LMFDB - Embedded newform 136.4.c.b.69.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.c (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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.8
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85990 + 2.13091i) q^{2} +3.39972i q^{3} +(-1.08156 - 7.92655i) q^{4} +21.1389i q^{5} +(-7.24451 - 6.32314i) q^{6} +36.0029 q^{7} +(18.9024 + 12.4379i) q^{8} +15.4419 q^{9} +O(q^{10})$	\(q+(-1.85990 + 2.13091i) q^{2} +3.39972i q^{3} +(-1.08156 - 7.92655i) q^{4} +21.1389i q^{5} +(-7.24451 - 6.32314i) q^{6} +36.0029 q^{7} +(18.9024 + 12.4379i) q^{8} +15.4419 q^{9} +(-45.0451 - 39.3162i) q^{10} +1.32292i q^{11} +(26.9481 - 3.67701i) q^{12} +22.9931i q^{13} +(-66.9617 + 76.7190i) q^{14} -71.8664 q^{15} +(-61.6605 + 17.1461i) q^{16} +17.0000 q^{17} +(-28.7203 + 32.9053i) q^{18} -50.4607i q^{19} +(167.558 - 22.8630i) q^{20} +122.400i q^{21} +(-2.81902 - 2.46049i) q^{22} +44.6733 q^{23} +(-42.2853 + 64.2628i) q^{24} -321.852 q^{25} +(-48.9962 - 42.7648i) q^{26} +144.291i q^{27} +(-38.9393 - 285.379i) q^{28} -74.4837i q^{29} +(133.664 - 153.141i) q^{30} -160.995 q^{31} +(78.1453 - 163.283i) q^{32} -4.49756 q^{33} +(-31.6183 + 36.2255i) q^{34} +761.061i q^{35} +(-16.7013 - 122.401i) q^{36} -371.209i q^{37} +(107.527 + 93.8517i) q^{38} -78.1702 q^{39} +(-262.923 + 399.575i) q^{40} -264.139 q^{41} +(-260.823 - 227.651i) q^{42} -144.753i q^{43} +(10.4862 - 1.43082i) q^{44} +326.424i q^{45} +(-83.0878 + 95.1948i) q^{46} +445.614 q^{47} +(-58.2920 - 209.629i) q^{48} +953.209 q^{49} +(598.612 - 685.838i) q^{50} +57.7953i q^{51} +(182.256 - 24.8684i) q^{52} -243.350i q^{53} +(-307.471 - 268.366i) q^{54} -27.9650 q^{55} +(680.540 + 447.799i) q^{56} +171.552 q^{57} +(158.718 + 138.532i) q^{58} +404.638i q^{59} +(77.7278 + 569.652i) q^{60} -474.840i q^{61} +(299.434 - 343.066i) q^{62} +555.952 q^{63} +(202.599 + 470.210i) q^{64} -486.048 q^{65} +(8.36500 - 9.58390i) q^{66} +424.323i q^{67} +(-18.3865 - 134.751i) q^{68} +151.877i q^{69} +(-1621.75 - 1415.50i) q^{70} -54.9686 q^{71} +(291.888 + 192.064i) q^{72} -648.234 q^{73} +(791.013 + 690.411i) q^{74} -1094.21i q^{75} +(-399.979 + 54.5763i) q^{76} +47.6289i q^{77} +(145.389 - 166.574i) q^{78} -157.149 q^{79} +(-362.449 - 1303.43i) q^{80} -73.6178 q^{81} +(491.271 - 562.856i) q^{82} -523.315i q^{83} +(970.210 - 132.383i) q^{84} +359.361i q^{85} +(308.455 + 269.225i) q^{86} +253.224 q^{87} +(-16.4543 + 25.0063i) q^{88} -603.481 q^{89} +(-695.580 - 607.115i) q^{90} +827.818i q^{91} +(-48.3169 - 354.105i) q^{92} -547.338i q^{93} +(-828.796 + 949.563i) q^{94} +1066.68 q^{95} +(555.117 + 265.673i) q^{96} -142.748 q^{97} +(-1772.87 + 2031.20i) q^{98} +20.4283i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.85990	+	2.13091i	−0.657573	+	0.753391i
$2$	−1.85990	+	2.13091i	−0.657573	+	0.753391i
$3$			3.39972i			0.654277i	0.944976	+	0.327139i	$0.106084\pi$
$3$			3.39972i			0.654277i	−0.944976	+	0.327139i	$0.893916\pi$
$4$	−1.08156	−	7.92655i	−0.135195	−	0.990819i
$5$			21.1389i			1.89072i	0.326030	+	0.945359i	$0.394289\pi$
$5$			21.1389i			1.89072i	−0.326030	+	0.945359i	$0.605711\pi$
$6$	−7.24451	−	6.32314i	−0.492926	−	0.430235i
$7$	36.0029			1.94397			0.971987	−	0.235034i	$-0.0755201\pi$
$7$	36.0029			1.94397			0.971987	+	0.235034i	$0.0755201\pi$
$8$	18.9024	+	12.4379i	0.835374	+	0.549681i
$9$	15.4419			0.571921
$10$	−45.0451	−	39.3162i	−1.42445	−	1.24329i
$11$			1.32292i			0.0362614i	0.999836	+	0.0181307i	$0.00577149\pi$
$11$			1.32292i			0.0362614i	−0.999836	+	0.0181307i	$0.994229\pi$
$12$	26.9481	−	3.67701i	0.648270	−	0.0884551i
$13$			22.9931i			0.490549i	0.969454	+	0.245274i	$0.0788781\pi$
$13$			22.9931i			0.490549i	−0.969454	+	0.245274i	$0.921122\pi$
$14$	−66.9617	+	76.7190i	−1.27831	+	1.46457i
$15$	−71.8664			−1.23705
$16$	−61.6605	+	17.1461i	−0.963445	+	0.267908i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	−28.7203	+	32.9053i	−0.376080	+	0.430880i
$19$		−	50.4607i		−	0.609288i	−0.952466	−	0.304644i	$-0.901462\pi$
$19$		−	50.4607i		−	0.609288i	0.952466	−	0.304644i	$-0.0985375\pi$
$20$	167.558	−	22.8630i	1.87336	−	0.255616i
$21$			122.400i			1.27190i
$22$	−2.81902	−	2.46049i	−0.0273190	−	0.0238445i
$23$	44.6733			0.405001			0.202501	−	0.979282i	$-0.435093\pi$
$23$	44.6733			0.405001			0.202501	+	0.979282i	$0.435093\pi$
$24$	−42.2853	+	64.2628i	−0.359644	+	0.546566i
$25$	−321.852			−2.57482
$26$	−48.9962	−	42.7648i	−0.369575	−	0.322572i
$27$			144.291i			1.02847i
$28$	−38.9393	−	285.379i	−0.262816	−	1.92613i
$29$		−	74.4837i		−	0.476940i	−0.971150	−	0.238470i	$-0.923354\pi$
$29$		−	74.4837i		−	0.476940i	0.971150	−	0.238470i	$-0.0766459\pi$
$30$	133.664	−	153.141i	0.813454	−	0.931985i
$31$	−160.995			−0.932759			−0.466379	−	0.884585i	$-0.654442\pi$
$31$	−160.995			−0.932759			−0.466379	+	0.884585i	$0.654442\pi$
$32$	78.1453	−	163.283i	0.431696	−	0.902019i
$33$	−4.49756			−0.0237250
$34$	−31.6183	+	36.2255i	−0.159485	+	0.182724i
$35$			761.061i			3.67551i
$36$	−16.7013	−	122.401i	−0.0773209	−	0.566671i
$37$		−	371.209i		−	1.64936i	−0.565599	−	0.824681i	$-0.691355\pi$
$37$		−	371.209i		−	1.64936i	0.565599	−	0.824681i	$-0.308645\pi$
$38$	107.527	+	93.8517i	0.459032	+	0.400652i
$39$	−78.1702			−0.320955
$40$	−262.923	+	399.575i	−1.03929	+	1.57946i
$41$	−264.139			−1.00614			−0.503068	−	0.864247i	$-0.667795\pi$
$41$	−264.139			−1.00614			−0.503068	+	0.864247i	$0.667795\pi$
$42$	−260.823	−	227.651i	−0.958236	−	0.836366i
$43$		−	144.753i		−	0.513362i	−0.966496	−	0.256681i	$-0.917371\pi$
$43$		−	144.753i		−	0.513362i	0.966496	−	0.256681i	$-0.0826289\pi$
$44$	10.4862	−	1.43082i	0.0359285	−	0.00490236i
$45$			326.424i			1.08134i
$46$	−83.0878	+	95.1948i	−0.266318	+	0.305124i
$47$	445.614			1.38297			0.691484	−	0.722392i	$-0.256957\pi$
$47$	445.614			1.38297			0.691484	+	0.722392i	$0.256957\pi$
$48$	−58.2920	−	209.629i	−0.175286	−	0.630360i
$49$	953.209			2.77904
$50$	598.612	−	685.838i	1.69313	−	1.93984i
$51$			57.7953i			0.158686i
$52$	182.256	−	24.8684i	0.486045	−	0.0663198i
$53$		−	243.350i		−	0.630693i	−0.948977	−	0.315346i	$-0.897879\pi$
$53$		−	243.350i		−	0.630693i	0.948977	−	0.315346i	$-0.102121\pi$
$54$	−307.471	−	268.366i	−0.774841	−	0.676296i
$55$	−27.9650			−0.0685601
$56$	680.540	+	447.799i	1.62395	+	1.06857i
$57$	171.552			0.398643
$58$	158.718	+	138.532i	0.359322	+	0.313623i
$59$			404.638i			0.892871i	0.894816	+	0.446436i	$0.147307\pi$
$59$			404.638i			0.892871i	−0.894816	+	0.446436i	$0.852693\pi$
$60$	77.7278	+	569.652i	0.167244	+	1.22570i
$61$		−	474.840i		−	0.996673i	−0.866984	−	0.498336i	$-0.833944\pi$
$61$		−	474.840i		−	0.996673i	0.866984	−	0.498336i	$-0.166056\pi$
$62$	299.434	−	343.066i	0.613357	−	0.702732i
$63$	555.952			1.11180
$64$	202.599	+	470.210i	0.395701	+	0.918379i
$65$	−486.048			−0.927490
$66$	8.36500	−	9.58390i	0.0156009	−	0.0178742i
$67$			424.323i			0.773721i	0.922138	+	0.386860i	$0.126440\pi$
$67$			424.323i			0.773721i	−0.922138	+	0.386860i	$0.873560\pi$
$68$	−18.3865	−	134.751i	−0.0327896	−	0.240309i
$69$			151.877i			0.264983i
$70$	−1621.75	−	1415.50i	−2.76909	−	2.41692i
$71$	−54.9686			−0.0918812			−0.0459406	−	0.998944i	$-0.514629\pi$
$71$	−54.9686			−0.0918812			−0.0459406	+	0.998944i	$0.514629\pi$
$72$	291.888	+	192.064i	0.477768	+	0.314374i
$73$	−648.234			−1.03932			−0.519658	−	0.854375i	$-0.673940\pi$
$73$	−648.234			−1.03932			−0.519658	+	0.854375i	$0.673940\pi$
$74$	791.013	+	690.411i	1.24261	+	1.08458i
$75$		−	1094.21i		−	1.68464i
$76$	−399.979	+	54.5763i	−0.603694	+	0.0823728i
$77$			47.6289i			0.0704912i
