LMFDB - Embedded newform 177.5.b.a.119.19

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			119.19
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.60

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} +O(q^{10})$	\(q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} -156.006 q^{10} +130.221i q^{11} +(-38.7533 + 29.7117i) q^{12} +134.782 q^{13} +417.419i q^{14} +(-184.558 - 240.721i) q^{15} -313.374 q^{16} +178.035i q^{17} +(-362.079 - 97.3314i) q^{18} +400.688 q^{19} +182.868i q^{20} +(-644.090 + 493.816i) q^{21} +602.768 q^{22} +68.8786i q^{23} +(-268.026 - 349.590i) q^{24} -510.908 q^{25} -623.878i q^{26} +(-278.163 - 673.845i) q^{27} +489.293 q^{28} -1463.81i q^{29} +(-1114.25 + 854.284i) q^{30} -240.021 q^{31} +667.412i q^{32} +(713.089 + 930.090i) q^{33} +824.088 q^{34} +3039.31i q^{35} +(-114.091 + 424.425i) q^{36} +223.236 q^{37} -1854.71i q^{38} +(962.663 - 738.062i) q^{39} -1649.63 q^{40} +200.831i q^{41} +(2285.78 + 2981.37i) q^{42} -3019.72 q^{43} -706.558i q^{44} +(-2636.37 - 708.689i) q^{45} +318.826 q^{46} -2568.51i q^{47} +(-2238.24 + 1716.03i) q^{48} +5731.18 q^{49} +2364.89i q^{50} +(974.915 + 1271.59i) q^{51} -731.302 q^{52} +3075.45i q^{53} +(-3119.09 + 1287.56i) q^{54} +4388.88 q^{55} +4413.86i q^{56} +(2861.87 - 2194.16i) q^{57} -6775.71 q^{58} -453.188i q^{59} +(1001.38 + 1306.11i) q^{60} +3522.17 q^{61} +1111.01i q^{62} +(-1896.22 + 7054.05i) q^{63} -1924.66 q^{64} -4542.58i q^{65} +(4305.20 - 3300.75i) q^{66} -5175.34 q^{67} -965.986i q^{68} +(377.178 + 491.957i) q^{69} +14068.4 q^{70} -3023.98i q^{71} +(-3828.69 - 1029.20i) q^{72} +4158.64 q^{73} -1033.32i q^{74} +(-3649.10 + 2797.72i) q^{75} -2174.06 q^{76} -11743.2i q^{77} +(-3416.34 - 4455.98i) q^{78} -11295.7 q^{79} +10561.7i q^{80} +(-5676.70 - 3289.65i) q^{81} +929.608 q^{82} -9462.92i q^{83} +(3494.72 - 2679.36i) q^{84} +6000.35 q^{85} +13977.7i q^{86} +(-8015.82 - 10455.1i) q^{87} +6373.78 q^{88} +3702.98i q^{89} +(-3280.38 + 12203.2i) q^{90} -12154.4 q^{91} -373.723i q^{92} +(-1714.32 + 1314.35i) q^{93} -11889.1 q^{94} -13504.5i q^{95} +(3654.74 + 4766.92i) q^{96} +8345.01 q^{97} -26528.5i q^{98} +(10186.3 + 2738.20i) 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 $

$2$		−	4.62880i		−	1.15720i	−0.815611	−	0.578600i	$-0.803599\pi$
$2$		−	4.62880i		−	1.15720i	0.815611	−	0.578600i	$-0.196401\pi$
$3$	7.14239	−	5.47598i	0.793598	−	0.608442i
$3$	7.14239	−	5.47598i	0.793598	−	0.608442i
$4$	−5.42582			−0.339114
$5$		−	33.7032i		−	1.34813i	−0.738672	−	0.674065i	$-0.764547\pi$
$5$		−	33.7032i		−	1.34813i	0.738672	−	0.674065i	$-0.235453\pi$
$6$	−25.3472	−	33.0607i	−0.704090	−	0.918353i
$7$	−90.1786			−1.84038			−0.920190	−	0.391472i	$-0.871966\pi$
$7$	−90.1786			−1.84038			−0.920190	+	0.391472i	$0.871966\pi$
$8$		−	48.9458i		−	0.764778i
$9$	21.0273	−	78.2231i	0.259597	−	0.965717i
$10$	−156.006			−1.56006
$11$			130.221i			1.07621i	0.842878	+	0.538104i	$0.180859\pi$
$11$			130.221i			1.07621i	−0.842878	+	0.538104i	$0.819141\pi$
$12$	−38.7533	+	29.7117i	−0.269120	+	0.206331i
$13$	134.782			0.797525			0.398763	−	0.917054i	$-0.369440\pi$
$13$	134.782			0.797525			0.398763	+	0.917054i	$0.369440\pi$
$14$			417.419i			2.12969i
$15$	−184.558	−	240.721i	−0.820259	−	1.06987i
$16$	−313.374			−1.22412
$17$			178.035i			0.616038i	0.951380	+	0.308019i	$0.0996660\pi$
$17$			178.035i			0.616038i	−0.951380	+	0.308019i	$0.900334\pi$
$18$	−362.079	−	97.3314i	−1.11753	−	0.300406i
$19$	400.688			1.10994			0.554970	−	0.831871i	$-0.312730\pi$
$19$	400.688			1.10994			0.554970	+	0.831871i	$0.312730\pi$
$20$			182.868i			0.457170i
$21$	−644.090	+	493.816i	−1.46052	+	1.11976i
$22$	602.768			1.24539
$23$			68.8786i			0.130205i	0.997879	+	0.0651026i	$0.0207375\pi$
$23$			68.8786i			0.130205i	−0.997879	+	0.0651026i	$0.979263\pi$
$24$	−268.026	−	349.590i	−0.465323	−	0.606926i
$25$	−510.908			−0.817453
$26$		−	623.878i		−	0.922897i
$27$	−278.163	−	673.845i	−0.381567	−	0.924341i
$28$	489.293			0.624099
$29$		−	1463.81i		−	1.74056i	−0.492553	−	0.870282i	$-0.663936\pi$
$29$		−	1463.81i		−	1.74056i	0.492553	−	0.870282i	$-0.336064\pi$
$30$	−1114.25	+	854.284i	−1.23806	+	0.949204i
$31$	−240.021			−0.249761			−0.124881	−	0.992172i	$-0.539855\pi$
$31$	−240.021			−0.249761			−0.124881	+	0.992172i	$0.539855\pi$
$32$			667.412i			0.651770i
$33$	713.089	+	930.090i	0.654810	+	0.854077i
$34$	824.088			0.712879
$35$			3039.31i			2.48107i
$36$	−114.091	+	424.425i	−0.0880329	+	0.327488i
$37$	223.236			0.163065			0.0815326	−	0.996671i	$-0.474019\pi$
$37$	223.236			0.163065			0.0815326	+	0.996671i	$0.474019\pi$
$38$		−	1854.71i		−	1.28442i
$39$	962.663	−	738.062i	0.632915	−	0.485248i
$40$	−1649.63			−1.03102
$41$			200.831i			0.119471i	0.998214	+	0.0597356i	$0.0190258\pi$
$41$			200.831i			0.119471i	−0.998214	+	0.0597356i	$0.980974\pi$
$42$	2285.78	+	2981.37i	1.29579	+	1.69012i
$43$	−3019.72			−1.63316			−0.816582	−	0.577229i	$-0.804134\pi$
$43$	−3019.72			−1.63316			−0.816582	+	0.577229i	$0.804134\pi$
$44$		−	706.558i		−	0.364957i
$45$	−2636.37	−	708.689i	−1.30191	−	0.349970i
$46$	318.826			0.150674
$47$		−	2568.51i		−	1.16275i	−0.813637	−	0.581373i	$-0.802516\pi$
$47$		−	2568.51i		−	1.16275i	0.813637	−	0.581373i	$-0.197484\pi$
$48$	−2238.24	+	1716.03i	−0.971456	+	0.744803i
$49$	5731.18			2.38700
$50$			2364.89i			0.945957i
$51$	974.915	+	1271.59i	0.374823	+	0.488886i
$52$	−731.302			−0.270452
$53$			3075.45i			1.09486i	0.836852	+	0.547429i	$0.184393\pi$
$53$			3075.45i			1.09486i	−0.836852	+	0.547429i	$0.815607\pi$
$54$	−3119.09	+	1287.56i	−1.06965	+	0.441550i
$55$	4388.88			1.45087
$56$			4413.86i			1.40748i
$57$	2861.87	−	2194.16i	0.880846	−	0.675334i
$58$	−6775.71			−2.01418
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	1001.38	+	1306.11i	0.278161	+	0.362809i
$61$	3522.17			0.946566			0.473283	−	0.880910i	$-0.343069\pi$
$61$	3522.17			0.946566			0.473283	+	0.880910i	$0.343069\pi$
$62$			1111.01i			0.289024i
$63$	−1896.22	+	7054.05i	−0.477756	+	1.77729i
$64$	−1924.66			−0.469887
$65$		−	4542.58i		−	1.07517i
$66$	4305.20	−	3300.75i	0.988339	−	0.757747i
$67$	−5175.34			−1.15289			−0.576446	−	0.817135i	$-0.695561\pi$
$67$	−5175.34			−1.15289			−0.576446	+	0.817135i	$0.695561\pi$
$68$		−	965.986i		−	0.208907i
$69$	377.178	+	491.957i	0.0792224	+	0.103331i
$70$	14068.4			2.87110
$71$		−	3023.98i		−	0.599877i	−0.953959	−	0.299939i	$-0.903034\pi$
$71$		−	3023.98i		−	0.599877i	0.953959	−	0.299939i	$-0.0969662\pi$
$72$	−3828.69	−	1029.20i	−0.738559	−	0.198534i
$73$	4158.64			0.780378			0.390189	−	0.920735i	$-0.372410\pi$
$73$	4158.64			0.780378			0.390189	+	0.920735i	$0.372410\pi$
$74$		−	1033.32i		−	0.188699i
$75$	−3649.10	+	2797.72i	−0.648729	+	0.497373i
$76$	−2174.06			−0.376396
$77$		−	11743.2i		−	1.98063i
$78$	−3416.34	−	4455.98i	−0.561529	−	0.732409i
$79$	−11295.7			−1.80991			−0.904956	−	0.425506i	$-0.860096\pi$
$79$	−11295.7			−1.80991			−0.904956	+	0.425506i	$0.860096\pi$
$80$			10561.7i			1.65027i
$81$	−5676.70	−	3289.65i	−0.865219	−	0.501394i
$82$	929.608			0.138252
