LMFDB - Embedded newform 177.5.b.a.119.73

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,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, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.73
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.08630i q^{2} +(-1.58963 + 8.85850i) q^{3} -34.2156 q^{4} +8.65783i q^{5} +(-62.7740 - 11.2646i) q^{6} -70.0243 q^{7} -129.081i q^{8} +(-75.9462 - 28.1634i) q^{9} +O(q^{10})$	\(q+7.08630i q^{2} +(-1.58963 + 8.85850i) q^{3} -34.2156 q^{4} +8.65783i q^{5} +(-62.7740 - 11.2646i) q^{6} -70.0243 q^{7} -129.081i q^{8} +(-75.9462 - 28.1634i) q^{9} -61.3520 q^{10} +225.973i q^{11} +(54.3901 - 303.099i) q^{12} +156.064 q^{13} -496.213i q^{14} +(-76.6954 - 13.7627i) q^{15} +367.259 q^{16} -15.4786i q^{17} +(199.575 - 538.177i) q^{18} +179.462 q^{19} -296.233i q^{20} +(111.313 - 620.310i) q^{21} -1601.31 q^{22} +621.607i q^{23} +(1143.47 + 205.191i) q^{24} +550.042 q^{25} +1105.91i q^{26} +(370.212 - 628.000i) q^{27} +2395.92 q^{28} -442.113i q^{29} +(97.5268 - 543.487i) q^{30} -258.752 q^{31} +537.204i q^{32} +(-2001.78 - 359.212i) q^{33} +109.686 q^{34} -606.259i q^{35} +(2598.55 + 963.629i) q^{36} -2503.21 q^{37} +1271.72i q^{38} +(-248.083 + 1382.49i) q^{39} +1117.56 q^{40} -241.937i q^{41} +(4395.70 + 788.794i) q^{42} +2192.78 q^{43} -7731.79i q^{44} +(243.834 - 657.529i) q^{45} -4404.89 q^{46} +2940.86i q^{47} +(-583.804 + 3253.36i) q^{48} +2502.40 q^{49} +3897.76i q^{50} +(137.117 + 24.6052i) q^{51} -5339.82 q^{52} -289.041i q^{53} +(4450.20 + 2623.43i) q^{54} -1956.43 q^{55} +9038.83i q^{56} +(-285.278 + 1589.77i) q^{57} +3132.94 q^{58} -453.188i q^{59} +(2624.18 + 470.900i) q^{60} -4432.23 q^{61} -1833.59i q^{62} +(5318.08 + 1972.12i) q^{63} +2069.35 q^{64} +1351.17i q^{65} +(2545.48 - 14185.2i) q^{66} -1621.56 q^{67} +529.609i q^{68} +(-5506.51 - 988.123i) q^{69} +4296.13 q^{70} -7336.07i q^{71} +(-3635.37 + 9803.23i) q^{72} -1743.91 q^{73} -17738.5i q^{74} +(-874.362 + 4872.55i) q^{75} -6140.41 q^{76} -15823.6i q^{77} +(-9796.75 - 1757.99i) q^{78} +2560.10 q^{79} +3179.66i q^{80} +(4974.64 + 4277.81i) q^{81} +1714.44 q^{82} -4640.76i q^{83} +(-3808.63 + 21224.3i) q^{84} +134.011 q^{85} +15538.7i q^{86} +(3916.46 + 702.795i) q^{87} +29168.8 q^{88} -8720.43i q^{89} +(4659.45 + 1727.88i) q^{90} -10928.3 q^{91} -21268.7i q^{92} +(411.319 - 2292.15i) q^{93} -20839.8 q^{94} +1553.75i q^{95} +(-4758.82 - 853.953i) q^{96} +12826.5 q^{97} +17732.8i q^{98} +(6364.16 - 17161.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * 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 $

$2$			7.08630i			1.77157i	0.464092	+	0.885787i	$0.346381\pi$
$2$			7.08630i			1.77157i	−0.464092	+	0.885787i	$0.653619\pi$
$3$	−1.58963	+	8.85850i	−0.176625	+	0.984278i
$3$	−1.58963	+	8.85850i	−0.176625	+	0.984278i
$4$	−34.2156			−2.13848
$5$			8.65783i			0.346313i	0.984894	+	0.173157i	$0.0553967\pi$
$5$			8.65783i			0.346313i	−0.984894	+	0.173157i	$0.944603\pi$
$6$	−62.7740	−	11.2646i	−1.74372	−	0.312905i
$7$	−70.0243			−1.42907			−0.714534	−	0.699601i	$-0.753361\pi$
$7$	−70.0243			−1.42907			−0.714534	+	0.699601i	$0.753361\pi$
$8$		−	129.081i		−	2.01690i
$9$	−75.9462	−	28.1634i	−0.937607	−	0.347697i
$10$	−61.3520			−0.613520
$11$			225.973i			1.86754i	0.357871	+	0.933771i	$0.383503\pi$
$11$			225.973i			1.86754i	−0.357871	+	0.933771i	$0.616497\pi$
$12$	54.3901	−	303.099i	0.377709	−	2.10486i
$13$	156.064			0.923455			0.461727	−	0.887022i	$-0.347230\pi$
$13$	156.064			0.923455			0.461727	+	0.887022i	$0.347230\pi$
$14$		−	496.213i		−	2.53170i
$15$	−76.6954	−	13.7627i	−0.340869	−	0.0611677i
$16$	367.259			1.43460
$17$		−	15.4786i		−	0.0535591i	−0.999641	−	0.0267795i	$-0.991475\pi$
$17$		−	15.4786i		−	0.0535591i	0.999641	−	0.0267795i	$-0.00852521\pi$
$18$	199.575	−	538.177i	0.615971	−	1.66104i
$19$	179.462			0.497125			0.248563	−	0.968616i	$-0.420042\pi$
$19$	179.462			0.497125			0.248563	+	0.968616i	$0.420042\pi$
$20$		−	296.233i		−	0.740583i
$21$	111.313	−	620.310i	0.252409	−	1.40660i
$22$	−1601.31			−3.30849
$23$			621.607i			1.17506i	0.809202	+	0.587530i	$0.199900\pi$
$23$			621.607i			1.17506i	−0.809202	+	0.587530i	$0.800100\pi$
$24$	1143.47	+	205.191i	1.98519	+	0.356235i
$25$	550.042			0.880067
$26$			1105.91i			1.63597i
$27$	370.212	−	628.000i	0.507835	−	0.861454i
$28$	2395.92			3.05603
$29$		−	442.113i		−	0.525699i	−0.964837	−	0.262850i	$-0.915338\pi$
$29$		−	442.113i		−	0.525699i	0.964837	−	0.262850i	$-0.0846623\pi$
$30$	97.5268	−	543.487i	0.108363	−	0.603874i
$31$	−258.752			−0.269252			−0.134626	−	0.990896i	$-0.542983\pi$
$31$	−258.752			−0.269252			−0.134626	+	0.990896i	$0.542983\pi$
$32$			537.204i			0.524613i
$33$	−2001.78	−	359.212i	−1.83818	−	0.329855i
$34$	109.686			0.0948838
$35$		−	606.259i		−	0.494905i
$36$	2598.55	+	963.629i	2.00505	+	0.743541i
$37$	−2503.21			−1.82850			−0.914248	−	0.405154i	$-0.867218\pi$
$37$	−2503.21			−1.82850			−0.914248	+	0.405154i	$0.867218\pi$
$38$			1271.72i			0.880694i
$39$	−248.083	+	1382.49i	−0.163105	+	0.908936i
$40$	1117.56			0.698478
$41$		−	241.937i		−	0.143925i	−0.997407	−	0.0719623i	$-0.977074\pi$
$41$		−	241.937i		−	0.143925i	0.997407	−	0.0719623i	$-0.0229261\pi$
$42$	4395.70	+	788.794i	2.49190	+	0.447162i
$43$	2192.78			1.18593			0.592964	−	0.805229i	$-0.297958\pi$
$43$	2192.78			1.18593			0.592964	+	0.805229i	$0.297958\pi$
$44$		−	7731.79i		−	3.99369i
$45$	243.834	−	657.529i	0.120412	−	0.324706i
$46$	−4404.89			−2.08171
$47$			2940.86i			1.33131i	0.746261	+	0.665654i	$0.231847\pi$
$47$			2940.86i			1.33131i	−0.746261	+	0.665654i	$0.768153\pi$
$48$	−583.804	+	3253.36i	−0.253387	+	1.41205i
$49$	2502.40			1.04223
$50$			3897.76i			1.55910i
$51$	137.117	+	24.6052i	0.0527170	+	0.00945988i
$52$	−5339.82			−1.97479
$53$		−	289.041i		−	0.102898i	−0.998676	−	0.0514491i	$-0.983616\pi$
$53$		−	289.041i		−	0.102898i	0.998676	−	0.0514491i	$-0.0163840\pi$
$54$	4450.20	+	2623.43i	1.52613	+	0.899668i
$55$	−1956.43			−0.646755
$56$			9038.83i			2.88228i
$57$	−285.278	+	1589.77i	−0.0878049	+	0.489310i
$58$	3132.94			0.931315
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	2624.18	+	470.900i	0.728939	+	0.130806i
$61$	−4432.23			−1.19114			−0.595570	−	0.803304i	$-0.703074\pi$
$61$	−4432.23			−1.19114			−0.595570	+	0.803304i	$0.703074\pi$
$62$		−	1833.59i		−	0.477001i
$63$	5318.08	+	1972.12i	1.33990	+	0.496882i
$64$	2069.35			0.505213
$65$			1351.17i			0.319805i
$66$	2545.48	−	14185.2i	0.584363	−	3.25647i
$67$	−1621.56			−0.361229			−0.180615	−	0.983554i	$-0.557809\pi$
$67$	−1621.56			−0.361229			−0.180615	+	0.983554i	$0.557809\pi$
$68$			529.609i			0.114535i
$69$	−5506.51	−	988.123i	−1.15659	−	0.207545i
$70$	4296.13			0.876761
$71$		−	7336.07i		−	1.45528i	−0.685958	−	0.727641i	$-0.740617\pi$
$71$		−	7336.07i		−	1.45528i	0.685958	−	0.727641i	$-0.259383\pi$
$72$	−3635.37	+	9803.23i	−0.701268	+	1.89106i
$73$	−1743.91			−0.327250			−0.163625	−	0.986523i	$-0.552319\pi$
$73$	−1743.91			−0.327250			−0.163625	+	0.986523i	$0.552319\pi$
$74$		−	17738.5i		−	3.23932i
$75$	−874.362	+	4872.55i	−0.155442	+	0.866231i
$76$	−6140.41			−1.06309
