LMFDB - Embedded newform 177.5.b.a.119.43

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			119.43
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.16718i q^{2} +(-7.53898 - 4.91567i) q^{3} +14.6377 q^{4} -22.4730i q^{5} +(5.73747 - 8.79934i) q^{6} -87.0284 q^{7} +35.7597i q^{8} +(32.6723 + 74.1183i) q^{9} +O(q^{10})$	\(q+1.16718i q^{2} +(-7.53898 - 4.91567i) q^{3} +14.6377 q^{4} -22.4730i q^{5} +(5.73747 - 8.79934i) q^{6} -87.0284 q^{7} +35.7597i q^{8} +(32.6723 + 74.1183i) q^{9} +26.2301 q^{10} +176.627i q^{11} +(-110.353 - 71.9541i) q^{12} -62.6893 q^{13} -101.578i q^{14} +(-110.470 + 169.424i) q^{15} +192.465 q^{16} -275.299i q^{17} +(-86.5093 + 38.1345i) q^{18} +639.203 q^{19} -328.954i q^{20} +(656.105 + 427.803i) q^{21} -206.156 q^{22} +459.067i q^{23} +(175.783 - 269.591i) q^{24} +119.962 q^{25} -73.1696i q^{26} +(118.025 - 719.382i) q^{27} -1273.89 q^{28} +559.739i q^{29} +(-197.748 - 128.938i) q^{30} +111.553 q^{31} +796.796i q^{32} +(868.242 - 1331.59i) q^{33} +321.323 q^{34} +1955.79i q^{35} +(478.248 + 1084.92i) q^{36} -238.912 q^{37} +746.064i q^{38} +(472.613 + 308.160i) q^{39} +803.629 q^{40} +1876.01i q^{41} +(-499.323 + 765.792i) q^{42} +1854.78 q^{43} +2585.42i q^{44} +(1665.66 - 734.247i) q^{45} -535.814 q^{46} +2042.58i q^{47} +(-1450.99 - 946.095i) q^{48} +5172.94 q^{49} +140.017i q^{50} +(-1353.28 + 2075.47i) q^{51} -917.626 q^{52} -243.223i q^{53} +(839.648 + 137.757i) q^{54} +3969.35 q^{55} -3112.11i q^{56} +(-4818.93 - 3142.11i) q^{57} -653.316 q^{58} +453.188i q^{59} +(-1617.03 + 2479.97i) q^{60} -4627.99 q^{61} +130.202i q^{62} +(-2843.42 - 6450.39i) q^{63} +2149.44 q^{64} +1408.82i q^{65} +(1554.20 + 1013.39i) q^{66} -5993.39 q^{67} -4029.74i q^{68} +(2256.63 - 3460.90i) q^{69} -2282.76 q^{70} +8085.89i q^{71} +(-2650.45 + 1168.35i) q^{72} +321.074 q^{73} -278.853i q^{74} +(-904.391 - 589.694i) q^{75} +9356.45 q^{76} -15371.6i q^{77} +(-359.678 + 551.624i) q^{78} -105.206 q^{79} -4325.28i q^{80} +(-4426.04 + 4843.23i) q^{81} -2189.64 q^{82} +12472.9i q^{83} +(9603.86 + 6262.05i) q^{84} -6186.81 q^{85} +2164.86i q^{86} +(2751.50 - 4219.86i) q^{87} -6316.13 q^{88} -4819.17i q^{89} +(856.998 + 1944.13i) q^{90} +5455.75 q^{91} +6719.69i q^{92} +(-840.994 - 548.357i) q^{93} -2384.05 q^{94} -14364.8i q^{95} +(3916.79 - 6007.03i) q^{96} -6900.62 q^{97} +6037.75i q^{98} +(-13091.3 + 5770.82i) 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 $

$2$			1.16718i			0.291795i	0.989300	+	0.145897i	$0.0466069\pi$
$2$			1.16718i			0.291795i	−0.989300	+	0.145897i	$0.953393\pi$
$3$	−7.53898	−	4.91567i	−0.837664	−	0.546186i
$3$	−7.53898	−	4.91567i	−0.837664	−	0.546186i
$4$	14.6377			0.914856
$5$		−	22.4730i		−	0.898922i	−0.893300	−	0.449461i	$-0.851616\pi$
$5$		−	22.4730i		−	0.898922i	0.893300	−	0.449461i	$-0.148384\pi$
$6$	5.73747	−	8.79934i	0.159374	−	0.244426i
$7$	−87.0284			−1.77609			−0.888045	−	0.459757i	$-0.847936\pi$
$7$	−87.0284			−1.77609			−0.888045	+	0.459757i	$0.847936\pi$
$8$			35.7597i			0.558745i
$9$	32.6723	+	74.1183i	0.403362	+	0.915040i
$10$	26.2301			0.262301
$11$			176.627i			1.45973i	0.683592	+	0.729865i	$0.260417\pi$
$11$			176.627i			1.45973i	−0.683592	+	0.729865i	$0.739583\pi$
$12$	−110.353	−	71.9541i	−0.766342	−	0.499681i
$13$	−62.6893			−0.370942			−0.185471	−	0.982650i	$-0.559381\pi$
$13$	−62.6893			−0.370942			−0.185471	+	0.982650i	$0.559381\pi$
$14$		−	101.578i		−	0.518254i
$15$	−110.470	+	169.424i	−0.490978	+	0.752995i
$16$	192.465			0.751817
$17$		−	275.299i		−	0.952592i	−0.879285	−	0.476296i	$-0.841979\pi$
$17$		−	275.299i		−	0.952592i	0.879285	−	0.476296i	$-0.158021\pi$
$18$	−86.5093	+	38.1345i	−0.267004	+	0.117699i
$19$	639.203			1.77064			0.885322	−	0.464978i	$-0.153938\pi$
$19$	639.203			1.77064			0.885322	+	0.464978i	$0.153938\pi$
$20$		−	328.954i		−	0.822384i
$21$	656.105	+	427.803i	1.48777	+	0.970075i
$22$	−206.156			−0.425941
$23$			459.067i			0.867802i	0.900960	+	0.433901i	$0.142863\pi$
$23$			459.067i			0.867802i	−0.900960	+	0.433901i	$0.857137\pi$
$24$	175.783	−	269.591i	0.305179	−	0.468041i
$25$	119.962			0.191939
$26$		−	73.1696i		−	0.108239i
$27$	118.025	−	719.382i	0.161900	−	0.986807i
$28$	−1273.89			−1.62487
$29$			559.739i			0.665564i	0.943004	+	0.332782i	$0.107987\pi$
$29$			559.739i			0.665564i	−0.943004	+	0.332782i	$0.892013\pi$
$30$	−197.748	−	128.938i	−0.219720	−	0.143265i
$31$	111.553			0.116080			0.0580400	−	0.998314i	$-0.481515\pi$
$31$	111.553			0.116080			0.0580400	+	0.998314i	$0.481515\pi$
$32$			796.796i			0.778121i
$33$	868.242	−	1331.59i	0.797283	−	1.22276i
$34$	321.323			0.277961
$35$			1955.79i			1.59657i
$36$	478.248	+	1084.92i	0.369018	+	0.837130i
$37$	−238.912			−0.174516			−0.0872579	−	0.996186i	$-0.527810\pi$
$37$	−238.912			−0.174516			−0.0872579	+	0.996186i	$0.527810\pi$
$38$			746.064i			0.516665i
$39$	472.613	+	308.160i	0.310725	+	0.202604i
$40$	803.629			0.502268
$41$			1876.01i			1.11601i	0.829838	+	0.558004i	$0.188433\pi$
$41$			1876.01i			1.11601i	−0.829838	+	0.558004i	$0.811567\pi$
$42$	−499.323	+	765.792i	−0.283063	+	0.434122i
$43$	1854.78			1.00313			0.501563	−	0.865121i	$-0.332759\pi$
$43$	1854.78			1.00313			0.501563	+	0.865121i	$0.332759\pi$
$44$			2585.42i			1.33544i
$45$	1665.66	−	734.247i	0.822550	−	0.362591i
$46$	−535.814			−0.253220
$47$			2042.58i			0.924661i	0.886708	+	0.462330i	$0.152987\pi$
$47$			2042.58i			0.924661i	−0.886708	+	0.462330i	$0.847013\pi$
$48$	−1450.99	−	946.095i	−0.629770	−	0.410632i
$49$	5172.94			2.15449
$50$			140.017i			0.0560069i
$51$	−1353.28	+	2075.47i	−0.520292	+	0.797952i
$52$	−917.626			−0.339359
$53$		−	243.223i		−	0.0865872i	−0.999062	−	0.0432936i	$-0.986215\pi$
$53$		−	243.223i		−	0.0865872i	0.999062	−	0.0432936i	$-0.0137851\pi$
$54$	839.648	+	137.757i	0.287945	+	0.0472416i
$55$	3969.35			1.31218
$56$		−	3112.11i		−	0.992381i
$57$	−4818.93	−	3142.11i	−1.48321	−	0.967101i
$58$	−653.316			−0.194208
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	−1617.03	+	2479.97i	−0.449174	+	0.688881i
$61$	−4627.99			−1.24375			−0.621875	−	0.783117i	$-0.713629\pi$
$61$	−4627.99			−1.24375			−0.621875	+	0.783117i	$0.713629\pi$
$62$			130.202i			0.0338715i
$63$	−2843.42	−	6450.39i	−0.716407	−	1.62519i
$64$	2149.44			0.524765
$65$			1408.82i			0.333448i
$66$	1554.20	+	1013.39i	0.356796	+	0.232643i
$67$	−5993.39			−1.33513			−0.667564	−	0.744553i	$-0.732663\pi$
$67$	−5993.39			−1.33513			−0.667564	+	0.744553i	$0.732663\pi$
$68$		−	4029.74i		−	0.871484i
$69$	2256.63	−	3460.90i	0.473981	−	0.726927i
$70$	−2282.76			−0.465870
$71$			8085.89i			1.60403i	0.597307	+	0.802013i	$0.296238\pi$
$71$			8085.89i			1.60403i	−0.597307	+	0.802013i	$0.703762\pi$
$72$	−2650.45	+	1168.35i	−0.511274	+	0.225377i
$73$	321.074			0.0602503			0.0301251	−	0.999546i	$-0.490409\pi$
$73$	321.074			0.0602503			0.0301251	+	0.999546i	$0.490409\pi$
$74$		−	278.853i		−	0.0509228i
$75$	−904.391	−	589.694i	−0.160781	−	0.104835i
$76$	9356.45			1.61988
$77$		−	15371.6i		−	2.59261i
$78$	−359.678	+	551.624i	−0.0591187	+	0.0906680i
$79$	−105.206			−0.0168572			−0.00842860	−	0.999964i	$-0.502683\pi$
