LMFDB - Embedded newform 177.3.b.a.119.14

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			119.14
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50430i q^{2} +(2.93642 - 0.614364i) q^{3} +1.73708 q^{4} +1.04714i q^{5} +(-0.924188 - 4.41725i) q^{6} -6.70636 q^{7} -8.63029i q^{8} +(8.24511 - 3.60806i) q^{9} +O(q^{10})$	\(q-1.50430i q^{2} +(2.93642 - 0.614364i) q^{3} +1.73708 q^{4} +1.04714i q^{5} +(-0.924188 - 4.41725i) q^{6} -6.70636 q^{7} -8.63029i q^{8} +(8.24511 - 3.60806i) q^{9} +1.57522 q^{10} -13.0295i q^{11} +(5.10080 - 1.06720i) q^{12} +15.6086 q^{13} +10.0884i q^{14} +(0.643327 + 3.07485i) q^{15} -6.03421 q^{16} +23.4435i q^{17} +(-5.42761 - 12.4031i) q^{18} -3.66427 q^{19} +1.81897i q^{20} +(-19.6927 + 4.12015i) q^{21} -19.6003 q^{22} -7.48394i q^{23} +(-5.30214 - 25.3422i) q^{24} +23.9035 q^{25} -23.4801i q^{26} +(21.9944 - 15.6603i) q^{27} -11.6495 q^{28} +55.2663i q^{29} +(4.62550 - 0.967757i) q^{30} -48.1479 q^{31} -25.4439i q^{32} +(-8.00486 - 38.2601i) q^{33} +35.2660 q^{34} -7.02251i q^{35} +(14.3224 - 6.26750i) q^{36} -61.5262 q^{37} +5.51216i q^{38} +(45.8335 - 9.58939i) q^{39} +9.03715 q^{40} +23.5016i q^{41} +(6.19793 + 29.6237i) q^{42} -2.28122 q^{43} -22.6333i q^{44} +(3.77816 + 8.63381i) q^{45} -11.2581 q^{46} +89.1953i q^{47} +(-17.7190 + 3.70720i) q^{48} -4.02479 q^{49} -35.9580i q^{50} +(14.4028 + 68.8399i) q^{51} +27.1135 q^{52} +11.9800i q^{53} +(-23.5578 - 33.0862i) q^{54} +13.6438 q^{55} +57.8778i q^{56} +(-10.7598 + 2.25120i) q^{57} +83.1371 q^{58} -7.68115i q^{59} +(1.11751 + 5.34127i) q^{60} +69.8136 q^{61} +72.4288i q^{62} +(-55.2947 + 24.1969i) q^{63} -62.4121 q^{64} +16.3445i q^{65} +(-57.5546 + 12.0417i) q^{66} -41.2944 q^{67} +40.7233i q^{68} +(-4.59787 - 21.9760i) q^{69} -10.5640 q^{70} -73.6101i q^{71} +(-31.1386 - 71.1577i) q^{72} +78.0150 q^{73} +92.5538i q^{74} +(70.1907 - 14.6855i) q^{75} -6.36514 q^{76} +87.3805i q^{77} +(-14.4253 - 68.9473i) q^{78} +16.5574 q^{79} -6.31868i q^{80} +(54.9638 - 59.4978i) q^{81} +35.3534 q^{82} +17.9481i q^{83} +(-34.2078 + 7.15704i) q^{84} -24.5487 q^{85} +3.43163i q^{86} +(33.9537 + 162.285i) q^{87} -112.448 q^{88} +11.3114i q^{89} +(12.9878 - 5.68348i) q^{90} -104.677 q^{91} -13.0002i q^{92} +(-141.382 + 29.5803i) q^{93} +134.177 q^{94} -3.83701i q^{95} +(-15.6318 - 74.7140i) q^{96} +29.9370 q^{97} +6.05450i q^{98} +(-47.0113 - 107.430i) 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 $

$2$		−	1.50430i		−	0.752150i	−0.926589	−	0.376075i	$-0.877274\pi$
$2$		−	1.50430i		−	0.752150i	0.926589	−	0.376075i	$-0.122726\pi$
$3$	2.93642	−	0.614364i	0.978806	−	0.204788i
$3$	2.93642	−	0.614364i	0.978806	−	0.204788i
$4$	1.73708			0.434271
$5$			1.04714i			0.209429i	0.994502	+	0.104714i	$0.0333928\pi$
$5$			1.04714i			0.209429i	−0.994502	+	0.104714i	$0.966607\pi$
$6$	−0.924188	−	4.41725i	−0.154031	−	0.736209i
$7$	−6.70636			−0.958051			−0.479025	−	0.877801i	$-0.659010\pi$
$7$	−6.70636			−0.958051			−0.479025	+	0.877801i	$0.659010\pi$
$8$		−	8.63029i		−	1.07879i
$9$	8.24511	−	3.60806i	0.916124	−	0.400896i
$10$	1.57522			0.157522
$11$		−	13.0295i		−	1.18450i	−0.805754	−	0.592250i	$-0.798240\pi$
$11$		−	13.0295i		−	1.18450i	0.805754	−	0.592250i	$-0.201760\pi$
$12$	5.10080	−	1.06720i	0.425067	−	0.0889335i
$13$	15.6086			1.20066			0.600332	−	0.799751i	$-0.295035\pi$
$13$	15.6086			1.20066			0.600332	+	0.799751i	$0.295035\pi$
$14$			10.0884i			0.720598i
$15$	0.643327	+	3.07485i	0.0428885	+	0.204990i
$16$	−6.03421			−0.377138
$17$			23.4435i			1.37903i	0.724272	+	0.689514i	$0.242176\pi$
$17$			23.4435i			1.37903i	−0.724272	+	0.689514i	$0.757824\pi$
$18$	−5.42761	−	12.4031i	−0.301534	−	0.689062i
$19$	−3.66427			−0.192856			−0.0964281	−	0.995340i	$-0.530742\pi$
$19$	−3.66427			−0.192856			−0.0964281	+	0.995340i	$0.530742\pi$
$20$			1.81897i			0.0909487i
$21$	−19.6927	+	4.12015i	−0.937746	+	0.196197i
$22$	−19.6003			−0.890922
$23$		−	7.48394i		−	0.325389i	−0.986677	−	0.162694i	$-0.947982\pi$
$23$		−	7.48394i		−	0.325389i	0.986677	−	0.162694i	$-0.0520184\pi$
$24$	−5.30214	−	25.3422i	−0.220923	−	1.05592i
$25$	23.9035			0.956140
$26$		−	23.4801i		−	0.903080i
$27$	21.9944	−	15.6603i	0.814609	−	0.580011i
$28$	−11.6495			−0.416053
$29$			55.2663i			1.90573i	0.303387	+	0.952867i	$0.401882\pi$
$29$			55.2663i			1.90573i	−0.303387	+	0.952867i	$0.598118\pi$
$30$	4.62550	−	0.967757i	0.154183	−	0.0322586i
$31$	−48.1479			−1.55316			−0.776579	−	0.630020i	$-0.783047\pi$
$31$	−48.1479			−1.55316			−0.776579	+	0.630020i	$0.783047\pi$
$32$		−	25.4439i		−	0.795122i
$33$	−8.00486	−	38.2601i	−0.242572	−	1.15940i
$34$	35.2660			1.03724
$35$		−	7.02251i		−	0.200643i
$36$	14.3224	−	6.26750i	0.397846	−	0.174097i
$37$	−61.5262			−1.66287			−0.831435	−	0.555622i	$-0.812480\pi$
$37$	−61.5262			−1.66287			−0.831435	+	0.555622i	$0.812480\pi$
$38$			5.51216i			0.145057i
$39$	45.8335	−	9.58939i	1.17522	−	0.245882i
$40$	9.03715			0.225929
$41$			23.5016i			0.573210i	0.958049	+	0.286605i	$0.0925267\pi$
$41$			23.5016i			0.573210i	−0.958049	+	0.286605i	$0.907473\pi$
$42$	6.19793	+	29.6237i	0.147570	+	0.705326i
$43$	−2.28122			−0.0530516			−0.0265258	−	0.999648i	$-0.508444\pi$
$43$	−2.28122			−0.0530516			−0.0265258	+	0.999648i	$0.508444\pi$
$44$		−	22.6333i		−	0.514394i
$45$	3.77816	+	8.63381i	0.0839590	+	0.191862i
$46$	−11.2581			−0.244741
$47$			89.1953i			1.89777i	0.315617	+	0.948887i	$0.397789\pi$
$47$			89.1953i			1.89777i	−0.315617	+	0.948887i	$0.602211\pi$
$48$	−17.7190	+	3.70720i	−0.369145	+	0.0772334i
$49$	−4.02479			−0.0821386
$50$		−	35.9580i		−	0.719160i
$51$	14.4028	+	68.8399i	0.282409	+	1.34980i
$52$	27.1135			0.521414
$53$			11.9800i			0.226038i	0.993593	+	0.113019i	$0.0360521\pi$
$53$			11.9800i			0.226038i	−0.993593	+	0.113019i	$0.963948\pi$
$54$	−23.5578	−	33.0862i	−0.436255	−	0.612708i
$55$	13.6438			0.248068
$56$			57.8778i			1.03353i
$57$	−10.7598	+	2.25120i	−0.188769	+	0.0394947i
$58$	83.1371			1.43340
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	1.11751	+	5.34127i	0.0186252	+	0.0890212i
$61$	69.8136			1.14449			0.572243	−	0.820084i	$-0.306073\pi$
$61$	69.8136			1.14449			0.572243	+	0.820084i	$0.306073\pi$
$62$			72.4288i			1.16821i
$63$	−55.2947	+	24.1969i	−0.877693	+	0.384079i
$64$	−62.4121			−0.975189
$65$			16.3445i			0.251454i
$66$	−57.5546	+	12.0417i	−0.872040	+	0.182450i
$67$	−41.2944			−0.616335			−0.308168	−	0.951332i	$-0.599716\pi$
$67$	−41.2944			−0.616335			−0.308168	+	0.951332i	$0.599716\pi$
$68$			40.7233i			0.598872i
$69$	−4.59787	−	21.9760i	−0.0666357	−	0.318492i
$70$	−10.5640			−0.150914
$71$		−	73.6101i		−	1.03676i	−0.855150	−	0.518381i	$-0.826535\pi$
$71$		−	73.6101i		−	1.03676i	0.855150	−	0.518381i	$-0.173465\pi$
$72$	−31.1386	−	71.1577i	−0.432481	−	0.988302i
$73$	78.0150			1.06870			0.534349	−	0.845264i	$-0.320557\pi$
$73$	78.0150			1.06870			0.534349	+	0.845264i	$0.320557\pi$
$74$			92.5538i			1.25073i
$75$	70.1907	−	14.6855i	0.935876	−	0.195806i
$76$	−6.36514			−0.0837518
$77$			87.3805i			1.13481i
$78$	−14.4253	−	68.9473i	−0.184940	−	0.883940i
$79$	16.5574			0.209588			0.104794	−	0.994494i	$-0.466582\pi$
