LMFDB - Embedded newform 189.3.k.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (of order $6$, degree $2$, 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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	189.19
Dual form			189.3.k.a.10.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826674 - 1.43184i) q^{2} +(0.633221 - 1.09677i) q^{4} -7.86923i q^{5} +(-5.81886 + 3.89113i) q^{7} -8.70726 q^{8} +O(q^{10})$	\(q+(-0.826674 - 1.43184i) q^{2} +(0.633221 - 1.09677i) q^{4} -7.86923i q^{5} +(-5.81886 + 3.89113i) q^{7} -8.70726 q^{8} +(-11.2675 + 6.50529i) q^{10} +0.712531 q^{11} +(11.3334 - 6.54333i) q^{13} +(10.3818 + 5.11499i) q^{14} +(4.66518 + 8.08032i) q^{16} +(-14.9400 + 8.62563i) q^{17} +(3.67616 + 2.12243i) q^{19} +(-8.63075 - 4.98297i) q^{20} +(-0.589031 - 1.02023i) q^{22} -15.4669 q^{23} -36.9248 q^{25} +(-18.7380 - 10.8184i) q^{26} +(0.583053 + 8.84591i) q^{28} +(8.42802 - 14.5978i) q^{29} +(-38.1282 - 22.0134i) q^{31} +(-9.70136 + 16.8033i) q^{32} +(24.7010 + 14.2612i) q^{34} +(30.6202 + 45.7900i) q^{35} +(23.2785 - 40.3196i) q^{37} -7.01823i q^{38} +68.5195i q^{40} +(47.7579 - 27.5730i) q^{41} +(-17.6802 + 30.6230i) q^{43} +(0.451190 - 0.781484i) q^{44} +(12.7860 + 22.1461i) q^{46} +(-1.12164 + 0.647579i) q^{47} +(18.7182 - 45.2839i) q^{49} +(30.5248 + 52.8705i) q^{50} -16.5735i q^{52} +(-36.4805 - 63.1860i) q^{53} -5.60707i q^{55} +(50.6663 - 33.8811i) q^{56} -27.8689 q^{58} +(45.0624 + 26.0168i) q^{59} +(81.9361 - 47.3058i) q^{61} +72.7914i q^{62} +69.4008 q^{64} +(-51.4910 - 89.1850i) q^{65} +(45.5040 - 78.8152i) q^{67} +21.8477i q^{68} +(40.2510 - 81.6966i) q^{70} -34.4191 q^{71} +(-28.6859 + 16.5618i) q^{73} -76.9750 q^{74} +(4.65564 - 2.68794i) q^{76} +(-4.14612 + 2.77255i) q^{77} +(-47.3266 - 81.9721i) q^{79} +(63.5859 - 36.7114i) q^{80} +(-78.9604 - 45.5878i) q^{82} +(79.2685 + 45.7657i) q^{83} +(67.8771 + 117.567i) q^{85} +58.4630 q^{86} -6.20419 q^{88} +(58.0738 + 33.5289i) q^{89} +(-40.4864 + 82.1743i) q^{91} +(-9.79394 + 16.9636i) q^{92} +(1.85446 + 1.07067i) q^{94} +(16.7019 - 28.9285i) q^{95} +(33.5610 + 19.3764i) q^{97} +(-80.3131 + 10.6334i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.826674	−	1.43184i	−0.413337	−	0.715920i	0.581915	−	0.813249i	$-0.302303\pi$
$2$	−0.826674	−	1.43184i	−0.413337	−	0.715920i	−0.995252	+	0.0973289i	$0.968970\pi$
$3$		0			0
$3$		0			0
$4$	0.633221	−	1.09677i	0.158305	−	0.274193i
$5$		−	7.86923i		−	1.57385i	−0.617051	−	0.786923i	$-0.711673\pi$
$5$		−	7.86923i		−	1.57385i	0.617051	−	0.786923i	$-0.288327\pi$
$6$		0			0
$7$	−5.81886	+	3.89113i	−0.831266	+	0.555875i
$7$	−5.81886	+	3.89113i	−0.831266	+	0.555875i
$8$	−8.70726			−1.08841
$9$		0			0
$10$	−11.2675	+	6.50529i	−1.12675	+	0.650529i
$11$	0.712531			0.0647755			0.0323878	−	0.999475i	$-0.489689\pi$
$11$	0.712531			0.0647755			0.0323878	+	0.999475i	$0.489689\pi$
$12$		0			0
$13$	11.3334	−	6.54333i	0.871798	−	0.503333i	0.00385293	−	0.999993i	$-0.498774\pi$
$13$	11.3334	−	6.54333i	0.871798	−	0.503333i	0.867945	+	0.496660i	$0.165440\pi$
$14$	10.3818	+	5.11499i	0.741555	+	0.365356i
$15$		0			0
$16$	4.66518	+	8.08032i	0.291573	+	0.505020i
$17$	−14.9400	+	8.62563i	−0.878825	+	0.507390i	−0.870271	−	0.492574i	$-0.836056\pi$
$17$	−14.9400	+	8.62563i	−0.878825	+	0.507390i	−0.00855411	+	0.999963i	$0.502723\pi$
$18$		0			0
$19$	3.67616	+	2.12243i	0.193482	+	0.111707i	0.593612	−	0.804752i	$-0.297702\pi$
$19$	3.67616	+	2.12243i	0.193482	+	0.111707i	−0.400130	+	0.916459i	$0.631035\pi$
$20$	−8.63075	−	4.98297i	−0.431538	−	0.249148i
$21$		0			0
$22$	−0.589031	−	1.02023i	−0.0267741	−	0.0463741i
$23$	−15.4669			−0.672472			−0.336236	−	0.941778i	$-0.609154\pi$
$23$	−15.4669			−0.672472			−0.336236	+	0.941778i	$0.609154\pi$
$24$		0			0
$25$	−36.9248			−1.47699
$26$	−18.7380	−	10.8184i	−0.720693	−	0.416092i
$27$		0			0
$28$	0.583053	+	8.84591i	0.0208233	+	0.315925i
$29$	8.42802	−	14.5978i	0.290621	−	0.503371i	−0.683335	−	0.730105i	$-0.739471\pi$
$29$	8.42802	−	14.5978i	0.290621	−	0.503371i	0.973957	+	0.226734i	$0.0728047\pi$
$30$		0			0
$31$	−38.1282	−	22.0134i	−1.22994	−	0.710108i	−0.262925	−	0.964816i	$-0.584687\pi$
$31$	−38.1282	−	22.0134i	−1.22994	−	0.710108i	−0.967018	+	0.254708i	$0.918021\pi$
$32$	−9.70136	+	16.8033i	−0.303168	+	0.525102i
$33$		0			0
$34$	24.7010	+	14.2612i	0.726501	+	0.419446i
$35$	30.6202	+	45.7900i	0.874863	+	1.30828i
$36$		0			0
$37$	23.2785	−	40.3196i	0.629150	−	1.08972i	−0.358573	−	0.933502i	$-0.616737\pi$
$37$	23.2785	−	40.3196i	0.629150	−	1.08972i	0.987723	−	0.156218i	$-0.0499301\pi$
$38$		−	7.01823i		−	0.184690i
$39$		0			0
$40$			68.5195i			1.71299i
$41$	47.7579	−	27.5730i	1.16483	−	0.672513i	0.212370	−	0.977189i	$-0.431882\pi$
$41$	47.7579	−	27.5730i	1.16483	−	0.672513i	0.952456	+	0.304677i	$0.0985484\pi$
$42$		0			0
$43$	−17.6802	+	30.6230i	−0.411167	+	0.712162i	−0.995018	−	0.0996988i	$-0.968212\pi$
$43$	−17.6802	+	30.6230i	−0.411167	+	0.712162i	0.583851	+	0.811861i	$0.301545\pi$
$44$	0.451190	−	0.781484i	0.0102543	−	0.0177610i
$45$		0			0
$46$	12.7860	+	22.1461i	0.277957	+	0.481436i
$47$	−1.12164	+	0.647579i	−0.0238647	+	0.0137783i	−0.511885	−	0.859054i	$-0.671053\pi$
$47$	−1.12164	+	0.647579i	−0.0238647	+	0.0137783i	0.488020	+	0.872832i	$0.337719\pi$
$48$		0			0
$49$	18.7182	−	45.2839i	0.382005	−	0.924160i
$50$	30.5248	+	52.8705i	0.610496	+	1.05741i
$51$		0			0
$52$		−	16.5735i		−	0.318721i
$53$	−36.4805	−	63.1860i	−0.688310	−	1.19219i	−0.972384	−	0.233386i	$-0.925019\pi$
$53$	−36.4805	−	63.1860i	−0.688310	−	1.19219i	0.284074	−	0.958802i	$-0.408314\pi$
$54$		0			0
$55$		−	5.60707i		−	0.101947i
$56$	50.6663	−	33.8811i	0.904756	−	0.605019i
$57$		0			0
$58$	−27.8689			−0.480498
$59$	45.0624	+	26.0168i	0.763769	+	0.440962i	0.830647	−	0.556799i	$-0.187971\pi$
$59$	45.0624	+	26.0168i	0.763769	+	0.440962i	−0.0668785	+	0.997761i	$0.521304\pi$
$60$		0			0
$61$	81.9361	−	47.3058i	1.34322	−	0.775506i	0.355937	−	0.934510i	$-0.384162\pi$
$61$	81.9361	−	47.3058i	1.34322	−	0.775506i	0.987278	+	0.159004i	$0.0508283\pi$
$62$			72.7914i			1.17406i
$63$		0			0
$64$	69.4008			1.08439
$65$	−51.4910	−	89.1850i	−0.792169	−	1.37208i
$66$		0			0
$67$	45.5040	−	78.8152i	0.679164	−	1.17635i	−0.296069	−	0.955167i	$-0.595676\pi$
$67$	45.5040	−	78.8152i	0.679164	−	1.17635i	0.975233	−	0.221180i	$-0.0709908\pi$
$68$			21.8477i			0.321290i
$69$		0			0
$70$	40.2510	−	81.6966i	0.575015	−	1.16709i
$71$	−34.4191			−0.484776			−0.242388	−	0.970179i	$-0.577931\pi$
$71$	−34.4191			−0.484776			−0.242388	+	0.970179i	$0.577931\pi$
$72$		0			0
$73$	−28.6859	+	16.5618i	−0.392957	+	0.226874i	−0.683441	−	0.730006i	$-0.739517\pi$
$73$	−28.6859	+	16.5618i	−0.392957	+	0.226874i	0.290483	+	0.956880i	$0.406184\pi$
$74$	−76.9750			−1.04020
$75$		0			0
$76$	4.65564	−	2.68794i	0.0612585	−	0.0353676i
$77$	−4.14612	+	2.77255i	−0.0538457	+	0.0360071i
$78$		0			0
$79$	−47.3266	−	81.9721i	−0.599071	−	1.03762i	−0.992959	−	0.118463i	$-0.962203\pi$
$79$	−47.3266	−	81.9721i	−0.599071	−	1.03762i	0.393888	−	0.919159i	$-0.371130\pi$
$80$	63.5859	−	36.7114i	0.794824	−	0.458892i
$81$		0			0
