LMFDB - Embedded newform 69.3.b.a.47.13

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			47.13
Root			$3.07980i$ of defining polynomial
Character	$\chi$	$=$	69.47
Dual form			69.3.b.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.07980i q^{2} +(-0.479940 + 2.96136i) q^{3} -5.48516 q^{4} -0.529218i q^{5} +(-9.12040 - 1.47812i) q^{6} +5.42850 q^{7} -4.57400i q^{8} +(-8.53932 - 2.84255i) q^{9} +O(q^{10})$	\(q+3.07980i q^{2} +(-0.479940 + 2.96136i) q^{3} -5.48516 q^{4} -0.529218i q^{5} +(-9.12040 - 1.47812i) q^{6} +5.42850 q^{7} -4.57400i q^{8} +(-8.53932 - 2.84255i) q^{9} +1.62989 q^{10} -6.59782i q^{11} +(2.63255 - 16.2435i) q^{12} +12.8269 q^{13} +16.7187i q^{14} +(1.56721 + 0.253993i) q^{15} -7.85365 q^{16} +30.3572i q^{17} +(8.75448 - 26.2994i) q^{18} -2.33061 q^{19} +2.90285i q^{20} +(-2.60536 + 16.0758i) q^{21} +20.3200 q^{22} -4.79583i q^{23} +(13.5453 + 2.19524i) q^{24} +24.7199 q^{25} +39.5041i q^{26} +(12.5162 - 23.9237i) q^{27} -29.7762 q^{28} -12.8345i q^{29} +(-0.782247 + 4.82668i) q^{30} +13.8659 q^{31} -42.4837i q^{32} +(19.5385 + 3.16656i) q^{33} -93.4941 q^{34} -2.87286i q^{35} +(46.8395 + 15.5918i) q^{36} +45.7562 q^{37} -7.17779i q^{38} +(-6.15612 + 37.9849i) q^{39} -2.42064 q^{40} -60.7229i q^{41} +(-49.5101 - 8.02397i) q^{42} -70.9391 q^{43} +36.1901i q^{44} +(-1.50433 + 4.51916i) q^{45} +14.7702 q^{46} -66.7279i q^{47} +(3.76928 - 23.2575i) q^{48} -19.5313 q^{49} +76.1324i q^{50} +(-89.8986 - 14.5696i) q^{51} -70.3573 q^{52} +24.9540i q^{53} +(73.6803 + 38.5473i) q^{54} -3.49169 q^{55} -24.8300i q^{56} +(1.11855 - 6.90176i) q^{57} +39.5277 q^{58} +42.0542i q^{59} +(-8.59638 - 1.39319i) q^{60} +94.7404 q^{61} +42.7042i q^{62} +(-46.3557 - 15.4308i) q^{63} +99.4265 q^{64} -6.78820i q^{65} +(-9.75236 + 60.1747i) q^{66} +55.1537 q^{67} -166.514i q^{68} +(14.2022 + 2.30171i) q^{69} +8.84784 q^{70} -4.00358i q^{71} +(-13.0018 + 39.0588i) q^{72} -89.8344 q^{73} +140.920i q^{74} +(-11.8641 + 73.2046i) q^{75} +12.7837 q^{76} -35.8163i q^{77} +(-116.986 - 18.9596i) q^{78} -70.5809 q^{79} +4.15630i q^{80} +(64.8398 + 48.5469i) q^{81} +187.014 q^{82} -43.8033i q^{83} +(14.2908 - 88.1781i) q^{84} +16.0656 q^{85} -218.478i q^{86} +(38.0076 + 6.15979i) q^{87} -30.1784 q^{88} -95.2462i q^{89} +(-13.9181 - 4.63303i) q^{90} +69.6306 q^{91} +26.3059i q^{92} +(-6.65480 + 41.0620i) q^{93} +205.508 q^{94} +1.23340i q^{95} +(125.809 + 20.3896i) q^{96} -43.0190 q^{97} -60.1526i q^{98} +(-18.7546 + 56.3409i) 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 $

$2$			3.07980i			1.53990i	0.638105	+	0.769950i	$0.279719\pi$
$2$			3.07980i			1.53990i	−0.638105	+	0.769950i	$0.720281\pi$
$3$	−0.479940	+	2.96136i	−0.159980	+	0.987120i
$3$	−0.479940	+	2.96136i	−0.159980	+	0.987120i
$4$	−5.48516			−1.37129
$5$		−	0.529218i		−	0.105844i	−0.998599	−	0.0529218i	$-0.983147\pi$
$5$		−	0.529218i		−	0.105844i	0.998599	−	0.0529218i	$-0.0168534\pi$
$6$	−9.12040	−	1.47812i	−1.52007	−	0.246353i
$7$	5.42850			0.775501			0.387750	−	0.921764i	$-0.373252\pi$
$7$	5.42850			0.775501			0.387750	+	0.921764i	$0.373252\pi$
$8$		−	4.57400i		−	0.571750i
$9$	−8.53932	−	2.84255i	−0.948813	−	0.315839i
$10$	1.62989			0.162989
$11$		−	6.59782i		−	0.599802i	−0.953970	−	0.299901i	$-0.903046\pi$
$11$		−	6.59782i		−	0.599802i	0.953970	−	0.299901i	$-0.0969536\pi$
$12$	2.63255	−	16.2435i	0.219379	−	1.35363i
$13$	12.8269			0.986681			0.493340	−	0.869836i	$-0.335776\pi$
$13$	12.8269			0.986681			0.493340	+	0.869836i	$0.335776\pi$
$14$			16.7187i			1.19419i
$15$	1.56721	+	0.253993i	0.104480	+	0.0169329i
$16$	−7.85365			−0.490853
$17$			30.3572i			1.78572i	0.450337	+	0.892859i	$0.351304\pi$
$17$			30.3572i			1.78572i	−0.450337	+	0.892859i	$0.648696\pi$
$18$	8.75448	−	26.2994i	0.486360	−	1.46108i
$19$	−2.33061			−0.122663			−0.0613317	−	0.998117i	$-0.519535\pi$
$19$	−2.33061			−0.122663			−0.0613317	+	0.998117i	$0.519535\pi$
$20$			2.90285i			0.145142i
$21$	−2.60536	+	16.0758i	−0.124065	+	0.765512i
$22$	20.3200			0.923635
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	13.5453	+	2.19524i	0.564386	+	0.0914685i
$25$	24.7199			0.988797
$26$			39.5041i			1.51939i
$27$	12.5162	−	23.9237i	0.463562	−	0.886064i
$28$	−29.7762			−1.06344
$29$		−	12.8345i		−	0.442569i	−0.975209	−	0.221285i	$-0.928975\pi$
$29$		−	12.8345i		−	0.442569i	0.975209	−	0.221285i	$-0.0710249\pi$
$30$	−0.782247	+	4.82668i	−0.0260749	+	0.160889i
$31$	13.8659			0.447287			0.223644	−	0.974671i	$-0.428205\pi$
$31$	13.8659			0.447287			0.223644	+	0.974671i	$0.428205\pi$
$32$		−	42.4837i		−	1.32761i
$33$	19.5385	+	3.16656i	0.592077	+	0.0959563i
$34$	−93.4941			−2.74983
$35$		−	2.87286i		−	0.0820818i
$36$	46.8395	+	15.5918i	1.30110	+	0.433107i
$37$	45.7562			1.23665			0.618327	−	0.785921i	$-0.287811\pi$
$37$	45.7562			1.23665			0.618327	+	0.785921i	$0.287811\pi$
$38$		−	7.17779i		−	0.188889i
$39$	−6.15612	+	37.9849i	−0.157849	+	0.973973i
$40$	−2.42064			−0.0605161
$41$		−	60.7229i		−	1.48105i	−0.672031	−	0.740523i	$-0.734578\pi$
$41$		−	60.7229i		−	1.48105i	0.672031	−	0.740523i	$-0.265422\pi$
$42$	−49.5101	−	8.02397i	−1.17881	−	0.191047i
$43$	−70.9391			−1.64975			−0.824873	−	0.565318i	$-0.808754\pi$
$43$	−70.9391			−1.64975			−0.824873	+	0.565318i	$0.808754\pi$
$44$			36.1901i			0.822502i
$45$	−1.50433	+	4.51916i	−0.0334296	+	0.100426i
$46$	14.7702			0.321091
$47$		−	66.7279i		−	1.41974i	−0.704331	−	0.709871i	$-0.748753\pi$
$47$		−	66.7279i		−	1.41974i	0.704331	−	0.709871i	$-0.251247\pi$
$48$	3.76928	−	23.2575i	0.0785267	−	0.484531i
$49$	−19.5313			−0.398599
$50$			76.1324i			1.52265i
$51$	−89.8986	−	14.5696i	−1.76272	−	0.285679i
$52$	−70.3573			−1.35303
$53$			24.9540i			0.470831i	0.971895	+	0.235415i	$0.0756451\pi$
$53$			24.9540i			0.470831i	−0.971895	+	0.235415i	$0.924355\pi$
$54$	73.6803	+	38.5473i	1.36445	+	0.713839i
$55$	−3.49169			−0.0634852
$56$		−	24.8300i		−	0.443392i
$57$	1.11855	−	6.90176i	0.0196237	−	0.121084i
$58$	39.5277			0.681512
$59$			42.0542i			0.712784i	0.934337	+	0.356392i	$0.115993\pi$
$59$			42.0542i			0.712784i	−0.934337	+	0.356392i	$0.884007\pi$
$60$	−8.59638	−	1.39319i	−0.143273	−	0.0232199i
$61$	94.7404			1.55312			0.776561	−	0.630043i	$-0.216963\pi$
$61$	94.7404			1.55312			0.776561	+	0.630043i	$0.216963\pi$
$62$			42.7042i			0.688778i
$63$	−46.3557	−	15.4308i	−0.735805	−	0.244933i
$64$	99.4265			1.55354
$65$		−	6.78820i		−	0.104434i
$66$	−9.75236	+	60.1747i	−0.147763	+	0.911738i
$67$	55.1537			0.823190			0.411595	−	0.911367i	$-0.364972\pi$
$67$	55.1537			0.823190			0.411595	+	0.911367i	$0.364972\pi$
$68$		−	166.514i		−	2.44874i
$69$	14.2022	+	2.30171i	0.205829	+	0.0333581i
$70$	8.84784			0.126398
$71$		−	4.00358i		−	0.0563884i	−0.999602	−	0.0281942i	$-0.991024\pi$
$71$		−	4.00358i		−	0.0563884i	0.999602	−	0.0281942i	$-0.00897568\pi$
$72$	−13.0018	+	39.0588i	−0.180581	+	0.542483i
$73$	−89.8344			−1.23061			−0.615304	−	0.788290i	$-0.710967\pi$
$73$	−89.8344			−1.23061			−0.615304	+	0.788290i	$0.710967\pi$
$74$			140.920i			1.90432i
$75$	−11.8641	+	73.2046i	−0.158188	+	0.976062i
$76$	12.7837			0.168207
$77$		−	35.8163i		−	0.465147i
$78$	−116.986	−	18.9596i	−1.49982	−	0.243072i
