LMFDB - Embedded newform 483.3.f.a.22.24

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			22.24
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.327978 q^{2} +1.73205 q^{3} -3.89243 q^{4} -3.00707i q^{5} -0.568074 q^{6} +2.64575i q^{7} +2.58854 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-0.327978 q^{2} +1.73205 q^{3} -3.89243 q^{4} -3.00707i q^{5} -0.568074 q^{6} +2.64575i q^{7} +2.58854 q^{8} +3.00000 q^{9} +0.986251i q^{10} +9.21875i q^{11} -6.74189 q^{12} +0.0704661 q^{13} -0.867748i q^{14} -5.20839i q^{15} +14.7207 q^{16} -4.13348i q^{17} -0.983934 q^{18} +18.2874i q^{19} +11.7048i q^{20} +4.58258i q^{21} -3.02355i q^{22} +(-7.16445 - 21.8557i) q^{23} +4.48349 q^{24} +15.9576 q^{25} -0.0231113 q^{26} +5.19615 q^{27} -10.2984i q^{28} +40.1946 q^{29} +1.70824i q^{30} +34.9897 q^{31} -15.1822 q^{32} +15.9673i q^{33} +1.35569i q^{34} +7.95595 q^{35} -11.6773 q^{36} +40.6571i q^{37} -5.99787i q^{38} +0.122051 q^{39} -7.78392i q^{40} +74.0663 q^{41} -1.50298i q^{42} -27.9302i q^{43} -35.8833i q^{44} -9.02120i q^{45} +(2.34978 + 7.16818i) q^{46} +16.0759 q^{47} +25.4971 q^{48} -7.00000 q^{49} -5.23373 q^{50} -7.15940i q^{51} -0.274285 q^{52} +84.4623i q^{53} -1.70422 q^{54} +27.7214 q^{55} +6.84864i q^{56} +31.6747i q^{57} -13.1829 q^{58} +49.2810 q^{59} +20.2733i q^{60} +8.08548i q^{61} -11.4759 q^{62} +7.93725i q^{63} -53.9035 q^{64} -0.211896i q^{65} -5.23694i q^{66} +72.1807i q^{67} +16.0893i q^{68} +(-12.4092 - 37.8551i) q^{69} -2.60937 q^{70} -14.2788 q^{71} +7.76563 q^{72} -120.606 q^{73} -13.3346i q^{74} +27.6393 q^{75} -71.1825i q^{76} -24.3905 q^{77} -0.0400300 q^{78} -144.623i q^{79} -44.2662i q^{80} +9.00000 q^{81} -24.2921 q^{82} +18.6072i q^{83} -17.8374i q^{84} -12.4296 q^{85} +9.16049i q^{86} +69.6190 q^{87} +23.8631i q^{88} +127.976i q^{89} +2.95875i q^{90} +0.186436i q^{91} +(27.8871 + 85.0717i) q^{92} +60.6040 q^{93} -5.27255 q^{94} +54.9914 q^{95} -26.2964 q^{96} -90.3864i q^{97} +2.29585 q^{98} +27.6563i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.327978			−0.163989			−0.0819945	−	0.996633i	$-0.526129\pi$
$2$	−0.327978			−0.163989			−0.0819945	+	0.996633i	$0.526129\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−3.89243			−0.973108
$5$		−	3.00707i		−	0.601413i	−0.953717	−	0.300707i	$-0.902778\pi$
$5$		−	3.00707i		−	0.601413i	0.953717	−	0.300707i	$-0.0972225\pi$
$6$	−0.568074			−0.0946791
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.58854			0.323568
$9$	3.00000			0.333333
$10$			0.986251i			0.0986251i
$11$			9.21875i			0.838068i	0.907970	+	0.419034i	$0.137631\pi$
$11$			9.21875i			0.838068i	−0.907970	+	0.419034i	$0.862369\pi$
$12$	−6.74189			−0.561824
$13$	0.0704661			0.00542047			0.00271024	−	0.999996i	$-0.499137\pi$
$13$	0.0704661			0.00542047			0.00271024	+	0.999996i	$0.499137\pi$
$14$		−	0.867748i		−	0.0619820i
$15$		−	5.20839i		−	0.347226i
$16$	14.7207			0.920046
$17$		−	4.13348i		−	0.243146i	−0.992582	−	0.121573i	$-0.961206\pi$
$17$		−	4.13348i		−	0.243146i	0.992582	−	0.121573i	$-0.0387938\pi$
$18$	−0.983934			−0.0546630
$19$			18.2874i			0.962495i	0.876585	+	0.481248i	$0.159816\pi$
$19$			18.2874i			0.962495i	−0.876585	+	0.481248i	$0.840184\pi$
$20$			11.7048i			0.585240i
$21$			4.58258i			0.218218i
$22$		−	3.02355i		−	0.137434i
$23$	−7.16445	−	21.8557i	−0.311498	−	0.950247i
$23$	−7.16445	−	21.8557i	−0.311498	−	0.950247i
$24$	4.48349			0.186812
$25$	15.9576			0.638302
$26$	−0.0231113			−0.000888897
$27$	5.19615			0.192450
$28$		−	10.2984i		−	0.367800i
$29$	40.1946			1.38602			0.693010	−	0.720928i	$-0.256284\pi$
$29$	40.1946			1.38602			0.693010	+	0.720928i	$0.256284\pi$
$30$			1.70824i			0.0569412i
$31$	34.9897			1.12870			0.564351	−	0.825535i	$-0.309127\pi$
$31$	34.9897			1.12870			0.564351	+	0.825535i	$0.309127\pi$
$32$	−15.1822			−0.474445
$33$			15.9673i			0.483859i
$34$			1.35569i			0.0398732i
$35$	7.95595			0.227313
$36$	−11.6773			−0.324369
$37$			40.6571i			1.09884i	0.835546	+	0.549420i	$0.185151\pi$
$37$			40.6571i			1.09884i	−0.835546	+	0.549420i	$0.814849\pi$
$38$		−	5.99787i		−	0.157839i
$39$	0.122051			0.00312951
$40$		−	7.78392i		−	0.194598i
$41$	74.0663			1.80650			0.903248	−	0.429120i	$-0.141176\pi$
$41$	74.0663			1.80650			0.903248	+	0.429120i	$0.141176\pi$
$42$		−	1.50298i		−	0.0357853i
$43$		−	27.9302i		−	0.649540i	−0.945793	−	0.324770i	$-0.894713\pi$
$43$		−	27.9302i		−	0.649540i	0.945793	−	0.324770i	$-0.105287\pi$
$44$		−	35.8833i		−	0.815531i
$45$		−	9.02120i		−	0.200471i
$46$	2.34978	+	7.16818i	0.0510822	+	0.155830i
$47$	16.0759			0.342041			0.171021	−	0.985267i	$-0.445294\pi$
$47$	16.0759			0.342041			0.171021	+	0.985267i	$0.445294\pi$
$48$	25.4971			0.531189
$49$	−7.00000			−0.142857
$50$	−5.23373			−0.104675
$51$		−	7.15940i		−	0.140380i
$52$	−0.274285			−0.00527470
$53$			84.4623i			1.59363i	0.604224	+	0.796814i	$0.293483\pi$
$53$			84.4623i			1.59363i	−0.604224	+	0.796814i	$0.706517\pi$
$54$	−1.70422			−0.0315597
$55$	27.7214			0.504025
$56$			6.84864i			0.122297i
$57$			31.6747i			0.555697i
$58$	−13.1829			−0.227292
$59$	49.2810			0.835271			0.417635	−	0.908615i	$-0.362859\pi$
$59$	49.2810			0.835271			0.417635	+	0.908615i	$0.362859\pi$
$60$			20.2733i			0.337888i
$61$			8.08548i			0.132549i	0.997801	+	0.0662744i	$0.0211113\pi$
$61$			8.08548i			0.132549i	−0.997801	+	0.0662744i	$0.978889\pi$
$62$	−11.4759			−0.185095
$63$			7.93725i			0.125988i
$64$	−53.9035			−0.842242
$65$		−	0.211896i		−	0.00325994i
$66$		−	5.23694i		−	0.0793475i
$67$			72.1807i			1.07732i	0.842522	+	0.538662i	$0.181070\pi$
$67$			72.1807i			1.07732i	−0.842522	+	0.538662i	$0.818930\pi$
$68$			16.0893i			0.236607i
$69$	−12.4092	−	37.8551i	−0.179843	−	0.548625i
$70$	−2.60937			−0.0372768
$71$	−14.2788			−0.201110			−0.100555	−	0.994932i	$-0.532062\pi$
$71$	−14.2788			−0.201110			−0.100555	+	0.994932i	$0.532062\pi$
$72$	7.76563			0.107856
$73$	−120.606			−1.65214			−0.826071	−	0.563566i	$-0.809429\pi$
$73$	−120.606			−1.65214			−0.826071	+	0.563566i	$0.809429\pi$
$74$		−	13.3346i		−	0.180198i
$75$	27.6393			0.368524
$76$		−	71.1825i		−	0.936612i
$77$	−24.3905			−0.316760
$78$	−0.0400300			−0.000513205
$79$		−	144.623i		−	1.83067i	−0.402696	−	0.915334i	$-0.631927\pi$
$79$		−	144.623i		−	1.83067i	0.402696	−	0.915334i	$-0.368073\pi$
$80$		−	44.2662i		−	0.553328i
$81$	9.00000			0.111111
