LMFDB - Embedded newform 77.5.d.a.34.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,5,Mod(34,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	77.d (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:	$7.95948715746$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.5
Character	$\chi$	$=$	77.34
Dual form			77.5.d.a.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.70412 q^{2} -7.64626i q^{3} +16.5370 q^{4} -9.31094i q^{5} +43.6152i q^{6} +(34.0002 - 35.2843i) q^{7} -3.06288 q^{8} +22.5346 q^{9} +O(q^{10})$	\(q-5.70412 q^{2} -7.64626i q^{3} +16.5370 q^{4} -9.31094i q^{5} +43.6152i q^{6} +(34.0002 - 35.2843i) q^{7} -3.06288 q^{8} +22.5346 q^{9} +53.1107i q^{10} +36.4829 q^{11} -126.446i q^{12} +119.989i q^{13} +(-193.941 + 201.266i) q^{14} -71.1939 q^{15} -247.120 q^{16} -528.958i q^{17} -128.540 q^{18} -300.735i q^{19} -153.975i q^{20} +(-269.793 - 259.975i) q^{21} -208.103 q^{22} -691.723 q^{23} +23.4196i q^{24} +538.306 q^{25} -684.431i q^{26} -791.653i q^{27} +(562.260 - 583.496i) q^{28} -1408.09 q^{29} +406.098 q^{30} +1517.21i q^{31} +1458.61 q^{32} -278.958i q^{33} +3017.24i q^{34} +(-328.530 - 316.574i) q^{35} +372.654 q^{36} +669.816 q^{37} +1715.43i q^{38} +917.467 q^{39} +28.5183i q^{40} -1343.68i q^{41} +(1538.93 + 1482.93i) q^{42} -502.866 q^{43} +603.316 q^{44} -209.819i q^{45} +3945.67 q^{46} +1193.46i q^{47} +1889.55i q^{48} +(-88.9687 - 2399.35i) q^{49} -3070.56 q^{50} -4044.56 q^{51} +1984.25i q^{52} +1058.76 q^{53} +4515.68i q^{54} -339.690i q^{55} +(-104.139 + 108.072i) q^{56} -2299.50 q^{57} +8031.91 q^{58} -2508.35i q^{59} -1177.33 q^{60} +1059.89i q^{61} -8654.37i q^{62} +(766.183 - 795.120i) q^{63} -4366.15 q^{64} +1117.21 q^{65} +1591.21i q^{66} +2934.81 q^{67} -8747.36i q^{68} +5289.10i q^{69} +(1873.98 + 1805.78i) q^{70} -7130.47 q^{71} -69.0208 q^{72} -5197.02i q^{73} -3820.71 q^{74} -4116.03i q^{75} -4973.25i q^{76} +(1240.43 - 1287.27i) q^{77} -5233.34 q^{78} -1341.21 q^{79} +2300.92i q^{80} -4227.88 q^{81} +7664.52i q^{82} -3788.29i q^{83} +(-4461.56 - 4299.19i) q^{84} -4925.10 q^{85} +2868.41 q^{86} +10766.6i q^{87} -111.743 q^{88} +3337.04i q^{89} +1196.83i q^{90} +(4233.73 + 4079.65i) q^{91} -11439.0 q^{92} +11601.0 q^{93} -6807.65i q^{94} -2800.13 q^{95} -11152.9i q^{96} +18179.1i q^{97} +(507.488 + 13686.2i) q^{98} +822.128 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	$ 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) $ 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$1$

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 $

$2$	−5.70412			−1.42603			−0.713015	−	0.701149i	$-0.752671\pi$
$2$	−5.70412			−1.42603			−0.713015	+	0.701149i	$0.752671\pi$
$3$		−	7.64626i		−	0.849585i	−0.905291	−	0.424792i	$-0.860347\pi$
$3$		−	7.64626i		−	0.849585i	0.905291	−	0.424792i	$-0.139653\pi$
$4$	16.5370			1.03356
$5$		−	9.31094i		−	0.372438i	−0.982508	−	0.186219i	$-0.940377\pi$
$5$		−	9.31094i		−	0.372438i	0.982508	−	0.186219i	$-0.0596233\pi$
$6$			43.6152i			1.21153i
$7$	34.0002	−	35.2843i	0.693882	−	0.720088i
$7$	34.0002	−	35.2843i	0.693882	−	0.720088i
$8$	−3.06288			−0.0478575
$9$	22.5346			0.278205
$10$			53.1107i			0.531107i
$11$	36.4829			0.301511
$11$	36.4829			0.301511
$12$		−	126.446i		−	0.878097i
$13$			119.989i			0.709993i	0.934868	+	0.354997i	$0.115518\pi$
$13$			119.989i			0.709993i	−0.934868	+	0.354997i	$0.884482\pi$
$14$	−193.941	+	201.266i	−0.989497	+	1.02687i
$15$	−71.1939			−0.316417
$16$	−247.120			−0.965314
$17$		−	528.958i		−	1.83031i	−0.403107	−	0.915153i	$-0.632070\pi$
$17$		−	528.958i		−	1.83031i	0.403107	−	0.915153i	$-0.367930\pi$
$18$	−128.540			−0.396729
$19$		−	300.735i		−	0.833062i	−0.909122	−	0.416531i	$-0.863246\pi$
$19$		−	300.735i		−	0.833062i	0.909122	−	0.416531i	$-0.136754\pi$
$20$		−	153.975i		−	0.384937i
$21$	−269.793	−	259.975i	−0.611776	−	0.589512i
$22$	−208.103			−0.429964
$23$	−691.723			−1.30760			−0.653802	−	0.756665i	$-0.726827\pi$
$23$	−691.723			−1.30760			−0.653802	+	0.756665i	$0.726827\pi$
$24$			23.4196i			0.0406590i
$25$	538.306			0.861290
$26$		−	684.431i		−	1.01247i
$27$		−	791.653i		−	1.08594i
$28$	562.260	−	583.496i	0.717169	−	0.744255i
$29$	−1408.09			−1.67430			−0.837152	−	0.546971i	$-0.815781\pi$
$29$	−1408.09			−1.67430			−0.837152	+	0.546971i	$0.815781\pi$
$30$	406.098			0.451220
$31$			1517.21i			1.57879i	0.613888	+	0.789393i	$0.289605\pi$
$31$			1517.21i			1.57879i	−0.613888	+	0.789393i	$0.710395\pi$
$32$	1458.61			1.42442
$33$		−	278.958i		−	0.256160i
$34$			3017.24i			2.61007i
$35$	−328.530	−	316.574i	−0.268188	−	0.258428i
$36$	372.654			0.287542
$37$	669.816			0.489274			0.244637	−	0.969615i	$-0.421331\pi$
$37$	669.816			0.489274			0.244637	+	0.969615i	$0.421331\pi$
$38$			1715.43i			1.18797i
$39$	917.467			0.603200
$40$			28.5183i			0.0178239i
$41$		−	1343.68i		−	0.799335i	−0.916660	−	0.399667i	$-0.869126\pi$
$41$		−	1343.68i		−	0.799335i	0.916660	−	0.399667i	$-0.130874\pi$
$42$	1538.93	+	1482.93i	0.872411	+	0.840661i
$43$	−502.866			−0.271966			−0.135983	−	0.990711i	$-0.543419\pi$
$43$	−502.866			−0.271966			−0.135983	+	0.990711i	$0.543419\pi$
$44$	603.316			0.311630
$45$		−	209.819i		−	0.103614i
$46$	3945.67			1.86468
$47$			1193.46i			0.540273i	0.962822	+	0.270136i	$0.0870688\pi$
$47$			1193.46i			0.540273i	−0.962822	+	0.270136i	$0.912931\pi$
$48$			1889.55i			0.820116i
$49$	−88.9687	−	2399.35i	−0.0370548	−	0.999313i
$50$	−3070.56			−1.22823
$51$	−4044.56			−1.55500
$52$			1984.25i			0.733821i
$53$	1058.76			0.376917			0.188458	−	0.982081i	$-0.439651\pi$
$53$	1058.76			0.376917			0.188458	+	0.982081i	$0.439651\pi$
$54$			4515.68i			1.54859i
$55$		−	339.690i		−	0.112294i
$56$	−104.139	+	108.072i	−0.0332074	+	0.0344616i
$57$	−2299.50			−0.707757
$58$	8031.91			2.38761
$59$		−	2508.35i		−	0.720583i	−0.932840	−	0.360291i	$-0.882677\pi$
$59$		−	2508.35i		−	0.720583i	0.932840	−	0.360291i	$-0.117323\pi$
$60$	−1177.33			−0.327036
$61$			1059.89i			0.284839i	0.989806	+	0.142420i	$0.0454882\pi$
$61$			1059.89i			0.284839i	−0.989806	+	0.142420i	$0.954512\pi$
$62$		−	8654.37i		−	2.25140i
$63$	766.183	−	795.120i	0.193042	−	0.200332i
$64$	−4366.15			−1.06596
$65$	1117.21			0.264428
$66$			1591.21i			0.365291i
$67$	2934.81			0.653779			0.326889	−	0.945063i	$-0.394000\pi$
$67$	2934.81			0.653779			0.326889	+	0.945063i	$0.394000\pi$
$68$		−	8747.36i		−	1.89173i
$69$			5289.10i			1.11092i
$70$	1873.98	+	1805.78i	0.382444	+	0.368526i
$71$	−7130.47			−1.41450			−0.707248	−	0.706966i	$-0.750063\pi$
$71$	−7130.47			−1.41450			−0.707248	+	0.706966i	$0.750063\pi$
$72$	−69.0208			−0.0133142
$73$		−	5197.02i		−	0.975234i	−0.873058	−	0.487617i	$-0.837866\pi$
$73$		−	5197.02i		−	0.975234i	0.873058	−	0.487617i	$-0.162134\pi$
$74$	−3820.71			−0.697719
$75$		−	4116.03i		−	0.731739i
$76$		−	4973.25i		−	0.861019i