$79$	−105.206			−0.0168572			−0.00842860	+	0.999964i	$0.502683\pi$
$80$		−	4325.28i		−	0.675825i
$81$	−4426.04	+	4843.23i	−0.674598	+	0.738185i
$82$	−2189.64			−0.325645
$83$			12472.9i			1.81055i	0.424821	+	0.905277i	$0.360337\pi$
$83$			12472.9i			1.81055i	−0.424821	+	0.905277i	$0.639663\pi$
$84$	9603.86	+	6262.05i	1.36109	+	0.887478i
$85$	−6186.81			−0.856305
$86$			2164.86i			0.292707i
$87$	2751.50	−	4219.86i	0.363522	−	0.557519i
$88$	−6316.13			−0.815616
$89$		−	4819.17i		−	0.608404i	−0.952608	−	0.304202i	$-0.901610\pi$
$89$		−	4819.17i		−	0.608404i	0.952608	−	0.304202i	$-0.0983898\pi$
$90$	856.998	+	1944.13i	0.105802	+	0.240016i
$91$	5455.75			0.658827
$92$			6719.69i			0.793914i
$93$	−840.994	−	548.357i	−0.0972360	−	0.0634012i
$94$	−2384.05			−0.269811
$95$		−	14364.8i		−	1.59167i
$96$	3916.79	−	6007.03i	0.424999	−	0.651804i
$97$	−6900.62			−0.733406			−0.366703	−	0.930338i	$-0.619513\pi$
$97$	−6900.62			−0.733406			−0.366703	+	0.930338i	$0.619513\pi$
$98$			6037.75i			0.628670i
$99$	−13091.3	+	5770.82i	−1.33571	+	0.588800i
$100$	1755.97			0.175597
$101$		−	13681.1i		−	1.34116i	−0.741839	−	0.670578i	$-0.766046\pi$
$101$		−	13681.1i		−	1.34116i	0.741839	−	0.670578i	$-0.233954\pi$
$102$	−2422.45	−	1579.52i	−0.232838	−	0.151819i
$103$	19144.4			1.80455			0.902274	−	0.431163i	$-0.141897\pi$
$103$	19144.4			1.80455			0.902274	+	0.431163i	$0.141897\pi$
$104$		−	2241.75i		−	0.207262i
$105$	9614.04	−	14744.7i	0.872021	−	1.33739i
$106$	283.885			0.0252657
$107$		−	11093.2i		−	0.968925i	−0.874812	−	0.484463i	$-0.839015\pi$
$107$		−	11093.2i		−	0.968925i	0.874812	−	0.484463i	$-0.160985\pi$
$108$	1727.62	−	10530.1i	0.148115	−	0.902786i
$109$	1446.69			0.121765			0.0608826	−	0.998145i	$-0.480608\pi$
$109$	1446.69			0.121765			0.0608826	+	0.998145i	$0.480608\pi$
$110$			4632.95i			0.382888i
$111$	1801.15	+	1174.41i	0.146186	+	0.0953180i
$112$	−16749.9			−1.33529
$113$			21528.9i			1.68603i	0.537889	+	0.843016i	$0.319222\pi$
$113$			21528.9i			1.68603i	−0.537889	+	0.843016i	$0.680778\pi$
$114$	3667.41	−	5624.56i	0.282195	−	0.432792i
$115$	10316.6			0.780087
$116$			8193.29i			0.608895i
$117$	−2048.21	−	4646.42i	−0.149624	−	0.339427i
$118$	−528.951			−0.0379885
$119$			23958.8i			1.69189i
$120$	−6058.54	−	3950.38i	−0.420732	−	0.274332i
$121$	−16556.2			−1.13081
$122$		−	5401.69i		−	0.362920i
$123$	9221.84	−	14143.2i	0.609547	−	0.934839i
$124$	1632.88			0.106196
$125$		−	16741.6i		−	1.07146i
$126$	7528.77	−	3318.78i	0.474223	−	0.209044i
$127$	15588.2			0.966471			0.483235	−	0.875490i	$-0.339462\pi$
$127$	15588.2			0.966471			0.483235	+	0.875490i	$0.339462\pi$
$128$			15257.5i			0.931245i
$129$	−13983.1	−	9117.49i	−0.840282	−	0.547893i
$130$	−1644.34			−0.0972985
$131$			9235.06i			0.538142i	0.963120	+	0.269071i	$0.0867167\pi$
$131$			9235.06i			0.538142i	−0.963120	+	0.269071i	$0.913283\pi$
$132$	12709.1	−	19491.4i	0.729399	−	1.11865i
$133$	−55628.8			−3.14482
$134$		−	6995.36i		−	0.389583i
$135$	−16166.7	−	2652.39i	−0.887063	−	0.145536i
$136$	9844.60			0.532256
$137$			28074.3i			1.49578i	0.663822	+	0.747891i	$0.268933\pi$
$137$			28074.3i			1.49578i	−0.663822	+	0.747891i	$0.731067\pi$
$138$	4039.49	+	2633.89i	0.212113	+	0.138305i
$139$	601.869			0.0311510			0.0155755	−	0.999879i	$-0.495042\pi$
$139$	601.869			0.0311510			0.0155755	+	0.999879i	$0.495042\pi$
$140$			28628.3i			1.46063i
$141$	10040.6	−	15398.9i	0.505037	−	0.774555i
$142$	−9437.69			−0.468046
$143$		−	11072.6i		−	0.541476i
$144$	6288.28	+	14265.2i	0.303254	+	0.687943i
$145$	12579.1			0.598290
$146$			374.751i			0.0175807i
$147$	−38998.7	−	25428.5i	−1.80474	−	1.17675i
$148$	−3497.12			−0.159657
$149$		−	11239.9i		−	0.506280i	−0.967430	−	0.253140i	$-0.918537\pi$
$149$		−	11239.9i		−	0.506280i	0.967430	−	0.253140i	$-0.0814633\pi$
$150$	688.279	−	1055.59i	0.0305902	−	0.0469150i
$151$	−12433.5			−0.545305			−0.272652	−	0.962113i	$-0.587901\pi$
$151$	−12433.5			−0.545305			−0.272652	+	0.962113i	$0.587901\pi$
$152$			22857.7i			0.989339i
$153$	20404.7	−	8994.66i	0.871660	−	0.384239i
$154$	17941.4			0.756510
$155$		−	2506.93i		−	0.104347i
$156$	6917.96	+	4510.75i	0.284269	+	0.185353i
$157$	−7084.45			−0.287413			−0.143707	−	0.989620i	$-0.545902\pi$
$157$	−7084.45			−0.287413			−0.143707	+	0.989620i	$0.545902\pi$
$158$		−	122.794i		−	0.00491884i
$159$	−1195.61	+	1833.66i	−0.0472927	+	0.0725310i
$160$	17906.4			0.699470
$161$		−	39951.9i		−	1.54129i
$162$	−5652.92	−	5165.98i	−0.215399	−	0.196844i
$163$	−22465.5			−0.845553			−0.422776	−	0.906234i	$-0.638944\pi$
$163$	−22465.5			−0.845553			−0.422776	+	0.906234i	$0.638944\pi$
$164$			27460.4i			1.02099i
$165$	−29924.9	−	19512.0i	−1.09917	−	0.716696i
$166$	−14558.1			−0.528310
$167$		−	11661.4i		−	0.418136i	−0.977901	−	0.209068i	$-0.932957\pi$
$167$		−	11661.4i		−	0.418136i	0.977901	−	0.209068i	$-0.0670430\pi$
$168$	−15298.1	+	23462.1i	−0.542024	+	0.831282i
$169$	−24631.1			−0.862402
$170$		−	7221.11i		−	0.249865i
$171$	20884.2	+	47376.6i	0.714211	+	1.62021i
$172$	27149.7			0.917715
$173$		−	213.966i		−	0.00714912i	−0.999994	−	0.00357456i	$-0.998862\pi$
$173$		−	213.966i		−	0.00714912i	0.999994	−	0.00357456i	$-0.00113782\pi$
$174$	4925.34	+	3211.49i	0.162681	+	0.106074i
$175$	−10440.1			−0.340901
$176$			33994.6i			1.09745i
$177$	2227.72	−	3416.57i	0.0711073	−	0.109055i
$178$	5624.84			0.177529
$179$			3004.55i			0.0937721i	0.998900	+	0.0468861i	$0.0149298\pi$
$179$			3004.55i			0.0937721i	−0.998900	+	0.0468861i	$0.985070\pi$
$180$	24381.5	−	10747.7i	0.752515	−	0.331719i
$181$	27135.6			0.828289			0.414144	−	0.910211i	$-0.364081\pi$
$181$	27135.6			0.828289			0.414144	+	0.910211i	$0.364081\pi$
$182$			6367.83i			0.192242i
$183$	34890.3	+	22749.7i	1.04184	+	0.679318i
$184$	−16416.1			−0.484880
$185$			5369.08i			0.156876i
$186$	640.031	−	981.591i	0.0185002	−	0.0283730i
$187$	48625.3			1.39053
$188$			29898.6i			0.845931i
$189$	−10271.5	+	62606.7i	−0.287549	+	1.75266i
$190$	16766.3			0.464441
$191$			21342.8i			0.585039i	0.956260	+	0.292519i	$0.0944936\pi$
$191$			21342.8i			0.585039i	−0.956260	+	0.292519i	$0.905506\pi$
$192$	−16204.6	−	10565.9i	−0.439577	−	0.286619i
$193$	55112.8			1.47958			0.739789	−	0.672839i	$-0.234925\pi$
$193$	55112.8			1.47958			0.739789	+	0.672839i	$0.234925\pi$
$194$		−	8054.26i		−	0.214004i
$195$	6925.29	−	10621.1i	0.182125	−	0.279318i
$196$	75719.9			1.97105
$197$		−	25131.8i		−	0.647575i	−0.946130	−	0.323788i	$-0.895044\pi$
$197$		−	25131.8i		−	0.647575i	0.946130	−	0.323788i	$-0.104956\pi$
$198$	−6735.59	−	15279.9i	−0.171809	−	0.389754i
$199$	−2741.44			−0.0692265			−0.0346132	−	0.999401i	$-0.511020\pi$
$199$	−2741.44			−0.0692265			−0.0346132	+	0.999401i	$0.511020\pi$
$200$			4289.81i			0.107245i
$201$	45184.0	+	29461.5i	1.11839	+	0.729228i
$202$	15968.3			0.391342
$203$		−	48713.2i		−	1.18210i
$204$	−19808.9	+	30380.1i	−0.475992	+	0.730011i
$205$	42159.6			1.00320
$206$			22345.0i			0.526558i
$207$	−34025.3	+	14998.8i	−0.794074	+	0.350039i
$208$	−12065.5			−0.278881
$209$			112901.i			2.58466i
$210$	17209.7	+	11221.3i	0.390242	+	0.254451i
$211$	−16563.4			−0.372035			−0.186018	−	0.982546i	$-0.559558\pi$
