LMFDB - Embedded newform 40.5.e.c.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,5,Mod(19,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("40.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	40.e (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:	$4.13479852335$
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} + 10 x^{18} - 20 x^{16} + 2640 x^{14} + 22400 x^{12} - 652288 x^{10} + 5734400 x^{8} + \cdots + 1099511627776 $ x^20 + 10x^18 - 20x^16 + 2640x^14 + 22400x^12 - 652288x^10 + 5734400x^8 + 173015040x^6 - 335544320x^4 + 42949672960*x^2 + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{33}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.9
Root			$-0.495691 - 3.96917i$ of defining polynomial
Character	$\chi$	$=$	40.19
Dual form			40.5.e.c.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.495691 - 3.96917i) q^{2} +10.2033i q^{3} +(-15.5086 + 3.93496i) q^{4} +(17.9141 - 17.4381i) q^{5} +(40.4986 - 5.05768i) q^{6} +84.8600 q^{7} +(23.3060 + 59.6056i) q^{8} -23.1073 q^{9} +(-78.0944 - 62.4601i) q^{10} +71.3055 q^{11} +(-40.1496 - 158.239i) q^{12} -109.279 q^{13} +(-42.0643 - 336.824i) q^{14} +(177.926 + 182.783i) q^{15} +(225.032 - 122.051i) q^{16} +151.344i q^{17} +(11.4541 + 91.7167i) q^{18} -368.470 q^{19} +(-209.204 + 340.931i) q^{20} +865.852i q^{21} +(-35.3455 - 283.023i) q^{22} +358.031 q^{23} +(-608.174 + 237.798i) q^{24} +(16.8280 - 624.773i) q^{25} +(54.1687 + 433.748i) q^{26} +590.697i q^{27} +(-1316.06 + 333.921i) q^{28} +387.610i q^{29} +(637.299 - 796.821i) q^{30} -1687.73i q^{31} +(-595.988 - 832.691i) q^{32} +727.551i q^{33} +(600.709 - 75.0197i) q^{34} +(1520.19 - 1479.79i) q^{35} +(358.361 - 90.9262i) q^{36} -1158.77 q^{37} +(182.647 + 1462.52i) q^{38} -1115.01i q^{39} +(1456.91 + 661.369i) q^{40} -2545.99 q^{41} +(3436.71 - 429.195i) q^{42} +1354.04i q^{43} +(-1105.85 + 280.584i) q^{44} +(-413.946 + 402.946i) q^{45} +(-177.473 - 1421.08i) q^{46} +901.424 q^{47} +(1245.33 + 2296.07i) q^{48} +4800.23 q^{49} +(-2488.17 + 242.901i) q^{50} -1544.21 q^{51} +(1694.77 - 430.009i) q^{52} -3409.47 q^{53} +(2344.57 - 292.803i) q^{54} +(1277.37 - 1243.43i) q^{55} +(1977.75 + 5058.14i) q^{56} -3759.61i q^{57} +(1538.49 - 192.135i) q^{58} -1454.37 q^{59} +(-3478.62 - 2134.57i) q^{60} -5324.84i q^{61} +(-6698.88 + 836.592i) q^{62} -1960.88 q^{63} +(-3009.66 + 2778.33i) q^{64} +(-1957.64 + 1905.62i) q^{65} +(2887.77 - 360.640i) q^{66} -657.048i q^{67} +(-595.532 - 2347.13i) q^{68} +3653.09i q^{69} +(-6627.10 - 5300.36i) q^{70} +6741.79i q^{71} +(-538.538 - 1377.32i) q^{72} +4130.26i q^{73} +(574.391 + 4599.34i) q^{74} +(6374.75 + 171.701i) q^{75} +(5714.45 - 1449.91i) q^{76} +6050.98 q^{77} +(-4425.66 + 552.700i) q^{78} +2307.14i q^{79} +(1902.90 - 6110.56i) q^{80} -7898.74 q^{81} +(1262.03 + 10105.5i) q^{82} -2146.14i q^{83} +(-3407.09 - 13428.1i) q^{84} +(2639.14 + 2711.18i) q^{85} +(5374.41 - 671.184i) q^{86} -3954.90 q^{87} +(1661.84 + 4250.21i) q^{88} +5117.03 q^{89} +(1804.55 + 1443.28i) q^{90} -9273.44 q^{91} +(-5552.55 + 1408.84i) q^{92} +17220.4 q^{93} +(-446.827 - 3577.90i) q^{94} +(-6600.80 + 6425.40i) q^{95} +(8496.19 - 6081.05i) q^{96} -9169.66i q^{97} +(-2379.43 - 19052.9i) q^{98} -1647.68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 12 q^{6} - 652 q^{9} - 240 q^{10} - 168 q^{11} + 660 q^{14} + 280 q^{16} + 728 q^{19} + 900 q^{20} - 1232 q^{24} - 1420 q^{25} + 4680 q^{26} + 1540 q^{30} - 2312 q^{34} + 4440 q^{35} - 7868 q^{36}+ \cdots - 62504 q^{99}+O(q^{100}) $ 20 * q - 20 * q^4 + 12 * q^6 - 652 * q^9 - 240 * q^10 - 168 * q^11 + 660 * q^14 + 280 * q^16 + 728 * q^19 + 900 * q^20 - 1232 * q^24 - 1420 * q^25 + 4680 * q^26 + 1540 * q^30 - 2312 * q^34 + 4440 * q^35 - 7868 * q^36 - 4640 * q^40 - 4728 * q^41 + 1368 * q^44 - 6260 * q^46 + 540 * q^49 - 2280 * q^50 + 4352 * q^51 + 10688 * q^54 + 12960 * q^56 + 8280 * q^59 - 3480 * q^60 - 19040 * q^64 + 9480 * q^65 + 2632 * q^66 - 11020 * q^70 - 12000 * q^74 - 16000 * q^75 + 22472 * q^76 + 22440 * q^80 - 10956 * q^81 + 29000 * q^84 + 7740 * q^86 + 22248 * q^89 + 28520 * q^90 - 39760 * q^91 + 8540 * q^94 - 1328 * q^96 - 62504 * q^99

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 $

$2$	−0.495691	−	3.96917i	−0.123923	−	0.992292i
$2$	−0.495691	−	3.96917i	−0.123923	−	0.992292i
$3$			10.2033i			1.13370i	0.823821	+	0.566850i	$0.191838\pi$
$3$			10.2033i			1.13370i	−0.823821	+	0.566850i	$0.808162\pi$
$4$	−15.5086	+	3.93496i	−0.969286	+	0.245935i
$5$	17.9141	−	17.4381i	0.716563	−	0.697522i
$5$	17.9141	−	17.4381i	0.716563	−	0.697522i
$6$	40.4986	−	5.05768i	1.12496	−	0.140491i
$7$	84.8600			1.73184			0.865919	−	0.500185i	$-0.166735\pi$
$7$	84.8600			1.73184			0.865919	+	0.500185i	$0.166735\pi$
$8$	23.3060	+	59.6056i	0.364156	+	0.931338i
$9$	−23.1073			−0.285275
$10$	−78.0944	−	62.4601i	−0.780944	−	0.624601i
$11$	71.3055			0.589301			0.294651	−	0.955605i	$-0.404797\pi$
$11$	71.3055			0.589301			0.294651	+	0.955605i	$0.404797\pi$
$12$	−40.1496	−	158.239i	−0.278816	−	1.09888i
$13$	−109.279			−0.646623			−0.323311	−	0.946293i	$-0.604796\pi$
$13$	−109.279			−0.646623			−0.323311	+	0.946293i	$0.604796\pi$
$14$	−42.0643	−	336.824i	−0.214614	−	1.71849i
$15$	177.926	+	182.783i	0.790781	+	0.812367i
$16$	225.032	−	122.051i	0.879032	−	0.476763i
$17$			151.344i			0.523681i	0.965111	+	0.261840i	$0.0843294\pi$
$17$			151.344i			0.523681i	−0.965111	+	0.261840i	$0.915671\pi$
$18$	11.4541	+	91.7167i	0.0353521	+	0.283076i
$19$	−368.470			−1.02069			−0.510346	−	0.859969i	$-0.670483\pi$
$19$	−368.470			−1.02069			−0.510346	+	0.859969i	$0.670483\pi$
$20$	−209.204	+	340.931i	−0.523009	+	0.852327i
$21$			865.852i			1.96338i
$22$	−35.3455	−	283.023i	−0.0730278	−	0.584759i
$23$	358.031			0.676807			0.338403	−	0.941001i	$-0.390113\pi$
$23$	358.031			0.676807			0.338403	+	0.941001i	$0.390113\pi$
$24$	−608.174	+	237.798i	−1.05586	+	0.412843i
$25$	16.8280	−	624.773i	0.0269248	−	0.999637i
$26$	54.1687	+	433.748i	0.0801312	+	0.641639i
$27$			590.697i			0.810283i
$28$	−1316.06	+	333.921i	−1.67865	+	0.425919i
$29$			387.610i			0.460892i	0.973085	+	0.230446i	$0.0740185\pi$
$29$			387.610i			0.460892i	−0.973085	+	0.230446i	$0.925982\pi$
$30$	637.299	−	796.821i	0.708110	−	0.885356i
$31$		−	1687.73i		−	1.75622i	−0.478457	−	0.878111i	$-0.658804\pi$
$31$		−	1687.73i		−	1.75622i	0.478457	−	0.878111i	$-0.341196\pi$
$32$	−595.988	−	832.691i	−0.582020	−	0.813175i
$33$			727.551i			0.668091i
$34$	600.709	−	75.0197i	0.519644	−	0.0648960i
$35$	1520.19	−	1479.79i	1.24097	−	1.20800i
$36$	358.361	−	90.9262i	0.276513	−	0.0701591i
$37$	−1158.77			−0.846434			−0.423217	−	0.906028i	$-0.639099\pi$
$37$	−1158.77			−0.846434			−0.423217	+	0.906028i	$0.639099\pi$
$38$	182.647	+	1462.52i	0.126487	+	1.01283i
$39$		−	1115.01i		−	0.733076i
$40$	1456.91	+	661.369i	0.910570	+	0.413355i
$41$	−2545.99			−1.51457			−0.757285	−	0.653084i	$-0.773475\pi$
$41$	−2545.99			−1.51457			−0.757285	+	0.653084i	$0.773475\pi$
$42$	3436.71	−	429.195i	1.94825	−	0.243308i
$43$			1354.04i			0.732308i	0.930554	+	0.366154i	$0.119326\pi$
$43$			1354.04i			0.732308i	−0.930554	+	0.366154i	$0.880674\pi$
$44$	−1105.85	+	280.584i	−0.571202	+	0.144930i
$45$	−413.946	+	402.946i	−0.204418	+	0.198986i
$46$	−177.473	−	1421.08i	−0.0838717	−	0.671590i
$47$	901.424			0.408069			0.204034	−	0.978964i	$-0.434595\pi$
$47$	901.424			0.408069			0.204034	+	0.978964i	$0.434595\pi$
$48$	1245.33	+	2296.07i	0.540506	+	0.996558i
$49$	4800.23			1.99926
$50$	−2488.17	+	242.901i	−0.995269	+	0.0971605i
$51$	−1544.21			−0.593697
$52$	1694.77	−	430.009i	0.626763	−	0.159027i
$53$	−3409.47			−1.21377			−0.606883	−	0.794791i	$-0.707580\pi$
$53$	−3409.47			−1.21377			−0.606883	+	0.794791i	$0.707580\pi$
$54$	2344.57	−	292.803i	0.804038	−	0.100413i
$55$	1277.37	−	1243.43i	0.422271	−	0.411051i
$56$	1977.75	+	5058.14i	0.630659	+	1.61293i
$57$		−	3759.61i		−	1.15716i
$58$	1538.49	−	192.135i	0.457339	−	0.0571150i
$59$	−1454.37			−0.417803			−0.208902	−	0.977937i	$-0.566989\pi$
$59$	−1454.37			−0.417803			−0.208902	+	0.977937i	$0.566989\pi$
$60$	−3478.62	−	2134.57i	−0.966283	−	0.592936i
$61$		−	5324.84i		−	1.43102i	−0.698601	−	0.715512i	$-0.746194\pi$
$61$		−	5324.84i		−	1.43102i	0.698601	−	0.715512i	$-0.253806\pi$
