LMFDB - Embedded newform 153.3.i.a.50.17

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			50.17
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.17

$q$-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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.129772	+	0.0749237i	−0.0648859	+	0.0374619i	−0.532092	−	0.846687i	$-0.678594\pi$
$2$	−0.129772	+	0.0749237i	−0.0648859	+	0.0374619i	0.467206	+	0.884148i	$0.345261\pi$
$3$	−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	−0.694221	−	0.719762i	$-0.744251\pi$
$5$	1.38111	−	2.39215i	0.276222	−	0.478430i	0.970443	+	0.241332i	$0.0775842\pi$
$6$	0.414284	+	0.174521i	0.0690473	+	0.0290868i
$7$	−2.73699	+	1.58020i	−0.390999	+	0.225743i	−0.682593	−	0.730799i	$-0.739148\pi$
$7$	−2.73699	+	1.58020i	−0.390999	+	0.225743i	0.291594	+	0.956542i	$0.405814\pi$
$8$		−	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	0.997946	+	0.0640648i	$0.0204064\pi$
$11$	6.09900	+	10.5638i	0.554455	+	0.960344i	−0.443491	+	0.896279i	$0.646260\pi$
$12$	11.8397	−	1.48653i	0.986640	−	0.123878i
$13$	−8.45595	+	14.6461i	−0.650458	+	1.12663i	0.332554	+	0.943084i	$0.392090\pi$
$13$	−8.45595	+	14.6461i	−0.650458	+	1.12663i	−0.983012	+	0.183542i	$0.941244\pi$
$14$	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	−0.997975	−	0.0636149i	$-0.979737\pi$
$23$	−10.2096	+	17.6835i	−0.443895	+	0.768849i	0.554079	+	0.832464i	$0.313070\pi$
$24$	−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	0.846719	−	0.532040i	$-0.178575\pi$
$29$	−1.08463	−	1.87864i	−0.0374011	−	0.0647807i	−0.884120	+	0.467260i	$0.845241\pi$
$30$	0.989651	−	0.749997i	0.0329884	−	0.0249999i
$31$	−38.1700	−	22.0374i	−1.23129	−	0.710885i	−0.263991	−	0.964525i	$-0.585039\pi$
$31$	−38.1700	−	22.0374i	−1.23129	−	0.710885i	−0.967299	+	0.253640i	$0.918372\pi$
$32$	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	$-0.680586\pi$
$37$		−	62.4071i		−	1.68668i	0.537381	−	0.843340i	$-0.319414\pi$
$38$	−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	0.178076	+	0.984017i	$0.443013\pi$
$41$	−31.2890	+	54.1941i	−0.763145	+	1.32181i	−0.941222	+	0.337790i	$0.890321\pi$
$42$	−1.40967	+	0.176991i	−0.0335635	+	0.00421407i
$43$	−14.0734	−	24.3759i	−0.327289	−	0.566881i	0.654684	−	0.755903i	$-0.272802\pi$
$43$	−14.0734	−	24.3759i	−0.327289	−	0.566881i	−0.981973	+	0.189022i	$0.939468\pi$
$44$	−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	−0.0422410	−	0.999107i	$-0.513450\pi$
$47$	37.6889	−	21.7597i	0.801891	−	0.462972i	0.844132	+	0.536136i	$0.180116\pi$
$48$	−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	$-0.782842\pi$
$53$		−	66.8350i		−	1.26104i	0.776174	−	0.630518i	$-0.217158\pi$
$54$	−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	0.951613	−	0.307299i	$-0.0994252\pi$
$59$	68.5161	+	39.5578i	1.16129	+	0.670471i	0.209678	+	0.977771i	$0.432759\pi$
$60$	12.7959	−	30.3754i	0.213265	−	0.506256i
$61$	−65.5511	+	37.8459i	−1.07461	+	0.620425i	−0.929437	−	0.368981i	$-0.879707\pi$
$61$	−65.5511	+	37.8459i	−1.07461	+	0.620425i	−0.145171	+	0.989407i	$0.546373\pi$
$62$	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	−0.934652	−	0.355563i	$-0.884289\pi$
$67$	−10.6797	+	18.4979i	−0.159399	+	0.276087i	0.775253	+	0.631651i	$0.217622\pi$
