LMFDB - Embedded newform 153.3.i.a.101.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.i (of order $6$, degree $2$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	153.101
Dual form			153.3.i.a.50.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.129772 - 0.0749237i) q^{2} +(-1.81198 + 2.39097i) q^{3} +(-1.98877 - 3.44466i) q^{4} +(1.38111 + 2.39215i) q^{5} +(0.414284 - 0.174521i) q^{6} +(-2.73699 - 1.58020i) q^{7} +1.19542i q^{8} +(-2.43349 - 8.66476i) q^{9} -0.413911i q^{10} +(6.09900 - 10.5638i) q^{11} +(11.8397 + 1.48653i) q^{12} +(-8.45595 - 14.6461i) q^{13} +(0.236789 + 0.410131i) q^{14} +(-8.22210 - 1.03233i) q^{15} +(-7.86553 + 13.6235i) q^{16} +(-4.71123 - 16.3341i) q^{17} +(-0.333398 + 1.30677i) q^{18} +9.05723 q^{19} +(5.49342 - 9.51489i) q^{20} +(8.73757 - 3.68078i) q^{21} +(-1.58296 + 0.913920i) q^{22} +(-10.2096 - 17.6835i) q^{23} +(-2.85820 - 2.16606i) q^{24} +(8.68508 - 15.0430i) q^{25} +2.53421i q^{26} +(25.1266 + 9.88192i) q^{27} +12.5706i q^{28} +(-1.08463 + 1.87864i) q^{29} +(0.989651 + 0.749997i) q^{30} +(-38.1700 + 22.0374i) q^{31} +(6.18249 - 3.56946i) q^{32} +(14.2065 + 33.7238i) q^{33} +(-0.612431 + 2.47269i) q^{34} -8.72972i q^{35} +(-25.0075 + 25.6148i) q^{36} +62.4071i q^{37} +(-1.17537 - 0.678602i) q^{38} +(50.3405 + 6.32050i) q^{39} +(-2.85961 + 1.65100i) q^{40} +(-31.2890 - 54.1941i) q^{41} +(-1.40967 - 0.176991i) q^{42} +(-14.0734 + 24.3759i) q^{43} -48.5181 q^{44} +(17.3665 - 17.7883i) q^{45} +3.05976i q^{46} +(37.6889 + 21.7597i) q^{47} +(-18.3212 - 43.4917i) q^{48} +(-19.5059 - 33.7853i) q^{49} +(-2.25415 + 1.30144i) q^{50} +(47.5911 + 18.3326i) q^{51} +(-33.6339 + 58.2557i) q^{52} +66.8350i q^{53} +(-2.52034 - 3.16498i) q^{54} +33.6935 q^{55} +(1.88900 - 3.27184i) q^{56} +(-16.4115 + 21.6556i) q^{57} +(0.281509 - 0.162529i) q^{58} +(68.5161 - 39.5578i) q^{59} +(12.7959 + 30.3754i) q^{60} +(-65.5511 - 37.8459i) q^{61} +6.60451 q^{62} +(-7.03163 + 27.5608i) q^{63} +61.8545 q^{64} +(23.3572 - 40.4558i) q^{65} +(0.683120 - 5.44080i) q^{66} +(-10.6797 - 18.4979i) q^{67} +(-46.8959 + 48.7135i) q^{68} +(60.7803 + 7.63127i) q^{69} +(-0.654064 + 1.13287i) q^{70} +80.2879 q^{71} +(10.3580 - 2.90903i) q^{72} -23.7538i q^{73} +(4.67578 - 8.09868i) q^{74} +(20.2302 + 48.0233i) q^{75} +(-18.0128 - 31.1990i) q^{76} +(-33.3858 + 19.2753i) q^{77} +(-6.05922 - 4.59192i) q^{78} +(-6.49716 - 3.75114i) q^{79} -43.4526 q^{80} +(-69.1562 + 42.1713i) q^{81} +9.37714i q^{82} +(-12.4098 - 7.16481i) q^{83} +(-30.0561 - 22.7777i) q^{84} +(32.5670 - 33.8292i) q^{85} +(3.65266 - 2.10887i) q^{86} +(-2.52645 - 5.99737i) q^{87} +(12.6281 + 7.29084i) q^{88} -115.581i q^{89} +(-3.58644 + 1.00725i) q^{90} +53.4484i q^{91} +(-40.6091 + 70.3370i) q^{92} +(16.4721 - 131.195i) q^{93} +(-3.26063 - 5.64758i) q^{94} +(12.5090 + 21.6663i) q^{95} +(-2.66803 + 21.2499i) q^{96} +(-9.98636 - 5.76563i) q^{97} +5.84583i q^{98} +(-106.375 - 27.1395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.129772	−	0.0749237i	−0.0648859	−	0.0374619i	0.467206	−	0.884148i	$-0.345261\pi$
$2$	−0.129772	−	0.0749237i	−0.0648859	−	0.0374619i	−0.532092	+	0.846687i	$0.678594\pi$
$3$	−1.81198	+	2.39097i	−0.603992	+	0.796991i
$3$	−1.81198	+	2.39097i	−0.603992	+	0.796991i
$4$	−1.98877	−	3.44466i	−0.497193	−	0.861164i
$5$	1.38111	+	2.39215i	0.276222	+	0.478430i	0.970443	−	0.241332i	$-0.0775842\pi$
$5$	1.38111	+	2.39215i	0.276222	+	0.478430i	−0.694221	+	0.719762i	$0.744251\pi$
$6$	0.414284	−	0.174521i	0.0690473	−	0.0290868i
$7$	−2.73699	−	1.58020i	−0.390999	−	0.225743i	0.291594	−	0.956542i	$-0.405814\pi$
$7$	−2.73699	−	1.58020i	−0.390999	−	0.225743i	−0.682593	+	0.730799i	$0.739148\pi$
$8$			1.19542i			0.149427i
$9$	−2.43349	−	8.66476i	−0.270388	−	0.962751i
$10$		−	0.413911i		−	0.0413911i
$11$	6.09900	−	10.5638i	0.554455	−	0.960344i	−0.443491	−	0.896279i	$-0.646260\pi$
$11$	6.09900	−	10.5638i	0.554455	−	0.960344i	0.997946	−	0.0640648i	$-0.0204064\pi$
$12$	11.8397	+	1.48653i	0.986640	+	0.123878i
$13$	−8.45595	−	14.6461i	−0.650458	−	1.12663i	−0.983012	−	0.183542i	$-0.941244\pi$
$13$	−8.45595	−	14.6461i	−0.650458	−	1.12663i	0.332554	−	0.943084i	$-0.392090\pi$
$14$	0.236789	+	0.410131i	0.0169135	+	0.0292951i
$15$	−8.22210	−	1.03233i	−0.548140	−	0.0688217i
$16$	−7.86553	+	13.6235i	−0.491595	+	0.851468i
$17$	−4.71123	−	16.3341i	−0.277131	−	0.960832i
$17$	−4.71123	−	16.3341i	−0.277131	−	0.960832i
$18$	−0.333398	+	1.30677i	−0.0185221	+	0.0725982i
$19$	9.05723			0.476696			0.238348	−	0.971180i	$-0.423394\pi$
$19$	9.05723			0.476696			0.238348	+	0.971180i	$0.423394\pi$
$20$	5.49342	−	9.51489i	0.274671	−	0.475745i
$21$	8.73757	−	3.68078i	0.416075	−	0.175275i
$22$	−1.58296	+	0.913920i	−0.0719525	+	0.0415418i
$23$	−10.2096	−	17.6835i	−0.443895	−	0.768849i	0.554079	−	0.832464i	$-0.313070\pi$
$23$	−10.2096	−	17.6835i	−0.443895	−	0.768849i	−0.997975	+	0.0636149i	$0.979737\pi$
$24$	−2.85820	−	2.16606i	−0.119092	−	0.0902526i
$25$	8.68508	−	15.0430i	0.347403	−	0.601720i
$26$			2.53421i			0.0974695i
$27$	25.1266	+	9.88192i	0.930616	+	0.365997i
$28$			12.5706i			0.448952i
$29$	−1.08463	+	1.87864i	−0.0374011	+	0.0647807i	−0.884120	−	0.467260i	$-0.845241\pi$
$29$	−1.08463	+	1.87864i	−0.0374011	+	0.0647807i	0.846719	+	0.532040i	$0.178575\pi$
$30$	0.989651	+	0.749997i	0.0329884	+	0.0249999i
$31$	−38.1700	+	22.0374i	−1.23129	+	0.710885i	−0.967299	−	0.253640i	$-0.918372\pi$
$31$	−38.1700	+	22.0374i	−1.23129	+	0.710885i	−0.263991	+	0.964525i	$0.585039\pi$
$32$	6.18249	−	3.56946i	0.193203	−	0.111546i
$33$	14.2065	+	33.7238i	0.430499	+	1.02193i
$34$	−0.612431	+	2.47269i	−0.0180127	+	0.0727263i
$35$		−	8.72972i		−	0.249421i
$36$	−25.0075	+	25.6148i	−0.694652	+	0.711522i
$37$			62.4071i			1.68668i	0.537381	+	0.843340i	$0.319414\pi$
$37$			62.4071i			1.68668i	−0.537381	+	0.843340i	$0.680586\pi$
$38$	−1.17537	−	0.678602i	−0.0309309	−	0.0178579i
$39$	50.3405	+	6.32050i	1.29078	+	0.162064i
$40$	−2.85961	+	1.65100i	−0.0714903	+	0.0412750i
$41$	−31.2890	−	54.1941i	−0.763145	−	1.32181i	−0.941222	−	0.337790i	$-0.890321\pi$
$41$	−31.2890	−	54.1941i	−0.763145	−	1.32181i	0.178076	−	0.984017i	$-0.443013\pi$
$42$	−1.40967	−	0.176991i	−0.0335635	−	0.00421407i
$43$	−14.0734	+	24.3759i	−0.327289	+	0.566881i	−0.981973	−	0.189022i	$-0.939468\pi$
$43$	−14.0734	+	24.3759i	−0.327289	+	0.566881i	0.654684	+	0.755903i	$0.272802\pi$
$44$	−48.5181			−1.10268
$45$	17.3665	−	17.7883i	0.385922	−	0.395295i
$46$			3.05976i			0.0665166i
$47$	37.6889	+	21.7597i	0.801891	+	0.462972i	0.844132	−	0.536136i	$-0.180116\pi$
$47$	37.6889	+	21.7597i	0.801891	+	0.462972i	−0.0422410	+	0.999107i	$0.513450\pi$
$48$	−18.3212	−	43.4917i	−0.381693	−	0.906077i
$49$	−19.5059	−	33.7853i	−0.398080	−	0.689495i
$50$	−2.25415	+	1.30144i	−0.0450831	+	0.0260287i
$51$	47.5911	+	18.3326i	0.933159	+	0.359464i
$52$	−33.6339	+	58.2557i	−0.646807	+	1.12030i
$53$			66.8350i			1.26104i	0.776174	+	0.630518i	$0.217158\pi$
$53$			66.8350i			1.26104i	−0.776174	+	0.630518i	$0.782842\pi$
$54$	−2.52034	−	3.16498i	−0.0466729	−	0.0586107i
$55$	33.6935			0.612610
$56$	1.88900	−	3.27184i	0.0337321	−	0.0584257i
$57$	−16.4115	+	21.6556i	−0.287921	+	0.379923i
$58$	0.281509	−	0.162529i	0.00485361	−	0.00280223i
$59$	68.5161	−	39.5578i	1.16129	−	0.670471i	0.209678	−	0.977771i	$-0.432759\pi$
$59$	68.5161	−	39.5578i	1.16129	−	0.670471i	0.951613	+	0.307299i	$0.0994252\pi$
$60$	12.7959	+	30.3754i	0.213265	+	0.506256i
$61$	−65.5511	−	37.8459i	−1.07461	−	0.620425i	−0.145171	−	0.989407i	$-0.546373\pi$
$61$	−65.5511	−	37.8459i	−1.07461	−	0.620425i	−0.929437	+	0.368981i	$0.879707\pi$
$62$	6.60451			0.106524
$63$	−7.03163	+	27.5608i	−0.111613	+	0.437473i
$64$	61.8545			0.966476
$65$	23.3572	−	40.4558i	0.359341	−	0.622397i
$66$	0.683120	−	5.44080i	0.0103503	−	0.0824364i
$67$	−10.6797	−	18.4979i	−0.159399	−	0.276087i	0.775253	−	0.631651i	$-0.217622\pi$
$67$	−10.6797	−	18.4979i	−0.159399	−	0.276087i	−0.934652	+	0.355563i	$0.884289\pi$
$68$	−46.8959	+	48.7135i	−0.689646	+	0.716375i
$69$	60.7803	+	7.63127i	0.880874	+	0.110598i
$70$	−0.654064	+	1.13287i	−0.00934377	+	0.0161839i
$71$	80.2879			1.13082			0.565408	−	0.824811i	$-0.308719\pi$
$71$	80.2879			1.13082			0.565408	+	0.824811i	$0.308719\pi$
$72$	10.3580	−	2.90903i	0.143861	−	0.0404033i
$73$		−	23.7538i		−	0.325394i	−0.986676	−	0.162697i	$-0.947981\pi$
$73$		−	23.7538i		−	0.325394i	0.986676	−	0.162697i	$-0.0520193\pi$
$74$	4.67578	−	8.09868i	0.0631862	−	0.109442i
$75$	20.2302	+	48.0233i	0.269736	+	0.640311i
$76$	−18.0128	−	31.1990i	−0.237010	−	0.410514i
$77$	−33.3858	+	19.2753i	−0.433582	+	0.250329i
$78$	−6.05922	−	4.59192i	−0.0776823	−	0.0588708i
$79$	−6.49716	−	3.75114i	−0.0822426	−	0.0474828i	0.458315	−	0.888790i	$-0.348453\pi$