$82$	−78.9604	−	45.5878i	−0.962931	−	0.555949i
$83$	79.2685	+	45.7657i	0.955043	+	0.551394i	0.894644	−	0.446780i	$-0.147429\pi$
$83$	79.2685	+	45.7657i	0.955043	+	0.551394i	0.0603988	+	0.998174i	$0.480763\pi$
$84$		0			0
$85$	67.8771	+	117.567i	0.798554	+	1.38314i
$86$	58.4630			0.679802
$87$		0			0
$88$	−6.20419			−0.0705022
$89$	58.0738	+	33.5289i	0.652515	+	0.376730i	0.789419	−	0.613855i	$-0.210382\pi$
$89$	58.0738	+	33.5289i	0.652515	+	0.376730i	−0.136904	+	0.990584i	$0.543715\pi$
$90$		0			0
$91$	−40.4864	+	82.1743i	−0.444906	+	0.903015i
$92$	−9.79394	+	16.9636i	−0.106456	+	0.184387i
$93$		0			0
$94$	1.85446	+	1.07067i	0.0197283	+	0.0113901i
$95$	16.7019	−	28.9285i	0.175810	−	0.304511i
$96$		0			0
$97$	33.5610	+	19.3764i	0.345989	+	0.199757i	0.662917	−	0.748693i	$-0.269318\pi$
$97$	33.5610	+	19.3764i	0.345989	+	0.199757i	−0.316928	+	0.948450i	$0.602651\pi$
$98$	−80.3131	+	10.6334i	−0.819522	+	0.108504i
$99$		0			0
$100$	−23.3816	+	40.4981i	−0.233816	+	0.404981i
$101$			92.4254i			0.915103i	0.889183	+	0.457552i	$0.151273\pi$
$101$			92.4254i			0.915103i	−0.889183	+	0.457552i	$0.848727\pi$
$102$		0			0
$103$			98.8726i			0.959928i	0.877288	+	0.479964i	$0.159350\pi$
$103$			98.8726i			0.959928i	−0.877288	+	0.479964i	$0.840650\pi$
$104$	−98.6827	+	56.9745i	−0.948872	+	0.547831i
$105$		0			0
$106$	−60.3149	+	104.468i	−0.569008	+	0.985551i
$107$	15.8732	−	27.4931i	0.148347	−	0.256945i	−0.782269	−	0.622940i	$-0.785938\pi$
$107$	15.8732	−	27.4931i	0.148347	−	0.256945i	0.930617	+	0.365995i	$0.119271\pi$
$108$		0			0
$109$	−31.2546	−	54.1346i	−0.286740	−	0.496648i	0.686290	−	0.727328i	$-0.259238\pi$
$109$	−31.2546	−	54.1346i	−0.286740	−	0.496648i	−0.973030	+	0.230680i	$0.925905\pi$
$110$	−8.02844	+	4.63522i	−0.0729858	+	0.0421384i
$111$		0			0
$112$	−58.5876	−	28.8655i	−0.523103	−	0.257727i
$113$	−50.0630	−	86.7116i	−0.443035	−	0.767360i	0.554878	−	0.831932i	$-0.312765\pi$
$113$	−50.0630	−	86.7116i	−0.443035	−	0.767360i	−0.997913	+	0.0645722i	$0.979432\pi$
$114$		0			0
$115$			121.712i			1.05837i
$116$	−10.6736	−	18.4872i	−0.0920138	−	0.159373i
$117$		0			0
$118$		−	86.0295i		−	0.729063i
$119$	53.3705	−	108.325i	0.448491	−	0.910293i
$120$		0			0
$121$	−120.492			−0.995804
$122$	−135.469	−	78.2130i	−1.11040	−	0.641090i
$123$		0			0
$124$	−48.2872	+	27.8787i	−0.389413	+	0.224828i
$125$			93.8394i			0.750715i
$126$		0			0
$127$	3.10525			0.0244508			0.0122254	−	0.999925i	$-0.496108\pi$
$127$	3.10525			0.0244508			0.0122254	+	0.999925i	$0.496108\pi$
$128$	−18.5664	−	32.1579i	−0.145050	−	0.251234i
$129$		0			0
$130$	−85.1325	+	147.454i	−0.654865	+	1.13426i
$131$		−	74.9897i		−	0.572441i	−0.958164	−	0.286220i	$-0.907601\pi$
$131$		−	74.9897i		−	0.572441i	0.958164	−	0.286220i	$-0.0923989\pi$
$132$		0			0
$133$	−29.6497	+	1.95428i	−0.222930	+	0.0146938i
$134$	−150.468			−1.12289
$135$		0			0
$136$	130.087	−	75.1056i	0.956519	−	0.552247i
$137$	35.1188			0.256342			0.128171	−	0.991752i	$-0.459089\pi$
$137$	35.1188			0.256342			0.128171	+	0.991752i	$0.459089\pi$
$138$		0			0
$139$	174.436	−	100.711i	1.25493	−	0.724537i	0.282849	−	0.959164i	$-0.408721\pi$
$139$	174.436	−	100.711i	1.25493	−	0.724537i	0.972085	+	0.234628i	$0.0753872\pi$
$140$	69.6105	−	4.58818i	0.497218	−	0.0327727i
$141$		0			0
$142$	28.4533	+	49.2826i	0.200376	+	0.347061i
$143$	8.07538	−	4.66233i	0.0564712	−	0.0326037i
$144$		0			0
$145$	−114.873	−	66.3220i	−0.792229	−	0.457393i
$146$	47.4277	+	27.3824i	0.324847	+	0.187551i
$147$		0			0
$148$	−29.4809	−	51.0625i	−0.199196	−	0.345017i
$149$	18.0431			0.121094			0.0605472	−	0.998165i	$-0.480715\pi$
$149$	18.0431			0.121094			0.0605472	+	0.998165i	$0.480715\pi$
$150$		0			0
$151$	−3.78901			−0.0250928			−0.0125464	−	0.999921i	$-0.503994\pi$
$151$	−3.78901			−0.0250928			−0.0125464	+	0.999921i	$0.503994\pi$
$152$	−32.0093	−	18.4806i	−0.210587	−	0.121583i
$153$		0			0
$154$	7.39734	+	3.64459i	0.0480346	+	0.0236661i
$155$	−173.228	+	300.040i	−1.11760	+	1.93574i
$156$		0			0
$157$	−120.870	−	69.7844i	−0.769873	−	0.444486i	0.0629562	−	0.998016i	$-0.479947\pi$
$157$	−120.870	−	69.7844i	−0.769873	−	0.444486i	−0.832829	+	0.553530i	$0.813280\pi$
$158$	−78.2473	+	135.528i	−0.495236	+	0.857774i
$159$		0			0
$160$	132.229	+	76.3423i	0.826430	+	0.477139i
$161$	89.9994	−	60.1835i	0.559003	−	0.373811i
$162$		0			0
$163$	−104.309	+	180.668i	−0.639930	+	1.10839i	0.345518	+	0.938412i	$0.387703\pi$
$163$	−104.309	+	180.668i	−0.639930	+	1.10839i	−0.985448	+	0.169979i	$0.945630\pi$
$164$		−	69.8393i		−	0.425849i
$165$		0			0
$166$		−	151.333i		−	0.911646i
$167$	113.021	−	65.2529i	0.676775	−	0.390736i	−0.121864	−	0.992547i	$-0.538887\pi$
$167$	113.021	−	65.2529i	0.676775	−	0.390736i	0.798639	+	0.601811i	$0.205554\pi$
$168$		0			0
$169$	1.13032	−	1.95777i	0.00668827	−	0.0115844i
$170$	112.224	−	194.378i	0.660143	−	1.14340i
$171$		0			0
$172$	22.3909	+	38.7823i	0.130180	+	0.225478i
$173$	−181.864	+	104.999i	−1.05123	+	0.606931i	−0.922995	−	0.384813i	$-0.874266\pi$
$173$	−181.864	+	104.999i	−1.05123	+	0.606931i	−0.128240	+	0.991743i	$0.540933\pi$
$174$		0			0
$175$	214.860	−	143.679i	1.22777	−	0.821024i
$176$	3.32408	+	5.75748i	0.0188868	+	0.0327129i
$177$		0			0
$178$		−	110.870i		−	0.622865i
$179$	−45.8709	−	79.4508i	−0.256262	−	0.443859i	0.708975	−	0.705233i	$-0.249158\pi$
$179$	−45.8709	−	79.4508i	−0.256262	−	0.443859i	−0.965238	+	0.261374i	$0.915824\pi$
$180$		0			0
$181$			135.692i			0.749677i	0.927090	+	0.374839i	$0.122302\pi$
$181$			135.692i			0.749677i	−0.927090	+	0.374839i	$0.877698\pi$
$182$	151.130	−	9.96128i	0.830382	−	0.0547323i
$183$		0			0
$184$	134.674			0.731923
$185$	−317.284	−	183.184i	−1.71505	−	0.990185i
$186$		0			0
$187$	−10.6452	+	6.14603i	−0.0569264	+	0.0328665i
$188$			1.64024i			0.00872470i
$189$		0			0
$190$	−55.2281			−0.290674
$191$	17.7468	+	30.7384i	0.0929154	+	0.160934i	0.908737	−	0.417370i	$-0.137048\pi$
$191$	17.7468	+	30.7384i	0.0929154	+	0.160934i	−0.815821	+	0.578304i	$0.803715\pi$
$192$		0			0
$193$	−150.297	+	260.321i	−0.778739	+	1.34882i	0.153930	+	0.988082i	$0.450807\pi$
$193$	−150.297	+	260.321i	−0.778739	+	1.34882i	−0.932669	+	0.360734i	$0.882526\pi$
$194$		−	64.0719i		−	0.330268i
$195$		0			0
$196$	−37.8133	−	49.2043i	−0.192925	−	0.251043i
$197$	229.095			1.16292			0.581460	−	0.813575i	$-0.302482\pi$
$197$	229.095			1.16292			0.581460	+	0.813575i	$0.302482\pi$
$198$		0			0
$199$	245.191	−	141.561i	1.23212	−	0.711363i	0.264646	−	0.964346i	$-0.414745\pi$
$199$	245.191	−	141.561i	1.23212	−	0.711363i	0.967471	+	0.252983i	$0.0814116\pi$
$200$	321.514			1.60757
$201$		0			0
$202$	132.338	−	76.4057i	0.655141	−	0.378246i
$203$	7.76028	+	117.737i	0.0382280	+	0.579984i
$204$		0			0
$205$	−216.979	−	375.818i	−1.05843	−	1.83326i
$206$	141.570	−	81.7354i	0.687232	−	0.396774i
$207$		0			0
$208$	105.744	+	61.0516i	0.508387	+	0.293517i
$209$	2.61938	+	1.51230i	0.0125329	+	0.00723587i
$210$		0			0
$211$	−3.55175	−	6.15180i	−0.0168329	−	0.0291555i	0.857486	−	0.514507i	$-0.172025\pi$
$211$	−3.55175	−	6.15180i	−0.0168329	−	0.0291555i	−0.874319	+	0.485351i	$0.838692\pi$
$212$	−92.4008			−0.435853
