LMFDB - Embedded newform 507.2.q.b.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0277086 + 0.00223687i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.97334 - 0.320699i) q^{4} +(0.676752 + 0.599550i) q^{5} +(-0.0222235 - 0.0166999i) q^{6} +(-0.402242 + 0.418779i) q^{7} +(-0.107943 - 0.0266056i) q^{8} +(0.428693 + 0.903450i) q^{9} +(0.0174108 + 0.0181265i) q^{10} +(-0.912090 + 1.92219i) q^{11} +(1.49644 + 1.32573i) q^{12} +(3.31516 - 1.41764i) q^{13} +(-0.0120823 + 0.0107040i) q^{14} +(-0.251545 - 0.868434i) q^{15} +(3.78975 + 1.26520i) q^{16} +(4.44533 - 4.62808i) q^{17} +(0.00985759 + 0.0259923i) q^{18} +(1.16027 - 2.00966i) q^{19} +(-1.14319 - 1.40015i) q^{20} +(0.563794 - 0.138963i) q^{21} +(-0.0295725 + 0.0512210i) q^{22} +(0.130762 + 0.226487i) q^{23} +(0.0770127 + 0.0801787i) q^{24} +(-0.504150 - 4.15205i) q^{25} +(0.0950298 - 0.0318652i) q^{26} +(0.120537 - 0.992709i) q^{27} +(0.928062 - 0.697393i) q^{28} +(3.01090 + 0.243065i) q^{29} +(-0.00502740 - 0.0246258i) q^{30} +(0.367054 - 3.02296i) q^{31} +(0.306734 + 0.130687i) q^{32} +(1.79823 - 1.13713i) q^{33} +(0.133526 - 0.118294i) q^{34} +(-0.523297 + 0.0422449i) q^{35} +(-0.556220 - 1.92029i) q^{36} +(-3.92427 + 1.67198i) q^{37} +(0.0366450 - 0.0530894i) q^{38} +(-3.55962 - 0.573669i) q^{39} +(-0.0570994 - 0.0827227i) q^{40} +(6.99227 + 4.42165i) q^{41} +(0.0159328 - 0.00258934i) q^{42} +(6.36721 + 2.71282i) q^{43} +(2.41630 - 3.50062i) q^{44} +(-0.251545 + 0.868434i) q^{45} +(0.00311662 + 0.00656813i) q^{46} +(4.16030 - 10.9698i) q^{47} +(-2.52685 - 3.09483i) q^{48} +(0.268285 + 6.65742i) q^{49} +(-0.00468171 - 0.116175i) q^{50} +(-6.23070 + 1.53573i) q^{51} +(-6.99657 + 1.73431i) q^{52} +(12.8330 + 3.16306i) q^{53} +(0.00556047 - 0.0272370i) q^{54} +(-1.76971 + 0.754001i) q^{55} +(0.0545612 - 0.0345024i) q^{56} +(-2.05474 + 1.07841i) q^{57} +(0.0828843 + 0.0134700i) q^{58} +(0.448278 - 0.149657i) q^{59} +(0.217878 + 1.79438i) q^{60} +(1.59181 - 5.49556i) q^{61} +(0.0169325 - 0.0829411i) q^{62} +(-0.550784 - 0.183879i) q^{63} +(-7.06723 - 3.70917i) q^{64} +(3.09349 + 1.02822i) q^{65} +(0.0523702 - 0.0274860i) q^{66} +(-12.6346 + 2.05331i) q^{67} +(-10.2564 + 7.70715i) q^{68} +(0.0105305 - 0.261312i) q^{69} -0.0145944 q^{70} +(-0.309919 + 7.69056i) q^{71} +(-0.0222376 - 0.108927i) q^{72} +(-7.46656 - 10.8172i) q^{73} +(-0.112476 + 0.0375501i) q^{74} +(-1.79303 + 3.77872i) q^{75} +(-2.93411 + 3.59363i) q^{76} +(-0.438090 - 1.15515i) q^{77} +(-0.0973491 - 0.0238580i) q^{78} +(-4.60560 + 12.1440i) q^{79} +(1.80617 + 3.12837i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.183856 + 0.138159i) q^{82} +(14.0741 + 7.38664i) q^{83} +(-1.15712 + 0.0934125i) q^{84} +(5.78315 - 0.466864i) q^{85} +(0.170359 + 0.0894111i) q^{86} +(-2.41487 - 1.81466i) q^{87} +(0.149595 - 0.183220i) q^{88} +(-5.94029 - 10.2889i) q^{89} +(-0.00891255 + 0.0235005i) q^{90} +(-0.739824 + 1.95855i) q^{91} +(-0.185404 - 0.488870i) q^{92} +(-1.92590 + 2.35880i) q^{93} +(0.139814 - 0.294653i) q^{94} +(1.99011 - 0.664395i) q^{95} +(-0.189401 - 0.274394i) q^{96} +(0.310961 + 1.52319i) q^{97} +(-0.00745800 + 0.185068i) q^{98} -2.12761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	0.0277086	+	0.00223687i	0.0195930	+	0.00158171i	0.0902592	−	0.995918i	$-0.471230\pi$
$2$	0.0277086	+	0.00223687i	0.0195930	+	0.00158171i	−0.0706662	+	0.997500i	$0.522513\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−1.97334	−	0.320699i	−0.986669	−	0.160349i
$5$	0.676752	+	0.599550i	0.302653	+	0.268127i	0.800756	−	0.598991i	$-0.204431\pi$
$5$	0.676752	+	0.599550i	0.302653	+	0.268127i	−0.498103	+	0.867118i	$0.665970\pi$
$6$	−0.0222235	−	0.0166999i	−0.00907272	−	0.00681771i
$7$	−0.402242	+	0.418779i	−0.152033	+	0.158284i	−0.792864	−	0.609399i	$-0.791411\pi$
$7$	−0.402242	+	0.418779i	−0.152033	+	0.158284i	0.640830	+	0.767683i	$0.278590\pi$
$8$	−0.107943	−	0.0266056i	−0.0381637	−	0.00940650i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	0.0174108	+	0.0181265i	0.00550577	+	0.00573211i
$11$	−0.912090	+	1.92219i	−0.275005	+	0.579562i	−0.993219	−	0.116261i	$-0.962909\pi$
$11$	−0.912090	+	1.92219i	−0.275005	+	0.579562i	0.718213	+	0.695823i	$0.244960\pi$
$12$	1.49644	+	1.32573i	0.431986	+	0.382706i
$13$	3.31516	−	1.41764i	0.919461	−	0.393182i
$13$	3.31516	−	1.41764i	0.919461	−	0.393182i
$14$	−0.0120823	+	0.0107040i	−0.00322914	+	0.00286077i
$15$	−0.251545	−	0.868434i	−0.0649487	−	0.224229i
$16$	3.78975	+	1.26520i	0.947437	+	0.316301i
$17$	4.44533	−	4.62808i	1.07815	−	1.12247i	0.0861445	−	0.996283i	$-0.472545\pi$
$17$	4.44533	−	4.62808i	1.07815	−	1.12247i	0.992006	−	0.126191i	$-0.0402752\pi$
$18$	0.00985759	+	0.0259923i	0.00232346	+	0.00612645i
$19$	1.16027	−	2.00966i	0.266185	−	0.461046i	−0.701688	−	0.712484i	$-0.747570\pi$
$19$	1.16027	−	2.00966i	0.266185	−	0.461046i	0.967873	+	0.251438i	$0.0809034\pi$
$20$	−1.14319	−	1.40015i	−0.255624	−	0.313083i
$21$	0.563794	−	0.138963i	0.123030	−	0.0303242i
$22$	−0.0295725	+	0.0512210i	−0.00630487	+	0.0109204i
$23$	0.130762	+	0.226487i	0.0272658	+	0.0472257i	0.879336	−	0.476201i	$-0.157987\pi$
$23$	0.130762	+	0.226487i	0.0272658	+	0.0472257i	−0.852071	+	0.523427i	$0.824653\pi$
$24$	0.0770127	+	0.0801787i	0.0157202	+	0.0163664i
$25$	−0.504150	−	4.15205i	−0.100830	−	0.830410i
$26$	0.0950298	−	0.0318652i	0.0186369	−	0.00624928i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	0.928062	−	0.697393i	0.175387	−	0.131795i
$29$	3.01090	+	0.243065i	0.559110	+	0.0451360i	0.356792	−	0.934184i	$-0.383870\pi$
$29$	3.01090	+	0.243065i	0.559110	+	0.0451360i	0.202318	+	0.979320i	$0.435153\pi$
$30$	−0.00502740	−	0.0246258i	−0.000917873	−	0.00449604i
$31$	0.367054	−	3.02296i	0.0659248	−	0.542940i	−0.921907	−	0.387412i	$-0.873369\pi$
$31$	0.367054	−	3.02296i	0.0659248	−	0.542940i	0.987832	−	0.155528i	$-0.0497078\pi$
$32$	0.306734	+	0.130687i	0.0542234	+	0.0231024i
$33$	1.79823	−	1.13713i	0.313032	−	0.197950i
$34$	0.133526	−	0.118294i	0.0228996	−	0.0202873i
$35$	−0.523297	+	0.0422449i	−0.0884534	+	0.00714069i
$36$	−0.556220	−	1.92029i	−0.0927033	−	0.320049i
$37$	−3.92427	+	1.67198i	−0.645146	+	0.274871i	−0.689655	−	0.724138i	$-0.742238\pi$
$37$	−3.92427	+	1.67198i	−0.645146	+	0.274871i	0.0445089	+	0.999009i	$0.485828\pi$
$38$	0.0366450	−	0.0530894i	0.00594460	−	0.00861224i
$39$	−3.55962	−	0.573669i	−0.569996	−	0.0918606i
$40$	−0.0570994	−	0.0827227i	−0.00902820	−	0.0130796i
$41$	6.99227	+	4.42165i	1.09201	+	0.690545i	0.953976	−	0.299882i	$-0.0969474\pi$
$41$	6.99227	+	4.42165i	1.09201	+	0.690545i	0.138034	+	0.990428i	$0.455922\pi$
$42$	0.0159328	−	0.00258934i	0.00245849	−	0.000399543i
$43$	6.36721	+	2.71282i	0.970991	+	0.413701i	0.818438	−	0.574595i	$-0.194840\pi$
$43$	6.36721	+	2.71282i	0.970991	+	0.413701i	0.152553	+	0.988295i	$0.451251\pi$
$44$	2.41630	−	3.50062i	0.364272	−	0.527738i
$45$	−0.251545	+	0.868434i	−0.0374981	+	0.129459i
$46$	0.00311662	+	0.00656813i	0.000459520	+	0.000968418i
$47$	4.16030	−	10.9698i	0.606843	−	1.60011i	−0.180485	−	0.983578i	$-0.557767\pi$
$47$	4.16030	−	10.9698i	0.606843	−	1.60011i	0.787328	−	0.616535i	$-0.211464\pi$
$48$	−2.52685	−	3.09483i	−0.364719	−	0.446700i
$49$	0.268285	+	6.65742i	0.0383264	+	0.951060i
$50$	−0.00468171	−	0.116175i	−0.000662094	−	0.0164297i
$51$	−6.23070	+	1.53573i	−0.872472	+	0.215045i
$52$	−6.99657	+	1.73431i	−0.970250	+	0.240505i
$53$	12.8330	+	3.16306i	1.76275	+	0.434480i	0.981770	−	0.190071i	$-0.0608718\pi$
$53$	12.8330	+	3.16306i	1.76275	+	0.434480i	0.780984	+	0.624551i	$0.214718\pi$
$54$	0.00556047	−	0.0272370i	0.000756684	−	0.00370649i