$79$	−6.49716	−	3.75114i	−0.0822426	−	0.0474828i	−0.540557	+	0.841307i	$0.681787\pi$
$80$	−43.4526			−0.543157
$81$	−69.1562	+	42.1713i	−0.853781	+	0.520633i
$82$			9.37714i			0.114355i
$83$	−12.4098	−	7.16481i	−0.149516	−	0.0863230i	0.423376	−	0.905954i	$-0.360845\pi$
$83$	−12.4098	−	7.16481i	−0.149516	−	0.0863230i	−0.572892	+	0.819631i	$0.694178\pi$
$84$	−30.0561	−	22.7777i	−0.357810	−	0.271163i
$85$	32.5670	−	33.8292i	0.383141	−	0.397991i
$86$	3.65266	−	2.10887i	0.0424728	−	0.0245217i
$87$	−2.52645	−	5.99737i	−0.0290396	−	0.0689353i
$88$	12.6281	+	7.29084i	0.143501	+	0.0828504i
$89$		−	115.581i		−	1.29867i	−0.760504	−	0.649333i	$-0.775048\pi$
$89$		−	115.581i		−	1.29867i	0.760504	−	0.649333i	$-0.224952\pi$
$90$	−3.58644	+	1.00725i	−0.0398494	+	0.0111917i
$91$			53.4484i			0.587346i
$92$	−40.6091	+	70.3370i	−0.441403	+	0.764533i
$93$	16.4721	−	131.195i	0.177120	−	1.41070i
$94$	−3.26063	−	5.64758i	−0.0346876	−	0.0600807i
$95$	12.5090	+	21.6663i	0.131674	+	0.228066i
$96$	−2.66803	+	21.2499i	−0.0277920	+	0.221353i
$97$	−9.98636	−	5.76563i	−0.102952	−	0.0594395i	0.447640	−	0.894214i	$-0.352265\pi$
$97$	−9.98636	−	5.76563i	−0.102952	−	0.0594395i	−0.550592	+	0.834774i	$0.685598\pi$
$98$			5.84583i			0.0596513i
$99$	−106.375	−	27.1395i	−1.07449	−	0.274137i
$100$	−69.0906			−0.690906
$101$	−64.3415	−	37.1476i	−0.637045	−	0.367798i	0.146431	−	0.989221i	$-0.453222\pi$
$101$	−64.3415	−	37.1476i	−0.637045	−	0.367798i	−0.783475	+	0.621423i	$0.786555\pi$
$102$	−4.80243	−	5.94476i	−0.0470827	−	0.0582820i
$103$	4.63237	+	8.02349i	0.0449744	+	0.0778980i	0.887636	−	0.460545i	$-0.152346\pi$
$103$	4.63237	+	8.02349i	0.0449744	+	0.0778980i	−0.842662	+	0.538443i	$0.819013\pi$
$104$	17.5082	−	10.1084i	0.168348	−	0.0971959i
$105$	20.8725	+	15.8180i	0.198786	+	0.150648i
$106$	5.00753	−	8.67329i	0.0472408	−	0.0818235i
$107$	45.5617			0.425811			0.212905	−	0.977073i	$-0.431707\pi$
$107$	45.5617			0.425811			0.212905	+	0.977073i	$0.431707\pi$
$108$	−15.9313	−	106.205i	−0.147512	−	0.983384i
$109$		−	158.516i		−	1.45428i	−0.686490	−	0.727140i	$-0.740849\pi$
$109$		−	158.516i		−	1.45428i	0.686490	−	0.727140i	$-0.259151\pi$
$110$	−4.37247	−	2.52445i	−0.0397497	−	0.0229495i
$111$	−149.214	−	113.080i	−1.34427	−	1.01874i
$112$	43.0557	−	24.8582i	0.384426	−	0.221949i
$113$	27.6157	+	47.8318i	0.244387	+	0.423291i	0.961959	−	0.273194i	$-0.0880800\pi$
$113$	27.6157	+	47.8318i	0.244387	+	0.423291i	−0.717572	+	0.696484i	$0.754747\pi$
$114$	3.75226	−	1.58067i	0.0329146	−	0.0138656i
$115$	28.2011	−	48.8458i	0.245227	−	0.424746i
$116$	8.62835			0.0743824
$117$	−106.328	+	108.910i	−0.908785	+	0.930856i
$118$	−11.8553			−0.100468
$119$	−12.9166	+	52.1511i	−0.108543	+	0.438244i
$120$	1.23406	−	9.82882i	0.0102838	−	0.0819069i
$121$	−13.8956	−	24.0679i	−0.114840	−	0.198909i
$122$	5.67112	+	9.82267i	0.0464846	+	0.0805137i
$123$	186.271	+	23.3873i	1.51440	+	0.190140i
$124$	151.823	+	87.6550i	1.22438	+	0.706895i
$125$	117.036			0.936285
$126$	2.97746	−	3.04977i	0.0236307	−	0.0242046i
$127$	164.891			1.29835			0.649176	−	0.760638i	$-0.275114\pi$
$127$	164.891			1.29835			0.649176	+	0.760638i	$0.275114\pi$
$128$	−32.7569	−	18.9122i	−0.255913	−	0.147752i
$129$	−32.7813	−	77.8176i	−0.254119	−	0.603237i
$130$	−6.06221	+	3.50002i	−0.0466324	+	0.0269232i
$131$	0.0321956	+	0.0557644i	0.000245768	+	0.000425682i	0.866148	−	0.499787i	$-0.166588\pi$
$131$	0.0321956	+	0.0557644i	0.000245768	+	0.000425682i	−0.865902	+	0.500213i	$0.833255\pi$
$132$	87.9136	−	116.005i	0.666012	−	0.878829i
$133$	−24.7896	−	14.3123i	−0.186388	−	0.107611i
$134$			3.20066i			0.0238856i
$135$	11.0636	+	73.7547i	0.0819524	+	0.546331i
$136$	19.5261	−	5.63188i	0.143574	−	0.0414109i
$137$	62.9889	+	36.3666i	0.459773	+	0.265450i	0.711949	−	0.702231i	$-0.247813\pi$
$137$	62.9889	+	36.3666i	0.459773	+	0.265450i	−0.252176	+	0.967681i	$0.581146\pi$
$138$	−7.31581	−	5.54421i	−0.0530131	−	0.0401755i
$139$	21.6096	−	12.4763i	0.155465	−	0.0897578i	−0.420249	−	0.907409i	$-0.638057\pi$
$139$	21.6096	−	12.4763i	0.155465	−	0.0897578i	0.575714	+	0.817651i	$0.304724\pi$
$140$	−30.0709	+	17.3614i	−0.214792	+	0.124010i
$141$	−120.318	+	50.6850i	−0.853320	+	0.359468i
$142$	−10.4191	−	6.01547i	−0.0733740	−	0.0423625i
$143$	−206.291			−1.44260
$144$	137.185	+	35.0003i	0.952674	+	0.243057i
$145$	−5.99198			−0.0413240
$146$	−1.77972	+	3.08257i	−0.0121899	+	0.0211135i
$147$	116.124	+	14.5799i	0.789958	+	0.0991831i
$148$	214.971	−	124.114i	1.45251	−	0.838606i
$149$	18.2046	−	10.5104i	0.122179	−	0.0705398i	−0.437665	−	0.899138i	$-0.644194\pi$
$149$	18.2046	−	10.5104i	0.122179	−	0.0705398i	0.559844	+	0.828598i	$0.310861\pi$
$150$	0.972773	−	7.74779i	0.00648516	−	0.0516519i
$151$	−121.688	+	210.770i	−0.805882	+	1.39583i	0.109811	+	0.993952i	$0.464975\pi$
$151$	−121.688	+	210.770i	−0.805882	+	1.39583i	−0.915694	+	0.401877i	$0.868358\pi$
$152$			10.8272i			0.0712313i
$153$	−130.067	+	80.5707i	−0.850109	+	0.526606i
$154$	5.77671			0.0375111
$155$	−105.434	−	60.8722i	−0.680218	−	0.392724i
$156$	−78.3439	−	185.976i	−0.502204	−	1.19215i
$157$	−22.7702	−	39.4391i	−0.145033	−	0.251205i	0.784352	−	0.620316i	$-0.212996\pi$
$157$	−22.7702	−	39.4391i	−0.145033	−	0.251205i	−0.929385	+	0.369111i	$0.879662\pi$
$158$	0.562099	+	0.973584i	0.00355759	+	0.00616192i
$159$	−159.801	−	121.103i	−1.00503	−	0.761656i
$160$	17.0774	+	9.85963i	0.106734	+	0.0616227i
$161$			64.5328i			0.400825i
$162$	12.1342	−	0.291196i	0.0749022	−	0.00179750i
$163$			157.251i			0.964732i	0.875970	+	0.482366i	$0.160222\pi$
$163$			157.251i			0.964732i	−0.875970	+	0.482366i	$0.839778\pi$
$164$	−124.453	+	215.559i	−0.758861	+	1.31439i
$165$	−61.0519	+	80.5603i	−0.370011	+	0.488244i
$166$	1.07363	+	1.85958i	0.00646764	+	0.0112023i
$167$	46.0342	+	79.7336i	0.275654	+	0.477447i	0.970300	−	0.241905i	$-0.0777722\pi$
$167$	46.0342	+	79.7336i	0.275654	+	0.477447i	−0.694646	+	0.719352i	$0.744439\pi$
$168$	4.40006	+	10.4450i	0.0261908	+	0.0621728i
$169$	−58.5063	+	101.336i	−0.346191	+	0.599621i
$170$	−6.76089	+	1.95003i	−0.0397699	+	0.0114708i
$171$	−22.0407	−	78.4788i	−0.128893	−	0.458940i
$172$	111.955			0.650903
$173$	22.7265	−	39.3635i	0.131367	−	0.227535i	−0.792837	−	0.609434i	$-0.791397\pi$
$173$	22.7265	−	39.3635i	0.131367	−	0.227535i	0.924204	+	0.381900i	$0.124730\pi$
$174$	−0.121484	+	0.967580i	−0.000698187	+	0.00556081i
$175$	−47.5419	+	27.4483i	−0.271668	+	0.156848i
$176$	95.9437	+	166.179i	0.545135	+	0.944201i
$177$	−29.5679	+	235.498i	−0.167050	+	1.33050i
$178$	−8.65978	+	14.9992i	−0.0486505	+	0.0842651i
$179$			294.556i			1.64556i	0.568357	+	0.822782i	$0.307579\pi$
$179$			294.556i			1.64556i	−0.568357	+	0.822782i	$0.692421\pi$
$180$	−95.8125	−	24.4448i	−0.532292	−	0.135804i
$181$		−	279.929i		−	1.54657i	−0.634058	−	0.773285i	$-0.718612\pi$
$181$		−	279.929i		−	1.54657i	0.634058	−	0.773285i	$-0.281388\pi$
$182$	4.00456	−	6.93610i	0.0220031	−	0.0381104i
$183$	209.266	−	88.1549i	1.14353	−	0.481721i
$184$	21.1392	−	12.2047i	0.114887	−	0.0663299i
$185$	−149.287	+	86.1911i	−0.806958	+	0.465898i
$186$	−11.9672	+	15.7912i	−0.0643398	+	0.0848989i
$187$	−201.284	−	49.8536i	−1.07639	−	0.266597i
$188$		−	173.100i		−	0.920746i
$189$	−53.1559	−	66.7519i	−0.281248	−	0.353184i
$190$		−	3.74889i		−	0.0197310i
$191$	247.642	+	142.976i	1.29656	+	0.748567i	0.979808	−	0.199942i	$-0.0640755\pi$
$191$	247.642	+	142.976i	1.29656	+	0.748567i	0.316749	+	0.948510i	$0.397409\pi$
$192$	−112.079	+	147.892i	−0.583743	+	0.770272i
$193$	−121.814	+	70.3291i	−0.631159	+	0.364400i	−0.781201	−	0.624280i	$-0.785392\pi$
$193$	−121.814	+	70.3291i	−0.631159	+	0.364400i	0.150042	+	0.988680i	$0.452059\pi$
$194$	0.863965	+	1.49643i	0.00445343	+	0.00771356i
$195$	54.4061	+	129.151i	0.279006	+	0.662315i
$196$	−77.5857	+	134.382i	−0.395845	+	0.685624i
$197$	347.281			1.76285			0.881423	−	0.472327i	$-0.156586\pi$
$197$	347.281			1.76285			0.881423	+	0.472327i	$0.156586\pi$
$198$	11.7710	+	11.4919i	0.0594496	+	0.0580400i
$199$		−	55.1047i		−	0.276908i	−0.990369	−	0.138454i	$-0.955787\pi$
$199$		−	55.1047i		−	0.276908i	0.990369	−	0.138454i	$-0.0442133\pi$
$200$	17.9826	+	10.3823i	0.0899131	+	0.0519114i
$201$	63.5793	+	7.98269i	0.316315	+	0.0397149i
$202$	5.56647	+	9.64141i	0.0275568	+	0.0477298i
$203$	5.93726	−	3.42788i	0.0292476	−	0.0168861i
$204$	−31.4983	−	200.394i	−0.154403	−	0.982326i
$205$	86.4269	−	149.696i	0.421595	−	0.730223i
$206$		−	1.38830i		−	0.00673931i
$207$	−128.379	+	131.496i	−0.620186	+	0.635248i
$208$	266.042			1.27905
$209$	55.2401	−	95.6786i	0.264307	−	0.457792i
$210$	−1.52352	−	3.61658i	−0.00725484	−	0.0172218i
$211$	285.929	−	165.081i	1.35511	−	0.782374i	0.366152	−	0.930555i	$-0.380675\pi$
$211$	285.929	−	165.081i	1.35511	−	0.782374i	0.988960	+	0.148181i	$0.0473419\pi$
