LMFDB - Embedded newform 363.3.h.q.323.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [24,0,-4,18,0,10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	363.323
Dual form			363.3.h.q.245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05778 + 2.83229i) q^{2} +(-2.95837 + 0.498071i) q^{3} +(-2.55135 - 7.85225i) q^{4} +(-4.64306 - 6.39063i) q^{5} +(4.67699 - 9.40388i) q^{6} +(0.560737 + 1.72577i) q^{7} +(14.1718 + 4.60468i) q^{8} +(8.50385 - 2.94695i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +(-0.0573816 - 0.0416901i) q^{13} +(-6.04176 - 1.96309i) q^{14} +(16.9189 + 16.5932i) q^{15} +(-15.4861 + 11.2513i) q^{16} +(-2.15151 - 2.96129i) q^{17} +(-9.15243 + 30.1496i) q^{18} +(8.13557 - 25.0387i) q^{19} +(-38.3347 + 52.7632i) q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(-44.2187 - 6.56379i) q^{24} +(-11.5567 + 35.5678i) q^{25} +(0.236157 - 0.0767322i) q^{26} +(-23.6897 + 12.9537i) q^{27} +(12.1205 - 8.80609i) q^{28} +(-28.7313 + 9.33537i) q^{29} +(-81.8122 + 13.7739i) q^{30} +(-34.1714 - 24.8270i) q^{31} -7.40958i q^{32} +12.8146 q^{34} +(8.42522 - 11.5963i) q^{35} +(-44.8365 - 59.2557i) q^{36} +(1.14339 + 3.51900i) q^{37} +(54.1758 + 74.5665i) q^{38} +(0.190520 + 0.0947546i) q^{39} +(-36.3736 - 111.946i) q^{40} +(67.5964 + 21.9634i) q^{41} +(18.8515 + 2.79830i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} +(19.3796 + 14.0801i) q^{46} +(26.0191 + 8.45412i) q^{47} +(40.2096 - 40.9986i) q^{48} +(36.9780 - 26.8661i) q^{49} +(-76.9573 - 105.923i) q^{50} +(7.83988 + 7.68899i) q^{51} +(-0.180961 + 0.556941i) q^{52} +(-12.7697 + 17.5760i) q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(-11.5969 + 78.1258i) q^{57} +(32.6823 - 100.586i) q^{58} +(-75.8954 + 24.6599i) q^{59} +(87.1283 - 175.186i) q^{60} +(-64.0476 + 46.5333i) q^{61} +(140.634 - 45.6949i) q^{62} +(9.85418 + 13.0232i) q^{63} +(-40.9582 - 29.7579i) q^{64} +0.560274i q^{65} -101.689 q^{67} +(-17.7636 + 24.4495i) q^{68} +(3.40798 + 20.2422i) q^{69} +(15.5069 + 47.7254i) q^{70} +(-27.2787 - 37.5458i) q^{71} +(134.084 - 2.60595i) q^{72} +(35.6914 + 109.847i) q^{73} +(-12.3197 - 4.00291i) q^{74} +(16.4736 - 110.979i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +(-50.8781 - 36.9651i) q^{79} +(143.806 + 46.7253i) q^{80} +(63.6310 - 50.1209i) q^{81} +(-201.305 + 146.257i) q^{82} +(49.6679 + 68.3620i) q^{83} +(-31.4709 + 32.0885i) q^{84} +(-8.93495 + 27.4990i) q^{85} +(28.5211 - 39.2559i) q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(235.170 - 81.4966i) q^{90} +(0.0397717 - 0.122405i) q^{91} +(-53.7279 + 17.4573i) q^{92} +(113.457 + 56.4275i) q^{93} +(-77.4862 + 56.2970i) q^{94} +(-197.787 + 64.2650i) q^{95} +(3.69050 + 21.9202i) q^{96} +(77.8815 + 56.5842i) q^{97} +160.017i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

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

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

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 $

$2$	−2.05778	+	2.83229i	−1.02889	+	1.41615i	−0.123113	+	0.992393i	$0.539288\pi$
$2$	−2.05778	+	2.83229i	−1.02889	+	1.41615i	−0.905777	+	0.423754i	$0.860712\pi$
$3$	−2.95837	+	0.498071i	−0.986122	+	0.166024i
$3$	−2.95837	+	0.498071i	−0.986122	+	0.166024i
$4$	−2.55135	−	7.85225i	−0.637838	−	1.96306i
$5$	−4.64306	−	6.39063i	−0.928613	−	1.27813i	−0.960398	−	0.278631i	$-0.910119\pi$
$5$	−4.64306	−	6.39063i	−0.928613	−	1.27813i	0.0317852	−	0.999495i	$-0.489881\pi$
$6$	4.67699	−	9.40388i	0.779498	−	1.56731i
$7$	0.560737	+	1.72577i	0.0801053	+	0.246539i	0.983087	−	0.183141i	$-0.0586265\pi$
$7$	0.560737	+	1.72577i	0.0801053	+	0.246539i	−0.902981	+	0.429680i	$0.858626\pi$
$8$	14.1718	+	4.60468i	1.77147	+	0.575585i
$9$	8.50385	−	2.94695i	0.944872	−	0.327439i
$10$	27.6545			2.76545
$11$		0			0
$11$		0			0
$12$	11.4588	+	21.9591i	0.954901	+	1.82992i
$13$	−0.0573816	−	0.0416901i	−0.00441397	−	0.00320693i	0.585576	−	0.810617i	$-0.300868\pi$
$13$	−0.0573816	−	0.0416901i	−0.00441397	−	0.00320693i	−0.589990	+	0.807411i	$0.700868\pi$
$14$	−6.04176	−	1.96309i	−0.431554	−	0.140220i
$15$	16.9189	+	16.5932i	1.12792	+	1.10622i
$16$	−15.4861	+	11.2513i	−0.967880	+	0.703206i
$17$	−2.15151	−	2.96129i	−0.126559	−	0.174194i	0.741035	−	0.671466i	$-0.234335\pi$
$17$	−2.15151	−	2.96129i	−0.126559	−	0.174194i	−0.867595	+	0.497272i	$0.834335\pi$
$18$	−9.15243	+	30.1496i	−0.508469	+	1.67498i
$19$	8.13557	−	25.0387i	0.428188	−	1.31783i	−0.471720	−	0.881748i	$-0.656367\pi$
$19$	8.13557	−	25.0387i	0.428188	−	1.31783i	0.899908	−	0.436079i	$-0.143633\pi$
$20$	−38.3347	+	52.7632i	−1.91674	+	2.63816i
$21$	−2.51842	−	4.82617i	−0.119925	−	0.229818i
$22$		0			0
$23$		−	6.84236i		−	0.297494i	−0.988875	−	0.148747i	$-0.952476\pi$
$23$		−	6.84236i		−	0.297494i	0.988875	−	0.148747i	$-0.0475240\pi$
$24$	−44.2187	−	6.56379i	−1.84245	−	0.273491i
$25$	−11.5567	+	35.5678i	−0.462267	+	1.42271i
$26$	0.236157	−	0.0767322i	0.00908298	−	0.00295124i
$27$	−23.6897	+	12.9537i	−0.877397	+	0.479766i
$28$	12.1205	−	8.80609i	0.432877	−	0.314503i
$29$	−28.7313	+	9.33537i	−0.990735	+	0.321909i	−0.759157	−	0.650907i	$-0.774389\pi$
$29$	−28.7313	+	9.33537i	−0.990735	+	0.321909i	−0.231578	+	0.972816i	$0.574389\pi$
$30$	−81.8122	+	13.7739i	−2.72707	+	0.459131i
$31$	−34.1714	−	24.8270i	−1.10230	−	0.800870i	−0.120869	−	0.992669i	$-0.538568\pi$
$31$	−34.1714	−	24.8270i	−1.10230	−	0.800870i	−0.981434	+	0.191799i	$0.938568\pi$
$32$		−	7.40958i		−	0.231549i
$33$		0			0
$34$	12.8146			0.376899
$35$	8.42522	−	11.5963i	0.240721	−	0.331324i
$36$	−44.8365	−	59.2557i	−1.24546	−	1.64599i
$37$	1.14339	+	3.51900i	0.0309025	+	0.0951080i	0.965318	−	0.261076i	$-0.0840775\pi$
$37$	1.14339	+	3.51900i	0.0309025	+	0.0951080i	−0.934416	+	0.356184i	$0.884077\pi$
$38$	54.1758	+	74.5665i	1.42568	+	1.96228i
$39$	0.190520	+	0.0947546i	0.00488514	+	0.00242960i
$40$	−36.3736	−	111.946i	−0.909339	−	2.79866i
$41$	67.5964	+	21.9634i	1.64869	+	0.535692i	0.978456	−	0.206456i	$-0.0661929\pi$
$41$	67.5964	+	21.9634i	1.64869	+	0.535692i	0.670236	+	0.742148i	$0.266193\pi$
$42$	18.8515	+	2.79830i	0.448845	+	0.0666263i
$43$	−13.8601			−0.322329			−0.161164	−	0.986928i	$-0.551525\pi$
$43$	−13.8601			−0.322329			−0.161164	+	0.986928i	$0.551525\pi$
$44$		0			0
$45$	−58.3168	−	40.6621i	−1.29593	−	0.903602i
$46$	19.3796	+	14.0801i	0.421295	+	0.306089i
$47$	26.0191	+	8.45412i	0.553598	+	0.179875i	0.572439	−	0.819948i	$-0.305997\pi$
$47$	26.0191	+	8.45412i	0.553598	+	0.179875i	−0.0188404	+	0.999823i	$0.505997\pi$
$48$	40.2096	−	40.9986i	0.837699	−	0.854138i
$49$	36.9780	−	26.8661i	0.754653	−	0.548287i
$50$	−76.9573	−	105.923i	−1.53915	−	2.11845i
$51$	7.83988	+	7.68899i	0.153723	+	0.150764i
$52$	−0.180961	+	0.556941i	−0.00348002	+	0.0107104i
$53$	−12.7697	+	17.5760i	−0.240938	+	0.331623i	−0.912312	−	0.409496i	$-0.865705\pi$
$53$	−12.7697	+	17.5760i	−0.240938	+	0.331623i	0.671374	+	0.741119i	$0.265705\pi$
$54$	12.0596	−	93.7520i	0.223326	−	1.73615i
$55$		0			0
$56$			27.0392i			0.482843i
$57$	−11.5969	+	78.1258i	−0.203455	+	1.37063i
$58$	32.6823	−	100.586i	0.563487	−	1.73424i
$59$	−75.8954	+	24.6599i	−1.28636	+	0.417964i	−0.870817	−	0.491608i	$-0.836409\pi$
$59$	−75.8954	+	24.6599i	−1.28636	+	0.417964i	−0.415546	+	0.909572i	$0.636409\pi$
$60$	87.1283	−	175.186i	1.45214	−	2.91977i
$61$	−64.0476	+	46.5333i	−1.04996	+	0.762842i	−0.972205	−	0.234131i	$-0.924776\pi$
$61$	−64.0476	+	46.5333i	−1.04996	+	0.762842i	−0.0777562	+	0.996972i	$0.524776\pi$
$62$	140.634	−	45.6949i	2.26830	−	0.737015i
$63$	9.85418	+	13.0232i	0.156416	+	0.206718i
$64$	−40.9582	−	29.7579i	−0.639973	−	0.464967i
$65$			0.560274i			0.00861961i
$66$		0			0
$67$	−101.689			−1.51775			−0.758874	−	0.651238i	$-0.774250\pi$
$67$	−101.689			−1.51775			−0.758874	+	0.651238i	$0.774250\pi$
$68$	−17.7636	+	24.4495i	−0.261229	+	0.359551i
$69$	3.40798	+	20.2422i	0.0493910	+	0.293365i
$70$	15.5069	+	47.7254i	0.221527	+	0.681791i
$71$	−27.2787	−	37.5458i	−0.384206	−	0.528815i	0.572486	−	0.819914i	$-0.305979\pi$
$71$	−27.2787	−	37.5458i	−0.384206	−	0.528815i	−0.956693	+	0.291099i	$0.905979\pi$
$72$	134.084	−	2.60595i	1.86228	−	0.0361937i
$73$	35.6914	+	109.847i	0.488923	+	1.50475i	0.826218	+	0.563351i	$0.190488\pi$
$73$	35.6914	+	109.847i	0.488923	+	1.50475i	−0.337295	+	0.941399i	$0.609512\pi$
$74$	−12.3197	−	4.00291i	−0.166482	−	0.0540933i
$75$	16.4736	−	110.979i	0.219648	−	1.47971i
$76$	−217.367			−2.86009
$77$		0			0
$78$	−0.660422	+	0.344625i	−0.00846695	+	0.00441827i
$79$	−50.8781	−	36.9651i	−0.644026	−	0.467912i	0.217205	−	0.976126i	$-0.430306\pi$
$79$	−50.8781	−	36.9651i	−0.644026	−	0.467912i	−0.861231	+	0.508214i	$0.830306\pi$
