LMFDB - Embedded newform 76.5.b.a.39.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.20
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.515277 + 3.96667i) q^{2} +1.66205i q^{3} +(-15.4690 + 4.08787i) q^{4} -27.3711 q^{5} +(-6.59279 + 0.856415i) q^{6} -39.8073i q^{7} +(-24.1861 - 59.2540i) q^{8} +78.2376 q^{9} +O(q^{10})$	\(q+(0.515277 + 3.96667i) q^{2} +1.66205i q^{3} +(-15.4690 + 4.08787i) q^{4} -27.3711 q^{5} +(-6.59279 + 0.856415i) q^{6} -39.8073i q^{7} +(-24.1861 - 59.2540i) q^{8} +78.2376 q^{9} +(-14.1037 - 108.572i) q^{10} -69.8049i q^{11} +(-6.79423 - 25.7102i) q^{12} -87.6129 q^{13} +(157.902 - 20.5118i) q^{14} -45.4921i q^{15} +(222.579 - 126.470i) q^{16} -440.917 q^{17} +(40.3141 + 310.343i) q^{18} -82.8191i q^{19} +(423.403 - 111.890i) q^{20} +66.1615 q^{21} +(276.893 - 35.9689i) q^{22} -429.510i q^{23} +(98.4829 - 40.1983i) q^{24} +124.179 q^{25} +(-45.1449 - 347.532i) q^{26} +264.660i q^{27} +(162.727 + 615.778i) q^{28} -405.559 q^{29} +(180.452 - 23.4410i) q^{30} -942.233i q^{31} +(616.356 + 817.729i) q^{32} +116.019 q^{33} +(-227.194 - 1748.97i) q^{34} +1089.57i q^{35} +(-1210.26 + 319.825i) q^{36} -1544.15 q^{37} +(328.516 - 42.6748i) q^{38} -145.617i q^{39} +(662.000 + 1621.85i) q^{40} -2006.79 q^{41} +(34.0915 + 262.441i) q^{42} +3322.91i q^{43} +(285.353 + 1079.81i) q^{44} -2141.45 q^{45} +(1703.73 - 221.317i) q^{46} -1869.66i q^{47} +(210.200 + 369.936i) q^{48} +816.380 q^{49} +(63.9864 + 492.576i) q^{50} -732.824i q^{51} +(1355.28 - 358.150i) q^{52} -2074.82 q^{53} +(-1049.82 + 136.373i) q^{54} +1910.64i q^{55} +(-2358.74 + 962.781i) q^{56} +137.649 q^{57} +(-208.975 - 1608.72i) q^{58} +72.9033i q^{59} +(185.966 + 703.716i) q^{60} +4601.99 q^{61} +(3737.53 - 485.511i) q^{62} -3114.43i q^{63} +(-2926.07 + 2866.24i) q^{64} +2398.06 q^{65} +(59.7819 + 460.209i) q^{66} +1190.81i q^{67} +(6820.53 - 1802.41i) q^{68} +713.866 q^{69} +(-4321.97 + 561.431i) q^{70} +5790.72i q^{71} +(-1892.26 - 4635.89i) q^{72} +5103.81 q^{73} +(-795.667 - 6125.15i) q^{74} +206.391i q^{75} +(338.554 + 1281.13i) q^{76} -2778.74 q^{77} +(577.614 - 75.0330i) q^{78} -4870.31i q^{79} +(-6092.23 + 3461.64i) q^{80} +5897.37 q^{81} +(-1034.05 - 7960.28i) q^{82} -11585.3i q^{83} +(-1023.45 + 270.460i) q^{84} +12068.4 q^{85} +(-13180.9 + 1712.22i) q^{86} -674.058i q^{87} +(-4136.22 + 1688.30i) q^{88} -7653.85 q^{89} +(-1103.44 - 8494.44i) q^{90} +3487.63i q^{91} +(1755.78 + 6644.09i) q^{92} +1566.04 q^{93} +(7416.34 - 963.395i) q^{94} +2266.85i q^{95} +(-1359.10 + 1024.41i) q^{96} +180.494 q^{97} +(420.662 + 3238.31i) q^{98} -5461.37i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.515277	+	3.96667i	0.128819	+	0.991668i
$2$	0.515277	+	3.96667i	0.128819	+	0.991668i
$3$			1.66205i			0.184672i	0.995728	+	0.0923359i	$0.0294334\pi$
$3$			1.66205i			0.184672i	−0.995728	+	0.0923359i	$0.970567\pi$
$4$	−15.4690	+	4.08787i	−0.966811	+	0.255492i
$5$	−27.3711			−1.09485			−0.547423	−	0.836856i	$-0.684391\pi$
$5$	−27.3711			−1.09485			−0.547423	+	0.836856i	$0.684391\pi$
$6$	−6.59279	+	0.856415i	−0.183133	+	0.0237893i
$7$		−	39.8073i		−	0.812394i	−0.913786	−	0.406197i	$-0.866855\pi$
$7$		−	39.8073i		−	0.812394i	0.913786	−	0.406197i	$-0.133145\pi$
$8$	−24.1861	−	59.2540i	−0.377907	−	0.925843i
$9$	78.2376			0.965896
$10$	−14.1037	−	108.572i	−0.141037	−	1.08572i
$11$		−	69.8049i		−	0.576900i	−0.957495	−	0.288450i	$-0.906860\pi$
$11$		−	69.8049i		−	0.576900i	0.957495	−	0.288450i	$-0.0931399\pi$
$12$	−6.79423	−	25.7102i	−0.0471822	−	0.178543i
$13$	−87.6129			−0.518420			−0.259210	−	0.965821i	$-0.583462\pi$
$13$	−87.6129			−0.518420			−0.259210	+	0.965821i	$0.583462\pi$
$14$	157.902	−	20.5118i	0.805625	−	0.104652i
$15$		−	45.4921i		−	0.202187i
$16$	222.579	−	126.470i	0.869448	−	0.494025i
$17$	−440.917			−1.52566			−0.762832	−	0.646597i	$-0.776192\pi$
$17$	−440.917			−1.52566			−0.762832	+	0.646597i	$0.776192\pi$
$18$	40.3141	+	310.343i	0.124426	+	0.957849i
$19$		−	82.8191i		−	0.229416i
$19$		−	82.8191i		−	0.229416i
$20$	423.403	−	111.890i	1.05851	−	0.279724i
$21$	66.1615			0.150026
$22$	276.893	−	35.9689i	0.572093	−	0.0743158i
$23$		−	429.510i		−	0.811929i	−0.913889	−	0.405964i	$-0.866936\pi$
$23$		−	429.510i		−	0.811929i	0.913889	−	0.405964i	$-0.133064\pi$
$24$	98.4829	−	40.1983i	0.170977	−	0.0697888i
$25$	124.179			0.198686
$26$	−45.1449	−	347.532i	−0.0667825	−	0.514100i
$27$			264.660i			0.363046i
$28$	162.727	+	615.778i	0.207560	+	0.785431i
$29$	−405.559			−0.482235			−0.241117	−	0.970496i	$-0.577514\pi$
$29$	−405.559			−0.482235			−0.241117	+	0.970496i	$0.577514\pi$
$30$	180.452	−	23.4410i	0.200502	−	0.0260456i
$31$		−	942.233i		−	0.980472i	−0.871590	−	0.490236i	$-0.836911\pi$
$31$		−	942.233i		−	0.980472i	0.871590	−	0.490236i	$-0.163089\pi$
$32$	616.356	+	817.729i	0.601910	+	0.798564i
$33$	116.019			0.106537
$34$	−227.194	−	1748.97i	−0.196535	−	1.51295i
$35$			1089.57i			0.889445i
$36$	−1210.26	+	319.825i	−0.933839	+	0.246779i
$37$	−1544.15			−1.12794			−0.563971	−	0.825795i	$-0.690727\pi$
$37$	−1544.15			−1.12794			−0.563971	+	0.825795i	$0.690727\pi$
$38$	328.516	−	42.6748i	0.227504	−	0.0295532i
$39$		−	145.617i		−	0.0957375i
$40$	662.000	+	1621.85i	0.413750	+	1.01366i
$41$	−2006.79			−1.19381			−0.596904	−	0.802313i	$-0.703603\pi$
$41$	−2006.79			−1.19381			−0.596904	+	0.802313i	$0.703603\pi$
$42$	34.0915	+	262.441i	0.0193263	+	0.148776i
$43$			3322.91i			1.79714i	0.438831	+	0.898570i	$0.355393\pi$
$43$			3322.91i			1.79714i	−0.438831	+	0.898570i	$0.644607\pi$
$44$	285.353	+	1079.81i	0.147393	+	0.557753i
$45$	−2141.45			−1.05751
$46$	1703.73	−	221.317i	0.805164	−	0.104592i
$47$		−	1869.66i		−	0.846384i	−0.906040	−	0.423192i	$-0.860910\pi$
$47$		−	1869.66i		−	0.846384i	0.906040	−	0.423192i	$-0.139090\pi$
$48$	210.200	+	369.936i	0.0912325	+	0.160562i
$49$	816.380			0.340017
$50$	63.9864	+	492.576i	0.0255946	+	0.197030i
$51$		−	732.824i		−	0.281747i
$52$	1355.28	−	358.150i	0.501214	−	0.132452i
$53$	−2074.82			−0.738634			−0.369317	−	0.929303i	$-0.620408\pi$
$53$	−2074.82			−0.738634			−0.369317	+	0.929303i	$0.620408\pi$
$54$	−1049.82	+	136.373i	−0.360021	+	0.0467673i
$55$			1910.64i			0.631616i
$56$	−2358.74	+	962.781i	−0.752149	+	0.307009i
$57$	137.649			0.0423666
$58$	−208.975	−	1608.72i	−0.0621211	−	0.478217i
$59$			72.9033i			0.0209432i	0.999945	+	0.0104716i	$0.00333328\pi$
$59$			72.9033i			0.0209432i	−0.999945	+	0.0104716i	$0.996667\pi$
$60$	185.966	+	703.716i	0.0516572	+	0.195477i
$61$	4601.99			1.23676			0.618380	−	0.785879i	$-0.287789\pi$
$61$	4601.99			1.23676			0.618380	+	0.785879i	$0.287789\pi$
$62$	3737.53	−	485.511i	0.972303	−	0.126304i
$63$		−	3114.43i		−	0.784688i
$64$	−2926.07	+	2866.24i	−0.714372	+	0.699766i
$65$	2398.06			0.567589
$66$	59.7819	+	460.209i	0.0137240	+	0.105649i
$67$			1190.81i			0.265273i	0.991165	+	0.132637i	$0.0423443\pi$
$67$			1190.81i			0.265273i	−0.991165	+	0.132637i	$0.957656\pi$
$68$	6820.53	−	1802.41i	1.47503	−	0.389795i
$69$	713.866			0.149940
$70$	−4321.97	+	561.431i	−0.882034	+	0.114578i
$71$			5790.72i			1.14872i	0.818601	+	0.574362i	$0.194750\pi$
$71$			5790.72i			1.14872i	−0.818601	+	0.574362i	$0.805250\pi$
$72$	−1892.26	−	4635.89i	−0.365019	−	0.894269i
$73$	5103.81			0.957743			0.478871	−	0.877885i	$-0.341046\pi$
$73$	5103.81			0.957743			0.478871	+	0.877885i	$0.341046\pi$
$74$	−795.667	−	6125.15i	−0.145301	−	1.11854i
$75$			206.391i			0.0366917i
$76$	338.554	+	1281.13i	0.0586139	+	0.221802i
$77$	−2778.74			−0.468670
$78$	577.614	−	75.0330i	0.0949398	−	0.0123328i
$79$		−	4870.31i		−	0.780373i	−0.920736	−	0.390187i	$-0.872411\pi$