$212$	230.223	−	132.920i	1.08596	−	0.626979i
$213$	−145.480	+	191.966i	−0.683003	+	0.901250i
$214$	−5.91263	−	3.41366i	−0.0276291	−	0.0159517i
$215$	−77.7477			−0.361617
$216$	−11.8130	+	30.0368i	−0.0546898	+	0.139059i
$217$	139.294			0.641910
$218$	−11.8766	+	20.5710i	−0.0544800	+	0.0943622i
$219$	56.7946	+	43.0412i	0.259336	+	0.196535i
$220$	−67.0088	−	116.063i	−0.304585	−	0.527558i
$221$	−199.394	+	207.122i	−0.902236	+	0.937204i
$222$	10.8913	+	25.8543i	0.0490601	+	0.116461i
$223$	−1.03255	+	1.78843i	−0.00463026	+	0.00801984i	−0.868331	−	0.495985i	$-0.834807\pi$
$223$	−1.03255	+	1.78843i	−0.00463026	+	0.00801984i	0.863701	+	0.504005i	$0.168141\pi$
$224$	−22.5619			−0.100723
$225$	−151.479	−	38.6471i	−0.673240	−	0.171765i
$226$		−	8.27629i		−	0.0366208i
$227$	99.7577	−	172.785i	0.439461	−	0.761169i	−0.558187	−	0.829715i	$-0.688503\pi$
$227$	99.7577	−	172.785i	0.439461	−	0.761169i	0.997648	+	0.0685463i	$0.0218361\pi$
$228$	107.235	+	13.4639i	0.470328	+	0.0590520i
$229$	69.4180	+	120.235i	0.303135	+	0.525046i	0.976844	−	0.213951i	$-0.0686332\pi$
$229$	69.4180	+	120.235i	0.303135	+	0.525046i	−0.673709	+	0.738997i	$0.735300\pi$
$230$	−7.31941	+	4.22587i	−0.0318235	+	0.0183733i
$231$	14.4075	−	114.751i	0.0623703	−	0.496757i
$232$	−2.24575	−	1.29659i	−0.00967997	−	0.00558873i
$233$	−325.344			−1.39633			−0.698164	−	0.715938i	$-0.745999\pi$
$233$	−325.344			−1.39633			−0.698164	+	0.715938i	$0.745999\pi$
$234$	21.9583	−	6.16697i	0.0938389	−	0.0263546i
$235$			120.210i			0.511532i
$236$	−272.526	−	157.343i	−1.15477	−	0.666708i
$237$	20.7416	−	8.73756i	0.0875171	−	0.0368674i
$238$	5.58357	−	5.79997i	0.0234604	−	0.0243696i
$239$	147.606	−	85.2204i	0.617598	−	0.356571i	−0.158335	−	0.987385i	$-0.550613\pi$
$239$	147.606	−	85.2204i	0.617598	−	0.356571i	0.775933	+	0.630815i	$0.217279\pi$
$240$	78.7350	−	103.894i	0.328063	−	0.432891i
$241$	−20.3122	−	11.7272i	−0.0842829	−	0.0486607i	0.457266	−	0.889330i	$-0.348829\pi$
$241$	−20.3122	−	11.7272i	−0.0842829	−	0.0486607i	−0.541549	+	0.840669i	$0.682162\pi$
$242$			4.16445i			0.0172085i
$243$	24.4790	−	241.764i	0.100737	−	0.994913i
$244$			301.068i			1.23389i
$245$	53.8796	−	93.3222i	0.219917	−	0.380907i
$246$	−22.4205	−	16.9911i	−0.0911402	−	0.0690697i
$247$	−76.5875	−	132.654i	−0.310071	−	0.537059i
$248$	−26.3439	−	45.6290i	−0.106225	−	0.183988i
$249$	39.6171	−	16.6891i	0.159105	−	0.0670243i
$250$	−15.1879	−	8.76875i	−0.0607517	−	0.0350750i
$251$		−	335.935i		−	1.33839i	−0.743088	−	0.669194i	$-0.766640\pi$
$251$		−	335.935i		−	1.33839i	0.743088	−	0.669194i	$-0.233360\pi$
$252$	108.922	−	30.5906i	0.432229	−	0.121391i
$253$	−249.073			−0.984479
$254$	−21.3982	−	12.3542i	−0.0842447	−	0.0486387i
$255$	21.8741	+	139.165i	0.0857807	+	0.545743i
$256$	−120.875	−	209.362i	−0.472168	−	0.817819i
$257$	−46.1536	+	26.6468i	−0.179586	+	0.103684i	−0.587098	−	0.809516i	$-0.699730\pi$
$257$	−46.1536	+	26.6468i	−0.179586	+	0.103684i	0.407512	+	0.913200i	$0.366396\pi$
$258$	−1.57630	+	12.5546i	−0.00610967	+	0.0486613i
$259$	98.6159	−	170.808i	0.380756	−	0.659489i
$260$	−185.809			−0.714648
$261$	18.9174	+	4.82643i	0.0724805	+	0.0184921i
$262$		−	0.00964885i		−	3.68277e-5i
$263$	43.3604	+	25.0342i	0.164869	+	0.0951869i	0.580164	−	0.814500i	$-0.302988\pi$
$263$	43.3604	+	25.0342i	0.164869	+	0.0951869i	−0.415295	+	0.909687i	$0.636322\pi$
$264$	−40.3140	+	16.9826i	−0.152705	+	0.0643281i
$265$	−159.879	+	92.3064i	−0.603318	+	0.348326i
$266$	2.14466	+	3.71465i	0.00806261	+	0.0139649i
$267$	276.352	+	209.430i	1.03502	+	0.784383i
$268$	−42.4792	+	73.5761i	−0.158504	+	0.274538i
$269$	299.181			1.11220			0.556098	−	0.831117i	$-0.312298\pi$
$269$	299.181			1.11220			0.556098	+	0.831117i	$0.312298\pi$
$270$	4.09024	−	10.4002i	0.0151490	−	0.0385193i
$271$	−159.041			−0.586868			−0.293434	−	0.955979i	$-0.594798\pi$
$271$	−159.041			−0.586868			−0.293434	+	0.955979i	$0.594798\pi$
$272$	259.584	+	64.2932i	0.954354	+	0.236372i
$273$	−127.794	−	96.8473i	−0.468109	−	0.354752i
$274$	−5.44945	−	9.43873i	−0.0198885	−	0.0344479i
$275$	−105.941	−	183.494i	−0.385238	−	0.667253i
$276$	−94.5912	−	224.544i	−0.342722	−	0.813566i
$277$	−175.498	−	101.324i	−0.633567	−	0.365790i	0.148565	−	0.988903i	$-0.452535\pi$
$277$	−175.498	−	101.324i	−0.633567	−	0.365790i	−0.782132	+	0.623112i	$0.785868\pi$
$278$	−3.73909			−0.0134500
$279$	283.836	+	277.106i	1.01733	+	0.993211i
$280$	10.4356			0.0372702
$281$	−368.933	−	213.003i	−1.31293	−	0.758019i	−0.330348	−	0.943859i	$-0.607166\pi$
$281$	−368.933	−	213.003i	−1.31293	−	0.758019i	−0.982580	+	0.185840i	$0.940499\pi$
$282$	19.4114	+	2.43720i	0.0688347	+	0.00864254i
$283$	−402.896	+	232.612i	−1.42366	+	0.821950i	−0.996609	−	0.0822775i	$-0.973781\pi$
$283$	−402.896	+	232.612i	−1.42366	+	0.821950i	−0.427050	+	0.904228i	$0.640447\pi$
$284$	−159.674	−	276.564i	−0.562234	−	0.973818i
$285$	−74.4695	−	9.35001i	−0.261296	−	0.0328071i
$286$	26.7708	+	15.4561i	0.0936042	+	0.0540424i
$287$			197.771i			0.689099i
$288$	−45.9736	−	44.8835i	−0.159630	−	0.155846i
$289$	−244.609	+	153.908i	−0.846396	+	0.532553i
$290$	0.777590	+	0.448942i	0.00268135	+	0.00154808i
$291$	31.8805	−	13.4299i	0.109555	−	0.0461510i
$292$	−81.8236	+	47.2409i	−0.280218	+	0.161784i
$293$	302.277	−	174.519i	1.03166	−	0.595630i	0.114201	−	0.993458i	$-0.463569\pi$
$293$	302.277	−	174.519i	1.03166	−	0.595630i	0.917460	+	0.397828i	$0.130236\pi$
$294$	−13.9772	−	10.5925i	−0.0475415	−	0.0360289i
$295$	189.257	+	109.267i	0.641548	+	0.370398i
$296$	−74.6024			−0.252035
$297$	257.638	−	205.162i	0.867467	−	0.690782i
$298$	−3.14992			−0.0105702
$299$	−172.664	+	299.062i	−0.577470	+	1.00021i
$300$	125.190	−	165.194i	0.417301	−	0.550645i
$301$	77.0376	−	44.4777i	0.255939	−	0.147766i
$302$	31.5834	−	18.2347i	0.104581	−	0.0603797i
$303$	205.404	−	86.5282i	0.677901	−	0.285572i
$304$	−71.2399	+	123.391i	−0.234342	+	0.405892i
$305$		−	209.078i		−	0.685500i
$306$	22.9156	−	0.710716i	0.0748877	−	0.00232260i
$307$	171.450			0.558468			0.279234	−	0.960223i	$-0.409920\pi$
$307$	171.450			0.558468			0.279234	+	0.960223i	$0.409920\pi$
$308$	132.794	+	76.6684i	0.431148	+	0.248923i
$309$	−27.5777	−	3.46251i	−0.0892482	−	0.0112055i
$310$	9.12155	+	15.7990i	0.0294244	+	0.0509645i
$311$	−213.902	−	370.488i	−0.687786	−	1.19128i	−0.972552	−	0.232684i	$-0.925249\pi$
$311$	−213.902	−	370.488i	−0.687786	−	1.19128i	0.284766	−	0.958597i	$-0.408084\pi$
$312$	−7.55562	+	60.1778i	−0.0242167	+	0.192878i
$313$	303.815	+	175.407i	0.970654	+	0.560407i	0.899436	−	0.437053i	$-0.143978\pi$
$313$	303.815	+	175.407i	0.970654	+	0.560407i	0.0712184	+	0.997461i	$0.477311\pi$
$314$			6.82412i			0.0217329i
$315$	−75.6410	+	21.2437i	−0.240130	+	0.0674404i
$316$			29.8407i			0.0944324i
$317$	85.4313	−	147.971i	0.269499	−	0.466787i	−0.699233	−	0.714894i	$-0.746475\pi$
$317$	85.4313	−	147.971i	0.269499	−	0.466787i	0.968733	+	0.248107i	$0.0798084\pi$
$318$	11.6641	+	27.6886i	0.0366795	+	0.0870712i
$319$	13.2304	+	22.9156i	0.0414745	+	0.0718359i
$320$	85.4278	+	147.965i	0.266962	+	0.462391i
$321$	−82.5568	+	108.937i	−0.257186	+	0.339367i
$322$	4.83504	−	8.37454i	0.0150157	−	0.0260079i
$323$	−42.6707	−	147.942i	−0.132108	−	0.458025i
$324$	282.802	+	154.350i	0.872844	+	0.476390i
$325$	−293.762			−0.903884
$326$	11.7819	−	20.4068i	0.0361407	−	0.0625975i
$327$	379.008	+	287.228i	1.15905	+	0.878373i
$328$	64.7844	−	37.4033i	0.197513	−	0.114034i
$329$	−68.7694	−	119.112i	−0.209025	−	0.362043i
$330$	13.9587	−	5.88022i	0.0422990	−	0.0178188i
$331$	277.160	−	480.056i	0.837343	−	1.45032i	−0.0547661	−	0.998499i	$-0.517441\pi$
$331$	277.160	−	480.056i	0.837343	−	1.45032i	0.892109	−	0.451821i	$-0.149225\pi$
$332$			56.9967i			0.171677i
$333$	540.743	−	151.867i	1.62385	−	0.456058i
$334$		−	13.7962i		−	0.0413061i
$335$	29.4998	−	51.0951i	0.0880590	−	0.152523i
$336$	−18.5806	+	147.988i	−0.0552993	+	0.440439i
$337$	−475.857	+	274.736i	−1.41204	+	0.815242i	−0.995580	−	0.0939126i	$-0.970063\pi$
$337$	−475.857	+	274.736i	−1.41204	+	0.815242i	−0.416460	+	0.909154i	$0.636729\pi$
$338$	15.1849	−	8.76702i	0.0449258	−	0.0259379i
$339$	−164.404	−	20.6417i	−0.484966	−	0.0608899i
$340$	−181.298	−	44.9035i	−0.533231	−	0.132069i
$341$			537.626i			1.57661i
$342$	−3.01966	+	11.8357i	−0.00882942	+	0.0346073i
$343$			278.153i			0.810942i
$344$	−29.1393	−	16.8236i	−0.0847072	−	0.0489057i
$345$	65.6891	+	155.935i	0.190403	+	0.451987i
$346$	−5.89852	+	3.40551i	−0.0170477	+	0.00984252i
$347$	−255.193	−	442.007i	−0.735426	−	1.27380i	−0.954536	−	0.298095i	$-0.903649\pi$
$347$	−255.193	−	442.007i	−0.735426	−	1.27380i	0.219110	−	0.975700i	$-0.429685\pi$
$348$	−15.6344	+	20.6301i	−0.0449263	+	0.0592820i
$349$	69.4543	−	120.298i	0.199010	−	0.344695i	−0.749198	−	0.662346i	$-0.769561\pi$
