LMFDB - Embedded newform 49.5.b.b.48.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,5,Mod(48,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("49.48");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	49.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:	$5.06512819111$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 66x^{6} + 212x^{5} + 2021x^{4} - 4400x^{3} - 25028x^{2} + 27264x + 127778 $ x^8 - 4x^7 - 66x^6 + 212x^5 + 2021x^4 - 4400x^3 - 25028x^2 + 27264*x + 127778
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			48.1
Root			$5.99086 + 1.84776i$ of defining polynomial
Character	$\chi$	$=$	49.48
Dual form			49.5.b.b.48.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.99086 q^{2} -7.89087i q^{3} +32.8721 q^{4} +22.0095i q^{5} +55.1639i q^{6} -117.950 q^{8} +18.7341 q^{9} +O(q^{10})$	\(q-6.99086 q^{2} -7.89087i q^{3} +32.8721 q^{4} +22.0095i q^{5} +55.1639i q^{6} -117.950 q^{8} +18.7341 q^{9} -153.865i q^{10} +44.7675 q^{11} -259.389i q^{12} -311.907i q^{13} +173.674 q^{15} +298.619 q^{16} -71.5536i q^{17} -130.968 q^{18} -278.920i q^{19} +723.499i q^{20} -312.963 q^{22} -514.843 q^{23} +930.729i q^{24} +140.580 q^{25} +2180.50i q^{26} -786.989i q^{27} +866.138 q^{29} -1214.13 q^{30} -683.378i q^{31} -200.403 q^{32} -353.255i q^{33} +500.221i q^{34} +615.830 q^{36} +1944.19 q^{37} +1949.89i q^{38} -2461.22 q^{39} -2596.03i q^{40} +102.538i q^{41} -885.919 q^{43} +1471.60 q^{44} +412.330i q^{45} +3599.20 q^{46} -2826.69i q^{47} -2356.37i q^{48} -982.778 q^{50} -564.621 q^{51} -10253.0i q^{52} -1329.80 q^{53} +5501.73i q^{54} +985.312i q^{55} -2200.92 q^{57} -6055.04 q^{58} +4841.74i q^{59} +5709.04 q^{60} +392.964i q^{61} +4777.40i q^{62} -3376.92 q^{64} +6864.93 q^{65} +2469.55i q^{66} +4246.54 q^{67} -2352.12i q^{68} +4062.56i q^{69} +1188.97 q^{71} -2209.69 q^{72} -0.214566i q^{73} -13591.6 q^{74} -1109.30i q^{75} -9168.67i q^{76} +17206.0 q^{78} -1578.96 q^{79} +6572.47i q^{80} -4692.57 q^{81} -716.829i q^{82} -9056.29i q^{83} +1574.86 q^{85} +6193.33 q^{86} -6834.58i q^{87} -5280.33 q^{88} +3485.66i q^{89} -2882.54i q^{90} -16924.0 q^{92} -5392.45 q^{93} +19761.0i q^{94} +6138.90 q^{95} +1581.36i q^{96} +7941.40i q^{97} +838.681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{2} + 52 q^{4} - 372 q^{8} - 352 q^{9}+O(q^{10}) $ 8 * q - 12 * q^2 + 52 * q^4 - 372 * q^8 - 352 * q^9	$ 8 q - 12 q^{2} + 52 q^{4} - 372 q^{8} - 352 q^{9} + 120 q^{11} - 632 q^{15} - 300 q^{16} + 340 q^{18} + 1952 q^{22} + 1752 q^{23} - 2192 q^{25} + 1248 q^{29} + 456 q^{30} + 3156 q^{32} + 4940 q^{36} + 2368 q^{37} - 7672 q^{39} - 8552 q^{43} + 264 q^{44} + 7208 q^{46} - 5556 q^{50} - 11976 q^{51} + 5496 q^{53} - 9200 q^{57} - 17496 q^{58} + 2856 q^{60} + 3980 q^{64} + 30240 q^{65} - 7440 q^{67} + 9984 q^{71} - 1508 q^{72} - 1080 q^{74} + 22456 q^{78} - 14096 q^{79} + 3432 q^{81} + 11912 q^{85} + 44496 q^{86} - 44464 q^{88} - 32232 q^{92} + 9584 q^{93} + 22488 q^{95} + 30144 q^{99}+O(q^{100}) $ 8 * q - 12 * q^2 + 52 * q^4 - 372 * q^8 - 352 * q^9 + 120 * q^11 - 632 * q^15 - 300 * q^16 + 340 * q^18 + 1952 * q^22 + 1752 * q^23 - 2192 * q^25 + 1248 * q^29 + 456 * q^30 + 3156 * q^32 + 4940 * q^36 + 2368 * q^37 - 7672 * q^39 - 8552 * q^43 + 264 * q^44 + 7208 * q^46 - 5556 * q^50 - 11976 * q^51 + 5496 * q^53 - 9200 * q^57 - 17496 * q^58 + 2856 * q^60 + 3980 * q^64 + 30240 * q^65 - 7440 * q^67 + 9984 * q^71 - 1508 * q^72 - 1080 * q^74 + 22456 * q^78 - 14096 * q^79 + 3432 * q^81 + 11912 * q^85 + 44496 * q^86 - 44464 * q^88 - 32232 * q^92 + 9584 * q^93 + 22488 * q^95 + 30144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−6.99086	−1.74771	−0.873857	−	0.486183i	$-0.838389\pi$
$2$	−6.99086	−1.74771	−0.873857	+	0.486183i	$0.838389\pi$
$3$	− 7.89087i	− 0.876764i	−0.898789	−	0.438382i	$-0.855552\pi$
$3$	− 7.89087i	− 0.876764i	0.898789	−	0.438382i	$-0.144448\pi$
$4$	32.8721	2.05450
$5$	22.0095i	0.880381i	0.897904	+	0.440191i	$0.145089\pi$
$5$	22.0095i	0.880381i	−0.897904	+	0.440191i	$0.854911\pi$
$6$	55.1639i	1.53233i
$7$	0	0
$7$	0	0
$8$	−117.950	−1.84297
$9$	18.7341	0.231286
$10$	− 153.865i	− 1.53865i
$11$	44.7675	0.369979	0.184990	−	0.982740i	$-0.440775\pi$
$11$	44.7675	0.369979	0.184990	+	0.982740i	$0.440775\pi$
$12$	− 259.389i	− 1.80131i
$13$	− 311.907i	− 1.84560i	−0.385274	−	0.922802i	$-0.625893\pi$
$13$	− 311.907i	− 1.84560i	0.385274	−	0.922802i	$-0.374107\pi$
$14$	0	0
$15$	173.674	0.771886
$16$	298.619	1.16648
$17$	− 71.5536i	− 0.247590i	−0.992308	−	0.123795i	$-0.960493\pi$
$17$	− 71.5536i	− 0.247590i	0.992308	−	0.123795i	$-0.0395066\pi$
$18$	−130.968	−0.404221
$19$	− 278.920i	− 0.772632i	−0.922367	−	0.386316i	$-0.873748\pi$
$19$	− 278.920i	− 0.772632i	0.922367	−	0.386316i	$-0.126252\pi$
$20$	723.499i	1.80875i
$21$	0	0
$22$	−312.963	−0.646618
$23$	−514.843	−0.973239	−0.486619	−	0.873614i	$-0.661770\pi$
$23$	−514.843	−0.973239	−0.486619	+	0.873614i	$0.661770\pi$
$24$	930.729i	1.61585i
$25$	140.580	0.224929
$26$	2180.50i	3.22559i
$27$	− 786.989i	− 1.07955i
$28$	0	0
$29$	866.138	1.02989	0.514945	−	0.857223i	$-0.327812\pi$
$29$	866.138	1.02989	0.514945	+	0.857223i	$0.327812\pi$
$30$	−1214.13	−1.34904
$31$	− 683.378i	− 0.711112i	−0.934655	−	0.355556i	$-0.884292\pi$
$31$	− 683.378i	− 0.711112i	0.934655	−	0.355556i	$-0.115708\pi$
$32$	−200.403	−0.195706
$33$	− 353.255i	− 0.324384i
$34$	500.221i	0.432717i
$35$	0	0
$36$	615.830	0.475177
$37$	1944.19	1.42016	0.710078	−	0.704123i	$-0.248660\pi$
$37$	1944.19	1.42016	0.710078	+	0.704123i	$0.248660\pi$
$38$	1949.89i	1.35034i
$39$	−2461.22	−1.61816
$40$	− 2596.03i	− 1.62252i
$41$	102.538i	0.0609983i	0.999535	+	0.0304991i	$0.00970969\pi$
$41$	102.538i	0.0609983i	−0.999535	+	0.0304991i	$0.990290\pi$
$42$	0	0
$43$	−885.919	−0.479134	−0.239567	−	0.970880i	$-0.577006\pi$
$43$	−885.919	−0.479134	−0.239567	+	0.970880i	$0.577006\pi$
$44$	1471.60	0.760124
$45$	412.330i	0.203620i
$46$	3599.20	1.70094
