LMFDB - Embedded newform 171.3.p.f.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19163381760000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 $ x^8 - 14x^6 + 177x^4 - 266*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$3.05907 - 1.76616i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.f.46.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.05907 - 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(-0.533068 - 0.923301i) q^{5} +0.477226 q^{7} -15.8150i q^{8} +O(q^{10})$	\(q+(3.05907 - 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(-0.533068 - 0.923301i) q^{5} +0.477226 q^{7} -15.8150i q^{8} +(-3.26139 - 1.88296i) q^{10} +11.1702 q^{11} +(-12.9772 - 7.49240i) q^{13} +(1.45987 - 0.842855i) q^{14} +(-10.9772 - 19.0131i) q^{16} +(6.11814 + 10.5969i) q^{17} +(-6.52277 + 17.8453i) q^{19} -9.03788 q^{20} +(34.1703 - 19.7282i) q^{22} +(-20.7411 + 35.9246i) q^{23} +(11.9317 - 20.6663i) q^{25} -52.9310 q^{26} +(2.02277 - 3.50355i) q^{28} +(30.5907 + 17.6616i) q^{29} -15.8903i q^{31} +(-12.3756 - 7.14507i) q^{32} +(37.4317 + 21.6112i) q^{34} +(-0.254394 - 0.440623i) q^{35} +24.3276i q^{37} +(11.5639 + 66.1102i) q^{38} +(-14.6020 + 8.43045i) q^{40} +(5.83947 - 3.37142i) q^{41} +(-31.6703 - 54.8546i) q^{43} +(47.3459 - 82.0056i) q^{44} +146.528i q^{46} +(-20.2080 + 35.0013i) q^{47} -48.7723 q^{49} -84.2928i q^{50} +(-110.011 + 63.5148i) q^{52} +(-26.3505 - 15.2134i) q^{53} +(-5.95445 - 10.3134i) q^{55} -7.54730i q^{56} +124.772 q^{58} +(69.1775 - 39.9396i) q^{59} +(-35.8861 + 62.1566i) q^{61} +(-28.0647 - 48.6095i) q^{62} +37.3406 q^{64} +15.9758i q^{65} +(7.62474 + 4.40215i) q^{67} +103.730 q^{68} +(-1.55642 - 0.898598i) q^{70} +(42.2697 - 24.4044i) q^{71} +(-56.7950 - 98.3719i) q^{73} +(42.9663 + 74.4199i) q^{74} +(103.363 + 123.526i) q^{76} +5.33068 q^{77} +(104.534 - 60.3525i) q^{79} +(-11.7032 + 20.2706i) q^{80} +(11.9089 - 20.6268i) q^{82} -65.4460 q^{83} +(6.52277 - 11.2978i) q^{85} +(-193.763 - 111.869i) q^{86} -176.655i q^{88} +(-133.279 - 76.9484i) q^{89} +(-6.19306 - 3.57557i) q^{91} +(175.827 + 304.541i) q^{92} +142.762i q^{94} +(19.9536 - 3.49026i) q^{95} +(-83.0911 + 47.9727i) q^{97} +(-149.198 + 86.1394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) $ 8 * q + 12 * q^4 - 40 * q^7	$ 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 - 40 * q^7 - 48 * q^10 - 60 * q^13 - 44 * q^16 - 96 * q^19 + 120 * q^22 - 36 * q^25 + 60 * q^28 + 168 * q^34 + 168 * q^40 - 100 * q^43 + 48 * q^49 - 420 * q^52 + 40 * q^55 + 560 * q^58 - 68 * q^61 - 8 * q^64 - 180 * q^67 + 360 * q^70 - 60 * q^73 + 564 * q^76 + 420 * q^79 - 80 * q^82 + 96 * q^85 + 60 * q^91 - 840 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.05907	−	1.76616i	1.52954	−	0.883078i	0.530155	−	0.847901i	$-0.322134\pi$
$2$	3.05907	−	1.76616i	1.52954	−	0.883078i	0.999381	−	0.0351770i	$-0.0111995\pi$
$3$		0			0
$3$		0			0
$4$	4.23861	−	7.34149i	1.05965	−	1.83537i
$5$	−0.533068	−	0.923301i	−0.106614	−	0.184660i	0.807783	−	0.589480i	$-0.200667\pi$
$5$	−0.533068	−	0.923301i	−0.106614	−	0.184660i	−0.914396	+	0.404820i	$0.867334\pi$
$6$		0			0
$7$	0.477226			0.0681751			0.0340875	−	0.999419i	$-0.489147\pi$
$7$	0.477226			0.0681751			0.0340875	+	0.999419i	$0.489147\pi$
$8$		−	15.8150i		−	1.97687i
$9$		0			0
$10$	−3.26139	−	1.88296i	−0.326139	−	0.188296i
$11$	11.1702			1.01547			0.507734	−	0.861514i	$-0.330483\pi$
$11$	11.1702			1.01547			0.507734	+	0.861514i	$0.330483\pi$
$12$		0			0
$13$	−12.9772	−	7.49240i	−0.998248	−	0.576339i	−0.0905186	−	0.995895i	$-0.528852\pi$
$13$	−12.9772	−	7.49240i	−0.998248	−	0.576339i	−0.907729	+	0.419556i	$0.862186\pi$
$14$	1.45987	−	0.842855i	0.104276	−	0.0602039i
$15$		0			0
$16$	−10.9772	−	19.0131i	−0.686077	−	1.18832i
$17$	6.11814	+	10.5969i	0.359891	+	0.623349i	0.987942	−	0.154823i	$-0.0494806\pi$
$17$	6.11814	+	10.5969i	0.359891	+	0.623349i	−0.628051	+	0.778172i	$0.716147\pi$
$18$		0			0
$19$	−6.52277	+	17.8453i	−0.343304	+	0.939224i
$19$	−6.52277	+	17.8453i	−0.343304	+	0.939224i
$20$	−9.03788			−0.451894
$21$		0			0
$22$	34.1703	−	19.7282i	1.55319	−	0.896738i
$23$	−20.7411	+	35.9246i	−0.901787	+	1.56194i	−0.0766135	+	0.997061i	$0.524411\pi$
$23$	−20.7411	+	35.9246i	−0.901787	+	1.56194i	−0.825173	+	0.564880i	$0.808923\pi$
$24$		0			0
$25$	11.9317	−	20.6663i	0.477267	−	0.826651i
$26$	−52.9310			−2.03581
$27$		0			0
$28$	2.02277	−	3.50355i	0.0722419	−	0.125127i
$29$	30.5907	+	17.6616i	1.05485	+	0.609019i	0.924004	−	0.382383i	$-0.124897\pi$
$29$	30.5907	+	17.6616i	1.05485	+	0.609019i	0.130848	+	0.991402i	$0.458230\pi$
$30$		0			0
$31$		−	15.8903i		−	0.512590i	−0.966599	−	0.256295i	$-0.917498\pi$
$31$		−	15.8903i		−	0.512590i	0.966599	−	0.256295i	$-0.0825018\pi$
$32$	−12.3756	−	7.14507i	−0.386738	−	0.223283i
$33$		0			0
$34$	37.4317	+	21.6112i	1.10093	+	0.635623i
$35$	−0.254394	−	0.440623i	−0.00726839	−	0.0125892i
$36$		0			0
$37$			24.3276i			0.657503i	0.944416	+	0.328751i	$0.106628\pi$
$37$			24.3276i			0.657503i	−0.944416	+	0.328751i	$0.893372\pi$
$38$	11.5639	+	66.1102i	0.304313	+	1.73974i
$39$		0			0
$40$	−14.6020	+	8.43045i	−0.365049	+	0.210761i
$41$	5.83947	−	3.37142i	0.142426	−	0.0822297i	−0.427094	−	0.904207i	$-0.640463\pi$
$41$	5.83947	−	3.37142i	0.142426	−	0.0822297i	0.569520	+	0.821978i	$0.307129\pi$
$42$		0			0
$43$	−31.6703	−	54.8546i	−0.736518	−	1.27569i	−0.954054	−	0.299635i	$-0.903135\pi$
$43$	−31.6703	−	54.8546i	−0.736518	−	1.27569i	0.217536	−	0.976052i	$-0.430198\pi$
$44$	47.3459	−	82.0056i	1.07604	−	1.86376i
$45$		0			0
$46$			146.528i			3.18539i
$47$	−20.2080	+	35.0013i	−0.429958	+	0.744709i	−0.996869	−	0.0790699i	$-0.974805\pi$
$47$	−20.2080	+	35.0013i	−0.429958	+	0.744709i	0.566911	+	0.823779i	$0.308138\pi$
$48$		0			0
$49$	−48.7723			−0.995352
$50$		−	84.2928i		−	1.68586i
$51$		0			0
$52$	−110.011	+	63.5148i	−2.11559	+	1.22144i
$53$	−26.3505	−	15.2134i	−0.497178	−	0.287046i	0.230369	−	0.973103i	$-0.426007\pi$
$53$	−26.3505	−	15.2134i	−0.497178	−	0.287046i	−0.727548	+	0.686057i	$0.759340\pi$
$54$		0			0
$55$	−5.95445	−	10.3134i	−0.108263	−	0.187517i
$56$		−	7.54730i		−	0.134773i
$57$		0			0
$58$	124.772			2.15125
$59$	69.1775	−	39.9396i	1.17250	−	0.676943i	0.218232	−	0.975897i	$-0.429971\pi$
$59$	69.1775	−	39.9396i	1.17250	−	0.676943i	0.954267	+	0.298954i	$0.0966378\pi$
$60$		0			0
$61$	−35.8861	+	62.1566i	−0.588297	+	1.01896i	0.406158	+	0.913803i	$0.366868\pi$
$61$	−35.8861	+	62.1566i	−0.588297	+	1.01896i	−0.994456	+	0.105158i	$0.966465\pi$
$62$	−28.0647	−	48.6095i	−0.452657	−	0.784024i
$63$		0			0
$64$	37.3406			0.583447
$65$			15.9758i			0.245782i
$66$		0			0
$67$	7.62474	+	4.40215i	0.113802	+	0.0657037i	0.555821	−	0.831302i	$-0.312404\pi$
$67$	7.62474	+	4.40215i	0.113802	+	0.0657037i	−0.442019	+	0.897006i	$0.645737\pi$
$68$	103.730			1.52544
$69$		0			0
$70$	−1.55642	−	0.898598i	−0.0222345	−	0.0128371i
$71$	42.2697	−	24.4044i	0.595347	−	0.343724i	−0.171862	−	0.985121i	$-0.554978\pi$
$71$	42.2697	−	24.4044i	0.595347	−	0.343724i	0.767209	+	0.641397i	$0.221645\pi$
$72$		0			0
