LMFDB - Embedded newform 25.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,6,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

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:	yes
Analytic conductor:	$4.00959549532$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{241}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 60 $ x^2 - x - 60
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.26209$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.2621 q^{2} -5.52417 q^{3} +73.3104 q^{4} -56.6896 q^{6} +68.9517 q^{7} +423.931 q^{8} -212.483 q^{9} +O(q^{10})$	\(q+10.2621 q^{2} -5.52417 q^{3} +73.3104 q^{4} -56.6896 q^{6} +68.9517 q^{7} +423.931 q^{8} -212.483 q^{9} -486.104 q^{11} -404.980 q^{12} -428.387 q^{13} +707.588 q^{14} +2004.49 q^{16} +1800.64 q^{17} -2180.52 q^{18} -1046.65 q^{19} -380.901 q^{21} -4988.45 q^{22} +686.855 q^{23} -2341.87 q^{24} -4396.14 q^{26} +2516.17 q^{27} +5054.88 q^{28} -1339.03 q^{29} +7990.30 q^{31} +7004.41 q^{32} +2685.33 q^{33} +18478.4 q^{34} -15577.3 q^{36} -1970.64 q^{37} -10740.9 q^{38} +2366.48 q^{39} +10772.2 q^{41} -3908.84 q^{42} +15017.7 q^{43} -35636.5 q^{44} +7048.57 q^{46} +895.337 q^{47} -11073.1 q^{48} -12052.7 q^{49} -9947.07 q^{51} -31405.2 q^{52} -19327.1 q^{53} +25821.2 q^{54} +29230.8 q^{56} +5781.90 q^{57} -13741.3 q^{58} +21193.7 q^{59} -27722.2 q^{61} +81997.1 q^{62} -14651.1 q^{63} +7736.31 q^{64} +27557.0 q^{66} -7719.33 q^{67} +132006. q^{68} -3794.31 q^{69} -51410.1 q^{71} -90078.4 q^{72} -43776.4 q^{73} -20222.9 q^{74} -76730.7 q^{76} -33517.7 q^{77} +24285.1 q^{78} -6225.68 q^{79} +37733.7 q^{81} +110545. q^{82} +52949.9 q^{83} -27924.0 q^{84} +154113. q^{86} +7397.05 q^{87} -206075. q^{88} +44631.2 q^{89} -29538.0 q^{91} +50353.6 q^{92} -44139.8 q^{93} +9188.03 q^{94} -38693.6 q^{96} -148018. q^{97} -123686. q^{98} +103289. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} + 20 q^{3} + 69 q^{4} - 191 q^{6} + 200 q^{7} + 615 q^{8} + 196 q^{9}+O(q^{10}) $ 2 * q + 5 * q^2 + 20 * q^3 + 69 * q^4 - 191 * q^6 + 200 * q^7 + 615 * q^8 + 196 * q^9	\( 2 q + 5 q^{2} + 20 q^{3} + 69 q^{4} - 191 q^{6} + 200 q^{7} + 615 q^{8} + 196 q^{9} - 196 q^{11} - 515 q^{12} - 360 q^{13} + 18 q^{14} + 1137 q^{16} + 1490 q^{17} - 4330 q^{18} - 3180 q^{19} + 2964 q^{21} - 6515 q^{22} + 1560 q^{23} + 2535 q^{24} - 4756 q^{26} + 6740 q^{27} + 4490 q^{28} - 3920 q^{29} - 1096 q^{31} + 5455 q^{32} + 10090 q^{33} + 20113 q^{34} - 17338 q^{36} + 2020 q^{37} + 485 q^{38} + 4112 q^{39} + 27754 q^{41} - 21510 q^{42} - 3000 q^{43} - 36887 q^{44} + 2454 q^{46} + 25760 q^{47} - 33215 q^{48} - 11686 q^{49} - 17876 q^{51} - 31700 q^{52} - 26980 q^{53} + 3595 q^{54} + 54270 q^{56} - 48670 q^{57} - 160 q^{58} + 11960 q^{59} - 24396 q^{61} + 129810 q^{62} + 38880 q^{63} + 43649 q^{64} - 11407 q^{66} - 40060 q^{67} + 133345 q^{68} + 18492 q^{69} - 87296 q^{71} - 12030 q^{72} - 70290 q^{73} - 41222 q^{74} - 67535 q^{76} + 4500 q^{77} + 15100 q^{78} + 65480 q^{79} + 46282 q^{81} + 21185 q^{82} + 92580 q^{83} - 42342 q^{84} + 248924 q^{86} - 58480 q^{87} - 150645 q^{88} - 72810 q^{89} - 20576 q^{91} + 46590 q^{92} - 276060 q^{93} - 121652 q^{94} - 78241 q^{96} - 126140 q^{97} - 125615 q^{98} + 221792 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 20 * q^3 + 69 * q^4 - 191 * q^6 + 200 * q^7 + 615 * q^8 + 196 * q^9 - 196 * q^11 - 515 * q^12 - 360 * q^13 + 18 * q^14 + 1137 * q^16 + 1490 * q^17 - 4330 * q^18 - 3180 * q^19 + 2964 * q^21 - 6515 * q^22 + 1560 * q^23 + 2535 * q^24 - 4756 * q^26 + 6740 * q^27 + 4490 * q^28 - 3920 * q^29 - 1096 * q^31 + 5455 * q^32 + 10090 * q^33 + 20113 * q^34 - 17338 * q^36 + 2020 * q^37 + 485 * q^38 + 4112 * q^39 + 27754 * q^41 - 21510 * q^42 - 3000 * q^43 - 36887 * q^44 + 2454 * q^46 + 25760 * q^47 - 33215 * q^48 - 11686 * q^49 - 17876 * q^51 - 31700 * q^52 - 26980 * q^53 + 3595 * q^54 + 54270 * q^56 - 48670 * q^57 - 160 * q^58 + 11960 * q^59 - 24396 * q^61 + 129810 * q^62 + 38880 * q^63 + 43649 * q^64 - 11407 * q^66 - 40060 * q^67 + 133345 * q^68 + 18492 * q^69 - 87296 * q^71 - 12030 * q^72 - 70290 * q^73 - 41222 * q^74 - 67535 * q^76 + 4500 * q^77 + 15100 * q^78 + 65480 * q^79 + 46282 * q^81 + 21185 * q^82 + 92580 * q^83 - 42342 * q^84 + 248924 * q^86 - 58480 * q^87 - 150645 * q^88 - 72810 * q^89 - 20576 * q^91 + 46590 * q^92 - 276060 * q^93 - 121652 * q^94 - 78241 * q^96 - 126140 * q^97 - 125615 * q^98 + 221792 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	10.2621	1.81410	0.907049	−	0.421025i	$-0.138330\pi$
$2$	10.2621	1.81410	0.907049	+	0.421025i	$0.138330\pi$
