LMFDB - Embedded newform 363.3.b.l.122.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 $ x^8 + 29x^6 + 282x^4 + 1061*x^2 + 1331
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.2
Root			$-3.06025i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.l.122.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.06025i q^{2} +(0.126437 + 2.99733i) q^{3} -5.36516 q^{4} +6.63932i q^{5} +(9.17261 - 0.386930i) q^{6} +3.06298 q^{7} +4.17774i q^{8} +(-8.96803 + 0.757950i) q^{9} +O(q^{10})$	\(q-3.06025i q^{2} +(0.126437 + 2.99733i) q^{3} -5.36516 q^{4} +6.63932i q^{5} +(9.17261 - 0.386930i) q^{6} +3.06298 q^{7} +4.17774i q^{8} +(-8.96803 + 0.757950i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} -16.2447 q^{13} -9.37349i q^{14} +(-19.9003 + 0.839458i) q^{15} -8.67570 q^{16} +0.805648i q^{17} +(2.31952 + 27.4444i) q^{18} -20.7018 q^{19} -35.6210i q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(-12.5221 + 0.528222i) q^{24} -19.0806 q^{25} +49.7128i q^{26} +(-3.40572 - 26.7843i) q^{27} -16.4334 q^{28} +3.78268i q^{29} +(2.56896 + 60.8999i) q^{30} -20.7800 q^{31} +43.2608i q^{32} +2.46549 q^{34} +20.3361i q^{35} +(48.1149 - 4.06652i) q^{36} +38.5536 q^{37} +63.3527i q^{38} +(-2.05393 - 48.6907i) q^{39} -27.7373 q^{40} +13.3726i q^{41} +(28.0955 - 1.18516i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +83.6135 q^{46} +19.8903i q^{47} +(-1.09693 - 26.0040i) q^{48} -39.6182 q^{49} +58.3915i q^{50} +(-2.41480 + 0.101864i) q^{51} +87.1552 q^{52} -17.6754i q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(-2.61748 - 62.0502i) q^{57} +11.5760 q^{58} +43.5255i q^{59} +(106.768 - 4.50383i) q^{60} -10.6547 q^{61} +63.5921i q^{62} +(-27.4689 + 2.32158i) q^{63} +97.6863 q^{64} -107.854i q^{65} +72.2963 q^{67} -4.32243i q^{68} +(-81.8944 + 3.45457i) q^{69} +62.2336 q^{70} +2.56990i q^{71} +(-3.16651 - 37.4660i) q^{72} +45.4788 q^{73} -117.984i q^{74} +(-2.41250 - 57.1910i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +98.2423 q^{79} -57.6008i q^{80} +(79.8510 - 13.5946i) q^{81} +40.9237 q^{82} +31.9006i q^{83} +(-2.07779 - 49.2563i) q^{84} -5.34895 q^{85} +132.853i q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(-182.213 + 15.4000i) q^{90} -49.7570 q^{91} -146.589i q^{92} +(-2.62737 - 62.2846i) q^{93} +60.8693 q^{94} -137.446i q^{95} +(-129.667 + 5.46978i) q^{96} -63.3019 q^{97} +121.242i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	$ 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) $ 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	3.06025i		−	1.53013i	−0.643955	−	0.765064i	$-0.722707\pi$
$2$		−	3.06025i		−	1.53013i	0.643955	−	0.765064i	$-0.277293\pi$
$3$	0.126437	+	2.99733i	0.0421458	+	0.999111i
$3$	0.126437	+	2.99733i	0.0421458	+	0.999111i
$4$	−5.36516			−1.34129
$5$			6.63932i			1.32786i	0.747793	+	0.663932i	$0.231114\pi$
$5$			6.63932i			1.32786i	−0.747793	+	0.663932i	$0.768886\pi$
$6$	9.17261	−	0.386930i	1.52877	−	0.0644884i
$7$	3.06298			0.437568			0.218784	−	0.975773i	$-0.429791\pi$
$7$	3.06298			0.437568			0.218784	+	0.975773i	$0.429791\pi$
$8$			4.17774i			0.522217i
$9$	−8.96803	+	0.757950i	−0.996447	+	0.0842166i
$10$	20.3180			2.03180
$11$		0			0
$11$		0			0
$12$	−0.678356	−	16.0812i	−0.0565297	−	1.34010i
$13$	−16.2447			−1.24959			−0.624795	−	0.780789i	$-0.714817\pi$
$13$	−16.2447			−1.24959			−0.624795	+	0.780789i	$0.714817\pi$
$14$		−	9.37349i		−	0.669535i
$15$	−19.9003	+	0.839458i	−1.32668	+	0.0559639i
$16$	−8.67570			−0.542231
$17$			0.805648i			0.0473910i	0.999719	+	0.0236955i	$0.00754322\pi$
$17$			0.805648i			0.0473910i	−0.999719	+	0.0236955i	$0.992457\pi$
$18$	2.31952	+	27.4444i	0.128862	+	1.52469i
$19$	−20.7018			−1.08957			−0.544784	−	0.838577i	$-0.683388\pi$
$19$	−20.7018			−1.08957			−0.544784	+	0.838577i	$0.683388\pi$
$20$		−	35.6210i		−	1.78105i
$21$	0.387274	+	9.18076i	0.0184416	+	0.437179i
$22$		0			0
$23$			27.3224i			1.18793i	0.804491	+	0.593965i	$0.202438\pi$
$23$			27.3224i			1.18793i	−0.804491	+	0.593965i	$0.797562\pi$
$24$	−12.5221	+	0.528222i	−0.521753	+	0.0220092i
$25$	−19.0806			−0.763224
$26$			49.7128i			1.91203i
$27$	−3.40572	−	26.7843i	−0.126138	−	0.992013i
$28$	−16.4334			−0.586906
$29$			3.78268i			0.130437i	0.997871	+	0.0652187i	$0.0207745\pi$
$29$			3.78268i			0.130437i	−0.997871	+	0.0652187i	$0.979226\pi$
$30$	2.56896	+	60.8999i	0.0856318	+	2.03000i
$31$	−20.7800			−0.670323			−0.335161	−	0.942161i	$-0.608791\pi$
$31$	−20.7800			−0.670323			−0.335161	+	0.942161i	$0.608791\pi$
$32$			43.2608i			1.35190i
$33$		0			0
$34$	2.46549			0.0725143
$35$			20.3361i			0.581031i
$36$	48.1149	−	4.06652i	1.33652	−	0.112959i
$37$	38.5536			1.04199			0.520995	−	0.853560i	$-0.325561\pi$
$37$	38.5536			1.04199			0.520995	+	0.853560i	$0.325561\pi$
$38$			63.3527i			1.66718i
$39$	−2.05393	−	48.6907i	−0.0526649	−	1.24848i
$40$	−27.7373			−0.693433
$41$			13.3726i			0.326162i	0.986613	+	0.163081i	$0.0521432\pi$
$41$			13.3726i			0.326162i	−0.986613	+	0.163081i	$0.947857\pi$
$42$	28.0955	−	1.18516i	0.668940	−	0.0282181i
$43$	−43.4125			−1.00959			−0.504797	−	0.863238i	$-0.668433\pi$
$43$	−43.4125			−1.00959			−0.504797	+	0.863238i	$0.668433\pi$
$44$		0			0
$45$	−5.03227	−	59.5416i	−0.111828	−	1.32315i
$46$	83.6135			1.81768
$47$			19.8903i			0.423198i	0.977357	+	0.211599i	$0.0678670\pi$
$47$			19.8903i			0.423198i	−0.977357	+	0.211599i	$0.932133\pi$
$48$	−1.09693	−	26.0040i	−0.0228528	−	0.541750i
$49$	−39.6182			−0.808534
$50$			58.3915i			1.16783i
$51$	−2.41480	+	0.101864i	−0.0473489	+	0.00199733i
$52$	87.1552			1.67606
$53$		−	17.6754i		−	0.333499i	−0.985999	−	0.166750i	$-0.946673\pi$
$53$		−	17.6754i		−	0.333499i	0.985999	−	0.166750i	$-0.0533271\pi$
$54$	−81.9669	+	10.4224i	−1.51791	+	0.193007i
$55$		0			0
$56$			12.7963i			0.228505i
$57$	−2.61748	−	62.0502i	−0.0459207	−	1.08860i
$58$	11.5760			0.199586
$59$			43.5255i			0.737721i	0.929485	+	0.368860i	$0.120252\pi$
$59$			43.5255i			0.737721i	−0.929485	+	0.368860i	$0.879748\pi$
$60$	106.768	−	4.50383i	1.77947	−	0.0750638i
$61$	−10.6547			−0.174668			−0.0873339	−	0.996179i	$-0.527835\pi$
$61$	−10.6547			−0.174668			−0.0873339	+	0.996179i	$0.527835\pi$
$62$			63.5921i			1.02568i
$63$	−27.4689	+	2.32158i	−0.436014	+	0.0368505i
$64$	97.6863			1.52635
$65$		−	107.854i		−	1.65929i
$66$		0			0
$67$	72.2963			1.07905			0.539525	−	0.841970i	$-0.318604\pi$
$67$	72.2963			1.07905			0.539525	+	0.841970i	$0.318604\pi$
$68$		−	4.32243i		−	0.0635651i
$69$	−81.8944	+	3.45457i	−1.18687	+	0.0500662i
$70$	62.2336			0.889052
$71$			2.56990i			0.0361957i	0.999836	+	0.0180979i	$0.00576105\pi$
$71$			2.56990i			0.0361957i	−0.999836	+	0.0180979i	$0.994239\pi$
$72$	−3.16651	−	37.4660i	−0.0439793	−	0.520362i
$73$	45.4788			0.622997			0.311499	−	0.950247i	$-0.399169\pi$
$73$	45.4788			0.622997			0.311499	+	0.950247i	$0.399169\pi$
$74$		−	117.984i		−	1.59438i
$75$	−2.41250	−	57.1910i	−0.0321667	−	0.762546i
$76$	111.068			1.46143
$77$		0			0
$78$	−149.006	+	6.28555i	−1.91033	+	0.0805840i
$79$	98.2423			1.24357			0.621786	−	0.783187i	$-0.286407\pi$
$79$	98.2423			1.24357			0.621786	+	0.783187i	$0.286407\pi$
$80$		−	57.6008i		−	0.720010i
$81$	79.8510	−	13.5946i	0.985815	−	0.167835i
$82$	40.9237			0.499069