$73$	−56.7950	−	98.3719i	−0.778014	−	1.34756i	−0.933085	−	0.359657i	$-0.882894\pi$
$73$	−56.7950	−	98.3719i	−0.778014	−	1.34756i	0.155071	−	0.987903i	$-0.450439\pi$
$74$	42.9663	+	74.4199i	0.580626	+	1.00567i
$75$		0			0
$76$	103.363	+	123.526i	1.36004	+	1.62534i
$77$	5.33068			0.0692296
$78$		0			0
$79$	104.534	−	60.3525i	1.32321	−	0.763956i	0.338971	−	0.940797i	$-0.389921\pi$
$79$	104.534	−	60.3525i	1.32321	−	0.763956i	0.984239	+	0.176841i	$0.0565877\pi$
$80$	−11.7032	+	20.2706i	−0.146290	+	0.253382i
$81$		0			0
$82$	11.9089	−	20.6268i	0.145231	−	0.251547i
$83$	−65.4460			−0.788506			−0.394253	−	0.919002i	$-0.628997\pi$
$83$	−65.4460			−0.788506			−0.394253	+	0.919002i	$0.628997\pi$
$84$		0			0
$85$	6.52277	−	11.2978i	0.0767385	−	0.132915i
$86$	−193.763	−	111.869i	−2.25306	−	1.30081i
$87$		0			0
$88$		−	176.655i		−	2.00745i
$89$	−133.279	−	76.9484i	−1.49751	−	0.864589i	−0.497517	−	0.867454i	$-0.665755\pi$
$89$	−133.279	−	76.9484i	−1.49751	−	0.864589i	−0.999996	+	0.00286509i	$0.999088\pi$
$90$		0			0
$91$	−6.19306	−	3.57557i	−0.0680556	−	0.0392919i
$92$	175.827	+	304.541i	1.91116	+	3.31023i
$93$		0			0
$94$			142.762i			1.51875i
$95$	19.9536	−	3.49026i	0.210038	−	0.0367395i
$96$		0			0
$97$	−83.0911	+	47.9727i	−0.856609	+	0.494564i	−0.862875	−	0.505417i	$-0.831339\pi$
$97$	−83.0911	+	47.9727i	−0.856609	+	0.494564i	0.00626610	+	0.999980i	$0.498005\pi$
$98$	−149.198	+	86.1394i	−1.52243	+	0.878974i
$99$		0			0
$100$	−101.148	−	175.193i	−1.01148	−	1.75193i
$101$	13.5811	−	23.5232i	0.134466	−	0.232902i	−0.790927	−	0.611910i	$-0.790401\pi$
$101$	13.5811	−	23.5232i	0.134466	−	0.232902i	0.925393	+	0.379008i	$0.123735\pi$
$102$		0			0
$103$			43.4453i			0.421799i	0.977508	+	0.210900i	$0.0676393\pi$
$103$			43.4453i			0.421799i	−0.977508	+	0.210900i	$0.932361\pi$
$104$	−118.492	+	205.234i	−1.13935	+	1.97341i
$105$		0			0
$106$	−107.477			−1.01394
$107$		−	35.9667i		−	0.336137i	−0.985775	−	0.168069i	$-0.946247\pi$
$107$		−	35.9667i		−	0.336137i	0.985775	−	0.168069i	$-0.0537530\pi$
$108$		0			0
$109$	−70.0455	+	40.4408i	−0.642620	+	0.371017i	−0.785623	−	0.618706i	$-0.787657\pi$
$109$	−70.0455	+	40.4408i	−0.642620	+	0.371017i	0.143003	+	0.989722i	$0.454324\pi$
$110$	−36.4302	−	21.0330i	−0.331184	−	0.191209i
$111$		0			0
$112$	−5.23861	−	9.07354i	−0.0467733	−	0.0810138i
$113$			19.9908i			0.176910i	0.996080	+	0.0884550i	$0.0281930\pi$
$113$			19.9908i			0.176910i	−0.996080	+	0.0884550i	$0.971807\pi$
$114$		0			0
$115$	44.2257			0.384571
$116$	259.324	−	149.721i	2.23556	−	1.29070i
$117$		0			0
$118$	141.079	−	244.356i	1.19559	−	2.07082i
$119$	2.91973	+	5.05713i	0.0245356	+	0.0424969i
$120$		0			0
$121$	3.77226			0.0311757
$122$			253.522i			2.07805i
$123$		0			0
$124$	−116.658	−	67.3527i	−0.940793	−	0.543167i
$125$	−52.0950			−0.416760
$126$		0			0
$127$	−35.7267	−	20.6268i	−0.281313	−	0.162416i	0.352705	−	0.935735i	$-0.385262\pi$
$127$	−35.7267	−	20.6268i	−0.281313	−	0.162416i	−0.634018	+	0.773319i	$0.718595\pi$
$128$	163.730	−	94.5296i	1.27914	−	0.738512i
$129$		0			0
$130$	28.2158	+	48.8713i	0.217045	+	0.375933i
$131$	−102.942	−	178.301i	−0.785819	−	1.36108i	−0.928509	−	0.371311i	$-0.878908\pi$
$131$	−102.942	−	178.301i	−0.785819	−	1.36108i	0.142689	−	0.989768i	$-0.454425\pi$
$132$		0			0
$133$	−3.11283	+	8.51622i	−0.0234048	+	0.0640317i
$134$	31.0995			0.232086
$135$		0			0
$136$	167.590	−	96.7582i	1.23228	−	0.711457i
$137$	90.1487	−	156.142i	0.658019	−	1.13972i	−0.323108	−	0.946362i	$-0.604728\pi$
$137$	90.1487	−	156.142i	0.658019	−	1.13972i	0.981128	−	0.193361i	$-0.0619389\pi$
$138$		0			0
$139$	35.8525	−	62.0983i	0.257932	−	0.446751i	−0.707756	−	0.706457i	$-0.750292\pi$
$139$	35.8525	−	62.0983i	0.257932	−	0.446751i	0.965688	+	0.259706i	$0.0836258\pi$
$140$	−4.31311			−0.0308079
$141$		0			0
$142$	86.2039	−	149.310i	0.607070	−	1.05148i
$143$	−144.958	−	83.6913i	−1.01369	−	0.585254i
$144$		0			0
$145$		−	37.6593i		−	0.259719i
$146$	−347.480	−	200.618i	−2.38000	−	1.37409i
$147$		0			0
$148$	178.601	+	103.115i	1.20676	+	0.696725i
$149$	109.036	+	188.856i	0.731786	+	1.26749i	0.956119	+	0.292978i	$0.0946464\pi$
$149$	109.036	+	188.856i	0.731786	+	1.26749i	−0.224333	+	0.974513i	$0.572020\pi$
$150$		0			0
$151$		−	26.1899i		−	0.173443i	−0.996233	−	0.0867217i	$-0.972361\pi$
$151$		−	26.1899i		−	0.173443i	0.996233	−	0.0867217i	$-0.0276391\pi$
$152$	282.222	+	103.157i	1.85672	+	0.678667i
$153$		0			0
$154$	16.3069	−	9.41481i	0.105889	−	0.0611352i
$155$	−14.6715	+	8.47060i	−0.0946549	+	0.0546490i
$156$		0			0
$157$	59.8861	+	103.726i	0.381440	+	0.660674i	0.991268	−	0.131860i	$-0.0420948\pi$
$157$	59.8861	+	103.726i	0.381440	+	0.660674i	−0.609828	+	0.792534i	$0.708762\pi$
$158$	213.184	−	369.245i	1.34927	−	2.33700i
$159$		0			0
$160$			15.2352i			0.0952202i
$161$	−9.89818	+	17.1442i	−0.0614794	+	0.106485i
$162$		0			0
$163$	252.885			1.55144			0.775721	−	0.631076i	$-0.217386\pi$
$163$	252.885			1.55144			0.775721	+	0.631076i	$0.217386\pi$
$164$		−	57.1606i		−	0.348540i
$165$		0			0
$166$	−200.204	+	115.588i	−1.20605	+	0.696312i
$167$	163.312	+	94.2882i	0.977916	+	0.564600i	0.901640	−	0.432487i	$-0.142364\pi$
$167$	163.312	+	94.2882i	0.977916	+	0.564600i	0.0762758	+	0.997087i	$0.475697\pi$
$168$		0			0
$169$	27.7723	+	48.1030i	0.164333	+	0.284633i
$170$		−	46.0809i		−	0.271064i
$171$		0			0
$172$	−536.952			−3.12182
$173$	168.946	−	97.5408i	0.976564	−	0.563820i	0.0753332	−	0.997158i	$-0.475998\pi$
$173$	168.946	−	97.5408i	0.976564	−	0.563820i	0.901231	+	0.433339i	$0.142665\pi$
$174$		0			0
$175$	5.69410	−	9.86247i	0.0325377	−	0.0563570i
$176$	−122.617	−	212.379i	−0.696689	−	1.20670i
$177$		0			0
$178$	−543.612			−3.05400
$179$			170.754i			0.953933i	0.878921	+	0.476966i	$0.158264\pi$
$179$			170.754i			0.953933i	−0.878921	+	0.476966i	$0.841736\pi$
$180$		0			0
$181$	1.70497	+	0.984365i	0.00941972	+	0.00543848i	0.504702	−	0.863293i	$-0.331602\pi$
$181$	1.70497	+	0.984365i	0.00941972	+	0.00543848i	−0.495283	+	0.868732i	$0.664936\pi$
$182$	−25.2600			−0.138791
$183$		0			0
$184$	568.146	+	328.020i	3.08775	+	1.78271i
$185$	22.4617	−	12.9683i	0.121415	−	0.0700988i
$186$		0			0
$187$	68.3406	+	118.369i	0.365458	+	0.632991i
$188$	171.308	+	296.714i	0.911213	+	1.57827i
$189$		0			0
$190$	54.8753	−	45.9182i	0.288817	−	0.241675i
$191$	12.1877			0.0638101			0.0319050	−	0.999491i	$-0.489843\pi$
$191$	12.1877			0.0638101			0.0319050	+	0.999491i	$0.489843\pi$
$192$		0			0
$193$	−245.884	+	141.961i	−1.27401	+	0.735550i	−0.975740	−	0.218931i	$-0.929743\pi$
$193$	−245.884	+	141.961i	−1.27401	+	0.735550i	−0.298270	+	0.954481i	$0.596410\pi$
$194$	−169.454	+	293.504i	−0.873476	+	1.51291i
$195$		0			0
$196$	−206.727	+	358.061i	−1.05473	+	1.82684i
$197$	−306.876			−1.55775			−0.778874	−	0.627181i	$-0.784209\pi$
$197$	−306.876			−1.55775			−0.778874	+	0.627181i	$0.784209\pi$
$198$		0			0
$199$	−76.7376	+	132.913i	−0.385616	+	0.667906i	−0.991854	−	0.127376i	$-0.959344\pi$
$199$	−76.7376	+	132.913i	−0.385616	+	0.667906i	0.606238	+	0.795283i	$0.292678\pi$
$200$	−326.836	−	188.699i	−1.63418	−	0.943495i