$79$	−70.5809			−0.893429			−0.446715	−	0.894676i	$-0.647406\pi$
$79$	−70.5809			−0.893429			−0.446715	+	0.894676i	$0.647406\pi$
$80$			4.15630i			0.0519537i
$81$	64.8398	+	48.5469i	0.800491	+	0.599344i
$82$	187.014			2.28066
$83$		−	43.8033i		−	0.527750i	−0.964557	−	0.263875i	$-0.914999\pi$
$83$		−	43.8033i		−	0.527750i	0.964557	−	0.263875i	$-0.0850007\pi$
$84$	14.2908	−	88.1781i	0.170129	−	1.04974i
$85$	16.0656			0.189007
$86$		−	218.478i		−	2.54044i
$87$	38.0076	+	6.15979i	0.436869	+	0.0708022i
$88$	−30.1784			−0.342936
$89$		−	95.2462i		−	1.07018i	−0.844795	−	0.535091i	$-0.820277\pi$
$89$		−	95.2462i		−	1.07018i	0.844795	−	0.535091i	$-0.179723\pi$
$90$	−13.9181	−	4.63303i	−0.154646	−	0.0514781i
$91$	69.6306			0.765172
$92$			26.3059i			0.285934i
$93$	−6.65480	+	41.0620i	−0.0715570	+	0.441526i
$94$	205.508			2.18626
$95$			1.23340i			0.0129831i
$96$	125.809	+	20.3896i	1.31052	+	0.212392i
$97$	−43.0190			−0.443495			−0.221747	−	0.975104i	$-0.571176\pi$
$97$	−43.0190			−0.443495			−0.221747	+	0.975104i	$0.571176\pi$
$98$		−	60.1526i		−	0.613802i
$99$	−18.7546	+	56.3409i	−0.189441	+	0.569100i
$100$	−135.593			−1.35593
$101$			125.747i			1.24502i	0.782614	+	0.622508i	$0.213886\pi$
$101$			125.747i			1.24502i	−0.782614	+	0.622508i	$0.786114\pi$
$102$	44.8715	−	276.870i	0.439917	−	2.71441i
$103$	−166.596			−1.61743			−0.808716	−	0.588199i	$-0.799837\pi$
$103$	−166.596			−1.61743			−0.808716	+	0.588199i	$0.799837\pi$
$104$		−	58.6700i		−	0.564134i
$105$	8.50759	+	1.37880i	0.0810246	+	0.0131314i
$106$	−76.8534			−0.725032
$107$			75.0930i			0.701804i	0.936412	+	0.350902i	$0.114125\pi$
$107$			75.0930i			0.701804i	−0.936412	+	0.350902i	$0.885875\pi$
$108$	−68.6532	+	131.226i	−0.635678	+	1.21505i
$109$	−60.4745			−0.554812			−0.277406	−	0.960753i	$-0.589475\pi$
$109$	−60.4745			−0.554812			−0.277406	+	0.960753i	$0.589475\pi$
$110$		−	10.7537i		−	0.0977609i
$111$	−21.9602	+	135.501i	−0.197840	+	1.22073i
$112$	−42.6336			−0.380657
$113$			49.0885i			0.434412i	0.976126	+	0.217206i	$0.0696943\pi$
$113$			49.0885i			0.434412i	−0.976126	+	0.217206i	$0.930306\pi$
$114$	21.2560	+	3.44491i	0.186456	+	0.0302185i
$115$	−2.53804			−0.0220699
$116$			70.3993i			0.606891i
$117$	−109.533	−	36.4610i	−0.936176	−	0.311632i
$118$	−129.519			−1.09762
$119$			164.794i			1.38483i
$120$	1.16176	−	7.16840i	0.00968136	−	0.0597366i
$121$	77.4688			0.640238
$122$			291.781i			2.39165i
$123$	179.822	+	29.1433i	1.46197	+	0.236938i
$124$	−76.0567			−0.613361
$125$		−	26.3127i		−	0.210502i
$126$	47.5238	−	142.766i	0.377173	−	1.13307i
$127$	−126.296			−0.994454			−0.497227	−	0.867620i	$-0.665648\pi$
$127$	−126.296			−0.994454			−0.497227	+	0.867620i	$0.665648\pi$
$128$			136.279i			1.06468i
$129$	34.0465	−	210.076i	0.263926	−	1.62850i
$130$	20.9063			0.160818
$131$		−	160.974i		−	1.22881i	−0.788990	−	0.614406i	$-0.789396\pi$
$131$		−	160.974i		−	1.22881i	0.788990	−	0.614406i	$-0.210604\pi$
$132$	−107.172	−	17.3691i	−0.811909	−	0.131584i
$133$	−12.6517			−0.0951256
$134$			169.862i			1.26763i
$135$	−12.6609	−	6.62379i	−0.0937843	−	0.0490651i
$136$	138.854			1.02098
$137$		−	43.4514i		−	0.317164i	−0.987346	−	0.158582i	$-0.949308\pi$
$137$		−	43.4514i		−	0.317164i	0.987346	−	0.158582i	$-0.0506921\pi$
$138$	−7.08881	+	43.7399i	−0.0513682	+	0.316956i
$139$	13.3168			0.0958042			0.0479021	−	0.998852i	$-0.484746\pi$
$139$	13.3168			0.0958042			0.0479021	+	0.998852i	$0.484746\pi$
$140$			15.7581i			0.112558i
$141$	197.605	+	32.0254i	1.40146	+	0.227130i
$142$	12.3302			0.0868325
$143$		−	84.6293i		−	0.591813i
$144$	67.0648	+	22.3244i	0.465728	+	0.155031i
$145$	−6.79225			−0.0468431
$146$		−	276.672i		−	1.89501i
$147$	9.37387	−	57.8393i	0.0637678	−	0.393465i
$148$	−250.980			−1.69581
$149$			115.676i			0.776347i	0.921586	+	0.388174i	$0.126894\pi$
$149$			115.676i			0.776347i	−0.921586	+	0.388174i	$0.873106\pi$
$150$	−225.456	−	36.5390i	−1.50304	−	0.243593i
$151$	−260.182			−1.72306			−0.861530	−	0.507707i	$-0.830493\pi$
$151$	−260.182			−1.72306			−0.861530	+	0.507707i	$0.830493\pi$
$152$			10.6602i			0.0701328i
$153$	86.2919	−	259.230i	0.563999	−	1.69431i
$154$	110.307			0.716279
$155$		−	7.33809i		−	0.0473425i
$156$	33.7673	−	208.353i	0.216457	−	1.33560i
$157$	278.139			1.77158			0.885792	−	0.464082i	$-0.153616\pi$
$157$	278.139			1.77158			0.885792	+	0.464082i	$0.153616\pi$
$158$		−	217.375i		−	1.37579i
$159$	−73.8979	−	11.9764i	−0.464767	−	0.0753235i
$160$	−22.4831			−0.140520
$161$		−	26.0342i		−	0.161703i
$162$	−149.515	+	199.694i	−0.922930	+	1.23268i
$163$	−32.7771			−0.201087			−0.100543	−	0.994933i	$-0.532058\pi$
$163$	−32.7771			−0.201087			−0.100543	+	0.994933i	$0.532058\pi$
$164$			333.075i			2.03094i
$165$	1.67580	−	10.3401i	0.0101564	−	0.0626675i
$166$	134.905			0.812682
$167$		−	258.078i		−	1.54538i	−0.634785	−	0.772689i	$-0.718911\pi$
$167$		−	258.078i		−	1.54538i	0.634785	−	0.772689i	$-0.281089\pi$
$168$	73.5305	+	11.9169i	0.437681	+	0.0709339i
$169$	−4.47186			−0.0264607
$170$			49.4788i			0.291052i
$171$	19.9018	+	6.62486i	0.116385	+	0.0387419i
$172$	389.112			2.26228
$173$		−	66.4001i		−	0.383816i	−0.981413	−	0.191908i	$-0.938533\pi$
$173$		−	66.4001i		−	0.383816i	0.981413	−	0.191908i	$-0.0614674\pi$
$174$	−18.9709	+	117.056i	−0.109028	+	0.672734i
$175$	134.192			0.766813
$176$			51.8170i			0.294415i
$177$	−124.538	−	20.1835i	−0.703603	−	0.114031i
$178$	293.339			1.64797
$179$		−	65.2306i		−	0.364417i	−0.983260	−	0.182208i	$-0.941675\pi$
$179$		−	65.2306i		−	0.364417i	0.983260	−	0.182208i	$-0.0583246\pi$
$180$	8.25149	−	24.7883i	0.0458416	−	0.137713i
$181$	−105.174			−0.581071			−0.290535	−	0.956864i	$-0.593833\pi$
$181$	−105.174			−0.581071			−0.290535	+	0.956864i	$0.593833\pi$
$182$			214.448i			1.17829i
$183$	−45.4697	+	280.560i	−0.248468	+	1.53312i
$184$	−21.9361			−0.119218
$185$		−	24.2150i		−	0.130892i
$186$	−126.463	−	20.4955i	−0.679906	−	0.110191i
$187$	200.291			1.07108
$188$			366.013i			1.94688i
$189$	67.9441	−	129.870i	0.359493	−	0.687144i
$190$	−3.79862			−0.0199927
$191$			108.804i			0.569655i	0.958579	+	0.284828i	$0.0919363\pi$
$191$			108.804i			0.569655i	−0.958579	+	0.284828i	$0.908064\pi$
$192$	−47.7188	+	294.438i	−0.248535	+	1.53353i
$193$	198.159			1.02673			0.513364	−	0.858171i	$-0.328399\pi$
$193$	198.159			1.02673			0.513364	+	0.858171i	$0.328399\pi$
$194$		−	132.490i		−	0.682937i
$195$	20.1023	+	3.25793i	0.103089	+	0.0167073i
$196$	107.133			0.546595
$197$			149.112i			0.756914i	0.925619	+	0.378457i	$0.123545\pi$
$197$			149.112i			0.756914i	−0.925619	+	0.378457i	$0.876455\pi$
$198$	−173.519	−	57.7605i	−0.876356	−	0.291720i
$199$	−21.6726			−0.108908			−0.0544538	−	0.998516i	$-0.517342\pi$
$199$	−21.6726			−0.108908			−0.0544538	+	0.998516i	$0.517342\pi$
$200$		−	113.069i		−	0.565344i
$201$	−26.4705	+	163.330i	−0.131694	+	0.812587i
$202$	−387.274			−1.91720
$203$		−	69.6722i		−	0.343213i
$204$	493.108	+	79.9168i	2.41720	+	0.391749i
$205$	−32.1357			−0.156759
$206$		−	513.081i		−	2.49068i
$207$	−13.6324	+	40.9531i	−0.0658570	+	0.197841i
$208$	−100.738			−0.484316
$209$			15.3769i			0.0735738i
$210$	−4.24643	+	26.2017i	−0.0202211	+	0.124770i
