LMFDB - Embedded newform 483.3.g.a.139.20

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			139.20
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79815 q^{2} -1.73205i q^{3} -0.766656 q^{4} +9.01598i q^{5} +3.11449i q^{6} +(6.86887 + 1.34858i) q^{7} +8.57116 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.79815 q^{2} -1.73205i q^{3} -0.766656 q^{4} +9.01598i q^{5} +3.11449i q^{6} +(6.86887 + 1.34858i) q^{7} +8.57116 q^{8} -3.00000 q^{9} -16.2121i q^{10} +7.87346 q^{11} +1.32789i q^{12} -11.5819i q^{13} +(-12.3513 - 2.42495i) q^{14} +15.6161 q^{15} -12.3456 q^{16} +11.8676i q^{17} +5.39445 q^{18} +3.15779i q^{19} -6.91215i q^{20} +(2.33581 - 11.8972i) q^{21} -14.1577 q^{22} +4.79583 q^{23} -14.8457i q^{24} -56.2879 q^{25} +20.8259i q^{26} +5.19615i q^{27} +(-5.26606 - 1.03390i) q^{28} +16.9230 q^{29} -28.0801 q^{30} +35.6665i q^{31} -12.0854 q^{32} -13.6372i q^{33} -21.3397i q^{34} +(-12.1588 + 61.9296i) q^{35} +2.29997 q^{36} -5.67016 q^{37} -5.67819i q^{38} -20.0604 q^{39} +77.2774i q^{40} -31.1263i q^{41} +(-4.20013 + 21.3930i) q^{42} +51.9215 q^{43} -6.03624 q^{44} -27.0479i q^{45} -8.62363 q^{46} +61.2855i q^{47} +21.3832i q^{48} +(45.3627 + 18.5264i) q^{49} +101.214 q^{50} +20.5553 q^{51} +8.87930i q^{52} +66.1931 q^{53} -9.34346i q^{54} +70.9870i q^{55} +(58.8742 + 11.5589i) q^{56} +5.46946 q^{57} -30.4301 q^{58} -21.3806i q^{59} -11.9722 q^{60} -5.91807i q^{61} -64.1338i q^{62} +(-20.6066 - 4.04574i) q^{63} +71.1138 q^{64} +104.422 q^{65} +24.5218i q^{66} -121.240 q^{67} -9.09837i q^{68} -8.30662i q^{69} +(21.8633 - 111.359i) q^{70} +12.8246 q^{71} -25.7135 q^{72} +109.816i q^{73} +10.1958 q^{74} +97.4934i q^{75} -2.42094i q^{76} +(54.0818 + 10.6180i) q^{77} +36.0715 q^{78} -133.346 q^{79} -111.308i q^{80} +9.00000 q^{81} +55.9697i q^{82} +106.728i q^{83} +(-1.79076 + 9.12108i) q^{84} -106.998 q^{85} -93.3627 q^{86} -29.3115i q^{87} +67.4847 q^{88} +21.5522i q^{89} +48.6362i q^{90} +(15.6190 - 79.5542i) q^{91} -3.67675 q^{92} +61.7762 q^{93} -110.200i q^{94} -28.4706 q^{95} +20.9325i q^{96} +139.695i q^{97} +(-81.5689 - 33.3133i) q^{98} -23.6204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.79815			−0.899075			−0.449538	−	0.893261i	$-0.648411\pi$
$2$	−1.79815			−0.899075			−0.449538	+	0.893261i	$0.648411\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−0.766656			−0.191664
$5$			9.01598i			1.80320i	0.432575	+	0.901598i	$0.357605\pi$
$5$			9.01598i			1.80320i	−0.432575	+	0.901598i	$0.642395\pi$
$6$			3.11449i			0.519081i
$7$	6.86887	+	1.34858i	0.981267	+	0.192654i
$7$	6.86887	+	1.34858i	0.981267	+	0.192654i
$8$	8.57116			1.07140
$9$	−3.00000			−0.333333
$10$		−	16.2121i		−	1.62121i
$11$	7.87346			0.715769			0.357885	−	0.933766i	$-0.383498\pi$
$11$	7.87346			0.715769			0.357885	+	0.933766i	$0.383498\pi$
$12$			1.32789i			0.110657i
$13$		−	11.5819i		−	0.890912i	−0.895304	−	0.445456i	$-0.853042\pi$
$13$		−	11.5819i		−	0.890912i	0.895304	−	0.445456i	$-0.146958\pi$
$14$	−12.3513	−	2.42495i	−0.882232	−	0.173211i
$15$	15.6161			1.04108
$16$	−12.3456			−0.771601
$17$			11.8676i			0.698094i	0.937105	+	0.349047i	$0.113495\pi$
$17$			11.8676i			0.698094i	−0.937105	+	0.349047i	$0.886505\pi$
$18$	5.39445			0.299692
$19$			3.15779i			0.166200i	0.996541	+	0.0830998i	$0.0264820\pi$
$19$			3.15779i			0.166200i	−0.996541	+	0.0830998i	$0.973518\pi$
$20$		−	6.91215i		−	0.345608i
$21$	2.33581	−	11.8972i	0.111229	−	0.566535i
$22$	−14.1577			−0.643531
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	14.8457i		−	0.618570i
$25$	−56.2879			−2.25151
$26$			20.8259i			0.800997i
$27$			5.19615i			0.192450i
$28$	−5.26606	−	1.03390i	−0.188074	−	0.0369249i
$29$	16.9230			0.583552			0.291776	−	0.956487i	$-0.405754\pi$
$29$	16.9230			0.583552			0.291776	+	0.956487i	$0.405754\pi$
$30$	−28.0801			−0.936005
$31$			35.6665i			1.15053i	0.817966	+	0.575267i	$0.195102\pi$
$31$			35.6665i			1.15053i	−0.817966	+	0.575267i	$0.804898\pi$
$32$	−12.0854			−0.377668
$33$		−	13.6372i		−	0.413250i
$34$		−	21.3397i		−	0.627639i
$35$	−12.1588	+	61.9296i	−0.347393	+	1.76942i
$36$	2.29997			0.0638880
$37$	−5.67016			−0.153248			−0.0766238	−	0.997060i	$-0.524414\pi$
$37$	−5.67016			−0.153248			−0.0766238	+	0.997060i	$0.524414\pi$
$38$		−	5.67819i		−	0.149426i
$39$	−20.0604			−0.514368
$40$			77.2774i			1.93194i
$41$		−	31.1263i		−	0.759178i	−0.925155	−	0.379589i	$-0.876065\pi$
$41$		−	31.1263i		−	0.759178i	0.925155	−	0.379589i	$-0.123935\pi$
$42$	−4.20013	+	21.3930i	−0.100003	+	0.509357i
$43$	51.9215			1.20748			0.603738	−	0.797182i	$-0.293677\pi$
$43$	51.9215			1.20748			0.603738	+	0.797182i	$0.293677\pi$
$44$	−6.03624			−0.137187
$45$		−	27.0479i		−	0.601065i
$46$	−8.62363			−0.187470
$47$			61.2855i			1.30395i	0.758242	+	0.651973i	$0.226059\pi$
$47$			61.2855i			1.30395i	−0.758242	+	0.651973i	$0.773941\pi$
$48$			21.3832i			0.445484i
$49$	45.3627	+	18.5264i	0.925769	+	0.378090i
$50$	101.214			2.02428
$51$	20.5553			0.403045
$52$			8.87930i			0.170756i
$53$	66.1931			1.24893			0.624463	−	0.781055i	$-0.285318\pi$
$53$	66.1931			1.24893			0.624463	+	0.781055i	$0.285318\pi$
$54$		−	9.34346i		−	0.173027i
$55$			70.9870i			1.29067i
$56$	58.8742	+	11.5589i	1.05132	+	0.206409i
$57$	5.46946			0.0959554
$58$	−30.4301			−0.524657
$59$		−	21.3806i		−	0.362384i	−0.983448	−	0.181192i	$-0.942004\pi$
$59$		−	21.3806i		−	0.362384i	0.983448	−	0.181192i	$-0.0579955\pi$
$60$	−11.9722			−0.199537
$61$		−	5.91807i		−	0.0970176i	−0.998823	−	0.0485088i	$-0.984553\pi$
$61$		−	5.91807i		−	0.0970176i	0.998823	−	0.0485088i	$-0.0154469\pi$
$62$		−	64.1338i		−	1.03442i
$63$	−20.6066	−	4.04574i	−0.327089	−	0.0642181i
$64$	71.1138			1.11115
$65$	104.422			1.60649
$66$			24.5218i			0.371543i
$67$	−121.240			−1.80956			−0.904778	−	0.425884i	$-0.859963\pi$
$67$	−121.240			−1.80956			−0.904778	+	0.425884i	$0.859963\pi$
$68$		−	9.09837i		−	0.133800i
$69$		−	8.30662i		−	0.120386i
$70$	21.8633	−	111.359i	0.312333	−	1.59084i
$71$	12.8246			0.180629			0.0903143	−	0.995913i	$-0.471213\pi$
$71$	12.8246			0.180629			0.0903143	+	0.995913i	$0.471213\pi$
$72$	−25.7135			−0.357132
$73$			109.816i			1.50433i	0.658973	+	0.752167i	$0.270991\pi$
$73$			109.816i			1.50433i	−0.658973	+	0.752167i	$0.729009\pi$
$74$	10.1958			0.137781
$75$			97.4934i			1.29991i
$76$		−	2.42094i		−	0.0318545i
$77$	54.0818	+	10.6180i	0.702361	+	0.137896i
$78$	36.0715			0.462456
$79$	−133.346			−1.68793			−0.843965	−	0.536399i	$-0.819784\pi$
$79$	−133.346			−1.68793			−0.843965	+	0.536399i	$0.819784\pi$
$80$		−	111.308i		−	1.39135i
$81$	9.00000			0.111111
