LMFDB - Embedded newform 87.3.b.a.59.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,3,Mod(59,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, 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("87.59");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	87.b (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:	$2.37057829993$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 $ x^18 + 54x^16 + 1187x^14 + 13673x^12 + 88449x^10 + 318861x^8 + 593533x^6 + 482583x^4 + 152462x^2 + 15341
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.8
Root			$-0.591999i$ of defining polynomial
Character	$\chi$	$=$	87.59
Dual form			87.3.b.a.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.591999i q^{2} +(1.87458 + 2.34221i) q^{3} +3.64954 q^{4} +5.79366i q^{5} +(1.38659 - 1.10975i) q^{6} -9.59672 q^{7} -4.52852i q^{8} +(-1.97189 + 8.78132i) q^{9} +O(q^{10})$	\(q-0.591999i q^{2} +(1.87458 + 2.34221i) q^{3} +3.64954 q^{4} +5.79366i q^{5} +(1.38659 - 1.10975i) q^{6} -9.59672 q^{7} -4.52852i q^{8} +(-1.97189 + 8.78132i) q^{9} +3.42984 q^{10} -11.6953i q^{11} +(6.84135 + 8.54798i) q^{12} +21.0935 q^{13} +5.68125i q^{14} +(-13.5700 + 10.8607i) q^{15} +11.9173 q^{16} -25.9337i q^{17} +(5.19853 + 1.16736i) q^{18} -9.59174 q^{19} +21.1442i q^{20} +(-17.9898 - 22.4775i) q^{21} -6.92358 q^{22} -5.25325i q^{23} +(10.6067 - 8.48907i) q^{24} -8.56649 q^{25} -12.4873i q^{26} +(-24.2642 + 11.8427i) q^{27} -35.0236 q^{28} +5.38516i q^{29} +(6.42951 + 8.03340i) q^{30} +8.67080 q^{31} -25.1691i q^{32} +(27.3927 - 21.9237i) q^{33} -15.3527 q^{34} -55.6001i q^{35} +(-7.19649 + 32.0478i) q^{36} -55.8395 q^{37} +5.67830i q^{38} +(39.5414 + 49.4053i) q^{39} +26.2367 q^{40} +62.0334i q^{41} +(-13.3067 + 10.6500i) q^{42} -23.0437 q^{43} -42.6823i q^{44} +(-50.8760 - 11.4245i) q^{45} -3.10992 q^{46} -34.6532i q^{47} +(22.3399 + 27.9128i) q^{48} +43.0970 q^{49} +5.07135i q^{50} +(60.7421 - 48.6147i) q^{51} +76.9814 q^{52} +22.0743i q^{53} +(7.01088 + 14.3644i) q^{54} +67.7583 q^{55} +43.4589i q^{56} +(-17.9805 - 22.4659i) q^{57} +3.18801 q^{58} -7.52808i q^{59} +(-49.5241 + 39.6365i) q^{60} +6.95229 q^{61} -5.13311i q^{62} +(18.9237 - 84.2719i) q^{63} +32.7690 q^{64} +122.208i q^{65} +(-12.9788 - 16.2165i) q^{66} -99.9467 q^{67} -94.6459i q^{68} +(12.3042 - 9.84765i) q^{69} -32.9152 q^{70} +137.582i q^{71} +(39.7664 + 8.92975i) q^{72} +39.2838 q^{73} +33.0569i q^{74} +(-16.0586 - 20.0645i) q^{75} -35.0054 q^{76} +112.236i q^{77} +(29.2479 - 23.4085i) q^{78} +8.63722 q^{79} +69.0446i q^{80} +(-73.2233 - 34.6316i) q^{81} +36.7237 q^{82} -54.4522i q^{83} +(-65.6546 - 82.0326i) q^{84} +150.251 q^{85} +13.6419i q^{86} +(-12.6132 + 10.0949i) q^{87} -52.9622 q^{88} -83.2696i q^{89} +(-6.76327 + 30.1185i) q^{90} -202.428 q^{91} -19.1719i q^{92} +(16.2541 + 20.3088i) q^{93} -20.5146 q^{94} -55.5713i q^{95} +(58.9513 - 47.1815i) q^{96} -41.9422 q^{97} -25.5134i q^{98} +(102.700 + 23.0618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.591999i		−	0.295999i	−0.988987	−	0.148000i	$-0.952717\pi$
$2$		−	0.591999i		−	0.295999i	0.988987	−	0.148000i	$-0.0472835\pi$
$3$	1.87458	+	2.34221i	0.624860	+	0.780737i
$3$	1.87458	+	2.34221i	0.624860	+	0.780737i
$4$	3.64954			0.912384
$5$			5.79366i			1.15873i	0.815068	+	0.579366i	$0.196700\pi$
$5$			5.79366i			1.15873i	−0.815068	+	0.579366i	$0.803300\pi$
$6$	1.38659	−	1.10975i	0.231098	−	0.184958i
$7$	−9.59672			−1.37096			−0.685480	−	0.728091i	$-0.740408\pi$
$7$	−9.59672			−1.37096			−0.685480	+	0.728091i	$0.740408\pi$
$8$		−	4.52852i		−	0.566065i
$9$	−1.97189	+	8.78132i	−0.219099	+	0.975703i
$10$	3.42984			0.342984
$11$		−	11.6953i		−	1.06320i	−0.846994	−	0.531602i	$-0.821590\pi$
$11$		−	11.6953i		−	1.06320i	0.846994	−	0.531602i	$-0.178410\pi$
$12$	6.84135	+	8.54798i	0.570113	+	0.712332i
$13$	21.0935			1.62257			0.811287	−	0.584648i	$-0.198767\pi$
$13$	21.0935			1.62257			0.811287	+	0.584648i	$0.198767\pi$
$14$			5.68125i			0.405803i
$15$	−13.5700	+	10.8607i	−0.904664	+	0.724046i
$16$	11.9173			0.744830
$17$		−	25.9337i		−	1.52551i	−0.646688	−	0.762755i	$-0.723846\pi$
$17$		−	25.9337i		−	1.52551i	0.646688	−	0.762755i	$-0.276154\pi$
$18$	5.19853	+	1.16736i	0.288807	+	0.0648532i
$19$	−9.59174			−0.504829			−0.252414	−	0.967619i	$-0.581225\pi$
$19$	−9.59174			−0.504829			−0.252414	+	0.967619i	$0.581225\pi$
$20$			21.1442i			1.05721i
$21$	−17.9898	−	22.4775i	−0.856659	−	1.07036i
$22$	−6.92358			−0.314708
$23$		−	5.25325i		−	0.228402i	−0.993458	−	0.114201i	$-0.963569\pi$
$23$		−	5.25325i		−	0.228402i	0.993458	−	0.114201i	$-0.0364308\pi$
$24$	10.6067	−	8.48907i	0.441947	−	0.353711i
$25$	−8.56649			−0.342660
$26$		−	12.4873i		−	0.480281i
$27$	−24.2642	+	11.8427i	−0.898673	+	0.438619i
$28$	−35.0236			−1.25084
$29$			5.38516i			0.185695i
$29$			5.38516i			0.185695i
$30$	6.42951	+	8.03340i	0.214317	+	0.267780i
$31$	8.67080			0.279703			0.139852	−	0.990172i	$-0.455337\pi$
$31$	8.67080			0.279703			0.139852	+	0.990172i	$0.455337\pi$
$32$		−	25.1691i		−	0.786534i
$33$	27.3927	−	21.9237i	0.830083	−	0.664355i
$34$	−15.3527			−0.451550
$35$		−	55.6001i		−	1.58858i
$36$	−7.19649	+	32.0478i	−0.199903	+	0.890216i
$37$	−55.8395			−1.50918			−0.754588	−	0.656199i	$-0.772163\pi$
$37$	−55.8395			−1.50918			−0.754588	+	0.656199i	$0.772163\pi$
$38$			5.67830i			0.149429i
$39$	39.5414	+	49.4053i	1.01388	+	1.26680i
$40$	26.2367			0.655917
$41$			62.0334i			1.51301i	0.653988	+	0.756505i	$0.273095\pi$
$41$			62.0334i			1.51301i	−0.653988	+	0.756505i	$0.726905\pi$
$42$	−13.3067	+	10.6500i	−0.316826	+	0.253570i
$43$	−23.0437			−0.535901			−0.267950	−	0.963433i	$-0.586346\pi$
$43$	−23.0437			−0.535901			−0.267950	+	0.963433i	$0.586346\pi$
$44$		−	42.6823i		−	0.970052i
$45$	−50.8760	−	11.4245i	−1.13058	−	0.253877i
$46$	−3.10992			−0.0676069
$47$		−	34.6532i		−	0.737302i	−0.929568	−	0.368651i	$-0.879820\pi$
$47$		−	34.6532i		−	0.737302i	0.929568	−	0.368651i	$-0.120180\pi$
$48$	22.3399	+	27.9128i	0.465414	+	0.581516i
$49$	43.0970			0.879531
$50$			5.07135i			0.101427i
$51$	60.7421	−	48.6147i	1.19102	−	0.953230i
$52$	76.9814			1.48041
$53$			22.0743i			0.416496i	0.978076	+	0.208248i	$0.0667761\pi$
$53$			22.0743i			0.416496i	−0.978076	+	0.208248i	$0.933224\pi$
$54$	7.01088	+	14.3644i	0.129831	+	0.266007i
$55$	67.7583			1.23197
$56$			43.4589i			0.776052i
$57$	−17.9805	−	22.4659i	−0.315447	−	0.394138i
$58$	3.18801			0.0549657
$59$		−	7.52808i		−	0.127595i	−0.997963	−	0.0637973i	$-0.979679\pi$
$59$		−	7.52808i		−	0.127595i	0.997963	−	0.0637973i	$-0.0203211\pi$
$60$	−49.5241	+	39.6365i	−0.825402	+	0.660608i
$61$	6.95229			0.113972			0.0569860	−	0.998375i	$-0.481851\pi$
$61$	6.95229			0.113972			0.0569860	+	0.998375i	$0.481851\pi$
$62$		−	5.13311i		−	0.0827920i
$63$	18.9237	−	84.2719i	0.300376	−	1.33765i
$64$	32.7690			0.512016
$65$			122.208i			1.88013i
$66$	−12.9788	−	16.2165i	−0.196649	−	0.245704i
$67$	−99.9467			−1.49174			−0.745871	−	0.666090i	$-0.767967\pi$
$67$	−99.9467			−1.49174			−0.745871	+	0.666090i	$0.767967\pi$
$68$		−	94.6459i		−	1.39185i
$69$	12.3042	−	9.84765i	0.178322	−	0.142720i
$70$	−32.9152			−0.470217
$71$			137.582i			1.93778i	0.247499	+	0.968888i	$0.420391\pi$