$80$	143.806	+	46.7253i	1.79757	+	0.584067i
$81$	63.6310	−	50.1209i	0.785567	−	0.618776i
$82$	−201.305	+	146.257i	−2.45494	+	1.78362i
$83$	49.6679	+	68.3620i	0.598409	+	0.823639i	0.995561	−	0.0941136i	$-0.0300017\pi$
$83$	49.6679	+	68.3620i	0.598409	+	0.823639i	−0.397153	+	0.917753i	$0.630002\pi$
$84$	−31.4709	+	32.0885i	−0.374654	+	0.382006i
$85$	−8.93495	+	27.4990i	−0.105117	+	0.323517i
$86$	28.5211	−	39.2559i	0.331641	−	0.456464i
$87$	80.3481	−	41.9277i	0.923541	−	0.481927i
$88$		0			0
$89$			45.3523i			0.509577i	0.966997	+	0.254788i	$0.0820058\pi$
$89$			45.3523i			0.509577i	−0.966997	+	0.254788i	$0.917994\pi$
$90$	235.170	−	81.4966i	2.61300	−	0.905518i
$91$	0.0397717	−	0.122405i	0.000437051	−	0.00134511i
$92$	−53.7279	+	17.4573i	−0.583999	+	0.189753i
$93$	113.457	+	56.4275i	1.21997	+	0.606747i
$94$	−77.4862	+	56.2970i	−0.824321	+	0.598905i
$95$	−197.787	+	64.2650i	−2.08197	+	0.676473i
$96$	3.69050	+	21.9202i	0.0384427	+	0.228336i
$97$	77.8815	+	56.5842i	0.802902	+	0.583342i	0.911764	−	0.410715i	$-0.134721\pi$
$97$	77.8815	+	56.5842i	0.802902	+	0.583342i	−0.108862	+	0.994057i	$0.534721\pi$
$98$			160.017i			1.63283i
$99$		0			0
$100$	308.772			3.08772
$101$	−32.7370	+	45.0587i	−0.324129	+	0.446126i	−0.939722	−	0.341939i	$-0.888917\pi$
$101$	−32.7370	+	45.0587i	−0.324129	+	0.446126i	0.615593	+	0.788064i	$0.288917\pi$
$102$	−37.9102	+	6.38257i	−0.371669	+	0.0625742i
$103$	40.3200	+	124.092i	0.391456	+	1.20478i	0.931687	+	0.363262i	$0.118337\pi$
$103$	40.3200	+	124.092i	0.391456	+	1.20478i	−0.540231	+	0.841517i	$0.681663\pi$
$104$	−0.621228	−	0.855046i	−0.00597334	−	0.00822160i
$105$	−19.1491	+	38.5025i	−0.182372	+	0.366691i
$106$	−23.5031	−	72.3352i	−0.221728	−	0.682408i
$107$	−55.2940	−	17.9661i	−0.516767	−	0.167908i	0.0390107	−	0.999239i	$-0.487579\pi$
$107$	−55.2940	−	17.9661i	−0.516767	−	0.167908i	−0.555778	+	0.831331i	$0.687579\pi$
$108$	162.156	+	152.968i	1.50145	+	1.41637i
$109$	49.0112			0.449644			0.224822	−	0.974400i	$-0.427820\pi$
$109$	49.0112			0.449644			0.224822	+	0.974400i	$0.427820\pi$
$110$		0			0
$111$	−5.13528	−	9.84099i	−0.0462638	−	0.0886575i
$112$	−28.1008	−	20.4164i	−0.250900	−	0.182289i
$113$	−49.6509	−	16.1325i	−0.439388	−	0.142766i	0.0809652	−	0.996717i	$-0.474200\pi$
$113$	−49.6509	−	16.1325i	−0.439388	−	0.142766i	−0.520353	+	0.853951i	$0.674200\pi$
$114$	−197.411	−	193.612i	−1.73168	−	1.69835i
$115$	−43.7270	+	31.7695i	−0.380235	+	0.276257i
$116$	146.607	+	201.788i	1.26386	+	1.73955i
$117$	−0.610823	−	0.185426i	−0.00522071	−	0.00158484i
$118$	86.3320	−	265.703i	0.731627	−	2.25172i
$119$	3.90409	−	5.37351i	0.0328074	−	0.0451556i
$120$	163.363	+	313.061i	1.36136	+	2.60884i
$121$		0			0
$122$		−	277.157i		−	2.27178i
$123$	−210.914	−	31.3079i	−1.71475	−	0.254536i
$124$	−107.764	+	331.665i	−0.869068	+	2.67471i
$125$	93.1432	−	30.2640i	0.745145	−	0.242112i
$126$	−57.1634	+	1.11098i	−0.453677	+	0.00881728i
$127$	47.3051	−	34.3692i	0.372481	−	0.270624i	−0.385758	−	0.922600i	$-0.626060\pi$
$127$	47.3051	−	34.3692i	0.372481	−	0.270624i	0.758239	+	0.651977i	$0.226060\pi$
$128$	196.754	−	63.9292i	1.53714	−	0.499447i
$129$	41.0033	−	6.90333i	0.317855	−	0.0535142i
$130$	−1.58686	−	1.15292i	−0.0122066	−	0.00886863i
$131$			147.683i			1.12735i	0.825997	+	0.563675i	$0.190613\pi$
$131$			147.683i			1.12735i	−0.825997	+	0.563675i	$0.809387\pi$
$132$		0			0
$133$	47.7730			0.359196
$134$	209.254	−	288.013i	1.56160	−	2.14935i
$135$	192.775	+	91.2474i	1.42796	+	0.675906i
$136$	−16.8548	−	51.8737i	−0.123932	−	0.381425i
$137$	−97.2514	−	133.855i	−0.709864	−	0.977044i	−0.999800	−	0.0199980i	$-0.993634\pi$
$137$	−97.2514	−	133.855i	−0.709864	−	0.977044i	0.289936	−	0.957046i	$-0.406366\pi$
$138$	−64.3447	−	32.0016i	−0.466266	−	0.231896i
$139$	−16.0986	−	49.5465i	−0.115818	−	0.356450i	0.876299	−	0.481767i	$-0.160005\pi$
$139$	−16.0986	−	49.5465i	−0.115818	−	0.356450i	−0.992117	+	0.125318i	$0.960005\pi$
$140$	−112.553	−	36.5707i	−0.803950	−	0.261219i
$141$	−81.1848	−	12.0510i	−0.575779	−	0.0854682i
$142$	162.474			1.14419
$143$		0			0
$144$	−98.5343	+	141.316i	−0.684266	+	0.981362i
$145$	193.060	+	140.267i	1.33145	+	0.967355i
$146$	−384.563	−	124.952i	−2.63399	−	0.855837i
$147$	−96.0131	+	97.8973i	−0.653151	+	0.665968i
$148$	24.7149	−	17.9564i	0.166992	−	0.121327i
$149$	−17.9536	−	24.7110i	−0.120494	−	0.165846i	0.744509	−	0.667612i	$-0.232684\pi$
$149$	−17.9536	−	24.7110i	−0.120494	−	0.165846i	−0.865003	+	0.501767i	$0.832684\pi$
$150$	280.425	+	275.028i	1.86950	+	1.83352i
$151$	−51.0733	+	157.187i	−0.338234	+	1.04098i	0.626873	+	0.779121i	$0.284334\pi$
$151$	−51.0733	+	157.187i	−0.338234	+	1.04098i	−0.965107	+	0.261855i	$0.915666\pi$
$152$	230.591	−	317.381i	1.51704	−	2.08803i
$153$	−27.0229	−	18.8420i	−0.176620	−	0.123150i
$154$		0			0
$155$			333.650i			2.15258i
$156$	0.257953	−	1.73777i	0.00165354	−	0.0111395i
$157$	−65.2412	+	200.792i	−0.415549	+	1.27893i	0.496210	+	0.868203i	$0.334725\pi$
$157$	−65.2412	+	200.792i	−0.415549	+	1.27893i	−0.911759	+	0.410726i	$0.865275\pi$
$158$	209.392	−	68.0355i	1.32526	−	0.430605i
$159$	29.0234	−	58.3565i	0.182537	−	0.367022i
$160$	−47.3519	+	34.4031i	−0.295949	+	0.215020i
$161$	11.8083	−	3.83676i	0.0733437	−	0.0238308i
$162$	11.0184	+	283.359i	0.0680149	+	1.74913i
$163$	70.7189	+	51.3803i	0.433858	+	0.315216i	0.783190	−	0.621783i	$-0.213591\pi$
$163$	70.7189	+	51.3803i	0.433858	+	0.315216i	−0.349332	+	0.936999i	$0.613591\pi$
$164$		−	586.820i		−	3.57817i
$165$		0			0
$166$	−295.827			−1.78209
$167$	24.3144	−	33.4659i	0.145595	−	0.200395i	−0.729991	−	0.683457i	$-0.760476\pi$
$167$	24.3144	−	33.4659i	0.145595	−	0.200395i	0.875586	+	0.483063i	$0.160476\pi$
$168$	−13.4674	−	79.9919i	−0.0801634	−	0.476142i
$169$	−52.2223	−	160.724i	−0.309008	−	0.951028i
$170$	−59.4989	−	81.8933i	−0.349994	−	0.481725i
$171$	−4.60420	−	236.901i	−0.0269251	−	1.38538i
$172$	35.3621	+	108.833i	0.205593	+	0.632751i
$173$	196.711	+	63.9152i	1.13706	+	0.369452i	0.816253	−	0.577694i	$-0.196047\pi$
$173$	196.711	+	63.9152i	1.13706	+	0.369452i	0.320803	+	0.947146i	$0.396047\pi$
$174$	−46.5873	+	313.847i	−0.267743	+	1.80372i
$175$	−67.8621			−0.387784
$176$		0			0
$177$	212.244	−	110.754i	1.19912	−	0.625730i
$178$	−128.451	−	93.3252i	−0.721635	−	0.524299i
$179$	131.523	+	42.7345i	0.734767	+	0.238740i	0.652414	−	0.757863i	$-0.273756\pi$
$179$	131.523	+	42.7345i	0.734767	+	0.238740i	0.0823532	+	0.996603i	$0.473756\pi$
$180$	−170.502	+	561.661i	−0.947234	+	3.12034i
$181$	50.1033	−	36.4022i	0.276814	−	0.201117i	−0.440713	−	0.897648i	$-0.645274\pi$
$181$	50.1033	−	36.4022i	0.276814	−	0.201117i	0.717526	+	0.696531i	$0.245274\pi$
$182$	0.264844	+	0.364527i	0.00145519	+	0.00200289i
$183$	166.299	−	169.563i	0.908740	−	0.926573i
$184$	31.5069	−	96.9682i	0.171233	−	0.527001i
$185$	17.1798	−	23.6459i	0.0928636	−	0.127816i
$186$	−393.289	+	205.228i	−2.11446	+	1.10338i
$187$		0			0
$188$		−	225.878i		−	1.20148i
$189$	−35.6388	−	33.6194i	−0.188565	−	0.177880i
$190$	224.986	−	692.435i	1.18413	−	3.64439i
$191$	23.1013	−	7.50608i	0.120949	−	0.0392988i	−0.247917	−	0.968781i	$-0.579746\pi$
$191$	23.1013	−	7.50608i	0.120949	−	0.0392988i	0.368866	+	0.929482i	$0.379746\pi$
$192$	135.991	+	67.6347i	0.708287	+	0.352264i
$193$	−163.270	+	118.623i	−0.845958	+	0.614625i	−0.924029	−	0.382323i	$-0.875124\pi$
$193$	−163.270	+	118.623i	−0.845958	+	0.614625i	0.0780703	+	0.996948i	$0.475124\pi$
$194$	−320.526	+	104.145i	−1.65220	+	0.536831i
$195$	−0.279056	−	1.65750i	−0.00143106	−	0.00849998i
$196$	−305.303	−	221.816i	−1.55767	−	1.13171i
$197$			64.9088i			0.329486i	0.986337	+	0.164743i	$0.0526795\pi$
$197$			64.9088i			0.329486i	−0.986337	+	0.164743i	$0.947320\pi$
$198$		0			0
$199$	136.263			0.684741			0.342370	−	0.939565i	$-0.388770\pi$
$199$	136.263			0.684741			0.342370	+	0.939565i	$0.388770\pi$
$200$	−327.557	+	450.843i	−1.63778	+	2.25422i
$201$	300.834	−	50.6484i	1.49668	−	0.251982i
$202$	−60.2537	−	185.442i	−0.298286	−	0.918029i
$203$	−32.2214	−	44.3490i	−0.158726	−	0.218468i
$204$	40.3736	−	81.1780i	0.197910	−	0.397931i
$205$	−173.494	−	533.961i	−0.846314	−	2.60469i
$206$	−434.435	−	141.157i	−2.10891	−	0.685226i
$207$	−20.1641	−	58.1864i	−0.0974111	−	0.281094i
$208$	1.35768			0.00652733
$209$		0			0
$210$	−69.6458	−	133.466i	−0.331647	−	0.635550i
$211$	1.00476	+	0.729998i	0.00476188	+	0.00345971i	0.590164	−	0.807284i	$-0.299063\pi$
$211$	1.00476	+	0.729998i	0.00476188	+	0.00345971i	−0.585402	+	0.810743i	$0.699063\pi$
$212$	170.591	+	55.4285i	0.804677	+	0.261455i
$213$	99.4007	+	97.4876i	0.466670	+	0.457688i