$213$		0			0
$214$	−52.4877			−0.245270
$215$	240.979	+	139.130i	1.12083	+	0.647114i
$216$		0			0
$217$	307.520	−	20.2693i	1.41714	−	0.0934068i
$218$	−51.6748	+	89.5033i	−0.237040	+	0.410566i
$219$		0			0
$220$	−6.14968	−	3.55052i	−0.0279531	−	0.0161387i
$221$	−112.881	+	195.515i	−0.510772	+	0.884683i
$222$		0			0
$223$	10.1660	+	5.86934i	0.0455874	+	0.0263199i	0.522621	−	0.852565i	$-0.324954\pi$
$223$	10.1660	+	5.86934i	0.0455874	+	0.0263199i	−0.477033	+	0.878885i	$0.658288\pi$
$224$	−8.93274	−	135.525i	−0.0398783	−	0.605022i
$225$		0			0
$226$	−82.7715	+	143.364i	−0.366246	+	0.634356i
$227$			119.055i			0.524472i	0.965004	+	0.262236i	$0.0844599\pi$
$227$			119.055i			0.524472i	−0.965004	+	0.262236i	$0.915540\pi$
$228$		0			0
$229$		−	11.4426i		−	0.0499678i	−0.999688	−	0.0249839i	$-0.992047\pi$
$229$		−	11.4426i		−	0.0499678i	0.999688	−	0.0249839i	$-0.00795346\pi$
$230$	174.273	−	100.616i	0.757707	−	0.437462i
$231$		0			0
$232$	−73.3849	+	127.106i	−0.316314	+	0.547873i
$233$	−40.9939	+	71.0035i	−0.175940	+	0.304736i	−0.940486	−	0.339832i	$-0.889630\pi$
$233$	−40.9939	+	71.0035i	−0.175940	+	0.304736i	0.764546	+	0.644569i	$0.222963\pi$
$234$		0			0
$235$	5.09595	+	8.82644i	0.0216849	+	0.0375593i
$236$	57.0689	−	32.9487i	0.241817	−	0.139613i
$237$		0			0
$238$	−199.224	+	13.1313i	−0.837075	+	0.0551734i
$239$	−48.9498	−	84.7835i	−0.204811	−	0.354743i	0.745262	−	0.666772i	$-0.232325\pi$
$239$	−48.9498	−	84.7835i	−0.204811	−	0.354743i	−0.950072	+	0.312029i	$0.898991\pi$
$240$		0			0
$241$			63.0850i			0.261764i	0.991398	+	0.130882i	$0.0417808\pi$
$241$			63.0850i			0.261764i	−0.991398	+	0.130882i	$0.958219\pi$
$242$	99.6078	+	172.526i	0.411603	+	0.712916i
$243$		0			0
$244$		−	119.820i		−	0.491067i
$245$	−356.349	−	147.298i	−1.45449	−	0.601217i
$246$		0			0
$247$	55.5511			0.224903
$248$	331.992	+	191.676i	1.33868	+	0.772887i
$249$		0			0
$250$	134.363	−	77.5745i	0.537452	−	0.310298i
$251$			181.337i			0.722460i	0.932477	+	0.361230i	$0.117643\pi$
$251$			181.337i			0.722460i	−0.932477	+	0.361230i	$0.882357\pi$
$252$		0			0
$253$	−11.0206			−0.0435597
$254$	−2.56703	−	4.44622i	−0.0101064	−	0.0175048i
$255$		0			0
$256$	108.105	−	187.243i	0.422285	−	0.731419i
$257$			196.743i			0.765536i	0.923845	+	0.382768i	$0.125029\pi$
$257$			196.743i			0.765536i	−0.923845	+	0.382768i	$0.874971\pi$
$258$		0			0
$259$	21.4342	+	325.194i	0.0827576	+	1.25558i
$260$	−130.421			−0.501618
$261$		0			0
$262$	−107.373	+	61.9920i	−0.409822	+	0.236611i
$263$	113.528			0.431666			0.215833	−	0.976430i	$-0.430753\pi$
$263$	113.528			0.431666			0.215833	+	0.976430i	$0.430753\pi$
$264$		0			0
$265$	−497.225	+	287.073i	−1.87632	+	1.08330i
$266$	27.3088	+	40.8381i	0.102665	+	0.153527i
$267$		0			0
$268$	−57.6282	−	99.8150i	−0.215031	−	0.372444i
$269$	461.950	−	266.707i	1.71729	−	0.991477i	0.793501	−	0.608568i	$-0.208256\pi$
$269$	461.950	−	266.707i	1.71729	−	0.991477i	0.923786	−	0.382908i	$-0.125077\pi$
$270$		0			0
$271$	250.882	+	144.847i	0.925765	+	0.534490i	0.885470	−	0.464697i	$-0.153837\pi$
$271$	250.882	+	144.847i	0.925765	+	0.534490i	0.0402950	+	0.999188i	$0.487170\pi$
$272$	−139.396	−	80.4801i	−0.512484	−	0.295883i
$273$		0			0
$274$	−29.0318	−	50.2845i	−0.105955	−	0.183520i
$275$	−26.3101			−0.0956731
$276$		0			0
$277$	392.430			1.41672			0.708358	−	0.705854i	$-0.249436\pi$
$277$	392.430			1.41672			0.708358	+	0.705854i	$0.249436\pi$
$278$	−288.403	−	166.510i	−1.03742	−	0.598955i
$279$		0			0
$280$	−266.618	−	398.705i	−0.952207	−	1.42395i
$281$	161.818	−	280.277i	0.575864	−	0.997426i	−0.420083	−	0.907486i	$-0.637999\pi$
$281$	161.818	−	280.277i	0.575864	−	0.997426i	0.995947	−	0.0899400i	$-0.0286675\pi$
$282$		0			0
$283$	93.3629	+	53.9031i	0.329904	+	0.190470i	0.655799	−	0.754936i	$-0.272332\pi$
$283$	93.3629	+	53.9031i	0.329904	+	0.190470i	−0.325894	+	0.945406i	$0.605665\pi$
$284$	−21.7949	+	37.7499i	−0.0767426	+	0.132922i
$285$		0			0
$286$	−13.3514	−	7.70844i	−0.0466833	−	0.0269526i
$287$	−170.606	+	346.276i	−0.594447	+	1.20653i
$288$		0			0
$289$	4.30286	−	7.45277i	0.0148888	−	0.0257881i
$290$			219.307i			0.756230i
$291$		0			0
$292$			41.9491i			0.143661i
$293$	74.3429	−	42.9219i	0.253730	−	0.146491i	−0.367741	−	0.929928i	$-0.619869\pi$
$293$	74.3429	−	42.9219i	0.253730	−	0.146491i	0.621471	+	0.783437i	$0.286535\pi$
$294$		0			0
$295$	204.732	−	354.606i	0.694007	−	1.20205i
$296$	−202.692	+	351.073i	−0.684771	+	1.18606i
$297$		0			0
$298$	−14.9157	−	25.8348i	−0.0500528	−	0.0866939i
$299$	−175.292	+	101.205i	−0.586260	+	0.338477i
$300$		0			0
$301$	−16.2794	−	246.987i	−0.0540845	−	0.820554i
$302$	3.13228	+	5.42526i	0.0103718	+	0.0179644i
$303$		0			0
$304$			39.6061i			0.130283i
$305$	−372.261	−	644.775i	−1.22053	−	2.11401i
$306$		0			0
$307$		−	353.739i		−	1.15225i	−0.817363	−	0.576123i	$-0.804565\pi$
$307$		−	353.739i		−	1.15225i	0.817363	−	0.576123i	$-0.195435\pi$
$308$	0.415443	+	6.30298i	0.00134884	+	0.0204642i
$309$		0			0
$310$	572.813			1.84778
$311$	−294.546	−	170.056i	−0.947094	−	0.546805i	−0.0549172	−	0.998491i	$-0.517489\pi$
$311$	−294.546	−	170.056i	−0.947094	−	0.546805i	−0.892177	+	0.451686i	$0.850823\pi$
$312$		0			0
$313$	−277.574	+	160.257i	−0.886817	+	0.512004i	−0.872900	−	0.487899i	$-0.837763\pi$
$313$	−277.574	+	160.257i	−0.886817	+	0.512004i	−0.0139172	+	0.999903i	$0.504430\pi$
$314$			230.756i			0.734890i
$315$		0			0
$316$	−119.873			−0.379344
$317$	96.4406	+	167.040i	0.304229	+	0.526940i	0.977089	−	0.212829i	$-0.0682679\pi$
$317$	96.4406	+	167.040i	0.304229	+	0.526940i	−0.672860	+	0.739770i	$0.734935\pi$
$318$		0			0
$319$	6.00522	−	10.4014i	0.0188252	−	0.0326061i
$320$		−	546.131i		−	1.70666i
$321$		0			0
$322$	−160.573	−	79.1127i	−0.498675	−	0.245692i
$323$	−73.2292			−0.226716
$324$		0			0
$325$	−418.483	+	241.611i	−1.28764	+	0.743420i
$326$	344.917			1.05803
$327$		0			0
$328$	−415.840	+	240.085i	−1.26781	+	0.731968i
$329$	4.00685	−	8.13261i	0.0121789	−	0.0247192i
$330$		0			0
$331$	308.710	+	534.702i	0.932659	+	1.61541i	0.778755	+	0.627328i	$0.215851\pi$
$331$	308.710	+	534.702i	0.932659	+	1.61541i	0.153904	+	0.988086i	$0.450815\pi$
$332$	100.389	−	57.9597i	0.302377	−	0.174577i
$333$		0			0
$334$	−186.864	−	107.886i	−0.559472	−	0.323011i
$335$	−620.215	−	358.082i	−1.85139	−	1.06890i
$336$		0			0
$337$	−4.22353	−	7.31537i	−0.0125327	−	0.0217073i	0.859691	−	0.510814i	$-0.170656\pi$
$337$	−4.22353	−	7.31537i	−0.0125327	−	0.0217073i	−0.872224	+	0.489107i	$0.837323\pi$
$338$	−3.73762			−0.0110580
$339$		0			0
$340$	171.925			0.505661
$341$	−27.1676	−	15.6852i	−0.0796703	−	0.0459976i
$342$		0			0
$343$	67.2864	+	336.335i	0.196170	+	0.980570i
$344$	153.946	−	266.642i	0.447517	−	0.775123i
$345$		0			0
$346$	300.684	+	173.600i	0.869028	+	0.501733i
$347$	175.317	−	303.658i	0.505237	−	0.875096i	−0.494744	−	0.869039i	$-0.664738\pi$
$347$	175.317	−	303.658i	0.505237	−	0.875096i	0.999982	−	0.00605798i	$-0.00192833\pi$
$348$		0			0
$349$	−275.145	−	158.855i	−0.788380	−	0.455171i	0.0510121	−	0.998698i	$-0.483755\pi$
$349$	−275.145	−	158.855i	−0.788380	−	0.455171i	−0.839392	+	0.543527i	$0.817089\pi$