$77$	1240.43	−	1287.27i	0.209213	−	0.217115i
$78$	−5233.34			−0.860181
$79$	−1341.21			−0.214903			−0.107452	−	0.994210i	$-0.534269\pi$
$79$	−1341.21			−0.214903			−0.107452	+	0.994210i	$0.534269\pi$
$80$			2300.92i			0.359519i
$81$	−4227.88			−0.644396
$82$			7664.52i			1.13987i
$83$		−	3788.29i		−	0.549904i	−0.961458	−	0.274952i	$-0.911338\pi$
$83$		−	3788.29i		−	0.549904i	0.961458	−	0.274952i	$-0.0886619\pi$
$84$	−4461.56	−	4299.19i	−0.632308	−	0.609296i
$85$	−4925.10			−0.681675
$86$	2868.41			0.387832
$87$			10766.6i			1.42246i
$88$	−111.743			−0.0144296
$89$			3337.04i			0.421290i	0.977563	+	0.210645i	$0.0675564\pi$
$89$			3337.04i			0.421290i	−0.977563	+	0.210645i	$0.932444\pi$
$90$			1196.83i			0.147757i
$91$	4233.73	+	4079.65i	0.511258	+	0.492652i
$92$	−11439.0			−1.35149
$93$	11601.0			1.34131
$94$		−	6807.65i		−	0.770445i
$95$	−2800.13			−0.310264
$96$		−	11152.9i		−	1.21017i
$97$			18179.1i			1.93209i	0.258367	+	0.966047i	$0.416816\pi$
$97$			18179.1i			1.93209i	−0.258367	+	0.966047i	$0.583184\pi$
$98$	507.488	+	13686.2i	0.0528413	+	1.42505i
$99$	822.128			0.0838821
$100$	8901.95			0.890195
$101$		−	19600.6i		−	1.92144i	−0.277518	−	0.960720i	$-0.589512\pi$
$101$		−	19600.6i		−	1.92144i	0.277518	−	0.960720i	$-0.410488\pi$
$102$	23070.6			2.21748
$103$		−	4246.38i		−	0.400262i	−0.979769	−	0.200131i	$-0.935863\pi$
$103$		−	4246.38i		−	0.400262i	0.979769	−	0.200131i	$-0.0641367\pi$
$104$		−	367.511i		−	0.0339785i
$105$	−2420.61	+	2512.03i	−0.219556	+	0.227848i
$106$	−6039.29			−0.537495
$107$	3000.11			0.262041			0.131021	−	0.991380i	$-0.458175\pi$
$107$	3000.11			0.262041			0.131021	+	0.991380i	$0.458175\pi$
$108$		−	13091.5i		−	1.12239i
$109$	10236.8			0.861608			0.430804	−	0.902446i	$-0.358230\pi$
$109$	10236.8			0.861608			0.430804	+	0.902446i	$0.358230\pi$
$110$			1937.63i			0.160135i
$111$		−	5121.59i		−	0.415680i
$112$	−8402.15	+	8719.48i	−0.669814	+	0.695111i
$113$	16426.1			1.28640			0.643202	−	0.765697i	$-0.277606\pi$
$113$	16426.1			1.28640			0.643202	+	0.765697i	$0.277606\pi$
$114$	13116.6			1.00928
$115$			6440.59i			0.487001i
$116$	−23285.5			−1.73049
$117$			2703.91i			0.197524i
$118$			14307.9i			1.02757i
$119$	−18663.9	−	17984.7i	−1.31798	−	1.27002i
$120$	218.058			0.0151429
$121$	1331.00			0.0909091
$122$		−	6045.72i		−	0.406189i
$123$	−10274.1			−0.679103
$124$			25090.1i			1.63177i
$125$		−	10831.5i		−	0.693214i
$126$	−4370.40	+	4535.46i	−0.275283	+	0.285680i
$127$	5844.55			0.362363			0.181181	−	0.983450i	$-0.442008\pi$
$127$	5844.55			0.362363			0.181181	+	0.983450i	$0.442008\pi$
$128$	1567.31			0.0956610
$129$			3845.05i			0.231059i
$130$	−6372.69			−0.377082
$131$			21914.6i			1.27700i	0.769622	+	0.638500i	$0.220445\pi$
$131$			21914.6i			1.27700i	−0.769622	+	0.638500i	$0.779555\pi$
$132$		−	4613.11i		−	0.264756i
$133$	−10611.2	−	10225.1i	−0.599878	−	0.578047i
$134$	−16740.5			−0.932307
$135$	−7371.03			−0.404446
$136$			1620.13i			0.0875938i
$137$	31913.9			1.70035			0.850175	−	0.526499i	$-0.176496\pi$
$137$	31913.9			1.70035			0.850175	+	0.526499i	$0.176496\pi$
$138$		−	30169.6i		−	1.58421i
$139$		−	21424.7i		−	1.10888i	−0.832222	−	0.554442i	$-0.812932\pi$
$139$		−	21424.7i		−	1.10888i	0.832222	−	0.554442i	$-0.187068\pi$
$140$	−5432.89	−	5235.17i	−0.277188	−	0.267101i
$141$	9125.53			0.459008
$142$	40673.0			2.01711
$143$			4377.54i			0.214071i
$144$	−5568.77			−0.268555
$145$			13110.6i			0.623573i
$146$			29644.4i			1.39071i
$147$	−18346.1	+	680.278i	−0.849001	+	0.0314812i
$148$	11076.7			0.505694
$149$	−5588.62			−0.251728			−0.125864	−	0.992047i	$-0.540170\pi$
$149$	−5588.62			−0.251728			−0.125864	+	0.992047i	$0.540170\pi$
$150$			23478.3i			1.04348i
$151$	13293.7			0.583032			0.291516	−	0.956566i	$-0.405840\pi$
$151$	13293.7			0.583032			0.291516	+	0.956566i	$0.405840\pi$
$152$			921.115i			0.0398682i
$153$		−	11919.9i		−	0.509201i
$154$	−7075.54	+	7342.76i	−0.298344	+	0.309612i
$155$	14126.7			0.587999
$156$	15172.1			0.623443
$157$			39400.5i			1.59846i	0.601024	+	0.799231i	$0.294760\pi$
$157$			39400.5i			1.59846i	−0.601024	+	0.799231i	$0.705240\pi$
$158$	7650.43			0.306459
$159$		−	8095.56i		−	0.320223i
$160$		−	13581.0i		−	0.530509i
$161$	−23518.7	+	24407.0i	−0.907324	+	0.941591i
$162$	24116.4			0.918928
$163$	−13163.6			−0.495449			−0.247724	−	0.968831i	$-0.579683\pi$
$163$	−13163.6			−0.495449			−0.247724	+	0.968831i	$0.579683\pi$
$164$		−	22220.4i		−	0.826160i
$165$	−2597.36			−0.0954034
$166$			21608.8i			0.784179i
$167$			32342.9i			1.15970i	0.814723	+	0.579850i	$0.196889\pi$
$167$			32342.9i			1.15970i	−0.814723	+	0.579850i	$0.803111\pi$
$168$	826.344	+	796.271i	0.0292781	+	0.0282125i
$169$	14163.7			0.495909
$170$	28093.3			0.972088
$171$		−	6776.96i		−	0.231762i
$172$	−8315.87			−0.281094
$173$			17662.1i			0.590135i	0.955476	+	0.295067i	$0.0953421\pi$
$173$			17662.1i			0.590135i	−0.955476	+	0.295067i	$0.904658\pi$
$174$		−	61414.1i		−	2.02847i
$175$	18302.5	−	18993.8i	0.597634	−	0.620205i
$176$	−9015.66			−0.291053
$177$	−19179.5			−0.612196
$178$		−	19034.8i		−	0.600772i
$179$	−31647.2			−0.987710			−0.493855	−	0.869544i	$-0.664413\pi$
$179$	−31647.2			−0.987710			−0.493855	+	0.869544i	$0.664413\pi$
$180$		−	3469.76i		−	0.107091i
$181$		−	13567.0i		−	0.414119i	−0.978328	−	0.207060i	$-0.933611\pi$
$181$		−	13567.0i		−	0.414119i	0.978328	−	0.207060i	$-0.0663894\pi$
$182$	−24149.7	−	23270.8i	−0.729069	−	0.702536i
$183$	8104.17			0.241995
$184$	2118.66			0.0625786
$185$		−	6236.61i		−	0.182224i
$186$	−66173.6			−1.91275
$187$		−	19297.9i		−	0.551858i
$188$			19736.2i			0.558404i
$189$	−27933.0	−	26916.4i	−0.781976	−	0.753517i
$190$	15972.3			0.442445
$191$	32663.5			0.895357			0.447679	−	0.894195i	$-0.352251\pi$
$191$	32663.5			0.895357			0.447679	+	0.894195i	$0.352251\pi$
$192$			33384.8i			0.905620i
$193$	7724.25			0.207368			0.103684	−	0.994610i	$-0.466937\pi$
$193$	7724.25			0.207368			0.103684	+	0.994610i	$0.466937\pi$
$194$		−	103696.i		−	2.75522i
$195$		−	8542.48i		−	0.224654i
$196$	−1471.27	−	39678.0i	−0.0382984	−	1.03285i
$197$	19379.6			0.499358			0.249679	−	0.968329i	$-0.419675\pi$
$197$	19379.6			0.499358			0.249679	+	0.968329i	$0.419675\pi$
$198$	−4689.52			−0.119618
$199$		−	32090.9i		−	0.810356i	−0.914238	−	0.405178i	$-0.867210\pi$
$199$		−	32090.9i		−	0.810356i	0.914238	−	0.405178i	$-0.132790\pi$
$200$	−1648.77			−0.0412192
$201$		−	22440.3i		−	0.555440i
$202$			111804.i			2.74003i
$203$	−47875.4	+	49683.5i	−1.16177	+	1.20565i
$204$	−66884.7			−1.60719
$205$	−12510.9			−0.297702
$206$			24221.8i			0.570785i
$207$	−15587.7			−0.363783
$208$		−	29651.7i		−	0.685366i
$209$		−	10971.7i		−	0.251178i
$210$	13807.4	−	14328.9i	0.313094	−	0.324919i
$211$	−25370.5			−0.569855			−0.284927	−	0.958549i	$-0.591969\pi$
$211$	−25370.5			−0.569855			−0.284927	+	0.958549i	$0.591969\pi$