$79$	16.5574			0.209588			0.104794	+	0.994494i	$0.466582\pi$
$80$		−	6.31868i		−	0.0789835i
$81$	54.9638	−	59.4978i	0.678565	−	0.734540i
$82$	35.3534			0.431140
$83$			17.9481i			0.216242i	0.994138	+	0.108121i	$0.0344834\pi$
$83$			17.9481i			0.216242i	−0.994138	+	0.108121i	$0.965517\pi$
$84$	−34.2078	+	7.15704i	−0.407236	+	0.0852028i
$85$	−24.5487			−0.288808
$86$			3.43163i			0.0399027i
$87$	33.9537	+	162.285i	0.390272	+	1.86535i
$88$	−112.448			−1.27782
$89$			11.3114i			0.127095i	0.997979	+	0.0635473i	$0.0202414\pi$
$89$			11.3114i			0.127095i	−0.997979	+	0.0635473i	$0.979759\pi$
$90$	12.9878	−	5.68348i	0.144309	−	0.0631498i
$91$	−104.677			−1.15030
$92$		−	13.0002i		−	0.141307i
$93$	−141.382	+	29.5803i	−1.52024	+	0.318068i
$94$	134.177			1.42741
$95$		−	3.83701i		−	0.0403896i
$96$	−15.6318	−	74.7140i	−0.162832	−	0.778270i
$97$	29.9370			0.308628			0.154314	−	0.988022i	$-0.450683\pi$
$97$	29.9370			0.308628			0.154314	+	0.988022i	$0.450683\pi$
$98$			6.05450i			0.0617806i
$99$	−47.0113	−	107.430i	−0.474861	−	1.08515i
$100$	41.5223			0.415223
$101$		−	168.802i		−	1.67131i	−0.549255	−	0.835655i	$-0.685089\pi$
$101$		−	168.802i		−	1.67131i	0.549255	−	0.835655i	$-0.314911\pi$
$102$	103.556	−	21.6662i	1.01525	−	0.212414i
$103$	93.0507			0.903404			0.451702	−	0.892169i	$-0.350817\pi$
$103$	93.0507			0.903404			0.451702	+	0.892169i	$0.350817\pi$
$104$		−	134.707i		−	1.29526i
$105$	−4.31438	−	20.6210i	−0.0410894	−	0.196391i
$106$	18.0215			0.170014
$107$			20.5910i			0.192439i	0.995360	+	0.0962194i	$0.0306751\pi$
$107$			20.5910i			0.192439i	−0.995360	+	0.0962194i	$0.969325\pi$
$108$	38.2062	−	27.2032i	0.353761	−	0.251882i
$109$	−135.021			−1.23872			−0.619362	−	0.785106i	$-0.712609\pi$
$109$	−135.021			−1.23872			−0.619362	+	0.785106i	$0.712609\pi$
$110$		−	20.5243i		−	0.186584i
$111$	−180.667	+	37.7995i	−1.62763	+	0.340536i
$112$	40.4676			0.361318
$113$		−	204.558i		−	1.81025i	−0.425150	−	0.905123i	$-0.639779\pi$
$113$		−	204.558i		−	1.81025i	0.425150	−	0.905123i	$-0.360221\pi$
$114$	3.38647	+	16.1860i	0.0297059	+	0.141983i
$115$	7.83675			0.0681457
$116$			96.0022i			0.827605i
$117$	128.695	−	56.3170i	1.09996	−	0.481342i
$118$	−11.5547			−0.0979216
$119$		−	157.220i		−	1.32118i
$120$	26.5369	−	5.55210i	0.221140	−	0.0462675i
$121$	−48.7680			−0.403042
$122$		−	105.021i		−	0.860825i
$123$	14.4385	+	69.0105i	0.117387	+	0.561061i
$124$	−83.6368			−0.674491
$125$			51.2089i			0.409672i
$126$	36.3995	+	83.1797i	0.288885	+	0.660157i
$127$	56.4029			0.444118			0.222059	−	0.975033i	$-0.428722\pi$
$127$	56.4029			0.444118			0.222059	+	0.975033i	$0.428722\pi$
$128$		−	7.88914i		−	0.0616339i
$129$	−6.69861	+	1.40150i	−0.0519272	+	0.0108643i
$130$	24.5870			0.189131
$131$			132.495i			1.01141i	0.862706	+	0.505706i	$0.168768\pi$
$131$			132.495i			1.01141i	−0.862706	+	0.505706i	$0.831232\pi$
$132$	−13.9051	−	66.4610i	−0.105342	−	0.503492i
$133$	24.5739			0.184766
$134$			62.1192i			0.463576i
$135$	16.3986	+	23.0313i	0.121471	+	0.170602i
$136$	202.324			1.48768
$137$		−	28.0963i		−	0.205082i	−0.994729	−	0.102541i	$-0.967303\pi$
$137$		−	28.0963i		−	0.205082i	0.994729	−	0.102541i	$-0.0326973\pi$
$138$	−33.0585	+	6.91657i	−0.239554	+	0.0501200i
$139$	−188.801			−1.35828			−0.679141	−	0.734008i	$-0.737647\pi$
$139$	−188.801			−1.35828			−0.679141	+	0.734008i	$0.737647\pi$
$140$		−	12.1987i		−	0.0871335i
$141$	54.7984	+	261.915i	0.388641	+	1.85755i
$142$	−110.732			−0.779800
$143$		−	203.373i		−	1.42219i
$144$	−49.7527	+	21.7718i	−0.345505	+	0.151193i
$145$	−57.8717			−0.399115
$146$		−	117.358i		−	0.803821i
$147$	−11.8185	+	2.47269i	−0.0803978	+	0.0168210i
$148$	−106.876			−0.722136
$149$		−	61.0699i		−	0.409865i	−0.978776	−	0.204932i	$-0.934303\pi$
$149$		−	61.0699i		−	0.409865i	0.978776	−	0.204932i	$-0.0656975\pi$
$150$	−22.0913	−	105.588i	−0.147275	−	0.703919i
$151$	93.7581			0.620915			0.310457	−	0.950587i	$-0.399518\pi$
$151$	93.7581			0.620915			0.310457	+	0.950587i	$0.399518\pi$
$152$			31.6237i			0.208051i
$153$	84.5855	+	193.294i	0.552847	+	1.26336i
$154$	131.446			0.853548
$155$		−	50.4177i		−	0.325276i
$156$	79.6166	−	16.6576i	0.510363	−	0.106779i
$157$	−17.5679			−0.111898			−0.0559488	−	0.998434i	$-0.517818\pi$
$157$	−17.5679			−0.111898			−0.0559488	+	0.998434i	$0.517818\pi$
$158$		−	24.9074i		−	0.157642i
$159$	7.36008	+	35.1783i	0.0462898	+	0.221247i
$160$	26.6434			0.166521
$161$			50.1900i			0.311739i
$162$	−89.5025	−	82.6820i	−0.552484	−	0.510383i
$163$	131.130			0.804481			0.402240	−	0.915534i	$-0.368232\pi$
$163$	131.130			0.804481			0.402240	+	0.915534i	$0.368232\pi$
$164$			40.8242i			0.248928i
$165$	40.0638	−	8.38224i	0.242811	−	0.0508014i
$166$	26.9993			0.162646
$167$		−	117.311i		−	0.702461i	−0.936289	−	0.351231i	$-0.885763\pi$
$167$		−	117.311i		−	0.702461i	0.936289	−	0.351231i	$-0.114237\pi$
$168$	35.5581	+	169.953i	0.211655	+	1.01163i
$169$	74.6298			0.441596
$170$			36.9286i			0.217227i
$171$	−30.2123	+	13.2209i	−0.176680	+	0.0773153i
$172$	−3.96266			−0.0230387
$173$			181.941i			1.05168i	0.850583	+	0.525840i	$0.176249\pi$
$173$			181.941i			1.05168i	−0.850583	+	0.525840i	$0.823751\pi$
$174$	244.125	−	51.0765i	1.40302	−	0.293543i
$175$	−160.305			−0.916030
$176$			78.6228i			0.446720i
$177$	−4.71902	−	22.5551i	−0.0266611	−	0.127430i
$178$	17.0158			0.0955942
$179$		−	300.060i		−	1.67632i	−0.545428	−	0.838158i	$-0.683633\pi$
$179$		−	300.060i		−	1.67632i	0.545428	−	0.838158i	$-0.316367\pi$
$180$	6.56297	+	14.9976i	0.0364610	+	0.0833203i
$181$	−95.6689			−0.528557			−0.264279	−	0.964446i	$-0.585134\pi$
$181$	−95.6689			−0.528557			−0.264279	+	0.964446i	$0.585134\pi$
$182$			157.466i			0.865196i
$183$	205.002	−	42.8910i	1.12023	−	0.234377i
$184$	−64.5886			−0.351025
$185$		−	64.4267i		−	0.348253i
$186$	44.4977	+	212.681i	0.239235	+	1.14345i
$187$	305.457			1.63346
$188$			154.940i			0.824147i
$189$	−147.503	+	105.023i	−0.780437	+	0.555680i
$190$	−5.77202			−0.0303790
$191$			122.292i			0.640274i	0.947371	+	0.320137i	$0.103729\pi$
$191$			122.292i			0.640274i	−0.947371	+	0.320137i	$0.896271\pi$
$192$	−183.268	+	38.3438i	−0.954521	+	0.199707i
$193$	−59.5916			−0.308765			−0.154382	−	0.988011i	$-0.549339\pi$
$193$	−59.5916			−0.308765			−0.154382	+	0.988011i	$0.549339\pi$
$194$		−	45.0342i		−	0.232135i
$195$	10.0415	+	47.9942i	0.0514947	+	0.246124i
$196$	−6.99140			−0.0356704
$197$			244.220i			1.23970i	0.784721	+	0.619849i	$0.212806\pi$
$197$			244.220i			1.23970i	−0.784721	+	0.619849i	$0.787194\pi$
$198$	−161.607	+	70.7190i	−0.816195	+	0.357167i
$199$	−321.030			−1.61321			−0.806607	−	0.591088i	$-0.798698\pi$
$199$	−321.030			−1.61321			−0.806607	+	0.591088i	$0.798698\pi$
$200$		−	206.294i		−	1.03147i
$201$	−121.258	+	25.3698i	−0.603273	+	0.126218i
$202$	−253.929			−1.25707
$203$		−	370.636i		−	1.82579i
$204$	25.0189	+	119.581i	0.122642	+	0.586179i
$205$	−24.6095			−0.120047
$206$		−	139.976i		−	0.679495i
$207$	−27.0025	−	61.7059i	−0.130447	−	0.298096i
$208$	−94.1858			−0.452817
$209$			47.7436i			0.228438i
$210$	−31.0202	+	6.49012i	−0.147715	+	0.0309053i
