LMFDB - Embedded newform 483.3.g.a.139.5

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			139.5
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.29495 q^{2} +1.73205i q^{3} +6.85669 q^{4} -6.17562i q^{5} -5.70702i q^{6} +(-6.91716 + 1.07376i) q^{7} -9.41266 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.29495 q^{2} +1.73205i q^{3} +6.85669 q^{4} -6.17562i q^{5} -5.70702i q^{6} +(-6.91716 + 1.07376i) q^{7} -9.41266 q^{8} -3.00000 q^{9} +20.3484i q^{10} +18.6871 q^{11} +11.8761i q^{12} +3.26619i q^{13} +(22.7917 - 3.53798i) q^{14} +10.6965 q^{15} +3.58748 q^{16} +14.6408i q^{17} +9.88485 q^{18} -21.5903i q^{19} -42.3444i q^{20} +(-1.85980 - 11.9809i) q^{21} -61.5731 q^{22} -4.79583 q^{23} -16.3032i q^{24} -13.1383 q^{25} -10.7619i q^{26} -5.19615i q^{27} +(-47.4288 + 7.36244i) q^{28} +8.81655 q^{29} -35.2444 q^{30} +13.8198i q^{31} +25.8301 q^{32} +32.3670i q^{33} -48.2408i q^{34} +(6.63113 + 42.7178i) q^{35} -20.5701 q^{36} -23.7342 q^{37} +71.1391i q^{38} -5.65721 q^{39} +58.1291i q^{40} -0.813534i q^{41} +(6.12796 + 39.4763i) q^{42} -55.9522 q^{43} +128.132 q^{44} +18.5269i q^{45} +15.8020 q^{46} -53.2456i q^{47} +6.21370i q^{48} +(46.6941 - 14.8547i) q^{49} +43.2901 q^{50} -25.3587 q^{51} +22.3953i q^{52} +9.55590 q^{53} +17.1211i q^{54} -115.405i q^{55} +(65.1089 - 10.1069i) q^{56} +37.3956 q^{57} -29.0501 q^{58} -70.3769i q^{59} +73.3426 q^{60} -73.6403i q^{61} -45.5355i q^{62} +(20.7515 - 3.22128i) q^{63} -99.4588 q^{64} +20.1708 q^{65} -106.648i q^{66} +63.1408 q^{67} +100.388i q^{68} -8.30662i q^{69} +(-21.8492 - 140.753i) q^{70} +40.6288 q^{71} +28.2380 q^{72} -17.4936i q^{73} +78.2029 q^{74} -22.7563i q^{75} -148.038i q^{76} +(-129.262 + 20.0655i) q^{77} +18.6402 q^{78} -30.8574 q^{79} -22.1549i q^{80} +9.00000 q^{81} +2.68056i q^{82} -140.993i q^{83} +(-12.7521 - 82.1491i) q^{84} +90.4163 q^{85} +184.360 q^{86} +15.2707i q^{87} -175.896 q^{88} -117.309i q^{89} -61.0451i q^{90} +(-3.50710 - 22.5928i) q^{91} -32.8836 q^{92} -23.9366 q^{93} +175.442i q^{94} -133.334 q^{95} +44.7390i q^{96} -62.3174i q^{97} +(-153.855 + 48.9455i) q^{98} -56.0613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.29495			−1.64747			−0.823737	−	0.566971i	$-0.808115\pi$
$2$	−3.29495			−1.64747			−0.823737	+	0.566971i	$0.808115\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	6.85669			1.71417
$5$		−	6.17562i		−	1.23512i	−0.786522	−	0.617562i	$-0.788120\pi$
$5$		−	6.17562i		−	1.23512i	0.786522	−	0.617562i	$-0.211880\pi$
$6$		−	5.70702i		−	0.951170i
$7$	−6.91716	+	1.07376i	−0.988165	+	0.153394i
$7$	−6.91716	+	1.07376i	−0.988165	+	0.153394i
$8$	−9.41266			−1.17658
$9$	−3.00000			−0.333333
$10$			20.3484i			2.03484i
$11$	18.6871			1.69883			0.849414	−	0.527727i	$-0.176955\pi$
$11$	18.6871			1.69883			0.849414	+	0.527727i	$0.176955\pi$
$12$			11.8761i			0.989679i
$13$			3.26619i			0.251246i	0.992078	+	0.125623i	$0.0400929\pi$
$13$			3.26619i			0.251246i	−0.992078	+	0.125623i	$0.959907\pi$
$14$	22.7917	−	3.53798i	1.62798	−	0.252713i
$15$	10.6965			0.713100
$16$	3.58748			0.224218
$17$			14.6408i			0.861226i	0.902537	+	0.430613i	$0.141703\pi$
$17$			14.6408i			0.861226i	−0.902537	+	0.430613i	$0.858297\pi$
$18$	9.88485			0.549158
$19$		−	21.5903i		−	1.13633i	−0.822913	−	0.568167i	$-0.807653\pi$
$19$		−	21.5903i		−	1.13633i	0.822913	−	0.568167i	$-0.192347\pi$
$20$		−	42.3444i		−	2.11722i
$21$	−1.85980	−	11.9809i	−0.0885621	−	0.570517i
$22$	−61.5731			−2.79878
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$		−	16.3032i		−	0.679301i
$25$	−13.1383			−0.525533
$26$		−	10.7619i		−	0.413921i
$27$		−	5.19615i		−	0.192450i
$28$	−47.4288	+	7.36244i	−1.69389	+	0.262944i
$29$	8.81655			0.304019			0.152010	−	0.988379i	$-0.451426\pi$
$29$	8.81655			0.304019			0.152010	+	0.988379i	$0.451426\pi$
$30$	−35.2444			−1.17481
$31$			13.8198i			0.445800i	0.974841	+	0.222900i	$0.0715523\pi$
$31$			13.8198i			0.445800i	−0.974841	+	0.222900i	$0.928448\pi$
$32$	25.8301			0.807190
$33$			32.3670i			0.980819i
$34$		−	48.2408i		−	1.41885i
$35$	6.63113	+	42.7178i	0.189461	+	1.22051i
$36$	−20.5701			−0.571391
$37$	−23.7342			−0.641464			−0.320732	−	0.947170i	$-0.603929\pi$
$37$	−23.7342			−0.641464			−0.320732	+	0.947170i	$0.603929\pi$
$38$			71.1391i			1.87208i
$39$	−5.65721			−0.145057
$40$			58.1291i			1.45323i
$41$		−	0.813534i		−	0.0198423i	−0.999951	−	0.00992115i	$-0.996842\pi$
$41$		−	0.813534i		−	0.0198423i	0.999951	−	0.00992115i	$-0.00315805\pi$
$42$	6.12796	+	39.4763i	0.145904	+	0.939913i
$43$	−55.9522			−1.30121			−0.650606	−	0.759415i	$-0.725485\pi$
$43$	−55.9522			−1.30121			−0.650606	+	0.759415i	$0.725485\pi$
$44$	128.132			2.91209
$45$			18.5269i			0.411708i
$46$	15.8020			0.343522
$47$		−	53.2456i		−	1.13289i	−0.824101	−	0.566443i	$-0.808319\pi$
$47$		−	53.2456i		−	1.13289i	0.824101	−	0.566443i	$-0.191681\pi$
$48$			6.21370i			0.129452i
$49$	46.6941	−	14.8547i	0.952940	−	0.303157i
$50$	43.2901			0.865803
$51$	−25.3587			−0.497229
$52$			22.3953i			0.430678i
$53$	9.55590			0.180300			0.0901500	−	0.995928i	$-0.471265\pi$
$53$	9.55590			0.180300			0.0901500	+	0.995928i	$0.471265\pi$
$54$			17.1211i			0.317057i
$55$		−	115.405i		−	2.09827i
$56$	65.1089	−	10.1069i	1.16266	−	0.180481i
$57$	37.3956			0.656063
$58$	−29.0501			−0.500864
$59$		−	70.3769i		−	1.19283i	−0.802677	−	0.596414i	$-0.796592\pi$
$59$		−	70.3769i		−	1.19283i	0.802677	−	0.596414i	$-0.203408\pi$
$60$	73.3426			1.22238
$61$		−	73.6403i		−	1.20722i	−0.797280	−	0.603609i	$-0.793729\pi$
$61$		−	73.6403i		−	1.20722i	0.797280	−	0.603609i	$-0.206271\pi$
$62$		−	45.5355i		−	0.734444i
$63$	20.7515	−	3.22128i	0.329388	−	0.0511314i
$64$	−99.4588			−1.55404
$65$	20.1708			0.310320
$66$		−	106.648i		−	1.61587i
$67$	63.1408			0.942399			0.471200	−	0.882027i	$-0.343821\pi$
$67$	63.1408			0.942399			0.471200	+	0.882027i	$0.343821\pi$
$68$			100.388i			1.47629i
$69$		−	8.30662i		−	0.120386i
$70$	−21.8492	−	140.753i	−0.312132	−	2.01075i
$71$	40.6288			0.572236			0.286118	−	0.958194i	$-0.407635\pi$
$71$	40.6288			0.572236			0.286118	+	0.958194i	$0.407635\pi$
$72$	28.2380			0.392194
$73$		−	17.4936i		−	0.239639i	−0.992796	−	0.119819i	$-0.961768\pi$
$73$		−	17.4936i		−	0.239639i	0.992796	−	0.119819i	$-0.0382316\pi$
$74$	78.2029			1.05680
$75$		−	22.7563i		−	0.303417i
$76$		−	148.038i		−	1.94787i
$77$	−129.262	+	20.0655i	−1.67872	+	0.260590i
$78$	18.6402			0.238977
$79$	−30.8574			−0.390600			−0.195300	−	0.980744i	$-0.562568\pi$
$79$	−30.8574			−0.390600			−0.195300	+	0.980744i	$0.562568\pi$
$80$		−	22.1549i		−	0.276937i
