LMFDB - Embedded newform 363.3.h.j.245.3

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			245.3
Root			$0.974642 + 1.34148i$ of defining polynomial
Character	$\chi$	$=$	363.245
Dual form			363.3.h.j.323.3

$q$-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} +(2.52902 + 1.61371i) q^{3} +(0.386428 - 1.18930i) q^{4} +(0.410570 - 0.565101i) q^{5} +(0.300138 + 4.96542i) q^{6} +(-0.806259 + 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(3.79191 + 8.16220i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} +(13.8479 - 10.0611i) q^{13} +(-4.11458 + 1.33691i) q^{14} +(1.95025 - 0.766614i) q^{15} +(7.63243 + 5.54529i) q^{16} +(-9.47072 + 13.0353i) q^{17} +(-7.25367 + 13.0420i) q^{18} +(4.92151 + 15.1469i) q^{19} +(-0.513421 - 0.706663i) q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(25.2819 + 6.55762i) q^{24} +(7.57465 + 23.3124i) q^{25} +(26.9935 + 8.77071i) q^{26} +(-3.58157 + 26.7614i) q^{27} +(2.63959 + 1.91777i) q^{28} +(-5.10329 - 1.65816i) q^{29} +(2.92919 + 1.86904i) q^{30} +(3.28671 - 2.38793i) q^{31} -19.1813i q^{32} -26.7172 q^{34} +(1.07122 + 1.47441i) q^{35} +(11.1726 - 1.35562i) q^{36} +(19.6322 - 60.4217i) q^{37} +(-15.5225 + 21.3649i) q^{38} +(51.2573 - 3.09828i) q^{39} +(1.87922 - 5.78366i) q^{40} +(-64.1371 + 20.8394i) q^{41} +(-12.5632 - 3.25865i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} +(31.0277 - 22.5429i) q^{46} +(-70.2078 + 22.8119i) q^{47} +(10.3541 + 26.3407i) q^{48} +(34.1345 + 24.8002i) q^{49} +(-23.8905 + 32.8825i) q^{50} +(-44.9868 + 17.6837i) q^{51} +(-6.61446 - 20.3572i) q^{52} +(-25.1873 - 34.6673i) q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(-11.9960 + 46.2486i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(-27.3316 - 8.88056i) q^{59} +(-0.158106 - 2.61568i) q^{60} +(-37.4585 - 27.2152i) q^{61} +(6.40673 + 2.08167i) q^{62} +(-23.3110 + 2.82843i) q^{63} +(56.2610 - 40.8760i) q^{64} -11.9562i q^{65} -77.2821 q^{67} +(11.8432 + 16.3008i) q^{68} +(37.3241 - 58.4949i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(24.2537 - 33.3824i) q^{71} +(53.3565 + 57.3820i) q^{72} +(17.5438 - 53.9942i) q^{73} +(100.189 - 32.5533i) q^{74} +(-18.4629 + 71.1808i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +(-41.1994 + 29.9331i) q^{79} +(6.26730 - 2.03637i) q^{80} +(-52.2429 + 61.9006i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(34.8026 - 47.9017i) q^{83} +(3.58085 + 9.10961i) q^{84} +(3.47788 + 10.7038i) q^{85} +(22.0875 + 30.4009i) q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(4.39190 + 9.45370i) q^{90} +(13.8007 + 42.4742i) q^{91} +(-27.5079 - 8.93786i) q^{92} +(12.1656 - 0.735356i) q^{93} +(-99.0291 - 71.9489i) q^{94} +(10.5801 + 3.43769i) q^{95} +(30.9530 - 48.5099i) 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	0.979891	−	0.199533i	$-0.0639425\pi$
$2$	0.974642	+	1.34148i	0.487321	+	0.670740i	−0.492570	+	0.870273i	$0.663943\pi$
$3$	2.52902	+	1.61371i	0.843007	+	0.537902i
$3$	2.52902	+	1.61371i	0.843007	+	0.537902i
$4$	0.386428	−	1.18930i	0.0966070	−	0.297326i
$5$	0.410570	−	0.565101i	0.0821140	−	0.113020i	−0.765984	−	0.642860i	$-0.777748\pi$
$5$	0.410570	−	0.565101i	0.0821140	−	0.113020i	0.848098	+	0.529839i	$0.177748\pi$
$6$	0.300138	+	4.96542i	0.0500229	+	0.827569i
$7$	−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
$9$	3.79191	+	8.16220i	0.421323	+	0.906911i
$10$	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
$15$	1.95025	−	0.766614i	0.130017	−	0.0511076i
$16$	7.63243	+	5.54529i	0.477027	+	0.346580i
$17$	−9.47072	+	13.0353i	−0.557101	+	0.766784i	−0.990954	−	0.134200i	$-0.957154\pi$
$17$	−9.47072	+	13.0353i	−0.557101	+	0.766784i	0.433853	+	0.900984i	$0.357154\pi$
$18$	−7.25367	+	13.0420i	−0.402981	+	0.724555i
$19$	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	$-0.832298\pi$
$23$		−	23.1295i		−	1.00563i	0.864395	−	0.502814i	$-0.167702\pi$
$24$	25.2819	+	6.55762i	1.05341	+	0.273234i
$25$	7.57465	+	23.3124i	0.302986	+	0.932495i
$26$	26.9935	+	8.77071i	1.03821	+	0.337335i
$27$	−3.58157	+	26.7614i	−0.132651	+	0.991163i
$28$	2.63959	+	1.91777i	0.0942710	+	0.0684919i
$29$	−5.10329	−	1.65816i	−0.175976	−	0.0571779i	0.219704	−	0.975567i	$-0.429491\pi$
$29$	−5.10329	−	1.65816i	−0.175976	−	0.0571779i	−0.395679	+	0.918389i	$0.629491\pi$
$30$	2.92919	+	1.86904i	0.0976397	+	0.0623014i
$31$	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
$36$	11.1726	−	1.35562i	0.310351	−	0.0376562i
$37$	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
$39$	51.2573	−	3.09828i	1.31429	−	0.0794430i
$40$	1.87922	−	5.78366i	0.0469806	−	0.144591i
$41$	−64.1371	+	20.8394i	−1.56432	+	0.508278i	−0.957958	−	0.286910i	$-0.907372\pi$
$41$	−64.1371	+	20.8394i	−1.56432	+	0.508278i	−0.606362	+	0.795188i	$0.707372\pi$
$42$	−12.5632	−	3.25865i	−0.299124	−	0.0775869i
$43$	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	−0.938198	−	0.346100i	$-0.887506\pi$
$47$	−70.2078	+	22.8119i	−1.49378	+	0.485360i	−0.555585	+	0.831460i	$0.687506\pi$
$48$	10.3541	+	26.3407i	0.215711	+	0.548764i
$49$	34.1345	+	24.8002i	0.696622	+	0.506126i
$50$	−23.8905	+	32.8825i	−0.477810	+	0.657649i
$51$	−44.9868	+	17.6837i	−0.882095	+	0.346739i
$52$	−6.61446	−	20.3572i	−0.127201	−	0.391485i
$53$	−25.1873	−	34.6673i	−0.475232	−	0.654100i	0.502348	−	0.864666i	$-0.332470\pi$
$53$	−25.1873	−	34.6673i	−0.475232	−	0.654100i	−0.977580	+	0.210565i	$0.932470\pi$
$54$	−39.3906	+	21.2782i	−0.729456	+	0.394040i
$55$		0			0
$56$			22.7154i			0.405632i
$57$	−11.9960	+	46.2486i	−0.210455	+	0.811379i
$58$	−2.74949	−	8.46207i	−0.0474051	−	0.145898i
$59$	−27.3316	−	8.88056i	−0.463247	−	0.150518i	0.0680891	−	0.997679i	$-0.478310\pi$
$59$	−27.3316	−	8.88056i	−0.463247	−	0.150518i	−0.531336	+	0.847161i	$0.678310\pi$
$60$	−0.158106	−	2.61568i	−0.00263510	−	0.0435946i
$61$	−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
$63$	−23.3110	+	2.82843i	−0.370016	+	0.0448957i
$64$	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
$69$	37.3241	−	58.4949i	0.540929	−	0.847752i
$70$	−0.933834	+	2.87405i	−0.0133405	+	0.0410578i
