LMFDB - Embedded newform 201.3.c.a.68.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.13
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84390i q^{2} +(1.97832 + 2.25527i) q^{3} +0.600017 q^{4} -2.65010i q^{5} +(4.15850 - 3.64784i) q^{6} +5.23167 q^{7} -8.48199i q^{8} +(-1.17249 + 8.92330i) q^{9} +O(q^{10})$	\(q-1.84390i q^{2} +(1.97832 + 2.25527i) q^{3} +0.600017 q^{4} -2.65010i q^{5} +(4.15850 - 3.64784i) q^{6} +5.23167 q^{7} -8.48199i q^{8} +(-1.17249 + 8.92330i) q^{9} -4.88653 q^{10} +2.95963i q^{11} +(1.18703 + 1.35320i) q^{12} +4.18795 q^{13} -9.64671i q^{14} +(5.97668 - 5.24274i) q^{15} -13.2399 q^{16} -10.9299i q^{17} +(16.4537 + 2.16196i) q^{18} +11.6954 q^{19} -1.59010i q^{20} +(10.3499 + 11.7988i) q^{21} +5.45727 q^{22} +21.9171i q^{23} +(19.1292 - 16.7801i) q^{24} +17.9770 q^{25} -7.72218i q^{26} +(-22.4440 + 15.0089i) q^{27} +3.13909 q^{28} -35.8437i q^{29} +(-9.66712 - 11.0204i) q^{30} -15.8581 q^{31} -9.51483i q^{32} +(-6.67476 + 5.85510i) q^{33} -20.1536 q^{34} -13.8644i q^{35} +(-0.703513 + 5.35413i) q^{36} -44.8823 q^{37} -21.5653i q^{38} +(8.28511 + 9.44496i) q^{39} -22.4781 q^{40} +23.6603i q^{41} +(21.7559 - 19.0843i) q^{42} -56.4133 q^{43} +1.77583i q^{44} +(23.6476 + 3.10721i) q^{45} +40.4130 q^{46} +31.9776i q^{47} +(-26.1928 - 29.8596i) q^{48} -21.6296 q^{49} -33.1478i q^{50} +(24.6498 - 21.6228i) q^{51} +2.51284 q^{52} +15.8120i q^{53} +(27.6749 + 41.3846i) q^{54} +7.84330 q^{55} -44.3750i q^{56} +(23.1373 + 26.3764i) q^{57} -66.0924 q^{58} +51.0166i q^{59} +(3.58611 - 3.14573i) q^{60} +77.1692 q^{61} +29.2407i q^{62} +(-6.13408 + 46.6838i) q^{63} -70.5041 q^{64} -11.0985i q^{65} +(10.7962 + 12.3076i) q^{66} +8.18535 q^{67} -6.55811i q^{68} +(-49.4290 + 43.3591i) q^{69} -25.5647 q^{70} +109.029i q^{71} +(75.6873 + 9.94504i) q^{72} -92.2321 q^{73} +82.7586i q^{74} +(35.5643 + 40.5430i) q^{75} +7.01746 q^{76} +15.4838i q^{77} +(17.4156 - 15.2770i) q^{78} -14.6748 q^{79} +35.0871i q^{80} +(-78.2505 - 20.9249i) q^{81} +43.6272 q^{82} +36.0122i q^{83} +(6.21013 + 7.07950i) q^{84} -28.9652 q^{85} +104.021i q^{86} +(80.8373 - 70.9104i) q^{87} +25.1035 q^{88} -59.9764i q^{89} +(5.72940 - 43.6039i) q^{90} +21.9100 q^{91} +13.1506i q^{92} +(-31.3723 - 35.7642i) q^{93} +58.9637 q^{94} -30.9940i q^{95} +(21.4585 - 18.8234i) q^{96} -115.641 q^{97} +39.8829i q^{98} +(-26.4096 - 3.47013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.84390i		−	0.921952i	−0.887413	−	0.460976i	$-0.847499\pi$
$2$		−	1.84390i		−	0.921952i	0.887413	−	0.460976i	$-0.152501\pi$
$3$	1.97832	+	2.25527i	0.659440	+	0.751757i
$3$	1.97832	+	2.25527i	0.659440	+	0.751757i
$4$	0.600017			0.150004
$5$		−	2.65010i		−	0.530019i	−0.964246	−	0.265010i	$-0.914625\pi$
$5$		−	2.65010i		−	0.530019i	0.964246	−	0.265010i	$-0.0853752\pi$
$6$	4.15850	−	3.64784i	0.693084	−	0.607973i
$7$	5.23167			0.747382			0.373691	−	0.927553i	$-0.378092\pi$
$7$	5.23167			0.747382			0.373691	+	0.927553i	$0.378092\pi$
$8$		−	8.48199i		−	1.06025i
$9$	−1.17249	+	8.92330i	−0.130277	+	0.991478i
$10$	−4.88653			−0.488653
$11$			2.95963i			0.269057i	0.990910	+	0.134529i	$0.0429520\pi$
$11$			2.95963i			0.269057i	−0.990910	+	0.134529i	$0.957048\pi$
$12$	1.18703	+	1.35320i	0.0989188	+	0.112767i
$13$	4.18795			0.322150			0.161075	−	0.986942i	$-0.448504\pi$
$13$	4.18795			0.322150			0.161075	+	0.986942i	$0.448504\pi$
$14$		−	9.64671i		−	0.689051i
$15$	5.97668	−	5.24274i	0.398446	−	0.349516i
$16$	−13.2399			−0.827495
$17$		−	10.9299i		−	0.642934i	−0.946921	−	0.321467i	$-0.895824\pi$
$17$		−	10.9299i		−	0.642934i	0.946921	−	0.321467i	$-0.104176\pi$
$18$	16.4537	+	2.16196i	0.914095	+	0.120109i
$19$	11.6954			0.615549			0.307775	−	0.951459i	$-0.400416\pi$
$19$	11.6954			0.615549			0.307775	+	0.951459i	$0.400416\pi$
$20$		−	1.59010i		−	0.0795051i
$21$	10.3499	+	11.7988i	0.492854	+	0.561850i
$22$	5.45727			0.248058
$23$			21.9171i			0.952917i	0.879197	+	0.476459i	$0.158080\pi$
$23$			21.9171i			0.952917i	−0.879197	+	0.476459i	$0.841920\pi$
$24$	19.1292	−	16.7801i	0.797049	−	0.699171i
$25$	17.9770			0.719079
$26$		−	7.72218i		−	0.297007i
$27$	−22.4440	+	15.0089i	−0.831260	+	0.555884i
$28$	3.13909			0.112110
$29$		−	35.8437i		−	1.23599i	−0.786182	−	0.617995i	$-0.787945\pi$
$29$		−	35.8437i		−	1.23599i	0.786182	−	0.617995i	$-0.212055\pi$
$30$	−9.66712	−	11.0204i	−0.322237	−	0.367348i
$31$	−15.8581			−0.511550			−0.255775	−	0.966736i	$-0.582331\pi$
$31$	−15.8581			−0.511550			−0.255775	+	0.966736i	$0.582331\pi$
$32$		−	9.51483i		−	0.297338i
$33$	−6.67476	+	5.85510i	−0.202266	+	0.177427i
$34$	−20.1536			−0.592754
$35$		−	13.8644i		−	0.396127i
$36$	−0.703513	+	5.35413i	−0.0195420	+	0.148726i
$37$	−44.8823			−1.21303			−0.606517	−	0.795070i	$-0.707434\pi$
$37$	−44.8823			−1.21303			−0.606517	+	0.795070i	$0.707434\pi$
$38$		−	21.5653i		−	0.567507i
$39$	8.28511	+	9.44496i	0.212439	+	0.242178i
$40$	−22.4781			−0.561952
$41$			23.6603i			0.577079i	0.957468	+	0.288540i	$0.0931697\pi$
$41$			23.6603i			0.577079i	−0.957468	+	0.288540i	$0.906830\pi$
$42$	21.7559	−	19.0843i	0.517998	−	0.454388i
$43$	−56.4133			−1.31194			−0.655969	−	0.754788i	$-0.727740\pi$
$43$	−56.4133			−1.31194			−0.655969	+	0.754788i	$0.727740\pi$
$44$			1.77583i			0.0403597i
$45$	23.6476	+	3.10721i	0.525502	+	0.0690491i
$46$	40.4130			0.878544
$47$			31.9776i			0.680375i	0.940358	+	0.340188i	$0.110491\pi$
$47$			31.9776i			0.680375i	−0.940358	+	0.340188i	$0.889509\pi$
$48$	−26.1928	−	29.8596i	−0.545683	−	0.622075i
$49$	−21.6296			−0.441420
$50$		−	33.1478i		−	0.662957i
$51$	24.6498	−	21.6228i	0.483330	−	0.423977i
$52$	2.51284			0.0483238
$53$			15.8120i			0.298340i	0.988812	+	0.149170i	$0.0476602\pi$
$53$			15.8120i			0.298340i	−0.988812	+	0.149170i	$0.952340\pi$
$54$	27.6749	+	41.3846i	0.512499	+	0.766382i
$55$	7.84330			0.142605
$56$		−	44.3750i		−	0.792411i
$57$	23.1373	+	26.3764i	0.405918	+	0.462744i
$58$	−66.0924			−1.13952
$59$			51.0166i			0.864688i	0.901709	+	0.432344i	$0.142313\pi$
$59$			51.0166i			0.864688i	−0.901709	+	0.432344i	$0.857687\pi$
$60$	3.58611	−	3.14573i	0.0597685	−	0.0524289i
$61$	77.1692			1.26507			0.632535	−	0.774532i	$-0.282015\pi$
$61$	77.1692			1.26507			0.632535	+	0.774532i	$0.282015\pi$
$62$			29.2407i			0.471625i
$63$	−6.13408	+	46.6838i	−0.0973664	+	0.741013i
$64$	−70.5041			−1.10163
$65$		−	11.0985i		−	0.170746i
$66$	10.7962	+	12.3076i	0.163579	+	0.186479i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$		−	6.55811i		−	0.0964427i
$69$	−49.4290	+	43.3591i	−0.716362	+	0.628392i
$70$	−25.5647			−0.365210
$71$			109.029i			1.53561i	0.640682	+	0.767807i	$0.278652\pi$
$71$			109.029i			1.53561i	−0.640682	+	0.767807i	$0.721348\pi$
$72$	75.6873	+	9.94504i	1.05121	+	0.138126i
$73$	−92.2321			−1.26345			−0.631727	−	0.775191i	$-0.717654\pi$
$73$	−92.2321			−1.26345			−0.631727	+	0.775191i	$0.717654\pi$
$74$			82.7586i			1.11836i
$75$	35.5643	+	40.5430i	0.474190	+	0.540573i
$76$	7.01746			0.0923350
$77$			15.4838i			0.201088i
$78$	17.4156	−	15.2770i	0.223277	−	0.195858i
$79$	−14.6748			−0.185757			−0.0928783	−	0.995677i	$-0.529607\pi$