$55$	−1.76971	+	0.754001i	−0.238627	+	0.101670i
$56$	0.0545612	−	0.0345024i	0.00729105	−	0.00461058i
$57$	−2.05474	+	1.07841i	−0.272158	+	0.142839i
$58$	0.0828843	+	0.0134700i	0.0108832	+	0.00176870i
$59$	0.448278	−	0.149657i	0.0583609	−	0.0194837i	−0.287338	−	0.957829i	$-0.592770\pi$
$59$	0.448278	−	0.149657i	0.0583609	−	0.0194837i	0.345699	+	0.938346i	$0.387642\pi$
$60$	0.217878	+	1.79438i	0.0281279	+	0.231654i
$61$	1.59181	−	5.49556i	0.203810	−	0.703634i	−0.791862	−	0.610700i	$-0.790888\pi$
$61$	1.59181	−	5.49556i	0.203810	−	0.703634i	0.995672	−	0.0929344i	$-0.0296247\pi$
$62$	0.0169325	−	0.0829411i	0.00215043	−	0.0105335i
$63$	−0.550784	−	0.183879i	−0.0693923	−	0.0231666i
$64$	−7.06723	−	3.70917i	−0.883404	−	0.463646i
$65$	3.09349	+	1.02822i	0.383700	+	0.127535i
$66$	0.0523702	−	0.0274860i	0.00644633	−	0.00338329i
$67$	−12.6346	+	2.05331i	−1.54356	+	0.250852i	−0.871778	−	0.489900i	$-0.837033\pi$
$67$	−12.6346	+	2.05331i	−1.54356	+	0.250852i	−0.671778	+	0.740753i	$0.734469\pi$
$68$	−10.2564	+	7.70715i	−1.24377	+	0.934629i
$69$	0.0105305	−	0.261312i	0.00126772	−	0.0314583i
$70$	−0.0145944			−0.00174436
$71$	−0.309919	+	7.69056i	−0.0367806	+	0.912702i	0.870498	+	0.492172i	$0.163797\pi$
$71$	−0.309919	+	7.69056i	−0.0367806	+	0.912702i	−0.907279	+	0.420530i	$0.861844\pi$
$72$	−0.0222376	−	0.108927i	−0.00262073	−	0.0128372i
$73$	−7.46656	−	10.8172i	−0.873895	−	1.26605i	−0.962855	−	0.270020i	$-0.912970\pi$
$73$	−7.46656	−	10.8172i	−0.873895	−	1.26605i	0.0889603	−	0.996035i	$-0.471646\pi$
$74$	−0.112476	+	0.0375501i	−0.0130751	+	0.00436511i
$75$	−1.79303	+	3.77872i	−0.207041	+	0.436329i
$76$	−2.93411	+	3.59363i	−0.336565	+	0.412218i
$77$	−0.438090	−	1.15515i	−0.0499250	−	0.131642i
$78$	−0.0973491	−	0.0238580i	−0.0110226	−	0.00270139i
$79$	−4.60560	+	12.1440i	−0.518170	+	1.36630i	0.379319	+	0.925266i	$0.376158\pi$
$79$	−4.60560	+	12.1440i	−0.518170	+	1.36630i	−0.897489	+	0.441036i	$0.854611\pi$
$80$	1.80617	+	3.12837i	0.201936	+	0.349763i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	0.183856	+	0.138159i	0.0203035	+	0.0152571i
$83$	14.0741	+	7.38664i	1.54483	+	0.810789i	0.999621	−	0.0275120i	$-0.00875844\pi$
$83$	14.0741	+	7.38664i	1.54483	+	0.810789i	0.545208	+	0.838301i	$0.316451\pi$
$84$	−1.15712	+	0.0934125i	−0.126252	+	0.0101921i
$85$	5.78315	−	0.466864i	0.627270	−	0.0506385i
$86$	0.170359	+	0.0894111i	0.0183702	+	0.00964145i
$87$	−2.41487	−	1.81466i	−0.258902	−	0.194552i
$88$	0.149595	−	0.183220i	0.0159469	−	0.0195314i
$89$	−5.94029	−	10.2889i	−0.629670	−	1.09062i	−0.987618	−	0.156878i	$-0.949857\pi$
$89$	−5.94029	−	10.2889i	−0.629670	−	1.09062i	0.357948	−	0.933741i	$-0.383476\pi$
$90$	−0.00891255	+	0.0235005i	−0.000939466	+	0.00247717i
$91$	−0.739824	+	1.95855i	−0.0775546	+	0.205312i
$92$	−0.185404	−	0.488870i	−0.0193297	−	0.0509682i
$93$	−1.92590	+	2.35880i	−0.199706	+	0.244596i
$94$	0.139814	−	0.294653i	0.0144208	−	0.0303911i
$95$	1.99011	−	0.664395i	0.204181	−	0.0681655i
$96$	−0.189401	−	0.274394i	−0.0193306	−	0.0280052i
$97$	0.310961	+	1.52319i	0.0315733	+	0.154656i	0.992521	−	0.122074i	$-0.0389544\pi$
$97$	0.310961	+	1.52319i	0.0315733	+	0.154656i	−0.960948	+	0.276730i	$0.910749\pi$
$98$	−0.00745800	+	0.185068i	−0.000753371	+	0.0186947i
$99$	−2.12761			−0.213833
$100$	−0.336698	+	8.35508i	−0.0336698	+	0.835508i
$101$	−7.54182	+	5.66731i	−0.750439	+	0.563918i	−0.905682	−	0.423958i	$-0.860640\pi$
$101$	−7.54182	+	5.66731i	−0.750439	+	0.563918i	0.155243	+	0.987876i	$0.450384\pi$
$102$	−0.176079	+	0.0286157i	−0.0174345	+	0.00283338i
$103$	−11.8507	+	6.21974i	−1.16769	+	0.612850i	−0.933231	−	0.359277i	$-0.883023\pi$
$103$	−11.8507	+	6.21974i	−1.16769	+	0.612850i	−0.234456	+	0.972127i	$0.575331\pi$
$104$	−0.395566	+	0.0648222i	−0.0387885	+	0.00635634i
$105$	0.464864	+	0.243979i	0.0453661	+	0.0238100i
$106$	0.348511	+	0.116350i	0.0338504	+	0.0113009i
$107$	−1.18661	+	5.81240i	−0.114714	+	0.561906i	0.881288	+	0.472579i	$0.156677\pi$
$107$	−1.18661	+	5.81240i	−0.114714	+	0.561906i	−0.996002	+	0.0893273i	$0.971528\pi$
$108$	−0.556220	+	1.92029i	−0.0535223	+	0.184780i
$109$	−1.73635	−	14.3001i	−0.166312	−	1.36970i	−0.801800	−	0.597592i	$-0.796124\pi$
$109$	−1.73635	−	14.3001i	−0.166312	−	1.36970i	0.635488	−	0.772111i	$-0.280799\pi$
$110$	−0.0507228	+	0.0169337i	−0.00483623	+	0.00161457i
$111$	4.21037	+	0.684252i	0.399631	+	0.0649463i
$112$	−2.05424	+	1.07815i	−0.194107	+	0.101875i
$113$	8.22967	−	5.20413i	0.774182	−	0.489563i	−0.0880257	−	0.996118i	$-0.528056\pi$
$113$	8.22967	−	5.20413i	0.774182	−	0.489563i	0.862207	+	0.506555i	$0.169081\pi$
$114$	−0.0593465	+	0.0252852i	−0.00555831	+	0.00236817i
$115$	−0.0472965	+	0.231674i	−0.00441042	+	0.0216037i
$116$	−5.86357	−	1.44524i	−0.544419	−	0.134187i
$117$	2.70195	+	2.38736i	0.249795	+	0.220711i
$118$	0.0127560	−	0.00314406i	0.00117428	−	0.000289434i
$119$	0.150041	+	3.72322i	0.0137542	+	0.341307i
$120$	0.00404735	+	0.100434i	0.000369471	+	0.00916834i
$121$	4.09400	+	5.01424i	0.372182	+	0.455840i
$122$	0.0563997	−	0.148714i	0.00510619	−	0.0134639i
$123$	−3.54658	−	7.47426i	−0.319785	−	0.673932i
$124$	−1.69378	+	5.84761i	−0.152106	+	0.525131i
$125$	4.71620	−	6.83260i	0.421830	−	0.611126i
$126$	−0.0148502	−	0.00632707i	−0.00132296	−	0.000563660i
$127$	6.27350	−	1.01954i	0.556683	−	0.0904698i	0.124440	−	0.992227i	$-0.460286\pi$
$127$	6.27350	−	1.01954i	0.556683	−	0.0904698i	0.432243	+	0.901757i	$0.357722\pi$
$128$	−0.751122	−	0.474981i	−0.0663905	−	0.0419828i
$129$	−3.93160	−	5.69590i	−0.346158	−	0.501496i
$130$	0.0834163	+	0.0354103i	0.00731610	+	0.00310569i
$131$	5.69597	−	8.25204i	0.497659	−	0.720984i	−0.491000	−	0.871159i	$-0.663369\pi$
$131$	5.69597	−	8.25204i	0.497659	−	0.720984i	0.988659	+	0.150176i	$0.0479839\pi$
$132$	−3.91320	+	1.66726i	−0.340600	+	0.145116i
$133$	0.374889	+	1.29427i	0.0325070	+	0.112227i
$134$	−0.354679	+	0.0286327i	−0.0306396	+	0.00247349i
$135$	0.676752	−	0.599550i	0.0582455	−	0.0516010i
$136$	−0.602976	+	0.381299i	−0.0517047	+	0.0326961i
$137$	−17.0024	−	7.24404i	−1.45261	−	0.618900i	−0.485727	−	0.874111i	$-0.661445\pi$
$137$	−17.0024	−	7.24404i	−1.45261	−	0.618900i	−0.966885	+	0.255211i	$0.917855\pi$
$138$	0.000876308	−	0.00721705i	7.45963e−5	−	0.000614356i
$139$	−1.93011	−	9.45431i	−0.163710	−	0.801904i	−0.975850	−	0.218442i	$-0.929903\pi$
$139$	−1.93011	−	9.45431i	−0.163710	−	0.801904i	0.812140	−	0.583462i	$-0.198302\pi$
$140$	1.04619	+	0.0844572i	0.0884192	+	0.00713793i
$141$	−9.37924	+	7.04804i	−0.789875	+	0.593552i
$142$	−0.0257903	+	0.212402i	−0.00216427	+	0.0178244i
$143$	−0.298763	+	7.66538i	−0.0249838	+	0.641011i
$144$	0.481588	+	3.96623i	0.0401323	+	0.330519i
$145$	1.89190	+	1.96968i	0.157114	+	0.163573i
$146$	−0.182692	−	0.316431i	−0.0151197	−	0.0261880i
$147$	3.33141	−	5.77018i	0.274770	−	0.475916i
$148$	8.28011	−	2.04087i	0.680621	−	0.167758i
$149$	4.04902	+	4.95915i	0.331709	+	0.406270i	0.913350	−	0.407176i	$-0.133486\pi$
$149$	4.04902	+	4.95915i	0.331709	+	0.406270i	−0.581641	+	0.813446i	$0.697589\pi$
$150$	−0.0581349	+	0.100693i	−0.00474669	+	0.00822151i
$151$	2.90756	+	7.66661i	0.236614	+	0.623899i	0.999750	−	0.0223377i	$-0.00711090\pi$
$151$	2.90756	+	7.66661i	0.236614	+	0.623899i	−0.763137	+	0.646237i	$0.776342\pi$
$152$	−0.178712	+	0.186059i	−0.0144954	+	0.0150914i
$153$	6.08692	+	2.03211i	0.492098	+	0.164286i
$154$	−0.00955497	−	0.0329876i	−0.000769961	−	0.00265822i
$155$	2.06082	−	1.82573i	0.165529	−	0.146646i
$156$	6.84036	+	2.27361i	0.547667	+	0.182034i
$157$	9.96820	+	8.83106i	0.795549	+	0.704795i	0.959511	−	0.281672i	$-0.0908889\pi$