$211$	47.4139			0.224711			0.112355	−	0.993668i	$-0.464161\pi$
$211$	47.4139			0.224711			0.112355	+	0.993668i	$0.464161\pi$
$212$			20.8103i			0.0981616i
$213$	−45.2234	−	216.150i	−0.212316	−	1.01479i
$214$	30.9750			0.144743
$215$		−	2.38876i		−	0.0111105i
$216$	−135.153	−	189.818i	−0.625708	−	0.878789i
$217$	322.897			1.48800
$218$			203.112i			0.931705i
$219$	229.085	−	47.9296i	1.04605	−	0.218857i
$220$	23.7003			0.107729
$221$			365.921i			1.65575i
$222$	56.8618	+	271.777i	0.256134	+	1.22422i
$223$	−70.5752			−0.316481			−0.158240	−	0.987401i	$-0.550582\pi$
$223$	−70.5752			−0.316481			−0.158240	+	0.987401i	$0.550582\pi$
$224$			170.636i			0.761767i
$225$	197.087	−	86.2453i	0.875942	−	0.383312i
$226$	−307.716			−1.36158
$227$		−	29.9031i		−	0.131732i	−0.997828	−	0.0658659i	$-0.979019\pi$
$227$		−	29.9031i		−	0.131732i	0.997828	−	0.0658659i	$-0.0209809\pi$
$228$	−18.6907	+	3.91052i	−0.0819768	+	0.0171514i
$229$	−226.006			−0.986925			−0.493462	−	0.869767i	$-0.664269\pi$
$229$	−226.006			−0.986925			−0.493462	+	0.869767i	$0.664269\pi$
$230$		−	11.7888i		−	0.0512558i
$231$	53.6835	+	256.586i	0.232396	+	1.11076i
$232$	476.964			2.05588
$233$			48.0830i			0.206365i	0.994662	+	0.103182i	$0.0329025\pi$
$233$			48.0830i			0.206365i	−0.994662	+	0.103182i	$0.967097\pi$
$234$	−84.7176	−	193.596i	−0.362041	−	0.827333i
$235$	−93.4003			−0.397448
$236$		−	13.3428i		−	0.0565372i
$237$	48.6196	−	10.1723i	0.205146	−	0.0429211i
$238$	−236.506			−0.993724
$239$		−	153.720i		−	0.643178i	−0.946879	−	0.321589i	$-0.895783\pi$
$239$		−	153.720i		−	0.643178i	0.946879	−	0.321589i	$-0.104217\pi$
$240$	−3.88197	−	18.5543i	−0.0161749	−	0.0773096i
$241$	−170.638			−0.708044			−0.354022	−	0.935237i	$-0.615186\pi$
$241$	−170.638			−0.708044			−0.354022	+	0.935237i	$0.615186\pi$
$242$			73.3617i			0.303148i
$243$	124.843	−	208.478i	0.513759	−	0.857935i
$244$	121.272			0.497017
$245$		−	4.21453i		−	0.0172022i
$246$	103.813	−	21.7199i	0.422002	−	0.0882923i
$247$	−57.1943			−0.231556
$248$			415.530i			1.67552i
$249$	11.0267	+	52.7031i	0.0442838	+	0.211659i
$250$	77.0336			0.308134
$251$		−	265.903i		−	1.05937i	−0.848193	−	0.529687i	$-0.822310\pi$
$251$		−	265.903i		−	1.05937i	0.848193	−	0.529687i	$-0.177690\pi$
$252$	−96.0514	+	42.0321i	−0.381156	+	0.166794i
$253$	−97.5120			−0.385423
$254$		−	84.8469i		−	0.334043i
$255$	−72.0852	+	15.0818i	−0.282687	+	0.0591444i
$256$	−261.516			−1.02155
$257$		−	156.363i		−	0.608415i	−0.952606	−	0.304207i	$-0.901608\pi$
$257$		−	156.363i		−	0.608415i	0.952606	−	0.304207i	$-0.0983916\pi$
$258$	2.10827	+	10.0767i	0.00817160	+	0.0390570i
$259$	412.617			1.59311
$260$			28.3917i			0.109199i
$261$	199.404	+	455.677i	0.764001	+	1.74589i
$262$	199.312			0.760733
$263$			171.710i			0.652889i	0.945216	+	0.326445i	$0.105851\pi$
$263$			171.710i			0.652889i	−0.945216	+	0.326445i	$0.894149\pi$
$264$	−330.196	+	69.0843i	−1.25074	+	0.261683i
$265$	−12.5448			−0.0473388
$266$		−	36.9665i		−	0.138972i
$267$	6.94934	+	33.2151i	0.0260275	+	0.124401i
$268$	−71.7319			−0.267656
$269$		−	181.352i		−	0.674173i	−0.941474	−	0.337086i	$-0.890559\pi$
$269$		−	181.352i		−	0.674173i	0.941474	−	0.337086i	$-0.109441\pi$
$270$	34.6460	−	24.6683i	0.128319	−	0.0913642i
$271$	150.686			0.556038			0.278019	−	0.960576i	$-0.410322\pi$
$271$	150.686			0.556038			0.278019	+	0.960576i	$0.410322\pi$
$272$		−	141.463i		−	0.520084i
$273$	−307.376	+	64.3099i	−1.12592	+	0.235567i
$274$	−42.2652			−0.154252
$275$		−	311.451i		−	1.13255i
$276$	−7.98687	−	38.1741i	−0.0289379	−	0.138312i
$277$	139.607			0.503998			0.251999	−	0.967728i	$-0.418912\pi$
$277$	139.607			0.503998			0.251999	+	0.967728i	$0.418912\pi$
$278$			284.013i			1.02163i
$279$	−396.985	+	173.721i	−1.42288	+	0.622654i
$280$	−60.6063			−0.216451
$281$		−	254.644i		−	0.906205i	−0.891458	−	0.453103i	$-0.850317\pi$
$281$		−	254.644i		−	0.906205i	0.891458	−	0.453103i	$-0.149683\pi$
$282$	393.998	−	82.4333i	1.39716	−	0.292317i
$283$	324.401			1.14629			0.573147	−	0.819452i	$-0.305722\pi$
$283$	324.401			1.14629			0.573147	+	0.819452i	$0.305722\pi$
$284$		−	127.867i		−	0.450235i
$285$	−2.35732	−	11.2671i	−0.00827131	−	0.0395336i
$286$	−305.934			−1.06970
$287$		−	157.610i		−	0.549164i
$288$	−91.8032	−	209.788i	−0.318761	−	0.728430i
$289$	−260.597			−0.901718
$290$			87.0564i			0.300195i
$291$	87.9075	−	18.3922i	0.302088	−	0.0632034i
$292$	135.518			0.464104
$293$			418.822i			1.42943i	0.699418	+	0.714713i	$0.253443\pi$
$293$			418.822i			1.42943i	−0.699418	+	0.714713i	$0.746557\pi$
$294$	3.71967	+	17.7785i	0.0126519	+	0.0604712i
$295$	8.04326			0.0272653
$296$			530.989i			1.79388i
$297$	−204.046	−	286.577i	−0.687023	−	0.964905i
$298$	−91.8673			−0.308280
$299$		−	116.814i		−	0.390683i
$300$	121.927	−	25.5099i	0.406423	−	0.0850328i
$301$	15.2987			0.0508261
$302$		−	141.040i		−	0.467021i
$303$	−103.706	−	495.674i	−0.342264	−	1.63589i
$304$	22.1110			0.0727335
$305$			73.1048i			0.239688i
$306$	290.772	−	127.242i	0.950236	−	0.415823i
$307$	390.523			1.27206			0.636031	−	0.771663i	$-0.280575\pi$
$307$	390.523			1.27206			0.636031	+	0.771663i	$0.280575\pi$
$308$			151.787i			0.492816i
$309$	273.236	−	57.1670i	0.884258	−	0.185007i
$310$	−75.8433			−0.244656
$311$		−	526.795i		−	1.69387i	−0.531693	−	0.846937i	$-0.678444\pi$
$311$		−	526.795i		−	1.69387i	0.531693	−	0.846937i	$-0.321556\pi$
$312$	−82.7593	−	395.557i	−0.265254	−	1.26781i
$313$	376.903			1.20416			0.602081	−	0.798435i	$-0.294338\pi$
$313$	376.903			1.20416			0.602081	+	0.798435i	$0.294338\pi$
$314$			26.4274i			0.0841637i
$315$	−25.3377	−	57.9014i	−0.0804370	−	0.183814i
$316$	28.7617			0.0910179
$317$			390.759i			1.23268i	0.787481	+	0.616339i	$0.211385\pi$
$317$			390.759i			1.23268i	−0.787481	+	0.616339i	$0.788615\pi$
$318$	52.9187	−	11.0718i	0.166411	−	0.0348169i
$319$	720.093			2.25734
$320$		−	65.3544i		−	0.204232i
$321$	12.6504	+	60.4637i	0.0394092	+	0.188360i
$322$	75.5007			0.234474
$323$		−	85.9032i		−	0.265954i
$324$	95.4766	−	103.353i	0.294681	−	0.318989i
$325$	373.101			1.14800
$326$		−	197.259i		−	0.605090i
$327$	−396.478	+	82.9520i	−1.21247	+	0.253676i
$328$	202.826			0.618371
$329$		−	598.176i		−	1.81816i
$330$	−12.6094	−	60.2679i	−0.0382103	−	0.182630i
$331$	−294.339			−0.889242			−0.444621	−	0.895719i	$-0.646662\pi$
$331$	−294.339			−0.889242			−0.444621	+	0.895719i	$0.646662\pi$
$332$			31.1773i			0.0939077i
$333$	−507.291	+	221.990i	−1.52339	+	0.666638i
$334$	−176.471			−0.528356
$335$		−	43.2412i		−	0.129078i
$336$	118.830	−	24.8618i	0.353660	−	0.0739935i
$337$	72.4236			0.214907			0.107453	−	0.994210i	$-0.465730\pi$
$337$	72.4236			0.214907			0.107453	+	0.994210i	$0.465730\pi$
$338$		−	112.266i		−	0.332146i
$339$	−125.673	−	600.667i	−0.370717	−	1.77188i
$340$	−42.6431			−0.125421
$341$			627.343i			1.83972i
$342$	19.8882	+	45.4484i	0.0581527	+	0.132890i
$343$	355.603			1.03674
$344$			19.6876i			0.0572313i
$345$	23.0120	−	4.81462i	0.0667014	−	0.0139554i
$346$	273.693			0.791022
$347$		−	138.584i		−	0.399378i	−0.979859	−	0.199689i	$-0.936007\pi$
$347$		−	138.584i		−	0.399378i	0.979859	−	0.199689i	$-0.0639931\pi$