$62$	−6698.88	+	836.592i	−1.74268	+	0.217636i
$63$	−1960.88			−0.494050
$64$	−3009.66	+	2778.33i	−0.734781	+	0.678304i
$65$	−1957.64	+	1905.62i	−0.463346	+	0.451034i
$66$	2887.77	−	360.640i	0.662941	−	0.0827916i
$67$		−	657.048i		−	0.146368i	−0.997318	−	0.0731842i	$-0.976684\pi$
$67$		−	657.048i		−	0.146368i	0.997318	−	0.0731842i	$-0.0233161\pi$
$68$	−595.532	−	2347.13i	−0.128791	−	0.507597i
$69$			3653.09i			0.767295i
$70$	−6627.10	−	5300.36i	−1.35247	−	1.08171i
$71$			6741.79i			1.33739i	0.743536	+	0.668696i	$0.233147\pi$
$71$			6741.79i			1.33739i	−0.743536	+	0.668696i	$0.766853\pi$
$72$	−538.538	−	1377.32i	−0.103885	−	0.265688i
$73$			4130.26i			0.775054i	0.921858	+	0.387527i	$0.126671\pi$
$73$			4130.26i			0.775054i	−0.921858	+	0.387527i	$0.873329\pi$
$74$	574.391	+	4599.34i	0.104892	+	0.839909i
$75$	6374.75	+	171.701i	1.13329	+	0.0305246i
$76$	5714.45	−	1449.91i	0.989344	−	0.251024i
$77$	6050.98			1.02057
$78$	−4425.66	+	552.700i	−0.727425	+	0.0908448i
$79$			2307.14i			0.369675i	0.982769	+	0.184837i	$0.0591758\pi$
$79$			2307.14i			0.369675i	−0.982769	+	0.184837i	$0.940824\pi$
$80$	1902.90	−	6110.56i	0.297329	−	0.954775i
$81$	−7898.74			−1.20389
$82$	1262.03	+	10105.5i	0.187690	+	1.50290i
$83$		−	2146.14i		−	0.311532i	−0.987794	−	0.155766i	$-0.950215\pi$
$83$		−	2146.14i		−	0.311532i	0.987794	−	0.155766i	$-0.0497846\pi$
$84$	−3407.09	−	13428.1i	−0.482865	−	1.90308i
$85$	2639.14	+	2711.18i	0.365279	+	0.375250i
$86$	5374.41	−	671.184i	0.726664	−	0.0907497i
$87$	−3954.90			−0.522513
$88$	1661.84	+	4250.21i	0.214598	+	0.548839i
$89$	5117.03			0.646008			0.323004	−	0.946398i	$-0.395307\pi$
$89$	5117.03			0.646008			0.323004	+	0.946398i	$0.395307\pi$
$90$	1804.55	+	1443.28i	0.222784	+	0.178183i
$91$	−9273.44			−1.11985
$92$	−5552.55	+	1408.84i	−0.656019	+	0.166450i
$93$	17220.4			1.99103
$94$	−446.827	−	3577.90i	−0.0505690	−	0.404923i
$95$	−6600.80	+	6425.40i	−0.731391	+	0.711956i
$96$	8496.19	−	6081.05i	0.921896	−	0.659836i
$97$		−	9169.66i		−	0.974563i	−0.873245	−	0.487281i	$-0.837989\pi$
$97$		−	9169.66i		−	0.974563i	0.873245	−	0.487281i	$-0.162011\pi$
$98$	−2379.43	−	19052.9i	−0.247754	−	1.98385i
$99$	−1647.68			−0.168113
$100$	2197.48	+	9755.57i	0.219748	+	0.975557i
$101$		−	536.675i		−	0.0526100i	−0.999654	−	0.0263050i	$-0.991626\pi$
$101$		−	536.675i		−	0.0526100i	0.999654	−	0.0263050i	$-0.00837411\pi$
$102$	765.449	+	6129.21i	0.0735725	+	0.589121i
$103$	3140.33			0.296007			0.148003	−	0.988987i	$-0.452715\pi$
$103$	3140.33			0.296007			0.148003	+	0.988987i	$0.452715\pi$
$104$	−2546.86	−	6513.66i	−0.235471	−	0.602224i
$105$	15098.8	+	15510.9i	1.36950	+	1.40689i
$106$	1690.04	+	13532.8i	0.150413	+	1.20441i
$107$			16703.3i			1.45893i	0.684017	+	0.729466i	$0.260231\pi$
$107$			16703.3i			1.45893i	−0.684017	+	0.729466i	$0.739769\pi$
$108$	−2324.37	−	9160.87i	−0.199277	−	0.785397i
$109$		−	15790.1i		−	1.32902i	−0.747279	−	0.664510i	$-0.768640\pi$
$109$		−	15790.1i		−	1.32902i	0.747279	−	0.664510i	$-0.231360\pi$
$110$	−5568.56	−	4453.74i	−0.460212	−	0.368078i
$111$		−	11823.3i		−	0.959602i
$112$	19096.2	−	10357.3i	1.52234	−	0.825676i
$113$		−	4460.76i		−	0.349343i	−0.984627	−	0.174672i	$-0.944114\pi$
$113$		−	4460.76i		−	0.349343i	0.984627	−	0.174672i	$-0.0558864\pi$
$114$	−14922.5	+	1863.60i	−1.14824	+	0.143398i
$115$	6413.79	−	6243.36i	0.484974	−	0.472088i
$116$	−1525.23	−	6011.28i	−0.113349	−	0.446736i
$117$	2525.15			0.184465
$118$	720.920	+	5772.65i	0.0517753	+	0.414583i
$119$			12843.0i			0.906930i
$120$	−6748.14	+	14865.3i	−0.468621	+	1.03231i
$121$	−9556.53			−0.652724
$122$	−21135.2	+	2639.47i	−1.41999	+	0.177336i
$123$		−	25977.5i		−	1.71707i
$124$	6641.15	+	26174.3i	0.431916	+	1.70228i
$125$	−10593.4	−	11485.7i	−0.677976	−	0.735084i
$126$	971.993	+	7783.08i	0.0612240	+	0.490242i
$127$	−10888.2			−0.675070			−0.337535	−	0.941313i	$-0.609593\pi$
$127$	−10888.2			−0.675070			−0.337535	+	0.941313i	$0.609593\pi$
$128$	12519.5	+	10568.7i	0.764132	+	0.645060i
$129$	−13815.7			−0.830218
$130$	8534.10	+	6825.59i	0.504976	+	0.403881i
$131$	−9105.25			−0.530578			−0.265289	−	0.964169i	$-0.585467\pi$
$131$	−9105.25			−0.530578			−0.265289	+	0.964169i	$0.585467\pi$
$132$	−2862.88	−	11283.3i	−0.164307	−	0.647571i
$133$	−31268.4			−1.76767
$134$	−2607.93	+	325.693i	−0.145240	+	0.0181384i
$135$	10300.6	+	10581.8i	0.565191	+	0.580619i
$136$	−9020.94	+	3527.21i	−0.487724	+	0.190701i
$137$		−	14976.2i		−	0.797921i	−0.916968	−	0.398960i	$-0.869371\pi$
$137$		−	14976.2i		−	0.797921i	0.916968	−	0.398960i	$-0.130629\pi$
$138$	14499.7	−	1810.81i	0.761381	−	0.0950853i
$139$	25598.6			1.32491			0.662456	−	0.749101i	$-0.269514\pi$
$139$	25598.6			1.32491			0.662456	+	0.749101i	$0.269514\pi$
$140$	−17753.0	+	28931.4i	−0.905767	+	1.47609i
$141$			9197.49i			0.462627i
$142$	26759.3	−	3341.84i	1.32708	−	0.165733i
$143$	−7792.21			−0.381056
$144$	−5199.88	+	2820.27i	−0.250766	+	0.136009i
$145$	6759.17	+	6943.68i	0.321482	+	0.330258i
$146$	16393.7	−	2047.33i	0.769080	−	0.0960468i
$147$			48978.1i			2.26656i
$148$	17970.8	−	4559.70i	0.820437	−	0.208168i
$149$			10269.8i			0.462585i	0.972884	+	0.231292i	$0.0742954\pi$
$149$			10269.8i			0.462585i	−0.972884	+	0.231292i	$0.925705\pi$
$150$	−2478.39	−	25387.6i	−0.110151	−	1.12834i
$151$		−	14739.4i		−	0.646435i	−0.946325	−	0.323217i	$-0.895236\pi$
$151$		−	14739.4i		−	0.646435i	0.946325	−	0.323217i	$-0.104764\pi$
$152$	−8587.55	−	21962.9i	−0.371691	−	0.950610i
$153$		−	3497.14i		−	0.149393i
$154$	−2999.42	−	24017.4i	−0.126472	−	1.01271i
$155$	−29430.7	−	30234.1i	−1.22500	−	1.25844i
$156$	4387.51	+	17292.2i	0.180289	+	0.710561i
$157$	−27740.2			−1.12541			−0.562705	−	0.826658i	$-0.690239\pi$
$157$	−27740.2			−1.12541			−0.562705	+	0.826658i	$0.690239\pi$
$158$	9157.42	−	1143.63i	0.366825	−	0.0458111i
$159$		−	34787.8i		−	1.37605i
$160$	−25197.1	−	4524.00i	−0.984261	−	0.176719i
$161$	30382.5			1.17212
$162$	3915.33	+	31351.4i	0.149190	+	1.19461i
$163$		−	3732.97i		−	0.140501i	−0.997529	−	0.0702505i	$-0.977620\pi$
$163$		−	3732.97i		−	0.140501i	0.997529	−	0.0702505i	$-0.0223799\pi$
$164$	39484.7	−	10018.4i	1.46805	−	0.372486i
$165$	12687.1	+	13033.4i	0.466008	+	0.478729i
$166$	−8518.41	+	1063.82i	−0.309131	+	0.0386059i
$167$	20717.4			0.742853			0.371427	−	0.928462i	$-0.378869\pi$
$167$	20717.4			0.742853			0.371427	+	0.928462i	$0.378869\pi$
$168$	−51609.7	+	20179.5i	−1.82857	+	0.714978i
$169$	−16619.0			−0.581879
$170$	9452.94	−	11819.1i	0.327091	−	0.408966i
$171$	8514.34			0.291178
$172$	−5328.09	−	20999.2i	−0.180100	−	0.709817i
$173$	35335.7			1.18065			0.590326	−	0.807165i	$-0.298999\pi$
$173$	35335.7			1.18065			0.590326	+	0.807165i	$0.298999\pi$
$174$	1960.41	+	15697.7i	0.0647512	+	0.518485i
$175$	1428.02	−	53018.3i	0.0466293	−	1.73121i
$176$	16046.0	−	8702.92i	0.518015	−	0.280957i
$177$		−	14839.4i		−	0.473664i
$178$	−2536.46	−	20310.3i	−0.0800551	−	0.641028i
$179$	23669.8			0.738734			0.369367	−	0.929284i	$-0.379575\pi$
$179$	23669.8			0.738734			0.369367	+	0.929284i	$0.379575\pi$
$180$	4834.13	−	7877.98i	0.149202	−	0.243148i
$181$			7525.59i			0.229712i	0.993382	+	0.114856i	$0.0366406\pi$
$181$			7525.59i			0.229712i	−0.993382	+	0.114856i	$0.963359\pi$
$182$	4596.76	+	36807.8i	0.138774	+	1.11121i
$183$	54330.9			1.62235
$184$	8344.25	+	21340.6i	0.246463	+	0.630336i
$185$	−20758.2	+	20206.7i	−0.606523	+	0.590407i
$186$	−8535.99	−	68350.7i	−0.246734	−	1.97568i
$187$			10791.6i			0.308606i
$188$	−13979.8	+	3547.07i	−0.395535	+	0.100358i
$189$			50126.5i			1.40328i
$190$	28775.5	+	23014.7i	0.797104	+	0.637525i
$191$			28925.8i			0.792901i	0.918056	+	0.396450i	$0.129758\pi$
$191$			28925.8i			0.792901i	−0.918056	+	0.396450i	$0.870242\pi$
$192$	−28348.2	−	30708.5i	−0.768994	−	0.833021i
$193$			48944.4i			1.31398i	0.753900	+	0.656990i	$0.228171\pi$
$193$			48944.4i			1.31398i	−0.753900	+	0.656990i	$0.771829\pi$
$194$	−36395.9	+	4545.32i	−0.967051	+	0.120770i
$195$	−19443.6	−	19974.3i	−0.511337	−	0.525295i
$196$	−74444.7	+	18888.7i	−1.93786	+	0.491688i
$197$	47883.5			1.23382			0.616912	−	0.787032i	$-0.288383\pi$
$197$	47883.5			1.23382			0.616912	+	0.787032i	$0.288383\pi$
$198$	816.738	+	6539.90i	0.0208330	+	0.166817i