$77$		−	15823.6i		−	2.66884i
$78$	−9796.75	−	1757.99i	−1.61025	−	0.288953i
$79$	2560.10			0.410206			0.205103	−	0.978740i	$-0.434247\pi$
$79$	2560.10			0.410206			0.205103	+	0.978740i	$0.434247\pi$
$80$			3179.66i			0.496823i
$81$	4974.64	+	4277.81i	0.758214	+	0.652006i
$82$	1714.44			0.254973
$83$		−	4640.76i		−	0.673648i	−0.941568	−	0.336824i	$-0.890647\pi$
$83$		−	4640.76i		−	0.673648i	0.941568	−	0.336824i	$-0.109353\pi$
$84$	−3808.63	+	21224.3i	−0.539771	+	3.00798i
$85$	134.011			0.0185482
$86$			15538.7i			2.10096i
$87$	3916.46	+	702.795i	0.517434	+	0.0928518i
$88$	29168.8			3.76664
$89$		−	8720.43i		−	1.10093i	−0.834860	−	0.550463i	$-0.814451\pi$
$89$		−	8720.43i		−	1.10093i	0.834860	−	0.550463i	$-0.185549\pi$
$90$	4659.45	+	1727.88i	0.575241	+	0.213319i
$91$	−10928.3			−1.31968
$92$		−	21268.7i		−	2.51284i
$93$	411.319	−	2292.15i	0.0475568	−	0.265019i
$94$	−20839.8			−2.35851
$95$			1553.75i			0.172161i
$96$	−4758.82	−	853.953i	−0.516365	−	0.0926599i
$97$	12826.5			1.36322			0.681610	−	0.731715i	$-0.261280\pi$
$97$	12826.5			1.36322			0.681610	+	0.731715i	$0.261280\pi$
$98$			17732.8i			1.84639i
$99$	6364.16	−	17161.8i	0.649338	−	1.75102i
$100$	−18820.0			−1.88200
$101$			9691.64i			0.950067i	0.879968	+	0.475034i	$0.157564\pi$
$101$			9691.64i			0.950067i	−0.879968	+	0.475034i	$0.842436\pi$
$102$	−174.359	+	971.651i	−0.0167589	+	0.0933921i
$103$	−19054.9			−1.79610			−0.898052	−	0.439889i	$-0.855018\pi$
$103$	−19054.9			−1.79610			−0.898052	+	0.439889i	$0.855018\pi$
$104$		−	20144.9i		−	1.86251i
$105$	5370.54	+	963.725i	0.487124	+	0.0874127i
$106$	2048.23			0.182292
$107$			13776.4i			1.20329i	0.798764	+	0.601644i	$0.205487\pi$
$107$			13776.4i			1.20329i	−0.798764	+	0.601644i	$0.794513\pi$
$108$	−12667.0	+	21487.4i	−1.08599	+	1.84220i
$109$	−5789.04			−0.487252			−0.243626	−	0.969869i	$-0.578337\pi$
$109$	−5789.04			−0.487252			−0.243626	+	0.969869i	$0.578337\pi$
$110$		−	13863.9i		−	1.14577i
$111$	3979.17	−	22174.7i	0.322959	−	1.79975i
$112$	−25717.0			−2.05015
$113$		−	16701.6i		−	1.30798i	−0.756502	−	0.653992i	$-0.773093\pi$
$113$		−	16701.6i		−	1.30798i	0.756502	−	0.653992i	$-0.226907\pi$
$114$	−11265.6	−	2021.57i	−0.866848	−	0.155553i
$115$	−5381.77			−0.406939
$116$			15127.2i			1.12420i
$117$	−11852.5	−	4395.29i	−0.865838	−	0.321082i
$118$	3211.42			0.230639
$119$			1083.88i			0.0765395i
$120$	−1776.51	+	9899.95i	−0.123369	+	0.687496i
$121$	−36422.6			−2.48771
$122$		−	31408.1i		−	2.11019i
$123$	2143.20	+	384.590i	0.141662	+	0.0254207i
$124$	8853.35			0.575790
$125$			10173.3i			0.651092i
$126$	−13975.1	+	37685.5i	−0.880264	+	2.37374i
$127$	30521.6			1.89234			0.946170	−	0.323670i	$-0.104917\pi$
$127$	30521.6			1.89234			0.946170	+	0.323670i	$0.104917\pi$
$128$			23259.3i			1.41964i
$129$	−3485.70	+	19424.8i	−0.209465	+	1.16728i
$130$	−9574.83			−0.566558
$131$		−	9964.10i		−	0.580625i	−0.956932	−	0.290312i	$-0.906241\pi$
$131$		−	9964.10i		−	0.580625i	0.956932	−	0.290312i	$-0.0937592\pi$
$132$	68492.1	+	12290.7i	3.93091	+	0.705387i
$133$	−12566.7			−0.710425
$134$		−	11490.9i		−	0.639945i
$135$	5437.12	+	3205.23i	0.298333	+	0.175870i
$136$	−1997.99			−0.108023
$137$		−	8591.87i		−	0.457769i	−0.973454	−	0.228885i	$-0.926492\pi$
$137$		−	8591.87i		−	0.457769i	0.973454	−	0.228885i	$-0.0735079\pi$
$138$	7002.14	−	39020.8i	0.367682	−	2.04898i
$139$	−33423.9			−1.72992			−0.864962	−	0.501837i	$-0.832658\pi$
$139$	−33423.9			−1.72992			−0.864962	+	0.501837i	$0.832658\pi$
$140$			20743.5i			1.05834i
$141$	−26051.6	−	4674.87i	−1.31038	−	0.235142i
$142$	51985.6			2.57814
$143$			35266.2i			1.72459i
$144$	−27891.9	−	10343.3i	−1.34510	−	0.498807i
$145$	3827.74			0.182057
$146$		−	12357.9i		−	0.579747i
$147$	−3977.89	+	22167.5i	−0.184085	+	1.02585i
$148$	85648.9			3.91020
$149$			38544.7i			1.73617i	0.496418	+	0.868084i	$0.334648\pi$
$149$			38544.7i			1.73617i	−0.496418	+	0.868084i	$0.665352\pi$
$150$	−34528.3	−	6195.99i	−1.53459	−	0.275377i
$151$	13143.4			0.576441			0.288221	−	0.957564i	$-0.406936\pi$
$151$	13143.4			0.576441			0.288221	+	0.957564i	$0.406936\pi$
$152$		−	23165.2i		−	1.00265i
$153$	−435.930	+	1175.54i	−0.0186223	+	0.0502173i
$154$	112131.			4.72805
$155$		−	2240.23i		−	0.0932457i
$156$	8488.33	−	47302.8i	0.348797	−	1.94374i
$157$	1902.76			0.0771942			0.0385971	−	0.999255i	$-0.487711\pi$
$157$	1902.76			0.0771942			0.0385971	+	0.999255i	$0.487711\pi$
$158$			18141.6i			0.726711i
$159$	2560.47	+	459.467i	0.101280	+	0.0181744i
$160$	−4651.02			−0.181680
$161$		−	43527.6i		−	1.67924i
$162$	−30313.8	+	35251.8i	−1.15508	+	1.34323i
$163$	16415.8			0.617854			0.308927	−	0.951086i	$-0.400030\pi$
$163$	16415.8			0.617854			0.308927	+	0.951086i	$0.400030\pi$
$164$			8278.04i			0.307779i
$165$	3110.00	−	17331.1i	0.114233	−	0.636586i
$166$	32885.8			1.19342
$167$			25416.2i			0.911333i	0.890151	+	0.455667i	$0.150599\pi$
$167$			25416.2i			0.911333i	−0.890151	+	0.455667i	$0.849401\pi$
$168$	−80070.5	−	14368.4i	−2.83696	−	0.509083i
$169$	−4205.07			−0.147231
$170$			949.641i			0.0328595i
$171$	−13629.5	−	5054.27i	−0.466108	−	0.172849i
$172$	−75027.4			−2.53608
$173$			23861.0i			0.797252i	0.917114	+	0.398626i	$0.130513\pi$
$173$			23861.0i			0.797252i	−0.917114	+	0.398626i	$0.869487\pi$
$174$	−4980.21	+	27753.2i	−0.164494	+	0.916673i
$175$	−38516.3			−1.25767
$176$			82990.4i			2.67918i
$177$	4014.56	+	720.399i	0.128142	+	0.0229946i
$178$	61795.6			1.95037
$179$		−	21390.9i		−	0.667610i	−0.942642	−	0.333805i	$-0.891667\pi$
$179$		−	21390.9i		−	0.667610i	0.942642	−	0.333805i	$-0.108333\pi$
$180$	−8342.94	+	22497.8i	−0.257498	+	0.694376i
$181$	36138.0			1.10308			0.551540	−	0.834148i	$-0.314040\pi$
$181$	36138.0			1.10308			0.551540	+	0.834148i	$0.314040\pi$
$182$		−	77440.9i		−	2.33791i
$183$	7045.59	−	39262.9i	0.210385	−	1.17241i
$184$	80237.8			2.36997
$185$		−	21672.4i		−	0.633233i
$186$	16242.9	+	2914.73i	0.469501	+	0.0842504i
$187$	3497.73			0.100024
$188$		−	100623.i		−	2.84697i
$189$	−25923.8	+	43975.3i	−0.725731	+	1.23108i
$190$	−11010.4			−0.304996
$191$			38862.2i			1.06527i	0.846344	+	0.532636i	$0.178799\pi$
$191$			38862.2i			1.06527i	−0.846344	+	0.532636i	$0.821201\pi$
$192$	−3289.50	+	18331.4i	−0.0892335	+	0.497271i
$193$	−32884.5			−0.882830			−0.441415	−	0.897303i	$-0.645523\pi$
$193$	−32884.5			−0.882830			−0.441415	+	0.897303i	$0.645523\pi$
$194$			90892.7i			2.41505i
$195$	−11969.4	−	2147.86i	−0.314777	−	0.0564856i
$196$	−85621.2			−2.22879
$197$			40794.8i			1.05117i	0.850742	+	0.525584i	$0.176153\pi$
$197$			40794.8i			1.05117i	−0.850742	+	0.525584i	$0.823847\pi$
$198$	121613.	+	45098.4i	3.10206	+	1.15035i
$199$	−22665.5			−0.572346			−0.286173	−	0.958178i	$-0.592383\pi$
$199$	−22665.5			−0.572346			−0.286173	+	0.958178i	$0.592383\pi$
$200$		−	71000.1i		−	1.77500i
$201$	2577.67	−	14364.6i	0.0638023	−	0.355550i
$202$	−68677.8			−1.68312
$203$			30958.7i			0.751260i
$204$	−4691.54	−	841.880i	−0.112734	−	0.0202297i
$205$	2094.65			0.0498430
$206$		−	135028.i		−	3.18193i
$207$	17506.6	−	47208.7i	0.408565	−	1.10174i
$208$	57315.8			1.32479
$209$			40553.5i			0.928402i