$78$	145.389	−	166.574i	0.211051	−	0.241805i
$79$	−157.149			−0.223806			−0.111903	−	0.993719i	$-0.535695\pi$
$79$	−157.149			−0.223806			−0.111903	+	0.993719i	$0.535695\pi$
$80$	−362.449	−	1303.43i	−0.506538	−	1.82160i
$81$	−73.6178			−0.100985
$82$	491.271	−	562.856i	0.661607	−	0.758013i
$83$		−	523.315i		−	0.692064i	−0.938223	−	0.346032i	$-0.887529\pi$
$83$		−	523.315i		−	0.692064i	0.938223	−	0.346032i	$-0.112471\pi$
$84$	970.210	−	132.383i	1.26022	−	0.171954i
$85$			359.361i			0.458567i
$86$	308.455	+	269.225i	0.386762	+	0.337573i
$87$	253.224			0.312051
$88$	−16.4543	+	25.0063i	−0.0199322	+	0.0302918i
$89$	−603.481			−0.718751			−0.359376	−	0.933193i	$-0.617010\pi$
$89$	−603.481			−0.718751			−0.359376	+	0.933193i	$0.617010\pi$
$90$	−695.580	−	607.115i	−0.814673	−	0.711062i
$91$			827.818i			0.953615i
$92$	−48.3169	−	354.105i	−0.0547542	−	0.401283i
$93$		−	547.338i		−	0.610283i
$94$	−828.796	+	949.563i	−0.909402	+	1.04191i
$95$	1066.68			1.15199
$96$	555.117	+	265.673i	0.590171	+	0.282449i
$97$	−142.748			−0.149422			−0.0747108	−	0.997205i	$-0.523803\pi$
$97$	−142.748			−0.149422			−0.0747108	+	0.997205i	$0.523803\pi$
$98$	−1772.87	+	2031.20i	−1.82742	+	2.09370i
$99$			20.4283i			0.0207387i
$100$	348.103	+	2551.18i	0.348103	+	2.55118i
$101$			850.033i			0.837440i	0.908115	+	0.418720i	$0.137521\pi$
$101$			850.033i			0.837440i	−0.908115	+	0.418720i	$0.862479\pi$
$102$	−123.157	−	107.493i	−0.119552	−	0.104347i
$103$	1264.69			1.20984			0.604920	−	0.796287i	$-0.293205\pi$
$103$	1264.69			1.20984			0.604920	+	0.796287i	$0.293205\pi$
$104$	−285.985	+	434.624i	−0.269646	+	0.409792i
$105$	−2587.40			−2.40480
$106$	518.557	+	452.606i	0.475158	+	0.414726i
$107$		−	565.627i		−	0.511040i	−0.966804	−	0.255520i	$-0.917753\pi$
$107$		−	565.627i		−	0.511040i	0.966804	−	0.255520i	$-0.0822466\pi$
$108$	1143.73	−	156.059i	1.01903	−	0.139044i
$109$		−	1351.13i		−	1.18730i	−0.804725	−	0.593648i	$-0.797687\pi$
$109$		−	1351.13i		−	1.18730i	0.804725	−	0.593648i	$-0.202313\pi$
$110$	52.0121	−	59.5910i	0.0450833	−	0.0516525i
$111$	1262.01			1.07914
$112$	−2219.96	+	617.309i	−1.87291	+	0.520806i
$113$	−454.029			−0.377978			−0.188989	−	0.981979i	$-0.560521\pi$
$113$	−454.029			−0.377978			−0.188989	+	0.981979i	$0.560521\pi$
$114$	−319.070	+	365.563i	−0.262137	+	0.300334i
$115$			944.344i			0.765743i
$116$	−590.399	+	80.5586i	−0.472562	+	0.0644800i
$117$			355.056i			0.280555i
$118$	−862.248	−	752.586i	−0.672681	−	0.587128i
$119$	612.049			0.471483
$120$	−1358.44	−	893.864i	−1.03340	−	0.679986i
$121$	1329.25			0.998685
$122$	1011.84	+	883.154i	0.750884	+	0.655385i
$123$		−	897.999i		−	0.658291i
$124$	174.126	+	1276.13i	0.126104	+	0.924195i
$125$		−	4161.23i		−	2.97754i
$126$	−1034.01	+	1184.68i	−0.731090	+	0.837620i
$127$	−2229.88			−1.55803			−0.779015	−	0.627005i	$-0.784281\pi$
$127$	−2229.88			−1.55803			−0.779015	+	0.627005i	$0.784281\pi$
$128$	−1378.79	−	442.823i	−0.952101	−	0.305784i
$129$	492.119			0.335881
$130$	904.000	−	1035.73i	0.609893	−	0.698762i
$131$			1673.41i			1.11608i	0.829815	+	0.558039i	$0.188446\pi$
$131$			1673.41i			1.11608i	−0.829815	+	0.558039i	$0.811554\pi$
$132$	4.86438	+	35.6501i	0.00320750	+	0.0235072i
$133$		−	1816.73i		−	1.18444i
$134$	−904.194	−	789.197i	−0.582914	−	0.508778i
$135$	−3050.14			−1.94455
$136$	321.340	+	211.444i	0.202608	+	0.133317i
$137$	−1174.82			−0.732642			−0.366321	−	0.930489i	$-0.619383\pi$
$137$	−1174.82			−0.732642			−0.366321	+	0.930489i	$0.619383\pi$
$138$	−323.636	−	282.476i	−0.199636	−	0.174246i
$139$		−	1715.44i		−	1.04677i	−0.852096	−	0.523386i	$-0.824669\pi$
$139$		−	1715.44i		−	1.04677i	0.852096	−	0.523386i	$-0.175331\pi$
$140$	6032.59	−	823.134i	3.64176	−	0.496911i
$141$			1514.96i			0.904844i
$142$	102.236	−	117.133i	0.0604186	−	0.0692225i
$143$	−30.4180			−0.0177880
$144$	−952.153	+	264.768i	−0.551014	+	0.153222i
$145$	1574.50			0.901760
$146$	1205.65	−	1381.33i	0.683426	−	0.783010i
$147$			3240.65i			1.81826i
$148$	−2942.41	+	401.485i	−1.63422	+	0.222986i
$149$		−	339.712i		−	0.186781i	−0.995630	−	0.0933903i	$-0.970230\pi$
$149$		−	339.712i		−	0.186781i	0.995630	−	0.0933903i	$-0.0297704\pi$
$150$	2331.66	+	2035.12i	1.26920	+	1.10778i
$151$	430.149			0.231821			0.115911	−	0.993260i	$-0.463021\pi$
$151$	430.149			0.231821			0.115911	+	0.993260i	$0.463021\pi$
$152$	627.623	−	953.826i	0.334914	−	0.508984i
$153$	262.512			0.138711
$154$	−101.493	−	88.5849i	−0.0531074	−	0.0463531i
$155$		−	3403.25i		−	1.76358i
$156$	84.5458	+	619.620i	0.0433915	+	0.318008i
$157$			3283.54i			1.66914i	0.550903	+	0.834569i	$0.314283\pi$
$157$			3283.54i			1.66914i	−0.550903	+	0.834569i	$0.685717\pi$
$158$	292.281	−	334.871i	0.147169	−	0.168613i
$159$	827.323			0.412648
$160$	3451.62	+	1651.91i	1.70546	+	0.816216i
$161$	1608.37			0.787312
$162$	136.922	−	156.873i	0.0664048	−	0.0760809i
$163$			2209.15i			1.06156i	0.847511	+	0.530778i	$0.178100\pi$
$163$			2209.15i			1.06156i	−0.847511	+	0.530778i	$0.821900\pi$
$164$	285.682	+	2093.71i	0.136025	+	0.996898i
$165$		−	95.0734i		−	0.0448573i
$166$	1115.14	+	973.313i	0.521395	+	0.455083i
$167$	1939.29			0.898604			0.449302	−	0.893380i	$-0.351673\pi$
$167$	1939.29			0.898604			0.449302	+	0.893380i	$0.351673\pi$
$168$	−1522.39	+	2313.65i	−0.699139	+	1.06251i
$169$	1668.32			0.759362
$170$	−765.766	−	668.375i	−0.345480	−	0.301541i
$171$		−	779.208i		−	0.348465i
$172$	−1147.39	+	156.559i	−0.508649	+	0.0694040i
$173$		−	1119.29i		−	0.491895i	−0.969283	−	0.245947i	$-0.920901\pi$
$173$		−	1119.29i		−	0.491895i	0.969283	−	0.245947i	$-0.0790990\pi$
$174$	−470.971	+	539.598i	−0.205197	+	0.235097i
$175$	−11587.6			−5.00538
$176$	−22.6829	−	81.5718i	−0.00971470	−	0.0349358i
$177$	−1375.66			−0.584185
$178$	1122.41	−	1285.96i	0.472632	−	0.541500i
$179$		−	1139.87i		−	0.475964i	−0.971270	−	0.237982i	$-0.923514\pi$
$179$		−	1139.87i		−	0.475964i	0.971270	−	0.237982i	$-0.0764859\pi$
$180$	2587.42	−	353.047i	1.07141	−	0.146192i
$181$		−	1793.25i		−	0.736414i	−0.929744	−	0.368207i	$-0.879972\pi$
$181$		−	1793.25i		−	0.736414i	0.929744	−	0.368207i	$-0.120028\pi$
$182$	−1764.01	−	1539.66i	−0.718444	−	0.627071i
$183$	1614.33			0.652100
$184$	844.431	+	555.641i	0.338328	+	0.222622i
$185$	7846.94			3.11848
$186$	1166.33	+	1017.99i	0.459781	+	0.401306i
$187$			22.4896i			0.00879467i
$188$	−481.958	−	3532.18i	−0.186970	−	1.37027i
$189$			5194.88i			1.99932i
$190$	−1983.92	+	2273.00i	−0.757519	+	0.867901i
$191$	3846.25			1.45709			0.728547	−	0.684996i	$-0.240196\pi$
$191$	3846.25			1.45709			0.728547	+	0.684996i	$0.240196\pi$
$192$	−1598.59	+	688.780i	−0.600875	+	0.258898i
$193$	1572.91			0.586635			0.293317	−	0.956015i	$-0.405241\pi$
$193$	1572.91			0.586635			0.293317	+	0.956015i	$0.405241\pi$
$194$	265.497	−	304.184i	0.0982557	−	0.112573i
$195$		−	1652.43i		−	0.606836i
$196$	−1030.95	−	7555.66i	−0.375712	−	2.75352i
$197$			1503.79i			0.543859i	0.962317	+	0.271930i	$0.0876618\pi$
$197$			1503.79i			0.543859i	−0.962317	+	0.271930i	$0.912338\pi$
$198$	−43.5310	−	37.9946i	−0.0156243	−	0.0136372i
$199$	1541.82			0.549230			0.274615	−	0.961554i	$-0.411450\pi$
$199$	1541.82			0.549230			0.274615	+	0.961554i	$0.411450\pi$
$200$	−6083.77	−	4003.15i	−2.15094	−	1.41533i
$201$	−1442.58			−0.506228
$202$	−1811.34	−	1580.97i	−0.630920	−	0.550678i
$203$		−	2681.63i		−	0.927160i
$204$	458.118	−	62.5091i	0.157229	−	0.0214535i
$205$		−	5583.60i		−	1.90232i
$206$	−2352.19	+	2694.94i	−0.795558	+	0.911482i
$207$	689.840			0.231629
$208$	−394.242	−	1417.76i	−0.131422	−	0.472617i
$209$	66.7554			0.0220936
$210$	4812.30	−	5513.51i	1.58133	−	1.81176i