$82$			55.9697i			0.682558i
$83$			106.728i			1.28588i	0.765915	+	0.642942i	$0.222286\pi$
$83$			106.728i			1.28588i	−0.765915	+	0.642942i	$0.777714\pi$
$84$	−1.79076	+	9.12108i	−0.0213186	+	0.108584i
$85$	−106.998			−1.25880
$86$	−93.3627			−1.08561
$87$		−	29.3115i		−	0.336914i
$88$	67.4847			0.766872
$89$			21.5522i			0.242160i	0.992643	+	0.121080i	$0.0386357\pi$
$89$			21.5522i			0.242160i	−0.992643	+	0.121080i	$0.961364\pi$
$90$			48.6362i			0.540403i
$91$	15.6190	−	79.5542i	0.171638	−	0.874222i
$92$	−3.67675			−0.0399647
$93$	61.7762			0.664261
$94$		−	110.200i		−	1.17235i
$95$	−28.4706			−0.299691
$96$			20.9325i			0.218047i
$97$			139.695i			1.44016i	0.693891	+	0.720080i	$0.255895\pi$
$97$			139.695i			1.44016i	−0.693891	+	0.720080i	$0.744105\pi$
$98$	−81.5689	−	33.3133i	−0.832336	−	0.339932i
$99$	−23.6204			−0.238590
$100$	43.1534			0.431534
$101$			79.6903i			0.789013i	0.918893	+	0.394506i	$0.129084\pi$
$101$			79.6903i			0.789013i	−0.918893	+	0.394506i	$0.870916\pi$
$102$	−36.9615			−0.362368
$103$			4.00668i			0.0388998i	0.999811	+	0.0194499i	$0.00619149\pi$
$103$			4.00668i			0.0388998i	−0.999811	+	0.0194499i	$0.993809\pi$
$104$		−	99.2700i		−	0.954519i
$105$	107.265	+	21.0596i	1.02157	+	0.200568i
$106$	−119.025			−1.12288
$107$	43.4026			0.405632			0.202816	−	0.979217i	$-0.434991\pi$
$107$	43.4026			0.405632			0.202816	+	0.979217i	$0.434991\pi$
$108$		−	3.98366i		−	0.0368858i
$109$	−67.2552			−0.617020			−0.308510	−	0.951221i	$-0.599830\pi$
$109$	−67.2552			−0.617020			−0.308510	+	0.951221i	$0.599830\pi$
$110$		−	127.645i		−	1.16041i
$111$			9.82101i			0.0884776i
$112$	−84.8004	−	16.6490i	−0.757146	−	0.148652i
$113$	−144.700			−1.28053			−0.640265	−	0.768155i	$-0.721175\pi$
$113$	−144.700			−1.28053			−0.640265	+	0.768155i	$0.721175\pi$
$114$	−9.83491			−0.0862711
$115$			43.2391i			0.375992i
$116$	−12.9741			−0.111846
$117$			34.7456i			0.296971i
$118$			38.4456i			0.325810i
$119$	−16.0044	+	81.5170i	−0.134491	+	0.685017i
$120$	133.848			1.11540
$121$	−59.0086			−0.487674
$122$			10.6416i			0.0872261i
$123$	−53.9123			−0.438311
$124$		−	27.3440i		−	0.220516i
$125$		−	282.091i		−	2.25672i
$126$	37.0538	+	7.27484i	0.294077	+	0.0577369i
$127$	−40.0840			−0.315622			−0.157811	−	0.987469i	$-0.550444\pi$
$127$	−40.0840			−0.315622			−0.157811	+	0.987469i	$0.550444\pi$
$128$	−79.5317			−0.621342
$129$		−	89.9307i		−	0.697137i
$130$	−187.766			−1.44435
$131$			196.769i			1.50205i	0.660273	+	0.751025i	$0.270440\pi$
$131$			196.769i			1.50205i	−0.660273	+	0.751025i	$0.729560\pi$
$132$			10.4551i			0.0792051i
$133$	−4.25854	+	21.6905i	−0.0320191	+	0.163086i
$134$	218.008			1.62693
$135$	−46.8484			−0.347025
$136$			101.719i			0.747935i
$137$	124.236			0.906836			0.453418	−	0.891298i	$-0.350205\pi$
$137$	124.236			0.906836			0.453418	+	0.891298i	$0.350205\pi$
$138$			14.9366i			0.108236i
$139$		−	132.662i		−	0.954400i	−0.878795	−	0.477200i	$-0.841652\pi$
$139$		−	132.662i		−	0.954400i	0.878795	−	0.477200i	$-0.158348\pi$
$140$	9.32159	−	47.4787i	0.0665828	−	0.339133i
$141$	106.150			0.752834
$142$	−23.0606			−0.162399
$143$		−	91.1893i		−	0.637688i
$144$	37.0368			0.257200
$145$			152.577i			1.05226i
$146$		−	197.466i		−	1.35251i
$147$	32.0887	−	78.5704i	0.218291	−	0.534493i
$148$	4.34707			0.0293721
$149$	4.14677			0.0278307			0.0139153	−	0.999903i	$-0.495570\pi$
$149$	4.14677			0.0278307			0.0139153	+	0.999903i	$0.495570\pi$
$150$		−	175.308i		−	1.16872i
$151$	183.469			1.21502			0.607512	−	0.794310i	$-0.292168\pi$
$151$	183.469			1.21502			0.607512	+	0.794310i	$0.292168\pi$
$152$			27.0660i			0.178066i
$153$		−	35.6028i		−	0.232698i
$154$	−97.2472	−	19.0927i	−0.631475	−	0.123979i
$155$	−321.569			−2.07464
$156$	15.3794			0.0985859
$157$		−	236.347i		−	1.50539i	−0.658368	−	0.752697i	$-0.728753\pi$
$157$		−	236.347i		−	1.50539i	0.658368	−	0.752697i	$-0.271247\pi$
$158$	239.777			1.51757
$159$		−	114.650i		−	0.721068i
$160$		−	108.962i		−	0.681010i
$161$	32.9419	+	6.46756i	0.204608	+	0.0401712i
$162$	−16.1834			−0.0998972
$163$	−52.3795			−0.321347			−0.160673	−	0.987008i	$-0.551367\pi$
$163$	−52.3795			−0.321347			−0.160673	+	0.987008i	$0.551367\pi$
$164$			23.8632i			0.145507i
$165$	122.953			0.745170
$166$		−	191.914i		−	1.15611i
$167$		−	218.335i		−	1.30740i	−0.756755	−	0.653699i	$-0.773216\pi$
$167$		−	218.335i		−	1.30740i	0.756755	−	0.653699i	$-0.226784\pi$
$168$	20.0206	−	101.973i	0.119170	−	0.606983i
$169$	34.8607			0.206276
$170$	192.399			1.13176
$171$		−	9.47338i		−	0.0553999i
$172$	−39.8059			−0.231430
$173$			29.0906i			0.168154i	0.996459	+	0.0840769i	$0.0267942\pi$
$173$			29.0906i			0.168154i	−0.996459	+	0.0840769i	$0.973206\pi$
$174$			52.7065i			0.302911i
$175$	−386.634	−	75.9086i	−2.20934	−	0.433764i
$176$	−97.2028			−0.552288
$177$	−37.0324			−0.209222
$178$		−	38.7542i		−	0.217720i
$179$	257.837			1.44043			0.720216	−	0.693750i	$-0.244043\pi$
$179$	257.837			1.44043			0.720216	+	0.693750i	$0.244043\pi$
$180$			20.7365i			0.115203i
$181$		−	28.0271i		−	0.154846i	−0.996998	−	0.0774228i	$-0.975331\pi$
$181$		−	28.0271i		−	0.154846i	0.996998	−	0.0774228i	$-0.0246691\pi$
$182$	−28.0854	+	143.050i	−0.154315	+	0.785991i
$183$	−10.2504			−0.0560131
$184$	41.1059			0.223401
$185$		−	51.1221i		−	0.276336i
$186$	−111.083			−0.597220
$187$			93.4391i			0.499675i
$188$		−	46.9849i		−	0.249920i
$189$	−7.00742	+	35.6917i	−0.0370763	+	0.188845i
$190$	51.1944			0.269444
$191$	200.695			1.05076			0.525381	−	0.850867i	$-0.323923\pi$
$191$	200.695			1.05076			0.525381	+	0.850867i	$0.323923\pi$
$192$		−	123.173i		−	0.641525i
$193$	300.693			1.55800			0.778998	−	0.627026i	$-0.215728\pi$
$193$	300.693			1.55800			0.778998	+	0.627026i	$0.215728\pi$
$194$		−	251.193i		−	1.29481i
$195$		−	180.864i		−	0.927506i
$196$	−34.7776	−	14.2034i	−0.177437	−	0.0724663i
$197$	−82.6662			−0.419625			−0.209813	−	0.977742i	$-0.567285\pi$
$197$	−82.6662			−0.419625			−0.209813	+	0.977742i	$0.567285\pi$
$198$	42.4730			0.214510
$199$		−	198.601i		−	0.997994i	−0.866604	−	0.498997i	$-0.833702\pi$
$199$		−	198.601i		−	0.997994i	0.866604	−	0.498997i	$-0.166298\pi$
$200$	−482.452			−2.41226
$201$			209.994i			1.04475i
$202$		−	143.295i		−	0.709382i
$203$	116.242	+	22.8220i	0.572620	+	0.112424i
$204$	−15.7588			−0.0772492
$205$	280.634			1.36895
$206$		−	7.20462i		−	0.0349739i
$207$	−14.3875			−0.0695048
$208$			142.985i			0.687428i
$209$			24.8628i			0.118961i
$210$	−192.879	−	37.8683i	−0.918471	−	0.180325i
$211$	−72.0711			−0.341569			−0.170785	−	0.985308i	$-0.554630\pi$