$82$	−24.2921			−0.296245
$83$			18.6072i			0.224183i	0.993698	+	0.112092i	$0.0357550\pi$
$83$			18.6072i			0.224183i	−0.993698	+	0.112092i	$0.964245\pi$
$84$		−	17.8374i		−	0.212349i
$85$	−12.4296			−0.146231
$86$			9.16049i			0.106517i
$87$	69.6190			0.800219
$88$			23.8631i			0.271172i
$89$			127.976i			1.43793i	0.695046	+	0.718965i	$0.255384\pi$
$89$			127.976i			1.43793i	−0.695046	+	0.718965i	$0.744616\pi$
$90$			2.95875i			0.0328750i
$91$			0.186436i			0.00204875i
$92$	27.8871	+	85.0717i	0.303121	+	0.924692i
$93$	60.6040			0.651656
$94$	−5.27255			−0.0560910
$95$	54.9914			0.578857
$96$	−26.2964			−0.273921
$97$		−	90.3864i		−	0.931818i	−0.884833	−	0.465909i	$-0.845727\pi$
$97$		−	90.3864i		−	0.931818i	0.884833	−	0.465909i	$-0.154273\pi$
$98$	2.29585			0.0234270
$99$			27.6563i			0.279356i
$100$	−62.1137			−0.621137
$101$	109.693			1.08606			0.543032	−	0.839712i	$-0.317276\pi$
$101$	109.693			1.08606			0.543032	+	0.839712i	$0.317276\pi$
$102$			2.34812i			0.0230208i
$103$		−	98.8500i		−	0.959709i	−0.877348	−	0.479855i	$-0.840689\pi$
$103$		−	98.8500i		−	0.959709i	0.877348	−	0.479855i	$-0.159311\pi$
$104$	0.182405			0.00175389
$105$	13.7801			0.131239
$106$		−	27.7018i		−	0.261337i
$107$		−	56.3531i		−	0.526665i	−0.964705	−	0.263332i	$-0.915178\pi$
$107$		−	56.3531i		−	0.526665i	0.964705	−	0.263332i	$-0.0848216\pi$
$108$	−20.2257			−0.187275
$109$			120.152i			1.10232i	0.834401	+	0.551158i	$0.185814\pi$
$109$			120.152i			1.10232i	−0.834401	+	0.551158i	$0.814186\pi$
$110$	−9.09200			−0.0826546
$111$			70.4201i			0.634415i
$112$			38.9474i			0.347745i
$113$			41.3436i			0.365873i	0.983125	+	0.182936i	$0.0585603\pi$
$113$			41.3436i			0.365873i	−0.983125	+	0.182936i	$0.941440\pi$
$114$		−	10.3886i		−	0.0911282i
$115$	−65.7214	+	21.5440i	−0.571491	+	0.187339i
$116$	−156.455			−1.34875
$117$	0.211398			0.00180682
$118$	−16.1631			−0.136975
$119$	10.9362			0.0919005
$120$		−	13.4821i		−	0.112351i
$121$	36.0146			0.297642
$122$		−	2.65186i		−	0.0217365i
$123$	128.287			1.04298
$124$	−136.195			−1.09835
$125$		−	123.162i		−	0.985296i
$126$		−	2.60324i		−	0.0206607i
$127$	6.53745			0.0514760			0.0257380	−	0.999669i	$-0.491806\pi$
$127$	6.53745			0.0514760			0.0257380	+	0.999669i	$0.491806\pi$
$128$	78.4081			0.612564
$129$		−	48.3765i		−	0.375012i
$130$			0.0694973i			0.000534594i
$131$	91.5247			0.698661			0.349331	−	0.936999i	$-0.386409\pi$
$131$	91.5247			0.698661			0.349331	+	0.936999i	$0.386409\pi$
$132$		−	62.1518i		−	0.470847i
$133$	−48.3840			−0.363789
$134$		−	23.6737i		−	0.176669i
$135$		−	15.6252i		−	0.115742i
$136$		−	10.6997i		−	0.0786742i
$137$		−	72.0109i		−	0.525627i	−0.964847	−	0.262813i	$-0.915350\pi$
$137$		−	72.0109i		−	0.525627i	0.964847	−	0.262813i	$-0.0846504\pi$
$138$	4.06994	+	12.4156i	0.0294923	+	0.0899685i
$139$	−228.903			−1.64679			−0.823393	−	0.567472i	$-0.807922\pi$
$139$	−228.903			−1.64679			−0.823393	+	0.567472i	$0.807922\pi$
$140$	−30.9680			−0.221200
$141$	27.8444			0.197478
$142$	4.68313			0.0329798
$143$			0.649610i			0.00454273i
$144$	44.1622			0.306682
$145$		−	120.868i		−	0.833570i
$146$	39.5562			0.270933
$147$	−12.1244			−0.0824786
$148$		−	158.255i		−	1.06929i
$149$			52.6490i			0.353349i	0.984269	+	0.176675i	$0.0565340\pi$
$149$			52.6490i			0.353349i	−0.984269	+	0.176675i	$0.943466\pi$
$150$	−9.06508			−0.0604339
$151$	−254.224			−1.68360			−0.841802	−	0.539786i	$-0.818505\pi$
$151$	−254.224			−1.68360			−0.841802	+	0.539786i	$0.818505\pi$
$152$			47.3377i			0.311433i
$153$		−	12.4004i		−	0.0810486i
$154$	7.99955			0.0519451
$155$		−	105.216i		−	0.678816i
$156$	−0.475075			−0.00304535
$157$			102.188i			0.650879i	0.945563	+	0.325439i	$0.105512\pi$
$157$			102.188i			0.650879i	−0.945563	+	0.325439i	$0.894488\pi$
$158$			47.4331i			0.300209i
$159$			146.293i			0.920082i
$160$			45.6540i			0.285338i
$161$	57.8247	−	18.9554i	0.359160	−	0.117735i
$162$	−2.95180			−0.0182210
$163$	−47.8507			−0.293563			−0.146781	−	0.989169i	$-0.546891\pi$
$163$	−47.8507			−0.293563			−0.146781	+	0.989169i	$0.546891\pi$
$164$	−288.298			−1.75791
$165$	48.0148			0.290999
$166$		−	6.10275i		−	0.0367635i
$167$	176.995			1.05985			0.529924	−	0.848045i	$-0.322220\pi$
$167$	176.995			1.05985			0.529924	+	0.848045i	$0.322220\pi$
$168$			11.8622i			0.0706083i
$169$	−168.995			−0.999971
$170$	4.07665			0.0239803
$171$			54.8622i			0.320832i
$172$			108.716i			0.632072i
$173$	−74.6896			−0.431732			−0.215866	−	0.976423i	$-0.569257\pi$
$173$	−74.6896			−0.431732			−0.215866	+	0.976423i	$0.569257\pi$
$174$	−22.8335			−0.131227
$175$			42.2197i			0.241256i
$176$			135.707i			0.771061i
$177$	85.3571			0.482244
$178$		−	41.9732i		−	0.235805i
$179$	−130.980			−0.731732			−0.365866	−	0.930668i	$-0.619227\pi$
$179$	−130.980			−0.731732			−0.365866	+	0.930668i	$0.619227\pi$
$180$			35.1144i			0.195080i
$181$			79.6209i			0.439894i	0.975512	+	0.219947i	$0.0705885\pi$
$181$			79.6209i			0.439894i	−0.975512	+	0.219947i	$0.929412\pi$
$182$		−	0.0611468i		−	0.000335972i
$183$			14.0045i			0.0765271i
$184$	−18.5455	−	56.5743i	−0.100791	−	0.307469i
$185$	122.258			0.660857
$186$	−19.8768			−0.106864
$187$	38.1055			0.203773
$188$	−62.5745			−0.332843
$189$			13.7477i			0.0727393i
$190$	−18.0360			−0.0949262
$191$		−	367.945i		−	1.92642i	−0.268757	−	0.963208i	$-0.586613\pi$
$191$		−	367.945i		−	1.92642i	0.268757	−	0.963208i	$-0.413387\pi$
$192$	−93.3636			−0.486269
$193$	−259.187			−1.34294			−0.671468	−	0.741033i	$-0.734336\pi$
$193$	−259.187			−1.34294			−0.671468	+	0.741033i	$0.734336\pi$
$194$			29.6447i			0.152808i
$195$		−	0.367015i		−	0.00188213i
$196$	27.2470			0.139015
$197$	−202.897			−1.02994			−0.514968	−	0.857209i	$-0.672196\pi$
$197$	−202.897			−1.02994			−0.514968	+	0.857209i	$0.672196\pi$
$198$		−	9.07064i		−	0.0458113i
$199$		−	121.073i		−	0.608405i	−0.952607	−	0.304202i	$-0.901610\pi$
$199$		−	121.073i		−	0.608405i	0.952607	−	0.304202i	$-0.0983899\pi$
$200$	41.3068			0.206534
$201$			125.021i			0.621993i
$202$	−35.9767			−0.178103
$203$			106.345i			0.523866i
$204$			27.8675i			0.136605i
$205$		−	222.722i		−	1.08645i
$206$			32.4206i			0.157382i
$207$	−21.4934	−	65.5670i	−0.103833	−	0.316749i
$208$	1.03731			0.00498708
$209$	−168.587			−0.806637
$210$	−4.51957			−0.0215218
$211$	126.504			0.599544			0.299772	−	0.954011i	$-0.403089\pi$