$211$		−	2123.21i		−	0.692740i	−0.938098	−	0.346370i	$-0.887414\pi$
$211$		−	2123.21i		−	0.692740i	0.938098	−	0.346370i	$-0.112586\pi$
$212$	−1928.93	+	263.198i	−0.624902	+	0.0852665i
$213$		−	186.878i		−	0.0601158i
$214$	1205.30	+	1052.01i	0.385013	+	0.336046i
$215$	3059.91			0.970623
$216$	−1794.67	+	2727.44i	−0.565332	+	0.859160i
$217$	−5796.28			−1.81326
$218$	2879.15	+	2512.97i	0.894497	+	0.780734i
$219$		−	2203.82i		−	0.680000i
$220$	30.2459	+	221.666i	0.00926898	+	0.0679306i
$221$			390.883i			0.118976i
$222$	−2347.21	+	2689.23i	−0.709613	+	0.813014i
$223$	5201.04			1.56183			0.780914	−	0.624638i	$-0.214754\pi$
$223$	5201.04			1.56183			0.780914	+	0.624638i	$0.214754\pi$
$224$	2813.46	−	5878.66i	0.839206	−	1.75350i
$225$	−4970.00			−1.47259
$226$	844.448	−	967.496i	0.248548	−	0.284765i
$227$			3554.85i			1.03940i	0.854349	+	0.519699i	$0.173956\pi$
$227$			3554.85i			1.03940i	−0.854349	+	0.519699i	$0.826044\pi$
$228$	−185.544	−	1359.82i	−0.0538946	−	0.394983i
$229$			3915.44i			1.12987i	0.825136	+	0.564934i	$0.191098\pi$
$229$			3915.44i			1.12987i	−0.825136	+	0.564934i	$0.808902\pi$
$230$	−2012.31	−	1756.38i	−0.576904	−	0.503532i
$231$	−161.925			−0.0461208
$232$	926.418	−	1407.92i	0.262165	−	0.398424i
$233$	1060.07			0.298059			0.149029	−	0.988833i	$-0.452385\pi$
$233$	1060.07			0.298059			0.149029	+	0.988833i	$0.452385\pi$
$234$	−756.594	−	660.369i	−0.211368	−	0.184486i
$235$			9419.78i			2.61480i
$236$	3207.39	−	437.641i	0.884674	−	0.120712i
$237$		−	534.263i		−	0.146431i
$238$	−1138.35	+	1304.22i	−0.310035	+	0.355211i
$239$	−4204.93			−1.13805			−0.569026	−	0.822320i	$-0.692680\pi$
$239$	−4204.93			−1.13805			−0.569026	+	0.822320i	$0.692680\pi$
$240$	4431.31	−	1232.23i	1.19183	−	0.331416i
$241$	−371.702			−0.0993503			−0.0496752	−	0.998765i	$-0.515819\pi$
$241$	−371.702			−0.0993503			−0.0496752	+	0.998765i	$0.515819\pi$
$242$	−2472.27	+	2832.51i	−0.656709	+	0.752400i
$243$			3645.57i			0.962400i
$244$	−3763.84	+	513.568i	−0.987522	+	0.134745i
$245$			20149.8i			5.25438i
$246$	1913.56	+	1670.19i	0.495951	+	0.432875i
$247$	1160.25			0.298886
$248$	−3043.18	−	2002.43i	−0.779203	−	0.512720i
$249$	1779.13			0.452802
$250$	8867.22	+	7739.47i	2.24325	+	1.95795i
$251$			24.8057i			0.00623793i	0.999995	+	0.00311896i	$0.000992799\pi$
$251$			24.8057i			0.00623793i	−0.999995	+	0.00311896i	$0.999007\pi$
$252$	−601.296	−	4406.79i	−0.150310	−	1.10159i
$253$			59.0992i			0.0146859i
$254$	4147.35	−	4751.68i	1.02452	−	1.17381i
$255$	−1221.73			−0.300030
$256$	3508.02	−	2114.47i	0.856451	−	0.516228i
$257$	−2671.29			−0.648368			−0.324184	−	0.945994i	$-0.605090\pi$
$257$	−2671.29			−0.648368			−0.324184	+	0.945994i	$0.605090\pi$
$258$	−915.291	+	1048.66i	−0.220866	+	0.253050i
$259$		−	13364.6i		−	3.20632i
$260$	525.691	+	3852.69i	0.125392	+	0.918975i
$261$		−	1150.17i		−	0.272772i
$262$	−3565.88	−	3112.37i	−0.840843	−	0.733903i
$263$	−6352.11			−1.48931			−0.744654	−	0.667450i	$-0.767386\pi$
$263$	−6352.11			−1.48931			−0.744654	+	0.667450i	$0.767386\pi$
$264$	−85.0145	−	55.9400i	−0.0198192	−	0.0130412i
$265$	5144.15			1.19246
$266$	3871.29	+	3378.93i	0.892347	+	0.778856i
$267$		−	2051.67i		−	0.470263i
$268$	3363.42	−	458.931i	0.766617	−	0.104603i
$269$			2258.87i			0.511991i	0.966678	+	0.255995i	$0.0824032\pi$
$269$			2258.87i			0.511991i	−0.966678	+	0.255995i	$0.917597\pi$
$270$	5672.95	−	6499.58i	1.27869	−	1.46501i
$271$	4013.00			0.899530			0.449765	−	0.893147i	$-0.351508\pi$
$271$	4013.00			0.899530			0.449765	+	0.893147i	$0.351508\pi$
$272$	−1048.23	+	291.484i	−0.233670	+	0.0649772i
$273$	−2814.35			−0.623928
$274$	2185.05	−	2503.44i	0.481766	−	0.551966i
$275$		−	425.784i		−	0.0933664i
$276$	1203.86	−	164.264i	0.262550	−	0.0358244i
$277$		−	3812.62i		−	0.826997i	−0.910505	−	0.413498i	$-0.864307\pi$
$277$		−	3812.62i		−	0.826997i	0.910505	−	0.413498i	$-0.135693\pi$
$278$	3655.44	+	3190.53i	0.788628	+	0.688329i
$279$	−2486.06			−0.533465
$280$	−9465.98	+	14385.9i	−2.02036	+	3.07043i
$281$	−2293.65			−0.486931			−0.243466	−	0.969909i	$-0.578284\pi$
$281$	−2293.65			−0.486931			−0.243466	+	0.969909i	$0.578284\pi$
$282$	−3228.25	−	2817.68i	−0.681701	−	0.595001i
$283$		−	3018.72i		−	0.634079i	−0.948412	−	0.317039i	$-0.897311\pi$
$283$		−	3018.72i		−	0.634079i	0.948412	−	0.317039i	$-0.102689\pi$
$284$	59.4518	+	435.711i	0.0124219	+	0.0910377i
$285$			3626.43i			0.753723i
$286$	56.5744	−	64.8180i	0.0116969	−	0.0134013i
$287$	−9509.76			−1.95590
$288$	1206.71	−	2521.39i	0.246896	−	0.515884i
$289$	289.000			0.0588235
$290$	−2928.41	+	3355.12i	−0.592973	+	0.679378i
$291$		−	485.305i		−	0.0977632i
$292$	701.104	+	5138.26i	0.140510	+	1.02977i
$293$		−	2099.19i		−	0.418552i	−0.977857	−	0.209276i	$-0.932889\pi$
$293$		−	2099.19i		−	0.418552i	0.977857	−	0.209276i	$-0.0671108\pi$
$294$	−6905.53	−	6027.28i	−1.36986	−	1.19564i
$295$	−8553.60			−1.68817
$296$	4617.05	−	7016.73i	0.906623	−	1.37783i
$297$	−190.885			−0.0372938
$298$	723.896	+	631.830i	0.140719	+	0.122822i
$299$			1027.18i			0.198673i
$300$	−8673.30	+	1183.45i	−1.66918	+	0.227756i
$301$		−	5211.51i		−	0.997962i
$302$	−800.033	+	916.609i	−0.152440	+	0.174652i
$303$	−2889.88			−0.547918
$304$	865.204	+	3111.43i	0.163233	+	0.587015i
$305$	10037.6			1.88443
$306$	−488.245	+	559.389i	−0.0912128	+	0.104504i
$307$		−	2231.40i		−	0.414829i	−0.978253	−	0.207415i	$-0.933495\pi$
$307$		−	2231.40i		−	0.414829i	0.978253	−	0.207415i	$-0.0665049\pi$
$308$	377.533	−	51.5136i	0.0698440	−	0.00953006i
$309$			4299.59i			0.791570i
$310$	7252.02	+	6329.70i	1.32867	+	1.15969i
$311$	1662.17			0.303064			0.151532	−	0.988452i	$-0.451579\pi$
$311$	1662.17			0.303064			0.151532	+	0.988452i	$0.451579\pi$
$312$	−1477.60	−	972.270i	−0.268118	−	0.176423i
$313$	−815.145			−0.147204			−0.0736018	−	0.997288i	$-0.523449\pi$
$313$	−815.145			−0.147204			−0.0736018	+	0.997288i	$0.523449\pi$
$314$	−6996.92	−	6107.04i	−1.25751	−	1.09758i
$315$			11752.2i			2.10210i
$316$	169.966	+	1245.65i	0.0302574	+	0.221751i
$317$			5671.98i			1.00495i	0.864591	+	0.502477i	$0.167578\pi$
$317$			5671.98i			1.00495i	−0.864591	+	0.502477i	$0.832422\pi$
$318$	−1538.74	+	1762.95i	−0.271346	+	0.310885i
$319$	98.5359			0.0172945
$320$	−9939.72	+	4282.71i	−1.73640	+	0.748159i
$321$	1922.98			0.334362
$322$	−2991.40	+	3427.29i	−0.517715	+	0.593153i
$323$		−	857.832i		−	0.147774i
$324$	79.6222	+	583.536i	0.0136526	+	0.100058i
$325$		−	7400.38i		−	1.26307i
$326$	−4707.50	−	4108.79i	−0.799767	−	0.698051i
$327$	4593.48			0.776820
$328$	−4992.85	−	3285.32i	−0.840500	−	0.553054i
$329$	16043.4			2.68845
$330$	202.593	+	176.827i	0.0337951	+	0.0294969i
$331$			626.406i			0.104019i	0.998647	+	0.0520096i	$0.0165627\pi$
$331$			626.406i			0.104019i	−0.998647	+	0.0520096i	$0.983437\pi$
$332$	−4148.09	+	565.997i	−0.685710	+	0.0935637i
$333$		−	5732.16i		−	0.943305i
$334$	−3606.88	+	4132.46i	−0.590898	+	0.677000i
$335$	−8969.71			−1.46289
$336$	−2098.68	−	7547.24i	−0.340751	−	1.22540i
$337$	−8153.84			−1.31801			−0.659003	−	0.752140i	$-0.729022\pi$
$337$	−8153.84			−1.31801			−0.659003	+	0.752140i	$0.729022\pi$
$338$	−3102.90	+	3555.04i	−0.499336	+	0.572096i
$339$		−	1543.57i		−	0.247302i
$340$	2848.49	−	388.671i	0.454357	−	0.0619960i
$341$		−	212.983i		−	0.0338231i
$342$	1660.42	+	1449.25i	0.262530	+	0.229141i
$343$	21969.3			3.45840
$344$	1800.41	−	2736.17i	0.282185	−	0.428849i
$345$	−3210.51			−0.501008
$346$	2385.10	+	2081.76i	0.370589	+	0.323457i
$347$		−	1514.80i		−	0.234348i	−0.993111	−	0.117174i	$-0.962617\pi$
$347$		−	1514.80i		−	0.234348i	0.993111	−	0.117174i	$-0.0373835\pi$