$79$	−14.6748			−0.185757			−0.0928783	+	0.995677i	$0.529607\pi$
$80$			35.0871i			0.438588i
$81$	−78.2505	−	20.9249i	−0.966056	−	0.258333i
$82$	43.6272			0.532040
$83$			36.0122i			0.433882i	0.976185	+	0.216941i	$0.0696079\pi$
$83$			36.0122i			0.433882i	−0.976185	+	0.216941i	$0.930392\pi$
$84$	6.21013	+	7.07950i	0.0739301	+	0.0842798i
$85$	−28.9652			−0.340767
$86$			104.021i			1.20954i
$87$	80.8373	−	70.9104i	0.929164	−	0.815062i
$88$	25.1035			0.285267
$89$		−	59.9764i		−	0.673892i	−0.941524	−	0.336946i	$-0.890606\pi$
$89$		−	59.9764i		−	0.673892i	0.941524	−	0.336946i	$-0.109394\pi$
$90$	5.72940	−	43.6039i	0.0636600	−	0.484488i
$91$	21.9100			0.240769
$92$			13.1506i			0.142942i
$93$	−31.3723	−	35.7642i	−0.337337	−	0.384561i
$94$	58.9637			0.627274
$95$		−	30.9940i		−	0.326253i
$96$	21.4585	−	18.8234i	0.223526	−	0.196077i
$97$	−115.641			−1.19218			−0.596089	−	0.802918i	$-0.703280\pi$
$97$	−115.641			−1.19218			−0.596089	+	0.802918i	$0.703280\pi$
$98$			39.8829i			0.406968i
$99$	−26.4096	−	3.47013i	−0.266764	−	0.0350518i
$100$	10.7865			0.107865
$101$			28.0274i			0.277499i	0.990327	+	0.138750i	$0.0443083\pi$
$101$			28.0274i			0.277499i	−0.990327	+	0.138750i	$0.955692\pi$
$102$	−39.8704	−	45.4519i	−0.390886	−	0.445607i
$103$	33.8847			0.328978			0.164489	−	0.986379i	$-0.447402\pi$
$103$	33.8847			0.328978			0.164489	+	0.986379i	$0.447402\pi$
$104$		−	35.5222i		−	0.341559i
$105$	31.2681	−	27.4283i	0.297791	−	0.261222i
$106$	29.1559			0.275056
$107$		−	99.8598i		−	0.933269i	−0.884450	−	0.466634i	$-0.845466\pi$
$107$		−	99.8598i		−	0.933269i	0.884450	−	0.466634i	$-0.154534\pi$
$108$	−13.4668	+	9.00557i	−0.124692	+	0.0833849i
$109$	−105.233			−0.965440			−0.482720	−	0.875775i	$-0.660351\pi$
$109$	−105.233			−0.965440			−0.482720	+	0.875775i	$0.660351\pi$
$110$		−	14.4623i		−	0.131475i
$111$	−88.7915	−	101.222i	−0.799924	−	0.911907i
$112$	−69.2669			−0.618455
$113$		−	64.0485i		−	0.566801i	−0.959002	−	0.283400i	$-0.908537\pi$
$113$		−	64.0485i		−	0.566801i	0.959002	−	0.283400i	$-0.0914625\pi$
$114$	48.6355	−	42.6630i	0.426627	−	0.374237i
$115$	58.0824			0.505065
$116$		−	21.5068i		−	0.185404i
$117$	−4.91033	+	37.3703i	−0.0419686	+	0.319405i
$118$	94.0697			0.797201
$119$		−	57.1815i		−	0.480517i
$120$	−44.4689	−	50.6942i	−0.370574	−	0.422452i
$121$	112.241			0.927608
$122$		−	142.293i		−	1.16633i
$123$	−53.3603	+	46.8076i	−0.433823	+	0.380549i
$124$	−9.51509			−0.0767346
$125$		−	113.893i		−	0.911145i
$126$	86.0805	+	11.3107i	0.683178	+	0.0897671i
$127$	79.0881			0.622741			0.311371	−	0.950289i	$-0.399212\pi$
$127$	79.0881			0.622741			0.311371	+	0.950289i	$0.399212\pi$
$128$			91.9435i			0.718308i
$129$	−111.604	−	127.227i	−0.865144	−	0.986258i
$130$	−20.4645			−0.157419
$131$		−	69.6262i		−	0.531497i	−0.964042	−	0.265749i	$-0.914381\pi$
$131$		−	69.6262i		−	0.531497i	0.964042	−	0.265749i	$-0.0856191\pi$
$132$	−4.00497	+	3.51315i	−0.0303407	+	0.0266148i
$133$	61.1867			0.460051
$134$		−	15.0930i		−	0.112634i
$135$	39.7750	+	59.4788i	0.294629	+	0.440584i
$136$	−92.7071			−0.681670
$137$			14.6893i			0.107221i	0.998562	+	0.0536107i	$0.0170730\pi$
$137$			14.6893i			0.107221i	−0.998562	+	0.0536107i	$0.982927\pi$
$138$	79.9500	+	91.1423i	0.579348	+	0.660451i
$139$	−122.074			−0.878230			−0.439115	−	0.898431i	$-0.644708\pi$
$139$	−122.074			−0.878230			−0.439115	+	0.898431i	$0.644708\pi$
$140$		−	8.31890i		−	0.0594207i
$141$	−72.1182	+	63.2621i	−0.511477	+	0.448667i
$142$	201.038			1.41576
$143$			12.3948i			0.0866768i
$144$	15.5237	−	118.144i	0.107803	−	0.820442i
$145$	−94.9893			−0.655099
$146$			170.067i			1.16484i
$147$	−42.7903	−	48.7806i	−0.291090	−	0.331841i
$148$	−26.9301			−0.181960
$149$		−	58.1673i		−	0.390385i	−0.980765	−	0.195192i	$-0.937467\pi$
$149$		−	58.1673i		−	0.390385i	0.980765	−	0.195192i	$-0.0625331\pi$
$150$	74.7574	−	65.5771i	0.498382	−	0.437181i
$151$	134.983			0.893930			0.446965	−	0.894551i	$-0.352505\pi$
$151$	134.983			0.893930			0.446965	+	0.894551i	$0.352505\pi$
$152$		−	99.2006i		−	0.652636i
$153$	97.5305	+	12.8152i	0.637455	+	0.0837592i
$154$	28.5507			0.185394
$155$			42.0254i			0.271131i
$156$	4.97120	+	5.66713i	0.0318667	+	0.0363278i
$157$	263.963			1.68130			0.840648	−	0.541582i	$-0.182175\pi$
$157$	263.963			1.68130			0.840648	+	0.541582i	$0.182175\pi$
$158$			27.0589i			0.171259i
$159$	−35.6604	+	31.2813i	−0.224279	+	0.196738i
$160$	−25.2152			−0.157595
$161$			114.663i			0.712193i
$162$	−38.5836	+	144.287i	−0.238170	+	0.890657i
$163$	62.7432			0.384928			0.192464	−	0.981304i	$-0.438352\pi$
$163$	62.7432			0.384928			0.192464	+	0.981304i	$0.438352\pi$
$164$			14.1965i			0.0865643i
$165$	15.5166	+	17.6888i	0.0940398	+	0.107205i
$166$	66.4031			0.400019
$167$		−	264.002i		−	1.58085i	−0.612558	−	0.790426i	$-0.709859\pi$
$167$		−	264.002i		−	1.58085i	0.612558	−	0.790426i	$-0.290141\pi$
$168$	100.078	−	87.7880i	0.595700	−	0.522548i
$169$	−151.461			−0.896219
$170$			53.4091i			0.314171i
$171$	−13.7128	+	104.362i	−0.0801917	+	0.610304i
$172$	−33.8489			−0.196796
$173$			131.624i			0.760835i	0.924815	+	0.380418i	$0.124220\pi$
$173$			131.624i			0.760835i	−0.924815	+	0.380418i	$0.875780\pi$
$174$	−130.752	−	149.056i	−0.751448	−	0.856645i
$175$	94.0497			0.537427
$176$		−	39.1852i		−	0.222643i
$177$	−115.056	+	100.927i	−0.650035	+	0.570210i
$178$	−110.591			−0.621296
$179$		−	164.251i		−	0.917604i	−0.888538	−	0.458802i	$-0.848279\pi$
$179$		−	164.251i		−	0.917604i	0.888538	−	0.458802i	$-0.151721\pi$
$180$	14.1890	+	1.86438i	0.0788275	+	0.0103576i
$181$	−30.1633			−0.166648			−0.0833240	−	0.996523i	$-0.526554\pi$
$181$	−30.1633			−0.166648			−0.0833240	+	0.996523i	$0.526554\pi$
$182$		−	40.3999i		−	0.221978i
$183$	152.666	+	174.038i	0.834238	+	0.951025i
$184$	185.901			1.01033
$185$			118.942i			0.642932i
$186$	−65.9458	+	57.8476i	−0.354547	+	0.311008i
$187$	32.3484			0.172986
$188$			19.1871i			0.102059i
$189$	−117.420	+	78.5215i	−0.621269	+	0.415458i
$190$	−57.1501			−0.300790
$191$			261.071i			1.36686i	0.730014	+	0.683432i	$0.239513\pi$
$191$			261.071i			1.36686i	−0.730014	+	0.683432i	$0.760487\pi$
$192$	−139.480	−	159.006i	−0.726457	−	0.828155i
$193$	275.614			1.42805			0.714025	−	0.700120i	$-0.246870\pi$
$193$	275.614			1.42805			0.714025	+	0.700120i	$0.246870\pi$
$194$			213.232i			1.09913i
$195$	25.0301	−	21.9563i	0.128359	−	0.112597i
$196$	−12.9781			−0.0662148
$197$			83.3036i			0.422861i	0.977393	+	0.211430i	$0.0678122\pi$
$197$			83.3036i			0.422861i	−0.977393	+	0.211430i	$0.932188\pi$
$198$	−6.39859	+	48.6969i	−0.0323161	+	0.245944i
$199$	143.984			0.723537			0.361769	−	0.932268i	$-0.382173\pi$
$199$	143.984			0.723537			0.361769	+	0.932268i	$0.382173\pi$
$200$		−	152.481i		−	0.762403i
$201$	16.1933	+	18.4602i	0.0805635	+	0.0918417i
$202$	51.6799			0.255841
$203$		−	187.523i		−	0.923757i
$204$	14.7903	−	12.9740i	0.0725015	−	0.0635982i
$205$	62.7020			0.305863
$206$		−	62.4802i		−	0.303302i
$207$	−195.573	−	25.6976i	−0.944796	−	0.124143i
$208$	−55.4481			−0.266577
$209$			34.6142i			0.165618i
$210$	−50.5752	−	57.6553i	−0.240834	−	0.274549i