$211$	−72.0711			−0.341569			−0.170785	+	0.985308i	$0.554630\pi$
$212$	−50.7473			−0.239374
$213$		−	22.2129i		−	0.104286i
$214$	−78.0444			−0.364694
$215$			468.123i			2.17732i
$216$			44.5371i			0.206190i
$217$	−48.0991	+	244.989i	−0.221655	+	1.12898i
$218$	120.935			0.554748
$219$	190.208			0.868528
$220$		−	54.4226i		−	0.247375i
$221$	137.449			0.621940
$222$		−	17.6597i		−	0.0795480i
$223$		−	342.921i		−	1.53776i	−0.639391	−	0.768882i	$-0.720813\pi$
$223$		−	342.921i		−	1.53776i	0.639391	−	0.768882i	$-0.279187\pi$
$224$	−83.0129	−	16.2981i	−0.370593	−	0.0727594i
$225$	168.864			0.750505
$226$	260.192			1.15129
$227$			335.899i			1.47973i	0.672755	+	0.739865i	$0.265111\pi$
$227$			335.899i			1.47973i	−0.672755	+	0.739865i	$0.734889\pi$
$228$	−4.19319			−0.0183912
$229$			160.020i			0.698779i	0.936978	+	0.349389i	$0.113611\pi$
$229$			160.020i			0.698779i	−0.936978	+	0.349389i	$0.886389\pi$
$230$		−	77.7504i		−	0.338045i
$231$	18.3909	−	93.6724i	0.0796143	−	0.405508i
$232$	145.050			0.625215
$233$	−119.759			−0.513987			−0.256994	−	0.966413i	$-0.582732\pi$
$233$	−119.759			−0.513987			−0.256994	+	0.966413i	$0.582732\pi$
$234$		−	62.4777i		−	0.266999i
$235$	−552.548			−2.35127
$236$			16.3916i			0.0694559i
$237$			230.963i			0.974526i
$238$	28.7783	−	146.580i	0.120917	−	0.615881i
$239$	−226.922			−0.949464			−0.474732	−	0.880130i	$-0.657455\pi$
$239$	−226.922			−0.949464			−0.474732	+	0.880130i	$0.657455\pi$
$240$	−192.791			−0.803295
$241$		−	403.095i		−	1.67259i	−0.548278	−	0.836296i	$-0.684716\pi$
$241$		−	403.095i		−	1.67259i	0.548278	−	0.836296i	$-0.315284\pi$
$242$	106.106			0.438456
$243$		−	15.5885i		−	0.0641500i
$244$			4.53713i			0.0185948i
$245$	−167.034	+	408.989i	−0.681771	+	1.66934i
$246$	96.9424			0.394075
$247$	36.5731			0.148069
$248$			305.704i			1.23268i
$249$	184.859			0.742405
$250$			507.241i			2.02896i
$251$			246.111i			0.980522i	0.871576	+	0.490261i	$0.163099\pi$
$251$			246.111i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$252$	15.7982	+	3.10169i	0.0626912	+	0.0123083i
$253$	37.7598			0.149248
$254$	72.0771			0.283768
$255$			185.326i			0.726769i
$256$	−141.445			−0.552520
$257$		−	283.570i		−	1.10338i	−0.834048	−	0.551692i	$-0.813982\pi$
$257$		−	283.570i		−	1.10338i	0.834048	−	0.551692i	$-0.186018\pi$
$258$			161.709i			0.626779i
$259$	−38.9476	−	7.64667i	−0.150377	−	0.0295238i
$260$	−80.0556			−0.307906
$261$	−50.7690			−0.194517
$262$		−	353.820i		−	1.35046i
$263$	−425.045			−1.61614			−0.808070	−	0.589087i	$-0.799488\pi$
$263$	−425.045			−1.61614			−0.808070	+	0.589087i	$0.799488\pi$
$264$		−	116.887i		−	0.442754i
$265$			596.795i			2.25206i
$266$	7.65749	−	39.0027i	0.0287875	−	0.146627i
$267$	37.3296			0.139811
$268$	92.9496			0.346827
$269$		−	54.2866i		−	0.201809i	−0.994896	−	0.100904i	$-0.967826\pi$
$269$		−	54.2866i		−	0.201809i	0.994896	−	0.100904i	$-0.0321736\pi$
$270$	84.2404			0.312002
$271$			164.878i			0.608406i	0.952607	+	0.304203i	$0.0983900\pi$
$271$			164.878i			0.608406i	−0.952607	+	0.304203i	$0.901610\pi$
$272$		−	146.513i		−	0.538650i
$273$	−137.792	−	27.0530i	−0.504732	−	0.0990952i
$274$	−223.396			−0.815313
$275$	−443.180			−1.61157
$276$			6.36832i			0.0230736i
$277$	190.165			0.686518			0.343259	−	0.939241i	$-0.388469\pi$
$277$	190.165			0.686518			0.343259	+	0.939241i	$0.388469\pi$
$278$			238.545i			0.858077i
$279$		−	107.000i		−	0.383511i
$280$	−104.215	+	530.808i	−0.372195	+	1.89574i
$281$	165.781			0.589966			0.294983	−	0.955502i	$-0.404686\pi$
$281$	165.781			0.589966			0.294983	+	0.955502i	$0.404686\pi$
$282$	−190.873			−0.676854
$283$		−	469.109i		−	1.65763i	−0.559524	−	0.828814i	$-0.689016\pi$
$283$		−	469.109i		−	1.65763i	0.559524	−	0.828814i	$-0.310984\pi$
$284$	−9.83208			−0.0346200
$285$			49.3125i			0.173026i
$286$			163.972i			0.573329i
$287$	41.9763	−	213.802i	0.146259	−	0.744956i
$288$	36.2562			0.125889
$289$	148.160			0.512664
$290$		−	274.357i		−	0.946059i
$291$	241.960			0.831476
$292$		−	84.1914i		−	0.288327i
$293$		−	240.172i		−	0.819700i	−0.912153	−	0.409850i	$-0.865581\pi$
$293$		−	240.172i		−	0.819700i	0.912153	−	0.409850i	$-0.134419\pi$
$294$	−57.7003	+	141.281i	−0.196260	+	0.480549i
$295$	192.767			0.653449
$296$	−48.5999			−0.164189
$297$			40.9117i			0.137750i
$298$	−7.45651			−0.0250219
$299$		−	55.5446i		−	0.185768i
$300$		−	74.7439i		−	0.249146i
$301$	356.642	+	70.0203i	1.18486	+	0.232625i
$302$	−329.904			−1.09240
$303$	138.028			0.455537
$304$		−	38.9849i		−	0.128240i
$305$	53.3572			0.174942
$306$			64.0192i			0.209213i
$307$			294.063i			0.957860i	0.877853	+	0.478930i	$0.158975\pi$
$307$			294.063i			0.957860i	−0.877853	+	0.478930i	$0.841025\pi$
$308$	−41.4621	−	8.14035i	−0.134617	−	0.0264297i
$309$	6.93978			0.0224588
$310$	578.229			1.86525
$311$			360.449i			1.15900i	0.814972	+	0.579500i	$0.196752\pi$
$311$			360.449i			1.15900i	−0.814972	+	0.579500i	$0.803248\pi$
$312$	−171.941			−0.551092
$313$		−	434.797i		−	1.38913i	−0.719432	−	0.694563i	$-0.755598\pi$
$313$		−	434.797i		−	1.38913i	0.719432	−	0.694563i	$-0.244402\pi$
$314$			424.987i			1.35346i
$315$	36.4763	−	185.789i	0.115798	−	0.589805i
$316$	102.231			0.323515
$317$	84.2626			0.265813			0.132906	−	0.991129i	$-0.457569\pi$
$317$	84.2626			0.265813			0.132906	+	0.991129i	$0.457569\pi$
$318$			206.157i			0.648294i
$319$	133.243			0.417688
$320$			641.160i			2.00363i
$321$		−	75.1756i		−	0.234192i
$322$	−59.2345	−	11.6296i	−0.183958	−	0.0361169i
$323$	−37.4754			−0.116023
$324$	−6.89990			−0.0212960
$325$			651.918i			2.00590i
$326$	94.1862			0.288915
$327$			116.489i			0.356237i
$328$		−	266.789i		−	0.813380i
$329$	−82.6483	+	420.962i	−0.251211	+	1.27952i
$330$	−221.088			−0.669964
$331$	588.268			1.77724			0.888622	−	0.458641i	$-0.151664\pi$
$331$	588.268			1.77724			0.888622	+	0.458641i	$0.151664\pi$
$332$		−	81.8239i		−	0.246458i
$333$	17.0105			0.0510826
$334$			392.600i			1.17545i
$335$		−	1093.10i		−	3.26298i
$336$	−28.8370	+	146.879i	−0.0858244	+	0.437139i
$337$	−154.322			−0.457929			−0.228965	−	0.973435i	$-0.573534\pi$
$337$	−154.322			−0.457929			−0.228965	+	0.973435i	$0.573534\pi$
$338$	−62.6847			−0.185458
$339$			250.627i			0.739314i
$340$	82.0307			0.241267
$341$			280.819i			0.823517i
$342$			17.0346i			0.0498087i
$343$	286.606	+	188.431i	0.835585	+	0.549361i
$344$	445.028			1.29369
$345$	74.8923			0.217079
$346$		−	52.3093i		−	0.151183i
$347$	563.917			1.62512			0.812560	−	0.582877i	$-0.198073\pi$
$347$	563.917			1.62512			0.812560	+	0.582877i	$0.198073\pi$
$348$			22.4718i			0.0645742i