$199$			29644.2i			0.748573i	0.927313	+	0.374286i	$0.122112\pi$
$199$			29644.2i			0.748573i	−0.927313	+	0.374286i	$0.877888\pi$
$200$	37632.2	−	13557.9i	0.940805	−	0.338948i
$201$	6704.06			0.165938
$202$	−2130.15	+	266.025i	−0.0522045	+	0.00651958i
$203$			32892.6i			0.798190i
$204$	23948.4	−	6076.39i	0.575462	−	0.146011i
$205$	−45609.1	+	44397.2i	−1.08529	+	1.05645i
$206$	−1556.63	−	12464.5i	−0.0366819	−	0.293725i
$207$	−8273.12			−0.193076
$208$	−24591.3	+	13337.7i	−0.568402	+	0.308286i
$209$	−26273.9			−0.601496
$210$	54081.2	−	67618.2i	1.22633	−	1.53329i
$211$	19653.5			0.441444			0.220722	−	0.975337i	$-0.429159\pi$
$211$	19653.5			0.441444			0.220722	+	0.975337i	$0.429159\pi$
$212$	52876.1	−	13416.1i	1.17649	−	0.298508i
$213$	−68788.5			−1.51620
$214$	66298.2	−	8279.68i	1.44769	−	0.180795i
$215$	23611.8	+	24256.3i	0.510802	+	0.524745i
$216$	−35208.8	+	13766.8i	−0.754648	+	0.295069i
$217$		−	143221.i		−	3.04149i
$218$	−62673.5	+	7827.00i	−1.31878	+	0.164696i
$219$	−42142.3			−0.878678
$220$	−14917.4	+	24310.2i	−0.308210	+	0.502277i
$221$		−	16538.7i		−	0.338624i
$222$	−46928.5	+	5860.68i	−0.952205	+	0.118916i
$223$	−60977.7			−1.22620			−0.613100	−	0.790005i	$-0.710078\pi$
$223$	−60977.7			−1.22620			−0.613100	+	0.790005i	$0.710078\pi$
$224$	−50575.6	−	70662.2i	−1.00796	−	1.40829i
$225$	−388.849	+	14436.8i	−0.00768097	+	0.285172i
$226$	−17705.5	+	2211.16i	−0.346650	+	0.0432915i
$227$			2698.14i			0.0523616i	0.999657	+	0.0261808i	$0.00833456\pi$
$227$			2698.14i			0.0523616i	−0.999657	+	0.0261808i	$0.991665\pi$
$228$	14793.9	+	58306.2i	0.284586	+	1.12162i
$229$		−	68901.3i		−	1.31388i	−0.753942	−	0.656941i	$-0.771850\pi$
$229$		−	68901.3i		−	1.31388i	0.753942	−	0.656941i	$-0.228150\pi$
$230$	−27960.2	−	22362.6i	−0.528548	−	0.422734i
$231$			61740.0i			1.15702i
$232$	−23103.7	+	9033.63i	−0.429246	+	0.167837i
$233$			83770.9i			1.54305i	0.636196	+	0.771527i	$0.280507\pi$
$233$			83770.9i			1.54305i	−0.636196	+	0.771527i	$0.719493\pi$
$234$	−1251.69	−	10022.7i	−0.0228595	−	0.183044i
$235$	16148.2	−	15719.1i	0.292407	−	0.284637i
$236$	22555.3	−	5722.90i	0.404971	−	0.102752i
$237$	−23540.4			−0.419100
$238$	50976.2	−	6366.18i	0.899939	−	0.112389i
$239$		−	36602.8i		−	0.640795i	−0.947283	−	0.320397i	$-0.896184\pi$
$239$		−	36602.8i		−	0.640795i	0.947283	−	0.320397i	$-0.103816\pi$
$240$	62347.9	+	19415.9i	1.08243	+	0.337082i
$241$	48755.9			0.839447			0.419724	−	0.907652i	$-0.362127\pi$
$241$	48755.9			0.839447			0.419724	+	0.907652i	$0.362127\pi$
$242$	4737.09	+	37931.5i	0.0808873	+	0.647693i
$243$		−	32746.8i		−	0.554570i
$244$	20953.0	+	82580.7i	0.351939	+	1.38707i
$245$	85991.6	−	83706.6i	1.43260	−	1.39453i
$246$	−103109.	+	12876.8i	−1.70383	+	0.212784i
$247$	40266.1			0.660003
$248$	100598.	−	39334.2i	1.63564	−	0.639538i
$249$	21897.8			0.353184
$250$	−40337.6	+	47740.2i	−0.645401	+	0.763844i
$251$	75319.3			1.19553			0.597763	−	0.801673i	$-0.296056\pi$
$251$	75319.3			1.19553			0.597763	+	0.801673i	$0.296056\pi$
$252$	30410.5	−	7716.00i	0.478876	−	0.121504i
$253$	25529.5			0.398843
$254$	5397.19	+	43217.1i	0.0836566	+	0.669867i
$255$	−27663.0	+	26928.0i	−0.425421	+	0.414117i
$256$	35743.0	−	54930.9i	0.545394	−	0.838180i
$257$			27190.5i			0.411672i	0.978587	+	0.205836i	$0.0659913\pi$
$257$			27190.5i			0.411672i	−0.978587	+	0.205836i	$0.934009\pi$
$258$	6848.29	+	54836.7i	0.102883	+	0.823819i
$259$	−98333.1			−1.46589
$260$	22861.6	−	37256.7i	0.338190	−	0.551134i
$261$		−	8956.62i		−	0.131481i
$262$	4513.39	+	36140.3i	0.0657507	+	0.526488i
$263$	−48135.0			−0.695905			−0.347952	−	0.937512i	$-0.613123\pi$
$263$	−48135.0			−0.695905			−0.347952	+	0.937512i	$0.613123\pi$
$264$	−43366.1	+	16956.3i	−0.622218	+	0.243289i
$265$	−61077.5	+	59454.6i	−0.869740	+	0.846630i
$266$	15499.5	+	124109.i	0.219055	+	1.75405i
$267$			52210.6i			0.732379i
$268$	2585.46	+	10189.9i	0.0359971	+	0.141873i
$269$		−	57856.4i		−	0.799553i	−0.916613	−	0.399776i	$-0.869088\pi$
$269$		−	57856.4i		−	0.799553i	0.916613	−	0.399776i	$-0.130912\pi$
$270$	36894.9	−	46130.1i	0.506104	−	0.632786i
$271$		−	135141.i		−	1.84013i	−0.391765	−	0.920065i	$-0.628136\pi$
$271$		−	135141.i		−	1.84013i	0.391765	−	0.920065i	$-0.371864\pi$
$272$	18471.7	+	34057.2i	0.249672	+	0.460332i
$273$		−	94619.7i		−	1.26957i
$274$	−59443.0	+	7423.55i	−0.791770	+	0.0988805i
$275$	1199.93	−	44549.8i	0.0158668	−	0.589088i
$276$	−14374.8	−	56654.3i	−0.188705	−	0.743729i
$277$	66626.3			0.868333			0.434166	−	0.900833i	$-0.357043\pi$
$277$	66626.3			0.868333			0.434166	+	0.900833i	$0.357043\pi$
$278$	−12689.0	−	101605.i	−0.164187	−	1.31470i
$279$			38998.8i			0.501006i
$280$	123634.	+	56123.8i	1.57696	+	0.715864i
$281$	70518.3			0.893078			0.446539	−	0.894764i	$-0.352656\pi$
$281$	70518.3			0.893078			0.446539	+	0.894764i	$0.352656\pi$
$282$	36506.4	−	4559.11i	0.459061	−	0.0573300i
$283$			5580.69i			0.0696811i	0.999393	+	0.0348406i	$0.0110923\pi$
$283$			5580.69i			0.0696811i	−0.999393	+	0.0348406i	$0.988908\pi$
$284$	−26528.7	−	104556.i	−0.328911	−	1.29632i
$285$	−65560.3	−	67349.9i	−0.807144	−	0.829177i
$286$	3862.53	+	30928.6i	0.0472214	+	0.378118i
$287$	−216053.			−2.62299
$288$	13771.7	+	19241.2i	0.166036	+	0.231978i
$289$	60616.1			0.725758
$290$	24210.2	−	30270.2i	0.287873	−	0.359931i
$291$	93560.8			1.10486
$292$	−16252.4	−	64054.5i	−0.190613	−	0.751249i
$293$	85817.1			0.999628			0.499814	−	0.866133i	$-0.333402\pi$
$293$	85817.1			0.999628			0.499814	+	0.866133i	$0.333402\pi$
$294$	194402.	−	24278.0i	2.24909	−	0.280878i
$295$	−26053.8	+	25361.5i	−0.299382	+	0.291427i
$296$	−27006.2	−	69069.1i	−0.308234	−	0.788316i
$297$			42119.9i			0.477501i
$298$	40762.7	−	5090.67i	0.459019	−	0.0573248i
$299$	−39125.3			−0.437639
$300$	−99539.0	+	22421.5i	−1.10599	+	0.249128i
$301$			114904.i			1.26824i
$302$	−58503.0	+	7306.16i	−0.641452	+	0.0801079i
$303$	5475.85			0.0596440
$304$	−82917.6	+	44972.2i	−0.897222	+	0.486628i
$305$	−92854.9	−	95389.5i	−0.998171	−	1.02542i
$306$	−13880.7	+	1733.50i	−0.148242	+	0.0185132i
$307$		−	24380.3i		−	0.258680i	−0.991600	−	0.129340i	$-0.958714\pi$
$307$		−	24380.3i		−	0.258680i	0.991600	−	0.129340i	$-0.0412858\pi$
$308$	−93842.2	+	23810.4i	−0.989228	+	0.250995i
$309$			32041.8i			0.335583i
$310$	−105416.	+	131802.i	−1.09694	+	1.37151i
$311$			145304.i			1.50230i	0.660133	+	0.751149i	$0.270500\pi$
$311$			145304.i			1.50230i	−0.660133	+	0.751149i	$0.729500\pi$
$312$	66460.8	−	25986.4i	0.682742	−	0.266954i
$313$			15.3803i			0.000156991i	1.00000		7.84956e-5i	$2.49859e-5\pi$
$313$			15.3803i			0.000156991i	−1.00000		7.84956e-5i	$0.999975\pi$
$314$	13750.6	+	110106.i	0.139464	+	1.11673i
$315$	−35127.4	+	34194.0i	−0.354018	+	0.344611i
$316$	−9078.50	−	35780.5i	−0.0909159	−	0.358320i
$317$	−19873.1			−0.197764			−0.0988819	−	0.995099i	$-0.531527\pi$
$317$	−19873.1			−0.197764			−0.0988819	+	0.995099i	$0.531527\pi$
$318$	−138079.	+	17244.0i	−1.36544	+	0.170523i
$319$			27638.7i			0.271604i
$320$	−5466.54	+	102254.i	−0.0533842	+	0.998574i
$321$	−170429.			−1.65399
$322$	−15060.3	−	120593.i	−0.145252	−	1.16308i
$323$		−	55765.7i		−	0.534517i
$324$	122498.	−	31081.2i	1.16692	−	0.296079i
$325$	−1838.95	+	68274.8i	−0.0174102	+	0.646388i
$326$	−14816.8	+	1850.40i	−0.139418	+	0.0174113i
$327$	161111.			1.50671
$328$	−59336.9	−	151756.i	−0.551540	−	1.41058i
$329$	76494.8			0.706708
$330$	45442.9	−	56817.7i	0.417290	−	0.521742i
$331$	−55183.9			−0.503682			−0.251841	−	0.967769i	$-0.581036\pi$
$331$	−55183.9			−0.503682			−0.251841	+	0.967769i	$0.581036\pi$
$332$	8444.99	+	33283.7i	0.0766167	+	0.301964i
$333$	26776.0			0.241466
$334$	−10269.4	−	82231.0i	−0.0920564	−	0.737127i
$335$	−11457.6	−	11770.4i	−0.102095	−	0.104882i
$336$	105678.	+	194845.i	0.936068	+	1.72588i
$337$			172509.i			1.51898i	0.650520	+	0.759489i	$0.274551\pi$
$337$			172509.i			1.51898i	−0.650520	+	0.759489i	$0.725449\pi$
$338$	8237.91	+	65963.8i	0.0721080	+	0.577394i
$339$	45514.5			0.396050
$340$	−51597.8	−	31661.7i	−0.446347	−	0.273890i
$341$		−	120344.i		−	1.03494i
$342$	−4220.48	−	33794.9i	−0.0360836	−	0.288934i
$343$	203598.			1.73056
$344$	−80708.3	+	31557.2i	−0.682027	+	0.266674i
$345$	63702.9	+	65441.8i	0.535206	+	0.549815i
