LMFDB - Embedded newform 361.3.f.k.333.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			333.11
Character	$\chi$	$=$	361.333
Dual form			361.3.f.k.116.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.496551 + 0.0875553i) q^{2} +(3.57601 + 4.26172i) q^{3} +(-3.51987 + 1.28113i) q^{4} +(-3.10600 - 1.13049i) q^{5} +(-2.14881 - 1.80306i) q^{6} +(-2.51371 + 4.35388i) q^{7} +(3.38227 - 1.95275i) q^{8} +(-3.81160 + 21.6166i) q^{9} +O(q^{10})$	\(q+(-0.496551 + 0.0875553i) q^{2} +(3.57601 + 4.26172i) q^{3} +(-3.51987 + 1.28113i) q^{4} +(-3.10600 - 1.13049i) q^{5} +(-2.14881 - 1.80306i) q^{6} +(-2.51371 + 4.35388i) q^{7} +(3.38227 - 1.95275i) q^{8} +(-3.81160 + 21.6166i) q^{9} +(1.64127 + 0.289400i) q^{10} +(-5.32930 - 9.23062i) q^{11} +(-18.0469 - 10.4194i) q^{12} +(-2.66997 + 3.18194i) q^{13} +(0.866981 - 2.38201i) q^{14} +(-6.28925 - 17.2796i) q^{15} +(9.96922 - 8.36516i) q^{16} +(-0.355036 - 2.01351i) q^{17} -11.0675i q^{18} +12.3811 q^{20} +(-27.5441 + 4.85676i) q^{21} +(3.45446 + 4.11686i) q^{22} +(-9.04706 + 3.29286i) q^{23} +(20.4171 + 7.43122i) q^{24} +(-10.7819 - 9.04706i) q^{25} +(1.04718 - 1.81377i) q^{26} +(-62.3929 + 36.0225i) q^{27} +(3.27007 - 18.5455i) q^{28} +(-26.8513 - 4.73461i) q^{29} +(4.63585 + 8.02954i) q^{30} +(26.7556 + 15.4473i) q^{31} +(-14.2594 + 16.9937i) q^{32} +(20.2807 - 55.7208i) q^{33} +(0.352586 + 0.968723i) q^{34} +(12.7296 - 10.6814i) q^{35} +(-14.2774 - 80.9710i) q^{36} +19.3174i q^{37} -23.1084 q^{39} +(-12.7129 + 2.24163i) q^{40} +(-40.9723 - 48.8289i) q^{41} +(13.2518 - 4.82326i) q^{42} +(62.6890 + 22.8169i) q^{43} +(30.5841 + 25.6631i) q^{44} +(36.2763 - 62.8324i) q^{45} +(4.20402 - 2.42719i) q^{46} +(-4.32959 + 24.5543i) q^{47} +(71.3000 + 12.5721i) q^{48} +(11.8625 + 20.5465i) q^{49} +(6.14586 + 3.54832i) q^{50} +(7.31139 - 8.71338i) q^{51} +(5.32147 - 14.6206i) q^{52} +(-21.2868 - 58.4851i) q^{53} +(27.8273 - 23.3499i) q^{54} +(6.11768 + 34.6951i) q^{55} +19.6346i q^{56} +13.7476 q^{58} +(15.5523 - 2.74229i) q^{59} +(44.2747 + 52.7646i) q^{60} +(-63.3905 + 23.0722i) q^{61} +(-14.6380 - 5.32779i) q^{62} +(-84.5349 - 70.9332i) q^{63} +(-20.4351 + 35.3947i) q^{64} +(11.8901 - 6.86475i) q^{65} +(-5.19175 + 29.4439i) q^{66} +(-56.9447 - 10.0409i) q^{67} +(3.82924 + 6.63244i) q^{68} +(-46.3856 - 26.7808i) q^{69} +(-5.38569 + 6.41842i) q^{70} +(-38.6990 + 106.325i) q^{71} +(29.3201 + 80.5563i) q^{72} +(-74.0509 + 62.1361i) q^{73} +(-1.69134 - 9.59207i) q^{74} -78.3016i q^{75} +53.5853 q^{77} +(11.4745 - 2.02326i) q^{78} +(31.7548 + 37.8439i) q^{79} +(-40.4212 + 14.7121i) q^{80} +(-190.998 - 69.5177i) q^{81} +(24.6201 + 20.6587i) q^{82} +(-48.0685 + 83.2571i) q^{83} +(90.7295 - 52.3827i) q^{84} +(-1.17351 + 6.65533i) q^{85} +(-33.1260 - 5.84102i) q^{86} +(-75.8429 - 131.364i) q^{87} +(-36.0502 - 20.8136i) q^{88} +(-31.6819 + 37.7570i) q^{89} +(-12.5117 + 34.3757i) q^{90} +(-7.14226 - 19.6232i) q^{91} +(27.6259 - 23.1809i) q^{92} +(29.8459 + 169.264i) q^{93} -12.5716i q^{94} -123.415 q^{96} +(-38.8683 + 6.85353i) q^{97} +(-7.68929 - 9.16374i) q^{98} +(219.848 - 80.0181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 24 q^{7}+O(q^{10}) $ 144 * q - 24 * q^7	$ 144 q - 24 q^{7} + 192 q^{11} + 528 q^{20} - 228 q^{26} + 1440 q^{30} + 408 q^{39} + 264 q^{45} - 336 q^{49} + 216 q^{58} + 24 q^{64} + 480 q^{68} - 144 q^{77} + 1704 q^{83} - 3216 q^{87} - 3624 q^{96}+O(q^{100}) $ 144 * q - 24 * q^7 + 192 * q^11 + 528 * q^20 - 228 * q^26 + 1440 * q^30 + 408 * q^39 + 264 * q^45 - 336 * q^49 + 216 * q^58 + 24 * q^64 + 480 * q^68 - 144 * q^77 + 1704 * q^83 - 3216 * q^87 - 3624 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.496551	+	0.0875553i	−0.248276	+	0.0437777i	−0.296401	−	0.955064i	$-0.595786\pi$
$2$	−0.496551	+	0.0875553i	−0.248276	+	0.0437777i	0.0481253	+	0.998841i	$0.484675\pi$
$3$	3.57601	+	4.26172i	1.19200	+	1.42057i	0.882910	+	0.469542i	$0.155581\pi$
$3$	3.57601	+	4.26172i	1.19200	+	1.42057i	0.309093	+	0.951032i	$0.399975\pi$
$4$	−3.51987	+	1.28113i	−0.879968	+	0.320282i
$5$	−3.10600	−	1.13049i	−0.621201	−	0.226099i	0.0121961	−	0.999926i	$-0.496118\pi$
$5$	−3.10600	−	1.13049i	−0.621201	−	0.226099i	−0.633397	+	0.773827i	$0.718340\pi$
$6$	−2.14881	−	1.80306i	−0.358135	−	0.300511i
$7$	−2.51371	+	4.35388i	−0.359102	+	0.621982i	−0.987811	−	0.155658i	$-0.950250\pi$
$7$	−2.51371	+	4.35388i	−0.359102	+	0.621982i	0.628709	+	0.777640i	$0.283584\pi$
$8$	3.38227	−	1.95275i	0.422783	−	0.244094i
$9$	−3.81160	+	21.6166i	−0.423511	+	2.40185i
$10$	1.64127	+	0.289400i	0.164127	+	0.0289400i
$11$	−5.32930	−	9.23062i	−0.484482	−	0.839147i	0.515359	−	0.856974i	$-0.327658\pi$
$11$	−5.32930	−	9.23062i	−0.484482	−	0.839147i	−0.999841	+	0.0178271i	$0.994325\pi$
$12$	−18.0469	−	10.4194i	−1.50391	−	0.868283i
$13$	−2.66997	+	3.18194i	−0.205382	+	0.244765i	−0.858896	−	0.512149i	$-0.828849\pi$
$13$	−2.66997	+	3.18194i	−0.205382	+	0.244765i	0.653514	+	0.756914i	$0.273294\pi$
$14$	0.866981	−	2.38201i	0.0619272	−	0.170144i
$15$	−6.28925	−	17.2796i	−0.419283	−	1.15197i
$16$	9.96922	−	8.36516i	0.623076	−	0.522823i
$17$	−0.355036	−	2.01351i	−0.0208844	−	0.118442i	0.972583	−	0.232555i	$-0.0747085\pi$
$17$	−0.355036	−	2.01351i	−0.0208844	−	0.118442i	−0.993468	+	0.114113i	$0.963597\pi$
$18$		−	11.0675i		−	0.614860i
$19$		0			0
$19$		0			0
$20$	12.3811			0.619053
$21$	−27.5441	+	4.85676i	−1.31162	+	0.231274i
$22$	3.45446	+	4.11686i	0.157021	+	0.187130i
$23$	−9.04706	+	3.29286i	−0.393351	+	0.143168i	−0.531120	−	0.847296i	$-0.678229\pi$
$23$	−9.04706	+	3.29286i	−0.393351	+	0.143168i	0.137770	+	0.990464i	$0.456007\pi$
$24$	20.4171	+	7.43122i	0.850712	+	0.309634i
$25$	−10.7819	−	9.04706i	−0.431274	−	0.361882i
$26$	1.04718	−	1.81377i	0.0402761	−	0.0697603i
$27$	−62.3929	+	36.0225i	−2.31085	+	1.33417i
$28$	3.27007	−	18.5455i	0.116788	−	0.662339i
$29$	−26.8513	−	4.73461i	−0.925907	−	0.163262i	−0.309689	−	0.950838i	$-0.600225\pi$
$29$	−26.8513	−	4.73461i	−0.925907	−	0.163262i	−0.616218	+	0.787576i	$0.711336\pi$
$30$	4.63585	+	8.02954i	0.154528	+	0.267651i
$31$	26.7556	+	15.4473i	0.863082	+	0.498301i	0.865043	−	0.501697i	$-0.167291\pi$
$31$	26.7556	+	15.4473i	0.863082	+	0.498301i	−0.00196095	+	0.999998i	$0.500624\pi$
$32$	−14.2594	+	16.9937i	−0.445608	+	0.531055i
$33$	20.2807	−	55.7208i	0.614567	−	1.68851i
$34$	0.352586	+	0.968723i	0.0103702	+	0.0284919i
$35$	12.7296	−	10.6814i	0.363704	−	0.305184i
$36$	−14.2774	−	80.9710i	−0.396593	−	2.24919i
$37$			19.3174i			0.522091i	0.965326	+	0.261046i	$0.0840673\pi$
$37$			19.3174i			0.522091i	−0.965326	+	0.261046i	$0.915933\pi$
$38$		0			0
$39$	−23.1084			−0.592522
$40$	−12.7129	+	2.24163i	−0.317823	+	0.0560407i
$41$	−40.9723	−	48.8289i	−0.999325	−	1.19095i	−0.981569	−	0.191107i	$-0.938792\pi$
$41$	−40.9723	−	48.8289i	−0.999325	−	1.19095i	−0.0177560	−	0.999842i	$-0.505652\pi$
$42$	13.2518	−	4.82326i	0.315519	−	0.114840i
$43$	62.6890	+	22.8169i	1.45788	+	0.530627i	0.944782	−	0.327701i	$-0.106274\pi$
$43$	62.6890	+	22.8169i	1.45788	+	0.530627i	0.513103	+	0.858327i	$0.328496\pi$
$44$	30.5841	+	25.6631i	0.695093	+	0.583252i
$45$	36.2763	−	62.8324i	0.806140	−	1.39628i
$46$	4.20402	−	2.42719i	0.0913917	−	0.0527650i
$47$	−4.32959	+	24.5543i	−0.0921190	+	0.522433i	0.903473	+	0.428645i	$0.141009\pi$
$47$	−4.32959	+	24.5543i	−0.0921190	+	0.522433i	−0.995592	+	0.0937882i	$0.970102\pi$
$48$	71.3000	+	12.5721i	1.48542	+	0.261919i
$49$	11.8625	+	20.5465i	0.242092	+	0.419316i
$50$	6.14586	+	3.54832i	0.122917	+	0.0709663i
$51$	7.31139	−	8.71338i	0.143361	−	0.170851i
$52$	5.32147	−	14.6206i	0.102336	−	0.281166i
$53$	−21.2868	−	58.4851i	−0.401638	−	1.10349i	−0.961476	−	0.274889i	$-0.911359\pi$
$53$	−21.2868	−	58.4851i	−0.401638	−	1.10349i	0.559838	−	0.828602i	$-0.310863\pi$
$54$	27.8273	−	23.3499i	0.515320	−	0.432405i
$55$	6.11768	+	34.6951i	0.111231	+	0.630820i
$56$			19.6346i			0.350618i
$57$		0			0
$58$	13.7476			0.237027
$59$	15.5523	−	2.74229i	0.263599	−	0.0464795i	−0.0402868	−	0.999188i	$-0.512827\pi$
$59$	15.5523	−	2.74229i	0.263599	−	0.0464795i	0.303885	+	0.952709i	$0.401716\pi$
$60$	44.2747	+	52.7646i	0.737912	+	0.879410i
$61$	−63.3905	+	23.0722i	−1.03919	+	0.378233i	−0.804572	−	0.593855i	$-0.797605\pi$
$61$	−63.3905	+	23.0722i	−1.03919	+	0.378233i	−0.234616	+	0.972088i	$0.575383\pi$
$62$	−14.6380	−	5.32779i	−0.236097	−	0.0859322i
$63$	−84.5349	−	70.9332i	−1.34182	−	1.12592i
$64$	−20.4351	+	35.3947i	−0.319299	+	0.553042i
$65$	11.8901	−	6.86475i	0.182925	−	0.105612i
$66$	−5.19175	+	29.4439i	−0.0786629	+	0.446119i
$67$	−56.9447	−	10.0409i	−0.849921	−	0.149864i	−0.268311	−	0.963332i	$-0.586466\pi$
$67$	−56.9447	−	10.0409i	−0.849921	−	0.149864i	−0.581609	+	0.813468i	$0.697577\pi$
$68$	3.82924	+	6.63244i	0.0563124	+	0.0975359i
$69$	−46.3856	−	26.7808i	−0.672256	−	0.388127i
$70$	−5.38569	+	6.41842i	−0.0769385	+	0.0916917i
$71$	−38.6990	+	106.325i	−0.545057	+	1.49753i	0.295250	+	0.955420i	$0.404597\pi$
$71$	−38.6990	+	106.325i	−0.545057	+	1.49753i	−0.840307	+	0.542111i	$0.817625\pi$
$72$	29.3201	+	80.5563i	0.407224	+	1.11884i