$211$	−16563.4			−0.372035			−0.186018	+	0.982546i	$0.559558\pi$
$212$		−	3560.23i		−	0.0792148i
$213$	39747.6	−	60959.4i	0.876096	−	1.34363i
$214$	12947.8			0.282727
$215$		−	41682.5i		−	0.901732i
$216$	25724.9	+	4220.54i	0.551374	+	0.0904609i
$217$	−9708.26			−0.206168
$218$			1688.55i			0.0355304i
$219$	−2420.57	−	1578.29i	−0.0504695	−	0.0329079i
$220$	58102.2			1.20046
$221$			17258.3i			0.353357i
$222$	−1370.75	+	2102.27i	−0.0278133	+	0.0426562i
$223$	−64261.7			−1.29224			−0.646119	−	0.763237i	$-0.723609\pi$
$223$	−64261.7			−1.29224			−0.646119	+	0.763237i	$0.723609\pi$
$224$		−	69343.9i		−	1.38201i
$225$	3919.44	+	8891.38i	0.0774211	+	0.175632i
$226$	−25128.1			−0.491975
$227$			49768.0i			0.965825i	0.875669	+	0.482913i	$0.160421\pi$
$227$			49768.0i			0.965825i	−0.875669	+	0.482913i	$0.839579\pi$
$228$	−70538.1	−	45993.2i	−1.35692	−	0.884758i
$229$	−58627.8			−1.11798			−0.558988	−	0.829175i	$-0.688810\pi$
$229$	−58627.8			−1.11798			−0.558988	+	0.829175i	$0.688810\pi$
$230$			12041.4i			0.227625i
$231$	−75561.7	+	115886.i	−1.41605	+	2.17174i
$232$	−20016.1			−0.371881
$233$		−	27155.6i		−	0.500205i	−0.968219	−	0.250103i	$-0.919536\pi$
$233$		−	27155.6i		−	0.500205i	0.968219	−	0.250103i	$-0.0804643\pi$
$234$	5423.21	−	2390.62i	0.0990431	−	0.0436596i
$235$	45902.9			0.831198
$236$			6633.62i			0.119104i
$237$	793.144	+	517.157i	0.0141207	+	0.00920716i
$238$	−27964.2			−0.493684
$239$		−	92859.5i		−	1.62566i	−0.582499	−	0.812831i	$-0.697925\pi$
$239$		−	92859.5i		−	1.62566i	0.582499	−	0.812831i	$-0.302075\pi$
$240$	−21261.6	+	32608.2i	−0.369126	+	0.566114i
$241$	−73629.9			−1.26771			−0.633855	−	0.773452i	$-0.718528\pi$
$241$	−73629.9			−1.26771			−0.633855	+	0.773452i	$0.718528\pi$
$242$		−	19324.0i		−	0.329964i
$243$	57175.5	−	14756.1i	0.968273	−	0.249896i
$244$	−67743.1			−1.13785
$245$		−	116252.i		−	1.93672i
$246$	16507.6	+	10763.5i	0.272781	+	0.177863i
$247$	−40071.1			−0.656807
$248$			3989.09i			0.0648591i
$249$	61312.7	−	94033.0i	0.988899	−	1.51664i
$250$	19540.4			0.312647
$251$		−	23684.0i		−	0.375930i	−0.982176	−	0.187965i	$-0.939811\pi$
$251$		−	23684.0i		−	0.375930i	0.982176	−	0.187965i	$-0.0601892\pi$
$252$	−41621.1	−	94418.9i	−0.655409	−	1.48682i
$253$	−81083.8			−1.26676
$254$			18194.2i			0.282011i
$255$	46642.2	+	30412.3i	0.717296	+	0.467702i
$256$	16582.7			0.253033
$257$		−	23634.3i		−	0.357830i	−0.983865	−	0.178915i	$-0.942741\pi$
$257$		−	23634.3i		−	0.357830i	0.983865	−	0.178915i	$-0.0572587\pi$
$258$	10641.7	−	16320.8i	0.159872	−	0.245190i
$259$	20792.1			0.309955
$260$			20621.9i			0.305057i
$261$	−41486.9	+	18288.0i	−0.609018	+	0.268463i
$262$	−10779.0			−0.157027
$263$			56966.1i			0.823579i	0.911279	+	0.411789i	$0.135096\pi$
$263$			56966.1i			0.823579i	−0.911279	+	0.411789i	$0.864904\pi$
$264$	47617.2	+	31048.0i	0.683213	+	0.445478i
$265$	−5465.97			−0.0778351
$266$		−	64928.7i		−	0.917643i
$267$	−23689.5	+	36331.6i	−0.332302	+	0.509638i
$268$	−87729.4			−1.22145
$269$			99475.8i			1.37472i	0.726319	+	0.687358i	$0.241229\pi$
$269$			99475.8i			1.37472i	−0.726319	+	0.687358i	$0.758771\pi$
$270$	3095.81	−	18869.5i	0.0424665	−	0.258840i
$271$	116423.			1.58525			0.792627	−	0.609706i	$-0.208713\pi$
$271$	116423.			1.58525			0.792627	+	0.609706i	$0.208713\pi$
$272$		−	52985.4i		−	0.716174i
$273$	−41130.7	−	26818.7i	−0.551876	−	0.359842i
$274$	−32767.8			−0.436461
$275$			21188.6i			0.280179i
$276$	33031.8	−	50659.6i	0.433625	−	0.665033i
$277$	59391.6			0.774043			0.387022	−	0.922071i	$-0.373504\pi$
$277$	59391.6			0.774043			0.387022	+	0.922071i	$0.373504\pi$
$278$			702.489i			0.00908971i
$279$	3644.69	+	8268.11i	0.0468223	+	0.106218i
$280$	−69938.5			−0.892073
$281$		−	36331.5i		−	0.460120i	−0.973176	−	0.230060i	$-0.926108\pi$
$281$		−	36331.5i		−	0.460120i	0.973176	−	0.230060i	$-0.0738923\pi$
$282$	17973.3	+	11719.2i	0.226011	+	0.147367i
$283$	84812.3			1.05898			0.529488	−	0.848318i	$-0.322384\pi$
$283$	84812.3			1.05898			0.529488	+	0.848318i	$0.322384\pi$
$284$			118359.i			1.46745i
$285$	−70612.8	+	108296.i	−0.869348	+	1.33329i
$286$	12923.7			0.158000
$287$		−	163266.i		−	1.98213i
$288$	−59057.2	+	26033.2i	−0.712012	+	0.313865i
$289$	7731.49			0.0925694
$290$			14682.0i			0.174578i
$291$	52023.6	+	33921.2i	0.614348	+	0.400576i
$292$	4699.78			0.0551203
$293$			46837.0i			0.545574i	0.962074	+	0.272787i	$0.0879454\pi$
$293$			46837.0i			0.545574i	−0.962074	+	0.272787i	$0.912055\pi$
$294$	29679.6	−	45518.4i	0.343371	−	0.526614i
$295$	10184.5			0.117030
$296$		−	8543.42i		−	0.0975098i
$297$	127063.	+	20846.5i	1.44047	+	0.236330i
$298$	13119.0			0.147730
$299$		−	28778.6i		−	0.321905i
$300$	−13238.2	−	8631.76i	−0.147091	−	0.0959085i
$301$	−161418.			−1.78164
$302$		−	14512.1i		−	0.159117i
$303$	−67251.9	+	103142.i	−0.732520	+	1.12344i
$304$	123024.			1.33120
$305$			104005.i			1.11803i
$306$	10498.4	+	23815.9i	0.112119	+	0.254346i
$307$	175115.			1.85801			0.929003	−	0.370071i	$-0.120667\pi$
$307$	175115.			1.85801			0.929003	+	0.370071i	$0.120667\pi$
$308$		−	225004.i		−	2.37186i
$309$	−144330.	−	94107.8i	−1.51160	−	0.985618i
$310$	2926.04			0.0304479
$311$		−	172388.i		−	1.78232i	−0.453689	−	0.891160i	$-0.649892\pi$
$311$		−	172388.i		−	1.78232i	0.453689	−	0.891160i	$-0.350108\pi$
$312$	−11019.7	+	16900.5i	−0.113204	+	0.173616i
$313$	−79879.2			−0.815352			−0.407676	−	0.913127i	$-0.633661\pi$
$313$	−79879.2			−0.815352			−0.407676	+	0.913127i	$0.633661\pi$
$314$		−	8268.82i		−	0.0838657i
$315$	−144960.	+	63900.3i	−1.46092	+	0.643994i
$316$	−1539.97			−0.0154219
$317$			19862.4i			0.197657i	0.995104	+	0.0988286i	$0.0315096\pi$
$317$			19862.4i			0.197657i	−0.995104	+	0.0988286i	$0.968490\pi$
$318$	−2140.21	−	1395.49i	−0.0211642	−	0.0137998i
$319$	−98865.2			−0.971544
$320$		−	48304.4i		−	0.471723i
$321$	−54530.6	+	83631.5i	−0.529213	+	0.811634i
$322$	46631.0			0.449742
$323$		−	175972.i		−	1.68670i
$324$	−64787.0	+	70893.8i	−0.617160	+	0.675333i
$325$	−7520.34			−0.0711985
$326$		−	26221.3i		−	0.246728i
$327$	−10906.6	−	7111.46i	−0.101998	−	0.0665064i
$328$	−67085.5			−0.623564
$329$		−	177762.i		−	1.64228i
$330$	22774.0	−	34927.7i	0.209128	−	0.320732i
$331$	148082.			1.35160			0.675799	−	0.737086i	$-0.263799\pi$
$331$	148082.			1.35160			0.675799	+	0.737086i	$0.263799\pi$
$332$			182575.i			1.65640i
$333$	−7805.81	−	17707.7i	−0.0703930	−	0.159689i
$334$	13610.9			0.122010
$335$			134690.i			1.20018i
$336$	126277.	+	82337.1i	1.11853	+	0.729319i
$337$	203759.			1.79414			0.897071	−	0.441886i	$-0.145691\pi$
$337$	203759.			1.79414			0.897071	+	0.441886i	$0.145691\pi$
$338$		−	28748.9i		−	0.251644i
$339$	105829.	−	162306.i	0.920886	−	1.41233i
$340$	−90560.6			−0.783396
$341$			19703.3i			0.169445i
$342$	−55297.0	+	24375.7i	−0.472769	+	0.208403i
$343$	−241237.			−2.05048
$344$			66326.3i			0.560491i
$345$	−77776.9	−	50713.2i	−0.653450	−	0.426072i
$346$	249.737			0.00208607
$347$			91453.2i			0.759522i	0.925085	+	0.379761i	$0.123994\pi$
$347$			91453.2i			0.759522i	−0.925085	+	0.379761i	$0.876006\pi$
$348$	40275.6	−	61769.1i	0.332570	−	0.510050i