$212$	17508.7			0.389566
$213$			54521.5i			1.20173i
$214$	−17113.0			−0.373679
$215$			4682.15i			0.101291i
$216$			2424.74i			0.0519705i
$217$	53533.9	+	51585.6i	1.13687	+	1.09549i
$218$	−58391.7			−1.22868
$219$	−39737.8			−0.828544
$220$		−	5617.44i		−	0.116063i
$221$	63469.1			1.29951
$222$			29214.1i			0.592771i
$223$		−	68553.9i		−	1.37855i	−0.724500	−	0.689275i	$-0.757929\pi$
$223$		−	68553.9i		−	1.37855i	0.724500	−	0.689275i	$-0.242071\pi$
$224$	49593.1	−	51466.1i	0.988382	−	1.02571i
$225$	12130.5			0.239616
$226$	−93696.3			−1.83445
$227$		−	26452.8i		−	0.513357i	−0.966497	−	0.256679i	$-0.917372\pi$
$227$		−	26452.8i		−	0.513357i	0.966497	−	0.256679i	$-0.0826282\pi$
$228$	−38026.8			−0.731509
$229$			40223.3i			0.767019i	0.923537	+	0.383510i	$0.125285\pi$
$229$			40223.3i			0.767019i	−0.923537	+	0.383510i	$0.874715\pi$
$230$		−	36737.9i		−	0.694478i
$231$	−9842.84	−	9484.63i	−0.184458	−	0.177745i
$232$	4312.80			0.0801279
$233$	90345.8			1.66416			0.832082	−	0.554653i	$-0.187149\pi$
$233$	90345.8			1.66416			0.832082	+	0.554653i	$0.187149\pi$
$234$		−	15423.4i		−	0.281675i
$235$	11112.3			0.201218
$236$		−	41480.5i		−	0.744766i
$237$			10255.3i			0.182579i
$238$	106461.	+	102587.i	1.87948	+	1.81108i
$239$	89912.2			1.57407			0.787033	−	0.616911i	$-0.211616\pi$
$239$	89912.2			1.57407			0.787033	+	0.616911i	$0.211616\pi$
$240$	17593.5			0.305442
$241$			21850.7i			0.376210i	0.982149	+	0.188105i	$0.0602345\pi$
$241$			21850.7i			0.376210i	−0.982149	+	0.188105i	$0.939765\pi$
$242$	−7592.18			−0.129639
$243$		−	31796.4i		−	0.538475i
$244$			17527.3i			0.294398i
$245$	−22340.2	+	828.382i	−0.372182	+	0.0138006i
$246$	58604.9			0.968421
$247$	36084.9			0.591468
$248$		−	4647.04i		−	0.0755567i
$249$	−28966.2			−0.467190
$250$			61784.0i			0.988544i
$251$			70220.9i			1.11460i	0.830311	+	0.557300i	$0.188163\pi$
$251$			70220.9i			1.11460i	−0.830311	+	0.557300i	$0.811837\pi$
$252$	12670.3	−	13148.9i	0.199520	−	0.207056i
$253$	−25236.0			−0.394258
$254$	−33338.0			−0.516740
$255$			37658.6i			0.579141i
$256$	60918.4			0.929540
$257$			83565.1i			1.26520i	0.774480	+	0.632599i	$0.218012\pi$
$257$			83565.1i			1.26520i	−0.774480	+	0.632599i	$0.781988\pi$
$258$		−	21932.6i		−	0.329496i
$259$	22773.9	−	23634.0i	0.339498	−	0.352320i
$260$	18475.2			0.273302
$261$	−31730.8			−0.465800
$262$		−	125003.i		−	1.82104i
$263$	−4685.91			−0.0677457			−0.0338729	−	0.999426i	$-0.510784\pi$
$263$	−4685.91			−0.0677457			−0.0338729	+	0.999426i	$0.510784\pi$
$264$			854.413i			0.0122591i
$265$		−	9858.05i		−	0.140378i
$266$	60527.8	+	58325.0i	0.855444	+	0.824312i
$267$	25515.9			0.357921
$268$	48532.9			0.675719
$269$			80057.0i			1.10636i	0.833063	+	0.553178i	$0.186585\pi$
$269$			80057.0i			1.10636i	−0.833063	+	0.553178i	$0.813415\pi$
$270$	42045.3			0.576752
$271$			9723.16i			0.132394i	0.997807	+	0.0661970i	$0.0210866\pi$
$271$			9723.16i			0.132394i	−0.997807	+	0.0661970i	$0.978913\pi$
$272$			130716.i			1.76682i
$273$	31194.1	−	32372.2i	0.418550	−	0.434357i
$274$	−182041.			−2.42475
$275$	19639.0			0.259689
$276$			87465.5i			1.14820i
$277$	69563.2			0.906609			0.453305	−	0.891356i	$-0.350245\pi$
$277$	69563.2			0.906609			0.453305	+	0.891356i	$0.350245\pi$
$278$			122209.i			1.58130i
$279$			34189.9i			0.439227i
$280$	1006.25	+	969.627i	0.0128348	+	0.0123677i
$281$	71167.0			0.901292			0.450646	−	0.892703i	$-0.351194\pi$
$281$	71167.0			0.901292			0.450646	+	0.892703i	$0.351194\pi$
$282$	−52053.1			−0.654558
$283$		−	88282.9i		−	1.10231i	−0.834403	−	0.551155i	$-0.814187\pi$
$283$		−	88282.9i		−	1.10231i	0.834403	−	0.551155i	$-0.185813\pi$
$284$	−117916.			−1.46197
$285$			21410.5i			0.263595i
$286$		−	24970.0i		−	0.305272i
$287$	−47410.9	−	45685.5i	−0.575592	−	0.554644i
$288$	32869.2			0.396282
$289$	−196276.			−2.35002
$290$		−	74784.6i		−	0.889234i
$291$	139002.			1.64148
$292$		−	85942.9i		−	1.00796i
$293$		−	11489.3i		−	0.133831i	−0.997759	−	0.0669157i	$-0.978684\pi$
$293$		−	11489.3i		−	0.133831i	0.997759	−	0.0669157i	$-0.0213158\pi$
$294$	104648.	−	3880.39i	1.21070	−	0.0448932i
$295$	−23355.1			−0.268372
$296$	−2051.56			−0.0234154
$297$		−	28881.8i		−	0.327424i
$298$	31878.1			0.358972
$299$		−	82999.0i		−	0.928391i
$300$		−	68066.7i		−	0.756296i
$301$	−17097.6	+	17743.3i	−0.188713	+	0.195840i
$302$	−75828.9			−0.831421
$303$	−149872.			−1.63243
$304$			74317.8i			0.804166i
$305$	9868.54			0.106085
$306$			67992.4i			0.726136i
$307$		−	55588.4i		−	0.589804i	−0.955528	−	0.294902i	$-0.904713\pi$
$307$		−	55588.4i		−	0.589804i	0.955528	−	0.294902i	$-0.0952869\pi$
$308$	20512.9	−	21287.6i	0.216235	−	0.224401i
$309$	−32468.9			−0.340056
$310$	−80580.3			−0.838504
$311$		−	121373.i		−	1.25488i	−0.778667	−	0.627438i	$-0.784104\pi$
$311$		−	121373.i		−	1.25488i	0.778667	−	0.627438i	$-0.215896\pi$
$312$	−2810.09			−0.0288676
$313$			37456.3i			0.382328i	0.981558	+	0.191164i	$0.0612262\pi$
$313$			37456.3i			0.382328i	−0.981558	+	0.191164i	$0.938774\pi$
$314$		−	224745.i		−	2.27945i
$315$	−7403.31	−	7133.88i	−0.0746113	−	0.0718960i
$316$	−22179.6			−0.222116
$317$	−37583.2			−0.374003			−0.187001	−	0.982360i	$-0.559877\pi$
$317$	−37583.2			−0.374003			−0.187001	+	0.982360i	$0.559877\pi$
$318$			46178.0i			0.456647i
$319$	−51371.1			−0.504821
$320$			40653.0i			0.397002i
$321$		−	22939.7i		−	0.222626i
$322$	134154.	−	139220.i	1.29387	−	1.34274i
$323$	−159076.			−1.52476
$324$	−69916.4			−0.666022
$325$			64590.8i			0.611510i
$326$	75086.6			0.706524
$327$		−	78273.0i		−	0.732009i
$328$			4115.53i			0.0382541i
$329$	42110.5	+	40578.0i	0.389044	+	0.374886i
$330$	14815.6			0.136048
$331$	−165588.			−1.51138			−0.755690	−	0.654930i	$-0.772698\pi$
$331$	−165588.			−1.51138			−0.755690	+	0.654930i	$0.772698\pi$
$332$		−	62646.7i		−	0.568358i
$333$	15094.1			0.136119
$334$		−	184487.i		−	1.65377i
$335$		−	27325.9i		−	0.243492i
$336$	66671.4	+	64245.0i	0.590556	+	0.569064i
$337$	82419.4			0.725721			0.362860	−	0.931843i	$-0.381800\pi$
$337$	82419.4			0.725721			0.362860	+	0.931843i	$0.381800\pi$
$338$	−80791.2			−0.707181
$339$		−	125598.i		−	1.09291i
$340$	−81446.2			−0.704552
$341$			55352.3i			0.476022i
$342$			38656.6i			0.330500i
$343$	−87684.5	−	78439.3i	−0.745306	−	0.666723i
$344$	1540.22			0.0130156
$345$	49246.4			0.413749
$346$		−	100747.i		−	0.841549i
$347$	92956.4			0.772005			0.386003	−	0.922498i	$-0.373856\pi$
$347$	92956.4			0.772005			0.386003	+	0.922498i	$0.373856\pi$
$348$			178047.i			1.47020i
$349$			35260.7i			0.289495i	0.989469	+	0.144747i	$0.0462369\pi$
$349$			35260.7i			0.289495i	−0.989469	+	0.144747i	$0.953763\pi$
$350$	−104400.	+	108343.i	−0.852244	+	0.884431i
$351$	94989.6			0.771013
$352$	53214.3			0.429480
$353$		−	7796.38i		−	0.0625668i	−0.999511	−	0.0312834i	$-0.990041\pi$
$353$		−	7796.38i		−	0.0625668i	0.999511	−	0.0312834i	$-0.00995943\pi$