$81$	9.00000			0.111111
$82$			2.68056i			0.0326897i
$83$		−	140.993i		−	1.69871i	−0.527821	−	0.849356i	$-0.676991\pi$
$83$		−	140.993i		−	1.69871i	0.527821	−	0.849356i	$-0.323009\pi$
$84$	−12.7521	−	82.1491i	−0.151811	−	0.977966i
$85$	90.4163			1.06372
$86$	184.360			2.14372
$87$			15.2707i			0.175525i
$88$	−175.896			−1.99881
$89$		−	117.309i		−	1.31808i	−0.752110	−	0.659038i	$-0.770964\pi$
$89$		−	117.309i		−	1.31808i	0.752110	−	0.659038i	$-0.229036\pi$
$90$		−	61.0451i		−	0.678279i
$91$	−3.50710	−	22.5928i	−0.0385396	−	0.248272i
$92$	−32.8836			−0.357430
$93$	−23.9366			−0.257383
$94$			175.442i			1.86640i
$95$	−133.334			−1.40351
$96$			44.7390i			0.466032i
$97$		−	62.3174i		−	0.642447i	−0.947003	−	0.321224i	$-0.895906\pi$
$97$		−	62.3174i		−	0.642447i	0.947003	−	0.321224i	$-0.104094\pi$
$98$	−153.855	+	48.9455i	−1.56995	+	0.499444i
$99$	−56.0613			−0.566276
$100$	−90.0855			−0.900855
$101$		−	166.315i		−	1.64669i	−0.567544	−	0.823343i	$-0.692106\pi$
$101$		−	166.315i		−	1.64669i	0.567544	−	0.823343i	$-0.307894\pi$
$102$	83.5556			0.819172
$103$			92.5486i			0.898530i	0.893399	+	0.449265i	$0.148314\pi$
$103$			92.5486i			0.898530i	−0.893399	+	0.449265i	$0.851686\pi$
$104$		−	30.7436i		−	0.295611i
$105$	−73.9893	+	11.4855i	−0.704660	+	0.109385i
$106$	−31.4862			−0.297040
$107$	−14.0784			−0.131574			−0.0657869	−	0.997834i	$-0.520956\pi$
$107$	−14.0784			−0.131574			−0.0657869	+	0.997834i	$0.520956\pi$
$108$		−	35.6284i		−	0.329893i
$109$	17.9547			0.164722			0.0823608	−	0.996603i	$-0.473754\pi$
$109$	17.9547			0.164722			0.0823608	+	0.996603i	$0.473754\pi$
$110$			380.252i			3.45684i
$111$		−	41.1088i		−	0.370349i
$112$	−24.8152	+	3.85209i	−0.221564	+	0.0343937i
$113$	117.574			1.04048			0.520238	−	0.854022i	$-0.325843\pi$
$113$	117.574			1.04048			0.520238	+	0.854022i	$0.325843\pi$
$114$	−123.217			−1.08085
$115$			29.6173i			0.257541i
$116$	60.4524			0.521141
$117$		−	9.79858i		−	0.0837485i
$118$			231.888i			1.96515i
$119$	−15.7207	−	101.273i	−0.132107	−	0.851034i
$120$	−100.683			−0.839021
$121$	228.208			1.88602
$122$			242.641i			1.98886i
$123$	1.40908			0.0114560
$124$			94.7581i			0.764178i
$125$		−	73.2532i		−	0.586026i
$126$	−68.3750	+	10.6139i	−0.542659	+	0.0842377i
$127$	−30.7007			−0.241738			−0.120869	−	0.992668i	$-0.538568\pi$
$127$	−30.7007			−0.241738			−0.120869	+	0.992668i	$0.538568\pi$
$128$	224.391			1.75306
$129$		−	96.9120i		−	0.751256i
$130$	−66.4617			−0.511244
$131$			106.463i			0.812696i	0.913718	+	0.406348i	$0.133198\pi$
$131$			106.463i			0.812696i	−0.913718	+	0.406348i	$0.866802\pi$
$132$			221.931i			1.68129i
$133$	23.1828	+	149.344i	0.174307	+	1.12289i
$134$	−208.046			−1.55258
$135$	−32.0895			−0.237700
$136$		−	137.809i		−	1.01330i
$137$	109.057			0.796033			0.398016	−	0.917378i	$-0.369699\pi$
$137$	109.057			0.796033			0.398016	+	0.917378i	$0.369699\pi$
$138$			27.3699i			0.198333i
$139$			119.876i			0.862418i	0.902252	+	0.431209i	$0.141913\pi$
$139$			119.876i			0.862418i	−0.902252	+	0.431209i	$0.858087\pi$
$140$	45.4676	+	292.903i	0.324769	+	2.09216i
$141$	92.2241			0.654072
$142$	−133.870			−0.942744
$143$			61.0357i			0.426823i
$144$	−10.7624			−0.0747392
$145$		−	54.4477i		−	0.375501i
$146$			57.6407i			0.394799i
$147$	25.7291	+	80.8765i	0.175028	+	0.550180i
$148$	−162.738			−1.09958
$149$	−57.1282			−0.383411			−0.191705	−	0.981453i	$-0.561402\pi$
$149$	−57.1282			−0.383411			−0.191705	+	0.981453i	$0.561402\pi$
$150$			74.9807i			0.499871i
$151$	−177.338			−1.17442			−0.587211	−	0.809434i	$-0.699774\pi$
$151$	−177.338			−1.17442			−0.587211	+	0.809434i	$0.699774\pi$
$152$			203.223i			1.33699i
$153$		−	43.9225i		−	0.287075i
$154$	425.911	−	66.1147i	2.76565	−	0.429316i
$155$	85.3459			0.550618
$156$	−38.7898			−0.248652
$157$		−	278.100i		−	1.77134i	−0.464318	−	0.885668i	$-0.653701\pi$
$157$		−	278.100i		−	1.77134i	0.464318	−	0.885668i	$-0.346299\pi$
$158$	101.674			0.643504
$159$			16.5513i			0.104096i
$160$		−	159.517i		−	0.996981i
$161$	33.1735	−	5.14957i	0.206047	−	0.0319849i
$162$	−29.6545			−0.183053
$163$	−271.093			−1.66315			−0.831574	−	0.555414i	$-0.812560\pi$
$163$	−271.093			−1.66315			−0.831574	+	0.555414i	$0.812560\pi$
$164$		−	5.57816i		−	0.0340132i
$165$	199.887			1.21143
$166$			464.565i			2.79859i
$167$		−	292.831i		−	1.75348i	−0.480968	−	0.876738i	$-0.659715\pi$
$167$		−	292.831i		−	1.75348i	0.480968	−	0.876738i	$-0.340285\pi$
$168$	17.5057	+	112.772i	0.104201	+	0.671261i
$169$	158.332			0.936876
$170$	−297.917			−1.75245
$171$			64.7710i			0.378778i
$172$	−383.647			−2.23050
$173$			303.399i			1.75375i	0.480715	+	0.876877i	$0.340377\pi$
$173$			303.399i			1.75375i	−0.480715	+	0.876877i	$0.659623\pi$
$174$		−	50.3162i		−	0.289174i
$175$	90.8799	−	14.1074i	0.519313	−	0.0806137i
$176$	67.0397			0.380907
$177$	121.896			0.688680
$178$			386.526i			2.17150i
$179$	−292.706			−1.63523			−0.817616	−	0.575764i	$-0.804705\pi$
$179$	−292.706			−1.63523			−0.817616	+	0.575764i	$0.804705\pi$
$180$			127.033i			0.705739i
$181$			21.6285i			0.119495i	0.998214	+	0.0597473i	$0.0190295\pi$
$181$			21.6285i			0.119495i	−0.998214	+	0.0597473i	$0.980971\pi$
$182$	11.5557	+	74.4420i	0.0634930	+	0.409022i
$183$	127.549			0.696988
$184$	45.1416			0.245335
$185$			146.573i			0.792288i
$186$	78.8699			0.424032
$187$			273.595i			1.46308i
$188$		−	365.089i		−	1.94196i
$189$	5.57941	+	35.9426i	0.0295207	+	0.190172i
$190$	439.328			2.31225
$191$	37.3713			0.195661			0.0978306	−	0.995203i	$-0.468810\pi$
$191$	37.3713			0.195661			0.0978306	+	0.995203i	$0.468810\pi$
$192$		−	172.268i		−	0.897227i
$193$	50.5070			0.261694			0.130847	−	0.991403i	$-0.458230\pi$
$193$	50.5070			0.261694			0.130847	+	0.991403i	$0.458230\pi$
$194$			205.333i			1.05842i
$195$			34.9368i			0.179163i
$196$	320.167	−	101.854i	1.63351	−	0.519664i
$197$	−168.711			−0.856402			−0.428201	−	0.903684i	$-0.640852\pi$
$197$	−168.711			−0.856402			−0.428201	+	0.903684i	$0.640852\pi$
$198$	184.719			0.932926
$199$		−	268.488i		−	1.34918i	−0.738191	−	0.674592i	$-0.764320\pi$
$199$		−	268.488i		−	1.34918i	0.738191	−	0.674592i	$-0.235680\pi$
$200$	123.667			0.618333
$201$			109.363i			0.544095i
$202$			548.001i			2.71287i
$203$	−60.9855	+	9.46685i	−0.300421	+	0.0466347i
$204$	−173.877			−0.852337
$205$	−5.02408			−0.0245077
$206$		−	304.943i		−	1.48031i
$207$	14.3875			0.0695048
$208$			11.7174i			0.0563336i
$209$		−	403.461i		−	1.93044i
$210$	243.791	−	37.8440i	1.16091	−	0.180210i
$211$	−359.772			−1.70508			−0.852540	−	0.522661i	$-0.824939\pi$