$350$	−383.345	−	188.870i	−1.09527	−	0.539629i
$351$		0			0
$352$	−6.91252	+	11.9728i	−0.0196378	+	0.0340137i
$353$			16.4624i			0.0466357i	0.999728	+	0.0233179i	$0.00742298\pi$
$353$			16.4624i			0.0466357i	−0.999728	+	0.0233179i	$0.992577\pi$
$354$		0			0
$355$			270.852i			0.762963i
$356$	73.5472	−	42.4625i	0.206593	−	0.119277i
$357$		0			0
$358$	−75.8406	+	131.360i	−0.211845	+	0.366927i
$359$	−248.876	+	431.065i	−0.693247	+	1.20074i	0.277522	+	0.960719i	$0.410487\pi$
$359$	−248.876	+	431.065i	−0.693247	+	1.20074i	−0.970768	+	0.240019i	$0.922846\pi$
$360$		0			0
$361$	−171.491	−	297.030i	−0.475043	−	0.822799i
$362$	194.289	−	112.173i	0.536709	−	0.309869i
$363$		0			0
$364$	64.4896	+	96.4389i	0.177169	+	0.264942i
$365$	130.329	+	225.736i	0.357065	+	0.618454i
$366$		0			0
$367$			219.197i			0.597267i	0.954368	+	0.298634i	$0.0965308\pi$
$367$			219.197i			0.597267i	−0.954368	+	0.298634i	$0.903469\pi$
$368$	−72.1556	−	124.977i	−0.196075	−	0.339612i
$369$		0			0
$370$			605.734i			1.63712i
$371$	458.139	+	225.720i	1.23488	+	0.608411i
$372$		0			0
$373$	−59.2697			−0.158900			−0.0794500	−	0.996839i	$-0.525316\pi$
$373$	−59.2697			−0.158900			−0.0794500	+	0.996839i	$0.525316\pi$
$374$	17.6003	+	10.1615i	0.0470595	+	0.0271698i
$375$		0			0
$376$	9.76640	−	5.63864i	0.0259745	−	0.0149964i
$377$		−	220.589i		−	0.585117i
$378$		0			0
$379$	−329.557			−0.869543			−0.434771	−	0.900541i	$-0.643171\pi$
$379$	−329.557			−0.869543			−0.434771	+	0.900541i	$0.643171\pi$
$380$	−21.1520	−	36.6364i	−0.0556632	−	0.0964115i
$381$		0			0
$382$	29.3417	−	50.8213i	0.0768107	−	0.133040i
$383$			290.422i			0.758283i	0.925339	+	0.379141i	$0.123781\pi$
$383$			290.422i			0.758283i	−0.925339	+	0.379141i	$0.876219\pi$
$384$		0			0
$385$	21.8178	+	32.6268i	0.0566697	+	0.0847449i
$386$	496.985			1.28753
$387$		0			0
$388$	42.5030	−	24.5391i	0.109544	−	0.0632452i
$389$	−197.625			−0.508033			−0.254017	−	0.967200i	$-0.581752\pi$
$389$	−197.625			−0.508033			−0.254017	+	0.967200i	$0.581752\pi$
$390$		0			0
$391$	231.075	−	133.411i	0.590985	−	0.341205i
$392$	−162.985	+	394.298i	−0.415777	+	1.00586i
$393$		0			0
$394$	−189.387	−	328.028i	−0.480678	−	0.832558i
$395$	−645.057	+	372.424i	−1.63306	+	0.942846i
$396$		0			0
$397$	−160.619	−	92.7331i	−0.404581	−	0.233585i	0.283878	−	0.958860i	$-0.408379\pi$
$397$	−160.619	−	92.7331i	−0.404581	−	0.233585i	−0.688459	+	0.725276i	$0.741712\pi$
$398$	−405.386	−	234.050i	−1.01856	−	0.588065i
$399$		0			0
$400$	−172.261	−	298.365i	−0.430652	−	0.745911i
$401$	444.865			1.10939			0.554694	−	0.832054i	$-0.312835\pi$
$401$	444.865			1.10939			0.554694	+	0.832054i	$0.312835\pi$
$402$		0			0
$403$	−576.162			−1.42968
$404$	101.370	+	58.5258i	0.250915	+	0.144866i
$405$		0			0
$406$	162.165	−	108.441i	0.399421	−	0.267097i
$407$	16.5867	−	28.7290i	0.0407535	−	0.0705872i
$408$		0			0
$409$	−64.9377	−	37.4918i	−0.158772	−	0.0916669i	0.418509	−	0.908213i	$-0.362553\pi$
$409$	−64.9377	−	37.4918i	−0.158772	−	0.0916669i	−0.577281	+	0.816546i	$0.695886\pi$
$410$	−358.741	+	621.357i	−0.874978	+	1.51551i
$411$		0			0
$412$	108.441	+	62.6083i	0.263206	+	0.151962i
$413$	−363.446	+	23.9555i	−0.880015	+	0.0580036i
$414$		0			0
$415$	360.141	−	623.783i	0.867810	−	1.50309i
$416$			253.917i			0.610377i
$417$		0			0
$418$		−	5.00071i		−	0.0119634i
$419$	250.153	−	144.426i	0.597025	−	0.344692i	−0.170845	−	0.985298i	$-0.554650\pi$
$419$	250.153	−	144.426i	0.597025	−	0.344692i	0.767870	+	0.640605i	$0.221317\pi$
$420$		0			0
$421$	324.455	−	561.973i	0.770678	−	1.33485i	−0.166514	−	0.986039i	$-0.553251\pi$
$421$	324.455	−	561.973i	0.770678	−	1.33485i	0.937192	−	0.348814i	$-0.113416\pi$
$422$	−5.87227	+	10.1711i	−0.0139153	+	0.0241021i
$423$		0			0
$424$	317.645	+	550.177i	0.749162	+	1.29759i
$425$	551.658	−	318.500i	1.29802	−	0.749411i
$426$		0			0
$427$	−292.702	+	594.090i	−0.685484	+	1.39131i
$428$	−20.1025	−	34.8185i	−0.0469684	−	0.0813516i
$429$		0			0
$430$		−	460.059i		−	1.06990i
$431$	335.357	+	580.856i	0.778092	+	1.34769i	0.933040	+	0.359772i	$0.117145\pi$
$431$	335.357	+	580.856i	0.778092	+	1.34769i	−0.154949	+	0.987923i	$0.549521\pi$
$432$		0			0
$433$		−	91.5049i		−	0.211328i	−0.994402	−	0.105664i	$-0.966303\pi$
$433$		−	91.5049i		−	0.211328i	0.994402	−	0.105664i	$-0.0336967\pi$
$434$	−283.241	−	423.563i	−0.652629	−	0.975952i
$435$		0			0
$436$	−79.1644			−0.181570
$437$	−56.8586	−	32.8273i	−0.130111	−	0.0751197i
$438$		0			0
$439$	445.282	−	257.083i	1.01431	−	0.585612i	0.101859	−	0.994799i	$-0.467521\pi$
$439$	445.282	−	257.083i	1.01431	−	0.585612i	0.912450	+	0.409187i	$0.134188\pi$
$440$			48.8222i			0.110960i
$441$		0			0
$442$	373.262			0.844484
$443$	−258.992	−	448.587i	−0.584631	−	1.01261i	−0.994921	−	0.100656i	$-0.967906\pi$
$443$	−258.992	−	448.587i	−0.584631	−	1.01261i	0.410290	−	0.911955i	$-0.365428\pi$
$444$		0			0
$445$	263.847	−	456.996i	0.592915	−	1.02696i
$446$		−	19.4081i		−	0.0435160i
$447$		0			0
$448$	−403.834	+	270.048i	−0.901415	+	0.602785i
$449$	706.722			1.57399			0.786995	−	0.616959i	$-0.211636\pi$
$449$	706.722			1.57399			0.786995	+	0.616959i	$0.211636\pi$
$450$		0			0
$451$	34.0290	−	19.6466i	0.0754523	−	0.0435624i
$452$	−126.804			−0.280539
$453$		0			0
$454$	170.468	−	98.4197i	0.375480	−	0.216784i
$455$	646.649	+	318.597i	1.42121	+	0.700213i
$456$		0			0
$457$	269.457	+	466.714i	0.589622	+	1.02126i	0.994282	+	0.106788i	$0.0340566\pi$
$457$	269.457	+	466.714i	0.589622	+	1.02126i	−0.404660	+	0.914467i	$0.632610\pi$
$458$	−16.3840	+	9.45933i	−0.0357730	+	0.0206536i
$459$		0			0
$460$	133.491	+	77.0708i	0.290197	+	0.167545i
$461$	101.379	+	58.5313i	0.219911	+	0.126966i	0.605909	−	0.795534i	$-0.292809\pi$
$461$	101.379	+	58.5313i	0.219911	+	0.126966i	−0.385998	+	0.922500i	$0.626143\pi$
$462$		0			0
$463$	12.2368	+	21.1948i	0.0264295	+	0.0457772i	0.878938	−	0.476937i	$-0.158253\pi$
$463$	12.2368	+	21.1948i	0.0264295	+	0.0457772i	−0.852508	+	0.522714i	$0.824920\pi$
$464$	157.273			0.338950
$465$		0			0
$466$	135.554			0.290889
$467$	294.670	+	170.128i	0.630986	+	0.364300i	0.781134	−	0.624364i	$-0.214642\pi$
$467$	294.670	+	170.128i	0.630986	+	0.364300i	−0.150148	+	0.988664i	$0.547975\pi$
$468$		0			0
$469$	41.8988	+	635.676i	0.0893365	+	1.35539i
$470$	8.42537	−	14.5932i	0.0179263	−	0.0310493i
$471$		0			0
$472$	−392.370	−	226.535i	−0.831291	−	0.479946i
$473$	−12.5977	+	21.8198i	−0.0266336	+	0.0461307i
$474$		0			0
$475$	−135.742	−	78.3704i	−0.285772	−	0.164990i
$476$	−85.0123	−	127.129i	−0.178597	−	0.267077i
$477$		0			0
$478$	−80.9310	+	140.177i	−0.169312	+	0.293256i
$479$			624.134i			1.30299i	0.758651	+	0.651497i	$0.225859\pi$
$479$			624.134i			1.30299i	−0.758651	+	0.651497i	$0.774141\pi$
$480$		0			0
$481$		−	609.277i		−	1.26669i
$482$	90.3277	−	52.1507i	0.187402	−	0.108197i
$483$		0			0
$484$	−76.2983	+	132.153i	−0.157641	+	0.273042i
$485$	152.478	−	264.099i	0.314387	−	0.544534i
$486$		0			0
$487$	−291.974	−	505.715i	−0.599537	−	1.03843i	−0.992889	−	0.119041i	$-0.962018\pi$
$487$	−291.974	−	505.715i	−0.599537	−	1.03843i	0.393352	−	0.919388i	$-0.371315\pi$
