$-0.477523\pi$
$157$	2095.39	−	1758.24i	1.06516	−	0.893777i	0.994605	+	0.103731i	$0.0330782\pi$
$158$	−856.597	−	151.041i	−0.431311	−	0.0760518i
$159$		0			0
$160$	−2273.69	+	1312.71i	−1.12344	+	0.648619i
$161$	362.376	+	995.620i	0.177386	+	0.487365i
$162$		0			0
$163$	−1996.64	−	3458.29i	−0.959442	−	1.66180i	−0.723858	−	0.689949i	$-0.757633\pi$
$163$	−1996.64	−	3458.29i	−0.959442	−	1.66180i	−0.235584	−	0.971854i	$-0.575700\pi$
$164$	−1084.86	+	1879.03i	−0.516544	+	0.894680i
$165$		0			0
$166$	530.021	+	631.654i	0.247817	+	0.295337i
$167$	419.497	+	352.000i	0.194381	+	0.163105i	0.734784	−	0.678301i	$-0.237284\pi$
$167$	419.497	+	352.000i	0.194381	+	0.163105i	−0.540403	+	0.841407i	$0.681728\pi$
$168$		0			0
$169$	−1848.40	−	672.763i	−0.841330	−	0.306219i
$170$	2013.72			0.908501
$171$		0			0
$172$	106.034			0.0470061
$173$	224.273	+	81.6286i	0.0985615	+	0.0358735i	0.390830	−	0.920463i	$-0.372188\pi$
$173$	224.273	+	81.6286i	0.0985615	+	0.0358735i	−0.292269	+	0.956336i	$0.594410\pi$
$174$		0			0
$175$	529.270	+	444.110i	0.228623	+	0.191838i
$176$	1523.39	+	1815.50i	0.652442	+	0.777550i
$177$		0			0
$178$	1209.28	−	2094.53i	0.509208	−	0.881974i
$179$	−974.838	−	1688.47i	−0.407055	−	0.705040i	0.587503	−	0.809222i	$-0.300111\pi$
$179$	−974.838	−	1688.47i	−0.407055	−	0.705040i	−0.994558	+	0.104182i	$0.966778\pi$
$180$		0			0
$181$	−1442.04	−	3961.97i	−0.592187	−	1.62702i	−0.766438	−	0.642319i	$-0.777973\pi$
$181$	−1442.04	−	3961.97i	−0.592187	−	1.62702i	0.174251	−	0.984701i	$-0.444250\pi$
$182$	838.826	−	484.296i	0.341637	−	0.197244i
$183$		0			0
$184$	−599.175	−	105.651i	−0.240064	−	0.0423298i
$185$	−3223.33	+	2704.69i	−1.28099	+	1.07488i
$186$		0			0
$187$	−226.448	−	1284.25i	−0.0885535	−	0.502212i
$188$	16.0003	−	43.9604i	0.00620713	−	0.0170540i
$189$		0			0
$190$	3310.76	−	1987.14i	1.26414	−	0.758750i
$191$			466.765i			0.176827i	0.996084	+	0.0884134i	$0.0281797\pi$
$191$			466.765i			0.176827i	−0.996084	+	0.0884134i	$0.971820\pi$
$192$		0			0
$193$	−3288.92	+	579.926i	−1.22664	+	0.216290i	−0.749182	−	0.662364i	$-0.769553\pi$
$193$	−3288.92	+	579.926i	−1.22664	+	0.216290i	−0.477460	+	0.878654i	$0.658442\pi$
$194$	2515.21	−	2997.51i	0.930833	−	1.10932i
$195$		0			0
$196$	−31.3875	+	178.007i	−0.0114386	+	0.0648714i
$197$	−3943.46	−	2276.76i	−1.42619	−	0.823412i	−0.429373	−	0.903127i	$-0.641265\pi$
$197$	−3943.46	−	2276.76i	−1.42619	−	0.823412i	−0.996818	+	0.0797156i	$0.974599\pi$
$198$		0			0
$199$	2100.16	−	764.394i	0.748121	−	0.272294i	0.0603064	−	0.998180i	$-0.480792\pi$
$199$	2100.16	−	764.394i	0.748121	−	0.272294i	0.687815	+	0.725886i	$0.258570\pi$
$200$	−372.824	+	135.697i	−0.131813	+	0.0479761i
$201$		0			0
$202$	3799.20	+	2193.47i	1.32332	+	0.764019i
$203$	550.078	−	3119.64i	0.190187	−	1.07860i
$204$		0			0
$205$	−3420.45	+	4076.33i	−1.16534	+	1.38880i
$206$	−2798.88	+	493.518i	−0.946637	+	0.166918i
$207$		0			0
$208$			1190.35i			0.396808i
$209$	−1639.61	−	1887.98i	−0.542650	−	0.624852i
$210$		0			0
$211$	−1723.25	+	4734.59i	−0.562244	+	1.54475i	0.254094	+	0.967179i	$0.418223\pi$
$211$	−1723.25	+	4734.59i	−0.562244	+	1.54475i	−0.816339	+	0.577574i	$0.804000\pi$
$212$	277.072	+	1571.35i	0.0897613	+	0.509062i
$213$		0			0
$214$	−5445.25	+	4569.11i	−1.73939	+	1.45952i
$215$	256.101	+	45.1575i	0.0812368	+	0.0143242i
$216$		0			0
$217$	3339.41	−	1928.01i	1.04467	−	0.603143i
$218$	−1696.51	−	4661.12i	−0.527074	−	1.44812i
$219$		0			0
$220$	−1011.60	−	1752.15i	−0.310010	−	0.536954i
$221$	327.492	−	567.232i	0.0996809	−	0.172652i
$222$		0			0
$223$	−772.977	−	921.198i	−0.232118	−	0.276628i	0.637395	−	0.770537i	$-0.280012\pi$
$223$	−772.977	−	921.198i	−0.232118	−	0.276628i	−0.869513	+	0.493909i	$0.835567\pi$
$224$	2755.19	+	2311.88i	0.821825	+	0.689593i
$225$		0			0
$226$	−960.239	−	349.498i	−0.282629	−	0.102869i
$227$	3313.62			0.968865			0.484433	−	0.874829i	$-0.339026\pi$
$227$	3313.62			0.968865			0.484433	+	0.874829i	$0.339026\pi$
$228$		0			0
$229$	2572.79			0.742422			0.371211	−	0.928549i	$-0.378943\pi$
$229$	2572.79			0.742422			0.371211	+	0.928549i	$0.378943\pi$
$230$	2643.19	+	962.042i	0.757769	+	0.275805i
$231$		0			0
$232$	1393.49	+	1169.27i	0.394340	+	0.330890i
$233$	−359.708	−	428.683i	−0.101138	−	0.120532i	0.713101	−	0.701061i	$-0.247290\pi$
$233$	−359.708	−	428.683i	−0.101138	−	0.120532i	−0.814239	+	0.580529i	$0.802846\pi$
$234$		0			0
$235$	57.3666	−	99.3618i	0.0159242	−	0.0275815i
$236$	−2055.69	−	3560.55i	−0.567008	−	0.982086i
$237$		0			0
$238$	−943.513	−	2592.28i	−0.256970	−	0.706019i
$239$	3915.56	−	2260.65i	1.05973	−	0.611837i	0.134375	−	0.990931i	$-0.457097\pi$
$239$	3915.56	−	2260.65i	1.05973	−	0.611837i	0.925359	+	0.379093i	$0.123764\pi$
$240$		0			0
$241$	−1958.06	−	345.259i	−0.523360	−	0.0922824i	−0.0942741	−	0.995546i	$-0.530053\pi$
$241$	−1958.06	−	345.259i	−0.523360	−	0.0922824i	−0.429086	+	0.903264i	$0.641164\pi$
$242$	1168.42	−	980.424i	0.310368	−	0.260430i
$243$		0			0
$244$	339.829	+	1927.27i	0.0891613	+	0.505659i
$245$	−151.618	+	416.567i	−0.0395368	+	0.108626i
$246$		0			0
$247$	−21.3174	−	1255.76i	−0.00549147	−	0.323489i
$248$			2214.29i			0.566966i
$249$		0			0
$250$	−3933.03	+	693.500i	−0.994987	+	0.175443i
$251$	3219.35	−	3836.67i	0.809576	−	0.964815i	−0.190281	−	0.981730i	$-0.560940\pi$
$251$	3219.35	−	3836.67i	0.809576	−	0.964815i	0.999857	+	0.0169147i	$0.00538437\pi$
$252$		0			0
$253$	316.309	−	1793.88i	0.0786016	−	0.445772i
$254$	−6452.22	−	3725.19i	−1.59389	−	0.920234i
$255$		0			0
$256$	−5025.21	+	1829.03i	−1.22686	+	0.446540i
$257$	1026.87	−	373.750i	0.249239	−	0.0907156i	−0.214380	−	0.976750i	$-0.568773\pi$
$257$	1026.87	−	373.750i	0.249239	−	0.0907156i	0.463619	+	0.886035i	$0.346551\pi$
$258$		0			0
$259$	4992.05	+	2882.16i	1.19765	+	0.691462i
$260$	176.459	−	1000.75i	0.0420904	−	0.238706i
$261$		0			0
$262$	5040.75	−	6007.33i	1.18862	−	1.41654i
$263$	5623.97	−	991.658i	1.31859	−	0.232503i	0.530301	−	0.847809i	$-0.322079\pi$