$83$		−	9462.92i		−	1.37363i	−0.726833	−	0.686814i	$-0.759009\pi$
$83$		−	9462.92i		−	1.37363i	0.726833	−	0.686814i	$-0.240991\pi$
$84$	3494.72	−	2679.36i	0.495284	−	0.379728i
$85$	6000.35			0.830498
$86$			13977.7i			1.88990i
$87$	−8015.82	−	10455.1i	−1.05903	−	1.38131i
$88$	6373.78			0.823060
$89$			3702.98i			0.467489i	0.972298	+	0.233744i	$0.0750979\pi$
$89$			3702.98i			0.467489i	−0.972298	+	0.233744i	$0.924902\pi$
$90$	−3280.38	+	12203.2i	−0.404986	+	1.50657i
$91$	−12154.4			−1.46775
$92$		−	373.723i		−	0.0441544i
$93$	−1714.32	+	1314.35i	−0.198210	+	0.151965i
$94$	−11889.1			−1.34553
$95$		−	13504.5i		−	1.49634i
$96$	3654.74	+	4766.92i	0.396564	+	0.517244i
$97$	8345.01			0.886917			0.443459	−	0.896295i	$-0.353751\pi$
$97$	8345.01			0.886917			0.443459	+	0.896295i	$0.353751\pi$
$98$		−	26528.5i		−	2.76224i
$99$	10186.3	+	2738.20i	1.03931	+	0.279380i
$100$	2772.10			0.277210
$101$		−	17854.1i		−	1.75023i	−0.483914	−	0.875116i	$-0.660785\pi$
$101$		−	17854.1i		−	1.75023i	0.483914	−	0.875116i	$-0.339215\pi$
$102$	5885.96	−	4512.69i	0.565740	−	0.433746i
$103$	−13628.6			−1.28463			−0.642314	−	0.766441i	$-0.722026\pi$
$103$	−13628.6			−1.28463			−0.642314	+	0.766441i	$0.722026\pi$
$104$		−	6597.00i		−	0.609930i
$105$	16643.2	+	21707.9i	1.50959	+	1.96897i
$106$	14235.7			1.26697
$107$			5939.18i			0.518751i	0.965777	+	0.259376i	$0.0835167\pi$
$107$			5939.18i			0.518751i	−0.965777	+	0.259376i	$0.916483\pi$
$108$	1509.26	+	3656.16i	0.129395	+	0.313457i
$109$	18993.4			1.59863			0.799317	−	0.600910i	$-0.205195\pi$
$109$	18993.4			1.59863			0.799317	+	0.600910i	$0.205195\pi$
$110$		−	20315.2i		−	1.67895i
$111$	1594.44	−	1222.44i	0.129408	−	0.0992157i
$112$	28259.6			2.25284
$113$			1215.68i			0.0952052i	0.998866	+	0.0476026i	$0.0151581\pi$
$113$			1215.68i			0.0952052i	−0.998866	+	0.0476026i	$0.984842\pi$
$114$	−10156.3	−	13247.0i	−0.781497	−	1.01932i
$115$	2321.43			0.175534
$116$			7942.40i			0.590250i
$117$	2834.10	−	10543.0i	0.207035	−	0.770184i
$118$	−2097.72			−0.150655
$119$		−	16054.9i		−	1.13374i
$120$	−11782.3	+	9033.34i	−0.818215	+	0.627316i
$121$	−2316.57			−0.158225
$122$		−	16303.5i		−	1.09537i
$123$	1099.75	+	1434.41i	0.0726913	+	0.0948121i
$124$	1302.31			0.0846976
$125$		−	3845.27i		−	0.246097i
$126$	32651.8	+	8777.21i	2.05668	+	0.552860i
$127$	12112.2			0.750960			0.375480	−	0.926831i	$-0.377478\pi$
$127$	12112.2			0.750960			0.375480	+	0.926831i	$0.377478\pi$
$128$			19587.5i			1.19552i
$129$	−21568.0	+	16535.9i	−1.29608	+	0.993686i
$130$	−21026.7			−1.24418
$131$		−	7500.56i		−	0.437070i	−0.975829	−	0.218535i	$-0.929872\pi$
$131$		−	7500.56i		−	0.437070i	0.975829	−	0.218535i	$-0.0701278\pi$
$132$	−3869.09	−	5046.51i	−0.222055	−	0.289630i
$133$	−36133.5			−2.04271
$134$			23955.6i			1.33413i
$135$	−22710.7	+	9374.98i	−1.24613	+	0.514402i
$136$	8714.06			0.471132
$137$			19710.8i			1.05018i	0.851048	+	0.525088i	$0.175968\pi$
$137$			19710.8i			1.05018i	−0.851048	+	0.525088i	$0.824032\pi$
$138$	2277.17	−	1745.88i	0.119574	−	0.0916762i
$139$	24368.1			1.26122			0.630612	−	0.776098i	$-0.282804\pi$
$139$	24368.1			1.26122			0.630612	+	0.776098i	$0.282804\pi$
$140$		−	16490.8i		−	0.841366i
$141$	−14065.1	−	18345.3i	−0.707463	−	0.922753i
$142$	−13997.4			−0.694179
$143$			17551.4i			0.858303i
$144$	−6589.41	+	24513.1i	−0.317776	+	1.18215i
$145$	−49335.3			−2.34651
$146$		−	19249.5i		−	0.903055i
$147$	40934.3	−	31383.8i	1.89432	−	1.45235i
$148$	−1211.24			−0.0552977
$149$			4538.71i			0.204437i	0.994762	+	0.102219i	$0.0325941\pi$
$149$			4538.71i			0.204437i	−0.994762	+	0.102219i	$0.967406\pi$
$150$	12950.1	+	16891.0i	0.575560	+	0.750710i
$151$	21114.9			0.926052			0.463026	−	0.886345i	$-0.346764\pi$
$151$	21114.9			0.926052			0.463026	+	0.886345i	$0.346764\pi$
$152$		−	19612.0i		−	0.848857i
$153$	13926.4	+	3743.60i	0.594918	+	0.159921i
$154$	−54356.8			−2.29199
$155$			8089.47i			0.336711i
$156$	−5223.24	+	4004.59i	−0.214630	+	0.164554i
$157$	35639.3			1.44587			0.722936	−	0.690915i	$-0.242792\pi$
$157$	35639.3			1.44587			0.722936	+	0.690915i	$0.242792\pi$
$158$			52285.4i			2.09443i
$159$	16841.1	+	21966.1i	0.666157	+	0.868877i
$160$	22494.0			0.878670
$161$		−	6211.38i		−	0.239627i
$162$	−15227.1	+	26276.3i	−0.580214	+	1.00123i
$163$	−9162.59			−0.344860			−0.172430	−	0.985022i	$-0.555162\pi$
$163$	−9162.59			−0.344860			−0.172430	+	0.985022i	$0.555162\pi$
$164$		−	1089.67i		−	0.0405144i
$165$	31347.0	−	24033.4i	1.15141	−	0.882769i
$166$	−43802.0			−1.58956
$167$			20236.1i			0.725593i	0.931868	+	0.362796i	$0.118178\pi$
$167$			20236.1i			0.725593i	−0.931868	+	0.362796i	$0.881822\pi$
$168$	24170.2	+	31525.5i	0.856371	+	1.11698i
$169$	−10394.9			−0.363954
$170$		−	27774.4i		−	0.961053i
$171$	8425.40	−	31343.1i	0.288137	−	1.07189i
$172$	16384.5			0.553829
$173$			385.341i			0.0128752i	0.999979	+	0.00643758i	$0.00204916\pi$
$173$			385.341i			0.0128752i	−0.999979	+	0.00643758i	$0.997951\pi$
$174$	−48394.7	+	37103.7i	−1.59845	+	1.22551i
$175$	46073.0			1.50442
$176$		−	40807.9i		−	1.31740i
$177$	−2481.65	−	3236.84i	−0.0792124	−	0.103318i
$178$	17140.4			0.540978
$179$		−	38311.8i		−	1.19571i	−0.801603	−	0.597857i	$-0.796019\pi$
$179$		−	38311.8i		−	1.19571i	0.801603	−	0.597857i	$-0.203981\pi$
$180$	14304.5	+	3845.22i	0.441497	+	0.118680i
$181$	10944.5			0.334071			0.167036	−	0.985951i	$-0.446581\pi$
$181$	10944.5			0.334071			0.167036	+	0.985951i	$0.446581\pi$
$182$			56260.5i			1.69848i
$183$	25156.7	−	19287.3i	0.751194	−	0.575931i
$184$	3371.32			0.0995781
$185$		−	7523.79i		−	0.219833i
$186$	6083.86	+	7935.25i	0.175854	+	0.229369i
$187$	−23183.9			−0.662985
$188$			13936.3i			0.394303i
$189$	25084.3	+	60766.4i	0.702229	+	1.70114i
$190$	−62509.6			−1.73157
$191$		−	7761.08i		−	0.212743i	−0.994326	−	0.106372i	$-0.966077\pi$
$191$		−	7761.08i		−	0.212743i	0.994326	−	0.106372i	$-0.0339233\pi$
$192$	−13746.6	+	10539.4i	−0.372901	+	0.285899i
$193$	−35665.8			−0.957497			−0.478749	−	0.877952i	$-0.658909\pi$
$193$	−35665.8			−0.957497			−0.478749	+	0.877952i	$0.658909\pi$
$194$		−	38627.4i		−	1.02634i
$195$	−24875.1	−	32444.9i	−0.654177	−	0.853251i
$196$	−31096.4			−0.809464
$197$		−	70264.2i		−	1.81051i	−0.424865	−	0.905257i	$-0.639679\pi$
$197$		−	70264.2i		−	1.81051i	0.424865	−	0.905257i	$-0.360321\pi$
$198$	12674.6	−	47150.4i	0.323299	−	1.20269i
$199$	13463.4			0.339978			0.169989	−	0.985446i	$-0.445627\pi$
$199$	13463.4			0.339978			0.169989	+	0.985446i	$0.445627\pi$
$200$			25006.8i			0.625170i
$201$	−36964.2	+	28340.0i	−0.914934	+	0.701468i
$202$	−82643.2			−2.02537
$203$			132005.i			3.20330i
$204$	−5289.72	−	6899.44i	−0.127108	−	0.165788i
$205$	6768.66			0.161063
$206$			63084.2i			1.48657i
$207$	5387.90	+	1448.33i	0.125741	+	0.0338009i
$208$	−42237.0			−0.976263
$209$			52178.1i			1.19453i
$210$	100482.	−	77038.1i	2.27850	−	1.74690i
$211$	39414.6			0.885303			0.442652	−	0.896694i	$-0.354038\pi$
$211$	39414.6			0.885303			0.442652	+	0.896694i	$0.354038\pi$
$212$		−	16686.9i		−	0.371282i