$71$			137.582i			1.93778i	−0.247499	+	0.968888i	$0.579609\pi$
$72$	39.7664	+	8.92975i	0.552311	+	0.124024i
$73$	39.2838			0.538134			0.269067	−	0.963121i	$-0.413285\pi$
$73$	39.2838			0.538134			0.269067	+	0.963121i	$0.413285\pi$
$74$			33.0569i			0.446715i
$75$	−16.0586	−	20.0645i	−0.214114	−	0.267527i
$76$	−35.0054			−0.460598
$77$			112.236i			1.45761i
$78$	29.2479	−	23.4085i	0.374973	−	0.300109i
$79$	8.63722			0.109332			0.0546659	−	0.998505i	$-0.482591\pi$
$79$	8.63722			0.109332			0.0546659	+	0.998505i	$0.482591\pi$
$80$			69.0446i			0.863058i
$81$	−73.2233	−	34.6316i	−0.903991	−	0.427551i
$82$	36.7237			0.447850
$83$		−	54.4522i		−	0.656051i	−0.944669	−	0.328025i	$-0.893617\pi$
$83$		−	54.4522i		−	0.656051i	0.944669	−	0.328025i	$-0.106383\pi$
$84$	−65.6546	−	82.0326i	−0.781602	−	0.976578i
$85$	150.251			1.76766
$86$			13.6419i			0.158626i
$87$	−12.6132	+	10.0949i	−0.144979	+	0.116034i
$88$	−52.9622			−0.601843
$89$		−	83.2696i		−	0.935614i	−0.883831	−	0.467807i	$-0.845044\pi$
$89$		−	83.2696i		−	0.935614i	0.883831	−	0.467807i	$-0.154956\pi$
$90$	−6.76327	+	30.1185i	−0.0751475	+	0.334650i
$91$	−202.428			−2.22448
$92$		−	19.1719i		−	0.208391i
$93$	16.2541	+	20.3088i	0.174776	+	0.218375i
$94$	−20.5146			−0.218241
$95$		−	55.5713i		−	0.584961i
$96$	58.9513	−	47.1815i	0.614076	−	0.491474i
$97$	−41.9422			−0.432394			−0.216197	−	0.976350i	$-0.569365\pi$
$97$	−41.9422			−0.432394			−0.216197	+	0.976350i	$0.569365\pi$
$98$		−	25.5134i		−	0.260341i
$99$	102.700	+	23.0618i	1.03737	+	0.232947i
$100$	−31.2637			−0.312637
$101$		−	63.9348i		−	0.633018i	−0.948589	−	0.316509i	$-0.897489\pi$
$101$		−	63.9348i		−	0.633018i	0.948589	−	0.316509i	$-0.102511\pi$
$102$	−28.7799	−	35.9592i	−0.282156	−	0.352541i
$103$	28.1857			0.273648			0.136824	−	0.990595i	$-0.456311\pi$
$103$	28.1857			0.273648			0.136824	+	0.990595i	$0.456311\pi$
$104$		−	95.5221i		−	0.918482i
$105$	130.227	−	104.227i	1.24026	−	0.992638i
$106$	13.0679			0.123282
$107$		−	20.5837i		−	0.192371i	−0.995363	−	0.0961854i	$-0.969336\pi$
$107$		−	20.5837i		−	0.192371i	0.995363	−	0.0961854i	$-0.0306642\pi$
$108$	−88.5530	+	43.2204i	−0.819935	+	0.400189i
$109$	53.4297			0.490181			0.245091	−	0.969500i	$-0.421182\pi$
$109$	53.4297			0.490181			0.245091	+	0.969500i	$0.421182\pi$
$110$		−	40.1128i		−	0.364662i
$111$	−104.676	−	130.788i	−0.943025	−	1.17827i
$112$	−114.367			−1.02113
$113$			31.6405i			0.280005i	0.990151	+	0.140002i	$0.0447110\pi$
$113$			31.6405i			0.280005i	−0.990151	+	0.140002i	$0.955289\pi$
$114$	−13.2998	+	10.6444i	−0.116665	+	0.0933722i
$115$	30.4356			0.264657
$116$			19.6534i			0.169426i
$117$	−41.5940	+	185.229i	−0.355505	+	1.58315i
$118$	−4.45662			−0.0377679
$119$			248.878i			2.09141i
$120$	49.1828	+	61.4518i	0.409857	+	0.512099i
$121$	−15.7790			−0.130405
$122$		−	4.11575i		−	0.0337356i
$123$	−145.295	+	116.287i	−1.18126	+	0.945420i
$124$	31.6444			0.255197
$125$			95.2102i			0.761681i
$126$	−49.8889	−	11.2028i	−0.395943	−	0.0889111i
$127$	139.865			1.10130			0.550648	−	0.834737i	$-0.314381\pi$
$127$	139.865			1.10130			0.550648	+	0.834737i	$0.314381\pi$
$128$		−	120.076i		−	0.938090i
$129$	−43.1974	−	53.9733i	−0.334863	−	0.418397i
$130$	72.3472			0.556517
$131$		−	16.6624i		−	0.127194i	−0.997976	−	0.0635969i	$-0.979743\pi$
$131$		−	16.6624i		−	0.127194i	0.997976	−	0.0635969i	$-0.0202572\pi$
$132$	99.9708	−	80.0114i	0.757355	−	0.606147i
$133$	92.0493			0.692100
$134$			59.1684i			0.441555i
$135$	−68.6127	−	140.578i	−0.508242	−	1.04132i
$136$	−117.441			−0.863537
$137$			91.6710i			0.669132i	0.942372	+	0.334566i	$0.108590\pi$
$137$			91.6710i			0.669132i	−0.942372	+	0.334566i	$0.891410\pi$
$138$	−5.82980	−	7.28408i	−0.0422449	−	0.0527832i
$139$	−96.5441			−0.694562			−0.347281	−	0.937761i	$-0.612895\pi$
$139$	−96.5441			−0.694562			−0.347281	+	0.937761i	$0.612895\pi$
$140$		−	202.915i		−	1.44939i
$141$	81.1650	−	64.9602i	0.575638	−	0.460711i
$142$	81.4485			0.573581
$143$		−	246.693i		−	1.72513i
$144$	−23.4996	+	104.649i	−0.163191	+	0.726732i
$145$	−31.1998			−0.215171
$146$		−	23.2560i		−	0.159287i
$147$	80.7889	+	100.942i	0.549584	+	0.686682i
$148$	−203.788			−1.37695
$149$			194.129i			1.30288i	0.758701	+	0.651440i	$0.225835\pi$
$149$			194.129i			1.30288i	−0.758701	+	0.651440i	$0.774165\pi$
$150$	−11.8782	+	9.50666i	−0.0791878	+	0.0633777i
$151$	52.4709			0.347489			0.173745	−	0.984791i	$-0.444413\pi$
$151$	52.4709			0.347489			0.173745	+	0.984791i	$0.444413\pi$
$152$			43.4364i			0.285766i
$153$	227.732	+	51.1384i	1.48844	+	0.334238i
$154$	66.4436			0.431452
$155$			50.2357i			0.324101i
$156$	144.308	+	180.307i	0.925051	+	1.15581i
$157$	145.640			0.927645			0.463822	−	0.885928i	$-0.346478\pi$
$157$	145.640			0.927645			0.463822	+	0.885928i	$0.346478\pi$
$158$		−	5.11322i		−	0.0323622i
$159$	−51.7026	+	41.3800i	−0.325173	+	0.260252i
$160$	145.821			0.911382
$161$			50.4140i			0.313130i
$162$	−20.5019	+	43.3481i	−0.126555	+	0.267581i
$163$	−170.407			−1.04544			−0.522719	−	0.852505i	$-0.675082\pi$
$163$	−170.407			−1.04544			−0.522719	+	0.852505i	$0.675082\pi$
$164$			226.393i			1.38045i
$165$	127.018	+	158.704i	0.769809	+	0.961844i
$166$	−32.2356			−0.194191
$167$		−	329.268i		−	1.97167i	−0.167731	−	0.985833i	$-0.553644\pi$
$167$		−	329.268i		−	1.97167i	0.167731	−	0.985833i	$-0.446356\pi$
$168$	−101.790	+	81.4673i	−0.605892	+	0.484924i
$169$	275.934			1.63275
$170$		−	88.9483i		−	0.523225i
$171$	18.9139	−	84.2282i	0.110607	−	0.492563i
$172$	−84.0990			−0.488948
$173$			223.353i			1.29106i	0.763735	+	0.645530i	$0.223363\pi$
$173$			223.353i			1.29106i	−0.763735	+	0.645530i	$0.776637\pi$
$174$	5.97619	+	7.46699i	0.0343459	+	0.0429137i
$175$	82.2102			0.469773
$176$		−	139.376i		−	0.791906i
$177$	17.6324	−	14.1120i	0.0996178	−	0.0797288i
$178$	−49.2955			−0.276941
$179$			22.3994i			0.125136i	0.998041	+	0.0625681i	$0.0199291\pi$
$179$			22.3994i			0.125136i	−0.998041	+	0.0625681i	$0.980071\pi$
$180$	−185.674	−	41.6940i	−1.03152	−	0.231634i
$181$	143.446			0.792521			0.396260	−	0.918138i	$-0.370308\pi$
$181$	143.446			0.792521			0.396260	+	0.918138i	$0.370308\pi$
$182$			119.837i			0.658446i
$183$	13.0326	+	16.2837i	0.0712165	+	0.0889820i
$184$	−23.7894			−0.129290
$185$		−	323.515i		−	1.74873i
$186$	12.0228	−	9.62242i	0.0646388	−	0.0517335i
$187$	−303.301			−1.62193
$188$		−	126.468i		−	0.672702i
$189$	232.856	−	113.651i	1.23204	−	0.601329i
$190$	−32.8981			−0.173148
$191$			36.2678i			0.189884i	0.995483	+	0.0949418i	$0.0302665\pi$
$191$			36.2678i			0.189884i	−0.995483	+	0.0949418i	$0.969734\pi$
$192$	61.4282	+	76.7519i	0.319938	+	0.399750i
$193$	−259.170			−1.34285			−0.671424	−	0.741073i	$-0.734317\pi$
$193$	−259.170			−1.34285			−0.671424	+	0.741073i	$0.734317\pi$
$194$			24.8297i			0.127988i
$195$	−286.238	+	229.090i	−1.46789	+	1.17482i
$196$	157.284			0.802470
$197$		−	119.924i		−	0.608753i	−0.952552	−	0.304377i	$-0.901552\pi$
$197$		−	119.924i		−	0.608753i	0.952552	−	0.304377i	$-0.0984481\pi$
$198$	13.6525	−	60.7982i	0.0689523	−	0.307061i
$199$	127.606			0.641236			0.320618	−	0.947209i	$-0.396109\pi$
$199$	127.606			0.641236			0.320618	+	0.947209i	$0.396109\pi$