$83$			31.9006i			0.384345i	0.981361	+	0.192172i	$0.0615533\pi$
$83$			31.9006i			0.384345i	−0.981361	+	0.192172i	$0.938447\pi$
$84$	−2.07779	−	49.2563i	−0.0247356	−	0.586384i
$85$	−5.34895			−0.0629289
$86$			132.853i			1.54481i
$87$	−11.3380	+	0.478272i	−0.130321	+	0.00549738i
$88$		0			0
$89$			18.5409i			0.208325i	0.994560	+	0.104162i	$0.0332161\pi$
$89$			18.5409i			0.208325i	−0.994560	+	0.104162i	$0.966784\pi$
$90$	−182.213	+	15.4000i	−2.02458	+	0.171112i
$91$	−49.7570			−0.546780
$92$		−	146.589i		−	1.59336i
$93$	−2.62737	−	62.2846i	−0.0282513	−	0.669727i
$94$	60.8693			0.647546
$95$		−	137.446i		−	1.44680i
$96$	−129.667	+	5.46978i	−1.35070	+	0.0569769i
$97$	−63.3019			−0.652597			−0.326298	−	0.945267i	$-0.605801\pi$
$97$	−63.3019			−0.652597			−0.326298	+	0.945267i	$0.605801\pi$
$98$			121.242i			1.23716i
$99$		0			0
$100$	102.371			1.02371
$101$			150.359i			1.48870i	0.667790	+	0.744350i	$0.267241\pi$
$101$			150.359i			1.48870i	−0.667790	+	0.744350i	$0.732759\pi$
$102$	0.311729	+	7.38989i	0.00305617	+	0.0724499i
$103$	−149.767			−1.45405			−0.727026	−	0.686610i	$-0.759098\pi$
$103$	−149.767			−1.45405			−0.727026	+	0.686610i	$0.759098\pi$
$104$		−	67.8659i		−	0.652557i
$105$	−60.9541	+	2.57124i	−0.580515	+	0.0244880i
$106$	−54.0914			−0.510296
$107$			20.7515i			0.193939i	0.995287	+	0.0969696i	$0.0309150\pi$
$107$			20.7515i			0.193939i	−0.995287	+	0.0969696i	$0.969085\pi$
$108$	18.2722	+	143.702i	0.169187	+	1.33058i
$109$	105.794			0.970583			0.485291	−	0.874352i	$-0.338714\pi$
$109$	105.794			0.970583			0.485291	+	0.874352i	$0.338714\pi$
$110$		0			0
$111$	4.87462	+	115.558i	0.0439155	+	1.04106i
$112$	−26.5735			−0.237263
$113$			132.769i			1.17495i	0.809244	+	0.587473i	$0.199877\pi$
$113$			132.769i			1.17495i	−0.809244	+	0.587473i	$0.800123\pi$
$114$	−189.889	+	8.01015i	−1.66570	+	0.0702644i
$115$	−181.402			−1.57741
$116$		−	20.2947i		−	0.174954i
$117$	145.683	−	12.3126i	1.24515	−	0.105236i
$118$	133.199			1.12881
$119$			2.46768i			0.0207368i
$120$	−3.50703	−	83.1381i	−0.0292253	−	0.692817i
$121$		0			0
$122$			32.6062i			0.267264i
$123$	−40.0823	+	1.69080i	−0.325872	+	0.0137463i
$124$	111.488			0.899097
$125$			39.3007i			0.314406i
$126$	7.10463	+	84.0617i	0.0563860	+	0.667156i
$127$	146.655			1.15477			0.577384	−	0.816473i	$-0.304074\pi$
$127$	146.655			1.15477			0.577384	+	0.816473i	$0.304074\pi$
$128$		−	125.902i		−	0.983607i
$129$	−5.48896	−	130.122i	−0.0425501	−	1.00870i
$130$	−330.059			−2.53892
$131$		−	149.467i		−	1.14097i	−0.821309	−	0.570484i	$-0.806756\pi$
$131$		−	149.467i		−	1.14097i	0.821309	−	0.570484i	$-0.193244\pi$
$132$		0			0
$133$	−63.4091			−0.476760
$134$		−	221.245i		−	1.65108i
$135$	177.830	−	22.6117i	1.31726	−	0.167494i
$136$	−3.36578			−0.0247484
$137$		−	152.207i		−	1.11100i	−0.831517	−	0.555500i	$-0.812527\pi$
$137$		−	152.207i		−	1.11100i	0.831517	−	0.555500i	$-0.187473\pi$
$138$	10.5719	+	250.618i	0.0766077	+	1.81607i
$139$	−111.836			−0.804573			−0.402286	−	0.915514i	$-0.631784\pi$
$139$	−111.836			−0.804573			−0.402286	+	0.915514i	$0.631784\pi$
$140$		−	109.106i		−	0.779331i
$141$	−59.6178	+	2.51487i	−0.422822	+	0.0178360i
$142$	7.86454			0.0553841
$143$		0			0
$144$	77.8039	−	6.57574i	0.540305	−	0.0456649i
$145$	−25.1145			−0.173203
$146$		−	139.177i		−	0.953265i
$147$	−5.00921	−	118.749i	−0.0340763	−	0.807816i
$148$	−206.846			−1.39761
$149$		−	259.695i		−	1.74292i	−0.490465	−	0.871461i	$-0.663173\pi$
$149$		−	259.695i		−	1.74292i	0.490465	−	0.871461i	$-0.336827\pi$
$150$	−175.019	+	7.38287i	−1.16679	+	0.0492191i
$151$	−88.0177			−0.582899			−0.291449	−	0.956586i	$-0.594137\pi$
$151$	−88.0177			−0.582899			−0.291449	+	0.956586i	$0.594137\pi$
$152$		−	86.4866i		−	0.568991i
$153$	−0.610640	−	7.22507i	−0.00399111	−	0.0472227i
$154$		0			0
$155$		−	137.965i		−	0.890098i
$156$	11.0197	+	261.233i	0.0706389	+	1.67457i
$157$	−7.65530			−0.0487598			−0.0243799	−	0.999703i	$-0.507761\pi$
$157$	−7.65530			−0.0487598			−0.0243799	+	0.999703i	$0.507761\pi$
$158$		−	300.646i		−	1.90282i
$159$	52.9792	−	2.23484i	0.333203	−	0.0140556i
$160$	−287.222			−1.79514
$161$			83.6879i			0.519800i
$162$	−41.6030	−	244.364i	−0.256809	−	1.50842i
$163$	262.547			1.61072			0.805359	−	0.592788i	$-0.201973\pi$
$163$	262.547			1.61072			0.805359	+	0.592788i	$0.201973\pi$
$164$		−	71.7464i		−	0.437478i
$165$		0			0
$166$	97.6240			0.588096
$167$		−	160.006i		−	0.958122i	−0.877782	−	0.479061i	$-0.840977\pi$
$167$		−	160.006i		−	0.958122i	0.877782	−	0.479061i	$-0.159023\pi$
$168$	−38.3548	+	1.61793i	−0.228302	+	0.00963054i
$169$	94.8889			0.561473
$170$			16.3692i			0.0962892i
$171$	185.654	−	15.6909i	1.08570	−	0.0917597i
$172$	232.915			1.35416
$173$			165.524i			0.956785i	0.878146	+	0.478392i	$0.158780\pi$
$173$			165.524i			0.956785i	−0.878146	+	0.478392i	$0.841220\pi$
$174$	1.46363	+	34.6971i	0.00841169	+	0.199408i
$175$	−58.4435			−0.333963
$176$		0			0
$177$	−130.461	+	5.50325i	−0.737065	+	0.0310918i
$178$	56.7398			0.318763
$179$			58.5371i			0.327023i	0.986541	+	0.163511i	$0.0522820\pi$
$179$			58.5371i			0.327023i	−0.986541	+	0.163511i	$0.947718\pi$
$180$	26.9989	+	319.450i	0.149994	+	1.77472i
$181$	284.678			1.57281			0.786403	−	0.617713i	$-0.211941\pi$
$181$	284.678			1.57281			0.786403	+	0.617713i	$0.211941\pi$
$182$			152.269i			0.836643i
$183$	−1.34716	−	31.9358i	−0.00736151	−	0.174513i
$184$	−114.146			−0.620357
$185$			255.970i			1.38362i
$186$	−190.607	+	8.04041i	−1.02477	+	0.0432280i
$187$		0			0
$188$		−	106.715i		−	0.567631i
$189$	−10.4316	−	82.0398i	−0.0551939	−	0.434073i
$190$	−420.619			−2.21379
$191$			137.443i			0.719595i	0.933031	+	0.359797i	$0.117154\pi$
$191$			137.443i			0.719595i	−0.933031	+	0.359797i	$0.882846\pi$
$192$	12.3512	+	292.798i	0.0643291	+	1.52499i
$193$	−298.094			−1.54453			−0.772265	−	0.635300i	$-0.780876\pi$
$193$	−298.094			−1.54453			−0.772265	+	0.635300i	$0.780876\pi$
$194$			193.720i			0.998556i
$195$	323.273	−	13.6367i	1.65781	−	0.0699318i
$196$	212.558			1.08448
$197$			58.1375i			0.295114i	0.989054	+	0.147557i	$0.0471410\pi$
$197$			58.1375i			0.295114i	−0.989054	+	0.147557i	$0.952859\pi$
$198$		0			0
$199$	−125.049			−0.628385			−0.314193	−	0.949359i	$-0.601734\pi$
$199$	−125.049			−0.628385			−0.314193	+	0.949359i	$0.601734\pi$
$200$		−	79.7138i		−	0.398569i
$201$	9.14095	+	216.696i	0.0454774	+	1.07809i
$202$	460.136			2.27790
$203$			11.5863i			0.0570752i
$204$	12.9558	−	0.546516i	0.0635086	−	0.00267900i
$205$	−88.7853			−0.433099
$206$			458.326i			2.22489i
$207$	−20.7090	−	245.028i	−0.100043	−	1.18371i
$208$	140.934			0.677566
$209$		0			0
$210$	7.86865	+	186.535i	0.0374698	+	0.888262i
$211$	48.3927			0.229349			0.114675	−	0.993403i	$-0.463417\pi$
$211$	48.3927			0.229349			0.114675	+	0.993403i	$0.463417\pi$
$212$			94.8316i			0.447319i
$213$	−7.70284	+	0.324931i	−0.0361636	+	0.00152550i
$214$	63.5048			0.296752
$215$		−	288.230i		−	1.34060i
$216$	111.898	−	14.2282i	0.518046	−	0.0658713i
$217$	−63.6486			−0.293312
$218$		−	323.755i		−	1.48512i
$219$	5.75021	+	136.315i	0.0262567	+	0.622444i
$220$		0			0
$221$		−	13.0875i		−	0.0592193i
$222$	353.637	−	14.9176i	1.59296	−	0.0671962i