$263$	5623.97	−	991.658i	1.31859	−	0.232503i	0.788288	+	0.615307i	$0.210968\pi$
$264$		0			0
$265$			3913.23i			0.907124i
$266$	−4109.30	−	3330.91i	−0.947208	−	0.767786i
$267$		0			0
$268$	−0.676811	+	1.85952i	−0.000154264	+	0.000423837i
$269$	88.0758	+	499.503i	0.0199631	+	0.113216i	0.993161	−	0.116753i	$-0.0372485\pi$
$269$	88.0758	+	499.503i	0.0199631	+	0.113216i	−0.973198	+	0.229969i	$0.926137\pi$
$270$		0			0
$271$	−6678.92	+	5604.28i	−1.49711	+	1.25622i	−0.611976	+	0.790876i	$0.709625\pi$
$271$	−6678.92	+	5604.28i	−1.49711	+	1.25622i	−0.885130	+	0.465345i	$0.845930\pi$
$272$	3338.73	+	588.709i	0.744266	+	0.131234i
$273$		0			0
$274$	−2649.99	+	1529.97i	−0.584277	+	0.337333i
$275$	−406.265	−	1116.20i	−0.0890862	−	0.244762i
$276$		0			0
$277$	2134.16	+	3696.47i	0.462920	+	0.801802i	0.999105	−	0.0422991i	$-0.0134682\pi$
$277$	2134.16	+	3696.47i	0.462920	+	0.801802i	−0.536185	+	0.844101i	$0.680135\pi$
$278$	−4903.96	+	8493.90i	−1.05799	+	1.83248i
$279$		0			0
$280$	1459.41	+	1739.26i	0.311488	+	0.371217i
$281$	3621.28	+	3038.62i	0.768782	+	0.645085i	0.940397	−	0.340080i	$-0.110454\pi$
$281$	3621.28	+	3038.62i	0.768782	+	0.645085i	−0.171615	+	0.985164i	$0.554898\pi$
$282$		0			0
$283$	−4175.27	−	1519.67i	−0.877010	−	0.319206i	−0.136008	−	0.990708i	$-0.543427\pi$
$283$	−4175.27	−	1519.67i	−0.877010	−	0.319206i	−0.741003	+	0.671502i	$0.765649\pi$
$284$	−236.456			−0.0494053
$285$		0			0
$286$	−1665.23			−0.344292
$287$	6850.13	+	2493.24i	1.40889	+	0.512793i
$288$		0			0
$289$	2334.55	+	1958.92i	0.475179	+	0.398722i
$290$	−5405.75	−	6442.32i	−1.09461	−	1.30450i
$291$		0			0
$292$	1298.13	−	2248.43i	0.260162	−	0.450615i
$293$	−3087.63	−	5347.92i	−0.615635	−	1.06631i	−0.990273	−	0.139140i	$-0.955566\pi$
$293$	−3087.63	−	5347.92i	−0.615635	−	1.06631i	0.374638	−	0.927171i	$-0.377767\pi$
$294$		0			0
$295$	−3448.67	−	9475.14i	−0.680642	−	1.87005i
$296$	−2866.64	+	1655.06i	−0.562906	+	0.324994i
$297$		0			0
$298$	12298.3	+	2168.52i	2.39068	+	0.421541i
$299$	700.855	−	588.087i	0.135557	−	0.113746i
$300$		0			0
$301$	−61.8624	−	350.839i	−0.0118462	−	0.0671829i
$302$	1188.27	−	3264.74i	0.226415	−	0.622069i
$303$		0			0
$304$	6070.15	−	2326.78i	1.14522	−	0.438980i
$305$			4799.58i			0.901060i
$306$		0			0
$307$	−2645.45	+	466.464i	−0.491803	+	0.0867182i	−0.414049	−	0.910254i	$-0.635886\pi$
$307$	−2645.45	+	466.464i	−0.491803	+	0.0867182i	−0.0777538	+	0.996973i	$0.524775\pi$
$308$	−1781.58	+	2123.20i	−0.329594	+	0.392795i
$309$		0			0
$310$	1777.64	−	10081.5i	0.325688	−	1.84707i
$311$	1261.31	+	728.219i	0.229976	+	0.132776i	0.610561	−	0.791969i	$-0.290944\pi$
$311$	1261.31	+	728.219i	0.229976	+	0.132776i	−0.380585	+	0.924746i	$0.624277\pi$
$312$		0			0
$313$	−4689.16	+	1706.71i	−0.846795	+	0.308208i	−0.728733	−	0.684798i	$-0.759890\pi$
$313$	−4689.16	+	1706.71i	−0.846795	+	0.308208i	−0.118062	+	0.993006i	$0.537668\pi$
$314$	−9348.22	+	3402.48i	−1.68010	+	0.611506i
$315$		0			0
$316$	1082.64	+	625.063i	0.192732	+	0.111274i
$317$	1196.68	−	6786.70i	0.212026	−	1.20246i	−0.673968	−	0.738760i	$-0.735412\pi$
$317$	1196.68	−	6786.70i	0.212026	−	1.20246i	0.885994	−	0.463697i	$-0.153477\pi$
$318$		0			0
$319$	−3500.70	+	4171.98i	−0.614426	+	0.732244i
$320$	1475.57	−	260.182i	0.257771	−	0.0454520i
$321$		0			0
$322$		−	3853.36i		−	0.666893i
$323$	−3532.73	−	561.264i	−0.608564	−	0.0966860i
$324$		0			0
$325$	204.052	−	560.629i	0.0348270	−	0.0956865i
$326$	2521.93	+	14302.6i	0.428456	+	2.42990i
$327$		0			0
$328$	−3206.73	+	2690.76i	−0.539823	+	0.452965i
$329$	−154.788	−	27.2933i	−0.0259385	−	0.00457365i
$330$		0			0
$331$	−3272.13	+	1889.16i	−0.543360	+	0.313709i	−0.746440	−	0.665453i	$-0.768238\pi$
$331$	−3272.13	+	1889.16i	−0.543360	+	0.313709i	0.203079	+	0.979162i	$0.434905\pi$
$332$	−405.327	−	1113.63i	−0.0670037	−	0.184091i
$333$		0			0
$334$	−995.812	−	1724.80i	−0.163139	−	0.282565i
$335$	−2.42660	+	4.20299i	−0.000395759	+	0.000685475i
$336$		0			0
$337$	−853.261	−	1016.88i	−0.137923	−	0.164370i	0.692661	−	0.721263i	$-0.256438\pi$
$337$	−853.261	−	1016.88i	−0.137923	−	0.164370i	−0.830585	+	0.556892i	$0.811994\pi$
$338$	5480.21	+	4598.44i	0.881905	+	0.740006i
$339$		0			0
$340$	−2719.65	−	989.872i	−0.433805	−	0.157892i
$341$	−6629.39			−1.05279
$342$		0			0
$343$	6631.02			1.04385
$344$	192.237	+	69.9686i	0.0301300	+	0.0109664i
$345$		0			0
$346$	−664.932	−	557.944i	−0.103315	−	0.0866915i
$347$	1850.12	+	2204.88i	0.286223	+	0.341107i	0.889928	−	0.456100i	$-0.150754\pi$
$347$	1850.12	+	2204.88i	0.286223	+	0.341107i	−0.603705	+	0.797208i	$0.706310\pi$
$348$		0			0
$349$	4675.53	−	8098.25i	0.717121	−	1.24209i	−0.245015	−	0.969519i	$-0.578793\pi$
$349$	4675.53	−	8098.25i	0.717121	−	1.24209i	0.962136	−	0.272570i	$-0.0878737\pi$
$350$	−1256.39	−	2176.14i	−0.191877	−	0.332341i
$351$		0			0
$352$	−2114.87	−	5810.55i	−0.320235	−	0.879839i
$353$	−4297.40	+	2481.10i	−0.647953	+	0.374096i	−0.787672	−	0.616095i	$-0.788714\pi$
$353$	−4297.40	+	2481.10i	−0.647953	+	0.374096i	0.139718	+	0.990191i	$0.455380\pi$
$354$		0			0
$355$	−571.104	−	100.701i	−0.0853833	−	0.0150554i
$356$	−2662.80	+	2234.35i	−0.396427	+	0.332642i
$357$		0			0
$358$	1231.30	+	6983.07i	0.181778	+	1.03091i
$359$	−1104.27	+	3033.95i	−0.162343	+	0.446033i	−0.994016	−	0.109232i	$-0.965161\pi$
$359$	−1104.27	+	3033.95i	−0.162343	+	0.446033i	0.831673	+	0.555265i	$0.187383\pi$
$360$		0			0
$361$	−6362.01	+	2563.33i	−0.927542	+	0.373718i
$362$			15334.1i			2.22635i
$363$		0			0
$364$	−1370.95	+	241.735i	−0.197410	+	0.0348087i
$365$	4092.88	−	4877.71i	0.586935	−	0.699482i
$366$		0			0
$367$	2254.38	−	12785.2i	0.320648	−	1.81848i	−0.217995	−	0.975950i	$-0.569952\pi$
$367$	2254.38	−	12785.2i	0.320648	−	1.81848i	0.538643	−	0.842534i	$-0.318937\pi$
$368$	4101.14	+	2367.79i	0.580942	+	0.335407i
$369$		0			0
$370$	14380.3	−	5234.01i	2.02053	−	0.735414i
$371$	5037.54	−	1833.52i	0.704949	−	0.256581i
$372$		0			0
$373$	9787.35	+	5650.73i	1.35863	+	0.784407i	0.989440	−	0.144946i	$-0.0463009\pi$
