LMFDB - Embedded newform 177.3.b.a.119.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(119,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.5
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.18759i q^{2} +(2.94308 + 0.581607i) q^{3} -6.16073 q^{4} +2.91835i q^{5} +(1.85393 - 9.38134i) q^{6} +12.1837 q^{7} +6.88752i q^{8} +(8.32347 + 3.42344i) q^{9} +O(q^{10})$	\(q-3.18759i q^{2} +(2.94308 + 0.581607i) q^{3} -6.16073 q^{4} +2.91835i q^{5} +(1.85393 - 9.38134i) q^{6} +12.1837 q^{7} +6.88752i q^{8} +(8.32347 + 3.42344i) q^{9} +9.30252 q^{10} -13.3732i q^{11} +(-18.1315 - 3.58312i) q^{12} -12.2071 q^{13} -38.8366i q^{14} +(-1.69734 + 8.58896i) q^{15} -2.68834 q^{16} -2.10350i q^{17} +(10.9125 - 26.5318i) q^{18} -3.44330 q^{19} -17.9792i q^{20} +(35.8576 + 7.08611i) q^{21} -42.6282 q^{22} +44.1928i q^{23} +(-4.00583 + 20.2705i) q^{24} +16.4832 q^{25} +38.9112i q^{26} +(22.5056 + 14.9164i) q^{27} -75.0603 q^{28} -41.6037i q^{29} +(27.3781 + 5.41041i) q^{30} -28.5455 q^{31} +36.1194i q^{32} +(7.77793 - 39.3583i) q^{33} -6.70509 q^{34} +35.5563i q^{35} +(-51.2786 - 21.0909i) q^{36} -16.7372 q^{37} +10.9758i q^{38} +(-35.9264 - 7.09973i) q^{39} -20.1002 q^{40} +7.60876i q^{41} +(22.5876 - 114.299i) q^{42} -46.0831 q^{43} +82.3884i q^{44} +(-9.99080 + 24.2908i) q^{45} +140.869 q^{46} -1.11928i q^{47} +(-7.91200 - 1.56356i) q^{48} +99.4419 q^{49} -52.5417i q^{50} +(1.22341 - 6.19077i) q^{51} +75.2045 q^{52} +30.2820i q^{53} +(47.5475 - 71.7385i) q^{54} +39.0276 q^{55} +83.9152i q^{56} +(-10.1339 - 2.00265i) q^{57} -132.616 q^{58} -7.68115i q^{59} +(10.4568 - 52.9142i) q^{60} -46.1565 q^{61} +90.9915i q^{62} +(101.410 + 41.7100i) q^{63} +104.380 q^{64} -35.6246i q^{65} +(-125.458 - 24.7928i) q^{66} +66.4936 q^{67} +12.9591i q^{68} +(-25.7029 + 130.063i) q^{69} +113.339 q^{70} +99.7802i q^{71} +(-23.5790 + 57.3280i) q^{72} -129.745 q^{73} +53.3515i q^{74} +(48.5114 + 9.58675i) q^{75} +21.2133 q^{76} -162.934i q^{77} +(-22.6310 + 114.519i) q^{78} +12.2886 q^{79} -7.84553i q^{80} +(57.5602 + 56.9897i) q^{81} +24.2536 q^{82} +41.1271i q^{83} +(-220.909 - 43.6556i) q^{84} +6.13875 q^{85} +146.894i q^{86} +(24.1970 - 122.443i) q^{87} +92.1079 q^{88} +75.0603i q^{89} +(77.4292 + 31.8466i) q^{90} -148.727 q^{91} -272.260i q^{92} +(-84.0119 - 16.6023i) q^{93} -3.56781 q^{94} -10.0488i q^{95} +(-21.0073 + 106.302i) q^{96} +186.423 q^{97} -316.980i q^{98} +(45.7822 - 111.311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	$ 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) $ 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	3.18759i		−	1.59379i	−0.604115	−	0.796897i	$-0.706473\pi$
$2$		−	3.18759i		−	1.59379i	0.604115	−	0.796897i	$-0.293527\pi$
$3$	2.94308	+	0.581607i	0.981027	+	0.193869i
$3$	2.94308	+	0.581607i	0.981027	+	0.193869i
$4$	−6.16073			−1.54018
$5$			2.91835i			0.583671i	0.956469	+	0.291835i	$0.0942660\pi$
$5$			2.91835i			0.583671i	−0.956469	+	0.291835i	$0.905734\pi$
$6$	1.85393	−	9.38134i	0.308988	−	1.56356i
$7$	12.1837			1.74052			0.870262	−	0.492588i	$-0.163949\pi$
$7$	12.1837			1.74052			0.870262	+	0.492588i	$0.163949\pi$
$8$			6.88752i			0.860939i
$9$	8.32347	+	3.42344i	0.924830	+	0.380382i
$10$	9.30252			0.930252
$11$		−	13.3732i		−	1.21574i	−0.794036	−	0.607871i	$-0.792024\pi$
$11$		−	13.3732i		−	1.21574i	0.794036	−	0.607871i	$-0.207976\pi$
$12$	−18.1315	−	3.58312i	−1.51096	−	0.298594i
$13$	−12.2071			−0.939006			−0.469503	−	0.882931i	$-0.655567\pi$
$13$	−12.2071			−0.939006			−0.469503	+	0.882931i	$0.655567\pi$
$14$		−	38.8366i		−	2.77404i
$15$	−1.69734	+	8.58896i	−0.113156	+	0.572597i
$16$	−2.68834			−0.168021
$17$		−	2.10350i		−	0.123735i	−0.998084	−	0.0618676i	$-0.980294\pi$
$17$		−	2.10350i		−	0.123735i	0.998084	−	0.0618676i	$-0.0197057\pi$
$18$	10.9125	−	26.5318i	0.606250	−	1.47399i
$19$	−3.44330			−0.181227			−0.0906133	−	0.995886i	$-0.528883\pi$
$19$	−3.44330			−0.181227			−0.0906133	+	0.995886i	$0.528883\pi$
$20$		−	17.9792i		−	0.898960i
$21$	35.8576	+	7.08611i	1.70750	+	0.337434i
$22$	−42.6282			−1.93764
$23$			44.1928i			1.92143i	0.277540	+	0.960714i	$0.410481\pi$
$23$			44.1928i			1.92143i	−0.277540	+	0.960714i	$0.589519\pi$
$24$	−4.00583	+	20.2705i	−0.166910	+	0.844605i
$25$	16.4832			0.659328
$26$			38.9112i			1.49658i
$27$	22.5056	+	14.9164i	0.833539	+	0.552461i
$28$	−75.0603			−2.68073
$29$		−	41.6037i		−	1.43461i	−0.696759	−	0.717305i	$-0.745375\pi$
$29$		−	41.6037i		−	1.43461i	0.696759	−	0.717305i	$-0.254625\pi$
$30$	27.3781	+	5.41041i	0.912603	+	0.180347i
$31$	−28.5455			−0.920824			−0.460412	−	0.887705i	$-0.652298\pi$
$31$	−28.5455			−0.920824			−0.460412	+	0.887705i	$0.652298\pi$
$32$			36.1194i			1.12873i
$33$	7.77793	−	39.3583i	0.235695	−	1.19268i
$34$	−6.70509			−0.197209
$35$			35.5563i			1.01589i
$36$	−51.2786	−	21.0909i	−1.42441	−	0.585857i
$37$	−16.7372			−0.452358			−0.226179	−	0.974086i	$-0.572623\pi$
$37$	−16.7372			−0.452358			−0.226179	+	0.974086i	$0.572623\pi$
$38$			10.9758i			0.288838i
$39$	−35.9264	−	7.09973i	−0.921191	−	0.182044i
$40$	−20.1002			−0.502505
$41$			7.60876i			0.185580i	0.995686	+	0.0927898i	$0.0295785\pi$
$41$			7.60876i			0.185580i	−0.995686	+	0.0927898i	$0.970422\pi$
$42$	22.5876	−	114.299i	0.537800	−	2.72141i
$43$	−46.0831			−1.07170			−0.535850	−	0.844313i	$-0.680009\pi$
$43$	−46.0831			−1.07170			−0.535850	+	0.844313i	$0.680009\pi$
$44$			82.3884i			1.87246i
$45$	−9.99080	+	24.2908i	−0.222018	+	0.539796i
$46$	140.869			3.06236
$47$		−	1.11928i		−	0.0238145i	−0.999929	−	0.0119072i	$-0.996210\pi$
$47$		−	1.11928i		−	0.0238145i	0.999929	−	0.0119072i	$-0.00379028\pi$
$48$	−7.91200	−	1.56356i	−0.164833	−	0.0325741i
$49$	99.4419			2.02943
$50$		−	52.5417i		−	1.05083i
$51$	1.22341	−	6.19077i	0.0239884	−	0.121388i
$52$	75.2045			1.44624
$53$			30.2820i			0.571358i	0.958325	+	0.285679i	$0.0922191\pi$
$53$			30.2820i			0.571358i	−0.958325	+	0.285679i	$0.907781\pi$
$54$	47.5475	−	71.7385i	0.880509	−	1.32849i
$55$	39.0276			0.709593
$56$			83.9152i			1.49849i
$57$	−10.1339	−	2.00265i	−0.177788	−	0.0351342i
$58$	−132.616			−2.28648
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	10.4568	−	52.9142i	0.174280	−	0.881904i
$61$	−46.1565			−0.756664			−0.378332	−	0.925670i	$-0.623502\pi$
$61$	−46.1565			−0.756664			−0.378332	+	0.925670i	$0.623502\pi$
$62$			90.9915i			1.46760i
$63$	101.410	+	41.7100i	1.60969	+	0.662064i
$64$	104.380			1.63094
$65$		−	35.6246i		−	0.548071i
$66$	−125.458	−	24.7928i	−1.90088	−	0.375649i
$67$	66.4936			0.992442			0.496221	−	0.868196i	$-0.334721\pi$
$67$	66.4936			0.992442			0.496221	+	0.868196i	$0.334721\pi$
$68$			12.9591i			0.190575i
$69$	−25.7029	+	130.063i	−0.372505	+	1.88497i
$70$	113.339			1.61913
$71$			99.7802i			1.40535i	0.711509	+	0.702677i	$0.248012\pi$
$71$			99.7802i			1.40535i	−0.711509	+	0.702677i	$0.751988\pi$
$72$	−23.5790	+	57.3280i	−0.327486	+	0.796222i
$73$	−129.745			−1.77733			−0.888663	−	0.458561i	$-0.848365\pi$
$73$	−129.745			−1.77733			−0.888663	+	0.458561i	$0.848365\pi$
$74$			53.3515i			0.720966i
$75$	48.5114	+	9.58675i	0.646819	+	0.127823i
$76$	21.2133			0.279122
$77$		−	162.934i		−	2.11603i
$78$	−22.6310	+	114.519i	−0.290141	+	1.46819i