$488$	−713.439	+	411.904i	−1.46197	+	0.844066i
$489$		0			0
$490$	83.6769	+	632.003i	0.170769	+	1.28980i
$491$	−204.905	−	354.906i	−0.417321	−	0.722822i	0.578348	−	0.815790i	$-0.303698\pi$
$491$	−204.905	−	354.906i	−0.417321	−	0.722822i	−0.995669	+	0.0929685i	$0.970364\pi$
$492$		0			0
$493$			290.788i			0.589833i
$494$	−45.9226	−	79.5403i	−0.0929607	−	0.161013i
$495$		0			0
$496$		−	410.785i		−	0.828195i
$497$	200.280	−	133.929i	0.402977	−	0.269475i
$498$		0			0
$499$	−84.7735			−0.169887			−0.0849434	−	0.996386i	$-0.527071\pi$
$499$	−84.7735			−0.169887			−0.0849434	+	0.996386i	$0.527071\pi$
$500$	102.920	+	59.4211i	0.205841	+	0.118842i
$501$		0			0
$502$	259.646	−	149.907i	0.517224	−	0.298619i
$503$		−	610.511i		−	1.21374i	−0.794801	−	0.606870i	$-0.792425\pi$
$503$		−	610.511i		−	1.21374i	0.794801	−	0.606870i	$-0.207575\pi$
$504$		0			0
$505$	727.317			1.44023
$506$	9.11045	+	15.7798i	0.0180048	+	0.0311853i
$507$		0			0
$508$	1.96631	−	3.40575i	0.00387069	−	0.00670423i
$509$		−	98.0281i		−	0.192590i	−0.995353	−	0.0962948i	$-0.969301\pi$
$509$		−	98.0281i		−	0.192590i	0.995353	−	0.0962948i	$-0.0306992\pi$
$510$		0			0
$511$	102.475	−	207.991i	0.200538	−	0.407028i
$512$	−506.001			−0.988284
$513$		0			0
$514$	281.704	−	162.642i	0.548063	−	0.316424i
$515$	778.052			1.51078
$516$		0			0
$517$	−0.799203	+	0.461420i	−0.00154585	+	0.000892495i
$518$	447.907	−	299.520i	0.864685	−	0.578223i
$519$		0			0
$520$	448.345	+	776.557i	0.862203	+	1.49338i
$521$	−287.126	+	165.772i	−0.551106	+	0.318181i	−0.749568	−	0.661927i	$-0.769739\pi$
$521$	−287.126	+	165.772i	−0.551106	+	0.318181i	0.198462	+	0.980109i	$0.436405\pi$
$522$		0			0
$523$	75.9105	+	43.8270i	0.145144	+	0.0837991i	0.570814	−	0.821080i	$-0.306628\pi$
$523$	75.9105	+	43.8270i	0.145144	+	0.0837991i	−0.425669	+	0.904879i	$0.639961\pi$
$524$	−82.2466	−	47.4851i	−0.156959	−	0.0906204i
$525$		0			0
$526$	−93.8508	−	162.554i	−0.178424	−	0.309039i
$527$	759.516			1.44121
$528$		0			0
$529$	−289.777			−0.547782
$530$	822.086	+	474.632i	1.55111	+	0.895532i
$531$		0			0
$532$	−16.6314	+	33.7564i	−0.0312621	+	0.0634520i
$533$	360.839	−	624.991i	0.676996	−	1.17259i
$534$		0			0
$535$	−216.350	−	124.910i	−0.404392	−	0.233476i
$536$	−396.215	+	686.264i	−0.739207	+	1.28034i
$537$		0			0
$538$	−763.764	−	440.960i	−1.41964	−	0.819628i
$539$	13.3373	−	32.2661i	0.0247446	−	0.0598630i
$540$		0			0
$541$	134.595	−	233.125i	0.248788	−	0.430914i	−0.714401	−	0.699736i	$-0.753301\pi$
$541$	134.595	−	233.125i	0.248788	−	0.430914i	0.963190	+	0.268822i	$0.0866343\pi$
$542$		−	478.964i		−	0.883698i
$543$		0			0
$544$		−	334.721i		−	0.615297i
$545$	−425.998	+	245.950i	−0.781648	+	0.451285i
$546$		0			0
$547$	286.703	−	496.584i	0.524137	−	0.907831i	−0.475469	−	0.879733i	$-0.657721\pi$
$547$	286.703	−	496.584i	0.524137	−	0.907831i	0.999605	−	0.0280984i	$-0.00894519\pi$
$548$	22.2380	−	38.5173i	0.0405803	−	0.0702871i
$549$		0			0
$550$	21.7499	+	37.6719i	0.0395452	+	0.0684943i
$551$	61.9655	−	35.7758i	0.112460	−	0.0649288i
$552$		0			0
$553$	594.351	+	292.830i	1.07477	+	0.529530i
$554$	−324.412	−	561.898i	−0.585581	−	1.01426i
$555$		0			0
$556$		−	255.088i		−	0.458792i
$557$	−424.276	−	734.868i	−0.761717	−	1.31933i	−0.941965	−	0.335711i	$-0.891024\pi$
$557$	−424.276	−	734.868i	−0.761717	−	1.31933i	0.180248	−	0.983621i	$-0.442310\pi$
$558$		0			0
$559$			462.749i			0.827816i
$560$	−227.149	+	461.039i	−0.405623	+	0.823284i
$561$		0			0
$562$	−535.082			−0.952103
$563$	−777.513	−	448.897i	−1.38102	−	0.797331i	−0.388738	−	0.921348i	$-0.627089\pi$
$563$	−777.513	−	448.897i	−1.38102	−	0.797331i	−0.992280	+	0.124017i	$0.960422\pi$
$564$		0			0
$565$	−682.354	+	393.957i	−1.20771	+	0.697270i
$566$		−	178.241i		−	0.314913i
$567$		0			0
$568$	299.696			0.527634
$569$	364.780	+	631.817i	0.641090	+	1.11040i	0.985190	+	0.171467i	$0.0548506\pi$
$569$	364.780	+	631.817i	0.641090	+	1.11040i	−0.344100	+	0.938933i	$0.611816\pi$
$570$		0			0
$571$	229.413	−	397.355i	0.401774	−	0.695894i	−0.592166	−	0.805816i	$-0.701727\pi$
$571$	229.413	−	397.355i	0.401774	−	0.695894i	0.993940	+	0.109922i	$0.0350602\pi$
$572$		−	11.8091i		−	0.0206453i
$573$		0			0
$574$	636.847	−	41.9760i	1.10949	−	0.0731288i
$575$	571.111			0.993237
$576$		0			0
$577$	−205.047	+	118.384i	−0.355367	+	0.205171i	−0.667046	−	0.745016i	$-0.732442\pi$
$577$	−205.047	+	118.384i	−0.355367	+	0.205171i	0.311680	+	0.950187i	$0.399108\pi$
$578$	−14.2282			−0.0246163
$579$		0			0
$580$	−145.480	+	83.9931i	−0.250828	+	0.144816i
$581$	−639.333	+	42.1398i	−1.10040	+	0.0725297i
$582$		0			0
$583$	−25.9935	−	45.0220i	−0.0445857	−	0.0772247i
$584$	249.775	−	144.208i	0.427697	−	0.246931i
$585$		0			0
$586$	−122.915	−	70.9648i	−0.209752	−	0.121100i
$587$	−504.674	−	291.374i	−0.859752	−	0.496378i	0.00417747	−	0.999991i	$-0.498670\pi$
$587$	−504.674	−	291.374i	−0.859752	−	0.496378i	−0.863929	+	0.503613i	$0.832004\pi$
$588$		0			0
$589$	−93.4436	−	161.849i	−0.158648	−	0.274786i
$590$	−676.986			−1.14743
$591$		0			0
$592$	434.394			0.733774
$593$	−740.999	−	427.816i	−1.24958	−	0.721444i	−0.278552	−	0.960421i	$-0.589854\pi$
$593$	−740.999	−	427.816i	−1.24958	−	0.721444i	−0.971025	+	0.238977i	$0.923188\pi$
$594$		0			0
$595$	−852.434	−	419.985i	−1.43266	−	0.705857i
$596$	11.4253	−	19.7891i	0.0191699	−	0.0332032i
$597$		0			0
$598$	289.818	+	167.327i	0.484646	+	0.279810i
$599$	245.138	−	424.591i	0.409245	−	0.708833i	−0.585561	−	0.810629i	$-0.699126\pi$
$599$	245.138	−	424.591i	0.409245	−	0.708833i	0.994805	+	0.101796i	$0.0324589\pi$
$600$		0			0
$601$	34.1740	+	19.7303i	0.0568618	+	0.0328292i	0.528161	−	0.849144i	$-0.322882\pi$
$601$	34.1740	+	19.7303i	0.0568618	+	0.0328292i	−0.471300	+	0.881973i	$0.656215\pi$
$602$	−340.188	+	227.487i	−0.565096	+	0.377885i
$603$		0			0
$604$	−2.39928	+	4.15568i	−0.00397232	+	0.00688026i
$605$			948.182i			1.56724i
$606$		0			0
$607$			77.6825i			0.127978i	0.997951	+	0.0639888i	$0.0203822\pi$
$607$			77.6825i			0.127978i	−0.997951	+	0.0639888i	$0.979618\pi$
$608$	−71.3275	+	41.1809i	−0.117315	+	0.0677318i
$609$		0			0
$610$	−615.476	+	1066.04i	−1.00898	+	1.74760i
$611$	−8.47464	+	14.6785i	−0.0138701	+	0.0240238i
$612$		0			0
$613$	209.028	+	362.047i	0.340992	+	0.590616i	0.984617	−	0.174725i	$-0.0559037\pi$
$613$	209.028	+	362.047i	0.340992	+	0.590616i	−0.643625	+	0.765341i	$0.722570\pi$
$614$	−506.498	+	292.427i	−0.824916	+	0.476265i
$615$		0			0
$616$	36.1013	−	24.1413i	0.0586060	−	0.0391904i
$617$	417.377	+	722.918i	0.676461	+	1.17167i	0.976039	+	0.217594i	$0.0698207\pi$
$617$	417.377	+	722.918i	0.676461	+	1.17167i	−0.299578	+	0.954072i	$0.596846\pi$
$618$		0			0
$619$			467.361i			0.755026i	0.926004	+	0.377513i	$0.123221\pi$
$619$			467.361i			0.755026i	−0.926004	+	0.377513i	$0.876779\pi$
$620$	219.384	+	379.984i	0.353845	+	0.612877i
$621$		0			0
$622$			562.325i			0.904059i
$623$	−468.389	+	30.8725i	−0.751828	+	0.0495546i
$624$		0			0
$625$	−184.677			−0.295483
$626$	458.926	+	264.961i	0.733108	+	0.423260i
$627$		0			0
$628$	−153.075	+	88.3779i	−0.243750	+	0.140729i
$629$			803.168i			1.27690i
$630$		0			0
