LMFDB - Embedded newform 483.3.f.a.22.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

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, 0, 1]))

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

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

chi := DirichletCharacter("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.21
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} +8.10909i q^{5} +1.29170 q^{6} -2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} +8.10909i q^{5} +1.29170 q^{6} -2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} -6.04744i q^{10} +17.3590i q^{11} +5.96491 q^{12} +11.7963 q^{13} +1.97310i q^{14} -14.0453i q^{15} +9.63540 q^{16} +14.5159i q^{17} -2.23728 q^{18} -7.64785i q^{19} -27.9264i q^{20} +4.58258i q^{21} -12.9456i q^{22} +(-0.920715 + 22.9816i) q^{23} -9.61518 q^{24} -40.7573 q^{25} -8.79723 q^{26} -5.19615 q^{27} +9.11155i q^{28} +4.85267 q^{29} +10.4745i q^{30} +3.69740 q^{31} -29.3910 q^{32} -30.0666i q^{33} -10.8254i q^{34} +21.4546 q^{35} -10.3315 q^{36} -27.2098i q^{37} +5.70347i q^{38} -20.4318 q^{39} +45.0162i q^{40} -75.2950 q^{41} -3.41751i q^{42} -10.9461i q^{43} -59.7815i q^{44} +24.3273i q^{45} +(0.686633 - 17.1387i) q^{46} -63.8078 q^{47} -16.6890 q^{48} -7.00000 q^{49} +30.3952 q^{50} -25.1422i q^{51} -40.6246 q^{52} -0.265774i q^{53} +3.87509 q^{54} -140.765 q^{55} -14.6874i q^{56} +13.2465i q^{57} -3.61893 q^{58} +109.616 q^{59} +48.3699i q^{60} +94.2884i q^{61} -2.75737 q^{62} -7.93725i q^{63} -16.6230 q^{64} +95.6573i q^{65} +22.4225i q^{66} +50.6910i q^{67} -49.9903i q^{68} +(1.59472 - 39.8052i) q^{69} -16.0000 q^{70} +32.1216 q^{71} +16.6540 q^{72} -125.902 q^{73} +20.2920i q^{74} +70.5937 q^{75} +26.3380i q^{76} +45.9275 q^{77} +15.2372 q^{78} -45.1325i q^{79} +78.1343i q^{80} +9.00000 q^{81} +56.1521 q^{82} -119.398i q^{83} -15.7817i q^{84} -117.710 q^{85} +8.16319i q^{86} -8.40507 q^{87} +96.3653i q^{88} +94.1931i q^{89} -18.1423i q^{90} -31.2101i q^{91} +(3.17080 - 79.1449i) q^{92} -6.40408 q^{93} +47.5853 q^{94} +62.0171 q^{95} +50.9067 q^{96} -53.8983i q^{97} +5.22033 q^{98} +52.0769i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * 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 $

$2$	−0.745761			−0.372880			−0.186440	−	0.982466i	$-0.559695\pi$
$2$	−0.745761			−0.372880			−0.186440	+	0.982466i	$0.559695\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−3.44384			−0.860960
$5$			8.10909i			1.62182i	0.585173	+	0.810909i	$0.301027\pi$
$5$			8.10909i			1.62182i	−0.585173	+	0.810909i	$0.698973\pi$
$6$	1.29170			0.215283
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	5.55132			0.693916
$9$	3.00000			0.333333
$10$		−	6.04744i		−	0.604744i
$11$			17.3590i			1.57809i	0.614337	+	0.789044i	$0.289424\pi$
$11$			17.3590i			1.57809i	−0.614337	+	0.789044i	$0.710576\pi$
$12$	5.96491			0.497076
$13$	11.7963			0.907409			0.453704	−	0.891152i	$-0.350102\pi$
$13$	11.7963			0.907409			0.453704	+	0.891152i	$0.350102\pi$
$14$			1.97310i			0.140936i
$15$		−	14.0453i		−	0.936357i
$16$	9.63540			0.602213
$17$			14.5159i			0.853874i	0.904281	+	0.426937i	$0.140407\pi$
$17$			14.5159i			0.853874i	−0.904281	+	0.426937i	$0.859593\pi$
$18$	−2.23728			−0.124293
$19$		−	7.64785i		−	0.402519i	−0.979538	−	0.201259i	$-0.935497\pi$
$19$		−	7.64785i		−	0.402519i	0.979538	−	0.201259i	$-0.0645034\pi$
$20$		−	27.9264i		−	1.39632i
$21$			4.58258i			0.218218i
$22$		−	12.9456i		−	0.588438i
$23$	−0.920715	+	22.9816i	−0.0400311	+	0.999198i
$23$	−0.920715	+	22.9816i	−0.0400311	+	0.999198i
$24$	−9.61518			−0.400632
$25$	−40.7573			−1.63029
$26$	−8.79723			−0.338355
$27$	−5.19615			−0.192450
$28$			9.11155i			0.325412i
$29$	4.85267			0.167333			0.0836667	−	0.996494i	$-0.473337\pi$
$29$	4.85267			0.167333			0.0836667	+	0.996494i	$0.473337\pi$
$30$			10.4745i			0.349149i
$31$	3.69740			0.119271			0.0596355	−	0.998220i	$-0.481006\pi$
$31$	3.69740			0.119271			0.0596355	+	0.998220i	$0.481006\pi$
$32$	−29.3910			−0.918469
$33$		−	30.0666i		−	0.911110i
$34$		−	10.8254i		−	0.318393i
$35$	21.4546			0.612989
$36$	−10.3315			−0.286987
$37$		−	27.2098i		−	0.735399i	−0.929945	−	0.367700i	$-0.880145\pi$
$37$		−	27.2098i		−	0.735399i	0.929945	−	0.367700i	$-0.119855\pi$
$38$			5.70347i			0.150091i
$39$	−20.4318			−0.523893
$40$			45.0162i			1.12540i
$41$	−75.2950			−1.83646			−0.918232	−	0.396043i	$-0.870383\pi$
$41$	−75.2950			−1.83646			−0.918232	+	0.396043i	$0.870383\pi$
$42$		−	3.41751i		−	0.0813692i
$43$		−	10.9461i		−	0.254561i	−0.991867	−	0.127281i	$-0.959375\pi$
$43$		−	10.9461i		−	0.254561i	0.991867	−	0.127281i	$-0.0406248\pi$
$44$		−	59.7815i		−	1.35867i
$45$			24.3273i			0.540606i
$46$	0.686633	−	17.1387i	0.0149268	−	0.372581i
$47$	−63.8078			−1.35761			−0.678806	−	0.734317i	$-0.737502\pi$
$47$	−63.8078			−1.35761			−0.678806	+	0.734317i	$0.737502\pi$
$48$	−16.6890			−0.347688
$49$	−7.00000			−0.142857
$50$	30.3952			0.607903
$51$		−	25.1422i		−	0.492984i
$52$	−40.6246			−0.781243
$53$		−	0.265774i		−	0.00501460i	−0.999997	−	0.00250730i	$-0.999202\pi$
$53$		−	0.265774i		−	0.00501460i	0.999997	−	0.00250730i	$-0.000798099\pi$
$54$	3.87509			0.0717609
$55$	−140.765			−2.55937
$56$		−	14.6874i		−	0.262275i
$57$			13.2465i			0.232394i
$58$	−3.61893			−0.0623953
$59$	109.616			1.85790			0.928950	−	0.370206i	$-0.120713\pi$
$59$	109.616			1.85790			0.928950	+	0.370206i	$0.120713\pi$
$60$			48.3699i			0.806166i
$61$			94.2884i			1.54571i	0.634582	+	0.772855i	$0.281172\pi$
$61$			94.2884i			1.54571i	−0.634582	+	0.772855i	$0.718828\pi$
$62$	−2.75737			−0.0444738
$63$		−	7.93725i		−	0.125988i
$64$	−16.6230			−0.259734
$65$			95.6573i			1.47165i
$66$			22.4225i			0.339735i
$67$			50.6910i			0.756581i	0.925687	+	0.378291i	$0.123488\pi$
$67$			50.6910i			0.756581i	−0.925687	+	0.378291i	$0.876512\pi$
$68$		−	49.9903i		−	0.735151i
$69$	1.59472	−	39.8052i	0.0231120	−	0.576887i
$70$	−16.0000			−0.228572
$71$	32.1216			0.452416			0.226208	−	0.974079i	$-0.427367\pi$
$71$	32.1216			0.452416			0.226208	+	0.974079i	$0.427367\pi$
$72$	16.6540			0.231305
$73$	−125.902			−1.72468			−0.862342	−	0.506327i	$-0.831003\pi$
$73$	−125.902			−1.72468			−0.862342	+	0.506327i	$0.831003\pi$
$74$			20.2920i			0.274216i
$75$	70.5937			0.941249
$76$			26.3380i			0.346553i
$77$	45.9275			0.596461
$78$	15.2372			0.195349
