LMFDB - Embedded newform 69.3.b.a.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,3,Mod(47,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, 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("69.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	69.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:	$1.88011382409$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 40x^{12} + 598x^{10} + 4207x^{8} + 14465x^{6} + 23786x^{4} + 17144x^{2} + 3887 $ x^14 + 40x^12 + 598x^10 + 4207x^8 + 14465x^6 + 23786x^4 + 17144x^2 + 3887
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.12
Root			$2.92693i$ of defining polynomial
Character	$\chi$	$=$	69.47
Dual form			69.3.b.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.92693i q^{2} +(2.91955 - 0.690107i) q^{3} -4.56694 q^{4} +2.77451i q^{5} +(2.01990 + 8.54532i) q^{6} -1.17249 q^{7} -1.65938i q^{8} +(8.04750 - 4.02960i) q^{9} +O(q^{10})$	\(q+2.92693i q^{2} +(2.91955 - 0.690107i) q^{3} -4.56694 q^{4} +2.77451i q^{5} +(2.01990 + 8.54532i) q^{6} -1.17249 q^{7} -1.65938i q^{8} +(8.04750 - 4.02960i) q^{9} -8.12081 q^{10} -8.93439i q^{11} +(-13.3334 + 3.15167i) q^{12} -10.2977 q^{13} -3.43179i q^{14} +(1.91471 + 8.10032i) q^{15} -13.4108 q^{16} -21.1076i q^{17} +(11.7944 + 23.5545i) q^{18} +27.2193 q^{19} -12.6710i q^{20} +(-3.42313 + 0.809141i) q^{21} +26.1504 q^{22} +4.79583i q^{23} +(-1.14515 - 4.84464i) q^{24} +17.3021 q^{25} -30.1405i q^{26} +(20.7142 - 17.3182i) q^{27} +5.35467 q^{28} +9.80746i q^{29} +(-23.7091 + 5.60423i) q^{30} -32.5049 q^{31} -45.8902i q^{32} +(-6.16568 - 26.0844i) q^{33} +61.7805 q^{34} -3.25308i q^{35} +(-36.7524 + 18.4029i) q^{36} -46.6160 q^{37} +79.6691i q^{38} +(-30.0645 + 7.10648i) q^{39} +4.60397 q^{40} +59.6097i q^{41} +(-2.36830 - 10.0193i) q^{42} -10.3738 q^{43} +40.8028i q^{44} +(11.1802 + 22.3279i) q^{45} -14.0371 q^{46} -21.5378i q^{47} +(-39.1536 + 9.25492i) q^{48} -47.6253 q^{49} +50.6420i q^{50} +(-14.5665 - 61.6246i) q^{51} +47.0287 q^{52} -75.1021i q^{53} +(50.6893 + 60.6291i) q^{54} +24.7886 q^{55} +1.94560i q^{56} +(79.4681 - 18.7842i) q^{57} -28.7058 q^{58} +65.9384i q^{59} +(-8.74436 - 36.9936i) q^{60} +29.5679 q^{61} -95.1398i q^{62} +(-9.43559 + 4.72465i) q^{63} +80.6740 q^{64} -28.5710i q^{65} +(76.3472 - 18.0465i) q^{66} -38.5701 q^{67} +96.3969i q^{68} +(3.30964 + 14.0017i) q^{69} +9.52154 q^{70} +138.781i q^{71} +(-6.68664 - 13.3539i) q^{72} -73.4107 q^{73} -136.442i q^{74} +(50.5142 - 11.9403i) q^{75} -124.309 q^{76} +10.4754i q^{77} +(-20.8002 - 87.9967i) q^{78} +28.2291 q^{79} -37.2085i q^{80} +(48.5247 - 64.8564i) q^{81} -174.474 q^{82} +119.305i q^{83} +(15.6332 - 3.69529i) q^{84} +58.5632 q^{85} -30.3635i q^{86} +(6.76820 + 28.6333i) q^{87} -14.8256 q^{88} -115.770i q^{89} +(-65.3523 + 32.7236i) q^{90} +12.0739 q^{91} -21.9023i q^{92} +(-94.8997 + 22.4319i) q^{93} +63.0397 q^{94} +75.5203i q^{95} +(-31.6691 - 133.978i) q^{96} +116.859 q^{97} -139.396i q^{98} +(-36.0020 - 71.8995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} - 24 q^{4} + 11 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 14 * q - 4 * q^3 - 24 * q^4 + 11 * q^6 - 4 * q^7 - 8 * q^9	$ 14 q - 4 q^{3} - 24 q^{4} + 11 q^{6} - 4 q^{7} - 8 q^{9} - 8 q^{10} + 19 q^{12} - 14 q^{15} + 72 q^{16} - 31 q^{18} + 8 q^{19} - 2 q^{21} - 84 q^{22} - 44 q^{24} + 38 q^{25} + 62 q^{27} + 76 q^{28} + 62 q^{30} - 144 q^{31} + 90 q^{33} - 68 q^{34} + 3 q^{36} + 48 q^{37} - 78 q^{39} + 120 q^{40} - 76 q^{42} - 48 q^{43} - 18 q^{45} - 317 q^{48} - 30 q^{49} + 18 q^{51} - 6 q^{52} + 312 q^{54} + 232 q^{55} + 76 q^{57} + 66 q^{58} - 36 q^{60} - 140 q^{61} - 206 q^{63} - 346 q^{64} + 398 q^{66} + 204 q^{67} + 80 q^{70} + 384 q^{72} - 224 q^{73} - 80 q^{75} + 100 q^{76} - 341 q^{78} - 344 q^{79} - 232 q^{81} - 62 q^{82} - 330 q^{84} + 480 q^{85} + 86 q^{87} + 436 q^{88} - 514 q^{90} - 172 q^{91} + 62 q^{93} + 514 q^{94} + 609 q^{96} - 24 q^{97} + 234 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 - 24 * q^4 + 11 * q^6 - 4 * q^7 - 8 * q^9 - 8 * q^10 + 19 * q^12 - 14 * q^15 + 72 * q^16 - 31 * q^18 + 8 * q^19 - 2 * q^21 - 84 * q^22 - 44 * q^24 + 38 * q^25 + 62 * q^27 + 76 * q^28 + 62 * q^30 - 144 * q^31 + 90 * q^33 - 68 * q^34 + 3 * q^36 + 48 * q^37 - 78 * q^39 + 120 * q^40 - 76 * q^42 - 48 * q^43 - 18 * q^45 - 317 * q^48 - 30 * q^49 + 18 * q^51 - 6 * q^52 + 312 * q^54 + 232 * q^55 + 76 * q^57 + 66 * q^58 - 36 * q^60 - 140 * q^61 - 206 * q^63 - 346 * q^64 + 398 * q^66 + 204 * q^67 + 80 * q^70 + 384 * q^72 - 224 * q^73 - 80 * q^75 + 100 * q^76 - 341 * q^78 - 344 * q^79 - 232 * q^81 - 62 * q^82 - 330 * q^84 + 480 * q^85 + 86 * q^87 + 436 * q^88 - 514 * q^90 - 172 * q^91 + 62 * q^93 + 514 * q^94 + 609 * q^96 - 24 * q^97 + 234 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.92693i			1.46347i	0.681591	+	0.731733i	$0.261288\pi$
$2$			2.92693i			1.46347i	−0.681591	+	0.731733i	$0.738712\pi$
$3$	2.91955	−	0.690107i	0.973182	−	0.230036i
$3$	2.91955	−	0.690107i	0.973182	−	0.230036i
$4$	−4.56694			−1.14173
$5$			2.77451i			0.554902i	0.960740	+	0.277451i	$0.0894897\pi$
$5$			2.77451i			0.554902i	−0.960740	+	0.277451i	$0.910510\pi$
$6$	2.01990	+	8.54532i	0.336649	+	1.42422i
$7$	−1.17249			−0.167498			−0.0837490	−	0.996487i	$-0.526689\pi$
$7$	−1.17249			−0.167498			−0.0837490	+	0.996487i	$0.526689\pi$
$8$		−	1.65938i		−	0.207423i
$9$	8.04750	−	4.02960i	0.894167	−	0.447733i
$10$	−8.12081			−0.812081
$11$		−	8.93439i		−	0.812217i	−0.913825	−	0.406109i	$-0.866885\pi$
$11$		−	8.93439i		−	0.812217i	0.913825	−	0.406109i	$-0.133115\pi$
$12$	−13.3334	+	3.15167i	−1.11112	+	0.262639i
$13$	−10.2977			−0.792127			−0.396064	−	0.918223i	$-0.629624\pi$
$13$	−10.2977			−0.792127			−0.396064	+	0.918223i	$0.629624\pi$
$14$		−	3.43179i		−	0.245128i
$15$	1.91471	+	8.10032i	0.127647	+	0.540021i
$16$	−13.4108			−0.838178
$17$		−	21.1076i		−	1.24162i	−0.783960	−	0.620811i	$-0.786803\pi$
$17$		−	21.1076i		−	1.24162i	0.783960	−	0.620811i	$-0.213197\pi$
$18$	11.7944	+	23.5545i	0.655242	+	1.30858i
$19$	27.2193			1.43260			0.716298	−	0.697795i	$-0.245835\pi$
$19$	27.2193			1.43260			0.716298	+	0.697795i	$0.245835\pi$
$20$		−	12.6710i		−	0.633551i
$21$	−3.42313	+	0.809141i	−0.163006	+	0.0385305i
$22$	26.1504			1.18865
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−1.14515	−	4.84464i	−0.0477146	−	0.201860i
$25$	17.3021			0.692083
$26$		−	30.1405i		−	1.15925i
$27$	20.7142	−	17.3182i	0.767193	−	0.641416i
$28$	5.35467			0.191238
$29$			9.80746i			0.338188i	0.985600	+	0.169094i	$0.0540842\pi$
$29$			9.80746i			0.338188i	−0.985600	+	0.169094i	$0.945916\pi$
$30$	−23.7091	+	5.60423i	−0.790303	+	0.186808i
$31$	−32.5049			−1.04855			−0.524273	−	0.851550i	$-0.675663\pi$
$31$	−32.5049			−1.04855			−0.524273	+	0.851550i	$0.675663\pi$
$32$		−	45.8902i		−	1.43407i
$33$	−6.16568	−	26.0844i	−0.186839	−	0.790435i
$34$	61.7805			1.81707
$35$		−	3.25308i		−	0.0929450i
$36$	−36.7524	+	18.4029i	−1.02090	+	0.511192i
$37$	−46.6160			−1.25989			−0.629946	−	0.776639i	$-0.716923\pi$
$37$	−46.6160			−1.25989			−0.629946	+	0.776639i	$0.716923\pi$
$38$			79.6691i			2.09656i
$39$	−30.0645	+	7.10648i	−0.770884	+	0.182218i
$40$	4.60397			0.115099
$41$			59.6097i			1.45389i	0.686693	+	0.726947i	$0.259062\pi$
$41$			59.6097i			1.45389i	−0.686693	+	0.726947i	$0.740938\pi$
$42$	−2.36830	−	10.0193i	−0.0563881	−	0.238554i
$43$	−10.3738			−0.241252			−0.120626	−	0.992698i	$-0.538490\pi$
$43$	−10.3738			−0.241252			−0.120626	+	0.992698i	$0.538490\pi$
$44$			40.8028i			0.927336i
$45$	11.1802	+	22.3279i	0.248448	+	0.496176i
$46$	−14.0371			−0.305154
$47$		−	21.5378i		−	0.458251i	−0.973397	−	0.229126i	$-0.926413\pi$