$211$	367.789			1.74308			0.871538	−	0.490327i	$-0.163123\pi$
$211$	367.789			1.74308			0.871538	+	0.490327i	$0.163123\pi$
$212$			9.48748i			0.0447523i
$213$	−245.889	+	215.693i	−1.15441	+	1.01265i
$214$	−184.132			−0.860429
$215$			149.501i			0.695352i
$216$	127.305	+	190.370i	0.589376	+	0.881342i
$217$	−82.9642			−0.382323
$218$			194.040i			0.890089i
$219$	−182.465	−	208.008i	−0.833173	−	0.949810i
$220$	4.70611			0.0213914
$221$		−	45.7738i		−	0.207121i
$222$	−186.643	+	163.723i	−0.840734	+	0.737491i
$223$	26.1052			0.117063			0.0585317	−	0.998286i	$-0.481358\pi$
$223$	26.1052			0.117063			0.0585317	+	0.998286i	$0.481358\pi$
$224$		−	49.7785i		−	0.222225i
$225$	−21.0778	+	160.414i	−0.0936792	+	0.712951i
$226$	−118.099			−0.522563
$227$		−	384.299i		−	1.69295i	−0.532431	−	0.846473i	$-0.678722\pi$
$227$		−	384.299i		−	1.69295i	0.532431	−	0.846473i	$-0.321278\pi$
$228$	13.8828	+	15.8263i	0.0608894	+	0.0694134i
$229$	167.902			0.733195			0.366597	−	0.930380i	$-0.380523\pi$
$229$	167.902			0.733195			0.366597	+	0.930380i	$0.380523\pi$
$230$		−	107.098i		−	0.465645i
$231$	−34.9202	+	30.6320i	−0.151170	+	0.132606i
$232$	−304.026			−1.31046
$233$		−	35.4348i		−	0.152081i	−0.997105	−	0.0760404i	$-0.975772\pi$
$233$		−	35.4348i		−	0.152081i	0.997105	−	0.0760404i	$-0.0242278\pi$
$234$	68.9073	+	9.05417i	0.294476	+	0.0386930i
$235$	84.7439			0.360612
$236$			30.6108i			0.129707i
$237$	−29.0314	−	33.0956i	−0.122495	−	0.139644i
$238$	−105.437			−0.443014
$239$		−	147.129i		−	0.615604i	−0.951450	−	0.307802i	$-0.900407\pi$
$239$		−	147.129i		−	0.615604i	0.951450	−	0.307802i	$-0.0995935\pi$
$240$	−79.1308	+	69.4135i	−0.329712	+	0.289223i
$241$	−405.845			−1.68400			−0.842002	−	0.539475i	$-0.818623\pi$
$241$	−405.845			−1.68400			−0.842002	+	0.539475i	$0.818623\pi$
$242$		−	206.961i		−	0.855210i
$243$	−107.613	−	217.872i	−0.442853	−	0.896594i
$244$	46.3028			0.189766
$245$			57.3205i			0.233961i
$246$	86.3087	+	98.3912i	0.350848	+	0.399964i
$247$	48.9799			0.198299
$248$			134.508i			0.542370i
$249$	−81.2173	+	71.2437i	−0.326174	+	0.286119i
$250$	−210.008			−0.840033
$251$		−	8.46262i		−	0.0337156i	−0.999858	−	0.0168578i	$-0.994634\pi$
$251$		−	8.46262i		−	0.0337156i	0.999858	−	0.0168578i	$-0.00536626\pi$
$252$	−3.68055	+	28.0111i	−0.0146054	+	0.111155i
$253$	−64.8665			−0.256389
$254$		−	145.831i		−	0.574138i
$255$	−57.3025	−	65.3244i	−0.224716	−	0.256174i
$256$	−112.481			−0.439380
$257$		−	424.914i		−	1.65336i	−0.562670	−	0.826681i	$-0.690226\pi$
$257$		−	424.914i		−	1.65336i	0.562670	−	0.826681i	$-0.309774\pi$
$258$	−234.595	+	205.786i	−0.909282	+	0.797622i
$259$	−234.809			−0.906600
$260$		−	6.65927i		−	0.0256126i
$261$	319.844	+	42.0264i	1.22546	+	0.161021i
$262$	−128.384			−0.490015
$263$		−	36.9497i		−	0.140493i	−0.997530	−	0.0702465i	$-0.977621\pi$
$263$		−	36.9497i		−	0.140493i	0.997530	−	0.0702465i	$-0.0223786\pi$
$264$	49.6629	+	56.6153i	0.188117	+	0.214452i
$265$	41.9034			0.158126
$266$		−	112.822i		−	0.424145i
$267$	135.263	−	118.653i	0.506603	−	0.444391i
$268$	4.91135			0.0183259
$269$			227.187i			0.844562i	0.906465	+	0.422281i	$0.138770\pi$
$269$			227.187i			0.844562i	−0.906465	+	0.422281i	$0.861230\pi$
$270$	109.673	−	73.3412i	0.406197	−	0.271634i
$271$	215.655			0.795774			0.397887	−	0.917434i	$-0.369744\pi$
$271$	215.655			0.795774			0.397887	+	0.917434i	$0.369744\pi$
$272$			144.711i			0.532024i
$273$	43.3450	+	49.4130i	0.158773	+	0.181000i
$274$	27.0857			0.0988530
$275$			53.2052i			0.193473i
$276$	−29.6582	+	26.0162i	−0.107457	+	0.0942614i
$277$	218.353			0.788279			0.394140	−	0.919051i	$-0.371043\pi$
$277$	218.353			0.788279			0.394140	+	0.919051i	$0.371043\pi$
$278$			225.093i			0.809686i
$279$	18.5934	−	141.506i	0.0666430	−	0.507190i
$280$	−117.598			−0.419993
$281$			479.193i			1.70531i	0.522473	+	0.852656i	$0.325009\pi$
$281$			479.193i			1.70531i	−0.522473	+	0.852656i	$0.674991\pi$
$282$	116.649	+	132.979i	0.413650	+	0.471557i
$283$	27.1739			0.0960210			0.0480105	−	0.998847i	$-0.484712\pi$
$283$	27.1739			0.0960210			0.0480105	+	0.998847i	$0.484712\pi$
$284$			65.4189i			0.230348i
$285$	69.9000	−	61.3162i	0.245263	−	0.215145i
$286$	22.8548			0.0799118
$287$			123.783i			0.431299i
$288$	84.9037	+	11.1560i	0.294804	+	0.0387362i
$289$	169.538			0.586636
$290$			175.151i			0.603970i
$291$	−228.776	−	260.803i	−0.786171	−	0.896229i
$292$	−55.3408			−0.189523
$293$			90.2981i			0.308185i	0.988056	+	0.154092i	$0.0492453\pi$
$293$			90.2981i			0.308185i	−0.988056	+	0.154092i	$0.950755\pi$
$294$	−89.9467	+	78.9012i	−0.305941	+	0.268371i
$295$	135.199			0.458301
$296$			380.691i			1.28612i
$297$	−44.4207	−	66.4259i	−0.149565	−	0.223656i
$298$	−107.255			−0.359916
$299$			91.7877i			0.306982i
$300$	21.3391	+	24.3265i	0.0711305	+	0.0810882i
$301$	−295.136			−0.980518
$302$		−	248.897i		−	0.824161i
$303$	−63.2094	+	55.4473i	−0.208612	+	0.182994i
$304$	−154.847			−0.509364
$305$		−	204.506i		−	0.670511i
$306$	23.6299	−	179.837i	0.0772220	−	0.587703i
$307$	21.4382			0.0698311			0.0349156	−	0.999390i	$-0.488884\pi$
$307$	21.4382			0.0698311			0.0349156	+	0.999390i	$0.488884\pi$
$308$			9.29054i			0.0301641i
$309$	67.0349	+	76.4193i	0.216941	+	0.247312i
$310$	77.4908			0.249970
$311$		−	0.188950i		−	0.000607555i	−1.00000		0.000303778i	$-0.999903\pi$
$311$		−	0.188950i		−	0.000607555i	1.00000		0.000303778i	$-9.66954e-5\pi$
$312$	80.1121	−	70.2742i	0.256769	−	0.225238i
$313$	278.100			0.888499			0.444249	−	0.895903i	$-0.353470\pi$
$313$	278.100			0.888499			0.444249	+	0.895903i	$0.353470\pi$
$314$		−	486.723i		−	1.55007i
$315$	123.717	+	16.2559i	0.392751	+	0.0516061i
$316$	−8.80511			−0.0278643
$317$			404.954i			1.27746i	0.769432	+	0.638729i	$0.220540\pi$
$317$			404.954i			1.27746i	−0.769432	+	0.638729i	$0.779460\pi$
$318$	57.6797	+	65.7544i	0.181383	+	0.206775i
$319$	106.084			0.332552
$320$			186.843i			0.583883i
$321$	225.211	−	197.555i	0.701591	−	0.615435i
$322$	211.428			0.656608
$323$		−	127.830i		−	0.395758i
$324$	−46.9516	−	12.5553i	−0.144912	−	0.0387510i
$325$	75.2867			0.231651
$326$		−	115.692i		−	0.354885i
$327$	−208.185	−	237.329i	−0.636650	−	0.725776i
$328$	200.686			0.611848
$329$			167.297i			0.508500i
$330$	32.6164	−	28.6111i	0.0988376	−	0.0867002i
$331$	113.390			0.342569			0.171285	−	0.985222i	$-0.445208\pi$
$331$	113.390			0.342569			0.171285	+	0.985222i	$0.445208\pi$
$332$			21.6079i			0.0650841i
$333$	52.6240	−	400.498i	0.158030	−	1.20270i
$334$	−486.795			−1.45747
$335$		−	21.6920i		−	0.0647522i
$336$	−137.032	−	156.216i	−0.407834	−	0.464927i
$337$	407.422			1.20897			0.604484	−	0.796618i	$-0.293380\pi$
$337$	407.422			1.20897			0.604484	+	0.796618i	$0.293380\pi$
$338$			279.280i			0.826271i
$339$	144.447	−	126.708i	0.426096	−	0.373771i
$340$	−17.3796			−0.0511165
$341$		−	46.9339i		−	0.137636i
$342$	192.433	+	25.2850i	0.562671	+	0.0739329i
$343$	−369.511			−1.07729
$344$			478.497i			1.39098i
$345$	114.906	+	130.992i	0.333060	+	0.379686i
$346$	242.703			0.701454
$347$		−	534.926i		−	1.54157i	−0.637093	−	0.770787i	$-0.719863\pi$
$347$		−	534.926i		−	1.54157i	0.637093	−	0.770787i	$-0.280137\pi$