$349$	−96102.8			−0.789015			−0.394507	−	0.918893i	$-0.629085\pi$
$349$	−96102.8			−0.789015			−0.394507	+	0.918893i	$0.629085\pi$
$350$		−	12185.5i		−	0.0994733i
$351$	−7398.91	+	45097.6i	−0.0600556	+	0.366049i
$352$	−140736.			−1.13585
$353$		−	144407.i		−	1.15888i	−0.815015	−	0.579440i	$-0.803271\pi$
$353$		−	144407.i		−	1.15888i	0.815015	−	0.579440i	$-0.196729\pi$
$354$	3987.75	+	2600.15i	0.0318216	+	0.0207488i
$355$	181715.			1.44189
$356$		−	70541.5i		−	0.556602i
$357$	117774.	−	180625.i	0.924085	−	1.41723i
$358$	−3506.85			−0.0273622
$359$		−	65323.9i		−	0.506854i	−0.967355	−	0.253427i	$-0.918442\pi$
$359$		−	65323.9i		−	0.506854i	0.967355	−	0.253427i	$-0.0815578\pi$
$360$	26256.4	+	59563.6i	0.202596	+	0.459596i
$361$	278259.			2.13518
$362$			31672.1i			0.241690i
$363$	124817.	+	81384.8i	0.947239	+	0.617632i
$364$	79859.5			0.602732
$365$		−	7215.51i		−	0.0541603i
$366$	−26553.0	+	40723.2i	−0.198221	+	0.304005i
$367$	−181932.			−1.35076			−0.675379	−	0.737470i	$-0.736020\pi$
$367$	−181932.			−1.35076			−0.675379	+	0.737470i	$0.736020\pi$
$368$			88354.5i			0.652428i
$369$	−139047.	+	61293.6i	−1.02119	+	0.450155i
$370$	−6266.68			−0.0457756
$371$			21167.3i			0.153787i
$372$	−12310.2	−	8026.69i	−0.0889569	−	0.0580030i
$373$	83721.3			0.601753			0.300876	−	0.953663i	$-0.402721\pi$
$373$	83721.3			0.601753			0.300876	+	0.953663i	$0.402721\pi$
$374$			56754.4i			0.405748i
$375$	−82296.1	+	126214.i	−0.585216	+	0.897524i
$376$	−73041.9			−0.516650
$377$		−	35089.7i		−	0.246886i
$378$	−73073.2	−	11988.7i	−0.511416	−	0.0839053i
$379$	9890.60			0.0688564			0.0344282	−	0.999407i	$-0.489039\pi$
$379$	9890.60			0.0688564			0.0344282	+	0.999407i	$0.489039\pi$
$380$		−	210268.i		−	1.45615i
$381$	−117519.	−	76626.5i	−0.809578	−	0.527873i
$382$	−24910.9			−0.170711
$383$			142775.i			0.973317i	0.873592	+	0.486659i	$0.161784\pi$
$383$			142775.i			0.973317i	−0.873592	+	0.486659i	$0.838216\pi$
$384$	75001.0	−	115026.i	0.508633	−	0.780071i
$385$	−345446.			−2.33055
$386$			64326.5i			0.431733i
$387$	60600.0	+	137473.i	0.404623	+	0.917900i
$388$	−101009.			−0.670961
$389$		−	155550.i		−	1.02795i	−0.857806	−	0.513973i	$-0.828173\pi$
$389$		−	155550.i		−	1.02795i	0.857806	−	0.513973i	$-0.171827\pi$
$390$	12396.7	+	8083.06i	0.0815035	+	0.0531431i
$391$	126381.			0.826661
$392$			184983.i			1.20381i
$393$	45396.5	−	69622.9i	0.293926	−	0.450783i
$394$	29333.3			0.188959
$395$			2364.29i			0.0151533i
$396$	−191627.	+	84471.6i	−1.22198	+	0.538667i
$397$	114856.			0.728738			0.364369	−	0.931255i	$-0.381285\pi$
$397$	114856.			0.728738			0.364369	+	0.931255i	$0.381285\pi$
$398$		−	3199.75i		−	0.0201999i
$399$	419384.	+	273453.i	2.63430	+	1.71766i
$400$	23088.5			0.144303
$401$			182479.i			1.13481i	0.823438	+	0.567406i	$0.192053\pi$
$401$			182479.i			1.13481i	−0.823438	+	0.567406i	$0.807947\pi$
$402$	−34386.9	+	52737.8i	−0.212785	+	0.326340i
$403$	−6993.17			−0.0430590
$404$		−	200260.i		−	1.22696i
$405$	108842.	+	99466.5i	0.663571	+	0.606411i
$406$	56857.1			0.344931
$407$		−	42198.4i		−	0.254746i
$408$	−74218.2	−	48392.8i	−0.445852	−	0.290711i
$409$	−160760.			−0.961017			−0.480509	−	0.876990i	$-0.659548\pi$
$409$	−160760.			−0.961017			−0.480509	+	0.876990i	$0.659548\pi$
$410$			49207.8i			0.292730i
$411$	138004.	−	211652.i	0.816975	−	1.25296i
$412$	280231.			1.65090
$413$		−	39440.2i		−	0.231227i
$414$	−17506.3	−	39713.6i	−0.102139	−	0.231707i
$415$	280304.			1.62755
$416$		−	49950.6i		−	0.288638i
$417$	−4537.48	−	2958.59i	−0.0260941	−	0.0170142i
$418$	−131775.			−0.754191
$419$			300749.i			1.71308i	0.516084	+	0.856538i	$0.327389\pi$
$419$			300749.i			1.71308i	−0.516084	+	0.856538i	$0.672611\pi$
$420$	140727.	−	215828.i	0.797774	−	1.22351i
$421$	−169665.			−0.957255			−0.478628	−	0.878018i	$-0.658866\pi$
$421$	−169665.			−0.957255			−0.478628	+	0.878018i	$0.658866\pi$
$422$		−	19332.4i		−	0.108558i
$423$	−151392.	+	66735.7i	−0.846102	+	0.372973i
$424$	8697.59			0.0483802
$425$		−	33025.4i		−	0.182840i
$426$	71150.5	+	46392.6i	0.392066	+	0.255640i
$427$	402766.			2.20901
$428$		−	162379.i		−	0.886427i
$429$	−54429.4	+	83476.3i	−0.295746	+	0.453575i
$430$	48651.0			0.263121
$431$		−	156475.i		−	0.842348i	−0.906980	−	0.421174i	$-0.861618\pi$
$431$		−	156475.i		−	0.842348i	0.906980	−	0.421174i	$-0.138382\pi$
$432$	22715.7	−	138456.i	0.121719	−	0.741898i
$433$	−220128.			−1.17408			−0.587042	−	0.809556i	$-0.699708\pi$
$433$	−220128.			−1.17408			−0.587042	+	0.809556i	$0.699708\pi$
$434$		−	11331.3i		−	0.0601589i
$435$	−94833.2	−	61834.5i	−0.501166	−	0.326778i
$436$	21176.2			0.111398
$437$			293437.i			1.53657i
$438$	1842.15	−	2825.24i	0.00960234	−	0.0147267i
$439$	26366.9			0.136814			0.0684069	−	0.997658i	$-0.478208\pi$
$439$	26366.9			0.136814			0.0684069	+	0.997658i	$0.478208\pi$
$440$			141943.i			0.733176i
$441$	169012.	+	383409.i	0.869041	+	1.97145i
$442$	−20143.5			−0.103108
$443$			160477.i			0.817722i	0.912597	+	0.408861i	$0.134074\pi$
$443$			160477.i			0.817722i	−0.912597	+	0.408861i	$0.865926\pi$
$444$	26364.7	+	17190.7i	0.133739	+	0.0872022i
$445$	−108301.			−0.546908
$446$		−	75004.9i		−	0.377068i
$447$	−55251.7	+	84737.4i	−0.276523	+	0.424092i
$448$	−187062.			−0.932030
$449$		−	72854.0i		−	0.361377i	−0.983540	−	0.180689i	$-0.942167\pi$
$449$		−	72854.0i		−	0.361377i	0.983540	−	0.180689i	$-0.0578326\pi$
$450$	−10377.8	+	4574.69i	−0.0512486	+	0.0225911i
$451$	−331354.			−1.62907
$452$			315134.i			1.54248i
$453$	93735.9	+	61119.0i	0.456782	+	0.297838i
$454$	−58088.2			−0.281823
$455$		−	122607.i		−	0.592234i
$456$	112361.	−	172324.i	0.540363	−	0.828733i
$457$	−67504.4			−0.323221			−0.161611	−	0.986855i	$-0.551669\pi$
$457$	−67504.4			−0.323221			−0.161611	+	0.986855i	$0.551669\pi$
$458$		−	68429.2i		−	0.326220i
$459$	−198045.	−	32492.2i	−0.940024	−	0.154225i
$460$	151012.			0.713667
$461$			15277.9i			0.0718891i	0.999354	+	0.0359445i	$0.0114440\pi$
$461$			15277.9i			0.0718891i	−0.999354	+	0.0359445i	$0.988556\pi$
$462$	−135260.	−	88194.0i	−0.633701	−	0.413195i
$463$	100111.			0.467002			0.233501	−	0.972357i	$-0.424982\pi$
$463$	100111.			0.467002			0.233501	+	0.972357i	$0.424982\pi$
$464$			107730.i			0.500382i
$465$	−12323.3	+	18899.7i	−0.0569928	+	0.0874076i
$466$	31695.5			0.145957
$467$			251433.i			1.15289i	0.817135	+	0.576447i	$0.195561\pi$
$467$			251433.i			1.15289i	−0.817135	+	0.576447i	$0.804439\pi$
$468$	−29981.0	−	68012.9i	−0.136885	−	0.310527i
$469$	521595.			2.37131
$470$			53576.9i			0.242539i
$471$	53409.5	+	34824.8i	0.240756	+	0.156981i
$472$	−16205.8			−0.0727424
$473$			327605.i			1.46429i
$474$	−603.615	+	925.741i	−0.00268660	+	0.00412034i
$475$	76680.1			0.339856
$476$			350702.i			1.54783i
$477$	18027.3	−	7946.68i	0.0792308	−	0.0349260i
$478$	108384.			0.474360
$479$			270225.i			1.17776i	0.808222	+	0.588878i	$0.200430\pi$
$479$			270225.i			1.17776i	−0.808222	+	0.588878i	$0.799570\pi$
$480$	−134996.	−	88022.2i	−0.585921	−	0.382041i
$481$	14977.2			0.0647353
$482$		−	85939.3i		−	0.369911i
$483$	−196390.	+	301196.i	−0.841833	+	1.29109i
$484$	−242344.			−1.03453
$485$			155078.i			0.659275i