$47$		−	21.5378i		−	0.458251i	0.973397	−	0.229126i	$-0.0735866\pi$
$48$	−39.1536	+	9.25492i	−0.815700	+	0.192811i
$49$	−47.6253			−0.971944
$50$			50.6420i			1.01284i
$51$	−14.5665	−	61.6246i	−0.285617	−	1.20832i
$52$	47.0287			0.904399
$53$		−	75.1021i		−	1.41702i	−0.705701	−	0.708510i	$-0.749368\pi$
$53$		−	75.1021i		−	1.41702i	0.705701	−	0.708510i	$-0.250632\pi$
$54$	50.6893	+	60.6291i	0.938691	+	1.12276i
$55$	24.7886			0.450701
$56$			1.94560i			0.0347429i
$57$	79.4681	−	18.7842i	1.39418	−	0.329548i
$58$	−28.7058			−0.494927
$59$			65.9384i			1.11760i	0.829303	+	0.558800i	$0.188738\pi$
$59$			65.9384i			1.11760i	−0.829303	+	0.558800i	$0.811262\pi$
$60$	−8.74436	−	36.9936i	−0.145739	−	0.616560i
$61$	29.5679			0.484720			0.242360	−	0.970186i	$-0.422078\pi$
$61$	29.5679			0.484720			0.242360	+	0.970186i	$0.422078\pi$
$62$		−	95.1398i		−	1.53451i
$63$	−9.43559	+	4.72465i	−0.149771	+	0.0749944i
$64$	80.6740			1.26053
$65$		−	28.5710i		−	0.439553i
$66$	76.3472	−	18.0465i	1.15678	−	0.273432i
$67$	−38.5701			−0.575673			−0.287837	−	0.957680i	$-0.592936\pi$
$67$	−38.5701			−0.575673			−0.287837	+	0.957680i	$0.592936\pi$
$68$			96.3969i			1.41760i
$69$	3.30964	+	14.0017i	0.0479657	+	0.202923i
$70$	9.52154			0.136022
$71$			138.781i			1.95466i	0.211729	+	0.977328i	$0.432091\pi$
$71$			138.781i			1.95466i	−0.211729	+	0.977328i	$0.567909\pi$
$72$	−6.68664	−	13.3539i	−0.0928700	−	0.185471i
$73$	−73.4107			−1.00563			−0.502813	−	0.864395i	$-0.667702\pi$
$73$	−73.4107			−1.00563			−0.502813	+	0.864395i	$0.667702\pi$
$74$		−	136.442i		−	1.84381i
$75$	50.5142	−	11.9403i	0.673523	−	0.159204i
$76$	−124.309			−1.63564
$77$			10.4754i			0.136045i
$78$	−20.8002	−	87.9967i	−0.266669	−	1.12816i
$79$	28.2291			0.357330			0.178665	−	0.983910i	$-0.442822\pi$
$79$	28.2291			0.357330			0.178665	+	0.983910i	$0.442822\pi$
$80$		−	37.2085i		−	0.465107i
$81$	48.5247	−	64.8564i	0.599070	−	0.800697i
$82$	−174.474			−2.12773
$83$			119.305i			1.43741i	0.695313	+	0.718707i	$0.255266\pi$
$83$			119.305i			1.43741i	−0.695313	+	0.718707i	$0.744734\pi$
$84$	15.6332	−	3.69529i	0.186110	−	0.0439916i
$85$	58.5632			0.688979
$86$		−	30.3635i		−	0.353064i
$87$	6.76820	+	28.6333i	0.0777954	+	0.329119i
$88$	−14.8256			−0.168472
$89$		−	115.770i		−	1.30079i	−0.759596	−	0.650395i	$-0.774603\pi$
$89$		−	115.770i		−	1.30079i	0.759596	−	0.650395i	$-0.225397\pi$
$90$	−65.3523	+	32.7236i	−0.726136	+	0.363596i
$91$	12.0739			0.132680
$92$		−	21.9023i		−	0.238068i
$93$	−94.8997	+	22.4319i	−1.02043	+	0.241203i
$94$	63.0397			0.670635
$95$			75.5203i			0.794951i
$96$	−31.6691	−	133.978i	−0.329887	−	1.39561i
$97$	116.859			1.20473			0.602365	−	0.798221i	$-0.294225\pi$
$97$	116.859			1.20473			0.602365	+	0.798221i	$0.294225\pi$
$98$		−	139.396i		−	1.42241i
$99$	−36.0020	−	71.8995i	−0.363657	−	0.726258i
$100$	−79.0175			−0.790175
$101$		−	13.7513i		−	0.136151i	−0.997680	−	0.0680755i	$-0.978314\pi$
$101$		−	13.7513i		−	0.136151i	0.997680	−	0.0680755i	$-0.0216859\pi$
$102$	180.371	−	42.6351i	1.76834	−	0.417991i
$103$	−114.628			−1.11290			−0.556448	−	0.830882i	$-0.687836\pi$
$103$	−114.628			−1.11290			−0.556448	+	0.830882i	$0.687836\pi$
$104$			17.0877i			0.164305i
$105$	−2.24497	−	9.49751i	−0.0213807	−	0.0904525i
$106$	219.819			2.07376
$107$			141.394i			1.32144i	0.750633	+	0.660720i	$0.229749\pi$
$107$			141.394i			1.32144i	−0.750633	+	0.660720i	$0.770251\pi$
$108$	−94.6005	+	79.0913i	−0.875930	+	0.732327i
$109$	203.451			1.86653			0.933263	−	0.359193i	$-0.116948\pi$
$109$	203.451			1.86653			0.933263	+	0.359193i	$0.116948\pi$
$110$			72.5545i			0.659586i
$111$	−136.098	+	32.1700i	−1.22610	+	0.289820i
$112$	15.7240			0.140393
$113$		−	23.1483i		−	0.204852i	−0.994741	−	0.102426i	$-0.967339\pi$
$113$		−	23.1483i		−	0.204852i	0.994741	−	0.102426i	$-0.0326605\pi$
$114$	54.9802	+	232.598i	0.482282	+	2.04033i
$115$	−13.3061			−0.115705
$116$		−	44.7900i		−	0.386121i
$117$	−82.8704	+	41.4954i	−0.708294	+	0.354662i
$118$	−192.997			−1.63557
$119$			24.7483i			0.207969i
$120$	13.4415	−	3.17723i	0.112013	−	0.0264769i
$121$	41.1767			0.340303
$122$			86.5434i			0.709372i
$123$	41.1371	+	174.033i	0.334448	+	1.41490i
$124$	148.448			1.19716
$125$			117.368i			0.938941i
$126$	−13.8287	−	27.6173i	−0.109752	−	0.219185i
$127$	94.6210			0.745048			0.372524	−	0.928023i	$-0.378493\pi$
$127$	94.6210			0.745048			0.372524	+	0.928023i	$0.378493\pi$
$128$			52.5668i			0.410678i
$129$	−30.2869	+	7.15906i	−0.234782	+	0.0554966i
$130$	83.6253			0.643272
$131$		−	117.953i		−	0.900407i	−0.892926	−	0.450203i	$-0.851351\pi$
$131$		−	117.953i		−	0.900407i	0.892926	−	0.450203i	$-0.148649\pi$
$132$	28.1583	+	119.126i	0.213320	+	0.902467i
$133$	−31.9143			−0.239957
$134$		−	112.892i		−	0.842478i
$135$	48.0497	+	57.4718i	0.355923	+	0.425717i
$136$	−35.0255			−0.257541
$137$		−	219.574i		−	1.60273i	−0.598176	−	0.801365i	$-0.704108\pi$
$137$		−	219.574i		−	1.60273i	0.598176	−	0.801365i	$-0.295892\pi$
$138$	−40.9819	+	9.68708i	−0.296970	+	0.0701963i
$139$	−35.1952			−0.253203			−0.126601	−	0.991954i	$-0.540407\pi$
$139$	−35.1952			−0.253203			−0.126601	+	0.991954i	$0.540407\pi$
$140$			14.8566i			0.106118i
$141$	−14.8634	−	62.8806i	−0.105414	−	0.445962i
$142$	−406.202			−2.86057
$143$			92.0032i			0.643379i
$144$	−107.924	+	54.0403i	−0.749471	+	0.375280i
$145$	−27.2109			−0.187661
$146$		−	214.868i		−	1.47170i
$147$	−139.044	+	32.8665i	−0.945879	+	0.223582i
$148$	212.892			1.43846
$149$		−	90.8018i		−	0.609408i	−0.952447	−	0.304704i	$-0.901442\pi$
$149$		−	90.8018i		−	0.609408i	0.952447	−	0.304704i	$-0.0985575\pi$
$150$	34.9484	+	147.852i	0.232989	+	0.985679i
$151$	46.4008			0.307290			0.153645	−	0.988126i	$-0.450899\pi$
$151$	46.4008			0.307290			0.153645	+	0.988126i	$0.450899\pi$
$152$		−	45.1672i		−	0.297153i
$153$	−85.0551	−	169.863i	−0.555916	−	1.11022i
$154$	−30.6609			−0.199097
$155$		−	90.1853i		−	0.581841i
$156$	137.303	−	32.4548i	0.880145	−	0.208044i
$157$	−142.055			−0.904807			−0.452404	−	0.891813i	$-0.649433\pi$
$157$	−142.055			−0.904807			−0.452404	+	0.891813i	$0.649433\pi$
$158$			82.6245i			0.522940i
$159$	−51.8285	−	219.264i	−0.325965	−	1.37902i
$160$	127.323			0.795768
$161$		−	5.62305i		−	0.0349257i
$162$	189.830	+	142.028i	1.17179	+	0.876719i
$163$	98.8470			0.606423			0.303212	−	0.952923i	$-0.401941\pi$
$163$	98.8470			0.606423			0.303212	+	0.952923i	$0.401941\pi$
$164$		−	272.234i		−	1.65996i
$165$	72.3714	−	17.1068i	0.438614	−	0.103677i
$166$	−349.199			−2.10361
$167$			71.8770i			0.430401i	0.976570	+	0.215201i	$0.0690405\pi$
$167$			71.8770i			0.430401i	−0.976570	+	0.215201i	$0.930959\pi$
$168$	1.34267	+	5.68027i	0.00799210	+	0.0338111i
$169$	−62.9583			−0.372534
$170$			171.411i			1.00830i
$171$	219.048	−	109.683i	1.28098	−	0.641421i
$172$	47.3766			0.275446
$173$			32.7607i			0.189368i	0.995507	+	0.0946840i	$0.0301841\pi$
$173$			32.7607i			0.189368i	−0.995507	+	0.0946840i	$0.969816\pi$
$174$	−83.8079	+	19.8101i	−0.481654	+	0.113851i
$175$	−20.2865			−0.115923
$176$			119.818i			0.680782i
$177$	45.5045	+	192.510i	0.257088	+	1.08763i
$178$	338.852			1.90366
$179$		−	67.8265i		−	0.378919i	−0.981889	−	0.189460i	$-0.939326\pi$
$179$		−	67.8265i		−	0.378919i	0.981889	−	0.189460i	$-0.0606736\pi$
$180$	−51.0591	−	101.970i	−0.283662	−	0.566500i
$181$	−22.7148			−0.125496			−0.0627480	−	0.998029i	$-0.519986\pi$
$181$	−22.7148			−0.125496			−0.0627480	+	0.998029i	$0.519986\pi$
$182$			35.3394i			0.194172i
$183$	86.3250	−	20.4050i	0.471721	−	0.111503i
$184$	7.95811			0.0432506
$185$		−	129.337i		−	0.699117i
$186$	−65.6566	−	277.765i	−0.352992	−	1.49336i