$349$	69.4543	−	120.298i	0.199010	−	0.344695i	0.948208	+	0.317651i	$0.102894\pi$
$350$	8.22613			0.0235032
$351$	−67.7376	−	451.569i	−0.192985	−	1.28652i
$352$		−	87.0806i		−	0.247388i
$353$	257.287	+	148.545i	0.728859	+	0.420807i	0.818005	−	0.575212i	$-0.195080\pi$
$353$	257.287	+	148.545i	0.728859	+	0.420807i	−0.0891457	+	0.996019i	$0.528414\pi$
$354$	21.4815	−	28.3456i	0.0606821	−	0.0800724i
$355$	110.886	+	192.061i	0.312356	+	0.541016i
$356$	−398.138	+	229.865i	−1.11836	+	0.645688i
$357$	−101.287	−	125.380i	−0.283717	−	0.351204i
$358$	22.0692	−	38.2250i	0.0616459	−	0.106774i
$359$		−	251.878i		−	0.701611i	−0.936448	−	0.350805i	$-0.885908\pi$
$359$		−	251.878i		−	0.701611i	0.936448	−	0.350805i	$-0.114092\pi$
$360$	21.2644	+	20.7602i	0.0590677	+	0.0576672i
$361$	−278.967			−0.772760
$362$	−20.9733	+	36.3269i	−0.0579374	+	0.100351i
$363$	82.7243	+	10.3864i	0.227891	+	0.0286128i
$364$	184.111	−	106.297i	0.505801	−	0.292024i
$365$	56.8226	−	32.8065i	0.155678	−	0.0898810i
$366$	−33.7616	−	4.23894i	−0.0922449	−	0.0115818i
$367$	−409.800	−	236.598i	−1.11662	−	0.644681i	−0.176084	−	0.984375i	$-0.556343\pi$
$367$	−409.800	−	236.598i	−1.11662	−	0.644681i	−0.940536	+	0.339694i	$0.889676\pi$
$368$	321.215			0.872867
$369$	−393.437	+	402.992i	−1.06623	+	1.09212i
$370$	25.8310			0.0698136
$371$	105.613	−	182.927i	0.284670	−	0.493064i
$372$	−484.680	+	204.176i	−1.30290	+	0.548859i
$373$	171.228	+	296.575i	0.459055	+	0.795107i	0.998911	−	0.0466504i	$-0.0148547\pi$
$373$	171.228	+	296.575i	0.459055	+	0.795107i	−0.539856	+	0.841757i	$0.681521\pi$
$374$	22.3858	+	21.5505i	0.0598550	+	0.0576218i
$375$	−212.066	+	279.829i	−0.565508	+	0.746210i
$376$	−26.0119	+	45.0538i	−0.0691805	+	0.119824i
$377$	36.6864			0.0973115
$378$	1.89683	+	12.6451i	0.00501808	+	0.0334528i
$379$		−	144.860i		−	0.382216i	−0.981569	−	0.191108i	$-0.938792\pi$
$379$		−	144.860i		−	0.382216i	0.981569	−	0.191108i	$-0.0612081\pi$
$380$	49.7552	−	86.1786i	0.130935	−	0.226786i
$381$	−298.778	+	394.249i	−0.784194	+	1.03477i
$382$	−21.4246	−	37.1086i	−0.0560855	−	0.0971429i
$383$	188.695	−	108.943i	0.492677	−	0.284447i	−0.233007	−	0.972475i	$-0.574857\pi$
$383$	188.695	−	108.943i	0.492677	−	0.284447i	0.725684	+	0.688028i	$0.241523\pi$
$384$	104.573	−	44.0524i	0.272326	−	0.114720i
$385$	−92.2189	−	53.2426i	−0.239530	−	0.138292i
$386$	21.0773			0.0546044
$387$	245.459	+	62.6243i	0.634260	+	0.161820i
$388$			45.8661i			0.118212i
$389$	65.1167	+	37.5951i	0.167395	+	0.0966456i	0.581357	−	0.813649i	$-0.302522\pi$
$389$	65.1167	+	37.5951i	0.167395	+	0.0966456i	−0.413962	+	0.910294i	$0.635855\pi$
$390$	2.61613	−	20.8365i	0.00670801	−	0.0534269i
$391$	−240.746	+	250.076i	−0.615718	+	0.639581i
$392$	40.3874	−	23.3177i	0.103029	−	0.0594839i
$393$	−0.191669	−	0.0240649i	−0.000487706	−	6.12339e-5i
$394$	−45.0672	−	26.0196i	−0.114384	−	0.0660395i
$395$		−	20.7229i		−	0.0524631i
$396$	118.068	+	420.398i	0.298153	+	1.06161i
$397$		−	547.908i		−	1.38012i	−0.723752	−	0.690060i	$-0.757584\pi$
$397$		−	547.908i		−	1.38012i	0.723752	−	0.690060i	$-0.242416\pi$
$398$	−4.12865	+	7.15104i	−0.0103735	+	0.0179674i
$399$	79.1382	−	33.3377i	0.198341	−	0.0835531i
$400$	136.625	+	236.642i	0.341563	+	0.591605i
$401$	352.711	+	610.913i	0.879577	+	1.52347i	0.851805	+	0.523858i	$0.175508\pi$
$401$	352.711	+	610.913i	0.879577	+	1.52347i	0.0277720	+	0.999614i	$0.491159\pi$
$402$	−7.65270	−	5.79953i	−0.0190366	−	0.0144267i
$403$	645.527	+	372.695i	1.60180	+	0.924802i
$404$			295.512i			0.731467i
$405$	−196.392	−	107.189i	−0.484919	−	0.264664i
$406$	−1.02732			−0.00253034
$407$	659.255	+	380.621i	1.61979	+	0.935187i
$408$	−21.9151	+	56.8911i	−0.0537135	+	0.139439i
$409$	281.335	+	487.286i	0.687860	+	1.19141i	0.972529	+	0.232783i	$0.0747832\pi$
$409$	281.335	+	487.286i	0.687860	+	1.19141i	−0.284668	+	0.958626i	$0.591883\pi$
$410$	−22.4315	+	12.9509i	−0.0547111	+	0.0315875i
$411$	−201.086	+	84.7092i	−0.489260	+	0.206105i
$412$	18.4255	−	31.9138i	0.0447220	−	0.0774607i
$413$	−250.037			−0.605417
$414$	26.5121	−	7.44591i	0.0640389	−	0.0179853i
$415$		−	39.5815i		−	0.0953772i
$416$	−104.558	−	60.3664i	−0.251340	−	0.145111i
$417$	−9.32557	+	74.2748i	−0.0223635	+	0.178117i
$418$	−14.3372	+	8.27759i	−0.0342995	+	0.0198028i
$419$	300.580	+	520.620i	0.717375	+	1.24253i	0.962036	+	0.272921i	$0.0879897\pi$
$419$	300.580	+	520.620i	0.717375	+	1.24253i	−0.244662	+	0.969608i	$0.578677\pi$
$420$	12.9770	−	103.357i	0.0308976	−	0.246088i
$421$	167.946	−	290.891i	0.398921	−	0.690952i	−0.594672	−	0.803969i	$-0.702718\pi$
$421$	167.946	−	290.891i	0.398921	−	0.690952i	0.993593	+	0.113017i	$0.0360513\pi$
$422$	−49.4739			−0.117237
$423$	96.8269	−	379.517i	0.228905	−	0.897204i
$424$	−79.8955			−0.188433
$425$	−286.632	−	70.9923i	−0.674428	−	0.167041i
$426$	33.2620	−	14.0119i	0.0780798	−	0.0328918i
$427$	119.608	+	207.168i	0.280113	+	0.485171i
$428$	−90.6120	−	156.945i	−0.211710	−	0.366693i
$429$	373.795	−	493.237i	0.871317	−	1.14974i
$430$	10.0895	+	5.82515i	0.0234638	+	0.0135469i
$431$	−260.303			−0.603952			−0.301976	−	0.953316i	$-0.597646\pi$
$431$	−260.303			−0.603952			−0.301976	+	0.953316i	$0.597646\pi$
$432$	−332.260	+	264.586i	−0.769121	+	0.612467i
$433$	−11.2018			−0.0258703			−0.0129351	−	0.999916i	$-0.504118\pi$
$433$	−11.2018			−0.0258703			−0.0129351	+	0.999916i	$0.504118\pi$
$434$	−18.0765	−	10.4365i	−0.0416509	−	0.0240471i
$435$	10.8573	−	14.3267i	0.0249594	−	0.0329349i
$436$	−546.035	+	315.253i	−1.25237	+	0.723058i
$437$	−92.4706	−	160.164i	−0.211603	−	0.366508i
$438$	−4.14552	−	9.84080i	−0.00946466	−	0.0224676i
$439$	214.805	+	124.018i	0.489305	+	0.282500i	0.724286	−	0.689500i	$-0.242170\pi$
$439$	214.805	+	124.018i	0.489305	+	0.282500i	−0.234981	+	0.972000i	$0.575503\pi$
$440$			40.2778i			0.0915404i
$441$	−245.274	+	251.230i	−0.556176	+	0.569683i
$442$	41.3941	−	11.9392i	0.0936518	−	0.0270118i
$443$	−713.529	−	411.956i	−1.61067	−	0.929923i	−0.989214	−	0.146478i	$-0.953206\pi$
$443$	−713.529	−	411.956i	−1.61067	−	0.929923i	−0.621461	−	0.783445i	$-0.713460\pi$
$444$	−92.7701	+	738.881i	−0.208942	+	1.66415i
$445$	276.488	−	159.630i	0.621321	−	0.358720i
$446$	0.267991	−	0.154725i	0.000600877	−	0.000346916i
$447$	−7.85614	+	62.5714i	−0.0175753	+	0.139981i
$448$	−169.295	−	97.7425i	−0.377891	−	0.218175i
$449$	−124.936			−0.278253			−0.139126	−	0.990275i	$-0.544429\pi$
$449$	−124.936			−0.278253			−0.139126	+	0.990275i	$0.544429\pi$
$450$	16.7621	+	16.3647i	0.0372491	+	0.0363660i
$451$	−763.325			−1.69252
$452$	109.843	−	190.253i	0.243015	−	0.420914i
$453$	−283.450	−	672.864i	−0.625717	−	1.48535i
$454$	−25.8915	+	14.9484i	−0.0570296	+	0.0329261i
$455$	−127.857	+	73.8181i	−0.281004	+	0.162238i
$456$	−25.8874	−	19.6185i	−0.0567707	−	0.0430231i
$457$	433.428	−	750.719i	0.948419	−	1.64271i	0.199663	−	0.979865i	$-0.436015\pi$
$457$	433.428	−	750.719i	0.948419	−	1.64271i	0.748756	−	0.662846i	$-0.230651\pi$
$458$		−	20.8042i		−	0.0454241i
$459$	43.0354	−	456.978i	0.0937589	−	0.995595i
$460$	−224.342			−0.487701
$461$	251.349	+	145.116i	0.545225	+	0.314786i	0.747194	−	0.664606i	$-0.231401\pi$
$461$	251.349	+	145.116i	0.545225	+	0.314786i	−0.201969	+	0.979392i	$0.564734\pi$
$462$	−10.4673	+	13.8120i	−0.0226564	+	0.0298960i
$463$	175.796	+	304.487i	0.379689	+	0.657640i	0.991017	−	0.133737i	$-0.0426978\pi$
$463$	175.796	+	304.487i	0.379689	+	0.657640i	−0.611328	+	0.791377i	$0.709364\pi$
$464$	−17.0624	−	29.5530i	−0.0367724	−	0.0636917i
$465$	336.587	−	141.790i	0.723844	−	0.304925i
$466$	42.2205	+	24.3760i	0.0906019	+	0.0523090i
$467$		−	394.357i		−	0.844447i	−0.906492	−	0.422224i	$-0.861250\pi$
$467$		−	394.357i		−	0.844447i	0.906492	−	0.422224i	$-0.138750\pi$
$468$	586.620	+	149.665i	1.25346	+	0.319798i
$469$			67.5046i			0.143933i
$470$	9.00658	−	15.5999i	0.0191629	−	0.0331912i
$471$	135.557	+	17.0198i	0.287807	+	0.0361355i
$472$	47.2880	+	81.9052i	0.100186	+	0.173528i
$473$	171.668	+	297.337i	0.362933	+	0.628619i
$474$	−3.34632	−	0.420147i	−0.00705975	−	0.000886386i
$475$	78.6628	−	136.248i	0.165606	−	0.286838i
$476$	205.331	−	59.2232i	0.431367	−	0.124419i
$477$	579.109	−	162.642i	1.21407	−	0.340969i
$478$	−25.5401			−0.0534312
$479$	−172.631	+	299.005i	−0.360398	+	0.624227i	−0.988026	−	0.154286i	$-0.950692\pi$
$479$	−172.631	+	299.005i	−0.360398	+	0.624227i	0.627628	+	0.778513i	$0.284026\pi$
$480$	−54.5179	+	22.9661i	−0.113579	+	0.0478461i
$481$	914.024	−	527.712i	1.90026	−	1.09711i
$482$	1.75730	+	3.04373i	0.00364584	+	0.00631479i
$483$	−154.296	−	116.932i	−0.319454	−	0.242095i
$484$	−55.2705	+	95.7313i	−0.114195	+	0.197792i
$485$		−	31.8519i		−	0.0656739i
$486$	−21.2905	+	29.5401i	−0.0438077	+	0.0607820i