$68$	−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	$0.0520193\pi$
$73$			23.7538i			0.325394i	−0.986676	+	0.162697i	$0.947981\pi$
$74$	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	−0.540557	−	0.841307i	$-0.681787\pi$
$79$	−6.49716	+	3.75114i	−0.0822426	+	0.0474828i	0.458315	+	0.888790i	$0.348453\pi$
$80$	−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	−0.572892	−	0.819631i	$-0.694178\pi$
$83$	−12.4098	+	7.16481i	−0.149516	+	0.0863230i	0.423376	+	0.905954i	$0.360845\pi$
$84$	−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	$0.224952\pi$
$89$			115.581i			1.29867i	−0.760504	+	0.649333i	$0.775048\pi$
$90$	−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	−0.550592	−	0.834774i	$-0.685598\pi$
$97$	−9.98636	+	5.76563i	−0.102952	+	0.0594395i	0.447640	+	0.894214i	$0.352265\pi$
$98$		−	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	−0.783475	−	0.621423i	$-0.786555\pi$
$101$	−64.3415	+	37.1476i	−0.637045	+	0.367798i	0.146431	+	0.989221i	$0.453222\pi$
$102$	−4.80243	+	5.94476i	−0.0470827	+	0.0582820i
$103$	4.63237	−	8.02349i	0.0449744	−	0.0778980i	−0.842662	−	0.538443i	$-0.819013\pi$
$103$	4.63237	−	8.02349i	0.0449744	−	0.0778980i	0.887636	+	0.460545i	$0.152346\pi$
$104$	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	$0.259151\pi$
$109$			158.516i			1.45428i	−0.686490	+	0.727140i	$0.740849\pi$
$110$	−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	−0.717572	−	0.696484i	$-0.754747\pi$
$113$	27.6157	−	47.8318i	0.244387	−	0.423291i	0.961959	+	0.273194i	$0.0880800\pi$
$114$	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	−0.865902	−	0.500213i	$-0.833255\pi$
$131$	0.0321956	−	0.0557644i	0.000245768	−	0.000425682i	0.866148	+	0.499787i	$0.166588\pi$
$132$	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	−0.252176	−	0.967681i	$-0.581146\pi$
$137$	62.9889	−	36.3666i	0.459773	−	0.265450i	0.711949	+	0.702231i	$0.247813\pi$
$138$	−7.31581	+	5.54421i	−0.0530131	+	0.0401755i
$139$	21.6096	+	12.4763i	0.155465	+	0.0897578i	0.575714	−	0.817651i	$-0.304724\pi$
$139$	21.6096	+	12.4763i	0.155465	+	0.0897578i	−0.420249	+	0.907409i	$0.638057\pi$
$140$	−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	0.559844	−	0.828598i	$-0.310861\pi$
$149$	18.2046	+	10.5104i	0.122179	+	0.0705398i	−0.437665	+	0.899138i	$0.644194\pi$
$150$	0.972773	+	7.74779i	0.00648516	+	0.0516519i
$151$	−121.688	−	210.770i	−0.805882	−	1.39583i	−0.915694	−	0.401877i	$-0.868358\pi$
$151$	−121.688	−	210.770i	−0.805882	−	1.39583i	0.109811	−	0.993952i	$-0.464975\pi$
$152$		−	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	−0.929385	−	0.369111i	$-0.879662\pi$
$157$	−22.7702	+	39.4391i	−0.145033	+	0.251205i	0.784352	+	0.620316i	$0.212996\pi$
$158$	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	$-0.839778\pi$
$163$		−	157.251i		−	0.964732i	0.875970	−	0.482366i	$-0.160222\pi$
$164$	−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	−0.694646	−	0.719352i	$-0.744439\pi$
$167$	46.0342	−	79.7336i	0.275654	−	0.477447i	0.970300	+	0.241905i	$0.0777722\pi$
$168$	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	0.924204	−	0.381900i	$-0.124730\pi$
$173$	22.7265	+	39.3635i	0.131367	+	0.227535i	−0.792837	+	0.609434i	$0.791397\pi$