$3$	−5.52417	−0.354376	−0.177188	−	0.984177i	$-0.556700\pi$
$3$	−5.52417	−0.354376	−0.177188	+	0.984177i	$0.556700\pi$
$4$	73.3104	2.29095
$5$	0	0
$5$	0	0
$6$	−56.6896	−0.642873
$7$	68.9517	0.531863	0.265931	−	0.963992i	$-0.414321\pi$
$7$	68.9517	0.531863	0.265931	+	0.963992i	$0.414321\pi$
$8$	423.931	2.34191
$9$	−212.483	−0.874418
$10$	0	0
$11$	−486.104	−1.21129	−0.605645	−	0.795735i	$-0.707085\pi$
$11$	−486.104	−1.21129	−0.605645	+	0.795735i	$0.707085\pi$
$12$	−404.980	−0.811858
$13$	−428.387	−0.703036	−0.351518	−	0.936181i	$-0.614334\pi$
$13$	−428.387	−0.703036	−0.351518	+	0.936181i	$0.614334\pi$
$14$	707.588	0.964851
$15$	0	0
$16$	2004.49	1.95751
$17$	1800.64	1.51114	0.755571	−	0.655066i	$-0.227359\pi$
$17$	1800.64	1.51114	0.755571	+	0.655066i	$0.227359\pi$
$18$	−2180.52	−1.58628
$19$	−1046.65	−0.665149	−0.332575	−	0.943077i	$-0.607917\pi$
$19$	−1046.65	−0.665149	−0.332575	+	0.943077i	$0.607917\pi$
$20$	0	0
$21$	−380.901	−0.188479
$22$	−4988.45	−2.19740
$23$	686.855	0.270736	0.135368	−	0.990795i	$-0.456778\pi$
$23$	686.855	0.270736	0.135368	+	0.990795i	$0.456778\pi$
$24$	−2341.87	−0.829917
$25$	0	0
$26$	−4396.14	−1.27538
$27$	2516.17	0.664249
$28$	5054.88	1.21847
$29$	−1339.03	−0.295663	−0.147831	−	0.989013i	$-0.547229\pi$
$29$	−1339.03	−0.295663	−0.147831	+	0.989013i	$0.547229\pi$
$30$	0	0
$31$	7990.30	1.49334	0.746670	−	0.665195i	$-0.231651\pi$
$31$	7990.30	1.49334	0.746670	+	0.665195i	$0.231651\pi$
$32$	7004.41	1.20920
$33$	2685.33	0.429252
$34$	18478.4	2.74136
$35$	0	0
$36$	−15577.3	−2.00325
$37$	−1970.64	−0.236648	−0.118324	−	0.992975i	$-0.537752\pi$
$37$	−1970.64	−0.236648	−0.118324	+	0.992975i	$0.537752\pi$
$38$	−10740.9	−1.20665
$39$	2366.48	0.249139
$40$	0	0
$41$	10772.2	1.00079	0.500395	−	0.865797i	$-0.333188\pi$
$41$	10772.2	1.00079	0.500395	+	0.865797i	$0.333188\pi$
$42$	−3908.84	−0.341920
$43$	15017.7	1.23861	0.619303	−	0.785152i	$-0.287415\pi$
$43$	15017.7	1.23861	0.619303	+	0.785152i	$0.287415\pi$
$44$	−35636.5	−2.77500
$45$	0	0
$46$	7048.57	0.491141
$47$	895.337	0.0591210	0.0295605	−	0.999563i	$-0.490589\pi$
$47$	895.337	0.0591210	0.0295605	+	0.999563i	$0.490589\pi$
$48$	−11073.1	−0.693693
$49$	−12052.7	−0.717122
$50$	0	0
$51$	−9947.07	−0.535513
$52$	−31405.2	−1.61062
$53$	−19327.1	−0.945098	−0.472549	−	0.881304i	$-0.656666\pi$
$53$	−19327.1	−0.945098	−0.472549	+	0.881304i	$0.656666\pi$
$54$	25821.2	1.20501
$55$	0	0
$56$	29230.8	1.24558
$57$	5781.90	0.235713
$58$	−13741.3	−0.536361
$59$	21193.7	0.792641	0.396321	−	0.918112i	$-0.370287\pi$
$59$	21193.7	0.792641	0.396321	+	0.918112i	$0.370287\pi$
$60$	0	0
$61$	−27722.2	−0.953900	−0.476950	−	0.878931i	$-0.658258\pi$
$61$	−27722.2	−0.953900	−0.476950	+	0.878931i	$0.658258\pi$
$62$	81997.1	2.70906
$63$	−14651.1	−0.465070
$64$	7736.31	0.236093
$65$	0	0
$66$	27557.0	0.778705
$67$	−7719.33	−0.210084	−0.105042	−	0.994468i	$-0.533498\pi$
$67$	−7719.33	−0.210084	−0.105042	+	0.994468i	$0.533498\pi$
$68$	132006.	3.46195
$69$	−3794.31	−0.0959422
$70$	0	0
$71$	−51410.1	−1.21033	−0.605163	−	0.796101i	$-0.706892\pi$
$71$	−51410.1	−1.21033	−0.605163	+	0.796101i	$0.706892\pi$
$72$	−90078.4	−2.04781
$73$	−43776.4	−0.961465	−0.480732	−	0.876867i	$-0.659629\pi$
$73$	−43776.4	−0.961465	−0.480732	+	0.876867i	$0.659629\pi$
$74$	−20222.9	−0.429303
$75$	0	0
$76$	−76730.7	−1.52382
$77$	−33517.7	−0.644240
$78$	24285.1	0.451963
$79$	−6225.68	−0.112233	−0.0561163	−	0.998424i	$-0.517872\pi$
$79$	−6225.68	−0.112233	−0.0561163	+	0.998424i	$0.517872\pi$
$80$	0	0
$81$	37733.7	0.639024
$82$	110545.	1.81553
$83$	52949.9	0.843664	0.421832	−	0.906674i	$-0.361387\pi$
$83$	52949.9	0.843664	0.421832	+	0.906674i	$0.361387\pi$
$84$	−27924.0	−0.431797
$85$	0	0
$86$	154113.	2.24695
$87$	7397.05	0.104776
$88$	−206075.	−2.83673
$89$	44631.2	0.597260	0.298630	−	0.954369i	$-0.403470\pi$
$89$	44631.2	0.597260	0.298630	+	0.954369i	$0.403470\pi$
$90$	0	0
$91$	−29538.0	−0.373919
$92$	50353.6	0.620242
$93$	−44139.8	−0.529204
$94$	9188.03	0.107251
$95$	0	0
$96$	−38693.6	−0.428510
$97$	−148018.	−1.59730	−0.798649	−	0.601797i	$-0.794452\pi$
$97$	−148018.	−1.59730	−0.798649	+	0.601797i	$0.794452\pi$
$98$	−123686.	−1.30093
$99$	103289.	1.05917
$100$	0	0
$101$	148476.	1.44828	0.724141	−	0.689652i	$-0.242237\pi$
$101$	148476.	1.44828	0.724141	+	0.689652i	$0.242237\pi$
$102$	−102078.	−0.971472
$103$	188391.	1.74972	0.874859	−	0.484378i	$-0.160954\pi$
$103$	188391.	1.74972	0.874859	+	0.484378i	$0.160954\pi$
$104$	−181607.	−1.64645
$105$	0	0
$106$	−198336.	−1.71450
$107$	67887.7	0.573234	0.286617	−	0.958045i	$-0.407469\pi$
$107$	67887.7	0.573234	0.286617	+	0.958045i	$0.407469\pi$
