LMFDB - Embedded newform 272.3.x.a.155.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,3,Mod(155,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.155"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 2, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	272.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.41146319060$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.17
Character	$\chi$	$=$	272.155
Dual form			272.3.x.a.179.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.51503 - 1.30564i) q^{2} +(-5.10521 - 2.11465i) q^{3} +(0.590634 + 3.95615i) q^{4} +(-1.23196 + 2.97420i) q^{5} +(4.97359 + 9.86931i) q^{6} +(5.08037 - 12.2651i) q^{7} +(4.27047 - 6.76485i) q^{8} +(15.2275 + 15.2275i) q^{9} +(5.74968 - 2.89752i) q^{10} +(10.2260 - 4.23573i) q^{11} +(5.35056 - 21.4460i) q^{12} +(-9.70987 - 9.70987i) q^{13} +(-23.7107 + 11.9489i) q^{14} +(12.5788 - 12.5788i) q^{15} +(-15.3023 + 4.67328i) q^{16} +(11.9786 - 12.0629i) q^{17} +(-3.18857 - 42.9517i) q^{18} +12.5646i q^{19} +(-12.4940 - 3.11714i) q^{20} +(-51.8728 + 51.8728i) q^{21} +(-21.0230 - 6.93411i) q^{22} +(5.48178 + 2.27063i) q^{23} +(-36.1069 + 25.5055i) q^{24} +(10.3495 + 10.3495i) q^{25} +(2.03320 + 27.3883i) q^{26} +(-26.5070 - 63.9937i) q^{27} +(51.5233 + 12.8545i) q^{28} +(-7.99702 - 3.31247i) q^{29} +(-35.4806 + 2.63394i) q^{30} +(-15.9667 - 38.5469i) q^{31} +(29.2850 + 12.8991i) q^{32} -61.1628 q^{33} +(-33.8977 + 2.63605i) q^{34} +(30.2201 + 30.2201i) q^{35} +(-51.2485 + 69.2363i) q^{36} +(-19.5907 - 8.11473i) q^{37} +(16.4047 - 19.0357i) q^{38} +(29.0380 + 70.1039i) q^{39} +(14.8590 + 21.0352i) q^{40} +(-9.19169 - 3.80732i) q^{41} +(146.316 - 10.8619i) q^{42} +26.4797i q^{43} +(22.7970 + 37.9537i) q^{44} +(-64.0494 + 26.5301i) q^{45} +(-5.34045 - 10.5973i) q^{46} -49.0795 q^{47} +(88.0039 + 8.50092i) q^{48} +(-89.9743 - 89.9743i) q^{49} +(-2.16713 - 29.1925i) q^{50} +(-86.6620 + 36.2533i) q^{51} +(32.6787 - 44.1487i) q^{52} -13.9860i q^{53} +(-43.3934 + 131.561i) q^{54} +35.6323i q^{55} +(-61.2760 - 86.7456i) q^{56} +(26.5697 - 64.1448i) q^{57} +(7.79084 + 15.4597i) q^{58} -51.9124i q^{59} +(57.1931 + 42.3342i) q^{60} +(4.84608 + 11.6995i) q^{61} +(-26.1383 + 79.2464i) q^{62} +(264.128 - 109.406i) q^{63} +(-27.5263 - 57.7781i) q^{64} +(40.8412 - 16.9170i) q^{65} +(92.6635 + 79.8563i) q^{66} +(-70.8700 - 70.8700i) q^{67} +(54.7977 + 40.2643i) q^{68} +(-23.1841 - 23.1841i) q^{69} +(-6.32795 - 85.2409i) q^{70} +(97.1042 - 40.2219i) q^{71} +(168.040 - 37.9832i) q^{72} +(-123.486 + 51.1496i) q^{73} +(19.0856 + 37.8724i) q^{74} +(-30.9508 - 74.7219i) q^{75} +(-49.7074 + 7.42106i) q^{76} -146.942i q^{77} +(47.5367 - 144.123i) q^{78} +(2.95218 - 7.12720i) q^{79} +(4.95248 - 51.2694i) q^{80} +188.940i q^{81} +(8.95472 + 17.7692i) q^{82} +58.4127i q^{83} +(-235.854 - 174.579i) q^{84} +(21.1205 + 50.4877i) q^{85} +(34.5728 - 40.1175i) q^{86} +(33.8218 + 33.8218i) q^{87} +(15.0155 - 87.2656i) q^{88} +127.045 q^{89} +(131.675 + 43.4312i) q^{90} +(-168.422 + 69.7628i) q^{91} +(-5.74523 + 23.0279i) q^{92} +230.554i q^{93} +(74.3570 + 64.0800i) q^{94} +(-37.3696 - 15.4790i) q^{95} +(-122.229 - 127.780i) q^{96} +(4.98961 + 12.0460i) q^{97} +(18.8402 + 253.787i) q^{98} +(220.216 + 91.2163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.51503	−	1.30564i	−0.757515	−	0.652818i
$2$	−1.51503	−	1.30564i	−0.757515	−	0.652818i
$3$	−5.10521	−	2.11465i	−1.70174	−	0.704883i	−0.701767	−	0.712407i	$-0.747605\pi$
$3$	−5.10521	−	2.11465i	−1.70174	−	0.704883i	−0.999972	+	0.00752390i	$0.997605\pi$
$4$	0.590634	+	3.95615i	0.147658	+	0.989038i
$5$	−1.23196	+	2.97420i	−0.246391	+	0.594841i	−0.997892	−	0.0648909i	$-0.979330\pi$
$5$	−1.23196	+	2.97420i	−0.246391	+	0.594841i	0.751501	+	0.659732i	$0.229330\pi$
$6$	4.97359	+	9.86931i	0.828932	+	1.64488i
$7$	5.08037	−	12.2651i	0.725767	−	1.75216i	0.0695587	−	0.997578i	$-0.477841\pi$
$7$	5.08037	−	12.2651i	0.725767	−	1.75216i	0.656209	−	0.754579i	$-0.272159\pi$
$8$	4.27047	−	6.76485i	0.533808	−	0.845606i
$9$	15.2275	+	15.2275i	1.69195	+	1.69195i
$10$	5.74968	−	2.89752i	0.574968	−	0.289752i
$11$	10.2260	−	4.23573i	0.929633	−	0.385067i	0.134094	−	0.990969i	$-0.457188\pi$
$11$	10.2260	−	4.23573i	0.929633	−	0.385067i	0.795539	+	0.605902i	$0.207188\pi$
$12$	5.35056	−	21.4460i	0.445880	−	1.78717i
$13$	−9.70987	−	9.70987i	−0.746913	−	0.746913i	0.226985	−	0.973898i	$-0.427113\pi$
$13$	−9.70987	−	9.70987i	−0.746913	−	0.746913i	−0.973898	+	0.226985i	$0.927113\pi$
$14$	−23.7107	+	11.9489i	−1.69362	+	0.853492i
$15$	12.5788	−	12.5788i	0.838586	−	0.838586i
$16$	−15.3023	+	4.67328i	−0.956394	+	0.292080i
$17$	11.9786	−	12.0629i	0.704622	−	0.709583i
$17$	11.9786	−	12.0629i	0.704622	−	0.709583i
$18$	−3.18857	−	42.9517i	−0.177143	−	2.38621i
$19$			12.5646i			0.661293i	0.943755	+	0.330647i	$0.107267\pi$
$19$			12.5646i			0.661293i	−0.943755	+	0.330647i	$0.892733\pi$
$20$	−12.4940	−	3.11714i	−0.624702	−	0.155857i
$21$	−51.8728	+	51.8728i	−2.47013	+	2.47013i
$22$	−21.0230	−	6.93411i	−0.955589	−	0.315187i
$23$	5.48178	+	2.27063i	0.238338	+	0.0987229i	0.498656	−	0.866800i	$-0.333827\pi$
$23$	5.48178	+	2.27063i	0.238338	+	0.0987229i	−0.260317	+	0.965523i	$0.583827\pi$
$24$	−36.1069	+	25.5055i	−1.50445	+	1.06273i
$25$	10.3495	+	10.3495i	0.413980	+	0.413980i
$26$	2.03320	+	27.3883i	0.0782000	+	1.05340i
$27$	−26.5070	−	63.9937i	−0.981742	−	2.37014i
$28$	51.5233	+	12.8545i	1.84012	+	0.459091i
$29$	−7.99702	−	3.31247i	−0.275759	−	0.114223i	0.240518	−	0.970645i	$-0.422683\pi$
$29$	−7.99702	−	3.31247i	−0.275759	−	0.114223i	−0.516277	+	0.856421i	$0.672683\pi$
$30$	−35.4806	+	2.63394i	−1.18269	+	0.0877980i
$31$	−15.9667	−	38.5469i	−0.515054	−	1.24345i	−0.940909	−	0.338658i	$-0.890027\pi$
$31$	−15.9667	−	38.5469i	−0.515054	−	1.24345i	0.425856	−	0.904791i	$-0.359973\pi$
$32$	29.2850	+	12.8991i	0.915158	+	0.403096i
$33$	−61.1628			−1.85342
$34$	−33.8977	+	2.63605i	−0.996990	+	0.0775308i
$35$	30.2201	+	30.2201i	0.863432	+	0.863432i
$36$	−51.2485	+	69.2363i	−1.42357	+	1.92323i
$37$	−19.5907	−	8.11473i	−0.529478	−	0.219317i	0.101897	−	0.994795i	$-0.467509\pi$
$37$	−19.5907	−	8.11473i	−0.529478	−	0.219317i	−0.631375	+	0.775478i	$0.717509\pi$
$38$	16.4047	−	19.0357i	0.431704	−	0.500940i
$39$	29.0380	+	70.1039i	0.744564	+	1.79754i
$40$	14.8590	+	21.0352i	0.371475	+	0.525881i
$41$	−9.19169	−	3.80732i	−0.224188	−	0.0928615i	0.267762	−	0.963485i	$-0.413716\pi$
$41$	−9.19169	−	3.80732i	−0.224188	−	0.0928615i	−0.491950	+	0.870623i	$0.663716\pi$
$42$	146.316	−	10.8619i	3.48371	−	0.258617i
$43$			26.4797i			0.615807i	0.951418	+	0.307903i	$0.0996273\pi$
$43$			26.4797i			0.615807i	−0.951418	+	0.307903i	$0.900373\pi$
$44$	22.7970	+	37.9537i	0.518114	+	0.862584i
$45$	−64.0494	+	26.5301i	−1.42332	+	0.589558i
$46$	−5.34045	−	10.5973i	−0.116097	−	0.230375i
$47$	−49.0795			−1.04425			−0.522123	−	0.852870i	$-0.674860\pi$
$47$	−49.0795			−1.04425			−0.522123	+	0.852870i	$0.674860\pi$
$48$	88.0039	+	8.50092i	1.83341	+	0.177103i
$49$	−89.9743	−	89.9743i	−1.83621	−	1.83621i
$50$	−2.16713	−	29.1925i	−0.0433427	−	0.583849i
$51$	−86.6620	+	36.2533i	−1.69925	+	0.710849i
$52$	32.6787	−	44.1487i	0.628437	−	0.849013i
$53$		−	13.9860i		−	0.263886i	−0.991257	−	0.131943i	$-0.957878\pi$
$53$		−	13.9860i		−	0.263886i	0.991257	−	0.131943i	$-0.0421216\pi$
$54$	−43.3934	+	131.561i	−0.803581	+	2.43631i
$55$			35.6323i			0.647861i
$56$	−61.2760	−	86.7456i	−1.09421	−	1.54903i
$57$	26.5697	−	64.1448i	0.466134	−	1.12535i
$58$	7.79084	+	15.4597i	0.134325	+	0.266546i
$59$		−	51.9124i		−	0.879872i	−0.898029	−	0.439936i	$-0.855001\pi$
$59$		−	51.9124i		−	0.879872i	0.898029	−	0.439936i	$-0.144999\pi$
$60$	57.1931	+	42.3342i	0.953219	+	0.705570i
$61$	4.84608	+	11.6995i	0.0794440	+	0.191795i	0.958611	−	0.284719i	$-0.0919003\pi$
$61$	4.84608	+	11.6995i	0.0794440	+	0.191795i	−0.879167	+	0.476514i	$0.841900\pi$
$62$	−26.1383	+	79.2464i	−0.421585	+	1.27817i
$63$	264.128	−	109.406i	4.19252	−	1.73660i
$64$	−27.5263	−	57.7781i	−0.430098	−	0.902782i
$65$	40.8412	−	16.9170i	0.628327	−	0.260262i
$66$	92.6635	+	79.8563i	1.40399	+	1.20994i
$67$	−70.8700	−	70.8700i	−1.05776	−	1.05776i	−0.998226	−	0.0595351i	$-0.981038\pi$
$67$	−70.8700	−	70.8700i	−1.05776	−	1.05776i	−0.0595351	−	0.998226i	$-0.518962\pi$
$68$	54.7977	+	40.2643i	0.805848	+	0.592122i
$69$	−23.1841	−	23.1841i	−0.336001	−	0.336001i
$70$	−6.32795	−	85.2409i	−0.0903993	−	1.21773i
$71$	97.1042	−	40.2219i	1.36767	−	0.566505i	0.426511	−	0.904482i	$-0.359743\pi$
$71$	97.1042	−	40.2219i	1.36767	−	0.566505i	0.941154	+	0.337977i	$0.109743\pi$
$72$	168.040	−	37.9832i	2.33389	−	0.527545i
$73$	−123.486	+	51.1496i	−1.69159	+	0.700680i	−0.999771	−	0.0213912i	$-0.993190\pi$
$73$	−123.486	+	51.1496i	−1.69159	+	0.700680i	−0.691819	+	0.722071i	$0.743190\pi$
$74$	19.0856	+	37.8724i	0.257914	+	0.511789i
$75$	−30.9508	−	74.7219i	−0.412678	−	0.996293i
