LMFDB - Embedded newform 180.3.f.h.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(19,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("180.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.f (of order $2$, degree $1$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-1.52274 + 1.29664i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.3.f.h.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52274 + 1.29664i) q^{2} +(0.637459 - 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +O(q^{10})$	\(q+(-1.52274 + 1.29664i) q^{2} +(0.637459 - 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +(3.14704 - 9.49190i) q^{10} -15.7955i q^{11} +5.18655i q^{13} +(1.27492 - 1.08561i) q^{14} +(-15.1873 - 5.03449i) q^{16} -27.3586i q^{17} -17.9667i q^{19} +(7.51545 + 18.5342i) q^{20} +(20.4811 + 24.0524i) q^{22} -19.1101 q^{23} +(11.5498 - 22.1721i) q^{25} +(-6.72508 - 7.89776i) q^{26} +(-0.533714 + 3.30621i) q^{28} +45.6495 q^{29} -13.6243i q^{31} +(29.6542 - 12.0262i) q^{32} +(35.4743 + 41.6600i) q^{34} +(3.57919 - 2.17123i) q^{35} -15.5597i q^{37} +(23.2964 + 27.3586i) q^{38} +(-35.4763 - 18.4780i) q^{40} -13.2990 q^{41} -27.9430 q^{43} +(-62.3746 - 10.0690i) q^{44} +(29.0997 - 24.7789i) q^{46} -55.6558 q^{47} -48.2990 q^{49} +(11.1618 + 48.7382i) q^{50} +(20.4811 + 3.30621i) q^{52} +15.5597i q^{53} +(40.9621 + 67.5245i) q^{55} +(-3.47425 - 5.72653i) q^{56} +(-69.5122 + 59.1909i) q^{58} +87.6625i q^{59} +38.0000 q^{61} +(17.6658 + 20.7462i) q^{62} +(-29.5619 + 56.7635i) q^{64} +(-13.4502 - 22.1721i) q^{65} -92.2015 q^{67} +(-108.036 - 17.4400i) q^{68} +(-2.63487 + 7.94713i) q^{70} -130.707i q^{71} +54.7173i q^{73} +(20.1752 + 23.6933i) q^{74} +(-70.9485 - 11.4531i) q^{76} +13.2249i q^{77} +13.6243i q^{79} +(77.9803 - 17.8628i) q^{80} +(20.2509 - 17.2440i) q^{82} +59.0048 q^{83} +(70.9485 + 116.956i) q^{85} +(42.5498 - 36.2319i) q^{86} +(108.036 - 65.5448i) q^{88} -39.8007 q^{89} -4.34246i q^{91} +(-12.1819 + 75.4635i) q^{92} +(84.7492 - 72.1654i) q^{94} +(46.5927 + 76.8064i) q^{95} -168.821i q^{97} +(73.5467 - 62.6263i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4} - 4 q^{5}+O(q^{10}) $ 8 * q - 10 * q^4 - 4 * q^5	$ 8 q - 10 q^{4} - 4 q^{5} - 42 q^{10} - 20 q^{14} - 46 q^{16} - 52 q^{20} + 32 q^{25} - 84 q^{26} + 184 q^{29} + 12 q^{34} - 6 q^{40} + 256 q^{41} - 348 q^{44} + 112 q^{46} - 24 q^{49} - 72 q^{50} + 244 q^{56} + 304 q^{61} - 10 q^{64} - 168 q^{65} - 104 q^{70} + 252 q^{74} - 24 q^{76} + 308 q^{80} + 24 q^{85} + 280 q^{86} - 560 q^{89} + 376 q^{94}+O(q^{100}) $ 8 * q - 10 * q^4 - 4 * q^5 - 42 * q^10 - 20 * q^14 - 46 * q^16 - 52 * q^20 + 32 * q^25 - 84 * q^26 + 184 * q^29 + 12 * q^34 - 6 * q^40 + 256 * q^41 - 348 * q^44 + 112 * q^46 - 24 * q^49 - 72 * q^50 + 244 * q^56 + 304 * q^61 - 10 * q^64 - 168 * q^65 - 104 * q^70 + 252 * q^74 - 24 * q^76 + 308 * q^80 + 24 * q^85 + 280 * q^86 - 560 * q^89 + 376 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.52274	+	1.29664i	−0.761369	+	0.648319i
$2$	−1.52274	+	1.29664i	−0.761369	+	0.648319i
$3$		0			0
$3$		0			0
$4$	0.637459	−	3.94888i	0.159365	−	0.987220i
$5$	−4.27492	+	2.59328i	−0.854983	+	0.518655i
$5$	−4.27492	+	2.59328i	−0.854983	+	0.518655i
$6$		0			0
$7$	−0.837253			−0.119608			−0.0598038	−	0.998210i	$-0.519048\pi$
$7$	−0.837253			−0.119608			−0.0598038	+	0.998210i	$0.519048\pi$
$8$	4.14959	+	6.83966i	0.518698	+	0.854957i
$9$		0			0
$10$	3.14704	−	9.49190i	0.314704	−	0.949190i
$11$		−	15.7955i		−	1.43596i	−0.696066	−	0.717978i	$-0.745068\pi$
$11$		−	15.7955i		−	1.43596i	0.696066	−	0.717978i	$-0.254932\pi$
$12$		0			0
$13$			5.18655i			0.398966i	0.979901	+	0.199483i	$0.0639262\pi$
$13$			5.18655i			0.398966i	−0.979901	+	0.199483i	$0.936074\pi$
$14$	1.27492	−	1.08561i	0.0910655	−	0.0775439i
$15$		0			0
$16$	−15.1873	−	5.03449i	−0.949206	−	0.314656i
$17$		−	27.3586i		−	1.60933i	−0.593728	−	0.804666i	$-0.702344\pi$
$17$		−	27.3586i		−	1.60933i	0.593728	−	0.804666i	$-0.297656\pi$
$18$		0			0
$19$		−	17.9667i		−	0.945618i	−0.881165	−	0.472809i	$-0.843240\pi$
$19$		−	17.9667i		−	0.945618i	0.881165	−	0.472809i	$-0.156760\pi$
$20$	7.51545	+	18.5342i	0.375773	+	0.926712i
$21$		0			0
$22$	20.4811	+	24.0524i	0.930958	+	1.09329i
$23$	−19.1101			−0.830874			−0.415437	−	0.909622i	$-0.636371\pi$
$23$	−19.1101			−0.830874			−0.415437	+	0.909622i	$0.636371\pi$
$24$		0			0
$25$	11.5498	−	22.1721i	0.461993	−	0.886883i
$26$	−6.72508	−	7.89776i	−0.258657	−	0.303760i
$27$		0			0
$28$	−0.533714	+	3.30621i	−0.0190612	+	0.118079i
$29$	45.6495			1.57412			0.787060	−	0.616876i	$-0.211602\pi$
$29$	45.6495			1.57412			0.787060	+	0.616876i	$0.211602\pi$
$30$		0			0
$31$		−	13.6243i		−	0.439493i	−0.975557	−	0.219747i	$-0.929477\pi$
$31$		−	13.6243i		−	0.439493i	0.975557	−	0.219747i	$-0.0705230\pi$
$32$	29.6542	−	12.0262i	0.926693	−	0.375819i
$33$		0			0
$34$	35.4743	+	41.6600i	1.04336	+	1.22529i
$35$	3.57919	−	2.17123i	0.102263	−	0.0620351i
$36$		0			0
$37$		−	15.5597i		−	0.420531i	−0.977644	−	0.210266i	$-0.932567\pi$
$37$		−	15.5597i		−	0.420531i	0.977644	−	0.210266i	$-0.0674329\pi$
$38$	23.2964	+	27.3586i	0.613062	+	0.719964i
$39$		0			0
$40$	−35.4763	−	18.4780i	−0.886907	−	0.461949i
$41$	−13.2990			−0.324366			−0.162183	−	0.986761i	$-0.551853\pi$
$41$	−13.2990			−0.324366			−0.162183	+	0.986761i	$0.551853\pi$
$42$		0			0
$43$	−27.9430			−0.649837			−0.324918	−	0.945742i	$-0.605337\pi$
$43$	−27.9430			−0.649837			−0.324918	+	0.945742i	$0.605337\pi$
$44$	−62.3746	−	10.0690i	−1.41760	−	0.228841i
$45$		0			0
$46$	29.0997	−	24.7789i	0.632601	−	0.538672i
$47$	−55.6558			−1.18417			−0.592083	−	0.805877i	$-0.701694\pi$
$47$	−55.6558			−1.18417			−0.592083	+	0.805877i	$0.701694\pi$
$48$		0			0
$49$	−48.2990			−0.985694
$50$	11.1618	+	48.7382i	0.223236	+	0.974764i
$51$		0			0
$52$	20.4811	+	3.30621i	0.393867	+	0.0635810i
$53$			15.5597i			0.293578i	0.989168	+	0.146789i	$0.0468939\pi$
$53$			15.5597i			0.293578i	−0.989168	+	0.146789i	$0.953106\pi$
$54$		0			0
$55$	40.9621	+	67.5245i	0.744766	+	1.22772i
$56$	−3.47425	−	5.72653i	−0.0620403	−	0.102259i
$57$		0			0
$58$	−69.5122	+	59.1909i	−1.19849	+	1.02053i
$59$			87.6625i			1.48581i	0.669400	+	0.742903i	$0.266551\pi$
$59$			87.6625i			1.48581i	−0.669400	+	0.742903i	$0.733449\pi$
$60$		0			0
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	17.6658	+	20.7462i	0.284932	+	0.334616i
$63$		0			0
$64$	−29.5619	+	56.7635i	−0.461904	+	0.886930i
$65$	−13.4502	−	22.1721i	−0.206926	−	0.341109i
$66$		0			0
$67$	−92.2015			−1.37614			−0.688071	−	0.725643i	$-0.741542\pi$
$67$	−92.2015			−1.37614			−0.688071	+	0.725643i	$0.741542\pi$
$68$	−108.036	−	17.4400i	−1.58876	−	0.256471i
$69$		0			0
$70$	−2.63487	+	7.94713i	−0.0376409	+	0.113530i
$71$		−	130.707i		−	1.84094i	−0.390816	−	0.920469i	$-0.627807\pi$
$71$		−	130.707i		−	1.84094i	0.390816	−	0.920469i	$-0.372193\pi$
$72$		0			0
