LMFDB - Embedded newform 483.3.f.a.22.14

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			22.14
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} -0.711109i q^{5} +3.04499 q^{6} +2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} -0.711109i q^{5} +3.04499 q^{6} +2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} +1.25015i q^{10} -8.01603i q^{11} +1.57505 q^{12} -19.1112 q^{13} -4.65129i q^{14} +1.23168i q^{15} -11.5357 q^{16} +25.4247i q^{17} -5.27407 q^{18} +5.80334i q^{19} +0.646650i q^{20} -4.58258i q^{21} +14.0924i q^{22} +(-19.3326 + 12.4600i) q^{23} -14.9489 q^{24} +24.4943 q^{25} +33.5979 q^{26} -5.19615 q^{27} -2.40593i q^{28} -13.4076 q^{29} -2.16532i q^{30} +49.8044 q^{31} -14.2431 q^{32} +13.8842i q^{33} -44.6973i q^{34} +1.88142 q^{35} -2.72806 q^{36} -61.8720i q^{37} -10.2024i q^{38} +33.1016 q^{39} -6.13741i q^{40} +11.2387 q^{41} +8.05627i q^{42} -69.0959i q^{43} +7.28941i q^{44} -2.13333i q^{45} +(33.9871 - 21.9050i) q^{46} -8.79613 q^{47} +19.9803 q^{48} -7.00000 q^{49} -43.0616 q^{50} -44.0369i q^{51} +17.3789 q^{52} -63.7575i q^{53} +9.13496 q^{54} -5.70027 q^{55} +22.8348i q^{56} -10.0517i q^{57} +23.5709 q^{58} +54.3128 q^{59} -1.12003i q^{60} -65.2892i q^{61} -87.5573 q^{62} +7.93725i q^{63} +71.1823 q^{64} +13.5902i q^{65} -24.4087i q^{66} +102.088i q^{67} -23.1201i q^{68} +(33.4850 - 21.5813i) q^{69} -3.30758 q^{70} +14.5341 q^{71} +25.8923 q^{72} +74.1461 q^{73} +108.772i q^{74} -42.4254 q^{75} -5.27729i q^{76} +21.2084 q^{77} -58.1934 q^{78} -70.0342i q^{79} +8.20311i q^{80} +9.00000 q^{81} -19.7579 q^{82} -68.9881i q^{83} +4.16719i q^{84} +18.0798 q^{85} +121.472i q^{86} +23.2227 q^{87} -69.1844i q^{88} +12.2196i q^{89} +3.75044i q^{90} -50.5635i q^{91} +(17.5802 - 11.3306i) q^{92} -86.2638 q^{93} +15.4638 q^{94} +4.12681 q^{95} +24.6697 q^{96} -135.825i q^{97} +12.3062 q^{98} -24.0481i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.75802			−0.879012			−0.439506	−	0.898240i	$-0.644846\pi$
$2$	−1.75802			−0.879012			−0.439506	+	0.898240i	$0.644846\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−0.909354			−0.227339
$5$		−	0.711109i		−	0.142222i	−0.997468	−	0.0711109i	$-0.977346\pi$
$5$		−	0.711109i		−	0.142222i	0.997468	−	0.0711109i	$-0.0226544\pi$
$6$	3.04499			0.507498
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	8.63076			1.07884
$9$	3.00000			0.333333
$10$			1.25015i			0.125015i
$11$		−	8.01603i		−	0.728730i	−0.931256	−	0.364365i	$-0.881286\pi$
$11$		−	8.01603i		−	0.728730i	0.931256	−	0.364365i	$-0.118714\pi$
$12$	1.57505			0.131254
$13$	−19.1112			−1.47009			−0.735047	−	0.678017i	$-0.762840\pi$
$13$	−19.1112			−1.47009			−0.735047	+	0.678017i	$0.762840\pi$
$14$		−	4.65129i		−	0.332235i
$15$			1.23168i			0.0821118i
$16$	−11.5357			−0.720979
$17$			25.4247i			1.49557i	0.663940	+	0.747786i	$0.268883\pi$
$17$			25.4247i			1.49557i	−0.663940	+	0.747786i	$0.731117\pi$
$18$	−5.27407			−0.293004
$19$			5.80334i			0.305439i	0.988270	+	0.152719i	$0.0488031\pi$
$19$			5.80334i			0.305439i	−0.988270	+	0.152719i	$0.951197\pi$
$20$			0.646650i			0.0323325i
$21$		−	4.58258i		−	0.218218i
$22$			14.0924i			0.640562i
$23$	−19.3326	+	12.4600i	−0.840547	+	0.541739i
$23$	−19.3326	+	12.4600i	−0.840547	+	0.541739i
$24$	−14.9489			−0.622871
$25$	24.4943			0.979773
$26$	33.5979			1.29223
$27$	−5.19615			−0.192450
$28$		−	2.40593i		−	0.0859259i
$29$	−13.4076			−0.462332			−0.231166	−	0.972914i	$-0.574254\pi$
$29$	−13.4076			−0.462332			−0.231166	+	0.972914i	$0.574254\pi$
$30$		−	2.16532i		−	0.0721772i
$31$	49.8044			1.60659			0.803297	−	0.595579i	$-0.203077\pi$
$31$	49.8044			1.60659			0.803297	+	0.595579i	$0.203077\pi$
$32$	−14.2431			−0.445096
$33$			13.8842i			0.420733i
$34$		−	44.6973i		−	1.31463i
$35$	1.88142			0.0537548
$36$	−2.72806			−0.0757795
$37$		−	61.8720i		−	1.67222i	−0.548566	−	0.836108i	$-0.684826\pi$
$37$		−	61.8720i		−	1.67222i	0.548566	−	0.836108i	$-0.315174\pi$
$38$		−	10.2024i		−	0.268484i
$39$	33.1016			0.848759
$40$		−	6.13741i		−	0.153435i
$41$	11.2387			0.274115			0.137057	−	0.990563i	$-0.456236\pi$
$41$	11.2387			0.274115			0.137057	+	0.990563i	$0.456236\pi$
$42$			8.05627i			0.191816i
$43$		−	69.0959i		−	1.60688i	−0.595385	−	0.803441i	$-0.703000\pi$
$43$		−	69.0959i		−	1.60688i	0.595385	−	0.803441i	$-0.297000\pi$
$44$			7.28941i			0.165669i
$45$		−	2.13333i		−	0.0474073i
$46$	33.9871	−	21.9050i	0.738850	−	0.476195i
$47$	−8.79613			−0.187152			−0.0935758	−	0.995612i	$-0.529830\pi$
$47$	−8.79613			−0.187152			−0.0935758	+	0.995612i	$0.529830\pi$
$48$	19.9803			0.416257
$49$	−7.00000			−0.142857
$50$	−43.0616			−0.861232
$51$		−	44.0369i		−	0.863469i
$52$	17.3789			0.334209
$53$		−	63.7575i		−	1.20297i	−0.798884	−	0.601485i	$-0.794576\pi$
$53$		−	63.7575i		−	1.20297i	0.798884	−	0.601485i	$-0.205424\pi$
$54$	9.13496			0.169166
$55$	−5.70027			−0.103641
$56$			22.8348i			0.407765i
$57$		−	10.0517i		−	0.176345i
$58$	23.5709			0.406395
$59$	54.3128			0.920556			0.460278	−	0.887775i	$-0.347750\pi$
$59$	54.3128			0.920556			0.460278	+	0.887775i	$0.347750\pi$
$60$		−	1.12003i		−	0.0186672i
$61$		−	65.2892i		−	1.07031i	−0.844753	−	0.535157i	$-0.820252\pi$
$61$		−	65.2892i		−	1.07031i	0.844753	−	0.535157i	$-0.179748\pi$
$62$	−87.5573			−1.41221
$63$			7.93725i			0.125988i
$64$	71.1823			1.11222
$65$			13.5902i			0.209079i
$66$		−	24.4087i		−	0.369829i
$67$			102.088i			1.52370i	0.647751	+	0.761852i	$0.275710\pi$
$67$			102.088i			1.52370i	−0.647751	+	0.761852i	$0.724290\pi$
$68$		−	23.1201i		−	0.340001i
$69$	33.4850	−	21.5813i	0.485290	−	0.312773i
$70$	−3.30758			−0.0472511
$71$	14.5341			0.204705			0.102353	−	0.994748i	$-0.467363\pi$
$71$	14.5341			0.204705			0.102353	+	0.994748i	$0.467363\pi$
$72$	25.8923			0.359615
$73$	74.1461			1.01570			0.507850	−	0.861446i	$-0.330441\pi$
$73$	74.1461			1.01570			0.507850	+	0.861446i	$0.330441\pi$
$74$			108.772i			1.46990i
$75$	−42.4254			−0.565672
$76$		−	5.27729i		−	0.0694380i
$77$	21.2084			0.275434
$78$	−58.1934			−0.746069
$79$		−	70.0342i		−	0.886509i	−0.896396	−	0.443255i	$-0.853824\pi$
$79$		−	70.0342i		−	0.886509i	0.896396	−	0.443255i	$-0.146176\pi$
$80$			8.20311i			0.102539i
$81$	9.00000			0.111111
$82$	−19.7579			−0.240950
$83$		−	68.9881i		−	0.831181i	−0.909552	−	0.415591i	$-0.863575\pi$