$211$	126.504			0.599544			0.299772	+	0.954011i	$0.403089\pi$
$212$		−	328.764i		−	1.55077i
$213$	−24.7316			−0.116111
$214$			18.4826i			0.0863672i
$215$	−83.9880			−0.390642
$216$	13.4505			0.0622707
$217$			92.5742i			0.426609i
$218$		−	39.4073i		−	0.180768i
$219$	−208.896			−0.953864
$220$	−107.904			−0.490471
$221$		−	0.291270i		−	0.00131797i
$222$		−	23.0962i		−	0.104037i
$223$	47.4745			0.212890			0.106445	−	0.994319i	$-0.466053\pi$
$223$	47.4745			0.212890			0.106445	+	0.994319i	$0.466053\pi$
$224$		−	40.1684i		−	0.179323i
$225$	47.8727			0.212767
$226$		−	13.5598i		−	0.0599991i
$227$			449.389i			1.97969i	0.142161	+	0.989844i	$0.454595\pi$
$227$			449.389i			1.97969i	−0.142161	+	0.989844i	$0.545405\pi$
$228$		−	123.292i		−	0.540753i
$229$		−	215.733i		−	0.942064i	−0.882116	−	0.471032i	$-0.843882\pi$
$229$		−	215.733i		−	0.942064i	0.882116	−	0.471032i	$-0.156118\pi$
$230$	21.5552	−	7.06595i	0.0937182	−	0.0307215i
$231$	−42.2456			−0.182881
$232$	104.045			0.448471
$233$	227.597			0.976812			0.488406	−	0.872616i	$-0.337578\pi$
$233$	227.597			0.976812			0.488406	+	0.872616i	$0.337578\pi$
$234$	−0.0693340			−0.000296299
$235$		−	48.3414i		−	0.205708i
$236$	−191.823			−0.812808
$237$		−	250.494i		−	1.05694i
$238$	−3.58682			−0.0150707
$239$	256.627			1.07375			0.536876	−	0.843661i	$-0.319604\pi$
$239$	256.627			1.07375			0.536876	+	0.843661i	$0.319604\pi$
$240$		−	76.6713i		−	0.319464i
$241$			469.422i			1.94781i	0.226957	+	0.973905i	$0.427122\pi$
$241$			469.422i			1.94781i	−0.226957	+	0.973905i	$0.572878\pi$
$242$	−11.8120			−0.0488099
$243$	15.5885			0.0641500
$244$		−	31.4722i		−	0.128984i
$245$			21.0495i			0.0859162i
$246$	−42.0752			−0.171037
$247$			1.28864i			0.00521718i
$248$	90.5724			0.365211
$249$			32.2286i			0.129432i
$250$			40.3944i			0.161578i
$251$		−	110.873i		−	0.441726i	−0.975305	−	0.220863i	$-0.929113\pi$
$251$		−	110.873i		−	0.441726i	0.975305	−	0.220863i	$-0.0708873\pi$
$252$		−	30.8952i		−	0.122600i
$253$	201.482	−	66.0473i	0.796372	−	0.261057i
$254$	−2.14414			−0.00844150
$255$	−21.5288			−0.0844266
$256$	189.898			0.741789
$257$	−161.663			−0.629037			−0.314519	−	0.949251i	$-0.601843\pi$
$257$	−161.663			−0.629037			−0.314519	+	0.949251i	$0.601843\pi$
$258$			15.8664i			0.0614978i
$259$	−107.569			−0.415322
$260$			0.824791i			0.00317227i
$261$	120.584			0.462006
$262$	−30.0181			−0.114573
$263$		−	208.933i		−	0.794423i	−0.917727	−	0.397211i	$-0.869978\pi$
$263$		−	208.933i		−	0.794423i	0.917727	−	0.397211i	$-0.130022\pi$
$264$			41.3322i			0.156561i
$265$	253.984			0.958429
$266$	15.8689			0.0596574
$267$			221.661i			0.830189i
$268$		−	280.958i		−	1.04835i
$269$	−97.2851			−0.361655			−0.180827	−	0.983515i	$-0.557878\pi$
$269$	−97.2851			−0.361655			−0.180827	+	0.983515i	$0.557878\pi$
$270$			5.12471i			0.0189804i
$271$	136.557			0.503899			0.251950	−	0.967740i	$-0.418928\pi$
$271$	136.557			0.503899			0.251950	+	0.967740i	$0.418928\pi$
$272$		−	60.8479i		−	0.223705i
$273$			0.322916i			0.00118284i
$274$			23.6180i			0.0861970i
$275$			147.109i			0.534941i
$276$	48.3019	+	147.349i	0.175007	+	0.533871i
$277$	336.193			1.21369			0.606847	−	0.794819i	$-0.292434\pi$
$277$	336.193			1.21369			0.606847	+	0.794819i	$0.292434\pi$
$278$	75.0752			0.270055
$279$	104.969			0.376234
$280$	20.5943			0.0735511
$281$		−	56.2734i		−	0.200261i	−0.994974	−	0.100131i	$-0.968074\pi$
$281$		−	56.2734i		−	0.200261i	0.994974	−	0.100131i	$-0.0319260\pi$
$282$	−9.13233			−0.0323842
$283$			177.951i			0.628801i	0.949290	+	0.314401i	$0.101804\pi$
$283$			177.951i			0.628801i	−0.949290	+	0.314401i	$0.898196\pi$
$284$	55.5793			0.195702
$285$	95.2480			0.334203
$286$		−	0.213058i		−	0.000744957i
$287$			195.961i			0.682791i
$288$	−45.5467			−0.158148
$289$	271.914			0.940880
$290$			39.6419i			0.136696i
$291$		−	156.554i		−	0.537985i
$292$	469.452			1.60771
$293$			266.462i			0.909427i	0.890638	+	0.454713i	$0.150258\pi$
$293$			266.462i			0.909427i	−0.890638	+	0.454713i	$0.849742\pi$
$294$	3.97652			0.0135256
$295$		−	148.191i		−	0.502343i
$296$			105.243i			0.355549i
$297$			47.9020i			0.161286i
$298$		−	17.2677i		−	0.0579453i
$299$	−0.504851	−	1.54008i	−0.00168847	−	0.00515079i
$300$	−107.584			−0.358614
$301$	73.8964			0.245503
$302$	83.3799			0.276093
$303$	189.993			0.627040
$304$			269.204i			0.885540i
$305$	24.3136			0.0797166
$306$			4.06707i			0.0132911i
$307$	−396.114			−1.29027			−0.645137	−	0.764067i	$-0.723200\pi$
$307$	−396.114			−1.29027			−0.645137	+	0.764067i	$0.723200\pi$
$308$	94.9384			0.308242
$309$		−	171.213i		−	0.554088i
$310$			34.5087i			0.111318i
$311$	99.3901			0.319582			0.159791	−	0.987151i	$-0.448918\pi$
$311$	99.3901			0.319582			0.159791	+	0.987151i	$0.448918\pi$
$312$	0.315934			0.00101261
$313$			217.393i			0.694547i	0.937764	+	0.347274i	$0.112892\pi$
$313$			217.393i			0.694547i	−0.937764	+	0.347274i	$0.887108\pi$
$314$		−	33.5154i		−	0.106737i
$315$	23.8678			0.0757709
$316$			562.934i			1.78144i
$317$	168.827			0.532577			0.266289	−	0.963893i	$-0.414203\pi$
$317$	168.827			0.532577			0.266289	+	0.963893i	$0.414203\pi$
$318$		−	47.9809i		−	0.150883i
$319$			370.544i			1.16158i
$320$			162.091i			0.506536i
$321$		−	97.6065i		−	0.304070i
$322$	−18.9652	+	6.21694i	−0.0588982	+	0.0193073i
$323$	75.5907			0.234027
$324$	−35.0319			−0.108123
$325$	1.12447			0.00345990
$326$	15.6940			0.0481410
$327$			208.110i			0.636422i
$328$	191.724			0.584524
$329$			42.5330i			0.129279i
$330$	−15.7478			−0.0477206
$331$	423.211			1.27858			0.639292	−	0.768964i	$-0.279227\pi$
$331$	423.211			1.27858			0.639292	+	0.768964i	$0.279227\pi$
$332$		−	72.4272i		−	0.218154i
$333$			121.971i			0.366280i
$334$	−58.0504			−0.173803
$335$	217.052			0.647917
$336$			67.4589i			0.200771i
$337$		−	577.326i		−	1.71313i	−0.516037	−	0.856566i	$-0.672593\pi$
$337$		−	577.326i		−	1.71313i	0.516037	−	0.856566i	$-0.327407\pi$
$338$	55.4266			0.163984
$339$			71.6093i			0.211237i
$340$	48.3815			0.142299
$341$			322.562i			0.945929i
$342$		−	17.9936i		−	0.0526129i
$343$		−	18.5203i		−	0.0539949i
$344$		−	72.2985i		−	0.210170i
$345$	−113.833	+	37.3153i	−0.329950	+	0.108160i
$346$	24.4966			0.0707993
$347$	336.111			0.968620			0.484310	−	0.874896i	$-0.339071\pi$
$347$	336.111			0.968620			0.484310	+	0.874896i	$0.339071\pi$
$348$	−270.987			−0.778699
