LMFDB - Embedded newform 483.3.g.a.139.11

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			139.11
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79612 q^{2} +1.73205i q^{3} +3.81828 q^{4} +8.09762i q^{5} -4.84302i q^{6} +(-5.87622 + 3.80395i) q^{7} +0.508111 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.79612 q^{2} +1.73205i q^{3} +3.81828 q^{4} +8.09762i q^{5} -4.84302i q^{6} +(-5.87622 + 3.80395i) q^{7} +0.508111 q^{8} -3.00000 q^{9} -22.6419i q^{10} -17.5747 q^{11} +6.61345i q^{12} -15.1280i q^{13} +(16.4306 - 10.6363i) q^{14} -14.0255 q^{15} -16.6939 q^{16} -0.845174i q^{17} +8.38836 q^{18} -14.3210i q^{19} +30.9190i q^{20} +(-6.58863 - 10.1779i) q^{21} +49.1410 q^{22} -4.79583 q^{23} +0.880073i q^{24} -40.5714 q^{25} +42.2996i q^{26} -5.19615i q^{27} +(-22.4371 + 14.5245i) q^{28} +53.7320 q^{29} +39.2169 q^{30} +42.4666i q^{31} +44.6456 q^{32} -30.4403i q^{33} +2.36321i q^{34} +(-30.8029 - 47.5834i) q^{35} -11.4548 q^{36} -49.6964 q^{37} +40.0431i q^{38} +26.2024 q^{39} +4.11449i q^{40} +12.1763i q^{41} +(18.4226 + 28.4587i) q^{42} +11.2595 q^{43} -67.1051 q^{44} -24.2929i q^{45} +13.4097 q^{46} +59.2081i q^{47} -28.9146i q^{48} +(20.0599 - 44.7057i) q^{49} +113.442 q^{50} +1.46388 q^{51} -57.7628i q^{52} +50.5529 q^{53} +14.5291i q^{54} -142.313i q^{55} +(-2.98577 + 1.93283i) q^{56} +24.8046 q^{57} -150.241 q^{58} +21.6840i q^{59} -53.5532 q^{60} -27.9661i q^{61} -118.742i q^{62} +(17.6287 - 11.4118i) q^{63} -58.0589 q^{64} +122.501 q^{65} +85.1146i q^{66} -40.8837 q^{67} -3.22711i q^{68} -8.30662i q^{69} +(86.1286 + 133.049i) q^{70} -61.4554 q^{71} -1.52433 q^{72} -108.405i q^{73} +138.957 q^{74} -70.2717i q^{75} -54.6814i q^{76} +(103.273 - 66.8533i) q^{77} -73.2651 q^{78} +123.870 q^{79} -135.180i q^{80} +9.00000 q^{81} -34.0464i q^{82} +5.63361i q^{83} +(-25.1573 - 38.8621i) q^{84} +6.84390 q^{85} -31.4830 q^{86} +93.0665i q^{87} -8.92989 q^{88} -97.3170i q^{89} +67.9257i q^{90} +(57.5461 + 88.8953i) q^{91} -18.3118 q^{92} -73.5543 q^{93} -165.553i q^{94} +115.966 q^{95} +77.3284i q^{96} -166.026i q^{97} +(-56.0899 + 125.002i) q^{98} +52.7241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.79612			−1.39806			−0.699030	−	0.715093i	$-0.746384\pi$
$2$	−2.79612			−1.39806			−0.699030	+	0.715093i	$0.746384\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.81828			0.954570
$5$			8.09762i			1.61952i	0.586759	+	0.809762i	$0.300404\pi$
$5$			8.09762i			1.61952i	−0.586759	+	0.809762i	$0.699596\pi$
$6$		−	4.84302i		−	0.807170i
$7$	−5.87622	+	3.80395i	−0.839460	+	0.543421i
$7$	−5.87622	+	3.80395i	−0.839460	+	0.543421i
$8$	0.508111			0.0635138
$9$	−3.00000			−0.333333
$10$		−	22.6419i		−	2.26419i
$11$	−17.5747			−1.59770			−0.798850	−	0.601530i	$-0.794558\pi$
$11$	−17.5747			−1.59770			−0.798850	+	0.601530i	$0.794558\pi$
$12$			6.61345i			0.551121i
$13$		−	15.1280i		−	1.16369i	−0.813300	−	0.581845i	$-0.802331\pi$
$13$		−	15.1280i		−	1.16369i	0.813300	−	0.581845i	$-0.197669\pi$
$14$	16.4306	−	10.6363i	1.17361	−	0.759735i
$15$	−14.0255			−0.935032
$16$	−16.6939			−1.04337
$17$		−	0.845174i		−	0.0497161i	−0.999691	−	0.0248581i	$-0.992087\pi$
$17$		−	0.845174i		−	0.0497161i	0.999691	−	0.0248581i	$-0.00791338\pi$
$18$	8.38836			0.466020
$19$		−	14.3210i		−	0.753734i	−0.926267	−	0.376867i	$-0.877001\pi$
$19$		−	14.3210i		−	0.753734i	0.926267	−	0.376867i	$-0.122999\pi$
$20$			30.9190i			1.54595i
$21$	−6.58863	−	10.1779i	−0.313744	−	0.484662i
$22$	49.1410			2.23368
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			0.880073i			0.0366697i
$25$	−40.5714			−1.62286
$26$			42.2996i			1.62691i
$27$		−	5.19615i		−	0.192450i
$28$	−22.4371	+	14.5245i	−0.801323	+	0.518734i
$29$	53.7320			1.85283			0.926413	−	0.376508i	$-0.122875\pi$
$29$	53.7320			1.85283			0.926413	+	0.376508i	$0.122875\pi$
$30$	39.2169			1.30723
$31$			42.4666i			1.36989i	0.728594	+	0.684945i	$0.240174\pi$
$31$			42.4666i			1.36989i	−0.728594	+	0.684945i	$0.759826\pi$
$32$	44.6456			1.39517
$33$		−	30.4403i		−	0.922433i
$34$			2.36321i			0.0695061i
$35$	−30.8029	−	47.5834i	−0.880084	−	1.35953i
$36$	−11.4548			−0.318190
$37$	−49.6964			−1.34315			−0.671573	−	0.740938i	$-0.734381\pi$
$37$	−49.6964			−1.34315			−0.671573	+	0.740938i	$0.734381\pi$
$38$			40.0431i			1.05377i
$39$	26.2024			0.671857
$40$			4.11449i			0.102862i
$41$			12.1763i			0.296984i	0.988914	+	0.148492i	$0.0474418\pi$
$41$			12.1763i			0.296984i	−0.988914	+	0.148492i	$0.952558\pi$
$42$	18.4226	+	28.4587i	0.438633	+	0.677587i
$43$	11.2595			0.261850			0.130925	−	0.991392i	$-0.458205\pi$
$43$	11.2595			0.261850			0.130925	+	0.991392i	$0.458205\pi$
$44$	−67.1051			−1.52512
$45$		−	24.2929i		−	0.539841i
$46$	13.4097			0.291516
$47$			59.2081i			1.25975i	0.776698	+	0.629874i	$0.216893\pi$
$47$			59.2081i			1.25975i	−0.776698	+	0.629874i	$0.783107\pi$
$48$		−	28.9146i		−	0.602388i
$49$	20.0599	−	44.7057i	0.409386	−	0.912361i
$50$	113.442			2.26885
$51$	1.46388			0.0287036
$52$		−	57.7628i		−	1.11082i
$53$	50.5529			0.953829			0.476915	−	0.878950i	$-0.341755\pi$
$53$	50.5529			0.953829			0.476915	+	0.878950i	$0.341755\pi$
$54$			14.5291i			0.269057i
$55$		−	142.313i		−	2.58751i
$56$	−2.98577	+	1.93283i	−0.0533173	+	0.0345148i
$57$	24.8046			0.435169
$58$	−150.241			−2.59036
$59$			21.6840i			0.367525i	0.982971	+	0.183762i	$0.0588277\pi$
$59$			21.6840i			0.367525i	−0.982971	+	0.183762i	$0.941172\pi$
$60$	−53.5532			−0.892554
$61$		−	27.9661i		−	0.458461i	−0.973372	−	0.229230i	$-0.926379\pi$
$61$		−	27.9661i		−	0.458461i	0.973372	−	0.229230i	$-0.0736209\pi$
$62$		−	118.742i		−	1.91519i
$63$	17.6287	−	11.4118i	0.279820	−	0.181140i
$64$	−58.0589			−0.907170
$65$	122.501			1.88462
$66$			85.1146i			1.28962i
$67$	−40.8837			−0.610205			−0.305103	−	0.952320i	$-0.598691\pi$
$67$	−40.8837			−0.610205			−0.305103	+	0.952320i	$0.598691\pi$
$68$		−	3.22711i		−	0.0474575i
$69$		−	8.30662i		−	0.120386i
$70$	86.1286	+	133.049i	1.23041	+	1.90070i
$71$	−61.4554			−0.865569			−0.432785	−	0.901497i	$-0.642469\pi$
$71$	−61.4554			−0.865569			−0.432785	+	0.901497i	$0.642469\pi$
$72$	−1.52433			−0.0211713
$73$		−	108.405i		−	1.48501i	−0.669843	−	0.742503i	$-0.733639\pi$
$73$		−	108.405i		−	1.48501i	0.669843	−	0.742503i	$-0.266361\pi$
$74$	138.957			1.87780
$75$		−	70.2717i		−	0.936956i
$76$		−	54.6814i		−	0.719492i
$77$	103.273	−	66.8533i	1.34121	−	0.868224i
$78$	−73.2651			−0.939296
$79$	123.870			1.56797			0.783985	−	0.620780i	$-0.213184\pi$
$79$	123.870			1.56797			0.783985	+	0.620780i	$0.213184\pi$
$80$		−	135.180i		−	1.68976i
