LMFDB - Embedded newform 483.3.g.a.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(139,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("483.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.1
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.94080 q^{2} +1.73205i q^{3} +11.5299 q^{4} +1.76571i q^{5} -6.82566i q^{6} +(-5.04591 - 4.85168i) q^{7} -29.6737 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.94080 q^{2} +1.73205i q^{3} +11.5299 q^{4} +1.76571i q^{5} -6.82566i q^{6} +(-5.04591 - 4.85168i) q^{7} -29.6737 q^{8} -3.00000 q^{9} -6.95831i q^{10} -5.51370 q^{11} +19.9703i q^{12} -13.2008i q^{13} +(19.8849 + 19.1195i) q^{14} -3.05830 q^{15} +70.8186 q^{16} +2.41240i q^{17} +11.8224 q^{18} +23.6880i q^{19} +20.3585i q^{20} +(8.40335 - 8.73978i) q^{21} +21.7284 q^{22} +4.79583 q^{23} -51.3964i q^{24} +21.8823 q^{25} +52.0216i q^{26} -5.19615i q^{27} +(-58.1788 - 55.9393i) q^{28} +1.32028 q^{29} +12.0522 q^{30} -44.1358i q^{31} -160.387 q^{32} -9.55001i q^{33} -9.50678i q^{34} +(8.56666 - 8.90963i) q^{35} -34.5896 q^{36} -3.45994 q^{37} -93.3496i q^{38} +22.8644 q^{39} -52.3953i q^{40} +76.4235i q^{41} +(-33.1159 + 34.4417i) q^{42} +19.3938 q^{43} -63.5723 q^{44} -5.29714i q^{45} -18.8994 q^{46} -64.1841i q^{47} +122.661i q^{48} +(1.92246 + 48.9623i) q^{49} -86.2335 q^{50} -4.17840 q^{51} -152.203i q^{52} +70.0629 q^{53} +20.4770i q^{54} -9.73560i q^{55} +(149.731 + 143.967i) q^{56} -41.0288 q^{57} -5.20297 q^{58} +35.6816i q^{59} -35.2619 q^{60} +72.4488i q^{61} +173.930i q^{62} +(15.1377 + 14.5550i) q^{63} +348.778 q^{64} +23.3088 q^{65} +37.6346i q^{66} +17.6813 q^{67} +27.8147i q^{68} +8.30662i q^{69} +(-33.7595 + 35.1110i) q^{70} +79.1093 q^{71} +89.0212 q^{72} -18.2265i q^{73} +13.6349 q^{74} +37.9012i q^{75} +273.120i q^{76} +(27.8216 + 26.7507i) q^{77} -90.1040 q^{78} +118.726 q^{79} +125.045i q^{80} +9.00000 q^{81} -301.169i q^{82} -23.8678i q^{83} +(96.8896 - 100.769i) q^{84} -4.25961 q^{85} -76.4271 q^{86} +2.28680i q^{87} +163.612 q^{88} -47.1823i q^{89} +20.8749i q^{90} +(-64.0459 + 66.6100i) q^{91} +55.2954 q^{92} +76.4455 q^{93} +252.937i q^{94} -41.8262 q^{95} -277.798i q^{96} +180.769i q^{97} +(-7.57604 - 192.950i) q^{98} +16.5411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.94080			−1.97040			−0.985199	−	0.171413i	$-0.945167\pi$
$2$	−3.94080			−1.97040			−0.985199	+	0.171413i	$0.945167\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	11.5299			2.88247
$5$			1.76571i			0.353142i	0.984288	+	0.176571i	$0.0565006\pi$
$5$			1.76571i			0.353142i	−0.984288	+	0.176571i	$0.943499\pi$
$6$		−	6.82566i		−	1.13761i
$7$	−5.04591	−	4.85168i	−0.720845	−	0.693097i
$7$	−5.04591	−	4.85168i	−0.720845	−	0.693097i
$8$	−29.6737			−3.70922
$9$	−3.00000			−0.333333
$10$		−	6.95831i		−	0.695831i
$11$	−5.51370			−0.501245			−0.250623	−	0.968085i	$-0.580635\pi$
$11$	−5.51370			−0.501245			−0.250623	+	0.968085i	$0.580635\pi$
$12$			19.9703i			1.66420i
$13$		−	13.2008i		−	1.01544i	−0.861521	−	0.507722i	$-0.830488\pi$
$13$		−	13.2008i		−	1.01544i	0.861521	−	0.507722i	$-0.169512\pi$
$14$	19.8849	+	19.1195i	1.42035	+	1.36568i
$15$	−3.05830			−0.203887
$16$	70.8186			4.42617
$17$			2.41240i			0.141906i	0.997480	+	0.0709530i	$0.0226040\pi$
$17$			2.41240i			0.141906i	−0.997480	+	0.0709530i	$0.977396\pi$
$18$	11.8224			0.656800
$19$			23.6880i			1.24674i	0.781928	+	0.623368i	$0.214236\pi$
$19$			23.6880i			1.24674i	−0.781928	+	0.623368i	$0.785764\pi$
$20$			20.3585i			1.01792i
$21$	8.40335	−	8.73978i	0.400160	−	0.416180i
$22$	21.7284			0.987653
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	51.3964i		−	2.14152i
$25$	21.8823			0.875290
$26$			52.0216i			2.00083i
$27$		−	5.19615i		−	0.192450i
$28$	−58.1788	−	55.9393i	−2.07781	−	1.99783i
$29$	1.32028			0.0455270			0.0227635	−	0.999741i	$-0.492754\pi$
$29$	1.32028			0.0455270			0.0227635	+	0.999741i	$0.492754\pi$
$30$	12.0522			0.401738
$31$		−	44.1358i		−	1.42374i	−0.702313	−	0.711868i	$-0.747849\pi$
$31$		−	44.1358i		−	1.42374i	0.702313	−	0.711868i	$-0.252151\pi$
$32$	−160.387			−5.01209
$33$		−	9.55001i		−	0.289394i
$34$		−	9.50678i		−	0.279611i
$35$	8.56666	−	8.90963i	0.244762	−	0.254561i
$36$	−34.5896			−0.960823
$37$	−3.45994			−0.0935119			−0.0467559	−	0.998906i	$-0.514888\pi$
$37$	−3.45994			−0.0935119			−0.0467559	+	0.998906i	$0.514888\pi$
$38$		−	93.3496i		−	2.45657i
$39$	22.8644			0.586267
$40$		−	52.3953i		−	1.30988i
$41$			76.4235i			1.86399i	0.362474	+	0.931994i	$0.381932\pi$
$41$			76.4235i			1.86399i	−0.362474	+	0.931994i	$0.618068\pi$
$42$	−33.1159	+	34.4417i	−0.788474	+	0.820040i
$43$	19.3938			0.451019			0.225510	−	0.974241i	$-0.427595\pi$
$43$	19.3938			0.451019			0.225510	+	0.974241i	$0.427595\pi$
$44$	−63.5723			−1.44482
$45$		−	5.29714i		−	0.117714i
$46$	−18.8994			−0.410856
$47$		−	64.1841i		−	1.36562i	−0.730596	−	0.682810i	$-0.760758\pi$
$47$		−	64.1841i		−	1.36562i	0.730596	−	0.682810i	$-0.239242\pi$
$48$			122.661i			2.55545i
$49$	1.92246	+	48.9623i	0.0392339	+	0.999230i
$50$	−86.2335			−1.72467
$51$	−4.17840			−0.0819294
$52$		−	152.203i		−	2.92699i
$53$	70.0629			1.32194			0.660971	−	0.750412i	$-0.270145\pi$
$53$	70.0629			1.32194			0.660971	+	0.750412i	$0.270145\pi$
$54$			20.4770i			0.379203i
$55$		−	9.73560i		−	0.177011i
$56$	149.731	+	143.967i	2.67377	+	2.57085i
$57$	−41.0288			−0.719804
$58$	−5.20297			−0.0897063
$59$			35.6816i			0.604773i	0.953185	+	0.302386i	$0.0977833\pi$
$59$			35.6816i			0.604773i	−0.953185	+	0.302386i	$0.902217\pi$
$60$	−35.2619			−0.587698
$61$			72.4488i			1.18768i	0.804581	+	0.593842i	$0.202390\pi$
$61$			72.4488i			1.18768i	−0.804581	+	0.593842i	$0.797610\pi$
$62$			173.930i			2.80533i
$63$	15.1377	+	14.5550i	0.240282	+	0.231032i
$64$	348.778			5.44965
$65$	23.3088			0.358597
$66$			37.6346i			0.570222i
$67$	17.6813			0.263900			0.131950	−	0.991256i	$-0.457876\pi$
$67$	17.6813			0.263900			0.131950	+	0.991256i	$0.457876\pi$
$68$			27.8147i			0.409040i
$69$			8.30662i			0.120386i
$70$	−33.7595	+	35.1110i	−0.482278	+	0.501586i
$71$	79.1093			1.11422			0.557108	−	0.830440i	$-0.311911\pi$
$71$	79.1093			1.11422			0.557108	+	0.830440i	$0.311911\pi$
$72$	89.0212			1.23641
$73$		−	18.2265i		−	0.249679i	−0.992177	−	0.124839i	$-0.960158\pi$
$73$		−	18.2265i		−	0.249679i	0.992177	−	0.124839i	$-0.0398415\pi$
$74$	13.6349			0.184256
$75$			37.9012i			0.505349i
$76$			273.120i			3.59368i
$77$	27.8216	+	26.7507i	0.361320	+	0.347411i
$78$	−90.1040			−1.15518
$79$	118.726			1.50287			0.751433	−	0.659810i	$-0.229363\pi$