$187$	−188.583			−1.00847
$188$			98.3617i			0.523201i
$189$	−24.2871	+	20.3054i	−0.128503	+	0.107436i
$190$	−221.043			−1.16338
$191$			26.2942i			0.137666i	0.997628	+	0.0688330i	$0.0219276\pi$
$191$			26.2942i			0.137666i	−0.997628	+	0.0688330i	$0.978072\pi$
$192$	235.532	−	55.6737i	1.22673	−	0.289967i
$193$	128.881			0.667776			0.333888	−	0.942613i	$-0.391639\pi$
$193$	128.881			0.667776			0.333888	+	0.942613i	$0.391639\pi$
$194$			342.038i			1.76308i
$195$	−19.7170	−	83.4143i	−0.101113	−	0.427765i
$196$	217.502			1.10970
$197$		−	347.172i		−	1.76230i	−0.472841	−	0.881148i	$-0.656772\pi$
$197$		−	347.172i		−	1.76230i	0.472841	−	0.881148i	$-0.343228\pi$
$198$	210.445	−	105.375i	1.06285	−	0.532199i
$199$	4.43323			0.0222776			0.0111388	−	0.999938i	$-0.496454\pi$
$199$	4.43323			0.0222776			0.0111388	+	0.999938i	$0.496454\pi$
$200$		−	28.7107i		−	0.143554i
$201$	−112.607	+	26.6175i	−0.560235	+	0.132425i
$202$	40.2490			0.199253
$203$		−	11.4991i		−	0.0566459i
$204$	66.5242	+	281.435i	0.326099	+	1.37959i
$205$	−165.388			−0.806770
$206$		−	335.509i		−	1.62869i
$207$	19.3253	+	38.5945i	0.0933588	+	0.186447i
$208$	138.100			0.663943
$209$		−	243.188i		−	1.16358i
$210$	27.7986	−	6.57088i	0.132374	−	0.0312899i
$211$	216.407			1.02563			0.512814	−	0.858500i	$-0.328603\pi$
$211$	216.407			1.02563			0.512814	+	0.858500i	$0.328603\pi$
$212$			342.986i			1.61786i
$213$	95.7735	+	405.177i	0.449641	+	1.90224i
$214$	−413.851			−1.93388
$215$		−	28.7823i		−	0.133871i
$216$	−28.7376	−	34.3728i	−0.133044	−	0.159133i
$217$	38.1116			0.175629
$218$			595.488i			2.73160i
$219$	−214.326	+	50.6613i	−0.978658	+	0.231330i
$220$	−113.208			−0.514581
$221$			217.359i			0.983523i
$222$	−94.1595	−	398.349i	−0.424142	−	1.79436i
$223$	−135.854			−0.609213			−0.304606	−	0.952478i	$-0.598525\pi$
$223$	−135.854			−0.609213			−0.304606	+	0.952478i	$0.598525\pi$
$224$			53.8056i			0.240203i
$225$	139.239	−	69.7205i	0.618838	−	0.309869i
$226$	67.7536			0.299795
$227$		−	163.531i		−	0.720401i	−0.932875	−	0.360201i	$-0.882708\pi$
$227$		−	163.531i		−	0.720401i	0.932875	−	0.360201i	$-0.117292\pi$
$228$	−362.925	+	85.7864i	−1.59178	+	0.376256i
$229$	−6.81594			−0.0297640			−0.0148820	−	0.999889i	$-0.504737\pi$
$229$	−6.81594			−0.0297640			−0.0148820	+	0.999889i	$0.504737\pi$
$230$		−	38.9460i		−	0.169331i
$231$	7.22918	+	30.5835i	0.0312951	+	0.132396i
$232$	16.2743			0.0701479
$233$			282.647i			1.21308i	0.795054	+	0.606538i	$0.207442\pi$
$233$			282.647i			1.21308i	−0.795054	+	0.606538i	$0.792558\pi$
$234$	−121.454	−	242.556i	−0.519035	−	1.03656i
$235$	59.7569			0.254285
$236$		−	301.136i		−	1.27600i
$237$	82.4160	−	19.4811i	0.347747	−	0.0821986i
$238$	−72.4367			−0.304356
$239$			347.523i			1.45407i	0.686600	+	0.727035i	$0.259102\pi$
$239$			347.523i			1.45407i	−0.686600	+	0.727035i	$0.740898\pi$
$240$	−25.6779	−	108.632i	−0.106991	−	0.452634i
$241$	84.4689			0.350493			0.175247	−	0.984525i	$-0.443928\pi$
$241$	84.4689			0.350493			0.175247	+	0.984525i	$0.443928\pi$
$242$			120.521i			0.498023i
$243$	96.9121	−	222.839i	0.398815	−	0.917031i
$244$	−135.035			−0.553422
$245$		−	132.137i		−	0.539334i
$246$	−509.384	+	120.405i	−2.07067	+	0.489453i
$247$	−280.295			−1.13480
$248$			53.9381i			0.217492i
$249$	82.3335	+	348.318i	0.330657	+	1.39887i
$250$	−343.527			−1.37411
$251$		−	193.749i		−	0.771909i	−0.922518	−	0.385955i	$-0.873872\pi$
$251$		−	193.749i		−	0.771909i	0.922518	−	0.385955i	$-0.126128\pi$
$252$	43.0917	−	21.5772i	0.170999	−	0.0856237i
$253$	42.8478			0.169359
$254$			276.949i			1.09035i
$255$	170.978	−	40.4149i	0.670502	−	0.158490i
$256$	168.837			0.659518
$257$			89.9521i			0.350008i	0.984568	+	0.175004i	$0.0559939\pi$
$257$			89.9521i			0.350008i	−0.984568	+	0.175004i	$0.944006\pi$
$258$	−20.9541	−	88.6477i	−0.0812174	−	0.343596i
$259$	54.6566			0.211029
$260$			130.482i			0.501853i
$261$	39.5201	+	78.9256i	0.151418	+	0.302397i
$262$	345.241			1.31772
$263$			261.816i			0.995498i	0.867321	+	0.497749i	$0.165840\pi$
$263$			261.816i			0.995498i	−0.867321	+	0.497749i	$0.834160\pi$
$264$	−43.2839	+	10.2312i	−0.163954	+	0.0387546i
$265$	208.372			0.786308
$266$		−	93.4109i		−	0.351169i
$267$	−79.8940	−	337.997i	−0.299228	−	1.26591i
$268$	176.147			0.657265
$269$		−	168.732i		−	0.627255i	−0.949546	−	0.313628i	$-0.898456\pi$
$269$		−	168.732i		−	0.627255i	0.949546	−	0.313628i	$-0.101544\pi$
$270$	−168.216	+	140.638i	−0.623023	+	0.520882i
$271$	533.955			1.97031			0.985157	−	0.171653i	$-0.0549108\pi$
$271$	533.955			1.97031			0.985157	+	0.171653i	$0.0549108\pi$
$272$			283.070i			1.04070i
$273$	35.2502	−	8.33225i	0.129122	−	0.0305211i
$274$	642.678			2.34554
$275$		−	154.584i		−	0.562122i
$276$	−15.1149	−	63.9446i	−0.0547641	−	0.231683i
$277$	−28.4625			−0.102753			−0.0513764	−	0.998679i	$-0.516361\pi$
$277$	−28.4625			−0.102753			−0.0513764	+	0.998679i	$0.516361\pi$
$278$		−	103.014i		−	0.370554i
$279$	−261.584	+	130.982i	−0.937576	+	0.469469i
$280$	−5.39809			−0.0192789
$281$			361.831i			1.28766i	0.765171	+	0.643828i	$0.222655\pi$
$281$			361.831i			1.28766i	−0.765171	+	0.643828i	$0.777345\pi$
$282$	184.047	−	43.5041i	0.652650	−	0.154270i
$283$	66.4429			0.234781			0.117390	−	0.993086i	$-0.462547\pi$
$283$	66.4429			0.234781			0.117390	+	0.993086i	$0.462547\pi$
$284$		−	633.802i		−	2.23170i
$285$	52.1171	+	220.485i	0.182867	+	0.773632i
$286$	−269.287			−0.941564
$287$		−	69.8915i		−	0.243524i
$288$	−184.919	−	369.301i	−0.642080	−	1.28230i
$289$	−156.530			−0.541626
$290$		−	79.6445i		−	0.274636i
$291$	341.175	−	80.6451i	1.17242	−	0.277131i
$292$	335.262			1.14816
$293$			299.159i			1.02102i	0.859871	+	0.510511i	$0.170544\pi$
$293$			299.159i			1.02102i	−0.859871	+	0.510511i	$0.829456\pi$
$294$	−96.1981	−	406.973i	−0.327205	−	1.38426i
$295$	−182.947			−0.620159
$296$			77.3537i			0.261330i
$297$	−154.728	−	185.069i	−0.520969	−	0.623127i
$298$	265.771			0.891848
$299$		−	49.3858i		−	0.165170i
$300$	−230.695	+	54.5305i	−0.768984	+	0.181768i
$301$	12.1632			0.0404092
$302$			135.812i			0.449709i
$303$	−9.48984	−	40.1474i	−0.0313196	−	0.132500i
$304$	−365.034			−1.20077
$305$			82.0366i			0.268972i
$306$	497.179	−	248.950i	1.62477	−	0.813564i
$307$	−238.324			−0.776299			−0.388149	−	0.921596i	$-0.626886\pi$
$307$	−238.324			−0.776299			−0.388149	+	0.921596i	$0.626886\pi$
$308$		−	47.8407i		−	0.155327i
$309$	−334.663	+	79.1058i	−1.08305	+	0.256006i
$310$	263.966			0.851504
$311$		−	211.794i		−	0.681010i	−0.940243	−	0.340505i	$-0.889402\pi$
$311$		−	211.794i		−	0.681010i	0.940243	−	0.340505i	$-0.110598\pi$
$312$	11.7924	+	49.8884i	0.0377960	+	0.159899i
$313$	−494.287			−1.57919			−0.789596	−	0.613627i	$-0.789710\pi$
$313$	−494.287			−1.57919			−0.789596	+	0.613627i	$0.789710\pi$
$314$		−	415.785i		−	1.32415i
$315$	−13.1086	−	26.1791i	−0.0416146	−	0.0831084i
$316$	−128.920			−0.407975
$317$		−	463.357i		−	1.46170i	−0.682541	−	0.730848i	$-0.739125\pi$
$317$		−	463.357i		−	1.46170i	0.682541	−	0.730848i	$-0.260875\pi$
$318$	641.771	−	151.698i	2.01815	−	0.477039i
$319$	87.6237			0.274682
$320$			223.831i			0.699472i
$321$	97.5770	+	412.807i	0.303978	+	1.28600i
$322$	16.4583			0.0511127
$323$		−	574.534i		−	1.77874i
$324$	−221.609	+	296.195i	−0.683978	+	0.914182i
$325$	−178.171			−0.548218
$326$			289.319i			0.887480i
$327$	593.986	−	140.403i	1.81647	−	0.429368i
$328$	98.9152			0.301571
$329$			25.2528i			0.0767561i
$330$	50.0703	+	211.826i	0.151728	+	0.641897i
$331$	−267.974			−0.809589			−0.404794	−	0.914408i	$-0.632657\pi$
$331$	−267.974			−0.809589			−0.404794	+	0.914408i	$0.632657\pi$
$332$		−	544.860i		−	1.64114i
$333$	−375.143	+	187.844i	−1.12655	+	0.564096i