$157$	9.96820	+	8.83106i	0.795549	+	0.704795i	−0.163962	+	0.986467i	$0.552427\pi$
$158$	−0.154779	+	0.326191i	−0.0123136	+	0.0259503i
$159$	−9.15581	−	9.53221i	−0.726103	−	0.755954i
$160$	0.129229	+	0.272345i	0.0102165	+	0.0215308i
$161$	−0.147446	−	0.0363421i	−0.0116204	−	0.00286416i
$162$	−0.0192569	+	0.0200486i	−0.00151296	+	0.00157516i
$163$	−16.2861	−	12.2382i	−1.27562	−	0.958569i	−0.275627	−	0.961265i	$-0.588886\pi$
$163$	−16.2861	−	12.2382i	−1.27562	−	0.958569i	−0.999996	+	0.00269553i	$0.999142\pi$
$164$	−12.3801	−	10.9678i	−0.966724	−	0.856442i
$165$	1.89873	+	0.308573i	0.147816	+	0.0240224i
$166$	0.373450	+	0.236156i	0.0289854	+	0.0183292i
$167$	5.69784	+	0.459977i	0.440912	+	0.0355941i	0.298930	−	0.954275i	$-0.403370\pi$
$167$	5.69784	+	0.459977i	0.440912	+	0.0355941i	0.141982	+	0.989869i	$0.454652\pi$
$168$	−0.0645549			−0.00498052
$169$	8.98062	−	9.39939i	0.690817	−	0.723030i
$170$	0.161288			0.0123702
$171$	2.31302	+	0.186727i	0.176881	+	0.0142793i
$172$	−11.6947	−	7.39526i	−0.891710	−	0.563883i
$173$	6.54548	+	1.06374i	0.497644	+	0.0808750i	0.404053	−	0.914736i	$-0.367601\pi$
$173$	6.54548	+	1.06374i	0.497644	+	0.0808750i	0.0935912	+	0.995611i	$0.470165\pi$
$174$	−0.0628537	−	0.0556835i	−0.00476493	−	0.00422136i
$175$	1.94158	+	1.45900i	0.146770	+	0.110290i
$176$	−5.88855	+	6.13063i	−0.443866	+	0.462114i
$177$	−0.458867	−	0.113101i	−0.0344906	−	0.00850116i
$178$	−0.141582	−	0.298379i	−0.0106121	−	0.0223644i
$179$	4.54373	+	4.73052i	0.339614	+	0.353576i	0.869006	−	0.494802i	$-0.164759\pi$
$179$	4.54373	+	4.73052i	0.339614	+	0.353576i	−0.529392	+	0.848378i	$0.677580\pi$
$180$	0.774889	−	1.63304i	0.0577568	−	0.121720i
$181$	−5.91557	−	5.24074i	−0.439701	−	0.389541i	0.414023	−	0.910266i	$-0.364123\pi$
$181$	−5.91557	−	5.24074i	−0.439701	−	0.389541i	−0.853724	+	0.520725i	$0.825662\pi$
$182$	−0.0248805	+	0.0526140i	−0.00184427	+	0.00390001i
$183$	−4.28257	+	3.79403i	−0.316577	+	0.280462i
$184$	−0.00808906	−	0.0279267i	−0.000596333	−	0.00205878i
$185$	−3.65819	−	1.22128i	−0.268956	−	0.0897906i
$186$	−0.0586404	+	0.0610511i	−0.00429972	+	0.00447648i
$187$	4.84150	+	12.7660i	0.354045	+	0.933541i
$188$	−11.7277	+	20.3130i	−0.855330	+	1.48147i
$189$	0.367240	+	0.449788i	0.0267128	+	0.0327173i
$190$	0.0566293	−	0.0139579i	0.00410832	−	0.00101261i
$191$	−2.13787	+	3.70290i	−0.154691	+	0.267933i	−0.932946	−	0.360015i	$-0.882772\pi$
$191$	−2.13787	+	3.70290i	−0.154691	+	0.267933i	0.778255	+	0.627948i	$0.216105\pi$
$192$	3.99073	+	6.91215i	0.288006	+	0.498841i
$193$	9.76265	+	10.1640i	0.702731	+	0.731620i	0.972909	−	0.231190i	$-0.0742619\pi$
$193$	9.76265	+	10.1640i	0.702731	+	0.731620i	−0.270178	+	0.962810i	$0.587082\pi$
$194$	0.00520913	+	0.0429011i	0.000373994	+	0.00308012i
$195$	−2.06504	−	2.52240i	−0.147880	−	0.180633i
$196$	1.60561	−	13.2234i	0.114686	−	0.944527i
$197$	−2.44551	+	1.83768i	−0.174235	+	0.130929i	−0.684282	−	0.729217i	$-0.739884\pi$
$197$	−2.44551	+	1.83768i	−0.174235	+	0.130929i	0.510047	+	0.860147i	$0.329628\pi$
$198$	−0.0589531	−	0.00475919i	−0.00418962	−	0.000338221i
$199$	−5.25650	−	25.7480i	−0.372623	−	1.82523i	−0.542857	−	0.839825i	$-0.682657\pi$
$199$	−5.25650	−	25.7480i	−0.372623	−	1.82523i	0.170234	−	0.985404i	$-0.445548\pi$
$200$	−0.0560482	+	0.461599i	−0.00396321	+	0.0326400i
$201$	11.7760	+	5.01729i	0.830617	+	0.353893i
$202$	−0.221651	+	0.140163i	−0.0155953	+	0.00986186i
$203$	−1.31290	+	1.16313i	−0.0921477	+	0.0816357i
$204$	12.7878	−	1.03234i	0.895323	−	0.0722780i
$205$	2.08104	+	7.18458i	0.145346	+	0.501793i
$206$	−0.342281	+	0.145832i	−0.0238478	+	0.0101606i
$207$	−0.148563	+	0.215230i	−0.0103258	+	0.0149595i
$208$	14.3572	−	1.17813i	0.995495	−	0.0816884i
$209$	2.80466	+	4.06325i	0.194002	+	0.281061i
$210$	0.0123350	+	0.00780018i	0.000851196	+	0.000538264i
$211$	−2.85581	+	0.464114i	−0.196602	+	0.0319509i	−0.257915	−	0.966168i	$-0.583035\pi$
$211$	−2.85581	+	0.464114i	−0.196602	+	0.0319509i	0.0613128	+	0.998119i	$0.480471\pi$
$212$	−24.3095	−	10.3573i	−1.66959	−	0.711344i
$213$	4.37228	−	6.33435i	0.299584	−	0.434022i
$214$	−0.0458810	+	0.158400i	−0.00313636	+	0.0108280i
$215$	2.68256	+	5.65337i	0.182949	+	0.385556i
$216$	−0.0394227	+	0.103949i	−0.00268238	+	0.00707285i
$217$	1.11831	+	1.36968i	0.0759156	+	0.0929797i
$218$	−0.0161243	−	0.400121i	−0.00109208	−	0.0270996i
$219$	0.529249	+	13.1332i	0.0357634	+	0.887459i
$220$	3.73404	−	0.920357i	0.251749	−	0.0620505i
$221$	8.17606	−	21.6447i	0.549981	−	1.45598i
$222$	0.115133	+	0.0283778i	0.00772723	+	0.00190459i
$223$	−2.58060	+	12.6406i	−0.172810	+	0.846478i	0.797257	+	0.603640i	$0.206284\pi$
$223$	−2.58060	+	12.6406i	−0.172810	+	0.846478i	−0.970067	+	0.242838i	$0.921922\pi$
$224$	−0.178110	+	0.0758857i	−0.0119005	+	0.00507033i
$225$	3.53505	−	2.23543i	0.235670	−	0.149029i
$226$	0.239674	−	0.125791i	0.0159429	−	0.00836746i
$227$	−11.6924	−	1.90020i	−0.776054	−	0.126121i	−0.240531	−	0.970642i	$-0.577321\pi$
$227$	−11.6924	−	1.90020i	−0.776054	−	0.126121i	−0.535523	+	0.844521i	$0.679886\pi$
$228$	4.40055	−	1.46912i	0.291434	−	0.0972948i
$229$	−0.834119	−	6.86959i	−0.0551201	−	0.453955i	−0.993972	−	0.109634i	$-0.965032\pi$
$229$	−0.834119	−	6.86959i	−0.0551201	−	0.453955i	0.938852	−	0.344321i	$-0.111891\pi$
$230$	−0.00182875	+	0.00631356i	−0.000120584	+	0.000416304i
$231$	−0.247118	+	1.21047i	−0.0162592	+	0.0796428i
$232$	−0.318539	−	0.106344i	−0.0209131	−	0.00698183i
$233$	10.8399	+	5.68922i	0.710145	+	0.372713i	0.780794	−	0.624788i	$-0.214815\pi$
$233$	10.8399	+	5.68922i	0.710145	+	0.372713i	−0.0706489	+	0.997501i	$0.522507\pi$
$234$	0.0695272	+	0.0721943i	0.00454513	+	0.00471949i
$235$	9.39245	−	4.92954i	0.612696	−	0.321568i
$236$	−0.932599	+	0.151562i	−0.0607071	+	0.00986586i
$237$	10.3831	−	7.80242i	0.674457	−	0.506822i
$238$	−0.00417095	+	0.103501i	−0.000270362	+	0.00670897i
$239$	−12.0491			−0.779391			−0.389696	−	0.920944i	$-0.627420\pi$
$239$	−12.0491			−0.779391			−0.389696	+	0.920944i	$0.627420\pi$
$240$	0.145454	−	3.60940i	0.00938902	−	0.232986i
$241$	1.71755	+	8.41309i	0.110637	+	0.541935i	0.996895	+	0.0787432i	$0.0250907\pi$
$241$	1.71755	+	8.41309i	0.110637	+	0.541935i	−0.886258	+	0.463192i	$0.846704\pi$
$242$	0.102223	+	0.148096i	0.00657114	+	0.00951994i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−4.90359	+	10.3341i	−0.313920	+	0.661573i
$245$	−3.80989	+	4.66627i	−0.243405	+	0.298117i
$246$	−0.0815520	−	0.215035i	−0.00519957	−	0.0137101i
$247$	0.997541	−	8.30718i	0.0634720	−	0.528573i
$248$	−0.120049	+	0.316542i	−0.00762309	+	0.0201004i
$249$	−7.94735	−	13.7652i	−0.503643	−	0.872335i
$250$	0.145963	−	0.178773i	0.00923153	−	0.0113066i
$251$	−2.19802	−	1.65170i	−0.138738	−	0.104255i	0.529108	−	0.848555i	$-0.322527\pi$
$251$	−2.19802	−	1.65170i	−0.138738	−	0.104255i	−0.667845	+	0.744300i	$0.732783\pi$
$252$	1.02791	+	0.539491i	0.0647525	+	0.0339847i
$253$	−0.554616	+	0.0447733i	−0.0348684	+	0.00281487i
$254$	0.176111	−	0.0142171i	0.0110502	−	0.000892062i
$255$	−5.13738	−	2.69631i	−0.321715	−	0.168849i
$256$	12.7417	+	9.57476i	0.796356	+	0.598422i
$257$	8.40637	−	10.2959i	0.524375	−	0.642243i	−0.442720	−	0.896660i	$-0.645986\pi$
$257$	8.40637	−	10.2959i	0.524375	−	0.642243i	0.967095	+	0.254417i	$0.0818837\pi$
$258$	−0.0961983	−	0.166620i	−0.00598904	−	0.0103733i
$259$	0.878321	−	2.31594i	0.0545762	−	0.143906i
$260$	−5.77475	−	3.02110i	−0.358135	−	0.187361i
$261$	1.07115	+	2.82440i	0.0663027	+	0.174826i
$262$	0.176286	−	0.215912i	0.0108910	−	0.0133391i
$263$	−2.12450	+	4.47729i	−0.131002	+	0.276081i	−0.958343	−	0.285618i	$-0.907801\pi$