$200$			38.7935i			0.193967i
$201$	−187.358	−	234.096i	−0.932131	−	1.16466i
$202$	−37.8493			−0.187373
$203$		−	51.6799i		−	0.254581i
$204$	221.680	−	177.421i	1.08667	−	0.869712i
$205$	−359.400			−1.75317
$206$		−	16.6859i		−	0.0809996i
$207$	46.1305	+	10.3588i	0.222853	+	0.0500427i
$208$	251.377			1.20854
$209$			112.178i			0.536736i
$210$	−61.7022	−	77.0943i	−0.293820	−	0.367116i
$211$	−158.883			−0.752999			−0.376500	−	0.926417i	$-0.622872\pi$
$211$	−158.883			−0.752999			−0.376500	+	0.926417i	$0.622872\pi$
$212$			80.5609i			0.380004i
$213$	−322.246	+	257.909i	−1.51289	+	1.21084i
$214$	−12.1855			−0.0569417
$215$		−	133.508i		−	0.620966i
$216$	53.6300	+	109.881i	0.248287	+	0.508707i
$217$	−83.2113			−0.383462
$218$		−	31.6303i		−	0.145093i
$219$	73.6407	+	92.0109i	0.336259	+	0.420141i
$220$	247.287			1.12403
$221$		−	547.031i		−	2.47525i
$222$	−77.4263	+	61.9679i	−0.348767	+	0.279135i
$223$	−400.363			−1.79535			−0.897675	−	0.440659i	$-0.854745\pi$
$223$	−400.363			−1.79535			−0.897675	+	0.440659i	$0.854745\pi$
$224$			241.541i			1.07831i
$225$	16.8922	−	75.2251i	0.0750764	−	0.334334i
$226$	18.7312			0.0828812
$227$			100.145i			0.441167i	0.975368	+	0.220583i	$0.0707961\pi$
$227$			100.145i			0.441167i	−0.975368	+	0.220583i	$0.929204\pi$
$228$	−65.6205	−	81.9900i	−0.287809	−	0.359605i
$229$	196.830			0.859521			0.429761	−	0.902943i	$-0.358598\pi$
$229$	196.830			0.859521			0.429761	+	0.902943i	$0.358598\pi$
$230$		−	18.0178i		−	0.0783383i
$231$	−262.880	+	210.396i	−1.13801	+	0.910804i
$232$	24.3868			0.105116
$233$		−	364.954i		−	1.56633i	−0.621816	−	0.783164i	$-0.713605\pi$
$233$		−	364.954i		−	1.56633i	0.621816	−	0.783164i	$-0.286395\pi$
$234$	109.655	+	24.6236i	0.468612	+	0.105229i
$235$	200.769			0.854335
$236$		−	27.4740i		−	0.116415i
$237$	16.1912	+	20.2302i	0.0683171	+	0.0853594i
$238$	147.336			0.619057
$239$		−	129.400i		−	0.541422i	−0.962661	−	0.270711i	$-0.912741\pi$
$239$		−	129.400i		−	0.541422i	0.962661	−	0.270711i	$-0.0872588\pi$
$240$	−161.717	+	129.430i	−0.673821	+	0.539291i
$241$	−78.9952			−0.327781			−0.163890	−	0.986479i	$-0.552404\pi$
$241$	−78.9952			−0.327781			−0.163890	+	0.986479i	$0.552404\pi$
$242$			9.34114i			0.0385997i
$243$	−56.1484	−	236.424i	−0.231063	−	0.972939i
$244$	25.3726			0.103986
$245$			249.690i			1.01914i
$246$	68.8415	+	86.0146i	0.279844	+	0.349653i
$247$	−202.323			−0.819122
$248$		−	39.2659i		−	0.158330i
$249$	127.538	−	102.075i	0.512203	−	0.409940i
$250$	56.3643			0.225457
$251$		−	102.882i		−	0.409890i	−0.978773	−	0.204945i	$-0.934298\pi$
$251$		−	102.882i		−	0.409890i	0.978773	−	0.204945i	$-0.0657015\pi$
$252$	69.0627	−	307.553i	0.274058	−	1.22045i
$253$	−61.4381			−0.242838
$254$		−	82.7997i		−	0.325983i
$255$	281.657	+	351.919i	1.10454	+	1.38007i
$256$	59.9915			0.234342
$257$			157.221i			0.611756i	0.952071	+	0.305878i	$0.0989500\pi$
$257$			157.221i			0.611756i	−0.952071	+	0.305878i	$0.901050\pi$
$258$	−31.9521	+	25.5728i	−0.123845	+	0.0991193i
$259$	535.876			2.06902
$260$			446.004i			1.71540i
$261$	−47.2889	−	10.6190i	−0.181183	−	0.0406857i
$262$	−9.86411			−0.0376493
$263$			407.396i			1.54903i	0.632553	+	0.774517i	$0.282007\pi$
$263$			407.396i			1.54903i	−0.632553	+	0.774517i	$0.717993\pi$
$264$	−99.2819	−	124.048i	−0.376068	−	0.469881i
$265$	−127.891			−0.482607
$266$		−	54.4931i		−	0.204861i
$267$	195.035	−	156.096i	0.730468	−	0.584628i
$268$	−364.759			−1.36104
$269$			119.369i			0.443752i	0.975075	+	0.221876i	$0.0712180\pi$
$269$			119.369i			0.443752i	−0.975075	+	0.221876i	$0.928782\pi$
$270$	−83.2222	+	40.6186i	−0.308230	+	0.150439i
$271$	310.345			1.14518			0.572591	−	0.819841i	$-0.305938\pi$
$271$	310.345			1.14518			0.572591	+	0.819841i	$0.305938\pi$
$272$		−	309.058i		−	1.13624i
$273$	−379.468	−	474.129i	−1.38999	−	1.73674i
$274$	54.2691			0.198063
$275$			100.187i			0.364317i
$276$	44.9047	−	35.9394i	0.162698	−	0.130215i
$277$	−34.2997			−0.123826			−0.0619128	−	0.998082i	$-0.519720\pi$
$277$	−34.2997			−0.123826			−0.0619128	+	0.998082i	$0.519720\pi$
$278$			57.1540i			0.205590i
$279$	−17.0979	+	76.1411i	−0.0612827	+	0.272907i
$280$	−251.786			−0.899236
$281$			418.400i			1.48897i	0.667641	+	0.744483i	$0.267304\pi$
$281$			418.400i			1.48897i	−0.667641	+	0.744483i	$0.732696\pi$
$282$	−38.4564	−	48.0496i	−0.136370	−	0.170389i
$283$	106.001			0.374562			0.187281	−	0.982306i	$-0.440032\pi$
$283$	106.001			0.374562			0.187281	+	0.982306i	$0.440032\pi$
$284$			502.111i			1.76800i
$285$	130.160	−	104.173i	0.456700	−	0.365519i
$286$	−146.042			−0.510637
$287$		−	595.317i		−	2.07428i
$288$	221.018	+	49.6307i	0.767423	+	0.172329i
$289$	−383.555			−1.32718
$290$			18.4703i			0.0636905i
$291$	−78.6241	−	98.2374i	−0.270186	−	0.337586i
$292$	143.368			0.490985
$293$			44.3924i			0.151510i	0.997126	+	0.0757550i	$0.0241367\pi$
$293$			44.3924i			0.151510i	−0.997126	+	0.0757550i	$0.975863\pi$
$294$	59.7577	−	47.8269i	0.203258	−	0.162677i
$295$	43.6152			0.147848
$296$			252.870i			0.854292i
$297$	138.504	+	283.776i	0.466342	+	0.955474i
$298$	114.924			0.385651
$299$		−	110.809i		−	0.370600i
$300$	−58.6064	−	73.2262i	−0.195355	−	0.244087i
$301$	221.144			0.734699
$302$		−	31.0627i		−	0.102857i
$303$	149.749	−	119.851i	0.494220	−	0.395548i
$304$	−114.307			−0.376011
$305$			40.2792i			0.132063i
$306$	30.2739	−	134.817i	0.0989342	−	0.440578i
$307$	−16.6849			−0.0543481			−0.0271740	−	0.999631i	$-0.508651\pi$
$307$	−16.6849			−0.0543481			−0.0271740	+	0.999631i	$0.508651\pi$
$308$			409.610i			1.32990i
$309$	52.8364	+	66.0169i	0.170992	+	0.213647i
$310$	29.7395			0.0959338
$311$			270.662i			0.870297i	0.900359	+	0.435148i	$0.143304\pi$
$311$			270.662i			0.870297i	−0.900359	+	0.435148i	$0.856696\pi$
$312$	223.733	−	179.064i	0.717093	−	0.573923i
$313$	−106.195			−0.339281			−0.169640	−	0.985506i	$-0.554261\pi$
$313$	−106.195			−0.339281			−0.169640	+	0.985506i	$0.554261\pi$
$314$		−	86.2189i		−	0.274582i
$315$	488.243	+	109.637i	1.54998	+	0.348055i
$316$	31.5218			0.0997527
$317$			125.017i			0.394374i	0.980366	+	0.197187i	$0.0631806\pi$
$317$			125.017i			0.394374i	−0.980366	+	0.197187i	$0.936819\pi$
$318$	24.4969	+	30.6079i	0.0770343	+	0.0962511i
$319$	62.9809			0.197432
$320$			189.853i			0.593289i
$321$	48.2113	−	38.5858i	0.150191	−	0.120205i
$322$	29.8450			0.0926864
$323$			248.749i			0.770121i
$324$	−267.231	−	126.389i	−0.824787	−	0.390091i
$325$	−180.697			−0.555991
$326$			100.880i			0.309449i
$327$	100.158	+	125.144i	0.306295	+	0.382702i
$328$	280.919			0.856461
$329$			332.557i			1.01081i
$330$	93.9527	−	75.1948i	0.284705	−	0.227863i
$331$	461.247			1.39350			0.696748	−	0.717316i	$-0.254630\pi$
$331$	461.247			1.39350			0.696748	+	0.717316i	$0.254630\pi$
$332$		−	198.725i		−	0.598570i
$333$	110.110	−	490.345i	0.330659	−	1.47251i
$334$	−194.926			−0.583612
$335$		−	579.057i		−	1.72853i
$336$	−214.390	−	267.871i	−0.638065	−	0.797235i
$337$	560.751			1.66395			0.831975	−	0.554813i	$-0.187210\pi$
$337$	560.751			1.66395			0.831975	+	0.554813i	$0.187210\pi$
$338$		−	163.353i		−	0.483293i
$339$	−74.1088	+	59.3128i	−0.218610	+	0.174964i
$340$	548.346			1.61278
$341$		−	101.407i		−	0.297382i