$73$	−74.0509	+	62.1361i	−1.01440	+	0.851180i	−0.988913	−	0.148496i	$-0.952557\pi$
$73$	−74.0509	+	62.1361i	−1.01440	+	0.851180i	−0.0254833	+	0.999675i	$0.508112\pi$
$74$	−1.69134	−	9.59207i	−0.0228559	−	0.129623i
$75$		−	78.3016i		−	1.04402i
$76$		0			0
$77$	53.5853			0.695913
$78$	11.4745	−	2.02326i	0.147109	−	0.0259393i
$79$	31.7548	+	37.8439i	0.401960	+	0.479037i	0.928617	−	0.371041i	$-0.120999\pi$
$79$	31.7548	+	37.8439i	0.401960	+	0.479037i	−0.526656	+	0.850078i	$0.676555\pi$
$80$	−40.4212	+	14.7121i	−0.505265	+	0.183901i
$81$	−190.998	−	69.5177i	−2.35800	−	0.858243i
$82$	24.6201	+	20.6587i	0.300245	+	0.251935i
$83$	−48.0685	+	83.2571i	−0.579139	+	1.00310i	0.416440	+	0.909163i	$0.363278\pi$
$83$	−48.0685	+	83.2571i	−0.579139	+	1.00310i	−0.995578	+	0.0939343i	$0.970056\pi$
$84$	90.7295	−	52.3827i	1.08011	−	0.623603i
$85$	−1.17351	+	6.65533i	−0.0138060	+	0.0782979i
$86$	−33.1260	−	5.84102i	−0.385187	−	0.0679188i
$87$	−75.8429	−	131.364i	−0.871758	−	1.50993i
$88$	−36.0502	−	20.8136i	−0.409662	−	0.236518i
$89$	−31.6819	+	37.7570i	−0.355976	+	0.424236i	−0.914079	−	0.405536i	$-0.867085\pi$
$89$	−31.6819	+	37.7570i	−0.355976	+	0.424236i	0.558103	+	0.829772i	$0.311529\pi$
$90$	−12.5117	+	34.3757i	−0.139019	+	0.381952i
$91$	−7.14226	−	19.6232i	−0.0784863	−	0.215639i
$92$	27.6259	−	23.1809i	0.300282	−	0.251966i
$93$	29.8459	+	169.264i	0.320924	+	1.82005i
$94$		−	12.5716i		−	0.133740i
$95$		0			0
$96$	−123.415			−1.28557
$97$	−38.8683	+	6.85353i	−0.400704	+	0.0706550i	−0.370369	−	0.928885i	$-0.620769\pi$
$97$	−38.8683	+	6.85353i	−0.400704	+	0.0706550i	−0.0303355	+	0.999540i	$0.509658\pi$
$98$	−7.68929	−	9.16374i	−0.0784622	−	0.0935076i
$99$	219.848	−	80.0181i	2.22069	−	0.808264i
$100$	49.5412	+	18.0315i	0.495412	+	0.180315i
$101$	144.313	+	121.093i	1.42885	+	1.19894i	0.946391	+	0.323024i	$0.104699\pi$
$101$	144.313	+	121.093i	1.42885	+	1.19894i	0.482456	+	0.875920i	$0.339745\pi$
$102$	−2.86758	+	4.96679i	−0.0281135	+	0.0486940i
$103$	70.5875	−	40.7537i	0.685316	−	0.395667i	−0.116539	−	0.993186i	$-0.537180\pi$
$103$	70.5875	−	40.7537i	0.685316	−	0.395667i	0.801855	+	0.597519i	$0.203847\pi$
$104$	−2.81699	+	15.9760i	−0.0270865	+	0.153615i
$105$	91.0425	+	16.0533i	0.867072	+	0.152888i
$106$	15.6907	+	27.1770i	0.148025	+	0.256387i
$107$	64.7149	+	37.3632i	0.604812	+	0.349188i	0.770932	−	0.636917i	$-0.219791\pi$
$107$	64.7149	+	37.3632i	0.604812	+	0.349188i	−0.166120	+	0.986105i	$0.553124\pi$
$108$	173.465	−	206.728i	1.60616	−	1.91415i
$109$	−13.8235	+	37.9797i	−0.126821	+	0.348437i	−0.986812	−	0.161872i	$-0.948247\pi$
$109$	−13.8235	+	37.9797i	−0.126821	+	0.348437i	0.859991	+	0.510309i	$0.170469\pi$
$110$	−6.07548	−	16.6922i	−0.0552316	−	0.151748i
$111$	−82.3253	+	69.0791i	−0.741669	+	0.622335i
$112$	11.3612	+	64.4323i	0.101439	+	0.575289i
$113$		−	30.5747i		−	0.270573i	−0.990807	−	0.135286i	$-0.956805\pi$
$113$		−	30.5747i		−	0.270573i	0.990807	−	0.135286i	$-0.0431955\pi$
$114$		0			0
$115$	31.8228			0.276720
$116$	100.579	−	17.7348i	0.867059	−	0.152886i
$117$	−58.6060	−	69.8440i	−0.500906	−	0.596957i
$118$	−7.48242	+	2.72338i	−0.0634103	+	0.0230795i
$119$	9.65901	+	3.51559i	0.0811682	+	0.0295428i
$120$	−55.0147	−	46.1628i	−0.458455	−	0.384690i
$121$	3.69713	−	6.40361i	0.0305548	−	0.0529224i
$122$	29.4565	−	17.0067i	0.241447	−	0.139399i
$123$	61.5778	−	349.225i	0.500633	−	2.83923i
$124$	−113.966	−	20.0953i	−0.919082	−	0.162059i
$125$	64.5776	+	111.852i	0.516621	+	0.894814i
$126$	48.1865	+	27.8205i	0.382432	+	0.220797i
$127$	−78.9307	+	94.0659i	−0.621501	+	0.740677i	−0.981328	−	0.192343i	$-0.938391\pi$
$127$	−78.9307	+	94.0659i	−0.621501	+	0.740677i	0.359826	+	0.933019i	$0.382836\pi$
$128$	37.3973	−	102.748i	0.292166	−	0.802720i
$129$	126.937	+	348.757i	0.984008	+	2.70354i
$130$	−5.30299	+	4.44974i	−0.0407922	+	0.0342288i
$131$	−20.1618	−	114.343i	−0.153907	−	0.872848i	−0.959779	−	0.280758i	$-0.909414\pi$
$131$	−20.1618	−	114.343i	−0.153907	−	0.872848i	0.805872	−	0.592090i	$-0.201697\pi$
$132$			222.112i			1.68267i
$133$		0			0
$134$	29.1551			0.217575
$135$	234.516	−	41.3515i	1.73715	−	0.306307i
$136$	−5.13270	−	6.11692i	−0.0377405	−	0.0449773i
$137$	−38.4167	+	13.9825i	−0.280414	+	0.102062i	−0.478399	−	0.878143i	$-0.658783\pi$
$137$	−38.4167	+	13.9825i	−0.280414	+	0.102062i	0.197985	+	0.980205i	$0.436560\pi$
$138$	25.3776	+	9.23670i	0.183896	+	0.0669326i
$139$	9.36335	+	7.85678i	0.0673622	+	0.0565236i	0.675847	−	0.737042i	$-0.263778\pi$
$139$	9.36335	+	7.85678i	0.0673622	+	0.0565236i	−0.608485	+	0.793565i	$0.708222\pi$
$140$	−31.1224	+	53.9056i	−0.222303	+	0.385040i
$141$	−120.126	+	69.3550i	−0.851960	+	0.491880i
$142$	9.90675	−	56.1839i	0.0697658	−	0.395662i
$143$	43.6003	+	7.68792i	0.304898	+	0.0537617i
$144$	142.828	+	247.386i	0.991862	+	1.71795i
$145$	78.0478	+	45.0609i	0.538261	+	0.310765i
$146$	31.3297	−	37.3373i	0.214587	−	0.255735i
$147$	−45.1429	+	124.029i	−0.307094	+	0.843735i
$148$	−24.7481	−	67.9947i	−0.167217	−	0.459424i
$149$	62.8703	−	52.7545i	0.421948	−	0.354057i	−0.406955	−	0.913448i	$-0.633410\pi$
$149$	62.8703	−	52.7545i	0.421948	−	0.354057i	0.828904	+	0.559391i	$0.188965\pi$
$150$	6.85573	+	38.8808i	0.0457048	+	0.259205i
$151$			137.096i			0.907922i	0.891022	+	0.453961i	$0.149989\pi$
$151$			137.096i			0.907922i	−0.891022	+	0.453961i	$0.850011\pi$
$152$		0			0
$153$	44.8785			0.293323
$154$	−26.6078	+	4.69168i	−0.172778	+	0.0304654i
$155$	−65.6398	−	78.2264i	−0.423482	−	0.504687i
$156$	81.3386	−	29.6048i	0.521401	−	0.189774i
$157$	57.5428	+	20.9439i	0.366514	+	0.133400i	0.518710	−	0.854950i	$-0.326412\pi$
$157$	57.5428	+	20.9439i	0.366514	+	0.133400i	−0.152196	+	0.988350i	$0.548635\pi$
$158$	−19.0813	−	16.0111i	−0.120768	−	0.101336i
$159$	173.125	−	299.862i	1.08884	−	1.88592i
$160$	63.5012	−	36.6624i	0.396883	−	0.229140i
$161$	8.40499	−	47.6671i	0.0522049	−	0.296069i
$162$	100.927	+	17.7962i	0.623007	+	0.109853i
$163$	−101.260	−	175.388i	−0.621229	−	1.07600i	−0.989257	−	0.146186i	$-0.953300\pi$
$163$	−101.260	−	175.388i	−0.621229	−	1.07600i	0.368028	−	0.929815i	$-0.380033\pi$
$164$	206.774	+	119.381i	1.26081	+	0.727932i
$165$	−125.984	+	150.142i	−0.763539	+	0.909950i
$166$	16.5789	−	45.5501i	0.0998727	−	0.274398i
$167$	−74.9775	−	205.999i	−0.448967	−	1.23353i	−0.933444	−	0.358722i	$-0.883212\pi$
$167$	−74.9775	−	205.999i	−0.448967	−	1.23353i	0.484477	−	0.874804i	$-0.339010\pi$
$168$	−83.6773	+	70.2136i	−0.498079	+	0.417938i
$169$	26.3505	+	149.441i	0.155920	+	0.884267i
$170$		−	3.40746i		−	0.0200439i
$171$		0			0
$172$	−249.889			−1.45284
$173$	70.4402	−	12.4205i	0.407169	−	0.0717948i	0.0336871	−	0.999432i	$-0.489275\pi$
$173$	70.4402	−	12.4205i	0.407169	−	0.0717948i	0.373482	+	0.927638i	$0.378164\pi$
$174$	49.1615	+	58.5884i	0.282537	+	0.336715i
$175$	66.4922	−	24.2012i	0.379956	−	0.138293i
$176$	−130.345	−	47.4415i	−0.740594	−	0.269554i
$177$	67.3021	+	56.4732i	0.380238	+	0.319057i
$178$	12.4258	−	21.5222i	0.0698081	−	0.120911i
$179$	114.387	−	66.0413i	0.639033	−	0.368946i	−0.145209	−	0.989401i	$-0.546386\pi$
$179$	114.387	−	66.0413i	0.639033	−	0.368946i	0.784242	+	0.620455i	$0.213052\pi$
$180$	−47.1916	+	267.637i	−0.262175	+	1.48687i
$181$	141.973	+	25.0337i	0.784382	+	0.138308i	0.551475	−	0.834191i	$-0.314065\pi$
$181$	141.973	+	25.0337i	0.784382	+	0.138308i	0.232907	+	0.972499i	$0.425176\pi$
$182$	5.26461	+	9.11857i	0.0289264	+	0.0501020i
$183$	−325.012	−	187.646i	−1.77602	−	1.02539i
$184$	−24.1694	+	28.8040i	−0.131356	+	0.156543i
$185$	21.8382	−	59.9999i	0.118044	−	0.324324i
$186$	−29.6400	−	81.4353i	−0.159355	−	0.437824i
$187$	−16.6938	+	14.0078i	−0.0892718	+	0.0749079i
$188$	−16.2177	−	91.9749i	−0.0862642	−	0.489228i
$189$		−	362.201i		−	1.91641i
$190$		0			0
$191$	331.007			1.73302			0.866511	−	0.499158i	$-0.166357\pi$
$191$	331.007			1.73302			0.866511	+	0.499158i	$0.166357\pi$
$192$	−223.918	+	39.4829i	−1.16624	+	0.205640i
$193$	−47.8181	−	56.9873i	−0.247762	−	0.295271i	0.627802	−	0.778373i	$-0.283955\pi$
$193$	−47.8181	−	56.9873i	−0.247762	−	0.295271i	−0.875564	+	0.483102i	$0.839510\pi$
$194$	18.7000	−	6.80626i	0.0963919	−	0.0350838i
$195$	71.7747	+	26.1239i	0.368075	+	0.133969i
$196$	−68.0772	−	57.1236i	−0.347333	−	0.291447i
$197$	−133.136	+	230.599i	−0.675820	+	1.17055i	0.300409	+	0.953811i	$0.402877\pi$
$197$	−133.136	+	230.599i	−0.675820	+	1.17055i	−0.976229	+	0.216744i	$0.930456\pi$
$198$	−102.160	+	58.9820i	−0.515958	+	0.297889i
$199$	−45.5932	+	258.572i	−0.229112	+	1.29936i	0.625555	+	0.780180i	$0.284873\pi$
$199$	−45.5932	+	258.572i	−0.229112	+	1.29936i	−0.854667	+	0.519177i	$0.826238\pi$
$200$	−54.1338	−	9.54525i	−0.270669	−	0.0477262i
$201$	−160.843	−	278.589i	−0.800215	−	1.38601i
$202$	−82.2614	−	47.4936i	−0.407235	−	0.235117i
$203$	88.1103	−	105.006i	0.434041	−	0.517270i
$204$	−14.5722	+	40.0368i	−0.0714324	+	0.196259i
$205$	72.0595	+	197.982i	0.351510	+	0.965765i
$206$	−31.4821	+	26.4166i	−0.152826	+	0.128236i
$207$	−36.6968	−	208.118i	−0.177279	−	1.00540i
$208$			54.0562i			0.259885i
$209$		0			0
$210$	−46.6128			−0.221966