$79$	118.726			1.50287			0.751433	+	0.659810i	$0.229363\pi$
$80$			125.045i			1.56307i
$81$	9.00000			0.111111
$82$		−	301.169i		−	3.67280i
$83$		−	23.8678i		−	0.287564i	−0.989609	−	0.143782i	$-0.954074\pi$
$83$		−	23.8678i		−	0.287564i	0.989609	−	0.143782i	$-0.0459264\pi$
$84$	96.8896	−	100.769i	1.15345	−	1.19963i
$85$	−4.25961			−0.0501130
$86$	−76.4271			−0.888687
$87$			2.28680i			0.0262850i
$88$	163.612			1.85923
$89$		−	47.1823i		−	0.530138i	−0.964229	−	0.265069i	$-0.914605\pi$
$89$		−	47.1823i		−	0.530138i	0.964229	−	0.265069i	$-0.0853948\pi$
$90$			20.8749i			0.231944i
$91$	−64.0459	+	66.6100i	−0.703801	+	0.731978i
$92$	55.2954			0.601037
$93$	76.4455			0.821995
$94$			252.937i			2.69081i
$95$	−41.8262			−0.440276
$96$		−	277.798i		−	2.89373i
$97$			180.769i			1.86360i	0.362969	+	0.931801i	$0.381763\pi$
$97$			180.769i			1.86360i	−0.362969	+	0.931801i	$0.618237\pi$
$98$	−7.57604	−	192.950i	−0.0773065	−	1.96888i
$99$	16.5411			0.167082
$100$	252.300			2.52300
$101$		−	81.6688i		−	0.808602i	−0.914626	−	0.404301i	$-0.867515\pi$
$101$		−	81.6688i		−	0.808602i	0.914626	−	0.404301i	$-0.132485\pi$
$102$	16.4662			0.161434
$103$			168.978i			1.64056i	0.571960	+	0.820282i	$0.306183\pi$
$103$			168.978i			1.64056i	−0.571960	+	0.820282i	$0.693817\pi$
$104$			391.716i			3.76650i
$105$	15.4319	+	14.8379i	0.146971	+	0.141313i
$106$	−276.104			−2.60475
$107$	−149.690			−1.39897			−0.699486	−	0.714646i	$-0.746588\pi$
$107$	−149.690			−1.39897			−0.699486	+	0.714646i	$0.746588\pi$
$108$		−	59.9110i		−	0.554732i
$109$	−9.03995			−0.0829353			−0.0414676	−	0.999140i	$-0.513203\pi$
$109$	−9.03995			−0.0829353			−0.0414676	+	0.999140i	$0.513203\pi$
$110$			38.3660i			0.348782i
$111$		−	5.99279i		−	0.0539891i
$112$	−357.345	−	343.589i	−3.19058	−	3.06776i
$113$	158.635			1.40385			0.701925	−	0.712251i	$-0.252324\pi$
$113$	158.635			1.40385			0.701925	+	0.712251i	$0.252324\pi$
$114$	161.686			1.41830
$115$			8.46806i			0.0736353i
$116$	15.2227			0.131230
$117$			39.6023i			0.338482i
$118$		−	140.614i		−	1.19164i
$119$	11.7042	−	12.1728i	0.0983545	−	0.102292i
$120$	90.7513			0.756261
$121$	−90.5991			−0.748753
$122$		−	285.506i		−	2.34021i
$123$	−132.369			−1.07617
$124$		−	508.881i		−	4.10388i
$125$			82.7806i			0.662245i
$126$	−59.6547	−	57.3584i	−0.473450	−	0.455226i
$127$	19.1260			0.150599			0.0752994	−	0.997161i	$-0.476009\pi$
$127$	19.1260			0.150599			0.0752994	+	0.997161i	$0.476009\pi$
$128$	−732.915			−5.72590
$129$			33.5911i			0.260396i
$130$	−91.8552			−0.706578
$131$			55.8432i			0.426284i	0.977021	+	0.213142i	$0.0683697\pi$
$131$			55.8432i			0.426284i	−0.977021	+	0.213142i	$0.931630\pi$
$132$		−	110.110i		−	0.834170i
$133$	114.927	−	119.528i	0.864109	−	0.898704i
$134$	−69.6783			−0.519987
$135$	9.17491			0.0679623
$136$		−	71.5849i		−	0.526360i
$137$	51.5528			0.376298			0.188149	−	0.982140i	$-0.439751\pi$
$137$	51.5528			0.376298			0.188149	+	0.982140i	$0.439751\pi$
$138$		−	32.7347i		−	0.237208i
$139$			223.117i			1.60516i	0.596547	+	0.802578i	$0.296539\pi$
$139$			223.117i			1.60516i	−0.596547	+	0.802578i	$0.703461\pi$
$140$	98.7726	−	102.727i	0.705519	−	0.733764i
$141$	111.170			0.788441
$142$	−311.754			−2.19545
$143$			72.7851i			0.508987i
$144$	−212.456			−1.47539
$145$			2.33124i			0.0160775i
$146$			71.8271i			0.491966i
$147$	−84.8051	+	3.32980i	−0.576906	+	0.0226517i
$148$	−39.8927			−0.269545
$149$	134.981			0.905915			0.452957	−	0.891532i	$-0.350369\pi$
$149$	134.981			0.905915			0.452957	+	0.891532i	$0.350369\pi$
$150$		−	149.361i		−	0.995739i
$151$	137.521			0.910732			0.455366	−	0.890304i	$-0.349508\pi$
$151$	137.521			0.910732			0.455366	+	0.890304i	$0.349508\pi$
$152$		−	702.911i		−	4.62442i
$153$		−	7.23720i		−	0.0473020i
$154$	−109.639	−	105.419i	−0.711944	−	0.684539i
$155$	77.9312			0.502782
$156$	263.624			1.68990
$157$			108.839i			0.693240i	0.938006	+	0.346620i	$0.112671\pi$
$157$			108.839i			0.693240i	−0.938006	+	0.346620i	$0.887329\pi$
$158$	−467.876			−2.96124
$159$			121.353i			0.763223i
$160$		−	283.197i		−	1.76998i
$161$	−24.1993	−	23.2678i	−0.150306	−	0.144521i
$162$	−35.4672			−0.218933
$163$	−17.2384			−0.105757			−0.0528786	−	0.998601i	$-0.516840\pi$
$163$	−17.2384			−0.105757			−0.0528786	+	0.998601i	$0.516840\pi$
$164$			881.154i			5.37289i
$165$	16.8626			0.102197
$166$			94.0581i			0.566615i
$167$		−	111.223i		−	0.666006i	−0.942926	−	0.333003i	$-0.891938\pi$
$167$		−	111.223i		−	0.666006i	0.942926	−	0.333003i	$-0.108062\pi$
$168$	−249.359	+	259.342i	−1.48428	+	1.54370i
$169$	−5.26056			−0.0311276
$170$	16.7862			0.0987426
$171$		−	71.0640i		−	0.415579i
$172$	223.608			1.30005
$173$		−	13.1451i		−	0.0759834i	−0.999278	−	0.0379917i	$-0.987904\pi$
$173$		−	13.1451i		−	0.0759834i	0.999278	−	0.0379917i	$-0.0120960\pi$
$174$		−	9.01180i		−	0.0517920i
$175$	−110.416	−	106.166i	−0.630948	−	0.606661i
$176$	−390.473			−2.21859
$177$	−61.8023			−0.349166
$178$			185.936i			1.04458i
$179$	330.112			1.84420			0.922100	−	0.386951i	$-0.126472\pi$
$179$	330.112			1.84420			0.922100	+	0.386951i	$0.126472\pi$
$180$		−	61.0754i		−	0.339308i
$181$		−	162.894i		−	0.899967i	−0.893037	−	0.449983i	$-0.851430\pi$
$181$		−	162.894i		−	0.899967i	0.893037	−	0.449983i	$-0.148570\pi$
$182$	252.392	−	262.496i	1.38677	−	1.44229i
$183$	−125.485			−0.685710
$184$	−142.310			−0.773425
$185$		−	6.10926i		−	0.0330230i
$186$	−301.256			−1.61966
$187$		−	13.3013i		−	0.0711297i
$188$		−	740.035i		−	3.93636i
$189$	−25.2101	+	26.2193i	−0.133387	+	0.138727i
$190$	164.829			0.867519
$191$	214.572			1.12342			0.561708	−	0.827336i	$-0.310145\pi$
$191$	214.572			1.12342			0.561708	+	0.827336i	$0.310145\pi$
$192$			604.101i			3.14636i
$193$	123.781			0.641352			0.320676	−	0.947189i	$-0.396090\pi$
$193$	123.781			0.641352			0.320676	+	0.947189i	$0.396090\pi$
$194$		−	712.376i		−	3.67204i
$195$			40.3720i			0.207036i
$196$	22.1658	+	564.529i	0.113091	+	2.88025i
$197$	127.652			0.647982			0.323991	−	0.946060i	$-0.394975\pi$
$197$	127.652			0.647982			0.323991	+	0.946060i	$0.394975\pi$
$198$	−65.1851			−0.329218
$199$		−	117.936i		−	0.592642i	−0.955088	−	0.296321i	$-0.904240\pi$
$199$		−	117.936i		−	0.592642i	0.955088	−	0.296321i	$-0.0957598\pi$
$200$	−649.328			−3.24664
$201$			30.6249i			0.152362i
$202$			321.840i			1.59327i
$203$	−6.66203	−	6.40559i	−0.0328179	−	0.0315546i
$204$	−48.1765			−0.236159
$205$	−134.942			−0.658253
$206$		−	665.908i		−	3.23256i
$207$	−14.3875			−0.0695048
$208$		−	934.861i		−	4.49453i
$209$		−	130.608i		−	0.624921i
$210$	−60.8141	−	58.4731i	−0.289591	−	0.278444i