$373$	9787.35	+	5650.73i	1.35863	+	0.784407i	0.369193	+	0.929353i	$0.379634\pi$
$374$	−823.570	+	4670.70i	−0.113866	+	0.645765i
$375$		0			0
$376$	58.0161	−	69.1409i	0.00795732	−	0.00948317i
$377$	−2693.84	+	474.996i	−0.368010	+	0.0648901i
$378$		0			0
$379$		−	1085.01i		−	0.147053i	−0.997293	−	0.0735267i	$-0.976575\pi$
$379$		−	1085.01i		−	0.147053i	0.997293	−	0.0735267i	$-0.0234254\pi$
$380$	−5448.19	+	1056.31i	−0.735490	+	0.142599i
$381$		0			0
$382$	580.607	−	1595.21i	0.0777656	−	0.213659i
$383$	−757.250	−	4294.58i	−0.101028	−	0.572957i	−0.992733	−	0.120340i	$-0.961602\pi$
$383$	−757.250	−	4294.58i	−0.101028	−	0.572957i	0.891705	−	0.452617i	$-0.149510\pi$
$384$		0			0
$385$	−5207.20	+	4369.36i	−0.689308	+	0.578398i
$386$	11961.5	+	2109.14i	1.57727	+	0.278115i
$387$		0			0
$388$	−4870.42	+	2811.94i	−0.637263	+	0.367924i
$389$	3827.19	+	10515.1i	0.498833	+	1.37053i	0.892403	+	0.451239i	$0.149018\pi$
$389$	3827.19	+	10515.1i	0.498833	+	1.37053i	−0.393570	+	0.919295i	$0.628760\pi$
$390$		0			0
$391$	−1302.86	−	2256.63i	−0.168513	−	0.291873i
$392$	−174.366	+	302.010i	−0.0224663	+	0.0389128i
$393$		0			0
$394$	10645.0	+	12686.2i	1.36114	+	1.62214i
$395$	2348.66	+	1970.76i	0.299175	+	0.251037i
$396$		0			0
$397$	6472.89	+	2355.94i	0.818300	+	0.297837i	0.717048	−	0.697024i	$-0.245493\pi$
$397$	6472.89	+	2355.94i	0.818300	+	0.297837i	0.101252	+	0.994861i	$0.467715\pi$
$398$	−8128.27			−1.02370
$399$		0			0
$400$	3088.09			0.386011
$401$	11087.8	+	4035.64i	1.38080	+	0.502569i	0.922420	−	0.386188i	$-0.126208\pi$
$401$	11087.8	+	4035.64i	1.38080	+	0.502569i	0.458378	+	0.888757i	$0.348431\pi$
$402$		0			0
$403$	−2550.70	−	2140.29i	−0.315284	−	0.264555i
$404$	−4052.82	−	4829.97i	−0.499098	−	0.594801i
$405$		0			0
$406$	−5760.45	+	9977.38i	−0.704153	+	1.21963i
$407$	−4955.10	−	8582.48i	−0.603477	−	1.04525i
$408$		0			0
$409$	3167.89	+	8703.70i	0.382988	+	1.05225i	0.970092	+	0.242739i	$0.0780458\pi$
$409$	3167.89	+	8703.70i	0.382988	+	1.05225i	−0.587104	+	0.809512i	$0.699732\pi$
$410$	16760.2	−	9676.49i	2.01884	−	1.16558i
$411$		0			0
$412$	4022.66	+	709.303i	0.481025	+	0.0848176i
$413$	−10581.6	+	8879.01i	−1.26074	+	1.05789i
$414$		0			0
$415$	−504.704	−	2862.32i	−0.0596987	−	0.338568i
$416$	1062.22	−	2918.43i	0.125192	−	0.343961i
$417$		0			0
$418$	3255.03	+	8491.80i	0.380882	+	0.993654i
$419$		−	13294.4i		−	1.55006i	−0.631925	−	0.775029i	$-0.717735\pi$
$419$		−	13294.4i		−	1.55006i	0.631925	−	0.775029i	$-0.282265\pi$
$420$		0			0
$421$	2877.93	−	507.457i	0.333164	−	0.0587457i	−0.00456412	−	0.999990i	$-0.501453\pi$
$421$	2877.93	−	507.457i	0.333164	−	0.0587457i	0.337728	+	0.941244i	$0.390342\pi$
$422$	11778.7	−	14037.3i	1.35871	−	1.61925i
$423$		0			0
$424$	−534.562	+	3031.65i	−0.0612279	+	0.347240i
$425$	−1471.55	−	849.601i	−0.167955	−	0.0969687i
$426$		0			0
$427$	6178.55	−	2248.81i	0.700237	−	0.254865i
$428$	9600.17	−	3494.17i	1.08421	−	0.394620i
$429$		0			0
$430$	−819.072	−	472.892i	−0.0918586	−	0.0530346i
$431$	−1097.00	+	6221.38i	−0.122600	+	0.695297i	0.860105	+	0.510117i	$0.170398\pi$
$431$	−1097.00	+	6221.38i	−0.122600	+	0.695297i	−0.982705	+	0.185180i	$0.940713\pi$
$432$		0			0
$433$	1830.97	−	2182.06i	0.203212	−	0.242178i	−0.654808	−	0.755795i	$-0.727250\pi$
$433$	1830.97	−	2182.06i	0.203212	−	0.242178i	0.858019	+	0.513617i	$0.171695\pi$
$434$	−13810.9	+	2435.24i	−1.52753	+	0.269344i
$435$		0			0
$436$			7129.07i			0.783075i
$437$	−4368.88	−	2424.45i	−0.478243	−	0.265394i
$438$		0			0
$439$	−1425.72	+	3917.13i	−0.155002	+	0.425864i	−0.992751	−	0.120191i	$-0.961649\pi$
$439$	−1425.72	+	3917.13i	−0.155002	+	0.425864i	0.837749	+	0.546056i	$0.183871\pi$
$440$	−677.822	−	3844.12i	−0.0734407	−	0.416503i
$441$		0			0
$442$	−1824.81	+	1531.19i	−0.196374	+	0.164777i
$443$	10107.8	+	1782.29i	1.08406	+	0.191149i	0.687010	−	0.726648i	$-0.258923\pi$
$443$	10107.8	+	1782.29i	1.08406	+	0.191149i	0.397050	+	0.917797i	$0.370034\pi$
$444$		0			0
$445$	−7382.91	+	4262.52i	−0.786480	+	0.454074i
$446$	1495.83	+	4109.76i	0.158811	+	0.436330i
$447$		0			0
$448$	−1026.30	−	1777.61i	−0.108233	−	0.187464i
$449$	−165.110	+	285.978i	−0.0173541	+	0.0300582i	−0.874572	−	0.484896i	$-0.838858\pi$
$449$	−165.110	+	285.978i	−0.0173541	+	0.0300582i	0.857218	+	0.514954i	$0.172191\pi$
$450$		0			0
$451$	−8055.91	−	9600.66i	−0.841105	−	1.00239i
$452$	1125.06	+	944.038i	0.117076	+	0.0982386i
$453$		0			0
$454$	−11324.5	−	4121.79i	−1.17068	−	0.426091i
$455$	−3414.15			−0.351775
$456$		0			0
$457$	−1887.93			−0.193247			−0.0966234	−	0.995321i	$-0.530804\pi$
$457$	−1887.93			−0.193247			−0.0966234	+	0.995321i	$0.530804\pi$
$458$	−8792.70	−	3200.28i	−0.897065	−	0.326505i
$459$		0			0
$460$	−3096.89	−	2598.60i	−0.313898	−	0.263392i
$461$	−3171.97	−	3780.20i	−0.320463	−	0.381912i	0.581631	−	0.813453i	$-0.302415\pi$
$461$	−3171.97	−	3780.20i	−0.320463	−	0.381912i	−0.902094	+	0.431540i	$0.857970\pi$
$462$		0			0
$463$	1743.29	−	3019.47i	0.174984	−	0.303081i	−0.765172	−	0.643826i	$-0.777346\pi$
$463$	1743.29	−	3019.47i	0.174984	−	0.303081i	0.940156	+	0.340745i	$0.110679\pi$
$464$	−7079.30	−	12261.7i	−0.708293	−	1.22680i
$465$		0			0
$466$	696.092	+	1912.50i	0.0691971	+	0.190117i
$467$	10763.7	−	6214.40i	1.06656	−	0.615777i	0.139319	−	0.990248i	$-0.455509\pi$
$467$	10763.7	−	6214.40i	1.06656	−	0.615777i	0.927239	+	0.374470i	$0.122175\pi$
$468$		0			0
$469$	6.54752	+	1.15451i	0.000644641	+	0.000113668i
$470$	−319.650	+	268.219i	−0.0313710	+	0.0263234i
$471$		0			0
$472$	−1377.41	−	7811.66i	−0.134323	−	0.761782i
$473$	−209.480	+	575.542i	−0.0203634	+	0.0559481i
$474$		0			0
$475$	−3257.77	+	55.3030i	−0.314688	+	0.00534205i
$476$			3964.83i			0.381781i
$477$		0			0
$478$	−16193.7	+	2855.39i	−1.54955	+	0.273227i
$479$	2107.53	−	2511.66i	0.201034	−	0.239584i	−0.656103	−	0.754671i	$-0.727796\pi$
$479$	2107.53	−	2511.66i	0.201034	−	0.239584i	0.857137	+	0.515088i	$0.172241\pi$
$480$		0			0
$481$	864.340	−	4901.91i	0.0819345	−	0.464674i