$334$	−210.379			−0.629878
$335$		−	107.013i		−	0.319442i
$336$	45.9070	−	10.8513i	0.136628	−	0.0322954i
$337$	−250.719			−0.743972			−0.371986	−	0.928238i	$-0.621323\pi$
$337$	−250.719			−0.743972			−0.371986	+	0.928238i	$0.621323\pi$
$338$		−	184.275i		−	0.545191i
$339$	−15.9748	−	67.5826i	−0.0471234	−	0.199359i
$340$	−267.454			−0.786631
$341$			290.412i			0.851647i
$342$	321.035	+	641.137i	0.938697	+	1.87467i
$343$	113.292			0.330297
$344$			17.2141i			0.0500411i
$345$	−38.8478	+	9.18263i	−0.112602	+	0.0266163i
$346$	−95.8882			−0.277134
$347$		−	95.7166i		−	0.275840i	−0.990443	−	0.137920i	$-0.955958\pi$
$347$		−	95.7166i		−	0.275840i	0.990443	−	0.137920i	$-0.0440417\pi$
$348$	−30.9099	−	130.767i	−0.0888216	−	0.375766i
$349$	−11.0463			−0.0316514			−0.0158257	−	0.999875i	$-0.505038\pi$
$349$	−11.0463			−0.0316514			−0.0158257	+	0.999875i	$0.505038\pi$
$350$		−	59.3771i		−	0.169649i
$351$	−213.308	+	178.337i	−0.607715	+	0.508083i
$352$	−410.000			−1.16477
$353$			67.4356i			0.191036i	0.995428	+	0.0955178i	$0.0304507\pi$
$353$			67.4356i			0.191036i	−0.995428	+	0.0955178i	$0.969549\pi$
$354$	−563.464	+	133.189i	−1.59171	+	0.376239i
$355$	−385.049			−1.08464
$356$			528.716i			1.48516i
$357$	17.0790	+	72.2539i	0.0478403	+	0.202392i
$358$	198.524			0.554536
$359$			452.049i			1.25919i	0.776924	+	0.629595i	$0.216779\pi$
$359$			452.049i			1.25919i	−0.776924	+	0.629595i	$0.783221\pi$
$360$	37.0505	−	18.5522i	0.102918	−	0.0515338i
$361$	379.891			1.05233
$362$		−	66.4846i		−	0.183659i
$363$	120.217	−	28.4163i	0.331177	−	0.0782819i
$364$	−55.1405			−0.151485
$365$		−	203.679i		−	0.558025i
$366$	59.7242	+	252.667i	0.163181	+	0.690348i
$367$	−603.624			−1.64475			−0.822377	−	0.568944i	$-0.807352\pi$
$367$	−603.624			−1.64475			−0.822377	+	0.568944i	$0.807352\pi$
$368$		−	64.3161i		−	0.174772i
$369$	240.203	+	479.709i	0.650957	+	1.30003i
$370$	378.560			1.02313
$371$			88.0561i			0.237348i
$372$	433.401	−	102.445i	1.16506	−	0.275390i
$373$	195.736			0.524761			0.262380	−	0.964965i	$-0.415493\pi$
$373$	195.736			0.524761			0.262380	+	0.964965i	$0.415493\pi$
$374$		−	551.971i		−	1.47586i
$375$	80.9962	+	342.660i	0.215990	+	0.913761i
$376$	−35.7394			−0.0950516
$377$		−	100.994i		−	0.267888i
$378$	−59.4325	−	71.0868i	−0.157229	−	0.188060i
$379$	522.722			1.37921			0.689607	−	0.724184i	$-0.257783\pi$
$379$	522.722			1.37921			0.689607	+	0.724184i	$0.257783\pi$
$380$		−	344.896i		−	0.907622i
$381$	276.251	−	65.2986i	0.725067	−	0.171387i
$382$	−76.9614			−0.201470
$383$			623.986i			1.62921i	0.580020	+	0.814603i	$0.303045\pi$
$383$			623.986i			1.62921i	−0.580020	+	0.814603i	$0.696955\pi$
$384$	36.2767	+	153.471i	0.0944707	+	0.399665i
$385$	−29.0642			−0.0754915
$386$			377.225i			0.977267i
$387$	−83.4835	+	41.8024i	−0.215720	+	0.108017i
$388$	−533.687			−1.37548
$389$		−	184.434i		−	0.474124i	−0.971495	−	0.237062i	$-0.923816\pi$
$389$		−	184.434i		−	0.474124i	0.971495	−	0.237062i	$-0.0761844\pi$
$390$	244.148	−	57.7104i	0.626020	−	0.147975i
$391$	101.228			0.258896
$392$			79.0285i			0.201603i
$393$	−81.4004	−	344.370i	−0.207126	−	0.876260i
$394$	1016.15			2.57906
$395$			78.3218i			0.198283i
$396$	164.419	+	328.360i	0.415199	+	0.829193i
$397$	577.611			1.45494			0.727470	−	0.686139i	$-0.240696\pi$
$397$	577.611			1.45494			0.727470	+	0.686139i	$0.240696\pi$
$398$			12.9758i			0.0326025i
$399$	−93.1752	+	22.0243i	−0.233522	+	0.0551986i
$400$	−232.036			−0.580089
$401$		−	124.700i		−	0.310971i	−0.987838	−	0.155486i	$-0.950306\pi$
$401$		−	124.700i		−	0.310971i	0.987838	−	0.155486i	$-0.0496943\pi$
$402$	−77.9076	−	329.594i	−0.193800	−	0.819885i
$403$	334.725			0.830582
$404$			62.8011i			0.155448i
$405$	179.945	+	134.632i	0.444309	+	0.332425i
$406$	33.6571			0.0828993
$407$			416.486i			1.02331i
$408$	−102.259	+	24.1714i	−0.250634	+	0.0592435i
$409$	−734.370			−1.79552			−0.897762	−	0.440480i	$-0.854808\pi$
$409$	−734.370			−1.79552			−0.897762	+	0.440480i	$0.854808\pi$
$410$		−	484.079i		−	1.18068i
$411$	−151.529	−	641.056i	−0.368685	−	1.55975i
$412$	523.500			1.27063
$413$		−	77.3118i		−	0.187196i
$414$	−112.963	+	56.5638i	−0.272859	+	0.136628i
$415$	−331.014			−0.797625
$416$			472.561i			1.13596i
$417$	−102.754	+	24.2884i	−0.246412	+	0.0582457i
$418$	711.795			1.70286
$419$		−	261.797i		−	0.624813i	−0.949948	−	0.312407i	$-0.898865\pi$
$419$		−	261.797i		−	0.624813i	0.949948	−	0.312407i	$-0.101135\pi$
$420$	10.2526	+	43.3745i	0.0244110	+	0.103273i
$421$	−300.230			−0.713134			−0.356567	−	0.934270i	$-0.616053\pi$
$421$	−300.230			−0.713134			−0.356567	+	0.934270i	$0.616053\pi$
$422$			633.410i			1.50097i
$423$	−86.7887	−	173.326i	−0.205174	−	0.409753i
$424$	−124.623			−0.293922
$425$		−	365.205i		−	0.859306i
$426$	−1185.92	+	280.323i	−2.78386	+	0.658034i
$427$	−34.6680			−0.0811897
$428$		−	645.738i		−	1.50873i
$429$	63.4921	+	268.608i	0.148000	+	0.626125i
$430$	84.2440			0.195916
$431$		−	315.367i		−	0.731711i	−0.930672	−	0.365855i	$-0.880776\pi$
$431$		−	315.367i		−	0.731711i	0.930672	−	0.365855i	$-0.119224\pi$
$432$	−277.795	+	232.252i	−0.643044	+	0.537621i
$433$	−254.801			−0.588454			−0.294227	−	0.955736i	$-0.595062\pi$
$433$	−254.801			−0.588454			−0.294227	+	0.955736i	$0.595062\pi$
$434$			111.550i			0.257028i
$435$	−79.4435	+	18.7784i	−0.182629	+	0.0431688i
$436$	−929.149			−2.13108
$437$			130.539i			0.298717i
$438$	−148.282	−	627.318i	−0.338544	−	1.43223i
$439$	−120.984			−0.275591			−0.137795	−	0.990461i	$-0.544002\pi$
$439$	−120.984			−0.275591			−0.137795	+	0.990461i	$0.544002\pi$
$440$		−	41.1337i		−	0.0934856i
$441$	−383.265	+	191.911i	−0.869081	+	0.435172i
$442$	−636.194			−1.43935
$443$			386.803i			0.873144i	0.899669	+	0.436572i	$0.143808\pi$
$443$			386.803i			0.873144i	−0.899669	+	0.436572i	$0.856192\pi$
$444$	621.549	−	146.918i	1.39989	−	0.330897i
$445$	321.206			0.721812
$446$		−	397.637i		−	0.891563i
$447$	−62.6629	−	265.100i	−0.140186	−	0.593065i
$448$	−94.5892			−0.211137
$449$			491.962i			1.09568i	0.836582	+	0.547842i	$0.184550\pi$
$449$			491.962i			1.09568i	−0.836582	+	0.547842i	$0.815450\pi$
$450$	204.067	+	407.542i	0.453482	+	0.905649i
$451$	532.576			1.18088
$452$			105.717i			0.233887i
$453$	135.469	−	32.0215i	0.299049	−	0.0706877i
$454$	478.645			1.05428
$455$			33.4991i			0.0736243i
$456$	−31.1702	−	131.868i	−0.0683557	−	0.289184i
$457$	532.919			1.16613			0.583063	−	0.812427i	$-0.301854\pi$
$457$	532.919			1.16613			0.583063	+	0.812427i	$0.301854\pi$
$458$		−	19.9498i		−	0.0435585i
$459$	−365.546	−	437.227i	−0.796397	−	0.952564i
$460$	60.7681			0.132104
$461$		−	374.158i		−	0.811623i	−0.913957	−	0.405812i	$-0.866989\pi$
$461$		−	374.158i		−	0.811623i	0.913957	−	0.405812i	$-0.133011\pi$
$462$	−89.5160	+	21.1593i	−0.193758	+	0.0457994i
$463$	636.479			1.37468			0.687342	−	0.726334i	$-0.258777\pi$
$463$	636.479			1.37468			0.687342	+	0.726334i	$0.258777\pi$
$464$		−	131.526i		−	0.283462i
$465$	−62.2375	−	263.300i	−0.133844	−	0.566237i
$466$	−827.288			−1.77530
$467$		−	28.0428i		−	0.0600488i	−0.999549	−	0.0300244i	$-0.990441\pi$
$467$		−	28.0428i		−	0.0600488i	0.999549	−	0.0300244i	$-0.00955850\pi$
$468$	378.464	−	189.507i	0.808683	−	0.404929i
$469$	45.2229			0.0964241
$470$			174.904i			0.372137i
$471$	−414.735	+	98.0330i	−0.880542	+	0.208138i
$472$	109.417			0.231815
$473$			92.6839i			0.195949i
$474$	57.0198	+	241.226i	0.120295	+	0.508916i
$475$	470.951			0.991475
$476$		−	113.024i		−	0.237446i
$477$	−302.631	−	604.384i	−0.634447	−	1.26705i
$478$	−1017.18			−2.12798
$479$		−	825.592i		−	1.72357i	−0.507270	−	0.861787i	$-0.669345\pi$