$76$	−49.7074	+	7.42106i	−0.654044	+	0.0976455i
$77$		−	146.942i		−	1.90833i
$78$	47.5367	−	144.123i	0.609445	−	1.84773i
$79$	2.95218	−	7.12720i	0.0373694	−	0.0902177i	−0.904093	−	0.427336i	$-0.859452\pi$
$79$	2.95218	−	7.12720i	0.0373694	−	0.0902177i	0.941462	+	0.337118i	$0.109452\pi$
$80$	4.95248	−	51.2694i	0.0619060	−	0.640868i
$81$			188.940i			2.33259i
$82$	8.95472	+	17.7692i	0.109204	+	0.216698i
$83$			58.4127i			0.703767i	0.936044	+	0.351883i	$0.114459\pi$
$83$			58.4127i			0.703767i	−0.936044	+	0.351883i	$0.885541\pi$
$84$	−235.854	−	174.579i	−2.80779	−	2.07832i
$85$	21.1205	+	50.4877i	0.248477	+	0.593973i
$86$	34.5728	−	40.1175i	0.402009	−	0.466483i
$87$	33.8218	+	33.8218i	0.388756	+	0.388756i
$88$	15.0155	−	87.2656i	0.170631	−	0.991655i
$89$	127.045			1.42747			0.713734	−	0.700417i	$-0.247003\pi$
$89$	127.045			1.42747			0.713734	+	0.700417i	$0.247003\pi$
$90$	131.675	+	43.4312i	1.46306	+	0.482569i
$91$	−168.422	+	69.7628i	−1.85079	+	0.766624i
$92$	−5.74523	+	23.0279i	−0.0624481	+	0.250303i
$93$			230.554i			2.47908i
$94$	74.3570	+	64.0800i	0.791032	+	0.681702i
$95$	−37.3696	−	15.4790i	−0.393364	−	0.162937i
$96$	−122.229	−	127.780i	−1.27322	−	1.33104i
$97$	4.98961	+	12.0460i	0.0514392	+	0.124185i	0.947510	−	0.319726i	$-0.103591\pi$
$97$	4.98961	+	12.0460i	0.0514392	+	0.124185i	−0.896071	+	0.443911i	$0.853591\pi$
$98$	18.8402	+	253.787i	0.192247	+	2.58967i
$99$	220.216	+	91.2163i	2.22440	+	0.921377i
$100$	−34.8314	+	47.0569i	−0.348314	+	0.470569i
$101$	10.4799	+	10.4799i	0.103761	+	0.103761i	0.757082	−	0.653320i	$-0.226625\pi$
$101$	10.4799	+	10.4799i	0.103761	+	0.103761i	−0.653320	+	0.757082i	$0.726625\pi$
$102$	178.629	+	58.2241i	1.75127	+	0.570824i
$103$	−92.1171			−0.894341			−0.447170	−	0.894449i	$-0.647568\pi$
$103$	−92.1171			−0.894341			−0.447170	+	0.894449i	$0.647568\pi$
$104$	−107.151	+	24.2201i	−1.03030	+	0.232886i
$105$	−90.3753	−	218.185i	−0.860717	−	2.07795i
$106$	−18.2606	+	21.1892i	−0.172270	+	0.199898i
$107$	4.99149	+	2.06754i	0.0466495	+	0.0193228i	0.405886	−	0.913924i	$-0.366963\pi$
$107$	4.99149	+	2.06754i	0.0466495	+	0.0193228i	−0.359237	+	0.933246i	$0.616963\pi$
$108$	237.513	−	142.663i	2.19919	−	1.32095i
$109$	45.1093	+	108.904i	0.413847	+	0.999116i	0.984095	+	0.177643i	$0.0568472\pi$
$109$	45.1093	+	108.904i	0.413847	+	0.999116i	−0.570248	+	0.821473i	$0.693153\pi$
$110$	46.5228	−	53.9841i	0.422935	−	0.490764i
$111$	82.8549	+	82.8549i	0.746440	+	0.746440i
$112$	−20.4232	+	211.426i	−0.182350	+	1.88773i
$113$	93.2650	+	38.6316i	0.825354	+	0.341873i	0.755062	−	0.655654i	$-0.227607\pi$
$113$	93.2650	+	38.6316i	0.825354	+	0.341873i	0.0702923	+	0.997526i	$0.477607\pi$
$114$	−124.004	+	62.4911i	−1.08775	+	0.548167i
$115$	−13.5066	+	13.5066i	−0.117449	+	0.117449i
$116$	8.38134	−	33.5939i	0.0722530	−	0.289603i
$117$		−	295.714i		−	2.52747i
$118$	−67.7787	+	78.6489i	−0.574396	+	0.666516i
$119$	−87.0973	−	208.202i	−0.731910	−	1.74960i
$120$	−31.3763	−	138.811i	−0.261469	−	1.15676i
$121$	1.06896	−	1.06896i	0.00883441	−	0.00883441i
$122$	7.93329	−	24.0523i	0.0650269	−	0.197150i
$123$	38.8744	+	38.8744i	0.316052	+	0.316052i
$124$	143.067	−	85.9337i	1.15377	−	0.693014i
$125$	−117.887	+	48.8303i	−0.943094	+	0.390642i
$126$	−543.006	−	179.103i	−4.30957	−	1.42145i
$127$	−52.2489	−	52.2489i	−0.411409	−	0.411409i	0.470820	−	0.882229i	$-0.343958\pi$
$127$	−52.2489	−	52.2489i	−0.411409	−	0.411409i	−0.882229	+	0.470820i	$0.843958\pi$
$128$	−33.7340	+	123.475i	−0.263547	+	0.964647i
$129$	55.9952	−	135.184i	0.434072	−	1.04794i
$130$	−83.9632	−	27.6940i	−0.645870	−	0.213031i
$131$	56.8796	−	137.319i	0.434195	−	1.04824i	−0.543725	−	0.839263i	$-0.682987\pi$
$131$	56.8796	−	137.319i	0.434195	−	1.04824i	0.977921	−	0.208977i	$-0.0670134\pi$
$132$	−36.1248	−	241.970i	−0.273673	−	1.83310i
$133$	154.106	+	63.8327i	1.15869	+	0.479945i
$134$	14.8398	+	199.901i	0.110745	+	1.49180i
$135$	222.986			1.65175
$136$	−30.4497	−	132.547i	−0.223895	−	0.974613i
$137$			46.4780i			0.339255i	0.985508	+	0.169628i	$0.0542565\pi$
$137$			46.4780i			0.339255i	−0.985508	+	0.169628i	$0.945744\pi$
$138$	4.85463	+	65.3945i	0.0351785	+	0.473873i
$139$	−5.83727	+	14.0924i	−0.0419947	+	0.101384i	−0.943485	−	0.331415i	$-0.892474\pi$
$139$	−5.83727	+	14.0924i	−0.0419947	+	0.101384i	0.901490	+	0.432799i	$0.142474\pi$
$140$	−101.706	+	137.404i	−0.726474	+	0.981461i
$141$	250.562	+	103.786i	1.77703	+	0.736071i
$142$	−199.631	−	65.8453i	−1.40585	−	0.463699i
$143$	−140.421	−	58.1643i	−0.981966	−	0.406744i
$144$	−304.178	−	161.854i	−2.11235	−	1.12398i
$145$	19.7039	−	19.7039i	0.135889	−	0.135889i
$146$	253.868	+	83.7346i	1.73882	+	0.573524i
$147$	269.074	+	649.602i	1.83044	+	4.41906i
$148$	20.5322	−	82.2966i	0.138731	−	0.556058i
$149$	−130.039	+	130.039i	−0.872747	+	0.872747i	−0.992771	−	0.120024i	$-0.961703\pi$
$149$	−130.039	+	130.039i	−0.872747	+	0.872747i	0.120024	+	0.992771i	$0.461703\pi$
$150$	−50.6681	+	153.617i	−0.337788	+	1.02411i
$151$	−124.402	−	124.402i	−0.823851	−	0.823851i	0.162807	−	0.986658i	$-0.447945\pi$
$151$	−124.402	−	124.402i	−0.823851	−	0.823851i	−0.986658	+	0.162807i	$0.947945\pi$
$152$	84.9974	+	53.6566i	0.559193	+	0.353004i
$153$	366.092	−	1.28444i	2.39276	−	0.00839505i
$154$	−191.852	+	222.621i	−1.24579	+	1.44559i
$155$	134.317			0.866559
$156$	−260.191	+	156.284i	−1.66789	+	1.00182i
$157$	−158.393	−	158.393i	−1.00888	−	1.00888i	−0.999960	−	0.00891508i	$-0.997162\pi$
$157$	−158.393	−	158.393i	−1.00888	−	1.00888i	−0.00891508	−	0.999960i	$-0.502838\pi$
$158$	−13.7782	+	6.94345i	−0.0872036	+	0.0439459i
$159$	−29.5754	+	71.4014i	−0.186009	+	0.449065i
$160$	−74.4423	+	71.2086i	−0.465265	+	0.445054i
$161$	55.6989	−	55.6989i	0.345956	−	0.345956i
$162$	246.686	−	286.250i	1.52276	−	1.76697i
$163$	−88.7593	+	36.7653i	−0.544535	+	0.225554i	−0.637956	−	0.770073i	$-0.720220\pi$
$163$	−88.7593	+	36.7653i	−0.544535	+	0.225554i	0.0934207	+	0.995627i	$0.470220\pi$
$164$	9.63343	−	38.6125i	0.0587404	−	0.235442i
$165$	75.3499	−	181.911i	0.456666	−	1.10249i
$166$	76.2656	−	88.4969i	0.459431	−	0.533114i
$167$	−34.7229	+	14.3827i	−0.207922	+	0.0861240i	−0.484214	−	0.874950i	$-0.660894\pi$
$167$	−34.7229	+	14.3827i	−0.207922	+	0.0861240i	0.276292	+	0.961074i	$0.410894\pi$
$168$	129.390	+	572.432i	0.770181	+	3.40733i
$169$			19.5630i			0.115757i
$170$	33.9203	−	104.066i	0.199531	−	0.612153i
$171$	−191.327	+	191.327i	−1.11887	+	1.11887i
$172$	−104.758	+	15.6398i	−0.609056	+	0.0909291i
$173$	85.6320	−	206.734i	0.494982	−	1.19499i	−0.457173	−	0.889378i	$-0.651138\pi$
$173$	85.6320	−	206.734i	0.494982	−	1.19499i	0.952155	−	0.305615i	$-0.0988621\pi$
$174$	−7.08212	−	95.3999i	−0.0407018	−	0.548275i
$175$	179.517	−	74.3583i	1.02581	−	0.424905i
$176$	−136.686	+	112.605i	−0.776625	+	0.639802i
$177$	−109.777	+	265.024i	−0.620207	+	1.49731i
$178$	−192.476	−	165.874i	−1.08133	−	0.931876i
$179$	−157.100			−0.877651			−0.438825	−	0.898572i	$-0.644605\pi$
$179$	−157.100			−0.877651			−0.438825	+	0.898572i	$0.644605\pi$
$180$	−142.787	−	237.720i	−0.793261	−	1.32066i
$181$	26.0338	+	62.8512i	0.143833	+	0.347244i	0.979335	−	0.202243i	$-0.0648231\pi$
$181$	26.0338	+	62.8512i	0.143833	+	0.347244i	−0.835502	+	0.549487i	$0.814823\pi$
$182$	346.249	+	114.205i	1.90247	+	0.627501i
$183$		−	69.9761i		−	0.382383i
$184$	38.7702	−	27.3867i	0.210708	−	0.148841i
$185$	48.2697	−	48.2697i	0.260917	−	0.260917i
$186$	301.020	−	349.297i	1.61839	−	1.87794i
$187$	71.3971	−	174.093i	0.381803	−	0.930978i
$188$	−28.9880	−	194.166i	−0.154192	−	1.03280i
$189$	−919.554			−4.86537
$190$	36.4062	+	72.2422i	0.191611	+	0.380222i
$191$	−92.7935			−0.485830			−0.242915	−	0.970048i	$-0.578104\pi$
$191$	−92.7935			−0.485830			−0.242915	+	0.970048i	$0.578104\pi$
$192$	18.3471	+	353.178i	0.0955578	+	1.83947i
$193$	107.220	+	44.4120i	0.555544	+	0.230114i	0.642749	−	0.766077i	$-0.277794\pi$
$193$	107.220	+	44.4120i	0.555544	+	0.230114i	−0.0872056	+	0.996190i	$0.527794\pi$
$194$	8.16824	−	24.7646i	0.0421044	−	0.127653i
$195$	−244.277			−1.25270
$196$	302.810	−	409.094i	1.54495	−	2.08721i
$197$	74.9225	−	31.0339i	0.380317	−	0.157533i	−0.184331	−	0.982864i	$-0.559012\pi$
$197$	74.9225	−	31.0339i	0.380317	−	0.157533i	0.564648	+	0.825332i	$0.309012\pi$
$198$	−214.538	−	425.717i	−1.08353	−	2.15009i
$199$	−10.9633	−	26.4678i	−0.0550920	−	0.133004i	0.893937	−	0.448193i	$-0.147932\pi$
$199$	−10.9633	−	26.4678i	−0.0550920	−	0.133004i	−0.949029	+	0.315189i	$0.897932\pi$
$200$	114.210	−	25.8156i	0.571049	−	0.129078i
$201$	211.941	+	511.672i	1.05443	+	2.54563i
$202$	−2.19444	−	29.5602i	−0.0108635	−	0.146338i
$203$	−81.2556	+	81.2556i	−0.400274	+	0.400274i
$204$	−194.609	−	321.436i	−0.953967	−	1.57567i
$205$	22.6475	−	22.6475i	0.110476	−	0.110476i
$206$	139.560	+	120.271i	0.677477	+	0.583841i
$207$	48.8979	+	118.050i	0.236222	+	0.570289i
$208$	193.960	+	103.206i	0.932501	+	0.496185i