$482$	6262.35	+	3615.57i	0.591789	+	0.341669i
$483$		0			0
$484$	−2059.97	+	749.768i	−0.193461	+	0.0704140i
$485$	−12960.9	+	4717.37i	−1.21345	+	0.441659i
$486$		0			0
$487$	−1540.54	−	889.431i	−0.143344	−	0.0827597i	0.426613	−	0.904434i	$-0.359707\pi$
$487$	−1540.54	−	889.431i	−0.143344	−	0.0827597i	−0.569957	+	0.821675i	$0.693040\pi$
$488$	−655.641	+	3718.32i	−0.0608186	+	0.344919i
$489$		0			0
$490$	1036.33	−	1235.05i	0.0955442	−	0.113865i
$491$	−12735.6	+	2245.64i	−1.17057	+	0.206403i	−0.724940	−	0.688812i	$-0.758132\pi$
$491$	−12735.6	+	2245.64i	−1.17057	+	0.206403i	−0.445633	+	0.895216i	$0.647021\pi$
$492$		0			0
$493$			7790.67i			0.711713i
$494$	−1489.18	+	4318.16i	−0.135630	+	0.393286i
$495$		0			0
$496$	5894.65	−	16195.4i	0.533624	−	1.46612i
$497$	137.953	+	782.371i	0.0124508	+	0.0706119i
$498$		0			0
$499$	11719.5	−	9833.86i	1.05138	−	0.882213i	0.0581421	−	0.998308i	$-0.481482\pi$
$499$	11719.5	−	9833.86i	1.05138	−	0.882213i	0.993238	+	0.116096i	$0.0370379\pi$
$500$	5652.70	+	996.724i	0.505593	+	0.0891497i
$501$		0			0
$502$	−15774.8	+	9107.58i	−1.40252	+	0.809743i
$503$	−2424.90	−	6662.35i	−0.214952	−	0.590576i	0.784616	−	0.619983i	$-0.212860\pi$
$503$	−2424.90	−	6662.35i	−0.214952	−	0.590576i	−0.999568	+	0.0294069i	$0.990638\pi$
$504$		0			0
$505$	−7731.66	−	13391.6i	−0.681296	−	1.18004i
$506$	−3312.41	+	5737.26i	−0.291017	+	0.504056i
$507$		0			0
$508$	6882.96	+	8202.79i	0.601145	+	0.716417i
$509$	−9050.24	−	7594.06i	−0.788104	−	0.661298i	0.157171	−	0.987571i	$-0.449763\pi$
$509$	−9050.24	−	7594.06i	−0.788104	−	0.661298i	−0.945275	+	0.326273i	$0.894207\pi$
$510$		0			0
$511$	−8196.81	−	2983.40i	−0.709600	−	0.258273i
$512$	9742.70			0.840958
$513$		0			0
$514$	−3974.31			−0.341050
$515$	9413.70	+	3426.31i	0.805470	+	0.293167i
$516$		0			0
$517$	207.002	+	173.695i	0.0176092	+	0.0147758i
$518$	−13475.6	−	16059.6i	−1.14302	−	1.36220i
$519$		0			0
$520$	980.274	−	1697.88i	0.0826690	−	0.143187i
$521$	−7946.82	−	13764.3i	−0.668247	−	1.15744i	−0.978394	−	0.206749i	$-0.933712\pi$
$521$	−7946.82	−	13764.3i	−0.668247	−	1.15744i	0.310147	−	0.950689i	$-0.399622\pi$
$522$		0			0
$523$	1678.92	+	4612.79i	0.140371	+	0.385666i	0.989880	−	0.141909i	$-0.0453239\pi$
$523$	1678.92	+	4612.79i	0.140371	+	0.385666i	−0.849509	+	0.527574i	$0.823102\pi$
$524$	−9760.84	+	5635.42i	−0.813748	+	0.469818i
$525$		0			0
$526$	−20453.9	−	3606.57i	−1.69550	−	0.298962i
$527$	−7264.65	+	6095.77i	−0.600481	+	0.503863i
$528$		0			0
$529$	1480.74	+	8397.69i	0.121701	+	0.690202i
$530$	4867.65	−	13373.8i	0.398938	−	1.09607i
$531$		0			0
$532$	3912.51	+	6518.58i	0.318851	+	0.531234i
$533$		−	6294.76i		−	0.511551i
$534$		0			0
$535$	24675.0	−	4350.87i	1.99401	−	0.351597i
$536$	−2.45408	+	2.92465i	−0.000197761	+	0.000235682i
$537$		0			0
$538$	320.324	−	1816.65i	0.0256694	−	0.145578i
$539$	−904.193	−	522.036i	−0.0722566	−	0.0417174i
$540$		0			0
$541$	−14890.1	+	5419.54i	−1.18332	+	0.430692i	−0.857372	−	0.514698i	$-0.827904\pi$
$541$	−14890.1	+	5419.54i	−1.18332	+	0.430692i	−0.325944	+	0.945389i	$0.605682\pi$
$542$	29796.9	−	10845.2i	2.36141	−	0.859484i
$543$		0			0
$544$	−7660.36	−	4422.71i	−0.603741	−	0.348570i
$545$	−3036.10	+	17218.6i	−0.238628	+	1.35333i
$546$		0			0
$547$	14302.6	−	17045.1i	1.11798	−	1.33235i	0.180792	−	0.983521i	$-0.442134\pi$
$547$	14302.6	−	17045.1i	1.11798	−	1.33235i	0.937185	−	0.348832i	$-0.113422\pi$
$548$	4331.06	−	763.683i	0.337616	−	0.0595309i
$549$		0			0
$550$			4320.06i			0.334924i
$551$	7687.86	+	12808.7i	0.594399	+	0.990321i
$552$		0			0
$553$	1436.53	−	3946.84i	0.110466	−	0.303502i
$554$	−2695.62	−	15287.6i	−0.206725	−	1.17240i
$555$		0			0
$556$	10798.4	−	9060.93i	0.823659	−	0.691132i
$557$	9402.00	+	1657.83i	0.715217	+	0.126112i	0.519403	−	0.854529i	$-0.326154\pi$
$557$	9402.00	+	1657.83i	0.715217	+	0.126112i	0.195813	+	0.980641i	$0.437265\pi$
$558$		0			0
$559$	−266.412	+	153.813i	−0.0201575	+	0.0116379i
$560$	−6044.14	−	16606.1i	−0.456092	−	1.25310i
$561$		0			0
$562$	−8596.29	−	14889.2i	−0.645218	−	1.11755i
$563$	−8862.29	+	15349.9i	−0.663412	+	1.14906i	0.316301	+	0.948659i	$0.397559\pi$
$563$	−8862.29	+	15349.9i	−0.663412	+	1.14906i	−0.979713	+	0.200405i	$0.935774\pi$
$564$		0			0
$565$	2315.27	+	2759.24i	0.172397	+	0.205455i
$566$	12379.0	+	10387.2i	0.919306	+	0.771389i
$567$		0			0
$568$	−428.689	−	156.030i	−0.0316679	−	0.0115262i
$569$	−3866.18			−0.284848			−0.142424	−	0.989806i	$-0.545490\pi$
$569$	−3866.18			−0.284848			−0.142424	+	0.989806i	$0.545490\pi$
$570$		0			0
$571$	7240.38			0.530649			0.265324	−	0.964159i	$-0.414521\pi$
$571$	7240.38			0.530649			0.265324	+	0.964159i	$0.414521\pi$
$572$	2249.00	+	818.570i	0.164398	+	0.0598359i
$573$		0			0
$574$	−20309.5	−	17041.7i	−1.47683	−	1.23921i
$575$	−1525.65	−	1818.20i	−0.110651	−	0.131868i
$576$		0			0
$577$	−7854.36	+	13604.1i	−0.566692	+	0.981539i	0.430198	+	0.902734i	$0.358444\pi$
$577$	−7854.36	+	13604.1i	−0.566692	+	0.981539i	−0.996890	+	0.0788047i	$0.974890\pi$
$578$	−5541.82	−	9598.71i	−0.398805	−	0.690750i
$579$		0			0
$580$	4133.99	+	11358.0i	0.295956	+	0.813132i
$581$	−3448.22	+	1990.83i	−0.246224	+	0.142158i
$582$		0			0
$583$	−9076.50	−	1600.43i	−0.644786	−	0.113693i
$584$	3837.14	−	3219.74i	0.271887	−	0.228140i
$585$		0			0
$586$	3899.93	+	22117.6i	0.274923	+	1.55916i
$587$	7664.97	−	21059.3i	0.538956	−	1.48077i	−0.309187	−	0.951001i	$-0.600057\pi$
$587$	7664.97	−	21059.3i	0.538956	−	1.48077i	0.848143	−	0.529767i	$-0.177721\pi$
$588$		0			0
$589$	−5928.50	+	17190.8i	−0.414736	+	1.20261i
$590$			36671.8i			2.55890i
$591$		0			0
$592$	25372.6	−	4473.88i	1.76150	−	0.310600i
$593$	−13204.5	+	15736.5i	−0.914405	+	1.08974i	0.0812567	+	0.996693i	$0.474107\pi$
$593$	−13204.5	+	15736.5i	−0.914405	+	1.08974i	−0.995661	+	0.0930518i	$0.970338\pi$
$594$		0			0
$595$	−1688.53	+	9576.11i	−0.116341	+	0.659802i
$596$	−15543.7	−	8974.14i	−1.06828	−	0.616770i
$597$		0			0
