LMFDB - Embedded newform 177.5.b.a.119.77

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			119.77
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.73459i q^{2} +(-8.52815 + 2.87588i) q^{3} -43.8239 q^{4} +0.620129i q^{5} +(-22.2437 - 65.9618i) q^{6} +71.8012 q^{7} -215.207i q^{8} +(64.4587 - 49.0518i) q^{9} +O(q^{10})$	\(q+7.73459i q^{2} +(-8.52815 + 2.87588i) q^{3} -43.8239 q^{4} +0.620129i q^{5} +(-22.2437 - 65.9618i) q^{6} +71.8012 q^{7} -215.207i q^{8} +(64.4587 - 49.0518i) q^{9} -4.79645 q^{10} +63.2025i q^{11} +(373.737 - 126.032i) q^{12} +204.993 q^{13} +555.353i q^{14} +(-1.78341 - 5.28856i) q^{15} +963.353 q^{16} -443.362i q^{17} +(379.396 + 498.562i) q^{18} -526.936 q^{19} -27.1765i q^{20} +(-612.332 + 206.491i) q^{21} -488.846 q^{22} -966.597i q^{23} +(618.907 + 1835.31i) q^{24} +624.615 q^{25} +1585.54i q^{26} +(-408.646 + 603.696i) q^{27} -3146.61 q^{28} -559.951i q^{29} +(40.9048 - 13.7940i) q^{30} +1278.62 q^{31} +4007.84i q^{32} +(-181.763 - 539.001i) q^{33} +3429.22 q^{34} +44.5261i q^{35} +(-2824.83 + 2149.64i) q^{36} +362.114 q^{37} -4075.64i q^{38} +(-1748.21 + 589.535i) q^{39} +133.456 q^{40} +2028.46i q^{41} +(-1597.13 - 4736.14i) q^{42} -487.652 q^{43} -2769.78i q^{44} +(30.4185 + 39.9727i) q^{45} +7476.24 q^{46} +34.7038i q^{47} +(-8215.62 + 2770.48i) q^{48} +2754.42 q^{49} +4831.15i q^{50} +(1275.05 + 3781.05i) q^{51} -8983.61 q^{52} -1648.43i q^{53} +(-4669.34 - 3160.71i) q^{54} -39.1937 q^{55} -15452.1i q^{56} +(4493.79 - 1515.40i) q^{57} +4330.99 q^{58} +453.188i q^{59} +(78.1562 + 231.765i) q^{60} -2514.15 q^{61} +9889.62i q^{62} +(4628.21 - 3521.98i) q^{63} -15585.3 q^{64} +127.122i q^{65} +(4168.95 - 1405.86i) q^{66} -2378.22 q^{67} +19429.8i q^{68} +(2779.81 + 8243.29i) q^{69} -344.391 q^{70} +884.945i q^{71} +(-10556.3 - 13871.9i) q^{72} +7907.46 q^{73} +2800.80i q^{74} +(-5326.81 + 1796.32i) q^{75} +23092.4 q^{76} +4538.02i q^{77} +(-4559.82 - 13521.7i) q^{78} -3006.62 q^{79} +597.403i q^{80} +(1748.84 - 6323.63i) q^{81} -15689.3 q^{82} -4564.48i q^{83} +(26834.8 - 9049.26i) q^{84} +274.942 q^{85} -3771.79i q^{86} +(1610.35 + 4775.35i) q^{87} +13601.6 q^{88} +2010.89i q^{89} +(-309.173 + 235.274i) q^{90} +14718.8 q^{91} +42360.1i q^{92} +(-10904.3 + 3677.16i) q^{93} -268.420 q^{94} -326.769i q^{95} +(-11526.0 - 34179.4i) q^{96} +7872.26 q^{97} +21304.3i q^{98} +(3100.20 + 4073.95i) 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 $

$2$			7.73459i			1.93365i	0.255443	+	0.966824i	$0.417779\pi$
$2$			7.73459i			1.93365i	−0.255443	+	0.966824i	$0.582221\pi$
$3$	−8.52815	+	2.87588i	−0.947572	+	0.319542i
$3$	−8.52815	+	2.87588i	−0.947572	+	0.319542i
$4$	−43.8239			−2.73899
$5$			0.620129i			0.0248052i	0.999923	+	0.0124026i	$0.00394797\pi$
$5$			0.620129i			0.0248052i	−0.999923	+	0.0124026i	$0.996052\pi$
$6$	−22.2437	−	65.9618i	−0.617881	−	1.83227i
$7$	71.8012			1.46533			0.732666	−	0.680589i	$-0.238276\pi$
$7$	71.8012			1.46533			0.732666	+	0.680589i	$0.238276\pi$
$8$		−	215.207i		−	3.36260i
$9$	64.4587	−	49.0518i	0.795786	−	0.605578i
$10$	−4.79645			−0.0479645
$11$			63.2025i			0.522335i	0.965294	+	0.261167i	$0.0841075\pi$
$11$			63.2025i			0.522335i	−0.965294	+	0.261167i	$0.915893\pi$
$12$	373.737	−	126.032i	2.59540	−	0.875223i
$13$	204.993			1.21298			0.606489	−	0.795092i	$-0.292577\pi$
$13$	204.993			1.21298			0.606489	+	0.795092i	$0.292577\pi$
$14$			555.353i			2.83344i
$15$	−1.78341	−	5.28856i	−0.00792629	−	0.0235047i
$16$	963.353			3.76310
$17$		−	443.362i		−	1.53412i	−0.641573	−	0.767062i	$-0.721718\pi$
$17$		−	443.362i		−	1.53412i	0.641573	−	0.767062i	$-0.278282\pi$
$18$	379.396	+	498.562i	1.17097	+	1.53877i
$19$	−526.936			−1.45966			−0.729829	−	0.683630i	$-0.760400\pi$
$19$	−526.936			−1.45966			−0.729829	+	0.683630i	$0.760400\pi$
$20$		−	27.1765i		−	0.0679412i
$21$	−612.332	+	206.491i	−1.38851	+	0.468235i
$22$	−488.846			−1.01001
$23$		−	966.597i		−	1.82722i	−0.406596	−	0.913608i	$-0.633284\pi$
$23$		−	966.597i		−	1.82722i	0.406596	−	0.913608i	$-0.366716\pi$
$24$	618.907	+	1835.31i	1.07449	+	3.18631i
$25$	624.615			0.999385
$26$			1585.54i			2.34547i
$27$	−408.646	+	603.696i	−0.560558	+	0.828116i
$28$	−3146.61			−4.01354
$29$		−	559.951i		−	0.665816i	−0.942959	−	0.332908i	$-0.891970\pi$
$29$		−	559.951i		−	0.665816i	0.942959	−	0.332908i	$-0.108030\pi$
$30$	40.9048	−	13.7940i	0.0454498	−	0.0153267i
$31$	1278.62			1.33051			0.665256	−	0.746615i	$-0.268322\pi$
$31$	1278.62			1.33051			0.665256	+	0.746615i	$0.268322\pi$
$32$			4007.84i			3.91390i
$33$	−181.763	−	539.001i	−0.166908	−	0.494950i
$34$	3429.22			2.96645
$35$			44.5261i			0.0363478i
$36$	−2824.83	+	2149.64i	−2.17965	+	1.65867i
$37$	362.114			0.264510			0.132255	−	0.991216i	$-0.457778\pi$
$37$	362.114			0.264510			0.132255	+	0.991216i	$0.457778\pi$
$38$		−	4075.64i		−	2.82246i
$39$	−1748.21	+	589.535i	−1.14938	+	0.387597i
$40$	133.456			0.0834100
$41$			2028.46i			1.20670i	0.797477	+	0.603349i	$0.206167\pi$
$41$			2028.46i			1.20670i	−0.797477	+	0.603349i	$0.793833\pi$
$42$	−1597.13	−	4736.14i	−0.905401	−	2.68488i
$43$	−487.652			−0.263738			−0.131869	−	0.991267i	$-0.542098\pi$
$43$	−487.652			−0.263738			−0.131869	+	0.991267i	$0.542098\pi$
$44$		−	2769.78i		−	1.43067i
$45$	30.4185	+	39.9727i	0.0150215	+	0.0197396i
$46$	7476.24			3.53319
$47$			34.7038i			0.0157102i	0.999969	+	0.00785510i	$0.00250038\pi$
$47$			34.7038i			0.0157102i	−0.999969	+	0.00785510i	$0.997500\pi$
$48$	−8215.62	+	2770.48i	−3.56581	+	1.20247i
$49$	2754.42			1.14720
$50$			4831.15i			1.93246i
$51$	1275.05	+	3781.05i	0.490216	+	1.45369i
$52$	−8983.61			−3.32234
$53$		−	1648.43i		−	0.586840i	−0.955984	−	0.293420i	$-0.905207\pi$
$53$		−	1648.43i		−	0.586840i	0.955984	−	0.293420i	$-0.0947934\pi$
$54$	−4669.34	−	3160.71i	−1.60128	−	1.08392i
$55$	−39.1937			−0.0129566
$56$		−	15452.1i		−	4.92733i
$57$	4493.79	−	1515.40i	1.38313	−	0.466422i
$58$	4330.99			1.28745
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	78.1562	+	231.765i	0.0217101	+	0.0643792i
$61$	−2514.15			−0.675664			−0.337832	−	0.941206i	$-0.609694\pi$
$61$	−2514.15			−0.675664			−0.337832	+	0.941206i	$0.609694\pi$
$62$			9889.62i			2.57274i
$63$	4628.21	−	3521.98i	1.16609	−	0.887372i
$64$	−15585.3			−3.80501
$65$			127.122i			0.0300881i
$66$	4168.95	−	1405.86i	0.957059	−	0.322741i
$67$	−2378.22			−0.529788			−0.264894	−	0.964277i	$-0.585337\pi$
$67$	−2378.22			−0.529788			−0.264894	+	0.964277i	$0.585337\pi$
$68$			19429.8i			4.20196i
$69$	2779.81	+	8243.29i	0.583872	+	1.73142i
$70$	−344.391			−0.0702839
$71$			884.945i			0.175550i	0.996140	+	0.0877748i	$0.0279756\pi$
$71$			884.945i			0.175550i	−0.996140	+	0.0877748i	$0.972024\pi$
$72$	−10556.3	−	13871.9i	−2.03632	−	2.67591i
$73$	7907.46			1.48385			0.741927	−	0.670480i	$-0.233912\pi$
$73$	7907.46			1.48385			0.741927	+	0.670480i	$0.233912\pi$
$74$			2800.80i			0.511468i
$75$	−5326.81	+	1796.32i	−0.946989	+	0.319345i
$76$	23092.4			3.99800
$77$			4538.02i			0.765394i
$78$	−4559.82	−	13521.7i	−0.749477	−	2.22251i
$79$	−3006.62			−0.481754			−0.240877	−	0.970556i	$-0.577435\pi$
