LMFDB - Embedded newform 40.6.d.a.21.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,6,Mod(21,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.21"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.12
Root			$3.18502 + 2.41984i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.6.d.a.21.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.765181 + 5.60486i) q^{2} +17.3148i q^{3} +(-30.8290 + 8.57748i) q^{4} +25.0000i q^{5} +(-97.0471 + 13.2490i) q^{6} -9.19080 q^{7} +(-71.6654 - 166.229i) q^{8} -56.8021 q^{9} +(-140.122 + 19.1295i) q^{10} +160.480i q^{11} +(-148.517 - 533.798i) q^{12} -368.546i q^{13} +(-7.03263 - 51.5132i) q^{14} -432.870 q^{15} +(876.854 - 528.870i) q^{16} -1261.09 q^{17} +(-43.4639 - 318.368i) q^{18} +2486.75i q^{19} +(-214.437 - 770.725i) q^{20} -159.137i q^{21} +(-899.467 + 122.796i) q^{22} -422.882 q^{23} +(2878.22 - 1240.87i) q^{24} -625.000 q^{25} +(2065.65 - 282.005i) q^{26} +3223.98i q^{27} +(283.343 - 78.8339i) q^{28} +5666.05i q^{29} +(-331.224 - 2426.18i) q^{30} +9387.13 q^{31} +(3635.20 + 4509.96i) q^{32} -2778.67 q^{33} +(-964.961 - 7068.23i) q^{34} -229.770i q^{35} +(1751.15 - 487.219i) q^{36} +3566.43i q^{37} +(-13937.9 + 1902.81i) q^{38} +6381.30 q^{39} +(4155.72 - 1791.63i) q^{40} -5949.95 q^{41} +(891.941 - 121.769i) q^{42} -10658.5i q^{43} +(-1376.51 - 4947.43i) q^{44} -1420.05i q^{45} +(-323.581 - 2370.20i) q^{46} +9243.94 q^{47} +(9157.27 + 15182.5i) q^{48} -16722.5 q^{49} +(-478.238 - 3503.04i) q^{50} -21835.5i q^{51} +(3161.20 + 11361.9i) q^{52} -8976.82i q^{53} +(-18070.0 + 2466.93i) q^{54} -4011.99 q^{55} +(658.662 + 1527.78i) q^{56} -43057.5 q^{57} +(-31757.4 + 4335.55i) q^{58} +27435.6i q^{59} +(13344.9 - 3712.93i) q^{60} -50515.3i q^{61} +(7182.86 + 52613.6i) q^{62} +522.057 q^{63} +(-22496.2 + 23825.7i) q^{64} +9213.66 q^{65} +(-2126.19 - 15574.1i) q^{66} +5964.39i q^{67} +(38878.1 - 10817.0i) q^{68} -7322.11i q^{69} +(1287.83 - 175.816i) q^{70} +67286.3 q^{71} +(4070.75 + 9442.16i) q^{72} +85768.5 q^{73} +(-19989.3 + 2728.96i) q^{74} -10821.7i q^{75} +(-21330.0 - 76663.9i) q^{76} -1474.94i q^{77} +(4882.86 + 35766.3i) q^{78} +56567.2 q^{79} +(13221.7 + 21921.3i) q^{80} -69625.4 q^{81} +(-4552.79 - 33348.6i) q^{82} +30208.1i q^{83} +(1364.99 + 4906.03i) q^{84} -31527.2i q^{85} +(59739.7 - 8155.72i) q^{86} -98106.4 q^{87} +(26676.4 - 11500.8i) q^{88} +113965. q^{89} +(7959.21 - 1086.60i) q^{90} +3387.24i q^{91} +(13037.0 - 3627.26i) q^{92} +162536. i q^{93} +(7073.29 + 51811.0i) q^{94} -62168.7 q^{95} +(-78089.1 + 62942.7i) q^{96} -138806. q^{97} +(-12795.8 - 93727.5i) q^{98} -9115.59i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24}+ \cdots + 216942 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.765181	+	5.60486i	0.135266	+	0.990809i
$2$	0.765181	+	5.60486i	0.135266	+	0.990809i
$3$			17.3148i			1.11074i	0.831602	+	0.555372i	$0.187424\pi$
$3$			17.3148i			1.11074i	−0.831602	+	0.555372i	$0.812576\pi$
$4$	−30.8290	+	8.57748i	−0.963406	+	0.268046i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	−97.0471	+	13.2490i	−1.10054	+	0.150246i
$7$	−9.19080			−0.0708938			−0.0354469	−	0.999372i	$-0.511285\pi$
$7$	−9.19080			−0.0708938			−0.0354469	+	0.999372i	$0.511285\pi$
$8$	−71.6654	−	166.229i	−0.395899	−	0.918294i
$9$	−56.8021			−0.233754
$10$	−140.122	+	19.1295i	−0.443103	+	0.0604929i
$11$			160.480i			0.399888i	0.979807	+	0.199944i	$0.0640760\pi$
$11$			160.480i			0.399888i	−0.979807	+	0.199944i	$0.935924\pi$
$12$	−148.517	−	533.798i	−0.297731	−	1.07010i
$13$		−	368.546i		−	0.604831i	−0.953176	−	0.302415i	$-0.902207\pi$
$13$		−	368.546i		−	0.604831i	0.953176	−	0.302415i	$-0.0977929\pi$
$14$	−7.03263	−	51.5132i	−0.00958954	−	0.0702423i
$15$	−432.870			−0.496740
$16$	876.854	−	528.870i	0.856303	−	0.516475i
$17$	−1261.09			−1.05833			−0.529167	−	0.848517i	$-0.677496\pi$
$17$	−1261.09			−1.05833			−0.529167	+	0.848517i	$0.677496\pi$
$18$	−43.4639	−	318.368i	−0.0316190	−	0.231605i
$19$			2486.75i			1.58033i	0.612894	+	0.790165i	$0.290005\pi$
$19$			2486.75i			1.58033i	−0.612894	+	0.790165i	$0.709995\pi$
$20$	−214.437	−	770.725i	−0.119874	−	0.430848i
$21$		−	159.137i		−	0.0787449i
$22$	−899.467	+	122.796i	−0.396213	+	0.0540914i
$23$	−422.882			−0.166686			−0.0833431	−	0.996521i	$-0.526560\pi$
$23$	−422.882			−0.166686			−0.0833431	+	0.996521i	$0.526560\pi$
$24$	2878.22	−	1240.87i	1.01999	−	0.439743i
$25$	−625.000			−0.200000
$26$	2065.65	−	282.005i	0.599272	−	0.0818132i
$27$			3223.98i			0.851104i
$28$	283.343	−	78.8339i	0.0682995	−	0.0190028i
$29$			5666.05i			1.25108i	0.780192	+	0.625540i	$0.215121\pi$
$29$			5666.05i			1.25108i	−0.780192	+	0.625540i	$0.784879\pi$
$30$	−331.224	−	2426.18i	−0.0671922	−	0.492175i
$31$	9387.13			1.75440			0.877200	−	0.480125i	$-0.159409\pi$
$31$	9387.13			1.75440			0.877200	+	0.480125i	$0.159409\pi$
$32$	3635.20	+	4509.96i	0.627557	+	0.778571i
$33$	−2778.67			−0.444174
$34$	−964.961	−	7068.23i	−0.143157	−	1.04861i
$35$		−	229.770i		−	0.0317047i
$36$	1751.15	−	487.219i	0.225200	−	0.0626568i
$37$			3566.43i			0.428281i	0.976803	+	0.214141i	$0.0686951\pi$
$37$			3566.43i			0.428281i	−0.976803	+	0.214141i	$0.931305\pi$
$38$	−13937.9	+	1902.81i	−1.56581	+	0.213765i
$39$	6381.30			0.671812
$40$	4155.72	−	1791.63i	0.410674	−	0.177051i
$41$	−5949.95			−0.552782			−0.276391	−	0.961045i	$-0.589138\pi$
$41$	−5949.95			−0.552782			−0.276391	+	0.961045i	$0.589138\pi$
$42$	891.941	−	121.769i	0.0780212	−	0.0106515i
$43$		−	10658.5i		−	0.879077i	−0.898224	−	0.439538i	$-0.855142\pi$
$43$		−	10658.5i		−	0.879077i	0.898224	−	0.439538i	$-0.144858\pi$
$44$	−1376.51	−	4947.43i	−0.107188	−	0.385255i
$45$		−	1420.05i		−	0.104538i
$46$	−323.581	−	2370.20i	−0.0225470	−	0.165154i
$47$	9243.94			0.610397			0.305198	−	0.952289i	$-0.401277\pi$
$47$	9243.94			0.610397			0.305198	+	0.952289i	$0.401277\pi$
$48$	9157.27	+	15182.5i	0.573671	+	0.951133i
$49$	−16722.5			−0.994974
$50$	−478.238	−	3503.04i	−0.0270533	−	0.198162i
$51$		−	21835.5i		−	1.17554i
$52$	3161.20	+	11361.9i	0.162122	+	0.582697i
$53$		−	8976.82i		−	0.438968i	−0.975616	−	0.219484i	$-0.929563\pi$
$53$		−	8976.82i		−	0.438968i	0.975616	−	0.219484i	$-0.0704374\pi$
$54$	−18070.0	+	2466.93i	−0.843282	+	0.115126i
$55$	−4011.99			−0.178835
$56$	658.662	+	1527.78i	0.0280668	+	0.0651014i
$57$	−43057.5			−1.75534
$58$	−31757.4	+	4335.55i	−1.23958	+	0.169229i
$59$			27435.6i			1.02609i	0.858363	+	0.513044i	$0.171482\pi$
$59$			27435.6i			1.02609i	−0.858363	+	0.513044i	$0.828518\pi$
$60$	13344.9	−	3712.93i	0.478562	−	0.133149i
$61$		−	50515.3i		−	1.73819i	−0.494642	−	0.869097i	$-0.664701\pi$
$61$		−	50515.3i		−	1.73819i	0.494642	−	0.869097i	$-0.335299\pi$
$62$	7182.86	+	52613.6i	0.237311	+	1.73828i
$63$	522.057			0.0165717
$64$	−22496.2	+	23825.7i	−0.686528	+	0.727103i
$65$	9213.66			0.270488
$66$	−2126.19	−	15574.1i	−0.0600817	−	0.440091i
$67$			5964.39i			0.162323i	0.996701	+	0.0811613i	$0.0258629\pi$
$67$			5964.39i			0.162323i	−0.996701	+	0.0811613i	$0.974137\pi$
$68$	38878.1	−	10817.0i	1.01961	−	0.283683i
$69$		−	7322.11i		−	0.185146i
$70$	1287.83	−	175.816i	0.0314133	−	0.00428857i
$71$	67286.3			1.58409			0.792046	−	0.610461i	$-0.209016\pi$
$71$	67286.3			1.58409			0.792046	+	0.610461i	$0.209016\pi$
$72$	4070.75	+	9442.16i	0.0925428	+	0.214655i
$73$	85768.5			1.88374			0.941869	−	0.335979i	$-0.109067\pi$
$73$	85768.5			1.88374			0.941869	+	0.335979i	$0.109067\pi$
$74$	−19989.3	+	2728.96i	−0.424345	+	0.0579320i
$75$		−	10821.7i		−	0.222149i
$76$	−21330.0	−	76663.9i	−0.423601	−	1.52250i
$77$		−	1474.94i		−	0.0283496i
$78$	4882.86	+	35766.3i	0.0908735	+	0.665638i
$79$	56567.2			1.01976			0.509879	−	0.860246i	$-0.329690\pi$
$79$	56567.2			1.01976			0.509879	+	0.860246i	$0.329690\pi$
$80$	13221.7	+	21921.3i	0.230974	+	0.382950i
$81$	−69625.4			−1.17911
$82$	−4552.79	−	33348.6i	−0.0747727	−	0.547701i
$83$			30208.1i			0.481314i	0.970610	+	0.240657i	$0.0773628\pi$