$223$	211.716			0.949401			0.474701	−	0.880147i	$-0.342556\pi$
$223$	211.716			0.949401			0.474701	+	0.880147i	$0.342556\pi$
$224$			132.507i			0.591548i
$225$	171.115	−	14.4621i	0.760513	−	0.0642762i
$226$	406.307			1.79782
$227$		−	121.385i		−	0.534736i	−0.963594	−	0.267368i	$-0.913846\pi$
$227$		−	121.385i		−	0.534736i	0.963594	−	0.267368i	$-0.0861540\pi$
$228$	14.0432	+	332.909i	0.0615929	+	1.46013i
$229$	322.944			1.41023			0.705117	−	0.709091i	$-0.250894\pi$
$229$	322.944			1.41023			0.705117	+	0.709091i	$0.250894\pi$
$230$			555.137i			2.41364i
$231$		0			0
$232$	−15.8030			−0.0681166
$233$			402.409i			1.72708i	0.504282	+	0.863539i	$0.331757\pi$
$233$			402.409i			1.72708i	−0.504282	+	0.863539i	$0.668243\pi$
$234$	−37.6798	−	445.826i	−0.161025	−	1.90524i
$235$	−132.058			−0.561949
$236$		−	233.521i		−	0.989497i
$237$	12.4215	+	294.465i	0.0524113	+	1.24247i
$238$	7.55173			0.0317299
$239$		−	0.321443i		−	0.00134495i	−1.00000		0.000672476i	$-0.999786\pi$
$239$		−	0.321443i		−	0.00134495i	1.00000		0.000672476i	$-0.000214056\pi$
$240$	172.649	−	7.28289i	0.719370	−	0.0303454i
$241$	−290.799			−1.20664			−0.603318	−	0.797500i	$-0.706155\pi$
$241$	−290.799			−1.20664			−0.603318	+	0.797500i	$0.706155\pi$
$242$		0			0
$243$	50.8438	+	237.621i	0.209234	+	0.977866i
$244$	57.1643			0.234280
$245$		−	263.038i		−	1.07362i
$246$	5.17428	+	122.662i	0.0210337	+	0.498626i
$247$	336.293			1.36151
$248$		−	86.8133i		−	0.350054i
$249$	−95.6168	+	4.03343i	−0.384003	+	0.0161985i
$250$	120.270			0.481081
$251$		−	112.621i		−	0.448691i	−0.974510	−	0.224345i	$-0.927976\pi$
$251$		−	112.621i		−	0.448691i	0.974510	−	0.224345i	$-0.0720244\pi$
$252$	147.375	−	12.4557i	0.584821	−	0.0494272i
$253$		0			0
$254$		−	448.803i		−	1.76694i
$255$	−0.676307	−	16.0326i	−0.00265219	−	0.0628730i
$256$	5.45390			0.0213043
$257$			196.568i			0.764858i	0.923985	+	0.382429i	$0.124912\pi$
$257$			196.568i			0.764858i	−0.923985	+	0.382429i	$0.875088\pi$
$258$	−398.206	+	16.7976i	−1.54343	+	0.0651071i
$259$	118.089			0.455942
$260$			578.651i			2.22558i
$261$	−2.86708	−	33.9232i	−0.0109850	−	0.129974i
$262$	−457.407			−1.74583
$263$		−	378.327i		−	1.43850i	−0.694749	−	0.719252i	$-0.744485\pi$
$263$		−	378.327i		−	1.43850i	0.694749	−	0.719252i	$-0.255515\pi$
$264$		0			0
$265$	117.353			0.442842
$266$			194.048i			0.729503i
$267$	−55.5732	+	2.34426i	−0.208139	+	0.00877999i
$268$	−387.881			−1.44732
$269$			201.154i			0.747785i	0.927472	+	0.373892i	$0.121977\pi$
$269$			201.154i			0.747785i	−0.927472	+	0.373892i	$0.878023\pi$
$270$	−69.1975	−	544.205i	−0.256287	−	2.01557i
$271$	−80.2146			−0.295995			−0.147997	−	0.988988i	$-0.547283\pi$
$271$	−80.2146			−0.295995			−0.147997	+	0.988988i	$0.547283\pi$
$272$		−	6.98956i		−	0.0256969i
$273$	−6.29114	−	149.138i	−0.0230445	−	0.546294i
$274$	−465.792			−1.69997
$275$		0			0
$276$	439.376	−	18.5343i	1.59194	−	0.0671533i
$277$	−218.915			−0.790306			−0.395153	−	0.918615i	$-0.629308\pi$
$277$	−218.915			−0.790306			−0.395153	+	0.918615i	$0.629308\pi$
$278$			342.245i			1.23110i
$279$	186.356	−	15.7502i	0.667941	−	0.0564523i
$280$	−84.9588			−0.303424
$281$			496.437i			1.76668i	0.468733	+	0.883340i	$0.344711\pi$
$281$			496.437i			1.76668i	−0.468733	+	0.883340i	$0.655289\pi$
$282$	7.69615	+	182.446i	0.0272913	+	0.646971i
$283$	307.702			1.08729			0.543643	−	0.839317i	$-0.317045\pi$
$283$	307.702			1.08729			0.543643	+	0.839317i	$0.317045\pi$
$284$		−	13.7879i		−	0.0485490i
$285$	411.971	−	17.3783i	1.44551	−	0.0609764i
$286$		0			0
$287$			40.9601i			0.142718i
$288$	−32.7895	−	387.964i	−0.113852	−	1.34710i
$289$	288.351			0.997754
$290$			76.8566i			0.265023i
$291$	−8.00372	−	189.737i	−0.0275042	−	0.652017i
$292$	−244.001			−0.835620
$293$			339.698i			1.15938i	0.814837	+	0.579690i	$0.196826\pi$
$293$			339.698i			1.15938i	−0.814837	+	0.579690i	$0.803174\pi$
$294$	−363.402	+	15.3295i	−1.23606	+	0.0521411i
$295$	−288.980			−0.979593
$296$			161.067i			0.544145i
$297$		0			0
$298$	−794.734			−2.66689
$299$		−	443.843i		−	1.48442i
$300$	12.9435	+	306.839i	0.0431448	+	1.02280i
$301$	−132.972			−0.441766
$302$			269.357i			0.891909i
$303$	−450.675	+	19.0109i	−1.48738	+	0.0627424i
$304$	179.603			0.590798
$305$		−	70.7402i		−	0.231935i
$306$	−22.1106	+	1.86871i	−0.0722567	+	0.00610691i
$307$	396.129			1.29032			0.645161	−	0.764047i	$-0.276790\pi$
$307$	396.129			1.29032			0.645161	+	0.764047i	$0.276790\pi$
$308$		0			0
$309$	−18.9362	−	448.903i	−0.0612821	−	1.45276i
$310$	−422.208			−1.36196
$311$		−	87.0358i		−	0.279858i	−0.990162	−	0.139929i	$-0.955313\pi$
$311$		−	87.0358i		−	0.279858i	0.990162	−	0.139929i	$-0.0446874\pi$
$312$	203.417	−	8.58078i	0.651977	−	0.0275025i
$313$	−598.914			−1.91346			−0.956731	−	0.290973i	$-0.906021\pi$
$313$	−598.914			−1.91346			−0.956731	+	0.290973i	$0.906021\pi$
$314$			23.4272i			0.0746088i
$315$	−15.4137	−	182.375i	−0.0489325	−	0.578967i
$316$	−527.085			−1.66799
$317$		−	2.45490i		−	0.00774416i	−0.999993	−	0.00387208i	$-0.998767\pi$
$317$		−	2.45490i		−	0.00774416i	0.999993	−	0.00387208i	$-0.00123252\pi$
$318$	−6.83917	−	162.130i	−0.0215068	−	0.509843i
$319$		0			0
$320$			648.571i			2.02678i
$321$	−62.1992	+	2.62376i	−0.193767	+	0.00817371i
$322$	256.106			0.795361
$323$		−	16.6783i		−	0.0516357i
$324$	−428.413	+	72.9373i	−1.32226	+	0.225115i
$325$	309.958			0.953717
$326$		−	803.461i		−	2.46460i
$327$	13.3762	+	317.099i	0.0409059	+	0.969720i
$328$	−55.8674			−0.170327
$329$			60.9235i			0.185178i
$330$		0			0
$331$	368.074			1.11200			0.556002	−	0.831181i	$-0.312335\pi$
$331$	368.074			1.11200			0.556002	+	0.831181i	$0.312335\pi$
$332$		−	171.152i		−	0.515518i
$333$	−345.750	+	29.2217i	−1.03829	+	0.0877529i
$334$	−489.660			−1.46605
$335$			479.999i			1.43283i
$336$	−3.35988	−	79.6496i	−0.00999963	−	0.237052i
$337$	−591.880			−1.75632			−0.878160	−	0.478368i	$-0.841229\pi$
$337$	−591.880			−1.75632			−0.878160	+	0.478368i	$0.841229\pi$
$338$		−	290.384i		−	0.859125i
$339$	−397.953	+	16.7869i	−1.17390	+	0.0495190i
$340$	28.6980			0.0844059
$341$		0			0
$342$	−48.0182	−	568.149i	−0.140404	−	1.66125i
$343$	−271.435			−0.791357
$344$		−	181.366i		−	0.527227i
$345$	−22.9360	−	543.723i	−0.0664812	−	1.57601i
$346$	506.545			1.46400
$347$		−	294.601i		−	0.848994i	−0.905429	−	0.424497i	$-0.860451\pi$
$347$		−	294.601i		−	0.848994i	0.905429	−	0.424497i	$-0.139549\pi$
$348$	60.8300	−	2.56601i	0.174799	−	0.00737358i
$349$	−412.008			−1.18054			−0.590269	−	0.807206i	$-0.700979\pi$
$349$	−412.008			−1.18054			−0.590269	+	0.807206i	$0.700979\pi$
$350$			178.852i			0.511005i
$351$	55.3248	+	435.102i	0.157620	+	1.23961i
$352$		0			0
$353$		−	135.577i		−	0.384070i	−0.981388	−	0.192035i	$-0.938491\pi$
$353$		−	135.577i		−	0.384070i	0.981388	−	0.192035i	$-0.0615086\pi$
$354$	16.8413	+	399.242i	0.0475744	+	1.12780i
$355$	−17.0624			−0.0480630
$356$		−	99.4748i		−	0.279424i
$357$	−7.39646	+	0.312007i	−0.0207184	+	0.000873968i
$358$	179.138			0.500386
$359$		−	278.775i		−	0.776533i	−0.921547	−	0.388267i	$-0.873074\pi$
$359$		−	278.775i		−	0.776533i	0.921547	−	0.388267i	$-0.126926\pi$
$360$	248.749	−	21.0235i	0.690970	−	0.0583986i
$361$	67.5639			0.187158
$362$		−	871.187i		−	2.40659i
$363$		0			0