$486$	17223.0	+	66734.1i	0.0729182	+	0.282537i
$487$	−82961.2			−0.349798			−0.174899	−	0.984586i	$-0.555960\pi$
$487$	−82961.2			−0.349798			−0.174899	+	0.984586i	$0.555960\pi$
$488$		−	165495.i		−	0.694939i
$489$	169367.	+	110433.i	0.708289	+	0.461829i
$490$	135687.			0.565125
$491$		−	209684.i		−	0.869767i	−0.900487	−	0.434883i	$-0.856790\pi$
$491$		−	209684.i		−	0.869767i	0.900487	−	0.434883i	$-0.143210\pi$
$492$	134986.	−	207024.i	0.557648	−	0.855243i
$493$	154096.			0.634011
$494$		−	46770.2i		−	0.191653i
$495$	129688.	+	294202.i	0.529285	+	1.20070i
$496$	21470.0			0.0872709
$497$		−	703702.i		−	2.84889i
$498$	109753.	+	71563.0i	0.442547	+	0.288556i
$499$	185392.			0.744542			0.372271	−	0.928124i	$-0.378579\pi$
$499$	185392.			0.744542			0.372271	+	0.928124i	$0.378579\pi$
$500$		−	245058.i		−	0.980232i
$501$	−57323.6	+	87915.0i	−0.228380	+	0.350257i
$502$	27643.4			0.109694
$503$			10583.2i			0.0418292i	0.999781	+	0.0209146i	$0.00665781\pi$
$503$			10583.2i			0.0418292i	−0.999781	+	0.0209146i	$0.993342\pi$
$504$	230664.	−	101680.i	0.908069	−	0.400289i
$505$	−307457.			−1.20559
$506$		−	94639.4i		−	0.369633i
$507$	185693.	+	121078.i	0.722403	+	0.471032i
$508$	228175.			0.884181
$509$		−	515029.i		−	1.98791i	−0.109799	−	0.993954i	$-0.535021\pi$
$509$		−	515029.i		−	1.98791i	0.109799	−	0.993954i	$-0.464979\pi$
$510$	−35496.6	+	54439.8i	−0.136473	+	0.209303i
$511$	−27942.5			−0.107010
$512$			263475.i			1.00508i
$513$	75442.0	−	459831.i	0.286667	−	1.74728i
$514$	27585.5			0.104413
$515$		−	430234.i		−	1.62215i
$516$	−204681.	−	133459.i	−0.768737	−	0.501243i
$517$	−360774.			−1.34975
$518$			24268.1i			0.0904434i
$519$	−1051.79	+	1613.08i	−0.00390475	+	0.00598856i
$520$	−50378.9			−0.186313
$521$		−	179347.i		−	0.660722i	−0.943855	−	0.330361i	$-0.892830\pi$
$521$		−	179347.i		−	0.660722i	0.943855	−	0.330361i	$-0.107170\pi$
$522$	−21345.4	−	48422.7i	−0.0783362	−	0.177708i
$523$	−252344.			−0.922549			−0.461274	−	0.887257i	$-0.652608\pi$
$523$	−252344.			−0.922549			−0.461274	+	0.887257i	$0.652608\pi$
$524$			135180.i			0.492323i
$525$	78707.7	+	51320.1i	0.285561	+	0.186196i
$526$	−66489.7			−0.240316
$527$		−	30710.4i		−	0.110577i
$528$	167106.	−	256284.i	0.599411	−	0.919294i
$529$	69098.1			0.246919
$530$		−	6379.77i		−	0.0227119i
$531$	−33589.5	+	14806.7i	−0.119128	+	0.0525133i
$532$	−814277.			−2.87706
$533$		−	117606.i		−	0.413975i
$534$	−42405.5	−	27649.8i	−0.148710	−	0.0969639i
$535$	−249299.			−0.870988
$536$		−	214322.i		−	0.745996i
$537$	14769.4	−	22651.3i	0.0512170	−	0.0785495i
$538$	−116106.			−0.401135
$539$			913682.i			3.14498i
$540$	−236643.	−	38824.8i	−0.811534	−	0.133144i
$541$	229623.			0.784552			0.392276	−	0.919848i	$-0.371688\pi$
$541$	229623.			0.784552			0.392276	+	0.919848i	$0.371688\pi$
$542$			135886.i			0.462569i
$543$	−204574.	−	133390.i	−0.693828	−	0.452399i
$544$	219357.			0.741232
$545$		−	32511.6i		−	0.109457i
$546$	31302.2	−	48006.9i	0.105000	−	0.161034i
$547$	−51233.1			−0.171229			−0.0856143	−	0.996328i	$-0.527285\pi$
$547$	−51233.1			−0.171229			−0.0856143	+	0.996328i	$0.527285\pi$
$548$			410943.i			1.36842i
$549$	−151207.	−	343019.i	−0.501681	−	1.13808i
$550$	−24730.9			−0.0817549
$551$			357787.i			1.17848i
$552$	123761.	+	80696.2i	0.406167	+	0.264835i
$553$	9155.89			0.0299399
$554$			69320.6i			0.225862i
$555$	26392.6	−	40477.4i	0.0856834	−	0.131409i
$556$	8809.97			0.0284987
$557$		−	343261.i		−	1.10641i	−0.833046	−	0.553203i	$-0.813405\pi$
$557$		−	343261.i		−	1.10641i	0.833046	−	0.553203i	$-0.186595\pi$
$558$	−9650.36	+	4254.01i	−0.0309938	+	0.0136625i
$559$	−116275.			−0.372102
$560$			376422.i			1.20032i
$561$	−366585.	−	239026.i	−1.16479	−	0.759485i
$562$	42405.4			0.134261
$563$		−	343030.i		−	1.08222i	−0.840952	−	0.541110i	$-0.818004\pi$
$563$		−	343030.i		−	1.08222i	0.840952	−	0.541110i	$-0.181996\pi$
$564$	146972.	−	225405.i	0.462036	−	0.708606i
$565$	483821.			1.51561
$566$			98991.1i			0.309004i
$567$	385191.	−	421499.i	1.19815	−	1.31108i
$568$	−289149.			−0.896242
$569$			410745.i			1.26867i	0.773060	+	0.634333i	$0.218725\pi$
$569$			410745.i			1.26867i	−0.773060	+	0.634333i	$0.781275\pi$
$570$	−126401.	−	82417.8i	−0.389046	−	0.253671i
$571$	−339329.			−1.04075			−0.520377	−	0.853936i	$-0.674209\pi$
$571$	−339329.			−1.04075			−0.520377	+	0.853936i	$0.674209\pi$
$572$		−	162078.i		−	0.495372i
$573$	104914.	−	160903.i	0.319540	−	0.490066i
$574$	190561.			0.578375
$575$			55070.7i			0.166565i
$576$	70227.2	+	159313.i	0.211670	+	0.480181i
$577$	−109383.			−0.328548			−0.164274	−	0.986415i	$-0.552528\pi$
$577$	−109383.			−0.328548			−0.164274	+	0.986415i	$0.552528\pi$
$578$			9024.04i			0.0270113i
$579$	−415494.	−	270916.i	−1.23939	−	0.808124i
$580$	184128.			0.547349
$581$		−	1.08550e6i		−	3.21571i
$582$	−39592.1	+	60720.9i	−0.116886	+	0.179264i
$583$	42959.9			0.126394
$584$			11481.5i			0.0336646i
$585$	−104419.	+	46029.4i	−0.305119	+	0.134500i
$586$	−54667.1			−0.159196
$587$			461407.i			1.33908i	0.742774	+	0.669542i	$0.233510\pi$
$587$			461407.i			1.33908i	−0.742774	+	0.669542i	$0.766490\pi$
$588$	−570850.	−	372214.i	−1.65108	−	1.07656i
$589$	71304.9			0.205536
$590$			11887.1i			0.0341487i
$591$	−123539.	+	189468.i	−0.353696	+	0.542451i
$592$	−45982.2			−0.131204
$593$			359207.i			1.02149i	0.859731	+	0.510747i	$0.170631\pi$
$593$			359207.i			1.02149i	−0.859731	+	0.510747i	$0.829369\pi$
$594$	−24331.6	+	148305.i	−0.0689600	+	0.420322i
$595$	538428.			1.52087
$596$		−	164526.i		−	0.463173i
$597$	20667.6	+	13476.0i	0.0579885	+	0.0378105i
$598$	33589.8			0.0939301
$599$			488438.i			1.36131i	0.732606	+	0.680653i	$0.238304\pi$
$599$			488438.i			1.36131i	−0.732606	+	0.680653i	$0.761696\pi$
$600$	21087.3	−	32340.7i	0.0585758	−	0.0898354i
$601$	605126.			1.67532			0.837658	−	0.546196i	$-0.183924\pi$
$601$	605126.			1.67532			0.837658	+	0.546196i	$0.183924\pi$
$602$		−	188404.i		−	0.519873i
$603$	−195818.	−	444219.i	−0.538540	−	1.22170i
$604$	−181998.			−0.498875
$605$			372068.i			1.01651i
$606$	−120385.	−	78495.1i	−0.327813	−	0.213746i
$607$	−180397.			−0.489611			−0.244805	−	0.969572i	$-0.578724\pi$
$607$	−180397.			−0.489611			−0.244805	+	0.969572i	$0.578724\pi$
$608$			509314.i			1.37778i
$609$	−239458.	+	367248.i	−0.645647	+	0.990204i
$610$	−121393.			−0.326236
$611$		−	128048.i		−	0.342996i
$612$	298677.	−	131661.i	0.797443	−	0.351524i
$613$	449928.			1.19735			0.598676	−	0.800991i	$-0.295694\pi$
$613$	449928.			1.19735			0.598676	+	0.800991i	$0.295694\pi$
$614$			204391.i			0.542157i
$615$	−317840.	−	207243.i	−0.840348	−	0.547936i
$616$	549683.			1.44861
$617$		−	43057.6i		−	0.113104i	−0.998400	−	0.0565522i	$-0.981989\pi$
$617$		−	43057.6i		−	0.113104i	0.998400	−	0.0565522i	$-0.0180107\pi$
$618$	109841.	−	168458.i	0.287598	−	0.441079i
$619$	48597.9			0.126834			0.0634171	−	0.997987i	$-0.479800\pi$
$619$	48597.9			0.126834			0.0634171	+	0.997987i	$0.479800\pi$
$620$		−	36695.7i		−	0.0954623i
$621$	330245.	+	54181.5i	0.856354	+	0.140497i
$622$	201207.			0.520072
$623$			419405.i			1.08058i
$624$	90961.5	+	59310.0i	0.233608	+	0.152321i
$625$	−301258.			−0.771220