$83$			30208.1i			0.481314i	−0.970610	+	0.240657i	$0.922637\pi$
$84$	1364.99	+	4906.03i	0.0211073	+	0.0758633i
$85$		−	31527.2i		−	0.473302i
$86$	59739.7	−	8155.72i	0.870997	−	0.118909i
$87$	−98106.4			−1.38963
$88$	26676.4	−	11500.8i	0.367215	−	0.158315i
$89$	113965.			1.52509			0.762544	−	0.646936i	$-0.223950\pi$
$89$	113965.			1.52509			0.762544	+	0.646936i	$0.223950\pi$
$90$	7959.21	−	1086.60i	0.103577	−	0.0141404i
$91$			3387.24i			0.0428787i
$92$	13037.0	−	3627.26i	0.160586	−	0.0446796i
$93$			162536.i			1.94869i
$94$	7073.29	+	51811.0i	0.0825661	+	0.604787i
$95$	−62168.7			−0.706745
$96$	−78089.1	+	62942.7i	−0.864794	+	0.697055i
$97$	−138806.			−1.49788			−0.748942	−	0.662635i	$-0.769438\pi$
$97$	−138806.			−1.49788			−0.748942	+	0.662635i	$0.769438\pi$
$98$	−12795.8	−	93727.5i	−0.134586	−	0.985830i
$99$		−	9115.59i		−	0.0934753i
$100$	19268.1	−	5360.92i	0.192681	−	0.0536092i
$101$			128473.i			1.25317i	0.779354	+	0.626584i	$0.215547\pi$
$101$			128473.i			1.25317i	−0.779354	+	0.626584i	$0.784453\pi$
$102$	122385.	−	16708.1i	1.16474	−	0.159011i
$103$	−117231.			−1.08880			−0.544401	−	0.838825i	$-0.683243\pi$
$103$	−117231.			−1.08880			−0.544401	+	0.838825i	$0.683243\pi$
$104$	−61263.1	+	26412.0i	−0.555412	+	0.239452i
$105$	3978.42			0.0352158
$106$	50313.9	−	6868.90i	0.434934	−	0.0593776i
$107$		−	17654.6i		−	0.149073i	−0.997218	−	0.0745366i	$-0.976252\pi$
$107$		−	17654.6i		−	0.149073i	0.997218	−	0.0745366i	$-0.0237477\pi$
$108$	−27653.6	−	99392.0i	−0.228135	−	0.819959i
$109$		−	75398.4i		−	0.607849i	−0.952696	−	0.303925i	$-0.901703\pi$
$109$		−	75398.4i		−	0.607849i	0.952696	−	0.303925i	$-0.0982971\pi$
$110$	−3069.90	−	22486.7i	−0.0241904	−	0.177192i
$111$	−61752.0			−0.475711
$112$	−8058.99	+	4860.74i	−0.0607066	+	0.0366149i
$113$	69211.7			0.509898			0.254949	−	0.966954i	$-0.417941\pi$
$113$	69211.7			0.509898			0.254949	+	0.966954i	$0.417941\pi$
$114$	−32946.8	−	241332.i	−0.237439	−	1.73921i
$115$		−	10572.0i		−	0.0745443i
$116$	−48600.4	−	174678.i	−0.335347	−	1.20530i
$117$			20934.2i			0.141381i
$118$	−153773.	+	20993.2i	−1.01666	+	0.138795i
$119$	11590.4			0.0750294
$120$	31021.8	+	71955.5i	0.196659	+	0.456154i
$121$	135297.			0.840089
$122$	283131.	−	38653.4i	1.72222	−	0.235119i
$123$		−	103022.i		−	0.613999i
$124$	−289396.	+	80517.9i	−1.69020	+	0.470260i
$125$		−	15625.0i		−	0.0894427i
$126$	399.469	+	2926.06i	0.00224159	+	0.0164194i
$127$	−118525.			−0.652078			−0.326039	−	0.945356i	$-0.605714\pi$
$127$	−118525.			−0.652078			−0.326039	+	0.945356i	$0.605714\pi$
$128$	−150754.	−	107857.i	−0.813285	−	0.581866i
$129$	184551.			0.976430
$130$	7050.12	+	51641.3i	0.0365880	+	0.268002i
$131$			83761.8i			0.426450i	0.977003	+	0.213225i	$0.0683967\pi$
$131$			83761.8i			0.426450i	−0.977003	+	0.213225i	$0.931603\pi$
$132$	85663.7	−	23834.0i	0.427920	−	0.119059i
$133$		−	22855.2i		−	0.112036i
$134$	−33429.6	+	4563.84i	−0.160831	+	0.0219568i
$135$	−80599.4			−0.380625
$136$	90376.3	+	209629.i	0.418994	+	0.971863i
$137$	174055.			0.792291			0.396145	−	0.918188i	$-0.370348\pi$
$137$	174055.			0.792291			0.396145	+	0.918188i	$0.370348\pi$
$138$	41039.5	−	5602.75i	0.183444	−	0.0250440i
$139$			310792.i			1.36437i	0.731179	+	0.682186i	$0.238971\pi$
$139$			310792.i			1.36437i	−0.731179	+	0.682186i	$0.761029\pi$
$140$	1970.85	+	7083.58i	0.00849832	+	0.0305445i
$141$			160057.i			0.677995i
$142$	51486.2	+	377130.i	0.214274	+	1.56953i
$143$	59144.2			0.241865
$144$	−49807.2	+	30040.9i	−0.200164	+	0.120728i
$145$	−141651.			−0.559500
$146$	65628.5	+	480721.i	0.254806	+	1.86643i
$147$		−	289547.i		−	1.10516i
$148$	−30590.9	−	109949.i	−0.114799	−	0.412609i
$149$		−	293656.i		−	1.08361i	−0.840504	−	0.541805i	$-0.817741\pi$
$149$		−	293656.i		−	1.08361i	0.840504	−	0.541805i	$-0.182259\pi$
$150$	60654.4	−	8280.60i	0.220107	−	0.0300493i
$151$	26058.5			0.0930052			0.0465026	−	0.998918i	$-0.485192\pi$
$151$	26058.5			0.0930052			0.0465026	+	0.998918i	$0.485192\pi$
$152$	413370.	−	178214.i	1.45121	−	0.625651i
$153$	71632.5			0.247390
$154$	8266.82	−	1128.60i	0.0280890	−	0.00383474i
$155$			234678.i			0.784592i
$156$	−196729.	+	54735.5i	−0.647228	+	0.180077i
$157$		−	427448.i		−	1.38399i	−0.721900	−	0.691997i	$-0.756731\pi$
$157$		−	427448.i		−	1.38399i	0.721900	−	0.691997i	$-0.243269\pi$
$158$	43284.2	+	317051.i	0.137939	+	1.01039i
$159$	155432.			0.487581
$160$	−112749.	+	90879.9i	−0.348188	+	0.280652i
$161$	3886.62			0.0118170
$162$	−53276.1	−	390241.i	−0.159494	−	1.16828i
$163$		−	547292.i		−	1.61343i	−0.590941	−	0.806715i	$-0.701243\pi$
$163$		−	547292.i		−	1.61343i	0.590941	−	0.806715i	$-0.298757\pi$
$164$	183431.	−	51035.5i	0.532553	−	0.148171i
$165$		−	69466.8i		−	0.198640i
$166$	−169312.	+	23114.7i	−0.476890	+	0.0651055i
$167$	−203146.			−0.563659			−0.281829	−	0.959465i	$-0.590941\pi$
$167$	−203146.			−0.563659			−0.281829	+	0.959465i	$0.590941\pi$
$168$	−26453.2	+	11404.6i	−0.0723110	+	0.0311750i
$169$	235467.			0.634180
$170$	176706.	−	24124.0i	0.468952	−	0.0640217i
$171$		−	141253.i		−	0.369408i
$172$	91423.4	+	328592.i	0.235633	+	0.846908i
$173$			94689.2i			0.240539i	0.992741	+	0.120269i	$0.0383759\pi$
$173$			94689.2i			0.240539i	−0.992741	+	0.120269i	$0.961624\pi$
$174$	−75069.2	−	549873.i	−0.187970	−	1.37686i
$175$	5744.25			0.0141788
$176$	84872.9	+	140717.i	0.206532	+	0.342425i
$177$	−475042.			−1.13972
$178$	87203.6	+	638756.i	0.206293	+	1.51107i
$179$			290099.i			0.676727i	0.941016	+	0.338363i	$0.109873\pi$
$179$			290099.i			0.676727i	−0.941016	+	0.338363i	$0.890127\pi$
$180$	12180.5	+	43778.8i	0.0280210	+	0.100712i
$181$			63999.0i			0.145203i	0.997361	+	0.0726017i	$0.0231302\pi$
$181$			63999.0i			0.145203i	−0.997361	+	0.0726017i	$0.976870\pi$
$182$	−18985.0	+	2591.85i	−0.0424847	+	0.00580005i
$183$	874662.			1.93069
$184$	30306.0	+	70295.2i	0.0659909	+	0.153067i
$185$	−89160.7			−0.191533
$186$	−910994.	+	124370.i	−1.93078	+	0.263592i
$187$		−	202379.i		−	0.423216i
$188$	−284981.	+	79289.6i	−0.588060	+	0.163615i
$189$		−	29630.9i		−	0.0603380i
$190$	−47570.3	−	348447.i	−0.0955987	−	0.700249i
$191$	−391768.			−0.777044			−0.388522	−	0.921439i	$-0.627014\pi$
$191$	−391768.			−0.777044			−0.388522	+	0.921439i	$0.627014\pi$
$192$	−412537.	−	389516.i	−0.807626	−	0.762557i
$193$	−641122.			−1.23893			−0.619466	−	0.785024i	$-0.712651\pi$
$193$	−641122.			−1.23893			−0.619466	+	0.785024i	$0.712651\pi$
$194$	−106212.	−	777988.i	−0.202613	−	1.48412i
$195$			159533.i			0.300444i
$196$	515539.	−	143437.i	0.958564	−	0.266699i
$197$			312130.i			0.573019i	0.958077	+	0.286510i	$0.0924951\pi$
$197$			312130.i			0.573019i	−0.958077	+	0.286510i	$0.907505\pi$
$198$	51091.7	−	6975.08i	0.0926162	−	0.0126441i
$199$	171473.			0.306946			0.153473	−	0.988153i	$-0.450954\pi$
$199$	171473.			0.306946			0.153473	+	0.988153i	$0.450954\pi$
$200$	44790.8	+	103893.i	0.0791798	+	0.183659i
$201$	−103272.			−0.180299
$202$	−720075.	+	98305.3i	−1.24165	+	0.169511i
$203$		−	52075.5i		−	0.0886938i
$204$	187293.	+	673166.i	0.315099	+	1.13252i
$205$		−	148749.i		−	0.247211i
$206$	−89702.8	−	657063.i	−0.147278	−	1.07879i
$207$	24020.6			0.0389635
$208$	−194913.	−	323161.i	−0.312380	−	0.517918i
$209$	−399073.			−0.631955
$210$	3044.21	+	22298.5i	0.00476351	+	0.0348921i
$211$		−	679022.i		−	1.04997i	−0.851111	−	0.524986i	$-0.824070\pi$
$211$		−	679022.i		−	1.04997i	0.851111	−	0.524986i	$-0.175930\pi$
$212$	76998.5	+	276746.i	0.117664	+	0.422905i
$213$			1.16505e6i			1.75952i
$214$	98951.8	−	13509.0i	0.147703	−	0.0201646i
$215$	266464.			0.393135
$216$	535919.	−	231048.i	0.781564	−	0.336951i
$217$	−86275.3			−0.124376
$218$	422598.	−	57693.5i	0.602263	−	0.0822215i
$219$			1.48506e6i			2.09235i
$220$	123686.	−	34412.8i	0.172291	−	0.0479361i
$221$			464769.i			0.640113i
$222$	−47251.5	−	346111.i	−0.0643477	−	0.471339i
$223$	976043.			1.31434			0.657169	−	0.753743i	$-0.271754\pi$