$348$	58.9803	+	281.903i	0.169484	+	0.810065i
$349$	220.208			0.630968			0.315484	−	0.948931i	$-0.397833\pi$
$349$	220.208			0.630968			0.315484	+	0.948931i	$0.397833\pi$
$350$			241.147i			0.688992i
$351$	343.303	−	244.436i	0.978072	−	0.696398i
$352$	−331.522			−0.941822
$353$		−	180.114i		−	0.510237i	−0.966910	−	0.255119i	$-0.917885\pi$
$353$		−	180.114i		−	0.510237i	0.966910	−	0.255119i	$-0.0821145\pi$
$354$	−33.9296	+	7.09882i	−0.0958462	+	0.0200532i
$355$	77.0803			0.217128
$356$			19.6489i			0.0551935i
$357$	−96.5905	−	461.665i	−0.270562	−	1.29318i
$358$	−451.381			−1.26084
$359$		−	272.973i		−	0.760370i	−0.924910	−	0.380185i	$-0.875860\pi$
$359$		−	272.973i		−	0.760370i	0.924910	−	0.380185i	$-0.124140\pi$
$360$	74.5123	−	32.6066i	0.206979	−	0.0905739i
$361$	−347.573			−0.962806
$362$			143.915i			0.397554i
$363$	−143.203	+	29.9613i	−0.394500	+	0.0825381i
$364$	−181.833			−0.499541
$365$			81.6928i			0.223816i
$366$	−64.5209	−	308.384i	−0.176287	−	0.842580i
$367$	−669.007			−1.82291			−0.911454	−	0.411403i	$-0.865039\pi$
$367$	−669.007			−1.82291			−0.911454	+	0.411403i	$0.865039\pi$
$368$			45.1597i			0.122716i
$369$	84.7952	+	193.773i	0.229797	+	0.525131i
$370$	−96.9171			−0.261938
$371$		−	80.3421i		−	0.216556i
$372$	−245.593	+	51.3835i	−0.660196	+	0.138128i
$373$	−462.122			−1.23893			−0.619467	−	0.785023i	$-0.712651\pi$
$373$	−462.122			−1.23893			−0.619467	+	0.785023i	$0.712651\pi$
$374$		−	459.499i		−	1.22861i
$375$	31.4610	+	150.371i	0.0838959	+	0.400989i
$376$	769.782			2.04729
$377$			862.632i			2.28815i
$378$	157.987	+	221.888i	0.417954	+	0.587005i
$379$	−672.675			−1.77487			−0.887434	−	0.460936i	$-0.847514\pi$
$379$	−672.675			−1.77487			−0.887434	+	0.460936i	$0.847514\pi$
$380$		−	6.66521i		−	0.0175400i
$381$	165.623	−	34.6520i	0.434705	−	0.0909500i
$382$	183.964			0.481582
$383$			357.495i			0.933408i	0.884414	+	0.466704i	$0.154559\pi$
$383$			357.495i			0.933408i	−0.884414	+	0.466704i	$0.845441\pi$
$384$	−4.84680	−	23.1658i	−0.0126219	−	0.0603276i
$385$	−91.4999			−0.237662
$386$			89.6435i			0.232237i
$387$	−18.8089	+	8.23077i	−0.0486018	+	0.0212681i
$388$	52.0030			0.134028
$389$		−	190.238i		−	0.489043i	−0.969644	−	0.244522i	$-0.921369\pi$
$389$		−	190.238i		−	0.489043i	0.969644	−	0.244522i	$-0.0786309\pi$
$390$	72.1977	−	15.1054i	0.185122	−	0.0387317i
$391$	175.450			0.448720
$392$			34.7351i			0.0886101i
$393$	81.4001	+	389.060i	0.207125	+	0.989976i
$394$	367.381			0.932438
$395$			17.3380i			0.0438937i
$396$	−81.6625	−	186.614i	−0.206218	−	0.471248i
$397$	−349.958			−0.881507			−0.440753	−	0.897628i	$-0.645289\pi$
$397$	−349.958			−0.881507			−0.440753	+	0.897628i	$0.645289\pi$
$398$			482.925i			1.21338i
$399$	72.1593	−	15.0973i	0.180850	−	0.0378379i
$400$	−144.239			−0.360597
$401$		−	321.766i		−	0.802410i	−0.915988	−	0.401205i	$-0.868592\pi$
$401$		−	321.766i		−	0.802410i	0.915988	−	0.401205i	$-0.131408\pi$
$402$	38.1638	+	182.408i	0.0949349	+	0.453751i
$403$	−751.523			−1.86482
$404$		−	293.223i		−	0.725801i
$405$	62.3027	+	57.5549i	0.153834	+	0.142111i
$406$	−557.547			−1.37327
$407$			801.656i			1.96967i
$408$	594.108	−	124.301i	1.45615	−	0.304659i
$409$	−115.657			−0.282780			−0.141390	−	0.989954i	$-0.545157\pi$
$409$	−115.657			−0.282780			−0.141390	+	0.989954i	$0.545157\pi$
$410$			37.0201i			0.0902929i
$411$	−17.2613	−	82.5024i	−0.0419984	−	0.200736i
$412$	161.637			0.392322
$413$			51.5125i			0.124728i
$414$	−92.8242	+	40.6199i	−0.224213	+	0.0981156i
$415$	−18.7942			−0.0452873
$416$		−	397.145i		−	0.954675i
$417$	−554.399	+	115.993i	−1.32949	+	0.278160i
$418$	71.8207			0.171820
$419$			182.313i			0.435115i	0.976047	+	0.217558i	$0.0698090\pi$
$419$			182.313i			0.435115i	−0.976047	+	0.217558i	$0.930191\pi$
$420$	−7.49444	−	35.8205i	−0.0178439	−	0.0852868i
$421$	204.208			0.485055			0.242527	−	0.970145i	$-0.422024\pi$
$421$	204.208			0.485055			0.242527	+	0.970145i	$0.422024\pi$
$422$		−	71.3247i		−	0.169016i
$423$	321.822	+	735.426i	0.760809	+	1.73860i
$424$	103.391			0.243846
$425$			560.381i			1.31854i
$426$	−325.154	+	68.0296i	−0.763273	+	0.159694i
$427$	−468.195			−1.09648
$428$			35.7682i			0.0835706i
$429$	−124.945	−	597.188i	−0.291247	−	1.39205i
$430$	−3.59341			−0.00835677
$431$			672.668i			1.56071i	0.625335	+	0.780357i	$0.284962\pi$
$431$			672.668i			1.56071i	−0.625335	+	0.780357i	$0.715038\pi$
$432$	−132.719	+	94.4975i	−0.307220	+	0.218744i
$433$	714.659			1.65048			0.825241	−	0.564781i	$-0.191039\pi$
$433$	714.659			1.65048			0.825241	+	0.564781i	$0.191039\pi$
$434$		−	485.733i		−	1.11920i
$435$	−169.936	+	35.5543i	−0.390657	+	0.0817341i
$436$	−234.542			−0.537941
$437$			27.4232i			0.0627532i
$438$	−72.1005	−	344.612i	−0.164613	−	0.786785i
$439$	169.013			0.384994			0.192497	−	0.981298i	$-0.438341\pi$
$439$	169.013			0.384994			0.192497	+	0.981298i	$0.438341\pi$
$440$		−	117.750i		−	0.267613i
$441$	−33.1849	+	14.5217i	−0.0752492	+	0.0329290i
$442$	550.455			1.24537
$443$			761.327i			1.71857i	0.511497	+	0.859285i	$0.329091\pi$
$443$			761.327i			1.71857i	−0.511497	+	0.859285i	$0.670909\pi$
$444$	−313.833	+	65.6609i	−0.706831	+	0.147885i
$445$	−11.8447			−0.0266173
$446$			106.166i			0.238041i
$447$	−37.5191	−	179.327i	−0.0839354	−	0.401178i
$448$	418.558			0.934281
$449$			653.549i			1.45557i	0.685807	+	0.727783i	$0.259449\pi$
$449$			653.549i			1.45557i	−0.685807	+	0.727783i	$0.740551\pi$
$450$	−129.739	−	296.478i	−0.288308	−	0.658840i
$451$	306.214			0.678967
$452$		−	355.334i		−	0.786137i
$453$	275.313	−	57.6016i	0.607755	−	0.127156i
$454$	−44.9832			−0.0990820
$455$		−	109.612i		−	0.240905i
$456$	19.4285	+	92.8605i	0.0426063	+	0.203641i
$457$	88.4462			0.193536			0.0967682	−	0.995307i	$-0.469149\pi$
$457$	88.4462			0.193536			0.0967682	+	0.995307i	$0.469149\pi$
$458$			339.980i			0.742315i
$459$	367.132	+	515.626i	0.799851	+	1.12337i
$460$	13.6131			0.0295937
$461$			559.306i			1.21325i	0.794990	+	0.606623i	$0.207476\pi$
$461$			559.306i			1.21325i	−0.794990	+	0.606623i	$0.792524\pi$
$462$	385.982	−	80.7560i	0.835459	−	0.174797i
$463$	527.519			1.13935			0.569675	−	0.821870i	$-0.307069\pi$
$463$	527.519			1.13935			0.569675	+	0.821870i	$0.307069\pi$
$464$		−	333.489i		−	0.718725i
$465$	−30.9748	−	148.047i	−0.0666126	−	0.318382i
$466$	72.3312			0.155217
$467$		−	479.699i		−	1.02719i	−0.858032	−	0.513597i	$-0.828313\pi$
$467$		−	479.699i		−	1.02719i	0.858032	−	0.513597i	$-0.171687\pi$
$468$	223.554	−	97.8272i	0.477679	−	0.209033i
$469$	276.935			0.590480
$470$			140.502i			0.298940i
$471$	−51.5867	+	10.7931i	−0.109526	+	0.0229153i
$472$	−66.2905			−0.140446
$473$			29.7231i			0.0628396i
$474$	−15.3022	−	73.1385i	−0.0322831	−	0.154301i
$475$	−87.5888			−0.184398
$476$		−	273.105i		−	0.573749i
$477$	43.2246	+	98.7764i	0.0906176	+	0.207079i
$478$	−231.240			−0.483767
$479$		−	526.747i		−	1.09968i	−0.835270	−	0.549841i	$-0.814688\pi$
$479$		−	526.747i		−	1.09968i	0.835270	−	0.549841i	$-0.185312\pi$
$480$	78.2362	−	16.3688i	0.162992	−	0.0341016i
$481$	−960.341			−1.99655
$482$			256.691i			0.532555i
$483$	30.8349	+	147.379i	0.0638404	+	0.305132i
$484$	−84.7141			−0.175029