$81$	9.00000			0.111111
$82$		−	34.0464i		−	0.415201i
$83$			5.63361i			0.0678749i	0.999424	+	0.0339374i	$0.0108047\pi$
$83$			5.63361i			0.0678749i	−0.999424	+	0.0339374i	$0.989195\pi$
$84$	−25.1573	−	38.8621i	−0.299491	−	0.462644i
$85$	6.84390			0.0805164
$86$	−31.4830			−0.366081
$87$			93.0665i			1.06973i
$88$	−8.92989			−0.101476
$89$		−	97.3170i		−	1.09345i	−0.837313	−	0.546725i	$-0.815874\pi$
$89$		−	97.3170i		−	1.09345i	0.837313	−	0.546725i	$-0.184126\pi$
$90$			67.9257i			0.754730i
$91$	57.5461	+	88.8953i	0.632374	+	0.976872i
$92$	−18.3118			−0.199042
$93$	−73.5543			−0.790907
$94$		−	165.553i		−	1.76120i
$95$	115.966			1.22069
$96$			77.3284i			0.805504i
$97$		−	166.026i		−	1.71161i	−0.517299	−	0.855805i	$-0.673062\pi$
$97$		−	166.026i		−	1.71161i	0.517299	−	0.855805i	$-0.326938\pi$
$98$	−56.0899	+	125.002i	−0.572346	+	1.27554i
$99$	52.7241			0.532567
$100$	−154.913			−1.54913
$101$			24.3301i			0.240893i	0.992720	+	0.120446i	$0.0384326\pi$
$101$			24.3301i			0.240893i	−0.992720	+	0.120446i	$0.961567\pi$
$102$	−4.09320			−0.0401294
$103$			122.719i			1.19145i	0.803190	+	0.595723i	$0.203135\pi$
$103$			122.719i			1.19145i	−0.803190	+	0.595723i	$0.796865\pi$
$104$		−	7.68669i		−	0.0739104i
$105$	82.4168	−	53.3522i	0.784922	−	0.508117i
$106$	−141.352			−1.33351
$107$	−25.7346			−0.240510			−0.120255	−	0.992743i	$-0.538371\pi$
$107$	−25.7346			−0.240510			−0.120255	+	0.992743i	$0.538371\pi$
$108$		−	19.8404i		−	0.183707i
$109$	−120.261			−1.10331			−0.551654	−	0.834073i	$-0.686003\pi$
$109$	−120.261			−1.10331			−0.551654	+	0.834073i	$0.686003\pi$
$110$			397.925i			3.61750i
$111$		−	86.0767i		−	0.775466i
$112$	98.0968	−	63.5026i	0.875864	−	0.566987i
$113$	33.8834			0.299853			0.149927	−	0.988697i	$-0.452096\pi$
$113$	33.8834			0.299853			0.149927	+	0.988697i	$0.452096\pi$
$114$	−69.3567			−0.608392
$115$		−	38.8348i		−	0.337694i
$116$	205.164			1.76865
$117$			45.3839i			0.387897i
$118$		−	60.6310i		−	0.513822i
$119$	3.21500	+	4.96643i	0.0270168	+	0.0417347i
$120$	−7.12650			−0.0593875
$121$	187.870			1.55265
$122$			78.1965i			0.640955i
$123$	−21.0900			−0.171464
$124$			162.149i			1.30766i
$125$		−	126.091i		−	1.00873i
$126$	−49.2918	+	31.9089i	−0.391205	+	0.253245i
$127$	−185.275			−1.45886			−0.729431	−	0.684054i	$-0.760215\pi$
$127$	−185.275			−1.45886			−0.729431	+	0.684054i	$0.760215\pi$
$128$	−16.2428			−0.126897
$129$			19.5021i			0.151179i
$130$	−342.526			−2.63482
$131$		−	125.868i		−	0.960825i	−0.877043	−	0.480412i	$-0.840487\pi$
$131$		−	125.868i		−	0.960825i	0.877043	−	0.480412i	$-0.159513\pi$
$132$		−	116.229i		−	0.880526i
$133$	54.4762	+	84.1531i	0.409595	+	0.632730i
$134$	114.316			0.853103
$135$	42.0765			0.311677
$136$		−	0.429442i		−	0.00315766i
$137$	−145.525			−1.06222			−0.531112	−	0.847302i	$-0.678226\pi$
$137$	−145.525			−1.06222			−0.531112	+	0.847302i	$0.678226\pi$
$138$			23.2263i			0.168307i
$139$		−	136.690i		−	0.983384i	−0.870769	−	0.491692i	$-0.836379\pi$
$139$		−	136.690i		−	0.983384i	0.870769	−	0.491692i	$-0.163621\pi$
$140$	−117.614	−	181.687i	−0.840102	−	1.29776i
$141$	−102.551			−0.727316
$142$	171.837			1.21012
$143$			265.870i			1.85923i
$144$	50.0816			0.347789
$145$			435.101i			3.00070i
$146$			303.114i			2.07613i
$147$	77.4325	+	34.7448i	0.526752	+	0.236359i
$148$	−189.755			−1.28213
$149$	−177.561			−1.19169			−0.595843	−	0.803101i	$-0.703182\pi$
$149$	−177.561			−1.19169			−0.595843	+	0.803101i	$0.703182\pi$
$150$			196.488i			1.30992i
$151$	201.063			1.33154			0.665772	−	0.746155i	$-0.268102\pi$
$151$	201.063			1.33154			0.665772	+	0.746155i	$0.268102\pi$
$152$		−	7.27663i		−	0.0478726i
$153$			2.53552i			0.0165720i
$154$	−288.763	+	186.930i	−1.87508	+	1.21383i
$155$	−343.878			−2.21857
$156$	100.048			0.641334
$157$			275.969i			1.75776i	0.477038	+	0.878882i	$0.341710\pi$
$157$			275.969i			1.75776i	−0.477038	+	0.878882i	$0.658290\pi$
$158$	−346.354			−2.19212
$159$			87.5603i			0.550694i
$160$			361.523i			2.25952i
$161$	28.1814	−	18.2431i	0.175040	−	0.113311i
$162$	−25.1651			−0.155340
$163$	30.5866			0.187648			0.0938239	−	0.995589i	$-0.470091\pi$
$163$	30.5866			0.187648			0.0938239	+	0.995589i	$0.470091\pi$
$164$			46.4926i			0.283492i
$165$	246.494			1.49390
$166$		−	15.7523i		−	0.0948931i
$167$		−	100.653i		−	0.602713i	−0.953512	−	0.301356i	$-0.902561\pi$
$167$		−	100.653i		−	0.602713i	0.953512	−	0.301356i	$-0.0974394\pi$
$168$	−3.34776	−	5.17151i	−0.0199271	−	0.0307828i
$169$	−59.8556			−0.354175
$170$	−19.1364			−0.112567
$171$			42.9629i			0.251245i
$172$	42.9921			0.249954
$173$		−	19.0908i		−	0.110351i	−0.998477	−	0.0551757i	$-0.982428\pi$
$173$		−	19.0908i		−	0.110351i	0.998477	−	0.0551757i	$-0.0175719\pi$
$174$		−	260.225i		−	1.49555i
$175$	238.407	−	154.332i	1.36232	−	0.881895i
$176$	293.390			1.66699
$177$	−37.5577			−0.212191
$178$			272.110i			1.52871i
$179$	0.650523			0.00363421			0.00181710	−	0.999998i	$-0.499422\pi$
$179$	0.650523			0.00363421			0.00181710	+	0.999998i	$0.499422\pi$
$180$		−	92.7569i		−	0.515316i
$181$		−	199.577i		−	1.10263i	−0.834296	−	0.551317i	$-0.814125\pi$
$181$		−	199.577i		−	1.10263i	0.834296	−	0.551317i	$-0.185875\pi$
$182$	−160.906	−	248.562i	−0.884097	−	1.36572i
$183$	48.4387			0.264692
$184$	−2.43681			−0.0132435
$185$		−	402.423i		−	2.17526i
$186$	205.667			1.10573
$187$			14.8537i			0.0794315i
$188$			226.073i			1.20252i
$189$	19.7659	+	30.5337i	0.104581	+	0.161554i
$190$	−324.254			−1.70660
$191$	21.0116			0.110008			0.0550042	−	0.998486i	$-0.482483\pi$
$191$	21.0116			0.110008			0.0550042	+	0.998486i	$0.482483\pi$
$192$		−	100.561i		−	0.523755i
$193$	16.1388			0.0836209			0.0418105	−	0.999126i	$-0.486687\pi$
$193$	16.1388			0.0836209			0.0418105	+	0.999126i	$0.486687\pi$
$194$			464.229i			2.39293i
$195$			212.177i			1.08809i
$196$	76.5944	−	170.699i	0.390788	−	0.870913i
$197$	−140.012			−0.710722			−0.355361	−	0.934729i	$-0.615642\pi$
$197$	−140.012			−0.710722			−0.355361	+	0.934729i	$0.615642\pi$
$198$	−147.423			−0.744560
$199$		−	114.645i		−	0.576108i	−0.957614	−	0.288054i	$-0.906992\pi$
$199$		−	114.645i		−	0.576108i	0.957614	−	0.288054i	$-0.0930083\pi$
$200$	−20.6148			−0.103074
$201$		−	70.8127i		−	0.352302i
$202$		−	68.0300i		−	0.336782i
$203$	−315.741	+	204.394i	−1.55537	+	1.00687i
$204$	5.58952			0.0273996
$205$	−98.5992			−0.480972
$206$		−	343.137i		−	1.66571i
$207$	14.3875			0.0695048
$208$			252.544i			1.21416i
$209$			251.686i			1.20424i
$210$	−230.447	+	149.179i	−1.09737	+	0.710377i
$211$	233.854			1.10831			0.554156	−	0.832413i	$-0.313041\pi$