$211$	−359.772			−1.70508			−0.852540	+	0.522661i	$0.824939\pi$
$212$	65.5219			0.309066
$213$			70.3711i			0.330381i
$214$	46.3876			0.216765
$215$			345.539i			1.60716i
$216$			48.9096i			0.226434i
$217$	−14.8391	−	95.5937i	−0.0683831	−	0.440524i
$218$	−59.1597			−0.271375
$219$	30.2999			0.138356
$220$		−	791.294i		−	3.59679i
$221$	−47.8198			−0.216379
$222$			135.451i			0.610141i
$223$			80.2136i			0.359702i	0.983694	+	0.179851i	$0.0575616\pi$
$223$			80.2136i			0.359702i	−0.983694	+	0.179851i	$0.942438\pi$
$224$	−178.671	+	27.7353i	−0.797637	+	0.123818i
$225$	39.4150			0.175178
$226$	−387.400			−1.71416
$227$			135.098i			0.595146i	0.954699	+	0.297573i	$0.0961772\pi$
$227$			135.098i			0.595146i	−0.954699	+	0.297573i	$0.903823\pi$
$228$	256.410			1.12461
$229$		−	82.7151i		−	0.361201i	−0.983557	−	0.180601i	$-0.942196\pi$
$229$		−	82.7151i		−	0.361201i	0.983557	−	0.180601i	$-0.0578042\pi$
$230$		−	97.5874i		−	0.424293i
$231$	−34.7544	−	223.888i	−0.150452	−	0.969211i
$232$	−82.9872			−0.357704
$233$	−342.059			−1.46806			−0.734032	−	0.679115i	$-0.762364\pi$
$233$	−342.059			−1.46806			−0.734032	+	0.679115i	$0.762364\pi$
$234$			32.2858i			0.137974i
$235$	−328.825			−1.39926
$236$		−	482.553i		−	2.04472i
$237$		−	53.4466i		−	0.225513i
$238$	51.7990	+	333.689i	0.217643	+	1.40206i
$239$	261.082			1.09239			0.546196	−	0.837658i	$-0.316075\pi$
$239$	261.082			1.09239			0.546196	+	0.837658i	$0.316075\pi$
$240$	38.3735			0.159889
$241$			318.890i			1.32319i	0.749860	+	0.661597i	$0.230121\pi$
$241$			318.890i			1.32319i	−0.749860	+	0.661597i	$0.769879\pi$
$242$	−751.935			−3.10717
$243$			15.5885i			0.0641500i
$244$		−	504.929i		−	2.06938i
$245$	−91.7371	−	288.365i	−0.374437	−	1.17700i
$246$	−4.64286			−0.0188734
$247$	70.5182			0.285499
$248$		−	130.081i		−	0.524521i
$249$	244.207			0.980752
$250$			241.366i			0.965463i
$251$			233.834i			0.931610i	0.884887	+	0.465805i	$0.154235\pi$
$251$			233.834i			0.931610i	−0.884887	+	0.465805i	$0.845765\pi$
$252$	142.286	−	22.0873i	0.564629	−	0.0876481i
$253$	−89.6202			−0.354230
$254$	101.157			0.398257
$255$			156.606i			0.614140i
$256$	−341.523			−1.33407
$257$		−	313.621i		−	1.22031i	−0.792280	−	0.610157i	$-0.791106\pi$
$257$		−	313.621i		−	1.22031i	0.792280	−	0.610157i	$-0.208894\pi$
$258$			319.320i			1.23767i
$259$	164.173	−	25.4848i	0.633872	−	0.0983968i
$260$	138.305			0.531942
$261$	−26.4497			−0.101340
$262$		−	350.791i		−	1.33890i
$263$	320.398			1.21824			0.609122	−	0.793077i	$-0.291522\pi$
$263$	320.398			1.21824			0.609122	+	0.793077i	$0.291522\pi$
$264$		−	304.660i		−	1.15402i
$265$		−	59.0136i		−	0.222693i
$266$	−76.3862	−	492.080i	−0.287166	−	1.84993i
$267$	203.185			0.760991
$268$	432.937			1.61544
$269$		−	366.289i		−	1.36167i	−0.732438	−	0.680834i	$-0.761617\pi$
$269$		−	366.289i		−	1.36167i	0.732438	−	0.680834i	$-0.238383\pi$
$270$	105.733			0.391605
$271$		−	37.5106i		−	0.138416i	−0.997602	−	0.0692078i	$-0.977953\pi$
$271$		−	37.5106i		−	0.138416i	0.997602	−	0.0692078i	$-0.0220472\pi$
$272$			52.5237i			0.193102i
$273$	39.1318	−	6.07448i	0.143340	−	0.0222508i
$274$	−359.336			−1.31144
$275$	−245.517			−0.892791
$276$		−	56.9560i		−	0.206362i
$277$	125.818			0.454216			0.227108	−	0.973870i	$-0.427073\pi$
$277$	125.818			0.454216			0.227108	+	0.973870i	$0.427073\pi$
$278$		−	394.986i		−	1.42081i
$279$		−	41.4594i		−	0.148600i
$280$	−62.4166	−	402.088i	−0.222916	−	1.43603i
$281$	523.002			1.86122			0.930609	−	0.366015i	$-0.119278\pi$
$281$	523.002			1.86122			0.930609	+	0.366015i	$0.119278\pi$
$282$	−303.874			−1.07757
$283$			299.760i			1.05922i	0.848240	+	0.529612i	$0.177662\pi$
$283$			299.760i			1.05922i	−0.848240	+	0.529612i	$0.822338\pi$
$284$	278.579			0.980912
$285$		−	230.941i		−	0.810319i
$286$		−	201.110i		−	0.703180i
$287$	0.873540	+	5.62734i	0.00304369	+	0.0196075i
$288$	−77.4903			−0.269063
$289$	74.6457			0.258290
$290$			179.402i			0.618629i
$291$	107.937			0.370917
$292$		−	119.949i		−	0.410783i
$293$			517.985i			1.76787i	0.467613	+	0.883933i	$0.345114\pi$
$293$			517.985i			1.76787i	−0.467613	+	0.883933i	$0.654886\pi$
$294$	−84.7762	−	266.484i	−0.288354	−	0.906408i
$295$	−434.621			−1.47329
$296$	223.402			0.754736
$297$		−	97.1011i		−	0.326940i
$298$	188.234			0.631659
$299$		−	15.6641i		−	0.0523883i
$300$		−	156.033i		−	0.520109i
$301$	387.030	−	60.0791i	1.28581	−	0.199598i
$302$	584.319			1.93483
$303$	288.067			0.950715
$304$		−	77.4549i		−	0.254786i
$305$	−454.775			−1.49107
$306$			144.723i			0.472949i
$307$			152.975i			0.498291i	0.968466	+	0.249146i	$0.0801498\pi$
$307$			152.975i			0.498291i	−0.968466	+	0.249146i	$0.919850\pi$
$308$	−886.308	+	137.583i	−2.87762	+	0.446697i
$309$	−160.299			−0.518767
$310$	−281.210			−0.907130
$311$			115.037i			0.369895i	0.982748	+	0.184947i	$0.0592115\pi$
$311$			115.037i			0.369895i	−0.982748	+	0.184947i	$0.940788\pi$
$312$	53.2494			0.170671
$313$		−	563.173i		−	1.79928i	−0.436636	−	0.899638i	$-0.643830\pi$
$313$		−	563.173i		−	1.79928i	0.436636	−	0.899638i	$-0.356170\pi$
$314$			916.325i			2.91823i
$315$	−19.8934	−	128.153i	−0.0631536	−	0.406836i
$316$	−211.580			−0.669557
$317$	−469.568			−1.48129			−0.740644	−	0.671897i	$-0.765480\pi$
$317$	−469.568			−1.48129			−0.740644	+	0.671897i	$0.765480\pi$
$318$		−	54.5357i		−	0.171496i
$319$	164.756			0.516476
$320$			614.220i			1.91944i
$321$		−	24.3845i		−	0.0759642i
$322$	−109.305	+	16.9676i	−0.339457	+	0.0526943i
$323$	316.101			0.978640
$324$	61.7102			0.190464
$325$		−	42.9123i		−	0.132038i
$326$	893.238			2.73999
$327$			31.0984i			0.0951021i
$328$			7.65753i			0.0233461i
$329$	57.1730	+	368.308i	0.173778	+	1.11948i
$330$	−658.616			−1.99581
$331$	306.543			0.926113			0.463057	−	0.886329i	$-0.346753\pi$
$331$	306.543			0.926113			0.463057	+	0.886329i	$0.346753\pi$
$332$		−	966.746i		−	2.91189i
$333$	71.2025			0.213821
$334$			964.862i			2.88881i
$335$		−	389.934i		−	1.16398i
$336$	−6.67201	−	42.9811i	−0.0198572	−	0.127920i
$337$	−185.669			−0.550946			−0.275473	−	0.961309i	$-0.588834\pi$
$337$	−185.669			−0.550946			−0.275473	+	0.961309i	$0.588834\pi$
$338$	−521.696			−1.54348
$339$			203.644i			0.600719i
$340$	619.957			1.82340
$341$			258.252i			0.757338i
$342$		−	213.417i		−	0.624027i
$343$	−307.040	+	152.891i	−0.895160	+	0.445745i
$344$	526.659			1.53099
$345$	−51.2986			−0.148692
$346$		−	999.686i		−	2.88927i
$347$	27.6667			0.0797310			0.0398655	−	0.999205i	$-0.487307\pi$
$347$	27.6667			0.0797310			0.0398655	+	0.999205i	$0.487307\pi$
$348$			104.707i			0.300881i