$348$	48.5037	−	42.5474i	0.139378	−	0.122263i
$349$	−104.706			−0.300017			−0.150009	−	0.988685i	$-0.547930\pi$
$349$	−104.706			−0.300017			−0.150009	+	0.988685i	$0.547930\pi$
$350$		−	173.419i		−	0.495482i
$351$	−93.9944	+	62.8564i	−0.267790	+	0.179078i
$352$	28.1604			0.0800010
$353$		−	518.724i		−	1.46947i	−0.678353	−	0.734737i	$-0.737306\pi$
$353$		−	518.724i		−	1.46947i	0.678353	−	0.734737i	$-0.262694\pi$
$354$	186.100	+	212.153i	0.525707	+	0.599301i
$355$	288.936			0.813905
$356$		−	35.9868i		−	0.101087i
$357$	128.960	−	113.123i	0.361232	−	0.316872i
$358$	−302.863			−0.845987
$359$			626.337i			1.74467i	0.488907	+	0.872336i	$0.337396\pi$
$359$			626.337i			1.74467i	−0.488907	+	0.872336i	$0.662604\pi$
$360$	26.3553	−	200.579i	0.0732092	−	0.557163i
$361$	−224.217			−0.621099
$362$			55.6182i			0.153642i
$363$	222.048	+	253.133i	0.611702	+	0.697336i
$364$	13.1464			0.0361164
$365$			244.424i			0.669655i
$366$	320.909	−	281.501i	0.876799	−	0.769128i
$367$	−51.8672			−0.141327			−0.0706637	−	0.997500i	$-0.522512\pi$
$367$	−51.8672			−0.141327			−0.0706637	+	0.997500i	$0.522512\pi$
$368$		−	290.180i		−	0.788534i
$369$	−211.128	−	27.7414i	−0.572161	−	0.0751799i
$370$	219.318			0.592752
$371$			82.7234i			0.222974i
$372$	−18.8239	−	21.4591i	−0.0506019	−	0.0576858i
$373$	−407.673			−1.09296			−0.546479	−	0.837473i	$-0.684032\pi$
$373$	−407.673			−1.09296			−0.546479	+	0.837473i	$0.684032\pi$
$374$		−	59.6473i		−	0.159485i
$375$	256.860	−	225.317i	0.684960	−	0.600846i
$376$	271.234			0.721367
$377$		−	150.112i		−	0.398174i
$378$	144.786	+	216.511i	0.383032	+	0.572780i
$379$	551.302			1.45462			0.727311	−	0.686308i	$-0.240770\pi$
$379$	551.302			1.45462			0.727311	+	0.686308i	$0.240770\pi$
$380$		−	18.5969i		−	0.0489393i
$381$	156.462	+	178.365i	0.410661	+	0.468150i
$382$	481.390			1.26018
$383$		−	602.728i		−	1.57370i	−0.617143	−	0.786851i	$-0.711710\pi$
$383$		−	602.728i		−	1.57370i	0.617143	−	0.786851i	$-0.288290\pi$
$384$	−207.357	+	181.894i	−0.539993	+	0.473682i
$385$	41.0336			0.106581
$386$		−	508.205i		−	1.31659i
$387$	66.1440	−	503.393i	0.170915	−	1.30076i
$388$	−69.3867			−0.178832
$389$			29.1658i			0.0749763i	0.999297	+	0.0374881i	$0.0119356\pi$
$389$			29.1658i			0.0749763i	−0.999297	+	0.0374881i	$0.988064\pi$
$390$	−40.4854	−	46.1530i	−0.103809	−	0.118341i
$391$	239.551			0.612663
$392$			183.462i			0.468015i
$393$	157.026	−	137.743i	0.399557	−	0.350491i
$394$	153.604			0.389857
$395$			38.8896i			0.0984546i
$396$	−15.8462	−	2.08214i	−0.0400157	−	0.00525792i
$397$	−755.864			−1.90394			−0.951970	−	0.306191i	$-0.900945\pi$
$397$	−755.864			−1.90394			−0.951970	+	0.306191i	$0.900945\pi$
$398$		−	265.493i		−	0.667067i
$399$	121.047	+	137.993i	0.303376	+	0.345846i
$400$	−238.014			−0.595034
$401$			345.628i			0.861914i	0.902372	+	0.430957i	$0.141824\pi$
$401$			345.628i			0.861914i	−0.902372	+	0.430957i	$0.858176\pi$
$402$	34.0388	−	29.8588i	0.0846737	−	0.0742757i
$403$	−66.4127			−0.164796
$404$			16.8169i			0.0416261i
$405$	−55.4531	+	207.372i	−0.136921	+	0.512028i
$406$	−345.774			−0.851660
$407$		−	132.835i		−	0.326375i
$408$	−183.404	−	209.080i	−0.449521	−	0.512450i
$409$	−607.758			−1.48596			−0.742980	−	0.669313i	$-0.766588\pi$
$409$	−607.758			−1.48596			−0.742980	+	0.669313i	$0.766588\pi$
$410$		−	115.616i		−	0.281991i
$411$	−33.1284	+	29.0602i	−0.0806044	+	0.0707062i
$412$	20.3314			0.0493481
$413$			266.902i			0.646252i
$414$	−47.3838	+	360.618i	−0.114454	+	0.871057i
$415$	95.4359			0.229966
$416$		−	39.8476i		−	0.0957876i
$417$	−241.502	−	275.310i	−0.579141	−	0.660216i
$418$	63.8252			0.152692
$419$			227.278i			0.542430i	0.962519	+	0.271215i	$0.0874254\pi$
$419$			227.278i			0.542430i	−0.962519	+	0.271215i	$0.912575\pi$
$420$	18.7614	−	16.4574i	0.0446699	−	0.0391844i
$421$	−363.242			−0.862809			−0.431404	−	0.902159i	$-0.641982\pi$
$421$	−363.242			−0.862809			−0.431404	+	0.902159i	$0.641982\pi$
$422$		−	678.168i		−	1.60703i
$423$	−285.346	−	37.4934i	−0.674577	−	0.0886370i
$424$	134.118			0.316315
$425$		−	196.486i		−	0.462321i
$426$	397.718	+	453.395i	0.933611	+	1.06431i
$427$	403.724			0.945490
$428$		−	59.9175i		−	0.139994i
$429$	−27.9536	+	24.5209i	−0.0651598	+	0.0571582i
$430$	275.665			0.641081
$431$		−	535.420i		−	1.24227i	−0.783702	−	0.621137i	$-0.786671\pi$
$431$		−	535.420i		−	1.24227i	0.783702	−	0.621137i	$-0.213329\pi$
$432$	297.157	−	198.716i	0.687863	−	0.459991i
$433$	−412.290			−0.952172			−0.476086	−	0.879399i	$-0.657945\pi$
$433$	−412.290			−0.952172			−0.476086	+	0.879399i	$0.657945\pi$
$434$			152.978i			0.352484i
$435$	−187.919	−	214.227i	−0.431999	−	0.492475i
$436$	−63.1415			−0.144820
$437$			256.330i			0.586568i
$438$	−383.548	+	336.448i	−0.875679	+	0.768145i
$439$	−571.175			−1.30108			−0.650541	−	0.759471i	$-0.725458\pi$
$439$	−571.175			−1.30108			−0.650541	+	0.759471i	$0.725458\pi$
$440$		−	66.5268i		−	0.151197i
$441$	25.3604	−	193.007i	0.0575067	−	0.437658i
$442$	−84.4025			−0.190956
$443$			169.431i			0.382462i	0.981545	+	0.191231i	$0.0612479\pi$
$443$			169.431i			0.382462i	−0.981545	+	0.191231i	$0.938752\pi$
$444$	−53.2764	−	60.7347i	−0.119992	−	0.136790i
$445$	−158.943			−0.357176
$446$		−	48.1354i		−	0.107927i
$447$	131.183	−	115.074i	0.293474	−	0.257435i
$448$	−368.854			−0.823336
$449$			577.214i			1.28555i	0.766053	+	0.642777i	$0.222218\pi$
$449$			577.214i			1.28555i	−0.766053	+	0.642777i	$0.777782\pi$
$450$	295.788	+	38.8655i	0.657307	+	0.0863677i
$451$	−70.0256			−0.155267
$452$		−	38.4302i		−	0.0850225i
$453$	267.041	+	304.424i	0.589494	+	0.672018i
$454$	−708.610			−1.56082
$455$		−	58.0636i		−	0.127612i
$456$	223.724	−	196.251i	0.490623	−	0.430374i
$457$	290.862			0.636459			0.318230	−	0.948014i	$-0.396912\pi$
$457$	290.862			0.636459			0.318230	+	0.948014i	$0.396912\pi$
$458$		−	309.594i		−	0.675970i
$459$	164.045	+	245.310i	0.357397	+	0.534445i
$460$	34.8504			0.0757618
$461$			684.043i			1.48382i	0.670497	+	0.741912i	$0.266081\pi$
$461$			684.043i			1.48382i	−0.670497	+	0.741912i	$0.733919\pi$
$462$	56.4824	+	64.3895i	0.122256	+	0.139371i
$463$	−100.144			−0.216295			−0.108147	−	0.994135i	$-0.534492\pi$
$463$	−100.144			−0.216295			−0.108147	+	0.994135i	$0.534492\pi$
$464$			474.568i			1.02278i
$465$	−94.7786	+	83.1397i	−0.203825	+	0.178795i
$466$	−65.3385			−0.140211
$467$			73.7813i			0.157990i	0.996875	+	0.0789950i	$0.0251711\pi$
$467$			73.7813i			0.157990i	−0.996875	+	0.0789950i	$0.974829\pi$
$468$	−2.94628	+	22.4228i	−0.00629546	+	0.0479120i
$469$	42.8231			0.0913073
$470$		−	156.260i		−	0.332467i
$471$	522.204	+	595.309i	1.10871	+	1.26393i
$472$	432.722			0.916784
$473$		−	166.962i		−	0.352986i
$474$	−61.0251	+	53.5312i	−0.128745	+	0.112935i
$475$	210.249			0.442629
$476$		−	34.3099i		−	0.0720796i
$477$	−141.096	−	18.5394i	−0.295798	−	0.0388667i
$478$	−271.293			−0.567558
$479$			523.399i			1.09269i	0.837560	+	0.546346i	$0.183982\pi$
$479$			523.399i			1.09269i	−0.837560	+	0.546346i	$0.816018\pi$
$480$	−49.8838	−	56.8671i	−0.103925	−	0.118473i
$481$	−187.965			−0.390779
$482$			748.339i			1.55257i