$211$	43.8273			0.207712			0.103856	−	0.994592i	$-0.466882\pi$
$211$	43.8273			0.207712			0.103856	+	0.994592i	$0.466882\pi$
$212$		−	136.877i		−	0.645646i
$213$	11.8560	+	1.92148i	0.0556621	+	0.00902102i
$214$	−231.271			−1.08071
$215$			37.5423i			0.174615i
$216$	−109.427	−	57.2489i	−0.506607	−	0.265041i
$217$	75.2712			0.346872
$218$		−	186.249i		−	0.854354i
$219$	43.1151	−	266.032i	0.196873	−	1.21476i
$220$	19.1525			0.0870567
$221$			389.387i			1.76193i
$222$	−417.315	−	67.6331i	−1.87980	−	0.304654i
$223$	249.480			1.11875			0.559373	−	0.828916i	$-0.311042\pi$
$223$	249.480			1.11875			0.559373	+	0.828916i	$0.311042\pi$
$224$		−	230.623i		−	1.02957i
$225$	−211.091	−	70.2677i	−0.938183	−	0.312301i
$226$	−151.183			−0.668950
$227$			56.5589i			0.249158i	0.992210	+	0.124579i	$0.0397580\pi$
$227$			56.5589i			0.249158i	−0.992210	+	0.124579i	$0.960242\pi$
$228$	−6.13543	+	37.8573i	−0.0269098	+	0.166041i
$229$	−421.300			−1.83974			−0.919868	−	0.392228i	$-0.871704\pi$
$229$	−421.300			−1.83974			−0.919868	+	0.392228i	$0.871704\pi$
$230$		−	7.81666i		−	0.0339855i
$231$	106.065	+	17.1897i	0.459156	+	0.0744142i
$232$	−58.7050			−0.253039
$233$			238.395i			1.02315i	0.859238	+	0.511576i	$0.170938\pi$
$233$			238.395i			1.02315i	−0.859238	+	0.511576i	$0.829062\pi$
$234$	112.292	−	337.338i	0.479882	−	1.44162i
$235$	−35.3136			−0.150271
$236$		−	230.674i		−	0.977433i
$237$	33.8746	−	209.016i	0.142931	−	0.881922i
$238$	−507.533			−2.13249
$239$		−	379.849i		−	1.58933i	−0.607050	−	0.794664i	$-0.707647\pi$
$239$		−	379.849i		−	1.58933i	0.607050	−	0.794664i	$-0.292353\pi$
$240$	−12.3083	−	1.99477i	−0.0512846	−	0.00831156i
$241$	286.397			1.18837			0.594184	−	0.804329i	$-0.297475\pi$
$241$	286.397			1.18837			0.594184	+	0.804329i	$0.297475\pi$
$242$			238.588i			0.985902i
$243$	−174.884	+	168.714i	−0.719687	+	0.694298i
$244$	−519.666			−2.12978
$245$			10.3363i			0.0421891i
$246$	−89.7556	+	553.817i	−0.364860	+	2.25129i
$247$	−29.8943			−0.121030
$248$		−	63.4226i		−	0.255736i
$249$	129.717	+	21.0229i	0.520953	+	0.0844295i
$250$	81.0378			0.324151
$251$			112.370i			0.447689i	0.974625	+	0.223844i	$0.0718607\pi$
$251$			112.370i			0.447689i	−0.974625	+	0.223844i	$0.928139\pi$
$252$	254.269	+	84.6404i	1.00900	+	0.335875i
$253$	−31.6420			−0.125067
$254$		−	388.965i		−	1.53136i
$255$	−7.71052	+	47.5760i	−0.0302373	+	0.186572i
$256$	−22.0059			−0.0859604
$257$		−	19.5154i		−	0.0759355i	−0.999279	−	0.0379677i	$-0.987912\pi$
$257$		−	19.5154i		−	0.0759355i	0.999279	−	0.0379677i	$-0.0120884\pi$
$258$	646.993	+	104.856i	2.50772	+	0.406420i
$259$	248.388			0.959026
$260$			37.2344i			0.143209i
$261$	−36.4827	+	109.598i	−0.139781	+	0.419915i
$262$	495.768			1.89225
$263$			333.847i			1.26938i	0.772766	+	0.634691i	$0.218873\pi$
$263$			333.847i			1.26938i	−0.772766	+	0.634691i	$0.781127\pi$
$264$	14.4838	−	89.3691i	0.0548630	−	0.338520i
$265$	13.2061			0.0498345
$266$		−	38.9647i		−	0.146484i
$267$	282.058	+	45.7124i	1.05640	+	0.171208i
$268$	−302.527			−1.12883
$269$			83.8115i			0.311567i	0.987791	+	0.155784i	$0.0497902\pi$
$269$			83.8115i			0.311567i	−0.987791	+	0.155784i	$0.950210\pi$
$270$	20.3999	−	38.9930i	0.0755553	−	0.144418i
$271$	−215.484			−0.795142			−0.397571	−	0.917571i	$-0.630147\pi$
$271$	−215.484			−0.795142			−0.397571	+	0.917571i	$0.630147\pi$
$272$		−	238.415i		−	0.876526i
$273$	−33.4185	+	206.201i	−0.122412	+	0.755317i
$274$	133.822			0.488400
$275$		−	163.098i		−	0.593082i
$276$	−77.9013	−	12.6253i	−0.282251	−	0.0457437i
$277$	97.8788			0.353353			0.176676	−	0.984269i	$-0.443465\pi$
$277$	97.8788			0.353353			0.176676	+	0.984269i	$0.443465\pi$
$278$			41.0130i			0.147529i
$279$	−118.405	−	39.4146i	−0.424392	−	0.141271i
$280$	−13.1405			−0.0469302
$281$			467.515i			1.66375i	0.554959	+	0.831877i	$0.312734\pi$
$281$			467.515i			1.66375i	−0.554959	+	0.831877i	$0.687266\pi$
$282$	−98.6317	+	608.585i	−0.349758	+	2.15810i
$283$	−25.1405			−0.0888357			−0.0444179	−	0.999013i	$-0.514143\pi$
$283$	−25.1405			−0.0888357			−0.0444179	+	0.999013i	$0.514143\pi$
$284$			21.9603i			0.0773249i
$285$	−3.65254	−	0.591957i	−0.0128159	−	0.00207704i
$286$	260.641			0.911333
$287$		−	329.635i		−	1.14855i
$288$	−120.762	+	362.781i	−0.419312	+	1.25966i
$289$	−632.559			−2.18879
$290$		−	20.9188i		−	0.0721337i
$291$	20.6465	−	127.395i	0.0709503	−	0.437783i
$292$	492.756			1.68752
$293$			200.595i			0.684625i	0.939586	+	0.342313i	$0.111210\pi$
$293$			200.595i			0.684625i	−0.939586	+	0.342313i	$0.888790\pi$
$294$	178.134	+	28.8696i	0.605896	+	0.0981960i
$295$	22.2559			0.0754436
$296$		−	209.289i		−	0.707057i
$297$	−157.845	−	82.5795i	−0.531463	−	0.278045i
$298$	−356.258			−1.19550
$299$		−	61.5154i		−	0.205737i
$300$	65.0764	−	401.539i	0.216921	−	1.33846i
$301$	−385.093			−1.27938
$302$		−	801.308i		−	2.65334i
$303$	−372.381	−	60.3508i	−1.22898	−	0.199177i
$304$	18.3038			0.0602098
$305$		−	50.1383i		−	0.164388i
$306$	798.375	+	265.762i	2.60907	+	0.868502i
$307$	346.163			1.12757			0.563784	−	0.825922i	$-0.309345\pi$
$307$	346.163			1.12757			0.563784	+	0.825922i	$0.309345\pi$
$308$			196.458i			0.637851i
$309$	79.9559	−	493.350i	0.258757	−	1.59660i
$310$	22.5998			0.0729027
$311$		−	22.0301i		−	0.0708362i	−0.999373	−	0.0354181i	$-0.988724\pi$
$311$		−	22.0301i		−	0.0708362i	0.999373	−	0.0354181i	$-0.0112763\pi$
$312$	173.743	+	28.1581i	0.556868	+	0.0902502i
$313$	544.363			1.73918			0.869589	−	0.493775i	$-0.164384\pi$
$313$	544.363			1.73918			0.869589	+	0.493775i	$0.164384\pi$
$314$			856.612i			2.72806i
$315$	−8.16626	+	24.5323i	−0.0259246	+	0.0778803i
$316$	387.148			1.22515
$317$		−	73.3279i		−	0.231318i	−0.993289	−	0.115659i	$-0.963102\pi$
$317$		−	73.3279i		−	0.231318i	0.993289	−	0.115659i	$-0.0368980\pi$
$318$	36.8850	−	227.591i	0.115991	−	0.715694i
$319$	−84.6797			−0.265454
$320$		−	52.6183i		−	0.164432i
$321$	−222.377	−	36.0401i	−0.692765	−	0.112275i
$322$	80.1801			0.249006
$323$		−	70.7506i		−	0.219042i
$324$	−355.657	−	266.287i	−1.09771	−	0.821875i
$325$	317.079			0.975627
$326$		−	100.947i		−	0.309653i
$327$	29.0241	−	179.087i	0.0887588	−	0.547666i
$328$	−277.746			−0.846788
$329$		−	362.233i		−	1.10101i
$330$	31.8456	+	5.16113i	0.0965017	+	0.0156398i
$331$	375.024			1.13300			0.566501	−	0.824061i	$-0.308297\pi$
$331$	375.024			1.13300			0.566501	+	0.824061i	$0.308297\pi$
$332$			240.268i			0.723699i
$333$	−390.727	−	130.064i	−1.17335	−	0.390584i
$334$	794.829			2.37973
$335$		−	29.1884i		−	0.0871294i
$336$	20.4616	−	126.253i	0.0608975	−	0.375754i
$337$	−310.109			−0.920206			−0.460103	−	0.887866i	$-0.652187\pi$
$337$	−310.109			−0.920206			−0.460103	+	0.887866i	$0.652187\pi$
$338$		−	13.7724i		−	0.0407468i
$339$	−145.369	−	23.5595i	−0.428816	−	0.0694972i
$340$	−88.1223			−0.259183
$341$		−	91.4848i		−	0.268284i
$342$	−20.4032	+	61.2935i	−0.0596586	+	0.179221i
$343$	−372.023			−1.08461
$344$			324.475i			0.943242i
$345$	1.21811	−	7.51606i	0.00353075	−	0.0217857i
$346$	204.499			0.591037
$347$			495.035i			1.42662i	0.700851	+	0.713308i	$0.252804\pi$
$347$			495.035i			1.42662i	−0.700851	+	0.713308i	$0.747196\pi$