$211$	−300.352			−1.42347			−0.711734	−	0.702450i	$-0.752090\pi$
$211$	−300.352			−1.42347			−0.711734	+	0.702450i	$0.752090\pi$
$212$	807.817			3.81046
$213$			137.021i			0.643293i
$214$	589.898			2.75653
$215$			34.2439i			0.159274i
$216$			154.189i			0.713839i
$217$	−214.133	+	222.706i	−0.986787	+	1.02629i
$218$	35.6246			0.163416
$219$	31.5693			0.144152
$220$		−	112.250i		−	0.510229i
$221$	31.8456			0.144098
$222$			23.6164i			0.106380i
$223$		−	128.456i		−	0.576036i	−0.957625	−	0.288018i	$-0.907004\pi$
$223$		−	128.456i		−	0.576036i	0.957625	−	0.288018i	$-0.0929962\pi$
$224$	809.299	+	778.146i	3.61294	+	3.47386i
$225$	−65.6468			−0.291763
$226$	−625.148			−2.76614
$227$		−	103.273i		−	0.454948i	−0.973784	−	0.227474i	$-0.926953\pi$
$227$		−	103.273i		−	0.454948i	0.973784	−	0.227474i	$-0.0730466\pi$
$228$	−473.057			−2.07481
$229$			201.980i			0.882010i	0.897505	+	0.441005i	$0.145378\pi$
$229$			201.980i			0.882010i	−0.897505	+	0.441005i	$0.854622\pi$
$230$		−	33.3709i		−	0.145091i
$231$	−46.3335	+	48.1885i	−0.200578	+	0.208608i
$232$	−39.1777			−0.168869
$233$	85.6550			0.367618			0.183809	−	0.982962i	$-0.441157\pi$
$233$	85.6550			0.367618			0.183809	+	0.982962i	$0.441157\pi$
$234$		−	156.065i		−	0.666943i
$235$	113.331			0.482258
$236$			411.404i			1.74324i
$237$			205.640i			0.867680i
$238$	−46.1238	+	47.9704i	−0.193798	+	0.201556i
$239$	−401.950			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−401.950			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$	−216.585			−0.902437
$241$			12.9719i			0.0538251i	0.999638	+	0.0269126i	$0.00856757\pi$
$241$			12.9719i			0.0538251i	−0.999638	+	0.0269126i	$0.991432\pi$
$242$	357.033			1.47534
$243$			15.5885i			0.0641500i
$244$			835.326i			3.42347i
$245$	−86.4533	+	3.39452i	−0.352871	+	0.0138552i
$246$	521.641			2.12049
$247$	312.700			1.26599
$248$			1309.68i			5.28095i
$249$	41.3402			0.166025
$250$		−	326.221i		−	1.30489i
$251$		−	82.4480i		−	0.328478i	−0.986421	−	0.164239i	$-0.947483\pi$
$251$		−	82.4480i		−	0.328478i	0.986421	−	0.164239i	$-0.0525168\pi$
$252$	174.536	+	167.818i	0.692604	+	0.665944i
$253$	−26.4428			−0.104517
$254$	−75.3719			−0.296740
$255$		−	7.37785i		−	0.0289328i
$256$	1493.16			5.83265
$257$			117.988i			0.459095i	0.973297	+	0.229548i	$0.0737247\pi$
$257$			117.988i			0.459095i	−0.973297	+	0.229548i	$0.926275\pi$
$258$		−	132.376i		−	0.513084i
$259$	17.4586	+	16.7865i	0.0674075	+	0.0648128i
$260$	268.747			1.03364
$261$	−3.96085			−0.0151757
$262$		−	220.067i		−	0.839950i
$263$	−314.985			−1.19766			−0.598831	−	0.800875i	$-0.704368\pi$
$263$	−314.985			−1.19766			−0.598831	+	0.800875i	$0.704368\pi$
$264$			283.384i			1.07343i
$265$			123.711i			0.466834i
$266$	−452.902	+	471.034i	−1.70264	+	1.77080i
$267$	81.7222			0.306076
$268$	203.863			0.760683
$269$		−	22.0026i		−	0.0817940i	−0.999163	−	0.0408970i	$-0.986978\pi$
$269$		−	22.0026i		−	0.0817940i	0.999163	−	0.0408970i	$-0.0130216\pi$
$270$	−36.1565			−0.133913
$271$		−	78.7277i		−	0.290508i	−0.989394	−	0.145254i	$-0.953600\pi$
$271$		−	78.7277i		−	0.290508i	0.989394	−	0.145254i	$-0.0464000\pi$
$272$			170.843i			0.628099i
$273$	−115.372	−	110.931i	−0.422608	−	0.406340i
$274$	−203.159			−0.741457
$275$	−120.652			−0.438735
$276$			95.7744i			0.347009i
$277$	48.8438			0.176331			0.0881657	−	0.996106i	$-0.471899\pi$
$277$	48.8438			0.176331			0.0881657	+	0.996106i	$0.471899\pi$
$278$		−	879.258i		−	3.16280i
$279$			132.408i			0.474579i
$280$	−254.205	+	264.382i	−0.907875	+	0.944221i
$281$	25.7831			0.0917548			0.0458774	−	0.998947i	$-0.485392\pi$
$281$	25.7831			0.0917548			0.0458774	+	0.998947i	$0.485392\pi$
$282$	−438.099			−1.55354
$283$		−	543.030i		−	1.91883i	−0.281993	−	0.959416i	$-0.590996\pi$
$283$		−	543.030i		−	1.91883i	0.281993	−	0.959416i	$-0.409004\pi$
$284$	912.121			3.21169
$285$		−	72.4451i		−	0.254193i
$286$		−	286.831i		−	1.00291i
$287$	370.782	−	385.626i	1.29192	−	1.34365i
$288$	481.161			1.67070
$289$	283.180			0.979863
$290$		−	9.18694i		−	0.0316791i
$291$	−313.102			−1.07595
$292$		−	210.150i		−	0.719691i
$293$			267.253i			0.912126i	0.889948	+	0.456063i	$0.150741\pi$
$293$			267.253i			0.912126i	−0.889948	+	0.456063i	$0.849259\pi$
$294$	334.200	−	13.1221i	1.13673	−	0.0446329i
$295$	−63.0034			−0.213571
$296$	102.669			0.346856
$297$			28.6500i			0.0964647i
$298$	−531.934			−1.78501
$299$		−	63.3087i		−	0.211735i
$300$			436.996i			1.45665i
$301$	−97.8595	−	94.0925i	−0.325115	−	0.312600i
$302$	−541.941			−1.79451
$303$	141.455			0.466847
$304$			1677.55i			5.51826i
$305$	−127.924			−0.419422
$306$			28.5203i			0.0932038i
$307$			43.6863i			0.142301i	0.997466	+	0.0711503i	$0.0226670\pi$
$307$			43.6863i			0.142301i	−0.997466	+	0.0711503i	$0.977333\pi$
$308$	320.780	+	308.432i	1.04149	+	1.00140i
$309$	−292.679			−0.947180
$310$	−307.111			−0.990681
$311$		−	250.893i		−	0.806729i	−0.915039	−	0.403365i	$-0.867841\pi$
$311$		−	250.893i		−	0.806729i	0.915039	−	0.403365i	$-0.132159\pi$
$312$	−678.473			−2.17459
$313$		−	44.2006i		−	0.141216i	−0.997504	−	0.0706080i	$-0.977506\pi$
$313$		−	44.2006i		−	0.141216i	0.997504	−	0.0706080i	$-0.0224939\pi$
$314$		−	428.911i		−	1.36596i
$315$	−25.7000	+	26.7289i	−0.0815873	+	0.0848536i
$316$	1368.90			4.33196
$317$	−444.319			−1.40164			−0.700818	−	0.713340i	$-0.747181\pi$
$317$	−444.319			−1.40164			−0.700818	+	0.713340i	$0.747181\pi$
$318$		−	478.226i		−	1.50385i
$319$	−7.27964			−0.0228202
$320$			615.841i			1.92450i
$321$		−	259.271i		−	0.807697i
$322$	95.3647	+	91.6938i	0.296164	+	0.284763i
$323$	−57.1450			−0.176919
$324$	103.769			0.320274
$325$		−	288.863i		−	0.888809i
$326$	67.9331			0.208384
$327$		−	15.6576i		−	0.0478827i
$328$		−	2267.77i		−	6.91393i
$329$	−311.401	+	323.867i	−0.946506	+	0.984400i
$330$	−66.4519			−0.201369
$331$	−265.484			−0.802065			−0.401033	−	0.916064i	$-0.631349\pi$
$331$	−265.484			−0.802065			−0.401033	+	0.916064i	$0.631349\pi$
$332$		−	275.193i		−	0.828894i
$333$	10.3798			0.0311706
$334$			438.307i			1.31230i
$335$			31.2200i			0.0931941i
$336$	595.114	−	618.939i	1.77117	−	1.84208i
$337$	498.779			1.48006			0.740028	−	0.672576i	$-0.234812\pi$
$337$	498.779			1.48006			0.740028	+	0.672576i	$0.234812\pi$
$338$	20.7308			0.0613337
$339$			274.764i			0.810513i
$340$	−49.1127			−0.144449
$341$			243.352i			0.713641i
$342$			280.049i			0.818856i
$343$	227.849	−	256.387i	0.664281	−	0.747483i
$344$	−575.487			−1.67293
$345$	−14.6671			−0.0425134
$346$			51.8023i			0.149717i
$347$	475.730			1.37098			0.685490	−	0.728082i	$-0.259588\pi$