$79$		−	45.1325i		−	0.571297i	−0.958334	−	0.285648i	$-0.907791\pi$
$79$		−	45.1325i		−	0.571297i	0.958334	−	0.285648i	$-0.0922090\pi$
$80$			78.1343i			0.976679i
$81$	9.00000			0.111111
$82$	56.1521			0.684781
$83$		−	119.398i		−	1.43853i	−0.694738	−	0.719263i	$-0.744480\pi$
$83$		−	119.398i		−	1.43853i	0.694738	−	0.719263i	$-0.255520\pi$
$84$		−	15.7817i		−	0.187877i
$85$	−117.710			−1.38483
$86$			8.16319i			0.0949208i
$87$	−8.40507			−0.0966100
$88$			96.3653i			1.09506i
$89$			94.1931i			1.05835i	0.848513	+	0.529175i	$0.177498\pi$
$89$			94.1931i			1.05835i	−0.848513	+	0.529175i	$0.822502\pi$
$90$		−	18.1423i		−	0.201581i
$91$		−	31.2101i		−	0.342968i
$92$	3.17080	−	79.1449i	0.0344652	−	0.860270i
$93$	−6.40408			−0.0688611
$94$	47.5853			0.506227
$95$	62.0171			0.652812
$96$	50.9067			0.530278
$97$		−	53.8983i		−	0.555652i	−0.960631	−	0.277826i	$-0.910386\pi$
$97$		−	53.8983i		−	0.555652i	0.960631	−	0.277826i	$-0.0896139\pi$
$98$	5.22033			0.0532686
$99$			52.0769i			0.526029i
$100$	140.362			1.40362
$101$	−26.2570			−0.259970			−0.129985	−	0.991516i	$-0.541493\pi$
$101$	−26.2570			−0.259970			−0.129985	+	0.991516i	$0.541493\pi$
$102$			18.7501i			0.183824i
$103$		−	51.4015i		−	0.499043i	−0.968369	−	0.249522i	$-0.919727\pi$
$103$		−	51.4015i		−	0.499043i	0.968369	−	0.249522i	$-0.0802734\pi$
$104$	65.4851			0.629665
$105$	−37.1605			−0.353910
$106$			0.198204i			0.00186984i
$107$		−	187.789i		−	1.75504i	−0.479540	−	0.877520i	$-0.659196\pi$
$107$		−	187.789i		−	1.75504i	0.479540	−	0.877520i	$-0.340804\pi$
$108$	17.8947			0.165692
$109$		−	79.7085i		−	0.731271i	−0.930758	−	0.365635i	$-0.880852\pi$
$109$		−	79.7085i		−	0.731271i	0.930758	−	0.365635i	$-0.119148\pi$
$110$	104.977			0.954339
$111$			47.1287i			0.424583i
$112$		−	25.4929i		−	0.227615i
$113$			1.05462i			0.00933291i	0.999989	+	0.00466645i	$0.00148538\pi$
$113$			1.05462i			0.00933291i	−0.999989	+	0.00466645i	$0.998515\pi$
$114$		−	9.87870i		−	0.0866553i
$115$	−186.359	−	7.46616i	−1.62052	−	0.0649231i
$116$	−16.7118			−0.144067
$117$	35.3889			0.302470
$118$	−81.7474			−0.692774
$119$	38.4053			0.322734
$120$		−	77.9703i		−	0.649752i
$121$	−180.334			−1.49036
$122$		−	70.3166i		−	0.576365i
$123$	130.415			1.06028
$124$	−12.7333			−0.102688
$125$		−	127.777i		−	1.02222i
$126$			5.91929i			0.0469785i
$127$	221.052			1.74057			0.870285	−	0.492549i	$-0.163935\pi$
$127$	221.052			1.74057			0.870285	+	0.492549i	$0.163935\pi$
$128$	129.961			1.01532
$129$			18.9592i			0.146971i
$130$		−	71.3375i		−	0.548750i
$131$	−120.544			−0.920183			−0.460091	−	0.887872i	$-0.652183\pi$
$131$	−120.544			−0.920183			−0.460091	+	0.887872i	$0.652183\pi$
$132$			103.545i			0.784429i
$133$	−20.2343			−0.152138
$134$		−	37.8033i		−	0.282114i
$135$		−	42.1360i		−	0.312119i
$136$			80.5822i			0.592516i
$137$			6.29977i			0.0459837i	0.999736	+	0.0229919i	$0.00731918\pi$
$137$			6.29977i			0.0459837i	−0.999736	+	0.0229919i	$0.992681\pi$
$138$	−1.18928	+	29.6852i	−0.00861799	+	0.215110i
$139$	87.3445			0.628378			0.314189	−	0.949361i	$-0.398268\pi$
$139$	87.3445			0.628378			0.314189	+	0.949361i	$0.398268\pi$
$140$	−73.8863			−0.527759
$141$	110.518			0.783818
$142$	−23.9550			−0.168697
$143$			204.772i			1.43197i
$144$	28.9062			0.200738
$145$			39.3507i			0.271384i
$146$	93.8927			0.643101
$147$	12.1244			0.0824786
$148$			93.7061i			0.633150i
$149$			75.8390i			0.508986i	0.967075	+	0.254493i	$0.0819086\pi$
$149$			75.8390i			0.508986i	−0.967075	+	0.254493i	$0.918091\pi$
$150$	−52.6460			−0.350973
$151$	17.1909			0.113847			0.0569237	−	0.998379i	$-0.481871\pi$
$151$	17.1909			0.113847			0.0569237	+	0.998379i	$0.481871\pi$
$152$		−	42.4557i		−	0.279314i
$153$			43.5476i			0.284625i
$154$	−34.2509			−0.222409
$155$			29.9825i			0.193436i
$156$	70.3639			0.451051
$157$			173.915i			1.10774i	0.832603	+	0.553870i	$0.186849\pi$
$157$			173.915i			1.10774i	−0.832603	+	0.553870i	$0.813151\pi$
$158$			33.6580i			0.213025i
$159$			0.460333i			0.00289518i
$160$		−	238.334i		−	1.48959i
$161$	60.8035	+	2.43598i	0.377662	+	0.0151303i
$162$	−6.71185			−0.0414312
$163$	−61.4799			−0.377177			−0.188589	−	0.982056i	$-0.560391\pi$
$163$	−61.4799			−0.377177			−0.188589	+	0.982056i	$0.560391\pi$
$164$	259.304			1.58112
$165$	243.813			1.47765
$166$			89.0421i			0.536398i
$167$	194.339			1.16371			0.581853	−	0.813294i	$-0.302328\pi$
$167$	194.339			1.16371			0.581853	+	0.813294i	$0.302328\pi$
$168$			25.4394i			0.151425i
$169$	−29.8470			−0.176610
$170$	87.7837			0.516375
$171$		−	22.9436i		−	0.134173i
$172$			37.6967i			0.219167i
$173$	−51.7714			−0.299257			−0.149628	−	0.988742i	$-0.547808\pi$
$173$	−51.7714			−0.299257			−0.149628	+	0.988742i	$0.547808\pi$
$174$	6.26817			0.0360240
$175$			107.834i			0.616192i
$176$			167.261i			0.950345i
$177$	−189.861			−1.07266
$178$		−	70.2455i		−	0.394638i
$179$	−288.189			−1.60999			−0.804997	−	0.593279i	$-0.797833\pi$
$179$	−288.189			−1.60999			−0.804997	+	0.593279i	$0.797833\pi$
$180$		−	83.7792i		−	0.465440i
$181$			85.6046i			0.472954i	0.971637	+	0.236477i	$0.0759927\pi$
$181$			85.6046i			0.472954i	−0.971637	+	0.236477i	$0.924007\pi$
$182$			23.2753i			0.127886i
$183$		−	163.312i		−	0.892416i
$184$	−5.11119	+	127.578i	−0.0277782	+	0.693359i
$185$	220.646			1.19268
$186$	4.77591			0.0256770
$187$	−251.980			−1.34749
$188$	219.744			1.16885
$189$			13.7477i			0.0727393i
$190$	−46.2499			−0.243421
$191$		−	33.4941i		−	0.175362i	−0.996149	−	0.0876810i	$-0.972054\pi$
$191$		−	33.4941i		−	0.175362i	0.996149	−	0.0876810i	$-0.0279456\pi$
$192$	28.7918			0.149957
$193$	185.943			0.963434			0.481717	−	0.876327i	$-0.340013\pi$
$193$	185.943			0.963434			0.481717	+	0.876327i	$0.340013\pi$
$194$			40.1952i			0.207192i
$195$		−	165.683i		−	0.849658i
$196$	24.1069			0.122994
$197$	−192.754			−0.978449			−0.489224	−	0.872158i	$-0.662720\pi$
$197$	−192.754			−0.978449			−0.489224	+	0.872158i	$0.662720\pi$
$198$		−	38.8369i		−	0.196146i
$199$		−	85.6702i		−	0.430503i	−0.976559	−	0.215252i	$-0.930943\pi$
$199$		−	85.6702i		−	0.430503i	0.976559	−	0.215252i	$-0.0690572\pi$
$200$	−226.257			−1.13128
$201$		−	87.7993i		−	0.436813i
$202$	19.5814			0.0969377
$203$		−	12.8390i		−	0.0632461i
$204$			86.5857i			0.424440i
$205$		−	610.574i		−	2.97841i
$206$			38.3332i			0.186083i