$174$	−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	$-0.692421\pi$
$179$		−	294.556i		−	1.64556i	0.568357	−	0.822782i	$-0.307579\pi$
$180$	−95.8125	+	24.4448i	−0.532292	+	0.135804i
$181$			279.929i			1.54657i	0.634058	+	0.773285i	$0.281388\pi$
$181$			279.929i			1.54657i	−0.634058	+	0.773285i	$0.718612\pi$
$182$	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	0.316749	−	0.948510i	$-0.397409\pi$
$191$	247.642	−	142.976i	1.29656	−	0.748567i	0.979808	+	0.199942i	$0.0640755\pi$
$192$	−112.079	−	147.892i	−0.583743	−	0.770272i
$193$	−121.814	−	70.3291i	−0.631159	−	0.364400i	0.150042	−	0.988680i	$-0.452059\pi$
$193$	−121.814	−	70.3291i	−0.631159	−	0.364400i	−0.781201	+	0.624280i	$0.785392\pi$
$194$	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	$0.0442133\pi$
$199$			55.1047i			0.276908i	−0.990369	+	0.138454i	$0.955787\pi$
$200$	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	0.988960	−	0.148181i	$-0.0473419\pi$
$211$	285.929	+	165.081i	1.35511	+	0.782374i	0.366152	+	0.930555i	$0.380675\pi$
$212$	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	0.863701	−	0.504005i	$-0.168141\pi$
$223$	−1.03255	−	1.78843i	−0.00463026	−	0.00801984i	−0.868331	+	0.495985i	$0.834807\pi$
$224$	−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	0.997648	−	0.0685463i	$-0.0218361\pi$
$227$	99.7577	+	172.785i	0.439461	+	0.761169i	−0.558187	+	0.829715i	$0.688503\pi$
$228$	107.235	−	13.4639i	0.470328	−	0.0590520i
$229$	69.4180	−	120.235i	0.303135	−	0.525046i	−0.673709	−	0.738997i	$-0.735300\pi$
$229$	69.4180	−	120.235i	0.303135	−	0.525046i	0.976844	+	0.213951i	$0.0686332\pi$
$230$	−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	0.775933	−	0.630815i	$-0.217279\pi$
$239$	147.606	+	85.2204i	0.617598	+	0.356571i	−0.158335	+	0.987385i	$0.550613\pi$
$240$	78.7350	+	103.894i	0.328063	+	0.432891i
$241$	−20.3122	+	11.7272i	−0.0842829	+	0.0486607i	−0.541549	−	0.840669i	$-0.682162\pi$
$241$	−20.3122	+	11.7272i	−0.0842829	+	0.0486607i	0.457266	+	0.889330i	$0.348829\pi$
$242$		−	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	$0.233360\pi$
$251$			335.935i			1.33839i	−0.743088	+	0.669194i	$0.766640\pi$
$252$	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	0.407512	−	0.913200i	$-0.366396\pi$
$257$	−46.1536	−	26.6468i	−0.179586	−	0.103684i	−0.587098	+	0.809516i	$0.699730\pi$
$258$	−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	−0.415295	−	0.909687i	$-0.636322\pi$
$263$	43.3604	−	25.0342i	0.164869	−	0.0951869i	0.580164	+	0.814500i	$0.302988\pi$
$264$	−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	−0.782132	−	0.623112i	$-0.785868\pi$
$277$	−175.498	+	101.324i	−0.633567	+	0.365790i	0.148565	+	0.988903i	$0.452535\pi$
$278$	−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	−0.982580	−	0.185840i	$-0.940499\pi$
$281$	−368.933	+	213.003i	−1.31293	+	0.758019i	−0.330348	+	0.943859i	$0.607166\pi$
$282$	19.4114	−	2.43720i	0.0688347	−	0.00864254i
$283$	−402.896	−	232.612i	−1.42366	−	0.821950i	−0.427050	−	0.904228i	$-0.640447\pi$
$283$	−402.896	−	232.612i	−1.42366	−	0.821950i	−0.996609	+	0.0822775i	$0.973781\pi$
$284$	−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	0.917460	−	0.397828i	$-0.130236\pi$