$210$	−6829.24	+	38057.3i	−0.154858	+	0.862977i
$211$	−29824.6			−0.669899			−0.334949	−	0.942236i	$-0.608719\pi$
$211$	−29824.6			−0.669899			−0.334949	+	0.942236i	$0.608719\pi$
$212$			9889.71i			0.220045i
$213$	64986.6	+	11661.6i	1.43240	+	0.257039i
$214$	−97624.0			−2.13171
$215$			18984.7i			0.410703i
$216$	−81063.1	−	47787.5i	−1.73746	−	1.02425i
$217$	18118.9			0.384780
$218$		−	41022.9i		−	0.863203i
$219$	2772.17	−	15448.5i	0.0578006	−	0.322105i
$220$	66940.6			1.38307
$221$		−	2415.64i		−	0.0494594i
$222$	157137.	+	28197.6i	3.18839	+	0.572145i
$223$	15909.7			0.319927			0.159964	−	0.987123i	$-0.448862\pi$
$223$	15909.7			0.319927			0.159964	+	0.987123i	$0.448862\pi$
$224$		−	37617.3i		−	0.749707i
$225$	−41773.6	−	15491.1i	−0.825157	−	0.305996i
$226$	118353.			2.31719
$227$			26000.0i			0.504570i	0.967653	+	0.252285i	$0.0811820\pi$
$227$			26000.0i			0.504570i	−0.967653	+	0.252285i	$0.918818\pi$
$228$	9760.97	−	54394.9i	0.187769	−	1.04638i
$229$	−27370.1			−0.521922			−0.260961	−	0.965349i	$-0.584039\pi$
$229$	−27370.1			−0.521922			−0.260961	+	0.965349i	$0.584039\pi$
$230$		−	38136.8i		−	0.720923i
$231$	140173.	+	25153.6i	2.62688	+	0.471385i
$232$	−57068.5			−1.06028
$233$		−	87779.4i		−	1.61689i	−0.588571	−	0.808446i	$-0.700309\pi$
$233$		−	87779.4i		−	1.61689i	0.588571	−	0.808446i	$-0.299691\pi$
$234$	31146.4	−	83990.0i	0.568821	−	1.53390i
$235$	−25461.5			−0.461049
$236$			15506.1i			0.278406i
$237$	−4069.60	+	22678.6i	−0.0724528	+	0.403757i
$238$	−7680.67			−0.135595
$239$		−	27127.4i		−	0.474911i	−0.971398	−	0.237455i	$-0.923687\pi$
$239$		−	27127.4i		−	0.474911i	0.971398	−	0.237455i	$-0.0763134\pi$
$240$	−28167.1	−	5054.48i	−0.489012	−	0.0877514i
$241$	13743.6			0.236628			0.118314	−	0.992976i	$-0.462251\pi$
$241$	13743.6			0.236628			0.118314	+	0.992976i	$0.462251\pi$
$242$		−	258101.i		−	4.40717i
$243$	−45802.8	+	37267.8i	−0.775675	+	0.631133i
$244$	151652.			2.54722
$245$			21665.4i			0.360939i
$246$	−2725.32	+	15187.4i	−0.0450347	+	0.250965i
$247$	28007.6			0.459073
$248$			33400.0i			0.543054i
$249$	41110.2	+	7377.08i	0.663057	+	0.118983i
$250$	−72091.2			−1.15346
$251$			78056.8i			1.23898i	0.785006	+	0.619488i	$0.212660\pi$
$251$			78056.8i			1.23898i	−0.785006	+	0.619488i	$0.787340\pi$
$252$	−181961.	−	67477.5i	−2.86535	−	1.06257i
$253$	−140466.			−2.19447
$254$			216285.i			3.35242i
$255$	−213.027	+	1187.14i	−0.00327608	+	0.0182566i
$256$	−131713.			−2.00978
$257$		−	78115.9i		−	1.18270i	−0.806416	−	0.591348i	$-0.798596\pi$
$257$		−	78115.9i		−	1.18270i	0.806416	−	0.591348i	$-0.201404\pi$
$258$	−137650.	−	24700.7i	−2.06793	−	0.371083i
$259$	175286.			2.61304
$260$		−	46231.3i		−	0.683895i
$261$	−12451.4	+	33576.8i	−0.182784	+	0.492899i
$262$	70608.6			1.02862
$263$		−	17157.0i		−	0.248045i	−0.992279	−	0.124022i	$-0.960421\pi$
$263$		−	17157.0i		−	0.248045i	0.992279	−	0.124022i	$-0.0395795\pi$
$264$	−46367.6	+	258392.i	−0.665283	+	3.70742i
$265$	2502.47			0.0356350
$266$		−	89051.5i		−	1.25857i
$267$	77249.9	+	13862.2i	1.08362	+	0.194451i
$268$	55482.7			0.772481
$269$			111286.i			1.53792i	0.639295	+	0.768961i	$0.279226\pi$
$269$			111286.i			1.53792i	−0.639295	+	0.768961i	$0.720774\pi$
$270$	−22713.2	+	38529.0i	−0.311567	+	0.528519i
$271$	−86909.3			−1.18339			−0.591695	−	0.806162i	$-0.701541\pi$
$271$	−86909.3			−1.18339			−0.591695	+	0.806162i	$0.701541\pi$
$272$		−	5684.64i		−	0.0768360i
$273$	17371.9	−	96808.0i	0.233089	−	1.29893i
$274$	60884.6			0.810972
$275$			124294.i			1.64356i
$276$	188409.	+	33809.3i	2.47333	+	0.443831i
$277$	−96252.5			−1.25445			−0.627224	−	0.778839i	$-0.715809\pi$
$277$	−96252.5			−1.25445			−0.627224	+	0.778839i	$0.715809\pi$
$278$		−	236851.i		−	3.06469i
$279$	19651.2	+	7287.34i	0.252453	+	0.0936182i
$280$	−78256.7			−0.998172
$281$			39522.8i			0.500535i	0.968177	+	0.250268i	$0.0805186\pi$
$281$			39522.8i			0.500535i	−0.968177	+	0.250268i	$0.919481\pi$
$282$	33127.5	−	184609.i	0.416572	−	2.32143i
$283$	−100369.			−1.25322			−0.626611	−	0.779333i	$-0.715558\pi$
$283$	−100369.			−1.25322			−0.626611	+	0.779333i	$0.715558\pi$
$284$			251008.i			3.11208i
$285$	−13763.9	−	2469.89i	−0.169454	−	0.0304080i
$286$	−249906.			−3.05524
$287$			16941.5i			0.205678i
$288$	15129.5	−	40798.6i	0.182406	−	0.491881i
$289$	83281.4			0.997131
$290$			27124.5i			0.322527i
$291$	−20389.4	+	113624.i	−0.240779	+	1.34179i
$292$	59669.1			0.699816
$293$		−	44745.7i		−	0.521214i	−0.965445	−	0.260607i	$-0.916077\pi$
$293$		−	44745.7i		−	0.521214i	0.965445	−	0.260607i	$-0.0839227\pi$
$294$	−157086.	−	28188.5i	−1.81736	−	0.326120i
$295$	3923.62			0.0450862
$296$			323118.i			3.68789i
$297$	141911.	+	83657.8i	1.60880	+	0.948404i
$298$	−273139.			−3.07575
$299$			97010.4i			1.08512i
$300$	29916.8	−	166717.i	0.332409	−	1.85241i
$301$	−153548.			−1.69477
$302$			93138.3i			1.02121i
$303$	−85853.4	−	15406.1i	−0.935131	−	0.167806i
$304$	65909.1			0.713178
$305$		−	38373.5i		−	0.412507i
$306$	−8330.21	−	3089.13i	−0.0889638	−	0.0329908i
$307$	−125274.			−1.32918			−0.664589	−	0.747209i	$-0.731393\pi$
$307$	−125274.			−1.32918			−0.664589	+	0.747209i	$0.731393\pi$
$308$			541413.i			5.70726i
$309$	30290.1	−	168798.i	0.317237	−	1.76787i
$310$	15874.9			0.165192
$311$			23197.4i			0.239839i	0.992784	+	0.119919i	$0.0382636\pi$
$311$			23197.4i			0.239839i	−0.992784	+	0.119919i	$0.961736\pi$
$312$	178454.	+	32022.9i	1.83323	+	0.328967i
$313$	−43815.3			−0.447236			−0.223618	−	0.974677i	$-0.571787\pi$
$313$	−43815.3			−0.447236			−0.223618	+	0.974677i	$0.571787\pi$
$314$			13483.5i			0.136755i
$315$	−17074.3	+	46043.0i	−0.172077	+	0.464026i
$316$	−87595.3			−0.877216
$317$		−	49751.8i		−	0.495096i	−0.968876	−	0.247548i	$-0.920375\pi$
$317$		−	49751.8i		−	0.495096i	0.968876	−	0.247548i	$-0.0796249\pi$
$318$	−3255.92	+	18144.2i	−0.0321973	+	0.179426i
$319$	99905.4			0.981765
$320$			17916.1i			0.174962i
$321$	−122039.	−	21899.4i	−1.18437	−	0.212531i
$322$	308449.			2.97490
$323$		−	2777.82i		−	0.0266256i
$324$	−170210.	−	146368.i	−1.62142	−	1.39430i
$325$	85841.7			0.812702
$326$			116327.i			1.09457i
$327$	9202.42	−	51282.2i	0.0860610	−	0.479591i
$328$	−31229.6			−0.290281
$329$		−	205931.i		−	1.90253i
$330$	122813.	+	22038.4i	1.12776	+	0.202373i
$331$	−61831.6			−0.564358			−0.282179	−	0.959362i	$-0.591057\pi$
$331$	−61831.6			−0.564358			−0.282179	+	0.959362i	$0.591057\pi$
$332$			158787.i			1.44058i
$333$	190109.	+	70499.1i	1.71441	+	0.635762i
$334$	−180107.			−1.61449
$335$		−	14039.2i		−	0.125099i
$336$	40880.5	−	227814.i	0.362108	−	2.01791i
$337$	−59090.1			−0.520302			−0.260151	−	0.965568i	$-0.583772\pi$
$337$	−59090.1			−0.520302			−0.260151	+	0.965568i	$0.583772\pi$
$338$		−	29798.4i		−	0.260831i
$339$	147952.	+	26549.4i	1.28742	+	0.231023i
$340$	−4585.26			−0.0396649
$341$		−	58470.8i		−	0.502840i
$342$	35816.1	−	96582.5i	0.306215	−	0.825745i
$343$	−7100.56			−0.0603538
$344$		−	283047.i		−	2.39189i
$345$	8555.01	−	47674.4i	0.0718757	−	0.400541i
$346$	−169086.			−1.41239
$347$		−	98499.7i		−	0.818043i	−0.912525	−	0.409021i	$-0.865870\pi$
$347$		−	98499.7i		−	0.818043i	0.912525	−	0.409021i	$-0.134130\pi$