$47$	− 2826.69i	− 1.27962i	−0.768532	−	0.639812i	$-0.779012\pi$
$47$	− 2826.69i	− 1.27962i	0.768532	−	0.639812i	$-0.220988\pi$
$48$	− 2356.37i	− 1.02273i
$49$	0	0
$50$	−982.778	−0.393111
$51$	−564.621	−0.217078
$52$	− 10253.0i	− 3.79180i
$53$	−1329.80	−0.473408	−0.236704	−	0.971582i	$-0.576067\pi$
$53$	−1329.80	−0.473408	−0.236704	+	0.971582i	$0.576067\pi$
$54$	5501.73i	1.88674i
$55$	985.312i	0.325723i
$56$	0	0
$57$	−2200.92	−0.677415
$58$	−6055.04	−1.79995
$59$	4841.74i	1.39090i	0.718572	+	0.695452i	$0.244796\pi$
$59$	4841.74i	1.39090i	−0.718572	+	0.695452i	$0.755204\pi$
$60$	5709.04	1.58584
$61$	392.964i	0.105607i	0.998605	+	0.0528036i	$0.0168157\pi$
$61$	392.964i	0.105607i	−0.998605	+	0.0528036i	$0.983184\pi$
$62$	4777.40i	1.24282i
$63$	0	0
$64$	−3376.92	−0.824444
$65$	6864.93	1.62484
$66$	2469.55i	0.566931i
$67$	4246.54	0.945987	0.472994	−	0.881066i	$-0.343173\pi$
$67$	4246.54	0.945987	0.472994	+	0.881066i	$0.343173\pi$
$68$	− 2352.12i	− 0.508676i
$69$	4062.56i	0.853300i
$70$	0	0
$71$	1188.97	0.235860	0.117930	−	0.993022i	$-0.462374\pi$
$71$	1188.97	0.235860	0.117930	+	0.993022i	$0.462374\pi$
$72$	−2209.69	−0.426253
$73$	− 0.214566i	0 4.02639e-5i	−1.00000		2.01319e-5i	$-0.999994\pi$
$73$	− 0.214566i	0 4.02639e-5i	1.00000		2.01319e-5i	$-6.40820e-6\pi$
$74$	−13591.6	−2.48203
$75$	− 1109.30i	− 0.197209i
$76$	− 9168.67i	− 1.58737i
$77$	0	0
$78$	17206.0	2.82808
$79$	−1578.96	−0.252998	−0.126499	−	0.991967i	$-0.540374\pi$
$79$	−1578.96	−0.252998	−0.126499	+	0.991967i	$0.540374\pi$
$80$	6572.47i	1.02695i
$81$	−4692.57	−0.715221
$82$	− 716.829i	− 0.106608i
$83$	− 9056.29i	− 1.31460i	−0.753628	−	0.657301i	$-0.771698\pi$
$83$	− 9056.29i	− 1.31460i	0.753628	−	0.657301i	$-0.228302\pi$
$84$	0	0
$85$	1574.86	0.217974
$86$	6193.33	0.837390
$87$	− 6834.58i	− 0.902970i
$88$	−5280.33	−0.681861
$89$	3485.66i	0.440053i	0.975494	+	0.220026i	$0.0706144\pi$
$89$	3485.66i	0.440053i	−0.975494	+	0.220026i	$0.929386\pi$
$90$	− 2882.54i	− 0.355869i
$91$	0	0
$92$	−16924.0	−1.99952
$93$	−5392.45	−0.623477
$94$	19761.0i	2.23642i
$95$	6138.90	0.680210
$96$	1581.36i	0.171588i
$97$	7941.40i	0.844022i	0.906591	+	0.422011i	$0.138676\pi$
$97$	7941.40i	0.844022i	−0.906591	+	0.422011i	$0.861324\pi$
$98$	0	0
$99$	838.681	0.0855710
$100$	4621.17	0.462117
$101$	− 576.940i	− 0.0565572i	−0.999600	−	0.0282786i	$-0.990997\pi$
$101$	− 576.940i	− 0.0565572i	0.999600	−	0.0282786i	$-0.00900255\pi$
$102$	3947.18	0.379391
$103$	14336.3i	1.35134i	0.737205	+	0.675669i	$0.236145\pi$
$103$	14336.3i	1.35134i	−0.737205	+	0.675669i	$0.763855\pi$
$104$	36789.5i	3.40140i
$105$	0	0
$106$	9296.45	0.827381
$107$	−21220.3	−1.85346	−0.926730	−	0.375727i	$-0.877393\pi$
$107$	−21220.3	−1.85346	−0.926730	+	0.375727i	$0.877393\pi$
$108$	− 25870.0i	− 2.21793i
$109$	8061.45	0.678516	0.339258	−	0.940693i	$-0.389824\pi$
$109$	8061.45	0.678516	0.339258	+	0.940693i	$0.389824\pi$
$110$	− 6888.17i	− 0.569271i
$111$	− 15341.4i	− 1.24514i
$112$	0	0
$113$	−4563.77	−0.357410	−0.178705	−	0.983903i	$-0.557191\pi$
$113$	−4563.77	−0.357410	−0.178705	+	0.983903i	$0.557191\pi$
$114$	15386.3	1.18393
$115$	− 11331.5i	− 0.856821i
$116$	28471.7	2.11591
$117$	− 5843.31i	− 0.426862i
$118$	− 33847.9i	− 2.43090i
$119$	0	0
$120$	−20484.9	−1.42256
$121$	−12636.9	−0.863115
$122$	− 2747.16i	− 0.184571i
$123$	809.115	0.0534811
$124$	− 22464.1i	− 1.46098i
$125$	16850.1i	1.07840i
$126$	0	0
$127$	21712.4	1.34617	0.673085	−	0.739565i	$-0.264969\pi$
$127$	21712.4	1.34617	0.673085	+	0.739565i	$0.264969\pi$
$128$	26814.0	1.63660
$129$	6990.68i	0.420088i
$130$	−47991.7	−2.83975
$131$	− 270.510i	− 0.0157631i	−0.999969	−	0.00788154i	$-0.997491\pi$
$131$	− 270.510i	− 0.0157631i	0.999969	−	0.00788154i	$-0.00250880\pi$
$132$	− 11612.2i	− 0.666449i
$133$	0	0
$134$	−29686.9	−1.65332
$135$	17321.3	0.950412
$136$	8439.76i	0.456302i
$137$	−8215.56	−0.437720	−0.218860	−	0.975756i	$-0.570234\pi$
$137$	−8215.56	−0.437720	−0.218860	+	0.975756i	$0.570234\pi$
$138$	− 28400.8i	− 1.49132i
$139$	11669.2i	0.603962i	0.953314	+	0.301981i	$0.0976480\pi$
$139$	11669.2i	0.603962i	−0.953314	+	0.301981i	$0.902352\pi$
$140$	0	0
$141$	−22305.0	−1.12193
$142$	−8311.90	−0.412215
$143$	− 13963.3i	− 0.682836i
$144$	5594.38	0.269791
$145$	19063.3i	0.906696i
$146$	1.50000i	0 7.03698e-5i
$147$	0	0
$148$	63909.7	2.91772
$149$	28307.7	1.27506	0.637531	−	0.770424i	$-0.279956\pi$
$149$	28307.7	1.27506	0.637531	+	0.770424i	$0.279956\pi$
$150$	7754.97i	0.344665i
$151$	22135.3	0.970802	0.485401	−	0.874292i	$-0.338674\pi$
$151$	22135.3	0.970802	0.485401	+	0.874292i	$0.338674\pi$
$152$	32898.7i	1.42394i
$153$	− 1340.50i	− 0.0572641i
$154$	0	0
$155$	15040.8	0.626049
$156$	−80905.3	−3.32451
$157$	44311.6i	1.79770i	0.438252	+	0.898852i	$0.355598\pi$
$157$	44311.6i	1.79770i	−0.438252	+	0.898852i	$0.644402\pi$
$158$	11038.3	0.442169
$159$	10493.3i	0.415066i
$160$	− 4410.78i	− 0.172296i
$161$	0	0
$162$	32805.1	1.25000
$163$	−25621.7	−0.964346	−0.482173	−	0.876076i	$-0.660152\pi$
$163$	−25621.7	−0.964346	−0.482173	+	0.876076i	$0.660152\pi$
$164$	3370.64i	0.125321i
$165$	7774.97	0.285582
$166$	63311.2i	2.29755i
$167$	− 5822.23i	− 0.208764i	−0.994537	−	0.104382i	$-0.966713\pi$
$167$	− 5822.23i	− 0.208764i	0.994537	−	0.104382i	$-0.0332865\pi$
$168$	0	0
$169$	−68725.1	−2.40626
$170$	−11009.6	−0.380956
$171$	− 5225.33i	− 0.178699i
$172$	−29122.0	−0.984383
$173$	− 39542.0i	− 1.32119i	−0.750741	−	0.660596i	$-0.770303\pi$
$173$	− 39542.0i	− 1.32119i	0.750741	−	0.660596i	$-0.229697\pi$
$174$	47779.6i	1.57813i
$175$	0	0
$176$	13368.4	0.431574
$177$	38205.5	1.21949
$178$	− 24367.7i	− 0.769087i
$179$	−48083.2	−1.50068	−0.750338	−	0.661054i	$-0.770109\pi$
$179$	−48083.2	−1.50068	−0.750338	+	0.661054i	$0.770109\pi$
$180$	13554.1i	0.418337i
$181$	47562.9i	1.45181i	0.687793	+	0.725907i	$0.258580\pi$
$181$	47562.9i	1.45181i	−0.687793	+	0.725907i	$0.741420\pi$
$182$	0	0
$183$	3100.83	0.0925925
$184$	60725.8	1.79365