$207$	−2.76214	+	68.9447i	−0.0133437	+	0.333066i
$208$	113.662			0.546453
$209$	132.759			0.635210
$210$	27.7128			0.131966
$211$	−125.041			−0.592613			−0.296307	−	0.955093i	$-0.595755\pi$
$211$	−125.041			−0.592613			−0.296307	+	0.955093i	$0.595755\pi$
$212$			0.915282i			0.00431737i
$213$	−55.6362			−0.261203
$214$			140.046i			0.654420i
$215$	88.7631			0.412851
$216$	−28.8455			−0.133544
$217$		−	9.78240i		−	0.0450802i
$218$			59.4435i			0.272676i
$219$	218.068			0.995746
$220$	484.774			2.20352
$221$			171.234i			0.774812i
$222$		−	35.1467i		−	0.158319i
$223$	38.1190			0.170937			0.0854687	−	0.996341i	$-0.472761\pi$
$223$	38.1190			0.170937			0.0854687	+	0.996341i	$0.472761\pi$
$224$			77.7613i			0.347149i
$225$	−122.272			−0.543430
$226$		−	0.786493i		−	0.00348006i
$227$			388.681i			1.71225i	0.516768	+	0.856126i	$0.327135\pi$
$227$			388.681i			1.71225i	−0.516768	+	0.856126i	$0.672865\pi$
$228$		−	45.6187i		−	0.200082i
$229$			347.374i			1.51692i	0.651722	+	0.758458i	$0.274047\pi$
$229$			347.374i			1.51692i	−0.651722	+	0.758458i	$0.725953\pi$
$230$	138.980	+	5.56797i	0.604259	+	0.0242085i
$231$	−79.5488			−0.344367
$232$	26.9387			0.116115
$233$	−382.241			−1.64052			−0.820260	−	0.571991i	$-0.806171\pi$
$233$	−382.241			−1.64052			−0.820260	+	0.571991i	$0.806171\pi$
$234$	−26.3917			−0.112785
$235$		−	517.423i		−	2.20180i
$236$	−377.500			−1.59958
$237$			78.1717i			0.329838i
$238$	−28.6412			−0.120341
$239$	331.712			1.38792			0.693958	−	0.720015i	$-0.255865\pi$
$239$	331.712			1.38792			0.693958	+	0.720015i	$0.255865\pi$
$240$		−	135.333i		−	0.563886i
$241$			265.451i			1.10146i	0.834685	+	0.550728i	$0.185650\pi$
$241$			265.451i			1.10146i	−0.834685	+	0.550728i	$0.814350\pi$
$242$	134.486			0.555727
$243$	−15.5885			−0.0641500
$244$		−	324.714i		−	1.33080i
$245$		−	56.7636i		−	0.231688i
$246$	−97.2583			−0.395359
$247$		−	90.2165i		−	0.365249i
$248$	20.5255			0.0827639
$249$			206.803i			0.830534i
$250$			95.2911i			0.381164i
$251$		−	229.727i		−	0.915248i	−0.889146	−	0.457624i	$-0.848701\pi$
$251$		−	229.727i		−	0.915248i	0.889146	−	0.457624i	$-0.151299\pi$
$252$			27.3346i			0.108471i
$253$	−398.936	−	15.9827i	−1.57682	−	0.0631726i
$254$	−164.852			−0.649024
$255$	203.880			0.799530
$256$	−30.4278			−0.118859
$257$	294.228			1.14486			0.572428	−	0.819955i	$-0.306001\pi$
$257$	294.228			1.14486			0.572428	+	0.819955i	$0.306001\pi$
$258$		−	14.1391i		−	0.0548026i
$259$	−71.9903			−0.277955
$260$		−	329.429i		−	1.26703i
$261$	14.5580			0.0557778
$262$	89.8969			0.343118
$263$		−	49.5368i		−	0.188353i	−0.995556	−	0.0941764i	$-0.969978\pi$
$263$		−	49.5368i		−	0.188353i	0.995556	−	0.0941764i	$-0.0300218\pi$
$264$		−	166.910i		−	0.632233i
$265$	2.15518			0.00813276
$266$	15.0900			0.0567292
$267$		−	163.147i		−	0.611038i
$268$		−	174.572i		−	0.651387i
$269$	−407.228			−1.51386			−0.756929	−	0.653498i	$-0.773301\pi$
$269$	−407.228			−1.51386			−0.756929	+	0.653498i	$0.773301\pi$
$270$			31.4234i			0.116383i
$271$	−136.566			−0.503932			−0.251966	−	0.967736i	$-0.581077\pi$
$271$	−136.566			−0.503932			−0.251966	+	0.967736i	$0.581077\pi$
$272$			139.866i			0.514214i
$273$			54.0575i			0.198013i
$274$		−	4.69812i		−	0.0171464i
$275$		−	707.504i		−	2.57274i
$276$	−5.49198	+	137.083i	−0.0198985	+	0.496677i
$277$	108.086			0.390202			0.195101	−	0.980783i	$-0.437497\pi$
$277$	108.086			0.390202			0.195101	+	0.980783i	$0.437497\pi$
$278$	−65.1381			−0.234310
$279$	11.0922			0.0397570
$280$	119.102			0.425363
$281$		−	256.248i		−	0.911915i	−0.890001	−	0.455958i	$-0.849297\pi$
$281$		−	256.248i		−	0.911915i	0.890001	−	0.455958i	$-0.150703\pi$
$282$	−82.4202			−0.292270
$283$		−	87.9114i		−	0.310641i	−0.987864	−	0.155321i	$-0.950359\pi$
$283$		−	87.9114i		−	0.310641i	0.987864	−	0.155321i	$-0.0496410\pi$
$284$	−110.622			−0.389513
$285$	−107.417			−0.376901
$286$		−	152.711i		−	0.533954i
$287$			199.212i			0.694118i
$288$	−88.1730			−0.306156
$289$	78.2899			0.270899
$290$		−	29.3462i		−	0.101194i
$291$			93.3545i			0.320806i
$292$	433.586			1.48488
$293$			553.764i			1.88998i	0.327101	+	0.944989i	$0.393928\pi$
$293$			553.764i			1.88998i	−0.327101	+	0.944989i	$0.606072\pi$
$294$	−9.04187			−0.0307547
$295$			888.886i			3.01317i
$296$		−	151.050i		−	0.510305i
$297$		−	90.1999i		−	0.303703i
$298$		−	56.5577i		−	0.189791i
$299$	−10.8610	+	271.098i	−0.0363245	+	0.906681i
$300$	−243.113			−0.810378
$301$	−28.9607			−0.0962150
$302$	−12.8203			−0.0424514
$303$	45.4784			0.150094
$304$		−	73.6902i		−	0.242402i
$305$	−764.592			−2.50686
$306$		−	32.4761i		−	0.106131i
$307$	166.279			0.541627			0.270813	−	0.962632i	$-0.412707\pi$
$307$	166.279			0.541627			0.270813	+	0.962632i	$0.412707\pi$
$308$	−158.167			−0.513529
$309$			89.0299i			0.288123i
$310$		−	22.3598i		−	0.0721283i
$311$	−343.603			−1.10483			−0.552417	−	0.833568i	$-0.686294\pi$
$311$	−343.603			−1.10483			−0.552417	+	0.833568i	$0.686294\pi$
$312$	−113.424			−0.363537
$313$			314.795i			1.00574i	0.864363	+	0.502868i	$0.167722\pi$
$313$			314.795i			1.00574i	−0.864363	+	0.502868i	$0.832278\pi$
$314$		−	129.699i		−	0.413054i
$315$	64.3639			0.204330
$316$			155.429i			0.491864i
$317$	−401.581			−1.26682			−0.633409	−	0.773818i	$-0.718345\pi$
$317$	−401.581			−1.26682			−0.633409	+	0.773818i	$0.718345\pi$
$318$		−	0.343299i		−	0.00107956i
$319$			84.2373i			0.264067i
$320$		−	134.797i		−	0.421241i
$321$			325.261i			1.01327i
$322$	−45.3449	−	1.81666i	−0.140823	−	0.00564180i
$323$	111.015			0.343700
$324$	−30.9946			−0.0956622
$325$	−480.785			−1.47934
$326$	45.8493			0.140642
$327$			138.059i			0.422199i
$328$	−417.987			−1.27435
$329$			168.820i			0.513129i
$330$	−181.826			−0.550988
$331$	−497.047			−1.50165			−0.750827	−	0.660499i	$-0.770345\pi$
$331$	−497.047			−1.50165			−0.750827	+	0.660499i	$0.770345\pi$
$332$			411.187i			1.23851i
$333$		−	81.6293i		−	0.245133i
$334$	−144.930			−0.433923
$335$	−411.057			−1.22704
$336$			44.1550i			0.131414i
$337$			357.790i			1.06169i	0.847468	+	0.530846i	$0.178126\pi$
$337$			357.790i			1.06169i	−0.847468	+	0.530846i	$0.821874\pi$
$338$	22.2588			0.0658543
$339$		−	1.82665i		−	0.00538836i
$340$	405.376			1.19228
$341$			64.1830i			0.188220i
$342$			17.1104i			0.0500304i
$343$			18.5203i			0.0539949i
$344$		−	60.7655i		−	0.176644i
$345$	322.784	+	12.9318i	0.935606	+	0.0374834i