$71$	24.2537	−	33.3824i	0.341601	−	0.470174i	−0.603307	−	0.797509i	$-0.706151\pi$
$71$	24.2537	−	33.3824i	0.341601	−	0.470174i	0.944908	+	0.327335i	$0.106151\pi$
$72$	53.3565	+	57.3820i	0.741062	+	0.796972i
$73$	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
$75$	−18.4629	+	71.1808i	−0.246172	+	0.949077i
$76$	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
$81$	−52.2429	+	61.9006i	−0.644974	+	0.764205i
$82$	−90.4664	−	65.7277i	−1.10325	−	0.801557i
$83$	34.8026	−	47.9017i	0.419309	−	0.577129i	−0.546149	−	0.837688i	$-0.683907\pi$
$83$	34.8026	−	47.9017i	0.419309	−	0.577129i	0.965458	+	0.260559i	$0.0839068\pi$
$84$	3.58085	+	9.10961i	0.0426292	+	0.108448i
$85$	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	$0.0688304\pi$
$89$			38.1909i			0.429112i	−0.976712	+	0.214556i	$0.931170\pi$
$90$	4.39190	+	9.45370i	0.0487989	+	0.105041i
$91$	13.8007	+	42.4742i	0.151656	+	0.466749i
$92$	−27.5079	−	8.93786i	−0.298999	−	0.0971507i
$93$	12.1656	−	0.735356i	0.130813	−	0.00790705i
$94$	−99.0291	−	71.9489i	−1.05350	−	0.765414i
$95$	10.5801	+	3.43769i	0.111370	+	0.0361862i
$96$	30.9530	−	48.5099i	0.322427	−	0.505312i
$97$	−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	0.389897	−	0.920858i	$-0.372510\pi$
$101$	−61.2440	−	84.2951i	−0.606376	−	0.834605i	−0.996273	+	0.0862537i	$0.972510\pi$
$102$	−67.5683	−	43.1137i	−0.662435	−	0.422683i
$103$	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
$105$	0.329879	+	5.45746i	0.00314171	+	0.0519758i
$106$	21.9569	−	67.5764i	0.207141	−	0.637514i
$107$	−27.0164	+	8.77818i	−0.252490	+	0.0820390i	−0.432527	−	0.901621i	$-0.642378\pi$
$107$	−27.0164	+	8.77818i	−0.252490	+	0.0820390i	0.180037	+	0.983660i	$0.442378\pi$
$108$	30.4434	+	14.6009i	0.281883	+	0.135194i
$109$	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	0.374114	−	0.927383i	$-0.377947\pi$
$113$	138.072	−	44.8625i	1.22188	−	0.397013i	0.847766	+	0.530370i	$0.177947\pi$
$114$	−73.7333	+	28.9835i	−0.646783	+	0.254241i
$115$	−13.0705	−	9.49626i	−0.113656	−	0.0825762i
$116$	−3.94411	+	5.42860i	−0.0340009	+	0.0467983i
$117$	134.630	+	74.8786i	1.15069	+	0.639988i
$118$	−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
$123$	−195.833	−	50.7951i	−1.59214	−	0.412968i
$124$	−1.56990	−	4.83165i	−0.0126605	−	0.0389650i
$125$	32.8917	+	10.6872i	0.263134	+	0.0854973i
$126$	−26.5142	−	28.5146i	−0.210430	−	0.226306i
$127$	−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
$129$	57.3132	+	36.5701i	0.444289	+	0.283489i
$130$	16.0391	−	11.6531i	0.123377	−	0.0896389i
$131$		−	84.5109i		−	0.645121i	−0.946549	−	0.322561i	$-0.895456\pi$
$131$		−	84.5109i		−	0.645121i	0.946549	−	0.322561i	$-0.104544\pi$
$132$		0			0
$133$	−41.5536			−0.312433
$134$	−75.3223	−	103.672i	−0.562107	−	0.773674i
$135$	13.6524	+	13.0114i	0.101129	+	0.0963806i
$136$	−43.3485	+	133.413i	−0.318739	+	0.980978i
$137$	−120.127	+	165.341i	−0.876841	+	1.20687i	0.100445	+	0.994943i	$0.467973\pi$
$137$	−120.127	+	165.341i	−0.876841	+	1.20687i	−0.977286	+	0.211925i	$0.932027\pi$
$138$	114.847	−	6.94202i	0.832227	−	0.0503045i
$139$	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
$141$	−214.369	−	55.6029i	−1.52035	−	0.394347i
$142$	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
$147$	46.3067	+	117.803i	0.315012	+	0.801382i
$148$	−64.2733	−	46.6973i	−0.434279	−	0.315522i
$149$	92.5187	−	127.341i	0.620931	−	0.854638i	−0.376490	−	0.926421i	$-0.622869\pi$
$149$	92.5187	−	127.341i	0.620931	−	0.854638i	0.997420	+	0.0717830i	$0.0228689\pi$
$150$	−113.482	+	44.6082i	−0.756548	+	0.297388i
$151$	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
$156$	16.1224	−	62.1577i	0.103349	−	0.398447i
$157$	−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
$159$	−7.75634	−	128.319i	−0.0487820	−	0.807040i
$160$	−10.8394	−	7.87526i	−0.0677461	−	0.0492204i
$161$	57.3937	+	18.6483i	0.356483	+	0.115828i
$162$	−133.956	−	9.75188i	−0.826892	−	0.0601968i
$163$	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	0.988956	−	0.148211i	$-0.0473516\pi$
$167$	90.5798	+	124.672i	0.542394	+	0.746542i	−0.446561	+	0.894753i	$0.647352\pi$
$168$	−36.6559	+	57.4477i	−0.218190	+	0.341951i
$169$	38.3149	−	117.921i	0.226715	−	0.697758i
$170$	−10.9693	+	15.0979i	−0.0645251	+	0.0888112i
$171$	−104.970	+	97.6058i	−0.613858	+	0.570794i
$172$	8.75731	−	26.9522i	0.0509146	−	0.156699i
$173$	−23.8744	+	7.75725i	−0.138002	+	0.0448396i	−0.377204	−	0.926130i	$-0.623114\pi$
$173$	−23.8744	+	7.75725i	−0.138002	+	0.0448396i	0.239202	+	0.970970i	$0.423114\pi$
$174$	6.70176	−	25.8376i	0.0385159	−	0.148492i
$175$	−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	−0.468567	−	0.883428i	$-0.655230\pi$
$179$	−58.7800	+	19.0988i	−0.328380	+	0.106697i	0.140187	+	0.990125i	$0.455230\pi$
$180$	3.82108	−	6.87024i	0.0212282	−	0.0381680i
$181$	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
$183$	−50.8161	−	129.275i	−0.277684	−	0.706420i
$184$	−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
$189$	−63.5184	−	30.4640i	−0.336076	−	0.161185i
$190$	5.70024	+	17.5435i	0.0300013	+	0.0923344i
$191$	−53.4521	−	17.3676i	−0.279854	−	0.0909301i	0.165727	−	0.986172i	$-0.447003\pi$
$191$	−53.4521	−	17.3676i	−0.279854	−	0.0909301i	−0.445581	+	0.895242i	$0.647003\pi$
$192$	208.247	−	12.5876i	1.08462	−	0.0655606i
$193$	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
$195$	19.2939	−	30.2376i	0.0989429	−	0.155065i
$196$	42.6854	−	31.0128i	0.217783	−	0.158228i
$197$			22.3374i			0.113388i	0.998392	+	0.0566938i	$0.0180559\pi$
$197$			22.3374i			0.113388i	−0.998392	+	0.0566938i	$0.981944\pi$
$198$		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
$201$	−195.448	−	124.711i	−0.972379	−	0.620450i
$202$	53.3892	−	164.315i	0.264303	−	0.813441i
$203$	8.22915	−	11.3265i	0.0405377	−	0.0557954i
$204$	3.64707	+	60.3364i	0.0178778	+	0.295767i
$205$	−14.5564	+	44.8000i	−0.0710068	+	0.218537i
$206$	85.7993	−	27.8779i	0.416501	−	0.135329i
$207$	188.787	−	87.7047i	0.912015	−	0.423694i
$208$	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