$348$	−273.877	−	2007.19i	−0.0421878	−	0.309186i
$349$			10015.4i			1.53614i	0.640364	+	0.768072i	$0.278784\pi$
$349$			10015.4i			1.53614i	−0.640364	+	0.768072i	$0.721216\pi$
$350$	21551.8	−	24692.2i	3.29140	−	3.77101i
$351$	−3317.69			−0.504516
$352$	216.010	+	103.380i	0.0327084	+	0.0156539i
$353$	399.079			0.0601723			0.0300862	−	0.999547i	$-0.490422\pi$
$353$	399.079			0.0601723			0.0300862	+	0.999547i	$0.490422\pi$
$354$	2558.58	−	2931.40i	0.384145	−	0.440120i
$355$		−	1161.97i		−	0.173722i
$356$	652.701	+	4783.52i	0.0971716	+	0.712152i
$357$			2080.80i			0.308481i
$358$	2428.95	+	2120.03i	0.358587	+	0.312981i
$359$	−4123.65			−0.606234			−0.303117	−	0.952953i	$-0.598027\pi$
$359$	−4123.65			−0.606234			−0.303117	+	0.952953i	$0.598027\pi$
$360$	−4060.02	+	6170.18i	−0.594394	+	0.903326i
$361$	4312.72			0.628768
$362$	3821.25	+	3335.25i	0.554808	+	0.484246i
$363$			4519.08i			0.653417i
$364$	6561.74	−	895.336i	0.944859	−	0.128924i
$365$		−	13702.9i		−	1.96505i
$366$	−3002.48	+	3439.98i	−0.428804	+	0.491286i
$367$	−6635.21			−0.943747			−0.471873	−	0.881666i	$-0.656422\pi$
$367$	−6635.21			−0.943747			−0.471873	+	0.881666i	$0.656422\pi$
$368$	−2754.58	+	765.973i	−0.390196	+	0.108503i
$369$	−4078.80			−0.575430
$370$	−14594.5	+	16721.1i	−2.05063	+	2.34943i
$371$		−	8761.31i		−	1.22605i
$372$	−4338.50	+	591.979i	−0.604680	+	0.0825072i
$373$		−	12174.1i		−	1.68995i	−0.534804	−	0.844976i	$-0.679615\pi$
$373$		−	12174.1i		−	1.68995i	0.534804	−	0.844976i	$-0.320385\pi$
$374$	−47.9234	−	41.8284i	−0.00662583	−	0.00578314i
$375$	14147.1			1.94813
$376$	8423.16	+	5542.49i	1.15530	+	0.760191i
$377$	1712.61			0.233963
$378$	−11069.8	−	9661.95i	−1.50627	−	1.31470i
$379$			11223.2i			1.52110i	0.649277	+	0.760552i	$0.275071\pi$
$379$			11223.2i			1.52110i	−0.649277	+	0.760552i	$0.724929\pi$
$380$	−1153.68	−	8455.11i	−0.155744	−	1.14142i
$381$		−	7580.98i		−	1.01938i
$382$	−7153.64	+	8196.02i	−0.958146	+	1.09776i
$383$	−736.925			−0.0983162			−0.0491581	−	0.998791i	$-0.515654\pi$
$383$	−736.925			−0.0983162			−0.0491581	+	0.998791i	$0.515654\pi$
$384$	1505.48	−	4687.50i	0.200068	−	0.622938i
$385$	−1006.82			−0.133279
$386$	−2925.45	+	3351.73i	−0.385755	+	0.441965i
$387$		−	2235.25i		−	0.293603i
$388$	154.391	+	1131.50i	0.0202011	+	0.148050i
$389$		−	12516.4i		−	1.63138i	−0.578487	−	0.815691i	$-0.696357\pi$
$389$		−	12516.4i		−	1.63138i	0.578487	−	0.815691i	$-0.303643\pi$
$390$	3521.18	+	3073.35i	0.457184	+	0.399039i
$391$	759.446			0.0982272
$392$	18017.9	+	11855.9i	2.32154	+	1.52758i
$393$	−5689.12			−0.730225
$394$	−3204.43	−	2796.89i	−0.409739	−	0.357627i
$395$		−	3321.95i		−	0.423154i
$396$	161.926	−	22.0945i	0.0205482	−	0.00280376i
$397$		−	6952.37i		−	0.878916i	−0.898263	−	0.439458i	$-0.855171\pi$
$397$		−	6952.37i		−	0.878916i	0.898263	−	0.439458i	$-0.144829\pi$
$398$	−2867.63	+	3285.48i	−0.361159	+	0.413785i
$399$	6176.39			0.774953
$400$	19845.6	−	5518.51i	2.48069	−	0.689813i
$401$	−14778.4			−1.84040			−0.920198	−	0.391454i	$-0.871972\pi$
$401$	−14778.4			−1.84040			−0.920198	+	0.391454i	$0.871972\pi$
$402$	2683.05	−	3074.01i	0.332882	−	0.381387i
$403$		−	3701.77i		−	0.457564i
$404$	6737.83	−	919.362i	0.829752	−	0.113218i
$405$		−	1556.20i		−	0.190934i
$406$	5714.31	+	4987.56i	0.698514	+	0.609676i
$407$	491.079			0.0598081
$408$	−718.850	+	1092.47i	−0.0872265	+	0.132562i
$409$	−1871.27			−0.226231			−0.113115	−	0.993582i	$-0.536083\pi$
$409$	−1871.27			−0.226231			−0.113115	+	0.993582i	$0.536083\pi$
$410$	11898.1	+	10384.9i	1.43319	+	1.25091i
$411$		−	3994.08i		−	0.479351i
$412$	−1367.84	−	10024.6i	−0.163564	−	1.19873i
$413$			14568.2i			1.73572i
$414$	−1283.03	+	1469.99i	−0.152313	+	0.174507i
$415$	11062.3			1.30850
$416$	3754.38	+	1796.80i	0.442485	+	0.211768i
$417$	5832.01			0.684879
$418$	−124.158	+	142.250i	−0.0145282	+	0.0166451i
$419$		−	1709.40i		−	0.199308i	−0.995022	−	0.0996538i	$-0.968226\pi$
$419$		−	1709.40i		−	0.199308i	0.995022	−	0.0996538i	$-0.0317735\pi$
$420$	2798.43	+	20509.1i	0.325117	+	2.38272i
$421$			3736.71i			0.432580i	0.976329	+	0.216290i	$0.0693956\pi$
$421$			3736.71i			0.432580i	−0.976329	+	0.216290i	$0.930604\pi$
$422$	4524.38	+	3948.96i	0.521904	+	0.455527i
$423$	6881.11			0.790948
$424$	3026.76	−	4599.89i	0.346680	−	0.526864i
$425$	−5471.49			−0.624485
$426$	398.220	+	347.574i	0.0452907	+	0.0395305i
$427$		−	17095.6i		−	1.93751i
$428$	−4483.47	+	611.760i	−0.506348	+	0.0690901i
$429$		−	103.413i		−	0.0116383i
$430$	−5691.11	+	6520.39i	−0.638256	+	0.731258i
$431$	−1214.16			−0.135694			−0.0678468	−	0.997696i	$-0.521613\pi$
$431$	−1214.16			−0.135694			−0.0678468	+	0.997696i	$0.521613\pi$
$432$	−2474.02	−	8897.03i	−0.275536	−	0.990876i
$433$	4290.25			0.476158			0.238079	−	0.971246i	$-0.423482\pi$
$433$	4290.25			0.476158			0.238079	+	0.971246i	$0.423482\pi$
$434$	10780.5	−	12351.4i	1.19235	−	1.36609i
$435$			5352.87i			0.590001i
$436$	−10709.8	+	1461.33i	−1.17639	+	0.160517i
$437$		−	2254.25i		−	0.246762i
$438$	4696.13	+	4098.87i	0.512306	+	0.447150i
$439$	7584.89			0.824617			0.412309	−	0.911044i	$-0.364723\pi$
$439$	7584.89			0.824617			0.412309	+	0.911044i	$0.364723\pi$
$440$	−528.605	−	347.825i	−0.0572733	−	0.0376862i
$441$	14719.3			1.58939
$442$	−832.936	−	727.002i	−0.0896351	−	0.0782352i
$443$			12323.7i			1.32171i	0.750514	+	0.660854i	$0.229806\pi$
$443$			12323.7i			1.32171i	−0.750514	+	0.660854i	$0.770194\pi$
$444$	−1364.94	−	10003.4i	−0.145894	−	1.06923i
$445$		−	12756.9i		−	1.35896i
$446$	−9673.41	+	11083.0i	−1.02702	+	1.17667i
$447$	1154.93			0.122206
$448$	7294.15	+	16928.9i	0.769233	+	1.78531i
$449$	−10994.8			−1.15563			−0.577815	−	0.816168i	$-0.696094\pi$
$449$	−10994.8			−1.15563			−0.577815	+	0.816168i	$0.696094\pi$
$450$	9243.69	−	10590.6i	0.968338	−	1.10944i
$451$		−	349.434i		−	0.0364838i
$452$	491.060	+	3598.89i	0.0511007	+	0.374508i
$453$			1462.39i			0.151675i
$454$	−7575.06	−	6611.65i	−0.783073	−	0.683481i
$455$	−17499.1			−1.80302
$456$	3242.75	+	2133.75i	0.333017	+	0.219127i
$457$	−15812.8			−1.61858			−0.809289	−	0.587411i	$-0.800147\pi$
$457$	−15812.8			−1.61858			−0.809289	+	0.587411i	$0.800147\pi$
$458$	−8343.46	−	7282.33i	−0.851232	−	0.742971i
$459$			2452.94i			0.249441i
$460$	7485.39	−	1021.36i	0.758713	−	0.103525i
$461$			5226.08i			0.527988i	0.964524	+	0.263994i	$0.0850400\pi$
$461$			5226.08i			0.527988i	−0.964524	+	0.263994i	$0.914960\pi$
$462$	301.164	−	345.048i	0.0303278	−	0.0347470i
$463$	10585.7			1.06254			0.531272	−	0.847202i	$-0.321714\pi$
$463$	10585.7			1.06254			0.531272	+	0.847202i	$0.321714\pi$
$464$	1277.10	+	4592.70i	0.127776	+	0.459506i
$465$	11570.1			1.15387
$466$	−1971.63	+	2258.92i	−0.195995	+	0.224555i
$467$		−	12269.4i		−	1.21576i	−0.794029	−	0.607880i	$-0.792020\pi$
$467$		−	12269.4i		−	1.21576i	0.794029	−	0.607880i	$-0.207980\pi$
$468$	2814.37	−	384.015i	0.277980	−	0.0379297i
$469$			15276.9i			1.50409i
$470$	−20072.7	−	17519.8i	−1.96997	−	1.71942i
$471$	−11163.1			−1.09208
$472$	−5032.84	+	7648.62i	−0.490795	+	0.745882i
$473$	191.496			0.0186152
$474$	1138.47	+	993.675i	0.110320	+	0.0962891i
$475$			16240.9i			1.56881i
$476$	−661.969	−	4851.44i	−0.0637422	−	0.467154i
$477$		−	3757.78i		−	0.360706i
$478$	7820.74	−	8960.33i	0.748352	−	0.857398i
$479$	−10339.1			−0.986235			−0.493118	−	0.869963i	$-0.664143\pi$
$479$	−10339.1			−0.986235			−0.493118	+	0.869963i	$0.664143\pi$
$480$	−5616.02	+	11734.5i	−0.534032	+	1.11585i
$481$	8535.24			0.809092
$482$	691.327	−	792.063i	0.0653301	−	0.0748496i
$483$			5468.01i			0.515120i
$484$	−1437.66	−	10536.4i	−0.135017	−	0.989516i