$349$			275.472i			0.789319i	0.918827	+	0.394660i	$0.129138\pi$
$349$			275.472i			0.789319i	−0.918827	+	0.394660i	$0.870862\pi$
$350$	695.226	+	136.495i	1.98636	+	0.389986i
$351$	60.1811			0.171456
$352$	−95.1539			−0.270323
$353$		−	297.152i		−	0.841791i	−0.907109	−	0.420896i	$-0.861716\pi$
$353$		−	297.152i		−	0.841791i	0.907109	−	0.420896i	$-0.138284\pi$
$354$	66.5897			0.188107
$355$			115.627i			0.325709i
$356$		−	16.5232i		−	0.0464133i
$357$	141.192	+	27.7204i	0.395495	+	0.0776483i
$358$	−463.630			−1.29506
$359$	−219.913			−0.612572			−0.306286	−	0.951940i	$-0.599086\pi$
$359$	−219.913			−0.612572			−0.306286	+	0.951940i	$0.599086\pi$
$360$		−	231.832i		−	0.643978i
$361$	351.028			0.972378
$362$			50.3969i			0.139218i
$363$			102.206i			0.281559i
$364$	−11.9744	+	60.9907i	−0.0328968	+	0.167557i
$365$	−990.102			−2.71261
$366$	18.4318			0.0503600
$367$		−	194.863i		−	0.530963i	−0.964116	−	0.265481i	$-0.914469\pi$
$367$		−	194.863i		−	0.530963i	0.964116	−	0.265481i	$-0.0855309\pi$
$368$	−59.2075			−0.160890
$369$			93.3789i			0.253059i
$370$			91.9252i			0.248446i
$371$	454.671	+	89.2666i	1.22553	+	0.240611i
$372$	−47.3611			−0.127315
$373$	−464.725			−1.24591			−0.622956	−	0.782257i	$-0.714068\pi$
$373$	−464.725			−1.24591			−0.622956	+	0.782257i	$0.714068\pi$
$374$		−	168.018i		−	0.449245i
$375$	−488.595			−1.30292
$376$			525.288i			1.39704i
$377$		−	196.000i		−	0.519893i
$378$	12.6004	−	64.1790i	0.0333344	−	0.169786i
$379$	−473.576			−1.24954			−0.624770	−	0.780809i	$-0.714807\pi$
$379$	−473.576			−1.24954			−0.624770	+	0.780809i	$0.714807\pi$
$380$	21.8272			0.0574399
$381$			69.4276i			0.182225i
$382$	−360.881			−0.944714
$383$		−	388.716i		−	1.01492i	−0.861674	−	0.507462i	$-0.830584\pi$
$383$		−	388.716i		−	1.01492i	0.861674	−	0.507462i	$-0.169416\pi$
$384$			137.753i			0.358732i
$385$	−95.7316	+	487.600i	−0.248653	+	1.26649i
$386$	−540.692			−1.40076
$387$	−155.765			−0.402492
$388$		−	107.098i		−	0.276027i
$389$	575.273			1.47885			0.739426	−	0.673238i	$-0.235097\pi$
$389$	575.273			1.47885			0.739426	+	0.673238i	$0.235097\pi$
$390$			325.220i			0.833898i
$391$			56.9150i			0.145563i
$392$	388.811	+	158.793i	0.991864	+	0.405084i
$393$	340.813			0.867209
$394$	148.646			0.377275
$395$		−	1202.25i		−	3.04367i
$396$	18.1087			0.0457291
$397$			275.783i			0.694669i	0.937741	+	0.347334i	$0.112913\pi$
$397$			275.783i			0.694669i	−0.937741	+	0.347334i	$0.887087\pi$
$398$			357.114i			0.897272i
$399$	37.5690	+	7.37600i	0.0941579	+	0.0184862i
$400$	694.908			1.73727
$401$	−638.868			−1.59319			−0.796593	−	0.604516i	$-0.793367\pi$
$401$	−638.868			−1.59319			−0.796593	+	0.604516i	$0.793367\pi$
$402$		−	377.601i		−	0.939306i
$403$	413.085			1.02502
$404$		−	61.0950i		−	0.151225i
$405$			81.1438i			0.200355i
$406$	−209.020	−	41.0374i	−0.514828	−	0.101077i
$407$	−44.6438			−0.109690
$408$	176.183			0.431820
$409$			155.642i			0.380542i	0.981732	+	0.190271i	$0.0609367\pi$
$409$			155.642i			0.380542i	−0.981732	+	0.190271i	$0.939063\pi$
$410$	−504.622			−1.23079
$411$		−	215.184i		−	0.523562i
$412$		−	3.07175i		−	0.00745570i
$413$	28.8335	−	146.861i	0.0698148	−	0.355595i
$414$	25.8709			0.0624900
$415$	−962.260			−2.31870
$416$			139.971i			0.336469i
$417$	−229.777			−0.551023
$418$		−	44.7070i		−	0.106955i
$419$			99.9079i			0.238444i	0.992868	+	0.119222i	$0.0380400\pi$
$419$			99.9079i			0.238444i	−0.992868	+	0.119222i	$0.961960\pi$
$420$	−82.2355	−	16.1455i	−0.195799	−	0.0384416i
$421$	−256.903			−0.610222			−0.305111	−	0.952317i	$-0.598694\pi$
$421$	−256.903			−0.610222			−0.305111	+	0.952317i	$0.598694\pi$
$422$	129.595			0.307096
$423$		−	183.856i		−	0.434649i
$424$	567.352			1.33809
$425$		−	668.002i		−	1.57177i
$426$			39.9421i			0.0937609i
$427$	7.98099	−	40.6505i	0.0186909	−	0.0952002i
$428$	−33.2749			−0.0777451
$429$	−157.945			−0.368169
$430$		−	841.756i		−	1.95757i
$431$	−545.760			−1.26626			−0.633132	−	0.774044i	$-0.718231\pi$
$431$	−545.760			−1.26626			−0.633132	+	0.774044i	$0.718231\pi$
$432$		−	64.1497i		−	0.148495i
$433$		−	609.727i		−	1.40815i	−0.710128	−	0.704073i	$-0.751363\pi$
$433$		−	609.727i		−	1.40815i	0.710128	−	0.704073i	$-0.248637\pi$
$434$	86.4895	−	440.526i	0.199285	−	1.01504i
$435$	264.272			0.607521
$436$	51.5616			0.118261
$437$			15.1442i			0.0346550i
$438$	−342.022			−0.780871
$439$		−	810.518i		−	1.84628i	−0.384462	−	0.923141i	$-0.625613\pi$
$439$		−	810.518i		−	1.84628i	0.384462	−	0.923141i	$-0.374387\pi$
$440$			608.441i			1.38282i
$441$	−136.088	−	55.5793i	−0.308590	−	0.126030i
$442$	−247.154			−0.559171
$443$	−406.479			−0.917559			−0.458780	−	0.888550i	$-0.651713\pi$
$443$	−406.479			−0.917559			−0.458780	+	0.888550i	$0.651713\pi$
$444$		−	7.52934i		−	0.0169580i
$445$	−194.314			−0.436662
$446$			616.624i			1.38257i
$447$		−	7.18241i		−	0.0160680i
$448$	488.471	+	95.9026i	1.09034	+	0.214068i
$449$	523.202			1.16526			0.582630	−	0.812737i	$-0.302023\pi$
$449$	523.202			1.16526			0.582630	+	0.812737i	$0.302023\pi$
$450$	−303.642			−0.674760
$451$		−	245.072i		−	0.543396i
$452$	110.935			0.245431
$453$		−	317.777i		−	0.701495i
$454$		−	603.996i		−	1.33039i
$455$	717.259	+	140.821i	1.57639	+	0.309497i
$456$	46.8796			0.102806
$457$	512.888			1.12229			0.561147	−	0.827716i	$-0.310360\pi$
$457$	512.888			1.12229			0.561147	+	0.827716i	$0.310360\pi$
$458$		−	287.741i		−	0.628255i
$459$	−61.6659			−0.134348
$460$		−	33.1495i		−	0.0720642i
$461$			763.171i			1.65547i	0.561120	+	0.827735i	$0.310371\pi$
$461$			763.171i			1.65547i	−0.561120	+	0.827735i	$0.689629\pi$
$462$	−33.0696	+	168.437i	−0.0715792	+	0.364582i
$463$	556.403			1.20173			0.600867	−	0.799349i	$-0.294822\pi$
$463$	556.403			1.20173			0.600867	+	0.799349i	$0.294822\pi$
$464$	−208.925			−0.450269
$465$			556.973i			1.19779i
$466$	215.345			0.462113
$467$		−	102.975i		−	0.220504i	−0.993904	−	0.110252i	$-0.964834\pi$
$467$		−	102.975i		−	0.220504i	0.993904	−	0.110252i	$-0.0351658\pi$
$468$		−	26.6379i		−	0.0569186i
$469$	−832.783	−	163.502i	−1.77566	−	0.348618i
$470$	993.565			2.11397
$471$	−409.365			−0.869139
$472$		−	183.257i		−	0.388256i
$473$	408.802			0.864275
$474$		−	415.306i		−	0.876172i
$475$		−	177.745i		−	0.374201i
$476$	12.2699	−	62.4955i	0.0257770	−	0.131293i
$477$	−198.579			−0.416309
$478$	408.040			0.853639
$479$			267.951i			0.559397i	0.960088	+	0.279699i	$0.0902346\pi$
$479$			267.951i			0.559397i	−0.960088	+	0.279699i	$0.909765\pi$
$480$	−188.727			−0.393181
$481$			65.6710i			0.136530i
$482$			724.825i			1.50379i
$483$	11.2021	−	57.0571i	0.0231928	−	0.118131i
$484$	45.2393			0.0934696