$209$	53.2202	+	128.485i	0.254642	+	0.614760i
$210$	−147.949	+	448.554i	−0.704519	+	2.13597i
$211$	262.686	−	108.808i	1.24496	−	0.515678i	0.339697	−	0.940535i	$-0.389676\pi$
$211$	262.686	−	108.808i	1.24496	−	0.515678i	0.905261	+	0.424857i	$0.139676\pi$
$212$	55.3307	−	8.26059i	0.260994	−	0.0389650i
$213$	−580.793			−2.72673
$214$	−4.86281	−	9.64946i	−0.0227234	−	0.0450910i
$215$	−78.7560	−	32.6218i	−0.366307	−	0.151729i
$216$	−546.105	−	93.9667i	−2.52826	−	0.435031i
$217$	−553.899			−2.55253
$218$	73.8463	−	223.889i	0.338745	−	1.02701i
$219$	738.586			3.37254
$220$	−140.967	+	21.0457i	−0.640759	+	0.0956621i
$221$	−233.440	+	0.819029i	−1.05629	+	0.00370601i
$222$	−17.3494	−	233.706i	−0.0781505	−	1.05273i
$223$	205.081	−	205.081i	0.919645	−	0.919645i	−0.0773584	−	0.997003i	$-0.524649\pi$
$223$	205.081	−	205.081i	0.919645	−	0.919645i	0.997003	+	0.0773584i	$0.0246486\pi$
$224$	306.987	−	293.652i	1.37048	−	1.31095i
$225$			315.194i			1.40086i
$226$	−90.8605	−	180.298i	−0.402038	−	0.797780i
$227$	−124.146	−	299.714i	−0.546897	−	1.32033i	−0.919775	−	0.392445i	$-0.871629\pi$
$227$	−124.146	−	299.714i	−0.546897	−	1.32033i	0.372879	−	0.927880i	$-0.378371\pi$
$228$	269.460	+	67.2275i	1.18184	+	0.294858i
$229$	25.5308			0.111488			0.0557441	−	0.998445i	$-0.482247\pi$
$229$	25.5308			0.111488			0.0557441	+	0.998445i	$0.482247\pi$
$230$	38.0976	−	2.82822i	0.165642	−	0.0122966i
$231$	−310.730	+	750.168i	−1.34515	+	3.24748i
$232$	−56.5594	+	39.9528i	−0.243790	+	0.172210i
$233$	−100.038	+	41.4369i	−0.429346	+	0.177841i	−0.586882	−	0.809672i	$-0.699645\pi$
$233$	−100.038	+	41.4369i	−0.429346	+	0.177841i	0.157537	+	0.987513i	$0.449645\pi$
$234$	−386.095	+	448.016i	−1.64998	+	1.91460i
$235$	60.4638	−	145.973i	0.257293	−	0.621160i
$236$	205.374	−	30.6612i	0.870227	−	0.129921i
$237$	−30.1431	+	30.1431i	−0.127186	+	0.127186i
$238$	−139.881	+	429.150i	−0.587737	+	1.80315i
$239$			115.616i			0.483749i	0.970308	+	0.241874i	$0.0777622\pi$
$239$			115.616i			0.483749i	−0.970308	+	0.241874i	$0.922238\pi$
$240$	−133.700	+	251.269i	−0.557085	+	1.04695i
$241$	−213.623	+	88.4854i	−0.886401	+	0.367159i	−0.778976	−	0.627054i	$-0.784261\pi$
$241$	−213.623	+	88.4854i	−0.886401	+	0.367159i	−0.107425	+	0.994213i	$0.534261\pi$
$242$	−3.01519	+	0.223836i	−0.0124595	+	0.000924941i
$243$	160.978	−	388.636i	0.662461	−	1.59932i
$244$	−43.4227	+	26.0819i	−0.177962	+	0.106893i
$245$	378.446	−	156.758i	1.54468	−	0.639827i
$246$	−8.14011	−	109.652i	−0.0330899	−	0.445739i
$247$	122.000	−	122.000i	0.493928	−	0.493928i
$248$	−328.949	−	56.6013i	−1.32641	−	0.228231i
$249$	123.522	−	298.209i	0.496073	−	1.19763i
$250$	242.357	+	79.9377i	0.969426	+	0.319751i
$251$	4.67971	+	4.67971i	0.0186443	+	0.0186443i	0.716367	−	0.697723i	$-0.245803\pi$
$251$	4.67971	+	4.67971i	0.0186443	+	0.0186443i	−0.697723	+	0.716367i	$0.745803\pi$
$252$	588.829	+	980.314i	2.33662	+	3.89014i
$253$	65.6742			0.259582
$254$	10.9407	+	147.377i	0.0430735	+	0.580223i
$255$	−1.06102	−	302.413i	−0.00416088	−	1.18593i
$256$	212.321	−	143.024i	0.829379	−	0.558687i
$257$	225.070	+	225.070i	0.875760	+	0.875760i	0.993093	−	0.117333i	$-0.0374344\pi$
$257$	225.070	+	225.070i	0.875760	+	0.875760i	−0.117333	+	0.993093i	$0.537434\pi$
$258$	−261.336	+	131.699i	−1.01293	+	0.510462i
$259$	−199.056	+	199.056i	−0.768556	+	0.768556i
$260$	91.0485	+	151.583i	0.350186	+	0.583010i
$261$	−71.3340	−	172.215i	−0.273310	−	0.659829i
$262$	−265.463	+	133.779i	−1.01322	+	0.510608i
$263$	−226.588	+	226.588i	−0.861553	+	0.861553i	−0.991518	−	0.129966i	$-0.958513\pi$
$263$	−226.588	+	226.588i	−0.861553	+	0.861553i	0.129966	+	0.991518i	$0.458513\pi$
$264$	−261.194	+	413.757i	−0.989370	+	1.56726i
$265$	41.5971	+	17.2301i	0.156970	+	0.0650193i
$266$	−150.133	−	297.914i	−0.564408	−	1.11998i
$267$	−648.590	−	268.655i	−2.42918	−	1.00620i
$268$	238.514	−	322.231i	0.889979	−	1.20235i
$269$	−103.475	+	249.810i	−0.384665	+	0.928663i	0.606385	+	0.795171i	$0.292619\pi$
$269$	−103.475	+	249.810i	−0.384665	+	0.928663i	−0.991050	+	0.133492i	$0.957381\pi$
$270$	−337.830	−	291.138i	−1.25122	−	1.07829i
$271$		−	73.9998i		−	0.273062i	−0.990636	−	0.136531i	$-0.956405\pi$
$271$		−	73.9998i		−	0.273062i	0.990636	−	0.136531i	$-0.0435954\pi$
$272$	−126.926	+	240.570i	−0.466641	+	0.884447i
$273$	1007.36			3.68995
$274$	60.6833	−	70.4155i	0.221472	−	0.256991i
$275$	149.671	+	61.9959i	0.544259	+	0.225439i
$276$	78.0265	−	105.413i	0.282705	−	0.381931i
$277$	192.024	−	463.588i	0.693229	−	1.67360i	−0.0449430	−	0.998990i	$-0.514311\pi$
$277$	192.024	−	463.588i	0.693229	−	1.67360i	0.738172	−	0.674613i	$-0.235689\pi$
$278$	27.2432	−	13.7291i	0.0979971	−	0.0493852i
$279$	343.841	−	830.107i	1.23241	−	2.97529i
$280$	333.488	−	75.3805i	1.19103	−	0.269216i
$281$	29.3847	+	29.3847i	0.104572	+	0.104572i	0.757457	−	0.652885i	$-0.226442\pi$
$281$	29.3847	+	29.3847i	0.104572	+	0.104572i	−0.652885	+	0.757457i	$0.726442\pi$
$282$	−244.102	−	484.381i	−0.865609	−	1.71766i
$283$	47.4927	−	19.6721i	0.167819	−	0.0695128i	−0.297193	−	0.954818i	$-0.596050\pi$
$283$	47.4927	−	19.6721i	0.167819	−	0.0695128i	0.465011	+	0.885305i	$0.346050\pi$
$284$	216.477	+	360.403i	0.762243	+	1.26902i
$285$	158.047	+	158.047i	0.554551	+	0.554551i
$286$	136.801	+	271.459i	0.478325	+	0.949159i
$287$	−93.3944	+	93.3944i	−0.325416	+	0.325416i
$288$	249.518	+	642.359i	0.866381	+	2.23041i
$289$	−2.02790	−	288.993i	−0.00701696	−	0.999975i
$290$	−55.5782	+	4.12591i	−0.191649	+	0.0142273i
$291$		−	72.0486i		−	0.247590i
$292$	−275.291	−	458.319i	−0.942777	−	1.56959i
$293$	224.417	−	224.417i	0.765928	−	0.765928i	−0.211459	−	0.977387i	$-0.567821\pi$
$293$	224.417	−	224.417i	0.765928	−	0.765928i	0.977387	+	0.211459i	$0.0678214\pi$
$294$	440.488	−	1335.48i	1.49826	−	4.54245i
$295$	154.398	+	63.9538i	0.523384	+	0.216793i
$296$	−138.556	+	97.8743i	−0.468095	+	0.330656i
$297$	−542.120	−	542.120i	−1.82532	−	1.82532i
$298$	366.797	−	27.2296i	1.23086	−	0.0913745i
$299$	−31.1799	−	75.2748i	−0.104280	−	0.251755i
$300$	277.331	−	166.580i	0.924436	−	0.555265i
$301$	324.776	+	134.527i	1.07899	+	0.446932i
$302$	26.0491	+	350.895i	0.0862552	+	1.16190i
$303$	−31.3407	−	75.6633i	−0.103435	−	0.249714i
$304$	−58.7177	−	192.267i	−0.193150	−	0.632457i
$305$	−40.7668			−0.133662
$306$	−556.318	−	476.037i	−1.81803	−	1.55568i
$307$	196.215	+	196.215i	0.639138	+	0.639138i	0.950343	−	0.311205i	$-0.100732\pi$
$307$	196.215	+	196.215i	0.639138	+	0.639138i	−0.311205	+	0.950343i	$0.600732\pi$
$308$	581.323	−	86.7887i	1.88741	−	0.281781i
$309$	470.278	+	194.795i	1.52193	+	0.630406i
$310$	−203.494	−	175.369i	−0.656432	−	0.565705i
$311$	37.0749	+	89.5068i	0.119212	+	0.287803i	0.972210	−	0.234111i	$-0.0752180\pi$
$311$	37.0749	+	89.5068i	0.119212	+	0.287803i	−0.852998	+	0.521915i	$0.825218\pi$
$312$	598.248	+	102.939i	1.91746	+	0.329932i
$313$	386.031	+	159.899i	1.23332	+	0.510860i	0.901622	−	0.432524i	$-0.142377\pi$
$313$	386.031	+	159.899i	1.23332	+	0.510860i	0.331703	+	0.943384i	$0.392377\pi$
$314$	33.1668	+	446.775i	0.105627	+	1.42285i
$315$			920.355i			2.92176i
$316$	29.9400	+	7.46973i	0.0947467	+	0.0236384i
$317$	294.975	−	122.182i	0.930519	−	0.385434i	0.134644	−	0.990894i	$-0.457011\pi$
$317$	294.975	−	122.182i	0.930519	−	0.385434i	0.795875	+	0.605460i	$0.207011\pi$
$318$	138.032	−	69.5606i	0.434062	−	0.218744i
$319$	−95.8080			−0.300338
$320$	205.755	−	10.6887i	0.642984	−	0.0334021i
$321$	−21.1105	−	21.1105i	−0.0657649	−	0.0657649i
$322$	−157.108	+	11.6631i	−0.487913	+	0.0362208i
$323$	151.565	+	150.506i	0.469243	+	0.465961i
$324$	−747.475	+	111.594i	−2.30702	+	0.344427i
$325$		−	200.984i		−	0.618414i
$326$	182.475	+	60.1867i	0.559739	+	0.184622i
$327$		−	651.367i		−	1.99195i
$328$	−65.0087	+	45.9213i	−0.198197	+	0.140004i
$329$	−249.342	+	601.965i	−0.757879	+	1.82968i
$330$	−351.666	+	177.221i	−1.06566	+	0.537033i
$331$			263.239i			0.795285i	0.917540	+	0.397642i	$0.130172\pi$
$331$			263.239i			0.795285i	−0.917540	+	0.397642i	$0.869828\pi$
$332$	−231.089	+	34.5005i	−0.696053	+	0.103917i
$333$	−174.750	−	421.885i	−0.524776	−	1.26692i
$334$	71.3848	+	23.5452i	0.213727	+	0.0704947i
$335$	298.091	−	123.473i	0.889823	−	0.368577i
$336$	551.357	−	1036.19i	1.64094	−	3.08390i
$337$	−420.852	+	174.323i	−1.24882	+	0.517278i	−0.906460	−	0.422291i	$-0.861226\pi$
$337$	−420.852	+	174.323i	−1.24882	+	0.517278i	−0.342360	+	0.939569i	$0.611226\pi$
$338$	25.5421	−	29.6385i	0.0755685	−	0.0876880i
$339$	−394.446	−	394.446i	−1.16356	−	1.16356i
$340$	−187.263	+	113.376i	−0.550772	+	0.333458i
$341$	−326.549	−	326.549i	−0.957622	−	0.957622i
$342$	539.670	−	40.0630i	1.57798	−	0.117143i
$343$	−959.657	+	397.503i	−2.79783	+	1.15890i
$344$	179.131	+	113.081i	0.520730	+	0.328723i
$345$	97.5159	−	40.3924i	0.282655	−	0.117079i
$346$	−399.654	+	201.404i	−1.15507	+	0.582092i
$347$	−22.0961	−	53.3448i	−0.0636776	−	0.153731i	0.888838	−	0.458222i	$-0.151514\pi$