$79$	12.2886			0.155551			0.0777757	−	0.996971i	$-0.475218\pi$
$79$	12.2886			0.155551			0.0777757	+	0.996971i	$0.475218\pi$
$80$		−	7.84553i		−	0.0980691i
$81$	57.5602	+	56.9897i	0.710619	+	0.703577i
$82$	24.2536			0.295776
$83$			41.1271i			0.495507i	0.968823	+	0.247754i	$0.0796923\pi$
$83$			41.1271i			0.495507i	−0.968823	+	0.247754i	$0.920308\pi$
$84$	−220.909	−	43.6556i	−2.62986	−	0.519710i
$85$	6.13875			0.0722206
$86$			146.894i			1.70807i
$87$	24.1970	−	122.443i	0.278127	−	1.40739i
$88$	92.1079			1.04668
$89$			75.0603i			0.843374i	0.906741	+	0.421687i	$0.138562\pi$
$89$			75.0603i			0.843374i	−0.906741	+	0.421687i	$0.861438\pi$
$90$	77.4292	+	31.8466i	0.860324	+	0.353851i
$91$	−148.727			−1.63436
$92$		−	272.260i		−	2.95935i
$93$	−84.0119	−	16.6023i	−0.903354	−	0.178519i
$94$	−3.56781			−0.0379554
$95$		−	10.0488i		−	0.105777i
$96$	−21.0073	+	106.302i	−0.218826	+	1.10732i
$97$	186.423			1.92189			0.960943	−	0.276747i	$-0.0892564\pi$
$97$	186.423			1.92189			0.960943	+	0.276747i	$0.0892564\pi$
$98$		−	316.980i		−	3.23449i
$99$	45.7822	−	111.311i	0.462446	−	1.12435i
$100$	−101.549			−1.01549
$101$		−	40.4331i		−	0.400328i	−0.979762	−	0.200164i	$-0.935853\pi$
$101$		−	40.4331i		−	0.400328i	0.979762	−	0.200164i	$-0.0641474\pi$
$102$	−19.7336	−	3.89973i	−0.193467	−	0.0382326i
$103$	−43.2601			−0.420001			−0.210001	−	0.977701i	$-0.567347\pi$
$103$	−43.2601			−0.420001			−0.210001	+	0.977701i	$0.567347\pi$
$104$		−	84.0765i		−	0.808428i
$105$	−20.6798	+	104.645i	−0.196950	+	0.996620i
$106$	96.5265			0.910627
$107$		−	105.027i		−	0.981557i	−0.871284	−	0.490779i	$-0.836712\pi$
$107$		−	105.027i		−	0.981557i	0.871284	−	0.490779i	$-0.163288\pi$
$108$	−138.651	−	91.8961i	−1.28380	−	0.850890i
$109$	−87.1490			−0.799532			−0.399766	−	0.916617i	$-0.630909\pi$
$109$	−87.1490			−0.799532			−0.399766	+	0.916617i	$0.630909\pi$
$110$		−	124.404i		−	1.13095i
$111$	−49.2591	−	9.73450i	−0.443775	−	0.0876982i
$112$	−32.7539			−0.292445
$113$			119.661i			1.05894i	0.848328	+	0.529472i	$0.177610\pi$
$113$			119.661i			1.05894i	−0.848328	+	0.529472i	$0.822390\pi$
$114$	−6.38363	+	32.3028i	−0.0559967	+	0.283358i
$115$	−128.970			−1.12148
$116$			256.309i			2.20956i
$117$	−101.605	−	41.7902i	−0.868421	−	0.357181i
$118$	−24.4843			−0.207494
$119$		−	25.6283i		−	0.215364i
$120$	−59.1566	−	11.6904i	−0.492972	−	0.0974202i
$121$	−57.8415			−0.478029
$122$			147.128i			1.20597i
$123$	−4.42531	+	22.3932i	−0.0359781	+	0.182059i
$124$	175.861			1.41824
$125$			121.063i			0.968502i
$126$	132.954	−	323.255i	1.05519	−	2.56551i
$127$	−197.855			−1.55791			−0.778955	−	0.627080i	$-0.784250\pi$
$127$	−197.855			−1.55791			−0.778955	+	0.627080i	$0.784250\pi$
$128$		−	188.244i		−	1.47066i
$129$	−135.626	−	26.8022i	−1.05137	−	0.207769i
$130$	−113.557			−0.873512
$131$		−	120.820i		−	0.922292i	−0.887324	−	0.461146i	$-0.847438\pi$
$131$		−	120.820i		−	0.922292i	0.887324	−	0.461146i	$-0.152562\pi$
$132$	−47.9177	+	242.476i	−0.363013	+	1.83694i
$133$	−41.9521			−0.315429
$134$		−	211.954i		−	1.58175i
$135$	−43.5315	+	65.6792i	−0.322455	+	0.486512i
$136$	14.4879			0.106529
$137$		−	174.325i		−	1.27244i	−0.771506	−	0.636222i	$-0.780496\pi$
$137$		−	174.325i		−	1.27244i	0.771506	−	0.636222i	$-0.219504\pi$
$138$	414.588	+	81.9302i	3.00426	+	0.593697i
$139$	1.76171			0.0126742			0.00633709	−	0.999980i	$-0.497983\pi$
$139$	1.76171			0.0126742			0.00633709	+	0.999980i	$0.497983\pi$
$140$		−	219.053i		−	1.56466i
$141$	0.650981	−	3.29413i	0.00461689	−	0.0233626i
$142$	318.058			2.23985
$143$			163.247i			1.14159i
$144$	−22.3763	−	9.20336i	−0.155391	−	0.0639122i
$145$	121.414			0.837341
$146$			413.573i			2.83269i
$147$	292.666	+	57.8361i	1.99092	+	0.393443i
$148$	103.114			0.696713
$149$		−	88.4441i		−	0.593584i	−0.954942	−	0.296792i	$-0.904083\pi$
$149$		−	88.4441i		−	0.593584i	0.954942	−	0.296792i	$-0.0959169\pi$
$150$	30.5586	−	154.635i	0.203724	−	1.03090i
$151$	79.9437			0.529428			0.264714	−	0.964327i	$-0.414722\pi$
$151$	79.9437			0.529428			0.264714	+	0.964327i	$0.414722\pi$
$152$		−	23.7158i		−	0.156025i
$153$	7.20119	−	17.5084i	0.0470666	−	0.114434i
$154$	−519.368			−3.37252
$155$		−	83.3060i		−	0.537458i
$156$	221.333	+	43.7395i	1.41880	+	0.280381i
$157$	71.8100			0.457388			0.228694	−	0.973498i	$-0.426554\pi$
$157$	71.8100			0.457388			0.228694	+	0.973498i	$0.426554\pi$
$158$		−	39.1709i		−	0.247917i
$159$	−17.6122	+	89.1223i	−0.110769	+	0.560518i
$160$	−105.409			−0.658807
$161$			538.431i			3.34429i
$162$	181.660	−	183.478i	1.12136	−	1.13258i
$163$	43.7644			0.268493			0.134247	−	0.990948i	$-0.457139\pi$
$163$	43.7644			0.268493			0.134247	+	0.990948i	$0.457139\pi$
$164$		−	46.8755i		−	0.285826i
$165$	114.862	+	22.6988i	0.696131	+	0.137568i
$166$	131.096			0.789737
$167$			97.8528i			0.585945i	0.956121	+	0.292973i	$0.0946445\pi$
$167$			97.8528i			0.585945i	−0.956121	+	0.292973i	$0.905356\pi$
$168$	−48.8057	+	246.969i	−0.290510	+	1.47006i
$169$	−19.9871			−0.118267
$170$		−	19.5678i		−	0.115105i
$171$	−28.6602	−	11.7879i	−0.167604	−	0.0689353i
$172$	283.905			1.65061
$173$		−	67.8975i		−	0.392471i	−0.980557	−	0.196235i	$-0.937128\pi$
$173$		−	67.8975i		−	0.392471i	0.980557	−	0.196235i	$-0.0628717\pi$
$174$	−390.299	−	77.1302i	−2.24310	−	0.443277i
$175$	200.826			1.14758
$176$			35.9516i			0.204270i
$177$	4.46741	−	22.6062i	0.0252396	−	0.127719i
$178$	239.261			1.34417
$179$		−	290.963i		−	1.62549i	−0.582620	−	0.812745i	$-0.697972\pi$
$179$		−	290.963i		−	1.62549i	0.582620	−	0.812745i	$-0.302028\pi$
$180$	61.5506	−	149.649i	0.341948	−	0.831384i
$181$	63.7495			0.352207			0.176104	−	0.984372i	$-0.443651\pi$
$181$	63.7495			0.352207			0.176104	+	0.984372i	$0.443651\pi$
$182$			474.081i			2.60484i
$183$	−135.842	−	26.8450i	−0.742308	−	0.146694i
$184$	−304.379			−1.65423
$185$		−	48.8452i		−	0.264028i
$186$	−52.9213	+	267.795i	−0.284523	+	1.43976i
$187$	−28.1304			−0.150430
$188$			6.89558i			0.0366786i
$189$	274.200	+	181.737i	1.45080	+	0.961572i
$190$	−32.0314			−0.168586
$191$		−	181.224i		−	0.948818i	−0.880305	−	0.474409i	$-0.842662\pi$
$191$		−	181.224i		−	0.948818i	0.880305	−	0.474409i	$-0.157338\pi$
$192$	307.200	+	60.7084i	1.60000	+	0.316190i
$193$	−267.431			−1.38565			−0.692826	−	0.721104i	$-0.743635\pi$
$193$	−267.431			−1.38565			−0.692826	+	0.721104i	$0.743635\pi$
$194$		−	594.240i		−	3.06309i
$195$	20.7195	−	104.846i	0.106254	−	0.537672i
$196$	−612.635			−3.12569
$197$		−	187.173i		−	0.950115i	−0.879955	−	0.475058i	$-0.842427\pi$
$197$		−	187.173i		−	0.950115i	0.879955	−	0.475058i	$-0.157573\pi$
$198$	−354.814	−	145.935i	−1.79199	−	0.737044i
$199$	−43.9546			−0.220877			−0.110439	−	0.993883i	$-0.535226\pi$
$199$	−43.9546			−0.220877			−0.110439	+	0.993883i	$0.535226\pi$
$200$			113.528i			0.567642i
$201$	195.696	+	38.6732i	0.973613	+	0.192404i
$202$	−128.884			−0.638040
$203$		−	506.886i		−	2.49698i
$204$	−7.53709	+	38.1396i	−0.0369465	+	0.186959i
$205$	−22.2051			−0.108317
$206$			137.895i			0.669395i
$207$	−151.291	+	367.838i	−0.730876	+	1.77699i
$208$	32.8168			0.157773
$209$			46.0479i			0.220325i
$210$	333.566	+	65.9187i	1.58841	+	0.313899i
$211$	−153.458			−0.727291			−0.363645	−	0.931537i	$-0.618468\pi$