$342$	−49.8630	−	11.1970i	−0.145798	−	0.0327397i
$343$	56.6492			0.165158
$344$			104.354i			0.303355i
$345$	57.0539	+	71.2864i	0.165374	+	0.206627i
$346$	132.225			0.382153
$347$		−	256.975i		−	0.740562i	−0.928920	−	0.370281i	$-0.879261\pi$
$347$		−	256.975i		−	0.740562i	0.928920	−	0.370281i	$-0.120739\pi$
$348$	−46.0323	+	36.8418i	−0.132277	+	0.105867i
$349$	−405.643			−1.16230			−0.581150	−	0.813796i	$-0.697397\pi$
$349$	−405.643			−1.16230			−0.581150	+	0.813796i	$0.697397\pi$
$350$		−	48.6683i		−	0.139052i
$351$	−511.816	+	249.804i	−1.45816	+	0.711692i
$352$	−294.359			−0.836247
$353$			276.988i			0.784668i	0.919823	+	0.392334i	$0.128332\pi$
$353$			276.988i			0.784668i	−0.919823	+	0.392334i	$0.871668\pi$
$354$	−8.35429	−	10.4383i	−0.0235997	−	0.0294868i
$355$	−797.104			−2.24536
$356$		−	303.896i		−	0.853639i
$357$	−582.925	+	466.542i	−1.63284	+	1.30684i
$358$	13.2604			0.0370403
$359$		−	252.513i		−	0.703380i	−0.936117	−	0.351690i	$-0.885607\pi$
$359$		−	252.513i		−	0.703380i	0.936117	−	0.351690i	$-0.114393\pi$
$360$	−51.7359	+	230.393i	−0.143711	+	0.639980i
$361$	−268.998			−0.745148
$362$		−	84.9200i		−	0.234586i
$363$	−29.5790	−	36.9577i	−0.0814848	−	0.101812i
$364$	−738.769			−2.02959
$365$			227.597i			0.623554i
$366$	9.63994	−	7.71530i	0.0263386	−	0.0210801i
$367$	377.542			1.02872			0.514362	−	0.857573i	$-0.328029\pi$
$367$	377.542			1.02872			0.514362	+	0.857573i	$0.328029\pi$
$368$		−	62.6044i		−	0.170121i
$369$	−544.735	−	122.323i	−1.47625	−	0.331499i
$370$	−191.521			−0.517623
$371$		−	211.841i		−	0.570999i
$372$	59.3200	+	74.1179i	0.159462	+	0.199242i
$373$	113.060			0.303111			0.151555	−	0.988449i	$-0.451572\pi$
$373$	113.060			0.303111			0.151555	+	0.988449i	$0.451572\pi$
$374$			179.554i			0.480090i
$375$	−223.002	+	178.479i	−0.594672	+	0.475944i
$376$	−156.928			−0.417360
$377$			113.592i			0.301305i
$378$	−67.2814	−	137.851i	−0.177993	−	0.364685i
$379$	405.803			1.07072			0.535360	−	0.844624i	$-0.320176\pi$
$379$	405.803			1.07072			0.535360	+	0.844624i	$0.320176\pi$
$380$		−	202.809i		−	0.533709i
$381$	262.188	+	327.592i	0.688156	+	0.859822i
$382$	21.4705			0.0562054
$383$		−	454.658i		−	1.18710i	−0.804798	−	0.593548i	$-0.797727\pi$
$383$		−	454.658i		−	1.18710i	0.804798	−	0.593548i	$-0.202273\pi$
$384$	281.242	−	225.091i	0.732401	−	0.586175i
$385$	−650.258			−1.68898
$386$			153.428i			0.397482i
$387$	45.4398	−	202.355i	0.117415	−	0.522880i
$388$	−153.070			−0.394509
$389$		−	562.968i		−	1.44722i	−0.690209	−	0.723610i	$-0.742482\pi$
$389$		−	562.968i		−	1.44722i	0.690209	−	0.723610i	$-0.257518\pi$
$390$	135.621	+	169.452i	0.347745	+	0.434493i
$391$	−136.236			−0.348430
$392$		−	195.166i		−	0.497872i
$393$	39.0268	−	31.2350i	0.0993048	−	0.0794783i
$394$	−70.9951			−0.180191
$395$			50.0411i			0.126686i
$396$	374.807	+	84.1648i	0.946482	+	0.212537i
$397$	484.369			1.22007			0.610037	−	0.792373i	$-0.291155\pi$
$397$	484.369			1.22007			0.610037	+	0.792373i	$0.291155\pi$
$398$		−	75.5425i		−	0.189805i
$399$	172.554	+	215.599i	0.432466	+	0.540348i
$400$	−102.089			−0.255223
$401$		−	274.521i		−	0.684591i	−0.939592	−	0.342295i	$-0.888796\pi$
$401$		−	274.521i		−	0.684591i	0.939592	−	0.342295i	$-0.111204\pi$
$402$	−138.585	+	110.916i	−0.344738	+	0.275910i
$403$	182.897			0.453840
$404$		−	233.333i		−	0.577556i
$405$	200.644	−	424.231i	0.495417	−	1.04748i
$406$	−30.5945			−0.0753558
$407$			653.058i			1.60456i
$408$	−220.153	−	275.071i	−0.539590	−	0.674195i
$409$	−137.445			−0.336051			−0.168026	−	0.985783i	$-0.553739\pi$
$409$	−137.445			−0.336051			−0.168026	+	0.985783i	$0.553739\pi$
$410$			212.765i			0.518938i
$411$	−214.713	+	171.845i	−0.522415	+	0.418114i
$412$	102.865			0.249672
$413$			72.2449i			0.174927i
$414$	6.13242	−	27.3092i	0.0148126	−	0.0659643i
$415$	315.478			0.760187
$416$		−	530.903i		−	1.27621i
$417$	−180.980	−	226.126i	−0.434004	−	0.542270i
$418$	66.4092			0.158874
$419$			624.266i			1.48990i	0.667122	+	0.744948i	$0.267526\pi$
$419$			624.266i			1.48990i	−0.667122	+	0.744948i	$0.732474\pi$
$420$	475.269	−	380.380i	1.13159	−	0.905667i
$421$	385.339			0.915295			0.457648	−	0.889134i	$-0.348692\pi$
$421$	385.339			0.915295			0.457648	+	0.889134i	$0.348692\pi$
$422$			94.0584i			0.222887i
$423$	304.301	+	68.3323i	0.719387	+	0.161542i
$424$	99.9637			0.235763
$425$			222.160i			0.522730i
$426$	152.682	+	190.769i	0.358408	+	0.447815i
$427$	−66.7191			−0.156251
$428$		−	75.1209i		−	0.175516i
$429$	577.808	−	462.447i	1.34687	−	1.07796i
$430$	−79.0363			−0.183805
$431$			336.616i			0.781010i	0.920601	+	0.390505i	$0.127700\pi$
$431$			336.616i			0.781010i	−0.920601	+	0.390505i	$0.872300\pi$
$432$	−289.163	+	141.133i	−0.669358	+	0.326697i
$433$	−819.659			−1.89298			−0.946488	−	0.322738i	$-0.895397\pi$
$433$	−819.659			−1.89298			−0.946488	+	0.322738i	$0.895397\pi$
$434$			49.2610i			0.113505i
$435$	−58.4866	−	73.0765i	−0.134452	−	0.167992i
$436$	194.994			0.447234
$437$			50.3878i			0.115304i
$438$	54.4704	−	43.5952i	0.124362	−	0.0995324i
$439$	−173.257			−0.394662			−0.197331	−	0.980337i	$-0.563227\pi$
$439$	−173.257			−0.394662			−0.197331	+	0.980337i	$0.563227\pi$
$440$		−	306.845i		−	0.697374i
$441$	−84.9827	+	378.449i	−0.192704	+	0.858161i
$442$	−323.842			−0.732673
$443$			172.338i			0.389025i	0.980900	+	0.194513i	$0.0623125\pi$
$443$			172.338i			0.389025i	−0.980900	+	0.194513i	$0.937687\pi$
$444$	−382.018	−	477.315i	−0.860401	−	1.07503i
$445$	482.436			1.08413
$446$			237.014i			0.531422i
$447$	−454.691	+	363.911i	−1.01721	+	0.814118i
$448$	−314.475			−0.701953
$449$			70.7383i			0.157546i	0.996893	+	0.0787731i	$0.0251003\pi$
$449$			70.7383i			0.157546i	−0.996893	+	0.0787731i	$0.974900\pi$
$450$	−44.5332	−	10.0002i	−0.0989626	−	0.0222226i
$451$	725.496			1.60864
$452$			115.473i			0.255472i
$453$	98.3610	+	122.898i	0.217132	+	0.271298i
$454$	59.2856			0.130585
$455$		−	1172.80i		−	2.57758i
$456$	−101.737	+	81.4250i	−0.223108	+	0.178564i
$457$	−46.7867			−0.102378			−0.0511890	−	0.998689i	$-0.516301\pi$
$457$	−46.7867			−0.102378			−0.0511890	+	0.998689i	$0.516301\pi$
$458$		−	116.523i		−	0.254418i
$459$	307.125	+	629.259i	0.669118	+	1.37093i
$460$	111.076			0.241469
$461$		−	582.934i		−	1.26450i	−0.774765	−	0.632250i	$-0.782132\pi$
$461$		−	582.934i		−	1.26450i	0.774765	−	0.632250i	$-0.217868\pi$
$462$	124.554	+	155.625i	0.269597	+	0.336850i
$463$	879.627			1.89984			0.949921	−	0.312489i	$-0.101163\pi$
$463$	879.627			1.89984			0.949921	+	0.312489i	$0.101163\pi$
$464$			64.1765i			0.138311i
$465$	−117.662	+	94.1709i	−0.253038	+	0.202518i
$466$	−216.053			−0.463632
$467$			12.3860i			0.0265225i	0.999912	+	0.0132612i	$0.00422131\pi$
$467$			12.3860i			0.0265225i	−0.999912	+	0.0132612i	$0.995779\pi$
$468$	−151.799	+	675.999i	−0.324357	+	1.44444i
$469$	959.161			2.04512
$470$		−	118.855i		−	0.252883i
$471$	273.014	+	341.120i	0.579649	+	0.724246i
$472$	−34.0911			−0.0722268
$473$			269.502i			0.569773i
$474$	11.9762	−	9.58515i	0.0252663	−	0.0202218i
$475$	82.1676			0.172984
$476$			908.290i			1.90817i
$477$	−193.841	−	43.5281i	−0.406376	−	0.0912538i
$478$	−76.6046			−0.160261
$479$		−	98.8167i		−	0.206298i	−0.994666	−	0.103149i	$-0.967108\pi$
