LMFDB - Embedded newform 363.3.h.j.245.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.2
Root			$-0.974642 - 1.34148i$ of defining polynomial
Character	$\chi$	$=$	363.245
Dual form			363.3.h.j.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.974642 - 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(4.81514 - 1.24895i) q^{6} +(-0.806259 + 2.48141i) q^{7} +(-8.28007 + 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} +1.15823 q^{10} +(2.89647 + 2.38419i) q^{12} +(13.8479 - 10.0611i) q^{13} +(4.11458 - 1.33691i) q^{14} +(-1.12718 - 1.76653i) q^{15} +(7.63243 + 5.54529i) q^{16} +(9.47072 - 13.0353i) q^{17} +(-1.79754 + 14.8148i) q^{18} +(4.92151 + 15.1469i) q^{19} +(0.513421 + 0.706663i) q^{20} +(-6.04332 - 4.97448i) q^{21} +23.1295i q^{23} +(1.57587 - 26.0710i) q^{24} +(7.57465 + 23.3124i) q^{25} +(-26.9935 - 8.77071i) q^{26} +(24.3448 - 11.6760i) q^{27} +(2.63959 + 1.91777i) q^{28} +(5.10329 + 1.65816i) q^{29} +(-1.27117 + 3.23382i) q^{30} +(3.28671 - 2.38793i) q^{31} +19.1813i q^{32} -26.7172 q^{34} +(-1.07122 - 1.47441i) q^{35} +(-9.83565 + 5.47038i) q^{36} +(19.6322 - 60.4217i) q^{37} +(15.5225 - 21.3649i) q^{38} +(12.8927 + 49.7060i) q^{39} +(1.87922 - 5.78366i) q^{40} +(64.1371 - 20.8394i) q^{41} +(-0.783092 + 12.9553i) q^{42} +22.6622 q^{43} +(6.16931 - 1.20834i) q^{45} +(31.0277 - 22.5429i) q^{46} +(70.2078 - 22.8119i) q^{47} +(-23.8593 + 15.2240i) q^{48} +(34.1345 + 24.8002i) q^{49} +(23.8905 - 32.8825i) q^{50} +(26.0009 + 40.7490i) q^{51} +(-6.61446 - 20.3572i) q^{52} +(25.1873 + 34.6673i) q^{53} +(-39.3906 - 21.2782i) q^{54} -22.7154i q^{56} +(-47.6920 - 2.88277i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(27.3316 + 8.88056i) q^{59} +(-2.53651 + 0.657920i) q^{60} +(-37.4585 - 27.2152i) q^{61} +(-6.40673 - 2.08167i) q^{62} +(20.5215 - 11.4136i) q^{63} +(56.2610 - 40.8760i) q^{64} +11.9562i q^{65} -77.2821 q^{67} +(-11.8432 - 16.3008i) q^{68} +(-64.5783 - 25.3848i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(-24.2537 + 33.3824i) q^{71} +(71.0615 + 33.0130i) q^{72} +(17.5438 - 53.9942i) q^{73} +(-100.189 + 32.5533i) q^{74} +(-73.4023 - 4.43685i) q^{75} +19.9160 q^{76} +(54.1137 - 65.7409i) q^{78} +(-41.1994 + 29.9331i) q^{79} +(-6.26730 + 2.03637i) q^{80} +(5.88115 + 80.7862i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(-34.8026 + 47.9017i) q^{83} +(-8.25147 + 5.26505i) q^{84} +(3.47788 + 10.7038i) q^{85} +(-22.0875 - 30.4009i) q^{86} +(-10.2306 + 12.4287i) q^{87} -38.1909i q^{89} +(-7.63383 - 7.09830i) q^{90} +(13.8007 + 42.4742i) q^{91} +(27.5079 + 8.93786i) q^{92} +(3.06001 + 11.7974i) q^{93} +(-99.0291 - 71.9489i) q^{94} +(-10.5801 - 3.43769i) q^{95} +(-53.5549 - 21.0516i) q^{96} +(-13.1808 + 9.57644i) q^{97} -69.9620i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.974642	−	1.34148i	−0.487321	−	0.670740i	0.492570	−	0.870273i	$-0.336057\pi$
$2$	−0.974642	−	1.34148i	−0.487321	−	0.670740i	−0.979891	+	0.199533i	$0.936057\pi$
$3$	−1.09751	+	2.79204i	−0.365836	+	0.930679i
$3$	−1.09751	+	2.79204i	−0.365836	+	0.930679i
$4$	0.386428	−	1.18930i	0.0966070	−	0.297326i
$5$	−0.410570	+	0.565101i	−0.0821140	+	0.113020i	−0.848098	−	0.529839i	$-0.822252\pi$
$5$	−0.410570	+	0.565101i	−0.0821140	+	0.113020i	0.765984	+	0.642860i	$0.222252\pi$
$6$	4.81514	−	1.24895i	0.802523	−	0.208158i
$7$	−0.806259	+	2.48141i	−0.115180	+	0.354487i	−0.991985	−	0.126360i	$-0.959671\pi$
$7$	−0.806259	+	2.48141i	−0.115180	+	0.354487i	0.876805	+	0.480847i	$0.159671\pi$
$8$	−8.28007	+	2.69036i	−1.03501	+	0.336295i
$9$	−6.59095	−	6.12857i	−0.732327	−	0.680953i
$10$	1.15823			0.115823
$11$		0			0
$11$		0			0
$12$	2.89647	+	2.38419i	0.241372	+	0.198683i
$13$	13.8479	−	10.0611i	1.06522	−	0.773930i	0.0901753	−	0.995926i	$-0.471257\pi$
$13$	13.8479	−	10.0611i	1.06522	−	0.773930i	0.975048	+	0.221996i	$0.0712573\pi$
$14$	4.11458	−	1.33691i	0.293898	−	0.0954933i
$15$	−1.12718	−	1.76653i	−0.0751453	−	0.117769i
$16$	7.63243	+	5.54529i	0.477027	+	0.346580i
$17$	9.47072	−	13.0353i	0.557101	−	0.766784i	−0.433853	−	0.900984i	$-0.642846\pi$
$17$	9.47072	−	13.0353i	0.557101	−	0.766784i	0.990954	+	0.134200i	$0.0428464\pi$
$18$	−1.79754	+	14.8148i	−0.0998636	+	0.823043i
$19$	4.92151	+	15.1469i	0.259027	+	0.797203i	0.993009	+	0.118035i	$0.0376594\pi$
$19$	4.92151	+	15.1469i	0.259027	+	0.797203i	−0.733983	+	0.679168i	$0.762341\pi$
$20$	0.513421	+	0.706663i	0.0256710	+	0.0353331i
$21$	−6.04332	−	4.97448i	−0.287777	−	0.236880i
$22$		0			0
$23$			23.1295i			1.00563i	0.864395	+	0.502814i	$0.167702\pi$
$23$			23.1295i			1.00563i	−0.864395	+	0.502814i	$0.832298\pi$
$24$	1.57587	−	26.0710i	0.0656614	−	1.08629i
$25$	7.57465	+	23.3124i	0.302986	+	0.932495i
$26$	−26.9935	−	8.77071i	−1.03821	−	0.337335i
$27$	24.3448	−	11.6760i	0.901661	−	0.432444i
$28$	2.63959	+	1.91777i	0.0942710	+	0.0684919i
$29$	5.10329	+	1.65816i	0.175976	+	0.0571779i	0.395679	−	0.918389i	$-0.370509\pi$
$29$	5.10329	+	1.65816i	0.175976	+	0.0571779i	−0.219704	+	0.975567i	$0.570509\pi$
$30$	−1.27117	+	3.23382i	−0.0423723	+	0.107794i
$31$	3.28671	−	2.38793i	0.106023	−	0.0770301i	−0.533511	−	0.845793i	$-0.679128\pi$
$31$	3.28671	−	2.38793i	0.106023	−	0.0770301i	0.639533	+	0.768763i	$0.279128\pi$
$32$			19.1813i			0.599415i
$33$		0			0
$34$	−26.7172			−0.785799
$35$	−1.07122	−	1.47441i	−0.0306064	−	0.0421260i
$36$	−9.83565	+	5.47038i	−0.273213	+	0.151955i
$37$	19.6322	−	60.4217i	0.530600	−	1.63302i	−0.222368	−	0.974963i	$-0.571379\pi$
$37$	19.6322	−	60.4217i	0.530600	−	1.63302i	0.752968	−	0.658057i	$-0.228621\pi$
$38$	15.5225	−	21.3649i	0.408486	−	0.562233i
$39$	12.8927	+	49.7060i	0.330583	+	1.27451i
$40$	1.87922	−	5.78366i	0.0469806	−	0.144591i
$41$	64.1371	−	20.8394i	1.56432	−	0.508278i	0.606362	−	0.795188i	$-0.292628\pi$
$41$	64.1371	−	20.8394i	1.56432	−	0.508278i	0.957958	+	0.286910i	$0.0926281\pi$
$42$	−0.783092	+	12.9553i	−0.0186450	+	0.308460i
$43$	22.6622			0.527028			0.263514	−	0.964656i	$-0.415118\pi$
$43$	22.6622			0.527028			0.263514	+	0.964656i	$0.415118\pi$
$44$		0			0
$45$	6.16931	−	1.20834i	0.137096	−	0.0268521i
$46$	31.0277	−	22.5429i	0.674515	−	0.490064i
$47$	70.2078	−	22.8119i	1.49378	−	0.485360i	0.555585	−	0.831460i	$-0.312494\pi$
$47$	70.2078	−	22.8119i	1.49378	−	0.485360i	0.938198	+	0.346100i	$0.112494\pi$
$48$	−23.8593	+	15.2240i	−0.497069	+	0.317167i
$49$	34.1345	+	24.8002i	0.696622	+	0.506126i
$50$	23.8905	−	32.8825i	0.477810	−	0.657649i
$51$	26.0009	+	40.7490i	0.509822	+	0.799000i
$52$	−6.61446	−	20.3572i	−0.127201	−	0.391485i
$53$	25.1873	+	34.6673i	0.475232	+	0.654100i	0.977580	−	0.210565i	$-0.0675304\pi$
$53$	25.1873	+	34.6673i	0.475232	+	0.654100i	−0.502348	+	0.864666i	$0.667530\pi$
$54$	−39.3906	−	21.2782i	−0.729456	−	0.394040i
$55$		0			0
$56$		−	22.7154i		−	0.405632i
$57$	−47.6920	−	2.88277i	−0.836702	−	0.0505749i
$58$	−2.74949	−	8.46207i	−0.0474051	−	0.145898i
$59$	27.3316	+	8.88056i	0.463247	+	0.150518i	0.531336	−	0.847161i	$-0.321690\pi$
$59$	27.3316	+	8.88056i	0.463247	+	0.150518i	−0.0680891	+	0.997679i	$0.521690\pi$
$60$	−2.53651	+	0.657920i	−0.0422752	+	0.0109653i
$61$	−37.4585	−	27.2152i	−0.614074	−	0.446151i	0.236772	−	0.971565i	$-0.423910\pi$
$61$	−37.4585	−	27.2152i	−0.614074	−	0.446151i	−0.850847	+	0.525414i	$0.823910\pi$
$62$	−6.40673	−	2.08167i	−0.103334	−	0.0335753i
$63$	20.5215	−	11.4136i	0.325739	−	0.181169i
$64$	56.2610	−	40.8760i	0.879079	−	0.638688i
$65$			11.9562i			0.183942i
$66$		0			0
$67$	−77.2821			−1.15346			−0.576732	−	0.816933i	$-0.695672\pi$
$67$	−77.2821			−1.15346			−0.576732	+	0.816933i	$0.695672\pi$
$68$	−11.8432	−	16.3008i	−0.174165	−	0.239717i
$69$	−64.5783	−	25.3848i	−0.935917	−	0.367896i
$70$	−0.933834	+	2.87405i	−0.0133405	+	0.0410578i
$71$	−24.2537	+	33.3824i	−0.341601	+	0.470174i	−0.944908	−	0.327335i	$-0.893849\pi$
$71$	−24.2537	+	33.3824i	−0.341601	+	0.470174i	0.603307	+	0.797509i	$0.293849\pi$
$72$	71.0615	+	33.0130i	0.986966	+	0.458514i
$73$	17.5438	−	53.9942i	0.240326	−	0.739647i	−0.756044	−	0.654521i	$-0.772871\pi$
$73$	17.5438	−	53.9942i	0.240326	−	0.739647i	0.996370	−	0.0851266i	$-0.0271295\pi$
$74$	−100.189	+	32.5533i	−1.35390	+	0.439910i
$75$	−73.4023	−	4.43685i	−0.978697	−	0.0591579i
$76$	19.9160			0.262053
$77$		0			0
$78$	54.1137	−	65.7409i	0.693766	−	0.842831i
$79$	−41.1994	+	29.9331i	−0.521512	+	0.378901i	−0.817173	−	0.576392i	$-0.804460\pi$
$79$	−41.1994	+	29.9331i	−0.521512	+	0.378901i	0.295661	+	0.955293i	$0.404460\pi$
$80$	−6.26730	+	2.03637i	−0.0783412	+	0.0254546i
$81$	5.88115	+	80.7862i	0.0726068	+	0.997361i
$82$	−90.4664	−	65.7277i	−1.10325	−	0.801557i