$213$	115.207	−	45.2864i	0.540880	−	0.212612i
$214$	−38.1071	−	27.6864i	−0.178071	−	0.129376i
$215$	9.30442	−	12.8064i	0.0432764	−	0.0595648i
$216$	42.3421	+	231.222i	0.196028	+	1.07047i
$217$	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
$222$	305.911	+	79.3473i	1.37798	+	0.357420i
$223$	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
$225$	−161.558	+	150.224i	−0.718035	+	0.667663i
$226$	194.753	+	141.497i	0.861740	+	0.626091i
$227$	−408.219	−	132.638i	−1.79832	−	0.584310i	−0.798478	−	0.602024i	$-0.794361\pi$
$227$	−408.219	−	132.638i	−1.79832	−	0.584310i	−0.999843	+	0.0177135i	$0.994361\pi$
$228$	50.3680	+	32.1386i	0.220912	+	0.140959i
$229$	−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	$0.0474768\pi$
$233$	192.141	+	264.459i	0.824638	+	1.13502i	−0.164259	+	0.986417i	$0.552523\pi$
$234$	30.7685	+	253.584i	0.131489	+	1.08369i
$235$	−15.9342	+	49.0404i	−0.0678051	+	0.208683i
$236$	−21.1233	+	29.0738i	−0.0895057	+	0.123194i
$237$	−152.498	+	9.21781i	−0.643450	+	0.0388937i
$238$	21.5410	−	66.2963i	0.0905083	−	0.278556i
$239$	−88.8791	+	28.8786i	−0.371879	+	0.120831i	−0.488993	−	0.872288i	$-0.662636\pi$
$239$	−88.8791	+	28.8786i	−0.371879	+	0.120831i	0.117114	+	0.993118i	$0.462636\pi$
$240$	19.1362	+	4.96355i	0.0797343	+	0.0206815i
$241$	−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
$246$	−122.726	−	312.213i	−0.498887	−	1.26916i
$247$	220.546	+	160.236i	0.892900	+	0.648730i
$248$	20.7898	−	28.6147i	0.0838297	−	0.115382i
$249$	165.316	−	64.9833i	0.663919	−	0.260977i
$250$	17.7210	+	54.5397i	0.0708841	+	0.218159i
$251$	−1.64009	−	2.25739i	−0.00653422	−	0.00899358i	0.805737	−	0.592273i	$-0.201769\pi$
$251$	−1.64009	−	2.25739i	−0.00653422	−	0.00899358i	−0.812272	+	0.583279i	$0.801769\pi$
$252$	−5.64417	+	28.8168i	−0.0223975	+	0.114353i
$253$		0			0
$254$		−	303.081i		−	1.19323i
$255$	−8.47718	+	32.6825i	−0.0332439	+	0.128167i
$256$	−66.1871	−	203.703i	−0.258543	−	0.795714i
$257$	380.619	+	123.671i	1.48101	+	0.481208i	0.934414	−	0.356190i	$-0.115924\pi$
$257$	380.619	+	123.671i	1.48101	+	0.481208i	0.546593	+	0.837398i	$0.315924\pi$
$258$	6.80178	+	112.527i	0.0263635	+	0.436152i
$259$	134.103	+	97.4312i	0.517770	+	0.376182i
$260$	−14.2196	−	4.62022i	−0.0546907	−	0.0177701i
$261$	−5.81698	−	47.9416i	−0.0222873	−	0.183684i
$262$	113.370	−	82.3678i	0.432708	−	0.314381i
$263$			379.212i			1.44187i	0.693003	+	0.720935i	$0.256287\pi$
$263$			379.212i			1.44187i	−0.693003	+	0.720935i	$0.743713\pi$
$264$		0			0
$265$	−29.9317			−0.112950
$266$	−40.4999	−	55.7433i	−0.152255	−	0.209561i
$267$	−61.6289	+	96.5857i	−0.230820	+	0.361744i
$268$	−29.8639	+	91.9118i	−0.111433	+	0.342954i
$269$	18.3393	−	25.2419i	0.0681760	−	0.0938362i	−0.773567	−	0.633714i	$-0.781530\pi$
$269$	18.3393	−	25.2419i	0.0681760	−	0.0938362i	0.841743	+	0.539878i	$0.181530\pi$
$270$	−4.14828	+	30.9959i	−0.0153640	+	0.114799i
$271$	−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
$273$	−33.6386	+	129.688i	−0.123218	+	0.475049i
$274$	−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
$279$	31.9537	+	17.7719i	0.114529	+	0.0636987i
$280$	12.8365	+	9.32625i	0.0458446	+	0.0333081i
$281$	−188.322	+	259.203i	−0.670184	+	0.922429i	−0.999765	−	0.0216982i	$-0.993093\pi$
$281$	−188.322	+	259.203i	−0.670184	+	0.922429i	0.329580	+	0.944127i	$0.393093\pi$
$282$	−134.343	−	341.764i	−0.476392	−	1.21193i
$283$	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
$288$	156.561	−	72.7337i	0.543616	−	0.252547i
$289$	9.08071	+	27.9475i	0.0314211	+	0.0967043i
$290$	−5.91079	−	1.92053i	−0.0203820	−	0.00662252i
$291$	−48.7882	+	2.94903i	−0.167657	+	0.0101341i
$292$	−57.4361	−	41.7298i	−0.196699	−	0.142910i
$293$	276.702	+	89.9060i	0.944377	+	0.306847i	0.740429	−	0.672135i	$-0.234623\pi$
$293$	276.702	+	89.9060i	0.944377	+	0.306847i	0.203948	+	0.978982i	$0.434623\pi$
$294$	−112.898	+	176.935i	−0.384007	+	0.601821i
$295$	−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
$300$	77.5209	+	49.4642i	0.258403	+	0.164881i
$301$	−18.2716	+	56.2343i	−0.0607030	+	0.186825i
$302$	−167.035	+	229.905i	−0.553097	+	0.761273i
$303$	−18.8599	−	312.014i	−0.0622438	−	1.02975i
$304$	−46.4306	+	142.899i	−0.152732	+	0.470061i
$305$	−30.7587	+	9.99411i	−0.100848	+	0.0327676i
$306$	−101.309	−	218.071i	−0.331075	−	0.712650i
$307$	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	−0.924618	−	0.380897i	$-0.875615\pi$
$311$	−450.565	+	146.398i	−1.44876	+	0.470732i	−0.524146	+	0.851628i	$0.675615\pi$
$312$	416.078	−	163.554i	1.33358	−	0.524212i
$313$	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
$315$	−7.97246	+	14.3344i	−0.0253094	+	0.0455059i
$316$	19.6790	+	60.5656i	0.0622752	+	0.191663i
$317$	−93.6204	−	128.857i	−0.295333	−	0.406490i	0.635405	−	0.772179i	$-0.280833\pi$
$317$	−93.6204	−	128.857i	−0.295333	−	0.406490i	−0.930737	+	0.365689i	$0.880833\pi$
$318$	164.578	−	135.470i	0.517541	−	0.426007i
$319$		0			0
$320$		−	48.5757i		−	0.151799i
$321$	−82.4906	−	21.3964i	−0.256980	−	0.0666555i
$322$	30.9219	+	95.1679i	0.0960308	+	0.295552i
$323$	−244.054	−	79.2981i	−0.755586	−	0.245505i
$324$	53.4304	+	86.0527i	0.164909	+	0.265595i
$325$	339.441	+	246.618i	1.04443	+	0.758825i
$326$	24.3465	+	7.91065i	0.0746825	+	0.0242658i
$327$	104.332	+	66.5718i	0.319059	+	0.203583i
$328$	−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
$333$	567.617	−	68.8716i	1.70456	−	0.206822i
$334$	−78.9626	+	243.022i	−0.236415	+	0.727611i
$335$	−31.7297	+	43.6722i	−0.0947155	+	0.130365i
$336$	−73.7101	+	4.45545i	−0.219375	+	0.0132603i
$337$	−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
$339$	421.583	+	109.350i	1.24361	+	0.322567i
$340$	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
$345$	−17.7314	−	45.1082i	−0.0513953	−	0.130748i
$346$	−33.6751	−	24.4664i	−0.0973270	−	0.0707122i
$347$	−81.4326	+	112.082i	−0.234676	+	0.323004i	−0.910071	−	0.414452i	$-0.863973\pi$
$347$	−81.4326	+	112.082i	−0.234676	+	0.323004i	0.675395	+	0.737456i	$0.263973\pi$
$348$	−18.7349	+	7.36441i	−0.0538359	+	0.0211621i