$364$	266.954			0.733391
$365$			301.948i			0.827256i
$366$	−97.7317	+	4.12264i	−0.267026	+	0.0112640i
$367$	−176.388			−0.480620			−0.240310	−	0.970696i	$-0.577249\pi$
$367$	−176.388			−0.480620			−0.240310	+	0.970696i	$0.577249\pi$
$368$		−	237.041i		−	0.644133i
$369$	−10.1358	−	119.926i	−0.0274683	−	0.325003i
$370$	783.333			2.11712
$371$		−	54.1395i		−	0.145929i
$372$	14.0962	+	334.167i	0.0378931	+	0.898298i
$373$	−163.109			−0.437289			−0.218645	−	0.975805i	$-0.570164\pi$
$373$	−163.109			−0.437289			−0.218645	+	0.975805i	$0.570164\pi$
$374$		0			0
$375$	−117.797	+	4.96908i	−0.314126	+	0.0132509i
$376$	−83.0964			−0.221001
$377$		−	61.4484i		−	0.162993i
$378$	−251.063	+	31.9235i	−0.664187	+	0.0844537i
$379$	53.2306			0.140450			0.0702250	−	0.997531i	$-0.477628\pi$
$379$	53.2306			0.140450			0.0702250	+	0.997531i	$0.477628\pi$
$380$			737.419i			1.94058i
$381$	18.5427	+	439.575i	0.0486685	+	1.15374i
$382$	420.609			1.10107
$383$			89.6653i			0.234113i	0.993125	+	0.117057i	$0.0373459\pi$
$383$			89.6653i			0.234113i	−0.993125	+	0.117057i	$0.962654\pi$
$384$	377.369	−	15.9187i	0.982733	−	0.0414549i
$385$		0			0
$386$			912.245i			2.36333i
$387$	389.325	−	32.9045i	1.00601	−	0.0850246i
$388$	339.625			0.875322
$389$			269.601i			0.693062i	0.938038	+	0.346531i	$0.112640\pi$
$389$			269.601i			0.693062i	−0.938038	+	0.346531i	$0.887360\pi$
$390$	−41.7318	−	989.298i	−0.107005	−	2.53666i
$391$	−22.0122			−0.0562972
$392$		−	165.514i		−	0.422230i
$393$	448.002	−	18.8982i	1.13995	−	0.0480870i
$394$	177.916			0.451562
$395$			652.262i			1.65130i
$396$		0			0
$397$	211.490			0.532720			0.266360	−	0.963874i	$-0.414179\pi$
$397$	211.490			0.532720			0.266360	+	0.963874i	$0.414179\pi$
$398$			382.681i			0.961509i
$399$	−8.01727	−	190.058i	−0.0200934	−	0.476336i
$400$	165.538			0.413844
$401$		−	449.798i		−	1.12169i	−0.827920	−	0.560846i	$-0.810476\pi$
$401$		−	449.798i		−	1.12169i	0.827920	−	0.560846i	$-0.189524\pi$
$402$	663.146	−	27.9736i	1.64962	−	0.0695861i
$403$	337.564			0.837628
$404$		−	806.698i		−	1.99678i
$405$	90.2591	+	530.157i	0.222862	+	1.30903i
$406$	35.4569			0.0873323
$407$		0			0
$408$	−0.425560	−	10.0884i	−0.00104304	−	0.0247264i
$409$	154.294			0.377247			0.188623	−	0.982049i	$-0.439597\pi$
$409$	154.294			0.377247			0.188623	+	0.982049i	$0.439597\pi$
$410$			271.706i			0.662697i
$411$	456.215	−	19.2446i	1.11001	−	0.0468239i
$412$	803.526			1.95031
$413$			133.318i			0.322803i
$414$	−749.848	+	63.3748i	−1.81123	+	0.153079i
$415$	−211.798			−0.510358
$416$		−	702.757i		−	1.68932i
$417$	−14.1402	−	335.209i	−0.0339093	−	0.803858i
$418$		0			0
$419$			755.530i			1.80317i	0.432599	+	0.901587i	$0.357597\pi$
$419$			755.530i			1.80317i	−0.432599	+	0.901587i	$0.642403\pi$
$420$	327.028	−	13.7951i	0.778639	−	0.0328455i
$421$	−436.890			−1.03774			−0.518872	−	0.854852i	$-0.673648\pi$
$421$	−436.890			−1.03774			−0.518872	+	0.854852i	$0.673648\pi$
$422$		−	148.094i		−	0.350933i
$423$	−15.0758	−	178.377i	−0.0356403	−	0.421694i
$424$	73.8433			0.174159
$425$		−	15.3722i		−	0.0361700i
$426$	0.994371	+	23.5727i	0.00233420	+	0.0553349i
$427$	−32.6352			−0.0764290
$428$		−	111.335i		−	0.260129i
$429$		0			0
$430$	−882.057			−2.05129
$431$		−	9.73407i		−	0.0225849i	−0.999936	−	0.0112924i	$-0.996405\pi$
$431$		−	9.73407i		−	0.0225849i	0.999936	−	0.0112924i	$-0.00359457\pi$
$432$	29.5470	+	232.373i	0.0683959	+	0.537900i
$433$	−59.2747			−0.136893			−0.0684466	−	0.997655i	$-0.521804\pi$
$433$	−59.2747			−0.136893			−0.0684466	+	0.997655i	$0.521804\pi$
$434$			194.781i			0.448804i
$435$	−3.17540	−	75.2764i	−0.00729978	−	0.173049i
$436$	−567.599			−1.30183
$437$		−	565.622i		−	1.29433i
$438$	417.159	−	17.5971i	0.952418	−	0.0401761i
$439$	−444.724			−1.01304			−0.506519	−	0.862229i	$-0.669068\pi$
$439$	−444.724			−1.01304			−0.506519	+	0.862229i	$0.669068\pi$
$440$		0			0
$441$	355.297	−	30.0286i	0.805662	−	0.0680920i
$442$	−40.0510			−0.0906131
$443$		−	535.351i		−	1.20847i	−0.796807	−	0.604234i	$-0.793479\pi$
$443$		−	535.351i		−	1.20847i	0.796807	−	0.604234i	$-0.206521\pi$
$444$	−26.1531	−	619.988i	−0.0589034	−	1.39637i
$445$	−123.099			−0.276627
$446$		−	647.906i		−	1.45270i
$447$	778.394	−	32.8352i	1.74137	−	0.0734568i
$448$	299.211			0.667881
$449$			769.414i			1.71362i	0.515635	+	0.856809i	$0.327556\pi$
$449$			769.414i			1.71362i	−0.515635	+	0.856809i	$0.672444\pi$
$450$	−44.2578	−	523.657i	−0.0983508	−	1.16368i
$451$		0			0
$452$		−	712.327i		−	1.57594i
$453$	−11.1287	−	263.818i	−0.0245667	−	0.582381i
$454$	−371.470			−0.818215
$455$		−	330.353i		−	0.726050i
$456$	259.229	−	10.9351i	0.568485	−	0.0239805i
$457$	−169.655			−0.371236			−0.185618	−	0.982622i	$-0.559429\pi$
$457$	−169.655			−0.371236			−0.185618	+	0.982622i	$0.559429\pi$
$458$		−	988.290i		−	2.15784i
$459$	21.5787	−	2.74381i	0.0470125	−	0.00597780i
$460$	973.252			2.11577
$461$			266.355i			0.577777i	0.957363	+	0.288888i	$0.0932857\pi$
$461$			266.355i			0.577777i	−0.957363	+	0.288888i	$0.906714\pi$
$462$		0			0
$463$	−704.848			−1.52235			−0.761175	−	0.648547i	$-0.775377\pi$
$463$	−704.848			−1.52235			−0.761175	+	0.648547i	$0.775377\pi$
$464$		−	32.8174i		−	0.0707272i
$465$	413.528	−	17.4439i	0.889307	−	0.0375138i
$466$	1231.47			2.64265
$467$			675.178i			1.44578i	0.690965	+	0.722888i	$0.257186\pi$
$467$			675.178i			1.44578i	−0.690965	+	0.722888i	$0.742814\pi$
$468$	−781.610	+	66.0592i	−1.67011	+	0.141152i
$469$	221.442			0.472158
$470$			404.131i			0.859854i
$471$	−0.967915	−	22.9455i	−0.00205502	−	0.0487165i
$472$	−181.838			−0.385250
$473$		0			0
$474$	901.138	−	38.0129i	1.90113	−	0.0801960i
$475$	395.003			0.831585
$476$		−	13.2395i		−	0.0278141i
$477$	13.3971	+	158.514i	0.0280862	+	0.332314i
$478$	−0.983699			−0.00205795
$479$			699.807i			1.46098i	0.682926	+	0.730488i	$0.260707\pi$
$479$			699.807i			1.46098i	−0.682926	+	0.730488i	$0.739293\pi$
$480$	−36.3156	−	860.902i	−0.0756575	−	1.79355i
$481$	−626.291			−1.30206
$482$			889.920i			1.84631i
$483$	−250.841	+	10.5813i	−0.519339	+	0.0219074i
$484$		0			0
$485$		−	420.282i		−	0.866560i
$486$	727.182	−	155.595i	1.49626	−	0.320154i
$487$	−653.347			−1.34157			−0.670787	−	0.741650i	$-0.734044\pi$
$487$	−653.347			−1.34157			−0.670787	+	0.741650i	$0.734044\pi$
$488$		−	44.5127i		−	0.0912145i
$489$	33.1957	+	786.941i	0.0678849	+	1.60929i
$490$	−804.963			−1.64278
$491$			61.8372i			0.125941i	0.998015	+	0.0629707i	$0.0200575\pi$
$491$			61.8372i			0.125941i	−0.998015	+	0.0629707i	$0.979943\pi$
$492$	215.048	−	9.07141i	0.437089	−	0.0184378i
$493$	−3.04751			−0.00618156
$494$		−	1029.14i		−	2.08329i
$495$		0			0
$496$	180.281			0.363470
$497$			7.87154i			0.0158381i
$498$	12.3433	+	292.612i	0.0247858	+	0.587574i
$499$	329.993			0.661309			0.330654	−	0.943752i	$-0.392731\pi$
$499$	329.993			0.661309			0.330654	+	0.943752i	$0.392731\pi$
$500$		−	210.855i		−	0.421709i
$501$	479.592	−	20.2308i	0.957270	−	0.0403808i
$502$	−344.650			−0.686554
$503$		−	347.179i		−	0.690217i	−0.938563	−	0.345109i	$-0.887842\pi$
$503$		−	347.179i		−	0.690217i	0.938563	−	0.345109i	$-0.112158\pi$
$504$	−9.69895	−	114.758i	−0.0192440	−	0.227694i
$505$	−998.280			−1.97679
$506$		0			0