$349$		−	172.121i		−	0.493184i	−0.969119	−	0.246592i	$-0.920689\pi$
$349$		−	172.121i		−	0.493184i	0.969119	−	0.246592i	$-0.0793108\pi$
$350$	−299.445	+	46.4832i	−0.855556	+	0.132809i
$351$	16.9716			0.0483522
$352$	482.690			1.37128
$353$			471.614i			1.33602i	0.744153	+	0.668009i	$0.232853\pi$
$353$			471.614i			1.33602i	−0.744153	+	0.668009i	$0.767147\pi$
$354$	−401.642			−1.13458
$355$		−	250.908i		−	0.706783i
$356$		−	804.350i		−	2.25941i
$357$	175.410	−	27.2291i	0.491344	−	0.0762720i
$358$	964.453			2.69400
$359$	425.042			1.18396			0.591980	−	0.805952i	$-0.298346\pi$
$359$	425.042			1.18396			0.591980	+	0.805952i	$0.298346\pi$
$360$		−	174.387i		−	0.484409i
$361$	−105.143			−0.291255
$362$		−	71.2649i		−	0.196864i
$363$			395.268i			1.08889i
$364$	−24.0471	−	154.912i	−0.0660635	−	0.425581i
$365$	−108.034			−0.295984
$366$	−420.267			−1.14827
$367$		−	383.085i		−	1.04383i	−0.852998	−	0.521915i	$-0.825218\pi$
$367$		−	383.085i		−	1.04383i	0.852998	−	0.521915i	$-0.174782\pi$
$368$	−17.2050			−0.0467526
$369$			2.44060i			0.00661410i
$370$		−	482.952i		−	1.30527i
$371$	−66.0997	+	10.2607i	−0.178166	+	0.0276570i
$372$	−164.126			−0.441199
$373$	711.450			1.90737			0.953686	−	0.300802i	$-0.0972545\pi$
$373$	711.450			1.90737			0.953686	+	0.300802i	$0.0972545\pi$
$374$		−	901.482i		−	2.41038i
$375$	126.878			0.338342
$376$			501.183i			1.33293i
$377$			28.7965i			0.0763834i
$378$	−18.3839	−	118.429i	−0.0486346	−	0.313304i
$379$	490.334			1.29376			0.646879	−	0.762592i	$-0.276074\pi$
$379$	490.334			1.29376			0.646879	+	0.762592i	$0.276074\pi$
$380$	−914.229			−2.40587
$381$		−	53.1752i		−	0.139568i
$382$	−123.137			−0.322347
$383$		−	187.274i		−	0.488967i	−0.969653	−	0.244484i	$-0.921382\pi$
$383$		−	187.274i		−	0.488967i	0.969653	−	0.244484i	$-0.0786184\pi$
$384$			388.657i			1.01213i
$385$	123.917	+	798.271i	0.321862	+	2.07343i
$386$	−166.418			−0.431135
$387$	167.856			0.433738
$388$		−	427.291i		−	1.10127i
$389$	−673.049			−1.73020			−0.865101	−	0.501597i	$-0.832746\pi$
$389$	−673.049			−1.73020			−0.865101	+	0.501597i	$0.832746\pi$
$390$		−	115.115i		−	0.295167i
$391$		−	70.2150i		−	0.179578i
$392$	−439.516	+	139.822i	−1.12121	+	0.356690i
$393$	−184.400			−0.469210
$394$	555.895			1.41090
$395$			190.564i			0.482440i
$396$	−384.395			−0.970696
$397$		−	499.360i		−	1.25783i	−0.777473	−	0.628916i	$-0.783499\pi$
$397$		−	499.360i		−	1.25783i	0.777473	−	0.628916i	$-0.216501\pi$
$398$			884.653i			2.22275i
$399$	−258.671	+	40.1538i	−0.648298	+	0.100636i
$400$	−47.1335			−0.117834
$401$	523.213			1.30477			0.652385	−	0.757888i	$-0.273768\pi$
$401$	523.213			1.30477			0.652385	+	0.757888i	$0.273768\pi$
$402$		−	360.346i		−	0.896382i
$403$	−45.1381			−0.112005
$404$		−	1140.37i		−	2.82271i
$405$		−	55.5806i		−	0.137236i
$406$	200.944	−	31.1928i	0.494936	−	0.0768295i
$407$	−443.523			−1.08974
$408$	238.693			0.585031
$409$			118.910i			0.290733i	0.989378	+	0.145367i	$0.0464361\pi$
$409$			118.910i			0.290733i	−0.989378	+	0.145367i	$0.953564\pi$
$410$	16.5541			0.0403759
$411$			188.891i			0.459590i
$412$			634.577i			1.54024i
$413$	75.5678	+	486.808i	0.182973	+	1.17871i
$414$	−47.4061			−0.114507
$415$	−870.720			−2.09812
$416$			84.3660i			0.202803i
$417$	−207.632			−0.497917
$418$			1329.38i			3.18035i
$419$		−	303.292i		−	0.723848i	−0.932208	−	0.361924i	$-0.882120\pi$
$419$		−	303.292i		−	0.723848i	0.932208	−	0.361924i	$-0.117880\pi$
$420$	−507.322	+	78.7523i	−1.20791	+	0.187505i
$421$	−104.240			−0.247601			−0.123801	−	0.992307i	$-0.539508\pi$
$421$	−104.240			−0.247601			−0.123801	+	0.992307i	$0.539508\pi$
$422$	1185.43			2.80908
$423$			159.737i			0.377629i
$424$	−89.9465			−0.212138
$425$		−	192.356i		−	0.452603i
$426$		−	231.869i		−	0.544294i
$427$	79.0719	+	509.381i	0.185180	+	1.19293i
$428$	−96.5313			−0.225540
$429$	−105.717			−0.246426
$430$		−	1138.54i		−	2.64776i
$431$	−834.590			−1.93640			−0.968202	−	0.250171i	$-0.919513\pi$
$431$	−834.590			−1.93640			−0.968202	+	0.250171i	$0.919513\pi$
$432$		−	18.6411i		−	0.0431507i
$433$			743.715i			1.71759i	0.512321	+	0.858794i	$0.328786\pi$
$433$			743.715i			1.71759i	−0.512321	+	0.858794i	$0.671214\pi$
$434$	48.8942	+	314.976i	0.112659	+	0.725752i
$435$	94.3062			0.216796
$436$	123.110			0.282361
$437$			103.544i			0.236942i
$438$	−99.8366			−0.227937
$439$		−	507.065i		−	1.15505i	−0.816374	−	0.577523i	$-0.804019\pi$
$439$		−	507.065i		−	1.15505i	0.816374	−	0.577523i	$-0.195981\pi$
$440$			1086.26i			2.46878i
$441$	−140.082	+	44.5641i	−0.317647	+	0.101052i
$442$	157.564			0.356479
$443$	−4.71685			−0.0106475			−0.00532376	−	0.999986i	$-0.501695\pi$
$443$	−4.71685			−0.0106475			−0.00532376	+	0.999986i	$0.501695\pi$
$444$		−	281.870i		−	0.634843i
$445$	−724.455			−1.62799
$446$		−	264.300i		−	0.592600i
$447$		−	98.9489i		−	0.221362i
$448$	687.972	−	106.795i	1.53565	−	0.238381i
$449$	512.840			1.14218			0.571092	−	0.820886i	$-0.306520\pi$
$449$	512.840			1.14218			0.571092	+	0.820886i	$0.306520\pi$
$450$	−129.870			−0.288601
$451$		−	15.2026i		−	0.0337087i
$452$	806.167			1.78356
$453$		−	307.158i		−	0.678053i
$454$		−	445.142i		−	0.980489i
$455$	−139.524	+	21.6585i	−0.306647	+	0.0476012i
$456$	−351.992			−0.771912
$457$	631.627			1.38212			0.691058	−	0.722800i	$-0.257145\pi$
$457$	631.627			1.38212			0.691058	+	0.722800i	$0.257145\pi$
$458$			272.542i			0.595070i
$459$	76.0761			0.165743
$460$			203.076i			0.441471i
$461$			478.587i			1.03815i	0.854729	+	0.519075i	$0.173724\pi$
$461$			478.587i			1.03815i	−0.854729	+	0.519075i	$0.826276\pi$
$462$	114.514	+	737.699i	0.247866	+	1.59675i
$463$	226.920			0.490108			0.245054	−	0.969509i	$-0.421194\pi$
$463$	226.920			0.490108			0.245054	+	0.969509i	$0.421194\pi$
$464$	31.6292			0.0681664
$465$			147.823i			0.317900i
$466$	1127.07			2.41860
$467$		−	74.3726i		−	0.159256i	−0.996825	−	0.0796281i	$-0.974627\pi$
$467$		−	74.3726i		−	0.159256i	0.996825	−	0.0796281i	$-0.0253733\pi$
$468$		−	67.1858i		−	0.143559i
$469$	−436.754	+	67.7979i	−0.931246	+	0.144559i
$470$	1083.46			2.30524
$471$	481.683			1.02268
$472$			662.434i			1.40346i
$473$	−1045.58			−2.21054
$474$			176.104i			0.371527i
$475$			283.661i			0.597181i
$476$	−107.792	−	694.398i	−0.226454	−	1.45882i
$477$	−28.6677			−0.0601000
$478$	−860.251			−1.79969
$479$			656.137i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$479$			656.137i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$480$	276.291			0.575607
$481$		−	77.5203i		−	0.161165i
$482$		−	1050.73i		−	2.17993i