$346$	38.6091			0.111587
$347$	529.547			1.52607			0.763035	−	0.646357i	$-0.223708\pi$
$347$	529.547			1.52607			0.763035	+	0.646357i	$0.223708\pi$
$348$	28.9457			0.0831773
$349$	324.799			0.930657			0.465328	−	0.885138i	$-0.345936\pi$
$349$	324.799			0.930657			0.465328	+	0.885138i	$0.345936\pi$
$350$		−	80.4181i		−	0.229766i
$351$	−61.2954			−0.174631
$352$		−	510.198i		−	1.44942i
$353$	−119.472			−0.338447			−0.169224	−	0.985578i	$-0.554126\pi$
$353$	−119.472			−0.338447			−0.169224	+	0.985578i	$0.554126\pi$
$354$	141.591			0.399973
$355$			260.477i			0.733737i
$356$		−	324.386i		−	0.911197i
$357$	−66.5200			−0.186331
$358$	214.920			0.600335
$359$			32.2603i			0.0898616i	0.998990	+	0.0449308i	$0.0143067\pi$
$359$			32.2603i			0.0898616i	−0.998990	+	0.0449308i	$0.985693\pi$
$360$			135.048i			0.375135i
$361$	302.510			0.837979
$362$		−	63.8406i		−	0.176355i
$363$	312.347			0.860461
$364$			107.483i			0.295282i
$365$		−	1020.95i		−	2.79712i
$366$			121.792i			0.332765i
$367$			10.7331i			0.0292455i	0.999893	+	0.0146228i	$0.00465474\pi$
$367$			10.7331i			0.0292455i	−0.999893	+	0.0146228i	$0.995345\pi$
$368$	−8.87146	+	221.437i	−0.0241072	+	0.601730i
$369$	−225.885			−0.612155
$370$	−164.549			−0.444728
$371$	−0.703171			−0.00189534
$372$	22.0546			0.0592867
$373$		−	209.138i		−	0.560693i	−0.959899	−	0.280346i	$-0.909551\pi$
$373$		−	209.138i		−	0.560693i	0.959899	−	0.280346i	$-0.0904493\pi$
$374$	187.917			0.502452
$375$			221.316i			0.590177i
$376$	−354.218			−0.942069
$377$	57.2436			0.151840
$378$		−	10.2525i		−	0.0271231i
$379$		−	227.488i		−	0.600232i	−0.953903	−	0.300116i	$-0.902975\pi$
$379$		−	227.488i		−	0.600232i	0.953903	−	0.300116i	$-0.0970254\pi$
$380$	−213.577			−0.562045
$381$	−382.874			−1.00492
$382$			24.9786i			0.0653891i
$383$		−	358.454i		−	0.935910i	−0.883752	−	0.467955i	$-0.844991\pi$
$383$		−	358.454i		−	0.935910i	0.883752	−	0.467955i	$-0.155009\pi$
$384$	−225.099			−0.586194
$385$			372.430i			0.967351i
$386$	−138.669			−0.359246
$387$		−	32.8384i		−	0.0848537i
$388$			185.617i			0.478394i
$389$		−	320.157i		−	0.823025i	−0.911404	−	0.411512i	$-0.865001\pi$
$389$		−	320.157i		−	0.823025i	0.911404	−	0.411512i	$-0.134999\pi$
$390$			123.560i			0.316821i
$391$	−333.597	−	13.3650i	−0.853189	−	0.0341815i
$392$	−38.8593			−0.0991308
$393$	208.788			0.531268
$394$	143.749			0.364844
$395$	365.983			0.926539
$396$		−	179.345i		−	0.452890i
$397$	636.060			1.60217			0.801083	−	0.598554i	$-0.204258\pi$
$397$	636.060			1.60217			0.801083	+	0.598554i	$0.204258\pi$
$398$			63.8894i			0.160526i
$399$	35.0469			0.0878368
$400$	−392.713			−0.981782
$401$		−	491.403i		−	1.22544i	−0.790299	−	0.612721i	$-0.790075\pi$
$401$		−	491.403i		−	1.22544i	0.790299	−	0.612721i	$-0.209925\pi$
$402$			65.4773i			0.162879i
$403$	43.6157			0.108227
$404$	90.4248			0.223824
$405$			72.9818i			0.180202i
$406$			9.57479i			0.0235832i
$407$	472.334			1.16053
$408$		−	139.573i		−	0.342089i
$409$	−519.008			−1.26897			−0.634484	−	0.772936i	$-0.718787\pi$
$409$	−519.008			−1.26897			−0.634484	+	0.772936i	$0.718787\pi$
$410$			455.342i			1.11059i
$411$		−	10.9115i		−	0.0265487i
$412$			177.018i			0.429656i
$413$		−	290.017i		−	0.702220i
$414$	2.05990	−	51.4162i	0.00497560	−	0.124194i
$415$	968.206			2.33303
$416$	−346.705			−0.833426
$417$	−151.285			−0.362794
$418$	−99.0064			−0.236857
$419$			287.924i			0.687170i	0.939122	+	0.343585i	$0.111641\pi$
$419$			287.924i			0.687170i	−0.939122	+	0.343585i	$0.888359\pi$
$420$	127.975			0.304702
$421$		−	534.001i		−	1.26841i	−0.773165	−	0.634206i	$-0.781327\pi$
$421$		−	534.001i		−	1.26841i	0.773165	−	0.634206i	$-0.218673\pi$
$422$	93.2509			0.220974
$423$	−191.423			−0.452538
$424$		−	1.47540i		−	0.00347971i
$425$		−	591.627i		−	1.39206i
$426$	41.4913			0.0973974
$427$	249.464			0.584224
$428$			646.717i			1.51102i
$429$		−	354.675i		−	0.826749i
$430$	−66.1960			−0.153944
$431$			513.030i			1.19033i	0.803605	+	0.595163i	$0.202912\pi$
$431$			513.030i			1.19033i	−0.803605	+	0.595163i	$0.797088\pi$
$432$	−50.0670			−0.115896
$433$		−	762.021i		−	1.75986i	−0.475101	−	0.879931i	$-0.657588\pi$
$433$		−	762.021i		−	1.75986i	0.475101	−	0.879931i	$-0.342412\pi$
$434$			7.29533i			0.0168095i
$435$		−	68.1574i		−	0.156684i
$436$			274.503i			0.629595i
$437$	175.760	+	7.04149i	0.402196	+	0.0161133i
$438$	−162.627			−0.371294
$439$	−486.445			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$439$	−486.445			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$440$	−781.434			−1.77599
$441$	−21.0000			−0.0476190
$442$		−	127.699i		−	0.288912i
$443$	568.520			1.28334			0.641670	−	0.766981i	$-0.278242\pi$
$443$	568.520			1.28334			0.641670	+	0.766981i	$0.278242\pi$
$444$		−	162.304i		−	0.365549i
$445$	−763.820			−1.71645
$446$	−28.4277			−0.0637392
$447$		−	131.357i		−	0.293863i
$448$			43.9802i			0.0981701i
$449$	181.778			0.404850			0.202425	−	0.979298i	$-0.435118\pi$
$449$	181.778			0.404850			0.202425	+	0.979298i	$0.435118\pi$
$450$	91.1855			0.202634
$451$		−	1307.04i		−	2.89810i
$452$		−	3.63194i		−	0.00803526i
$453$	−29.7756			−0.0657298
$454$		−	289.863i		−	0.638465i
$455$	253.085			0.556232
$456$			73.5355i			0.161262i
$457$			842.429i			1.84339i	0.387915	+	0.921695i	$0.373195\pi$
$457$			842.429i			1.84339i	−0.387915	+	0.921695i	$0.626805\pi$
$458$		−	259.058i		−	0.565628i
$459$		−	75.4266i		−	0.164328i
$460$	641.792	+	25.7123i	1.39520	+	0.0558962i
$461$	−819.955			−1.77865			−0.889323	−	0.457281i	$-0.848824\pi$
$461$	−819.955			−1.77865			−0.889323	+	0.457281i	$0.848824\pi$
$462$	59.3244			0.128408
$463$	598.844			1.29340			0.646700	−	0.762745i	$-0.276149\pi$
$463$	598.844			1.29340			0.646700	+	0.762745i	$0.276149\pi$
$464$	46.7574			0.100770
$465$		−	51.9313i		−	0.111680i
$466$	285.060			0.611718
$467$			688.578i			1.47447i	0.675636	+	0.737236i	$0.263869\pi$
$467$			688.578i			1.47447i	−0.675636	+	0.737236i	$0.736131\pi$
$468$	−121.874			−0.260414
$469$	134.116			0.285961
$470$			385.874i			0.821008i
$471$		−	301.230i		−	0.639554i
$472$	608.514			1.28923
$473$	190.013			0.401720
$474$		−	58.2974i		−	0.122990i
$475$			311.706i			0.656223i
$476$	−132.262			−0.277861
$477$		−	0.797321i		−	0.00167153i
$478$	−247.378			−0.517527
$479$			515.560i			1.07633i	0.842841	+	0.538163i	$0.180882\pi$