$487$			592.593i			1.21682i	0.793622	+	0.608412i	$0.208193\pi$
$487$			592.593i			1.21682i	−0.793622	+	0.608412i	$0.791807\pi$
$488$	45.2416	−	78.3608i	0.0927082	−	0.160575i
$489$	−375.984	−	284.936i	−0.768882	−	0.582690i
$490$	−13.9841	+	8.07373i	−0.0285390	+	0.0164770i
$491$	107.710	−	62.1865i	0.219369	−	0.126653i	−0.386289	−	0.922378i	$-0.626243\pi$
$491$	107.710	−	62.1865i	0.219369	−	0.126653i	0.605658	+	0.795725i	$0.292910\pi$
$492$	−289.890	−	688.152i	−0.589208	−	1.39868i
$493$	35.7959	+	8.86584i	0.0726084	+	0.0179835i
$494$			22.9529i			0.0464634i
$495$	−81.9930	−	291.947i	−0.165642	−	0.589791i
$496$		−	693.344i		−	1.39787i
$497$	−219.747	−	126.871i	−0.442147	−	0.255274i
$498$	−6.39159	−	0.802496i	−0.0128345	−	0.00161144i
$499$	272.670	−	157.426i	0.546434	−	0.315484i	−0.201249	−	0.979540i	$-0.564500\pi$
$499$	272.670	−	157.426i	0.546434	−	0.315484i	0.747682	+	0.664056i	$0.231167\pi$
$500$	−232.757	−	403.147i	−0.465514	−	0.806295i
$501$	−274.054	−	34.4088i	−0.547014	−	0.0686802i
$502$	−25.1695	+	43.5949i	−0.0501385	+	0.0868425i
$503$	−158.607			−0.315323			−0.157661	−	0.987493i	$-0.550395\pi$
$503$	−158.607			−0.315323			−0.157661	+	0.987493i	$0.550395\pi$
$504$	−32.9466	−	8.40572i	−0.0653702	−	0.0166780i
$505$		−	205.220i		−	0.406375i
$506$	32.3227	+	18.6615i	0.0638788	+	0.0368804i
$507$	−136.279	−	323.505i	−0.268795	−	0.638077i
$508$	−327.930	−	567.992i	−0.645532	−	1.11809i
$509$	−575.309	+	332.155i	−1.13027	+	0.652563i	−0.944003	−	0.329936i	$-0.892973\pi$
$509$	−575.309	+	332.155i	−1.13027	+	0.652563i	−0.186269	+	0.982499i	$0.559640\pi$
$510$	7.58809	−	19.6985i	0.0148786	−	0.0386245i
$511$	−37.5357	+	65.0138i	−0.0734555	+	0.127229i
$512$			187.523i			0.366256i
$513$	227.578	+	89.5029i	0.443621	+	0.174470i
$514$	7.98591			0.0155368
$515$	−12.7956	+	22.1626i	−0.0248458	+	0.0430343i
$516$	−202.860	+	267.682i	−0.393140	+	0.518764i
$517$	459.729	−	265.425i	0.889224	−	0.513394i
$518$	−25.5951	+	14.7773i	−0.0494114	+	0.0285277i
$519$	52.9371	+	125.664i	0.101998	+	0.242127i
$520$	48.3615	+	27.9215i	0.0930029	+	0.0536953i
$521$	924.333			1.77415			0.887076	−	0.461624i	$-0.152733\pi$
$521$	924.333			1.77415			0.887076	+	0.461624i	$0.152733\pi$
$522$	−2.09333	−	2.04370i	−0.00401021	−	0.00391513i
$523$	−619.916			−1.18531			−0.592654	−	0.805457i	$-0.701920\pi$
$523$	−619.916			−1.18531			−0.592654	+	0.805457i	$0.701920\pi$
$524$	0.128059	−	0.221805i	0.000244388	−	0.000423293i
$525$	20.5166	−	163.407i	0.0390792	−	0.311252i
$526$	−3.75131	−	6.49745i	−0.00713176	−	0.0123526i
$527$	539.790	+	519.650i	1.02427	+	0.986054i
$528$	−571.178	−	71.7142i	−1.08178	−	0.135822i
$529$	56.0286	−	97.0444i	0.105914	−	0.183449i
$530$	27.6638			0.0521958
$531$	−509.493	−	497.413i	−0.959496	−	0.936747i
$532$			113.855i			0.214014i
$533$	−529.156	+	916.525i	−0.992788	+	1.71956i
$534$	−20.1713	−	47.8834i	−0.0377740	−	0.0896694i
$535$	62.9257	+	108.991i	0.117618	+	0.203721i
$536$	22.1126	−	12.7667i	0.0412549	−	0.0238185i
$537$	−704.275	−	533.728i	−1.31150	−	0.993907i
$538$	−38.8252	−	22.4157i	−0.0721658	−	0.0416649i
$539$	−475.867			−0.882869
$540$	232.057	−	184.792i	0.429735	−	0.342207i
$541$		−	757.243i		−	1.39971i	−0.714285	−	0.699855i	$-0.753248\pi$
$541$		−	757.243i		−	1.39971i	0.714285	−	0.699855i	$-0.246752\pi$
$542$	20.6390	+	11.9160i	0.0380794	+	0.0219852i
$543$	669.303	+	507.225i	1.23260	+	0.934116i
$544$	−87.4312	−	84.1691i	−0.160719	−	0.154723i
$545$	379.195	−	218.928i	0.695771	−	0.401704i
$546$	9.32786	+	22.1428i	0.0170840	+	0.0405546i
$547$	670.522	+	387.126i	1.22582	+	0.707726i	0.966152	−	0.257972i	$-0.0830544\pi$
$547$	670.522	+	387.126i	1.22582	+	0.707726i	0.259666	+	0.965699i	$0.416388\pi$
$548$		−	289.300i		−	0.527920i
$549$	−168.408	+	660.083i	−0.306754	+	1.20234i
$550$			31.7499i			0.0577270i
$551$	−9.82377	+	17.0153i	−0.0178290	+	0.0308807i
$552$	−9.12254	+	72.6577i	−0.0165263	+	0.131626i
$553$	11.8551	+	20.5337i	0.0214378	+	0.0371314i
$554$	15.1831	+	26.2979i	0.0274064	+	0.0474692i
$555$	64.4245	−	513.118i	0.116080	−	0.924537i
$556$	−85.9533	−	49.6252i	−0.154592	−	0.0892539i
$557$		−	375.595i		−	0.674318i	−0.941448	−	0.337159i	$-0.890534\pi$
$557$		−	375.595i		−	0.674318i	0.941448	−	0.337159i	$-0.109466\pi$
$558$	−16.0720	−	57.2265i	−0.0288029	−	0.102557i
$559$	476.017			0.851550
$560$	118.929	+	68.6639i	0.212374	+	0.122614i
$561$	483.920	−	390.931i	0.862603	−	0.696847i
$562$	31.9180	+	55.2836i	0.0567936	+	0.0983695i
$563$	−267.021	+	154.165i	−0.474283	+	0.273827i	−0.718031	−	0.696011i	$-0.754956\pi$
$563$	−267.021	+	154.165i	−0.474283	+	0.273827i	0.243748	+	0.969839i	$0.421623\pi$
$564$	413.878	+	313.653i	0.733826	+	0.556123i
$565$	−76.2807	+	132.122i	−0.135010	+	0.233844i
$566$	69.7126			0.123167
$567$	255.919	−	6.14155i	0.451356	−	0.0108317i
$568$			95.9774i			0.168974i
$569$	127.010	+	73.3291i	0.223216	+	0.128874i	0.607438	−	0.794367i	$-0.292197\pi$
$569$	127.010	+	73.3291i	0.223216	+	0.128874i	−0.384223	+	0.923240i	$0.625531\pi$
$570$	8.96350	+	6.79290i	0.0157254	+	0.0119174i
$571$	−431.255	+	248.985i	−0.755262	+	0.436051i	−0.827592	−	0.561330i	$-0.810290\pi$
$571$	−431.255	+	248.985i	−0.755262	+	0.436051i	0.0723301	+	0.997381i	$0.476956\pi$
$572$	410.267	+	710.603i	0.717250	+	1.24231i
$573$	−790.574	+	333.036i	−1.37971	+	0.581215i
$574$	14.8178	−	25.6651i	0.0258149	−	0.0447128i
$575$	−354.684			−0.616842
$576$	−150.522	−	535.954i	−0.261324	−	0.930476i
$577$	442.364			0.766662			0.383331	−	0.923611i	$-0.374777\pi$
$577$	442.364			0.766662			0.383331	+	0.923611i	$0.374777\pi$
$578$	43.2746	−	1.64590i	0.0748696	−	0.00284758i
$579$	52.5683	−	418.688i	0.0907915	−	0.723122i
$580$	11.9167	+	20.6403i	0.0205460	+	0.0355868i
$581$	22.6437	+	39.2200i	0.0389736	+	0.0675043i
$582$	−5.14341	−	0.645780i	−0.00883747	−	0.00110959i
$583$	706.030	+	407.626i	1.21103	+	0.699188i
$584$	28.3956			0.0486226
$585$	−407.380	−	103.936i	−0.696376	−	0.177668i
$586$	−52.3026			−0.0892536
$587$	−396.514	−	228.928i	−0.675492	−	0.389996i	0.122662	−	0.992448i	$-0.460857\pi$
$587$	−396.514	−	228.928i	−0.675492	−	0.389996i	−0.798155	+	0.602453i	$0.794190\pi$
$588$	−180.721	−	429.003i	−0.307349	−	0.729597i
$589$	−345.714	+	199.598i	−0.586951	+	0.338877i
$590$	−16.3734	−	28.3596i	−0.0277516	−	0.0480672i
$591$	−629.264	+	830.338i	−1.06474	+	1.40497i
$592$	−850.203	−	490.865i	−1.43615	−	0.829164i
$593$			578.833i			0.976109i	0.872813	+	0.488055i	$0.162293\pi$
$593$			578.833i			0.976109i	−0.872813	+	0.488055i	$0.837707\pi$
$594$	−48.8056	+	7.32109i	−0.0821644	+	0.0123251i
$595$	−142.593	+	41.1278i	−0.239651	+	0.0691223i
$596$	−72.4097	−	41.8057i	−0.121493	−	0.0701439i
$597$	131.754	+	99.8484i	0.220693	+	0.167250i
$598$	44.8137	−	25.8732i	0.0749393	−	0.0432662i
$599$	−432.584	+	249.752i	−0.722176	+	0.416949i	−0.815553	−	0.578682i	$-0.803567\pi$
$599$	−432.584	+	249.752i	−0.722176	+	0.416949i	0.0933770	+	0.995631i	$0.470234\pi$
$600$	−57.4078	+	24.1835i	−0.0956796	+	0.0403059i
$601$	−720.962	−	416.247i	−1.19960	−	0.692591i	−0.239136	−	0.970986i	$-0.576864\pi$
$601$	−720.962	−	416.247i	−1.19960	−	0.692591i	−0.960467	+	0.278395i	$0.910198\pi$
$602$	−13.3297			−0.0221424
$603$	−134.290	+	137.552i	−0.222704	+	0.228112i
$604$	968.041			1.60272
$605$	38.3828	−	66.4809i	0.0634426	−	0.109886i
$606$	−33.1387	−	4.16072i	−0.0546843	−	0.00686588i
$607$	945.923	−	546.129i	1.55836	−	0.899718i	0.560942	−	0.827855i	$-0.310439\pi$
$607$	945.923	−	546.129i	1.55836	−	0.899718i	0.997415	−	0.0718628i	$-0.0228944\pi$
$608$	55.9962	−	32.3294i	0.0920990	−	0.0531734i
$609$	−2.56220	+	20.4070i	−0.00420723	+	0.0335091i
$610$	−15.6649	+	27.1324i	−0.0256801	+	0.0444793i
$611$		−	735.995i		−	1.20458i
$612$	536.212	+	287.798i	0.876163	+	0.470259i
$613$	53.8085			0.0877790			0.0438895	−	0.999036i	$-0.486025\pi$
$613$	53.8085			0.0877790			0.0438895	+	0.999036i	$0.486025\pi$
$614$	−22.2493	−	12.8456i	−0.0362367	−	0.0209212i
$615$	201.315	+	477.889i	0.327342	+	0.777056i
$616$	−23.0420	−	39.9099i	−0.0374058	−	0.0647888i
$617$	−70.0923	−	121.403i	−0.113602	−	0.196764i	0.803618	−	0.595145i	$-0.202905\pi$
$617$	−70.0923	−	121.403i	−0.113602	−	0.196764i	−0.917220	+	0.398381i	$0.869572\pi$
$618$	3.31938	+	2.51556i	0.00537116	+	0.00407049i
$619$	274.717	+	158.608i	0.443807	+	0.256232i	0.705211	−	0.708997i	$-0.250852\pi$
$619$	274.717	+	158.608i	0.443807	+	0.256232i	−0.261404	+	0.965230i	$0.584185\pi$
$620$			484.244i			0.781039i
$621$	−81.7853	−	545.218i	−0.131699	−	0.877967i
$622$			64.1052i			0.103063i
$623$	−182.642	+	316.345i	−0.293165	+	0.507776i
$624$	−482.062	+	636.099i	−0.772535	+	1.01939i
$625$	−55.4880	−	96.1080i	−0.0887807	−	0.153773i
$626$	−26.2844	−	45.5259i	−0.0419878	−	0.0727250i
$627$	128.671	+	305.445i	0.205217	+	0.487153i