$483$	−258.596	+	226.840i	−0.535396	+	0.469649i
$484$	67.3462			0.139145
$485$			306.461i			0.631878i
$486$	−401.736	+	198.429i	−0.826617	+	0.408289i
$487$	−654.906			−1.34478			−0.672389	−	0.740198i	$-0.734732\pi$
$487$	−654.906			−1.34478			−0.672389	+	0.740198i	$0.734732\pi$
$488$		−	654.549i		−	1.34129i
$489$	124.126	+	141.503i	0.253837	+	0.289372i
$490$	105.693			0.215701
$491$			561.636i			1.14386i	0.820302	+	0.571931i	$0.193805\pi$
$491$			561.636i			1.14386i	−0.820302	+	0.571931i	$0.806195\pi$
$492$	−32.0170	+	28.0853i	−0.0650753	+	0.0570840i
$493$	−391.767			−0.794660
$494$		−	90.3143i		−	0.182822i
$495$	−9.19618	+	69.9881i	−0.0185781	+	0.141390i
$496$	209.959			0.423305
$497$			570.402i			1.14769i
$498$	131.367	+	149.757i	0.263788	+	0.300717i
$499$	927.301			1.85832			0.929159	−	0.369680i	$-0.120533\pi$
$499$	927.301			1.85832			0.929159	+	0.369680i	$0.120533\pi$
$500$		−	68.3378i		−	0.136676i
$501$	595.396	−	522.281i	1.18842	−	1.04248i
$502$	−15.6043			−0.0310842
$503$		−	814.607i		−	1.61950i	−0.586778	−	0.809748i	$-0.699604\pi$
$503$		−	814.607i		−	1.61950i	0.586778	−	0.809748i	$-0.300396\pi$
$504$	395.972	+	52.0292i	0.785658	+	0.103233i
$505$	74.2754			0.147080
$506$			119.608i			0.236379i
$507$	−299.639	−	341.586i	−0.591003	−	0.673739i
$508$	47.4542			0.0934138
$509$		−	878.211i		−	1.72537i	−0.505745	−	0.862683i	$-0.668782\pi$
$509$		−	878.211i		−	1.72537i	0.505745	−	0.862683i	$-0.331218\pi$
$510$	−120.452	+	105.660i	−0.236180	+	0.207177i
$511$	−482.529			−0.944283
$512$			575.179i			1.12340i
$513$	−262.493	+	175.535i	−0.511682	+	0.342174i
$514$	−783.501			−1.52432
$515$		−	89.7979i		−	0.174365i
$516$	−66.9640	−	76.3384i	−0.129775	−	0.147943i
$517$	−94.6420			−0.183060
$518$			432.966i			0.835842i
$519$	−296.849	+	260.396i	−0.571963	+	0.501726i
$520$	−94.1372			−0.181033
$521$		−	853.975i		−	1.63911i	−0.573002	−	0.819554i	$-0.694221\pi$
$521$		−	853.975i		−	1.63911i	0.573002	−	0.819554i	$-0.305779\pi$
$522$	77.4926	−	589.762i	0.148453	−	1.12981i
$523$	−525.979			−1.00570			−0.502848	−	0.864375i	$-0.667714\pi$
$523$	−525.979			−1.00570			−0.502848	+	0.864375i	$0.667714\pi$
$524$		−	41.7768i		−	0.0797268i
$525$	186.061	+	212.108i	0.354401	+	0.404014i
$526$	−68.1316			−0.129528
$527$			173.327i			0.328893i
$528$	88.3733	−	77.5210i	0.167374	−	0.146820i
$529$	48.6410			0.0919489
$530$		−	77.2659i		−	0.145785i
$531$	−455.236	−	59.8164i	−0.857319	−	0.112649i
$532$	36.7131			0.0690095
$533$			99.0880i			0.185906i
$534$	−218.784	−	249.412i	−0.409708	−	0.467063i
$535$	−264.638			−0.494651
$536$		−	69.4281i		−	0.129530i
$537$	370.431	−	324.942i	0.689815	−	0.605105i
$538$	418.912			0.778646
$539$		−	64.0155i		−	0.118767i
$540$	23.8656	+	35.6883i	0.0441956	+	0.0660894i
$541$	−298.428			−0.551623			−0.275812	−	0.961212i	$-0.588947\pi$
$541$	−298.428			−0.551623			−0.275812	+	0.961212i	$0.588947\pi$
$542$		−	397.647i		−	0.733665i
$543$	−59.6727	−	68.0264i	−0.109894	−	0.125279i
$544$	−103.996			−0.191169
$545$			278.878i			0.511702i
$546$	91.1128	−	79.9241i	0.166873	−	0.146381i
$547$	923.627			1.68853			0.844266	−	0.535924i	$-0.180037\pi$
$547$	923.627			1.68853			0.844266	+	0.535924i	$0.180037\pi$
$548$			8.81385i			0.0160837i
$549$	−90.4801	+	688.604i	−0.164809	+	1.25429i
$550$	98.1053			0.178373
$551$		−	419.208i		−	0.760813i
$552$	367.771	+	419.256i	0.666252	+	0.759522i
$553$	−76.7736			−0.138831
$554$		−	402.623i		−	0.726756i
$555$	−268.247	+	235.306i	−0.483328	+	0.423975i
$556$	−73.2464			−0.131738
$557$			32.0462i			0.0575335i	0.999586	+	0.0287668i	$0.00915801\pi$
$557$			32.0462i			0.0575335i	−0.999586	+	0.0287668i	$0.990842\pi$
$558$	−260.924	−	34.2844i	−0.467605	−	0.0614416i
$559$	−236.256			−0.422641
$560$			183.564i			0.327793i
$561$	63.9955	+	72.9543i	0.114074	+	0.130043i
$562$	883.585			1.57222
$563$			350.101i			0.621849i	0.950435	+	0.310924i	$0.100639\pi$
$563$			350.101i			0.621849i	−0.950435	+	0.310924i	$0.899361\pi$
$564$	−43.2721	+	37.9583i	−0.0767237	+	0.0673019i
$565$	−169.735			−0.300415
$566$		−	50.1061i		−	0.0885267i
$567$	−409.381	−	109.472i	−0.722013	−	0.193073i
$568$	924.779			1.62813
$569$			259.456i			0.455986i	0.973663	+	0.227993i	$0.0732163\pi$
$569$			259.456i			0.455986i	−0.973663	+	0.227993i	$0.926784\pi$
$570$	−113.061	−	128.889i	−0.198353	−	0.226121i
$571$	800.537			1.40199			0.700996	−	0.713165i	$-0.252739\pi$
$571$	800.537			1.40199			0.700996	+	0.713165i	$0.252739\pi$
$572$			7.43707i			0.0130019i
$573$	−588.785	+	516.482i	−1.02755	+	0.901365i
$574$	228.244			0.397637
$575$			394.003i			0.685223i
$576$	82.6653	−	629.129i	0.143516	−	1.09224i
$577$	−733.488			−1.27121			−0.635605	−	0.772014i	$-0.719249\pi$
$577$	−733.488			−1.27121			−0.635605	+	0.772014i	$0.719249\pi$
$578$		−	312.612i		−	0.540850i
$579$	545.252	+	621.583i	0.941714	+	1.07355i
$580$	−56.9952			−0.0982675
$581$			188.404i			0.324276i
$582$	−480.895	+	421.841i	−0.826280	+	0.724812i
$583$	−46.7978			−0.0802706
$584$			782.312i			1.33958i
$585$	99.0350	+	13.0128i	0.169291	+	0.0222442i
$586$	166.501			0.284131
$587$		−	849.871i		−	1.44782i	−0.689894	−	0.723911i	$-0.742343\pi$
$587$		−	849.871i		−	1.44782i	0.689894	−	0.723911i	$-0.257657\pi$
$588$	−25.6749	−	29.2691i	−0.0436647	−	0.0497775i
$589$	−185.467			−0.314884
$590$		−	249.294i		−	0.422532i
$591$	−187.872	+	164.801i	−0.317888	+	0.278851i
$592$	594.237			1.00378
$593$			531.871i			0.896915i	0.893804	+	0.448458i	$0.148026\pi$
$593$			531.871i			0.896915i	−0.893804	+	0.448458i	$0.851974\pi$
$594$	−122.483	+	81.9075i	−0.206200	+	0.137891i
$595$	−151.537			−0.254683
$596$		−	34.9013i		−	0.0585593i
$597$	284.847	+	324.723i	0.477130	+	0.543924i
$598$	169.248			0.283023
$599$			519.468i			0.867226i	0.901099	+	0.433613i	$0.142762\pi$
$599$			519.468i			0.867226i	−0.901099	+	0.433613i	$0.857238\pi$
$600$	343.885	−	301.656i	0.573142	−	0.502760i
$601$	−1102.03			−1.83366			−0.916832	−	0.399273i	$-0.869263\pi$
$601$	−1102.03			−1.83366			−0.916832	+	0.399273i	$0.869263\pi$
$602$			544.203i			0.903991i
$603$	−9.59724	+	73.0404i	−0.0159158	+	0.121128i
$604$	80.9923			0.134093
$605$		−	297.448i		−	0.491650i
$606$	102.239	+	116.552i	0.168712	+	0.192330i
$607$	1158.66			1.90883			0.954417	−	0.298476i	$-0.0964782\pi$
$607$	1158.66			1.90883			0.954417	+	0.298476i	$0.0964782\pi$
$608$		−	111.280i		−	0.183026i
$609$	422.914	−	370.980i	0.694441	−	0.609163i
$610$	−377.089			−0.618179
$611$			133.921i			0.219183i
$612$	58.5199	+	7.68931i	0.0956208	+	0.0125642i
$613$	614.940			1.00317			0.501583	−	0.865110i	$-0.332751\pi$
$613$	614.940			1.00317			0.501583	+	0.865110i	$0.332751\pi$
$614$		−	39.5299i		−	0.0643810i
$615$	124.045	+	141.410i	0.201699	+	0.229935i
$616$	131.334			0.213204
$617$		−	1034.11i		−	1.67602i	−0.545654	−	0.838011i	$-0.683719\pi$
$617$		−	1034.11i		−	1.67602i	0.545654	−	0.838011i	$-0.316281\pi$
$618$	140.910	−	123.606i	0.228009	−	0.200010i
$619$	−522.566			−0.844211			−0.422105	−	0.906547i	$-0.638709\pi$
$619$	−522.566			−0.844211			−0.422105	+	0.906547i	$0.638709\pi$
$620$			25.2159i			0.0406708i
$621$	−328.951	−	491.908i	−0.529712	−	0.792122i