$346$	−17515.6	−	140253.i	−0.146310	−	1.17155i
$347$			53756.2i			0.446447i	0.974767	+	0.223223i	$0.0716579\pi$
$347$			53756.2i			0.446447i	−0.974767	+	0.223223i	$0.928342\pi$
$348$	61334.9	−	15562.4i	0.506465	−	0.128504i
$349$			101720.i			0.835136i	0.908646	+	0.417568i	$0.137117\pi$
$349$			101720.i			0.835136i	−0.908646	+	0.417568i	$0.862883\pi$
$350$	−211146.	+	20612.6i	−1.72364	+	0.168266i
$351$		−	64550.9i		−	0.523948i
$352$	−42497.2	−	59375.4i	−0.342985	−	0.479205i
$353$		−	119472.i		−	0.958778i	−0.877603	−	0.479389i	$-0.840858\pi$
$353$		−	119472.i		−	0.958778i	0.877603	−	0.479389i	$-0.159142\pi$
$354$	−58900.1	+	7355.76i	−0.470013	+	0.0586977i
$355$	117564.	+	120773.i	0.932861	+	0.958325i
$356$	−79357.9	+	20135.3i	−0.626167	+	0.158876i
$357$	−131041.			−1.02819
$358$	−11732.9	−	93949.3i	−0.0915459	−	0.733039i
$359$			66348.7i			0.514806i	0.966304	+	0.257403i	$0.0828668\pi$
$359$			66348.7i			0.514806i	−0.966304	+	0.257403i	$0.917133\pi$
$360$	−33665.3	−	15282.4i	−0.259763	−	0.117920i
$361$	5449.20			0.0418137
$362$	29870.3	−	3730.37i	0.227941	−	0.0284665i
$363$		−	97508.1i		−	0.739993i
$364$	143818.	−	36490.6i	1.08545	−	0.275409i
$365$	72023.8	+	73989.8i	0.540618	+	0.555375i
$366$	−26931.3	−	215648.i	−0.201046	−	1.60985i
$367$	146492.			1.08763			0.543817	−	0.839204i	$-0.316979\pi$
$367$	146492.			1.08763			0.543817	+	0.839204i	$0.316979\pi$
$368$	80568.4	−	43698.1i	0.594935	−	0.322676i
$369$	58831.0			0.432069
$370$	90493.3	+	72376.7i	0.661018	+	0.528683i
$371$	−289328.			−2.10205
$372$	−267064.	+	67761.6i	−1.92988	+	0.489663i
$373$	−113125.			−0.813092			−0.406546	−	0.913630i	$-0.633267\pi$
$373$	−113125.			−0.813092			−0.406546	+	0.913630i	$0.633267\pi$
$374$	42833.8	−	5349.32i	0.306227	−	0.0382433i
$375$	117192.	−	108087.i	0.833364	−	0.768622i
$376$	21008.6	+	53729.9i	0.148601	+	0.380050i
$377$		−	42357.7i		−	0.298023i
$378$	198961.	−	24847.3i	1.39246	−	0.173898i
$379$	43592.1			0.303480			0.151740	−	0.988420i	$-0.451512\pi$
$379$	43592.1			0.303480			0.151740	+	0.988420i	$0.451512\pi$
$380$	77085.3	−	125623.i	0.533832	−	0.869964i
$381$		−	111096.i		−	0.765327i
$382$	114811.	−	14338.3i	0.786789	−	0.0982584i
$383$	−99396.2			−0.677598			−0.338799	−	0.940859i	$-0.610021\pi$
$383$	−99396.2			−0.677598			−0.338799	+	0.940859i	$0.610021\pi$
$384$	−107835.	+	127741.i	−0.731304	+	0.866296i
$385$	108398.	−	105517.i	0.731306	−	0.711873i
$386$	194269.	−	24261.3i	1.30385	−	0.162832i
$387$		−	31288.2i		−	0.208909i
$388$	36082.2	+	142208.i	0.239679	+	0.944630i
$389$			99896.0i			0.660159i	0.943953	+	0.330080i	$0.107076\pi$
$389$			99896.0i			0.660159i	−0.943953	+	0.330080i	$0.892924\pi$
$390$	−69643.5	+	87076.0i	−0.457880	+	0.572492i
$391$			54185.7i			0.354431i
$392$	111874.	+	286120.i	0.728043	+	1.86199i
$393$		−	92903.6i		−	0.601516i
$394$	−23735.4	−	190058.i	−0.152899	−	1.22431i
$395$	40232.0	+	41330.3i	0.257856	+	0.264895i
$396$	25553.1	−	6483.54i	0.162950	−	0.0413449i
$397$	55234.5			0.350453			0.175226	−	0.984528i	$-0.443934\pi$
$397$	55234.5			0.350453			0.175226	+	0.984528i	$0.443934\pi$
$398$	117663.	−	14694.4i	0.742803	−	0.0927652i
$399$		−	319041.i		−	2.00401i
$400$	−72467.6	−	142648.i	−0.452922	−	0.891550i
$401$	−40688.8			−0.253038			−0.126519	−	0.991964i	$-0.540380\pi$
$401$	−40688.8			−0.253038			−0.126519	+	0.991964i	$0.540380\pi$
$402$	−3323.14	−	26609.5i	−0.0205635	−	0.164659i
$403$			184434.i			1.13561i
$404$	2111.79	+	8323.07i	0.0129386	+	0.0509942i
$405$	−141499.	+	137739.i	−0.862665	+	0.839743i
$406$	130556.	−	16304.6i	0.792037	−	0.0989139i
$407$	−82626.5			−0.498804
$408$	−35989.2	−	92043.4i	−0.216198	−	0.552933i
$409$	−313804.			−1.87591			−0.937955	−	0.346757i	$-0.887283\pi$
$409$	−313804.			−1.87591			−0.937955	+	0.346757i	$0.887283\pi$
$410$	198828.	+	159023.i	1.18280	+	0.946002i
$411$	152806.			0.904603
$412$	−48702.1	+	12357.1i	−0.286915	+	0.0727984i
$413$	−123418.			−0.723567
$414$	4100.91	+	32837.4i	0.0239265	+	0.191588i
$415$	−37424.6	−	38446.2i	−0.217301	−	0.223232i
$416$	65129.2	+	90995.8i	0.376347	+	0.525817i
$417$			261190.i			1.50205i
$418$	13023.7	+	104286.i	0.0745390	+	0.596859i
$419$	264287.			1.50538			0.752692	−	0.658373i	$-0.228755\pi$
$419$	264287.			1.50538			0.752692	+	0.658373i	$0.228755\pi$
$420$	−295196.	−	181140.i	−1.67344	−	1.02687i
$421$			179764.i			1.01424i	0.861877	+	0.507118i	$0.169289\pi$
$421$			179764.i			1.01424i	−0.861877	+	0.507118i	$0.830711\pi$
$422$	−9742.08	−	78008.2i	−0.0547050	−	0.438042i
$423$	−20829.4			−0.116412
$424$	−79461.0	−	203224.i	−0.442000	−	1.13043i
$425$	94555.6	+	2546.81i	0.523491	+	0.0141000i
$426$	34097.8	+	273033.i	0.187892	+	1.50451i
$427$		−	451866.i		−	2.47830i
$428$	−65726.8	−	259045.i	−0.358802	−	1.41412i
$429$		−	79506.2i		−	0.432003i
$430$	84573.3	−	105743.i	0.457400	−	0.571892i
$431$		−	151073.i		−	0.813266i	−0.913592	−	0.406633i	$-0.866703\pi$
$431$		−	151073.i		−	0.813266i	0.913592	−	0.406633i	$-0.133297\pi$
$432$	72095.3	+	132926.i	0.386313	+	0.712265i
$433$			133641.i			0.712796i	0.934334	+	0.356398i	$0.115995\pi$
$433$			133641.i			0.712796i	−0.934334	+	0.356398i	$0.884005\pi$
$434$	−568467.	+	70993.2i	−3.01805	+	0.376910i
$435$	−70848.4	+	68965.8i	−0.374413	+	0.364465i
$436$	62133.3	+	244882.i	0.326852	+	1.28820i
$437$	−131924.			−0.690812
$438$	20889.5	+	167270.i	0.108888	+	0.871905i
$439$		−	74613.0i		−	0.387156i	−0.981085	−	0.193578i	$-0.937991\pi$
$439$		−	74613.0i		−	0.387156i	0.981085	−	0.193578i	$-0.0620092\pi$
$440$	103886.	+	47159.2i	0.536600	+	0.243591i
$441$	−110920.			−0.570339
$442$	−65645.0	+	8198.10i	−0.336014	+	0.0419632i
$443$			110554.i			0.563334i	0.959512	+	0.281667i	$0.0908874\pi$
$443$			110554.i			0.563334i	−0.959512	+	0.281667i	$0.909113\pi$
$444$	46524.0	+	183362.i	0.236000	+	0.930129i
$445$	91666.8	−	89231.1i	0.462905	−	0.450605i
$446$	30226.1	+	242031.i	0.151954	+	1.21675i
$447$	−104786.			−0.524432
$448$	−255400.	+	235770.i	−1.27252	+	1.17471i
$449$	9722.73			0.0482276			0.0241138	−	0.999709i	$-0.492324\pi$
$449$	9722.73			0.0482276			0.0241138	+	0.999709i	$0.492324\pi$
$450$	57494.9	−	5612.79i	0.283925	−	0.0277175i
$451$	−181543.			−0.892539
$452$	17552.9	+	69180.1i	0.0859157	+	0.338613i
$453$	150390.			0.732863
$454$	10709.4	−	1337.44i	0.0519580	−	0.00648879i
$455$	−166125.	+	161711.i	−0.802440	+	0.781117i
$456$	224094.	−	87621.4i	1.07771	−	0.421386i
$457$		−	331629.i		−	1.58789i	−0.607990	−	0.793945i	$-0.708024\pi$
$457$		−	331629.i		−	1.58789i	0.607990	−	0.793945i	$-0.291976\pi$
$458$	−273481.	+	34153.7i	−1.30375	+	0.162820i
$459$	−89398.3			−0.424330
$460$	−74901.4	+	122064.i	−0.353976	+	0.576860i
$461$		−	86774.7i		−	0.408311i	−0.978938	−	0.204156i	$-0.934555\pi$
$461$		−	86774.7i		−	0.408311i	0.978938	−	0.204156i	$-0.0654449\pi$
$462$	245056.	−	30603.9i	1.14811	−	0.143382i
$463$	−35664.8			−0.166371			−0.0831856	−	0.996534i	$-0.526509\pi$
$463$	−35664.8			−0.166371			−0.0831856	+	0.996534i	$0.526509\pi$
$464$	47308.3	+	87224.7i	0.219736	+	0.405139i
$465$	308487.	−	300290.i	1.42670	−	1.38879i
$466$	332501.	−	41524.5i	1.53116	−	0.191220i
$467$		−	293718.i		−	1.34678i	−0.739288	−	0.673389i	$-0.764838\pi$
$467$		−	293718.i		−	1.34678i	0.739288	−	0.673389i	$-0.235162\pi$
$468$	−39161.4	+	9936.35i	−0.178800	+	0.0453665i
$469$		−	55757.1i		−	0.253486i
$470$	−70396.2	−	56303.0i	−0.318679	−	0.254880i
$471$		−	283042.i		−	1.27588i
$472$	−33895.6	−	86688.9i	−0.152146	−	0.389116i
$473$			96550.3i			0.431550i
$474$	11668.8	+	93435.9i	0.0519360	+	0.415869i
$475$	−6200.61	+	230210.i	−0.0274819	+	1.02032i
$476$	−50536.8	−	199177.i	−0.223046	−	0.879075i
$477$	78783.6			0.346257
$478$	−145283.	+	18143.7i	−0.635855	+	0.0794090i
$479$			435529.i			1.89822i	0.314945	+	0.949110i	$0.398014\pi$
$479$			435529.i			1.89822i	−0.314945	+	0.949110i	$0.601986\pi$
$480$	46159.7	−	257093.i	0.200346	−	1.11586i
$481$	126629.			0.547323
$482$	−24167.9	−	193520.i	−0.104027	−	0.832977i
$483$			310002.i			1.32883i
$484$	148208.	−	37604.6i	0.632676	−	0.160528i
$485$	−159901.	−	164266.i	−0.679779	−	0.698335i
$486$	−129978.	+	16232.3i	−0.550295	+	0.0687238i
$487$	187286.			0.789672			0.394836	−	0.918752i	$-0.370801\pi$
$487$	187286.			0.789672			0.394836	+	0.918752i	$0.370801\pi$