$349$	125.305			0.359040			0.179520	−	0.983754i	$-0.442546\pi$
$349$	125.305			0.359040			0.179520	+	0.983754i	$0.442546\pi$
$350$		−	13.8471i		−	0.0395632i
$351$	0.366153			0.00104317
$352$		−	139.961i		−	0.397617i
$353$	98.1599			0.278073			0.139037	−	0.990287i	$-0.455599\pi$
$353$	98.1599			0.278073			0.139037	+	0.990287i	$0.455599\pi$
$354$	−27.9952			−0.0790826
$355$			42.9373i			0.120950i
$356$		−	498.137i		−	1.39926i
$357$	18.9420			0.0530588
$358$	42.9585			0.119996
$359$		−	460.554i		−	1.28288i	−0.767173	−	0.641440i	$-0.778337\pi$
$359$		−	460.554i		−	1.28288i	0.767173	−	0.641440i	$-0.221663\pi$
$360$		−	23.3517i		−	0.0648660i
$361$	26.5705			0.0736024
$362$		−	26.1139i		−	0.0721378i
$363$	62.3792			0.171843
$364$		−	0.725689i		−	0.00199365i
$365$			362.671i			0.993620i
$366$		−	4.59315i		−	0.0125496i
$367$			249.164i			0.678920i	0.940620	+	0.339460i	$0.110244\pi$
$367$			249.164i			0.678920i	−0.940620	+	0.339460i	$0.889756\pi$
$368$	−105.466	−	321.732i	−0.286593	−	0.874271i
$369$	222.199			0.602165
$370$	−40.0981			−0.108373
$371$	−223.466			−0.602335
$372$	−235.897			−0.634132
$373$		−	197.507i		−	0.529509i	−0.964316	−	0.264755i	$-0.914709\pi$
$373$		−	197.507i		−	0.529509i	0.964316	−	0.264755i	$-0.0852909\pi$
$374$	−12.4978			−0.0334165
$375$		−	213.323i		−	0.568861i
$376$	41.6133			0.110674
$377$	2.83236			0.00751288
$378$		−	4.50895i		−	0.0119284i
$379$		−	741.067i		−	1.95532i	−0.210190	−	0.977660i	$-0.567408\pi$
$379$		−	741.067i		−	1.95532i	0.210190	−	0.977660i	$-0.432592\pi$
$380$	−214.050			−0.563291
$381$	11.3232			0.0297197
$382$			120.678i			0.315911i
$383$			644.445i			1.68263i	0.540549	+	0.841313i	$0.318217\pi$
$383$			644.445i			1.68263i	−0.540549	+	0.841313i	$0.681783\pi$
$384$	135.807			0.353664
$385$			73.3439i			0.190504i
$386$	85.0075			0.220227
$387$		−	83.7906i		−	0.216513i
$388$			351.823i			0.906759i
$389$		−	49.1616i		−	0.126379i	−0.998002	−	0.0631897i	$-0.979873\pi$
$389$		−	49.1616i		−	0.126379i	0.998002	−	0.0631897i	$-0.0201273\pi$
$390$			0.120373i			0.000308648i
$391$	−90.3400	+	29.6141i	−0.231049	+	0.0757395i
$392$	−18.1198			−0.0462240
$393$	158.525			0.403372
$394$	66.5459			0.168898
$395$	−434.890			−1.10099
$396$		−	107.650i		−	0.271844i
$397$	203.753			0.513233			0.256616	−	0.966513i	$-0.417392\pi$
$397$	203.753			0.513233			0.256616	+	0.966513i	$0.417392\pi$
$398$			39.7091i			0.0997716i
$399$	−83.8035			−0.210034
$400$	234.907			0.587268
$401$			82.3959i			0.205476i	0.994708	+	0.102738i	$0.0327603\pi$
$401$			82.3959i			0.205476i	−0.994708	+	0.102738i	$0.967240\pi$
$402$		−	41.0040i		−	0.102000i
$403$	2.46559			0.00611809
$404$	−426.971			−1.05686
$405$		−	27.0636i		−	0.0668237i
$406$		−	34.8787i		−	0.0859082i
$407$	−374.807			−0.920903
$408$		−	18.5324i		−	0.0454226i
$409$	−565.600			−1.38289			−0.691443	−	0.722431i	$-0.743025\pi$
$409$	−565.600			−1.38289			−0.691443	+	0.722431i	$0.743025\pi$
$410$			73.0480i			0.178166i
$411$		−	124.727i		−	0.303471i
$412$			384.767i			0.933900i
$413$			130.385i			0.315703i
$414$	7.04935	+	21.5045i	0.0170274	+	0.0519433i
$415$	55.9531			0.134827
$416$	−1.06983			−0.00257172
$417$	−396.472			−0.950772
$418$	55.2928			0.132280
$419$		−	729.782i		−	1.74172i	−0.491529	−	0.870861i	$-0.663562\pi$
$419$		−	729.782i		−	1.74172i	0.491529	−	0.870861i	$-0.336438\pi$
$420$	−53.6381			−0.127710
$421$		−	488.027i		−	1.15921i	−0.814898	−	0.579605i	$-0.803207\pi$
$421$		−	488.027i		−	1.15921i	0.814898	−	0.579605i	$-0.196793\pi$
$422$	−41.4904			−0.0983186
$423$	48.2278			0.114014
$424$			218.634i			0.515647i
$425$		−	65.9603i		−	0.155201i
$426$	8.11142			0.0190409
$427$	−21.3922			−0.0500987
$428$			219.351i			0.512501i
$429$			1.12516i			0.00262274i
$430$	27.5462			0.0640609
$431$			499.700i			1.15940i	0.814831	+	0.579698i	$0.196830\pi$
$431$			499.700i			1.15940i	−0.814831	+	0.579698i	$0.803170\pi$
$432$	76.4912			0.177063
$433$			250.440i			0.578382i	0.957271	+	0.289191i	$0.0933863\pi$
$433$			250.440i			0.578382i	−0.957271	+	0.289191i	$0.906614\pi$
$434$		−	30.3623i		−	0.0699592i
$435$		−	209.349i		−	0.481262i
$436$		−	467.685i		−	1.07267i
$437$	399.684	−	131.019i	0.914608	−	0.299815i
$438$	68.5134			0.156423
$439$	−570.739			−1.30009			−0.650044	−	0.759896i	$-0.725250\pi$
$439$	−570.739			−1.30009			−0.650044	+	0.759896i	$0.725250\pi$
$440$	71.7580			0.163086
$441$	−21.0000			−0.0476190
$442$			0.0955302i			0.000216132i
$443$	−519.651			−1.17303			−0.586514	−	0.809939i	$-0.699500\pi$
$443$	−519.651			−1.17303			−0.586514	+	0.809939i	$0.699500\pi$
$444$		−	274.105i		−	0.617355i
$445$	384.831			0.864790
$446$	−15.5706			−0.0349116
$447$			91.1908i			0.204006i
$448$		−	142.615i		−	0.318338i
$449$	−483.613			−1.07709			−0.538545	−	0.842597i	$-0.681026\pi$
$449$	−483.613			−1.07709			−0.538545	+	0.842597i	$0.681026\pi$
$450$	−15.7012			−0.0348915
$451$			682.799i			1.51397i
$452$		−	160.927i		−	0.356034i
$453$	−440.329			−0.972030
$454$		−	147.390i		−	0.324647i
$455$	0.560625			0.00123214
$456$			81.9914i			0.179806i
$457$		−	123.292i		−	0.269786i	−0.990860	−	0.134893i	$-0.956931\pi$
$457$		−	123.292i		−	0.269786i	0.990860	−	0.134893i	$-0.0430690\pi$
$458$			70.7555i			0.154488i
$459$		−	21.4782i		−	0.0467935i
$460$	255.816	−	83.8585i	0.556122	−	0.182301i
$461$	464.422			1.00742			0.503711	−	0.863872i	$-0.331968\pi$
$461$	464.422			1.00742			0.503711	+	0.863872i	$0.331968\pi$
$462$	13.8556			0.0299905
$463$	184.085			0.397591			0.198795	−	0.980041i	$-0.436297\pi$
$463$	184.085			0.397591			0.198795	+	0.980041i	$0.436297\pi$
$464$	591.694			1.27520
$465$		−	182.240i		−	0.391914i
$466$	−74.6469			−0.160186
$467$		−	740.843i		−	1.58639i	−0.608970	−	0.793193i	$-0.708417\pi$
$467$		−	740.843i		−	1.58639i	0.608970	−	0.793193i	$-0.291583\pi$
$468$	−0.822854			−0.00175823
$469$	−190.972			−0.407190
$470$			15.8549i			0.0337339i
$471$			176.995i			0.375785i
$472$	127.566			0.270267
$473$	257.482			0.544359
$474$			82.1565i			0.173326i
$475$			291.822i			0.614363i
$476$	−42.5683			−0.0894291
$477$			253.387i			0.531209i
$478$	−84.1679			−0.176084
$479$			290.201i			0.605848i	0.953015	+	0.302924i	$0.0979628\pi$
$479$			290.201i			0.605848i	−0.953015	+	0.302924i	$0.902037\pi$
$480$			79.0751i			0.164740i
$481$			2.86495i			0.00595623i
$482$		−	153.960i		−	0.319419i
$483$	100.155	−	32.8317i	0.207361	−	0.0679744i