$211$	−153.458			−0.727291			−0.363645	+	0.931537i	$0.618468\pi$
$212$		−	186.559i		−	0.879995i
$213$	−58.0329	+	293.661i	−0.272455	+	1.37869i
$214$	−334.782			−1.56440
$215$		−	134.487i		−	0.625520i
$216$	−102.737	+	155.007i	−0.475635	+	0.717627i
$217$	−347.790			−1.60272
$218$			277.795i			1.27429i
$219$	−381.850	−	75.4605i	−1.74361	−	0.344568i
$220$	−240.439			−1.09290
$221$			25.6776i			0.116188i
$222$	−31.0296	+	157.018i	−0.139773	+	0.707287i
$223$	348.282			1.56180			0.780901	−	0.624654i	$-0.214760\pi$
$223$	348.282			1.56180			0.780901	+	0.624654i	$0.214760\pi$
$224$			440.067i			1.96458i
$225$	137.197	+	56.4292i	0.609766	+	0.250796i
$226$	381.429			1.68774
$227$			135.891i			0.598641i	0.954153	+	0.299320i	$0.0967599\pi$
$227$			135.891i			0.598641i	−0.954153	+	0.299320i	$0.903240\pi$
$228$	62.4324	+	12.3378i	0.273826	+	0.0541131i
$229$	243.213			1.06207			0.531033	−	0.847351i	$-0.321804\pi$
$229$	243.213			1.06207			0.531033	+	0.847351i	$0.321804\pi$
$230$			411.105i			1.78741i
$231$	94.7637	−	479.529i	0.410233	−	2.07588i
$232$	286.546			1.23511
$233$		−	455.367i		−	1.95436i	−0.212406	−	0.977181i	$-0.568130\pi$
$233$		−	455.367i		−	1.95436i	0.212406	−	0.977181i	$-0.431870\pi$
$234$	−133.210	+	323.876i	−0.569273	+	1.38408i
$235$	3.26646			0.0138998
$236$			47.3215i			0.200515i
$237$	36.1662	+	7.14711i	0.152600	+	0.0301566i
$238$	−81.6926			−0.343246
$239$		−	195.311i		−	0.817199i	−0.912714	−	0.408600i	$-0.866017\pi$
$239$		−	195.311i		−	0.817199i	0.912714	−	0.408600i	$-0.133983\pi$
$240$	4.56302	−	23.0900i	0.0190126	−	0.0962085i
$241$	27.4728			0.113995			0.0569976	−	0.998374i	$-0.481847\pi$
$241$	27.4728			0.113995			0.0569976	+	0.998374i	$0.481847\pi$
$242$			184.375i			0.761880i
$243$	136.259	+	201.203i	0.560735	+	0.827995i
$244$	284.358			1.16540
$245$			290.207i			1.18452i
$246$	71.3804	+	14.1061i	0.290164	+	0.0573418i
$247$	42.0327			0.170173
$248$		−	196.608i		−	0.792774i
$249$	−23.9198	+	121.040i	−0.0960635	+	0.486106i
$250$	385.898			1.54359
$251$		−	239.932i		−	0.955903i	−0.878386	−	0.477952i	$-0.841379\pi$
$251$		−	239.932i		−	0.955903i	0.878386	−	0.477952i	$-0.158621\pi$
$252$	−624.762	−	256.964i	−2.47921	−	1.01970i
$253$	590.998			2.33596
$254$			630.679i			2.48299i
$255$	18.0669	+	3.57034i	0.0708504	+	0.0140013i
$256$	−182.524			−0.712986
$257$			334.481i			1.30148i	0.759300	+	0.650741i	$0.225542\pi$
$257$			334.481i			1.30148i	−0.759300	+	0.650741i	$0.774458\pi$
$258$	−85.4346	+	432.321i	−0.331142	+	1.67566i
$259$	−203.921			−0.787340
$260$			219.473i			0.844129i
$261$	142.428	−	346.287i	0.545700	−	1.32677i
$262$	−385.125			−1.46994
$263$		−	351.568i		−	1.33676i	−0.743820	−	0.668380i	$-0.766988\pi$
$263$		−	351.568i		−	1.33676i	0.743820	−	0.668380i	$-0.233012\pi$
$264$	271.081	+	53.5706i	1.02682	+	0.202919i
$265$	−88.3735			−0.333485
$266$			133.726i			0.502730i
$267$	−43.6556	+	220.909i	−0.163504	+	0.827373i
$268$	−409.649			−1.52854
$269$			243.044i			0.903508i	0.892143	+	0.451754i	$0.149202\pi$
$269$			243.044i			0.903508i	−0.892143	+	0.451754i	$0.850798\pi$
$270$	209.358	+	138.760i	0.775401	+	0.513928i
$271$	−69.7893			−0.257525			−0.128763	−	0.991675i	$-0.541101\pi$
$271$	−69.7893			−0.257525			−0.128763	+	0.991675i	$0.541101\pi$
$272$			5.65492i			0.0207901i
$273$	−437.716	−	86.5008i	−1.60336	−	0.316853i
$274$	−555.676			−2.02801
$275$		−	220.433i		−	0.801573i
$276$	158.348	−	801.284i	0.573726	−	2.90320i
$277$	74.2229			0.267953			0.133976	−	0.990985i	$-0.457225\pi$
$277$	74.2229			0.267953			0.133976	+	0.990985i	$0.457225\pi$
$278$		−	5.61561i		−	0.0202000i
$279$	−237.598	−	97.7238i	−0.851605	−	0.350265i
$280$	−244.894			−0.874623
$281$		−	342.390i		−	1.21847i	−0.792990	−	0.609235i	$-0.791476\pi$
$281$		−	342.390i		−	1.21847i	0.792990	−	0.609235i	$-0.208524\pi$
$282$	−10.5003	−	2.07506i	−0.0372353	−	0.00735837i
$283$	490.428			1.73296			0.866481	−	0.499209i	$-0.166376\pi$
$283$	490.428			1.73296			0.866481	+	0.499209i	$0.166376\pi$
$284$		−	614.719i		−	2.16450i
$285$	5.84445	−	29.5744i	0.0205068	−	0.103770i
$286$	520.365			1.81946
$287$			92.7027i			0.323006i
$288$	−123.652	+	300.638i	−0.429349	+	1.04388i
$289$	284.575			0.984690
$290$		−	387.019i		−	1.33455i
$291$	548.658	+	108.425i	1.88542	+	0.372594i
$292$	799.322			2.73741
$293$			400.366i			1.36644i	0.730214	+	0.683219i	$0.239421\pi$
$293$			400.366i			1.36644i	−0.730214	+	0.683219i	$0.760579\pi$
$294$	184.358	−	932.898i	0.627068	−	3.17312i
$295$	22.4163			0.0759875
$296$		−	115.278i		−	0.389453i
$297$	199.480	−	300.970i	0.671650	−	1.01337i
$298$	−281.923			−0.946052
$299$		−	539.466i		−	1.80423i
$300$	−298.866	−	59.0614i	−0.996219	−	0.196871i
$301$	−561.461			−1.86532
$302$		−	254.828i		−	0.843800i
$303$	23.5162	−	118.998i	0.0776111	−	0.392732i
$304$	9.25677			0.0304499
$305$		−	134.701i		−	0.441643i
$306$	−55.8096	−	22.9544i	−0.182384	−	0.0750145i
$307$	209.512			0.682450			0.341225	−	0.939982i	$-0.389158\pi$
$307$	209.512			0.682450			0.341225	+	0.939982i	$0.389158\pi$
$308$			1003.79i			3.25907i
$309$	−127.318	−	25.1604i	−0.412033	−	0.0814252i
$310$	−265.545			−0.856598
$311$		−	383.028i		−	1.23160i	−0.787902	−	0.615801i	$-0.788833\pi$
$311$		−	383.028i		−	1.23160i	0.787902	−	0.615801i	$-0.211167\pi$
$312$	48.8995	−	247.444i	0.156729	−	0.793090i
$313$	28.8222			0.0920837			0.0460418	−	0.998940i	$-0.485339\pi$
$313$	28.8222			0.0920837			0.0460418	+	0.998940i	$0.485339\pi$
$314$		−	228.901i		−	0.728983i
$315$	−121.725	+	295.952i	−0.386427	+	0.939529i
$316$	−75.7065			−0.239577
$317$			357.739i			1.12851i	0.825599	+	0.564257i	$0.190837\pi$
$317$			357.739i			1.12851i	−0.825599	+	0.564257i	$0.809163\pi$
$318$	284.085	+	56.1405i	0.893350	+	0.176542i
$319$	−556.373			−1.74412
$320$			304.619i			0.951935i
$321$	61.0842	−	309.102i	0.190294	−	0.962935i
$322$	1716.30			5.33012
$323$			7.24298i			0.0224241i
$324$	−354.613	−	351.098i	−1.09448	−	1.08364i
$325$	−201.212			−0.619113
$326$		−	139.503i		−	0.427923i
$327$	−256.487	−	50.6865i	−0.784363	−	0.155004i
$328$	−52.4055			−0.159773
$329$		−	13.6369i		−	0.0414497i
$330$	72.3543	−	366.131i	0.219255	−	1.10949i
$331$	−132.781			−0.401152			−0.200576	−	0.979678i	$-0.564281\pi$
$331$	−132.781			−0.401152			−0.200576	+	0.979678i	$0.564281\pi$
$332$		−	253.373i		−	0.763171i
$333$	−139.312	−	57.2989i	−0.418354	−	0.172069i
$334$	311.915			0.933876
$335$			194.052i			0.579260i
$336$	−96.3973	−	19.0499i	−0.286897	−	0.0566961i
$337$	203.625			0.604228			0.302114	−	0.953272i	$-0.402308\pi$
$337$	203.625			0.604228			0.302114	+	0.953272i	$0.402308\pi$
$338$			63.7108i			0.188493i
$339$	−69.5955	+	352.171i	−0.205296	+	1.03885i
$340$	−37.8192			−0.111233
$341$			381.744i			1.11948i
$342$	−37.5751	+	91.3571i	−0.109869	+	0.267126i
$343$	614.568			1.79174
$344$		−	317.398i		−	0.922668i
$345$	−379.570	−	75.0101i	−1.10020	−	0.217421i
$346$	−216.429			−0.625518
$347$			191.457i			0.551750i	0.961194	+	0.275875i	$0.0889676\pi$
$347$			191.457i			0.551750i	−0.961194	+	0.275875i	$0.911032\pi$
$348$	−149.071	+	754.339i	−0.428366	+	2.16764i
$349$	376.372			1.07843			0.539215	−	0.842168i	$-0.318721\pi$
$349$	376.372			1.07843			0.539215	+	0.842168i	$0.318721\pi$
$350$		−	640.151i		−	1.82900i