$73$			54.7173i			0.749552i	0.927115	+	0.374776i	$0.122280\pi$
$73$			54.7173i			0.749552i	−0.927115	+	0.374776i	$0.877720\pi$
$74$	20.1752	+	23.6933i	0.272638	+	0.320179i
$75$		0			0
$76$	−70.9485	−	11.4531i	−0.933533	−	0.150698i
$77$			13.2249i			0.171751i
$78$		0			0
$79$			13.6243i			0.172459i	0.996275	+	0.0862297i	$0.0274819\pi$
$79$			13.6243i			0.172459i	−0.996275	+	0.0862297i	$0.972518\pi$
$80$	77.9803	−	17.8628i	0.974753	−	0.223285i
$81$		0			0
$82$	20.2509	−	17.2440i	0.246962	−	0.210293i
$83$	59.0048			0.710901			0.355451	−	0.934695i	$-0.384327\pi$
$83$	59.0048			0.710901			0.355451	+	0.934695i	$0.384327\pi$
$84$		0			0
$85$	70.9485	+	116.956i	0.834688	+	1.37595i
$86$	42.5498	−	36.2319i	0.494766	−	0.421302i
$87$		0			0
$88$	108.036	−	65.5448i	1.22768	−	0.744828i
$89$	−39.8007			−0.447198			−0.223599	−	0.974681i	$-0.571781\pi$
$89$	−39.8007			−0.447198			−0.223599	+	0.974681i	$0.571781\pi$
$90$		0			0
$91$		−	4.34246i		−	0.0477193i
$92$	−12.1819	+	75.4635i	−0.132412	+	0.820255i
$93$		0			0
$94$	84.7492	−	72.1654i	0.901587	−	0.767717i
$95$	46.5927	+	76.8064i	0.490450	+	0.808488i
$96$		0			0
$97$		−	168.821i		−	1.74043i	−0.492675	−	0.870214i	$-0.663981\pi$
$97$		−	168.821i		−	1.74043i	0.492675	−	0.870214i	$-0.336019\pi$
$98$	73.5467	−	62.6263i	0.750477	−	0.639044i
$99$		0			0
$100$	−80.1923	−	59.7427i	−0.801923	−	0.597427i
$101$	−44.5498			−0.441087			−0.220544	−	0.975377i	$-0.570783\pi$
$101$	−44.5498			−0.441087			−0.220544	+	0.975377i	$0.570783\pi$
$102$		0			0
$103$	126.466			1.22782			0.613911	−	0.789375i	$-0.289595\pi$
$103$	126.466			1.22782			0.613911	+	0.789375i	$0.289595\pi$
$104$	−35.4743	+	21.5220i	−0.341099	+	0.206943i
$105$		0			0
$106$	−20.1752	−	23.6933i	−0.190333	−	0.223521i
$107$	104.383			0.975546			0.487773	−	0.872971i	$-0.337809\pi$
$107$	104.383			0.975546			0.487773	+	0.872971i	$0.337809\pi$
$108$		0			0
$109$	−0.501656			−0.00460235			−0.00230117	−	0.999997i	$-0.500732\pi$
$109$	−0.501656			−0.00460235			−0.00230117	+	0.999997i	$0.500732\pi$
$110$	−149.929	−	49.7090i	−1.36300	−	0.451900i
$111$		0			0
$112$	12.7156	+	4.21515i	0.113532	+	0.0376352i
$113$			16.9855i			0.150314i	0.997172	+	0.0751572i	$0.0239459\pi$
$113$			16.9855i			0.150314i	−0.997172	+	0.0751572i	$0.976054\pi$
$114$		0			0
$115$	81.6941	−	49.5578i	0.710384	−	0.430937i
$116$	29.0997	−	180.264i	0.250859	−	1.55400i
$117$		0			0
$118$	−113.667	−	133.487i	−0.963276	−	1.13125i
$119$			22.9061i			0.192488i
$120$		0			0
$121$	−128.498			−1.06197
$122$	−57.8640	+	49.2723i	−0.474295	+	0.403871i
$123$		0			0
$124$	−53.8007	−	8.68492i	−0.433876	−	0.0700397i
$125$	8.12376	+	124.736i	0.0649901	+	0.997886i
$126$		0			0
$127$	−8.45598			−0.0665825			−0.0332913	−	0.999446i	$-0.510599\pi$
$127$	−8.45598			−0.0665825			−0.0332913	+	0.999446i	$0.510599\pi$
$128$	−28.5867	−	124.767i	−0.223334	−	0.974742i
$129$		0			0
$130$	49.2302	+	16.3223i	0.378694	+	0.125556i
$131$			51.7290i			0.394878i	0.980315	+	0.197439i	$0.0632624\pi$
$131$			51.7290i			0.394878i	−0.980315	+	0.197439i	$0.936738\pi$
$132$		0			0
$133$			15.0427i			0.113103i
$134$	140.399	−	119.552i	1.04775	−	0.892179i
$135$		0			0
$136$	187.124	−	113.527i	1.37591	−	0.834757i
$137$			53.8083i			0.392762i	0.980528	+	0.196381i	$0.0629189\pi$
$137$			53.8083i			0.392762i	−0.980528	+	0.196381i	$0.937081\pi$
$138$		0			0
$139$		−	13.6243i		−	0.0980165i	−0.998798	−	0.0490082i	$-0.984394\pi$
$139$		−	13.6243i		−	0.0980165i	0.998798	−	0.0490082i	$-0.0156061\pi$
$140$	−6.29234	−	15.5179i	−0.0449453	−	0.110842i
$141$		0			0
$142$	169.479	+	199.032i	1.19352	+	1.40163i
$143$	81.9243			0.572897
$144$		0			0
$145$	−195.148	+	118.382i	−1.34585	+	0.816426i
$146$	−70.9485	−	83.3200i	−0.485949	−	0.570685i
$147$		0			0
$148$	−61.4432	−	9.91864i	−0.415157	−	0.0670178i
$149$	33.6495			0.225836			0.112918	−	0.993604i	$-0.463980\pi$
$149$	33.6495			0.225836			0.112918	+	0.993604i	$0.463980\pi$
$150$		0			0
$151$		−	139.988i		−	0.927076i	−0.886077	−	0.463538i	$-0.846580\pi$
$151$		−	139.988i		−	0.927076i	0.886077	−	0.463538i	$-0.153420\pi$
$152$	122.886	−	74.5546i	0.808463	−	0.490490i
$153$		0			0
$154$	−17.1478	−	20.1380i	−0.111350	−	0.130766i
$155$	35.3315	+	58.2427i	0.227945	+	0.375759i
$156$		0			0
$157$			21.2631i			0.135434i	0.997705	+	0.0677170i	$0.0215715\pi$
$157$			21.2631i			0.135434i	−0.997705	+	0.0677170i	$0.978428\pi$
$158$	−17.6658	−	20.7462i	−0.111809	−	0.131305i
$159$		0			0
$160$	−95.5819	+	128.313i	−0.597387	+	0.801953i
$161$	16.0000			0.0993789
$162$		0			0
$163$	210.211			1.28964			0.644819	−	0.764335i	$-0.276933\pi$
$163$	210.211			1.28964			0.644819	+	0.764335i	$0.276933\pi$
$164$	−8.47757	+	52.5162i	−0.0516925	+	0.320221i
$165$		0			0
$166$	−89.8488	+	76.5079i	−0.541258	+	0.460891i
$167$	−238.384			−1.42745			−0.713725	−	0.700426i	$-0.752994\pi$
$167$	−238.384			−1.42745			−0.713725	+	0.700426i	$0.752994\pi$
$168$		0			0
$169$	142.100			0.840826
$170$	−259.685	−	86.0986i	−1.52756	−	0.506462i
$171$		0			0
$172$	−17.8125	+	110.343i	−0.103561	+	0.641532i
$173$			2.33481i			0.0134960i	0.999977	+	0.00674800i	$0.00214797\pi$
$173$			2.33481i			0.0134960i	−0.999977	+	0.00674800i	$0.997852\pi$
$174$		0			0
$175$	−9.67014	+	18.5637i	−0.0552579	+	0.106078i
$176$	−79.5224	+	239.891i	−0.451832	+	1.36302i
$177$		0			0
$178$	60.6060	−	51.6071i	0.340483	−	0.289927i
$179$		−	227.054i		−	1.26846i	−0.773145	−	0.634229i	$-0.781318\pi$
$179$		−	227.054i		−	1.26846i	0.773145	−	0.634229i	$-0.218682\pi$
$180$		0			0
$181$	114.096			0.630367			0.315183	−	0.949031i	$-0.397934\pi$
$181$	114.096			0.630367			0.315183	+	0.949031i	$0.397934\pi$
$182$	5.63060	+	6.61243i	0.0309374	+	0.0363320i
$183$		0			0
$184$	−79.2990	−	130.707i	−0.430973	−	0.710362i
$185$	40.3505	+	66.5163i	0.218111	+	0.359547i
$186$		0			0
$187$	−432.144			−2.31093
$188$	−35.4783	+	219.778i	−0.188714	+	1.16903i
$189$		0			0
$190$	−170.539	−	56.5420i	−0.897571	−	0.297589i
$191$			139.392i			0.729798i	0.931047	+	0.364899i	$0.118897\pi$
$191$			139.392i			0.729798i	−0.931047	+	0.364899i	$0.881103\pi$
$192$		0			0
$193$		−	182.046i		−	0.943245i	−0.881801	−	0.471623i	$-0.843669\pi$
$193$		−	182.046i		−	0.943245i	0.881801	−	0.471623i	$-0.156331\pi$
$194$	218.900	+	257.071i	1.12835	+	1.32511i
$195$		0			0
$196$	−30.7886	+	190.727i	−0.157085	+	0.973097i
$197$		−	258.027i		−	1.30978i	−0.755724	−	0.654890i	$-0.772715\pi$
$197$		−	258.027i		−	1.30978i	0.755724	−	0.654890i	$-0.227285\pi$
$198$		0			0
$199$			256.474i			1.28881i	0.764683	+	0.644407i	$0.222896\pi$
$199$			256.474i			1.28881i	−0.764683	+	0.644407i	$0.777104\pi$
$200$	199.577	−	13.0080i	0.997883	−	0.0650401i
$201$		0			0
$202$	67.8377	−	57.7650i	0.335830	−	0.285965i
$203$	−38.2202			−0.188277
$204$		0			0
$205$	56.8522	−	34.4880i	0.277328	−	0.168234i
$206$	−192.574	+	163.980i	−0.934825	+	0.796020i
$207$		0			0