$211$	233.854			1.10831			0.554156	+	0.832413i	$0.313041\pi$
$212$	193.025			0.910497
$213$		−	106.444i		−	0.499737i
$214$	71.9569			0.336247
$215$			91.1754i			0.424072i
$216$		−	2.64022i		−	0.0122232i
$217$	−161.541	−	249.543i	−0.744428	−	1.14997i
$218$	336.263			1.54249
$219$	187.764			0.857368
$220$		−	543.392i		−	2.46996i
$221$	−12.7858			−0.0578542
$222$			240.681i			1.08415i
$223$		−	195.368i		−	0.876089i	−0.898953	−	0.438044i	$-0.855671\pi$
$223$		−	195.368i		−	0.876089i	0.898953	−	0.438044i	$-0.144329\pi$
$224$	−262.347	+	169.829i	−1.17119	+	0.758167i
$225$	121.714			0.540952
$226$	−94.7421			−0.419213
$227$		−	155.715i		−	0.685969i	−0.939341	−	0.342984i	$-0.888562\pi$
$227$		−	155.715i		−	0.685969i	0.939341	−	0.342984i	$-0.111438\pi$
$228$	94.7110			0.415399
$229$		−	282.577i		−	1.23396i	−0.786978	−	0.616980i	$-0.788356\pi$
$229$		−	282.577i		−	1.23396i	0.786978	−	0.616980i	$-0.211644\pi$
$230$			108.587i			0.472116i
$231$	115.793	+	178.874i	0.501270	+	0.774345i
$232$	27.3018			0.117680
$233$	−118.808			−0.509908			−0.254954	−	0.966953i	$-0.582060\pi$
$233$	−118.808			−0.509908			−0.254954	+	0.966953i	$0.582060\pi$
$234$		−	126.899i		−	0.542303i
$235$	−479.445			−2.04019
$236$			82.7955i			0.350828i
$237$			214.549i			0.905268i
$238$	−8.98952	−	13.8867i	−0.0377711	−	0.0583476i
$239$	267.504			1.11926			0.559632	−	0.828741i	$-0.310942\pi$
$239$	267.504			1.11926			0.559632	+	0.828741i	$0.310942\pi$
$240$	234.139			0.975581
$241$		−	476.873i		−	1.97873i	−0.145463	−	0.989364i	$-0.546467\pi$
$241$		−	476.873i		−	1.97873i	0.145463	−	0.989364i	$-0.453533\pi$
$242$	−525.307			−2.17069
$243$			15.5885i			0.0641500i
$244$		−	106.782i		−	0.437633i
$245$	362.010	+	162.438i	1.47759	+	0.663011i
$246$	58.9702			0.239716
$247$	−216.647			−0.877113
$248$			21.5777i			0.0870070i
$249$	−9.75771			−0.0391876
$250$			352.566i			1.41026i
$251$			110.096i			0.438631i	0.975654	+	0.219315i	$0.0703824\pi$
$251$			110.096i			0.438631i	−0.975654	+	0.219315i	$0.929618\pi$
$252$	67.3112	−	43.5736i	0.267108	−	0.172911i
$253$	84.2853			0.333144
$254$	518.052			2.03958
$255$			11.8540i			0.0464862i
$256$	277.652			1.08458
$257$			149.908i			0.583299i	0.956525	+	0.291649i	$0.0942040\pi$
$257$			149.908i			0.583299i	−0.956525	+	0.291649i	$0.905796\pi$
$258$		−	54.5301i		−	0.211357i
$259$	292.027	−	189.043i	1.12752	−	0.729895i
$260$	467.741			1.79901
$261$	−161.196			−0.617609
$262$			351.942i			1.34329i
$263$	−373.611			−1.42057			−0.710287	−	0.703912i	$-0.751435\pi$
$263$	−373.611			−1.42057			−0.710287	+	0.703912i	$0.751435\pi$
$264$		−	15.4670i		−	0.0585872i
$265$			409.358i			1.54475i
$266$	−152.322	−	235.302i	−0.572639	−	0.884594i
$267$	168.558			0.631303
$268$	−156.106			−0.582483
$269$		−	453.557i		−	1.68609i	−0.537847	−	0.843043i	$-0.680762\pi$
$269$		−	453.557i		−	1.68609i	0.537847	−	0.843043i	$-0.319238\pi$
$270$	−117.651			−0.435744
$271$		−	40.4250i		−	0.149170i	−0.997215	−	0.0745849i	$-0.976237\pi$
$271$		−	40.4250i		−	0.149170i	0.997215	−	0.0745849i	$-0.0237632\pi$
$272$			14.1092i			0.0518721i
$273$	−153.971	+	99.6727i	−0.563997	+	0.365101i
$274$	406.904			1.48505
$275$	713.030			2.59284
$276$		−	31.7170i		−	0.114917i
$277$	396.209			1.43036			0.715179	−	0.698941i	$-0.246345\pi$
$277$	396.209			1.43036			0.715179	+	0.698941i	$0.246345\pi$
$278$			382.202i			1.37483i
$279$		−	127.400i		−	0.456630i
$280$	−15.6513	−	24.1776i	−0.0558975	−	0.0863487i
$281$	−479.724			−1.70720			−0.853601	−	0.520928i	$-0.825586\pi$
$281$	−479.724			−1.70720			−0.853601	+	0.520928i	$0.825586\pi$
$282$	286.746			1.01683
$283$		−	118.618i		−	0.419145i	−0.977793	−	0.209573i	$-0.932793\pi$
$283$		−	118.618i		−	0.419145i	0.977793	−	0.209573i	$-0.0672073\pi$
$284$	−234.654			−0.826246
$285$			200.858i			0.704766i
$286$		−	743.403i		−	2.59931i
$287$	−46.3181	−	71.5508i	−0.161387	−	0.249306i
$288$	−133.937			−0.465058
$289$	288.286			0.997528
$290$		−	1216.59i		−	4.19515i
$291$	287.566			0.988198
$292$		−	413.922i		−	1.41754i
$293$			404.759i			1.38143i	0.723128	+	0.690714i	$0.242704\pi$
$293$			404.759i			1.38143i	−0.723128	+	0.690714i	$0.757296\pi$
$294$	−216.511	−	97.1506i	−0.736430	−	0.330444i
$295$	−175.589			−0.595215
$296$	−25.2513			−0.0853084
$297$			91.3208i			0.307478i
$298$	496.482			1.66605
$299$			72.5512i			0.242646i
$300$		−	268.317i		−	0.894391i
$301$	−66.1635	+	42.8307i	−0.219812	+	0.142295i
$302$	−562.197			−1.86158
$303$	−42.1411			−0.139079
$304$			239.072i			0.786421i
$305$	226.459			0.742488
$306$		−	7.08962i		−	0.0231687i
$307$			7.35898i			0.0239706i	0.999928	+	0.0119853i	$0.00381513\pi$
$307$			7.35898i			0.0239706i	−0.999928	+	0.0119853i	$0.996185\pi$
$308$	394.325	−	255.265i	1.28027	−	0.828781i
$309$	−212.556			−0.687882
$310$	961.525			3.10169
$311$		−	145.220i		−	0.466945i	−0.972363	−	0.233472i	$-0.924991\pi$
$311$		−	145.220i		−	0.466945i	0.972363	−	0.233472i	$-0.0750088\pi$
$312$	13.3137			0.0426722
$313$			147.472i			0.471155i	0.971856	+	0.235578i	$0.0756982\pi$
$313$			147.472i			0.471155i	−0.971856	+	0.235578i	$0.924302\pi$
$314$		−	771.642i		−	2.45746i
$315$	92.4088	+	142.750i	0.293361	+	0.453175i
$316$	472.969			1.49674
$317$	−212.810			−0.671324			−0.335662	−	0.941982i	$-0.608960\pi$
$317$	−212.810			−0.671324			−0.335662	+	0.941982i	$0.608960\pi$
$318$		−	244.829i		−	0.769902i
$319$	−944.323			−2.96026
$320$		−	470.139i		−	1.46918i
$321$		−	44.5736i		−	0.138859i
$322$	−78.7984	+	51.0099i	−0.244716	+	0.158416i
$323$	−12.1037			−0.0374728
$324$	34.3645			0.106063
$325$			613.763i			1.88850i
$326$	−85.5237			−0.262343
$327$		−	208.298i		−	0.636995i
$328$			6.18692i			0.0188626i
$329$	−225.225	−	347.920i	−0.684574	−	1.05751i
$330$	−689.226			−2.08856
$331$	−505.835			−1.52820			−0.764101	−	0.645097i	$-0.776817\pi$
$331$	−505.835			−1.52820			−0.764101	+	0.645097i	$0.776817\pi$
$332$			21.5107i			0.0647913i
$333$	149.089			0.447715
$334$			281.438i			0.842628i
$335$		−	331.061i		−	0.988241i
$336$	109.990	+	169.909i	0.327350	+	0.505680i
$337$	−393.472			−1.16757			−0.583787	−	0.811907i	$-0.698430\pi$
$337$	−393.472			−1.16757			−0.583787	+	0.811907i	$0.698430\pi$
$338$	167.363			0.495158
$339$			58.6878i			0.173120i
$340$	26.1319			0.0768586
$341$		−	746.338i		−	2.18867i
$342$		−	120.129i		−	0.351255i
$343$	52.1816	+	339.007i	0.152133	+	0.988360i
$344$	5.72109			0.0166311
$345$	67.2639			0.194968
$346$			53.3801i			0.154278i
$347$	−300.823			−0.866926			−0.433463	−	0.901171i	$-0.642709\pi$
$347$	−300.823			−0.866926			−0.433463	+	0.901171i	$0.642709\pi$