$108$	184462.	1.52176
$109$	−219292.	−1.76790	−0.883949	−	0.467582i	$-0.845125\pi$
$109$	−219292.	−1.76790	−0.883949	+	0.467582i	$0.845125\pi$
$110$	0	0
$111$	10886.2	0.0838625
$112$	138213.	1.04112
$113$	−80783.9	−0.595153	−0.297577	−	0.954698i	$-0.596178\pi$
$113$	−80783.9	−0.595153	−0.297577	+	0.954698i	$0.596178\pi$
$114$	59334.4	0.427606
$115$	0	0
$116$	−98165.1	−0.677348
$117$	91025.1	0.614747
$118$	217492.	1.43793
$119$	124157.	0.803721
$120$	0	0
$121$	75246.5	0.467221
$122$	−284487.	−1.73047
$123$	−59507.3	−0.354656
$124$	585772.	3.42117
$125$	0	0
$126$	−150351.	−0.843683
$127$	161301.	0.887417	0.443708	−	0.896171i	$-0.353663\pi$
$127$	161301.	0.887417	0.443708	+	0.896171i	$0.353663\pi$
$128$	−144750.	−0.780899
$129$	−82960.5	−0.438932
$130$	0	0
$131$	−193006.	−0.982636	−0.491318	−	0.870980i	$-0.663485\pi$
$131$	−193006.	−0.982636	−0.491318	+	0.870980i	$0.663485\pi$
$132$	196862.	0.983395
$133$	−72168.5	−0.353768
$134$	−79216.4	−0.381113
$135$	0	0
$136$	763349.	3.53896
$137$	250340.	1.13954	0.569768	−	0.821806i	$-0.307033\pi$
$137$	250340.	1.13954	0.569768	+	0.821806i	$0.307033\pi$
$138$	−38937.5	−0.174049
$139$	−218650.	−0.959871	−0.479935	−	0.877304i	$-0.659340\pi$
$139$	−218650.	−0.959871	−0.479935	+	0.877304i	$0.659340\pi$
$140$	0	0
$141$	−4946.00	−0.0209511
$142$	−527575.	−2.19565
$143$	208241.	0.851580
$144$	−425920.	−1.71168
$145$	0	0
$146$	−449238.	−1.74419
$147$	66581.1	0.254131
$148$	−144469.	−0.542150
$149$	−38740.0	−0.142953	−0.0714766	−	0.997442i	$-0.522771\pi$
$149$	−38740.0	−0.142953	−0.0714766	+	0.997442i	$0.522771\pi$
$150$	0	0
$151$	−154945.	−0.553013	−0.276507	−	0.961012i	$-0.589177\pi$
$151$	−154945.	−0.553013	−0.276507	+	0.961012i	$0.589177\pi$
$152$	−443709.	−1.55772
$153$	−382607.	−1.32137
$154$	−343962.	−1.16871
$155$	0	0
$156$	173488.	0.570766
$157$	−344442.	−1.11523	−0.557617	−	0.830098i	$-0.688284\pi$
$157$	−344442.	−1.11523	−0.557617	+	0.830098i	$0.688284\pi$
$158$	−63888.5	−0.203601
$159$	106766.	0.334920
$160$	0	0
$161$	47359.8	0.143994
$162$	387227.	1.15925
$163$	366203.	1.07957	0.539787	−	0.841801i	$-0.318505\pi$
$163$	366203.	1.07957	0.539787	+	0.841801i	$0.318505\pi$
$164$	789712.	2.29276
$165$	0	0
$166$	543376.	1.53049
$167$	249272.	0.691644	0.345822	−	0.938300i	$-0.387600\pi$
$167$	249272.	0.691644	0.345822	+	0.938300i	$0.387600\pi$
$168$	−161476.	−0.441402
$169$	−187778.	−0.505740
$170$	0	0
$171$	222397.	0.581618
$172$	1.10096e6	2.83758
$173$	−61460.1	−0.156127	−0.0780635	−	0.996948i	$-0.524874\pi$
$173$	−61460.1	−0.156127	−0.0780635	+	0.996948i	$0.524874\pi$
$174$	75909.2	0.190073
$175$	0	0
$176$	−974389.	−2.37111
$177$	−117078.	−0.280893
$178$	458009.	1.08349
$179$	606803.	1.41552	0.707759	−	0.706454i	$-0.249706\pi$
$179$	606803.	1.41552	0.707759	+	0.706454i	$0.249706\pi$
$180$	0	0
$181$	153684.	0.348685	0.174343	−	0.984685i	$-0.444220\pi$
$181$	153684.	0.348685	0.174343	+	0.984685i	$0.444220\pi$
$182$	−303121.	−0.678325
$183$	153142.	0.338039
$184$	291179.	0.634039
$185$	0	0
$186$	−452966.	−0.960027
$187$	−875301.	−1.83043
$188$	65637.6	0.135443
$189$	173494.	0.353289
$190$	0	0
$191$	182315.	0.361608	0.180804	−	0.983519i	$-0.442130\pi$
$191$	182315.	0.361608	0.180804	+	0.983519i	$0.442130\pi$
$192$	−42736.7	−0.0836659
$193$	−102080.	−0.197265	−0.0986323	−	0.995124i	$-0.531447\pi$
$193$	−102080.	−0.197265	−0.0986323	+	0.995124i	$0.531447\pi$
$194$	−1.51898e6	−2.89766
$195$	0	0
$196$	−883586.	−1.64289
$197$	−404656.	−0.742882	−0.371441	−	0.928456i	$-0.621136\pi$
$197$	−404656.	−0.742882	−0.371441	+	0.928456i	$0.621136\pi$
$198$	1.05996e6	1.92144
$199$	−167297.	−0.299472	−0.149736	−	0.988726i	$-0.547842\pi$
$199$	−167297.	−0.299472	−0.149736	+	0.988726i	$0.547842\pi$
$200$	0	0
$201$	42642.9	0.0744487
$202$	1.52367e6	2.62732
$203$	−92328.5	−0.157252
$204$	−729224.	−1.22683
$205$	0	0
$206$	1.93329e6	3.17416
$207$	−145945.	−0.236736
$208$	−858695.	−1.37620
$209$	508783.	0.805688
$210$	0	0
$211$	−460778.	−0.712502	−0.356251	−	0.934390i	$-0.615945\pi$
$211$	−460778.	−0.712502	−0.356251	+	0.934390i	$0.615945\pi$
$212$	−1.41688e6	−2.16517
$213$	283998.	0.428911
$214$	696670.	1.03990
$215$	0	0
$216$	1.06668e6	1.55561
$217$	550944.	0.794252
$218$	−2.25040e6	−3.20714
$219$	241829.	0.340720
$220$	0	0
$221$	−771372.	−1.06239
$222$	111715.	0.152135
$223$	−1.08298e6	−1.45834	−0.729172	−	0.684330i	$-0.760095\pi$
$223$	−1.08298e6	−1.45834	−0.729172	+	0.684330i	$0.760095\pi$
$224$	482966.	0.643126
$225$	0	0
$226$	−829012.	−1.07967
$227$	412201.	0.530938	0.265469	−	0.964119i	$-0.414473\pi$