$201$		0			0
$202$		−	95.9453i		−	0.474977i
$203$	14.5987	+	8.42855i	0.0719146	+	0.0415199i
$204$		0			0
$205$	−6.22567	−	3.59439i	−0.0303691	−	0.0175336i
$206$	76.7312	+	132.902i	0.372481	+	0.645157i
$207$		0			0
$208$			328.983i			1.58165i
$209$	−72.8604	+	199.334i	−0.348614	+	0.953752i
$210$		0			0
$211$	238.078	−	137.454i	1.12833	−	0.651443i	0.184817	−	0.982773i	$-0.440831\pi$
$211$	238.078	−	137.454i	1.12833	−	0.651443i	0.943515	+	0.331330i	$0.107497\pi$
$212$	−223.379	+	128.968i	−1.05367	+	0.608339i
$213$		0			0
$214$	−63.5228	−	110.025i	−0.296835	−	0.514134i
$215$	−33.7648	+	58.4824i	−0.157046	+	0.272011i
$216$		0			0
$217$		−	7.58325i		−	0.0349458i
$218$	−142.850	+	247.423i	−0.655273	+	1.13497i
$219$		0			0
$220$	−100.954			−0.458884
$221$		−	183.358i		−	0.829676i
$222$		0			0
$223$	347.646	−	200.714i	1.55895	−	0.900062i	0.561595	−	0.827412i	$-0.310188\pi$
$223$	347.646	−	200.714i	1.55895	−	0.900062i	0.997358	−	0.0726498i	$-0.0231455\pi$
$224$	−5.90596	−	3.40981i	−0.0263659	−	0.0152224i
$225$		0			0
$226$	35.3069	+	61.1534i	0.156225	+	0.270590i
$227$			338.864i			1.49279i	0.665501	+	0.746397i	$0.268218\pi$
$227$			338.864i			1.49279i	−0.665501	+	0.746397i	$0.731782\pi$
$228$		0			0
$229$	−222.453			−0.971412			−0.485706	−	0.874122i	$-0.661437\pi$
$229$	−222.453			−0.971412			−0.485706	+	0.874122i	$0.661437\pi$
$230$	135.289	−	78.1094i	0.588215	−	0.339606i
$231$		0			0
$232$	279.317	−	483.791i	1.20395	−	2.08531i
$233$	116.802	+	202.307i	0.501296	+	0.868271i	0.999999	+	0.00149765i	$0.000476716\pi$
$233$	116.802	+	202.307i	0.501296	+	0.868271i	−0.498702	+	0.866773i	$0.666190\pi$
$234$		0			0
$235$	43.0890			0.183358
$236$		−	677.154i		−	2.86930i
$237$		0			0
$238$	17.8634	+	10.3134i	0.0750561	+	0.0433337i
$239$	322.917			1.35112			0.675558	−	0.737307i	$-0.263903\pi$
$239$	322.917			1.35112			0.675558	+	0.737307i	$0.263903\pi$
$240$		0			0
$241$	201.841	+	116.533i	0.837513	+	0.483538i	0.856418	−	0.516283i	$-0.172685\pi$
$241$	201.841	+	116.533i	0.837513	+	0.483538i	−0.0189052	+	0.999821i	$0.506018\pi$
$242$	11.5396	−	6.66239i	0.0476843	−	0.0275305i
$243$		0			0
$244$	304.215	+	526.915i	1.24678	+	2.15949i
$245$	25.9989	+	45.0315i	0.106118	+	0.183802i
$246$		0			0
$247$	218.351	−	182.711i	0.884014	−	0.739720i
$248$	−251.304			−1.01332
$249$		0			0
$250$	−159.362	+	92.0079i	−0.637449	+	0.368032i
$251$	−134.042	+	232.167i	−0.534031	+	0.924969i	0.465178	+	0.885217i	$0.345990\pi$
$251$	−134.042	+	232.167i	−0.534031	+	0.924969i	−0.999210	+	0.0397521i	$0.987343\pi$
$252$		0			0
$253$	−231.681	+	401.284i	−0.915736	+	1.58610i
$254$	−145.721			−0.573704
$255$		0			0
$256$	259.227	−	448.994i	1.01260	−	1.75388i
$257$	414.568	+	239.351i	1.61310	+	0.931326i	0.988645	+	0.150267i	$0.0480133\pi$
$257$	414.568	+	239.351i	1.61310	+	0.931326i	0.624458	+	0.781059i	$0.285320\pi$
$258$		0			0
$259$			11.6098i			0.0448253i
$260$	117.287	+	67.7154i	0.451102	+	0.260444i
$261$		0			0
$262$	−629.816	−	363.624i	−2.40388	−	1.38788i
$263$	−133.812	−	231.769i	−0.508790	−	0.881250i	−0.999948	−	0.0101794i	$-0.996760\pi$
$263$	−133.812	−	231.769i	−0.508790	−	0.881250i	0.491158	−	0.871070i	$-0.336574\pi$
$264$		0			0
$265$			32.4392i			0.122412i
$266$	5.51858	+	31.5495i	0.0207465	+	0.118607i
$267$		0			0
$268$	64.6366	−	37.3180i	0.241182	−	0.139246i
$269$	16.7552	−	9.67363i	0.0622871	−	0.0359615i	−0.468533	−	0.883446i	$-0.655217\pi$
$269$	16.7552	−	9.67363i	0.0622871	−	0.0359615i	0.530820	+	0.847485i	$0.321884\pi$
$270$		0			0
$271$	117.499	+	203.514i	0.433576	+	0.750975i	0.997178	−	0.0750712i	$-0.0239184\pi$
$271$	117.499	+	203.514i	0.433576	+	0.750975i	−0.563603	+	0.826046i	$0.690585\pi$
$272$	134.320	−	232.650i	0.493825	−	0.855330i
$273$		0			0
$274$		−	636.866i		−	2.32433i
$275$	133.279	−	230.845i	0.484650	−	0.839438i
$276$		0			0
$277$	−107.636			−0.388576			−0.194288	−	0.980945i	$-0.562240\pi$
$277$	−107.636			−0.388576			−0.194288	+	0.980945i	$0.562240\pi$
$278$		−	253.284i		−	0.911095i
$279$		0			0
$280$	−6.96843	+	4.02323i	−0.0248873	+	0.0143687i
$281$	−364.932	−	210.694i	−1.29869	−	0.749799i	−0.318513	−	0.947919i	$-0.603183\pi$
$281$	−364.932	−	210.694i	−1.29869	−	0.749799i	−0.980178	+	0.198119i	$0.936517\pi$
$282$		0			0
$283$	−10.4772	−	18.1471i	−0.0370220	−	0.0641240i	0.846921	−	0.531719i	$-0.178454\pi$
$283$	−10.4772	−	18.1471i	−0.0370220	−	0.0641240i	−0.883943	+	0.467595i	$0.845120\pi$
$284$		−	413.763i		−	1.45691i
$285$		0			0
$286$	−591.247			−2.06730
$287$	2.78674	−	1.60893i	0.00970991	−	0.00560602i
$288$		0			0
$289$	69.6366	−	120.614i	0.240957	−	0.417350i
$290$	−66.5121	−	115.202i	−0.229352	−	0.397250i
$291$		0			0
$292$	−962.929			−3.29770
$293$			308.437i			1.05269i	0.850272	+	0.526344i	$0.176437\pi$
$293$			308.437i			1.05269i	−0.850272	+	0.526344i	$0.823563\pi$
$294$		0			0
$295$	−73.7526	−	42.5811i	−0.250009	−	0.144343i
$296$	384.740			1.29980
$297$		0			0
$298$	667.099	+	385.150i	2.23859	+	1.29245i
$299$	538.324	−	310.801i	1.80041	−	1.03947i
$300$		0			0
$301$	−15.1139	−	26.1780i	−0.0502122	−	0.0869701i
$302$	−46.2555	−	80.1169i	−0.153164	−	0.265288i
$303$		0			0
$304$	410.896	−	71.8732i	1.35163	−	0.236425i
$305$	76.5190			0.250882
$306$		0			0
$307$	−17.8634	+	10.3134i	−0.0581868	+	0.0335942i	−0.528811	−	0.848739i	$-0.677362\pi$
$307$	−17.8634	+	10.3134i	−0.0581868	+	0.0335942i	0.470624	+	0.882334i	$0.344029\pi$
$308$	22.5947	−	39.1352i	0.0733594	−	0.127062i
$309$		0			0
$310$	−29.9208	+	51.8244i	−0.0965187	+	0.167175i
$311$	−294.737			−0.947707			−0.473854	−	0.880604i	$-0.657137\pi$
$311$	−294.737			−0.947707			−0.473854	+	0.880604i	$0.657137\pi$
$312$		0			0
$313$	25.7267	−	44.5600i	0.0821940	−	0.142364i	−0.821998	−	0.569490i	$-0.807141\pi$
$313$	25.7267	−	44.5600i	0.0821940	−	0.142364i	0.904192	+	0.427126i	$0.140474\pi$
$314$	366.392	+	211.536i	1.16685	+	0.673683i
$315$		0			0
$316$		−	1023.24i		−	3.23811i
$317$	42.0638	+	24.2856i	0.132693	+	0.0766106i	0.564877	−	0.825175i	$-0.308924\pi$
$317$	42.0638	+	24.2856i	0.132693	+	0.0766106i	−0.432184	+	0.901786i	$0.642257\pi$
$318$		0			0
$319$	341.703	+	197.282i	1.07117	+	0.618440i
$320$	−19.9051	−	34.4766i	−0.0622034	−	0.107739i
$321$		0			0
$322$			69.9269i			0.217164i
$323$	−229.012	+	40.0585i	−0.709017	+	0.124020i
$324$		0			0
$325$	−309.680	+	178.794i	−0.952862	+	0.550135i
$326$	773.594	−	446.634i	2.37299	−	1.37004i
$327$		0			0
$328$	−53.3188	−	92.3509i	−0.162557	−	0.281558i
$329$	−9.64379	+	16.7035i	−0.0293124	+	0.0507706i
$330$		0			0
$331$		−	351.908i		−	1.06317i	−0.847006	−	0.531583i	$-0.821597\pi$
$331$		−	351.908i		−	1.06317i	0.847006	−	0.531583i	$-0.178403\pi$
$332$	−277.400	+	480.471i	−0.835543	+	1.44720i
$333$		0			0
$334$	666.111			1.99434
$335$		−	9.38658i		−	0.0280196i
$336$		0			0
$337$	85.1791	−	49.1782i	0.252757	−	0.145929i	−0.368269	−	0.929719i	$-0.620049\pi$
$337$	85.1791	−	49.1782i	0.252757	−	0.145929i	0.621026	+	0.783790i	$0.286716\pi$
$338$	169.915	+	98.1003i	0.502706	+	0.290237i
$339$		0			0
$340$	−55.2950	−	95.7738i	−0.162632	−	0.281688i
$341$		−	177.497i		−	0.520519i