$79$	−3006.62			−0.481754			−0.240877	+	0.970556i	$0.577435\pi$
$80$			597.403i			0.0933443i
$81$	1748.84	−	6323.63i	0.266551	−	0.963821i
$82$	−15689.3			−2.33333
$83$		−	4564.48i		−	0.662576i	−0.943530	−	0.331288i	$-0.892517\pi$
$83$		−	4564.48i		−	0.662576i	0.943530	−	0.331288i	$-0.107483\pi$
$84$	26834.8	−	9049.26i	3.80311	−	1.28249i
$85$	274.942			0.0380542
$86$		−	3771.79i		−	0.509977i
$87$	1610.35	+	4775.35i	0.212756	+	0.630908i
$88$	13601.6			1.75641
$89$			2010.89i			0.253868i	0.991911	+	0.126934i	$0.0405137\pi$
$89$			2010.89i			0.253868i	−0.991911	+	0.126934i	$0.959486\pi$
$90$	−309.173	+	235.274i	−0.0381695	+	0.0290462i
$91$	14718.8			1.77742
$92$			42360.1i			5.00474i
$93$	−10904.3	+	3677.16i	−1.26076	+	0.425154i
$94$	−268.420			−0.0303780
$95$		−	326.769i		−	0.0362071i
$96$	−11526.0	−	34179.4i	−1.25065	−	3.70870i
$97$	7872.26			0.836673			0.418337	−	0.908292i	$-0.362613\pi$
$97$	7872.26			0.836673			0.418337	+	0.908292i	$0.362613\pi$
$98$			21304.3i			2.21827i
$99$	3100.20	+	4073.95i	0.316314	+	0.415667i
$100$	−27373.1			−2.73731
$101$		−	4233.74i		−	0.415032i	−0.978232	−	0.207516i	$-0.933462\pi$
$101$		−	4233.74i		−	0.415032i	0.978232	−	0.207516i	$-0.0665380\pi$
$102$	−29244.9	+	9862.01i	−2.81093	+	0.947906i
$103$	10764.8			1.01468			0.507341	−	0.861745i	$-0.330628\pi$
$103$	10764.8			1.01468			0.507341	+	0.861745i	$0.330628\pi$
$104$		−	44115.9i		−	4.07877i
$105$	−128.051	−	379.725i	−0.0116146	−	0.0344422i
$106$	12750.0			1.13474
$107$		−	8243.20i		−	0.719993i	−0.932954	−	0.359997i	$-0.882778\pi$
$107$		−	8243.20i		−	0.719993i	0.932954	−	0.359997i	$-0.117222\pi$
$108$	17908.5	−	26456.3i	1.53536	−	2.26820i
$109$	4786.90			0.402903			0.201452	−	0.979498i	$-0.435434\pi$
$109$	4786.90			0.402903			0.201452	+	0.979498i	$0.435434\pi$
$110$		−	303.148i		−	0.0250535i
$111$	−3088.16	+	1041.39i	−0.250642	+	0.0845219i
$112$	69169.9			5.51418
$113$		−	2505.20i		−	0.196194i	−0.995177	−	0.0980971i	$-0.968724\pi$
$113$		−	2505.20i		−	0.196194i	0.995177	−	0.0980971i	$-0.0312756\pi$
$114$	11721.0	+	34757.7i	0.901895	+	2.67449i
$115$	599.415			0.0453244
$116$			24539.2i			1.82367i
$117$	13213.6	−	10055.3i	0.965272	−	0.734553i
$118$	−3505.22			−0.251740
$119$		−	31833.9i		−	2.24800i
$120$	−1138.13	+	383.803i	−0.0790370	+	0.0266530i
$121$	10646.4			0.727166
$122$		−	19445.9i		−	1.30650i
$123$	−5833.60	−	17299.0i	−0.385590	−	1.14343i
$124$	−56034.2			−3.64427
$125$			774.923i			0.0495951i
$126$	27241.1	+	35797.3i	1.71587	+	2.25481i
$127$	16718.1			1.03652			0.518262	−	0.855222i	$-0.326579\pi$
$127$	16718.1			1.03652			0.518262	+	0.855222i	$0.326579\pi$
$128$		−	56420.8i		−	3.44365i
$129$	4158.77	−	1402.43i	0.249911	−	0.0842754i
$130$	−983.240			−0.0581799
$131$			36.1996i			0.00210941i	0.999999	+	0.00105470i	$0.000335723\pi$
$131$			36.1996i			0.00210941i	−0.999999	+	0.00105470i	$0.999664\pi$
$132$	7965.55	+	23621.1i	0.457160	+	1.35567i
$133$	−37834.7			−2.13888
$134$		−	18394.6i		−	1.02442i
$135$	−374.370	−	253.414i	−0.0205416	−	0.0139047i
$136$	−95414.4			−5.15865
$137$		−	976.041i		−	0.0520028i	−0.999662	−	0.0260014i	$-0.991723\pi$
$137$		−	976.041i		−	0.0520028i	0.999662	−	0.0260014i	$-0.00827744\pi$
$138$	−63758.5	+	21500.7i	−3.34796	+	1.12900i
$139$	−5174.94			−0.267840			−0.133920	−	0.990992i	$-0.542757\pi$
$139$	−5174.94			−0.267840			−0.133920	+	0.990992i	$0.542757\pi$
$140$		−	1951.31i		−	0.0995564i
$141$	−99.8039	−	295.959i	−0.00502006	−	0.0148865i
$142$	−6844.69			−0.339451
$143$			12956.1i			0.633581i
$144$	62096.5	−	47254.2i	2.99462	−	2.27885i
$145$	347.242			0.0165157
$146$			61161.0i			2.86925i
$147$	−23490.1	+	7921.36i	−1.08705	+	0.366577i
$148$	−15869.2			−0.724490
$149$			24593.4i			1.10776i	0.832596	+	0.553881i	$0.186854\pi$
$149$			24593.4i			1.10776i	−0.832596	+	0.553881i	$0.813146\pi$
$150$	−13893.8	−	41200.7i	−0.617501	−	1.83114i
$151$	16890.9			0.740798			0.370399	−	0.928873i	$-0.379221\pi$
$151$	16890.9			0.740798			0.370399	+	0.928873i	$0.379221\pi$
$152$			113400.i			4.90825i
$153$	−21747.7	−	28578.5i	−0.929031	−	1.22083i
$154$	−35099.7			−1.48000
$155$			792.911i			0.0330036i
$156$	76613.6	−	25835.8i	3.14816	−	1.06163i
$157$	−16131.7			−0.654458			−0.327229	−	0.944945i	$-0.606115\pi$
$157$	−16131.7			−0.654458			−0.327229	+	0.944945i	$0.606115\pi$
$158$		−	23255.0i		−	0.931542i
$159$	4740.69	+	14058.1i	0.187520	+	0.556073i
$160$	−2485.38			−0.0970850
$161$		−	69402.9i		−	2.67748i
$162$	48910.7	+	13526.6i	1.86369	+	0.515416i
$163$	−40515.1			−1.52490			−0.762451	−	0.647046i	$-0.776004\pi$
$163$	−40515.1			−1.52490			−0.762451	+	0.647046i	$0.776004\pi$
$164$		−	88895.0i		−	3.30514i
$165$	334.250	−	112.716i	0.0122773	−	0.00414018i
$166$	35304.4			1.28119
$167$			20215.8i			0.724866i	0.932010	+	0.362433i	$0.118054\pi$
$167$			20215.8i			0.724866i	−0.932010	+	0.362433i	$0.881946\pi$
$168$	44438.3	+	131778.i	1.57449	+	4.66900i
$169$	13461.3			0.471317
$170$			2126.56i			0.0735834i
$171$	−33965.6	+	25847.2i	−1.16158	+	0.883936i
$172$	21370.8			0.722378
$173$		−	49862.1i		−	1.66601i	−0.553264	−	0.833006i	$-0.686618\pi$
$173$		−	49862.1i		−	1.66601i	0.553264	−	0.833006i	$-0.313382\pi$
$174$	−36935.3	+	12455.4i	−1.21995	+	0.411395i
$175$	44848.2			1.46443
$176$			60886.3i			1.96560i
$177$	−1303.31	−	3864.85i	−0.0416008	−	0.123363i
$178$	−15553.4			−0.490892
$179$		−	32152.1i		−	1.00347i	−0.865022	−	0.501733i	$-0.832696\pi$
$179$		−	32152.1i		−	1.00347i	0.865022	−	0.501733i	$-0.167304\pi$
$180$	−1333.06	−	1751.76i	−0.0411437	−	0.0540667i
$181$	26929.6			0.822003			0.411001	−	0.911635i	$-0.365179\pi$
$181$	26929.6			0.822003			0.411001	+	0.911635i	$0.365179\pi$
$182$			113844.i			3.43690i
$183$	21441.0	−	7230.37i	0.640240	−	0.215903i
$184$	−208018.			−6.14420
$185$			224.557i			0.00656121i
$186$	−28441.3	−	84340.2i	−0.822098	−	2.43786i
$187$	28021.6			0.801326
$188$		−	1520.86i		−	0.0430302i
$189$	−29341.3	+	43346.1i	−0.821403	+	1.21346i
$190$	2527.42			0.0700117
$191$			32685.5i			0.895958i	0.894044	+	0.447979i	$0.147856\pi$
$191$			32685.5i			0.895958i	−0.894044	+	0.447979i	$0.852144\pi$
$192$	132914.	−	44821.5i	3.60552	−	1.21586i
$193$	27244.8			0.731425			0.365712	−	0.930728i	$-0.380825\pi$
$193$	27244.8			0.731425			0.365712	+	0.930728i	$0.380825\pi$
$194$			60888.7i			1.61783i
$195$	−365.588	−	1084.12i	−0.00961442	−	0.0285107i
$196$	−120709.			−3.14216
$197$			32019.8i			0.825062i	0.910944	+	0.412531i	$0.135355\pi$
$197$			32019.8i			0.825062i	−0.910944	+	0.412531i	$0.864645\pi$
$198$	−31510.4	+	23978.8i	−0.803753	+	0.611641i
$199$	25668.1			0.648169			0.324085	−	0.946028i	$-0.394944\pi$
$199$	25668.1			0.648169			0.324085	+	0.946028i	$0.394944\pi$
$200$		−	134421.i		−	3.36053i
$201$	20281.8	−	6839.47i	0.502013	−	0.169289i
$202$	32746.3			0.802526
$203$		−	40205.2i		−	0.975641i
$204$	−55877.8	−	165701.i	−1.34270	−	3.98166i
$205$	−1257.91			−0.0299323
$206$			83261.0i			1.96204i
$207$	−47413.3	−	62305.6i	−1.10652	−	1.45407i
$208$	197481.			4.56456
$209$		−	33303.7i		−	0.762430i
$210$	2937.02	−	990.425i	0.0665990	−	0.0224586i
$211$	−42406.1			−0.952497			−0.476249	−	0.879311i	$-0.658004\pi$