$263$	−2.12450	+	4.47729i	−0.131002	+	0.276081i	0.827341	+	0.561700i	$0.189852\pi$
$264$	−0.224361	+	0.0749027i	−0.0138085	+	0.00460995i
$265$	6.78838	+	9.83466i	0.417007	+	0.604138i
$266$	0.00749256	+	0.0367010i	0.000459398	+	0.00225028i
$267$	−0.478383	+	11.8709i	−0.0292766	+	0.726490i
$268$	25.5907			1.56320
$269$	0.745028	−	18.4877i	0.0454252	−	1.12721i	−0.802349	−	0.596856i	$-0.796416\pi$
$269$	0.745028	−	18.4877i	0.0454252	−	1.12721i	0.847774	−	0.530358i	$-0.177943\pi$
$270$	0.0200930	−	0.0150989i	0.00122282	−	0.000918890i
$271$	−5.13277	+	0.834156i	−0.311794	+	0.0506714i	−0.314295	−	0.949325i	$-0.601768\pi$
$271$	−5.13277	+	0.834156i	−0.311794	+	0.0506714i	0.00250106	+	0.999997i	$0.499204\pi$
$272$	22.7021	−	11.9150i	1.37652	−	0.722453i
$273$	1.67207	−	1.25994i	0.101198	−	0.0762550i
$274$	−0.454909	−	0.238755i	−0.0274821	−	0.0144237i
$275$	8.44085	+	2.81797i	0.509003	+	0.169930i
$276$	−0.104583	+	0.512280i	−0.00629514	+	0.0308356i
$277$	1.25225	−	4.32326i	0.0752403	−	0.259760i	−0.914076	−	0.405542i	$-0.867083\pi$
$277$	1.25225	−	4.32326i	0.0752403	−	0.259760i	0.989317	+	0.145782i	$0.0465699\pi$
$278$	−0.0323327	−	0.266284i	−0.00193918	−	0.0159706i
$279$	2.88845	−	0.964305i	0.172927	−	0.0577315i
$280$	0.0576103	+	0.00936259i	0.00344287	+	0.000559522i
$281$	−11.8440	+	6.21620i	−0.706552	+	0.370827i	−0.779409	−	0.626515i	$-0.784481\pi$
$281$	−11.8440	+	6.21620i	−0.706552	+	0.370827i	0.0728570	+	0.997342i	$0.476788\pi$
$282$	−0.275652	+	0.174312i	−0.0164148	+	0.0103801i
$283$	13.2891	−	5.66194i	0.789953	−	0.336567i	0.0409730	−	0.999160i	$-0.486954\pi$
$283$	13.2891	−	5.66194i	0.789953	−	0.336567i	0.748980	+	0.662593i	$0.230544\pi$
$284$	3.07793	−	15.0767i	0.182641	−	0.894637i
$285$	−2.03712	−	0.502104i	−0.120668	−	0.0297421i
$286$	−0.0254248	+	0.211729i	−0.00150340	+	0.0125198i
$287$	−4.66428	+	1.14964i	−0.275324	+	0.0678612i
$288$	0.0134252	+	0.333143i	0.000791088	+	0.0196307i
$289$	−0.973632	−	24.1604i	−0.0572725	−	1.42120i
$290$	0.0480161	+	0.0588091i	0.00281961	+	0.00345339i
$291$	0.551271	−	1.45358i	0.0323161	−	0.0852105i
$292$	11.2650	+	23.7405i	0.659234	+	1.38931i
$293$	−7.39139	+	25.5180i	−0.431810	+	1.49078i	0.389891	+	0.920861i	$0.372513\pi$
$293$	−7.39139	+	25.5180i	−0.431810	+	1.49078i	−0.821701	+	0.569919i	$0.806974\pi$
$294$	0.105216	−	0.152432i	0.00613633	−	0.00889000i
$295$	0.393100	+	0.167484i	0.0228872	+	0.00975132i
$296$	0.468082	−	0.0760708i	0.0272067	−	0.00442152i
$297$	1.79823	+	1.13713i	0.104344	+	0.0659832i
$298$	0.101100	+	0.146469i	0.00585656	+	0.00848470i
$299$	0.754573	+	0.565467i	0.0436381	+	0.0327018i
$300$	4.75008	−	6.88168i	0.274246	−	0.397314i
$301$	−3.69723	+	1.57524i	−0.213105	+	0.0907956i
$302$	0.0634153	+	0.218935i	0.00364914	+	0.0125983i
$303$	9.40325	−	0.759109i	0.540203	−	0.0436097i
$304$	6.93977	−	6.14810i	0.398023	−	0.352618i
$305$	4.37212	−	2.76476i	0.250347	−	0.158310i
$306$	0.164115	+	0.0699227i	0.00938181	+	0.00399722i
$307$	1.60148	−	13.1893i	0.0914010	−	0.752755i	−0.872891	−	0.487915i	$-0.837758\pi$
$307$	1.60148	−	13.1893i	0.0914010	−	0.752755i	0.964292	−	0.264840i	$-0.0853192\pi$
$308$	0.494046	+	2.42000i	0.0281509	+	0.137892i
$309$	13.3404	+	1.07695i	0.758907	+	0.0612653i
$310$	0.0611864	−	0.0459786i	0.00347516	−	0.00261141i
$311$	2.53153	−	20.8490i	0.143550	−	1.18224i	−0.725751	−	0.687957i	$-0.758508\pi$
$311$	2.53153	−	20.8490i	0.143550	−	1.18224i	0.869301	−	0.494283i	$-0.164569\pi$
$312$	0.368974	+	0.156630i	0.0208890	+	0.00886740i
$313$	2.59447	+	21.3674i	0.146648	+	1.20776i	0.861233	+	0.508209i	$0.169692\pi$
$313$	2.59447	+	21.3674i	0.146648	+	1.20776i	−0.714585	+	0.699549i	$0.753384\pi$
$314$	0.256451	+	0.266994i	0.0144724	+	0.0150674i
$315$	−0.262500	−	0.454663i	−0.0147902	−	0.0256174i
$316$	12.9829	−	22.4871i	0.730348	−	1.26500i
$317$	21.1149	−	5.20437i	1.18593	−	0.292306i	0.403464	−	0.914995i	$-0.367806\pi$
$317$	21.1149	−	5.20437i	1.18593	−	0.292306i	0.782469	+	0.622689i	$0.213960\pi$
$318$	−0.232373	−	0.284605i	−0.0130308	−	0.0159599i
$319$	−3.21343	+	5.56582i	−0.179917	+	0.311626i
$320$	−2.55893	−	6.74735i	−0.143049	−	0.377188i
$321$	4.10944	−	4.27838i	0.229367	−	0.238796i
$322$	−0.00400423	−	0.00133681i	−0.000223147	−	7.44974e-5i
$323$	−4.14304	−	14.3034i	−0.230525	−	0.795863i
$324$	1.49644	−	1.32573i	0.0831357	−	0.0736518i
$325$	−7.55744	−	13.0500i	−0.419211	−	0.723885i
$326$	−0.423890	−	0.375534i	−0.0234771	−	0.0207989i
$327$	−6.17538	+	13.0143i	−0.341499	+	0.719695i
$328$	−0.637128	−	0.663320i	−0.0351795	−	0.0366257i
$329$	2.92048	+	6.15477i	0.161011	+	0.339324i
$330$	0.0519209	+	0.0127974i	0.00285815	+	0.000704471i
$331$	0.820717	−	0.854457i	0.0451107	−	0.0469652i	−0.698265	−	0.715840i	$-0.746044\pi$
$331$	0.820717	−	0.854457i	0.0451107	−	0.0469652i	0.743375	+	0.668874i	$0.233224\pi$
$332$	−25.4040	−	19.0899i	−1.39423	−	1.04769i
$333$	−3.19285	−	2.82862i	−0.174967	−	0.155008i
$334$	0.156851	+	0.0254907i	0.00858248	+	0.00139479i
$335$	−9.78152	−	6.18546i	−0.534422	−	0.337948i
$336$	2.31245	+	0.186681i	0.126155	+	0.0101843i
$337$	−12.9445			−0.705131			−0.352565	−	0.935787i	$-0.614691\pi$
$337$	−12.9445			−0.705131			−0.352565	+	0.935787i	$0.614691\pi$
$338$	0.269866	−	0.240356i	0.0146788	−	0.0130736i
$339$	−9.73706			−0.528844
$340$	−11.5618	−	0.933367i	−0.627028	−	0.0506189i
$341$	5.47591	+	3.46276i	0.296537	+	0.187519i
$342$	0.0636731	+	0.0103479i	0.00344305	+	0.000559550i
$343$	−5.93835	−	5.26092i	−0.320641	−	0.284063i
$344$	−0.615121	−	0.462234i	−0.0331651	−	0.0249220i
$345$	0.163796	−	0.170530i	0.00881849	−	0.00918102i
$346$	0.178987	+	0.0441163i	0.00962240	+	0.00237171i
$347$	4.58934	+	9.67182i	0.246368	+	0.519210i	0.988533	−	0.151008i	$-0.0482518\pi$
$347$	4.58934	+	9.67182i	0.246368	+	0.519210i	−0.742164	+	0.670218i	$0.766201\pi$
$348$	4.18340	+	4.35538i	0.224254	+	0.233473i
$349$	−13.1220	+	27.6539i	−0.702402	+	1.48028i	0.166886	+	0.985976i	$0.446629\pi$
$349$	−13.1220	+	27.6539i	−0.702402	+	1.48028i	−0.869288	+	0.494305i	$0.835422\pi$
$350$	0.0505350	+	0.0447701i	0.00270121	+	0.00239306i
$351$	−1.00770	−	3.46187i	−0.0537871	−	0.184781i
$352$	−0.530974	+	0.470402i	−0.0283010	+	0.0250725i
$353$	6.24809	+	21.5709i	0.332552	+	1.14810i	0.936380	+	0.350989i	$0.114155\pi$
$353$	6.24809	+	21.5709i	0.332552	+	1.14810i	−0.603827	+	0.797115i	$0.706358\pi$
$354$	−0.0124616	−	0.00416029i	−0.000662326	−	0.000221117i
$355$	−4.82061	+	5.01879i	−0.255852	+	0.266370i
$356$	8.42257	+	22.2085i	0.446395	+	1.17705i
$357$	1.86312	−	3.22702i	0.0986068	−	0.170792i
$358$	0.115319	+	0.141240i	0.00609480	+	0.00746477i
$359$	−13.3751	+	3.29666i	−0.705910	+	0.173991i	−0.575898	−	0.817521i	$-0.695348\pi$
$359$	−13.3751	+	3.29666i	−0.705910	+	0.173991i	−0.130011	+	0.991513i	$0.541501\pi$
$360$	0.0502578	−	0.0870491i	0.00264882	−	0.00458789i
$361$	6.80752	+	11.7910i	0.358291	+	0.620578i
$362$	−0.152190	−	0.158446i	−0.00799891	−	0.00832775i
$363$	−0.780268	−	6.42609i	−0.0409535	−	0.337282i
$364$	2.08803	−	3.62763i	0.109442	−	0.190139i
$365$	1.43243	−	11.7971i	0.0749768	−	0.617489i
$366$	−0.127151	+	0.0955478i	−0.00664629	+	0.00499436i
$367$	−34.8864	−	2.81632i	−1.82106	−	0.147011i	−0.877789	−	0.479048i	$-0.840982\pi$
$367$	−34.8864	−	2.81632i	−1.82106	−	0.147011i	−0.943266	+	0.332037i	$0.892264\pi$
$368$	0.209004	+	1.02377i	0.0108951	+	0.0533676i
$369$	−0.997202	+	8.21270i	−0.0519123	+	0.427536i
$370$	−0.0986317	−	0.0420230i	−0.00512762	−	0.00218467i
$371$	−6.48662	+	4.10189i	−0.336768	+	0.212959i
$372$	4.55691	−	4.03707i	0.236265	−	0.209312i
$373$	18.4635	−	1.49053i	0.956003	−	0.0771765i	0.407391	−	0.913254i	$-0.366439\pi$