$354$	109402.			0.873010
$355$			66391.4i			0.526811i
$356$			55184.4i			0.435428i
$357$	−137516.	+	142709.i	−1.07899	+	1.11974i
$358$	180519.			1.40850
$359$	−96330.9			−0.747440			−0.373720	−	0.927541i	$-0.621918\pi$
$359$	−96330.9			−0.747440			−0.373720	+	0.927541i	$0.621918\pi$
$360$			642.649i			0.00495871i
$361$	39879.3			0.306008
$362$			77387.5i			0.590546i
$363$		−	10177.2i		−	0.0772350i
$364$	70013.0	+	67465.0i	0.528416	+	0.509185i
$365$	−48389.1			−0.363214
$366$	−46227.2			−0.345092
$367$			8038.25i			0.0596800i	0.999555	+	0.0298400i	$0.00949978\pi$
$367$			8038.25i			0.0596800i	−0.999555	+	0.0298400i	$0.990500\pi$
$368$	170939.			1.26225
$369$		−	30279.4i		−	0.222379i
$370$			35574.4i			0.259857i
$371$	35998.1	−	37357.6i	0.261536	−	0.271414i
$372$	191846.			1.38633
$373$	185043.			1.33001			0.665004	−	0.746840i	$-0.268430\pi$
$373$	185043.			1.33001			0.665004	+	0.746840i	$0.268430\pi$
$374$			110078.i			0.786966i
$375$	−82820.3			−0.588945
$376$		−	3655.43i		−	0.0258561i
$377$		−	168955.i		−	1.18874i
$378$	159333.	+	153534.i	1.11512	+	1.07454i
$379$	−3185.62			−0.0221777			−0.0110888	−	0.999939i	$-0.503530\pi$
$379$	−3185.62			−0.0221777			−0.0110888	+	0.999939i	$0.503530\pi$
$380$	−46305.6			−0.320676
$381$		−	44688.9i		−	0.307858i
$382$	−186317.			−1.27681
$383$		−	97882.4i		−	0.667278i	−0.942701	−	0.333639i	$-0.891723\pi$
$383$		−	97882.4i		−	0.667278i	0.942701	−	0.333639i	$-0.108277\pi$
$384$		−	11984.1i		−	0.0812722i
$385$	−11985.7	−	11549.5i	−0.0808617	−	0.0779189i
$386$	−44060.0			−0.295713
$387$	−11331.9			−0.0756625
$388$			300627.i			1.99693i
$389$	−279823.			−1.84920			−0.924601	−	0.380937i	$-0.875602\pi$
$389$	−279823.			−1.84920			−0.924601	+	0.380937i	$0.875602\pi$
$390$			48727.3i			0.320364i
$391$			365893.i			2.39332i
$392$	272.500	+	7348.92i	0.00177335	+	0.0478246i
$393$	167565.			1.08492
$394$	−110544.			−0.712100
$395$			12487.9i			0.0800381i
$396$	13595.5			0.0866972
$397$		−	178304.i		−	1.13130i	−0.824644	−	0.565652i	$-0.808624\pi$
$397$		−	178304.i		−	1.13130i	0.824644	−	0.565652i	$-0.191376\pi$
$398$			183050.i			1.15559i
$399$	−78183.6	+	81136.4i	−0.491100	+	0.509648i
$400$	−133026.			−0.831415
$401$	180071.			1.11983			0.559917	−	0.828548i	$-0.310833\pi$
$401$	180071.			1.11983			0.559917	+	0.828548i	$0.310833\pi$
$402$			128002.i			0.792074i
$403$	−182049.			−1.12093
$404$		−	324135.i		−	1.98592i
$405$			39365.6i			0.239997i
$406$	273087.	−	283400.i	1.65672	−	1.71929i
$407$	24436.8			0.147522
$408$	12388.0			0.0744184
$409$		−	191943.i		−	1.14743i	−0.819056	−	0.573714i	$-0.805502\pi$
$409$		−	191943.i		−	1.14743i	0.819056	−	0.573714i	$-0.194498\pi$
$410$	71363.9			0.424532
$411$		−	244022.i		−	1.44459i
$412$		−	70222.2i		−	0.413694i
$413$	−88505.4	−	85284.5i	−0.518883	−	0.500000i
$414$	88914.2			0.518765
$415$	−35272.5			−0.204805
$416$			175017.i			1.01133i
$417$	−163819.			−0.942091
$418$			62583.8i			0.358187i
$419$			211909.i			1.20704i	0.797347	+	0.603521i	$0.206236\pi$
$419$			211909.i			1.20704i	−0.797347	+	0.603521i	$0.793764\pi$
$420$	−40029.5	+	41541.3i	−0.226925	+	0.235495i
$421$	205981.			1.16215			0.581075	−	0.813850i	$-0.302632\pi$
$421$	205981.			1.16215			0.581075	+	0.813850i	$0.302632\pi$
$422$	144716.			0.812630
$423$			26894.2i			0.150307i
$424$	−3242.85			−0.0180383
$425$		−	284742.i		−	1.57642i
$426$		−	310997.i		−	1.71371i
$427$	37397.4	+	36036.4i	0.205109	+	0.197645i
$428$	49612.7			0.270835
$429$	33471.8			0.181872
$430$		−	26707.6i		−	0.144443i
$431$	−82904.4			−0.446296			−0.223148	−	0.974785i	$-0.571633\pi$
$431$	−82904.4			−0.446296			−0.223148	+	0.974785i	$0.571633\pi$
$432$			195634.i			1.04828i
$433$		−	116644.i		−	0.622136i	−0.950388	−	0.311068i	$-0.899313\pi$
$433$		−	116644.i		−	0.622136i	0.950388	−	0.311068i	$-0.100687\pi$
$434$	−305364.	−	294250.i	−1.62120	−	1.56220i
$435$	100247.			0.529779
$436$	169285.			0.890523
$437$			208025.i			1.08932i
$438$	226669.			1.18153
$439$			335864.i			1.74275i	0.490618	+	0.871375i	$0.336771\pi$
$439$			335864.i			1.74275i	−0.490618	+	0.871375i	$0.663229\pi$
$440$			1040.43i			0.00537411i
$441$	−2004.88	−	54068.5i	−0.0103089	−	0.278014i
$442$	−362035.			−1.85313
$443$	−116560.			−0.593938			−0.296969	−	0.954887i	$-0.595976\pi$
$443$	−116560.			−0.593938			−0.296969	+	0.954887i	$0.595976\pi$
$444$		−	84695.5i		−	0.429630i
$445$	31070.9			0.156904
$446$			391040.i			1.96585i
$447$			42732.0i			0.213864i
$448$	−148450.	+	154057.i	−0.739648	+	0.767582i
$449$	312508.			1.55013			0.775066	−	0.631880i	$-0.217716\pi$
$449$	312508.			1.55013			0.775066	+	0.631880i	$0.217716\pi$
$450$	−69194.0			−0.341699
$451$		−	49021.4i		−	0.241008i
$452$	271638.			1.32958
$453$		−	101647.i		−	0.495335i
$454$			150890.i			0.732063i
$455$	37985.4	−	39420.0i	0.183482	−	0.190412i
$456$	7043.09			0.0338714
$457$	102807.			0.492254			0.246127	−	0.969238i	$-0.420842\pi$
$457$	102807.			0.492254			0.246127	+	0.969238i	$0.420842\pi$
$458$		−	229438.i		−	1.09379i
$459$	−418752.			−1.98761
$460$			106508.i			0.503345i
$461$			106079.i			0.499146i	0.968356	+	0.249573i	$0.0802903\pi$
$461$			106079.i			0.499146i	−0.968356	+	0.249573i	$0.919710\pi$
$462$	56144.7	+	54101.4i	0.263042	+	0.253469i
$463$	331461.			1.54622			0.773108	−	0.634274i	$-0.218701\pi$
$463$	331461.			1.54622			0.773108	+	0.634274i	$0.218701\pi$
$464$	347967.			1.61623
$465$		−	108016.i		−	0.499555i
$466$	−515343.			−2.37315
$467$			48704.0i			0.223322i	0.993746	+	0.111661i	$0.0356170\pi$
$467$			48704.0i			0.223322i	−0.993746	+	0.111661i	$0.964383\pi$
$468$			44714.4i			0.204153i
$469$	99784.3	−	103553.i	0.453645	−	0.470778i
$470$	−63385.6			−0.286943
$471$	301267.			1.35803
$472$			7682.77i			0.0344853i
$473$	−18346.0			−0.0820010
$474$		−	58497.2i		−	0.260363i
$475$		−	161888.i		−	0.717508i
$476$	−308645.	−	297412.i	−1.36221	−	1.31264i
$477$	23858.8			0.104860
$478$	−512870.			−2.24466
$479$			35719.4i			0.155680i	0.996966	+	0.0778401i	$0.0248024\pi$
$479$			35719.4i			0.155680i	−0.996966	+	0.0778401i	$0.975198\pi$
$480$	−103844.			−0.450712
$481$			80370.5i			0.347381i
$482$		−	124639.i		−	0.536487i
$483$	186622.	+	179830.i	0.799961	+	0.770848i
$484$	22010.7			0.0939600
$485$	169264.			0.719584
$486$			181370.i			0.767881i
$487$	−26388.9			−0.111266			−0.0556331	−	0.998451i	$-0.517718\pi$
$487$	−26388.9			−0.111266			−0.0556331	+	0.998451i	$0.517718\pi$
$488$		−	3246.30i		−	0.0136317i
$489$			100652.i			0.420926i
$490$	127431.	−	4725.19i	0.530742	−	0.0196801i
$491$	−217484.			−0.902119			−0.451060	−	0.892494i	$-0.648954\pi$
$491$	−217484.			−0.902119			−0.451060	+	0.892494i	$0.648954\pi$
$492$	−169903.			−0.701893
$493$			744821.i			3.06449i
$494$	−205832.			−0.843451
$495$		−	7654.79i		−	0.0312408i
$496$		−	374934.i		−	1.52402i