$485$		−	3017.54i		−	0.282514i
$486$	−7768.38	−	6780.38i	−0.725063	−	0.632849i
$487$	5138.18			0.478097			0.239049	−	0.971008i	$-0.423164\pi$
$487$	5138.18			0.478097			0.239049	+	0.971008i	$0.423164\pi$
$488$	5906.00	−	8975.60i	0.547852	−	0.832595i
$489$	−7510.49			−0.694552
$490$	−42937.4	−	37476.5i	−3.95860	−	3.45514i
$491$			8771.11i			0.806180i	0.915160	+	0.403090i	$0.132064\pi$
$491$			8771.11i			0.806180i	−0.915160	+	0.403090i	$0.867936\pi$
$492$	−7118.03	+	971.240i	−0.652248	+	0.0889977i
$493$		−	1266.22i		−	0.115675i
$494$	−2157.94	+	2472.38i	−0.196539	+	0.225178i
$495$	−431.832			−0.0392110
$496$	9927.01	−	2760.43i	0.898662	−	0.249893i
$497$	−1979.03			−0.178615
$498$	−3309.00	+	3791.16i	−0.297750	+	0.341137i
$499$		−	10907.2i		−	0.978502i	−0.872143	−	0.489251i	$-0.837270\pi$
$499$		−	10907.2i		−	0.978502i	0.872143	−	0.489251i	$-0.162730\pi$
$500$	−32984.2	+	4500.63i	−2.95020	+	0.402548i
$501$			6593.06i			0.587936i
$502$	−52.8587	−	46.1360i	−0.00469960	−	0.00410189i
$503$	18065.6			1.60140			0.800700	−	0.599066i	$-0.204461\pi$
$503$	18065.6			1.60140			0.800700	+	0.599066i	$0.204461\pi$
$504$	10508.8	+	6914.86i	0.928770	+	0.611136i
$505$	−17968.7			−1.58336
$506$	−125.935	−	109.918i	−0.0110642	−	0.00965705i
$507$			5671.82i			0.496833i
$508$	2411.75	+	17675.3i	0.210638	+	1.54373i
$509$			21694.5i			1.88918i	0.328249	+	0.944591i	$0.393541\pi$
$509$			21694.5i			1.88918i	−0.328249	+	0.944591i	$0.606459\pi$
$510$	2272.29	−	2603.39i	0.197291	−	0.226040i
$511$	−23338.3			−2.02040
$512$	−2018.81	+	11408.0i	−0.174257	+	0.984700i
$513$	7281.01			0.626636
$514$	4968.33	−	5692.29i	0.426350	−	0.488475i
$515$			26734.1i			2.28747i
$516$	−532.256	−	3900.81i	−0.0454095	−	0.332797i
$517$			589.511i			0.0501483i
$518$	28478.8	+	24856.8i	2.41561	+	2.10839i
$519$	3805.27			0.321836
$520$	−9187.46	−	6045.40i	−0.774802	−	0.509824i
$521$	−16531.5			−1.39013			−0.695065	−	0.718947i	$-0.744624\pi$
$521$	−16531.5			−1.39013			−0.695065	+	0.718947i	$0.744624\pi$
$522$	2450.90	+	2139.19i	0.205504	+	0.179368i
$523$		−	21109.8i		−	1.76495i	−0.470361	−	0.882474i	$-0.655876\pi$
$523$		−	21109.8i		−	1.76495i	0.470361	−	0.882474i	$-0.344124\pi$
$524$	13264.4	−	1809.89i	1.10583	−	0.150888i
$525$		−	39394.7i		−	3.27491i
$526$	11814.3	−	13535.8i	0.979329	−	1.12203i
$527$	−2736.91			−0.226227
$528$	277.322	−	77.1156i	0.0228577	−	0.00635611i
$529$	−10171.3			−0.835974
$530$	−9567.59	+	10961.7i	−0.784131	+	0.898390i
$531$			6248.37i			0.510652i
$532$	−14400.4	+	1964.91i	−1.17357	+	0.160131i
$533$		−	6073.37i		−	0.493559i
$534$	4371.92	+	3815.89i	0.354291	+	0.309232i
$535$	11956.7			0.966233
$536$	−5277.67	+	8020.71i	−0.425300	+	0.646347i
$537$	3875.23			0.311412
$538$	−4813.44	−	4201.26i	−0.385729	−	0.336671i
$539$			1261.02i			0.100772i
$540$	3298.91	+	24177.1i	0.262894	+	1.92670i
$541$			1140.05i			0.0905998i	0.998973	+	0.0452999i	$0.0144243\pi$
$541$			1140.05i			0.0905998i	−0.998973	+	0.0452999i	$0.985576\pi$
$542$	−7463.77	+	8551.35i	−0.591507	+	0.677697i
$543$	6096.54			0.481819
$544$	1328.47	−	2775.81i	0.104702	−	0.218772i
$545$	28561.5			2.24484
$546$	5234.41	−	5997.14i	0.410279	−	0.470062i
$547$			1815.52i			0.141913i	0.997479	+	0.0709563i	$0.0226051\pi$
$547$			1815.52i			0.141913i	−0.997479	+	0.0709563i	$0.977395\pi$
$548$	1270.64	+	9312.30i	0.0990496	+	0.725916i
$549$		−	7332.42i		−	0.570018i
$550$	907.308	+	791.915i	0.0703414	+	0.0613952i
$551$	−3758.50			−0.290594
$552$	−1889.02	+	2870.83i	−0.145656	+	0.221360i
$553$	−5657.82			−0.435072
$554$	8124.35	+	7091.08i	0.623051	+	0.543811i
$555$			26677.4i			2.04035i
$556$	−13597.5	+	1855.35i	−1.03716	+	0.141518i
$557$			12853.9i			0.977803i	0.872339	+	0.488901i	$0.162602\pi$
$557$			12853.9i			0.977803i	−0.872339	+	0.488901i	$0.837398\pi$
$558$	4623.82	−	5297.58i	0.350792	−	0.401907i
$559$	3328.31			0.251829
$560$	−13049.2	−	46927.4i	−0.984697	−	3.54115i
$561$	−76.4585			−0.00575415
$562$	4265.96	−	4887.57i	0.320193	−	0.366850i
$563$			7349.70i			0.550183i	0.961418	+	0.275091i	$0.0887081\pi$
$563$			7349.70i			0.550183i	−0.961418	+	0.275091i	$0.911292\pi$
$564$	12008.4	−	1638.53i	0.896536	−	0.122330i
$565$		−	9597.67i		−	0.714650i
$566$	6432.62	+	5614.51i	0.477709	+	0.416953i
$567$	−2650.46			−0.196312
$568$	−1039.04	−	683.692i	−0.0767552	−	0.0505054i
$569$	1835.93			0.135266			0.0676328	−	0.997710i	$-0.478455\pi$
$569$	1835.93			0.135266			0.0676328	+	0.997710i	$0.478455\pi$
$570$	−7727.59	−	6744.78i	−0.567848	−	0.495628i
$571$			8306.81i			0.608808i	0.952543	+	0.304404i	$0.0984572\pi$
$571$			8306.81i			0.608808i	−0.952543	+	0.304404i	$0.901543\pi$
$572$	32.8989	+	241.110i	0.00240485	+	0.0176247i
$573$			13076.2i			0.953344i
$574$	17687.2	−	20264.5i	1.28615	−	1.47356i
$575$	−14378.2			−1.04280
$576$	3128.51	+	7260.93i	0.226310	+	0.525241i
$577$	−20957.8			−1.51210			−0.756051	−	0.654513i	$-0.772874\pi$
$577$	−20957.8			−1.51210			−0.756051	+	0.654513i	$0.772874\pi$
$578$	−537.510	+	615.833i	−0.0386808	+	0.0443171i
$579$			5347.46i			0.383822i
$580$	−1702.92	−	12480.4i	−0.121914	−	0.893481i
$581$		−	18840.9i		−	1.34535i
$582$	1034.14	+	902.618i	0.0736539	+	0.0642865i
$583$	321.932			0.0228698
$584$	−12253.2	−	8062.64i	−0.868217	−	0.571292i
$585$	−7505.50			−0.530451
$586$	4473.18	+	3904.27i	0.315333	+	0.275229i
$587$		−	1119.97i		−	0.0787500i	−0.999225	−	0.0393750i	$-0.987463\pi$
$587$		−	1119.97i		−	0.0787500i	0.999225	−	0.0393750i	$-0.0125367\pi$
$588$	25687.2	−	3504.96i	1.80157	−	0.245820i
$589$			8123.91i			0.568319i
$590$	15908.8	−	18227.0i	1.11009	−	1.27185i
$591$	−5112.46			−0.355835
$592$	6364.78	+	22888.9i	0.441877	+	1.58907i
$593$	−17060.2			−1.18141			−0.590707	−	0.806886i	$-0.701151\pi$
$593$	−17060.2			−1.18141			−0.590707	+	0.806886i	$0.701151\pi$
$594$	355.026	−	406.759i	0.0245234	−	0.0280968i
$595$			12938.0i			0.891442i
$596$	−2692.75	+	367.419i	−0.185066	+	0.0252518i
$597$			5241.77i			0.359349i
$598$	−2188.82	−	1910.44i	−0.149678	−	0.130642i
$599$	14554.2			0.992769			0.496385	−	0.868103i	$-0.334661\pi$
$599$	14554.2			0.992769			0.496385	+	0.868103i	$0.334661\pi$
$600$	13609.6	−	20683.1i	0.926018	−	1.40731i
$601$	−15344.2			−1.04143			−0.520717	−	0.853730i	$-0.674335\pi$
$601$	−15344.2			−1.04143			−0.520717	+	0.853730i	$0.674335\pi$
$602$	11105.3	+	9692.88i	0.751855	+	0.656233i
$603$			6552.34i			0.442507i
$604$	−465.232	−	3409.60i	−0.0313411	−	0.229693i
$605$			28098.9i			1.88823i
$606$	5374.88	−	6158.07i	0.360296	−	0.412796i
$607$	17195.4			1.14982			0.574908	−	0.818218i	$-0.305038\pi$
$607$	17195.4			1.14982			0.574908	+	0.818218i	$0.305038\pi$
$608$	−8239.37	−	3943.27i	−0.549590	−	0.263027i
$609$	9116.80			0.606620
$610$	−18668.9	+	21389.2i	−1.23915	+	1.41971i
$611$			10246.0i			0.678413i
$612$	−283.923	−	2080.81i	−0.0187531	−	0.137438i
$613$		−	5210.05i		−	0.343282i	−0.985160	−	0.171641i	$-0.945093\pi$
$613$		−	5210.05i		−	0.343282i	0.985160	−	0.171641i	$-0.0549070\pi$
$614$	4754.91	+	4150.17i	0.312529	+	0.272781i
$615$	18982.7			1.24464
$616$	−592.402	+	900.299i	−0.0387477	+	0.0588865i
$617$	−9605.27			−0.626732			−0.313366	−	0.949632i	$-0.601457\pi$
$617$	−9605.27			−0.626732			−0.313366	+	0.949632i	$0.601457\pi$
$618$	−9162.04	−	7996.80i	−0.596362	−	0.520515i
$619$			10970.5i			0.712345i	0.934420	+	0.356172i	$0.115918\pi$
$619$			10970.5i			0.712345i	−0.934420	+	0.356172i	$0.884082\pi$
$620$	−26976.0	+	3680.82i	−1.74739	+	0.238428i
$621$			6445.94i			0.416533i
$622$	−3091.46	+	3541.93i	−0.199286	+	0.228325i
$623$	−21727.1			−1.39723
$624$	4820.01	−	1340.31i	0.309222	−	0.0859863i
$625$	47732.3			3.05487