$485$			31.3483i			0.0646356i
$486$	−313.614	−	187.802i	−0.645295	−	0.386423i
$487$	19.2910			0.0396120			0.0198060	−	0.999804i	$-0.493695\pi$
$487$	19.2910			0.0396120			0.0198060	+	0.999804i	$0.493695\pi$
$488$		−	602.512i		−	1.23466i
$489$	385.054	−	80.5618i	0.787431	−	0.164748i
$490$	−6.33992			−0.0129386
$491$		−	453.229i		−	0.923074i	−0.887121	−	0.461537i	$-0.847298\pi$
$491$		−	453.229i		−	0.923074i	0.887121	−	0.461537i	$-0.152702\pi$
$492$	25.0810	+	119.877i	0.0509775	+	0.243653i
$493$	−1295.63			−2.62806
$494$			86.0373i			0.174165i
$495$	112.494	−	49.2275i	0.227261	−	0.0994495i
$496$	290.534			0.585755
$497$			493.655i			0.993270i
$498$	79.2813	−	16.5874i	0.159199	−	0.0333081i
$499$	184.228			0.369194			0.184597	−	0.982814i	$-0.440902\pi$
$499$	184.228			0.369194			0.184597	+	0.982814i	$0.440902\pi$
$500$			88.9542i			0.177908i
$501$	−72.0717	−	344.474i	−0.143856	−	0.687574i
$502$	−399.997			−0.796807
$503$			877.043i			1.74362i	0.489840	+	0.871812i	$0.337055\pi$
$503$			877.043i			1.74362i	−0.489840	+	0.871812i	$0.662945\pi$
$504$	208.827	+	477.209i	0.414339	+	0.946843i
$505$	176.760			0.350020
$506$			146.687i			0.289896i
$507$	219.144	−	45.8499i	0.432237	−	0.0904337i
$508$	97.9766			0.192867
$509$		−	664.179i		−	1.30487i	−0.757844	−	0.652435i	$-0.773747\pi$
$509$		−	664.179i		−	1.30487i	0.757844	−	0.652435i	$-0.226253\pi$
$510$	22.6876	+	108.438i	0.0444855	+	0.212623i
$511$	−523.196			−1.02387
$512$			361.842i			0.706722i
$513$	−80.5936	+	57.3835i	−0.157102	+	0.111859i
$514$	−235.216			−0.457619
$515$			97.4373i			0.189199i
$516$	−11.6360	+	2.43452i	−0.0225505	+	0.00471806i
$517$	1162.17			2.24791
$518$		−	620.699i		−	1.19826i
$519$	111.778	+	534.254i	0.215372	+	1.02939i
$520$	141.058			0.271265
$521$		−	5.86686i		−	0.0112608i	−0.999984	−	0.00563039i	$-0.998208\pi$
$521$		−	5.86686i		−	0.0112608i	0.999984	−	0.00563039i	$-0.00179222\pi$
$522$	685.475	−	299.964i	1.31317	−	0.574643i
$523$	−454.910			−0.869809			−0.434904	−	0.900477i	$-0.643218\pi$
$523$	−454.910			−0.869809			−0.434904	+	0.900477i	$0.643218\pi$
$524$			230.155i			0.439226i
$525$	−470.724	+	98.4859i	−0.896616	+	0.187592i
$526$	258.303			0.491070
$527$		−	1128.75i		−	2.14185i
$528$	48.3030	+	230.869i	0.0914830	+	0.437253i
$529$	472.991			0.894122
$530$			18.8711i			0.0356058i
$531$	−27.7141	−	63.3319i	−0.0521922	−	0.119269i
$532$	42.6869			0.0802385
$533$			366.828i			0.688233i
$534$	49.9654	−	10.4539i	0.0935682	−	0.0195766i
$535$	−21.5617			−0.0403022
$536$			356.383i			0.664894i
$537$	−184.346	−	881.103i	−0.343289	−	1.64079i
$538$	−272.808			−0.507079
$539$			52.4411i			0.0972933i
$540$	28.4857	+	40.0073i	0.0527512	+	0.0740876i
$541$	698.822			1.29172			0.645862	−	0.763454i	$-0.276498\pi$
$541$	698.822			1.29172			0.645862	+	0.763454i	$0.276498\pi$
$542$		−	226.677i		−	0.418224i
$543$	−280.924	+	58.7755i	−0.517355	+	0.108242i
$544$	596.494			1.09650
$545$		−	141.386i		−	0.259424i
$546$	96.7413	+	462.385i	0.177182	+	0.846860i
$547$	−697.807			−1.27570			−0.637849	−	0.770161i	$-0.720176\pi$
$547$	−697.807			−1.27570			−0.637849	+	0.770161i	$0.720176\pi$
$548$		−	48.8055i		−	0.0890612i
$549$	575.621	−	251.892i	1.04849	−	0.458819i
$550$	−468.515			−0.851846
$551$		−	202.511i		−	0.367533i
$552$	−189.659	+	39.6809i	−0.343585	+	0.0718857i
$553$	−111.040			−0.200796
$554$		−	210.011i		−	0.379082i
$555$	−39.5815	−	189.184i	−0.0713180	−	0.340872i
$556$	−327.963			−0.589862
$557$		−	292.583i		−	0.525283i	−0.964893	−	0.262642i	$-0.915406\pi$
$557$		−	292.583i		−	0.525283i	0.964893	−	0.262642i	$-0.0845937\pi$
$558$	261.328	+	597.184i	0.468329	+	1.07022i
$559$	−35.6067			−0.0636971
$560$			42.3753i			0.0756702i
$561$	896.949	−	187.662i	1.59884	−	0.334513i
$562$	−383.060			−0.681602
$563$		−	392.030i		−	0.696324i	−0.937434	−	0.348162i	$-0.886806\pi$
$563$		−	392.030i		−	0.696324i	0.937434	−	0.348162i	$-0.113194\pi$
$564$	95.1894	+	454.968i	0.168776	+	0.806681i
$565$	214.201			0.379117
$566$		−	487.997i		−	0.862185i
$567$	−368.607	+	399.013i	−0.650100	+	0.703727i
$568$	−635.276			−1.11844
$569$			72.4547i			0.127337i	0.997971	+	0.0636685i	$0.0202800\pi$
$569$			72.4547i			0.127337i	−0.997971	+	0.0636685i	$0.979720\pi$
$570$	−16.9491	+	3.54612i	−0.0297352	+	0.00622127i
$571$	−757.963			−1.32743			−0.663716	−	0.747985i	$-0.731022\pi$
$571$	−757.963			−1.32743			−0.663716	+	0.747985i	$0.731022\pi$
$572$		−	353.276i		−	0.617615i
$573$	75.1321	+	359.102i	0.131121	+	0.626704i
$574$	−237.093			−0.413054
$575$		−	178.892i		−	0.311117i
$576$	−514.595	+	225.187i	−0.893394	+	0.390949i
$577$	316.962			0.549327			0.274663	−	0.961540i	$-0.411434\pi$
$577$	316.962			0.549327			0.274663	+	0.961540i	$0.411434\pi$
$578$			392.015i			0.678227i
$579$	−174.986	+	36.6109i	−0.302221	+	0.0632313i
$580$	−100.528			−0.173324
$581$		−	120.366i		−	0.207171i
$582$	−27.6674	−	132.239i	−0.0475385	−	0.227215i
$583$	156.093			0.267742
$584$		−	673.292i		−	1.15290i
$585$	58.9719	+	134.762i	0.100807	+	0.230363i
$586$	630.033			1.07514
$587$		−	193.204i		−	0.329138i	−0.986366	−	0.164569i	$-0.947377\pi$
$587$		−	193.204i		−	0.329138i	0.986366	−	0.164569i	$-0.0526234\pi$
$588$	−20.5297	+	4.29527i	−0.0349144	+	0.00730488i
$589$	176.427			0.299536
$590$		−	12.0995i		−	0.0205076i
$591$	150.040	+	717.134i	0.253875	+	1.21342i
$592$	371.262			0.627132
$593$		−	496.895i		−	0.837934i	−0.908001	−	0.418967i	$-0.862392\pi$
$593$		−	496.895i		−	0.837934i	0.908001	−	0.418967i	$-0.137608\pi$
$594$	−431.097	+	306.946i	−0.725753	+	0.516744i
$595$	164.632			0.276693
$596$		−	106.083i		−	0.177992i
$597$	−942.677	+	197.229i	−1.57902	+	0.330367i
$598$	−175.723			−0.293852
$599$			406.669i			0.678914i	0.940622	+	0.339457i	$0.110243\pi$
$599$			406.669i			0.678914i	−0.940622	+	0.339457i	$0.889757\pi$
$600$	−126.740	−	605.766i	−0.211233	−	1.00961i
$601$	−778.606			−1.29552			−0.647758	−	0.761846i	$-0.724293\pi$
$601$	−778.606			−1.29552			−0.647758	+	0.761846i	$0.724293\pi$
$602$		−	23.0138i		−	0.0382288i
$603$	−340.477	+	148.993i	−0.564639	+	0.247086i
$604$	162.866			0.269645
$605$		−	51.0671i		−	0.0844084i
$606$	−745.642	+	156.005i	−1.23043	+	0.257434i
$607$	341.880			0.563229			0.281614	−	0.959528i	$-0.409130\pi$
$607$	341.880			0.563229			0.281614	+	0.959528i	$0.409130\pi$
$608$			93.2333i			0.153344i
$609$	−227.705	−	1088.34i	−0.373900	−	1.78710i
$610$	109.972			0.180281
$611$			1392.22i			2.27859i
$612$	146.932	+	335.768i	0.240085	+	0.548640i
$613$	−528.209			−0.861678			−0.430839	−	0.902429i	$-0.641782\pi$
$613$	−528.209			−0.861678			−0.430839	+	0.902429i	$0.641782\pi$
$614$		−	587.464i		−	0.956782i
$615$	−72.2639	+	15.1192i	−0.117502	+	0.0245841i
$616$	754.119			1.22422
$617$			86.9691i			0.140955i	0.997513	+	0.0704774i	$0.0224523\pi$
$617$			86.9691i			0.140955i	−0.997513	+	0.0704774i	$0.977548\pi$
$618$	−85.9963	−	411.028i	−0.139153	−	0.665094i
$619$	1041.28			1.68220			0.841100	−	0.540880i	$-0.181909\pi$
$619$	1041.28			1.68220			0.841100	+	0.540880i	$0.181909\pi$
$620$		−	87.5797i		−	0.141258i
$621$	−117.201	−	164.605i	−0.188729	−	0.265064i
$622$	−792.458			−1.27405