$213$	−16559.3	−	21598.4i	−0.364991	−	0.476062i
$214$	27491.3			0.600299
$215$			101774.i			2.20172i
$216$	−32981.9	+	13614.9i	−0.706916	+	0.291814i
$217$	21644.7			0.459656
$218$		−	87916.5i		−	1.84994i
$219$	29702.6	−	22772.6i	0.619307	−	0.474815i
$220$	−23813.3			−0.492010
$221$			23995.8i			0.491305i
$222$	−5658.42	−	7380.35i	−0.114813	−	0.149751i
$223$	47200.5			0.949154			0.474577	−	0.880214i	$-0.342601\pi$
$223$	47200.5			0.949154			0.474577	+	0.880214i	$0.342601\pi$
$224$		−	60186.3i		−	1.19950i
$225$	−10743.0	+	39964.8i	−0.212208	+	0.789428i
$226$	5627.12			0.110172
$227$		−	39356.4i		−	0.763772i	−0.924209	−	0.381886i	$-0.875275\pi$
$227$		−	39356.4i		−	0.763772i	0.924209	−	0.381886i	$-0.124725\pi$
$228$	−15528.0	+	11905.1i	−0.298707	+	0.229015i
$229$	46289.3			0.882693			0.441347	−	0.897337i	$-0.354501\pi$
$229$	46289.3			0.882693			0.441347	+	0.897337i	$0.354501\pi$
$230$		−	10745.5i		−	0.203128i
$231$	−64305.3	−	83874.2i	−1.20510	−	1.57183i
$232$	−71647.6			−1.33115
$233$		−	33537.3i		−	0.617754i	−0.951102	−	0.308877i	$-0.900047\pi$
$233$		−	33537.3i		−	0.617754i	0.951102	−	0.308877i	$-0.0999532\pi$
$234$	−48801.7	−	13118.5i	−0.891257	−	0.239581i
$235$	−86566.9			−1.56753
$236$			2458.92i			0.0441489i
$237$	−80677.9	+	61854.8i	−1.43634	+	1.10123i
$238$	−74315.1			−1.31197
$239$			49320.1i			0.863433i	0.902009	+	0.431716i	$0.142092\pi$
$239$			49320.1i			0.863433i	−0.902009	+	0.431716i	$0.857908\pi$
$240$	57835.7	+	75435.8i	1.00409	+	1.30965i
$241$	95764.7			1.64881			0.824406	−	0.565999i	$-0.191509\pi$
$241$	95764.7			1.64881			0.824406	+	0.565999i	$0.191509\pi$
$242$			10722.9i			0.183098i
$243$	−58559.2	+	7589.58i	−0.991706	+	0.128530i
$244$	−19110.7			−0.320994
$245$		−	193159.i		−	3.21798i
$246$	6639.62	−	5090.51i	0.109717	−	0.0841184i
$247$	54005.4			0.885205
$248$			11748.0i			0.191012i
$249$	−51818.7	−	67587.8i	−0.835773	−	1.09011i
$250$	−17799.0			−0.284784
$251$			54762.3i			0.869229i	0.900617	+	0.434614i	$0.143115\pi$
$251$			54762.3i			0.869229i	−0.900617	+	0.434614i	$0.856885\pi$
$252$	10288.5	−	38274.0i	0.162014	−	0.602703i
$253$	−8969.46			−0.140128
$254$		−	56065.1i		−	0.869011i
$255$	42856.8	−	32857.8i	0.659082	−	0.505310i
$256$	59872.0			0.913574
$257$			85189.9i			1.28980i	0.764267	+	0.644899i	$0.223101\pi$
$257$			85189.9i			1.28980i	−0.764267	+	0.644899i	$0.776899\pi$
$258$	76541.5	+	99834.1i	1.14989	+	1.49982i
$259$	−20131.1			−0.300102
$260$			24647.2i			0.364604i
$261$	−114504.	−	30780.1i	−1.68089	−	0.451845i
$262$	−34718.6			−0.505778
$263$		−	64508.2i		−	0.932617i	−0.884622	−	0.466309i	$-0.845584\pi$
$263$		−	64508.2i		−	0.932617i	0.884622	−	0.466309i	$-0.154416\pi$
$264$	45524.0	−	34902.7i	0.653179	−	0.500784i
$265$	103653.			1.47601
$266$			167255.i			2.36383i
$267$	20277.4	+	26448.1i	0.284440	+	0.370998i
$268$	28080.5			0.390962
$269$			11006.7i			0.152108i	0.997104	+	0.0760542i	$0.0242322\pi$
$269$			11006.7i			0.152108i	−0.997104	+	0.0760542i	$0.975768\pi$
$270$	43394.9	+	105124.i	0.595267	+	1.44202i
$271$	−2180.15			−0.0296858			−0.0148429	−	0.999890i	$-0.504725\pi$
$271$	−2180.15			−0.0296858			−0.0148429	+	0.999890i	$0.504725\pi$
$272$		−	55791.4i		−	0.754101i
$273$	−86811.6	+	66557.4i	−1.16480	+	0.893040i
$274$	91237.3			1.21527
$275$		−	66531.1i		−	0.879750i
$276$	−2046.50	−	2669.28i	−0.0268654	−	0.0350409i
$277$	−11249.7			−0.146615			−0.0733077	−	0.997309i	$-0.523356\pi$
$277$	−11249.7			−0.146615			−0.0733077	+	0.997309i	$0.523356\pi$
$278$		−	112795.i		−	1.45949i
$279$	−5046.99	+	18775.2i	−0.0648372	+	0.241199i
$280$	148761.			1.89747
$281$			83004.0i			1.05120i	0.850731	+	0.525601i	$0.176160\pi$
$281$			83004.0i			1.05120i	−0.850731	+	0.525601i	$0.823840\pi$
$282$	−84916.6	+	65104.5i	−1.06781	+	0.818677i
$283$	52296.8			0.652983			0.326492	−	0.945200i	$-0.394134\pi$
$283$	52296.8			0.652983			0.326492	+	0.945200i	$0.394134\pi$
$284$			16407.6i			0.203427i
$285$	−73950.3	−	96454.3i	−0.910437	−	1.18749i
$286$	81242.2			0.993229
$287$		−	18110.7i		−	0.219872i
$288$	52207.1	+	14033.9i	0.629425	+	0.169197i
$289$	51824.6			0.620498
$290$			228363.i			2.71538i
$291$	59603.2	−	45697.1i	0.703856	−	0.539638i
$292$	−22564.0			−0.264637
$293$		−	27668.3i		−	0.322290i	−0.986931	−	0.161145i	$-0.948481\pi$
$293$		−	27668.3i		−	0.322290i	0.986931	−	0.161145i	$-0.0515187\pi$
$294$	−145270.	−	189477.i	−1.68066	−	2.19211i
$295$	−15273.9			−0.175511
$296$		−	10926.5i		−	0.124709i
$297$	87748.9	−	36222.7i	0.994784	−	0.410646i
$298$	21008.8			0.236575
$299$			9283.58i			0.103842i
$300$	19799.4	−	15179.9i	0.219993	−	0.168666i
$301$	272314.			3.00564
$302$		−	97736.7i		−	1.07163i
$303$	−97768.7	−	127521.i	−1.06491	−	1.38898i
$304$	−125565.			−1.35869
$305$		−	118709.i		−	1.27609i
$306$	17328.4	−	64462.7i	0.185061	−	0.688440i
$307$	46064.3			0.488751			0.244376	−	0.969681i	$-0.421417\pi$
$307$	46064.3			0.488751			0.244376	+	0.969681i	$0.421417\pi$
$308$			63716.4i			0.671660i
$309$	−97340.9	+	74630.0i	−1.01948	+	0.781622i
$310$	37444.6			0.389642
$311$		−	4093.35i		−	0.0423212i	−0.999776	−	0.0211606i	$-0.993264\pi$
$311$		−	4093.35i		−	0.0423212i	0.999776	−	0.0211606i	$-0.00673613\pi$
$312$	−36125.0	−	47118.3i	−0.371107	−	0.484039i
$313$	38229.6			0.390221			0.195110	−	0.980781i	$-0.437493\pi$
$313$	38229.6			0.390221			0.195110	+	0.980781i	$0.437493\pi$
$314$		−	164967.i		−	1.67316i
$315$	237744.	+	63908.6i	2.39601	+	0.644078i
$316$	61288.2			0.613766
$317$			35832.0i			0.356577i	0.983978	+	0.178288i	$0.0570560\pi$
$317$			35832.0i			0.356577i	−0.983978	+	0.178288i	$0.942944\pi$
$318$	101677.	−	77954.2i	1.00547	−	0.770878i
$319$	190620.			1.87321
$320$			64867.1i			0.633468i
$321$	32522.8	+	42419.9i	0.315630	+	0.411680i
$322$	−28751.2			−0.277297
$323$			71336.5i			0.683764i
$324$	30800.8	+	17849.0i	0.293408	+	0.170030i
$325$	−68861.1			−0.651939
$326$			42411.8i			0.399073i
$327$	135658.	−	104007.i	1.26867	−	0.972676i
$328$	9829.83			0.0913689
$329$			231624.i			2.13989i
$330$	−111246.	−	145099.i	−1.02154	−	1.33241i
$331$	−50899.9			−0.464580			−0.232290	−	0.972647i	$-0.574622\pi$
$331$	−50899.9			−0.464580			−0.232290	+	0.972647i	$0.574622\pi$
$332$			51344.2i			0.465816i
$333$	4694.06	−	17462.2i	0.0423312	−	0.157475i
$334$	93668.7			0.839656
$335$			174426.i			1.55425i
$336$	201841.	−	154749.i	1.78785	−	1.37072i
$337$	−219364.			−1.93155			−0.965774	−	0.259384i	$-0.916481\pi$
$337$	−219364.			−1.93155			−0.965774	+	0.259384i	$0.916481\pi$
$338$			48115.9i			0.421168i
$339$	6657.01	+	8682.82i	0.0579269	+	0.0755547i
$340$	−32556.8			−0.281634
$341$		−	31255.8i		−	0.268795i
$342$	−145081.	−	38999.5i	−1.24039	−	0.333432i
$343$	−300311.			−2.55260
$344$			147803.i			1.24901i
$345$	16580.6	−	12712.1i	0.139303	−	0.106802i
$346$	1783.67			0.0148991
$347$		−	18664.6i		−	0.155010i	−0.996992	−	0.0775051i	$-0.975305\pi$
$347$		−	18664.6i		−	0.155010i	0.996992	−	0.0775051i	$-0.0246954\pi$
$348$	43492.4	+	56727.7i	0.359133	+	0.468421i
$349$	129387.			1.06228			0.531141	−	0.847284i	$-0.321763\pi$