$214$	164.668	−	119.639i	0.769478	−	0.559059i
$215$	64.3535	+	88.5750i	0.299318	+	0.411977i
$216$	−395.372	+	74.4928i	−1.83043	+	0.344874i
$217$	23.6845	−	72.8934i	0.109145	−	0.335914i
$218$	−100.854	+	138.814i	−0.462634	+	0.636761i
$219$	−160.300	−	307.190i	−0.731962	−	1.40269i
$220$		0			0
$221$			0.259620i			0.00117475i
$222$	38.4398	+	5.70598i	0.173152	+	0.0257026i
$223$	38.3982	−	118.178i	0.172189	−	0.529944i	−0.827305	−	0.561754i	$-0.810127\pi$
$223$	38.3982	−	118.178i	0.172189	−	0.529944i	0.999494	+	0.0318093i	$0.0101269\pi$
$224$	12.7872	−	4.15482i	0.0570859	−	0.0185483i
$225$	6.54032	+	336.520i	0.0290681	+	1.49565i
$226$	147.863	−	107.429i	0.654260	−	0.475347i
$227$	−45.3725	+	14.7424i	−0.199879	+	0.0649446i	−0.407246	−	0.913319i	$-0.633511\pi$
$227$	−45.3725	+	14.7424i	−0.199879	+	0.0649446i	0.207367	+	0.978263i	$0.433511\pi$
$228$	643.051	−	108.264i	2.82040	−	0.474843i
$229$	59.2260	+	43.0302i	0.258629	+	0.187905i	0.709542	−	0.704663i	$-0.248902\pi$
$229$	59.2260	+	43.0302i	0.258629	+	0.187905i	−0.450913	+	0.892568i	$0.648902\pi$
$230$		−	189.222i		−	0.822706i
$231$		0			0
$232$	−450.160			−1.94034
$233$	−108.973	+	149.988i	−0.467694	+	0.643726i	−0.976082	−	0.217402i	$-0.930242\pi$
$233$	−108.973	+	149.988i	−0.467694	+	0.643726i	0.508388	+	0.861128i	$0.330242\pi$
$234$	1.78212	−	1.34846i	0.00761590	−	0.00576266i
$235$	−66.7813	−	205.532i	−0.284176	−	0.874603i
$236$	387.271	+	533.033i	1.64098	+	2.25862i
$237$	168.927	+	84.0153i	0.712773	+	0.354495i
$238$	7.18561	+	22.1150i	0.0301916	+	0.0929203i
$239$	−333.790	−	108.455i	−1.39661	−	0.453787i	−0.488518	−	0.872554i	$-0.662462\pi$
$239$	−333.790	−	108.455i	−1.39661	−	0.453787i	−0.908094	+	0.418767i	$0.862462\pi$
$240$	−448.703	−	66.6051i	−1.86959	−	0.277521i
$241$	−175.508			−0.728248			−0.364124	−	0.931351i	$-0.618631\pi$
$241$	−175.508			−0.728248			−0.364124	+	0.931351i	$0.618631\pi$
$242$		0			0
$243$	−163.280	+	179.969i	−0.671934	+	0.740611i
$244$	528.799	+	384.195i	2.16721	+	1.57457i
$245$	−343.382	−	111.572i	−1.40156	−	0.455395i
$246$	522.688	−	532.945i	2.12475	−	2.16644i
$247$	−1.51070	+	1.09759i	−0.00611619	+	0.00444368i
$248$	−369.948	−	509.190i	−1.49173	−	2.05319i
$249$	−180.985	−	177.502i	−0.726847	−	0.712858i
$250$	−105.952	+	326.086i	−0.423806	+	1.30434i
$251$	−81.7075	+	112.461i	−0.325528	+	0.448051i	−0.940145	−	0.340775i	$-0.889311\pi$
$251$	−81.7075	+	112.461i	−0.325528	+	0.448051i	0.614617	+	0.788826i	$0.289311\pi$
$252$	77.1202	−	110.604i	0.306032	−	0.438906i
$253$		0			0
$254$			204.706i			0.805930i
$255$	12.7364	−	85.8022i	0.0499468	−	0.336479i
$256$	−161.232	+	496.220i	−0.629811	+	1.93836i
$257$	406.456	−	132.065i	1.58154	−	0.513873i	0.619087	−	0.785323i	$-0.287503\pi$
$257$	406.456	−	132.065i	1.58154	−	0.513873i	0.962453	+	0.271449i	$0.0875029\pi$
$258$	−64.8236	+	130.339i	−0.251254	+	0.505190i
$259$	−5.43184	+	3.94646i	−0.0209724	+	0.0152373i
$260$	4.39941	−	1.42946i	0.0169208	−	0.00549791i
$261$	−216.816	+	164.056i	−0.830712	+	0.628569i
$262$	−418.281	−	303.899i	−1.59649	−	1.15992i
$263$			201.638i			0.766686i	0.923606	+	0.383343i	$0.125227\pi$
$263$			201.638i			0.766686i	−0.923606	+	0.383343i	$0.874773\pi$
$264$		0			0
$265$	171.613			0.647595
$266$	−98.3064	+	135.307i	−0.369573	+	0.508673i
$267$	−22.5887	−	134.169i	−0.0846018	−	0.502505i
$268$	259.445	+	798.488i	0.968077	+	2.97943i
$269$	−201.640	−	277.534i	−0.749591	−	1.03172i	−0.998009	−	0.0630705i	$-0.979911\pi$
$269$	−201.640	−	277.534i	−0.749591	−	1.03172i	0.248418	−	0.968653i	$-0.420089\pi$
$270$	−655.128	+	358.228i	−2.42640	+	1.32677i
$271$	125.951	+	387.638i	0.464765	+	1.43040i	0.859278	+	0.511509i	$0.170913\pi$
$271$	125.951	+	387.638i	0.464765	+	1.43040i	−0.394513	+	0.918890i	$0.629087\pi$
$272$	66.6368	+	21.6516i	0.244988	+	0.0796015i
$273$	−0.0566929	+	0.381927i	−0.000207666	+	0.00139900i
$274$	579.239			2.11401
$275$		0			0
$276$	150.252	−	78.4053i	0.544391	−	0.284077i
$277$	−402.078	−	292.127i	−1.45154	−	1.05461i	−0.985467	−	0.169865i	$-0.945667\pi$
$277$	−402.078	−	292.127i	−1.45154	−	1.05461i	−0.466078	−	0.884744i	$-0.654333\pi$
$278$	173.458	+	56.3598i	0.623949	+	0.202733i
$279$	−363.752	−	110.423i	−1.30377	−	0.395783i
$280$	172.798	−	125.545i	0.617134	−	0.448374i
$281$	227.477	+	313.095i	0.809525	+	1.11422i	0.991396	+	0.130893i	$0.0417845\pi$
$281$	227.477	+	313.095i	0.809525	+	1.11422i	−0.181871	+	0.983322i	$0.558215\pi$
$282$	201.193	−	205.141i	0.713449	−	0.727450i
$283$	68.5261	−	210.902i	0.242142	−	0.745235i	−0.753952	−	0.656930i	$-0.771855\pi$
$283$	68.5261	−	210.902i	0.242142	−	0.745235i	0.996093	−	0.0883055i	$-0.0281452\pi$
$284$	−225.222	+	309.991i	−0.793035	+	1.09152i
$285$	553.118	−	288.631i	1.94077	−	1.01274i
$286$		0			0
$287$			128.971i			0.449378i
$288$	−21.8357	−	63.0099i	−0.0758183	−	0.218785i
$289$	85.1656	−	262.113i	0.294691	−	0.906965i
$290$	−794.552	+	258.165i	−2.73983	+	0.890226i
$291$	−258.585	−	128.606i	−0.888607	−	0.441946i
$292$	771.483	−	560.515i	2.64207	−	1.91957i
$293$	421.089	−	136.820i	1.43716	−	0.466963i	0.516151	−	0.856497i	$-0.327364\pi$
$293$	421.089	−	136.820i	1.43716	−	0.466963i	0.921012	+	0.389535i	$0.127364\pi$
$294$	−79.6998	−	473.389i	−0.271088	−	1.61017i
$295$	509.979	+	370.522i	1.72874	+	1.25601i
$296$			55.1353i			0.186268i
$297$		0			0
$298$	106.933			0.358837
$299$	−0.285259	+	0.392625i	−0.000954043	+	0.00131313i
$300$	−913.462	+	153.791i	−3.04487	+	0.512635i
$301$	−7.77188	−	23.9194i	−0.0258202	−	0.0794664i
$302$	−340.103	−	468.112i	−1.12617	−	1.55004i
$303$	74.4057	−	149.605i	0.245563	−	0.493747i
$304$	155.730	+	479.288i	0.512270	+	1.57660i
$305$	594.755	+	193.247i	1.95002	+	0.633598i
$306$	108.973	−	37.7640i	0.356122	−	0.123412i
$307$	−324.906			−1.05832			−0.529162	−	0.848521i	$-0.677494\pi$
$307$	−324.906			−1.05832			−0.529162	+	0.848521i	$0.677494\pi$
$308$		0			0
$309$	−181.088	−	347.028i	−0.586046	−	1.12307i
$310$	−944.994	−	686.579i	−3.04837	−	2.21477i
$311$	−111.277	−	36.1562i	−0.357805	−	0.116258i	0.124598	−	0.992207i	$-0.460236\pi$
$311$	−111.277	−	36.1562i	−0.357805	−	0.116258i	−0.482403	+	0.875949i	$0.660236\pi$
$312$	2.26369	+	2.22012i	0.00725542	+	0.00711578i
$313$	118.178	−	85.8611i	0.377564	−	0.274317i	−0.382776	−	0.923841i	$-0.625032\pi$
$313$	118.178	−	85.8611i	0.377564	−	0.274317i	0.760341	+	0.649524i	$0.225032\pi$
$314$	−434.449	−	597.968i	−1.38360	−	1.90436i
$315$	37.4730	−	123.442i	0.118962	−	0.391880i
$316$	−160.451	+	493.818i	−0.507757	+	1.56272i
$317$	−39.7124	+	54.6595i	−0.125276	+	0.172427i	−0.867048	−	0.498225i	$-0.833986\pi$
$317$	−39.7124	+	54.6595i	−0.125276	+	0.172427i	0.741772	+	0.670652i	$0.233986\pi$
$318$	105.559	+	202.288i	0.331946	+	0.636125i
$319$		0			0
$320$			399.917i			1.24974i
$321$	172.528	+	25.6100i	0.537472	+	0.0797819i
$322$	−13.4321	+	41.3399i	−0.0417147	+	0.128385i
$323$	−91.6508	+	29.7791i	−0.283749	+	0.0921955i
$324$	−555.907	−	371.770i	−1.71576	−	1.14744i
$325$	2.14597	−	1.55914i	0.00660298	−	0.00479734i
$326$	−291.048	+	94.5672i	−0.892785	+	0.290083i
$327$	−144.993	+	24.4110i	−0.443403	+	0.0746515i
$328$	856.825	+	622.520i	2.61227	+	1.89793i
$329$			49.6436i			0.150892i
$330$		0			0
$331$	303.465			0.916814			0.458407	−	0.888742i	$-0.348420\pi$
$331$	303.465			0.916814			0.458407	+	0.888742i	$0.348420\pi$
$332$	410.076	−	564.421i	1.23517	−	1.70006i
$333$	20.0935	+	26.5555i	0.0603410	+	0.0797463i
$334$	44.7515	+	137.731i	0.133987	+	0.412368i
$335$	472.149	+	649.857i	1.40940	+	1.93987i
$336$	93.3012	+	46.4030i	0.277682	+	0.138104i
$337$	171.640	+	528.253i	0.509317	+	1.56752i	0.793390	+	0.608714i	$0.208314\pi$
$337$	171.640	+	528.253i	0.509317	+	1.56752i	−0.284072	+	0.958803i	$0.591686\pi$
$338$	562.679	+	182.825i	1.66473	+	0.540904i
$339$	154.921	+	22.9963i	0.456993	+	0.0678357i
$340$	238.725			0.702132
$341$		0			0
$342$	680.447	+	474.449i	1.98961	+	1.38728i
$343$	139.033	+	101.013i	0.405344	+	0.294500i
$344$	−196.422	−	63.8215i	−0.570995	−	0.185528i
$345$	113.537	−	115.765i	0.329092	−	0.335551i
$346$	−585.814	+	425.619i	−1.69310	+	1.23011i
$347$	−228.043	−	313.874i	−0.657184	−	0.904537i	0.342200	−	0.939627i	$-0.388828\pi$
$347$	−228.043	−	313.874i	−0.657184	−	0.904537i	−0.999384	+	0.0350905i	$0.988828\pi$
$348$	−534.223	−	523.941i	−1.53512	−	1.50558i
$349$	−139.687	+	429.911i	−0.400248	+	1.23184i	0.524551	+	0.851379i	$0.324233\pi$
$349$	−139.687	+	429.911i	−0.400248	+	1.23184i	−0.924799	+	0.380457i	$0.875767\pi$
$350$	139.645	−	192.205i	0.398987	−	0.549158i
$351$	1.89939	+	0.244325i	0.00541138	+	0.000696082i
$352$		0			0
$353$		−	304.454i		−	0.862476i	−0.902238	−	0.431238i	$-0.858077\pi$