$83$	−34.8026	+	47.9017i	−0.419309	+	0.577129i	−0.965458	−	0.260559i	$-0.916093\pi$
$83$	−34.8026	+	47.9017i	−0.419309	+	0.577129i	0.546149	+	0.837688i	$0.316093\pi$
$84$	−8.25147	+	5.26505i	−0.0982317	+	0.0626792i
$85$	3.47788	+	10.7038i	0.0409163	+	0.125927i
$86$	−22.0875	−	30.4009i	−0.256832	−	0.353499i
$87$	−10.2306	+	12.4287i	−0.117593	+	0.142859i
$88$		0			0
$89$		−	38.1909i		−	0.429112i	−0.976712	−	0.214556i	$-0.931170\pi$
$89$		−	38.1909i		−	0.429112i	0.976712	−	0.214556i	$-0.0688304\pi$
$90$	−7.63383	−	7.09830i	−0.0848204	−	0.0788700i
$91$	13.8007	+	42.4742i	0.151656	+	0.466749i
$92$	27.5079	+	8.93786i	0.298999	+	0.0971507i
$93$	3.06001	+	11.7974i	0.0329033	+	0.126854i
$94$	−99.0291	−	71.9489i	−1.05350	−	0.765414i
$95$	−10.5801	−	3.43769i	−0.111370	−	0.0361862i
$96$	−53.5549	−	21.0516i	−0.557863	−	0.219288i
$97$	−13.1808	+	9.57644i	−0.135885	+	0.0987262i	−0.653651	−	0.756796i	$-0.726764\pi$
$97$	−13.1808	+	9.57644i	−0.135885	+	0.0987262i	0.517766	+	0.855522i	$0.326764\pi$
$98$		−	69.9620i		−	0.713898i
$99$		0			0
$100$	30.6525			0.306525
$101$	61.2440	+	84.2951i	0.606376	+	0.834605i	0.996273	−	0.0862537i	$-0.0274895\pi$
$101$	61.2440	+	84.2951i	0.606376	+	0.834605i	−0.389897	+	0.920858i	$0.627490\pi$
$102$	29.3224	−	74.5954i	0.287474	−	0.731327i
$103$	16.8125	−	51.7437i	0.163229	−	0.502366i	−0.835673	−	0.549227i	$-0.814922\pi$
$103$	16.8125	−	51.7437i	0.163229	−	0.502366i	0.998901	+	0.0468618i	$0.0149220\pi$
$104$	−87.5936	+	120.562i	−0.842246	+	1.15925i
$105$	5.29229	−	1.37271i	0.0504027	−	0.0130735i
$106$	21.9569	−	67.5764i	0.207141	−	0.637514i
$107$	27.0164	−	8.77818i	0.252490	−	0.0820390i	−0.180037	−	0.983660i	$-0.557622\pi$
$107$	27.0164	−	8.77818i	0.252490	−	0.0820390i	0.432527	+	0.901621i	$0.357622\pi$
$108$	−4.47878	−	33.4653i	−0.0414702	−	0.309864i
$109$	41.2540			0.378477			0.189238	−	0.981931i	$-0.439398\pi$
$109$	41.2540			0.378477			0.189238	+	0.981931i	$0.439398\pi$
$110$		0			0
$111$	147.153	+	121.127i	1.32570	+	1.09124i
$112$	−19.9139	+	14.4683i	−0.177802	+	0.129181i
$113$	−138.072	+	44.8625i	−1.22188	+	0.397013i	−0.847766	−	0.530370i	$-0.822053\pi$
$113$	−138.072	+	44.8625i	−1.22188	+	0.397013i	−0.374114	+	0.927383i	$0.622053\pi$
$114$	42.6154	+	66.7875i	0.373820	+	0.585855i
$115$	−13.0705	−	9.49626i	−0.113656	−	0.0825762i
$116$	3.94411	−	5.42860i	0.0340009	−	0.0467983i
$117$	−152.931	−	18.5558i	−1.30710	−	0.158596i
$118$	−14.7254	−	45.3201i	−0.124791	−	0.384069i
$119$	24.7101	+	34.0106i	0.207648	+	0.285803i
$120$	14.0857	+	11.5945i	0.117381	+	0.0966207i
$121$		0			0
$122$			76.7749i			0.629303i
$123$	−12.2067	+	201.945i	−0.0992412	+	1.64183i
$124$	−1.56990	−	4.83165i	−0.0126605	−	0.0389650i
$125$	−32.8917	−	10.6872i	−0.263134	−	0.0854973i
$126$	−35.3123	−	16.4050i	−0.280256	−	0.130198i
$127$	−147.873	−	107.436i	−1.16436	−	0.845955i	−0.174034	−	0.984740i	$-0.555680\pi$
$127$	−147.873	−	107.436i	−1.16436	−	0.845955i	−0.990323	+	0.138785i	$0.955680\pi$
$128$	−36.6987	−	11.9241i	−0.286709	−	0.0931574i
$129$	−24.8720	+	63.2737i	−0.192806	+	0.490494i
$130$	16.0391	−	11.6531i	0.123377	−	0.0896389i
$131$			84.5109i			0.645121i	0.946549	+	0.322561i	$0.104544\pi$
$131$			84.5109i			0.645121i	−0.946549	+	0.322561i	$0.895456\pi$
$132$		0			0
$133$	−41.5536			−0.312433
$134$	75.3223	+	103.672i	0.562107	+	0.773674i
$135$	−3.39714	+	18.5511i	−0.0251640	+	0.137416i
$136$	−43.3485	+	133.413i	−0.318739	+	0.980978i
$137$	120.127	−	165.341i	0.876841	−	1.20687i	−0.100445	−	0.994943i	$-0.532027\pi$
$137$	120.127	−	165.341i	0.876841	−	1.20687i	0.977286	−	0.211925i	$-0.0679733\pi$
$138$	28.8875	+	111.372i	0.209330	+	0.807040i
$139$	15.5254	−	47.7824i	0.111694	−	0.343758i	−0.879549	−	0.475808i	$-0.842156\pi$
$139$	15.5254	−	47.7824i	0.111694	−	0.343758i	0.991243	+	0.132050i	$0.0421558\pi$
$140$	−2.16747	+	0.704254i	−0.0154819	+	0.00503039i
$141$	−13.3620	+	221.059i	−0.0947663	+	1.56779i
$142$	68.4204			0.481834
$143$		0			0
$144$	−16.3203	−	83.3246i	−0.113335	−	0.578643i
$145$	−3.03229	+	2.20308i	−0.0209123	+	0.0151937i
$146$	−89.5311	+	29.0904i	−0.613227	+	0.199249i
$147$	−106.706	+	68.0864i	−0.725890	+	0.463172i
$148$	−64.2733	−	46.6973i	−0.434279	−	0.315522i
$149$	−92.5187	+	127.341i	−0.620931	+	0.854638i	−0.997420	−	0.0717830i	$-0.977131\pi$
$149$	−92.5187	+	127.341i	−0.620931	+	0.854638i	0.376490	+	0.926421i	$0.377131\pi$
$150$	65.5890	+	102.792i	0.437260	+	0.685280i
$151$	52.9598	+	162.993i	0.350727	+	1.07943i	0.958446	+	0.285274i	$0.0920847\pi$
$151$	52.9598	+	162.993i	0.350727	+	1.07943i	−0.607719	+	0.794152i	$0.707915\pi$
$152$	−81.5009	−	112.176i	−0.536190	−	0.738002i
$153$	−142.309	+	27.8731i	−0.930124	+	0.182177i
$154$		0			0
$155$			2.83774i			0.0183080i
$156$	64.0976	+	3.87442i	0.410882	+	0.0248360i
$157$	−20.1905	−	62.1401i	−0.128602	−	0.395797i	0.865938	−	0.500151i	$-0.166722\pi$
$157$	−20.1905	−	62.1401i	−0.128602	−	0.395797i	−0.994540	+	0.104355i	$0.966722\pi$
$158$	80.3094	+	26.0941i	0.508287	+	0.165153i
$159$	−124.436	+	32.2761i	−0.782615	+	0.202995i
$160$	−10.8394	−	7.87526i	−0.0677461	−	0.0492204i
$161$	−57.3937	−	18.6483i	−0.356483	−	0.115828i
$162$	102.641	−	86.6271i	0.633587	−	0.534735i
$163$	12.4900	−	9.07449i	0.0766256	−	0.0556717i	−0.548813	−	0.835945i	$-0.684920\pi$
$163$	12.4900	−	9.07449i	0.0766256	−	0.0556717i	0.625439	+	0.780273i	$0.284920\pi$
$164$		−	84.3314i		−	0.514216i
$165$		0			0
$166$	98.1792			0.591441
$167$	−90.5798	−	124.672i	−0.542394	−	0.746542i	0.446561	−	0.894753i	$-0.352648\pi$
$167$	−90.5798	−	124.672i	−0.542394	−	0.746542i	−0.988956	+	0.148211i	$0.952648\pi$
$168$	63.4222	+	24.9303i	0.377513	+	0.148395i
$169$	38.3149	−	117.921i	0.226715	−	0.697758i
$170$	10.9693	−	15.0979i	0.0645251	−	0.0888112i
$171$	60.3912	−	129.994i	0.353165	−	0.760199i
$172$	8.75731	−	26.9522i	0.0509146	−	0.156699i
$173$	23.8744	−	7.75725i	0.138002	−	0.0448396i	−0.239202	−	0.970970i	$-0.576886\pi$
$173$	23.8744	−	7.75725i	0.138002	−	0.0448396i	0.377204	+	0.926130i	$0.376886\pi$
$174$	26.6440	+	1.61051i	0.153127	+	0.00925582i
$175$	−63.9548			−0.365456
$176$		0			0
$177$	−54.7915	+	66.5642i	−0.309556	+	0.376069i
$178$	−51.2323	+	37.2225i	−0.287822	+	0.209115i
$179$	58.7800	−	19.0988i	0.328380	−	0.106697i	−0.140187	−	0.990125i	$-0.544770\pi$
$179$	58.7800	−	19.0988i	0.328380	−	0.106697i	0.468567	+	0.883428i	$0.344770\pi$
$180$	0.946908	−	7.80411i	0.00526060	−	0.0433562i
$181$	120.062	+	87.2301i	0.663325	+	0.481934i	0.867784	−	0.496941i	$-0.165544\pi$
$181$	120.062	+	87.2301i	0.663325	+	0.481934i	−0.204459	+	0.978875i	$0.565544\pi$
$182$	43.5275	−	59.9104i	0.239162	−	0.329178i
$183$	117.097	−	74.7167i	0.639874	−	0.408288i
$184$	−62.2265	−	191.513i	−0.338187	−	1.04083i
$185$	26.0840	+	35.9015i	0.140995	+	0.194062i
$186$	12.8435	−	15.6032i	0.0690513	−	0.0838880i
$187$		0			0
$188$		−	92.3135i		−	0.491029i
$189$	9.34471	+	69.8234i	0.0494429	+	0.369436i
$190$	5.70024	+	17.5435i	0.0300013	+	0.0923344i
$191$	53.4521	+	17.3676i	0.279854	+	0.0909301i	0.445581	−	0.895242i	$-0.352997\pi$
$191$	53.4521	+	17.3676i	0.279854	+	0.0909301i	−0.165727	+	0.986172i	$0.552997\pi$
$192$	52.3804	+	201.945i	0.272815	+	1.05180i
$193$	122.139	+	88.7392i	0.632844	+	0.459788i	0.857384	−	0.514676i	$-0.172088\pi$
$193$	122.139	+	88.7392i	0.632844	+	0.459788i	−0.224540	+	0.974465i	$0.572088\pi$
$194$	25.6932	+	8.34822i	0.132439	+	0.0430321i
$195$	−33.3823	−	13.1221i	−0.171191	−	0.0672928i
$196$	42.6854	−	31.0128i	0.217783	−	0.158228i
$197$		−	22.3374i		−	0.113388i	−0.998392	−	0.0566938i	$-0.981944\pi$
$197$		−	22.3374i		−	0.113388i	0.998392	−	0.0566938i	$-0.0180559\pi$
$198$		0			0
$199$	−150.930			−0.758444			−0.379222	−	0.925306i	$-0.623808\pi$
$199$	−150.930			−0.758444			−0.379222	+	0.925306i	$0.623808\pi$
$200$	−125.437	−	172.650i	−0.627186	−	0.863248i
$201$	84.8178	−	215.774i	0.421979	−	1.07350i
$202$	53.3892	−	164.315i	0.264303	−	0.813441i
$203$	−8.22915	+	11.3265i	−0.0405377	+	0.0557954i
$204$	58.5104	−	15.1764i	0.286815	−	0.0743942i
$205$	−14.5564	+	44.8000i	−0.0710068	+	0.218537i
$206$	−85.7993	+	27.8779i	−0.416501	+	0.135329i
$207$	141.751	−	152.445i	0.684785	−	0.736449i
$208$	161.485			0.776369
$209$		0			0
$210$	−6.99955	−	5.76159i	−0.0333312	−	0.0274362i
$211$	146.900	−	106.729i	0.696207	−	0.505824i	−0.182488	−	0.983208i	$-0.558415\pi$
$211$	146.900	−	106.729i	0.696207	−	0.505824i	0.878695	+	0.477384i	$0.158415\pi$
$212$	50.9630	−	16.5589i	0.240392	−	0.0781079i
$213$	−66.5861	−	104.355i	−0.312611	−	0.489928i
$214$	−38.1071	−	27.6864i	−0.178071	−	0.129376i
$215$	−9.30442	+	12.8064i	−0.0432764	+	0.0595648i
$216$	−170.164	+	162.174i	−0.787798	+	0.750807i