$79$		−	4870.31i		−	0.780373i	0.920736	−	0.390187i	$-0.127589\pi$
$80$	−6092.23	+	3461.64i	−0.951911	+	0.540881i
$81$	5897.37			0.898852
$82$	−1034.05	−	7960.28i	−0.153785	−	1.18386i
$83$		−	11585.3i		−	1.68171i	−0.541260	−	0.840855i	$-0.682053\pi$
$83$		−	11585.3i		−	1.68171i	0.541260	−	0.840855i	$-0.317947\pi$
$84$	−1023.45	+	270.460i	−0.145047	+	0.0383305i
$85$	12068.4			1.67037
$86$	−13180.9	+	1712.22i	−1.78217	+	0.231506i
$87$		−	674.058i		−	0.0890551i
$88$	−4136.22	+	1688.30i	−0.534119	+	0.218015i
$89$	−7653.85			−0.966273			−0.483137	−	0.875545i	$-0.660503\pi$
$89$	−7653.85			−0.966273			−0.483137	+	0.875545i	$0.660503\pi$
$90$	−1103.44	−	8494.44i	−0.136227	−	1.04870i
$91$			3487.63i			0.421161i
$92$	1755.78	+	6644.09i	0.207441	+	0.784982i
$93$	1566.04			0.181065
$94$	7416.34	−	963.395i	0.839332	−	0.109031i
$95$			2266.85i			0.251175i
$96$	−1359.10	+	1024.41i	−0.147472	+	0.111156i
$97$	180.494			0.0191831			0.00959155	−	0.999954i	$-0.496947\pi$
$97$	180.494			0.0191831			0.00959155	+	0.999954i	$0.496947\pi$
$98$	420.662	+	3238.31i	0.0438007	+	0.337184i
$99$		−	5461.37i		−	0.557225i
$100$	−1920.92	+	507.626i	−0.192092	+	0.0507626i
$101$	−2846.27			−0.279018			−0.139509	−	0.990221i	$-0.544552\pi$
$101$	−2846.27			−0.279018			−0.139509	+	0.990221i	$0.544552\pi$
$102$	2906.87	−	377.607i	0.279400	−	0.0362945i
$103$		−	17434.3i		−	1.64335i	−0.569956	−	0.821675i	$-0.693040\pi$
$103$		−	17434.3i		−	1.64335i	0.569956	−	0.821675i	$-0.306960\pi$
$104$	2119.01	+	5191.41i	0.195915	+	0.479975i
$105$	−1810.92			−0.164255
$106$	−1069.11	−	8230.15i	−0.0951504	−	0.732480i
$107$			19738.2i			1.72401i	0.506896	+	0.862007i	$0.330793\pi$
$107$			19738.2i			1.72401i	−0.506896	+	0.862007i	$0.669207\pi$
$108$	−1081.90	−	4094.02i	−0.0927552	−	0.350997i
$109$	5519.61			0.464575			0.232287	−	0.972647i	$-0.425379\pi$
$109$	5519.61			0.464575			0.232287	+	0.972647i	$0.425379\pi$
$110$	−7578.87	+	984.508i	−0.626353	+	0.0813643i
$111$		−	2566.45i		−	0.208299i
$112$	−5034.44	−	8860.25i	−0.401343	−	0.706334i
$113$	1809.76			0.141731			0.0708654	−	0.997486i	$-0.477424\pi$
$113$	1809.76			0.141731			0.0708654	+	0.997486i	$0.477424\pi$
$114$	70.9275	+	546.009i	0.00545764	+	0.0420136i
$115$			11756.2i			0.888936i
$116$	6273.59	−	1657.87i	0.466230	−	0.123207i
$117$	−6854.63			−0.500740
$118$	−289.184	+	37.5654i	−0.0207687	+	0.00269789i
$119$			17551.7i			1.23944i
$120$	−2695.59	+	1100.27i	−0.187194	+	0.0764079i
$121$	9768.28			0.667187
$122$	2371.30	+	18254.6i	0.159319	+	1.22646i
$123$		−	3335.38i		−	0.220463i
$124$	3851.73	+	14575.4i	0.250503	+	0.947931i
$125$	13708.0			0.877315
$126$	12353.9	−	1604.79i	0.778150	−	0.101083i
$127$			8780.18i			0.544372i	0.962245	+	0.272186i	$0.0877467\pi$
$127$			8780.18i			0.544372i	−0.962245	+	0.272186i	$0.912253\pi$
$128$	−12877.2	−	10129.8i	−0.785960	−	0.618277i
$129$	−5522.83			−0.331881
$130$	1235.67	+	9512.34i	0.0731164	+	0.562860i
$131$			17992.3i			1.04844i	0.851582	+	0.524222i	$0.175644\pi$
$131$			17992.3i			1.04844i	−0.851582	+	0.524222i	$0.824356\pi$
$132$	−1794.69	+	474.270i	−0.103001	+	0.0272194i
$133$	−3296.80			−0.186376
$134$	−4723.56	+	613.598i	−0.263063	+	0.0341723i
$135$		−	7244.05i		−	0.397479i
$136$	10664.0	+	26126.1i	0.576559	+	1.41253i
$137$	−8337.57			−0.444220			−0.222110	−	0.975022i	$-0.571294\pi$
$137$	−8337.57			−0.444220			−0.222110	+	0.975022i	$0.571294\pi$
$138$	367.839	+	2831.67i	0.0193152	+	0.148691i
$139$		−	15231.1i		−	0.788318i	−0.919042	−	0.394159i	$-0.871036\pi$
$139$		−	15231.1i		−	0.788318i	0.919042	−	0.394159i	$-0.128964\pi$
$140$	−4454.02	−	16854.5i	−0.227246	−	0.859925i
$141$	3107.47			0.156303
$142$	−22969.9	+	2983.83i	−1.13915	+	0.147978i
$143$			6115.81i			0.299076i
$144$	17414.0	−	9894.74i	0.839796	−	0.477177i
$145$	11100.6			0.527972
$146$	2629.88	+	20245.2i	0.123376	+	0.949763i
$147$			1356.86i			0.0627915i
$148$	23886.5	−	6312.30i	1.09051	−	0.288180i
$149$	977.417			0.0440258			0.0220129	−	0.999758i	$-0.492993\pi$
$149$	977.417			0.0440258			0.0220129	+	0.999758i	$0.492993\pi$
$150$	−818.684	+	106.348i	−0.0363859	+	0.00472659i
$151$		−	22670.3i		−	0.994269i	−0.867673	−	0.497135i	$-0.834385\pi$
$151$		−	22670.3i		−	0.994269i	0.867673	−	0.497135i	$-0.165615\pi$
$152$	−4907.36	+	2003.07i	−0.212403	+	0.0866979i
$153$	−34496.3			−1.47363
$154$	−1431.82	−	11022.4i	−0.0603737	−	0.464765i
$155$			25790.0i			1.07346i
$156$	595.263	+	2252.54i	0.0244602	+	0.0925601i
$157$	−42424.9			−1.72116			−0.860581	−	0.509314i	$-0.829899\pi$
$157$	−42424.9			−1.72116			−0.860581	+	0.509314i	$0.829899\pi$
$158$	19318.9	−	2509.56i	0.773871	−	0.100527i
$159$		−	3448.45i		−	0.136405i
$160$	−16870.4	−	22382.2i	−0.658999	−	0.874303i
$161$	−17097.6			−0.659606
$162$	3038.78	+	23392.9i	0.115789	+	0.891363i
$163$		−	22875.1i		−	0.860969i	−0.902598	−	0.430485i	$-0.858343\pi$
$163$		−	22875.1i		−	0.860969i	0.902598	−	0.430485i	$-0.141657\pi$
$164$	31043.0	−	8203.50i	1.15419	−	0.305008i
$165$	−3175.57			−0.116642
$166$	45955.1	−	5969.64i	1.66770	−	0.216637i
$167$		−	25550.9i		−	0.916164i	−0.888910	−	0.458082i	$-0.848537\pi$
$167$		−	25550.9i		−	0.916164i	0.888910	−	0.458082i	$-0.151463\pi$
$168$	−1600.19	−	3920.33i	−0.0566960	−	0.138901i
$169$	−20885.0			−0.731241
$170$	6218.57	+	47871.3i	0.215175	+	1.65645i
$171$		−	6479.57i		−	0.221592i
$172$	−13583.6	−	51402.0i	−0.459155	−	1.73749i
$173$	−39661.0			−1.32517			−0.662584	−	0.748987i	$-0.730540\pi$
$173$	−39661.0			−1.32517			−0.662584	+	0.748987i	$0.730540\pi$
$174$	2673.77	−	347.327i	0.0883131	−	0.0114720i
$175$		−	4943.21i		−	0.161411i
$176$	−8828.25	−	15537.1i	−0.285003	−	0.501584i
$177$	−121.169			−0.00386762
$178$	−3943.85	−	30360.3i	−0.124475	−	0.958222i
$179$		−	44678.5i		−	1.39442i	−0.716868	−	0.697209i	$-0.754425\pi$
$179$		−	44678.5i		−	1.39442i	0.716868	−	0.697209i	$-0.245575\pi$
$180$	33126.1	−	8753.98i	1.02241	−	0.270185i
$181$	−8223.10			−0.251003			−0.125501	−	0.992093i	$-0.540054\pi$
$181$	−8223.10			−0.251003			−0.125501	+	0.992093i	$0.540054\pi$
$182$	−13834.3	+	1797.10i	−0.417652	+	0.0542536i
$183$			7648.71i			0.228395i
$184$	−25450.2	+	10388.2i	−0.751719	+	0.306834i
$185$	42265.2			1.23492
$186$	806.942	+	6211.95i	0.0233247	+	0.179557i
$187$			30778.1i			0.880155i
$188$	7642.94	+	28921.8i	0.216244	+	0.818294i
$189$	10535.4			0.294936
$190$	−8991.86	+	1168.06i	−0.249082	+	0.0323561i
$191$			34761.7i			0.952872i	0.879209	+	0.476436i	$0.158072\pi$
$191$			34761.7i			0.952872i	−0.879209	+	0.476436i	$0.841928\pi$
$192$	−4763.82	−	4863.26i	−0.129227	−	0.131924i
$193$	57400.1			1.54098			0.770492	−	0.637450i	$-0.220011\pi$
$193$	57400.1			1.54098			0.770492	+	0.637450i	$0.220011\pi$
$194$	93.0044	+	715.960i	0.00247115	+	0.0190233i
$195$			3985.69i			0.104818i
$196$	−12628.6	+	3337.26i	−0.328732	+	0.0868716i
$197$	−11114.7			−0.286394			−0.143197	−	0.989694i	$-0.545738\pi$
$197$	−11114.7			−0.286394			−0.143197	+	0.989694i	$0.545738\pi$
$198$	21663.4	−	2814.12i	0.552583	−	0.0717814i
$199$		−	29911.3i		−	0.755318i	−0.925945	−	0.377659i	$-0.876729\pi$
$199$		−	29911.3i		−	0.755318i	0.925945	−	0.377659i	$-0.123271\pi$
$200$	−3003.39	−	7358.08i	−0.0750848	−	0.183952i
$201$	−1979.18			−0.0489884
$202$	−1466.62	−	11290.2i	−0.0359430	−	0.276694i
$203$			16144.2i			0.391764i
$204$	2995.69	+	11336.0i	0.0719841	+	0.272396i
$205$	54928.1			1.30703
$206$	69156.2	−	8983.50i	1.62966	−	0.211695i
$207$		−	33603.9i		−	0.784239i
$208$	−19500.8	+	11080.4i	−0.450739	+	0.256112i
$209$	−5781.18			−0.132350
$210$	−933.124	−	7183.31i	−0.0211593	−	0.162887i
$211$			23814.6i			0.534908i	0.963571	+	0.267454i	$0.0861823\pi$