$623$		−	75.8584i		−	0.121763i
$624$	−276.569	+	57.8644i	−0.443220	+	0.0927315i
$625$	543.964			0.870343
$626$		−	566.975i		−	0.905710i
$627$	29.3320	+	140.195i	0.0467815	+	0.223597i
$628$	−30.5169			−0.0485938
$629$		−	1442.39i		−	2.29314i
$630$	−87.1011	+	38.1154i	−0.138256	+	0.0605007i
$631$	1006.88			1.59569			0.797844	−	0.602863i	$-0.205974\pi$
$631$	1006.88			1.59569			0.797844	+	0.602863i	$0.205974\pi$
$632$		−	142.896i		−	0.226101i
$633$	139.227	−	29.1294i	0.219948	−	0.0460181i
$634$	587.819			0.927159
$635$			59.0619i			0.0930109i
$636$	12.7851	+	61.1076i	0.0201023	+	0.0960812i
$637$	−62.8216			−0.0986210
$638$		−	1083.24i		−	1.69786i
$639$	−265.590	−	606.923i	−0.415633	−	0.949802i
$640$	8.26105			0.0129079
$641$			658.137i			1.02674i	0.858169	+	0.513368i	$0.171602\pi$
$641$			658.137i			1.02674i	−0.858169	+	0.513368i	$0.828398\pi$
$642$	90.9555	−	19.0299i	0.141675	−	0.0296416i
$643$	374.939			0.583110			0.291555	−	0.956554i	$-0.405827\pi$
$643$	374.939			0.583110			0.291555	+	0.956554i	$0.405827\pi$
$644$			87.1841i			0.135379i
$645$	−1.46757	−	7.01440i	−0.00227530	−	0.0108750i
$646$	−129.224			−0.200037
$647$		−	434.057i		−	0.670877i	−0.942062	−	0.335439i	$-0.891116\pi$
$647$		−	434.057i		−	0.670877i	0.942062	−	0.335439i	$-0.108884\pi$
$648$	−513.483	−	474.353i	−0.792412	−	0.732027i
$649$	−100.082			−0.154209
$650$		−	561.256i		−	0.863470i
$651$	948.160	−	198.376i	1.45647	−	0.304725i
$652$	227.784			0.349362
$653$		−	773.408i		−	1.18439i	−0.805794	−	0.592196i	$-0.798261\pi$
$653$		−	773.408i		−	1.18439i	0.805794	−	0.592196i	$-0.201739\pi$
$654$	124.785	+	596.421i	0.190802	+	0.911959i
$655$	−138.741			−0.211818
$656$		−	141.814i		−	0.216179i
$657$	643.242	−	281.483i	0.979060	−	0.428437i
$658$	−899.835			−1.36753
$659$		−	238.350i		−	0.361685i	−0.983512	−	0.180843i	$-0.942118\pi$
$659$		−	238.350i		−	0.361685i	0.983512	−	0.180843i	$-0.0578824\pi$
$660$	69.5941	−	14.5606i	0.105446	−	0.0220616i
$661$	−1049.70			−1.58806			−0.794028	−	0.607882i	$-0.792019\pi$
$661$	−1049.70			−1.58806			−0.794028	+	0.607882i	$0.792019\pi$
$662$			442.774i			0.668843i
$663$	224.809	+	1074.50i	0.339078	+	1.62066i
$664$	154.897			0.233279
$665$			25.7324i			0.0386953i
$666$	333.940	+	763.117i	0.501411	+	1.14582i
$667$	413.610			0.620104
$668$		−	203.779i		−	0.305058i
$669$	−207.238	+	43.3589i	−0.309773	+	0.0648115i
$670$	−65.0477			−0.0970861
$671$		−	909.637i		−	1.35564i
$672$	104.833	+	501.058i	0.156001	+	0.745623i
$673$	591.009			0.878171			0.439086	−	0.898445i	$-0.355302\pi$
$673$	591.009			0.878171			0.439086	+	0.898445i	$0.355302\pi$
$674$		−	108.947i		−	0.161642i
$675$	525.744	−	374.336i	0.778880	−	0.554571i
$676$	129.638			0.191772
$677$			70.4446i			0.104054i	0.998646	+	0.0520270i	$0.0165682\pi$
$677$			70.4446i			0.104054i	−0.998646	+	0.0520270i	$0.983432\pi$
$678$	−903.584	+	189.050i	−1.33272	+	0.278835i
$679$	−200.768			−0.295682
$680$			211.862i			0.311562i
$681$	−18.3714	−	87.8080i	−0.0269771	−	0.128940i
$682$	943.712			1.38374
$683$		−	796.448i		−	1.16610i	−0.812435	−	0.583051i	$-0.801859\pi$
$683$		−	796.448i		−	1.16610i	0.812435	−	0.583051i	$-0.198141\pi$
$684$	−52.4813	+	22.9658i	−0.0767270	+	0.0335758i
$685$	29.4208			0.0429501
$686$		−	534.934i		−	0.779787i
$687$	−663.648	+	138.850i	−0.966008	+	0.202111i
$688$	13.7653			0.0200078
$689$			186.992i			0.271396i
$690$	−7.24263	−	34.6169i	−0.0104966	−	0.0501695i
$691$	962.387			1.39275			0.696373	−	0.717680i	$-0.254796\pi$
$691$	962.387			1.39275			0.696373	+	0.717680i	$0.254796\pi$
$692$			316.046i			0.456714i
$693$	315.274	+	720.462i	0.454941	+	1.03963i
$694$	−208.472			−0.300392
$695$		−	197.702i		−	0.284463i
$696$	1400.57	−	293.030i	2.01231	−	0.421020i
$697$	−550.959			−0.790472
$698$		−	331.259i		−	0.474582i
$699$	29.5405	+	141.192i	0.0422610	+	0.201991i
$700$	−278.464			−0.397805
$701$			160.133i			0.228435i	0.993456	+	0.114217i	$0.0364360\pi$
$701$			160.133i			0.228435i	−0.993456	+	0.114217i	$0.963564\pi$
$702$	−367.705	−	516.431i	−0.523796	−	0.735657i
$703$	225.449			0.320695
$704$			813.199i			1.15511i
$705$	−274.262	+	57.3818i	−0.389025	+	0.0813926i
$706$	−270.945			−0.383775
$707$			1132.05i			1.60120i
$708$	−8.19733	−	39.1800i	−0.0115782	−	0.0553390i
$709$	−131.019			−0.184794			−0.0923972	−	0.995722i	$-0.529453\pi$
$709$	−131.019			−0.184794			−0.0923972	+	0.995722i	$0.529453\pi$
$710$		−	115.952i		−	0.163312i
$711$	136.518	−	59.7403i	0.192008	−	0.0840229i
$712$	97.6209			0.137108
$713$			360.336i			0.505380i
$714$	−694.482	+	145.301i	−0.972664	+	0.203503i
$715$	212.961			0.297847
$716$		−	521.230i		−	0.727975i
$717$	−94.4399	−	451.385i	−0.131715	−	0.629547i
$718$	−410.633			−0.571912
$719$			842.287i			1.17147i	0.810503	+	0.585735i	$0.199194\pi$
$719$			842.287i			1.17147i	−0.810503	+	0.585735i	$0.800806\pi$
$720$	−22.7982	−	52.0982i	−0.0316642	−	0.0723587i
$721$	−624.031			−0.865507
$722$			522.854i			0.724175i
$723$	−501.066	+	104.834i	−0.693037	+	0.144999i
$724$	−166.185			−0.229537
$725$			1321.06i			1.82215i
$726$	45.0708	+	215.421i	0.0620810	+	0.296723i
$727$	−826.548			−1.13693			−0.568465	−	0.822708i	$-0.692462\pi$
$727$	−826.548			−1.13693			−0.568465	+	0.822708i	$0.692462\pi$
$728$			903.394i			1.24093i
$729$	238.511	−	688.878i	0.327175	−	0.944964i
$730$	122.890			0.168343
$731$		−	53.4797i		−	0.0731596i
$732$	356.106	−	74.5052i	0.486483	−	0.101783i
$733$	1184.81			1.61638			0.808191	−	0.588920i	$-0.200447\pi$
$733$	1184.81			1.61638			0.808191	+	0.588920i	$0.200447\pi$
$734$			1006.39i			1.37110i
$735$	−2.58926	−	12.3756i	−0.00352280	−	0.0168376i
$736$	−190.421			−0.258724
$737$			538.046i			0.730049i
$738$	291.493	−	127.557i	0.394977	−	0.172842i
$739$	180.722			0.244549			0.122275	−	0.992496i	$-0.460981\pi$
$739$	180.722			0.244549			0.122275	+	0.992496i	$0.460981\pi$
$740$		−	111.915i		−	0.151236i
$741$	−167.946	+	35.1381i	−0.226648	+	0.0474199i
$742$	−120.859			−0.162882
$743$			623.820i			0.839596i	0.907618	+	0.419798i	$0.137899\pi$
$743$			623.820i			0.839596i	−0.907618	+	0.419798i	$0.862101\pi$
$744$	255.287	+	1220.17i	0.343128	+	1.64001i
$745$	63.9489			0.0858374
$746$			695.170i			0.931863i
$747$	64.7579	+	147.984i	0.0866906	+	0.198105i
$748$	530.604			0.709364
$749$		−	138.090i		−	0.184366i
$750$	226.203	−	47.3267i	0.301604	−	0.0631023i
$751$	−619.258			−0.824578			−0.412289	−	0.911053i	$-0.635271\pi$
$751$	−619.258			−0.824578			−0.412289	+	0.911053i	$0.635271\pi$
$752$		−	538.224i		−	0.715723i
$753$	−163.361	−	780.802i	−0.216947	−	1.03692i
$754$	1297.66			1.72103
$755$			98.1781i			0.130037i
$756$	−256.224	+	182.434i	−0.338921	+	0.241315i
$757$	−452.664			−0.597971			−0.298986	−	0.954258i	$-0.596648\pi$
$757$	−452.664			−0.597971			−0.298986	+	0.954258i	$0.596648\pi$
$758$			1011.90i			1.33497i
$759$	−286.336	+	59.9079i	−0.377254	+	0.0789301i
$760$	−33.1145			−0.0435718
$761$		−	220.417i		−	0.289642i	−0.989458	−	0.144821i	$-0.953739\pi$
$761$		−	220.417i		−	0.289642i	0.989458	−	0.144821i	$-0.0462606\pi$
$762$	−52.1269	−	249.146i	−0.0684080	−	0.326963i
$763$	905.498			1.18676
$764$			212.432i			0.278052i