$628$	−90.5695	+	156.871i	−0.144219	+	0.249795i
$629$	1019.37	−	294.015i	1.62062	−	0.467432i
$630$	11.4077	+	2.91047i	0.0181075	+	0.00461980i
$631$	−152.848			−0.242232			−0.121116	−	0.992638i	$-0.538647\pi$
$631$	−152.848			−0.242232			−0.121116	+	0.992638i	$0.538647\pi$
$632$	4.48417	−	7.76681i	0.00709520	−	0.0122893i
$633$	−123.392	+	982.770i	−0.194931	+	1.55256i
$634$	−22.1731	+	12.8017i	−0.0349734	+	0.0201919i
$635$	227.732	+	394.444i	0.358633	+	0.621171i
$636$	−99.3522	+	791.305i	−0.156214	+	1.24419i
$637$	−329.882	+	571.373i	−0.517869	+	0.896975i
$638$		−	3.96507i		−	0.00621484i
$639$	−195.380	−	695.676i	−0.305759	−	1.08869i
$640$		−	104.479i		−	0.163249i
$641$	318.805	−	552.187i	0.497356	−	0.861447i	−0.502639	−	0.864496i	$-0.667637\pi$
$641$	318.805	−	552.187i	0.497356	−	0.861447i	0.999995	+	0.00304989i	$0.000970811\pi$
$642$	18.8755	−	7.95146i	0.0294011	−	0.0123855i
$643$	−121.948	+	70.4067i	−0.189655	+	0.109497i	−0.591821	−	0.806069i	$-0.701591\pi$
$643$	−121.948	+	70.4067i	−0.189655	+	0.109497i	0.402166	+	0.915567i	$0.368257\pi$
$644$	222.293	−	128.341i	0.345176	−	0.199288i
$645$	140.877	−	185.893i	0.218414	−	0.288205i
$646$	−5.54693	+	22.3958i	−0.00858657	+	0.0346684i
$647$			997.613i			1.54191i	0.636892	+	0.770953i	$0.280220\pi$
$647$			997.613i			1.54191i	−0.636892	+	0.770953i	$0.719780\pi$
$648$	−50.4122	−	82.6704i	−0.0777966	−	0.127578i
$649$		−	965.053i		−	1.48698i
$650$	38.1221	+	22.0098i	0.0586493	+	0.0338612i
$651$	−252.398	+	333.049i	−0.387708	+	0.511596i
$652$	541.677	−	312.737i	0.830793	−	0.479658i
$653$	−327.153	−	566.646i	−0.501000	−	0.867758i	−0.999999	−	0.00115542i	$-0.999632\pi$
$653$	−327.153	−	566.646i	−0.501000	−	0.867758i	0.498999	−	0.866603i	$-0.333701\pi$
$654$	−27.6644	−	65.6708i	−0.0423003	−	0.100414i
$655$	−0.0889312	+	0.154033i	−0.000135773	+	0.000235165i
$656$	984.416			1.50063
$657$	−205.821	+	57.8046i	−0.313274	+	0.0879827i
$658$			20.6098i			0.0313219i
$659$	−63.6237	−	36.7332i	−0.0965459	−	0.0557408i	0.450950	−	0.892549i	$-0.351085\pi$
$659$	−63.6237	−	36.7332i	−0.0965459	−	0.0557408i	−0.547496	+	0.836809i	$0.684419\pi$
$660$	398.921	+	50.0865i	0.604425	+	0.0758886i
$661$	559.494	+	969.071i	0.846435	+	1.46607i	0.884369	+	0.466788i	$0.154589\pi$
$661$	559.494	+	969.071i	0.846435	+	1.46607i	−0.0379339	+	0.999280i	$0.512078\pi$
$662$	−71.9352	+	41.5318i	−0.108663	+	0.0627368i
$663$	−133.926	−	852.046i	−0.202000	−	1.28514i
$664$	8.56492	−	14.8349i	0.0128990	−	0.0223417i
$665$		−	79.0671i		−	0.118898i
$666$	−81.5516	−	20.8064i	−0.122450	−	0.0312409i
$667$	44.2946			0.0664087
$668$	183.103	−	317.144i	0.274107	−	0.474767i
$669$	−2.40512	−	5.70937i	−0.00359510	−	0.00853419i
$670$	−7.65647	+	4.42047i	−0.0114276	+	0.00659771i
$671$	−799.592	+	461.645i	−1.19164	+	0.687995i
$672$	40.8815	−	53.9448i	0.0608356	−	0.0802750i
$673$	−505.859	−	292.058i	−0.751648	−	0.433964i	0.0746413	−	0.997210i	$-0.476219\pi$
$673$	−505.859	−	292.058i	−0.751648	−	0.433964i	−0.826289	+	0.563246i	$0.809552\pi$
$674$	82.3371			0.122162
$675$	366.880	−	292.154i	0.543526	−	0.432821i
$676$	465.423			0.688496
$677$	−533.325	+	923.745i	−0.787776	+	1.36447i	0.139550	+	0.990215i	$0.455434\pi$
$677$	−533.325	+	923.745i	−0.787776	+	1.36447i	−0.927326	+	0.374254i	$0.877899\pi$
$678$	19.7884	+	14.9964i	0.0291864	+	0.0221186i
$679$	18.2217	+	31.5609i	0.0268361	+	0.0464815i
$680$	40.4400	+	38.9311i	0.0594705	+	0.0572516i
$681$	232.367	+	551.601i	0.341214	+	0.809986i
$682$	40.2809	−	69.7686i	0.0590629	−	0.102300i
$683$	−1096.38			−1.60524			−0.802621	−	0.596489i	$-0.796562\pi$
$683$	−1096.38			−1.60524			−0.802621	+	0.596489i	$0.796562\pi$
$684$	−226.498	+	231.999i	−0.331138	+	0.339180i
$685$			200.905i			0.293292i
$686$	20.8403	−	36.0964i	0.0303794	−	0.0526186i
$687$	−413.263	−	51.8872i	−0.601548	−	0.0755273i
$688$	−221.390	−	383.458i	−0.321787	−	0.557352i
$689$	978.874	−	565.153i	1.42072	−	0.820252i
$690$	3.15867	−	25.1577i	0.00457778	−	0.0364604i
$691$	−450.025	−	259.822i	−0.651267	−	0.376009i	0.137675	−	0.990478i	$-0.456037\pi$
$691$	−450.025	−	259.822i	−0.651267	−	0.376009i	−0.788941	+	0.614468i	$0.789371\pi$
$692$	−180.792			−0.261259
$693$	248.260	+	242.374i	0.358240	+	0.349746i
$694$			76.4800i			0.110202i
$695$	59.6905	+	34.4623i	0.0858857	+	0.0495861i
$696$	7.16935	−	3.02015i	0.0103008	−	0.00433930i
$697$	−737.804	+	766.399i	−1.05854	+	1.09957i
$698$	−18.0264	+	10.4076i	−0.0258258	+	0.0149105i
$699$	589.516	−	777.889i	0.843370	−	1.11286i
$700$	189.100	+	109.177i	0.270143	+	0.155967i
$701$			926.951i			1.32233i	0.750242	+	0.661163i	$0.229937\pi$
$701$			926.951i			1.32233i	−0.750242	+	0.661163i	$0.770063\pi$
$702$	−25.0428	+	63.6761i	−0.0356736	+	0.0907067i
$703$			565.236i			0.804034i
$704$	377.250	−	653.417i	0.535867	−	0.928149i
$705$	−287.419	−	217.817i	−0.407686	−	0.308961i
$706$	−22.2591	−	38.5538i	−0.0315284	−	0.0546088i
$707$	117.401	+	203.345i	0.166056	+	0.287617i
$708$	870.013	−	366.501i	1.22883	−	0.517656i
$709$	865.153	+	499.496i	1.22024	+	0.704508i	0.964970	−	0.262361i	$-0.0845010\pi$
$709$	865.153	+	499.496i	1.22024	+	0.704508i	0.255274	+	0.966869i	$0.417834\pi$
$710$		−	33.2321i		−	0.0468058i
$711$	−16.6919	+	65.4247i	−0.0234767	+	0.0920179i
$712$	138.168			0.194056
$713$	779.400	+	449.987i	1.09313	+	0.631117i
$714$	3.75028	+	23.8596i	0.00525249	+	0.0334168i
$715$	−284.911	−	493.480i	−0.398477	−	0.690182i
$716$	1014.64	−	585.805i	1.41710	−	0.818163i
$717$	−63.6989	+	507.339i	−0.0888409	+	0.707586i
$718$	−18.8717	+	32.6867i	−0.0262836	+	0.0455246i
$719$	−659.825			−0.917698			−0.458849	−	0.888514i	$-0.651738\pi$
$719$	−659.825			−0.917698			−0.458849	+	0.888514i	$0.651738\pi$
$720$	105.742	+	376.506i	0.146863	+	0.522926i
$721$		−	29.2803i		−	0.0406107i
$722$	36.2020	+	20.9012i	0.0501412	+	0.0289491i
$723$	64.8446	−	27.3164i	0.0896883	−	0.0377820i
$724$	−964.260	+	556.716i	−1.33185	+	0.768944i
$725$	18.8402	+	32.6322i	0.0259865	+	0.0450100i
$726$	−9.95708	−	7.54588i	−0.0137150	−	0.0103938i
$727$	−373.310	+	646.592i	−0.513494	+	0.889398i	0.486383	+	0.873746i	$0.338316\pi$
$727$	−373.310	+	646.592i	−0.513494	+	0.889398i	−0.999877	+	0.0156524i	$0.995017\pi$
$728$	−63.8931			−0.0877652
$729$	533.695	+	496.599i	0.732092	+	0.681206i
$730$	−9.83196			−0.0134684
$731$	464.462	+	115.037i	0.635379	+	0.157369i
$732$	−719.845	−	545.528i	−0.983395	−	0.745256i
$733$	−333.459	−	577.568i	−0.454924	−	0.787951i	0.543760	−	0.839241i	$-0.317000\pi$
$733$	−333.459	−	577.568i	−0.454924	−	0.787951i	−0.998684	+	0.0512897i	$0.983667\pi$
$734$	35.4536	+	61.4074i	0.0483019	+	0.0836613i
$735$	125.502	+	297.922i	0.170751	+	0.405336i
$736$	−126.241	−	72.8854i	−0.171523	−	0.0990291i
$737$	−260.543			−0.353518
$738$	81.2507	−	22.8192i	0.110096	−	0.0309203i
$739$	−1026.55			−1.38911			−0.694554	−	0.719440i	$-0.744398\pi$
$739$	−1026.55			−1.38911			−0.694554	+	0.719440i	$0.744398\pi$
$740$	593.797	+	342.829i	0.802429	+	0.463282i
$741$	455.946	+	57.2462i	0.615311	+	0.0772553i
$742$	−27.4111	+	15.8258i	−0.0369422	+	0.0213286i
$743$	−609.448	−	1055.59i	−0.820253	−	1.42072i	−0.905494	−	0.424359i	$-0.860500\pi$
$743$	−609.448	−	1055.59i	−0.820253	−	1.42072i	0.0852417	−	0.996360i	$-0.472834\pi$
$744$	156.832	+	19.6910i	0.210796	+	0.0264665i
$745$	50.2851	+	29.0321i	0.0674968	+	0.0389693i
$746$		−	51.3161i		−	0.0687883i
$747$	−31.8822	+	124.964i	−0.0426803	+	0.167287i
$748$	228.580	+	792.502i	0.305588	+	1.05949i
$749$	−124.702	−	71.9968i	−0.166491	−	0.0961238i
$750$	48.4859	−	20.4251i	0.0646479	−	0.0272335i
$751$	−84.1112	+	48.5616i	−0.111999	+	0.0646626i	−0.554953	−	0.831882i	$-0.687264\pi$
$751$	−84.1112	+	48.5616i	−0.111999	+	0.0646626i	0.442954	+	0.896544i	$0.353930\pi$
$752$	−592.886	+	342.303i	−0.788412	+	0.455190i
$753$	803.212	+	608.706i	1.06668	+	0.808375i
$754$	−4.76086	−	2.74868i	−0.00631414	−	0.00364547i
$755$	−672.259			−0.890409
$756$	−124.222	+	315.858i	−0.164315	+	0.417802i
$757$	−183.164			−0.241960			−0.120980	−	0.992655i	$-0.538604\pi$
$757$	−183.164			−0.241960			−0.120980	+	0.992655i	$0.538604\pi$
$758$	−10.8535	+	18.7987i	−0.0143185	+	0.0248004i
$759$	451.314	−	595.527i	0.594617	−	0.784620i
$760$	−25.9002	+	14.9535i	−0.0340792	+	0.0196756i
$761$	−926.306	+	534.803i	−1.21722	+	0.702764i	−0.964323	−	0.264729i	$-0.914717\pi$
$761$	−926.306	+	534.803i	−1.21722	+	0.702764i	−0.252899	+	0.967493i	$0.581384\pi$
$762$	68.3116	−	28.7768i	0.0896477	−	0.0377649i
$763$	−250.488	+	433.858i	−0.328293	+	0.568621i
$764$		−	1137.39i		−	1.48873i
$765$	−372.374	−	199.862i	−0.486763	−	0.261258i
$766$	−32.6498			−0.0426237
$767$	−1158.74	−	668.998i	−1.51074	−	0.872227i
$768$	719.600	+	90.3493i	0.936979	+	0.117642i
$769$	−316.206	−	547.685i	−0.411192	−	0.712205i	0.583829	−	0.811877i	$-0.301554\pi$