$211$			23814.6i			0.534908i	−0.963571	+	0.267454i	$0.913818\pi$
$212$	32095.4	−	8481.61i	0.714120	−	0.188715i
$213$	−9624.45			−0.212137
$214$	−78295.2	+	10170.7i	−1.70965	+	0.222086i
$215$		−	90951.8i		−	1.96759i
$216$	15682.2	−	6401.09i	0.336123	−	0.137198i
$217$	−37507.7			−0.796529
$218$	2844.13	+	21894.5i	0.0598462	+	0.460704i
$219$			8482.77i			0.176868i
$220$	−7810.44	−	29555.6i	−0.161373	−	0.610653i
$221$	38630.0			0.790934
$222$	10180.3	−	1322.43i	0.206564	−	0.0268329i
$223$			24049.9i			0.483619i	0.970324	+	0.241809i	$0.0777409\pi$
$223$			24049.9i			0.483619i	−0.970324	+	0.241809i	$0.922259\pi$
$224$	32551.6	−	24535.5i	0.648748	−	0.488988i
$225$	9715.43			0.191910
$226$	932.528	+	7178.73i	0.0182577	+	0.140550i
$227$			61002.8i			1.18385i	0.805992	+	0.591927i	$0.201632\pi$
$227$			61002.8i			1.18385i	−0.805992	+	0.591927i	$0.798368\pi$
$228$	−2129.29	+	562.692i	−0.0409605	+	0.0108243i
$229$	−19904.3			−0.379557			−0.189778	−	0.981827i	$-0.560777\pi$
$229$	−19904.3			−0.379557			−0.189778	+	0.981827i	$0.560777\pi$
$230$	−46632.9	+	6057.69i	−0.881530	+	0.114512i
$231$		−	4618.40i		−	0.0865501i
$232$	9808.88	+	24031.0i	0.182240	+	0.446474i
$233$	14637.8			0.269628			0.134814	−	0.990871i	$-0.456956\pi$
$233$	14637.8			0.269628			0.134814	+	0.990871i	$0.456956\pi$
$234$	−3532.03	−	27190.1i	−0.0645049	−	0.496568i
$235$			51174.8i			0.926660i
$236$	−298.019	−	1127.74i	−0.00535082	−	0.0202481i
$237$	8094.68			0.144113
$238$	−69621.8	+	9043.99i	−1.22911	+	0.159664i
$239$		−	22617.6i		−	0.395960i	−0.980206	−	0.197980i	$-0.936562\pi$
$239$		−	22617.6i		−	0.395960i	0.980206	−	0.197980i	$-0.0634381\pi$
$240$	−5753.40	−	10125.6i	−0.0998854	−	0.175791i
$241$	37894.3			0.652439			0.326219	−	0.945294i	$-0.394225\pi$
$241$	37894.3			0.652439			0.326219	+	0.945294i	$0.394225\pi$
$242$	5033.37	+	38747.6i	0.0859465	+	0.661628i
$243$			31239.2i			0.529038i
$244$	−71188.0	+	18812.3i	−1.19571	+	0.315982i
$245$	−22345.2			−0.372266
$246$	13230.4	−	1718.64i	0.218626	−	0.0283998i
$247$			7256.02i			0.118934i
$248$	−55831.1	+	22788.9i	−0.907763	+	0.370527i
$249$	19255.3			0.310564
$250$	7063.44	+	54375.3i	0.113015	+	0.870005i
$251$			79523.9i			1.26226i	0.775675	+	0.631132i	$0.217409\pi$
$251$			79523.9i			1.26226i	−0.775675	+	0.631132i	$0.782591\pi$
$252$	12731.4	+	48177.0i	0.200481	+	0.758645i
$253$	−29981.9			−0.468401
$254$	−34828.1	+	4524.23i	−0.539837	+	0.0701257i
$255$			20058.2i			0.308469i
$256$	33546.5	−	56299.2i	0.511879	−	0.859058i
$257$	−117892.			−1.78491			−0.892455	−	0.451137i	$-0.851019\pi$
$257$	−117892.			−1.78491			−0.892455	+	0.451137i	$0.851019\pi$
$258$	−2845.79	−	21907.3i	−0.0427527	−	0.329116i
$259$			61468.5i			0.916333i
$260$	−37095.6	+	9802.98i	−0.548752	+	0.145014i
$261$	−31730.0			−0.465789
$262$	−71369.7	+	9271.05i	−1.03971	+	0.135060i
$263$		−	11065.3i		−	0.159974i	−0.996796	−	0.0799871i	$-0.974512\pi$
$263$		−	11065.3i		−	0.159974i	0.996796	−	0.0799871i	$-0.0254879\pi$
$264$	−2806.04	−	6874.58i	−0.0402611	−	0.0986367i
$265$	56790.3			0.808690
$266$	−1698.77	−	13077.3i	−0.0240088	−	0.184823i
$267$		−	12721.1i		−	0.178443i
$268$	−4867.88	−	18420.6i	−0.0677751	−	0.256469i
$269$	120549.			1.66594			0.832968	−	0.553321i	$-0.186640\pi$
$269$	120549.			1.66594			0.832968	+	0.553321i	$0.186640\pi$
$270$	28734.8	−	3732.69i	0.394167	−	0.0512029i
$271$		−	120931.i		−	1.64664i	−0.567576	−	0.823321i	$-0.692119\pi$
$271$		−	120931.i		−	1.64664i	0.567576	−	0.823321i	$-0.307881\pi$
$272$	−98138.6	+	55762.9i	−1.32648	+	0.753716i
$273$	−5796.61			−0.0777765
$274$	−4296.16	−	33072.4i	−0.0572241	−	0.440519i
$275$		−	8668.27i		−	0.114622i
$276$	−11042.8	+	2918.19i	−0.144964	+	0.0383086i
$277$	143491.			1.87010			0.935048	−	0.354520i	$-0.115356\pi$
$277$	143491.			1.87010			0.935048	+	0.354520i	$0.115356\pi$
$278$	60416.8	−	7848.24i	0.781750	−	0.101551i
$279$		−	73718.1i		−	0.947034i
$280$	64561.4	−	26352.4i	0.823487	−	0.336128i
$281$	−40509.9			−0.513036			−0.256518	−	0.966539i	$-0.582575\pi$
$281$	−40509.9			−0.513036			−0.256518	+	0.966539i	$0.582575\pi$
$282$	1601.21	+	12326.3i	0.0201349	+	0.155001i
$283$		−	26900.1i		−	0.335877i	−0.985797	−	0.167939i	$-0.946289\pi$
$283$		−	26900.1i		−	0.335877i	0.985797	−	0.167939i	$-0.0537111\pi$
$284$	−23671.7	−	89576.5i	−0.293490	−	1.11060i
$285$	−3767.61			−0.0463849
$286$	−24259.4	+	3151.34i	−0.296584	+	0.0385268i
$287$			79884.9i			0.969841i
$288$	48222.2	+	63977.2i	0.581383	+	0.771330i
$289$	110887.			1.32765
$290$	5719.89	+	44032.5i	0.0680130	+	0.523573i
$291$			299.989i			0.00354258i
$292$	−78950.8	+	20863.7i	−0.925957	+	0.244696i
$293$	13297.2			0.154890			0.0774451	−	0.996997i	$-0.475324\pi$
$293$	13297.2			0.154890			0.0774451	+	0.996997i	$0.475324\pi$
$294$	−5382.23	+	699.160i	−0.0622683	+	0.00808876i
$295$		−	1995.45i		−	0.0229296i
$296$	37347.0	+	91497.2i	0.426257	+	1.04430i
$297$	18474.6			0.209441
$298$	503.641	+	3877.09i	0.00567137	+	0.0436590i
$299$			37630.7i			0.420920i
$300$	−843.698	−	3192.65i	−0.00937442	−	0.0354739i
$301$	132276.			1.45998
$302$	89925.8	−	11681.5i	0.985985	−	0.128081i
$303$		−	4730.63i		−	0.0515268i
$304$	−10474.2	−	18433.8i	−0.113337	−	0.199465i
$305$	−125962.			−1.35406
$306$	−17775.1	−	136835.i	−0.189832	−	1.46135i
$307$			3398.98i			0.0360639i	0.999837	+	0.0180319i	$0.00574005\pi$
$307$			3398.98i			0.0360639i	−0.999837	+	0.0180319i	$0.994260\pi$
$308$	42984.3	−	11359.1i	0.453115	−	0.119741i
$309$	28976.6			0.303480
$310$	−102300.	+	13289.0i	−1.06452	+	0.138283i
$311$		−	169055.i		−	1.74787i	−0.486047	−	0.873933i	$-0.661562\pi$
$311$		−	169055.i		−	1.74787i	0.486047	−	0.873933i	$-0.338438\pi$
$312$	−8628.37	+	3521.89i	−0.0886379	+	0.0361799i
$313$	−1819.67			−0.0185739			−0.00928696	−	0.999957i	$-0.502956\pi$
$313$	−1819.67			−0.0185739			−0.00928696	+	0.999957i	$0.502956\pi$
$314$	−21860.6	−	168286.i	−0.221719	−	1.70682i
$315$			85245.4i			0.859112i
$316$	19909.2	+	75338.7i	0.199379	+	0.754474i
$317$	−75259.9			−0.748937			−0.374468	−	0.927240i	$-0.622175\pi$
$317$	−75259.9			−0.748937			−0.374468	+	0.927240i	$0.622175\pi$
$318$	13678.9	−	1776.91i	0.135268	−	0.0175716i
$319$			28310.0i			0.278201i
$320$	80089.8	−	78452.2i	0.782127	−	0.766135i
$321$	−32805.9			−0.318377
$322$	−8810.02	−	67820.7i	−0.0849699	−	0.654110i
$323$			36516.3i			0.350011i
$324$	−91226.3	+	24107.7i	−0.869020	+	0.229649i
$325$	−10879.6			−0.103003
$326$	90738.0	−	11787.0i	0.853796	−	0.110909i
$327$			9173.85i			0.0857939i
$328$	48536.3	+	118910.i	0.451148	+	1.10528i
$329$	−74426.2			−0.687597
$330$	−1636.30	−	12596.4i	−0.0150257	−	0.115670i
$331$			127025.i			1.15940i	0.814831	+	0.579699i	$0.196830\pi$
$331$			127025.i			1.15940i	−0.814831	+	0.579699i	$0.803170\pi$
$332$	47359.2	+	179213.i	0.429664	+	1.62590i
$333$	−120811.			−1.08948
$334$	101352.	−	13165.8i	0.908531	−	0.118020i
$335$		−	32593.8i		−	0.290433i
$336$	14726.1	−	8367.48i	0.130440	−	0.0741167i
$337$	185171.			1.63047			0.815235	−	0.579131i	$-0.196608\pi$
$337$	185171.			1.63047			0.815235	+	0.579131i	$0.196608\pi$
$338$	−10761.6	−	82843.9i	−0.0941980	−	0.725148i
$339$			3007.91i			0.0261737i
$340$	−186686.	+	49334.0i	−1.61493	+	0.426765i
$341$	−65772.5			−0.565634
$342$	25702.3	−	3338.77i	0.219746	−	0.0285453i
$343$		−	128075.i		−	1.08862i
$344$	196896.	−	80368.1i	1.66387	−	0.679152i
$345$	−19539.3			−0.164161
$346$	−20436.4	−	157322.i	−0.170707	−	1.31413i
$347$		−	161035.i		−	1.33740i	−0.743532	−	0.668700i	$-0.766851\pi$
$347$		−	161035.i		−	1.33740i	0.743532	−	0.668700i	$-0.233149\pi$
$348$	2755.46	+	10427.0i	0.0227529	+	0.0860995i
$349$	−199146.			−1.63501			−0.817504	−	0.575923i	$-0.804643\pi$