$488$	317390.	−	124101.i	1.33277	−	0.521116i
$489$	38088.6			0.159286
$490$	−374871.	−	299822.i	−1.56131	−	1.24874i
$491$	−287674.			−1.19327			−0.596634	−	0.802513i	$-0.703496\pi$
$491$	−287674.			−1.19327			−0.596634	+	0.802513i	$0.703496\pi$
$492$	102221.	+	402875.i	0.422287	+	1.66433i
$493$	−58662.4			−0.241360
$494$	−19959.6	−	159823.i	−0.0817894	−	0.654916i
$495$	−29516.6	+	28732.3i	−0.120464	+	0.117263i
$496$	−205989.	−	379793.i	−0.837301	−	1.54377i
$497$			572109.i			2.31615i
$498$	−10854.5	−	86915.9i	−0.0437675	−	0.350462i
$499$	175430.			0.704537			0.352268	−	0.935899i	$-0.385410\pi$
$499$	175430.			0.704537			0.352268	+	0.935899i	$0.385410\pi$
$500$	209484.	+	136442.i	0.837936	+	0.545769i
$501$			211386.i			0.842172i
$502$	−37335.1	−	298955.i	−0.148153	−	1.18631i
$503$	−95682.5			−0.378178			−0.189089	−	0.981960i	$-0.560553\pi$
$503$	−95682.5			−0.378178			−0.189089	+	0.981960i	$0.560553\pi$
$504$	−45700.3	−	116880.i	−0.179911	−	0.460128i
$505$	−9358.57	−	9614.03i	−0.0366967	−	0.0376984i
$506$	−12654.8	−	101331.i	−0.0494257	−	0.395769i
$507$		−	169569.i		−	0.659676i
$508$	168861.	−	42844.7i	0.654336	−	0.166023i
$509$		−	370388.i		−	1.42962i	−0.699318	−	0.714811i	$-0.746513\pi$
$509$		−	370388.i		−	1.42962i	0.699318	−	0.714811i	$-0.253487\pi$
$510$	120594.	+	96451.2i	0.463644	+	0.370823i
$511$			350494.i			1.34227i
$512$	−235748.	−	114641.i	−0.899306	−	0.437321i
$513$		−	217654.i		−	0.827050i
$514$	107924.	−	13478.1i	0.408499	−	0.0510155i
$515$	56256.2	−	54761.3i	0.212107	−	0.206471i
$516$	214261.	−	54364.1i	0.804719	−	0.204180i
$517$	64276.4			0.240475
$518$	48742.8	+	390300.i	0.181656	+	1.45459i
$519$			360541.i			1.33850i
$520$	−159210.	−	72273.9i	−0.588795	−	0.267285i
$521$	−259622.			−0.956458			−0.478229	−	0.878235i	$-0.658721\pi$
$521$	−259622.			−0.956458			−0.478229	+	0.878235i	$0.658721\pi$
$522$	−35550.3	+	4439.71i	−0.130468	+	0.0162935i
$523$			108562.i			0.396895i	0.980111	+	0.198448i	$0.0635900\pi$
$523$			108562.i			0.396895i	−0.980111	+	0.198448i	$0.936410\pi$
$524$	141209.	−	35828.8i	0.514282	−	0.130488i
$525$	540961.	+	14570.5i	1.96267	+	0.0528637i
$526$	23860.1	+	191056.i	0.0862384	+	0.690541i
$527$	255427.			0.919700
$528$	88798.5	+	163722.i	0.318521	+	0.587273i
$529$	−151655.			−0.541933
$530$	266261.	+	212956.i	0.947884	+	0.758119i
$531$	33606.6			0.119189
$532$	484928.	−	123040.i	1.71338	−	0.434733i
$533$	278224.			0.979356
$534$	207233.	−	25880.3i	0.726734	−	0.0907584i
$535$	291273.	+	299224.i	1.01764	+	1.04542i
$536$	39163.8	−	15313.1i	0.136319	−	0.0533009i
$537$			241510.i			0.837502i
$538$	−229642.	+	28678.9i	−0.793390	+	0.0990827i
$539$	342282.			1.17817
$540$	−201387.	−	123576.i	−0.690626	−	0.423786i
$541$		−	280006.i		−	0.956694i	−0.878171	−	0.478347i	$-0.841236\pi$
$541$		−	280006.i		−	0.956694i	0.878171	−	0.478347i	$-0.158764\pi$
$542$	−536397.	+	66988.2i	−1.82595	+	0.228034i
$543$	−76785.8			−0.260424
$544$	126023.	−	90199.1i	0.425844	−	0.304793i
$545$	−275348.	−	282865.i	−0.927021	−	0.952326i
$546$	−375561.	+	46902.1i	−1.25978	+	0.157328i
$547$			72377.7i			0.241897i	0.992659	+	0.120948i	$0.0385936\pi$
$547$			72377.7i			0.241897i	−0.992659	+	0.120948i	$0.961406\pi$
$548$	58930.7	+	232259.i	0.196237	+	0.773414i
$549$			123043.i			0.408235i
$550$	−177420.	+	17320.2i	−0.586513	+	0.0572568i
$551$		−	142823.i		−	0.470429i
$552$	−217745.	+	85138.9i	−0.714611	+	0.279415i
$553$			195784.i			0.640216i
$554$	−33026.0	−	264451.i	−0.107606	−	0.861640i
$555$	−206175.	−	211803.i	−0.669344	−	0.687615i
$556$	−396998.	+	100730.i	−1.28422	+	0.325842i
$557$	402974.			1.29887			0.649437	−	0.760416i	$-0.275005\pi$
$557$	402974.			1.29887			0.649437	+	0.760416i	$0.275005\pi$
$558$	154793.	−	19331.4i	0.497144	−	0.0620861i
$559$		−	147968.i		−	0.473527i
$560$	161481.	−	518542.i	0.514925	−	1.65352i
$561$	−110110.			−0.349866
$562$	−34955.3	−	279899.i	−0.110673	−	0.886194i
$563$		−	244892.i		−	0.772606i	−0.922372	−	0.386303i	$-0.873752\pi$
$563$		−	244892.i		−	0.772606i	0.922372	−	0.386303i	$-0.126248\pi$
$564$	−36191.8	−	142640.i	−0.113776	−	0.448418i
$565$	−77787.0	−	79910.4i	−0.243675	−	0.250326i
$566$	22150.7	−	2766.30i	0.0691440	−	0.00863508i
$567$	−670288.			−2.08495
$568$	−401849.	+	157124.i	−1.24556	+	0.487019i
$569$	644997.			1.99220			0.996100	−	0.0882331i	$-0.0281220\pi$
$569$	644997.			1.99220			0.996100	+	0.0882331i	$0.0281220\pi$
$570$	−234825.	+	293605.i	−0.722762	+	0.903677i
$571$	198216.			0.607947			0.303973	−	0.952681i	$-0.401687\pi$
$571$	198216.			0.607947			0.303973	+	0.952681i	$0.401687\pi$
$572$	120846.	−	30662.0i	0.369352	−	0.0937149i
$573$	−295139.			−0.898911
$574$	107096.	+	857551.i	0.325048	+	2.60277i
$575$	6024.94	−	223688.i	0.0182229	−	0.676561i
$576$	69545.1	−	64199.8i	0.209615	−	0.193503i
$577$			218459.i			0.656172i	0.944648	+	0.328086i	$0.106404\pi$
$577$			218459.i			0.656172i	−0.944648	+	0.328086i	$0.893596\pi$
$578$	−30046.8	−	240595.i	−0.0899379	−	0.720164i
$579$	−499394.			−1.48966
$580$	−132148.	−	81089.5i	−0.392831	−	0.241051i
$581$		−	182122.i		−	0.539523i
$582$	−46377.2	−	371358.i	−0.136917	−	1.09634i
$583$	−243114.			−0.715274
$584$	−246187.	+	96259.8i	−0.721837	+	0.282240i
$585$	45235.7	−	44033.7i	0.132181	−	0.128669i
$586$	−42538.7	−	340622.i	−0.123877	−	0.991923i
$587$			330673.i			0.959673i	0.877358	+	0.479836i	$0.159304\pi$
$587$			330673.i			0.959673i	−0.877358	+	0.479836i	$0.840696\pi$
$588$	−192727.	−	759581.i	−0.557427	−	2.19695i
$589$			621878.i			1.79256i
$590$	113578.	+	90840.3i	0.326281	+	0.260960i
$591$			488569.i			1.39879i
$592$	−260760.	+	141429.i	−0.744042	+	0.403548i
$593$		−	499960.i		−	1.42176i	−0.703314	−	0.710879i	$-0.748297\pi$
$593$		−	499960.i		−	1.42176i	0.703314	−	0.710879i	$-0.251703\pi$
$594$	167181.	−	20878.4i	0.473820	−	0.0591732i
$595$	223958.	+	230071.i	0.632604	+	0.649873i
$596$	−40411.4	−	159271.i	−0.113766	−	0.448377i
$597$	−302469.			−0.848657
$598$	19394.1	+	155295.i	0.0542334	+	0.434265i
$599$		−	407848.i		−	1.13670i	−0.822788	−	0.568348i	$-0.807583\pi$
$599$		−	407848.i		−	1.13670i	0.822788	−	0.568348i	$-0.192417\pi$
$600$	138335.	+	383973.i	0.384265	+	1.06659i
$601$	441217.			1.22153			0.610763	−	0.791813i	$-0.290863\pi$
$601$	441217.			1.22153			0.610763	+	0.791813i	$0.290863\pi$
$602$	456072.	−	56956.7i	1.25846	−	0.157164i
$603$			15182.6i			0.0417553i
$604$	57998.8	+	228587.i	0.158981	+	0.626580i
$605$	−171196.	+	166647.i	−0.467718	+	0.455290i
$606$	−2714.33	−	21734.6i	−0.00739124	−	0.0591842i
$607$	−71921.7			−0.195201			−0.0976006	−	0.995226i	$-0.531117\pi$
$607$	−71921.7			−0.195201			−0.0976006	+	0.995226i	$0.531117\pi$
$608$	219604.	+	306822.i	0.594064	+	0.830001i
$609$	−335613.			−0.904908
$610$	−332590.	+	415840.i	−0.893818	+	1.11755i
$611$	−98506.9			−0.263866
$612$	13761.1	+	54235.7i	0.0367410	+	0.144805i
$613$	527274.			1.40319			0.701593	−	0.712577i	$-0.252472\pi$
$613$	527274.			1.40319			0.701593	+	0.712577i	$0.252472\pi$
$614$	−96769.6	+	12085.1i	−0.256686	+	0.0320563i
$615$	−452998.	−	465363.i	−1.19769	−	1.23039i
$616$	141024.	+	360673.i	0.371648	+	0.950499i
$617$		−	91867.0i		−	0.241318i	−0.992694	−	0.120659i	$-0.961499\pi$
$617$		−	91867.0i		−	0.241318i	0.992694	−	0.120659i	$-0.0385007\pi$
$618$	127179.	−	15882.8i	0.332996	−	0.0415863i
$619$	−633381.			−1.65304			−0.826521	−	0.562906i	$-0.809683\pi$
$619$	−633381.			−1.65304			−0.826521	+	0.562906i	$0.809683\pi$
$620$	575399.	+	353079.i	1.49687	+	0.918520i
$621$			211488.i			0.548405i
$622$	576735.	−	72025.7i	1.49072	−	0.186169i
$623$	434231.			1.11878
$624$	−136088.	−	250913.i	−0.349503	−	0.644397i
$625$	−390059.	−	21027.4i	−0.998550	−	0.0538300i
$626$	61.0469	−	7.62386i	0.000155781	−	1.94548e-5i
$627$		−	268081.i		−	0.681915i
$628$	430211.	−	109157.i	1.09084	−	0.276777i
$629$		−	175372.i		−	0.443261i
$630$	153134.	+	122477.i	0.385826	+	0.308584i
$631$			128753.i			0.323368i	0.986843	+	0.161684i	$0.0516926\pi$
$631$			128753.i			0.323368i	−0.986843	+	0.161684i	$0.948307\pi$
$632$	−137518.	+	53770.1i	−0.344292	+	0.134619i
$633$			200531.i			0.500465i
$634$	9850.91	+	78879.6i	0.0245074	+	0.196239i
$635$	−195052.	+	189869.i	−0.483730	+	0.470877i
$636$	136889.	+	539510.i	0.338418	+	1.33378i