$208$	26.1117	−	78.7697i	0.125537	−	0.378700i
$209$	−283.794			−1.35787
$210$		0			0
$211$			211.855i			1.00405i	0.864852	+	0.502027i	$0.167412\pi$
$211$			211.855i			1.00405i	−0.864852	+	0.502027i	$0.832588\pi$
$212$	61.4432	+	9.91864i	0.289826	+	0.0467860i
$213$		0			0
$214$	−158.949	+	135.348i	−0.742750	+	0.632465i
$215$	119.454	−	72.4639i	0.555600	−	0.337041i
$216$		0			0
$217$			11.4070i			0.0525667i
$218$	0.763890	−	0.650466i	0.00350408	−	0.00298379i
$219$		0			0
$220$	292.758	−	118.710i	1.33072	−	0.539593i
$221$	141.897			0.642068
$222$		0			0
$223$	−349.843			−1.56880			−0.784401	−	0.620255i	$-0.787029\pi$
$223$	−349.843			−1.56880			−0.784401	+	0.620255i	$0.787029\pi$
$224$	−24.8281	+	10.0690i	−0.110840	+	0.0449508i
$225$		0			0
$226$	−22.0241	−	25.8645i	−0.0974517	−	0.114445i
$227$	−185.554			−0.817418			−0.408709	−	0.912665i	$-0.634021\pi$
$227$	−185.554			−0.817418			−0.408709	+	0.912665i	$0.634021\pi$
$228$		0			0
$229$	263.897			1.15239			0.576194	−	0.817313i	$-0.304537\pi$
$229$	263.897			1.15239			0.576194	+	0.817313i	$0.304537\pi$
$230$	−60.1402	+	181.391i	−0.261479	+	0.788657i
$231$		0			0
$232$	189.427	+	312.227i	0.816494	+	1.34581i
$233$		−	58.4780i		−	0.250978i	−0.992095	−	0.125489i	$-0.959950\pi$
$233$		−	58.4780i		−	0.250978i	0.992095	−	0.125489i	$-0.0400500\pi$
$234$		0			0
$235$	237.924	−	144.331i	1.01244	−	0.614174i
$236$	346.169	+	55.8812i	1.46682	+	0.236785i
$237$		0			0
$238$	−29.7009	−	34.8800i	−0.124794	−	0.146555i
$239$		−	113.337i		−	0.474212i	−0.971484	−	0.237106i	$-0.923801\pi$
$239$		−	113.337i		−	0.474212i	0.971484	−	0.237106i	$-0.0761989\pi$
$240$		0			0
$241$	−77.7940			−0.322797			−0.161398	−	0.986889i	$-0.551600\pi$
$241$	−77.7940			−0.322797			−0.161398	+	0.986889i	$0.551600\pi$
$242$	195.669	−	166.616i	0.808551	−	0.688495i
$243$		0			0
$244$	24.2234	−	150.057i	0.0992763	−	0.614989i
$245$	206.474	−	125.253i	0.842752	−	0.511235i
$246$		0			0
$247$	93.1855			0.377269
$248$	93.1855	−	56.5351i	0.375748	−	0.227964i
$249$		0			0
$250$	−174.107	−	179.406i	−0.696430	−	0.717625i
$251$			106.226i			0.423212i	0.977355	+	0.211606i	$0.0678693\pi$
$251$			106.226i			0.423212i	−0.977355	+	0.211606i	$0.932131\pi$
$252$		0			0
$253$			301.854i			1.19310i
$254$	12.8762	−	10.9644i	0.0506939	−	0.0431667i
$255$		0			0
$256$	205.308	+	152.921i	0.801983	+	0.597346i
$257$		−	381.078i		−	1.48279i	−0.671067	−	0.741397i	$-0.734164\pi$
$257$		−	381.078i		−	1.48279i	0.671067	−	0.741397i	$-0.265836\pi$
$258$		0			0
$259$			13.0274i			0.0502988i
$260$	−96.1288	+	38.9793i	−0.369726	+	0.149920i
$261$		0			0
$262$	−67.0738	−	78.7697i	−0.256007	−	0.300648i
$263$	−11.4914			−0.0436934			−0.0218467	−	0.999761i	$-0.506955\pi$
$263$	−11.4914			−0.0436934			−0.0218467	+	0.999761i	$0.506955\pi$
$264$		0			0
$265$	−40.3505	−	66.5163i	−0.152266	−	0.251005i
$266$	−19.5050	−	22.9061i	−0.0733269	−	0.0861132i
$267$		0			0
$268$	−58.7746	+	364.093i	−0.219308	+	1.35855i
$269$	77.9518			0.289784			0.144892	−	0.989447i	$-0.453717\pi$
$269$	77.9518			0.289784			0.144892	+	0.989447i	$0.453717\pi$
$270$		0			0
$271$			86.6851i			0.319871i	0.987127	+	0.159936i	$0.0511287\pi$
$271$			86.6851i			0.319871i	−0.987127	+	0.159936i	$0.948871\pi$
$272$	−137.737	+	415.504i	−0.506386	+	1.52759i
$273$		0			0
$274$	−69.7700	−	81.9360i	−0.254635	−	0.299036i
$275$	−350.220	−	182.436i	−1.27353	−	0.663402i
$276$		0			0
$277$		−	287.328i		−	1.03729i	−0.854991	−	0.518643i	$-0.826437\pi$
$277$		−	287.328i		−	1.03729i	0.854991	−	0.518643i	$-0.173563\pi$
$278$	17.6658	+	20.7462i	0.0635459	+	0.0746267i
$279$		0			0
$280$	29.7026	+	15.4707i	0.106081	+	0.0552526i
$281$	224.598			0.799281			0.399641	−	0.916672i	$-0.369135\pi$
$281$	224.598			0.799281			0.399641	+	0.916672i	$0.369135\pi$
$282$		0			0
$283$	84.1224			0.297252			0.148626	−	0.988893i	$-0.452515\pi$
$283$	84.1224			0.297252			0.148626	+	0.988893i	$0.452515\pi$
$284$	−516.145	−	83.3200i	−1.81741	−	0.293380i
$285$		0			0
$286$	−124.749	+	106.226i	−0.436186	+	0.371420i
$287$	11.1346			0.0387967
$288$		0			0
$289$	−459.495			−1.58995
$290$	143.661	−	433.301i	0.495381	−	1.49414i
$291$		0			0
$292$	216.072	+	34.8800i	0.739972	+	0.119452i
$293$			246.620i			0.841706i	0.907129	+	0.420853i	$0.138269\pi$
$293$			246.620i			0.841706i	−0.907129	+	0.420853i	$0.861731\pi$
$294$		0			0
$295$	−227.333	−	374.750i	−0.770621	−	1.27034i
$296$	106.423	−	64.5661i	0.359536	−	0.218129i
$297$		0			0
$298$	−51.2394	+	43.6312i	−0.171944	+	0.146414i
$299$		−	99.1156i		−	0.331490i
$300$		0			0
$301$	23.3954			0.0777255
$302$	181.514	+	213.166i	0.601041	+	0.705846i
$303$		0			0
$304$	−90.4535	+	272.866i	−0.297544	+	0.897586i
$305$	−162.447	+	98.5445i	−0.532613	+	0.323097i
$306$		0			0
$307$	115.811			0.377236			0.188618	−	0.982051i	$-0.439599\pi$
$307$	115.811			0.377236			0.188618	+	0.982051i	$0.439599\pi$
$308$	52.2233	+	8.43030i	0.169556	+	0.0273711i
$309$		0			0
$310$	−129.320	−	42.8761i	−0.417162	−	0.138310i
$311$			203.767i			0.655201i	0.944816	+	0.327600i	$0.106240\pi$
$311$			203.767i			0.655201i	−0.944816	+	0.327600i	$0.893760\pi$
$312$		0			0
$313$		−	99.0614i		−	0.316490i	−0.987400	−	0.158245i	$-0.949416\pi$
$313$		−	99.0614i		−	0.316490i	0.987400	−	0.158245i	$-0.0505836\pi$
$314$	−27.5706	−	32.3782i	−0.0878045	−	0.103115i
$315$		0			0
$316$	53.8007	+	8.68492i	0.170255	+	0.0274839i
$317$			471.192i			1.48641i	0.669063	+	0.743206i	$0.266696\pi$
$317$			471.192i			1.48641i	−0.669063	+	0.743206i	$0.733304\pi$
$318$		0			0
$319$		−	721.057i		−	2.26037i
$320$	−20.8289	−	319.321i	−0.0650902	−	0.997879i
$321$		0			0
$322$	−24.3638	+	20.7462i	−0.0756640	+	0.0644292i
$323$	−491.546			−1.52181
$324$		0			0
$325$	114.997	+	59.9038i	0.353836	+	0.184319i
$326$	−320.096	+	272.568i	−0.981891	+	0.836098i
$327$		0			0
$328$	−55.1854	−	90.9607i	−0.168248	−	0.277319i
$329$	46.5980			0.141635
$330$		0			0
$331$		−	270.695i		−	0.817810i	−0.912577	−	0.408905i	$-0.865911\pi$
$331$		−	270.695i		−	0.817810i	0.912577	−	0.408905i	$-0.134089\pi$
$332$	37.6131	−	233.003i	0.113293	−	0.701816i
$333$		0			0
$334$	362.997	−	309.098i	1.08682	−	0.925444i
$335$	394.154	−	239.104i	1.17658	−	0.713743i
$336$		0			0
$337$		−	377.317i		−	1.11964i	−0.828615	−	0.559818i	$-0.810871\pi$
$337$		−	377.317i		−	1.11964i	0.828615	−	0.559818i	$-0.189129\pi$
$338$	−216.380	+	184.252i	−0.640179	+	0.545124i
$339$		0			0
$340$	507.071	−	205.613i	1.49139	−	0.604743i
$341$	−215.203			−0.631093
$342$		0			0
$343$	81.4639			0.237504
$344$	−115.952	−	191.121i	−0.337069	−	0.555583i
$345$		0			0
$346$	−3.02740	−	3.55530i	−0.00874971	−	0.0102754i
$347$	462.222			1.33205			0.666025	−	0.745929i	$-0.267994\pi$
$347$	462.222			1.33205			0.666025	+	0.745929i	$0.267994\pi$
$348$		0			0
$349$	200.598			0.574779			0.287390	−	0.957814i	$-0.407213\pi$
$349$	200.598			0.574779			0.287390	+	0.957814i	$0.407213\pi$
$350$	−9.34526	−	40.8062i	−0.0267007	−	0.116589i