$211$	−267.887	+	47.2357i	−1.26961	+	0.223866i	−0.767562	−	0.640975i	$-0.778530\pi$
$211$	−267.887	+	47.2357i	−1.26961	+	0.223866i	−0.502046	+	0.864841i	$0.667419\pi$
$212$	149.854	+	178.589i	0.706858	+	0.842400i
$213$	−591.514	+	215.294i	−2.77706	+	1.01077i
$214$	−35.4056	−	12.8866i	−0.165447	−	0.0602177i
$215$	−168.918	−	141.739i	−0.785665	−	0.659251i
$216$	−140.686	+	243.676i	−0.651325	+	1.12813i
$217$	−134.511	+	77.6602i	−0.619869	+	0.357881i
$218$	3.53874	−	20.0692i	0.0162327	−	0.0920604i
$219$	−529.614	−	93.3852i	−2.41833	−	0.426416i
$220$	−65.9823	−	114.285i	−0.299920	−	0.519476i
$221$	7.35479	+	4.24629i	0.0332796	+	0.0192140i
$222$	34.8305	−	41.5093i	0.156894	−	0.186979i
$223$	−39.1769	+	107.638i	−0.175681	+	0.482680i	−0.996013	−	0.0892079i	$-0.971566\pi$
$223$	−39.1769	+	107.638i	−0.175681	+	0.482680i	0.820332	+	0.571888i	$0.193789\pi$
$224$	−38.1445	−	104.801i	−0.170288	−	0.467863i
$225$	236.663	−	198.584i	1.05184	−	0.882595i
$226$	2.67698	+	15.1819i	0.0118450	+	0.0671766i
$227$		−	403.991i		−	1.77970i	−0.456258	−	0.889848i	$-0.650811\pi$
$227$		−	403.991i		−	1.77970i	0.456258	−	0.889848i	$-0.349189\pi$
$228$		0			0
$229$	−109.482			−0.478087			−0.239043	−	0.971009i	$-0.576834\pi$
$229$	−109.482			−0.478087			−0.239043	+	0.971009i	$0.576834\pi$
$230$	−15.8016	+	2.78625i	−0.0687027	+	0.0121141i
$231$	191.621	+	228.366i	0.829530	+	0.988595i
$232$	−100.064	+	36.4202i	−0.431309	+	0.156984i
$233$	−171.340	−	62.3628i	−0.735366	−	0.267651i	−0.0529316	−	0.998598i	$-0.516857\pi$
$233$	−171.340	−	62.3628i	−0.735366	−	0.267651i	−0.682434	+	0.730947i	$0.739079\pi$
$234$	35.2161	+	29.5498i	0.150496	+	0.126281i
$235$	41.2063	−	71.3713i	0.175346	−	0.303708i
$236$	−51.2290	+	29.5770i	−0.217072	+	0.125326i
$237$	−47.7248	+	270.661i	−0.201370	+	1.14203i
$238$	−5.10400	−	0.899973i	−0.0214454	−	0.00378140i
$239$	138.117	+	239.226i	0.577895	+	1.00094i	0.995720	+	0.0924165i	$0.0294591\pi$
$239$	138.117	+	239.226i	0.577895	+	1.00094i	−0.417825	+	0.908527i	$0.637208\pi$
$240$	−207.245	−	119.653i	−0.863523	−	0.498555i
$241$	96.7207	−	115.267i	0.401331	−	0.478287i	−0.527095	−	0.849807i	$-0.676719\pi$
$241$	96.7207	−	115.267i	0.401331	−	0.478287i	0.928425	+	0.371519i	$0.121163\pi$
$242$	−1.27514	+	3.50342i	−0.00526918	+	0.0144770i
$243$	−164.979	−	453.275i	−0.678925	−	1.86533i
$244$	193.568	−	162.423i	0.793311	−	0.665667i
$245$	−13.6174	−	77.2279i	−0.0555811	−	0.315216i
$246$			178.800i			0.726828i
$247$		0			0
$248$	120.659			0.486529
$249$	−526.712	+	92.8735i	−2.11531	+	0.372986i
$250$	−41.8593	−	49.8860i	−0.167437	−	0.199544i
$251$	362.654	−	131.995i	1.44484	−	0.525877i	0.503691	−	0.863884i	$-0.331975\pi$
$251$	362.654	−	131.995i	1.44484	−	0.525877i	0.941144	+	0.338007i	$0.109753\pi$
$252$	388.427	+	141.376i	1.54138	+	0.561015i
$253$	78.6097	+	65.9613i	0.310710	+	0.260717i
$254$	30.9571	−	53.6193i	0.121878	−	0.211100i
$255$	−32.5596	+	18.7983i	−0.127685	+	0.0737189i
$256$	18.8147	−	106.703i	0.0734948	−	0.416810i
$257$	392.792	+	69.2598i	1.52837	+	0.269493i	0.873717	−	0.486435i	$-0.161703\pi$
$257$	392.792	+	69.2598i	1.52837	+	0.269493i	0.654655	+	0.755928i	$0.272814\pi$
$258$	−93.5663	−	162.062i	−0.362660	−	0.628145i
$259$	−84.1055	−	48.5583i	−0.324732	−	0.187484i
$260$	−33.0570	+	39.3958i	−0.127142	+	0.151522i
$261$	204.693	−	562.388i	0.784263	−	2.15474i
$262$	20.0227	+	55.0119i	0.0764225	+	0.209969i
$263$	−46.7234	+	39.2055i	−0.177655	+	0.149071i	−0.727279	−	0.686342i	$-0.759215\pi$
$263$	−46.7234	+	39.2055i	−0.177655	+	0.149071i	0.549624	+	0.835412i	$0.314771\pi$
$264$	−40.2141	−	228.066i	−0.152326	−	0.863885i
$265$			205.719i			0.776300i
$266$		0			0
$267$	−274.204			−1.02698
$268$	213.302	−	37.6109i	0.795902	−	0.140339i
$269$	−106.783	−	127.259i	−0.396962	−	0.473081i	0.530129	−	0.847917i	$-0.322143\pi$
$269$	−106.783	−	127.259i	−0.396962	−	0.473081i	−0.927091	+	0.374836i	$0.877699\pi$
$270$	−112.829	+	41.0662i	−0.417883	+	0.152097i
$271$	179.052	+	65.1697i	0.660710	+	0.240479i	0.650543	−	0.759470i	$-0.274541\pi$
$271$	179.052	+	65.1697i	0.660710	+	0.240479i	0.0101670	+	0.999948i	$0.496764\pi$
$272$	−20.3827	−	17.1031i	−0.0749365	−	0.0628792i
$273$	58.0878	−	100.611i	0.212776	−	0.368538i
$274$	17.8516	−	10.3066i	0.0651518	−	0.0376154i
$275$	−26.0501	+	147.738i	−0.0947278	+	0.537228i
$276$	197.581	+	34.8389i	0.715874	+	0.126228i
$277$	48.8669	+	84.6399i	0.176415	+	0.305559i	0.940650	−	0.339378i	$-0.110217\pi$
$277$	48.8669	+	84.6399i	0.176415	+	0.305559i	−0.764235	+	0.644938i	$0.776883\pi$
$278$	−5.33728	−	3.08148i	−0.0191989	−	0.0110845i
$279$	−435.901	+	519.486i	−1.56237	+	1.86196i
$280$	22.1968	−	60.9852i	0.0792743	−	0.217804i
$281$	−89.2166	−	245.121i	−0.317497	−	0.872315i	−0.991088	−	0.133211i	$-0.957471\pi$
$281$	−89.2166	−	245.121i	−0.317497	−	0.872315i	0.673591	−	0.739104i	$-0.264751\pi$
$282$	53.5765	−	44.9560i	0.189988	−	0.159419i
$283$	−51.9445	−	294.592i	−0.183549	−	1.04096i	−0.927805	−	0.373066i	$-0.878307\pi$
$283$	−51.9445	−	294.592i	−0.183549	−	1.04096i	0.744256	−	0.667895i	$-0.232804\pi$
$284$		−	423.828i		−	1.49235i
$285$		0			0
$286$	−22.3229			−0.0780521
$287$	315.588	−	55.6466i	1.09961	−	0.193891i
$288$	−312.996	−	373.015i	−1.08679	−	1.29519i
$289$	267.643	−	97.4141i	0.926100	−	0.337073i
$290$	−42.7001	−	15.5415i	−0.147242	−	0.0535915i
$291$	−168.201	−	141.138i	−0.578011	−	0.485009i
$292$	181.046	−	313.580i	0.620019	−	1.07390i
$293$	−439.492	+	253.741i	−1.49997	+	0.866010i	−1.00000		3.02106e-5i	$-0.999990\pi$
$293$	−439.492	+	253.741i	−1.49997	+	0.866010i	−0.499974	+	0.866041i	$0.666657\pi$
$294$	11.5563	−	65.5393i	0.0393073	−	0.222923i
$295$	−51.4057	−	9.06421i	−0.174257	−	0.0307261i
$296$	37.7221	+	65.3365i	0.127439	+	0.220732i
$297$	665.021	+	383.950i	2.23913	+	1.29276i
$298$	−26.5994	+	31.6999i	−0.0892597	+	0.106376i
$299$	13.6777	−	37.5791i	0.0457447	−	0.125682i
$300$	100.315	+	275.612i	0.334382	+	0.918706i
$301$	−256.924	+	215.585i	−0.853569	+	0.716229i
$302$	−12.0035	−	68.0752i	−0.0397467	−	0.225415i
$303$			1048.05i			3.45893i
$304$		0			0
$305$	222.974			0.731063
$306$	−22.2845	+	3.92935i	−0.0728250	+	0.0128410i
$307$	30.1912	+	35.9804i	0.0983426	+	0.117200i	0.812971	−	0.582304i	$-0.197849\pi$
$307$	30.1912	+	35.9804i	0.0983426	+	0.117200i	−0.714628	+	0.699504i	$0.753404\pi$
$308$	−188.613	+	68.6497i	−0.612381	+	0.222889i
$309$	426.103	+	155.089i	1.37897	+	0.501905i
$310$	39.4426	+	33.0963i	0.127234	+	0.106762i
$311$	48.0701	−	83.2599i	0.154566	−	0.267717i	−0.778335	−	0.627850i	$-0.783935\pi$
$311$	48.0701	−	83.2599i	0.154566	−	0.267717i	0.932901	+	0.360133i	$0.117269\pi$
$312$	−78.1587	+	45.1249i	−0.250509	+	0.144631i
$313$	9.67789	−	54.8860i	0.0309198	−	0.175355i	−0.965437	−	0.260636i	$-0.916068\pi$
$313$	9.67789	−	54.8860i	0.0309198	−	0.175355i	0.996357	+	0.0852813i	$0.0271789\pi$
$314$	−30.4067	−	5.36151i	−0.0968365	−	0.0170749i
$315$	182.376	+	315.885i	0.578972	+	1.00281i
$316$	−160.256	−	92.5239i	−0.507139	−	0.292797i
$317$	237.386	−	282.906i	0.748852	−	0.892448i	−0.248236	−	0.968700i	$-0.579851\pi$
$317$	237.386	−	282.906i	0.748852	−	0.892448i	0.997089	+	0.0762520i	$0.0242953\pi$
$318$	−59.7110	+	164.055i	−0.187770	+	0.515895i
$319$	99.3953	+	273.086i	0.311584	+	0.856070i
$320$	103.485	−	86.8342i	0.323391	−	0.271357i
$321$	72.1896	+	409.408i	0.224890	+	1.27541i
$322$			24.4050i			0.0757921i
$323$		0			0
$324$	761.351			2.34985
$325$	57.5744	−	10.1519i	0.177152	−	0.0312367i
$326$	65.6371	+	78.2233i	0.201341	+	0.239949i
$327$	−211.292	+	76.9039i	−0.646152	+	0.235180i
$328$	−233.930	−	85.1436i	−0.713202	−	0.259584i
$329$	−96.0232	−	80.5730i	−0.291864	−	0.244903i
$330$	49.4117	−	85.5836i	0.149732	−	0.259344i
$331$	−319.730	+	184.596i	−0.965951	+	0.557692i	−0.898000	−	0.439996i	$-0.854980\pi$
$331$	−319.730	+	184.596i	−0.965951	+	0.557692i	−0.0679517	+	0.997689i	$0.521646\pi$
$332$	62.5320	−	354.636i	0.188349	−	1.06818i
$333$	−417.577	−	73.6301i	−1.25398	−	0.221111i
$334$	55.2664	+	95.7243i	0.165468	+	0.286600i
$335$	165.519	+	95.5626i	0.494087	+	0.285262i
$336$	−233.965	+	278.829i	−0.696325	+	0.829847i
$337$	42.0296	−	115.475i	0.124717	−	0.342657i	−0.861584	−	0.507616i	$-0.830527\pi$
$337$	42.0296	−	115.475i	0.124717	−	0.342657i	0.986300	+	0.164959i	$0.0527492\pi$
$338$	−26.1687	−	71.8980i	−0.0774223	−	0.212716i
$339$	130.301	−	109.336i	0.384369	−	0.322524i
$340$	−4.39571	−	24.9293i	−0.0129286	−	0.0733215i
$341$		−	329.294i		−	0.965671i
$342$		0			0
$343$	−365.619			−1.06595
$344$	256.587	−	45.2432i	0.745892	−	0.131521i
$345$	113.799	+	135.620i	0.329851	+	0.393101i
$346$	−33.8897	+	12.3348i	−0.0979470	+	0.0356498i
$347$	−251.294	−	91.4636i	−0.724191	−	0.263584i	−0.0464869	−	0.998919i	$-0.514803\pi$
$347$	−251.294	−	91.4636i	−0.724191	−	0.263584i	−0.677704	+	0.735335i	$0.737025\pi$
$348$	435.251	+	365.219i	1.25072	+	1.04948i
$349$	116.771	−	202.253i	0.334586	−	0.579521i	−0.648819	−	0.760943i	$-0.724737\pi$
$349$	116.771	−	202.253i	0.334586	−	0.579521i	0.983405	+	0.181422i	$0.0580700\pi$
$350$	−30.8978	+	17.8389i	−0.0882796	+	0.0509682i