$223$	976043.			1.31434			0.657169	+	0.753743i	$0.271754\pi$
$224$	−33410.4	−	41450.2i	−0.0444899	−	0.0551959i
$225$	35501.3			0.0467507
$226$	52959.5	+	387922.i	0.0689720	+	0.505212i
$227$			243426.i			0.313547i	0.987635	+	0.156773i	$0.0501092\pi$
$227$			243426.i			0.313547i	−0.987635	+	0.156773i	$0.949891\pi$
$228$	1.32742e6	−	369325.i	1.69111	−	0.470513i
$229$		−	1.33345e6i		−	1.68030i	−0.542354	−	0.840150i	$-0.682467\pi$
$229$		−	1.33345e6i		−	1.68030i	0.542354	−	0.840150i	$-0.317533\pi$
$230$	59254.9	−	8089.54i	0.0738592	−	0.0100833i
$231$	25538.2			0.0314892
$232$	941861.	−	406059.i	1.14886	−	0.495301i
$233$	−1.01947e6			−1.23023			−0.615114	−	0.788438i	$-0.710890\pi$
$233$	−1.01947e6			−1.23023			−0.615114	+	0.788438i	$0.710890\pi$
$234$	−117333.	+	16018.5i	−0.140082	+	0.0191241i
$235$			231098.i			0.272978i
$236$	−235328.	−	845812.i	−0.275039	−	0.988539i
$237$			979449.i			1.13269i
$238$	8868.77	+	64962.7i	0.0101489	+	0.0743398i
$239$	−975796.			−1.10501			−0.552503	−	0.833511i	$-0.686327\pi$
$239$	−975796.			−1.10501			−0.552503	+	0.833511i	$0.686327\pi$
$240$	−379564.	+	228932.i	−0.425360	+	0.256554i
$241$	359018.			0.398175			0.199087	−	0.979982i	$-0.436202\pi$
$241$	359018.			0.398175			0.199087	+	0.979982i	$0.436202\pi$
$242$	103527.	+	758323.i	0.113636	+	0.832368i
$243$		−	422124.i		−	0.458589i
$244$	433294.	+	1.55734e6i	0.465916	+	1.67459i
$245$		−	418063.i		−	0.444966i
$246$	577425.	−	78830.6i	0.608356	−	0.0830534i
$247$	916482.			0.955832
$248$	−672732.	−	1.56041e6i	−0.694565	−	1.61106i
$249$	−523047.			−0.534616
$250$	87576.0	−	11956.0i	0.0886207	−	0.0120986i
$251$			208180.i			0.208572i	0.994547	+	0.104286i	$0.0332557\pi$
$251$			208180.i			0.208572i	−0.994547	+	0.104286i	$0.966744\pi$
$252$	−16094.5	+	4477.93i	−0.0159653	+	0.00444198i
$253$		−	67864.0i		−	0.0666558i
$254$	−90692.8	−	664314.i	−0.0882041	−	0.646084i
$255$	545887.			0.525717
$256$	489169.	−	927483.i	0.466508	−	0.884517i
$257$	1.82101e6			1.71981			0.859904	−	0.510456i	$-0.170523\pi$
$257$	1.82101e6			1.71981			0.859904	+	0.510456i	$0.170523\pi$
$258$	141215.	+	1.03438e6i	0.132078	+	0.967456i
$259$		−	32778.3i		−	0.0303625i
$260$	−284048.	+	79029.9i	−0.260590	+	0.0725034i
$261$		−	321844.i		−	0.292445i
$262$	−469474.	+	64093.0i	−0.422531	+	0.0576843i
$263$	−1.74901e6			−1.55921			−0.779603	−	0.626274i	$-0.784579\pi$
$263$	−1.74901e6			−1.55921			−0.779603	+	0.626274i	$0.784579\pi$
$264$	199135.	+	461896.i	0.175848	+	0.407882i
$265$	224421.			0.196313
$266$	128100.	−	17488.4i	0.111006	−	0.0151546i
$267$			1.97327e6i			1.69398i
$268$	−51159.4	−	183876.i	−0.0435099	−	0.156383i
$269$		−	1.48042e6i		−	1.24740i	−0.781665	−	0.623699i	$-0.785629\pi$
$269$		−	1.48042e6i		−	1.24740i	0.781665	−	0.623699i	$-0.214371\pi$
$270$	−61673.2	−	451749.i	−0.0514858	−	0.377127i
$271$	1.04418e6			0.863680			0.431840	−	0.901950i	$-0.357864\pi$
$271$	1.04418e6			0.863680			0.431840	+	0.901950i	$0.357864\pi$
$272$	−1.10579e6	+	666951.i	−0.906255	+	0.546603i
$273$	−58649.3			−0.0476273
$274$	133183.	+	975553.i	0.107170	+	0.785009i
$275$		−	100300.i		−	0.0799776i
$276$	62805.3	+	225733.i	0.0496276	+	0.178371i
$277$		−	22792.5i		−	0.0178481i	−0.999960	−	0.00892407i	$-0.997159\pi$
$277$		−	22792.5i		−	0.0178481i	0.999960	−	0.00892407i	$-0.00284066\pi$
$278$	−1.74195e6	+	237812.i	−1.35183	+	0.184553i
$279$	−533209.			−0.410098
$280$	−38194.4	+	16466.6i	−0.0291142	+	0.0125518i
$281$	181092.			0.136815			0.0684074	−	0.997657i	$-0.478208\pi$
$281$	181092.			0.136815			0.0684074	+	0.997657i	$0.478208\pi$
$282$	−897097.	+	122473.i	−0.671764	+	0.0917099i
$283$		−	1.00940e6i		−	0.749200i	−0.927187	−	0.374600i	$-0.877780\pi$
$283$		−	1.00940e6i		−	0.749200i	0.927187	−	0.374600i	$-0.122220\pi$
$284$	−2.07437e6	+	577146.i	−1.52612	+	0.424610i
$285$		−	1.07644e6i		−	0.785013i
$286$	45256.1	+	331495.i	0.0327161	+	0.239642i
$287$	54684.8			0.0391888
$288$	−206487.	−	256176.i	−0.146694	−	0.181994i
$289$	170486.			0.120073
$290$	−108389.	−	793935.i	−0.0756815	−	0.554358i
$291$		−	2.40339e6i		−	1.66377i
$292$	−2.64416e6	+	735677.i	−1.81481	+	0.504929i
$293$			2.25558e6i			1.53493i	0.641090	+	0.767465i	$0.278482\pi$
$293$			2.25558e6i			1.53493i	−0.641090	+	0.767465i	$0.721518\pi$
$294$	1.62287e6	−	221556.i	1.09500	−	0.149491i
$295$	−685890.			−0.458880
$296$	592844.	−	255589.i	0.393288	−	0.169556i
$297$	−517383.			−0.340346
$298$	1.64590e6	−	224700.i	1.07365	−	0.146576i
$299$			155852.i			0.100817i
$300$	92823.3	+	333624.i	0.0595462	+	0.214020i
$301$			97960.6i			0.0623211i
$302$	19939.5	+	146054.i	0.0125805	+	0.0921504i
$303$	−2.22449e6			−1.39195
$304$	1.31517e6	+	2.18051e6i	0.816200	+	1.35324i
$305$	1.26288e6			0.777344
$306$	54811.9	+	401490.i	0.0334635	+	0.245116i
$307$		−	2.42181e6i		−	1.46654i	−0.679938	−	0.733270i	$-0.737993\pi$
$307$		−	2.42181e6i		−	1.46654i	0.679938	−	0.733270i	$-0.262007\pi$
$308$	12651.2	+	45470.8i	0.00759900	+	0.0273122i
$309$		−	2.02983e6i		−	1.20938i
$310$	−1.31534e6	+	179572.i	−0.777381	+	0.106129i
$311$	−1.04918e6			−0.615107			−0.307554	−	0.951531i	$-0.599510\pi$
$311$	−1.04918e6			−0.615107			−0.307554	+	0.951531i	$0.599510\pi$
$312$	−457318.	−	1.06076e6i	−0.265970	−	0.616921i
$313$	919355.			0.530423			0.265212	−	0.964190i	$-0.414558\pi$
$313$	919355.			0.530423			0.265212	+	0.964190i	$0.414558\pi$
$314$	2.39579e6	−	327075.i	1.37127	−	0.187208i
$315$			13051.4i			0.00741109i
$316$	−1.74391e6	+	485204.i	−0.982441	+	0.273342i
$317$			761677.i			0.425719i	0.977083	+	0.212859i	$0.0682776\pi$
$317$			761677.i			0.425719i	−0.977083	+	0.212859i	$0.931722\pi$
$318$	118934.	+	871174.i	0.0659533	+	0.483100i
$319$	−909285.			−0.500292
$320$	−595643.	−	562404.i	−0.325170	−	0.307025i
$321$	305686.			0.165582
$322$	2973.97	+	21784.0i	0.00159844	+	0.0117084i
$323$		−	3.13601e6i		−	1.67252i
$324$	2.14648e6	−	597211.i	1.13596	−	0.316057i
$325$			230341.i			0.120966i
$326$	3.06750e6	−	418778.i	1.59860	−	0.218243i
$327$	1.30551e6			0.675165
$328$	426405.	+	989054.i	0.218846	+	0.507616i
$329$	−84959.2			−0.0432734
$330$	389352.	−	53154.7i	0.196815	−	0.0268694i
$331$			1.27292e6i			0.638605i	0.947653	+	0.319302i	$0.103449\pi$
$331$			1.27292e6i			0.638605i	−0.947653	+	0.319302i	$0.896551\pi$
$332$	−259109.	−	931285.i	−0.129014	−	0.463700i
$333$		−	202581.i		−	0.100112i
$334$	−155443.	−	1.13860e6i	−0.0762440	−	0.558478i
$335$	−149110.			−0.0725928
$336$	−84162.7	−	139540.i	−0.0406697	−	0.0674295i
$337$	1.61635e6			0.775286			0.387643	−	0.921810i	$-0.373289\pi$
$337$	1.61635e6			0.775286			0.387643	+	0.921810i	$0.373289\pi$
$338$	180175.	+	1.31976e6i	0.0857832	+	0.628351i
$339$			1.19839e6i			0.566367i
$340$	270424.	+	971952.i	0.126867	+	0.455982i
$341$			1.50644e6i			0.701564i
$342$	791701.	−	108084.i	0.366013	−	0.0499684i
$343$	308163.			0.141431
$344$	−1.77176e6	+	763848.i	−0.807251	+	0.348026i
$345$	183053.			0.0827997
$346$	−530720.	+	72454.4i	−0.238328	+	0.0325368i
$347$			349978.i			0.156033i	0.996952	+	0.0780167i	$0.0248587\pi$
$347$			349978.i			0.156033i	−0.996952	+	0.0780167i	$0.975141\pi$
$348$	3.02452e6	−	841505.i	1.33878	−	0.372485i
$349$			2.38580e6i			1.04850i	0.851563	+	0.524252i	$0.175655\pi$
$349$			2.38580e6i			1.04850i	−0.851563	+	0.524252i	$0.824345\pi$
$350$	4395.40	+	32195.7i	0.00191791	+	0.0140485i
$351$	1.18819e6			0.514774
$352$	−723758.	+	583375.i	−0.311341	+	0.250952i
$353$	3.84764e6			1.64345			0.821727	−	0.569882i	$-0.193011\pi$
$353$	3.84764e6			1.64345			0.821727	+	0.569882i	$0.193011\pi$
$354$	−363493.	−	2.66254e6i	−0.154166	−	1.12925i
$355$			1.68216e6i			0.708428i
$356$	−3.51342e6	+	977529.i	−1.46928	+	0.408794i
$357$			200686.i			0.0833385i
$358$	−1.62596e6	+	221978.i	−0.670507	+	0.0915383i
$359$	−2.69844e6			−1.10503			−0.552517	−	0.833501i	$-0.686333\pi$
$359$	−2.69844e6			−1.10503			−0.552517	+	0.833501i	$0.686333\pi$
$360$	−236054.	+	101769.i	−0.0959965	+	0.0413864i
$361$	−3.70781e6			−1.49744