$765$	−202.407	+	88.5731i	−0.264584	+	0.115782i
$766$	537.780			0.702063
$767$		−	119.892i		−	0.156313i
$768$	−767.921	+	160.666i	−0.999897	+	0.209201i
$769$	582.680			0.757712			0.378856	−	0.925456i	$-0.376318\pi$
$769$	582.680			0.757712			0.378856	+	0.925456i	$0.376318\pi$
$770$			137.643i			0.178757i
$771$	−96.0636	−	459.146i	−0.124596	−	0.595520i
$772$	−103.515			−0.134087
$773$			152.912i			0.197816i	0.995097	+	0.0989080i	$0.0315350\pi$
$773$			152.912i			0.197816i	−0.995097	+	0.0989080i	$0.968465\pi$
$774$	12.3815	+	28.2942i	0.0159968	+	0.0365558i
$775$	−1150.90			−1.48504
$776$		−	258.365i		−	0.332944i
$777$	1211.62	−	253.497i	1.55935	−	0.326251i
$778$	−286.175			−0.367834
$779$		−	86.1162i		−	0.110547i
$780$	17.4429	+	83.3700i	0.0223626	+	0.106885i
$781$	−959.103			−1.22804
$782$		−	263.929i		−	0.337505i
$783$	865.486	+	1215.55i	1.10535	+	1.55243i
$784$	24.2865			0.0309776
$785$		−	18.3961i		−	0.0234345i
$786$	585.263	−	122.450i	0.744610	−	0.155789i
$787$	−688.818			−0.875245			−0.437622	−	0.899159i	$-0.644179\pi$
$787$	−688.818			−0.875245			−0.437622	+	0.899159i	$0.644179\pi$
$788$			424.231i			0.538364i
$789$	105.492	+	504.212i	0.133704	+	0.639052i
$790$	26.0816			0.0330146
$791$			1371.84i			1.73431i
$792$	−927.150	+	405.721i	−1.17064	+	0.512274i
$793$	1089.70			1.37414
$794$			526.442i			0.663025i
$795$	−36.8367	+	7.70706i	−0.0463355	+	0.00969442i
$796$	−557.655			−0.700572
$797$		−	804.310i		−	1.00917i	−0.863362	−	0.504586i	$-0.831645\pi$
$797$		−	804.310i		−	1.00917i	0.863362	−	0.504586i	$-0.168355\pi$
$798$	−22.7109	−	108.549i	−0.0284598	−	0.136026i
$799$	−2091.05			−2.61708
$800$		−	608.198i		−	0.760248i
$801$	40.8123	+	93.2640i	0.0509517	+	0.116434i
$802$	−484.033			−0.603532
$803$		−	1016.50i		−	1.26587i
$804$	−210.635	+	44.0695i	−0.261984	+	0.0548128i
$805$	−52.5561			−0.0652870
$806$			1130.52i			1.40262i
$807$	−111.417	−	532.527i	−0.138063	−	0.659885i
$808$	−1456.81			−1.80299
$809$		−	353.926i		−	0.437485i	−0.975783	−	0.218743i	$-0.929804\pi$
$809$		−	353.926i		−	0.437485i	0.975783	−	0.218743i	$-0.0701955\pi$
$810$	86.5798	−	93.7219i	0.106889	−	0.115706i
$811$	432.829			0.533697			0.266849	−	0.963738i	$-0.414018\pi$
$811$	432.829			0.533697			0.266849	+	0.963738i	$0.414018\pi$
$812$		−	643.825i		−	0.792888i
$813$	442.478	−	92.5762i	0.544253	−	0.113870i
$814$	1205.93			1.48149
$815$			137.312i			0.168481i
$816$	−86.9097	−	415.394i	−0.106507	−	0.509062i
$817$	8.35899			0.0102313
$818$			173.983i			0.212693i
$819$	−863.075	+	377.682i	−1.05382	+	0.461150i
$820$	−42.7488			−0.0521327
$821$		−	1197.58i		−	1.45868i	−0.684151	−	0.729341i	$-0.739827\pi$
$821$		−	1197.58i		−	1.45868i	0.684151	−	0.729341i	$-0.260173\pi$
$822$	−124.108	+	25.9662i	−0.150983	+	0.0315891i
$823$	−607.281			−0.737887			−0.368944	−	0.929452i	$-0.620280\pi$
$823$	−607.281			−0.737887			−0.368944	+	0.929452i	$0.620280\pi$
$824$		−	803.054i		−	0.974580i
$825$	−191.344	−	914.550i	−0.231932	−	1.10855i
$826$	77.4902			0.0938138
$827$		−	23.5361i		−	0.0284596i	−0.999899	−	0.0142298i	$-0.995470\pi$
$827$		−	23.5361i		−	0.0284596i	0.999899	−	0.0142298i	$-0.00452963\pi$
$828$	−46.9056	−	107.188i	−0.0566493	−	0.129454i
$829$	1538.85			1.85627			0.928137	−	0.372238i	$-0.121410\pi$
$829$	1538.85			1.85627			0.928137	+	0.372238i	$0.121410\pi$
$830$			28.2721i			0.0340628i
$831$	409.946	−	85.7698i	0.493316	−	0.103213i
$832$	−974.168			−1.17088
$833$		−	94.3552i		−	0.113271i
$834$	174.488	+	833.982i	0.209218	+	0.999979i
$835$	122.841			0.147116
$836$			82.9346i			0.0992041i
$837$	−1058.99	+	754.009i	−1.26522	+	0.900848i
$838$	274.254			0.327272
$839$			1080.29i			1.28759i	0.765196	+	0.643797i	$0.222642\pi$
$839$			1080.29i			1.28759i	−0.765196	+	0.643797i	$0.777358\pi$
$840$	−177.966	+	37.2344i	−0.211864	+	0.0443266i
$841$	−2213.36			−2.63183
$842$		−	307.190i		−	0.364834i
$843$	−156.444	−	747.741i	−0.185580	−	0.886999i
$844$	82.3619			0.0975852
$845$			78.1480i			0.0924829i
$846$	1106.30	−	484.117i	1.30768	−	0.572243i
$847$	327.056			0.386134
$848$		−	72.2898i		−	0.0852474i
$849$	952.579	−	199.301i	1.12200	−	0.234748i
$850$	842.981			0.991742
$851$			460.458i			0.541079i
$852$	−78.5568	−	375.471i	−0.0922028	−	0.440693i
$853$	638.949			0.749061			0.374531	−	0.927215i	$-0.377804\pi$
$853$	638.949			0.749061			0.374531	+	0.927215i	$0.377804\pi$
$854$			704.305i			0.824714i
$855$	−13.8442	−	31.6366i	−0.0161920	−	0.0370019i
$856$	177.706			0.207600
$857$			166.017i			0.193719i	0.995298	+	0.0968596i	$0.0308798\pi$
$857$			166.017i			0.193719i	−0.995298	+	0.0968596i	$0.969120\pi$
$858$	−898.350	+	187.955i	−1.04703	+	0.219062i
$859$	−156.022			−0.181632			−0.0908159	−	0.995868i	$-0.528947\pi$
$859$	−156.022			−0.181632			−0.0908159	+	0.995868i	$0.528947\pi$
$860$		−	4.14947i		−	0.00482497i
$861$	−96.8300	−	462.809i	−0.112462	−	0.537525i
$862$	1011.89			1.17389
$863$			451.761i			0.523477i	0.965139	+	0.261739i	$0.0842959\pi$
$863$			451.761i			0.523477i	−0.965139	+	0.261739i	$0.915704\pi$
$864$	−398.459	−	559.624i	−0.461179	−	0.647713i
$865$	−190.518			−0.220252
$866$		−	1075.06i		−	1.24141i
$867$	−765.221	+	160.101i	−0.882608	+	0.184661i
$868$	560.898			0.646196
$869$		−	215.735i		−	0.248257i
$870$	53.4844	+	255.634i	0.0614763	+	0.293832i
$871$	−644.550			−0.740012
$872$			1165.27i			1.33632i
$873$	246.834	−	108.014i	0.282742	−	0.123728i
$874$	41.2527			0.0471998
$875$		−	343.425i		−	0.392486i
$876$	397.939	−	83.2577i	0.454268	−	0.0950431i
$877$	1099.82			1.25407			0.627035	−	0.778991i	$-0.284268\pi$
$877$	1099.82			1.25407			0.627035	+	0.778991i	$0.284268\pi$
$878$		−	254.245i		−	0.289573i
$879$	257.309	+	1229.84i	0.292729	+	1.39913i
$880$	−82.3293			−0.0935560
$881$			188.686i			0.214172i	0.994250	+	0.107086i	$0.0341521\pi$
$881$			188.686i			0.214172i	−0.994250	+	0.107086i	$0.965848\pi$
$882$	21.8450	+	49.9200i	0.0247676	+	0.0565986i
$883$	72.1884			0.0817536			0.0408768	−	0.999164i	$-0.486985\pi$
$883$	72.1884			0.0817536			0.0408768	+	0.999164i	$0.486985\pi$
$884$			635.635i			0.719044i
$885$	23.6184	−	4.94149i	0.0266874	−	0.00558361i
$886$	1145.26			1.29262
$887$			292.868i			0.330178i	0.986279	+	0.165089i	$0.0527911\pi$
$887$			292.868i			0.330178i	−0.986279	+	0.165089i	$0.947209\pi$
$888$	326.221	+	1559.21i	0.367366	+	1.75586i
$889$	−378.258			−0.425487
$890$			17.8179i			0.0200202i
$891$	−775.226	−	716.151i	−0.870063	−	0.803761i
$892$	−122.595			−0.137438
$893$		−	326.836i		−	0.365998i
$894$	−269.761	+	56.4400i	−0.301746	+	0.0631320i
$895$	314.206			0.351068
$896$			52.9074i			0.0590484i
$897$	−71.7664	−	343.015i	−0.0800072	−	0.382403i
$898$	983.134			1.09480
$899$		−	2660.96i		−	2.95991i
$900$	342.356	−	149.815i	0.380396	−	0.166461i
$901$	−280.853			−0.311712
$902$		−	460.638i		−	0.510685i
$903$	44.9233	−	9.39895i	0.0497489	−	0.0104086i
$904$	−1765.39			−1.95287
$905$		−	100.179i		−	0.110695i
$906$	−86.6501	−	414.153i	−0.0956403	−	0.457123i
$907$	−383.046			−0.422322			−0.211161	−	0.977451i	$-0.567724\pi$
$907$	−383.046			−0.422322			−0.211161	+	0.977451i	$0.567724\pi$
$908$		−	51.9442i		−	0.0572072i
$909$	−609.049	−	1391.79i	−0.670021	−	1.53113i