$351$	51.9652	−	294.710i	0.148049	−	0.839628i
$352$	232.856	+	41.0587i	0.661522	+	0.116644i
$353$	−20.6612	−	35.7862i	−0.0585302	−	0.101377i	0.835276	−	0.549831i	$-0.185308\pi$
$353$	−20.6612	−	35.7862i	−0.0585302	−	0.101377i	−0.893806	+	0.448454i	$0.851975\pi$
$354$	−38.3635	−	22.1492i	−0.108371	−	0.0625682i
$355$	240.399	−	286.496i	0.677179	−	0.807031i
$356$	63.1446	−	173.488i	0.177372	−	0.487327i
$357$	19.5582	+	53.7358i	0.0547850	+	0.150520i
$358$	−51.0166	+	42.8080i	−0.142505	+	0.119576i
$359$	42.2098	+	239.384i	0.117576	+	0.666807i	0.985442	+	0.170009i	$0.0543798\pi$
$359$	42.2098	+	239.384i	0.117576	+	0.666807i	−0.867866	+	0.496798i	$0.834509\pi$
$360$		−	283.354i		−	0.787096i
$361$		0			0
$362$	−72.6887			−0.200798
$363$	40.5114	−	7.14325i	0.111602	−	0.0196784i
$364$	50.2797	+	59.9210i	0.138131	+	0.164618i
$365$	300.247	−	109.281i	0.822594	−	0.299400i
$366$	177.815	+	64.7192i	0.485832	+	0.176828i
$367$	−307.657	−	258.155i	−0.838303	−	0.703420i	0.118878	−	0.992909i	$-0.462070\pi$
$367$	−307.657	−	258.155i	−0.838303	−	0.703420i	−0.957181	+	0.289489i	$0.906515\pi$
$368$	−62.6468	+	108.507i	−0.170236	+	0.294857i
$369$	1211.69	−	699.568i	3.28370	−	1.89585i
$370$	−5.59046	+	31.7051i	−0.0151093	+	0.0856893i
$371$	308.146	+	54.3344i	0.830581	+	0.146454i
$372$	−321.903	−	557.553i	−0.865332	−	1.49880i
$373$	−523.753	−	302.389i	−1.40416	−	0.810694i	−0.409347	−	0.912379i	$-0.634244\pi$
$373$	−523.753	−	302.389i	−1.40416	−	0.810694i	−0.994817	+	0.101684i	$0.967577\pi$
$374$	7.06288	−	8.41721i	0.0188847	−	0.0225059i
$375$	−245.751	+	675.195i	−0.655335	+	1.80052i
$376$	33.3047	+	91.5039i	0.0885763	+	0.243362i
$377$	86.7573	−	72.7980i	0.230126	−	0.193098i
$378$	31.7126	+	179.851i	0.0838959	+	0.475797i
$379$		−	31.3786i		−	0.0827931i	−0.999143	−	0.0413965i	$-0.986819\pi$
$379$		−	31.3786i		−	0.0827931i	0.999143	−	0.0413965i	$-0.0131807\pi$
$380$		0			0
$381$	−683.139			−1.79302
$382$	−164.362	+	28.9815i	−0.430267	+	0.0758677i
$383$	−276.227	−	329.195i	−0.721220	−	0.859517i	0.273528	−	0.961864i	$-0.411809\pi$
$383$	−276.227	−	329.195i	−0.721220	−	0.859517i	−0.994749	+	0.102347i	$0.967365\pi$
$384$	571.617	−	208.052i	1.48859	−	0.541801i
$385$	−166.436	−	60.5778i	−0.432302	−	0.157345i
$386$	28.7336	+	24.1104i	0.0744395	+	0.0624622i
$387$	−732.171	+	1268.16i	−1.89191	+	3.27689i
$388$	128.031	−	73.9189i	0.329978	−	0.190513i
$389$	−105.477	+	598.191i	−0.271150	+	1.53777i	0.479783	+	0.877387i	$0.340715\pi$
$389$	−105.477	+	598.191i	−0.271150	+	1.53777i	−0.750932	+	0.660379i	$0.770396\pi$
$390$	−37.9271	−	6.68757i	−0.0972490	−	0.0171476i
$391$	9.84223	+	17.0472i	0.0251719	+	0.0435991i
$392$	80.2443	+	46.3291i	0.204705	+	0.118186i
$393$	415.200	−	494.816i	1.05649	−	1.25907i
$394$	45.9189	−	126.161i	0.116545	−	0.320206i
$395$	−55.8484	−	153.442i	−0.141388	−	0.388461i
$396$	−671.324	+	563.307i	−1.69526	+	1.42249i
$397$	36.8724	+	209.114i	0.0928777	+	0.526736i	0.995377	+	0.0960444i	$0.0306191\pi$
$397$	36.8724	+	209.114i	0.0928777	+	0.526736i	−0.902499	+	0.430691i	$0.858270\pi$
$398$		−	132.386i		−	0.332629i
$399$		0			0
$400$	−183.167			−0.457917
$401$	299.042	−	52.7292i	0.745741	−	0.131494i	0.212150	−	0.977237i	$-0.431953\pi$
$401$	299.042	−	52.7292i	0.745741	−	0.131494i	0.533591	+	0.845743i	$0.320842\pi$
$402$	104.259	+	124.251i	0.259350	+	0.309082i
$403$	−120.589	+	43.8908i	−0.299228	+	0.108910i
$404$	−663.101	−	241.349i	−1.64134	−	0.597399i
$405$	514.652	+	431.845i	1.27075	+	1.06628i
$406$	−34.5575	+	59.8553i	−0.0851169	+	0.147427i
$407$	178.311	−	102.948i	0.438112	−	0.252944i
$408$	7.71401	−	43.7483i	0.0189069	−	0.107226i
$409$	−483.069	−	85.1782i	−1.18110	−	0.208260i	−0.451587	−	0.892227i	$-0.649142\pi$
$409$	−483.069	−	85.1782i	−1.18110	−	0.208260i	−0.729512	+	0.683968i	$0.760253\pi$
$410$	−53.1156	−	91.9989i	−0.129550	−	0.224388i
$411$	−196.968	−	113.720i	−0.479241	−	0.276690i
$412$	−196.248	+	233.880i	−0.476331	+	0.567669i
$413$	−27.1544	+	74.6062i	−0.0657492	+	0.180645i
$414$	36.4437	+	100.128i	0.0880283	+	0.241856i
$415$	243.423	−	204.256i	0.586561	−	0.492183i
$416$	−16.0009	−	90.7455i	−0.0384636	−	0.218138i
$417$			67.9999i			0.163069i
$418$		0			0
$419$	−20.9810			−0.0500739			−0.0250370	−	0.999687i	$-0.507970\pi$
$419$	−20.9810			−0.0500739			−0.0250370	+	0.999687i	$0.507970\pi$
$420$	−341.024	+	60.1318i	−0.811963	+	0.143171i
$421$	448.747	+	534.796i	1.06591	+	1.27030i	0.961217	+	0.275794i	$0.0889408\pi$
$421$	448.747	+	534.796i	1.06591	+	1.27030i	0.104691	+	0.994505i	$0.466615\pi$
$422$	128.884	−	46.9099i	0.305412	−	0.111161i
$423$	−514.280	−	187.182i	−1.21579	−	0.442512i
$424$	−186.205	−	156.244i	−0.439162	−	0.368500i
$425$	−14.3884	+	24.9214i	−0.0338550	+	0.0586385i
$426$	274.867	−	158.694i	0.645227	−	0.372522i
$427$	58.8916	−	333.991i	0.137920	−	0.782181i
$428$	−275.655	−	48.6054i	−0.644054	−	0.113564i
$429$	123.151	+	213.305i	0.287066	+	0.497213i
$430$	96.2864	+	55.5910i	0.223922	+	0.129281i
$431$	299.711	−	357.182i	0.695385	−	0.828728i	−0.296610	−	0.954999i	$-0.595856\pi$
$431$	299.711	−	357.182i	0.695385	−	0.828728i	0.991996	+	0.126270i	$0.0403007\pi$
$432$	−320.673	+	881.043i	−0.742300	+	2.03945i
$433$	165.547	+	454.836i	0.382325	+	1.05043i	0.970375	+	0.241605i	$0.0776739\pi$
$433$	165.547	+	454.836i	0.382325	+	1.05043i	−0.588049	+	0.808825i	$0.700104\pi$
$434$	59.9922	−	50.3395i	0.138231	−	0.115990i
$435$	87.0626	+	493.756i	0.200144	+	1.13507i
$436$		−	151.393i		−	0.347232i
$437$		0			0
$438$	271.157			0.619079
$439$	−342.212	+	60.3412i	−0.779526	+	0.137451i	−0.549232	−	0.835670i	$-0.685080\pi$
$439$	−342.212	+	60.3412i	−0.779526	+	0.137451i	−0.230294	+	0.973121i	$0.573969\pi$
$440$	88.4425	+	105.402i	0.201006	+	0.239549i
$441$	−489.361	+	178.113i	−1.10966	+	0.403884i
$442$	−4.02382	−	1.46455i	−0.00910366	−	0.00331346i
$443$	63.6751	+	53.4298i	0.143736	+	0.120609i	0.711821	−	0.702361i	$-0.247871\pi$
$443$	63.6751	+	53.4298i	0.143736	+	0.120609i	−0.568084	+	0.822970i	$0.692315\pi$
$444$	201.275	−	348.619i	0.453323	−	0.785178i
$445$	141.088	−	81.4572i	0.317052	−	0.183050i
$446$	10.0291	−	56.8777i	0.0224867	−	0.127528i
$447$	449.650	+	79.2854i	1.00593	+	0.177372i
$448$	−102.736	−	177.944i	−0.229321	−	0.397196i
$449$	108.702	+	62.7592i	0.242098	+	0.139775i	0.616141	−	0.787636i	$-0.288695\pi$
$449$	108.702	+	62.7592i	0.242098	+	0.139775i	−0.374042	+	0.927412i	$0.622029\pi$
$450$	−100.128	+	119.328i	−0.222507	+	0.265174i
$451$	−232.367	+	638.424i	−0.515227	+	1.41557i
$452$	39.1702	+	107.619i	0.0866597	+	0.238096i
$453$	−584.266	+	490.257i	−1.28977	+	1.08225i
$454$	35.3716	+	200.602i	0.0779109	+	0.441855i
$455$			69.0240i			0.151701i
$456$		0			0
$457$	763.151			1.66992			0.834958	−	0.550314i	$-0.185492\pi$
$457$	763.151			1.66992			0.834958	+	0.550314i	$0.185492\pi$
$458$	54.3633	−	9.58572i	0.118697	−	0.0209295i
$459$	94.6833	+	112.839i	0.206282	+	0.245837i
$460$	−112.012	+	40.7691i	−0.243505	+	0.0886284i
$461$	−102.490	−	37.3033i	−0.222321	−	0.0809183i	0.228458	−	0.973554i	$-0.426632\pi$
$461$	−102.490	−	37.3033i	−0.222321	−	0.0809183i	−0.450779	+	0.892635i	$0.648854\pi$
$462$	−115.144	−	96.6177i	−0.249230	−	0.209129i
$463$	−0.476643	+	0.825570i	−0.00102947	+	0.00178309i	−0.866540	−	0.499108i	$-0.833661\pi$
$463$	−0.476643	+	0.825570i	−0.00102947	+	0.00178309i	0.865510	+	0.500891i	$0.166994\pi$
$464$	−307.292	+	177.415i	−0.662268	+	0.382360i
$465$	98.6509	−	559.477i	0.212152	−	1.20318i
$466$	90.5394	+	15.9645i	0.194291	+	0.0342587i
$467$	185.392	+	321.108i	0.396984	+	0.687597i	0.993352	−	0.115114i	$-0.0367234\pi$
$467$	185.392	+	321.108i	0.396984	+	0.687597i	−0.596368	+	0.802711i	$0.703390\pi$
$468$	295.765	+	170.760i	0.631977	+	0.364872i
$469$	186.859	−	222.690i	0.398421	−	0.474819i
$470$	−14.2121	+	39.0473i	−0.0302384	+	0.0830794i
$471$	116.517	+	320.127i	0.247381	+	0.679674i
$472$	47.2470	−	39.6450i	0.100100	−	0.0839936i
$473$	−123.474	−	700.257i	−0.261045	−	1.48046i
$474$		−	138.575i		−	0.292353i
$475$		0			0
$476$	−38.5024			−0.0808875
$477$	1345.39	−	237.228i	2.82052	−	0.497333i
$478$	−89.5276	−	106.695i	−0.187296	−	0.223211i
$479$	59.5645	−	21.6797i	0.124352	−	0.0452604i	−0.279095	−	0.960264i	$-0.590034\pi$
$479$	59.5645	−	21.6797i	0.124352	−	0.0452604i	0.403447	+	0.915003i	$0.367812\pi$
$480$	383.326	+	139.519i	0.798596	+	0.290665i
$481$	−61.4668	−	51.5768i	−0.127790	−	0.107228i
$482$	−37.9345	+	65.7045i	−0.0787023	+	0.136316i
$483$	233.200	−	134.638i	0.482816	−	0.278754i
$484$	−4.80956	+	27.2764i	−0.00993712	+	0.0563562i
$485$	128.473	+	22.6533i	0.264893	+	0.0467078i
$486$	121.607	+	210.630i	0.250220	+	0.433394i
$487$	299.678	+	173.019i	0.615355	+	0.355275i	0.775058	−	0.631890i	$-0.217720\pi$
$487$	299.678	+	173.019i	0.615355	+	0.355275i	−0.159704	+	0.987165i	$0.551054\pi$
$488$	−169.349	+	201.822i	−0.347027	+	0.413570i
$489$	385.347	−	1058.73i	0.788031	−	2.16510i
$490$	13.5234	+	37.1553i	0.0275988	+	0.0758272i
$491$	205.028	−	172.039i	0.417572	−	0.350384i	−0.409667	−	0.912235i	$-0.634355\pi$
$491$	205.028	−	172.039i	0.417572	−	0.350384i	0.827239	+	0.561851i	$0.189911\pi$