$185$	42790.8i	1.25028i
$186$	37697.8	1.08966
$187$	− 3203.28i	− 0.0916034i
$188$	− 92919.0i	− 2.62899i
$189$	0	0
$190$	−42916.2	−1.18881
$191$	9825.68	0.269337	0.134668	−	0.990891i	$-0.457003\pi$
$191$	9825.68	0.269337	0.134668	+	0.990891i	$0.457003\pi$
$192$	26646.9i	0.722842i
$193$	−9734.63	−0.261339	−0.130670	−	0.991426i	$-0.541713\pi$
$193$	−9734.63	−0.261339	−0.130670	+	0.991426i	$0.541713\pi$
$194$	− 55517.2i	− 1.47511i
$195$	− 54170.3i	− 1.42460i
$196$	0	0
$197$	58038.9	1.49550	0.747750	−	0.663981i	$-0.231134\pi$
$197$	58038.9	1.49550	0.747750	+	0.663981i	$0.231134\pi$
$198$	−5863.10	−0.149554
$199$	− 62566.0i	− 1.57991i	−0.613165	−	0.789955i	$-0.710104\pi$
$199$	− 62566.0i	− 1.57991i	0.613165	−	0.789955i	$-0.289896\pi$
$200$	−16581.5	−0.414537
$201$	− 33508.9i	− 0.829407i
$202$	4033.30i	0.0988458i
$203$	0	0
$204$	−18560.2	−0.445988
$205$	−2256.82	−0.0537018
$206$	− 100223.i	− 2.36175i
$207$	−9645.15	−0.225096
$208$	− 93141.5i	− 2.15286i
$209$	− 12486.6i	− 0.285858i
$210$	0	0
$211$	26674.3	0.599140	0.299570	−	0.954074i	$-0.403157\pi$
$211$	26674.3	0.599140	0.299570	+	0.954074i	$0.403157\pi$
$212$	−43713.3	−0.972618
$213$	− 9382.00i	− 0.206793i
$214$	148348.	3.23932
$215$	− 19498.7i	− 0.421821i
$216$	92825.5i	1.98957i
$217$	0	0
$218$	−56356.4	−1.18585
$219$	−1.69311	−3.53019e−5 0
$220$	32389.2i	0.669199i
$221$	−22318.1	−0.456954
$222$	107249.i	2.17615i
$223$	− 21285.7i	− 0.428035i	−0.976830	−	0.214017i	$-0.931345\pi$
$223$	− 21285.7i	− 0.428035i	0.976830	−	0.214017i	$-0.0686549\pi$
$224$	0	0
$225$	2633.65	0.0520228
$226$	31904.7	0.624651
$227$	21567.9i	0.418559i	0.977856	+	0.209280i	$0.0671119\pi$
$227$	21567.9i	0.418559i	−0.977856	+	0.209280i	$0.932888\pi$
$228$	−72348.8	−1.39175
$229$	19922.3i	0.379900i	0.981794	+	0.189950i	$0.0608326\pi$
$229$	19922.3i	0.379900i	−0.981794	+	0.189950i	$0.939167\pi$
$230$	79216.6i	1.49748i
$231$	0	0
$232$	−102161.	−1.89806
$233$	4027.85	0.0741927	0.0370964	−	0.999312i	$-0.488189\pi$
$233$	4027.85	0.0741927	0.0370964	+	0.999312i	$0.488189\pi$
$234$	40849.8i	0.746032i
$235$	62214.1	1.12656
$236$	159158.i	2.85762i
$237$	12459.4i	0.221820i
$238$	0	0
$239$	35321.2	0.618358	0.309179	−	0.951004i	$-0.399946\pi$
$239$	35321.2	0.618358	0.309179	+	0.951004i	$0.399946\pi$
$240$	51862.6	0.900392
$241$	− 79235.5i	− 1.36422i	−0.731248	−	0.682112i	$-0.761062\pi$
$241$	− 79235.5i	− 1.36422i	0.731248	−	0.682112i	$-0.238938\pi$
$242$	88342.5	1.50848
$243$	− 26717.7i	− 0.452467i
$244$	12917.5i	0.216970i
$245$	0	0
$246$	−5656.41	−0.0934696
$247$	−86997.1	−1.42597
$248$	80604.6i	1.31056i
$249$	−71462.0	−1.15259
$250$	− 117796.i	− 1.88474i
$251$	− 100747.i	− 1.59914i	−0.600575	−	0.799569i	$-0.705061\pi$
$251$	− 100747.i	− 1.59914i	0.600575	−	0.799569i	$-0.294939\pi$
$252$	0	0
$253$	−23048.3	−0.360078
$254$	−151788.	−2.35272
$255$	− 12427.0i	− 0.191112i
$256$	−133422.	−2.03586
$257$	49021.5i	0.742198i	0.928593	+	0.371099i	$0.121019\pi$
$257$	49021.5i	0.742198i	−0.928593	+	0.371099i	$0.878981\pi$
$258$	− 48870.8i	− 0.734193i
$259$	0	0
$260$	225664.	3.33823
$261$	16226.3	0.238199
$262$	1891.10i	0.0275494i
$263$	−2870.93	−0.0415060	−0.0207530	−	0.999785i	$-0.506606\pi$
$263$	−2870.93	−0.0415060	−0.0207530	+	0.999785i	$0.506606\pi$
$264$	41666.4i	0.597831i
$265$	− 29268.3i	− 0.416779i
$266$	0	0
$267$	27504.9	0.385822
$268$	139592.	1.94353
$269$	46932.4i	0.648587i	0.945957	+	0.324294i	$0.105127\pi$
$269$	46932.4i	0.648587i	−0.945957	+	0.324294i	$0.894873\pi$
$270$	−121090.	−1.66105
$271$	− 58557.8i	− 0.797345i	−0.917093	−	0.398673i	$-0.869471\pi$
$271$	− 58557.8i	− 0.797345i	0.917093	−	0.398673i	$-0.130529\pi$
$272$	− 21367.3i	− 0.288810i
$273$	0	0
$274$	57433.8	0.765009
$275$	6293.44	0.0832190
$276$	133545.i	1.75311i
$277$	59620.0	0.777020	0.388510	−	0.921444i	$-0.372990\pi$
$277$	59620.0	0.777020	0.388510	+	0.921444i	$0.372990\pi$
$278$	− 81577.4i	− 1.05555i
$279$	− 12802.5i	− 0.164470i
$280$	0	0
$281$	−47369.7	−0.599912	−0.299956	−	0.953953i	$-0.596972\pi$
$281$	−47369.7	−0.599912	−0.299956	+	0.953953i	$0.596972\pi$
$282$	155931.	1.96081
$283$	94657.0i	1.18190i	0.806709	+	0.590949i	$0.201246\pi$
$283$	94657.0i	1.18190i	−0.806709	+	0.590949i	$0.798754\pi$
$284$	39083.8	0.484574
$285$	− 48441.3i	− 0.596384i
$286$	97615.4i	1.19340i
$287$	0	0
$288$	−3754.38	−0.0452640
$289$	78401.1	0.938699
$290$	− 133269.i	− 1.58465i
$291$	62664.6	0.740008
$292$	− 7.05324i	0 8.27223e-5i
$293$	73528.8i	0.856490i	0.903663	+	0.428245i	$0.140868\pi$
$293$	73528.8i	0.856490i	−0.903663	+	0.428245i	$0.859132\pi$
$294$	0	0
$295$	−106564.	−1.22453
$296$	−229318.	−2.61731
$297$	− 35231.6i	− 0.399410i
$298$	−197895.	−2.22844
$299$	160583.i	1.79621i
$300$	− 36465.1i	− 0.405167i
$301$	0	0
$302$	−154744.	−1.69668
$303$	−4552.56	−0.0495873
$304$	− 83290.9i	− 0.901261i
$305$	−8648.96	−0.0929745
$306$	9371.22i	0.100081i
$307$	117853.i	1.25045i	0.780445	+	0.625224i	$0.214992\pi$
$307$	117853.i	1.25045i	−0.780445	+	0.625224i	$0.785008\pi$
$308$	0	0
$309$	113126.	1.18480
$310$	−105148.	−1.09416
$311$	4319.53i	0.0446597i	0.999751	+	0.0223298i	$0.00710840\pi$
$311$	4319.53i	0.0446597i	−0.999751	+	0.0223298i	$0.992892\pi$
$312$	290301.	2.98222
$313$	119271.i	1.21744i	0.793387	+	0.608718i	$0.208316\pi$
$313$	119271.i	1.21744i	−0.793387	+	0.608718i	$0.791684\pi$
$314$	− 309776.i	− 3.14187i
$315$	0	0
$316$	−51903.8	−0.519786
$317$	−13998.6	−0.139305	−0.0696524	−	0.997571i	$-0.522189\pi$
$317$	−13998.6	−0.139305	−0.0696524	+	0.997571i	$0.522189\pi$
$318$	− 73357.1i	− 0.725417i
$319$	38774.8	0.381038
$320$	− 74324.5i	− 0.725825i
$321$	167446.i	1.62505i
$322$	0	0
$323$	−19957.7	−0.191296
$324$	−154254.	−1.46942
$325$	− 43848.0i	− 0.415129i
$326$	179118.	1.68540
$327$	− 63611.9i	− 0.594898i
$328$	− 12094.4i	− 0.112418i
$329$	0	0
$330$	−54353.7	−0.499116
$331$	30753.0	0.280692	0.140346	−	0.990102i	$-0.455178\pi$
$331$	30753.0	0.280692	0.140346	+	0.990102i	$0.455178\pi$