$349$	−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	$-0.880464\pi$
$353$		−	258.939i		−	0.733538i	0.930312	−	0.366769i	$-0.119536\pi$
$354$	35.8925	−	138.378i	0.101391	−	0.390898i
$355$	−8.90657	−	27.4116i	−0.0250889	−	0.0772157i
$356$	45.4206	+	14.7580i	0.127586	+	0.0414552i
$357$	−7.60940	−	125.888i	−0.0213149	−	0.352629i
$358$	−82.9101	−	60.2377i	−0.231592	−	0.168262i
$359$	246.358	+	80.0466i	0.686234	+	0.222971i	0.631323	−	0.775520i	$-0.282512\pi$
$359$	246.358	+	80.0466i	0.686234	+	0.222971i	0.0549113	+	0.998491i	$0.482512\pi$
$360$	54.3332	−	6.59249i	0.150925	−	0.0183125i
$361$	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
$366$	123.892	−	194.165i	0.338503	−	0.530507i
$367$	−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
$369$	−413.297	−	444.479i	−1.12005	−	1.20455i
$370$	22.7386	−	69.9823i	0.0614557	−	0.189141i
$371$	106.331	−	34.5492i	0.286607	−	0.0931244i
$372$	3.82656	−	14.7527i	0.0102864	−	0.0396578i
$373$	−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
$378$	−21.0409	−	114.900i	−0.0556636	−	0.303968i
$379$	−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
$381$	−200.604	−	510.333i	−0.526521	−	1.33946i
$382$	−28.7983	−	88.6321i	−0.0753883	−	0.232021i
$383$	292.542	+	402.649i	0.763817	+	1.05130i	0.996887	+	0.0788436i	$0.0251228\pi$
$383$	292.542	+	402.649i	0.763817	+	1.05130i	−0.233070	+	0.972460i	$0.574877\pi$
$384$	73.5699	+	89.3774i	0.191588	+	0.232754i
$385$		0			0
$386$			250.336i			0.648538i
$387$	85.9330	+	184.973i	0.222049	+	0.477967i
$388$	6.29584	+	19.3766i	0.0162264	+	0.0499397i
$389$	−392.101	−	127.401i	−1.00797	−	0.327510i	−0.241926	−	0.970295i	$-0.577779\pi$
$389$	−392.101	−	127.401i	−1.00797	−	0.327510i	−0.766047	+	0.642785i	$0.777779\pi$
$390$	59.3677	−	3.58852i	0.152225	−	0.00920133i
$391$	301.500	+	219.053i	0.771100	+	0.560237i
$392$	349.357	+	113.513i	0.891217	+	0.289574i
$393$	136.376	−	213.730i	0.347012	−	0.543842i
$394$	−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
$399$	−105.090	−	67.0553i	−0.263383	−	0.168058i
$400$	−71.4608	+	219.934i	−0.178652	+	0.549835i
$401$	426.743	−	587.361i	1.06420	−	1.46474i	0.188382	−	0.982096i	$-0.439676\pi$
$401$	426.743	−	587.361i	1.06420	−	1.46474i	0.875816	−	0.482646i	$-0.160324\pi$
$402$	−23.1953	−	383.738i	−0.0576996	−	0.954571i
$403$	21.4888	−	66.1357i	0.0533221	−	0.164108i
$404$	−123.919	+	40.2636i	−0.306729	+	0.0996624i
$405$	13.5307	+	54.9370i	0.0334092	+	0.135647i
$406$	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
$411$	−570.616	+	224.301i	−1.38836	+	0.545744i
$412$	−55.0420	−	39.9904i	−0.133597	−	0.0970640i
$413$	44.0727	−	60.6608i	0.106713	−	0.146878i
$414$	301.654	+	167.773i	0.728633	+	0.405250i
$415$	−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	$0.239763\pi$
$419$			573.195i			1.36801i	−0.729478	+	0.684004i	$0.760237\pi$
$420$	6.61804	+	1.71659i	0.0157572	+	0.00408711i
$421$	−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
$423$	−452.417	−	486.549i	−1.06954	−	1.15023i
$424$	−301.820	−	219.285i	−0.711839	−	0.517182i
$425$	−375.622	−	122.047i	−0.883816	−	0.287169i
$426$	173.037	+	110.410i	0.406190	+	0.259179i
$427$	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	0.650701	−	0.759334i	$-0.274475\pi$
$431$	−117.467	−	161.680i	−0.272546	−	0.375127i	−0.923247	+	0.384207i	$0.874475\pi$
$432$	−175.736	+	184.394i	−0.406796	+	0.426837i
$433$	−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
$435$	−11.2238	+	0.678432i	−0.0258020	+	0.00155961i
$436$	15.9417	−	49.0635i	0.0365635	−	0.112531i
$437$	350.338	−	113.832i	0.801690	−	0.260485i
$438$	273.369	+	70.9065i	0.624131	+	0.161887i
$439$	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	−0.0738308	−	0.997271i	$-0.523522\pi$
$443$	200.511	−	65.1499i	0.452620	−	0.147065i	0.526451	+	0.850206i	$0.323522\pi$
$444$	−87.1929	−	221.817i	−0.196380	−	0.499587i
$445$	21.5817	+	15.6801i	0.0484983	+	0.0352361i
$446$	−183.266	+	252.244i	−0.410911	+	0.565570i
$447$	439.473	−	172.750i	0.983161	−	0.386466i
$448$	56.0693	+	172.563i	0.125155	+	0.385186i
$449$	−140.640	−	193.574i	−0.313229	−	0.431123i	0.623156	−	0.782098i	$-0.285850\pi$
$449$	−140.640	−	193.574i	−0.313229	−	0.431123i	−0.936385	+	0.350975i	$0.885850\pi$
$450$	−358.984	−	70.3118i	−0.797742	−	0.156248i
$451$		0			0
$452$		−	181.546i		−	0.401651i
$453$	−129.087	+	497.675i	−0.284960	+	1.09862i
$454$	−219.936	−	676.892i	−0.484440	−	1.49095i
$455$	29.6684	+	9.63983i	0.0652052	+	0.0211864i
$456$	25.0979	+	415.215i	0.0550393	+	0.910559i
$457$	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
$459$	−314.923	−	300.137i	−0.686108	−	0.653892i
$460$	−16.3447	+	11.8751i	−0.0355320	+	0.0258155i
$461$		−	393.125i		−	0.852766i	−0.904543	−	0.426383i	$-0.859788\pi$
$461$		−	393.125i		−	0.852766i	0.904543	−	0.426383i	$-0.140212\pi$
$462$		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
$465$	4.57927	−	7.17670i	0.00984790	−	0.0154338i
$466$	−167.498	+	515.506i	−0.359438	+	1.10624i
$467$	248.580	−	342.141i	0.532291	−	0.732636i	−0.455186	−	0.890396i	$-0.650427\pi$
$467$	248.580	−	342.141i	0.532291	−	0.732636i	0.987477	+	0.157760i	$0.0504274\pi$
$468$	141.078	−	131.181i	0.301449	−	0.280302i
$469$	62.3094	−	191.769i	0.132856	−	0.408888i
$470$	−81.3168	+	26.4214i	−0.173014	+	0.0562158i
$471$	49.2135	−	189.735i	0.104487	−	0.402835i
$472$	−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
$477$	187.454	−	337.039i	0.392985	−	0.706580i
$478$	−125.365	−	91.0832i	−0.262270	−	0.190551i
$479$	317.236	−	436.638i	0.662289	−	0.911562i	−0.337266	−	0.941409i	$-0.609502\pi$
$479$	317.236	−	436.638i	0.662289	−	0.911562i	0.999554	+	0.0298475i	$0.00950216\pi$
$480$	−14.7046	−	37.4083i	−0.0306347	−	0.0779339i
$481$	−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
$486$	−323.042	−	240.829i	−0.664696	−	0.495533i
$487$	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
$489$	46.2310	−	2.79446i	0.0945418	−	0.00571464i
$490$	39.5356	+	28.7243i	0.0806849	+	0.0586210i
$491$	54.0905	+	17.5751i	0.110164	+	0.0357944i	0.363580	−	0.931563i	$-0.381554\pi$