$373$	18.4635	−	1.49053i	0.956003	−	0.0771765i	0.548612	+	0.836077i	$0.315157\pi$
$374$	0.105595	+	0.364558i	0.00546021	+	0.0188508i
$375$	−7.63788	+	3.25420i	−0.394418	+	0.168046i
$376$	−0.740935	+	1.07343i	−0.0382108	+	0.0553579i
$377$	10.3262	−	3.46256i	0.531827	−	0.178331i
$378$	0.00916962	+	0.0132845i	0.000471634	+	0.000683280i
$379$	−16.4925	−	10.4292i	−0.847161	−	0.535712i	0.0389205	−	0.999242i	$-0.487608\pi$
$379$	−16.4925	−	10.4292i	−0.847161	−	0.535712i	−0.886081	+	0.463530i	$0.846582\pi$
$380$	−4.14022	+	0.672852i	−0.212389	+	0.0345166i
$381$	−5.84721	−	2.49126i	−0.299562	−	0.127631i
$382$	−0.0675205	+	0.0978203i	−0.00345465	+	0.00500492i
$383$	−8.19478	+	28.2917i	−0.418734	+	1.44564i	0.423191	+	0.906041i	$0.360910\pi$
$383$	−8.19478	+	28.2917i	−0.418734	+	1.44564i	−0.841924	+	0.539595i	$0.818577\pi$
$384$	0.380980	+	0.802898i	0.0194418	+	0.0409727i
$385$	0.396091	−	1.04441i	0.0201867	−	0.0532279i
$386$	0.247774	+	0.303468i	0.0126114	+	0.0154461i
$387$	0.278682	+	6.91543i	0.0141662	+	0.351531i
$388$	−0.125147	−	3.10549i	−0.00635337	−	0.157657i
$389$	−26.3569	+	6.49640i	−1.33635	+	0.329381i	−0.841810	−	0.539774i	$-0.818510\pi$
$389$	−26.3569	+	6.49640i	−1.33635	+	0.329381i	−0.494540	+	0.869155i	$0.664664\pi$
$390$	−0.0515771	−	0.0745116i	−0.00261171	−	0.00377304i
$391$	1.62948	+	0.401630i	0.0824062	+	0.0203113i
$392$	0.148165	−	0.725761i	0.00748347	−	0.0366565i
$393$	−9.22461	+	3.93024i	−0.465320	+	0.198254i
$394$	−0.0718724	+	0.0454494i	−0.00362088	+	0.00228971i
$395$	−10.3978	+	5.45716i	−0.523168	+	0.274580i
$396$	4.19849	+	0.682321i	0.210982	+	0.0342879i
$397$	23.4652	−	7.83383i	1.17768	−	0.393169i	0.340582	−	0.940215i	$-0.389376\pi$
$397$	23.4652	−	7.83383i	1.17768	−	0.393169i	0.837103	+	0.547046i	$0.184248\pi$
$398$	−0.0880553	−	0.725201i	−0.00441382	−	0.0363510i
$399$	0.374889	−	1.29427i	0.0187679	−	0.0647944i
$400$	3.34259	−	16.3731i	0.167129	−	0.818654i
$401$	−5.29167	−	1.76662i	−0.264253	−	0.0882207i	0.181454	−	0.983399i	$-0.441920\pi$
$401$	−5.29167	−	1.76662i	−0.264253	−	0.0882207i	−0.445707	+	0.895179i	$0.647048\pi$
$402$	0.315075	+	0.165364i	0.0157145	+	0.00824760i
$403$	−3.06861	−	10.5420i	−0.152859	−	0.525132i
$404$	16.7001	−	8.76486i	0.830859	−	0.436068i
$405$	−0.892423	+	0.145033i	−0.0443449	+	0.00720674i
$406$	−0.0389805	+	0.0292920i	−0.00193457	+	0.00145374i
$407$	0.365435	−	9.06818i	0.0181140	−	0.449493i
$408$	0.713420			0.0353196
$409$	−0.439813	+	10.9138i	−0.0217473	+	0.539654i	0.951193	+	0.308597i	$0.0998595\pi$
$409$	−0.439813	+	10.9138i	−0.0217473	+	0.539654i	−0.972940	+	0.231057i	$0.925782\pi$
$410$	0.0415918	+	0.203730i	0.00205407	+	0.0100615i
$411$	10.4986	+	15.2098i	0.517856	+	0.750243i
$412$	25.3802	−	8.47314i	1.25039	−	0.417442i
$413$	−0.117643	+	0.247928i	−0.00578885	+	0.0121997i
$414$	−0.00459791	+	0.00563142i	−0.000225975	+	0.000276769i
$415$	5.09599	+	13.4370i	0.250152	+	0.659598i
$416$	1.20214	−	0.00158800i	0.0589397	−	7.78582e-5i
$417$	−3.42169	+	9.02227i	−0.167561	+	0.441822i
$418$	0.0686244	+	0.118861i	0.00335653	+	0.00581368i
$419$	−16.8003	+	20.5767i	−0.820750	+	1.00524i	0.179021	+	0.983845i	$0.442707\pi$
$419$	−16.8003	+	20.5767i	−0.820750	+	1.00524i	−0.999771	+	0.0213912i	$0.993190\pi$
$420$	−0.839090	−	0.630535i	−0.0409434	−	0.0307670i
$421$	14.4279	+	7.57237i	0.703175	+	0.369055i	0.778105	−	0.628134i	$-0.216181\pi$
$421$	14.4279	+	7.57237i	0.703175	+	0.369055i	−0.0749301	+	0.997189i	$0.523873\pi$
$422$	−0.0801688	+	0.00647189i	−0.00390256	+	0.000315047i
$423$	11.6942	−	0.944052i	0.568591	−	0.0459014i
$424$	−1.30108	−	0.682862i	−0.0631862	−	0.0331627i
$425$	−21.4571	−	16.1240i	−1.04082	−	0.782128i
$426$	0.135319	−	0.165736i	0.00655624	−	0.00802993i
$427$	1.66113	+	2.87716i	0.0803878	+	0.139236i
$428$	4.20561	−	11.0893i	0.203286	−	0.536021i
$429$	4.34939	−	6.31902i	0.209991	−	0.305085i
$430$	0.0616841	+	0.162648i	0.00297467	+	0.00784357i
$431$	8.22846	−	10.0780i	0.396351	−	0.485442i	−0.537419	−	0.843315i	$-0.680601\pi$
$431$	8.22846	−	10.0780i	0.396351	−	0.485442i	0.933770	+	0.357873i	$0.116498\pi$
$432$	1.71278	−	3.60961i	0.0824063	−	0.173668i
$433$	−24.5105	+	8.18279i	−1.17790	+	0.393240i	−0.837181	−	0.546926i	$-0.815798\pi$
$433$	−24.5105	+	8.18279i	−1.17790	+	0.393240i	−0.340716	+	0.940166i	$0.610670\pi$
$434$	0.0279230	+	0.0404534i	0.00134035	+	0.00194183i
$435$	−0.546291	−	2.67591i	−0.0261927	−	0.128300i
$436$	−1.15963	+	28.7758i	−0.0555360	+	1.37811i
$437$	0.606880			0.0290310
$438$	−0.0147125	+	0.365087i	−0.000702990	+	0.0174445i
$439$	−3.89644	+	2.92798i	−0.185967	+	0.139745i	−0.689648	−	0.724144i	$-0.742235\pi$
$439$	−3.89644	+	2.92798i	−0.185967	+	0.139745i	0.503682	+	0.863889i	$0.331978\pi$
$440$	0.211088	−	0.0343052i	0.0100632	−	0.00163544i
$441$	−5.89964	+	3.09637i	−0.280935	+	0.147446i
$442$	0.274964	−	0.581456i	0.0130787	−	0.0276571i
$443$	14.8346	+	7.78579i	0.704812	+	0.369914i	0.778738	−	0.627350i	$-0.215860\pi$
$443$	14.8346	+	7.78579i	0.704812	+	0.369914i	−0.0739255	+	0.997264i	$0.523553\pi$
$444$	−8.08904	−	2.70052i	−0.383889	−	0.128161i
$445$	2.14860	−	10.5245i	0.101853	−	0.498910i
$446$	−0.0997804	+	0.344482i	−0.00472474	+	0.0163117i
$447$	−0.771697	−	6.35549i	−0.0365000	−	0.300604i
$448$	4.39606	−	1.46762i	0.207694	−	0.0693386i
$449$	−34.9591	−	5.68140i	−1.64982	−	0.268122i	−0.736823	−	0.676086i	$-0.763675\pi$
$449$	−34.9591	−	5.68140i	−1.64982	−	0.268122i	−0.912998	+	0.407964i	$0.866239\pi$
$450$	0.102952	−	0.0540332i	0.00485319	−	0.00254715i
$451$	−14.8768	+	9.40753i	−0.700522	+	0.442983i
$452$	−17.9089	+	7.63025i	−0.842362	+	0.358897i
$453$	1.64010	−	8.03373i	0.0770585	−	0.377458i
$454$	−0.319731	−	0.0788066i	−0.0150057	−	0.00369858i
$455$	−1.67493	+	0.881894i	−0.0785218	+	0.0413438i
$456$	0.250488	−	0.0617396i	0.0117302	−	0.00289122i
$457$	−0.0165686	−	0.411144i	−0.000775044	−	0.0192325i	0.998755	−	0.0498803i	$-0.0158840\pi$
$457$	−0.0165686	−	0.411144i	−0.000775044	−	0.0192325i	−0.999530	+	0.0306478i	$0.990243\pi$
$458$	−0.00774591	−	0.192213i	−0.000361943	−	0.00898152i
$459$	−4.05851	−	4.97077i	−0.189435	−	0.232016i
$460$	0.167629	−	0.442002i	0.00781576	−	0.0206085i
$461$	1.61337	+	3.40011i	0.0751422	+	0.158359i	0.937545	−	0.347864i	$-0.113093\pi$
$461$	1.61337	+	3.40011i	0.0751422	+	0.158359i	−0.862403	+	0.506222i	$0.831041\pi$
$462$	−0.00955497	+	0.0329876i	−0.000444537	+	0.00153472i
$463$	−11.5738	+	16.7675i	−0.537879	+	0.779252i	−0.993849	−	0.110743i	$-0.964677\pi$
$463$	−11.5738	+	16.7675i	−0.537879	+	0.779252i	0.455970	+	0.889995i	$0.349292\pi$
$464$	11.1030	+	4.73056i	0.515445	+	0.219611i
$465$	−2.71757	+	0.441649i	−0.126024	+	0.0204810i
$466$	0.287633	+	0.181888i	0.0133243	+	0.00842580i
$467$	1.37898	+	1.99779i	0.0638114	+	0.0924468i	0.853590	−	0.520945i	$-0.174420\pi$
$467$	1.37898	+	1.99779i	0.0638114	+	0.0924468i	−0.789779	+	0.613391i	$0.789805\pi$
$468$	−4.56624	−	5.57757i	−0.211074	−	0.257823i
$469$	4.22227	−	6.11701i	0.194966	−	0.282457i
$470$	0.271279	−	0.115581i	0.0125132	−	0.00533136i
$471$	−3.70513	−	12.7916i	−0.170723	−	0.589405i
$472$	−0.0523703	+	0.00422777i	−0.00241054	+	0.000194599i
$473$	−11.0220	+	9.76465i	−0.506793	+	0.448979i
$474$	0.305156	−	0.192969i	0.0140163	−	0.00886335i
$475$	−8.92914	−	3.80435i	−0.409697	−	0.174556i
$476$	0.897950	−	7.39529i	0.0411575	−	0.338962i
$477$	2.64376	+	12.9500i	0.121050	+	0.592940i
$478$	−0.333864	−	0.0269523i	−0.0152706	−	0.00123277i
$479$	2.73837	−	2.05775i	0.125119	−	0.0940212i	−0.536340	−	0.844002i	$-0.680194\pi$
$479$	2.73837	−	2.05775i	0.125119	−	0.0940212i	0.661460	+	0.749981i	$0.269937\pi$