$227$	412201.	0.530938	0.265469	+	0.964119i	$0.414473\pi$
$228$	423874.	0.540007
$229$	−433163.	−0.545836	−0.272918	−	0.962037i	$-0.587989\pi$
$229$	−433163.	−0.545836	−0.272918	+	0.962037i	$0.587989\pi$
$230$	0	0
$231$	185158.	0.228303
$232$	−567658.	−0.692416
$233$	760097.	0.917232	0.458616	−	0.888635i	$-0.348345\pi$
$233$	760097.	0.917232	0.458616	+	0.888635i	$0.348345\pi$
$234$	934108.	1.11521
$235$	0	0
$236$	1.55372e6	1.81590
$237$	34391.7	0.0397725
$238$	1.27411e6	1.45803
$239$	−988624.	−1.11953	−0.559766	−	0.828651i	$-0.689109\pi$
$239$	−988624.	−1.11953	−0.559766	+	0.828651i	$0.689109\pi$
$240$	0	0
$241$	−358878.	−0.398020	−0.199010	−	0.979997i	$-0.563773\pi$
$241$	−358878.	−0.398020	−0.199010	+	0.979997i	$0.563773\pi$
$242$	772186.	0.847585
$243$	−819877.	−0.890703
$244$	−2.03232e6	−2.18534
$245$	0	0
$246$	−610669.	−0.643381
$247$	448373.	0.467624
$248$	3.38734e6	3.49727
$249$	−292504.	−0.298974
$250$	0	0
$251$	−851049.	−0.852649	−0.426324	−	0.904570i	$-0.640192\pi$
$251$	−851049.	−0.852649	−0.426324	+	0.904570i	$0.640192\pi$
$252$	−1.07408e6	−1.06545
$253$	−333883.	−0.327939
$254$	1.65528e6	1.60986
$255$	0	0
$256$	−1.73300e6	−1.65272
$257$	−76358.4	−0.0721147	−0.0360574	−	0.999350i	$-0.511480\pi$
$257$	−76358.4	−0.0721147	−0.0360574	+	0.999350i	$0.511480\pi$
$258$	−851348.	−0.796266
$259$	−135879.	−0.125864
$260$	0	0
$261$	284522.	0.258533
$262$	−1.98064e6	−1.78260
$263$	1.19420e6	1.06460	0.532301	−	0.846555i	$-0.321327\pi$
$263$	1.19420e6	1.06460	0.532301	+	0.846555i	$0.321327\pi$
$264$	1.13839e6	1.00527
$265$	0	0
$266$	−740600.	−0.641770
$267$	−246551.	−0.211655
$268$	−565907.	−0.481292
$269$	1.02930e6	0.867286	0.433643	−	0.901085i	$-0.357228\pi$
$269$	1.02930e6	0.867286	0.433643	+	0.901085i	$0.357228\pi$
$270$	0	0
$271$	2.12144e6	1.75472	0.877359	−	0.479834i	$-0.159303\pi$
$271$	2.12144e6	1.75472	0.877359	+	0.479834i	$0.159303\pi$
$272$	3.60937e6	2.95807
$273$	163173.	0.132508
$274$	2.56901e6	2.06723
$275$	0	0
$276$	−278162.	−0.219799
$277$	1.85145e6	1.44982	0.724908	−	0.688845i	$-0.241882\pi$
$277$	1.85145e6	1.44982	0.724908	+	0.688845i	$0.241882\pi$
$278$	−2.24381e6	−1.74130
$279$	−1.69781e6	−1.30580
$280$	0	0
$281$	90653.2	0.0684884	0.0342442	−	0.999413i	$-0.489098\pi$
$281$	90653.2	0.0684884	0.0342442	+	0.999413i	$0.489098\pi$
$282$	−50756.3	−0.0380073
$283$	−929308.	−0.689753	−0.344877	−	0.938648i	$-0.612079\pi$
$283$	−929308.	−0.689753	−0.344877	+	0.938648i	$0.612079\pi$
$284$	−3.76890e6	−2.77280
$285$	0	0
$286$	2.13698e6	1.54485
$287$	742759.	0.532283
$288$	−1.48832e6	−1.05734
$289$	1.82246e6	1.28355
$290$	0	0
$291$	817679.	0.566044
$292$	−3.20927e6	−2.20267
$293$	2.72733e6	1.85596	0.927979	−	0.372632i	$-0.121545\pi$
$293$	2.72733e6	1.85596	0.927979	+	0.372632i	$0.121545\pi$
$294$	683261.	0.461018
$295$	0	0
$296$	−835417.	−0.554209
$297$	−1.22312e6	−0.804597
$298$	−397553.	−0.259331
$299$	−294240.	−0.190337
$300$	0	0
$301$	1.03550e6	0.658768
$302$	−1.59006e6	−1.00322
$303$	−820208.	−0.513236
$304$	−2.09800e6	−1.30203
$305$	0	0
$306$	−3.92635e6	−2.39709
$307$	−2.29648e6	−1.39064	−0.695322	−	0.718698i	$-0.744738\pi$
$307$	−2.29648e6	−1.39064	−0.695322	+	0.718698i	$0.744738\pi$
$308$	−2.45720e6	−1.47592
$309$	−1.04071e6	−0.620058
$310$	0	0
$311$	984847.	0.577388	0.288694	−	0.957421i	$-0.406779\pi$
$311$	984847.	0.577388	0.288694	+	0.957421i	$0.406779\pi$
$312$	1.00323e6	0.583462
$313$	2.06650e6	1.19227	0.596135	−	0.802884i	$-0.296702\pi$
$313$	2.06650e6	1.19227	0.596135	+	0.802884i	$0.296702\pi$
$314$	−3.53469e6	−2.02315
$315$	0	0
$316$	−456407.	−0.257119
$317$	1.14349e6	0.639125	0.319563	−	0.947565i	$-0.396464\pi$
$317$	1.14349e6	0.639125	0.319563	+	0.947565i	$0.396464\pi$
$318$	1.09564e6	0.607578
$319$	650910.	0.358133
$320$	0	0
$321$	−375024.	−0.203140
$322$	486010.	0.261220
$323$	−1.88465e6	−1.00514
$324$	2.76628e6	1.46397
$325$	0	0
$326$	3.75801e6	1.95845
$327$	1.21141e6	0.626501
$328$	4.56666e6	2.34376
$329$	61735.0	0.0314443
$330$	0	0
$331$	205230.	0.102961	0.0514804	−	0.998674i	$-0.483606\pi$
$331$	205230.	0.102961	0.0514804	+	0.998674i	$0.483606\pi$
$332$	3.88178e6	1.93279
$333$	418729.	0.206929
$334$	2.55805e6	1.25471
$335$	0	0
$336$	−763511.	−0.368950
$337$	488213.	0.234172	0.117086	−	0.993122i	$-0.462645\pi$
$337$	488213.	0.234172	0.117086	+	0.993122i	$0.462645\pi$
$338$	−1.92699e6	−0.917462
$339$	446265.	0.210908
$340$	0	0
$341$	−3.88412e6	−1.80887
$342$	2.28225e6	1.05511
$343$	−1.98992e6	−0.913273
$344$	6.36648e6	2.90070
$345$	0	0
$346$	−630709.	−0.283230
$347$	−3.82809e6	−1.70670	−0.853351	−	0.521336i	$-0.825434\pi$