$626$		−	93233.3i		−	0.237915i
$627$	554982.	−	851155.i	1.41171	−	2.16508i
$628$	−103700.			−0.262942
$629$			65772.2i			0.166242i
$630$	−74583.1	−	169194.i	−0.187914	−	0.426290i
$631$	−249698.			−0.627129			−0.313565	−	0.949567i	$-0.601523\pi$
$631$	−249698.			−0.627129			−0.313565	+	0.949567i	$0.601523\pi$
$632$		−	3762.12i		−	0.00941887i
$633$	124871.	+	81420.2i	0.311641	+	0.203200i
$634$	−23183.0			−0.0576754
$635$		−	350315.i		−	0.868782i
$636$	−17500.9	+	26840.5i	−0.0432660	+	0.0663554i
$637$	−324288.			−0.799193
$638$		−	115393.i		−	0.283491i
$639$	−599313.	+	264185.i	−1.46775	+	0.647003i
$640$	342883.			0.837117
$641$			192927.i			0.469545i	0.972050	+	0.234772i	$0.0754345\pi$
$641$			192927.i			0.469545i	−0.972050	+	0.234772i	$0.924565\pi$
$642$	−97613.0	−	63647.0i	−0.236831	−	0.154422i
$643$	−639242.			−1.54612			−0.773061	−	0.634332i	$-0.781275\pi$
$643$	−639242.			−1.54612			−0.773061	+	0.634332i	$0.781275\pi$
$644$		−	584804.i		−	1.41006i
$645$	−204898.	+	314244.i	−0.492513	+	0.755348i
$646$	205391.			0.492171
$647$		−	401397.i		−	0.958884i	−0.877574	−	0.479442i	$-0.840839\pi$
$647$		−	401397.i		−	0.958884i	0.877574	−	0.479442i	$-0.159161\pi$
$648$	−173193.	−	158274.i	−0.412457	−	0.376928i
$649$	−80045.3			−0.190041
$650$		−	8777.58i		−	0.0207753i
$651$	73190.4	+	47722.6i	0.172700	+	0.112606i
$652$	−328843.			−0.773559
$653$		−	526944.i		−	1.23577i	−0.786268	−	0.617886i	$-0.787989\pi$
$653$		−	526944.i		−	1.23577i	0.786268	−	0.617886i	$-0.212011\pi$
$654$	8300.35	−	12729.9i	0.0194062	−	0.0297626i
$655$	207540.			0.483748
$656$			361066.i			0.839033i
$657$	10490.2	+	23797.4i	0.0243027	+	0.0551315i
$658$	207480.			0.479209
$659$		−	423139.i		−	0.974343i	−0.873306	−	0.487172i	$-0.838029\pi$
$659$		−	423139.i		−	0.974343i	0.873306	−	0.487172i	$-0.161971\pi$
$660$	−438031.	−	285611.i	−1.00558	−	0.655673i
$661$	−338181.			−0.774010			−0.387005	−	0.922078i	$-0.626490\pi$
$661$	−338181.			−0.774010			−0.387005	+	0.922078i	$0.626490\pi$
$662$			172839.i			0.394389i
$663$	84836.1	−	130110.i	0.192998	−	0.295994i
$664$	−446027.			−1.01164
$665$			1.25015e6i			2.82695i
$666$	20668.1	−	9110.78i	0.0465964	−	0.0205403i
$667$	−256958.			−0.577578
$668$		−	170696.i		−	0.382534i
$669$	484468.	+	315889.i	1.08246	+	0.705802i
$670$	−157207.			−0.350205
$671$		−	817429.i		−	1.81554i
$672$	−340872.	+	522782.i	−0.754836	+	1.15766i
$673$	−1045.44			−0.00230817			−0.00115408	−	0.999999i	$-0.500367\pi$
$673$	−1045.44			−0.00230817			−0.00115408	+	0.999999i	$0.500367\pi$
$674$			237823.i			0.523521i
$675$	14158.5	−	86298.6i	0.0310750	−	0.189407i
$676$	−360542.			−0.788973
$677$		−	221844.i		−	0.484029i	−0.970273	−	0.242014i	$-0.922192\pi$
$677$		−	221844.i		−	0.484029i	0.970273	−	0.242014i	$-0.0778081\pi$
$678$	189440.	+	123522.i	0.412110	+	0.268710i
$679$	600550.			1.30259
$680$		−	221238.i		−	0.478456i
$681$	244643.	−	375200.i	0.527520	−	0.809037i
$682$	−22997.3			−0.0494433
$683$		−	445211.i		−	0.954387i	−0.878798	−	0.477194i	$-0.841654\pi$
$683$		−	445211.i		−	0.954387i	0.878798	−	0.477194i	$-0.158346\pi$
$684$	305697.	+	693484.i	0.653400	+	1.48226i
$685$	630916.			1.34459
$686$		−	281567.i		−	0.598320i
$687$	441994.	+	288195.i	0.936489	+	0.610623i
$688$	356980.			0.754167
$689$			15247.5i			0.0321189i
$690$	59191.4	−	90779.6i	0.124326	−	0.190673i
$691$	591550.			1.23890			0.619448	−	0.785037i	$-0.287356\pi$
$691$	591550.			1.23890			0.619448	+	0.785037i	$0.287356\pi$
$692$		−	3131.97i		−	0.00654041i
$693$	1.13932e6	−	502225.i	2.37234	−	1.04576i
$694$	−106742.			−0.221624
$695$		−	13525.8i		−	0.0280023i
$696$	150901.	+	98392.6i	0.311511	+	0.203116i
$697$	516463.			1.06310
$698$		−	112169.i		−	0.230230i
$699$	−133488.	+	204726.i	−0.273205	+	0.419004i
$700$	−152819.			−0.311876
$701$		−	257419.i		−	0.523847i	−0.965089	−	0.261923i	$-0.915643\pi$
$701$		−	257419.i		−	0.523847i	0.965089	−	0.261923i	$-0.0843568\pi$
$702$	−52636.9	−	8635.86i	−0.106811	−	0.0175239i
$703$	−152713.			−0.309005
$704$			379649.i			0.766015i
$705$	−346061.	−	225644.i	−0.696265	−	0.453988i
$706$	168549.			0.338155
$707$			1.19065e6i			2.38201i
$708$	32608.7	−	50010.7i	0.0650530	−	0.0997692i
$709$	−119925.			−0.238570			−0.119285	−	0.992860i	$-0.538060\pi$
$709$	−119925.			−0.238570			−0.119285	+	0.992860i	$0.538060\pi$
$710$			212094.i			0.420737i
$711$	−3437.32	−	7797.67i	−0.00679955	−	0.0154250i
$712$	172332.			0.339943
$713$			51210.3i			0.100734i
$714$	210822.	+	137463.i	0.413541	+	0.269643i
$715$	−248836.			−0.486744
$716$			43979.7i			0.0857880i
$717$	−456467.	+	700066.i	−0.887914	+	1.36176i
$718$	76244.7			0.147897
$719$			849612.i			1.64347i	0.569867	+	0.821737i	$0.306995\pi$
$719$			849612.i			1.64347i	−0.569867	+	0.821737i	$0.693005\pi$
$720$	320582.	−	141317.i	0.618407	−	0.272602i
$721$	−1.66611e6			−3.20504
$722$			324778.i			0.623035i
$723$	555094.	+	361940.i	1.06192	+	0.692405i
$724$	397202.			0.757765
$725$			67147.5i			0.127748i
$726$	−94990.6	+	145683.i	−0.180222	+	0.276399i
$727$	15489.3			0.0293065			0.0146533	−	0.999893i	$-0.495336\pi$
$727$	15489.3			0.0293065			0.0146533	+	0.999893i	$0.495336\pi$
$728$			195096.i			0.368116i
$729$	−503581.	−	169810.i	−0.947577	−	0.319528i
$730$	8421.79			0.0158037
$731$		−	510619.i		−	0.955569i
$732$	510714.	+	333003.i	0.953137	+	0.621478i
$733$	890710.			1.65779			0.828893	−	0.559408i	$-0.188971\pi$
$733$	890710.			1.65779			0.828893	+	0.559408i	$0.188971\pi$
$734$		−	212348.i		−	0.394144i
$735$	−571455.	+	876419.i	−1.05781	+	1.62232i
$736$	−365783.			−0.675255
$737$		−	1.05860e6i		−	1.94892i
$738$	−71540.6	−	162292.i	−0.131353	−	0.297979i
$739$	−2030.85			−0.00371868			−0.00185934	−	0.999998i	$-0.500592\pi$
$739$	−2030.85			−0.00371868			−0.00185934	+	0.999998i	$0.500592\pi$
$740$			78591.0i			0.143519i
$741$	302095.	+	196977.i	0.550184	+	0.358739i
$742$	−24706.1			−0.0448741
$743$		−	442006.i		−	0.800664i	−0.916370	−	0.400332i	$-0.868895\pi$
$743$		−	442006.i		−	0.800664i	0.916370	−	0.400332i	$-0.131105\pi$
$744$	19609.1	−	30073.7i	0.0354251	−	0.0543301i
$745$	−252595.			−0.455106
$746$			97717.7i			0.175588i
$747$	−924471.	+	407519.i	−1.65673	+	0.730309i
$748$	711762.			1.27213
$749$			965425.i			1.72090i
$750$	−147315.	−	96054.3i	−0.261893	−	0.170763i
$751$	−1.09401e6			−1.93972			−0.969861	−	0.243657i	$-0.921653\pi$
$751$	−1.09401e6			−1.93972			−0.969861	+	0.243657i	$0.921653\pi$
$752$			393125.i			0.695176i
$753$	−116423.	+	178553.i	−0.205328	+	0.314903i
$754$	40955.9			0.0720401
$755$			279419.i			0.490187i
$756$	−150352.	+	916417.i	−0.263066	+	1.60343i
$757$	−790749.			−1.37990			−0.689949	−	0.723858i	$-0.742367\pi$
$757$	−790749.			−1.37990			−0.689949	+	0.723858i	$0.742367\pi$
$758$			11544.1i			0.0200919i
$759$	611289.	+	398581.i	1.06112	+	0.691884i
$760$	513682.			0.889338
$761$		−	881986.i		−	1.52297i	−0.648181	−	0.761487i	$-0.724470\pi$
$761$		−	881986.i		−	1.52297i	0.648181	−	0.761487i	$-0.275530\pi$
$762$	89436.9	−	137166.i	0.154031	−	0.236231i
$763$	−125903.			−0.216266
$764$			312409.i			0.535226i
$765$	−202137.	−	458555.i	−0.345401	−	0.783554i
$766$	−166644.			−0.284009