$348$	−134004.	−	24046.6i	−1.10652	−	0.198561i
$349$	−47248.8			−0.387918			−0.193959	−	0.981010i	$-0.562133\pi$
$349$	−47248.8			−0.387918			−0.193959	+	0.981010i	$0.562133\pi$
$350$		−	272938.i		−	2.22806i
$351$	57776.7	−	98008.1i	0.468963	−	0.795514i
$352$	−121393.			−0.979737
$353$		−	115826.i		−	0.929513i	−0.885438	−	0.464757i	$-0.846142\pi$
$353$		−	115826.i		−	0.929513i	0.885438	−	0.464757i	$-0.153858\pi$
$354$	−5104.96	+	28448.4i	−0.0407367	+	0.227013i
$355$	63514.5			0.503983
$356$			298375.i			2.35430i
$357$	−9601.52	−	1722.96i	−0.0753361	−	0.0135188i
$358$	151582.			1.18272
$359$			66309.4i			0.514501i	0.966345	+	0.257250i	$0.0828165\pi$
$359$			66309.4i			0.514501i	−0.966345	+	0.257250i	$0.917184\pi$
$360$	−84874.7	−	31474.5i	−0.654898	−	0.242858i
$361$	−98114.3			−0.752866
$362$			256085.i			1.95419i
$363$	57898.4	−	322650.i	0.439393	−	2.44860i
$364$	373917.			2.82210
$365$		−	15098.5i		−	0.113331i
$366$	278229.	+	49927.2i	2.07702	+	0.372713i
$367$	227240.			1.68714			0.843572	−	0.537016i	$-0.180449\pi$
$367$	227240.			1.68714			0.843572	+	0.537016i	$0.180449\pi$
$368$			228291.i			1.68575i
$369$	−6813.79	+	18374.2i	−0.0500421	+	0.134945i
$370$	153577.			1.12182
$371$			20239.9i			0.147048i
$372$	−14073.5	+	78427.4i	−0.101699	+	0.566738i
$373$	252202.			1.81272			0.906361	−	0.422504i	$-0.138849\pi$
$373$	252202.			1.81272			0.906361	+	0.422504i	$0.138849\pi$
$374$			24786.0i			0.177200i
$375$	−90120.4	−	16171.8i	−0.640856	−	0.114999i
$376$	379610.			2.68511
$377$		−	68997.9i		−	0.485459i
$378$	−311622.	−	183704.i	−2.18094	−	1.28569i
$379$	−20628.3			−0.143610			−0.0718049	−	0.997419i	$-0.522876\pi$
$379$	−20628.3			−0.143610			−0.0718049	+	0.997419i	$0.522876\pi$
$380$		−	53162.7i		−	0.368162i
$381$	−48517.9	+	270375.i	−0.334235	+	1.86259i
$382$	−275389.			−1.88721
$383$			269587.i			1.83781i	0.394474	+	0.918907i	$0.370927\pi$
$383$			269587.i			1.83781i	−0.394474	+	0.918907i	$0.629073\pi$
$384$	−206043.	−	36973.6i	−1.39732	−	0.250744i
$385$	136998.			0.924256
$386$		−	233030.i		−	1.56400i
$387$	−166533.	−	61756.3i	−1.11193	−	0.412343i
$388$	−438868.			−2.91522
$389$		−	151849.i		−	1.00349i	−0.865015	−	0.501746i	$-0.832691\pi$
$389$		−	151849.i		−	1.00349i	0.865015	−	0.501746i	$-0.167309\pi$
$390$	15220.4	−	84818.6i	0.100068	−	0.557650i
$391$	9621.58			0.0629351
$392$		−	323013.i		−	2.10207i
$393$	88267.0	+	15839.2i	0.571496	+	0.102553i
$394$	−289084.			−1.86222
$395$			22164.9i			0.142060i
$396$	−217754.	+	587200.i	−1.38859	+	3.74452i
$397$	−116775.			−0.740919			−0.370459	−	0.928849i	$-0.620800\pi$
$397$	−116775.			−0.740919			−0.370459	+	0.928849i	$0.620800\pi$
$398$		−	160614.i		−	1.01395i
$399$	19976.4	−	111322.i	0.125479	−	0.699256i
$400$	202008.			1.26255
$401$			131648.i			0.818700i	0.912377	+	0.409350i	$0.134245\pi$
$401$			131648.i			0.818700i	−0.912377	+	0.409350i	$0.865755\pi$
$402$	101792.	+	18266.2i	0.629884	+	0.113030i
$403$	−40381.8			−0.248642
$404$		−	331605.i		−	2.03170i
$405$	−37036.6	+	43069.6i	−0.225798	+	0.262580i
$406$	−219382.			−1.33091
$407$		−	565657.i		−	3.41479i
$408$	3176.06	−	17699.2i	0.0190796	−	0.106325i
$409$	−130585.			−0.780630			−0.390315	−	0.920681i	$-0.627634\pi$
$409$	−130585.			−0.780630			−0.390315	+	0.920681i	$0.627634\pi$
$410$			14843.3i			0.0883006i
$411$	76111.1	+	13657.9i	0.450572	+	0.0808536i
$412$	651974.			3.84093
$413$			31734.1i			0.186049i
$414$	334535.	+	124057.i	1.95182	+	0.723803i
$415$	40178.9			0.233293
$416$			83838.1i			0.484456i
$417$	53131.5	−	296085.i	0.305548	−	1.70273i
$418$	−287374.			−1.64473
$419$		−	21577.2i		−	0.122904i	−0.998110	−	0.0614522i	$-0.980427\pi$
$419$		−	21577.2i		−	0.122904i	0.998110	−	0.0614522i	$-0.0195732\pi$
$420$	−183756.	−	32974.5i	−1.04170	−	0.186930i
$421$	−115411.			−0.651152			−0.325576	−	0.945516i	$-0.605558\pi$
$421$	−115411.			−0.651152			−0.325576	+	0.945516i	$0.605558\pi$
$422$		−	211346.i		−	1.18678i
$423$	82824.7	−	223347.i	0.462891	−	1.24824i
$424$	−37309.8			−0.207535
$425$		−	8513.86i		−	0.0471356i
$426$	−82637.7	+	460515.i	−0.455365	+	2.53761i
$427$	310364.			1.70222
$428$		−	471369.i		−	2.57320i
$429$	−312405.	−	56060.0i	−1.69748	−	0.304606i
$430$	−134531.			−0.727590
$431$		−	17024.2i		−	0.0916459i	−0.998950	−	0.0458229i	$-0.985409\pi$
$431$		−	17024.2i		−	0.0916459i	0.998950	−	0.0458229i	$-0.0145910\pi$
$432$	135964.	−	230638.i	0.728543	−	1.23585i
$433$	125401.			0.668844			0.334422	−	0.942423i	$-0.391459\pi$
$433$	125401.			0.668844			0.334422	+	0.942423i	$0.391459\pi$
$434$			128396.i			0.681666i
$435$	−6084.68	+	33908.1i	−0.0321558	+	0.179194i
$436$	198076.			1.04198
$437$			111555.i			0.584152i
$438$	109472.	+	19644.4i	0.570633	+	0.102398i
$439$	277022.			1.43743			0.718713	−	0.695307i	$-0.244732\pi$
$439$	277022.			1.43743			0.718713	+	0.695307i	$0.244732\pi$
$440$			252539.i			1.30444i
$441$	−190048.	−	70476.2i	−0.977205	−	0.362381i
$442$	17118.0			0.0876209
$443$		−	241189.i		−	1.22900i	−0.788918	−	0.614499i	$-0.789358\pi$
$443$		−	241189.i		−	1.22900i	0.788918	−	0.614499i	$-0.210642\pi$
$444$	−136150.	+	758722.i	−0.690639	+	3.84872i
$445$	75500.0			0.381265
$446$			112741.i			0.566775i
$447$	−341448.	−	61271.6i	−1.70887	−	0.306651i
$448$	−144905.			−0.721984
$449$			58868.2i			0.292004i	0.989284	+	0.146002i	$0.0466405\pi$
$449$			58868.2i			0.292004i	−0.989284	+	0.146002i	$0.953359\pi$
$450$	109774.	−	296020.i	0.542096	−	1.46183i
$451$	54671.2			0.268785
$452$			571457.i			2.79709i
$453$	−20893.2	+	116431.i	−0.101814	+	0.567378i
$454$	−184244.			−0.893883
$455$		−	94615.1i		−	0.457022i
$456$	205209.	+	36824.1i	0.986886	+	0.177093i
$457$	198349.			0.949726			0.474863	−	0.880060i	$-0.342498\pi$
$457$	198349.			0.949726			0.474863	+	0.880060i	$0.342498\pi$
$458$		−	193953.i		−	0.924624i
$459$	−9720.54	−	5730.35i	−0.0461387	−	0.0271992i
$460$	184141.			0.870230
$461$			368156.i			1.73233i	0.499761	+	0.866163i	$0.333421\pi$
$461$			368156.i			1.73233i	−0.499761	+	0.866163i	$0.666579\pi$
$462$	−178246.	+	993309.i	−0.835094	+	4.65372i
$463$	258187.			1.20441			0.602203	−	0.798343i	$-0.294290\pi$
$463$	258187.			1.20441			0.602203	+	0.798343i	$0.294290\pi$
$464$		−	162370.i		−	0.754170i
$465$	19845.1	+	3561.13i	0.0917797	+	0.0164695i
$466$	622031.			2.86444
$467$		−	78827.9i		−	0.361448i	−0.983534	−	0.180724i	$-0.942156\pi$
$467$		−	78827.9i		−	0.361448i	0.983534	−	0.180724i	$-0.0578441\pi$
$468$	405539.	+	150388.i	1.85157	+	0.686627i
$469$	113549.			0.516221
$470$		−	180427.i		−	0.816783i
$471$	−3024.68	+	16855.6i	−0.0136344	+	0.0759806i
$472$	−58498.0			−0.262577
$473$			495508.i			2.21477i
$474$	−160708.	−	28838.4i	−0.715286	−	0.128355i
$475$	98711.7			0.437504
$476$		−	37085.5i		−	0.163678i
$477$	−8140.38	+	21951.5i	−0.0357773	+	0.0964780i
$478$	192233.			0.841340
$479$			240842.i			1.04969i	0.851197	+	0.524846i	$0.175877\pi$
$479$			240842.i			1.04969i	−0.851197	+	0.524846i	$0.824123\pi$
$480$	7393.39	−	41201.1i	0.0320894	−	0.178824i
$481$	−390661.			−1.68853
$482$			97391.2i			0.419204i
$483$	385589.	+	69192.6i	1.65284	+	0.296596i
$484$	1.24622e6			5.31991