$497$	−242438.	+	251594.i	−0.981493	+	1.01856i
$498$	165227.			0.666227
$499$	324880.			1.30473			0.652366	−	0.757904i	$-0.273776\pi$
$499$	324880.			1.30473			0.652366	+	0.757904i	$0.273776\pi$
$500$		−	179120.i		−	0.716479i
$501$	247302.			0.985263
$502$		−	400548.i		−	1.58945i
$503$			102481.i			0.405048i	0.979277	+	0.202524i	$0.0649144\pi$
$503$			102481.i			0.405048i	−0.979277	+	0.202524i	$0.935086\pi$
$504$	−2346.72	+	2435.35i	−0.00923849	+	0.00958740i
$505$	−182500.			−0.715617
$506$	143949.			0.562223
$507$		−	108299.i		−	0.421317i
$508$	96651.0			0.374523
$509$			76518.3i			0.295345i	0.989036	+	0.147673i	$0.0471782\pi$
$509$			76518.3i			0.295345i	−0.989036	+	0.147673i	$0.952822\pi$
$510$		−	214809.i		−	0.825871i
$511$	−183373.	−	176700.i	−0.702255	−	0.676697i
$512$	−372562.			−1.42121
$513$	−238078.			−0.904659
$514$		−	476665.i		−	1.80421i
$515$	−39537.8			−0.149072
$516$			63585.4i			0.238813i
$517$			43540.9i			0.162898i
$518$	−129905.	+	134811.i	−0.484135	+	0.502419i
$519$	135049.			0.501370
$520$	−3421.87			−0.0126549
$521$		−	67565.7i		−	0.248915i	−0.992225	−	0.124457i	$-0.960281\pi$
$521$		−	67565.7i		−	0.248915i	0.992225	−	0.124457i	$-0.0397190\pi$
$522$	180996.			0.664245
$523$			156345.i			0.571583i	0.958292	+	0.285791i	$0.0922565\pi$
$523$			156345.i			0.571583i	−0.958292	+	0.285791i	$0.907744\pi$
$524$			362401.i			1.31986i
$525$	−145232.	−	139946.i	−0.526917	−	0.507741i
$526$	26729.0			0.0966074
$527$	802543.			2.88966
$528$			68936.1i			0.247274i
$529$	198639.			0.709829
$530$			56231.5i			0.200183i
$531$		−	56524.7i		−	0.200470i
$532$	−175478.	−	169092.i	−0.620010	−	0.597446i
$533$	161227.			0.567522
$534$	−145545.			−0.510407
$535$		−	27933.9i		−	0.0975941i
$536$	−8988.97			−0.0312882
$537$			241983.i			0.839144i
$538$		−	456654.i		−	1.57770i
$539$	−3245.83	−	87535.2i	−0.0111725	−	0.301304i
$540$	−121895.			−0.418020
$541$	−440458.			−1.50491			−0.752455	−	0.658644i	$-0.771130\pi$
$541$	−440458.			−1.50491			−0.752455	+	0.658644i	$0.771130\pi$
$542$		−	55462.0i		−	0.188798i
$543$	−103737.			−0.351829
$544$		−	771544.i		−	2.60713i
$545$		−	95313.8i		−	0.320895i
$546$	−177935.	+	184655.i	−0.596864	+	0.619406i
$547$	242937.			0.811932			0.405966	−	0.913888i	$-0.366935\pi$
$547$	242937.			0.811932			0.405966	+	0.913888i	$0.366935\pi$
$548$	527759.			1.75741
$549$			23884.2i			0.0792438i
$550$	−112023.			−0.370324
$551$			423462.i			1.39480i
$552$		−	16199.8i		−	0.0531659i
$553$	−45601.5	+	47323.8i	−0.149118	+	0.154749i
$554$	−396797.			−1.29285
$555$	−47686.8			−0.154815
$556$		−	354300.i		−	1.14610i
$557$	18437.4			0.0594276			0.0297138	−	0.999558i	$-0.490540\pi$
$557$	18437.4			0.0594276			0.0297138	+	0.999558i	$0.490540\pi$
$558$		−	195023.i		−	0.626351i
$559$		−	60338.3i		−	0.193094i
$560$	81186.5	+	78231.9i	0.258886	+	0.249464i
$561$	−147557.			−0.468850
$562$	−405945.			−1.28527
$563$			368367.i			1.16216i	0.813848	+	0.581078i	$0.197369\pi$
$563$			368367.i			1.16216i	−0.813848	+	0.581078i	$0.802631\pi$
$564$	150909.			0.474412
$565$		−	152942.i		−	0.479105i
$566$			503576.i			1.57193i
$567$	−143749.	+	149178.i	−0.447135	+	0.464022i
$568$	21839.8			0.0676941
$569$	253590.			0.783264			0.391632	−	0.920122i	$-0.371911\pi$
$569$	253590.			0.783264			0.391632	+	0.920122i	$0.371911\pi$
$570$		−	122128.i		−	0.375895i
$571$	−358387.			−1.09921			−0.549604	−	0.835425i	$-0.685222\pi$
$571$	−358387.			−1.09921			−0.549604	+	0.835425i	$0.685222\pi$
$572$			72391.2i			0.221255i
$573$		−	249754.i		−	0.760682i
$574$	270437.	+	260595.i	0.820811	+	0.790939i
$575$	−372359.			−1.12623
$576$	−98389.7			−0.296555
$577$		−	644156.i		−	1.93482i	−0.253222	−	0.967408i	$-0.581490\pi$
$577$		−	644156.i		−	1.93482i	0.253222	−	0.967408i	$-0.418510\pi$
$578$	1.11958e6			3.35120
$579$		−	59061.6i		−	0.176177i
$580$			216810.i			0.644501i
$581$	−133667.	−	128803.i	−0.395979	−	0.381568i
$582$	−792884.			−2.34080
$583$	38626.6			0.113645
$584$			15917.8i			0.0466722i
$585$	25175.9			0.0735654
$586$			65536.2i			0.190847i
$587$		−	110409.i		−	0.320427i	−0.987082	−	0.160214i	$-0.948782\pi$
$587$		−	110409.i		−	0.320427i	0.987082	−	0.160214i	$-0.0512183\pi$
$588$	−303388.	+	11249.7i	−0.877494	+	0.0325377i
$589$	456280.			1.31523
$590$	133220.			0.382707
$591$		−	148182.i		−	0.424247i
$592$	−165525.			−0.472303
$593$		−	161041.i		−	0.457960i	−0.973431	−	0.228980i	$-0.926461\pi$
$593$		−	161041.i		−	0.457960i	0.973431	−	0.228980i	$-0.0735391\pi$
$594$			164745.i			0.466917i
$595$	−167455.	+	173779.i	−0.473002	+	0.490866i
$596$	−92418.7			−0.260176
$597$	−245376.			−0.688466
$598$			473436.i			1.32391i
$599$	378048.			1.05364			0.526822	−	0.849976i	$-0.323384\pi$
$599$	378048.			1.05364			0.526822	+	0.849976i	$0.323384\pi$
$600$			12606.9i			0.0350192i
$601$			486671.i			1.34737i	0.739019	+	0.673685i	$0.235290\pi$
$601$			486671.i			1.34737i	−0.739019	+	0.673685i	$0.764710\pi$
$602$	97526.5	−	101210.i	0.269110	−	0.279273i
$603$	66134.9			0.181885
$604$	219838.			0.602599
$605$		−	12392.9i		−	0.0338580i
$606$	854885.			2.32789
$607$		−	269656.i		−	0.731867i	−0.930641	−	0.365933i	$-0.880750\pi$
$607$		−	269656.i		−	0.731867i	0.930641	−	0.365933i	$-0.119250\pi$
$608$		−	438655.i		−	1.18663i
$609$	379893.	+	366068.i	1.02430	+	0.987022i
$610$	−56291.3			−0.151280
$611$	−143202.			−0.383590
$612$		−	197119.i		−	0.526290i
$613$	−567517.			−1.51028			−0.755141	−	0.655562i	$-0.772432\pi$
$613$	−567517.			−1.51028			−0.755141	+	0.655562i	$0.772432\pi$
$614$			317083.i			0.841077i
$615$			95661.9i			0.252923i
$616$	−3799.27	+	3942.76i	−0.0100124	+	0.0103906i
$617$	−577598.			−1.51724			−0.758622	−	0.651531i	$-0.774127\pi$
$617$	−577598.			−1.51724			−0.758622	+	0.651531i	$0.774127\pi$
$618$	185207.			0.484930
$619$		−	65269.9i		−	0.170346i	−0.996366	−	0.0851729i	$-0.972856\pi$
$619$		−	65269.9i		−	0.170346i	0.996366	−	0.0851729i	$-0.0271443\pi$
$620$	233612.			0.607733
$621$			547605.i			1.41999i
$622$			692325.i			1.78949i
$623$	117745.	+	113460.i	0.303366	+	0.292326i
$624$	−226725.			−0.582277
$625$	235590.			0.603111
$626$		−	213655.i		−	0.545211i
$627$	−83892.4			−0.213397
$628$			651564.i			1.65211i
$629$		−	354305.i		−	0.895521i
$630$	42229.4	+	40692.5i	0.106398	+	0.102526i
$631$	67577.4			0.169724			0.0848619	−	0.996393i	$-0.472955\pi$
$631$	67577.4			0.169724			0.0848619	+	0.996393i	$0.472955\pi$
$632$	4107.97			0.0102847
$633$			193990.i			0.484140i
$634$	214379.			0.533339
$635$		−	54418.2i		−	0.134957i
$636$		−	133876.i		−	0.330970i
$637$	287895.	−	10675.3i	0.709506	−	0.0263087i
$638$	293027.			0.719890
$639$	−160683.			−0.393520
$640$		−	14593.1i		−	0.0356278i
$641$	276369.			0.672624			0.336312	−	0.941751i	$-0.390820\pi$
$641$	276369.			0.672624			0.336312	+	0.941751i	$0.390820\pi$
$642$			130850.i			0.317472i
$643$			143792.i			0.347787i	0.984764	+	0.173894i	$0.0556349\pi$