$622$	−0.348405			−0.000560137
$623$		−	313.777i		−	0.503655i
$624$	−109.694	−	125.050i	−0.175792	−	0.200401i
$625$	147.597			0.236155
$626$		−	512.790i		−	0.819153i
$627$	−78.0643	+	68.4779i	−0.124504	+	0.109215i
$628$	158.382			0.252201
$629$			490.558i			0.779901i
$630$	29.9743	−	228.122i	0.0475783	−	0.362098i
$631$	−443.977			−0.703608			−0.351804	−	0.936074i	$-0.614432\pi$
$631$	−443.977			−0.703608			−0.351804	+	0.936074i	$0.614432\pi$
$632$			124.471i			0.196948i
$633$	727.605	+	829.464i	1.14946	+	1.31037i
$634$	746.697			1.17776
$635$		−	209.591i		−	0.330065i
$636$	−21.3968	+	18.7693i	−0.0336428	+	0.0295115i
$637$	−90.5836			−0.142203
$638$		−	195.609i		−	0.306597i
$639$	−972.894	−	127.835i	−1.52253	−	0.200054i
$640$	243.659			0.380717
$641$		−	757.644i		−	1.18197i	−0.806682	−	0.590986i	$-0.798739\pi$
$641$		−	757.644i		−	1.18197i	0.806682	−	0.590986i	$-0.201261\pi$
$642$	−364.272	−	415.267i	−0.567402	−	0.646834i
$643$	471.391			0.733111			0.366556	−	0.930396i	$-0.380537\pi$
$643$	471.391			0.733111			0.366556	+	0.930396i	$0.380537\pi$
$644$			68.7998i			0.106832i
$645$	−337.164	+	295.760i	−0.522736	+	0.458543i
$646$	−235.706			−0.364870
$647$			452.186i			0.698896i	0.936956	+	0.349448i	$0.113631\pi$
$647$			452.186i			0.698896i	−0.936956	+	0.349448i	$0.886369\pi$
$648$	−177.485	+	663.720i	−0.273897	+	1.02426i
$649$	−150.990			−0.232650
$650$		−	138.822i		−	0.213572i
$651$	−164.130	−	187.107i	−0.252119	−	0.287414i
$652$	37.6470			0.0577407
$653$		−	221.234i		−	0.338796i	−0.985548	−	0.169398i	$-0.945818\pi$
$653$		−	221.234i		−	0.338796i	0.985548	−	0.169398i	$-0.0541824\pi$
$654$	−437.612	+	383.872i	−0.669131	+	0.586961i
$655$	−184.516			−0.281704
$656$		−	313.260i		−	0.477530i
$657$	108.141	−	823.015i	0.164598	−	1.25269i
$658$	308.479			0.468813
$659$		−	693.305i		−	1.05206i	−0.850467	−	0.526028i	$-0.823681\pi$
$659$		−	693.305i		−	1.05206i	0.850467	−	0.526028i	$-0.176319\pi$
$660$	9.31020	+	10.6136i	0.0141064	+	0.0160811i
$661$	398.001			0.602120			0.301060	−	0.953605i	$-0.402660\pi$
$661$	398.001			0.602120			0.301060	+	0.953605i	$0.402660\pi$
$662$		−	209.081i		−	0.315832i
$663$	103.232	−	90.5552i	0.155705	−	0.136584i
$664$	305.455			0.460023
$665$		−	162.151i		−	0.243836i
$666$	−738.480	−	97.0335i	−1.10883	−	0.145696i
$667$	785.590			1.17780
$668$		−	158.406i		−	0.237134i
$669$	51.6444	+	58.8742i	0.0771964	+	0.0880032i
$670$	−39.9979			−0.0596984
$671$			228.392i			0.340376i
$672$	112.264	−	98.4778i	0.167059	−	0.146544i
$673$	165.897			0.246503			0.123252	−	0.992375i	$-0.460668\pi$
$673$	165.897			0.246503			0.123252	+	0.992375i	$0.460668\pi$
$674$		−	751.247i		−	1.11461i
$675$	−403.476	+	269.814i	−0.597742	+	0.399725i
$676$	−90.8792			−0.134437
$677$		−	254.517i		−	0.375948i	−0.982174	−	0.187974i	$-0.939808\pi$
$677$		−	254.517i		−	0.375948i	0.982174	−	0.187974i	$-0.0601920\pi$
$678$	−233.638	−	266.346i	−0.344599	−	0.392840i
$679$	−604.998			−0.891013
$680$			245.683i			0.361298i
$681$	866.698	−	760.267i	1.27268	−	1.11640i
$682$	−86.5417			−0.126894
$683$		−	73.8480i		−	0.108123i	−0.998538	−	0.0540615i	$-0.982783\pi$
$683$		−	73.8480i		−	0.108123i	0.998538	−	0.0540615i	$-0.0172167\pi$
$684$	−8.22789	+	62.6189i	−0.0120291	+	0.0915481i
$685$	38.9282			0.0568294
$686$			681.343i			0.993211i
$687$	332.163	+	378.663i	0.483498	+	0.551184i
$688$	746.907			1.08562
$689$			66.2200i			0.0961104i
$690$	241.536	−	211.875i	0.350052	−	0.307065i
$691$	−409.739			−0.592966			−0.296483	−	0.955038i	$-0.595814\pi$
$691$	−409.739			−0.592966			−0.296483	+	0.955038i	$0.595814\pi$
$692$			78.9769i			0.114128i
$693$	−138.167	−	18.1546i	−0.199375	−	0.0261971i
$694$	−986.353			−1.42126
$695$			323.508i			0.465479i
$696$	−601.461	−	685.661i	−0.864169	−	0.985145i
$697$	258.604			0.371024
$698$			193.068i			0.276601i
$699$	79.9151	−	70.1015i	0.114328	−	0.100288i
$700$	56.4314			0.0806163
$701$		−	216.682i		−	0.309104i	−0.987985	−	0.154552i	$-0.950607\pi$
$701$		−	216.682i		−	0.309104i	0.987985	−	0.154552i	$-0.0493934\pi$
$702$	115.901	+	173.317i	0.165101	+	0.246890i
$703$	−524.918			−0.746683
$704$		−	208.666i		−	0.296400i
$705$	167.651	+	191.120i	0.237802	+	0.271093i
$706$	−956.477			−1.35478
$707$			146.630i			0.207398i
$708$	−69.0356	+	60.5580i	−0.0975079	+	0.0855339i
$709$	792.254			1.11742			0.558712	−	0.829362i	$-0.311296\pi$
$709$	792.254			1.11742			0.558712	+	0.829362i	$0.311296\pi$
$710$		−	532.771i		−	0.750381i
$711$	17.2060	−	130.947i	0.0241997	−	0.184174i
$712$	−508.719			−0.714493
$713$		−	347.562i		−	0.487465i
$714$	−208.589	−	237.790i	−0.292141	−	0.333039i
$715$	32.8474			0.0459404
$716$		−	98.5534i		−	0.137644i
$717$	331.817	−	291.069i	0.462785	−	0.405954i
$718$	1154.91			1.60850
$719$			997.625i			1.38752i	0.720207	+	0.693759i	$0.244047\pi$
$719$			997.625i			1.38752i	−0.720207	+	0.693759i	$0.755953\pi$
$720$	−313.092	−	41.1392i	−0.434850	−	0.0571378i
$721$	177.274			0.245872
$722$			413.434i			0.572623i
$723$	−802.892	−	915.290i	−1.11050	−	1.26596i
$724$	−18.0985			−0.0249979
$725$		−	644.362i		−	0.888775i
$726$	466.753	−	409.435i	0.642910	−	0.563960i
$727$	894.163			1.22994			0.614968	−	0.788552i	$-0.289169\pi$
$727$	894.163			1.22994			0.614968	+	0.788552i	$0.289169\pi$
$728$		−	185.840i		−	0.255275i
$729$	278.467	−	673.719i	0.381985	−	0.924168i
$730$	450.695			0.617390
$731$			616.590i			0.843489i
$732$	91.6019	+	104.425i	0.125139	+	0.142658i
$733$	626.003			0.854029			0.427015	−	0.904245i	$-0.359565\pi$
$733$	626.003			0.854029			0.427015	+	0.904245i	$0.359565\pi$
$734$			95.6381i			0.130297i
$735$	−129.273	+	113.398i	−0.175882	+	0.154283i
$736$	208.537			0.283339
$737$			24.2256i			0.0328706i
$738$	−51.1525	+	389.299i	−0.0693123	+	0.527505i
$739$	876.313			1.18581			0.592905	−	0.805272i	$-0.297981\pi$
$739$	876.313			1.18581			0.592905	+	0.805272i	$0.297981\pi$
$740$			71.3674i			0.0964424i
$741$	96.8980	+	110.463i	0.130767	+	0.149073i
$742$	152.534			0.205572
$743$			44.4875i			0.0598755i	0.999552	+	0.0299378i	$0.00953091\pi$
$743$			44.4875i			0.0598755i	−0.999552	+	0.0299378i	$0.990469\pi$
$744$	−303.352	+	266.100i	−0.407731	+	0.357661i
$745$	−154.149			−0.206911
$746$			751.710i			1.00765i
$747$	−321.348	−	42.2239i	−0.430184	−	0.0565247i
$748$	19.4096			0.0259486
$749$		−	522.434i		−	0.697508i
$750$	−415.464	−	473.625i	−0.553951	−	0.631500i
$751$	−443.773			−0.590910			−0.295455	−	0.955357i	$-0.595471\pi$
$751$	−443.773			−0.590910			−0.295455	+	0.955357i	$0.595471\pi$
$752$		−	423.381i		−	0.563007i
$753$	19.0855	−	16.7418i	0.0253460	−	0.0222335i
$754$	−276.792			−0.367098
$755$		−	357.719i		−	0.473800i
$756$	−70.4538	+	47.1142i	−0.0931929	+	0.0623204i
$757$	629.413			0.831458			0.415729	−	0.909489i	$-0.363527\pi$
$757$	629.413			0.831458			0.415729	+	0.909489i	$0.363527\pi$
$758$		−	1016.55i		−	1.34109i
$759$	−128.327	−	146.291i	−0.169073	−	0.192742i
$760$	−262.891			−0.345910
$761$			1124.48i			1.47764i	0.673905	+	0.738818i	$0.264616\pi$
$761$			1124.48i			1.47764i	−0.673905	+	0.738818i	$0.735384\pi$
$762$	328.888	−	288.501i	0.431612	−	0.378610i
$763$	−550.545			−0.721552