$211$	−42406.1			−0.952497			−0.476249	+	0.879311i	$0.658004\pi$
$212$			72240.8i			1.60735i
$213$	−2544.99	−	7546.95i	−0.0560954	−	0.166346i
$214$	63757.8			1.39221
$215$		−	302.408i		−	0.00654208i
$216$	129919.	+	87943.4i	2.78462	+	1.88493i
$217$	91806.7			1.94964
$218$			37024.7i			0.779073i
$219$	−67436.0	+	22740.9i	−1.40606	+	0.474153i
$220$	1717.62			0.0354881
$221$		−	90886.2i		−	1.86086i
$222$	−8054.76	−	23885.7i	−0.163436	−	0.484653i
$223$	−53628.8			−1.07842			−0.539211	−	0.842171i	$-0.681277\pi$
$223$	−53628.8			−1.07842			−0.539211	+	0.842171i	$0.681277\pi$
$224$			287768.i			5.73516i
$225$	40261.9	−	30638.5i	0.795297	−	0.605205i
$226$	19376.7			0.379371
$227$			42594.5i			0.826613i	0.910592	+	0.413306i	$0.135626\pi$
$227$			42594.5i			0.826613i	−0.910592	+	0.413306i	$0.864374\pi$
$228$	−196936.	+	66410.9i	−3.78839	+	1.27753i
$229$	−15094.4			−0.287836			−0.143918	−	0.989590i	$-0.545970\pi$
$229$	−15094.4			−0.287836			−0.143918	+	0.989590i	$0.545970\pi$
$230$			4636.23i			0.0876415i
$231$	−13050.8	−	38700.9i	−0.244575	−	0.725266i
$232$	−120505.			−2.23887
$233$			1764.28i			0.0324979i	0.999868	+	0.0162489i	$0.00517243\pi$
$233$			1764.28i			0.0324979i	−0.999868	+	0.0162489i	$0.994828\pi$
$234$	77773.6	+	102202.i	1.42037	+	1.86650i
$235$	−21.5209			−0.000389694
$236$		−	19860.5i		−	0.356587i
$237$	25640.9	−	8646.68i	0.456496	−	0.153940i
$238$	246222.			4.34684
$239$			99155.8i			1.73589i	0.496659	+	0.867946i	$0.334560\pi$
$239$			99155.8i			1.73589i	−0.496659	+	0.867946i	$0.665440\pi$
$240$	−1718.06	−	5094.75i	−0.0298274	−	0.0884505i
$241$	−73745.9			−1.26971			−0.634854	−	0.772632i	$-0.718940\pi$
$241$	−73745.9			−1.26971			−0.634854	+	0.772632i	$0.718940\pi$
$242$			82345.9i			1.40608i
$243$	3271.57	+	58958.3i	0.0554044	+	0.998464i
$244$	110180.			1.85064
$245$			1708.10i			0.0284564i
$246$	133801.	−	45120.5i	2.21100	−	0.745596i
$247$	−108018.			−1.77053
$248$		−	275168.i		−	4.47398i
$249$	13126.9	+	38926.6i	0.211721	+	0.627838i
$250$	−5993.72			−0.0958994
$251$			34624.4i			0.549585i	0.961504	+	0.274793i	$0.0886092\pi$
$251$			34624.4i			0.549585i	−0.961504	+	0.274793i	$0.911391\pi$
$252$	−202826.	+	154347.i	−3.19392	+	2.43051i
$253$	61091.4			0.954419
$254$			129308.i			2.00427i
$255$	−2344.74	+	790.698i	−0.0360591	+	0.0121599i
$256$	187026.			2.85380
$257$		−	85104.8i		−	1.28851i	−0.764811	−	0.644255i	$-0.777168\pi$
$257$		−	85104.8i		−	1.28851i	0.764811	−	0.644255i	$-0.222832\pi$
$258$	10847.2	+	32166.4i	0.162959	+	0.483240i
$259$	26000.2			0.387594
$260$		−	5571.00i		−	0.0824113i
$261$	−27466.6	−	36093.7i	−0.403203	−	0.529847i
$262$	−279.989			−0.00407885
$263$			112176.i			1.62176i	0.585210	+	0.810882i	$0.301012\pi$
$263$			112176.i			1.62176i	−0.585210	+	0.810882i	$0.698988\pi$
$264$	−115997.	+	39116.5i	−1.66432	+	0.561245i
$265$	1022.24			0.0145567
$266$		−	292636.i		−	4.13585i
$267$	−5783.07	−	17149.2i	−0.0811215	−	0.240558i
$268$	104223.			1.45109
$269$		−	26041.8i		−	0.359887i	−0.983677	−	0.179944i	$-0.942408\pi$
$269$		−	26041.8i		−	0.359887i	0.983677	−	0.179944i	$-0.0575915\pi$
$270$	1960.05	−	2895.60i	0.0268868	−	0.0397201i
$271$	−122251.			−1.66461			−0.832307	−	0.554315i	$-0.812980\pi$
$271$	−122251.			−1.66461			−0.832307	+	0.554315i	$0.812980\pi$
$272$		−	427114.i		−	5.77306i
$273$	−125524.	+	42329.4i	−1.68423	+	0.567958i
$274$	7549.28			0.100555
$275$			39477.3i			0.522014i
$276$	−121822.	−	361253.i	−1.59922	−	4.74235i
$277$	27696.8			0.360969			0.180485	−	0.983578i	$-0.442233\pi$
$277$	27696.8			0.360969			0.180485	+	0.983578i	$0.442233\pi$
$278$		−	40026.0i		−	0.517909i
$279$	82418.3	−	62718.7i	1.05880	−	0.805728i
$280$	9582.30			0.122223
$281$		−	138592.i		−	1.75520i	−0.479396	−	0.877599i	$-0.659144\pi$
$281$		−	138592.i		−	1.75520i	0.479396	−	0.877599i	$-0.340856\pi$
$282$	2289.13	−	771.942i	0.0287853	−	0.00970704i
$283$	34002.8			0.424563			0.212281	−	0.977209i	$-0.431911\pi$
$283$	34002.8			0.424563			0.212281	+	0.977209i	$0.431911\pi$
$284$		−	38781.8i		−	0.480829i
$285$	939.746	+	2786.73i	0.0115697	+	0.0343088i
$286$	−100210.			−1.22512
$287$			145646.i			1.76821i
$288$	196592.	+	258340.i	2.37017	+	3.11463i
$289$	−113049.			−1.35353
$290$			2685.78i			0.0319355i
$291$	−67135.8	+	22639.6i	−0.792808	+	0.267352i
$292$	−346536.			−4.06427
$293$		−	85177.2i		−	0.992175i	−0.868272	−	0.496088i	$-0.834769\pi$
$293$		−	85177.2i		−	0.992175i	0.868272	−	0.496088i	$-0.165231\pi$
$294$	−61268.5	−	181686.i	−0.708831	−	2.10197i
$295$	−281.035			−0.00322936
$296$		−	77929.3i		−	0.889441i
$297$	−38155.1	−	25827.5i	−0.432554	−	0.292799i
$298$	−190220.			−2.14202
$299$		−	198146.i		−	2.21637i
$300$	233442.	−	78721.6i	2.59380	−	0.874685i
$301$	−35014.0			−0.386464
$302$			130644.i			1.43244i
$303$	12175.7	+	36106.0i	0.132620	+	0.393273i
$304$	−507626.			−5.49283
$305$		−	1559.10i		−	0.0167600i
$306$	221043.	−	168209.i	2.36066	−	1.79642i
$307$	181337.			1.92402			0.962011	−	0.273009i	$-0.0880190\pi$
$307$	181337.			1.92402			0.962011	+	0.273009i	$0.0880190\pi$
$308$		−	198874.i		−	2.09641i
$309$	−91803.5	+	30958.1i	−0.961485	+	0.324233i
$310$	−6132.84			−0.0638173
$311$			54923.1i			0.567851i	0.958846	+	0.283925i	$0.0916368\pi$
$311$			54923.1i			0.567851i	−0.958846	+	0.283925i	$0.908363\pi$
$312$	126872.	+	376227.i	1.30334	+	3.86493i
$313$	54353.5			0.554803			0.277401	−	0.960754i	$-0.410527\pi$
$313$	54353.5			0.554803			0.277401	+	0.960754i	$0.410527\pi$
$314$		−	124772.i		−	1.26549i
$315$	2184.08	+	2870.09i	0.0220114	+	0.0289251i
$316$	131762.			1.31952
$317$		−	22871.8i		−	0.227605i	−0.993503	−	0.113802i	$-0.963697\pi$
$317$		−	22871.8i		−	0.227605i	0.993503	−	0.113802i	$-0.0363031\pi$
$318$	−108734.	+	36667.3i	−1.07525	+	0.362597i
$319$	35390.3			0.347779
$320$		−	9664.92i		−	0.0943840i
$321$	23706.4	+	70299.3i	0.230068	+	0.682246i
$322$	536803.			5.17730
$323$			233623.i			2.23930i
$324$	−76641.1	+	277126.i	−0.730082	+	2.63990i
$325$	128042.			1.21223
$326$		−	313368.i		−	2.94862i
$327$	−40823.4	+	13766.5i	−0.381780	+	0.128744i
$328$	436538.			4.05765
$329$			2491.78i			0.0230206i
$330$	871.815	+	2585.29i	0.00800565	+	0.0237400i
$331$	−77310.0			−0.705634			−0.352817	−	0.935692i	$-0.614776\pi$
$331$	−77310.0			−0.705634			−0.352817	+	0.935692i	$0.614776\pi$
$332$			200034.i			1.81479i
$333$	23341.4	−	17762.3i	0.210493	−	0.160181i
$334$	−156361.			−1.40164
$335$		−	1474.80i		−	0.0131415i
$336$	−589892.	+	198924.i	−5.22509	+	1.76201i
$337$	4371.86			0.0384952			0.0192476	−	0.999815i	$-0.493873\pi$
$337$	4371.86			0.0384952			0.0192476	+	0.999815i	$0.493873\pi$
$338$			104118.i			0.911361i
$339$	7204.65	+	21364.8i	0.0626922	+	0.185908i
$340$	−12049.0			−0.104230
$341$			80812.1i			0.694973i
$342$	−199917.	−	262710.i	−1.70922	−	2.24608i
$343$	25375.9			0.215692
$344$			104946.i			0.886848i
$345$	−5111.90	+	1723.84i	−0.0429482	+	0.0144830i
$346$	385663.			3.22148
$347$			71853.0i			0.596741i	0.954450	+	0.298370i	$0.0964431\pi$
$347$			71853.0i			0.596741i	−0.954450	+	0.298370i	$0.903557\pi$
$348$	−70571.8	−	209274.i	−0.582737	−	1.72805i
$349$	185348.			1.52173			0.760863	−	0.648913i	$-0.224776\pi$