$342$		0			0
$343$	−46.6594			−0.136033
$344$	−867.522	+	500.864i	−2.52187	+	1.45600i
$345$		0			0
$346$	344.545	−	596.769i	0.995793	−	1.72476i
$347$	42.8027	+	74.1365i	0.123351	+	0.213650i	0.921087	−	0.389357i	$-0.127303\pi$
$347$	42.8027	+	74.1365i	0.123351	+	0.213650i	−0.797736	+	0.603006i	$0.793969\pi$
$348$		0			0
$349$	146.137			0.418730			0.209365	−	0.977838i	$-0.432860\pi$
$349$	146.137			0.418730			0.209365	+	0.977838i	$0.432860\pi$
$350$		−	40.2267i		−	0.114933i
$351$		0			0
$352$	−138.238	−	79.8115i	−0.392720	−	0.226737i
$353$	−517.025			−1.46466			−0.732330	−	0.680949i	$-0.761567\pi$
$353$	−517.025			−1.46466			−0.732330	+	0.680949i	$0.761567\pi$
$354$		0			0
$355$	−45.0652	−	26.0184i	−0.126944	−	0.0732913i
$356$	−1129.83	+	652.309i	−3.17369	+	1.83233i
$357$		0			0
$358$	301.578	+	522.349i	0.842397	+	1.45907i
$359$	−112.210	−	194.354i	−0.312563	−	0.541376i	0.666353	−	0.745636i	$-0.267854\pi$
$359$	−112.210	−	194.354i	−0.312563	−	0.541376i	−0.978917	+	0.204261i	$0.934521\pi$
$360$		0			0
$361$	−275.907	−	232.801i	−0.764285	−	0.644879i
$362$	6.95417			0.0192104
$363$		0			0
$364$	−52.5000	+	30.3109i	−0.144231	+	0.0832717i
$365$	−60.5512	+	104.878i	−0.165894	+	0.287337i
$366$		0			0
$367$	171.714	−	297.417i	0.467885	−	0.810400i	−0.531442	−	0.847095i	$-0.678350\pi$
$367$	171.714	−	297.417i	0.467885	−	0.810400i	0.999327	+	0.0366945i	$0.0116828\pi$
$368$	910.719			2.47478
$369$		0			0
$370$	45.8080	−	79.3417i	0.123805	−	0.214437i
$371$	−12.5751	−	7.26024i	−0.0338952	−	0.0195694i
$372$		0			0
$373$			497.699i			1.33431i	0.744918	+	0.667156i	$0.232489\pi$
$373$			497.699i			1.33431i	−0.744918	+	0.667156i	$0.767511\pi$
$374$	418.117	+	241.400i	1.11796	+	0.645455i
$375$		0			0
$376$	553.545	+	319.589i	1.47219	+	0.849971i
$377$	−264.655	−	458.396i	−0.702003	−	1.21590i
$378$		0			0
$379$			73.4149i			0.193707i	0.995299	+	0.0968535i	$0.0308778\pi$
$379$			73.4149i			0.193707i	−0.995299	+	0.0968535i	$0.969122\pi$
$380$	58.9520	−	161.283i	0.155137	−	0.424430i
$381$		0			0
$382$	37.2831	−	21.5254i	0.0975998	−	0.0563493i
$383$	−228.528	+	131.941i	−0.596678	+	0.344492i	−0.767734	−	0.640769i	$-0.778616\pi$
$383$	−228.528	+	131.941i	−0.596678	+	0.344492i	0.171055	+	0.985261i	$0.445282\pi$
$384$		0			0
$385$	−2.84162	−	4.92182i	−0.00738082	−	0.0127840i
$386$	−501.451	+	868.539i	−1.29910	+	2.25010i
$387$		0			0
$388$			813.350i			2.09626i
$389$	193.951	−	335.933i	0.498589	−	0.863582i	−0.501409	−	0.865210i	$-0.667185\pi$
$389$	193.951	−	335.933i	0.498589	−	0.863582i	0.999999	+	0.00162809i	$0.000518236\pi$
$390$		0			0
$391$	−507.588			−1.29818
$392$			771.331i			1.96768i
$393$		0			0
$394$	−938.756	+	541.991i	−2.38263	+	1.37561i
$395$	−111.447	−	64.3440i	−0.282145	−	0.162896i
$396$		0			0
$397$	−207.294	−	359.044i	−0.522151	−	0.904392i	−0.999668	−	0.0257696i	$-0.991796\pi$
$397$	−207.294	−	359.044i	−0.522151	−	0.904392i	0.477517	−	0.878623i	$-0.341537\pi$
$398$			542.122i			1.36212i
$399$		0			0
$400$	−523.907			−1.30977
$401$	359.226	−	207.399i	0.895824	−	0.517204i	0.0199812	−	0.999800i	$-0.493639\pi$
$401$	359.226	−	207.399i	0.895824	−	0.517204i	0.875843	+	0.482596i	$0.160306\pi$
$402$		0			0
$403$	−119.056	+	206.212i	−0.295425	+	0.511692i
$404$	−115.130	−	199.411i	−0.284975	−	0.493592i
$405$		0			0
$406$	59.5445			0.146661
$407$			271.743i			0.667673i
$408$		0			0
$409$	−385.954	−	222.831i	−0.943654	−	0.544819i	−0.0525501	−	0.998618i	$-0.516735\pi$
$409$	−385.954	−	222.831i	−0.943654	−	0.544819i	−0.891104	+	0.453799i	$0.850068\pi$
$410$	−25.3930			−0.0619342
$411$		0			0
$412$	318.953	+	184.148i	0.774159	+	0.446961i
$413$	33.0133	−	19.0602i	0.0799352	−	0.0461506i
$414$		0			0
$415$	34.8872	+	60.4263i	0.0840655	+	0.145606i
$416$	107.068	+	185.446i	0.257374	+	0.445785i
$417$		0			0
$418$	129.170	+	738.461i	0.309020	+	1.76665i
$419$	352.866			0.842162			0.421081	−	0.907023i	$-0.361651\pi$
$419$	352.866			0.842162			0.421081	+	0.907023i	$0.361651\pi$
$420$		0			0
$421$	281.887	−	162.748i	0.669566	−	0.386574i	−0.126346	−	0.991986i	$-0.540325\pi$
$421$	281.887	−	162.748i	0.669566	−	0.386574i	0.795912	+	0.605412i	$0.206992\pi$
$422$	485.532	−	840.966i	1.15055	−	1.99281i
$423$		0			0
$424$	−240.600	+	416.731i	−0.567453	+	0.982857i
$425$	291.999			0.687056
$426$		0			0
$427$	−17.1258	+	29.6627i	−0.0401072	+	0.0694677i
$428$	−264.049	−	152.449i	−0.616937	−	0.356189i
$429$		0			0
$430$			238.536i			0.554735i
$431$	−166.026	−	95.8551i	−0.385211	−	0.222402i	0.294872	−	0.955537i	$-0.404723\pi$
$431$	−166.026	−	95.8551i	−0.385211	−	0.222402i	−0.680083	+	0.733135i	$0.738056\pi$
$432$		0			0
$433$	−253.975	−	146.633i	−0.586548	−	0.338643i	0.177184	−	0.984178i	$-0.443301\pi$
$433$	−253.975	−	146.633i	−0.586548	−	0.338643i	−0.763731	+	0.645534i	$0.776635\pi$
$434$	−13.3932	−	23.1977i	−0.0308599	−	0.0534509i
$435$		0			0
$436$			685.652i			1.57260i
$437$	−505.795	−	604.459i	−1.15743	−	1.38320i
$438$		0			0
$439$	202.351	−	116.828i	0.460937	−	0.266122i	−0.251501	−	0.967857i	$-0.580924\pi$
$439$	202.351	−	116.828i	0.460937	−	0.266122i	0.712438	+	0.701735i	$0.247591\pi$
$440$	−163.106	+	94.1694i	−0.370696	+	0.214021i
$441$		0			0
$442$	−323.840	−	560.907i	−0.732669	−	1.26902i
$443$	−200.275	+	346.887i	−0.452089	+	0.783040i	−0.998516	−	0.0544663i	$-0.982654\pi$
$443$	−200.275	+	346.887i	−0.452089	+	0.783040i	0.546427	+	0.837507i	$0.315988\pi$
$444$		0			0
$445$			164.075i			0.368708i
$446$	708.984	−	1228.00i	1.58965	−	2.75335i
$447$		0			0
$448$	17.8199			0.0397765
$449$		−	243.737i		−	0.542844i	−0.962460	−	0.271422i	$-0.912506\pi$
$449$		−	243.737i		−	0.542844i	0.962460	−	0.271422i	$-0.0874939\pi$
$450$		0			0
$451$	65.2277	−	37.6593i	0.144629	−	0.0835017i
$452$	146.763	+	84.7334i	0.324696	+	0.187463i
$453$		0			0
$454$	598.487	+	1036.61i	1.31825	+	2.28328i
$455$			7.62408i			0.0167562i
$456$		0			0
$457$	4.08902			0.00894753			0.00447377	−	0.999990i	$-0.498576\pi$
$457$	4.08902			0.00894753			0.00447377	+	0.999990i	$0.498576\pi$
$458$	−680.501	+	392.887i	−1.48581	+	0.857833i
$459$		0			0
$460$	187.455	−	324.682i	0.407512	−	0.705831i
$461$	391.718	+	678.476i	0.849715	+	1.47175i	0.881463	+	0.472253i	$0.156559\pi$
$461$	391.718	+	678.476i	0.849715	+	1.47175i	−0.0317484	+	0.999496i	$0.510108\pi$
$462$		0			0
$463$	−219.978			−0.475115			−0.237558	−	0.971373i	$-0.576347\pi$
$463$	−219.978			−0.475115			−0.237558	+	0.971373i	$0.576347\pi$
$464$		−	775.500i		−	1.67134i
$465$		0			0
$466$	714.612	+	412.581i	1.53350	+	0.885368i
$467$	−445.983			−0.954995			−0.477498	−	0.878633i	$-0.658456\pi$
$467$	−445.983			−0.954995			−0.477498	+	0.878633i	$0.658456\pi$
$468$		0			0
$469$	3.63872	+	2.10082i	0.00775847	+	0.00447935i
$470$	131.812	−	76.1019i	0.280452	−	0.161919i
$471$		0			0
$472$	−631.643	−	1094.04i	−1.33823	−	2.31788i
$473$	−353.762	−	612.734i	−0.747911	−	1.29542i
$474$		0			0
$475$	290.967	+	347.725i	0.612563	+	0.732053i
$476$	49.5025			0.103997
$477$		0			0
$478$	987.826	−	570.321i	2.06658	−	1.19314i
$479$	315.684	−	546.781i	0.659048	−	1.14150i	−0.321815	−	0.946803i	$-0.604293\pi$