$351$	−274.727	−	182.086i	−0.782698	−	0.518764i
$352$	483.030			1.37225
$353$			514.841i			1.45847i	0.684261	+	0.729237i	$0.260125\pi$
$353$			514.841i			1.45847i	−0.684261	+	0.729237i	$0.739875\pi$
$354$	−72.0594	−	14.2403i	−0.203558	−	0.0402267i
$355$	−291.194			−0.820265
$356$		−	462.426i		−	1.29895i
$357$	14.9056	−	75.4263i	0.0417525	−	0.211278i
$358$	−927.469			−2.59070
$359$			204.536i			0.569738i	0.958566	+	0.284869i	$0.0919501\pi$
$359$			204.536i			0.569738i	−0.958566	+	0.284869i	$0.908050\pi$
$360$	−167.303	−	68.8118i	−0.464732	−	0.191144i
$361$	−349.144			−0.967157
$362$		−	203.207i		−	0.561346i
$363$	−170.232	−	33.6410i	−0.468959	−	0.0926750i
$364$	916.267			2.51722
$365$		−	378.641i		−	1.03737i
$366$	−85.5707	+	433.010i	−0.233800	+	1.18309i
$367$	72.5182			0.197597			0.0987986	−	0.995107i	$-0.468500\pi$
$367$	72.5182			0.197597			0.0987986	+	0.995107i	$0.468500\pi$
$368$		−	118.805i		−	0.322841i
$369$	−26.0481	+	63.3313i	−0.0705911	+	0.171629i
$370$	−155.698			−0.420807
$371$			368.946i			0.994463i
$372$	517.574	+	102.282i	1.39133	+	0.274952i
$373$	33.8148			0.0906563			0.0453282	−	0.998972i	$-0.485567\pi$
$373$	33.8148			0.0906563			0.0453282	+	0.998972i	$0.485567\pi$
$374$			89.6683i			0.239755i
$375$	−70.4109	+	356.298i	−0.187763	+	0.950127i
$376$	7.70906			0.0205028
$377$			507.860i			1.34711i
$378$	579.303	−	874.038i	1.53255	−	2.31227i
$379$	70.9565			0.187220			0.0936102	−	0.995609i	$-0.470159\pi$
$379$	70.9565			0.187220			0.0936102	+	0.995609i	$0.470159\pi$
$380$			61.9078i			0.162915i
$381$	−582.302	−	115.074i	−1.52835	−	0.302031i
$382$	−577.668			−1.51222
$383$			152.819i			0.399006i	0.979897	+	0.199503i	$0.0639328\pi$
$383$			152.819i			0.399006i	−0.979897	+	0.199503i	$0.936067\pi$
$384$	109.484	−	554.019i	0.285115	−	1.44276i
$385$	475.500			1.23506
$386$			852.460i			2.20845i
$387$	−383.571	−	157.762i	−0.991139	−	0.407655i
$388$	−1148.50			−2.96005
$389$			448.180i			1.15213i	0.817403	+	0.576067i	$0.195413\pi$
$389$			448.180i			1.15213i	−0.817403	+	0.576067i	$0.804587\pi$
$390$	−334.206	−	66.0453i	−0.856940	−	0.169347i
$391$	92.9596			0.237748
$392$			684.908i			1.74721i
$393$	70.2699	−	355.584i	0.178804	−	0.904794i
$394$	−596.630			−1.51429
$395$			35.8624i			0.0907908i
$396$	−282.051	+	685.757i	−0.712251	+	1.73171i
$397$	244.470			0.615795			0.307897	−	0.951420i	$-0.400375\pi$
$397$	244.470			0.615795			0.307897	+	0.951420i	$0.400375\pi$
$398$			140.109i			0.352033i
$399$	−123.468	−	24.3996i	−0.309445	−	0.0611520i
$400$	−44.3124			−0.110781
$401$			3.27174i			0.00815896i	0.999992	+	0.00407948i	$0.00129854\pi$
$401$			3.27174i			0.00815896i	−0.999992	+	0.00407948i	$0.998701\pi$
$402$	123.274	−	623.799i	0.306652	−	1.55174i
$403$	348.458			0.864660
$404$			249.097i			0.616577i
$405$	−166.316	+	167.981i	−0.410657	+	0.414768i
$406$	−1615.75			−3.97967
$407$			223.830i			0.549951i
$408$	42.6390	+	8.42625i	0.104507	+	0.0206526i
$409$	−523.908			−1.28095			−0.640474	−	0.767980i	$-0.721262\pi$
$409$	−523.908			−1.28095			−0.640474	+	0.767980i	$0.721262\pi$
$410$			70.7806i			0.172636i
$411$	101.389	−	513.052i	0.246687	−	1.24830i
$412$	266.514			0.646878
$413$		−	93.5846i		−	0.226597i
$414$	1172.52	+	482.255i	2.83216	+	1.16487i
$415$	−120.023			−0.289213
$416$		−	440.912i		−	1.05989i
$417$	5.18486	+	1.02462i	0.0124337	+	0.00245713i
$418$	146.782			0.351152
$419$		−	596.864i		−	1.42450i	−0.701928	−	0.712248i	$-0.747677\pi$
$419$		−	596.864i		−	1.42450i	0.701928	−	0.712248i	$-0.252323\pi$
$420$	127.403	−	644.690i	0.303339	−	1.53498i
$421$	745.944			1.77184			0.885919	−	0.463839i	$-0.153529\pi$
$421$	745.944			1.77184			0.885919	+	0.463839i	$0.153529\pi$
$422$			489.162i			1.15915i
$423$	3.83178	−	9.31629i	0.00905859	−	0.0220243i
$424$	−208.568			−0.491905
$425$		−	34.6724i		−	0.0815821i
$426$	936.072	+	184.985i	2.19735	+	0.434237i
$427$	−562.356			−1.31699
$428$			647.041i			1.51178i
$429$	−94.9458	+	480.450i	−0.221319	+	1.11993i
$430$	−428.689			−0.996950
$431$			514.240i			1.19313i	0.802564	+	0.596566i	$0.203469\pi$
$431$			514.240i			1.19313i	−0.802564	+	0.596566i	$0.796531\pi$
$432$	−60.5026	−	40.1005i	−0.140052	−	0.0928251i
$433$	94.8594			0.219075			0.109537	−	0.993983i	$-0.465063\pi$
$433$	94.8594			0.219075			0.109537	+	0.993983i	$0.465063\pi$
$434$			1108.61i			2.55440i
$435$	357.333	+	70.6155i	0.821454	+	0.162334i
$436$	536.901			1.23142
$437$		−	152.169i		−	0.348214i
$438$	−240.537	+	1217.18i	−0.549172	+	2.77895i
$439$	−229.998			−0.523912			−0.261956	−	0.965080i	$-0.584368\pi$
$439$	−229.998			−0.523912			−0.261956	+	0.965080i	$0.584368\pi$
$440$			268.803i			0.610917i
$441$	827.701	+	340.433i	1.87687	+	0.771957i
$442$	81.8496			0.185180
$443$		−	567.587i		−	1.28123i	−0.767860	−	0.640617i	$-0.778679\pi$
$443$		−	567.587i		−	1.28123i	0.767860	−	0.640617i	$-0.221321\pi$
$444$	303.472	+	59.9716i	0.683495	+	0.135071i
$445$	−219.053			−0.492253
$446$		−	1110.18i		−	2.48919i
$447$	51.4397	−	260.298i	0.115078	−	0.582323i
$448$	1271.74			2.83870
$449$		−	718.237i		−	1.59964i	−0.600242	−	0.799819i	$-0.704929\pi$
$449$		−	718.237i		−	1.59964i	0.600242	−	0.799819i	$-0.295071\pi$
$450$	179.873	−	437.329i	0.399718	−	0.971842i
$451$	101.753			0.225617
$452$		−	737.196i		−	1.63097i
$453$	235.281	+	46.4958i	0.519384	+	0.102640i
$454$	433.166			0.954110
$455$		−	434.039i		−	0.953931i
$456$	13.7933	−	69.7976i	0.0302484	−	0.153065i
$457$	−649.904			−1.42211			−0.711055	−	0.703137i	$-0.751782\pi$
$457$	−649.904			−1.42211			−0.711055	+	0.703137i	$0.751782\pi$
$458$		−	775.263i		−	1.69271i
$459$	31.3767	−	47.3404i	0.0683588	−	0.103138i
$460$	794.552			1.72729
$461$			657.743i			1.42677i	0.700771	+	0.713387i	$0.252840\pi$
$461$			657.743i			1.42677i	−0.700771	+	0.713387i	$0.747160\pi$
$462$	−1528.54	−	302.068i	−3.30853	−	0.653827i
$463$	46.1887			0.0997597			0.0498798	−	0.998755i	$-0.484116\pi$
$463$	46.1887			0.0997597			0.0498798	+	0.998755i	$0.484116\pi$
$464$			111.845i			0.241045i
$465$	48.4514	−	245.177i	0.104197	−	0.527261i
$466$	−1451.52			−3.11485
$467$		−	406.250i		−	0.869914i	−0.900451	−	0.434957i	$-0.856764\pi$
$467$		−	406.250i		−	0.869914i	0.900451	−	0.434957i	$-0.143236\pi$
$468$	625.962	+	257.458i	1.33753	+	0.550124i
$469$	810.137			1.72737
$470$		−	10.4121i		−	0.0221535i
$471$	211.343	+	41.7652i	0.448711	+	0.0886735i
$472$	52.9040			0.112085
$473$			616.276i			1.30291i
$474$	22.7821	−	115.283i	0.0480634	−	0.243213i
$475$	−56.7567			−0.119488
$476$			157.889i			0.331700i
$477$	−103.668	+	252.051i	−0.217334	+	0.528409i
$478$	−622.570			−1.30245
$479$		−	569.676i		−	1.18930i	−0.803984	−	0.594651i	$-0.797290\pi$
$479$		−	569.676i		−	1.18930i	0.803984	−	0.594651i	$-0.202710\pi$
$480$	−310.228	−	61.3067i	−0.646308	−	0.127722i
$481$	204.313			0.424767
$482$		−	87.5721i		−	0.181685i
$483$	−313.155	+	1584.65i	−0.648355	+	3.28084i
$484$	356.346			0.736252
$485$			544.048i			1.12175i
$486$	641.352	−	434.337i	1.31965	−	0.893697i
$487$	−478.590			−0.982731			−0.491366	−	0.870953i	$-0.663502\pi$
$487$	−478.590			−0.982731			−0.491366	+	0.870953i	$0.663502\pi$
$488$		−	317.904i		−	0.651442i
$489$	128.802	+	25.4537i	0.263399	+	0.0520525i
$490$	925.060			1.88788