$626$	1516.09	−	1737.00i	0.0967971	−	0.110902i
$627$			226.950i			0.0144554i
$628$	26027.1	−	3551.34i	1.65381	−	0.225659i
$629$		−	6310.55i		−	0.400029i
$630$	−25042.9	−	21857.9i	−1.58370	−	1.38229i
$631$	21720.1			1.37031			0.685154	−	0.728398i	$-0.259735\pi$
$631$	21720.1			1.37031			0.685154	+	0.728398i	$0.259735\pi$
$632$	−2970.49	−	1954.60i	−0.186962	−	0.123022i
$633$	7218.34			0.453244
$634$	−12086.5	−	10549.3i	−0.757123	−	0.660831i
$635$		−	47137.2i		−	2.94580i
$636$	−894.800	−	6557.82i	−0.0557879	−	0.408859i
$637$			21917.2i			1.36325i
$638$	−183.267	+	209.971i	−0.0113724	+	0.0130295i
$639$	−848.818			−0.0525488
$640$	9360.78	−	29146.1i	0.578152	−	1.80015i
$641$	21736.8			1.33939			0.669696	−	0.742635i	$-0.266424\pi$
$641$	21736.8			1.33939			0.669696	+	0.742635i	$0.266424\pi$
$642$	−3576.54	+	4097.69i	−0.219867	+	0.251905i
$643$		−	16220.6i		−	0.994831i	−0.867513	−	0.497415i	$-0.834283\pi$
$643$		−	16220.6i		−	0.994831i	0.867513	−	0.497415i	$-0.165717\pi$
$644$	−1739.55	−	12748.8i	−0.106441	−	0.780084i
$645$			10402.8i			0.635056i
$646$	1827.96	+	1595.48i	0.111332	+	0.0971723i
$647$	11372.7			0.691045			0.345523	−	0.938410i	$-0.387702\pi$
$647$	11372.7			0.691045			0.345523	+	0.938410i	$0.387702\pi$
$648$	−1391.55	−	915.649i	−0.0843600	−	0.0555094i
$649$	−535.303			−0.0323767
$650$	15769.5	+	13763.9i	0.951588	+	0.830564i
$651$		−	19705.8i		−	1.18637i
$652$	17510.9	−	2389.33i	1.05181	−	0.143517i
$653$		−	2019.60i		−	0.121031i	−0.998167	−	0.0605155i	$-0.980726\pi$
$653$		−	2019.60i		−	0.121031i	0.998167	−	0.0605155i	$-0.0192745\pi$
$654$	−8543.41	+	9788.31i	−0.510816	+	0.585249i
$655$	−35374.0			−2.11019
$656$	16286.9	−	4528.95i	0.969355	−	0.269551i
$657$	−10009.9			−0.594407
$658$	−29839.1	+	34187.0i	−1.76785	+	2.02546i
$659$		−	2381.04i		−	0.140747i	−0.997521	−	0.0703734i	$-0.977581\pi$
$659$		−	2381.04i		−	0.140747i	0.997521	−	0.0703734i	$-0.0224191\pi$
$660$	−753.604	+	102.828i	−0.0444454	+	0.00606448i
$661$		−	10353.6i		−	0.609239i	−0.952474	−	0.304619i	$-0.901471\pi$
$661$		−	10353.6i		−	0.609239i	0.952474	−	0.304619i	$-0.0985292\pi$
$662$	−1334.82	−	1165.05i	−0.0783672	−	0.0684003i
$663$	−1328.89			−0.0778430
$664$	6508.93	−	9891.90i	0.380415	−	0.578133i
$665$	38403.7			2.23944
$666$	12214.7	+	10661.2i	0.710677	+	0.620292i
$667$		−	3327.43i		−	0.193161i
$668$	−2097.46	−	15371.9i	−0.121487	−	0.890354i
$669$			17682.1i			1.02187i
$670$	16682.7	−	19113.7i	0.961956	−	1.10213i
$671$	628.175			0.0361407
$672$	19985.8	+	9564.99i	1.14728	+	0.549074i
$673$	−9430.32			−0.540137			−0.270068	−	0.962841i	$-0.587046\pi$
$673$	−9430.32			−0.540137			−0.270068	+	0.962841i	$0.587046\pi$
$674$	15165.3	−	17375.1i	0.866686	−	0.992974i
$675$		−	46440.3i		−	2.64813i
$676$	−1804.39	−	13224.0i	−0.102662	−	0.752390i
$677$			23598.4i			1.33967i	0.742508	+	0.669837i	$0.233636\pi$
$677$			23598.4i			1.33967i	−0.742508	+	0.669837i	$0.766364\pi$
$678$	3289.22	+	2870.89i	0.186315	+	0.162619i
$679$	−5139.36			−0.290472
$680$	−4469.68	+	6792.77i	−0.252066	+	0.383075i
$681$	−12085.5			−0.680055
$682$	453.848	+	396.127i	0.0254820	+	0.0222412i
$683$		−	15278.0i		−	0.855923i	−0.903797	−	0.427961i	$-0.859232\pi$
$683$		−	15278.0i		−	0.855923i	0.903797	−	0.427961i	$-0.140768\pi$
$684$	−6176.43	+	842.760i	−0.345266	+	0.0471107i
$685$		−	24834.5i		−	1.38522i
$686$	−40860.7	+	46814.6i	−2.27415	+	2.60553i
$687$	−13311.4			−0.739247
$688$	2481.94	+	8925.51i	0.137534	+	0.494596i
$689$	5595.37			0.309386
$690$	5971.22	−	6841.30i	0.329450	−	0.377455i
$691$		−	9266.06i		−	0.510127i	−0.966924	−	0.255063i	$-0.917904\pi$
$691$		−	9266.06i		−	0.510127i	0.966924	−	0.255063i	$-0.0820963\pi$
$692$	−8872.08	+	1210.58i	−0.487379	+	0.0665018i
$693$			735.480i			0.0403154i
$694$	3227.90	+	2817.37i	0.176555	+	0.154101i
$695$	36262.4			1.97915
$696$	4786.53	+	3149.57i	0.260680	+	0.171529i
$697$	−4490.36			−0.244024
$698$	−21342.0	−	18627.7i	−1.15732	−	1.01013i
$699$			3603.95i			0.195013i
$700$	12532.7	+	91849.8i	0.676703	+	4.95942i
$701$			677.706i			0.0365144i	0.999833	+	0.0182572i	$0.00581177\pi$
$701$			677.706i			0.0365144i	−0.999833	+	0.0182572i	$0.994188\pi$
$702$	6170.56	−	7069.70i	0.331756	−	0.380098i
$703$	−18731.5			−1.00494
$704$	−622.050	+	268.022i	−0.0333017	+	0.0143487i
$705$	−32024.6			−1.71081
$706$	−742.246	+	850.402i	−0.0395677	+	0.0453333i
$707$			30603.7i			1.62796i
$708$	1487.86	+	10904.2i	0.0789790	+	0.578822i
$709$		−	21334.8i		−	1.13011i	−0.825055	−	0.565053i	$-0.808856\pi$
$709$		−	21334.8i		−	1.13011i	0.825055	−	0.565053i	$-0.191144\pi$
$710$	2476.06	+	2161.15i	0.130880	+	0.114235i
$711$	−2426.68			−0.127999
$712$	−11407.2	−	7506.02i	−0.600426	−	0.395084i
$713$	−7192.17			−0.377768
$714$	−4434.00	−	3870.07i	−0.232406	−	0.202849i
$715$		−	643.002i		−	0.0336321i
$716$	−9035.20	+	1232.83i	−0.471594	+	0.0643480i
$717$		−	14295.6i		−	0.744602i
$718$	7669.57	−	8787.14i	0.398643	−	0.456731i
$719$	36141.9			1.87464			0.937318	−	0.348474i	$-0.113300\pi$
$719$	36141.9			1.87464			0.937318	+	0.348474i	$0.113300\pi$
$720$	−5596.90	−	20127.4i	−0.289700	−	1.04181i
$721$	45532.5			2.35190
$722$	−8021.22	+	9190.02i	−0.413461	+	0.473708i
$723$		−	1263.68i		−	0.0650026i
$724$	−14214.3	+	1939.50i	−0.729653	+	0.0995596i
$725$			23972.7i			1.22803i
$726$	−9629.76	−	8405.03i	−0.492278	−	0.429669i
$727$	−36614.9			−1.86791			−0.933956	−	0.357387i	$-0.883668\pi$
$727$	−36614.9			−1.86791			−0.933956	+	0.357387i	$0.883668\pi$
$728$	−10296.3	+	15647.7i	−0.524184	+	0.796625i
$729$	−14381.6			−0.730661
$730$	29199.7	+	25486.1i	1.48045	+	1.29217i
$731$		−	2460.79i		−	0.124509i
$732$	−1745.99	−	12796.0i	−0.0881608	−	0.646113i
$733$		−	23692.7i		−	1.19387i	−0.802289	−	0.596936i	$-0.796385\pi$
$733$		−	23692.7i		−	1.19387i	0.802289	−	0.596936i	$-0.203615\pi$
$734$	12340.8	−	14139.0i	0.620583	−	0.711010i
$735$	−68503.7			−3.43782
$736$	3491.01	−	7294.39i	0.174837	−	0.365319i
$737$	−561.345			−0.0280562
$738$	7586.15	−	8691.55i	0.378387	−	0.433524i
$739$			19337.2i			0.962558i	0.876567	+	0.481279i	$0.159828\pi$
$739$			19337.2i			0.962558i	−0.876567	+	0.481279i	$0.840172\pi$
$740$	−8486.94	−	62199.2i	−0.421603	−	3.08985i
$741$			3944.52i			0.195554i
$742$	18669.6	+	16295.1i	0.923695	+	0.806218i
$743$	−3141.98			−0.155139			−0.0775693	−	0.996987i	$-0.524716\pi$
$743$	−3141.98			−0.155139			−0.0775693	+	0.996987i	$0.524716\pi$
$744$	6807.72	−	10346.0i	0.335461	−	0.509815i
$745$	7181.13			0.353149
$746$	25942.0	+	22642.6i	1.27319	+	1.11127i
$747$		−	8080.97i		−	0.395806i
$748$	178.265	−	24.3239i	0.00871393	−	0.00118900i
$749$		−	20364.2i		−	0.993448i
$750$	−26312.1	+	30146.1i	−1.28104	+	1.46771i
$751$	−14579.1			−0.708387			−0.354194	−	0.935172i	$-0.615245\pi$
$751$	−14579.1			−0.708387			−0.354194	+	0.935172i	$0.615245\pi$
$752$	−27476.7	+	7640.54i	−1.33241	+	0.370508i
$753$	−84.3324			−0.00408133
$754$	−3185.28	+	3649.42i	−0.153848	+	0.176265i
$755$			9092.87i			0.438309i
$756$	41177.5	−	5618.58i	1.98097	−	0.270299i
$757$			26557.2i			1.27508i	0.770416	+	0.637541i	$0.220048\pi$
$757$			26557.2i			1.27508i	−0.770416	+	0.637541i	$0.779952\pi$
$758$	−23915.7	−	20874.0i	−1.14599	−	1.00024i
$759$	−200.921			−0.00960865
$760$	20162.8	+	13267.3i	0.962345	+	0.633229i
$761$	25342.3			1.20717			0.603585	−	0.797299i	$-0.293739\pi$
$761$	25342.3			1.20717			0.603585	+	0.797299i	$0.293739\pi$
$762$	16154.4	+	14099.8i	0.767994	+	0.670320i
$763$		−	48644.8i		−	2.30807i
$764$	−4159.95	−	30487.5i	−0.196992	−	1.44372i
$765$			5549.21i			0.262264i
$766$	1370.61	−	1570.32i	0.0646501	−	0.0740705i
$767$	−9303.88			−0.437997