$479$	315.684	−	546.781i	0.659048	−	1.14150i	0.980862	−	0.194702i	$-0.0623739\pi$
$480$		0			0
$481$	182.272	−	315.705i	0.378944	−	0.656351i
$482$	823.260			1.70801
$483$		0			0
$484$	15.9891	−	27.6940i	0.0330354	−	0.0572190i
$485$	88.5864	+	51.1454i	0.182652	+	0.105454i
$486$		0			0
$487$		−	792.723i		−	1.62777i	−0.581027	−	0.813884i	$-0.697349\pi$
$487$		−	792.723i		−	1.62777i	0.581027	−	0.813884i	$-0.302651\pi$
$488$	983.004	+	567.538i	2.01435	+	1.16299i
$489$		0			0
$490$	159.065	+	91.8363i	0.324623	+	0.187421i
$491$	−67.9055	−	117.616i	−0.138300	−	0.239543i	0.788553	−	0.614967i	$-0.210831\pi$
$491$	−67.9055	−	117.616i	−0.138300	−	0.239543i	−0.926853	+	0.375424i	$0.877497\pi$
$492$		0			0
$493$			432.224i			0.876722i
$494$	345.257	−	944.568i	0.698901	−	1.91208i
$495$		0			0
$496$	−302.124	+	174.431i	−0.609120	+	0.351676i
$497$	20.1722	−	11.6464i	0.0405878	−	0.0234334i
$498$		0			0
$499$	−236.577	−	409.764i	−0.474102	−	0.821170i	0.525458	−	0.850820i	$-0.323894\pi$
$499$	−236.577	−	409.764i	−0.474102	−	0.821170i	−0.999560	+	0.0296501i	$0.990561\pi$
$500$	−220.811	+	382.455i	−0.441621	+	0.764910i
$501$		0			0
$502$			946.955i			1.88636i
$503$	359.444	−	622.575i	0.714601	−	1.23772i	−0.248513	−	0.968629i	$-0.579942\pi$
$503$	359.444	−	622.575i	0.714601	−	1.23772i	0.963113	−	0.269096i	$-0.0867249\pi$
$504$		0			0
$505$	−28.9586			−0.0573438
$506$			1636.74i			3.23466i
$507$		0			0
$508$	−302.863	+	174.858i	−0.596188	+	0.344209i
$509$	578.570	+	334.037i	1.13668	+	0.656262i	0.945606	−	0.325314i	$-0.105470\pi$
$509$	578.570	+	334.037i	1.13668	+	0.656262i	0.191073	+	0.981576i	$0.438803\pi$
$510$		0			0
$511$	−27.1040	−	46.9456i	−0.0530412	−	0.0918700i
$512$		−	1075.10i		−	2.09981i
$513$		0			0
$514$	1690.92			3.28973
$515$	40.1131	−	23.1593i	0.0778895	−	0.0449695i
$516$		0			0
$517$	−225.727	+	390.970i	−0.436609	+	0.756228i
$518$	20.5046	+	35.5151i	0.0395842	+	0.0685619i
$519$		0			0
$520$	252.657			0.485880
$521$			772.856i			1.48341i	0.670727	+	0.741704i	$0.265982\pi$
$521$			772.856i			1.48341i	−0.670727	+	0.741704i	$0.734018\pi$
$522$		0			0
$523$	−599.415	−	346.072i	−1.14611	−	0.661706i	−0.198172	−	0.980167i	$-0.563501\pi$
$523$	−599.415	−	346.072i	−1.14611	−	0.661706i	−0.947936	+	0.318461i	$0.896834\pi$
$524$	−1745.33			−3.33078
$525$		0			0
$526$	−818.679	−	472.665i	−1.55642	−	0.898602i
$527$	168.388	−	97.2190i	0.319522	−	0.184476i
$528$		0			0
$529$	−595.886	−	1032.11i	−1.12644	−	1.95105i
$530$	57.2927	+	99.2338i	0.108099	+	0.187234i
$531$		0			0
$532$	49.3276	+	58.9498i	0.0927211	+	0.110808i
$533$	−101.040			−0.189569
$534$		0			0
$535$	−33.2081	+	19.1727i	−0.0620712	+	0.0358368i
$536$	69.6197	−	120.585i	0.129888	−	0.224972i
$537$		0			0
$538$	34.1703	−	59.1847i	0.0635135	−	0.110009i
$539$	−544.793			−1.01075
$540$		0			0
$541$	−488.635	+	846.340i	−0.903206	+	1.56440i	−0.0798991	+	0.996803i	$0.525460\pi$
$541$	−488.635	+	846.340i	−0.903206	+	1.56440i	−0.823307	+	0.567596i	$0.807874\pi$
$542$	718.875	+	415.043i	1.32634	+	0.765762i
$543$		0			0
$544$		−	174.858i		−	0.321431i
$545$	74.6781	+	43.1154i	0.137024	+	0.0791109i
$546$		0			0
$547$	166.215	+	95.9642i	0.303866	+	0.175437i	0.644178	−	0.764875i	$-0.277199\pi$
$547$	166.215	+	95.9642i	0.303866	+	0.175437i	−0.340312	+	0.940312i	$0.610533\pi$
$548$	−764.211	−	1323.65i	−1.39454	−	2.41542i
$549$		0			0
$550$		−	941.563i		−	1.71193i
$551$	−514.711	+	430.697i	−0.934141	+	0.781664i
$552$		0			0
$553$	49.8861	−	28.8018i	0.0902100	−	0.0520828i
$554$	−329.265	+	190.101i	−0.594341	+	0.343143i
$555$		0			0
$556$	−303.930	−	526.422i	−0.546636	−	0.946801i
$557$	−161.531	+	279.780i	−0.290002	+	0.502299i	−0.973810	−	0.227364i	$-0.926989\pi$
$557$	−161.531	+	279.780i	−0.290002	+	0.502299i	0.683808	+	0.729662i	$0.260323\pi$
$558$		0			0
$559$			949.147i			1.69794i
$560$	−5.58508	+	9.67363i	−0.00997335	+	0.0172743i
$561$		0			0
$562$	−1488.47			−2.64852
$563$			328.512i			0.583503i	0.956494	+	0.291752i	$0.0942381\pi$
$563$			328.512i			0.583503i	−0.956494	+	0.291752i	$0.905762\pi$
$564$		0			0
$565$	18.4576	−	10.6565i	0.0326683	−	0.0188610i
$566$	−64.1012	−	37.0088i	−0.113253	−	0.0653866i
$567$		0			0
$568$	−385.954	−	668.493i	−0.679497	−	1.17692i
$569$			1069.96i			1.88042i	0.340590	+	0.940212i	$0.389373\pi$
$569$			1069.96i			1.88042i	−0.340590	+	0.940212i	$0.610627\pi$
$570$		0			0
$571$	226.109			0.395987			0.197994	−	0.980203i	$-0.436557\pi$
$571$	226.109			0.395987			0.197994	+	0.980203i	$0.436557\pi$
$572$	−1228.84	+	709.470i	−2.14832	+	1.24033i
$573$		0			0
$574$	5.68323	−	9.84365i	0.00990110	−	0.0171492i
$575$	494.952	+	857.282i	0.860786	+	1.49093i
$576$		0			0
$577$	563.905			0.977305			0.488652	−	0.872479i	$-0.337489\pi$
$577$	563.905			0.977305			0.488652	+	0.872479i	$0.337489\pi$
$578$		−	491.957i		−	0.851136i
$579$		0			0
$580$	−276.475	−	159.623i	−0.476681	−	0.275212i
$581$	−31.2325			−0.0537564
$582$		0			0
$583$	−294.339	−	169.936i	−0.504869	−	0.291486i
$584$	−1555.75	+	898.211i	−2.66395	+	1.53803i
$585$		0			0
$586$	544.748	+	943.532i	0.929605	+	1.61012i
$587$	−138.379	−	239.680i	−0.235740	−	0.408313i	0.723748	−	0.690065i	$-0.242418\pi$
$587$	−138.379	−	239.680i	−0.235740	−	0.408313i	−0.959487	+	0.281752i	$0.909085\pi$
$588$		0			0
$589$	283.566	+	103.649i	0.481437	+	0.175974i
$590$	−300.819			−0.509863
$591$		0			0
$592$	462.543	−	267.050i	0.781323	−	0.451097i
$593$	130.080	−	225.306i	0.219360	−	0.379942i	−0.735253	−	0.677793i	$-0.762937\pi$
$593$	130.080	−	225.306i	0.219360	−	0.379942i	0.954612	+	0.297851i	$0.0962699\pi$
$594$		0			0
$595$	3.11283	−	5.39159i	0.00523166	−	0.00906149i
$596$	1848.65			3.10176
$597$		0			0
$598$	1097.85	−	1901.53i	1.83587	−	3.17981i
$599$	660.820	+	381.524i	1.10320	+	0.636936i	0.937061	−	0.349166i	$-0.113535\pi$
$599$	660.820	+	381.524i	1.10320	+	0.636936i	0.166144	+	0.986102i	$0.446868\pi$
$600$		0			0
$601$		−	628.679i		−	1.04606i	−0.852316	−	0.523028i	$-0.824802\pi$
$601$		−	628.679i		−	1.04606i	0.852316	−	0.523028i	$-0.175198\pi$
$602$	−92.4688	−	53.3869i	−0.153603	−	0.0886826i
$603$		0			0
$604$	−192.273	−	111.009i	−0.318333	−	0.183790i
$605$	−2.01087	−	3.48293i	−0.00332375	−	0.00575691i
$606$		0			0
$607$			56.3825i			0.0928871i	0.998921	+	0.0464436i	$0.0147888\pi$
$607$			56.3825i			0.0928871i	−0.998921	+	0.0464436i	$0.985211\pi$
$608$	208.229	−	174.241i	0.342482	−	0.286580i
$609$		0			0
$610$	234.077	−	135.144i	0.383733	−	0.221548i
$611$	524.488	−	302.813i	0.858410	−	0.495603i
$612$		0			0
$613$	14.0673	+	24.3653i	0.0229483	+	0.0397476i	0.877271	−	0.479995i	$-0.159361\pi$
$613$	14.0673	+	24.3653i	0.0229483	+	0.0397476i	−0.854323	+	0.519742i	$0.826028\pi$
$614$	−36.4302	+	63.0989i	−0.0593325	+	0.102767i
$615$		0			0
$616$		−	84.3045i		−	0.136858i
$617$	−66.9966	+	116.042i	−0.108584	+	0.188074i	−0.915197	−	0.403007i	$-0.867965\pi$
$617$	−66.9966	+	116.042i	−0.108584	+	0.188074i	0.806613	+	0.591081i	$0.201298\pi$
$618$		0			0
$619$	586.929			0.948188			0.474094	−	0.880474i	$-0.342776\pi$
$619$	586.929			0.948188			0.474094	+	0.880474i	$0.342776\pi$