$353$		−	304.454i		−	0.862476i	0.902238	−	0.431238i	$-0.141923\pi$
$354$	−123.063	+	829.045i	−0.347635	+	2.34193i
$355$	−113.285	+	348.656i	−0.319113	+	0.982128i
$356$	356.118	−	115.710i	1.00033	−	0.325027i
$357$	−8.87332	+	17.8413i	−0.0248552	+	0.0499757i
$358$	−391.683	+	284.574i	−1.09409	+	0.794900i
$359$	−288.279	+	93.6674i	−0.803004	+	0.260912i	−0.681632	−	0.731695i	$-0.738730\pi$
$359$	−288.279	+	93.6674i	−0.803004	+	0.260912i	−0.121372	+	0.992607i	$0.538730\pi$
$360$	−639.216	−	844.783i	−1.77560	−	2.34662i
$361$	−268.695	−	195.218i	−0.744307	−	0.540771i
$362$			216.815i			0.598936i
$363$		0			0
$364$	−1.06262			−0.00291929
$365$	536.273	−	738.116i	1.46924	−	2.02224i
$366$	138.044	+	819.932i	0.377169	+	2.24025i
$367$	−129.776	−	399.409i	−0.353612	−	1.08831i	−0.956810	−	0.290715i	$-0.906107\pi$
$367$	−129.776	−	399.409i	−0.353612	−	1.08831i	0.603197	−	0.797592i	$-0.293893\pi$
$368$	76.9854	+	105.961i	0.209200	+	0.287938i
$369$	639.554	−	12.4298i	1.73321	−	0.0336852i
$370$	31.6200	+	97.3163i	0.0854594	+	0.263017i
$371$	−37.4926	−	12.1821i	−0.101058	−	0.0328359i
$372$	153.614	−	1034.86i	0.412941	−	2.78188i
$373$	198.795			0.532963			0.266482	−	0.963840i	$-0.414139\pi$
$373$	198.795			0.532963			0.266482	+	0.963840i	$0.414139\pi$
$374$		0			0
$375$	−260.478	+	135.924i	−0.694608	+	0.362464i
$376$	329.808	+	239.620i	0.877149	+	0.637286i
$377$	2.03784	+	0.662135i	0.00540541	+	0.00175633i
$378$	168.557	−	31.7581i	0.445917	−	0.0840161i
$379$	−58.5806	+	42.5613i	−0.154566	+	0.112299i	−0.662380	−	0.749168i	$-0.730454\pi$
$379$	−58.5806	+	42.5613i	−0.154566	+	0.112299i	0.507814	+	0.861467i	$0.330454\pi$
$380$	1009.25	+	1389.11i	2.65592	+	3.65556i
$381$	−122.828	+	125.238i	−0.322382	+	0.328708i
$382$	−26.2781	+	80.8756i	−0.0687908	+	0.211716i
$383$	−308.532	+	424.658i	−0.805566	+	1.10877i	0.186426	+	0.982469i	$0.440309\pi$
$383$	−308.532	+	424.658i	−0.805566	+	1.10877i	−0.991992	+	0.126298i	$0.959691\pi$
$384$	−550.229	+	287.123i	−1.43289	+	0.747717i
$385$		0			0
$386$		−	706.528i		−	1.83038i
$387$	−117.864	+	40.8451i	−0.304559	+	0.105543i
$388$	245.610	−	755.911i	0.633016	−	1.94822i
$389$	−354.669	+	115.239i	−0.911745	+	0.296244i	−0.727076	−	0.686557i	$-0.759121\pi$
$389$	−354.669	+	115.239i	−0.911745	+	0.296244i	−0.184669	+	0.982801i	$0.559121\pi$
$390$	5.26875	+	2.62040i	0.0135096	+	0.00671896i
$391$	−20.2622	+	14.7214i	−0.0518216	+	0.0376506i
$392$	647.753	−	210.468i	1.65243	−	0.536907i
$393$	−73.5565	−	436.900i	−0.187167	−	1.11170i
$394$	−183.841	−	133.568i	−0.466601	−	0.339005i
$395$			496.774i			1.25766i
$396$		0			0
$397$	−184.584			−0.464947			−0.232474	−	0.972603i	$-0.574682\pi$
$397$	−184.584			−0.464947			−0.232474	+	0.972603i	$0.574682\pi$
$398$	−280.400	+	385.938i	−0.704523	+	0.969693i
$399$	−141.330	+	23.7943i	−0.354211	+	0.0596350i
$400$	−221.216	−	680.834i	−0.553041	−	1.70208i
$401$	−53.3656	−	73.4514i	−0.133081	−	0.183171i	0.737276	−	0.675592i	$-0.236112\pi$
$401$	−53.3656	−	73.4514i	−0.133081	−	0.183171i	−0.870357	+	0.492421i	$0.836112\pi$
$402$	−475.598	+	956.272i	−1.18308	+	2.37879i
$403$	0.925768	+	2.84922i	0.00229719	+	0.00707003i
$404$	437.336	+	142.099i	1.08251	+	0.351730i
$405$	−615.747	−	173.927i	−1.52036	−	0.429450i
$406$	191.914			0.472694
$407$		0			0
$408$	75.6995	+	145.067i	0.185538	+	0.355555i
$409$	444.897	+	323.237i	1.08777	+	0.790310i	0.979021	−	0.203760i	$-0.0653161\pi$
$409$	444.897	+	323.237i	1.08777	+	0.790310i	0.108747	+	0.994069i	$0.465316\pi$
$410$	1869.35	+	607.388i	4.55938	+	1.48143i
$411$	354.374	+	347.554i	0.862225	+	0.845630i
$412$	871.533	−	633.206i	2.11537	−	1.53691i
$413$	−85.1147	−	117.150i	−0.206089	−	0.283657i
$414$	206.294	+	62.6242i	0.498295	+	0.151266i
$415$	206.265	−	634.819i	0.497024	−	1.52968i
$416$	−0.308906	+	0.425173i	−0.000742563	+	0.00102205i
$417$	72.3034	+	138.558i	0.173389	+	0.332275i
$418$		0			0
$419$		−	298.402i		−	0.712176i	−0.934452	−	0.356088i	$-0.884110\pi$
$419$		−	298.402i		−	0.712176i	0.934452	−	0.356088i	$-0.115890\pi$
$420$	351.188	+	52.1300i	0.836161	+	0.124119i
$421$	−37.8855	+	116.600i	−0.0899894	+	0.276959i	−0.985915	−	0.167244i	$-0.946513\pi$
$421$	−37.8855	+	116.600i	−0.0899894	+	0.276959i	0.895926	+	0.444203i	$0.146513\pi$
$422$	−4.13514	+	1.34359i	−0.00979891	+	0.00318386i
$423$	246.177	−	4.78448i	0.581978	−	0.0113108i
$424$	−261.902	+	190.283i	−0.617692	+	0.448780i
$425$	130.191	−	42.3016i	0.306332	−	0.0995332i
$426$	−480.658	+	80.9238i	−1.12831	+	0.189962i
$427$	−116.220	−	84.4386i	−0.272177	−	0.197748i
$428$			480.021i			1.12154i
$429$		0			0
$430$	−383.296			−0.891385
$431$	−347.398	+	478.153i	−0.806028	+	1.10940i	0.185896	+	0.982569i	$0.440481\pi$
$431$	−347.398	+	478.153i	−0.806028	+	1.10940i	−0.991924	+	0.126833i	$0.959519\pi$
$432$	221.115	−	467.142i	0.511840	−	1.08135i
$433$	198.492	+	610.896i	0.458411	+	1.41084i	0.867083	+	0.498163i	$0.165992\pi$
$433$	198.492	+	610.896i	0.458411	+	1.41084i	−0.408672	+	0.912681i	$0.634008\pi$
$434$	157.718	+	217.080i	0.363405	+	0.500184i
$435$	−641.005	−	318.802i	−1.47358	−	0.732878i
$436$	−125.045	−	384.848i	−0.286800	−	0.882679i
$437$	−171.324	−	55.6665i	−0.392046	−	0.127383i
$438$	1199.91	+	178.114i	2.73953	+	0.406654i
$439$	−476.217			−1.08478			−0.542388	−	0.840128i	$-0.682480\pi$
$439$	−476.217			−1.08478			−0.542388	+	0.840128i	$0.682480\pi$
$440$		0			0
$441$	235.282	−	337.437i	0.533520	−	0.765164i
$442$	−0.735321	−	0.534242i	−0.00166362	−	0.00120869i
$443$	−102.449	−	33.2878i	−0.231262	−	0.0751417i	0.191093	−	0.981572i	$-0.438797\pi$
$443$	−102.449	−	33.2878i	−0.231262	−	0.0751417i	−0.422356	+	0.906430i	$0.638797\pi$
$444$	−64.1720	+	65.4313i	−0.144532	+	0.147368i
$445$	289.830	−	210.574i	0.651303	−	0.473200i
$446$	255.698	+	351.939i	0.573315	+	0.789100i
$447$	65.4211	+	64.1620i	0.146356	+	0.143539i
$448$	28.3885	−	87.3709i	0.0633672	−	0.195024i
$449$	131.943	−	181.604i	0.293860	−	0.404464i	−0.636403	−	0.771357i	$-0.719578\pi$
$449$	131.943	−	181.604i	0.293860	−	0.404464i	0.930263	+	0.366893i	$0.119578\pi$
$450$	−966.582	−	673.961i	−2.14796	−	1.49769i
$451$		0			0
$452$			431.031i			0.953608i
$453$	72.8030	−	490.456i	0.160713	−	1.08268i
$454$	51.6118	−	158.845i	0.113682	−	0.349879i
$455$	−0.966905	+	0.314166i	−0.00212507	+	0.000690476i
$456$	−524.093	+	1053.78i	−1.14933	+	2.31092i
$457$	57.6734	−	41.9021i	0.126200	−	0.0916896i	−0.522895	−	0.852397i	$-0.675148\pi$
$457$	57.6734	−	41.9021i	0.126200	−	0.0916896i	0.649095	+	0.760708i	$0.275148\pi$
$458$	−243.748	+	79.1986i	−0.532202	+	0.172923i
$459$	89.3282	+	42.2823i	0.194615	+	0.0921182i
$460$	361.025	+	262.300i	0.784837	+	0.570217i
$461$		−	876.537i		−	1.90138i	−0.310141	−	0.950691i	$-0.600376\pi$
$461$		−	876.537i		−	1.90138i	0.310141	−	0.950691i	$-0.399624\pi$
$462$		0			0
$463$	−824.691			−1.78119			−0.890595	−	0.454797i	$-0.849712\pi$
$463$	−824.691			−1.78119			−0.890595	+	0.454797i	$0.849712\pi$
$464$	339.901	−	467.833i	0.732544	−	1.00826i
$465$	−166.181	−	987.058i	−0.357379	−	2.12271i
$466$	−200.568	−	617.285i	−0.430404	−	1.32465i
$467$	−188.715	−	259.743i	−0.404100	−	0.556196i	0.557667	−	0.830065i	$-0.311697\pi$
$467$	−188.715	−	259.743i	−0.404100	−	0.556196i	−0.961767	+	0.273869i	$0.911697\pi$
$468$	0.102412	+	5.26942i	0.000218829	+	0.0112595i
$469$	−57.0208	−	175.492i	−0.121580	−	0.374183i
$470$	719.547	+	233.795i	1.53095	+	0.497436i
$471$	92.9987	−	626.510i	0.197450	−	1.33017i
$472$	−1189.12			−2.51933
$473$		0			0
$474$	−585.571	+	305.566i	−1.23538	+	0.644654i
$475$	796.552	+	578.729i	1.67695	+	1.21838i
$476$	−52.1549	−	16.9461i	−0.109569	−	0.0356011i
$477$	−56.7962	+	187.096i	−0.119070	+	0.392234i
$478$	994.044	−	722.215i	2.07959	−	1.51091i
$479$	−254.639	−	350.481i	−0.531606	−	0.731693i	0.455768	−	0.890099i	$-0.349365\pi$
$479$	−254.639	−	350.481i	−0.531606	−	0.731693i	−0.987374	+	0.158406i	$0.949365\pi$
$480$	122.949	−	125.362i	0.256144	−	0.261170i
$481$	0.0810979	−	0.249594i	0.000168603	−	0.000518906i
$482$	361.156	−	497.089i	0.749287	−	1.03131i
$483$	−33.0224	+	17.2319i	−0.0683694	+	0.0356769i
$484$		0			0
$485$		−	760.436i		−	1.56791i
$486$	−173.730	−	832.792i	−0.357468	−	1.71356i
$487$	−108.946	+	335.301i	−0.223708	+	0.688504i	0.774712	+	0.632315i	$0.217895\pi$
$487$	−108.946	+	335.301i	−0.223708	+	0.688504i	−0.998420	+	0.0561891i	$0.982105\pi$
$488$	−1121.94	+	364.540i	−2.29905	+	0.747008i
$489$	−234.803	−	116.779i	−0.480170	−	0.238811i
$490$	1022.61	−	742.969i	2.08696	−	1.51626i
$491$	424.537	−	137.940i	0.864637	−	0.280938i	0.157073	−	0.987587i	$-0.449794\pi$