$347$	475.730			1.37098			0.685490	+	0.728082i	$0.259588\pi$
$348$			26.3665i			0.0757658i
$349$		−	268.326i		−	0.768843i	−0.923158	−	0.384421i	$-0.874401\pi$
$349$		−	268.326i		−	0.768843i	0.923158	−	0.384421i	$-0.125599\pi$
$350$	435.127	+	418.377i	1.24322	+	1.19536i
$351$	−68.5933			−0.195422
$352$	884.325			2.51229
$353$		−	451.994i		−	1.28044i	−0.768193	−	0.640218i	$-0.778844\pi$
$353$		−	451.994i		−	1.28044i	0.768193	−	0.640218i	$-0.221156\pi$
$354$	243.550			0.687995
$355$			139.684i			0.393477i
$356$		−	544.006i		−	1.52811i
$357$	21.0838	+	20.2723i	0.0590584	+	0.0567850i
$358$	−1300.90			−3.63381
$359$	294.697			0.820884			0.410442	−	0.911887i	$-0.365374\pi$
$359$	294.697			0.820884			0.410442	+	0.911887i	$0.365374\pi$
$360$			157.186i			0.436627i
$361$	−200.121			−0.554353
$362$			641.932i			1.77329i
$363$		−	156.922i		−	0.432293i
$364$	−738.442	+	768.005i	−2.02869	+	2.10990i
$365$	32.1828			0.0881721
$366$	494.511			1.35112
$367$		−	582.353i		−	1.58679i	−0.608706	−	0.793396i	$-0.708311\pi$
$367$		−	582.353i		−	1.58679i	0.608706	−	0.793396i	$-0.291689\pi$
$368$	339.634			0.922919
$369$		−	229.270i		−	0.621329i
$370$			24.0753i			0.0650685i
$371$	−353.531	−	339.923i	−0.952914	−	0.916233i
$372$	881.408			2.36938
$373$	−599.910			−1.60834			−0.804169	−	0.594401i	$-0.797389\pi$
$373$	−599.910			−1.60834			−0.804169	+	0.594401i	$0.797389\pi$
$374$			52.4175i			0.140154i
$375$	−143.380			−0.382347
$376$			1904.58i			5.06538i
$377$		−	17.4288i		−	0.0462301i
$378$	99.3477	−	103.325i	0.262825	−	0.273347i
$379$	397.728			1.04941			0.524707	−	0.851283i	$-0.324175\pi$
$379$	397.728			1.04941			0.524707	+	0.851283i	$0.324175\pi$
$380$	−482.251			−1.26908
$381$			33.1273i			0.0869483i
$382$	−845.586			−2.21358
$383$			425.785i			1.11171i	0.831279	+	0.555855i	$0.187609\pi$
$383$			425.785i			1.11171i	−0.831279	+	0.555855i	$0.812391\pi$
$384$		−	1269.45i		−	3.30585i
$385$	−47.2340	+	49.1250i	−0.122686	+	0.127597i
$386$	−487.796			−1.26372
$387$	−58.1815			−0.150340
$388$			2084.25i			5.37178i
$389$	379.716			0.976134			0.488067	−	0.872806i	$-0.337702\pi$
$389$	379.716			0.976134			0.488067	+	0.872806i	$0.337702\pi$
$390$		−	159.098i		−	0.407943i
$391$			11.5695i			0.0295894i
$392$	−57.0466	−	1452.89i	−0.145527	−	3.70636i
$393$	−96.7233			−0.246115
$394$	−503.052			−1.27678
$395$			209.637i			0.530725i
$396$	190.717			0.481608
$397$		−	173.737i		−	0.437625i	−0.975767	−	0.218812i	$-0.929782\pi$
$397$		−	173.737i		−	0.437625i	0.975767	−	0.218812i	$-0.0702182\pi$
$398$			464.761i			1.16774i
$399$	207.028	+	199.059i	0.518867	+	0.498894i
$400$	1549.67			3.87418
$401$	590.188			1.47179			0.735895	−	0.677095i	$-0.236761\pi$
$401$	590.188			1.47179			0.735895	+	0.677095i	$0.236761\pi$
$402$		−	120.686i		−	0.300215i
$403$	−582.628			−1.44573
$404$		−	941.632i		−	2.33077i
$405$			15.8914i			0.0392380i
$406$	26.2537	+	25.2431i	0.0646643	+	0.0621752i
$407$	19.0771			0.0468724
$408$	123.989			0.303894
$409$			636.682i			1.55668i	0.627843	+	0.778340i	$0.283938\pi$
$409$			636.682i			1.55668i	−0.627843	+	0.778340i	$0.716062\pi$
$410$	531.779			1.29702
$411$			89.2921i			0.217256i
$412$			1948.30i			4.72888i
$413$	173.116	−	180.046i	0.419166	−	0.435947i
$414$	56.6982			0.136952
$415$	42.1437			0.101551
$416$			2117.23i			5.08950i
$417$	−386.450			−0.926738
$418$			514.702i			1.23134i
$419$		−	651.647i		−	1.55524i	−0.628732	−	0.777622i	$-0.716426\pi$
$419$		−	651.647i		−	1.55524i	0.628732	−	0.777622i	$-0.283574\pi$
$420$	177.928	+	171.079i	0.423639	+	0.407331i
$421$	−98.0246			−0.232838			−0.116419	−	0.993200i	$-0.537141\pi$
$421$	−98.0246			−0.232838			−0.116419	+	0.993200i	$0.537141\pi$
$422$	1183.62			2.80480
$423$			192.552i			0.455207i
$424$	−2079.03			−4.90337
$425$			52.7888i			0.124209i
$426$		−	539.973i		−	1.26754i
$427$	351.498	−	365.570i	0.823180	−	0.856136i
$428$	−1725.91			−4.03249
$429$	−126.068			−0.293864
$430$		−	134.948i		−	0.313833i
$431$	6.32715			0.0146802			0.00734008	−	0.999973i	$-0.497664\pi$
$431$	6.32715			0.0146802			0.00734008	+	0.999973i	$0.497664\pi$
$432$		−	367.984i		−	0.851816i
$433$			750.754i			1.73384i	0.498445	+	0.866921i	$0.333904\pi$
$433$			750.754i			1.73384i	−0.498445	+	0.866921i	$0.666096\pi$
$434$	843.854	−	877.638i	1.94436	−	2.02221i
$435$	−4.03782			−0.00928236
$436$	−104.230			−0.239059
$437$			113.604i			0.259963i
$438$	−124.408			−0.284037
$439$		−	718.511i		−	1.63670i	−0.574720	−	0.818350i	$-0.694889\pi$
$439$		−	718.511i		−	1.63670i	0.574720	−	0.818350i	$-0.305111\pi$
$440$			288.892i			0.656572i
$441$	−5.76739	−	146.887i	−0.0130780	−	0.333077i
$442$	−125.497			−0.283930
$443$	−337.384			−0.761589			−0.380795	−	0.924660i	$-0.624349\pi$
$443$	−337.384			−0.761589			−0.380795	+	0.924660i	$0.624349\pi$
$444$		−	69.0962i		−	0.155622i
$445$	83.3104			0.187214
$446$			506.219i			1.13502i
$447$			233.794i			0.523030i
$448$	−1759.90	−	1692.16i	−3.92835	−	3.77714i
$449$	−210.417			−0.468634			−0.234317	−	0.972160i	$-0.575285\pi$
$449$	−210.417			−0.468634			−0.234317	+	0.972160i	$0.575285\pi$
$450$	258.701			0.574890
$451$		−	421.376i		−	0.934315i
$452$	1829.04			4.04655
$453$			238.193i			0.525812i
$454$			406.978i			0.896428i
$455$	−117.614	−	113.087i	−0.258492	−	0.248542i
$456$	1217.48			2.66991
$457$	292.274			0.639550			0.319775	−	0.947494i	$-0.396393\pi$
$457$	292.274			0.639550			0.319775	+	0.947494i	$0.396393\pi$
$458$		−	795.964i		−	1.73791i
$459$	12.5352			0.0273098
$460$			97.6357i			0.212252i
$461$			385.990i			0.837288i	0.908150	+	0.418644i	$0.137495\pi$
$461$			385.990i			0.837288i	−0.908150	+	0.418644i	$0.862505\pi$
$462$	182.591	−	189.901i	0.395219	−	0.411041i
$463$	−186.544			−0.402904			−0.201452	−	0.979498i	$-0.564566\pi$
$463$	−186.544			−0.402904			−0.201452	+	0.979498i	$0.564566\pi$
$464$	93.5006			0.201510
$465$			134.981i			0.290281i
$466$	−337.549			−0.724354
$467$			504.057i			1.07935i	0.841873	+	0.539676i	$0.181453\pi$
$467$			504.057i			1.07935i	−0.841873	+	0.539676i	$0.818547\pi$
$468$			456.610i			0.975663i
$469$	−89.2181	−	85.7838i	−0.190231	−	0.182908i
$470$	−446.613			−0.950241
$471$	−188.514			−0.400242
$472$		−	1058.81i		−	2.24323i
$473$	−106.932			−0.226071
$474$		−	810.386i		−	1.70967i
$475$			518.347i			1.09126i
$476$	134.948	−	140.351i	0.283504	−	0.294854i
$477$	−210.189			−0.440647
$478$	1584.00			3.31382
$479$		−	884.470i		−	1.84649i	−0.384209	−	0.923246i	$-0.625526\pi$
$479$		−	884.470i		−	1.84649i	0.384209	−	0.923246i	$-0.374474\pi$
$480$	490.512			1.02190
$481$			45.6739i			0.0949561i