$598$	−3126.74	+	1138.04i	−0.213816	+	0.0778227i
$599$	−1666.77	+	606.654i	−0.113693	+	0.0413810i	−0.398240	−	0.917281i	$-0.630379\pi$
$599$	−1666.77	+	606.654i	−0.113693	+	0.0413810i	0.284547	+	0.958662i	$0.408157\pi$
$600$		0			0
$601$	19474.0	+	11243.3i	1.32173	+	0.763102i	0.984005	−	0.178143i	$-0.0570089\pi$
$601$	19474.0	+	11243.3i	1.32173	+	0.763102i	0.337726	+	0.941244i	$0.390342\pi$
$602$	−224.988	+	1275.97i	−0.0152323	+	0.0863865i
$603$		0			0
$604$	−3209.66	+	3825.13i	−0.216224	+	0.257686i
$605$	−5294.68	+	933.594i	−0.355800	+	0.0627372i
$606$		0			0
$607$		−	15274.4i		−	1.02136i	−0.859770	−	0.510682i	$-0.829393\pi$
$607$		−	15274.4i		−	1.02136i	0.859770	−	0.510682i	$-0.170607\pi$
$608$	−16958.7	+	287.887i	−1.13120	+	0.0192029i
$609$		0			0
$610$	5970.18	−	16402.9i	0.396271	−	1.08875i
$611$	23.5680	+	133.661i	0.00156049	+	0.00884998i
$612$		0			0
$613$	−18373.0	+	15416.8i	−1.21057	+	1.01579i	−0.211303	+	0.977421i	$0.567771\pi$
$613$	−18373.0	+	15416.8i	−1.21057	+	1.01579i	−0.999264	+	0.0383657i	$0.987785\pi$
$614$	9621.25	+	1696.49i	0.632381	+	0.111506i
$615$		0			0
$616$	−4630.99	+	2673.70i	−0.302902	+	0.174881i
$617$	1994.06	+	5478.62i	0.130110	+	0.357473i	0.987592	−	0.157039i	$-0.0501950\pi$
$617$	1994.06	+	5478.62i	0.130110	+	0.357473i	−0.857483	+	0.514513i	$0.827973\pi$
$618$		0			0
$619$	6933.09	+	12008.5i	0.450185	+	0.779743i	0.998397	−	0.0565963i	$-0.0180248\pi$
$619$	6933.09	+	12008.5i	0.450185	+	0.779743i	−0.548212	+	0.836339i	$0.684691\pi$
$620$	−7356.53	+	12741.9i	−0.476525	+	0.825365i
$621$		0			0
$622$	−3404.80	−	4057.68i	−0.219486	−	0.261573i
$623$	8946.40	+	7506.92i	0.575329	+	0.482758i
$624$		0			0
$625$	17849.4	+	6496.65i	1.14236	+	0.415786i
$626$	18148.5			1.15872
$627$		0			0
$628$	14297.9			0.908516
$629$	−13321.6	−	4848.65i	−0.844460	−	0.307358i
$630$		0			0
$631$	3386.13	+	2841.30i	0.213629	+	0.179256i	0.743323	−	0.668933i	$-0.233249\pi$
$631$	3386.13	+	2841.30i	0.213629	+	0.179256i	−0.529694	+	0.848189i	$0.677693\pi$
$632$	1550.34	+	1847.62i	0.0975777	+	0.116289i
$633$		0			0
$634$	−12531.7	+	21705.5i	−0.785010	+	1.35968i
$635$	13130.8	+	22743.2i	0.820597	+	1.42131i
$636$		0			0
$637$	−179.355	−	492.775i	−0.0111559	−	0.0306506i
$638$	17153.4	−	9903.53i	1.06444	−	0.614553i
$639$		0			0
$640$	15317.8	+	2700.94i	0.946078	+	0.166819i
$641$	16396.9	−	13758.6i	1.01036	−	0.847790i	0.0219716	−	0.999759i	$-0.493006\pi$
$641$	16396.9	−	13758.6i	1.01036	−	0.847790i	0.988385	+	0.151968i	$0.0485612\pi$
$642$		0			0
$643$	−2117.42	−	12008.5i	−0.129864	−	0.736498i	−0.978299	−	0.207198i	$-0.933566\pi$
$643$	−2117.42	−	12008.5i	−0.129864	−	0.736498i	0.848435	−	0.529300i	$-0.177545\pi$
$644$	−1894.18	+	5204.21i	−0.115902	+	0.318439i
$645$		0			0
$646$	11375.2	+	6312.51i	0.692804	+	0.384462i
$647$		−	5526.23i		−	0.335794i	−0.985805	−	0.167897i	$-0.946302\pi$
$647$		−	5526.23i		−	0.335794i	0.985805	−	0.167897i	$-0.0536976\pi$
$648$		0			0
$649$	23387.5	−	4123.84i	1.41454	−	0.249422i
$650$	−1394.73	+	1662.17i	−0.0841627	+	0.100301i
$651$		0			0
$652$	3624.61	−	20556.2i	0.217716	−	1.23473i
$653$	8261.98	+	4770.05i	0.495124	+	0.285860i	0.726698	−	0.686957i	$-0.241054\pi$
$653$	8261.98	+	4770.05i	0.495124	+	0.285860i	−0.231574	+	0.972817i	$0.574387\pi$
$654$		0			0
$655$	−25975.0	+	9454.11i	−1.54951	+	0.563974i
$656$	30617.2	−	11143.7i	1.82226	−	0.663247i
$657$		0			0
$658$	495.050	+	285.818i	0.0293299	+	0.0169336i
$659$	−1529.56	+	8674.56i	−0.0904146	+	0.512766i	0.905642	+	0.424044i	$0.139390\pi$
$659$	−1529.56	+	8674.56i	−0.0904146	+	0.512766i	−0.996056	+	0.0887229i	$0.971721\pi$
$660$		0			0
$661$	20213.8	−	24089.8i	1.18945	−	1.41753i	0.304073	−	0.952649i	$-0.401653\pi$
$661$	20213.8	−	24089.8i	1.18945	−	1.41753i	0.885374	−	0.464880i	$-0.153902\pi$
$662$	13532.7	−	2386.17i	0.794504	−	0.140093i
$663$		0			0
$664$		−	2286.44i		−	0.133631i
$665$	6673.63	+	17410.3i	0.389161	+	1.01525i
$666$		0			0
$667$	−3721.95	+	10226.0i	−0.216064	+	0.593630i
$668$	497.057	+	2818.95i	0.0287900	+	0.163276i
$669$		0			0
$670$	13.5212	−	11.3456i	0.000779655	−	0.000654208i
$671$	−11132.3	−	1962.93i	−0.640476	−	0.112933i
$672$		0			0
$673$	22577.1	−	13034.9i	1.29314	−	0.746593i	0.313928	−	0.949447i	$-0.398355\pi$
$673$	22577.1	−	13034.9i	1.29314	−	0.746593i	0.979209	+	0.202853i	$0.0650215\pi$
$674$	1651.20	+	4536.62i	0.0943645	+	0.259264i
$675$		0			0
$676$	−5140.93	−	8904.35i	−0.292497	−	0.506620i
$677$	−10775.8	+	18664.2i	−0.611738	+	1.05956i	0.379209	+	0.925311i	$0.376196\pi$
$677$	−10775.8	+	18664.2i	−0.611738	+	1.05956i	−0.990947	+	0.134250i	$0.957137\pi$
$678$		0			0
$679$	12145.4	+	14474.4i	0.686450	+	0.818079i
$680$	−4277.47	−	3589.22i	−0.241225	−	0.202412i
$681$		0			0
$682$	22656.5	+	8246.28i	1.27208	+	0.463000i
$683$	10420.4			0.583787			0.291893	−	0.956451i	$-0.405715\pi$
$683$	10420.4			0.583787			0.291893	+	0.956451i	$0.405715\pi$
$684$		0			0
$685$	10785.9			0.601617
$686$	−22662.0	−	8248.30i	−1.26128	−	0.459069i
$687$		0			0
$688$	−1219.77	−	1023.51i	−0.0675919	−	0.0567163i
$689$	−2975.55	−	3546.12i	−0.164527	−	0.196076i
$690$		0			0
$691$	−5403.97	+	9359.94i	−0.297506	+	0.515295i	−0.975565	−	0.219712i	$-0.929488\pi$
$691$	−5403.97	+	9359.94i	−0.297506	+	0.515295i	0.678059	+	0.735008i	$0.262821\pi$
$692$	623.766	+	1080.39i	0.0342659	+	0.0593503i
$693$		0			0
$694$	−3580.27	−	9836.70i	−0.195829	−	0.538035i
$695$	29939.8	−	17285.7i	1.63407	−	0.943433i
$696$		0			0
$697$	−17655.7	−	3113.18i	−0.959482	−	0.169183i
$698$	−26052.3	+	21860.5i	−1.41274	+	1.18543i
$699$		0			0
$700$	627.126	+	3556.61i	0.0338616	+	0.192039i
$701$	360.375	−	990.121i	0.0194168	−	0.0533472i	−0.929606	−	0.368556i	$-0.879852\pi$
$701$	360.375	−	990.121i	0.0194168	−	0.0533472i	0.949022	+	0.315209i	$0.102075\pi$
$702$		0			0
$703$	−26686.6	+	5174.09i	−1.43173	+	0.277588i
$704$			3528.90i			0.188921i
$705$		0			0
$706$	17772.9	−	3133.85i	0.947440	−	0.167059i
$707$	−13616.6	+	16227.6i	−0.724334	+	0.863227i
$708$		0			0