$293$	302.277	+	174.519i	1.03166	+	0.595630i	0.114201	+	0.993458i	$0.463569\pi$
$294$	−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	0.284766	+	0.958597i	$0.408084\pi$
$311$	−213.902	+	370.488i	−0.687786	+	1.19128i	−0.972552	+	0.232684i	$0.925249\pi$
$312$	−7.55562	−	60.1778i	−0.0242167	−	0.192878i
$313$	303.815	−	175.407i	0.970654	−	0.560407i	0.0712184	−	0.997461i	$-0.477311\pi$
$313$	303.815	−	175.407i	0.970654	−	0.560407i	0.899436	+	0.437053i	$0.143978\pi$
$314$		−	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	0.968733	−	0.248107i	$-0.0798084\pi$
$317$	85.4313	+	147.971i	0.269499	+	0.466787i	−0.699233	+	0.714894i	$0.746475\pi$
$318$	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	0.892109	+	0.451821i	$0.149225\pi$
$331$	277.160	+	480.056i	0.837343	+	1.45032i	−0.0547661	+	0.998499i	$0.517441\pi$
$332$		−	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	−0.416460	−	0.909154i	$-0.636729\pi$
$337$	−475.857	−	274.736i	−1.41204	−	0.815242i	−0.995580	+	0.0939126i	$0.970063\pi$
$338$	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	0.219110	+	0.975700i	$0.429685\pi$
$347$	−255.193	+	442.007i	−0.735426	+	1.27380i	−0.954536	+	0.298095i	$0.903649\pi$
$348$	−15.6344	−	20.6301i	−0.0449263	−	0.0592820i
$349$	69.4543	+	120.298i	0.199010	+	0.344695i	0.948208	−	0.317651i	$-0.102894\pi$
$349$	69.4543	+	120.298i	0.199010	+	0.344695i	−0.749198	+	0.662346i	$0.769561\pi$
$350$	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	−0.0891457	−	0.996019i	$-0.528414\pi$
$353$	257.287	−	148.545i	0.728859	−	0.420807i	0.818005	+	0.575212i	$0.195080\pi$
$354$	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	$0.114092\pi$
$359$			251.878i			0.701611i	−0.936448	+	0.350805i	$0.885908\pi$
$360$	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	−0.940536	−	0.339694i	$-0.889676\pi$
$367$	−409.800	+	236.598i	−1.11662	+	0.644681i	−0.176084	+	0.984375i	$0.556343\pi$
$368$	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	−0.539856	−	0.841757i	$-0.681521\pi$
$373$	171.228	−	296.575i	0.459055	−	0.795107i	0.998911	+	0.0466504i	$0.0148547\pi$
$374$	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	$0.0612081\pi$
$379$			144.860i			0.382216i	−0.981569	+	0.191108i	$0.938792\pi$
$380$	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	0.725684	−	0.688028i	$-0.241523\pi$
$383$	188.695	+	108.943i	0.492677	+	0.284447i	−0.233007	+	0.972475i	$0.574857\pi$
$384$	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	−0.413962	−	0.910294i	$-0.635855\pi$
$389$	65.1167	−	37.5951i	0.167395	−	0.0966456i	0.581357	+	0.813649i	$0.302522\pi$
$390$	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	$0.242416\pi$
$397$			547.908i			1.38012i	−0.723752	+	0.690060i	$0.757584\pi$
$398$	−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	0.0277720	−	0.999614i	$-0.491159\pi$
$401$	352.711	−	610.913i	0.879577	−	1.52347i	0.851805	−	0.523858i	$-0.175508\pi$
$402$	−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	−0.284668	−	0.958626i	$-0.591883\pi$
$409$	281.335	−	487.286i	0.687860	−	1.19141i	0.972529	−	0.232783i	$-0.0747832\pi$
$410$	−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	−0.244662	−	0.969608i	$-0.578677\pi$