$347$	−3.82809e6	−1.70670	−0.853351	+	0.521336i	$0.825434\pi$
$348$	542281.	0.240036
$349$	1.45476e6	0.639333	0.319667	−	0.947530i	$-0.396429\pi$
$349$	1.45476e6	0.639333	0.319667	+	0.947530i	$0.396429\pi$
$350$	0	0
$351$	−1.07789e6	−0.466991
$352$	−3.40487e6	−1.46469
$353$	−778492.	−0.332520	−0.166260	−	0.986082i	$-0.553169\pi$
$353$	−778492.	−0.332520	−0.166260	+	0.986082i	$0.553169\pi$
$354$	−1.20146e6	−0.509567
$355$	0	0
$356$	3.27193e6	1.36829
$357$	−685867.	−0.284819
$358$	6.22707e6	2.56789
$359$	−2.12510e6	−0.870247	−0.435124	−	0.900371i	$-0.643295\pi$
$359$	−2.12510e6	−0.870247	−0.435124	+	0.900371i	$0.643295\pi$
$360$	0	0
$361$	−1.38061e6	−0.557577
$362$	1.57712e6	0.632549
$363$	−415675.	−0.165572
$364$	−2.16544e6	−0.856630
$365$	0	0
$366$	1.57156e6	0.613236
$367$	4.10801e6	1.59208	0.796042	−	0.605242i	$-0.206923\pi$
$367$	4.10801e6	1.59208	0.796042	+	0.605242i	$0.206923\pi$
$368$	1.37679e6	0.529967
$369$	−2.28891e6	−0.875109
$370$	0	0
$371$	−1.33263e6	−0.502662
$372$	−3.23591e6	−1.21238
$373$	−4.54570e6	−1.69172	−0.845860	−	0.533405i	$-0.820912\pi$
$373$	−4.54570e6	−1.69172	−0.845860	+	0.533405i	$0.820912\pi$
$374$	−8.98241e6	−3.32058
$375$	0	0
$376$	379561.	0.138456
$377$	573624.	0.207861
$378$	1.78041e6	0.640901
$379$	1.40554e6	0.502626	0.251313	−	0.967906i	$-0.419138\pi$
$379$	1.40554e6	0.502626	0.251313	+	0.967906i	$0.419138\pi$
$380$	0	0
$381$	−891054.	−0.314479
$382$	1.87093e6	0.655993
$383$	4.64417e6	1.61775	0.808874	−	0.587982i	$-0.200078\pi$
$383$	4.64417e6	1.61775	0.808874	+	0.587982i	$0.200078\pi$
$384$	799627.	0.276732
$385$	0	0
$386$	−1.04756e6	−0.357857
$387$	−3.19102e6	−1.08306
$388$	−1.08513e7	−3.65933
$389$	3.53606e6	1.18480	0.592400	−	0.805644i	$-0.298181\pi$
$389$	3.53606e6	1.18480	0.592400	+	0.805644i	$0.298181\pi$
$390$	0	0
$391$	1.23678e6	0.409120
$392$	−5.10950e6	−1.67944
$393$	1.06620e6	0.348223
$394$	−4.15261e6	−1.34766
$395$	0	0
$396$	7.57217e6	2.42651
$397$	−2.95611e6	−0.941336	−0.470668	−	0.882310i	$-0.655987\pi$
$397$	−2.95611e6	−0.941336	−0.470668	+	0.882310i	$0.655987\pi$
$398$	−1.71682e6	−0.543272
$399$	398671.	0.125367
$400$	0	0
$401$	−799254.	−0.248213	−0.124106	−	0.992269i	$-0.539606\pi$
$401$	−799254.	−0.248213	−0.124106	+	0.992269i	$0.539606\pi$
$402$	437605.	0.135057
$403$	−3.42294e6	−1.04987
$404$	1.08848e7	3.31794
$405$	0	0
$406$	−947484.	−0.285270
$407$	957937.	0.286649
$408$	−4.21687e6	−1.25412
$409$	898422.	0.265566	0.132783	−	0.991145i	$-0.457609\pi$
$409$	898422.	0.265566	0.132783	+	0.991145i	$0.457609\pi$
$410$	0	0
$411$	−1.38292e6	−0.403824
$412$	1.38111e7	4.00852
$413$	1.46134e6	0.421576
$414$	−1.49770e6	−0.429462
$415$	0	0
$416$	−3.00060e6	−0.850108
$417$	1.20786e6	0.340155
$418$	5.22118e6	1.46160
$419$	2.31259e6	0.643523	0.321761	−	0.946821i	$-0.395725\pi$
$419$	2.31259e6	0.643523	0.321761	+	0.946821i	$0.395725\pi$
$420$	0	0
$421$	4.43296e6	1.21896	0.609478	−	0.792803i	$-0.291379\pi$
$421$	4.43296e6	1.21896	0.609478	+	0.792803i	$0.291379\pi$
$422$	−4.72855e6	−1.29255
$423$	−190244.	−0.0516965
$424$	−8.19336e6	−2.21334
$425$	0	0
$426$	2.91442e6	0.778086
$427$	−1.91149e6	−0.507344
$428$	4.97688e6	1.31325
$429$	−1.15036e6	−0.301780
$430$	0	0
$431$	5.97999e6	1.55063	0.775314	−	0.631576i	$-0.217592\pi$
$431$	5.97999e6	1.55063	0.775314	+	0.631576i	$0.217592\pi$
$432$	5.04363e6	1.30027
$433$	2.06419e6	0.529089	0.264545	−	0.964373i	$-0.414778\pi$
$433$	2.06419e6	0.529089	0.264545	+	0.964373i	$0.414778\pi$
$434$	5.65384e6	1.44085
$435$	0	0
$436$	−1.60764e7	−4.05017
$437$	−718899.	−0.180080
$438$	2.48167e6	0.618099
$439$	−4.09148e6	−1.01326	−0.506628	−	0.862165i	$-0.669108\pi$
$439$	−4.09148e6	−1.01326	−0.506628	+	0.862165i	$0.669108\pi$
$440$	0	0
$441$	2.56099e6	0.627064
$442$	−7.91589e6	−1.92728
$443$	2.75822e6	0.667759	0.333879	−	0.942616i	$-0.391642\pi$
$443$	2.75822e6	0.667759	0.333879	+	0.942616i	$0.391642\pi$
$444$	798070.	0.192125
$445$	0	0
$446$	−1.11137e7	−2.64558
$447$	214006.	0.0506592
$448$	533431.	0.125569
$449$	−3.76648e6	−0.881698	−0.440849	−	0.897581i	$-0.645323\pi$
$449$	−3.76648e6	−0.881698	−0.440849	+	0.897581i	$0.645323\pi$
$450$	0	0
$451$	−5.23640e6	−1.21225
$452$	−5.92231e6	−1.36347
$453$	855944.	0.195975
$454$	4.23004e6	0.963174
$455$	0	0
$456$	2.45113e6	0.552019
$457$	480604.	0.107646	0.0538229	−	0.998550i	$-0.482859\pi$
$457$	480604.	0.107646	0.0538229	+	0.998550i	$0.482859\pi$
$458$	−4.44515e6	−0.990200
$459$	4.53073e6	1.00377
$460$	0	0
$461$	4.52514e6	0.991699	0.495849	−	0.868409i	$-0.334857\pi$
$461$	4.52514e6	0.991699	0.495849	+	0.868409i	$0.334857\pi$
$462$	1.90010e6	0.414164