$349$	185348.			1.52173			0.760863	+	0.648913i	$0.224776\pi$
$350$			346882.i			2.83169i
$351$	−83769.8	+	123754.i	−0.679944	+	1.00449i
$352$	−253305.			−2.04437
$353$		−	146210.i		−	1.17335i	−0.809822	−	0.586676i	$-0.800436\pi$
$353$		−	146210.i		−	1.17335i	0.809822	−	0.586676i	$-0.199564\pi$
$354$	29893.1	−	10080.6i	0.238541	−	0.0804413i
$355$	−548.781			−0.00435454
$356$		−	88125.1i		−	0.695344i
$357$	91550.4	+	271484.i	0.718330	+	2.13014i
$358$	248683.			1.94035
$359$		−	71968.3i		−	0.558409i	−0.960232	−	0.279205i	$-0.909929\pi$
$359$		−	71968.3i		−	0.558409i	0.960232	−	0.279205i	$-0.0900708\pi$
$360$	8602.39	−	6546.25i	0.0663765	−	0.0505112i
$361$	147341.			1.13060
$362$			208290.i			1.58946i
$363$	−90794.4	+	30617.8i	−0.689043	+	0.232360i
$364$	−645035.			−4.86833
$365$			4903.65i			0.0368073i
$366$	55924.0	+	165837.i	0.417480	+	1.23800i
$367$	263314.			1.95498			0.977489	−	0.210988i	$-0.0676681\pi$
$367$	263314.			1.95498			0.977489	+	0.210988i	$0.0676681\pi$
$368$		−	931174.i		−	6.87599i
$369$	99499.6	+	130752.i	0.730749	+	0.960273i
$370$	−1736.86			−0.0126871
$371$		−	118360.i		−	0.859915i
$372$	477868.	−	161147.i	3.45320	−	1.16449i
$373$	94196.4			0.677043			0.338522	−	0.940959i	$-0.390073\pi$
$373$	94196.4			0.677043			0.338522	+	0.940959i	$0.390073\pi$
$374$			216735.i			1.54948i
$375$	−2228.58	−	6608.66i	−0.0158477	−	0.0469949i
$376$	7468.49			0.0528272
$377$		−	114786.i		−	0.807620i
$378$	−335265.	−	226943.i	−2.34641	−	1.58830i
$379$	102807.			0.715720			0.357860	−	0.933775i	$-0.383507\pi$
$379$	102807.			0.715720			0.357860	+	0.933775i	$0.383507\pi$
$380$			14320.3i			0.0991710i
$381$	−142574.	+	48079.2i	−0.982182	+	0.331213i
$382$	−252809.			−1.73247
$383$		−	58900.9i		−	0.401536i	−0.979639	−	0.200768i	$-0.935656\pi$
$383$		−	58900.9i		−	0.401536i	0.979639	−	0.200768i	$-0.0643437\pi$
$384$	162259.	+	481165.i	1.10039	+	3.26311i
$385$	−2814.16			−0.0189857
$386$			210728.i			1.41432i
$387$	−31433.4	+	23920.2i	−0.209879	+	0.159714i
$388$	−344993.			−2.29164
$389$			179102.i			1.18359i	0.806088	+	0.591795i	$0.201581\pi$
$389$			179102.i			1.18359i	−0.806088	+	0.591795i	$0.798419\pi$
$390$	8385.22	−	2827.68i	0.0551296	−	0.0185909i
$391$	−428552.			−2.80318
$392$		−	592769.i		−	3.85757i
$393$	−104.105	−	308.715i	−0.000674044	−	0.00199882i
$394$	−247660.			−1.59538
$395$		−	1864.50i		−	0.0119500i
$396$	−135863.	−	178536.i	−0.866383	−	1.13851i
$397$	45669.8			0.289767			0.144883	−	0.989449i	$-0.453719\pi$
$397$	45669.8			0.289767			0.144883	+	0.989449i	$0.453719\pi$
$398$			198533.i			1.25333i
$399$	322660.	−	108808.i	2.02675	−	0.683462i
$400$	601725.			3.76078
$401$			54669.9i			0.339985i	0.985445	+	0.169992i	$0.0543743\pi$
$401$			54669.9i			0.339985i	−0.985445	+	0.169992i	$0.945626\pi$
$402$	52900.5	+	156872.i	0.327346	+	0.970716i
$403$	262109.			1.61388
$404$			185539.i			1.13677i
$405$	3921.47	+	1084.51i	0.0239077	+	0.00661185i
$406$	310971.			1.88655
$407$			22886.5i			0.138163i
$408$	813708.	−	274400.i	4.88819	−	1.64840i
$409$	259180.			1.54937			0.774684	−	0.632348i	$-0.217909\pi$
$409$	259180.			1.54937			0.774684	+	0.632348i	$0.217909\pi$
$410$		−	9729.40i		−	0.0578786i
$411$	2806.97	+	8323.83i	0.0166171	+	0.0492764i
$412$	−471754.			−2.77921
$413$			32539.4i			0.190770i
$414$	481908.	−	366723.i	2.81167	−	2.13962i
$415$	2830.57			0.0164353
$416$			821580.i			4.74748i
$417$	44132.7	−	14882.5i	0.253798	−	0.0855861i
$418$	257591.			1.47427
$419$		−	102683.i		−	0.584888i	−0.956283	−	0.292444i	$-0.905532\pi$
$419$		−	102683.i		−	0.584888i	0.956283	−	0.292444i	$-0.0944685\pi$
$420$	5611.71	+	16641.0i	0.0318124	+	0.0943369i
$421$	−216357.			−1.22069			−0.610346	−	0.792135i	$-0.708970\pi$
$421$	−216357.			−1.22069			−0.610346	+	0.792135i	$0.708970\pi$
$422$		−	327994.i		−	1.84179i
$423$	1702.29	+	2236.96i	0.00951375	+	0.0125020i
$424$	−354754.			−1.97331
$425$		−	276931.i		−	1.53318i
$426$	58372.5	−	19684.5i	0.321654	−	0.108469i
$427$	−180519.			−0.990072
$428$			361249.i			1.97206i
$429$	−37260.1	−	110492.i	−0.202456	−	0.600364i
$430$	2339.00			0.0126501
$431$			140988.i			0.758976i	0.925197	+	0.379488i	$0.123900\pi$
$431$			140988.i			0.758976i	−0.925197	+	0.379488i	$0.876100\pi$
$432$	−393671.	+	581572.i	−2.10943	+	3.11628i
$433$	133663.			0.712911			0.356455	−	0.934312i	$-0.383985\pi$
$433$	133663.			0.712911			0.356455	+	0.934312i	$0.383985\pi$
$434$			710087.i			3.76992i
$435$	−2961.33	+	998.625i	−0.0156498	+	0.00527745i
$436$	−209780.			−1.10355
$437$			509335.i			2.66711i
$438$	−175891.	−	521590.i	−0.916846	−	2.71882i
$439$	−13250.2			−0.0687531			−0.0343765	−	0.999409i	$-0.510945\pi$
$439$	−13250.2			−0.0687531			−0.0343765	+	0.999409i	$0.510945\pi$
$440$			8434.75i			0.0435679i
$441$	177546.	−	135109.i	0.912923	−	0.694717i
$442$	702968.			3.59825
$443$		−	195021.i		−	0.993743i	−0.867824	−	0.496871i	$-0.834482\pi$
$443$		−	195021.i		−	0.993743i	0.867824	−	0.496871i	$-0.165518\pi$
$444$	135335.	−	45638.0i	0.686507	−	0.231505i
$445$	−1247.01			−0.00629725
$446$		−	414797.i		−	2.08529i
$447$	−70727.6	−	209736.i	−0.353976	−	1.04968i
$448$	−1.11905e6			−5.57560
$449$		−	62270.2i		−	0.308879i	−0.988002	−	0.154439i	$-0.950643\pi$
$449$		−	62270.2i		−	0.308879i	0.988002	−	0.154439i	$-0.0493571\pi$
$450$	236976.	+	311409.i	1.17025	+	1.53782i
$451$	−128204.			−0.630300
$452$			109788.i			0.537375i
$453$	−144048.	+	48576.2i	−0.701960	+	0.236716i
$454$	−329451.			−1.59838
$455$			9127.55i			0.0440891i
$456$	−326125.	−	967094.i	−1.56839	−	4.65092i
$457$	−178424.			−0.854319			−0.427159	−	0.904176i	$-0.640486\pi$
$457$	−178424.			−0.854319			−0.427159	+	0.904176i	$0.640486\pi$
$458$		−	116749.i		−	0.556574i
$459$	267656.	+	181178.i	1.27043	+	0.859964i
$460$	−26268.7			−0.124143
$461$		−	37707.0i		−	0.177427i	−0.996057	−	0.0887135i	$-0.971724\pi$
$461$		−	37707.0i		−	0.177427i	0.996057	−	0.0887135i	$-0.0282756\pi$
$462$	299336.	−	100942.i	1.40241	−	0.472922i
$463$	−234321.			−1.09308			−0.546538	−	0.837435i	$-0.684054\pi$
$463$	−234321.			−1.09308			−0.546538	+	0.837435i	$0.684054\pi$
$464$		−	539430.i		−	2.50553i
$465$	−2280.31	−	6762.07i	−0.0105460	−	0.0312733i
$466$	−13646.0			−0.0628395
$467$			254624.i			1.16753i	0.811924	+	0.583763i	$0.198420\pi$
$467$			254624.i			1.16753i	−0.811924	+	0.583763i	$0.801580\pi$
$468$	−579072.	+	440662.i	−2.64387	+	2.01194i
$469$	−170759.			−0.776316
$470$		−	166.455i		−	0.000753532i
$471$	137574.	−	46392.8i	0.620146	−	0.209127i
$472$	97529.0			0.437774
$473$		−	30820.9i		−	0.137760i
$474$	66878.5	+	198322.i	0.297667	+	0.882703i
$475$	−329133.			−1.45876
$476$			1.39509e6i			6.15726i
$477$	−80858.6	−	106256.i	−0.355377	−	0.466999i
$478$	−766930.			−3.35660
$479$		−	157553.i		−	0.686680i	−0.939211	−	0.343340i	$-0.888442\pi$
$479$		−	157553.i		−	0.686680i	0.939211	−	0.343340i	$-0.111558\pi$
$480$	21195.7	−	7147.63i	0.0919951	−	0.0310227i
$481$	74230.9			0.320844
$482$		−	570394.i		−	2.45517i
$483$	199594.	+	591878.i	0.855566	+	2.53710i
$484$	−466569.			−1.99170
$485$			4881.82i			0.0207538i
$486$	−456018.	+	25304.3i	−1.93068	+	0.107133i