$419$	300.580	−	520.620i	0.717375	−	1.24253i	0.962036	−	0.272921i	$-0.0879897\pi$
$420$	12.9770	+	103.357i	0.0308976	+	0.246088i
$421$	167.946	+	290.891i	0.398921	+	0.690952i	0.993593	−	0.113017i	$-0.0360513\pi$
$421$	167.946	+	290.891i	0.398921	+	0.690952i	−0.594672	+	0.803969i	$0.702718\pi$
$422$	−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	−0.234981	−	0.972000i	$-0.575503\pi$
$439$	214.805	−	124.018i	0.489305	−	0.282500i	0.724286	+	0.689500i	$0.242170\pi$
$440$		−	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	−0.621461	+	0.783445i	$0.713460\pi$
$443$	−713.529	+	411.956i	−1.61067	+	0.929923i	−0.989214	+	0.146478i	$0.953206\pi$
$444$	−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	0.748756	+	0.662846i	$0.230651\pi$
$457$	433.428	+	750.719i	0.948419	+	1.64271i	0.199663	+	0.979865i	$0.436015\pi$
$458$			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	−0.201969	−	0.979392i	$-0.564734\pi$
$461$	251.349	−	145.116i	0.545225	−	0.314786i	0.747194	+	0.664606i	$0.231401\pi$
$462$	−10.4673	−	13.8120i	−0.0226564	−	0.0298960i
$463$	175.796	−	304.487i	0.379689	−	0.657640i	−0.611328	−	0.791377i	$-0.709364\pi$
$463$	175.796	−	304.487i	0.379689	−	0.657640i	0.991017	+	0.133737i	$0.0426978\pi$
$464$	−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	$0.138750\pi$
$467$			394.357i			0.844447i	−0.906492	+	0.422224i	$0.861250\pi$
$468$	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	0.627628	−	0.778513i	$-0.284026\pi$
$479$	−172.631	−	299.005i	−0.360398	−	0.624227i	−0.988026	+	0.154286i	$0.950692\pi$
$480$	−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	$-0.791807\pi$
$487$		−	592.593i		−	1.21682i	0.793622	−	0.608412i	$-0.208193\pi$
$488$	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	0.605658	−	0.795725i	$-0.292910\pi$
$491$	107.710	+	62.1865i	0.219369	+	0.126653i	−0.386289	+	0.922378i	$0.626243\pi$
$492$	−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	0.747682	−	0.664056i	$-0.231167\pi$
$499$	272.670	+	157.426i	0.546434	+	0.315484i	−0.201249	+	0.979540i	$0.564500\pi$
$500$	−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	−0.186269	−	0.982499i	$-0.559640\pi$
$509$	−575.309	−	332.155i	−1.13027	−	0.652563i	−0.944003	+	0.329936i	$0.892973\pi$
$510$	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	$0.246752\pi$
$541$			757.243i			1.39971i	−0.714285	+	0.699855i	$0.753248\pi$
$542$	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	0.259666	−	0.965699i	$-0.416388\pi$
$547$	670.522	−	387.126i	1.22582	−	0.707726i	0.966152	+	0.257972i	$0.0830544\pi$
$548$			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	$0.109466\pi$
$557$			375.595i			0.674318i	−0.941448	+	0.337159i	$0.890534\pi$
$558$	−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	0.243748	−	0.969839i	$-0.421623\pi$
$563$	−267.021	−	154.165i	−0.474283	−	0.273827i	−0.718031	+	0.696011i	$0.754956\pi$
$564$	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	−0.384223	−	0.923240i	$-0.625531\pi$
$569$	127.010	−	73.3291i	0.223216	−	0.128874i	0.607438	+	0.794367i	$0.292197\pi$
$570$	8.96350	−	6.79290i	0.0157254	−	0.0119174i
$571$	−431.255	−	248.985i	−0.755262	−	0.436051i	0.0723301	−	0.997381i	$-0.476956\pi$