$764$			156.647i			0.205035i
$765$	33.9614	−	258.465i	0.0443940	−	0.337863i
$766$	−1111.37			−1.45088
$767$			213.655i			0.278559i
$768$	−222.524	−	253.676i	−0.289745	−	0.330307i
$769$	−265.673			−0.345478			−0.172739	−	0.984968i	$-0.555262\pi$
$769$	−265.673			−0.345478			−0.172739	+	0.984968i	$0.555262\pi$
$770$		−	75.6620i		−	0.0982624i
$771$	958.297	−	840.617i	1.24293	−	1.09029i
$772$	165.373			0.214213
$773$			1070.51i			1.38488i	0.721476	+	0.692439i	$0.243464\pi$
$773$			1070.51i			1.38488i	−0.721476	+	0.692439i	$0.756536\pi$
$774$	−928.208	−	121.963i	−1.19924	−	0.157575i
$775$	−285.080			−0.367845
$776$			980.869i			1.26401i
$777$	−464.528	−	529.559i	−0.597849	−	0.681543i
$778$	53.7789			0.0691245
$779$			276.717i			0.355221i
$780$	15.0185	−	13.1742i	0.0192544	−	0.0168900i
$781$	−322.684			−0.413168
$782$		−	441.709i		−	0.564846i
$783$	537.974	+	804.477i	0.687067	+	1.02743i
$784$	286.374			0.365273
$785$		−	699.529i		−	0.891119i
$786$	−253.985	−	289.541i	−0.323136	−	0.368372i
$787$	895.533			1.13791			0.568954	−	0.822369i	$-0.307348\pi$
$787$	895.533			1.13791			0.568954	+	0.822369i	$0.307348\pi$
$788$			49.9835i			0.0634309i
$789$	83.3315	−	73.0983i	0.105617	−	0.0926468i
$790$	71.7086			0.0907704
$791$		−	335.081i		−	0.423617i
$792$	−29.4336	+	224.006i	−0.0371637	+	0.282836i
$793$	323.181			0.407542
$794$			1393.74i			1.75534i
$795$	82.8985	+	94.5036i	0.104275	+	0.118872i
$796$	86.3928			0.108534
$797$		−	216.959i		−	0.272220i	−0.990694	−	0.136110i	$-0.956540\pi$
$797$		−	216.959i		−	0.272220i	0.990694	−	0.136110i	$-0.0434601\pi$
$798$	254.445	−	223.199i	0.318854	−	0.279698i
$799$	349.512			0.437436
$800$		−	171.048i		−	0.213810i
$801$	535.187	+	70.3216i	0.668149	+	0.0877923i
$802$	637.304			0.794644
$803$		−	272.973i		−	0.339941i
$804$	9.71622	+	11.0764i	0.0120849	+	0.0137766i
$805$	303.868			0.377476
$806$			122.459i			0.151934i
$807$	−512.369	+	449.449i	−0.634905	+	0.556938i
$808$	237.728			0.294218
$809$			858.258i			1.06089i	0.847720	+	0.530443i	$0.177975\pi$
$809$			858.258i			1.06089i	−0.847720	+	0.530443i	$0.822025\pi$
$810$	382.373	+	102.250i	0.472066	+	0.126235i
$811$	−204.337			−0.251957			−0.125979	−	0.992033i	$-0.540207\pi$
$811$	−204.337			−0.251957			−0.125979	+	0.992033i	$0.540207\pi$
$812$		−	112.517i		−	0.138567i
$813$	426.634	+	486.360i	0.524765	+	0.598228i
$814$	−244.935			−0.300903
$815$		−	166.276i		−	0.204019i
$816$	−326.362	+	286.284i	−0.399953	+	0.350838i
$817$	−659.778			−0.807562
$818$			1120.65i			1.36998i
$819$	−25.6892	+	195.509i	−0.0313666	+	0.238717i
$820$	37.6222			0.0458808
$821$		−	735.330i		−	0.895652i	−0.894121	−	0.447826i	$-0.852198\pi$
$821$		−	735.330i		−	0.895652i	0.894121	−	0.447826i	$-0.147802\pi$
$822$	53.5843	+	61.0857i	0.0651877	+	0.0743134i
$823$	57.6599			0.0700607			0.0350303	−	0.999386i	$-0.488847\pi$
$823$	57.6599			0.0700607			0.0350303	+	0.999386i	$0.488847\pi$
$824$		−	287.410i		−	0.348799i
$825$	−119.992	+	105.257i	−0.145445	+	0.127584i
$826$	492.142			0.595814
$827$			801.051i			0.968623i	0.874896	+	0.484311i	$0.160930\pi$
$827$			801.051i			0.968623i	−0.874896	+	0.484311i	$0.839070\pi$
$828$	−117.347	−	15.4190i	−0.141723	−	0.0186219i
$829$	1416.27			1.70841			0.854203	−	0.519940i	$-0.174046\pi$
$829$	1416.27			1.70841			0.854203	+	0.519940i	$0.174046\pi$
$830$		−	175.975i		−	0.212018i
$831$	431.973	+	492.446i	0.519823	+	0.592594i
$832$	−295.268			−0.354889
$833$			236.409i			0.283804i
$834$	−507.645	+	445.306i	−0.608687	+	0.533940i
$835$	−699.631			−0.837882
$836$			20.7691i			0.0248434i
$837$	355.918	−	238.011i	0.425231	−	0.284363i
$838$	419.079			0.500094
$839$			68.0663i			0.0811279i	0.999177	+	0.0405640i	$0.0129155\pi$
$839$			68.0663i			0.0811279i	−0.999177	+	0.0405640i	$0.987085\pi$
$840$	−232.647	−	265.215i	−0.276960	−	0.315733i
$841$	−443.772			−0.527672
$842$			669.784i			0.795468i
$843$	−1080.71	+	947.997i	−1.28198	+	1.12455i
$844$	220.680			0.261469
$845$			401.386i			0.475014i
$846$	−69.1343	+	526.151i	−0.0817190	+	0.621928i
$847$	587.206			0.693278
$848$		−	209.350i		−	0.246875i
$849$	53.7588	+	61.2846i	0.0633201	+	0.0721844i
$850$	−362.302			−0.426237
$851$		−	983.689i		−	1.15592i
$852$	−147.537	+	129.420i	−0.173166	+	0.151901i
$853$	−904.904			−1.06085			−0.530424	−	0.847732i	$-0.677967\pi$
$853$	−904.904			−1.06085			−0.530424	+	0.847732i	$0.677967\pi$
$854$		−	744.429i		−	0.871697i
$855$	276.569	+	36.3402i	0.323473	+	0.0425031i
$856$	−847.010			−0.989497
$857$		−	935.072i		−	1.09110i	−0.838079	−	0.545549i	$-0.816321\pi$
$857$		−	935.072i		−	1.09110i	0.838079	−	0.545549i	$-0.183679\pi$
$858$	45.2141	+	51.5437i	0.0526971	+	0.0600743i
$859$	588.055			0.684581			0.342291	−	0.939594i	$-0.388797\pi$
$859$	588.055			0.684581			0.342291	+	0.939594i	$0.388797\pi$
$860$			89.7029i			0.104306i
$861$	−279.164	+	244.882i	−0.324232	+	0.284416i
$862$	−987.264			−1.14532
$863$			897.798i			1.04032i	0.854068	+	0.520161i	$0.174128\pi$
$863$			897.798i			1.04032i	−0.854068	+	0.520161i	$0.825872\pi$
$864$	142.807	+	213.551i	0.165286	+	0.247165i
$865$	348.818			0.403257
$866$			760.224i			0.877857i
$867$	335.400	+	382.354i	0.386852	+	0.441008i
$868$	−49.7799			−0.0573501
$869$		−	43.4319i		−	0.0499791i
$870$	−395.013	+	346.505i	−0.454038	+	0.398282i
$871$	34.2799			0.0393569
$872$			892.585i			1.02361i
$873$	135.588	−	1031.90i	0.155313	−	1.18202i
$874$	472.648			0.540787
$875$		−	595.852i		−	0.680974i
$876$	−109.482	−	124.808i	−0.124979	−	0.142475i
$877$	−791.844			−0.902901			−0.451450	−	0.892296i	$-0.649093\pi$
$877$	−791.844			−0.902901			−0.451450	+	0.892296i	$0.649093\pi$
$878$			1053.19i			1.19954i
$879$	−203.647	+	178.639i	−0.231680	+	0.203229i
$880$	−103.845			−0.118005
$881$			504.103i			0.572194i	0.958201	+	0.286097i	$0.0923580\pi$
$881$			504.103i			0.572194i	−0.958201	+	0.286097i	$0.907642\pi$
$882$	−355.887	−	46.7622i	−0.403500	−	0.0530184i
$883$	−1450.34			−1.64252			−0.821259	−	0.570555i	$-0.806728\pi$
$883$	−1450.34			−1.64252			−0.821259	+	0.570555i	$0.806728\pi$
$884$		−	27.4650i		−	0.0310690i
$885$	267.467	+	304.910i	0.302222	+	0.344531i
$886$	312.414			0.352611
$887$			1272.73i			1.43487i	0.696627	+	0.717433i	$0.254683\pi$
$887$			1272.73i			1.43487i	−0.696627	+	0.717433i	$0.745317\pi$
$888$	−858.561	+	753.129i	−0.966848	+	0.848118i
$889$	413.763			0.465426
$890$			293.076i			0.329299i
$891$	61.9300	−	231.593i	0.0695062	−	0.259924i
$892$	15.6635			0.0175600
$893$			373.993i			0.418805i
$894$	−212.185	−	241.889i	−0.237343	−	0.270569i
$895$	−435.281			−0.486348
$896$			481.018i			0.536851i
$897$	−207.006	+	181.586i	−0.230776	+	0.202437i
$898$	1064.33			1.18522
$899$			568.411i			0.632271i
$900$	−12.6470	+	96.2511i	−0.0140523	+	0.106946i
$901$	172.824			0.191813
$902$			129.120i			0.143149i
$903$	−583.874	−	665.611i	−0.646593	−	0.737111i
$904$	−543.259			−0.600950
$905$			79.9356i			0.0883267i
$906$	561.329	−	492.398i	0.619569	−	0.543485i
$907$	−929.502			−1.02481			−0.512405	−	0.858744i	$-0.671245\pi$
$907$	−929.502			−1.02481			−0.512405	+	0.858744i	$0.671245\pi$
$908$		−	230.586i		−	0.253949i