$643$			143792.i			0.347787i	−0.984764	+	0.173894i	$0.944365\pi$
$644$	−388928.	+	403617.i	−0.937773	+	0.973191i
$645$	35801.0			0.0860549
$646$	907391.			2.17435
$647$			323146.i			0.771953i	0.922509	+	0.385976i	$0.126135\pi$
$647$			323146.i			0.771953i	−0.922509	+	0.385976i	$0.873865\pi$
$648$	12949.5			0.0308392
$649$		−	91511.8i		−	0.217264i
$650$		−	368433.i		−	0.872032i
$651$	394437.	−	409334.i	0.930713	−	0.965864i
$652$	−217685.			−0.512076
$653$	136793.			0.320801			0.160401	−	0.987052i	$-0.448721\pi$
$653$	136793.			0.320801			0.160401	+	0.987052i	$0.448721\pi$
$654$			446478.i			1.04387i
$655$	204046.			0.475603
$656$			332051.i			0.771609i
$657$		−	117113.i		−	0.271315i
$658$	−240203.	−	231462.i	−0.554788	−	0.534598i
$659$	−262556.			−0.604576			−0.302288	−	0.953217i	$-0.597750\pi$
$659$	−262556.			−0.604576			−0.302288	+	0.953217i	$0.597750\pi$
$660$	−42952.4			−0.0986052
$661$			311791.i			0.713610i	0.934179	+	0.356805i	$0.116134\pi$
$661$			311791.i			0.713610i	−0.934179	+	0.356805i	$0.883866\pi$
$662$	944535.			2.15527
$663$		−	485302.i		−	1.10404i
$664$			11603.1i			0.0263170i
$665$	−95205.0	+	98800.7i	−0.215286	+	0.223417i
$666$	−86098.3			−0.194109
$667$	974007.			2.18933
$668$			534853.i			1.19862i
$669$	−524181.			−1.17120
$670$			155870.i			0.347226i
$671$			38667.7i			0.0858823i
$672$	−393523.	−	379202.i	−0.871429	−	0.839715i
$673$	−245754.			−0.542589			−0.271295	−	0.962496i	$-0.587452\pi$
$673$	−245754.			−0.542589			−0.271295	+	0.962496i	$0.587452\pi$
$674$	−470130.			−1.03490
$675$		−	426152.i		−	0.935313i
$676$	234224.			0.512552
$677$		−	826671.i		−	1.80366i	−0.432089	−	0.901831i	$-0.642223\pi$
$677$		−	826671.i		−	1.80366i	0.432089	−	0.901831i	$-0.357777\pi$
$678$			716427.i			1.55852i
$679$	641436.	+	618093.i	1.39128	+	1.34065i
$680$	15085.0			0.0326232
$681$	−202265.			−0.436141
$682$		−	315736.i		−	0.678821i
$683$	209436.			0.448961			0.224481	−	0.974479i	$-0.427931\pi$
$683$	209436.			0.448961			0.224481	+	0.974479i	$0.427931\pi$
$684$		−	112070.i		−	0.239540i
$685$		−	297148.i		−	0.633275i
$686$	500163.	+	447427.i	1.06283	+	0.950767i
$687$	307558.			0.651648
$688$	124268.			0.262533
$689$			127039.i			0.267609i
$690$	−280908.			−0.590018
$691$		−	319620.i		−	0.669388i	−0.942327	−	0.334694i	$-0.891367\pi$
$691$		−	319620.i		−	0.669388i	0.942327	−	0.334694i	$-0.108633\pi$
$692$			292078.i			0.609940i
$693$	27952.6	−	29008.2i	0.0582043	−	0.0604025i
$694$	−530234.			−1.10090
$695$	−199484.			−0.412990
$696$		−	32976.8i		−	0.0680755i
$697$	−710752.			−1.46303
$698$		−	201131.i		−	0.412828i
$699$		−	690808.i		−	1.41385i
$700$	302668.	−	314099.i	0.617691	−	0.641019i
$701$	−738918.			−1.50370			−0.751849	−	0.659336i	$-0.770838\pi$
$701$	−738918.			−1.50370			−0.751849	+	0.659336i	$0.770838\pi$
$702$	−541832.			−1.09949
$703$		−	201437.i		−	0.407595i
$704$	−159290.			−0.321398
$705$		−	84967.3i		−	0.170952i
$706$			44471.5i			0.0892220i
$707$	−691595.	−	666425.i	−1.38361	−	1.33325i
$708$	−317171.			−0.632742
$709$	−536581.			−1.06744			−0.533719	−	0.845662i	$-0.679206\pi$
$709$	−536581.			−1.06744			−0.533719	+	0.845662i	$0.679206\pi$
$710$		−	378704.i		−	0.751248i
$711$	−30223.7			−0.0597873
$712$		−	10220.9i		−	0.0201619i
$713$		−	1.04949e6i		−	2.06443i
$714$	784407.	−	814032.i	1.53867	−	1.59678i
$715$	40759.0			0.0797281
$716$	−523349.			−1.02086
$717$		−	687492.i		−	1.33730i
$718$	549483.			1.06587
$719$			586018.i			1.13358i	0.823861	+	0.566792i	$0.191816\pi$
$719$			586018.i			1.13358i	−0.823861	+	0.566792i	$0.808184\pi$
$720$			51850.4i			0.100020i
$721$	−149831.	−	144378.i	−0.288224	−	0.277735i
$722$	−227476.			−0.436376
$723$	167076.			0.319622
$724$		−	224356.i		−	0.428017i
$725$	−757983.			−1.44206
$726$			58051.8i			0.110139i
$727$			521107.i			0.985958i	0.870041	+	0.492979i	$0.164092\pi$
$727$			521107.i			0.985958i	−0.870041	+	0.492979i	$0.835908\pi$
$728$	−12967.4	−	12495.5i	−0.0244675	−	0.0235771i
$729$	−585582.			−1.10188
$730$	276017.			0.517953
$731$			265995.i			0.497782i
$732$	134018.			0.250116
$733$			469783.i			0.874357i	0.899375	+	0.437179i	$0.144022\pi$
$733$			469783.i			0.874357i	−0.899375	+	0.437179i	$0.855978\pi$
$734$		−	45851.1i		−	0.0851055i
$735$	6334.03	+	170819.i	0.0117248	+	0.316200i
$736$	−1.00895e6			−1.86258
$737$	107070.			0.197122
$738$			172717.i			0.317119i
$739$	−918282.			−1.68146			−0.840731	−	0.541453i	$-0.817874\pi$
$739$	−918282.			−1.68146			−0.840731	+	0.541453i	$0.817874\pi$
$740$		−	103135.i		−	0.188339i
$741$		−	275915.i		−	0.502503i
$742$	−205337.	+	213092.i	−0.372958	+	0.387044i
$743$	−1.00924e6			−1.82816			−0.914082	−	0.405529i	$-0.867087\pi$
$743$	−1.00924e6			−1.82816			−0.914082	+	0.405529i	$0.867087\pi$
$744$	−35532.5			−0.0641918
$745$			52035.3i			0.0937530i
$746$	−1.05551e6			−1.89663
$747$		−	85367.7i		−	0.152986i
$748$		−	319129.i		−	0.570378i
$749$	102005.	−	105857.i	0.181826	−	0.188693i
$750$	472417.			0.839852
$751$	621193.			1.10140			0.550702	−	0.834702i	$-0.314360\pi$
$751$	621193.			1.10140			0.550702	+	0.834702i	$0.314360\pi$
$752$		−	294929.i		−	0.521533i
$753$	536928.			0.946947
$754$			963740.i			1.69518i
$755$		−	123777.i		−	0.217143i
$756$	−461926.	−	445115.i	−0.808219	−	0.778805i
$757$	503988.			0.879485			0.439742	−	0.898124i	$-0.355070\pi$
$757$	503988.			0.879485			0.439742	+	0.898124i	$0.355070\pi$
$758$	18171.2			0.0316260
$759$			192961.i			0.334955i
$760$	8576.45			0.0148484
$761$			362373.i			0.625729i	0.949798	+	0.312864i	$0.101289\pi$
$761$			362373.i			0.625729i	−0.949798	+	0.312864i	$0.898711\pi$
$762$			254911.i			0.439014i
$763$	348052.	−	361197.i	0.597854	−	0.620434i
$764$	540155.			0.925405
$765$	−110985.			−0.189646
$766$			558333.i			0.951559i
$767$	300974.			0.511609
$768$		−	465798.i		−	0.789724i
$769$			476694.i			0.806097i	0.915179	+	0.403048i	$0.132049\pi$
$769$			476694.i			0.806097i	−0.915179	+	0.403048i	$0.867951\pi$
$770$	68368.0	+	65879.9i	0.115311	+	0.111115i
$771$	638961.			1.07489
$772$	127736.			0.214327
$773$		−	1.00148e6i		−	1.67604i	−0.545639	−	0.838020i	$-0.683713\pi$
$773$		−	1.00148e6i		−	1.67604i	0.545639	−	0.838020i	$-0.316287\pi$
$774$	64638.5			0.107897
$775$			816726.i			1.35979i
$776$		−	55680.3i		−	0.0924651i
$777$	−180712.	−	174135.i	−0.299326	−	0.288433i
$778$	1.59614e6			2.63702
$779$	−404093.			−0.665895
$780$		−	141267.i		−	0.232194i
$781$	−260140.			−0.426486
$782$		−	2.08709e6i		−	3.41294i
$783$			1.11472e6i			1.81820i
$784$	21986.0	+	592928.i	0.0357695	+	0.964651i
$785$	366856.			0.595327
$786$	−955810.			−1.54713
$787$			955012.i			1.54191i	0.636889	+	0.770956i	$0.280221\pi$
$787$			955012.i			1.54191i	−0.636889	+	0.770956i	$0.719779\pi$
$788$	320480.			0.516117
$789$			35829.7i			0.0575558i
$790$		−	71232.7i		−	0.114137i