$484$	−140.184			−0.289637
$485$	−271.798			−0.560408
$486$	−5.11267			−0.0105199
$487$	−470.867			−0.966872			−0.483436	−	0.875380i	$-0.660611\pi$
$487$	−470.867			−0.966872			−0.483436	+	0.875380i	$0.660611\pi$
$488$			20.9296i			0.0428885i
$489$	−82.8799			−0.169489
$490$		−	6.90376i		−	0.0140893i
$491$	441.819			0.899836			0.449918	−	0.893070i	$-0.351453\pi$
$491$	441.819			0.899836			0.449918	+	0.893070i	$0.351453\pi$
$492$	−499.347			−1.01493
$493$		−	166.143i		−	0.337005i
$494$		−	0.422646i		−	0.000855560i
$495$	83.1642			0.168008
$496$	515.075			1.03846
$497$		−	37.7782i		−	0.0760124i
$498$		−	10.5703i		−	0.0212254i
$499$	−514.773			−1.03161			−0.515805	−	0.856706i	$-0.672507\pi$
$499$	−514.773			−1.03161			−0.515805	+	0.856706i	$0.672507\pi$
$500$			479.400i			0.958799i
$501$	306.564			0.611904
$502$			36.3639i			0.0724381i
$503$		−	87.6862i		−	0.174326i	−0.996194	−	0.0871632i	$-0.972220\pi$
$503$		−	87.6862i		−	0.174326i	0.996194	−	0.0871632i	$-0.0277802\pi$
$504$			20.5459i			0.0407657i
$505$		−	329.853i		−	0.653174i
$506$	−66.0816	+	21.6621i	−0.130596	+	0.0428104i
$507$	−292.708			−0.577333
$508$	−25.4466			−0.0500917
$509$	202.288			0.397423			0.198712	−	0.980058i	$-0.436324\pi$
$509$	202.288			0.397423			0.198712	+	0.980058i	$0.436324\pi$
$510$	7.06096			0.0138450
$511$		−	319.094i		−	0.624451i
$512$	−375.915			−0.734209
$513$			95.0242i			0.185232i
$514$	53.0217			0.103155
$515$	−297.249			−0.577182
$516$			188.302i			0.364927i
$517$			148.200i			0.286654i
$518$	35.2801			0.0681083
$519$	−129.366			−0.249261
$520$		−	0.548502i		−	0.00105481i
$521$		−	423.505i		−	0.812870i	−0.913680	−	0.406435i	$-0.866772\pi$
$521$		−	423.505i		−	0.812870i	0.913680	−	0.406435i	$-0.133228\pi$
$522$	−39.5488			−0.0757640
$523$		−	3.01355i		−	0.00576205i	−0.999996	−	0.00288103i	$-0.999083\pi$
$523$		−	3.01355i		−	0.00576205i	0.999996	−	0.00288103i	$-0.000917061\pi$
$524$	−356.253			−0.679873
$525$			73.1267i			0.139289i
$526$			68.5255i			0.130277i
$527$		−	144.629i		−	0.274439i
$528$			235.051i			0.445173i
$529$	−426.341	+	313.168i	−0.805938	+	0.592000i
$530$	−83.3010			−0.157172
$531$	147.843			0.278424
$532$	188.331			0.354006
$533$	5.21917			0.00979206
$534$		−	72.6997i		−	0.136142i
$535$	−169.458			−0.316743
$536$			186.843i			0.348587i
$537$	−226.864			−0.422466
$538$	31.9074			0.0593073
$539$		−	64.5313i		−	0.119724i
$540$			60.8199i			0.112629i
$541$	672.961			1.24392			0.621961	−	0.783048i	$-0.286336\pi$
$541$	672.961			1.24392			0.621961	+	0.783048i	$0.286336\pi$
$542$	−44.7876			−0.0826339
$543$			137.907i			0.253973i
$544$			62.7555i			0.115359i
$545$	361.306			0.662947
$546$		−	0.105909i		−	0.000193973i
$547$	543.021			0.992726			0.496363	−	0.868115i	$-0.334669\pi$
$547$	543.021			0.992726			0.496363	+	0.868115i	$0.334669\pi$
$548$			280.297i			0.511492i
$549$			24.2564i			0.0441829i
$550$		−	48.2484i		−	0.0877244i
$551$			735.055i			1.33404i
$552$	−32.1217	−	97.9896i	−0.0581916	−	0.177517i
$553$	382.636			0.691927
$554$	−110.264			−0.199032
$555$	211.758			0.381546
$556$	890.990			1.60250
$557$		−	289.827i		−	0.520337i	−0.965563	−	0.260168i	$-0.916222\pi$
$557$		−	289.827i		−	0.520337i	0.965563	−	0.260168i	$-0.0837780\pi$
$558$	−34.4276			−0.0616982
$559$		−	1.96813i		−	0.00352081i
$560$	117.117			0.209138
$561$	66.0007			0.117648
$562$			18.4564i			0.0328406i
$563$		−	1047.34i		−	1.86029i	−0.367189	−	0.930146i	$-0.619680\pi$
$563$		−	1047.34i		−	1.86029i	0.367189	−	0.930146i	$-0.380320\pi$
$564$	−108.382			−0.192167
$565$	124.323			0.220041
$566$		−	58.3639i		−	0.103116i
$567$			23.8118i			0.0419961i
$568$	−36.9613			−0.0650727
$569$			77.3747i			0.135984i	0.997686	+	0.0679918i	$0.0216592\pi$
$569$			77.3747i			0.135984i	−0.997686	+	0.0679918i	$0.978341\pi$
$570$	−31.2392			−0.0548057
$571$			190.835i			0.334212i	0.985939	+	0.167106i	$0.0534422\pi$
$571$			190.835i			0.334212i	−0.985939	+	0.167106i	$0.946558\pi$
$572$		−	2.52856i		−	0.00442056i
$573$		−	637.300i		−	1.11222i
$574$		−	64.2709i		−	0.111970i
$575$	−114.327	−	348.763i	−0.198830	−	0.606545i
$576$	−161.711			−0.280747
$577$	487.051			0.844109			0.422054	−	0.906571i	$-0.361309\pi$
$577$	487.051			0.844109			0.422054	+	0.906571i	$0.361309\pi$
$578$	−89.1819			−0.154294
$579$	−448.925			−0.775345
$580$			470.469i			0.811154i
$581$	−49.2300			−0.0847332
$582$			51.3462i			0.0882237i
$583$	−778.637			−1.33557
$584$	−312.195			−0.534580
$585$		−	0.635689i		−	0.00108665i
$586$		−	87.3936i		−	0.149136i
$587$	−1086.75			−1.85136			−0.925682	−	0.378302i	$-0.876508\pi$
$587$	−1086.75			−1.85136			−0.925682	+	0.378302i	$0.876508\pi$
$588$	47.1932			0.0802606
$589$			639.872i			1.08637i
$590$			48.6034i			0.0823786i
$591$	−351.429			−0.594634
$592$			598.502i			1.01098i
$593$	−143.713			−0.242349			−0.121175	−	0.992631i	$-0.538666\pi$
$593$	−143.713			−0.242349			−0.121175	+	0.992631i	$0.538666\pi$
$594$		−	15.7108i		−	0.0264492i
$595$		−	32.8858i		−	0.0552702i
$596$		−	204.933i		−	0.343847i
$597$		−	209.704i		−	0.351263i
$598$	0.165580	+	0.505114i	0.000276890	+	0.000844672i
$599$	−469.609			−0.783989			−0.391994	−	0.919968i	$-0.628215\pi$
$599$	−469.609			−0.783989			−0.391994	+	0.919968i	$0.628215\pi$
$600$	71.5455			0.119243
$601$	−155.429			−0.258617			−0.129309	−	0.991604i	$-0.541276\pi$
$601$	−155.429			−0.258617			−0.129309	+	0.991604i	$0.541276\pi$
$602$	−24.2364			−0.0402598
$603$			216.542i			0.359108i
$604$	989.550			1.63833
$605$		−	108.298i		−	0.179006i
$606$	−62.3135			−0.102828
$607$	−999.043			−1.64587			−0.822935	−	0.568136i	$-0.807665\pi$
$607$	−999.043			−1.64587			−0.822935	+	0.568136i	$0.807665\pi$
$608$		−	277.644i		−	0.456651i
$609$			184.195i			0.302454i
$610$	−7.97431			−0.0130726
$611$	1.13281			0.00185403
$612$			48.2679i			0.0788691i
$613$			89.0968i			0.145345i	0.997356	+	0.0726727i	$0.0231529\pi$
$613$			89.0968i			0.145345i	−0.997356	+	0.0726727i	$0.976847\pi$
$614$	129.917			0.211591
$615$		−	385.766i		−	0.627262i
$616$	−63.1359			−0.102493
$617$		−	113.190i		−	0.183452i	−0.995784	−	0.0917262i	$-0.970762\pi$
$617$		−	113.190i		−	0.183452i	0.995784	−	0.0917262i	$-0.0292385\pi$
$618$			56.1542i			0.0908644i
$619$		−	1110.47i		−	1.79397i	−0.442062	−	0.896984i	$-0.645753\pi$
$619$		−	1110.47i		−	1.79397i	0.442062	−	0.896984i	$-0.354247\pi$