$480$	0.0363357	−	0.299252i	0.00165849	−	0.0136589i
$481$	−10.6393	+	11.1061i	−0.485113	+	0.506393i
$482$	0.0287718	+	0.236957i	0.00131052	+	0.0107931i
$483$	0.105196	+	0.109521i	0.00478659	+	0.00498337i
$484$	−6.47078	−	11.2077i	−0.294127	−	0.509442i
$485$	−0.702784	+	1.21726i	−0.0319118	+	0.0552728i
$486$	0.0269910	−	0.00665269i	0.00122434	−	0.000301772i
$487$	−2.55724	−	3.13205i	−0.115879	−	0.141927i	0.713408	−	0.700749i	$-0.247151\pi$
$487$	−2.55724	−	3.13205i	−0.115879	−	0.141927i	−0.829287	+	0.558823i	$0.811253\pi$
$488$	−0.318038	+	0.550857i	−0.0143969	+	0.0249361i
$489$	7.22393	+	19.0479i	0.326678	+	0.861378i
$490$	−0.116005	+	0.120774i	−0.00524057	+	0.00545601i
$491$	1.16389	+	0.388563i	0.0525256	+	0.0175356i	0.342809	−	0.939405i	$-0.388621\pi$
$491$	1.16389	+	0.388563i	0.0525256	+	0.0175356i	−0.290284	+	0.956941i	$0.593750\pi$
$492$	4.60162	+	15.8866i	0.207457	+	0.716225i
$493$	14.5094	−	12.8542i	0.653469	−	0.578923i
$494$	0.0462226	−	0.227949i	0.00207965	−	0.0102559i
$495$	−1.43986	−	1.27561i	−0.0647170	−	0.0573343i
$496$	5.21570	−	10.9919i	0.234192	−	0.493549i
$497$	−3.09598	−	3.22326i	−0.138874	−	0.144583i
$498$	−0.189419	−	0.399193i	−0.00848808	−	0.0178883i
$499$	−4.01360	−	0.989263i	−0.179673	−	0.0442855i	0.148452	−	0.988920i	$-0.452571\pi$
$499$	−4.01360	−	0.989263i	−0.179673	−	0.0442855i	−0.328126	+	0.944634i	$0.606417\pi$
$500$	−11.4979	+	11.9705i	−0.514200	+	0.535339i
$501$	−4.56992	−	3.43407i	−0.204169	−	0.153423i
$502$	−0.0572094	−	0.0506831i	−0.00255338	−	0.00226210i
$503$	13.1253	+	2.13306i	0.585227	+	0.0951086i	0.445814	−	0.895126i	$-0.352914\pi$
$503$	13.1253	+	2.13306i	0.585227	+	0.0951086i	0.139413	+	0.990234i	$0.455478\pi$
$504$	0.0545612	+	0.0345024i	0.00243035	+	0.00153686i
$505$	−8.50177	−	0.686334i	−0.378324	−	0.0305415i
$506$	−0.0154678			−0.000687629
$507$	−12.6140	+	3.14444i	−0.560207	+	0.139649i
$508$	−12.7067			−0.563769
$509$	−27.8532	−	2.24855i	−1.23457	−	0.0996650i	−0.554107	−	0.832445i	$-0.686940\pi$
$509$	−27.8532	−	2.24855i	−1.23457	−	0.0996650i	−0.680465	+	0.732780i	$0.738222\pi$
$510$	−0.136319	−	0.0862027i	−0.00603629	−	0.00381712i
$511$	7.53337	+	1.22429i	0.333257	+	0.0541595i
$512$	1.66204	+	1.47244i	0.0734526	+	0.0650734i
$513$	−1.85515	−	1.39405i	−0.0819067	−	0.0615489i
$514$	0.255960	−	0.266482i	0.0112899	−	0.0117540i
$515$	−11.7491	−	2.89588i	−0.517725	−	0.127608i
$516$	5.93170	+	12.5008i	0.261129	+	0.550317i
$517$	17.2915	+	18.0023i	0.760479	+	0.791742i
$518$	0.0295176	−	0.0622069i	0.00129693	−	0.00273322i
$519$	−4.96364	−	4.39740i	−0.217880	−	0.193025i
$520$	−0.306564	−	0.193293i	−0.0134437	−	0.00847647i
$521$	−9.01742	+	7.98873i	−0.395060	+	0.349993i	−0.837146	−	0.546980i	$-0.815777\pi$
$521$	−9.01742	+	7.98873i	−0.395060	+	0.349993i	0.442085	+	0.896973i	$0.354239\pi$
$522$	0.0233624	+	0.0806563i	0.00102254	+	0.00353023i
$523$	30.0830	+	10.0432i	1.31544	+	0.439158i	0.885894	−	0.463888i	$-0.153546\pi$
$523$	30.0830	+	10.0432i	1.31544	+	0.439158i	0.429544	+	0.903046i	$0.358674\pi$
$524$	−13.8865	+	14.4574i	−0.606634	+	0.631573i
$525$	−0.861218	−	2.27084i	−0.0375866	−	0.0991078i
$526$	−0.0688821	+	0.119307i	−0.00300340	+	0.00520205i
$527$	−12.3588	−	15.1368i	−0.538358	−	0.659369i
$528$	8.25356	−	2.03432i	0.359190	−	0.0885324i
$529$	11.4658	−	19.8594i	0.498513	−	0.863450i
$530$	0.166098	+	0.287690i	0.00721483	+	0.0124964i
$531$	0.327382	+	0.340840i	0.0142071	+	0.0147912i
$532$	−0.324713	−	2.67425i	−0.0140781	−	0.115944i
$533$	29.4488	+	4.74598i	1.27557	+	0.205571i
$534$	−0.0398091	+	0.327858i	−0.00172271	+	0.0141878i
$535$	−4.28787	+	3.22212i	−0.185381	+	0.139305i
$536$	1.41844	+	0.114509i	0.0612674	+	0.00494602i
$537$	−1.31201	−	6.42666i	−0.0566175	−	0.277331i
$538$	0.0619983	−	0.510602i	0.00267294	−	0.0220136i
$539$	−13.0415	−	5.55647i	−0.561738	−	0.239334i
$540$	−1.52774	+	0.966081i	−0.0657432	+	0.0415735i
$541$	−25.3834	+	22.4878i	−1.09132	+	0.966824i	−0.999581	−	0.0289587i	$-0.990781\pi$
$541$	−25.3834	+	22.4878i	−1.09132	+	0.966824i	−0.0917385	+	0.995783i	$0.529242\pi$
$542$	−0.144088	+	0.0116320i	−0.00618911	+	0.000499637i
$543$	2.19879	+	7.59109i	0.0943590	+	0.325765i
$544$	1.96836	−	0.838640i	0.0843928	−	0.0359564i
$545$	7.39856	−	10.7187i	0.316919	−	0.459137i
$546$	0.0491492	−	0.0311710i	0.00210339	−	0.00133400i
$547$	−8.13256	−	11.7820i	−0.347723	−	0.503764i	0.609629	−	0.792687i	$-0.291318\pi$
$547$	−8.13256	−	11.7820i	−0.347723	−	0.503764i	−0.957352	+	0.288923i	$0.906703\pi$
$548$	31.2283	+	19.7476i	1.33401	+	0.843575i
$549$	5.64736	−	0.917786i	0.241024	−	0.0391701i
$550$	0.227581	+	0.0969633i	0.00970410	+	0.00413453i
$551$	3.98195	−	5.76885i	0.169637	−	0.245761i
$552$	−0.00808906	+	0.0279267i	−0.000344293	+	0.00118864i
$553$	−3.23307	−	6.81354i	−0.137484	−	0.289741i
$554$	0.0443687	−	0.116991i	0.00188505	−	0.00497046i
$555$	2.43913	+	2.98740i	0.103535	+	0.126808i
$556$	0.776777	+	19.2755i	0.0329427	+	0.817465i
$557$	1.12698	+	27.9658i	0.0477519	+	1.18495i	0.828458	+	0.560052i	$0.189219\pi$
$557$	1.12698	+	27.9658i	0.0477519	+	1.18495i	−0.780706	+	0.624899i	$0.785140\pi$
$558$	0.0821920	−	0.0202585i	0.00347946	−	0.000857611i
$559$	24.9541	−	0.0329639i	1.05545	−	0.00139423i
$560$	−2.03661	−	0.501980i	−0.0860626	−	0.0212125i
$561$	2.73099	−	13.3773i	0.115303	−	0.564790i
$562$	−0.342085	+	0.145749i	−0.0144300	+	0.00614805i
$563$	−4.38696	+	2.77415i	−0.184888	+	0.116916i	−0.623703	−	0.781661i	$-0.714373\pi$
$563$	−4.38696	+	2.77415i	−0.184888	+	0.116916i	0.438815	+	0.898577i	$0.355398\pi$
$564$	20.7687	−	10.9003i	0.874520	−	0.458984i
$565$	8.68958	+	1.41219i	0.365573	+	0.0594114i
$566$	0.380887	−	0.127159i	0.0160099	−	0.00534488i
$567$	−0.0699917	−	0.576434i	−0.00293938	−	0.0242079i
$568$	0.238066	−	0.821898i	0.00998901	−	0.0344861i
$569$	5.96715	−	29.2291i	0.250156	−	1.22535i	−0.639528	−	0.768768i	$-0.720870\pi$
$569$	5.96715	−	29.2291i	0.250156	−	1.22535i	0.889684	−	0.456577i	$-0.150925\pi$
$570$	−0.0553226	−	0.0184694i	−0.00231721	−	0.000773597i
$571$	−22.5609	−	11.8408i	−0.944142	−	0.495524i	−0.0789025	−	0.996882i	$-0.525142\pi$
$571$	−22.5609	−	11.8408i	−0.944142	−	0.495524i	−0.865240	+	0.501358i	$0.832834\pi$
$572$	3.04784	−	15.0306i	0.127436	−	0.628460i
$573$	3.78598	−	1.98704i	0.158162	−	0.0830097i
$574$	−0.131813	+	0.0214216i	−0.00550175	+	0.000894121i
$575$	0.874460	−	0.657114i	0.0364675	−	0.0274035i
$576$	0.321381	−	7.97499i	0.0133909	−	0.332291i
$577$	−22.0009			−0.915909			−0.457954	−	0.888976i	$-0.651418\pi$
$577$	−22.0009			−0.915909			−0.457954	+	0.888976i	$0.651418\pi$
$578$	0.0270658	−	0.671631i	0.00112579	−	0.0279362i
$579$	−2.81899	−	13.8083i	−0.117153	−	0.573854i
$580$	−3.10169	−	4.49357i	−0.128791	−	0.186586i
$581$	−8.75455	+	2.92270i	−0.363200	+	0.121254i
$582$	0.0185264	−	0.0390437i	0.000767946	−	0.00161841i
$583$	−17.7849	+	21.7825i	−0.736575	+	0.902140i
$584$	0.518166	+	1.36629i	0.0214419	+	0.0565376i
$585$	0.397211	+	3.23560i	0.0164227	+	0.133776i
$586$	−0.261886	+	0.690537i	−0.0108184	+	0.0285258i
$587$	23.5267	+	40.7494i	0.971050	+	1.68191i	0.692399	+	0.721515i	$0.256554\pi$
$587$	23.5267	+	40.7494i	0.971050	+	1.68191i	0.278651	+	0.960393i	$0.410113\pi$
$588$	−8.42449	+	10.3181i	−0.347420	+	0.425512i
$589$	−5.64922	−	4.24512i	−0.232772	−	0.174917i
$590$	0.0105176	+	0.00552008i	0.000433004	+	0.000227258i
$591$	3.04910	−	0.246149i	0.125423	−	0.0101252i
$592$	−16.9874	+	1.37136i	−0.698178	+	0.0563627i
$593$	−24.2317	−	12.7178i	−0.995075	−	0.522256i	−0.113116	−	0.993582i	$-0.536083\pi$
$593$	−24.2317	−	12.7178i	−0.995075	−	0.522256i	−0.881959	+	0.471326i	$0.843775\pi$