$463$	7.39975e6	1.60422	0.802111	−	0.597175i	$-0.203710\pi$
$463$	7.39975e6	1.60422	0.802111	+	0.597175i	$0.203710\pi$
$464$	−2.68407e6	−0.578761
$465$	0	0
$466$	7.80018e6	1.66395
$467$	1.84711e6	0.391923	0.195962	−	0.980612i	$-0.437217\pi$
$467$	1.84711e6	0.391923	0.195962	+	0.980612i	$0.437217\pi$
$468$	6.67309e6	1.40836
$469$	−532261.	−0.111736
$470$	0	0
$471$	1.90276e6	0.395212
$472$	8.98467e6	1.85630
$473$	−7.30018e6	−1.50031
$474$	352931.	0.0721513
$475$	0	0
$476$	9.10203e6	1.84128
$477$	4.10669e6	0.826410
$478$	−1.01453e7	−2.03094
$479$	−3.05088e6	−0.607555	−0.303778	−	0.952743i	$-0.598248\pi$
$479$	−3.05088e6	−0.607555	−0.303778	+	0.952743i	$0.598248\pi$
$480$	0	0
$481$	844197.	0.166372
$482$	−3.68284e6	−0.722047
$483$	−261624.	−0.0510281
$484$	5.51635e6	1.07038
$485$	0	0
$486$	−8.41365e6	−1.61582
$487$	7.28136e6	1.39120	0.695601	−	0.718429i	$-0.255138\pi$
$487$	7.28136e6	1.39120	0.695601	+	0.718429i	$0.255138\pi$
$488$	−1.17523e7	−2.23395
$489$	−2.02297e6	−0.382575
$490$	0	0
$491$	−6.60475e6	−1.23638	−0.618191	−	0.786028i	$-0.712134\pi$
$491$	−6.60475e6	−1.23638	−0.618191	+	0.786028i	$0.712134\pi$
$492$	−4.36251e6	−0.812500
$493$	−2.41112e6	−0.446788
$494$	4.60124e6	0.848316
$495$	0	0
$496$	1.60164e7	2.92322
$497$	−3.54481e6	−0.643727
$498$	−3.00171e6	−0.542369
$499$	4.87006e6	0.875555	0.437777	−	0.899083i	$-0.355766\pi$
$499$	4.87006e6	0.875555	0.437777	+	0.899083i	$0.355766\pi$
$500$	0	0
$501$	−1.37702e6	−0.245102
$502$	−8.73354e6	−1.54679
$503$	−1.16752e6	−0.205753	−0.102876	−	0.994694i	$-0.532805\pi$
$503$	−1.16752e6	−0.205753	−0.102876	+	0.994694i	$0.532805\pi$
$504$	−6.21105e6	−1.08915
$505$	0	0
$506$	−3.42634e6	−0.594914
$507$	1.03732e6	0.179222
$508$	1.18250e7	2.03303
$509$	−7.41468e6	−1.26852	−0.634261	−	0.773119i	$-0.718695\pi$
$509$	−7.41468e6	−1.26852	−0.634261	+	0.773119i	$0.718695\pi$
$510$	0	0
$511$	−3.01846e6	−0.511367
$512$	−1.31522e7	−2.21730
$513$	−2.63356e6	−0.441824
$514$	−783596.	−0.130823
$515$	0	0
$516$	−6.08187e6	−1.00557
$517$	−435227.	−0.0716127
$518$	−1.39440e6	−0.228330
$519$	339516.	0.0553277
$520$	0	0
$521$	−811897.	−0.131041	−0.0655204	−	0.997851i	$-0.520871\pi$
$521$	−811897.	−0.131041	−0.0655204	+	0.997851i	$0.520871\pi$
$522$	2.91979e6	0.469003
$523$	5.06828e6	0.810226	0.405113	−	0.914267i	$-0.367232\pi$
$523$	5.06828e6	0.810226	0.405113	+	0.914267i	$0.367232\pi$
$524$	−1.41494e7	−2.25117
$525$	0	0
$526$	1.22550e7	1.93129
$527$	1.43877e7	2.25665
$528$	5.38270e6	0.840263
$529$	−5.96457e6	−0.926702
$530$	0	0
$531$	−4.50331e6	−0.693099
$532$	−5.29071e6	−0.810465
$533$	−4.61465e6	−0.703592
$534$	−2.53012e6	−0.383962
$535$	0	0
$536$	−3.27247e6	−0.491998
$537$	−3.35209e6	−0.501626
$538$	1.05628e7	1.57334
$539$	5.85886e6	0.868642
$540$	0	0
$541$	1.52830e6	0.224499	0.112250	−	0.993680i	$-0.464194\pi$
$541$	1.52830e6	0.224499	0.112250	+	0.993680i	$0.464194\pi$
$542$	2.17704e7	3.18323
$543$	−848980.	−0.123566
$544$	1.26124e7	1.82727
$545$	0	0
$546$	1.67449e6	0.240382
$547$	−1.23234e7	−1.76101	−0.880506	−	0.474036i	$-0.842797\pi$
$547$	−1.23234e7	−1.76101	−0.880506	+	0.474036i	$0.842797\pi$
$548$	1.83525e7	2.61062
$549$	5.89050e6	0.834107
$550$	0	0
$551$	1.40150e6	0.196660
$552$	−1.60853e6	−0.224688
$553$	−429271.	−0.0596923
$554$	1.89998e7	2.63011
$555$	0	0
$556$	−1.60293e7	−2.19902
$557$	−4.08606e6	−0.558042	−0.279021	−	0.960285i	$-0.590010\pi$
$557$	−4.08606e6	−0.558042	−0.279021	+	0.960285i	$0.590010\pi$
$558$	−1.74230e7	−2.36885
$559$	−6.43339e6	−0.870784
$560$	0	0
$561$	4.83531e6	0.648661
$562$	930291.	0.124245
$563$	24160.3	0.00321241	0.00160621	−	0.999999i	$-0.499489\pi$
$563$	24160.3	0.00321241	0.00160621	+	0.999999i	$0.499489\pi$
$564$	−362593.	−0.0479979
$565$	0	0
$566$	−9.53664e6	−1.25128
$567$	2.60180e6	0.339873
$568$	−2.17943e7	−2.83448
$569$	1.42000e7	1.83869	0.919344	−	0.393454i	$-0.128720\pi$
$569$	1.42000e7	1.83869	0.919344	+	0.393454i	$0.128720\pi$
$570$	0	0
$571$	−767642.	−0.0985300	−0.0492650	−	0.998786i	$-0.515688\pi$
$571$	−767642.	−0.0985300	−0.0492650	+	0.998786i	$0.515688\pi$
$572$	1.52662e7	1.95093
$573$	−1.00714e6	−0.128145
$574$	7.62225e6	0.965614
$575$	0	0
$576$	−1.64384e6	−0.206444
$577$	−1.51488e6	−0.189426	−0.0947129	−	0.995505i	$-0.530193\pi$
$577$	−1.51488e6	−0.189426	−0.0947129	+	0.995505i	$0.530193\pi$
$578$	1.87023e7	2.32849
$579$	563910.	0.0699059
$580$	0	0
$581$	3.65098e6	0.448714
$582$	8.39109e6	1.02686
$583$	9.39498e6	1.14479
$584$	−1.85582e7	−2.25167
$585$	0	0
$586$	2.79881e7	3.36689
$587$	−1.28973e7	−1.54491	−0.772455	−	0.635070i	$-0.780971\pi$
$587$	−1.28973e7	−1.54491	−0.772455	+	0.635070i	$0.780971\pi$