$348$	−208.478	−	33.7874i	−0.599074	−	0.0970904i
$349$	107.856			0.309042			0.154521	−	0.987989i	$-0.450617\pi$
$349$	107.856			0.309042			0.154521	+	0.987989i	$0.450617\pi$
$350$			413.285i			1.18081i
$351$	160.543	−	306.866i	0.457388	−	0.874263i
$352$	−280.300			−0.796306
$353$		−	362.638i		−	1.02730i	−0.857999	−	0.513651i	$-0.828293\pi$
$353$		−	362.638i		−	1.02730i	0.857999	−	0.513651i	$-0.171707\pi$
$354$	62.1612	−	383.551i	0.175596	−	1.08348i
$355$	−2.11877			−0.00596835
$356$			522.441i			1.46753i
$357$	−488.015	−	79.0913i	−1.36699	−	0.221544i
$358$	200.897			0.561165
$359$			175.820i			0.489749i	0.969555	+	0.244874i	$0.0787467\pi$
$359$			175.820i			0.489749i	−0.969555	+	0.244874i	$0.921253\pi$
$360$	20.6706	+	6.88080i	0.0574184	+	0.0191133i
$361$	−355.568			−0.984954
$362$		−	323.914i		−	0.894790i
$363$	−37.1804	+	229.413i	−0.102425	+	0.631992i
$364$	−381.935			−1.04927
$365$			47.5420i			0.130252i
$366$	−864.070	−	140.038i	−2.36085	−	0.382616i
$367$	75.8998			0.206812			0.103406	−	0.994639i	$-0.467026\pi$
$367$	75.8998			0.206812			0.103406	+	0.994639i	$0.467026\pi$
$368$			37.6648i			0.102350i
$369$	−172.608	+	518.532i	−0.467772	+	1.40524i
$370$	74.5774			0.201561
$371$			135.463i			0.365130i
$372$	36.5027	−	225.231i	0.0981255	−	0.605461i
$373$	−71.3113			−0.191183			−0.0955915	−	0.995421i	$-0.530474\pi$
$373$	−71.3113			−0.191183			−0.0955915	+	0.995421i	$0.530474\pi$
$374$			616.857i			1.64935i
$375$	77.9214	+	12.6285i	0.207790	+	0.0336760i
$376$	−305.213			−0.811737
$377$		−	164.626i		−	0.436674i
$378$	399.974	+	209.254i	1.05813	+	0.553583i
$379$	−12.7395			−0.0336136			−0.0168068	−	0.999859i	$-0.505350\pi$
$379$	−12.7395			−0.0336136			−0.0168068	+	0.999859i	$0.505350\pi$
$380$		−	6.76539i		−	0.0178037i
$381$	60.6143	−	374.007i	0.159093	−	0.981646i
$382$	−335.095			−0.877212
$383$		−	164.389i		−	0.429213i	−0.976701	−	0.214607i	$-0.931153\pi$
$383$		−	164.389i		−	0.429213i	0.976701	−	0.214607i	$-0.0688470\pi$
$384$	−403.571	−	65.4057i	−1.05097	−	0.170327i
$385$	−18.9546			−0.0492328
$386$			610.289i			1.58106i
$387$	605.771	+	201.648i	1.56530	+	0.521054i
$388$	235.966			0.608160
$389$			100.512i			0.258385i	0.991620	+	0.129192i	$0.0412385\pi$
$389$			100.512i			0.258385i	−0.991620	+	0.129192i	$0.958762\pi$
$390$	−10.0338	+	61.9111i	−0.0257276	+	0.158746i
$391$	145.588			0.372348
$392$			89.3363i			0.227899i
$393$	476.703	+	77.2580i	1.21298	+	0.196585i
$394$	−459.235			−1.16557
$395$			37.3527i			0.0945638i
$396$	102.872	−	309.039i	0.259778	−	0.780401i
$397$	−47.2606			−0.119044			−0.0595221	−	0.998227i	$-0.518958\pi$
$397$	−47.2606			−0.119044			−0.0595221	+	0.998227i	$0.518958\pi$
$398$		−	66.7472i		−	0.167707i
$399$	6.07206	−	37.4662i	0.0152182	−	0.0939004i
$400$	−194.142			−0.485354
$401$			282.744i			0.705096i	0.935794	+	0.352548i	$0.114685\pi$
$401$			282.744i			0.705096i	−0.935794	+	0.352548i	$0.885315\pi$
$402$	−503.024	−	81.5237i	−1.25130	−	0.202795i
$403$	177.856			0.441330
$404$		−	689.740i		−	1.70728i
$405$	25.6919	−	34.3144i	0.0634368	−	0.0847269i
$406$	214.576			0.528513
$407$		−	301.891i		−	0.741748i
$408$	−66.6414	+	411.196i	−0.163337	+	1.00783i
$409$	−1.80407			−0.00441092			−0.00220546	−	0.999998i	$-0.500702\pi$
$409$	−1.80407			−0.00441092			−0.00220546	+	0.999998i	$0.500702\pi$
$410$		−	98.9714i		−	0.241394i
$411$	128.675	+	20.8541i	0.313079	+	0.0507398i
$412$	913.804			2.21797
$413$			228.292i			0.552764i
$414$	−126.127	−	41.9850i	−0.304655	−	0.101413i
$415$	−23.1815			−0.0558590
$416$		−	544.932i		−	1.30993i
$417$	−6.39126	+	39.4358i	−0.0153268	+	0.0945702i
$418$	−47.3578			−0.113296
$419$		−	678.621i		−	1.61962i	−0.586692	−	0.809810i	$-0.699570\pi$
$419$		−	678.621i		−	1.61962i	0.586692	−	0.809810i	$-0.300430\pi$
$420$	−46.6655	−	7.56295i	−0.111108	−	0.0180070i
$421$	−413.758			−0.982798			−0.491399	−	0.870935i	$-0.663514\pi$
$421$	−413.758			−0.982798			−0.491399	+	0.870935i	$0.663514\pi$
$422$			134.979i			0.319856i
$423$	−189.677	+	569.811i	−0.448410	+	1.34707i
$424$	114.140			0.269197
$425$			750.428i			1.76571i
$426$	−5.91776	+	36.5142i	−0.0138915	+	0.0857141i
$427$	514.299			1.20445
$428$		−	411.897i		−	0.962376i
$429$	250.618	+	40.6170i	0.584191	+	0.0946783i
$430$	−115.623			−0.268890
$431$			584.826i			1.35690i	0.734645	+	0.678452i	$0.237349\pi$
$431$			584.826i			1.35690i	−0.734645	+	0.678452i	$0.762651\pi$
$432$	−98.2977	+	187.889i	−0.227541	+	0.434928i
$433$	−671.106			−1.54990			−0.774949	−	0.632024i	$-0.782225\pi$
$433$	−671.106			−1.54990			−0.774949	+	0.632024i	$0.782225\pi$
$434$			231.820i			0.534147i
$435$	3.25987	−	20.1143i	0.00749396	−	0.0462398i
$436$	331.712			0.760808
$437$			11.1772i			0.0255771i
$438$	819.325	+	132.786i	1.87061	+	0.303164i
$439$	29.2093			0.0665360			0.0332680	−	0.999446i	$-0.489409\pi$
$439$	29.2093			0.0665360			0.0332680	+	0.999446i	$0.489409\pi$
$440$			15.9710i			0.0362976i
$441$	166.784	+	55.5188i	0.378196	+	0.125893i
$442$	−1199.23			−2.71320
$443$		−	425.993i		−	0.961610i	−0.876827	−	0.480805i	$-0.840344\pi$
$443$		−	425.993i		−	0.961610i	0.876827	−	0.480805i	$-0.159656\pi$
$444$	120.455	−	743.243i	0.271296	−	1.67397i
$445$	−50.4060			−0.113272
$446$			768.350i			1.72276i
$447$	−342.558	−	55.5174i	−0.766348	−	0.124200i
$448$	539.737			1.20477
$449$		−	745.944i		−	1.66135i	−0.556761	−	0.830673i	$-0.687956\pi$
$449$		−	745.944i		−	1.66135i	0.556761	−	0.830673i	$-0.312044\pi$
$450$	216.410	−	650.119i	0.480912	−	1.44471i
$451$	−400.639			−0.888334
$452$		−	269.258i		−	0.595704i
$453$	124.872	−	770.493i	0.275655	−	1.70087i
$454$	−174.190			−0.383678
$455$		−	36.8498i		−	0.0809886i
$456$	−31.5686	−	5.11625i	−0.0692295	−	0.0112198i
$457$	−436.582			−0.955321			−0.477661	−	0.878544i	$-0.658515\pi$
$457$	−436.582			−0.955321			−0.477661	+	0.878544i	$0.658515\pi$
$458$		−	1297.52i		−	2.83301i
$459$	726.258	+	379.956i	1.58226	+	0.827791i
$460$	13.9216			0.0302643
$461$			393.630i			0.853861i	0.904284	+	0.426931i	$0.140405\pi$
$461$			393.630i			0.853861i	−0.904284	+	0.426931i	$0.859595\pi$
$462$	−52.9407	+	326.659i	−0.114590	+	0.707054i
$463$	511.349			1.10443			0.552213	−	0.833703i	$-0.313783\pi$
$463$	511.349			1.10443			0.552213	+	0.833703i	$0.313783\pi$
$464$			100.798i			0.217237i
$465$	21.7307	+	3.52184i	0.0467328	+	0.00757386i
$466$	−734.207			−1.57555
$467$		−	439.744i		−	0.941636i	−0.882230	−	0.470818i	$-0.843959\pi$
$467$		−	439.744i		−	0.941636i	0.882230	−	0.470818i	$-0.156041\pi$
$468$	600.804	+	199.994i	1.28377	+	0.427338i
$469$	299.402			0.638384
$470$		−	108.759i		−	0.231402i
$471$	−133.490	+	823.669i	−0.283418	+	1.74877i
$472$	192.356			0.407534
$473$			468.043i			0.989521i
$474$	643.726	+	104.327i	1.35807	+	0.220099i
$475$	−57.6124			−0.121289
$476$		−	903.923i		−	1.89900i
$477$	70.9331	−	213.090i	0.148707	−	0.446730i
$478$	1169.86			2.44740
$479$			488.124i			1.01905i	0.860456	+	0.509524i	$0.170179\pi$
$479$			488.124i			1.01905i	−0.860456	+	0.509524i	$0.829821\pi$
$480$	10.7906	−	66.5807i	0.0224803	−	0.138710i
$481$	586.908			1.22018
$482$			882.044i			1.82997i
$483$	77.0966	+	12.4948i	0.159620	+	0.0258693i
$484$	−424.929			−0.877952