$479$		−	825.592i		−	1.72357i	0.507270	−	0.861787i	$-0.330655\pi$
$480$	371.725	−	87.8664i	0.774427	−	0.183055i
$481$	480.036			0.997995
$482$			247.235i			0.512935i
$483$	−3.88050	−	16.4167i	−0.00803417	−	0.0339891i
$484$	−188.051			−0.388536
$485$			324.226i			0.668508i
$486$	652.234	+	283.655i	1.34204	+	0.583653i
$487$	−95.3294			−0.195748			−0.0978742	−	0.995199i	$-0.531204\pi$
$487$	−95.3294			−0.195748			−0.0978742	+	0.995199i	$0.531204\pi$
$488$		−	49.0645i		−	0.100542i
$489$	288.588	−	68.2150i	0.590160	−	0.139499i
$490$	386.756			0.789298
$491$			123.297i			0.251115i	0.992086	+	0.125557i	$0.0400719\pi$
$491$			123.297i			0.251115i	−0.992086	+	0.125557i	$0.959928\pi$
$492$	−187.870	−	794.799i	−0.381850	−	1.61544i
$493$	207.012			0.419902
$494$		−	820.405i		−	1.66074i
$495$	199.486	−	99.8880i	0.403002	−	0.201794i
$496$	435.919			0.878868
$497$		−	162.718i		−	0.327401i
$498$	−1019.50	+	240.985i	−2.04719	+	0.483905i
$499$	876.831			1.75718			0.878589	−	0.477579i	$-0.158486\pi$
$499$	876.831			1.75718			0.878589	+	0.477579i	$0.158486\pi$
$500$		−	536.010i		−	1.07202i
$501$	49.6028	+	209.848i	0.0990076	+	0.418859i
$502$	567.091			1.12966
$503$		−	228.064i		−	0.453407i	−0.973964	−	0.226703i	$-0.927205\pi$
$503$		−	228.064i		−	0.453407i	0.973964	−	0.226703i	$-0.0727948\pi$
$504$	7.83999	+	15.6572i	0.0155555	+	0.0310659i
$505$	38.1530			0.0755506
$506$			125.413i			0.247851i
$507$	−183.810	+	43.4480i	−0.362544	+	0.0856962i
$508$	−432.128			−0.850646
$509$		−	318.234i		−	0.625215i	−0.949882	−	0.312607i	$-0.898798\pi$
$509$		−	318.234i		−	0.625215i	0.949882	−	0.312607i	$-0.101202\pi$
$510$	118.292	+	500.441i	0.231944	+	0.981257i
$511$	86.0731			0.168440
$512$			704.441i			1.37586i
$513$	563.827	−	471.391i	1.09908	−	0.918890i
$514$	−263.284			−0.512225
$515$		−	318.038i		−	0.617549i
$516$	138.318	−	32.6949i	0.268059	−	0.0633623i
$517$	−192.427			−0.372199
$518$			159.976i			0.308835i
$519$	22.6084	+	95.6463i	0.0435614	+	0.184290i
$520$	−47.4101			−0.0911733
$521$			692.586i			1.32934i	0.747137	+	0.664670i	$0.231428\pi$
$521$			692.586i			1.32934i	−0.747137	+	0.664670i	$0.768572\pi$
$522$	−231.010	+	115.673i	−0.442548	+	0.221595i
$523$	−243.893			−0.466335			−0.233167	−	0.972437i	$-0.574909\pi$
$523$	−243.893			−0.466335			−0.233167	+	0.972437i	$0.574909\pi$
$524$			538.685i			1.02802i
$525$	−59.2272	+	13.9998i	−0.112814	+	0.0266663i
$526$	−766.318			−1.45688
$527$			686.100i			1.30190i
$528$	82.6870	+	349.813i	0.156604	+	0.662525i
$529$	−23.0000			−0.0434783
$530$			609.890i			1.15074i
$531$	265.705	+	530.639i	0.500386	+	0.999321i
$532$	145.750			0.273967
$533$		−	613.840i		−	1.15167i
$534$	989.295	−	233.844i	1.85261	−	0.437911i
$535$	−392.300			−0.733270
$536$			64.0025i			0.119408i
$537$	−46.8076	−	198.023i	−0.0871649	−	0.368757i
$538$	493.866			0.917967
$539$			425.503i			0.789430i
$540$	−219.440	−	262.470i	−0.406370	−	0.486056i
$541$	453.686			0.838606			0.419303	−	0.907846i	$-0.362274\pi$
$541$	453.686			0.838606			0.419303	+	0.907846i	$0.362274\pi$
$542$			1562.85i			2.88349i
$543$	−66.3168	+	15.6756i	−0.122130	+	0.0288686i
$544$	−968.630			−1.78057
$545$			564.478i			1.03574i
$546$	24.3879	+	103.175i	0.0446666	+	0.188965i
$547$	−254.534			−0.465326			−0.232663	−	0.972557i	$-0.574744\pi$
$547$	−254.534			−0.465326			−0.232663	+	0.972557i	$0.574744\pi$
$548$			1002.78i			1.82989i
$549$	237.948	−	119.147i	0.433421	−	0.217025i
$550$	452.456			0.822646
$551$			266.952i			0.484487i
$552$	23.2341	−	5.49195i	0.0420907	−	0.00994918i
$553$	−33.0982			−0.0598520
$554$		−	83.3080i		−	0.150375i
$555$	−89.2562	−	377.605i	−0.160822	−	0.680369i
$556$	160.734			0.289090
$557$		−	428.256i		−	0.768861i	−0.923154	−	0.384431i	$-0.874398\pi$
$557$		−	428.256i		−	0.768861i	0.923154	−	0.384431i	$-0.125602\pi$
$558$	−383.375	−	765.638i	−0.687052	−	1.37211i
$559$	106.826			0.191102
$560$			43.6265i			0.0779045i
$561$	−550.578	+	130.143i	−0.981422	+	0.231983i
$562$	−1059.06			−1.88444
$563$		−	710.838i		−	1.26259i	−0.775543	−	0.631295i	$-0.782524\pi$
$563$		−	710.838i		−	1.26259i	0.775543	−	0.631295i	$-0.217476\pi$
$564$	67.8801	+	287.172i	0.120355	+	0.509170i
$565$	64.2253			0.113673
$566$			194.474i			0.343594i
$567$	−56.8945	+	76.0433i	−0.100343	+	0.134115i
$568$	230.290			0.405440
$569$			295.041i			0.518526i	0.965807	+	0.259263i	$0.0834796\pi$
$569$			295.041i			0.518526i	−0.965807	+	0.259263i	$0.916520\pi$
$570$	−645.345	+	152.543i	−1.13218	+	0.267620i
$571$	−471.766			−0.826210			−0.413105	−	0.910683i	$-0.635556\pi$
$571$	−471.766			−0.826210			−0.413105	+	0.910683i	$0.635556\pi$
$572$		−	420.173i		−	0.734568i
$573$	18.1458	+	76.7671i	0.0316681	+	0.133974i
$574$	204.568			0.356390
$575$			82.9779i			0.144309i
$576$	649.225	−	325.084i	1.12713	−	0.564382i
$577$	−845.564			−1.46545			−0.732724	−	0.680526i	$-0.761752\pi$
$577$	−845.564			−1.46545			−0.732724	+	0.680526i	$0.761752\pi$
$578$		−	458.152i		−	0.792651i
$579$	376.273	−	88.9415i	0.649867	−	0.153612i
$580$	124.270			0.214259
$581$		−	139.884i		−	0.240764i
$582$	236.043	+	998.596i	0.405572	+	1.71580i
$583$	−670.991			−1.15093
$584$			121.816i			0.208590i
$585$	−115.130	−	229.925i	−0.196803	−	0.393034i
$586$	−875.620			−1.49423
$587$		−	179.014i		−	0.304965i	−0.988306	−	0.152483i	$-0.951273\pi$
$587$		−	179.014i		−	0.304965i	0.988306	−	0.152483i	$-0.0487268\pi$
$588$	635.006	−	150.099i	1.07994	−	0.255271i
$589$	−884.762			−1.50214
$590$		−	535.473i		−	0.907581i
$591$	−239.586	−	1013.59i	−0.405391	−	1.71503i
$592$	625.160			1.05601
$593$			69.2659i			0.116806i	0.998293	+	0.0584029i	$0.0186008\pi$
$593$			69.2659i			0.116806i	−0.998293	+	0.0584029i	$0.981399\pi$
$594$	541.684	−	452.878i	0.911926	−	0.762421i
$595$	−68.6646			−0.115403
$596$			414.686i			0.695782i
$597$	12.9430	−	3.05941i	0.0216801	−	0.00512463i
$598$	144.549			0.241721
$599$			743.613i			1.24142i	0.784039	+	0.620712i	$0.213156\pi$
$599$			743.613i			1.24142i	−0.784039	+	0.620712i	$0.786844\pi$
$600$	−19.8135	−	83.8224i	−0.0330225	−	0.139704i
$601$	−879.809			−1.46391			−0.731954	−	0.681354i	$-0.761391\pi$
$601$	−879.809			−1.46391			−0.731954	+	0.681354i	$0.761391\pi$
$602$			35.6008i			0.0591375i
$603$	−310.393	+	155.422i	−0.514748	+	0.257748i
$604$	−211.910			−0.350844
$605$			114.245i			0.188835i
$606$	117.509	−	27.7761i	0.193909	−	0.0458352i
$607$	1008.65			1.66170			0.830852	−	0.556493i	$-0.187853\pi$
$607$	1008.65			1.66170			0.830852	+	0.556493i	$0.187853\pi$
$608$		−	1249.10i		−	2.05444i
$609$	−7.93562	−	33.5722i	−0.0130306	−	0.0551267i
$610$	−240.116			−0.393632
$611$			221.789i			0.362993i
$612$	388.441	+	775.755i	0.634708	+	1.26757i
$613$	119.085			0.194267			0.0971334	−	0.995271i	$-0.469033\pi$
$613$	119.085			0.194267			0.0971334	+	0.995271i	$0.469033\pi$
$614$		−	697.558i		−	1.13609i
$615$	−482.857	+	114.135i	−0.785134	+	0.185586i
$616$	17.3828			0.0282188
$617$		−	314.384i		−	0.509537i	−0.967002	−	0.254769i	$-0.918001\pi$
$617$		−	314.384i		−	0.509537i	0.967002	−	0.254769i	$-0.0819993\pi$
$618$	−231.537	−	979.535i	−0.374656	−	1.58501i
$619$	−119.714			−0.193399			−0.0966996	−	0.995314i	$-0.530829\pi$
$619$	−119.714			−0.193399			−0.0966996	+	0.995314i	$0.530829\pi$
$620$			411.871i			0.664307i
$621$	83.0554	+	99.3419i	0.133745	+	0.159971i
$622$	619.907			0.996635
$623$			135.739i			0.217880i
$624$	403.190	−	95.3039i	0.646138	−	0.152731i
$625$	106.914			0.171063
$626$		−	1446.75i		−	2.31109i
$627$	−167.826	−	709.998i	−0.267665	−	1.13237i
$628$	648.755			1.03305
$629$			983.951i			1.56431i
$630$	76.6246	−	38.3680i	0.121626	−	0.0609015i
$631$	−9.99471			−0.0158395			−0.00791974	−	0.999969i	$-0.502521\pi$