$620$			143.614i			0.231636i
$621$		0			0
$622$	−901.622	+	520.551i	−1.44955	+	0.836900i
$623$	−63.6040	−	36.7218i	−0.102093	−	0.0589434i
$624$		0			0
$625$	−270.522	−	468.557i	−0.432835	−	0.749692i
$626$		−	181.749i		−	0.290335i
$627$		0			0
$628$	1015.34			1.61678
$629$	−257.798	+	148.840i	−0.409854	+	0.236629i
$630$		0			0
$631$	−163.649	+	283.448i	−0.259348	+	0.449204i	−0.966067	−	0.258290i	$-0.916841\pi$
$631$	−163.649	+	283.448i	−0.259348	+	0.449204i	0.706719	+	0.707494i	$0.250174\pi$
$632$	−954.473	−	1653.19i	−1.51024	−	2.61581i
$633$		0			0
$634$	171.568			0.270612
$635$			43.9820i			0.0692630i
$636$		0			0
$637$	632.929	+	365.421i	0.993608	+	0.573660i
$638$	1393.72			2.18452
$639$		0			0
$640$	−174.558	−	100.781i	−0.272748	−	0.157471i
$641$	234.307	−	135.277i	0.365534	−	0.211041i	−0.305972	−	0.952041i	$-0.598981\pi$
$641$	234.307	−	135.277i	0.365534	−	0.211041i	0.671506	+	0.741000i	$0.265648\pi$
$642$		0			0
$643$	−402.896	−	697.836i	−0.626588	−	1.08528i	−0.988232	−	0.152966i	$-0.951118\pi$
$643$	−402.896	−	697.836i	−0.626588	−	1.08528i	0.361644	−	0.932316i	$-0.382216\pi$
$644$	83.9091	+	145.335i	0.130294	+	0.225675i
$645$		0			0
$646$	−629.816	+	527.013i	−0.974947	+	0.815810i
$647$	590.952			0.913372			0.456686	−	0.889628i	$-0.349036\pi$
$647$	590.952			0.913372			0.456686	+	0.889628i	$0.349036\pi$
$648$		0			0
$649$	772.723	−	446.132i	1.19064	−	0.687414i
$650$	−631.556	+	1093.89i	−0.971624	+	1.68290i
$651$		0			0
$652$	1071.88	−	1856.55i	1.64399	−	2.84748i
$653$	−990.945			−1.51753			−0.758763	−	0.651366i	$-0.774196\pi$
$653$	−990.945			−1.51753			−0.758763	+	0.651366i	$0.774196\pi$
$654$		0			0
$655$	−109.751	+	190.093i	−0.167558	+	0.290219i
$656$	−128.202	−	74.0177i	−0.195430	−	0.112832i
$657$		0			0
$658$			68.1297i			0.103541i
$659$	446.552	+	257.817i	0.677620	+	0.391224i	0.798958	−	0.601387i	$-0.205385\pi$
$659$	446.552	+	257.817i	0.677620	+	0.391224i	−0.121338	+	0.992611i	$0.538718\pi$
$660$		0			0
$661$	1142.22	+	659.462i	1.72802	+	0.997673i	0.898100	+	0.439791i	$0.144948\pi$
$661$	1142.22	+	659.462i	1.72802	+	0.997673i	0.829921	+	0.557882i	$0.188386\pi$
$662$	−621.525	−	1076.51i	−0.938859	−	1.62615i
$663$		0			0
$664$			1035.03i			1.55877i
$665$	9.52238	−	1.66564i	0.0143194	−	0.00250472i
$666$		0			0
$667$	−1268.97	+	732.640i	−1.90250	+	1.09841i
$668$	1384.43	−	799.303i	2.07250	−	1.19656i
$669$		0			0
$670$	−16.5782	−	28.7142i	−0.0247435	−	0.0428570i
$671$	−400.853	+	694.299i	−0.597397	+	1.03472i
$672$		0			0
$673$		−	569.028i		−	0.845510i	−0.906244	−	0.422755i	$-0.861063\pi$
$673$		−	569.028i		−	0.845510i	0.906244	−	0.422755i	$-0.138937\pi$
$674$	173.713	−	300.879i	0.257734	−	0.446408i
$675$		0			0
$676$	470.863			0.696543
$677$		−	909.084i		−	1.34281i	−0.741090	−	0.671406i	$-0.765691\pi$
$677$		−	909.084i		−	1.34281i	0.741090	−	0.671406i	$-0.234309\pi$
$678$		0			0
$679$	−39.6532	+	22.8938i	−0.0583994	+	0.0337169i
$680$	−178.674	−	103.157i	−0.262756	−	0.151702i
$681$		0			0
$682$	−313.487	−	542.976i	−0.459658	−	0.796152i
$683$		−	85.6567i		−	0.125412i	−0.998032	−	0.0627062i	$-0.980027\pi$
$683$		−	85.6567i		−	0.125412i	0.998032	−	0.0627062i	$-0.0199731\pi$
$684$		0			0
$685$	−192.222			−0.280615
$686$	−142.735	+	82.4078i	−0.208068	+	0.120128i
$687$		0			0
$688$	−695.304	+	1204.30i	−1.01062	+	1.75044i
$689$	227.971	+	394.856i	0.330872	+	0.573086i
$690$		0			0
$691$	−12.0911			−0.0174980			−0.00874899	−	0.999962i	$-0.502785\pi$
$691$	−12.0911			−0.0174980			−0.00874899	+	0.999962i	$0.502785\pi$
$692$		−	1653.75i		−	2.38981i
$693$		0			0
$694$	261.873	+	151.193i	0.377339	+	0.217857i
$695$	−76.4473			−0.109996
$696$		0			0
$697$	71.4534	+	41.2536i	0.102516	+	0.0591874i
$698$	447.042	−	258.100i	0.640462	−	0.369771i
$699$		0			0
$700$	−48.2702	−	83.6064i	−0.0689574	−	0.119438i
$701$	−13.8355	−	23.9638i	−0.0197368	−	0.0341851i	0.855988	−	0.516995i	$-0.172949\pi$
$701$	−13.8355	−	23.9638i	−0.0197368	−	0.0341851i	−0.875725	+	0.482810i	$0.839616\pi$
$702$		0			0
$703$	−434.132	−	158.683i	−0.617543	−	0.225723i
$704$	417.100			0.592471
$705$		0			0
$706$	−1581.62	+	913.147i	−2.24025	+	1.29341i
$707$	6.48125	−	11.2258i	0.00916725	−	0.0158781i
$708$		0			0
$709$	−330.042	+	571.650i	−0.465504	+	0.806277i	−0.999224	−	0.0393844i	$-0.987460\pi$
$709$	−330.042	+	571.650i	−0.465504	+	0.806277i	0.533720	+	0.845661i	$0.320794\pi$
$710$	−183.810			−0.258888
$711$		0			0
$712$	−1216.94	+	2107.80i	−1.70918	+	2.96039i
$713$	570.853	+	329.582i	0.800635	+	0.462247i
$714$		0			0
$715$			178.453i			0.249584i
$716$	1253.59	+	723.760i	1.75082	+	1.01084i
$717$		0			0
$718$	−686.519	−	396.362i	−0.956154	−	0.552036i
$719$	−216.159	−	374.398i	−0.300638	−	0.520720i	0.675643	−	0.737229i	$-0.263866\pi$
$719$	−216.159	−	374.398i	−0.300638	−	0.520720i	−0.976281	+	0.216509i	$0.930533\pi$
$720$		0			0
$721$			20.7332i			0.0287562i
$722$	−1255.18	−	224.861i	−1.73848	−	0.311442i
$723$		0			0
$724$	14.4534	−	8.34468i	0.0199633	−	0.0115258i
$725$	729.997	−	421.464i	1.00689	−	0.581330i
$726$		0			0
$727$	517.896	+	897.022i	0.712374	+	1.23387i	0.963964	+	0.266034i	$0.0857134\pi$
$727$	517.896	+	897.022i	0.712374	+	1.23387i	−0.251590	+	0.967834i	$0.580953\pi$
$728$	−56.5474	+	97.9430i	−0.0776751	+	0.134537i
$729$		0			0
$730$			427.772i			0.585989i
$731$	387.527	−	671.216i	0.530132	−	0.918216i
$732$		0			0
$733$	416.182			0.567779			0.283890	−	0.958857i	$-0.408375\pi$
$733$	416.182			0.567779			0.283890	+	0.958857i	$0.408375\pi$
$734$		−	1213.09i		−	1.65272i
$735$		0			0
$736$	513.368	−	296.393i	0.697511	−	0.402708i
$737$	85.1695	+	49.1726i	0.115562	+	0.0667200i
$738$		0			0
$739$	330.536	+	572.505i	0.447274	+	0.774702i	0.998208	−	0.0598475i	$-0.0190614\pi$
$739$	330.536	+	572.505i	0.447274	+	0.774702i	−0.550933	+	0.834549i	$0.685728\pi$
$740$		−	219.870i		−	0.297122i
$741$		0			0
$742$	−51.2909			−0.0691252
$743$	99.0651	−	57.1953i	0.133331	−	0.0769788i	−0.431851	−	0.901945i	$-0.642139\pi$
$743$	99.0651	−	57.1953i	0.133331	−	0.0769788i	0.565182	+	0.824966i	$0.308806\pi$
$744$		0			0
$745$	116.247	−	201.346i	0.156037	−	0.270264i
$746$	879.013	+	1522.50i	1.17830	+	2.04088i
$747$		0			0
$748$	1158.68			1.54903
$749$		−	17.1642i		−	0.0229162i
$750$		0			0
$751$	−118.013	−	68.1348i	−0.157141	−	0.0907254i	0.419367	−	0.907817i	$-0.362252\pi$
$751$	−118.013	−	68.1348i	−0.157141	−	0.0907254i	−0.576509	+	0.817091i	$0.695585\pi$
$752$	887.312			1.17994
$753$		0			0
$754$	−1619.20	−	934.844i	−2.14748	−	1.23985i
$755$	−24.1812	+	13.9610i	−0.0320281	+	0.0184914i
$756$		0			0
$757$	101.860	+	176.427i	0.134558	+	0.233061i	0.925428	−	0.378922i	$-0.123705\pi$
$757$	101.860	+	176.427i	0.134558	+	0.233061i	−0.790871	+	0.611983i	$0.790372\pi$
$758$	129.662	+	224.582i	0.171058	+	0.296282i
$759$		0			0
$760$	−55.1983	−	315.566i	−0.0726293	−	0.415218i
$761$	−976.891			−1.28369			−0.641847	−	0.766833i	$-0.721832\pi$
$761$	−976.891			−1.28369			−0.641847	+	0.766833i	$0.721832\pi$
$762$		0			0
$763$	−33.4275	+	19.2994i	−0.0438107	+	0.0252941i
$764$	51.6590	−	89.4761i	0.0676166	−	0.117115i