$492$	230.657	+	1308.12i	0.468814	+	2.65878i
$493$			55.7462i			0.113076i
$494$		0			0
$495$	−773.309			−1.56224
$496$	395.951	−	69.8169i	0.798289	−	0.140760i
$497$	−365.646	−	435.760i	−0.735707	−	0.876781i
$498$	253.408	−	92.2329i	0.508851	−	0.185207i
$499$	219.330	+	79.8295i	0.439539	+	0.159979i	0.552304	−	0.833643i	$-0.313749\pi$
$499$	219.330	+	79.8295i	0.439539	+	0.159979i	−0.112766	+	0.993622i	$0.535971\pi$
$500$	−370.602	−	310.972i	−0.741203	−	0.621943i
$501$	609.790	−	1056.19i	1.21715	−	2.10816i
$502$	−168.519	+	97.2946i	−0.335695	+	0.193814i
$503$	20.6888	−	117.332i	0.0411308	−	0.233264i	−0.957312	−	0.289058i	$-0.906658\pi$
$503$	20.6888	−	117.332i	0.0411308	−	0.233264i	0.998442	+	0.0557940i	$0.0177690\pi$
$504$	−424.434	−	74.8392i	−0.842132	−	0.148491i
$505$	−311.343	−	539.262i	−0.616521	−	1.06785i
$506$	−44.8090	−	25.8705i	−0.0885553	−	0.0511274i
$507$	−542.647	+	646.701i	−1.07031	+	1.27555i
$508$	157.315	−	432.221i	0.309676	−	0.850828i
$509$	−57.8441	−	158.925i	−0.113643	−	0.312231i	0.869812	−	0.493382i	$-0.164240\pi$
$509$	−57.8441	−	158.925i	−0.113643	−	0.312231i	−0.983455	+	0.181152i	$0.942017\pi$
$510$	14.5216	−	12.1851i	0.0284738	−	0.0238923i
$511$	−84.3902	−	478.601i	−0.165147	−	0.936597i
$512$			492.000i			0.960938i
$513$		0			0
$514$	−201.105			−0.391255
$515$	−265.317	+	46.7825i	−0.515179	+	0.0908399i
$516$	−893.605	−	1064.96i	−1.73179	−	2.06387i
$517$	249.725	−	90.8926i	0.483028	−	0.175808i
$518$	46.0142	+	16.7478i	0.0888305	+	0.0323317i
$519$	304.827	+	255.781i	0.587336	+	0.492833i
$520$	26.8103	−	46.4368i	0.0515583	−	0.0893015i
$521$	434.924	−	251.104i	0.834787	−	0.481965i	−0.0207018	−	0.999786i	$-0.506590\pi$
$521$	434.924	−	251.104i	0.834787	−	0.481965i	0.855489	+	0.517821i	$0.173257\pi$
$522$	−52.4002	+	297.176i	−0.100384	+	0.569304i
$523$	1000.13	+	176.350i	1.91229	+	0.337189i	0.997735	−	0.0672702i	$-0.0214290\pi$
$523$	1000.13	+	176.350i	1.91229	+	0.337189i	0.914556	+	0.404459i	$0.132540\pi$
$524$	217.455	+	376.643i	0.414991	+	0.718785i
$525$	340.916	+	196.828i	0.649363	+	0.374910i
$526$	19.7679	−	23.5584i	0.0375815	−	0.0447879i
$527$	21.6041	−	59.3568i	0.0409945	−	0.112632i
$528$	−263.931	−	725.144i	−0.499869	−	1.37338i
$529$	−334.231	+	280.453i	−0.631817	+	0.530157i
$530$	−18.0118	−	102.150i	−0.0339846	−	0.192736i
$531$			346.641i			0.652808i
$532$		0			0
$533$	264.766			0.496746
$534$	136.156	−	24.0080i	0.254975	−	0.0449589i
$535$	−158.766	−	189.210i	−0.296759	−	0.353663i
$536$	−212.209	+	77.2379i	−0.395913	+	0.144101i
$537$	690.498	+	251.321i	1.28584	+	0.468009i
$538$	64.1653	+	53.8410i	0.119266	+	0.100076i
$539$	126.438	−	218.997i	0.234578	−	0.406302i
$540$	−772.489	+	445.997i	−1.43054	+	0.825920i
$541$	43.6914	−	247.786i	0.0807604	−	0.458015i	−0.917431	−	0.397895i	$-0.869741\pi$
$541$	43.6914	−	247.786i	0.0807604	−	0.458015i	0.998191	−	0.0601194i	$-0.0191482\pi$
$542$	−94.6146	−	16.6831i	−0.174566	−	0.0307806i
$543$	401.010	+	694.571i	0.738509	+	1.27914i
$544$	39.2796	+	22.6781i	0.0722052	+	0.0416877i
$545$	85.8715	−	102.338i	0.157562	−	0.187776i
$546$	−20.0345	+	55.0444i	−0.0366933	+	0.100814i
$547$	77.3033	+	212.389i	0.141322	+	0.388280i	0.990081	−	0.140501i	$-0.0448714\pi$
$547$	77.3033	+	212.389i	0.141322	+	0.388280i	−0.848758	+	0.528781i	$0.822649\pi$
$548$	117.308	−	98.4335i	0.214067	−	0.179623i
$549$	−257.125	−	1458.23i	−0.468352	−	2.65616i
$550$		−	75.6401i		−	0.137528i
$551$		0			0
$552$	−209.185			−0.378958
$553$	−244.590	+	43.1279i	−0.442297	+	0.0779889i
$554$	−31.6756	−	37.7495i	−0.0571762	−	0.0681399i
$555$	333.796	−	121.492i	0.601435	−	0.218904i
$556$	−43.0233	−	15.6592i	−0.0773801	−	0.0281641i
$557$	775.468	+	650.695i	1.39222	+	1.16821i	0.964430	+	0.264338i	$0.0851533\pi$
$557$	775.468	+	650.695i	1.39222	+	1.16821i	0.427793	+	0.903877i	$0.359291\pi$
$558$	170.963	−	296.117i	0.306385	−	0.530675i
$559$	−239.980	+	138.552i	−0.429302	+	0.247858i
$560$	37.5525	−	212.971i	0.0670580	−	0.380305i
$561$	−119.394	−	21.0525i	−0.212824	−	0.0375267i
$562$	65.7622	+	113.903i	0.117015	+	0.202675i
$563$	−231.065	−	133.406i	−0.410418	−	0.236955i	0.280551	−	0.959839i	$-0.409483\pi$
$563$	−231.065	−	133.406i	−0.410418	−	0.236955i	−0.690969	+	0.722884i	$0.742816\pi$
$564$	333.977	−	398.018i	0.592158	−	0.705706i
$565$	−34.5645	+	94.9653i	−0.0611762	+	0.168080i
$566$	51.5862	+	141.732i	0.0911417	+	0.250410i
$567$	782.786	−	656.836i	1.38058	−	1.15844i
$568$	76.7354	+	435.188i	0.135098	+	0.766176i
$569$			883.651i			1.55299i	0.630124	+	0.776494i	$0.283004\pi$
$569$			883.651i			1.55299i	−0.630124	+	0.776494i	$0.716996\pi$
$570$		0			0
$571$	365.568			0.640224			0.320112	−	0.947380i	$-0.396280\pi$
$571$	365.568			0.640224			0.320112	+	0.947380i	$0.396280\pi$
$572$	−163.317	+	28.7972i	−0.285519	+	0.0503447i
$573$	1183.68	+	1410.66i	2.06577	+	2.46189i
$574$	−151.833	+	55.2628i	−0.264518	+	0.0962766i
$575$	127.335	+	46.3461i	0.221452	+	0.0806019i
$576$	−687.223	−	576.649i	−1.19310	−	1.00113i
$577$	−316.678	+	548.503i	−0.548836	+	0.950612i	0.449519	+	0.893271i	$0.351596\pi$
$577$	−316.678	+	548.503i	−0.548836	+	0.950612i	−0.998355	+	0.0573410i	$0.981738\pi$
$578$	−124.369	+	71.8046i	−0.215172	+	0.124229i
$579$	71.8664	−	407.574i	0.124122	−	0.703928i
$580$	−332.447	−	58.6194i	−0.573185	−	0.101068i
$581$	−241.661	−	418.569i	−0.415939	−	0.720428i
$582$	95.8779	+	55.3551i	0.164739	+	0.0951119i
$583$	−426.409	+	508.175i	−0.731406	+	0.871655i
$584$	−129.124	+	354.764i	−0.221102	+	0.607473i
$585$	103.073	+	283.189i	0.176192	+	0.484084i
$586$	196.014	−	164.475i	0.334495	−	0.280675i
$587$	−23.1674	−	131.389i	−0.0394674	−	0.223831i	0.958694	−	0.284439i	$-0.0918072\pi$
$587$	−23.1674	−	131.389i	−0.0394674	−	0.223831i	−0.998162	+	0.0606078i	$0.980696\pi$
$588$		−	494.400i		−	0.840817i
$589$		0			0
$590$	26.3192			0.0446088
$591$	−1458.85	+	257.234i	−2.46844	+	0.435252i
$592$	161.593	+	192.579i	0.272961	+	0.325303i
$593$	14.7902	−	5.38321i	0.0249414	−	0.00907792i	−0.329519	−	0.944149i	$-0.606887\pi$
$593$	14.7902	−	5.38321i	0.0249414	−	0.00907792i	0.354461	+	0.935071i	$0.384664\pi$
$594$	−363.834	−	132.425i	−0.612514	−	0.222937i
$595$	−26.0266	−	21.8389i	−0.0437422	−	0.0367040i
$596$	−153.710	+	266.234i	−0.257903	+	0.446701i
$597$	−1265.00	+	730.351i	−2.11894	+	1.22337i
$598$	−3.50141	+	19.8575i	−0.00585520	+	0.0332065i
$599$	−238.781	−	42.1035i	−0.398632	−	0.0702896i	−0.0292615	−	0.999572i	$-0.509316\pi$
$599$	−238.781	−	42.1035i	−0.398632	−	0.0702896i	−0.369371	+	0.929282i	$0.620427\pi$
$600$	−152.904	−	264.837i	−0.254839	−	0.441395i
$601$	−23.1113	−	13.3433i	−0.0384548	−	0.0222019i	0.480649	−	0.876913i	$-0.340401\pi$
$601$	−23.1113	−	13.3433i	−0.0384548	−	0.0222019i	−0.519104	+	0.854711i	$0.673734\pi$
$602$	108.700	−	129.544i	0.180565	−	0.215189i
$603$	434.100	−	1192.68i	0.719901	−	1.97791i
$604$	−175.638	−	482.561i	−0.290791	−	0.798942i
$605$	−18.7225	+	15.7101i	−0.0309463	+	0.0259671i
$606$	−91.7628	−	520.413i	−0.151424	−	0.858767i
$607$		−	705.287i		−	1.16192i	−0.813931	−	0.580961i	$-0.802677\pi$
$607$		−	705.287i		−	1.16192i	0.813931	−	0.580961i	$-0.197323\pi$
$608$		0			0
$609$	762.589			1.25220
$610$	−110.718	+	19.5226i	−0.181505	+	0.0320042i
$611$	−66.5706	−	79.3358i	−0.108954	−	0.129846i
$612$	−157.967	+	57.4951i	−0.258115	+	0.0939463i
$613$	746.206	+	271.597i	1.21730	+	0.443062i	0.869231	−	0.494407i	$-0.164615\pi$
$613$	746.206	+	271.597i	1.21730	+	0.443062i	0.348071	+	0.937468i	$0.386837\pi$
$614$	−18.1417	−	15.2227i	−0.0295468	−	0.0247927i
$615$	−586.058	+	1015.08i	−0.952940	+	1.65054i
$616$	181.240	−	104.639i	0.294220	−	0.169868i
$617$	−178.356	+	1011.51i	−0.289070	+	1.63939i	0.401306	+	0.915944i	$0.368556\pi$
$617$	−178.356	+	1011.51i	−0.289070	+	1.63939i	−0.690376	+	0.723451i	$0.742555\pi$
$618$	−225.160	−	39.7019i	−0.364337	−	0.0642425i
$619$	340.432	+	589.645i	0.549971	+	0.952577i	0.998276	+	0.0586965i	$0.0186944\pi$
$619$	340.432	+	589.645i	0.549971	+	0.952577i	−0.448305	+	0.893880i	$0.647972\pi$
$620$	331.262	+	191.254i	0.534293	+	0.308474i
$621$	445.855	−	531.349i	0.717963	−	0.855635i
$622$	−16.5794	+	45.5516i	−0.0266550	+	0.0732341i
$623$	−84.7501	−	232.849i	−0.136035	−	0.373754i
$624$	−230.372	+	193.305i	−0.369186	+	0.309784i
$625$	−13.0296	−	73.8943i	−0.0208473	−	0.118231i
$626$			28.1011i			0.0448899i
$627$		0			0
$628$	−229.375			−0.365247
$629$	38.8957	−	6.85836i	0.0618373	−	0.0109036i
$630$	−118.217	−	140.885i	−0.187645	−	0.223627i
$631$	−577.097	+	210.046i	−0.914575	+	0.332878i	−0.756078	−	0.654482i	$-0.772887\pi$
$631$	−577.097	+	210.046i	−0.914575	+	0.332878i	−0.158497	+	0.987360i	$0.550665\pi$
$632$	181.303	+	65.9890i	0.286872	+	0.104413i
$633$	−1159.27	−	972.745i	−1.83139	−	1.53672i
$634$	−93.1044	+	161.262i	−0.146852	+	0.254356i
$635$	351.500	−	202.939i	0.553543	−	0.319588i
$636$	−225.217	+	1277.27i	−0.354115	+	2.00829i
$637$	−97.0502	−	17.1126i	−0.152355	−	0.0268643i
$638$	−73.2650	−	126.899i	−0.114835	−	0.198901i
$639$	−2150.88	−	1241.81i	−3.36600	−	1.94336i
$640$	−232.312	+	276.859i	−0.362988	+	0.432592i