$507$	11.9975	+	284.414i	0.0236637	+	0.560974i
$508$	−786.830			−1.54888
$509$			856.194i			1.68211i	0.540950	+	0.841055i	$0.318065\pi$
$509$			856.194i			1.68211i	−0.540950	+	0.841055i	$0.681935\pi$
$510$	−49.0639	+	2.06967i	−0.0962036	+	0.00405818i
$511$	139.300			0.272604
$512$		−	520.297i		−	1.01621i
$513$	70.5045	+	554.484i	0.137436	+	1.08086i
$514$	601.549			1.17033
$515$		−	994.354i		−	1.93078i
$516$	29.4492	+	698.125i	0.0570720	+	1.35295i
$517$		0			0
$518$		−	361.382i		−	0.697649i
$519$	−496.130	+	20.9284i	−0.955935	+	0.0403244i
$520$	450.584			0.866507
$521$		−	712.659i		−	1.36787i	−0.729544	−	0.683934i	$-0.760268\pi$
$521$		−	712.659i		−	1.36787i	0.729544	−	0.683934i	$-0.239732\pi$
$522$	−103.814	+	8.77400i	−0.198877	+	0.0168084i
$523$	−503.925			−0.963527			−0.481764	−	0.876301i	$-0.660004\pi$
$523$	−503.925			−0.963527			−0.481764	+	0.876301i	$0.660004\pi$
$524$			801.914i			1.53037i
$525$	−7.38943	−	175.175i	−0.0140751	−	0.333666i
$526$	−1157.78			−2.20109
$527$		−	16.7414i		−	0.0317673i
$528$		0			0
$529$	−217.513			−0.411179
$530$		−	359.130i		−	0.677604i
$531$	−32.9901	−	390.338i	−0.0621283	−	0.735100i
$532$	340.200			0.639473
$533$		−	217.234i		−	0.407568i
$534$	7.17403	+	170.068i	0.0134345	+	0.318480i
$535$	−137.776			−0.257525
$536$			302.035i			0.563498i
$537$	−175.455	+	7.40127i	−0.326732	+	0.0137826i
$538$	615.583			1.14421
$539$		0			0
$540$	−954.086	+	121.315i	−1.76683	+	0.224658i
$541$	586.637			1.08436			0.542179	−	0.840263i	$-0.317600\pi$
$541$	586.637			1.08436			0.542179	+	0.840263i	$0.317600\pi$
$542$			245.477i			0.452910i
$543$	35.9939	+	853.275i	0.0662871	+	1.57141i
$544$	−34.8530			−0.0640679
$545$			702.397i			1.28880i
$546$	−456.401	+	19.2525i	−0.835900	+	0.0352610i
$547$	−688.847			−1.25932			−0.629659	−	0.776872i	$-0.716805\pi$
$547$	−688.847			−1.25932			−0.629659	+	0.776872i	$0.716805\pi$
$548$			816.614i			1.49017i
$549$	95.5519	−	8.07575i	0.174047	−	0.0147099i
$550$		0			0
$551$		−	78.3083i		−	0.142120i
$552$	−14.4323	−	342.133i	−0.0261454	−	0.619806i
$553$	300.914			0.544148
$554$			669.935i			1.20927i
$555$	−767.228	+	32.3642i	−1.38239	+	0.0583138i
$556$	600.016			1.07917
$557$			618.806i			1.11096i	0.831529	+	0.555481i	$0.187466\pi$
$557$			618.806i			1.11096i	−0.831529	+	0.555481i	$0.812534\pi$
$558$	−48.1996	−	570.296i	−0.0863792	−	1.02204i
$559$	705.222			1.26158
$560$		−	176.430i		−	0.315053i
$561$		0			0
$562$	1519.22			2.70325
$563$		−	569.270i		−	1.01114i	−0.862787	−	0.505568i	$-0.831283\pi$
$563$		−	569.270i		−	1.01114i	0.862787	−	0.505568i	$-0.168717\pi$
$564$	319.859	−	13.4927i	0.567126	−	0.0239232i
$565$	−881.496			−1.56017
$566$		−	941.645i		−	1.66368i
$567$	244.582	−	41.6400i	0.431361	−	0.0734392i
$568$	−10.7364			−0.0189020
$569$			901.528i			1.58441i	0.610256	+	0.792204i	$0.291066\pi$
$569$			901.528i			1.58441i	−0.610256	+	0.792204i	$0.708934\pi$
$570$	−53.1820	−	1260.74i	−0.0933017	−	2.21182i
$571$	804.182			1.40837			0.704187	−	0.710014i	$-0.251312\pi$
$571$	804.182			1.40837			0.704187	+	0.710014i	$0.251312\pi$
$572$		0			0
$573$	−411.961	+	17.3779i	−0.718955	+	0.0303279i
$574$	125.348			0.218377
$575$		−	521.328i		−	0.906658i
$576$	−876.053	+	74.0413i	−1.52093	+	0.128544i
$577$	−787.100			−1.36412			−0.682062	−	0.731294i	$-0.738917\pi$
$577$	−787.100			−1.36412			−0.682062	+	0.731294i	$0.738917\pi$
$578$		−	882.427i		−	1.52669i
$579$	−37.6902	−	893.489i	−0.0650954	−	1.54316i
$580$	134.743			0.232316
$581$			97.7108i			0.168177i
$582$	−580.643	+	24.4934i	−0.997669	+	0.0420849i
$583$		0			0
$584$			189.998i			0.325340i
$585$	81.7475	+	967.233i	0.139739	+	1.65339i
$586$	1039.56			1.77400
$587$		−	182.527i		−	0.310948i	−0.987840	−	0.155474i	$-0.950309\pi$
$587$		−	182.527i		−	0.310948i	0.987840	−	0.155474i	$-0.0496906\pi$
$588$	26.8752	+	637.107i	0.0457062	+	1.08352i
$589$	430.183			0.730362
$590$			884.352i			1.49890i
$591$	−174.258	+	7.35075i	−0.294852	+	0.0124378i
$592$	−334.480			−0.565000
$593$			685.071i			1.15526i	0.816297	+	0.577632i	$0.196023\pi$
$593$			685.071i			1.15526i	−0.816297	+	0.577632i	$0.803977\pi$
$594$		0			0
$595$	−16.3837			−0.0275357
$596$			1393.31i			2.33776i
$597$	−15.8108	−	374.813i	−0.0264838	−	0.627827i
$598$	−1358.27			−2.27136
$599$		−	360.876i		−	0.602463i	−0.953551	−	0.301232i	$-0.902602\pi$
$599$		−	360.876i		−	0.602463i	0.953551	−	0.301232i	$-0.0973978\pi$
$600$	238.929	−	10.0788i	0.398215	−	0.0167980i
$601$	419.487			0.697982			0.348991	−	0.937126i	$-0.386524\pi$
$601$	419.487			0.697982			0.348991	+	0.937126i	$0.386524\pi$
$602$			406.927i			0.675958i
$603$	−648.355	+	54.7970i	−1.07522	+	0.0908739i
$604$	472.229			0.781836
$605$		0			0
$606$	58.1783	+	1379.18i	0.0960039	+	2.27588i
$607$	−1007.72			−1.66017			−0.830084	−	0.557639i	$-0.811707\pi$
$607$	−1007.72			−1.66017			−0.830084	+	0.557639i	$0.811707\pi$
$608$		−	895.576i		−	1.47299i
$609$	−34.7279	+	1.46494i	−0.0570245	+	0.00240548i
$610$	−216.483			−0.354890
$611$		−	323.111i		−	0.528823i
$612$	3.27618	+	38.7636i	0.00535324	+	0.0633393i
$613$	552.248			0.900893			0.450447	−	0.892803i	$-0.351265\pi$
$613$	552.248			0.900893			0.450447	+	0.892803i	$0.351265\pi$
$614$		−	1212.26i		−	1.97436i
$615$	−11.2258	−	266.119i	−0.0182533	−	0.432714i
$616$		0			0
$617$		−	675.556i		−	1.09490i	−0.836837	−	0.547452i	$-0.815598\pi$
$617$		−	675.556i		−	1.09490i	0.836837	−	0.547452i	$-0.184402\pi$
$618$	−1373.76	+	57.9495i	−2.22291	+	0.0937695i
$619$	−269.119			−0.434765			−0.217382	−	0.976087i	$-0.569752\pi$
$619$	−269.119			−0.434765			−0.217382	+	0.976087i	$0.569752\pi$
$620$			740.205i			1.19388i
$621$	731.813	−	93.0525i	1.17844	−	0.149843i
$622$	−266.352			−0.428218
$623$			56.7903i			0.0911562i
$624$	17.8193	+	422.426i	0.0285565	+	0.676964i
$625$	−737.946			−1.18071
$626$			1832.83i			2.92784i
$627$		0			0
$628$	41.0719			0.0654011
$629$			31.0606i			0.0493810i
$630$	−558.113	+	47.1699i	−0.885893	+	0.0748729i
$631$	93.3489			0.147938			0.0739690	−	0.997261i	$-0.476433\pi$
$631$	93.3489			0.147938			0.0739690	+	0.997261i	$0.476433\pi$
$632$			410.430i			0.649415i
$633$	6.11864	+	145.049i	0.00966609	+	0.229145i
$634$	−7.51261			−0.0118495
$635$			973.693i			1.53337i
$636$	−284.242	+	11.9902i	−0.446921	+	0.0188526i
$637$	643.584			1.01034
$638$		0			0
$639$	−1.94785	−	23.0469i	−0.00304828	−	0.0360672i
$640$	835.902			1.30610
$641$		−	14.7703i		−	0.0230425i	−0.999934	−	0.0115213i	$-0.996333\pi$
$641$		−	14.7703i		−	0.0230425i	0.999934	−	0.0115213i	$-0.00366741\pi$
$642$	8.02938	+	190.345i	0.0125068	+	0.296488i
$643$	−436.040			−0.678133			−0.339067	−	0.940762i	$-0.610111\pi$
$643$	−436.040			−0.678133			−0.339067	+	0.940762i	$0.610111\pi$
$644$		−	448.999i		−	0.697203i
$645$	863.921	−	36.4430i	1.33941	−	0.0565008i
$646$	−51.0400			−0.0790092
$647$		−	314.372i		−	0.485892i	−0.970040	−	0.242946i	$-0.921886\pi$
$647$		−	314.372i		−	0.485892i	0.970040	−	0.242946i	$-0.0781137\pi$
$648$	56.7948	+	333.596i	0.0876462	+	0.514809i
$649$		0			0
$650$		−	948.550i		−	1.45931i
$651$	−8.04756	−	190.776i	−0.0123618	−	0.293051i
$652$	−1408.61			−2.16044
$653$		−	191.919i		−	0.293904i	−0.989144	−	0.146952i	$-0.953054\pi$
$653$		−	191.919i		−	0.293904i	0.989144	−	0.146952i	$-0.0469463\pi$