$767$		−	28410.0i		−	0.0482926i
$768$	−125017.	−	81515.3i	−0.211956	−	0.138203i
$769$	−36739.2			−0.0621266			−0.0310633	−	0.999517i	$-0.509889\pi$
$769$	−36739.2			−0.0621266			−0.0310633	+	0.999517i	$0.509889\pi$
$770$		−	403198.i		−	0.680044i
$771$	−116178.	+	178178.i	−0.195442	+	0.299741i
$772$	806724.			1.35360
$773$			816495.i			1.36645i	0.730207	+	0.683226i	$0.239424\pi$
$773$			816495.i			1.36645i	−0.730207	+	0.683226i	$0.760576\pi$
$774$	−160456.	+	70731.0i	−0.267839	+	0.118067i
$775$	13382.1			0.0222803
$776$		−	246764.i		−	0.409787i
$777$	−156751.	−	102207.i	−0.259639	−	0.169293i
$778$	181554.			0.299949
$779$			1.19915e6i			1.97605i
$780$	101370.	−	155468.i	0.166618	−	0.255535i
$781$	−1.42819e6			−2.34144
$782$			147509.i			0.241215i
$783$	402667.	+	66063.3i	0.656784	+	0.107755i
$784$	995610.			1.61978
$785$			159209.i			0.258362i
$786$	81262.4	+	52985.9i	0.131536	+	0.0857660i
$787$	−205656.			−0.332041			−0.166021	−	0.986122i	$-0.553092\pi$
$787$	−205656.			−0.332041			−0.166021	+	0.986122i	$0.553092\pi$
$788$		−	367871.i		−	0.592438i
$789$	280027.	−	429466.i	0.449827	−	0.689882i
$790$	−2759.56			−0.00442166
$791$		−	1.87363e6i		−	2.99454i
$792$	−206363.	−	468141.i	−0.328989	−	0.746322i
$793$	290125.			0.461359
$794$			134057.i			0.212642i
$795$	41207.8	+	26868.9i	0.0651997	+	0.0425124i
$796$	−40128.3			−0.0633323
$797$		−	1.04258e6i		−	1.64131i	−0.571422	−	0.820656i	$-0.693608\pi$
$797$		−	1.04258e6i		−	1.64131i	0.571422	−	0.820656i	$-0.306392\pi$
$798$	−319168.	+	489496.i	−0.501204	+	0.768676i
$799$	562319.			0.880824
$800$			95585.3i			0.149352i
$801$	357189.	−	157454.i	0.556714	−	0.245407i
$802$	−212986.			−0.331132
$803$			56710.4i			0.0879491i
$804$	661390.	+	431249.i	1.02316	+	0.667138i
$805$	−897841.			−1.38550
$806$		−	8162.28i		−	0.0125644i
$807$	488990.	−	749946.i	0.750850	−	1.15155i
$808$	489233.			0.749364
$809$		−	932975.i		−	1.42552i	−0.701408	−	0.712760i	$-0.747445\pi$
$809$		−	932975.i		−	1.42552i	0.701408	−	0.712760i	$-0.252555\pi$
$810$	−116095.	+	127038.i	−0.176948	+	0.193627i
$811$	−435568.			−0.662238			−0.331119	−	0.943589i	$-0.607426\pi$
$811$	−435568.			−0.662238			−0.331119	+	0.943589i	$0.607426\pi$
$812$		−	713049.i		−	1.08145i
$813$	−877708.	−	572296.i	−1.32791	−	0.865844i
$814$	49253.1			0.0743335
$815$			504868.i			0.760086i
$816$	−260459.	+	399456.i	−0.391164	+	0.599914i
$817$	1.18558e6			1.77618
$818$		−	187636.i		−	0.280420i
$819$	178252.	+	404370.i	0.265746	+	0.602853i
$820$	617120.			0.917787
$821$			479977.i			0.712089i	0.934469	+	0.356044i	$0.115875\pi$
$821$			479977.i			0.712089i	−0.934469	+	0.356044i	$0.884125\pi$
$822$	247035.	+	161076.i	0.365608	+	0.238389i
$823$	−629784.			−0.929806			−0.464903	−	0.885362i	$-0.653911\pi$
$823$	−629784.			−0.929806			−0.464903	+	0.885362i	$0.653911\pi$
$824$			684599.i			1.00828i
$825$	104156.	−	159740.i	0.153030	−	0.234696i
$826$	46033.8			0.0674709
$827$		−	17111.6i		−	0.0250195i	−0.999922	−	0.0125098i	$-0.996018\pi$
$827$		−	17111.6i		−	0.0250195i	0.999922	−	0.0125098i	$-0.00398208\pi$
$828$	−498052.	+	219548.i	−0.726463	+	0.320235i
$829$	878281.			1.27798			0.638990	−	0.769215i	$-0.279352\pi$
$829$	878281.			1.27798			0.638990	+	0.769215i	$0.279352\pi$
$830$			327165.i			0.474910i
$831$	−447752.	−	291950.i	−0.648388	−	0.422772i
$832$	−134747.			−0.194658
$833$		−	1.42410e6i		−	2.05235i
$834$	3453.20	−	5296.05i	0.00496467	−	0.00761412i
$835$	−262067.			−0.375871
$836$			1.65260e6i			2.36459i
$837$	13166.0	−	80249.2i	0.0187934	−	0.114549i
$838$	−351028.			−0.499867
$839$		−	425705.i		−	0.604763i	−0.953187	−	0.302381i	$-0.902218\pi$
$839$		−	425705.i		−	0.604763i	0.953187	−	0.302381i	$-0.0977816\pi$
$840$	527265.	+	343795.i	0.747258	+	0.487238i
$841$	393973.			0.557024
$842$		−	198029.i		−	0.279322i
$843$	−178594.	+	273903.i	−0.251311	+	0.385426i
$844$	−242450.			−0.340359
$845$			553535.i			0.775232i
$846$	−77892.5	−	176702.i	−0.108832	−	0.246888i
$847$	1.44086e6			2.00842
$848$		−	46812.0i		−	0.0650977i
$849$	−639398.	−	416909.i	−0.887066	−	0.578397i
$850$	38546.6			0.0533517
$851$		−	109677.i		−	0.151445i
$852$	581813.	−	892305.i	0.801502	−	1.22923i
$853$	137821.			0.189417			0.0947083	−	0.995505i	$-0.469808\pi$
$853$	137821.			0.189417			0.0947083	+	0.995505i	$0.469808\pi$
$854$			470101.i			0.644577i
$855$	1.06470e6	−	469333.i	1.45644	−	0.642020i
$856$	396690.			0.541382
$857$		−	555414.i		−	0.756232i	−0.925758	−	0.378116i	$-0.876572\pi$
$857$		−	555414.i		−	0.756232i	0.925758	−	0.378116i	$-0.123428\pi$
$858$	−97431.8	−	63528.9i	−0.132351	−	0.0862972i
$859$	748789.			1.01478			0.507392	−	0.861716i	$-0.330610\pi$
$859$	748789.			1.01478			0.507392	+	0.861716i	$0.330610\pi$
$860$		−	610136.i		−	0.824954i
$861$	−802562.	+	1.23086e6i	−1.08261	+	1.66036i
$862$	182635.			0.245793
$863$			407607.i			0.547294i	0.961830	+	0.273647i	$0.0882300\pi$
$863$			407607.i			0.547294i	−0.961830	+	0.273647i	$0.911770\pi$
$864$	573201.	+	94042.0i	0.767856	+	0.125978i
$865$	−4808.47			−0.00642650
$866$		−	256929.i		−	0.342592i
$867$	−58287.5	−	38005.5i	−0.0775421	−	0.0505601i
$868$	−142107.			−0.188614
$869$		−	18582.2i		−	0.0246069i
$870$	72172.0	−	110687.i	0.0953520	−	0.146238i
$871$	375721.			0.495255
$872$			51733.2i			0.0680357i
$873$	−225459.	−	511462.i	−0.295828	−	0.671096i
$874$	−342494.			−0.448363
$875$			1.45699e6i			1.90301i
$876$	−35431.5	−	23102.6i	−0.0461723	−	0.0301059i
$877$	117354.			0.152581			0.0762905	−	0.997086i	$-0.475692\pi$
$877$	117354.			0.152581			0.0762905	+	0.997086i	$0.475692\pi$
$878$			30774.9i			0.0399216i
$879$	230235.	−	353103.i	0.297985	−	0.457007i
$880$	763962.			0.986521
$881$			1.10900e6i			1.42882i	0.699725	+	0.714412i	$0.253306\pi$
$881$			1.10900e6i			1.42882i	−0.699725	+	0.714412i	$0.746694\pi$
$882$	−447507.	+	197267.i	−0.575258	+	0.253582i
$883$	674171.			0.864666			0.432333	−	0.901714i	$-0.357690\pi$
$883$	674171.			0.864666			0.432333	+	0.901714i	$0.357690\pi$
$884$			252622.i			0.323270i
$885$	−76780.8	−	50063.7i	−0.0980315	−	0.0639199i
$886$	−187306.			−0.238607
$887$			476121.i			0.605160i	0.953124	+	0.302580i	$0.0978479\pi$
$887$			476121.i			0.605160i	−0.953124	+	0.302580i	$0.902152\pi$
$888$	−41996.6	+	64408.6i	−0.0532585	+	0.0816804i
$889$	−1.35662e6			−1.71654
$890$		−	126407.i		−	0.159585i
$891$	−855447.	−	781759.i	−1.07755	−	0.984730i
$892$	−940643.			−1.18221
$893$			1.30562e6i			1.63725i
$894$	−98903.8	−	64488.7i	−0.123748	−	0.0806879i
$895$	67521.5			0.0842938
$896$		−	1.32784e6i		−	1.65397i
$897$	−141466.	+	216961.i	−0.175820	+	0.269648i
$898$	85033.7			0.105448
$899$			62440.5i			0.0772587i
$900$	57371.6	+	130149.i	0.0708291	+	0.160678i
$901$	−66959.2			−0.0824822
$902$		−	386750.i		−	0.475354i
$903$	1.21693e6	+	793480.i	1.49242	+	0.973107i
$904$	−769868.			−0.942061
$905$		−	609819.i		−	0.744567i
$906$	−71336.8	+	109407.i	−0.0869075	+	0.133287i
$907$	192323.			0.233785			0.116893	−	0.993145i	$-0.462707\pi$
$907$	192323.			0.233785			0.116893	+	0.993145i	$0.462707\pi$
$908$			728489.i			0.883591i
$909$	1.01402e6	−	446994.i	1.22721	−	0.540971i
$910$	143105.			0.172811