$641$	−85.6701	+	235.377i	−0.133651	+	0.367202i	−0.988407	−	0.151827i	$-0.951484\pi$
$641$	−85.6701	+	235.377i	−0.133651	+	0.367202i	0.854756	+	0.519029i	$0.173706\pi$
$642$	−71.6917	−	196.971i	−0.111669	−	0.306809i
$643$	−287.355	+	241.120i	−0.446898	+	0.374992i	−0.838283	−	0.545235i	$-0.816440\pi$
$643$	−287.355	+	241.120i	−0.446898	+	0.374992i	0.391385	+	0.920227i	$0.371996\pi$
$644$	31.4832	+	178.550i	0.0488869	+	0.277252i
$645$		−	1226.74i		−	1.90192i
$646$		0			0
$647$	−862.929			−1.33374			−0.666869	−	0.745175i	$-0.732366\pi$
$647$	−862.929			−1.33374			−0.666869	+	0.745175i	$0.732366\pi$
$648$	−781.758	+	137.845i	−1.20642	+	0.212724i
$649$	−108.196	−	128.943i	−0.166712	−	0.198679i
$650$	−27.6998	+	10.0819i	−0.0426150	+	0.0155106i
$651$	−811.980	−	295.537i	−1.24728	−	0.453973i
$652$	581.119	+	487.616i	0.891286	+	0.747878i
$653$	−41.8448	+	72.4774i	−0.0640809	+	0.110991i	−0.896286	−	0.443477i	$-0.853745\pi$
$653$	−41.8448	+	72.4774i	−0.0640809	+	0.110991i	0.832205	+	0.554468i	$0.187078\pi$
$654$	98.1837	−	56.6864i	0.150128	−	0.0866765i
$655$	−66.6415	+	377.943i	−0.101743	+	0.577012i
$656$	−816.924	−	144.046i	−1.24531	−	0.219582i
$657$	−1060.92	−	1837.57i	−1.61480	−	2.79691i
$658$	54.7350	+	31.6013i	0.0831839	+	0.0480263i
$659$	−280.820	+	334.668i	−0.426130	+	0.507842i	−0.935802	−	0.352527i	$-0.885322\pi$
$659$	−280.820	+	334.668i	−0.426130	+	0.507842i	0.509672	+	0.860369i	$0.329767\pi$
$660$	251.096	−	689.882i	0.380449	−	1.04528i
$661$	−279.129	−	766.900i	−0.422283	−	1.16021i	−0.950397	−	0.311039i	$-0.899323\pi$
$661$	−279.129	−	766.900i	−0.422283	−	1.16021i	0.528115	−	0.849173i	$-0.322899\pi$
$662$	142.600	−	119.655i	0.215408	−	0.180748i
$663$	8.20429	+	46.5289i	0.0123745	+	0.0701793i
$664$			375.464i			0.565457i
$665$		0			0
$666$	213.795			0.321013
$667$	258.516	−	45.5833i	0.387580	−	0.0683408i
$668$	527.822	+	629.034i	0.790153	+	0.941668i
$669$	−598.818	+	217.952i	−0.895094	+	0.325788i
$670$	−90.5558	−	32.9596i	−0.135158	−	0.0491935i
$671$	550.798	+	462.174i	0.820861	+	0.688784i
$672$	310.228	−	537.332i	0.461650	−	0.799600i
$673$	741.181	−	427.921i	1.10131	−	0.635841i	0.164745	−	0.986336i	$-0.447320\pi$
$673$	741.181	−	427.921i	1.10131	−	0.635841i	0.936565	+	0.350495i	$0.113987\pi$
$674$	−10.7593	+	61.0193i	−0.0159634	+	0.0905330i
$675$	998.609	+	176.082i	1.47942	+	0.260862i
$676$	−284.204	−	492.256i	−0.420420	−	0.728189i
$677$	−62.9559	−	36.3476i	−0.0929924	−	0.0536892i	0.452783	−	0.891621i	$-0.350431\pi$
$677$	−62.9559	−	36.3476i	−0.0929924	−	0.0536892i	−0.545775	+	0.837932i	$0.683765\pi$
$678$	−55.1282	+	65.6992i	−0.0813100	+	0.0969015i
$679$	67.8643	−	186.456i	0.0999474	−	0.274603i
$680$	9.02707	+	24.8017i	0.0132751	+	0.0364730i
$681$	1721.70	−	1444.67i	2.52819	−	2.12140i
$682$	28.8314	+	163.511i	0.0422748	+	0.239752i
$683$		−	593.349i		−	0.868739i	−0.900735	−	0.434370i	$-0.856971\pi$
$683$		−	593.349i		−	0.868739i	0.900735	−	0.434370i	$-0.143029\pi$
$684$		0			0
$685$	135.130			0.197269
$686$	181.549	−	32.0119i	0.264648	−	0.0466646i
$687$	−391.508	−	466.581i	−0.569881	−	0.679158i
$688$	815.828	−	296.937i	1.18580	−	0.431595i
$689$	242.931	+	88.4197i	0.352585	+	0.128331i
$690$	−68.3810	−	57.3785i	−0.0991029	−	0.0831572i
$691$	174.163	−	301.659i	0.252045	−	0.436554i	−0.712044	−	0.702135i	$-0.752230\pi$
$691$	174.163	−	301.659i	0.252045	−	0.436554i	0.964089	+	0.265581i	$0.0855637\pi$
$692$	−232.028	+	133.962i	−0.335301	+	0.193586i
$693$	−204.245	+	1158.33i	−0.294726	+	1.67148i
$694$	132.788	+	23.4142i	0.191338	+	0.0337380i
$695$	−20.2006	−	34.9884i	−0.0290656	−	0.0503430i
$696$	−513.042	−	296.205i	−0.737129	−	0.425582i
$697$	−83.7707	+	99.8341i	−0.120188	+	0.143234i
$698$	−40.2743	+	110.653i	−0.0576996	+	0.158528i
$699$	−346.942	−	953.214i	−0.496340	−	1.36368i
$700$	−203.039	+	170.370i	−0.290056	+	0.243386i
$701$	130.826	+	741.952i	0.186628	+	1.05842i	0.923846	+	0.382764i	$0.125028\pi$
$701$	130.826	+	741.952i	0.186628	+	1.05842i	−0.737218	+	0.675655i	$0.763861\pi$
$702$			150.888i			0.214940i
$703$		0			0
$704$	435.620			0.618778
$705$	451.519	−	79.6149i	0.640452	−	0.112929i
$706$	13.3926	+	15.9607i	0.0189697	+	0.0226072i
$707$	−889.988	+	323.929i	−1.25882	+	0.458174i
$708$	−309.244	−	112.556i	−0.436786	−	0.158977i
$709$	126.001	+	105.727i	0.177716	+	0.149121i	0.727307	−	0.686313i	$-0.240772\pi$
$709$	126.001	+	105.727i	0.177716	+	0.149121i	−0.549591	+	0.835434i	$0.685216\pi$
$710$	−94.2860	+	163.308i	−0.132797	+	0.230011i
$711$	−939.095	+	542.187i	−1.32081	+	0.762570i
$712$	−33.4265	+	189.571i	−0.0469473	+	0.266251i
$713$	−292.925	−	51.6506i	−0.410835	−	0.0724412i
$714$	−14.4165	−	24.9701i	−0.0201912	−	0.0349722i
$715$	−126.732	−	73.1686i	−0.177247	−	0.102334i
$716$	−318.020	+	379.001i	−0.444162	+	0.529331i
$717$	−525.605	+	1444.09i	−0.733062	+	2.01407i
$718$	−41.9186	−	115.171i	−0.0583825	−	0.160405i
$719$	−769.601	+	645.772i	−1.07038	+	0.898152i	−0.995086	−	0.0990094i	$-0.968433\pi$
$719$	−769.601	+	645.772i	−1.07038	+	0.898152i	−0.0752897	+	0.997162i	$0.523988\pi$
$720$	−163.957	−	929.847i	−0.227718	−	1.29145i
$721$			409.772i			0.568339i
$722$		0			0
$723$	837.111			1.15783
$724$	−531.799	+	93.7705i	−0.734529	+	0.129517i
$725$	246.673	+	293.973i	0.340238	+	0.405480i
$726$	−19.4905	+	7.09397i	−0.0268465	+	0.00977131i
$727$	37.8713	+	13.7840i	0.0520926	+	0.0189602i	0.367935	−	0.929851i	$-0.380065\pi$
$727$	37.8713	+	13.7840i	0.0520926	+	0.0189602i	−0.315842	+	0.948812i	$0.602287\pi$
$728$	−62.4762	−	52.4238i	−0.0858190	−	0.0720107i
$729$	427.115	−	739.785i	0.585892	−	1.01479i
$730$	−139.520	+	80.5518i	−0.191123	+	0.110345i
$731$	23.6852	−	134.326i	0.0324011	−	0.183756i
$732$	1384.40	+	244.107i	1.89126	+	0.333480i
$733$	401.131	+	694.780i	0.547246	+	0.947858i	0.998462	+	0.0554428i	$0.0176570\pi$
$733$	401.131	+	694.780i	0.547246	+	0.947858i	−0.451216	+	0.892415i	$0.649010\pi$
$734$	175.370	+	101.250i	0.238924	+	0.137943i
$735$	280.428	−	334.201i	0.381535	−	0.454695i
$736$	73.0481	−	200.698i	0.0992501	−	0.272687i
$737$	210.792	+	579.145i	0.286013	+	0.785815i
$738$	−540.414	+	453.461i	−0.732268	+	0.614445i
$739$	−13.3551	−	75.7404i	−0.0180718	−	0.102490i	0.974438	−	0.224658i	$-0.0721265\pi$
$739$	−13.3551	−	75.7404i	−0.0180718	−	0.102490i	−0.992509	+	0.122168i	$0.961015\pi$
$740$			239.170i			0.323202i
$741$		0			0
$742$	−157.767			−0.212624
$743$	−912.618	+	160.919i	−1.22829	+	0.216580i	−0.749890	−	0.661563i	$-0.769894\pi$
$743$	−912.618	+	160.919i	−1.22829	+	0.216580i	−0.478398	+	0.878143i	$0.658782\pi$
$744$	431.478	+	514.216i	0.579944	+	0.691150i
$745$	−254.914	+	92.7811i	−0.342167	+	0.124538i
$746$	286.546	+	104.294i	0.384110	+	0.139805i
$747$	−1616.52	−	1356.42i	−2.16402	−	1.81583i
$748$	40.8144	−	70.6925i	0.0545646	−	0.0945087i
$749$	−325.349	+	187.840i	−0.434378	+	0.250788i
$750$	62.9109	−	356.785i	0.0838812	−	0.475714i
$751$	−1273.87	−	224.618i	−1.69624	−	0.299092i	−0.759858	−	0.650089i	$-0.774732\pi$
$751$	−1273.87	−	224.618i	−1.69624	−	0.299092i	−0.936377	+	0.350996i	$0.885843\pi$
$752$	162.238	+	281.005i	0.215743	+	0.373677i
$753$	1859.38	+	1073.51i	2.46929	+	1.42565i
$754$	−36.7056	+	43.7440i	−0.0486811	+	0.0580159i
$755$	154.986	−	425.821i	0.205280	−	0.564002i
$756$	464.026	+	1274.90i	0.613792	+	1.68638i
$757$	373.503	−	313.406i	0.493399	−	0.414011i	−0.361844	−	0.932239i	$-0.617853\pi$
$757$	373.503	−	313.406i	0.493399	−	0.414011i	0.855242	+	0.518228i	$0.173408\pi$
$758$	2.74736	+	15.5811i	0.00362449	+	0.0205555i
$759$			570.891i			0.752162i
$760$		0			0
$761$	−271.919			−0.357318			−0.178659	−	0.983911i	$-0.557176\pi$
$761$	−271.919			−0.357318			−0.178659	+	0.983911i	$0.557176\pi$
$762$	339.214	−	59.8125i	0.445162	−	0.0784941i
$763$	−130.611	−	155.656i	−0.171180	−	0.204005i
$764$	−1165.10	+	424.063i	−1.52501	+	0.555056i
$765$	−139.393	−	50.7348i	−0.182213	−	0.0663200i
$766$	165.984	+	139.277i	0.216689	+	0.181824i
$767$	−32.7983	+	56.8084i	−0.0427619	+	0.0740657i
$768$	522.021	−	301.389i	0.679715	−	0.392434i
$769$	133.111	−	754.908i	0.173096	−	0.981675i	−0.767223	−	0.641380i	$-0.778362\pi$
$769$	133.111	−	754.908i	0.173096	−	0.981675i	0.940319	−	0.340295i	$-0.110527\pi$
$770$	87.9479	+	15.5076i	0.114218	+	0.0201397i
$771$	1109.46	+	1921.64i	1.43899	+	2.49240i
$772$	241.322	+	139.327i	0.312593	+	0.180476i
$773$	−667.535	+	795.538i	−0.863565	+	1.02916i	0.135698	+	0.990750i	$0.456672\pi$
$773$	−667.535	+	795.538i	−0.863565	+	1.02916i	−0.999262	+	0.0384059i	$0.987772\pi$
$774$	252.526	−	693.810i	0.326261	−	0.896395i
$775$	−148.722	−	408.610i	−0.191899	−	0.527239i
$776$	−118.080	+	99.0806i	−0.152165	+	0.127681i
$777$	−93.8199	−	532.079i	−0.120746	−	0.684787i
$778$		−	306.268i		−	0.393660i
$779$		0			0
$780$	−286.106			−0.366803
$781$	1187.68	−	209.420i	1.52072	−	0.268144i
$782$	−6.37974	−	7.60308i	−0.00815824	−	0.00972261i
$783$	1845.88	−	671.846i	2.35745	−	0.858041i
$784$	290.135	+	105.600i	0.370070	+	0.134694i
$785$	−155.051	−	130.103i	−0.197517	−	0.165737i
$786$	−162.844	+	282.054i	−0.207181	+	0.358848i