$332$	− 297699.i	− 2.70085i
$333$	36422.8	0.328462
$334$	40702.4i	0.364860i
$335$	93464.3i	0.832830i
$336$	0	0
$337$	−22396.7	−0.197208	−0.0986040	−	0.995127i	$-0.531438\pi$
$337$	−22396.7	−0.197208	−0.0986040	+	0.995127i	$0.531438\pi$
$338$	480447.	4.20545
$339$	36012.2i	0.313364i
$340$	51769.0	0.447828
$341$	− 30593.1i	− 0.263097i
$342$	36529.5i	0.312314i
$343$	0	0
$344$	104494.	0.883031
$345$	−89415.1	−0.751230
$346$	276432.i	2.30907i
$347$	−213803.	−1.77564	−0.887820	−	0.460190i	$-0.847781\pi$
$347$	−213803.	−1.77564	−0.887820	+	0.460190i	$0.847781\pi$
$348$	− 224667.i	− 1.85516i
$349$	− 63672.4i	− 0.522758i	−0.965236	−	0.261379i	$-0.915823\pi$
$349$	− 63672.4i	− 0.522758i	0.965236	−	0.261379i	$-0.0841772\pi$
$350$	0	0
$351$	−245468.	−1.99242
$352$	−8971.55	−0.0724073
$353$	140790.i	1.12985i	0.825142	+	0.564926i	$0.191095\pi$
$353$	140790.i	1.12985i	−0.825142	+	0.564926i	$0.808905\pi$
$354$	−267089.	−2.13133
$355$	26168.6i	0.207646i
$356$	114581.i	0.904090i
$357$	0	0
$358$	336142.	2.62275
$359$	−36765.1	−0.285264	−0.142632	−	0.989776i	$-0.545557\pi$
$359$	−36765.1	−0.285264	−0.142632	+	0.989776i	$0.545557\pi$
$360$	− 48634.4i	− 0.375265i
$361$	52524.6	0.403041
$362$	− 332505.i	− 2.53735i
$363$	99715.9i	0.756748i
$364$	0	0
$365$	4.72250	3.54476e−5 0
$366$	−21677.5	−0.161825
$367$	− 24768.2i	− 0.183892i	−0.995764	−	0.0919459i	$-0.970691\pi$
$367$	− 24768.2i	− 0.183892i	0.995764	−	0.0919459i	$-0.0293087\pi$
$368$	−153742.	−1.13527
$369$	1920.96i	0.0141080i
$370$	− 299144.i	− 2.18513i
$371$	0	0
$372$	−177261.	−1.28094
$373$	−32192.6	−0.231387	−0.115693	−	0.993285i	$-0.536909\pi$
$373$	−32192.6	−0.231387	−0.115693	+	0.993285i	$0.536909\pi$
$374$	22393.7i	0.160096i
$375$	132962.	0.945506
$376$	333408.i	2.35831i
$377$	− 270154.i	− 1.90077i
$378$	0	0
$379$	187516.	1.30545	0.652726	−	0.757594i	$-0.273625\pi$
$379$	187516.	1.30545	0.652726	+	0.757594i	$0.273625\pi$
$380$	201798.	1.39749
$381$	− 171330.i	− 1.18027i
$382$	−68689.9	−0.470724
$383$	− 25640.4i	− 0.174794i	−0.996174	−	0.0873972i	$-0.972145\pi$
$383$	− 25640.4i	− 0.174794i	0.996174	−	0.0873972i	$-0.0278549\pi$
$384$	− 211586.i	− 1.43491i
$385$	0	0
$386$	68053.4	0.456746
$387$	−16596.9	−0.110817
$388$	261050.i	1.73405i
$389$	72456.0	0.478823	0.239412	−	0.970918i	$-0.423045\pi$
$389$	72456.0	0.478823	0.239412	+	0.970918i	$0.423045\pi$
$390$	378697.i	2.48979i
$391$	36838.9i	0.240965i
$392$	0	0
$393$	−2134.56	−0.0138205
$394$	−405741.	−2.61371
$395$	− 34752.2i	− 0.222735i
$396$	27569.2	0.175806
$397$	127601.i	0.809607i	0.914404	+	0.404803i	$0.132660\pi$
$397$	127601.i	0.809607i	−0.914404	+	0.404803i	$0.867340\pi$
$398$	437390.i	2.76123i
$399$	0	0
$400$	41980.1	0.262375
$401$	−138450.	−0.861000	−0.430500	−	0.902591i	$-0.641663\pi$
$401$	−138450.	−0.861000	−0.430500	+	0.902591i	$0.641663\pi$
$402$	234256.i	1.44957i
$403$	−213151.	−1.31243
$404$	− 18965.2i	− 0.116197i
$405$	− 103281.i	− 0.629667i
$406$	0	0
$407$	87036.7	0.525428
$408$	66597.1	0.400069
$409$	− 76736.7i	− 0.458729i	−0.973341	−	0.229365i	$-0.926335\pi$
$409$	− 76736.7i	− 0.458729i	0.973341	−	0.229365i	$-0.0736648\pi$
$410$	15777.1	0.0938553
$411$	64828.0i	0.383777i
$412$	471265.i	2.77633i
$413$	0	0
$414$	67427.8	0.393404
$415$	199325.	1.15735
$416$	62507.2i	0.361196i
$417$	92079.8	0.529532
$418$	87291.7i	0.499598i
$419$	179909.i	1.02476i	0.858757	+	0.512382i	$0.171237\pi$
$419$	179909.i	1.02476i	−0.858757	+	0.512382i	$0.828763\pi$
$420$	0	0
$421$	−6114.46	−0.0344980	−0.0172490	−	0.999851i	$-0.505491\pi$
$421$	−6114.46	−0.0344980	−0.0172490	+	0.999851i	$0.505491\pi$
$422$	−186476.	−1.04713
$423$	− 52955.6i	− 0.295959i
$424$	156850.	0.872476
$425$	− 10059.0i	− 0.0556902i
$426$	65588.2i	0.361415i
$427$	0	0
$428$	−697554.	−3.80794
$429$	−110183.	−0.598685
$430$	136312.i	0.737222i
$431$	225295.	1.21282	0.606412	−	0.795150i	$-0.292608\pi$
$431$	225295.	1.21282	0.606412	+	0.795150i	$0.292608\pi$
$432$	− 235010.i	− 1.25927i
$433$	− 291349.i	− 1.55395i	−0.629531	−	0.776976i	$-0.716753\pi$
$433$	− 291349.i	− 1.55395i	0.629531	−	0.776976i	$-0.283247\pi$
$434$	0	0
$435$	150426.	0.794958
$436$	264997.	1.39401
$437$	143600.i	0.751955i
$438$	11.8363	6.16976e−5 0
$439$	− 270847.i	− 1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$439$	− 270847.i	− 1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$440$	− 116218.i	− 0.600298i
$441$	0	0
$442$	156023.	0.798625
$443$	63184.3	0.321960	0.160980	−	0.986958i	$-0.448535\pi$
$443$	63184.3	0.321960	0.160980	+	0.986958i	$0.448535\pi$
$444$	− 504303.i	− 2.55815i
$445$	−76717.7	−0.387414
$446$	148806.i	0.748082i
$447$	− 223372.i	− 1.11793i
$448$	0	0
$449$	328951.	1.63169	0.815846	−	0.578269i	$-0.196272\pi$
$449$	328951.	1.63169	0.815846	+	0.578269i	$0.196272\pi$
$450$	−18411.5	−0.0909210
$451$	4590.38i	0.0225681i
$452$	−150021.	−0.734301
$453$	− 174666.i	− 0.851164i
$454$	− 150778.i	− 0.731522i
$455$	0	0
$456$	259599.	1.24846
$457$	−31227.4	−0.149521	−0.0747607	−	0.997202i	$-0.523819\pi$
$457$	−31227.4	−0.149521	−0.0747607	+	0.997202i	$0.523819\pi$
$458$	− 139274.i	− 0.663957i
$459$	−56312.0	−0.267285
$460$	− 372488.i	− 1.76034i
$461$	− 193095.i	− 0.908591i	−0.890851	−	0.454296i	$-0.849891\pi$
$461$	− 193095.i	− 0.908591i	0.890851	−	0.454296i	$-0.150109\pi$
$462$	0	0
$463$	−246667.	−1.15067	−0.575333	−	0.817919i	$-0.695127\pi$
$463$	−246667.	−1.15067	−0.575333	+	0.817919i	$0.695127\pi$
$464$	258646.	1.20135
$465$	− 118685.i	− 0.548897i
$466$	−28158.1	−0.129668
$467$	334087.i	1.53188i	0.642910	+	0.765942i	$0.277727\pi$
$467$	334087.i	1.53188i	−0.642910	+	0.765942i	$0.722273\pi$
$468$	− 192082.i	− 0.876989i
$469$	0	0
$470$	−434930.	−1.96890
$471$	349657.	1.57616
$472$	− 571084.i	− 2.56340i
$473$	−39660.4	−0.177270
$474$	− 87101.8i	− 0.387677i
$475$	− 39210.7i	− 0.173787i
$476$	0	0
$477$	−24912.7	−0.109492
$478$	−246925.	−1.08071
$479$	150428.i	0.655628i	0.944742	+	0.327814i	$0.106312\pi$