$620$			409.548i			0.660561i
$621$	−37.2276	−	113.565i	−0.0599478	−	0.182875i
$622$	−32.5977			−0.0524079
$623$	−338.592			−0.543486
$624$	1.79668			0.00287929
$625$	28.5826			0.0457322
$626$		−	71.3002i		−	0.113898i
$627$	−292.001			−0.465712
$628$		−	397.760i		−	0.633375i
$629$	168.055			0.267178
$630$	−7.82812			−0.0124256
$631$		−	269.827i		−	0.427618i	−0.976876	−	0.213809i	$-0.931413\pi$
$631$		−	269.827i		−	0.427618i	0.976876	−	0.213809i	$-0.0685870\pi$
$632$		−	374.362i		−	0.592345i
$633$	219.111			0.346147
$634$	−55.3715			−0.0873367
$635$		−	19.6585i		−	0.0309583i
$636$		−	569.435i		−	0.895339i
$637$	−0.493263			−0.000774353
$638$		−	121.530i		−	0.190486i
$639$	−42.8364			−0.0670367
$640$		−	235.778i		−	0.368404i
$641$			671.024i			1.04684i	0.852075	+	0.523419i	$0.175344\pi$
$641$			671.024i			1.04684i	−0.852075	+	0.523419i	$0.824656\pi$
$642$			32.0128i			0.0498641i
$643$			552.899i			0.859875i	0.902859	+	0.429937i	$0.141464\pi$
$643$			552.899i			0.859875i	−0.902859	+	0.429937i	$0.858536\pi$
$644$	−225.079	+	73.7824i	−0.349501	+	0.114569i
$645$	−145.471			−0.225537
$646$	−24.7921			−0.0383778
$647$	−79.6475			−0.123103			−0.0615514	−	0.998104i	$-0.519605\pi$
$647$	−79.6475			−0.123103			−0.0615514	+	0.998104i	$0.519605\pi$
$648$	23.2969			0.0359520
$649$			454.309i			0.700014i
$650$	−0.368800			−0.000567385
$651$			160.343i			0.246303i
$652$	186.256			0.285668
$653$	−517.157			−0.791971			−0.395986	−	0.918257i	$-0.629597\pi$
$653$	−517.157			−0.791971			−0.395986	+	0.918257i	$0.629597\pi$
$654$		−	68.2555i		−	0.104366i
$655$		−	275.221i		−	0.420184i
$656$	1090.31			1.66206
$657$	−361.819			−0.550714
$658$		−	13.9499i		−	0.0212004i
$659$		−	696.706i		−	1.05722i	−0.848866	−	0.528609i	$-0.822714\pi$
$659$		−	696.706i		−	1.05722i	0.848866	−	0.528609i	$-0.177286\pi$
$660$	−186.894			−0.283173
$661$			556.242i			0.841516i	0.907173	+	0.420758i	$0.138236\pi$
$661$			556.242i			0.841516i	−0.907173	+	0.420758i	$0.861764\pi$
$662$	−138.804			−0.209674
$663$		−	0.504495i		−	0.000760928i
$664$			48.1655i			0.0725384i
$665$			145.494i			0.218788i
$666$		−	40.0039i		−	0.0600659i
$667$	−287.972	−	878.479i	−0.431742	−	1.31706i
$668$	−688.940			−1.03135
$669$	82.2283			0.122912
$670$	−71.1883			−0.106251
$671$	−74.5380			−0.111085
$672$		−	69.5738i		−	0.103532i
$673$	−138.551			−0.205870			−0.102935	−	0.994688i	$-0.532823\pi$
$673$	−138.551			−0.205870			−0.102935	+	0.994688i	$0.532823\pi$
$674$			189.350i			0.280935i
$675$	82.9179			0.122841
$676$	657.801			0.973079
$677$			331.254i			0.489296i	0.969612	+	0.244648i	$0.0786724\pi$
$677$			331.254i			0.489296i	−0.969612	+	0.244648i	$0.921328\pi$
$678$		−	23.4863i		−	0.0346405i
$679$	239.140			0.352194
$680$	−32.1747			−0.0473157
$681$			778.365i			1.14297i
$682$		−	105.793i		−	0.155122i
$683$	−781.426			−1.14411			−0.572054	−	0.820216i	$-0.693853\pi$
$683$	−781.426			−1.14411			−0.572054	+	0.820216i	$0.693853\pi$
$684$		−	213.547i		−	0.312204i
$685$	−216.541			−0.316119
$686$			6.07423i			0.00885457i
$687$		−	373.660i		−	0.543901i
$688$		−	411.153i		−	0.597606i
$689$			5.95173i			0.00863822i
$690$	37.3347	−	12.2386i	0.0541082	−	0.0177371i
$691$	−116.189			−0.168146			−0.0840730	−	0.996460i	$-0.526793\pi$
$691$	−116.189			−0.168146			−0.0840730	+	0.996460i	$0.526793\pi$
$692$	290.724			0.420122
$693$	−73.1716			−0.105587
$694$	−110.237			−0.158843
$695$			688.327i			0.990399i
$696$	180.212			0.258925
$697$		−	306.152i		−	0.439242i
$698$	−41.0973			−0.0588786
$699$	394.210			0.563963
$700$		−	164.337i		−	0.234768i
$701$		−	922.576i		−	1.31609i	−0.752981	−	0.658043i	$-0.771385\pi$
$701$		−	922.576i		−	1.31609i	0.752981	−	0.658043i	$-0.228615\pi$
$702$	−0.120090			−0.000171068
$703$	−743.513			−1.05763
$704$		−	496.923i		−	0.705857i
$705$		−	83.7298i		−	0.118766i
$706$	−32.1943			−0.0456009
$707$			290.219i			0.410494i
$708$	−332.247			−0.469275
$709$			842.621i			1.18846i	0.804294	+	0.594232i	$0.202544\pi$
$709$			842.621i			1.18846i	−0.804294	+	0.594232i	$0.797456\pi$
$710$		−	14.0825i		−	0.0198345i
$711$		−	433.868i		−	0.610223i
$712$			331.271i			0.465268i
$713$	−250.682	−	764.725i	−0.351588	−	1.07254i
$714$	−6.21255			−0.00870105
$715$	1.95342			0.00273205
$716$	509.831			0.712054
$717$	444.491			0.619931
$718$			151.051i			0.210378i
$719$	563.888			0.784267			0.392133	−	0.919908i	$-0.371737\pi$
$719$	563.888			0.784267			0.392133	+	0.919908i	$0.371737\pi$
$720$		−	132.799i		−	0.184443i
$721$	261.533			0.362736
$722$	−8.71453			−0.0120700
$723$			813.063i			1.12457i
$724$		−	309.919i		−	0.428065i
$725$	641.407			0.884699
$726$	−20.4590			−0.0281804
$727$			820.880i			1.12913i	0.825387	+	0.564567i	$0.190957\pi$
$727$			820.880i			1.12913i	−0.825387	+	0.564567i	$0.809043\pi$
$728$			0.482597i			0.000662908i
$729$	27.0000			0.0370370
$730$		−	118.948i		−	0.162943i
$731$	−115.449			−0.157933
$732$		−	54.5114i		−	0.0744691i
$733$		−	169.968i		−	0.231879i	−0.993256	−	0.115940i	$-0.963012\pi$
$733$		−	169.968i		−	0.231879i	0.993256	−	0.115940i	$-0.0369879\pi$
$734$		−	81.7202i		−	0.111335i
$735$			36.4587i			0.0496037i
$736$	108.773	+	331.818i	0.147789	+	0.450840i
$737$	−665.416			−0.902871
$738$	−72.8763			−0.0987484
$739$	−1097.78			−1.48549			−0.742747	−	0.669572i	$-0.766477\pi$
$739$	−1097.78			−1.48549			−0.742747	+	0.669572i	$0.766477\pi$
$740$	−475.883			−0.643085
$741$			2.23200i			0.00301214i
$742$	73.2920			0.0987763
$743$			1185.75i			1.59590i	0.602727	+	0.797948i	$0.294081\pi$
$743$			1185.75i			1.59590i	−0.602727	+	0.797948i	$0.705919\pi$
$744$	156.876			0.210855
$745$	158.319			0.212509
$746$			64.7779i			0.0868336i
$747$			55.8216i			0.0747277i
$748$	−148.323			−0.198293
$749$	149.096			0.199061
$750$			69.9652i			0.0932869i
$751$		−	933.071i		−	1.24244i	−0.783637	−	0.621219i	$-0.786638\pi$
$751$		−	933.071i		−	1.24244i	0.783637	−	0.621219i	$-0.213362\pi$
$752$	236.650			0.314694
$753$		−	192.038i		−	0.255030i
$754$	−0.928950			−0.00123203
$755$			764.469i			1.01254i
$756$		−	53.5121i		−	0.0707832i
$757$		−	1006.42i		−	1.32949i	−0.747071	−	0.664744i	$-0.768541\pi$
$757$		−	1006.42i		−	1.32949i	0.747071	−	0.664744i	$-0.231459\pi$
$758$			243.053i			0.320651i
$759$	348.977	−	114.397i	0.459785	−	0.150721i
$760$	142.348			0.187300
$761$	−107.786			−0.141637			−0.0708187	−	0.997489i	$-0.522561\pi$