$347$	−22.0961	−	53.3448i	−0.0636776	−	0.153731i	−0.952515	+	0.304491i	$0.901514\pi$
$348$	−113.828	+	153.780i	−0.327092	+	0.441898i
$349$		−	661.905i		−	1.89658i	−0.317412	−	0.948288i	$-0.602814\pi$
$349$		−	661.905i		−	1.89658i	0.317412	−	0.948288i	$-0.397186\pi$
$350$	−369.058	−	121.728i	−1.05445	−	0.347795i
$351$	−363.990	+	878.750i	−1.03701	+	2.50356i
$352$	354.105	+	7.86178i	1.00598	+	0.0223346i
$353$			316.147i			0.895601i	0.894133	+	0.447801i	$0.147793\pi$
$353$			316.147i			0.895601i	−0.894133	+	0.447801i	$0.852207\pi$
$354$	512.340	−	258.191i	1.44729	−	0.729354i
$355$			338.359i			0.953125i
$356$	75.0369	+	502.608i	0.210778	+	1.41182i
$357$	4.37548	+	1247.10i	0.0122562	+	3.49327i
$358$	238.011	+	205.115i	0.664834	+	0.572946i
$359$	135.755	+	135.755i	0.378147	+	0.378147i	0.870433	−	0.492287i	$-0.163839\pi$
$359$	135.755	+	135.755i	0.378147	+	0.378147i	−0.492287	+	0.870433i	$0.663839\pi$
$360$	−94.0485	+	546.580i	−0.261246	+	1.51828i
$361$	203.132			0.562691
$362$	42.6187	−	129.212i	0.117731	−	0.356940i
$363$	−7.71777	+	3.19680i	−0.0212611	+	0.00880662i
$364$	−375.468	−	625.100i	−1.03151	−	1.71731i
$365$		−	430.287i		−	1.17887i
$366$	−91.3633	+	106.016i	−0.249626	+	0.289661i
$367$	551.260	+	228.339i	1.50207	+	0.622178i	0.973903	−	0.226963i	$-0.0728796\pi$
$367$	551.260	+	228.339i	1.50207	+	0.622178i	0.528167	+	0.849141i	$0.322880\pi$
$368$	−94.4951	−	9.12796i	−0.256780	−	0.0248042i
$369$	−81.9905	−	197.943i	−0.222197	−	0.536430i
$370$	−136.153	+	10.1074i	−0.367980	+	0.0273174i
$371$	−171.539	−	71.0540i	−0.462370	−	0.191520i
$372$	−912.108	+	136.173i	−2.45190	+	0.366057i
$373$	224.168	+	224.168i	0.600988	+	0.600988i	0.940575	−	0.339587i	$-0.110287\pi$
$373$	224.168	+	224.168i	0.600988	+	0.600988i	−0.339587	+	0.940575i	$0.610287\pi$
$374$	−335.471	+	170.538i	−0.896980	+	0.455983i
$375$	705.096			1.88026
$376$	−209.592	+	332.015i	−0.557427	+	0.883020i
$377$	45.4863	+	109.814i	0.120653	+	0.291283i
$378$	1393.15	+	1200.60i	3.68559	+	3.17620i
$379$	−94.2102	−	39.0231i	−0.248576	−	0.102963i	0.254917	−	0.966963i	$-0.417952\pi$
$379$	−94.2102	−	39.0231i	−0.248576	−	0.102963i	−0.503493	+	0.864000i	$0.667952\pi$
$380$	39.1655	−	156.982i	0.103067	−	0.413111i
$381$	156.254	+	377.230i	0.410115	+	0.990105i
$382$	140.585	+	121.154i	0.368023	+	0.317158i
$383$	−443.407	−	443.407i	−1.15772	−	1.15772i	−0.984964	−	0.172757i	$-0.944732\pi$
$383$	−443.407	−	443.407i	−1.15772	−	1.15772i	−0.172757	−	0.984964i	$-0.555268\pi$
$384$	433.325	−	559.030i	1.12845	−	1.45581i
$385$	437.034	+	181.025i	1.13515	+	0.470196i
$386$	−104.456	−	207.276i	−0.270611	−	0.536983i
$387$	−403.220	+	403.220i	−1.04191	+	1.04191i
$388$	−44.7087	+	26.8544i	−0.115229	+	0.0692124i
$389$		−	377.707i		−	0.970968i	−0.874245	−	0.485484i	$-0.838643\pi$
$389$		−	377.707i		−	0.970968i	0.874245	−	0.485484i	$-0.161357\pi$
$390$	370.087	+	318.936i	0.948941	+	0.817786i
$391$	93.0542	−	38.9274i	0.237990	−	0.0995585i
$392$	−992.894	+	224.430i	−2.53289	+	0.572526i
$393$	−580.765	+	580.765i	−1.47777	+	1.47777i
$394$	−154.029	−	50.8041i	−0.390936	−	0.128944i
$395$	17.5608	+	17.5608i	0.0444577	+	0.0444577i
$396$	−230.799	+	925.083i	−0.582826	+	2.33607i
$397$	580.865	−	240.602i	1.46314	−	0.606051i	0.497855	−	0.867260i	$-0.334121\pi$
$397$	580.865	−	240.602i	1.46314	−	0.606051i	0.965282	+	0.261209i	$0.0841213\pi$
$398$	−17.9475	+	54.4136i	−0.0450943	+	0.136718i
$399$	−651.759	−	651.759i	−1.63348	−	1.63348i
$400$	−206.737	−	110.005i	−0.516843	−	0.275013i
$401$	180.627	−	436.072i	0.450441	−	1.08746i	−0.521713	−	0.853121i	$-0.674707\pi$
$401$	180.627	−	436.072i	0.450441	−	1.08746i	0.972154	−	0.234341i	$-0.0752932\pi$
$402$	346.959	−	1051.92i	0.863082	−	2.61671i
$403$	−219.251	+	529.320i	−0.544048	+	1.31345i
$404$	−35.2702	+	47.6498i	−0.0873025	+	0.117945i
$405$	−561.946	−	232.766i	−1.38752	−	0.574730i
$406$	229.195	−	17.0145i	0.564520	−	0.0419077i
$407$	−234.705			−0.576672
$408$	−124.839	+	741.073i	−0.305978	+	1.81636i
$409$		−	649.546i		−	1.58813i	−0.607831	−	0.794066i	$-0.707960\pi$
$409$		−	649.546i		−	1.58813i	0.607831	−	0.794066i	$-0.292040\pi$
$410$	−63.8810	+	4.74228i	−0.155807	+	0.0115665i
$411$	98.2846	−	237.280i	0.239135	−	0.577324i
$412$	−54.4075	−	364.429i	−0.132057	−	0.884537i
$413$	−636.711	−	263.735i	−1.54167	−	0.638582i
$414$	80.0483	−	242.692i	0.193353	−	0.586212i
$415$	−173.731	−	71.9618i	−0.418629	−	0.173402i
$416$	−159.106	−	409.602i	−0.382466	−	0.984621i
$417$	59.6010	−	59.6010i	0.142928	−	0.142928i
$418$	87.1241	−	264.145i	0.208431	−	0.631925i
$419$	−264.189	−	637.810i	−0.630524	−	1.52222i	−0.838966	−	0.544184i	$-0.816839\pi$
$419$	−264.189	−	637.810i	−0.630524	−	1.52222i	0.208442	−	0.978035i	$-0.433161\pi$
$420$	809.795	−	486.406i	1.92808	−	1.15811i
$421$	75.1403	−	75.1403i	0.178480	−	0.178480i	−0.612213	−	0.790693i	$-0.709720\pi$
$421$	75.1403	−	75.1403i	0.178480	−	0.178480i	0.790693	+	0.612213i	$0.209720\pi$
$422$	−540.041	−	178.125i	−1.27972	−	0.422096i
$423$	−747.359	−	747.359i	−1.76681	−	1.76681i
$424$	−94.6130	−	59.7266i	−0.223144	−	0.140865i
$425$	248.817	−	0.872981i	0.585452	−	0.00205407i
$426$	879.919	+	758.304i	2.06554	+	1.78006i
$427$	168.115			0.393712
$428$	−5.23138	+	20.9683i	−0.0122228	+	0.0489913i
$429$	593.883	+	593.883i	1.38434	+	1.38434i
$430$	76.7255	+	152.250i	0.178431	+	0.354069i
$431$	25.5047	−	61.5738i	0.0591756	−	0.142863i	−0.891526	−	0.452969i	$-0.850365\pi$
$431$	25.5047	−	61.5738i	0.0591756	−	0.142863i	0.950702	+	0.310107i	$0.100365\pi$
$432$	704.679	+	855.376i	1.63120	+	1.98004i
$433$	−277.814	+	277.814i	−0.641603	+	0.641603i	−0.950949	−	0.309346i	$-0.899890\pi$
$433$	−277.814	+	277.814i	−0.641603	+	0.641603i	0.309346	+	0.950949i	$0.399890\pi$
$434$	839.173	+	723.190i	1.93358	+	1.66634i
$435$	−142.260	+	58.9259i	−0.327034	+	0.135462i
$436$	−404.196	+	242.782i	−0.927056	+	0.556839i
$437$	−28.5295	+	68.8762i	−0.0652848	+	0.157611i
$438$	−1118.98	−	964.324i	−2.55475	−	2.20165i
$439$	−669.640	+	277.374i	−1.52538	+	0.631831i	−0.978660	−	0.205487i	$-0.934122\pi$
$439$	−669.640	+	277.374i	−1.52538	+	0.631831i	−0.546716	+	0.837318i	$0.684122\pi$
$440$	241.047	+	152.167i	0.547835	+	0.345833i
$441$		−	2740.17i		−	6.21354i
$442$	354.737	+	303.546i	0.802573	+	0.686756i
$443$	−522.268	+	522.268i	−1.17893	+	1.17893i	−0.198919	+	0.980016i	$0.563743\pi$
$443$	−522.268	+	522.268i	−1.17893	+	1.17893i	−0.980016	+	0.198919i	$0.936257\pi$
$444$	−278.850	+	376.723i	−0.628040	+	0.848476i
$445$	−156.513	+	377.857i	−0.351715	+	0.849116i
$446$	−578.464	+	42.9429i	−1.29701	+	0.0962846i
$447$	938.866	−	388.891i	2.10037	−	0.870002i
$448$	−848.497	+	44.0783i	−1.89397	+	0.0983890i
$449$	106.032	−	255.985i	0.236152	−	0.570122i	−0.760726	−	0.649073i	$-0.775157\pi$
$449$	106.032	−	255.985i	0.236152	−	0.570122i	0.996878	+	0.0789510i	$0.0251571\pi$
$450$	411.529	−	477.529i	0.914508	−	1.06117i
$451$	−110.121			−0.244170
$452$	−97.7472	+	391.788i	−0.216255	+	0.866787i
$453$	372.031	+	898.162i	0.821260	+	1.98270i
$454$	−203.233	+	616.164i	−0.447649	+	1.35719i
$455$		−	586.867i		−	1.28982i
$456$	−320.465	−	453.668i	−0.702774	−	0.994886i
$457$	51.6330	−	51.6330i	0.112983	−	0.112983i	−0.648355	−	0.761338i	$-0.724543\pi$
$457$	51.6330	−	51.6330i	0.112983	−	0.112983i	0.761338	+	0.648355i	$0.224543\pi$
$458$	−38.6799	−	33.3339i	−0.0844540	−	0.0727814i
$459$	−1089.47	−	446.800i	−2.37357	−	0.973421i
$460$	−61.4117	−	45.4568i	−0.133504	−	0.0988191i
$461$	489.583			1.06200			0.531001	−	0.847371i	$-0.321816\pi$
$461$	489.583			1.06200			0.531001	+	0.847371i	$0.321816\pi$
$462$	1450.21	−	730.828i	3.13899	−	1.58188i
$463$	599.404			1.29461			0.647304	−	0.762232i	$-0.275896\pi$
$463$	599.404			1.29461			0.647304	+	0.762232i	$0.275896\pi$
$464$	137.853	+	13.3162i	0.297097	+	0.0286987i
$465$	−685.715	−	284.033i	−1.47466	−	0.610823i
$466$	205.661	+	67.8343i	0.441333	+	0.145567i
$467$	283.087			0.606182			0.303091	−	0.952962i	$-0.401981\pi$
$467$	283.087			0.606182			0.303091	+	0.952962i	$0.401981\pi$
$468$	1169.89	−	174.659i	2.49977	−	0.373203i
$469$	−1229.27	+	509.182i	−2.62105	+	1.08568i
$470$	−282.191	+	142.209i	−0.600407	+	0.302573i
$471$	473.686	+	1143.58i	1.00570	+	2.42798i
$472$	−351.180	−	221.690i	−0.744025	−	0.469683i
$473$	112.161	+	270.780i	0.237127	+	0.572474i
$474$	85.0235	−	6.31181i	0.179374	−	0.0133161i
$475$	−130.037	+	130.037i	−0.273762	+	0.273762i
$476$	772.238	−	467.542i	1.62235	−	0.982231i
$477$	212.972	−	212.972i	0.446481	−	0.446481i
$478$	150.952	−	175.162i	0.315800	−	0.366447i
$479$	18.4463	+	44.5333i	0.0385101	+	0.0929715i	0.941964	−	0.335713i	$-0.108977\pi$
$479$	18.4463	+	44.5333i	0.0385101	+	0.0929715i	−0.903454	+	0.428684i	$0.858977\pi$
$480$	530.625	−	206.116i	1.10547	−	0.429408i
$481$	111.430	+	269.016i	0.231663	+	0.559285i
$482$	439.175	+	144.855i	0.911151	+	0.300530i
$483$	−402.139	+	166.571i	−0.832585	+	0.344868i