$482$		−	51.1195i		−	0.106057i
$483$	40.3011	−	41.9145i	0.0834390	−	0.0867795i
$484$	−1044.60			−2.15826
$485$	−319.187			−0.658117
$486$		−	61.4309i		−	0.126401i
$487$	−259.445			−0.532741			−0.266371	−	0.963871i	$-0.585824\pi$
$487$	−259.445			−0.532741			−0.266371	+	0.963871i	$0.585824\pi$
$488$		−	2149.83i		−	4.40538i
$489$		−	29.8578i		−	0.0610589i
$490$	340.695	−	13.3771i	0.695296	−	0.0273002i
$491$	−899.263			−1.83149			−0.915746	−	0.401757i	$-0.868400\pi$
$491$	−899.263			−1.83149			−0.915746	+	0.401757i	$0.868400\pi$
$492$	−1526.20			−3.10204
$493$			3.18505i			0.00646055i
$494$	−1232.29			−2.49451
$495$			29.2068i			0.0590037i
$496$		−	3125.64i		−	6.30169i
$497$	−399.179	−	383.813i	−0.803176	−	0.772259i
$498$	−162.913			−0.327136
$499$	−841.192			−1.68576			−0.842878	−	0.538105i	$-0.819140\pi$
$499$	−841.192			−1.68576			−0.842878	+	0.538105i	$0.819140\pi$
$500$			954.450i			1.90890i
$501$	192.644			0.384519
$502$			324.911i			0.647233i
$503$			764.836i			1.52055i	0.649602	+	0.760274i	$0.274935\pi$
$503$			764.836i			1.52055i	−0.649602	+	0.760274i	$0.725065\pi$
$504$	−449.193	−	431.902i	−0.891256	−	0.856949i
$505$	144.204			0.285552
$506$	104.206			0.205940
$507$		−	9.11155i		−	0.0179715i
$508$	220.521			0.434097
$509$		−	67.2860i		−	0.132193i	−0.997813	−	0.0660963i	$-0.978946\pi$
$509$		−	67.2860i		−	0.132193i	0.997813	−	0.0660963i	$-0.0210545\pi$
$510$			29.0746i			0.0570091i
$511$	−88.4293	+	91.9695i	−0.173051	+	0.179980i
$512$	−2952.57			−5.76674
$513$	123.086			0.239935
$514$		−	464.965i		−	0.904601i
$515$	−298.367			−0.579353
$516$			387.301i			0.750584i
$517$			353.892i			0.684510i
$518$	−68.8006	−	66.1522i	−0.132820	−	0.127707i
$519$	22.7680			0.0438690
$520$	−691.658			−1.33011
$521$		−	490.202i		−	0.940886i	−0.882430	−	0.470443i	$-0.844094\pi$
$521$		−	490.202i		−	0.940886i	0.882430	−	0.470443i	$-0.155906\pi$
$522$	15.6089			0.0299021
$523$		−	340.744i		−	0.651518i	−0.945453	−	0.325759i	$-0.894380\pi$
$523$		−	340.744i		−	0.651518i	0.945453	−	0.325759i	$-0.105620\pi$
$524$			643.866i			1.22875i
$525$	183.884	−	191.246i	0.350256	−	0.364278i
$526$	1241.29			2.35987
$527$	106.473			0.202037
$528$		−	676.318i		−	1.28091i
$529$	23.0000			0.0434783
$530$		−	487.520i		−	0.919848i
$531$		−	107.045i		−	0.201591i
$532$	1325.09	−	1378.14i	2.49077	−	2.59049i
$533$	1008.85			1.89278
$534$	−322.050			−0.603091
$535$		−	264.309i		−	0.494036i
$536$	−524.669			−0.978861
$537$			571.771i			1.06475i
$538$			86.7077i			0.161167i
$539$	−10.5999	−	269.963i	−0.0196658	−	0.500859i
$540$	105.786			0.195899
$541$	1022.64			1.89028			0.945139	−	0.326668i	$-0.105926\pi$
$541$	1022.64			1.89028			0.945139	+	0.326668i	$0.105926\pi$
$542$			310.250i			0.572417i
$543$	282.141			0.519596
$544$		−	386.918i		−	0.711246i
$545$		−	15.9619i		−	0.0292880i
$546$	454.657	+	437.156i	0.832705	+	0.800651i
$547$	441.287			0.806740			0.403370	−	0.915037i	$-0.367839\pi$
$547$	441.287			0.806740			0.403370	+	0.915037i	$0.367839\pi$
$548$	594.398			1.08467
$549$		−	217.346i		−	0.395895i
$550$	475.466			0.864483
$551$			31.2749i			0.0567602i
$552$		−	246.489i		−	0.446537i
$553$	−599.083	−	576.022i	−1.08333	−	1.04163i
$554$	−192.484			−0.347443
$555$	10.5815			0.0190658
$556$			2572.51i			4.62682i
$557$	151.199			0.271453			0.135726	−	0.990746i	$-0.456663\pi$
$557$	151.199			0.271453			0.135726	+	0.990746i	$0.456663\pi$
$558$		−	521.791i		−	0.935110i
$559$		−	256.014i		−	0.457985i
$560$	606.680	−	630.968i	1.08336	−	1.12673i
$561$	23.0384			0.0410667
$562$	−101.606			−0.180794
$563$		−	35.9828i		−	0.0639126i	−0.999489	−	0.0319563i	$-0.989826\pi$
$563$		−	35.9828i		−	0.0639126i	0.999489	−	0.0319563i	$-0.0101737\pi$
$564$	1281.78			2.27266
$565$			280.104i			0.495759i
$566$			2139.97i			3.78087i
$567$	−45.4132	−	43.6651i	−0.0800938	−	0.0770107i
$568$	−2347.47			−4.13287
$569$	610.314			1.07261			0.536304	−	0.844025i	$-0.319820\pi$
$569$	610.314			1.07261			0.536304	+	0.844025i	$0.319820\pi$
$570$			285.491i			0.500862i
$571$	1026.83			1.79830			0.899149	−	0.437642i	$-0.144186\pi$
$571$	1026.83			1.79830			0.899149	+	0.437642i	$0.144186\pi$
$572$			839.204i			1.46714i
$573$			371.650i			0.648604i
$574$	−1461.18	+	1519.67i	−2.54560	+	2.64752i
$575$	104.944			0.182511
$576$	−1046.33			−1.81655
$577$			542.951i			0.940990i	0.882403	+	0.470495i	$0.155925\pi$
$577$			542.951i			0.940990i	−0.882403	+	0.470495i	$0.844075\pi$
$578$	−1115.96			−1.93072
$579$			214.395i			0.370285i
$580$			26.8789i			0.0463430i
$581$	−115.799	+	120.435i	−0.199310	+	0.207289i
$582$	1233.87			2.12005
$583$	−386.306			−0.662617
$584$			540.850i			0.926112i
$585$	−69.9263			−0.119532
$586$		−	1053.19i		−	1.79725i
$587$			421.078i			0.717340i	0.933464	+	0.358670i	$0.116770\pi$
$587$			421.078i			0.717340i	−0.933464	+	0.358670i	$0.883230\pi$
$588$	−977.793	+	38.3922i	−1.66291	+	0.0652929i
$589$	1045.49			1.77503
$590$	248.284			0.420820
$591$			221.100i			0.374112i
$592$	−245.028			−0.413899
$593$			124.143i			0.209347i	0.994507	+	0.104674i	$0.0333798\pi$
$593$			124.143i			0.209347i	−0.994507	+	0.104674i	$0.966620\pi$
$594$		−	112.904i		−	0.190074i
$595$	21.4936	+	20.6662i	0.0361237	+	0.0347332i
$596$	1556.32			2.61127
$597$	204.271			0.342162
$598$			249.487i			0.417202i
$599$	598.745			0.999574			0.499787	−	0.866148i	$-0.333412\pi$
$599$	598.745			0.999574			0.499787	+	0.866148i	$0.333412\pi$
$600$		−	1124.67i		−	1.87445i
$601$			403.448i			0.671294i	0.941988	+	0.335647i	$0.108955\pi$
$601$			403.448i			0.671294i	−0.941988	+	0.335647i	$0.891045\pi$
$602$	385.644	+	370.800i	0.640605	+	0.615946i
$603$	−53.0438			−0.0879665
$604$	1585.60			2.62516
$605$		−	159.972i		−	0.264417i
$606$	−557.444			−0.919874
$607$			230.507i			0.379748i	0.981808	+	0.189874i	$0.0608080\pi$
$607$			230.507i			0.379748i	−0.981808	+	0.189874i	$0.939192\pi$
$608$		−	3799.25i		−	6.24876i
$609$	11.0948	−	11.5390i	0.0182181	−	0.0189474i
$610$	504.121			0.826428
$611$	−847.280			−1.38671
$612$		−	83.4441i		−	0.136347i
$613$	−819.205			−1.33639			−0.668193	−	0.743988i	$-0.732932\pi$
$613$	−819.205			−1.33639			−0.668193	+	0.743988i	$0.732932\pi$
$614$		−	172.159i		−	0.280389i
$615$		−	233.726i		−	0.380043i
$616$	−825.572	−	793.793i	−1.34021	−	1.28862i
$617$	−176.101			−0.285414			−0.142707	−	0.989765i	$-0.545581\pi$
$617$	−176.101			−0.285414			−0.142707	+	0.989765i	$0.545581\pi$
$618$	1153.39			1.86632
$619$		−	996.824i		−	1.61038i	−0.593019	−	0.805189i	$-0.702064\pi$
$619$		−	996.824i		−	1.61038i	0.593019	−	0.805189i	$-0.297936\pi$