$765$		0			0
$766$	−466.055	+	807.232i	−0.608427	+	1.05383i
$767$	−1196.98			−1.56059
$768$		0			0
$769$	357.908	−	619.915i	0.465420	−	0.806131i	−0.533801	−	0.845610i	$-0.679237\pi$
$769$	357.908	−	619.915i	0.465420	−	0.806131i	0.999220	+	0.0394796i	$0.0125700\pi$
$770$	−17.3854	−	10.0375i	−0.0225785	−	0.0130357i
$771$		0			0
$772$			2406.87i			3.11771i
$773$	−320.373	−	184.967i	−0.414454	−	0.239285i	0.278248	−	0.960509i	$-0.410246\pi$
$773$	−320.373	−	184.967i	−0.414454	−	0.239285i	−0.692702	+	0.721224i	$0.743580\pi$
$774$		0			0
$775$	−328.393	−	189.598i	−0.423733	−	0.244642i
$776$	758.686	+	1314.08i	0.977688	+	1.69340i
$777$		0			0
$778$		−	1370.19i		−	1.76117i
$779$	22.0743	+	126.198i	0.0283367	+	0.162000i
$780$		0			0
$781$	472.158	−	272.601i	0.604556	−	0.349041i
$782$	−1552.75	+	896.479i	−1.98561	+	1.14639i
$783$		0			0
$784$	535.384	+	927.312i	0.682888	+	1.18280i
$785$	63.8468	−	110.586i	0.0813335	−	0.140874i
$786$		0			0
$787$		−	162.672i		−	0.206699i	−0.994645	−	0.103350i	$-0.967044\pi$
$787$		−	162.672i		−	0.206699i	0.994645	−	0.103350i	$-0.0329561\pi$
$788$	−1300.73	+	2252.93i	−1.65067	+	2.85905i
$789$		0			0
$790$	−454.566			−0.575400
$791$			9.54014i			0.0120609i
$792$		0			0
$793$	931.405	−	537.747i	1.17453	−	0.678117i
$794$	−1268.25	−	732.227i	−1.59730	−	0.922200i
$795$		0			0
$796$	650.522	+	1126.74i	0.817238	+	1.41550i
$797$			103.395i			0.129730i	0.997894	+	0.0648652i	$0.0206617\pi$
$797$			103.395i			0.129730i	−0.997894	+	0.0648652i	$0.979338\pi$
$798$		0			0
$799$	−494.542			−0.618952
$800$	−295.324	+	170.505i	−0.369155	+	0.213132i
$801$		0			0
$802$	732.598	−	1268.90i	0.913464	−	1.58217i
$803$	−634.409	−	1098.83i	−0.790049	−	1.36840i
$804$		0			0
$805$	21.1056			0.0262182
$806$			841.089i			1.04353i
$807$		0			0
$808$	−372.018	−	214.784i	−0.460418	−	0.265822i
$809$	940.571			1.16263			0.581317	−	0.813677i	$-0.302538\pi$
$809$	940.571			1.16263			0.581317	+	0.813677i	$0.302538\pi$
$810$		0			0
$811$	884.720	+	510.794i	1.09090	+	0.629832i	0.933816	−	0.357753i	$-0.116457\pi$
$811$	884.720	+	510.794i	1.09090	+	0.629832i	0.157085	+	0.987585i	$0.449790\pi$
$812$	123.756	−	71.4507i	0.152409	−	0.0879935i
$813$		0			0
$814$	479.940	+	831.281i	0.589607	+	1.02123i
$815$	−134.805	−	233.489i	−0.165405	−	0.286490i
$816$		0			0
$817$	1185.47	−	207.361i	1.45101	−	0.253808i
$818$	−1574.22			−1.92447
$819$		0			0
$820$	−52.7764	+	30.4705i	−0.0643615	+	0.0371591i
$821$	−638.601	+	1106.09i	−0.777833	+	1.34725i	0.155356	+	0.987859i	$0.450348\pi$
$821$	−638.601	+	1106.09i	−0.777833	+	1.34725i	−0.933188	+	0.359387i	$0.882986\pi$
$822$		0			0
$823$	−242.137	+	419.393i	−0.294212	+	0.509590i	−0.974801	−	0.223075i	$-0.928391\pi$
$823$	−242.137	+	419.393i	−0.294212	+	0.509590i	0.680589	+	0.732665i	$0.261724\pi$
$824$	687.086			0.833842
$825$		0			0
$826$	67.3266	−	116.613i	0.0815092	−	0.141178i
$827$	769.904	+	444.504i	0.930961	+	0.537490i	0.887115	−	0.461548i	$-0.152706\pi$
$827$	769.904	+	444.504i	0.930961	+	0.537490i	0.0438453	+	0.999038i	$0.486039\pi$
$828$		0			0
$829$		−	188.951i		−	0.227927i	−0.993485	−	0.113963i	$-0.963645\pi$
$829$		−	188.951i		−	0.227927i	0.993485	−	0.113963i	$-0.0363547\pi$
$830$	213.445	+	123.232i	0.257162	+	0.148473i
$831$		0			0
$832$	−484.577	−	279.771i	−0.582424	−	0.336263i
$833$	−298.396	−	516.836i	−0.358218	−	0.620452i
$834$		0			0
$835$		−	201.048i		−	0.240776i
$836$	1154.58	+	1379.80i	1.38108	+	1.65048i
$837$		0			0
$838$	1079.44	−	623.216i	1.28812	−	0.743694i
$839$	−146.484	+	84.5725i	−0.174593	+	0.100802i	−0.584750	−	0.811214i	$-0.698807\pi$
$839$	−146.484	+	84.5725i	−0.174593	+	0.100802i	0.410157	+	0.912015i	$0.365474\pi$
$840$		0			0
$841$	203.361	+	352.232i	0.241809	+	0.418825i
$842$	574.875	−	995.713i	0.682750	−	1.18256i
$843$		0			0
$844$		−	2330.47i		−	2.76121i
$845$	29.6090	−	51.2843i	0.0350402	−	0.0606915i
$846$		0			0
$847$	1.80022			0.00212540
$848$			668.005i			0.787742i
$849$		0			0
$850$	893.245	−	515.715i	1.05088	−	0.606724i
$851$	−873.960	−	504.581i	−1.02698	−	0.592927i
$852$		0			0
$853$	253.769	+	439.541i	0.297502	+	0.515288i	0.975564	−	0.219716i	$-0.0705132\pi$
$853$	253.769	+	439.541i	0.297502	+	0.515288i	−0.678062	+	0.735005i	$0.737180\pi$
$854$			120.987i			0.141671i
$855$		0			0
$856$	−568.812			−0.664500
$857$	761.557	−	439.685i	0.888631	−	0.513051i	0.0151366	−	0.999885i	$-0.495182\pi$
$857$	761.557	−	439.685i	0.888631	−	0.513051i	0.873494	+	0.486834i	$0.161848\pi$
$858$		0			0
$859$	−584.193	+	1011.85i	−0.680085	+	1.17794i	0.294869	+	0.955538i	$0.404724\pi$
$859$	−584.193	+	1011.85i	−0.680085	+	1.17794i	−0.974955	+	0.222404i	$0.928609\pi$
$860$	286.232	+	495.769i	0.332828	+	0.576475i
$861$		0			0
$862$	−677.180			−0.785592
$863$			1078.16i			1.24932i	0.780899	+	0.624658i	$0.214762\pi$
$863$			1078.16i			1.24932i	−0.780899	+	0.624658i	$0.785238\pi$
$864$		0			0
$865$	−180.119	−	103.992i	−0.208230	−	0.120222i
$866$	−1035.90			−1.19619
$867$		0			0
$868$	−55.6724	−	32.1425i	−0.0641387	−	0.0370305i
$869$	1167.66	−	674.147i	1.34368	−	0.775773i
$870$		0			0
$871$	−65.9653	−	114.255i	−0.0757352	−	0.131177i
$872$	639.570	+	1107.77i	0.733452	+	1.27038i
$873$		0			0
$874$	−2614.83	−	955.769i	−2.99180	−	1.09356i
$875$	−24.8611			−0.0284126
$876$		0			0
$877$	−884.225	+	510.507i	−1.00824	+	0.582106i	−0.910675	−	0.413123i	$-0.864438\pi$
$877$	−884.225	+	510.507i	−1.00824	+	0.582106i	−0.0975626	+	0.995229i	$0.531105\pi$
$878$	412.672	−	714.768i	0.470013	−	0.814087i
$879$		0			0
$880$	−130.727	+	226.425i	−0.148553	+	0.257301i
$881$	−111.944			−0.127065			−0.0635325	−	0.997980i	$-0.520237\pi$
$881$	−111.944			−0.127065			−0.0635325	+	0.997980i	$0.520237\pi$
$882$		0			0
$883$	−670.488	+	1161.32i	−0.759330	+	1.31520i	0.183863	+	0.982952i	$0.441140\pi$
$883$	−670.488	+	1161.32i	−0.759330	+	1.31520i	−0.943193	+	0.332246i	$0.892194\pi$
$884$	−1346.12	−	777.185i	−1.52277	−	0.879169i
$885$		0			0
$886$			1414.87i			1.59692i
$887$	−1218.13	−	703.287i	−1.37331	−	0.792882i	−0.381969	−	0.924175i	$-0.624754\pi$
$887$	−1218.13	−	703.287i	−1.37331	−	0.792882i	−0.991344	+	0.131293i	$0.958087\pi$
$888$		0			0
$889$	−17.0497	−	9.84365i	−0.0191785	−	0.0110727i
$890$	289.782	+	501.917i	0.325598	+	0.563952i
$891$		0			0
$892$		−	3402.99i		−	3.81501i
$893$	−492.796	−	588.923i	−0.551843	−	0.659489i
$894$		0			0
$895$	157.657	−	91.0235i	0.176153	−	0.101702i
$896$	78.1361	−	45.1119i	0.0872055	−	0.0503481i
$897$		0			0
$898$	−430.477	−	745.608i	−0.479373	−	0.830299i
$899$	280.647	−	486.095i	0.312177	−	0.540706i
$900$		0			0
$901$		−	372.312i		−	0.413221i
$902$	133.024	−	230.405i	0.147477	−	0.255438i
$903$		0			0
$904$	316.154			0.349728
$905$		−	2.09893i		−	0.00231926i
$906$		0			0
$907$	1155.56	−	667.165i	1.27405	−	0.735574i	0.298303	−	0.954471i	$-0.403579\pi$
$907$	1155.56	−	667.165i	1.27405	−	0.735574i	0.975748	+	0.218898i	$0.0702461\pi$
$908$	2487.77	+	1436.31i	2.73983	+	1.58184i
$909$		0			0
$910$	13.4653	+	23.3226i	0.0147971	+	0.0256293i
$911$		−	378.747i		−	0.415749i	−0.978156	−	0.207874i	$-0.933345\pi$