$910$	−164.889			−0.181197
$911$			1278.75i			1.40367i	0.712337	+	0.701837i	$0.247637\pi$
$911$			1278.75i			1.40367i	−0.712337	+	0.701837i	$0.752363\pi$
$912$	64.9271	−	13.5842i	0.0711920	−	0.0148950i
$913$	233.855			0.256139
$914$		−	133.050i		−	0.145568i
$915$	44.9130	+	214.666i	0.0490853	+	0.234608i
$916$	−392.591			−0.428593
$917$		−	888.558i		−	0.968983i
$918$	775.656	−	552.276i	0.844941	−	0.601608i
$919$	−963.384			−1.04830			−0.524148	−	0.851627i	$-0.675616\pi$
$919$	−963.384			−1.04830			−0.524148	+	0.851627i	$0.675616\pi$
$920$		−	67.6335i		−	0.0735146i
$921$	1146.74	−	239.924i	1.24510	−	0.260503i
$922$	841.364			0.912543
$923$		−	1148.95i		−	1.24480i
$924$	93.2526	+	445.711i	0.100923	+	0.482371i
$925$	−1470.69			−1.58994
$926$		−	793.546i		−	0.856961i
$927$	767.213	−	335.733i	0.827630	−	0.362171i
$928$	1406.19			1.51529
$929$			414.537i			0.446219i	0.974793	+	0.223109i	$0.0716207\pi$
$929$			414.537i			0.446219i	−0.974793	+	0.223109i	$0.928379\pi$
$930$	−222.708	+	46.5954i	−0.239471	+	0.0501026i
$931$	14.7479			0.0158410
$932$			83.5241i			0.0896182i
$933$	−323.644	−	1546.89i	−0.346885	−	1.65798i
$934$	−721.611			−0.772603
$935$			319.857i			0.342093i
$936$	−486.032	−	1110.68i	−0.519265	−	1.18662i
$937$	−1719.61			−1.83523			−0.917617	−	0.397467i	$-0.869889\pi$
$937$	−1719.61			−1.83523			−0.917617	+	0.397467i	$0.869889\pi$
$938$		−	416.594i		−	0.444130i
$939$	1106.74	−	231.556i	1.17864	−	0.246598i
$940$	−162.244			−0.172600
$941$		−	275.664i		−	0.292948i	−0.989215	−	0.146474i	$-0.953207\pi$
$941$		−	275.664i		−	0.292948i	0.989215	−	0.146474i	$-0.0467925\pi$
$942$	16.2361	+	77.6019i	0.0172357	+	0.0823799i
$943$	175.885			0.186516
$944$			46.3496i			0.0490992i
$945$	−109.975	−	154.456i	−0.116375	−	0.163446i
$946$	44.7125			0.0472648
$947$			1081.25i			1.14176i	0.821032	+	0.570882i	$0.193398\pi$
$947$			1081.25i			1.14176i	−0.821032	+	0.570882i	$0.806602\pi$
$948$	84.4563	−	17.6701i	0.0890889	−	0.0186394i
$949$	1217.71			1.28315
$950$			131.760i			0.138695i
$951$	240.068	+	1147.43i	0.252438	+	1.20655i
$952$	−1356.86			−1.42527
$953$			1239.80i			1.30095i	0.759529	+	0.650474i	$0.225430\pi$
$953$			1239.80i			1.30095i	−0.759529	+	0.650474i	$0.774570\pi$
$954$	148.589	−	65.0227i	0.155754	−	0.0681580i
$955$	−128.058			−0.134092
$956$		−	267.024i		−	0.279314i
$957$	2114.49	−	442.399i	2.20950	−	0.462277i
$958$	−792.386			−0.827125
$959$			188.423i			0.196479i
$960$	−40.1514	−	191.908i	−0.0418244	−	0.199904i
$961$	1357.22			1.41230
$962$			1444.64i			1.50170i
$963$	74.2935	+	169.775i	0.0771479	+	0.176298i
$964$	−296.413			−0.307483
$965$		−	62.4009i		−	0.0646641i
$966$	221.702	−	46.3850i	0.229505	−	0.0480175i
$967$	45.3464			0.0468939			0.0234469	−	0.999725i	$-0.492536\pi$
$967$	45.3464			0.0468939			0.0234469	+	0.999725i	$0.492536\pi$
$968$			420.882i			0.434796i
$969$	−52.7759	−	252.248i	−0.0544643	−	0.260318i
$970$	47.1572			0.0486157
$971$		−	1457.27i		−	1.50079i	−0.660991	−	0.750394i	$-0.729864\pi$
$971$		−	1457.27i		−	1.50079i	0.660991	−	0.750394i	$-0.270136\pi$
$972$	216.863	−	362.144i	0.223110	−	0.372576i
$973$	1266.17			1.30130
$974$		−	29.0195i		−	0.0297941i
$975$	1095.58	−	229.220i	1.12367	−	0.235097i
$976$	−421.270			−0.431629
$977$			1393.65i			1.42646i	0.700932	+	0.713228i	$0.252767\pi$
$977$			1393.65i			1.42646i	−0.700932	+	0.713228i	$0.747233\pi$
$978$	−121.189	−	579.236i	−0.123915	−	0.592266i
$979$	147.382			0.150544
$980$		−	7.32100i		−	0.00747040i
$981$	−1113.26	+	487.164i	−1.13482	+	0.496599i
$982$	−681.792			−0.694290
$983$		−	986.913i		−	1.00398i	−0.864873	−	0.501990i	$-0.832601\pi$
$983$		−	986.913i		−	1.00398i	0.864873	−	0.501990i	$-0.167399\pi$
$984$	595.581	−	124.609i	0.605265	−	0.126635i
$985$	−255.734			−0.259628
$986$			1949.02i			1.97670i
$987$	−367.498	−	1756.49i	−0.372338	−	1.77963i
$988$	−99.3512			−0.100558
$989$			17.0725i			0.0172624i
$990$	−74.0529	−	169.225i	−0.0748009	−	0.170934i
$991$	604.569			0.610059			0.305030	−	0.952343i	$-0.401334\pi$
$991$	604.569			0.610059			0.305030	+	0.952343i	$0.401334\pi$
$992$			1225.07i			1.23495i
$993$	−864.303	+	180.831i	−0.870396	+	0.182106i
$994$	742.606			0.747088
$995$		−	336.164i		−	0.337853i
$996$	19.1542	+	91.5497i	0.0192312	+	0.0919174i
$997$	−1579.57			−1.58432			−0.792161	−	0.610313i	$-0.791044\pi$
$997$	−1579.57			−1.58432			−0.792161	+	0.610313i	$0.791044\pi$
$998$		−	277.134i		−	0.277689i
$999$	−1353.23	+	963.518i	−1.35459	+	0.964482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.b.a.119.14	✓	38
3.2	odd	2	inner	177.3.b.a.119.25	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.b.a.119.14	✓	38	1.1	even	1	trivial
177.3.b.a.119.25	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)

\(f(q)\)	\(=\)	\(q-1.50430i q^{2} +(2.93642 - 0.614364i) q^{3} +1.73708 q^{4} +1.04714i q^{5} +(-0.924188 - 4.41725i) q^{6} -6.70636 q^{7} -8.63029i q^{8} +(8.24511 - 3.60806i) q^{9} +O(q^{10})\)	\(q-1.50430i q^{2} +(2.93642 - 0.614364i) q^{3} +1.73708 q^{4} +1.04714i q^{5} +(-0.924188 - 4.41725i) q^{6} -6.70636 q^{7} -8.63029i q^{8} +(8.24511 - 3.60806i) q^{9} +1.57522 q^{10} -13.0295i q^{11} +(5.10080 - 1.06720i) q^{12} +15.6086 q^{13} +10.0884i q^{14} +(0.643327 + 3.07485i) q^{15} -6.03421 q^{16} +23.4435i q^{17} +(-5.42761 - 12.4031i) q^{18} -3.66427 q^{19} +1.81897i q^{20} +(-19.6927 + 4.12015i) q^{21} -19.6003 q^{22} -7.48394i q^{23} +(-5.30214 - 25.3422i) q^{24} +23.9035 q^{25} -23.4801i q^{26} +(21.9944 - 15.6603i) q^{27} -11.6495 q^{28} +55.2663i q^{29} +(4.62550 - 0.967757i) q^{30} -48.1479 q^{31} -25.4439i q^{32} +(-8.00486 - 38.2601i) q^{33} +35.2660 q^{34} -7.02251i q^{35} +(14.3224 - 6.26750i) q^{36} -61.5262 q^{37} +5.51216i q^{38} +(45.8335 - 9.58939i) q^{39} +9.03715 q^{40} +23.5016i q^{41} +(6.19793 + 29.6237i) q^{42} -2.28122 q^{43} -22.6333i q^{44} +(3.77816 + 8.63381i) q^{45} -11.2581 q^{46} +89.1953i q^{47} +(-17.7190 + 3.70720i) q^{48} -4.02479 q^{49} -35.9580i q^{50} +(14.4028 + 68.8399i) q^{51} +27.1135 q^{52} +11.9800i q^{53} +(-23.5578 - 33.0862i) q^{54} +13.6438 q^{55} +57.8778i q^{56} +(-10.7598 + 2.25120i) q^{57} +83.1371 q^{58} -7.68115i q^{59} +(1.11751 + 5.34127i) q^{60} +69.8136 q^{61} +72.4288i q^{62} +(-55.2947 + 24.1969i) q^{63} -62.4121 q^{64} +16.3445i q^{65} +(-57.5546 + 12.0417i) q^{66} -41.2944 q^{67} +40.7233i q^{68} +(-4.59787 - 21.9760i) q^{69} -10.5640 q^{70} -73.6101i q^{71} +(-31.1386 - 71.1577i) q^{72} +78.0150 q^{73} +92.5538i q^{74} +(70.1907 - 14.6855i) q^{75} -6.36514 q^{76} +87.3805i q^{77} +(-14.4253 - 68.9473i) q^{78} +16.5574 q^{79} -6.31868i q^{80} +(54.9638 - 59.4978i) q^{81} +35.3534 q^{82} +17.9481i q^{83} +(-34.2078 + 7.15704i) q^{84} -24.5487 q^{85} +3.43163i q^{86} +(33.9537 + 162.285i) q^{87} -112.448 q^{88} +11.3114i q^{89} +(12.9878 - 5.68348i) q^{90} -104.677 q^{91} -13.0002i q^{92} +(-141.382 + 29.5803i) q^{93} +134.177 q^{94} -3.83701i q^{95} +(-15.6318 - 74.7140i) q^{96} +29.9370 q^{97} +6.05450i q^{98} +(-47.0113 - 107.430i) 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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