$620$	898.538			1.44925
$621$		−	24.9199i		−	0.0401286i
$622$			988.718i			1.58958i
$623$	−228.913	+	238.078i	−0.367437	+	0.382147i
$624$	1619.23			2.59492
$625$	400.890			0.641424
$626$			174.186i			0.278252i
$627$	226.221			0.360798
$628$			1254.90i			1.99824i
$629$		−	8.34676i		−	0.0132699i
$630$	101.278	−	105.333i	0.160759	−	0.167195i
$631$	545.806			0.864986			0.432493	−	0.901637i	$-0.357634\pi$
$631$	545.806			0.864986			0.432493	+	0.901637i	$0.357634\pi$
$632$	−3523.05			−5.57445
$633$		−	520.224i		−	0.821839i
$634$	1750.97			2.76178
$635$			33.7711i			0.0531828i
$636$			1399.18i			2.19997i
$637$	646.340	−	25.3780i	1.01466	−	0.0398399i
$638$	28.6876			0.0449649
$639$	−237.328			−0.371405
$640$		−	1294.12i		−	2.02206i
$641$	372.433			0.581019			0.290509	−	0.956872i	$-0.406175\pi$
$641$	372.433			0.581019			0.290509	+	0.956872i	$0.406175\pi$
$642$			1021.73i			1.59148i
$643$		−	360.640i		−	0.560871i	−0.959873	−	0.280435i	$-0.909521\pi$
$643$		−	360.640i		−	0.560871i	0.959873	−	0.280435i	$-0.0904789\pi$
$644$	−279.016	−	268.275i	−0.433254	−	0.416576i
$645$	−59.3122			−0.0919569
$646$	225.197			0.348602
$647$			1004.04i			1.55183i	0.630835	+	0.775917i	$0.282713\pi$
$647$			1004.04i			1.55183i	−0.630835	+	0.775917i	$0.717287\pi$
$648$	−267.064			−0.412135
$649$		−	196.737i		−	0.303139i
$650$			1138.35i			1.75131i
$651$	−385.737	−	370.889i	−0.592531	−	0.569722i
$652$	−198.757			−0.304842
$653$	−281.954			−0.431782			−0.215891	−	0.976417i	$-0.569266\pi$
$653$	−281.954			−0.431782			−0.215891	+	0.976417i	$0.569266\pi$
$654$			61.7036i			0.0943480i
$655$	−98.6031			−0.150539
$656$			5412.21i			8.25032i
$657$			54.6796i			0.0832262i
$658$	1227.17	−	1276.30i	1.86499	−	1.93966i
$659$	415.895			0.631100			0.315550	−	0.948909i	$-0.397811\pi$
$659$	415.895			0.631100			0.315550	+	0.948909i	$0.397811\pi$
$660$	194.423			0.294581
$661$			428.779i			0.648682i	0.945940	+	0.324341i	$0.105143\pi$
$661$			428.779i			0.648682i	−0.945940	+	0.324341i	$0.894857\pi$
$662$	1046.22			1.58039
$663$			55.1581i			0.0831948i
$664$			708.247i			1.06664i
$665$	211.051	+	202.927i	0.317370	+	0.305154i
$666$	−40.9048			−0.0614186
$667$	6.33185			0.00949303
$668$		−	1282.39i		−	1.91974i
$669$	222.492			0.332574
$670$		−	123.032i		−	0.183630i
$671$		−	399.461i		−	0.595321i
$672$	−1347.79	+	1401.75i	−2.00564	+	2.08593i
$673$	657.308			0.976683			0.488342	−	0.872653i	$-0.337602\pi$
$673$	657.308			0.976683			0.488342	+	0.872653i	$0.337602\pi$
$674$	−1965.59			−2.91630
$675$		−	113.704i		−	0.168450i
$676$	−60.6536			−0.0897243
$677$			1331.79i			1.96720i	0.180371	+	0.983599i	$0.442270\pi$
$677$			1331.79i			1.96720i	−0.180371	+	0.983599i	$0.557730\pi$
$678$		−	1082.79i		−	1.59703i
$679$	877.035	−	912.147i	1.29166	−	1.34337i
$680$	126.398			0.185880
$681$	178.874			0.262664
$682$		−	959.000i		−	1.40616i
$683$	−189.458			−0.277391			−0.138695	−	0.990335i	$-0.544291\pi$
$683$	−189.458			−0.277391			−0.138695	+	0.990335i	$0.544291\pi$
$684$		−	819.360i		−	1.19789i
$685$			91.0274i			0.132887i
$686$	−897.905	+	1010.37i	−1.30890	+	1.47284i
$687$	−349.840			−0.509229
$688$	1373.44			1.99628
$689$		−	924.885i		−	1.34236i
$690$	57.8001			0.0837682
$691$			1137.65i			1.64638i	0.567763	+	0.823192i	$0.307809\pi$
$691$			1137.65i			1.64638i	−0.567763	+	0.823192i	$0.692191\pi$
$692$		−	151.562i		−	0.219020i
$693$	−83.4649	−	80.2520i	−0.120440	−	0.115804i
$694$	−1874.75			−2.70138
$695$	−393.960			−0.566849
$696$		−	67.8578i		−	0.0974968i
$697$	−184.364			−0.264511
$698$			1057.42i			1.51493i
$699$			148.359i			0.212244i
$700$	−1273.08	−	1224.08i	−1.81869	−	1.74868i
$701$	−662.130			−0.944551			−0.472276	−	0.881451i	$-0.656567\pi$
$701$	−662.130			−0.944551			−0.472276	+	0.881451i	$0.656567\pi$
$702$	270.312			0.385060
$703$		−	81.9591i		−	0.116585i
$704$	−1923.06			−2.73161
$705$			196.295i			0.278432i
$706$			1781.22i			2.52297i
$707$	−396.231	+	412.094i	−0.560440	+	0.582877i
$708$	−712.573			−1.00646
$709$	69.6714			0.0982672			0.0491336	−	0.998792i	$-0.484354\pi$
$709$	69.6714			0.0982672			0.0491336	+	0.998792i	$0.484354\pi$
$710$		−	550.467i		−	0.775306i
$711$	−356.179			−0.500955
$712$			1400.08i			1.96640i
$713$		−	211.668i		−	0.296870i
$714$	−83.0872	−	79.8888i	−0.116369	−	0.111889i
$715$	−128.518			−0.179745
$716$	3806.15			5.31585
$717$		−	696.198i		−	0.970988i
$718$	−1161.34			−1.61747
$719$			650.068i			0.904129i	0.891985	+	0.452064i	$0.149312\pi$
$719$			650.068i			0.904129i	−0.891985	+	0.452064i	$0.850688\pi$
$720$		−	375.136i		−	0.521022i
$721$	819.827	−	852.648i	1.13707	−	1.18259i
$722$	788.638			1.09230
$723$	−22.4679			−0.0310760
$724$		−	1878.15i		−	2.59413i
$725$	28.8908			0.0398493
$726$			618.399i			0.851789i
$727$		−	507.838i		−	0.698539i	−0.937022	−	0.349269i	$-0.886430\pi$
$727$		−	507.838i		−	0.698539i	0.937022	−	0.349269i	$-0.113570\pi$
$728$	1900.48	−	1976.57i	2.61055	−	2.71506i
$729$	−27.0000			−0.0370370
$730$	−126.826			−0.173734
$731$			46.7857i			0.0640023i
$732$	−1446.83			−1.97654
$733$			749.268i			1.02219i	0.859523	+	0.511097i	$0.170761\pi$
$733$			749.268i			1.02219i	−0.859523	+	0.511097i	$0.829239\pi$
$734$			2294.93i			3.12661i
$735$	−5.87947	−	149.741i	−0.00799928	−	0.203730i
$736$	−769.189			−1.04509
$737$	−97.4892			−0.132278
$738$			903.508i			1.22427i
$739$	434.719			0.588253			0.294127	−	0.955766i	$-0.404971\pi$
$739$	434.719			0.588253			0.294127	+	0.955766i	$0.404971\pi$
$740$		−	70.4390i		−	0.0951879i
$741$			541.612i			0.730921i
$742$	1393.20	+	1339.57i	1.87762	+	1.80534i
$743$	655.651			0.882437			0.441219	−	0.897400i	$-0.354546\pi$
$743$	655.651			0.882437			0.441219	+	0.897400i	$0.354546\pi$
$744$	−2268.42			−3.04896
$745$			238.338i			0.319917i
$746$	2364.12			3.16907
$747$			71.6034i			0.0958546i
$748$		−	153.362i		−	0.205029i
$749$	755.322	+	726.247i	1.00844	+	0.969623i
$750$	565.032			0.753376
$751$	−749.098			−0.997467			−0.498734	−	0.866755i	$-0.666201\pi$
$751$	−749.098			−0.997467			−0.498734	+	0.866755i	$0.666201\pi$
$752$		−	4545.43i		−	6.04446i
$753$	142.804			0.189647
$754$			68.6832i			0.0910918i
$755$			242.822i			0.321618i
$756$	−290.669	+	302.306i	−0.384483	+	0.399875i
$757$	−619.781			−0.818733			−0.409367	−	0.912370i	$-0.634250\pi$
$757$	−619.781			−0.818733			−0.409367	+	0.912370i	$0.634250\pi$
$758$	−1567.36			−2.06776
$759$		−	45.8002i		−	0.0603428i
$760$	1241.14			1.63308
$761$		−	395.108i		−	0.519195i	−0.965717	−	0.259598i	$-0.916410\pi$
$761$		−	395.108i		−	0.519195i	0.965717	−	0.259598i	$-0.0835900\pi$
$762$		−	130.548i		−	0.171323i