$349$	129387.			1.06228			0.531141	+	0.847284i	$0.321763\pi$
$350$		−	213263.i		−	1.74092i
$351$	−37491.2	−	90821.9i	−0.304310	−	0.737185i
$352$	−86911.3			−0.701440
$353$			187137.i			1.50180i	0.660418	+	0.750898i	$0.270379\pi$
$353$			187137.i			1.50180i	−0.660418	+	0.750898i	$0.729621\pi$
$354$	−14982.7	+	11487.0i	−0.119559	+	0.0916647i
$355$	−101918.			−0.808712
$356$		−	20091.7i		−	0.158532i
$357$	−87916.5	−	114671.i	−0.689817	−	0.899737i
$358$	−177338.			−1.38368
$359$		−	11341.9i		−	0.0880030i	−0.999031	−	0.0440015i	$-0.985989\pi$
$359$		−	11341.9i		−	0.0880030i	0.999031	−	0.0440015i	$-0.0140106\pi$
$360$	−34687.3	+	129039.i	−0.267649	+	0.995673i
$361$	30230.0			0.231966
$362$		−	50660.0i		−	0.386588i
$363$	−16545.8	+	12685.5i	−0.125567	+	0.0962705i
$364$	65947.8			0.497734
$365$		−	140159.i		−	1.05205i
$366$	−89277.3	−	116446.i	−0.666468	−	0.869282i
$367$	−246051.			−1.82681			−0.913403	−	0.407055i	$-0.866556\pi$
$367$	−246051.			−1.82681			−0.913403	+	0.407055i	$0.866556\pi$
$368$		−	21584.7i		−	0.159386i
$369$	15709.6	+	4222.94i	0.115375	+	0.0310143i
$370$	−34826.1			−0.254391
$371$		−	277340.i		−	2.01495i
$372$	9301.60	−	7131.42i	0.0672158	−	0.0515336i
$373$	128003.			0.920032			0.460016	−	0.887911i	$-0.347844\pi$
$373$	128003.			0.920032			0.460016	+	0.887911i	$0.347844\pi$
$374$			107314.i			0.767207i
$375$	−21056.6	−	27464.4i	−0.149736	−	0.195302i
$376$	−125718.			−0.889242
$377$		−	197296.i		−	1.38814i
$378$	281276.	−	116110.i	1.96856	−	0.812620i
$379$	250015.			1.74055			0.870277	−	0.492563i	$-0.163940\pi$
$379$	250015.			1.74055			0.870277	+	0.492563i	$0.163940\pi$
$380$			73273.0i			0.507431i
$381$	86510.2	−	66326.3i	0.595960	−	0.456915i
$382$	−35924.5			−0.246187
$383$			218308.i			1.48823i	0.668049	+	0.744117i	$0.267130\pi$
$383$			218308.i			1.48823i	−0.668049	+	0.744117i	$0.732870\pi$
$384$	107260.	+	139901.i	0.727407	+	0.948765i
$385$	−395783.			−2.67015
$386$			165090.i			1.10802i
$387$	−63496.7	+	236212.i	−0.423964	+	1.57717i
$388$	−45278.5			−0.300766
$389$		−	114908.i		−	0.759365i	−0.925117	−	0.379683i	$-0.876033\pi$
$389$		−	114908.i		−	0.759365i	0.925117	−	0.379683i	$-0.123967\pi$
$390$	−150181.	+	115142.i	−0.987383	+	0.757014i
$391$	−12262.8			−0.0802113
$392$		−	280517.i		−	1.82552i
$393$	−41072.9	−	53571.9i	−0.265932	−	0.346858i
$394$	−325239.			−2.09513
$395$			380700.i			2.43999i
$396$	−55269.1	−	14857.0i	−0.352446	−	0.0947417i
$397$	−81107.2			−0.514610			−0.257305	−	0.966330i	$-0.582835\pi$
$397$	−81107.2			−0.514610			−0.257305	+	0.966330i	$0.582835\pi$
$398$		−	62319.7i		−	0.393422i
$399$	−258079.	+	197866.i	−1.62109	+	1.24287i
$400$	160105.			1.00066
$401$		−	92221.4i		−	0.573513i	−0.958004	−	0.286756i	$-0.907423\pi$
$401$		−	92221.4i		−	0.573513i	0.958004	−	0.286756i	$-0.0925770\pi$
$402$	131180.	+	171100.i	0.811740	+	1.05876i
$403$	−32350.4			−0.199191
$404$			96873.3i			0.593528i
$405$	−110872.	+	191323.i	−0.675944	+	1.16643i
$406$	611024.			3.70686
$407$			29070.1i			0.175492i
$408$	62239.1	−	47718.0i	0.373889	−	0.286656i
$409$	−184450.			−1.10264			−0.551319	−	0.834295i	$-0.685875\pi$
$409$	−184450.			−1.10264			−0.551319	+	0.834295i	$0.685875\pi$
$410$		−	31330.8i		−	0.186382i
$411$	107936.	+	140782.i	0.638972	+	0.833419i
$412$	73946.5			0.435636
$413$			40867.8i			0.239597i
$414$	6704.05	−	24939.5i	0.0391144	−	0.145508i
$415$	−318931.			−1.85183
$416$			89955.0i			0.519803i
$417$	174046.	−	133439.i	1.00091	−	0.767382i
$418$	241522.			1.38231
$419$		−	137728.i		−	0.784499i	−0.919859	−	0.392250i	$-0.871697\pi$
$419$		−	137728.i		−	0.784499i	0.919859	−	0.392250i	$-0.128303\pi$
$420$	−90303.1	−	117783.i	−0.511922	−	0.667706i
$421$	−208082.			−1.17401			−0.587003	−	0.809585i	$-0.699692\pi$
$421$	−208082.			−1.17401			−0.587003	+	0.809585i	$0.699692\pi$
$422$		−	182442.i		−	1.02447i
$423$	−200916.	−	54008.8i	−1.12288	−	0.301845i
$424$	150531.			0.837323
$425$		−	90959.4i		−	0.503582i
$426$	−99974.9	+	76649.5i	−0.550899	+	0.422367i
$427$	−317625.			−1.74204
$428$		−	32225.0i		−	0.175916i
$429$	96111.3	+	125359.i	0.522228	+	0.681148i
$430$	471093.			2.54783
$431$			182971.i			0.984981i	0.870318	+	0.492491i	$0.163913\pi$
$431$			182971.i			0.984981i	−0.870318	+	0.492491i	$0.836087\pi$
$432$	87168.8	+	211165.i	0.467083	+	1.13150i
$433$	−123677.			−0.659649			−0.329825	−	0.944042i	$-0.606990\pi$
$433$	−123677.			−0.659649			−0.329825	+	0.944042i	$0.606990\pi$
$434$		−	100189.i		−	0.531914i
$435$	−352372.	+	270159.i	−1.86218	+	1.42771i
$436$	−103055.			−0.542119
$437$			27598.8i			0.144520i
$438$	−105410.	−	137487.i	−0.549456	−	0.716663i
$439$	23268.2			0.120735			0.0603675	−	0.998176i	$-0.480773\pi$
$439$	23268.2			0.120735			0.0603675	+	0.998176i	$0.480773\pi$
$440$		−	214817.i		−	1.10959i
$441$	120511.	−	448311.i	0.619657	−	2.30516i
$442$	111072.			0.568539
$443$			207356.i			1.05660i	0.849059	+	0.528298i	$0.177170\pi$
$443$			207356.i			1.05660i	−0.849059	+	0.528298i	$0.822830\pi$
$444$	−8651.15	+	6632.73i	−0.0438842	+	0.0336455i
$445$	124802.			0.630235
$446$		−	218482.i		−	1.09836i
$447$	24853.9	+	32417.2i	0.124388	+	0.162241i
$448$	173563.			0.864770
$449$			269010.i			1.33437i	0.744892	+	0.667185i	$0.232501\pi$
$449$			269010.i			1.33437i	−0.744892	+	0.667185i	$0.767499\pi$
$450$	184989.	+	49727.4i	0.913527	+	0.245567i
$451$	−26152.5			−0.128576
$452$		−	6596.04i		−	0.0322854i
$453$	150811.	−	115625.i	0.734913	−	0.563449i
$454$	−182173.			−0.883838
$455$			409644.i			1.97872i
$456$	−107395.	−	140076.i	−0.516480	−	0.673652i
$457$	−265318.			−1.27038			−0.635190	−	0.772356i	$-0.719078\pi$
$457$	−265318.			−1.27038			−0.635190	+	0.772356i	$0.719078\pi$
$458$		−	214264.i		−	1.02145i
$459$	119968.	−	49522.6i	0.569429	−	0.235060i
$460$	−12595.7			−0.0595259
$461$		−	135910.i		−	0.639514i	−0.947500	−	0.319757i	$-0.896399\pi$
$461$		−	135910.i		−	0.639514i	0.947500	−	0.319757i	$-0.103601\pi$
$462$	−388237.	+	297657.i	−1.81892	+	1.39454i
$463$	−79162.9			−0.369283			−0.184642	−	0.982806i	$-0.559112\pi$
$463$	−79162.9			−0.369283			−0.184642	+	0.982806i	$0.559112\pi$
$464$			458721.i			2.13065i
$465$	44297.8	+	57778.1i	0.204869	+	0.267213i
$466$	−155237.			−0.714866
$467$			264929.i			1.21478i	0.794405	+	0.607388i	$0.207783\pi$
$467$			264929.i			1.21478i	−0.794405	+	0.607388i	$0.792217\pi$
$468$	−15377.3	+	57204.7i	−0.0702084	+	0.261180i
$469$	466705.			2.12176
$470$			400701.i			1.81395i
$471$	254550.	−	195160.i	1.14744	−	0.879729i
$472$	−22181.6			−0.0995656
$473$		−	393232.i		−	1.75762i
$474$	286314.	+	373442.i	1.27434	+	1.66214i
$475$	−204715.			−0.907323
$476$			87111.3i			0.384468i
$477$	240572.	+	64668.6i	1.05732	+	0.284221i
$478$	228293.			0.999165
$479$			256028.i			1.11588i	0.829883	+	0.557938i	$0.188407\pi$
$479$			256028.i			1.11588i	−0.829883	+	0.557938i	$0.811593\pi$
$480$	160661.	−	123176.i	0.697311	−	0.534620i
$481$	30088.2			0.130049
$482$		−	443276.i		−	1.90801i
$483$	−34013.4	−	44364.0i	−0.145799	−	0.190168i
$484$	12569.3			0.0536562
$485$		−	281254.i		−	1.19568i
$486$	35130.7	+	271059.i	0.148735	+	1.14760i