$479$		−	98.8167i		−	0.206298i	0.994666	−	0.103149i	$-0.0328918\pi$
$480$	273.353	+	341.544i	0.569486	+	0.711549i
$481$	−1177.85			−2.44875
$482$			46.7650i			0.0970229i
$483$	−118.080	+	94.5051i	−0.244472	+	0.195663i
$484$	−57.5860			−0.118979
$485$		−	242.999i		−	0.501029i
$486$	−139.963	+	33.2398i	−0.287989	+	0.0683946i
$487$	−372.714			−0.765326			−0.382663	−	0.923888i	$-0.624993\pi$
$487$	−372.714			−0.765326			−0.382663	+	0.923888i	$0.624993\pi$
$488$		−	31.4836i		−	0.0645155i
$489$	−319.441	−	399.128i	−0.653253	−	0.816212i
$490$	147.816			0.301665
$491$		−	168.548i		−	0.343274i	−0.985160	−	0.171637i	$-0.945094\pi$
$491$		−	168.548i		−	0.343274i	0.985160	−	0.171637i	$-0.0549057\pi$
$492$	−530.260	+	424.392i	−1.07776	+	0.862586i
$493$	139.657			0.283280
$494$			119.775i			0.242460i
$495$	−133.612	+	595.008i	−0.269923	+	1.20204i
$496$	103.332			0.208331
$497$		−	1320.34i		−	2.65661i
$498$	−60.4283	−	75.5026i	−0.121342	−	0.151612i
$499$	−64.2216			−0.128701			−0.0643503	−	0.997927i	$-0.520498\pi$
$499$	−64.2216			−0.128701			−0.0643503	+	0.997927i	$0.520498\pi$
$500$			347.473i			0.694946i
$501$	771.215	−	617.240i	1.53935	−	1.23202i
$502$	−60.9062			−0.121327
$503$			540.746i			1.07504i	0.843251	+	0.537521i	$0.180639\pi$
$503$			540.746i			1.07504i	−0.843251	+	0.537521i	$0.819361\pi$
$504$	−381.627	−	85.6963i	−0.757196	−	0.170032i
$505$	370.417			0.733498
$506$			36.3713i			0.0718800i
$507$	517.262	+	646.296i	1.02024	+	1.27475i
$508$	510.441			1.00481
$509$			331.526i			0.651328i	0.945486	+	0.325664i	$0.105588\pi$
$509$			331.526i			0.651328i	−0.945486	+	0.325664i	$0.894412\pi$
$510$	208.336	−	166.741i	0.408501	−	0.326943i
$511$	−376.996			−0.737761
$512$		−	515.817i		−	1.00746i
$513$	232.736	−	113.592i	0.453676	−	0.221427i
$514$	93.0749			0.181080
$515$			163.299i			0.317085i
$516$	−157.650	−	196.977i	−0.305524	−	0.381739i
$517$	−405.278			−0.783903
$518$		−	317.238i		−	0.612429i
$519$	−523.140	+	418.694i	−1.00798	+	0.806732i
$520$	553.423			1.06427
$521$		−	560.227i		−	1.07529i	−0.843171	−	0.537646i	$-0.819314\pi$
$521$		−	560.227i		−	1.07529i	0.843171	−	0.537646i	$-0.180686\pi$
$522$	−6.28641	+	27.9950i	−0.0120429	+	0.0536302i
$523$	569.804			1.08949			0.544746	−	0.838601i	$-0.316626\pi$
$523$	569.804			1.08949			0.544746	+	0.838601i	$0.316626\pi$
$524$		−	60.8100i		−	0.116050i
$525$	154.110	+	192.554i	0.293542	+	0.366769i
$526$	241.178			0.458513
$527$		−	224.866i		−	0.426690i
$528$	326.447	−	261.271i	0.618270	−	0.494831i
$529$	501.403			0.947832
$530$			75.7112i			0.142851i
$531$	66.1065	+	14.8446i	0.124494	+	0.0279559i
$532$	335.937			0.631461
$533$			1308.50i			2.45497i
$534$	−92.4085	−	115.460i	−0.173050	−	0.216218i
$535$	119.255			0.222906
$536$			452.611i			0.844423i
$537$	−52.4641	+	41.9895i	−0.0976984	+	0.0781927i
$538$	70.6665			0.131350
$539$		−	504.031i		−	0.935122i
$540$	−250.405	−	513.046i	−0.463712	−	0.950085i
$541$	−775.645			−1.43373			−0.716863	−	0.697214i	$-0.754423\pi$
$541$	−775.645			−1.43373			−0.716863	+	0.697214i	$0.754423\pi$
$542$		−	183.724i		−	0.338973i
$543$	268.902	+	335.981i	0.495215	+	0.618750i
$544$	−652.726			−1.19986
$545$			309.554i			0.567989i
$546$	−280.684	+	224.645i	−0.514073	+	0.411437i
$547$	−810.832			−1.48232			−0.741162	−	0.671326i	$-0.765725\pi$
$547$	−810.832			−1.48232			−0.741162	+	0.671326i	$0.765725\pi$
$548$			334.557i			0.610505i
$549$	−13.7092	+	61.0503i	−0.0249711	+	0.111203i
$550$	59.3108			0.107838
$551$		−	51.6531i		−	0.0937443i
$552$	−44.5952	−	55.7199i	−0.0807885	−	0.100942i
$553$	−82.8889			−0.149890
$554$			20.3054i			0.0366523i
$555$	757.741	−	606.456i	1.36530	−	1.09271i
$556$	−352.341			−0.633707
$557$		−	18.0342i		−	0.0323775i	−0.999869	−	0.0161887i	$-0.994847\pi$
$557$		−	18.0342i		−	0.0323775i	0.999869	−	0.0161887i	$-0.00515326\pi$
$558$	45.0755	+	10.1219i	0.0807804	+	0.0181397i
$559$	−486.072			−0.869539
$560$		−	662.602i		−	1.18322i
$561$	−568.562	−	710.394i	−1.01348	−	1.26630i
$562$	247.692			0.440733
$563$			39.9304i			0.0709243i	0.999371	+	0.0354622i	$0.0112903\pi$
$563$			39.9304i			0.0709243i	−0.999371	+	0.0354622i	$0.988710\pi$
$564$	296.215	−	237.075i	0.525203	−	0.420345i
$565$	−183.315			−0.324450
$566$		−	62.7525i		−	0.110870i
$567$	702.703	+	332.350i	1.23934	+	0.586155i
$568$	623.043			1.09691
$569$		−	761.946i		−	1.33910i	−0.742768	−	0.669549i	$-0.766488\pi$
$569$		−	761.946i		−	1.33910i	0.742768	−	0.669549i	$-0.233512\pi$
$570$	−61.6702	−	77.0543i	−0.108193	−	0.135183i
$571$	−1064.02			−1.86344			−0.931718	−	0.363182i	$-0.881690\pi$
$571$	−1064.02			−1.86344			−0.931718	+	0.363182i	$0.881690\pi$
$572$		−	900.317i		−	1.57398i
$573$	−84.9467	+	67.9869i	−0.148249	+	0.118651i
$574$	−352.427			−0.613984
$575$			45.0019i			0.0782642i
$576$	−64.6170	+	287.755i	−0.112182	+	0.499575i
$577$	973.716			1.68755			0.843774	−	0.536698i	$-0.180329\pi$
$577$	973.716			1.68755			0.843774	+	0.536698i	$0.180329\pi$
$578$			227.064i			0.392844i
$579$	−485.835	−	607.030i	−0.839093	−	1.04841i
$580$	−113.865			−0.196319
$581$			522.563i			0.899419i
$582$	−58.1565	+	46.5454i	−0.0999252	+	0.0799748i
$583$	258.164			0.442820
$584$		−	177.897i		−	0.304619i
$585$	−1073.15	−	240.982i	−1.83445	−	0.411935i
$586$	26.2803			0.0448469
$587$			58.2841i			0.0992915i	0.998767	+	0.0496458i	$0.0158092\pi$
$587$			58.2841i			0.0992915i	−0.998767	+	0.0496458i	$0.984191\pi$
$588$	294.842	+	368.393i	0.501432	+	0.626518i
$589$	−83.1681			−0.141202
$590$		−	25.8201i		−	0.0437629i
$591$	280.888	−	224.808i	0.475276	−	0.380386i
$592$	−665.455			−1.12408
$593$		−	1049.87i		−	1.77043i	−0.465180	−	0.885216i	$-0.654010\pi$
$593$		−	1049.87i		−	1.77043i	0.465180	−	0.885216i	$-0.345990\pi$
$594$	167.995	−	81.9940i	0.282820	−	0.138037i
$595$	−1441.91			−2.42339
$596$			708.481i			1.18873i
$597$	239.208	+	298.880i	0.400683	+	0.500636i
$598$	−65.5990			−0.109697
$599$			737.946i			1.23196i	0.787761	+	0.615982i	$0.211240\pi$
$599$			737.946i			1.23196i	−0.787761	+	0.615982i	$0.788760\pi$
$600$	−90.8625	+	72.7216i	−0.151438	+	0.121203i
$601$	1149.40			1.91247			0.956237	−	0.292595i	$-0.0945186\pi$
$601$	1149.40			1.91247			0.956237	+	0.292595i	$0.0945186\pi$
$602$		−	130.917i		−	0.217470i
$603$	197.084	−	877.665i	0.326839	−	1.45550i
$604$	191.495			0.317044
$605$		−	91.4180i		−	0.151104i
$606$	−70.9517	−	88.6511i	−0.117082	−	0.146289i
$607$	−852.763			−1.40488			−0.702441	−	0.711742i	$-0.747907\pi$
$607$	−852.763			−1.40488			−0.702441	+	0.711742i	$0.747907\pi$
$608$			241.415i			0.397065i
$609$	121.045	−	96.8782i	0.198761	−	0.159077i
$610$	23.8452			0.0390905
$611$		−	730.956i		−	1.19633i
$612$	831.116	+	186.631i	1.35803	+	0.304953i
$613$	−823.924			−1.34408			−0.672042	−	0.740513i	$-0.734583\pi$
$613$	−823.924			−1.34408			−0.672042	+	0.740513i	$0.734583\pi$
$614$			9.87742i			0.0160870i
$615$	−673.725	−	841.791i	−1.09549	−	1.36877i
$616$	508.263			0.825102
$617$		−	47.3880i		−	0.0768038i	−0.999262	−	0.0384019i	$-0.987773\pi$
$617$		−	47.3880i		−	0.0768038i	0.999262	−	0.0384019i	$-0.0122267\pi$
$618$	39.0819	−	31.2791i	0.0632394	−	0.0506134i
$619$	−505.631			−0.816852			−0.408426	−	0.912792i	$-0.633922\pi$