$571$	−431.255	−	248.985i	−0.755262	−	0.436051i	−0.827592	+	0.561330i	$0.810290\pi$
$572$	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	−0.798155	−	0.602453i	$-0.794190\pi$
$587$	−396.514	+	228.928i	−0.675492	+	0.389996i	0.122662	+	0.992448i	$0.460857\pi$
$588$	−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	$-0.837707\pi$
$593$		−	578.833i		−	0.976109i	0.872813	−	0.488055i	$-0.162293\pi$
$594$	−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	0.0933770	−	0.995631i	$-0.470234\pi$
$599$	−432.584	−	249.752i	−0.722176	−	0.416949i	−0.815553	+	0.578682i	$0.803567\pi$
$600$	−57.4078	−	24.1835i	−0.0956796	−	0.0403059i
$601$	−720.962	+	416.247i	−1.19960	+	0.692591i	−0.960467	−	0.278395i	$-0.910198\pi$
$601$	−720.962	+	416.247i	−1.19960	+	0.692591i	−0.239136	+	0.970986i	$0.576864\pi$
$602$	−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	0.997415	+	0.0718628i	$0.0228944\pi$
$607$	945.923	+	546.129i	1.55836	+	0.899718i	0.560942	+	0.827855i	$0.310439\pi$
$608$	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	−0.917220	−	0.398381i	$-0.869572\pi$
$617$	−70.0923	+	121.403i	−0.113602	+	0.196764i	0.803618	+	0.595145i	$0.202905\pi$
$618$	3.31938	−	2.51556i	0.00537116	−	0.00407049i
$619$	274.717	−	158.608i	0.443807	−	0.256232i	−0.261404	−	0.965230i	$-0.584185\pi$
$619$	274.717	−	158.608i	0.443807	−	0.256232i	0.705211	+	0.708997i	$0.250852\pi$
$620$		−	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	0.999995	−	0.00304989i	$-0.000970811\pi$
$641$	318.805	+	552.187i	0.497356	+	0.861447i	−0.502639	+	0.864496i	$0.667637\pi$
$642$	18.8755	+	7.95146i	0.0294011	+	0.0123855i
$643$	−121.948	−	70.4067i	−0.189655	−	0.109497i	0.402166	−	0.915567i	$-0.368257\pi$
$643$	−121.948	−	70.4067i	−0.189655	−	0.109497i	−0.591821	+	0.806069i	$0.701591\pi$
$644$	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	$-0.719780\pi$
$647$		−	997.613i		−	1.54191i	0.636892	−	0.770953i	$-0.280220\pi$
$648$	−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	0.498999	+	0.866603i	$0.333701\pi$
$653$	−327.153	+	566.646i	−0.501000	+	0.867758i	−0.999999	+	0.00115542i	$0.999632\pi$
$654$	−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	−0.547496	−	0.836809i	$-0.684419\pi$
$659$	−63.6237	+	36.7332i	−0.0965459	+	0.0557408i	0.450950	+	0.892549i	$0.351085\pi$
$660$	398.921	−	50.0865i	0.604425	−	0.0758886i
$661$	559.494	−	969.071i	0.846435	−	1.46607i	−0.0379339	−	0.999280i	$-0.512078\pi$
$661$	559.494	−	969.071i	0.846435	−	1.46607i	0.884369	−	0.466788i	$-0.154589\pi$
$662$	−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	−0.826289	−	0.563246i	$-0.809552\pi$
$673$	−505.859	+	292.058i	−0.751648	+	0.433964i	0.0746413	+	0.997210i	$0.476219\pi$
$674$	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	−0.927326	−	0.374254i	$-0.877899\pi$
$677$	−533.325	−	923.745i	−0.787776	−	1.36447i	0.139550	−	0.990215i	$-0.455434\pi$
$678$	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	−0.788941	−	0.614468i	$-0.789371\pi$
$691$	−450.025	+	259.822i	−0.651267	+	0.376009i	0.137675	+	0.990478i	$0.456037\pi$
$692$	−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	$-0.770063\pi$
$701$		−	926.951i		−	1.32233i	0.750242	−	0.661163i	$-0.229937\pi$