$761$	−107.786			−0.141637			−0.0708187	+	0.997489i	$0.522561\pi$
$762$	−3.71376			−0.00487370
$763$	−317.893			−0.416636
$764$			1432.20i			1.87461i
$765$	−37.2889			−0.0487437
$766$		−	211.364i		−	0.275932i
$767$	3.47264			0.00452756
$768$	328.913			0.428272
$769$			1378.73i			1.79288i	0.443161	+	0.896442i	$0.353857\pi$
$769$			1378.73i			1.79288i	−0.443161	+	0.896442i	$0.646143\pi$
$770$		−	24.0552i		−	0.0312405i
$771$	−280.008			−0.363175
$772$	1008.87			1.30682
$773$		−	1139.98i		−	1.47475i	−0.675485	−	0.737373i	$-0.736066\pi$
$773$		−	1139.98i		−	1.47475i	0.675485	−	0.737373i	$-0.263934\pi$
$774$			27.4815i			0.0355058i
$775$	558.351			0.720453
$776$		−	233.969i		−	0.301506i
$777$	−186.314			−0.239787
$778$			16.1239i			0.0207248i
$779$			1354.48i			1.73874i
$780$			1.42858i			0.00183151i
$781$		−	131.633i		−	0.168544i
$782$	29.6295	−	9.71278i	0.0378894	−	0.0124204i
$783$	208.857			0.266740
$784$	−103.045			−0.131435
$785$	307.286			0.391447
$786$	−51.9928			−0.0661486
$787$		−	832.403i		−	1.05769i	−0.848718	−	0.528845i	$-0.822625\pi$
$787$		−	832.403i		−	1.05769i	0.848718	−	0.528845i	$-0.177375\pi$
$788$	789.764			1.00224
$789$		−	361.883i		−	0.458660i
$790$	142.634			0.180550
$791$	−109.385			−0.138287
$792$			71.5894i			0.0903906i
$793$			0.569752i			0.000718477i
$794$	−66.8266			−0.0841645
$795$	439.913			0.553349
$796$			471.266i			0.592043i
$797$			841.525i			1.05587i	0.849286	+	0.527933i	$0.177033\pi$
$797$			841.525i			1.05587i	−0.849286	+	0.527933i	$0.822967\pi$
$798$	27.4857			0.0344432
$799$		−	66.4496i		−	0.0831660i
$800$	−242.272			−0.302839
$801$			383.927i			0.479310i
$802$		−	27.0240i		−	0.0336958i
$803$		−	1111.84i		−	1.38461i
$804$		−	486.634i		−	0.605266i
$805$	−57.0000	−	173.883i	−0.0708075	−	0.216003i
$806$	−0.808660			−0.00100330
$807$	−168.503			−0.208801
$808$	283.944			0.351416
$809$	1275.41			1.57653			0.788263	−	0.615339i	$-0.210981\pi$
$809$	1275.41			1.57653			0.788263	+	0.615339i	$0.210981\pi$
$810$			8.87626i			0.0109583i
$811$	−836.277			−1.03117			−0.515584	−	0.856839i	$-0.672425\pi$
$811$	−836.277			−1.03117			−0.515584	+	0.856839i	$0.672425\pi$
$812$		−	413.940i		−	0.509778i
$813$	236.523			0.290926
$814$	122.929			0.151018
$815$			143.890i			0.176552i
$816$		−	105.392i		−	0.129156i
$817$	510.771			0.625179
$818$	185.504			0.226778
$819$			0.559308i			0.000682915i
$820$			866.931i			1.05723i
$821$	113.132			0.137798			0.0688988	−	0.997624i	$-0.478051\pi$
$821$	113.132			0.137798			0.0688988	+	0.997624i	$0.478051\pi$
$822$			40.9075i			0.0497659i
$823$	319.434			0.388133			0.194067	−	0.980988i	$-0.437832\pi$
$823$	319.434			0.388133			0.194067	+	0.980988i	$0.437832\pi$
$824$		−	255.878i		−	0.310531i
$825$			254.800i			0.308848i
$826$		−	42.7634i		−	0.0517717i
$827$			691.081i			0.835649i	0.908528	+	0.417824i	$0.137207\pi$
$827$			691.081i			0.835649i	−0.908528	+	0.417824i	$0.862793\pi$
$828$	83.6614	+	255.215i	0.101040	+	0.308231i
$829$	831.786			1.00336			0.501680	−	0.865053i	$-0.332715\pi$
$829$	831.786			1.00336			0.501680	+	0.865053i	$0.332715\pi$
$830$	−18.3514			−0.0221101
$831$	582.304			0.700727
$832$	−3.79837			−0.00456535
$833$			28.9344i			0.0347351i
$834$	130.034			0.155916
$835$		−	532.235i		−	0.637407i
$836$	656.214			0.784945
$837$	181.812			0.217219
$838$			239.352i			0.285623i
$839$		−	798.714i		−	0.951984i	−0.879450	−	0.475992i	$-0.842089\pi$
$839$		−	798.714i		−	0.951984i	0.879450	−	0.475992i	$-0.157911\pi$
$840$	35.6704			0.0424647
$841$	774.603			0.921050
$842$			160.062i			0.190098i
$843$		−	97.4683i		−	0.115621i
$844$	−492.407			−0.583421
$845$			508.179i			0.601395i
$846$	−15.8177			−0.0186970
$847$			95.2858i			0.112498i
$848$			1243.35i			1.46621i
$849$			308.220i			0.363039i
$850$			21.6335i			0.0254512i
$851$	888.588	−	291.286i	1.04417	−	0.342286i
$852$	96.2661			0.112988
$853$	−1389.74			−1.62924			−0.814622	−	0.579993i	$-0.803055\pi$
$853$	−1389.74			−1.62924			−0.814622	+	0.579993i	$0.803055\pi$
$854$	7.01615			0.00821564
$855$	164.974			0.192952
$856$		−	145.872i		−	0.170412i
$857$	−983.647			−1.14778			−0.573890	−	0.818933i	$-0.694566\pi$
$857$	−983.647			−1.14778			−0.573890	+	0.818933i	$0.694566\pi$
$858$		−	0.369027i		−	0.000430101i
$859$	−357.902			−0.416650			−0.208325	−	0.978060i	$-0.566801\pi$
$859$	−357.902			−0.416650			−0.208325	+	0.978060i	$0.566801\pi$
$860$	326.917			0.380136
$861$			339.414i			0.394210i
$862$		−	163.891i		−	0.190128i
$863$	1418.86			1.64410			0.822051	−	0.569414i	$-0.192830\pi$
$863$	1418.86			1.64410			0.822051	+	0.569414i	$0.192830\pi$
$864$	−78.8893			−0.0913070
$865$			224.597i			0.259649i
$866$		−	82.1386i		−	0.0948483i
$867$	470.969			0.543217
$868$		−	360.338i		−	0.415137i
$869$	1333.24			1.53422
$870$			68.6618i			0.0789216i
$871$			5.08630i			0.00583960i
$872$			311.020i			0.356674i
$873$		−	271.159i		−	0.310606i
$874$	−131.087	+	42.9714i	−0.149986	+	0.0491664i
$875$	325.856			0.372407
$876$	813.114			0.928213
$877$	−198.888			−0.226783			−0.113391	−	0.993550i	$-0.536171\pi$
$877$	−198.888			−0.226783			−0.113391	+	0.993550i	$0.536171\pi$
$878$	187.190			0.213200
$879$			461.526i			0.525058i
$880$	408.079			0.463726
$881$		−	604.427i		−	0.686069i	−0.939323	−	0.343034i	$-0.888545\pi$
$881$		−	604.427i		−	0.686069i	0.939323	−	0.343034i	$-0.111455\pi$
$882$	6.88754			0.00780900
$883$	−1154.76			−1.30777			−0.653884	−	0.756595i	$-0.726861\pi$
$883$	−1154.76			−1.30777			−0.653884	+	0.756595i	$0.726861\pi$
$884$			1.13375i			0.00128252i
$885$		−	256.674i		−	0.290028i
$886$	170.434			0.192364
$887$	56.8741			0.0641196			0.0320598	−	0.999486i	$-0.489793\pi$
$887$	56.8741			0.0641196			0.0320598	+	0.999486i	$0.489793\pi$
$888$			182.285i			0.205276i
$889$			17.2965i			0.0194561i
$890$	−126.216			−0.141816
$891$			82.9688i			0.0931187i
$892$	−184.791			−0.207165
$893$			293.987i			0.329213i
$894$		−	29.9086i		−	0.0334548i
$895$			393.865i			0.440073i
$896$			207.448i			0.231527i
$897$	−0.874428	−	2.66751i	−0.000974836	−	0.00297381i
$898$	158.615			0.176631
$899$	1406.40			1.56440
$900$	−186.341			−0.207046
$901$	349.123			0.387484
$902$		−	223.943i		−	0.248274i
$903$	127.992			0.141741
$904$			107.020i			0.118385i
$905$	239.425			0.264558
$906$	144.418			0.159402
$907$		−	399.528i		−	0.440493i	−0.975444	−	0.220247i	$-0.929314\pi$
$907$		−	399.528i		−	0.440493i	0.975444	−	0.220247i	$-0.0706863\pi$