$217$	3.27551	+	10.0810i	0.0150945	+	0.0464561i
$218$	−40.2078	−	55.3414i	−0.184440	−	0.253859i
$219$	131.499	+	108.242i	0.600454	+	0.494256i
$220$		0			0
$221$		−	275.798i		−	1.24795i
$222$	19.0681	−	315.459i	0.0858923	−	1.42098i
$223$	58.1059	+	178.831i	0.260564	+	0.801935i	0.992682	+	0.120757i	$0.0385321\pi$
$223$	58.1059	+	178.831i	0.260564	+	0.801935i	−0.732118	+	0.681178i	$0.761468\pi$
$224$	−47.5967	−	15.4651i	−0.212485	−	0.0690406i
$225$	92.9476	−	200.073i	0.413100	−	0.889211i
$226$	194.753	+	141.497i	0.861740	+	0.626091i
$227$	408.219	+	132.638i	1.79832	+	0.584310i	0.999843	−	0.0177135i	$-0.00563869\pi$
$227$	408.219	+	132.638i	1.79832	+	0.584310i	0.798478	+	0.602024i	$0.205639\pi$
$228$	−21.8580	+	55.6062i	−0.0958684	+	0.243887i
$229$	−109.845	+	79.8068i	−0.479671	+	0.348501i	−0.801198	−	0.598399i	$-0.795804\pi$
$229$	−109.845	+	79.8068i	−0.479671	+	0.348501i	0.321527	+	0.946900i	$0.395804\pi$
$230$			26.7892i			0.116475i
$231$		0			0
$232$	−46.7166			−0.201365
$233$	−192.141	−	264.459i	−0.824638	−	1.13502i	−0.988897	−	0.148600i	$-0.952523\pi$
$233$	−192.141	−	264.459i	−0.824638	−	1.13502i	0.164259	−	0.986417i	$-0.447477\pi$
$234$	124.161	+	223.239i	0.530601	+	0.954012i
$235$	−15.9342	+	49.0404i	−0.0678051	+	0.208683i
$236$	21.1233	−	29.0738i	0.0895057	−	0.123194i
$237$	−38.3577	−	147.882i	−0.161847	−	0.623976i
$238$	21.5410	−	66.2963i	0.0905083	−	0.278556i
$239$	88.8791	−	28.8786i	0.371879	−	0.120831i	−0.117114	−	0.993118i	$-0.537364\pi$
$239$	88.8791	−	28.8786i	0.371879	−	0.120831i	0.488993	+	0.872288i	$0.337364\pi$
$240$	1.19280	−	19.7335i	0.00497000	−	0.0822227i
$241$	−206.766			−0.857952			−0.428976	−	0.903316i	$-0.641125\pi$
$241$	−206.766			−0.857952			−0.428976	+	0.903316i	$0.641125\pi$
$242$		0			0
$243$	−232.013	−	72.2432i	−0.954785	−	0.297297i
$244$	−46.8421	+	34.0328i	−0.191976	+	0.139479i
$245$	−28.0292	+	9.10724i	−0.114405	+	0.0371724i
$246$	282.802	−	180.449i	1.14960	−	0.733531i
$247$	220.546	+	160.236i	0.892900	+	0.648730i
$248$	−20.7898	+	28.6147i	−0.0838297	+	0.115382i
$249$	−95.5472	−	149.743i	−0.383724	−	0.601377i
$250$	17.7210	+	54.5397i	0.0708841	+	0.218159i
$251$	1.64009	+	2.25739i	0.00653422	+	0.00899358i	0.812272	−	0.583279i	$-0.198231\pi$
$251$	1.64009	+	2.25739i	0.00653422	+	0.00899358i	−0.805737	+	0.592273i	$0.798231\pi$
$252$	−5.64417	−	28.8168i	−0.0223975	−	0.114353i
$253$		0			0
$254$			303.081i			1.19323i
$255$	−33.7025	−	2.03717i	−0.132167	−	0.00798889i
$256$	−66.1871	−	203.703i	−0.258543	−	0.795714i
$257$	−380.619	−	123.671i	−1.48101	−	0.481208i	−0.546593	−	0.837398i	$-0.684076\pi$
$257$	−380.619	−	123.671i	−1.48101	−	0.481208i	−0.934414	+	0.356190i	$0.884076\pi$
$258$	109.122	−	28.3040i	0.422952	−	0.109705i
$259$	134.103	+	97.4312i	0.517770	+	0.376182i
$260$	14.2196	+	4.62022i	0.0546907	+	0.0177701i
$261$	−23.4734	−	42.2047i	−0.0899362	−	0.161704i
$262$	113.370	−	82.3678i	0.432708	−	0.314381i
$263$		−	379.212i		−	1.44187i	−0.693003	−	0.720935i	$-0.743713\pi$
$263$		−	379.212i		−	1.44187i	0.693003	−	0.720935i	$-0.256287\pi$
$264$		0			0
$265$	−29.9317			−0.112950
$266$	40.4999	+	55.7433i	0.152255	+	0.209561i
$267$	106.631	+	41.9149i	0.399365	+	0.156985i
$268$	−29.8639	+	91.9118i	−0.111433	+	0.342954i
$269$	−18.3393	+	25.2419i	−0.0681760	+	0.0938362i	−0.841743	−	0.539878i	$-0.818470\pi$
$269$	−18.3393	+	25.2419i	−0.0681760	+	0.0938362i	0.773567	+	0.633714i	$0.218470\pi$
$270$	28.1969	−	13.5235i	0.104433	−	0.0500870i
$271$	−160.104	+	492.748i	−0.590788	+	1.81826i	−0.0161246	+	0.999870i	$0.505133\pi$
$271$	−160.104	+	492.748i	−0.590788	+	1.81826i	−0.574664	+	0.818390i	$0.694867\pi$
$272$	144.569	−	46.9734i	0.531505	−	0.172696i
$273$	−133.736	−	8.08374i	−0.489875	−	0.0296108i
$274$	−338.882			−1.23680
$275$		0			0
$276$	−55.1450	+	66.9937i	−0.199801	+	0.242731i
$277$	297.684	−	216.280i	1.07467	−	0.780795i	0.0979254	−	0.995194i	$-0.468779\pi$
$277$	297.684	−	216.280i	1.07467	−	0.780795i	0.976746	+	0.214399i	$0.0687793\pi$
$278$	−79.2308	+	25.7436i	−0.285003	+	0.0926031i
$279$	−36.2971	−	4.40410i	−0.130097	−	0.0157853i
$280$	12.8365	+	9.32625i	0.0458446	+	0.0333081i
$281$	188.322	−	259.203i	0.670184	−	0.922429i	−0.329580	−	0.944127i	$-0.606907\pi$
$281$	188.322	−	259.203i	0.670184	−	0.922429i	0.999765	+	0.0216982i	$0.00690730\pi$
$282$	309.569	−	197.528i	1.09776	−	0.700456i
$283$	49.6883	+	152.925i	0.175577	+	0.540371i	0.999659	−	0.0260993i	$-0.00830861\pi$
$283$	49.6883	+	152.925i	0.175577	+	0.540371i	−0.824082	+	0.566470i	$0.808309\pi$
$284$	30.3294	+	41.7449i	0.106794	+	0.146989i
$285$	21.2100	−	25.7672i	0.0744209	−	0.0904113i
$286$		0			0
$287$			175.953i			0.613075i
$288$	117.554	−	126.423i	0.408174	−	0.438968i
$289$	9.08071	+	27.9475i	0.0314211	+	0.0967043i
$290$	5.91079	+	1.92053i	0.0203820	+	0.00662252i
$291$	−12.2717	−	47.3116i	−0.0421707	−	0.162583i
$292$	−57.4361	−	41.7298i	−0.196699	−	0.142910i
$293$	−276.702	−	89.9060i	−0.944377	−	0.306847i	−0.203948	−	0.978982i	$-0.565377\pi$
$293$	−276.702	−	89.9060i	−0.944377	−	0.306847i	−0.740429	+	0.672135i	$0.765377\pi$
$294$	195.336	+	76.7839i	0.664410	+	0.261170i
$295$	−16.2399	+	11.7990i	−0.0550506	+	0.0399966i
$296$			553.114i			1.86863i
$297$		0			0
$298$	260.998			0.875832
$299$	232.707	+	320.294i	0.778286	+	1.07122i
$300$	−33.6414	+	85.5830i	−0.112138	+	0.285277i
$301$	−18.2716	+	56.2343i	−0.0607030	+	0.186825i
$302$	167.035	−	229.905i	0.553097	−	0.761273i
$303$	−302.571	+	78.4808i	−0.998583	+	0.259012i
$304$	−46.4306	+	142.899i	−0.152732	+	0.470061i
$305$	30.7587	−	9.99411i	0.100848	−	0.0327676i
$306$	176.091	+	163.738i	0.575462	+	0.535092i
$307$	281.800			0.917915			0.458957	−	0.888458i	$-0.348223\pi$
$307$	281.800			0.917915			0.458957	+	0.888458i	$0.348223\pi$
$308$		0			0
$309$	126.018	+	103.730i	0.407826	+	0.335697i
$310$	3.80676	−	2.76578i	0.0122799	−	0.00892186i
$311$	450.565	−	146.398i	1.44876	−	0.470732i	0.524146	−	0.851628i	$-0.324385\pi$
$311$	450.565	−	146.398i	1.44876	−	0.470732i	0.924618	+	0.380897i	$0.124385\pi$
$312$	−240.480	−	376.883i	−0.770768	−	1.20796i
$313$	24.2496	+	17.6184i	0.0774748	+	0.0562887i	0.625848	−	0.779945i	$-0.284753\pi$
$313$	24.2496	+	17.6184i	0.0774748	+	0.0562887i	−0.548374	+	0.836233i	$0.684753\pi$
$314$	−63.6811	+	87.6495i	−0.202806	+	0.279139i
$315$	−1.97567	+	16.2828i	−0.00627197	+	0.0516915i
$316$	19.6790	+	60.5656i	0.0622752	+	0.191663i
$317$	93.6204	+	128.857i	0.295333	+	0.406490i	0.930737	−	0.365689i	$-0.119167\pi$
$317$	93.6204	+	128.857i	0.295333	+	0.406490i	−0.635405	+	0.772179i	$0.719167\pi$
$318$	164.578	+	135.470i	0.517541	+	0.426007i
$319$		0			0
$320$			48.5757i			0.151799i
$321$	−5.14181	+	85.0651i	−0.0160181	+	0.265000i
$322$	30.9219	+	95.1679i	0.0960308	+	0.295552i
$323$	244.054	+	79.2981i	0.755586	+	0.245505i
$324$	98.3519	+	24.2236i	0.303555	+	0.0747641i
$325$	339.441	+	246.618i	1.04443	+	0.758825i
$326$	−24.3465	−	7.91065i	−0.0746825	−	0.0242658i
$327$	−45.2766	+	115.183i	−0.138461	+	0.352241i
$328$	−474.994	+	345.103i	−1.44815	+	1.05214i
$329$			192.607i			0.585431i
$330$		0			0
$331$	332.709			1.00516			0.502582	−	0.864530i	$-0.332384\pi$
$331$	332.709			1.00516			0.502582	+	0.864530i	$0.332384\pi$
$332$	43.5209	+	59.9014i	0.131087	+	0.180426i
$333$	−499.694	+	277.919i	−1.50058	+	0.834591i
$334$	−78.9626	+	243.022i	−0.236415	+	0.727611i
$335$	31.7297	−	43.6722i	0.0947155	−	0.130365i
$336$	−18.5403	−	71.4793i	−0.0551794	−	0.212736i
$337$	−17.1212	+	52.6936i	−0.0508047	+	0.156361i	−0.973240	−	0.229791i	$-0.926196\pi$
$337$	−17.1212	+	52.6936i	−0.0508047	+	0.156361i	0.922435	+	0.386152i	$0.126196\pi$
$338$	−195.532	+	63.5322i	−0.578497	+	0.187965i
$339$	26.2782	−	434.741i	0.0775167	−	1.28242i
$340$	14.0740			0.0413942
$341$		0			0
$342$	−233.244	+	45.6840i	−0.682000	+	0.133579i
$343$	−192.491	+	139.853i	−0.561197	+	0.407733i
$344$	−187.645	+	60.9694i	−0.545478	+	0.177237i
$345$	40.8589	−	26.0710i	0.118432	−	0.0755682i
$346$	−33.6751	−	24.4664i	−0.0973270	−	0.0707122i
$347$	81.4326	−	112.082i	0.234676	−	0.323004i	−0.675395	−	0.737456i	$-0.736027\pi$
$347$	81.4326	−	112.082i	0.234676	−	0.323004i	0.910071	+	0.414452i	$0.136027\pi$
$348$	10.8282	+	16.9700i	0.0311154	+	0.0487645i
$349$	−69.9974	−	215.430i	−0.200566	−	0.617277i	−0.999866	−	0.0163462i	$-0.994797\pi$
$349$	−69.9974	−	215.430i	−0.200566	−	0.617277i	0.799301	−	0.600931i	$-0.205203\pi$
$350$	62.3330	+	85.7940i	0.178094	+	0.245126i
$351$	219.652	−	406.624i	0.625788	−	1.15847i
$352$		0			0
$353$			258.939i			0.733538i	0.930312	+	0.366769i	$0.119536\pi$
$353$			258.939i			0.733538i	−0.930312	+	0.366769i	$0.880464\pi$