$479$	150428.i	0.655628i	−0.944742	+	0.327814i	$0.893688\pi$
$480$	−34804.9	−0.151063
$481$	− 606408.i	− 2.62105i
$482$	553924.i	2.38427i
$483$	0	0
$484$	−415400.	−1.77327
$485$	−174787.	−0.743061
$486$	186780.i	0.790782i
$487$	−280063.	−1.18086	−0.590429	−	0.807089i	$-0.701042\pi$
$487$	−280063.	−1.18086	−0.590429	+	0.807089i	$0.701042\pi$
$488$	− 46350.2i	− 0.194631i
$489$	202178.i	0.845503i
$490$	0	0
$491$	−227539.	−0.943829	−0.471914	−	0.881644i	$-0.656437\pi$
$491$	−227539.	−0.943829	−0.471914	+	0.881644i	$0.656437\pi$
$492$	26597.3	0.109877
$493$	− 61975.3i	− 0.254991i
$494$	608184.	2.49219
$495$	18459.0i	0.0753351i
$496$	− 204070.i	− 0.829499i
$497$	0	0
$498$	499581.	2.01441
$499$	230599.	0.926098	0.463049	−	0.886333i	$-0.346755\pi$
$499$	230599.	0.926098	0.463049	+	0.886333i	$0.346755\pi$
$500$	553896.i	2.21559i
$501$	−45942.5	−0.183037
$502$	704310.i	2.79483i
$503$	434537.i	1.71748i	0.512415	+	0.858738i	$0.328751\pi$
$503$	434537.i	1.71748i	−0.512415	+	0.858738i	$0.671249\pi$
$504$	0	0
$505$	12698.2	0.0497919
$506$	161127.	0.629314
$507$	542301.i	2.10972i
$508$	713730.	2.76571
$509$	227244.i	0.877118i	0.898703	+	0.438559i	$0.144511\pi$
$509$	227244.i	0.877118i	−0.898703	+	0.438559i	$0.855489\pi$
$510$	86875.6i	0.334009i
$511$	0	0
$512$	503711.	1.92151
$513$	−219507.	−0.834092
$514$	− 342702.i	− 1.29715i
$515$	−315536.	−1.18969
$516$	229798.i	0.863071i
$517$	− 126544.i	− 0.473434i
$518$	0	0
$519$	−312021.	−1.15837
$520$	−809720.	−2.99452
$521$	− 238110.i	− 0.877207i	−0.898681	−	0.438603i	$-0.855473\pi$
$521$	− 238110.i	− 0.877207i	0.898681	−	0.438603i	$-0.144527\pi$
$522$	−113436.	−0.416303
$523$	− 199292.i	− 0.728595i	−0.931283	−	0.364298i	$-0.881309\pi$
$523$	− 199292.i	− 0.728595i	0.931283	−	0.364298i	$-0.118691\pi$
$524$	− 8892.23i	− 0.0323853i
$525$	0	0
$526$	20070.3	0.0725406
$527$	−48898.2	−0.176064
$528$	− 105489.i	− 0.378389i
$529$	−14777.4	−0.0528063
$530$	204611.i	0.728411i
$531$	90705.8i	0.321696i
$532$	0	0
$533$	31982.4	0.112579
$534$	−192283.	−0.674307
$535$	− 467048.i	− 1.63175i
$536$	−500880.	−1.74343
$537$	379418.i	1.31574i
$538$	− 328098.i	− 1.13354i
$539$	0	0
$540$	569386.	1.95263
$541$	279663.	0.955522	0.477761	−	0.878490i	$-0.341448\pi$
$541$	279663.	0.955522	0.477761	+	0.878490i	$0.341448\pi$
$542$	409369.i	1.39353i
$543$	375312.	1.27290
$544$	14339.6i	0.0484550i
$545$	177429.i	0.597353i
$546$	0	0
$547$	322945.	1.07933	0.539664	−	0.841881i	$-0.318551\pi$
$547$	322945.	1.07933	0.539664	+	0.841881i	$0.318551\pi$
$548$	−270062.	−0.899297
$549$	7361.85i	0.0244254i
$550$	−43996.5	−0.145443
$551$	− 241583.i	− 0.795726i
$552$	− 479180.i	− 1.57261i
$553$	0	0
$554$	−416795.	−1.35801
$555$	337657.	1.09620
$556$	383589.i	1.24084i
$557$	−408009.	−1.31510	−0.657551	−	0.753410i	$-0.728407\pi$
$557$	−408009.	−1.31510	−0.657551	+	0.753410i	$0.728407\pi$
$558$	89500.5i	0.287446i
$559$	276325.i	0.884292i
$560$	0	0
$561$	−25276.7	−0.0803145
$562$	331154.	1.04847
$563$	580596.i	1.83171i	0.401507	+	0.915856i	$0.368487\pi$
$563$	580596.i	1.83171i	−0.401507	+	0.915856i	$0.631513\pi$
$564$	−733212.	−2.30500
$565$	− 100447.i	− 0.314657i
$566$	− 661733.i	− 2.06562i
$567$	0	0
$568$	−140239.	−0.434682
$569$	337535.	1.04255	0.521273	−	0.853390i	$-0.325458\pi$
$569$	337535.	1.04255	0.521273	+	0.853390i	$0.325458\pi$
$570$	338646.i	1.04231i
$571$	218308.	0.669571	0.334786	−	0.942294i	$-0.391336\pi$
$571$	218308.	0.669571	0.334786	+	0.942294i	$0.391336\pi$
$572$	− 459003.i	− 1.40289i
$573$	− 77533.2i	− 0.236145i
$574$	0	0
$575$	−72376.9	−0.218909
$576$	−63263.7	−0.190682
$577$	228354.i	0.685893i	0.939355	+	0.342947i	$0.111425\pi$
$577$	228354.i	0.685893i	−0.939355	+	0.342947i	$0.888575\pi$
$578$	−548091.	−1.64058
$579$	76814.7i	0.229133i
$580$	626649.i	1.86281i
$581$	0	0
$582$	−438079.	−1.29332
$583$	−59531.9	−0.175151
$584$	25.3081i	0 7.42052e-5i
$585$	128609.	0.375801
$586$	− 514029.i	− 1.49690i
$587$	− 235281.i	− 0.682827i	−0.939913	−	0.341413i	$-0.889094\pi$
$587$	− 235281.i	− 0.682827i	0.939913	−	0.341413i	$-0.110906\pi$
$588$	0	0
$589$	−190608.	−0.549427
$590$	744976.	2.14012
$591$	− 457977.i	− 1.31120i
$592$	580574.	1.65659
$593$	56404.5i	0.160400i	0.996779	+	0.0802000i	$0.0255559\pi$
$593$	56404.5i	0.160400i	−0.996779	+	0.0802000i	$0.974444\pi$
$594$	246299.i	0.698054i
$595$	0	0
$596$	930531.	2.61962
$597$	−493700.	−1.38521
$598$	− 1.12261e6i	− 3.13927i
$599$	108643.	0.302795	0.151397	−	0.988473i	$-0.451623\pi$
$599$	108643.	0.302795	0.151397	+	0.988473i	$0.451623\pi$
$600$	130842.i	0.363451i
$601$	− 11012.9i	− 0.0304897i	−0.999884	−	0.0152448i	$-0.995147\pi$
$601$	− 11012.9i	− 0.0304897i	0.999884	−	0.0152448i	$-0.00485277\pi$
$602$	0	0
$603$	79555.2	0.218793
$604$	727631.	1.99452
$605$	− 278132.i	− 0.759871i
$606$	31826.3	0.0866644
$607$	− 191265.i	− 0.519109i	−0.965728	−	0.259554i	$-0.916424\pi$
$607$	− 191265.i	− 0.519109i	0.965728	−	0.259554i	$-0.0835757\pi$
$608$	55896.4i	0.151209i
$609$	0	0
$610$	60463.6	0.162493
$611$	−881664.	−2.36168
$612$	− 44064.9i	− 0.117649i
$613$	310998.	0.827631	0.413816	−	0.910361i	$-0.364196\pi$
$613$	310998.	0.827631	0.413816	+	0.910361i	$0.364196\pi$
$614$	− 823897.i	− 2.18543i
$615$	17808.2i	0.0470837i
$616$	0	0
$617$	452960.	1.18984	0.594922	−	0.803784i	$-0.297183\pi$
$617$	452960.	1.18984	0.594922	+	0.803784i	$0.297183\pi$
$618$	−790849.	−2.07070
$619$	698778.i	1.82372i	0.410504	+	0.911859i	$0.365353\pi$
$619$	698778.i	1.82372i	−0.410504	+	0.911859i	$0.634647\pi$
$620$	494423.	1.28622
$621$	405176.i	1.05066i
$622$	− 30197.2i	− 0.0780524i
$623$	0	0
$624$	−734968.	−1.88755
$625$	−282999.	−0.724478
$626$	− 833806.i	− 2.12773i
$627$	−98529.8	−0.250630
$628$	1.45661e6i	3.69339i
$629$	− 139114.i	− 0.351617i
$630$	0	0
$631$	−401495.	−1.00837	−0.504187	−	0.863595i	$-0.668208\pi$
$631$	−401495.	−1.00837	−0.504187	+	0.863595i	$0.668208\pi$
$632$	186239.	0.466269
$633$	− 210484.i	− 0.525304i
$634$	97862.2	0.243465