$491$	424.537	−	137.940i	0.864637	−	0.280938i	0.707564	+	0.706649i	$0.249794\pi$
$492$	292.278	+	1736.03i	0.594061	+	3.52851i
$493$	89.4604	+	64.9968i	0.181461	+	0.131839i
$494$		−	6.53734i		−	0.0132335i
$495$		0			0
$496$	808.517			1.63007
$497$	49.4994	−	68.1300i	0.0995963	−	0.137083i
$498$	875.164	−	147.343i	1.75736	−	0.295869i
$499$	27.7403	+	85.3758i	0.0555917	+	0.171094i	0.974997	−	0.222217i	$-0.0713295\pi$
$499$	27.7403	+	85.3758i	0.0555917	+	0.171094i	−0.919405	+	0.393311i	$0.871329\pi$
$500$	−475.282	−	654.169i	−0.950564	−	1.30834i
$501$	−55.2625	+	111.115i	−0.110304	+	0.221786i
$502$	−150.386	−	462.839i	−0.299573	−	0.921990i
$503$	−928.252	−	301.607i	−1.84543	−	0.599617i	−0.997591	−	0.0693646i	$-0.977903\pi$
$503$	−928.252	−	301.607i	−1.84543	−	0.599617i	−0.847840	−	0.530252i	$-0.822097\pi$
$504$	79.6832	+	229.937i	0.158102	+	0.456225i
$505$	439.954			0.871195
$506$		0			0
$507$	234.545	+	449.469i	0.462612	+	0.886527i
$508$	−390.567	−	283.764i	−0.768834	−	0.558590i
$509$	−305.922	−	99.3999i	−0.601025	−	0.195285i	−0.00732728	−	0.999973i	$-0.502332\pi$
$509$	−305.922	−	99.3999i	−0.601025	−	0.195285i	−0.593697	+	0.804688i	$0.702332\pi$
$510$	216.808	+	212.635i	0.425114	+	0.416932i
$511$	−169.557	+	123.190i	−0.331814	+	0.241077i
$512$	−587.258	−	808.291i	−1.14699	−	1.57869i
$513$	131.614	+	698.546i	0.256558	+	1.36169i
$514$	−462.349	+	1422.96i	−0.899511	+	2.76841i
$515$	605.819	−	833.839i	1.17635	−	1.61910i
$516$	−158.821	−	304.356i	−0.307792	−	0.589836i
$517$		0			0
$518$		−	23.5055i		−	0.0453774i
$519$	−613.777	−	91.1086i	−1.18261	−	0.175546i
$520$	−2.57989	+	7.94007i	−0.00496132	+	0.0152694i
$521$	−291.387	+	94.6773i	−0.559284	+	0.181722i	−0.574999	−	0.818154i	$-0.694998\pi$
$521$	−291.387	+	94.6773i	−0.559284	+	0.181722i	0.0157151	+	0.999877i	$0.494998\pi$
$522$	−18.4960	−	951.678i	−0.0354330	−	1.82314i
$523$	−543.341	+	394.761i	−1.03889	+	0.754800i	−0.970069	−	0.242828i	$-0.921925\pi$
$523$	−543.341	+	394.761i	−1.03889	+	0.754800i	−0.0688243	+	0.997629i	$0.521925\pi$
$524$	1159.64	−	376.791i	2.21306	−	0.719066i
$525$	200.761	−	33.8001i	0.382402	−	0.0643812i
$526$	−571.099	−	414.928i	−1.08574	−	0.788836i
$527$			154.607i			0.293372i
$528$		0			0
$529$	482.182			0.911497
$530$	−353.141	+	486.057i	−0.666304	+	0.917089i
$531$	−572.731	+	433.364i	−1.07859	+	0.816128i
$532$	−121.886	−	375.126i	−0.229108	−	0.705123i
$533$	−2.96313	−	4.07840i	−0.00555934	−	0.00765177i
$534$	426.488	+	212.112i	0.798666	+	0.397214i
$535$	141.919	+	436.782i	0.265269	+	0.816414i
$536$	−1441.11	−	468.246i	−2.68864	−	0.873593i
$537$	−410.379	−	60.9164i	−0.764206	−	0.113438i
$538$	1200.99			2.23232
$539$		0			0
$540$	224.661	−	1746.52i	0.416038	−	3.23430i
$541$	148.941	+	108.212i	0.275307	+	0.200022i	0.716868	−	0.697209i	$-0.245575\pi$
$541$	148.941	+	108.212i	0.275307	+	0.200022i	−0.441561	+	0.897231i	$0.645575\pi$
$542$	−1357.08	−	440.944i	−2.50385	−	0.813549i
$543$	−130.093	+	132.646i	−0.239582	+	0.244283i
$544$	−21.9419	+	15.9418i	−0.0403345	+	0.0293047i
$545$	−227.562	−	313.212i	−0.417545	−	0.574701i
$546$	−0.965066	−	0.946492i	−0.00176752	−	0.00173350i
$547$	187.610	−	577.405i	0.342980	−	1.05558i	−0.619676	−	0.784858i	$-0.712736\pi$
$547$	187.610	−	577.405i	0.342980	−	1.05558i	0.962656	−	0.270727i	$-0.0872640\pi$
$548$	−802.941	+	1105.15i	−1.46522	+	2.01670i
$549$	−407.520	+	584.458i	−0.742295	+	1.06459i
$550$		0			0
$551$			795.344i			1.44346i
$552$	−44.9118	+	302.560i	−0.0813620	+	0.548116i
$553$	35.2640	−	108.532i	0.0637686	−	0.196260i
$554$	1654.78	−	537.670i	2.98696	−	0.970523i
$555$	−39.0467	+	78.5100i	−0.0703544	+	0.141459i
$556$	−347.979	+	252.821i	−0.625861	+	0.454714i
$557$	−386.247	+	125.499i	−0.693441	+	0.225313i	−0.634471	−	0.772947i	$-0.718782\pi$
$557$	−386.247	+	125.499i	−0.693441	+	0.225313i	−0.0589706	+	0.998260i	$0.518782\pi$
$558$	1061.27	−	803.026i	1.90192	−	1.43911i
$559$	0.795316	+	0.577831i	0.00142275	+	0.00103369i
$560$			274.376i			0.489958i
$561$		0			0
$562$	−1354.87			−2.41081
$563$	189.430	−	260.728i	0.336465	−	0.463104i	−0.606940	−	0.794748i	$-0.707603\pi$
$563$	189.430	−	260.728i	0.336465	−	0.463104i	0.943405	+	0.331643i	$0.107603\pi$
$564$	112.503	+	668.230i	0.199474	+	1.18480i
$565$	127.435	+	392.205i	0.225549	+	0.694168i
$566$	456.323	+	628.075i	0.806225	+	1.10967i
$567$	122.177	+	81.7078i	0.215480	+	0.144105i
$568$	−213.700	−	657.700i	−0.376232	−	1.15792i
$569$	414.675	+	134.736i	0.728779	+	0.236795i	0.649825	−	0.760084i	$-0.274842\pi$
$569$	414.675	+	134.736i	0.728779	+	0.236795i	0.0789537	+	0.996878i	$0.474842\pi$
$570$	−320.708	+	2160.53i	−0.562646	+	3.79041i
$571$	155.637			0.272569			0.136284	−	0.990670i	$-0.456484\pi$
$571$	155.637			0.272569			0.136284	+	0.990670i	$0.456484\pi$
$572$		0			0
$573$	−64.6036	+	33.7118i	−0.112746	+	0.0588339i
$574$	−365.285	−	265.395i	−0.636385	−	0.462361i
$575$	243.368	+	79.0749i	0.423248	+	0.137522i
$576$	−435.998	−	132.355i	−0.756941	−	0.229783i
$577$	−678.174	+	492.722i	−1.17534	+	0.853938i	−0.991639	−	0.129043i	$-0.958809\pi$
$577$	−678.174	+	492.722i	−1.17534	+	0.853938i	−0.183706	+	0.982981i	$0.558809\pi$
$578$	567.128	+	780.585i	0.981190	+	1.35049i
$579$	423.930	−	432.249i	0.732176	−	0.746544i
$580$	608.843	−	1873.83i	1.04973	−	3.23074i
$581$	−90.1265	+	124.049i	−0.155123	+	0.213509i
$582$	896.361	−	467.744i	1.54014	−	0.803684i
$583$		0			0
$584$			1721.07i			2.94704i
$585$	1.65110	+	4.76449i	0.00282240	+	0.00814443i
$586$	−478.994	+	1474.19i	−0.817396	+	2.51569i
$587$	−580.367	+	188.573i	−0.988699	+	0.321248i	−0.758341	−	0.651858i	$-0.773990\pi$
$587$	−580.367	+	188.573i	−0.988699	+	0.321248i	−0.230358	+	0.973106i	$0.573990\pi$
$588$	1013.68	+	504.149i	1.72394	+	0.857396i
$589$	−899.640	+	653.626i	−1.52740	+	1.10972i
$590$	−2098.85	+	681.958i	−3.55738	+	1.15586i
$591$	−32.3292	−	192.024i	−0.0547025	−	0.324913i
$592$	−57.2999	−	41.6308i	−0.0967904	−	0.0703224i
$593$		−	626.517i		−	1.05652i	−0.849083	−	0.528260i	$-0.822845\pi$
$593$		−	626.517i		−	1.05652i	0.849083	−	0.528260i	$-0.177155\pi$
$594$		0			0
$595$	−52.4671			−0.0881799
$596$	−148.231	+	204.023i	−0.248710	+	0.342320i
$597$	−403.117	+	67.8688i	−0.675238	+	0.113683i
$598$	−0.525029	−	1.61587i	−0.000877975	−	0.00270213i
$599$	673.968	+	927.638i	1.12516	+	1.54864i	0.796958	+	0.604035i	$0.206441\pi$
$599$	673.968	+	927.638i	1.12516	+	1.54864i	0.328198	+	0.944609i	$0.393559\pi$
$600$	744.481	−	1496.91i	1.24080	−	2.49484i
$601$	188.992	+	581.657i	0.314462	+	0.967816i	0.975975	+	0.217882i	$0.0699148\pi$
$601$	188.992	+	581.657i	0.314462	+	0.967816i	−0.661513	+	0.749934i	$0.730085\pi$
$602$	83.7396	+	27.2086i	0.139102	+	0.0451971i
$603$	−864.749	+	299.673i	−1.43408	+	0.496970i
$604$	1364.58			2.25924
$605$		0			0
$606$	270.616	+	518.594i	0.446560	+	0.855766i
$607$	90.2465	+	65.5679i	0.148676	+	0.108020i	0.659637	−	0.751585i	$-0.270710\pi$
$607$	90.2465	+	65.5679i	0.148676	+	0.108020i	−0.510960	+	0.859604i	$0.670710\pi$
$608$	−185.526	−	60.2812i	−0.305142	−	0.0991467i
$609$	117.412	+	115.152i	0.192794	+	0.189084i
$610$	−1771.21	+	1286.86i	−2.90362	+	2.10960i
$611$	−1.14056	−	1.56985i	−0.00186672	−	0.00256932i
$612$	−79.0074	+	260.263i	−0.129097	+	0.425266i
$613$	−223.735	+	688.587i	−0.364984	+	1.12331i	0.585006	+	0.811029i	$0.301092\pi$
$613$	−223.735	+	688.587i	−0.364984	+	1.12331i	−0.949991	+	0.312278i	$0.898908\pi$
$614$	668.585	−	920.228i	1.08890	−	1.49874i
$615$	779.210	+	1493.24i	1.26701	+	2.42803i
$616$		0			0
$617$		−	305.723i		−	0.495499i	−0.968824	−	0.247749i	$-0.920309\pi$
$617$		−	305.723i		−	0.495499i	0.968824	−	0.247749i	$-0.0796910\pi$
$618$	1355.52	+	201.213i	2.19341	+	0.325588i
$619$	306.245	−	942.525i	0.494741	−	1.52266i	−0.322618	−	0.946529i	$-0.604563\pi$
$619$	306.245	−	942.525i	0.494741	−	1.52266i	0.817359	−	0.576128i	$-0.195437\pi$
$620$	2619.90	−	851.258i	4.22565	−	1.37300i
$621$	88.6337	+	162.093i	0.142727	+	0.261020i
$622$	331.389	−	240.769i	0.532780	−	0.387088i
$623$	−78.2677	+	25.4307i	−0.125630	+	0.0408198i
$624$	−4.01653	+	0.676223i	−0.00643674	+	0.00108369i
$625$	130.518	+	94.8272i	0.208829	+	0.151723i
$626$			511.397i			0.816928i
$627$		0			0
$628$	1743.12			2.77567
$629$	7.96077	−	10.9571i	0.0126562	−	0.0174198i
$630$	272.513	+	360.151i	0.432560	+	0.571669i
$631$	−167.008	−	513.999i	−0.264673	−	0.814578i	−0.991769	−	0.128043i	$-0.959131\pi$
$631$	−167.008	−	513.999i	−0.264673	−	0.814578i	0.727096	−	0.686536i	$-0.240869\pi$
$632$	−550.819	−	758.137i	−0.871549	−	1.19958i
$633$	−3.33603	−	1.65916i	−0.00527019	−	0.00262111i
$634$	−73.0921	−	224.954i	−0.115287	−	0.354818i
$635$	−439.282	−	142.731i	−0.691782	−	0.224774i