$654$	970.402	−	40.9347i	1.48380	−	0.0625913i
$655$	992.359			1.51505
$656$		−	116.017i		−	0.176855i
$657$	−407.855	+	34.4706i	−0.620784	+	0.0524667i
$658$	186.441			0.283346
$659$		−	127.678i		−	0.193745i	−0.995297	−	0.0968724i	$-0.969116\pi$
$659$		−	127.678i		−	0.193745i	0.995297	−	0.0968724i	$-0.0308839\pi$
$660$		0			0
$661$	580.599			0.878364			0.439182	−	0.898398i	$-0.355268\pi$
$661$	580.599			0.878364			0.439182	+	0.898398i	$0.355268\pi$
$662$		−	1126.40i		−	1.70151i
$663$	39.2275	−	1.65474i	0.0591667	−	0.00249584i
$664$	−133.272			−0.200711
$665$		−	420.993i		−	0.633073i
$666$	89.4259	+	1058.08i	0.134273	+	1.58871i
$667$	−103.352			−0.154950
$668$			858.459i			1.28512i
$669$	26.7689	+	634.585i	0.0400132	+	0.948558i
$670$	1468.92			2.19241
$671$		0			0
$672$	−397.167	+	16.7538i	−0.591023	+	0.0249313i
$673$	546.461			0.811977			0.405989	−	0.913878i	$-0.366927\pi$
$673$	546.461			0.811977			0.405989	+	0.913878i	$0.366927\pi$
$674$			1811.30i			2.68739i
$675$	64.9832	+	511.062i	0.0962715	+	0.757128i
$676$	−509.094			−0.753098
$677$		−	29.1664i		−	0.0430819i	−0.999768	−	0.0215409i	$-0.993143\pi$
$677$		−	29.1664i		−	0.0430819i	0.999768	−	0.0215409i	$-0.00685722\pi$
$678$	51.3723	+	1217.84i	0.0757704	+	1.79622i
$679$	−193.892			−0.285556
$680$		−	22.3465i		−	0.0328625i
$681$	363.832	−	15.3476i	0.534261	−	0.0225369i
$682$		0			0
$683$		−	82.4506i		−	0.120718i	−0.998177	−	0.0603592i	$-0.980775\pi$
$683$		−	82.4506i		−	0.120718i	0.998177	−	0.0603592i	$-0.0192246\pi$
$684$	−996.064	+	84.1842i	−1.45623	+	0.123076i
$685$	1010.55			1.47526
$686$			830.661i			1.21088i
$687$	40.8321	+	967.970i	0.0594354	+	1.40898i
$688$	376.634			0.547433
$689$			287.132i			0.416737i
$690$	−1663.93	+	70.1900i	−2.41149	+	0.101725i
$691$	967.715			1.40046			0.700228	−	0.713919i	$-0.253082\pi$
$691$	967.715			1.40046			0.700228	+	0.713919i	$0.253082\pi$
$692$		−	888.061i		−	1.28333i
$693$		0			0
$694$	−901.554			−1.29907
$695$		−	742.513i		−	1.06836i
$696$	−1.99809	−	47.3670i	−0.00287083	−	0.0680561i
$697$	−10.7736			−0.0154572
$698$			1260.85i			1.80638i
$699$	−1206.16	+	50.8795i	−1.72554	+	0.0727890i
$700$	313.558			0.447941
$701$		−	314.100i		−	0.448075i	−0.974581	−	0.224037i	$-0.928076\pi$
$701$		−	314.100i		−	0.448075i	0.974581	−	0.224037i	$-0.0719237\pi$
$702$	1331.52	−	169.308i	1.89676	−	0.241179i
$703$	−798.129			−1.13532
$704$		0			0
$705$	−16.6971	−	395.822i	−0.0236838	−	0.561450i
$706$	−414.899			−0.587675
$707$			460.545i			0.651408i
$708$	699.941	−	29.5258i	0.988618	−	0.0417031i
$709$	327.352			0.461709			0.230855	−	0.972988i	$-0.425848\pi$
$709$	327.352			0.461709			0.230855	+	0.972988i	$0.425848\pi$
$710$			52.2152i			0.0735426i
$711$	−881.039	+	74.4627i	−1.23916	+	0.104730i
$712$	−77.4589			−0.108791
$713$		−	567.759i		−	0.796297i
$714$	0.954820	+	22.6351i	0.00133728	+	0.0317018i
$715$		0			0
$716$		−	314.061i		−	0.438632i
$717$	0.963473	−	0.0406424i	0.00134376	−	5.66840e-5i
$718$	−853.124			−1.18820
$719$		−	1106.21i		−	1.53853i	−0.638928	−	0.769266i	$-0.720622\pi$
$719$		−	1106.21i		−	1.53853i	0.638928	−	0.769266i	$-0.279378\pi$
$720$	43.6585	+	516.565i	0.0606368	+	0.717452i
$721$	−458.734			−0.636247
$722$		−	206.763i		−	0.286375i
$723$	−36.7679	−	871.623i	−0.0508546	−	1.20556i
$724$	−1527.34			−2.10959
$725$		−	72.1759i		−	0.0995530i
$726$		0			0
$727$	577.040			0.793727			0.396864	−	0.917878i	$-0.370099\pi$
$727$	577.040			0.793727			0.396864	+	0.917878i	$0.370099\pi$
$728$		−	207.872i		−	0.285538i
$729$	−705.802	+	182.440i	−0.968178	+	0.250261i
$730$	924.039			1.26581
$731$		−	34.9752i		−	0.0478457i
$732$	7.22770	+	171.341i	0.00987391	+	0.234072i
$733$	−619.302			−0.844886			−0.422443	−	0.906389i	$-0.638827\pi$
$733$	−619.302			−0.844886			−0.422443	+	0.906389i	$0.638827\pi$
$734$			539.791i			0.735410i
$735$	788.412	−	33.2578i	1.07267	−	0.0452487i
$736$	−1181.99			−1.60596
$737$		0			0
$738$	−367.005	+	31.0181i	−0.497297	+	0.0420299i
$739$	1119.31			1.51462			0.757311	−	0.653055i	$-0.226513\pi$
$739$	1119.31			1.51462			0.757311	+	0.653055i	$0.226513\pi$
$740$		−	1373.32i		−	1.85584i
$741$	42.5200	+	1007.98i	0.0573819	+	1.36030i
$742$	−165.681			−0.223289
$743$		−	1148.58i		−	1.54586i	−0.634489	−	0.772932i	$-0.718790\pi$
$743$		−	1148.58i		−	1.54586i	0.634489	−	0.772932i	$-0.281210\pi$
$744$	260.209	−	10.9764i	0.349743	−	0.0147533i
$745$	1724.20			2.31436
$746$			499.155i			0.669108i
$747$	−24.1791	−	286.086i	−0.0323682	−	0.382979i
$748$		0			0
$749$			63.5613i			0.0848616i
$750$	15.2066	+	360.490i	0.0202755	+	0.480654i
$751$	−273.658			−0.364391			−0.182196	−	0.983262i	$-0.558320\pi$
$751$	−273.658			−0.364391			−0.182196	+	0.983262i	$0.558320\pi$
$752$		−	172.562i		−	0.229471i
$753$	337.564	−	14.2395i	0.448292	−	0.0189104i
$754$	−188.048			−0.249400
$755$		−	584.378i		−	0.774011i
$756$	55.9674	+	440.157i	0.0740310	+	0.582218i
$757$	−558.006			−0.737128			−0.368564	−	0.929602i	$-0.620150\pi$
$757$	−558.006			−0.737128			−0.368564	+	0.929602i	$0.620150\pi$
$758$		−	162.899i		−	0.214906i
$759$		0			0
$760$	574.212			0.755543
$761$			421.755i			0.554211i	0.960839	+	0.277106i	$0.0893752\pi$
$761$			421.755i			0.554211i	−0.960839	+	0.277106i	$0.910625\pi$
$762$	1345.21	−	56.7454i	1.76537	−	0.0744691i
$763$	324.043			0.424696
$764$		−	737.401i		−	0.965185i
$765$	47.9696	−	4.05424i	0.0627053	−	0.00529966i
$766$	274.399			0.358223
$767$		−	707.057i		−	0.921847i
$768$	0.689576	+	16.3472i	0.000897886	+	0.0212854i
$769$	108.997			0.141738			0.0708692	−	0.997486i	$-0.477423\pi$
$769$	108.997			0.141738			0.0708692	+	0.997486i	$0.477423\pi$
$770$		0			0
$771$	−589.181	+	24.8536i	−0.764178	+	0.0322355i
$772$	1599.32			2.07166
$773$		−	1031.61i		−	1.33456i	−0.744808	−	0.667279i	$-0.767459\pi$
$773$		−	1031.61i		−	1.33456i	0.744808	−	0.667279i	$-0.232541\pi$
$774$	−100.696	−	1191.43i	−0.130098	−	1.53932i
$775$	396.495			0.511607
$776$		−	264.459i		−	0.340797i
$777$	14.9308	+	353.952i	0.0192160	+	0.455536i
$778$	825.048			1.06047
$779$		−	276.838i		−	0.355376i
$780$	−1734.41	+	73.1631i	−2.22360	+	0.0937988i
$781$		0			0
$782$			67.3630i			0.0861420i
$783$	101.317	−	12.8828i	0.129396	−	0.0164531i
$784$	343.715			0.438413
$785$		−	50.8260i		−	0.0647465i
$786$	−57.8333	−	1371.00i	−0.0735792	−	1.74428i
$787$	−207.427			−0.263567			−0.131783	−	0.991279i	$-0.542070\pi$
$787$	−207.427			−0.263567			−0.131783	+	0.991279i	$0.542070\pi$
$788$		−	311.917i		−	0.395834i
$789$	1133.97	−	47.8346i	1.43723	−	0.0606269i
$790$	1996.09			2.52669
$791$			406.668i			0.514119i
$792$		0			0
$793$	173.082			0.218263
$794$		−	647.213i		−	0.815129i
$795$	14.8378	+	351.746i	0.0186639	+	0.442448i
$796$	670.906			0.842847
$797$		−	222.399i		−	0.279046i	−0.990219	−	0.139523i	$-0.955443\pi$
$797$		−	222.399i		−	0.279046i	0.990219	−	0.139523i	$-0.0445569\pi$
$798$	−581.627	+	24.5349i	−0.728855	+	0.0307455i
$799$	−16.0246			−0.0200558
$800$		−	825.443i		−	1.03180i
$801$	−14.0531	−	166.275i	−0.0175444	−	0.207584i
$802$	−1376.50			−1.71633
$803$		0			0
$804$	−49.0426	−	1162.61i	−0.0609983	−	1.44603i
$805$	−555.631			−0.690225
$806$		−	1033.03i		−	1.28168i
$807$	−602.926	+	25.4334i	−0.747121	+	0.0315160i
$808$	−628.159			−0.777424