$787$	164.535	−	94.9942i	0.209066	−	0.120704i	−0.391811	−	0.920046i	$-0.628151\pi$
$787$	164.535	−	94.9942i	0.209066	−	0.120704i	0.600877	+	0.799341i	$0.294818\pi$
$788$	173.196	−	982.245i	0.219792	−	1.24650i
$789$	−334.166	−	58.9225i	−0.423531	−	0.0746800i
$790$	41.1662	+	71.3020i	0.0521092	+	0.0902557i
$791$	133.119	+	76.8561i	0.168292	+	0.0971631i
$792$	587.329	−	699.951i	0.741577	−	0.883777i
$793$	95.8359	−	263.307i	0.120852	−	0.332039i
$794$	−36.6181	−	100.607i	−0.0461185	−	0.126710i
$795$	−876.719	+	735.655i	−1.10279	+	0.925352i
$796$	−170.782	−	968.552i	−0.214550	−	1.21677i
$797$			753.381i			0.945270i	0.881258	+	0.472635i	$0.156697\pi$
$797$			753.381i			0.945270i	−0.881258	+	0.472635i	$0.843303\pi$
$798$		0			0
$799$	50.9775			0.0638016
$800$	307.487	−	54.2182i	0.384358	−	0.0677728i
$801$	−695.420	−	828.769i	−0.868190	−	1.03467i
$802$	−143.873	+	52.3655i	−0.179393	+	0.0652936i
$803$	968.194	+	352.394i	1.20572	+	0.438847i
$804$	923.056	+	774.536i	1.14808	+	0.963353i
$805$	−79.9933	+	138.552i	−0.0993705	+	0.172115i
$806$	56.0357	−	32.3522i	0.0695232	−	0.0401392i
$807$	160.485	−	910.157i	0.198866	−	1.12783i
$808$	724.572	+	127.762i	0.896747	+	0.158121i
$809$	−579.462	−	1003.66i	−0.716270	−	1.24062i	−0.962468	−	0.271396i	$-0.912515\pi$
$809$	−579.462	−	1003.66i	−0.716270	−	1.24062i	0.246198	−	0.969220i	$-0.420819\pi$
$810$	−293.361	−	169.372i	−0.362175	−	0.209102i
$811$	−189.313	+	225.614i	−0.233431	+	0.278192i	−0.870026	−	0.493006i	$-0.835898\pi$
$811$	−189.313	+	225.614i	−0.233431	+	0.278192i	0.636595	+	0.771199i	$0.280342\pi$
$812$	−175.611	+	482.488i	−0.216270	+	0.594197i
$813$	362.558	+	996.119i	0.445950	+	1.22524i
$814$	−79.5270	+	66.7311i	−0.0976991	+	0.0819793i
$815$	116.240	+	659.231i	0.142626	+	0.808872i
$816$		−	148.027i		−	0.181405i
$817$		0			0
$818$	247.326			0.302355
$819$	451.411	−	79.5959i	0.551173	−	0.0971867i
$820$	−507.281	−	604.553i	−0.618635	−	0.737260i
$821$	1108.38	−	403.417i	1.35003	−	0.491372i	0.437076	−	0.899425i	$-0.356014\pi$
$821$	1108.38	−	403.417i	1.35003	−	0.491372i	0.912958	+	0.408052i	$0.133792\pi$
$822$	107.761	+	39.2220i	0.131097	+	0.0477153i
$823$	697.170	+	584.995i	0.847109	+	0.710808i	0.959151	−	0.282895i	$-0.0912948\pi$
$823$	697.170	+	584.995i	0.847109	+	0.710808i	−0.112042	+	0.993703i	$0.535739\pi$
$824$	159.164	−	275.680i	0.193160	−	0.334563i
$825$	−722.773	+	417.293i	−0.876088	+	0.505810i
$826$	6.95139	−	39.4233i	0.00841573	−	0.0477280i
$827$	575.392	+	101.457i	0.695758	+	0.122681i	0.510332	−	0.859977i	$-0.329522\pi$
$827$	575.392	+	101.457i	0.695758	+	0.122681i	0.185426	+	0.982658i	$0.440634\pi$
$828$	395.794	+	685.536i	0.478013	+	0.827942i
$829$	594.252	+	343.092i	0.716830	+	0.413862i	0.813585	−	0.581446i	$-0.197513\pi$
$829$	594.252	+	343.092i	0.716830	+	0.413862i	−0.0967546	+	0.995308i	$0.530846\pi$
$830$	−102.988	+	122.736i	−0.124082	+	0.147875i
$831$	−185.963	+	510.930i	−0.223783	+	0.614838i
$832$	−58.0627	−	159.526i	−0.0697869	−	0.191738i
$833$	37.1588	−	31.1800i	0.0446084	−	0.0374309i
$834$	−5.95375	−	33.7654i	−0.00713879	−	0.0404861i
$835$			724.595i			0.867778i
$836$		0			0
$837$	−2225.81			−2.65927
$838$	10.4181	−	1.83700i	0.0124321	−	0.00219212i
$839$	−540.139	−	643.712i	−0.643789	−	0.767237i	0.341175	−	0.940000i	$-0.389175\pi$
$839$	−540.139	−	643.712i	−0.643789	−	0.767237i	−0.984964	+	0.172763i	$0.944731\pi$
$840$	339.278	−	123.487i	0.403902	−	0.147008i
$841$	−91.7055	−	33.3781i	−0.109043	−	0.0396886i
$842$	−269.650	−	226.263i	−0.320249	−	0.268721i
$843$	725.596	−	1256.77i	0.860731	−	1.49083i
$844$	882.414	−	509.462i	1.04551	−	0.603628i
$845$	87.0974	−	493.954i	0.103074	−	0.584561i
$846$	271.755	+	47.9177i	0.321223	+	0.0566403i
$847$	18.5870	+	32.1937i	0.0219445	+	0.0380090i
$848$	−701.450	−	404.982i	−0.827182	−	0.477574i
$849$	1069.71	−	1274.84i	1.25997	−	1.50157i
$850$	4.96256	−	13.6345i	0.00583830	−	0.0160406i
$851$	−63.6095	−	174.766i	−0.0747467	−	0.205365i
$852$	1806.24	−	1515.61i	2.12000	−	1.77889i
$853$	61.4866	+	348.708i	0.0720828	+	0.408802i	0.999404	+	0.0345341i	$0.0109947\pi$
$853$	61.4866	+	348.708i	0.0720828	+	0.408802i	−0.927321	+	0.374268i	$0.877894\pi$
$854$			171.000i			0.200234i
$855$		0			0
$856$	291.844			0.340939
$857$	−1032.34	+	182.029i	−1.20459	+	0.212402i	−0.739683	−	0.672956i	$-0.765024\pi$
$857$	−1032.34	+	182.029i	−1.20459	+	0.212402i	−0.464910	+	0.885358i	$0.653913\pi$
$858$	−79.8269	−	95.1340i	−0.0930384	−	0.110879i
$859$	−319.720	+	116.368i	−0.372200	+	0.135470i	−0.521346	−	0.853346i	$-0.674570\pi$
$859$	−319.720	+	116.368i	−0.372200	+	0.135470i	0.149146	+	0.988815i	$0.452348\pi$
$860$	776.156	+	282.498i	0.902507	+	0.328486i
$861$	1365.69	+	1145.95i	1.58617	+	1.33096i
$862$	−117.549	+	203.600i	−0.136367	+	0.236195i
$863$	973.829	−	562.241i	1.12842	−	0.651495i	0.184885	−	0.982760i	$-0.440809\pi$
$863$	973.829	−	562.241i	1.12842	−	0.651495i	0.943538	+	0.331265i	$0.107475\pi$
$864$	277.530	−	1573.95i	0.321215	−	1.82170i
$865$	−232.829	−	41.0540i	−0.269166	−	0.0474613i
$866$	−122.026	−	211.355i	−0.140907	−	0.244059i
$867$	1372.25	+	792.266i	1.58275	+	0.913802i
$868$	373.971	−	445.681i	0.430842	−	0.513457i
$869$	180.092	−	494.799i	0.207240	−	0.569388i
$870$	−86.4620	−	237.552i	−0.0993816	−	0.273049i
$871$	183.990	−	154.386i	0.211240	−	0.177251i
$872$	27.4102	+	155.451i	0.0314338	+	0.178270i
$873$		−	866.325i		−	0.992354i
$874$		0			0
$875$	−649.318			−0.742078
$876$	1983.81	−	349.799i	2.26462	−	0.399314i
$877$	−411.038	−	489.856i	−0.468687	−	0.558559i	0.478978	−	0.877827i	$-0.341007\pi$
$877$	−411.038	−	489.856i	−0.468687	−	0.558559i	−0.947664	+	0.319268i	$0.896563\pi$
$878$	164.642	−	59.9250i	0.187520	−	0.0682517i
$879$	−2653.00	−	965.614i	−3.01820	−	1.09854i
$880$	351.219	+	294.707i	0.399112	+	0.334895i
$881$	160.656	−	278.264i	0.182356	−	0.315851i	−0.760326	−	0.649542i	$-0.774961\pi$
$881$	160.656	−	278.264i	0.182356	−	0.315851i	0.942683	+	0.333691i	$0.108294\pi$
$882$	227.398	−	131.288i	0.257821	−	0.148853i
$883$	−107.764	+	611.161i	−0.122043	+	0.692142i	0.860977	+	0.508644i	$0.169853\pi$
$883$	−107.764	+	611.161i	−0.122043	+	0.692142i	−0.983020	+	0.183498i	$0.941258\pi$
$884$	−31.3280	−	5.52397i	−0.0354389	−	0.00624884i
$885$	−145.198	−	251.490i	−0.164066	−	0.284170i
$886$	−36.2960	−	20.9555i	−0.0409662	−	0.0236518i
$887$	−161.097	+	191.988i	−0.181620	+	0.216446i	−0.849171	−	0.528117i	$-0.822898\pi$
$887$	−161.097	+	191.988i	−0.181620	+	0.216446i	0.667551	+	0.744564i	$0.267343\pi$
$888$	−143.552	+	394.405i	−0.161657	+	0.444150i
$889$	−211.142	−	580.109i	−0.237505	−	0.652541i
$890$	−62.9254	+	52.8007i	−0.0707027	+	0.0593266i
$891$	376.196	+	2133.51i	0.422218	+	2.39452i
$892$		−	429.061i		−	0.481010i
$893$		0			0
$894$	−230.216			−0.257512
$895$	−429.945	+	75.8110i	−0.480386	+	0.0847050i
$896$	353.347	+	421.102i	0.394360	+	0.469980i
$897$	209.063	−	76.0927i	0.233069	−	0.0848302i
$898$	−59.4711	−	21.6457i	−0.0662261	−	0.0241043i
$899$	−645.284	−	541.458i	−0.717780	−	0.602289i
$900$	−578.612	+	1002.19i	−0.642903	+	1.11354i
$901$	−110.202	+	63.6254i	−0.122311	+	0.0706165i
$902$	59.4848	−	337.355i	0.0659477	−	0.374008i
$903$	−1837.53	−	324.006i	−2.03491	−	0.358810i
$904$	−59.7049	−	103.412i	−0.0660452	−	0.114394i
$905$	−412.669	−	238.254i	−0.455988	−	0.263265i
$906$	247.193	−	294.593i	0.272840	−	0.325158i
$907$	−259.217	+	712.193i	−0.285796	+	0.785219i	0.710847	+	0.703347i	$0.248312\pi$
$907$	−259.217	+	712.193i	−0.285796	+	0.785219i	−0.996643	+	0.0818717i	$0.973910\pi$
$908$	517.564	+	1422.00i	0.570005	+	1.56608i
$909$	−3167.70	+	2658.01i	−3.48481	+	2.92411i
$910$	−6.04342	−	34.2739i	−0.00664112	−	0.0376637i
$911$		−	410.330i		−	0.450417i	−0.974311	−	0.225208i	$-0.927694\pi$
$911$		−	410.330i		−	0.450417i	0.974311	−	0.225208i	$-0.0723063\pi$
$912$		0			0
$913$	1024.69			1.12233
$914$	−378.944	+	66.8180i	−0.414599	+	0.0731050i
$915$	797.357	+	950.253i	0.871429	+	1.03853i
$916$	385.362	−	140.260i	0.420701	−	0.153123i
$917$	548.516	+	199.644i	0.598164	+	0.217714i
$918$	−56.8948	−	47.7404i	−0.0619769	−	0.0520048i
$919$	−498.853	+	864.038i	−0.542821	+	0.940194i	0.455919	+	0.890021i	$0.349311\pi$
$919$	−498.853	+	864.038i	−0.542821	+	0.940194i	−0.998741	+	0.0501729i	$0.984023\pi$
$920$	107.633	−	62.1420i	0.116992	−	0.0675456i
$921$	−45.3747	+	257.333i	−0.0492668	+	0.279406i
$922$	54.1576	+	9.54945i	0.0587393	+	0.0103573i
$923$	−234.994	−	407.021i	−0.254598	−	0.440977i
$924$	−967.049	−	558.326i	−1.04659	−	0.604249i
$925$	174.765	−	208.277i	0.188936	−	0.225165i
$926$	0.164395	−	0.451670i	0.000177532	−	0.000487765i
$927$	611.907	+	1681.20i	0.660094	+	1.81359i
$928$	463.344	−	388.791i	0.499293	−	0.418956i
$929$	230.495	+	1307.20i	0.248111	+	1.40711i	0.813155	+	0.582047i	$0.197748\pi$
$929$	230.495	+	1307.20i	0.248111	+	1.40711i	−0.565044	+	0.825061i	$0.691141\pi$
$930$			286.446i			0.308007i
$931$		0			0
$932$	682.991			0.732823
$933$	526.730	−	92.8767i	0.564555	−	0.0995463i
$934$	−120.171	−	143.214i	−0.128663	−	0.153334i
$935$	67.6868	−	24.6360i	0.0723923	−	0.0263486i
$936$	−334.609	−	121.788i	−0.357488	−	0.130115i