$909$	−250.097	−	32.8619i	−0.275134	−	0.0361517i
$910$	−107.064			−0.117652
$911$			782.061i			0.858465i	0.903194	+	0.429232i	$0.141216\pi$
$911$			782.061i			0.858465i	−0.903194	+	0.429232i	$0.858784\pi$
$912$	−306.336	−	349.221i	−0.335895	−	0.382918i
$913$	−106.583			−0.116739
$914$		−	536.321i		−	0.586785i
$915$	461.216	−	404.579i	0.504061	−	0.442162i
$916$	100.744			0.109982
$917$		−	364.261i		−	0.397232i
$918$	452.329	−	302.484i	0.492733	−	0.329503i
$919$	−1494.90			−1.62666			−0.813328	−	0.581805i	$-0.802347\pi$
$919$	−1494.90			−1.62666			−0.813328	+	0.581805i	$0.802347\pi$
$920$		−	492.655i		−	0.535494i
$921$	42.4116	+	48.3488i	0.0460495	+	0.0524960i
$922$	1261.31			1.36802
$923$			456.606i			0.494698i
$924$	−20.9527	+	18.3797i	−0.0226761	+	0.0198914i
$925$	−806.848			−0.872268
$926$			184.657i			0.199413i
$927$	−39.7295	+	302.364i	−0.0428581	+	0.326174i
$928$	−341.047			−0.367507
$929$		−	1438.78i		−	1.54875i	−0.632730	−	0.774373i	$-0.718066\pi$
$929$		−	1438.78i		−	1.54875i	0.632730	−	0.774373i	$-0.281934\pi$
$930$	153.302	+	174.763i	0.164840	+	0.187917i
$931$	−252.967			−0.271716
$932$		−	21.2615i		−	0.0228128i
$933$	0.426133	−	0.373803i	0.000456734	−	0.000400647i
$934$	136.046			0.145659
$935$		−	85.7263i		−	0.0916859i
$936$	316.975	+	41.6493i	0.338648	+	0.0444972i
$937$	−673.826			−0.719131			−0.359565	−	0.933120i	$-0.617075\pi$
$937$	−673.826			−0.719131			−0.359565	+	0.933120i	$0.617075\pi$
$938$		−	78.9617i		−	0.0841809i
$939$	550.171	+	627.191i	0.585912	+	0.667935i
$940$	50.8477			0.0540933
$941$		−	1644.39i		−	1.74750i	−0.486379	−	0.873748i	$-0.661682\pi$
$941$		−	1644.39i		−	1.74750i	0.486379	−	0.873748i	$-0.338318\pi$
$942$	1097.69	−	962.895i	1.16528	−	1.02218i
$943$	−518.564			−0.549909
$944$		−	675.455i		−	0.715525i
$945$	208.090	+	311.174i	0.220201	+	0.329284i
$946$	−307.863			−0.325436
$947$		−	781.824i		−	0.825580i	−0.910826	−	0.412790i	$-0.864554\pi$
$947$		−	781.824i		−	0.825580i	0.910826	−	0.412790i	$-0.135446\pi$
$948$	−17.4193	−	19.8579i	−0.0183748	−	0.0209471i
$949$	−386.264			−0.407022
$950$		−	387.679i		−	0.408083i
$951$	−913.281	+	801.130i	−0.960338	+	0.842408i
$952$	−485.013			−0.509468
$953$		−	328.757i		−	0.344971i	−0.985012	−	0.172485i	$-0.944820\pi$
$953$		−	328.757i		−	0.344971i	0.985012	−	0.172485i	$-0.0551798\pi$
$954$	−34.1850	+	260.167i	−0.0358333	+	0.272711i
$955$	691.863			0.724464
$956$		−	88.2801i		−	0.0923432i
$957$	209.868	+	239.248i	0.219298	+	0.249998i
$958$	965.098			1.00741
$959$			76.8498i			0.0801354i
$960$	−421.381	+	369.635i	−0.438938	+	0.385036i
$961$	−709.522			−0.738317
$962$			346.589i			0.360280i
$963$	891.079	+	117.084i	0.925315	+	0.121583i
$964$	−243.514			−0.252607
$965$		−	730.403i		−	0.756894i
$966$	418.272	+	476.827i	0.432994	+	0.493610i
$967$	−750.511			−0.776123			−0.388062	−	0.921633i	$-0.626855\pi$
$967$	−750.511			−0.776123			−0.388062	+	0.921633i	$0.626855\pi$
$968$		−	952.024i		−	0.983496i
$969$	288.291	−	252.888i	0.297513	−	0.260979i
$970$	565.084			0.582561
$971$		−	451.198i		−	0.464674i	−0.972635	−	0.232337i	$-0.925363\pi$
$971$		−	451.198i		−	0.464674i	0.972635	−	0.232337i	$-0.0746372\pi$
$972$	−64.5698	−	130.727i	−0.0664298	−	0.134493i
$973$	−638.651			−0.656373
$974$			1207.58i			1.23982i
$975$	148.941	+	169.792i	0.152760	+	0.174146i
$976$	−1021.71			−1.04684
$977$			1572.87i			1.60989i	0.593347	+	0.804947i	$0.297806\pi$
$977$			1572.87i			1.60989i	−0.593347	+	0.804947i	$0.702194\pi$
$978$	260.918	−	228.877i	0.266787	−	0.234025i
$979$	177.508			0.181315
$980$			34.3932i			0.0350951i
$981$	123.384	−	939.025i	0.125774	−	0.957212i
$982$	1035.60			1.05459
$983$		−	700.872i		−	0.712992i	−0.934297	−	0.356496i	$-0.883971\pi$
$983$		−	700.872i		−	0.712992i	0.934297	−	0.356496i	$-0.116029\pi$
$984$	397.022	+	452.601i	0.403477	+	0.459961i
$985$	220.762			0.224124
$986$			722.382i			0.732638i
$987$	−377.299	+	330.967i	−0.382269	+	0.335326i
$988$	29.3888			0.0297457
$989$		−	1236.42i		−	1.25017i
$990$	129.051	+	16.9569i	0.130355	+	0.0171282i
$991$	635.398			0.641168			0.320584	−	0.947220i	$-0.396121\pi$
$991$	635.398			0.641168			0.320584	+	0.947220i	$0.396121\pi$
$992$			150.887i			0.152103i
$993$	224.323	+	255.726i	0.225904	+	0.257529i
$994$	1051.77			1.05812
$995$		−	381.571i		−	0.383489i
$996$	−48.7317	+	42.7474i	−0.0489274	+	0.0429191i
$997$	758.582			0.760865			0.380432	−	0.924809i	$-0.375775\pi$
$997$	758.582			0.760865			0.380432	+	0.924809i	$0.375775\pi$
$998$		−	1709.85i		−	1.71328i
$999$	1007.34	−	673.632i	1.00835	−	0.674307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.13	✓	44
3.2	odd	2	inner	201.3.c.a.68.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.13	✓	44	1.1	even	1	trivial
201.3.c.a.68.32	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.84390i q^{2} +(1.97832 + 2.25527i) q^{3} +0.600017 q^{4} -2.65010i q^{5} +(4.15850 - 3.64784i) q^{6} +5.23167 q^{7} -8.48199i q^{8} +(-1.17249 + 8.92330i) q^{9} +O(q^{10})\)	\(q-1.84390i q^{2} +(1.97832 + 2.25527i) q^{3} +0.600017 q^{4} -2.65010i q^{5} +(4.15850 - 3.64784i) q^{6} +5.23167 q^{7} -8.48199i q^{8} +(-1.17249 + 8.92330i) q^{9} -4.88653 q^{10} +2.95963i q^{11} +(1.18703 + 1.35320i) q^{12} +4.18795 q^{13} -9.64671i q^{14} +(5.97668 - 5.24274i) q^{15} -13.2399 q^{16} -10.9299i q^{17} +(16.4537 + 2.16196i) q^{18} +11.6954 q^{19} -1.59010i q^{20} +(10.3499 + 11.7988i) q^{21} +5.45727 q^{22} +21.9171i q^{23} +(19.1292 - 16.7801i) q^{24} +17.9770 q^{25} -7.72218i q^{26} +(-22.4440 + 15.0089i) q^{27} +3.13909 q^{28} -35.8437i q^{29} +(-9.66712 - 11.0204i) q^{30} -15.8581 q^{31} -9.51483i q^{32} +(-6.67476 + 5.85510i) q^{33} -20.1536 q^{34} -13.8644i q^{35} +(-0.703513 + 5.35413i) q^{36} -44.8823 q^{37} -21.5653i q^{38} +(8.28511 + 9.44496i) q^{39} -22.4781 q^{40} +23.6603i q^{41} +(21.7559 - 19.0843i) q^{42} -56.4133 q^{43} +1.77583i q^{44} +(23.6476 + 3.10721i) q^{45} +40.4130 q^{46} +31.9776i q^{47} +(-26.1928 - 29.8596i) q^{48} -21.6296 q^{49} -33.1478i q^{50} +(24.6498 - 21.6228i) q^{51} +2.51284 q^{52} +15.8120i q^{53} +(27.6749 + 41.3846i) q^{54} +7.84330 q^{55} -44.3750i q^{56} +(23.1373 + 26.3764i) q^{57} -66.0924 q^{58} +51.0166i q^{59} +(3.58611 - 3.14573i) q^{60} +77.1692 q^{61} +29.2407i q^{62} +(-6.13408 + 46.6838i) q^{63} -70.5041 q^{64} -11.0985i q^{65} +(10.7962 + 12.3076i) q^{66} +8.18535 q^{67} -6.55811i q^{68} +(-49.4290 + 43.3591i) q^{69} -25.5647 q^{70} +109.029i q^{71} +(75.6873 + 9.94504i) q^{72} -92.2321 q^{73} +82.7586i q^{74} +(35.5643 + 40.5430i) q^{75} +7.01746 q^{76} +15.4838i q^{77} +(17.4156 - 15.2770i) q^{78} -14.6748 q^{79} +35.0871i q^{80} +(-78.2505 - 20.9249i) q^{81} +43.6272 q^{82} +36.0122i q^{83} +(6.21013 + 7.07950i) q^{84} -28.9652 q^{85} +104.021i q^{86} +(80.8373 - 70.9104i) q^{87} +25.1035 q^{88} -59.9764i q^{89} +(5.72940 - 43.6039i) q^{90} +21.9100 q^{91} +13.1506i q^{92} +(-31.3723 - 35.7642i) q^{93} +58.9637 q^{94} -30.9940i q^{95} +(21.4585 - 18.8234i) q^{96} -115.641 q^{97} +39.8829i q^{98} +(-26.4096 - 3.47013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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