$631$	−1062.07			−1.68316			−0.841580	−	0.540133i	$-0.818374\pi$
$631$	−1062.07			−1.68316			−0.841580	+	0.540133i	$0.818374\pi$
$632$	412.085	+	713.752i	0.652033	+	1.12935i
$633$		0			0
$634$	159.450	−	276.175i	0.251498	−	0.435607i
$635$		−	24.4359i		−	0.0384818i
$636$		0			0
$637$	−84.1662	−	635.699i	−0.132129	−	0.997957i
$638$	−19.8574			−0.0311245
$639$		0			0
$640$	−253.058	+	146.103i	−0.395404	+	0.228286i
$641$	−214.455			−0.334564			−0.167282	−	0.985909i	$-0.553499\pi$
$641$	−214.455			−0.334564			−0.167282	+	0.985909i	$0.553499\pi$
$642$		0			0
$643$	206.180	−	119.038i	0.320654	−	0.185130i	−0.331030	−	0.943620i	$-0.607396\pi$
$643$	206.180	−	119.038i	0.320654	−	0.185130i	0.651684	+	0.758491i	$0.274063\pi$
$644$	−9.01799	−	136.818i	−0.0140031	−	0.212451i
$645$		0			0
$646$	60.5366	+	104.853i	0.0937100	+	0.162310i
$647$	707.038	−	408.209i	1.09279	−	0.630925i	0.158475	−	0.987363i	$-0.449342\pi$
$647$	707.038	−	408.209i	1.09279	−	0.630925i	0.934319	+	0.356438i	$0.116009\pi$
$648$		0			0
$649$	32.1083	+	18.5377i	0.0494735	+	0.0285636i
$650$	691.898	+	399.468i	1.06446	+	0.614565i
$651$		0			0
$652$	132.101	+	228.805i	0.202609	+	0.350929i
$653$	−924.162			−1.41526			−0.707628	−	0.706585i	$-0.750235\pi$
$653$	−924.162			−1.41526			−0.707628	+	0.706585i	$0.750235\pi$
$654$		0			0
$655$	−590.112			−0.900934
$656$	445.598	+	257.266i	0.679265	+	0.392174i
$657$		0			0
$658$	−14.9570	+	0.985845i	−0.0227309	+	0.00149825i
$659$	−374.087	+	647.937i	−0.567658	+	0.983212i	0.429139	+	0.903238i	$0.358817\pi$
$659$	−374.087	+	647.937i	−0.567658	+	0.983212i	−0.996797	+	0.0799738i	$0.974516\pi$
$660$		0			0
$661$	1058.09	+	610.887i	1.60074	+	0.924186i	0.991340	+	0.131322i	$0.0419222\pi$
$661$	1058.09	+	610.887i	1.60074	+	0.924186i	0.609398	+	0.792864i	$0.291411\pi$
$662$	510.405	−	884.048i	0.771005	−	1.33542i
$663$		0			0
$664$	−690.212	−	398.494i	−1.03948	−	0.600141i
$665$	15.3786	+	233.320i	0.0231258	+	0.350858i
$666$		0			0
$667$	−130.355	+	225.781i	−0.195435	+	0.338503i
$668$		−	165.278i		−	0.247422i
$669$		0			0
$670$			1184.07i			1.76726i
$671$	58.3820	−	33.7069i	0.0870075	−	0.0502338i
$672$		0			0
$673$	4.31743	−	7.47801i	0.00641520	−	0.0111115i	−0.862800	−	0.505545i	$-0.831291\pi$
$673$	4.31743	−	7.47801i	0.00641520	−	0.0111115i	0.869215	+	0.494434i	$0.164625\pi$
$674$	−6.98296	+	12.0948i	−0.0103605	+	0.0179449i
$675$		0			0
$676$	−1.43148	−	2.47940i	−0.00211758	−	0.00366775i
$677$	697.272	−	402.570i	1.02994	−	0.594638i	0.112975	−	0.993598i	$-0.463962\pi$
$677$	697.272	−	402.570i	1.02994	−	0.594638i	0.916968	+	0.398960i	$0.130629\pi$
$678$		0			0
$679$	−270.683	+	17.8413i	−0.398649	+	0.0262758i
$680$	−591.023	−	1023.68i	−0.869152	−	1.50542i
$681$		0			0
$682$			51.8662i			0.0760501i
$683$	−414.817	−	718.484i	−0.607345	−	1.05195i	−0.991676	−	0.128757i	$-0.958901\pi$
$683$	−414.817	−	718.484i	−0.607345	−	1.05195i	0.384331	−	0.923195i	$-0.374432\pi$
$684$		0			0
$685$		−	276.358i		−	0.403442i
$686$	425.955	−	374.383i	0.620925	−	0.545748i
$687$		0			0
$688$	−329.925			−0.479542
$689$	−826.894	−	477.407i	−1.20014	−	0.692899i
$690$		0			0
$691$	278.141	−	160.585i	0.402520	−	0.232395i	−0.285051	−	0.958512i	$-0.592011\pi$
$691$	278.141	−	160.585i	0.402520	−	0.232395i	0.687571	+	0.726118i	$0.258677\pi$
$692$			265.950i			0.384321i
$693$		0			0
$694$	−579.721			−0.835333
$695$	−792.515	−	1372.68i	−1.14031	−	1.97507i
$696$		0			0
$697$	−475.669	+	823.883i	−0.682452	+	1.18204i
$698$			525.284i			0.752556i
$699$		0			0
$700$	−21.5291	−	326.634i	−0.0307559	−	0.466620i
$701$	−1005.22			−1.43398			−0.716990	−	0.697084i	$-0.754481\pi$
$701$	−1005.22			−1.43398			−0.716990	+	0.697084i	$0.754481\pi$
$702$		0			0
$703$	171.151	−	98.8142i	0.243458	−	0.140561i
$704$	49.4503			0.0702418
$705$		0			0
$706$	23.5715	−	13.6090i	0.0333875	−	0.0192763i
$707$	−359.639	−	537.811i	−0.508683	−	0.760694i
$708$		0			0
$709$	−169.337	−	293.300i	−0.238839	−	0.413682i	0.721542	−	0.692370i	$-0.243434\pi$
$709$	−169.337	−	293.300i	−0.238839	−	0.413682i	−0.960382	+	0.278689i	$0.910100\pi$
$710$	387.817	−	223.906i	0.546221	−	0.315361i
$711$		0			0
$712$	−505.664	−	291.945i	−0.710202	−	0.410035i
$713$	589.724	+	340.477i	0.827102	+	0.477528i
$714$		0			0
$715$	−36.6889	−	63.5471i	−0.0513132	−	0.0888770i
$716$	−116.186			−0.162271
$717$		0			0
$718$	822.955			1.14618
$719$	−439.689	−	253.854i	−0.611528	−	0.353066i	0.162035	−	0.986785i	$-0.448194\pi$
$719$	−439.689	−	253.854i	−0.611528	−	0.353066i	−0.773563	+	0.633719i	$0.781528\pi$
$720$		0			0
$721$	−384.726	−	575.326i	−0.533601	−	0.797955i
$722$	−283.533	+	491.094i	−0.392706	+	0.680186i
$723$		0			0
$724$	148.823	+	85.9228i	0.205556	+	0.118678i
$725$	−311.203	+	539.020i	−0.429246	+	0.743476i
$726$		0			0
$727$	1069.58	+	617.521i	1.47122	+	0.849410i	0.999477	−	0.0323253i	$-0.0102912\pi$
$727$	1069.58	+	617.521i	1.47122	+	0.849410i	0.471744	+	0.881735i	$0.343625\pi$
$728$	352.526	−	715.513i	0.484238	−	0.982848i
$729$		0			0
$730$	215.479	−	373.220i	0.295176	−	0.511260i
$731$		−	610.011i		−	0.834488i
$732$		0			0
$733$		−	620.994i		−	0.847195i	−0.905851	−	0.423597i	$-0.860767\pi$
$733$		−	620.994i		−	0.847195i	0.905851	−	0.423597i	$-0.139233\pi$
$734$	313.855	−	181.204i	0.427596	−	0.246872i
$735$		0			0
$736$	150.050	−	259.893i	0.203872	−	0.353116i
$737$	32.4230	−	56.1583i	0.0439932	−	0.0761985i
$738$		0			0
$739$	84.0942	+	145.655i	0.113795	+	0.197098i	0.917297	−	0.398203i	$-0.130366\pi$
$739$	84.0942	+	145.655i	0.113795	+	0.197098i	−0.803503	+	0.595301i	$0.797033\pi$
$740$	−401.823	+	231.992i	−0.543004	+	0.313503i
$741$		0			0
$742$	−55.5362	−	842.580i	−0.0748467	−	1.13555i
$743$	699.942	+	1212.33i	0.942048	+	1.63167i	0.761557	+	0.648098i	$0.224435\pi$
$743$	699.942	+	1212.33i	0.942048	+	1.63167i	0.180491	+	0.983577i	$0.442231\pi$
$744$		0			0
$745$		−	141.985i		−	0.190584i
$746$	48.9967	+	84.8648i	0.0656793	+	0.113760i
$747$		0			0
$748$			15.5672i			0.0208117i
$749$	14.6156	+	221.743i	0.0195134	+	0.296052i
$750$		0			0
$751$	−563.842			−0.750788			−0.375394	−	0.926865i	$-0.622493\pi$
$751$	−563.842			−0.750788			−0.375394	+	0.926865i	$0.622493\pi$
$752$	−10.4653	−	6.04214i	−0.0139166	−	0.00803476i
$753$		0			0
$754$	−315.849	+	182.355i	−0.418897	+	0.241850i
$755$			29.8166i			0.0394922i
$756$		0			0
$757$	453.694			0.599332			0.299666	−	0.954044i	$-0.403125\pi$
$757$	453.694			0.599332			0.299666	+	0.954044i	$0.403125\pi$
$758$	272.436	+	471.873i	0.359414	+	0.622523i
$759$		0			0
$760$	−145.428	+	251.888i	−0.191352	+	0.331432i
$761$		−	943.979i		−	1.24045i	−0.784426	−	0.620223i	$-0.787042\pi$
$761$		−	943.979i		−	1.24045i	0.784426	−	0.620223i	$-0.212958\pi$
$762$		0			0
$763$	392.511	+	193.386i	0.514431	+	0.253455i
$764$	44.9507			0.0588360
$765$		0			0
$766$	415.838	−	240.084i	0.542870	−	0.313426i
$767$	680.945			0.887803
$768$		0			0
$769$	150.045	−	86.6282i	0.195116	−	0.112651i	−0.399259	−	0.916838i	$-0.630733\pi$
$769$	150.045	−	86.6282i	0.195116	−	0.112651i	0.594376	+	0.804188i	$0.297399\pi$
$770$	28.6801	−	58.2114i	0.0372469	−	0.0755992i
$771$		0			0
$772$	190.342	+	329.682i	0.246557	+	0.427049i