$491$	54.0905	+	17.5751i	0.110164	+	0.0357944i	−0.253416	+	0.967357i	$0.581554\pi$
$492$	−136.086	+	213.276i	−0.276598	+	0.433488i
$493$	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
$498$	248.297	+	158.432i	0.498589	+	0.318137i
$499$	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
$501$	27.8937	+	461.469i	0.0556761	+	0.921095i
$502$	1.42974	−	4.40029i	0.00284809	−	0.00876552i
$503$	−435.748	+	141.583i	−0.866297	+	0.281477i	−0.708256	−	0.705955i	$-0.750518\pi$
$503$	−435.748	+	141.583i	−0.866297	+	0.281477i	−0.158041	+	0.987433i	$0.550518\pi$
$504$	−185.407	+	86.1346i	−0.367872	+	0.170902i
$505$	−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	−0.0407663	−	0.999169i	$-0.512980\pi$
$509$	261.397	−	84.9330i	0.513550	−	0.166862i	0.554316	+	0.832306i	$0.312980\pi$
$510$	−52.1051	+	20.4818i	−0.102167	+	0.0401603i
$511$	119.837	+	87.0667i	0.234515	+	0.170385i
$512$	299.479	−	412.197i	0.584920	−	0.805073i
$513$	−422.978	+	77.4570i	−0.824518	+	0.150988i
$514$	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
$519$	−72.8967	−	18.9079i	−0.140456	−	0.0364315i
$520$	−32.1666	−	98.9985i	−0.0618588	−	0.190382i
$521$	−236.239	−	76.7587i	−0.453434	−	0.147330i	0.0733915	−	0.997303i	$-0.476618\pi$
$521$	−236.239	−	76.7587i	−0.453434	−	0.147330i	−0.526825	+	0.849974i	$0.676618\pi$
$522$	58.6433	−	54.5293i	0.112343	−	0.104462i
$523$	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
$525$	−161.743	−	103.204i	−0.308082	−	0.196579i
$526$	−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
$531$	−31.1538	−	256.760i	−0.0586701	−	0.483540i
$532$	−16.0575	+	49.4198i	−0.0301832	+	0.0928943i
$533$	−678.497	+	933.871i	−1.27298	+	1.75210i
$534$	−189.634	+	11.4625i	−0.355120	+	0.0214654i
$535$	−6.13159	+	18.8711i	−0.0114609	+	0.0352731i
$536$	−639.901	+	207.916i	−1.19384	+	0.387904i
$537$	−179.476	−	46.5524i	−0.334219	−	0.0866898i
$538$	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
$543$	162.875	+	414.351i	0.299955	+	0.763078i
$544$	250.034	+	181.661i	0.459622	+	0.333935i
$545$	16.9376	−	23.3127i	0.0310782	−	0.0427755i
$546$	−206.760	+	81.2743i	−0.378681	+	0.148854i
$547$	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
$552$	151.674	−	584.757i	0.274772	−	1.05934i
$553$	−41.0590	−	126.367i	−0.0742478	−	0.228511i
$554$	580.271	+	188.541i	1.04742	+	0.340327i
$555$	−8.03247	−	132.888i	−0.0144729	−	0.239437i
$556$	−50.8282	−	36.9289i	−0.0914177	−	0.0664188i
$557$	513.595	+	166.877i	0.922074	+	0.299600i	0.731317	−	0.682037i	$-0.238906\pi$
$557$	513.595	+	166.877i	0.922074	+	0.299600i	0.190757	+	0.981637i	$0.438906\pi$
$558$	7.30269	+	60.1865i	0.0130873	+	0.107861i
$559$	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	0.929317	−	0.369282i	$-0.120396\pi$
$563$	163.796	+	225.446i	0.290934	+	0.400437i	−0.638383	+	0.769719i	$0.720396\pi$
$564$	−148.967	+	233.463i	−0.264126	+	0.413941i
$565$	31.3366	−	96.4441i	0.0554630	−	0.170698i
$566$	−156.717	+	215.703i	−0.276886	+	0.381101i
$567$	−111.479	−	179.544i	−0.196613	−	0.316656i
$568$	111.012	−	341.659i	0.195443	−	0.601513i
$569$	1017.22	−	330.514i	1.78773	−	0.580869i	0.788321	−	0.615264i	$-0.210950\pi$
$569$	1017.22	−	330.514i	1.78773	−	0.580869i	0.999408	+	0.0343952i	$0.0109505\pi$
$570$	−13.8941	+	53.5665i	−0.0243756	+	0.0939764i
$571$	−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
$576$	546.975	+	304.216i	0.949609	+	0.528152i
$577$	−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
$579$	165.693	+	421.520i	0.286171	+	0.728013i
$580$	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
$585$	97.5892	−	45.3370i	0.166819	−	0.0774991i
$586$	149.079	+	458.817i	0.254400	+	0.782964i
$587$	−0.704580	−	0.228932i	−0.00120031	−	0.000390003i	0.308417	−	0.951251i	$-0.400201\pi$
$587$	−0.704580	−	0.228932i	−0.00120031	−	0.000390003i	−0.309617	+	0.950861i	$0.600201\pi$
$588$	157.998	−	9.55027i	0.268704	−	0.0162420i
$589$	52.3452	+	38.0310i	0.0888714	+	0.0645688i
$590$	−31.6562	−	10.2857i	−0.0536546	−	0.0174334i
$591$	−36.0459	+	56.4917i	−0.0609914	+	0.0955866i
$592$	484.897	−	352.299i	0.819083	−	0.595099i
$593$		−	498.413i		−	0.840494i	−0.907410	−	0.420247i	$-0.861943\pi$
$593$		−	498.413i		−	0.840494i	0.907410	−	0.420247i	$-0.138057\pi$
$594$		0			0
$595$	−29.3647			−0.0493524
$596$	−115.695	−	159.241i	−0.194120	−	0.267183i
$597$	−381.706	−	243.557i	−0.639374	−	0.407968i
$598$	202.862	−	624.344i	0.339234	−	1.04405i
$599$	112.504	−	154.848i	0.187819	−	0.258511i	−0.704715	−	0.709490i	$-0.748925\pi$
$599$	112.504	−	154.848i	0.187819	−	0.258511i	0.892534	+	0.450979i	$0.148925\pi$
$600$	38.6280	+	639.054i	0.0643800	+	1.06509i
$601$	−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
$603$	−293.046	−	630.791i	−0.485981	−	1.04609i
$604$	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
$609$	39.0893	−	15.3654i	0.0641860	−	0.0252306i
$610$	−43.3856	−	31.5215i	−0.0711239	−	0.0516746i
$611$	−742.718	+	1022.26i	−1.21558	+	1.67310i
$612$	−88.1417	+	158.477i	−0.144022	+	0.258950i
$613$	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	$-0.728863\pi$
$617$		−	928.547i		−	1.50494i	0.658628	−	0.752469i	$-0.271137\pi$
$618$	261.975	+	67.9510i	0.423908	+	0.109953i
$619$	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
$621$	618.976	+	82.8397i	0.996741	+	0.133397i
$622$	−635.529	−	461.739i	−1.02175	−	0.742346i
$623$	−94.7674	−	30.7918i	−0.152115	−	0.0494250i
$624$	408.399	+	260.589i	0.654485	+	0.417610i
$625$	−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
$630$	−26.9995	+	3.27598i	−0.0428564	+	0.00519996i
$631$	−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
$633$	543.741	−	32.8668i	0.858991	−	0.0519222i
$634$	81.6132	−	251.180i	0.128728	−	0.396183i
$635$	−121.425	+	39.4533i	−0.191220	+	0.0621311i
$636$	−155.608	−	40.3615i	−0.244666	−	0.0634615i
$637$	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	0.0745928	−	0.997214i	$-0.476234\pi$
$641$	462.217	−	150.183i	0.721087	−	0.234296i	0.646495	+	0.762919i	$0.276234\pi$
$642$	−51.6959	−	131.513i	−0.0805233	−	0.204849i