$349$	−199146.			−1.63501			−0.817504	+	0.575923i	$0.804643\pi$
$350$	19608.1	−	2547.12i	0.160066	−	0.0207929i
$351$		−	23187.7i		−	0.188210i
$352$	57081.5	−	43024.7i	0.460691	−	0.347242i
$353$	−71926.4			−0.577217			−0.288609	−	0.957447i	$-0.593193\pi$
$353$	−71926.4			−0.577217			−0.288609	+	0.957447i	$0.593193\pi$
$354$	−62.4355	−	480.637i	−0.000498224	−	0.00383540i
$355$		−	158499.i		−	1.25768i
$356$	118397.	−	31288.0i	0.934204	−	0.246875i
$357$	−29171.7			−0.228889
$358$	177225.	−	23021.8i	1.38280	−	0.179628i
$359$		−	131216.i		−	1.01812i	−0.860732	−	0.509059i	$-0.829994\pi$
$359$		−	131216.i		−	1.01812i	0.860732	−	0.509059i	$-0.170006\pi$
$360$	51793.3	+	126890.i	0.399639	+	0.979086i
$361$	−6859.00			−0.0526316
$362$	−4237.17	−	32618.3i	−0.0323340	−	0.248911i
$363$			16235.3i			0.123211i
$364$	−14257.0	−	53950.1i	−0.107603	−	0.407183i
$365$	−139697.			−1.04858
$366$	−30339.9	+	3941.21i	−0.226492	+	0.0294217i
$367$			36469.9i			0.270771i	0.990793	+	0.135386i	$0.0432273\pi$
$367$			36469.9i			0.270771i	−0.990793	+	0.135386i	$0.956773\pi$
$368$	−54320.3	−	95599.8i	−0.401113	−	0.705930i
$369$	−157006.			−1.15309
$370$	21778.3	+	167652.i	0.159082	+	1.22463i
$371$			82593.1i			0.600062i
$372$	−24225.0	+	6401.75i	−0.175056	+	0.0462608i
$373$	70829.7			0.509094			0.254547	−	0.967060i	$-0.418074\pi$
$373$	70829.7			0.509094			0.254547	+	0.967060i	$0.418074\pi$
$374$	−122087.	+	15859.3i	−0.872821	+	0.113381i
$375$			22783.4i			0.162015i
$376$	−110785.	+	45219.8i	−0.783619	+	0.319855i
$377$	35532.2			0.250000
$378$	5428.65	+	41790.5i	0.0379934	+	0.292479i
$379$		−	90500.7i		−	0.630048i	−0.949084	−	0.315024i	$-0.897987\pi$
$379$		−	90500.7i		−	0.630048i	0.949084	−	0.315024i	$-0.102013\pi$
$380$	−9266.60	−	35065.9i	−0.0641731	−	0.242838i
$381$	−14593.1			−0.100530
$382$	−137888.	+	17911.9i	−0.944932	+	0.122748i
$383$		−	87363.0i		−	0.595566i	−0.954634	−	0.297783i	$-0.903753\pi$
$383$		−	87363.0i		−	0.595566i	0.954634	−	0.297783i	$-0.0962472\pi$
$384$	16836.3	−	21402.5i	0.114178	−	0.145145i
$385$	76057.3			0.513121
$386$	29577.0	+	227687.i	0.198508	+	1.52814i
$387$			259977.i			1.73585i
$388$	−2792.06	+	737.836i	−0.0185464	+	0.00490113i
$389$	209582.			1.38502			0.692508	−	0.721410i	$-0.256506\pi$
$389$	209582.			1.38502			0.692508	+	0.721410i	$0.256506\pi$
$390$	−15809.9	+	2053.74i	−0.103944	+	0.0135025i
$391$			189378.i			1.23873i
$392$	−19745.0	−	48373.8i	−0.128495	−	0.314802i
$393$	−29904.1			−0.193618
$394$	−5727.14	−	44088.3i	−0.0368931	−	0.284008i
$395$			133306.i			0.854388i
$396$	22325.4	+	84481.7i	0.142367	+	0.538732i
$397$	−148427.			−0.941740			−0.470870	−	0.882203i	$-0.656060\pi$
$397$	−148427.			−0.941740			−0.470870	+	0.882203i	$0.656060\pi$
$398$	118648.	−	15412.6i	0.749025	−	0.0972995i
$399$		−	5479.44i		−	0.0344184i
$400$	27639.5	−	15704.9i	0.172747	−	0.0981557i
$401$	−96097.0			−0.597615			−0.298807	−	0.954313i	$-0.596589\pi$
$401$	−96097.0			−0.597615			−0.298807	+	0.954313i	$0.596589\pi$
$402$	−1019.83	−	7850.77i	−0.00631066	−	0.0485803i
$403$			82551.8i			0.508296i
$404$	44028.8	−	11635.2i	0.269758	−	0.0712870i
$405$	−161418.			−0.984104
$406$	−64038.8	+	8318.74i	−0.388500	+	0.0504668i
$407$			107789.i			0.650710i
$408$	−43422.7	+	17724.1i	−0.260854	+	0.106474i
$409$	271142.			1.62088			0.810439	−	0.585823i	$-0.199229\pi$
$409$	271142.			1.62088			0.810439	+	0.585823i	$0.199229\pi$
$410$	28303.2	+	217882.i	0.168371	+	1.29614i
$411$		−	13857.4i		−	0.0820349i
$412$	71269.2	+	269691.i	0.419863	+	1.58881i
$413$	2902.08			0.0170141
$414$	133295.	−	17315.3i	0.777705	−	0.101025i
$415$			317103.i			1.84121i
$416$	−54000.8	−	71643.6i	−0.312042	−	0.413991i
$417$	25314.8			0.145580
$418$	−2978.91	−	22932.0i	−0.0170492	−	0.131247i
$419$			32770.3i			0.186660i	0.995635	+	0.0933302i	$0.0297512\pi$
$419$			32770.3i			0.186660i	−0.995635	+	0.0933302i	$0.970249\pi$
$420$	28013.0	−	7402.79i	0.158804	−	0.0419659i
$421$	51738.8			0.291912			0.145956	−	0.989291i	$-0.453374\pi$
$421$	51738.8			0.291912			0.145956	+	0.989291i	$0.453374\pi$
$422$	−94464.8	+	12271.1i	−0.530451	+	0.0689064i
$423$		−	146278.i		−	0.817519i
$424$	50181.8	+	122942.i	0.279135	+	0.683860i
$425$	−54752.4			−0.303128
$426$	−4959.26	−	38177.0i	−0.0273273	−	0.210370i
$427$		−	183193.i		−	1.00474i
$428$	−80687.4	−	305331.i	−0.440472	−	1.66680i
$429$	−10164.8			−0.0552309
$430$	360776.	−	46865.4i	1.95120	−	0.253463i
$431$		−	331119.i		−	1.78250i	−0.453513	−	0.891250i	$-0.649829\pi$
$431$		−	331119.i		−	1.78250i	0.453513	−	0.891250i	$-0.350171\pi$
$432$	33471.7	+	58907.7i	0.179354	+	0.315649i
$433$	−320967.			−1.71192			−0.855961	−	0.517040i	$-0.827034\pi$
$433$	−320967.			−1.71192			−0.855961	+	0.517040i	$0.827034\pi$
$434$	−19326.9	−	148781.i	−0.102608	−	0.789892i
$435$			18449.7i			0.0975016i
$436$	−85382.8	+	22563.5i	−0.449156	+	0.118695i
$437$	−35571.6			−0.186269
$438$	−33648.4	+	4370.98i	−0.175394	+	0.0227840i
$439$			286114.i			1.48460i	0.670065	+	0.742302i	$0.266266\pi$
$439$			286114.i			1.48460i	−0.670065	+	0.742302i	$0.733734\pi$
$440$	113213.	−	46210.8i	0.584777	−	0.238692i
$441$	63871.6			0.328421
$442$	19905.2	+	153233.i	0.101888	+	0.784344i
$443$		−	348679.i		−	1.77672i	−0.459148	−	0.888360i	$-0.651845\pi$
$443$		−	348679.i		−	1.77672i	0.459148	−	0.888360i	$-0.348155\pi$
$444$	10491.3	+	39700.4i	0.0532187	+	0.201386i
$445$	209495.			1.05792
$446$	−95398.0	+	12392.4i	−0.479589	+	0.0622994i
$447$			1624.51i			0.00813033i
$448$	114097.	+	116479.i	0.568485	+	0.580351i
$449$	345739.			1.71497			0.857484	−	0.514510i	$-0.172026\pi$
$449$	345739.			1.71497			0.857484	+	0.514510i	$0.172026\pi$
$450$	5006.14	+	38537.9i	0.0247217	+	0.190311i
$451$			140084.i			0.688707i
$452$	−27995.1	+	7398.07i	−0.137027	+	0.0362111i
$453$	37679.1			0.183614
$454$	−241978.	+	31433.3i	−1.17399	+	0.152503i
$455$		−	95460.4i		−	0.461106i
$456$	−3329.19	−	8156.26i	−0.0160106	−	0.0392249i
$457$	−254466.			−1.21842			−0.609211	−	0.793008i	$-0.708514\pi$
$457$	−254466.			−1.21842			−0.609211	+	0.793008i	$0.708514\pi$
$458$	−10256.3	−	78954.0i	−0.0488942	−	0.376394i
$459$		−	116693.i		−	0.553885i
$460$	−48057.8	−	181856.i	−0.227116	−	0.859433i
$461$	−69189.1			−0.325564			−0.162782	−	0.986662i	$-0.552047\pi$
$461$	−69189.1			−0.325564			−0.162782	+	0.986662i	$0.552047\pi$
$462$	18319.7	−	2379.76i	0.0858289	−	0.0111493i
$463$			291341.i			1.35906i	0.733647	+	0.679531i	$0.237817\pi$
$463$			291341.i			1.35906i	−0.733647	+	0.679531i	$0.762183\pi$
$464$	−90268.8	+	51291.2i	−0.419278	+	0.238236i
$465$	−42864.2			−0.198239
$466$	7542.55	+	58063.5i	0.0347333	+	0.267382i
$467$			26265.5i			0.120435i	0.998185	+	0.0602175i	$0.0191794\pi$
$467$			26265.5i			0.120435i	−0.998185	+	0.0602175i	$0.980821\pi$
$468$	106034.	−	28020.8i	0.484121	−	0.127935i
$469$	47402.9			0.215506
$470$	−202994.	+	26369.2i	−0.918939	+	0.119372i
$471$		−	70512.1i		−	0.317850i
$472$	4319.81	−	1763.24i	0.0193901	−	0.00791459i
$473$	231955.			1.03677
$474$	4171.00	+	32108.9i	0.0185645	+	0.142912i
$475$		−	10284.4i		−	0.0455816i
$476$	−71749.1	−	271507.i	−0.316667	−	1.19830i
$477$	−162329.			−0.713444
$478$	89716.7	−	11654.3i	0.392661	−	0.0510073i
$479$		−	71783.6i		−	0.312863i	−0.987689	−	0.156431i	$-0.950001\pi$
$479$		−	71783.6i		−	0.312863i	0.987689	−	0.156431i	$-0.0499990\pi$
$480$	37200.2	−	28039.3i	0.161459	−	0.121698i
$481$	135288.			0.584747
$482$	19526.1	+	150314.i	0.0840467	+	0.647003i
$483$		−	28417.1i		−	0.121811i
$484$	−151105.	+	39931.5i	−0.645044	+	0.170461i
$485$	−4940.32			−0.0210025
$486$	−123916.	+	16096.8i	−0.524630	+	0.0681503i