$619$	−505.631			−0.816852			−0.408426	+	0.912792i	$0.633922\pi$
$620$			183.337i			0.295705i
$621$	62.2128	+	127.466i	0.100182	+	0.205259i
$622$	160.232			0.257607
$623$			799.115i			1.28269i
$624$	471.226	+	588.777i	0.755170	+	0.943552i
$625$	−765.777			−1.22524
$626$			62.8673i			0.100427i
$627$	−262.744	+	210.286i	−0.419050	+	0.335385i
$628$	531.520			0.846369
$629$			1448.12i			2.30226i
$630$	64.9052	−	289.039i	0.103024	−	0.458792i
$631$	−254.186			−0.402830			−0.201415	−	0.979506i	$-0.564554\pi$
$631$	−254.186			−0.402830			−0.201415	+	0.979506i	$0.564554\pi$
$632$		−	39.1138i		−	0.0618889i
$633$	−297.839	−	372.137i	−0.470519	−	0.587894i
$634$	74.0096			0.116734
$635$			810.328i			1.27611i
$636$	−188.690	+	151.018i	−0.296683	+	0.237449i
$637$	909.066			1.42710
$638$		−	37.2846i		−	0.0584398i
$639$	−1208.15	−	271.297i	−1.89069	−	0.424565i
$640$	695.677			1.08700
$641$		−	429.687i		−	0.670339i	−0.942158	−	0.335169i	$-0.891206\pi$
$641$		−	429.687i		−	0.670339i	0.942158	−	0.335169i	$-0.108794\pi$
$642$	−22.8427	−	28.5410i	−0.0355806	−	0.0444564i
$643$	972.930			1.51311			0.756556	−	0.653929i	$-0.226881\pi$
$643$	972.930			1.51311			0.756556	+	0.653929i	$0.226881\pi$
$644$			183.988i			0.285695i
$645$	312.703	−	250.271i	0.484810	−	0.388017i
$646$	147.259			0.227955
$647$		−	477.680i		−	0.738300i	−0.929370	−	0.369150i	$-0.879649\pi$
$647$		−	477.680i		−	0.738300i	0.929370	−	0.369150i	$-0.120351\pi$
$648$	−156.830	+	331.593i	−0.242022	+	0.511717i
$649$	−88.0429			−0.135659
$650$			106.972i			0.164573i
$651$	−155.986	−	194.898i	−0.239610	−	0.299383i
$652$	−621.905			−0.953842
$653$			1265.67i			1.93823i	0.246604	+	0.969116i	$0.420685\pi$
$653$			1265.67i			1.93823i	−0.246604	+	0.969116i	$0.579315\pi$
$654$	74.0849	−	59.2936i	0.113280	−	0.0906631i
$655$	96.5362			0.147383
$656$			739.269i			1.12693i
$657$	−77.4634	+	344.964i	−0.117905	+	0.525059i
$658$	196.873			0.299199
$659$			390.420i			0.592443i	0.955119	+	0.296221i	$0.0957266\pi$
$659$			390.420i			0.592443i	−0.955119	+	0.296221i	$0.904273\pi$
$660$	463.559	+	579.197i	0.702362	+	0.877571i
$661$	−523.839			−0.792495			−0.396248	−	0.918144i	$-0.629688\pi$
$661$	−523.839			−0.792495			−0.396248	+	0.918144i	$0.629688\pi$
$662$		−	273.058i		−	0.412474i
$663$	1281.26	−	1025.45i	1.93252	−	1.54669i
$664$	−246.588			−0.371367
$665$			533.302i			0.801958i
$666$	−290.284	−	65.1847i	−0.435861	−	0.0978749i
$667$	28.2896			0.0424132
$668$		−	1201.68i		−	1.79892i
$669$	−750.513	−	937.734i	−1.12184	−	1.40169i
$670$	−342.801			−0.511644
$671$		−	81.3088i		−	0.121176i
$672$	−565.739	+	452.787i	−0.841873	+	0.673791i
$673$	313.476			0.465789			0.232894	−	0.972502i	$-0.425180\pi$
$673$	313.476			0.465789			0.232894	+	0.972502i	$0.425180\pi$
$674$		−	331.964i		−	0.492528i
$675$	207.859	−	101.451i	0.307939	−	0.150297i
$676$	1007.03			1.48969
$677$		−	417.075i		−	0.616064i	−0.951376	−	0.308032i	$-0.900330\pi$
$677$		−	417.075i		−	0.616064i	0.951376	−	0.308032i	$-0.0996704\pi$
$678$	35.1131	+	43.8723i	0.0517892	+	0.0647084i
$679$	402.508			0.592795
$680$		−	680.413i		−	1.00061i
$681$	−234.560	+	187.730i	−0.344435	+	0.275668i
$682$	−60.0330			−0.0880249
$683$		−	189.165i		−	0.276962i	−0.990365	−	0.138481i	$-0.955778\pi$
$683$		−	189.165i		−	0.276962i	0.990365	−	0.138481i	$-0.0442220\pi$
$684$	69.0269	−	307.394i	0.100917	−	0.449406i
$685$	−531.111			−0.775344
$686$		−	33.5362i		−	0.0488866i
$687$	368.975	+	461.018i	0.537081	+	0.671060i
$688$	−274.619			−0.399155
$689$			465.623i			0.675795i
$690$	42.2015	−	33.7759i	0.0611616	−	0.0489505i
$691$	140.199			0.202893			0.101446	−	0.994841i	$-0.467653\pi$
$691$	140.199			0.202893			0.101446	+	0.994841i	$0.467653\pi$
$692$			815.136i			1.17794i
$693$	−985.581	−	221.317i	−1.42220	−	0.319361i
$694$	−152.129			−0.219206
$695$		−	559.343i		−	0.804811i
$696$	45.7151	+	57.1190i	0.0656826	+	0.0820676i
$697$	1608.75			2.30811
$698$			240.140i			0.344040i
$699$	854.799	−	684.136i	1.22289	−	0.978736i
$700$	300.029			0.428613
$701$			927.437i			1.32302i	0.749936	+	0.661510i	$0.230084\pi$
$701$			927.437i			1.32302i	−0.749936	+	0.661510i	$0.769916\pi$
$702$	147.884	+	302.994i	0.210661	+	0.431616i
$703$	535.598			0.761875
$704$		−	383.242i		−	0.544378i
$705$	376.357	+	470.242i	0.533840	+	0.667010i
$706$	163.976			0.232261
$707$			613.565i			0.867842i
$708$	64.3499	−	51.5023i	0.0908897	−	0.0727433i
$709$	763.851			1.07736			0.538682	−	0.842509i	$-0.318923\pi$
$709$	763.851			1.07736			0.538682	+	0.842509i	$0.318923\pi$
$710$			471.885i			0.664626i
$711$	−17.0317	+	75.8462i	−0.0239545	+	0.106675i
$712$	−377.088			−0.529618
$713$		−	45.5499i		−	0.0638849i
$714$	276.192	+	345.091i	0.386824	+	0.483320i
$715$	1429.26			1.99896
$716$			81.7474i			0.114172i
$717$	303.082	−	242.571i	0.422708	−	0.338313i
$718$	−149.488			−0.208200
$719$		−	957.517i		−	1.33173i	−0.746070	−	0.665867i	$-0.768062\pi$
$719$		−	957.517i		−	1.33173i	0.746070	−	0.665867i	$-0.231938\pi$
$720$	−606.303	−	136.149i	−0.842088	−	0.189095i
$721$	−270.491			−0.375160
$722$			159.247i			0.220563i
$723$	−148.083	−	185.023i	−0.204817	−	0.255910i
$724$	523.513			0.723084
$725$		−	46.1320i		−	0.0636303i
$726$	−21.8789	+	17.5107i	−0.0301362	+	0.0241194i
$727$	192.761			0.265145			0.132573	−	0.991173i	$-0.457676\pi$
$727$	192.761			0.265145			0.132573	+	0.991173i	$0.457676\pi$
$728$			916.699i			1.25920i
$729$	448.500	−	574.708i	0.615226	−	0.788350i
$730$	134.737			0.184571
$731$			597.608i			0.817522i
$732$	47.5631	+	59.4280i	0.0649768	+	0.0811858i
$733$	211.579			0.288648			0.144324	−	0.989530i	$-0.453899\pi$
$733$	211.579			0.288648			0.144324	+	0.989530i	$0.453899\pi$
$734$		−	223.504i		−	0.304502i
$735$	−584.825	+	468.063i	−0.795681	+	0.636821i
$736$	−132.220			−0.179646
$737$			1168.90i			1.58603i
$738$	−72.4151	+	322.483i	−0.0981235	+	0.436968i
$739$	−929.012			−1.25712			−0.628560	−	0.777761i	$-0.716356\pi$
$739$	−929.012			−1.25712			−0.628560	+	0.777761i	$0.716356\pi$
$740$		−	1180.68i		−	1.59551i
$741$	−379.271	−	473.883i	−0.511837	−	0.639518i
$742$	−125.409			−0.169015
$743$			714.016i			0.960990i	0.876997	+	0.480495i	$0.159543\pi$
$743$			714.016i			0.960990i	−0.876997	+	0.480495i	$0.840457\pi$
$744$	91.9689	−	73.6071i	0.123614	−	0.0989342i
$745$	−1124.72			−1.50969
$746$		−	66.9316i		−	0.0897206i
$747$	478.162	+	107.374i	0.640110	+	0.143740i
$748$	−1106.91			−1.47982
$749$			197.536i			0.263733i
$750$	105.659	+	132.017i	0.140879	+	0.176023i
$751$	309.044			0.411510			0.205755	−	0.978603i	$-0.434035\pi$
$751$	309.044			0.411510			0.205755	+	0.978603i	$0.434035\pi$
$752$		−	412.971i		−	0.549164i
$753$	240.972	−	192.861i	0.320016	−	0.256124i
$754$	67.2462			0.0891860
$755$			303.999i			0.402647i
$756$	849.818	−	414.774i	1.12410	−	0.548643i
$757$	−349.474			−0.461656			−0.230828	−	0.972995i	$-0.574143\pi$
$757$	−349.474			−0.461656			−0.230828	+	0.972995i	$0.574143\pi$
$758$		−	240.235i		−	0.316933i
$759$	−115.171	−	143.901i	−0.151740	−	0.189593i
$760$	−251.656			−0.331126
$761$		−	1364.48i		−	1.79301i	−0.443035	−	0.896504i	$-0.646098\pi$
$761$		−	1364.48i		−	1.79301i	0.443035	−	0.896504i	$-0.353902\pi$
$762$	193.934	−	155.215i	0.254507	−	0.203694i