$483$	8.91931	+	57.4582i	0.0184665	+	0.118961i
$484$	1564.75			3.23296
$485$	−384.849			−0.793503
$486$		−	51.3632i		−	0.105686i
$487$	−12.9840			−0.0266613			−0.0133306	−	0.999911i	$-0.504243\pi$
$487$	−12.9840			−0.0266613			−0.0133306	+	0.999911i	$0.504243\pi$
$488$			693.152i			1.42039i
$489$		−	469.547i		−	0.960219i
$490$	302.269	+	950.149i	0.616876	+	1.93908i
$491$	344.825			0.702291			0.351146	−	0.936321i	$-0.385792\pi$
$491$	344.825			0.702291			0.351146	+	0.936321i	$0.385792\pi$
$492$	9.66165			0.0196375
$493$			129.082i			0.261829i
$494$	−232.354			−0.470352
$495$			346.214i			0.699422i
$496$			49.5782i			0.0999561i
$497$	−281.035	+	43.6255i	−0.565464	+	0.0877776i
$498$	−804.650			−1.61576
$499$	−459.798			−0.921438			−0.460719	−	0.887546i	$-0.652408\pi$
$499$	−459.798			−0.921438			−0.460719	+	0.887546i	$0.652408\pi$
$500$		−	502.275i		−	1.00455i
$501$	507.197			1.01237
$502$		−	770.472i		−	1.53480i
$503$			581.897i			1.15685i	0.815735	+	0.578426i	$0.196333\pi$
$503$			581.897i			1.15685i	−0.815735	+	0.578426i	$0.803667\pi$
$504$	−195.327	+	30.3208i	−0.387553	+	0.0601603i
$505$	−1027.10			−2.03386
$506$	295.294			0.583585
$507$			274.239i			0.540905i
$508$	−210.506			−0.414381
$509$		−	151.503i		−	0.297649i	−0.988864	−	0.148824i	$-0.952451\pi$
$509$		−	151.503i		−	0.297649i	0.988864	−	0.148824i	$-0.0475489\pi$
$510$		−	516.008i		−	1.01178i
$511$	18.7840	+	121.006i	0.0367592	+	0.236803i
$512$	227.736			0.444797
$513$	−112.187			−0.218688
$514$			1033.36i			2.01044i
$515$	571.545			1.10980
$516$		−	664.496i		−	1.28778i
$517$		−	995.007i		−	1.92458i
$518$	−540.942	+	83.9711i	−1.04429	+	0.162106i
$519$	−525.503			−1.01253
$520$	−189.861			−0.365117
$521$		−	132.063i		−	0.253479i	−0.991936	−	0.126740i	$-0.959549\pi$
$521$		−	132.063i		−	0.253479i	0.991936	−	0.126740i	$-0.0404513\pi$
$522$	87.1503			0.166955
$523$			624.639i			1.19434i	0.802115	+	0.597169i	$0.203708\pi$
$523$			624.639i			1.19434i	−0.802115	+	0.597169i	$0.796292\pi$
$524$			729.986i			1.39310i
$525$	24.4347	+	157.409i	0.0465423	+	0.299826i
$526$	−1055.70			−2.00703
$527$	−202.333			−0.383934
$528$			116.116i			0.219917i
$529$	23.0000			0.0434783
$530$			194.447i			0.366881i
$531$			211.131i			0.397609i
$532$	158.958	+	1024.00i	0.298792	+	1.92482i
$533$	2.65716			0.00498529
$534$	−669.483			−1.25371
$535$			86.9429i			0.162510i
$536$	−594.323			−1.10881
$537$		−	506.983i		−	0.944102i
$538$			1206.90i			2.24331i
$539$	872.578	−	277.592i	1.61888	−	0.515013i
$540$	−220.028			−0.407459
$541$	−98.2510			−0.181610			−0.0908050	−	0.995869i	$-0.528944\pi$
$541$	−98.2510			−0.181610			−0.0908050	+	0.995869i	$0.528944\pi$
$542$			123.596i			0.228036i
$543$	−37.4617			−0.0689902
$544$			378.174i			0.695173i
$545$		−	110.881i		−	0.203452i
$546$	−128.937	+	20.0151i	−0.236149	+	0.0366577i
$547$	92.3144			0.168765			0.0843824	−	0.996433i	$-0.473108\pi$
$547$	92.3144			0.168765			0.0843824	+	0.996433i	$0.473108\pi$
$548$	747.767			1.36454
$549$			220.921i			0.402406i
$550$	808.968			1.47085
$551$		−	190.352i		−	0.345467i
$552$			78.1875i			0.141644i
$553$	213.446	−	33.1334i	0.385978	−	0.0599158i
$554$	−414.563			−0.748309
$555$	−253.872			−0.457428
$556$			821.954i			1.47833i
$557$	−252.163			−0.452717			−0.226359	−	0.974044i	$-0.572682\pi$
$557$	−252.163			−0.452717			−0.226359	+	0.974044i	$0.572682\pi$
$558$			136.607i			0.244815i
$559$		−	182.750i		−	0.326924i
$560$	23.7891	+	153.249i	0.0424805	+	0.273659i
$561$	−473.881			−0.844707
$562$	−1723.27			−3.06631
$563$		−	603.228i		−	1.07145i	−0.844391	−	0.535727i	$-0.820038\pi$
$563$		−	603.228i		−	1.07145i	0.844391	−	0.535727i	$-0.179962\pi$
$564$	632.353			1.12119
$565$		−	726.091i		−	1.28512i
$566$		−	987.696i		−	1.74505i
$567$	−62.2544	+	9.66383i	−0.109796	+	0.0170438i
$568$	−382.425			−0.673283
$569$	917.263			1.61206			0.806031	−	0.591874i	$-0.201612\pi$
$569$	917.263			1.61206			0.806031	+	0.591874i	$0.201612\pi$
$570$			760.939i			1.33498i
$571$	65.0859			0.113986			0.0569929	−	0.998375i	$-0.481849\pi$
$571$	65.0859			0.113986			0.0569929	+	0.998375i	$0.481849\pi$
$572$			418.503i			0.731649i
$573$			64.7290i			0.112965i
$574$	−2.87827	−	18.5418i	−0.00501441	−	0.0323028i
$575$	63.0092			0.109581
$576$	298.376			0.518014
$577$			937.455i			1.62471i	0.583166	+	0.812353i	$0.301814\pi$
$577$			937.455i			1.62471i	−0.583166	+	0.812353i	$0.698186\pi$
$578$	−245.954			−0.425526
$579$			87.4807i			0.151089i
$580$		−	373.331i		−	0.643675i
$581$	151.393	+	975.271i	0.260572	+	1.67861i
$582$	−355.647			−0.611077
$583$	178.572			0.306299
$584$			164.662i			0.281955i
$585$	−60.5123			−0.103440
$586$		−	1706.73i		−	2.91252i
$587$		−	601.022i		−	1.02389i	−0.859019	−	0.511943i	$-0.828926\pi$
$587$		−	601.022i		−	1.02389i	0.859019	−	0.511943i	$-0.171074\pi$
$588$	176.417	+	554.546i	0.300028	+	0.943105i
$589$	298.374			0.506578
$590$	1432.05			2.42721
$591$		−	292.216i		−	0.494444i
$592$	−85.1459			−0.143827
$593$			293.746i			0.495356i	0.968842	+	0.247678i	$0.0796676\pi$
$593$			293.746i			0.495356i	−0.968842	+	0.247678i	$0.920332\pi$
$594$			319.943i			0.538625i
$595$	−625.424	+	97.0853i	−1.05113	+	0.163169i
$596$	−391.710			−0.657232
$597$	465.034			0.778951
$598$			51.6124i			0.0863084i
$599$	230.999			0.385641			0.192820	−	0.981234i	$-0.438237\pi$
$599$	230.999			0.385641			0.192820	+	0.981234i	$0.438237\pi$
$600$			214.197i			0.356995i
$601$		−	361.950i		−	0.602246i	−0.953585	−	0.301123i	$-0.902639\pi$
$601$		−	361.950i		−	0.602246i	0.953585	−	0.301123i	$-0.0973614\pi$
$602$	−1275.24	+	197.958i	−2.11834	+	0.328833i
$603$	−189.422			−0.314133
$604$	−1215.95			−2.01316
$605$		−	1409.33i		−	2.32947i
$606$	−949.165			−1.56628
$607$		−	1104.05i		−	1.81886i	−0.415859	−	0.909429i	$-0.636519\pi$
$607$		−	1104.05i		−	1.81886i	0.415859	−	0.909429i	$-0.363481\pi$
$608$		−	557.681i		−	0.917238i
$609$	−16.3971	−	105.630i	−0.0269246	−	0.173448i
$610$	1498.46			2.45649
$611$	173.910			0.284632
$612$		−	301.163i		−	0.492097i
$613$	−643.060			−1.04904			−0.524519	−	0.851399i	$-0.675755\pi$
$613$	−643.060			−1.04904			−0.524519	+	0.851399i	$0.675755\pi$
$614$		−	504.046i		−	0.820922i
$615$		−	8.70197i		−	0.0141495i
$616$	1216.70	−	188.869i	1.97516	−	0.306606i
$617$	923.669			1.49703			0.748516	−	0.663117i	$-0.230767\pi$
$617$	923.669			1.49703			0.748516	+	0.663117i	$0.230767\pi$
$618$	528.177			0.854655
$619$			1118.81i			1.80745i	0.428111	+	0.903726i	$0.359179\pi$
$619$			1118.81i			1.80745i	−0.428111	+	0.903726i	$0.640821\pi$
$620$	585.191			0.943856
$621$			24.9199i			0.0401286i