$487$			443034.i			1.86801i	0.357259	+	0.934006i	$0.383711\pi$
$487$			443034.i			1.86801i	−0.357259	+	0.934006i	$0.616289\pi$
$488$	−111304.	−	272686.i	−0.467381	−	1.14505i
$489$	38019.5			0.158997
$490$	−11514.0	−	88636.3i	−0.0479550	−	0.369164i
$491$		−	192738.i		−	0.799475i	−0.916630	−	0.399737i	$-0.869101\pi$
$491$		−	192738.i		−	0.799475i	0.916630	−	0.399737i	$-0.130899\pi$
$492$	13634.6	+	51594.9i	0.0563264	+	0.213146i
$493$	178818.			0.735728
$494$	−28782.3	+	3738.86i	−0.117943	+	0.0153209i
$495$			149484.i			0.610075i
$496$	−119165.	−	209721.i	−0.484378	−	0.852469i
$497$	230513.			0.933216
$498$	9921.82	+	76379.5i	0.0400067	+	0.307977i
$499$		−	422929.i		−	1.69850i	−0.527988	−	0.849252i	$-0.677053\pi$
$499$		−	422929.i		−	1.69850i	0.527988	−	0.849252i	$-0.322947\pi$
$500$	−212049.	+	56036.7i	−0.848198	+	0.224147i
$501$	42466.8			0.169190
$502$	−315445.	+	40976.9i	−1.25175	+	0.162604i
$503$		−	183719.i		−	0.726138i	−0.931762	−	0.363069i	$-0.881729\pi$
$503$		−	183719.i		−	0.726138i	0.931762	−	0.363069i	$-0.118271\pi$
$504$	−184542.	+	75325.7i	−0.726498	+	0.296539i
$505$	77905.5			0.305482
$506$	−15449.0	−	118928.i	−0.0603392	−	0.464499i
$507$		−	34711.8i		−	0.135040i
$508$	−35892.3	−	135820.i	−0.139083	−	0.526305i
$509$	302299.			1.16681			0.583406	−	0.812181i	$-0.301720\pi$
$509$	302299.			1.16681			0.583406	+	0.812181i	$0.301720\pi$
$510$	−79564.4	+	10335.5i	−0.305899	+	0.0397368i
$511$		−	203169.i		−	0.778064i
$512$	240606.	+	104058.i	0.917840	+	0.396950i
$513$	21918.9			0.0832884
$514$	−60746.8	−	467637.i	−0.229931	−	1.77004i
$515$			477197.i			1.79921i
$516$	85432.5	−	22576.6i	0.320866	−	0.0847929i
$517$	−130512.			−0.488279
$518$	−243826.	+	31673.3i	−0.908698	+	0.118041i
$519$		−	65918.4i		−	0.244721i
$520$	−57999.7	−	142095.i	−0.214496	−	0.525499i
$521$	−93213.6			−0.343403			−0.171701	−	0.985149i	$-0.554926\pi$
$521$	−93213.6			−0.343403			−0.171701	+	0.985149i	$0.554926\pi$
$522$	−16349.7	−	125862.i	−0.0600026	−	0.461908i
$523$		−	439154.i		−	1.60551i	−0.596309	−	0.802755i	$-0.703367\pi$
$523$		−	439154.i		−	1.60551i	0.596309	−	0.802755i	$-0.296633\pi$
$524$	−73550.4	−	278323.i	−0.267869	−	1.01365i
$525$	8215.85			0.0298081
$526$	43892.2	−	5701.67i	0.158641	−	0.0206078i
$527$			415446.i			1.49587i
$528$	25823.3	−	14673.0i	0.0926284	−	0.0526320i
$529$	95361.9			0.340772
$530$	29262.7	+	225268.i	0.104175	+	0.801952i
$531$			5703.78i			0.0202290i
$532$	50998.2	−	13476.9i	0.180190	−	0.0476175i
$533$	175821.			0.618893
$534$	50460.2	−	6554.87i	0.176957	−	0.0229870i
$535$		−	540258.i		−	1.88753i
$536$	70560.3	−	28801.0i	0.245601	−	0.100249i
$537$	74257.8			0.257510
$538$	62116.0	+	478178.i	0.214605	+	1.65206i
$539$		−	56987.3i		−	0.196156i
$540$	29612.7	+	112058.i	0.101553	+	0.384287i
$541$	87034.4			0.297370			0.148685	−	0.988885i	$-0.452496\pi$
$541$	87034.4			0.297370			0.148685	+	0.988885i	$0.452496\pi$
$542$	479694.	−	62313.0i	1.63292	−	0.212119i
$543$		−	13667.2i		−	0.0463531i
$544$	−271762.	−	360550.i	−0.918313	−	1.21834i
$545$	−151078.			−0.508638
$546$	−2986.86	−	22993.2i	−0.0100191	−	0.0771285i
$547$			282452.i			0.943996i	0.881600	+	0.471998i	$0.156467\pi$
$547$			282452.i			0.943996i	−0.881600	+	0.471998i	$0.843533\pi$
$548$	128974.	−	34082.9i	0.429477	−	0.113495i
$549$	360048.			1.19458
$550$	34384.2	−	4466.56i	0.113667	−	0.0147655i
$551$			33588.0i			0.110632i
$552$	−17265.6	−	42299.4i	−0.0566635	−	0.138821i
$553$	−193874.			−0.633970
$554$	73937.5	+	569180.i	0.240905	+	1.85452i
$555$			70246.7i			0.228055i
$556$	62262.8	+	235610.i	0.201409	+	0.762155i
$557$	70244.1			0.226412			0.113206	−	0.993572i	$-0.463888\pi$
$557$	70244.1			0.226412			0.113206	+	0.993572i	$0.463888\pi$
$558$	292415.	−	37985.2i	0.939143	−	0.121996i
$559$		−	291130.i		−	0.931672i
$560$	137798.	+	242515.i	0.439408	+	0.773326i
$561$	−51154.7			−0.162540
$562$	−20873.8	−	160689.i	−0.0660890	−	0.508762i
$563$			236028.i			0.744639i	0.928105	+	0.372320i	$0.121438\pi$
$563$			236028.i			0.744639i	−0.928105	+	0.372320i	$0.878562\pi$
$564$	−48069.3	+	12702.9i	−0.151116	+	0.0399342i
$565$	−49535.2			−0.155173
$566$	106704.	−	13861.0i	0.333079	−	0.0432675i
$567$		−	234758.i		−	0.730222i
$568$	343123.	−	140055.i	1.06354	−	0.434111i
$569$	−94761.3			−0.292689			−0.146345	−	0.989234i	$-0.546751\pi$
$569$	−94761.3			−0.292689			−0.146345	+	0.989234i	$0.546751\pi$
$570$	−1941.36	−	14944.9i	−0.00597527	−	0.0459984i
$571$			620968.i			1.90457i	0.305210	+	0.952285i	$0.401273\pi$
$571$			620968.i			1.90457i	−0.305210	+	0.952285i	$0.598727\pi$
$572$	−25000.6	−	94605.3i	−0.0764116	−	0.289150i
$573$	−57775.6			−0.175969
$574$	−316877.	+	41162.8i	−0.961761	+	0.124934i
$575$		−	53336.0i		−	0.161319i
$576$	−228929.	+	224248.i	−0.690010	+	0.675901i
$577$	234114.			0.703195			0.351597	−	0.936151i	$-0.385639\pi$
$577$	234114.			0.703195			0.351597	+	0.936151i	$0.385639\pi$
$578$	57137.3	+	439851.i	0.171027	+	1.31659i
$579$			95401.6i			0.284576i
$580$	−171715.	+	45377.9i	−0.510449	+	0.134893i
$581$	−461179.			−1.36621
$582$	−1189.96	+	154.578i	−0.00351306	+	0.000456352i
$583$			144833.i			0.426118i
$584$	−123441.	−	302421.i	−0.361938	−	0.886720i
$585$	187619.			0.548232
$586$	6851.73	+	52745.5i	0.0199529	+	0.153600i
$587$			267180.i			0.775403i	0.921785	+	0.387701i	$0.126731\pi$
$587$			267180.i			0.775403i	−0.921785	+	0.387701i	$0.873269\pi$
$588$	−5546.68	−	20989.3i	−0.0160427	−	0.0607075i
$589$	−78034.9			−0.224936
$590$	7915.28	−	1028.21i	0.0227385	−	0.00295377i
$591$		−	18473.1i		−	0.0528890i
$592$	−343695.	+	195290.i	−0.980687	+	0.557232i
$593$	235410.			0.669447			0.334724	−	0.942316i	$-0.391357\pi$
$593$	235410.			0.669447			0.334724	+	0.942316i	$0.391357\pi$
$594$	9519.53	+	73282.6i	0.0269800	+	0.207696i
$595$		−	480410.i		−	1.35699i
$596$	−15119.6	+	3995.56i	−0.0425646	+	0.0112482i
$597$	49714.0			0.139486
$598$	−149268.	+	19390.2i	−0.417413	+	0.0542226i
$599$			184974.i			0.515533i	0.966207	+	0.257766i	$0.0829865\pi$
$599$			184974.i			0.515533i	−0.966207	+	0.257766i	$0.917014\pi$
$600$	12229.5	−	4991.77i	0.0339707	−	0.0138660i
$601$	−661984.			−1.83273			−0.916365	−	0.400344i	$-0.868891\pi$
$601$	−661984.			−1.83273			−0.916365	+	0.400344i	$0.868891\pi$
$602$	68158.8	+	524696.i	0.188074	+	1.44782i
$603$			93166.2i			0.256226i
$604$	92673.4	+	350687.i	0.254028	+	0.961271i
$605$	−267369.			−0.730466
$606$	18764.8	−	2437.58i	0.0510975	−	0.00663765i
$607$		−	78426.0i		−	0.212854i	−0.994321	−	0.106427i	$-0.966059\pi$
$607$		−	78426.0i		−	0.212854i	0.994321	−	0.106427i	$-0.0339411\pi$
$608$	67723.6	−	51046.1i	0.183203	−	0.138088i
$609$	−26832.4			−0.0723478
$610$	−64905.1	−	499648.i	−0.174429	−	1.34278i
$611$			163807.i			0.438782i
$612$	533622.	−	141016.i	1.42472	−	0.376501i
$613$	−411844.			−1.09600			−0.548001	−	0.836477i	$-0.684611\pi$
$613$	−411844.			−1.09600			−0.548001	+	0.836477i	$0.684611\pi$
$614$	−13482.6	+	1751.42i	−0.0357634	+	0.00464572i
$615$			91293.0i			0.241372i
$616$	67206.8	+	164652.i	0.177114	+	0.433915i
$617$	−258720.			−0.679609			−0.339805	−	0.940496i	$-0.610361\pi$
$617$	−258720.			−0.679609			−0.339805	+	0.940496i	$0.610361\pi$
$618$	14931.0	+	114941.i	0.0390941	+	0.300952i
$619$		−	343992.i		−	0.897774i	−0.893589	−	0.448887i	$-0.851821\pi$
$619$		−	343992.i		−	0.897774i	0.893589	−	0.448887i	$-0.148179\pi$
$620$	−105426.	−	398945.i	−0.274262	−	1.03784i
$621$	113674.			0.294767
$622$	670587.	−	87110.3i	1.73330	−	0.225159i
$623$			304679.i			0.784994i
$624$	−18416.2	−	32411.2i	−0.0472967	−	0.0832387i
$625$	−452816.			−1.15921
$626$	−937.634	−	7218.03i	−0.00239268	−	0.0184192i