$637$	−524565.			−1.29277
$638$	109703.	−	13700.3i	0.269511	−	0.0336579i
$639$		−	155785.i		−	0.381525i
$640$	408573.	−	28988.7i	0.997492	−	0.0707733i
$641$	391151.			0.951980			0.475990	−	0.879451i	$-0.342090\pi$
$641$	391151.			0.951980			0.475990	+	0.879451i	$0.342090\pi$
$642$	84480.0	+	676461.i	0.204967	+	1.64124i
$643$		−	720581.i		−	1.74285i	−0.490525	−	0.871427i	$-0.663195\pi$
$643$		−	720581.i		−	1.74285i	0.490525	−	0.871427i	$-0.336805\pi$
$644$	−471189.	+	119554.i	−1.13612	+	0.288265i
$645$	−247495.	+	240918.i	−0.594903	+	0.579096i
$646$	−221343.	+	27642.5i	−0.530397	+	0.0662388i
$647$	403682.			0.964341			0.482171	−	0.876077i	$-0.339849\pi$
$647$	403682.			0.964341			0.482171	+	0.876077i	$0.339849\pi$
$648$	−184088.	−	470810.i	−0.438405	−	1.12123i
$649$	−103705.			−0.246212
$650$	271906.	−	26544.1i	0.643563	−	0.0628262i
$651$	1.46132e6			3.44814
$652$	14689.1	+	57893.1i	0.0345541	+	0.136186i
$653$	−404377.			−0.948332			−0.474166	−	0.880436i	$-0.657250\pi$
$653$	−404377.			−0.948332			−0.474166	+	0.880436i	$0.657250\pi$
$654$	−79861.2	−	639476.i	−0.186716	−	1.49510i
$655$	−163112.	+	158778.i	−0.380192	+	0.370090i
$656$	−572930.	+	310742.i	−1.33136	+	0.722091i
$657$		−	95439.1i		−	0.221104i
$658$	−37917.8	−	303621.i	−0.0875772	−	0.701261i
$659$	179720.			0.413834			0.206917	−	0.978359i	$-0.433657\pi$
$659$	179720.			0.413834			0.206917	+	0.978359i	$0.433657\pi$
$660$	−248044.	−	152206.i	−0.569432	−	0.349418i
$661$		−	512413.i		−	1.17278i	−0.810028	−	0.586391i	$-0.800548\pi$
$661$		−	512413.i		−	1.17278i	0.810028	−	0.586391i	$-0.199452\pi$
$662$	27354.1	+	219034.i	0.0624176	+	0.499799i
$663$	168750.			0.383898
$664$	127922.	−	50018.0i	0.290142	−	0.113446i
$665$	−560144.	+	545260.i	−1.26665	+	1.23299i
$666$	−13272.6	−	106278.i	−0.0299232	−	0.239605i
$667$			138776.i			0.311935i
$668$	−321298.	+	81522.3i	−0.720037	+	0.182694i
$669$		−	622174.i		−	1.39014i
$670$	−41039.3	+	51311.8i	−0.0914218	+	0.114306i
$671$		−	379690.i		−	0.843304i
$672$	720987.	−	516038.i	1.59657	−	1.14273i
$673$		−	136431.i		−	0.301220i	−0.988593	−	0.150610i	$-0.951876\pi$
$673$		−	136431.i		−	0.301220i	0.988593	−	0.150610i	$-0.0481238\pi$
$674$	684716.	−	85511.0i	1.50727	−	0.188236i
$675$	369052.	+	9940.24i	0.809990	+	0.0218167i
$676$	257738.	−	65395.3i	0.564007	−	0.143104i
$677$	−185710.			−0.405190			−0.202595	−	0.979263i	$-0.564937\pi$
$677$	−185710.			−0.405190			−0.202595	+	0.979263i	$0.564937\pi$
$678$	−22561.1	−	180655.i	−0.0490796	−	0.392997i
$679$		−	778138.i		−	1.68778i
$680$	−100094.	+	220495.i	−0.216466	+	0.476848i
$681$	−27529.9			−0.0593623
$682$	−477667.	+	59653.6i	−1.02697	+	0.128253i
$683$			521505.i			1.11794i	0.829189	+	0.558968i	$0.188802\pi$
$683$			521505.i			1.11794i	−0.829189	+	0.558968i	$0.811198\pi$
$684$	−132045.	+	33503.6i	−0.282235	+	0.0716109i
$685$	−261156.	−	268284.i	−0.556568	−	0.571761i
$686$	−100922.	−	808116.i	−0.214455	−	1.71722i
$687$	703020.			1.48955
$688$	165262.	+	304702.i	0.349137	+	0.643723i
$689$	372584.			0.784849
$690$	228172.	−	285286.i	0.479253	−	0.599215i
$691$	−159485.			−0.334012			−0.167006	−	0.985956i	$-0.553410\pi$
$691$	−159485.			−0.334012			−0.167006	+	0.985956i	$0.553410\pi$
$692$	−548007.	+	139045.i	−1.14439	+	0.290363i
$693$	−139822.			−0.291144
$694$	213367.	−	26646.5i	0.443005	−	0.0553249i
$695$	458576.	−	446391.i	0.949383	−	0.924156i
$696$	−92172.8	−	235734.i	−0.190276	−	0.486636i
$697$		−	385320.i		−	0.793152i
$698$	403745.	−	50421.8i	0.828698	−	0.103492i
$699$	−854739.			−1.74936
$700$	186478.	+	827858.i	0.380568	+	1.68951i
$701$			924458.i			1.88127i	0.339418	+	0.940635i	$0.389770\pi$
$701$			924458.i			1.88127i	−0.339418	+	0.940635i	$0.610230\pi$
$702$	−256213.	+	31997.3i	−0.519909	+	0.0649290i
$703$	426971.			0.863949
$704$	−214605.	+	198110.i	−0.433007	+	0.399726i
$705$	160386.	+	164765.i	0.322693	+	0.331502i
$706$	−474206.	+	59221.3i	−0.951387	+	0.118814i
$707$		−	45542.2i		−	0.0911120i
$708$	58392.5	+	230138.i	0.116490	+	0.459116i
$709$			49979.9i			0.0994267i	0.998764	+	0.0497134i	$0.0158308\pi$
$709$			49979.9i			0.0994267i	−0.998764	+	0.0497134i	$0.984169\pi$
$710$	421093.	−	526496.i	0.835336	−	1.04443i
$711$		−	53311.7i		−	0.105459i
$712$	119257.	+	305004.i	0.235248	+	0.601652i
$713$		−	604259.i		−	1.18862i
$714$	64956.0	+	520125.i	0.127416	+	1.02026i
$715$	−139590.	+	135881.i	−0.273050	+	0.265795i
$716$	−367084.	+	93139.6i	−0.716044	+	0.181680i
$717$	373470.			0.726469
$718$	263349.	−	32888.4i	0.510838	−	0.0637961i
$719$			823502.i			1.59297i	0.604659	+	0.796484i	$0.293309\pi$
$719$			823502.i			1.59297i	−0.604659	+	0.796484i	$0.706691\pi$
$720$	−43971.0	+	141198.i	−0.0848205	+	0.272374i
$721$	266489.			0.512635
$722$	−2701.12	−	21628.8i	−0.00518166	−	0.0414914i
$723$			497471.i			0.951681i
$724$	−29612.9	−	116711.i	−0.0564942	−	0.222657i
$725$	242168.	+	6522.70i	0.460725	+	0.0124094i
$726$	−387026.	+	48333.9i	−0.734289	+	0.0917019i
$727$	−791865.			−1.49824			−0.749122	−	0.662432i	$-0.769524\pi$
$727$	−791865.			−1.49824			−0.749122	+	0.662432i	$0.769524\pi$
$728$	−216127.	−	552749.i	−0.407798	−	1.04295i
$729$	−305673.			−0.575177
$730$	257976.	−	322550.i	0.484099	−	0.605274i
$731$	−204925.			−0.383496
$732$	−842595.	+	213790.i	−1.57252	+	0.398993i
$733$	−586208.			−1.09105			−0.545524	−	0.838095i	$-0.683669\pi$
$733$	−586208.			−1.09105			−0.545524	+	0.838095i	$0.683669\pi$
$734$	−72614.9	−	581452.i	−0.134782	−	1.07925i
$735$	854084.	+	877398.i	1.58098	+	1.62413i
$736$	−213382.	−	298129.i	−0.393915	−	0.550362i
$737$		−	46851.1i		−	0.0862551i
$738$	−29162.0	−	233510.i	−0.0535432	−	0.428739i
$739$	51496.3			0.0942947			0.0471474	−	0.998888i	$-0.484987\pi$
$739$	51496.3			0.0942947			0.0471474	+	0.998888i	$0.484987\pi$
$740$	242419.	−	395060.i	0.442693	−	0.721438i
$741$			410847.i			0.748245i
$742$	143417.	+	1.14839e6i	0.260491	+	2.08584i
$743$	−333510.			−0.604132			−0.302066	−	0.953287i	$-0.597676\pi$
$743$	−333510.			−0.604132			−0.302066	+	0.953287i	$0.597676\pi$
$744$	401338.	+	1.02643e6i	0.725044	+	1.85432i
$745$	179086.	+	183975.i	0.322663	+	0.331471i
$746$	56074.9	+	449011.i	0.100761	+	0.806825i
$747$			49591.6i			0.0888724i
$748$	−42464.7	−	167363.i	−0.0758970	−	0.299127i
$749$			1.41744e6i			2.52663i
$750$	−487108.	−	411576.i	−0.865970	−	0.731691i
$751$		−	315513.i		−	0.559419i	−0.960085	−	0.279710i	$-0.909762\pi$
$751$		−	315513.i		−	0.559419i	0.960085	−	0.279710i	$-0.0902382\pi$
$752$	202849.	−	110020.i	0.358705	−	0.194552i
$753$			768505.i			1.35537i
$754$	−168125.	+	20996.3i	−0.295726	+	0.0369318i
$755$	−257026.	−	264042.i	−0.450903	−	0.463211i
$756$	−197246.	−	777391.i	−0.345115	−	1.36018i
$757$	559184.			0.975806			0.487903	−	0.872898i	$-0.337762\pi$
$757$	559184.			0.975806			0.487903	+	0.872898i	$0.337762\pi$
$758$	−21608.2	−	173024.i	−0.0376080	−	0.301140i
$759$			260486.i			0.452168i
$760$	−536828.	−	243695.i	−0.929412	−	0.421909i
$761$	−432702.			−0.747170			−0.373585	−	0.927596i	$-0.621872\pi$
$761$	−432702.			−0.747170			−0.373585	+	0.927596i	$0.621872\pi$
$762$	−440957.	+	55069.1i	−0.759428	+	0.0948414i
$763$		−	1.33995e6i		−	2.30165i
$764$	−113822.	−	448598.i	−0.195002	−	0.768548i
$765$	−60983.4	−	62648.1i	−0.104205	−	0.107050i
$766$	49269.8	+	394520.i	0.0839698	+	0.672375i
$767$	158933.			0.270161
$768$	560477.	+	364696.i	0.950244	+	0.618313i
$769$	258310.			0.436805			0.218403	−	0.975859i	$-0.429915\pi$
$769$	258310.			0.436805			0.218403	+	0.975859i	$0.429915\pi$
$770$	−472548.	−	377945.i	−0.797011	−	0.637451i
$771$	−277433.			−0.466712
$772$	−192594.	−	759059.i	−0.323154	−	1.27362i
$773$	280428.			0.469312			0.234656	−	0.972078i	$-0.424604\pi$
$773$	280428.			0.469312			0.234656	+	0.972078i	$0.424604\pi$
$774$	−124188.	+	15509.2i	−0.207299	+	0.0258886i
$775$	−1.05445e6	−	28401.1i	−1.75558	−	0.0472859i
$776$	546563.	−	213708.i	0.907647	−	0.354893i
$777$		−	1.00332e6i		−	1.66187i
$778$	396504.	−	49517.5i	0.655071	−	0.0818087i
$779$	938122.			1.54591
$780$	380141.	+	233264.i	0.624820	+	0.383406i
$781$			480727.i			0.788127i
$782$	215072.	−	26859.4i	0.351699	−	0.0439220i
$783$	−228960.			−0.373453
$784$	1.08021e6	−	585874.i	1.75741	−	0.953173i
$785$	−496940.	+	483735.i	−0.806426	+	0.784998i