$702$	−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	0.255274	−	0.966869i	$-0.417834\pi$
$709$	865.153	−	499.496i	1.22024	−	0.704508i	0.964970	+	0.262361i	$0.0845010\pi$
$710$			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	−0.999877	−	0.0156524i	$-0.995017\pi$
$727$	−373.310	−	646.592i	−0.513494	−	0.889398i	0.486383	−	0.873746i	$-0.338316\pi$
$728$	−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	−0.998684	−	0.0512897i	$-0.983667\pi$
$733$	−333.459	+	577.568i	−0.454924	+	0.787951i	0.543760	+	0.839241i	$0.317000\pi$
$734$	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	0.0852417	+	0.996360i	$0.472834\pi$
$743$	−609.448	+	1055.59i	−0.820253	+	1.42072i	−0.905494	+	0.424359i	$0.860500\pi$
$744$	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	0.442954	−	0.896544i	$-0.353930\pi$
$751$	−84.1112	−	48.5616i	−0.111999	−	0.0646626i	−0.554953	+	0.831882i	$0.687264\pi$
$752$	−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	−0.252899	−	0.967493i	$-0.581384\pi$
$761$	−926.306	−	534.803i	−1.21722	−	0.702764i	−0.964323	+	0.264729i	$0.914717\pi$
$762$	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	−0.995020	−	0.0996721i	$-0.968221\pi$
$769$	−316.206	+	547.685i	−0.411192	+	0.712205i	0.583829	+	0.811877i	$0.301554\pi$
$770$	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	$-0.998479\pi$
$773$		−	7.38633i		−	0.00955541i	0.999989	−	0.00477771i	$-0.00152080\pi$
$774$	−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	0.712882	−	0.701284i	$-0.247389\pi$
$787$	363.589	+	209.918i	0.461994	+	0.266732i	−0.250888	+	0.968016i	$0.580723\pi$
$788$	−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	0.949470	+	0.313859i	$0.101622\pi$
$797$	1351.72	+	780.418i	1.69601	+	0.979194i	0.746545	+	0.665335i	$0.231711\pi$
$798$	−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	$0.0574475\pi$
$811$			291.146i			0.358997i	−0.983758	+	0.179498i	$0.942553\pi$
$812$	−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	0.807135	−	0.590367i	$-0.201017\pi$
$821$	−88.4256	−	153.158i	−0.107705	−	0.186550i	−0.914840	+	0.403816i	$0.867683\pi$
$822$	32.4420	−	4.07325i	0.0394672	−	0.00495530i
$823$	38.5079	+	22.2325i	0.0467896	+	0.0270140i	0.523212	−	0.852202i	$-0.324733\pi$
$823$	38.5079	+	22.2325i	0.0467896	+	0.0270140i	−0.476423	+	0.879216i	$0.658067\pi$
$824$	−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	0.989670	+	0.143366i	$0.0457925\pi$
$839$	519.335	+	899.515i	0.618993	+	1.07213i	−0.370677	+	0.928762i	$0.620874\pi$
$840$	−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	−0.611041	−	0.791599i	$-0.709249\pi$
$853$	−197.058	+	113.771i	−0.231017	+	0.133378i	0.380024	+	0.924977i	$0.375916\pi$
$854$			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	0.998572	+	0.0534180i	$0.0170116\pi$
$857$	467.534	+	809.793i	0.545547	+	0.944916i	−0.453025	+	0.891498i	$0.649655\pi$
$858$	−85.4632	−	36.0021i	−0.0996075	−	0.0419605i
$859$	−264.570	+	458.248i	−0.307997	+	0.533467i	−0.977924	−	0.208960i	$-0.932992\pi$
$859$	−264.570	+	458.248i	−0.307997	+	0.533467i	0.669927	+	0.742427i	$0.266325\pi$
$860$	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	$0.0502815\pi$
$863$			271.514i			0.314616i	−0.987550	+	0.157308i	$0.949718\pi$