$351$		0			0
$352$	−189.960	−	468.403i	−0.539660	−	1.33069i
$353$		−	250.897i		−	0.710757i	−0.934722	−	0.355379i	$-0.884352\pi$
$353$		−	250.897i		−	0.710757i	0.934722	−	0.355379i	$-0.115648\pi$
$354$		0			0
$355$	338.958	+	558.760i	0.954812	+	1.57397i
$356$	−25.3713	+	157.168i	−0.0712676	+	0.441483i
$357$		0			0
$358$	294.407	+	345.744i	0.822366	+	0.965764i
$359$			215.601i			0.600560i	0.953851	+	0.300280i	$0.0970801\pi$
$359$			215.601i			0.600560i	−0.953851	+	0.300280i	$0.902920\pi$
$360$		0			0
$361$	38.1960			0.105806
$362$	−173.739	+	147.942i	−0.479941	+	0.408679i
$363$		0			0
$364$	−17.1478	−	2.76814i	−0.0471095	−	0.00760478i
$365$	−141.897	−	233.912i	−0.388759	−	0.640854i
$366$		0			0
$367$	67.0637			0.182735			0.0913675	−	0.995817i	$-0.470876\pi$
$367$	67.0637			0.182735			0.0913675	+	0.995817i	$0.470876\pi$
$368$	290.231	+	96.2097i	0.788670	+	0.261439i
$369$		0			0
$370$	−147.691	−	48.9668i	−0.399164	−	0.132343i
$371$		−	13.0274i		−	0.0351142i
$372$		0			0
$373$			567.402i			1.52119i	0.649230	+	0.760593i	$0.275091\pi$
$373$			567.402i			1.52119i	−0.649230	+	0.760593i	$0.724909\pi$
$374$	658.042	−	560.334i	1.75947	−	1.49822i
$375$		0			0
$376$	−230.949	−	380.667i	−0.614225	−	1.01241i
$377$			236.764i			0.628020i
$378$		0			0
$379$			240.298i			0.634031i	0.948420	+	0.317016i	$0.102681\pi$
$379$			240.298i			0.634031i	−0.948420	+	0.317016i	$0.897319\pi$
$380$	333.000	−	135.028i	0.876316	−	0.355337i
$381$		0			0
$382$	−180.740	−	212.257i	−0.473142	−	0.555646i
$383$	670.068			1.74952			0.874762	−	0.484553i	$-0.161018\pi$
$383$	670.068			1.74952			0.874762	+	0.484553i	$0.161018\pi$
$384$		0			0
$385$	−34.2957	−	56.5351i	−0.0890797	−	0.146845i
$386$	236.048	+	277.209i	0.611524	+	0.718157i
$387$		0			0
$388$	−666.655	−	107.617i	−1.71818	−	0.277363i
$389$	474.640			1.22015			0.610077	−	0.792342i	$-0.291139\pi$
$389$	474.640			1.22015			0.610077	+	0.792342i	$0.291139\pi$
$390$		0			0
$391$			522.826i			1.33715i
$392$	−200.421	−	330.349i	−0.511278	−	0.842726i
$393$		0			0
$394$	334.567	+	392.907i	0.849156	+	0.997226i
$395$	−35.3315	−	58.2427i	−0.0894469	−	0.147450i
$396$		0			0
$397$			499.460i			1.25809i	0.777371	+	0.629043i	$0.216553\pi$
$397$			499.460i			1.25809i	−0.777371	+	0.629043i	$0.783447\pi$
$398$	−332.554	−	390.542i	−0.835562	−	0.981262i
$399$		0			0
$400$	−287.036	+	278.586i	−0.717590	+	0.696466i
$401$	−344.694			−0.859587			−0.429793	−	0.902927i	$-0.641414\pi$
$401$	−344.694			−0.859587			−0.429793	+	0.902927i	$0.641414\pi$
$402$		0			0
$403$	70.6631			0.175343
$404$	−28.3987	+	175.922i	−0.0702938	+	0.435450i
$405$		0			0
$406$	58.1993	−	49.5578i	0.143348	−	0.122063i
$407$	−245.773			−0.603864
$408$		0			0
$409$	−501.890			−1.22712			−0.613558	−	0.789650i	$-0.710262\pi$
$409$	−501.890			−1.22712			−0.613558	+	0.789650i	$0.710262\pi$
$410$	−41.8524	+	126.233i	−0.102079	+	0.307885i
$411$		0			0
$412$	80.6166	−	499.397i	0.195671	−	1.21213i
$413$		−	73.3957i		−	0.177714i
$414$		0			0
$415$	−252.241	+	153.016i	−0.607809	+	0.368713i
$416$	62.3746	+	153.803i	0.149939	+	0.369719i
$417$		0			0
$418$	432.144	−	367.978i	1.03384	−	0.880331i
$419$			218.369i			0.521167i	0.965451	+	0.260584i	$0.0839150\pi$
$419$			218.369i			0.521167i	−0.965451	+	0.260584i	$0.916085\pi$
$420$		0			0
$421$	281.698			0.669116			0.334558	−	0.942375i	$-0.391413\pi$
$421$	281.698			0.669116			0.334558	+	0.942375i	$0.391413\pi$
$422$	−274.700	−	322.600i	−0.650947	−	0.764455i
$423$		0			0
$424$	−106.423	+	64.5661i	−0.250997	+	0.152279i
$425$	−606.598	−	315.988i	−1.42729	−	0.743501i
$426$		0			0
$427$	−31.8156			−0.0745097
$428$	66.5401	−	412.197i	0.155468	−	0.963078i
$429$		0			0
$430$	−87.9376	+	265.232i	−0.204506	+	0.616819i
$431$			441.081i			1.02339i	0.859167	+	0.511694i	$0.170982\pi$
$431$			441.081i			1.02339i	−0.859167	+	0.511694i	$0.829018\pi$
$432$		0			0
$433$		−	123.443i		−	0.285089i	−0.989788	−	0.142544i	$-0.954472\pi$
$433$		−	123.443i		−	0.285089i	0.989788	−	0.142544i	$-0.0455283\pi$
$434$	−14.7907	−	17.3698i	−0.0340800	−	0.0400227i
$435$		0			0
$436$	−0.319785	+	1.98098i	−0.000733451	+	0.00454353i
$437$			343.346i			0.785690i
$438$		0			0
$439$			330.728i			0.753368i	0.926342	+	0.376684i	$0.122936\pi$
$439$			330.728i			0.753368i	−0.926342	+	0.376684i	$0.877064\pi$
$440$	−291.869	+	560.366i	−0.663338	+	1.27356i
$441$		0			0
$442$	−216.072	+	183.989i	−0.488850	+	0.416265i
$443$	154.952			0.349780			0.174890	−	0.984588i	$-0.444043\pi$
$443$	154.952			0.349780			0.174890	+	0.984588i	$0.444043\pi$
$444$		0			0
$445$	170.145	−	103.214i	0.382347	−	0.231942i
$446$	532.718	−	453.619i	1.19444	−	1.01708i
$447$		0			0
$448$	24.7508	−	47.5254i	0.0552473	−	0.106084i
$449$	95.8970			0.213579			0.106790	−	0.994282i	$-0.465943\pi$
$449$	95.8970			0.213579			0.106790	+	0.994282i	$0.465943\pi$
$450$		0			0
$451$			210.065i			0.465775i
$452$	67.0738	+	10.8276i	0.148393	+	0.0239548i
$453$		0			0
$454$	282.550	−	240.596i	0.622356	−	0.529948i
$455$	11.2612	+	18.5637i	0.0247499	+	0.0407992i
$456$		0			0
$457$			485.718i			1.06284i	0.847108	+	0.531420i	$0.178341\pi$
$457$			485.718i			1.06284i	−0.847108	+	0.531420i	$0.821659\pi$
$458$	−401.846	+	342.179i	−0.877393	+	0.747116i
$459$		0			0
$460$	−143.621	−	354.191i	−0.312220	−	0.769981i
$461$	−353.650			−0.767136			−0.383568	−	0.923513i	$-0.625305\pi$
$461$	−353.650			−0.767136			−0.383568	+	0.923513i	$0.625305\pi$
$462$		0			0
$463$	−421.720			−0.910842			−0.455421	−	0.890276i	$-0.650511\pi$
$463$	−421.720			−0.910842			−0.455421	+	0.890276i	$0.650511\pi$
$464$	−693.292	−	229.822i	−1.49416	−	0.495306i
$465$		0			0
$466$	75.8248	+	89.0466i	0.162714	+	0.191087i
$467$	640.974			1.37254			0.686268	−	0.727349i	$-0.259248\pi$
$467$	640.974			1.37254			0.686268	+	0.727349i	$0.259248\pi$
$468$		0			0
$469$	77.1960			0.164597
$470$	−175.151	+	528.279i	−0.372661	+	1.12400i
$471$		0			0
$472$	−599.582	+	363.763i	−1.27030	+	0.770684i
$473$			441.374i			0.933137i
$474$		0			0
$475$	−398.360	−	207.513i	−0.838653	−	0.436869i
$476$	90.4535	+	14.6017i	0.190028	+	0.0306758i
$477$		0			0
$478$	146.957	+	172.582i	0.307441	+	0.361050i
$479$			221.137i			0.461664i	0.972994	+	0.230832i	$0.0741448\pi$
$479$			221.137i			0.461664i	−0.972994	+	0.230832i	$0.925855\pi$
$480$		0			0
$481$	80.7010			0.167778
$482$	118.460	−	100.871i	0.245767	−	0.209275i
$483$		0			0
$484$	−81.9124	+	507.424i	−0.169240	+	1.04840i
$485$	437.801	+	721.698i	0.902682	+	1.48804i
$486$		0			0
$487$	889.949			1.82741			0.913705	−	0.406377i	$-0.133208\pi$
$487$	889.949			1.82741			0.913705	+	0.406377i	$0.133208\pi$
$488$	157.684	+	259.907i	0.323123	+	0.532596i
$489$		0			0
$490$	−151.999	+	458.449i	−0.310201	+	0.935611i
$491$		−	552.843i		−	1.12595i	−0.826473	−	0.562977i	$-0.809656\pi$
$491$		−	552.843i		−	1.12595i	0.826473	−	0.562977i	$-0.190344\pi$
$492$		0			0