$487$	−9062.55			−0.0382114			−0.0191057	−	0.999817i	$-0.506082\pi$
$487$	−9062.55			−0.0382114			−0.0191057	+	0.999817i	$0.506082\pi$
$488$			541061.i			2.27199i
$489$	345519.	−	116516.i	1.44495	−	0.487270i
$490$	−13211.4			−0.0550247
$491$			200856.i			0.833148i	0.909102	+	0.416574i	$0.136769\pi$
$491$			200856.i			0.833148i	−0.909102	+	0.416574i	$0.863231\pi$
$492$	255651.	+	758110.i	1.05613	+	3.13186i
$493$	−248261.			−1.02144
$494$		−	835479.i		−	3.42359i
$495$	−2526.38	+	1922.52i	−0.0103107	+	0.00784623i
$496$	1.23176e6			5.00685
$497$			63540.2i			0.257238i
$498$	−301081.	+	101531.i	−1.21402	+	0.409393i
$499$	280290.			1.12566			0.562829	−	0.826573i	$-0.309713\pi$
$499$	280290.			1.12566			0.562829	+	0.826573i	$0.309713\pi$
$500$		−	33960.2i		−	0.135841i
$501$	−58138.1	−	172403.i	−0.231625	−	0.686863i
$502$	−267806.			−1.06270
$503$		−	254469.i		−	1.00577i	−0.864353	−	0.502886i	$-0.832272\pi$
$503$		−	254469.i		−	1.00577i	0.864353	−	0.502886i	$-0.167728\pi$
$504$	−757953.	−	996022.i	−2.98388	−	3.92110i
$505$	2625.47			0.0102949
$506$			472517.i			1.84551i
$507$	−114800.	+	38713.0i	−0.446607	+	0.150605i
$508$	−732653.			−2.83904
$509$		−	250109.i		−	0.965370i	−0.875794	−	0.482685i	$-0.839662\pi$
$509$		−	250109.i		−	0.965370i	0.875794	−	0.482685i	$-0.160338\pi$
$510$	−6115.73	−	18135.6i	−0.0235130	−	0.0697256i
$511$	567766.			2.17434
$512$			543841.i			2.07459i
$513$	215331.	−	318110.i	0.818222	−	1.20877i
$514$	658251.			2.49153
$515$			6675.55i			0.0251694i
$516$	−182254.	+	61459.9i	−0.684505	+	0.230830i
$517$	−2193.37			−0.00820599
$518$			201101.i			0.749471i
$519$	143397.	+	425231.i	0.532360	+	1.57867i
$520$	27357.6			0.101175
$521$		−	190802.i		−	0.702924i	−0.936202	−	0.351462i	$-0.885685\pi$
$521$		−	190802.i		−	0.702924i	0.936202	−	0.351462i	$-0.114315\pi$
$522$	279170.	−	212443.i	1.02454	−	0.779653i
$523$	−397545.			−1.45339			−0.726697	−	0.686958i	$-0.758946\pi$
$523$	−397545.			−1.45339			−0.726697	+	0.686958i	$0.758946\pi$
$524$		−	1586.41i		−	0.00577766i
$525$	−382472.	+	128978.i	−1.38765	+	0.467946i
$526$	−867634.			−3.13592
$527$		−	566892.i		−	2.04117i
$528$	−175102.	−	519248.i	−0.628090	−	1.86255i
$529$	−654469.			−2.33872
$530$			7906.62i			0.0281475i
$531$	22229.7	+	29211.9i	0.0788395	+	0.103603i
$532$	1.65806e6			5.85839
$533$			415821.i			1.46370i
$534$	132642.	−	44729.7i	0.465155	−	0.156860i
$535$	5111.85			0.0178596
$536$			511809.i			1.78147i
$537$	92465.4	+	274198.i	0.320649	+	0.950857i
$538$	201423.			0.695895
$539$			174086.i			0.599221i
$540$	16406.3	+	11105.6i	0.0562632	+	0.0380850i
$541$	43502.7			0.148635			0.0743177	−	0.997235i	$-0.476322\pi$
$541$	43502.7			0.148635			0.0743177	+	0.997235i	$0.476322\pi$
$542$		−	945561.i		−	3.21878i
$543$	−229660.	+	77446.3i	−0.778907	+	0.262664i
$544$	1.77692e6			6.00441
$545$			2968.49i			0.00999409i
$546$	−327400.	−	970877.i	−1.09823	−	3.25671i
$547$	−11223.2			−0.0375095			−0.0187547	−	0.999824i	$-0.505970\pi$
$547$	−11223.2			−0.0375095			−0.0187547	+	0.999824i	$0.505970\pi$
$548$			42773.9i			0.142435i
$549$	−162059.	+	123323.i	−0.537684	+	0.409167i
$550$	−305341.			−1.00939
$551$			295059.i			0.971863i
$552$	1.77401e6	−	598234.i	5.82208	−	1.96333i
$553$	−215879.			−0.705929
$554$			214224.i			0.697988i
$555$	−645.799	−	1915.06i	−0.00209658	−	0.00621722i
$556$	226786.			0.733613
$557$			142448.i			0.459140i	0.973292	+	0.229570i	$0.0737320\pi$
$557$			142448.i			0.459140i	−0.973292	+	0.229570i	$0.926268\pi$
$558$	485104.	+	637472.i	1.55800	+	2.04735i
$559$	−99965.5			−0.319909
$560$			42894.3i			0.136780i
$561$	−238972.	+	80586.6i	−0.759314	+	0.256057i
$562$	1.07195e6			3.39393
$563$			80736.3i			0.254714i	0.991857	+	0.127357i	$0.0406493\pi$
$563$			80736.3i			0.254714i	−0.991857	+	0.127357i	$0.959351\pi$
$564$	4373.80	+	12970.1i	0.0137499	+	0.0407742i
$565$	1553.55			0.00486663
$566$			262998.i			0.820955i
$567$	125569.	−	454044.i	0.390586	−	1.41232i
$568$	190446.			0.590304
$569$			597848.i			1.84657i	0.384112	+	0.923287i	$0.374508\pi$
$569$			597848.i			1.84657i	−0.384112	+	0.923287i	$0.625492\pi$
$570$	−21554.2	+	7268.55i	−0.0663412	+	0.0223717i
$571$	84790.5			0.260061			0.130030	−	0.991510i	$-0.458492\pi$
$571$	84790.5			0.260061			0.130030	+	0.991510i	$0.458492\pi$
$572$		−	567787.i		−	1.73538i
$573$	−93999.3	−	278746.i	−0.286296	−	0.848985i
$574$	−1.12651e6			−3.41910
$575$		−	603752.i		−	1.82609i
$576$	−1.00461e6	+	764488.i	−3.02798	+	2.30423i
$577$	−315750.			−0.948402			−0.474201	−	0.880417i	$-0.657263\pi$
$577$	−315750.			−0.948402			−0.474201	+	0.880417i	$0.657263\pi$
$578$		−	874385.i		−	2.61726i
$579$	−232348.	+	78352.8i	−0.693078	+	0.233721i
$580$	−15217.5			−0.0452363
$581$		−	327736.i		−	0.970893i
$582$	−175108.	−	519268.i	−0.516965	−	1.53301i
$583$	104185.			0.306527
$584$		−	1.70174e6i		−	4.98961i
$585$	6235.58	+	8194.14i	0.0182207	+	0.0239437i
$586$	658811.			1.91852
$587$			255826.i			0.742454i	0.928542	+	0.371227i	$0.121063\pi$
$587$			255826.i			0.742454i	−0.928542	+	0.371227i	$0.878937\pi$
$588$	1.02943e6	−	347145.i	2.97743	−	1.00405i
$589$	−673753.			−1.94209
$590$		−	2173.69i		−	0.00624444i
$591$	−92085.0	−	273070.i	−0.263642	−	0.781806i
$592$	348843.			0.995375
$593$		−	469997.i		−	1.33655i	−0.743914	−	0.668275i	$-0.767033\pi$
$593$		−	469997.i		−	1.33655i	0.743914	−	0.668275i	$-0.232967\pi$
$594$	199765.	−	295114.i	0.566170	−	0.836407i
$595$	19741.1			0.0557620
$596$		−	1.07778e6i		−	3.03415i
$597$	−218902.	+	73818.4i	−0.614187	+	0.207117i
$598$	1.53258e6			4.28569
$599$			407616.i			1.13605i	0.823011	+	0.568025i	$0.192292\pi$
$599$			407616.i			1.13605i	−0.823011	+	0.568025i	$0.807708\pi$
$600$	386579.	+	1.14637e6i	1.07383	+	3.18435i
$601$	−222294.			−0.615431			−0.307715	−	0.951478i	$-0.599564\pi$
$601$	−222294.			−0.615431			−0.307715	+	0.951478i	$0.599564\pi$
$602$		−	270819.i		−	0.747286i
$603$	−153297.	+	116656.i	−0.421598	+	0.320828i
$604$	−740227.			−2.02904
$605$			6602.17i			0.0180375i
$606$	−279265.	+	94174.2i	−0.760452	+	0.256441i
$607$	−163249.			−0.443071			−0.221535	−	0.975152i	$-0.571107\pi$
$607$	−163249.			−0.443071			−0.221535	+	0.975152i	$0.571107\pi$
$608$		−	2.11187e6i		−	5.71296i
$609$	115625.	+	342876.i	0.311758	+	0.924490i
$610$	12059.0			0.0324079
$611$			7114.06i			0.0190561i
$612$	953069.	+	1.25242e6i	2.54461	+	3.34386i
$613$	−288936.			−0.768919			−0.384459	−	0.923142i	$-0.625612\pi$
$613$	−288936.			−0.768919			−0.384459	+	0.923142i	$0.625612\pi$
$614$			1.40257e6i			3.72038i
$615$	10727.6	−	3617.58i	0.0283631	−	0.00956463i
$616$	976612.			2.57372
$617$		−	412795.i		−	1.08434i	−0.840270	−	0.542168i	$-0.817604\pi$
$617$		−	412795.i		−	1.08434i	0.840270	−	0.542168i	$-0.182396\pi$
$618$	−239448.	−	710063.i	−0.626953	−	1.85917i
$619$	499803.			1.30442			0.652211	−	0.758038i	$-0.273842\pi$
$619$	499803.			1.30442			0.652211	+	0.758038i	$0.273842\pi$
$620$		−	34748.5i		−	0.0903966i
$621$	583531.	+	394997.i	1.51315	+	1.02426i
$622$	−424808.			−1.09802
$623$			144384.i			0.372001i
$624$	−1.68415e6	+	567931.i	−4.32525	+	1.45857i
$625$	389904.			0.998154
$626$			420402.i			1.07279i
$627$	95777.3	+	284019.i	0.243628	+	0.722458i