$636$	−532.279	−	79.0112i	−0.836917	−	0.124231i
$637$	−3.24190			−0.00508933
$638$		0			0
$639$	−342.619	−	238.895i	−0.536181	−	0.373858i
$640$	−1322.09	−	960.554i	−2.06576	−	1.50087i
$641$	270.883	+	88.0153i	0.422595	+	0.137309i	0.512591	−	0.858633i	$-0.328686\pi$
$641$	270.883	+	88.0153i	0.422595	+	0.137309i	−0.0899965	+	0.995942i	$0.528686\pi$
$642$	−427.561	+	435.951i	−0.665982	+	0.679052i
$643$	−131.317	+	95.4072i	−0.204225	+	0.148378i	−0.685197	−	0.728358i	$-0.740284\pi$
$643$	−131.317	+	95.4072i	−0.204225	+	0.148378i	0.480972	+	0.876736i	$0.340284\pi$
$644$	−60.2544	−	82.9331i	−0.0935628	−	0.128778i
$645$	−234.498	−	229.984i	−0.363562	−	0.356565i
$646$	104.254	−	320.861i	0.161384	−	0.496689i
$647$	−163.579	+	225.146i	−0.252826	+	0.347985i	−0.916499	−	0.400038i	$-0.868997\pi$
$647$	−163.579	+	225.146i	−0.252826	+	0.347985i	0.663672	+	0.748023i	$0.268997\pi$
$648$	1132.55	−	417.300i	1.74777	−	0.643982i
$649$		0			0
$650$			9.28637i			0.0142867i
$651$	−33.7613	+	227.442i	−0.0518607	+	0.349373i
$652$	223.022	−	686.391i	0.342058	−	1.05275i
$653$	−568.393	+	184.682i	−0.870433	+	0.282821i	−0.709979	−	0.704222i	$-0.751296\pi$
$653$	−568.393	+	184.682i	−0.870433	+	0.282821i	−0.160454	+	0.987043i	$0.551296\pi$
$654$	229.225	−	460.895i	0.350496	−	0.704732i
$655$	943.786	−	685.701i	1.44090	−	1.04687i
$656$	−1293.92	+	420.420i	−1.97244	+	0.640884i
$657$	627.227	+	828.940i	0.954684	+	1.26170i
$658$	−140.605	−	102.156i	−0.213686	−	0.155252i
$659$		−	187.267i		−	0.284169i	−0.989855	−	0.142085i	$-0.954620\pi$
$659$		−	187.267i		−	0.284169i	0.989855	−	0.142085i	$-0.0453805\pi$
$660$		0			0
$661$	218.982			0.331289			0.165645	−	0.986186i	$-0.447030\pi$
$661$	218.982			0.331289			0.165645	+	0.986186i	$0.447030\pi$
$662$	−624.465	+	859.503i	−0.943301	+	1.29834i
$663$	−0.129309	−	0.768052i	−0.000195037	−	0.00115845i
$664$	389.096	+	1197.52i	0.585988	+	1.80349i
$665$	−221.813	−	305.300i	−0.333554	−	0.459097i
$666$	−116.561	+	2.26538i	−0.175017	+	0.00340147i
$667$	63.8760	+	196.590i	0.0957660	+	0.294738i
$668$	−324.817	−	105.539i	−0.486253	−	0.157993i
$669$	−54.7351	+	368.737i	−0.0818164	+	0.551177i
$670$	−2812.17			−4.19726
$671$		0			0
$672$	−35.7599	+	18.6604i	−0.0532141	+	0.0277685i
$673$	−496.850	−	360.983i	−0.738261	−	0.536378i	0.153905	−	0.988086i	$-0.450815\pi$
$673$	−496.850	−	360.983i	−0.738261	−	0.536378i	−0.892166	+	0.451707i	$0.850815\pi$
$674$	−1849.37	−	600.895i	−2.74387	−	0.891536i
$675$	−186.960	−	992.292i	−0.276977	−	1.47006i
$676$	−1128.81	+	820.125i	−1.66983	+	1.21320i
$677$	479.292	+	659.688i	0.707964	+	0.974429i	0.999838	+	0.0179723i	$0.00572108\pi$
$677$	479.292	+	659.688i	0.707964	+	0.974429i	−0.291874	+	0.956457i	$0.594279\pi$
$678$	−383.925	+	391.459i	−0.566261	+	0.577373i
$679$	−53.9803	+	166.134i	−0.0794997	+	0.244675i
$680$	−253.248	+	348.566i	−0.372424	+	0.512597i
$681$	126.886	−	66.2122i	0.186323	−	0.0972279i
$682$		0			0
$683$		−	95.9038i		−	0.140416i	−0.997532	−	0.0702078i	$-0.977634\pi$
$683$		−	95.9038i		−	0.140416i	0.997532	−	0.0702078i	$-0.0223662\pi$
$684$	−1848.46	+	640.570i	−2.70242	+	0.936506i
$685$	−403.874	+	1243.00i	−0.589597	+	1.81459i
$686$	−572.199	+	185.919i	−0.834109	+	0.271018i
$687$	−196.644	−	97.8004i	−0.286236	−	0.142359i
$688$	214.639	−	155.944i	0.311976	−	0.226663i
$689$	1.46549	−	0.476168i	0.00212699	−	0.000691100i
$690$	94.2461	+	559.789i	0.136589	+	0.811288i
$691$	−239.639	−	174.108i	−0.346801	−	0.251965i	0.400725	−	0.916198i	$-0.368758\pi$
$691$	−239.639	−	174.108i	−0.346801	−	0.251965i	−0.747526	+	0.664233i	$0.768758\pi$
$692$		−	1707.69i		−	2.46776i
$693$		0			0
$694$	1358.25			1.95713
$695$	−241.887	+	332.928i	−0.348038	+	0.479033i
$696$	1331.74	−	224.211i	1.91341	−	0.322143i
$697$	−80.3939	−	247.427i	−0.115343	−	0.354989i
$698$	−930.189	−	1280.30i	−1.33265	−	1.83423i
$699$	247.676	−	497.996i	0.354330	−	0.712440i
$700$	173.140	+	532.870i	0.247343	+	0.761243i
$701$	−707.749	−	229.962i	−1.00963	−	0.328048i	−0.242922	−	0.970046i	$-0.578106\pi$
$701$	−707.749	−	229.962i	−1.00963	−	0.328048i	−0.766707	+	0.641998i	$0.778106\pi$
$702$	−4.60053	+	4.87687i	−0.00655347	+	0.00694711i
$703$	97.4133			0.138568
$704$		0			0
$705$	299.933	+	574.776i	0.425436	+	0.815285i
$706$	862.303	+	626.500i	1.22139	+	0.887394i
$707$	−96.1178	−	31.2306i	−0.135952	−	0.0441734i
$708$	−1411.18	−	1384.02i	−1.99319	−	1.95483i
$709$	637.240	−	462.982i	0.898787	−	0.653007i	−0.0393674	−	0.999225i	$-0.512534\pi$
$709$	637.240	−	462.982i	0.898787	−	0.653007i	0.938154	+	0.346218i	$0.112534\pi$
$710$	−754.379	−	1038.31i	−1.06251	−	1.46241i
$711$	−541.594	−	164.410i	−0.761735	−	0.231238i
$712$	−208.833	+	642.722i	−0.293305	+	0.902700i
$713$	−169.875	+	233.813i	−0.238254	+	0.327928i
$714$	−32.2725	−	61.8454i	−0.0451996	−	0.0866182i
$715$		0			0
$716$		−	1141.78i		−	1.59467i
$717$	1041.49	+	154.598i	1.45257	+	0.215618i
$718$	327.921	−	1009.24i	0.456714	−	1.40562i
$719$	464.851	−	151.039i	0.646525	−	0.210069i	0.0326435	−	0.999467i	$-0.489607\pi$
$719$	464.851	−	151.039i	0.646525	−	0.210069i	0.613881	+	0.789398i	$0.289607\pi$
$720$	1360.60	−	26.4435i	1.88972	−	0.0367270i
$721$	−191.546	+	139.166i	−0.265667	+	0.193018i
$722$	1105.83	−	359.306i	1.53162	−	0.497654i
$723$	519.216	−	87.4153i	0.718141	−	0.120906i
$724$	−413.670	−	300.549i	−0.571367	−	0.415123i
$725$		−	1129.80i		−	1.55834i
$726$		0			0
$727$	270.772			0.372452			0.186226	−	0.982507i	$-0.440374\pi$
$727$	270.772			0.372452			0.186226	+	0.982507i	$0.440374\pi$
$728$	1.12727	−	1.55155i	0.00154845	−	0.00213125i
$729$	393.404	−	613.738i	0.539649	−	0.841890i
$730$	987.029	+	3037.76i	1.35209	+	4.16132i
$731$	29.8202	+	41.0439i	0.0407936	+	0.0561476i
$732$	−1755.74	−	873.210i	−2.39855	−	1.19291i
$733$	−125.540	−	386.373i	−0.171269	−	0.527112i	0.828174	−	0.560471i	$-0.189380\pi$
$733$	−125.540	−	386.373i	−0.171269	−	0.527112i	−0.999443	+	0.0333585i	$0.989380\pi$
$734$	1398.29	+	454.333i	1.90503	+	0.618982i
$735$	1071.42	+	159.041i	1.45772	+	0.216382i
$736$	−50.6990			−0.0688845
$737$		0			0
$738$	−1280.86	+	1836.98i	−1.73558	+	2.48914i
$739$	−751.623	−	546.086i	−1.01708	−	0.738953i	−0.0513986	−	0.998678i	$-0.516368\pi$
$739$	−751.623	−	546.086i	−1.01708	−	0.738953i	−0.965682	+	0.259726i	$0.916368\pi$
$740$	−229.505	−	74.5708i	−0.310142	−	0.100771i
$741$	3.92253	−	3.99950i	0.00529356	−	0.00539744i
$742$	111.655	−	81.1221i	0.150478	−	0.109329i
$743$	−426.474	−	586.991i	−0.573989	−	0.790029i	0.419031	−	0.907972i	$-0.362370\pi$
$743$	−426.474	−	586.991i	−0.573989	−	0.790029i	−0.993020	+	0.117943i	$0.962370\pi$
$744$	1348.06	+	1322.11i	1.81190	+	1.77703i
$745$	−74.5592	+	229.470i	−0.100079	+	0.308013i
$746$	−409.077	+	563.046i	−0.548361	+	0.754754i
$747$	623.828	+	434.972i	0.835111	+	0.582291i
$748$		0			0
$749$		−	105.499i		−	0.140853i
$750$	151.030	−	1017.45i	0.201373	−	1.35660i
$751$	339.950	−	1046.26i	0.452664	−	1.39316i	−0.421193	−	0.906971i	$-0.638388\pi$
$751$	339.950	−	1046.26i	0.452664	−	1.39316i	0.873856	−	0.486184i	$-0.161612\pi$
$752$	−498.054	+	161.828i	−0.662306	+	0.215196i
$753$	185.707	−	373.396i	0.246623	−	0.495878i
$754$	−6.06879	+	4.40923i	−0.00804879	+	0.00584779i
$755$	1241.66	−	403.441i	1.64459	−	0.534359i
$756$	−173.061	+	365.619i	−0.228916	+	0.483624i
$757$	1020.40	+	741.362i	1.34795	+	0.979342i	0.999111	+	0.0421594i	$0.0134237\pi$
$757$	1020.40	+	741.362i	1.34795	+	0.979342i	0.348838	+	0.937183i	$0.386576\pi$
$758$		−	253.499i		−	0.334431i
$759$		0			0
$760$	−3098.91			−4.07752
$761$	68.5586	−	94.3628i	0.0900901	−	0.123998i	−0.761593	−	0.648056i	$-0.775582\pi$
$761$	68.5586	−	94.3628i	0.0900901	−	0.123998i	0.851683	+	0.524057i	$0.175582\pi$
$762$	−101.958	−	605.596i	−0.133803	−	0.794745i
$763$	27.4824	+	84.5820i	0.0360188	+	0.110855i
$764$	−117.879	−	162.247i	−0.154292	−	0.212365i
$765$	5.05659	+	260.178i	0.00660993	+	0.340102i
$766$	−567.864	−	1747.71i	−0.741337	−	2.28160i
$767$	5.38307	+	1.74907i	0.00701834	+	0.00228040i
$768$	229.829	−	1548.30i	0.299257	−	2.01602i
$769$	−1252.94			−1.62930			−0.814652	−	0.579949i	$-0.803072\pi$
$769$	−1252.94			−1.62930			−0.814652	+	0.579949i	$0.803072\pi$
$770$		0			0
$771$	−1136.67	+	593.142i	−1.47428	+	0.769315i
$772$	1348.01	+	979.389i	1.74613	+	1.26864i
$773$	1111.09	+	361.014i	1.43737	+	0.467030i	0.921076	−	0.389382i	$-0.127311\pi$
$773$	1111.09	+	361.014i	1.43737	+	0.467030i	0.516293	+	0.856412i	$0.327311\pi$
$774$	126.854	−	417.877i	0.163894	−	0.539893i
$775$	1277.95	−	928.484i	1.64897	−	1.19804i
$776$	843.165	+	1160.52i	1.08655	+	1.49551i
$777$	14.1037	−	14.3805i	0.0181515	−	0.0185077i