$83$		−	68.9881i		−	0.831181i	0.909552	−	0.415591i	$-0.136425\pi$
$84$			4.16719i			0.0496093i
$85$	18.0798			0.212703
$86$			121.472i			1.41247i
$87$	23.2227			0.266928
$88$		−	69.1844i		−	0.786187i
$89$			12.2196i			0.137299i	0.997641	+	0.0686497i	$0.0218691\pi$
$89$			12.2196i			0.137299i	−0.997641	+	0.0686497i	$0.978131\pi$
$90$			3.75044i			0.0416715i
$91$		−	50.5635i		−	0.555643i
$92$	17.5802	−	11.3306i	0.191089	−	0.123158i
$93$	−86.2638			−0.927568
$94$	15.4638			0.164508
$95$	4.12681			0.0434401
$96$	24.6697			0.256976
$97$		−	135.825i		−	1.40026i	−0.714016	−	0.700130i	$-0.753125\pi$
$97$		−	135.825i		−	1.40026i	0.714016	−	0.700130i	$-0.246875\pi$
$98$	12.3062			0.125573
$99$		−	24.0481i		−	0.242910i
$100$	−22.2740			−0.222740
$101$	86.7443			0.858854			0.429427	−	0.903102i	$-0.358716\pi$
$101$	86.7443			0.858854			0.429427	+	0.903102i	$0.358716\pi$
$102$			77.4179i			0.758999i
$103$		−	15.5070i		−	0.150554i	−0.997163	−	0.0752769i	$-0.976016\pi$
$103$		−	15.5070i		−	0.150554i	0.997163	−	0.0752769i	$-0.0239841\pi$
$104$	−164.944			−1.58600
$105$	−3.25871			−0.0310353
$106$			112.087i			1.05743i
$107$		−	39.3116i		−	0.367398i	−0.982982	−	0.183699i	$-0.941193\pi$
$107$		−	39.3116i		−	0.367398i	0.982982	−	0.183699i	$-0.0588072\pi$
$108$	4.72514			0.0437513
$109$		−	119.619i		−	1.09742i	−0.836012	−	0.548711i	$-0.815119\pi$
$109$		−	119.619i		−	1.09742i	0.836012	−	0.548711i	$-0.184881\pi$
$110$	10.0212			0.0911020
$111$			107.165i			0.965454i
$112$		−	30.5205i		−	0.272504i
$113$			188.364i			1.66694i	0.552565	+	0.833470i	$0.313649\pi$
$113$			188.364i			1.66694i	−0.552565	+	0.833470i	$0.686351\pi$
$114$			17.6711i			0.155009i
$115$	8.86042	+	13.7476i	0.0770471	+	0.119544i
$116$	12.1923			0.105106
$117$	−57.3336			−0.490031
$118$	−95.4832			−0.809180
$119$	−67.2675			−0.565273
$120$			10.6303i			0.0885859i
$121$	56.7432			0.468952
$122$			114.780i			0.940818i
$123$	−19.4660			−0.158260
$124$	−45.2899			−0.365241
$125$		−	35.1959i		−	0.281567i
$126$		−	13.9539i		−	0.110745i
$127$	77.7836			0.612469			0.306235	−	0.951956i	$-0.400931\pi$
$127$	77.7836			0.612469			0.306235	+	0.951956i	$0.400931\pi$
$128$	−68.1678			−0.532561
$129$			119.678i			0.927733i
$130$		−	23.8918i		−	0.183783i
$131$	−79.4552			−0.606528			−0.303264	−	0.952907i	$-0.598076\pi$
$131$	−79.4552			−0.606528			−0.303264	+	0.952907i	$0.598076\pi$
$132$		−	12.6256i		−	0.0956488i
$133$	−15.3542			−0.115445
$134$		−	179.473i		−	1.33935i
$135$			3.69503i			0.0273706i
$136$			219.435i			1.61349i
$137$			113.187i			0.826184i	0.910689	+	0.413092i	$0.135551\pi$
$137$			113.187i			0.826184i	−0.910689	+	0.413092i	$0.864449\pi$
$138$	−58.8674	+	37.9405i	−0.426575	+	0.274931i
$139$	121.495			0.874067			0.437033	−	0.899445i	$-0.356029\pi$
$139$	121.495			0.874067			0.437033	+	0.899445i	$0.356029\pi$
$140$	−1.71088			−0.0122205
$141$	15.2353			0.108052
$142$	−25.5512			−0.179938
$143$			153.196i			1.07130i
$144$	−34.6070			−0.240326
$145$			9.53429i			0.0657537i
$146$	−130.350			−0.892812
$147$	12.1244			0.0824786
$148$			56.2635i			0.380159i
$149$		−	21.8043i		−	0.146338i	−0.997320	−	0.0731688i	$-0.976689\pi$
$149$		−	21.8043i		−	0.146338i	0.997320	−	0.0731688i	$-0.0233112\pi$
$150$	74.5849			0.497232
$151$	44.0474			0.291704			0.145852	−	0.989306i	$-0.453408\pi$
$151$	44.0474			0.291704			0.145852	+	0.989306i	$0.453408\pi$
$152$			50.0872i			0.329521i
$153$			76.2742i			0.498524i
$154$	−37.2849			−0.242110
$155$		−	35.4164i		−	0.228493i
$156$	−30.1011			−0.192956
$157$		−	282.497i		−	1.79934i	−0.436569	−	0.899671i	$-0.643807\pi$
$157$		−	282.497i		−	1.79934i	0.436569	−	0.899671i	$-0.356193\pi$
$158$			123.122i			0.779252i
$159$			110.431i			0.694536i
$160$			10.1284i			0.0633024i
$161$	−32.9660	−	51.1492i	−0.204758	−	0.317697i
$162$	−15.8222			−0.0976680
$163$	−318.274			−1.95260			−0.976299	−	0.216426i	$-0.930560\pi$
$163$	−318.274			−1.95260			−0.976299	+	0.216426i	$0.930560\pi$
$164$	−10.2200			−0.0623169
$165$	9.87316			0.0598374
$166$			121.283i			0.730618i
$167$	−40.9876			−0.245435			−0.122717	−	0.992442i	$-0.539161\pi$
$167$	−40.9876			−0.245435			−0.122717	+	0.992442i	$0.539161\pi$
$168$		−	39.5511i		−	0.235423i
$169$	196.238			1.16117
$170$	−31.7846			−0.186968
$171$			17.4100i			0.101813i
$172$			62.8327i			0.365306i
$173$	205.900			1.19017			0.595086	−	0.803662i	$-0.297118\pi$
$173$	205.900			1.19017			0.595086	+	0.803662i	$0.297118\pi$
$174$	−40.8260			−0.234632
$175$			64.8059i			0.370319i
$176$			92.4702i			0.525399i
$177$	−94.0726			−0.531484
$178$		−	21.4824i		−	0.120688i
$179$	−250.038			−1.39686			−0.698430	−	0.715678i	$-0.746118\pi$
$179$	−250.038			−1.39686			−0.698430	+	0.715678i	$0.746118\pi$
$180$			1.93995i			0.0107775i
$181$			31.4840i			0.173945i	0.996211	+	0.0869724i	$0.0277192\pi$
$181$			31.4840i			0.173945i	−0.996211	+	0.0869724i	$0.972281\pi$
$182$			88.8918i			0.488417i
$183$			113.084i			0.617946i
$184$	−166.855	+	107.539i	−0.906820	+	0.584452i
$185$	−43.9977			−0.237825
$186$	151.654			0.815343
$187$	203.805			1.08987
$188$	7.99880			0.0425468
$189$		−	13.7477i		−	0.0727393i
$190$	−7.25502			−0.0381843
$191$		−	356.198i		−	1.86491i	−0.361288	−	0.932454i	$-0.617663\pi$
$191$		−	356.198i		−	1.86491i	0.361288	−	0.932454i	$-0.382337\pi$
$192$	−123.291			−0.642142
$193$	−17.4493			−0.0904107			−0.0452053	−	0.998978i	$-0.514394\pi$
$193$	−17.4493			−0.0904107			−0.0452053	+	0.998978i	$0.514394\pi$
$194$			238.784i			1.23084i
$195$		−	23.5388i		−	0.120712i
$196$	6.36548			0.0324769
$197$	216.442			1.09869			0.549346	−	0.835595i	$-0.314877\pi$
$197$	216.442			1.09869			0.549346	+	0.835595i	$0.314877\pi$
$198$			42.2771i			0.213521i
$199$			79.5233i			0.399615i	0.979835	+	0.199807i	$0.0640316\pi$
$199$			79.5233i			0.399615i	−0.979835	+	0.199807i	$0.935968\pi$
$200$	211.405			1.05702
$201$		−	176.822i		−	0.879711i
$202$	−152.498			−0.754943
$203$		−	35.4733i		−	0.174745i
$204$			40.0452i			0.196300i
$205$		−	7.99195i		−	0.0389851i
$206$			27.2617i			0.132338i
$207$	−57.9977	+	37.3800i	−0.280182	+	0.180580i
$208$	220.460			1.05991
$209$	46.5197			0.222582
$210$	5.72889			0.0272804
$211$	−137.441			−0.651378			−0.325689	−	0.945477i	$-0.605596\pi$
$211$	−137.441			−0.651378			−0.325689	+	0.945477i	$0.605596\pi$
$212$			57.9781i			0.273482i
$213$	−25.1737			−0.118187