$622$		−	379.042i		−	0.609393i
$623$	125.961	+	811.443i	0.202185	+	1.30248i
$624$	−20.2951			−0.0325242
$625$	−780.843			−1.24935
$626$			1855.63i			2.96426i
$627$	698.815			1.11454
$628$		−	1906.85i		−	3.03638i
$629$		−	347.488i		−	0.552446i
$630$	65.5477	+	422.259i	0.104044	+	0.670252i
$631$	−704.827			−1.11700			−0.558500	−	0.829504i	$-0.688623\pi$
$631$	−704.827			−1.11700			−0.558500	+	0.829504i	$0.688623\pi$
$632$	290.451			0.459574
$633$		−	623.144i		−	0.984429i
$634$	1547.20			2.44039
$635$			189.596i			0.298577i
$636$			113.487i			0.178439i
$637$	48.5183	+	152.512i	0.0761670	+	0.239422i
$638$	−542.862			−0.850882
$639$	−121.886			−0.190745
$640$		−	1385.76i		−	2.16524i
$641$	373.468			0.582633			0.291316	−	0.956627i	$-0.405907\pi$
$641$	373.468			0.582633			0.291316	+	0.956627i	$0.405907\pi$
$642$			80.3457i			0.125149i
$643$		−	461.828i		−	0.718239i	−0.933292	−	0.359119i	$-0.883077\pi$
$643$		−	461.828i		−	0.718239i	0.933292	−	0.359119i	$-0.116923\pi$
$644$	227.461	−	35.3090i	0.353200	−	0.0548276i
$645$	−598.492			−0.927894
$646$	−1041.54			−1.61229
$647$			362.430i			0.560170i	0.959975	+	0.280085i	$0.0903627\pi$
$647$			362.430i			0.560170i	−0.959975	+	0.280085i	$0.909637\pi$
$648$	−84.7140			−0.130731
$649$		−	1315.14i		−	2.02641i
$650$			141.394i			0.217529i
$651$	165.573	−	25.7021i	0.254337	−	0.0394810i
$652$	−1858.80			−2.85092
$653$	884.027			1.35379			0.676896	−	0.736078i	$-0.263324\pi$
$653$	884.027			1.35379			0.676896	+	0.736078i	$0.263324\pi$
$654$		−	102.468i		−	0.156678i
$655$	657.477			1.00378
$656$		−	2.91854i		−	0.00444899i
$657$			52.4809i			0.0798797i
$658$	−188.382	−	1213.56i	−0.286295	−	1.84431i
$659$	−911.585			−1.38328			−0.691642	−	0.722240i	$-0.743113\pi$
$659$	−911.585			−1.38328			−0.691642	+	0.722240i	$0.743113\pi$
$660$	1370.56			2.07661
$661$		−	85.4704i		−	0.129305i	−0.997908	−	0.0646523i	$-0.979406\pi$
$661$		−	85.4704i		−	0.129305i	0.997908	−	0.0646523i	$-0.0205938\pi$
$662$	−1010.05			−1.52575
$663$		−	82.8263i		−	0.124927i
$664$			1327.12i			1.99868i
$665$	922.291	−	143.168i	1.38690	−	0.215291i
$666$	−234.609			−0.352265
$667$	−42.2827			−0.0633923
$668$		−	2007.85i		−	3.00576i
$669$	−138.934			−0.207674
$670$			1284.81i			1.91763i
$671$		−	1376.12i		−	2.05086i
$672$	−48.0389	−	309.467i	−0.0714865	−	0.460516i
$673$	852.855			1.26724			0.633622	−	0.773643i	$-0.281567\pi$
$673$	852.855			1.26724			0.633622	+	0.773643i	$0.281567\pi$
$674$	611.769			0.907669
$675$			68.2688i			0.101139i
$676$	1085.63			1.60597
$677$		−	585.534i		−	0.864896i	−0.901659	−	0.432448i	$-0.857650\pi$
$677$		−	585.534i		−	0.864896i	0.901659	−	0.432448i	$-0.142350\pi$
$678$		−	670.996i		−	0.989669i
$679$	66.9139	+	431.059i	0.0985476	+	0.634844i
$680$	−851.059			−1.25156
$681$	−233.997			−0.343608
$682$		−	850.928i		−	1.24769i
$683$	165.791			0.242739			0.121370	−	0.992607i	$-0.461271\pi$
$683$	165.791			0.242739			0.121370	+	0.992607i	$0.461271\pi$
$684$			444.115i			0.649291i
$685$		−	673.492i		−	0.983200i
$686$	1011.68	−	503.767i	1.47475	−	0.734354i
$687$	143.267			0.208540
$688$	−200.727			−0.291755
$689$			31.2114i			0.0452996i
$690$	169.026			0.244966
$691$			188.310i			0.272518i	0.990673	+	0.136259i	$0.0435080\pi$
$691$			188.310i			0.272518i	−0.990673	+	0.136259i	$0.956492\pi$
$692$			2080.32i			3.00624i
$693$	387.785	−	60.1964i	0.559574	−	0.0868634i
$694$	−91.1602			−0.131355
$695$	740.310			1.06519
$696$		−	143.738i		−	0.206520i
$697$	11.9108			0.0170887
$698$			567.131i			0.812509i
$699$		−	592.463i		−	0.847587i
$700$	623.135	−	96.7301i	0.890193	−	0.138186i
$701$	280.460			0.400085			0.200042	−	0.979787i	$-0.435892\pi$
$701$	280.460			0.400085			0.200042	+	0.979787i	$0.435892\pi$
$702$	−55.9207			−0.0796591
$703$			512.429i			0.728917i
$704$	−1858.60			−2.64005
$705$		−	569.541i		−	0.807860i
$706$		−	1553.95i		−	2.20106i
$707$	178.583	+	1150.43i	0.252592	+	1.62720i
$708$	835.806			1.18052
$709$	−1089.95			−1.53731			−0.768654	−	0.639665i	$-0.779073\pi$
$709$	−1089.95			−1.53731			−0.768654	+	0.639665i	$0.779073\pi$
$710$			826.729i			1.16441i
$711$	92.5723			0.130200
$712$			1104.19i			1.55083i
$713$		−	66.2774i		−	0.0929557i
$714$	−577.967	+	89.7186i	−0.809478	+	0.125656i
$715$	376.933			0.527180
$716$	−2007.00			−2.80307
$717$			452.207i			0.630693i
$718$	−1400.49			−1.95055
$719$			686.206i			0.954389i	0.878798	+	0.477195i	$0.158346\pi$
$719$			686.206i			0.954389i	−0.878798	+	0.477195i	$0.841654\pi$
$720$			66.4648i			0.0923122i
$721$	−99.3749	−	640.173i	−0.137829	−	0.887896i
$722$	346.441			0.479835
$723$	−552.333			−0.763946
$724$			148.300i			0.204834i
$725$	−115.835			−0.159772
$726$		−	1302.39i		−	1.79392i
$727$			1325.91i			1.82381i	0.410402	+	0.911905i	$0.365388\pi$
$727$			1325.91i			1.82381i	−0.410402	+	0.911905i	$0.634612\pi$
$728$	33.0112	+	212.658i	0.0453450	+	0.292113i
$729$	−27.0000			−0.0370370
$730$	355.967			0.487626
$731$		−	819.187i		−	1.12064i
$732$	874.563			1.19476
$733$			96.6264i			0.131823i	0.997825	+	0.0659116i	$0.0209955\pi$
$733$			96.6264i			0.131823i	−0.997825	+	0.0659116i	$0.979004\pi$
$734$			1262.25i			1.71968i
$735$	499.463	−	158.893i	0.679541	−	0.216181i
$736$	−123.877			−0.168311
$737$	1179.92			1.60097
$738$		−	8.04167i		−	0.0108966i
$739$	529.063			0.715917			0.357959	−	0.933737i	$-0.383473\pi$
$739$	529.063			0.715917			0.357959	+	0.933737i	$0.383473\pi$
$740$			1005.01i			1.35812i
$741$			122.141i			0.164833i
$742$	217.795	−	33.8086i	0.293524	−	0.0455642i
$743$	−205.001			−0.275910			−0.137955	−	0.990439i	$-0.544053\pi$
$743$	−205.001			−0.275910			−0.137955	+	0.990439i	$0.544053\pi$
$744$	225.307			0.302832
$745$			352.802i			0.473560i
$746$	−2344.19			−3.14235
$747$			422.979i			0.566237i
$748$			1875.96i			2.50797i
$749$	97.3825	−	15.1168i	0.130017	−	0.0201827i
$750$	−418.058			−0.557410
$751$	607.228			0.808559			0.404279	−	0.914636i	$-0.367522\pi$
$751$	607.228			0.808559			0.404279	+	0.914636i	$0.367522\pi$
$752$		−	191.018i		−	0.254013i
$753$	−405.012			−0.537865
$754$		−	94.8832i		−	0.125840i
$755$			1095.17i			1.45056i
$756$	38.2563	+	246.447i	0.0506036	+	0.325989i
$757$	−650.858			−0.859786			−0.429893	−	0.902880i	$-0.641449\pi$
$757$	−650.858			−0.859786			−0.429893	+	0.902880i	$0.641449\pi$
$758$	−1615.63			−2.13143
$759$		−	155.227i		−	0.204515i
$760$	1255.03			1.65135
$761$		−	813.820i		−	1.06941i	−0.845039	−	0.534704i	$-0.820423\pi$
$761$		−	813.820i		−	1.06941i	0.845039	−	0.534704i	$-0.179577\pi$
$762$			175.210i			0.229934i