$348$			355.354i			1.02113i
$349$		−	562.703i		−	1.61233i	−0.591692	−	0.806164i	$-0.701540\pi$
$349$		−	562.703i		−	1.61233i	0.591692	−	0.806164i	$-0.298460\pi$
$350$	−666.613	+	431.529i	−1.90461	+	1.23294i
$351$	−78.6073			−0.223952
$352$	−784.632			−2.22907
$353$		−	164.649i		−	0.466429i	−0.972425	−	0.233214i	$-0.925076\pi$
$353$		−	164.649i		−	0.466429i	0.972425	−	0.233214i	$-0.0749244\pi$
$354$	105.016			0.296655
$355$		−	497.642i		−	1.40181i
$356$		−	371.583i		−	1.04377i
$357$	−8.60211	+	5.56854i	−0.0240955	+	0.0155982i
$358$	−1.81894			−0.00508084
$359$	−103.201			−0.287469			−0.143735	−	0.989616i	$-0.545911\pi$
$359$	−103.201			−0.287469			−0.143735	+	0.989616i	$0.545911\pi$
$360$		−	12.3435i		−	0.0342874i
$361$	155.910			0.431884
$362$			558.041i			1.54155i
$363$			325.401i			0.896420i
$364$	219.727	+	339.427i	0.603645	+	0.932492i
$365$	877.825			2.40500
$366$	−135.440			−0.370056
$367$			32.0510i			0.0873324i	0.999046	+	0.0436662i	$0.0139038\pi$
$367$			32.0510i			0.0873324i	−0.999046	+	0.0436662i	$0.986096\pi$
$368$	80.0609			0.217557
$369$		−	36.5290i		−	0.0989945i
$370$			1125.22i			3.04114i
$371$	−297.060	+	192.301i	−0.800702	+	0.518331i
$372$	−280.851			−0.754976
$373$	−535.827			−1.43653			−0.718267	−	0.695768i	$-0.755064\pi$
$373$	−535.827			−1.43653			−0.718267	+	0.695768i	$0.755064\pi$
$374$		−	41.5327i		−	0.111050i
$375$	218.396			0.582391
$376$			30.0843i			0.0800114i
$377$		−	812.856i		−	2.15612i
$378$	−55.2678	−	85.3760i	−0.146211	−	0.225862i
$379$	−103.633			−0.273437			−0.136718	−	0.990610i	$-0.543656\pi$
$379$	−103.633			−0.273437			−0.136718	+	0.990610i	$0.543656\pi$
$380$	442.789			1.16523
$381$		−	320.907i		−	0.842274i
$382$	−58.7509			−0.153798
$383$			80.5648i			0.210352i	0.994454	+	0.105176i	$0.0335406\pi$
$383$			80.5648i			0.210352i	−0.994454	+	0.105176i	$0.966459\pi$
$384$		−	28.1333i		−	0.0732638i
$385$	541.352	+	836.264i	1.40611	+	2.17211i
$386$	−45.1261			−0.116907
$387$	−33.7786			−0.0872832
$388$		−	633.934i		−	1.63385i
$389$	659.477			1.69531			0.847656	−	0.530545i	$-0.178013\pi$
$389$	659.477			1.69531			0.847656	+	0.530545i	$0.178013\pi$
$390$		−	593.273i		−	1.52121i
$391$			4.05331i			0.0103665i
$392$	10.1927	−	22.7154i	0.0260017	−	0.0579476i
$393$	218.010			0.554732
$394$	391.491			0.993631
$395$			1003.05i			2.53936i
$396$	201.315			0.508372
$397$		−	61.2089i		−	0.154179i	−0.997024	−	0.0770893i	$-0.975437\pi$
$397$		−	61.2089i		−	0.154179i	0.997024	−	0.0770893i	$-0.0245626\pi$
$398$			320.562i			0.805433i
$399$	−145.757	+	94.3555i	−0.365307	+	0.236480i
$400$	677.293			1.69323
$401$	183.178			0.456803			0.228402	−	0.973567i	$-0.426650\pi$
$401$	183.178			0.456803			0.228402	+	0.973567i	$0.426650\pi$
$402$			198.001i			0.492539i
$403$	642.434			1.59413
$404$			92.8993i			0.229949i
$405$			72.8786i			0.179947i
$406$	882.849	−	571.509i	2.17451	−	1.40766i
$407$	873.400			2.14595
$408$	0.743815			0.00182308
$409$			761.647i			1.86222i	0.364741	+	0.931109i	$0.381158\pi$
$409$			761.647i			1.86222i	−0.364741	+	0.931109i	$0.618842\pi$
$410$	275.695			0.672427
$411$		−	252.056i		−	0.613275i
$412$			468.576i			1.13732i
$413$	−82.4847	−	127.420i	−0.199721	−	0.308523i
$414$	−40.2291			−0.0971718
$415$	−45.6189			−0.109925
$416$		−	675.397i		−	1.62355i
$417$	236.755			0.567757
$418$		−	703.745i		−	1.68360i
$419$			397.025i			0.947555i	0.880645	+	0.473777i	$0.157110\pi$
$419$			397.025i			0.947555i	−0.880645	+	0.473777i	$0.842890\pi$
$420$	314.691	−	203.714i	0.749263	−	0.485033i
$421$	236.745			0.562340			0.281170	−	0.959658i	$-0.409277\pi$
$421$	236.745			0.562340			0.281170	+	0.959658i	$0.409277\pi$
$422$	−653.883			−1.54949
$423$		−	177.624i		−	0.419916i
$424$	25.6865			0.0605813
$425$			34.2899i			0.0806821i
$426$			297.630i			0.698661i
$427$	106.382	+	164.335i	0.249137	+	0.384859i
$428$	−98.2618			−0.229584
$429$	−460.500			−1.07343
$430$		−	254.937i		−	0.592877i
$431$	−568.327			−1.31862			−0.659312	−	0.751870i	$-0.729152\pi$
$431$	−568.327			−1.31862			−0.659312	+	0.751870i	$0.729152\pi$
$432$			86.7438i			0.200796i
$433$			189.716i			0.438144i	0.975709	+	0.219072i	$0.0703029\pi$
$433$			189.716i			0.438144i	−0.975709	+	0.219072i	$0.929697\pi$
$434$	451.687	+	697.752i	1.04075	+	1.60772i
$435$	−753.617			−1.73245
$436$	−459.189			−1.05319
$437$			68.6809i			0.157164i
$438$	−525.009			−1.19865
$439$			545.353i			1.24226i	0.783707	+	0.621131i	$0.213327\pi$
$439$			545.353i			1.24226i	−0.783707	+	0.621131i	$0.786673\pi$
$440$		−	72.3109i		−	0.164343i
$441$	−60.1798	+	134.117i	−0.136462	+	0.304120i
$442$	35.7505			0.0808836
$443$	−379.787			−0.857307			−0.428654	−	0.903469i	$-0.641012\pi$
$443$	−379.787			−0.857307			−0.428654	+	0.903469i	$0.641012\pi$
$444$		−	328.665i		−	0.740237i
$445$	788.036			1.77087
$446$			546.271i			1.22482i
$447$		−	307.545i		−	0.688020i
$448$	341.167	−	220.853i	0.761533	−	0.492976i
$449$	−253.496			−0.564578			−0.282289	−	0.959329i	$-0.591094\pi$
$449$	−253.496			−0.564578			−0.282289	+	0.959329i	$0.591094\pi$
$450$	−340.327			−0.756283
$451$		−	213.995i		−	0.474491i
$452$	129.376			0.286231
$453$			348.252i			0.768768i
$454$			435.397i			0.959025i
$455$	−719.840	+	465.986i	−1.58207	+	1.02414i
$456$	12.6035			0.0276392
$457$	−788.403			−1.72517			−0.862586	−	0.505911i	$-0.831156\pi$
$457$	−788.403			−1.72517			−0.862586	+	0.505911i	$0.831156\pi$
$458$			790.119i			1.72515i
$459$	−4.39165			−0.00956787
$460$		−	148.282i		−	0.322353i
$461$			185.425i			0.402223i	0.979568	+	0.201112i	$0.0644554\pi$
$461$			185.425i			0.402223i	−0.979568	+	0.201112i	$0.935545\pi$
$462$	−323.772	−	500.152i	−0.700805	−	1.08258i
$463$	−374.433			−0.808712			−0.404356	−	0.914602i	$-0.632504\pi$
$463$	−374.433			−0.808712			−0.404356	+	0.914602i	$0.632504\pi$
$464$	−896.994			−1.93318
$465$		−	595.615i		−	1.28089i
$466$	332.203			0.712881
$467$		−	184.592i		−	0.395273i	−0.980275	−	0.197636i	$-0.936673\pi$
$467$		−	184.592i		−	0.395273i	0.980275	−	0.197636i	$-0.0633265\pi$
$468$			173.289i			0.370275i
$469$	240.242	−	155.520i	0.512243	−	0.331598i
$470$	1340.58			2.85231
$471$	−477.993			−1.01485
$472$			11.0179i			0.0233429i
$473$	−197.883			−0.418357
$474$		−	599.903i		−	1.26562i
$475$			581.021i			1.22320i
$476$	12.2758	+	18.9632i	0.0257894	+	0.0398387i
$477$	−151.659			−0.317943
$478$	−747.974			−1.56480
$479$			184.885i			0.385982i	0.981201	+	0.192991i	$0.0618188\pi$
$479$			184.885i			0.385982i	−0.981201	+	0.192991i	$0.938181\pi$
$480$	−626.176			−1.30453
$481$			751.806i			1.56301i
$482$			1333.39i			2.76638i
$483$	31.5980	+	48.8116i	0.0654202	+	0.101059i