$362$	−358706.	+	48970.9i	−0.143869	+	0.0196411i
$363$			2.34264e6i			0.933125i
$364$	−29053.9	−	104425.i	−0.0114935	−	0.0413096i
$365$			2.14421e6i			0.842434i
$366$	669275.	+	4.90236e6i	0.261157	+	1.91295i
$367$	1.14096e6			0.442186			0.221093	−	0.975253i	$-0.429038\pi$
$367$	1.14096e6			0.442186			0.221093	+	0.975253i	$0.429038\pi$
$368$	−370806.	+	223650.i	−0.142734	+	0.0860892i
$369$	337970.			0.129215
$370$	−68224.1	−	499734.i	−0.0259080	−	0.189773i
$371$			82504.2i			0.0311201i
$372$	−1.39415e6	−	5.01083e6i	−0.522339	−	1.87738i
$373$		−	461958.i		−	0.171922i	−0.996299	−	0.0859608i	$-0.972604\pi$
$373$		−	461958.i		−	0.171922i	0.996299	−	0.0859608i	$-0.0273960\pi$
$374$	1.13431e6	−	154857.i	0.419326	−	0.0572468i
$375$	270544.			0.0993480
$376$	−662470.	−	1.53661e6i	−0.241655	−	0.560524i
$377$	2.08820e6			0.756691
$378$	166077.	−	22673.1i	0.0597835	−	0.00816170i
$379$			4.36174e6i			1.55977i	0.625920	+	0.779887i	$0.284723\pi$
$379$			4.36174e6i			1.55977i	−0.625920	+	0.779887i	$0.715277\pi$
$380$	1.91660e6	−	533250.i	0.680882	−	0.189440i
$381$		−	2.05223e6i		−	0.724292i
$382$	−299774.	−	2.19581e6i	−0.105108	−	0.769903i
$383$	−417638.			−0.145480			−0.0727400	−	0.997351i	$-0.523174\pi$
$383$	−417638.			−0.145480			−0.0727400	+	0.997351i	$0.523174\pi$
$384$	1.86752e6	−	2.61027e6i	0.646304	−	0.903352i
$385$	36873.4			0.0126783
$386$	−490574.	−	3.59340e6i	−0.167586	−	1.22754i
$387$			605428.i			0.205487i
$388$	4.27924e6	−	1.19060e6i	1.44307	−	0.401502i
$389$		−	1.92396e6i		−	0.644647i	−0.946630	−	0.322323i	$-0.895536\pi$
$389$		−	1.92396e6i		−	0.644647i	0.946630	−	0.322323i	$-0.104464\pi$
$390$	−894159.	+	122071.i	−0.297682	+	0.0406399i
$391$	533291.			0.176410
$392$	1.19843e6	+	2.77977e6i	0.393909	+	0.913679i
$393$	−1.45032e6			−0.473677
$394$	−1.74944e6	+	238836.i	−0.567753	+	0.0775102i
$395$			1.41418e6i			0.456049i
$396$	78188.8	+	281025.i	0.0250557	+	0.0900547i
$397$		−	2.95436e6i		−	0.940778i	−0.882459	−	0.470389i	$-0.844114\pi$
$397$		−	2.95436e6i		−	0.940778i	0.882459	−	0.470389i	$-0.155886\pi$
$398$	131208.	+	961080.i	0.0415194	+	0.304125i
$399$	395733.			0.124443
$400$	−548034.	+	330544.i	−0.171261	+	0.103295i
$401$	−1.57105e6			−0.487898			−0.243949	−	0.969788i	$-0.578443\pi$
$401$	−1.57105e6			−0.487898			−0.243949	+	0.969788i	$0.578443\pi$
$402$	−79021.9	−	578826.i	−0.0243884	−	0.178642i
$403$		−	3.45959e6i		−	1.06112i
$404$	−1.10198e6	−	3.96070e6i	−0.335907	−	1.20731i
$405$		−	1.74064e6i		−	0.527315i
$406$	291876.	−	39847.2i	0.0878787	−	0.0119973i
$407$	−572339.			−0.171265
$408$	−3.62969e6	+	1.56485e6i	−1.07949	+	0.465395i
$409$	−5.18294e6			−1.53203			−0.766016	−	0.642821i	$-0.777764\pi$
$409$	−5.18294e6			−1.53203			−0.766016	+	0.642821i	$0.777764\pi$
$410$	833716.	−	113820.i	0.244939	−	0.0334394i
$411$			3.01372e6i			0.880033i
$412$	3.61411e6	−	1.00554e6i	1.04896	−	0.291849i
$413$		−	252155.i		−	0.0727432i
$414$	18380.1	+	134632.i	0.00527045	+	0.0386054i
$415$	−755202.			−0.215250
$416$	1.66213e6	−	1.33974e6i	0.470903	−	0.379565i
$417$	−5.38130e6			−1.51547
$418$	−305363.	−	2.23675e6i	−0.0854822	−	0.626147i
$419$		−	4.81218e6i		−	1.33908i	−0.742776	−	0.669540i	$-0.766491\pi$
$419$		−	4.81218e6i		−	1.33908i	0.742776	−	0.669540i	$-0.233509\pi$
$420$	−122651.	+	34124.8i	−0.0339271	+	0.00943946i
$421$			4.66983e6i			1.28409i	0.766667	+	0.642045i	$0.221914\pi$
$421$			4.66983e6i			1.28409i	−0.766667	+	0.642045i	$0.778086\pi$
$422$	3.80583e6	−	519575.i	1.04032	−	0.142026i
$423$	−525075.			−0.142683
$424$	−1.49221e6	+	643327.i	−0.403102	+	0.173787i
$425$	788180.			0.211667
$426$	−6.52994e6	+	891473.i	−1.74335	+	0.238004i
$427$			464276.i			0.123227i
$428$	151432.	+	544275.i	0.0399585	+	0.143618i
$429$			1.02407e6i			0.268650i
$430$	203893.	+	1.49349e6i	0.0531779	+	0.389522i
$431$	−3.07756e6			−0.798020			−0.399010	−	0.916947i	$-0.630646\pi$
$431$	−3.07756e6			−0.798020			−0.399010	+	0.916947i	$0.630646\pi$
$432$	1.70506e6	+	2.82696e6i	0.439574	+	0.728803i
$433$	−2.60694e6			−0.668206			−0.334103	−	0.942537i	$-0.608433\pi$
$433$	−2.60694e6			−0.668206			−0.334103	+	0.942537i	$0.608433\pi$
$434$	−66016.3	−	483561.i	−0.0168239	−	0.123233i
$435$		−	2.45266e6i		−	0.621462i
$436$	646728.	+	2.32446e6i	0.162932	+	0.585606i
$437$		−	1.05160e6i		−	0.263419i
$438$	−8.32358e6	+	1.13634e6i	−2.07312	+	0.283025i
$439$	7.17040e6			1.77575			0.887876	−	0.460083i	$-0.152180\pi$
$439$	7.17040e6			1.77575			0.887876	+	0.460083i	$0.152180\pi$
$440$	287521.	+	666910.i	0.0708007	+	0.164223i
$441$	949875.			0.232579
$442$	−2.60497e6	+	355633.i	−0.634230	+	0.0865857i
$443$			5.08067e6i			1.23002i	0.788520	+	0.615009i	$0.210848\pi$
$443$			5.08067e6i			1.23002i	−0.788520	+	0.615009i	$0.789152\pi$
$444$	1.90375e6	−	529676.i	0.458303	−	0.127513i
$445$			2.84912e6i			0.682041i
$446$	746850.	+	5.47059e6i	0.177786	+	1.30226i
$447$	5.08459e6			1.20361
$448$	206758.	−	218978.i	0.0486706	−	0.0515471i
$449$	3.18246e6			0.744984			0.372492	−	0.928035i	$-0.378503\pi$
$449$	3.18246e6			0.744984			0.372492	+	0.928035i	$0.378503\pi$
$450$	27165.0	+	198980.i	0.00632380	+	0.0463211i
$451$		−	954846.i		−	0.221051i
$452$	−2.13373e6	+	593662.i	−0.491239	+	0.136676i
$453$			451198.i			0.103305i
$454$	−1.36437e6	+	186265.i	−0.310665	+	0.0424123i
$455$	−84680.9			−0.0191760
$456$	3.08573e6	+	7.15741e6i	0.694938	+	1.61192i
$457$	−1.54454e6			−0.345946			−0.172973	−	0.984927i	$-0.555337\pi$
$457$	−1.54454e6			−0.345946			−0.172973	+	0.984927i	$0.555337\pi$
$458$	7.47378e6	−	1.02033e6i	1.66486	−	0.227288i
$459$		−	4.06572e6i		−	0.900753i
$460$	90681.5	+	325926.i	0.0199813	+	0.0718164i
$461$		−	888536.i		−	0.194725i	−0.995249	−	0.0973627i	$-0.968959\pi$
$461$		−	888536.i		−	0.194725i	0.995249	−	0.0973627i	$-0.0310407\pi$
$462$	19541.4	+	143138.i	0.00425942	+	0.0311998i
$463$	3.53164e6			0.765640			0.382820	−	0.923823i	$-0.374953\pi$
$463$	3.53164e6			0.765640			0.382820	+	0.923823i	$0.374953\pi$
$464$	2.99660e6	+	4.96829e6i	0.646151	+	1.07130i
$465$	−4.06341e6			−0.871481
$466$	−780081.	−	5.71400e6i	−0.166408	−	1.21892i
$467$		−	7.13335e6i		−	1.51357i	−0.653666	−	0.756783i	$-0.726770\pi$
$467$		−	7.13335e6i		−	1.51357i	0.653666	−	0.756783i	$-0.273230\pi$
$468$	−179563.	−	645381.i	−0.0378967	−	0.136208i
$469$		−	54817.5i		−	0.0115077i
$470$	−1.29528e6	+	176832.i	−0.270469	+	0.0369247i
$471$	7.40118e6			1.53726
$472$	4.56059e6	−	1.96618e6i	0.942250	−	0.406227i
$473$	1.71048e6			0.351532
$474$	−5.48968e6	+	749457.i	−1.12228	+	0.153215i
$475$		−	1.55422e6i		−	0.316066i
$476$	−357321.	+	99416.5i	−0.0722838	+	0.0201113i
$477$			509903.i			0.102610i
$478$	−746661.	−	5.46920e6i	−0.149470	−	1.09485i
$479$	5.02213e6			1.00011			0.500057	−	0.865992i	$-0.333312\pi$
$479$	5.02213e6			1.00011			0.500057	+	0.865992i	$0.333312\pi$
$480$	−1.57357e6	−	1.95223e6i	−0.311733	−	0.386747i
$481$	1.31439e6			0.259038
$482$	274714.	+	2.01225e6i	0.0538596	+	0.394515i
$483$			67296.1i			0.0131257i
$484$	−4.17108e6	+	1.16051e6i	−0.809347	+	0.225183i
$485$		−	3.47015e6i		−	0.669874i
$486$	2.36595e6	−	323001.i	0.454375	−	0.0620317i
$487$	−9.04360e6			−1.72790			−0.863951	−	0.503576i	$-0.832017\pi$
$487$	−9.04360e6			−1.72790			−0.863951	+	0.503576i	$0.832017\pi$
$488$	−8.39710e6	+	3.62020e6i	−1.59617	+	0.688149i
$489$	9.47625e6			1.79211
$490$	2.34319e6	−	319894.i	0.440876	−	0.0601889i
$491$			1.91922e6i			0.359270i	0.983733	+	0.179635i	$0.0574916\pi$
$491$			1.91922e6i			0.359270i	−0.983733	+	0.179635i	$0.942508\pi$
$492$	883670.	+	3.17607e6i	0.164580	+	0.591531i
$493$		−	7.14538e6i		−	1.32406i
$494$	701275.	+	5.13675e6i	0.129292	+	0.947047i
$495$	227890.			0.0418034
$496$	8.23114e6	−	4.96457e6i	1.50230	−	0.906103i
$497$	−618415.			−0.112302
$498$	−400226.	−	2.93161e6i	−0.0723156	−	0.529703i
$499$		−	1.22004e6i		−	0.219342i	−0.993968	−	0.109671i	$-0.965020\pi$
$499$		−	1.22004e6i		−	0.219342i	0.993968	−	0.109671i	$-0.0349797\pi$
$500$	134023.	+	481703.i	0.0239748	+	0.0861697i