$491$			454.446i			0.925552i	0.886475	+	0.462776i	$0.153147\pi$
$491$			454.446i			0.925552i	−0.886475	+	0.462776i	$0.846853\pi$
$492$	27.2631	−	137.958i	0.0554129	−	0.280403i
$493$	−87.5133			−0.177512
$494$		−	133.983i		−	0.271221i
$495$	324.845	+	133.609i	0.656253	+	0.269916i
$496$	76.7401			0.154718
$497$			1215.69i			2.44605i
$498$	385.827	+	76.2465i	0.774753	+	0.153105i
$499$	−158.942			−0.318520			−0.159260	−	0.987237i	$-0.550911\pi$
$499$	−158.942			−0.318520			−0.159260	+	0.987237i	$0.550911\pi$
$500$		−	745.834i		−	1.49167i
$501$	−56.9119	+	287.989i	−0.113597	+	0.574828i
$502$	−764.804			−1.52351
$503$			455.984i			0.906529i	0.891376	+	0.453265i	$0.149741\pi$
$503$			455.984i			0.906529i	−0.891376	+	0.453265i	$0.850259\pi$
$504$	−287.278	+	698.466i	−0.569997	+	1.38584i
$505$	117.998			0.233660
$506$		−	1883.86i		−	3.72304i
$507$	−58.8238	−	11.6247i	−0.116023	−	0.0229283i
$508$	1218.93			2.39947
$509$			831.857i			1.63430i	0.576428	+	0.817148i	$0.304446\pi$
$509$			831.857i			1.63430i	−0.576428	+	0.817148i	$0.695554\pi$
$510$	11.3808	−	57.5897i	0.0223153	−	0.112921i
$511$	−1580.77			−3.09348
$512$		−	171.165i		−	0.334307i
$513$	−77.4935	−	51.3618i	−0.151059	−	0.100121i
$514$	1066.19			2.07430
$515$		−	126.248i		−	0.245142i
$516$	835.557	+	165.121i	1.61930	+	0.320003i
$517$	−14.9683			−0.0289523
$518$			650.017i			1.25486i
$519$	39.4896	−	199.828i	0.0760880	−	0.385025i
$520$	245.365			0.471856
$521$		−	886.146i		−	1.70086i	−0.526091	−	0.850428i	$-0.676343\pi$
$521$		−	886.146i		−	1.70086i	0.526091	−	0.850428i	$-0.323657\pi$
$522$	−1103.82	−	454.001i	−2.11460	−	0.869734i
$523$	−116.013			−0.221823			−0.110912	−	0.993830i	$-0.535377\pi$
$523$	−116.013			−0.221823			−0.110912	+	0.993830i	$0.535377\pi$
$524$			744.341i			1.42050i
$525$	591.047	+	116.802i	1.12580	+	0.222480i
$526$	−1120.65			−2.13052
$527$			60.0455i			0.113938i
$528$	−20.9097	+	105.809i	−0.0396017	+	0.200395i
$529$	−1424.01			−2.69189
$530$			281.699i			0.531507i
$531$	26.2959	−	63.9338i	0.0495215	−	0.120403i
$532$	258.455			0.485819
$533$		−	92.8808i		−	0.174260i
$534$	704.166	+	139.156i	1.31866	+	0.260592i
$535$	306.505			0.572906
$536$			457.976i			0.854433i
$537$	169.226	−	856.327i	0.315132	−	1.59465i
$538$	774.723			1.44001
$539$		−	1329.85i		−	2.46726i
$540$	268.186	−	404.632i	0.496640	−	0.749318i
$541$	391.559			0.723769			0.361885	−	0.932223i	$-0.382133\pi$
$541$	391.559			0.723769			0.361885	+	0.932223i	$0.382133\pi$
$542$			222.460i			0.410442i
$543$	187.620	+	37.0772i	0.345525	+	0.0682821i
$544$	75.9771			0.139664
$545$		−	254.332i		−	0.466664i
$546$	−275.729	+	1395.26i	−0.504998	+	2.55542i
$547$	390.455			0.713812			0.356906	−	0.934140i	$-0.383832\pi$
$547$	390.455			0.713812			0.356906	+	0.934140i	$0.383832\pi$
$548$			1073.97i			1.95979i
$549$	−384.182	−	158.014i	−0.699785	−	0.287821i
$550$	−702.649			−1.27754
$551$			143.254i			0.259990i
$552$	−895.812	−	177.029i	−1.62285	−	0.320705i
$553$	149.720			0.270741
$554$		−	236.592i		−	0.427062i
$555$	28.4087	−	143.755i	0.0511869	−	0.259019i
$556$	−10.8534			−0.0195205
$557$		−	417.528i		−	0.749602i	−0.927105	−	0.374801i	$-0.877711\pi$
$557$		−	417.528i		−	0.749602i	0.927105	−	0.374801i	$-0.122289\pi$
$558$	−311.503	+	757.365i	−0.558250	+	1.35728i
$559$	562.540			1.00633
$560$		−	95.5874i		−	0.170692i
$561$	−82.7902	−	16.3609i	−0.147576	−	0.0291637i
$562$	−1091.40			−1.94199
$563$			142.520i			0.253144i	0.991957	+	0.126572i	$0.0403975\pi$
$563$			142.520i			0.253144i	−0.991957	+	0.126572i	$0.959602\pi$
$564$	−4.01052	+	20.2943i	−0.00711085	+	0.0359827i
$565$	−349.212			−0.618074
$566$		−	1563.28i		−	2.76199i
$567$	701.294	+	694.344i	1.23685	+	1.22459i
$568$	−687.238			−1.20993
$569$			441.466i			0.775863i	0.921688	+	0.387932i	$0.126810\pi$
$569$			441.466i			0.775863i	−0.921688	+	0.387932i	$0.873190\pi$
$570$	−94.2711	−	18.6297i	−0.165388	−	0.0326837i
$571$	560.119			0.980943			0.490472	−	0.871457i	$-0.336825\pi$
$571$	560.119			0.980943			0.490472	+	0.871457i	$0.336825\pi$
$572$		−	1005.72i		−	1.75826i
$573$	105.401	−	533.358i	0.183946	−	0.930816i
$574$	295.498			0.514805
$575$			728.440i			1.26685i
$576$	868.807	+	357.340i	1.50835	+	0.620381i
$577$	521.847			0.904414			0.452207	−	0.891913i	$-0.350637\pi$
$577$	521.847			0.904414			0.452207	+	0.891913i	$0.350637\pi$
$578$		−	907.109i		−	1.56939i
$579$	−787.071	−	155.540i	−1.35936	−	0.268635i
$580$	−748.001			−1.28966
$581$			501.079i			0.862442i
$582$	345.614	−	1748.90i	0.593839	−	3.00498i
$583$	404.966			0.694624
$584$		−	893.619i		−	1.53017i
$585$	121.959	−	296.520i	0.208476	−	0.506872i
$586$	1276.20			2.17782
$587$		−	393.477i		−	0.670319i	−0.942161	−	0.335160i	$-0.891210\pi$
$587$		−	393.477i		−	0.670319i	0.942161	−	0.335160i	$-0.108790\pi$
$588$	−1803.03	−	356.313i	−3.06638	−	0.605974i
$589$	98.2910			0.166878
$590$		−	71.4540i		−	0.121108i
$591$	108.861	−	550.865i	0.184198	−	0.932089i
$592$	44.9954			0.0760057
$593$		−	815.002i		−	1.37437i	−0.726482	−	0.687185i	$-0.758846\pi$
$593$		−	815.002i		−	1.37437i	0.726482	−	0.687185i	$-0.241154\pi$
$594$	−959.370	−	635.860i	−1.61510	−	1.07047i
$595$	74.7926			0.125702
$596$			544.880i			0.914228i
$597$	−129.362	−	25.5643i	−0.216687	−	0.0428213i
$598$	−1719.60			−2.87558
$599$			248.629i			0.415074i	0.978227	+	0.207537i	$0.0665447\pi$
$599$			248.629i			0.415074i	−0.978227	+	0.207537i	$0.933455\pi$
$600$	−66.0289	+	334.123i	−0.110048	+	0.556872i
$601$	463.227			0.770761			0.385381	−	0.922758i	$-0.374070\pi$
$601$	463.227			0.770761			0.385381	+	0.922758i	$0.374070\pi$
$602$			1789.71i			2.97294i
$603$	553.457	+	227.637i	0.917840	+	0.377507i
$604$	−492.511			−0.815416
$605$		−	168.802i		−	0.279012i
$606$	−379.316	−	74.9599i	−0.625935	−	0.123696i
$607$	61.8284			0.101859			0.0509295	−	0.998702i	$-0.483782\pi$
$607$	61.8284			0.101859			0.0509295	+	0.998702i	$0.483782\pi$
$608$		−	124.370i		−	0.204556i
$609$	294.809	−	1491.81i	0.484086	−	2.44960i
$610$	−429.372			−0.703888
$611$			13.6631i			0.0223619i
$612$	−44.3646	+	107.864i	−0.0724911	+	0.176249i
$613$	356.755			0.581981			0.290991	−	0.956726i	$-0.406015\pi$
$613$	356.755			0.581981			0.290991	+	0.956726i	$0.406015\pi$
$614$		−	667.839i		−	1.08769i
$615$	−65.3513	−	12.9146i	−0.106262	−	0.0209994i
$616$	1122.21			1.82177
$617$			225.517i			0.365506i	0.983159	+	0.182753i	$0.0585008\pi$
$617$			225.517i			0.365506i	−0.983159	+	0.182753i	$0.941499\pi$
$618$	−80.2010	+	405.838i	−0.129775	+	0.656695i
$619$	−1105.63			−1.78616			−0.893080	−	0.449898i	$-0.851460\pi$
$619$	−1105.63			−1.78616			−0.893080	+	0.449898i	$0.851460\pi$
$620$			513.226i			0.827784i
$621$	−659.200	+	994.584i	−1.06151	+	1.60158i
$622$	−1220.94			−1.96292
$623$			914.510i			1.46791i
$624$	96.5825	+	19.0865i	0.154780	+	0.0305873i
$625$	58.7762			0.0940419
$626$		−	91.8733i		−	0.146763i
$627$	−26.7818	+	135.523i	−0.0427142	+	0.216145i
$628$	−442.402			−0.704462
$629$			35.2068i			0.0559726i
$630$	943.372	+	388.008i	1.49742	+	0.615886i
$631$	130.411			0.206674			0.103337	−	0.994646i	$-0.467048\pi$
$631$	130.411			0.206674			0.103337	+	0.994646i	$0.467048\pi$
$632$			84.6376i			0.133920i
$633$	−451.641	−	89.2525i	−0.713492	−	0.140999i