$354$	142.697	+	8.62538i	0.403098	+	0.0243655i
$355$	−8.90657	−	27.4116i	−0.0250889	−	0.0772157i
$356$	−45.4206	−	14.7580i	−0.127586	−	0.0414552i
$357$	−122.078	+	31.6647i	−0.341957	+	0.0886967i
$358$	−82.9101	−	60.2377i	−0.231592	−	0.168262i
$359$	−246.358	−	80.0466i	−0.686234	−	0.222971i	−0.0549113	−	0.998491i	$-0.517488\pi$
$359$	−246.358	−	80.0466i	−0.686234	−	0.222971i	−0.631323	+	0.775520i	$0.717488\pi$
$360$	−47.8314	+	26.6028i	−0.132865	+	0.0738967i
$361$	86.8492	−	63.0996i	0.240580	−	0.174791i
$362$		−	246.079i		−	0.679775i
$363$		0			0
$364$	55.8476			0.153428
$365$	23.3093	+	32.0824i	0.0638610	+	0.0878971i
$366$	−214.358	−	84.2612i	−0.585679	−	0.230222i
$367$	−61.4255	+	189.048i	−0.167372	+	0.515118i	−0.999203	−	0.0399105i	$-0.987293\pi$
$367$	−61.4255	+	189.048i	−0.167372	+	0.515118i	0.831831	+	0.555029i	$0.187293\pi$
$368$	−128.259	+	176.534i	−0.348531	+	0.479712i
$369$	−550.440	−	255.718i	−1.49171	−	0.693002i
$370$	22.7386	−	69.9823i	0.0614557	−	0.189141i
$371$	−106.331	+	34.5492i	−0.286607	+	0.0931244i
$372$	15.2131	+	0.919567i	0.0408955	+	0.00247195i
$373$	−670.467			−1.79750			−0.898750	−	0.438462i	$-0.855523\pi$
$373$	−670.467			−1.79750			−0.898750	+	0.438462i	$0.855523\pi$
$374$		0			0
$375$	65.9379	−	80.1056i	0.175834	−	0.213615i
$376$	−519.953	+	377.768i	−1.38285	+	1.00470i
$377$	87.3527	−	28.3826i	0.231705	−	0.0752855i
$378$	84.5590	−	80.5886i	0.223701	−	0.213197i
$379$	−317.451	−	230.642i	−0.837601	−	0.608553i	0.0840983	−	0.996457i	$-0.473199\pi$
$379$	−317.451	−	230.642i	−0.837601	−	0.608553i	−0.921700	+	0.387905i	$0.873199\pi$
$380$	−8.17691	+	11.2546i	−0.0215182	+	0.0296173i
$381$	462.258	−	294.956i	1.21328	−	0.774161i
$382$	−28.7983	−	88.6321i	−0.0753883	−	0.232021i
$383$	−292.542	−	402.649i	−0.763817	−	1.05130i	−0.996887	−	0.0788436i	$-0.974877\pi$
$383$	−292.542	−	402.649i	−0.763817	−	1.05130i	0.233070	−	0.972460i	$-0.425123\pi$
$384$	73.5699	−	89.3774i	0.191588	−	0.232754i
$385$		0			0
$386$		−	250.336i		−	0.648538i
$387$	−149.365	−	138.887i	−0.385957	−	0.358881i
$388$	6.29584	+	19.3766i	0.0162264	+	0.0499397i
$389$	392.101	+	127.401i	1.00797	+	0.327510i	0.766047	−	0.642785i	$-0.222221\pi$
$389$	392.101	+	127.401i	1.00797	+	0.327510i	0.241926	+	0.970295i	$0.422221\pi$
$390$	14.9328	+	57.5710i	0.0382891	+	0.147618i
$391$	301.500	+	219.053i	0.771100	+	0.560237i
$392$	−349.357	−	113.513i	−0.891217	−	0.289574i
$393$	−235.958	−	92.7515i	−0.600401	−	0.236009i
$394$	−29.9651	+	21.7709i	−0.0760535	+	0.0552561i
$395$		−	35.5715i		−	0.0900544i
$396$		0			0
$397$	171.230			0.431310			0.215655	−	0.976470i	$-0.430811\pi$
$397$	171.230			0.431310			0.215655	+	0.976470i	$0.430811\pi$
$398$	147.103	+	202.470i	0.369605	+	0.508718i
$399$	45.6055	−	116.019i	0.114299	−	0.290775i
$400$	−71.4608	+	219.934i	−0.178652	+	0.549835i
$401$	−426.743	+	587.361i	−1.06420	+	1.46474i	−0.188382	+	0.982096i	$0.560324\pi$
$401$	−426.743	+	587.361i	−1.06420	+	1.46474i	−0.875816	+	0.482646i	$0.839676\pi$
$402$	−372.124	+	96.5215i	−0.925681	+	0.240103i
$403$	21.4888	−	66.1357i	0.0533221	−	0.164108i
$404$	123.919	−	40.2636i	0.306729	−	0.0996624i
$405$	−48.0670	−	29.8450i	−0.118684	−	0.0736912i
$406$	23.2147			0.0571790
$407$		0			0
$408$	−324.919	−	267.453i	−0.796369	−	0.655521i
$409$	243.830	−	177.153i	0.596161	−	0.433137i	−0.248353	−	0.968670i	$-0.579889\pi$
$409$	243.830	−	177.153i	0.596161	−	0.433137i	0.844514	+	0.535533i	$0.179889\pi$
$410$	74.2855	−	24.1368i	0.181184	−	0.0588703i
$411$	329.797	+	516.863i	0.802426	+	1.25757i
$412$	−55.0420	−	39.9904i	−0.133597	−	0.0970640i
$413$	−44.0727	+	60.6608i	−0.106713	+	0.146878i
$414$	−342.658	−	41.5762i	−0.827676	−	0.100426i
$415$	−12.7804	−	39.3340i	−0.0307961	−	0.0947808i
$416$	192.985	+	265.621i	0.463905	+	0.638511i
$417$	116.371	+	95.7892i	0.279067	+	0.229710i
$418$		0			0
$419$		−	573.195i		−	1.36801i	−0.729478	−	0.684004i	$-0.760237\pi$
$419$		−	573.195i		−	1.36801i	0.729478	−	0.684004i	$-0.239763\pi$
$420$	0.412516	−	6.82459i	0.000982181	−	0.0162490i
$421$	−172.827	−	531.908i	−0.410516	−	1.26344i	−0.916200	−	0.400721i	$-0.868760\pi$
$421$	−172.827	−	531.908i	−0.410516	−	1.26344i	0.505684	−	0.862719i	$-0.331240\pi$
$422$	−286.349	−	93.0404i	−0.678552	−	0.220475i
$423$	−602.540	−	279.922i	−1.42445	−	0.661754i
$424$	−301.820	−	219.285i	−0.711839	−	0.517182i
$425$	375.622	+	122.047i	0.883816	+	0.287169i
$426$	−75.0920	+	191.032i	−0.176272	+	0.448433i
$427$	97.7334	−	71.0075i	0.228884	−	0.166294i
$428$		−	35.5229i		−	0.0829973i
$429$		0			0
$430$	26.2480			0.0610420
$431$	117.467	+	161.680i	0.272546	+	0.375127i	0.923247	−	0.384207i	$-0.125525\pi$
$431$	117.467	+	161.680i	0.272546	+	0.375127i	−0.650701	+	0.759334i	$0.725525\pi$
$432$	250.557	+	45.8828i	0.579993	+	0.106210i
$433$	−31.9791	+	98.4214i	−0.0738547	+	0.227301i	−0.981169	−	0.193152i	$-0.938129\pi$
$433$	−31.9791	+	98.4214i	−0.0738547	+	0.227301i	0.907314	+	0.420453i	$0.138129\pi$
$434$	10.3310	−	14.2194i	0.0238041	−	0.0327635i
$435$	−2.82313	−	10.8842i	−0.00648996	−	0.0250211i
$436$	15.9417	−	49.0635i	0.0365635	−	0.112531i
$437$	−350.338	+	113.832i	−0.801690	+	0.260485i
$438$	17.0397	−	281.901i	0.0389034	−	0.643610i
$439$	662.550			1.50923			0.754613	−	0.656171i	$-0.227825\pi$
$439$	662.550			1.50923			0.754613	+	0.656171i	$0.227825\pi$
$440$		0			0
$441$	−72.9890	−	372.652i	−0.165508	−	0.845016i
$442$	−369.977	+	268.804i	−0.837051	+	0.608153i
$443$	−200.511	+	65.1499i	−0.452620	+	0.147065i	−0.526451	−	0.850206i	$-0.676478\pi$
$443$	−200.511	+	65.1499i	−0.452620	+	0.147065i	0.0738308	+	0.997271i	$0.476478\pi$
$444$	200.921	−	128.203i	0.452525	−	0.288745i
$445$	21.5817	+	15.6801i	0.0484983	+	0.0352361i
$446$	183.266	−	252.244i	0.410911	−	0.565570i
$447$	−254.001	−	398.074i	−0.568235	−	0.890545i
$448$	56.0693	+	172.563i	0.125155	+	0.385186i
$449$	140.640	+	193.574i	0.313229	+	0.431123i	0.936385	−	0.350975i	$-0.114150\pi$
$449$	140.640	+	193.574i	0.313229	+	0.431123i	−0.623156	+	0.782098i	$0.714150\pi$
$450$	−358.984	+	70.3118i	−0.797742	+	0.156248i
$451$		0			0
$452$			181.546i			0.401651i
$453$	−513.207	−	31.0211i	−1.13291	−	0.0684793i
$454$	−219.936	−	676.892i	−0.484440	−	1.49095i
$455$	−29.6684	−	9.63983i	−0.0652052	−	0.0211864i
$456$	402.649	−	104.439i	0.883001	−	0.229033i
$457$	21.5908	+	15.6866i	0.0472446	+	0.0343252i	0.611157	−	0.791509i	$-0.290704\pi$
$457$	21.5908	+	15.6866i	0.0472446	+	0.0343252i	−0.563912	+	0.825835i	$0.690704\pi$
$458$	214.118	+	69.5713i	0.467507	+	0.151902i
$459$	78.3626	−	427.923i	0.170725	−	0.932294i
$460$	−16.3447	+	11.8751i	−0.0355320	+	0.0258155i
$461$			393.125i			0.852766i	0.904543	+	0.426383i	$0.140212\pi$
$461$			393.125i			0.852766i	−0.904543	+	0.426383i	$0.859788\pi$
$462$		0			0
$463$	106.954			0.231002			0.115501	−	0.993307i	$-0.463153\pi$
$463$	106.954			0.231002			0.115501	+	0.993307i	$0.463153\pi$
$464$	29.7556	+	40.9550i	0.0641283	+	0.0882651i
$465$	−7.92307	−	3.11444i	−0.0170389	−	0.00669772i
$466$	−167.498	+	515.506i	−0.359438	+	1.10624i
$467$	−248.580	+	342.141i	−0.532291	+	0.732636i	−0.987477	−	0.157760i	$-0.949573\pi$
$467$	−248.580	+	342.141i	−0.532291	+	0.732636i	0.455186	+	0.890396i	$0.349573\pi$
$468$	−81.1652	+	174.711i	−0.173430	+	0.373313i
$469$	62.3094	−	191.769i	0.132856	−	0.408888i
$470$	81.3168	−	26.4214i	0.173014	−	0.0562158i
$471$	195.657	+	11.8266i	0.415407	+	0.0251095i
$472$	−250.199			−0.530083
$473$		0			0
$474$	−160.996	+	195.588i	−0.339654	+	0.412634i
$475$	−315.831	+	229.464i	−0.664906	+	0.483083i
$476$	49.9976	−	16.2452i	0.105037	−	0.0341286i
$477$	46.4532	−	382.853i	0.0973862	−	0.802626i
$478$	−125.365	−	91.0832i	−0.262270	−	0.190551i
$479$	−317.236	+	436.638i	−0.662289	+	0.911562i	−0.999554	−	0.0298475i	$-0.990498\pi$
$479$	−317.236	+	436.638i	−0.662289	+	0.911562i	0.337266	+	0.941409i	$0.390498\pi$
$480$	33.8843	−	21.6208i	0.0705924	−	0.0450432i
$481$	−336.043	−	1034.24i	−0.698635	−	2.15018i
$482$	201.523	+	277.373i	0.418098	+	0.575462i
$483$	115.057	−	139.779i	0.238213	−	0.289397i
$484$		0			0
$485$		−	11.3803i		−	0.0234645i
$486$	129.217	+	381.652i	0.265878	+	0.785291i
$487$	188.700	+	580.759i	0.387474	+	1.19252i	0.934669	+	0.355518i	$0.115696\pi$
$487$	188.700	+	580.759i	0.387474	+	1.19252i	−0.547195	+	0.837005i	$0.684304\pi$
$488$	383.378	+	124.567i	0.785610	+	0.255260i
$489$	11.6285	+	44.8318i	0.0237801	+	0.0916805i
$490$	39.5356	+	28.7243i	0.0806849	+	0.0586210i
$491$	−54.0905	−	17.5751i	−0.110164	−	0.0357944i	0.253416	−	0.967357i	$-0.418446\pi$
$491$	−54.0905	−	17.5751i	−0.110164	−	0.0357944i	−0.363580	+	0.931563i	$0.618446\pi$