$627$		−	9608.58i		−	0.0244413i
$628$	656270.	−	173428.i	1.66404	−	0.439743i
$629$	680843.			1.72086
$630$	−338140.	+	43925.0i	−0.851954	+	0.110670i
$631$			85415.7i			0.214526i	0.994231	+	0.107263i	$0.0342086\pi$
$631$			85415.7i			0.214526i	−0.994231	+	0.107263i	$0.965791\pi$
$632$	−288585.	+	117794.i	−0.722503	+	0.294909i
$633$	−39581.0			−0.0987823
$634$	−38779.7	−	298531.i	−0.0964775	−	0.742697i
$635$		−	240323.i		−	0.596003i
$636$	14096.8	+	53344.1i	0.0348504	+	0.131878i
$637$	−71525.5			−0.176271
$638$	−112297.	+	14587.5i	−0.275883	+	0.0358377i
$639$			453052.i			1.10955i
$640$	352463.	+	277265.i	0.860505	+	0.676917i
$641$	−497286.			−1.21029			−0.605146	−	0.796114i	$-0.706885\pi$
$641$	−497286.			−1.21029			−0.605146	+	0.796114i	$0.706885\pi$
$642$	−16904.1	−	130130.i	−0.0410131	−	0.315724i
$643$			79010.5i			0.191101i	0.995425	+	0.0955505i	$0.0304612\pi$
$643$			79010.5i			0.191101i	−0.995425	+	0.0955505i	$0.969539\pi$
$644$	264483.	−	69893.0i	0.637714	−	0.168524i
$645$	151166.			0.363358
$646$	−144848.	+	18816.0i	−0.347095	+	0.0450882i
$647$			567446.i			1.35555i	0.735268	+	0.677776i	$0.237056\pi$
$647$			567446.i			1.35555i	−0.735268	+	0.677776i	$0.762944\pi$
$648$	−142634.	−	349443.i	−0.339683	−	0.832196i
$649$	5089.01			0.0120821
$650$	−5606.04	−	43156.0i	−0.0132687	−	0.102144i
$651$		−	62339.6i		−	0.147096i
$652$	93510.5	+	353854.i	0.219971	+	0.832395i
$653$	−580634.			−1.36168			−0.680842	−	0.732431i	$-0.738386\pi$
$653$	−580634.			−1.36168			−0.680842	+	0.732431i	$0.738386\pi$
$654$	−36389.7	+	4727.08i	−0.0850791	+	0.0110519i
$655$		−	492471.i		−	1.14788i
$656$	−446669.	+	253800.i	−1.03795	+	0.589771i
$657$	399310.			0.925080
$658$	−38350.1	−	295224.i	−0.0885758	−	0.681868i
$659$		−	471686.i		−	1.08613i	−0.839690	−	0.543066i	$-0.817264\pi$
$659$		−	471686.i		−	1.08613i	0.839690	−	0.543066i	$-0.182736\pi$
$660$	49122.8	−	12981.3i	0.112770	−	0.0298010i
$661$	−255760.			−0.585369			−0.292684	−	0.956209i	$-0.594548\pi$
$661$	−255760.			−0.585369			−0.292684	+	0.956209i	$0.594548\pi$
$662$	−503866.	+	65453.0i	−1.14974	+	0.149353i
$663$			64204.9i			0.146063i
$664$	−686475.	+	280203.i	−1.55700	+	0.635530i
$665$	90237.2			0.204053
$666$	−62251.1	−	479217.i	−0.140345	−	1.08040i
$667$			174192.i			0.391540i
$668$	104449.	+	395246.i	0.234073	+	0.885758i
$669$	−39972.0			−0.0893107
$670$	129289.	−	16794.9i	0.288013	−	0.0374134i
$671$		−	321241.i		−	0.713487i
$672$	40779.1	+	54102.2i	0.0903023	+	0.119805i
$673$	−276308.			−0.610046			−0.305023	−	0.952345i	$-0.598664\pi$
$673$	−276308.			−0.610046			−0.305023	+	0.952345i	$0.598664\pi$
$674$	95414.3	+	734512.i	0.210036	+	1.61688i
$675$			32865.1i			0.0721320i
$676$	323069.	−	85375.1i	0.706972	−	0.186826i
$677$	−342538.			−0.747363			−0.373681	−	0.927557i	$-0.621905\pi$
$677$	−342538.			−0.747363			−0.373681	+	0.927557i	$0.621905\pi$
$678$	−11931.4	+	1549.91i	−0.0259556	+	0.00337168i
$679$		−	7184.97i		−	0.0155842i
$680$	−291887.	−	715100.i	−0.631243	−	1.54650i
$681$	−101389.			−0.218624
$682$	−33891.1	−	260898.i	−0.0728646	−	0.560921i
$683$		−	806555.i		−	1.72899i	−0.502642	−	0.864495i	$-0.667638\pi$
$683$		−	806555.i		−	1.72899i	0.502642	−	0.864495i	$-0.332362\pi$
$684$	26487.6	+	100232.i	0.0566149	+	0.214237i
$685$	228209.			0.486352
$686$	508032.	−	65994.2i	1.07955	−	0.140235i
$687$		−	33081.9i		−	0.0700934i
$688$	420250.	+	739609.i	0.887832	+	1.56252i
$689$	181781.			0.382923
$690$	−10068.2	−	77506.1i	−0.0211472	−	0.162794i
$691$		−	159893.i		−	0.334869i	−0.985883	−	0.167434i	$-0.946452\pi$
$691$		−	159893.i		−	0.334869i	0.985883	−	0.167434i	$-0.0535482\pi$
$692$	613515.	−	162129.i	1.28119	−	0.338570i
$693$	−217402.			−0.452686
$694$	638773.	−	82977.7i	1.32626	−	0.172283i
$695$			416892.i			0.863086i
$696$	−39940.6	+	16302.8i	−0.0824511	+	0.0336546i
$697$	884827.			1.82135
$698$	−102615.	−	789945.i	−0.210621	−	1.62138i
$699$			24328.8i			0.0497927i
$700$	20207.2	+	76466.4i	0.0412392	+	0.156054i
$701$	−17458.3			−0.0355277			−0.0177638	−	0.999842i	$-0.505655\pi$
$701$	−17458.3			−0.0355277			−0.0177638	+	0.999842i	$0.505655\pi$
$702$	91977.8	−	11948.1i	0.186642	−	0.0242451i
$703$			127885.i			0.258768i
$704$	200078.	+	204254.i	0.403695	+	0.412121i
$705$	−85054.8			−0.171128
$706$	−37062.1	−	285309.i	−0.0743567	−	0.572408i
$707$			113302.i			0.226673i
$708$	1874.36	−	495.322i	0.00373926	−	0.000988146i
$709$	354740.			0.705696			0.352848	−	0.935681i	$-0.385213\pi$
$709$	354740.			0.705696			0.352848	+	0.935681i	$0.385213\pi$
$710$	628712.	−	81670.7i	1.24720	−	0.162013i
$711$		−	381041.i		−	0.753760i
$712$	185116.	+	453521.i	0.365162	+	0.894618i
$713$	−404699.			−0.796073
$714$	−15031.5	−	115715.i	−0.0294854	−	0.226982i
$715$		−	167397.i		−	0.327442i
$716$	182640.	+	691131.i	0.356262	+	1.34814i
$717$	37591.5			0.0731226
$718$	520491.	−	67612.6i	1.00963	−	0.131153i
$719$			581820.i			1.12546i	0.826640	+	0.562731i	$0.190249\pi$
$719$			581820.i			1.12546i	−0.826640	+	0.562731i	$0.809751\pi$
$720$	−476641.	+	270830.i	−0.919447	+	0.522435i
$721$	−694012.			−1.33505
$722$	−3534.29	−	27207.4i	−0.00677996	−	0.0521931i
$723$			62982.1i			0.120487i
$724$	127203.	−	33615.0i	0.242672	−	0.0641292i
$725$	−50361.8			−0.0958131
$726$	−64400.2	+	8365.70i	−0.122184	+	0.0158719i
$727$			107083.i			0.202605i	0.994856	+	0.101302i	$0.0323010\pi$
$727$			107083.i			0.202605i	−0.994856	+	0.101302i	$0.967699\pi$
$728$	206656.	−	84352.1i	0.389929	−	0.159160i
$729$	425766.			0.801154
$730$	−71982.7	−	554133.i	−0.135077	−	1.03984i
$731$		−	1.46513e6i		−	2.74183i
$732$	−31267.0	−	118318.i	−0.0583530	−	0.220815i
$733$	−408469.			−0.760241			−0.380121	−	0.924937i	$-0.624118\pi$
$733$	−408469.			−0.760241			−0.380121	+	0.924937i	$0.624118\pi$
$734$	−144664.	+	18792.1i	−0.268515	+	0.0348805i
$735$		−	37138.8i		−	0.0687470i
$736$	351223.	−	264731.i	0.648377	−	0.488708i
$737$	83124.4			0.153036
$738$	−80901.8	−	622793.i	−0.148541	−	1.14349i
$739$		−	233345.i		−	0.427278i	−0.976913	−	0.213639i	$-0.931468\pi$
$739$		−	233345.i		−	0.427278i	0.976913	−	0.213639i	$-0.0685316\pi$
$740$	−653800.	+	172775.i	−1.19394	+	0.315513i
$741$	−12059.8			−0.0219637
$742$	−327620.	+	42558.3i	−0.595062	+	0.0772995i
$743$			718838.i			1.30213i	0.759023	+	0.651064i	$0.225677\pi$
$743$			718838.i			1.30213i	−0.759023	+	0.651064i	$0.774323\pi$
$744$	−37876.2	−	92793.8i	−0.0684259	−	0.167638i
$745$	−26753.0			−0.0482014
$746$	36496.9	+	280958.i	0.0655811	+	0.504852i
$747$		−	906406.i		−	1.62436i
$748$	−125817.	−	476106.i	−0.224873	−	0.850944i
$749$	785726.			1.40058
$750$	−90374.3	+	11739.8i	−0.160665	+	0.0208707i
$751$			1.01541e6i			1.80037i	0.435506	+	0.900186i	$0.356570\pi$
$751$			1.01541e6i			1.80037i	−0.435506	+	0.900186i	$0.643430\pi$
$752$	−236457.	−	416147.i	−0.418135	−	0.735887i
$753$	−132172.			−0.233105
$754$	18308.9	+	140945.i	0.0322048	+	0.247917i
$755$			620513.i			1.08857i
$756$	−162972.	+	43067.4i	−0.285147	+	0.0753538i
$757$	−581969.			−1.01557			−0.507783	−	0.861485i	$-0.669535\pi$
$757$	−581969.			−1.01557			−0.507783	+	0.861485i	$0.669535\pi$
$758$	358987.	−	46633.0i	0.624799	−	0.0811624i
$759$		−	49831.3i		−	0.0865005i
$760$	134320.	−	54826.2i	0.232548	−	0.0949207i
$761$	761623.			1.31514			0.657568	−	0.753395i	$-0.271585\pi$
$761$	761623.			1.31514			0.657568	+	0.753395i	$0.271585\pi$
$762$	−7519.47	−	57885.9i	−0.0129502	−	0.0996926i
$763$		−	219721.i		−	0.377418i
$764$	−142101.	−	537728.i	−0.243451	−	0.921247i
$765$	944202.			1.61340
$766$	346540.	−	45016.2i	0.590604	−	0.0767204i
$767$		−	6387.27i		−	0.0108574i
$768$	93571.9	+	55755.8i	0.158644	+	0.0945295i