$763$	−512.750			−0.672019
$764$			132.361i			0.173247i
$765$	−296.278	+	1319.40i	−0.387292	+	1.72471i
$766$	−269.157			−0.351380
$767$		−	158.793i		−	0.207032i
$768$	112.459	+	140.513i	0.146431	+	0.182959i
$769$	−565.496			−0.735365			−0.367683	−	0.929951i	$-0.619849\pi$
$769$	−565.496			−0.735365			−0.367683	+	0.929951i	$0.619849\pi$
$770$			384.952i			0.499937i
$771$	−368.245	+	294.724i	−0.477621	+	0.382262i
$772$	−945.850			−1.22519
$773$		−	911.843i		−	1.17962i	−0.807544	−	0.589808i	$-0.799203\pi$
$773$		−	911.843i		−	1.17962i	0.807544	−	0.589808i	$-0.200797\pi$
$774$	−119.794	−	26.9003i	−0.154772	−	0.0347549i
$775$	−74.2784			−0.0958430
$776$			189.936i			0.244763i
$777$	1004.54	+	1255.13i	1.29285	+	1.61536i
$778$	−333.277			−0.428376
$779$		−	595.008i		−	0.763810i
$780$	−1044.63	+	836.071i	−1.33928	+	1.07189i
$781$	1609.06			2.06025
$782$			80.6516i			0.103135i
$783$	−63.7750	−	130.667i	−0.0814495	−	0.166879i
$784$	513.599			0.655101
$785$			843.790i			1.07489i
$786$	−18.4911	−	23.1038i	−0.0235255	−	0.0293942i
$787$	−57.4282			−0.0729710			−0.0364855	−	0.999334i	$-0.511616\pi$
$787$	−57.4282			−0.0729710			−0.0364855	+	0.999334i	$0.511616\pi$
$788$		−	437.669i		−	0.555417i
$789$	−954.207	+	763.697i	−1.20939	+	0.967930i
$790$	29.6243			0.0374991
$791$		−	303.645i		−	0.383875i
$792$	104.436	−	465.078i	0.131863	−	0.587220i
$793$	146.648			0.184928
$794$		−	286.746i		−	0.361141i
$795$	−239.742	−	299.547i	−0.301562	−	0.376789i
$796$	465.702			0.585053
$797$		−	574.353i		−	0.720644i	−0.932828	−	0.360322i	$-0.882667\pi$
$797$		−	574.353i		−	0.720644i	0.932828	−	0.360322i	$-0.117333\pi$
$798$	127.634	−	102.152i	0.159943	−	0.128010i
$799$	−898.684			−1.12476
$800$			215.611i			0.269513i
$801$	731.218	+	164.199i	0.912881	+	0.204992i
$802$	−162.516			−0.202638
$803$		−	459.434i		−	0.572147i
$804$	−683.771	−	854.343i	−0.850461	−	1.06262i
$805$	−292.081			−0.362834
$806$		−	108.275i		−	0.134336i
$807$	−279.588	+	223.767i	−0.346453	+	0.277283i
$808$	−289.530			−0.358329
$809$		−	516.585i		−	0.638548i	−0.947663	−	0.319274i	$-0.896561\pi$
$809$		−	516.585i		−	0.638548i	0.947663	−	0.319274i	$-0.103439\pi$
$810$	−251.144	−	118.781i	−0.310054	−	0.146643i
$811$	1219.71			1.50396			0.751981	−	0.659185i	$-0.229098\pi$
$811$	1219.71			1.50396			0.751981	+	0.659185i	$0.229098\pi$
$812$		−	188.608i		−	0.232276i
$813$	581.766	+	726.892i	0.715579	+	0.894086i
$814$	386.609			0.474950
$815$		−	987.277i		−	1.21138i
$816$	723.880	−	579.355i	0.887107	−	0.709994i
$817$	221.030			0.270538
$818$			81.3673i			0.0994710i
$819$	399.166	−	1777.59i	0.487383	−	2.17044i
$820$	−1311.64			−1.59957
$821$		−	760.688i		−	0.926539i	−0.886218	−	0.463269i	$-0.846676\pi$
$821$		−	760.688i		−	0.926539i	0.886218	−	0.463269i	$-0.153324\pi$
$822$	101.732	+	127.110i	0.123761	+	0.154635i
$823$	−809.343			−0.983406			−0.491703	−	0.870763i	$-0.663625\pi$
$823$	−809.343			−0.983406			−0.491703	+	0.870763i	$0.663625\pi$
$824$		−	127.640i		−	0.154902i
$825$	−234.660	+	187.809i	−0.284436	+	0.227647i
$826$	42.7689			0.0517783
$827$			240.652i			0.290995i	0.989359	+	0.145497i	$0.0464782\pi$
$827$			240.652i			0.290995i	−0.989359	+	0.145497i	$0.953522\pi$
$828$	168.355	+	37.8050i	0.203327	+	0.0456582i
$829$	−1477.23			−1.78194			−0.890970	−	0.454062i	$-0.849974\pi$
$829$	−1477.23			−1.78194			−0.890970	+	0.454062i	$0.849974\pi$
$830$		−	186.762i		−	0.225015i
$831$	−64.2975	−	80.3370i	−0.0773737	−	0.0966751i
$832$	691.212			0.830784
$833$		−	1117.66i		−	1.34173i
$834$	−133.867	+	107.140i	−0.160512	+	0.128465i
$835$	1907.67			2.28463
$836$			409.397i			0.489710i
$837$	−210.390	+	102.686i	−0.251362	+	0.122683i
$838$	369.565			0.441008
$839$			790.443i			0.942125i	0.882100	+	0.471062i	$0.156129\pi$
$839$			790.443i			0.942125i	−0.882100	+	0.471062i	$0.843871\pi$
$840$	−471.994	−	589.736i	−0.561897	−	0.702067i
$841$	−29.0000			−0.0344828
$842$		−	228.120i		−	0.270927i
$843$	−979.980	+	784.324i	−1.16249	+	0.930396i
$844$	−579.849			−0.687025
$845$			1598.67i			1.89192i
$846$	40.4527	−	180.146i	0.0478164	−	0.212938i
$847$	151.426			0.178780
$848$			263.065i			0.310218i
$849$	198.708	+	248.277i	0.234049	+	0.292434i
$850$	131.519			0.154728
$851$			293.339i			0.344699i
$852$	−1176.05	+	941.248i	−1.38034	+	1.10475i
$853$	143.410			0.168124			0.0840619	−	0.996461i	$-0.473211\pi$
$853$	143.410			0.168124			0.0840619	+	0.996461i	$0.473211\pi$
$854$			39.4977i			0.0462502i
$855$	487.989	+	109.581i	0.570748	+	0.128164i
$856$	−93.2136			−0.108894
$857$		−	1071.85i		−	1.25070i	−0.780346	−	0.625348i	$-0.784957\pi$
$857$		−	1071.85i		−	1.25070i	0.780346	−	0.625348i	$-0.215043\pi$
$858$	−273.768	−	342.062i	−0.319077	−	0.398673i
$859$	686.666			0.799379			0.399689	−	0.916651i	$-0.369118\pi$
$859$	686.666			0.799379			0.399689	+	0.916651i	$0.369118\pi$
$860$		−	487.241i		−	0.566559i
$861$	1394.36	−	1115.97i	1.61946	−	1.29613i
$862$	199.276			0.231179
$863$			1573.31i			1.82307i	0.411224	+	0.911535i	$0.365102\pi$
$863$			1573.31i			1.82307i	−0.411224	+	0.911535i	$0.634898\pi$
$864$	298.070	+	610.707i	0.344989	+	0.706837i
$865$	−1294.03			−1.49599
$866$			485.237i			0.560320i
$867$	−719.004	−	898.365i	−0.829301	−	1.03618i
$868$	−303.683			−0.349865
$869$		−	101.014i		−	0.116242i
$870$	−43.2612	+	34.6240i	−0.0497255	+	0.0397977i
$871$	−2108.22			−2.42046
$872$		−	241.958i		−	0.277474i
$873$	82.7055	−	368.308i	0.0947371	−	0.421888i
$874$	29.8295			0.0341299
$875$		−	913.705i		−	1.04423i
$876$	268.754	+	335.797i	0.306797	+	0.383330i
$877$	299.913			0.341976			0.170988	−	0.985273i	$-0.445304\pi$
$877$	299.913			0.341976			0.170988	+	0.985273i	$0.445304\pi$
$878$			102.568i			0.116820i
$879$	−103.976	+	83.2172i	−0.118289	+	0.0946726i
$880$	807.494			0.917607
$881$		−	271.490i		−	0.308161i	−0.988058	−	0.154081i	$-0.950758\pi$
$881$		−	271.490i		−	0.308161i	0.988058	−	0.154081i	$-0.0492416\pi$
$882$	224.041	+	50.3096i	0.254015	+	0.0570404i
$883$	1279.48			1.44901			0.724507	−	0.689267i	$-0.242067\pi$
$883$	1279.48			1.44901			0.724507	+	0.689267i	$0.242067\pi$
$884$		−	1996.41i		−	2.25838i
$885$	81.7601	+	102.156i	0.0923843	+	0.115430i
$886$	102.024			0.115151
$887$			920.613i			1.03790i	0.854806	+	0.518948i	$0.173676\pi$
$887$			920.613i			1.03790i	−0.854806	+	0.518948i	$0.826324\pi$
$888$	−592.275	+	474.026i	−0.666977	+	0.533813i
$889$	−1342.24			−1.50983
$890$		−	285.601i		−	0.320901i
$891$	−405.026	+	856.365i	−0.454574	+	0.961128i
$892$	−1461.14			−1.63805
$893$			332.384i			0.372211i
$894$	215.435	+	269.176i	0.240978	+	0.301092i
$895$	−129.774			−0.144999
$896$			1152.33i			1.28608i
$897$	259.539	−	207.721i	0.289341	−	0.231573i
$898$	41.8770			0.0466336
$899$			46.6937i			0.0519396i
$900$	61.6487	−	274.537i	0.0684985	−	0.305041i
$901$	572.467			0.635368
$902$		−	429.493i		−	0.476156i
$903$	414.553	+	517.966i	0.459084	+	0.573606i
$904$	143.285			0.158501
$905$			831.079i			0.918319i
$906$	72.7554	−	58.2296i	0.0803040	−	0.0642711i
$907$	481.775			0.531174			0.265587	−	0.964087i	$-0.414434\pi$
$907$	481.775			0.531174			0.265587	+	0.964087i	$0.414434\pi$
$908$			365.482i			0.402514i
$909$	561.432	+	126.073i	0.617637	+	0.138694i
$910$	−694.296			−0.762963