$768$	7188.62	+	11926.3i	0.337757	+	0.560356i
$769$	8237.67			0.386291			0.193146	−	0.981170i	$-0.438131\pi$
$769$	8237.67			0.386291			0.193146	+	0.981170i	$0.438131\pi$
$770$	1872.59	−	2145.45i	0.0876407	−	0.100411i
$771$		−	9081.66i		−	0.424213i
$772$	−1701.20	−	12467.8i	−0.0793101	−	0.581249i
$773$		−	26852.0i		−	1.24942i	−0.780858	−	0.624709i	$-0.785218\pi$
$773$		−	26852.0i		−	1.24942i	0.780858	−	0.624709i	$-0.214782\pi$
$774$	4763.12	+	4157.34i	0.221197	+	0.193065i
$775$	51816.5			2.40168
$776$	−2698.28	−	1775.49i	−0.124823	−	0.0821343i
$777$	45436.0			2.09782
$778$	26671.4	+	23279.3i	1.22907	+	1.07275i
$779$			13328.6i			0.613026i
$780$	−13098.1	+	1787.20i	−0.601264	+	0.0820412i
$781$		−	72.7189i		−	0.00333174i
$782$	−1412.49	+	1618.31i	−0.0645916	+	0.0740035i
$783$	10747.3			0.490520
$784$	−58775.3	+	16343.8i	−2.67745	+	0.744525i
$785$	−69410.3			−3.15587
$786$	10581.2	−	12123.0i	0.480176	−	0.550145i
$787$			14269.9i			0.646339i	0.946341	+	0.323169i	$0.104748\pi$
$787$			14269.9i			0.646339i	−0.946341	+	0.323169i	$0.895252\pi$
$788$	11919.8	−	1626.44i	0.538866	−	0.0735271i
$789$		−	21595.4i		−	0.974421i
$790$	7078.79	+	6178.50i	0.318800	+	0.278254i
$791$	−16346.4			−0.734779
$792$	−254.085	+	386.144i	−0.0113996	+	0.0173245i
$793$	10918.0			0.488917
$794$	14814.9	+	12930.7i	0.662167	+	0.577951i
$795$			17488.7i			0.780201i
$796$	−1667.57	−	12221.3i	−0.0742533	−	0.544188i
$797$			5985.21i			0.266006i	0.991116	+	0.133003i	$0.0424620\pi$
$797$			5985.21i			0.266006i	−0.991116	+	0.133003i	$0.957538\pi$
$798$	−11487.4	+	13161.3i	−0.509588	+	0.583842i
$799$	7575.43			0.335419
$800$	−25151.3	+	52553.0i	−1.11154	+	2.32253i
$801$	−9318.88			−0.411069
$802$	27486.3	−	31491.5i	1.21019	−	1.38654i
$803$		−	857.561i		−	0.0376870i
$804$	1560.24	+	11434.7i	0.0684395	+	0.501580i
$805$			33999.1i			1.48859i
$806$	7888.14	+	6884.91i	0.344724	+	0.300882i
$807$	−7679.52			−0.334984
$808$	−10572.6	+	16067.6i	−0.460325	+	0.699576i
$809$	24655.1			1.07148			0.535739	−	0.844384i	$-0.320033\pi$
$809$	24655.1			1.07148			0.535739	+	0.844384i	$0.320033\pi$
$810$	3316.12	+	2894.37i	0.143848	+	0.125553i
$811$			1336.11i			0.0578511i	0.999582	+	0.0289255i	$0.00920857\pi$
$811$			1336.11i			0.0578511i	−0.999582	+	0.0289255i	$0.990791\pi$
$812$	−21256.1	+	2900.34i	−0.918648	+	0.125347i
$813$			13643.1i			0.588542i
$814$	−913.357	+	1046.45i	−0.0393282	+	0.0450589i
$815$	−46698.9			−2.00711
$816$	−990.964	−	3563.69i	−0.0425131	−	0.152885i
$817$	−7304.31			−0.312785
$818$	3480.37	−	3987.51i	0.148763	−	0.170440i
$819$			12783.1i			0.545393i
$820$	−44258.7	+	6039.00i	−1.88485	+	0.257184i
$821$			23963.6i			1.01868i	0.860565	+	0.509340i	$0.170111\pi$
$821$			23963.6i			1.01868i	−0.860565	+	0.509340i	$0.829889\pi$
$822$	8511.02	+	7428.58i	0.361139	+	0.315208i
$823$	−32712.5			−1.38552			−0.692762	−	0.721167i	$-0.743606\pi$
$823$	−32712.5			−1.38552			−0.692762	+	0.721167i	$0.743606\pi$
$824$	23905.6	+	15730.0i	1.01067	+	0.665026i
$825$	1447.55			0.0610875
$826$	−31043.4	−	27095.3i	−1.30767	−	1.14136i
$827$		−	41923.9i		−	1.76280i	−0.472368	−	0.881401i	$-0.656601\pi$
$827$		−	41923.9i		−	1.76280i	0.472368	−	0.881401i	$-0.343399\pi$
$828$	−746.103	−	5468.05i	−0.0313151	−	0.229502i
$829$		−	21043.1i		−	0.881615i	−0.897602	−	0.440807i	$-0.854692\pi$
$829$		−	21043.1i		−	0.881615i	0.897602	−	0.440807i	$-0.145308\pi$
$830$	−20574.7	+	23572.8i	−0.860434	+	0.985811i
$831$	12961.9			0.541085
$832$	−10811.6	+	4658.38i	−0.450510	+	0.194111i
$833$	16204.6			0.674015
$834$	−10846.9	+	12427.5i	−0.450358	+	0.515982i
$835$			40994.5i			1.69901i
$836$	−72.2000	−	529.140i	−0.00298695	−	0.0218908i
$837$		−	23230.1i		−	0.959317i
$838$	3642.59	+	3179.32i	0.150156	+	0.131059i
$839$	15634.6			0.643345			0.321673	−	0.946851i	$-0.395755\pi$
$839$	15634.6			0.643345			0.321673	+	0.946851i	$0.395755\pi$
$840$	−48907.9	−	32181.7i	−2.00891	−	1.32187i
$841$	18841.2			0.772528
$842$	−7962.59	−	6949.90i	−0.325902	−	0.284453i
$843$		−	7797.78i		−	0.318588i
$844$	−16829.8	+	2296.39i	−0.686380	+	0.0936550i
$845$			35266.4i			1.43574i
$846$	−12798.2	+	14663.0i	−0.520106	+	0.595893i
$847$	47856.9			1.94142
$848$	4172.50	+	15005.1i	0.168967	+	0.607637i
$849$	10262.8			0.414863
$850$	10176.4	−	11659.3i	0.410645	−	0.470481i
$851$		−	16583.1i		−	0.667993i
$852$	−1481.30	+	202.120i	−0.0595639	+	0.00812736i
$853$		−	49098.9i		−	1.97083i	−0.170178	−	0.985413i	$-0.554434\pi$
$853$		−	49098.9i		−	1.97083i	0.170178	−	0.985413i	$-0.445566\pi$
$854$	36429.2	+	31796.1i	1.45970	+	1.27405i
$855$	16471.6			0.658849
$856$	7035.20	−	10691.7i	0.280909	−	0.426910i
$857$	30953.5			1.23378			0.616890	−	0.787049i	$-0.288392\pi$
$857$	30953.5			1.23378			0.616890	+	0.787049i	$0.288392\pi$
$858$	220.363	+	192.337i	0.00876816	+	0.00765301i
$859$			31986.2i			1.27049i	0.772309	+	0.635246i	$0.219101\pi$
$859$			31986.2i			1.27049i	−0.772309	+	0.635246i	$0.780899\pi$
$860$	−3309.47	−	24254.5i	−0.131223	−	0.961712i
$861$		−	32330.6i		−	1.27970i
$862$	2258.21	−	2587.26i	0.0892285	−	0.102230i
$863$	5417.61			0.213694			0.106847	−	0.994275i	$-0.465925\pi$
$863$	5417.61			0.213694			0.106847	+	0.994275i	$0.465925\pi$
$864$	23560.2	+	11275.6i	0.927702	+	0.443988i
$865$	23660.5			0.930035
$866$	−7979.43	+	9142.15i	−0.313109	+	0.358733i
$867$			982.520i			0.0384869i
$868$	6269.03	+	45944.5i	0.245144	+	1.79661i
$869$		−	207.895i		−	0.00811550i
$870$	−11406.5	−	9955.79i	−0.444501	−	0.387969i
$871$	−9756.50			−0.379548
$872$	16805.2	−	25539.6i	0.652634	−	0.991836i
$873$	−2204.30			−0.0854574
$874$	4803.60	+	4192.67i	0.185909	+	0.162264i
$875$		−	149817.i		−	5.78826i
$876$	−17468.7	+	2383.56i	−0.673757	+	0.0919327i
$877$			38749.6i			1.49200i	0.665948	+	0.745998i	$0.268027\pi$
$877$			38749.6i			1.49200i	−0.665948	+	0.745998i	$0.731973\pi$
$878$	−14107.1	+	16162.7i	−0.542246	+	0.621259i
$879$	7136.66			0.273849
$880$	1724.34	−	479.491i	0.0660538	−	0.0183678i
$881$	−33654.7			−1.28701			−0.643506	−	0.765441i	$-0.722521\pi$
$881$	−33654.7			−1.28701			−0.643506	+	0.765441i	$0.722521\pi$
$882$	−27376.5	+	31365.6i	−1.04514	+	1.19743i
$883$		−	2077.27i		−	0.0791682i	−0.999216	−	0.0395841i	$-0.987397\pi$
$883$		−	2077.27i		−	0.0791682i	0.999216	−	0.0395841i	$-0.0126033\pi$
$884$	3098.35	−	422.763i	0.117883	−	0.0160849i
$885$		−	29079.9i		−	1.10453i
$886$	−26260.7	−	22920.8i	−0.995763	−	0.869120i
$887$	−29795.2			−1.12787			−0.563936	−	0.825818i	$-0.690714\pi$
$887$	−29795.2			−1.12787			−0.563936	+	0.825818i	$0.690714\pi$
$888$	23854.9	+	15696.7i	0.901486	+	0.593183i
$889$	−80282.2			−3.02877
$890$	27183.8	+	23726.6i	1.02383	+	0.893613i
$891$		−	97.3904i		−	0.00366184i
$892$	−5625.24	−	41226.3i	−0.211151	−	1.54749i
$893$		−	22486.0i		−	0.842625i
$894$	−2148.05	+	2461.05i	−0.0803595	+	0.0920690i
$895$	24095.5			0.899914
$896$	−49640.4	−	15942.9i	−1.85086	−	0.594437i
$897$	−3492.12			−0.129987
$898$	20449.2	−	23429.0i	0.759911	−	0.870641i
$899$			11991.5i			0.444870i
$900$	5375.36	+	39395.0i	0.199087	+	1.45907i
$901$		−	4136.95i		−	0.152965i
$902$	744.613	+	649.912i	0.0274866	+	0.0239908i
$903$	17717.7			0.652944
$904$	−8582.23	−	5647.16i	−0.315753	−	0.207767i
$905$	37907.2			1.39235
$906$	−3116.22	−	2719.89i	−0.114271	−	0.0997377i
$907$			28087.5i			1.02826i	0.857713	+	0.514130i	$0.171885\pi$
$907$			28087.5i			1.02826i	−0.857713	+	0.514130i	$0.828115\pi$
$908$	28177.7	−	3844.78i	1.02986	−	0.140522i
$909$			13126.1i			0.478950i
$910$	32546.6	−	37289.1i	1.18562	−	1.35838i
$911$	−42586.7			−1.54880			−0.774401	−	0.632695i	$-0.781949\pi$