$214$			69.1108i			0.322948i
$215$	−49.1347			−0.228534
$216$	−44.8467			−0.207624
$217$			131.770i			0.607236i
$218$			210.293i			0.964646i
$219$	−128.425			−0.586414
$220$	5.18357			0.0235617
$221$		−	485.897i		−	2.19863i
$222$		−	188.399i		−	0.848645i
$223$	−206.967			−0.928105			−0.464052	−	0.885808i	$-0.653605\pi$
$223$	−206.967			−0.928105			−0.464052	+	0.885808i	$0.653605\pi$
$224$		−	37.6837i		−	0.168231i
$225$	73.4830			0.326591
$226$		−	331.149i		−	1.46526i
$227$			332.026i			1.46267i	0.682019	+	0.731335i	$0.261102\pi$
$227$			332.026i			1.46267i	−0.682019	+	0.731335i	$0.738898\pi$
$228$			9.14053i			0.0400901i
$229$		−	1.54210i		−	0.00673406i	−0.999994	−	0.00336703i	$-0.998928\pi$
$229$		−	1.54210i		−	0.00673406i	0.999994	−	0.00336703i	$-0.00107176\pi$
$230$	−15.5768	−	24.1685i	−0.0677253	−	0.105081i
$231$	−36.7341			−0.159022
$232$	−115.718			−0.498785
$233$	78.1284			0.335315			0.167658	−	0.985845i	$-0.446380\pi$
$233$	78.1284			0.335315			0.167658	+	0.985845i	$0.446380\pi$
$234$	100.794			0.430743
$235$			6.25501i			0.0266170i
$236$	−49.3896			−0.209278
$237$			121.303i			0.511826i
$238$	118.258			0.496882
$239$	−292.092			−1.22214			−0.611072	−	0.791575i	$-0.709261\pi$
$239$	−292.092			−1.22214			−0.611072	+	0.791575i	$0.709261\pi$
$240$		−	14.2082i		−	0.0592009i
$241$		−	394.307i		−	1.63613i	−0.575126	−	0.818065i	$-0.695047\pi$
$241$		−	394.307i		−	1.63613i	0.575126	−	0.818065i	$-0.304953\pi$
$242$	−99.7559			−0.412214
$243$	−15.5885			−0.0641500
$244$			59.3710i			0.243324i
$245$			4.97776i			0.0203174i
$246$	34.2217			0.139113
$247$		−	110.909i		−	0.449023i
$248$	429.850			1.73327
$249$			119.491i			0.479883i
$250$			61.8751i			0.247501i
$251$			107.173i			0.426984i	0.976945	+	0.213492i	$0.0684838\pi$
$251$			107.173i			0.426984i	−0.976945	+	0.213492i	$0.931516\pi$
$252$		−	7.21778i		−	0.0286420i
$253$	99.8797	+	154.971i	0.394782	+	0.612532i
$254$	−136.745			−0.538368
$255$	−31.3151			−0.122804
$256$	−164.889			−0.644096
$257$	−42.3722			−0.164872			−0.0824362	−	0.996596i	$-0.526270\pi$
$257$	−42.3722			−0.164872			−0.0824362	+	0.996596i	$0.526270\pi$
$258$		−	210.396i		−	0.815488i
$259$	163.698			0.632038
$260$		−	12.3583i		−	0.0475318i
$261$	−40.2229			−0.154111
$262$	139.684			0.533145
$263$			40.5143i			0.154047i	0.997029	+	0.0770234i	$0.0245416\pi$
$263$			40.5143i			0.154047i	−0.997029	+	0.0770234i	$0.975458\pi$
$264$			119.831i			0.453905i
$265$	−45.3385			−0.171089
$266$	26.9930			0.101478
$267$		−	21.1651i		−	0.0792699i
$268$		−	92.8343i		−	0.346397i
$269$	517.952			1.92547			0.962737	−	0.270440i	$-0.0871690\pi$
$269$	517.952			1.92547			0.962737	+	0.270440i	$0.0871690\pi$
$270$		−	6.49595i		−	0.0240591i
$271$	265.958			0.981395			0.490697	−	0.871330i	$-0.336742\pi$
$271$	265.958			0.981395			0.490697	+	0.871330i	$0.336742\pi$
$272$		−	293.291i		−	1.07828i
$273$			87.5786i			0.320801i
$274$		−	198.986i		−	0.726225i
$275$		−	196.347i		−	0.713990i
$276$	−30.4497	+	19.6251i	−0.110325	+	0.0711054i
$277$	426.483			1.53965			0.769824	−	0.638256i	$-0.220344\pi$
$277$	426.483			1.53965			0.769824	+	0.638256i	$0.220344\pi$
$278$	−213.591			−0.768315
$279$	149.413			0.535531
$280$	16.2381			0.0579931
$281$		−	365.313i		−	1.30005i	−0.759914	−	0.650024i	$-0.774759\pi$
$281$		−	365.313i		−	1.30005i	0.759914	−	0.650024i	$-0.225241\pi$
$282$	−26.7841			−0.0949790
$283$			517.783i			1.82962i	0.403882	+	0.914811i	$0.367660\pi$
$283$			517.783i			1.82962i	−0.403882	+	0.914811i	$0.632340\pi$
$284$	−13.2166			−0.0465374
$285$	−7.14784			−0.0250801
$286$		−	269.322i		−	0.941686i
$287$			29.7348i			0.103606i
$288$	−42.7292			−0.148365
$289$	−357.417			−1.23674
$290$		−	16.7615i		−	0.0577983i
$291$			235.256i			0.808440i
$292$	−67.4250			−0.230908
$293$		−	478.496i		−	1.63309i	−0.577280	−	0.816546i	$-0.695886\pi$
$293$		−	478.496i		−	1.63309i	0.577280	−	0.816546i	$-0.304114\pi$
$294$	−21.3149			−0.0724997
$295$		−	38.6223i		−	0.130923i
$296$		−	534.002i		−	1.80406i
$297$			41.6525i			0.140244i
$298$			38.3325i			0.128632i
$299$	369.469	−	238.126i	1.23568	−	0.796407i
$300$	38.5797			0.128599
$301$	182.811			0.607344
$302$	−77.4363			−0.256411
$303$	−150.245			−0.495860
$304$		−	66.9453i		−	0.220215i
$305$	−46.4277			−0.152222
$306$		−	134.092i		−	0.438208i
$307$	−395.306			−1.28764			−0.643821	−	0.765176i	$-0.722652\pi$
$307$	−395.306			−1.28764			−0.643821	+	0.765176i	$0.722652\pi$
$308$	−19.2860			−0.0626168
$309$			26.8590i			0.0869222i
$310$			62.2628i			0.200848i
$311$	584.020			1.87788			0.938939	−	0.344084i	$-0.111810\pi$
$311$	584.020			1.87788			0.938939	+	0.344084i	$0.111810\pi$
$312$	285.692			0.915679
$313$			121.168i			0.387118i	0.981089	+	0.193559i	$0.0620031\pi$
$313$			121.168i			0.387118i	−0.981089	+	0.193559i	$0.937997\pi$
$314$			496.636i			1.58164i
$315$	5.64425			0.0179183
$316$			63.6859i			0.201538i
$317$	−557.796			−1.75961			−0.879805	−	0.475335i	$-0.842327\pi$
$317$	−557.796			−1.75961			−0.879805	+	0.475335i	$0.842327\pi$
$318$		−	194.141i		−	0.610505i
$319$			107.476i			0.336915i
$320$		−	50.6184i		−	0.158182i
$321$			68.0898i			0.212118i
$322$	57.9551	+	89.9215i	0.179985	+	0.279259i
$323$	−147.548			−0.456806
$324$	−8.18419			−0.0252598
$325$	−468.116			−1.44036
$326$	559.532			1.71636
$327$			207.186i			0.633596i
$328$	96.9986			0.295727
$329$		−	23.2724i		−	0.0707367i
$330$	−17.3573			−0.0525977
$331$	511.085			1.54406			0.772031	−	0.635585i	$-0.219241\pi$
$331$	511.085			1.54406			0.772031	+	0.635585i	$0.219241\pi$
$332$			62.7346i			0.188960i
$333$		−	185.616i		−	0.557405i
$334$	72.0572			0.215740
$335$	72.5958			0.216704
$336$			52.8630i			0.157330i
$337$		−	486.160i		−	1.44261i	−0.692617	−	0.721305i	$-0.743542\pi$
$337$		−	486.160i		−	1.44261i	0.692617	−	0.721305i	$-0.256458\pi$
$338$	−344.992			−1.02069
$339$		−	326.256i		−	0.962408i
$340$	−16.4409			−0.0483556
$341$		−	399.234i		−	1.17077i
$342$		−	30.6072i		−	0.0894947i
$343$		−	18.5203i		−	0.0539949i
$344$		−	596.350i		−	1.73358i
$345$	−15.3467	−	23.8115i	−0.0444832	−	0.0690188i
$346$	−361.976			−1.04617
$347$	237.184			0.683528			0.341764	−	0.939786i	$-0.388976\pi$
$347$	237.184			0.683528			0.341764	+	0.939786i	$0.388976\pi$
$348$	−21.1177			−0.0606829
$349$	132.541			0.379775			0.189887	−	0.981806i	$-0.439188\pi$