$635$	477879.i	1.18514i
$636$	344936.i	0.852756i
$637$	0	0
$638$	−271069.	−0.665946
$639$	22274.3	0.0545510
$640$	590164.i	1.44083i
$641$	736931.	1.79354	0.896769	−	0.442498i	$-0.145908\pi$
$641$	736931.	1.79354	0.896769	+	0.442498i	$0.145908\pi$
$642$	− 1.17059e6i	− 2.84012i
$643$	− 328825.i	− 0.795323i	−0.917532	−	0.397661i	$-0.869822\pi$
$643$	− 328825.i	− 0.795323i	0.917532	−	0.397661i	$-0.130178\pi$
$644$	0	0
$645$	−153862.	−0.369837
$646$	139522.	0.334331
$647$	− 581489.i	− 1.38910i	−0.719445	−	0.694549i	$-0.755604\pi$
$647$	− 581489.i	− 1.38910i	0.719445	−	0.694549i	$-0.244396\pi$
$648$	553489.	1.31813
$649$	216753.i	0.514606i
$650$	306535.i	0.725527i
$651$	0	0
$652$	−842238.	−1.98125
$653$	596467.	1.39881	0.699407	−	0.714723i	$-0.253447\pi$
$653$	596467.	1.39881	0.699407	+	0.714723i	$0.253447\pi$
$654$	444701.i	1.03971i
$655$	5953.81	0.0138775
$656$	30619.9i	0.0711534i
$657$	− 4.01971i	0 9.31246e-6i
$658$	0	0
$659$	−82075.1	−0.188991	−0.0944954	−	0.995525i	$-0.530124\pi$
$659$	−82075.1	−0.188991	−0.0944954	+	0.995525i	$0.530124\pi$
$660$	255579.	0.586729
$661$	− 154358.i	− 0.353286i	−0.984275	−	0.176643i	$-0.943476\pi$
$661$	− 154358.i	− 0.353286i	0.984275	−	0.176643i	$-0.0565238\pi$
$662$	−214989.	−0.490570
$663$	176109.i	0.400641i
$664$	1.06819e6i	2.42277i
$665$	0	0
$666$	−254627.	−0.574057
$667$	−445925.	−1.00233
$668$	− 191389.i	− 0.428907i
$669$	−167963.	−0.375285
$670$	− 653395.i	− 1.45555i
$671$	17592.0i	0.0390725i
$672$	0	0
$673$	675260.	1.49087	0.745437	−	0.666576i	$-0.232241\pi$
$673$	675260.	1.49087	0.745437	+	0.666576i	$0.232241\pi$
$674$	156572.	0.344663
$675$	− 110635.i	− 0.242821i
$676$	−2.25913e6	−4.94366
$677$	208893.i	0.455772i	0.973688	+	0.227886i	$0.0731813\pi$
$677$	208893.i	0.455772i	−0.973688	+	0.227886i	$0.926819\pi$
$678$	− 251756.i	− 0.547671i
$679$	0	0
$680$	−185755.	−0.401720
$681$	170190.	0.366978
$682$	213872.i	0.459818i
$683$	−42319.7	−0.0907196	−0.0453598	−	0.998971i	$-0.514443\pi$
$683$	−42319.7	−0.0907196	−0.0453598	+	0.998971i	$0.514443\pi$
$684$	− 171767.i	− 0.367137i
$685$	− 180821.i	− 0.385360i
$686$	0	0
$687$	157205.	0.333083
$688$	−264553.	−0.558902
$689$	414775.i	0.873723i
$690$	625088.	1.31293
$691$	23511.6i	0.0492409i	0.999697	+	0.0246205i	$0.00783773\pi$
$691$	23511.6i	0.0492409i	−0.999697	+	0.0246205i	$0.992162\pi$
$692$	− 1.29983e6i	− 2.71440i
$693$	0	0
$694$	1.49467e6	3.10331
$695$	−256833.	−0.531717
$696$	806140.i	1.66415i
$697$	7336.98	0.0151026
$698$	445125.i	0.913631i
$699$	− 31783.2i	− 0.0650495i
$700$	0	0
$701$	−161942.	−0.329552	−0.164776	−	0.986331i	$-0.552690\pi$
$701$	−161942.	−0.329552	−0.164776	+	0.986331i	$0.552690\pi$
$702$	1.71603e6	3.48217
$703$	− 542274.i	− 1.09726i
$704$	−151176.	−0.305027
$705$	− 490923.i	− 0.987724i
$706$	− 984240.i	− 1.97466i
$707$	0	0
$708$	1.25589e6	2.50546
$709$	61606.0	0.122555	0.0612774	−	0.998121i	$-0.480483\pi$
$709$	61606.0	0.122555	0.0612774	+	0.998121i	$0.480483\pi$
$710$	− 182941.i	− 0.362906i
$711$	−29580.5	−0.0585149
$712$	− 411134.i	− 0.811005i
$713$	351833.i	0.692081i
$714$	0	0
$715$	307326.	0.601156
$716$	−1.58059e6	−3.08314
$717$	− 278715.i	− 0.542153i
$718$	257020.	0.498560
$719$	− 241921.i	− 0.467968i	−0.972240	−	0.233984i	$-0.924824\pi$
$719$	− 241921.i	− 0.467968i	0.972240	−	0.233984i	$-0.0751763\pi$
$720$	123130.i	0.237519i
$721$	0	0
$722$	−367192.	−0.704400
$723$	−625237.	−1.19610
$724$	1.56349e6i	2.98276i
$725$	121762.	0.231652
$726$	− 697100.i	− 1.32258i
$727$	− 75734.6i	− 0.143293i	−0.997430	−	0.0716466i	$-0.977175\pi$
$727$	− 75734.6i	− 0.143293i	0.997430	−	0.0716466i	$-0.0228254\pi$
$728$	0	0
$729$	−590924.	−1.11193
$730$	−33.0143	−6.19522e−5 0
$731$	63390.8i	0.118629i
$732$	101931.	0.190232
$733$	349506.i	0.650499i	0.945628	+	0.325250i	$0.105448\pi$
$733$	349506.i	0.650499i	−0.945628	+	0.325250i	$0.894552\pi$
$734$	173151.i	0.321390i
$735$	0	0
$736$	103176.	0.190469
$737$	190107.	0.349996
$738$	− 13429.2i	− 0.0246568i
$739$	−869563.	−1.59225	−0.796127	−	0.605130i	$-0.793121\pi$
$739$	−869563.	−1.59225	−0.796127	+	0.605130i	$0.793121\pi$
$740$	1.40662e6i	2.56870i
$741$	686483.i	1.25024i
$742$	0	0
$743$	95108.3	0.172282	0.0861412	−	0.996283i	$-0.472546\pi$
$743$	95108.3	0.172282	0.0861412	+	0.996283i	$0.472546\pi$
$744$	636040.	1.14905
$745$	623038.i	1.12254i
$746$	225054.	0.404398
$747$	− 169662.i	− 0.304048i
$748$	− 105298.i	− 0.188199i
$749$	0	0
$750$	−929516.	−1.65247
$751$	753206.	1.33547	0.667735	−	0.744399i	$-0.267264\pi$
$751$	753206.	1.33547	0.667735	+	0.744399i	$0.267264\pi$
$752$	− 844104.i	− 1.49266i
$753$	−794984.	−1.40207
$754$	1.88861e6i	3.32200i
$755$	487187.i	0.854676i
$756$	0	0
$757$	−293022.	−0.511338	−0.255669	−	0.966764i	$-0.582296\pi$
$757$	−293022.	−0.511338	−0.255669	+	0.966764i	$0.582296\pi$
$758$	−1.31090e6	−2.28156
$759$	181871.i	0.315704i
$760$	−724084.	−1.25361
$761$	− 521576.i	− 0.900634i	−0.892869	−	0.450317i	$-0.851311\pi$
$761$	− 521576.i	− 0.900634i	0.892869	−	0.450317i	$-0.148689\pi$
$762$	1.19774e6i	2.06278i
$763$	0	0
$764$	322990.	0.553354
$765$	29503.7	0.0504143
$766$	179248.i	0.305490i
$767$	1.51017e6	2.56706
$768$	1.05282e6i	1.78497i
$769$	920553.i	1.55667i	0.627850	+	0.778334i	$0.283935\pi$
$769$	920553.i	1.55667i	−0.627850	+	0.778334i	$0.716065\pi$
$770$	0	0
$771$	386822.	0.650732
$772$	−319997.	−0.536922
$773$	456997.i	0.764811i	0.923995	+	0.382406i	$0.124904\pi$
$773$	456997.i	0.764811i	−0.923995	+	0.382406i	$0.875096\pi$
$774$	116027.	0.193676
$775$	− 96069.6i	− 0.159949i
$776$	− 936690.i	− 1.55551i
$777$	0	0
$778$	−506530.	−0.836846
$779$	28599.9	0.0471292
$780$	− 1.78069e6i	− 2.92684i
$781$	53227.1	0.0872632
$782$	− 257536.i	− 0.421137i
$783$	− 681641.i	− 1.11181i
$784$	0	0
$785$	−975278.	−1.58267
$786$	14922.4	0.0241543
$787$	326745.i	0.527546i	0.964585	+	0.263773i	$0.0849669\pi$
$787$	326745.i	0.527546i	−0.964585	+	0.263773i	$0.915033\pi$
$788$	1.90786e6	3.07251
$789$	22654.1i	0.0363910i