$484$	717.341			1.48211
$485$	1344.42			2.77199
$486$		−	43.5872i		−	0.0896856i
$487$	−428.490			−0.879855			−0.439928	−	0.898033i	$-0.644996\pi$
$487$	−428.490			−0.879855			−0.439928	+	0.898033i	$0.644996\pi$
$488$		−	14.2099i		−	0.0291186i
$489$			52.9775i			0.108338i
$490$	−1012.22	−	454.195i	−2.06576	−	0.926928i
$491$	3.51842			0.00716583			0.00358291	−	0.999994i	$-0.498860\pi$
$491$	3.51842			0.00716583			0.00358291	+	0.999994i	$0.498860\pi$
$492$	−80.5276			−0.163674
$493$		−	45.4129i		−	0.0921154i
$494$	605.771			1.22626
$495$			426.940i			0.862504i
$496$		−	708.932i		−	1.42930i
$497$	361.126	−	233.773i	0.726611	−	0.470369i
$498$	27.2837			0.0547866
$499$	277.849			0.556812			0.278406	−	0.960463i	$-0.410194\pi$
$499$	277.849			0.556812			0.278406	+	0.960463i	$0.410194\pi$
$500$		−	481.452i		−	0.962904i
$501$	174.336			0.347976
$502$		−	307.843i		−	0.613232i
$503$			125.570i			0.249643i	0.992179	+	0.124821i	$0.0398357\pi$
$503$			125.570i			0.249643i	−0.992179	+	0.124821i	$0.960164\pi$
$504$	8.95731	−	5.79848i	0.0177724	−	0.0115049i
$505$	−197.016			−0.390131
$506$	−235.672			−0.465754
$507$		−	103.673i		−	0.204483i
$508$	−707.434			−1.39259
$509$			246.457i			0.484199i	0.970251	+	0.242100i	$0.0778361\pi$
$509$			246.457i			0.484199i	−0.970251	+	0.242100i	$0.922164\pi$
$510$		−	33.1451i		−	0.0649905i
$511$	412.369	+	637.014i	0.806984	+	1.24660i
$512$	−711.377			−1.38941
$513$	−74.4139			−0.145056
$514$		−	419.160i		−	0.815486i
$515$	−993.732			−1.92958
$516$			74.4644i			0.144311i
$517$		−	1040.57i		−	2.01270i
$518$	−816.542	+	528.586i	−1.57634	+	1.02044i
$519$	33.0662			0.0637114
$520$	62.2438			0.119700
$521$			460.844i			0.884537i	0.896883	+	0.442268i	$0.145826\pi$
$521$			460.844i			0.884537i	−0.896883	+	0.442268i	$0.854174\pi$
$522$	450.723			0.863454
$523$		−	422.861i		−	0.808530i	−0.914642	−	0.404265i	$-0.867527\pi$
$523$		−	422.861i		−	0.808530i	0.914642	−	0.404265i	$-0.132473\pi$
$524$		−	480.599i		−	0.917174i
$525$	267.310	+	412.932i	0.509162	+	0.786537i
$526$	1044.66			1.98605
$527$	35.8917			0.0681057
$528$			508.166i			0.962435i
$529$	23.0000			0.0434783
$530$		−	1144.61i		−	2.15965i
$531$		−	65.0519i		−	0.122508i
$532$	208.005	+	321.320i	0.390987	+	0.603985i
$533$	184.203			0.345597
$534$	−471.308			−0.882599
$535$		−	208.389i		−	0.389512i
$536$	−20.7735			−0.0387565
$537$			1.12674i			0.00209821i
$538$			1268.20i			2.35725i
$539$	−352.547	+	785.689i	−0.654077	+	1.45768i
$540$	160.660			0.297518
$541$	184.766			0.341527			0.170763	−	0.985312i	$-0.445377\pi$
$541$	184.766			0.341527			0.170763	+	0.985312i	$0.445377\pi$
$542$			113.033i			0.208548i
$543$	345.677			0.636606
$544$		−	37.7333i		−	0.0693627i
$545$		−	973.824i		−	1.78683i
$546$	430.522	−	278.697i	0.788501	−	0.510433i
$547$	−283.298			−0.517912			−0.258956	−	0.965889i	$-0.583378\pi$
$547$	−283.298			−0.517912			−0.258956	+	0.965889i	$0.583378\pi$
$548$	−555.654			−1.01397
$549$			83.8983i			0.152820i
$550$	−1993.72			−3.62494
$551$		−	769.493i		−	1.39654i
$552$		−	4.22068i		−	0.00764617i
$553$	−727.885	+	471.194i	−1.31625	+	0.852069i
$554$	−1107.85			−1.99973
$555$	697.016			1.25589
$556$		−	521.922i		−	0.938709i
$557$	758.855			1.36240			0.681198	−	0.732099i	$-0.261459\pi$
$557$	758.855			1.36240			0.681198	+	0.732099i	$0.261459\pi$
$558$			356.225i			0.638396i
$559$		−	170.334i		−	0.304712i
$560$	514.220	+	794.350i	0.918250	+	1.41848i
$561$	−25.7273			−0.0458598
$562$	1341.36			2.38677
$563$			4.48006i			0.00795749i	0.999992	+	0.00397874i	$0.00126648\pi$
$563$			4.48006i			0.00795749i	−0.999992	+	0.00397874i	$0.998734\pi$
$564$	−391.570			−0.694274
$565$			274.375i			0.485620i
$566$			331.670i			0.585990i
$567$	−52.8860	+	34.2355i	−0.0932733	+	0.0603802i
$568$	−31.2262			−0.0549756
$569$	−771.052			−1.35510			−0.677550	−	0.735476i	$-0.736958\pi$
$569$	−771.052			−1.35510			−0.677550	+	0.735476i	$0.736958\pi$
$570$		−	561.624i		−	0.985305i
$571$	−699.765			−1.22551			−0.612754	−	0.790274i	$-0.709938\pi$
$571$	−699.765			−1.22551			−0.612754	+	0.790274i	$0.709938\pi$
$572$			1015.16i			1.77476i
$573$			36.3932i			0.0635134i
$574$	129.511	+	200.064i	0.225629	+	0.348544i
$575$	194.574			0.338389
$576$	174.177			0.302390
$577$		−	1000.51i		−	1.73399i	−0.498313	−	0.866997i	$-0.666047\pi$
$577$		−	1000.51i		−	1.73399i	0.498313	−	0.866997i	$-0.333953\pi$
$578$	−806.081			−1.39460
$579$			27.9533i			0.0482786i
$580$			1661.34i			2.86437i
$581$	−21.4300	−	33.1044i	−0.0368847	−	0.0569782i
$582$	−804.068			−1.38156
$583$	−888.453			−1.52393
$584$		−	55.0819i		−	0.0943184i
$585$	−367.502			−0.628208
$586$		−	1131.75i		−	1.93132i
$587$			590.031i			1.00516i	0.864530	+	0.502582i	$0.167616\pi$
$587$			590.031i			1.00516i	−0.864530	+	0.502582i	$0.832384\pi$
$588$	295.659	+	132.665i	0.502822	+	0.225622i
$589$	608.162			1.03253
$590$	490.966			0.832146
$591$		−	242.508i		−	0.410336i
$592$	829.625			1.40139
$593$		−	956.704i		−	1.61333i	−0.591009	−	0.806665i	$-0.701270\pi$
$593$		−	956.704i		−	1.61333i	0.591009	−	0.806665i	$-0.298730\pi$
$594$		−	255.344i		−	0.429872i
$595$	−40.2163	+	26.0338i	−0.0675903	+	0.0437544i
$596$	−677.979			−1.13755
$597$	198.572			0.332616
$598$		−	202.862i		−	0.339234i
$599$	−319.765			−0.533831			−0.266915	−	0.963720i	$-0.586004\pi$
$599$	−319.765			−0.533831			−0.266915	+	0.963720i	$0.586004\pi$
$600$		−	35.7058i		−	0.0595097i
$601$			110.650i			0.184109i	0.995754	+	0.0920547i	$0.0293435\pi$
$601$			110.650i			0.184109i	−0.995754	+	0.0920547i	$0.970657\pi$
$602$	185.001	−	119.760i	0.307311	−	0.198936i
$603$	122.651			0.203402
$604$	767.716			1.27105
$605$			1521.30i			2.51455i
$606$	117.831			0.194441
$607$		−	897.557i		−	1.47868i	−0.673334	−	0.739339i	$-0.735138\pi$
$607$		−	897.557i		−	1.47868i	0.673334	−	0.739339i	$-0.264862\pi$
$608$		−	639.367i		−	1.05159i
$609$	−354.020	−	546.879i	−0.581314	−	0.897996i
$610$	−633.205			−1.03804
$611$	895.699			1.46596
$612$			9.68134i			0.0158192i
$613$	407.170			0.664225			0.332113	−	0.943240i	$-0.392239\pi$
$613$	407.170			0.664225			0.332113	+	0.943240i	$0.392239\pi$
$614$		−	20.5766i		−	0.0335123i
$615$		−	170.779i		−	0.277689i
$616$	52.4740	−	33.9689i	0.0851851	−	0.0551443i
$617$	658.570			1.06737			0.533687	−	0.845682i	$-0.320806\pi$
$617$	658.570			1.06737			0.533687	+	0.845682i	$0.320806\pi$
$618$	594.331			0.961700
$619$		−	421.737i		−	0.681320i	−0.940187	−	0.340660i	$-0.889350\pi$
$619$		−	421.737i		−	0.681320i	0.940187	−	0.340660i	$-0.110650\pi$
$620$	−1313.02			−2.11778
$621$			24.9199i			0.0401286i