$349$	132.541			0.379775			0.189887	+	0.981806i	$0.439188\pi$
$350$		−	113.930i		−	0.325515i
$351$	99.3048			0.282920
$352$			114.173i			0.324355i
$353$	183.098			0.518691			0.259346	−	0.965785i	$-0.416493\pi$
$353$	183.098			0.518691			0.259346	+	0.965785i	$0.416493\pi$
$354$	165.382			0.467180
$355$		−	10.3353i		−	0.0291135i
$356$		−	11.1120i		−	0.0312135i
$357$	116.511			0.326361
$358$	439.573			1.22786
$359$			299.975i			0.835584i	0.908543	+	0.417792i	$0.137196\pi$
$359$			299.975i			0.835584i	−0.908543	+	0.417792i	$0.862804\pi$
$360$		−	18.4122i		−	0.0511451i
$361$	327.321			0.906707
$362$		−	55.3496i		−	0.152899i
$363$	−98.2821			−0.270750
$364$			45.9801i			0.126319i
$365$		−	52.7259i		−	0.144455i
$366$		−	198.805i		−	0.543182i
$367$		−	135.980i		−	0.370517i	−0.982690	−	0.185259i	$-0.940688\pi$
$367$		−	135.980i		−	0.370517i	0.982690	−	0.185259i	$-0.0593123\pi$
$368$	223.014	−	143.734i	0.606016	−	0.390582i
$369$	33.7161			0.0913716
$370$	77.3490			0.209051
$371$	168.686			0.454680
$372$	78.4444			0.210872
$373$			4.36491i			0.0117022i	0.999983	+	0.00585109i	$0.00186247\pi$
$373$			4.36491i			0.0117022i	−0.999983	+	0.00585109i	$0.998138\pi$
$374$	−358.295			−0.958007
$375$			60.9610i			0.162563i
$376$	−75.9172			−0.201908
$377$	256.236			0.679671
$378$			24.1688i			0.0639387i
$379$			152.822i			0.403225i	0.979465	+	0.201612i	$0.0646182\pi$
$379$			152.822i			0.403225i	−0.979465	+	0.201612i	$0.935382\pi$
$380$	−3.75273			−0.00987560
$381$	−134.725			−0.353609
$382$			626.204i			1.63928i
$383$			408.302i			1.06606i	0.846096	+	0.533031i	$0.178947\pi$
$383$			408.302i			1.06606i	−0.846096	+	0.533031i	$0.821053\pi$
$384$	118.070			0.307474
$385$		−	15.0815i		−	0.0391727i
$386$	30.6762			0.0794720
$387$		−	207.288i		−	0.535627i
$388$			123.513i			0.318333i
$389$			653.238i			1.67928i	0.543146	+	0.839638i	$0.317233\pi$
$389$			653.238i			1.67928i	−0.543146	+	0.839638i	$0.682767\pi$
$390$			41.3818i			0.106107i
$391$	−316.792	−	491.525i	−0.810210	−	1.25710i
$392$	−60.4153			−0.154121
$393$	137.620			0.350179
$394$	−380.510			−0.965762
$395$	−49.8020			−0.126081
$396$			21.8682i			0.0552228i
$397$	−347.048			−0.874176			−0.437088	−	0.899419i	$-0.643990\pi$
$397$	−347.048			−0.874176			−0.437088	+	0.899419i	$0.643990\pi$
$398$		−	139.804i		−	0.351266i
$399$	26.5942			0.0666522
$400$	−282.558			−0.706395
$401$			75.2554i			0.187669i	0.995588	+	0.0938347i	$0.0299125\pi$
$401$			75.2554i			0.187669i	−0.995588	+	0.0938347i	$0.970087\pi$
$402$			310.857i			0.773276i
$403$	−951.823			−2.36184
$404$	−78.8813			−0.195251
$405$		−	6.39998i		−	0.0158024i
$406$			62.3628i			0.153603i
$407$	−495.968			−1.21859
$408$		−	380.072i		−	0.931549i
$409$	−120.274			−0.294068			−0.147034	−	0.989131i	$-0.546973\pi$
$409$	−120.274			−0.294068			−0.147034	+	0.989131i	$0.546973\pi$
$410$			14.0500i			0.0342684i
$411$		−	196.046i		−	0.476998i
$412$			14.1014i			0.0342267i
$413$			143.698i			0.347938i
$414$	101.961	−	65.7149i	0.246283	−	0.158732i
$415$	−49.0580			−0.118212
$416$	272.203			0.654333
$417$	−210.436			−0.504643
$418$	−81.7828			−0.195653
$419$			223.088i			0.532430i	0.963914	+	0.266215i	$0.0857731\pi$
$419$			223.088i			0.532430i	−0.963914	+	0.266215i	$0.914227\pi$
$420$	2.96332			0.00705553
$421$			475.998i			1.13064i	0.824873	+	0.565318i	$0.191247\pi$
$421$			475.998i			1.13064i	−0.824873	+	0.565318i	$0.808753\pi$
$422$	241.624			0.572569
$423$	−26.3884			−0.0623839
$424$		−	550.275i		−	1.29782i
$425$			622.761i			1.46532i
$426$	44.2560			0.103887
$427$	172.739			0.404541
$428$			35.7482i			0.0835239i
$429$		−	265.343i		−	0.618516i
$430$	86.3800			0.200884
$431$		−	589.612i		−	1.36801i	−0.729477	−	0.684005i	$-0.760237\pi$
$431$		−	589.612i		−	1.36801i	0.729477	−	0.684005i	$-0.239763\pi$
$432$	59.9410			0.138752
$433$		−	28.3248i		−	0.0654153i	−0.999465	−	0.0327077i	$-0.989587\pi$
$433$		−	28.3248i		−	0.0654153i	0.999465	−	0.0327077i	$-0.0104130\pi$
$434$		−	231.655i		−	0.533767i
$435$		−	16.5139i		−	0.0379629i
$436$			108.776i			0.249486i
$437$	−72.3095	−	112.193i	−0.165468	−	0.256736i
$438$	225.774			0.515465
$439$	770.570			1.75528			0.877642	−	0.479316i	$-0.159115\pi$
$439$	770.570			1.75528			0.877642	+	0.479316i	$0.159115\pi$
$440$	−49.1977			−0.111813
$441$	−21.0000			−0.0476190
$442$			854.219i			1.93262i
$443$	−192.079			−0.433588			−0.216794	−	0.976217i	$-0.569560\pi$
$443$	−192.079			−0.433588			−0.216794	+	0.976217i	$0.569560\pi$
$444$		−	97.4513i		−	0.219485i
$445$	8.68950			0.0195270
$446$	363.853			0.815815
$447$			37.7662i			0.0844880i
$448$			188.331i			0.420381i
$449$	−810.000			−1.80401			−0.902004	−	0.431727i	$-0.857904\pi$
$449$	−810.000			−1.80401			−0.902004	+	0.431727i	$0.857904\pi$
$450$	−129.185			−0.287077
$451$		−	90.0899i		−	0.199756i
$452$		−	171.290i		−	0.378960i
$453$	−76.2923			−0.168416
$454$		−	583.709i		−	1.28570i
$455$	−35.9562			−0.0790246
$456$		−	86.7536i		−	0.190249i
$457$		−	84.0185i		−	0.183848i	−0.995766	−	0.0919239i	$-0.970698\pi$
$457$		−	84.0185i		−	0.183848i	0.995766	−	0.0919239i	$-0.0293017\pi$
$458$			2.71105i			0.00591931i
$459$		−	132.111i		−	0.287823i
$460$	−8.05726	−	12.5014i	−0.0175158	−	0.0271770i
$461$	156.389			0.339240			0.169620	−	0.985510i	$-0.445746\pi$
$461$	156.389			0.339240			0.169620	+	0.985510i	$0.445746\pi$
$462$	64.5794			0.139782
$463$	729.911			1.57648			0.788241	−	0.615366i	$-0.210992\pi$
$463$	729.911			1.57648			0.788241	+	0.615366i	$0.210992\pi$
$464$	154.666			0.333332
$465$			61.3430i			0.131920i
$466$	−137.352			−0.294746
$467$			278.356i			0.596051i	0.954558	+	0.298026i	$0.0963281\pi$
$467$			278.356i			0.596051i	−0.954558	+	0.298026i	$0.903672\pi$
$468$	52.1366			0.111403
$469$	−270.100			−0.575906
$470$		−	10.9964i		−	0.0233967i
$471$			489.298i			1.03885i
$472$	468.761			0.993138
$473$	−553.875			−1.17098
$474$		−	213.253i		−	0.449901i
$475$			142.149i			0.299261i
$476$	61.1700			0.128508
$477$		−	191.272i		−	0.400990i
$478$	513.505			1.07428
$479$			195.302i			0.407728i	0.978999	+	0.203864i	$0.0653501\pi$
$479$			195.302i			0.407728i	−0.978999	+	0.203864i	$0.934650\pi$
$480$		−	17.5429i		−	0.0365477i
$481$			1182.45i			2.45831i
$482$			693.201i			1.43818i
$483$	57.0989	+	88.5930i	0.118217	+	0.183422i
$484$	−51.5997			−0.106611
$485$	−96.5865			−0.199147