$493$		−	1248.91i		−	2.53328i
$494$	−141.897	+	120.828i	−0.287241	+	0.244591i
$495$		0			0
$496$	−68.5914	+	206.916i	−0.138289	+	0.417169i
$497$			109.435i			0.220190i
$498$		0			0
$499$		−	533.302i		−	1.06874i	−0.845250	−	0.534371i	$-0.820549\pi$
$499$		−	533.302i		−	1.06874i	0.845250	−	0.534371i	$-0.179451\pi$
$500$	497.745	+	47.4341i	0.995490	+	0.0948683i
$501$		0			0
$502$	−137.737	−	161.755i	−0.274376	−	0.322220i
$503$	−574.914			−1.14297			−0.571485	−	0.820612i	$-0.693633\pi$
$503$	−574.914			−1.14297			−0.571485	+	0.820612i	$0.693633\pi$
$504$		0			0
$505$	190.447	−	115.530i	0.377122	−	0.228772i
$506$	−391.395	−	459.644i	−0.773509	−	0.908388i
$507$		0			0
$508$	−5.39034	+	33.3917i	−0.0106109	+	0.0657316i
$509$	−207.547			−0.407753			−0.203877	−	0.978997i	$-0.565354\pi$
$509$	−207.547			−0.407753			−0.203877	+	0.978997i	$0.565354\pi$
$510$		0			0
$511$		−	45.8122i		−	0.0896521i
$512$	−510.913	+	33.3518i	−0.997876	+	0.0651403i
$513$		0			0
$514$	494.120	+	580.282i	0.961324	+	1.12895i
$515$	−540.630	+	327.960i	−1.04977	+	0.636816i
$516$		0			0
$517$			879.112i			1.70041i
$518$	−16.8918	−	19.8373i	−0.0326096	−	0.0382959i
$519$		0			0
$520$	95.8369	−	184.000i	0.184302	−	0.353845i
$521$	712.900			1.36833			0.684165	−	0.729327i	$-0.260167\pi$
$521$	712.900			1.36833			0.684165	+	0.729327i	$0.260167\pi$
$522$		0			0
$523$	139.548			0.266822			0.133411	−	0.991061i	$-0.457407\pi$
$523$	139.548			0.266822			0.133411	+	0.991061i	$0.457407\pi$
$524$	204.272	+	32.9751i	0.389831	+	0.0629296i
$525$		0			0
$526$	17.4983	−	14.9002i	0.0332668	−	0.0283273i
$527$	−372.742			−0.707290
$528$		0			0
$529$	−163.804			−0.309648
$530$	147.691	+	48.9668i	0.278662	+	0.0923902i
$531$		0			0
$532$	59.4019	+	9.58911i	0.111658	+	0.0180246i
$533$		−	68.9760i		−	0.129411i
$534$		0			0
$535$	−446.230	+	270.695i	−0.834075	+	0.505972i
$536$	−382.598	−	630.627i	−0.713802	−	1.17654i
$537$		0			0
$538$	−118.700	+	101.075i	−0.220632	+	0.187872i
$539$			762.908i			1.41541i
$540$		0			0
$541$	−946.688			−1.74988			−0.874942	−	0.484227i	$-0.839101\pi$
$541$	−946.688			−1.74988			−0.874942	+	0.484227i	$0.839101\pi$
$542$	−112.399	−	131.999i	−0.207379	−	0.243540i
$543$		0			0
$544$	−329.021	−	811.298i	−0.604818	−	1.49136i
$545$	2.14454	−	1.30093i	0.00393493	−	0.00238703i
$546$		0			0
$547$	50.3388			0.0920271			0.0460136	−	0.998941i	$-0.485348\pi$
$547$	50.3388			0.0920271			0.0460136	+	0.998941i	$0.485348\pi$
$548$	212.483	+	34.3006i	0.387742	+	0.0625923i
$549$		0			0
$550$	769.845	−	176.307i	1.39972	−	0.320557i
$551$		−	820.173i		−	1.48852i
$552$		0			0
$553$		−	11.4070i		−	0.0206275i
$554$	372.561	+	437.525i	0.672492	+	0.789757i
$555$		0			0
$556$	−53.8007	−	8.68492i	−0.0967638	−	0.0156204i
$557$		−	790.157i		−	1.41859i	−0.704910	−	0.709297i	$-0.749013\pi$
$557$		−	790.157i		−	1.41859i	0.704910	−	0.709297i	$-0.250987\pi$
$558$		0			0
$559$		−	144.928i		−	0.259263i
$560$	−65.2892	+	14.9557i	−0.116588	+	0.0267066i
$561$		0			0
$562$	−342.004	+	291.222i	−0.608548	+	0.518189i
$563$	354.133			0.629010			0.314505	−	0.949256i	$-0.398162\pi$
$563$	354.133			0.629010			0.314505	+	0.949256i	$0.398162\pi$
$564$		0			0
$565$	−44.0482	−	72.6117i	−0.0779614	−	0.128516i
$566$	−128.096	+	109.076i	−0.226319	+	0.192714i
$567$		0			0
$568$	893.989	−	542.378i	1.57392	−	0.954891i
$569$	−55.4983			−0.0975366			−0.0487683	−	0.998810i	$-0.515530\pi$
$569$	−55.4983			−0.0975366			−0.0487683	+	0.998810i	$0.515530\pi$
$570$		0			0
$571$		−	791.134i		−	1.38552i	−0.721167	−	0.692762i	$-0.756394\pi$
$571$		−	791.134i		−	1.38552i	0.721167	−	0.692762i	$-0.243606\pi$
$572$	52.2233	−	323.509i	0.0912995	−	0.565575i
$573$		0			0
$574$	−16.9551	+	14.4376i	−0.0295386	+	0.0251526i
$575$	−220.719	+	423.711i	−0.383858	+	0.736888i
$576$		0			0
$577$			201.759i			0.349668i	0.984598	+	0.174834i	$0.0559389\pi$
$577$			201.759i			0.349668i	−0.984598	+	0.174834i	$0.944061\pi$
$578$	699.690	−	595.799i	1.21054	−	1.03079i
$579$		0			0
$580$	343.077	+	846.079i	0.591512	+	1.45876i
$581$	−49.4020			−0.0850292
$582$		0			0
$583$	245.773			0.421566
$584$	−374.248	+	227.054i	−0.640835	+	0.388791i
$585$		0			0
$586$	−319.777	−	375.537i	−0.545694	−	0.640848i
$587$	444.556			0.757335			0.378668	−	0.925533i	$-0.376382\pi$
$587$	444.556			0.757335			0.378668	+	0.925533i	$0.376382\pi$
$588$		0			0
$589$	−244.784			−0.415593
$590$	832.084	+	275.877i	1.41031	+	0.467588i
$591$		0			0
$592$	−78.3350	+	236.309i	−0.132323	+	0.399171i
$593$		−	563.908i		−	0.950942i	−0.879731	−	0.475471i	$-0.842278\pi$
$593$		−	563.908i		−	0.950942i	0.879731	−	0.475471i	$-0.157722\pi$
$594$		0			0
$595$	−59.4019	−	97.9217i	−0.0998351	−	0.164574i
$596$	21.4502	−	132.878i	0.0359902	−	0.222949i
$597$		0			0
$598$	128.517	+	150.927i	0.214911	+	0.252386i
$599$		−	845.034i		−	1.41074i	−0.708839	−	0.705371i	$-0.750781\pi$
$599$		−	845.034i		−	1.41074i	0.708839	−	0.705371i	$-0.249219\pi$
$600$		0			0
$601$	672.296			1.11863			0.559314	−	0.828956i	$-0.311065\pi$
$601$	672.296			1.11863			0.559314	+	0.828956i	$0.311065\pi$
$602$	−35.6250	+	30.3353i	−0.0591777	+	0.0503909i
$603$		0			0
$604$	−552.797	−	89.2368i	−0.915227	−	0.147743i
$605$	549.320	−	333.232i	0.907967	−	0.550796i
$606$		0			0
$607$	882.664			1.45414			0.727071	−	0.686562i	$-0.240881\pi$
$607$	882.664			1.45414			0.727071	+	0.686562i	$0.240881\pi$
$608$	−216.072	−	532.789i	−0.355381	−	0.876298i
$609$		0			0
$610$	119.587	−	360.692i	0.196045	−	0.591299i
$611$		−	288.662i		−	0.472442i
$612$		0			0
$613$		−	469.374i		−	0.765701i	−0.923810	−	0.382850i	$-0.874943\pi$
$613$		−	469.374i		−	0.765701i	0.923810	−	0.382850i	$-0.125057\pi$
$614$	−176.350	+	150.166i	−0.287216	+	0.244569i
$615$		0			0
$616$	−90.4535	+	54.8777i	−0.146840	+	0.0890871i
$617$		−	218.994i		−	0.354934i	−0.984127	−	0.177467i	$-0.943210\pi$
$617$		−	218.994i		−	0.354934i	0.984127	−	0.177467i	$-0.0567902\pi$
$618$		0			0
$619$			879.610i			1.42102i	0.703689	+	0.710509i	$0.251535\pi$
$619$			879.610i			1.42102i	−0.703689	+	0.710509i	$0.748465\pi$
$620$	252.516	−	102.393i	0.407284	−	0.165149i
$621$		0			0
$622$	−264.213	−	310.284i	−0.424779	−	0.498849i
$623$	33.3232			0.0534884
$624$		0			0
$625$	−358.203	−	512.168i	−0.573124	−	0.819468i
$626$	128.447	+	150.845i	0.205187	+	0.240966i
$627$		0			0
$628$	83.9656	+	13.5544i	0.133703	+	0.0215834i
$629$	−425.691			−0.676774
$630$		0			0
$631$		−	635.566i		−	1.00724i	−0.863926	−	0.503618i	$-0.832002\pi$
$631$		−	635.566i		−	1.00724i	0.863926	−	0.503618i	$-0.167998\pi$
$632$	−93.1855	+	56.5351i	−0.147445	+	0.0894543i
$633$		0			0
$634$	−610.966	−	717.502i	−0.963669	−	1.13171i
$635$	36.1486	−	21.9287i	0.0569270	−	0.0345334i
$636$		0			0
$637$		−	250.505i		−	0.393258i
$638$	934.951	+	1097.98i	1.46544	+	1.72097i
$639$		0			0
$640$	445.761	+	459.235i	0.696502	+	0.717555i
$641$	296.309			0.462260			0.231130	−	0.972923i	$-0.425758\pi$