$484$	4.86035	+	3.59762i	0.0100420	+	0.00743309i
$485$	−41.9742			−0.0865447
$486$	−751.303	+	378.616i	−1.54589	+	0.779045i
$487$	86.7080	+	35.9156i	0.178045	+	0.0737488i	0.469925	−	0.882706i	$-0.344281\pi$
$487$	86.7080	+	35.9156i	0.178045	+	0.0737488i	−0.291880	+	0.956455i	$0.594281\pi$
$488$	99.8402	+	17.1792i	0.204590	+	0.0352033i
$489$	530.881			1.08565
$490$	−778.026	−	256.620i	−1.58781	−	0.523715i
$491$	773.537			1.57543			0.787716	−	0.616039i	$-0.211264\pi$
$491$	773.537			1.57543			0.787716	+	0.616039i	$0.211264\pi$
$492$	−130.833	+	176.754i	−0.265920	+	0.359255i
$493$	−135.751	+	56.7887i	−0.275357	+	0.115190i
$494$	−344.122	+	25.5463i	−0.696603	+	0.0517131i
$495$	−542.592	+	542.592i	−1.09615	+	1.09615i
$496$	424.467	+	515.240i	0.855781	+	1.03879i
$497$		−	1395.34i		−	2.80752i
$498$	−576.492	+	290.521i	−1.15762	+	0.583375i
$499$	−75.2758	−	181.732i	−0.150853	−	0.364192i	0.830330	−	0.557273i	$-0.188152\pi$
$499$	−75.2758	−	181.732i	−0.150853	−	0.364192i	−0.981183	+	0.193080i	$0.938152\pi$
$500$	−262.808	−	437.537i	−0.525616	−	0.875074i
$501$	207.682			0.414536
$502$	−0.979908	−	13.1999i	−0.00195201	−	0.0262946i
$503$	87.5285	−	211.312i	0.174013	−	0.420104i	−0.812678	−	0.582713i	$-0.801991\pi$
$503$	87.5285	−	211.312i	0.174013	−	0.420104i	0.986691	+	0.162609i	$0.0519910\pi$
$504$	387.839	−	2254.00i	0.769523	−	4.47222i
$505$	−44.0800	+	18.2585i	−0.0872872	+	0.0361555i
$506$	−99.4985	−	85.7466i	−0.196637	−	0.169460i
$507$	41.3689	−	99.8733i	0.0815954	−	0.196989i
$508$	175.845	−	237.565i	0.346151	−	0.467647i
$509$	111.933	−	111.933i	0.219908	−	0.219908i	−0.588551	−	0.808460i	$-0.700302\pi$
$509$	111.933	−	111.933i	0.219908	−	0.219908i	0.808460	+	0.588551i	$0.200302\pi$
$510$	−393.233	+	459.550i	−0.771046	+	0.901079i
$511$			1774.43i			3.47246i
$512$	−508.410	−	60.5284i	−0.992987	−	0.118219i
$513$	804.053	−	333.050i	1.56735	−	0.649219i
$514$	−47.1286	−	634.848i	−0.0916900	−	1.23511i
$515$	113.484	−	273.975i	0.220358	−	0.531990i
$516$	567.883	+	141.681i	1.10055	+	0.274576i
$517$	−501.885	+	207.888i	−0.970765	+	0.402104i
$518$	561.470	−	41.6814i	1.08392	−	0.0804659i
$519$	−874.339	+	874.339i	−1.68466	+	1.68466i
$520$	59.9702	−	348.528i	0.115327	−	0.670246i
$521$	−329.055	+	794.410i	−0.631584	+	1.52478i	0.206047	+	0.978542i	$0.433940\pi$
$521$	−329.055	+	794.410i	−0.631584	+	1.52478i	−0.837631	+	0.546237i	$0.816060\pi$
$522$	−116.777	+	354.048i	−0.223712	+	0.678253i
$523$	−142.698	−	142.698i	−0.272845	−	0.272845i	0.557400	−	0.830244i	$-0.311799\pi$
$523$	−142.698	−	142.698i	−0.272845	−	0.272845i	−0.830244	+	0.557400i	$0.811799\pi$
$524$	576.852	+	143.919i	1.10086	+	0.274654i
$525$	−1073.71			−2.04517
$526$	639.130	−	47.4465i	1.21508	−	0.0902025i
$527$	−656.246	−	269.132i	−1.24525	−	0.510688i
$528$	935.932	−	285.831i	1.77260	−	0.541346i
$529$	−349.165	−	349.165i	−0.660048	−	0.660048i
$530$	−40.5247	−	80.4148i	−0.0764617	−	0.151726i
$531$	790.498	−	790.498i	1.48870	−	1.48870i
$532$	−161.512	+	647.368i	−0.303594	+	1.21686i
$533$	52.2815	+	126.219i	0.0980891	+	0.236808i
$534$	631.869	+	1253.84i	1.18327	+	2.34802i
$535$	−12.2986	+	12.2986i	−0.0229880	+	0.0229880i
$536$	−782.073	+	176.777i	−1.45909	+	0.329807i
$537$	802.027	+	332.210i	1.49353	+	0.618641i
$538$	482.928	−	243.370i	0.897637	−	0.452360i
$539$	−1301.18	−	538.967i	−2.41406	−	0.999938i
$540$	131.703	+	882.166i	0.243894	+	1.63364i
$541$	255.640	−	617.171i	0.472533	−	1.14080i	−0.490507	−	0.871437i	$-0.663188\pi$
$541$	255.640	−	617.171i	0.472533	−	1.14080i	0.963040	−	0.269359i	$-0.0868117\pi$
$542$	−96.6168	+	112.112i	−0.178260	+	0.206849i
$543$		−	375.921i		−	0.692305i
$544$	506.393	−	198.751i	0.930870	−	0.365351i
$545$	−379.474			−0.696283
$546$	−1526.17	−	1315.24i	−2.79519	−	2.40886i
$547$	730.435	+	302.556i	1.33535	+	0.553119i	0.932176	−	0.362005i	$-0.117908\pi$
$547$	730.435	+	302.556i	1.33535	+	0.553119i	0.403171	+	0.915124i	$0.367908\pi$
$548$	−183.874	+	27.4515i	−0.335536	+	0.0500939i
$549$	−104.360	+	251.948i	−0.190091	+	0.458921i
$550$	−145.812	−	289.342i	−0.265114	−	0.526076i
$551$	41.6198	−	100.479i	0.0755350	−	0.182358i
$552$	−255.843	+	57.8299i	−0.463485	+	0.104764i
$553$	−72.4177	−	72.4177i	−0.130954	−	0.130954i
$554$	−896.199	+	451.636i	−1.61769	+	0.815227i
$555$	−348.501	+	144.354i	−0.627929	+	0.260097i
$556$	−59.1994	−	14.7697i	−0.106474	−	0.0265642i
$557$	632.748	+	632.748i	1.13599	+	1.13599i	0.989161	+	0.146832i	$0.0469076\pi$
$557$	632.748	+	632.748i	1.13599	+	1.13599i	0.146832	+	0.989161i	$0.453092\pi$
$558$	−1604.75	+	808.705i	−2.87589	+	1.44929i
$559$	257.114	−	257.114i	0.459954	−	0.459954i
$560$	−603.664	−	321.211i	−1.07797	−	0.573590i
$561$	−732.643	+	737.802i	−1.30596	+	1.31516i
$562$	−6.15301	−	82.8844i	−0.0109484	−	0.147481i
$563$			204.606i			0.363421i	0.983352	+	0.181711i	$0.0581634\pi$
$563$			204.606i			0.363421i	−0.983352	+	0.181711i	$0.941837\pi$
$564$	−262.603	+	1052.56i	−0.465608	+	1.86624i
$565$	−229.797	+	229.797i	−0.406720	+	0.406720i
$566$	−97.6374	−	32.2043i	−0.172504	−	0.0568980i
$567$	2317.37	+	959.885i	4.08707	+	1.69292i
$568$	142.585	−	828.661i	0.251031	−	1.45891i
$569$	479.170	+	479.170i	0.842127	+	0.842127i	0.989135	−	0.147008i	$-0.0469643\pi$
$569$	479.170	+	479.170i	0.842127	+	0.842127i	−0.147008	+	0.989135i	$0.546964\pi$
$570$	−33.0943	−	445.798i	−0.0580602	−	0.782102i
$571$	−93.6301	−	226.043i	−0.163976	−	0.395872i	0.820439	−	0.571734i	$-0.193729\pi$
$571$	−93.6301	−	226.043i	−0.163976	−	0.395872i	−0.984415	+	0.175861i	$0.943729\pi$
$572$	147.170	−	589.881i	0.257289	−	1.03126i
$573$	473.731	+	196.226i	0.826755	+	0.342453i
$574$	263.434	−	19.5563i	0.458945	−	0.0340703i
$575$	33.2338	+	80.2335i	0.0577979	+	0.139536i
$576$	460.660	−	1298.97i	0.799757	−	2.25516i
$577$	230.599			0.399652			0.199826	−	0.979831i	$-0.435962\pi$
$577$	230.599			0.399652			0.199826	+	0.979831i	$0.435962\pi$
$578$	−374.247	+	440.481i	−0.647486	+	0.762077i
$579$	−453.465	−	453.465i	−0.783187	−	0.783187i
$580$	89.5897	+	66.3140i	0.154465	+	0.114335i
$581$	716.437	+	296.758i	1.23311	+	0.510771i
$582$	−94.0691	+	109.156i	−0.161631	+	0.187553i
$583$	−59.2409	−	143.020i	−0.101614	−	0.245317i
$584$	−181.324	+	1053.80i	−0.310486	+	1.80445i
$585$	879.515	+	364.307i	1.50344	+	0.622747i
$586$	−633.005	+	46.9918i	−1.08021	+	0.0801909i
$587$			235.208i			0.400696i	0.979725	+	0.200348i	$0.0642072\pi$
$587$			235.208i			0.400696i	−0.979725	+	0.200348i	$0.935793\pi$
$588$	−2411.00	+	1448.18i	−4.10034	+	2.46288i
$589$	484.326	−	200.614i	0.822285	−	0.340601i
$590$	−150.418	−	298.480i	−0.254945	−	0.505898i
$591$	−448.121			−0.758242
$592$	337.705	+	32.6213i	0.570448	+	0.0551036i
$593$	−47.6716	−	47.6716i	−0.0803905	−	0.0803905i	0.665768	−	0.746159i	$-0.268104\pi$
$593$	−47.6716	−	47.6716i	−0.0803905	−	0.0803905i	−0.746159	+	0.665768i	$0.768104\pi$
$594$	113.517	+	1529.14i	0.191107	+	2.57431i
$595$	726.537	−	2.54907i	1.22107	−	0.00428415i
$596$	−591.261	−	437.650i	−0.992049	−	0.734312i
$597$			158.307i			0.265171i
$598$	−51.0430	+	154.753i	−0.0853562	+	0.258785i
$599$			357.358i			0.596592i	0.954473	+	0.298296i	$0.0964182\pi$
$599$			357.358i			0.596592i	−0.954473	+	0.298296i	$0.903582\pi$
$600$	−637.657	−	109.720i	−1.06276	−	0.182866i
$601$	−399.736	+	965.047i	−0.665118	+	1.60574i	0.124559	+	0.992212i	$0.460248\pi$
$601$	−399.736	+	965.047i	−0.665118	+	1.60574i	−0.789676	+	0.613524i	$0.789752\pi$
$602$	−316.403	−	627.851i	−0.525586	−	1.04294i
$603$		−	2158.35i		−	3.57935i
$604$	418.676	−	565.627i	0.693172	−	0.936469i
$605$	1.86240	+	4.49623i	0.00307835	+	0.00743179i
$606$	−51.3064	+	155.552i	−0.0846641	+	0.256686i
$607$	−112.750	+	46.7025i	−0.185749	+	0.0769399i	−0.473620	−	0.880730i	$-0.657053\pi$
$607$	−112.750	+	46.7025i	−0.185749	+	0.0769399i	0.287870	+	0.957669i	$0.407053\pi$
$608$	−162.071	+	367.954i	−0.266565	+	0.605188i
$609$	586.655	−	243.000i	0.963308	−	0.399015i
$610$	61.7629	+	53.2265i	0.101251	+	0.0872566i
$611$	476.556	+	476.556i	0.779960	+	0.779960i
$612$	221.308	+	1447.56i	0.361614	+	2.36529i
$613$	250.114	+	250.114i	0.408016	+	0.408016i	0.881046	−	0.473030i	$-0.156840\pi$
$613$	250.114	+	250.114i	0.408016	+	0.408016i	−0.473030	+	0.881046i	$0.656840\pi$
$614$	−41.0866	−	553.458i	−0.0669162	−	0.901398i
$615$	−163.512	+	67.7289i	−0.265873	+	0.110128i
$616$	−994.037	−	627.509i	−1.61370	−	1.01868i
$617$	−319.156	+	132.199i	−0.517271	+	0.214261i	−0.626018	−	0.779809i	$-0.715316\pi$
$617$	−319.156	+	132.199i	−0.517271	+	0.214261i	0.108747	+	0.994069i	$0.465316\pi$
$618$	−458.153	−	909.132i	−0.741348	−	1.47109i
$619$	294.246	+	710.373i	0.475357	+	1.14761i	0.961764	+	0.273881i	$0.0883075\pi$
$619$	294.246	+	710.373i	0.475357	+	1.14761i	−0.486406	+	0.873733i	$0.661693\pi$
$620$	79.3320	+	531.377i	0.127955	+	0.857060i
$621$		−	410.987i		−	0.661814i
$622$	60.6936	−	184.012i	0.0975781	−	0.295839i
$623$	645.434	−	1558.22i	1.03601	−	2.50115i