$479$			515.560i			1.07633i	−0.842841	+	0.538163i	$0.819118\pi$
$480$			412.807i			0.860014i
$481$		−	320.975i		−	0.667308i
$482$		−	197.963i		−	0.410712i
$483$	−105.315	−	4.21925i	−0.218043	−	0.00873550i
$484$	621.041			1.28314
$485$	437.066			0.901166
$486$	11.6253			0.0239203
$487$	42.9540			0.0882013			0.0441007	−	0.999027i	$-0.485958\pi$
$487$	42.9540			0.0882013			0.0441007	+	0.999027i	$0.485958\pi$
$488$			523.425i			1.07259i
$489$	106.486			0.217763
$490$			42.3321i			0.0863920i
$491$	16.5663			0.0337400			0.0168700	−	0.999858i	$-0.494630\pi$
$491$	16.5663			0.0337400			0.0168700	+	0.999858i	$0.494630\pi$
$492$	−449.128			−0.912862
$493$			70.4406i			0.142882i
$494$			67.2799i			0.136194i
$495$	−422.296			−0.853123
$496$	35.6259			0.0718265
$497$		−	84.9857i		−	0.170997i
$498$		−	154.225i		−	0.309690i
$499$	410.775			0.823196			0.411598	−	0.911366i	$-0.364971\pi$
$499$	410.775			0.823196			0.411598	+	0.911366i	$0.364971\pi$
$500$			440.044i			0.880088i
$501$	−336.605			−0.671866
$502$			171.322i			0.341278i
$503$			707.969i			1.40749i	0.710452	+	0.703746i	$0.248491\pi$
$503$			707.969i			1.40749i	−0.710452	+	0.703746i	$0.751509\pi$
$504$		−	44.0623i		−	0.0874251i
$505$		−	212.920i		−	0.421624i
$506$	297.511	+	11.9192i	0.587966	+	0.0235558i
$507$	51.6966			0.101966
$508$	−761.269			−1.49856
$509$	928.365			1.82390			0.911950	−	0.410301i	$-0.134576\pi$
$509$	928.365			1.82390			0.911950	+	0.410301i	$0.134576\pi$
$510$	−152.046			−0.298129
$511$			333.105i			0.651869i
$512$	−497.151			−0.970998
$513$			39.7394i			0.0774648i
$514$	−219.424			−0.426895
$515$	416.819			0.809357
$516$		−	65.2926i		−	0.126536i
$517$		−	1107.64i		−	2.14243i
$518$	53.6875			0.103644
$519$	89.6707			0.172776
$520$			531.025i			1.02120i
$521$			268.873i			0.516070i	0.966136	+	0.258035i	$0.0830750\pi$
$521$			268.873i			0.516070i	−0.966136	+	0.258035i	$0.916925\pi$
$522$	−10.8568			−0.0207984
$523$			807.315i			1.54362i	0.635851	+	0.771812i	$0.280649\pi$
$523$			807.315i			1.54362i	−0.635851	+	0.771812i	$0.719351\pi$
$524$	415.134			0.792241
$525$		−	186.773i		−	0.355759i
$526$			36.9426i			0.0702330i
$527$			53.6709i			0.101842i
$528$		−	289.704i		−	0.548682i
$529$	−527.305	−	42.3189i	−0.996795	−	0.0799980i
$530$	−1.60725			−0.00303255
$531$	328.848			0.619300
$532$	69.6838			0.130985
$533$	−888.204			−1.66642
$534$			121.669i			0.227844i
$535$	1522.80			2.84635
$536$			281.402i			0.525004i
$537$	499.158			0.929530
$538$	303.694			0.564488
$539$		−	121.513i		−	0.225441i
$540$			145.110i			0.268722i
$541$	−78.0316			−0.144236			−0.0721179	−	0.997396i	$-0.522976\pi$
$541$	−78.0316			−0.144236			−0.0721179	+	0.997396i	$0.522976\pi$
$542$	101.845			0.187906
$543$		−	148.272i		−	0.273060i
$544$		−	426.636i		−	0.784257i
$545$	646.363			1.18599
$546$		−	40.3140i		−	0.0738351i
$547$	417.888			0.763963			0.381982	−	0.924170i	$-0.375242\pi$
$547$	417.888			0.763963			0.381982	+	0.924170i	$0.375242\pi$
$548$		−	21.6954i		−	0.0395902i
$549$			282.865i			0.515237i
$550$			527.629i			0.959325i
$551$		−	37.1125i		−	0.0673548i
$552$	8.85284	−	220.972i	0.0160377	−	0.400311i
$553$	−119.409			−0.215930
$554$	−80.6063			−0.145499
$555$	−382.171			−0.688596
$556$	−300.801			−0.541008
$557$		−	895.207i		−	1.60719i	−0.595173	−	0.803597i	$-0.702917\pi$
$557$		−	895.207i		−	1.60719i	0.595173	−	0.803597i	$-0.297083\pi$
$558$	−8.27212			−0.0148246
$559$		−	129.124i		−	0.230991i
$560$	206.724			0.369150
$561$	436.443			0.777973
$562$			191.100i			0.340035i
$563$			537.325i			0.954396i	0.878796	+	0.477198i	$0.158347\pi$
$563$			537.325i			0.954396i	−0.878796	+	0.477198i	$0.841653\pi$
$564$	−380.608			−0.674836
$565$	−8.55199			−0.0151363
$566$			65.5609i			0.115832i
$567$		−	23.8118i		−	0.0419961i
$568$	178.317			0.313939
$569$			348.018i			0.611632i	0.952091	+	0.305816i	$0.0989292\pi$
$569$			348.018i			0.611632i	−0.952091	+	0.305816i	$0.901071\pi$
$570$	80.1072			0.140539
$571$			660.161i			1.15615i	0.815984	+	0.578075i	$0.196196\pi$
$571$			660.161i			1.15615i	−0.815984	+	0.578075i	$0.803804\pi$
$572$		−	705.202i		−	1.23287i
$573$			58.0136i			0.101245i
$574$		−	148.564i		−	0.258823i
$575$	37.5258	−	936.666i	0.0652623	−	1.62898i
$576$	−49.8689			−0.0865779
$577$	285.015			0.493960			0.246980	−	0.969021i	$-0.420562\pi$
$577$	285.015			0.493960			0.246980	+	0.969021i	$0.420562\pi$
$578$	−58.3856			−0.101013
$579$	−322.062			−0.556239
$580$		−	135.518i		−	0.233651i
$581$	−315.897			−0.543712
$582$		−	69.6201i		−	0.119622i
$583$	4.61356			0.00791347
$584$	−698.922			−1.19678
$585$			286.972i			0.490550i
$586$		−	412.975i		−	0.704736i
$587$	−446.694			−0.760978			−0.380489	−	0.924785i	$-0.624244\pi$
$587$	−446.694			−0.760978			−0.380489	+	0.924785i	$0.624244\pi$
$588$	−41.7544			−0.0710108
$589$		−	28.2772i		−	0.0480088i
$590$		−	662.896i		−	1.12355i
$591$	333.860			0.564908
$592$		−	262.177i		−	0.442867i
$593$	19.3952			0.0327069			0.0163534	−	0.999866i	$-0.494794\pi$
$593$	19.3952			0.0327069			0.0163534	+	0.999866i	$0.494794\pi$
$594$			67.2675i			0.113245i
$595$			311.432i			0.523416i
$596$		−	261.177i		−	0.438217i
$597$			148.385i			0.248551i
$598$	8.09974	−	202.174i	0.0135447	−	0.338084i
$599$	506.473			0.845530			0.422765	−	0.906239i	$-0.361059\pi$
$599$	506.473			0.845530			0.422765	+	0.906239i	$0.361059\pi$
$600$	391.888			0.653147
$601$	425.353			0.707742			0.353871	−	0.935294i	$-0.384865\pi$
$601$	425.353			0.707742			0.353871	+	0.935294i	$0.384865\pi$
$602$	21.5978			0.0358767
$603$			152.073i			0.252194i
$604$	−59.2029			−0.0980180
$605$		−	1462.34i		−	2.41710i
$606$	−33.9160			−0.0559670
$607$	633.633			1.04388			0.521938	−	0.852983i	$-0.325209\pi$
$607$	633.633			1.04388			0.521938	+	0.852983i	$0.325209\pi$
$608$			224.778i			0.369701i
$609$			22.2377i			0.0365151i
$610$	570.203			0.934759
$611$	−752.697			−1.23191
$612$		−	149.971i		−	0.245050i
$613$		−	25.9856i		−	0.0423909i	−0.999775	−	0.0211954i	$-0.993253\pi$
$613$		−	25.9856i		−	0.0423909i	0.999775	−	0.0211954i	$-0.00674722\pi$
$614$	−124.005			−0.201962
$615$			1057.54i			1.71959i
$616$	254.959			0.413894
$617$		−	158.782i		−	0.257345i	−0.991687	−	0.128672i	$-0.958928\pi$
$617$		−	158.782i		−	0.257345i	0.991687	−	0.128672i	$-0.0410715\pi$
$618$		−	66.3950i		−	0.107435i
$619$		−	801.920i		−	1.29551i	−0.761849	−	0.647755i	$-0.775708\pi$