$486$	27.4049			0.0563886
$487$	−356.792			−0.732632			−0.366316	−	0.930491i	$-0.619381\pi$
$487$	−356.792			−0.732632			−0.366316	+	0.930491i	$0.619381\pi$
$488$		−	563.495i		−	1.15470i
$489$	551.266			1.12733
$490$		−	8.75102i		−	0.0178592i
$491$	−336.651			−0.685644			−0.342822	−	0.939400i	$-0.611383\pi$
$491$	−336.651			−0.685644			−0.342822	+	0.939400i	$0.611383\pi$
$492$	17.7015			0.0359787
$493$		−	340.885i		−	0.691451i
$494$			194.980i			0.394697i
$495$	−17.1008			−0.0345471
$496$	−574.527			−1.15832
$497$			38.4535i			0.0773713i
$498$		−	210.068i		−	0.421823i
$499$	−168.599			−0.337873			−0.168936	−	0.985627i	$-0.554033\pi$
$499$	−168.599			−0.337873			−0.168936	+	0.985627i	$0.554033\pi$
$500$			32.0055i			0.0640110i
$501$	70.9927			0.141702
$502$		−	188.413i		−	0.375324i
$503$			804.464i			1.59933i	0.600445	+	0.799666i	$0.294990\pi$
$503$			804.464i			1.59933i	−0.600445	+	0.799666i	$0.705010\pi$
$504$			68.5045i			0.135922i
$505$		−	61.6846i		−	0.122148i
$506$	−175.591	−	272.442i	−0.347018	−	0.538423i
$507$	−339.895			−0.670404
$508$	−70.7329			−0.139238
$509$	62.7242			0.123230			0.0616152	−	0.998100i	$-0.480375\pi$
$509$	62.7242			0.123230			0.0616152	+	0.998100i	$0.480375\pi$
$510$	55.0526			0.107946
$511$			196.172i			0.383898i
$512$	562.549			1.09873
$513$		−	30.1550i		−	0.0587817i
$514$	74.4913			0.144925
$515$	−11.0272			−0.0214120
$516$		−	108.829i		−	0.210910i
$517$			70.5100i			0.136383i
$518$	−287.785			−0.555569
$519$	−356.629			−0.687146
$520$			117.293i			0.225564i
$521$		−	497.634i		−	0.955152i	−0.878590	−	0.477576i	$-0.841515\pi$
$521$		−	497.634i		−	0.955152i	0.878590	−	0.477576i	$-0.158485\pi$
$522$	70.7128			0.135465
$523$			84.1903i			0.160976i	0.996756	+	0.0804878i	$0.0256478\pi$
$523$			84.1903i			0.160976i	−0.996756	+	0.0804878i	$0.974352\pi$
$524$	72.2529			0.137887
$525$		−	112.247i		−	0.213804i
$526$		−	71.2251i		−	0.135409i
$527$			1266.26i			2.40278i
$528$		−	160.163i		−	0.303339i
$529$	218.497	−	481.768i	0.413038	−	0.910714i
$530$	79.7062			0.150389
$531$	162.938			0.306852
$532$	13.9624			0.0262451
$533$	−214.785			−0.402974
$534$			37.2087i			0.0696791i
$535$	−27.9549			−0.0522521
$536$			881.098i			1.64384i
$537$	433.079			0.806478
$538$	−910.572			−1.69251
$539$			56.1122i			0.104104i
$540$		−	3.36009i		−	0.00622239i
$541$	71.2344			0.131672			0.0658359	−	0.997830i	$-0.479029\pi$
$541$	71.2344			0.131672			0.0658359	+	0.997830i	$0.479029\pi$
$542$	−467.560			−0.862657
$543$		−	54.5319i		−	0.100427i
$544$		−	362.126i		−	0.665674i
$545$	−85.0621			−0.156077
$546$		−	153.965i		−	0.281987i
$547$	−504.297			−0.921933			−0.460966	−	0.887418i	$-0.652497\pi$
$547$	−504.297			−0.921933			−0.460966	+	0.887418i	$0.652497\pi$
$548$		−	102.927i		−	0.187823i
$549$		−	195.867i		−	0.356771i
$550$			345.183i			0.627606i
$551$		−	77.8090i		−	0.141214i
$552$	289.001	−	186.263i	0.523553	−	0.337434i
$553$	185.293			0.335069
$554$	−749.766			−1.35337
$555$	76.2063			0.137309
$556$	−110.482			−0.198709
$557$			243.692i			0.437507i	0.975780	+	0.218754i	$0.0701991\pi$
$557$			243.692i			0.437507i	−0.975780	+	0.218754i	$0.929801\pi$
$558$	−262.672			−0.470738
$559$			1320.51i			2.36227i
$560$	−21.7034			−0.0387561
$561$	−353.001			−0.629236
$562$			642.230i			1.14276i
$563$			790.151i			1.40346i	0.712441	+	0.701732i	$0.247590\pi$
$563$			790.151i			1.40346i	−0.712441	+	0.701732i	$0.752410\pi$
$564$	−13.8543			−0.0245644
$565$	133.948			0.237075
$566$		−	910.274i		−	1.60826i
$567$			23.8118i			0.0419961i
$568$	125.440			0.220845
$569$		−	739.643i		−	1.29990i	−0.759977	−	0.649950i	$-0.774790\pi$
$569$		−	739.643i		−	1.29990i	0.759977	−	0.649950i	$-0.225210\pi$
$570$	12.5661			0.0220457
$571$		−	692.965i		−	1.21360i	−0.794855	−	0.606799i	$-0.792453\pi$
$571$		−	692.965i		−	1.21360i	0.794855	−	0.606799i	$-0.207547\pi$
$572$		−	139.310i		−	0.243548i
$573$			616.952i			1.07671i
$574$		−	52.2745i		−	0.0910706i
$575$	−473.538	+	305.199i	−0.823545	+	0.530781i
$576$	213.547			0.370741
$577$	−932.406			−1.61596			−0.807978	−	0.589213i	$-0.799438\pi$
$577$	−932.406			−1.61596			−0.807978	+	0.589213i	$0.799438\pi$
$578$	628.347			1.08711
$579$	30.2230			0.0521986
$580$		−	8.67005i		−	0.0149484i
$581$	182.525			0.314157
$582$		−	413.586i		−	0.710628i
$583$	−511.082			−0.876641
$584$	639.937			1.09578
$585$			40.7705i			0.0696931i
$586$			841.207i			1.43551i
$587$	253.018			0.431035			0.215518	−	0.976500i	$-0.430856\pi$
$587$	253.018			0.431035			0.215518	+	0.976500i	$0.430856\pi$
$588$	−11.0253			−0.0187506
$589$			289.032i			0.490716i
$590$			67.8990i			0.115083i
$591$	−374.889			−0.634330
$592$			713.734i			1.20563i
$593$	91.0966			0.153620			0.0768100	−	0.997046i	$-0.475527\pi$
$593$	91.0966			0.153620			0.0768100	+	0.997046i	$0.475527\pi$
$594$		−	73.2261i		−	0.123276i
$595$			47.8345i			0.0803942i
$596$			19.8278i			0.0332682i
$597$		−	137.738i		−	0.230718i
$598$	−649.535	+	418.630i	−1.08618	+	0.700051i
$599$	−426.693			−0.712342			−0.356171	−	0.934421i	$-0.615918\pi$
$599$	−426.693			−0.712342			−0.356171	+	0.934421i	$0.615918\pi$
$600$	−366.164			−0.610273
$601$	243.004			0.404332			0.202166	−	0.979351i	$-0.435202\pi$
$601$	243.004			0.404332			0.202166	+	0.979351i	$0.435202\pi$
$602$	−321.385			−0.533862
$603$			306.265i			0.507901i
$604$	−40.0547			−0.0663156
$605$		−	40.3506i		−	0.0666952i
$606$	264.135			0.435866
$607$	242.034			0.398738			0.199369	−	0.979924i	$-0.436111\pi$
$607$	242.034			0.398738			0.199369	+	0.979924i	$0.436111\pi$
$608$		−	82.6574i		−	0.135950i
$609$			61.4415i			0.100889i
$610$	81.6210			0.133805
$611$	168.105			0.275130
$612$		−	69.3603i		−	0.113334i
$613$		−	118.345i		−	0.193058i	−0.995330	−	0.0965291i	$-0.969226\pi$
$613$		−	118.345i		−	0.193058i	0.995330	−	0.0965291i	$-0.0307741\pi$
$614$	694.957			1.13185
$615$			13.8425i			0.0225081i
$616$	183.045			0.297151
$617$		−	1152.80i		−	1.86840i	−0.356749	−	0.934200i	$-0.616115\pi$
$617$		−	1152.80i		−	1.86840i	0.356749	−	0.934200i	$-0.383885\pi$
$618$		−	47.2187i		−	0.0764057i
$619$		−	12.3379i		−	0.0199319i	−0.999950	−	0.00996596i	$-0.996828\pi$
$619$		−	12.3379i		−	0.0199319i	0.999950	−	0.00996596i	$-0.00317232\pi$
$620$			32.2060i			0.0519452i
$621$	100.455	−	64.7440i	0.161763	−	0.104258i
$622$	−1026.72			−1.65068
$623$	−32.3302			−0.0518943