$631$	−9.99471			−0.0158395			−0.00791974	+	0.999969i	$0.502521\pi$
$632$		−	46.8428i		−	0.0741183i
$633$	631.812	−	149.344i	0.998123	−	0.235931i
$634$	1356.22			2.13914
$635$			262.527i			0.413429i
$636$	236.697	+	1001.36i	0.372165	+	1.57447i
$637$	490.429			0.769904
$638$			256.469i			0.401988i
$639$	559.230	+	1116.84i	0.875165	+	1.74779i
$640$	−145.847			−0.227886
$641$			1164.14i			1.81613i	0.418824	+	0.908067i	$0.362442\pi$
$641$			1164.14i			1.81613i	−0.418824	+	0.908067i	$0.637558\pi$
$642$	−1208.26	+	285.601i	−1.88202	+	0.444862i
$643$	−1186.79			−1.84571			−0.922857	−	0.385143i	$-0.874152\pi$
$643$	−1186.79			−1.84571			−0.922857	+	0.385143i	$0.874152\pi$
$644$			25.6801i			0.0398759i
$645$	−19.8629	−	84.0314i	−0.0307952	−	0.130281i
$646$	1681.62			2.60313
$647$			738.437i			1.14132i	0.821185	+	0.570662i	$0.193313\pi$
$647$			738.437i			1.14132i	−0.821185	+	0.570662i	$0.806687\pi$
$648$	−107.622	−	80.5209i	−0.166083	−	0.124261i
$649$	589.119			0.907733
$650$		−	521.494i		−	0.802299i
$651$	111.269	−	26.3011i	0.170919	−	0.0404010i
$652$	−451.428			−0.692374
$653$		−	1188.54i		−	1.82012i	−0.414477	−	0.910060i	$-0.636036\pi$
$653$		−	1188.54i		−	1.82012i	0.414477	−	0.910060i	$-0.363964\pi$
$654$	410.951	+	1738.56i	0.628365	+	2.65834i
$655$	327.263			0.499638
$656$		−	799.416i		−	1.21862i
$657$	−590.773	+	295.816i	−0.899198	+	0.450252i
$658$	−73.9132			−0.112330
$659$		−	986.465i		−	1.49691i	−0.663185	−	0.748456i	$-0.730796\pi$
$659$		−	986.465i		−	1.49691i	0.663185	−	0.748456i	$-0.269204\pi$
$660$	−330.515	+	78.1255i	−0.500781	+	0.118372i
$661$	−1028.35			−1.55575			−0.777873	−	0.628421i	$-0.783702\pi$
$661$	−1028.35			−1.55575			−0.777873	+	0.628421i	$0.783702\pi$
$662$		−	784.342i		−	1.18481i
$663$	150.001	+	634.588i	0.226245	+	0.957147i
$664$	197.973			0.298152
$665$		−	88.5465i		−	0.133153i
$666$	−549.806	−	1098.02i	−0.825535	−	1.64867i
$667$	−47.0349			−0.0705171
$668$		−	328.258i		−	0.491403i
$669$	−396.633	+	93.7541i	−0.592875	+	0.140141i
$670$	313.220			0.467493
$671$		−	264.171i		−	0.393698i
$672$	37.1316	+	157.088i	0.0552554	+	0.233762i
$673$	390.788			0.580665			0.290333	−	0.956926i	$-0.406234\pi$
$673$	390.788			0.580665			0.290333	+	0.956926i	$0.406234\pi$
$674$		−	733.836i		−	1.08878i
$675$	358.399	−	299.642i	0.530961	−	0.443914i
$676$	287.526			0.425335
$677$		−	870.038i		−	1.28514i	−0.766228	−	0.642569i	$-0.777869\pi$
$677$		−	870.038i		−	1.28514i	0.766228	−	0.642569i	$-0.222131\pi$
$678$	197.810	−	46.7572i	0.291755	−	0.0689634i
$679$	−137.015			−0.201790
$680$		−	97.1787i		−	0.142910i
$681$	−112.854	−	477.437i	−0.165718	−	0.701082i
$682$	−850.015			−1.24636
$683$			390.139i			0.571214i	0.958347	+	0.285607i	$0.0921952\pi$
$683$			390.139i			0.571214i	−0.958347	+	0.285607i	$0.907805\pi$
$684$	−1000.38	+	500.915i	−1.46254	+	0.732332i
$685$	609.210			0.889358
$686$			331.597i			0.483378i
$687$	−19.8995	+	4.70373i	−0.0289657	+	0.00684677i
$688$	139.122			0.202212
$689$			773.375i			1.12246i
$690$	−26.8769	−	113.705i	−0.0389521	−	0.164790i
$691$	946.042			1.36909			0.684546	−	0.728970i	$-0.260001\pi$
$691$	946.042			1.36909			0.684546	+	0.728970i	$0.260001\pi$
$692$		−	149.616i		−	0.216208i
$693$	42.2118	+	84.3012i	0.0609117	+	0.121647i
$694$	280.156			0.403683
$695$		−	97.6495i		−	0.140503i
$696$	47.5136	−	11.2310i	0.0682667	−	0.0161365i
$697$	1258.22			1.80519
$698$		−	32.3319i		−	0.0463208i
$699$	195.057	+	825.201i	0.279051	+	1.18054i
$700$	92.6469			0.132353
$701$		−	311.015i		−	0.443674i	−0.975084	−	0.221837i	$-0.928795\pi$
$701$		−	311.015i		−	0.443674i	0.975084	−	0.221837i	$-0.0712053\pi$
$702$	−521.981	−	624.338i	−0.743563	−	0.889370i
$703$	−1268.86			−1.80492
$704$		−	720.773i		−	1.02383i
$705$	174.463	−	41.2386i	0.247465	−	0.0584945i
$706$	−197.379			−0.279574
$707$			16.1232i			0.0228050i
$708$	−207.816	−	879.181i	−0.293526	−	1.24178i
$709$	783.797			1.10550			0.552748	−	0.833349i	$-0.313579\pi$
$709$	783.797			1.10550			0.552748	+	0.833349i	$0.313579\pi$
$710$		−	1127.01i		−	1.58734i
$711$	227.173	−	113.752i	0.319513	−	0.159988i
$712$	−192.107			−0.269813
$713$		−	155.888i		−	0.218637i
$714$	−211.482	+	49.9891i	−0.296194	+	0.0700127i
$715$	−255.264			−0.357013
$716$			309.759i			0.432625i
$717$	239.828	+	1014.61i	0.334488	+	1.41508i
$718$	−1323.12			−1.84278
$719$			146.695i			0.204026i	0.994783	+	0.102013i	$0.0325283\pi$
$719$			146.695i			0.204026i	−0.994783	+	0.102013i	$0.967472\pi$
$720$	−149.936	−	299.436i	−0.208244	−	0.415883i
$721$	134.400			0.186408
$722$			1111.92i			1.54005i
$723$	246.611	−	58.2926i	0.341094	−	0.0806259i
$724$	103.737			0.143283
$725$			169.689i			0.234054i
$726$	83.1727	+	351.868i	0.114563	+	0.484667i
$727$	464.286			0.638633			0.319316	−	0.947648i	$-0.396547\pi$
$727$	464.286			0.638633			0.319316	+	0.947648i	$0.396547\pi$
$728$		−	20.0351i		−	0.0275208i
$729$	129.157	−	717.467i	0.177170	−	0.984180i
$730$	596.155			0.816650
$731$			218.967i			0.299544i
$732$	−394.241	+	93.1885i	−0.538580	+	0.127307i
$733$	−1166.95			−1.59202			−0.796009	−	0.605285i	$-0.793059\pi$
$733$	−1166.95			−1.59202			−0.796009	+	0.605285i	$0.793059\pi$
$734$		−	1766.77i		−	2.40704i
$735$	−91.1886	−	385.780i	−0.124066	−	0.524871i
$736$	220.081			0.299024
$737$			344.600i			0.467571i
$738$	−1404.08	+	703.058i	−1.90254	+	0.952654i
$739$	−626.936			−0.848357			−0.424178	−	0.905579i	$-0.639437\pi$
$739$	−626.936			−0.848357			−0.424178	+	0.905579i	$0.639437\pi$
$740$			590.672i			0.798206i
$741$	−818.335	+	193.434i	−1.10437	+	0.261044i
$742$	−257.734			−0.347351
$743$		−	39.3632i		−	0.0529788i	−0.999649	−	0.0264894i	$-0.991567\pi$
$743$		−	39.3632i		−	0.0529788i	0.999649	−	0.0264894i	$-0.00843282\pi$
$744$	37.2230	+	157.475i	0.0500310	+	0.211660i
$745$	251.931			0.338162
$746$			572.905i			0.767970i
$747$	480.753	+	960.111i	0.643578	+	1.28529i
$748$	861.248			1.15140
$749$		−	165.783i		−	0.221339i
$750$	−1002.94	+	237.070i	−1.33726	+	0.316094i
$751$	396.358			0.527774			0.263887	−	0.964554i	$-0.414995\pi$
$751$	396.358			0.527774			0.263887	+	0.964554i	$0.414995\pi$
$752$			288.840i			0.384096i
$753$	−133.708	−	565.660i	−0.177567	−	0.751208i
$754$	295.602			0.392045
$755$			128.740i			0.170516i
$756$	110.918	−	92.7334i	0.146717	−	0.122663i
$757$	−535.118			−0.706893			−0.353447	−	0.935455i	$-0.614990\pi$
$757$	−535.118			−0.706893			−0.353447	+	0.935455i	$0.614990\pi$
$758$			1529.97i			2.01843i
$759$	125.096	−	29.5696i	0.164817	−	0.0389586i
$760$	125.317			0.164891
$761$		−	170.888i		−	0.224557i	−0.993677	−	0.112279i	$-0.964185\pi$
$761$		−	170.888i		−	0.224557i	0.993677	−	0.112279i	$-0.0358149\pi$
$762$	191.125	+	808.567i	0.250820	+	1.06111i
$763$	−238.544			−0.312639
$764$		−	120.084i		−	0.157178i
$765$	471.288	−	235.986i	0.616063	−	0.308479i
$766$	−1826.36			−2.38429
$767$		−	679.011i		−	0.885281i
$768$	492.926	−	116.515i	0.641831	−	0.151713i
$769$	−1254.56			−1.63142			−0.815710	−	0.578460i	$-0.803654\pi$
$769$	−1254.56			−1.63142			−0.815710	+	0.578460i	$0.803654\pi$
$770$		−	85.0691i		−	0.110479i
$771$	62.0766	+	262.619i	0.0805144	+	0.340622i
$772$	−588.590			−0.762422
$773$			435.821i			0.563805i	0.959443	+	0.281902i	$0.0909655\pi$
$773$			435.821i			0.563805i	−0.959443	+	0.281902i	$0.909035\pi$
$774$	−122.353	−	244.351i	−0.158079	−	0.315698i
$775$	−562.403			−0.725681
$776$		−	193.913i		−	0.249888i
$777$	159.573	−	37.7189i	0.205370	−	0.0485443i
$778$	539.826			0.693864
$779$			1622.53i			2.08284i
$780$	90.0464	+	380.948i	0.115444	+	0.488394i
$781$	1239.92			1.58761
$782$			296.289i			0.378886i
$783$	169.848	+	203.154i	0.216919	+	0.259456i
$784$	638.695			0.814662