$485$	−1259.49			−2.59689
$486$			28.0304i			0.0576757i
$487$	155.018			0.318313			0.159156	−	0.987253i	$-0.449123\pi$
$487$	155.018			0.318313			0.159156	+	0.987253i	$0.449123\pi$
$488$		−	50.7248i		−	0.103944i
$489$			90.7240i			0.185530i
$490$	300.352	−	735.423i	0.612963	−	1.50086i
$491$	586.469			1.19444			0.597219	−	0.802078i	$-0.296272\pi$
$491$	586.469			1.19444			0.597219	+	0.802078i	$0.296272\pi$
$492$	41.3322			0.0840085
$493$			200.835i			0.407374i
$494$	−65.7639			−0.133125
$495$		−	212.961i		−	0.430224i
$496$		−	440.325i		−	0.887752i
$497$	88.0906	+	17.2950i	0.177245	+	0.0347988i
$498$	−332.404			−0.667478
$499$	524.664			1.05143			0.525716	−	0.850660i	$-0.323798\pi$
$499$	524.664			1.05143			0.525716	+	0.850660i	$0.323798\pi$
$500$			216.266i			0.432533i
$501$	−378.168			−0.754826
$502$		−	442.545i		−	0.881563i
$503$			548.894i			1.09124i	0.838032	+	0.545621i	$0.183706\pi$
$503$			548.894i			1.09124i	−0.838032	+	0.545621i	$0.816294\pi$
$504$	−176.623	−	34.6767i	−0.350442	−	0.0688029i
$505$	−718.486			−1.42274
$506$	−67.8978			−0.134185
$507$		−	60.3804i		−	0.119094i
$508$	30.7307			0.0604935
$509$			195.945i			0.384961i	0.981301	+	0.192481i	$0.0616532\pi$
$509$			195.945i			0.384961i	−0.981301	+	0.192481i	$0.938347\pi$
$510$		−	333.244i		−	0.653420i
$511$	−148.096	+	754.314i	−0.289816	+	1.47615i
$512$	572.467			1.11810
$513$	−16.4084			−0.0319851
$514$			509.901i			0.992026i
$515$	−36.1242			−0.0701440
$516$			68.9459i			0.133616i
$517$			482.529i			0.933325i
$518$	70.0336	+	13.7499i	0.135200	+	0.0265441i
$519$	50.3864			0.0970837
$520$	895.016			1.72118
$521$		−	336.646i		−	0.646153i	−0.946373	−	0.323076i	$-0.895283\pi$
$521$		−	336.646i		−	0.646153i	0.946373	−	0.323076i	$-0.104717\pi$
$522$	91.2903			0.174886
$523$		−	491.755i		−	0.940258i	−0.882598	−	0.470129i	$-0.844207\pi$
$523$		−	491.755i		−	0.940258i	0.882598	−	0.470129i	$-0.155793\pi$
$524$		−	150.854i		−	0.287889i
$525$	−131.478	+	669.669i	−0.250434	+	1.27556i
$526$	764.294			1.45303
$527$	−423.276			−0.803181
$528$			168.360i			0.318864i
$529$	23.0000			0.0434783
$530$		−	1073.13i		−	2.02477i
$531$			64.1419i			0.120795i
$532$	3.26483	−	16.6291i	0.00613690	−	0.0312578i
$533$	−360.500			−0.676360
$534$	−67.1242			−0.125701
$535$			391.317i			0.731434i
$536$	−1039.17			−1.93875
$537$		−	446.587i		−	0.831634i
$538$			97.6154i			0.181441i
$539$	357.161	+	145.867i	0.662637	+	0.270625i
$540$	35.9166			0.0665122
$541$	−686.463			−1.26888			−0.634439	−	0.772973i	$-0.718769\pi$
$541$	−686.463			−1.26888			−0.634439	+	0.772973i	$0.718769\pi$
$542$		−	296.475i		−	0.547002i
$543$	−48.5443			−0.0894002
$544$		−	143.425i		−	0.263648i
$545$		−	606.372i		−	1.11261i
$546$	247.771	+	48.6453i	0.453792	+	0.0890940i
$547$	−115.192			−0.210589			−0.105295	−	0.994441i	$-0.533579\pi$
$547$	−115.192			−0.210589			−0.105295	+	0.994441i	$0.533579\pi$
$548$	−95.2467			−0.173808
$549$			17.7542i			0.0323392i
$550$	796.905			1.44892
$551$			53.4393i			0.0969861i
$552$		−	71.1974i		−	0.128981i
$553$	−915.939	−	179.828i	−1.65631	−	0.325187i
$554$	−341.946			−0.617231
$555$	−88.5460			−0.159542
$556$			101.706i			0.182924i
$557$	578.016			1.03773			0.518866	−	0.854856i	$-0.326354\pi$
$557$	578.016			1.03773			0.518866	+	0.854856i	$0.326354\pi$
$558$			192.401i			0.344805i
$559$		−	601.347i		−	1.07576i
$560$	150.107	−	764.558i	0.268049	−	1.36528i
$561$	161.841			0.288487
$562$	−298.098			−0.530424
$563$		−	817.474i		−	1.45200i	−0.687696	−	0.725998i	$-0.741378\pi$
$563$		−	817.474i		−	1.45200i	0.687696	−	0.725998i	$-0.258622\pi$
$564$	−81.3802			−0.144291
$565$		−	1304.61i		−	2.30904i
$566$			843.528i			1.49033i
$567$	61.8198	+	12.1372i	0.109030	+	0.0214060i
$568$	109.922			0.193525
$569$	1116.35			1.96195			0.980974	−	0.194138i	$-0.0621908\pi$
$569$	1116.35			1.96195			0.980974	+	0.194138i	$0.0621908\pi$
$570$		−	88.6713i		−	0.155564i
$571$	−682.021			−1.19443			−0.597216	−	0.802080i	$-0.703727\pi$
$571$	−682.021			−1.19443			−0.597216	+	0.802080i	$0.703727\pi$
$572$			69.9108i			0.122222i
$573$		−	347.615i		−	0.606657i
$574$	−75.4796	+	384.449i	−0.131498	+	0.669771i
$575$	−269.947			−0.469473
$576$	−213.341			−0.370384
$577$			112.978i			0.195803i	0.995196	+	0.0979016i	$0.0312131\pi$
$577$			112.978i			0.195803i	−0.995196	+	0.0979016i	$0.968787\pi$
$578$	−266.414			−0.460924
$579$		−	520.816i		−	0.899509i
$580$		−	116.974i		−	0.201680i
$581$	−143.932	+	733.103i	−0.247731	+	1.26179i
$582$	−435.080			−0.747560
$583$	521.169			0.893943
$584$			941.254i			1.61174i
$585$	−313.265			−0.535496
$586$			431.866i			0.736972i
$587$			751.028i			1.27943i	0.768611	+	0.639717i	$0.220948\pi$
$587$			751.028i			1.27943i	−0.768611	+	0.639717i	$0.779052\pi$
$588$	−24.6010	+	60.2365i	−0.0418384	+	0.102443i
$589$	−112.628			−0.191218
$590$	−346.625			−0.587500
$591$			143.182i			0.242271i
$592$	70.0017			0.118246
$593$			404.985i			0.682943i	0.939892	+	0.341471i	$0.110925\pi$
$593$			404.985i			0.682943i	−0.939892	+	0.341471i	$0.889075\pi$
$594$		−	73.5654i		−	0.123848i
$595$	−734.955	−	144.295i	−1.23522	−	0.242513i
$596$	−3.17914			−0.00533414
$597$	−343.987			−0.576192
$598$			99.8776i			0.167019i
$599$	650.936			1.08670			0.543352	−	0.839505i	$-0.317155\pi$
$599$	650.936			1.08670			0.543352	+	0.839505i	$0.317155\pi$
$600$			835.632i			1.39272i
$601$			449.219i			0.747453i	0.927539	+	0.373726i	$0.121920\pi$
$601$			449.219i			0.747453i	−0.927539	+	0.373726i	$0.878080\pi$
$602$	−641.296	−	125.907i	−1.06528	−	0.209148i
$603$	363.721			0.603185
$604$	−140.657			−0.232876
$605$		−	532.020i		−	0.879372i
$606$	−248.194			−0.409562
$607$		−	117.259i		−	0.193177i	−0.995324	−	0.0965886i	$-0.969207\pi$
$607$		−	117.259i		−	0.193177i	0.995324	−	0.0965886i	$-0.0307931\pi$
$608$		−	38.1632i		−	0.0627683i
$609$	39.5289	−	201.337i	0.0649078	−	0.330602i
$610$	−95.9443			−0.157286
$611$	709.799			1.16170
$612$			27.2951i			0.0445999i
$613$	256.685			0.418735			0.209368	−	0.977837i	$-0.432859\pi$
$613$	256.685			0.418735			0.209368	+	0.977837i	$0.432859\pi$
$614$		−	528.769i		−	0.861188i
$615$		−	486.072i		−	0.790361i
$616$	463.544	+	91.0085i	0.752506	+	0.147741i
$617$	396.512			0.642645			0.321323	−	0.946970i	$-0.395873\pi$
$617$	396.512			0.642645			0.321323	+	0.946970i	$0.395873\pi$
$618$	−12.4788			−0.0201922
$619$			297.714i			0.480959i	0.970654	+	0.240480i	$0.0773047\pi$
$619$			297.714i			0.480959i	−0.970654	+	0.240480i	$0.922695\pi$
$620$	246.533			0.397633
$621$			24.9199i			0.0401286i
$622$		−	648.141i		−	1.04203i
$623$	−29.0649	+	148.039i	−0.0466531	+	0.237623i