$588$	4.88109e6	0.582201
$589$	−8.36307e6	−0.993294
$590$	0	0
$591$	2.23539e6	0.263260
$592$	−3.95012e6	−0.463240
$593$	−5.43125e6	−0.634254	−0.317127	−	0.948383i	$-0.602718\pi$
$593$	−5.43125e6	−0.634254	−0.317127	+	0.948383i	$0.602718\pi$
$594$	−1.25518e7	−1.45962
$595$	0	0
$596$	−2.84004e6	−0.327499
$597$	924180.	0.106126
$598$	−3.01951e6	−0.345290
$599$	3.92217e6	0.446642	0.223321	−	0.974745i	$-0.428310\pi$
$599$	3.92217e6	0.446642	0.223321	+	0.974745i	$0.428310\pi$
$600$	0	0
$601$	−5.64824e6	−0.637863	−0.318931	−	0.947778i	$-0.603324\pi$
$601$	−5.64824e6	−0.637863	−0.318931	+	0.947778i	$0.603324\pi$
$602$	1.06264e7	1.19507
$603$	1.64023e6	0.183701
$604$	−1.13591e7	−1.26693
$605$	0	0
$606$	−8.41704e6	−0.931061
$607$	−1.07148e7	−1.18035	−0.590177	−	0.807274i	$-0.700942\pi$
$607$	−1.07148e7	−1.18035	−0.590177	+	0.807274i	$0.700942\pi$
$608$	−7.33119e6	−0.804296
$609$	510039.	0.0557263
$610$	0	0
$611$	−383551.	−0.0415642
$612$	−2.80491e7	−3.02719
$613$	4.08748e6	0.439344	0.219672	−	0.975574i	$-0.429501\pi$
$613$	4.08748e6	0.439344	0.219672	+	0.975574i	$0.429501\pi$
$614$	−2.35666e7	−2.52276
$615$	0	0
$616$	−1.42092e7	−1.50875
$617$	−7.83395e6	−0.828453	−0.414227	−	0.910174i	$-0.635948\pi$
$617$	−7.83395e6	−0.828453	−0.414227	+	0.910174i	$0.635948\pi$
$618$	−1.06798e7	−1.12485
$619$	1.23423e7	1.29470	0.647352	−	0.762191i	$-0.275876\pi$
$619$	1.23423e7	1.29470	0.647352	+	0.762191i	$0.275876\pi$
$620$	0	0
$621$	1.72824e6	0.179836
$622$	1.01066e7	1.04744
$623$	3.07739e6	0.317660
$624$	4.74358e6	0.487691
$625$	0	0
$626$	2.12066e7	2.16290
$627$	−2.81061e6	−0.285516
$628$	−2.52512e7	−2.55495
$629$	−3.54842e6	−0.357609
$630$	0	0
$631$	−1.31578e6	−0.131556	−0.0657780	−	0.997834i	$-0.520953\pi$
$631$	−1.31578e6	−0.131556	−0.0657780	+	0.997834i	$0.520953\pi$
$632$	−2.63926e6	−0.262839
$633$	2.54542e6	0.252494
$634$	1.17346e7	1.15944
$635$	0	0
$636$	7.82708e6	0.767285
$637$	5.16320e6	0.504163
$638$	6.67969e6	0.649688
$639$	1.09238e7	1.05833
$640$	0	0
$641$	6.55744e6	0.630360	0.315180	−	0.949032i	$-0.397935\pi$
$641$	6.55744e6	0.630360	0.315180	+	0.949032i	$0.397935\pi$
$642$	−3.84852e6	−0.368516
$643$	−4.69954e6	−0.448258	−0.224129	−	0.974559i	$-0.571954\pi$
$643$	−4.69954e6	−0.448258	−0.224129	+	0.974559i	$0.571954\pi$
$644$	3.47197e6	0.329884
$645$	0	0
$646$	−1.93405e7	−1.82341
$647$	2.05827e7	1.93305	0.966523	−	0.256580i	$-0.0825956\pi$
$647$	2.05827e7	1.93305	0.966523	+	0.256580i	$0.0825956\pi$
$648$	1.59965e7	1.49654
$649$	−1.03023e7	−0.960117
$650$	0	0
$651$	−3.04351e6	−0.281464
$652$	2.68465e7	2.47325
$653$	−1.42466e7	−1.30746	−0.653731	−	0.756727i	$-0.726797\pi$
$653$	−1.42466e7	−1.30746	−0.653731	+	0.756727i	$0.726797\pi$
$654$	1.24316e7	1.13653
$655$	0	0
$656$	2.15927e7	1.95905
$657$	9.30177e6	0.840722
$658$	633530.	0.0570430
$659$	−1.35369e7	−1.21425	−0.607123	−	0.794608i	$-0.707676\pi$
$659$	−1.35369e7	−1.21425	−0.607123	+	0.794608i	$0.707676\pi$
$660$	0	0
$661$	−1.30443e7	−1.16122	−0.580612	−	0.814180i	$-0.697187\pi$
$661$	−1.30443e7	−1.16122	−0.580612	+	0.814180i	$0.697187\pi$
$662$	2.10609e6	0.186781
$663$	4.26119e6	0.376485
$664$	2.24471e7	1.97579
$665$	0	0
$666$	4.29703e6	0.375390
$667$	−919721.	−0.0800464
$668$	1.82743e7	1.58452
$669$	5.98260e6	0.516802
$670$	0	0
$671$	1.34759e7	1.15545
$672$	−2.66799e6	−0.227908
$673$	4.75951e6	0.405065	0.202532	−	0.979276i	$-0.435083\pi$
$673$	4.75951e6	0.405065	0.202532	+	0.979276i	$0.435083\pi$
$674$	5.01008e6	0.424810
$675$	0	0
$676$	−1.37661e7	−1.15863
$677$	−1.51397e7	−1.26954	−0.634770	−	0.772701i	$-0.718905\pi$
$677$	−1.51397e7	−1.26954	−0.634770	+	0.772701i	$0.718905\pi$
$678$	4.57961e6	0.382608
$679$	−1.02061e7	−0.849543
$680$	0	0
$681$	−2.27707e6	−0.188152
$682$	−3.98592e7	−3.28146
$683$	−2.34145e7	−1.92058	−0.960292	−	0.278998i	$-0.909998\pi$
$683$	−2.34145e7	−1.92058	−0.960292	+	0.278998i	$0.909998\pi$
$684$	1.63040e7	1.33246
$685$	0	0
$686$	−2.04208e7	−1.65677
$687$	2.39287e6	0.193431
$688$	3.01028e7	2.42458
$689$	8.27947e6	0.664438
$690$	0	0
$691$	−1.62194e7	−1.29223	−0.646113	−	0.763242i	$-0.723606\pi$
$691$	−1.62194e7	−1.29223	−0.646113	+	0.763242i	$0.723606\pi$
$692$	−4.50567e6	−0.357679
$693$	7.12196e6	0.563334
$694$	−3.92841e7	−3.09613
$695$	0	0
$696$	3.13584e6	0.245375
$697$	1.93968e7	1.51234
$698$	1.49289e7	1.15981
$699$	−4.19891e6	−0.325045
$700$	0	0
$701$	−1.89605e7	−1.45732	−0.728659	−	0.684876i	$-0.759856\pi$
$701$	−1.89605e7	−1.45732	−0.728659	+	0.684876i	$0.759856\pi$
$702$	−1.10614e7	−0.847167
$703$	2.06258e6	0.157406
$704$	−3.76065e6	−0.285977
$705$	0	0
$706$	−7.98895e6	−0.603223