$763$	45.6148	+	43.8589i	0.0597835	+	0.0574822i
$764$	2473.99			3.23821
$765$	12.7788			0.0167043
$766$		−	1677.93i		−	2.19051i
$767$	471.025			0.614113
$768$			2586.23i			3.36748i
$769$		−	964.989i		−	1.25486i	−0.778672	−	0.627431i	$-0.784106\pi$
$769$		−	964.989i		−	1.25486i	0.778672	−	0.627431i	$-0.215894\pi$
$770$	186.140	−	193.592i	0.241740	−	0.251418i
$771$	−204.360			−0.265059
$772$	1427.18			1.84868
$773$			469.817i			0.607784i	0.952706	+	0.303892i	$0.0982863\pi$
$773$			469.817i			0.607784i	−0.952706	+	0.303892i	$0.901714\pi$
$774$	229.281			0.296229
$775$		−	965.792i		−	1.24618i
$776$		−	5364.10i		−	6.91251i
$777$	−29.0751	+	30.2391i	−0.0374197	+	0.0389178i
$778$	−1496.38			−1.92337
$779$	−1810.32			−2.32390
$780$			465.484i			0.596775i
$781$	−436.185			−0.558495
$782$		−	45.5929i		−	0.0583030i
$783$		−	6.86039i		−	0.00876167i
$784$	136.146	+	3467.44i	0.173656	+	4.42276i
$785$	−192.178			−0.244812
$786$	381.167			0.484945
$787$		−	611.572i		−	0.777093i	−0.921429	−	0.388547i	$-0.872977\pi$
$787$		−	611.572i		−	0.777093i	0.921429	−	0.388547i	$-0.127023\pi$
$788$	1471.82			1.86779
$789$		−	545.570i		−	0.691471i
$790$		−	826.135i		−	1.04574i
$791$	−800.458	−	769.646i	−1.01196	−	0.973003i
$792$	−490.836			−0.619742
$793$	956.380			1.20603
$794$			684.662i			0.862295i
$795$	−214.274			−0.269527
$796$		−	1359.79i		−	1.70827i
$797$			1181.77i			1.48278i	0.671076	+	0.741388i	$0.265832\pi$
$797$			1181.77i			1.48278i	−0.671076	+	0.741388i	$0.734168\pi$
$798$	−815.855	−	784.450i	−1.02237	−	0.983019i
$799$	154.838			0.193790
$800$	−3509.63			−4.38704
$801$			141.547i			0.176713i
$802$	−2325.81			−2.90001
$803$			100.496i			0.125150i
$804$			353.101i			0.439180i
$805$	41.0843	−	42.7291i	0.0510364	−	0.0530796i
$806$	2296.02			2.84866
$807$	38.1096			0.0472238
$808$			2423.42i			2.99928i
$809$	−363.867			−0.449773			−0.224887	−	0.974385i	$-0.572201\pi$
$809$	−363.867			−0.449773			−0.224887	+	0.974385i	$0.572201\pi$
$810$		−	62.6248i		−	0.0773146i
$811$			1354.22i			1.66981i	0.550391	+	0.834907i	$0.314479\pi$
$811$			1354.22i			1.66981i	−0.550391	+	0.834907i	$0.685521\pi$
$812$	−76.8124	−	73.8556i	−0.0945966	−	0.0909552i
$813$	136.360			0.167725
$814$	−75.1788			−0.0923573
$815$		−	30.4381i		−	0.0373473i
$816$	−295.909			−0.362633
$817$			459.401i			0.562302i
$818$		−	2509.04i		−	3.06728i
$819$	192.138	−	199.830i	0.234600	−	0.243993i
$820$	−1555.86			−1.89740
$821$	−789.560			−0.961705			−0.480853	−	0.876801i	$-0.659673\pi$
$821$	−789.560			−0.961705			−0.480853	+	0.876801i	$0.659673\pi$
$822$		−	351.882i		−	0.428080i
$823$	−1112.03			−1.35119			−0.675595	−	0.737273i	$-0.736113\pi$
$823$	−1112.03			−1.35119			−0.675595	+	0.737273i	$0.736113\pi$
$824$		−	5014.21i		−	6.08521i
$825$		−	208.976i		−	0.253304i
$826$	−682.213	+	709.525i	−0.825924	+	0.858989i
$827$	−481.677			−0.582438			−0.291219	−	0.956656i	$-0.594061\pi$
$827$	−481.677			−0.582438			−0.291219	+	0.956656i	$0.594061\pi$
$828$	−165.886			−0.200346
$829$			858.422i			1.03549i	0.855535	+	0.517746i	$0.173229\pi$
$829$			858.422i			1.03549i	−0.855535	+	0.517746i	$0.826771\pi$
$830$	−166.080			−0.200096
$831$			84.6000i			0.101805i
$832$		−	4604.14i		−	5.53382i
$833$	−118.117	+	4.63775i	−0.141797	+	0.00556753i
$834$	1522.92			1.82604
$835$	196.388			0.235195
$836$		−	1505.90i		−	1.80132i
$837$	−229.337			−0.273998
$838$			2568.01i			3.06445i
$839$			235.458i			0.280642i	0.990106	+	0.140321i	$0.0448134\pi$
$839$			235.458i			0.280642i	−0.990106	+	0.140321i	$0.955187\pi$
$840$	−457.923	−	440.296i	−0.545146	−	0.524162i
$841$	−839.257			−0.997927
$842$	386.295			0.458783
$843$			44.6576i			0.0529747i
$844$	−3463.02			−4.10310
$845$		−	9.28863i		−	0.0109925i
$846$		−	758.810i		−	0.896938i
$847$	457.155	+	439.558i	0.539735	+	0.518958i
$848$	4961.76			5.85113
$849$	940.555			1.10784
$850$		−	208.030i		−	0.244741i
$851$	−16.5933			−0.0194986
$852$			1579.84i			1.85427i
$853$		−	420.775i		−	0.493289i	−0.969106	−	0.246644i	$-0.920672\pi$
$853$		−	420.775i		−	0.493289i	0.969106	−	0.246644i	$-0.0793279\pi$
$854$	−1385.18	+	1440.64i	−1.62199	+	1.68693i
$855$	125.479			0.146759
$856$	4441.86			5.18909
$857$			221.400i			0.258343i	0.991622	+	0.129171i	$0.0412317\pi$
$857$			221.400i			0.258343i	−0.991622	+	0.129171i	$0.958768\pi$
$858$	496.806			0.579029
$859$			572.033i			0.665930i	0.942939	+	0.332965i	$0.108049\pi$
$859$			572.033i			0.665930i	−0.942939	+	0.332965i	$0.891951\pi$
$860$			394.828i			0.459103i
$861$	667.924	+	642.213i	0.775754	+	0.745892i
$862$	−24.9340			−0.0289258
$863$	−1360.72			−1.57673			−0.788364	−	0.615209i	$-0.789072\pi$
$863$	−1360.72			−1.57673			−0.788364	+	0.615209i	$0.789072\pi$
$864$			833.395i			0.964578i
$865$	23.2105			0.0268329
$866$		−	2958.57i		−	3.41636i
$867$			490.483i			0.565724i
$868$	−2468.93	+	2567.77i	−2.84439	+	2.95826i
$869$	−654.621			−0.753304
$870$	15.9122			0.0182899
$871$		−	233.406i		−	0.267975i
$872$	268.249			0.307625
$873$		−	542.308i		−	0.621201i
$874$		−	447.689i		−	0.512230i
$875$	401.625	−	417.704i	0.459000	−	0.477375i
$876$	363.990			0.415514
$877$	−49.8393			−0.0568293			−0.0284146	−	0.999596i	$-0.509046\pi$
$877$	−49.8393			−0.0568293			−0.0284146	+	0.999596i	$0.509046\pi$
$878$			2831.51i			3.22495i
$879$	−462.896			−0.526616
$880$		−	689.462i		−	0.783480i
$881$		−	601.564i		−	0.682819i	−0.939915	−	0.341410i	$-0.889096\pi$
$881$		−	601.564i		−	0.682819i	0.939915	−	0.341410i	$-0.110904\pi$
$882$	22.7281	+	578.851i	0.0257688	+	0.656294i
$883$	−389.183			−0.440751			−0.220376	−	0.975415i	$-0.570728\pi$
$883$	−389.183			−0.440751			−0.220376	+	0.975415i	$0.570728\pi$
$884$	367.176			0.415357
$885$		−	109.125i		−	0.123305i
$886$	1329.56			1.50063
$887$		−	24.2233i		−	0.0273093i	−0.999907	−	0.0136546i	$-0.995653\pi$
$887$		−	24.2233i		−	0.0273093i	0.999907	−	0.0136546i	$-0.00434654\pi$
$888$			177.829i			0.200257i
$889$	−96.5084	−	92.7934i	−0.108558	−	0.104380i
$890$	−328.309			−0.368887
$891$	−49.6233			−0.0556939
$892$		−	1481.08i		−	1.66041i
$893$	1520.39			1.70257
$894$		−	921.336i		−	1.03058i
$895$			582.883i			0.651265i
$896$	3698.22	+	3555.87i	4.12748	+	3.96860i
$897$	109.654			0.122245
$898$	829.209			0.923396
$899$		−	58.2718i		−	0.0648185i
$900$	−756.900			−0.841000
$901$			169.020i			0.187591i
$902$			1660.56i			1.84097i
$903$	162.973	−	169.498i	0.180480	−	0.187705i
$904$	−4707.29			−5.20718
$905$	287.624			0.317817
$906$		−	938.669i		−	1.03606i
$907$	−327.821			−0.361434			−0.180717	−	0.983535i	$-0.557842\pi$
$907$	−327.821			−0.361434			−0.180717	+	0.983535i	$0.557842\pi$