$624$	−381.849			−0.611937
$625$	587.330			0.939728
$626$		−	213.016i		−	0.340281i
$627$	−80.5746			−0.128508
$628$			256.890i			0.409060i
$629$	1573.08			2.50092
$630$	−9.92273			−0.0157504
$631$		−	51.6407i		−	0.0818395i	−0.999162	−	0.0409198i	$-0.986971\pi$
$631$		−	51.6407i		−	0.0818395i	0.999162	−	0.0409198i	$-0.0130288\pi$
$632$		−	604.448i		−	0.956406i
$633$	238.054			0.376073
$634$	980.619			1.54672
$635$		−	55.3126i		−	0.0871065i
$636$		−	100.421i		−	0.157895i
$637$	133.778			0.210013
$638$		−	188.945i		−	0.296153i
$639$	43.6022			0.0682350
$640$			48.4747i			0.0757418i
$641$		−	700.130i		−	1.09225i	−0.837705	−	0.546123i	$-0.816103\pi$
$641$		−	700.130i		−	1.09225i	0.837705	−	0.546123i	$-0.183897\pi$
$642$		−	119.703i		−	0.186454i
$643$		−	839.673i		−	1.30587i	−0.757415	−	0.652934i	$-0.773538\pi$
$643$		−	839.673i		−	1.30587i	0.757415	−	0.652934i	$-0.226462\pi$
$644$	29.9778	+	46.5127i	0.0465494	+	0.0722248i
$645$	85.1038			0.131944
$646$	259.393			0.401538
$647$	−790.982			−1.22254			−0.611269	−	0.791423i	$-0.709341\pi$
$647$	−790.982			−1.22254			−0.611269	+	0.791423i	$0.709341\pi$
$648$	77.6768			0.119872
$649$		−	435.373i		−	0.670837i
$650$	822.959			1.26609
$651$		−	228.233i		−	0.350588i
$652$	289.423			0.443901
$653$	341.232			0.522561			0.261280	−	0.965263i	$-0.415855\pi$
$653$	341.232			0.522561			0.261280	+	0.965263i	$0.415855\pi$
$654$		−	364.238i		−	0.556939i
$655$			56.5013i			0.0862615i
$656$	−129.646			−0.197631
$657$	222.438			0.338566
$658$			40.9134i			0.0621783i
$659$		−	682.936i		−	1.03632i	−0.855283	−	0.518161i	$-0.826617\pi$
$659$		−	682.936i		−	1.03632i	0.855283	−	0.518161i	$-0.173383\pi$
$660$	−8.97821			−0.0136033
$661$		−	562.849i		−	0.851511i	−0.904838	−	0.425755i	$-0.860008\pi$
$661$		−	562.849i		−	0.851511i	0.904838	−	0.425755i	$-0.139992\pi$
$662$	−898.499			−1.35725
$663$			841.599i			1.26938i
$664$		−	595.419i		−	0.896716i
$665$			10.9185i			0.0164188i
$666$			326.317i			0.489965i
$667$	259.204	−	167.059i	0.388612	−	0.250463i
$668$	37.2723			0.0557968
$669$	358.478			0.535842
$670$	−127.625			−0.190485
$671$	−523.360			−0.779970
$672$			65.2700i			0.0971280i
$673$	28.5552			0.0424297			0.0212149	−	0.999775i	$-0.493247\pi$
$673$	28.5552			0.0424297			0.0212149	+	0.999775i	$0.493247\pi$
$674$			854.680i			1.26807i
$675$	−127.276			−0.188557
$676$	−178.450			−0.263980
$677$			663.295i			0.979757i	0.871791	+	0.489878i	$0.162959\pi$
$677$			663.295i			0.979757i	−0.871791	+	0.489878i	$0.837041\pi$
$678$			573.566i			0.845968i
$679$	359.360			0.529248
$680$	156.042			0.229474
$681$		−	575.086i		−	0.844473i
$682$			701.862i			1.02912i
$683$	−24.5205			−0.0359012			−0.0179506	−	0.999839i	$-0.505714\pi$
$683$	−24.5205			−0.0359012			−0.0179506	+	0.999839i	$0.505714\pi$
$684$		−	15.8319i		−	0.0231460i
$685$	80.4885			0.117501
$686$			32.5590i			0.0474622i
$687$			2.67099i			0.00388791i
$688$			797.067i			1.15853i
$689$			1218.48i			1.76848i
$690$	26.9798	+	41.8612i	0.0391012	+	0.0606683i
$691$	−421.109			−0.609419			−0.304710	−	0.952445i	$-0.598559\pi$
$691$	−421.109			−0.609419			−0.304710	+	0.952445i	$0.598559\pi$
$692$	−187.236			−0.270572
$693$	63.6253			0.0918114
$694$	−416.976			−0.600829
$695$		−	86.3964i		−	0.124311i
$696$	200.430			0.287973
$697$			285.741i			0.409959i
$698$	−233.011			−0.333826
$699$	−135.322			−0.193594
$700$		−	58.9315i		−	0.0841879i
$701$		−	1159.54i		−	1.65413i	−0.562109	−	0.827063i	$-0.690010\pi$
$701$		−	1159.54i		−	1.65413i	0.562109	−	0.827063i	$-0.309990\pi$
$702$	−174.580			−0.248690
$703$	359.064			0.510759
$704$		−	570.600i		−	0.810511i
$705$		−	10.8340i		−	0.0153674i
$706$	−321.891			−0.455936
$707$			229.504i			0.324616i
$708$	85.5453			0.120827
$709$		−	156.174i		−	0.220273i	−0.993916	−	0.110137i	$-0.964871\pi$
$709$		−	156.174i		−	0.220273i	0.993916	−	0.110137i	$-0.0351289\pi$
$710$			18.1697i			0.0255911i
$711$		−	210.103i		−	0.295503i
$712$			105.465i			0.148125i
$713$	−962.848	+	620.563i	−1.35042	+	0.870355i
$714$	−204.829			−0.286875
$715$	108.939			0.152362
$716$	227.373			0.317560
$717$	505.919			0.705605
$718$		−	527.362i		−	0.734488i
$719$	−498.495			−0.693317			−0.346659	−	0.937991i	$-0.612684\pi$
$719$	−498.495			−0.693317			−0.346659	+	0.937991i	$0.612684\pi$
$720$			24.6093i			0.0341796i
$721$	41.0278			0.0569040
$722$	−575.438			−0.797006
$723$			682.960i			0.944620i
$724$		−	28.6301i		−	0.0395444i
$725$	−328.411			−0.452980
$726$	172.782			0.237992
$727$		−	1060.14i		−	1.45824i	−0.684385	−	0.729121i	$-0.739929\pi$
$727$		−	1060.14i		−	1.45824i	0.684385	−	0.729121i	$-0.260071\pi$
$728$		−	436.401i		−	0.599453i
$729$	27.0000			0.0370370
$730$			92.6934i			0.126977i
$731$	1756.74			2.40321
$732$		−	102.834i		−	0.140483i
$733$		−	807.046i		−	1.10102i	−0.834829	−	0.550509i	$-0.814434\pi$
$733$		−	807.046i		−	1.10102i	0.834829	−	0.550509i	$-0.185566\pi$
$734$			239.056i			0.325689i
$735$		−	8.62174i		−	0.0117303i
$736$	275.355	−	177.469i	0.374124	−	0.241126i
$737$	818.342			1.11037
$738$	−59.2737			−0.0803167
$739$	−603.367			−0.816463			−0.408232	−	0.912878i	$-0.633854\pi$
$739$	−603.367			−0.816463			−0.408232	+	0.912878i	$0.633854\pi$
$740$	40.0095			0.0540669
$741$			192.100i			0.259244i
$742$	−296.555			−0.399669
$743$			578.041i			0.777982i	0.921241	+	0.388991i	$0.127176\pi$
$743$			578.041i			0.777982i	−0.921241	+	0.388991i	$0.872824\pi$
$744$	−744.522			−1.00070
$745$	−15.5052			−0.0208124
$746$		−	7.67362i		−	0.0102864i
$747$		−	206.964i		−	0.277060i
$748$	−185.331			−0.247769
$749$	104.009			0.138864
$750$		−	107.171i		−	0.142895i
$751$		−	138.968i		−	0.185044i	−0.995711	−	0.0925222i	$-0.970507\pi$
$751$		−	138.968i		−	0.185044i	0.995711	−	0.0925222i	$-0.0294929\pi$
$752$	101.469			0.134932
$753$		−	185.629i		−	0.246519i
$754$	−450.469			−0.597439
$755$		−	31.3225i		−	0.0414867i
$756$			12.5016i			0.0165364i
$757$			804.571i			1.06284i	0.847108	+	0.531421i	$0.178342\pi$
$757$			804.571i			1.06284i	−0.847108	+	0.531421i	$0.821658\pi$
$758$		−	268.665i		−	0.354439i
$759$	−172.997	−	268.417i	−0.227927	−	0.353645i
$760$	35.6175			0.0468651
$761$	142.923			0.187810			0.0939049	−	0.995581i	$-0.470065\pi$
$761$	142.923			0.187810			0.0939049	+	0.995581i	$0.470065\pi$
$762$	236.850			0.310827
$763$	316.482			0.414786
$764$			323.910i			0.423966i