$485$			22.7664i			0.0469411i
$486$	−519.607	−	538.608i	−1.06915	−	1.10825i
$487$	−198.019			−0.406610			−0.203305	−	0.979115i	$-0.565168\pi$
$487$	−198.019			−0.406610			−0.203305	+	0.979115i	$0.565168\pi$
$488$		−	433.342i		−	0.887996i
$489$	15.7311	−	97.0649i	0.0321698	−	0.198497i
$490$	−31.8338			−0.0649670
$491$		−	191.809i		−	0.390650i	−0.980739	−	0.195325i	$-0.937424\pi$
$491$		−	191.809i		−	0.390650i	0.980739	−	0.195325i	$-0.0625762\pi$
$492$	−986.355	−	159.856i	−2.00479	−	0.324910i
$493$	389.620			0.790303
$494$		−	92.0685i		−	0.186374i
$495$	29.8166	+	9.92530i	0.0602356	+	0.0200511i
$496$	−108.898			−0.219553
$497$		−	21.7334i		−	0.0437292i
$498$	−64.7464	+	399.503i	−0.130013	+	0.802215i
$499$	315.059			0.631381			0.315690	−	0.948862i	$-0.397764\pi$
$499$	315.059			0.631381			0.315690	+	0.948862i	$0.397764\pi$
$500$			144.329i			0.288659i
$501$	764.262	+	123.862i	1.52547	+	0.247230i
$502$	−346.077			−0.689395
$503$		−	296.480i		−	0.589422i	−0.955586	−	0.294711i	$-0.904777\pi$
$503$		−	296.480i		−	0.589422i	0.955586	−	0.294711i	$-0.0952235\pi$
$504$	−70.5804	+	212.031i	−0.140041	+	0.420696i
$505$	66.5474			0.131777
$506$		−	97.4511i		−	0.192591i
$507$	2.14622	−	13.2428i	0.00423318	−	0.0261199i
$508$	692.752			1.36369
$509$			357.291i			0.701948i	0.936385	+	0.350974i	$0.114149\pi$
$509$			357.291i			0.701948i	−0.936385	+	0.350974i	$0.885851\pi$
$510$	−146.524	−	23.7468i	−0.287303	−	0.0465624i
$511$	−487.667			−0.954338
$512$			477.342i			0.932309i
$513$	−29.1703	+	55.7568i	−0.0568621	+	0.108688i
$514$	60.1036			0.116933
$515$			88.1654i			0.171195i
$516$	−186.751	+	1152.30i	−0.361920	+	2.23314i
$517$	−440.259			−0.851564
$518$			764.985i			1.47680i
$519$	196.635	+	31.8681i	0.378872	+	0.0614028i
$520$	−31.0492			−0.0597100
$521$		−	807.009i		−	1.54896i	−0.632597	−	0.774481i	$-0.718011\pi$
$521$		−	807.009i		−	1.54896i	0.632597	−	0.774481i	$-0.281989\pi$
$522$	−337.539	−	112.359i	−0.646627	−	0.215248i
$523$	317.746			0.607545			0.303773	−	0.952745i	$-0.401754\pi$
$523$	317.746			0.607545			0.303773	+	0.952745i	$0.401754\pi$
$524$			882.970i			1.68506i
$525$	−64.4042	+	397.392i	−0.122675	+	0.756936i
$526$	−1028.18			−1.95472
$527$			420.930i			0.798729i
$528$	−153.449	−	24.8691i	−0.290623	−	0.0471005i
$529$	−23.0000			−0.0434783
$530$			40.6722i			0.0767400i
$531$	119.541	−	359.114i	0.225125	−	0.676298i
$532$	69.3966			0.130445
$533$		−	778.884i		−	1.46132i
$534$	−140.785	+	868.683i	−0.263643	+	1.62675i
$535$	39.7406			0.0742815
$536$		−	252.273i		−	0.470658i
$537$	193.171	+	31.3068i	0.359723	+	0.0582994i
$538$	−258.123			−0.479782
$539$			128.864i			0.239080i
$540$	69.4470	+	36.3325i	0.128605	+	0.0672825i
$541$	4.23807			0.00783377			0.00391689	−	0.999992i	$-0.498753\pi$
$541$	4.23807			0.00783377			0.00391689	+	0.999992i	$0.498753\pi$
$542$		−	663.646i		−	1.22444i
$543$	50.4771	−	311.457i	0.0929597	−	0.573587i
$544$	1289.68			2.37074
$545$			32.0042i			0.0587233i
$546$	−635.059	−	102.922i	−1.16311	−	0.188502i
$547$	−1.95837			−0.00358020			−0.00179010	−	0.999998i	$-0.500570\pi$
$547$	−1.95837			−0.00358020			−0.00179010	+	0.999998i	$0.500570\pi$
$548$			238.338i			0.434923i
$549$	−809.018	−	269.304i	−1.47362	−	0.490536i
$550$	502.308			0.913287
$551$			29.9122i			0.0542870i
$552$	10.5280	−	64.9608i	0.0190725	−	0.117683i
$553$	−383.149			−0.692855
$554$			301.447i			0.544128i
$555$	71.7094	+	11.6218i	0.129206	+	0.0209401i
$556$	−73.0447			−0.131375
$557$		−	851.578i		−	1.52887i	−0.644704	−	0.764433i	$-0.723019\pi$
$557$		−	851.578i		−	1.52887i	0.644704	−	0.764433i	$-0.276981\pi$
$558$	121.389	−	364.665i	0.217543	−	0.653521i
$559$	−909.925			−1.62777
$560$			22.5625i			0.0402901i
$561$	−96.1278	+	593.135i	−0.171351	+	1.05728i
$562$	−1439.85			−2.56202
$563$		−	494.170i		−	0.877744i	−0.898550	−	0.438872i	$-0.855378\pi$
$563$		−	494.170i		−	0.877744i	0.898550	−	0.438872i	$-0.144622\pi$
$564$	−1083.90	−	175.664i	−1.92180	−	0.311462i
$565$	25.9785			0.0459797
$566$		−	77.4277i		−	0.136798i
$567$	351.983	+	263.537i	0.620782	+	0.464792i
$568$	−18.3123			−0.0322400
$569$			676.484i			1.18890i	0.804133	+	0.594450i	$0.202630\pi$
$569$			676.484i			1.18890i	−0.804133	+	0.594450i	$0.797370\pi$
$570$	1.82311	−	11.2491i	0.00319844	−	0.0197352i
$571$	695.733			1.21845			0.609223	−	0.792999i	$-0.291481\pi$
$571$	695.733			1.21845			0.609223	+	0.792999i	$0.291481\pi$
$572$			464.205i			0.811547i
$573$	−322.208	−	52.2195i	−0.562318	−	0.0911334i
$574$	1015.21			1.76866
$575$		−	118.553i		−	0.206178i
$576$	−849.034	−	282.625i	−1.47402	−	0.490668i
$577$	756.194			1.31056			0.655281	−	0.755385i	$-0.272550\pi$
$577$	756.194			1.31056			0.655281	+	0.755385i	$0.272550\pi$
$578$		−	1948.16i		−	3.37051i
$579$	−95.1043	+	586.819i	−0.164256	+	1.01350i
$580$	37.2566			0.0642355
$581$		−	237.786i		−	0.409271i
$582$	392.350	+	63.5872i	0.674141	+	0.109256i
$583$	164.642			0.282405
$584$			410.902i			0.703600i
$585$	−19.2958	+	57.9666i	−0.0329843	+	0.0990882i
$586$	−617.793			−1.05425
$587$			354.212i			0.603427i	0.953399	+	0.301714i	$0.0975587\pi$
$587$			354.212i			0.603427i	−0.953399	+	0.301714i	$0.902441\pi$
$588$	−51.4172	+	317.258i	−0.0874442	+	0.539555i
$589$	−32.3160			−0.0548658
$590$			68.5436i			0.116176i
$591$	−441.575	−	71.5648i	−0.747165	−	0.121091i
$592$	−359.354			−0.607016
$593$		−	353.117i		−	0.595476i	−0.954648	−	0.297738i	$-0.903768\pi$
$593$		−	353.117i		−	0.595476i	0.954648	−	0.297738i	$-0.0962321\pi$
$594$	254.328	−	486.129i	0.428162	−	0.818400i
$595$	87.2121			0.146575
$596$		−	634.500i		−	1.06460i
$597$	10.4015	−	64.1804i	0.0174230	−	0.107505i
$598$	189.455			0.316815
$599$		−	627.885i		−	1.04822i	−0.851650	−	0.524111i	$-0.824398\pi$
$599$		−	627.885i		−	1.04822i	0.851650	−	0.524111i	$-0.175602\pi$
$600$	334.838	+	54.2663i	0.558063	+	0.0904438i
$601$	−461.824			−0.768426			−0.384213	−	0.923244i	$-0.625527\pi$
$601$	−461.824			−0.768426			−0.384213	+	0.923244i	$0.625527\pi$
$602$		−	1186.01i		−	1.97012i
$603$	−470.975	−	156.777i	−0.781053	−	0.259995i
$604$	1427.14			2.36281
$605$		−	40.9979i		−	0.0677651i
$606$	185.868	−	1146.86i	0.306713	−	1.89250i
$607$	−733.211			−1.20793			−0.603963	−	0.797012i	$-0.706413\pi$
$607$	−733.211			−1.20793			−0.603963	+	0.797012i	$0.706413\pi$
$608$			99.0126i			0.162850i
$609$	206.324	+	33.4385i	0.338792	+	0.0549071i
$610$	154.416			0.253141
$611$		−	855.909i		−	1.40083i
$612$	−473.325	+	1421.92i	−0.773407	+	2.32339i
$613$	837.302			1.36591			0.682954	−	0.730461i	$-0.260695\pi$
$613$	837.302			1.36591			0.682954	+	0.730461i	$0.260695\pi$
$614$			1066.11i			1.73634i
$615$	15.4232	−	95.1653i	0.0250784	−	0.154740i
$616$	−163.824			−0.265947
$617$		−	524.030i		−	0.849320i	−0.905353	−	0.424660i	$-0.860394\pi$
$617$		−	524.030i		−	0.849320i	0.905353	−	0.424660i	$-0.139606\pi$
$618$	1519.42	+	246.248i	2.45860	+	0.398460i
$619$	−520.432			−0.840762			−0.420381	−	0.907348i	$-0.638104\pi$
$619$	−520.432			−0.840762			−0.420381	+	0.907348i	$0.638104\pi$
$620$			40.2506i			0.0649203i
$621$	−114.734	−	60.0255i	−0.184757	−	0.0966594i
$622$	67.8482			0.109081
$623$		−	517.044i		−	0.829927i