$492$	235.456	+	92.5545i	0.478570	+	0.188119i
$493$	69.9465	−	50.8191i	0.141879	−	0.103081i
$494$		−	452.031i		−	0.915043i
$495$		0			0
$496$	38.3274			0.0772729
$497$	−63.2806	−	87.0983i	−0.127325	−	0.175248i
$498$	−107.753	+	274.120i	−0.216371	+	0.550442i
$499$	144.891	−	445.930i	0.290363	−	0.893646i	−0.694376	−	0.719612i	$-0.744320\pi$
$499$	144.891	−	445.930i	0.290363	−	0.893646i	0.984740	−	0.174034i	$-0.0556804\pi$
$500$	−25.4205	+	34.9884i	−0.0508411	+	0.0699767i
$501$	447.502	−	116.073i	0.893218	−	0.231683i
$502$	1.42974	−	4.40029i	0.00284809	−	0.00876552i
$503$	435.748	−	141.583i	0.866297	−	0.281477i	0.158041	−	0.987433i	$-0.449482\pi$
$503$	435.748	−	141.583i	0.866297	−	0.281477i	0.708256	+	0.705955i	$0.249482\pi$
$504$	−139.213	+	149.716i	−0.276216	+	0.297055i
$505$	−72.7802			−0.144119
$506$		0			0
$507$	287.189	+	236.396i	0.566448	+	0.466265i
$508$	−184.917	+	134.350i	−0.364009	+	0.264468i
$509$	−261.397	+	84.9330i	−0.513550	+	0.166862i	−0.554316	−	0.832306i	$-0.687020\pi$
$509$	−261.397	+	84.9330i	−0.513550	+	0.166862i	0.0407663	+	0.999169i	$0.487020\pi$
$510$	30.1150	+	47.1967i	0.0590491	+	0.0925426i
$511$	119.837	+	87.0667i	0.234515	+	0.170385i
$512$	−299.479	+	412.197i	−0.584920	+	0.805073i
$513$	296.668	+	311.284i	0.578300	+	0.606792i
$514$	205.065	+	631.127i	0.398960	+	1.22787i
$515$	22.3377	+	30.7452i	0.0433741	+	0.0596994i
$516$	65.6404	+	54.0310i	0.127210	+	0.104711i
$517$		0			0
$518$		−	274.856i		−	0.530610i
$519$	−4.54380	+	75.1717i	−0.00875491	+	0.144840i
$520$	−32.1666	−	98.9985i	−0.0618588	−	0.190382i
$521$	236.239	+	76.7587i	0.453434	+	0.147330i	0.526825	−	0.849974i	$-0.323382\pi$
$521$	236.239	+	76.7587i	0.453434	+	0.147330i	−0.0733915	+	0.997303i	$0.523382\pi$
$522$	−33.7387	+	72.6235i	−0.0646335	+	0.139126i
$523$	113.737	+	82.6347i	0.217470	+	0.158001i	0.691187	−	0.722676i	$-0.257088\pi$
$523$	113.737	+	82.6347i	0.217470	+	0.158001i	−0.473717	+	0.880677i	$0.657088\pi$
$524$	100.509	+	32.6574i	0.191811	+	0.0623232i
$525$	70.1909	−	178.564i	0.133697	−	0.340122i
$526$	−508.705	+	369.596i	−0.967119	+	0.702653i
$527$		−	65.4587i		−	0.124210i
$528$		0			0
$529$	−5.97152			−0.0112883
$530$	29.1727	+	40.1527i	0.0550428	+	0.0757599i
$531$	−125.716	−	226.035i	−0.236753	−	0.425678i
$532$	−16.0575	+	49.4198i	−0.0301832	+	0.0928943i
$533$	678.497	−	933.871i	1.27298	−	1.75210i
$534$	−47.6986	−	183.895i	−0.0893232	−	0.344372i
$535$	−6.13159	+	18.8711i	−0.0114609	+	0.0352731i
$536$	639.901	−	207.916i	1.19384	−	0.387904i
$537$	−11.1871	+	185.077i	−0.0208326	+	0.344650i
$538$	51.7358			0.0961633
$539$		0			0
$540$	20.7501	+	11.2089i	0.0384262	+	0.0207572i
$541$	486.149	−	353.208i	0.898612	−	0.652880i	−0.0394969	−	0.999220i	$-0.512576\pi$
$541$	486.149	−	353.208i	0.898612	−	0.652880i	0.938109	+	0.346340i	$0.112576\pi$
$542$	817.055	−	265.477i	1.50748	−	0.489811i
$543$	−375.319	+	239.481i	−0.691195	+	0.441034i
$544$	250.034	+	181.661i	0.459622	+	0.333935i
$545$	−16.9376	+	23.3127i	−0.0310782	+	0.0427755i
$546$	119.500	+	187.283i	0.218865	+	0.343009i
$547$	191.860	+	590.485i	0.350750	+	1.07950i	0.958433	+	0.285318i	$0.0920992\pi$
$547$	191.860	+	590.485i	0.350750	+	1.07950i	−0.607683	+	0.794180i	$0.707901\pi$
$548$	−150.220	−	206.760i	−0.274124	−	0.377299i
$549$	80.0967	+	408.941i	0.145896	+	0.744884i
$550$		0			0
$551$			85.4594i			0.155099i
$552$	603.007	+	36.4491i	1.09240	+	0.0660310i
$553$	−41.0590	−	126.367i	−0.0742478	−	0.228511i
$554$	−580.271	−	188.541i	−1.04742	−	0.340327i
$555$	−128.866	+	33.4252i	−0.232191	+	0.0602256i
$556$	−50.8282	−	36.9289i	−0.0914177	−	0.0664188i
$557$	−513.595	−	166.877i	−0.922074	−	0.299600i	−0.190757	−	0.981637i	$-0.561094\pi$
$557$	−513.595	−	166.877i	−0.922074	−	0.299600i	−0.731317	+	0.682037i	$0.761094\pi$
$558$	29.4687	+	52.9843i	0.0528113	+	0.0949539i
$559$	313.824	−	228.006i	0.561402	−	0.407883i
$560$		−	17.1936i		−	0.0307028i
$561$		0			0
$562$	−531.261			−0.945305
$563$	−163.796	−	225.446i	−0.290934	−	0.400437i	0.638383	−	0.769719i	$-0.279604\pi$
$563$	−163.796	−	225.446i	−0.290934	−	0.400437i	−0.929317	+	0.369282i	$0.879604\pi$
$564$	257.743	+	101.315i	0.456991	+	0.179636i
$565$	31.3366	−	96.4441i	0.0554630	−	0.170698i
$566$	156.717	−	215.703i	0.276886	−	0.381101i
$567$	−205.206	−	50.5411i	−0.361915	−	0.0891377i
$568$	111.012	−	341.659i	0.195443	−	0.601513i
$569$	−1017.22	+	330.514i	−1.78773	+	0.580869i	−0.999408	−	0.0343952i	$-0.989050\pi$
$569$	−1017.22	+	330.514i	−1.78773	+	0.580869i	−0.788321	+	0.615264i	$0.789050\pi$
$570$	−55.2383	−	3.33891i	−0.0969093	−	0.00585774i
$571$	−470.660			−0.824274			−0.412137	−	0.911122i	$-0.635217\pi$
$571$	−470.660			−0.824274			−0.412137	+	0.911122i	$0.635217\pi$
$572$		0			0
$573$	−107.155	+	130.179i	−0.187007	+	0.227189i
$574$	236.037	−	171.491i	0.411214	−	0.298764i
$575$	−539.203	+	175.198i	−0.937744	+	0.304691i
$576$	−621.325	−	75.3882i	−1.07869	−	0.130882i
$577$	−185.383	−	134.689i	−0.321288	−	0.233429i	0.415437	−	0.909622i	$-0.363629\pi$
$577$	−185.383	−	134.689i	−0.321288	−	0.233429i	−0.736725	+	0.676193i	$0.763629\pi$
$578$	28.6406	−	39.4204i	0.0495512	−	0.0682014i
$579$	−381.812	+	243.625i	−0.659433	+	0.420768i
$580$	1.44837	+	4.45764i	0.00249720	+	0.00768558i
$581$	−90.8039	−	124.981i	−0.156289	−	0.215113i
$582$	−51.5071	+	62.5741i	−0.0885001	+	0.107516i
$583$		0			0
$584$			494.275i			0.846361i
$585$	73.2747	−	78.8030i	0.125256	−	0.134706i
$586$	149.079	+	458.817i	0.254400	+	0.782964i
$587$	0.704580	+	0.228932i	0.00120031	+	0.000390003i	0.309617	−	0.950861i	$-0.399799\pi$
$587$	0.704580	+	0.228932i	0.00120031	+	0.000390003i	−0.308417	+	0.951251i	$0.599799\pi$
$588$	39.7412	+	153.216i	0.0675870	+	0.260571i
$589$	52.3452	+	38.0310i	0.0888714	+	0.0645688i
$590$	31.6562	+	10.2857i	0.0536546	+	0.0174334i
$591$	62.3667	+	24.5155i	0.105527	+	0.0414813i
$592$	484.897	−	352.299i	0.819083	−	0.595099i
$593$			498.413i			0.840494i	0.907410	+	0.420247i	$0.138057\pi$
$593$			498.413i			0.840494i	−0.907410	+	0.420247i	$0.861943\pi$
$594$		0			0
$595$	−29.3647			−0.0493524
$596$	115.695	+	159.241i	0.194120	+	0.267183i
$597$	165.647	−	421.403i	0.277466	−	0.705868i
$598$	202.862	−	624.344i	0.339234	−	1.04405i
$599$	−112.504	+	154.848i	−0.187819	+	0.258511i	−0.892534	−	0.450979i	$-0.851075\pi$
$599$	−112.504	+	154.848i	−0.187819	+	0.258511i	0.704715	+	0.709490i	$0.251075\pi$
$600$	619.713	−	160.741i	1.03285	−	0.267902i
$601$	−256.922	+	790.726i	−0.427491	+	1.31568i	0.473097	+	0.881010i	$0.343136\pi$
$601$	−256.922	+	790.726i	−0.427491	+	1.31568i	−0.900588	+	0.434673i	$0.856864\pi$
$602$	93.2454	−	30.2973i	0.154893	−	0.0503277i
$603$	509.362	+	473.629i	0.844713	+	0.785454i
$604$	214.314			0.354824
$605$		0			0
$606$	400.178	+	329.402i	0.660361	+	0.543567i
$607$	638.876	−	464.171i	1.05251	−	0.764697i	0.0798256	−	0.996809i	$-0.474564\pi$
$607$	638.876	−	464.171i	1.05251	−	0.764697i	0.972689	+	0.232112i	$0.0745636\pi$
$608$	−290.536	+	94.4010i	−0.477856	+	0.155265i
$609$	−22.5923	−	35.4070i	−0.0370974	−	0.0581396i
$610$	−43.3856	−	31.5215i	−0.0711239	−	0.0516746i
$611$	742.718	−	1022.26i	1.21558	−	1.67310i
$612$	−21.8426	+	180.019i	−0.0356905	+	0.294149i
$613$	85.6583	+	263.629i	0.139736	+	0.430064i	0.996297	−	0.0859829i	$-0.0274030\pi$
$613$	85.6583	+	263.629i	0.139736	+	0.430064i	−0.856560	+	0.516047i	$0.827403\pi$
$614$	−274.654	−	378.029i	−0.447319	−	0.615682i
$615$	−109.107	−	89.8104i	−0.177411	−	0.146033i
$616$		0			0
$617$			928.547i			1.50494i	0.658628	+	0.752469i	$0.271137\pi$
$617$			928.547i			1.50494i	−0.658628	+	0.752469i	$0.728863\pi$
$618$	16.3294	−	270.151i	0.0264230	−	0.437137i
$619$	295.319	+	908.900i	0.477091	+	1.46834i	0.843117	+	0.537731i	$0.180718\pi$
$619$	295.319	+	908.900i	0.477091	+	1.46834i	−0.366025	+	0.930605i	$0.619282\pi$
$620$	3.37493	+	1.09658i	0.00544343	+	0.00176868i
$621$	270.060	+	563.083i	0.434878	+	0.906735i
$622$	−635.529	−	461.739i	−1.02175	−	0.742346i
$623$	94.7674	+	30.7918i	0.152115	+	0.0494250i
$624$	−177.231	+	450.871i	−0.284024	+	0.722550i
$625$	−476.224	+	345.997i	−0.761958	+	0.553595i
$626$		−	49.7019i		−	0.0793961i
$627$		0			0
$628$	−81.7055			−0.130104
$629$	−601.686	−	828.149i	−0.956575	−	1.31661i
$630$	23.7687	−	13.2196i	0.0377280	−	0.0209835i
$631$	−1.62527	+	5.00208i	−0.00257571	+	0.00792722i	−0.952336	−	0.305051i	$-0.901327\pi$
$631$	−1.62527	+	5.00208i	−0.00257571	+	0.00792722i	0.949760	+	0.312978i	$0.101327\pi$
$632$	260.603	−	358.690i	0.412347	−	0.567547i
$633$	136.767	+	527.285i	0.216062	+	0.832994i
$634$	81.6132	−	251.180i	0.128728	−	0.396183i
$635$	121.425	−	39.4533i	0.191220	−	0.0621311i