$487$	118044.			0.497720			0.248860	−	0.968540i	$-0.419944\pi$
$487$	118044.			0.497720			0.248860	+	0.968540i	$0.419944\pi$
$488$		−	172396.i		−	0.723913i
$489$	−65442.8	+	50174.2i	−0.273681	+	0.209827i
$490$	−894097.			−3.72385
$491$		−	262067.i		−	1.08705i	−0.839393	−	0.543525i	$-0.817089\pi$
$491$		−	262067.i		−	1.08705i	0.839393	−	0.543525i	$-0.182911\pi$
$492$	−5967.03	−	7782.87i	−0.0246506	−	0.0321521i
$493$	260610.			1.07225
$494$		−	249981.i		−	1.02436i
$495$	92286.4	−	343311.i	0.376641	−	1.40113i
$496$	75216.1			0.305737
$497$			272698.i			1.10400i
$498$	−312851.	+	239859.i	−1.26147	+	0.967157i
$499$	434790.			1.74614			0.873069	−	0.487597i	$-0.162127\pi$
$499$	434790.			1.74614			0.873069	+	0.487597i	$0.162127\pi$
$500$			20863.8i			0.0834551i
$501$	110812.	+	144534.i	0.441481	+	0.575829i
$502$	253484.			1.00587
$503$			40412.2i			0.159726i	0.996806	+	0.0798632i	$0.0254483\pi$
$503$			40412.2i			0.159726i	−0.996806	+	0.0798632i	$0.974552\pi$
$504$	345266.	+	92811.7i	1.35923	+	0.365378i
$505$	−601741.			−2.35954
$506$			41517.8i			0.162156i
$507$	−74244.3	+	56922.2i	−0.288833	+	0.221445i
$508$	−65718.8			−0.254661
$509$		−	8123.63i		−	0.0313556i	−0.999877	−	0.0156778i	$-0.995009\pi$
$509$		−	8123.63i		−	0.0313556i	0.999877	−	0.0156778i	$-0.00499060\pi$
$510$	−152092.	−	198376.i	−0.584745	−	0.762690i
$511$	−375020.			−1.43619
$512$			36263.6i			0.138335i
$513$	−111456.	−	270002.i	−0.423517	−	1.02596i
$514$	394327.			1.49256
$515$			459329.i			1.73185i
$516$	117024.	−	89721.0i	0.439518	−	0.336973i
$517$	334474.			1.25136
$518$			93183.1i			0.347278i
$519$	2110.12	+	2752.25i	0.00783378	+	0.0102177i
$520$	−222340.			−0.822264
$521$			349679.i			1.28823i	0.764928	+	0.644116i	$0.222774\pi$
$521$			349679.i			1.28823i	−0.764928	+	0.644116i	$0.777226\pi$
$522$	−142475.	+	530017.i	−0.522875	+	1.94513i
$523$	−33077.4			−0.120928			−0.0604641	−	0.998170i	$-0.519258\pi$
$523$	−33077.4			−0.120928			−0.0604641	+	0.998170i	$0.519258\pi$
$524$			40696.7i			0.148217i
$525$	329071.	−	252295.i	1.19391	−	0.915354i
$526$	−298596.			−1.07923
$527$		−	42732.0i		−	0.153862i
$528$	−223463.	−	291466.i	−0.801564	−	1.04549i
$529$	275097.			0.983047
$530$		−	479788.i		−	1.70804i
$531$	−35449.7	−	9529.33i	−0.125726	−	0.0337966i
$532$	196054.			0.692712
$533$			27068.4i			0.0952813i
$534$	122423.	−	93860.2i	0.429320	−	0.329154i
$535$	200170.			0.699344
$536$			253311.i			0.881707i
$537$	−209795.	−	273638.i	−0.727522	−	0.948916i
$538$	50947.9			0.176020
$539$			746321.i			2.56891i
$540$	123225.	−	50867.0i	0.422581	−	0.174441i
$541$	347488.			1.18726			0.593630	−	0.804738i	$-0.297694\pi$
$541$	347488.			1.18726			0.593630	+	0.804738i	$0.297694\pi$
$542$			10091.5i			0.0343524i
$543$	78169.9	−	59931.9i	0.265118	−	0.203263i
$544$	−118823.			−0.401515
$545$		−	640138.i		−	2.15516i
$546$	308081.	+	401834.i	1.03343	+	1.34791i
$547$	−115572.			−0.386260			−0.193130	−	0.981173i	$-0.561864\pi$
$547$	−115572.			−0.386260			−0.193130	+	0.981173i	$0.561864\pi$
$548$		−	106947.i		−	0.356130i
$549$	74061.9	−	275515.i	0.245726	−	0.914115i
$550$	−307959.			−1.01805
$551$		−	586533.i		−	1.93192i
$552$	24079.2	−	18461.3i	0.0790250	−	0.0605875i
$553$	1.01863e6			3.33092
$554$			52072.4i			0.169663i
$555$	−41200.1	−	53737.8i	−0.133756	−	0.174459i
$556$	−132217.			−0.427699
$557$		−	407655.i		−	1.31396i	−0.753908	−	0.656980i	$-0.771834\pi$
$557$		−	407655.i		−	1.31396i	0.753908	−	0.656980i	$-0.228166\pi$
$558$	86906.5	+	23361.5i	0.279115	+	0.0750297i
$559$	−407003.			−1.30249
$560$		−	952440.i		−	3.03712i
$561$	−165588.	+	126955.i	−0.526144	+	0.403388i
$562$	384209.			1.21645
$563$		−	169358.i		−	0.534304i	−0.963654	−	0.267152i	$-0.913917\pi$
$563$		−	169358.i		−	0.534304i	0.963654	−	0.267152i	$-0.0860826\pi$
$564$	76314.7	+	99538.1i	0.239911	+	0.312919i
$565$	40972.2			0.128349
$566$		−	242071.i		−	0.755633i
$567$	511917.	+	296656.i	1.59233	+	0.922755i
$568$	−148011.			−0.458773
$569$			304678.i			0.941057i	0.882385	+	0.470529i	$0.155937\pi$
$569$			304678.i			0.941057i	−0.882385	+	0.470529i	$0.844063\pi$
$570$	−446468.	+	342301.i	−1.37417	+	1.05356i
$571$	−451694.			−1.38539			−0.692695	−	0.721230i	$-0.743577\pi$
$571$	−451694.			−1.38539			−0.692695	+	0.721230i	$0.743577\pi$
$572$		−	95231.1i		−	0.291063i
$573$	−42499.5	−	55432.6i	−0.129442	−	0.168833i
$574$	−83830.7			−0.254436
$575$		−	35190.6i		−	0.106437i
$576$	−40470.4	+	150553.i	−0.121981	+	0.453778i
$577$	−459751.			−1.38093			−0.690464	−	0.723366i	$-0.742594\pi$
$577$	−459751.			−1.38093			−0.690464	+	0.723366i	$0.742594\pi$
$578$		−	239886.i		−	0.718041i
$579$	−254739.	+	195305.i	−0.759868	+	0.582582i
$580$	267685.			0.795733
$581$			853353.i			2.52800i
$582$	−211523.	−	275892.i	−0.624469	−	0.814503i
$583$	−400489.			−1.17829
$584$		−	203548.i		−	0.596816i
$585$	−355335.	−	95518.3i	−1.03831	−	0.279110i
$586$	−128071.			−0.372954
$587$		−	537822.i		−	1.56085i	−0.625247	−	0.780427i	$-0.715002\pi$
$587$		−	537822.i		−	1.56085i	0.625247	−	0.780427i	$-0.284998\pi$
$588$	−222102.	+	170283.i	−0.642390	+	0.492512i
$589$	−96173.4			−0.277220
$590$			70699.8i			0.203102i
$591$	−384765.	−	501854.i	−1.10159	−	1.43682i
$592$	−69956.4			−0.199611
$593$			87783.0i			0.249632i	0.992180	+	0.124816i	$0.0398341\pi$
$593$			87783.0i			0.249632i	−0.992180	+	0.124816i	$0.960166\pi$
$594$	−167668.	−	406172.i	−0.475200	−	1.15116i
$595$	−541103.			−1.52843
$596$		−	24626.2i		−	0.0693275i
$597$	96161.1	−	73725.6i	0.269806	−	0.206857i
$598$	42971.9			0.120166
$599$			10152.6i			0.0282960i	0.999900	+	0.0141480i	$0.00450361\pi$
$599$			10152.6i			0.0282960i	−0.999900	+	0.0141480i	$0.995496\pi$
$600$	136937.	+	178608.i	0.380380	+	0.496134i
$601$	537739.			1.48875			0.744376	−	0.667761i	$-0.232747\pi$
$601$	537739.			1.48875			0.744376	+	0.667761i	$0.232747\pi$
$602$		−	1.26049e6i		−	3.47813i
$603$	−108824.	+	404831.i	−0.299287	+	1.11337i
$604$	−114566.			−0.314037
$605$			78075.8i			0.213307i
$606$	−590269.	+	452552.i	−1.60733	+	1.23232i
$607$	334916.			0.908989			0.454494	−	0.890750i	$-0.349820\pi$
$607$	334916.			0.908989			0.454494	+	0.890750i	$0.349820\pi$
$608$			267424.i			0.723425i
$609$	722855.	+	942829.i	1.94902	+	2.54213i
$610$	−549479.			−1.47670
$611$		−	346188.i		−	0.927319i
$612$	−75562.4	−	20312.1i	−0.201745	−	0.0542316i
$613$	193709.			0.515500			0.257750	−	0.966212i	$-0.417019\pi$
$613$	193709.			0.515500			0.257750	+	0.966212i	$0.417019\pi$
$614$		−	213223.i		−	0.565584i
$615$	48344.4	−	37065.0i	0.127819	−	0.0979973i
$616$	−574779.			−1.51474
$617$		−	397810.i		−	1.04497i	−0.852647	−	0.522487i	$-0.825004\pi$
$617$		−	397810.i		−	1.04497i	0.852647	−	0.522487i	$-0.174996\pi$
$618$	345448.	+	450572.i	0.904494	+	1.17974i
$619$	−53881.4			−0.140624			−0.0703118	−	0.997525i	$-0.522399\pi$
$619$	−53881.4			−0.140624			−0.0703118	+	0.997525i	$0.522399\pi$
$620$		−	43892.1i		−	0.114183i
$621$	46413.5	−	19159.4i	0.120354	−	0.0496821i
$622$	−18947.3			−0.0489741
$623$		−	333929.i		−	0.860357i
$624$	−301673.	+	231289.i	−0.774761	+	0.593999i