$634$	1140.33			1.79862
$635$		−	577.410i		−	0.909307i
$636$	108.504	−	549.058i	0.170604	−	0.863299i
$637$	−1213.90			−1.90564
$638$			1773.49i			2.77976i
$639$	−341.591	+	830.517i	−0.534571	+	1.29971i
$640$	549.364			0.858381
$641$			19.7410i			0.0307972i	0.999881	+	0.0153986i	$0.00490172\pi$
$641$			19.7410i			0.0307972i	−0.999881	+	0.0153986i	$0.995098\pi$
$642$	−985.290	−	194.711i	−1.53472	−	0.303289i
$643$	879.551			1.36789			0.683943	−	0.729535i	$-0.260263\pi$
$643$	879.551			1.36789			0.683943	+	0.729535i	$0.260263\pi$
$644$		−	3317.13i		−	5.15082i
$645$	78.2185	−	395.806i	0.121269	−	0.613652i
$646$	23.0877			0.0357394
$647$			611.023i			0.944394i	0.881493	+	0.472197i	$0.156539\pi$
$647$			611.023i			0.944394i	−0.881493	+	0.472197i	$0.843461\pi$
$648$	−392.517	+	396.447i	−0.605737	+	0.611800i
$649$	−102.721			−0.158276
$650$			641.381i			0.986740i
$651$	−1023.57	−	202.277i	−1.57231	−	0.310717i
$652$	−269.620			−0.413528
$653$		−	441.041i		−	0.675407i	−0.941253	−	0.337704i	$-0.890350\pi$
$653$		−	441.041i		−	0.675407i	0.941253	−	0.337704i	$-0.109650\pi$
$654$	−161.568	+	817.574i	−0.247045	+	1.25011i
$655$	352.596			0.538315
$656$		−	20.4549i		−	0.0311813i
$657$	−1079.93	−	444.173i	−1.64372	−	0.676062i
$658$	−43.4690			−0.0660623
$659$			38.8201i			0.0589076i	0.999566	+	0.0294538i	$0.00937680\pi$
$659$			38.8201i			0.0589076i	−0.999566	+	0.0294538i	$0.990623\pi$
$660$	−707.631	−	139.841i	−1.07217	−	0.211880i
$661$	−951.942			−1.44016			−0.720078	−	0.693894i	$-0.755894\pi$
$661$	−951.942			−1.44016			−0.720078	+	0.693894i	$0.755894\pi$
$662$			423.252i			0.639354i
$663$	−14.9343	+	75.5712i	−0.0225253	+	0.113984i
$664$	−283.263			−0.426602
$665$		−	122.431i		−	0.184107i
$666$	−182.645	+	444.069i	−0.274242	+	0.666770i
$667$	1838.59			2.75650
$668$		−	602.845i		−	0.902462i
$669$	1025.02	+	202.563i	1.53217	+	0.302785i
$670$	618.558			0.923221
$671$			617.259i			0.919909i
$672$	−255.946	+	1295.15i	−0.380872	+	1.92731i
$673$	−435.673			−0.647360			−0.323680	−	0.946167i	$-0.604920\pi$
$673$	−435.673			−0.647360			−0.323680	+	0.946167i	$0.604920\pi$
$674$		−	649.073i		−	0.963016i
$675$	370.964	+	245.871i	0.549576	+	0.364253i
$676$	123.135			0.182153
$677$			138.438i			0.204488i	0.994759	+	0.102244i	$0.0326022\pi$
$677$			138.438i			0.204488i	−0.994759	+	0.102244i	$0.967398\pi$
$678$	1122.58	+	221.842i	1.65572	+	0.327200i
$679$	2271.32			3.34509
$680$			42.2808i			0.0621776i
$681$	−79.0354	+	399.940i	−0.116058	+	0.587283i
$682$	1216.84			1.78423
$683$		−	610.846i		−	0.894358i	−0.894445	−	0.447179i	$-0.852429\pi$
$683$		−	610.846i		−	0.894358i	0.894445	−	0.447179i	$-0.147571\pi$
$684$	176.568	+	72.6222i	0.258140	+	0.106173i
$685$	508.741			0.742688
$686$		−	1958.99i		−	2.85567i
$687$	715.796	+	141.454i	1.04192	+	0.205902i
$688$	123.887			0.180068
$689$		−	369.654i		−	0.536509i
$690$	−239.101	+	1209.91i	−0.346524	+	1.75350i
$691$	150.187			0.217347			0.108674	−	0.994077i	$-0.465340\pi$
$691$	150.187			0.217347			0.108674	+	0.994077i	$0.465340\pi$
$692$			418.298i			0.604477i
$693$	557.795	−	1356.18i	0.804899	−	1.95697i
$694$	610.287			0.879376
$695$			5.14130i			0.00739755i
$696$	843.329	+	166.657i	1.21168	+	0.239450i
$697$	16.0050			0.0229627
$698$		−	1199.72i		−	1.71880i
$699$	264.844	−	1340.18i	0.378891	−	1.91728i
$700$	−1237.23			−1.76748
$701$			484.616i			0.691321i	0.938360	+	0.345661i	$0.112345\pi$
$701$			484.616i			0.691321i	−0.938360	+	0.345661i	$0.887655\pi$
$702$	−580.416	+	875.717i	−0.826804	+	1.24746i
$703$	57.6314			0.0819793
$704$		−	1395.90i		−	1.98281i
$705$	9.61345	+	1.89979i	0.0136361	+	0.00269474i
$706$	1641.10			2.32451
$707$		−	492.624i		−	0.696780i
$708$	−27.5225	+	139.271i	−0.0388736	+	0.196710i
$709$	−626.486			−0.883619			−0.441809	−	0.897109i	$-0.645663\pi$
$709$	−626.486			−0.883619			−0.441809	+	0.897109i	$0.645663\pi$
$710$			928.207i			1.30733i
$711$	102.283	+	42.0691i	0.143858	+	0.0591689i
$712$	−516.979			−0.726094
$713$		−	1261.51i		−	1.76930i
$714$	−240.428	−	47.5130i	−0.336734	−	0.0665448i
$715$	−476.414			−0.666313
$716$			1792.54i			2.50355i
$717$	113.594	−	574.815i	0.158430	−	0.801695i
$718$	651.977			0.908045
$719$			1027.95i			1.42969i	0.699284	+	0.714844i	$0.253502\pi$
$719$			1027.95i			1.42969i	−0.699284	+	0.714844i	$0.746498\pi$
$720$	26.8587	−	65.3020i	0.0373037	−	0.0906972i
$721$	−527.067			−0.731022
$722$			1112.93i			1.54145i
$723$	80.8548	+	15.9784i	0.111832	+	0.0221001i
$724$	−392.743			−0.542463
$725$		−	685.763i		−	0.945879i
$726$	−107.234	+	542.631i	−0.147705	+	0.747425i
$727$	−554.861			−0.763220			−0.381610	−	0.924323i	$-0.624630\pi$
$727$	−554.861			−0.763220			−0.381610	+	0.924323i	$0.624630\pi$
$728$		−	1024.36i		−	1.40709i
$729$	284.000	+	671.405i	0.389574	+	0.920995i
$730$	−1206.95			−1.65336
$731$			96.9357i			0.132607i
$732$	836.888	+	165.385i	1.14329	+	0.225935i
$733$	175.837			0.239886			0.119943	−	0.992781i	$-0.461729\pi$
$733$	175.837			0.239886			0.119943	+	0.992781i	$0.461729\pi$
$734$		−	231.158i		−	0.314929i
$735$	−168.786	+	854.102i	−0.229641	+	1.16204i
$736$	−1596.22			−2.16877
$737$		−	889.230i		−	1.20655i
$738$	201.874	+	83.0307i	0.273542	+	0.112508i
$739$	−139.389			−0.188618			−0.0943090	−	0.995543i	$-0.530064\pi$
$739$	−139.389			−0.188618			−0.0943090	+	0.995543i	$0.530064\pi$
$740$			300.922i			0.406651i
$741$	123.706	+	24.4465i	0.166944	+	0.0329913i
$742$	1176.05			1.58497
$743$		−	100.461i		−	0.135210i	−0.997712	−	0.0676048i	$-0.978464\pi$
$743$		−	100.461i		−	0.135210i	0.997712	−	0.0676048i	$-0.0215357\pi$
$744$	114.349	−	578.633i	0.153694	−	0.777733i
$745$	258.111			0.346458
$746$		−	107.788i		−	0.144488i
$747$	−140.796	+	342.320i	−0.188482	+	0.458260i
$748$	173.304			0.231690
$749$		−	1279.61i		−	1.70842i
$750$	1135.73	+	224.441i	1.51431	+	0.299255i
$751$	−153.159			−0.203940			−0.101970	−	0.994787i	$-0.532515\pi$
$751$	−153.159			−0.203940			−0.101970	+	0.994787i	$0.532515\pi$
$752$			3.00900i			0.00400134i
$753$	139.546	−	706.139i	0.185320	−	0.937767i
$754$	1618.85			2.14702
$755$			233.304i			0.309012i
$756$	−1689.27	−	1119.63i	−2.23449	−	1.48100i
$757$	−947.893			−1.25217			−0.626085	−	0.779755i	$-0.715344\pi$
$757$	−947.893			−1.25217			−0.626085	+	0.779755i	$0.715344\pi$
$758$		−	226.180i		−	0.298391i
$759$	1739.36	+	343.729i	2.29164	+	0.452871i
$760$	69.2112			0.0910673
$761$			1068.30i			1.40381i	0.712272	+	0.701904i	$0.247666\pi$
$761$			1068.30i			1.40381i	−0.712272	+	0.701904i	$0.752334\pi$
$762$	−366.808	+	1856.14i	−0.481375	+	2.43588i
$763$	−1061.79			−1.39161
$764$			1116.47i			1.46135i
$765$	51.0957	+	21.0156i	0.0667918	+	0.0274714i
$766$	487.125			0.635934
$767$			93.7644i			0.122248i
$768$	−537.184	−	106.157i	−0.699458	−	0.138226i
$769$	908.642			1.18159			0.590795	−	0.806822i	$-0.298814\pi$
$769$	908.642			1.18159			0.590795	+	0.806822i	$0.298814\pi$
$770$		−	1515.70i		−	1.96844i
$771$	−194.536	+	984.405i	−0.252317	+	1.27679i
$772$	1647.57			2.13416
$773$			606.118i			0.784112i	0.919941	+	0.392056i	$0.128236\pi$
$773$			606.118i			0.784112i	−0.919941	+	0.392056i	$0.871764\pi$
$774$	−502.882	+	1222.67i	−0.649718	+	1.57967i
$775$	−470.522			−0.607125
$776$			1283.99i			1.65463i