$809$			752.614i			0.930301i	0.885231	+	0.465151i	$0.154000\pi$
$809$			752.614i			0.930301i	−0.885231	+	0.465151i	$0.846000\pi$
$810$	1622.41	−	276.216i	2.00298	−	0.341007i
$811$	−232.246			−0.286369			−0.143185	−	0.989696i	$-0.545734\pi$
$811$	−232.246			−0.286369			−0.143185	+	0.989696i	$0.545734\pi$
$812$		−	62.1622i		−	0.0765544i
$813$	−10.1421	−	240.430i	−0.0124749	−	0.295732i
$814$		0			0
$815$			1743.13i			2.13881i
$816$	20.9500	−	0.883741i	0.0256741	−	0.00108302i
$817$	898.717			1.10002
$818$		−	472.179i		−	0.577236i
$819$	446.222	−	37.7133i	0.544838	−	0.0460480i
$820$	476.347			0.580911
$821$			484.963i			0.590698i	0.955389	+	0.295349i	$0.0954359\pi$
$821$			484.963i			0.590698i	−0.955389	+	0.295349i	$0.904564\pi$
$822$	−58.8935	−	1396.13i	−0.0716466	−	1.69846i
$823$	156.891			0.190633			0.0953164	−	0.995447i	$-0.469614\pi$
$823$	156.891			0.190633			0.0953164	+	0.995447i	$0.469614\pi$
$824$		−	625.689i		−	0.759331i
$825$		0			0
$826$	407.986			0.493930
$827$			157.726i			0.190721i	0.995443	+	0.0953605i	$0.0304004\pi$
$827$			157.726i			0.190721i	−0.995443	+	0.0953605i	$0.969600\pi$
$828$	111.107	+	1314.61i	0.134187	+	1.58770i
$829$	1306.62			1.57614			0.788069	−	0.615587i	$-0.211081\pi$
$829$	1306.62			1.57614			0.788069	+	0.615587i	$0.211081\pi$
$830$			648.157i			0.780912i
$831$	−27.6790	−	656.161i	−0.0333080	−	0.789604i
$832$	−1586.88			−1.90731
$833$		−	31.9183i		−	0.0383173i
$834$	−1025.82	+	43.2726i	−1.23001	+	0.0518856i
$835$	1062.33			1.27226
$836$		0			0
$837$	70.7709	+	556.579i	0.0845530	+	0.664969i
$838$	2312.11			2.75908
$839$			1283.32i			1.52959i	0.644276	+	0.764793i	$0.277159\pi$
$839$			1283.32i			1.52959i	−0.644276	+	0.764793i	$0.722841\pi$
$840$	−10.7420	−	254.650i	−0.0127880	−	0.303155i
$841$	826.691			0.982986
$842$			1337.00i			1.58788i
$843$	−1487.99	+	62.7681i	−1.76511	+	0.0744581i
$844$	−259.634			−0.307624
$845$			629.998i			0.745560i
$846$	−545.878	+	46.1359i	−0.645246	+	0.0545342i
$847$		0			0
$848$			153.347i			0.180834i
$849$	38.9050	+	922.285i	0.0458245	+	1.08632i
$850$	−47.0430			−0.0553447
$851$			1053.38i			1.23781i
$852$	41.3270	−	1.74331i	0.0485058	−	0.00204613i
$853$	−496.632			−0.582218			−0.291109	−	0.956690i	$-0.594024\pi$
$853$	−496.632			−0.582218			−0.291109	+	0.956690i	$0.594024\pi$
$854$			99.8720i			0.116946i
$855$	104.177	+	1232.62i	0.121844	+	1.44166i
$856$	−86.6942			−0.101278
$857$		−	479.970i		−	0.560059i	−0.959991	−	0.280029i	$-0.909656\pi$
$857$		−	479.970i		−	0.560059i	0.959991	−	0.280029i	$-0.0903442\pi$
$858$		0			0
$859$	658.810			0.766950			0.383475	−	0.923551i	$-0.374727\pi$
$859$	658.810			0.766950			0.383475	+	0.923551i	$0.374727\pi$
$860$			1546.40i			1.79814i
$861$	−122.771	+	5.17888i	−0.142591	+	0.00601496i
$862$	−29.7887			−0.0345577
$863$		−	538.814i		−	0.624350i	−0.950025	−	0.312175i	$-0.898942\pi$
$863$		−	538.814i		−	0.624350i	0.950025	−	0.312175i	$-0.101058\pi$
$864$	1158.71	−	147.334i	1.34110	−	0.170526i
$865$	−1098.97			−1.27048
$866$			181.396i			0.209464i
$867$	36.4583	+	864.284i	0.0420511	+	0.996868i
$868$	341.485			0.393416
$869$		0			0
$870$	−230.365	+	9.71754i	−0.264787	+	0.0111696i
$871$	−1174.43			−1.34837
$872$			441.977i			0.506855i
$873$	567.693	−	47.9796i	0.650279	−	0.0549595i
$874$	−1730.95			−1.98049
$875$			120.377i			0.137574i
$876$	−30.8508	−	731.352i	−0.0352178	−	0.834877i
$877$	−84.7147			−0.0965961			−0.0482980	−	0.998833i	$-0.515380\pi$
$877$	−84.7147			−0.0965961			−0.0482980	+	0.998833i	$0.515380\pi$
$878$			1360.97i			1.55008i
$879$	−1018.19	+	42.9505i	−1.15835	+	0.0488629i
$880$		0			0
$881$			364.734i			0.414000i	0.978341	+	0.207000i	$0.0663701\pi$
$881$			364.734i			0.414000i	−0.978341	+	0.207000i	$0.933630\pi$
$882$	−91.8951	−	1087.30i	−0.104189	−	1.23277i
$883$	222.790			0.252310			0.126155	−	0.992011i	$-0.459736\pi$
$883$	222.790			0.252310			0.126155	+	0.992011i	$0.459736\pi$
$884$			70.2164i			0.0794303i
$885$	−36.5378	−	866.169i	−0.0412857	−	0.978723i
$886$	−1638.31			−1.84911
$887$		−	1363.47i		−	1.53717i	−0.639750	−	0.768583i	$-0.720962\pi$
$887$		−	1363.47i		−	1.53717i	0.639750	−	0.768583i	$-0.279038\pi$
$888$	−482.771	+	20.3649i	−0.543661	+	0.0229334i
$889$	449.202			0.505289
$890$			376.714i			0.423274i
$891$		0			0
$892$	−1135.89			−1.27342
$893$		−	411.764i		−	0.461102i
$894$	−100.484	−	2382.08i	−0.112398	−	2.66452i
$895$	−388.646			−0.434242
$896$		−	385.634i		−	0.430395i
$897$	1330.35	−	56.1183i	1.48311	−	0.0625622i
$898$	2354.60			2.62205
$899$		−	78.6041i		−	0.0874351i
$900$	−918.062	+	77.5917i	−1.02007	+	0.0862130i
$901$	14.2402			0.0158049
$902$		0			0
$903$	−16.8126	−	398.560i	−0.0186186	−	0.441373i
$904$	−554.674			−0.613577
$905$			1890.07i			2.08847i
$906$	−807.352	+	34.0567i	−0.891117	+	0.0375902i
$907$	657.241			0.724632			0.362316	−	0.932055i	$-0.381986\pi$
$907$	657.241			0.724632			0.362316	+	0.932055i	$0.381986\pi$
$908$			651.251i			0.717237i
$909$	−113.964	−	1348.42i	−0.125373	−	1.48341i
$910$	−1010.96			−1.11095
$911$			348.442i			0.382483i	0.981543	+	0.191241i	$0.0612513\pi$
$911$			348.442i			0.382483i	−0.981543	+	0.191241i	$0.938749\pi$
$912$	22.7085	+	538.329i	0.0248996	+	0.590273i
$913$		0			0
$914$			519.188i			0.568039i
$915$	212.032	−	8.94420i	0.231729	−	0.00977508i
$916$	−1732.64			−1.89153
$917$		−	457.814i		−	0.499251i
$918$	−8.39676	−	66.0364i	−0.00914680	−	0.0719351i
$919$	−639.410			−0.695767			−0.347883	−	0.937538i	$-0.613099\pi$
$919$	−639.410			−0.695767			−0.347883	+	0.937538i	$0.613099\pi$
$920$		−	757.851i		−	0.823751i
$921$	50.0855	+	1187.33i	0.0543816	+	1.28918i
$922$	815.115			0.884072
$923$		−	41.7471i		−	0.0452298i
$924$		0			0
$925$	−735.627			−0.795272
$926$			2157.01i			2.32939i
$927$	1343.12	−	113.516i	1.44889	−	0.122455i
$928$	−163.642			−0.176338
$929$			314.446i			0.338478i	0.985575	+	0.169239i	$0.0541310\pi$
$929$			314.446i			0.338478i	−0.985575	+	0.169239i	$0.945869\pi$
$930$	−53.3829	−	1265.50i	−0.0574010	−	1.36075i
$931$	820.167			0.880953
$932$		−	2158.99i		−	2.31651i
$933$	260.875	−	11.0046i	0.279609	−	0.0117948i
$934$	2066.22			2.21222
$935$		0			0
$936$	51.4389	+	608.623i	0.0549561	+	0.650238i
$937$	−1520.09			−1.62230			−0.811150	−	0.584839i	$-0.801158\pi$
$937$	−1520.09			−1.62230			−0.811150	+	0.584839i	$0.801158\pi$
$938$		−	677.669i		−	0.722461i
$939$	−75.7250	−	1795.14i	−0.0806443	−	1.91176i
$940$	708.512			0.753737
$941$		−	1122.30i		−	1.19267i	−0.802735	−	0.596336i	$-0.796623\pi$
$941$		−	1122.30i		−	1.19267i	0.802735	−	0.596336i	$-0.203377\pi$
$942$	−70.2190	+	2.96207i	−0.0745425	+	0.00314444i
$943$	−365.373			−0.387458
$944$		−	377.614i		−	0.400015i
$945$	544.689	−	69.2591i	0.576390	−	0.0732900i
$946$		0			0
$947$		−	865.333i		−	0.913762i	−0.889528	−	0.456881i	$-0.848967\pi$
$947$		−	865.333i		−	0.913762i	0.889528	−	0.456881i	$-0.151033\pi$
$948$	−66.6432	−	1579.85i	−0.0702988	−	1.66651i
$949$	−738.787			−0.778490
$950$		−	1208.81i		−	1.27243i
$951$	7.35815	−	0.310391i	0.00773728	−	0.000326383i
$952$	−10.3093			−0.0108291
$953$		−	507.196i		−	0.532210i	−0.963944	−	0.266105i	$-0.914263\pi$
$953$		−	507.196i		−	0.532210i	0.963944	−	0.266105i	$-0.0857368\pi$
$954$	485.093	−	40.9985i	0.508483	−	0.0429754i