$769$	135064.			0.228396			0.114198	−	0.993458i	$-0.463570\pi$
$769$	135064.			0.228396			0.114198	+	0.993458i	$0.463570\pi$
$770$	39190.6	+	301694.i	0.0660998	+	0.508845i
$771$		−	195941.i		−	0.329622i
$772$	−887921.	+	234644.i	−1.48984	+	0.393709i
$773$	−583726.			−0.976899			−0.488450	−	0.872592i	$-0.662437\pi$
$773$	−583726.			−0.976899			−0.488450	+	0.872592i	$0.662437\pi$
$774$	−1.03124e6	+	133960.i	−1.72139	+	0.223611i
$775$		−	117005.i		−	0.194806i
$776$	−4365.43	−	10695.0i	−0.00724943	−	0.0177606i
$777$	−102164.			−0.169221
$778$	107993.	+	831343.i	0.178417	+	1.37348i
$779$			166201.i			0.273878i
$780$	−16293.0	−	61654.6i	−0.0267801	−	0.101339i
$781$	404221.			0.662699
$782$	−751202.	+	97582.3i	−1.22841	+	0.159572i
$783$		−	107335.i		−	0.175073i
$784$	181709.	−	103248.i	0.295627	−	0.167977i
$785$	1.16122e6			1.88440
$786$	−15408.9	−	118620.i	−0.0249417	−	0.192005i
$787$		−	681426.i		−	1.10019i	−0.835101	−	0.550097i	$-0.814591\pi$
$787$		−	681426.i		−	1.10019i	0.835101	−	0.550097i	$-0.185409\pi$
$788$	171933.	−	45435.4i	0.276889	−	0.0731715i
$789$	18391.0			0.0295427
$790$	−528781.	+	68689.5i	−0.847269	+	0.110062i
$791$		−	72041.6i		−	0.115141i
$792$	−323608.	+	132089.i	−0.515903	+	0.210579i
$793$	−403193.			−0.641161
$794$	−76480.9	−	588760.i	−0.121314	−	0.933894i
$795$			94388.1i			0.149342i
$796$	122274.	+	462698.i	0.192978	+	0.730250i
$797$	438597.			0.690476			0.345238	−	0.938515i	$-0.387798\pi$
$797$	438597.			0.690476			0.345238	+	0.938515i	$0.387798\pi$
$798$	21735.1	−	2823.43i	0.0341316	−	0.00443375i
$799$			824366.i			1.29130i
$800$	76538.3	+	101544.i	0.119591	+	0.158663i
$801$	−598819.			−0.933320
$802$	−49516.6	−	381185.i	−0.0769843	−	0.592635i
$803$		−	356271.i		−	0.552522i
$804$	30615.9	−	8090.64i	0.0473626	−	0.0125162i
$805$	467982.			0.722166
$806$	−327456.	+	42537.1i	−0.504061	+	0.0654783i
$807$			200358.i			0.307651i
$808$	68840.0	+	168653.i	0.105443	+	0.258327i
$809$	421910.			0.644649			0.322324	−	0.946629i	$-0.395536\pi$
$809$	421910.			0.644649			0.322324	+	0.946629i	$0.395536\pi$
$810$	−83174.8	−	640291.i	−0.126772	−	0.975904i
$811$		−	423519.i		−	0.643918i	−0.946754	−	0.321959i	$-0.895659\pi$
$811$		−	423519.i		−	0.643918i	0.946754	−	0.321959i	$-0.104341\pi$
$812$	−65995.5	−	249734.i	−0.100093	−	0.378762i
$813$	200993.			0.304088
$814$	−427565.	+	55541.4i	−0.645288	+	0.0838239i
$815$			626117.i			0.942628i
$816$	−92680.5	−	163111.i	−0.139190	−	0.244964i
$817$	275200.			0.412292
$818$	139713.	+	1.07553e6i	0.208800	+	1.60737i
$819$			272864.i			0.406798i
$820$	−849682.	+	224539.i	−1.26366	+	0.333937i
$821$	−592927.			−0.879659			−0.439830	−	0.898081i	$-0.644961\pi$
$821$	−592927.			−0.879659			−0.439830	+	0.898081i	$0.644961\pi$
$822$	54967.9	−	7140.42i	0.0813514	−	0.0105677i
$823$		−	737893.i		−	1.08942i	−0.838626	−	0.544708i	$-0.816640\pi$
$823$		−	737893.i		−	1.08942i	0.838626	−	0.544708i	$-0.183360\pi$
$824$	−1.03305e6	+	421667.i	−1.52149	+	0.621034i
$825$	14407.1			0.0211674
$826$	1495.38	+	11511.6i	0.00219175	+	0.0168724i
$827$			573222.i			0.838131i	0.907956	+	0.419065i	$0.137642\pi$
$827$			573222.i			0.838131i	−0.907956	+	0.419065i	$0.862358\pi$
$828$	137368.	+	519817.i	0.200367	+	0.758211i
$829$	−570919.			−0.830740			−0.415370	−	0.909653i	$-0.636348\pi$
$829$	−570919.			−0.830740			−0.415370	+	0.909653i	$0.636348\pi$
$830$	−1.25784e6	+	163396.i	−1.82587	+	0.237184i
$831$			238488.i			0.345354i
$832$	256361.	−	251120.i	0.370345	−	0.362772i
$833$	−359956.			−0.518751
$834$	13044.1	+	100415.i	0.0187535	+	0.144367i
$835$			699357.i			1.00306i
$836$	89428.9	−	23632.7i	0.127957	−	0.0338143i
$837$	249372.			0.355956
$838$	−129989.	+	16885.8i	−0.185105	+	0.0240455i
$839$		−	406559.i		−	0.577563i	−0.957395	−	0.288782i	$-0.906750\pi$
$839$		−	406559.i		−	0.577563i	0.957395	−	0.288782i	$-0.0932501\pi$
$840$	43798.9	+	107304.i	0.0620733	+	0.152075i
$841$	−542803.			−0.767450
$842$	26659.8	+	205231.i	0.0376039	+	0.289480i
$843$		−	67329.3i		−	0.0947434i
$844$	−97351.1	−	368388.i	−0.136665	−	0.517155i
$845$	571645.			0.800596
$846$	580237.	−	75373.7i	0.810708	−	0.105312i
$847$		−	388849.i		−	0.542018i
$848$	−461811.	+	262404.i	−0.642204	+	0.364904i
$849$	44709.2			0.0620271
$850$	−28212.7	−	217185.i	−0.0390487	−	0.300602i
$851$			663230.i			0.915809i
$852$	148880.	−	39343.5i	0.205096	−	0.0541993i
$853$	247344.			0.339941			0.169970	−	0.985449i	$-0.445633\pi$
$853$	247344.			0.339941			0.169970	+	0.985449i	$0.445633\pi$
$854$	726665.	−	94394.9i	0.996365	−	0.129429i
$855$			177353.i			0.242609i
$856$	1.16957e6	−	477390.i	1.59617	−	0.651518i
$857$	−547454.			−0.745394			−0.372697	−	0.927953i	$-0.621567\pi$
$857$	−547454.			−0.745394			−0.372697	+	0.927953i	$0.621567\pi$
$858$	−5237.67	−	40320.3i	−0.00711481	−	0.0547708i
$859$			1.09264e6i			1.48078i	0.672178	+	0.740389i	$0.265359\pi$
$859$			1.09264e6i			1.48078i	−0.672178	+	0.740389i	$0.734641\pi$
$860$	371799.	+	1.40693e6i	0.502703	+	1.90229i
$861$	−132772.			−0.179102
$862$	1.31344e6	−	170618.i	1.76765	−	0.229620i
$863$			1.48571e6i			1.99487i	0.0716026	+	0.997433i	$0.477189\pi$
$863$			1.48571e6i			1.99487i	−0.0716026	+	0.997433i	$0.522811\pi$
$864$	−216420.	+	163125.i	−0.289915	+	0.218521i
$865$	1.08557e6			1.45085
$866$	−165387.	−	1.27317e6i	−0.220529	−	1.69766i
$867$			184299.i			0.245179i
$868$	580207.	−	153327.i	0.770093	−	0.203507i
$869$	−339971.			−0.450197
$870$	−73184.0	+	9506.73i	−0.0966892	+	0.0125601i
$871$		−	104330.i		−	0.137523i
$872$	−133498.	−	327059.i	−0.175566	−	0.430124i
$873$	14121.4			0.0185289
$874$	−18329.3	−	141101.i	−0.0239951	−	0.184717i
$875$		−	545680.i		−	0.712725i
$876$	−34676.5	−	131220.i	−0.0451884	−	0.170998i
$877$	−760810.			−0.989184			−0.494592	−	0.869125i	$-0.664683\pi$
$877$	−760810.			−0.989184			−0.494592	+	0.869125i	$0.664683\pi$
$878$	−1.13492e6	+	147428.i	−1.47223	+	0.191246i
$879$			22100.5i			0.0286039i
$880$	241639.	+	425267.i	0.312034	+	0.549157i
$881$	983729.			1.26743			0.633714	−	0.773567i	$-0.281529\pi$
$881$	983729.			1.26743			0.633714	+	0.773567i	$0.281529\pi$
$882$	32911.6	+	253358.i	0.0423070	+	0.325685i
$883$		−	281309.i		−	0.360797i	−0.983594	−	0.180398i	$-0.942261\pi$
$883$		−	281309.i		−	0.360797i	0.983594	−	0.180398i	$-0.0577387\pi$
$884$	−597567.	+	157915.i	−0.764684	+	0.202077i
$885$	3316.52			0.00423445
$886$	1.38310e6	−	179667.i	1.76192	−	0.228876i
$887$		−	1.08735e6i		−	1.38205i	−0.722833	−	0.691023i	$-0.757161\pi$
$887$		−	1.08735e6i		−	1.38205i	0.722833	−	0.691023i	$-0.242839\pi$
$888$	−152073.	+	62072.4i	−0.192852	+	0.0787177i
$889$	349515.			0.442245
$890$	107948.	+	830996.i	0.136280	+	1.04911i
$891$		−	411665.i		−	0.518548i
$892$	−98312.8	−	372027.i	−0.123561	−	0.467568i
$893$	−154844.			−0.194174
$894$	−6443.91	+	837.074i	−0.00806258	+	0.00104734i
$895$			1.22290e6i			1.52667i
$896$	−403242.	+	512605.i	−0.502284	+	0.638509i
$897$	−62543.9			−0.0777320
$898$	178152.	+	1.37143e6i	0.220921	+	1.70068i
$899$			382131.i			0.472817i
$900$	−150288.	+	39715.5i	−0.185541	+	0.0490314i
$901$	914825.			1.12691
$902$	−555666.	+	72182.0i	−0.682969	+	0.0887188i
$903$			219849.i			0.269618i
$904$	−43771.0	−	107236.i	−0.0535611	−	0.131221i
$905$	225075.			0.274809
$906$	19415.2	+	149461.i	0.0236530	+	0.182084i
$907$		−	1.03371e6i		−	1.25656i	−0.777988	−	0.628279i	$-0.783760\pi$
$907$		−	1.03371e6i		−	1.25656i	0.777988	−	0.628279i	$-0.216240\pi$
$908$	−249371.	−	943650.i	−0.302465	−	1.14456i
$909$	−222685.			−0.269503
$910$	378660.	−	49188.6i	0.457264	−	0.0593993i
$911$			1.17357e6i			1.41407i	0.707179	+	0.707035i	$0.249968\pi$
$911$			1.17357e6i			1.41407i	−0.707179	+	0.707035i	$0.750032\pi$