$908$		−	1190.73i		−	1.31137i
$909$			245.006i			0.269534i
$910$	463.493	+	445.652i	0.509333	+	0.489727i
$911$	−1533.23			−1.68302			−0.841511	−	0.540239i	$-0.818334\pi$
$911$	−1533.23			−1.68302			−0.841511	+	0.540239i	$0.818334\pi$
$912$	−2905.61			−3.18597
$913$			131.600i			0.144140i
$914$	−1151.79			−1.26017
$915$		−	221.570i		−	0.242153i
$916$			2328.81i			2.54237i
$917$	270.933	−	281.780i	0.295456	−	0.307285i
$918$	−49.3987			−0.0538112
$919$	−202.306			−0.220137			−0.110069	−	0.993924i	$-0.535107\pi$
$919$	−202.306			−0.220137			−0.110069	+	0.993924i	$0.535107\pi$
$920$		−	251.279i		−	0.273129i
$921$	−75.6668			−0.0821572
$922$		−	1521.11i		−	1.64979i
$923$		−	1044.30i		−	1.13142i
$924$	−534.220	+	555.608i	−0.578160	+	0.601307i
$925$	−75.7113			−0.0818501
$926$	735.134			0.793881
$927$		−	506.934i		−	0.546855i
$928$	−211.756			−0.228185
$929$		−	834.874i		−	0.898680i	−0.893361	−	0.449340i	$-0.851659\pi$
$929$		−	834.874i		−	0.898680i	0.893361	−	0.449340i	$-0.148341\pi$
$930$		−	531.932i		−	0.571970i
$931$	−1159.82	+	45.5393i	−1.24578	+	0.0489144i
$932$	987.591			1.05965
$933$	434.559			0.465765
$934$		−	1986.39i		−	2.12675i
$935$	23.4862			0.0251189
$936$		−	1175.15i		−	1.25550i
$937$		−	1732.66i		−	1.84916i	−0.380991	−	0.924579i	$-0.624417\pi$
$937$		−	1732.66i		−	1.84916i	0.380991	−	0.924579i	$-0.375583\pi$
$938$	351.591	+	338.057i	0.374830	+	0.360401i
$939$	76.5577			0.0815311
$940$	1306.69			1.39010
$941$			642.939i			0.683251i	0.939836	+	0.341625i	$0.110977\pi$
$941$			642.939i			0.683251i	−0.939836	+	0.341625i	$0.889023\pi$
$942$	742.896			0.788636
$943$			366.514i			0.388668i
$944$			2526.92i			2.67682i
$945$	−46.2958	−	44.5137i	−0.0489903	−	0.0471044i
$946$	421.396			0.445450
$947$	−1170.04			−1.23552			−0.617760	−	0.786366i	$-0.711960\pi$
$947$	−1170.04			−1.23552			−0.617760	+	0.786366i	$0.711960\pi$
$948$			2371.01i			2.50106i
$949$	−240.605			−0.253535
$950$		−	2042.70i		−	2.15021i
$951$		−	769.582i		−	0.809235i
$952$	−347.307	+	361.211i	−0.364818	+	0.379424i
$953$	1054.33			1.10632			0.553162	−	0.833074i	$-0.313421\pi$
$953$	1054.33			1.10632			0.553162	+	0.833074i	$0.313421\pi$
$954$	828.311			0.868251
$955$			378.873i			0.396726i
$956$	−4634.44			−4.84774
$957$		−	12.6087i		−	0.0131752i
$958$			3485.52i			3.63833i
$959$	−260.131	−	250.118i	−0.271252	−	0.260811i
$960$	−1066.67			−1.11111
$961$	−986.973			−1.02703
$962$		−	179.992i		−	0.187101i
$963$	449.070			0.466324
$964$			149.564i			0.155149i
$965$			218.562i			0.226489i
$966$	−158.818	+	165.177i	−0.164408	+	0.170990i
$967$	1572.14			1.62579			0.812895	−	0.582410i	$-0.197890\pi$
$967$	1572.14			1.62579			0.812895	+	0.582410i	$0.197890\pi$
$968$	2688.41			2.77729
$969$		−	98.9780i		−	0.102144i
$970$	1257.85			1.29675
$971$		−	269.102i		−	0.277139i	−0.990353	−	0.138569i	$-0.955750\pi$
$971$		−	269.102i		−	0.277139i	0.990353	−	0.138569i	$-0.0442504\pi$
$972$			179.733i			0.184911i
$973$	1082.49	−	1125.83i	1.11253	−	1.15707i
$974$	1022.42			1.04971
$975$	500.325			0.513154
$976$			5130.72i			5.25689i
$977$	1329.66			1.36096			0.680479	−	0.732768i	$-0.261772\pi$
$977$	1329.66			1.36096			0.680479	+	0.732768i	$0.261772\pi$
$978$			117.664i			0.120310i
$979$			260.149i			0.265729i
$980$	−996.796	+	39.1384i	−1.01714	+	0.0399371i
$981$	27.1198			0.0276451
$982$	3543.81			3.60877
$983$			502.517i			0.511208i	0.966782	+	0.255604i	$0.0822743\pi$
$983$			502.517i			0.511208i	−0.966782	+	0.255604i	$0.917726\pi$
$984$	3927.89			3.99176
$985$			225.397i			0.228830i
$986$		−	12.5516i		−	0.0127299i
$987$	−560.955	−	539.362i	−0.568343	−	0.546466i
$988$	3605.39			3.64918
$989$	93.0095			0.0940440
$990$		−	115.098i		−	0.116261i
$991$	495.383			0.499882			0.249941	−	0.968261i	$-0.419589\pi$
$991$	495.383			0.499882			0.249941	+	0.968261i	$0.419589\pi$
$992$			7078.81i			7.13590i
$993$		−	459.831i		−	0.463073i
$994$	1573.08	+	1512.53i	1.58258	+	1.52166i
$995$	208.241			0.209287
$996$	476.648			0.478562
$997$		−	799.290i		−	0.801695i	−0.916145	−	0.400848i	$-0.868716\pi$
$997$		−	799.290i		−	0.801695i	0.916145	−	0.400848i	$-0.131284\pi$
$998$	3314.97			3.32161
$999$			17.9784i			0.0179964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.1	✓	60
7.6	odd	2	inner	483.3.g.a.139.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.1	✓	60	1.1	even	1	trivial
483.3.g.a.139.2	yes	60	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.94080 q^{2} +1.73205i q^{3} +11.5299 q^{4} +1.76571i q^{5} -6.82566i q^{6} +(-5.04591 - 4.85168i) q^{7} -29.6737 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.94080 q^{2} +1.73205i q^{3} +11.5299 q^{4} +1.76571i q^{5} -6.82566i q^{6} +(-5.04591 - 4.85168i) q^{7} -29.6737 q^{8} -3.00000 q^{9} -6.95831i q^{10} -5.51370 q^{11} +19.9703i q^{12} -13.2008i q^{13} +(19.8849 + 19.1195i) q^{14} -3.05830 q^{15} +70.8186 q^{16} +2.41240i q^{17} +11.8224 q^{18} +23.6880i q^{19} +20.3585i q^{20} +(8.40335 - 8.73978i) q^{21} +21.7284 q^{22} +4.79583 q^{23} -51.3964i q^{24} +21.8823 q^{25} +52.0216i q^{26} -5.19615i q^{27} +(-58.1788 - 55.9393i) q^{28} +1.32028 q^{29} +12.0522 q^{30} -44.1358i q^{31} -160.387 q^{32} -9.55001i q^{33} -9.50678i q^{34} +(8.56666 - 8.90963i) q^{35} -34.5896 q^{36} -3.45994 q^{37} -93.3496i q^{38} +22.8644 q^{39} -52.3953i q^{40} +76.4235i q^{41} +(-33.1159 + 34.4417i) q^{42} +19.3938 q^{43} -63.5723 q^{44} -5.29714i q^{45} -18.8994 q^{46} -64.1841i q^{47} +122.661i q^{48} +(1.92246 + 48.9623i) q^{49} -86.2335 q^{50} -4.17840 q^{51} -152.203i q^{52} +70.0629 q^{53} +20.4770i q^{54} -9.73560i q^{55} +(149.731 + 143.967i) q^{56} -41.0288 q^{57} -5.20297 q^{58} +35.6816i q^{59} -35.2619 q^{60} +72.4488i q^{61} +173.930i q^{62} +(15.1377 + 14.5550i) q^{63} +348.778 q^{64} +23.3088 q^{65} +37.6346i q^{66} +17.6813 q^{67} +27.8147i q^{68} +8.30662i q^{69} +(-33.7595 + 35.1110i) q^{70} +79.1093 q^{71} +89.0212 q^{72} -18.2265i q^{73} +13.6349 q^{74} +37.9012i q^{75} +273.120i q^{76} +(27.8216 + 26.7507i) q^{77} -90.1040 q^{78} +118.726 q^{79} +125.045i q^{80} +9.00000 q^{81} -301.169i q^{82} -23.8678i q^{83} +(96.8896 - 100.769i) q^{84} -4.25961 q^{85} -76.4271 q^{86} +2.28680i q^{87} +163.612 q^{88} -47.1823i q^{89} +20.8749i q^{90} +(-64.0459 + 66.6100i) q^{91} +55.2954 q^{92} +76.4455 q^{93} +252.937i q^{94} -41.8262 q^{95} -277.798i q^{96} +180.769i q^{97} +(-7.57604 - 192.950i) q^{98} +16.5411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Introduction

L-functions

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