$624$	−771.963	−	937.049i	−1.23712	−	1.50168i
$625$		−	44.8661i		−	0.0717857i
$626$	−376.078	−	746.267i	−0.600764	−	1.19212i
$627$		−	768.485i		−	1.22565i
$628$	533.076	−	720.181i	0.848847	−	1.14679i
$629$	−332.556	+	139.118i	−0.528705	+	0.221173i
$630$	1201.65	−	1394.37i	1.90738	−	2.21328i
$631$	17.8887	+	17.8887i	0.0283498	+	0.0283498i	0.721140	−	0.692790i	$-0.243619\pi$
$631$	17.8887	+	17.8887i	0.0283498	+	0.0283498i	−0.692790	+	0.721140i	$0.743619\pi$
$632$	−35.6072	−	50.4075i	−0.0563405	−	0.0797588i
$633$	−1571.16			−2.48208
$634$	−606.421	−	200.019i	−0.956500	−	0.315487i
$635$	219.767	−	91.0306i	0.346090	−	0.143355i
$636$	−299.943	−	74.8329i	−0.471609	−	0.117662i
$637$			1747.28i			2.74298i
$638$	145.152	+	125.090i	0.227511	+	0.196066i
$639$	2091.14	+	866.177i	3.27251	+	1.35552i
$640$	−325.680	−	252.447i	−0.508876	−	0.394449i
$641$	−89.3018	−	215.594i	−0.139316	−	0.336339i	0.838787	−	0.544460i	$-0.183265\pi$
$641$	−89.3018	−	215.594i	−0.139316	−	0.336339i	−0.978103	+	0.208121i	$0.933265\pi$
$642$	4.42044	+	59.5457i	0.00688542	+	0.0927503i
$643$	110.259	+	45.6706i	0.171475	+	0.0710274i	0.466770	−	0.884379i	$-0.345418\pi$
$643$	110.259	+	45.6706i	0.171475	+	0.0710274i	−0.295294	+	0.955406i	$0.595418\pi$
$644$	253.251	+	187.456i	0.393247	+	0.291081i
$645$	333.083	+	333.083i	0.516407	+	0.516407i
$646$	−33.1208	−	425.909i	−0.0512706	−	0.659303i
$647$	−493.080			−0.762102			−0.381051	−	0.924554i	$-0.624438\pi$
$647$	−493.080			−0.762102			−0.381051	+	0.924554i	$0.624438\pi$
$648$	1278.15	+	806.861i	1.97245	+	1.24516i
$649$	−219.887	−	530.855i	−0.338809	−	0.817958i
$650$	−262.412	+	304.497i	−0.403711	+	0.468458i
$651$	2827.77	+	1171.30i	4.34373	+	1.79923i
$652$	−197.873	−	329.430i	−0.303487	−	0.505261i
$653$	−47.0212	−	113.519i	−0.0720080	−	0.173843i	0.883778	−	0.467907i	$-0.154992\pi$
$653$	−47.0212	−	113.519i	−0.0720080	−	0.173843i	−0.955786	+	0.294065i	$0.904992\pi$
$654$	−850.447	+	986.840i	−1.30038	+	1.50893i
$655$	338.343	+	338.343i	0.516554	+	0.516554i
$656$	158.447	+	15.3055i	0.241535	+	0.0233316i
$657$	−2659.27	−	1101.50i	−4.04759	−	1.67657i
$658$	1163.71	−	586.446i	1.76855	−	0.891255i
$659$	−755.256	+	755.256i	−1.14606	+	1.14606i	−0.158745	+	0.987320i	$0.550745\pi$
$659$	−755.256	+	755.256i	−1.14606	+	1.14606i	−0.987320	+	0.158745i	$0.949255\pi$
$660$	764.171	+	190.653i	1.15783	+	0.288868i
$661$		−	595.400i		−	0.900756i	−0.892838	−	0.450378i	$-0.851289\pi$
$661$		−	595.400i		−	0.900756i	0.892838	−	0.450378i	$-0.148711\pi$
$662$	343.694	−	398.815i	0.519176	−	0.602440i
$663$	1193.49	+	489.462i	1.80014	+	0.738253i
$664$	395.153	+	249.449i	0.595109	+	0.375677i
$665$	−379.703	+	379.703i	−0.570982	+	0.570982i
$666$	−286.075	+	867.328i	−0.429543	+	1.30229i
$667$	−36.3165	−	36.3165i	−0.0544475	−	0.0544475i
$668$	−77.4087	−	128.874i	−0.115881	−	0.192926i
$669$	−1480.66	+	613.308i	−2.21324	+	0.916753i
$670$	−612.827	−	202.132i	−0.914667	−	0.301689i
$671$	99.1117	+	99.1117i	0.147707	+	0.147707i
$672$	−2188.21	+	849.986i	−3.25626	+	1.26486i
$673$	435.011	−	1050.21i	0.646376	−	1.56049i	−0.171556	−	0.985174i	$-0.554879\pi$
$673$	435.011	−	1050.21i	0.646376	−	1.56049i	0.817932	−	0.575315i	$-0.195121\pi$
$674$	865.206	+	285.375i	1.28369	+	0.423406i
$675$	387.968	−	936.636i	0.574767	−	1.38761i
$676$	−77.3942	+	11.5546i	−0.114489	+	0.0170926i
$677$	39.4975	+	16.3604i	0.0583419	+	0.0241660i	0.411664	−	0.911336i	$-0.364948\pi$
$677$	39.4975	+	16.3604i	0.0583419	+	0.0241660i	−0.353322	+	0.935502i	$0.614948\pi$
$678$	82.5950	+	1112.60i	0.121822	+	1.64100i
$679$	173.094			0.254925
$680$	431.736	+	72.7289i	0.634906	+	0.106954i
$681$			1792.63i			2.63235i
$682$	68.3778	+	921.085i	0.100261	+	1.35057i
$683$	349.053	−	842.689i	0.511059	−	1.23381i	−0.432209	−	0.901773i	$-0.642266\pi$
$683$	349.053	−	842.689i	0.511059	−	1.23381i	0.943268	−	0.332032i	$-0.107734\pi$
$684$	−869.924	−	643.915i	−1.27182	−	0.941397i
$685$	−138.235	−	57.2588i	−0.201803	−	0.0835895i
$686$	1972.90	+	650.733i	2.87595	+	0.948590i
$687$	−130.340	−	53.9887i	−0.189724	−	0.0785861i
$688$	−123.747	−	405.200i	−0.179865	−	0.588954i
$689$	−135.802	+	135.802i	−0.197100	+	0.197100i
$690$	−200.477	−	66.1245i	−0.290547	−	0.0958326i
$691$	−1.54901	−	3.73964i	−0.00224169	−	0.00541192i	0.922755	−	0.385388i	$-0.125932\pi$
$691$	−1.54901	−	3.73964i	−0.00224169	−	0.00541192i	−0.924996	+	0.379976i	$0.875932\pi$
$692$	868.448	+	216.669i	1.25498	+	0.313106i
$693$	2237.55	−	2237.55i	3.22880	−	3.22880i
$694$	−36.1725	+	109.668i	−0.0521218	+	0.158024i
$695$	−34.7225	−	34.7225i	−0.0499604	−	0.0499604i
$696$	373.234	−	84.3644i	0.536255	−	0.121213i
$697$	−156.031	+	65.2723i	−0.223860	+	0.0936475i
$698$	−864.206	+	1002.81i	−1.23812	+	1.43668i
$699$	598.337			0.855991
$700$	400.202	+	666.278i	0.571717	+	0.951825i
$701$	463.779	+	463.779i	0.661597	+	0.661597i	0.955756	−	0.294160i	$-0.0950397\pi$
$701$	463.779	+	463.779i	0.661597	+	0.661597i	−0.294160	+	0.955756i	$0.595040\pi$
$702$	1698.78	−	856.094i	2.41992	−	1.21951i
$703$	101.958	−	246.149i	0.145033	−	0.350140i
$704$	−526.215	−	474.243i	−0.747464	−	0.673640i
$705$	−617.361	+	617.361i	−0.875690	+	0.875690i
$706$	412.773	−	478.973i	0.584664	−	0.678431i
$707$	181.778	−	75.2951i	0.257112	−	0.106499i
$708$	−1113.31	−	277.761i	−1.57248	−	0.392318i
$709$	44.9987	−	108.637i	0.0634679	−	0.153225i	−0.888964	−	0.457978i	$-0.848574\pi$
$709$	44.9987	−	108.637i	0.0634679	−	0.153225i	0.952431	+	0.304753i	$0.0985739\pi$
$710$	441.774	−	512.625i	0.622217	−	0.722007i
$711$	153.484	−	63.5752i	0.215871	−	0.0894165i
$712$	542.540	−	859.437i	0.761994	−	1.20707i
$713$		−	247.560i		−	0.347209i
$714$	1621.63	−	1895.10i	2.27119	−	2.65421i
$715$	345.985	−	345.985i	0.483895	−	0.483895i
$716$	−92.7883	−	621.510i	−0.129593	−	0.868030i
$717$	244.487	−	590.244i	0.340986	−	0.823214i
$718$	−28.4264	−	382.918i	−0.0395911	−	0.533313i
$719$	−212.075	+	87.8443i	−0.294958	+	0.122176i	−0.525255	−	0.850945i	$-0.676030\pi$
$719$	−212.075	+	87.8443i	−0.294958	+	0.122176i	0.230297	+	0.973120i	$0.426030\pi$
$720$	856.120	−	705.292i	1.18906	−	0.979573i
$721$	−467.989	+	1129.83i	−0.649083	+	1.56703i
$722$	−307.751	−	265.216i	−0.426247	−	0.367335i
$723$	1277.71			1.76723
$724$	−233.273	+	140.116i	−0.322200	+	0.193530i
$725$	−48.4827	−	117.048i	−0.0668726	−	0.161445i
$726$	15.8665	+	5.23333i	0.0218547	+	0.00720845i
$727$		−	742.599i		−	1.02146i	−0.859742	−	0.510728i	$-0.829376\pi$
$727$		−	742.599i		−	1.02146i	0.859742	−	0.510728i	$-0.170624\pi$
$728$	−247.307	+	1437.27i	−0.339707	+	1.97427i
$729$	−441.250	+	441.250i	−0.605281	+	0.605281i
$730$	−561.798	+	651.898i	−0.769586	+	0.893011i
$731$	319.422	+	317.189i	0.436966	+	0.433911i
$732$	276.836	−	41.3303i	0.378192	−	0.0564621i
$733$	−33.8658			−0.0462016			−0.0231008	−	0.999733i	$-0.507354\pi$
$733$	−33.8658			−0.0462016			−0.0231008	+	0.999733i	$0.507354\pi$
$734$	−537.047	−	1065.68i	−0.731672	−	1.45189i
$735$	−2263.54			−3.07964
$736$	131.245	+	137.205i	0.178322	+	0.186420i
$737$	−1024.90	−	424.528i	−1.39064	−	0.576021i
$738$	−134.223	+	406.939i	−0.181874	+	0.551408i
$739$	224.024			0.303144			0.151572	−	0.988446i	$-0.451566\pi$
$739$	224.024			0.303144			0.151572	+	0.988446i	$0.451566\pi$
$740$	219.472	+	162.453i	0.296584	+	0.219531i
$741$	−880.825	+	364.850i	−1.18870	+	0.492375i
$742$	167.117	+	331.617i	0.225225	+	0.446923i
$743$	−7.50163	−	18.1105i	−0.0100964	−	0.0243749i	0.918751	−	0.394838i	$-0.129199\pi$
$743$	−7.50163	−	18.1105i	−0.0100964	−	0.0243749i	−0.928847	+	0.370463i	$0.879199\pi$
$744$	1559.66	+	984.574i	2.09632	+	1.32335i
$745$	−226.561	−	546.966i	−0.304108	−	0.734183i
$746$	−46.9398	−	632.304i	−0.0629220	−	0.847592i
$747$	−889.480	+	889.480i	−1.19074	+	1.19074i
$748$	730.908	+	179.633i	0.977150	+	0.240151i
$749$	50.7173	−	50.7173i	0.0677133	−	0.0677133i
$750$	−1068.24	−	920.598i	−1.42432	−	1.22746i
$751$	−78.9620	−	190.631i	−0.105142	−	0.253836i	0.862549	−	0.505973i	$-0.168867\pi$
$751$	−78.9620	−	190.631i	−0.105142	−	0.253836i	−0.967692	+	0.252137i	$0.918867\pi$
$752$	751.030	−	229.362i	0.998710	−	0.305003i
$753$	−13.9950	−	33.7868i	−0.0185856	−	0.0448697i
$754$	74.4634	−	225.760i	0.0987579	−	0.299416i
$755$	523.253	−	216.738i	0.693050	−	0.287071i
$756$	−543.120	−	3637.90i	−0.718413	−	4.81203i
$757$	−248.885			−0.328779			−0.164389	−	0.986396i	$-0.552565\pi$
$757$	−248.885			−0.328779			−0.164389	+	0.986396i	$0.552565\pi$
$758$	91.7813	+	182.125i	0.121084	+	0.240271i
$759$	−335.281	−	138.878i	−0.441741	−	0.182975i
$760$	−264.299	+	186.697i	−0.347761	+	0.245654i
$761$	1366.54			1.79572			0.897859	−	0.440282i	$-0.145122\pi$
$761$	1366.54			1.79572			0.897859	+	0.440282i	$0.145122\pi$
$762$	255.796	−	775.526i	0.335690	−	1.01775i
$763$	1564.89			2.05096
$764$	−54.8070	−	367.105i	−0.0717369	−	0.480504i
$765$	−447.189	+	1090.41i	−0.584561	+	1.42538i
$766$	92.8474	+	1250.70i	0.121211	+	1.63277i