$777$	−600.157	−	118.602i	−0.772402	−	0.152641i
$778$	1428.61			1.83626
$779$		−	26.1993i		−	0.0336319i
$780$	−127.647	+	645.928i	−0.163650	+	0.828113i
$781$	1334.38			1.70855
$782$		−	296.317i		−	0.378922i
$783$	620.579	−	936.315i	0.792566	−	1.19580i
$784$	−267.334			−0.340987
$785$			209.567i			0.266964i
$786$	−1133.46	−	223.992i	−1.44206	−	0.284977i
$787$	−1402.16			−1.78165			−0.890826	−	0.454345i	$-0.849873\pi$
$787$	−1402.16			−1.78165			−0.890826	+	0.454345i	$0.849873\pi$
$788$			1153.12i			1.46335i
$789$	204.474	−	1034.69i	0.259156	−	1.31140i
$790$	114.315			0.144702
$791$			1457.91i			1.84312i
$792$	766.657	+	315.325i	0.968001	+	0.398138i
$793$	563.436			0.710512
$794$		−	779.272i		−	0.981450i
$795$	−260.091	−	51.3987i	−0.327158	−	0.0646524i
$796$	270.792			0.340191
$797$		−	735.167i		−	0.922418i	−0.887292	−	0.461209i	$-0.847416\pi$
$797$		−	735.167i		−	0.922418i	0.887292	−	0.461209i	$-0.152584\pi$
$798$	−77.7761	+	393.567i	−0.0974637	+	0.493192i
$799$	−2.35440			−0.00294669
$800$			595.363i			0.744204i
$801$	−256.964	+	624.762i	−0.320804	+	0.779977i
$802$	10.4290			0.0130037
$803$			1735.10i			2.16077i
$804$	−1205.63	−	238.255i	−1.49954	−	0.296337i
$805$	−1571.33			−1.95197
$806$		−	1110.74i		−	1.37809i
$807$	−141.356	+	715.297i	−0.175162	+	0.886366i
$808$	278.484			0.344658
$809$		−	827.182i		−	1.02247i	−0.859440	−	0.511237i	$-0.829187\pi$
$809$		−	827.182i		−	1.02247i	0.859440	−	0.511237i	$-0.170813\pi$
$810$	535.455	+	530.148i	0.661055	+	0.654503i
$811$	−996.744			−1.22903			−0.614515	−	0.788905i	$-0.710648\pi$
$811$	−996.744			−1.22903			−0.614515	+	0.788905i	$0.710648\pi$
$812$			3122.79i			3.84580i
$813$	−205.396	−	40.5900i	−0.252639	−	0.0499261i
$814$	713.478			0.876508
$815$			127.720i			0.156712i
$816$	−3.28894	+	16.6429i	−0.00403056	+	0.0203957i
$817$	158.678			0.194220
$818$			1670.00i			2.04157i
$819$	−1237.93	−	509.158i	−1.51151	−	0.621682i
$820$	136.799			0.166829
$821$			1443.77i			1.75855i	0.476318	+	0.879273i	$0.341971\pi$
$821$			1443.77i			1.75855i	−0.476318	+	0.879273i	$0.658029\pi$
$822$	−1635.40	−	323.185i	−1.98954	−	0.393169i
$823$	895.823			1.08848			0.544242	−	0.838928i	$-0.316817\pi$
$823$	895.823			1.08848			0.544242	+	0.838928i	$0.316817\pi$
$824$		−	297.955i		−	0.361595i
$825$	128.205	−	648.751i	0.155400	−	0.786365i
$826$	−298.309			−0.361149
$827$			151.631i			0.183351i	0.995789	+	0.0916756i	$0.0292223\pi$
$827$			151.631i			0.183351i	−0.995789	+	0.0916756i	$0.970778\pi$
$828$	932.065	−	2266.15i	1.12568	−	2.73689i
$829$	−724.289			−0.873690			−0.436845	−	0.899537i	$-0.643904\pi$
$829$	−724.289			−0.873690			−0.436845	+	0.899537i	$0.643904\pi$
$830$			382.585i			0.460946i
$831$	218.444	+	43.1686i	0.262869	+	0.0519477i
$832$	−1274.18			−1.53147
$833$		−	209.176i		−	0.251112i
$834$	3.26608	−	16.5272i	0.00391616	−	0.0198168i
$835$	−285.569			−0.341999
$836$		−	283.688i		−	0.339340i
$837$	−642.433	−	425.798i	−0.767543	−	0.508719i
$838$	−1902.56			−2.27035
$839$			284.547i			0.339150i	0.985517	+	0.169575i	$0.0542395\pi$
$839$			284.547i			0.339150i	−0.985517	+	0.169575i	$0.945760\pi$
$840$	−720.745	−	142.432i	−0.858029	−	0.169562i
$841$	−889.869			−1.05811
$842$		−	2377.76i		−	2.82395i
$843$	199.137	−	1007.68i	0.236224	−	1.19535i
$844$	945.415			1.12016
$845$		−	58.3295i		−	0.0690290i
$846$	−29.6965	−	12.2142i	−0.0351023	−	0.0144375i
$847$	−704.722			−0.832021
$848$		−	81.4082i		−	0.0960002i
$849$	1443.37	+	285.237i	1.70008	+	0.335968i
$850$	−110.521			−0.130025
$851$		−	739.666i		−	0.869173i
$852$	357.525	−	1809.17i	0.419630	−	2.12344i
$853$	−633.721			−0.742932			−0.371466	−	0.928447i	$-0.621145\pi$
$853$	−633.721			−0.742932			−0.371466	+	0.928447i	$0.621145\pi$
$854$			1792.56i			2.09902i
$855$	34.4014	−	83.6407i	0.0402355	−	0.0978254i
$856$	723.373			0.845061
$857$			26.5411i			0.0309698i	0.999880	+	0.0154849i	$0.00492919\pi$
$857$			26.5411i			0.0309698i	−0.999880	+	0.0154849i	$0.995071\pi$
$858$	1531.48	+	302.648i	1.78494	+	0.352737i
$859$	−703.528			−0.819008			−0.409504	−	0.912308i	$-0.634298\pi$
$859$	−703.528			−0.819008			−0.409504	+	0.912308i	$0.634298\pi$
$860$			828.536i			0.963414i
$861$	−53.9165	+	272.832i	−0.0626208	+	0.316878i
$862$	1639.19			1.90161
$863$			207.245i			0.240145i	0.992765	+	0.120072i	$0.0383126\pi$
$863$			207.245i			0.240145i	−0.992765	+	0.120072i	$0.961687\pi$
$864$	−538.773	+	812.887i	−0.623579	+	0.940841i
$865$	198.149			0.229074
$866$		−	302.373i		−	0.349160i
$867$	837.528	+	165.511i	0.966007	+	0.190901i
$868$	2142.64			2.46848
$869$		−	164.337i		−	0.189110i
$870$	225.093	−	1139.03i	0.258728	−	1.30923i
$871$	−811.693			−0.931909
$872$		−	600.240i		−	0.688349i
$873$	1551.68	+	638.207i	1.77742	+	0.731050i
$874$	−485.054			−0.554981
$875$			1474.99i			1.68570i
$876$	2352.47	+	464.892i	2.68547	+	0.530698i
$877$	−1109.52			−1.26513			−0.632567	−	0.774505i	$-0.717999\pi$
$877$	−1109.52			−1.26513			−0.632567	+	0.774505i	$0.717999\pi$
$878$			733.138i			0.835009i
$879$	−232.856	+	1178.31i	−0.264910	+	1.34051i
$880$	−104.920			−0.119227
$881$		−	837.583i		−	0.950718i	−0.879792	−	0.475359i	$-0.842318\pi$
$881$		−	837.583i		−	0.950718i	0.879792	−	0.475359i	$-0.157682\pi$
$882$	1085.16	−	2638.37i	1.23034	−	2.99135i
$883$	221.130			0.250431			0.125215	−	0.992130i	$-0.460038\pi$
$883$	221.130			0.250431			0.125215	+	0.992130i	$0.460038\pi$
$884$		−	158.193i		−	0.178951i
$885$	65.9730	+	13.0375i	0.0745458	+	0.0147316i
$886$	−1809.23			−2.04202
$887$			886.067i			0.998948i	0.866329	+	0.499474i	$0.166473\pi$
$887$			886.067i			0.998948i	−0.866329	+	0.499474i	$0.833527\pi$
$888$	67.0465	−	339.273i	0.0755028	−	0.382064i
$889$	−2410.60			−2.71158
$890$			698.250i			0.784550i
$891$	762.133	−	769.762i	0.855368	−	0.863930i
$892$	−2145.67			−2.40546
$893$			3.85402i			0.00431581i
$894$	−829.724	−	163.969i	−0.928103	−	0.183410i
$895$	849.132			0.948751
$896$		−	2293.51i		−	2.55972i
$897$	313.757	−	1587.69i	0.349785	−	1.77000i
$898$	−2289.44			−2.54949
$899$			1187.60i			1.32102i
$900$	−845.236	−	347.645i	−0.939151	−	0.386272i
$901$	63.6981			0.0706971
$902$		−	324.347i		−	0.359587i
$903$	−1652.43	−	326.550i	−1.82993	−	0.361628i
$904$	−824.164			−0.911686
$905$			186.044i			0.205573i
$906$	148.210	−	749.979i	0.163587	−	0.827791i
$907$	241.096			0.265817			0.132909	−	0.991128i	$-0.457568\pi$
$907$	241.096			0.265817			0.132909	+	0.991128i	$0.457568\pi$
$908$		−	837.190i		−	0.922016i
$909$	138.420	−	336.543i	0.152277	−	0.370235i
$910$	−1383.54			−1.52037
$911$		−	437.393i		−	0.480124i	−0.970758	−	0.240062i	$-0.922832\pi$
$911$		−	437.393i		−	0.480124i	0.970758	−	0.240062i	$-0.0771677\pi$
$912$	27.2434	+	5.38380i	0.0298722	+	0.00590329i
$913$	549.999			0.602409
$914$			2071.63i			2.26655i
$915$	78.3431	−	396.436i	0.0856209	−	0.433264i
$916$	−1498.37			−1.63577
$917$		−	1472.03i		−	1.60527i
$918$	−150.902	−	100.016i	−0.164381	−	0.108950i
$919$	93.6771			0.101934			0.0509669	−	0.998700i	$-0.483770\pi$
$919$	93.6771			0.101934			0.0509669	+	0.998700i	$0.483770\pi$
$920$		−	888.286i		−	0.965528i
$921$	616.612	+	121.854i	0.669503	+	0.132306i
$922$	2096.61			2.27398
$923$		−	1218.02i		−	1.31964i
$924$	−583.814	+	2954.25i	−0.631833	+	3.19724i