$625$	−448916.			−1.14922
$626$		−	176957.i		−	0.451564i
$627$	285726.	+	372676.i	0.726800	+	0.947974i
$628$	−193373.			−0.490316
$629$			39743.8i			0.100454i
$630$	295820.	−	1.10047e6i	0.745327	−	2.77267i
$631$	742614.			1.86511			0.932555	−	0.361029i	$-0.117574\pi$
$631$	742614.			1.86511			0.932555	+	0.361029i	$0.117574\pi$
$632$			552875.i			1.38418i
$633$	281514.	−	215833.i	0.702575	−	0.538656i
$634$	165859.			0.412631
$635$		−	408221.i		−	1.01239i
$636$	−91377.0	−	119184.i	−0.225903	−	0.294648i
$637$	772458.			1.90369
$638$		−	882342.i		−	2.16768i
$639$	−236545.	−	63586.3i	−0.579312	−	0.155726i
$640$	660161.			1.61172
$641$		−	378409.i		−	0.920969i	−0.887668	−	0.460485i	$-0.847676\pi$
$641$		−	378409.i		−	0.920969i	0.887668	−	0.460485i	$-0.152324\pi$
$642$	196353.	−	150542.i	0.476396	−	0.365247i
$643$	809650.			1.95828			0.979141	−	0.203182i	$-0.0651284\pi$
$643$	809650.			1.95828			0.979141	+	0.203182i	$0.0651284\pi$
$644$			33701.8i			0.0812609i
$645$	557314.	+	726912.i	1.33962	+	1.74728i
$646$	330202.			0.791253
$647$		−	158470.i		−	0.378563i	−0.981923	−	0.189282i	$-0.939384\pi$
$647$		−	158470.i		−	0.378563i	0.981923	−	0.189282i	$-0.0606159\pi$
$648$	−161014.	+	277851.i	−0.383455	+	0.661700i
$649$	59014.6			0.140110
$650$			318744.i			0.754425i
$651$	154595.	−	118526.i	0.364782	−	0.279674i
$652$	49714.6			0.116947
$653$			145679.i			0.341641i	0.985302	+	0.170820i	$0.0546418\pi$
$653$			145679.i			0.341641i	−0.985302	+	0.170820i	$0.945358\pi$
$654$	−481429.	−	627934.i	−1.12558	−	1.46811i
$655$	−252793.			−0.589227
$656$		−	62935.2i		−	0.146247i
$657$	87445.0	−	325301.i	0.202584	−	0.753625i
$658$	1.07214e6			2.47629
$659$		−	288401.i		−	0.664088i	−0.943264	−	0.332044i	$-0.892262\pi$
$659$		−	288401.i		−	0.664088i	0.943264	−	0.332044i	$-0.107738\pi$
$660$	−170084.	+	130401.i	−0.390458	+	0.299359i
$661$	−292254.			−0.668894			−0.334447	−	0.942415i	$-0.608550\pi$
$661$	−292254.			−0.668894			−0.334447	+	0.942415i	$0.608550\pi$
$662$			235605.i			0.537612i
$663$	131401.	+	171388.i	0.298931	+	0.389899i
$664$	−463170.			−1.05052
$665$			1.21782e6i			2.75384i
$666$	−80829.3	−	21727.9i	−0.182230	−	0.0489857i
$667$	100826.			0.226631
$668$		−	109797.i		−	0.246059i
$669$	337124.	−	258469.i	0.753247	−	0.577505i
$670$	807382.			1.79858
$671$			458662.i			1.01870i
$672$	−329579.	−	429874.i	−0.729829	−	0.951925i
$673$	−65987.4			−0.145690			−0.0728452	−	0.997343i	$-0.523208\pi$
$673$	−65987.4			−0.145690			−0.0728452	+	0.997343i	$0.523208\pi$
$674$			1.01539e6i			2.23519i
$675$	142115.	+	344273.i	0.311913	+	0.755605i
$676$	56400.8			0.123422
$677$		−	556849.i		−	1.21496i	−0.794337	−	0.607478i	$-0.792181\pi$
$677$		−	556849.i		−	1.21496i	0.794337	−	0.607478i	$-0.207819\pi$
$678$	40191.1	−	30814.0i	0.0874320	−	0.0670330i
$679$	−752541.			−1.63226
$680$		−	293692.i		−	0.635147i
$681$	−215515.	−	281099.i	−0.464711	−	0.606129i
$682$	−144677.			−0.311050
$683$			726005.i			1.55632i	0.628068	+	0.778158i	$0.283846\pi$
$683$			726005.i			1.55632i	−0.628068	+	0.778158i	$0.716154\pi$
$684$	−45714.8	+	170062.i	−0.0977112	+	0.363492i
$685$	664317.			1.41577
$686$			1.39008e6i			2.95387i
$687$	330616.	−	253479.i	0.700504	−	0.537068i
$688$	946301.			1.99918
$689$			414515.i			0.873176i
$690$	−58841.9	−	76748.1i	−0.123591	−	0.161202i
$691$	−273276.			−0.572329			−0.286165	−	0.958180i	$-0.592380\pi$
$691$	−273276.			−0.572329			−0.286165	+	0.958180i	$0.592380\pi$
$692$		−	2090.79i		−	0.00436615i
$693$	−918587.	−	246927.i	−1.91273	−	0.514166i
$694$	−86394.9			−0.179378
$695$		−	821284.i		−	1.70029i
$696$	−511735.	+	392341.i	−1.05639	+	0.809925i
$697$	−35754.9			−0.0735987
$698$		−	598907.i		−	1.22927i
$699$	−183649.	−	239536.i	−0.375868	−	0.490249i
$700$	−249984.			−0.510171
$701$		−	122895.i		−	0.250090i	−0.992151	−	0.125045i	$-0.960092\pi$
$701$		−	122895.i		−	0.250090i	0.992151	−	0.125045i	$-0.0399076\pi$
$702$	−420397.	+	173540.i	−0.853071	+	0.352147i
$703$	89448.2			0.180993
$704$		−	250631.i		−	0.505696i
$705$	−618294.	+	474039.i	−1.24399	+	0.953752i
$706$	866222.			1.73788
$707$			1.61006e6i			3.22109i
$708$	13465.0	+	17562.5i	0.0268620	+	0.0350365i
$709$	−649498.			−1.29207			−0.646034	−	0.763309i	$-0.723574\pi$
$709$	−649498.			−1.29207			−0.646034	+	0.763309i	$0.723574\pi$
$710$			471758.i			0.935842i
$711$	−237518.	+	883581.i	−0.469847	+	1.74786i
$712$	181245.			0.357525
$713$		−	16532.3i		−	0.0325202i
$714$	−530787.	+	406948.i	−1.04118	+	0.798257i
$715$	591540.			1.15710
$716$			207873.i			0.405483i
$717$	270076.	+	352263.i	0.525349	+	0.685219i
$718$	−52499.5			−0.101837
$719$		−	531825.i		−	1.02875i	−0.857565	−	0.514376i	$-0.828023\pi$
$719$		−	531825.i		−	1.02875i	0.857565	−	0.514376i	$-0.171977\pi$
$720$	826169.	+	222084.i	1.59369	+	0.428404i
$721$	1.22901e6			2.36420
$722$		−	139929.i		−	0.268431i
$723$	683988.	−	524405.i	1.30849	−	1.00321i
$724$	−59383.0			−0.113288
$725$			747875.i			1.42283i
$726$	58718.5	+	76587.3i	0.111404	+	0.145306i
$727$	−549128.			−1.03897			−0.519487	−	0.854478i	$-0.673877\pi$
$727$	−549128.			−1.03897			−0.519487	+	0.854478i	$0.673877\pi$
$728$			594908.i			1.12250i
$729$	−376692.	+	374877.i	−0.708813	+	0.705397i
$730$	−648771.			−1.21743
$731$		−	537615.i		−	1.00609i
$732$	−136496.	+	104650.i	−0.254740	+	0.195306i
$733$	62572.4			0.116460			0.0582298	−	0.998303i	$-0.481454\pi$
$733$	62572.4			0.116460			0.0582298	+	0.998303i	$0.481454\pi$
$734$			1.13892e6i			2.11398i
$735$	−1.05774e6	−	1.37962e6i	−1.95795	−	2.55378i
$736$	−45970.4			−0.0848639
$737$		−	673939.i		−	1.24075i
$738$	19547.2	−	72716.8i	0.0358898	−	0.133512i
$739$	180670.			0.330823			0.165412	−	0.986225i	$-0.447105\pi$
$739$	180670.			0.330823			0.165412	+	0.986225i	$0.447105\pi$
$740$			40822.7i			0.0745485i
$741$	385728.	−	295733.i	0.702497	−	0.538596i
$742$	−1.28375e6			−2.33171
$743$			678464.i			1.22899i	0.788920	+	0.614497i	$0.210641\pi$
$743$			678464.i			1.22899i	−0.788920	+	0.614497i	$0.789359\pi$
$744$	64331.8	+	83908.7i	0.116220	+	0.151587i
$745$	152969.			0.275608
$746$		−	592502.i		−	1.06466i
$747$	−740219.	−	198980.i	−1.32654	−	0.356589i
$748$	125792.			0.224827
$749$		−	535587.i		−	0.954699i
$750$	−127127.	+	97466.9i	−0.226004	+	0.173275i
$751$	11030.3			0.0195572			0.00977858	−	0.999952i	$-0.496887\pi$
$751$	11030.3			0.0195572			0.00977858	+	0.999952i	$0.496887\pi$
$752$			804902.i			1.42334i
$753$	299877.	+	391133.i	0.528875	+	0.689819i
$754$	−913242.			−1.60636
$755$		−	711640.i		−	1.24844i
$756$	−136103.	−	329708.i	−0.238136	−	0.576880i
$757$	−248825.			−0.434213			−0.217106	−	0.976148i	$-0.569662\pi$
$757$	−248825.			−0.434213			−0.217106	+	0.976148i	$0.569662\pi$
$758$		−	1.15727e6i		−	2.01417i
$759$	−64063.3	+	49116.5i	−0.111205	+	0.0852598i
$760$	−660988.			−1.14437
$761$			29077.7i			0.0502100i	0.999685	+	0.0251050i	$0.00799201\pi$
$761$			29077.7i			0.0502100i	−0.999685	+	0.0251050i	$0.992008\pi$
$762$	−307011.	−	400439.i	−0.528743	−	0.689646i
$763$	−1.71279e6			−2.94209
$764$			42110.3i			0.0721442i