$622$			406.052i			0.652816i
$623$	370.189	+	571.856i	0.594204	+	0.917907i
$624$	−437.419			−0.700993
$625$	6.75370			0.0108059
$626$		−	412.348i		−	0.658703i
$627$	−435.934			−0.695269
$628$			1053.73i			1.67791i
$629$			42.0021i			0.0667761i
$630$	−258.386	−	399.146i	−0.410136	−	0.633566i
$631$	−832.568			−1.31944			−0.659721	−	0.751510i	$-0.729326\pi$
$631$	−832.568			−1.31944			−0.659721	+	0.751510i	$0.729326\pi$
$632$	62.9395			0.0995878
$633$			405.047i			0.639884i
$634$	595.041			0.938551
$635$		−	1500.29i		−	2.36266i
$636$			334.330i			0.525676i
$637$	−676.307	−	303.466i	−1.06171	−	0.476399i
$638$	2640.44			4.13862
$639$	184.366			0.288523
$640$		−	131.528i		−	0.205512i
$641$	−187.603			−0.292672			−0.146336	−	0.989235i	$-0.546748\pi$
$641$	−187.603			−0.292672			−0.146336	+	0.989235i	$0.546748\pi$
$642$			124.633i			0.194133i
$643$		−	928.896i		−	1.44463i	−0.691565	−	0.722314i	$-0.743079\pi$
$643$		−	928.896i		−	1.44463i	0.691565	−	0.722314i	$-0.256921\pi$
$644$	107.604	−	69.6573i	0.167087	−	0.108163i
$645$	−157.920			−0.244838
$646$	33.8434			0.0523891
$647$			342.216i			0.528928i	0.964396	+	0.264464i	$0.0851950\pi$
$647$			342.216i			0.528928i	−0.964396	+	0.264464i	$0.914805\pi$
$648$	4.57300			0.00705709
$649$		−	381.089i		−	0.587195i
$650$		−	1716.15i		−	2.64024i
$651$	432.221	−	279.797i	0.663935	−	0.429796i
$652$	116.788			0.179123
$653$	−457.012			−0.699865			−0.349933	−	0.936775i	$-0.613796\pi$
$653$	−457.012			−0.699865			−0.349933	+	0.936775i	$0.613796\pi$
$654$			582.425i			0.890557i
$655$	1019.23			1.55608
$656$		−	203.270i		−	0.309863i
$657$			325.216i			0.495002i
$658$	629.755	+	972.826i	0.957075	+	1.47846i
$659$	335.610			0.509271			0.254636	−	0.967037i	$-0.418044\pi$
$659$	335.610			0.509271			0.254636	+	0.967037i	$0.418044\pi$
$660$	941.182			1.42603
$661$			285.325i			0.431657i	0.976431	+	0.215828i	$0.0692452\pi$
$661$			285.325i			0.431657i	−0.976431	+	0.215828i	$0.930755\pi$
$662$	1414.37			2.13652
$663$		−	22.1456i		−	0.0334021i
$664$			2.86250i			0.00431099i
$665$	−681.439	+	441.127i	−1.02472	+	0.663349i
$666$	−416.871			−0.625933
$667$	−257.690			−0.386341
$668$		−	384.321i		−	0.575331i
$669$	338.387			0.505810
$670$			925.685i			1.38162i
$671$			491.496i			0.732482i
$672$	−294.153	−	454.399i	−0.437728	−	0.676188i
$673$	346.691			0.515143			0.257572	−	0.966259i	$-0.417078\pi$
$673$	346.691			0.515143			0.257572	+	0.966259i	$0.417078\pi$
$674$	1100.20			1.63234
$675$			210.815i			0.312319i
$676$	−228.545			−0.338085
$677$			61.9651i			0.0915290i	0.998952	+	0.0457645i	$0.0145724\pi$
$677$			61.9651i			0.0915290i	−0.998952	+	0.0457645i	$0.985428\pi$
$678$		−	164.098i		−	0.242033i
$679$	631.555	+	975.606i	0.930125	+	1.43683i
$680$	3.47746			0.00511391
$681$	269.706			0.396044
$682$			2086.85i			3.05990i
$683$	−764.903			−1.11992			−0.559958	−	0.828521i	$-0.689183\pi$
$683$	−764.903			−1.11992			−0.559958	+	0.828521i	$0.689183\pi$
$684$			164.044i			0.239831i
$685$		−	1178.40i		−	1.72030i
$686$	−145.906	−	947.905i	−0.212691	−	1.38179i
$687$	489.438			0.712428
$688$	−187.965			−0.273205
$689$		−	764.764i		−	1.10996i
$690$	−188.078			−0.272576
$691$		−	383.890i		−	0.555557i	−0.960645	−	0.277779i	$-0.910402\pi$
$691$		−	383.890i		−	0.555557i	0.960645	−	0.277779i	$-0.0895981\pi$
$692$		−	72.8939i		−	0.105338i
$693$	−309.818	+	200.560i	−0.447068	+	0.289408i
$694$	841.138			1.21201
$695$	1106.87			1.59261
$696$			47.2881i			0.0679427i
$697$	10.2911			0.0147649
$698$			1573.38i			2.25413i
$699$		−	205.782i		−	0.294395i
$700$	910.303	−	589.281i	1.30043	−	0.841830i
$701$	915.587			1.30612			0.653058	−	0.757308i	$-0.273486\pi$
$701$	915.587			1.30612			0.653058	+	0.757308i	$0.273486\pi$
$702$	219.795			0.313099
$703$			711.700i			1.01238i
$704$	1020.37			1.44939
$705$		−	830.423i		−	1.17790i
$706$			460.379i			0.652095i
$707$	−92.5507	−	142.969i	−0.130906	−	0.202220i
$708$	−143.406			−0.202551
$709$	−330.186			−0.465706			−0.232853	−	0.972512i	$-0.574806\pi$
$709$	−330.186			−0.465706			−0.232853	+	0.972512i	$0.574806\pi$
$710$			1391.47i			1.95981i
$711$	−371.609			−0.522657
$712$		−	49.4478i		−	0.0694491i
$713$		−	203.663i		−	0.285642i
$714$	24.0525	−	15.5703i	0.0336870	−	0.0218072i
$715$	−2152.91			−3.01106
$716$	2.48388			0.00346911
$717$			463.331i			0.646208i
$718$	288.564			0.401899
$719$		−	275.272i		−	0.382854i	−0.981507	−	0.191427i	$-0.938689\pi$
$719$		−	275.272i		−	0.382854i	0.981507	−	0.191427i	$-0.0613114\pi$
$720$			405.541i			0.563252i
$721$	−466.817	−	721.124i	−0.647458	−	1.00017i
$722$	−435.944			−0.603800
$723$	825.969			1.14242
$724$		−	762.040i		−	1.05254i
$725$	−2179.98			−3.00687
$726$		−	909.859i		−	1.25325i
$727$			996.804i			1.37112i	0.728016	+	0.685560i	$0.240443\pi$
$727$			996.804i			1.37112i	−0.728016	+	0.685560i	$0.759557\pi$
$728$	29.2398	+	45.1687i	0.0401645	+	0.0620449i
$729$	−27.0000			−0.0370370
$730$	−2454.50			−3.36233
$731$		−	9.51627i		−	0.0130182i
$732$	184.952			0.252667
$733$			627.513i			0.856089i	0.903758	+	0.428044i	$0.140797\pi$
$733$			627.513i			0.856089i	−0.903758	+	0.428044i	$0.859203\pi$
$734$		−	89.6184i		−	0.122096i
$735$	−281.350	+	627.019i	−0.382789	+	0.853087i
$736$	−214.113			−0.290914
$737$	718.519			0.974925
$738$			102.139i			0.138400i
$739$	555.262			0.751369			0.375685	−	0.926748i	$-0.377408\pi$
$739$	555.262			0.751369			0.375685	+	0.926748i	$0.377408\pi$
$740$		−	1536.56i		−	2.07644i
$741$		−	375.244i		−	0.506402i
$742$	830.616	−	537.696i	1.11943	−	0.724658i
$743$	259.159			0.348800			0.174400	−	0.984675i	$-0.444201\pi$
$743$	259.159			0.348800			0.174400	+	0.984675i	$0.444201\pi$
$744$	−37.3737			−0.0502335
$745$		−	1437.82i		−	1.92996i
$746$	1498.24			2.00836
$747$		−	16.9008i		−	0.0226250i
$748$			56.7155i			0.0758229i
$749$	151.222	−	97.8931i	0.201899	−	0.130698i
$750$	−610.662			−0.814217
$751$	−321.188			−0.427680			−0.213840	−	0.976869i	$-0.568597\pi$
$751$	−321.188			−0.427680			−0.213840	+	0.976869i	$0.568597\pi$
$752$		−	988.412i		−	1.31438i
$753$	−190.693			−0.253244
$754$			2272.84i			3.01438i
$755$			1628.13i			2.15647i
$756$	75.4718	+	116.586i	0.0998304	+	0.154215i
$757$	29.1544			0.0385131			0.0192565	−	0.999815i	$-0.493870\pi$
$757$	29.1544			0.0385131			0.0192565	+	0.999815i	$0.493870\pi$
$758$	289.769			0.382281
$759$			145.986i			0.192340i
$760$	58.9234			0.0775307
$761$		−	1324.19i		−	1.74007i	−0.492992	−	0.870034i	$-0.664097\pi$
$761$		−	1324.19i		−	1.74007i	0.492992	−	0.870034i	$-0.335903\pi$
$762$			897.293i			1.17755i
$763$	706.678	−	457.465i	0.926183	−	0.599561i