$641$	296.309			0.462260			0.231130	+	0.972923i	$0.425758\pi$
$642$		0			0
$643$	−591.032			−0.919179			−0.459590	−	0.888131i	$-0.652003\pi$
$643$	−591.032			−0.919179			−0.459590	+	0.888131i	$0.652003\pi$
$644$	10.1993	−	63.1821i	0.0158375	−	0.0981088i
$645$		0			0
$646$	748.495	−	637.357i	1.15866	−	0.986621i
$647$	−166.507			−0.257352			−0.128676	−	0.991687i	$-0.541073\pi$
$647$	−166.507			−0.257352			−0.128676	+	0.991687i	$0.541073\pi$
$648$		0			0
$649$	1384.67			2.13355
$650$	−252.783	+	57.8913i	−0.388897	+	0.0890635i
$651$		0			0
$652$	134.001	−	830.098i	0.205523	−	1.27316i
$653$		−	621.335i		−	0.951509i	−0.879578	−	0.475754i	$-0.842175\pi$
$653$		−	621.335i		−	0.951509i	0.879578	−	0.475754i	$-0.157825\pi$
$654$		0			0
$655$	−134.148	−	221.137i	−0.204806	−	0.337614i
$656$	201.976	+	66.9538i	0.307890	+	0.102064i
$657$		0			0
$658$	−70.9565	+	60.4208i	−0.107837	+	0.0918249i
$659$		−	702.113i		−	1.06542i	−0.846297	−	0.532711i	$-0.821173\pi$
$659$		−	702.113i		−	1.06542i	0.846297	−	0.532711i	$-0.178827\pi$
$660$		0			0
$661$	358.193			0.541895			0.270948	−	0.962594i	$-0.412663\pi$
$661$	358.193			0.541895			0.270948	+	0.962594i	$0.412663\pi$
$662$	350.994	+	412.197i	0.530202	+	0.622655i
$663$		0			0
$664$	244.846	+	403.573i	0.368743	+	0.607790i
$665$	−39.0099	−	64.3064i	−0.0586616	−	0.0967013i
$666$		0			0
$667$	−872.367			−1.30790
$668$	−151.960	+	941.351i	−0.227485	+	1.40921i
$669$		0			0
$670$	−290.161	+	875.167i	−0.433077	+	1.30622i
$671$		−	600.230i		−	0.894530i
$672$		0			0
$673$			714.176i			1.06118i	0.847628	+	0.530592i	$0.178030\pi$
$673$			714.176i			1.06118i	−0.847628	+	0.530592i	$0.821970\pi$
$674$	489.244	+	574.555i	0.725882	+	0.852456i
$675$		0			0
$676$	90.5827	−	561.134i	0.133998	−	0.830081i
$677$			509.833i			0.753077i	0.926401	+	0.376538i	$0.122886\pi$
$677$			509.833i			0.753077i	−0.926401	+	0.376538i	$0.877114\pi$
$678$		0			0
$679$			141.346i			0.208168i
$680$	−505.532	+	970.582i	−0.743429	+	1.42733i
$681$		0			0
$682$	327.697	−	279.040i	0.480494	−	0.409150i
$683$	−1263.93			−1.85055			−0.925275	−	0.379298i	$-0.876166\pi$
$683$	−1263.93			−1.85055			−0.925275	+	0.379298i	$0.876166\pi$
$684$		0			0
$685$	−139.540	−	230.026i	−0.203708	−	0.335805i
$686$	−124.048	+	105.629i	−0.180828	+	0.153978i
$687$		0			0
$688$	424.378	+	140.679i	0.616829	+	0.204475i
$689$	−80.7010			−0.117128
$690$		0			0
$691$		−	512.351i		−	0.741463i	−0.928740	−	0.370731i	$-0.879107\pi$
$691$		−	512.351i		−	0.741463i	0.928740	−	0.370731i	$-0.120893\pi$
$692$	9.21987	+	1.48834i	0.0133235	+	0.00215078i
$693$		0			0
$694$	−703.842	+	599.334i	−1.01418	+	0.863594i
$695$	35.3315	+	58.2427i	0.0508368	+	0.0838024i
$696$		0			0
$697$			363.843i			0.522012i
$698$	−305.458	+	260.103i	−0.437619	+	0.372640i
$699$		0			0
$700$	67.1413	+	50.0198i	0.0959162	+	0.0714568i
$701$	−1092.03			−1.55781			−0.778907	−	0.627139i	$-0.784226\pi$
$701$	−1092.03			−1.55781			−0.778907	+	0.627139i	$0.784226\pi$
$702$		0			0
$703$	−279.556			−0.397662
$704$	896.609	+	466.945i	1.27359	+	0.663274i
$705$		0			0
$706$	325.323	+	382.051i	0.460798	+	0.541148i
$707$	37.2995			0.0527574
$708$		0			0
$709$	416.887			0.587993			0.293997	−	0.955806i	$-0.405015\pi$
$709$	416.887			0.587993			0.293997	+	0.955806i	$0.405015\pi$
$710$	−1240.65	−	411.338i	−1.74740	−	0.579350i
$711$		0			0
$712$	−165.156	−	272.223i	−0.231961	−	0.382336i
$713$			260.362i			0.365163i
$714$		0			0
$715$	−350.220	+	212.452i	−0.489818	+	0.297136i
$716$	−896.609	−	144.738i	−1.25225	−	0.202147i
$717$		0			0
$718$	−279.556	−	328.304i	−0.389354	−	0.457247i
$719$		−	395.268i		−	0.549747i	−0.961480	−	0.274874i	$-0.911364\pi$
$719$		−	395.268i		−	0.549747i	0.961480	−	0.274874i	$-0.0886361\pi$
$720$		0			0
$721$	−105.884			−0.146857
$722$	−58.1625	+	49.5264i	−0.0805575	+	0.0685962i
$723$		0			0
$724$	72.7317	−	450.553i	0.100458	−	0.622310i
$725$	527.244	−	1012.14i	0.727233	−	1.39606i
$726$		0			0
$727$	597.583			0.821985			0.410993	−	0.911639i	$-0.365182\pi$
$727$	597.583			0.821985			0.410993	+	0.911639i	$0.365182\pi$
$728$	29.7009	−	18.0194i	0.0407980	−	0.0247519i
$729$		0			0
$730$	519.371	+	172.197i	0.711467	+	0.235887i
$731$			764.482i			1.04580i
$732$		0			0
$733$		−	23.8650i		−	0.0325580i	−0.999867	−	0.0162790i	$-0.994818\pi$
$733$		−	23.8650i		−	0.0325580i	0.999867	−	0.0162790i	$-0.00518200\pi$
$734$	−102.120	+	86.9574i	−0.139129	+	0.118471i
$735$		0			0
$736$	−566.694	+	229.822i	−0.769965	+	0.312258i
$737$			1456.37i			1.97608i
$738$		0			0
$739$		−	125.767i		−	0.170186i	−0.996373	−	0.0850928i	$-0.972881\pi$
$739$		−	125.767i		−	0.170186i	0.996373	−	0.0850928i	$-0.0271187\pi$
$740$	288.386	−	116.938i	0.389711	−	0.158024i
$741$		0			0
$742$	16.8918	+	19.8373i	0.0227652	+	0.0267349i
$743$	−148.841			−0.200325			−0.100162	−	0.994971i	$-0.531936\pi$
$743$	−148.841			−0.200325			−0.100162	+	0.994971i	$0.531936\pi$
$744$		0			0
$745$	−143.849	+	87.2625i	−0.193086	+	0.117131i
$746$	−735.715	−	864.004i	−0.986213	−	1.15818i
$747$		0			0
$748$	−275.474	+	1706.48i	−0.368280	+	2.28140i
$749$	−87.3954			−0.116683
$750$		0			0
$751$			463.390i			0.617030i	0.951219	+	0.308515i	$0.0998321\pi$
$751$			463.390i			0.617030i	−0.951219	+	0.308515i	$0.900168\pi$
$752$	845.261	+	280.199i	1.12402	+	0.372605i
$753$		0			0
$754$	−306.997	−	360.529i	−0.407157	−	0.478155i
$755$	363.029	+	598.439i	0.480833	+	0.792634i
$756$		0			0
$757$		−	719.363i		−	0.950281i	−0.879910	−	0.475141i	$-0.842397\pi$
$757$		−	719.363i		−	0.950281i	0.879910	−	0.475141i	$-0.157603\pi$
$758$	−311.579	−	365.910i	−0.411054	−	0.482731i
$759$		0			0
$760$	−331.989	+	637.393i	−0.436827	+	0.838675i
$761$	1107.49			1.45530			0.727651	−	0.685947i	$-0.240612\pi$
$761$	1107.49			1.45530			0.727651	+	0.685947i	$0.240612\pi$
$762$		0			0
$763$	0.420013			0.000550476
$764$	550.440	+	88.8563i	0.720472	+	0.116304i
$765$		0			0
$766$	−1020.34	+	868.835i	−1.33203	+	1.13425i
$767$	−454.666			−0.592785
$768$		0			0
$769$	−231.691			−0.301289			−0.150644	−	0.988588i	$-0.548135\pi$
$769$	−231.691			−0.301289			−0.150644	+	0.988588i	$0.548135\pi$
$770$	125.529	+	41.6191i	0.163025	+	0.0540507i
$771$		0			0
$772$	−718.879	−	116.047i	−0.931190	−	0.150320i
$773$		−	519.956i		−	0.672647i	−0.941746	−	0.336324i	$-0.890816\pi$
$773$		−	519.956i		−	0.672647i	0.941746	−	0.336324i	$-0.109184\pi$
$774$		0			0
$775$	−302.079	−	157.358i	−0.389779	−	0.203043i
$776$	1154.68	−	700.539i	1.48799	−	0.902756i
$777$		0			0
$778$	−722.751	+	615.436i	−0.928986	+	0.791049i
$779$			238.940i			0.306726i
$780$		0			0
$781$	−2064.58			−2.64351
$782$	−677.917	−	796.127i	−0.866901	−	1.01807i
$783$		0			0
$784$	733.531	+	243.161i	0.935626	+	0.310154i
$785$	−55.1412	−	90.8982i	−0.0702436	−	0.115794i
$786$		0			0
$787$	46.0288			0.0584864			0.0292432	−	0.999572i	$-0.490690\pi$
$787$	46.0288			0.0584864			0.0292432	+	0.999572i	$0.490690\pi$