$501$		−	3.51742e6i		−	0.626081i
$502$	−1.16682e6	+	159296.i	−0.206655	+	0.0282127i
$503$	7.08742e6			1.24902			0.624508	−	0.781018i	$-0.285300\pi$
$503$	7.08742e6			1.24902			0.624508	+	0.781018i	$0.285300\pi$
$504$	−37413.4	−	86781.1i	−0.00656071	−	0.0152177i
$505$	−3.21183e6			−0.560434
$506$	380368.	−	51928.3i	0.0660432	−	0.00901628i
$507$			4.07706e6i			0.704412i
$508$	3.65399e6	−	1.01664e6i	0.628215	−	0.174787i
$509$			5.58984e6i			0.956324i	0.878272	+	0.478162i	$0.158697\pi$
$509$			5.58984e6i			0.956324i	−0.878272	+	0.478162i	$0.841303\pi$
$510$	417703.	+	3.05962e6i	0.0711118	+	0.520886i
$511$	−788281.			−0.133545
$512$	5.57272e6	+	2.03203e6i	0.939490	+	0.342575i
$513$	−8.01722e6			−1.34502
$514$	1.39340e6	+	1.02065e7i	0.232632	+	1.70400i
$515$		−	2.93077e6i		−	0.486927i
$516$	−5.68951e6	+	1.58298e6i	−0.940698	+	0.261728i
$517$			1.48346e6i			0.244090i
$518$	183718.	−	25081.4i	0.0300834	−	0.00410702i
$519$	−1.63952e6			−0.267177
$520$	−660300.	−	1.53158e6i	−0.107086	−	0.248388i
$521$	8.47810e6			1.36837			0.684186	−	0.729308i	$-0.260158\pi$
$521$	8.47810e6			1.36837			0.684186	+	0.729308i	$0.260158\pi$
$522$	1.80389e6	−	246269.i	0.289757	−	0.0395579i
$523$			6.21299e6i			0.993223i	0.867973	+	0.496611i	$0.165423\pi$
$523$			6.21299e6i			0.993223i	−0.867973	+	0.496611i	$0.834577\pi$
$524$	−718465.	−	2.58229e6i	−0.114308	−	0.410844i
$525$			99460.5i			0.0157490i
$526$	−1.33831e6	−	9.80298e6i	−0.210908	−	1.54488i
$527$	−1.18380e7			−1.85674
$528$	−2.43649e6	+	1.46956e6i	−0.380347	+	0.229404i
$529$	−6.25751e6			−0.972216
$530$	171722.	+	1.25785e6i	0.0265545	+	0.194508i
$531$		−	1.55840e6i		−	0.239852i
$532$	196040.	+	704603.i	0.0300307	+	0.107936i
$533$			2.19283e6i			0.334339i
$534$	−1.10599e7	+	1.50991e6i	−1.67842	+	0.229139i
$535$	441366.			0.0666675
$536$	991454.	−	427440.i	0.149060	−	0.0642633i
$537$	−5.02300e6			−0.751670
$538$	8.29757e6	−	1.13279e6i	1.23593	−	0.168731i
$539$		−	2.68363e6i		−	0.397878i
$540$	2.48480e6	−	691340.i	0.366697	−	0.102025i
$541$		−	7.13892e6i		−	1.04867i	−0.851512	−	0.524335i	$-0.824314\pi$
$541$		−	7.13892e6i		−	1.04867i	0.851512	−	0.524335i	$-0.175686\pi$
$542$	798989.	+	5.85250e6i	0.116827	+	0.855742i
$543$	−1.10813e6			−0.161284
$544$	−4.58430e6	−	5.68746e6i	−0.664165	−	0.823989i
$545$	1.88496e6			0.271838
$546$	−44877.4	−	328721.i	−0.00644237	−	0.0471896i
$547$			7.31142e6i			1.04480i	0.852700	+	0.522400i	$0.174963\pi$
$547$			7.31142e6i			1.04480i	−0.852700	+	0.522400i	$0.825037\pi$
$548$	−5.36593e6	+	1.49295e6i	−0.763298	+	0.212370i
$549$			2.86938e6i			0.406309i
$550$	562167.	−	76747.6i	0.0792426	−	0.0108183i
$551$	−1.40900e7			−1.97712
$552$	−1.21715e6	+	524742.i	−0.170018	+	0.0732990i
$553$	−519898.			−0.0722945
$554$	127749.	−	17440.4i	0.0176841	−	0.00241425i
$555$		−	1.54380e6i		−	0.212745i
$556$	−2.66581e6	−	9.58140e6i	−0.365715	−	1.31444i
$557$		−	1.92783e6i		−	0.263288i	−0.991297	−	0.131644i	$-0.957974\pi$
$557$		−	1.92783e6i		−	0.263288i	0.991297	−	0.131644i	$-0.0420256\pi$
$558$	−408002.	−	2.98857e6i	−0.0554724	−	0.406329i
$559$	−3.92817e6			−0.531692
$560$	−121518.	−	201475.i	−0.0163747	−	0.0271488i
$561$	3.50415e6			0.470084
$562$	138568.	+	1.01499e6i	0.0185064	+	0.135557i
$563$			1.29516e7i			1.72208i	0.508539	+	0.861039i	$0.330186\pi$
$563$			1.29516e7i			1.72208i	−0.508539	+	0.861039i	$0.669814\pi$
$564$	−1.37288e6	−	4.93439e6i	−0.181734	−	0.653185i
$565$			1.73029e6i			0.228033i
$566$	5.65756e6	−	772375.i	0.742314	−	0.101341i
$567$	639914.			0.0835918
$568$	−4.82210e6	−	1.11849e7i	−0.627141	−	1.45466i
$569$	7.26039e6			0.940112			0.470056	−	0.882637i	$-0.344234\pi$
$569$	7.26039e6			0.940112			0.470056	+	0.882637i	$0.344234\pi$
$570$	6.03329e6	−	823670.i	0.777798	−	0.106186i
$571$			1.83619e6i			0.235682i	0.993032	+	0.117841i	$0.0375973\pi$
$571$			1.83619e6i			0.235682i	−0.993032	+	0.117841i	$0.962403\pi$
$572$	−1.82336e6	+	507308.i	−0.233014	+	0.0648309i
$573$		−	6.78339e6i		−	0.863098i
$574$	41843.8	+	306501.i	0.00530092	+	0.0388286i
$575$	264301.			0.0333372
$576$	1.27783e6	−	1.35335e6i	0.160478	−	0.169963i
$577$	2.04937e6			0.256260			0.128130	−	0.991757i	$-0.459102\pi$
$577$	2.04937e6			0.256260			0.128130	+	0.991757i	$0.459102\pi$
$578$	130453.	+	955550.i	0.0162418	+	0.118969i
$579$		−	1.11009e7i		−	1.37614i
$580$	4.36696e6	−	1.21501e6i	0.539026	−	0.149972i
$581$		−	277637.i		−	0.0341222i
$582$	1.34707e7	−	1.83903e6i	1.64848	−	0.225052i
$583$	1.44060e6			0.175538
$584$	−6.14663e6	−	1.42572e7i	−0.745770	−	1.72983i
$585$	−523356.			−0.0632277
$586$	−1.26422e7	+	1.72593e6i	−1.52082	+	0.207624i
$587$			2.38716e6i			0.285947i	0.989726	+	0.142974i	$0.0456664\pi$
$587$			2.38716e6i			0.285947i	−0.989726	+	0.142974i	$0.954334\pi$
$588$	2.48358e6	+	8.92645e6i	0.296234	+	1.06472i
$589$			2.33434e7i			2.77253i
$590$	−524830.	−	3.84432e6i	−0.0620710	−	0.454663i
$591$	−5.40446e6			−0.636478
$592$	1.88618e6	+	3.12724e6i	0.221196	+	0.366738i
$593$	1.01237e7			1.18223			0.591116	−	0.806587i	$-0.298688\pi$
$593$	1.01237e7			1.18223			0.591116	+	0.806587i	$0.298688\pi$
$594$	−395892.	−	2.89986e6i	−0.0460374	−	0.337218i
$595$			289760.i			0.0335542i
$596$	2.51883e6	+	9.05311e6i	0.290457	+	1.04396i
$597$			2.96901e6i			0.340939i
$598$	−873527.	+	119255.i	−0.0998903	+	0.0136371i
$599$	3.96697e6			0.451743			0.225872	−	0.974157i	$-0.427477\pi$
$599$	3.96697e6			0.451743			0.225872	+	0.974157i	$0.427477\pi$
$600$	−1.79889e6	+	775544.i	−0.203998	+	0.0879485i
$601$	5.94578e6			0.671464			0.335732	−	0.941958i	$-0.391016\pi$
$601$	5.94578e6			0.671464			0.335732	+	0.941958i	$0.391016\pi$
$602$	−549056.	+	74957.6i	−0.0617483	+	0.00842994i
$603$		−	338790.i		−	0.0379435i
$604$	−803358.	+	223516.i	−0.0896018	+	0.0249297i
$605$			3.38243e6i			0.375699i
$606$	−1.70214e6	−	1.24680e7i	−0.188284	−	1.37916i
$607$	−900508.			−0.0992010			−0.0496005	−	0.998769i	$-0.515795\pi$
$607$	−900508.			−0.0992010			−0.0496005	+	0.998769i	$0.515795\pi$
$608$	−1.12151e7	+	9.03981e6i	−1.23040	+	0.991746i
$609$	901677.			0.0985162
$610$	966334.	+	7.07828e6i	0.105148	+	0.770200i
$611$		−	3.40682e6i		−	0.369187i
$612$	−2.20836e6	+	614426.i	−0.238337	+	0.0663118i
$613$			4.07379e6i			0.437872i	0.975739	+	0.218936i	$0.0702586\pi$
$613$			4.07379e6i			0.437872i	−0.975739	+	0.218936i	$0.929741\pi$
$614$	1.35739e7	−	1.85312e6i	1.45306	−	0.198373i
$615$	2.57555e6			0.274589
$616$	−245177.	+	105702.i	−0.0260333	+	0.0112236i
$617$	3.83021e6			0.405051			0.202525	−	0.979277i	$-0.435085\pi$
$617$	3.83021e6			0.405051			0.202525	+	0.979277i	$0.435085\pi$
$618$	1.13769e7	−	1.55319e6i	1.19826	−	0.163588i
$619$			9.65601e6i			1.01291i	0.862266	+	0.506455i	$0.169045\pi$
$619$			9.65601e6i			1.01291i	−0.862266	+	0.506455i	$0.830955\pi$
$620$	−2.01295e6	−	7.23490e6i	−0.210307	−	0.755881i
$621$		−	1.36336e6i		−	0.141867i
$622$	−802816.	−	5.88053e6i	−0.0832032	−	0.609454i
$623$	−1.04743e6			−0.108119
$624$	5.59547e6	−	3.37488e6i	0.575275	−	0.346974i
$625$	390625.			0.0400000
$626$	703473.	+	5.15286e6i	0.0717483	+	0.525548i
$627$		−	6.90986e6i		−	0.701941i
$628$	3.66643e6	+	1.31778e7i	0.370974	+	1.33335i
$629$		−	4.49758e6i		−	0.453265i
$630$	−73151.5	+	9986.71i	−0.00734297	+	0.00100247i
$631$	8.80367e6			0.880218			0.440109	−	0.897944i	$-0.354940\pi$
$631$	8.80367e6			0.880218			0.440109	+	0.897944i	$0.354940\pi$
$632$	−4.05391e6	−	9.40311e6i	−0.403721	−	0.936437i
$633$	1.17571e7			1.16625
$634$	−4.26910e6	+	582821.i	−0.421806	+	0.0575854i
$635$		−	2.96312e6i		−	0.291618i
$636$	−4.79181e6	+	1.33321e6i	−0.469739	+	0.130694i
$637$			6.16303e6i			0.601791i
$638$	−695768.	−	5.09642e6i	−0.0676726	−	0.495694i
$639$	−3.82201e6			−0.370288
$640$	2.69642e6	−	3.76884e6i	0.260218	−	0.363712i
$641$	−8.42581e6			−0.809966			−0.404983	−	0.914324i	$-0.632722\pi$
$641$	−8.42581e6			−0.809966			−0.404983	+	0.914324i	$0.632722\pi$
$642$	233906.	+	1.71333e6i	0.0223977	+	0.164060i