$925$	−275.883			−0.298252
$926$		−	147.231i		−	0.158996i
$927$	−360.074	−	148.098i	−0.388429	−	0.159761i
$928$	1502.70			1.61929
$929$			632.098i			0.680407i	0.940352	+	0.340203i	$0.110496\pi$
$929$			632.098i			0.680407i	−0.940352	+	0.340203i	$0.889504\pi$
$930$	−781.522	−	154.443i	−0.840346	−	0.166068i
$931$	−342.409			−0.367786
$932$			2805.39i			3.01007i
$933$	222.772	−	1127.28i	0.238769	−	1.20823i
$934$	−1294.96			−1.38646
$935$		−	82.0946i		−	0.0878017i
$936$	287.830	−	699.808i	0.307511	−	0.747658i
$937$	1763.82			1.88241			0.941207	−	0.337830i	$-0.109693\pi$
$937$	1763.82			1.88241			0.941207	+	0.337830i	$0.109693\pi$
$938$		−	2582.38i		−	2.75307i
$939$	84.8261	+	16.7632i	0.0903366	+	0.0178522i
$940$	−20.1238			−0.0214082
$941$			964.481i			1.02495i	0.858701	+	0.512477i	$0.171272\pi$
$941$			964.481i			1.02495i	−0.858701	+	0.512477i	$0.828728\pi$
$942$	133.130	−	673.674i	0.141327	−	0.715153i
$943$	−336.253			−0.356578
$944$			20.6495i			0.0218745i
$945$	−530.373	+	800.214i	−0.561241	+	0.846787i
$946$	1964.44			2.07657
$947$		−	532.682i		−	0.562495i	−0.959635	−	0.281247i	$-0.909252\pi$
$947$		−	532.682i		−	0.562495i	0.959635	−	0.281247i	$-0.0907481\pi$
$948$	−222.810	−	44.0314i	−0.235032	−	0.0464466i
$949$	1583.81			1.66892
$950$			180.917i			0.190439i
$951$	−208.064	+	1052.86i	−0.218784	+	1.10710i
$952$	176.516			0.185416
$953$			1383.10i			1.45132i	0.688056	+	0.725658i	$0.258464\pi$
$953$			1383.10i			1.45132i	−0.688056	+	0.725658i	$0.741536\pi$
$954$	803.435	+	330.452i	0.842175	+	0.346386i
$955$	528.876			0.553797
$956$			1203.26i			1.25864i
$957$	−1637.45	−	323.591i	−1.71103	−	0.338130i
$958$	−1815.89			−1.89550
$959$		−	2123.92i		−	2.21472i
$960$	−177.169	+	896.519i	−0.184551	+	0.933874i
$961$	−146.152			−0.152083
$962$		−	651.266i		−	0.676991i
$963$	359.552	−	874.186i	0.373366	−	0.907773i
$964$	−169.253			−0.175573
$965$		−	780.458i		−	0.808765i
$966$	5051.21	+	998.211i	5.22899	+	1.03334i
$967$	−1571.05			−1.62467			−0.812333	−	0.583194i	$-0.801803\pi$
$967$	−1571.05			−1.62467			−0.812333	+	0.583194i	$0.801803\pi$
$968$		−	398.384i		−	0.411554i
$969$	−4.21257	+	21.3167i	−0.00434734	+	0.0219987i
$970$	1734.20			1.78784
$971$		−	584.360i		−	0.601813i	−0.953654	−	0.300906i	$-0.902711\pi$
$971$		−	584.360i		−	0.601813i	0.953654	−	0.300906i	$-0.0972892\pi$
$972$	−839.453	−	1239.56i	−0.863635	−	1.27526i
$973$	21.4641			0.0220597
$974$			1525.55i			1.56627i
$975$	−592.183	−	117.026i	−0.607367	−	0.120027i
$976$	124.084			0.127136
$977$			433.880i			0.444095i	0.975036	+	0.222047i	$0.0712739\pi$
$977$			433.880i			0.444095i	−0.975036	+	0.222047i	$0.928726\pi$
$978$	81.1359	−	410.569i	0.0829610	−	0.419804i
$979$	1003.79			1.02533
$980$		−	1787.89i		−	1.82437i
$981$	−725.382	−	298.349i	−0.739431	−	0.304127i
$982$	1448.59			1.47514
$983$		−	1661.50i		−	1.69024i	−0.534580	−	0.845118i	$-0.679530\pi$
$983$		−	1661.50i		−	1.69024i	0.534580	−	0.845118i	$-0.320470\pi$
$984$	−154.234	−	30.4794i	−0.156741	−	0.0309750i
$985$	546.236			0.554555
$986$			278.957i			0.282917i
$987$	7.93134	−	40.1346i	0.00803581	−	0.0406633i
$988$	−258.952			−0.262097
$989$		−	2036.54i		−	2.05919i
$990$	425.889	−	1035.47i	0.430191	−	1.04593i
$991$	−365.343			−0.368661			−0.184330	−	0.982864i	$-0.559012\pi$
$991$	−365.343			−0.368661			−0.184330	+	0.982864i	$0.559012\pi$
$992$		−	1031.05i		−	1.03936i
$993$	−390.786	−	77.2265i	−0.393541	−	0.0777709i
$994$	3875.12			3.89851
$995$		−	128.275i		−	0.128920i
$996$	147.363	−	745.697i	0.147955	−	0.748692i
$997$	1276.56			1.28040			0.640202	−	0.768207i	$-0.278851\pi$
$997$	1276.56			1.28040			0.640202	+	0.768207i	$0.278851\pi$
$998$			506.641i			0.507656i
$999$	−376.681	−	249.660i	−0.377058	−	0.249910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.5	✓	38
3.2	odd	2	inner	177.3.b.a.119.34	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.5	✓	38	1.1	even	1	trivial
177.3.b.a.119.34	yes	38	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.18759i q^{2} +(2.94308 + 0.581607i) q^{3} -6.16073 q^{4} +2.91835i q^{5} +(1.85393 - 9.38134i) q^{6} +12.1837 q^{7} +6.88752i q^{8} +(8.32347 + 3.42344i) q^{9} +O(q^{10})\)	\(q-3.18759i q^{2} +(2.94308 + 0.581607i) q^{3} -6.16073 q^{4} +2.91835i q^{5} +(1.85393 - 9.38134i) q^{6} +12.1837 q^{7} +6.88752i q^{8} +(8.32347 + 3.42344i) q^{9} +9.30252 q^{10} -13.3732i q^{11} +(-18.1315 - 3.58312i) q^{12} -12.2071 q^{13} -38.8366i q^{14} +(-1.69734 + 8.58896i) q^{15} -2.68834 q^{16} -2.10350i q^{17} +(10.9125 - 26.5318i) q^{18} -3.44330 q^{19} -17.9792i q^{20} +(35.8576 + 7.08611i) q^{21} -42.6282 q^{22} +44.1928i q^{23} +(-4.00583 + 20.2705i) q^{24} +16.4832 q^{25} +38.9112i q^{26} +(22.5056 + 14.9164i) q^{27} -75.0603 q^{28} -41.6037i q^{29} +(27.3781 + 5.41041i) q^{30} -28.5455 q^{31} +36.1194i q^{32} +(7.77793 - 39.3583i) q^{33} -6.70509 q^{34} +35.5563i q^{35} +(-51.2786 - 21.0909i) q^{36} -16.7372 q^{37} +10.9758i q^{38} +(-35.9264 - 7.09973i) q^{39} -20.1002 q^{40} +7.60876i q^{41} +(22.5876 - 114.299i) q^{42} -46.0831 q^{43} +82.3884i q^{44} +(-9.99080 + 24.2908i) q^{45} +140.869 q^{46} -1.11928i q^{47} +(-7.91200 - 1.56356i) q^{48} +99.4419 q^{49} -52.5417i q^{50} +(1.22341 - 6.19077i) q^{51} +75.2045 q^{52} +30.2820i q^{53} +(47.5475 - 71.7385i) q^{54} +39.0276 q^{55} +83.9152i q^{56} +(-10.1339 - 2.00265i) q^{57} -132.616 q^{58} -7.68115i q^{59} +(10.4568 - 52.9142i) q^{60} -46.1565 q^{61} +90.9915i q^{62} +(101.410 + 41.7100i) q^{63} +104.380 q^{64} -35.6246i q^{65} +(-125.458 - 24.7928i) q^{66} +66.4936 q^{67} +12.9591i q^{68} +(-25.7029 + 130.063i) q^{69} +113.339 q^{70} +99.7802i q^{71} +(-23.5790 + 57.3280i) q^{72} -129.745 q^{73} +53.3515i q^{74} +(48.5114 + 9.58675i) q^{75} +21.2133 q^{76} -162.934i q^{77} +(-22.6310 + 114.519i) q^{78} +12.2886 q^{79} -7.84553i q^{80} +(57.5602 + 56.9897i) q^{81} +24.2536 q^{82} +41.1271i q^{83} +(-220.909 - 43.6556i) q^{84} +6.13875 q^{85} +146.894i q^{86} +(24.1970 - 122.443i) q^{87} +92.1079 q^{88} +75.0603i q^{89} +(77.4292 + 31.8466i) q^{90} -148.727 q^{91} -272.260i q^{92} +(-84.0119 - 16.6023i) q^{93} -3.56781 q^{94} -10.0488i q^{95} +(-21.0073 + 106.302i) q^{96} +186.423 q^{97} -316.980i q^{98} +(45.7822 - 111.311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9	\( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) 38 * q - 76 * q^4 - 8 * q^6 - 12 * q^7 + 20 * q^9 + 36 * q^10 - 4 * q^13 - 17 * q^15 + 100 * q^16 - 2 * q^18 - 28 * q^19 - 11 * q^21 + 84 * q^22 - 6 * q^24 - 166 * q^25 + 3 * q^27 + 12 * q^28 + 102 * q^30 - 40 * q^31 - 46 * q^33 - 148 * q^34 - 96 * q^36 + 112 * q^37 + 62 * q^39 - 56 * q^40 + 14 * q^42 + 164 * q^43 + 55 * q^45 - 4 * q^46 - 124 * q^48 + 242 * q^49 + 52 * q^51 + 8 * q^52 + 18 * q^54 - 228 * q^55 - 147 * q^57 - 80 * q^58 + 128 * q^60 + 12 * q^61 + 86 * q^63 + 48 * q^64 - 24 * q^66 + 124 * q^67 - 240 * q^69 + 148 * q^70 + 166 * q^72 - 192 * q^73 - 78 * q^75 - 304 * q^76 + 244 * q^78 + 64 * q^79 - 156 * q^81 - 180 * q^82 + 300 * q^84 - 52 * q^85 - 83 * q^87 - 96 * q^88 - 376 * q^90 - 332 * q^91 + 454 * q^93 + 768 * q^94 - 722 * q^96 + 416 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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