$764$	80.2282			0.105011
$765$	−20.5317			−0.0268388
$766$		−	225.269i		−	0.294084i
$767$	328.035			0.427685
$768$			480.908i			0.626182i
$769$			690.747i			0.898241i	0.893471	+	0.449121i	$0.148263\pi$
$769$			690.747i			0.898241i	−0.893471	+	0.449121i	$0.851737\pi$
$770$	−1513.69	−	2338.29i	−1.96583	−	3.03674i
$771$	−259.648			−0.336768
$772$	61.6226			0.0798220
$773$			1041.98i			1.34797i	0.738746	+	0.673984i	$0.235418\pi$
$773$			1041.98i			1.34797i	−0.738746	+	0.673984i	$0.764582\pi$
$774$	94.4490			0.122027
$775$		−	1722.93i		−	2.22314i
$776$		−	84.3596i		−	0.108711i
$777$	327.432	+	505.806i	0.421405	+	0.650973i
$778$	−1843.98			−2.37015
$779$	174.377			0.223847
$780$			810.152i			1.03866i
$781$	1080.06			1.38292
$782$		−	11.3335i		−	0.0144930i
$783$		−	279.200i		−	0.356577i
$784$	−334.878	+	746.311i	−0.427140	+	0.951927i
$785$	−2234.69			−2.84674
$786$	−609.581			−0.775549
$787$			667.331i			0.847943i	0.905676	+	0.423971i	$0.139364\pi$
$787$			667.331i			0.847943i	−0.905676	+	0.423971i	$0.860636\pi$
$788$	−534.606			−0.678434
$789$		−	647.113i		−	0.820169i
$790$		−	2804.64i		−	3.55018i
$791$	−199.107	+	128.891i	−0.251715	+	0.162947i
$792$	26.7897			0.0338254
$793$	−423.070			−0.533506
$794$			171.147i			0.215551i
$795$	−709.030			−0.891861
$796$		−	437.749i		−	0.549935i
$797$			160.611i			0.201519i	0.994911	+	0.100760i	$0.0321273\pi$
$797$			160.611i			0.201519i	−0.994911	+	0.100760i	$0.967873\pi$
$798$	407.555	−	263.829i	0.510721	−	0.330613i
$799$	50.0412			0.0626298
$800$	−1811.33			−2.26417
$801$			291.951i			0.364483i
$802$	−512.188			−0.638638
$803$			1905.19i			2.37259i
$804$		−	270.383i		−	0.336297i
$805$	147.726	+	228.202i	0.183510	+	0.283481i
$806$	−1796.32			−2.22869
$807$	785.584			0.973462
$808$			12.3624i			0.0153000i
$809$	−323.809			−0.400259			−0.200129	−	0.979769i	$-0.564136\pi$
$809$	−323.809			−0.400259			−0.200129	+	0.979769i	$0.564136\pi$
$810$		−	203.777i		−	0.251577i
$811$			618.216i			0.762288i	0.924516	+	0.381144i	$0.124470\pi$
$811$			618.216i			0.762288i	−0.924516	+	0.381144i	$0.875530\pi$
$812$	−1205.59	+	780.433i	−1.48471	+	0.961124i
$813$	70.0182			0.0861233
$814$	−2442.13			−3.00016
$815$			247.678i			0.303900i
$816$	−24.4379			−0.0299484
$817$		−	161.247i		−	0.197365i
$818$		−	2129.66i		−	2.60349i
$819$	−172.638	−	266.686i	−0.210791	−	0.325624i
$820$	−376.479			−0.459121
$821$	1540.09			1.87587			0.937936	−	0.346809i	$-0.112735\pi$
$821$	1540.09			1.87587			0.937936	+	0.346809i	$0.112735\pi$
$822$			704.778i			0.857395i
$823$	282.829			0.343657			0.171828	−	0.985127i	$-0.445033\pi$
$823$	282.829			0.343657			0.171828	+	0.985127i	$0.445033\pi$
$824$			62.3549i			0.0756734i
$825$			1235.00i			1.49698i
$826$	230.637	+	356.281i	0.279222	+	0.431333i
$827$	606.065			0.732847			0.366424	−	0.930448i	$-0.380582\pi$
$827$	606.065			0.732847			0.366424	+	0.930448i	$0.380582\pi$
$828$	54.9355			0.0663472
$829$		−	1184.88i		−	1.42929i	−0.699488	−	0.714645i	$-0.746588\pi$
$829$		−	1184.88i		−	1.42929i	0.699488	−	0.714645i	$-0.253412\pi$
$830$	127.556			0.153682
$831$			686.254i			0.825818i
$832$			878.313i			1.05566i
$833$	−37.7841	−	16.9541i	−0.0453591	−	0.0203531i
$834$	−661.994			−0.793758
$835$	815.050			0.976107
$836$			961.009i			1.14953i
$837$	220.663			0.263636
$838$		−	1110.13i		−	1.32474i
$839$		−	451.969i		−	0.538699i	−0.963042	−	0.269350i	$-0.913191\pi$
$839$		−	451.969i		−	0.538699i	0.963042	−	0.269350i	$-0.0868087\pi$
$840$	41.8769	−	27.1088i	0.0498534	−	0.0322724i
$841$	2046.13			2.43297
$842$	−661.968			−0.786185
$843$		−	830.906i		−	0.985653i
$844$	892.919			1.05796
$845$		−	484.688i		−	0.573595i
$846$			496.659i			0.587067i
$847$	−1103.97	+	714.649i	−1.30338	+	0.843741i
$848$	−843.924			−0.995193
$849$	205.453			0.241994
$850$		−	95.8787i		−	0.112798i
$851$	238.336			0.280065
$852$		−	406.433i		−	0.477034i
$853$		−	615.375i		−	0.721424i	−0.932677	−	0.360712i	$-0.882534\pi$
$853$		−	615.375i		−	0.721424i	0.932677	−	0.360712i	$-0.117466\pi$
$854$	−297.456	−	459.500i	−0.348309	−	0.538056i
$855$	−347.897			−0.406897
$856$	−13.0760			−0.0152757
$857$			1674.73i			1.95418i	0.212826	+	0.977090i	$0.431733\pi$
$857$			1674.73i			1.95418i	−0.212826	+	0.977090i	$0.568267\pi$
$858$	1287.61			1.50071
$859$			1497.48i			1.74328i	0.490144	+	0.871641i	$0.336944\pi$
$859$			1497.48i			1.74328i	−0.490144	+	0.871641i	$0.663056\pi$
$860$			348.133i			0.404806i
$861$	123.930	−	80.2254i	0.143937	−	0.0931769i
$862$	1589.11			1.84351
$863$	445.101			0.515760			0.257880	−	0.966177i	$-0.416976\pi$
$863$	445.101			0.515760			0.257880	+	0.966177i	$0.416976\pi$
$864$		−	231.985i		−	0.268501i
$865$	154.590			0.178717
$866$		−	530.469i		−	0.612551i
$867$			499.325i			0.575923i
$868$	−616.808	−	952.826i	−0.710609	−	1.09773i
$869$	−2176.97			−2.50515
$870$	2107.20			2.42207
$871$			618.488i			0.710090i
$872$	−61.1057			−0.0700753
$873$			498.078i			0.570536i
$874$		−	192.040i		−	0.219725i
$875$	479.645	+	740.940i	0.548166	+	0.846789i
$876$	716.934			0.818418
$877$	1170.57			1.33474			0.667371	−	0.744725i	$-0.267419\pi$
$877$	1170.57			1.33474			0.667371	+	0.744725i	$0.267419\pi$
$878$		−	1524.87i		−	1.73676i
$879$	−701.062			−0.797568
$880$			2375.76i			2.69972i
$881$		−	1586.44i		−	1.80072i	−0.435141	−	0.900362i	$-0.643301\pi$
$881$		−	1586.44i		−	1.80072i	0.435141	−	0.900362i	$-0.356699\pi$
$882$	168.270	−	375.007i	0.190782	−	0.425178i
$883$	−323.900			−0.366818			−0.183409	−	0.983037i	$-0.558713\pi$
$883$	−323.900			−0.366818			−0.183409	+	0.983037i	$0.558713\pi$
$884$	−48.8197			−0.0552259
$885$		−	304.128i		−	0.343648i
$886$	1061.93			1.19857
$887$		−	1525.96i		−	1.72036i	−0.509992	−	0.860179i	$-0.670352\pi$
$887$		−	1525.96i		−	1.72036i	0.509992	−	0.860179i	$-0.329648\pi$
$888$		−	43.7365i		−	0.0492528i
$889$	1088.72	−	704.779i	1.22466	−	0.792777i
$890$	−2203.44			−2.47578
$891$	−158.172			−0.177522
$892$		−	745.969i		−	0.836288i
$893$	847.917			0.949515
$894$			859.933i			0.961893i
$895$			5.26769i			0.00588569i
$896$	95.4461	−	61.7867i	0.106525	−	0.0689583i
$897$	−125.662			−0.140092
$898$	708.804			0.789314
$899$			2281.82i			2.53817i
$900$	464.739			0.516377
$901$		−	42.7261i		−	0.0474207i
$902$			598.356i			0.663366i
$903$	−74.1849	−	114.599i	−0.0821539	−	0.126909i
$904$	17.2165			0.0190448
$905$	1616.10			1.78574
$906$		−	973.753i		−	1.07478i
$907$	−765.500			−0.843991			−0.421996	−	0.906598i	$-0.638670\pi$
$907$	−765.500			−0.843991			−0.421996	+	0.906598i	$0.638670\pi$
$908$		−	594.563i		−	0.654805i
$909$		−	72.9904i		−	0.0802975i