$773$	1000.17	−	577.446i	1.29387	−	0.747019i	0.314536	−	0.949246i	$-0.398151\pi$
$773$	1000.17	−	577.446i	1.29387	−	0.747019i	0.979339	+	0.202226i	$0.0648177\pi$
$774$		0			0
$775$	1407.88	+	812.840i	1.81662	+	1.04883i
$776$	−292.224	−	168.716i	−0.376577	−	0.217417i
$777$		0			0
$778$	163.371	+	282.967i	0.209989	+	0.363711i
$779$	234.087			0.300497
$780$		0			0
$781$	−24.5247			−0.0314016
$782$	−382.047	−	220.575i	−0.488552	−	0.282065i
$783$		0			0
$784$	453.232	−	60.0077i	0.578102	−	0.0765404i
$785$	−549.150	+	951.155i	−0.699554	+	1.21166i
$786$		0			0
$787$	−270.673	−	156.273i	−0.343930	−	0.198568i	0.318079	−	0.948064i	$-0.396962\pi$
$787$	−270.673	−	156.273i	−0.343930	−	0.198568i	−0.662008	+	0.749496i	$0.730296\pi$
$788$	145.068	−	251.265i	0.184097	−	0.318865i
$789$		0			0
$790$	1066.50	+	615.746i	1.35000	+	0.779426i
$791$	628.716	+	309.761i	0.794836	+	0.391607i
$792$		0			0
$793$	619.075	−	1072.27i	0.780675	−	1.35217i
$794$			306.640i			0.386197i
$795$		0			0
$796$		−	358.558i		−	0.450450i
$797$	−255.222	+	147.352i	−0.320228	+	0.184884i	−0.651494	−	0.758654i	$-0.725857\pi$
$797$	−255.222	+	147.352i	−0.320228	+	0.184884i	0.331266	+	0.943537i	$0.392524\pi$
$798$		0			0
$799$	11.1715	−	19.3497i	0.0139819	−	0.0242174i
$800$	358.221	−	620.457i	0.447777	−	0.775572i
$801$		0			0
$802$	−367.758	−	636.975i	−0.458551	−	0.794234i
$803$	−20.4396	+	11.8008i	−0.0254540	+	0.0146959i
$804$		0			0
$805$	−473.598	−	708.227i	−0.588320	−	0.879785i
$806$	476.298	+	824.973i	0.590941	+	1.02354i
$807$		0			0
$808$		−	804.772i		−	0.996005i
$809$	674.311	+	1167.94i	0.833512	+	1.44368i	0.895236	+	0.445591i	$0.147007\pi$
$809$	674.311	+	1167.94i	0.833512	+	1.44368i	−0.0617248	+	0.998093i	$0.519660\pi$
$810$		0			0
$811$			108.718i			0.134054i	0.997751	+	0.0670270i	$0.0213514\pi$
$811$			108.718i			0.134054i	−0.997751	+	0.0670270i	$0.978649\pi$
$812$	134.044	+	66.0422i	0.165079	+	0.0813328i
$813$		0			0
$814$	−54.8471			−0.0673797
$815$	1421.72	+	820.829i	1.74444	+	1.00715i
$816$		0			0
$817$	−129.990	+	75.0500i	−0.159107	+	0.0918604i
$818$			123.974i			0.151557i
$819$		0			0
$820$	−549.582			−0.670222
$821$	168.555	+	291.946i	0.205304	+	0.355598i	0.950230	−	0.311550i	$-0.100848\pi$
$821$	168.555	+	291.946i	0.205304	+	0.355598i	−0.744925	+	0.667148i	$0.767515\pi$
$822$		0			0
$823$	−164.071	+	284.179i	−0.199357	+	0.345296i	−0.948320	−	0.317315i	$-0.897219\pi$
$823$	−164.071	+	284.179i	−0.199357	+	0.345296i	0.748963	+	0.662612i	$0.230552\pi$
$824$		−	860.909i		−	1.04479i
$825$		0			0
$826$	334.752	+	500.593i	0.405268	+	0.606045i
$827$	−329.273			−0.398154			−0.199077	−	0.979984i	$-0.563794\pi$
$827$	−329.273			−0.398154			−0.199077	+	0.979984i	$0.563794\pi$
$828$		0			0
$829$	−950.667	+	548.868i	−1.14676	+	0.662084i	−0.948097	−	0.317983i	$-0.896995\pi$
$829$	−950.667	+	548.868i	−1.14676	+	0.662084i	−0.198667	+	0.980067i	$0.563661\pi$
$830$	−1190.88			−1.43479
$831$		0			0
$832$	786.546	−	454.113i	0.945368	−	0.545808i
$833$	110.951	+	837.998i	0.133194	+	1.00600i
$834$		0			0
$835$	−513.491	−	889.392i	−0.614959	−	1.06514i
$836$	3.31729	−	1.91524i	0.00396805	−	0.00229096i
$837$		0			0
$838$	−413.590	−	238.787i	−0.493545	−	0.284948i
$839$	354.194	+	204.494i	0.422162	+	0.243735i	0.696002	−	0.718040i	$-0.254961\pi$
$839$	354.194	+	204.494i	0.422162	+	0.243735i	−0.273840	+	0.961775i	$0.588294\pi$
$840$		0			0
$841$	278.437	+	482.267i	0.331078	+	0.573445i
$842$	−1072.88			−1.27420
$843$		0			0
$844$	−8.99617			−0.0106590
$845$	−15.4061	−	8.89474i	−0.0182321	−	0.0105263i
$846$		0			0
$847$	701.128	−	468.851i	0.827778	−	0.553543i
$848$	340.375	−	589.548i	0.401386	−	0.695221i
$849$		0			0
$850$	−912.082	−	526.591i	−1.07304	−	0.619519i
$851$	−360.046	+	623.618i	−0.423085	+	0.732806i
$852$		0			0
$853$	−87.1029	−	50.2889i	−0.102114	−	0.0589553i	0.448074	−	0.893997i	$-0.352110\pi$
$853$	−87.1029	−	50.2889i	−0.102114	−	0.0589553i	−0.550187	+	0.835041i	$0.685444\pi$
$854$	1092.61	−	72.0163i	1.27940	−	0.0843283i
$855$		0			0
$856$	−138.212	+	239.390i	−0.161462	+	0.279661i
$857$		−	1155.67i		−	1.34851i	−0.738498	−	0.674255i	$-0.764465\pi$
$857$		−	1155.67i		−	1.34851i	0.738498	−	0.674255i	$-0.235535\pi$
$858$		0			0
$859$			128.897i			0.150054i	0.997181	+	0.0750271i	$0.0239043\pi$
$859$			128.897i			0.150054i	−0.997181	+	0.0750271i	$0.976096\pi$
$860$	305.187	−	176.200i	0.354868	−	0.204883i
$861$		0			0
$862$	554.462	−	960.357i	0.643228	−	1.11410i
$863$	−232.536	+	402.764i	−0.269451	+	0.466703i	−0.968720	−	0.248156i	$-0.920176\pi$
$863$	−232.536	+	402.764i	−0.269451	+	0.466703i	0.699269	+	0.714858i	$0.253509\pi$
$864$		0			0
$865$	826.262	+	1431.13i	0.955216	+	1.65448i
$866$	−131.020	+	75.6447i	−0.151294	+	0.0873495i
$867$		0			0
$868$	172.497	−	350.114i	0.198730	−	0.403357i
$869$	−33.7217	−	58.4076i	−0.0388051	−	0.0672125i
$870$		0			0
$871$		−	1190.99i		−	1.36738i
$872$	272.142	+	471.364i	0.312090	+	0.540555i
$873$		0			0
$874$			108.550i			0.124199i
$875$	−365.141	−	546.038i	−0.417304	−	0.624043i
$876$		0			0
$877$	1304.19			1.48711			0.743553	−	0.668677i	$-0.233139\pi$
$877$	1304.19			1.48711			0.743553	+	0.668677i	$0.233139\pi$
$878$	−736.205	−	425.048i	−0.838502	−	0.484110i
$879$		0			0
$880$	45.3070	−	26.1580i	0.0514852	−	0.0297250i
$881$		−	533.780i		−	0.605880i	−0.953010	−	0.302940i	$-0.902032\pi$
$881$		−	533.780i		−	0.605880i	0.953010	−	0.302940i	$-0.0979681\pi$
$882$		0			0
$883$	139.576			0.158070			0.0790351	−	0.996872i	$-0.474816\pi$
$883$	139.576			0.158070			0.0790351	+	0.996872i	$0.474816\pi$
$884$	142.957	+	247.609i	0.161716	+	0.280100i
$885$		0			0
$886$	−428.203	+	741.670i	−0.483299	+	0.837099i
$887$			762.221i			0.859324i	0.902990	+	0.429662i	$0.141367\pi$
$887$			762.221i			0.859324i	−0.902990	+	0.429662i	$0.858633\pi$
$888$		0			0
$889$	−18.0690	+	12.0829i	−0.0203251	+	0.0135916i
$890$	−872.461			−0.980294
$891$		0			0
$892$	12.8747	−	7.43319i	0.0144335	−	0.00833317i
$893$	−5.49777			−0.00615651
$894$		0			0
$895$	−625.217	+	360.969i	−0.698566	+	0.403317i
$896$	233.166	+	114.878i	0.260230	+	0.128212i
$897$		0			0
$898$	−584.228	−	1011.91i	−0.650588	−	1.12685i
$899$	−642.691	+	371.058i	−0.714896	+	0.412745i
$900$		0			0
$901$	1090.04	+	629.333i	1.20981	+	0.698483i
$902$	−56.2617	−	32.4827i	−0.0623744	−	0.0360119i
$903$		0			0
$904$	435.911	+	755.021i	0.482203	+	0.835200i
$905$	1067.79			1.17988
$906$		0			0
$907$	−1579.47			−1.74142			−0.870712	−	0.491794i	$-0.836341\pi$
$907$	−1579.47			−1.74142			−0.870712	+	0.491794i	$0.836341\pi$
$908$	130.576	+	75.3883i	0.143806	+	0.0830267i
$909$		0			0
$910$	−78.3876	−	1189.27i	−0.0861402	−	1.30689i
$911$	483.093	−	836.741i	0.530288	−	0.918487i	−0.469087	−	0.883152i	$-0.655417\pi$
$911$	483.093	−	836.741i	0.530288	−	0.918487i	0.999376	−	0.0353346i	$-0.0112497\pi$
$912$		0			0
$913$	56.4813	+	32.6095i	0.0618634	+	0.0357169i
$914$	445.506	−	771.640i	0.487425	−	0.844245i
$915$		0			0
$916$	−12.5500	−	7.24572i	−0.0137008	−	0.00791018i
$917$	291.795	+	436.355i	0.318206	+	0.475850i
$918$		0			0
$919$	−831.073	+	1439.46i	−0.904323	+	1.56633i	−0.0824996	+	0.996591i	$0.526290\pi$