$911$	−42586.7			−1.54880			−0.774401	+	0.632695i	$0.781949\pi$
$912$	−10578.0	+	2941.45i	−0.384071	+	0.106800i
$913$	692.304			0.0250952
$914$	29410.1	−	33695.6i	1.06433	−	1.21942i
$915$			34125.0i			1.23294i
$916$	31036.0	−	4234.79i	1.11949	−	0.152753i
$917$			60247.5i			2.16963i
$918$	−5227.00	−	4562.22i	−0.187927	−	0.164026i
$919$	−5275.59			−0.189364			−0.0946820	−	0.995508i	$-0.530183\pi$
$919$	−5275.59			−0.189364			−0.0946820	+	0.995508i	$0.530183\pi$
$920$	−11745.6	+	17850.3i	−0.420915	+	0.639682i
$921$	7586.14			0.271413
$922$	−11136.3	−	9719.97i	−0.397782	−	0.347191i
$923$		−	1263.90i		−	0.0450722i
$924$	175.132	+	1283.51i	0.00623530	+	0.0456973i
$925$			119474.i			4.24680i
$926$	−19688.2	+	22557.1i	−0.698700	+	0.800510i
$927$	19529.2			0.691933
$928$	−12161.9	−	5820.55i	−0.430209	−	0.205893i
$929$	−21538.2			−0.760651			−0.380326	−	0.924853i	$-0.624188\pi$
$929$	−21538.2			−0.760651			−0.380326	+	0.924853i	$0.624188\pi$
$930$	−21519.2	+	24654.9i	−0.758756	+	0.869317i
$931$		−	48099.6i		−	1.69323i
$932$	−1146.53	−	8402.72i	−0.0402961	−	0.295322i
$933$			5650.90i			0.198288i
$934$	26145.0	+	22819.8i	0.915943	+	0.799451i
$935$	−475.405			−0.0166283
$936$	−4416.15	+	6711.41i	−0.154216	+	0.234369i
$937$	27121.0			0.945576			0.472788	−	0.881176i	$-0.343248\pi$
$937$	27121.0			0.945576			0.472788	+	0.881176i	$0.343248\pi$
$938$	−32553.6	−	28413.4i	−1.13317	−	0.989051i
$939$		−	2771.27i		−	0.0963119i
$940$	74666.3	−	10188.1i	2.59080	−	0.353508i
$941$			37778.5i			1.30876i	0.756166	+	0.654380i	$0.227070\pi$
$941$			37778.5i			1.30876i	−0.756166	+	0.654380i	$0.772930\pi$
$942$	20762.3	−	23787.6i	0.718122	−	0.822762i
$943$	−11799.9			−0.407486
$944$	−6937.96	−	24950.2i	−0.239207	−	0.860232i
$945$	−109814.			−3.78016
$946$	−356.163	+	408.061i	−0.0122409	+	0.0140245i
$947$		−	34635.6i		−	1.18850i	−0.804281	−	0.594249i	$-0.797449\pi$
$947$		−	34635.6i		−	1.18850i	0.804281	−	0.594249i	$-0.202551\pi$
$948$	−4234.87	+	577.838i	−0.145087	+	0.0197967i
$949$		−	14904.9i		−	0.509835i
$950$	−34607.9	−	30206.4i	−1.18192	−	1.03160i
$951$	−19283.2			−0.657518
$952$	11569.2	+	7612.59i	0.393865	+	0.259165i
$953$	17330.3			0.589069			0.294534	−	0.955641i	$-0.404835\pi$
$953$	17330.3			0.589069			0.294534	+	0.955641i	$0.404835\pi$
$954$	8007.50	+	6989.09i	0.271753	+	0.237191i
$955$			81305.5i			2.75496i
$956$	4547.89	+	33330.6i	0.153859	+	1.12760i
$957$			334.995i			0.0113154i
$958$	19229.7	−	22031.7i	0.648522	−	0.743020i
$959$	−42297.1			−1.42424
$960$	−14560.0	−	33792.3i	−0.489504	−	1.13609i
$961$	−3871.66			−0.129961
$962$	−15874.7	+	18187.8i	−0.532037	+	0.609563i
$963$		−	8734.35i		−	0.292275i
$964$	402.018	+	2946.31i	0.0134317	+	0.0984382i
$965$			33249.5i			1.10916i
$966$	−11651.8	−	10169.9i	−0.388087	−	0.338729i
$967$	10669.2			0.354808			0.177404	−	0.984138i	$-0.443230\pi$
$967$	10669.2			0.354808			0.177404	+	0.984138i	$0.443230\pi$
$968$	25126.0	+	16533.0i	0.834276	+	0.548958i
$969$	2916.39			0.0966852
$970$	6430.11	+	5612.32i	0.212844	+	0.185774i
$971$		−	34329.6i		−	1.13459i	−0.823514	−	0.567296i	$-0.807990\pi$
$971$		−	34329.6i		−	1.13459i	0.823514	−	0.567296i	$-0.192010\pi$
$972$	28896.8	−	3942.90i	0.953565	−	0.130112i
$973$		−	61760.7i		−	2.03490i
$974$	−9556.49	+	10949.0i	−0.314384	+	0.360194i
$975$	25159.2			0.826401
$976$	8141.65	+	29278.9i	0.267016	+	0.960239i
$977$	474.154			0.0155266			0.00776332	−	0.999970i	$-0.497529\pi$
$977$	474.154			0.0155266			0.00776332	+	0.999970i	$0.497529\pi$
$978$	13968.7	−	16004.2i	0.456719	−	0.523269i
$979$		−	798.356i		−	0.0260629i
$980$	159718.	−	21793.2i	5.20614	−	0.710366i
$981$		−	20864.1i		−	0.679040i
$982$	−18690.5	−	16313.4i	−0.607369	−	0.530123i
$983$	9073.76			0.294413			0.147207	−	0.989106i	$-0.452972\pi$
$983$	9073.76			0.294413			0.147207	+	0.989106i	$0.452972\pi$
$984$	11169.2	−	16974.3i	0.361850	−	0.549920i
$985$	−31788.4			−1.02829
$986$	2698.21	+	2355.04i	0.0871485	+	0.0760648i
$987$			54543.1i			1.75899i
$988$	−1254.88	−	9196.76i	−0.0404079	−	0.296142i
$989$		−	6466.57i		−	0.207912i
$990$	803.164	−	920.196i	0.0257841	−	0.0295412i
$991$	−24588.7			−0.788178			−0.394089	−	0.919072i	$-0.628940\pi$
$991$	−24588.7			−0.788178			−0.394089	+	0.919072i	$0.628940\pi$
$992$	−12581.0	+	26287.7i	−0.402668	+	0.841366i
$993$	−2129.61			−0.0680574
$994$	3680.79	−	4217.13i	0.117452	−	0.134567i
$995$			32592.4i			1.03844i
$996$	−1924.23	−	14102.3i	−0.0612166	−	0.448645i
$997$		−	40948.3i		−	1.30075i	−0.759614	−	0.650374i	$-0.774612\pi$
$997$		−	40948.3i		−	1.30075i	0.759614	−	0.650374i	$-0.225388\pi$
$998$	23242.2	+	20286.2i	0.737194	+	0.643437i
$999$	53562.0			1.69632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.8	yes	24
4.3	odd	2		544.4.c.a.273.10		24
8.3	odd	2		544.4.c.a.273.15		24
8.5	even	2	inner	136.4.c.b.69.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.7	✓	24	8.5	even	2	inner
136.4.c.b.69.8	yes	24	1.1	even	1	trivial
544.4.c.a.273.10		24	4.3	odd	2
544.4.c.a.273.15		24	8.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85990 + 2.13091i) q^{2} +3.39972i q^{3} +(-1.08156 - 7.92655i) q^{4} +21.1389i q^{5} +(-7.24451 - 6.32314i) q^{6} +36.0029 q^{7} +(18.9024 + 12.4379i) q^{8} +15.4419 q^{9} +O(q^{10})\)	\(q+(-1.85990 + 2.13091i) q^{2} +3.39972i q^{3} +(-1.08156 - 7.92655i) q^{4} +21.1389i q^{5} +(-7.24451 - 6.32314i) q^{6} +36.0029 q^{7} +(18.9024 + 12.4379i) q^{8} +15.4419 q^{9} +(-45.0451 - 39.3162i) q^{10} +1.32292i q^{11} +(26.9481 - 3.67701i) q^{12} +22.9931i q^{13} +(-66.9617 + 76.7190i) q^{14} -71.8664 q^{15} +(-61.6605 + 17.1461i) q^{16} +17.0000 q^{17} +(-28.7203 + 32.9053i) q^{18} -50.4607i q^{19} +(167.558 - 22.8630i) q^{20} +122.400i q^{21} +(-2.81902 - 2.46049i) q^{22} +44.6733 q^{23} +(-42.2853 + 64.2628i) q^{24} -321.852 q^{25} +(-48.9962 - 42.7648i) q^{26} +144.291i q^{27} +(-38.9393 - 285.379i) q^{28} -74.4837i q^{29} +(133.664 - 153.141i) q^{30} -160.995 q^{31} +(78.1453 - 163.283i) q^{32} -4.49756 q^{33} +(-31.6183 + 36.2255i) q^{34} +761.061i q^{35} +(-16.7013 - 122.401i) q^{36} -371.209i q^{37} +(107.527 + 93.8517i) q^{38} -78.1702 q^{39} +(-262.923 + 399.575i) q^{40} -264.139 q^{41} +(-260.823 - 227.651i) q^{42} -144.753i q^{43} +(10.4862 - 1.43082i) q^{44} +326.424i q^{45} +(-83.0878 + 95.1948i) q^{46} +445.614 q^{47} +(-58.2920 - 209.629i) q^{48} +953.209 q^{49} +(598.612 - 685.838i) q^{50} +57.7953i q^{51} +(182.256 - 24.8684i) q^{52} -243.350i q^{53} +(-307.471 - 268.366i) q^{54} -27.9650 q^{55} +(680.540 + 447.799i) q^{56} +171.552 q^{57} +(158.718 + 138.532i) q^{58} +404.638i q^{59} +(77.7278 + 569.652i) q^{60} -474.840i q^{61} +(299.434 - 343.066i) q^{62} +555.952 q^{63} +(202.599 + 470.210i) q^{64} -486.048 q^{65} +(8.36500 - 9.58390i) q^{66} +424.323i q^{67} +(-18.3865 - 134.751i) q^{68} +151.877i q^{69} +(-1621.75 - 1415.50i) q^{70} -54.9686 q^{71} +(291.888 + 192.064i) q^{72} -648.234 q^{73} +(791.013 + 690.411i) q^{74} -1094.21i q^{75} +(-399.979 + 54.5763i) q^{76} +47.6289i q^{77} +(145.389 - 166.574i) q^{78} -157.149 q^{79} +(-362.449 - 1303.43i) q^{80} -73.6178 q^{81} +(491.271 - 562.856i) q^{82} -523.315i q^{83} +(970.210 - 132.383i) q^{84} +359.361i q^{85} +(308.455 + 269.225i) q^{86} +253.224 q^{87} +(-16.4543 + 25.0063i) q^{88} -603.481 q^{89} +(-695.580 - 607.115i) q^{90} +827.818i q^{91} +(-48.3169 - 354.105i) q^{92} -547.338i q^{93} +(-828.796 + 949.563i) q^{94} +1066.68 q^{95} +(555.117 + 265.673i) q^{96} -142.748 q^{97} +(-1772.87 + 2031.20i) q^{98} +20.4283i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

L-functions

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