$643$	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
$645$	44.1969	−	17.3732i	0.0685223	−	0.0269351i
$646$	−131.489	−	404.681i	−0.203543	−	0.626441i
$647$	676.121	+	930.601i	1.04501	+	1.43833i	0.893057	+	0.449945i	$0.148556\pi$
$647$	676.121	+	930.601i	1.04501	+	1.43833i	0.151953	+	0.988388i	$0.451444\pi$
$648$	−266.040	+	653.093i	−0.410556	+	1.00786i
$649$		0			0
$650$			695.717i			1.07033i
$651$	−7.98389	+	30.7807i	−0.0122640	+	0.0472822i
$652$	−5.96585	−	18.3610i	−0.00915007	−	0.0281610i
$653$	575.439	+	186.971i	0.881224	+	0.286327i	0.714465	−	0.699671i	$-0.246670\pi$
$653$	575.439	+	186.971i	0.881224	+	0.286327i	0.166758	+	0.985998i	$0.446670\pi$
$654$	12.3819	+	204.843i	0.0189325	+	0.313216i
$655$	−47.7572	−	34.6976i	−0.0729117	−	0.0529735i
$656$	−605.083	−	196.603i	−0.922382	−	0.299700i
$657$	507.236	−	61.5452i	0.772049	−	0.0936761i
$658$	258.378	−	187.723i	0.392672	−	0.285293i
$659$			956.314i			1.45116i	0.688138	+	0.725580i	$0.258428\pi$
$659$			956.314i			1.45116i	−0.688138	+	0.725580i	$0.741572\pi$
$660$		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
$663$	−445.056	+	697.498i	−0.671276	+	1.05203i
$664$	159.295	−	490.261i	0.239903	−	0.738345i
$665$	−17.0607	+	23.4820i	−0.0256551	+	0.0353113i
$666$	645.614	+	694.322i	0.969390	+	1.04253i
$667$	−38.3523	+	118.036i	−0.0574997	+	0.176966i
$668$	183.276	−	59.5499i	0.274365	−	0.0891466i
$669$	−141.630	+	546.034i	−0.211705	+	0.816195i
$670$	−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
$675$	−651.001	+	119.213i	−0.964446	+	0.176612i
$676$	−125.438	−	91.1361i	−0.185559	−	0.134817i
$677$	158.543	−	218.215i	0.234184	−	0.322327i	−0.675710	−	0.737168i	$-0.736163\pi$
$677$	158.543	−	218.215i	0.234184	−	0.322327i	0.909894	+	0.414841i	$0.136163\pi$
$678$	264.202	+	672.122i	0.389678	+	0.991331i
$679$	−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	$0.0595383\pi$
$683$			254.016i			0.371913i	−0.982558	+	0.185956i	$0.940462\pi$
$684$	75.5196	+	162.558i	0.110409	+	0.237658i
$685$	44.1137	+	135.768i	0.0643996	+	0.198201i
$686$	−375.219	−	121.916i	−0.546966	−	0.177720i
$687$	−406.584	+	24.5762i	−0.591826	+	0.0357733i
$688$	172.968	+	125.668i	0.251407	+	0.182658i
$689$	−697.582	−	226.658i	−1.01246	−	0.328967i
$690$	43.2299	−	67.7506i	0.0626521	−	0.0981892i
$691$	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
$696$	−118.147	−	75.3869i	−0.169752	−	0.108315i
$697$	335.776	−	1033.41i	0.481745	−	1.48266i
$698$	220.772	−	303.867i	0.316293	−	0.435339i
$699$	59.1691	+	978.882i	0.0846482	+	1.40040i
$700$	−24.7139	+	76.0616i	−0.0353056	+	0.108659i
$701$	304.289	−	98.8694i	0.434078	−	0.141040i	−0.0838238	−	0.996481i	$-0.526713\pi$
$701$	304.289	−	98.8694i	0.434078	−	0.141040i	0.517902	+	0.855440i	$0.326713\pi$
$702$	−331.396	+	690.970i	−0.472073	+	0.984288i
$703$	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
$708$	−100.338	+	39.4414i	−0.141720	+	0.0557082i
$709$	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
$711$	−400.545	−	222.774i	−0.563354	−	0.313325i
$712$	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
$717$	−271.379	−	70.3902i	−0.378492	−	0.0981732i
$718$	132.730	+	408.501i	0.184861	+	0.568943i
$719$	765.742	+	248.805i	1.06501	+	0.346043i	0.788542	−	0.614981i	$-0.210836\pi$
$719$	765.742	+	248.805i	1.06501	+	0.346043i	0.276467	+	0.961023i	$0.410836\pi$
$720$	40.3862	+	43.4332i	0.0560920	+	0.0603239i
$721$	114.842	+	83.4376i	0.159282	+	0.115725i
$722$	169.294	+	55.0069i	0.234479	+	0.0761868i
$723$	−522.917	−	333.660i	−0.723260	−	0.461494i
$724$	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
$729$	−703.345	−	191.696i	−0.964808	−	0.262957i
$730$	20.3198	−	62.5378i	0.0278353	−	0.0856682i
$731$	−214.627	+	295.409i	−0.293608	+	0.404117i
$732$	−173.384	+	10.4803i	−0.236863	+	0.0143173i
$733$	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
$735$	85.5829	+	22.1985i	0.116439	+	0.0302020i
$736$	−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
$741$	299.192	+	761.138i	0.403768	+	1.02718i
$742$	149.982	+	108.968i	0.202132	+	0.146858i
$743$	229.421	−	315.771i	0.308776	−	0.424994i	−0.626223	−	0.779644i	$-0.715400\pi$
$743$	229.421	−	315.771i	0.308776	−	0.424994i	0.934999	+	0.354650i	$0.115400\pi$
$744$	98.7534	−	38.8185i	0.132733	−	0.0521755i
$745$	−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
$750$	−43.1942	+	166.529i	−0.0575922	+	0.222038i
$751$	−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
$753$	−0.505060	−	8.35561i	−0.000670730	−	0.0110964i
$754$	−123.212	−	89.5190i	−0.163412	−	0.118725i
$755$	113.851	+	36.9926i	0.150797	+	0.0489968i
$756$	−60.7761	+	63.7704i	−0.0803917	+	0.0843524i
$757$	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	0.735674	−	0.677336i	$-0.236866\pi$
$761$	−103.379	−	142.289i	−0.135847	−	0.186977i	−0.871521	+	0.490359i	$0.836866\pi$
$762$	489.083	−	766.498i	0.641842	−	1.00590i
$763$	−33.2614	+	102.368i	−0.0435929	+	0.134165i
$764$	−41.3108	+	56.8594i	−0.0540717	+	0.0744233i
$765$	−74.1789	+	68.9751i	−0.0969659	+	0.0901635i
$766$	−255.022	+	784.878i	−0.332927	+	1.02464i
$767$	−467.833	+	152.008i	−0.609951	+	0.198185i
$768$	161.328	−	621.976i	0.210062	−	0.809864i
$769$	−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	−0.748945	−	0.662632i	$-0.769439\pi$
$773$	−746.230	+	242.465i	−0.965368	+	0.313667i	−0.216424	+	0.976300i	$0.569439\pi$
$774$	−164.384	+	295.560i	−0.212383	+	0.381861i
$775$	80.5641	+	58.5332i	0.103954	+	0.0755268i
$776$	−83.3742	+	114.755i	−0.107441	+	0.147880i
$777$	181.923	+	462.808i	0.234135	+	0.595634i
$778$	−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
$783$	62.6525	−	130.632i	0.0800159	−	0.166836i
$784$	123.005	+	378.571i	0.156894	+	0.482871i
$785$	−43.4051	−	14.1032i	−0.0552931	−	0.0179658i
$786$	419.632	−	25.3649i	0.533883	−	0.0322708i
$787$	−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
$789$	−611.936	+	959.035i	−0.775585	+	1.21551i
$790$	−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
$795$	−75.6979	−	48.3009i	−0.0952175	−	0.0607559i