$709$	−4796.08	+	27199.9i	−0.254049	+	1.44078i	0.544455	+	0.838790i	$0.316737\pi$
$709$	−4796.08	+	27199.9i	−0.254049	+	1.44078i	−0.798503	+	0.601991i	$0.794374\pi$
$710$	1826.53	+	1054.55i	0.0965471	+	0.0557415i
$711$		0			0
$712$	−6301.95	+	2293.72i	−0.331707	+	0.120732i
$713$	−12447.7	+	4530.61i	−0.653817	+	0.237970i
$714$		0			0
$715$	5083.32	+	2934.86i	0.265882	+	0.153507i
$716$	1769.68	−	10036.3i	0.0923686	−	0.523848i
$717$		0			0
$718$	7547.85	−	8995.17i	0.392316	−	0.467544i
$719$	2033.51	−	358.562i	0.105476	−	0.0185982i	−0.120661	−	0.992694i	$-0.538501\pi$
$719$	2033.51	−	358.562i	0.105476	−	0.0185982i	0.226137	+	0.974096i	$0.427390\pi$
$720$		0			0
$721$		−	13723.7i		−	0.708874i
$722$	24931.2	−	846.694i	1.28510	−	0.0436436i
$723$		0			0
$724$	7537.68	−	20709.6i	0.386928	−	1.06308i
$725$	1232.27	+	6988.53i	0.0631245	+	0.357997i
$726$		0			0
$727$	11286.9	−	9470.81i	0.575801	−	0.483154i	−0.307764	−	0.951463i	$-0.599581\pi$
$727$	11286.9	−	9470.81i	0.575801	−	0.483154i	0.883565	+	0.468309i	$0.155136\pi$
$728$	−2645.00	−	466.386i	−0.134657	−	0.0237437i
$729$		0			0
$730$	−20055.1	+	11578.8i	−1.01681	+	0.587056i
$731$	299.661	+	823.311i	0.0151619	+	0.0416570i
$732$		0			0
$733$	6550.21	+	11345.3i	0.330065	+	0.571689i	0.982524	−	0.186135i	$-0.0595961\pi$
$733$	6550.21	+	11345.3i	0.330065	+	0.571689i	−0.652460	+	0.757824i	$0.726263\pi$
$734$	−23608.0	+	40890.3i	−1.18718	+	2.05625i
$735$		0			0
$736$	−7942.00	−	9464.90i	−0.397753	−	0.474023i
$737$	−8.75616	−	7.34729i	−0.000437636	−	0.000367220i
$738$		0			0
$739$	−25913.1	−	9431.61i	−1.28989	−	0.469482i	−0.396200	−	0.918164i	$-0.629671\pi$
$739$	−25913.1	−	9431.61i	−1.28989	−	0.469482i	−0.893692	+	0.448682i	$0.851894\pi$
$740$	−21994.4			−1.09261
$741$		0			0
$742$	−19496.9			−0.964627
$743$	−10790.6	−	3927.45i	−0.532796	−	0.193922i	0.0615901	−	0.998102i	$-0.480383\pi$
$743$	−10790.6	−	3927.45i	−0.532796	−	0.193922i	−0.594387	+	0.804179i	$0.702605\pi$
$744$		0			0
$745$	−33720.1	−	28294.6i	−1.65827	−	1.39145i
$746$	−26420.1	−	31486.2i	−1.29666	−	1.54530i
$747$		0			0
$748$	3408.23	−	5903.23i	0.166601	−	0.288561i
$749$	−17162.2	−	29725.8i	−0.837241	−	1.45014i
$750$		0			0
$751$	3542.37	+	9732.58i	0.172121	+	0.472899i	0.995519	−	0.0945663i	$-0.0301464\pi$
$751$	3542.37	+	9732.58i	0.172121	+	0.472899i	−0.823398	+	0.567465i	$0.807924\pi$
$752$	−608.392	+	351.255i	−0.0295024	+	0.0170332i
$753$		0			0
$754$	9797.24	+	1727.52i	0.473202	+	0.0834383i
$755$	−9381.21	+	7871.77i	−0.452208	+	0.379448i
$756$		0			0
$757$	−2770.76	−	15713.8i	−0.133032	−	0.754460i	−0.976210	−	0.216826i	$-0.930429\pi$
$757$	−2770.76	−	15713.8i	−0.133032	−	0.754460i	0.843179	−	0.537634i	$-0.180682\pi$
$758$	−1349.64	+	3708.11i	−0.0646717	+	0.177684i
$759$		0			0
$760$	−10574.4	−	1680.02i	−0.504704	−	0.0801852i
$761$		−	785.685i		−	0.0374258i	−0.999825	−	0.0187129i	$-0.994043\pi$
$761$		−	785.685i		−	0.0374258i	0.999825	−	0.0187129i	$-0.00595686\pi$
$762$		0			0
$763$	23588.2	−	4159.23i	1.11920	−	0.197345i
$764$	−1568.29	+	1869.02i	−0.0742655	+	0.0885061i
$765$		0			0
$766$	−2754.05	+	15619.0i	−0.129906	+	0.736732i
$767$	10329.9	+	5963.94i	0.486297	+	0.280763i
$768$		0			0
$769$	3744.21	−	1362.78i	0.175578	−	0.0639052i	−0.252735	−	0.967535i	$-0.581330\pi$
$769$	3744.21	−	1362.78i	0.175578	−	0.0639052i	0.428313	+	0.903630i	$0.359108\pi$
$770$	23231.0	−	8455.41i	1.08726	−	0.395730i
$771$		0			0
$772$	−15118.0	−	8728.37i	−0.704804	−	0.406919i
$773$	2619.42	−	14855.5i	0.121881	−	0.691223i	−0.861230	−	0.508215i	$-0.830306\pi$
$773$	2619.42	−	14855.5i	0.121881	−	0.691223i	0.983111	−	0.183008i	$-0.0585833\pi$
$774$		0			0
$775$	−5552.49	+	6617.20i	−0.257357	+	0.306706i
$776$	−10685.4	+	1884.13i	−0.494310	+	0.0871602i
$777$		0			0
$778$		−	40696.8i		−	1.87539i
$779$	−32099.9	+	12304.4i	−1.47638	+	0.565917i
$780$		0			0
$781$	467.140	−	1283.46i	0.0214028	−	0.0588037i
$782$	1645.63	+	9332.82i	0.0752526	+	0.426779i
$783$		0			0
$784$	2079.30	−	1744.74i	0.0947201	−	0.0794796i
$785$	34533.1	+	6089.13i	1.57012	+	0.276854i
$786$		0			0
$787$	−23483.6	+	13558.3i	−1.06366	+	0.614104i	−0.926442	−	0.376436i	$-0.877149\pi$
$787$	−23483.6	+	13558.3i	−1.06366	+	0.614104i	−0.137218	+	0.990541i	$0.543816\pi$
$788$	−8140.65	−	22366.3i	−0.368019	−	1.01112i
$789$		0			0
$790$	−5575.31	−	9656.71i	−0.251089	−	0.434899i
$791$	2467.19	−	4273.30i	0.110902	−	0.192087i
$792$		0			0
$793$	−3649.51	−	4349.32i	−0.163427	−	0.194765i
$794$	−19191.1	−	16103.2i	−0.857765	−	0.719750i
$795$		0			0
$796$	10977.7	+	3995.57i	0.488813	+	0.177914i
$797$	10093.7			0.448605			0.224302	−	0.974520i	$-0.427990\pi$
$797$	10093.7			0.448605			0.224302	+	0.974520i	$0.427990\pi$
$798$		0			0
$799$	386.552			0.0171154
$800$	−7571.19	−	2755.69i	−0.334602	−	0.121785i
$801$		0			0
$802$	−32873.6	−	27584.2i	−1.44739	−	1.21450i
$803$	9639.64	+	11488.1i	0.423631	+	0.504864i
$804$		0			0
$805$	−6791.28	+	11762.8i	−0.297343	+	0.515013i
$806$	6054.92	+	10487.4i	0.264610	+	0.458317i
$807$		0			0
$808$	−4160.51	−	11430.9i	−0.181146	−	0.497696i
$809$	19457.2	−	11233.6i	0.845586	−	0.488199i	−0.0135733	−	0.999908i	$-0.504321\pi$
$809$	19457.2	−	11233.6i	0.845586	−	0.488199i	0.859159	+	0.511709i	$0.170987\pi$
$810$		0			0
$811$	4820.06	+	849.906i	0.208699	+	0.0367993i	0.277020	−	0.960864i	$-0.410653\pi$
$811$	4820.06	+	849.906i	0.208699	+	0.0367993i	−0.0683210	+	0.997663i	$0.521764\pi$
$812$	12684.4	−	10643.4i	0.548194	−	0.459990i
$813$		0			0
$814$	6258.71	+	35494.9i	0.269493	+	1.52837i
$815$	17508.8	−	48105.0i	0.752522	−	2.06754i
$816$		0			0
$817$	1305.12	+	1057.90i	0.0558878	+	0.0453014i
$818$		−	33686.1i		−	1.43986i
$819$		0			0
$820$	−27392.3	+	4830.00i	−1.16656	+	0.205696i
$821$	−13065.9	+	15571.3i	−0.555422	+	0.661927i	−0.968571	−	0.248737i	$-0.919985\pi$
$821$	−13065.9	+	15571.3i	−0.555422	+	0.661927i	0.413149	+	0.910664i	$0.364429\pi$
$822$		0			0
$823$	−6338.87	+	35949.5i	−0.268480	+	1.52263i	0.490458	+	0.871465i	$0.336829\pi$