$643$		−	559011.i		−	0.0533204i	−0.999645	−	0.0266602i	$-0.991513\pi$
$643$		−	559011.i		−	0.0533204i	0.999645	−	0.0266602i	$-0.00848720\pi$
$644$	−119821.	+	33337.4i	−0.0113846	+	0.00316751i
$645$			4.61376e6i			0.436673i
$646$	1.75769e7	−	2.39961e6i	1.65715	−	0.226235i
$647$	−1.60950e7			−1.51158			−0.755790	−	0.654814i	$-0.772747\pi$
$647$	−1.60950e7			−1.51158			−0.755790	+	0.654814i	$0.772747\pi$
$648$	4.98973e6	+	1.15738e7i	0.466810	+	1.08277i
$649$	−4.40286e6			−0.410320
$650$	−1.29103e6	+	176253.i	−0.119854	+	0.0163626i
$651$		−	1.49384e6i		−	0.138150i
$652$	4.69438e6	+	1.68725e7i	0.432473	+	1.55439i
$653$		−	2.03856e7i		−	1.87085i	−0.353520	−	0.935427i	$-0.615015\pi$
$653$		−	2.03856e7i		−	1.87085i	0.353520	−	0.935427i	$-0.384985\pi$
$654$	998951.	+	7.31720e6i	0.0913271	+	0.668960i
$655$	−2.09405e6			−0.190714
$656$	−5.21723e6	+	3.14675e6i	−0.473348	+	0.285498i
$657$	−4.87184e6			−0.440331
$658$	−65009.2	−	476185.i	−0.00585343	−	0.0428757i
$659$		−	6.70475e6i		−	0.601408i	−0.953718	−	0.300704i	$-0.902778\pi$
$659$		−	6.70475e6i		−	0.601408i	0.953718	−	0.300704i	$-0.0972216\pi$
$660$	595850.	+	2.14159e6i	0.0532448	+	0.191371i
$661$		−	5.17558e6i		−	0.460739i	−0.973103	−	0.230370i	$-0.926006\pi$
$661$		−	5.17558e6i		−	0.460739i	0.973103	−	0.230370i	$-0.0739935\pi$
$662$	−7.13456e6	+	974017.i	−0.632736	+	0.0863817i
$663$	−8.04739e6			−0.711002
$664$	5.02146e6	−	2.16487e6i	0.441987	−	0.190552i
$665$	571380.			0.0501038
$666$	1.13544e6	−	155011.i	0.0991922	−	0.0135418i
$667$		−	2.39607e6i		−	0.208538i
$668$	6.26278e6	−	1.74248e6i	0.543032	−	0.151087i
$669$			1.69000e7i			1.45989i
$670$	−114096.	−	835739.i	−0.00981936	−	0.0719257i
$671$	8.10668e6			0.695083
$672$	717702.	−	578494.i	0.0613085	−	0.0494169i
$673$	−2.31161e6			−0.196733			−0.0983664	−	0.995150i	$-0.531362\pi$
$673$	−2.31161e6			−0.196733			−0.0983664	+	0.995150i	$0.531362\pi$
$674$	1.23680e6	+	9.05945e6i	0.104870	+	0.768160i
$675$		−	2.01499e6i		−	0.170221i
$676$	−7.25920e6	+	2.01971e6i	−0.610973	+	0.169989i
$677$		−	1.01425e7i		−	0.850496i	−0.905077	−	0.425248i	$-0.860187\pi$
$677$		−	1.01425e7i		−	0.850496i	0.905077	−	0.425248i	$-0.139813\pi$
$678$	−6.71679e6	+	916983.i	−0.561161	+	0.0766103i
$679$	1.27574e6			0.106191
$680$	−5.24073e6	+	2.25941e6i	−0.434630	+	0.187380i
$681$	−4.21487e6			−0.348270
$682$	−8.44342e6	+	1.15270e6i	−0.695116	+	0.0948979i
$683$		−	5.34488e6i		−	0.438416i	−0.975678	−	0.219208i	$-0.929653\pi$
$683$		−	5.34488e6i		−	0.438416i	0.975678	−	0.219208i	$-0.0703473\pi$
$684$	1.21159e6	+	4.35468e6i	0.0990183	+	0.355890i
$685$			4.35137e6i			0.354323i
$686$	235801.	+	1.72721e6i	0.0191309	+	0.140131i
$687$	2.30883e7			1.86638
$688$	−5.63698e6	−	9.34599e6i	−0.454021	−	0.752756i
$689$	−3.30837e6			−0.265501
$690$	140069.	+	1.02599e6i	0.0112000	+	0.0820387i
$691$			5.80594e6i			0.462570i	0.972886	+	0.231285i	$0.0742930\pi$
$691$			5.80594e6i			0.462570i	−0.972886	+	0.231285i	$0.925707\pi$
$692$	−812195.	−	2.91917e6i	−0.0644755	−	0.231737i
$693$			83779.6i			0.00662682i
$694$	−1.96158e6	+	267797.i	−0.154599	+	0.0211060i
$695$	−7.76980e6			−0.610166
$696$	7.03083e6	+	1.63081e7i	0.550153	+	1.27609i
$697$	7.50341e6			0.585028
$698$	−1.33721e7	+	1.82557e6i	−1.03887	+	0.141827i
$699$		−	1.76520e7i		−	1.36647i
$700$	−177090.	+	49271.2i	−0.0136599	+	0.00380056i
$701$		−	6.84282e6i		−	0.525945i	−0.964803	−	0.262972i	$-0.915297\pi$
$701$		−	6.84282e6i		−	0.525945i	0.964803	−	0.262972i	$-0.0847028\pi$
$702$	909177.	+	6.65962e6i	0.0696315	+	0.510043i
$703$	−8.86881e6			−0.676826
$704$	−3.82355e6	−	3.61018e6i	−0.290760	−	0.274534i
$705$	−4.00142e6			−0.303209
$706$	2.94414e6	+	2.15655e7i	0.222304	+	1.62835i
$707$		−	1.18077e6i		−	0.0888418i
$708$	1.46451e7	−	4.07466e6i	1.09801	−	0.305498i
$709$		−	1.09625e7i		−	0.819019i	−0.912306	−	0.409509i	$-0.865700\pi$
$709$		−	1.09625e7i		−	0.819019i	0.912306	−	0.409509i	$-0.134300\pi$
$710$	−9.42826e6	+	1.28716e6i	−0.701917	+	0.0958264i
$711$	−3.21314e6			−0.238372
$712$	−8.16732e6	−	1.89442e7i	−0.603781	−	1.40048i
$713$	−3.96965e6			−0.292434
$714$	−1.12482e6	+	153561.i	−0.0825726	+	0.0112729i
$715$			1.47861e6i			0.108165i
$716$	−2.48831e6	−	8.94345e6i	−0.181394	−	0.651963i
$717$		−	1.68957e7i		−	1.22738i
$718$	−2.06479e6	−	1.51244e7i	−0.149474	−	1.09488i
$719$	4.16072e6			0.300156			0.150078	−	0.988674i	$-0.452048\pi$
$719$	4.16072e6			0.300156			0.150078	+	0.988674i	$0.452048\pi$
$720$	−751024.	−	1.24518e6i	−0.0539911	−	0.0895160i
$721$	1.07744e6			0.0771893
$722$	−2.83715e6	−	2.07818e7i	−0.202553	−	1.48368i
$723$			6.21633e6i			0.442271i
$724$	−548950.	−	1.97303e6i	−0.0389212	−	0.139890i
$725$		−	3.54128e6i		−	0.250216i
$726$	−1.31302e7	+	1.79255e6i	−0.924549	+	0.126220i
$727$	2.27412e7			1.59580			0.797899	−	0.602791i	$-0.205945\pi$
$727$	2.27412e7			1.59580			0.797899	+	0.602791i	$0.205945\pi$
$728$	563057.	−	242748.i	0.0393753	−	0.0169756i
$729$	−9.61000e6			−0.669737
$730$	−1.20180e7	+	1.64071e6i	−0.834691	+	0.113953i
$731$			1.34414e7i			0.930358i
$732$	−2.69649e7	+	7.50239e6i	−1.86004	+	0.517514i
$733$		−	2.60697e7i		−	1.79216i	−0.443898	−	0.896078i	$-0.646405\pi$
$733$		−	2.60697e7i		−	1.79216i	0.443898	−	0.896078i	$-0.353595\pi$
$734$	873041.	+	6.39492e6i	0.0598129	+	0.438122i
$735$	7.23868e6			0.494244
$736$	−1.53726e6	−	1.90718e6i	−0.104605	−	0.129777i
$737$	−957163.			−0.0649109
$738$	258608.	+	1.89427e6i	0.0174784	+	0.128027i
$739$		−	467568.i		−	0.0314944i	−0.999876	−	0.0157472i	$-0.994987\pi$
$739$		−	467568.i		−	0.0314944i	0.999876	−	0.0157472i	$-0.00501270\pi$
$740$	2.74873e6	−	764774.i	0.184524	−	0.0513397i
$741$			1.58687e7i			1.06168i
$742$	−462425.	+	63130.7i	−0.0308341	+	0.00420950i
$743$	1.98379e6			0.131833			0.0659165	−	0.997825i	$-0.479003\pi$
$743$	1.98379e6			0.131833			0.0659165	+	0.997825i	$0.479003\pi$
$744$	2.70182e7	−	1.16482e7i	1.78947	−	0.771485i
$745$	7.34140e6			0.484605
$746$	2.58921e6	−	353482.i	0.170341	−	0.0232552i
$747$		−	1.71588e6i		−	0.112509i
$748$	1.73590e6	+	6.23914e6i	0.113441	+	0.407728i
$749$			162260.i			0.0105684i
$750$	207015.	+	1.51636e6i	0.0134384	+	0.0984349i
$751$	1.55338e7			1.00503			0.502515	−	0.864568i	$-0.332408\pi$
$751$	1.55338e7			1.00503			0.502515	+	0.864568i	$0.332408\pi$
$752$	8.10558e6	−	4.88884e6i	0.522684	−	0.315254i
$753$	−3.60460e6			−0.231670
$754$	1.59785e6	+	1.17041e7i	0.102355	+	0.749737i
$755$			651463.i			0.0415932i
$756$	254159.	+	913492.i	0.0161734	+	0.0581300i
$757$		−	2.40224e6i		−	0.152362i	−0.997094	−	0.0761811i	$-0.975727\pi$
$757$		−	2.40224e6i		−	0.152362i	0.997094	−	0.0761811i	$-0.0242727\pi$
$758$	−2.44470e7	+	3.33752e6i	−1.54544	+	0.210985i
$759$	1.17505e6			0.0740376
$760$	4.45534e6	+	1.03342e7i	0.279800	+	0.649000i
$761$	−2.53929e7			−1.58946			−0.794732	−	0.606960i	$-0.792389\pi$
$761$	−2.53929e7			−1.58946			−0.794732	+	0.606960i	$0.792389\pi$
$762$	1.15025e7	−	1.57033e6i	0.717635	−	0.0979722i
$763$			692972.i			0.0430928i
$764$	1.20778e7	−	3.36038e6i	0.748609	−	0.208284i
$765$			1.79081e6i			0.110636i
$766$	−319569.	−	2.34081e6i	−0.0196785	−	0.144143i
$767$	1.01113e7			0.620609
$768$	1.60592e7	+	8.46987e6i	0.982472	+	0.518171i
$769$	−1.96036e6			−0.119542			−0.0597709	−	0.998212i	$-0.519037\pi$
$769$	−1.96036e6			−0.119542			−0.0597709	+	0.998212i	$0.519037\pi$
$770$	28214.9	+	206671.i	0.00171495	+	0.0125618i
$771$			3.15305e7i			1.91027i
$772$	1.97651e7	−	5.49921e6i	1.19359	−	0.332091i
$773$			3.14540e7i			1.89334i	0.322211	+	0.946668i	$0.395574\pi$
$773$			3.14540e7i			1.89334i	−0.322211	+	0.946668i	$0.604426\pi$
$774$	−3.39334e6	+	463262.i	−0.203599	+	0.0277955i
$775$	−5.86696e6			−0.350880
$776$	9.94757e6	+	2.30736e7i	0.593011	+	1.37550i
$777$	567550.			0.0337250
$778$	1.07835e7	−	1.47218e6i	0.638722	−	0.0871990i
$779$		−	1.47960e7i		−	0.873577i
$780$	−1.36839e6	−	4.91823e6i	−0.0805327	−	0.289449i
$781$			1.07981e7i			0.633460i
$782$	408065.	+	2.98902e6i	0.0238623	+	0.174788i
$783$	−1.82672e7			−1.06480