$628$	706955.			1.79256
$629$		−	160547.i		−	0.405790i
$630$	−22199.0	+	16893.0i	−0.0559309	+	0.0425623i
$631$	−689137.			−1.73080			−0.865400	−	0.501081i	$-0.832936\pi$
$631$	−689137.			−1.73080			−0.865400	+	0.501081i	$0.832936\pi$
$632$			647045.i			1.61995i
$633$	361646.	−	121955.i	0.902560	−	0.304363i
$634$	176904.			0.440108
$635$			10367.4i			0.0257112i
$636$	−207756.	−	616080.i	−0.513616	−	1.52308i
$637$	564638.			1.39152
$638$			273730.i			0.672482i
$639$	43408.2	+	57042.4i	0.106309	+	0.139700i
$640$	34988.2			0.0854204
$641$		−	250518.i		−	0.609710i	−0.952399	−	0.304855i	$-0.901392\pi$
$641$		−	250518.i		−	0.609710i	0.952399	−	0.304855i	$-0.0986081\pi$
$642$	−543736.	+	183360.i	−1.31922	+	0.444870i
$643$	277817.			0.671950			0.335975	−	0.941871i	$-0.390934\pi$
$643$	277817.			0.671950			0.335975	+	0.941871i	$0.390934\pi$
$644$			3.04151e6i			7.33360i
$645$	869.687	+	2578.98i	0.00209047	+	0.00619909i
$646$	−1.80698e6			−4.33001
$647$			705078.i			1.68434i	0.539215	+	0.842168i	$0.318721\pi$
$647$			705078.i			1.68434i	−0.539215	+	0.842168i	$0.681279\pi$
$648$	−1.36089e6	−	376363.i	−3.24095	−	0.896306i
$649$	−28642.6			−0.0680022
$650$			990353.i			2.34403i
$651$	−782941.	+	264025.i	−1.84743	+	0.622992i
$652$	1.77553e6			4.17670
$653$			58074.5i			0.136194i	0.997679	+	0.0680972i	$0.0216928\pi$
$653$			58074.5i			0.136194i	−0.997679	+	0.0680972i	$0.978307\pi$
$654$	−106478.	−	315752.i	−0.248946	−	0.738228i
$655$	−22.4484			−5.23242e−5
$656$			1.95412e6i			4.54092i
$657$	509705.	−	387875.i	1.18083	−	0.898589i
$658$	−19272.9			−0.0445138
$659$		−	745763.i		−	1.71724i	−0.512615	−	0.858619i	$-0.671323\pi$
$659$		−	745763.i		−	1.71724i	0.512615	−	0.858619i	$-0.328677\pi$
$660$	−14648.1	+	4939.67i	−0.0336275	+	0.0113399i
$661$	226416.			0.518209			0.259104	−	0.965849i	$-0.416573\pi$
$661$	226416.			0.518209			0.259104	+	0.965849i	$0.416573\pi$
$662$		−	597961.i		−	1.36445i
$663$	261377.	+	775091.i	0.594622	+	1.76330i
$664$	−982307.			−2.22798
$665$		−	23462.4i		−	0.0530554i
$666$	137384.	+	180536.i	0.309734	+	0.407020i
$667$	−541247.			−1.21659
$668$		−	885935.i		−	1.98540i
$669$	457354.	−	154230.i	1.02188	−	0.344601i
$670$	11407.0			0.0254110
$671$		−	158900.i		−	0.352923i
$672$	−827584.	−	2.45412e6i	−1.83262	−	5.43448i
$673$	−515622.			−1.13842			−0.569208	−	0.822194i	$-0.692750\pi$
$673$	−515622.			−1.13842			−0.569208	+	0.822194i	$0.692750\pi$
$674$			33814.5i			0.0744361i
$675$	−255247.	+	377078.i	−0.560213	+	0.827606i
$676$	−589926.			−1.29093
$677$			722728.i			1.57688i	0.615114	+	0.788438i	$0.289110\pi$
$677$			722728.i			1.57688i	−0.615114	+	0.788438i	$0.710890\pi$
$678$	−165248.	+	55725.1i	−0.359481	+	0.121225i
$679$	565238.			1.22600
$680$		−	59169.3i		−	0.127961i
$681$	−122497.	−	363253.i	−0.264137	−	0.783275i
$682$	−625049.			−1.34383
$683$		−	821439.i		−	1.76090i	−0.474142	−	0.880448i	$-0.657242\pi$
$683$		−	821439.i		−	1.76090i	0.474142	−	0.880448i	$-0.342758\pi$
$684$	1.48851e6	−	1.13272e6i	3.18155	−	2.42110i
$685$	605.272			0.00128994
$686$			196272.i			0.417071i
$687$	128727.	−	43409.7i	0.272745	−	0.0919756i
$688$	−469781.			−0.992473
$689$		−	337918.i		−	0.711824i
$690$	−13333.2	−	39538.5i	−0.0280051	−	0.0830466i
$691$	−506557.			−1.06089			−0.530447	−	0.847718i	$-0.677976\pi$
$691$	−506557.			−1.06089			−0.530447	+	0.847718i	$0.677976\pi$
$692$			2.18515e6i			4.56320i
$693$	222598.	+	292515.i	0.463505	+	0.609090i
$694$	−555753.			−1.15389
$695$		−	3209.13i		−	0.00664382i
$696$	1.02769e6	−	346558.i	2.12149	−	0.715414i
$697$	899341.			1.85122
$698$			1.43359e6i			2.94248i
$699$	−5073.84	−	15046.0i	−0.0103844	−	0.0307941i
$700$	−1.96542e6			−4.01107
$701$		−	831341.i		−	1.69178i	−0.533360	−	0.845888i	$-0.679071\pi$
$701$		−	831341.i		−	1.69178i	0.533360	−	0.845888i	$-0.320929\pi$
$702$	−957185.	−	647925.i	−1.94232	−	1.31477i
$703$	−190811.			−0.386094
$704$		−	985032.i		−	1.98749i
$705$	183.533	−	61.8913i	0.000369263	−	0.000124524i
$706$	1.13088e6			2.26885
$707$		−	303988.i		−	0.608160i
$708$	57116.2	+	169373.i	0.113944	+	0.337892i
$709$	−417159.			−0.829869			−0.414935	−	0.909851i	$-0.636196\pi$
$709$	−417159.			−0.829869			−0.414935	+	0.909851i	$0.636196\pi$
$710$		−	4244.59i		−	0.00842014i
$711$	−193803.	+	147480.i	−0.383373	+	0.291739i
$712$	432757.			0.853658
$713$		−	1.23591e6i		−	2.43113i
$714$	−2.09982e6	+	708105.i	−4.11894	+	1.38900i
$715$	−8034.46			−0.0157161
$716$			1.40903e6i			2.74849i
$717$	−285160.	−	845616.i	−0.554690	−	1.64488i
$718$	556646.			1.07977
$719$		−	150325.i		−	0.290787i	−0.989374	−	0.145393i	$-0.953555\pi$
$719$		−	150325.i		−	0.290787i	0.989374	−	0.145393i	$-0.0464448\pi$
$720$	29303.7	+	38507.8i	0.0565272	+	0.0742821i
$721$	772923.			1.48685
$722$			1.13962e6i			2.18618i
$723$	628916.	−	212084.i	1.20314	−	0.405725i
$724$	−1.18016e6			−2.25146
$725$		−	349754.i		−	0.665406i
$726$	−236816.	−	702258.i	−0.449302	−	1.33237i
$727$	−479152.			−0.906577			−0.453289	−	0.891364i	$-0.649749\pi$
$727$	−479152.			−0.906577			−0.453289	+	0.891364i	$0.649749\pi$
$728$		−	3.16758e6i		−	5.97674i
$729$	−197457.	−	493397.i	−0.371551	−	0.928413i
$730$	−37927.7			−0.0711723
$731$			216206.i			0.404607i
$732$	−939629.	+	316863.i	−1.75362	+	0.591357i
$733$	1.03624e6			1.92865			0.964325	−	0.264720i	$-0.0852796\pi$
$733$	1.03624e6			1.92865			0.964325	+	0.264720i	$0.0852796\pi$
$734$			2.03663e6i			3.78024i
$735$	−4912.27	−	14566.9i	−0.00909301	−	0.0269645i
$736$	3.87396e6			7.15154
$737$		−	150310.i		−	0.276727i
$738$	−1.01131e6	+	769588.i	−1.85683	+	1.41301i
$739$	−900360.			−1.64865			−0.824323	−	0.566120i	$-0.808444\pi$
$739$	−900360.			−1.64865			−0.824323	+	0.566120i	$0.808444\pi$
$740$		−	9840.98i		−	0.0179711i
$741$	921198.	−	310648.i	1.67771	−	0.565759i
$742$	915463.			1.66277
$743$			464398.i			0.841226i	0.907240	+	0.420613i	$0.138185\pi$
$743$			464398.i			0.841226i	−0.907240	+	0.420613i	$0.861815\pi$
$744$	791349.	+	2.34667e6i	1.42962	+	4.23942i
$745$	−15251.1			−0.0274782
$746$			728571.i			1.30916i
$747$	−223896.	−	294221.i	−0.401241	−	0.527269i
$748$	−1.22802e6			−2.19483
$749$		−	591872.i		−	1.05503i
$750$	51115.3	−	17237.2i	0.0908716	−	0.0306439i
$751$	−469386.			−0.832243			−0.416121	−	0.909309i	$-0.636611\pi$
$751$	−469386.			−0.832243			−0.416121	+	0.909309i	$0.636611\pi$
$752$			33432.0i			0.0591190i
$753$	−99575.5	−	295282.i	−0.175615	−	0.520772i
$754$	887825.			1.56165
$755$			10474.6i			0.0183756i
$756$	1.28585e6	−	1.89960e6i	2.24982	−	3.32367i
$757$	−162448.			−0.283480			−0.141740	−	0.989904i	$-0.545270\pi$
$757$	−162448.			−0.283480			−0.141740	+	0.989904i	$0.545270\pi$
$758$			795168.i			1.38395i
$759$	−520997.	+	175691.i	−0.904381	+	0.304977i
$760$	−70322.8			−0.121750
$761$			863476.i			1.49101i	0.666499	+	0.745506i	$0.267792\pi$
$761$			863476.i			1.49101i	−0.666499	+	0.745506i	$0.732208\pi$
$762$	−371873.	−	1.10276e6i	−0.640449	−	1.89919i
$763$	343705.			0.590387
$764$		−	1.43240e6i		−	2.45402i
$765$	17722.4	−	13486.4i	0.0302830	−	0.0230448i
$766$	455575.			0.776429
$767$			92900.5i			0.157916i
$768$	−1.59499e6	+	537865.i	−2.70418	+	0.911907i