$636$	−9.69935	+	160.464i	−0.0152506	+	0.252302i
$637$	722.207			1.13376
$638$		0			0
$639$	364.441	−	71.3807i	0.570330	−	0.111707i
$640$	21.8058	−	15.8428i	0.0340715	−	0.0247544i
$641$	−462.217	+	150.183i	−0.721087	+	0.234296i	−0.646495	−	0.762919i	$-0.723766\pi$
$641$	−462.217	+	150.183i	−0.721087	+	0.234296i	−0.0745928	+	0.997214i	$0.523766\pi$
$642$	119.124	−	76.0103i	0.185552	−	0.118396i
$643$	597.765	+	434.302i	0.929650	+	0.675430i	0.945907	−	0.324437i	$-0.105175\pi$
$643$	597.765	+	434.302i	0.929650	+	0.675430i	−0.0162570	+	0.999868i	$0.505175\pi$
$644$	−44.3570	+	61.0522i	−0.0688774	+	0.0948016i
$645$	−25.5444	−	40.0335i	−0.0396037	−	0.0620674i
$646$	−131.489	−	404.681i	−0.203543	−	0.626441i
$647$	−676.121	−	930.601i	−1.04501	−	1.43833i	−0.893057	−	0.449945i	$-0.851444\pi$
$647$	−676.121	−	930.601i	−1.04501	−	1.43833i	−0.151953	−	0.988388i	$-0.548556\pi$
$648$	−266.040	−	653.093i	−0.410556	−	1.00786i
$649$		0			0
$650$		−	695.717i		−	1.07033i
$651$	−31.7413	−	1.91862i	−0.0487578	−	0.00294720i
$652$	−5.96585	−	18.3610i	−0.00915007	−	0.0281610i
$653$	−575.439	−	186.971i	−0.881224	−	0.286327i	−0.166758	−	0.985998i	$-0.553330\pi$
$653$	−575.439	−	186.971i	−0.881224	−	0.286327i	−0.714465	+	0.699671i	$0.753330\pi$
$654$	198.644	−	51.5242i	0.303736	−	0.0787831i
$655$	−47.7572	−	34.6976i	−0.0729117	−	0.0529735i
$656$	605.083	+	196.603i	0.922382	+	0.299700i
$657$	−446.538	+	248.355i	−0.679662	+	0.378013i
$658$	258.378	−	187.723i	0.392672	−	0.285293i
$659$		−	956.314i		−	1.45116i	−0.688138	−	0.725580i	$-0.741572\pi$
$659$		−	956.314i		−	1.45116i	0.688138	−	0.725580i	$-0.258428\pi$
$660$		0			0
$661$	57.8747			0.0875563			0.0437781	−	0.999041i	$-0.486061\pi$
$661$	57.8747			0.0875563			0.0437781	+	0.999041i	$0.486061\pi$
$662$	−324.272	−	446.323i	−0.489837	−	0.674203i
$663$	770.037	+	302.690i	1.16144	+	0.456547i
$664$	159.295	−	490.261i	0.239903	−	0.738345i
$665$	17.0607	−	23.4820i	0.0256551	−	0.0353113i
$666$	859.845	+	399.458i	1.29106	+	0.599786i
$667$	−38.3523	+	118.036i	−0.0574997	+	0.176966i
$668$	−183.276	+	59.5499i	−0.274365	+	0.0891466i
$669$	−563.076	−	34.0355i	−0.841668	−	0.0508751i
$670$	−89.5104			−0.133598
$671$		0			0
$672$	95.4169	−	115.919i	0.141989	−	0.172498i
$673$	688.997	−	500.586i	1.02377	−	0.743813i	0.0567178	−	0.998390i	$-0.481936\pi$
$673$	688.997	−	500.586i	1.02377	−	0.743813i	0.967052	+	0.254578i	$0.0819365\pi$
$674$	87.3744	−	28.3897i	0.129636	−	0.0421212i
$675$	456.599	+	479.095i	0.676443	+	0.709770i
$676$	−125.438	−	91.1361i	−0.185559	−	0.134817i
$677$	−158.543	+	218.215i	−0.234184	+	0.322327i	−0.909894	−	0.414841i	$-0.863837\pi$
$677$	−158.543	+	218.215i	−0.234184	+	0.322327i	0.675710	+	0.737168i	$0.263837\pi$
$678$	−608.807	+	388.465i	−0.897946	+	0.572957i
$679$	−13.1359	−	40.4282i	−0.0193460	−	0.0595408i
$680$	−57.5942	−	79.2717i	−0.0846974	−	0.116576i
$681$	−818.355	+	994.191i	−1.20170	+	1.45990i
$682$		0			0
$683$		−	254.016i		−	0.371913i	−0.982558	−	0.185956i	$-0.940462\pi$
$683$		−	254.016i		−	0.371913i	0.982558	−	0.185956i	$-0.0595383\pi$
$684$	−131.265	−	122.057i	−0.191908	−	0.178445i
$685$	44.1137	+	135.768i	0.0643996	+	0.198201i
$686$	375.219	+	121.916i	0.546966	+	0.177720i
$687$	−102.268	−	394.279i	−0.148862	−	0.573914i
$688$	172.968	+	125.668i	0.251407	+	0.182658i
$689$	697.582	+	226.658i	1.01246	+	0.328967i
$690$	−74.7965	−	29.4014i	−0.108401	−	0.0426108i
$691$	306.290	−	222.532i	0.443256	−	0.322044i	−0.343672	−	0.939090i	$-0.611671\pi$
$691$	306.290	−	222.532i	0.443256	−	0.322044i	0.786927	+	0.617046i	$0.211671\pi$
$692$		−	31.3914i		−	0.0453634i
$693$		0			0
$694$	−229.724			−0.331014
$695$	20.6276	+	28.3915i	0.0296800	+	0.0408510i
$696$	51.2719	−	130.435i	0.0736666	−	0.187406i
$697$	335.776	−	1033.41i	0.481745	−	1.48266i
$698$	−220.772	+	303.867i	−0.316293	+	0.435339i
$699$	949.256	−	246.218i	1.35802	−	0.352243i
$700$	−24.7139	+	76.0616i	−0.0353056	+	0.108659i
$701$	−304.289	+	98.8694i	−0.434078	+	0.141040i	−0.517902	−	0.855440i	$-0.673287\pi$
$701$	−304.289	+	98.8694i	−0.434078	+	0.141040i	0.0838238	+	0.996481i	$0.473287\pi$
$702$	−759.559	+	101.654i	−1.08199	+	0.144807i
$703$	1011.82			1.43929
$704$		0			0
$705$	−119.435	−	98.3111i	−0.169411	−	0.139448i
$706$	347.361	−	252.373i	0.492013	−	0.357468i
$707$	−258.549	+	84.0077i	−0.365699	+	0.118823i
$708$	57.9921	+	90.8859i	0.0819097	+	0.128370i
$709$	184.876	+	134.320i	0.260755	+	0.189450i	0.710480	−	0.703717i	$-0.248478\pi$
$709$	184.876	+	134.320i	0.260755	+	0.189450i	−0.449725	+	0.893167i	$0.648478\pi$
$710$	−28.0914	+	38.6645i	−0.0395653	+	0.0544570i
$711$	454.991	+	55.2061i	0.639931	+	0.0776457i
$712$	102.747	+	316.223i	0.144308	+	0.444134i
$713$	55.2316	+	76.0198i	0.0774636	+	0.106620i
$714$	161.460	+	132.904i	0.226135	+	0.186140i
$715$		0			0
$716$		−	77.2875i		−	0.107943i
$717$	−16.9156	+	279.848i	−0.0235922	+	0.390304i
$718$	132.730	+	408.501i	0.184861	+	0.568943i
$719$	−765.742	−	248.805i	−1.06501	−	0.346043i	−0.276467	−	0.961023i	$-0.589164\pi$
$719$	−765.742	−	248.805i	−1.06501	−	0.346043i	−0.788542	+	0.614981i	$0.789164\pi$
$720$	53.7874	+	24.9880i	0.0747048	+	0.0347056i
$721$	114.842	+	83.4376i	0.159282	+	0.115725i
$722$	−169.294	−	55.0069i	−0.234479	−	0.0761868i
$723$	226.928	−	577.300i	0.313870	−	0.798478i
$724$	150.138	−	109.082i	0.207373	−	0.150665i
$725$			131.530i			0.181420i
$726$		0			0
$727$	−1002.31			−1.37869			−0.689345	−	0.724434i	$-0.742101\pi$
$727$	−1002.31			−1.37869			−0.689345	+	0.724434i	$0.742101\pi$
$728$	−228.541	−	314.560i	−0.313930	−	0.432088i
$729$	456.342	−	568.501i	0.625984	−	0.779836i
$730$	20.3198	−	62.5378i	0.0278353	−	0.0856682i
$731$	214.627	−	295.409i	0.293608	−	0.404117i
$732$	−43.6112	−	168.136i	−0.0595781	−	0.229694i
$733$	223.915	−	689.141i	0.305478	−	0.940165i	−0.674020	−	0.738713i	$-0.735434\pi$
$733$	223.915	−	689.141i	0.305478	−	0.940165i	0.979498	−	0.201452i	$-0.0645660\pi$
$734$	313.472	−	101.853i	0.427074	−	0.138765i
$735$	5.33456	−	88.2538i	0.00725790	−	0.120073i
$736$	−443.653			−0.602789
$737$		0			0
$738$	193.442	+	987.637i	0.262117	+	1.33826i
$739$	−696.026	+	505.693i	−0.941849	+	0.684293i	−0.948865	−	0.315682i	$-0.897767\pi$
$739$	−696.026	+	505.693i	−0.941849	+	0.684293i	0.00701624	+	0.999975i	$0.497767\pi$
$740$	52.7774	−	17.1484i	0.0713208	−	0.0231735i
$741$	−689.438	+	439.913i	−0.930415	+	0.593675i
$742$	149.982	+	108.968i	0.202132	+	0.146858i
$743$	−229.421	+	315.771i	−0.308776	+	0.424994i	−0.934999	−	0.354650i	$-0.884600\pi$
$743$	−229.421	+	315.771i	−0.308776	+	0.424994i	0.626223	+	0.779644i	$0.284600\pi$
$744$	−57.0762	−	89.4507i	−0.0767154	−	0.120229i
$745$	−33.9752	−	104.565i	−0.0456043	−	0.140355i
$746$	653.465	+	899.418i	0.875959	+	1.20565i
$747$	522.951	−	102.427i	0.700069	−	0.137118i
$748$		0			0
$749$			74.1164i			0.0989538i
$750$	−171.726	−	10.3801i	−0.228968	−	0.0138401i
$751$	−266.909	−	821.461i	−0.355405	−	1.09382i	−0.955774	−	0.294101i	$-0.904980\pi$
$751$	−266.909	−	821.461i	−0.355405	−	1.09382i	0.600370	−	0.799722i	$-0.295020\pi$
$752$	662.355	+	215.212i	0.880791	+	0.286186i
$753$	−8.10273	+	2.10168i	−0.0107606	+	0.00279108i
$754$	−123.212	−	89.5190i	−0.163412	−	0.118725i
$755$	−113.851	−	36.9926i	−0.150797	−	0.0489968i
$756$	86.6523	+	15.8680i	0.114619	+	0.0209895i
$757$	683.966	−	496.931i	0.903522	−	0.656447i	−0.0358461	−	0.999357i	$-0.511413\pi$
$757$	683.966	−	496.931i	0.903522	−	0.656447i	0.939368	+	0.342910i	$0.111413\pi$
$758$			650.647i			0.858373i
$759$		0			0
$760$	96.8528			0.127438
$761$	103.379	+	142.289i	0.135847	+	0.186977i	0.871521	−	0.490359i	$-0.163134\pi$
$761$	103.379	+	142.289i	0.135847	+	0.186977i	−0.735674	+	0.677336i	$0.763134\pi$
$762$	−846.213	−	332.634i	−1.11052	−	0.436528i
$763$	−33.2614	+	102.368i	−0.0435929	+	0.134165i
$764$	41.3108	−	56.8594i	0.0540717	−	0.0744233i
$765$	42.6767	−	91.8628i	0.0557865	−	0.120082i
$766$	−255.022	+	784.878i	−0.332927	+	1.02464i
$767$	467.833	−	152.008i	0.609951	−	0.198185i
$768$	641.387	+	38.7690i	0.835139	+	0.0504805i
$769$	−1341.04			−1.74388			−0.871941	−	0.489611i	$-0.837139\pi$
$769$	−1341.04			−1.74388			−0.871941	+	0.489611i	$0.837139\pi$
$770$		0			0
$771$	763.025	−	926.972i	0.989657	−	1.20230i
$772$	152.736	−	110.969i	0.197844	−	0.143742i
$773$	746.230	−	242.465i	0.965368	−	0.313667i	0.216424	−	0.976300i	$-0.430561\pi$
$773$	746.230	−	242.465i	0.965368	−	0.313667i	0.748945	+	0.662632i	$0.230561\pi$
$774$	−40.7363	+	335.736i	−0.0526309	+	0.433767i
$775$	80.5641	+	58.5332i	0.103954	+	0.0755268i
$776$	83.3742	−	114.755i	0.107441	−	0.147880i
$777$	−419.210	+	267.488i	−0.539524	+	0.344257i