$485$			111050.i			0.472102i
$486$	−264090.	−	324572.i	−1.11810	−	1.37417i
$487$	−132259.			−0.557656			−0.278828	−	0.960341i	$-0.589946\pi$
$487$	−132259.			−0.557656			−0.278828	+	0.960341i	$0.589946\pi$
$488$			572118.i			2.40240i
$489$	−26094.9	+	145419.i	−0.109129	+	0.608140i
$490$	−153527.			−0.639431
$491$		−	159708.i		−	0.662467i	−0.943549	−	0.331233i	$-0.892535\pi$
$491$		−	159708.i		−	0.662467i	0.943549	−	0.331233i	$-0.107465\pi$
$492$	−73331.0	−	13159.0i	−0.302941	−	0.0543616i
$493$	−6843.28			−0.0281560
$494$			198470.i			0.813281i
$495$	148584.	+	55099.9i	0.606402	+	0.224874i
$496$	−95028.8			−0.386271
$497$			513703.i			2.07970i
$498$	−52276.2	+	291319.i	−0.210788	+	1.17466i
$499$	438821.			1.76233			0.881163	−	0.472813i	$-0.156761\pi$
$499$	438821.			1.76233			0.881163	+	0.472813i	$0.156761\pi$
$500$		−	348086.i		−	1.39235i
$501$	−225149.	−	40402.2i	−0.897005	−	0.160964i
$502$	−553134.			−2.19494
$503$		−	231337.i		−	0.914343i	−0.889379	−	0.457171i	$-0.848863\pi$
$503$		−	231337.i		−	0.914343i	0.889379	−	0.457171i	$-0.151137\pi$
$504$	254564.	−	686464.i	1.00216	−	2.70245i
$505$	−83908.6			−0.329021
$506$		−	995385.i		−	3.88768i
$507$	6684.50	−	37250.7i	0.0260048	−	0.144917i
$508$	−1.04431e6			−4.04672
$509$		−	317545.i		−	1.22566i	−0.790215	−	0.612830i	$-0.790031\pi$
$509$		−	317545.i		−	1.22566i	0.790215	−	0.612830i	$-0.209969\pi$
$510$	−8412.40	−	1509.57i	−0.0323429	−	0.00580382i
$511$	122116.			0.467662
$512$		−	561207.i		−	2.14083i
$513$	66439.1	−	112702.i	0.252458	−	0.428251i
$514$	553553.			2.09523
$515$		−	164974.i		−	0.622015i
$516$	119266.	−	664630.i	0.447936	−	2.49621i
$517$	−664553.			−2.48627
$518$			1.24213e6i			4.62920i
$519$	−211372.	−	37930.0i	−0.784718	−	0.140815i
$520$	174411.			0.645013
$521$			203095.i			0.748210i	0.927386	+	0.374105i	$0.122050\pi$
$521$			203095.i			0.748210i	−0.927386	+	0.374105i	$0.877950\pi$
$522$	−237935.	−	88234.5i	−0.873208	−	0.323815i
$523$	188696.			0.689858			0.344929	−	0.938629i	$-0.387903\pi$
$523$	188696.			0.689858			0.344929	+	0.938629i	$0.387903\pi$
$524$			340928.i			1.24165i
$525$	61226.6	−	341197.i	0.222137	−	1.23790i
$526$	121580.			0.439430
$527$			4005.10i			0.0144209i
$528$	−735171.	−	131924.i	−2.63706	−	0.473211i
$529$	−106554.			−0.380767
$530$			17733.2i			0.0631300i
$531$	−12763.3	+	34417.9i	−0.0452663	+	0.122066i
$532$	429978.			1.51923
$533$		−	37757.7i		−	0.132908i
$534$	−98231.9	+	547416.i	−0.344485	+	1.91971i
$535$	−119274.			−0.416715
$536$			209313.i			0.728562i
$537$	189491.	+	34003.6i	0.657114	+	0.117917i
$538$	−788603.			−2.72454
$539$			565474.i			1.94641i
$540$	−186034.	−	109669.i	−0.637978	−	0.376094i
$541$	−424126.			−1.44911			−0.724553	−	0.689219i	$-0.757954\pi$
$541$	−424126.			−1.44911			−0.724553	+	0.689219i	$0.757954\pi$
$542$		−	615865.i		−	2.09646i
$543$	−57446.0	+	320129.i	−0.194832	+	1.08574i
$544$	8315.14			0.0280978
$545$		−	50120.5i		−	0.168742i
$546$	686011.	+	123102.i	2.30115	+	0.412934i
$547$	−133095.			−0.444823			−0.222412	−	0.974953i	$-0.571393\pi$
$547$	−133095.			−0.444823			−0.222412	+	0.974953i	$0.571393\pi$
$548$			293976.i			0.978929i
$549$	336611.	+	124827.i	1.11682	+	0.414155i
$550$	−880787.			−2.91169
$551$		−	79342.6i		−	0.261338i
$552$	−127548.	+	710787.i	−0.418597	+	2.33271i
$553$	−179269.			−0.586212
$554$		−	682074.i		−	2.22235i
$555$	191985.	+	34451.0i	0.623277	+	0.111845i
$556$	1.14362e6			3.69940
$557$		−	23822.6i		−	0.0767854i	−0.999263	−	0.0383927i	$-0.987776\pi$
$557$		−	23822.6i		−	0.0767854i	0.999263	−	0.0383927i	$-0.0122238\pi$
$558$	−51640.2	+	139254.i	−0.165852	+	0.447239i
$559$	342214.			1.09515
$560$		−	222654.i		−	0.709993i
$561$	−5560.09	+	30984.7i	−0.0176667	+	0.0984512i
$562$	−280070.			−0.886736
$563$		−	225139.i		−	0.710286i	−0.934812	−	0.355143i	$-0.884432\pi$
$563$		−	225139.i		−	0.710286i	0.934812	−	0.355143i	$-0.115568\pi$
$564$	891372.	+	159953.i	2.80221	+	0.502847i
$565$	144600.			0.452972
$566$		−	711246.i		−	2.22017i
$567$	−348346.	−	299551.i	−1.08354	−	0.931760i
$568$	−946950.			−2.93515
$569$			356315.i			1.10055i	0.834983	+	0.550275i	$0.185477\pi$
$569$			356315.i			1.10055i	−0.834983	+	0.550275i	$0.814523\pi$
$570$	17502.4	−	97535.3i	0.0538700	−	0.300201i
$571$	50591.2			0.155168			0.0775841	−	0.996986i	$-0.475279\pi$
$571$	50591.2			0.155168			0.0775841	+	0.996986i	$0.475279\pi$
$572$		−	1.20665e6i		−	3.68800i
$573$	−344261.	−	61776.4i	−1.04852	−	0.188154i
$574$	−120052.			−0.364374
$575$			341910.i			1.03413i
$576$	−157160.	−	58280.1i	−0.473692	−	0.175661i
$577$	25449.4			0.0764409			0.0382205	−	0.999269i	$-0.487831\pi$
$577$	25449.4			0.0764409			0.0382205	+	0.999269i	$0.487831\pi$
$578$			590157.i			1.76649i
$579$	52274.2	−	291308.i	0.155930	−	0.868951i
$580$	−130969.			−0.389324
$581$			324966.i			0.962688i
$582$	−805174.	−	144486.i	−2.37708	−	0.426558i
$583$	65315.3			0.192167
$584$			225107.i			0.660029i
$585$	38053.7	−	102617.i	0.111195	−	0.299851i
$586$	317081.			0.923370
$587$		−	479696.i		−	1.39216i	−0.717963	−	0.696081i	$-0.754925\pi$
$587$		−	479696.i		−	1.39216i	0.717963	−	0.696081i	$-0.245075\pi$
$588$	136106.	−	758476.i	0.393661	−	2.19375i
$589$	−46436.1			−0.133852
$590$			27804.0i			0.0798735i
$591$	−361381.	−	64848.5i	−1.03464	−	0.185663i
$592$	−919326.			−2.62317
$593$		−	84236.0i		−	0.239546i	−0.992801	−	0.119773i	$-0.961783\pi$
$593$		−	84236.0i		−	0.239546i	0.992801	−	0.119773i	$-0.0382166\pi$
$594$	−592824.	+	1.00562e6i	−1.68017	+	2.85011i
$595$	−9384.01			−0.0265066
$596$		−	1.31883e6i		−	3.71275i
$597$	36029.7	−	200782.i	0.101091	−	0.563348i
$598$	−687444.			−1.92236
$599$			505826.i			1.40977i	0.709323	+	0.704883i	$0.249001\pi$
$599$			505826.i			1.40977i	−0.709323	+	0.704883i	$0.750999\pi$
$600$	628955.	+	112864.i	1.74710	+	0.313510i
$601$	−4842.12			−0.0134056			−0.00670281	−	0.999978i	$-0.502134\pi$
$601$	−4842.12			−0.0134056			−0.00670281	+	0.999978i	$0.502134\pi$
$602$		−	1.08809e6i		−	3.00241i
$603$	123151.	+	45668.7i	0.338691	+	0.125598i
$604$	−449711.			−1.23271
$605$		−	315341.i		−	0.861528i
$606$	109172.	−	608383.i	0.297281	−	1.65665i
$607$	535910.			1.45450			0.727252	−	0.686371i	$-0.240797\pi$
$607$	535910.			1.45450			0.727252	+	0.686371i	$0.240797\pi$
$608$			96407.8i			0.260798i
$609$	−274247.	−	49212.7i	−0.739448	−	0.132691i
$610$	271926.			0.730788
$611$			458962.i			1.22940i
$612$	14915.6	−	40221.8i	0.0398234	−	0.107389i
$613$	341628.			0.909143			0.454571	−	0.890710i	$-0.349792\pi$
$613$	341628.			0.909143			0.454571	+	0.890710i	$0.349792\pi$
$614$		−	887727.i		−	2.35474i
$615$	−3329.72	+	18555.5i	−0.00880354	+	0.0490594i
$616$	−2.04253e6			−5.38278
$617$			374929.i			0.984870i	0.870349	+	0.492435i	$0.163893\pi$
$617$			374929.i			0.984870i	−0.870349	+	0.492435i	$0.836107\pi$
$618$	1.19615e6	+	214645.i	3.13191	+	0.562010i
$619$	176698.			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$619$	176698.			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$620$			76650.8i			0.199404i
$621$	390369.	+	230126.i	1.01226	+	0.596737i
$622$	−164384.			−0.424892
$623$			610642.i			1.57330i
$624$	−91110.8	+	507732.i	−0.233992	+	1.30396i