$788$	−1018.92	−	164.481i	−1.29304	−	0.208733i
$789$		0			0
$790$	129.320	+	42.8761i	0.163697	+	0.0542736i
$791$		−	14.2212i		−	0.0179788i
$792$		0			0
$793$			197.089i			0.248536i
$794$	−647.619	−	760.546i	−0.815641	−	0.957867i
$795$		0			0
$796$	1012.78	+	163.491i	1.27234	+	0.205391i
$797$		−	15.3098i		−	0.0192093i	−0.999954	−	0.00960463i	$-0.996943\pi$
$797$		−	15.3098i		−	0.0192093i	0.999954	−	0.00960463i	$-0.00305730\pi$
$798$		0			0
$799$			1522.67i			1.90572i
$800$	75.8546	−	796.396i	0.0948183	−	0.995495i
$801$		0			0
$802$	524.879	−	446.944i	0.654463	−	0.557287i
$803$	864.288			1.07632
$804$		0			0
$805$	−68.3987	+	41.4924i	−0.0849673	+	0.0515434i
$806$	−107.601	+	91.6245i	−0.133500	+	0.113678i
$807$		0			0
$808$	−184.863	−	304.706i	−0.228791	−	0.377111i
$809$	313.093			0.387012			0.193506	−	0.981099i	$-0.438014\pi$
$809$	313.093			0.387012			0.193506	+	0.981099i	$0.438014\pi$
$810$		0			0
$811$			1056.89i			1.30319i	0.758566	+	0.651596i	$0.225900\pi$
$811$			1056.89i			1.30319i	−0.758566	+	0.651596i	$0.774100\pi$
$812$	−24.3638	+	150.927i	−0.0300047	+	0.185871i
$813$		0			0
$814$	374.248	−	318.678i	0.459764	−	0.391497i
$815$	−898.635	+	545.136i	−1.10262	+	0.668878i
$816$		0			0
$817$			502.045i			0.614498i
$818$	764.247	−	650.770i	0.934288	−	0.795563i
$819$		0			0
$820$	−99.9481	−	246.487i	−0.121888	−	0.300594i
$821$	−308.659			−0.375955			−0.187978	−	0.982173i	$-0.560193\pi$
$821$	−308.659			−0.375955			−0.187978	+	0.982173i	$0.560193\pi$
$822$		0			0
$823$	109.680			0.133269			0.0666344	−	0.997777i	$-0.478774\pi$
$823$	109.680			0.133269			0.0666344	+	0.997777i	$0.478774\pi$
$824$	524.780	+	864.982i	0.636869	+	1.04974i
$825$		0			0
$826$	95.1677	+	111.762i	0.115215	+	0.135306i
$827$	711.971			0.860908			0.430454	−	0.902613i	$-0.358354\pi$
$827$	711.971			0.860908			0.430454	+	0.902613i	$0.358354\pi$
$828$		0			0
$829$	−118.688			−0.143170			−0.0715849	−	0.997435i	$-0.522806\pi$
$829$	−118.688			−0.143170			−0.0715849	+	0.997435i	$0.522806\pi$
$830$	185.690	−	560.068i	0.223723	−	0.674781i
$831$		0			0
$832$	−294.407	−	153.324i	−0.353854	−	0.184284i
$833$			1321.40i			1.58631i
$834$		0			0
$835$	1019.07	−	618.196i	1.22045	−	0.740355i
$836$	−180.907	+	1120.67i	−0.216396	+	1.34051i
$837$		0			0
$838$	−283.146	−	332.519i	−0.337883	−	0.396800i
$839$			1413.67i			1.68495i	0.538736	+	0.842475i	$0.318902\pi$
$839$			1413.67i			1.68495i	−0.538736	+	0.842475i	$0.681098\pi$
$840$		0			0
$841$	1242.88			1.47786
$842$	−428.952	+	365.260i	−0.509444	+	0.433800i
$843$		0			0
$844$	836.591	+	135.049i	0.991222	+	0.160011i
$845$	−607.464	+	368.504i	−0.718893	+	0.436099i
$846$		0			0
$847$	107.586			0.127020
$848$	78.3350	−	236.309i	0.0923762	−	0.278666i
$849$		0			0
$850$	1333.41	−	305.372i	1.56872	−	0.359261i
$851$			297.347i			0.349409i
$852$		0			0
$853$			1308.03i			1.53344i	0.641979	+	0.766722i	$0.278114\pi$
$853$			1308.03i			1.53344i	−0.641979	+	0.766722i	$0.721886\pi$
$854$	48.4469	−	41.2534i	0.0567293	−	0.0483060i
$855$		0			0
$856$	433.148	+	713.947i	0.506014	+	0.834050i
$857$		−	719.755i		−	0.839854i	−0.907558	−	0.419927i	$-0.862056\pi$
$857$		−	719.755i		−	0.839854i	0.907558	−	0.419927i	$-0.137944\pi$
$858$		0			0
$859$		−	1402.44i		−	1.63264i	−0.577601	−	0.816319i	$-0.696011\pi$
$859$		−	1402.44i		−	1.63264i	0.577601	−	0.816319i	$-0.303989\pi$
$860$	−210.004	−	517.902i	−0.244191	−	0.602212i
$861$		0			0
$862$	−571.922	−	671.650i	−0.663483	−	0.779176i
$863$	−72.4412			−0.0839411			−0.0419706	−	0.999119i	$-0.513364\pi$
$863$	−72.4412			−0.0839411			−0.0419706	+	0.999119i	$0.513364\pi$
$864$		0			0
$865$	−6.05480	−	9.98111i	−0.00699977	−	0.0115389i
$866$	160.061	+	187.972i	0.184828	+	0.217058i
$867$		0			0
$868$	45.0448	+	7.27148i	0.0518949	+	0.00837728i
$869$	215.203			0.247644
$870$		0			0
$871$		−	478.208i		−	0.549033i
$872$	−2.08166	−	3.43115i	−0.00238723	−	0.00393481i
$873$		0			0
$874$	−445.196	−	522.826i	−0.509378	−	0.598200i
$875$	−6.80164	−	104.435i	−0.00777331	−	0.119355i
$876$		0			0
$877$		−	1382.21i		−	1.57606i	−0.615635	−	0.788032i	$-0.711100\pi$
$877$		−	1382.21i		−	1.57606i	0.615635	−	0.788032i	$-0.288900\pi$
$878$	−428.835	−	503.613i	−0.488423	−	0.573591i
$879$		0			0
$880$	−282.152	−	1231.74i	−0.320628	−	1.39970i
$881$	1131.38			1.28419			0.642097	−	0.766623i	$-0.278064\pi$
$881$	1131.38			1.28419			0.642097	+	0.766623i	$0.278064\pi$
$882$		0			0
$883$	−1077.39			−1.22014			−0.610072	−	0.792346i	$-0.708860\pi$
$883$	−1077.39			−1.22014			−0.610072	+	0.792346i	$0.708860\pi$
$884$	90.4535	−	560.334i	0.102323	−	0.633862i
$885$		0			0
$886$	−235.952	+	200.917i	−0.266311	+	0.226769i
$887$	766.896			0.864595			0.432297	−	0.901731i	$-0.357703\pi$
$887$	766.896			0.864595			0.432297	+	0.901731i	$0.357703\pi$
$888$		0			0
$889$	7.07980			0.00796378
$890$	−125.254	+	377.784i	−0.140735	+	0.424476i
$891$		0			0
$892$	−223.010	+	1381.49i	−0.250011	+	1.54875i
$893$			999.954i			1.11977i
$894$		0			0
$895$	588.814	+	970.637i	0.657893	+	1.08451i
$896$	23.9344	+	104.462i	0.0267124	+	0.116587i
$897$		0			0
$898$	−146.026	+	124.344i	−0.162612	+	0.138467i
$899$		−	621.942i		−	0.691815i
$900$		0			0
$901$	425.691			0.472465
$902$	−272.378	−	319.873i	−0.301971	−	0.354627i
$903$		0			0
$904$	−116.175	+	70.4829i	−0.128512	+	0.0779678i
$905$	−487.752	+	295.883i	−0.538953	+	0.326943i
$906$		0			0
$907$	1086.43			1.19783			0.598913	−	0.800814i	$-0.295600\pi$
$907$	1086.43			1.19783			0.598913	+	0.800814i	$0.295600\pi$
$908$	−118.283	+	732.730i	−0.130268	+	0.806971i
$909$		0			0
$910$	−41.2182	−	13.6659i	−0.0452947	−	0.0150174i
$911$			237.746i			0.260973i	0.991450	+	0.130486i	$0.0416539\pi$
$911$			237.746i			0.260973i	−0.991450	+	0.130486i	$0.958346\pi$
$912$		0			0
$913$		−	932.012i		−	1.02082i
$914$	−629.801	−	739.621i	−0.689060	−	0.809214i
$915$		0			0
$916$	168.223	−	1042.10i	0.183650	−	1.13766i
$917$		−	43.3103i		−	0.0472304i
$918$		0			0
$919$		−	344.517i		−	0.374882i	−0.982276	−	0.187441i	$-0.939981\pi$
$919$		−	344.517i		−	0.374882i	0.982276	−	0.187441i	$-0.0600194\pi$
$920$	677.955	+	353.116i	0.736908	+	0.383821i
$921$		0			0
$922$	538.515	−	458.555i	0.584073	−	0.497349i
$923$	677.917			0.734471
$924$		0			0
$925$	−344.990	−	179.711i	−0.372962	−	0.194283i
$926$	642.169	−	546.818i	0.693487	−	0.590516i
$927$		0			0
$928$	1353.70	−	548.991i	1.45873	−	0.591585i
$929$	−1478.10			−1.59106			−0.795531	−	0.605913i	$-0.792808\pi$
$929$	−1478.10			−1.59106			−0.795531	+	0.605913i	$0.792808\pi$
$930$		0			0
$931$			867.776i			0.932090i
$932$	−230.922	−	37.2773i	−0.247771	−	0.0399971i
$933$		0			0
$934$	−976.035	+	831.111i	−1.04501	+	0.889841i
$935$	1847.38	−	1120.67i	1.97581	−	1.19858i
$936$		0			0
$937$			246.887i			0.263486i	0.991284	+	0.131743i	$0.0420574\pi$
$937$			246.887i			0.263486i	−0.991284	+	0.131743i	$0.957943\pi$
$938$	−117.549	+	100.095i	−0.125319	+	0.106711i