$908$		−	1749.22i		−	1.92645i
$909$	329.078			0.362022
$910$	−0.183873			−0.000202058
$911$		−	958.134i		−	1.05174i	−0.850565	−	0.525869i	$-0.823740\pi$
$911$		−	958.134i		−	1.05174i	0.850565	−	0.525869i	$-0.176260\pi$
$912$			466.275i			0.511267i
$913$	−171.535			−0.187881
$914$			40.4370i			0.0442418i
$915$	42.1123			0.0460244
$916$			839.724i			0.916729i
$917$			242.151i			0.264069i
$918$			7.04437i			0.00767361i
$919$		−	188.607i		−	0.205231i	−0.994721	−	0.102616i	$-0.967279\pi$
$919$		−	188.607i		−	0.205231i	0.994721	−	0.102616i	$-0.0327211\pi$
$920$	−170.123	+	55.7675i	−0.184916	+	0.0606169i
$921$	−686.090			−0.744940
$922$	−152.320			−0.165206
$923$	−1.00617			−0.00109011
$924$	164.438			0.177963
$925$			648.788i			0.701392i
$926$	−60.3756			−0.0652005
$927$		−	296.550i		−	0.319903i
$928$	−610.244			−0.657590
$929$	691.354			0.744192			0.372096	−	0.928194i	$-0.378639\pi$
$929$	691.354			0.744192			0.372096	+	0.928194i	$0.378639\pi$
$930$			59.7708i			0.0642696i
$931$		−	128.012i		−	0.137499i
$932$	−885.907			−0.950544
$933$	172.149			0.184511
$934$			242.980i			0.260150i
$935$		−	114.586i		−	0.122552i
$936$	0.547214			0.000584630
$937$			1191.54i			1.27165i	0.771831	+	0.635827i	$0.219341\pi$
$937$			1191.54i			1.27165i	−0.771831	+	0.635827i	$0.780659\pi$
$938$	62.6347			0.0667747
$939$			376.536i			0.400997i
$940$			188.166i			0.200176i
$941$			32.1890i			0.0342072i	0.999854	+	0.0171036i	$0.00544451\pi$
$941$			32.1890i			0.0342072i	−0.999854	+	0.0171036i	$0.994555\pi$
$942$		−	58.0504i		−	0.0616246i
$943$	−530.645	−	1618.77i	−0.562720	−	1.71662i
$944$	725.452			0.768487
$945$	41.3403			0.0437464
$946$	−84.4483			−0.0892688
$947$	−703.977			−0.743376			−0.371688	−	0.928358i	$-0.621221\pi$
$947$	−703.977			−0.743376			−0.371688	+	0.928358i	$0.621221\pi$
$948$			975.030i			1.02851i
$949$	−8.49866			−0.00895539
$950$		−	95.7113i		−	0.100749i
$951$	292.417			0.307484
$952$	28.3087			0.0297361
$953$			830.251i			0.871197i	0.900141	+	0.435598i	$0.143463\pi$
$953$			830.251i			0.871197i	−0.900141	+	0.435598i	$0.856537\pi$
$954$		−	83.1053i		−	0.0871125i
$955$	−1106.44			−1.15857
$956$	−998.902			−1.04488
$957$			641.800i			0.670638i
$958$		−	95.1796i		−	0.0993524i
$959$	190.523			0.198668
$960$			280.750i			0.292448i
$961$	263.282			0.273967
$962$		−	0.939639i		−	0.000976756i
$963$		−	169.059i		−	0.175555i
$964$		−	1827.19i		−	1.89543i
$965$			779.392i			0.807660i
$966$	−32.8487	+	10.7681i	−0.0340049	+	0.0111471i
$967$	−884.214			−0.914389			−0.457194	−	0.889367i	$-0.651146\pi$
$967$	−884.214			−0.914389			−0.457194	+	0.889367i	$0.651146\pi$
$968$	93.2254			0.0963072
$969$	130.927			0.135115
$970$	89.1436			0.0919006
$971$			211.929i			0.218259i	0.994028	+	0.109129i	$0.0348063\pi$
$971$			211.929i			0.218259i	−0.994028	+	0.109129i	$0.965194\pi$
$972$	−60.6770			−0.0624249
$973$		−	605.621i		−	0.622427i
$974$	154.434			0.158556
$975$	1.94763			0.00199757
$976$			119.024i			0.121951i
$977$		−	1366.41i		−	1.39857i	−0.714841	−	0.699287i	$-0.753501\pi$
$977$		−	1366.41i		−	1.39857i	0.714841	−	0.699287i	$-0.246499\pi$
$978$	27.1828			0.0277942
$979$	−1179.78			−1.20508
$980$		−	81.9336i		−	0.0836057i
$981$			360.457i			0.367438i
$982$	−144.907			−0.147563
$983$		−	313.182i		−	0.318598i	−0.987230	−	0.159299i	$-0.949077\pi$
$983$		−	313.182i		−	0.318598i	0.987230	−	0.159299i	$-0.0509233\pi$
$984$	332.075			0.337475
$985$			610.126i			0.619417i
$986$			54.4914i			0.0552651i
$987$			73.6692i			0.0746395i
$988$		−	5.01595i		−	0.00507688i
$989$	−610.434	+	200.105i	−0.617223	+	0.202330i
$990$	−27.2760			−0.0275515
$991$	997.180			1.00624			0.503118	−	0.864218i	$-0.332186\pi$
$991$	997.180			1.00624			0.503118	+	0.864218i	$0.332186\pi$
$992$	−531.223			−0.535507
$993$	733.024			0.738191
$994$			12.3904i			0.0124652i
$995$	−364.073			−0.365902
$996$		−	125.448i		−	0.125951i
$997$	798.253			0.800655			0.400328	−	0.916372i	$-0.368896\pi$
$997$	798.253			0.800655			0.400328	+	0.916372i	$0.368896\pi$
$998$	168.834			0.169173
$999$			211.260i			0.211472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.24	yes	48
23.22	odd	2	inner	483.3.f.a.22.23	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.23	✓	48	23.22	odd	2	inner
483.3.f.a.22.24	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.327978 q^{2} +1.73205 q^{3} -3.89243 q^{4} -3.00707i q^{5} -0.568074 q^{6} +2.64575i q^{7} +2.58854 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-0.327978 q^{2} +1.73205 q^{3} -3.89243 q^{4} -3.00707i q^{5} -0.568074 q^{6} +2.64575i q^{7} +2.58854 q^{8} +3.00000 q^{9} +0.986251i q^{10} +9.21875i q^{11} -6.74189 q^{12} +0.0704661 q^{13} -0.867748i q^{14} -5.20839i q^{15} +14.7207 q^{16} -4.13348i q^{17} -0.983934 q^{18} +18.2874i q^{19} +11.7048i q^{20} +4.58258i q^{21} -3.02355i q^{22} +(-7.16445 - 21.8557i) q^{23} +4.48349 q^{24} +15.9576 q^{25} -0.0231113 q^{26} +5.19615 q^{27} -10.2984i q^{28} +40.1946 q^{29} +1.70824i q^{30} +34.9897 q^{31} -15.1822 q^{32} +15.9673i q^{33} +1.35569i q^{34} +7.95595 q^{35} -11.6773 q^{36} +40.6571i q^{37} -5.99787i q^{38} +0.122051 q^{39} -7.78392i q^{40} +74.0663 q^{41} -1.50298i q^{42} -27.9302i q^{43} -35.8833i q^{44} -9.02120i q^{45} +(2.34978 + 7.16818i) q^{46} +16.0759 q^{47} +25.4971 q^{48} -7.00000 q^{49} -5.23373 q^{50} -7.15940i q^{51} -0.274285 q^{52} +84.4623i q^{53} -1.70422 q^{54} +27.7214 q^{55} +6.84864i q^{56} +31.6747i q^{57} -13.1829 q^{58} +49.2810 q^{59} +20.2733i q^{60} +8.08548i q^{61} -11.4759 q^{62} +7.93725i q^{63} -53.9035 q^{64} -0.211896i q^{65} -5.23694i q^{66} +72.1807i q^{67} +16.0893i q^{68} +(-12.4092 - 37.8551i) q^{69} -2.60937 q^{70} -14.2788 q^{71} +7.76563 q^{72} -120.606 q^{73} -13.3346i q^{74} +27.6393 q^{75} -71.1825i q^{76} -24.3905 q^{77} -0.0400300 q^{78} -144.623i q^{79} -44.2662i q^{80} +9.00000 q^{81} -24.2921 q^{82} +18.6072i q^{83} -17.8374i q^{84} -12.4296 q^{85} +9.16049i q^{86} +69.6190 q^{87} +23.8631i q^{88} +127.976i q^{89} +2.95875i q^{90} +0.186436i q^{91} +(27.8871 + 85.0717i) q^{92} +60.6040 q^{93} -5.27255 q^{94} +54.9914 q^{95} -26.2964 q^{96} -90.3864i q^{97} +2.29585 q^{98} +27.6563i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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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