$784$	−1.46632e7	+	8.84404e6i	−0.851999	+	0.513879i
$785$	1.06862e7			0.618941
$786$	−1.10976e6	−	8.12884e6i	−0.0640725	−	0.469323i
$787$			2.21797e7i			1.27650i	0.769831	+	0.638248i	$0.220340\pi$
$787$			2.21797e7i			1.27650i	−0.769831	+	0.638248i	$0.779660\pi$
$788$	−2.67728e6	−	9.62264e6i	−0.153596	−	0.552050i
$789$		−	3.02838e7i		−	1.73188i
$790$	−7.92629e6	+	1.08210e6i	−0.451858	+	0.0616881i
$791$	−636111.			−0.0361486
$792$	−1.51528e6	+	653272.i	−0.0858378	+	0.0370068i
$793$	−1.86172e7			−1.05131
$794$	1.65588e7	−	2.26062e6i	0.932131	−	0.127255i
$795$			3.88580e6i			0.218053i
$796$	−5.28633e6	+	1.47080e6i	−0.295714	+	0.0822757i
$797$			2.05722e7i			1.14719i	0.819139	+	0.573595i	$0.194452\pi$
$797$			2.05722e7i			1.14719i	−0.819139	+	0.573595i	$0.805548\pi$
$798$	302808.	+	2.21803e6i	0.0168329	+	0.123299i
$799$	−1.16574e7			−0.646004
$800$	−2.27200e6	−	2.81873e6i	−0.125511	−	0.155714i
$801$	−6.47344e6			−0.356495
$802$	−1.20214e6	−	8.80553e6i	−0.0659962	−	0.483414i
$803$			1.37641e7i			0.753285i
$804$	3.18378e6	−	885814.i	0.173701	−	0.0483284i
$805$			97165.6i			0.00528473i
$806$	1.93906e7	−	2.64722e6i	1.05136	−	0.143533i
$807$	2.56332e7			1.38554
$808$	2.13560e7	−	9.20708e6i	1.15078	−	0.496128i
$809$	−3.45753e7			−1.85735			−0.928676	−	0.370892i	$-0.879052\pi$
$809$	−3.45753e7			−1.85735			−0.928676	+	0.370892i	$0.879052\pi$
$810$	9.75603e6	−	1.33190e6i	0.522469	−	0.0713280i
$811$		−	2.43908e7i		−	1.30219i	−0.758997	−	0.651094i	$-0.774310\pi$
$811$		−	2.43908e7i		−	1.30219i	0.758997	−	0.651094i	$-0.225690\pi$
$812$	446676.	+	1.60544e6i	0.0237740	+	0.0854482i
$813$			1.80798e7i			0.959328i
$814$	−437944.	−	3.20788e6i	−0.0231663	−	0.169691i
$815$	1.36823e7			0.721548
$816$	−1.15481e7	−	1.91465e7i	−0.607136	−	1.00662i
$817$	2.65051e7			1.38923
$818$	−3.96589e6	−	2.90497e7i	−0.207232	−	1.51795i
$819$		−	192402.i		−	0.0100231i
$820$	1.27589e6	+	4.58577e6i	0.0662641	+	0.238165i
$821$		−	5.77124e6i		−	0.298821i	−0.988775	−	0.149410i	$-0.952262\pi$
$821$		−	5.77124e6i		−	0.298821i	0.988775	−	0.149410i	$-0.0477376\pi$
$822$	−1.68915e7	+	2.30604e6i	−0.871944	+	0.119039i
$823$	−9.22421e6			−0.474711			−0.237356	−	0.971423i	$-0.576281\pi$
$823$	−9.22421e6			−0.474711			−0.237356	+	0.971423i	$0.576281\pi$
$824$	8.40139e6	+	1.94872e7i	0.431055	+	0.999840i
$825$	1.73667e6			0.0888347
$826$	1.41329e6	−	192944.i	0.0720747	−	0.00983970i
$827$		−	1.36273e7i		−	0.692859i	−0.938076	−	0.346430i	$-0.887394\pi$
$827$		−	1.36273e7i		−	0.692859i	0.938076	−	0.346430i	$-0.112606\pi$
$828$	−740531.	+	206036.i	−0.0375377	+	0.0104440i
$829$			5.64154e6i			0.285109i	0.989787	+	0.142555i	$0.0455317\pi$
$829$			5.64154e6i			0.285109i	−0.989787	+	0.142555i	$0.954468\pi$
$830$	−577867.	−	4.23281e6i	−0.0291161	−	0.213272i
$831$	394648.			0.0198247
$832$	8.78088e6	+	8.29087e6i	0.439774	+	0.415233i
$833$	2.10886e7			1.05302
$834$	−4.11767e6	−	3.01614e7i	−0.204992	−	1.50154i
$835$		−	5.07864e6i		−	0.252076i
$836$	1.23030e7	−	3.42304e6i	0.608829	−	0.169393i
$837$			3.02639e7i			1.49318i
$838$	2.69716e7	−	3.68219e6i	1.32677	−	0.181132i
$839$	1.01209e7			0.496379			0.248189	−	0.968712i	$-0.420164\pi$
$839$	1.01209e7			0.496379			0.248189	+	0.968712i	$0.420164\pi$
$840$	−285115.	−	661329.i	−0.0139419	−	0.0323385i
$841$	−1.15929e7			−0.565201
$842$	−2.61737e7	+	3.57327e6i	−1.27229	+	0.173694i
$843$			3.13557e6i			0.151966i
$844$	5.82430e6	+	2.09336e7i	0.281441	+	1.01155i
$845$			5.88667e6i			0.283614i
$846$	−401778.	−	2.94298e6i	−0.0193001	−	0.141371i
$847$	−1.24349e6			−0.0595572
$848$	−4.74757e6	−	7.87136e6i	−0.226716	−	0.375890i
$849$	1.74776e7			0.832170
$850$	603101.	+	4.41764e6i	0.0286314	+	0.209722i
$851$		−	1.50818e6i		−	0.0713886i
$852$	−9.99317e6	−	3.59173e7i	−0.471633	−	1.69513i
$853$		−	8.59170e6i		−	0.404302i	−0.979354	−	0.202151i	$-0.935207\pi$
$853$		−	8.59170e6i		−	0.404302i	0.979354	−	0.202151i	$-0.0647932\pi$
$854$	−2.60220e6	+	355255.i	−0.122095	+	0.0166685i
$855$	3.53131e6			0.165204
$856$	−2.93471e6	+	1.26523e6i	−0.136893	+	0.0590179i
$857$	−1.17834e7			−0.548049			−0.274024	−	0.961723i	$-0.588355\pi$
$857$	−1.17834e7			−0.548049			−0.274024	+	0.961723i	$0.588355\pi$
$858$	−5.73977e6	+	783599.i	−0.266181	+	0.0363392i
$859$		−	2.83473e6i		−	0.131078i	−0.997850	−	0.0655389i	$-0.979123\pi$
$859$		−	2.83473e6i		−	0.131078i	0.997850	−	0.0655389i	$-0.0208767\pi$
$860$	−8.21481e6	+	2.28559e6i	−0.378749	+	0.105378i
$861$			946856.i			0.0435287i
$862$	−2.35489e6	−	1.72493e7i	−0.107945	−	0.790685i
$863$	2.08041e7			0.950870			0.475435	−	0.879751i	$-0.342291\pi$
$863$	2.08041e7			0.950870			0.475435	+	0.879751i	$0.342291\pi$
$864$	−1.45400e7	+	1.17198e7i	−0.662645	+	0.534116i
$865$	−2.36723e6			−0.107572
$866$	−1.99478e6	−	1.46115e7i	−0.0903858	−	0.662065i
$867$			2.95193e6i			0.133370i
$868$	2.65978e6	−	740024.i	0.119825	−	0.0333385i
$869$			9.07789e6i			0.407789i
$870$	1.37468e7	−	1.87673e6i	0.615750	−	0.0840628i
$871$	2.19815e6			0.0981776
$872$	−1.25334e7	+	5.40345e6i	−0.558184	+	0.240647i
$873$	7.88447e6			0.350136
$874$	5.89408e6	−	804665.i	0.260998	−	0.0356317i
$875$			143606.i			0.00634094i
$876$	−1.27381e7	−	4.57830e7i	−0.560847	−	2.01579i
$877$		−	2.82780e7i		−	1.24151i	−0.784006	−	0.620754i	$-0.786827\pi$
$877$		−	2.82780e7i		−	1.24151i	0.784006	−	0.620754i	$-0.213173\pi$
$878$	5.48666e6	+	4.01891e7i	0.240199	+	1.75943i
$879$	−3.90549e7			−1.70492
$880$	−3.51793e6	+	2.12182e6i	−0.153137	+	0.0923639i
$881$	−1.63898e6			−0.0711432			−0.0355716	−	0.999367i	$-0.511325\pi$
$881$	−1.63898e6			−0.0711432			−0.0355716	+	0.999367i	$0.511325\pi$
$882$	726827.	+	5.32392e6i	0.0314601	+	0.230441i
$883$		−	2.72729e7i		−	1.17714i	−0.808445	−	0.588572i	$-0.799690\pi$
$883$		−	2.72729e7i		−	1.17714i	0.808445	−	0.588572i	$-0.200310\pi$
$884$	−3.98655e6	−	1.43284e7i	−0.171580	−	0.616689i
$885$		−	1.18760e7i		−	0.509699i
$886$	−2.84765e7	+	3.88763e6i	−1.21871	+	0.166380i
$887$	−3.68277e7			−1.57168			−0.785842	−	0.618427i	$-0.787770\pi$
$887$	−3.68277e7			−1.57168			−0.785842	+	0.618427i	$0.787770\pi$
$888$	4.42548e6	+	1.02650e7i	0.188334	+	0.436843i
$889$	1.08934e6			0.0462283
$890$	−1.59689e7	+	2.18009e6i	−0.675772	+	0.0922571i
$891$		−	1.11735e7i		−	0.471513i
$892$	−3.00904e7	+	8.37199e6i	−1.26624	+	0.352303i
$893$			2.29873e7i			0.964628i
$894$	3.89063e6	+	2.84984e7i	0.162808	+	1.19255i
$895$	−7.25247e6			−0.302641
$896$	1.38555e6	+	991291.i	0.0576569	+	0.0412507i
$897$	−2.69854e6			−0.111982
$898$	2.43516e6	+	1.78373e7i	0.100771	+	0.738137i
$899$			5.31879e7i			2.19490i
$900$	−1.09447e6	+	304512.i	−0.0450399	+	0.0125314i
$901$			1.13206e7i			0.464575i
$902$	5.35178e6	−	730631.i	0.219019	−	0.0299007i
$903$	−1.69617e6			−0.0692228
$904$	−4.96008e6	−	1.15050e7i	−0.201868	−	0.468236i
$905$	−1.59998e6			−0.0649370
$906$	−2.52890e6	+	345248.i	−0.102356	+	0.0139737i
$907$		−	1.18940e7i		−	0.480077i	−0.970763	−	0.240038i	$-0.922840\pi$
$907$		−	1.18940e7i		−	0.480077i	0.970763	−	0.240038i	$-0.0771600\pi$
$908$	−2.08798e6	−	7.50458e6i	−0.0840450	−	0.302073i
$909$		−	7.29756e6i		−	0.292933i
$910$	−64796.3	−	474625.i	−0.00259386	−	0.0189997i
$911$	−3.24936e7			−1.29719			−0.648593	−	0.761135i	$-0.724642\pi$
$911$	−3.24936e7			−1.29719			−0.648593	+	0.761135i	$0.724642\pi$
$912$	−3.77552e7	+	2.27718e7i	−1.50310	+	0.906590i
$913$	−4.84779e6			−0.192472
$914$	−1.18185e6	−	8.65692e6i	−0.0467948	−	0.342766i
$915$			2.18665e7i			0.863431i
$916$	1.14376e7	+	4.11088e7i	0.450398	+	1.61881i
$917$		−	769839.i		−	0.0302327i
$918$	2.27878e7	−	3.11101e6i	0.892474	−	0.121841i
$919$	6.30861e6			0.246402			0.123201	−	0.992382i	$-0.460684\pi$
$919$	6.30861e6			0.246402			0.123201	+	0.992382i	$0.460684\pi$
$920$	−1.75738e6	+	757650.i	−0.0684536	+	0.0295120i
$921$	4.19331e7			1.62895
$922$	4.98012e6	−	679891.i	0.192936	−	0.0263398i
$923$		−	2.47981e7i		−	0.958108i
$924$	−787318.	+	219054.i	−0.0303368	+	0.00844055i
$925$		−	2.22902e6i		−	0.0856563i