$796$	−58.3237	+	179.502i	−0.0732709	+	0.225505i
$797$	203.605	−	280.238i	0.255464	−	0.351616i	−0.661951	−	0.749547i	$-0.730272\pi$
$797$	203.605	−	280.238i	0.255464	−	0.351616i	0.917416	+	0.397931i	$0.130272\pi$
$798$	−12.4718	−	206.331i	−0.0156288	−	0.258560i
$799$	367.558	−	1131.23i	0.460022	−	1.41580i
$800$	447.162	−	145.292i	0.558952	−	0.181615i
$801$	−311.722	+	144.816i	−0.389166	+	0.180795i
$802$	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
$807$	87.1137	−	34.2431i	0.107948	−	0.0424326i
$808$	−733.888	−	533.201i	−0.908277	−	0.659902i
$809$	307.526	−	423.274i	0.380131	−	0.523206i	−0.575488	−	0.817810i	$-0.695188\pi$
$809$	307.526	−	423.274i	0.380131	−	0.523206i	0.955619	+	0.294604i	$0.0951878\pi$
$810$	−60.5093	+	71.6951i	−0.0747028	+	0.0885125i
$811$	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
$816$	−441.420	−	114.495i	−0.540956	−	0.140313i
$817$	111.532	+	343.261i	0.136514	+	0.420148i
$818$	475.294	+	154.432i	0.581044	+	0.188793i
$819$	−294.352	+	273.702i	−0.359404	+	0.334191i
$820$	47.6558	+	34.6239i	0.0581168	+	0.0422243i
$821$	92.9928	+	30.2152i	0.113268	+	0.0368029i	0.365102	−	0.930967i	$-0.381034\pi$
$821$	92.9928	+	30.2152i	0.113268	+	0.0368029i	−0.251835	+	0.967770i	$0.581034\pi$
$822$	−857.041	−	546.856i	−1.04263	−	0.665275i
$823$	−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	$-0.933303\pi$
$827$	−722.545	−	994.498i	−0.873694	−	1.20254i	0.104433	−	0.994532i	$-0.466697\pi$
$828$	−31.3548	−	258.417i	−0.0378682	−	0.312097i
$829$	−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
$831$	1101.86	−	66.6027i	1.32595	−	0.0801477i
$832$	367.840	−	1132.09i	0.442115	−	1.36069i
$833$	−646.556	+	210.079i	−0.776178	+	0.252195i
$834$	241.919	+	62.7490i	0.290071	+	0.0752386i
$835$	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	−0.620343	−	0.784331i	$-0.713007\pi$
$839$	−554.741	+	180.246i	−0.661193	+	0.214835i	−0.0408501	+	0.999165i	$0.513007\pi$
$840$	17.4139	+	44.3006i	0.0207309	+	0.0527388i
$841$	−657.089	−	477.403i	−0.781319	−	0.567661i
$842$	545.099	−	750.264i	0.647386	−	0.891050i
$843$	−894.547	+	351.633i	−1.06115	+	0.417121i
$844$	−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
$849$	−121.113	+	466.933i	−0.142654	+	0.549980i
$850$	−202.373	−	622.841i	−0.238086	−	0.732754i
$851$	−1397.52	−	454.082i	−1.64221	−	0.533587i
$852$	−9.33984	−	154.516i	−0.0109623	−	0.181357i
$853$	−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
$855$	12.0597	+	99.3925i	0.0141050	+	0.116249i
$856$	−200.082	+	145.368i	−0.233740	+	0.169822i
$857$			580.461i			0.677317i	0.940909	+	0.338659i	$0.109973\pi$
$857$			580.461i			0.677317i	−0.940909	+	0.338659i	$0.890027\pi$
$858$		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
$861$	283.936	−	444.988i	0.329774	−	0.516827i
$862$	102.402	−	315.160i	0.118795	−	0.365614i
$863$	−369.257	+	508.239i	−0.427876	+	0.588921i	−0.967464	−	0.253008i	$-0.918580\pi$
$863$	−369.257	+	508.239i	−0.427876	+	0.588921i	0.539588	+	0.841929i	$0.318580\pi$
$864$	513.318	+	68.6991i	0.594118	+	0.0795129i
$865$	−5.41846	+	16.6763i	−0.00626412	+	0.0192790i
$866$	−163.198	+	53.0264i	−0.188451	+	0.0612314i
$867$	−22.1338	+	85.3335i	−0.0255292	+	0.0984239i
$868$	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
$873$	−128.145	−	71.2716i	−0.146787	−	0.0816399i
$874$	494.158	+	359.026i	0.565398	+	0.410785i
$875$	−53.0385	+	73.0012i	−0.0606154	+	0.0834299i
$876$	−77.9176	−	198.220i	−0.0889470	−	0.226279i
$877$	−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	$0.0237269\pi$
$881$			131.219i			0.148943i	−0.997223	+	0.0744714i	$0.976273\pi$
$882$	−571.043	+	265.289i	−0.647441	+	0.300781i
$883$	−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
$885$	−60.1113	+	3.63346i	−0.0679223	+	0.00410561i
$886$	282.823	+	205.483i	0.319214	+	0.231922i
$887$	1136.31	+	369.209i	1.28107	+	0.416245i	0.868957	−	0.494888i	$-0.164791\pi$
$887$	1136.31	+	369.209i	1.28107	+	0.416245i	0.412113	+	0.911133i	$0.364791\pi$
$888$	892.563	−	1398.84i	1.00514	−	1.57527i
$889$	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
$894$	660.070	+	421.174i	0.738333	+	0.471112i
$895$	−13.3406	+	41.0580i	−0.0149057	+	0.0458749i
$896$	−59.1774	+	81.4507i	−0.0660462	+	0.0909048i
$897$	−71.6614	−	1185.55i	−0.0798901	−	1.32169i
$898$	122.602	−	377.331i	0.136528	−	0.420190i
$899$	−20.7326	+	6.73643i	−0.0230618	+	0.00749325i
$900$	116.232	+	250.192i	0.129146	+	0.277991i
$901$	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
$906$	−793.435	+	311.888i	−0.875756	+	0.344247i
$907$	−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
$909$	455.802	−	819.524i	0.501432	−	0.901567i
$910$	15.9844	+	49.1949i	0.0175653	+	0.0540603i
$911$	−103.220	−	142.070i	−0.113304	−	0.155950i	0.748598	−	0.663024i	$-0.230727\pi$
$911$	−103.220	−	142.070i	−0.113304	−	0.155950i	−0.861903	+	0.507074i	$0.830727\pi$
$912$	−348.020	+	286.468i	−0.381601	+	0.314110i
$913$		0			0
$914$			44.2524i			0.0484162i
$915$	−93.9170	−	24.3602i	−0.102642	−	0.0266231i
$916$	52.4674	+	161.478i	0.0572788	+	0.176286i
$917$	209.706	+	68.1377i	0.228687	+	0.0743050i
$918$	95.6894	−	714.989i	0.104237	−	0.778855i
$919$	−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
$921$	712.678	+	454.742i	0.773809	+	0.493748i
$922$	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
$927$	486.093	−	58.9799i	0.524373	−	0.0636245i
$928$	−31.8056	+	97.8877i	−0.0342733	+	0.105482i
$929$	916.652	−	1261.66i	0.986708	−	1.35809i	0.0535724	−	0.998564i	$-0.482939\pi$
$929$	916.652	−	1261.66i	0.986708	−	1.35809i	0.933136	−	0.359524i	$-0.117061\pi$
$930$	14.0905	−	0.851711i	0.0151511	−	0.000915818i
$931$	−207.651	+	639.084i	−0.223041	+	0.686449i
$932$	388.770	−	126.319i	0.417136	−	0.135536i
$933$	−1375.73	−	356.837i	−1.47453	−	0.382462i
$934$	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
$939$	32.8969	+	83.6890i	0.0350340	+	0.0891256i
$940$	52.1664	+	37.9011i	0.0554962	+	0.0403204i
$941$	−689.641	+	949.209i	−0.732881	+	1.00872i	0.266116	+	0.963941i	$0.414260\pi$
$941$	−689.641	+	949.209i	−0.732881	+	1.00872i	−0.998997	+	0.0447831i	$0.985740\pi$