$910$	2012.76	−	1302.95i	2.21182	−	1.43182i
$911$	−112.398			−0.123378			−0.0616892	−	0.998095i	$-0.519649\pi$
$911$	−112.398			−0.123378			−0.0616892	+	0.998095i	$0.519649\pi$
$912$	−414.085			−0.454040
$913$		−	99.0091i		−	0.108444i
$914$	2204.47			2.41189
$915$			392.238i			0.428675i
$916$		−	1078.96i		−	1.17790i
$917$	478.796	+	739.628i	0.522133	+	0.806574i
$918$	12.2796			0.0133765
$919$	−1306.97			−1.42217			−0.711085	−	0.703106i	$-0.751796\pi$
$919$	−1306.97			−1.42217			−0.711085	+	0.703106i	$0.751796\pi$
$920$		−	19.7324i		−	0.0214482i
$921$	−12.7461			−0.0138394
$922$		−	518.470i		−	0.562332i
$923$			929.696i			1.00725i
$924$	442.131	+	682.990i	0.478497	+	0.739167i
$925$	2016.25			2.17973
$926$	1046.96			1.13063
$927$		−	368.157i		−	0.397149i
$928$	2398.89			2.58502
$929$			464.386i			0.499877i	0.968262	+	0.249939i	$0.0804104\pi$
$929$			464.386i			0.499877i	−0.968262	+	0.249939i	$0.919590\pi$
$930$			1665.41i			1.79076i
$931$	−640.228	−	287.277i	−0.687678	−	0.308569i
$932$	−453.644			−0.486743
$933$	251.528			0.269591
$934$			516.142i			0.552615i
$935$	−120.279			−0.128641
$936$			23.0601i			0.0246368i
$937$			251.354i			0.268254i	0.990964	+	0.134127i	$0.0428230\pi$
$937$			251.354i			0.268254i	−0.990964	+	0.134127i	$0.957177\pi$
$938$	−671.745	+	434.851i	−0.716146	+	0.463594i
$939$	−255.428			−0.272022
$940$	−1830.65			−1.94750
$941$		−	274.467i		−	0.291675i	−0.989309	−	0.145838i	$-0.953412\pi$
$941$		−	274.467i		−	0.291675i	0.989309	−	0.145838i	$-0.0465877\pi$
$942$	1336.52			1.41882
$943$		−	58.3956i		−	0.0619253i
$944$		−	361.989i		−	0.383463i
$945$	−247.251	+	160.057i	−0.261641	+	0.169372i
$946$	553.304			0.584888
$947$	465.562			0.491618			0.245809	−	0.969318i	$-0.420946\pi$
$947$	465.562			0.491618			0.245809	+	0.969318i	$0.420946\pi$
$948$			819.206i			0.864142i
$949$	−1639.95			−1.72809
$950$		−	1624.60i		−	1.71011i
$951$		−	368.597i		−	0.387589i
$952$	1.63358	+	2.52350i	0.00171594	+	0.00265073i
$953$	−319.387			−0.335138			−0.167569	−	0.985860i	$-0.553592\pi$
$953$	−319.387			−0.335138			−0.167569	+	0.985860i	$0.553592\pi$
$954$	424.056			0.444503
$955$			170.144i			0.178161i
$956$	1021.41			1.06842
$957$		−	1635.62i		−	1.70911i
$958$		−	516.961i		−	0.539626i
$959$	855.135	−	553.568i	0.891694	−	0.577235i
$960$	814.304			0.848233
$961$	−842.413			−0.876600
$962$		−	2102.14i		−	2.18518i
$963$	77.2037			0.0801700
$964$		−	1820.84i		−	1.88883i
$965$			130.686i			0.135426i
$966$	−88.3517	−	136.483i	−0.0914614	−	0.141287i
$967$	−1231.04			−1.27305			−0.636524	−	0.771257i	$-0.719629\pi$
$967$	−1231.04			−1.27305			−0.636524	+	0.771257i	$0.719629\pi$
$968$	95.4588			0.0986145
$969$		−	20.9642i		−	0.0216349i
$970$	−3759.15			−3.87541
$971$		−	452.534i		−	0.466049i	−0.972471	−	0.233025i	$-0.925138\pi$
$971$		−	452.534i		−	0.466049i	0.972471	−	0.233025i	$-0.0748622\pi$
$972$			59.5211i			0.0612357i
$973$	519.963	+	803.222i	0.534392	+	0.825511i
$974$	1198.11			1.23009
$975$	−1063.07			−1.09033
$976$			466.862i			0.478342i
$977$	−538.081			−0.550748			−0.275374	−	0.961337i	$-0.588802\pi$
$977$	−538.081			−0.550748			−0.275374	+	0.961337i	$0.588802\pi$
$978$		−	148.131i		−	0.151464i
$979$			1710.32i			1.74700i
$980$	1382.25	+	620.232i	1.41046	+	0.632890i
$981$	360.782			0.367769
$982$	−9.83792			−0.0100182
$983$		−	1701.60i		−	1.73103i	−0.500884	−	0.865515i	$-0.666992\pi$
$983$		−	1701.60i		−	1.73103i	0.500884	−	0.865515i	$-0.333008\pi$
$984$	−10.7161			−0.0108903
$985$		−	1133.77i		−	1.15103i
$986$			126.980i			0.128783i
$987$	602.615	−	390.101i	0.610552	−	0.395239i
$988$	−827.219			−0.837266
$989$	−53.9988			−0.0545994
$990$		−	1193.77i		−	1.20583i
$991$	1217.38			1.22844			0.614218	−	0.789137i	$-0.289472\pi$
$991$	1217.38			1.22844			0.614218	+	0.789137i	$0.289472\pi$
$992$			1895.95i			1.91124i
$993$		−	876.132i		−	0.882308i
$994$	−1009.75	+	653.658i	−1.01584	+	0.657604i
$995$	928.355			0.933020
$996$	−37.2577			−0.0374073
$997$		−	384.224i		−	0.385380i	−0.981260	−	0.192690i	$-0.938279\pi$
$997$		−	384.224i		−	0.385380i	0.981260	−	0.192690i	$-0.0617212\pi$
$998$	−776.900			−0.778457
$999$			258.230i			0.258489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.11	✓	60
7.6	odd	2	inner	483.3.g.a.139.12	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.11	✓	60	1.1	even	1	trivial
483.3.g.a.139.12	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)

\(f(q)\)	\(=\)	\(q-2.79612 q^{2} +1.73205i q^{3} +3.81828 q^{4} +8.09762i q^{5} -4.84302i q^{6} +(-5.87622 + 3.80395i) q^{7} +0.508111 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.79612 q^{2} +1.73205i q^{3} +3.81828 q^{4} +8.09762i q^{5} -4.84302i q^{6} +(-5.87622 + 3.80395i) q^{7} +0.508111 q^{8} -3.00000 q^{9} -22.6419i q^{10} -17.5747 q^{11} +6.61345i q^{12} -15.1280i q^{13} +(16.4306 - 10.6363i) q^{14} -14.0255 q^{15} -16.6939 q^{16} -0.845174i q^{17} +8.38836 q^{18} -14.3210i q^{19} +30.9190i q^{20} +(-6.58863 - 10.1779i) q^{21} +49.1410 q^{22} -4.79583 q^{23} +0.880073i q^{24} -40.5714 q^{25} +42.2996i q^{26} -5.19615i q^{27} +(-22.4371 + 14.5245i) q^{28} +53.7320 q^{29} +39.2169 q^{30} +42.4666i q^{31} +44.6456 q^{32} -30.4403i q^{33} +2.36321i q^{34} +(-30.8029 - 47.5834i) q^{35} -11.4548 q^{36} -49.6964 q^{37} +40.0431i q^{38} +26.2024 q^{39} +4.11449i q^{40} +12.1763i q^{41} +(18.4226 + 28.4587i) q^{42} +11.2595 q^{43} -67.1051 q^{44} -24.2929i q^{45} +13.4097 q^{46} +59.2081i q^{47} -28.9146i q^{48} +(20.0599 - 44.7057i) q^{49} +113.442 q^{50} +1.46388 q^{51} -57.7628i q^{52} +50.5529 q^{53} +14.5291i q^{54} -142.313i q^{55} +(-2.98577 + 1.93283i) q^{56} +24.8046 q^{57} -150.241 q^{58} +21.6840i q^{59} -53.5532 q^{60} -27.9661i q^{61} -118.742i q^{62} +(17.6287 - 11.4118i) q^{63} -58.0589 q^{64} +122.501 q^{65} +85.1146i q^{66} -40.8837 q^{67} -3.22711i q^{68} -8.30662i q^{69} +(86.1286 + 133.049i) q^{70} -61.4554 q^{71} -1.52433 q^{72} -108.405i q^{73} +138.957 q^{74} -70.2717i q^{75} -54.6814i q^{76} +(103.273 - 66.8533i) q^{77} -73.2651 q^{78} +123.870 q^{79} -135.180i q^{80} +9.00000 q^{81} -34.0464i q^{82} +5.63361i q^{83} +(-25.1573 - 38.8621i) q^{84} +6.84390 q^{85} -31.4830 q^{86} +93.0665i q^{87} -8.92989 q^{88} -97.3170i q^{89} +67.9257i q^{90} +(57.5461 + 88.8953i) q^{91} -18.3118 q^{92} -73.5543 q^{93} -165.553i q^{94} +115.966 q^{95} +77.3284i q^{96} -166.026i q^{97} +(-56.0899 + 125.002i) q^{98} +52.7241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 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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