$765$	126171.	−	469366.i	0.215595	−	0.802026i
$766$	1.01050e6			1.72219
$767$		−	61081.4i		−	0.103829i
$768$	427629.	−	327858.i	0.725011	−	0.555857i
$769$	−85639.0			−0.144817			−0.0724084	−	0.997375i	$-0.523069\pi$
$769$	−85639.0			−0.144817			−0.0724084	+	0.997375i	$0.523069\pi$
$770$			1.83200e6i			3.08990i
$771$	466498.	+	608459.i	0.784768	+	1.02358i
$772$	193516.			0.324701
$773$		−	380679.i		−	0.637089i	−0.947908	−	0.318544i	$-0.896806\pi$
$773$		−	380679.i		−	0.637089i	0.947908	−	0.318544i	$-0.103194\pi$
$774$	1.09338e6	+	293914.i	1.82511	+	0.490612i
$775$	122628.			0.204168
$776$		−	408453.i		−	0.678295i
$777$	−143784.	+	110238.i	−0.238160	+	0.182595i
$778$	−531886.			−0.878738
$779$			80470.6i			0.132606i
$780$	134968.	+	176040.i	0.221841	+	0.289349i
$781$	393787.			0.645593
$782$			56762.1i			0.0928206i
$783$	−986384.	+	407179.i	−1.60888	+	0.664143i
$784$	−1.79600e6			−2.92196
$785$		−	1.20116e6i		−	1.94922i
$786$	−247974.	+	190118.i	−0.401385	+	0.307737i
$787$	−408153.			−0.658983			−0.329491	−	0.944159i	$-0.606877\pi$
$787$	−408153.			−0.658983			−0.329491	+	0.944159i	$0.606877\pi$
$788$			381241.i			0.613970i
$789$	−353246.	−	460743.i	−0.567444	−	0.740124i
$790$	1.76219e6			2.82356
$791$		−	109628.i		−	0.175214i
$792$	134024.	−	498577.i	0.213664	−	0.794844i
$793$	474725.			0.754911
$794$			375429.i			0.595508i
$795$	740328.	−	567600.i	1.17136	−	0.898066i
$796$	−73050.3			−0.115291
$797$		−	921058.i		−	1.45001i	−0.688745	−	0.725004i	$-0.741838\pi$
$797$		−	921058.i		−	1.45001i	0.688745	−	0.725004i	$-0.258162\pi$
$798$	915884.	+	1.19460e6i	1.43825	+	1.87593i
$799$	457283.			0.716295
$800$		−	340986.i		−	0.532791i
$801$	289658.	+	77863.8i	0.451462	+	0.121359i
$802$	−426875.			−0.663669
$803$			541543.i			0.839850i
$804$	200561.	−	153768.i	0.310267	−	0.237878i
$805$	−209343.			−0.323048
$806$			149744.i			0.230504i
$807$	60272.5	+	78614.2i	0.0925491	+	0.120713i
$808$	−873883.			−1.33854
$809$		−	770817.i		−	1.17775i	−0.808223	−	0.588876i	$-0.799570\pi$
$809$		−	770817.i		−	1.17775i	0.808223	−	0.588876i	$-0.200430\pi$
$810$	885598.	+	513203.i	1.34979	+	0.782203i
$811$	−107089.			−0.162818			−0.0814088	−	0.996681i	$-0.525942\pi$
$811$	−107089.			−0.162818			−0.0814088	+	0.996681i	$0.525942\pi$
$812$		−	716235.i		−	1.08628i
$813$	−15571.5	+	11938.5i	−0.0235586	+	0.0180621i
$814$	134560.			0.203080
$815$			308809.i			0.464916i
$816$	−305513.	−	398484.i	−0.458827	−	0.598454i
$817$	−1.20997e6			−1.81271
$818$			853784.i			1.27597i
$819$	−255575.	+	950757.i	−0.381023	+	1.41743i
$820$	−36725.5			−0.0546186
$821$			590121.i			0.875498i	0.899097	+	0.437749i	$0.144224\pi$
$821$			590121.i			0.875498i	−0.899097	+	0.437749i	$0.855776\pi$
$822$	651652.	−	499613.i	0.964433	−	0.739419i
$823$	797252.			1.17705			0.588526	−	0.808478i	$-0.299708\pi$
$823$	797252.			1.17705			0.588526	+	0.808478i	$0.299708\pi$
$824$			667064.i			0.982456i
$825$	−364323.	−	475190.i	−0.535277	−	0.698168i
$826$	189169.			0.277262
$827$		−	684278.i		−	1.00051i	−0.865878	−	0.500255i	$-0.833240\pi$
$827$		−	684278.i		−	1.00051i	0.865878	−	0.500255i	$-0.166760\pi$
$828$	−29233.8	−	7858.40i	−0.0426407	−	0.0114623i
$829$	−905345.			−1.31736			−0.658681	−	0.752422i	$-0.728885\pi$
$829$	−905345.			−1.31736			−0.658681	+	0.752422i	$0.728885\pi$
$830$			1.47627e6i			2.14294i
$831$	−80349.3	+	61602.8i	−0.116354	+	0.0892070i
$832$	−259409.			−0.374747
$833$			1.02035e6i			1.47048i
$834$	−617664.	−	805627.i	−0.888015	−	1.15825i
$835$	682020.			0.978193
$836$		−	283109.i		−	0.405081i
$837$	66764.8	+	161737.i	0.0953008	+	0.230865i
$838$	−637514.			−0.907824
$839$			403317.i			0.572958i	0.958087	+	0.286479i	$0.0924849\pi$
$839$			403317.i			0.572958i	−0.958087	+	0.286479i	$0.907515\pi$
$840$	1.06251e6	−	814614.i	1.50583	−	1.15450i
$841$	−1.43547e6			−2.02957
$842$			963171.i			1.35856i
$843$	454528.	+	592847.i	0.639596	+	0.834233i
$844$	−213857.			−0.300219
$845$			350341.i			0.490657i
$846$	−249996.	+	930003.i	−0.349295	+	1.29940i
$847$	208905.			0.291193
$848$		−	963766.i		−	1.34023i
$849$	373524.	−	286376.i	0.518206	−	0.397302i
$850$	−421033.			−0.582745
$851$			15376.2i			0.0212320i
$852$	89847.6	+	117189.i	0.123773	+	0.161439i
$853$	25096.7			0.0344920			0.0172460	−	0.999851i	$-0.494510\pi$
$853$	25096.7			0.0344920			0.0172460	+	0.999851i	$0.494510\pi$
$854$			1.47022e6i			2.01589i
$855$	−1.05636e6	−	283963.i	−1.44504	−	0.388445i
$856$	290698.			0.396729
$857$		−	1.38432e6i		−	1.88485i	−0.334422	−	0.942423i	$-0.608541\pi$
$857$		−	1.38432e6i		−	1.88485i	0.334422	−	0.942423i	$-0.391459\pi$
$858$	580263.	−	444880.i	0.788225	−	0.604322i
$859$	238678.			0.323464			0.161732	−	0.986835i	$-0.448292\pi$
$859$	238678.			0.323464			0.161732	+	0.986835i	$0.448292\pi$
$860$		−	552210.i		−	0.746633i
$861$	−99173.6	−	129353.i	−0.133780	−	0.174490i
$862$	846937.			1.13982
$863$			643128.i			0.863527i	0.901987	+	0.431763i	$0.142108\pi$
$863$			643128.i			0.863527i	−0.901987	+	0.431763i	$0.857892\pi$
$864$	449732.	−	185649.i	0.602458	−	0.248694i
$865$	12987.2			0.0173574
$866$			572477.i			0.763347i
$867$	370151.	−	283790.i	0.492426	−	0.377537i
$868$	−117440.			−0.155876
$869$		−	1.47093e6i		−	1.94784i
$870$	1.25051e6	+	1.63106e6i	1.65215	+	2.15492i
$871$	−697541.			−0.919461
$872$		−	929645.i		−	1.22260i
$873$	175473.	−	652772.i	0.230241	−	0.856511i
$874$	127750.			0.167239
$875$			346761.i			0.452912i
$876$	−161161.	+	123560.i	−0.210016	+	0.161016i
$877$	959743.			1.24783			0.623916	−	0.781492i	$-0.285541\pi$
$877$	959743.			1.24783			0.623916	+	0.781492i	$0.285541\pi$
$878$		−	107704.i		−	0.139715i
$879$	−151511.	−	197617.i	−0.196095	−	0.255769i
$880$	−1.37536e6			−1.77603
$881$			189085.i			0.243615i	0.992554	+	0.121808i	$0.0388691\pi$
$881$			189085.i			0.243615i	−0.992554	+	0.121808i	$0.961131\pi$
$882$	−2.07514e6	−	557824.i	−2.66754	−	0.717067i
$883$	−546610.			−0.701061			−0.350531	−	0.936551i	$-0.613999\pi$
$883$	−546610.			−0.701061			−0.350531	+	0.936551i	$0.613999\pi$
$884$		−	130197.i		−	0.166609i
$885$	−109092.	+	83639.5i	−0.139286	+	0.106789i
$886$	959809.			1.22269
$887$			507730.i			0.645335i	0.946512	+	0.322668i	$0.104580\pi$
$887$			507730.i			0.645335i	−0.946512	+	0.322668i	$0.895420\pi$
$888$	−59833.1	−	78041.1i	−0.0758780	−	0.0989686i
$889$	−1.09226e6			−1.38205
$890$		−	577686.i		−	0.729309i
$891$	428382.	−	739227.i	0.539604	−	0.931156i
$892$	−256102.			−0.321872
$893$		−	1.02917e6i		−	1.29058i
$894$	150053.	−	115044.i	0.187745	−	0.143942i
$895$	−1.29123e6			−1.61198
$896$		−	1.76637e6i		−	2.20022i
$897$	50836.7	+	66306.9i	0.0631818	+	0.0824088i
$898$	1.24520e6			1.54413
$899$			351346.i			0.434726i
$900$	58289.8	−	216842.i	0.0719627	−	0.267706i
$901$	−547538.			−0.674473
$902$			121055.i			0.148788i
$903$	1.94497e6	−	1.49119e6i	2.38527	−	1.82876i
$904$	59502.2			0.0728109
$905$		−	368865.i		−	0.450371i
$906$	−535204.	−	698073.i	−0.652023	−	0.850442i
$907$	988484.			1.20159			0.600793	−	0.799404i	$-0.294851\pi$
$907$	988484.			1.20159			0.600793	+	0.799404i	$0.294851\pi$