$791$	558491.	−	579584.i	0.892613	−	0.926324i
$792$	−2518.08			−0.00401438
$793$	−127175.			−0.202234
$794$			1.01707e6i			1.61327i
$795$	−75377.2			−0.119263
$796$		−	530686.i		−	0.837551i
$797$		−	468669.i		−	0.737819i	−0.929465	−	0.368909i	$-0.879731\pi$
$797$		−	468669.i		−	0.737819i	0.929465	−	0.368909i	$-0.120269\pi$
$798$	445968.	−	462812.i	0.700323	−	0.726772i
$799$	631292.			0.988864
$800$	785179.			1.22684
$801$			75198.9i			0.117205i
$802$	−1.02714e6			−1.59692
$803$		−	189602.i		−	0.294044i
$804$		−	371095.i		−	0.574081i
$805$	227252.	+	218981.i	0.350684	+	0.337921i
$806$	1.03843e6			1.59848
$807$	612137.			0.939943
$808$			60034.3i			0.0919553i
$809$	−381745.			−0.583280			−0.291640	−	0.956528i	$-0.594201\pi$
$809$	−381745.			−0.583280			−0.291640	+	0.956528i	$0.594201\pi$
$810$		−	224546.i		−	0.342243i
$811$			443158.i			0.673778i	0.941544	+	0.336889i	$0.109375\pi$
$811$			443158.i			0.673778i	−0.941544	+	0.336889i	$0.890625\pi$
$812$	−791713.	+	821614.i	−1.20076	+	1.24611i
$813$	74345.8			0.112480
$814$	−139390.			−0.210370
$815$			122565.i			0.184524i
$816$	999492.			1.50106
$817$			151230.i			0.226565i
$818$			1.09486e6i			1.63627i
$819$	95405.5	+	91933.4i	0.142235	+	0.137058i
$820$	−206893.			−0.307693
$821$	389480.			0.577828			0.288914	−	0.957355i	$-0.406706\pi$
$821$	389480.			0.577828			0.288914	+	0.957355i	$0.406706\pi$
$822$			1.39193e6i			2.06003i
$823$	−248695.			−0.367171			−0.183585	−	0.983004i	$-0.558770\pi$
$823$	−248695.			−0.367171			−0.183585	+	0.983004i	$0.558770\pi$
$824$			13006.1i			0.0191555i
$825$		−	150165.i		−	0.220628i
$826$	504845.	+	486473.i	0.739943	+	0.713014i
$827$	−357647.			−0.522930			−0.261465	−	0.965213i	$-0.584206\pi$
$827$	−357647.			−0.522930			−0.261465	+	0.965213i	$0.584206\pi$
$828$	−257773.			−0.375991
$829$			23651.9i			0.0344158i	0.999852	+	0.0172079i	$0.00547771\pi$
$829$			23651.9i			0.0344158i	−0.999852	+	0.0172079i	$0.994522\pi$
$830$	201199.			0.292058
$831$		−	531899.i		−	0.770242i
$832$		−	523890.i		−	0.756822i
$833$	−1.26916e6	+	47060.7i	−1.82905	+	0.0678217i
$834$	934444.			1.34345
$835$	301142.			0.431916
$836$		−	181438.i		−	0.259607i
$837$	1.20111e6			1.71447
$838$		−	1.20876e6i		−	1.72128i
$839$			179538.i			0.255054i	0.991835	+	0.127527i	$0.0407039\pi$
$839$			179538.i			0.255054i	−0.991835	+	0.127527i	$0.959296\pi$
$840$	7414.03	−	7694.04i	0.0105074	−	0.0109042i
$841$	1.27543e6			1.80329
$842$	−1.17494e6			−1.65726
$843$		−	544161.i		−	0.765725i
$844$	−419551.			−0.588979
$845$		−	131877.i		−	0.184695i
$846$		−	153408.i		−	0.214342i
$847$	45254.3	−	46963.5i	0.0630802	−	0.0654626i
$848$	−261641.			−0.363843
$849$	−675034.			−0.936506
$850$			1.62420e6i			2.24803i
$851$	−463327.			−0.639777
$852$			901619.i			1.24206i
$853$		−	1.14070e6i		−	1.56774i	−0.620925	−	0.783870i	$-0.713243\pi$
$853$		−	1.14070e6i		−	1.56774i	0.620925	−	0.783870i	$-0.286757\pi$
$854$	−213319.	−	205556.i	−0.292492	−	0.281847i
$855$	−63099.9			−0.0863170
$856$	−9188.97			−0.0125406
$857$			1.20460e6i			1.64013i	0.572267	+	0.820067i	$0.306064\pi$
$857$			1.20460e6i			1.64013i	−0.572267	+	0.820067i	$0.693936\pi$
$858$	−190927.			−0.259354
$859$			1.13396e6i			1.53678i	0.639984	+	0.768388i	$0.278941\pi$
$859$			1.13396e6i			1.53678i	−0.639984	+	0.768388i	$0.721059\pi$
$860$			77428.6i			0.104690i
$861$	−349323.	+	362516.i	−0.471217	+	0.489014i
$862$	472896.			0.636431
$863$	−1.12135e6			−1.50563			−0.752815	−	0.658232i	$-0.771305\pi$
$863$	−1.12135e6			−1.50563			−0.752815	+	0.658232i	$0.771305\pi$
$864$		−	1.15471e6i		−	1.54684i
$865$	164451.			0.219788
$866$			665349.i			0.887184i
$867$			1.50078e6i			1.99654i
$868$	885288.	+	853069.i	1.17502	+	1.13226i
$869$	−48931.3			−0.0647958
$870$	−571823.			−0.755480
$871$			352145.i			0.464178i
$872$	−31353.9			−0.0412343
$873$			409659.i			0.537519i
$874$		−	1.18660e6i		−	1.55340i
$875$	−382181.	−	368273.i	−0.499176	−	0.481009i
$876$	−657142.			−0.856350
$877$	957066.			1.24435			0.622175	−	0.782878i	$-0.286249\pi$
$877$	957066.			1.24435			0.622175	+	0.782878i	$0.286249\pi$
$878$		−	1.91581e6i		−	2.48521i
$879$	−87850.1			−0.113701
$880$			83944.3i			0.108399i
$881$			953648.i			1.22867i	0.789044	+	0.614336i	$0.210576\pi$
$881$			953648.i			1.22867i	−0.789044	+	0.614336i	$0.789424\pi$
$882$	11436.1	+	308413.i	0.0147007	+	0.396457i
$883$	867214.			1.11226			0.556128	−	0.831097i	$-0.312286\pi$
$883$	867214.			1.11226			0.556128	+	0.831097i	$0.312286\pi$
$884$	1.04959e6			1.34312
$885$			178579.i			0.228005i
$886$	664871.			0.846974
$887$			26876.5i			0.0341606i	0.999854	+	0.0170803i	$0.00543710\pi$
$887$			26876.5i			0.0341606i	−0.999854	+	0.0170803i	$0.994563\pi$
$888$			15686.8i			0.0198934i
$889$	198716.	−	206221.i	0.251437	−	0.260933i
$890$	−177232.			−0.223750
$891$	−154245.			−0.194293
$892$		−	1.13367e6i		−	1.42481i
$893$	358916.			0.450081
$894$		−	243749.i		−	0.304977i
$895$			294665.i			0.367860i
$896$	53288.9	−	55301.5i	0.0663775	−	0.0688844i
$897$	−634633.			−0.788747
$898$	−1.78258e6			−2.21053
$899$		−	2.13637e6i		−	2.64337i
$900$	200602.			0.247657
$901$		−	560040.i		−	0.689873i
$902$			279624.i			0.343685i
$903$	135670.	+	130732.i	0.166383	+	0.160327i
$904$	−50311.1			−0.0615640
$905$	−126321.			−0.154233
$906$			579808.i			0.706363i
$907$	−549461.			−0.667917			−0.333958	−	0.942588i	$-0.608385\pi$
$907$	−549461.			−0.667917			−0.333958	+	0.942588i	$0.608385\pi$
$908$		−	437449.i		−	0.530586i
$909$		−	441693.i		−	0.534555i
$910$	−216673.	+	224856.i	−0.261651	+	0.271533i
$911$	1.07874e6			1.29981			0.649904	−	0.760016i	$-0.274809\pi$
$911$	1.07874e6			1.29981			0.649904	+	0.760016i	$0.274809\pi$
$912$	568254.			0.683207
$913$		−	138208.i		−	0.165802i
$914$	−586422.			−0.701969
$915$		−	75457.5i		−	0.0901281i
$916$			665170.i			0.792760i
$917$	773242.	+	745102.i	0.919553	+	0.886088i
$918$	2.38861e6			2.83439
$919$	309032.			0.365908			0.182954	−	0.983121i	$-0.441434\pi$
$919$	309032.			0.365908			0.182954	+	0.983121i	$0.441434\pi$
$920$		−	19726.7i		−	0.0233066i
$921$	−425044.			−0.501088
$922$		−	605087.i		−	0.711797i
$923$		−	855577.i		−	1.00428i
$924$	−162771.	−	156847.i	−0.190648	−	0.183710i
$925$	360566.			0.421407
$926$	−1.89069e6			−2.20495
$927$		−	95690.6i		−	0.111355i
$928$	−2.05385e6			−2.38492
$929$		−	910533.i		−	1.05503i	−0.849546	−	0.527515i	$-0.823124\pi$
$929$		−	910533.i		−	1.05503i	0.849546	−	0.527515i	$-0.176876\pi$
$930$			616138.i			0.712381i
$931$	−721570.	+	26756.0i	−0.832490	+	0.0308690i
$932$	1.49404e6			1.72001
$933$	−928049.			−1.06612
$934$		−	277813.i		−	0.318463i
$935$	−179682.			−0.205533
$936$		−	8281.73i		−	0.00945300i
$937$		−	1.46700e6i		−	1.67091i	−0.549561	−	0.835453i	$-0.685205\pi$
$937$		−	1.46700e6i		−	1.67091i	0.549561	−	0.835453i	$-0.314795\pi$
$938$	−569181.	+	590678.i	−0.646912	+	0.671344i