$926$	2.70235e6	+	1.97944e7i	0.103565	+	0.758603i
$927$	6.65896e6			0.254511
$928$	−2.55537e7	+	2.05972e7i	−0.974054	+	0.785123i
$929$	−9.87673e6			−0.375469			−0.187734	−	0.982220i	$-0.560114\pi$
$929$	−9.87673e6			−0.375469			−0.187734	+	0.982220i	$0.560114\pi$
$930$	−3.10924e6	−	2.27748e7i	−0.117882	−	0.863472i
$931$		−	4.15847e7i		−	1.57239i
$932$	3.14293e7	−	8.74450e6i	1.18521	−	0.329758i
$933$		−	1.81664e7i		−	0.683227i
$934$	3.99815e7	−	5.45831e6i	1.49966	−	0.204734i
$935$	5.05948e6			0.189268
$936$	3.47987e6	−	1.50026e6i	0.129830	−	0.0559727i
$937$	1.06437e7			0.396046			0.198023	−	0.980197i	$-0.436548\pi$
$937$	1.06437e7			0.396046			0.198023	+	0.980197i	$0.436548\pi$
$938$	307245.	−	41945.3i	0.0114019	−	0.00155660i
$939$			1.59184e7i			0.589165i
$940$	−1.98224e6	−	7.12453e6i	−0.0731706	−	0.262988i
$941$		−	4.65943e7i		−	1.71537i	−0.514174	−	0.857686i	$-0.671901\pi$
$941$		−	4.65943e7i		−	1.71537i	0.514174	−	0.857686i	$-0.328099\pi$
$942$	5.66324e6	+	4.14826e7i	0.207940	+	1.52314i
$943$	2.51613e6			0.0921410
$944$	1.45099e7	+	2.40570e7i	0.529948	+	0.878641i
$945$	740774.			0.0269840
$946$	1.30883e6	+	9.58701e6i	0.0475505	+	0.348302i
$947$			2.99997e7i			1.08703i	0.839399	+	0.543516i	$0.182907\pi$
$947$			2.99997e7i			1.08703i	−0.839399	+	0.543516i	$0.817093\pi$
$948$	−8.40120e6	−	3.01954e7i	−0.303613	−	1.09124i
$949$		−	3.16097e7i		−	1.13934i
$950$	8.71118e6	−	1.18926e6i	0.313161	−	0.0427531i
$951$	−1.31883e7			−0.472865
$952$	−830631.	−	1.92666e6i	−0.0297041	−	0.0688991i
$953$	−1.52026e7			−0.542233			−0.271116	−	0.962547i	$-0.587393\pi$
$953$	−1.52026e7			−0.542233			−0.271116	+	0.962547i	$0.587393\pi$
$954$	−2.85794e6	+	390168.i	−0.101667	+	0.0138797i
$955$		−	9.79421e6i		−	0.347505i
$956$	3.00828e7	−	8.36987e6i	1.06457	−	0.296192i
$957$		−	1.57441e7i		−	0.555697i
$958$	3.84284e6	+	2.81484e7i	0.135282	+	0.990922i
$959$	−1.59970e6			−0.0561685
$960$	9.73791e6	−	1.03134e7i	0.341026	−	0.361181i
$961$	5.94891e7			2.07792
$962$	1.00575e6	+	7.36700e6i	0.0350390	+	0.256657i
$963$			1.00282e6i			0.0348464i
$964$	−1.10682e7	+	3.07947e6i	−0.383604	+	0.106729i
$965$		−	1.60280e7i		−	0.554067i
$966$	−377186.	+	51493.7i	−0.0130051	+	0.00177546i
$967$	−4.59930e7			−1.58171			−0.790853	−	0.612006i	$-0.790363\pi$
$967$	−4.59930e7			−1.58171			−0.790853	+	0.612006i	$0.790363\pi$
$968$	−9.69613e6	−	2.24903e7i	−0.332591	−	0.771449i
$969$	5.42993e7			1.85774
$970$	1.94497e7	−	2.65529e6i	0.663718	−	0.0906114i
$971$		−	3.27040e7i		−	1.11315i	−0.830799	−	0.556573i	$-0.812116\pi$
$971$		−	3.27040e7i		−	1.11315i	0.830799	−	0.556573i	$-0.187884\pi$
$972$	3.62076e6	+	1.30136e7i	0.122923	+	0.441808i
$973$		−	2.85643e6i		−	0.0967255i
$974$	−6.92000e6	−	5.06882e7i	−0.233727	−	1.71202i
$975$	−3.98832e6			−0.134362
$976$	−2.67160e7	−	4.42945e7i	−0.897733	−	1.48842i
$977$	1.60025e7			0.536353			0.268177	−	0.963370i	$-0.413579\pi$
$977$	1.60025e7			0.536353			0.268177	+	0.963370i	$0.413579\pi$
$978$	7.25105e6	+	5.31131e7i	0.242412	+	1.77564i
$979$			1.82890e7i			0.609865i
$980$	3.58593e6	+	1.28885e7i	0.119271	+	0.428683i
$981$			4.28279e6i			0.142087i
$982$	−1.07570e7	+	1.46855e6i	−0.355968	+	0.0485971i
$983$	5.81035e7			1.91787			0.958933	−	0.283634i	$-0.0915400\pi$
$983$	5.81035e7			1.91787			0.958933	+	0.283634i	$0.0915400\pi$
$984$	−1.71253e7	+	7.38312e6i	−0.563832	+	0.243082i
$985$	−7.80324e6			−0.256262
$986$	4.00489e7	−	5.46751e6i	1.31189	−	0.179101i
$987$		−	1.47105e6i		−	0.0480657i
$988$	−2.82542e7	+	7.86110e6i	−0.920854	+	0.256207i
$989$			4.50731e6i			0.146530i
$990$	174377.	+	1.27729e6i	0.00565459	+	0.0414192i
$991$	−1.47014e7			−0.475527			−0.237764	−	0.971323i	$-0.576414\pi$
$991$	−1.47014e7			−0.475527			−0.237764	+	0.971323i	$0.576414\pi$
$992$	3.41241e7	+	4.23356e7i	1.10099	+	1.36593i
$993$	−2.20404e7			−0.709327
$994$	−473200.	−	3.46613e6i	−0.0151907	−	0.111270i
$995$			4.28681e6i			0.137270i
$996$	1.61250e7	−	4.48642e6i	0.515053	−	0.143302i
$997$			3.26322e7i			1.03970i	0.854257	+	0.519850i	$0.174012\pi$
$997$			3.26322e7i			1.03970i	−0.854257	+	0.519850i	$0.825988\pi$
$998$	6.83815e6	−	933550.i	0.217326	−	0.0296696i
$999$	−1.14981e7			−0.364512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.d.a.21.12	yes	20
3.2	odd	2		360.6.k.b.181.9		20
4.3	odd	2		160.6.d.a.81.5		20
5.2	odd	4		200.6.f.b.149.2		20
5.3	odd	4		200.6.f.c.149.19		20
5.4	even	2		200.6.d.b.101.9		20
8.3	odd	2		160.6.d.a.81.16		20
8.5	even	2	inner	40.6.d.a.21.11	✓	20
20.3	even	4		800.6.f.b.49.15		20
20.7	even	4		800.6.f.c.49.6		20
20.19	odd	2		800.6.d.c.401.16		20
24.5	odd	2		360.6.k.b.181.10		20
40.3	even	4		800.6.f.c.49.5		20
40.13	odd	4		200.6.f.b.149.1		20
40.19	odd	2		800.6.d.c.401.5		20
40.27	even	4		800.6.f.b.49.16		20
40.29	even	2		200.6.d.b.101.10		20
40.37	odd	4		200.6.f.c.149.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.11	✓	20	8.5	even	2	inner
40.6.d.a.21.12	yes	20	1.1	even	1	trivial
160.6.d.a.81.5		20	4.3	odd	2
160.6.d.a.81.16		20	8.3	odd	2
200.6.d.b.101.9		20	5.4	even	2
200.6.d.b.101.10		20	40.29	even	2
200.6.f.b.149.1		20	40.13	odd	4
200.6.f.b.149.2		20	5.2	odd	4
200.6.f.c.149.19		20	5.3	odd	4
200.6.f.c.149.20		20	40.37	odd	4
360.6.k.b.181.9		20	3.2	odd	2
360.6.k.b.181.10		20	24.5	odd	2
800.6.d.c.401.5		20	40.19	odd	2
800.6.d.c.401.16		20	20.19	odd	2
800.6.f.b.49.15		20	20.3	even	4
800.6.f.b.49.16		20	40.27	even	4
800.6.f.c.49.5		20	40.3	even	4
800.6.f.c.49.6		20	20.7	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.765181 + 5.60486i) q^{2} +17.3148i q^{3} +(-30.8290 + 8.57748i) q^{4} +25.0000i q^{5} +(-97.0471 + 13.2490i) q^{6} -9.19080 q^{7} +(-71.6654 - 166.229i) q^{8} -56.8021 q^{9} +(-140.122 + 19.1295i) q^{10} +160.480i q^{11} +(-148.517 - 533.798i) q^{12} -368.546i q^{13} +(-7.03263 - 51.5132i) q^{14} -432.870 q^{15} +(876.854 - 528.870i) q^{16} -1261.09 q^{17} +(-43.4639 - 318.368i) q^{18} +2486.75i q^{19} +(-214.437 - 770.725i) q^{20} -159.137i q^{21} +(-899.467 + 122.796i) q^{22} -422.882 q^{23} +(2878.22 - 1240.87i) q^{24} -625.000 q^{25} +(2065.65 - 282.005i) q^{26} +3223.98i q^{27} +(283.343 - 78.8339i) q^{28} +5666.05i q^{29} +(-331.224 - 2426.18i) q^{30} +9387.13 q^{31} +(3635.20 + 4509.96i) q^{32} -2778.67 q^{33} +(-964.961 - 7068.23i) q^{34} -229.770i q^{35} +(1751.15 - 487.219i) q^{36} +3566.43i q^{37} +(-13937.9 + 1902.81i) q^{38} +6381.30 q^{39} +(4155.72 - 1791.63i) q^{40} -5949.95 q^{41} +(891.941 - 121.769i) q^{42} -10658.5i q^{43} +(-1376.51 - 4947.43i) q^{44} -1420.05i q^{45} +(-323.581 - 2370.20i) q^{46} +9243.94 q^{47} +(9157.27 + 15182.5i) q^{48} -16722.5 q^{49} +(-478.238 - 3503.04i) q^{50} -21835.5i q^{51} +(3161.20 + 11361.9i) q^{52} -8976.82i q^{53} +(-18070.0 + 2466.93i) q^{54} -4011.99 q^{55} +(658.662 + 1527.78i) q^{56} -43057.5 q^{57} +(-31757.4 + 4335.55i) q^{58} +27435.6i q^{59} +(13344.9 - 3712.93i) q^{60} -50515.3i q^{61} +(7182.86 + 52613.6i) q^{62} +522.057 q^{63} +(-22496.2 + 23825.7i) q^{64} +9213.66 q^{65} +(-2126.19 - 15574.1i) q^{66} +5964.39i q^{67} +(38878.1 - 10817.0i) q^{68} -7322.11i q^{69} +(1287.83 - 175.816i) q^{70} +67286.3 q^{71} +(4070.75 + 9442.16i) q^{72} +85768.5 q^{73} +(-19989.3 + 2728.96i) q^{74} -10821.7i q^{75} +(-21330.0 - 76663.9i) q^{76} -1474.94i q^{77} +(4882.86 + 35766.3i) q^{78} +56567.2 q^{79} +(13221.7 + 21921.3i) q^{80} -69625.4 q^{81} +(-4552.79 - 33348.6i) q^{82} +30208.1i q^{83} +(1364.99 + 4906.03i) q^{84} -31527.2i q^{85} +(59739.7 - 8155.72i) q^{86} -98106.4 q^{87} +(26676.4 - 11500.8i) q^{88} +113965. q^{89} +(7959.21 - 1086.60i) q^{90} +3387.24i q^{91} +(13037.0 - 3627.26i) q^{92} +162536. i q^{93} +(7073.29 + 51811.0i) q^{94} -62168.7 q^{95} +(-78089.1 + 62942.7i) q^{96} -138806. q^{97} +(-12795.8 - 93727.5i) q^{98} -9115.59i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24}+ \cdots + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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