$778$	403.440	−	1241.66i	0.518561	−	1.59597i
$779$	1099.87	−	1513.84i	1.41190	−	1.94331i
$780$	−12.3031	+	6.42008i	−0.0157732	+	0.00823087i
$781$		0			0
$782$		−	87.6820i		−	0.112125i
$783$	559.709	−	593.329i	0.714826	−	0.757763i
$784$	−270.366	+	832.101i	−0.344854	+	1.06135i
$785$	1586.10	−	515.357i	2.02052	−	0.656505i
$786$	1388.79	+	690.710i	1.76691	+	0.878767i
$787$	895.443	−	650.578i	1.13779	−	0.826655i	0.150983	−	0.988536i	$-0.451756\pi$
$787$	895.443	−	650.578i	1.13779	−	0.826655i	0.986810	+	0.161881i	$0.0517561\pi$
$788$	509.680	−	165.605i	0.646802	−	0.210159i
$789$	−100.430	−	596.520i	−0.127288	−	0.756045i
$790$	−1407.01	−	1022.25i	−1.78102	−	1.29399i
$791$		−	94.7321i		−	0.119762i
$792$		0			0
$793$	5.61513			0.00708088
$794$	379.834	−	522.796i	0.478380	−	0.658434i
$795$	−507.693	+	85.4752i	−0.638607	+	0.107516i
$796$	−347.656	−	1069.97i	−0.436753	−	1.34419i
$797$	38.1748	+	52.5432i	0.0478982	+	0.0659262i	0.832294	−	0.554334i	$-0.187027\pi$
$797$	38.1748	+	52.5432i	0.0478982	+	0.0659262i	−0.784396	+	0.620260i	$0.787027\pi$
$798$	223.434	−	449.251i	0.279992	−	0.562972i
$799$	−30.9451	−	95.2394i	−0.0387298	−	0.119198i
$800$	263.542	+	85.6301i	0.329428	+	0.107038i
$801$	133.651	+	385.669i	0.166855	+	0.481485i
$802$	317.851			0.396322
$803$		0			0
$804$	−1165.24	−	2233.00i	−1.44930	−	2.77736i
$805$	−79.3462	−	57.6484i	−0.0985667	−	0.0716129i
$806$	−9.97485	−	3.24103i	−0.0123757	−	0.00402112i
$807$	734.756	+	720.615i	0.910478	+	0.892955i
$808$	−671.422	+	487.817i	−0.830968	+	0.603734i
$809$	377.536	+	519.633i	0.466669	+	0.642315i	0.975875	−	0.218329i	$-0.0700607\pi$
$809$	377.536	+	519.633i	0.466669	+	0.642315i	−0.509206	+	0.860645i	$0.670061\pi$
$810$	1759.69	−	1386.07i	2.17245	−	1.71120i
$811$	−28.1962	+	86.7791i	−0.0347673	+	0.107003i	−0.966934	−	0.255026i	$-0.917916\pi$
$811$	−28.1962	+	86.7791i	−0.0347673	+	0.107003i	0.932167	+	0.362029i	$0.117916\pi$
$812$	−266.031	+	366.160i	−0.327625	+	0.450936i
$813$	−565.681	−	1084.04i	−0.695795	−	1.33339i
$814$		0			0
$815$		−	690.500i		−	0.847239i
$816$	−207.920	−	30.8635i	−0.254804	−	0.0378229i
$817$	−112.760	+	347.040i	−0.138017	+	0.424774i
$818$	−1831.00	+	594.929i	−2.23839	+	0.727297i
$819$	−0.0225081	−	1.15812i	−2.74825e−5	−	0.00141406i
$820$	−3750.15	+	2724.64i	−4.57335	+	3.32274i
$821$	−860.864	+	279.712i	−1.04856	+	0.340696i	−0.782101	−	0.623151i	$-0.785852\pi$
$821$	−860.864	+	279.712i	−1.04856	+	0.340696i	−0.266454	+	0.963848i	$0.585852\pi$
$822$	−1713.60	+	288.502i	−2.08467	+	0.350976i
$823$	−506.080	−	367.688i	−0.614921	−	0.446766i	0.236223	−	0.971699i	$-0.424090\pi$
$823$	−506.080	−	367.688i	−0.614921	−	0.446766i	−0.851144	+	0.524933i	$0.824090\pi$
$824$			1944.27i			2.35955i
$825$		0			0
$826$	506.951			0.613742
$827$	−533.996	+	734.983i	−0.645703	+	0.888734i	−0.998904	−	0.0468139i	$-0.985093\pi$
$827$	−533.996	+	734.983i	−0.645703	+	0.888734i	0.353201	+	0.935548i	$0.385093\pi$
$828$	−405.448	+	306.787i	−0.489672	+	0.370516i
$829$	−181.306	−	558.004i	−0.218705	−	0.673104i	−0.998870	−	0.0475305i	$-0.984865\pi$
$829$	−181.306	−	558.004i	−0.218705	−	0.673104i	0.780165	−	0.625574i	$-0.215135\pi$
$830$	1373.54	+	1890.52i	1.65487	+	2.27774i
$831$	1334.99	+	663.954i	1.60649	+	0.798982i
$832$	1.10964	+	3.41511i	0.00133370	+	0.00410470i
$833$	−159.117	−	51.7002i	−0.191016	−	0.0620650i
$834$	−541.223	−	80.3387i	−0.648948	−	0.0963294i
$835$	−326.761			−0.391331
$836$		0			0
$837$	1131.11	+	145.498i	1.35139	+	0.173833i
$838$	845.162	+	614.046i	1.00855	+	0.732752i
$839$	973.790	+	316.404i	1.16066	+	0.377120i	0.825147	−	0.564917i	$-0.191092\pi$
$839$	973.790	+	316.404i	1.16066	+	0.377120i	0.335508	+	0.942037i	$0.391092\pi$
$840$	−448.668	+	457.473i	−0.534129	+	0.544611i
$841$	57.9563	−	42.1077i	0.0689135	−	0.0500686i
$842$	−252.284	−	347.239i	−0.299625	−	0.412398i
$843$	−828.902	−	812.949i	−0.983276	−	0.964352i
$844$	3.16864	−	9.75208i	0.00375432	−	0.0115546i
$845$	−784.655	+	1079.98i	−0.928585	+	1.27809i
$846$	−493.027	+	707.090i	−0.582774	+	0.835803i
$847$		0			0
$848$		−	415.860i		−	0.490401i
$849$	−97.6812	+	658.055i	−0.115054	+	0.775094i
$850$	−148.094	+	455.787i	−0.174228	+	0.536219i
$851$	24.0782	−	7.82349i	0.0282940	−	0.00919329i
$852$	511.891	−	1029.24i	0.600811	−	1.20803i
$853$	−319.388	+	232.049i	−0.374429	+	0.272038i	−0.759045	−	0.651038i	$-0.774334\pi$
$853$	−319.388	+	232.049i	−0.374429	+	0.272038i	0.384616	+	0.923077i	$0.374334\pi$
$854$	478.309	−	155.412i	0.560081	−	0.181981i
$855$	−1492.57	+	1129.37i	−1.74569	+	1.32090i
$856$	−700.885	−	509.223i	−0.818791	−	0.594887i
$857$			1.34510i			0.00156955i	1.00000		0.000784774i	$0.000249801\pi$
$857$			1.34510i			0.00156955i	−1.00000		0.000784774i	$0.999750\pi$
$858$		0			0
$859$	847.638			0.986772			0.493386	−	0.869810i	$-0.335759\pi$
$859$	847.638			0.986772			0.493386	+	0.869810i	$0.335759\pi$
$860$	531.324	−	731.305i	0.617819	−	0.850355i
$861$	−64.2369	−	381.545i	−0.0746074	−	0.443141i
$862$	−639.399	−	1967.87i	−0.741762	−	2.28291i
$863$	−273.561	−	376.524i	−0.316988	−	0.436296i	0.620557	−	0.784162i	$-0.286907\pi$
$863$	−273.561	−	376.524i	−0.316988	−	0.436296i	−0.937545	+	0.347865i	$0.886907\pi$
$864$	95.9813	+	175.531i	0.111089	+	0.203161i
$865$	−504.882	−	1553.87i	−0.583679	−	1.79638i
$866$	−2138.69	−	694.902i	−2.46962	−	0.802427i
$867$	−121.400	+	817.844i	−0.140023	+	0.943303i
$868$	−632.804			−0.729037
$869$		0			0
$870$	2221.99	−	1159.49i	2.55401	−	1.33275i
$871$	5.83508	+	4.23943i	0.00669929	+	0.00486732i
$872$	694.574	+	225.681i	0.796530	+	0.258808i
$873$	829.043	+	251.671i	0.949649	+	0.288282i
$874$	510.211	−	370.690i	0.583765	−	0.424130i
$875$	104.458	+	143.774i	0.119380	+	0.164313i
$876$	−2003.15	+	2042.46i	−2.28670	+	2.33158i
$877$	160.979	−	495.443i	0.183557	−	0.564929i	−0.816364	−	0.577538i	$-0.804014\pi$
$877$	160.979	−	495.443i	0.183557	−	0.564929i	0.999921	+	0.0126089i	$0.00401364\pi$
$878$	979.949	−	1348.78i	1.11612	−	1.53620i
$879$	−1177.59	+	614.496i	−1.33969	+	0.699085i
$880$		0			0
$881$		−	606.759i		−	0.688717i	−0.938838	−	0.344358i	$-0.888096\pi$
$881$		−	606.759i		−	0.688717i	0.938838	−	0.344358i	$-0.111904\pi$
$882$	471.562	+	1360.76i	0.534651	+	1.54281i
$883$	−34.5371	+	106.294i	−0.0391134	+	0.120379i	−0.968707	−	0.248208i	$-0.920158\pi$
$883$	−34.5371	+	106.294i	−0.0391134	+	0.120379i	0.929593	+	0.368587i	$0.120158\pi$
$884$	2.03860	−	0.662383i	0.00230611	−	0.000749302i
$885$	−1693.25	−	842.133i	−1.91328	−	0.951562i
$886$	305.099	−	221.667i	0.344355	−	0.250189i
$887$	10.8413	−	3.52254i	0.0122224	−	0.00397130i	−0.302899	−	0.953023i	$-0.597955\pi$
$887$	10.8413	−	3.52254i	0.0122224	−	0.00397130i	0.315122	+	0.949051i	$0.397955\pi$
$888$	−27.4613	−	163.110i	−0.0309249	−	0.183683i
$889$	85.8391	+	62.3657i	0.0965569	+	0.0701527i
$890$			1254.20i			1.40921i
$891$		0			0
$892$	−1025.93			−1.15014
$893$	423.361	−	582.706i	0.474088	−	0.652527i
$894$	−316.348	+	53.2604i	−0.353857	+	0.0595754i
$895$	−337.571	−	1038.94i	−0.377174	−	1.16082i
$896$	220.654	+	303.705i	0.246266	+	0.338956i
$897$	0.648345	−	1.30361i	0.000722792	−	0.00145330i
$898$	242.846	+	747.404i	0.270430	+	0.832298i
$899$	1213.56	+	394.309i	1.34990	+	0.438608i
$900$	2625.75	−	909.937i	2.91751	−	1.01104i
$901$	79.5220			0.0882597
$902$		0			0
$903$	34.9056	+	66.8914i	0.0386552	+	0.0740768i
$904$	−629.355	−	457.253i	−0.696189	−	0.505811i
$905$	−465.265	−	151.174i	−0.514106	−	0.167043i
$906$	1239.30	+	1215.45i	1.36788	+	1.34156i
$907$	−1290.64	+	937.708i	−1.42298	+	1.03386i	−0.431711	+	0.902012i	$0.642090\pi$
$907$	−1290.64	+	937.708i	−1.42298	+	1.03386i	−0.991270	+	0.131845i	$0.957910\pi$
$908$	231.522	+	318.663i	0.254981	+	0.350951i
$909$	−145.605	+	479.647i	−0.160182	+	0.527664i
$910$	1.09987	−	3.38504i	0.00120865	−	0.00371983i
$911$	−355.865	+	489.806i	−0.390631	+	0.537658i	−0.958362	−	0.285557i	$-0.907822\pi$
$911$	−355.865	+	489.806i	−0.390631	+	0.537658i	0.567731	+	0.823214i	$0.307822\pi$
$912$	−699.425	−	1340.34i	−0.766914	−	1.46967i
$913$		0			0
$914$			249.573i			0.273056i
$915$	−1855.75	−	275.467i	−2.02814	−	0.301056i
$916$	186.778	−	574.843i	0.203906	−	0.627558i
$917$	−254.867	+	82.8112i	−0.277935	+	0.0903066i
$918$	−303.574	+	165.996i	−0.330690	+	0.180824i
$919$	297.362	−	216.046i	0.323571	−	0.235088i	−0.414127	−	0.910219i	$-0.635913\pi$
$919$	297.362	−	216.046i	0.323571	−	0.235088i	0.737698	+	0.675131i	$0.235913\pi$
$920$	−765.977	+	248.881i	−0.832583	+	0.270523i
$921$	961.190	−	161.826i	1.04364	−	0.175707i
$922$	2482.61	+	1803.72i	2.69263	+	1.95631i
$923$			3.29169i			0.00356630i
$924$		0			0
$925$	−138.377			−0.149597