$763$	−124.195	+	19.2790i	−0.162772	+	0.0252673i
$764$	256.244			0.335397
$765$	−271.249			−0.354574
$766$			617.060i			0.805561i
$767$	229.864			0.299693
$768$		−	591.535i		−	0.770228i
$769$			506.793i			0.659028i	0.944151	+	0.329514i	$0.106885\pi$
$769$			506.793i			0.659028i	−0.944151	+	0.329514i	$0.893115\pi$
$770$	−408.299	−	2630.26i	−0.530259	−	3.41593i
$771$	543.207			0.704549
$772$	346.311			0.448589
$773$		−	1390.41i		−	1.79872i	−0.437207	−	0.899361i	$-0.644032\pi$
$773$		−	1390.41i		−	1.79872i	0.437207	−	0.899361i	$-0.355968\pi$
$774$	−553.079			−0.714572
$775$		−	181.569i		−	0.234283i
$776$			586.573i			0.755893i
$777$	44.1409	+	284.356i	0.0568094	+	0.365966i
$778$	2217.66			2.85047
$779$	−17.5645			−0.0225475
$780$			239.551i			0.307117i
$781$	759.234			0.972131
$782$			231.355i			0.295850i
$783$		−	45.8121i		−	0.0585085i
$784$	167.514	−	53.2910i	0.213666	−	0.0679732i
$785$	−1717.44			−2.18782
$786$	607.588			0.773012
$787$			1146.86i			1.45725i	0.684912	+	0.728625i	$0.259840\pi$
$787$			1146.86i			1.45725i	−0.684912	+	0.728625i	$0.740160\pi$
$788$	−1156.80			−1.46802
$789$			554.946i			0.703353i
$790$		−	627.898i		−	0.794808i
$791$	−813.276	+	126.246i	−1.02816	+	0.159603i
$792$	527.687			0.666271
$793$	240.523			0.303308
$794$			1645.36i			2.07225i
$795$	102.215			0.128572
$796$		−	1840.94i		−	2.31273i
$797$		−	176.205i		−	0.221085i	−0.993871	−	0.110543i	$-0.964741\pi$
$797$		−	176.205i		−	0.221085i	0.993871	−	0.110543i	$-0.0352588\pi$
$798$	852.308	−	132.305i	1.06806	−	0.165796i
$799$	779.561			0.975671
$800$	−339.364			−0.424205
$801$			351.926i			0.439359i
$802$	−1723.96			−2.14958
$803$		−	326.906i		−	0.407106i
$804$			749.869i			0.932672i
$805$	−31.8018	−	204.867i	−0.0395053	−	0.254493i
$806$	148.728			0.184526
$807$	634.431			0.786160
$808$			1565.47i			1.93746i
$809$	−162.123			−0.200399			−0.100200	−	0.994967i	$-0.531948\pi$
$809$	−162.123			−0.200399			−0.100200	+	0.994967i	$0.531948\pi$
$810$			183.135i			0.226093i
$811$			776.407i			0.957346i	0.877993	+	0.478673i	$0.158882\pi$
$811$			776.407i			0.957346i	−0.877993	+	0.478673i	$0.841118\pi$
$812$	−418.159	+	64.9113i	−0.514974	+	0.0799400i
$813$	64.9703			0.0799143
$814$	1461.39			1.79531
$815$			1674.17i			2.05419i
$816$	−90.9738			−0.111487
$817$			1208.03i			1.47861i
$818$		−	391.802i		−	0.478975i
$819$	10.5213	+	67.7783i	0.0128465	+	0.0827574i
$820$	−34.4486			−0.0420105
$821$	537.716			0.654952			0.327476	−	0.944859i	$-0.393802\pi$
$821$	537.716			0.654952			0.327476	+	0.944859i	$0.393802\pi$
$822$		−	622.388i		−	0.757163i
$823$	531.113			0.645338			0.322669	−	0.946512i	$-0.395420\pi$
$823$	531.113			0.645338			0.322669	+	0.946512i	$0.395420\pi$
$824$		−	871.129i		−	1.05720i
$825$		−	425.249i		−	0.515453i
$826$	−248.992	−	1604.01i	−0.301443	−	1.94190i
$827$	987.154			1.19366			0.596828	−	0.802369i	$-0.296427\pi$
$827$	987.154			1.19366			0.596828	+	0.802369i	$0.296427\pi$
$828$	98.6507			0.119143
$829$		−	62.9942i		−	0.0759882i	−0.999278	−	0.0379941i	$-0.987903\pi$
$829$		−	62.9942i		−	0.0759882i	0.999278	−	0.0379941i	$-0.0120968\pi$
$830$	2868.98			3.45660
$831$			217.923i			0.262242i
$832$		−	324.851i		−	0.390446i
$833$	217.486	+	683.641i	0.261087	+	0.820697i
$834$	684.136			0.820306
$835$	−1808.41			−2.16576
$836$		−	2766.41i		−	3.30910i
$837$	71.8098			0.0857942
$838$			999.334i			1.19252i
$839$		−	961.226i		−	1.14568i	−0.819667	−	0.572840i	$-0.805842\pi$
$839$		−	961.226i		−	1.14568i	0.819667	−	0.572840i	$-0.194158\pi$
$840$	696.437	−	108.109i	0.829091	−	0.128701i
$841$	−763.268			−0.907572
$842$	343.466			0.407917
$843$			905.866i			1.07457i
$844$	−2466.85			−2.92280
$845$		−	977.799i		−	1.15716i
$846$		−	526.325i		−	0.622134i
$847$	−1578.55	+	245.041i	−1.86370	+	0.289304i
$848$	34.2816			0.0404264
$849$	−519.200			−0.611543
$850$			633.804i			0.745652i
$851$	113.825			0.133754
$852$			482.513i			0.566330i
$853$			244.370i			0.286483i	0.989688	+	0.143241i	$0.0457525\pi$
$853$			244.370i			0.286483i	−0.989688	+	0.143241i	$0.954247\pi$
$854$	−260.538	−	1678.39i	−0.305080	−	1.96532i
$855$	400.002			0.467838
$856$	132.515			0.154808
$857$			622.245i			0.726073i	0.931775	+	0.363036i	$0.118260\pi$
$857$			622.245i			0.726073i	−0.931775	+	0.363036i	$0.881740\pi$
$858$	348.332			0.405981
$859$			241.220i			0.280815i	0.990094	+	0.140407i	$0.0448413\pi$
$859$			241.220i			0.280815i	−0.990094	+	0.140407i	$0.955159\pi$
$860$			2369.26i			2.75495i
$861$	−9.74685	+	1.51302i	−0.0113204	+	0.00175728i
$862$	2749.93			3.19018
$863$	−696.263			−0.806793			−0.403397	−	0.915025i	$-0.632170\pi$
$863$	−696.263			−0.806793			−0.403397	+	0.915025i	$0.632170\pi$
$864$		−	134.217i		−	0.155344i
$865$	1873.68			2.16610
$866$		−	2450.50i		−	2.82968i
$867$			129.290i			0.149124i
$868$	−101.747	−	655.457i	−0.117220	−	0.755134i
$869$	−576.636			−0.663563
$870$	−310.734			−0.357166
$871$			206.230i			0.236774i
$872$	−169.001			−0.193809
$873$			186.952i			0.214149i
$874$		−	341.171i		−	0.390356i
$875$	78.6563	+	506.704i	0.0898929	+	0.579090i
$876$	207.757			0.237166
$877$	−1025.59			−1.16943			−0.584717	−	0.811238i	$-0.698794\pi$
$877$	−1025.59			−1.16943			−0.584717	+	0.811238i	$0.698794\pi$
$878$			1670.75i			1.90291i
$879$	−897.176			−1.02068
$880$		−	414.012i		−	0.470468i
$881$			1082.45i			1.22866i	0.789050	+	0.614329i	$0.210573\pi$
$881$			1082.45i			1.22866i	−0.789050	+	0.614329i	$0.789427\pi$
$882$	461.564	−	146.837i	0.523315	−	0.166481i
$883$	−1023.34			−1.15894			−0.579468	−	0.814995i	$-0.696739\pi$
$883$	−1023.34			−1.15894			−0.579468	+	0.814995i	$0.696739\pi$
$884$	−327.886			−0.370911
$885$		−	752.786i		−	0.850606i
$886$	15.5418			0.0175415
$887$			796.873i			0.898391i	0.893434	+	0.449195i	$0.148289\pi$
$887$			796.873i			0.898391i	−0.893434	+	0.449195i	$0.851711\pi$
$888$			386.943i			0.435747i
$889$	212.362	−	32.9652i	0.238877	−	0.0370812i
$890$	2387.04			2.68207
$891$	168.184			0.188759
$892$			550.000i			0.616592i
$893$	−1149.59			−1.28734
$894$			326.032i			0.364689i
$895$			1807.65i			2.01972i
$896$	−1552.15	+	240.942i	−1.73231	+	0.268909i
$897$	27.1310			0.0302464
$898$	−1689.78			−1.88172
$899$			121.843i			0.135532i
$900$	270.257			0.300285
$901$			139.906i			0.155279i
$902$			50.0918i			0.0555342i
$903$	104.060	+	670.355i	0.115238	+	0.742365i
$904$	−1106.68			−1.22421
$905$	133.570			0.147591
$906$			1012.07i			1.11707i
$907$	527.672			0.581777			0.290889	−	0.956757i	$-0.406049\pi$
$907$	527.672			0.581777			0.290889	+	0.956757i	$0.406049\pi$
$908$			926.327i			1.02018i
$909$			498.946i			0.548895i