$864$	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	0.549585	−	0.835438i	$-0.314786\pi$
$877$	88.4609	+	51.0729i	0.100868	+	0.0582359i	−0.448718	+	0.893674i	$0.648119\pi$
$878$	−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	0.438120	+	0.898916i	$0.355644\pi$
$887$	−496.209	+	859.460i	−0.559424	+	0.968952i	−0.997545	+	0.0700351i	$0.977689\pi$
$888$	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	−0.462246	−	0.886752i	$-0.652956\pi$
$907$	67.6442	−	39.0544i	0.0745801	−	0.0430589i	0.536826	+	0.843693i	$0.319623\pi$
$908$	−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	0.513799	−	0.857911i	$-0.328238\pi$
$911$	−442.812	−	766.974i	−0.486073	−	0.841903i	−0.999872	+	0.0160076i	$0.994904\pi$
$912$	−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	0.955782	−	0.294076i	$-0.0950118\pi$
$929$	207.366	+	359.168i	0.223214	+	0.386618i	−0.732568	+	0.680694i	$0.761678\pi$
$930$	−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	−0.102458	−	0.994737i	$-0.532671\pi$
$941$	762.435	−	1320.58i	0.810239	−	1.40337i	0.912697	−	0.408637i	$-0.133996\pi$
$942$	−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	0.739909	−	0.672707i	$-0.234868\pi$
$947$	−201.357	−	348.761i	−0.212626	−	0.368280i	−0.952536	+	0.304427i	$0.901535\pi$
$948$	−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	$0.114533\pi$
$953$			671.106i			0.704203i	−0.935962	+	0.352102i	$0.885467\pi$
$954$	−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	−0.996309	−	0.0858390i	$-0.972643\pi$
$967$	−409.830	+	709.846i	−0.423816	+	0.734070i	0.572493	+	0.819909i	$0.305976\pi$
$968$	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	$-0.850723\pi$
$971$		−	877.715i		−	0.903929i	0.892036	−	0.451965i	$-0.149277\pi$
$972$	−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	−0.0840537	−	0.996461i	$-0.526787\pi$
$977$	−966.293	−	557.890i	−0.989041	−	0.571023i	−0.904988	+	0.425438i	$0.860120\pi$
$978$	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	0.997824	+	0.0659348i	$0.0210029\pi$
$983$	546.561	+	946.671i	0.556013	+	0.963043i	−0.441811	+	0.897108i	$0.645664\pi$
$984$	−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	$0.110169\pi$
$991$			672.370i			0.678477i	−0.940700	+	0.339238i	$0.889831\pi$
$992$	−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	−0.626830	−	0.779156i	$-0.715648\pi$
$997$	−264.679	+	152.813i	−0.265476	+	0.153272i	0.361354	+	0.932429i	$0.382315\pi$
$998$	−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.50.17	✓	68
3.2	odd	2		459.3.i.a.152.18		68
9.2	odd	6	inner	153.3.i.a.101.18	yes	68
9.7	even	3		459.3.i.a.305.17		68
17.16	even	2	inner	153.3.i.a.50.18	yes	68
51.50	odd	2		459.3.i.a.152.17		68
153.16	even	6		459.3.i.a.305.18		68
153.101	odd	6	inner	153.3.i.a.101.17	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.17	✓	68	1.1	even	1	trivial
153.3.i.a.50.18	yes	68	17.16	even	2	inner
153.3.i.a.101.17	yes	68	153.101	odd	6	inner
153.3.i.a.101.18	yes	68	9.2	odd	6	inner
459.3.i.a.152.17		68	51.50	odd	2
459.3.i.a.152.18		68	3.2	odd	2
459.3.i.a.305.17		68	9.7	even	3
459.3.i.a.305.18		68	153.16	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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