$769$	−316.206	−	547.685i	−0.411192	−	0.712205i	−0.995020	+	0.0996721i	$0.968221\pi$
$770$	7.97827	+	13.8188i	0.0103614	+	0.0179465i
$771$	19.9175	−	158.635i	0.0258333	−	0.205753i
$772$	484.519	+	279.737i	0.627616	+	0.362354i
$773$			7.38633i			0.00955541i	0.999989	+	0.00477771i	$0.00152080\pi$
$773$			7.38633i			0.00955541i	−0.999989	+	0.00477771i	$0.998479\pi$
$774$	−27.1616	−	26.5175i	−0.0350924	−	0.0342604i
$775$			765.588i			0.987855i
$776$	6.89232	−	11.9379i	0.00888186	−	0.0153838i
$777$	229.707	+	545.287i	0.295633	+	0.701785i
$778$	−5.63353	−	9.75757i	−0.00724105	−	0.0125419i
$779$	−283.391	−	490.848i	−0.363789	−	0.630100i
$780$	336.681	−	444.263i	0.431642	−	0.569568i
$781$	489.676	−	848.144i	0.626986	−	1.08597i
$782$	49.9786	−	14.4153i	0.0639113	−	0.0184338i
$783$	−45.8177	+	36.4856i	−0.0585156	+	0.0465972i
$784$	613.697			0.782777
$785$	62.8963	−	108.940i	0.0801226	−	0.138776i
$786$	0.0230701	+	0.0174835i	2.93513e−5	+	2.22436e-5i
$787$	363.589	−	209.918i	0.461994	−	0.266732i	−0.250888	−	0.968016i	$-0.580723\pi$
$787$	363.589	−	209.918i	0.461994	−	0.266732i	0.712882	+	0.701284i	$0.247389\pi$
$788$	−690.663	−	1196.26i	−0.876475	−	1.51810i
$789$	−138.424	+	58.3123i	−0.175442	+	0.0739066i
$790$	−1.55264	+	2.68925i	−0.00196537	+	0.00340411i
$791$		−	174.554i		−	0.220675i
$792$	32.4430	−	127.162i	0.0409634	−	0.160558i
$793$			1280.09i			1.61424i
$794$	−41.0513	+	71.1029i	−0.0517019	+	0.0895503i
$795$	68.9954	−	549.524i	0.0867867	−	0.691225i
$796$	−189.817	+	109.591i	−0.238463	+	0.137677i
$797$	1351.72	−	780.418i	1.69601	−	0.979194i	0.746545	−	0.665335i	$-0.231711\pi$
$797$	1351.72	−	780.418i	1.69601	−	0.979194i	0.949470	−	0.313859i	$-0.101622\pi$
$798$	−12.7677	−	1.60305i	−0.0159996	−	0.00200883i
$799$	177.865	−	718.130i	0.222609	−	0.898786i
$800$		−	124.004i		−	0.155005i
$801$	−1001.48	+	281.266i	−1.25029	+	0.351144i
$802$		−	105.706i		−	0.131802i
$803$	−250.930	−	144.874i	−0.312490	−	0.180416i
$804$	−98.9471	−	234.884i	−0.123069	−	0.292145i
$805$	−154.372	+	89.1269i	−0.191767	+	0.110717i
$806$	−55.8475	−	96.7306i	−0.0692896	−	0.120013i
$807$	−542.108	+	715.332i	−0.671757	+	0.886409i
$808$	44.4068	−	76.9148i	0.0549589	−	0.0951916i
$809$	474.700			0.586774			0.293387	−	0.955994i	$-0.405218\pi$
$809$	474.700			0.586774			0.293387	+	0.955994i	$0.405218\pi$
$810$	17.4552	+	28.6246i	0.0215496	+	0.0353390i
$811$		−	291.146i		−	0.358997i	−0.983758	−	0.179498i	$-0.942553\pi$
$811$		−	291.146i		−	0.358997i	0.983758	−	0.179498i	$-0.0574475\pi$
$812$	−23.6157	−	13.6345i	−0.0290834	−	0.0167913i
$813$	288.179	−	380.263i	0.354463	−	0.467728i
$814$	−57.0351	−	98.7878i	−0.0700677	−	0.121361i
$815$	−376.169	+	217.181i	−0.461557	+	0.266480i
$816$	−624.084	+	504.161i	−0.764809	+	0.617845i
$817$	−127.466	+	220.778i	−0.156017	+	0.270230i
$818$		−	84.3147i		−	0.103074i
$819$	463.118	−	130.066i	0.565468	−	0.158811i
$820$	−687.534			−0.838456
$821$	−88.4256	+	153.158i	−0.107705	+	0.186550i	−0.914840	−	0.403816i	$-0.867683\pi$
$821$	−88.4256	+	153.158i	−0.107705	+	0.186550i	0.807135	+	0.590367i	$0.201017\pi$
$822$	32.4420	+	4.07325i	0.0394672	+	0.00495530i
$823$	38.5079	−	22.2325i	0.0467896	−	0.0270140i	−0.476423	−	0.879216i	$-0.658067\pi$
$823$	38.5079	−	22.2325i	0.0467896	−	0.0270140i	0.523212	+	0.852202i	$0.324733\pi$
$824$	−9.59141	+	5.53760i	−0.0116401	+	0.00672039i
$825$	630.692	+	79.1865i	0.764475	+	0.0959836i
$826$	32.4478	+	18.7337i	0.0392830	+	0.0226801i
$827$	900.292			1.08862			0.544312	−	0.838883i	$-0.316791\pi$
$827$	900.292			1.08862			0.544312	+	0.838883i	$0.316791\pi$
$828$	708.276	+	180.704i	0.855405	+	0.218241i
$829$	−537.393			−0.648242			−0.324121	−	0.946016i	$-0.605069\pi$
$829$	−537.393			−0.648242			−0.324121	+	0.946016i	$0.605069\pi$
$830$	−2.96560	+	5.13656i	−0.00357301	+	0.00618863i
$831$	560.261	−	236.015i	0.674201	−	0.284013i
$832$	−523.038	−	905.929i	−0.628652	−	1.08886i
$833$	−459.956	+	477.783i	−0.552168	+	0.573569i
$834$	6.77515	−	8.94007i	0.00812368	−	0.0107195i
$835$	−127.157	+	220.242i	−0.152283	+	0.263763i
$836$	−439.440			−0.525646
$837$	−1176.86	+	176.534i	−1.40604	+	0.210913i
$838$		−	90.0823i		−	0.107497i
$839$	519.335	−	899.515i	0.618993	−	1.07213i	−0.370677	−	0.928762i	$-0.620874\pi$
$839$	519.335	−	899.515i	0.618993	−	1.07213i	0.989670	−	0.143366i	$-0.0457925\pi$
$840$	−18.9091	+	24.9513i	−0.0225109	+	0.0297040i
$841$	418.147	+	724.252i	0.497202	+	0.861180i
$842$	−43.5893	+	25.1663i	−0.0517687	+	0.0298887i
$843$	1177.78	−	496.151i	1.39713	−	0.588554i
$844$	−1137.29	−	656.617i	−1.34750	−	0.777982i
$845$	−323.214			−0.382502
$846$	−41.0002	+	41.9960i	−0.0484636	+	0.0496406i
$847$			87.8316i			0.103697i
$848$	−910.526	−	525.692i	−1.07373	−	0.619920i
$849$	173.868	−	1384.80i	0.204792	−	1.63109i
$850$	31.8777	+	30.6883i	0.0375032	+	0.0361039i
$851$	1103.58	−	637.151i	1.29680	−	0.748709i
$852$	950.583	+	119.350i	1.11571	+	0.140083i
$853$	−197.058	−	113.771i	−0.231017	−	0.133378i	0.380024	−	0.924977i	$-0.375916\pi$
$853$	−197.058	−	113.771i	−0.231017	−	0.133378i	−0.611041	+	0.791599i	$0.709249\pi$
$854$		−	35.8461i		−	0.0419743i
$855$	157.292	−	161.112i	0.183968	−	0.188436i
$856$			54.4652i			0.0636276i
$857$	467.534	−	809.793i	0.545547	−	0.944916i	−0.453025	−	0.891498i	$-0.649655\pi$
$857$	467.534	−	809.793i	0.545547	−	0.944916i	0.998572	−	0.0534180i	$-0.0170116\pi$
$858$	−85.4632	+	36.0021i	−0.0996075	+	0.0419605i
$859$	−264.570	−	458.248i	−0.307997	−	0.533467i	0.669927	−	0.742427i	$-0.266325\pi$
$859$	−264.570	−	458.248i	−0.307997	−	0.533467i	−0.977924	+	0.208960i	$0.932992\pi$
$860$	154.622	+	267.814i	0.179794	+	0.311412i
$861$	−472.866	−	358.357i	−0.549205	−	0.416210i
$862$	33.7800	+	19.5029i	0.0391880	+	0.0226252i
$863$		−	271.514i		−	0.314616i	−0.987550	−	0.157308i	$-0.949718\pi$
$863$		−	271.514i		−	0.314616i	0.987550	−	0.157308i	$-0.0502815\pi$
$864$	190.618	−	28.5937i	0.220623	−	0.0330945i
$865$	125.551			0.145146
$866$	1.45368	+	0.839284i	0.00167862	+	0.000969150i
$867$	75.2352	−	863.730i	0.0867765	−	0.996228i
$868$	−277.025	−	479.821i	−0.319153	−	0.552790i
$869$	−79.2524	+	45.7564i	−0.0911995	+	0.0526541i
$870$	−2.48238	+	1.04572i	−0.00285331	+	0.00120198i
$871$	−180.615	+	312.834i	−0.207365	+	0.359166i
$872$	189.493			0.217308
$873$	−25.6561	+	100.560i	−0.0293884	+	0.115189i
$874$			27.7130i			0.0317082i
$875$	−320.325	−	184.940i	−0.366086	−	0.211360i
$876$	35.3107	−	281.237i	0.0403090	−	0.321047i
$877$	88.4609	−	51.0729i	0.100868	−	0.0582359i	−0.448718	−	0.893674i	$-0.648119\pi$
$877$	88.4609	−	51.0729i	0.100868	−	0.0582359i	0.549585	+	0.835438i	$0.314786\pi$
$878$	−18.5837	−	32.1880i	−0.0211660	−	0.0366605i
$879$	−130.446	+	1038.96i	−0.148403	+	1.18198i
$880$	−265.017	+	459.024i	−0.301156	+	0.521618i
$881$	1034.23			1.17392			0.586961	−	0.809615i	$-0.300324\pi$
$881$	1034.23			1.17392			0.586961	+	0.809615i	$0.300324\pi$
$882$	50.6527	−	14.2258i	0.0574294	−	0.0161290i
$883$	823.510			0.932628			0.466314	−	0.884619i	$-0.345582\pi$
$883$	823.510			0.932628			0.466314	+	0.884619i	$0.345582\pi$
$884$	1110.01	+	274.926i	1.25567	+	0.311002i
$885$	−604.183	+	254.517i	−0.682693	+	0.287590i
$886$	61.7306	+	106.921i	0.0696733	+	0.120678i
$887$	−496.209	−	859.460i	−0.559424	−	0.968952i	−0.997545	−	0.0700351i	$-0.977689\pi$
$887$	−496.209	−	859.460i	−0.559424	−	0.968952i	0.438120	−	0.898916i	$-0.355644\pi$
$888$	135.178	−	178.372i	0.152227	−	0.200870i
$889$	−451.304	−	260.561i	−0.507654	−	0.293094i
$890$	−47.8404			−0.0537533
$891$	23.7041	+	987.754i	0.0266040	+	1.10859i
$892$	8.21401			0.00920853
$893$	341.357	+	197.082i	0.382259	+	0.220697i
$894$	5.70759	−	7.53138i	0.00638432	−	0.00842436i
$895$	−704.622	+	406.814i	−0.787288	+	0.454541i
$896$	59.7702	+	103.525i	0.0667078	+	0.115541i
$897$	−402.187	−	954.727i	−0.448369	−	1.06436i
$898$	16.2131	+	9.36064i	0.0180547	+	0.0104239i
$899$		−	95.6101i		−	0.106352i
$900$	168.131	+	598.653i	0.186813	+	0.665170i
$901$	1091.69	−	314.875i	1.21164	−	0.349473i
$902$	99.0581	+	57.1912i	0.109820	+	0.0634049i
$903$	−33.2453	+	264.787i	−0.0368165	+	0.293230i
$904$	−57.1789	+	33.0123i	−0.0632510	+	0.0365180i
$905$	669.633	−	386.613i	0.739926	−	0.427196i
$906$	−13.6297	+	108.556i	−0.0150438	+	0.119819i
$907$	67.6442	+	39.0544i	0.0745801	+	0.0430589i	0.536826	−	0.843693i	$-0.319623\pi$
$907$	67.6442	+	39.0544i	0.0745801	+	0.0430589i	−0.462246	+	0.886752i	$0.652956\pi$
$908$	−793.581			−0.873988
$909$	−165.300	+	647.902i	−0.181849	+	0.712764i
$910$	22.1229			0.0243109
$911$	−442.812	+	766.974i	−0.486073	+	0.841903i	−0.999872	−	0.0160076i	$-0.994904\pi$
$911$	−442.812	+	766.974i	−0.486073	+	0.841903i	0.513799	+	0.857911i	$0.328238\pi$
$912$	−165.940	−	393.914i	−0.181952	−	0.431924i