$790$	242948.i	0.389277i
$791$	0	0
$792$	−98922.5	−0.157705
$793$	122568.	0.194909
$794$	− 892042.i	− 1.41496i
$795$	−230953.	−0.365417
$796$	− 2.05667e6i	− 3.24593i
$797$	− 580079.i	− 0.913210i	−0.889669	−	0.456605i	$-0.849065\pi$
$797$	− 580079.i	− 0.913210i	0.889669	−	0.456605i	$-0.150935\pi$
$798$	0	0
$799$	−202260.	−0.316823
$800$	−28172.8	−0.0440199
$801$	65300.8i	0.101778i
$802$	967881.	1.50478
$803$	− 9.60560i	0 1.48968e-5i
$804$	− 1.10151e6i	− 1.70402i
$805$	0	0
$806$	1.49010e6	2.29375
$807$	370338.	0.568657
$808$	68050.1i	0.104233i
$809$	−805118.	−1.23016	−0.615081	−	0.788464i	$-0.710877\pi$
$809$	−805118.	−1.23016	−0.615081	+	0.788464i	$0.710877\pi$
$810$	722024.i	1.10048i
$811$	− 633160.i	− 0.962657i	−0.876540	−	0.481328i	$-0.840154\pi$
$811$	− 633160.i	− 0.962657i	0.876540	−	0.481328i	$-0.159846\pi$
$812$	0	0
$813$	−462072.	−0.699083
$814$	−608461.	−0.918299
$815$	− 563922.i	− 0.848992i
$816$	−168607.	−0.253218
$817$	247101.i	0.370194i
$818$	536455.i	0.801728i
$819$	0	0
$820$	−74186.2	−0.110330
$821$	615635.	0.913350	0.456675	−	0.889634i	$-0.349040\pi$
$821$	615635.	0.913350	0.456675	+	0.889634i	$0.349040\pi$
$822$	− 453203.i	− 0.670732i
$823$	128756.	0.190094	0.0950469	−	0.995473i	$-0.469700\pi$
$823$	128756.	0.190094	0.0950469	+	0.995473i	$0.469700\pi$
$824$	− 1.69097e6i	− 2.49048i
$825$	− 49660.7i	− 0.0729634i
$826$	0	0
$827$	1.05631e6	1.54447	0.772235	−	0.635337i	$-0.219139\pi$
$827$	1.05631e6	1.54447	0.772235	+	0.635337i	$0.219139\pi$
$828$	−317056.	−0.462461
$829$	632640.i	0.920551i	0.887776	+	0.460276i	$0.152249\pi$
$829$	632640.i	0.920551i	−0.887776	+	0.460276i	$0.847751\pi$
$830$	−1.39345e6	−2.02272
$831$	− 470454.i	− 0.681263i
$832$	1.05329e6i	1.52160i
$833$	0	0
$834$	−643717.	−0.925471
$835$	128145.	0.183792
$836$	− 410459.i	− 0.587296i
$837$	−537811.	−0.767678
$838$	− 1.25772e6i	− 1.79100i
$839$	− 249268.i	− 0.354114i	−0.984201	−	0.177057i	$-0.943342\pi$
$839$	− 249268.i	− 0.354114i	0.984201	−	0.177057i	$-0.0566577\pi$
$840$	0	0
$841$	42913.2	0.0606735
$842$	42745.3	0.0602926
$843$	373788.i	0.525981i
$844$	876839.	1.23094
$845$	− 1.51261e6i	− 2.11842i
$846$	370205.i	0.517251i
$847$	0	0
$848$	−397105.	−0.552222
$849$	746926.	1.03624
$850$	70321.3i	0.0973306i
$851$	−1.00096e6	−1.38215
$852$	− 308406.i	− 0.424857i
$853$	1.16100e6i	1.59564i	0.602898	+	0.797818i	$0.294012\pi$
$853$	1.16100e6i	1.59564i	−0.602898	+	0.797818i	$0.705988\pi$
$854$	0	0
$855$	115007.	0.157323
$856$	2.50293e6	3.41587
$857$	− 221233.i	− 0.301224i	−0.988593	−	0.150612i	$-0.951876\pi$
$857$	− 221233.i	− 0.301224i	0.988593	−	0.150612i	$-0.0481244\pi$
$858$	770271.	1.04633
$859$	1.14237e6i	1.54818i	0.633077	+	0.774089i	$0.281792\pi$
$859$	1.14237e6i	1.54818i	−0.633077	+	0.774089i	$0.718208\pi$
$860$	− 640962.i	− 0.866633i
$861$	0	0
$862$	−1.57501e6	−2.11967
$863$	1.12087e6	1.50499	0.752494	−	0.658599i	$-0.228851\pi$
$863$	1.12087e6	1.50499	0.752494	+	0.658599i	$0.228851\pi$
$864$	157715.i	0.211274i
$865$	870301.	1.16315
$866$	2.03678e6i	2.71586i
$867$	− 618653.i	− 0.823017i
$868$	0	0
$869$	−70686.2	−0.0936042
$870$	−1.05161e6	−1.38936
$871$	− 1.32453e6i	− 1.74592i
$872$	−950849.	−1.25049
$873$	148775.i	0.195210i
$874$	− 1.00389e6i	− 1.31420i
$875$	0	0
$876$	−55.6562	−7.25279e−5 0
$877$	−734113.	−0.954473	−0.477236	−	0.878775i	$-0.658361\pi$
$877$	−734113.	−0.954473	−0.477236	+	0.878775i	$0.658361\pi$
$878$	1.89345e6i	2.45621i
$879$	580206.	0.750939
$880$	294233.i	0.379950i
$881$	− 567852.i	− 0.731616i	−0.930690	−	0.365808i	$-0.880793\pi$
$881$	− 567852.i	− 0.731616i	0.930690	−	0.365808i	$-0.119207\pi$
$882$	0	0
$883$	40795.8	0.0523232	0.0261616	−	0.999658i	$-0.491672\pi$
$883$	40795.8	0.0523232	0.0261616	+	0.999658i	$0.491672\pi$
$884$	−733642.	−0.938814
$885$	840886.i	1.07362i
$886$	−441712.	−0.562694
$887$	− 139089.i	− 0.176785i	−0.996086	−	0.0883925i	$-0.971827\pi$
$887$	− 139089.i	− 0.176785i	0.996086	−	0.0883925i	$-0.0281730\pi$
$888$	1.80952e6i	2.29476i
$889$	0	0
$890$	536323.	0.677090
$891$	−210075.	−0.264617
$892$	− 699706.i	− 0.879399i
$893$	−788420.	−0.988677
$894$	1.56156e6i	1.95382i
$895$	− 1.05829e6i	− 1.32117i
$896$	0	0
$897$	1.26714e6	1.57485
$898$	−2.29965e6	−2.85173
$899$	− 591900.i	− 0.732367i
$900$	86573.7	0.106881
$901$	95152.2i	0.117211i
$902$	− 32090.7i	− 0.0394426i
$903$	0	0
$904$	538298.	0.658697
$905$	−1.04684e6	−1.27815
$906$	1.22107e6i	1.48759i
$907$	743411.	0.903680	0.451840	−	0.892099i	$-0.350768\pi$
$907$	743411.	0.903680	0.451840	+	0.892099i	$0.350768\pi$
$908$	708983.i	0.859932i
$909$	− 10808.5i	− 0.0130809i
$910$	0	0
$911$	−549043.	−0.661560	−0.330780	−	0.943708i	$-0.607312\pi$
$911$	−549043.	−0.661560	−0.330780	+	0.943708i	$0.607312\pi$
$912$	−657238.	−0.790193
$913$	− 405427.i	− 0.486375i
$914$	218306.	0.261321
$915$	68247.8i	0.0815167i
$916$	654888.i	0.780506i
$917$	0	0
$918$	393669.	0.467138
$919$	−1.64010e6	−1.94195	−0.970976	−	0.239178i	$-0.923122\pi$
$919$	−1.64010e6	−1.94195	−0.970976	+	0.239178i	$0.923122\pi$
$920$	1.33655e6i	1.57910i
$921$	929967.	1.09635
$922$	1.34990e6i	1.58796i
$923$	− 370848.i	− 0.435303i
$924$	0	0
$925$	273316.	0.319434
$926$	1.72441e6	2.01103
$927$	268579.i	0.312545i
$928$	−173577.	−0.201556
$929$	− 1.08792e6i	− 1.26057i	−0.776365	−	0.630283i	$-0.782939\pi$
$929$	− 1.08792e6i	− 1.26057i	0.776365	−	0.630283i	$-0.217061\pi$
$930$	829712.i	0.959315i
$931$	0	0
$932$	132404.	0.152429
$933$	34084.9	0.0391560
$934$	− 2.33555e6i	− 2.67729i
$935$	70502.7	0.0806459
$936$	689220.i	0.786694i
$937$	347157.i	0.395409i	0.980262	+	0.197704i	$0.0633486\pi$
$937$	347157.i	0.395409i	−0.980262	+	0.197704i	$0.936651\pi$
$938$	0	0
$939$	941152.	1.06740
$940$	2.04510e6	2.31451
$941$	167333.i	0.188975i	0.995526	+	0.0944873i	$0.0301212\pi$
$941$	167333.i	0.188975i	−0.995526	+	0.0944873i	$0.969879\pi$
$942$	−2.44440e6	−2.75468
$943$	− 52791.1i	− 0.0593659i
$944$	1.44584e6i	1.62247i
$945$	0	0
$946$	277260.	0.309817