$765$	54.2393			0.0709010
$766$		−	717.804i		−	0.937080i
$767$	−1037.98			−1.35330
$768$	285.595			0.371869
$769$			544.852i			0.708520i	0.935147	+	0.354260i	$0.115267\pi$
$769$			544.852i			0.708520i	−0.935147	+	0.354260i	$0.884733\pi$
$770$			26.5136i			0.0344333i
$771$	73.3908			0.0951891
$772$	15.8676			0.0205538
$773$		−	221.017i		−	0.285921i	−0.989728	−	0.142961i	$-0.954338\pi$
$773$		−	221.017i		−	0.285921i	0.989728	−	0.142961i	$-0.0456622\pi$
$774$			364.417i			0.470822i
$775$	1219.93			1.57410
$776$		−	1172.27i		−	1.51066i
$777$	−283.533			−0.364907
$778$		−	1148.41i		−	1.47610i
$779$			65.2220i			0.0837253i
$780$			21.4051i			0.0274425i
$781$		−	116.506i		−	0.149175i
$782$	556.928	+	864.113i	0.712184	+	1.10500i
$783$	69.6681			0.0889759
$784$	80.7496			0.102997
$785$	−200.886			−0.255906
$786$	−241.940			−0.307812
$787$			533.056i			0.677327i	0.940908	+	0.338663i	$0.109975\pi$
$787$			533.056i			0.677327i	−0.940908	+	0.338663i	$0.890025\pi$
$788$	−196.823			−0.249775
$789$		−	70.1729i		−	0.0889390i
$790$	87.5530			0.110827
$791$	−498.365			−0.630044
$792$		−	207.553i		−	0.262062i
$793$			1247.75i			1.57346i
$794$	610.118			0.768410
$795$	78.5286			0.0987781
$796$		−	72.3149i		−	0.0908478i
$797$		−	126.679i		−	0.158945i	−0.996837	−	0.0794723i	$-0.974676\pi$
$797$		−	126.679i		−	0.158945i	0.996837	−	0.0794723i	$-0.0253235\pi$
$798$	−46.7533			−0.0585881
$799$		−	223.639i		−	0.279899i
$800$	−348.875			−0.436093
$801$			36.6589i			0.0457665i
$802$		−	132.301i		−	0.164964i
$803$		−	594.357i		−	0.740171i
$804$			160.794i			0.199992i
$805$	−36.3727	+	23.4425i	−0.0451834	+	0.0291211i
$806$	1673.33			2.07609
$807$	−897.120			−1.11167
$808$	748.669			0.926570
$809$	−15.3007			−0.0189131			−0.00945656	−	0.999955i	$-0.503010\pi$
$809$	−15.3007			−0.0189131			−0.00945656	+	0.999955i	$0.503010\pi$
$810$			11.2513i			0.0138905i
$811$	1102.85			1.35987			0.679933	−	0.733275i	$-0.262009\pi$
$811$	1102.85			1.35987			0.679933	+	0.733275i	$0.262009\pi$
$812$			32.2578i			0.0397263i
$813$	−460.653			−0.566609
$814$	871.923			1.07116
$815$			226.327i			0.277702i
$816$			507.995i			0.622543i
$817$	400.987			0.490804
$818$	211.444			0.258489
$819$		−	151.691i		−	0.185214i
$820$			7.26751i			0.00886282i
$821$	−818.210			−0.996602			−0.498301	−	0.867004i	$-0.666043\pi$
$821$	−818.210			−0.996602			−0.498301	+	0.867004i	$0.666043\pi$
$822$			344.653i			0.419286i
$823$	−972.988			−1.18225			−0.591123	−	0.806582i	$-0.701315\pi$
$823$	−972.988			−1.18225			−0.591123	+	0.806582i	$0.701315\pi$
$824$		−	133.837i		−	0.162424i
$825$			340.084i			0.412222i
$826$		−	252.625i		−	0.305841i
$827$			479.613i			0.579944i	0.957035	+	0.289972i	$0.0936459\pi$
$827$			479.613i			0.579944i	−0.957035	+	0.289972i	$0.906354\pi$
$828$	52.7405	−	33.9917i	0.0636962	−	0.0410527i
$829$	−1279.03			−1.54286			−0.771431	−	0.636313i	$-0.780459\pi$
$829$	−1279.03			−1.54286			−0.771431	+	0.636313i	$0.780459\pi$
$830$	86.2452			0.103910
$831$	−738.690			−0.888917
$832$	−1360.38			−1.63507
$833$		−	177.973i		−	0.213653i
$834$	369.951			0.443587
$835$			29.1467i			0.0349062i
$836$	−42.3029			−0.0506016
$837$	−258.791			−0.309189
$838$		−	392.194i		−	0.468012i
$839$			448.957i			0.535110i	0.963543	+	0.267555i	$0.0862157\pi$
$839$			448.957i			0.535110i	−0.963543	+	0.267555i	$0.913784\pi$
$840$	−28.1252			−0.0334823
$841$	−661.235			−0.786249
$842$		−	836.816i		−	0.993843i
$843$			632.741i			0.750583i
$844$	124.982			0.148083
$845$		−	139.547i		−	0.165144i
$846$	46.3914			0.0548362
$847$			150.128i			0.177247i
$848$			735.484i			0.867316i
$849$		−	896.826i		−	1.05633i
$850$		−	1094.83i		−	1.28803i
$851$	770.924	+	1196.14i	0.905904	+	1.40558i
$852$	22.8918			0.0268684
$853$	861.052			1.00944			0.504720	−	0.863283i	$-0.331596\pi$
$853$	861.052			1.00944			0.504720	+	0.863283i	$0.331596\pi$
$854$	−303.679			−0.355596
$855$	12.3804			0.0144800
$856$		−	339.289i		−	0.396366i
$857$	791.635			0.923728			0.461864	−	0.886951i	$-0.347181\pi$
$857$	791.635			0.923728			0.461864	+	0.886951i	$0.347181\pi$
$858$			466.480i			0.543683i
$859$	−1239.94			−1.44347			−0.721736	−	0.692169i	$-0.756655\pi$
$859$	−1239.94			−1.44347			−0.721736	+	0.692169i	$0.756655\pi$
$860$	44.6809			0.0519545
$861$		−	51.5022i		−	0.0598168i
$862$			1036.55i			1.20250i
$863$	1478.24			1.71291			0.856454	−	0.516223i	$-0.172663\pi$
$863$	1478.24			1.71291			0.856454	+	0.516223i	$0.172663\pi$
$864$	74.0092			0.0856588
$865$		−	146.417i		−	0.169268i
$866$			49.7957i			0.0575008i
$867$	619.064			0.714030
$868$		−	119.826i		−	0.138048i
$869$	−561.397			−0.646026
$870$			29.0318i			0.0333699i
$871$		−	1951.03i		−	2.23999i
$872$		−	1032.40i		−	1.18395i
$873$		−	407.476i		−	0.466753i
$874$	127.122	+	197.239i	0.145448	+	0.225674i
$875$	93.1195			0.106422
$876$	116.784			0.133315
$877$	765.506			0.872869			0.436434	−	0.899736i	$-0.356241\pi$
$877$	765.506			0.872869			0.436434	+	0.899736i	$0.356241\pi$
$878$	−1354.68			−1.54292
$879$			828.779i			0.942866i
$880$	65.7564			0.0747232
$881$		−	1228.09i		−	1.39398i	−0.717083	−	0.696988i	$-0.754523\pi$
$881$		−	1228.09i		−	1.39398i	0.717083	−	0.696988i	$-0.245477\pi$
$882$	36.9185			0.0418577
$883$	665.576			0.753767			0.376883	−	0.926261i	$-0.376996\pi$
$883$	665.576			0.753767			0.376883	+	0.926261i	$0.376996\pi$
$884$			441.853i			0.499833i
$885$			66.8959i			0.0755886i
$886$	337.680			0.381129
$887$	−4.28591			−0.00483192			−0.00241596	−	0.999997i	$-0.500769\pi$
$887$	−4.28591			−0.00483192			−0.00241596	+	0.999997i	$0.500769\pi$
$888$			924.919i			1.04157i
$889$			205.796i			0.231492i
$890$	−15.2763			−0.0171644
$891$		−	72.1443i		−	0.0809700i
$892$	188.207			0.210994
$893$		−	51.0469i		−	0.0571634i
$894$		−	66.3938i		−	0.0742660i
$895$			177.804i			0.198664i
$896$		−	180.355i		−	0.201289i
$897$	−639.939	+	412.446i	−0.713421	+	0.459806i
$898$	1424.00			1.58574
$899$	−667.759			−0.742780
$900$	−66.8221			−0.0742467
$901$	1621.02			1.79913
$902$			158.380i			0.175588i
$903$	−316.637			−0.350650
$904$			1625.73i			1.79837i
$905$	22.3886			0.0247387
$906$	134.124			0.148039
$907$		−	812.413i		−	0.895714i	−0.894105	−	0.447857i	$-0.852187\pi$
$907$		−	812.413i		−	0.895714i	0.894105	−	0.447857i	$-0.147813\pi$
$908$		−	301.929i		−	0.332521i
$909$	260.233			0.286285