$624$	247.657			0.396887
$625$	1136.13			1.81780
$626$			781.830i			1.24893i
$627$	43.0636			0.0686820
$628$			181.197i			0.288530i
$629$		−	67.2913i		−	0.106981i
$630$	−65.5898	+	334.076i	−0.104111	+	0.530279i
$631$	1140.67			1.80772			0.903860	−	0.427829i	$-0.140722\pi$
$631$	1140.67			1.80772			0.903860	+	0.427829i	$0.140722\pi$
$632$	−1142.93			−1.80844
$633$			124.831i			0.197205i
$634$	−151.517			−0.238985
$635$		−	361.397i		−	0.569129i
$636$			87.8969i			0.138203i
$637$	214.570	−	525.384i	0.336845	−	0.824778i
$638$	−239.590			−0.375533
$639$	−38.4739			−0.0602095
$640$		−	717.056i		−	1.12040i
$641$	1214.52			1.89473			0.947363	−	0.320162i	$-0.103738\pi$
$641$	1214.52			1.89473			0.947363	+	0.320162i	$0.103738\pi$
$642$			135.177i			0.210556i
$643$		−	292.518i		−	0.454927i	−0.973787	−	0.227463i	$-0.926957\pi$
$643$		−	292.518i		−	0.454927i	0.973787	−	0.227463i	$-0.0730432\pi$
$644$	−25.2551	−	4.95839i	−0.0392160	−	0.00769937i
$645$	810.813			1.25707
$646$	67.3865			0.104313
$647$		−	821.359i		−	1.26949i	−0.772722	−	0.634744i	$-0.781105\pi$
$647$		−	821.359i		−	1.26949i	0.772722	−	0.634744i	$-0.218895\pi$
$648$	77.1405			0.119044
$649$		−	168.340i		−	0.259383i
$650$		−	1172.25i		−	1.80346i
$651$	424.333	+	83.3102i	0.651817	+	0.127973i
$652$	40.1571			0.0615906
$653$	−755.516			−1.15699			−0.578497	−	0.815685i	$-0.696360\pi$
$653$	−755.516			−1.15699			−0.578497	+	0.815685i	$0.696360\pi$
$654$		−	209.466i		−	0.320284i
$655$	−1774.06			−2.70849
$656$			384.273i			0.585782i
$657$		−	329.449i		−	0.501445i
$658$	148.614	−	756.952i	0.225857	−	1.15038i
$659$	−411.343			−0.624193			−0.312096	−	0.950050i	$-0.601031\pi$
$659$	−411.343			−0.624193			−0.312096	+	0.950050i	$0.601031\pi$
$660$	−94.2627			−0.142822
$661$			1152.87i			1.74413i	0.489394	+	0.872063i	$0.337218\pi$
$661$			1152.87i			1.74413i	−0.489394	+	0.872063i	$0.662782\pi$
$662$	−1057.79			−1.59788
$663$		−	238.068i		−	0.359077i
$664$			914.786i			1.37769i
$665$	−195.561	−	38.3949i	−0.294076	−	0.0577366i
$666$	−30.5874			−0.0459271
$667$	81.1598			0.121679
$668$			167.388i			0.250581i
$669$	−593.957			−0.887829
$670$			1965.56i			2.93367i
$671$		−	46.5957i		−	0.0694422i
$672$	−28.2291	+	143.783i	−0.0420076	+	0.213962i
$673$	−240.609			−0.357518			−0.178759	−	0.983893i	$-0.557208\pi$
$673$	−240.609			−0.357518			−0.178759	+	0.983893i	$0.557208\pi$
$674$	277.495			0.411713
$675$		−	292.480i		−	0.433304i
$676$	−26.7261			−0.0395357
$677$			122.944i			0.181601i	0.995869	+	0.0908006i	$0.0289426\pi$
$677$			122.944i			0.181601i	−0.995869	+	0.0908006i	$0.971057\pi$
$678$		−	450.666i		−	0.664699i
$679$	−188.390	+	959.549i	−0.277453	+	1.41318i
$680$	−917.098			−1.34867
$681$	581.794			0.854323
$682$		−	504.955i		−	0.740403i
$683$	70.0178			0.102515			0.0512575	−	0.998685i	$-0.483677\pi$
$683$	70.0178			0.102515			0.0512575	+	0.998685i	$0.483677\pi$
$684$			7.26283i			0.0106182i
$685$			1120.11i			1.63520i
$686$	−515.360	−	338.827i	−0.751254	−	0.493916i
$687$	277.163			0.403440
$688$	−641.003			−0.931690
$689$		−	766.638i		−	1.11268i
$690$	−134.668			−0.195171
$691$		−	963.110i		−	1.39379i	−0.717172	−	0.696896i	$-0.754564\pi$
$691$		−	963.110i		−	1.39379i	0.717172	−	0.696896i	$-0.245436\pi$
$692$		−	22.3025i		−	0.0322290i
$693$	−162.245	−	31.8540i	−0.234120	−	0.0459653i
$694$	−1014.01			−1.46111
$695$	1196.07			1.72097
$696$		−	251.234i		−	0.360968i
$697$	369.394			0.529978
$698$		−	495.341i		−	0.709657i
$699$			207.429i			0.296751i
$700$	296.415	+	58.1958i	0.423450	+	0.0831369i
$701$	−800.369			−1.14175			−0.570877	−	0.821036i	$-0.693397\pi$
$701$	−800.369			−1.14175			−0.570877	+	0.821036i	$0.693397\pi$
$702$	−108.215			−0.154152
$703$		−	17.9052i		−	0.0254697i
$704$	559.912			0.795329
$705$			957.042i			1.35751i
$706$			534.324i			0.756833i
$707$	−107.469	+	547.382i	−0.152007	+	0.774232i
$708$	28.3911			0.0401004
$709$	136.201			0.192102			0.0960512	−	0.995376i	$-0.469379\pi$
$709$	136.201			0.192102			0.0960512	+	0.995376i	$0.469379\pi$
$710$		−	207.914i		−	0.292836i
$711$	400.039			0.562643
$712$			184.728i			0.259449i
$713$			171.051i			0.239903i
$714$	−253.884	−	49.8455i	−0.355579	−	0.0698116i
$715$	822.161			1.14988
$716$	−197.673			−0.276079
$717$			393.040i			0.548173i
$718$	395.437			0.550748
$719$		−	611.061i		−	0.849876i	−0.905223	−	0.424938i	$-0.860296\pi$
$719$		−	611.061i		−	0.849876i	0.905223	−	0.424938i	$-0.139704\pi$
$720$			333.923i			0.463782i
$721$	−5.40333	+	27.5214i	−0.00749421	+	0.0381711i
$722$	−631.202			−0.874241
$723$	−698.180			−0.965671
$724$			21.4871i			0.0296783i
$725$	−952.559			−1.31387
$726$		−	183.781i		−	0.253142i
$727$		−	965.093i		−	1.32750i	−0.747954	−	0.663750i	$-0.768964\pi$
$727$		−	965.093i		−	1.32750i	0.747954	−	0.663750i	$-0.231036\pi$
$728$	133.873	−	681.872i	0.183892	−	0.936638i
$729$	−27.0000			−0.0370370
$730$	1780.35			2.43884
$731$			616.184i			0.842933i
$732$	7.85854			0.0107357
$733$			264.784i			0.361234i	0.983554	+	0.180617i	$0.0578094\pi$
$733$			264.784i			0.361234i	−0.983554	+	0.180617i	$0.942191\pi$
$734$			350.393i			0.477375i
$735$	708.389	+	289.311i	0.963795	+	0.393621i
$736$	−57.9595			−0.0787493
$737$	−954.581			−1.29522
$738$		−	167.909i		−	0.227519i
$739$	−600.107			−0.812053			−0.406026	−	0.913861i	$-0.633086\pi$
$739$	−600.107			−0.812053			−0.406026	+	0.913861i	$0.633086\pi$
$740$			39.1931i			0.0529636i
$741$		−	63.3465i		−	0.0854878i
$742$	−817.567	−	160.515i	−1.10184	−	0.216327i
$743$	1019.85			1.37261			0.686304	−	0.727315i	$-0.259232\pi$
$743$	1019.85			1.37261			0.686304	+	0.727315i	$0.259232\pi$
$744$	529.494			0.711686
$745$			37.3872i			0.0501841i
$746$	835.645			1.12017
$747$		−	320.185i		−	0.428628i
$748$		−	71.6357i		−	0.0957696i
$749$	298.127	+	58.5319i	0.398033	+	0.0781467i
$750$	878.568			1.17142
$751$	1373.55			1.82897			0.914483	−	0.404623i	$-0.132597\pi$
$751$	1373.55			1.82897			0.914483	+	0.404623i	$0.132597\pi$
$752$		−	756.607i		−	1.00613i
$753$	426.277			0.566105
$754$			352.437i			0.467423i
$755$			1654.15i			2.19093i
$756$	5.37228	−	27.3632i	0.00710620	−	0.0361948i
$757$	254.443			0.336120			0.168060	−	0.985777i	$-0.446250\pi$
$757$	254.443			0.336120			0.168060	+	0.985777i	$0.446250\pi$
$758$	851.561			1.12343
$759$		−	65.4019i		−	0.0861685i
$760$	−244.026			−0.321087
$761$			545.582i			0.716928i	0.933544	+	0.358464i	$0.116699\pi$
$761$			545.582i			0.716928i	−0.933544	+	0.358464i	$0.883301\pi$
$762$		−	124.841i		−	0.163834i
$763$	−461.967	−	90.6990i	−0.605462	−	0.118872i
$764$	−153.864			−0.201393