$619$		−	801.920i		−	1.29551i	0.761849	−	0.647755i	$-0.224292\pi$
$620$		−	103.255i		−	0.166540i
$621$	4.78417	−	119.416i	0.00770399	−	0.192296i
$622$	256.246			0.411971
$623$	249.212			0.400018
$624$	−196.869			−0.315495
$625$	17.2234			0.0275574
$626$		−	234.762i		−	0.375019i
$627$	−229.945			−0.366739
$628$		−	598.936i		−	0.953720i
$629$	394.973			0.627938
$630$	−48.0000			−0.0761906
$631$			755.002i			1.19652i	0.801303	+	0.598258i	$0.204140\pi$
$631$			755.002i			1.19652i	−0.801303	+	0.598258i	$0.795860\pi$
$632$		−	250.545i		−	0.396432i
$633$	216.578			0.342145
$634$	299.483			0.472371
$635$			1792.53i			2.82289i
$636$		−	1.58531i		−	0.00249263i
$637$	−82.5742			−0.129630
$638$		−	62.8209i		−	0.0984653i
$639$	96.3647			0.150805
$640$			1053.86i			1.64666i
$641$			474.103i			0.739631i	0.929105	+	0.369815i	$0.120579\pi$
$641$			474.103i			0.739631i	−0.929105	+	0.369815i	$0.879421\pi$
$642$		−	242.567i		−	0.377830i
$643$		−	92.0437i		−	0.143147i	−0.997435	−	0.0715737i	$-0.977198\pi$
$643$		−	92.0437i		−	0.143147i	0.997435	−	0.0715737i	$-0.0228021\pi$
$644$	−209.398	−	8.38914i	−0.325152	−	0.0130266i
$645$	−153.742			−0.238360
$646$	−82.7907			−0.128159
$647$	861.523			1.33156			0.665782	−	0.746146i	$-0.268098\pi$
$647$	861.523			1.33156			0.665782	+	0.746146i	$0.268098\pi$
$648$	49.9619			0.0771017
$649$			1902.82i			2.93193i
$650$	358.551			0.551617
$651$			16.9436i			0.0260270i
$652$	211.727			0.324735
$653$	946.887			1.45006			0.725028	−	0.688719i	$-0.241827\pi$
$653$	946.887			1.45006			0.725028	+	0.688719i	$0.241827\pi$
$654$		−	102.959i		−	0.157430i
$655$		−	977.501i		−	1.49237i
$656$	−725.498			−1.10594
$657$	−377.706			−0.574894
$658$		−	125.899i		−	0.191336i
$659$		−	284.771i		−	0.432126i	−0.976379	−	0.216063i	$-0.930678\pi$
$659$		−	284.771i		−	0.432126i	0.976379	−	0.216063i	$-0.0693217\pi$
$660$	−839.652			−1.27220
$661$			193.575i			0.292852i	0.989222	+	0.146426i	$0.0467771\pi$
$661$			193.575i			0.292852i	−0.989222	+	0.146426i	$0.953223\pi$
$662$	370.678			0.559937
$663$		−	296.585i		−	0.447338i
$664$		−	662.815i		−	0.998216i
$665$		−	164.082i		−	0.246740i
$666$			60.8759i			0.0914053i
$667$	−4.46792	+	111.522i	−0.00669854	+	0.167199i
$668$	−669.272			−1.00190
$669$	−66.0241			−0.0986907
$670$	306.550			0.457538
$671$	−1636.75			−2.43927
$672$		−	134.686i		−	0.200426i
$673$	913.275			1.35702			0.678511	−	0.734590i	$-0.262626\pi$
$673$	913.275			1.35702			0.678511	+	0.734590i	$0.262626\pi$
$674$		−	266.826i		−	0.395884i
$675$	211.781			0.313750
$676$	102.788			0.152054
$677$			286.078i			0.422567i	0.977425	+	0.211284i	$0.0677644\pi$
$677$			286.078i			0.422567i	−0.977425	+	0.211284i	$0.932236\pi$
$678$			1.36225i			0.00200921i
$679$	−142.601			−0.210017
$680$	−653.448			−0.960953
$681$		−	673.215i		−	0.988569i
$682$		−	47.8652i		−	0.0701836i
$683$	950.616			1.39182			0.695912	−	0.718127i	$-0.255000\pi$
$683$	950.616			1.39182			0.695912	+	0.718127i	$0.255000\pi$
$684$			79.0140i			0.115518i
$685$	−51.0854			−0.0745772
$686$		−	13.8117i		−	0.0201336i
$687$		−	601.669i		−	0.875791i
$688$		−	105.470i		−	0.153300i
$689$		−	3.13515i		−	0.00455029i
$690$	−240.720	−	9.64400i	−0.348869	−	0.0139768i
$691$	−742.374			−1.07435			−0.537174	−	0.843472i	$-0.680508\pi$
$691$	−742.374			−1.07435			−0.537174	+	0.843472i	$0.680508\pi$
$692$	178.292			0.257648
$693$	137.783			0.198820
$694$	−394.915			−0.569042
$695$			708.284i			1.01911i
$696$	−46.6592			−0.0670391
$697$		−	1092.97i		−	1.56811i
$698$	−242.223			−0.347024
$699$	662.061			0.947155
$700$		−	371.362i		−	0.530517i
$701$			270.705i			0.386169i	0.981182	+	0.193085i	$0.0618492\pi$
$701$			270.705i			0.386169i	−0.981182	+	0.193085i	$0.938151\pi$
$702$	45.7117			0.0651164
$703$	−208.096			−0.296012
$704$		−	288.557i		−	0.409883i
$705$			896.203i			1.27121i
$706$	89.0974			0.126200
$707$			69.4694i			0.0982594i
$708$	653.850			0.923517
$709$			392.483i			0.553572i	0.960932	+	0.276786i	$0.0892694\pi$
$709$			392.483i			0.553572i	−0.960932	+	0.276786i	$0.910731\pi$
$710$		−	194.253i		−	0.273596i
$711$		−	135.397i		−	0.190432i
$712$			522.896i			0.734405i
$713$	−3.40425	+	84.9720i	−0.00477454	+	0.119175i
$714$	49.6080			0.0694790
$715$	−1660.51			−2.32239
$716$	992.477			1.38614
$717$	−574.542			−0.801314
$718$		−	24.0585i		−	0.0335076i
$719$	126.909			0.176507			0.0882536	−	0.996098i	$-0.471871\pi$
$719$	126.909			0.176507			0.0882536	+	0.996098i	$0.471871\pi$
$720$			234.403i			0.325560i
$721$	−135.995			−0.188621
$722$	−225.600			−0.312466
$723$		−	459.775i		−	0.635926i
$724$		−	294.809i		−	0.407194i
$725$	−197.781			−0.272802
$726$	−232.936			−0.320849
$727$		−	335.134i		−	0.460982i	−0.973075	−	0.230491i	$-0.925967\pi$
$727$		−	335.134i		−	0.460982i	0.973075	−	0.230491i	$-0.0740332\pi$
$728$		−	173.257i		−	0.237991i
$729$	27.0000			0.0370370
$730$			761.384i			1.04299i
$731$	158.892			0.217363
$732$			562.421i			0.768335i
$733$		−	839.520i		−	1.14532i	−0.819793	−	0.572660i	$-0.805911\pi$
$733$		−	839.520i		−	1.14532i	0.819793	−	0.572660i	$-0.194089\pi$
$734$		−	8.00433i		−	0.0109051i
$735$			98.3174i			0.133765i
$736$	27.0607	−	675.451i	0.0367673	−	0.917733i
$737$	−879.943			−1.19395
$738$	168.456			0.228260
$739$	146.458			0.198184			0.0990921	−	0.995078i	$-0.468406\pi$
$739$	146.458			0.198184			0.0990921	+	0.995078i	$0.468406\pi$
$740$	−759.871			−1.02685
$741$			156.260i			0.210877i
$742$	0.524397			0.000706735
$743$		−	1227.58i		−	1.65219i	−0.563531	−	0.826095i	$-0.690558\pi$
$743$		−	1227.58i		−	1.65219i	0.563531	−	0.826095i	$-0.309442\pi$
$744$	−35.5511			−0.0477838
$745$	−614.985			−0.825483
$746$			155.967i			0.209071i
$747$		−	358.193i		−	0.479509i
$748$	867.780			1.16013
$749$	−496.844			−0.663343
$750$		−	165.049i		−	0.220065i
$751$		−	5.77510i		−	0.00768987i	−0.999993	−	0.00384494i	$-0.998776\pi$
$751$		−	5.77510i		−	0.00768987i	0.999993	−	0.00384494i	$-0.00122388\pi$
$752$	−614.814			−0.817572
$753$			397.899i			0.528419i
$754$	−42.6900			−0.0566180
$755$			139.403i			0.184640i
$756$		−	47.3450i		−	0.0626256i
$757$		−	451.516i		−	0.596455i	−0.954495	−	0.298227i	$-0.903605\pi$
$757$		−	451.516i		−	0.596455i	0.954495	−	0.298227i	$-0.0963954\pi$
$758$			169.652i			0.223815i
$759$	690.978	+	27.6828i	0.910379	+	0.0364727i
$760$	344.277			0.452996
$761$	258.765			0.340033			0.170016	−	0.985441i	$-0.445618\pi$