$594$	0.0472830	+	0.0355309i	0.00194004	+	0.00145785i
$595$	−2.13072	+	2.60965i	−0.0873508	+	0.106985i
$596$	−6.39970	−	11.0846i	−0.262142	−	0.454043i
$597$	−9.31870	+	24.5714i	−0.381389	+	1.00564i
$598$	0.0196433	+	0.0173562i	0.000803275	+	0.000709748i
$599$	8.01648	+	21.1377i	0.327545	+	0.863664i	0.993095	+	0.117311i	$0.0374276\pi$
$599$	8.01648	+	21.1377i	0.327545	+	0.863664i	−0.665551	+	0.746353i	$0.731803\pi$
$600$	0.294080	−	0.360183i	0.0120058	−	0.0147044i
$601$	5.32712	−	11.2267i	0.217298	−	0.457945i	−0.765304	−	0.643669i	$-0.777412\pi$
$601$	5.32712	−	11.2267i	0.217298	−	0.457945i	0.982602	+	0.185723i	$0.0594628\pi$
$602$	−0.105969	+	0.0353776i	−0.00431897	+	0.00144189i
$603$	−7.27141	−	10.5345i	−0.296115	−	0.428996i
$604$	−3.27893	−	16.0613i	−0.133418	−	0.653523i
$605$	−0.235664	+	5.84795i	−0.00958112	+	0.237753i
$606$	0.262249			0.0106532
$607$	−0.807466	+	20.0371i	−0.0327740	+	0.813279i	0.896314	+	0.443420i	$0.146235\pi$
$607$	−0.807466	+	20.0371i	−0.0327740	+	0.813279i	−0.929088	+	0.369859i	$0.879406\pi$
$608$	0.618531	−	0.464796i	0.0250848	−	0.0188500i
$609$	1.73131	−	0.281365i	0.0701560	−	0.0114015i
$610$	0.127330	−	0.0668280i	0.00515544	−	0.00270578i
$611$	−1.75913	−	42.2645i	−0.0711667	−	1.70984i
$612$	−11.3598	−	5.96211i	−0.459195	−	0.241004i
$613$	4.89352	+	1.63370i	0.197648	+	0.0659844i	0.413768	−	0.910382i	$-0.364212\pi$
$613$	4.89352	+	1.63370i	0.197648	+	0.0659844i	−0.216121	+	0.976367i	$0.569341\pi$
$614$	0.0738776	−	0.361876i	0.00298146	−	0.0146041i
$615$	2.08104	−	7.18458i	0.0839155	−	0.289710i
$616$	0.0165554	+	0.136346i	0.000667037	+	0.00549354i
$617$	−9.98644	+	3.33396i	−0.402039	+	0.134220i	−0.510495	−	0.859881i	$-0.670538\pi$
$617$	−9.98644	+	3.33396i	−0.402039	+	0.134220i	0.108456	+	0.994101i	$0.465409\pi$
$618$	0.367234	+	0.0596814i	0.0147723	+	0.00240074i
$619$	4.21369	−	2.21151i	0.169362	−	0.0888882i	−0.377912	−	0.925842i	$-0.623358\pi$
$619$	4.21369	−	2.21151i	0.169362	−	0.0888882i	0.547274	+	0.836953i	$0.315665\pi$
$620$	−4.65220	+	2.94187i	−0.186837	+	0.118148i
$621$	0.240597	−	0.102509i	0.00965482	−	0.00411353i
$622$	0.116782	−	0.572036i	0.00468253	−	0.0229366i
$623$	6.69820	+	1.65096i	0.268358	+	0.0661443i
$624$	−12.7643	−	6.67771i	−0.510979	−	0.267322i
$625$	−13.0169	+	3.20837i	−0.520675	+	0.128335i
$626$	0.0240932	+	0.597866i	0.000962957	+	0.0238955i
$627$	−0.198802	−	4.93322i	−0.00793938	−	0.197014i
$628$	−16.8385	−	20.6234i	−0.671930	−	0.822965i
$629$	−9.70664	+	25.5943i	−0.387029	+	1.02051i
$630$	−0.00625649	−	0.0131853i	−0.000249265	−	0.000525314i
$631$	1.24564	−	4.30046i	0.0495883	−	0.171199i	−0.931902	−	0.362710i	$-0.881852\pi$
$631$	1.24564	−	4.30046i	0.0495883	−	0.171199i	0.981490	+	0.191511i	$0.0613388\pi$
$632$	0.820240	−	1.18832i	0.0326274	−	0.0472689i
$633$	2.66175	+	1.13407i	0.105795	+	0.0450751i
$634$	0.596708	−	0.0969745i	0.0236983	−	0.00385135i
$635$	4.85687	+	3.07130i	0.192739	+	0.121881i
$636$	15.0105	+	21.7465i	0.595207	+	0.862306i
$637$	10.3272	+	21.6901i	0.409179	+	0.859393i
$638$	−0.101490	+	0.147033i	−0.00401802	+	0.00582110i
$639$	−7.08090	+	3.01689i	−0.280116	+	0.119346i
$640$	−0.223549	−	0.771780i	−0.00883654	−	0.0305073i
$641$	0.181168	−	0.0146254i	0.00715571	−	0.000577669i	−0.0768882	−	0.997040i	$-0.524498\pi$
$641$	0.181168	−	0.0146254i	0.00715571	−	0.000577669i	0.0840439	+	0.996462i	$0.473216\pi$
$642$	0.123437	−	0.109356i	0.00487168	−	0.00431593i
$643$	24.8089	−	15.6882i	0.978366	−	0.618681i	0.0533368	−	0.998577i	$-0.483014\pi$
$643$	24.8089	−	15.6882i	0.978366	−	0.618681i	0.925030	+	0.379895i	$0.124040\pi$
$644$	0.279305	+	0.119001i	0.0110062	+	0.00468929i
$645$	0.754262	−	6.21190i	0.0296990	−	0.244593i
$646$	−0.0828030	−	0.405596i	−0.00325784	−	0.0159580i
$647$	−4.64766	−	0.375198i	−0.182718	−	0.0147506i	−0.0112314	−	0.999937i	$-0.503575\pi$
$647$	−4.64766	−	0.375198i	−0.182718	−	0.0147506i	−0.171487	+	0.985186i	$0.554857\pi$
$648$	0.0888770	−	0.0667867i	0.00349142	−	0.00262363i
$649$	−0.121201	+	0.998176i	−0.00475754	+	0.0391818i
$650$	−0.180215	−	0.378504i	−0.00706862	−	0.0148461i
$651$	−0.213136	−	1.75533i	−0.00835347	−	0.0687970i
$652$	28.2132	+	29.3730i	1.10491	+	1.15034i
$653$	−9.32762	−	16.1559i	−0.365018	−	0.632230i	0.623761	−	0.781615i	$-0.285604\pi$
$653$	−9.32762	−	16.1559i	−0.365018	−	0.632230i	−0.988779	+	0.149385i	$0.952270\pi$
$654$	−0.200223	+	0.346796i	−0.00782933	+	0.0135608i
$655$	8.80227	−	2.16956i	0.343933	−	0.0847719i
$656$	20.9047	+	25.6036i	0.816191	+	0.999652i
$657$	6.57193	−	11.3829i	0.256395	−	0.444090i
$658$	0.0671550	+	0.177073i	0.00261797	+	0.00690303i
$659$	15.5854	−	16.2262i	0.607123	−	0.632082i	−0.344706	−	0.938711i	$-0.612022\pi$
$659$	15.5854	−	16.2262i	0.607123	−	0.632082i	0.951829	+	0.306629i	$0.0992010\pi$
$660$	−3.64787	−	1.21784i	−0.141993	−	0.0474043i
$661$	0.528468	+	1.82448i	0.0205550	+	0.0709642i	0.970140	−	0.242545i	$-0.0779824\pi$
$661$	0.528468	+	1.82448i	0.0205550	+	0.0709642i	−0.949585	+	0.313510i	$0.898495\pi$
$662$	0.0246523	−	0.0218400i	0.000958138	−	0.000848836i
$663$	−18.4787	+	13.9241i	−0.717652	+	0.540765i
$664$	−1.32267	−	1.17179i	−0.0513297	−	0.0454741i
$665$	−0.522271	+	1.10066i	−0.0202528	+	0.0426819i
$666$	−0.0821424	−	0.0855193i	−0.00318295	−	0.00331381i
$667$	0.338661	+	0.713712i	0.0131130	+	0.0276350i
$668$	−11.0962	−	2.73498i	−0.429327	−	0.105820i
$669$	8.93708	−	9.30448i	0.345527	−	0.359732i
$670$	−0.257197	−	0.193271i	−0.00993637	−	0.00746670i
$671$	9.11163	+	8.07220i	0.351751	+	0.311624i
$672$	0.191095	+	0.0310560i	0.00737166	+	0.00119801i
$673$	−23.4250	−	14.8131i	−0.902968	−	0.571002i	0.000337779	−	1.00000i	$-0.499892\pi$
$673$	−23.4250	−	14.8131i	−0.902968	−	0.571002i	−0.903306	+	0.428998i	$0.858867\pi$
$674$	−0.358674	−	0.0289552i	−0.0138156	−	0.00111531i
$675$	−4.18255			−0.160986
$676$	−20.7362	+	15.6681i	−0.797545	+	0.602619i
$677$	48.4389			1.86166			0.930829	−	0.365454i	$-0.119086\pi$
$677$	48.4389			1.86166			0.930829	+	0.365454i	$0.119086\pi$
$678$	−0.269801	−	0.0217806i	−0.0103616	−	0.000836478i
$679$	−0.762961	−	0.482467i	−0.0292797	−	0.0185154i
$680$	−0.636673	−	0.103469i	−0.0244153	−	0.00396787i
$681$	8.86673	+	7.85524i	0.339774	+	0.301013i
$682$	0.143984	+	0.108197i	0.00551345	+	0.00414309i
$683$	4.65829	−	4.84979i	0.178245	−	0.185572i	−0.626087	−	0.779754i	$-0.715344\pi$
$683$	4.65829	−	4.84979i	0.178245	−	0.185572i	0.804331	+	0.594181i	$0.202524\pi$
$684$	−4.50450	−	1.11026i	−0.172234	−	0.0424518i
$685$	−7.16324	−	15.0962i	−0.273693	−	0.576796i
$686$	−0.152776	−	0.159056i	−0.00583300	−	0.00607280i
$687$	−2.96657	+	6.25192i	−0.113182	+	0.238526i
$688$	20.6979	+	18.3367i	0.789099	+	0.699081i
$689$	47.0277	−	7.70652i	1.79161	−	0.293595i
$690$	0.00492002	−	0.00435876i	0.000187302	−	0.000165935i
$691$	−9.70211	−	33.4956i	−0.369086	−	1.27423i	−0.903346	−	0.428912i	$-0.858897\pi$
$691$	−9.70211	−	33.4956i	−0.369086	−	1.27423i	0.534261	−	0.845320i	$-0.320590\pi$
$692$	−12.5753	−	4.19825i	−0.478041	−	0.159594i
$693$	0.855814	−	0.890997i	0.0325097	−	0.0338462i
$694$	0.105530	+	0.278259i	0.00400585	+	0.0105626i
$695$	4.36212	−	7.55542i	0.165465	−	0.286593i
$696$	0.212389	+	0.260129i	0.00805058	+	0.00986017i
$697$	51.5467	−	12.7051i	1.95247	−	0.481241i
$698$	−0.425450	+	0.736901i	−0.0161035	+	0.0278921i
$699$	−6.12108	−	10.6020i	−0.231521	−	0.401005i
$700$	−3.36350	−	3.50177i	−0.127128	−	0.132354i
$701$	−2.45743	−	20.2388i	−0.0928158	−	0.764407i	−0.962591	−	0.270959i	$-0.912659\pi$
$701$	−2.45743	−	20.2388i	−0.0928158	−	0.764407i	0.869775	−	0.493448i	$-0.164264\pi$