$769$	−899906.			−1.52175			−0.760877	−	0.648896i	$-0.775231\pi$
$769$	−899906.			−1.52175			−0.760877	+	0.648896i	$0.775231\pi$
$770$		−	21766.4i		−	0.0367117i
$771$	244751.	+	725787.i	0.411733	+	1.22096i
$772$	−1.19398e6			−2.00337
$773$			736093.i			1.23189i	0.787787	+	0.615947i	$0.211227\pi$
$773$			736093.i			1.23189i	−0.787787	+	0.615947i	$0.788773\pi$
$774$	−185013.	−	243125.i	−0.308831	−	0.405833i
$775$	798647.			1.32969
$776$		−	1.69416e6i		−	2.81340i
$777$	−221734.	+	74773.4i	−0.367274	+	0.123853i
$778$	−1.38528e6			−2.28865
$779$		−	1.06887e6i		−	1.76137i
$780$	16021.5	+	47510.3i	0.0263338	+	0.0780906i
$781$	−55930.8			−0.0916957
$782$		−	3.31468e6i		−	5.42035i
$783$	338040.	+	228822.i	0.551372	+	0.373228i
$784$	2.65348e6			4.31701
$785$		−	10003.8i		−	0.0162339i
$786$	2387.79	−	805.213i	0.00386501	−	0.00130336i
$787$	−63528.7			−0.102570			−0.0512850	−	0.998684i	$-0.516332\pi$
$787$	−63528.7			−0.102570			−0.0512850	+	0.998684i	$0.516332\pi$
$788$		−	1.40323e6i		−	2.25984i
$789$	−322604.	−	956652.i	−0.518221	−	1.53674i
$790$	14421.1			0.0231071
$791$		−	179877.i		−	0.287490i
$792$	876741.	−	667183.i	1.39772	−	1.06364i
$793$	−515383.			−0.819566
$794$			353237.i			0.560307i
$795$	−8717.83	+	2939.84i	−0.0137935	+	0.00465146i
$796$	−1.12488e6			−1.77533
$797$			854920.i			1.34589i	0.739694	+	0.672944i	$0.234970\pi$
$797$			854920.i			1.34589i	−0.739694	+	0.672944i	$0.765030\pi$
$798$	841585.	+	2.49564e6i	1.32158	+	3.91901i
$799$	15386.3			0.0241014
$800$			2.50336e6i			3.91149i
$801$	98637.8	+	129619.i	0.153737	+	0.202025i
$802$	−422850.			−0.657411
$803$			499772.i			0.775069i
$804$	−888829.	+	299732.i	−1.37501	+	0.463683i
$805$	43038.8			0.0664153
$806$			2.02731e6i			3.12068i
$807$	74892.9	+	222088.i	0.114999	+	0.341019i
$808$	−911130.			−1.39559
$809$		−	32729.9i		−	0.0500089i	−0.999687	−	0.0250045i	$-0.992040\pi$
$809$		−	32729.9i		−	0.0500089i	0.999687	−	0.0250045i	$-0.00795999\pi$
$810$	−8388.23	+	30331.0i	−0.0127850	+	0.0462292i
$811$	208112.			0.316414			0.158207	−	0.987406i	$-0.449429\pi$
$811$	208112.			0.316414			0.158207	+	0.987406i	$0.449429\pi$
$812$			1.76195e6i			2.67227i
$813$	1.04257e6	−	351578.i	1.57734	−	0.531914i
$814$	−177018.			−0.267158
$815$		−	25124.6i		−	0.0378255i
$816$	1.22833e6	+	3.64249e6i	1.84473	+	5.47039i
$817$	256962.			0.384968
$818$			2.00465e6i			2.99593i
$819$	948753.	−	721983.i	1.41444	−	1.07636i
$820$	55126.4			0.0819845
$821$			839175.i			1.24499i	0.782623	+	0.622496i	$0.213881\pi$
$821$			839175.i			1.24499i	−0.782623	+	0.622496i	$0.786119\pi$
$822$	−64381.4	+	21710.8i	−0.0952833	+	0.0321316i
$823$	297088.			0.438616			0.219308	−	0.975656i	$-0.429620\pi$
$823$	297088.			0.438616			0.219308	+	0.975656i	$0.429620\pi$
$824$		−	2.31665e6i		−	3.41197i
$825$	−113532.	−	336668.i	−0.166805	−	0.494646i
$826$	−251679.			−0.368882
$827$			609715.i			0.891489i	0.895160	+	0.445745i	$0.147061\pi$
$827$			609715.i			0.891489i	−0.895160	+	0.445745i	$0.852939\pi$
$828$	2.07784e6	+	2.73047e6i	3.03076	+	3.98270i
$829$	66695.5			0.0970482			0.0485241	−	0.998822i	$-0.484548\pi$
$829$	66695.5			0.0970482			0.0485241	+	0.998822i	$0.484548\pi$
$830$			21893.3i			0.0317801i
$831$	−236203.	+	79652.6i	−0.342045	+	0.115345i
$832$	−3.19489e6			−4.61540
$833$		−	1.22120e6i		−	1.75994i
$834$	115110.	+	341348.i	0.165493	+	0.490756i
$835$	−12536.4			−0.0179804
$836$			1.45950e6i			2.08829i
$837$	−522504.	+	771899.i	−0.745829	+	1.10182i
$838$	794215.			1.13097
$839$		−	811996.i		−	1.15353i	−0.816909	−	0.576766i	$-0.804314\pi$
$839$		−	811996.i		−	1.15353i	0.816909	−	0.576766i	$-0.195686\pi$
$840$	−81719.3	+	27557.5i	−0.115815	+	0.0390554i
$841$	393736.			0.556690
$842$		−	1.67343e6i		−	2.36039i
$843$	398574.	+	1.18193e6i	0.560859	+	1.66318i
$844$	1.85840e6			2.60889
$845$			8347.74i			0.0116911i
$846$	−17302.0	+	13166.5i	−0.0241744	+	0.0183962i
$847$	764428.			1.06554
$848$		−	1.58802e6i		−	2.20834i
$849$	−289981.	+	97787.9i	−0.402304	+	0.135666i
$850$	2.14194e6			2.96463
$851$		−	350018.i		−	0.483316i
$852$	111532.	+	330737.i	0.153645	+	0.455620i
$853$	−146391.			−0.201195			−0.100597	−	0.994927i	$-0.532075\pi$
$853$	−146391.			−0.201195			−0.100597	+	0.994927i	$0.532075\pi$
$854$		−	1.39624e6i		−	1.91445i
$855$	−16028.6	−	21063.1i	−0.0219262	−	0.0288131i
$856$	−1.77399e6			−2.42105
$857$		−	251181.i		−	0.341999i	−0.985271	−	0.170999i	$-0.945300\pi$
$857$		−	251181.i		−	0.341999i	0.985271	−	0.170999i	$-0.0546996\pi$
$858$	854607.	−	288192.i	1.16089	−	0.391478i
$859$	869910.			1.17893			0.589465	−	0.807794i	$-0.299339\pi$
$859$	869910.			1.17893			0.589465	+	0.807794i	$0.299339\pi$
$860$			13252.7i			0.0179187i
$861$	−418859.	−	1.24209e6i	−0.565018	−	1.67551i
$862$	−1.09049e6			−1.46759
$863$			456928.i			0.613516i	0.951788	+	0.306758i	$0.0992442\pi$
$863$			456928.i			0.613516i	−0.951788	+	0.306758i	$0.900756\pi$
$864$	−2.41952e6	−	1.63779e6i	−3.24116	−	2.19397i
$865$	30920.9			0.0413257
$866$			1.03383e6i			1.37852i
$867$	964095.	−	325114.i	1.28257	−	0.432511i
$868$	−4.02333e6			−5.34006
$869$		−	190026.i		−	0.251637i
$870$	−7723.96	−	22904.7i	−0.0102047	−	0.0302612i
$871$	−487519.			−0.642622
$872$		−	1.03017e6i		−	1.35480i
$873$	507435.	−	386148.i	0.665813	−	0.506671i
$874$	−3.93950e6			−5.15725
$875$			55640.5i			0.0726732i
$876$	2.95531e6	−	996594.i	3.85119	−	1.29870i
$877$	382783.			0.497684			0.248842	−	0.968544i	$-0.419950\pi$
$877$	382783.			0.497684			0.248842	+	0.968544i	$0.419950\pi$
$878$		−	102485.i		−	0.132944i
$879$	244959.	+	726404.i	0.317041	+	0.940158i
$880$	−37757.4			−0.0487570
$881$			868608.i			1.11911i	0.828794	+	0.559554i	$0.189028\pi$
$881$			868608.i			1.11911i	−0.828794	+	0.559554i	$0.810972\pi$
$882$	1.04501e6	+	1.37325e6i	1.34334	+	1.76527i
$883$	60577.1			0.0776939			0.0388470	−	0.999245i	$-0.487632\pi$
$883$	60577.1			0.0776939			0.0388470	+	0.999245i	$0.487632\pi$
$884$			3.98299e6i			5.09688i
$885$	2396.71	−	808.222i	0.00306005	−	0.00103191i
$886$	1.50841e6			1.92155
$887$			1.22832e6i			1.56122i	0.625018	+	0.780610i	$0.285092\pi$
$887$			1.22832e6i			1.56122i	−0.625018	+	0.780610i	$0.714908\pi$
$888$	224115.	+	664592.i	0.284214	+	0.842810i
$889$	1.20038e6			1.51885
$890$		−	9645.13i		−	0.0121767i
$891$	399669.	+	110531.i	0.503437	+	0.139229i
$892$	2.35022e6			2.95379
$893$		−	18286.7i		−	0.0229315i
$894$	1.62222e6	−	547049.i	2.02972	−	0.684465i
$895$	19938.4			0.0248912
$896$		−	4.05108e6i		−	5.04609i
$897$	569843.	+	1.68982e6i	0.708224	+	2.10017i
$898$	481635.			0.597263
$899$		−	715966.i		−	0.885876i
$900$	−1.76443e6	+	1.34270e6i	−2.17831	+	1.65765i
$901$	−730852.			−0.900285
$902$		−	991604.i		−	1.21878i
$903$	298605.	−	100696.i	0.366203	−	0.123491i
$904$	−539136.			−0.659723
$905$			16699.9i			0.0203899i
$906$	−375717.	−	1.11416e6i	−0.457725	−	1.35734i
$907$	298870.			0.363302			0.181651	−	0.983363i	$-0.441856\pi$
$907$	298870.			0.363302			0.181651	+	0.983363i	$0.441856\pi$
$908$		−	1.86666e6i		−	2.26409i
$909$	−207673.	−	272902.i	−0.251334	−	0.330277i
$910$	−70597.9			−0.0852528
$911$		−	563963.i		−	0.679539i	−0.940509	−	0.339769i	$-0.889651\pi$