$786$	−368750.	+	46051.4i	−0.596880	+	0.0745415i
$787$			1.17964e6i			1.90459i	0.305177	+	0.952296i	$0.401284\pi$
$787$			1.17964e6i			1.90459i	−0.305177	+	0.952296i	$0.598716\pi$
$788$	−742605.	+	188420.i	−1.19593	+	0.303440i
$789$		−	491136.i		−	0.788947i
$790$	144104.	−	180175.i	0.230899	−	0.288695i
$791$		−	378540.i		−	0.605005i
$792$	−38400.7	−	98210.7i	−0.0612193	−	0.156570i
$793$			581894.i			0.925332i
$794$	−27379.2	−	219235.i	−0.0434291	−	0.347751i
$795$	−606633.	−	623192.i	−0.959824	−	0.986024i
$796$	−116649.	−	459740.i	−0.184100	−	0.725582i
$797$	−627511.			−0.987881			−0.493940	−	0.869496i	$-0.664444\pi$
$797$	−627511.			−0.987881			−0.493940	+	0.869496i	$0.664444\pi$
$798$	−1.26633e6	+	158146.i	−1.98856	+	0.248343i
$799$			136425.i			0.213698i
$800$	−530272.	+	358345.i	−0.828550	+	0.559914i
$801$	−118241.			−0.184290
$802$	20169.1	+	161501.i	0.0313572	+	0.251088i
$803$			294510.i			0.456740i
$804$	−103970.	+	26380.2i	−0.160841	+	0.0408099i
$805$	544274.	−	529812.i	0.839897	−	0.817579i
$806$	732048.	−	91422.1i	1.12686	−	0.140728i
$807$	590326.			0.906453
$808$	31988.8	−	12507.7i	0.0489977	−	0.0191582i
$809$	−328656.			−0.502163			−0.251081	−	0.967966i	$-0.580786\pi$
$809$	−328656.			−0.502163			−0.251081	+	0.967966i	$0.580786\pi$
$810$	616848.	+	493356.i	0.940174	+	0.751953i
$811$	510808.			0.776634			0.388317	−	0.921526i	$-0.373057\pi$
$811$	510808.			0.776634			0.388317	+	0.921526i	$0.373057\pi$
$812$	−129431.	−	510118.i	−0.196303	−	0.773675i
$813$	1.37888e6			2.08616
$814$	40957.2	+	327958.i	0.0618132	+	0.494960i
$815$	−65095.8	−	66872.7i	−0.0980026	−	0.100678i
$816$	−347496.	+	188472.i	−0.521879	+	0.283053i
$817$		−	498923.i		−	0.747462i
$818$	155550.	+	1.24554e6i	0.232468	+	1.86145i
$819$	214284.			0.319464
$820$	532631.	−	868007.i	0.792135	−	1.29091i
$821$			37920.6i			0.0562586i	0.999604	+	0.0281293i	$0.00895502\pi$
$821$			37920.6i			0.0562586i	−0.999604	+	0.0281293i	$0.991045\pi$
$822$	−75744.7	−	606514.i	−0.112101	−	0.897630i
$823$	−449975.			−0.664337			−0.332168	−	0.943220i	$-0.607780\pi$
$823$	−449975.			−0.664337			−0.332168	+	0.943220i	$0.607780\pi$
$824$	73188.5	+	187182.i	0.107793	+	0.275682i
$825$	454554.	+	12243.2i	0.667849	+	0.0179882i
$826$	61177.3	+	489867.i	0.0896664	+	0.717990i
$827$			41920.8i			0.0612940i	0.999530	+	0.0306470i	$0.00975678\pi$
$827$			41920.8i			0.0612940i	−0.999530	+	0.0306470i	$0.990243\pi$
$828$	128304.	−	32554.4i	0.187146	−	0.0474842i
$829$		−	1.28858e6i		−	1.87500i	−0.347985	−	0.937500i	$-0.613134\pi$
$829$		−	1.28858e6i		−	1.87500i	0.347985	−	0.937500i	$-0.386866\pi$
$830$	−134048.	+	167602.i	−0.194583	+	0.243289i
$831$			679808.i			0.984429i
$832$	328894.	−	303614.i	0.475126	−	0.438607i
$833$			726484.i			1.04697i
$834$	1.03671e6	−	129470.i	1.49047	−	0.186138i
$835$	371134.	−	361272.i	0.532301	−	0.518157i
$836$	407471.	−	103387.i	0.583021	−	0.147929i
$837$	996936.			1.42304
$838$	−131004.	−	1.04900e6i	−0.186551	−	1.49378i
$839$		−	506198.i		−	0.719112i	−0.933124	−	0.359556i	$-0.882928\pi$
$839$		−	506198.i		−	0.719112i	0.933124	−	0.359556i	$-0.117072\pi$
$840$	−572647.	+	1.26147e6i	−0.811575	+	1.78780i
$841$	557039.			0.787579
$842$	713514.	−	89107.4i	1.00642	−	0.125687i
$843$			719519.i			1.01248i
$844$	−304799.	+	77335.9i	−0.427886	+	0.108567i
$845$	−297715.	+	289804.i	−0.416953	+	0.405874i
$846$	10325.0	+	82675.6i	0.0144261	+	0.115514i
$847$	−810968.			−1.13041
$848$	−767241.	+	416130.i	−1.06694	+	0.578679i
$849$	−56941.5			−0.0789975
$850$	−36761.6	−	376569.i	−0.0508811	−	0.521203i
$851$	−414874.			−0.572872
$852$	1.06681e6	−	270680.i	1.46963	−	0.372887i
$853$	−656590.			−0.902395			−0.451197	−	0.892424i	$-0.649003\pi$
$853$	−656590.			−0.902395			−0.451197	+	0.892424i	$0.649003\pi$
$854$	−1.79353e6	+	223986.i	−2.45920	+	0.307118i
$855$	152527.	−	148474.i	0.208648	−	0.203103i
$856$	−995611.	+	389287.i	−1.35876	+	0.531279i
$857$		−	388067.i		−	0.528379i	−0.964471	−	0.264189i	$-0.914896\pi$
$857$		−	388067.i		−	0.528379i	0.964471	−	0.264189i	$-0.0851044\pi$
$858$	−315573.	+	39410.5i	−0.428673	+	0.0535349i
$859$	282145.			0.382372			0.191186	−	0.981554i	$-0.438767\pi$
$859$	282145.			0.382372			0.191186	+	0.981554i	$0.438767\pi$
$860$	−461633.	−	283270.i	−0.624166	−	0.383004i
$861$		−	2.20445e6i		−	2.97368i
$862$	−599634.	+	74885.5i	−0.806997	+	0.100782i
$863$	1.01110e6			1.35761			0.678804	−	0.734320i	$-0.262499\pi$
$863$	1.01110e6			1.35761			0.678804	+	0.734320i	$0.262499\pi$
$864$	491868.	−	352048.i	0.658902	−	0.471601i
$865$	633007.	−	616186.i	0.846011	−	0.823531i
$866$	530445.	−	66244.8i	0.707301	−	0.0883316i
$867$			618484.i			0.822792i
$868$	563568.	+	2.22115e6i	0.748009	+	2.94807i
$869$			164512.i			0.217850i
$870$	308856.	+	247023.i	0.408054	+	0.326362i
$871$			71801.7i			0.0946452i
$872$	941178.	−	368003.i	1.23777	−	0.483970i
$873$			211886.i			0.278018i
$874$	65393.3	+	523627.i	0.0856072	+	0.685487i
$875$	−898955.	−	974676.i	−1.17414	−	1.27305i
$876$	653567.	−	165828.i	0.851691	−	0.216098i
$877$	190192.			0.247283			0.123641	−	0.992327i	$-0.460543\pi$
$877$	190192.			0.247283			0.123641	+	0.992327i	$0.460543\pi$
$878$	−296152.	+	36985.0i	−0.384172	+	0.0479774i
$879$			875617.i			1.13328i
$880$	135688.	−	435716.i	0.175216	−	0.562650i
$881$	237801.			0.306380			0.153190	−	0.988197i	$-0.451045\pi$
$881$	237801.			0.306380			0.153190	+	0.988197i	$0.451045\pi$
$882$	54982.1	+	440261.i	0.0706780	+	0.565943i
$883$		−	175861.i		−	0.225552i	−0.993620	−	0.112776i	$-0.964026\pi$
$883$		−	175861.i		−	0.225552i	0.993620	−	0.112776i	$-0.0359743\pi$
$884$	65079.3	+	256492.i	0.0832795	+	0.328224i
$885$	−258770.	−	265834.i	−0.330391	−	0.339410i
$886$	438807.	−	54800.5i	0.558992	−	0.0698099i
$887$	−1.36691e6			−1.73738			−0.868688	−	0.495360i	$-0.835036\pi$
$887$	−1.36691e6			−1.73738			−0.868688	+	0.495360i	$0.835036\pi$
$888$	704732.	−	275552.i	0.893713	−	0.349445i
$889$	−923974.			−1.16911
$890$	−399611.	−	319610.i	−0.504496	−	0.403497i
$891$	−563224.			−0.709456
$892$	945678.	−	239945.i	1.18854	−	0.301566i
$893$	−332148.			−0.416513
$894$	51941.6	+	415914.i	0.0649891	+	0.520390i
$895$	424022.	−	412755.i	0.529349	−	0.515283i
$896$	1.06241e6	+	896857.i	1.32335	+	1.11714i
$897$		−	399207.i		−	0.496151i
$898$	−4819.47	−	38591.2i	−0.00597650	−	0.0478559i
$899$	654181.			0.809428
$900$	−50777.8	−	225425.i	−0.0626886	−	0.278302i
$901$		−	516002.i		−	0.635626i
$902$	89989.3	+	720575.i	0.110606	+	0.885659i
$903$	−1.17240e6			−1.43780
$904$	265887.	−	103962.i	0.325356	−	0.127215i
$905$	131232.	+	134814.i	0.160229	+	0.164603i
$906$	−74547.0	−	596923.i	−0.0908183	−	0.727214i
$907$			699123.i			0.849843i	0.905230	+	0.424922i	$0.139698\pi$
$907$			699123.i			0.849843i	−0.905230	+	0.424922i	$0.860302\pi$
$908$	−10617.1	−	41844.3i	−0.0128775	−	0.0507534i
$909$			12401.1i			0.0150083i
$910$	724204.	+	579220.i	0.874537	+	0.699456i
$911$			1.27217e6i			1.53288i	0.642315	+	0.766441i	$0.277974\pi$
$911$			1.27217e6i			1.53288i	−0.642315	+	0.766441i	$0.722026\pi$
$912$	−458865.	−	846033.i	−0.551690	−	1.01718i
$913$		−	153032.i		−	0.183586i
$914$	−1.31629e6	+	164386.i	−1.57565	+	0.196776i
$915$	973288.	−	947426.i	1.16252	−	1.13163i
$916$	271124.	+	1.06856e6i	0.323130	+	1.27353i
$917$	−772672.			−0.918875
$918$	44313.9	+	354837.i	0.0525841	+	0.421059i
$919$			507149.i			0.600488i	0.953862	+	0.300244i	$0.0970681\pi$
$919$			507149.i			0.600488i	−0.953862	+	0.300244i	$0.902932\pi$
$920$	521619.	+	236790.i	0.616280	+	0.279762i
$921$	248760.			0.293265
$922$	−344424.	+	43013.4i	−0.405164	+	0.0505991i
$923$		−	736738.i		−	0.864788i
$924$	−242944.	−	957500.i	−0.284553	−	1.12149i
$925$	−19499.7	+	723967.i	−0.0227900	+	0.846127i
$926$	17678.7	+	141560.i	0.0206172	+	0.165089i
$927$	−72564.6			−0.0844433
$928$	322759.	−	231011.i	0.374786	−	0.268248i
$929$	−31736.2			−0.0367725			−0.0183862	−	0.999831i	$-0.505853\pi$
$929$	−31736.2			−0.0367725			−0.0183862	+	0.999831i	$0.505853\pi$
$930$	−1.34482e6	−	1.07559e6i	−1.55488	−	1.24360i
$931$	−1.76874e6			−2.04063
$932$	−329635.	−	1.29917e6i	−0.379491	−	1.49566i
$933$	−1.48258e6			−1.70315
$934$	−1.16581e6	+	145593.i	−1.33640	+	0.166896i
$935$	188185.	+	193322.i	0.215260	+	0.221135i