$908$			213541.i			0.259006i
$909$	−1.39660e6	−	375424.i	−1.69023	−	0.454354i
$910$	1.89616e6			2.28977
$911$		−	241299.i		−	0.290750i	−0.989377	−	0.145375i	$-0.953561\pi$
$911$		−	241299.i		−	0.290750i	0.989377	−	0.145375i	$-0.0464388\pi$
$912$	−896834.	+	687592.i	−1.07826	+	0.826687i
$913$	1.23227e6			1.47831
$914$			1.22810e6i			1.47009i
$915$	−650046.	−	847863.i	−0.776429	−	1.01271i
$916$	−251158.			−0.299334
$917$			676390.i			0.804375i
$918$	−229231.	−	555308.i	−0.272011	−	0.658944i
$919$	754769.			0.893682			0.446841	−	0.894613i	$-0.352549\pi$
$919$	754769.			0.893682			0.446841	+	0.894613i	$0.352549\pi$
$920$		−	113624.i		−	0.134244i
$921$	329009.	−	252247.i	0.387872	−	0.297377i
$922$	−629101.			−0.740046
$923$		−	407577.i		−	0.478417i
$924$	348909.	+	455087.i	0.408666	+	0.533028i
$925$	−114053.			−0.133298
$926$			366430.i			0.427335i
$927$	−286574.	+	1.06607e6i	−0.333485	+	1.24059i
$928$	976968.			1.13445
$929$			642720.i			0.744716i	0.928089	+	0.372358i	$0.121451\pi$
$929$			642720.i			0.744716i	−0.928089	+	0.372358i	$0.878549\pi$
$930$	267444.	−	205046.i	0.309219	−	0.237074i
$931$	2.29642e6			2.64942
$932$			181967.i			0.209489i
$933$	−22415.1	−	29236.3i	−0.0257500	−	0.0335860i
$934$	1.22631e6			1.40574
$935$			781373.i			0.893789i
$936$	−516038.	−	138717.i	−0.589019	−	0.158336i
$937$	1.17137e6			1.33418			0.667089	−	0.744978i	$-0.267540\pi$
$937$	1.17137e6			1.33418			0.667089	+	0.744978i	$0.267540\pi$
$938$		−	2.16028e6i		−	2.45530i
$939$	273050.	−	209344.i	0.309679	−	0.237427i
$940$	469697.			0.531572
$941$			415284.i			0.468992i	0.972117	+	0.234496i	$0.0753441\pi$
$941$			415284.i			0.468992i	−0.972117	+	0.234496i	$0.924656\pi$
$942$	−903358.	−	1.17826e6i	−1.01802	−	1.32782i
$943$	−13833.0			−0.0155558
$944$			142017.i			0.159366i
$945$	2.04802e6	−	845422.i	2.29335	−	0.946695i
$946$	−1.82019e6			−2.03393
$947$			1.49323e6i			1.66505i	0.553986	+	0.832526i	$0.313106\pi$
$947$			1.49323e6i			1.66505i	−0.553986	+	0.832526i	$0.686894\pi$
$948$	437744.	−	335613.i	0.487084	−	0.373441i
$949$	560508.			0.622371
$950$			947585.i			1.04996i
$951$	196215.	+	255926.i	0.216956	+	0.282979i
$952$	−785821.			−0.867062
$953$		−	200448.i		−	0.220707i	−0.993892	−	0.110353i	$-0.964802\pi$
$953$		−	200448.i		−	0.220707i	0.993892	−	0.110353i	$-0.0351982\pi$
$954$	299338.	−	1.11356e6i	0.328901	−	1.22353i
$955$	−261574.			−0.286805
$956$		−	267602.i		−	0.292802i
$957$	1.36148e6	−	1.04383e6i	1.48658	−	1.13974i
$958$	1.18510e6			1.29129
$959$		−	1.77749e6i		−	1.93272i
$960$	355211.	+	463306.i	0.385429	+	0.502719i
$961$	−865911.			−0.937619
$962$		−	139272.i		−	0.150492i
$963$	464581.	+	124885.i	0.500967	+	0.134666i
$964$	−519602.			−0.559135
$965$			1.20205e6i			1.29083i
$966$	−205352.	+	157441.i	−0.220062	+	0.168719i
$967$	−1.09646e6			−1.17257			−0.586286	−	0.810104i	$-0.699411\pi$
$967$	−1.09646e6			−1.17257			−0.586286	+	0.810104i	$0.699411\pi$
$968$			113386.i			0.121007i
$969$	390637.	+	509512.i	0.416031	+	0.542634i
$970$	−1.30187e6			−1.38364
$971$			138690.i			0.147098i	0.997292	+	0.0735489i	$0.0234325\pi$
$971$			138690.i			0.147098i	−0.997292	+	0.0735489i	$0.976568\pi$
$972$	317732.	−	41179.7i	0.336301	−	0.0435864i
$973$	−2.19748e6			−2.32113
$974$		−	546401.i		−	0.575962i
$975$	−491832.	+	377082.i	−0.517378	+	0.396667i
$976$	−1.10376e6			−1.15871
$977$			1.57902e6i			1.65424i	0.562024	+	0.827121i	$0.310023\pi$
$977$			1.57902e6i			1.65424i	−0.562024	+	0.827121i	$0.689977\pi$
$978$	232246.	+	302922.i	0.242813	+	0.316703i
$979$	−482206.			−0.503115
$980$			1.04805e6i			1.09126i
$981$	399380.	−	1.48572e6i	0.415000	−	1.54383i
$982$	−1.21306e6			−1.25794
$983$			1.35450e6i			1.40176i	0.713280	+	0.700879i	$0.247209\pi$
$983$			1.35450e6i			1.40176i	−0.713280	+	0.700879i	$0.752791\pi$
$984$	70208.5	−	53828.0i	0.0725102	−	0.0555927i
$985$	−2.36813e6			−2.44081
$986$		−	1.20631e6i		−	1.24081i
$987$	1.26837e6	+	1.65435e6i	1.30200	+	1.69822i
$988$	−293024.			−0.300185
$989$		−	207994.i		−	0.212647i
$990$	−1.58912e6	−	427175.i	−1.62139	−	0.435849i
$991$	−464718.			−0.473198			−0.236599	−	0.971607i	$-0.576033\pi$
$991$	−464718.			−0.473198			−0.236599	+	0.971607i	$0.576033\pi$
$992$		−	160193.i		−	0.162787i
$993$	−363546.	+	278726.i	−0.368690	+	0.282670i
$994$	1.26227e6			1.27755
$995$		−	453762.i		−	0.458334i
$996$	281159.	+	366720.i	0.283422	+	0.369671i
$997$	1.89045e6			1.90184			0.950920	−	0.309438i	$-0.100141\pi$
$997$	1.89045e6			1.90184			0.950920	+	0.309438i	$0.100141\pi$
$998$		−	2.01256e6i		−	2.02063i
$999$	−62096.0	−	150427.i	−0.0622204	−	0.150728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.19	✓	78
3.2	odd	2	inner	177.5.b.a.119.60	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.19	✓	78	1.1	even	1	trivial
177.5.b.a.119.60	yes	78	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} +O(q^{10})\)	\(q-4.62880i q^{2} +(7.14239 - 5.47598i) q^{3} -5.42582 q^{4} -33.7032i q^{5} +(-25.3472 - 33.0607i) q^{6} -90.1786 q^{7} -48.9458i q^{8} +(21.0273 - 78.2231i) q^{9} -156.006 q^{10} +130.221i q^{11} +(-38.7533 + 29.7117i) q^{12} +134.782 q^{13} +417.419i q^{14} +(-184.558 - 240.721i) q^{15} -313.374 q^{16} +178.035i q^{17} +(-362.079 - 97.3314i) q^{18} +400.688 q^{19} +182.868i q^{20} +(-644.090 + 493.816i) q^{21} +602.768 q^{22} +68.8786i q^{23} +(-268.026 - 349.590i) q^{24} -510.908 q^{25} -623.878i q^{26} +(-278.163 - 673.845i) q^{27} +489.293 q^{28} -1463.81i q^{29} +(-1114.25 + 854.284i) q^{30} -240.021 q^{31} +667.412i q^{32} +(713.089 + 930.090i) q^{33} +824.088 q^{34} +3039.31i q^{35} +(-114.091 + 424.425i) q^{36} +223.236 q^{37} -1854.71i q^{38} +(962.663 - 738.062i) q^{39} -1649.63 q^{40} +200.831i q^{41} +(2285.78 + 2981.37i) q^{42} -3019.72 q^{43} -706.558i q^{44} +(-2636.37 - 708.689i) q^{45} +318.826 q^{46} -2568.51i q^{47} +(-2238.24 + 1716.03i) q^{48} +5731.18 q^{49} +2364.89i q^{50} +(974.915 + 1271.59i) q^{51} -731.302 q^{52} +3075.45i q^{53} +(-3119.09 + 1287.56i) q^{54} +4388.88 q^{55} +4413.86i q^{56} +(2861.87 - 2194.16i) q^{57} -6775.71 q^{58} -453.188i q^{59} +(1001.38 + 1306.11i) q^{60} +3522.17 q^{61} +1111.01i q^{62} +(-1896.22 + 7054.05i) q^{63} -1924.66 q^{64} -4542.58i q^{65} +(4305.20 - 3300.75i) q^{66} -5175.34 q^{67} -965.986i q^{68} +(377.178 + 491.957i) q^{69} +14068.4 q^{70} -3023.98i q^{71} +(-3828.69 - 1029.20i) q^{72} +4158.64 q^{73} -1033.32i q^{74} +(-3649.10 + 2797.72i) q^{75} -2174.06 q^{76} -11743.2i q^{77} +(-3416.34 - 4455.98i) q^{78} -11295.7 q^{79} +10561.7i q^{80} +(-5676.70 - 3289.65i) q^{81} +929.608 q^{82} -9462.92i q^{83} +(3494.72 - 2679.36i) q^{84} +6000.35 q^{85} +13977.7i q^{86} +(-8015.82 - 10455.1i) q^{87} +6373.78 q^{88} +3702.98i q^{89} +(-3280.38 + 12203.2i) q^{90} -12154.4 q^{91} -373.723i q^{92} +(-1714.32 + 1314.35i) q^{93} -11889.1 q^{94} -13504.5i q^{95} +(3654.74 + 4766.92i) q^{96} +8345.01 q^{97} -26528.5i q^{98} +(10186.3 + 2738.20i) 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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