$765$	320.994			0.419600
$766$			698.970i			0.912493i
$767$	−247.628			−0.322852
$768$			244.990i			0.318998i
$769$		−	768.665i		−	0.999564i	−0.866151	−	0.499782i	$-0.833413\pi$
$769$		−	768.665i		−	0.999564i	0.866151	−	0.499782i	$-0.166587\pi$
$770$	172.140	−	876.778i	0.223558	−	1.13867i
$771$	−491.158			−0.637040
$772$	−230.528			−0.298612
$773$		−	1474.33i		−	1.90728i	−0.300945	−	0.953642i	$-0.597302\pi$
$773$		−	1474.33i		−	1.90728i	0.300945	−	0.953642i	$-0.402698\pi$
$774$	280.088			0.361871
$775$		−	2007.59i		−	2.59044i
$776$			1197.35i			1.54298i
$777$	−13.2444	+	67.4592i	−0.0170456	+	0.0868201i
$778$	−1034.43			−1.32960
$779$	98.2904			0.126175
$780$			138.660i			0.177770i
$781$	100.974			0.129288
$782$		−	102.342i		−	0.130872i
$783$			87.9345i			0.112305i
$784$	−560.030	−	228.720i	−0.714324	−	0.291735i
$785$	2130.90			2.71452
$786$	−612.833			−0.779686
$787$		−	574.064i		−	0.729434i	−0.931118	−	0.364717i	$-0.881166\pi$
$787$		−	574.064i		−	0.729434i	0.931118	−	0.364717i	$-0.118834\pi$
$788$	63.3765			0.0804271
$789$			736.199i			0.933079i
$790$			2161.82i			2.73648i
$791$	−993.924	−	195.139i	−1.25654	−	0.246699i
$792$	−202.454			−0.255624
$793$	−68.5423			−0.0864341
$794$		−	495.900i		−	0.624559i
$795$	1033.68			1.30023
$796$			152.259i			0.191280i
$797$		−	446.159i		−	0.559798i	−0.960029	−	0.279899i	$-0.909699\pi$
$797$		−	446.159i		−	0.559798i	0.960029	−	0.279899i	$-0.0903010\pi$
$798$	−67.5547	−	13.2632i	−0.0846550	−	0.0166205i
$799$	−727.312			−0.910277
$800$	680.260			0.850326
$801$		−	64.6567i		−	0.0807200i
$802$	1148.78			1.43239
$803$			864.635i			1.07676i
$804$		−	160.993i		−	0.200240i
$805$	−58.3114	+	297.004i	−0.0724365	+	0.368949i
$806$	−742.788			−0.921573
$807$	−94.0271			−0.116514
$808$			683.038i			0.845344i
$809$	568.604			0.702848			0.351424	−	0.936216i	$-0.385698\pi$
$809$	568.604			0.702848			0.351424	+	0.936216i	$0.385698\pi$
$810$		−	145.909i		−	0.180134i
$811$		−	671.934i		−	0.828525i	−0.910157	−	0.414263i	$-0.864040\pi$
$811$		−	671.934i		−	0.828525i	0.910157	−	0.414263i	$-0.135960\pi$
$812$	−89.1175	−	17.4966i	−0.109751	−	0.0215476i
$813$	285.577			0.351263
$814$	80.2763			0.0986196
$815$		−	472.253i		−	0.579451i
$816$	−253.768			−0.310990
$817$			163.957i			0.200682i
$818$		−	279.867i		−	0.342136i
$819$	−46.8571	+	238.663i	−0.0572126	+	0.291407i
$820$	−215.150			−0.262378
$821$	243.623			0.296740			0.148370	−	0.988932i	$-0.452597\pi$
$821$	243.623			0.296740			0.148370	+	0.988932i	$0.452597\pi$
$822$			386.933i			0.470721i
$823$	−1513.67			−1.83920			−0.919602	−	0.392851i	$-0.871489\pi$
$823$	−1513.67			−1.83920			−0.919602	+	0.392851i	$0.871489\pi$
$824$			34.3419i			0.0416771i
$825$			767.611i			0.930438i
$826$	−51.8470	+	264.078i	−0.0627687	+	0.319707i
$827$	69.5570			0.0841077			0.0420538	−	0.999115i	$-0.486610\pi$
$827$	69.5570			0.0841077			0.0420538	+	0.999115i	$0.486610\pi$
$828$	11.0303			0.0133216
$829$		−	508.583i		−	0.613490i	−0.951792	−	0.306745i	$-0.900760\pi$
$829$		−	508.583i		−	0.613490i	0.951792	−	0.306745i	$-0.0992399\pi$
$830$	1730.29			2.08469
$831$		−	329.376i		−	0.396361i
$832$		−	823.630i		−	0.989939i
$833$	−219.864	+	538.346i	−0.263943	+	0.646274i
$834$	413.173			0.495411
$835$	1968.51			2.35749
$836$		−	19.0612i		−	0.0228005i
$837$	−185.329			−0.221420
$838$		−	179.649i		−	0.214379i
$839$		−	1298.10i		−	1.54719i	−0.633678	−	0.773597i	$-0.718456\pi$
$839$		−	1298.10i		−	1.54719i	0.633678	−	0.773597i	$-0.281544\pi$
$840$	919.387	+	180.505i	1.09451	+	0.214887i
$841$	−554.612			−0.659468
$842$	461.951			0.548635
$843$		−	287.140i		−	0.340617i
$844$	55.2538			0.0654665
$845$			314.303i			0.371956i
$846$			330.601i			0.390782i
$847$	−405.322	−	79.5777i	−0.478538	−	0.0939524i
$848$	−817.194			−0.963672
$849$	−812.520			−0.957032
$850$			1201.17i			1.41314i
$851$	−27.1932			−0.0319544
$852$			17.0297i			0.0199879i
$853$		−	376.966i		−	0.441930i	−0.975282	−	0.220965i	$-0.929079\pi$
$853$		−	376.966i		−	0.441930i	0.975282	−	0.220965i	$-0.0709206\pi$
$854$	−14.3510	+	73.0956i	−0.0168045	+	0.0855921i
$855$	85.4118			0.0998968
$856$	372.011			0.434592
$857$			1539.79i			1.79672i	0.439259	+	0.898361i	$0.355241\pi$
$857$			1539.79i			1.79672i	−0.439259	+	0.898361i	$0.644759\pi$
$858$	284.008			0.331012
$859$		−	929.180i		−	1.08170i	−0.841119	−	0.540850i	$-0.818103\pi$
$859$		−	929.180i		−	1.08170i	0.841119	−	0.540850i	$-0.181897\pi$
$860$		−	358.889i		−	0.417313i
$861$	−370.317	−	72.7050i	−0.430100	−	0.0844425i
$862$	981.358			1.13847
$863$	−571.085			−0.661744			−0.330872	−	0.943676i	$-0.607343\pi$
$863$	−571.085			−0.661744			−0.330872	+	0.943676i	$0.607343\pi$
$864$		−	62.7975i		−	0.0726823i
$865$	−262.280			−0.303214
$866$			1096.38i			1.26603i
$867$		−	256.621i		−	0.295987i
$868$	36.8755	−	187.822i	0.0424833	−	0.216385i
$869$	−1049.90			−1.20817
$870$	−475.200			−0.546207
$871$			1404.19i			1.61215i
$872$	−576.456			−0.661073
$873$		−	419.086i		−	0.480053i
$874$		−	27.2316i		−	0.0311575i
$875$	380.422	−	1937.64i	0.434767	−	2.21445i
$876$	−145.824			−0.166465
$877$	237.910			0.271277			0.135638	−	0.990758i	$-0.456691\pi$
$877$	237.910			0.271277			0.135638	+	0.990758i	$0.456691\pi$
$878$			1457.43i			1.65995i
$879$	−415.990			−0.473254
$880$		−	876.378i		−	0.995884i
$881$		−	4.48350i		−	0.00508910i	−0.999997	−	0.00254455i	$-0.999190\pi$
$881$		−	4.48350i		−	0.00508910i	0.999997	−	0.00254455i	$-0.000809956\pi$
$882$	244.707	+	99.9399i	0.277445	+	0.113311i
$883$	−1672.55			−1.89416			−0.947082	−	0.320991i	$-0.895984\pi$
$883$	−1672.55			−1.89416			−0.947082	+	0.320991i	$0.895984\pi$
$884$	−105.376			−0.119204
$885$		−	333.883i		−	0.377269i
$886$	730.910			0.824954
$887$			197.933i			0.223149i	0.993756	+	0.111575i	$0.0355894\pi$
$887$			197.933i			0.223149i	−0.993756	+	0.111575i	$0.964411\pi$
$888$			84.1775i			0.0947945i
$889$	−275.332	−	54.0565i	−0.309710	−	0.0608060i
$890$	349.407			0.392592
$891$	70.8612			0.0795299
$892$			262.903i			0.294734i
$893$	−193.527			−0.216715
$894$			12.9151i			0.0144464i
$895$			2324.65i			2.59738i
$896$	−546.293	−	107.255i	−0.609702	−	0.119704i
$897$	−96.2061			−0.107253
$898$	−940.796			−1.04766
$899$			603.585i			0.671396i
$900$	−129.460			−0.143845
$901$			785.553i			0.871868i
$902$			440.676i			0.488554i
$903$	121.279	−	617.722i	0.134306	−	0.684077i
$904$	−1240.25			−1.37195
$905$	252.691			0.279217
$906$			571.411i			0.630696i
$907$	79.0573			0.0871635			0.0435817	−	0.999050i	$-0.486123\pi$
$907$	79.0573			0.0871635			0.0435817	+	0.999050i	$0.486123\pi$
$908$		−	257.519i		−	0.283611i