$823$	−6338.87	+	35949.5i	−0.268480	+	1.52263i	−0.758938	+	0.651162i	$0.774282\pi$
$824$	6824.92	+	3940.37i	0.288540	+	0.166589i
$825$		0			0
$826$	47208.0	−	17182.3i	1.98859	−	0.723788i
$827$	6498.43	−	2365.24i	0.273244	−	0.0994526i	−0.201764	−	0.979434i	$-0.564667\pi$
$827$	6498.43	−	2365.24i	0.273244	−	0.0994526i	0.475008	+	0.879982i	$0.342445\pi$
$828$		0			0
$829$	−12847.8	−	7417.70i	−0.538268	−	0.310769i	0.206109	−	0.978529i	$-0.433920\pi$
$829$	−12847.8	−	7417.70i	−0.538268	−	0.310769i	−0.744377	+	0.667760i	$0.767253\pi$
$830$	−1835.56	+	10410.0i	−0.0767631	+	0.435345i
$831$		0			0
$832$	−1139.30	+	1357.77i	−0.0474738	+	0.0565770i
$833$	−1470.85	+	259.351i	−0.0611789	+	0.0107875i
$834$		0			0
$835$			7020.19i			0.290951i
$836$	−221.852	−	13068.8i	−0.00917812	−	0.540661i
$837$		0			0
$838$	−16536.9	+	45434.7i	−0.681691	+	1.87293i
$839$	1101.10	+	6244.67i	0.0453091	+	0.256960i	0.999045	−	0.0436838i	$-0.0139094\pi$
$839$	1101.10	+	6244.67i	0.0453091	+	0.256960i	−0.953736	+	0.300644i	$0.902798\pi$
$840$		0			0
$841$	6241.00	−	5236.82i	0.255894	−	0.214721i
$842$	−10466.8	−	1845.58i	−0.428395	−	0.0755377i
$843$		0			0
$844$	−22808.1	+	13168.2i	−0.930197	+	0.537050i
$845$	−8624.54	−	23695.7i	−0.351116	−	0.964684i
$846$		0			0
$847$	3682.61	+	6378.46i	0.149393	+	0.258756i
$848$	11980.3	−	20750.6i	0.485149	−	0.840303i
$849$		0			0
$850$	3972.33	+	4734.03i	0.160294	+	0.191031i
$851$	−15169.4	−	12728.6i	−0.611044	−	0.512727i
$852$		0			0
$853$	8256.21	+	3005.02i	0.331404	+	0.120621i	0.502363	−	0.864657i	$-0.332464\pi$
$853$	8256.21	+	3005.02i	0.331404	+	0.120621i	−0.170959	+	0.985278i	$0.554687\pi$
$854$	−23913.0			−0.958179
$855$		0			0
$856$	19710.5			0.787023
$857$	38469.3	+	14001.7i	1.53336	+	0.558096i	0.964441	−	0.264299i	$-0.0851406\pi$
$857$	38469.3	+	14001.7i	1.53336	+	0.558096i	0.568916	+	0.822395i	$0.307363\pi$
$858$		0			0
$859$	32724.0	+	27458.7i	1.29980	+	1.09066i	0.990180	+	0.139800i	$0.0446459\pi$
$859$	32724.0	+	27458.7i	1.29980	+	1.09066i	0.309619	+	0.950861i	$0.399799\pi$
$860$	873.751	+	1041.30i	0.0346450	+	0.0412883i
$861$		0			0
$862$	11487.8	−	19897.5i	0.453917	−	0.786207i
$863$	9577.00	+	16587.8i	0.377758	+	0.654295i	0.990736	−	0.135805i	$-0.0433619\pi$
$863$	9577.00	+	16587.8i	0.377758	+	0.654295i	−0.612978	+	0.790100i	$0.710029\pi$
$864$		0			0
$865$	1046.44	+	2875.08i	0.0411332	+	0.113012i
$866$	−8971.72	+	5179.83i	−0.352046	+	0.203254i
$867$		0			0
$868$	19849.6	+	3500.02i	0.776198	+	0.136865i
$869$	−5531.62	+	4641.58i	−0.215935	+	0.181191i
$870$		0			0
$871$	−0.996924	−	5.65384i	−3.87824e−5	−	0.000219946i
$872$	−4704.24	+	12924.8i	−0.182690	+	0.501937i
$873$		0			0
$874$	11915.2	+	13720.2i	0.461143	+	0.530998i
$875$		−	19284.8i		−	0.745080i
$876$		0			0
$877$	−3819.28	+	673.442i	−0.147056	+	0.0259299i	−0.246691	−	0.969094i	$-0.579343\pi$
$877$	−3819.28	+	673.442i	−0.147056	+	0.0259299i	0.0996356	+	0.995024i	$0.468232\pi$
$878$	9745.01	−	11613.6i	0.374576	−	0.446403i
$879$		0			0
$880$	−5275.79	+	29920.5i	−0.202099	+	1.14616i
$881$	−15994.1	−	9234.20i	−0.611640	−	0.353130i	0.161967	−	0.986796i	$-0.448216\pi$
$881$	−15994.1	−	9234.20i	−0.611640	−	0.353130i	−0.773607	+	0.633666i	$0.781549\pi$
$882$		0			0
$883$	−5094.76	+	1854.34i	−0.194170	+	0.0706722i	−0.437275	−	0.899328i	$-0.644056\pi$
$883$	−5094.76	+	1854.34i	−0.194170	+	0.0706722i	0.243105	+	0.970000i	$0.421834\pi$
$884$	3217.19	−	1170.96i	0.122405	−	0.0445517i
$885$		0			0
$886$	−32327.4	−	18664.2i	−1.22580	−	0.707716i
$887$	4279.09	−	24267.9i	0.161982	−	0.918645i	−0.790140	−	0.612926i	$-0.789992\pi$
$887$	4279.09	−	24267.9i	0.161982	−	0.918645i	0.952122	−	0.305718i	$-0.0988966\pi$
$888$		0			0
$889$	23125.2	−	27559.5i	0.872434	−	1.03973i
$890$	30533.8	−	5383.93i	1.14999	−	0.202775i
$891$		0			0
$892$		−	6285.79i		−	0.235946i
$893$	635.530	−	381.451i	0.0238155	−	0.0142942i
$894$		0			0
$895$	8548.46	−	23486.7i	0.319267	−	0.877178i
$896$	−3700.10	−	20984.3i	−0.137959	−	0.782406i
$897$		0			0
$898$	920.002	−	771.973i	0.0341880	−	0.0286872i
$899$	39003.4	+	6877.35i	1.44698	+	0.255142i
$900$		0			0
$901$	−11417.9	+	6592.11i	−0.422180	+	0.243746i
$902$	15589.5	+	42831.7i	0.575468	+	1.58109i
$903$		0			0
$904$	1416.76	+	2453.91i	0.0521248	+	0.0902828i
$905$	27025.2	−	46809.0i	0.992649	−	1.71932i
$906$		0			0
$907$	−18846.2	−	22460.0i	−0.689943	−	0.822242i	0.301406	−	0.953496i	$-0.402544\pi$
$907$	−18846.2	−	22460.0i	−0.689943	−	0.822242i	−0.991349	+	0.131254i	$0.958100\pi$
$908$	13268.4	+	11133.5i	0.484940	+	0.406913i
$909$		0			0
$910$	11668.1	+	4246.85i	0.425049	+	0.154705i
$911$	−46962.2			−1.70793			−0.853966	−	0.520329i	$-0.825809\pi$
$911$	−46962.2			−1.70793			−0.853966	+	0.520329i	$0.825809\pi$
$912$		0			0
$913$	6845.39			0.248137
$914$	6452.15	+	2348.39i	0.233499	+	0.0849867i
$915$		0			0
$916$	10301.9	+	8644.35i	0.371600	+	0.311810i
$917$	24340.8	+	29008.2i	0.876557	+	1.04464i
$918$		0			0
$919$	−16777.0	+	29058.7i	−0.602202	+	1.04304i	0.390285	+	0.920694i	$0.372376\pi$
$919$	−16777.0	+	29058.7i	−0.602202	+	1.04304i	−0.992487	+	0.122350i	$0.960957\pi$
$920$	−3899.83	−	6754.71i	−0.139754	−	0.242061i
$921$		0			0
$922$	6138.26	+	16864.7i	0.219255	+	0.602397i
$923$	594.098	−	343.003i	0.0211863	−	0.0122319i
$924$		0			0
$925$	−12716.9	−	2242.33i	−0.452031	−	0.0797052i
$926$	−9713.74	+	8150.79i	−0.344723	+	0.289257i
$927$		0			0
$928$	6414.73	+	36379.8i	0.226912	+	1.28688i
$929$	94.7034	−	260.195i	0.00334458	−	0.00918917i	−0.938009	−	0.346611i	$-0.887333\pi$
$929$	94.7034	−	260.195i	0.00334458	−	0.00918917i	0.941354	+	0.337421i	$0.109555\pi$
$930$		0			0
$931$	−2162.30	+	1877.84i	−0.0761187	+	0.0661050i
$932$		−	2925.12i		−	0.102806i
$933$		0			0
$934$	−44515.7	+	7849.31i	−1.55953	+	0.274986i
$935$	10745.8	−	12806.4i	0.375856	−	0.447928i
$936$		0			0
$937$	2500.73	−	14182.4i	0.0871883	−	0.494469i	−0.909675	−	0.415322i	$-0.863669\pi$
$937$	2500.73	−	14182.4i	0.0871883	−	0.494469i	0.996863	−	0.0791477i	$-0.0252199\pi$