$939$		0			0
$940$	−418.279	−	1031.54i	−0.444977	−	1.09738i
$941$	−1658.64			−1.76264			−0.881318	−	0.472525i	$-0.843343\pi$
$941$	−1658.64			−1.76264			−0.881318	+	0.472525i	$0.843343\pi$
$942$		0			0
$943$	254.145			0.269507
$944$	441.336	−	1331.36i	0.467517	−	1.41033i
$945$		0			0
$946$	−572.302	−	672.097i	−0.604971	−	0.710462i
$947$	6.00750			0.00634372			0.00317186	−	0.999995i	$-0.498990\pi$
$947$	6.00750			0.00634372			0.00317186	+	0.999995i	$0.498990\pi$
$948$		0			0
$949$	−283.794			−0.299045
$950$	875.667	−	200.541i	0.921755	−	0.211096i
$951$		0			0
$952$	−156.670	+	95.0509i	−0.164569	+	0.0998434i
$953$		−	1089.55i		−	1.14329i	−0.820503	−	0.571643i	$-0.806306\pi$
$953$		−	1089.55i		−	1.14329i	0.820503	−	0.571643i	$-0.193694\pi$
$954$		0			0
$955$	−361.481	−	595.887i	−0.378514	−	0.623966i
$956$	−447.553	−	72.2475i	−0.468152	−	0.0755727i
$957$		0			0
$958$	−286.735	−	336.734i	−0.299306	−	0.351497i
$959$		−	45.0512i		−	0.0469773i
$960$		0			0
$961$	775.379			0.806846
$962$	−122.886	+	104.640i	−0.127741	+	0.108773i
$963$		0			0
$964$	−49.5905	+	307.199i	−0.0514424	+	0.318671i
$965$	472.096	+	778.233i	0.489219	+	0.806459i
$966$		0			0
$967$	−1699.27			−1.75726			−0.878630	−	0.477502i	$-0.841542\pi$
$967$	−1699.27			−1.75726			−0.878630	+	0.477502i	$0.841542\pi$
$968$	−533.215	−	878.885i	−0.550842	−	0.907939i
$969$		0			0
$970$	−1602.44	−	531.287i	−1.65200	−	0.547719i
$971$			197.851i			0.203760i	0.994797	+	0.101880i	$0.0324857\pi$
$971$			197.851i			0.203760i	−0.994797	+	0.101880i	$0.967514\pi$
$972$		0			0
$973$			11.4070i			0.0117235i
$974$	−1355.16	+	1153.94i	−1.39133	+	1.18475i
$975$		0			0
$976$	−577.117	−	191.311i	−0.591309	−	0.196015i
$977$		−	847.868i		−	0.867828i	−0.900954	−	0.433914i	$-0.857132\pi$
$977$		−	847.868i		−	0.867828i	0.900954	−	0.433914i	$-0.142868\pi$
$978$		0			0
$979$			628.672i			0.642157i
$980$	−362.989	−	895.185i	−0.370397	−	0.913454i
$981$		0			0
$982$	716.837	+	841.835i	0.729977	+	0.857266i
$983$	96.0512			0.0977123			0.0488562	−	0.998806i	$-0.484442\pi$
$983$	96.0512			0.0977123			0.0488562	+	0.998806i	$0.484442\pi$
$984$		0			0
$985$	669.135	+	1103.04i	0.679324	+	1.11984i
$986$	1619.38	+	1901.76i	1.64238	+	1.92876i
$987$		0			0
$988$	59.4019	−	367.978i	0.0601234	−	0.372448i
$989$	533.993			0.539933
$990$		0			0
$991$		−	1184.45i		−	1.19520i	−0.801793	−	0.597602i	$-0.796120\pi$
$991$		−	1184.45i		−	1.19520i	0.801793	−	0.597602i	$-0.203880\pi$
$992$	−163.849	−	404.017i	−0.165170	−	0.407275i
$993$		0			0
$994$	−141.897	−	166.640i	−0.142754	−	0.167646i
$995$	−665.108	−	1096.40i	−0.668450	−	1.10191i
$996$		0			0
$997$			1887.35i			1.89303i	0.322655	+	0.946517i	$0.395425\pi$
$997$			1887.35i			1.89303i	−0.322655	+	0.946517i	$0.604575\pi$
$998$	691.500	+	812.079i	0.692886	+	0.813706i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.f.h.19.2		8
3.2	odd	2		60.3.f.b.19.7	yes	8
4.3	odd	2	inner	180.3.f.h.19.8		8
5.2	odd	4		900.3.c.r.451.3		8
5.3	odd	4		900.3.c.r.451.6		8
5.4	even	2	inner	180.3.f.h.19.7		8
12.11	even	2		60.3.f.b.19.1	✓	8
15.2	even	4		300.3.c.f.151.6		8
15.8	even	4		300.3.c.f.151.3		8
15.14	odd	2		60.3.f.b.19.2	yes	8
20.3	even	4		900.3.c.r.451.5		8
20.7	even	4		900.3.c.r.451.4		8
20.19	odd	2	inner	180.3.f.h.19.1		8
24.5	odd	2		960.3.j.e.319.6		8
24.11	even	2		960.3.j.e.319.2		8
60.23	odd	4		300.3.c.f.151.4		8
60.47	odd	4		300.3.c.f.151.5		8
60.59	even	2		60.3.f.b.19.8	yes	8
120.29	odd	2		960.3.j.e.319.1		8
120.59	even	2		960.3.j.e.319.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.1	✓	8	12.11	even	2
60.3.f.b.19.2	yes	8	15.14	odd	2
60.3.f.b.19.7	yes	8	3.2	odd	2
60.3.f.b.19.8	yes	8	60.59	even	2
180.3.f.h.19.1		8	20.19	odd	2	inner
180.3.f.h.19.2		8	1.1	even	1	trivial
180.3.f.h.19.7		8	5.4	even	2	inner
180.3.f.h.19.8		8	4.3	odd	2	inner
300.3.c.f.151.3		8	15.8	even	4
300.3.c.f.151.4		8	60.23	odd	4
300.3.c.f.151.5		8	60.47	odd	4
300.3.c.f.151.6		8	15.2	even	4
900.3.c.r.451.3		8	5.2	odd	4
900.3.c.r.451.4		8	20.7	even	4
900.3.c.r.451.5		8	20.3	even	4
900.3.c.r.451.6		8	5.3	odd	4
960.3.j.e.319.1		8	120.29	odd	2
960.3.j.e.319.2		8	24.11	even	2
960.3.j.e.319.5		8	120.59	even	2
960.3.j.e.319.6		8	24.5	odd	2

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52274 + 1.29664i) q^{2} +(0.637459 - 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +O(q^{10})\)	\(q+(-1.52274 + 1.29664i) q^{2} +(0.637459 - 3.94888i) q^{4} +(-4.27492 + 2.59328i) q^{5} -0.837253 q^{7} +(4.14959 + 6.83966i) q^{8} +(3.14704 - 9.49190i) q^{10} -15.7955i q^{11} +5.18655i q^{13} +(1.27492 - 1.08561i) q^{14} +(-15.1873 - 5.03449i) q^{16} -27.3586i q^{17} -17.9667i q^{19} +(7.51545 + 18.5342i) q^{20} +(20.4811 + 24.0524i) q^{22} -19.1101 q^{23} +(11.5498 - 22.1721i) q^{25} +(-6.72508 - 7.89776i) q^{26} +(-0.533714 + 3.30621i) q^{28} +45.6495 q^{29} -13.6243i q^{31} +(29.6542 - 12.0262i) q^{32} +(35.4743 + 41.6600i) q^{34} +(3.57919 - 2.17123i) q^{35} -15.5597i q^{37} +(23.2964 + 27.3586i) q^{38} +(-35.4763 - 18.4780i) q^{40} -13.2990 q^{41} -27.9430 q^{43} +(-62.3746 - 10.0690i) q^{44} +(29.0997 - 24.7789i) q^{46} -55.6558 q^{47} -48.2990 q^{49} +(11.1618 + 48.7382i) q^{50} +(20.4811 + 3.30621i) q^{52} +15.5597i q^{53} +(40.9621 + 67.5245i) q^{55} +(-3.47425 - 5.72653i) q^{56} +(-69.5122 + 59.1909i) q^{58} +87.6625i q^{59} +38.0000 q^{61} +(17.6658 + 20.7462i) q^{62} +(-29.5619 + 56.7635i) q^{64} +(-13.4502 - 22.1721i) q^{65} -92.2015 q^{67} +(-108.036 - 17.4400i) q^{68} +(-2.63487 + 7.94713i) q^{70} -130.707i q^{71} +54.7173i q^{73} +(20.1752 + 23.6933i) q^{74} +(-70.9485 - 11.4531i) q^{76} +13.2249i q^{77} +13.6243i q^{79} +(77.9803 - 17.8628i) q^{80} +(20.2509 - 17.2440i) q^{82} +59.0048 q^{83} +(70.9485 + 116.956i) q^{85} +(42.5498 - 36.2319i) q^{86} +(108.036 - 65.5448i) q^{88} -39.8007 q^{89} -4.34246i q^{91} +(-12.1819 + 75.4635i) q^{92} +(84.7492 - 72.1654i) q^{94} +(46.5927 + 76.8064i) q^{95} -168.821i q^{97} +(73.5467 - 62.6263i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4} - 4 q^{5}+O(q^{10}) \) 8 * q - 10 * q^4 - 4 * q^5	\( 8 q - 10 q^{4} - 4 q^{5} - 42 q^{10} - 20 q^{14} - 46 q^{16} - 52 q^{20} + 32 q^{25} - 84 q^{26} + 184 q^{29} + 12 q^{34} - 6 q^{40} + 256 q^{41} - 348 q^{44} + 112 q^{46} - 24 q^{49} - 72 q^{50} + 244 q^{56} + 304 q^{61} - 10 q^{64} - 168 q^{65} - 104 q^{70} + 252 q^{74} - 24 q^{76} + 308 q^{80} + 24 q^{85} + 280 q^{86} - 560 q^{89} + 376 q^{94}+O(q^{100}) \) 8 * q - 10 * q^4 - 4 * q^5 - 42 * q^10 - 20 * q^14 - 46 * q^16 - 52 * q^20 + 32 * q^25 - 84 * q^26 + 184 * q^29 + 12 * q^34 - 6 * q^40 + 256 * q^41 - 348 * q^44 + 112 * q^46 - 24 * q^49 - 72 * q^50 + 244 * q^56 + 304 * q^61 - 10 * q^64 - 168 * q^65 - 104 * q^70 + 252 * q^74 - 24 * q^76 + 308 * q^80 + 24 * q^85 + 280 * q^86 - 560 * q^89 + 376 * q^94

Introduction

L-functions

Modular forms

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