$624$	48.3480	−	298.321i	0.0774808	−	0.478078i
$625$	604.073			0.966517
$626$			1676.53i			2.67816i
$627$	−45.5366	−	7.38000i	−0.0726261	−	0.0117703i
$628$	−1525.64			−2.42936
$629$			1389.03i			2.20832i
$630$	−75.5545	−	25.1504i	−0.119928	−	0.0399213i
$631$	216.308			0.342801			0.171401	−	0.985201i	$-0.445171\pi$
$631$	216.308			0.342801			0.171401	+	0.985201i	$0.445171\pi$
$632$			322.837i			0.510818i
$633$	−21.0345	+	129.789i	−0.0332298	+	0.205037i
$634$	225.835			0.356207
$635$			66.8380i			0.105257i
$636$	405.342	+	65.6927i	0.637330	+	0.103290i
$637$	−250.526			−0.393290
$638$		−	260.797i		−	0.408772i
$639$	−11.3804	+	34.1878i	−0.0178097	+	0.0535020i
$640$	72.1213			0.112690
$641$			1236.22i			1.92859i	0.264834	+	0.964294i	$0.414683\pi$
$641$			1236.22i			1.92859i	−0.264834	+	0.964294i	$0.585317\pi$
$642$	110.996	−	684.878i	0.172891	−	1.06679i
$643$	−264.922			−0.412009			−0.206004	−	0.978551i	$-0.566046\pi$
$643$	−264.922			−0.412009			−0.206004	+	0.978551i	$0.566046\pi$
$644$			142.802i			0.221742i
$645$	−111.176	−	18.0180i	−0.172366	−	0.0279349i
$646$	217.898			0.337303
$647$			126.440i			0.195425i	0.995215	+	0.0977123i	$0.0311525\pi$
$647$			126.440i			0.195425i	−0.995215	+	0.0977123i	$0.968847\pi$
$648$	222.053	−	296.577i	0.342675	−	0.457681i
$649$	277.466			0.427529
$650$			976.539i			1.50237i
$651$	−36.1256	+	222.905i	−0.0554925	+	0.342404i
$652$	179.788			0.275748
$653$		−	640.167i		−	0.980347i	−0.871625	−	0.490174i	$-0.836933\pi$
$653$		−	640.167i		−	0.980347i	0.871625	−	0.490174i	$-0.163067\pi$
$654$	551.551	+	89.3884i	0.843350	+	0.136680i
$655$	−85.1905			−0.130062
$656$			476.897i			0.726977i
$657$	767.124	+	255.359i	1.16762	+	0.388674i
$658$	1115.60			1.69545
$659$			481.987i			0.731392i	0.930734	+	0.365696i	$0.119169\pi$
$659$			481.987i			0.731392i	−0.930734	+	0.365696i	$0.880831\pi$
$660$	−9.19203	+	56.7174i	−0.0139273	+	0.0859354i
$661$	−76.3324			−0.115480			−0.0577401	−	0.998332i	$-0.518389\pi$
$661$	−76.3324			−0.115480			−0.0577401	+	0.998332i	$0.518389\pi$
$662$			1155.00i			1.74471i
$663$	−1153.12	−	186.883i	−1.73924	−	0.281874i
$664$	−200.356			−0.301741
$665$			6.69551i			0.0100684i
$666$	400.572	−	1203.36i	0.601460	−	1.80685i
$667$	−61.5521			−0.0922820
$668$			1415.60i			2.11916i
$669$	−119.736	+	738.802i	−0.178977	+	1.10434i
$670$	89.8942			0.134171
$671$		−	625.080i		−	0.931565i
$672$	682.957	+	110.685i	1.01631	+	0.164710i
$673$	−420.058			−0.624158			−0.312079	−	0.950056i	$-0.601025\pi$
$673$	−420.058			−0.624158			−0.312079	+	0.950056i	$0.601025\pi$
$674$		−	955.074i		−	1.41702i
$675$	309.399	−	591.393i	0.458369	−	0.876138i
$676$	24.5289			0.0362853
$677$			273.409i			0.403854i	0.979401	+	0.201927i	$0.0647204\pi$
$677$			273.409i			0.403854i	−0.979401	+	0.201927i	$0.935280\pi$
$678$	72.5586	−	447.707i	0.107019	−	0.660334i
$679$	−233.529			−0.343930
$680$		−	73.4839i		−	0.108065i
$681$	−167.491	−	27.1449i	−0.245949	−	0.0398603i
$682$	281.755			0.413130
$683$			844.570i			1.23656i	0.785958	+	0.618280i	$0.212170\pi$
$683$			844.570i			1.23656i	−0.785958	+	0.618280i	$0.787830\pi$
$684$	−109.164	−	36.3384i	−0.159597	−	0.0531264i
$685$	−22.9953			−0.0335697
$686$		−	1145.76i		−	1.67020i
$687$	202.199	−	1247.62i	0.294321	−	1.81604i
$688$	557.131			0.809784
$689$			320.082i			0.464560i
$690$	23.1479	+	3.75153i	0.0335477	+	0.00543699i
$691$	18.9489			0.0274225			0.0137112	−	0.999906i	$-0.495635\pi$
$691$	18.9489			0.0274225			0.0137112	+	0.999906i	$0.495635\pi$
$692$			364.215i			0.526322i
$693$	−101.810	+	305.847i	−0.146911	+	0.441337i
$694$	−1524.61			−2.19684
$695$		−	7.04748i		−	0.0101403i
$696$	28.1749	−	173.847i	0.0404811	−	0.249780i
$697$	1843.38			2.64473
$698$			332.174i			0.475894i
$699$	−705.972	−	114.415i	−1.00997	−	0.163684i
$700$	−736.066			−1.05152
$701$		−	1100.30i		−	1.56961i	−0.619740	−	0.784807i	$-0.712762\pi$
$701$		−	1100.30i		−	1.56961i	0.619740	−	0.784807i	$-0.287238\pi$
$702$	945.086	+	494.441i	1.34628	+	0.704331i
$703$	−106.640			−0.151692
$704$		−	655.998i		−	0.931816i
$705$	16.9484	−	104.576i	0.0240403	−	0.148335i
$706$	1116.85			1.58194
$707$			682.616i			0.965510i
$708$	683.110	+	110.710i	0.964844	+	0.156370i
$709$	128.116			0.180699			0.0903495	−	0.995910i	$-0.471202\pi$
$709$	128.116			0.180699			0.0903495	+	0.995910i	$0.471202\pi$
$710$		−	6.52537i		−	0.00919067i
$711$	602.713	+	200.630i	0.847697	+	0.282180i
$712$	−435.656			−0.611876
$713$		−	66.4986i		−	0.0932659i
$714$	243.585	−	1502.99i	0.341156	−	2.10503i
$715$	−44.7874			−0.0626397
$716$			357.800i			0.499721i
$717$	1124.87	+	182.305i	1.56886	+	0.254261i
$718$	−541.490			−0.754164
$719$			944.130i			1.31311i	0.754276	+	0.656557i	$0.227988\pi$
$719$			944.130i			1.31311i	−0.754276	+	0.656557i	$0.772012\pi$
$720$	11.8145	−	35.4919i	0.0164090	−	0.0492944i
$721$	−904.365			−1.25432
$722$		−	1095.08i		−	1.51673i
$723$	−137.453	+	848.124i	−0.190115	+	1.17306i
$724$	576.895			0.796816
$725$		−	317.268i		−	0.437611i
$726$	−706.546	−	114.508i	−0.973204	−	0.157725i
$727$	−838.941			−1.15398			−0.576988	−	0.816752i	$-0.695772\pi$
$727$	−838.941			−1.15398			−0.576988	+	0.816752i	$0.695772\pi$
$728$		−	318.490i		−	0.437487i
$729$	−415.691	−	598.868i	−0.570220	−	0.821492i
$730$	−146.420			−0.200575
$731$		−	2153.51i		−	2.94598i
$732$	249.409	−	1538.92i	0.340722	−	2.10235i
$733$	387.644			0.528845			0.264423	−	0.964407i	$-0.414819\pi$
$733$	387.644			0.528845			0.264423	+	0.964407i	$0.414819\pi$
$734$			233.756i			0.318469i
$735$	−30.6096	−	4.96082i	−0.0416458	−	0.00674942i
$736$	−203.744			−0.276827
$737$		−	363.894i		−	0.493751i
$738$	−1596.97	−	531.598i	−2.16392	−	0.720322i
$739$	−1163.00			−1.57375			−0.786877	−	0.617110i	$-0.788304\pi$
$739$	−1163.00			−1.57375			−0.786877	+	0.617110i	$0.788304\pi$
$740$			132.823i			0.179491i
$741$	14.3475	−	88.5279i	0.0193623	−	0.119471i
$742$	−417.199			−0.562263
$743$			644.723i			0.867729i	0.900978	+	0.433865i	$0.142850\pi$
$743$			644.723i			0.867729i	−0.900978	+	0.433865i	$0.857150\pi$
$744$	187.817	+	30.4390i	0.252443	+	0.0409127i
$745$	61.2177			0.0821714
$746$		−	219.624i		−	0.294403i
$747$	−124.513	+	374.050i	−0.166684	+	0.500736i
$748$	−1098.63			−1.46876
$749$			407.643i			0.544249i
$750$	−38.8933	+	239.982i	−0.0518577	+	0.319976i
$751$	−1405.83			−1.87195			−0.935974	−	0.352069i	$-0.885478\pi$
$751$	−1405.83			−1.87195			−0.935974	+	0.352069i	$0.885478\pi$
$752$			524.058i			0.696885i
$753$	−332.768	−	53.9308i	−0.441923	−	0.0716212i
$754$	507.016			0.672435
$755$			137.693i			0.182375i
$756$	−372.684	+	712.359i	−0.492969	+	0.942273i
$757$	−223.285			−0.294960			−0.147480	−	0.989065i	$-0.547116\pi$
$757$	−223.285			−0.294960			−0.147480	+	0.989065i	$0.547116\pi$
$758$		−	39.2352i		−	0.0517615i
$759$	15.1863	−	93.7035i	0.0200083	−	0.123457i
$760$	5.64156			0.00742311
$761$		−	916.953i		−	1.20493i	−0.798145	−	0.602466i	$-0.794185\pi$
$761$		−	916.953i		−	1.20493i	0.798145	−	0.602466i	$-0.205815\pi$
$762$	1151.87	+	186.680i	1.51164	+	0.244987i
$763$	−328.286			−0.430257
$764$		−	596.808i		−	0.781162i
$765$	−137.189	−	45.6672i	−0.179332	−	0.0596957i
$766$	506.284			0.660946
$767$			539.424i			0.703290i