$913$	−151.375	+	87.3963i	−0.165799	+	0.0957244i
$914$	−112.493	+	64.9480i	−0.123078	+	0.0710591i
$915$	499.898	+	378.843i	0.546337	+	0.414036i
$916$	276.113	−	478.242i	0.301434	−	0.522098i
$917$		−	0.203502i		−	0.000221922i
$918$	−39.8233	+	56.0785i	−0.0433805	+	0.0610877i
$919$	−11.6428			−0.0126690			−0.00633450	−	0.999980i	$-0.502016\pi$
$919$	−11.6428			−0.0126690			−0.00633450	+	0.999980i	$0.502016\pi$
$920$	58.3910	+	33.7120i	0.0634684	+	0.0366435i
$921$	−310.662	+	409.931i	−0.337310	+	0.445093i
$922$	−21.7453	−	37.6640i	−0.0235849	−	0.0408503i
$923$	−678.911	−	1175.91i	−0.735548	−	1.27401i
$924$	−423.931	+	178.584i	−0.458799	+	0.193273i
$925$	938.790	+	542.011i	1.01491	+	0.585958i
$926$		−	52.6851i		−	0.0568954i
$927$	58.2488	−	59.6635i	0.0628359	−	0.0643619i
$928$			15.4862i			0.0166877i
$929$	207.366	−	359.168i	0.223214	−	0.386618i	−0.732568	−	0.680694i	$-0.761678\pi$
$929$	207.366	−	359.168i	0.223214	−	0.386618i	0.955782	+	0.294076i	$0.0950118\pi$
$930$	−54.3030	−	6.81801i	−0.0583903	−	0.00733119i
$931$	−176.670	−	306.001i	−0.189763	−	0.328680i
$932$	647.036	+	1120.70i	0.694244	+	1.20247i
$933$	1273.41	+	159.883i	1.36486	+	0.171364i
$934$	−29.5467	+	51.1764i	−0.0316346	+	0.0547927i
$935$	−158.738	−	550.355i	−0.169773	−	0.588615i
$936$	−130.193	−	127.106i	−0.139095	−	0.135797i
$937$	434.596			0.463817			0.231908	−	0.972738i	$-0.425503\pi$
$937$	434.596			0.463817			0.231908	+	0.972738i	$0.425503\pi$
$938$	5.05770	−	8.76019i	0.00539200	−	0.00933922i
$939$	−969.899	+	408.578i	−1.03291	+	0.435121i
$940$	414.082	−	239.070i	0.440513	−	0.254330i
$941$	762.435	+	1320.58i	0.810239	+	1.40337i	0.912697	+	0.408637i	$0.133996\pi$
$941$	762.435	+	1320.58i	0.810239	+	1.40337i	−0.102458	+	0.994737i	$0.532671\pi$
$942$	−16.3163	−	12.3651i	−0.0173209	−	0.0131265i
$943$	−638.895	+	1106.60i	−0.677513	+	1.17349i
$944$			1244.57i			1.31840i
$945$	86.2664	−	219.349i	0.0912872	−	0.232115i
$946$		−	51.4479i		−	0.0543847i
$947$	−201.357	+	348.761i	−0.212626	+	0.368280i	−0.952536	−	0.304427i	$-0.901535\pi$
$947$	−201.357	+	348.761i	−0.212626	+	0.368280i	0.739909	+	0.672707i	$0.234868\pi$
$948$	−71.3482	−	54.0705i	−0.0752618	−	0.0570364i
$949$	−347.901	+	200.861i	−0.366598	+	0.211655i
$950$	−20.4164	+	11.7874i	−0.0214910	+	0.0124078i
$951$	198.996	+	472.384i	0.209249	+	0.496724i
$952$	−62.3422	−	15.4408i	−0.0654855	−	0.0162193i
$953$		−	671.106i		−	0.704203i	−0.935962	−	0.352102i	$-0.885467\pi$
$953$		−	671.106i		−	0.704203i	0.935962	−	0.352102i	$-0.114533\pi$
$954$	−87.3378	−	22.2826i	−0.0915490	−	0.0233571i
$955$			789.864i			0.827082i
$956$	−587.110	−	338.968i	−0.614132	−	0.354569i
$957$	−78.7637	−	9.88917i	−0.0823027	−	0.0103335i
$958$	44.8051	−	25.8683i	0.0467695	−	0.0270024i
$959$	−114.933	−	199.070i	−0.119847	−	0.207581i
$960$	−508.574	−	63.8539i	−0.529764	−	0.0665145i
$961$	490.798	−	850.087i	0.510716	−	0.884586i
$962$	−158.153			−0.164400
$963$	−110.874	−	394.782i	−0.115134	−	0.409950i
$964$			93.2912i			0.0967751i
$965$	−336.476	−	194.264i	−0.348680	−	0.201310i
$966$	11.2623	+	26.7349i	0.0116587	+	0.0276759i
$967$	−409.830	−	709.846i	−0.423816	−	0.734070i	0.572493	−	0.819909i	$-0.305976\pi$
$967$	−409.830	−	709.846i	−0.423816	−	0.734070i	−0.996309	+	0.0858390i	$0.972643\pi$
$968$	28.7712	−	16.6110i	0.0297223	−	0.0171602i
$969$	431.044	+	166.043i	0.444834	+	0.171355i
$970$	−2.38646	+	4.13347i	−0.00246027	+	0.00426131i
$971$			877.715i			0.903929i	0.892036	+	0.451965i	$0.149277\pi$
$971$			877.715i			0.903929i	−0.892036	+	0.451965i	$0.850723\pi$
$972$	−881.477	+	396.492i	−0.906869	+	0.407913i
$973$	−78.8605			−0.0810488
$974$	44.3993	−	76.9018i	0.0455845	−	0.0789546i
$975$	532.290	−	702.378i	0.545939	−	0.720387i
$976$	1031.19	−	595.357i	1.05654	−	0.609996i
$977$	−966.293	+	557.890i	−0.989041	+	0.571023i	−0.904988	−	0.425438i	$-0.860120\pi$
$977$	−966.293	+	557.890i	−0.989041	+	0.571023i	−0.0840537	+	0.996461i	$0.526787\pi$
$978$	27.4436	+	65.1467i	0.0280609	+	0.0666121i
$979$	−1220.98	−	704.930i	−1.24717	−	0.720051i
$980$	−428.617			−0.437365
$981$	−1373.51	+	385.749i	−1.40011	+	0.393220i
$982$	−18.6370			−0.0189786
$983$	546.561	−	946.671i	0.556013	−	0.963043i	−0.441811	−	0.897108i	$-0.645664\pi$
$983$	546.561	−	946.671i	0.556013	−	0.963043i	0.997824	−	0.0659348i	$-0.0210029\pi$
$984$	−27.9575	+	222.672i	−0.0284121	+	0.226292i
$985$	479.633	+	830.748i	0.486937	+	0.843399i
$986$	−3.98104	−	3.83250i	−0.00403756	−	0.00388692i
$987$	409.402	+	51.4024i	0.414794	+	0.0520795i
$988$	−304.630	+	527.635i	−0.308330	+	0.534044i
$989$	574.735			0.581128
$990$	−11.2334	+	44.0296i	−0.0113468	+	0.0444744i
$991$		−	672.370i		−	0.678477i	−0.940700	−	0.339238i	$-0.889831\pi$
$991$		−	672.370i		−	0.678477i	0.940700	−	0.339238i	$-0.110169\pi$
$992$	−157.324	+	272.492i	−0.158592	+	0.274690i
$993$	645.592	+	1532.53i	0.650143	+	1.54334i
$994$	19.0113	+	32.9286i	0.0191261	+	0.0331273i
$995$	131.819	−	76.1056i	0.132481	−	0.0764881i
$996$	−136.278	−	103.277i	−0.136825	−	0.103691i
$997$	−264.679	−	152.813i	−0.265476	−	0.153272i	0.361354	−	0.932429i	$-0.382315\pi$
$997$	−264.679	−	152.813i	−0.265476	−	0.153272i	−0.626830	+	0.779156i	$0.715648\pi$
$998$	−47.1799			−0.0472744
$999$	−616.702	+	1568.08i	−0.617320	+	1.56965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.101.17	yes	68
3.2	odd	2		459.3.i.a.305.18		68
9.4	even	3		459.3.i.a.152.17		68
9.5	odd	6	inner	153.3.i.a.50.18	yes	68
17.16	even	2	inner	153.3.i.a.101.18	yes	68
51.50	odd	2		459.3.i.a.305.17		68
153.50	odd	6	inner	153.3.i.a.50.17	✓	68
153.67	even	6		459.3.i.a.152.18		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.17	✓	68	153.50	odd	6	inner
153.3.i.a.50.18	yes	68	9.5	odd	6	inner
153.3.i.a.101.17	yes	68	1.1	even	1	trivial
153.3.i.a.101.18	yes	68	17.16	even	2	inner
459.3.i.a.152.17		68	9.4	even	3
459.3.i.a.152.18		68	153.67	even	6
459.3.i.a.305.17		68	51.50	odd	2
459.3.i.a.305.18		68	3.2	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.129772 - 0.0749237i) q^{2} +(-1.81198 + 2.39097i) q^{3} +(-1.98877 - 3.44466i) q^{4} +(1.38111 + 2.39215i) q^{5} +(0.414284 - 0.174521i) q^{6} +(-2.73699 - 1.58020i) q^{7} +1.19542i q^{8} +(-2.43349 - 8.66476i) q^{9} -0.413911i q^{10} +(6.09900 - 10.5638i) q^{11} +(11.8397 + 1.48653i) q^{12} +(-8.45595 - 14.6461i) q^{13} +(0.236789 + 0.410131i) q^{14} +(-8.22210 - 1.03233i) q^{15} +(-7.86553 + 13.6235i) q^{16} +(-4.71123 - 16.3341i) q^{17} +(-0.333398 + 1.30677i) q^{18} +9.05723 q^{19} +(5.49342 - 9.51489i) q^{20} +(8.73757 - 3.68078i) q^{21} +(-1.58296 + 0.913920i) q^{22} +(-10.2096 - 17.6835i) q^{23} +(-2.85820 - 2.16606i) q^{24} +(8.68508 - 15.0430i) q^{25} +2.53421i q^{26} +(25.1266 + 9.88192i) q^{27} +12.5706i q^{28} +(-1.08463 + 1.87864i) q^{29} +(0.989651 + 0.749997i) q^{30} +(-38.1700 + 22.0374i) q^{31} +(6.18249 - 3.56946i) q^{32} +(14.2065 + 33.7238i) q^{33} +(-0.612431 + 2.47269i) q^{34} -8.72972i q^{35} +(-25.0075 + 25.6148i) q^{36} +62.4071i q^{37} +(-1.17537 - 0.678602i) q^{38} +(50.3405 + 6.32050i) q^{39} +(-2.85961 + 1.65100i) q^{40} +(-31.2890 - 54.1941i) q^{41} +(-1.40967 - 0.176991i) q^{42} +(-14.0734 + 24.3759i) q^{43} -48.5181 q^{44} +(17.3665 - 17.7883i) q^{45} +3.05976i q^{46} +(37.6889 + 21.7597i) q^{47} +(-18.3212 - 43.4917i) q^{48} +(-19.5059 - 33.7853i) q^{49} +(-2.25415 + 1.30144i) q^{50} +(47.5911 + 18.3326i) q^{51} +(-33.6339 + 58.2557i) q^{52} +66.8350i q^{53} +(-2.52034 - 3.16498i) q^{54} +33.6935 q^{55} +(1.88900 - 3.27184i) q^{56} +(-16.4115 + 21.6556i) q^{57} +(0.281509 - 0.162529i) q^{58} +(68.5161 - 39.5578i) q^{59} +(12.7959 + 30.3754i) q^{60} +(-65.5511 - 37.8459i) q^{61} +6.60451 q^{62} +(-7.03163 + 27.5608i) q^{63} +61.8545 q^{64} +(23.3572 - 40.4558i) q^{65} +(0.683120 - 5.44080i) q^{66} +(-10.6797 - 18.4979i) q^{67} +(-46.8959 + 48.7135i) q^{68} +(60.7803 + 7.63127i) q^{69} +(-0.654064 + 1.13287i) q^{70} +80.2879 q^{71} +(10.3580 - 2.90903i) q^{72} -23.7538i q^{73} +(4.67578 - 8.09868i) q^{74} +(20.2302 + 48.0233i) q^{75} +(-18.0128 - 31.1990i) q^{76} +(-33.3858 + 19.2753i) q^{77} +(-6.05922 - 4.59192i) q^{78} +(-6.49716 - 3.75114i) q^{79} -43.4526 q^{80} +(-69.1562 + 42.1713i) q^{81} +9.37714i q^{82} +(-12.4098 - 7.16481i) q^{83} +(-30.0561 - 22.7777i) q^{84} +(32.5670 - 33.8292i) q^{85} +(3.65266 - 2.10887i) q^{86} +(-2.52645 - 5.99737i) q^{87} +(12.6281 + 7.29084i) q^{88} -115.581i q^{89} +(-3.58644 + 1.00725i) q^{90} +53.4484i q^{91} +(-40.6091 + 70.3370i) q^{92} +(16.4721 - 131.195i) q^{93} +(-3.26063 - 5.64758i) q^{94} +(12.5090 + 21.6663i) q^{95} +(-2.66803 + 21.2499i) q^{96} +(-9.98636 - 5.76563i) q^{97} +5.84583i q^{98} +(-106.375 - 27.1395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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