$910$	459.726	−	71.3638i	0.505193	−	0.0784218i
$911$	−1510.85			−1.65845			−0.829224	−	0.558916i	$-0.811217\pi$
$911$	−1510.85			−1.65845			−0.829224	+	0.558916i	$0.811217\pi$
$912$	134.156			0.147101
$913$		−	2634.75i		−	2.88582i
$914$	−2081.18			−2.27700
$915$		−	787.693i		−	0.860867i
$916$		−	567.152i		−	0.619162i
$917$	−114.316	−	736.423i	−0.124663	−	0.803078i
$918$	−250.667			−0.273057
$919$	−921.851			−1.00310			−0.501551	−	0.865128i	$-0.667237\pi$
$919$	−921.851			−1.00310			−0.501551	+	0.865128i	$0.667237\pi$
$920$		−	278.777i		−	0.303019i
$921$	−264.961			−0.287689
$922$		−	1576.92i		−	1.71033i
$923$			132.701i			0.143772i
$924$	−238.300	−	1535.13i	−0.257901	−	1.66140i
$925$	311.827			0.337111
$926$	−747.690			−0.807440
$927$		−	277.646i		−	0.299510i
$928$	227.732			0.245401
$929$			122.245i			0.131588i	0.997833	+	0.0657939i	$0.0209580\pi$
$929$			122.245i			0.131588i	−0.997833	+	0.0657939i	$0.979042\pi$
$930$		−	487.071i		−	0.523732i
$931$	−320.718	−	1008.14i	−0.344488	−	1.08286i
$932$	−2345.39			−2.51652
$933$	−199.251			−0.213559
$934$			245.054i			0.262371i
$935$	1689.62			1.80708
$936$			92.2307i			0.0985371i
$937$		−	1588.93i		−	1.69576i	−0.530190	−	0.847879i	$-0.677879\pi$
$937$		−	1588.93i		−	1.69576i	0.530190	−	0.847879i	$-0.322121\pi$
$938$	1439.08	−	223.391i	1.53420	−	0.238157i
$939$	975.445			1.03881
$940$	−2254.65			−2.39857
$941$		−	1132.07i		−	1.20304i	−0.798856	−	0.601522i	$-0.794561\pi$
$941$		−	1132.07i		−	1.20304i	0.798856	−	0.601522i	$-0.205439\pi$
$942$	−1587.12			−1.68484
$943$			3.90157i			0.00413741i
$944$		−	252.476i		−	0.267453i
$945$	221.968	−	34.4564i	0.234887	−	0.0364618i
$946$	3445.15			3.64181
$947$	1190.19			1.25680			0.628399	−	0.777891i	$-0.283710\pi$
$947$	1190.19			1.25680			0.628399	+	0.777891i	$0.283710\pi$
$948$		−	366.467i		−	0.386569i
$949$	57.1376			0.0602082
$950$		−	934.649i		−	0.983841i
$951$		−	813.316i		−	0.855222i
$952$	147.974	+	953.249i	0.155435	+	1.00131i
$953$	1525.03			1.60024			0.800121	−	0.599838i	$-0.204768\pi$
$953$	1525.03			1.60024			0.800121	+	0.599838i	$0.204768\pi$
$954$	94.4586			0.0990132
$955$		−	230.791i		−	0.241666i
$956$	1790.16			1.87255
$957$			285.366i			0.298188i
$958$		−	2161.94i		−	2.25672i
$959$	−754.361	+	117.100i	−0.786612	+	0.122107i
$960$	−1063.86			−1.10819
$961$	770.013			0.801262
$962$			255.426i			0.265515i
$963$	42.2352			0.0438579
$964$			2186.53i			2.26818i
$965$		−	311.912i		−	0.323225i
$966$	−29.3887	−	189.322i	−0.0304231	−	0.195985i
$967$	−678.121			−0.701262			−0.350631	−	0.936514i	$-0.614033\pi$
$967$	−678.121			−0.701262			−0.350631	+	0.936514i	$0.614033\pi$
$968$	−2148.05			−2.21906
$969$			547.503i			0.565018i
$970$	1268.06			1.30728
$971$		−	1359.05i		−	1.39964i	−0.714317	−	0.699822i	$-0.753263\pi$
$971$		−	1359.05i		−	1.39964i	0.714317	−	0.699822i	$-0.246737\pi$
$972$			106.885i			0.109964i
$973$	−128.718	−	829.202i	−0.132290	−	0.852212i
$974$	42.7818			0.0439238
$975$	74.3263			0.0762321
$976$		−	264.183i		−	0.270679i
$977$	−116.477			−0.119219			−0.0596094	−	0.998222i	$-0.518986\pi$
$977$	−116.477			−0.119219			−0.0596094	+	0.998222i	$0.518986\pi$
$978$			1547.13i			1.58194i
$979$		−	2192.16i		−	2.23918i
$980$	−629.013	−	1977.23i	−0.641850	−	2.01758i
$981$	−53.8640			−0.0549072
$982$	−1136.18			−1.15701
$983$			225.983i			0.229891i	0.993372	+	0.114945i	$0.0366693\pi$
$983$			225.983i			0.229891i	−0.993372	+	0.114945i	$0.963331\pi$
$984$	−13.2632			−0.0134789
$985$			1041.90i			1.05776i
$986$		−	425.318i		−	0.431357i
$987$	−637.929	+	99.0265i	−0.646331	+	0.100331i
$988$	483.522			0.489395
$989$	268.337			0.271322
$990$		−	1140.76i		−	1.15228i
$991$	−313.193			−0.316037			−0.158019	−	0.987436i	$-0.550511\pi$
$991$	−313.193			−0.316037			−0.158019	+	0.987436i	$0.550511\pi$
$992$			356.967i			0.359845i
$993$			530.949i			0.534692i
$994$	925.998	−	143.744i	0.931587	−	0.144611i
$995$	−1658.08			−1.66641
$996$	1674.45			1.68118
$997$		−	1777.33i		−	1.78268i	−0.453336	−	0.891340i	$-0.649766\pi$
$997$		−	1777.33i		−	1.78268i	0.453336	−	0.891340i	$-0.350234\pi$
$998$	1515.01			1.51805
$999$			123.326i			0.123450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.5	✓	60
7.6	odd	2	inner	483.3.g.a.139.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.5	✓	60	1.1	even	1	trivial
483.3.g.a.139.6	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)

\(f(q)\)	\(=\)	\(q-3.29495 q^{2} +1.73205i q^{3} +6.85669 q^{4} -6.17562i q^{5} -5.70702i q^{6} +(-6.91716 + 1.07376i) q^{7} -9.41266 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.29495 q^{2} +1.73205i q^{3} +6.85669 q^{4} -6.17562i q^{5} -5.70702i q^{6} +(-6.91716 + 1.07376i) q^{7} -9.41266 q^{8} -3.00000 q^{9} +20.3484i q^{10} +18.6871 q^{11} +11.8761i q^{12} +3.26619i q^{13} +(22.7917 - 3.53798i) q^{14} +10.6965 q^{15} +3.58748 q^{16} +14.6408i q^{17} +9.88485 q^{18} -21.5903i q^{19} -42.3444i q^{20} +(-1.85980 - 11.9809i) q^{21} -61.5731 q^{22} -4.79583 q^{23} -16.3032i q^{24} -13.1383 q^{25} -10.7619i q^{26} -5.19615i q^{27} +(-47.4288 + 7.36244i) q^{28} +8.81655 q^{29} -35.2444 q^{30} +13.8198i q^{31} +25.8301 q^{32} +32.3670i q^{33} -48.2408i q^{34} +(6.63113 + 42.7178i) q^{35} -20.5701 q^{36} -23.7342 q^{37} +71.1391i q^{38} -5.65721 q^{39} +58.1291i q^{40} -0.813534i q^{41} +(6.12796 + 39.4763i) q^{42} -55.9522 q^{43} +128.132 q^{44} +18.5269i q^{45} +15.8020 q^{46} -53.2456i q^{47} +6.21370i q^{48} +(46.6941 - 14.8547i) q^{49} +43.2901 q^{50} -25.3587 q^{51} +22.3953i q^{52} +9.55590 q^{53} +17.1211i q^{54} -115.405i q^{55} +(65.1089 - 10.1069i) q^{56} +37.3956 q^{57} -29.0501 q^{58} -70.3769i q^{59} +73.3426 q^{60} -73.6403i q^{61} -45.5355i q^{62} +(20.7515 - 3.22128i) q^{63} -99.4588 q^{64} +20.1708 q^{65} -106.648i q^{66} +63.1408 q^{67} +100.388i q^{68} -8.30662i q^{69} +(-21.8492 - 140.753i) q^{70} +40.6288 q^{71} +28.2380 q^{72} -17.4936i q^{73} +78.2029 q^{74} -22.7563i q^{75} -148.038i q^{76} +(-129.262 + 20.0655i) q^{77} +18.6402 q^{78} -30.8574 q^{79} -22.1549i q^{80} +9.00000 q^{81} +2.68056i q^{82} -140.993i q^{83} +(-12.7521 - 82.1491i) q^{84} +90.4163 q^{85} +184.360 q^{86} +15.2707i q^{87} -175.896 q^{88} -117.309i q^{89} -61.0451i q^{90} +(-3.50710 - 22.5928i) q^{91} -32.8836 q^{92} -23.9366 q^{93} +175.442i q^{94} -133.334 q^{95} +44.7390i q^{96} -62.3174i q^{97} +(-153.855 + 48.9455i) q^{98} -56.0613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 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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