$911$		−	1331.08i		−	1.46112i	−0.682848	−	0.730560i	$-0.739259\pi$
$911$		−	1331.08i		−	1.46112i	0.682848	−	0.730560i	$-0.260741\pi$
$912$	−214.278	−	267.732i	−0.234954	−	0.293566i
$913$	−636.832			−0.697516
$914$			27.6977i			0.0303038i
$915$	−94.3423	+	75.5066i	−0.103106	+	0.0825209i
$916$	718.340			0.784214
$917$			159.904i			0.174378i
$918$	372.520	−	181.818i	0.405796	−	0.198058i
$919$	599.380			0.652209			0.326105	−	0.945334i	$-0.394264\pi$
$919$	599.380			0.652209			0.326105	+	0.945334i	$0.394264\pi$
$920$		−	137.828i		−	0.149813i
$921$	−31.2771	−	39.0794i	−0.0339600	−	0.0424315i
$922$	−345.096			−0.374291
$923$			2902.08i			3.14419i
$924$	−959.392	+	767.847i	−1.03830	+	0.831003i
$925$	478.349			0.517134
$926$		−	520.738i		−	0.562352i
$927$	−55.5792	+	247.508i	−0.0599560	+	0.266999i
$928$	135.540			0.146056
$929$		−	470.013i		−	0.505934i	−0.967475	−	0.252967i	$-0.918594\pi$
$929$		−	470.013i		−	0.505934i	0.967475	−	0.252967i	$-0.0814064\pi$
$930$	55.7490	+	69.6561i	0.0599452	+	0.0748990i
$931$	−413.376			−0.444012
$932$		−	1331.91i		−	1.42909i
$933$	−633.948	+	507.379i	−0.679473	+	0.543814i
$934$	7.33250			0.00785064
$935$		−	1757.22i		−	1.87938i
$936$	838.811	+	188.359i	0.896165	+	0.201239i
$937$	1645.52			1.75615			0.878077	−	0.478520i	$-0.158826\pi$
$937$	1645.52			1.75615			0.878077	+	0.478520i	$0.158826\pi$
$938$		−	567.822i		−	0.605354i
$939$	−199.071	−	248.731i	−0.212003	−	0.264889i
$940$	732.713			0.779482
$941$			1059.13i			1.12554i	0.826614	+	0.562769i	$0.190264\pi$
$941$			1059.13i			1.12554i	−0.826614	+	0.562769i	$0.809736\pi$
$942$	201.943	−	161.624i	0.214376	−	0.171576i
$943$	325.877			0.345575
$944$		−	89.7142i		−	0.0950363i
$945$	658.457	+	1349.09i	0.696780	+	1.42761i
$946$	159.545			0.168652
$947$		−	965.803i		−	1.01985i	−0.860217	−	0.509927i	$-0.829672\pi$
$947$		−	965.803i		−	1.01985i	0.860217	−	0.509927i	$-0.170328\pi$
$948$	59.0902	+	73.8308i	0.0623315	+	0.0778806i
$949$	828.632			0.873163
$950$		−	48.6431i		−	0.0512033i
$951$	−292.815	+	234.354i	−0.307902	+	0.246429i
$952$	1127.05			1.18387
$953$		−	1825.37i		−	1.91539i	−0.287778	−	0.957697i	$-0.592916\pi$
$953$		−	1825.37i		−	1.91539i	0.287778	−	0.957697i	$-0.407084\pi$
$954$	−25.7686	+	114.754i	−0.0270111	+	0.120287i
$955$	−210.123			−0.220024
$956$		−	472.250i		−	0.493985i
$957$	118.063	+	147.514i	0.123368	+	0.154143i
$958$	−58.4994			−0.0610641
$959$		−	879.741i		−	0.917353i
$960$	−444.674	+	355.894i	−0.463203	+	0.370723i
$961$	−885.817			−0.921766
$962$			697.286i			0.724829i
$963$	180.752	+	40.5888i	0.187697	+	0.0421483i
$964$	−288.296			−0.299062
$965$		−	1501.54i		−	1.55600i
$966$	55.9469	+	69.9033i	0.0579161	+	0.0723637i
$967$	338.117			0.349655			0.174828	−	0.984599i	$-0.444063\pi$
$967$	338.117			0.349655			0.174828	+	0.984599i	$0.444063\pi$
$968$			71.4554i			0.0738175i
$969$	−582.622	+	466.300i	−0.601261	+	0.481218i
$970$	−143.855			−0.148304
$971$		−	535.373i		−	0.551363i	−0.961249	−	0.275681i	$-0.911097\pi$
$971$		−	535.373i		−	0.551363i	0.961249	−	0.275681i	$-0.0889035\pi$
$972$	−204.916	−	862.839i	−0.210819	−	0.887694i
$973$	926.506			0.952216
$974$			220.646i			0.226536i
$975$	−338.731	−	423.230i	−0.347417	−	0.434082i
$976$	82.8523			0.0848896
$977$			1076.35i			1.10169i	0.834608	+	0.550844i	$0.185694\pi$
$977$			1076.35i			1.10169i	−0.834608	+	0.550844i	$0.814306\pi$
$978$	−236.283	+	189.109i	−0.241598	+	0.193363i
$979$	−973.859			−0.994749
$980$			911.251i			0.929848i
$981$	−105.358	+	469.184i	−0.107398	+	0.478271i
$982$	−99.7800			−0.101609
$983$			1369.52i			1.39320i	0.717459	+	0.696601i	$0.245305\pi$
$983$			1369.52i			1.39320i	−0.717459	+	0.696601i	$0.754695\pi$
$984$	526.606	+	657.972i	0.535169	+	0.668671i
$985$	694.801			0.705382
$986$		−	82.6768i		−	0.0838507i
$987$	−778.918	+	623.405i	−0.789177	+	0.631616i
$988$	−738.386			−0.747354
$989$			121.055i			0.122401i
$990$	352.244	+	79.0982i	0.355802	+	0.0798972i
$991$	−1341.80			−1.35399			−0.676994	−	0.735989i	$-0.736718\pi$
$991$	−1341.80			−1.35399			−0.676994	+	0.735989i	$0.736718\pi$
$992$		−	218.236i		−	0.219996i
$993$	864.645	+	1080.34i	0.870741	+	1.08795i
$994$	−781.638			−0.786356
$995$			739.305i			0.743020i
$996$	465.456	−	372.527i	0.467326	−	0.374023i
$997$	316.615			0.317567			0.158784	−	0.987313i	$-0.449243\pi$
$997$	316.615			0.317567			0.158784	+	0.987313i	$0.449243\pi$
$998$			38.0191i			0.0380953i
$999$	1354.90	−	661.292i	1.35626	−	0.661954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.3.b.a.59.8	✓	18
3.2	odd	2	inner	87.3.b.a.59.11	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.3.b.a.59.8	✓	18	1.1	even	1	trivial
87.3.b.a.59.11	yes	18	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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	87.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.591999i q^{2} +(1.87458 + 2.34221i) q^{3} +3.64954 q^{4} +5.79366i q^{5} +(1.38659 - 1.10975i) q^{6} -9.59672 q^{7} -4.52852i q^{8} +(-1.97189 + 8.78132i) q^{9} +O(q^{10})\)	\(q-0.591999i q^{2} +(1.87458 + 2.34221i) q^{3} +3.64954 q^{4} +5.79366i q^{5} +(1.38659 - 1.10975i) q^{6} -9.59672 q^{7} -4.52852i q^{8} +(-1.97189 + 8.78132i) q^{9} +3.42984 q^{10} -11.6953i q^{11} +(6.84135 + 8.54798i) q^{12} +21.0935 q^{13} +5.68125i q^{14} +(-13.5700 + 10.8607i) q^{15} +11.9173 q^{16} -25.9337i q^{17} +(5.19853 + 1.16736i) q^{18} -9.59174 q^{19} +21.1442i q^{20} +(-17.9898 - 22.4775i) q^{21} -6.92358 q^{22} -5.25325i q^{23} +(10.6067 - 8.48907i) q^{24} -8.56649 q^{25} -12.4873i q^{26} +(-24.2642 + 11.8427i) q^{27} -35.0236 q^{28} +5.38516i q^{29} +(6.42951 + 8.03340i) q^{30} +8.67080 q^{31} -25.1691i q^{32} +(27.3927 - 21.9237i) q^{33} -15.3527 q^{34} -55.6001i q^{35} +(-7.19649 + 32.0478i) q^{36} -55.8395 q^{37} +5.67830i q^{38} +(39.5414 + 49.4053i) q^{39} +26.2367 q^{40} +62.0334i q^{41} +(-13.3067 + 10.6500i) q^{42} -23.0437 q^{43} -42.6823i q^{44} +(-50.8760 - 11.4245i) q^{45} -3.10992 q^{46} -34.6532i q^{47} +(22.3399 + 27.9128i) q^{48} +43.0970 q^{49} +5.07135i q^{50} +(60.7421 - 48.6147i) q^{51} +76.9814 q^{52} +22.0743i q^{53} +(7.01088 + 14.3644i) q^{54} +67.7583 q^{55} +43.4589i q^{56} +(-17.9805 - 22.4659i) q^{57} +3.18801 q^{58} -7.52808i q^{59} +(-49.5241 + 39.6365i) q^{60} +6.95229 q^{61} -5.13311i q^{62} +(18.9237 - 84.2719i) q^{63} +32.7690 q^{64} +122.208i q^{65} +(-12.9788 - 16.2165i) q^{66} -99.9467 q^{67} -94.6459i q^{68} +(12.3042 - 9.84765i) q^{69} -32.9152 q^{70} +137.582i q^{71} +(39.7664 + 8.92975i) q^{72} +39.2838 q^{73} +33.0569i q^{74} +(-16.0586 - 20.0645i) q^{75} -35.0054 q^{76} +112.236i q^{77} +(29.2479 - 23.4085i) q^{78} +8.63722 q^{79} +69.0446i q^{80} +(-73.2233 - 34.6316i) q^{81} +36.7237 q^{82} -54.4522i q^{83} +(-65.6546 - 82.0326i) q^{84} +150.251 q^{85} +13.6419i q^{86} +(-12.6132 + 10.0949i) q^{87} -52.9622 q^{88} -83.2696i q^{89} +(-6.76327 + 30.1185i) q^{90} -202.428 q^{91} -19.1719i q^{92} +(16.2541 + 20.3088i) q^{93} -20.5146 q^{94} -55.5713i q^{95} +(58.9513 - 47.1815i) q^{96} -41.9422 q^{97} -25.5134i q^{98} +(102.700 + 23.0618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

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