$761$	258.765			0.340033			0.170016	+	0.985441i	$0.445618\pi$
$762$	285.532			0.374714
$763$	−210.889			−0.276394
$764$			115.349i			0.150980i
$765$	−353.131			−0.461609
$766$			267.321i			0.348983i
$767$	1293.07			1.68587
$768$	52.7025			0.0686230
$769$			295.640i			0.384447i	0.981351	+	0.192223i	$0.0615698\pi$
$769$			295.640i			0.384447i	−0.981351	+	0.192223i	$0.938430\pi$
$770$		−	277.744i		−	0.360706i
$771$	−509.618			−0.660983
$772$	−640.357			−0.829478
$773$			1385.11i			1.79186i	0.444195	+	0.895930i	$0.353490\pi$
$773$			1385.11i			1.79186i	−0.444195	+	0.895930i	$0.646510\pi$
$774$			24.4896i			0.0316403i
$775$	−150.696			−0.194446
$776$		−	299.207i		−	0.385576i
$777$	124.691			0.160477
$778$			238.760i			0.306890i
$779$			575.845i			0.739211i
$780$			570.587i			0.731522i
$781$			557.597i			0.713953i
$782$	248.784	+	9.96707i	0.318138	+	0.0127456i
$783$	−25.2152			−0.0322033
$784$	−67.4478			−0.0860304
$785$	−1410.29			−1.79655
$786$	−155.706			−0.198099
$787$		−	548.275i		−	0.696665i	−0.937371	−	0.348332i	$-0.886748\pi$
$787$		−	548.275i		−	0.696665i	0.937371	−	0.348332i	$-0.113252\pi$
$788$	663.815			0.842405
$789$			85.8002i			0.108746i
$790$	−272.936			−0.345488
$791$	2.79026			0.00352751
$792$			289.096i			0.365020i
$793$			1112.25i			1.40259i
$794$	−474.348			−0.597416
$795$	−3.73288			−0.00469545
$796$			295.034i			0.370646i
$797$		−	78.2129i		−	0.0981341i	−0.998795	−	0.0490670i	$-0.984375\pi$
$797$		−	78.2129i		−	0.0981341i	0.998795	−	0.0490670i	$-0.0156248\pi$
$798$	−26.1366			−0.0327526
$799$		−	926.225i		−	1.15923i
$800$	1197.90			1.49737
$801$			282.579i			0.352783i
$802$			366.469i			0.456944i
$803$		−	2185.53i		−	2.72170i
$804$			302.367i			0.376078i
$805$	−19.7536	+	493.061i	−0.0245386	+	0.612498i
$806$	−32.5269			−0.0403559
$807$	705.339			0.874026
$808$	−145.761			−0.180397
$809$	514.417			0.635868			0.317934	−	0.948113i	$-0.397011\pi$
$809$	514.417			0.635868			0.317934	+	0.948113i	$0.397011\pi$
$810$		−	54.4269i		−	0.0671938i
$811$	1305.27			1.60946			0.804731	−	0.593640i	$-0.202310\pi$
$811$	1305.27			1.60946			0.804731	+	0.593640i	$0.202310\pi$
$812$			44.2153i			0.0544523i
$813$	236.539			0.290945
$814$	−352.248			−0.432737
$815$		−	498.546i		−	0.611712i
$816$		−	242.255i		−	0.296881i
$817$	−83.7144			−0.102466
$818$	387.056			0.473173
$819$		−	93.6303i		−	0.114323i
$820$			2102.72i			2.56429i
$821$	−920.132			−1.12075			−0.560373	−	0.828240i	$-0.689342\pi$
$821$	−920.132			−1.12075			−0.560373	+	0.828240i	$0.689342\pi$
$822$			8.13739i			0.00989950i
$823$	−1234.57			−1.50009			−0.750045	−	0.661387i	$-0.769968\pi$
$823$	−1234.57			−1.50009			−0.750045	+	0.661387i	$0.769968\pi$
$824$		−	285.346i		−	0.346294i
$825$			1225.43i			1.48537i
$826$			216.283i			0.261844i
$827$			830.171i			1.00383i	0.864916	+	0.501917i	$0.167372\pi$
$827$			830.171i			1.00383i	−0.864916	+	0.501917i	$0.832628\pi$
$828$	9.51239	−	237.435i	0.0114884	−	0.286757i
$829$	−925.808			−1.11678			−0.558388	−	0.829580i	$-0.688580\pi$
$829$	−925.808			−1.11678			−0.558388	+	0.829580i	$0.688580\pi$
$830$	−722.050			−0.869940
$831$	−187.210			−0.225283
$832$	−196.090			−0.235685
$833$		−	101.611i		−	0.121982i
$834$	112.822			0.135279
$835$			1575.91i			1.88732i
$836$	−457.200			−0.546891
$837$	−19.2122			−0.0229537
$838$		−	214.723i		−	0.256232i
$839$		−	31.1776i		−	0.0371604i	−0.999827	−	0.0185802i	$-0.994085\pi$
$839$		−	31.1776i		−	0.0371604i	0.999827	−	0.0185802i	$-0.00591461\pi$
$840$	−206.290			−0.245583
$841$	−817.452			−0.972000
$842$			398.237i			0.472966i
$843$			443.835i			0.526495i
$844$	430.623			0.510216
$845$		−	242.032i		−	0.286429i
$846$	142.756			0.168742
$847$			477.118i			0.563304i
$848$		−	2.56084i		−	0.00301985i
$849$			152.267i			0.179349i
$850$			441.212i			0.519073i
$851$	625.323	+	25.0524i	0.734810	+	0.0294388i
$852$	191.602			0.224885
$853$	−253.172			−0.296802			−0.148401	−	0.988927i	$-0.547413\pi$
$853$	−253.172			−0.296802			−0.148401	+	0.988927i	$0.547413\pi$
$854$	−186.040			−0.217846
$855$	186.051			0.217604
$856$		−	1042.48i		−	1.21785i
$857$	−35.3789			−0.0412823			−0.0206412	−	0.999787i	$-0.506571\pi$
$857$	−35.3789			−0.0412823			−0.0206412	+	0.999787i	$0.506571\pi$
$858$			264.503i			0.308278i
$859$	−1087.85			−1.26642			−0.633210	−	0.773980i	$-0.718263\pi$
$859$	−1087.85			−1.26642			−0.633210	+	0.773980i	$0.718263\pi$
$860$	−305.686			−0.355449
$861$		−	345.045i		−	0.400749i
$862$		−	382.598i		−	0.443849i
$863$	−76.3577			−0.0884794			−0.0442397	−	0.999021i	$-0.514087\pi$
$863$	−76.3577			−0.0884794			−0.0442397	+	0.999021i	$0.514087\pi$
$864$	152.720			0.176759
$865$		−	419.819i		−	0.485339i
$866$			568.285i			0.656218i
$867$	−135.602			−0.156404
$868$			33.6890i			0.0388122i
$869$	783.453			0.901557
$870$			50.8291i			0.0584243i
$871$			597.966i			0.686529i
$872$		−	442.488i		−	0.507440i
$873$		−	161.695i		−	0.185217i
$874$	−131.075	−	5.25127i	−0.149971	−	0.00600832i
$875$	−338.066			−0.386362
$876$	−750.993			−0.857298
$877$	−260.023			−0.296491			−0.148246	−	0.988951i	$-0.547363\pi$
$877$	−260.023			−0.296491			−0.148246	+	0.988951i	$0.547363\pi$
$878$	362.772			0.413180
$879$		−	959.147i		−	1.09118i
$880$	−1356.33			−1.54129
$881$		−	171.372i		−	0.194520i	−0.995259	−	0.0972598i	$-0.968992\pi$
$881$		−	171.372i		−	0.194520i	0.995259	−	0.0972598i	$-0.0310078\pi$
$882$	15.6610			0.0177562
$883$	−1303.61			−1.47634			−0.738168	−	0.674616i	$-0.764309\pi$
$883$	−1303.61			−1.47634			−0.738168	+	0.674616i	$0.764309\pi$
$884$		−	589.701i		−	0.667083i
$885$		−	1539.60i		−	1.73966i
$886$	−423.980			−0.478532
$887$	10.4214			0.0117490			0.00587452	−	0.999983i	$-0.498130\pi$
$887$	10.4214			0.0117490			0.00587452	+	0.999983i	$0.498130\pi$
$888$			261.627i			0.294625i
$889$		−	584.850i		−	0.657873i
$890$	569.627			0.640030
$891$			156.231i			0.175343i
$892$	−131.276			−0.147170
$893$			487.993i			0.546464i
$894$			97.9609i			0.109576i
$895$		−	2336.95i		−	2.61112i
$896$		−	343.844i		−	0.383754i
$897$	18.8119	−	469.555i	0.0209720	−	0.523473i
$898$	−135.563			−0.150961
$899$	17.9422			0.0199580
$900$	421.085			0.467872
$901$	3.85793			0.00428183
$902$			974.742i			1.08065i
$903$	50.1614			0.0555498
$904$			5.85453i			0.00647625i
$905$	−694.175			−0.767044
$906$	22.2055			0.0245093