$702$	−0.0201783	−	0.0981778i	−0.000761580	−	0.00370548i
$703$	−1.19314	+	9.82639i	−0.0450001	+	0.370609i
$704$	13.5757	−	10.2015i	0.511652	−	0.384482i
$705$	−10.5731	−	0.853547i	−0.398205	−	0.0321464i
$706$	0.124875	+	0.611677i	0.00469973	+	0.0230208i
$707$	0.660291	−	5.43799i	0.0248328	−	0.204517i
$708$	0.869229	+	0.370344i	0.0326676	+	0.0139184i
$709$	20.5100	−	12.9698i	0.770270	−	0.487089i	−0.0906165	−	0.995886i	$-0.528884\pi$
$709$	20.5100	−	12.9698i	0.770270	−	0.487089i	0.860887	+	0.508796i	$0.169909\pi$
$710$	−0.144799	+	0.128281i	−0.00543421	+	0.00481429i
$711$	−12.9459	+	1.04510i	−0.485507	+	0.0391942i
$712$	0.367472	+	1.26866i	0.0137716	+	0.0475450i
$713$	0.732656	−	0.312156i	0.0274382	−	0.0116903i
$714$	0.0588430	−	0.0852488i	0.00220214	−	0.00319035i
$715$	−4.79797	+	5.00844i	−0.179434	+	0.187305i
$716$	−7.44924	−	10.7921i	−0.278391	−	0.403319i
$717$	10.1838	+	6.43983i	0.380320	+	0.240500i
$718$	−0.377979	+	0.0614276i	−0.0141061	+	0.00229246i
$719$	48.4088	+	20.6251i	1.80534	+	0.769185i	0.978345	+	0.206981i	$0.0663638\pi$
$719$	48.4088	+	20.6251i	1.80534	+	0.769185i	0.826999	+	0.562204i	$0.190046\pi$
$720$	−2.05204	+	2.97289i	−0.0764750	+	0.110793i
$721$	2.16217	−	7.46468i	0.0805235	−	0.277999i
$722$	0.162252	+	0.341940i	0.00603841	+	0.0127257i
$723$	3.04486	−	8.02863i	0.113239	−	0.298588i
$724$	9.99272	+	12.2389i	0.371377	+	0.454854i
$725$	−0.508728	−	12.6240i	−0.0188937	−	0.468842i
$726$	−0.00724584	−	0.179804i	−0.000268918	−	0.00667314i
$727$	−13.6243	+	3.35808i	−0.505296	+	0.124544i	−0.483720	−	0.875223i	$-0.660715\pi$
$727$	−13.6243	+	3.35808i	−0.505296	+	0.124544i	−0.0215760	+	0.999767i	$0.506868\pi$
$728$	0.131967	−	0.191729i	0.00489104	−	0.00710595i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	0.0660794	−	0.323678i	0.00244571	−	0.0119799i
$731$	40.8595	−	17.4086i	1.51124	−	0.643880i
$732$	9.66770	−	6.11348i	0.357328	−	0.225961i
$733$	7.43517	−	3.90228i	0.274624	−	0.144134i	−0.321789	−	0.946811i	$-0.604284\pi$
$733$	7.43517	−	3.90228i	0.274624	−	0.144134i	0.596413	+	0.802677i	$0.296592\pi$
$734$	−0.960355	−	0.156073i	−0.0354474	−	0.00576076i
$735$	5.71405	−	1.90763i	0.210766	−	0.0703640i
$736$	0.0105103	+	0.0865599i	0.000387414	+	0.00319064i
$737$	7.57699	−	26.1588i	0.279102	−	0.963572i
$738$	−0.0460019	+	0.225332i	−0.00169335	+	0.00829459i
$739$	−29.9329	−	9.99305i	−1.10110	−	0.367600i	−0.292681	−	0.956210i	$-0.594547\pi$
$739$	−29.9329	−	9.99305i	−1.10110	−	0.367600i	−0.808417	+	0.588610i	$0.799675\pi$
$740$	6.82718	+	3.58318i	0.250972	+	0.131720i
$741$	−5.28302	+	6.48800i	−0.194076	+	0.238343i
$742$	−0.188911	+	0.0991481i	−0.00693514	+	0.00363984i
$743$	−19.6051	+	3.18614i	−0.719242	+	0.116888i	−0.509007	−	0.860763i	$-0.669987\pi$
$743$	−19.6051	+	3.18614i	−0.719242	+	0.116888i	−0.210236	+	0.977651i	$0.567423\pi$
$744$	0.270645	−	0.203376i	0.00992232	−	0.00745614i
$745$	−0.233076	+	5.78371i	−0.00853923	+	0.211899i
$746$	0.514932			0.0188530
$747$	−0.640015	+	15.8818i	−0.0234169	+	0.581085i
$748$	−5.45988	−	26.7442i	−0.199633	−	0.977867i
$749$	−1.95681	−	2.83492i	−0.0715001	−	0.103586i
$750$	−0.218915	+	0.0730844i	−0.00799363	+	0.00266866i
$751$	−3.27095	+	6.89339i	−0.119359	+	0.251543i	−0.954332	−	0.298747i	$-0.903431\pi$
$751$	−3.27095	+	6.89339i	−0.119359	+	0.251543i	0.834974	+	0.550290i	$0.185483\pi$
$752$	29.6456	−	36.3092i	1.08106	−	1.32406i
$753$	0.974963	+	2.57077i	0.0355296	+	0.0936840i
$754$	0.293870	−	0.0728445i	0.0107021	−	0.00265284i
$755$	−2.62882	+	6.93162i	−0.0956724	+	0.252267i
$756$	−0.580443	−	1.00536i	−0.0211105	−	0.0365645i
$757$	0.512766	−	0.628025i	0.0186368	−	0.0228260i	−0.765202	−	0.643790i	$-0.777361\pi$
$757$	0.512766	−	0.628025i	0.0186368	−	0.0228260i	0.783839	+	0.620964i	$0.213259\pi$
$758$	−0.433655	−	0.325870i	−0.0157511	−	0.0118361i
$759$	0.492686	+	0.258582i	0.0178834	+	0.00938592i
$760$	−0.232495	+	0.0187689i	−0.00843348	+	0.000680821i
$761$	−0.164106	+	0.0132480i	−0.00594882	+	0.000480239i	−0.0834406	−	0.996513i	$-0.526591\pi$
$761$	−0.164106	+	0.0132480i	−0.00594882	+	0.000480239i	0.0774918	+	0.996993i	$0.475309\pi$
$762$	−0.156446	−	0.0821090i	−0.00566743	−	0.00297450i
$763$	6.68702	+	5.02497i	0.242086	+	0.181916i
$764$	5.40626	−	6.62146i	0.195592	−	0.239556i
$765$	2.90098	+	5.02465i	0.104885	+	0.181666i
$766$	−0.290351	+	0.765593i	−0.0104908	+	0.0276620i
$767$	1.27396	−	1.13163i	0.0459999	−	0.0408609i
$768$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0277086 + 0.00223687i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-1.97334 - 0.320699i) q^{4} +(0.676752 + 0.599550i) q^{5} +(-0.0222235 - 0.0166999i) q^{6} +(-0.402242 + 0.418779i) q^{7} +(-0.107943 - 0.0266056i) q^{8} +(0.428693 + 0.903450i) q^{9} +(0.0174108 + 0.0181265i) q^{10} +(-0.912090 + 1.92219i) q^{11} +(1.49644 + 1.32573i) q^{12} +(3.31516 - 1.41764i) q^{13} +(-0.0120823 + 0.0107040i) q^{14} +(-0.251545 - 0.868434i) q^{15} +(3.78975 + 1.26520i) q^{16} +(4.44533 - 4.62808i) q^{17} +(0.00985759 + 0.0259923i) q^{18} +(1.16027 - 2.00966i) q^{19} +(-1.14319 - 1.40015i) q^{20} +(0.563794 - 0.138963i) q^{21} +(-0.0295725 + 0.0512210i) q^{22} +(0.130762 + 0.226487i) q^{23} +(0.0770127 + 0.0801787i) q^{24} +(-0.504150 - 4.15205i) q^{25} +(0.0950298 - 0.0318652i) q^{26} +(0.120537 - 0.992709i) q^{27} +(0.928062 - 0.697393i) q^{28} +(3.01090 + 0.243065i) q^{29} +(-0.00502740 - 0.0246258i) q^{30} +(0.367054 - 3.02296i) q^{31} +(0.306734 + 0.130687i) q^{32} +(1.79823 - 1.13713i) q^{33} +(0.133526 - 0.118294i) q^{34} +(-0.523297 + 0.0422449i) q^{35} +(-0.556220 - 1.92029i) q^{36} +(-3.92427 + 1.67198i) q^{37} +(0.0366450 - 0.0530894i) q^{38} +(-3.55962 - 0.573669i) q^{39} +(-0.0570994 - 0.0827227i) q^{40} +(6.99227 + 4.42165i) q^{41} +(0.0159328 - 0.00258934i) q^{42} +(6.36721 + 2.71282i) q^{43} +(2.41630 - 3.50062i) q^{44} +(-0.251545 + 0.868434i) q^{45} +(0.00311662 + 0.00656813i) q^{46} +(4.16030 - 10.9698i) q^{47} +(-2.52685 - 3.09483i) q^{48} +(0.268285 + 6.65742i) q^{49} +(-0.00468171 - 0.116175i) q^{50} +(-6.23070 + 1.53573i) q^{51} +(-6.99657 + 1.73431i) q^{52} +(12.8330 + 3.16306i) q^{53} +(0.00556047 - 0.0272370i) q^{54} +(-1.76971 + 0.754001i) q^{55} +(0.0545612 - 0.0345024i) q^{56} +(-2.05474 + 1.07841i) q^{57} +(0.0828843 + 0.0134700i) q^{58} +(0.448278 - 0.149657i) q^{59} +(0.217878 + 1.79438i) q^{60} +(1.59181 - 5.49556i) q^{61} +(0.0169325 - 0.0829411i) q^{62} +(-0.550784 - 0.183879i) q^{63} +(-7.06723 - 3.70917i) q^{64} +(3.09349 + 1.02822i) q^{65} +(0.0523702 - 0.0274860i) q^{66} +(-12.6346 + 2.05331i) q^{67} +(-10.2564 + 7.70715i) q^{68} +(0.0105305 - 0.261312i) q^{69} -0.0145944 q^{70} +(-0.309919 + 7.69056i) q^{71} +(-0.0222376 - 0.108927i) q^{72} +(-7.46656 - 10.8172i) q^{73} +(-0.112476 + 0.0375501i) q^{74} +(-1.79303 + 3.77872i) q^{75} +(-2.93411 + 3.59363i) q^{76} +(-0.438090 - 1.15515i) q^{77} +(-0.0973491 - 0.0238580i) q^{78} +(-4.60560 + 12.1440i) q^{79} +(1.80617 + 3.12837i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.183856 + 0.138159i) q^{82} +(14.0741 + 7.38664i) q^{83} +(-1.15712 + 0.0934125i) q^{84} +(5.78315 - 0.466864i) q^{85} +(0.170359 + 0.0894111i) q^{86} +(-2.41487 - 1.81466i) q^{87} +(0.149595 - 0.183220i) q^{88} +(-5.94029 - 10.2889i) q^{89} +(-0.00891255 + 0.0235005i) q^{90} +(-0.739824 + 1.95855i) q^{91} +(-0.185404 - 0.488870i) q^{92} +(-1.92590 + 2.35880i) q^{93} +(0.139814 - 0.294653i) q^{94} +(1.99011 - 0.664395i) q^{95} +(-0.189401 - 0.274394i) q^{96} +(0.310961 + 1.52319i) q^{97} +(-0.00745800 + 0.185068i) q^{98} -2.12761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more