$768$	10.5615	−	65.1673i	0.0137519	−	0.0848533i
$769$	−339.172			−0.441056			−0.220528	−	0.975381i	$-0.570778\pi$
$769$	−339.172			−0.441056			−0.220528	+	0.975381i	$0.570778\pi$
$770$		−	58.3765i		−	0.0758136i
$771$	57.7922	+	9.36623i	0.0749575	+	0.0121482i
$772$	−1086.93			−1.40794
$773$			1441.87i			1.86529i	0.360796	+	0.932645i	$0.382505\pi$
$773$			1441.87i			1.86529i	−0.360796	+	0.932645i	$0.617495\pi$
$774$	−621.035	+	1865.65i	−0.802371	+	2.41041i
$775$	342.764			0.442276
$776$			196.769i			0.253568i
$777$	−119.211	+	735.566i	−0.153425	+	0.946674i
$778$	−309.556			−0.397887
$779$			141.521i			0.181670i
$780$	−110.264	−	17.8703i	−0.141365	−	0.0229106i
$781$	−26.4149			−0.0338219
$782$			448.382i			0.573378i
$783$	−307.049	−	160.639i	−0.392145	−	0.205158i
$784$	153.392			0.195654
$785$		−	147.196i		−	0.187511i
$786$	−237.939	+	1468.15i	−0.302721	+	1.86787i
$787$	1214.49			1.54318			0.771592	−	0.636118i	$-0.219461\pi$
$787$	1214.49			1.54318			0.771592	+	0.636118i	$0.219461\pi$
$788$		−	817.904i		−	1.03795i
$789$	−988.643	−	160.227i	−1.25303	−	0.203076i
$790$	−115.039			−0.145619
$791$			266.477i			0.336886i
$792$	257.703	+	85.7837i	0.325382	+	0.108313i
$793$	1215.22			1.53243
$794$		−	145.553i		−	0.183316i
$795$	−6.33815	+	39.1081i	−0.00797252	+	0.0491926i
$796$	118.878			0.149344
$797$			47.4182i			0.0594959i	0.999557	+	0.0297480i	$0.00947047\pi$
$797$			47.4182i			0.0594959i	−0.999557	+	0.0297480i	$0.990530\pi$
$798$	115.389	+	18.7007i	0.144597	+	0.0234345i
$799$	2025.67			2.53526
$800$		−	1050.19i		−	1.31274i
$801$	−270.742	+	813.337i	−0.338005	+	1.01540i
$802$	−870.794			−1.08578
$803$			592.711i			0.738121i
$804$	145.195	−	895.892i	0.180591	−	1.11429i
$805$	−13.7778			−0.0171152
$806$			547.761i			0.679604i
$807$	−248.196	−	40.2245i	−0.307554	−	0.0498445i
$808$	575.164			0.711837
$809$		−	391.405i		−	0.483814i	−0.970299	−	0.241907i	$-0.922227\pi$
$809$		−	391.405i		−	0.483814i	0.970299	−	0.241907i	$-0.0777728\pi$
$810$	105.681	+	79.1259i	0.130471	+	0.0976862i
$811$	672.347			0.829034			0.414517	−	0.910041i	$-0.363950\pi$
$811$	672.347			0.829034			0.414517	+	0.910041i	$0.363950\pi$
$812$			382.163i			0.470644i
$813$	103.419	−	638.125i	0.127207	−	0.784901i
$814$	929.765			1.14222
$815$			17.3463i			0.0212837i
$816$	706.033	+	114.425i	0.865236	+	0.140227i
$817$	165.331			0.202364
$818$		−	5.55616i		−	0.00679237i
$819$	−594.598	−	197.929i	−0.726005	−	0.241671i
$820$	176.269			0.214963
$821$			555.614i			0.676753i	0.941011	+	0.338376i	$0.109878\pi$
$821$			555.614i			0.676753i	−0.941011	+	0.338376i	$0.890122\pi$
$822$	−64.2263	+	396.294i	−0.0781342	+	0.482109i
$823$	−1111.22			−1.35021			−0.675103	−	0.737723i	$-0.735901\pi$
$823$	−1111.22			−1.35021			−0.675103	+	0.737723i	$0.735901\pi$
$824$			762.008i			0.924766i
$825$	482.991	+	78.2771i	0.585444	+	0.0948813i
$826$	−703.092			−0.851201
$827$			1337.40i			1.61717i	0.588380	+	0.808585i	$0.299766\pi$
$827$			1337.40i			1.61717i	−0.588380	+	0.808585i	$0.700234\pi$
$828$	74.7759	−	224.634i	0.0903090	−	0.271298i
$829$	−41.2955			−0.0498136			−0.0249068	−	0.999690i	$-0.507929\pi$
$829$	−41.2955			−0.0498136			−0.0249068	+	0.999690i	$0.507929\pi$
$830$		−	71.3943i		−	0.0860172i
$831$	−46.9759	+	289.854i	−0.0565294	+	0.348802i
$832$	1275.33			1.53285
$833$		−	592.917i		−	0.711785i
$834$	−121.454	−	19.6838i	−0.145629	−	0.0236017i
$835$	−136.580			−0.163568
$836$		−	84.3448i		−	0.100891i
$837$	173.548	−	331.724i	0.207345	−	0.396325i
$838$	2090.02			2.49405
$839$			522.269i			0.622490i	0.950330	+	0.311245i	$0.100746\pi$
$839$			522.269i			0.622490i	−0.950330	+	0.311245i	$0.899254\pi$
$840$	6.30664	−	38.9137i	0.00750790	−	0.0463258i
$841$	676.276			0.804133
$842$		−	1274.29i		−	1.51341i
$843$	−1384.48	−	224.379i	−1.64233	−	0.266167i
$844$	−240.400			−0.284834
$845$			2.36659i			0.00280070i
$846$	−1754.90	−	584.168i	−2.07435	−	0.690506i
$847$	420.540			0.496505
$848$		−	195.980i		−	0.231109i
$849$	12.0659	−	74.4501i	0.0142119	−	0.0876915i
$850$	−2311.17			−2.71902
$851$		−	219.439i		−	0.257860i
$852$	−65.0323	−	10.5396i	−0.0763289	−	0.0123704i
$853$	535.649			0.627959			0.313979	−	0.949430i	$-0.398338\pi$
$853$	535.649			0.627959			0.313979	+	0.949430i	$0.398338\pi$
$854$			1583.94i			1.85473i
$855$	3.50600	−	10.5324i	0.00410058	−	0.0123186i
$856$	343.475			0.401256
$857$		−	990.233i		−	1.15546i	−0.816226	−	0.577732i	$-0.803938\pi$
$857$		−	990.233i		−	1.15546i	0.816226	−	0.577732i	$-0.196062\pi$
$858$	−125.092	+	771.852i	−0.145795	+	0.899595i
$859$	−924.814			−1.07662			−0.538308	−	0.842748i	$-0.680936\pi$
$859$	−924.814			−1.07662			−0.538308	+	0.842748i	$0.680936\pi$
$860$		−	205.925i		−	0.239448i
$861$	976.167	+	158.205i	1.13376	+	0.183745i
$862$	−1801.15			−2.08950
$863$		−	214.613i		−	0.248682i	−0.992240	−	0.124341i	$-0.960318\pi$
$863$		−	214.613i		−	0.248682i	0.992240	−	0.124341i	$-0.0396817\pi$
$864$	−1016.37	−	531.733i	−1.17635	−	0.615432i
$865$	−35.1401			−0.0406244
$866$		−	2066.87i		−	2.38669i
$867$	303.591	−	1873.24i	0.350162	−	2.16060i
$868$	−412.874			−0.475662
$869$			465.680i			0.535881i
$870$	61.9480	+	10.0398i	0.0712046	+	0.0115399i
$871$	707.449			0.812226
$872$			276.610i			0.317213i
$873$	367.353	+	122.284i	0.420793	+	0.140073i
$874$	−34.4235			−0.0393861
$875$		−	142.839i		−	0.163244i
$876$	−236.493	+	1459.23i	−0.269970	+	1.66579i
$877$	482.517			0.550191			0.275095	−	0.961417i	$-0.411291\pi$
$877$	482.517			0.550191			0.275095	+	0.961417i	$0.411291\pi$
$878$			89.9587i			0.102459i
$879$	−594.035	−	96.2736i	−0.675807	−	0.109526i
$880$	27.4225			0.0311619
$881$		−	231.528i		−	0.262802i	−0.991329	−	0.131401i	$-0.958053\pi$
$881$		−	231.528i		−	0.262802i	0.991329	−	0.131401i	$-0.0419475\pi$
$882$	−170.987	+	513.662i	−0.193863	+	0.582383i
$883$	1351.26			1.53031			0.765155	−	0.643846i	$-0.222662\pi$
$883$	1351.26			1.53031			0.765155	+	0.643846i	$0.222662\pi$
$884$		−	2135.85i		−	2.41612i
$885$	−10.6815	+	65.9077i	−0.0120695	+	0.0744719i
$886$	1311.97			1.48078
$887$			1155.27i			1.30245i	0.758884	+	0.651226i	$0.225745\pi$
$887$			1155.27i			1.30245i	−0.758884	+	0.651226i	$0.774255\pi$
$888$	619.780	+	100.446i	0.697950	+	0.113115i
$889$	−685.597			−0.771200
$890$		−	155.240i		−	0.174427i
$891$	320.304	−	427.801i	0.359488	−	0.480136i
$892$	−1368.44			−1.53413
$893$			155.516i			0.174150i
$894$	170.982	−	1055.01i	0.191256	−	1.18010i
$895$	−34.5212			−0.0385712
$896$			739.791i			0.825660i
$897$	182.169	+	29.5237i	0.203087	+	0.0329138i
$898$	2297.36			2.55830
$899$		−	177.962i		−	0.197956i
$900$	1157.87	+	385.429i	1.28652	+	0.428255i
$901$	−757.534			−0.840771
$902$		−	1233.89i		−	1.36795i
$903$	184.822	−	1140.40i	0.204675	−	1.26290i
$904$	224.531			0.248375
$905$			55.6599i			0.0615026i
$906$	2372.96	+	384.580i	2.61916	+	0.424481i
$907$	−764.023			−0.842363			−0.421181	−	0.906976i	$-0.638384\pi$
$907$	−764.023			−0.842363			−0.421181	+	0.906976i	$0.638384\pi$
$908$		−	310.235i		−	0.341668i
$909$	357.441	−	1073.79i	0.393224	−	1.18129i
$910$	113.490			0.124714
$911$		−	462.715i		−	0.507920i	−0.967215	−	0.253960i	$-0.918267\pi$