$778$	−211.252	−	650.167i	−0.271532	−	0.835690i
$779$	631.303	+	868.914i	0.810402	+	1.11542i
$780$	−28.5060	+	34.6309i	−0.0365461	+	0.0443986i
$781$		0			0
$782$		−	617.954i		−	0.790222i
$783$	143.599	−	19.2184i	0.183396	−	0.0245446i
$784$	123.005	+	378.571i	0.156894	+	0.482871i
$785$	43.4051	+	14.1032i	0.0552931	+	0.0179658i
$786$	105.550	+	406.932i	0.134287	+	0.517725i
$787$	−1171.82	−	851.375i	−1.48897	−	1.08180i	−0.974526	−	0.224273i	$-0.927999\pi$
$787$	−1171.82	−	851.375i	−1.48897	−	1.08180i	−0.514442	−	0.857525i	$-0.672001\pi$
$788$	−26.5659	−	8.63178i	−0.0337130	−	0.0109540i
$789$	1058.77	+	416.189i	1.34192	+	0.527489i
$790$	−47.7184	+	34.6695i	−0.0604031	+	0.0438854i
$791$		−	378.785i		−	0.478869i
$792$		0			0
$793$	−792.536			−0.999415
$794$	−166.888	−	229.702i	−0.210186	−	0.289297i
$795$	32.8503	−	83.5704i	0.0413211	−	0.105120i
$796$	−58.3237	+	179.502i	−0.0732709	+	0.225505i
$797$	−203.605	+	280.238i	−0.255464	+	0.351616i	−0.917416	−	0.397931i	$-0.869728\pi$
$797$	−203.605	+	280.238i	−0.255464	+	0.351616i	0.661951	+	0.749547i	$0.269728\pi$
$798$	−200.086	+	51.8984i	−0.250735	+	0.0650355i
$799$	367.558	−	1131.23i	0.460022	−	1.41580i
$800$	−447.162	+	145.292i	−0.558952	+	0.181615i
$801$	−234.056	+	251.714i	−0.292205	+	0.314250i
$802$	1203.85			1.50107
$803$		0			0
$804$	−223.845	−	184.255i	−0.278414	−	0.229173i
$805$	34.1023	−	24.7768i	0.0423631	−	0.0307786i
$806$	−109.664	+	35.6318i	−0.136059	+	0.0442082i
$807$	−50.3488	−	78.9074i	−0.0623901	−	0.0977787i
$808$	−733.888	−	533.201i	−0.908277	−	0.659902i
$809$	−307.526	+	423.274i	−0.380131	+	0.523206i	−0.955619	−	0.294604i	$-0.904812\pi$
$809$	−307.526	+	423.274i	−0.380131	+	0.523206i	0.575488	+	0.817810i	$0.304812\pi$
$810$	6.81172	+	93.5690i	0.00840954	+	0.115517i
$811$	319.359	+	982.886i	0.393784	+	1.21194i	0.929904	+	0.367802i	$0.119889\pi$
$811$	319.359	+	982.886i	0.393784	+	1.21194i	−0.536120	+	0.844142i	$0.680111\pi$
$812$	10.2906	+	14.1638i	0.0126732	+	0.0174431i
$813$	−1200.06	−	987.811i	−1.47608	−	1.21502i
$814$		0			0
$815$			10.7838i			0.0132317i
$816$	−27.5146	+	455.196i	−0.0337189	+	0.557839i
$817$	111.532	+	343.261i	0.136514	+	0.420148i
$818$	−475.294	−	154.432i	−0.581044	−	0.188793i
$819$	169.346	−	364.524i	0.206772	−	0.445084i
$820$	47.6558	+	34.6239i	0.0581168	+	0.0422243i
$821$	−92.9928	−	30.2152i	−0.113268	−	0.0368029i	0.251835	−	0.967770i	$-0.418966\pi$
$821$	−92.9928	−	30.2152i	−0.113268	−	0.0368029i	−0.365102	+	0.930967i	$0.618966\pi$
$822$	371.927	−	946.172i	0.452465	−	1.15106i
$823$	−583.839	+	424.184i	−0.709404	+	0.515412i	−0.882981	−	0.469408i	$-0.844467\pi$
$823$	−583.839	+	424.184i	−0.709404	+	0.515412i	0.173578	+	0.984820i	$0.444467\pi$
$824$			473.673i			0.574846i
$825$		0			0
$826$	124.330			0.150521
$827$	722.545	+	994.498i	0.873694	+	1.20254i	0.978128	+	0.208005i	$0.0666971\pi$
$827$	722.545	+	994.498i	0.873694	+	1.20254i	−0.104433	+	0.994532i	$0.533303\pi$
$828$	−126.527	−	227.493i	−0.152810	−	0.274750i
$829$	−59.7651	+	183.938i	−0.0720930	+	0.221879i	−0.980610	−	0.195968i	$-0.937215\pi$
$829$	−59.7651	+	183.938i	−0.0720930	+	0.221879i	0.908517	+	0.417847i	$0.137215\pi$
$830$	−40.3095	+	55.4812i	−0.0485656	+	0.0668448i
$831$	277.151	+	1068.51i	0.333515	+	1.28582i
$832$	367.840	−	1132.09i	0.442115	−	1.36069i
$833$	646.556	−	210.079i	0.776178	−	0.252195i
$834$	15.0793	−	249.469i	0.0180807	−	0.299124i
$835$	107.642			0.128912
$836$		0			0
$837$	52.1329	−	96.5094i	0.0622854	−	0.115304i
$838$	−768.930	+	558.660i	−0.917577	+	0.666659i
$839$	554.741	−	180.246i	0.661193	−	0.214835i	0.0408501	−	0.999165i	$-0.486993\pi$
$839$	554.741	−	180.246i	0.661193	−	0.214835i	0.620343	+	0.784331i	$0.286993\pi$
$840$	−40.1274	+	25.6043i	−0.0477707	+	0.0304813i
$841$	−657.089	−	477.403i	−0.781319	−	0.567661i
$842$	−545.099	+	750.264i	−0.647386	+	0.891050i
$843$	517.019	+	810.279i	0.613308	+	0.961185i
$844$	−70.1668	−	215.951i	−0.0831360	−	0.255866i
$845$	50.9064	+	70.0667i	0.0602443	+	0.0829192i
$846$	211.752	+	1081.12i	0.250297	+	1.27792i
$847$		0			0
$848$			404.267i			0.476730i
$849$	−481.506	−	29.1049i	−0.567144	−	0.0342814i
$850$	−202.373	−	622.841i	−0.238086	−	0.732754i
$851$	1397.52	+	454.082i	1.64221	+	0.533587i
$852$	−149.840	+	38.8655i	−0.175869	+	0.0456168i
$853$	−348.868	−	253.468i	−0.408990	−	0.297148i	0.364203	−	0.931320i	$-0.381341\pi$
$853$	−348.868	−	253.468i	−0.408990	−	0.297148i	−0.773193	+	0.634171i	$0.781341\pi$
$854$	−190.510	−	61.9005i	−0.223080	−	0.0724830i
$855$	48.6649	+	87.4988i	0.0569180	+	0.102338i
$856$	−200.082	+	145.368i	−0.233740	+	0.169822i
$857$		−	580.461i		−	0.677317i	−0.940909	−	0.338659i	$-0.890027\pi$
$857$		−	580.461i		−	0.677317i	0.940909	−	0.338659i	$-0.109973\pi$
$858$		0			0
$859$	−812.241			−0.945566			−0.472783	−	0.881179i	$-0.656751\pi$
$859$	−812.241			−0.945566			−0.472783	+	0.881179i	$0.656751\pi$
$860$	11.6352	+	16.0145i	0.0135294	+	0.0186216i
$861$	−491.266	−	193.110i	−0.570576	−	0.224285i
$862$	102.402	−	315.160i	0.118795	−	0.365614i
$863$	369.257	−	508.239i	0.427876	−	0.588921i	−0.539588	−	0.841929i	$-0.681420\pi$
$863$	369.257	−	508.239i	0.427876	−	0.588921i	0.967464	+	0.253008i	$0.0814199\pi$
$864$	223.961	+	466.965i	0.259214	+	0.540469i
$865$	−5.41846	+	16.6763i	−0.00626412	+	0.0192790i
$866$	163.198	−	53.0264i	0.188451	−	0.0612314i
$867$	−87.9967	−	5.31902i	−0.101496	−	0.00613497i
$868$	13.2551			0.0152708
$869$		0			0
$870$	−11.8493	+	14.3953i	−0.0136199	+	0.0165464i
$871$	−1070.19	+	777.542i	−1.22870	+	0.892700i
$872$	−341.586	+	110.988i	−0.391727	+	0.127280i
$873$	145.564	+	17.6619i	0.166740	+	0.0202313i
$874$	494.158	+	359.026i	0.565398	+	0.410785i
$875$	53.0385	−	73.0012i	0.0606154	−	0.0834299i
$876$	179.548	−	114.565i	0.204963	−	0.130782i
$877$	−371.068	−	1142.03i	−0.423111	−	1.30220i	−0.904791	−	0.425855i	$-0.859973\pi$
$877$	−371.068	−	1142.03i	−0.423111	−	1.30220i	0.481680	−	0.876347i	$-0.340027\pi$
$878$	−645.749	−	888.797i	−0.735477	−	1.01230i
$879$	554.704	−	673.891i	0.631063	−	0.766656i
$880$		0			0
$881$		−	131.219i		−	0.148943i	−0.997223	−	0.0744714i	$-0.976273\pi$
$881$		−	131.219i		−	0.148943i	0.997223	−	0.0744714i	$-0.0237269\pi$
$882$	−428.767	+	461.116i	−0.486131	+	0.522807i
$883$	−39.2451	−	120.784i	−0.0444452	−	0.136788i	0.926371	−	0.376611i	$-0.122911\pi$
$883$	−39.2451	−	120.784i	−0.0444452	−	0.136788i	−0.970817	+	0.239823i	$0.922911\pi$
$884$	−328.007	−	106.576i	−0.371048	−	0.120561i
$885$	−15.1198	−	58.2920i	−0.0170845	−	0.0658667i
$886$	282.823	+	205.483i	0.319214	+	0.231922i
$887$	−1136.31	−	369.209i	−1.28107	−	0.416245i	−0.412113	−	0.911133i	$-0.635209\pi$
$887$	−1136.31	−	369.209i	−1.28107	−	0.416245i	−0.868957	+	0.494888i	$0.835209\pi$
$888$	−1544.31	−	607.047i	−1.73909	−	0.683612i
$889$	385.818	−	280.313i	0.433991	−	0.315313i
$890$		−	44.2339i		−	0.0497010i
$891$		0			0
$892$	235.138			0.263608
$893$	691.057	+	951.158i	0.773860	+	1.06513i
$894$	−286.448	+	728.716i	−0.320411	+	0.815119i
$895$	−13.3406	+	41.0580i	−0.0149057	+	0.0458749i
$896$	59.1774	−	81.4507i	0.0660462	−	0.0909048i
$897$	−1149.67	+	298.202i	−1.28169	+	0.332443i
$898$	122.602	−	377.331i	0.136528	−	0.420190i
$899$	20.7326	−	6.73643i	0.0230618	−	0.00749325i
$900$	−202.029	−	187.856i	−0.224477	−	0.208729i
$901$	690.442			0.766306
$902$		0			0
$903$	−136.955	−	112.733i	−0.151667	−	0.124842i
$904$	1022.55	−	742.929i	1.13114	−	0.821824i
$905$	−98.5876	+	32.0331i	−0.108937	+	0.0353956i
$906$	458.579	+	718.692i	0.506158	+	0.793258i
$907$	−424.397	−	308.342i	−0.467913	−	0.339958i	0.328715	−	0.944429i	$-0.393385\pi$
$907$	−424.397	−	308.342i	−0.467913	−	0.339958i	−0.796627	+	0.604471i	$0.793385\pi$
$908$	315.494	−	434.241i	0.347461	−	0.478239i
$909$	112.953	−	930.922i	0.124261	−	1.02412i
$910$	15.9844	+	49.1949i	0.0175653	+	0.0540603i
$911$	103.220	+	142.070i	0.113304	+	0.155950i	0.861903	−	0.507074i	$-0.169273\pi$
$911$	103.220	+	142.070i	0.113304	+	0.155950i	−0.748598	+	0.663024i	$0.769273\pi$
$912$	−348.020	−	286.468i	−0.381601	−	0.314110i
$913$		0			0
$914$		−	44.2524i		−	0.0484162i
$915$	−5.85404	+	96.8481i	−0.00639786	+	0.105845i
$916$	52.4674	+	161.478i	0.0572788	+	0.176286i
$917$	−209.706	−	68.1377i	−0.228687	−	0.0743050i
$918$	−650.425	+	311.950i	−0.708524	+	0.339815i
$919$	−1055.86	−	767.124i	−1.14892	−	0.834738i	−0.160581	−	0.987023i	$-0.551337\pi$
$919$	−1055.86	−	767.124i	−1.14892	−	0.834738i	−0.988337	+	0.152285i	$0.951337\pi$
$920$	133.773	+	43.4654i	0.145405	+	0.0472450i
$921$	−309.278	+	786.796i	−0.335807	+	0.854284i
$922$	527.369	−	383.156i	0.571984	−	0.415571i
$923$			706.294i			0.765216i
$924$		0			0