$936$	58851.0	+	150513.i	0.0671742	+	0.171800i
$937$			1.23459e6i			1.40619i	0.711096	+	0.703094i	$0.248199\pi$
$937$			1.23459e6i			1.40619i	−0.711096	+	0.703094i	$0.751801\pi$
$938$	−221309.	+	27638.3i	−0.251532	+	0.0314127i
$939$	−156.930			−0.000177981
$940$	−188581.	+	307323.i	−0.213424	+	0.347808i
$941$			126651.i			0.143031i	0.997439	+	0.0715156i	$0.0227836\pi$
$941$			126651.i			0.143031i	−0.997439	+	0.0715156i	$0.977216\pi$
$942$	−1.12344e6	+	140301.i	−1.26604	+	0.158110i
$943$	−911544.			−1.02507
$944$	−327281.	+	177508.i	−0.367263	+	0.199193i
$945$	874110.	+	897970.i	0.978819	+	1.00554i
$946$	383224.	−	47859.1i	0.428224	−	0.0534789i
$947$			213933.i			0.238549i	0.992861	+	0.119275i	$0.0380569\pi$
$947$			213933.i			0.238549i	−0.992861	+	0.119275i	$0.961943\pi$
$948$	365079.	−	92630.6i	0.406228	−	0.103071i
$949$		−	451352.i		−	0.501168i
$950$	916817.	−	89501.9i	1.01586	−	0.0991711i
$951$		−	202771.i		−	0.224205i
$952$	−765517.	+	299320.i	−0.844659	+	0.330264i
$953$		−	281174.i		−	0.309592i	−0.987946	−	0.154796i	$-0.950528\pi$
$953$		−	281174.i		−	0.309592i	0.987946	−	0.154796i	$-0.0494720\pi$
$954$	−39052.3	−	312705.i	−0.0429092	−	0.343588i
$955$	504410.	+	518179.i	0.553066	+	0.568163i
$956$	144031.	+	567658.i	0.157594	+	0.621113i
$957$	−282006.			−0.307918
$958$	1.72869e6	−	215888.i	1.88359	−	0.235233i
$959$		−	1.27088e6i		−	1.38187i
$960$	−1.04333e6	−	55776.8i	−1.13208	−	0.0605217i
$961$	−1.92491e6			−2.08431
$962$	−62769.0	−	502613.i	−0.0678258	−	0.543104i
$963$		−	385968.i		−	0.416197i
$964$	−756135.	+	191853.i	−0.813665	+	0.206449i
$965$	853496.	+	876794.i	0.916530	+	0.941549i
$966$	1.23045e6	−	153665.i	1.31859	−	0.164672i
$967$	1.15290e6			1.23293			0.616467	−	0.787381i	$-0.288563\pi$
$967$	1.15290e6			1.23293			0.616467	+	0.787381i	$0.288563\pi$
$968$	−222724.	−	569623.i	−0.237693	−	0.607907i
$969$	568994.			0.605982
$970$	−572738.	+	716099.i	−0.608712	+	0.761079i
$971$	857201.			0.909169			0.454584	−	0.890704i	$-0.349788\pi$
$971$	857201.			0.909169			0.454584	+	0.890704i	$0.349788\pi$
$972$	128857.	+	507856.i	0.136388	+	0.537537i
$973$	2.17230e6			2.29453
$974$	−92835.8	−	743368.i	−0.0978583	−	0.783585i
$975$	−696628.	−	18763.4i	−0.732810	−	0.0197379i
$976$	−649903.	−	1.19826e6i	−0.682259	−	1.25792i
$977$		−	1.68459e6i		−	1.76484i	−0.470464	−	0.882419i	$-0.655914\pi$
$977$		−	1.68459e6i		−	1.76484i	0.470464	−	0.882419i	$-0.344086\pi$
$978$	−18880.2	−	151180.i	−0.0197391	−	0.158058i
$979$	364872.			0.380693
$980$	−1.00423e6	+	1.63654e6i	−1.04563	+	1.70402i
$981$			364866.i			0.379136i
$982$	142597.	+	1.14183e6i	0.147873	+	1.18407i
$983$	501269.			0.518756			0.259378	−	0.965776i	$-0.416482\pi$
$983$	501269.			0.518756			0.259378	+	0.965776i	$0.416482\pi$
$984$	1.54841e6	−	605432.i	1.59917	−	0.625281i
$985$	857788.	−	834995.i	0.884112	−	0.860620i
$986$	29078.4	+	232841.i	0.0299100	+	0.239500i
$987$			780500.i			0.801195i
$988$	−624471.	+	158446.i	−0.639732	+	0.162318i
$989$			484787.i			0.495631i
$990$	128674.	+	102914.i	0.131287	+	0.105003i
$991$		−	650776.i		−	0.662650i	−0.943517	−	0.331325i	$-0.892504\pi$
$991$		−	650776.i		−	0.662650i	0.943517	−	0.331325i	$-0.107496\pi$
$992$	−1.40536e6	+	1.00587e6i	−1.42811	+	1.02216i
$993$		−	563058.i		−	0.571024i
$994$	2.27080e6	−	283589.i	2.29829	−	0.287023i
$995$	516938.	+	531049.i	0.522146	+	0.536400i
$996$	−339603.	+	86166.8i	−0.342336	+	0.0868603i
$997$	724549.			0.728916			0.364458	−	0.931220i	$-0.381254\pi$
$997$	724549.			0.728916			0.364458	+	0.931220i	$0.381254\pi$
$998$	−86959.2	−	696313.i	−0.0873081	−	0.699106i
$999$		−	684480.i		−	0.685851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.5.e.c.19.9	✓	20
4.3	odd	2		160.5.e.c.79.6		20
5.2	odd	4		200.5.g.i.51.19		20
5.3	odd	4		200.5.g.i.51.2		20
5.4	even	2	inner	40.5.e.c.19.12	yes	20
8.3	odd	2	inner	40.5.e.c.19.11	yes	20
8.5	even	2		160.5.e.c.79.5		20
20.3	even	4		800.5.g.i.751.16		20
20.7	even	4		800.5.g.i.751.5		20
20.19	odd	2		160.5.e.c.79.15		20
40.3	even	4		200.5.g.i.51.1		20
40.13	odd	4		800.5.g.i.751.15		20
40.19	odd	2	inner	40.5.e.c.19.10	yes	20
40.27	even	4		200.5.g.i.51.20		20
40.29	even	2		160.5.e.c.79.16		20
40.37	odd	4		800.5.g.i.751.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.5.e.c.19.9	✓	20	1.1	even	1	trivial
40.5.e.c.19.10	yes	20	40.19	odd	2	inner
40.5.e.c.19.11	yes	20	8.3	odd	2	inner
40.5.e.c.19.12	yes	20	5.4	even	2	inner
160.5.e.c.79.5		20	8.5	even	2
160.5.e.c.79.6		20	4.3	odd	2
160.5.e.c.79.15		20	20.19	odd	2
160.5.e.c.79.16		20	40.29	even	2
200.5.g.i.51.1		20	40.3	even	4
200.5.g.i.51.2		20	5.3	odd	4
200.5.g.i.51.19		20	5.2	odd	4
200.5.g.i.51.20		20	40.27	even	4
800.5.g.i.751.5		20	20.7	even	4
800.5.g.i.751.6		20	40.37	odd	4
800.5.g.i.751.15		20	40.13	odd	4
800.5.g.i.751.16		20	20.3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.495691 - 3.96917i) q^{2} +10.2033i q^{3} +(-15.5086 + 3.93496i) q^{4} +(17.9141 - 17.4381i) q^{5} +(40.4986 - 5.05768i) q^{6} +84.8600 q^{7} +(23.3060 + 59.6056i) q^{8} -23.1073 q^{9} +(-78.0944 - 62.4601i) q^{10} +71.3055 q^{11} +(-40.1496 - 158.239i) q^{12} -109.279 q^{13} +(-42.0643 - 336.824i) q^{14} +(177.926 + 182.783i) q^{15} +(225.032 - 122.051i) q^{16} +151.344i q^{17} +(11.4541 + 91.7167i) q^{18} -368.470 q^{19} +(-209.204 + 340.931i) q^{20} +865.852i q^{21} +(-35.3455 - 283.023i) q^{22} +358.031 q^{23} +(-608.174 + 237.798i) q^{24} +(16.8280 - 624.773i) q^{25} +(54.1687 + 433.748i) q^{26} +590.697i q^{27} +(-1316.06 + 333.921i) q^{28} +387.610i q^{29} +(637.299 - 796.821i) q^{30} -1687.73i q^{31} +(-595.988 - 832.691i) q^{32} +727.551i q^{33} +(600.709 - 75.0197i) q^{34} +(1520.19 - 1479.79i) q^{35} +(358.361 - 90.9262i) q^{36} -1158.77 q^{37} +(182.647 + 1462.52i) q^{38} -1115.01i q^{39} +(1456.91 + 661.369i) q^{40} -2545.99 q^{41} +(3436.71 - 429.195i) q^{42} +1354.04i q^{43} +(-1105.85 + 280.584i) q^{44} +(-413.946 + 402.946i) q^{45} +(-177.473 - 1421.08i) q^{46} +901.424 q^{47} +(1245.33 + 2296.07i) q^{48} +4800.23 q^{49} +(-2488.17 + 242.901i) q^{50} -1544.21 q^{51} +(1694.77 - 430.009i) q^{52} -3409.47 q^{53} +(2344.57 - 292.803i) q^{54} +(1277.37 - 1243.43i) q^{55} +(1977.75 + 5058.14i) q^{56} -3759.61i q^{57} +(1538.49 - 192.135i) q^{58} -1454.37 q^{59} +(-3478.62 - 2134.57i) q^{60} -5324.84i q^{61} +(-6698.88 + 836.592i) q^{62} -1960.88 q^{63} +(-3009.66 + 2778.33i) q^{64} +(-1957.64 + 1905.62i) q^{65} +(2887.77 - 360.640i) q^{66} -657.048i q^{67} +(-595.532 - 2347.13i) q^{68} +3653.09i q^{69} +(-6627.10 - 5300.36i) q^{70} +6741.79i q^{71} +(-538.538 - 1377.32i) q^{72} +4130.26i q^{73} +(574.391 + 4599.34i) q^{74} +(6374.75 + 171.701i) q^{75} +(5714.45 - 1449.91i) q^{76} +6050.98 q^{77} +(-4425.66 + 552.700i) q^{78} +2307.14i q^{79} +(1902.90 - 6110.56i) q^{80} -7898.74 q^{81} +(1262.03 + 10105.5i) q^{82} -2146.14i q^{83} +(-3407.09 - 13428.1i) q^{84} +(2639.14 + 2711.18i) q^{85} +(5374.41 - 671.184i) q^{86} -3954.90 q^{87} +(1661.84 + 4250.21i) q^{88} +5117.03 q^{89} +(1804.55 + 1443.28i) q^{90} -9273.44 q^{91} +(-5552.55 + 1408.84i) q^{92} +17220.4 q^{93} +(-446.827 - 3577.90i) q^{94} +(-6600.80 + 6425.40i) q^{95} +(8496.19 - 6081.05i) q^{96} -9169.66i q^{97} +(-2379.43 - 19052.9i) q^{98} -1647.68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 12 q^{6} - 652 q^{9} - 240 q^{10} - 168 q^{11} + 660 q^{14} + 280 q^{16} + 728 q^{19} + 900 q^{20} - 1232 q^{24} - 1420 q^{25} + 4680 q^{26} + 1540 q^{30} - 2312 q^{34} + 4440 q^{35} - 7868 q^{36}+ \cdots - 62504 q^{99}+O(q^{100}) \) 20 * q - 20 * q^4 + 12 * q^6 - 652 * q^9 - 240 * q^10 - 168 * q^11 + 660 * q^14 + 280 * q^16 + 728 * q^19 + 900 * q^20 - 1232 * q^24 - 1420 * q^25 + 4680 * q^26 + 1540 * q^30 - 2312 * q^34 + 4440 * q^35 - 7868 * q^36 - 4640 * q^40 - 4728 * q^41 + 1368 * q^44 - 6260 * q^46 + 540 * q^49 - 2280 * q^50 + 4352 * q^51 + 10688 * q^54 + 12960 * q^56 + 8280 * q^59 - 3480 * q^60 - 19040 * q^64 + 9480 * q^65 + 2632 * q^66 - 11020 * q^70 - 12000 * q^74 - 16000 * q^75 + 22472 * q^76 + 22440 * q^80 - 10956 * q^81 + 29000 * q^84 + 7740 * q^86 + 22248 * q^89 + 28520 * q^90 - 39760 * q^91 + 8540 * q^94 - 1328 * q^96 - 62504 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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