$911$		−	1.48648e6i		−	1.79110i	−0.444956	−	0.895552i	$-0.646781\pi$
$911$		−	1.48648e6i		−	1.79110i	0.444956	−	0.895552i	$-0.353219\pi$
$912$	−927477.	−	604747.i	−1.11510	−	0.727083i
$913$	−2.20306e6			−2.64292
$914$		−	78789.8i		−	0.0943143i
$915$	511255.	−	784092.i	0.610654	−	0.936536i
$916$	−858176.			−1.02279
$917$		−	803712.i		−	0.955789i
$918$	37924.2	−	231154.i	0.0450020	−	0.274294i
$919$	423660.			0.501633			0.250816	−	0.968035i	$-0.419301\pi$
$919$	423660.			0.501633			0.250816	+	0.968035i	$0.419301\pi$
$920$			368920.i			0.435869i
$921$	−1.32019e6	−	860809.i	−1.55639	−	1.01482i
$922$	−17832.1			−0.0209769
$923$		−	506899.i		−	0.595001i
$924$	−1.10605e6	+	1.69630e6i	−1.29548	+	1.98683i
$925$	−28660.4			−0.0334964
$926$			116847.i			0.136269i
$927$	625494.	+	1.41895e6i	0.727886	+	1.65123i
$928$	−445998.			−0.517890
$929$		−	538425.i		−	0.623869i	−0.950104	−	0.311935i	$-0.899023\pi$
$929$		−	538425.i		−	0.623869i	0.950104	−	0.311935i	$-0.100977\pi$
$930$	−22059.3	−	14383.5i	−0.0255051	−	0.0166302i
$931$	3.30656e6			3.81484
$932$		−	397496.i		−	0.457615i
$933$	−847402.	+	1.29963e6i	−0.973478	+	1.49299i
$934$	−293468.			−0.336408
$935$		−	1.09276e6i		−	1.24997i
$936$	166155.	−	73243.2i	0.189653	−	0.0836017i
$937$	−1.51272e6			−1.72297			−0.861487	−	0.507780i	$-0.830466\pi$
$937$	−1.51272e6			−1.72297			−0.861487	+	0.507780i	$0.830466\pi$
$938$			608795.i			0.691935i
$939$	602207.	+	392660.i	0.682991	+	0.445334i
$940$	671913.			0.760426
$941$		−	19155.6i		−	0.0216330i	−0.999941	−	0.0108165i	$-0.996557\pi$
$941$		−	19155.6i		−	0.0216330i	0.999941	−	0.0108165i	$-0.00344307\pi$
$942$	−40646.8	+	62338.5i	−0.0458063	+	0.0702513i
$943$	−861214.			−0.968474
$944$			87222.8i			0.0978782i
$945$	1.40696e6	+	230833.i	1.57550	+	0.258484i
$946$	−382373.			−0.427273
$947$			553216.i			0.616871i	0.951245	+	0.308436i	$0.0998054\pi$
$947$			553216.i			0.616871i	−0.951245	+	0.308436i	$0.900195\pi$
$948$	11609.8	+	7569.99i	0.0129184	+	0.00842322i
$949$	−20127.9			−0.0223494
$950$			89499.4i			0.0991683i
$951$	97637.0	−	149742.i	0.107958	−	0.165570i
$952$	−856760.			−0.945334
$953$		−	1.11705e6i		−	1.22995i	−0.788546	−	0.614976i	$-0.789166\pi$
$953$		−	1.11705e6i		−	1.22995i	0.788546	−	0.614976i	$-0.210834\pi$
$954$	9275.20	+	21041.1i	0.0101912	+	0.0231191i
$955$	479638.			0.525904
$956$		−	1.35925e6i		−	1.48725i
$957$	745343.	+	485989.i	0.813827	+	0.530643i
$958$	−315401.			−0.343663
$959$		−	2.44326e6i		−	2.65664i
$960$	−237449.	+	364166.i	−0.257648	+	0.395145i
$961$	−911077.			−0.986525
$962$			17481.1i			0.0188894i
$963$	822211.	−	362441.i	0.886606	−	0.390828i
$964$	−1.07777e6			−1.15977
$965$		−	1.23855e6i		−	1.33003i
$966$	−351550.	−	229223.i	−0.376733	−	0.245643i
$967$	−1.84182e6			−1.96968			−0.984838	−	0.173477i	$-0.944500\pi$
$967$	−1.84182e6			−1.96968			−0.984838	+	0.173477i	$0.944500\pi$
$968$		−	592044.i		−	0.631834i
$969$	−865020.	+	1.32665e6i	−0.921252	+	1.41289i
$970$	−181004.			−0.192373
$971$			842859.i			0.893956i	0.894545	+	0.446978i	$0.147500\pi$
$971$			842859.i			0.893956i	−0.894545	+	0.446978i	$0.852500\pi$
$972$	836918.	−	215995.i	0.885830	−	0.228618i
$973$	−52379.7			−0.0553270
$974$		−	96830.6i		−	0.102069i
$975$	56695.6	+	36967.5i	0.0596404	+	0.0388876i
$976$	−890727.			−0.935071
$977$		−	773136.i		−	0.809966i	−0.914324	−	0.404983i	$-0.867277\pi$
$977$		−	773136.i		−	0.809966i	0.914324	−	0.404983i	$-0.132723\pi$
$978$	−128895.	+	197681.i	−0.134759	+	0.206675i
$979$	851197.			0.888105
$980$		−	1.70166e6i		−	1.77182i
$981$	47266.8	+	107226.i	0.0491155	+	0.111420i
$982$	244739.			0.253793
$983$		−	388255.i		−	0.401800i	−0.979612	−	0.200900i	$-0.935613\pi$
$983$		−	388255.i		−	0.401800i	0.979612	−	0.200900i	$-0.0643867\pi$
$984$	505756.	+	329770.i	0.522337	+	0.340582i
$985$	−564787.			−0.582120
$986$			179857.i			0.185001i
$987$	−873820.	+	1.34014e6i	−0.896990	+	1.37568i
$988$	−586549.			−0.600884
$989$			851469.i			0.870515i
$990$	−343386.	+	151369.i	−0.350358	+	0.154443i
$991$	35726.0			0.0363778			0.0181889	−	0.999835i	$-0.494210\pi$
$991$	35726.0			0.0363778			0.0181889	+	0.999835i	$0.494210\pi$
$992$			88884.9i			0.0903243i
$993$	−1.11639e6	−	727925.i	−1.13219	−	0.738224i
$994$	821347.			0.831292
$995$			61608.5i			0.0622292i
$996$	897477.	−	1.37643e6i	0.904700	−	1.38750i
$997$	303969.			0.305801			0.152900	−	0.988242i	$-0.451139\pi$
$997$	303969.			0.305801			0.152900	+	0.988242i	$0.451139\pi$
$998$			216385.i			0.217253i
$999$	−28197.6	+	171869.i	−0.0282541	+	0.172213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.43	yes	78
3.2	odd	2	inner	177.5.b.a.119.36	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.36	✓	78	3.2	odd	2	inner
177.5.b.a.119.43	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)

\(f(q)\)	\(=\)	\(q+1.16718i q^{2} +(-7.53898 - 4.91567i) q^{3} +14.6377 q^{4} -22.4730i q^{5} +(5.73747 - 8.79934i) q^{6} -87.0284 q^{7} +35.7597i q^{8} +(32.6723 + 74.1183i) q^{9} +O(q^{10})\)	\(q+1.16718i q^{2} +(-7.53898 - 4.91567i) q^{3} +14.6377 q^{4} -22.4730i q^{5} +(5.73747 - 8.79934i) q^{6} -87.0284 q^{7} +35.7597i q^{8} +(32.6723 + 74.1183i) q^{9} +26.2301 q^{10} +176.627i q^{11} +(-110.353 - 71.9541i) q^{12} -62.6893 q^{13} -101.578i q^{14} +(-110.470 + 169.424i) q^{15} +192.465 q^{16} -275.299i q^{17} +(-86.5093 + 38.1345i) q^{18} +639.203 q^{19} -328.954i q^{20} +(656.105 + 427.803i) q^{21} -206.156 q^{22} +459.067i q^{23} +(175.783 - 269.591i) q^{24} +119.962 q^{25} -73.1696i q^{26} +(118.025 - 719.382i) q^{27} -1273.89 q^{28} +559.739i q^{29} +(-197.748 - 128.938i) q^{30} +111.553 q^{31} +796.796i q^{32} +(868.242 - 1331.59i) q^{33} +321.323 q^{34} +1955.79i q^{35} +(478.248 + 1084.92i) q^{36} -238.912 q^{37} +746.064i q^{38} +(472.613 + 308.160i) q^{39} +803.629 q^{40} +1876.01i q^{41} +(-499.323 + 765.792i) q^{42} +1854.78 q^{43} +2585.42i q^{44} +(1665.66 - 734.247i) q^{45} -535.814 q^{46} +2042.58i q^{47} +(-1450.99 - 946.095i) q^{48} +5172.94 q^{49} +140.017i q^{50} +(-1353.28 + 2075.47i) q^{51} -917.626 q^{52} -243.223i q^{53} +(839.648 + 137.757i) q^{54} +3969.35 q^{55} -3112.11i q^{56} +(-4818.93 - 3142.11i) q^{57} -653.316 q^{58} +453.188i q^{59} +(-1617.03 + 2479.97i) q^{60} -4627.99 q^{61} +130.202i q^{62} +(-2843.42 - 6450.39i) q^{63} +2149.44 q^{64} +1408.82i q^{65} +(1554.20 + 1013.39i) q^{66} -5993.39 q^{67} -4029.74i q^{68} +(2256.63 - 3460.90i) q^{69} -2282.76 q^{70} +8085.89i q^{71} +(-2650.45 + 1168.35i) q^{72} +321.074 q^{73} -278.853i q^{74} +(-904.391 - 589.694i) q^{75} +9356.45 q^{76} -15371.6i q^{77} +(-359.678 + 551.624i) q^{78} -105.206 q^{79} -4325.28i q^{80} +(-4426.04 + 4843.23i) q^{81} -2189.64 q^{82} +12472.9i q^{83} +(9603.86 + 6262.05i) q^{84} -6186.81 q^{85} +2164.86i q^{86} +(2751.50 - 4219.86i) q^{87} -6316.13 q^{88} -4819.17i q^{89} +(856.998 + 1944.13i) q^{90} +5455.75 q^{91} +6719.69i q^{92} +(-840.994 - 548.357i) q^{93} -2384.05 q^{94} -14364.8i q^{95} +(3916.79 - 6007.03i) q^{96} -6900.62 q^{97} +6037.75i q^{98} +(-13091.3 + 5770.82i) 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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