$911$		−	563963.i		−	0.679539i	0.940509	−	0.339769i	$-0.110349\pi$
$912$	4.32911e6	−	1.45987e6i	5.20486	−	1.75519i
$913$	288487.			0.346086
$914$		−	1.38003e6i		−	1.65195i
$915$	4483.77	+	13296.2i	0.00535551	+	0.0158813i
$916$	661496.			0.788382
$917$			2599.17i			0.00309098i
$918$	−1.40134e6	+	2.07021e6i	−1.66287	+	2.45657i
$919$	−1.39354e6			−1.65002			−0.825011	−	0.565116i	$-0.808831\pi$
$919$	−1.39354e6			−1.65002			−0.825011	+	0.565116i	$0.808831\pi$
$920$		−	128998.i		−	0.152408i
$921$	−1.54647e6	+	521503.i	−1.82315	+	0.614806i
$922$	291648.			0.343081
$923$			181408.i			0.212938i
$924$	571936.	+	1.69603e6i	0.669890	+	1.98650i
$925$	226182.			0.264347
$926$		−	1.81238e6i		−	2.11362i
$927$	693882.	−	528031.i	0.807470	−	0.614469i
$928$	2.24419e6			2.60594
$929$		−	343003.i		−	0.397435i	−0.980057	−	0.198718i	$-0.936322\pi$
$929$		−	343003.i		−	0.397435i	0.980057	−	0.198718i	$-0.0636776\pi$
$930$	52301.8	−	17637.3i	0.0604715	−	0.0203923i
$931$	−1.45140e6			−1.67451
$932$		−	77317.6i		−	0.0890115i
$933$	−157952.	−	468392.i	−0.181452	−	0.538080i
$934$	−1.96942e6			−2.25758
$935$			17377.0i			0.0198770i
$936$	−2.16397e6	−	2.84365e6i	−2.47001	−	3.24583i
$937$	−150942.			−0.171921			−0.0859607	−	0.996299i	$-0.527396\pi$
$937$	−150942.			−0.171921			−0.0859607	+	0.996299i	$0.527396\pi$
$938$		−	1.32075e6i		−	1.50112i
$939$	−463535.	+	156314.i	−0.525716	+	0.177283i
$940$	943.129			0.00106737
$941$			131326.i			0.148310i	0.997247	+	0.0741550i	$0.0236260\pi$
$941$			131326.i			0.148310i	−0.997247	+	0.0741550i	$0.976374\pi$
$942$	358830.	+	1.06408e6i	0.404377	+	1.19914i
$943$	1.96070e6			2.20490
$944$			436580.i			0.489914i
$945$	−26880.2	−	18195.4i	−0.0301002	−	0.0203750i
$946$	238387.			0.266379
$947$		−	1.65428e6i		−	1.84463i	−0.386441	−	0.922314i	$-0.626296\pi$
$947$		−	1.65428e6i		−	1.84463i	0.386441	−	0.922314i	$-0.373704\pi$
$948$	−1.12369e6	+	378931.i	−1.25034	+	0.421642i
$949$	1.62098e6			1.79988
$950$		−	2.54571e6i		−	2.82073i
$951$	65776.4	+	195054.i	0.0727292	+	0.215672i
$952$	−6.85087e6			−7.55913
$953$		−	151783.i		−	0.167123i	−0.996503	−	0.0835615i	$-0.973370\pi$
$953$		−	151783.i		−	0.167123i	0.996503	−	0.0835615i	$-0.0266295\pi$
$954$	821845.	−	625408.i	0.903012	−	0.687174i
$955$	−20269.2			−0.0222244
$956$		−	4.34540e6i		−	4.75460i
$957$	−301814.	+	101778.i	−0.329545	+	0.111130i
$958$	1.21860e6			1.32780
$959$		−	70081.0i		−	0.0762014i
$960$	27795.1	+	82423.9i	0.0301596	+	0.0894356i
$961$	711354.			0.770262
$962$			574146.i			0.620400i
$963$	−404344.	−	531346.i	−0.436012	−	0.572961i
$964$	3.23183e6			3.47772
$965$			16895.3i			0.0181431i
$966$	−4.57794e6	+	1.54378e6i	−4.90586	+	1.65436i
$967$	−1.21992e6			−1.30461			−0.652303	−	0.757959i	$-0.726197\pi$
$967$	−1.21992e6			−1.30461			−0.652303	+	0.757959i	$0.726197\pi$
$968$		−	2.29118e6i		−	2.44517i
$969$	−671872.	−	1.99238e6i	−0.715548	−	2.12189i
$970$	−37758.9			−0.0401306
$971$			1.47791e6i			1.56751i	0.621071	+	0.783754i	$0.286698\pi$
$971$			1.47791e6i			1.56751i	−0.621071	+	0.783754i	$0.713302\pi$
$972$	−143373.	−	2.58378e6i	−0.151752	−	2.73479i
$973$	−371567.			−0.392475
$974$		−	70095.2i		−	0.0738874i
$975$	−1.09196e6	+	368233.i	−1.14868	+	0.387359i
$976$	−2.42201e6			−2.54259
$977$			442576.i			0.463659i	0.972756	+	0.231830i	$0.0744712\pi$
$977$			442576.i			0.463659i	−0.972756	+	0.231830i	$0.925529\pi$
$978$	901207.	+	2.67245e6i	0.942208	+	2.79403i
$979$	−127093.			−0.132604
$980$		−	74855.4i		−	0.0779419i
$981$	308557.	−	234806.i	0.320625	−	0.243989i
$982$	−1.55354e6			−1.61102
$983$			1.41860e6i			1.46809i	0.679100	+	0.734046i	$0.262370\pi$
$983$			1.41860e6i			1.46809i	−0.679100	+	0.734046i	$0.737630\pi$
$984$	−3.72286e6	+	1.25543e6i	−3.84491	+	1.29659i
$985$	−19856.4			−0.0204658
$986$		−	1.92020e6i		−	1.97511i
$987$	−7166.04	−	21250.3i	−0.00735606	−	0.0218137i
$988$	4.73379e6			4.84948
$989$			471363.i			0.481907i
$990$	−14869.9	−	19540.5i	−0.0151719	−	0.0199372i
$991$	−331119.			−0.337161			−0.168580	−	0.985688i	$-0.553918\pi$
$991$	−331119.			−0.337161			−0.168580	+	0.985688i	$0.553918\pi$
$992$			5.12451e6i			5.20749i
$993$	659311.	−	222334.i	0.668639	−	0.225480i
$994$	−491457.			−0.497408
$995$			15917.6i			0.0160780i
$996$	−575272.	−	1.70592e6i	−0.579902	−	1.71965i
$997$	115116.			0.115809			0.0579047	−	0.998322i	$-0.481558\pi$
$997$	115116.			0.115809			0.0579047	+	0.998322i	$0.481558\pi$
$998$			2.16793e6i			2.17663i
$999$	−147976.	+	218607.i	−0.148273	+	0.219045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.77	yes	78
3.2	odd	2	inner	177.5.b.a.119.2	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.2	✓	78	3.2	odd	2	inner
177.5.b.a.119.77	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)

\(f(q)\)	\(=\)	\(q+7.73459i q^{2} +(-8.52815 + 2.87588i) q^{3} -43.8239 q^{4} +0.620129i q^{5} +(-22.2437 - 65.9618i) q^{6} +71.8012 q^{7} -215.207i q^{8} +(64.4587 - 49.0518i) q^{9} +O(q^{10})\)	\(q+7.73459i q^{2} +(-8.52815 + 2.87588i) q^{3} -43.8239 q^{4} +0.620129i q^{5} +(-22.2437 - 65.9618i) q^{6} +71.8012 q^{7} -215.207i q^{8} +(64.4587 - 49.0518i) q^{9} -4.79645 q^{10} +63.2025i q^{11} +(373.737 - 126.032i) q^{12} +204.993 q^{13} +555.353i q^{14} +(-1.78341 - 5.28856i) q^{15} +963.353 q^{16} -443.362i q^{17} +(379.396 + 498.562i) q^{18} -526.936 q^{19} -27.1765i q^{20} +(-612.332 + 206.491i) q^{21} -488.846 q^{22} -966.597i q^{23} +(618.907 + 1835.31i) q^{24} +624.615 q^{25} +1585.54i q^{26} +(-408.646 + 603.696i) q^{27} -3146.61 q^{28} -559.951i q^{29} +(40.9048 - 13.7940i) q^{30} +1278.62 q^{31} +4007.84i q^{32} +(-181.763 - 539.001i) q^{33} +3429.22 q^{34} +44.5261i q^{35} +(-2824.83 + 2149.64i) q^{36} +362.114 q^{37} -4075.64i q^{38} +(-1748.21 + 589.535i) q^{39} +133.456 q^{40} +2028.46i q^{41} +(-1597.13 - 4736.14i) q^{42} -487.652 q^{43} -2769.78i q^{44} +(30.4185 + 39.9727i) q^{45} +7476.24 q^{46} +34.7038i q^{47} +(-8215.62 + 2770.48i) q^{48} +2754.42 q^{49} +4831.15i q^{50} +(1275.05 + 3781.05i) q^{51} -8983.61 q^{52} -1648.43i q^{53} +(-4669.34 - 3160.71i) q^{54} -39.1937 q^{55} -15452.1i q^{56} +(4493.79 - 1515.40i) q^{57} +4330.99 q^{58} +453.188i q^{59} +(78.1562 + 231.765i) q^{60} -2514.15 q^{61} +9889.62i q^{62} +(4628.21 - 3521.98i) q^{63} -15585.3 q^{64} +127.122i q^{65} +(4168.95 - 1405.86i) q^{66} -2378.22 q^{67} +19429.8i q^{68} +(2779.81 + 8243.29i) q^{69} -344.391 q^{70} +884.945i q^{71} +(-10556.3 - 13871.9i) q^{72} +7907.46 q^{73} +2800.80i q^{74} +(-5326.81 + 1796.32i) q^{75} +23092.4 q^{76} +4538.02i q^{77} +(-4559.82 - 13521.7i) q^{78} -3006.62 q^{79} +597.403i q^{80} +(1748.84 - 6323.63i) q^{81} -15689.3 q^{82} -4564.48i q^{83} +(26834.8 - 9049.26i) q^{84} +274.942 q^{85} -3771.79i q^{86} +(1610.35 + 4775.35i) q^{87} +13601.6 q^{88} +2010.89i q^{89} +(-309.173 + 235.274i) q^{90} +14718.8 q^{91} +42360.1i q^{92} +(-10904.3 + 3677.16i) q^{93} -268.420 q^{94} -326.769i q^{95} +(-11526.0 - 34179.4i) q^{96} +7872.26 q^{97} +21304.3i q^{98} +(3100.20 + 4073.95i) 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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