$955$	−912.526			−0.955524
$956$			1.72460i			0.00180397i
$957$		0			0
$958$	2141.59			2.23548
$959$		−	466.206i		−	0.486138i
$960$	−1943.98	+	82.0035i	−2.02498	+	0.0854203i
$961$	−529.192			−0.550668
$962$			1916.61i			1.99232i
$963$	−15.7286	−	186.100i	−0.0163329	−	0.193250i
$964$	1560.19			1.61845
$965$		−	1979.14i		−	2.05093i
$966$	32.3814	+	767.636i	0.0335211	+	0.794654i
$967$	569.116			0.588537			0.294269	−	0.955723i	$-0.404924\pi$
$967$	569.116			0.588537			0.294269	+	0.955723i	$0.404924\pi$
$968$		0			0
$969$	49.9906	−	2.10876i	0.0515899	−	0.00217623i
$970$	−1286.17			−1.32595
$971$		−	1253.34i		−	1.29077i	−0.763856	−	0.645386i	$-0.776696\pi$
$971$		−	1253.34i		−	1.29077i	0.763856	−	0.645386i	$-0.223304\pi$
$972$	−272.785	−	1274.88i	−0.280643	−	1.31160i
$973$	−342.550			−0.352055
$974$			1999.41i			2.05278i
$975$	39.1902	+	929.048i	0.0401951	+	0.952869i
$976$	92.4373			0.0947103
$977$		−	1141.65i		−	1.16852i	−0.811566	−	0.584261i	$-0.801384\pi$
$977$		−	1141.65i		−	1.16852i	0.811566	−	0.584261i	$-0.198616\pi$
$978$	2408.24	−	101.587i	2.46241	−	0.103873i
$979$		0			0
$980$			1411.24i			1.44004i
$981$	−948.759	+	80.1862i	−0.967135	+	0.0817392i
$982$	189.238			0.192706
$983$			665.261i			0.676766i	0.941008	+	0.338383i	$0.109880\pi$
$983$			665.261i			0.676766i	−0.941008	+	0.338383i	$0.890120\pi$
$984$	−7.06372	−	167.453i	−0.00717858	−	0.170176i
$985$	−385.994			−0.391872
$986$			9.32615i			0.00945857i
$987$	−182.608	+	7.70300i	−0.185013	+	0.00780446i
$988$	−1804.27			−1.82618
$989$		−	1186.13i		−	1.19933i
$990$		0			0
$991$	−1471.97			−1.48534			−0.742670	−	0.669658i	$-0.766441\pi$
$991$	−1471.97			−1.48534			−0.742670	+	0.669658i	$0.766441\pi$
$992$		−	898.959i		−	0.906209i
$993$	46.5382	+	1103.24i	0.0468663	+	1.11102i
$994$	24.0889			0.0242343
$995$		−	830.238i		−	0.834410i
$996$	512.999	−	21.6400i	0.515060	−	0.0217269i
$997$	−620.792			−0.622660			−0.311330	−	0.950302i	$-0.600775\pi$
$997$	−620.792			−0.622660			−0.311330	+	0.950302i	$0.600775\pi$
$998$		−	1009.86i		−	1.01189i
$999$	−131.303	−	1032.63i	−0.131434	−	1.03367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.l.122.2		8
3.2	odd	2	inner	363.3.b.l.122.7		8
11.2	odd	10		363.3.h.o.323.4		16
11.3	even	5		363.3.h.j.251.1		16
11.4	even	5		363.3.h.j.269.4		16
11.5	even	5		363.3.h.n.245.4		16
11.6	odd	10		363.3.h.o.245.1		16
11.7	odd	10		33.3.h.b.5.1	✓	16
11.8	odd	10		33.3.h.b.20.4	yes	16
11.9	even	5		363.3.h.n.323.1		16
11.10	odd	2		363.3.b.m.122.7		8
33.2	even	10		363.3.h.o.323.1		16
33.5	odd	10		363.3.h.n.245.1		16
33.8	even	10		33.3.h.b.20.1	yes	16
33.14	odd	10		363.3.h.j.251.4		16
33.17	even	10		363.3.h.o.245.4		16
33.20	odd	10		363.3.h.n.323.4		16
33.26	odd	10		363.3.h.j.269.1		16
33.29	even	10		33.3.h.b.5.4	yes	16
33.32	even	2		363.3.b.m.122.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.1	✓	16	11.7	odd	10
33.3.h.b.5.4	yes	16	33.29	even	10
33.3.h.b.20.1	yes	16	33.8	even	10
33.3.h.b.20.4	yes	16	11.8	odd	10
363.3.b.l.122.2		8	1.1	even	1	trivial
363.3.b.l.122.7		8	3.2	odd	2	inner
363.3.b.m.122.2		8	33.32	even	2
363.3.b.m.122.7		8	11.10	odd	2
363.3.h.j.251.1		16	11.3	even	5
363.3.h.j.251.4		16	33.14	odd	10
363.3.h.j.269.1		16	33.26	odd	10
363.3.h.j.269.4		16	11.4	even	5
363.3.h.n.245.1		16	33.5	odd	10
363.3.h.n.245.4		16	11.5	even	5
363.3.h.n.323.1		16	11.9	even	5
363.3.h.n.323.4		16	33.20	odd	10
363.3.h.o.245.1		16	11.6	odd	10
363.3.h.o.245.4		16	33.17	even	10
363.3.h.o.323.1		16	33.2	even	10
363.3.h.o.323.4		16	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.06025i q^{2} +(0.126437 + 2.99733i) q^{3} -5.36516 q^{4} +6.63932i q^{5} +(9.17261 - 0.386930i) q^{6} +3.06298 q^{7} +4.17774i q^{8} +(-8.96803 + 0.757950i) q^{9} +O(q^{10})\)	\(q-3.06025i q^{2} +(0.126437 + 2.99733i) q^{3} -5.36516 q^{4} +6.63932i q^{5} +(9.17261 - 0.386930i) q^{6} +3.06298 q^{7} +4.17774i q^{8} +(-8.96803 + 0.757950i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} -16.2447 q^{13} -9.37349i q^{14} +(-19.9003 + 0.839458i) q^{15} -8.67570 q^{16} +0.805648i q^{17} +(2.31952 + 27.4444i) q^{18} -20.7018 q^{19} -35.6210i q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(-12.5221 + 0.528222i) q^{24} -19.0806 q^{25} +49.7128i q^{26} +(-3.40572 - 26.7843i) q^{27} -16.4334 q^{28} +3.78268i q^{29} +(2.56896 + 60.8999i) q^{30} -20.7800 q^{31} +43.2608i q^{32} +2.46549 q^{34} +20.3361i q^{35} +(48.1149 - 4.06652i) q^{36} +38.5536 q^{37} +63.3527i q^{38} +(-2.05393 - 48.6907i) q^{39} -27.7373 q^{40} +13.3726i q^{41} +(28.0955 - 1.18516i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +83.6135 q^{46} +19.8903i q^{47} +(-1.09693 - 26.0040i) q^{48} -39.6182 q^{49} +58.3915i q^{50} +(-2.41480 + 0.101864i) q^{51} +87.1552 q^{52} -17.6754i q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(-2.61748 - 62.0502i) q^{57} +11.5760 q^{58} +43.5255i q^{59} +(106.768 - 4.50383i) q^{60} -10.6547 q^{61} +63.5921i q^{62} +(-27.4689 + 2.32158i) q^{63} +97.6863 q^{64} -107.854i q^{65} +72.2963 q^{67} -4.32243i q^{68} +(-81.8944 + 3.45457i) q^{69} +62.2336 q^{70} +2.56990i q^{71} +(-3.16651 - 37.4660i) q^{72} +45.4788 q^{73} -117.984i q^{74} +(-2.41250 - 57.1910i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +98.2423 q^{79} -57.6008i q^{80} +(79.8510 - 13.5946i) q^{81} +40.9237 q^{82} +31.9006i q^{83} +(-2.07779 - 49.2563i) q^{84} -5.34895 q^{85} +132.853i q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(-182.213 + 15.4000i) q^{90} -49.7570 q^{91} -146.589i q^{92} +(-2.62737 - 62.2846i) q^{93} +60.8693 q^{94} -137.446i q^{95} +(-129.667 + 5.46978i) q^{96} -63.3019 q^{97} +121.242i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9	\( 8 q + 5 q^{3} - 26 q^{4} - q^{6} - 28 q^{7} + 11 q^{9} + 6 q^{10} + 53 q^{12} - 44 q^{13} - 54 q^{15} - 14 q^{16} - q^{18} - 68 q^{19} + 6 q^{21} - 33 q^{24} + 42 q^{25} - 25 q^{27} + 118 q^{28} - 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} - 38 q^{39} - 58 q^{40} + 174 q^{42} + 78 q^{43} - 36 q^{45} + 286 q^{46} - 285 q^{48} - 140 q^{49} - 58 q^{51} + 102 q^{52} - 523 q^{54} + 22 q^{57} - 68 q^{58} + 262 q^{60} - 22 q^{61} - 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} - 489 q^{72} + 378 q^{73} - 33 q^{75} + 450 q^{76} - 246 q^{78} + 252 q^{79} + 11 q^{81} - 200 q^{82} - 450 q^{84} + 156 q^{85} - 66 q^{87} - 598 q^{90} - 148 q^{91} + 380 q^{93} + 460 q^{94} - 399 q^{96} - 324 q^{97}+O(q^{100}) \) 8 * q + 5 * q^3 - 26 * q^4 - q^6 - 28 * q^7 + 11 * q^9 + 6 * q^10 + 53 * q^12 - 44 * q^13 - 54 * q^15 - 14 * q^16 - q^18 - 68 * q^19 + 6 * q^21 - 33 * q^24 + 42 * q^25 - 25 * q^27 + 118 * q^28 - 10 * q^30 + 2 * q^31 - 66 * q^34 - 7 * q^36 + 140 * q^37 - 38 * q^39 - 58 * q^40 + 174 * q^42 + 78 * q^43 - 36 * q^45 + 286 * q^46 - 285 * q^48 - 140 * q^49 - 58 * q^51 + 102 * q^52 - 523 * q^54 + 22 * q^57 - 68 * q^58 + 262 * q^60 - 22 * q^61 - 246 * q^63 - 52 * q^64 + 184 * q^67 - 176 * q^69 + 374 * q^70 - 489 * q^72 + 378 * q^73 - 33 * q^75 + 450 * q^76 - 246 * q^78 + 252 * q^79 + 11 * q^81 - 200 * q^82 - 450 * q^84 + 156 * q^85 - 66 * q^87 - 598 * q^90 - 148 * q^91 + 380 * q^93 + 460 * q^94 - 399 * q^96 - 324 * q^97

Introduction

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