$925$	1557.28			1.68355
$926$	−104.242	−	143.476i	−0.112572	−	0.154942i
$927$	−427.925	+	238.003i	−0.461624	+	0.256745i
$928$	−31.8056	+	97.8877i	−0.0342733	+	0.105482i
$929$	−916.652	+	1261.66i	−0.986708	+	1.35809i	−0.0535724	+	0.998564i	$0.517061\pi$
$929$	−916.652	+	1261.66i	−0.986708	+	1.35809i	−0.933136	+	0.359524i	$0.882939\pi$
$930$	3.54419	+	13.6641i	0.00381096	+	0.0146926i
$931$	−207.651	+	639.084i	−0.223041	+	0.686449i
$932$	−388.770	+	126.319i	−0.417136	+	0.135536i
$933$	−85.7523	+	1418.67i	−0.0919102	+	1.52054i
$934$	701.251			0.750804
$935$		0			0
$936$	1316.20	−	257.795i	1.40620	−	0.275422i
$937$	−581.968	+	422.824i	−0.621097	+	0.451253i	−0.853305	−	0.521413i	$-0.825405\pi$
$937$	−581.968	+	422.824i	−0.621097	+	0.451253i	0.232208	+	0.972666i	$0.425405\pi$
$938$	−317.983	+	103.319i	−0.339001	+	0.110148i
$939$	−75.8053	+	48.3695i	−0.0807298	+	0.0515117i
$940$	52.1664	+	37.9011i	0.0554962	+	0.0403204i
$941$	689.641	−	949.209i	0.732881	−	1.00872i	−0.266116	−	0.963941i	$-0.585740\pi$
$941$	689.641	−	949.209i	0.732881	−	1.00872i	0.998997	−	0.0447831i	$-0.0142597\pi$
$942$	−174.830	−	273.996i	−0.185595	−	0.290866i
$943$	482.004	+	1483.46i	0.511139	+	1.57312i
$944$	159.361	+	219.342i	0.168815	+	0.232353i
$945$	−43.2940	−	23.3867i	−0.0458137	−	0.0247478i
$946$		0			0
$947$			266.119i			0.281013i	0.990080	+	0.140506i	$0.0448730\pi$
$947$			266.119i			0.281013i	−0.990080	+	0.140506i	$0.955127\pi$
$948$	−190.699	−	11.5269i	−0.201160	−	0.0121592i
$949$	−300.296	−	924.216i	−0.316434	−	0.973884i
$950$	615.643	+	200.035i	0.648046	+	0.210563i
$951$	−462.524	+	119.969i	−0.486356	+	0.126151i
$952$	−296.102	−	215.131i	−0.311032	−	0.225978i
$953$	−121.881	−	39.6016i	−0.127892	−	0.0415547i	0.244372	−	0.969682i	$-0.421418\pi$
$953$	−121.881	−	39.6016i	−0.127892	−	0.0415547i	−0.372264	+	0.928127i	$0.621418\pi$
$954$	−558.864	+	310.828i	−0.585811	+	0.325816i
$955$	−31.7603	+	23.0752i	−0.0332569	+	0.0241625i
$956$		−	116.864i		−	0.122242i
$957$		0			0
$958$	894.933			0.934168
$959$	313.425	+	431.393i	0.326825	+	0.449836i
$960$	−135.625	−	53.3122i	−0.141276	−	0.0555336i
$961$	−291.865	+	898.268i	−0.303710	+	0.934723i
$962$	−1059.88	+	1458.80i	−1.10175	+	1.51643i
$963$	−231.862	−	107.716i	−0.240770	−	0.111854i
$964$	−79.9003	+	245.908i	−0.0828841	+	0.255091i
$965$	−100.293	+	32.5872i	−0.103931	+	0.0337692i
$966$	−299.649	−	18.1125i	−0.310196	−	0.0187500i
$967$	−1324.17			−1.36936			−0.684682	−	0.728842i	$-0.740059\pi$
$967$	−1324.17			−1.36936			−0.684682	+	0.728842i	$0.740059\pi$
$968$		0			0
$969$	−489.255	+	594.379i	−0.504907	+	0.613394i
$970$	−15.2664	+	11.0917i	−0.0157386	+	0.0114348i
$971$	556.252	−	180.737i	0.572865	−	0.186135i	−0.00823681	−	0.999966i	$-0.502622\pi$
$971$	556.252	−	180.737i	0.572865	−	0.186135i	0.581102	+	0.813831i	$0.302622\pi$
$972$	−175.575	+	248.017i	−0.180633	+	0.255161i
$973$	106.050	+	77.0500i	0.108993	+	0.0791881i
$974$	595.161	−	819.169i	0.611048	−	0.841036i
$975$	−1061.11	+	677.066i	−1.08831	+	0.694427i
$976$	−134.984	−	415.437i	−0.138303	−	0.425652i
$977$	−406.363	−	559.311i	−0.415930	−	0.572478i	0.548722	−	0.836005i	$-0.315114\pi$
$977$	−406.363	−	559.311i	−0.415930	−	0.572478i	−0.964652	+	0.263526i	$0.915114\pi$
$978$	48.8073	−	59.2943i	0.0499052	−	0.0606281i
$979$		0			0
$980$			36.8545i			0.0376066i
$981$	−271.903	−	252.828i	−0.277169	−	0.257725i
$982$	29.1423	+	89.6907i	0.0296764	+	0.0913347i
$983$	−623.407	−	202.557i	−0.634188	−	0.206060i	−0.0257588	−	0.999668i	$-0.508200\pi$
$983$	−623.407	−	202.557i	−0.634188	−	0.206060i	−0.608430	+	0.793608i	$0.708200\pi$
$984$	−442.231	−	1704.96i	−0.449422	−	1.73268i
$985$	12.6229	+	9.17105i	0.0128151	+	0.00931071i
$986$	−136.346	−	44.3013i	−0.138281	−	0.0449304i
$987$	−537.765	−	211.388i	−0.544848	−	0.214172i
$988$	275.795	−	200.377i	0.279144	−	0.202810i
$989$			524.164i			0.529994i
$990$		0			0
$991$	95.0559			0.0959192			0.0479596	−	0.998849i	$-0.484728\pi$
$991$	95.0559			0.0959192			0.0479596	+	0.998849i	$0.484728\pi$
$992$	45.8036	+	63.0433i	0.0461730	+	0.0635517i
$993$	−365.151	+	928.937i	−0.367726	+	0.935485i
$994$	−55.1646	+	169.779i	−0.0554976	+	0.170804i
$995$	61.9675	−	85.2909i	0.0622789	−	0.0857195i
$996$	−215.012	+	55.7697i	−0.215875	+	0.0559937i
$997$	241.467	−	743.158i	0.242193	−	0.745394i	−0.753892	−	0.656998i	$-0.771826\pi$
$997$	241.467	−	743.158i	0.242193	−	0.745394i	0.996085	−	0.0883960i	$-0.0281741\pi$
$998$	−739.422	+	240.253i	−0.740904	+	0.240734i
$999$	−227.541	−	1700.18i	−0.227769	−	1.70188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.j.245.2		16
3.2	odd	2	inner	363.3.h.j.245.3		16
11.2	odd	10		363.3.b.m.122.4		8
11.3	even	5		363.3.h.n.269.2		16
11.4	even	5	inner	363.3.h.j.323.3		16
11.5	even	5		363.3.h.n.251.3		16
11.6	odd	10		363.3.h.o.251.2		16
11.7	odd	10		33.3.h.b.26.2	yes	16
11.8	odd	10		363.3.h.o.269.3		16
11.9	even	5		363.3.b.l.122.5		8
11.10	odd	2		33.3.h.b.14.3	yes	16
33.2	even	10		363.3.b.m.122.5		8
33.5	odd	10		363.3.h.n.251.2		16
33.8	even	10		363.3.h.o.269.2		16
33.14	odd	10		363.3.h.n.269.3		16
33.17	even	10		363.3.h.o.251.3		16
33.20	odd	10		363.3.b.l.122.4		8
33.26	odd	10	inner	363.3.h.j.323.2		16
33.29	even	10		33.3.h.b.26.3	yes	16
33.32	even	2		33.3.h.b.14.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.2	✓	16	33.32	even	2
33.3.h.b.14.3	yes	16	11.10	odd	2
33.3.h.b.26.2	yes	16	11.7	odd	10
33.3.h.b.26.3	yes	16	33.29	even	10
363.3.b.l.122.4		8	33.20	odd	10
363.3.b.l.122.5		8	11.9	even	5
363.3.b.m.122.4		8	11.2	odd	10
363.3.b.m.122.5		8	33.2	even	10
363.3.h.j.245.2		16	1.1	even	1	trivial
363.3.h.j.245.3		16	3.2	odd	2	inner
363.3.h.j.323.2		16	33.26	odd	10	inner
363.3.h.j.323.3		16	11.4	even	5	inner
363.3.h.n.251.2		16	33.5	odd	10
363.3.h.n.251.3		16	11.5	even	5
363.3.h.n.269.2		16	11.3	even	5
363.3.h.n.269.3		16	33.14	odd	10
363.3.h.o.251.2		16	11.6	odd	10
363.3.h.o.251.3		16	33.17	even	10
363.3.h.o.269.2		16	33.8	even	10
363.3.h.o.269.3		16	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.974642 - 1.34148i) q^{2} +(-1.09751 + 2.79204i) q^{3} +(0.386428 - 1.18930i) q^{4} +(-0.410570 + 0.565101i) q^{5} +(4.81514 - 1.24895i) q^{6} +(-0.806259 + 2.48141i) q^{7} +(-8.28007 + 2.69036i) q^{8} +(-6.59095 - 6.12857i) q^{9} +1.15823 q^{10} +(2.89647 + 2.38419i) q^{12} +(13.8479 - 10.0611i) q^{13} +(4.11458 - 1.33691i) q^{14} +(-1.12718 - 1.76653i) q^{15} +(7.63243 + 5.54529i) q^{16} +(9.47072 - 13.0353i) q^{17} +(-1.79754 + 14.8148i) q^{18} +(4.92151 + 15.1469i) q^{19} +(0.513421 + 0.706663i) q^{20} +(-6.04332 - 4.97448i) q^{21} +23.1295i q^{23} +(1.57587 - 26.0710i) q^{24} +(7.57465 + 23.3124i) q^{25} +(-26.9935 - 8.77071i) q^{26} +(24.3448 - 11.6760i) q^{27} +(2.63959 + 1.91777i) q^{28} +(5.10329 + 1.65816i) q^{29} +(-1.27117 + 3.23382i) q^{30} +(3.28671 - 2.38793i) q^{31} +19.1813i q^{32} -26.7172 q^{34} +(-1.07122 - 1.47441i) q^{35} +(-9.83565 + 5.47038i) q^{36} +(19.6322 - 60.4217i) q^{37} +(15.5225 - 21.3649i) q^{38} +(12.8927 + 49.7060i) q^{39} +(1.87922 - 5.78366i) q^{40} +(64.1371 - 20.8394i) q^{41} +(-0.783092 + 12.9553i) q^{42} +22.6622 q^{43} +(6.16931 - 1.20834i) q^{45} +(31.0277 - 22.5429i) q^{46} +(70.2078 - 22.8119i) q^{47} +(-23.8593 + 15.2240i) q^{48} +(34.1345 + 24.8002i) q^{49} +(23.8905 - 32.8825i) q^{50} +(26.0009 + 40.7490i) q^{51} +(-6.61446 - 20.3572i) q^{52} +(25.1873 + 34.6673i) q^{53} +(-39.3906 - 21.2782i) q^{54} -22.7154i q^{56} +(-47.6920 - 2.88277i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(27.3316 + 8.88056i) q^{59} +(-2.53651 + 0.657920i) q^{60} +(-37.4585 - 27.2152i) q^{61} +(-6.40673 - 2.08167i) q^{62} +(20.5215 - 11.4136i) q^{63} +(56.2610 - 40.8760i) q^{64} +11.9562i q^{65} -77.2821 q^{67} +(-11.8432 - 16.3008i) q^{68} +(-64.5783 - 25.3848i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(-24.2537 + 33.3824i) q^{71} +(71.0615 + 33.0130i) q^{72} +(17.5438 - 53.9942i) q^{73} +(-100.189 + 32.5533i) q^{74} +(-73.4023 - 4.43685i) q^{75} +19.9160 q^{76} +(54.1137 - 65.7409i) q^{78} +(-41.1994 + 29.9331i) q^{79} +(-6.26730 + 2.03637i) q^{80} +(5.88115 + 80.7862i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(-34.8026 + 47.9017i) q^{83} +(-8.25147 + 5.26505i) q^{84} +(3.47788 + 10.7038i) q^{85} +(-22.0875 - 30.4009i) q^{86} +(-10.2306 + 12.4287i) q^{87} -38.1909i q^{89} +(-7.63383 - 7.09830i) q^{90} +(13.8007 + 42.4742i) q^{91} +(27.5079 + 8.93786i) q^{92} +(3.06001 + 11.7974i) q^{93} +(-99.0291 - 71.9489i) q^{94} +(-10.5801 - 3.43769i) q^{95} +(-53.5549 - 21.0516i) q^{96} +(-13.1808 + 9.57644i) q^{97} -69.9620i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more