$912$	30637.8	−	17408.5i	0.0368356	−	0.0209302i
$913$	−808711.			−0.970178
$914$	−131121.	−	1.00938e6i	−0.156956	−	1.20827i
$915$		−	209354.i		−	0.250057i
$916$	307900.	−	81366.4i	0.366960	−	0.0969737i
$917$	716226.			0.851749
$918$	462883.	−	60129.3i	0.549270	−	0.0713511i
$919$		−	450288.i		−	0.533162i	−0.963812	−	0.266581i	$-0.914106\pi$
$919$		−	450288.i		−	0.533162i	0.963812	−	0.266581i	$-0.0858940\pi$
$920$	696601.	−	284336.i	0.823016	−	0.335935i
$921$	−5649.27			−0.00665998
$922$	−35651.6	−	274451.i	−0.0419389	−	0.322851i
$923$		−	507342.i		−	0.595521i
$924$	18879.4	+	71441.9i	0.0221128	+	0.0836776i
$925$	−191751.			−0.224106
$926$	−1.15565e6	+	150121.i	−1.34774	+	0.175074i
$927$		−	1.36402e6i		−	1.58731i
$928$	−249969.	−	331638.i	−0.290262	−	0.385095i
$929$	1.20182e6			1.39254			0.696271	−	0.717779i	$-0.254841\pi$
$929$	1.20182e6			1.39254			0.696271	+	0.717779i	$0.254841\pi$
$930$	−22086.9	−	170028.i	−0.0255370	−	0.196587i
$931$		−	67611.9i		−	0.0780052i
$932$	−226432.	+	59837.6i	−0.260679	+	0.0688878i
$933$	280978.			0.322781
$934$	−104187.	+	13534.0i	−0.119431	+	0.0155143i
$935$		−	842432.i		−	0.963633i
$936$	165786.	+	406164.i	0.189233	+	0.463607i
$937$	−516411.			−0.588189			−0.294094	−	0.955776i	$-0.595018\pi$
$937$	−516411.			−0.588189			−0.294094	+	0.955776i	$0.595018\pi$
$938$	24425.7	+	188032.i	0.0277613	+	0.213711i
$939$		−	3024.37i		−	0.00343008i
$940$	−209196.	−	791621.i	−0.236754	−	0.895905i
$941$	654287.			0.738906			0.369453	−	0.929249i	$-0.379545\pi$
$941$	654287.			0.738906			0.369453	+	0.929249i	$0.379545\pi$
$942$	279699.	−	36333.3i	0.315202	−	0.0409452i
$943$			861937.i			0.969286i
$944$	9220.11	+	16226.7i	0.0103465	+	0.0182090i
$945$	−288366.			−0.322909
$946$	119521.	+	920091.i	0.133556	+	1.02813i
$947$		−	518684.i		−	0.578366i	−0.957274	−	0.289183i	$-0.906616\pi$
$947$		−	518684.i		−	0.578366i	0.957274	−	0.289183i	$-0.0933837\pi$
$948$	−125216.	+	33090.0i	−0.139330	+	0.0368197i
$949$	−447160.			−0.496513
$950$	40794.7	−	5299.29i	0.0452019	−	0.00587179i
$951$		−	125085.i		−	0.138308i
$952$	1.04001e6	−	424506.i	1.14753	−	0.468393i
$953$	−1.57632e6			−1.73563			−0.867817	−	0.496884i	$-0.834478\pi$
$953$	−1.57632e6			−1.73563			−0.867817	+	0.496884i	$0.834478\pi$
$954$	−83644.6	−	643907.i	−0.0919054	−	0.707500i
$955$		−	951467.i		−	1.04325i
$956$	92458.0	+	349872.i	0.101165	+	0.382819i
$957$	−47052.5			−0.0513759
$958$	284742.	−	36988.4i	0.310256	−	0.0403028i
$959$			331896.i			0.360882i
$960$	130391.	+	133113.i	0.141484	+	0.144437i
$961$	35717.4			0.0386752
$962$	69710.7	+	536642.i	0.0753268	+	0.579875i
$963$			1.54427e6i			1.66522i
$964$	−586186.	+	154907.i	−0.630785	+	0.166693i
$965$	−1.57111e6			−1.68714
$966$	112721.	−	14642.7i	0.120796	−	0.0156916i
$967$		−	1.73026e6i		−	1.85037i	−0.379519	−	0.925184i	$-0.623910\pi$
$967$		−	1.73026e6i		−	1.85037i	0.379519	−	0.925184i	$-0.376090\pi$
$968$	−236256.	−	578810.i	−0.252135	−	0.617710i
$969$	−60691.8			−0.0646372
$970$	−2545.63	−	19596.6i	−0.00270553	−	0.0208275i
$971$		−	869433.i		−	0.922142i	−0.887363	−	0.461071i	$-0.847465\pi$
$971$		−	869433.i		−	0.922142i	0.887363	−	0.461071i	$-0.152535\pi$
$972$	−127702.	−	483238.i	−0.135165	−	0.511480i
$973$	−606309.			−0.640425
$974$	−1.75737e6	+	228285.i	−1.85245	+	0.240636i
$975$		−	18082.5i		−	0.0190217i
$976$	1.02430e6	−	582015.i	1.07530	−	0.610991i
$977$	−1.48414e6			−1.55484			−0.777418	−	0.628984i	$-0.783471\pi$
$977$	−1.48414e6			−1.55484			−0.777418	+	0.628984i	$0.783471\pi$
$978$	19590.6	+	150811.i	0.0204819	+	0.157672i
$979$			534276.i			0.557443i
$980$	345658.	−	91344.5i	0.359911	−	0.0951109i
$981$	431841.			0.448731
$982$	764529.	−	99313.6i	0.792813	−	0.102988i
$983$			78721.6i			0.0814679i	0.999170	+	0.0407340i	$0.0129696\pi$
$983$			78721.6i			0.0814679i	−0.999170	+	0.0407340i	$0.987030\pi$
$984$	−197634.	+	80669.6i	−0.204114	+	0.0833144i
$985$	304221.			0.313558
$986$	92140.8	+	709312.i	0.0947759	+	0.729598i
$987$		−	123700.i		−	0.126980i
$988$	−29661.7	−	112243.i	−0.0303866	−	0.114986i
$989$	1.42722e6			1.45915
$990$	−592953.	+	77025.6i	−0.604992	+	0.0785895i
$991$		−	333428.i		−	0.339512i	−0.985486	−	0.169756i	$-0.945702\pi$
$991$		−	333428.i		−	0.339512i	0.985486	−	0.169756i	$-0.0542979\pi$
$992$	770492.	−	580751.i	0.782969	−	0.590156i
$993$	−211121.			−0.214108
$994$	118778.	+	914369.i	0.120216	+	0.925441i
$995$			818707.i			0.826956i
$996$	−297860.	+	78713.2i	−0.300257	+	0.0793467i
$997$	−1.21834e6			−1.22568			−0.612842	−	0.790205i	$-0.709974\pi$
$997$	−1.21834e6			−1.22568			−0.612842	+	0.790205i	$0.709974\pi$
$998$	1.67762e6	−	217926.i	1.68435	−	0.218800i
$999$		−	408676.i		−	0.409494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.20	yes	36
4.3	odd	2	inner	76.5.b.a.39.19	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.19	✓	36	4.3	odd	2	inner
76.5.b.a.39.20	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.515277 + 3.96667i) q^{2} +1.66205i q^{3} +(-15.4690 + 4.08787i) q^{4} -27.3711 q^{5} +(-6.59279 + 0.856415i) q^{6} -39.8073i q^{7} +(-24.1861 - 59.2540i) q^{8} +78.2376 q^{9} +O(q^{10})\)	\(q+(0.515277 + 3.96667i) q^{2} +1.66205i q^{3} +(-15.4690 + 4.08787i) q^{4} -27.3711 q^{5} +(-6.59279 + 0.856415i) q^{6} -39.8073i q^{7} +(-24.1861 - 59.2540i) q^{8} +78.2376 q^{9} +(-14.1037 - 108.572i) q^{10} -69.8049i q^{11} +(-6.79423 - 25.7102i) q^{12} -87.6129 q^{13} +(157.902 - 20.5118i) q^{14} -45.4921i q^{15} +(222.579 - 126.470i) q^{16} -440.917 q^{17} +(40.3141 + 310.343i) q^{18} -82.8191i q^{19} +(423.403 - 111.890i) q^{20} +66.1615 q^{21} +(276.893 - 35.9689i) q^{22} -429.510i q^{23} +(98.4829 - 40.1983i) q^{24} +124.179 q^{25} +(-45.1449 - 347.532i) q^{26} +264.660i q^{27} +(162.727 + 615.778i) q^{28} -405.559 q^{29} +(180.452 - 23.4410i) q^{30} -942.233i q^{31} +(616.356 + 817.729i) q^{32} +116.019 q^{33} +(-227.194 - 1748.97i) q^{34} +1089.57i q^{35} +(-1210.26 + 319.825i) q^{36} -1544.15 q^{37} +(328.516 - 42.6748i) q^{38} -145.617i q^{39} +(662.000 + 1621.85i) q^{40} -2006.79 q^{41} +(34.0915 + 262.441i) q^{42} +3322.91i q^{43} +(285.353 + 1079.81i) q^{44} -2141.45 q^{45} +(1703.73 - 221.317i) q^{46} -1869.66i q^{47} +(210.200 + 369.936i) q^{48} +816.380 q^{49} +(63.9864 + 492.576i) q^{50} -732.824i q^{51} +(1355.28 - 358.150i) q^{52} -2074.82 q^{53} +(-1049.82 + 136.373i) q^{54} +1910.64i q^{55} +(-2358.74 + 962.781i) q^{56} +137.649 q^{57} +(-208.975 - 1608.72i) q^{58} +72.9033i q^{59} +(185.966 + 703.716i) q^{60} +4601.99 q^{61} +(3737.53 - 485.511i) q^{62} -3114.43i q^{63} +(-2926.07 + 2866.24i) q^{64} +2398.06 q^{65} +(59.7819 + 460.209i) q^{66} +1190.81i q^{67} +(6820.53 - 1802.41i) q^{68} +713.866 q^{69} +(-4321.97 + 561.431i) q^{70} +5790.72i q^{71} +(-1892.26 - 4635.89i) q^{72} +5103.81 q^{73} +(-795.667 - 6125.15i) q^{74} +206.391i q^{75} +(338.554 + 1281.13i) q^{76} -2778.74 q^{77} +(577.614 - 75.0330i) q^{78} -4870.31i q^{79} +(-6092.23 + 3461.64i) q^{80} +5897.37 q^{81} +(-1034.05 - 7960.28i) q^{82} -11585.3i q^{83} +(-1023.45 + 270.460i) q^{84} +12068.4 q^{85} +(-13180.9 + 1712.22i) q^{86} -674.058i q^{87} +(-4136.22 + 1688.30i) q^{88} -7653.85 q^{89} +(-1103.44 - 8494.44i) q^{90} +3487.63i q^{91} +(1755.78 + 6644.09i) q^{92} +1566.04 q^{93} +(7416.34 - 963.395i) q^{94} +2266.85i q^{95} +(-1359.10 + 1024.41i) q^{96} +180.494 q^{97} +(420.662 + 3238.31i) q^{98} -5461.37i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Introduction

L-functions

Modular forms

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Database

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