$911$		−	378.747i		−	0.415749i	0.978156	−	0.207874i	$-0.0666545\pi$
$912$		0			0
$913$	−731.041			−0.800703
$914$	12.5086	−	7.22185i	0.0136856	−	0.00790137i
$915$		0			0
$916$	−942.894	+	1633.14i	−1.02936	+	1.78290i
$917$	−49.1267	−	85.0899i	−0.0535733	−	0.0927916i
$918$		0			0
$919$	−452.655			−0.492552			−0.246276	−	0.969200i	$-0.579207\pi$
$919$	−452.655			−0.492552			−0.246276	+	0.969200i	$0.579207\pi$
$920$		−	699.427i		−	0.760247i
$921$		0			0
$922$	2396.59	+	1383.67i	2.59934	+	1.50073i
$923$	−731.390			−0.792406
$924$		0			0
$925$	502.761	+	290.269i	0.543525	+	0.313804i
$926$	−672.929	+	388.516i	−0.726705	+	0.419564i
$927$		0			0
$928$	−252.386	−	437.146i	−0.271968	−	0.471062i
$929$	−823.417	−	1426.20i	−0.886348	−	1.53520i	−0.844161	−	0.536089i	$-0.819901\pi$
$929$	−823.417	−	1426.20i	−0.886348	−	1.53520i	−0.0421865	−	0.999110i	$-0.513432\pi$
$930$		0			0
$931$	318.130	−	870.354i	0.341708	−	0.934859i
$932$	1980.31			2.12480
$933$		0			0
$934$	−1364.29	+	787.675i	−1.46070	+	0.843335i
$935$	72.8604	−	126.198i	0.0779255	−	0.134971i
$936$		0			0
$937$	558.953	−	968.136i	0.596535	−	1.03323i	−0.396793	−	0.917908i	$-0.629877\pi$
$937$	558.953	−	968.136i	0.596535	−	1.03323i	0.993328	−	0.115321i	$-0.0367897\pi$
$938$	14.8415			0.0158225
$939$		0			0
$940$	182.638	−	316.338i	0.194295	−	0.336530i
$941$	−1529.54	−	883.078i	−1.62544	−	0.938446i	−0.985431	−	0.170076i	$-0.945599\pi$
$941$	−1529.54	−	883.078i	−1.62544	−	0.938446i	−0.640006	−	0.768370i	$-0.721068\pi$
$942$		0			0
$943$			279.708i			0.296615i
$944$	−1518.75	−	876.852i	−1.60885	−	0.928869i
$945$		0			0
$946$	−2164.37	−	1249.60i	−2.28791	−	1.32093i
$947$	650.983	+	1127.54i	0.687416	+	1.19064i	0.972671	+	0.232187i	$0.0745883\pi$
$947$	650.983	+	1127.54i	0.687416	+	1.19064i	−0.285255	+	0.958452i	$0.592078\pi$
$948$		0			0
$949$			1702.13i			1.79360i
$950$	1504.23	+	549.823i	1.58340	+	0.578761i
$951$		0			0
$952$	79.9783	−	46.1755i	0.0840108	−	0.0485036i
$953$	−727.416	+	419.974i	−0.763291	+	0.440686i	−0.830476	−	0.557054i	$-0.811931\pi$
$953$	−727.416	+	419.974i	−0.763291	+	0.440686i	0.0671852	+	0.997741i	$0.478598\pi$
$954$		0			0
$955$	−6.49689	−	11.2529i	−0.00680302	−	0.0117832i
$956$	1368.72	−	2370.69i	1.43171	−	2.47980i
$957$		0			0
$958$		−	2230.19i		−	2.32796i
$959$	43.0212	−	74.5150i	0.0448605	−	0.0777007i
$960$		0			0
$961$	708.499			0.737252
$962$		−	1287.68i		−	1.33855i
$963$		0			0
$964$	1711.05	−	987.874i	1.77495	−	1.02477i
$965$	262.146	+	151.350i	0.271654	+	0.156839i
$966$		0			0
$967$	−370.759	−	642.174i	−0.383412	−	0.664089i	0.608136	−	0.793833i	$-0.291918\pi$
$967$	−370.759	−	642.174i	−0.383412	−	0.664089i	−0.991547	+	0.129744i	$0.958584\pi$
$968$		−	59.6581i		−	0.0616302i
$969$		0			0
$970$	361.323			0.372498
$971$	1265.77	−	730.790i	1.30357	−	0.752616i	0.322554	−	0.946551i	$-0.395458\pi$
$971$	1265.77	−	730.790i	1.30357	−	0.752616i	0.981014	+	0.193935i	$0.0621251\pi$
$972$		0			0
$973$	17.1097	−	29.6349i	0.0175845	−	0.0304573i
$974$	−1400.07	−	2425.00i	−1.43745	−	2.48973i
$975$		0			0
$976$	1575.72			1.61447
$977$			340.557i			0.348574i	0.984695	+	0.174287i	$0.0557621\pi$
$977$			340.557i			0.348574i	−0.984695	+	0.174287i	$0.944238\pi$
$978$		0			0
$979$	−1488.74	−	859.526i	−1.52068	−	0.877963i
$980$	440.798			0.449794
$981$		0			0
$982$	−415.455	−	239.863i	−0.423071	−	0.244260i
$983$	397.752	−	229.642i	0.404631	−	0.233614i	−0.283849	−	0.958869i	$-0.591612\pi$
$983$	397.752	−	229.642i	0.404631	−	0.233614i	0.688480	+	0.725255i	$0.258278\pi$
$984$		0			0
$985$	163.586	+	283.339i	0.166077	+	0.287654i
$986$	763.375	+	1322.20i	0.774214	+	1.34098i
$987$		0			0
$988$	−415.862	−	2377.47i	−0.420913	−	2.40634i
$989$	2627.51			2.65673
$990$		0			0
$991$	108.241	−	62.4928i	0.109224	−	0.0630603i	−0.444393	−	0.895832i	$-0.646581\pi$
$991$	108.241	−	62.4928i	0.109224	−	0.0630603i	0.553617	+	0.832772i	$0.313247\pi$
$992$	−113.537	+	196.652i	−0.114453	+	0.198238i
$993$		0			0
$994$	41.1387	−	71.2544i	0.0413870	−	0.0716845i
$995$	163.625			0.164448
$996$		0			0
$997$	−122.478	+	212.139i	−0.122847	+	0.212777i	−0.920889	−	0.389824i	$-0.872536\pi$
$997$	−122.478	+	212.139i	−0.122847	+	0.212777i	0.798042	+	0.602601i	$0.205869\pi$
$998$	−1447.41	−	835.664i	−1.45031	−	0.837339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.f.145.4	yes	8
3.2	odd	2	inner	171.3.p.f.145.1	yes	8
19.8	odd	6	inner	171.3.p.f.46.4	yes	8
57.8	even	6	inner	171.3.p.f.46.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.p.f.46.1	✓	8	57.8	even	6	inner
171.3.p.f.46.4	yes	8	19.8	odd	6	inner
171.3.p.f.145.1	yes	8	3.2	odd	2	inner
171.3.p.f.145.4	yes	8	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.05907 - 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(-0.533068 - 0.923301i) q^{5} +0.477226 q^{7} -15.8150i q^{8} +O(q^{10})\)	\(q+(3.05907 - 1.76616i) q^{2} +(4.23861 - 7.34149i) q^{4} +(-0.533068 - 0.923301i) q^{5} +0.477226 q^{7} -15.8150i q^{8} +(-3.26139 - 1.88296i) q^{10} +11.1702 q^{11} +(-12.9772 - 7.49240i) q^{13} +(1.45987 - 0.842855i) q^{14} +(-10.9772 - 19.0131i) q^{16} +(6.11814 + 10.5969i) q^{17} +(-6.52277 + 17.8453i) q^{19} -9.03788 q^{20} +(34.1703 - 19.7282i) q^{22} +(-20.7411 + 35.9246i) q^{23} +(11.9317 - 20.6663i) q^{25} -52.9310 q^{26} +(2.02277 - 3.50355i) q^{28} +(30.5907 + 17.6616i) q^{29} -15.8903i q^{31} +(-12.3756 - 7.14507i) q^{32} +(37.4317 + 21.6112i) q^{34} +(-0.254394 - 0.440623i) q^{35} +24.3276i q^{37} +(11.5639 + 66.1102i) q^{38} +(-14.6020 + 8.43045i) q^{40} +(5.83947 - 3.37142i) q^{41} +(-31.6703 - 54.8546i) q^{43} +(47.3459 - 82.0056i) q^{44} +146.528i q^{46} +(-20.2080 + 35.0013i) q^{47} -48.7723 q^{49} -84.2928i q^{50} +(-110.011 + 63.5148i) q^{52} +(-26.3505 - 15.2134i) q^{53} +(-5.95445 - 10.3134i) q^{55} -7.54730i q^{56} +124.772 q^{58} +(69.1775 - 39.9396i) q^{59} +(-35.8861 + 62.1566i) q^{61} +(-28.0647 - 48.6095i) q^{62} +37.3406 q^{64} +15.9758i q^{65} +(7.62474 + 4.40215i) q^{67} +103.730 q^{68} +(-1.55642 - 0.898598i) q^{70} +(42.2697 - 24.4044i) q^{71} +(-56.7950 - 98.3719i) q^{73} +(42.9663 + 74.4199i) q^{74} +(103.363 + 123.526i) q^{76} +5.33068 q^{77} +(104.534 - 60.3525i) q^{79} +(-11.7032 + 20.2706i) q^{80} +(11.9089 - 20.6268i) q^{82} -65.4460 q^{83} +(6.52277 - 11.2978i) q^{85} +(-193.763 - 111.869i) q^{86} -176.655i q^{88} +(-133.279 - 76.9484i) q^{89} +(-6.19306 - 3.57557i) q^{91} +(175.827 + 304.541i) q^{92} +142.762i q^{94} +(19.9536 - 3.49026i) q^{95} +(-83.0911 + 47.9727i) q^{97} +(-149.198 + 86.1394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) \) 8 * q + 12 * q^4 - 40 * q^7	\( 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 - 40 * q^7 - 48 * q^10 - 60 * q^13 - 44 * q^16 - 96 * q^19 + 120 * q^22 - 36 * q^25 + 60 * q^28 + 168 * q^34 + 168 * q^40 - 100 * q^43 + 48 * q^49 - 420 * q^52 + 40 * q^55 + 560 * q^58 - 68 * q^61 - 8 * q^64 - 180 * q^67 + 360 * q^70 - 60 * q^73 + 564 * q^76 + 420 * q^79 - 80 * q^82 + 96 * q^85 + 60 * q^91 - 840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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