$909$		−	239.071i		−	0.263004i
$910$	−1289.74	−	253.217i	−1.41730	−	0.278261i
$911$	−1187.07			−1.30304			−0.651521	−	0.758630i	$-0.725869\pi$
$911$	−1187.07			−1.30304			−0.651521	+	0.758630i	$0.725869\pi$
$912$	−67.5238			−0.0740393
$913$			840.322i			0.920396i
$914$	−922.250			−1.00903
$915$		−	92.4174i		−	0.101003i
$916$		−	122.681i		−	0.133931i
$917$	−265.358	+	1351.58i	−0.289376	+	1.47391i
$918$	110.884			0.120789
$919$	−1423.93			−1.54943			−0.774717	−	0.632308i	$-0.782108\pi$
$919$	−1423.93			−1.54943			−0.774717	+	0.632308i	$0.782108\pi$
$920$			370.609i			0.402836i
$921$	509.332			0.553021
$922$		−	1372.30i		−	1.48839i
$923$		−	148.533i		−	0.160924i
$924$	−14.0995	+	71.8145i	−0.0152592	+	0.0777213i
$925$	319.161			0.345039
$926$	−1000.50			−1.08045
$927$		−	12.0200i		−	0.0129666i
$928$	−204.521			−0.220389
$929$		−	107.110i		−	0.115297i	−0.998337	−	0.0576483i	$-0.981640\pi$
$929$		−	107.110i		−	0.115297i	0.998337	−	0.0576483i	$-0.0183602\pi$
$930$		−	1001.52i		−	1.07690i
$931$	−58.5026	+	143.246i	−0.0628385	+	0.153862i
$932$	91.8140			0.0985129
$933$	624.316			0.669149
$934$			185.165i			0.198250i
$935$	−842.445			−0.901011
$936$			297.810i			0.318173i
$937$		−	1324.86i		−	1.41394i	−0.707245	−	0.706968i	$-0.750062\pi$
$937$		−	1324.86i		−	1.41394i	0.707245	−	0.706968i	$-0.249938\pi$
$938$	1497.47	+	294.001i	1.59645	+	0.313434i
$939$	−753.090			−0.802013
$940$	423.615			0.450654
$941$			624.033i			0.663159i	0.943427	+	0.331580i	$0.107582\pi$
$941$			624.033i			0.663159i	−0.943427	+	0.331580i	$0.892418\pi$
$942$	736.099			0.781421
$943$		−	149.276i		−	0.158300i
$944$			263.957i			0.279616i
$945$	−321.795	−	63.1788i	−0.340524	−	0.0668558i
$946$	−735.088			−0.777048
$947$	−5.74614			−0.00606773			−0.00303387	−	0.999995i	$-0.500966\pi$
$947$	−5.74614			−0.00606773			−0.00303387	+	0.999995i	$0.500966\pi$
$948$		−	177.069i		−	0.186782i
$949$	1271.88			1.34023
$950$			319.613i			0.336435i
$951$		−	145.947i		−	0.153467i
$952$	−137.176	+	698.695i	−0.144093	+	0.733924i
$953$	660.066			0.692619			0.346310	−	0.938120i	$-0.387435\pi$
$953$	660.066			0.692619			0.346310	+	0.938120i	$0.387435\pi$
$954$	357.075			0.374293
$955$			1809.47i			1.89473i
$956$	173.971			0.181978
$957$		−	230.783i		−	0.241153i
$958$		−	481.817i		−	0.502940i
$959$	853.364	+	167.543i	0.889848	+	0.174706i
$960$	1110.52			1.15679
$961$	−311.101			−0.323727
$962$		−	118.086i		−	0.122751i
$963$	−130.208			−0.135211
$964$			309.035i			0.320576i
$965$			2711.04i			2.80937i
$966$	−20.1431	+	102.597i	−0.0208521	+	0.106208i
$967$	−505.785			−0.523045			−0.261523	−	0.965197i	$-0.584225\pi$
$967$	−505.785			−0.523045			−0.261523	+	0.965197i	$0.584225\pi$
$968$	−505.772			−0.522492
$969$			64.9094i			0.0669859i
$970$	2264.75			2.33480
$971$			1321.25i			1.36071i	0.732881	+	0.680357i	$0.238175\pi$
$971$			1321.25i			1.36071i	−0.732881	+	0.680357i	$0.761825\pi$
$972$			11.9510i			0.0122953i
$973$	178.905	−	911.235i	0.183869	−	0.936521i
$974$	−278.746			−0.286187
$975$	1129.15			1.15811
$976$			73.0623i			0.0748589i
$977$	−1381.51			−1.41403			−0.707017	−	0.707197i	$-0.749959\pi$
$977$	−1381.51			−1.41403			−0.707017	+	0.707197i	$0.749959\pi$
$978$		−	163.135i		−	0.166805i
$979$			169.691i			0.173331i
$980$	128.058	−	313.554i	0.130671	−	0.319953i
$981$	201.766			0.205673
$982$	−1054.56			−1.07389
$983$			239.591i			0.243735i	0.992546	+	0.121867i	$0.0388883\pi$
$983$			239.591i			0.243735i	−0.992546	+	0.121867i	$0.961112\pi$
$984$	−462.091			−0.469605
$985$		−	745.316i		−	0.756666i
$986$		−	361.132i		−	0.366260i
$987$	729.127	+	143.151i	0.738731	+	0.145037i
$988$	−28.0390			−0.0283795
$989$	249.007			0.251776
$990$			382.936i			0.386804i
$991$	−817.862			−0.825290			−0.412645	−	0.910892i	$-0.635395\pi$
$991$	−817.862			−0.825290			−0.412645	+	0.910892i	$0.635395\pi$
$992$		−	431.044i		−	0.434520i
$993$		−	1018.91i		−	1.02609i
$994$	−158.400	−	31.0991i	−0.159356	−	0.0312868i
$995$	1790.58			1.79958
$996$	−141.723			−0.142292
$997$		−	689.336i		−	0.691410i	−0.938343	−	0.345705i	$-0.887640\pi$
$997$		−	689.336i		−	0.691410i	0.938343	−	0.345705i	$-0.112360\pi$
$998$	−943.425			−0.945316
$999$		−	29.4630i		−	0.0294925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.20	yes	60
7.6	odd	2	inner	483.3.g.a.139.19	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.19	✓	60	7.6	odd	2	inner
483.3.g.a.139.20	yes	60	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.79815 q^{2} -1.73205i q^{3} -0.766656 q^{4} +9.01598i q^{5} +3.11449i q^{6} +(6.86887 + 1.34858i) q^{7} +8.57116 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.79815 q^{2} -1.73205i q^{3} -0.766656 q^{4} +9.01598i q^{5} +3.11449i q^{6} +(6.86887 + 1.34858i) q^{7} +8.57116 q^{8} -3.00000 q^{9} -16.2121i q^{10} +7.87346 q^{11} +1.32789i q^{12} -11.5819i q^{13} +(-12.3513 - 2.42495i) q^{14} +15.6161 q^{15} -12.3456 q^{16} +11.8676i q^{17} +5.39445 q^{18} +3.15779i q^{19} -6.91215i q^{20} +(2.33581 - 11.8972i) q^{21} -14.1577 q^{22} +4.79583 q^{23} -14.8457i q^{24} -56.2879 q^{25} +20.8259i q^{26} +5.19615i q^{27} +(-5.26606 - 1.03390i) q^{28} +16.9230 q^{29} -28.0801 q^{30} +35.6665i q^{31} -12.0854 q^{32} -13.6372i q^{33} -21.3397i q^{34} +(-12.1588 + 61.9296i) q^{35} +2.29997 q^{36} -5.67016 q^{37} -5.67819i q^{38} -20.0604 q^{39} +77.2774i q^{40} -31.1263i q^{41} +(-4.20013 + 21.3930i) q^{42} +51.9215 q^{43} -6.03624 q^{44} -27.0479i q^{45} -8.62363 q^{46} +61.2855i q^{47} +21.3832i q^{48} +(45.3627 + 18.5264i) q^{49} +101.214 q^{50} +20.5553 q^{51} +8.87930i q^{52} +66.1931 q^{53} -9.34346i q^{54} +70.9870i q^{55} +(58.8742 + 11.5589i) q^{56} +5.46946 q^{57} -30.4301 q^{58} -21.3806i q^{59} -11.9722 q^{60} -5.91807i q^{61} -64.1338i q^{62} +(-20.6066 - 4.04574i) q^{63} +71.1138 q^{64} +104.422 q^{65} +24.5218i q^{66} -121.240 q^{67} -9.09837i q^{68} -8.30662i q^{69} +(21.8633 - 111.359i) q^{70} +12.8246 q^{71} -25.7135 q^{72} +109.816i q^{73} +10.1958 q^{74} +97.4934i q^{75} -2.42094i q^{76} +(54.0818 + 10.6180i) q^{77} +36.0715 q^{78} -133.346 q^{79} -111.308i q^{80} +9.00000 q^{81} +55.9697i q^{82} +106.728i q^{83} +(-1.79076 + 9.12108i) q^{84} -106.998 q^{85} -93.3627 q^{86} -29.3115i q^{87} +67.4847 q^{88} +21.5522i q^{89} +48.6362i q^{90} +(15.6190 - 79.5542i) q^{91} -3.67675 q^{92} +61.7762 q^{93} -110.200i q^{94} -28.4706 q^{95} +20.9325i q^{96} +139.695i q^{97} +(-81.5689 - 33.3133i) q^{98} -23.6204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 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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