$919$	−831.073	+	1439.46i	−0.904323	+	1.56633i	−0.821823	+	0.569742i	$0.807043\pi$
$920$		−	1059.78i		−	1.15193i
$921$		0			0
$922$		−	193.545i		−	0.209919i
$923$	−390.084	+	225.215i	−0.422627	+	0.244004i
$924$		0			0
$925$	−859.556	+	1488.80i	−0.929250	+	1.60951i
$926$	20.2317	−	35.0424i	0.0218485	−	0.0378428i
$927$		0			0
$928$	163.527	+	283.236i	0.176214	+	0.305211i
$929$	−427.869	+	247.030i	−0.460569	+	0.265910i	−0.712284	−	0.701892i	$-0.752339\pi$
$929$	−427.869	+	247.030i	−0.460569	+	0.265910i	0.251714	+	0.967802i	$0.419006\pi$
$930$		0			0
$931$	164.923	−	126.742i	0.177146	−	0.136136i
$932$	51.9164	+	89.9219i	0.0557043	+	0.0964827i
$933$		0			0
$934$		−	562.561i		−	0.602314i
$935$	48.3645	+	83.7698i	0.0517268	+	0.0895934i
$936$		0			0
$937$		−	582.125i		−	0.621265i	−0.950530	−	0.310632i	$-0.899459\pi$
$937$		−	582.125i		−	0.621265i	0.950530	−	0.310632i	$-0.100541\pi$
$938$	875.551	−	585.489i	0.933423	−	0.624189i
$939$		0			0
$940$	12.9075			0.0137313
$941$	667.636	+	385.460i	0.709496	+	0.409628i	0.810874	−	0.585220i	$-0.198992\pi$
$941$	667.636	+	385.460i	0.709496	+	0.409628i	−0.101378	+	0.994848i	$0.532325\pi$
$942$		0			0
$943$	−738.664	+	426.468i	−0.783313	+	0.452246i
$944$			485.491i			0.514291i
$945$		0			0
$946$	41.6567			0.0440345
$947$	−539.437	−	934.333i	−0.569628	−	0.986624i	−0.996603	−	0.0823605i	$-0.973754\pi$
$947$	−539.437	−	934.333i	−0.569628	−	0.986624i	0.426975	−	0.904263i	$-0.359579\pi$
$948$		0			0
$949$	−216.739	+	375.402i	−0.228386	+	0.395577i
$950$			259.147i			0.272786i
$951$		0			0
$952$	−464.711	+	943.212i	−0.488141	+	0.990769i
$953$	−759.145			−0.796584			−0.398292	−	0.917259i	$-0.630397\pi$
$953$	−759.145			−0.796584			−0.398292	+	0.917259i	$0.630397\pi$
$954$		0			0
$955$	241.888	−	139.654i	0.253286	−	0.146235i
$956$	−123.984			−0.129691
$957$		0			0
$958$	893.661	−	515.955i	0.932840	−	0.538576i
$959$	−204.351	+	136.652i	−0.213088	+	0.142494i
$960$		0			0
$961$	488.675	+	846.411i	0.508507	+	0.880760i
$962$	−872.387	+	503.673i	−0.906847	+	0.523569i
$963$		0			0
$964$	69.1899	+	39.9468i	0.0717737	+	0.0414386i
$965$	2048.53	+	1182.72i	2.12283	+	1.22562i
$966$		0			0
$967$	266.196	+	461.064i	0.275280	+	0.476799i	0.970206	−	0.242283i	$-0.0778962\pi$
$967$	266.196	+	461.064i	0.275280	+	0.476799i	−0.694926	+	0.719081i	$0.744563\pi$
$968$	1049.16			1.08384
$969$		0			0
$970$	−504.197			−0.519791
$971$	−1161.79	−	670.759i	−1.19649	−	0.690792i	−0.236717	−	0.971579i	$-0.576072\pi$
$971$	−1161.79	−	670.759i	−1.19649	−	0.690792i	−0.959770	+	0.280786i	$0.909405\pi$
$972$		0			0
$973$	−623.140	+	1264.77i	−0.640431	+	1.29987i
$974$	−482.735	+	836.122i	−0.495621	+	0.858441i
$975$		0			0
$976$	764.493	+	441.380i	0.783292	+	0.452234i
$977$	−293.739	+	508.771i	−0.300654	+	0.520748i	−0.976284	−	0.216493i	$-0.930538\pi$
$977$	−293.739	+	508.771i	−0.300654	+	0.520748i	0.675630	+	0.737241i	$0.263872\pi$
$978$		0			0
$979$	41.3794	+	23.8904i	0.0422670	+	0.0244029i
$980$	−387.201	+	297.561i	−0.395103	+	0.303634i
$981$		0			0
$982$	−338.779	+	586.782i	−0.344989	+	0.597538i
$983$			61.0729i			0.0621291i	0.999517	+	0.0310646i	$0.00988975\pi$
$983$			61.0729i			0.0621291i	−0.999517	+	0.0310646i	$0.990110\pi$
$984$		0			0
$985$		−	1802.80i		−	1.83026i
$986$	416.362	−	240.387i	0.422274	−	0.243800i
$987$		0			0
$988$	35.1761	−	60.9268i	0.0356034	−	0.0616668i
$989$	273.457	−	473.641i	0.276498	−	0.478909i
$990$		0			0
$991$	−72.0849	−	124.855i	−0.0727395	−	0.125989i	0.827362	−	0.561670i	$-0.189841\pi$
$991$	−72.0849	−	124.855i	−0.0727395	−	0.125989i	−0.900101	+	0.435681i	$0.856508\pi$
$992$	739.792	−	427.119i	0.745758	−	0.430564i
$993$		0			0
$994$	−357.331	−	176.053i	−0.359488	−	0.177116i
$995$	−1113.98	−	1929.47i	−1.11958	−	1.93916i
$996$		0			0
$997$			838.743i			0.841267i	0.907231	+	0.420633i	$0.138192\pi$
$997$			838.743i			0.841267i	−0.907231	+	0.420633i	$0.861808\pi$
$998$	70.0800	+	121.382i	0.0702205	+	0.121625i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.19.5		28
3.2	odd	2		63.3.k.a.61.10	yes	28
7.3	odd	6		189.3.t.a.73.10		28
9.4	even	3		189.3.t.a.145.10		28
9.5	odd	6		63.3.t.a.40.5	yes	28
21.2	odd	6		441.3.l.a.97.10		28
21.5	even	6		441.3.l.b.97.10		28
21.11	odd	6		441.3.t.a.178.5		28
21.17	even	6		63.3.t.a.52.5	yes	28
21.20	even	2		441.3.k.b.313.10		28
63.5	even	6		441.3.l.a.391.10		28
63.23	odd	6		441.3.l.b.391.10		28
63.31	odd	6	inner	189.3.k.a.10.5		28
63.32	odd	6		441.3.k.b.31.10		28
63.41	even	6		441.3.t.a.166.5		28
63.59	even	6		63.3.k.a.31.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.10	✓	28	63.59	even	6
63.3.k.a.61.10	yes	28	3.2	odd	2
63.3.t.a.40.5	yes	28	9.5	odd	6
63.3.t.a.52.5	yes	28	21.17	even	6
189.3.k.a.10.5		28	63.31	odd	6	inner
189.3.k.a.19.5		28	1.1	even	1	trivial
189.3.t.a.73.10		28	7.3	odd	6
189.3.t.a.145.10		28	9.4	even	3
441.3.k.b.31.10		28	63.32	odd	6
441.3.k.b.313.10		28	21.20	even	2
441.3.l.a.97.10		28	21.2	odd	6
441.3.l.a.391.10		28	63.5	even	6
441.3.l.b.97.10		28	21.5	even	6
441.3.l.b.391.10		28	63.23	odd	6
441.3.t.a.166.5		28	63.41	even	6
441.3.t.a.178.5		28	21.11	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.826674 - 1.43184i) q^{2} +(0.633221 - 1.09677i) q^{4} -7.86923i q^{5} +(-5.81886 + 3.89113i) q^{7} -8.70726 q^{8} +O(q^{10})\)	\(q+(-0.826674 - 1.43184i) q^{2} +(0.633221 - 1.09677i) q^{4} -7.86923i q^{5} +(-5.81886 + 3.89113i) q^{7} -8.70726 q^{8} +(-11.2675 + 6.50529i) q^{10} +0.712531 q^{11} +(11.3334 - 6.54333i) q^{13} +(10.3818 + 5.11499i) q^{14} +(4.66518 + 8.08032i) q^{16} +(-14.9400 + 8.62563i) q^{17} +(3.67616 + 2.12243i) q^{19} +(-8.63075 - 4.98297i) q^{20} +(-0.589031 - 1.02023i) q^{22} -15.4669 q^{23} -36.9248 q^{25} +(-18.7380 - 10.8184i) q^{26} +(0.583053 + 8.84591i) q^{28} +(8.42802 - 14.5978i) q^{29} +(-38.1282 - 22.0134i) q^{31} +(-9.70136 + 16.8033i) q^{32} +(24.7010 + 14.2612i) q^{34} +(30.6202 + 45.7900i) q^{35} +(23.2785 - 40.3196i) q^{37} -7.01823i q^{38} +68.5195i q^{40} +(47.7579 - 27.5730i) q^{41} +(-17.6802 + 30.6230i) q^{43} +(0.451190 - 0.781484i) q^{44} +(12.7860 + 22.1461i) q^{46} +(-1.12164 + 0.647579i) q^{47} +(18.7182 - 45.2839i) q^{49} +(30.5248 + 52.8705i) q^{50} -16.5735i q^{52} +(-36.4805 - 63.1860i) q^{53} -5.60707i q^{55} +(50.6663 - 33.8811i) q^{56} -27.8689 q^{58} +(45.0624 + 26.0168i) q^{59} +(81.9361 - 47.3058i) q^{61} +72.7914i q^{62} +69.4008 q^{64} +(-51.4910 - 89.1850i) q^{65} +(45.5040 - 78.8152i) q^{67} +21.8477i q^{68} +(40.2510 - 81.6966i) q^{70} -34.4191 q^{71} +(-28.6859 + 16.5618i) q^{73} -76.9750 q^{74} +(4.65564 - 2.68794i) q^{76} +(-4.14612 + 2.77255i) q^{77} +(-47.3266 - 81.9721i) q^{79} +(63.5859 - 36.7114i) q^{80} +(-78.9604 - 45.5878i) q^{82} +(79.2685 + 45.7657i) q^{83} +(67.8771 + 117.567i) q^{85} +58.4630 q^{86} -6.20419 q^{88} +(58.0738 + 33.5289i) q^{89} +(-40.4864 + 82.1743i) q^{91} +(-9.79394 + 16.9636i) q^{92} +(1.85446 + 1.07067i) q^{94} +(16.7019 - 28.9285i) q^{95} +(33.5610 + 19.3764i) q^{97} +(-80.3131 + 10.6334i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Introduction

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