$625$	255697.			0.654585
$626$		−	310488.i		−	0.792313i
$627$	−359244.	−	64465.0i	−0.913806	−	0.163979i
$628$	−65104.1			−0.165078
$629$			38746.1i			0.0979325i
$630$	−326275.	−	120994.i	−0.822057	−	0.304847i
$631$	414056.			1.03992			0.519960	−	0.854190i	$-0.325947\pi$
$631$	414056.			1.03992			0.519960	+	0.854190i	$0.325947\pi$
$632$		−	330461.i		−	0.827343i
$633$	47409.9	−	264201.i	0.118321	−	0.659367i
$634$	352556.			0.877100
$635$			264251.i			0.655343i
$636$	−87608.0	−	15721.0i	−0.216586	−	0.0388655i
$637$	390534.			0.962455
$638$			707960.i			1.73927i
$639$	−206609.	+	557147.i	−0.505997	+	1.36448i
$640$	−201375.			−0.491639
$641$			275394.i			0.670252i	0.942173	+	0.335126i	$0.108779\pi$
$641$			275394.i			0.670252i	−0.942173	+	0.335126i	$0.891221\pi$
$642$	155186.	−	864802.i	0.376514	−	2.09820i
$643$	267744.			0.647586			0.323793	−	0.946128i	$-0.395042\pi$
$643$	267744.			0.647586			0.323793	+	0.946128i	$0.395042\pi$
$644$			1.48932e6i			3.59102i
$645$	−168176.	−	30178.6i	−0.404246	−	0.0725405i
$646$	19684.4			0.0471692
$647$			680208.i			1.62493i	0.583013	+	0.812463i	$0.301874\pi$
$647$			680208.i			1.62493i	−0.583013	+	0.812463i	$0.698126\pi$
$648$	552185.	−	642133.i	1.31503	−	1.52924i
$649$	102408.			0.243133
$650$			608300.i			1.43976i
$651$	−28802.3	+	160506.i	−0.0679618	+	0.378730i
$652$	−561675.			−1.32127
$653$			714728.i			1.67616i	0.545550	+	0.838078i	$0.316321\pi$
$653$			714728.i			1.67616i	−0.545550	+	0.838078i	$0.683679\pi$
$654$	363401.	+	65211.1i	0.849632	+	0.152463i
$655$	86267.5			0.201078
$656$		−	88853.6i		−	0.206475i
$657$	132444.	+	49114.6i	0.306832	+	0.113784i
$658$	1.45929e6			3.37047
$659$		−	257886.i		−	0.593824i	−0.954905	−	0.296912i	$-0.904043\pi$
$659$		−	257886.i		−	0.593824i	0.954905	−	0.296912i	$-0.0959568\pi$
$660$	−106411.	+	592993.i	−0.244285	+	1.36133i
$661$	−157805.			−0.361174			−0.180587	−	0.983559i	$-0.557800\pi$
$661$	−157805.			−0.361174			−0.180587	+	0.983559i	$0.557800\pi$
$662$		−	438157.i		−	0.999802i
$663$	21399.0	+	3839.97i	0.0486818	+	0.00873577i
$664$	−599036.			−1.35868
$665$		−	108801.i		−	0.246030i
$666$	−499577.	+	1.34717e6i	−1.12630	+	3.03721i
$667$	274821.			0.617728
$668$		−	869630.i		−	1.94886i
$669$	−25290.4	+	140936.i	−0.0565072	+	0.314897i
$670$	99485.9			0.221621
$671$		−	1.00156e6i		−	2.22450i
$672$	333233.	+	59797.5i	0.737920	+	0.132417i
$673$	−160084.			−0.353441			−0.176720	−	0.984261i	$-0.556549\pi$
$673$	−160084.			−0.353441			−0.176720	+	0.984261i	$0.556549\pi$
$674$		−	418730.i		−	0.921753i
$675$	203632.	−	345426.i	0.446929	−	0.758137i
$676$	143879.			0.314851
$677$		−	402856.i		−	0.878968i	−0.898251	−	0.439484i	$-0.855161\pi$
$677$		−	402856.i		−	0.878968i	0.898251	−	0.439484i	$-0.144839\pi$
$678$	−188137.	+	1.04843e6i	−0.409274	+	2.28076i
$679$	−898170.			−1.94813
$680$		−	17298.3i		−	0.0374098i
$681$	−230321.	−	41330.3i	−0.496637	−	0.0891198i
$682$	414341.			0.890819
$683$			37881.8i			0.0812061i	0.999175	+	0.0406031i	$0.0129279\pi$
$683$			37881.8i			0.0812061i	−0.999175	+	0.0406031i	$0.987072\pi$
$684$	466341.	+	172935.i	0.996761	+	0.369633i
$685$	74387.0			0.158532
$686$		−	50316.7i		−	0.106921i
$687$	43508.3	−	242458.i	0.0921847	−	0.513717i
$688$	805318.			1.70134
$689$		−	45108.8i		−	0.0950218i
$690$	337835.	+	60623.3i	0.709589	+	0.127333i
$691$	−559150.			−1.17104			−0.585521	−	0.810658i	$-0.699110\pi$
$691$	−559150.			−1.17104			−0.585521	+	0.810658i	$0.699110\pi$
$692$		−	816418.i		−	1.70490i
$693$	−445646.	+	1.20174e6i	−0.927948	+	2.50233i
$694$	697998.			1.44922
$695$		−	289378.i		−	0.599096i
$696$	90717.7	−	505542.i	0.187272	−	1.04361i
$697$	−3744.84			−0.00770847
$698$		−	334819.i		−	0.687225i
$699$	777594.	+	139537.i	1.59147	+	0.285584i
$700$	1.31786e6			2.68951
$701$			628916.i			1.27984i	0.768440	+	0.639921i	$0.221033\pi$
$701$			628916.i			1.27984i	−0.768440	+	0.639921i	$0.778967\pi$
$702$	694515.	+	409423.i	1.40931	+	0.830803i
$703$	−449232.			−0.908992
$704$			467617.i			0.943507i
$705$	40474.2	−	225550.i	0.0814330	−	0.453801i
$706$	820775.			1.64670
$707$		−	678650.i		−	1.35771i
$708$	−137361.	−	24648.9i	−0.274029	−	0.0491735i
$709$	−244960.			−0.487307			−0.243653	−	0.969862i	$-0.578346\pi$
$709$	−244960.			−0.487307			−0.243653	+	0.969862i	$0.578346\pi$
$710$			450083.i			0.892844i
$711$	−194430.	−	72101.1i	−0.384612	−	0.142627i
$712$	−1.12564e6			−2.22045
$713$		−	160842.i		−	0.316388i
$714$	12209.4	−	68039.2i	0.0239496	−	0.133464i
$715$	−305328.			−0.597249
$716$			731903.i			1.42767i
$717$	240308.	+	43122.4i	0.467445	+	0.0838813i
$718$	−469888.			−0.911476
$719$		−	689940.i		−	1.33461i	−0.744785	−	0.667304i	$-0.767448\pi$
$719$		−	689940.i		−	1.33461i	0.744785	−	0.667304i	$-0.232552\pi$
$720$	89550.3	−	241483.i	0.172744	−	0.465824i
$721$	1.33430e6			2.56675
$722$		−	695267.i		−	1.33376i
$723$	−21847.2	+	121748.i	−0.0417945	+	0.232908i
$724$	−1.23648e6			−2.35891
$725$		−	243181.i		−	0.462651i
$726$	2.28639e6	+	410285.i	4.33788	+	0.778417i
$727$	−35938.5			−0.0679973			−0.0339986	−	0.999422i	$-0.510824\pi$
$727$	−35938.5			−0.0679973			−0.0339986	+	0.999422i	$0.510824\pi$
$728$			1.41063e6i			2.66165i
$729$	−257327.	−	464986.i	−0.484206	−	0.874954i
$730$	106993.			0.200774
$731$		−	33941.1i		−	0.0635172i
$732$	−241069.	+	1.34341e6i	−0.449904	+	2.50718i
$733$	−165921.			−0.308811			−0.154406	−	0.988008i	$-0.549346\pi$
$733$	−165921.			−0.308811			−0.154406	+	0.988008i	$0.549346\pi$
$734$			1.61029e6i			2.98890i
$735$	−191923.	−	34439.9i	−0.355265	−	0.0637510i
$736$	−333929.			−0.616452
$737$		−	366428.i		−	0.674611i
$738$	−130205.	−	48284.5i	−0.239065	−	0.0886534i
$739$	−748038.			−1.36973			−0.684865	−	0.728670i	$-0.740139\pi$
$739$	−748038.			−1.36973			−0.684865	+	0.728670i	$0.740139\pi$
$740$			741534.i			1.35415i
$741$	−44521.6	+	248105.i	−0.0810838	+	0.451855i
$742$	−143426.			−0.260507
$743$			534864.i			0.968871i	0.874827	+	0.484435i	$0.160975\pi$
$743$			534864.i			0.968871i	−0.874827	+	0.484435i	$0.839025\pi$
$744$	−295874.	−	53093.5i	−0.534516	−	0.0959171i
$745$	−333713.			−0.601258
$746$			1.78718e6i			3.21137i
$747$	−130700.	+	352448.i	−0.234225	+	0.631617i
$748$	−119677.			−0.213898
$749$		−	964686.i		−	1.71958i
$750$	114598.	−	638620.i	0.203730	−	1.13532i
$751$	−911644.			−1.61639			−0.808194	−	0.588917i	$-0.799555\pi$
$751$	−911644.			−1.61639			−0.808194	+	0.588917i	$0.799555\pi$
$752$			1.08006e6i			1.90990i
$753$	−691466.	−	124081.i	−1.21950	−	0.218835i
$754$	488939.			0.860028
$755$			113794.i			0.199629i
$756$	887000.	−	1.50464e6i	1.55196	−	2.63263i
$757$	−738108.			−1.28804			−0.644019	−	0.765010i	$-0.722734\pi$
$757$	−738108.			−1.28804			−0.644019	+	0.765010i	$0.722734\pi$
$758$		−	146178.i		−	0.254416i
$759$	223289.	−	1.24432e6i	0.387600	−	2.15997i
$760$	200561.			0.347231
$761$		−	931700.i		−	1.60882i	−0.594076	−	0.804409i	$-0.702482\pi$
$761$		−	931700.i		−	1.60882i	0.594076	−	0.804409i	$-0.297518\pi$
$762$	−1.91596e6	−	343812.i	−3.29972	−	0.592122i
$763$	405373.			0.696316
$764$		−	1.32969e6i		−	2.27806i
$765$	−10177.6	−	3774.21i	−0.0173909	−	0.00644915i