$938$	−20.9406	−	12.0900i	−0.000728928	−	0.000420847i
$939$		0			0
$940$	563.554	−	205.117i	0.0195544	−	0.00711721i
$941$	−29494.6	+	10735.1i	−1.02178	+	0.371898i	−0.797946	−	0.602729i	$-0.794080\pi$
$941$	−29494.6	+	10735.1i	−1.02178	+	0.371898i	−0.223835	+	0.974627i	$0.571858\pi$
$942$		0			0
$943$	−21687.5	−	12521.3i	−0.748930	−	0.432395i
$944$	−10721.0	+	60801.6i	−0.369637	+	2.09632i
$945$		0			0
$946$	1431.83	−	1706.39i	0.0492101	−	0.0586463i
$947$	−51442.3	+	9070.67i	−1.76521	+	0.311253i	−0.959636	−	0.281246i	$-0.909252\pi$
$947$	−51442.3	+	9070.67i	−1.76521	+	0.311253i	−0.805571	+	0.592500i	$0.798141\pi$
$948$		0			0
$949$			7532.26i			0.257648i
$950$	11202.5	+	3863.32i	0.382585	+	0.131940i
$951$		0			0
$952$	−2616.26	+	7188.13i	−0.0890689	+	0.244715i
$953$	−8533.57	−	48396.3i	−0.290063	−	1.64503i	−0.686620	−	0.727016i	$-0.740906\pi$
$953$	−8533.57	−	48396.3i	−0.290063	−	1.64503i	0.396558	−	0.918010i	$-0.370205\pi$
$954$		0			0
$955$	−4583.80	+	3846.27i	−0.155318	+	0.130327i
$956$	23274.2	+	4103.88i	0.787388	+	0.138838i
$957$		0			0
$958$	−10326.9	+	5962.23i	−0.348274	+	0.201076i
$959$	−5053.65	−	13884.8i	−0.170168	−	0.467532i
$960$		0			0
$961$	9209.47	+	15951.3i	0.309136	+	0.535439i
$962$	−9051.42	+	15677.5i	−0.303357	+	0.525430i
$963$		0			0
$964$	−6680.41	−	7961.40i	−0.223197	−	0.265995i
$965$	−32796.7	−	27519.7i	−1.09405	−	0.918021i
$966$		0			0
$967$	−21225.5	−	7725.46i	−0.705860	−	0.256912i	−0.0359492	−	0.999354i	$-0.511445\pi$
$967$	−21225.5	−	7725.46i	−0.705860	−	0.256912i	−0.669911	+	0.742442i	$0.733668\pi$
$968$	−4229.41			−0.140432
$969$		0			0
$970$	50162.7			1.66044
$971$	−29507.8	−	10740.0i	−0.975234	−	0.354956i	−0.195248	−	0.980754i	$-0.562551\pi$
$971$	−29507.8	−	10740.0i	−0.975234	−	0.354956i	−0.779985	+	0.625798i	$0.784773\pi$
$972$		0			0
$973$	−36280.2	−	30442.7i	−1.19536	−	1.00303i
$974$	4158.55	+	4955.97i	0.136806	+	0.163038i
$975$		0			0
$976$	14693.9	−	25450.6i	0.481906	−	0.834686i
$977$	23328.9	+	40406.9i	0.763929	+	1.32316i	0.940811	+	0.338932i	$0.110066\pi$
$977$	23328.9	+	40406.9i	0.763929	+	1.32316i	−0.176882	+	0.984232i	$0.556601\pi$
$978$		0			0
$979$	−6867.21	−	18867.5i	−0.224185	−	0.615943i
$980$	−2006.74	+	1158.59i	−0.0654111	+	0.0377651i
$981$		0			0
$982$	46318.3	+	8167.17i	1.50517	+	0.265402i
$983$	1552.55	−	1302.74i	0.0503750	−	0.0422696i	−0.617253	−	0.786765i	$-0.711754\pi$
$983$	1552.55	−	1302.74i	0.0503750	−	0.0422696i	0.667628	+	0.744495i	$0.267310\pi$
$984$		0			0
$985$	−10136.6	−	57487.3i	−0.327896	−	1.85959i
$986$	9690.79	−	26625.2i	0.313000	−	0.859959i
$987$		0			0
$988$	4133.88	−	5099.92i	0.133114	−	0.164221i
$989$			1223.83i			0.0393484i
$990$		0			0
$991$	21577.5	−	3804.70i	0.691658	−	0.121958i	0.183240	−	0.983068i	$-0.441342\pi$
$991$	21577.5	−	3804.70i	0.691658	−	0.121958i	0.508418	+	0.861110i	$0.330230\pi$
$992$	−28904.3	+	34446.7i	−0.925112	+	1.10251i
$993$		0			0
$994$	501.723	−	2845.41i	0.0160097	−	0.0907958i
$995$	24812.5	+	14325.5i	0.790561	+	0.456431i
$996$		0			0
$997$	−21098.1	+	7679.07i	−0.670193	+	0.243930i	−0.654631	−	0.755949i	$-0.727176\pi$
$997$	−21098.1	+	7679.07i	−0.670193	+	0.243930i	−0.0155621	+	0.999879i	$0.504954\pi$
$998$	−52284.7	+	19030.1i	−1.65836	+	0.603594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.y.a.53.4	✓	120
3.2	odd	2	inner	171.4.y.a.53.17	yes	120
19.14	odd	18	inner	171.4.y.a.71.17	yes	120
57.14	even	18	inner	171.4.y.a.71.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.y.a.53.4	✓	120	1.1	even	1	trivial
171.4.y.a.53.17	yes	120	3.2	odd	2	inner
171.4.y.a.71.4	yes	120	57.14	even	18	inner
171.4.y.a.71.17	yes	120	19.14	odd	18	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.41758 - 1.24390i) q^{2} +(4.00419 + 3.35992i) q^{4} +(8.24027 + 9.82037i) q^{5} +(8.78095 - 15.2090i) q^{7} +(5.04239 + 8.73367i) q^{8} +O(q^{10})\)	\(q+(-3.41758 - 1.24390i) q^{2} +(4.00419 + 3.35992i) q^{4} +(8.24027 + 9.82037i) q^{5} +(8.78095 - 15.2090i) q^{7} +(5.04239 + 8.73367i) q^{8} +(-15.9462 - 43.8119i) q^{10} +(-26.1479 + 15.0965i) q^{11} +(-14.9344 - 2.63335i) q^{13} +(-48.9280 + 41.0555i) q^{14} +(-13.6304 - 77.3017i) q^{16} +(-14.7722 + 40.5862i) q^{17} +(15.7637 + 81.3050i) q^{19} +67.0093i q^{20} +(108.141 - 19.0681i) q^{22} +(-38.7796 + 46.2158i) q^{23} +(-6.83160 + 38.7439i) q^{25} +(47.7640 + 27.5766i) q^{26} +(86.2617 - 31.3967i) q^{28} +(169.499 - 61.6927i) q^{29} +(190.151 + 109.784i) q^{31} +(-35.5628 + 201.687i) q^{32} +(100.970 - 120.331i) q^{34} +(221.716 - 39.0945i) q^{35} +328.229i q^{37} +(47.2615 - 297.474i) q^{38} +(-44.2172 + 121.486i) q^{40} +(72.0795 + 408.783i) q^{41} +(15.5396 - 13.0393i) q^{43} +(-155.424 - 27.4054i) q^{44} +(190.020 - 109.708i) q^{46} +(-3.06102 - 8.41010i) q^{47} +(17.2900 + 29.9471i) q^{49} +(71.5409 - 123.913i) q^{50} +(-50.9526 - 60.7229i) q^{52} +(233.838 + 196.214i) q^{53} +(-363.718 - 132.383i) q^{55} +177.108 q^{56} -656.017 q^{58} +(-739.115 - 269.016i) q^{59} +(286.803 + 240.656i) q^{61} +(-513.296 - 611.723i) q^{62} +(58.4391 - 101.220i) q^{64} +(-97.2034 - 168.361i) q^{65} +(0.129481 + 0.355746i) q^{67} +(-195.517 + 112.882i) q^{68} +(-806.360 - 142.183i) q^{70} +(-34.6533 + 29.0775i) q^{71} +(-86.2498 - 489.147i) q^{73} +(408.282 - 1121.75i) q^{74} +(-210.057 + 378.526i) q^{76} +530.245i q^{77} +(235.529 - 41.5301i) q^{79} +(646.813 - 770.842i) q^{80} +(262.147 - 1486.71i) q^{82} +(-196.347 - 113.361i) q^{83} +(-520.298 + 189.373i) q^{85} +(-69.3272 + 25.2330i) q^{86} +(-263.695 - 152.244i) q^{88} +(-115.476 + 654.899i) q^{89} +(-171.189 + 204.015i) q^{91} +(-310.562 + 54.7605i) q^{92} +32.5497i q^{94} +(-668.548 + 824.780i) q^{95} +(-367.982 + 1011.02i) q^{97} +(-21.8387 - 123.854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 36 q^{4}+O(q^{10}) \) 120 * q - 36 * q^4	\( 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) \) 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

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