$937$	−618.002	−	518.565i	−0.659554	−	0.553432i	0.250399	−	0.968143i	$-0.419438\pi$
$937$	−618.002	−	518.565i	−0.659554	−	0.553432i	−0.909953	+	0.414711i	$0.863883\pi$
$938$	−73.2874	+	126.938i	−0.0781316	+	0.135328i
$939$	268.517	−	155.028i	0.285961	−	0.165100i
$940$	−53.6049	+	304.009i	−0.0570265	+	0.323413i
$941$	−381.745	−	67.3119i	−0.405680	−	0.0715323i	−0.0329149	−	0.999458i	$-0.510479\pi$
$941$	−381.745	−	67.3119i	−0.405680	−	0.0715323i	−0.372765	+	0.927926i	$0.621590\pi$
$942$	−85.8852	−	148.758i	−0.0911733	−	0.157917i
$943$	531.466	+	306.842i	0.563591	+	0.325389i
$944$	132.105	−	157.436i	0.139941	−	0.166776i
$945$	−409.466	+	1125.00i	−0.433297	+	1.19047i
$946$	122.622	+	336.902i	0.129622	+	0.356134i
$947$	−400.768	+	336.285i	−0.423198	+	0.355105i	−0.829378	−	0.558688i	$-0.811305\pi$
$947$	−400.768	+	336.285i	−0.423198	+	0.355105i	0.406180	+	0.913793i	$0.366861\pi$
$948$	−178.766	−	1013.83i	−0.188572	−	1.06944i
$949$		−	401.527i		−	0.423106i
$950$		0			0
$951$	2054.56			2.16042
$952$	39.5344	−	6.97099i	0.0415278	−	0.00732247i
$953$	331.840	+	395.472i	0.348206	+	0.414976i	0.911513	−	0.411272i	$-0.134915\pi$
$953$	331.840	+	395.472i	0.348206	+	0.414976i	−0.563307	+	0.826248i	$0.690471\pi$
$954$	−647.283	+	235.592i	−0.678493	+	0.246951i
$955$	−1028.11	−	374.202i	−1.07656	−	0.391834i
$956$	−792.633	−	665.098i	−0.829114	−	0.695709i
$957$	−808.379	+	1400.15i	−0.844701	+	1.46307i
$958$	−27.6787	+	15.9803i	−0.0288921	+	0.0166809i
$959$	35.6903	−	202.410i	0.0372161	−	0.211063i
$960$	740.127	+	130.504i	0.770965	+	0.135942i
$961$	−3.26030	−	5.64700i	−0.00339261	−	0.00587617i
$962$	35.0372	+	20.2288i	0.0364212	+	0.0210278i
$963$	−1054.33	+	1256.50i	−1.09484	+	1.30478i
$964$	−192.772	+	529.638i	−0.199971	+	0.549417i
$965$	84.0993	+	231.061i	0.0871495	+	0.239441i
$966$	−104.007	+	87.2726i	−0.107668	+	0.0903444i
$967$	85.6849	+	485.943i	0.0886090	+	0.502527i	0.996519	+	0.0833623i	$0.0265659\pi$
$967$	85.6849	+	485.943i	0.0886090	+	0.502527i	−0.907910	+	0.419165i	$0.862323\pi$
$968$		−	28.8783i		−	0.0298329i
$969$		0			0
$970$	−65.7768			−0.0678112
$971$	132.449	−	23.3543i	0.136405	−	0.0240518i	−0.105029	−	0.994469i	$-0.533494\pi$
$971$	132.449	−	23.3543i	0.136405	−	0.0240518i	0.241434	+	0.970417i	$0.422382\pi$
$972$	1161.41	+	1384.11i	1.19487	+	1.42398i
$973$	−57.7442	+	21.0172i	−0.0593466	+	0.0216004i
$974$	−163.954	−	59.6744i	−0.168331	−	0.0612673i
$975$	249.151	+	209.063i	0.255540	+	0.214423i
$976$	−438.950	+	760.284i	−0.449744	+	0.778979i
$977$	605.791	−	349.754i	0.620053	−	0.357988i	−0.156837	−	0.987625i	$-0.550130\pi$
$977$	605.791	−	349.754i	0.620053	−	0.357988i	0.776890	+	0.629637i	$0.216796\pi$
$978$	−98.6469	+	559.454i	−0.100866	+	0.572039i
$979$	517.362	+	91.2249i	0.528460	+	0.0931817i
$980$	146.870	+	254.387i	0.149868	+	0.259578i
$981$	−768.303	−	443.580i	−0.783184	−	0.452171i
$982$	−86.7439	+	103.377i	−0.0883339	+	0.105272i
$983$	−208.246	+	572.152i	−0.211848	+	0.582047i	−0.999416	−	0.0341810i	$-0.989118\pi$
$983$	−208.246	+	572.152i	−0.211848	+	0.582047i	0.787568	+	0.616228i	$0.211340\pi$
$984$	−473.678	−	1301.42i	−0.481380	−	1.32258i
$985$	674.213	−	565.732i	0.684481	−	0.574347i
$986$	−4.88088	−	27.6808i	−0.00495018	−	0.0280739i
$987$		−	697.354i		−	0.706539i
$988$		0			0
$989$	−642.285			−0.649428
$990$	383.987	−	67.7073i	0.387866	−	0.0683912i
$991$	598.041	+	712.717i	0.603472	+	0.719190i	0.978135	−	0.207971i	$-0.0666860\pi$
$991$	598.041	+	712.717i	0.603472	+	0.719190i	−0.374663	+	0.927161i	$0.622242\pi$
$992$	−644.027	+	234.407i	−0.649221	+	0.236297i
$993$	−1930.05	−	702.482i	−1.94366	−	0.707434i
$994$	219.715	+	184.363i	0.221041	+	0.185476i
$995$	433.927	−	751.583i	0.436107	−	0.755360i
$996$	1734.98	−	1001.69i	1.74194	−	1.00571i
$997$	−224.653	+	1274.07i	−0.225329	+	1.27790i	0.636727	+	0.771090i	$0.280288\pi$
$997$	−224.653	+	1274.07i	−0.225329	+	1.27790i	−0.862056	+	0.506814i	$0.830823\pi$
$998$	−115.898	−	20.4359i	−0.116130	−	0.0204769i
$999$	−695.861	−	1205.27i	−0.696558	−	1.20647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.k.333.11		144
19.2	odd	18	inner	361.3.f.k.116.11		144
19.3	odd	18	inner	361.3.f.k.299.14		144
19.4	even	9		361.3.d.g.293.11		48
19.5	even	9	inner	361.3.f.k.307.11		144
19.6	even	9		361.3.b.d.360.14	yes	24
19.7	even	3	inner	361.3.f.k.262.14		144
19.8	odd	6	inner	361.3.f.k.127.11		144
19.9	even	9		361.3.d.g.69.14		48
19.10	odd	18		361.3.d.g.69.11		48
19.11	even	3	inner	361.3.f.k.127.14		144
19.12	odd	6	inner	361.3.f.k.262.11		144
19.13	odd	18		361.3.b.d.360.11	✓	24
19.14	odd	18	inner	361.3.f.k.307.14		144
19.15	odd	18		361.3.d.g.293.14		48
19.16	even	9	inner	361.3.f.k.299.11		144
19.17	even	9	inner	361.3.f.k.116.14		144
19.18	odd	2	inner	361.3.f.k.333.14		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.3.b.d.360.11	✓	24	19.13	odd	18
361.3.b.d.360.14	yes	24	19.6	even	9
361.3.d.g.69.11		48	19.10	odd	18
361.3.d.g.69.14		48	19.9	even	9
361.3.d.g.293.11		48	19.4	even	9
361.3.d.g.293.14		48	19.15	odd	18
361.3.f.k.116.11		144	19.2	odd	18	inner
361.3.f.k.116.14		144	19.17	even	9	inner
361.3.f.k.127.11		144	19.8	odd	6	inner
361.3.f.k.127.14		144	19.11	even	3	inner
361.3.f.k.262.11		144	19.12	odd	6	inner
361.3.f.k.262.14		144	19.7	even	3	inner
361.3.f.k.299.11		144	19.16	even	9	inner
361.3.f.k.299.14		144	19.3	odd	18	inner
361.3.f.k.307.11		144	19.5	even	9	inner
361.3.f.k.307.14		144	19.14	odd	18	inner
361.3.f.k.333.11		144	1.1	even	1	trivial
361.3.f.k.333.14		144	19.18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.496551 + 0.0875553i) q^{2} +(3.57601 + 4.26172i) q^{3} +(-3.51987 + 1.28113i) q^{4} +(-3.10600 - 1.13049i) q^{5} +(-2.14881 - 1.80306i) q^{6} +(-2.51371 + 4.35388i) q^{7} +(3.38227 - 1.95275i) q^{8} +(-3.81160 + 21.6166i) q^{9} +O(q^{10})\)	\(q+(-0.496551 + 0.0875553i) q^{2} +(3.57601 + 4.26172i) q^{3} +(-3.51987 + 1.28113i) q^{4} +(-3.10600 - 1.13049i) q^{5} +(-2.14881 - 1.80306i) q^{6} +(-2.51371 + 4.35388i) q^{7} +(3.38227 - 1.95275i) q^{8} +(-3.81160 + 21.6166i) q^{9} +(1.64127 + 0.289400i) q^{10} +(-5.32930 - 9.23062i) q^{11} +(-18.0469 - 10.4194i) q^{12} +(-2.66997 + 3.18194i) q^{13} +(0.866981 - 2.38201i) q^{14} +(-6.28925 - 17.2796i) q^{15} +(9.96922 - 8.36516i) q^{16} +(-0.355036 - 2.01351i) q^{17} -11.0675i q^{18} +12.3811 q^{20} +(-27.5441 + 4.85676i) q^{21} +(3.45446 + 4.11686i) q^{22} +(-9.04706 + 3.29286i) q^{23} +(20.4171 + 7.43122i) q^{24} +(-10.7819 - 9.04706i) q^{25} +(1.04718 - 1.81377i) q^{26} +(-62.3929 + 36.0225i) q^{27} +(3.27007 - 18.5455i) q^{28} +(-26.8513 - 4.73461i) q^{29} +(4.63585 + 8.02954i) q^{30} +(26.7556 + 15.4473i) q^{31} +(-14.2594 + 16.9937i) q^{32} +(20.2807 - 55.7208i) q^{33} +(0.352586 + 0.968723i) q^{34} +(12.7296 - 10.6814i) q^{35} +(-14.2774 - 80.9710i) q^{36} +19.3174i q^{37} -23.1084 q^{39} +(-12.7129 + 2.24163i) q^{40} +(-40.9723 - 48.8289i) q^{41} +(13.2518 - 4.82326i) q^{42} +(62.6890 + 22.8169i) q^{43} +(30.5841 + 25.6631i) q^{44} +(36.2763 - 62.8324i) q^{45} +(4.20402 - 2.42719i) q^{46} +(-4.32959 + 24.5543i) q^{47} +(71.3000 + 12.5721i) q^{48} +(11.8625 + 20.5465i) q^{49} +(6.14586 + 3.54832i) q^{50} +(7.31139 - 8.71338i) q^{51} +(5.32147 - 14.6206i) q^{52} +(-21.2868 - 58.4851i) q^{53} +(27.8273 - 23.3499i) q^{54} +(6.11768 + 34.6951i) q^{55} +19.6346i q^{56} +13.7476 q^{58} +(15.5523 - 2.74229i) q^{59} +(44.2747 + 52.7646i) q^{60} +(-63.3905 + 23.0722i) q^{61} +(-14.6380 - 5.32779i) q^{62} +(-84.5349 - 70.9332i) q^{63} +(-20.4351 + 35.3947i) q^{64} +(11.8901 - 6.86475i) q^{65} +(-5.19175 + 29.4439i) q^{66} +(-56.9447 - 10.0409i) q^{67} +(3.82924 + 6.63244i) q^{68} +(-46.3856 - 26.7808i) q^{69} +(-5.38569 + 6.41842i) q^{70} +(-38.6990 + 106.325i) q^{71} +(29.3201 + 80.5563i) q^{72} +(-74.0509 + 62.1361i) q^{73} +(-1.69134 - 9.59207i) q^{74} -78.3016i q^{75} +53.5853 q^{77} +(11.4745 - 2.02326i) q^{78} +(31.7548 + 37.8439i) q^{79} +(-40.4212 + 14.7121i) q^{80} +(-190.998 - 69.5177i) q^{81} +(24.6201 + 20.6587i) q^{82} +(-48.0685 + 83.2571i) q^{83} +(90.7295 - 52.3827i) q^{84} +(-1.17351 + 6.65533i) q^{85} +(-33.1260 - 5.84102i) q^{86} +(-75.8429 - 131.364i) q^{87} +(-36.0502 - 20.8136i) q^{88} +(-31.6819 + 37.7570i) q^{89} +(-12.5117 + 34.3757i) q^{90} +(-7.14226 - 19.6232i) q^{91} +(27.6259 - 23.1809i) q^{92} +(29.8459 + 169.264i) q^{93} -12.5716i q^{94} -123.415 q^{96} +(-38.8683 + 6.85353i) q^{97} +(-7.68929 - 9.16374i) q^{98} +(219.848 - 80.0181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 24 q^{7}+O(q^{10}) \) 144 * q - 24 * q^7	\( 144 q - 24 q^{7} + 192 q^{11} + 528 q^{20} - 228 q^{26} + 1440 q^{30} + 408 q^{39} + 264 q^{45} - 336 q^{49} + 216 q^{58} + 24 q^{64} + 480 q^{68} - 144 q^{77} + 1704 q^{83} - 3216 q^{87} - 3624 q^{96}+O(q^{100}) \) 144 * q - 24 * q^7 + 192 * q^11 + 528 * q^20 - 228 * q^26 + 1440 * q^30 + 408 * q^39 + 264 * q^45 - 336 * q^49 + 216 * q^58 + 24 * q^64 + 480 * q^68 - 144 * q^77 + 1704 * q^83 - 3216 * q^87 - 3624 * q^96

Introduction

L-functions

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