$766$	−1.91037e6			−3.25582
$767$		−	70726.2i		−	0.120224i
$768$	209374.	−	1.16678e6i	0.354977	−	1.97818i
$769$	−1.09188e6			−1.84639			−0.923193	−	0.384336i	$-0.874430\pi$
$769$	−1.09188e6			−1.84639			−0.923193	+	0.384336i	$0.874430\pi$
$770$			970807.i			1.63739i
$771$	691990.	+	124175.i	1.16410	+	0.208894i
$772$	1.12517e6			1.88791
$773$		−	641269.i		−	1.07320i	−0.843836	−	0.536601i	$-0.819708\pi$
$773$		−	641269.i		−	1.07320i	0.843836	−	0.536601i	$-0.180292\pi$
$774$	437623.	−	1.18010e6i	0.730497	−	1.96987i
$775$	−142324.			−0.236960
$776$		−	1.65567e6i		−	2.74947i
$777$	−278639.	+	1.55277e6i	−0.461530	+	2.57196i
$778$	1.07605e6			1.77776
$779$		−	43418.6i		−	0.0715486i
$780$	409540.	+	73490.5i	0.673143	+	0.120793i
$781$	1.65775e6			2.71780
$782$			68181.4i			0.111494i
$783$	−277647.	−	163676.i	−0.452866	−	0.266969i
$784$	919029.			1.49519
$785$			16473.8i			0.0267334i
$786$	−112241.	+	625486.i	−0.181680	+	1.01245i
$787$	402369.			0.649643			0.324822	−	0.945775i	$-0.394696\pi$
$787$	402369.			0.649643			0.324822	+	0.945775i	$0.394696\pi$
$788$		−	1.39582e6i		−	2.24790i
$789$	151985.	+	27273.2i	0.244145	+	0.0438110i
$790$	−157067.			−0.251670
$791$			1.16952e6i			1.86920i
$792$	−2.21526e6	−	821495.i	−3.53163	−	1.30965i
$793$	−691711.			−1.09996
$794$		−	827506.i		−	1.31259i
$795$	−3977.99	+	22168.1i	−0.00629404	+	0.0350747i
$796$	775513.			1.22395
$797$			338721.i			0.533243i	0.963801	+	0.266622i	$0.0859074\pi$
$797$			338721.i			0.533243i	−0.963801	+	0.266622i	$0.914093\pi$
$798$	788863.	+	141559.i	1.23878	+	0.222296i
$799$	45520.3			0.0713035
$800$			295484.i			0.461695i
$801$	−245597.	+	662283.i	−0.382788	+	1.03224i
$802$	−932896.			−1.45039
$803$		−	394077.i		−	0.611153i
$804$	−88196.7	+	491493.i	−0.136440	+	0.760336i
$805$	376855.			0.581543
$806$		−	286157.i		−	0.440489i
$807$	−985824.	−	176903.i	−1.51374	−	0.271636i
$808$	1.25101e6			1.91619
$809$		−	444127.i		−	0.678594i	−0.940679	−	0.339297i	$-0.889811\pi$
$809$		−	444127.i		−	0.678594i	0.940679	−	0.339297i	$-0.110189\pi$
$810$	−305204.	−	262452.i	−0.465179	−	0.400019i
$811$	−961721.			−1.46220			−0.731101	−	0.682269i	$-0.760993\pi$
$811$	−961721.			−1.46220			−0.731101	+	0.682269i	$0.760993\pi$
$812$		−	1.05927e6i		−	1.60655i
$813$	138153.	−	769886.i	0.209016	−	1.16478i
$814$	4.00842e6			6.04956
$815$			142125.i			0.213971i
$816$	50357.4	+	9036.46i	0.0756280	+	0.0135712i
$817$	393521.			0.589555
$818$		−	925361.i		−	1.38294i
$819$	829960.	+	307777.i	1.23734	+	0.458848i
$820$	−71669.9			−0.106588
$821$			65970.3i			0.0978728i	0.998802	+	0.0489364i	$0.0155832\pi$
$821$			65970.3i			0.0978728i	−0.998802	+	0.0489364i	$0.984417\pi$
$822$	−96783.8	+	539346.i	−0.143238	+	0.798222i
$823$	−228850.			−0.337871			−0.168935	−	0.985627i	$-0.554033\pi$
$823$	−228850.			−0.337871			−0.168935	+	0.985627i	$0.554033\pi$
$824$			2.45963e6i			3.62255i
$825$	−1.10106e6	−	197582.i	−1.61772	−	0.290295i
$826$	−224878.			−0.329599
$827$			824936.i			1.20617i	0.797676	+	0.603086i	$0.206062\pi$
$827$			824936.i			1.20617i	−0.797676	+	0.603086i	$0.793938\pi$
$828$	−598999.	+	1.61527e6i	−0.873706	+	2.35606i
$829$	−557367.			−0.811022			−0.405511	−	0.914090i	$-0.632906\pi$
$829$	−557367.			−0.811022			−0.405511	+	0.914090i	$0.632906\pi$
$830$			284720.i			0.413297i
$831$	153006.	−	852653.i	0.221567	−	1.23473i
$832$	322951.			0.466542
$833$		−	38733.6i		−	0.0558210i
$834$	2.09815e6	+	376506.i	3.01651	+	0.541302i
$835$	−220049.			−0.315607
$836$		−	1.38756e6i		−	1.98537i
$837$	−95793.0	+	162496.i	−0.136736	+	0.231949i
$838$	152903.			0.217734
$839$			361932.i			0.514165i	0.966389	+	0.257083i	$0.0827613\pi$
$839$			361932.i			0.514165i	−0.966389	+	0.257083i	$0.917239\pi$
$840$	124399.	−	693237.i	0.176302	−	0.982479i
$841$	511817.			0.723640
$842$		−	817835.i		−	1.15356i
$843$	−350113.	−	62826.5i	−0.492666	−	0.0884072i
$844$	1.02047e6			1.43256
$845$		−	36406.8i		−	0.0509882i
$846$	1.58270e6	+	586920.i	2.21136	+	0.820046i
$847$	2.55047e6			3.55511
$848$		−	106153.i		−	0.147618i
$849$	159550.	−	889121.i	0.221351	−	1.23352i
$850$	60331.7			0.0835042
$851$		−	1.55601e6i		−	2.14859i
$852$	−2.22356e6	−	399010.i	−3.06316	−	0.549673i
$853$	−443032.			−0.608888			−0.304444	−	0.952530i	$-0.598471\pi$
$853$	−443032.			−0.608888			−0.304444	+	0.952530i	$0.598471\pi$
$854$			2.19933e6i			3.01561i
$855$	43759.1	−	118002.i	0.0598599	−	0.161419i
$856$	1.77828e6			2.42691
$857$			1.05613e6i			1.43799i	0.695014	+	0.718996i	$0.255398\pi$
$857$			1.05613e6i			1.43799i	−0.695014	+	0.718996i	$0.744602\pi$
$858$	397258.	−	2.21380e6i	0.539633	−	3.00721i
$859$	−434895.			−0.589384			−0.294692	−	0.955592i	$-0.595217\pi$
$859$	−434895.			−0.589384			−0.294692	+	0.955592i	$0.595217\pi$
$860$		−	649574.i		−	0.878278i
$861$	−150076.	−	26930.7i	−0.202444	−	0.0363279i
$862$	120639.			0.162357
$863$		−	19733.9i		−	0.0264967i	−0.999912	−	0.0132483i	$-0.995783\pi$
$863$		−	19733.9i		−	0.0264967i	0.999912	−	0.0132483i	$-0.00421720\pi$
$864$	337364.	+	198879.i	0.451930	+	0.266417i
$865$	−206584.			−0.276099
$866$			888628.i			1.18491i
$867$	−132386.	+	737749.i	−0.176119	+	0.981455i
$868$	−619949.			−0.822843
$869$			578512.i			0.766077i
$870$	−240283.	−	43117.9i	−0.317456	−	0.0569664i
$871$	−253067.			−0.333579
$872$			747257.i			0.982736i
$873$	−974127.	−	361240.i	−1.27817	−	0.473988i
$874$	−790512.			−1.03487
$875$		−	712379.i		−	0.930455i
$876$	−94851.6	+	528579.i	−0.123605	+	0.688813i
$877$	412672.			0.536545			0.268273	−	0.963343i	$-0.413547\pi$
$877$	412672.			0.536545			0.268273	+	0.963343i	$0.413547\pi$
$878$			1.96306e6i			2.54651i
$879$	396380.	+	71129.0i	0.513020	+	0.0920596i
$880$	−718517.			−0.927837
$881$		−	1.25288e6i		−	1.61420i	−0.590414	−	0.807101i	$-0.701035\pi$
$881$		−	1.25288e6i		−	1.61420i	0.590414	−	0.807101i	$-0.298965\pi$
$882$	499416.	−	1.34674e6i	0.641985	−	1.73119i
$883$	261200.			0.335006			0.167503	−	0.985872i	$-0.446430\pi$
$883$	261200.			0.335006			0.167503	+	0.985872i	$0.446430\pi$
$884$			82652.8i			0.105768i
$885$	−6237.10	+	34757.4i	−0.00796335	+	0.0443773i
$886$	1.70914e6			2.17726
$887$		−	804200.i		−	1.02216i	−0.859534	−	0.511078i	$-0.829246\pi$
$887$		−	804200.i		−	1.02216i	0.859534	−	0.511078i	$-0.170754\pi$
$888$	−2.86234e6	−	513637.i	−3.62991	−	0.651374i
$889$	−2.13725e6			−2.70428
$890$			535016.i			0.675439i
$891$	−966668.	+	1.12413e6i	−1.21765	+	1.41600i
$892$	−544359.			−0.684157
$893$			527773.i			0.661826i
$894$	434189.	−	2.41960e6i	0.543255	−	3.02739i
$895$	185199.			0.231202
$896$		−	1.62872e6i		−	2.02876i
$897$	−859367.	−	154210.i	−1.06806	−	0.191659i
$898$	−417158.			−0.517306
$899$			114397.i			0.141546i
$900$	1.42931e6	+	530037.i	1.76458	+	0.654366i
$901$	−4473.94			−0.00551113
$902$			387416.i			0.476173i
$903$	244084.	−	1.36020e6i	0.299339	−	1.66813i
$904$	−2.15587e6			−2.63807
$905$			312877.i			0.382012i
$906$	−825066.	−	148055.i	−1.00515	−	0.180371i
$907$	109017.			0.132519			0.0662596	−	0.997802i	$-0.478893\pi$
$907$	109017.			0.132519			0.0662596	+	0.997802i	$0.478893\pi$
$908$		−	889605.i		−	1.07901i
$909$	272950.	−	736043.i	0.330335	−	0.890790i