$926$	1697.03	−	2335.77i	1.83265	−	2.52243i
$927$	708.569	+	936.441i	0.764368	+	1.01018i
$928$	69.1712	+	212.887i	0.0745379	+	0.229404i
$929$	982.652	+	1352.50i	1.05775	+	1.45587i	0.881890	+	0.471456i	$0.156271\pi$
$929$	982.652	+	1352.50i	1.05775	+	1.45587i	0.175862	+	0.984415i	$0.443729\pi$
$930$	3137.60	+	1560.48i	3.37377	+	1.67793i
$931$	−371.855	−	1144.45i	−0.399415	−	1.22927i
$932$	1455.77	+	473.009i	1.56199	+	0.507520i
$933$	347.207	+	51.5392i	0.372141	+	0.0552403i
$934$	1124.00			1.20343
$935$		0			0
$936$	−7.80261	−	5.44046i	−0.00833612	−	0.00581246i
$937$	−809.725	−	588.299i	−0.864167	−	0.627854i	0.0648482	−	0.997895i	$-0.479344\pi$
$937$	−809.725	−	588.299i	−0.864167	−	0.627854i	−0.929015	+	0.370041i	$0.879344\pi$
$938$	614.381	+	199.625i	0.654991	+	0.212819i
$939$	−306.848	+	312.869i	−0.326781	+	0.333194i
$940$	−1443.50	+	1048.77i	−1.53564	+	1.11571i
$941$	−207.090	−	285.035i	−0.220074	−	0.302906i	0.684677	−	0.728847i	$-0.259943\pi$
$941$	−207.090	−	285.035i	−0.220074	−	0.302906i	−0.904751	+	0.425940i	$0.859943\pi$
$942$	1583.09	+	1552.62i	1.68056	+	1.64822i
$943$	150.281	−	462.518i	0.159365	−	0.490476i
$944$	897.866	−	1235.81i	0.951130	−	1.30912i
$945$	−49.3760	+	383.851i	−0.0522497	+	0.406192i
$946$		0			0
$947$			1536.20i			1.62217i	0.584927	+	0.811086i	$0.301123\pi$
$947$			1536.20i			1.62217i	−0.584927	+	0.811086i	$0.698877\pi$
$948$	228.717	−	1540.81i	0.241263	−	1.62533i
$949$	2.53150	−	7.79116i	0.00266755	−	0.00820986i
$950$	−3278.26	+	1065.17i	−3.45080	+	1.12123i
$951$	90.2596	−	181.482i	0.0949102	−	0.190833i
$952$	80.0711	−	58.1750i	0.0841083	−	0.0611082i
$953$	853.431	−	277.296i	0.895520	−	0.290972i	0.175133	−	0.984545i	$-0.443964\pi$
$953$	853.431	−	277.296i	0.895520	−	0.290972i	0.720387	+	0.693573i	$0.243964\pi$
$954$	−413.036	−	545.865i	−0.432951	−	0.572186i
$955$	−155.230	−	112.781i	−0.162544	−	0.118095i
$956$			2897.71i			3.03108i
$957$		0			0
$958$	1516.66			1.58315
$959$	176.471	−	242.891i	0.184015	−	0.253275i
$960$	−199.187	−	1183.10i	−0.207486	−	1.23240i
$961$	254.340	+	782.779i	0.264662	+	0.814546i
$962$	0.540041	+	0.743302i	0.000561373	+	0.000772663i
$963$	−523.158	+	10.1676i	−0.543258	+	0.0105583i
$964$	447.782	+	1378.13i	0.464504	+	1.42960i
$965$	1516.15	+	492.626i	1.57114	+	0.510493i
$966$	19.1470	−	128.989i	0.0198209	−	0.133529i
$967$	1717.58			1.77620			0.888099	−	0.459652i	$-0.152026\pi$
$967$	1717.58			1.77620			0.888099	+	0.459652i	$0.152026\pi$
$968$		0			0
$969$	256.304	−	133.746i	0.264504	−	0.138025i
$970$	2153.78	+	1564.81i	2.22039	+	1.61321i
$971$	1425.38	+	463.135i	1.46795	+	0.476967i	0.930489	−	0.366319i	$-0.119382\pi$
$971$	1425.38	+	463.135i	1.46795	+	0.476967i	0.537465	+	0.843286i	$0.319382\pi$
$972$	1829.74	+	822.951i	1.88245	+	0.846658i
$973$	76.4788	−	55.5651i	0.0786011	−	0.0571070i
$974$	−725.484	−	998.544i	−0.744850	−	1.02520i
$975$	−5.57199	+	5.68134i	−0.00571487	+	0.00582701i
$976$	468.287	−	1441.24i	0.479802	−	1.47668i
$977$	33.1740	−	45.6602i	0.0339550	−	0.0467351i	−0.791702	−	0.610908i	$-0.790805\pi$
$977$	33.1740	−	45.6602i	0.0339550	−	0.0467351i	0.825657	+	0.564172i	$0.190805\pi$
$978$	813.925	−	424.727i	0.832234	−	0.434281i
$979$		0			0
$980$			2980.98i			3.04182i
$981$	416.784	−	144.434i	0.424856	−	0.147231i
$982$	−482.917	+	1486.26i	−0.491768	+	1.51351i
$983$	45.2279	−	14.6954i	0.0460101	−	0.0149496i	−0.285922	−	0.958253i	$-0.592300\pi$
$983$	45.2279	−	14.6954i	0.0460101	−	0.0149496i	0.331932	+	0.943303i	$0.392300\pi$
$984$	−2844.86	−	1414.88i	−2.89112	−	1.43789i
$985$	414.808	−	301.376i	0.421125	−	0.305965i
$986$	−368.180	+	119.629i	−0.373408	+	0.121327i
$987$	−24.7260	−	146.864i	−0.0250517	−	0.148798i
$988$	12.4729	+	9.06206i	0.0126244	+	0.00917213i
$989$			94.8360i			0.0958908i
$990$		0			0
$991$	−218.685			−0.220671			−0.110336	−	0.993894i	$-0.535193\pi$
$991$	−218.685			−0.220671			−0.110336	+	0.993894i	$0.535193\pi$
$992$	−183.957	+	253.196i	−0.185441	+	0.255238i
$993$	−897.761	+	151.147i	−0.904090	+	0.152213i
$994$	91.1053	+	280.393i	0.0916553	+	0.282086i
$995$	−632.680	−	870.809i	−0.635859	−	0.875185i
$996$	−932.032	+	1874.01i	−0.935775	+	1.88153i
$997$	203.226	+	625.464i	0.203837	+	0.627346i	0.999759	+	0.0219472i	$0.00698656\pi$
$997$	203.226	+	625.464i	0.203837	+	0.627346i	−0.795922	+	0.605399i	$0.793013\pi$
$998$	−298.893	−	97.1161i	−0.299492	−	0.0973107i
$999$	−72.6706	−	68.5529i	−0.0727433	−	0.0686215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.323.1		24
3.2	odd	2	inner	363.3.h.q.323.6		24
11.2	odd	10		363.3.h.p.269.1		24
11.3	even	5	inner	363.3.h.q.245.6		24
11.4	even	5	inner	363.3.h.q.251.1		24
11.5	even	5		363.3.b.j.122.1	✓	6
11.6	odd	10		363.3.b.k.122.6	yes	6
11.7	odd	10		363.3.h.p.251.6		24
11.8	odd	10		363.3.h.p.245.1		24
11.9	even	5	inner	363.3.h.q.269.6		24
11.10	odd	2		363.3.h.p.323.6		24
33.2	even	10		363.3.h.p.269.6		24
33.5	odd	10		363.3.b.j.122.6	yes	6
33.8	even	10		363.3.h.p.245.6		24
33.14	odd	10	inner	363.3.h.q.245.1		24
33.17	even	10		363.3.b.k.122.1	yes	6
33.20	odd	10	inner	363.3.h.q.269.1		24
33.26	odd	10	inner	363.3.h.q.251.6		24
33.29	even	10		363.3.h.p.251.1		24
33.32	even	2		363.3.h.p.323.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.1	✓	6	11.5	even	5
363.3.b.j.122.6	yes	6	33.5	odd	10
363.3.b.k.122.1	yes	6	33.17	even	10
363.3.b.k.122.6	yes	6	11.6	odd	10
363.3.h.p.245.1		24	11.8	odd	10
363.3.h.p.245.6		24	33.8	even	10
363.3.h.p.251.1		24	33.29	even	10
363.3.h.p.251.6		24	11.7	odd	10
363.3.h.p.269.1		24	11.2	odd	10
363.3.h.p.269.6		24	33.2	even	10
363.3.h.p.323.1		24	33.32	even	2
363.3.h.p.323.6		24	11.10	odd	2
363.3.h.q.245.1		24	33.14	odd	10	inner
363.3.h.q.245.6		24	11.3	even	5	inner
363.3.h.q.251.1		24	11.4	even	5	inner
363.3.h.q.251.6		24	33.26	odd	10	inner
363.3.h.q.269.1		24	33.20	odd	10	inner
363.3.h.q.269.6		24	11.9	even	5	inner
363.3.h.q.323.1		24	1.1	even	1	trivial
363.3.h.q.323.6		24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-2.05778 + 2.83229i) q^{2} +(-2.95837 + 0.498071i) q^{3} +(-2.55135 - 7.85225i) q^{4} +(-4.64306 - 6.39063i) q^{5} +(4.67699 - 9.40388i) q^{6} +(0.560737 + 1.72577i) q^{7} +(14.1718 + 4.60468i) q^{8} +(8.50385 - 2.94695i) q^{9} +27.6545 q^{10} +(11.4588 + 21.9591i) q^{12} +(-0.0573816 - 0.0416901i) q^{13} +(-6.04176 - 1.96309i) q^{14} +(16.9189 + 16.5932i) q^{15} +(-15.4861 + 11.2513i) q^{16} +(-2.15151 - 2.96129i) q^{17} +(-9.15243 + 30.1496i) q^{18} +(8.13557 - 25.0387i) q^{19} +(-38.3347 + 52.7632i) q^{20} +(-2.51842 - 4.82617i) q^{21} -6.84236i q^{23} +(-44.2187 - 6.56379i) q^{24} +(-11.5567 + 35.5678i) q^{25} +(0.236157 - 0.0767322i) q^{26} +(-23.6897 + 12.9537i) q^{27} +(12.1205 - 8.80609i) q^{28} +(-28.7313 + 9.33537i) q^{29} +(-81.8122 + 13.7739i) q^{30} +(-34.1714 - 24.8270i) q^{31} -7.40958i q^{32} +12.8146 q^{34} +(8.42522 - 11.5963i) q^{35} +(-44.8365 - 59.2557i) q^{36} +(1.14339 + 3.51900i) q^{37} +(54.1758 + 74.5665i) q^{38} +(0.190520 + 0.0947546i) q^{39} +(-36.3736 - 111.946i) q^{40} +(67.5964 + 21.9634i) q^{41} +(18.8515 + 2.79830i) q^{42} -13.8601 q^{43} +(-58.3168 - 40.6621i) q^{45} +(19.3796 + 14.0801i) q^{46} +(26.0191 + 8.45412i) q^{47} +(40.2096 - 40.9986i) q^{48} +(36.9780 - 26.8661i) q^{49} +(-76.9573 - 105.923i) q^{50} +(7.83988 + 7.68899i) q^{51} +(-0.180961 + 0.556941i) q^{52} +(-12.7697 + 17.5760i) q^{53} +(12.0596 - 93.7520i) q^{54} +27.0392i q^{56} +(-11.5969 + 78.1258i) q^{57} +(32.6823 - 100.586i) q^{58} +(-75.8954 + 24.6599i) q^{59} +(87.1283 - 175.186i) q^{60} +(-64.0476 + 46.5333i) q^{61} +(140.634 - 45.6949i) q^{62} +(9.85418 + 13.0232i) q^{63} +(-40.9582 - 29.7579i) q^{64} +0.560274i q^{65} -101.689 q^{67} +(-17.7636 + 24.4495i) q^{68} +(3.40798 + 20.2422i) q^{69} +(15.5069 + 47.7254i) q^{70} +(-27.2787 - 37.5458i) q^{71} +(134.084 - 2.60595i) q^{72} +(35.6914 + 109.847i) q^{73} +(-12.3197 - 4.00291i) q^{74} +(16.4736 - 110.979i) q^{75} -217.367 q^{76} +(-0.660422 + 0.344625i) q^{78} +(-50.8781 - 36.9651i) q^{79} +(143.806 + 46.7253i) q^{80} +(63.6310 - 50.1209i) q^{81} +(-201.305 + 146.257i) q^{82} +(49.6679 + 68.3620i) q^{83} +(-31.4709 + 32.0885i) q^{84} +(-8.93495 + 27.4990i) q^{85} +(28.5211 - 39.2559i) q^{86} +(80.3481 - 41.9277i) q^{87} +45.3523i q^{89} +(235.170 - 81.4966i) q^{90} +(0.0397717 - 0.122405i) q^{91} +(-53.7279 + 17.4573i) q^{92} +(113.457 + 56.4275i) q^{93} +(-77.4862 + 56.2970i) q^{94} +(-197.787 + 64.2650i) q^{95} +(3.69050 + 21.9202i) q^{96} +(77.8815 + 56.5842i) q^{97} +160.017i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

L-functions

Modular forms

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