$785$		−	394.133i		−	0.502080i
$786$	1007.95	−	238.253i	1.28238	−	0.303121i
$787$	1266.41			1.60916			0.804582	−	0.593841i	$-0.202389\pi$
$787$	1266.41			1.60916			0.804582	+	0.593841i	$0.202389\pi$
$788$			1585.51i			2.01207i
$789$	180.681	+	764.384i	0.229000	+	0.968801i
$790$	−229.243			−0.290181
$791$			27.1411i			0.0343124i
$792$	−119.309	+	59.7410i	−0.150642	+	0.0754306i
$793$	−304.480			−0.383960
$794$			1690.63i			2.12926i
$795$	608.351	−	143.799i	0.765221	−	0.180879i
$796$	−20.2463			−0.0254350
$797$		−	1128.40i		−	1.41581i	−0.706306	−	0.707906i	$-0.749640\pi$
$797$		−	1128.40i		−	1.41581i	0.706306	−	0.707906i	$-0.250360\pi$
$798$	−64.4635	−	272.717i	−0.0807813	−	0.341751i
$799$	−454.611			−0.568975
$800$		−	793.995i		−	0.992494i
$801$	−466.508	−	931.663i	−0.582407	−	1.16312i
$802$	364.987			0.455096
$803$			655.880i			0.816787i
$804$	514.270	−	121.560i	0.639639	−	0.151194i
$805$	15.6012			0.0193804
$806$			979.716i			1.21553i
$807$	−116.443	−	492.620i	−0.144291	−	0.610434i
$808$	−22.8186			−0.0282408
$809$		−	1139.33i		−	1.40832i	−0.710044	−	0.704158i	$-0.751325\pi$
$809$		−	1139.33i		−	1.40832i	0.710044	−	0.704158i	$-0.248675\pi$
$810$	−394.060	+	526.687i	−0.486493	+	0.650231i
$811$	338.987			0.417986			0.208993	−	0.977917i	$-0.432981\pi$
$811$	338.987			0.417986			0.208993	+	0.977917i	$0.432981\pi$
$812$			52.5157i			0.0646745i
$813$	1558.91	−	368.486i	1.91748	−	0.453243i
$814$	−1219.03			−1.49757
$815$			274.252i			0.336506i
$816$	195.349	+	826.437i	0.239398	+	1.01279i
$817$	−282.369			−0.345617
$818$		−	2149.45i		−	2.62769i
$819$	97.1644	−	48.6528i	0.118638	−	0.0594051i
$820$	755.315			0.921116
$821$			1227.56i			1.49521i	0.664146	+	0.747603i	$0.268795\pi$
$821$			1227.56i			1.49521i	−0.664146	+	0.747603i	$0.731205\pi$
$822$	1876.33	−	443.517i	2.28264	−	0.539558i
$823$	−218.962			−0.266053			−0.133026	−	0.991112i	$-0.542470\pi$
$823$	−218.962			−0.266053			−0.133026	+	0.991112i	$0.542470\pi$
$824$			190.212i			0.230840i
$825$	−106.679	−	451.314i	−0.129308	−	0.547047i
$826$	226.287			0.273955
$827$		−	1585.10i		−	1.91669i	−0.285611	−	0.958346i	$-0.592196\pi$
$827$		−	1585.10i		−	1.91669i	0.285611	−	0.958346i	$-0.407804\pi$
$828$	−88.2573	−	176.258i	−0.106591	−	0.212873i
$829$	−382.666			−0.461599			−0.230800	−	0.973001i	$-0.574134\pi$
$829$	−382.666			−0.461599			−0.230800	+	0.973001i	$0.574134\pi$
$830$		−	968.856i		−	1.16730i
$831$	−83.0977	+	19.6422i	−0.0999973	+	0.0236368i
$832$	−830.753			−0.998502
$833$			1005.25i			1.20679i
$834$	−71.0906	−	300.754i	−0.0852406	−	0.360616i
$835$	−199.424			−0.238831
$836$			1110.62i			1.32850i
$837$	−673.314	+	562.928i	−0.804437	+	0.672555i
$838$	766.262			0.914393
$839$			872.462i			1.03988i	0.854202	+	0.519941i	$0.174046\pi$
$839$			872.462i			1.03988i	−0.854202	+	0.519941i	$0.825954\pi$
$840$	−15.7600	+	3.72526i	−0.0187619	+	0.00443484i
$841$	744.814			0.885629
$842$		−	878.752i		−	1.04365i
$843$	249.702	+	1056.38i	0.296207	+	1.25312i
$844$	−988.319			−1.17099
$845$		−	174.679i		−	0.206720i
$846$	507.312	−	254.025i	0.599660	−	0.300266i
$847$	−48.2791			−0.0570002
$848$			1007.18i			1.18771i
$849$	193.983	−	45.8527i	0.228484	−	0.0540079i
$850$	1068.93			1.25757
$851$		−	223.563i		−	0.262706i
$852$	−437.391	−	1850.42i	−0.513370	−	2.17185i
$853$	−495.808			−0.581252			−0.290626	−	0.956837i	$-0.593863\pi$
$853$	−495.808			−0.581252			−0.290626	+	0.956837i	$0.593863\pi$
$854$		−	101.471i		−	0.118818i
$855$	304.317	+	607.750i	0.355926	+	0.710819i
$856$	234.627			0.274097
$857$		−	745.026i		−	0.869341i	−0.900589	−	0.434671i	$-0.856865\pi$
$857$		−	745.026i		−	0.869341i	0.900589	−	0.434671i	$-0.143135\pi$
$858$	−786.197	+	185.837i	−0.916313	+	0.216593i
$859$	−1095.94			−1.27584			−0.637919	−	0.770104i	$-0.720204\pi$
$859$	−1095.94			−1.27584			−0.637919	+	0.770104i	$0.720204\pi$
$860$			131.447i			0.152845i
$861$	−48.2326	−	204.052i	−0.0560193	−	0.236994i
$862$	923.059			1.07083
$863$		−	46.3124i		−	0.0536644i	−0.999640	−	0.0268322i	$-0.991458\pi$
$863$		−	46.3124i		−	0.0536644i	0.999640	−	0.0268322i	$-0.00854197\pi$
$864$	−794.737	−	950.578i	−0.919834	−	1.10021i
$865$	−90.8948			−0.105081
$866$		−	745.784i		−	0.861183i
$867$	−456.996	+	108.022i	−0.527101	+	0.124593i
$868$	−174.053			−0.200522
$869$		−	252.209i		−	0.290229i
$870$	−54.9632	−	232.526i	−0.0631761	−	0.267271i
$871$	397.182			0.456006
$872$		−	337.603i		−	0.387160i
$873$	940.422	−	470.894i	1.07723	−	0.539398i
$874$	−382.080			−0.437162
$875$		−	137.612i		−	0.157271i
$876$	978.813	−	231.367i	1.11737	−	0.264117i
$877$	396.570			0.452190			0.226095	−	0.974105i	$-0.427404\pi$
$877$	396.570			0.452190			0.226095	+	0.974105i	$0.427404\pi$
$878$		−	354.113i		−	0.403318i
$879$	206.452	+	873.410i	0.234872	+	0.993641i
$880$	−332.436			−0.377768
$881$		−	622.240i		−	0.706288i	−0.935569	−	0.353144i	$-0.885113\pi$
$881$		−	622.240i		−	0.706288i	0.935569	−	0.353144i	$-0.114887\pi$
$882$	−561.710	−	1121.79i	−0.636859	−	1.27187i
$883$	−52.3972			−0.0593400			−0.0296700	−	0.999560i	$-0.509446\pi$
$883$	−52.3972			−0.0593400			−0.0296700	+	0.999560i	$0.509446\pi$
$884$		−	992.662i		−	1.12292i
$885$	−534.122	+	126.253i	−0.603527	+	0.142659i
$886$	−1132.15			−1.27782
$887$			280.139i			0.315828i	0.987453	+	0.157914i	$0.0504769\pi$
$887$			280.139i			0.315828i	−0.987453	+	0.157914i	$0.949523\pi$
$888$	53.3824	+	225.838i	0.0601153	+	0.254322i
$889$	−110.942			−0.124794
$890$			940.149i			1.05635i
$891$	−579.452	−	433.538i	−0.650339	−	0.486575i
$892$	620.439			0.695559
$893$		−	586.244i		−	0.656488i
$894$	775.930	−	183.410i	0.867931	−	0.205157i
$895$	188.186			0.210263
$896$		−	61.6339i		−	0.0687878i
$897$	−34.0815	−	144.184i	−0.0379950	−	0.160740i
$898$	−1439.94			−1.60350
$899$		−	318.791i		−	0.354606i
$900$	−635.894	+	318.409i	−0.706548	+	0.353788i
$901$	−1585.22			−1.75940
$902$			1558.81i			1.72818i
$903$	35.5110	−	8.39389i	0.0393255	−	0.00929556i
$904$	−38.4119			−0.0424910
$905$		−	63.0224i		−	0.0696380i
$906$	93.7249	+	396.510i	0.103449	+	0.437649i
$907$	1161.05			1.28009			0.640047	−	0.768335i	$-0.278915\pi$
$907$	1161.05			1.28009			0.640047	+	0.768335i	$0.278915\pi$
$908$			746.836i			0.822507i
$909$	−55.4121	−	110.663i	−0.0609594	−	0.121742i
$910$	−98.0495			−0.107747
$911$		−	1086.01i		−	1.19211i	−0.802945	−	0.596054i	$-0.796735\pi$
$911$		−	1086.01i		−	1.19211i	0.802945	−	0.596054i	$-0.203265\pi$
$912$	−1065.73	+	251.912i	−1.16857	+	0.276220i
$913$	1065.92			1.16749
$914$			1559.82i			1.70658i
$915$	56.6140	+	239.510i	0.0618733	+	0.261759i
$916$	31.1280			0.0339825
$917$			138.299i			0.150816i
$918$	1279.73	−	1069.93i	1.39405	−	1.16550i
$919$	−602.306			−0.655393			−0.327697	−	0.944783i	$-0.606272\pi$
$919$	−602.306			−0.655393			−0.327697	+	0.944783i	$0.606272\pi$
$920$			22.0799i			0.0239999i
$921$	−695.797	+	164.469i	−0.755480	+	0.178576i
$922$	1095.14			1.18778
$923$		−	1429.12i		−	1.54834i
$924$	−33.0152	−	139.673i	−0.0357307	−	0.151161i
$925$	−806.554			−0.871950
$926$			1862.93i			2.01180i
$927$	−922.472	+	461.906i	−0.995115	+	0.498281i
$928$	450.066			0.484985
$929$		−	221.269i		−	0.238180i	−0.992883	−	0.119090i	$-0.962002\pi$
$929$		−	221.269i		−	0.238180i	0.992883	−	0.119090i	$-0.0379977\pi$
$930$	770.662	−	182.165i	0.828669	−	0.195876i
$931$	−1296.33			−1.39240
$932$		−	1290.83i		−	1.38501i
$933$	−146.161	−	618.342i	−0.156656	−	0.662746i
$934$	82.0794			0.0878794
$935$		−	523.227i		−	0.559601i
$936$	68.8567	+	137.514i	0.0735649	+	0.146916i
$937$	1409.68			1.50446			0.752230	−	0.658901i	$-0.228978\pi$
$937$	1409.68			1.50446			0.752230	+	0.658901i	$0.228978\pi$
$938$			132.364i			0.141113i