$767$	−504.063	+	504.063i	−0.657188	+	0.657188i
$768$	−1386.39	+	281.183i	−1.80519	+	0.366123i
$769$			344.739i			0.448295i	0.974555	+	0.224147i	$0.0719597\pi$
$769$			344.739i			0.448295i	−0.974555	+	0.224147i	$0.928040\pi$
$770$	−425.767	−	844.866i	−0.552944	−	1.09723i
$771$	−673.088	−	1624.98i	−0.873006	−	2.10762i
$772$	−112.373	+	450.410i	−0.145561	+	0.583432i
$773$	−423.145			−0.547406			−0.273703	−	0.961814i	$-0.588249\pi$
$773$	−423.145			−0.547406			−0.273703	+	0.961814i	$0.588249\pi$
$774$	1137.35	−	84.4323i	1.46944	−	0.109086i
$775$	233.694	−	564.188i	0.301541	−	0.727985i
$776$	102.797	+	17.6880i	0.132470	+	0.0227938i
$777$	1437.16	−	595.290i	1.84962	−	0.766139i
$778$	−493.147	+	572.237i	−0.633865	+	0.735523i
$779$	47.8374	−	115.490i	0.0614087	−	0.148254i
$780$	−144.278	−	966.397i	−0.184972	−	1.23897i
$781$	822.615	−	822.615i	1.05328	−	1.05328i
$782$	−191.805	−	62.5187i	−0.245275	−	0.0799472i
$783$			599.562i			0.765725i
$784$	1797.29	+	956.339i	2.29246	+	1.21982i
$785$	666.228	−	275.961i	0.848698	−	0.351542i
$786$	1638.14	−	121.609i	2.08415	−	0.154719i
$787$	27.8626	−	67.2663i	0.0354036	−	0.0854718i	−0.905189	−	0.425010i	$-0.860271\pi$
$787$	27.8626	−	67.2663i	0.0354036	−	0.0854718i	0.940592	+	0.339538i	$0.110271\pi$
$788$	167.027	+	278.075i	0.211963	+	0.352887i
$789$	1635.94	−	677.627i	2.07343	−	0.858843i
$790$	−3.67715	−	49.5331i	−0.00465462	−	0.0627002i
$791$	947.642	−	947.642i	1.19803	−	1.19803i
$792$	1557.49	−	1100.19i	1.96652	−	1.38913i
$793$	66.5455	−	160.655i	0.0839162	−	0.202592i
$794$	−1194.17	−	393.878i	−1.50399	−	0.496069i
$795$	−175.927	−	175.927i	−0.221292	−	0.221292i
$796$	98.2353	−	59.0053i	0.123411	−	0.0741273i
$797$	1058.78			1.32846			0.664230	−	0.747528i	$-0.268759\pi$
$797$	1058.78			1.32846			0.664230	+	0.747528i	$0.268759\pi$
$798$	136.475	+	1838.39i	0.171022	+	2.30375i
$799$	−587.902	+	592.042i	−0.735798	+	0.740979i
$800$	169.587	+	436.584i	0.211983	+	0.545730i
$801$	1934.57	+	1934.57i	2.41520	+	2.41520i
$802$	−843.007	+	424.830i	−1.05113	+	0.529713i
$803$	−1046.11	+	1046.11i	−1.30275	+	1.30275i
$804$	−1899.07	+	1140.68i	−2.36203	+	1.41876i
$805$	97.0414	+	234.279i	0.120548	+	0.291029i
$806$	1023.27	−	515.673i	1.26957	−	0.639793i
$807$	1056.52	−	1056.52i	1.30920	−	1.30920i
$808$	115.649	−	26.1408i	0.143130	−	0.0323525i
$809$	757.336	+	313.699i	0.936139	+	0.387761i	0.798004	−	0.602652i	$-0.205889\pi$
$809$	757.336	+	313.699i	0.936139	+	0.387761i	0.138135	+	0.990413i	$0.455889\pi$
$810$	547.458	+	1086.34i	0.675874	+	1.34116i
$811$	852.850	+	353.262i	1.05160	+	0.435588i	0.840464	−	0.541867i	$-0.182283\pi$
$811$	852.850	+	353.262i	1.05160	+	0.435588i	0.211140	+	0.977456i	$0.432283\pi$
$812$	−369.452	−	273.467i	−0.454990	−	0.336783i
$813$	−156.484	+	377.785i	−0.192477	+	0.464680i
$814$	355.586	+	306.440i	0.436838	+	0.376462i
$815$		−	309.281i		−	0.379486i
$816$	1156.71	−	959.755i	1.41753	−	1.17617i
$817$	−332.706			−0.407229
$818$	−848.070	+	984.082i	−1.03676	+	1.20303i
$819$	−3626.97	−	1502.34i	−4.42853	−	1.83436i
$820$	102.973	+	76.2206i	0.125577	+	0.0929520i
$821$	373.288	−	901.196i	0.454674	−	1.09768i	−0.515850	−	0.856679i	$-0.672524\pi$
$821$	373.288	−	901.196i	0.454674	−	1.09768i	0.970525	−	0.241002i	$-0.0774761\pi$
$822$	−458.705	+	231.163i	−0.558036	+	0.281220i
$823$	199.744	−	482.224i	0.242702	−	0.585934i	−0.754848	−	0.655900i	$-0.772289\pi$
$823$	199.744	−	482.224i	0.242702	−	0.585934i	0.997549	+	0.0699662i	$0.0222892\pi$
$824$	−393.383	+	623.158i	−0.477406	+	0.756260i
$825$	−633.004	−	633.004i	−0.767278	−	0.767278i
$826$	620.296	+	1230.88i	0.750964	+	1.49017i
$827$	−75.9625	+	31.4647i	−0.0918531	+	0.0380468i	−0.428137	−	0.903714i	$-0.640830\pi$
$827$	−75.9625	+	31.4647i	−0.0918531	+	0.0380468i	0.336284	+	0.941761i	$0.390830\pi$
$828$	−438.143	+	263.172i	−0.529158	+	0.317840i
$829$	−612.361	−	612.361i	−0.738675	−	0.738675i	0.233647	−	0.972322i	$-0.424934\pi$
$829$	−612.361	−	612.361i	−0.738675	−	0.738675i	−0.972322	+	0.233647i	$0.924934\pi$
$830$	169.252	+	335.854i	0.203918	+	0.404643i
$831$	−1960.65	+	1960.65i	−2.35939	+	2.35939i
$832$	−293.741	+	828.294i	−0.353054	+	0.995545i
$833$	−2163.12	+	7.58935i	−2.59678	+	0.00911086i
$834$	−168.115	+	12.4802i	−0.201576	+	0.0149642i
$835$		−	120.992i		−	0.144900i
$836$	−476.872	+	286.435i	−0.570421	+	0.342625i
$837$	−2043.53	+	2043.53i	−2.44149	+	2.44149i
$838$	−432.492	+	1311.24i	−0.516100	+	1.56472i
$839$	−611.388	−	253.245i	−0.728710	−	0.301842i	−0.0126885	−	0.999919i	$-0.504039\pi$
$839$	−611.388	−	253.245i	−0.728710	−	0.301842i	−0.716022	+	0.698078i	$0.754039\pi$
$840$	−1861.93	−	320.378i	−2.21659	−	0.381402i
$841$	−541.697	−	541.697i	−0.644111	−	0.644111i
$842$	−211.946	+	15.7340i	−0.251717	+	0.0186865i
$843$	−87.8768	−	212.153i	−0.104243	−	0.251665i
$844$	585.613	+	974.961i	0.693854	+	1.15517i
$845$	−58.1844	−	24.1008i	−0.0688572	−	0.0285216i
$846$	156.493	+	2108.05i	0.184980	+	2.49179i
$847$	−7.68021	−	18.5417i	−0.00906755	−	0.0218910i
$848$	65.3603	+	214.018i	0.0770759	+	0.252379i
$849$	−284.060			−0.334582
$850$	−378.105	−	323.542i	−0.444830	−	0.380637i
$851$	−88.9663	−	88.9663i	−0.104543	−	0.104543i
$852$	−343.036	−	2297.71i	−0.402624	−	2.69684i
$853$	−1181.93	−	489.572i	−1.38562	−	0.573941i	−0.439639	−	0.898174i	$-0.644894\pi$
$853$	−1181.93	−	489.572i	−1.38562	−	0.573941i	−0.945977	+	0.324233i	$0.894894\pi$
$854$	−254.700	−	219.497i	−0.298243	−	0.257022i
$855$	−333.339	−	804.753i	−0.389871	−	0.941231i
$856$	35.3026	−	24.9373i	0.0412414	−	0.0291324i
$857$	−934.539	−	387.099i	−1.09048	−	0.451691i	−0.236304	−	0.971679i	$-0.575936\pi$
$857$	−934.539	−	387.099i	−1.09048	−	0.451691i	−0.854173	+	0.519988i	$0.825936\pi$
$858$	−124.356	−	1675.14i	−0.144937	−	1.95238i
$859$			956.423i			1.11341i	0.830709	+	0.556707i	$0.187935\pi$
$859$			956.423i			1.11341i	−0.830709	+	0.556707i	$0.812065\pi$
$860$	82.5409	−	330.838i	0.0959778	−	0.384696i
$861$	674.295	−	279.302i	0.783153	−	0.324393i
$862$	−119.033	+	59.9863i	−0.138090	+	0.0695897i
$863$	−470.605			−0.545313			−0.272657	−	0.962111i	$-0.587902\pi$
$863$	−470.605			−0.545313			−0.272657	+	0.962111i	$0.587902\pi$
$864$	49.1987	−	2215.97i	0.0569429	−	2.56478i
$865$	509.374	+	509.374i	0.588871	+	0.588871i
$866$	783.621	−	58.1729i	0.904874	−	0.0671743i
$867$	−600.766	+	1479.66i	−0.692925	+	1.70664i
$868$	−327.151	−	2191.31i	−0.376902	−	2.52455i
$869$		−	85.3872i		−	0.0982591i
$870$	292.464	+	96.4648i	0.336165	+	0.110879i
$871$			1376.28i			1.58011i
$872$	929.354	+	159.911i	1.06577	+	0.183384i
$873$	−107.451	+	259.410i	−0.123082	+	0.297147i
$874$	133.150	−	67.1005i	0.152346	−	0.0767740i
$875$			1693.97i			1.93596i
$876$	436.234	+	2921.96i	0.497984	+	3.33557i
$877$	−264.239	−	637.929i	−0.301299	−	0.727399i	−0.999929	−	0.0119164i	$-0.996207\pi$
$877$	−264.239	−	637.929i	−0.301299	−	0.727399i	0.698630	−	0.715483i	$-0.253793\pi$
$878$	1376.67	+	454.076i	1.56797	+	0.517170i
$879$	−1620.26	+	671.134i	−1.84330	+	0.763520i
$880$	−166.520	−	545.257i	−0.189227	−	0.619610i
$881$	−297.636	+	123.285i	−0.337839	+	0.139937i	−0.545152	−	0.838337i	$-0.683528\pi$
$881$	−297.636	+	123.285i	−0.337839	+	0.139937i	0.207313	+	0.978275i	$0.433528\pi$
$882$	−3577.66	+	4151.44i	−4.05631	+	4.70685i
$883$	484.657	+	484.657i	0.548875	+	0.548875i	0.926115	−	0.377240i	$-0.123127\pi$
$883$	484.657	+	484.657i	0.548875	+	0.548875i	−0.377240	+	0.926115i	$0.623127\pi$
$884$	−141.118	−	923.039i	−0.159635	−	1.04416i
$885$	−652.996	−	652.996i	−0.737849	−	0.737849i
$886$	1473.14	−	109.360i	1.66269	−	0.123432i
$887$	823.135	−	340.954i	0.927999	−	0.384390i	0.133080	−	0.991105i	$-0.457513\pi$
$887$	823.135	−	340.954i	0.927999	−	0.384390i	0.794919	+	0.606715i	$0.207513\pi$
$888$	914.329	−	206.672i	1.02965	−	0.232738i
$889$	−906.282	+	375.394i	−1.01944	+	0.422266i
$890$	730.465	−	368.115i	0.820748	−	0.413612i
$891$	800.299	+	1932.09i	0.898203	+	2.16845i
$892$	932.459	+	690.204i	1.04536	+	0.773771i
$893$		−	616.663i		−	0.690552i
$894$	−1930.16	−	636.635i	−2.15902	−	0.712119i
$895$	193.540	−	467.246i	0.216245	−	0.522063i
$896$	1343.05	+	1041.05i	1.49894	+	1.16188i
$897$			450.229i			0.501927i
$898$	−494.865	+	249.385i	−0.551074	+	0.277712i
$899$			361.150i			0.401724i
$900$	−1246.96	+	186.164i	−1.38551	+	0.206849i
$901$	−168.712	−	167.532i	−0.187249	−	0.185940i
$902$	166.836	+	143.777i	0.184962	+	0.159398i
$903$	−1373.57	−	1373.57i	−1.52112	−	1.52112i
$904$	659.622	−	465.948i	0.729670	−	0.515430i
$905$	−219.005			−0.241994
$906$	609.034	−	1846.48i	0.672223	−	2.03806i
$907$	965.217	−	399.806i	1.06419	−	0.440800i	0.219251	−	0.975669i	$-0.429639\pi$
$907$	965.217	−	399.806i	1.06419	−	0.440800i	0.844935	+	0.534868i	$0.179639\pi$
$908$	1112.39	−	668.160i	1.22510	−	0.735859i
$909$			319.165i			0.351116i
$910$	−766.234	+	889.121i	−0.842015	+	0.977056i
$911$	210.139	+	87.0426i	0.230669	+	0.0955462i	0.495024	−	0.868879i	$-0.335159\pi$