$939$	286401.			0.324820
$940$	183763.			0.207971
$941$		−	204465.i		−	0.230909i	−0.993313	−	0.115454i	$-0.963168\pi$
$941$		−	204465.i		−	0.230909i	0.993313	−	0.115454i	$-0.0368324\pi$
$942$	−1.71846e6			−1.93659
$943$			929455.i			1.04521i
$944$			619864.i			0.695589i
$945$	−250617.	+	260082.i	−0.280638	+	0.291237i
$946$	104648.			0.116936
$947$	−104322.			−0.116325			−0.0581627	−	0.998307i	$-0.518524\pi$
$947$	−104322.			−0.116325			−0.0581627	+	0.998307i	$0.518524\pi$
$948$			169591.i			0.188706i
$949$	623585.			0.692410
$950$			923427.i			1.02319i
$951$			287371.i			0.317747i
$952$	57165.4	+	55085.0i	0.0630753	+	0.0607798i
$953$	−456470.			−0.502605			−0.251302	−	0.967909i	$-0.580859\pi$
$953$	−456470.			−0.502605			−0.251302	+	0.967909i	$0.580859\pi$
$954$	−136093.			−0.149534
$955$		−	304128.i		−	0.333465i
$956$	1.48687e6			1.62689
$957$			392797.i			0.428889i
$958$		−	203748.i		−	0.222005i
$959$	1.08508e6	−	1.12606e6i	1.17984	−	1.22440i
$960$	310844.			0.337287
$961$	−1.37842e6			−1.49257
$962$		−	458443.i		−	0.495376i
$963$	67606.4			0.0729013
$964$			361343.i			0.388836i
$965$		−	71920.0i		−	0.0772316i
$966$	−1.06452e6	−	1.02577e6i	−1.14077	−	1.09925i
$967$	−503765.			−0.538735			−0.269368	−	0.963037i	$-0.586815\pi$
$967$	−503765.			−0.538735			−0.269368	+	0.963037i	$0.586815\pi$
$968$	−4076.69			−0.00435068
$969$			1.21634e6i			1.29541i
$970$	−965503.			−1.02615
$971$			1.57433e6i			1.66977i	0.550426	+	0.834884i	$0.314465\pi$
$971$			1.57433e6i			1.66977i	−0.550426	+	0.834884i	$0.685535\pi$
$972$		−	525816.i		−	0.556546i
$973$	−755958.	−	728446.i	−0.798494	−	0.769435i
$974$	150525.			0.158669
$975$	493878.			0.519530
$976$		−	261920.i		−	0.274959i
$977$	1.40972e6			1.47688			0.738438	−	0.674321i	$-0.235564\pi$
$977$	1.40972e6			1.47688			0.738438	+	0.674321i	$0.235564\pi$
$978$		−	574132.i		−	0.600252i
$979$			121745.i			0.127024i
$980$	−369439.	+	13698.9i	−0.384672	+	0.0142638i
$981$	230682.			0.239704
$982$	1.24055e6			1.28645
$983$		−	282743.i		−	0.292607i	−0.989240	−	0.146303i	$-0.953262\pi$
$983$		−	282743.i		−	0.292607i	0.989240	−	0.146303i	$-0.0467376\pi$
$984$	31468.4			0.0325001
$985$		−	180442.i		−	0.185980i
$986$		−	4.24854e6i		−	4.37005i
$987$	310270.	−	321988.i	0.318497	−	0.330526i
$988$	596734.			0.611318
$989$	347844.			0.355625
$990$			43663.8i			0.0445504i
$991$	1.07155e6			1.09110			0.545549	−	0.838079i	$-0.316321\pi$
$991$	1.07155e6			1.09110			0.545549	+	0.838079i	$0.316321\pi$
$992$			2.21302e6i			2.24886i
$993$			1.26613e6i			1.28405i
$994$	1.38289e6	−	1.43512e6i	1.39964	−	1.45250i
$995$	−298796.			−0.301807
$996$	−479014.			−0.482869
$997$			1.08526e6i			1.09180i	0.837851	+	0.545900i	$0.183812\pi$
$997$			1.08526e6i			1.09180i	−0.837851	+	0.545900i	$0.816188\pi$
$998$	−1.85315e6			−1.86059
$999$		−	530262.i		−	0.531324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.5.d.a.34.5	✓	28
7.6	odd	2	inner	77.5.d.a.34.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.5.d.a.34.5	✓	28	1.1	even	1	trivial
77.5.d.a.34.6	yes	28	7.6	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	77.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.70412 q^{2} -7.64626i q^{3} +16.5370 q^{4} -9.31094i q^{5} +43.6152i q^{6} +(34.0002 - 35.2843i) q^{7} -3.06288 q^{8} +22.5346 q^{9} +O(q^{10})\)	\(q-5.70412 q^{2} -7.64626i q^{3} +16.5370 q^{4} -9.31094i q^{5} +43.6152i q^{6} +(34.0002 - 35.2843i) q^{7} -3.06288 q^{8} +22.5346 q^{9} +53.1107i q^{10} +36.4829 q^{11} -126.446i q^{12} +119.989i q^{13} +(-193.941 + 201.266i) q^{14} -71.1939 q^{15} -247.120 q^{16} -528.958i q^{17} -128.540 q^{18} -300.735i q^{19} -153.975i q^{20} +(-269.793 - 259.975i) q^{21} -208.103 q^{22} -691.723 q^{23} +23.4196i q^{24} +538.306 q^{25} -684.431i q^{26} -791.653i q^{27} +(562.260 - 583.496i) q^{28} -1408.09 q^{29} +406.098 q^{30} +1517.21i q^{31} +1458.61 q^{32} -278.958i q^{33} +3017.24i q^{34} +(-328.530 - 316.574i) q^{35} +372.654 q^{36} +669.816 q^{37} +1715.43i q^{38} +917.467 q^{39} +28.5183i q^{40} -1343.68i q^{41} +(1538.93 + 1482.93i) q^{42} -502.866 q^{43} +603.316 q^{44} -209.819i q^{45} +3945.67 q^{46} +1193.46i q^{47} +1889.55i q^{48} +(-88.9687 - 2399.35i) q^{49} -3070.56 q^{50} -4044.56 q^{51} +1984.25i q^{52} +1058.76 q^{53} +4515.68i q^{54} -339.690i q^{55} +(-104.139 + 108.072i) q^{56} -2299.50 q^{57} +8031.91 q^{58} -2508.35i q^{59} -1177.33 q^{60} +1059.89i q^{61} -8654.37i q^{62} +(766.183 - 795.120i) q^{63} -4366.15 q^{64} +1117.21 q^{65} +1591.21i q^{66} +2934.81 q^{67} -8747.36i q^{68} +5289.10i q^{69} +(1873.98 + 1805.78i) q^{70} -7130.47 q^{71} -69.0208 q^{72} -5197.02i q^{73} -3820.71 q^{74} -4116.03i q^{75} -4973.25i q^{76} +(1240.43 - 1287.27i) q^{77} -5233.34 q^{78} -1341.21 q^{79} +2300.92i q^{80} -4227.88 q^{81} +7664.52i q^{82} -3788.29i q^{83} +(-4461.56 - 4299.19i) q^{84} -4925.10 q^{85} +2868.41 q^{86} +10766.6i q^{87} -111.743 q^{88} +3337.04i q^{89} +1196.83i q^{90} +(4233.73 + 4079.65i) q^{91} -11439.0 q^{92} +11601.0 q^{93} -6807.65i q^{94} -2800.13 q^{95} -11152.9i q^{96} +18179.1i q^{97} +(507.488 + 13686.2i) q^{98} +822.128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9}+O(q^{10}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9	\( 28 q + 256 q^{4} - 50 q^{7} + 180 q^{8} - 800 q^{9} + 360 q^{14} - 68 q^{15} + 2008 q^{16} - 1740 q^{18} + 1238 q^{21} + 300 q^{23} - 4008 q^{25} + 24 q^{28} - 2052 q^{29} + 1604 q^{30} - 780 q^{32} + 294 q^{35} - 2712 q^{36} + 1884 q^{37} + 7696 q^{39} + 7488 q^{42} + 1748 q^{43} - 2904 q^{44} - 9628 q^{46} - 9140 q^{49} + 8220 q^{50} + 15640 q^{51} - 4392 q^{53} + 5736 q^{56} - 11860 q^{57} - 9056 q^{58} + 19408 q^{60} - 14412 q^{63} + 8560 q^{64} - 7104 q^{65} - 9524 q^{67} - 22744 q^{70} - 8748 q^{71} - 67764 q^{72} + 13980 q^{74} - 726 q^{77} + 13880 q^{78} + 41624 q^{79} + 51188 q^{81} + 56956 q^{84} + 29584 q^{85} + 24 q^{86} - 7260 q^{88} + 9104 q^{91} - 32928 q^{92} + 18252 q^{93} - 56412 q^{95} - 15372 q^{98}+O(q^{100}) \) 28 * q + 256 * q^4 - 50 * q^7 + 180 * q^8 - 800 * q^9 + 360 * q^14 - 68 * q^15 + 2008 * q^16 - 1740 * q^18 + 1238 * q^21 + 300 * q^23 - 4008 * q^25 + 24 * q^28 - 2052 * q^29 + 1604 * q^30 - 780 * q^32 + 294 * q^35 - 2712 * q^36 + 1884 * q^37 + 7696 * q^39 + 7488 * q^42 + 1748 * q^43 - 2904 * q^44 - 9628 * q^46 - 9140 * q^49 + 8220 * q^50 + 15640 * q^51 - 4392 * q^53 + 5736 * q^56 - 11860 * q^57 - 9056 * q^58 + 19408 * q^60 - 14412 * q^63 + 8560 * q^64 - 7104 * q^65 - 9524 * q^67 - 22744 * q^70 - 8748 * q^71 - 67764 * q^72 + 13980 * q^74 - 726 * q^77 + 13880 * q^78 + 41624 * q^79 + 51188 * q^81 + 56956 * q^84 + 29584 * q^85 + 24 * q^86 - 7260 * q^88 + 9104 * q^91 - 32928 * q^92 + 18252 * q^93 - 56412 * q^95 - 15372 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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