$911$		−	462.715i		−	0.507920i	0.967215	−	0.253960i	$-0.0817332\pi$
$912$	−8.78471	+	54.2041i	−0.00963236	+	0.0594343i
$913$	−289.006			−0.316546
$914$		−	1344.58i		−	1.47110i
$915$	148.478	+	24.0634i	0.162271	+	0.0262988i
$916$	2310.90			2.52281
$917$		−	873.849i		−	0.952944i
$918$	−1170.19	+	2236.73i	−1.27471	+	2.43652i
$919$	1351.19			1.47028			0.735139	−	0.677916i	$-0.237117\pi$
$919$	1351.19			1.47028			0.735139	+	0.677916i	$0.237117\pi$
$920$			11.6090i			0.0126185i
$921$	−166.138	+	1025.11i	−0.180388	+	1.11305i
$922$	−1212.30			−1.31486
$923$		−	51.3533i		−	0.0556374i
$924$	−581.783	−	94.2881i	−0.629636	−	0.102043i
$925$	1131.09			1.22280
$926$			1574.85i			1.70071i
$927$	1422.61	+	473.556i	1.53464	+	0.510848i
$928$	−545.257			−0.587561
$929$		−	796.429i		−	0.857297i	−0.903471	−	0.428648i	$-0.858990\pi$
$929$		−	796.429i		−	0.857297i	0.903471	−	0.428648i	$-0.141010\pi$
$930$	−10.8466	+	66.9263i	−0.0116630	+	0.0719638i
$931$	45.5198			0.0488935
$932$		−	1307.63i		−	1.40304i
$933$	65.2390	+	10.5731i	0.0699239	+	0.0113324i
$934$	1354.32			1.45003
$935$		−	105.998i		−	0.113367i
$936$	−166.772	+	501.001i	−0.178176	+	0.535258i
$937$	165.538			0.176668			0.0883339	−	0.996091i	$-0.471846\pi$
$937$	165.538			0.176668			0.0883339	+	0.996091i	$0.471846\pi$
$938$			922.098i			0.983047i
$939$	−261.262	+	1612.06i	−0.278234	+	1.71678i
$940$	193.701			0.206065
$941$		−	613.257i		−	0.651707i	−0.945420	−	0.325854i	$-0.894348\pi$
$941$		−	613.257i		−	0.651707i	0.945420	−	0.325854i	$-0.105652\pi$
$942$	−2536.74	−	411.122i	−2.69293	−	0.436435i
$943$	−291.217			−0.308820
$944$		−	330.280i		−	0.349872i
$945$	−68.7296	−	35.9573i	−0.0727298	−	0.0380500i
$946$	−1441.48			−1.52376
$947$			703.632i			0.743011i	0.928431	+	0.371506i	$0.121158\pi$
$947$			703.632i			0.743011i	−0.928431	+	0.371506i	$0.878842\pi$
$948$	−185.808	+	1146.48i	−0.196000	+	1.20937i
$949$	−1152.29			−1.21422
$950$		−	177.435i		−	0.186773i
$951$	217.150	+	35.1930i	0.228339	+	0.0370063i
$952$	753.768			0.791773
$953$		−	1341.12i		−	1.40727i	−0.710564	−	0.703633i	$-0.751560\pi$
$953$		−	1341.12i		−	1.40727i	0.710564	−	0.703633i	$-0.248440\pi$
$954$	656.275	+	218.460i	0.687920	+	0.228993i
$955$	57.5811			0.0602944
$956$			2083.53i			2.17943i
$957$	40.6412	−	250.767i	0.0424673	−	0.262035i
$958$	−1503.32			−1.56923
$959$		−	235.876i		−	0.245961i
$960$	155.822	+	25.2536i	0.162314	+	0.0263059i
$961$	−768.737			−0.799934
$962$			1807.56i			1.87896i
$963$	213.456	−	641.243i	0.221657	−	0.665880i
$964$	−1570.93			−1.62960
$965$		−	104.869i		−	0.108673i
$966$	−38.4816	+	237.442i	−0.0398360	+	0.245799i
$967$	511.669			0.529131			0.264565	−	0.964368i	$-0.414772\pi$
$967$	511.669			0.529131			0.264565	+	0.964368i	$0.414772\pi$
$968$		−	354.342i		−	0.366056i
$969$	209.518	+	33.9561i	0.216221	+	0.0350424i
$970$	−70.1160			−0.0722846
$971$			366.530i			0.377477i	0.982027	+	0.188738i	$0.0604398\pi$
$971$			366.530i			0.377477i	−0.982027	+	0.188738i	$0.939560\pi$
$972$	959.267	−	925.426i	0.986900	−	0.952084i
$973$	72.2902			0.0742962
$974$		−	609.858i		−	0.626138i
$975$	−152.179	+	938.985i	−0.156081	+	0.963061i
$976$	−744.058			−0.762355
$977$		−	777.865i		−	0.796177i	−0.917347	−	0.398088i	$-0.869674\pi$
$977$		−	777.865i		−	0.796177i	0.917347	−	0.398088i	$-0.130326\pi$
$978$	298.940	+	48.4485i	0.305665	+	0.0495383i
$979$	−628.417			−0.641897
$980$		−	56.6965i		−	0.0578536i
$981$	516.411	+	171.902i	0.526412	+	0.175231i
$982$	590.734			0.601562
$983$			714.476i			0.726832i	0.931627	+	0.363416i	$0.118390\pi$
$983$			714.476i			0.726832i	−0.931627	+	0.363416i	$0.881610\pi$
$984$	133.302	−	822.507i	0.135469	−	0.835881i
$985$	78.9128			0.0801146
$986$			1199.95i			1.21699i
$987$	1072.70	+	173.850i	1.08683	+	0.176140i
$988$	163.975			0.165967
$989$			340.212i			0.343996i
$990$	−30.5679	+	91.8292i	−0.0308767	+	0.0927567i
$991$	−1765.74			−1.78177			−0.890886	−	0.454226i	$-0.849916\pi$
$991$	−1765.74			−1.78177			−0.890886	+	0.454226i	$0.849916\pi$
$992$		−	589.075i		−	0.593825i
$993$	−179.989	+	1110.58i	−0.181258	+	1.11841i
$994$	66.9346			0.0673386
$995$			11.4695i			0.0115272i
$996$	−711.520	−	115.314i	−0.714378	−	0.115777i
$997$	−1567.09			−1.57181			−0.785903	−	0.618350i	$-0.787802\pi$
$997$	−1567.09			−1.57181			−0.785903	+	0.618350i	$0.787802\pi$
$998$			970.318i			0.972263i
$999$	572.693	−	1094.66i	0.573266	−	1.09576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.3.b.a.47.13	yes	14
3.2	odd	2	inner	69.3.b.a.47.2	✓	14
4.3	odd	2		1104.3.g.b.737.7		14
12.11	even	2		1104.3.g.b.737.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.3.b.a.47.2	✓	14	3.2	odd	2	inner
69.3.b.a.47.13	yes	14	1.1	even	1	trivial
1104.3.g.b.737.7		14	4.3	odd	2
1104.3.g.b.737.8		14	12.11	even	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)

\(f(q)\)	\(=\)	\(q+3.07980i q^{2} +(-0.479940 + 2.96136i) q^{3} -5.48516 q^{4} -0.529218i q^{5} +(-9.12040 - 1.47812i) q^{6} +5.42850 q^{7} -4.57400i q^{8} +(-8.53932 - 2.84255i) q^{9} +O(q^{10})\)	\(q+3.07980i q^{2} +(-0.479940 + 2.96136i) q^{3} -5.48516 q^{4} -0.529218i q^{5} +(-9.12040 - 1.47812i) q^{6} +5.42850 q^{7} -4.57400i q^{8} +(-8.53932 - 2.84255i) q^{9} +1.62989 q^{10} -6.59782i q^{11} +(2.63255 - 16.2435i) q^{12} +12.8269 q^{13} +16.7187i q^{14} +(1.56721 + 0.253993i) q^{15} -7.85365 q^{16} +30.3572i q^{17} +(8.75448 - 26.2994i) q^{18} -2.33061 q^{19} +2.90285i q^{20} +(-2.60536 + 16.0758i) q^{21} +20.3200 q^{22} -4.79583i q^{23} +(13.5453 + 2.19524i) q^{24} +24.7199 q^{25} +39.5041i q^{26} +(12.5162 - 23.9237i) q^{27} -29.7762 q^{28} -12.8345i q^{29} +(-0.782247 + 4.82668i) q^{30} +13.8659 q^{31} -42.4837i q^{32} +(19.5385 + 3.16656i) q^{33} -93.4941 q^{34} -2.87286i q^{35} +(46.8395 + 15.5918i) q^{36} +45.7562 q^{37} -7.17779i q^{38} +(-6.15612 + 37.9849i) q^{39} -2.42064 q^{40} -60.7229i q^{41} +(-49.5101 - 8.02397i) q^{42} -70.9391 q^{43} +36.1901i q^{44} +(-1.50433 + 4.51916i) q^{45} +14.7702 q^{46} -66.7279i q^{47} +(3.76928 - 23.2575i) q^{48} -19.5313 q^{49} +76.1324i q^{50} +(-89.8986 - 14.5696i) q^{51} -70.3573 q^{52} +24.9540i q^{53} +(73.6803 + 38.5473i) q^{54} -3.49169 q^{55} -24.8300i q^{56} +(1.11855 - 6.90176i) q^{57} +39.5277 q^{58} +42.0542i q^{59} +(-8.59638 - 1.39319i) q^{60} +94.7404 q^{61} +42.7042i q^{62} +(-46.3557 - 15.4308i) q^{63} +99.4265 q^{64} -6.78820i q^{65} +(-9.75236 + 60.1747i) q^{66} +55.1537 q^{67} -166.514i q^{68} +(14.2022 + 2.30171i) q^{69} +8.84784 q^{70} -4.00358i q^{71} +(-13.0018 + 39.0588i) q^{72} -89.8344 q^{73} +140.920i q^{74} +(-11.8641 + 73.2046i) q^{75} +12.7837 q^{76} -35.8163i q^{77} +(-116.986 - 18.9596i) q^{78} -70.5809 q^{79} +4.15630i q^{80} +(64.8398 + 48.5469i) q^{81} +187.014 q^{82} -43.8033i q^{83} +(14.2908 - 88.1781i) q^{84} +16.0656 q^{85} -218.478i q^{86} +(38.0076 + 6.15979i) q^{87} -30.1784 q^{88} -95.2462i q^{89} +(-13.9181 - 4.63303i) q^{90} +69.6306 q^{91} +26.3059i q^{92} +(-6.65480 + 41.0620i) q^{93} +205.508 q^{94} +1.23340i q^{95} +(125.809 + 20.3896i) q^{96} -43.0190 q^{97} -60.1526i q^{98} +(-18.7546 + 56.3409i) 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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