$947$	−527122.	−0.587775	−0.293887	−	0.955840i	$-0.594949\pi$
$947$	−527122.	−0.587775	−0.293887	+	0.955840i	$0.594949\pi$
$948$	409566.i	0.455730i
$949$	−66.9247	−7.43112e−5 0
$950$	274116.i	0.303730i
$951$	110461.i	0.122137i
$952$	0	0
$953$	−1.67904e6	−1.84873	−0.924366	−	0.381506i	$-0.875406\pi$
$953$	−1.67904e6	−1.84873	−0.924366	+	0.381506i	$0.875406\pi$
$954$	174161.	0.191361
$955$	216259.i	0.237119i
$956$	1.16108e6	1.27042
$957$	− 305967.i	− 0.334080i
$958$	− 1.05162e6i	− 1.14585i
$959$	0	0
$960$	−586485.	−0.636377
$961$	456515.	0.494320
$962$	4.23931e6i	4.58084i
$963$	−397544.	−0.428679
$964$	− 2.60463e6i	− 2.80280i
$965$	− 214255.i	− 0.230078i
$966$	0	0
$967$	797832.	0.853215	0.426608	−	0.904437i	$-0.359709\pi$
$967$	797832.	0.853215	0.426608	+	0.904437i	$0.359709\pi$
$968$	1.49052e6	1.59070
$969$	157484.i	0.167722i
$970$	1.22191e6	1.29866
$971$	933679.i	0.990283i	0.868812	+	0.495141i	$0.164884\pi$
$971$	933679.i	0.990283i	−0.868812	+	0.495141i	$0.835116\pi$
$972$	− 878266.i	− 0.929594i
$973$	0	0
$974$	1.95788e6	2.06380
$975$	−345999.	−0.363970
$976$	117347.i	0.123189i
$977$	−1.43977e6	−1.50835	−0.754176	−	0.656672i	$-0.771963\pi$
$977$	−1.43977e6	−1.50835	−0.754176	+	0.656672i	$0.771963\pi$
$978$	− 1.41339e6i	− 1.47770i
$979$	156044.i	0.162811i
$980$	0	0
$981$	151024.	0.156931
$982$	1.59069e6	1.64954
$983$	− 1.49826e6i	− 1.55053i	−0.631639	−	0.775263i	$-0.717618\pi$
$983$	− 1.49826e6i	− 1.55053i	0.631639	−	0.775263i	$-0.282382\pi$
$984$	−95435.3	−0.0985641
$985$	1.27741e6i	1.31661i
$986$	433260.i	0.445651i
$987$	0	0
$988$	−2.85977e6	−2.92966
$989$	456110.	0.466312
$990$	− 129044.i	− 0.131664i
$991$	−989082.	−1.00713	−0.503564	−	0.863958i	$-0.667978\pi$
$991$	−989082.	−1.00713	−0.503564	+	0.863958i	$0.667978\pi$
$992$	136951.i	0.139169i
$993$	− 242668.i	− 0.246101i
$994$	0	0
$995$	1.37705e6	1.39092
$996$	−2.34910e6	−2.36801
$997$	− 1.23700e6i	− 1.24446i	−0.782836	−	0.622228i	$-0.786228\pi$
$997$	− 1.23700e6i	− 1.24446i	0.782836	−	0.622228i	$-0.213772\pi$
$998$	−1.61209e6	−1.61855
$999$	− 1.53006e6i	− 1.53312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.5.b.b.48.1	✓	8
3.2	odd	2		441.5.d.g.244.7		8
4.3	odd	2		784.5.c.g.97.6		8
7.2	even	3		49.5.d.c.31.8		16
7.3	odd	6		49.5.d.c.19.8		16
7.4	even	3		49.5.d.c.19.7		16
7.5	odd	6		49.5.d.c.31.7		16
7.6	odd	2	inner	49.5.b.b.48.2	yes	8
21.20	even	2		441.5.d.g.244.8		8
28.27	even	2		784.5.c.g.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.5.b.b.48.1	✓	8	1.1	even	1	trivial
49.5.b.b.48.2	yes	8	7.6	odd	2	inner
49.5.d.c.19.7		16	7.4	even	3
49.5.d.c.19.8		16	7.3	odd	6
49.5.d.c.31.7		16	7.5	odd	6
49.5.d.c.31.8		16	7.2	even	3
441.5.d.g.244.7		8	3.2	odd	2
441.5.d.g.244.8		8	21.20	even	2
784.5.c.g.97.3		8	28.27	even	2
784.5.c.g.97.6		8	4.3	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	49.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.99086 q^{2} -7.89087i q^{3} +32.8721 q^{4} +22.0095i q^{5} +55.1639i q^{6} -117.950 q^{8} +18.7341 q^{9} +O(q^{10})\)	\(q-6.99086 q^{2} -7.89087i q^{3} +32.8721 q^{4} +22.0095i q^{5} +55.1639i q^{6} -117.950 q^{8} +18.7341 q^{9} -153.865i q^{10} +44.7675 q^{11} -259.389i q^{12} -311.907i q^{13} +173.674 q^{15} +298.619 q^{16} -71.5536i q^{17} -130.968 q^{18} -278.920i q^{19} +723.499i q^{20} -312.963 q^{22} -514.843 q^{23} +930.729i q^{24} +140.580 q^{25} +2180.50i q^{26} -786.989i q^{27} +866.138 q^{29} -1214.13 q^{30} -683.378i q^{31} -200.403 q^{32} -353.255i q^{33} +500.221i q^{34} +615.830 q^{36} +1944.19 q^{37} +1949.89i q^{38} -2461.22 q^{39} -2596.03i q^{40} +102.538i q^{41} -885.919 q^{43} +1471.60 q^{44} +412.330i q^{45} +3599.20 q^{46} -2826.69i q^{47} -2356.37i q^{48} -982.778 q^{50} -564.621 q^{51} -10253.0i q^{52} -1329.80 q^{53} +5501.73i q^{54} +985.312i q^{55} -2200.92 q^{57} -6055.04 q^{58} +4841.74i q^{59} +5709.04 q^{60} +392.964i q^{61} +4777.40i q^{62} -3376.92 q^{64} +6864.93 q^{65} +2469.55i q^{66} +4246.54 q^{67} -2352.12i q^{68} +4062.56i q^{69} +1188.97 q^{71} -2209.69 q^{72} -0.214566i q^{73} -13591.6 q^{74} -1109.30i q^{75} -9168.67i q^{76} +17206.0 q^{78} -1578.96 q^{79} +6572.47i q^{80} -4692.57 q^{81} -716.829i q^{82} -9056.29i q^{83} +1574.86 q^{85} +6193.33 q^{86} -6834.58i q^{87} -5280.33 q^{88} +3485.66i q^{89} -2882.54i q^{90} -16924.0 q^{92} -5392.45 q^{93} +19761.0i q^{94} +6138.90 q^{95} +1581.36i q^{96} +7941.40i q^{97} +838.681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} + 52 q^{4} - 372 q^{8} - 352 q^{9}+O(q^{10}) \) 8 * q - 12 * q^2 + 52 * q^4 - 372 * q^8 - 352 * q^9	\( 8 q - 12 q^{2} + 52 q^{4} - 372 q^{8} - 352 q^{9} + 120 q^{11} - 632 q^{15} - 300 q^{16} + 340 q^{18} + 1952 q^{22} + 1752 q^{23} - 2192 q^{25} + 1248 q^{29} + 456 q^{30} + 3156 q^{32} + 4940 q^{36} + 2368 q^{37} - 7672 q^{39} - 8552 q^{43} + 264 q^{44} + 7208 q^{46} - 5556 q^{50} - 11976 q^{51} + 5496 q^{53} - 9200 q^{57} - 17496 q^{58} + 2856 q^{60} + 3980 q^{64} + 30240 q^{65} - 7440 q^{67} + 9984 q^{71} - 1508 q^{72} - 1080 q^{74} + 22456 q^{78} - 14096 q^{79} + 3432 q^{81} + 11912 q^{85} + 44496 q^{86} - 44464 q^{88} - 32232 q^{92} + 9584 q^{93} + 22488 q^{95} + 30144 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 + 52 * q^4 - 372 * q^8 - 352 * q^9 + 120 * q^11 - 632 * q^15 - 300 * q^16 + 340 * q^18 + 1952 * q^22 + 1752 * q^23 - 2192 * q^25 + 1248 * q^29 + 456 * q^30 + 3156 * q^32 + 4940 * q^36 + 2368 * q^37 - 7672 * q^39 - 8552 * q^43 + 264 * q^44 + 7208 * q^46 - 5556 * q^50 - 11976 * q^51 + 5496 * q^53 - 9200 * q^57 - 17496 * q^58 + 2856 * q^60 + 3980 * q^64 + 30240 * q^65 - 7440 * q^67 + 9984 * q^71 - 1508 * q^72 - 1080 * q^74 + 22456 * q^78 - 14096 * q^79 + 3432 * q^81 + 11912 * q^85 + 44496 * q^86 - 44464 * q^88 - 32232 * q^92 + 9584 * q^93 + 22488 * q^95 + 30144 * q^99

Introduction

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Database

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