$910$	63.2118			0.0694635
$911$		−	551.157i		−	0.605002i	−0.953149	−	0.302501i	$-0.902178\pi$
$911$		−	551.157i		−	0.605002i	0.953149	−	0.302501i	$-0.0978215\pi$
$912$			115.953i			0.127141i
$913$	−553.011			−0.605707
$914$			147.706i			0.161604i
$915$	80.4152			0.0878854
$916$			1.40231i			0.00153091i
$917$		−	210.219i		−	0.229246i
$918$			232.254i			0.253000i
$919$		−	899.360i		−	0.978629i	−0.872107	−	0.489314i	$-0.837247\pi$
$919$		−	899.360i		−	0.978629i	0.872107	−	0.489314i	$-0.162753\pi$
$920$	76.4721	+	118.652i	0.0831219	+	0.128970i
$921$	684.690			0.743420
$922$	−274.936			−0.298196
$923$	−277.763			−0.300936
$924$	33.4043			0.0361518
$925$		−	1515.51i		−	1.63839i
$926$	−1283.20			−1.38575
$927$		−	46.5211i		−	0.0501846i
$928$	190.966			0.205782
$929$	−426.862			−0.459485			−0.229743	−	0.973251i	$-0.573788\pi$
$929$	−426.862			−0.459485			−0.229743	+	0.973251i	$0.573788\pi$
$930$		−	107.842i		−	0.115960i
$931$		−	40.6234i		−	0.0436341i
$932$	−71.0464			−0.0762301
$933$	−1011.55			−1.08419
$934$		−	489.356i		−	0.523936i
$935$		−	144.928i		−	0.155003i
$936$	−494.833			−0.528667
$937$			425.634i			0.454252i	0.973865	+	0.227126i	$0.0729329\pi$
$937$			425.634i			0.454252i	−0.973865	+	0.227126i	$0.927067\pi$
$938$	474.842			0.506228
$939$		−	209.869i		−	0.223503i
$940$		−	5.68802i		−	0.00605108i
$941$			1307.90i			1.38991i	0.719055	+	0.694953i	$0.244575\pi$
$941$			1307.90i			1.38991i	−0.719055	+	0.694953i	$0.755425\pi$
$942$		−	860.198i		−	0.913161i
$943$	−217.273	+	140.034i	−0.230406	+	0.148499i
$944$	−626.534			−0.663701
$945$	−9.77613			−0.0103451
$946$	973.725			1.02931
$947$	660.525			0.697492			0.348746	−	0.937217i	$-0.386608\pi$
$947$	660.525			0.697492			0.348746	+	0.937217i	$0.386608\pi$
$948$		−	110.307i		−	0.116358i
$949$	−1417.02			−1.49317
$950$		−	249.901i		−	0.263054i
$951$	966.131			1.01591
$952$	−580.570			−0.609842
$953$		−	143.346i		−	0.150416i	−0.997168	−	0.0752078i	$-0.976038\pi$
$953$		−	143.346i		−	0.150416i	0.997168	−	0.0752078i	$-0.0239620\pi$
$954$			336.261i			0.352475i
$955$	−253.295			−0.265231
$956$	265.615			0.277840
$957$		−	186.154i		−	0.194518i
$958$		−	343.345i		−	0.358398i
$959$	−299.465			−0.312268
$960$			87.6736i			0.0913267i
$961$	1519.48			1.58114
$962$		−	2078.77i		−	2.16088i
$963$		−	117.935i		−	0.122466i
$964$			358.565i			0.371955i
$965$			12.4083i			0.0128584i
$966$	−100.381	−	155.749i	−0.103914	−	0.161230i
$967$	681.391			0.704644			0.352322	−	0.935879i	$-0.385392\pi$
$967$	681.391			0.704644			0.352322	+	0.935879i	$0.385392\pi$
$968$	489.737			0.505927
$969$	255.561			0.263737
$970$	169.801			0.175053
$971$		−	812.942i		−	0.837221i	−0.908166	−	0.418611i	$-0.862517\pi$
$971$		−	812.942i		−	0.837221i	0.908166	−	0.418611i	$-0.137483\pi$
$972$	14.1754			0.0145838
$973$			321.446i			0.330366i
$974$	627.248			0.643992
$975$	810.801			0.831591
$976$			753.153i			0.771673i
$977$		−	654.475i		−	0.669882i	−0.942239	−	0.334941i	$-0.891284\pi$
$977$		−	654.475i		−	0.669882i	0.942239	−	0.334941i	$-0.108716\pi$
$978$	−969.138			−0.990939
$979$	97.9531			0.100054
$980$		−	4.52655i		−	0.00461893i
$981$		−	358.857i		−	0.365807i
$982$	591.841			0.602689
$983$		−	1694.86i		−	1.72417i	−0.506760	−	0.862087i	$-0.669157\pi$
$983$		−	1694.86i		−	1.72417i	0.506760	−	0.862087i	$-0.330843\pi$
$984$	−168.007			−0.170738
$985$		−	153.914i		−	0.156258i
$986$			599.284i			0.607793i
$987$			40.3089i			0.0408398i
$988$			100.855i			0.102080i
$989$	860.935	+	1335.80i	0.870510	+	1.35066i
$990$	30.0636			0.0303673
$991$	−995.227			−1.00427			−0.502133	−	0.864791i	$-0.667451\pi$
$991$	−995.227			−1.00427			−0.502133	+	0.864791i	$0.667451\pi$
$992$	−709.368			−0.715089
$993$	−885.224			−0.891465
$994$		−	67.6022i		−	0.0680102i
$995$	56.5498			0.0568339
$996$		−	108.659i		−	0.109096i
$997$	27.1125			0.0271941			0.0135970	−	0.999908i	$-0.495672\pi$
$997$	27.1125			0.0271941			0.0135970	+	0.999908i	$0.495672\pi$
$998$	296.400			0.296994
$999$			321.496i			0.321818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.14	yes	48
23.22	odd	2	inner	483.3.f.a.22.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.13	✓	48	23.22	odd	2	inner
483.3.f.a.22.14	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)

\(f(q)\)	\(=\)	\(q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} -0.711109i q^{5} +3.04499 q^{6} +2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.75802 q^{2} -1.73205 q^{3} -0.909354 q^{4} -0.711109i q^{5} +3.04499 q^{6} +2.64575i q^{7} +8.63076 q^{8} +3.00000 q^{9} +1.25015i q^{10} -8.01603i q^{11} +1.57505 q^{12} -19.1112 q^{13} -4.65129i q^{14} +1.23168i q^{15} -11.5357 q^{16} +25.4247i q^{17} -5.27407 q^{18} +5.80334i q^{19} +0.646650i q^{20} -4.58258i q^{21} +14.0924i q^{22} +(-19.3326 + 12.4600i) q^{23} -14.9489 q^{24} +24.4943 q^{25} +33.5979 q^{26} -5.19615 q^{27} -2.40593i q^{28} -13.4076 q^{29} -2.16532i q^{30} +49.8044 q^{31} -14.2431 q^{32} +13.8842i q^{33} -44.6973i q^{34} +1.88142 q^{35} -2.72806 q^{36} -61.8720i q^{37} -10.2024i q^{38} +33.1016 q^{39} -6.13741i q^{40} +11.2387 q^{41} +8.05627i q^{42} -69.0959i q^{43} +7.28941i q^{44} -2.13333i q^{45} +(33.9871 - 21.9050i) q^{46} -8.79613 q^{47} +19.9803 q^{48} -7.00000 q^{49} -43.0616 q^{50} -44.0369i q^{51} +17.3789 q^{52} -63.7575i q^{53} +9.13496 q^{54} -5.70027 q^{55} +22.8348i q^{56} -10.0517i q^{57} +23.5709 q^{58} +54.3128 q^{59} -1.12003i q^{60} -65.2892i q^{61} -87.5573 q^{62} +7.93725i q^{63} +71.1823 q^{64} +13.5902i q^{65} -24.4087i q^{66} +102.088i q^{67} -23.1201i q^{68} +(33.4850 - 21.5813i) q^{69} -3.30758 q^{70} +14.5341 q^{71} +25.8923 q^{72} +74.1461 q^{73} +108.772i q^{74} -42.4254 q^{75} -5.27729i q^{76} +21.2084 q^{77} -58.1934 q^{78} -70.0342i q^{79} +8.20311i q^{80} +9.00000 q^{81} -19.7579 q^{82} -68.9881i q^{83} +4.16719i q^{84} +18.0798 q^{85} +121.472i q^{86} +23.2227 q^{87} -69.1844i q^{88} +12.2196i q^{89} +3.75044i q^{90} -50.5635i q^{91} +(17.5802 - 11.3306i) q^{92} -86.2638 q^{93} +15.4638 q^{94} +4.12681 q^{95} +24.6697 q^{96} -135.825i q^{97} +12.3062 q^{98} -24.0481i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 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

Varieties

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Database

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