$907$		−	1765.32i		−	1.94633i	−0.230117	−	0.973163i	$-0.573911\pi$
$907$		−	1765.32i		−	1.94633i	0.230117	−	0.973163i	$-0.426089\pi$
$908$		−	1338.56i		−	1.47418i
$909$	−78.7709			−0.0866566
$910$	−188.741			−0.207408
$911$			1118.37i			1.22763i	0.789452	+	0.613813i	$0.210365\pi$
$911$			1118.37i			1.22763i	−0.789452	+	0.613813i	$0.789635\pi$
$912$			127.635i			0.139951i
$913$	2072.62			2.27012
$914$		−	628.251i		−	0.687364i
$915$	1324.31			1.44734
$916$		−	1196.30i		−	1.30600i
$917$			318.929i			0.347796i
$918$			56.2502i			0.0612747i
$919$		−	324.342i		−	0.352929i	−0.984307	−	0.176464i	$-0.943534\pi$
$919$		−	324.342i		−	0.352929i	0.984307	−	0.176464i	$-0.0564660\pi$
$920$	−1034.54	−	41.4471i	−1.12450	−	0.0450511i
$921$	−288.004			−0.312708
$922$	611.491			0.663222
$923$	378.916			0.410527
$924$	273.953			0.296486
$925$			1109.00i			1.19891i
$926$	−446.594			−0.482283
$927$		−	154.204i		−	0.166348i
$928$	−142.625			−0.153690
$929$	713.804			0.768357			0.384179	−	0.923259i	$-0.374485\pi$
$929$	713.804			0.768357			0.384179	+	0.923259i	$0.374485\pi$
$930$			38.7283i			0.0416433i
$931$			53.5350i			0.0575027i
$932$	1316.38			1.41242
$933$	595.138			0.637876
$934$		−	513.515i		−	0.549801i
$935$		−	2043.33i		−	2.18538i
$936$	196.455			0.209888
$937$			1505.22i			1.60642i	0.595696	+	0.803210i	$0.296876\pi$
$937$			1505.22i			1.60642i	−0.595696	+	0.803210i	$0.703124\pi$
$938$	−100.018			−0.106629
$939$		−	545.241i		−	0.580662i
$940$			1781.92i			1.89566i
$941$			295.128i			0.313632i	0.987628	+	0.156816i	$0.0501230\pi$
$941$			295.128i			0.313632i	−0.987628	+	0.156816i	$0.949877\pi$
$942$			224.645i			0.238477i
$943$	69.3253	−	1730.40i	0.0735156	−	1.83499i
$944$	1056.20			1.11885
$945$	−111.481			−0.117970
$946$	−141.705			−0.149793
$947$	−902.823			−0.953350			−0.476675	−	0.879080i	$-0.658158\pi$
$947$	−902.823			−0.953350			−0.476675	+	0.879080i	$0.658158\pi$
$948$		−	269.211i		−	0.283978i
$949$	−1485.18			−1.56499
$950$		−	232.458i		−	0.244692i
$951$	695.559			0.731397
$952$	213.201			0.223950
$953$			511.572i			0.536802i	0.963307	+	0.268401i	$0.0864952\pi$
$953$			511.572i			0.536802i	−0.963307	+	0.268401i	$0.913505\pi$
$954$			0.594611i			0.000623281i
$955$	271.607			0.284405
$956$	−1142.36			−1.19494
$957$		−	145.903i		−	0.152459i
$958$		−	384.484i		−	0.401341i
$959$	16.6676			0.0173802
$960$			233.475i			0.243203i
$961$	−947.329			−0.985774
$962$			239.371i			0.248826i
$963$		−	563.368i		−	0.585014i
$964$		−	914.171i		−	0.948310i
$965$			1507.83i			1.56251i
$966$	78.5396	+	3.14655i	0.0813039	+	0.00325730i
$967$	−341.109			−0.352750			−0.176375	−	0.984323i	$-0.556437\pi$
$967$	−341.109			−0.352750			−0.176375	+	0.984323i	$0.556437\pi$
$968$	−1001.09			−1.03419
$969$	−192.284			−0.198435
$970$	−325.946			−0.336027
$971$			1720.22i			1.77160i	0.464071	+	0.885798i	$0.346388\pi$
$971$			1720.22i			1.77160i	−0.464071	+	0.885798i	$0.653612\pi$
$972$	53.6842			0.0552306
$973$		−	231.092i		−	0.237504i
$974$	−32.0334			−0.0328885
$975$	832.745			0.854097
$976$			908.506i			0.930847i
$977$			241.901i			0.247596i	0.992307	+	0.123798i	$0.0395074\pi$
$977$			241.901i			0.247596i	−0.992307	+	0.123798i	$0.960493\pi$
$978$	−79.4133			−0.0811997
$979$	−1635.10			−1.67017
$980$			195.485i			0.199474i
$981$		−	239.125i		−	0.243757i
$982$	−12.3545			−0.0125810
$983$		−	495.443i		−	0.504011i	−0.967726	−	0.252006i	$-0.918910\pi$
$983$		−	495.443i		−	0.504011i	0.967726	−	0.252006i	$-0.0810901\pi$
$984$	723.975			0.735747
$985$		−	1563.06i		−	1.58686i
$986$		−	52.5318i		−	0.0532777i
$987$		−	292.404i		−	0.296255i
$988$			310.691i			0.314465i
$989$	251.559	+	10.0783i	0.254357	+	0.0101904i
$990$	314.932			0.318113
$991$	−323.525			−0.326463			−0.163232	−	0.986588i	$-0.552192\pi$
$991$	−323.525			−0.326463			−0.163232	+	0.986588i	$0.552192\pi$
$992$	−108.670			−0.109547
$993$	860.911			0.866980
$994$			63.3790i			0.0637616i
$995$	694.707			0.698198
$996$		−	712.196i		−	0.715056i
$997$	−1144.19			−1.14763			−0.573816	−	0.818984i	$-0.694538\pi$
$997$	−1144.19			−1.14763			−0.573816	+	0.818984i	$0.694538\pi$
$998$	−306.340			−0.306954
$999$			141.386i			0.141528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.21	✓	48
23.22	odd	2	inner	483.3.f.a.22.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.21	✓	48	1.1	even	1	trivial
483.3.f.a.22.22	yes	48	23.22	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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} +8.10909i q^{5} +1.29170 q^{6} -2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-0.745761 q^{2} -1.73205 q^{3} -3.44384 q^{4} +8.10909i q^{5} +1.29170 q^{6} -2.64575i q^{7} +5.55132 q^{8} +3.00000 q^{9} -6.04744i q^{10} +17.3590i q^{11} +5.96491 q^{12} +11.7963 q^{13} +1.97310i q^{14} -14.0453i q^{15} +9.63540 q^{16} +14.5159i q^{17} -2.23728 q^{18} -7.64785i q^{19} -27.9264i q^{20} +4.58258i q^{21} -12.9456i q^{22} +(-0.920715 + 22.9816i) q^{23} -9.61518 q^{24} -40.7573 q^{25} -8.79723 q^{26} -5.19615 q^{27} +9.11155i q^{28} +4.85267 q^{29} +10.4745i q^{30} +3.69740 q^{31} -29.3910 q^{32} -30.0666i q^{33} -10.8254i q^{34} +21.4546 q^{35} -10.3315 q^{36} -27.2098i q^{37} +5.70347i q^{38} -20.4318 q^{39} +45.0162i q^{40} -75.2950 q^{41} -3.41751i q^{42} -10.9461i q^{43} -59.7815i q^{44} +24.3273i q^{45} +(0.686633 - 17.1387i) q^{46} -63.8078 q^{47} -16.6890 q^{48} -7.00000 q^{49} +30.3952 q^{50} -25.1422i q^{51} -40.6246 q^{52} -0.265774i q^{53} +3.87509 q^{54} -140.765 q^{55} -14.6874i q^{56} +13.2465i q^{57} -3.61893 q^{58} +109.616 q^{59} +48.3699i q^{60} +94.2884i q^{61} -2.75737 q^{62} -7.93725i q^{63} -16.6230 q^{64} +95.6573i q^{65} +22.4225i q^{66} +50.6910i q^{67} -49.9903i q^{68} +(1.59472 - 39.8052i) q^{69} -16.0000 q^{70} +32.1216 q^{71} +16.6540 q^{72} -125.902 q^{73} +20.2920i q^{74} +70.5937 q^{75} +26.3380i q^{76} +45.9275 q^{77} +15.2372 q^{78} -45.1325i q^{79} +78.1343i q^{80} +9.00000 q^{81} +56.1521 q^{82} -119.398i q^{83} -15.7817i q^{84} -117.710 q^{85} +8.16319i q^{86} -8.40507 q^{87} +96.3653i q^{88} +94.1931i q^{89} -18.1423i q^{90} -31.2101i q^{91} +(3.17080 - 79.1449i) q^{92} -6.40408 q^{93} +47.5853 q^{94} +62.0171 q^{95} +50.9067 q^{96} -53.8983i q^{97} +5.22033 q^{98} +52.0769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

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