$911$	210.139	+	87.0426i	0.230669	+	0.0955462i	−0.264355	+	0.964425i	$0.585159\pi$
$912$	−106.810	+	1105.73i	−0.117117	+	1.21242i
$913$	247.420	+	597.326i	0.270997	+	0.654245i
$914$	−145.639	+	10.8117i	−0.159343	+	0.0118290i
$915$	208.123	+	86.2075i	0.227457	+	0.0942158i
$916$	15.0793	+	101.004i	0.0164622	+	0.110266i
$917$	−1395.27	−	1395.27i	−1.52156	−	1.52156i
$918$	1067.22	+	2099.36i	1.16255	+	2.28689i
$919$	−321.119			−0.349422			−0.174711	−	0.984620i	$-0.555899\pi$
$919$	−321.119			−0.349422			−0.174711	+	0.984620i	$0.555899\pi$
$920$	33.6906	+	149.050i	0.0366203	+	0.162011i
$921$	−586.795	−	1416.65i	−0.637128	−	1.53816i
$922$	−741.733	−	639.217i	−0.804483	−	0.693294i
$923$	−1333.42	−	552.320i	−1.44466	−	0.598396i
$924$	−3151.31	−	786.220i	−3.41051	−	0.850888i
$925$	−118.770	−	286.737i	−0.128400	−	0.309986i
$926$	−908.115	−	782.603i	−0.980686	−	0.845143i
$927$	−1402.71	−	1402.71i	−1.51318	−	1.51318i
$928$	−191.465	−	200.160i	−0.206320	−	0.215690i
$929$	1401.89	+	580.682i	1.50903	+	0.625062i	0.975358	−	0.220629i	$-0.0708109\pi$
$929$	1401.89	+	580.682i	1.50903	+	0.625062i	0.533674	+	0.845690i	$0.320811\pi$
$930$	668.037	+	1325.61i	0.718319	+	1.42539i
$931$	1130.49	−	1130.49i	1.21427	−	1.21427i
$932$	−223.016	−	371.290i	−0.239288	−	0.398380i
$933$		−	535.352i		−	0.573796i
$934$	−428.885	−	369.608i	−0.459192	−	0.395726i
$935$	429.830	+	426.824i	0.459711	+	0.456497i
$936$	−2000.46	−	1262.84i	−2.13724	−	1.34919i
$937$	−252.969	+	252.969i	−0.269978	+	0.269978i	−0.829091	−	0.559113i	$-0.811142\pi$
$937$	−252.969	+	252.969i	−0.269978	+	0.269978i	0.559113	+	0.829091i	$0.311142\pi$
$938$	2527.19	+	833.557i	2.69424	+	0.888654i
$939$	−1632.64	−	1632.64i	−1.73870	−	1.73870i
$940$	613.202	+	152.988i	0.652342	+	0.162753i
$941$	603.624	−	250.029i	0.641471	−	0.265706i	−0.0381470	−	0.999272i	$-0.512146\pi$
$941$	603.624	−	250.029i	0.641471	−	0.265706i	0.679618	+	0.733566i	$0.262146\pi$
$942$	775.448	−	2351.02i	0.823194	−	2.49577i
$943$	−41.7418	−	41.7418i	−0.0442649	−	0.0442649i
$944$	242.601	+	794.380i	0.256993	+	0.841504i
$945$	1132.85	−	2734.94i	1.19878	−	2.89412i
$946$	183.613	−	556.681i	0.194094	−	0.588458i
$947$	96.1499	−	232.126i	0.101531	−	0.245118i	−0.864949	−	0.501860i	$-0.832649\pi$
$947$	96.1499	−	232.126i	0.101531	−	0.245118i	0.966480	+	0.256742i	$0.0826492\pi$
$948$	−137.054	−	101.447i	−0.144572	−	0.107012i
$949$	1695.69	+	702.378i	1.78682	+	0.740124i
$950$	366.791	−	27.2291i	0.386095	−	0.0286622i
$951$	−1764.28			−1.85519
$952$	−1780.40	−	299.921i	−1.87017	−	0.315043i
$953$			406.822i			0.426886i	0.976956	+	0.213443i	$0.0684678\pi$
$953$			406.822i			0.426886i	−0.976956	+	0.213443i	$0.931532\pi$
$954$	−600.722	+	44.5952i	−0.629687	+	0.0467455i
$955$	114.317	−	275.987i	0.119704	−	0.288991i
$956$	−457.395	+	68.2867i	−0.478446	+	0.0714296i
$957$	489.120	+	202.600i	0.511097	+	0.211703i
$958$	30.1976	−	91.5535i	0.0315215	−	0.0955674i
$959$	570.057	+	236.125i	0.594429	+	0.246220i
$960$	−1073.03	−	380.531i	−1.11774	−	0.396387i
$961$	−551.402	+	551.402i	−0.573780	+	0.573780i
$962$	182.417	−	553.054i	0.189622	−	0.574900i
$963$	44.5245	+	107.492i	0.0462352	+	0.111622i
$964$	−476.235	−	792.862i	−0.494020	−	0.822471i
$965$	−264.180	+	264.180i	−0.273762	+	0.273762i
$966$	826.734	+	272.686i	0.855832	+	0.282284i
$967$	927.973	+	927.973i	0.959641	+	0.959641i	0.999217	−	0.0395754i	$-0.0126005\pi$
$967$	927.973	+	927.973i	0.959641	+	0.959641i	−0.0395754	+	0.999217i	$0.512601\pi$
$968$	−2.66640	−	11.7963i	−0.00275455	−	0.0121863i
$969$	−455.507	−	1088.87i	−0.470080	−	1.12371i
$970$	63.5921	+	54.8029i	0.0655589	+	0.0564979i
$971$	−201.718			−0.207742			−0.103871	−	0.994591i	$-0.533123\pi$
$971$	−201.718			−0.207742			−0.103871	+	0.994591i	$0.533123\pi$
$972$	1632.58	+	407.313i	1.67961	+	0.419046i
$973$	143.189	+	143.189i	0.147163	+	0.147163i
$974$	−84.4726	−	167.622i	−0.0867275	−	0.172097i
$975$	−425.012	+	1026.07i	−0.435909	+	1.05238i
$976$	−128.831	−	156.382i	−0.131999	−	0.160227i
$977$	258.369	−	258.369i	0.264452	−	0.264452i	−0.562408	−	0.826860i	$-0.690125\pi$
$977$	258.369	−	258.369i	0.264452	−	0.264452i	0.826860	+	0.562408i	$0.190125\pi$
$978$	−804.300	−	693.137i	−0.822393	−	0.708729i
$979$	1299.15	−	538.127i	1.32702	−	0.549670i
$980$	843.680	+	1404.61i	0.860898	+	1.43327i
$981$	−971.428	+	2345.23i	−0.990243	+	2.39066i
$982$	−1171.93	−	1009.96i	−1.19341	−	1.02847i
$983$	376.302	−	155.870i	0.382810	−	0.158565i	−0.182976	−	0.983117i	$-0.558573\pi$
$983$	376.302	−	155.870i	0.382810	−	0.158565i	0.565786	+	0.824552i	$0.308573\pi$
$984$	428.991	−	96.9675i	0.435967	−	0.0985442i
$985$			261.067i			0.265043i
$986$	279.812	+	91.2046i	0.283785	+	0.0924996i
$987$	2545.89	−	2545.89i	2.57942	−	2.57942i
$988$	554.709	+	410.594i	0.561447	+	0.415581i
$989$	−60.1255	+	145.156i	−0.0607942	+	0.146770i
$990$	1530.47	−	113.616i	1.54593	−	0.114764i
$991$	208.743	−	86.4643i	0.210639	−	0.0872496i	−0.274869	−	0.961482i	$-0.588635\pi$
$991$	208.743	−	86.4643i	0.210639	−	0.0872496i	0.485508	+	0.874232i	$0.338635\pi$
$992$	29.6351	−	1334.80i	0.0298741	−	1.34557i
$993$	556.659	−	1343.89i	0.560583	−	1.35337i
$994$	−1821.80	+	2113.98i	−1.83280	+	2.12674i
$995$	92.2269			0.0926904
$996$	1252.72	+	312.541i	1.25775	+	0.313796i
$997$	−106.842	−	257.941i	−0.107164	−	0.258717i	0.861197	−	0.508272i	$-0.169716\pi$
$997$	−106.842	−	257.941i	−0.107164	−	0.258717i	−0.968361	+	0.249555i	$0.919716\pi$
$998$	−123.230	+	373.612i	−0.123477	+	0.374361i
$999$			1468.78i			1.47025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.x.a.155.17	✓	280
16.3	odd	4		272.3.z.a.19.21	yes	280
17.9	even	8		272.3.z.a.43.21	yes	280
272.179	odd	8	inner	272.3.x.a.179.17	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.3.x.a.155.17	✓	280	1.1	even	1	trivial
272.3.x.a.179.17	yes	280	272.179	odd	8	inner
272.3.z.a.19.21	yes	280	16.3	odd	4
272.3.z.a.43.21	yes	280	17.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	272.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51503 - 1.30564i) q^{2} +(-5.10521 - 2.11465i) q^{3} +(0.590634 + 3.95615i) q^{4} +(-1.23196 + 2.97420i) q^{5} +(4.97359 + 9.86931i) q^{6} +(5.08037 - 12.2651i) q^{7} +(4.27047 - 6.76485i) q^{8} +(15.2275 + 15.2275i) q^{9} +(5.74968 - 2.89752i) q^{10} +(10.2260 - 4.23573i) q^{11} +(5.35056 - 21.4460i) q^{12} +(-9.70987 - 9.70987i) q^{13} +(-23.7107 + 11.9489i) q^{14} +(12.5788 - 12.5788i) q^{15} +(-15.3023 + 4.67328i) q^{16} +(11.9786 - 12.0629i) q^{17} +(-3.18857 - 42.9517i) q^{18} +12.5646i q^{19} +(-12.4940 - 3.11714i) q^{20} +(-51.8728 + 51.8728i) q^{21} +(-21.0230 - 6.93411i) q^{22} +(5.48178 + 2.27063i) q^{23} +(-36.1069 + 25.5055i) q^{24} +(10.3495 + 10.3495i) q^{25} +(2.03320 + 27.3883i) q^{26} +(-26.5070 - 63.9937i) q^{27} +(51.5233 + 12.8545i) q^{28} +(-7.99702 - 3.31247i) q^{29} +(-35.4806 + 2.63394i) q^{30} +(-15.9667 - 38.5469i) q^{31} +(29.2850 + 12.8991i) q^{32} -61.1628 q^{33} +(-33.8977 + 2.63605i) q^{34} +(30.2201 + 30.2201i) q^{35} +(-51.2485 + 69.2363i) q^{36} +(-19.5907 - 8.11473i) q^{37} +(16.4047 - 19.0357i) q^{38} +(29.0380 + 70.1039i) q^{39} +(14.8590 + 21.0352i) q^{40} +(-9.19169 - 3.80732i) q^{41} +(146.316 - 10.8619i) q^{42} +26.4797i q^{43} +(22.7970 + 37.9537i) q^{44} +(-64.0494 + 26.5301i) q^{45} +(-5.34045 - 10.5973i) q^{46} -49.0795 q^{47} +(88.0039 + 8.50092i) q^{48} +(-89.9743 - 89.9743i) q^{49} +(-2.16713 - 29.1925i) q^{50} +(-86.6620 + 36.2533i) q^{51} +(32.6787 - 44.1487i) q^{52} -13.9860i q^{53} +(-43.3934 + 131.561i) q^{54} +35.6323i q^{55} +(-61.2760 - 86.7456i) q^{56} +(26.5697 - 64.1448i) q^{57} +(7.79084 + 15.4597i) q^{58} -51.9124i q^{59} +(57.1931 + 42.3342i) q^{60} +(4.84608 + 11.6995i) q^{61} +(-26.1383 + 79.2464i) q^{62} +(264.128 - 109.406i) q^{63} +(-27.5263 - 57.7781i) q^{64} +(40.8412 - 16.9170i) q^{65} +(92.6635 + 79.8563i) q^{66} +(-70.8700 - 70.8700i) q^{67} +(54.7977 + 40.2643i) q^{68} +(-23.1841 - 23.1841i) q^{69} +(-6.32795 - 85.2409i) q^{70} +(97.1042 - 40.2219i) q^{71} +(168.040 - 37.9832i) q^{72} +(-123.486 + 51.1496i) q^{73} +(19.0856 + 37.8724i) q^{74} +(-30.9508 - 74.7219i) q^{75} +(-49.7074 + 7.42106i) q^{76} -146.942i q^{77} +(47.5367 - 144.123i) q^{78} +(2.95218 - 7.12720i) q^{79} +(4.95248 - 51.2694i) q^{80} +188.940i q^{81} +(8.95472 + 17.7692i) q^{82} +58.4127i q^{83} +(-235.854 - 174.579i) q^{84} +(21.1205 + 50.4877i) q^{85} +(34.5728 - 40.1175i) q^{86} +(33.8218 + 33.8218i) q^{87} +(15.0155 - 87.2656i) q^{88} +127.045 q^{89} +(131.675 + 43.4312i) q^{90} +(-168.422 + 69.7628i) q^{91} +(-5.74523 + 23.0279i) q^{92} +230.554i q^{93} +(74.3570 + 64.0800i) q^{94} +(-37.3696 - 15.4790i) q^{95} +(-122.229 - 127.780i) q^{96} +(4.98961 + 12.0460i) q^{97} +(18.8402 + 253.787i) q^{98} +(220.216 + 91.2163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

Introduction

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