$910$	670470.			0.809649
$911$			453728.i			0.546712i	0.961913	+	0.273356i	$0.0881338\pi$
$911$			453728.i			0.546712i	−0.961913	+	0.273356i	$0.911866\pi$
$912$	−104771.	+	583856.i	−0.125965	+	0.701966i
$913$	1.04868e6			1.25807
$914$			1.40556e6i			1.68251i
$915$	339932.	+	60999.6i	0.406022	+	0.0728592i
$916$	936486.			1.11612
$917$			697729.i			0.829752i
$918$	40607.0	−	68882.6i	0.0481854	−	0.0817381i
$919$	−330226.			−0.391003			−0.195502	−	0.980703i	$-0.562634\pi$
$919$	−330226.			−0.391003			−0.195502	+	0.980703i	$0.562634\pi$
$920$			694686.i			0.820754i
$921$	199138.	−	1.10974e6i	0.234766	−	1.30828i
$922$	−2.60886e6			−3.06895
$923$		−	1.14490e6i		−	1.34389i
$924$	−4.79611e6	−	860645.i	−5.61753	−	1.00805i
$925$	−1.37687e6			−1.60920
$926$			1.82959e6i			2.13369i
$927$	1.44714e6	+	536651.i	1.68404	+	0.624500i
$928$	237505.			0.275789
$929$		−	1.48562e6i		−	1.72138i	−0.509131	−	0.860689i	$-0.670033\pi$
$929$		−	1.48562e6i		−	1.72138i	0.509131	−	0.860689i	$-0.329967\pi$
$930$	−25235.2	+	140628.i	−0.0291770	+	0.162595i
$931$	449087.			0.518120
$932$			3.00343e6i			3.45768i
$933$	−205495.	−	36875.3i	−0.236068	−	0.0423616i
$934$	558598.			0.640332
$935$			30282.8i			0.0346396i
$936$	−567350.	+	1.52993e6i	−0.647589	+	1.74630i
$937$	544687.			0.620395			0.310197	−	0.950672i	$-0.399605\pi$
$937$	544687.			0.620395			0.310197	+	0.950672i	$0.399605\pi$
$938$			804639.i			0.914524i
$939$	69650.0	−	388138.i	0.0789933	−	0.440205i
$940$	871179.			0.985943
$941$			269431.i			0.304277i	0.988359	+	0.152138i	$0.0486159\pi$
$941$			269431.i			0.304277i	−0.988359	+	0.152138i	$0.951384\pi$
$942$	−119444.	−	21433.8i	−0.134605	−	0.0241544i
$943$	150390.			0.169120
$944$		−	166437.i		−	0.186770i
$945$	−380730.	−	224444.i	−0.426338	−	0.251330i
$946$	−3.51132e6			−3.92363
$947$			775388.i			0.864608i	0.901728	+	0.432304i	$0.142299\pi$
$947$			775388.i			0.864608i	−0.901728	+	0.432304i	$0.857701\pi$
$948$	139244.	−	775963.i	0.154939	−	0.863425i
$949$	−272162.			−0.302200
$950$			699501.i			0.775070i
$951$	440726.	+	79086.7i	0.487313	+	0.0874465i
$952$	139908.			0.154372
$953$			16310.0i			0.0179584i	0.999960	+	0.00897920i	$0.00285821\pi$
$953$			16310.0i			0.0179584i	−0.999960	+	0.00897920i	$0.997142\pi$
$954$	−155555.	−	57685.2i	−0.170918	−	0.0633822i
$955$	−336462.			−0.368918
$956$			928180.i			1.01559i
$957$	−158812.	+	885013.i	−0.173405	+	0.966330i
$958$	−1.70668e6			−1.85961
$959$			601640.i			0.654183i
$960$	−158710.	−	28480.0i	−0.172211	−	0.0309027i
$961$	−856569.			−0.927503
$962$		−	2.76834e6i		−	2.99136i
$963$	387992.	−	1.04627e6i	0.418379	−	1.12821i
$964$	−470245.			−0.506023
$965$		−	284709.i		−	0.305736i
$966$	−490320.	+	2.73240e6i	−0.525442	+	2.92813i
$967$	1.64756e6			1.76193			0.880967	−	0.473178i	$-0.156893\pi$
$967$	1.64756e6			1.76193			0.880967	+	0.473178i	$0.156893\pi$
$968$			4.70148e6i			5.01746i
$969$	24607.3	+	4415.70i	0.0262070	+	0.00470275i
$970$	−786934.			−0.836363
$971$			1.68663e6i			1.78888i	0.447186	+	0.894441i	$0.352426\pi$
$971$			1.68663e6i			1.78888i	−0.447186	+	0.894441i	$0.647574\pi$
$972$	1.56717e6	−	1.27514e6i	1.65876	−	1.34966i
$973$	2.34048e6			2.47218
$974$		−	937224.i		−	0.987929i
$975$	−136456.	+	760429.i	−0.143544	+	0.799925i
$976$	−1.62778e6			−1.70881
$977$		−	211107.i		−	0.221163i	−0.993867	−	0.110582i	$-0.964729\pi$
$977$		−	211107.i		−	0.221163i	0.993867	−	0.110582i	$-0.0352714\pi$
$978$	−1.03048e6	−	184916.i	−1.07737	−	0.193329i
$979$	1.97058e6			2.05602
$980$		−	741294.i		−	0.771860i
$981$	439655.	+	163039.i	0.456851	+	0.169416i
$982$	1.13174e6			1.17361
$983$		−	164036.i		−	0.169759i	−0.996391	−	0.0848796i	$-0.972949\pi$
$983$		−	164036.i		−	0.169759i	0.996391	−	0.0848796i	$-0.0270506\pi$
$984$	49643.4	−	276647.i	0.0512710	−	0.285717i
$985$	−353194.			−0.364033
$986$		−	48493.5i		−	0.0498804i
$987$	1.82424e6	+	327354.i	1.87262	+	0.336034i
$988$	−958296.			−0.981716
$989$			1.36305e6i			1.39354i
$990$	−390454.	+	1.05291e6i	−0.398382	+	1.07429i
$991$	−1.71373e6			−1.74500			−0.872501	−	0.488613i	$-0.837503\pi$
$991$	−1.71373e6			−1.74500			−0.872501	+	0.488613i	$0.837503\pi$
$992$		−	139002.i		−	0.141253i
$993$	98289.2	−	547736.i	0.0996798	−	0.555485i
$994$	−3.64026e6			−3.68433
$995$		−	196234.i		−	0.198211i
$996$	−1.40661e6	−	252411.i	−1.41793	−	0.254443i
$997$	−677731.			−0.681816			−0.340908	−	0.940097i	$-0.610734\pi$
$997$	−677731.			−0.681816			−0.340908	+	0.940097i	$0.610734\pi$
$998$			3.10962e6i			3.12209i
$999$	−926719.	+	1.57202e6i	−0.928575	+	1.57517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.73	yes	78
3.2	odd	2	inner	177.5.b.a.119.6	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.6	✓	78	3.2	odd	2	inner
177.5.b.a.119.73	yes	78	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.08630i q^{2} +(-1.58963 + 8.85850i) q^{3} -34.2156 q^{4} +8.65783i q^{5} +(-62.7740 - 11.2646i) q^{6} -70.0243 q^{7} -129.081i q^{8} +(-75.9462 - 28.1634i) q^{9} +O(q^{10})\)	\(q+7.08630i q^{2} +(-1.58963 + 8.85850i) q^{3} -34.2156 q^{4} +8.65783i q^{5} +(-62.7740 - 11.2646i) q^{6} -70.0243 q^{7} -129.081i q^{8} +(-75.9462 - 28.1634i) q^{9} -61.3520 q^{10} +225.973i q^{11} +(54.3901 - 303.099i) q^{12} +156.064 q^{13} -496.213i q^{14} +(-76.6954 - 13.7627i) q^{15} +367.259 q^{16} -15.4786i q^{17} +(199.575 - 538.177i) q^{18} +179.462 q^{19} -296.233i q^{20} +(111.313 - 620.310i) q^{21} -1601.31 q^{22} +621.607i q^{23} +(1143.47 + 205.191i) q^{24} +550.042 q^{25} +1105.91i q^{26} +(370.212 - 628.000i) q^{27} +2395.92 q^{28} -442.113i q^{29} +(97.5268 - 543.487i) q^{30} -258.752 q^{31} +537.204i q^{32} +(-2001.78 - 359.212i) q^{33} +109.686 q^{34} -606.259i q^{35} +(2598.55 + 963.629i) q^{36} -2503.21 q^{37} +1271.72i q^{38} +(-248.083 + 1382.49i) q^{39} +1117.56 q^{40} -241.937i q^{41} +(4395.70 + 788.794i) q^{42} +2192.78 q^{43} -7731.79i q^{44} +(243.834 - 657.529i) q^{45} -4404.89 q^{46} +2940.86i q^{47} +(-583.804 + 3253.36i) q^{48} +2502.40 q^{49} +3897.76i q^{50} +(137.117 + 24.6052i) q^{51} -5339.82 q^{52} -289.041i q^{53} +(4450.20 + 2623.43i) q^{54} -1956.43 q^{55} +9038.83i q^{56} +(-285.278 + 1589.77i) q^{57} +3132.94 q^{58} -453.188i q^{59} +(2624.18 + 470.900i) q^{60} -4432.23 q^{61} -1833.59i q^{62} +(5318.08 + 1972.12i) q^{63} +2069.35 q^{64} +1351.17i q^{65} +(2545.48 - 14185.2i) q^{66} -1621.56 q^{67} +529.609i q^{68} +(-5506.51 - 988.123i) q^{69} +4296.13 q^{70} -7336.07i q^{71} +(-3635.37 + 9803.23i) q^{72} -1743.91 q^{73} -17738.5i q^{74} +(-874.362 + 4872.55i) q^{75} -6140.41 q^{76} -15823.6i q^{77} +(-9796.75 - 1757.99i) q^{78} +2560.10 q^{79} +3179.66i q^{80} +(4974.64 + 4277.81i) q^{81} +1714.44 q^{82} -4640.76i q^{83} +(-3808.63 + 21224.3i) q^{84} +134.011 q^{85} +15538.7i q^{86} +(3916.46 + 702.795i) q^{87} +29168.8 q^{88} -8720.43i q^{89} +(4659.45 + 1727.88i) q^{90} -10928.3 q^{91} -21268.7i q^{92} +(411.319 - 2292.15i) q^{93} -20839.8 q^{94} +1553.75i q^{95} +(-4758.82 - 853.953i) q^{96} +12826.5 q^{97} +17732.8i q^{98} +(6364.16 - 17161.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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