$942$	302.491	−	118.905i	0.321116	−	0.126226i
$943$	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	$-0.955127\pi$
$947$		−	266.119i		−	0.281013i	0.990080	−	0.140506i	$-0.0448730\pi$
$948$	−47.9666	+	184.928i	−0.0505976	+	0.195072i
$949$	−300.296	−	924.216i	−0.316434	−	0.973884i
$950$	−615.643	−	200.035i	−0.648046	−	0.210563i
$951$	−28.8301	−	476.959i	−0.0303155	−	0.501534i
$952$	−296.102	−	215.131i	−0.311032	−	0.225978i
$953$	121.881	+	39.6016i	0.127892	+	0.0415547i	0.372264	−	0.928127i	$-0.378582\pi$
$953$	121.881	+	39.6016i	0.127892	+	0.0415547i	−0.244372	+	0.969682i	$0.578582\pi$
$954$	634.831	−	77.0269i	0.665441	−	0.0807410i
$955$	−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
$960$	78.3868	−	122.849i	0.0816529	−	0.127968i
$961$	−291.865	+	898.268i	−0.303710	+	0.934723i
$962$	1059.88	−	1458.80i	1.10175	−	1.51643i
$963$	−174.093	−	187.228i	−0.180782	−	0.194421i
$964$	−79.9003	+	245.908i	−0.0828841	+	0.255091i
$965$	100.293	−	32.5872i	0.103931	−	0.0337692i
$966$	−75.3708	+	290.581i	−0.0780236	+	0.300808i
$967$	−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	−0.581102	−	0.813831i	$-0.697378\pi$
$971$	−556.252	+	180.737i	−0.572865	+	0.186135i	0.00823681	+	0.999966i	$0.497378\pi$
$972$	−3.73711	+	303.850i	−0.00384477	+	0.312603i
$973$	106.050	+	77.0500i	0.108993	+	0.0791881i
$974$	−595.161	+	819.169i	−0.611048	+	0.841036i
$975$	460.484	+	1171.46i	0.472292	+	1.20150i
$976$	−134.984	−	415.437i	−0.138303	−	0.425652i
$977$	406.363	+	559.311i	0.415930	+	0.572478i	0.964652	−	0.263526i	$-0.0848856\pi$
$977$	406.363	+	559.311i	0.415930	+	0.572478i	−0.548722	+	0.836005i	$0.684886\pi$
$978$	48.8073	+	59.2943i	0.0499052	+	0.0606281i
$979$		0			0
$980$		−	36.8545i		−	0.0376066i
$981$	156.431	+	336.723i	0.159461	+	0.343245i
$982$	29.1423	+	89.6907i	0.0296764	+	0.0913347i
$983$	623.407	+	202.557i	0.634188	+	0.206060i	0.608430	−	0.793608i	$-0.291800\pi$
$983$	623.407	+	202.557i	0.634188	+	0.206060i	0.0257588	+	0.999668i	$0.491800\pi$
$984$	−1758.17	+	106.273i	−1.78675	+	0.108001i
$985$	12.6229	+	9.17105i	0.0128151	+	0.00931071i
$986$	136.346	+	44.3013i	0.138281	+	0.0449304i
$987$	310.811	−	487.107i	0.314904	−	0.493523i
$988$	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
$993$	841.429	+	536.895i	0.847361	+	0.540680i
$994$	−55.1646	+	169.779i	−0.0554976	+	0.170804i
$995$	−61.9675	+	85.2909i	−0.0622789	+	0.0857195i
$996$	−13.4021	−	221.722i	−0.0134559	−	0.222612i
$997$	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
$999$	1546.66	+	741.790i	1.54820	+	0.742532i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.2	✓	16	11.10	odd	2
33.3.h.b.14.3	yes	16	33.32	even	2
33.3.h.b.26.2	yes	16	33.29	even	10
33.3.h.b.26.3	yes	16	11.7	odd	10
363.3.b.l.122.4		8	11.9	even	5
363.3.b.l.122.5		8	33.20	odd	10
363.3.b.m.122.4		8	33.2	even	10
363.3.b.m.122.5		8	11.2	odd	10
363.3.h.j.245.2		16	3.2	odd	2	inner
363.3.h.j.245.3		16	1.1	even	1	trivial
363.3.h.j.323.2		16	11.4	even	5	inner
363.3.h.j.323.3		16	33.26	odd	10	inner
363.3.h.n.251.2		16	11.5	even	5
363.3.h.n.251.3		16	33.5	odd	10
363.3.h.n.269.2		16	33.14	odd	10
363.3.h.n.269.3		16	11.3	even	5
363.3.h.o.251.2		16	33.17	even	10
363.3.h.o.251.3		16	11.6	odd	10
363.3.h.o.269.2		16	11.8	odd	10
363.3.h.o.269.3		16	33.8	even	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} +(2.52902 + 1.61371i) q^{3} +(0.386428 - 1.18930i) q^{4} +(0.410570 - 0.565101i) q^{5} +(0.300138 + 4.96542i) q^{6} +(-0.806259 + 2.48141i) q^{7} +(8.28007 - 2.69036i) q^{8} +(3.79191 + 8.16220i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} +(13.8479 - 10.0611i) q^{13} +(-4.11458 + 1.33691i) q^{14} +(1.95025 - 0.766614i) q^{15} +(7.63243 + 5.54529i) q^{16} +(-9.47072 + 13.0353i) q^{17} +(-7.25367 + 13.0420i) q^{18} +(4.92151 + 15.1469i) q^{19} +(-0.513421 - 0.706663i) q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(25.2819 + 6.55762i) q^{24} +(7.57465 + 23.3124i) q^{25} +(26.9935 + 8.77071i) q^{26} +(-3.58157 + 26.7614i) q^{27} +(2.63959 + 1.91777i) q^{28} +(-5.10329 - 1.65816i) q^{29} +(2.92919 + 1.86904i) q^{30} +(3.28671 - 2.38793i) q^{31} -19.1813i q^{32} -26.7172 q^{34} +(1.07122 + 1.47441i) q^{35} +(11.1726 - 1.35562i) q^{36} +(19.6322 - 60.4217i) q^{37} +(-15.5225 + 21.3649i) q^{38} +(51.2573 - 3.09828i) q^{39} +(1.87922 - 5.78366i) q^{40} +(-64.1371 + 20.8394i) q^{41} +(-12.5632 - 3.25865i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} +(31.0277 - 22.5429i) q^{46} +(-70.2078 + 22.8119i) q^{47} +(10.3541 + 26.3407i) q^{48} +(34.1345 + 24.8002i) q^{49} +(-23.8905 + 32.8825i) q^{50} +(-44.9868 + 17.6837i) q^{51} +(-6.61446 - 20.3572i) q^{52} +(-25.1873 - 34.6673i) q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(-11.9960 + 46.2486i) q^{57} +(-2.74949 - 8.46207i) q^{58} +(-27.3316 - 8.88056i) q^{59} +(-0.158106 - 2.61568i) q^{60} +(-37.4585 - 27.2152i) q^{61} +(6.40673 + 2.08167i) q^{62} +(-23.3110 + 2.82843i) q^{63} +(56.2610 - 40.8760i) q^{64} -11.9562i q^{65} -77.2821 q^{67} +(11.8432 + 16.3008i) q^{68} +(37.3241 - 58.4949i) q^{69} +(-0.933834 + 2.87405i) q^{70} +(24.2537 - 33.3824i) q^{71} +(53.3565 + 57.3820i) q^{72} +(17.5438 - 53.9942i) q^{73} +(100.189 - 32.5533i) q^{74} +(-18.4629 + 71.1808i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +(-41.1994 + 29.9331i) q^{79} +(6.26730 - 2.03637i) q^{80} +(-52.2429 + 61.9006i) q^{81} +(-90.4664 - 65.7277i) q^{82} +(34.8026 - 47.9017i) q^{83} +(3.58085 + 9.10961i) q^{84} +(3.47788 + 10.7038i) q^{85} +(22.0875 + 30.4009i) q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(4.39190 + 9.45370i) q^{90} +(13.8007 + 42.4742i) q^{91} +(-27.5079 - 8.93786i) q^{92} +(12.1656 - 0.735356i) q^{93} +(-99.0291 - 71.9489i) q^{94} +(10.5801 + 3.43769i) q^{95} +(30.9530 - 48.5099i) 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

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Representations

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Database

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