$939$	−1443.09	+	341.111i	−1.53684	+	0.363271i
$940$	−272.906			−0.290325
$941$		−	12.9186i		−	0.0137286i	−0.999976	−	0.00686431i	$-0.997815\pi$
$941$		−	12.9186i		−	0.0137286i	0.999976	−	0.00686431i	$-0.00218500\pi$
$942$	−286.936	−	1213.90i	−0.304603	−	1.28864i
$943$	−285.878			−0.303158
$944$		−	884.289i		−	0.936747i
$945$	−56.3376	−	67.3849i	−0.0596165	−	0.0713068i
$946$	−271.279			−0.286765
$947$		−	185.226i		−	0.195592i	−0.995206	−	0.0977960i	$-0.968821\pi$
$947$		−	185.226i		−	0.195592i	0.995206	−	0.0977960i	$-0.0311793\pi$
$948$	−376.389	+	88.9688i	−0.397034	+	0.0938489i
$949$	755.959			0.796584
$950$			1378.44i			1.45099i
$951$	−319.766	−	1352.79i	−0.336242	−	1.42250i
$952$	41.0669			0.0431375
$953$			100.275i			0.105220i	0.998615	+	0.0526100i	$0.0167540\pi$
$953$			100.275i			0.105220i	−0.998615	+	0.0526100i	$0.983246\pi$
$954$	1768.99	−	885.781i	1.85429	−	0.928492i
$955$	−72.9536			−0.0763912
$956$		−	1587.11i		−	1.66016i
$957$	255.821	−	60.4697i	0.267316	−	0.0631867i
$958$	2416.45			2.52239
$959$			257.447i			0.268454i
$960$	154.467	+	653.485i	0.160904	+	0.680714i
$961$	95.5706			0.0994492
$962$			1405.03i			1.46053i
$963$	569.761	+	1137.87i	0.591653	+	1.18159i
$964$	−385.764			−0.400170
$965$			357.581i			0.370550i
$966$	48.0507	−	11.3580i	0.0497419	−	0.0117577i
$967$	163.698			0.169285			0.0846423	−	0.996411i	$-0.473025\pi$
$967$	163.698			0.169285			0.0846423	+	0.996411i	$0.473025\pi$
$968$		−	68.3279i		−	0.0705866i
$969$	−396.490	−	1677.38i	−0.409174	−	1.73104i
$970$	−948.988			−0.978338
$971$			1175.44i			1.21054i	0.796020	+	0.605271i	$0.206935\pi$
$971$			1175.44i			1.21054i	−0.796020	+	0.605271i	$0.793065\pi$
$972$	−442.591	+	1017.69i	−0.455341	+	1.04701i
$973$	41.2659			0.0424110
$974$		−	279.023i		−	0.286471i
$975$	−520.178	+	122.957i	−0.533516	+	0.126110i
$976$	−396.531			−0.406282
$977$			934.901i			0.956910i	0.878112	+	0.478455i	$0.158803\pi$
$977$			934.901i			0.956910i	−0.878112	+	0.478455i	$0.841197\pi$
$978$	199.661	+	844.679i	0.204152	+	0.863680i
$979$	−1034.34			−1.05652
$980$			603.461i			0.615776i
$981$	1637.28	−	819.827i	1.66899	−	0.835706i
$982$	−360.883			−0.367498
$983$			874.483i			0.889606i	0.895628	+	0.444803i	$0.146726\pi$
$983$			874.483i			0.889606i	−0.895628	+	0.444803i	$0.853274\pi$
$984$	288.787	−	68.2621i	0.293483	−	0.0693720i
$985$	963.233			0.977902
$986$			605.909i			0.614513i
$987$	17.4271	+	73.7266i	0.0176566	+	0.0746977i
$988$	1280.09			1.29564
$989$		−	49.7512i		−	0.0503045i
$990$	292.365	+	583.882i	0.295319	+	0.589780i
$991$	1154.08			1.16456			0.582282	−	0.812987i	$-0.302160\pi$
$991$	1154.08			1.16456			0.582282	+	0.812987i	$0.302160\pi$
$992$			1491.66i			1.50369i
$993$	−782.362	+	184.931i	−0.787877	+	0.186234i
$994$	476.266			0.479141
$995$			12.3001i			0.0123619i
$996$	−376.012	−	1590.74i	−0.377522	−	1.59713i
$997$	683.826			0.685884			0.342942	−	0.939357i	$-0.388577\pi$
$997$	683.826			0.685884			0.342942	+	0.939357i	$0.388577\pi$
$998$			2566.43i			2.57157i
$999$	−965.614	+	807.307i	−0.966581	+	0.808116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.3.b.a.47.12	yes	14
3.2	odd	2	inner	69.3.b.a.47.3	✓	14
4.3	odd	2		1104.3.g.b.737.2		14
12.11	even	2		1104.3.g.b.737.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.3.b.a.47.3	✓	14	3.2	odd	2	inner
69.3.b.a.47.12	yes	14	1.1	even	1	trivial
1104.3.g.b.737.1		14	12.11	even	2
1104.3.g.b.737.2		14	4.3	odd	2

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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	69.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.92693i q^{2} +(2.91955 - 0.690107i) q^{3} -4.56694 q^{4} +2.77451i q^{5} +(2.01990 + 8.54532i) q^{6} -1.17249 q^{7} -1.65938i q^{8} +(8.04750 - 4.02960i) q^{9} +O(q^{10})\)	\(q+2.92693i q^{2} +(2.91955 - 0.690107i) q^{3} -4.56694 q^{4} +2.77451i q^{5} +(2.01990 + 8.54532i) q^{6} -1.17249 q^{7} -1.65938i q^{8} +(8.04750 - 4.02960i) q^{9} -8.12081 q^{10} -8.93439i q^{11} +(-13.3334 + 3.15167i) q^{12} -10.2977 q^{13} -3.43179i q^{14} +(1.91471 + 8.10032i) q^{15} -13.4108 q^{16} -21.1076i q^{17} +(11.7944 + 23.5545i) q^{18} +27.2193 q^{19} -12.6710i q^{20} +(-3.42313 + 0.809141i) q^{21} +26.1504 q^{22} +4.79583i q^{23} +(-1.14515 - 4.84464i) q^{24} +17.3021 q^{25} -30.1405i q^{26} +(20.7142 - 17.3182i) q^{27} +5.35467 q^{28} +9.80746i q^{29} +(-23.7091 + 5.60423i) q^{30} -32.5049 q^{31} -45.8902i q^{32} +(-6.16568 - 26.0844i) q^{33} +61.7805 q^{34} -3.25308i q^{35} +(-36.7524 + 18.4029i) q^{36} -46.6160 q^{37} +79.6691i q^{38} +(-30.0645 + 7.10648i) q^{39} +4.60397 q^{40} +59.6097i q^{41} +(-2.36830 - 10.0193i) q^{42} -10.3738 q^{43} +40.8028i q^{44} +(11.1802 + 22.3279i) q^{45} -14.0371 q^{46} -21.5378i q^{47} +(-39.1536 + 9.25492i) q^{48} -47.6253 q^{49} +50.6420i q^{50} +(-14.5665 - 61.6246i) q^{51} +47.0287 q^{52} -75.1021i q^{53} +(50.6893 + 60.6291i) q^{54} +24.7886 q^{55} +1.94560i q^{56} +(79.4681 - 18.7842i) q^{57} -28.7058 q^{58} +65.9384i q^{59} +(-8.74436 - 36.9936i) q^{60} +29.5679 q^{61} -95.1398i q^{62} +(-9.43559 + 4.72465i) q^{63} +80.6740 q^{64} -28.5710i q^{65} +(76.3472 - 18.0465i) q^{66} -38.5701 q^{67} +96.3969i q^{68} +(3.30964 + 14.0017i) q^{69} +9.52154 q^{70} +138.781i q^{71} +(-6.68664 - 13.3539i) q^{72} -73.4107 q^{73} -136.442i q^{74} +(50.5142 - 11.9403i) q^{75} -124.309 q^{76} +10.4754i q^{77} +(-20.8002 - 87.9967i) q^{78} +28.2291 q^{79} -37.2085i q^{80} +(48.5247 - 64.8564i) q^{81} -174.474 q^{82} +119.305i q^{83} +(15.6332 - 3.69529i) q^{84} +58.5632 q^{85} -30.3635i q^{86} +(6.76820 + 28.6333i) q^{87} -14.8256 q^{88} -115.770i q^{89} +(-65.3523 + 32.7236i) q^{90} +12.0739 q^{91} -21.9023i q^{92} +(-94.8997 + 22.4319i) q^{93} +63.0397 q^{94} +75.5203i q^{95} +(-31.6691 - 133.978i) q^{96} +116.859 q^{97} -139.396i q^{98} +(-36.0020 - 71.8995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} - 24 q^{4} + 11 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 14 * q - 4 * q^3 - 24 * q^4 + 11 * q^6 - 4 * q^7 - 8 * q^9	\( 14 q - 4 q^{3} - 24 q^{4} + 11 q^{6} - 4 q^{7} - 8 q^{9} - 8 q^{10} + 19 q^{12} - 14 q^{15} + 72 q^{16} - 31 q^{18} + 8 q^{19} - 2 q^{21} - 84 q^{22} - 44 q^{24} + 38 q^{25} + 62 q^{27} + 76 q^{28} + 62 q^{30} - 144 q^{31} + 90 q^{33} - 68 q^{34} + 3 q^{36} + 48 q^{37} - 78 q^{39} + 120 q^{40} - 76 q^{42} - 48 q^{43} - 18 q^{45} - 317 q^{48} - 30 q^{49} + 18 q^{51} - 6 q^{52} + 312 q^{54} + 232 q^{55} + 76 q^{57} + 66 q^{58} - 36 q^{60} - 140 q^{61} - 206 q^{63} - 346 q^{64} + 398 q^{66} + 204 q^{67} + 80 q^{70} + 384 q^{72} - 224 q^{73} - 80 q^{75} + 100 q^{76} - 341 q^{78} - 344 q^{79} - 232 q^{81} - 62 q^{82} - 330 q^{84} + 480 q^{85} + 86 q^{87} + 436 q^{88} - 514 q^{90} - 172 q^{91} + 62 q^{93} + 514 q^{94} + 609 q^{96} - 24 q^{97} + 234 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 - 24 * q^4 + 11 * q^6 - 4 * q^7 - 8 * q^9 - 8 * q^10 + 19 * q^12 - 14 * q^15 + 72 * q^16 - 31 * q^18 + 8 * q^19 - 2 * q^21 - 84 * q^22 - 44 * q^24 + 38 * q^25 + 62 * q^27 + 76 * q^28 + 62 * q^30 - 144 * q^31 + 90 * q^33 - 68 * q^34 + 3 * q^36 + 48 * q^37 - 78 * q^39 + 120 * q^40 - 76 * q^42 - 48 * q^43 - 18 * q^45 - 317 * q^48 - 30 * q^49 + 18 * q^51 - 6 * q^52 + 312 * q^54 + 232 * q^55 + 76 * q^57 + 66 * q^58 - 36 * q^60 - 140 * q^61 - 206 * q^63 - 346 * q^64 + 398 * q^66 + 204 * q^67 + 80 * q^70 + 384 * q^72 - 224 * q^73 - 80 * q^75 + 100 * q^76 - 341 * q^78 - 344 * q^79 - 232 * q^81 - 62 * q^82 - 330 * q^84 + 480 * q^85 + 86 * q^87 + 436 * q^88 - 514 * q^90 - 172 * q^91 + 62 * q^93 + 514 * q^94 + 609 * q^96 - 24 * q^97 + 234 * q^99

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