$707$	1.02377e7	0.770287
$708$	−8.58301e6	−0.643512
$709$	128325.	0.00958732	0.00479366	−	0.999989i	$-0.498474\pi$
$709$	128325.	0.00958732	0.00479366	+	0.999989i	$0.498474\pi$
$710$	0	0
$711$	1.32285e6	0.0981382
$712$	1.89206e7	1.39873
$713$	5.48817e6	0.404300
$714$	−7.03843e6	−0.516690
$715$	0	0
$716$	4.44850e7	3.24288
$717$	5.46133e6	0.396735
$718$	−2.18079e7	−1.57871
$719$	−2.41874e7	−1.74489	−0.872444	−	0.488714i	$-0.837466\pi$
$719$	−2.41874e7	−1.74489	−0.872444	+	0.488714i	$0.837466\pi$
$720$	0	0
$721$	1.29899e7	0.930610
$722$	−1.41680e7	−1.01150
$723$	1.98251e6	0.141049
$724$	1.12667e7	0.798821
$725$	0	0
$726$	−4.26569e6	−0.300364
$727$	−513307.	−0.0360198	−0.0180099	−	0.999838i	$-0.505733\pi$
$727$	−513307.	−0.0360198	−0.0180099	+	0.999838i	$0.505733\pi$
$728$	−1.25221e7	−0.875685
$729$	−4.64015e6	−0.323380
$730$	0	0
$731$	2.70416e7	1.87171
$732$	1.12269e7	0.774431
$733$	1.64153e7	1.12847	0.564234	−	0.825615i	$-0.309172\pi$
$733$	1.64153e7	1.12847	0.564234	+	0.825615i	$0.309172\pi$
$734$	4.21567e7	2.88820
$735$	0	0
$736$	4.81101e6	0.327372
$737$	3.75240e6	0.254472
$738$	−2.34890e7	−1.58753
$739$	1.16112e7	0.782109	0.391054	−	0.920368i	$-0.372110\pi$
$739$	1.16112e7	0.782109	0.391054	+	0.920368i	$0.372110\pi$
$740$	0	0
$741$	−2.47689e6	−0.165715
$742$	−1.36756e7	−0.911879
$743$	−5.72590e6	−0.380515	−0.190257	−	0.981734i	$-0.560932\pi$
$743$	−5.72590e6	−0.380515	−0.190257	+	0.981734i	$0.560932\pi$
$744$	−1.87122e7	−1.23935
$745$	0	0
$746$	−4.66483e7	−3.06894
$747$	−1.12510e7	−0.737715
$748$	−6.41687e7	−4.19343
$749$	4.68097e6	0.304882
$750$	0	0
$751$	1.15324e7	0.746137	0.373069	−	0.927804i	$-0.378306\pi$
$751$	1.15324e7	0.746137	0.373069	+	0.927804i	$0.378306\pi$
$752$	1.79469e6	0.115730
$753$	4.70134e6	0.302158
$754$	5.88658e6	0.377081
$755$	0	0
$756$	1.27189e7	0.809368
$757$	8.63293e6	0.547544	0.273772	−	0.961795i	$-0.411729\pi$
$757$	8.63293e6	0.547544	0.273772	+	0.961795i	$0.411729\pi$
$758$	1.44238e7	0.911812
$759$	1.84443e6	0.116214
$760$	0	0
$761$	−3.52622e6	−0.220723	−0.110361	−	0.993892i	$-0.535201\pi$
$761$	−3.52622e6	−0.220723	−0.110361	+	0.993892i	$0.535201\pi$
$762$	−9.14408e6	−0.570496
$763$	−1.51206e7	−0.940280
$764$	1.33656e7	0.828427
$765$	0	0
$766$	4.76588e7	2.93475
$767$	−9.07910e6	−0.557255
$768$	9.57341e6	0.585685
$769$	1.40471e7	0.856585	0.428293	−	0.903640i	$-0.359115\pi$
$769$	1.40471e7	0.856585	0.428293	+	0.903640i	$0.359115\pi$
$770$	0	0
$771$	421817.	0.0255557
$772$	−7.48356e6	−0.451924
$773$	2.44760e7	1.47330	0.736651	−	0.676274i	$-0.236406\pi$
$773$	2.44760e7	1.47330	0.736651	+	0.676274i	$0.236406\pi$
$774$	−3.27465e7	−1.96477
$775$	0	0
$776$	−6.27496e7	−3.74073
$777$	750619.	0.0446033
$778$	3.62873e7	2.14934
$779$	−1.12747e7	−0.665675
$780$	0	0
$781$	2.49907e7	1.46606
$782$	1.26920e7	0.742184
$783$	−3.36924e6	−0.196393
$784$	−2.41594e7	−1.40377
$785$	0	0
$786$	1.09414e7	0.631710
$787$	−4.35977e6	−0.250915	−0.125458	−	0.992099i	$-0.540040\pi$
$787$	−4.35977e6	−0.250915	−0.125458	+	0.992099i	$0.540040\pi$
$788$	−2.96655e7	−1.70191
$789$	−6.59697e6	−0.377270
$790$	0	0
$791$	−5.57019e6	−0.316540
$792$	4.37875e7	2.48049
$793$	1.18758e7	0.670626
$794$	−3.03359e7	−1.70768
$795$	0	0
$796$	−1.22647e7	−0.686076
$797$	−1.06887e7	−0.596044	−0.298022	−	0.954559i	$-0.596327\pi$
$797$	−1.06887e7	−0.596044	−0.298022	+	0.954559i	$0.596327\pi$
$798$	4.09120e6	0.227428
$799$	1.61218e6	0.0893403
$800$	0	0
$801$	−9.48339e6	−0.522255
$802$	−8.20202e6	−0.450282
$803$	2.12799e7	1.16461
$804$	3.12617e6	0.170558
$805$	0	0
$806$	−3.51265e7	−1.90457
$807$	−5.68605e6	−0.307345
$808$	6.29436e7	3.39175
$809$	9.12014e6	0.489926	0.244963	−	0.969532i	$-0.421224\pi$
$809$	9.12014e6	0.489926	0.244963	+	0.969532i	$0.421224\pi$
$810$	0	0
$811$	5.22575e6	0.278995	0.139497	−	0.990222i	$-0.455451\pi$
$811$	5.22575e6	0.278995	0.139497	+	0.990222i	$0.455451\pi$
$812$	−6.76865e6	−0.360256
$813$	−1.17192e7	−0.621830
$814$	9.83044e6	0.520010
$815$	0	0
$816$	−1.99388e7	−1.04827
$817$	−1.57184e7	−0.823857
$818$	9.21968e6	0.481762
$819$	6.27633e6	0.326961
$820$	0	0
$821$	9.00437e6	0.466225	0.233112	−	0.972450i	$-0.425109\pi$
$821$	9.00437e6	0.466225	0.233112	+	0.972450i	$0.425109\pi$
$822$	−1.41916e7	−0.732576
$823$	−2.78867e7	−1.43515	−0.717574	−	0.696482i	$-0.754748\pi$
$823$	−2.78867e7	−1.43515	−0.717574	+	0.696482i	$0.754748\pi$
$824$	7.98650e7	4.09768
$825$	0	0
$826$	1.49964e7	0.764781
$827$	−6.64309e6	−0.337758	−0.168879	−	0.985637i	$-0.554015\pi$
$827$	−6.64309e6	−0.337758	−0.168879	+	0.985637i	$0.554015\pi$
$828$	−1.06993e7	−0.542351
$829$	2.17030e7	1.09682	0.548408	−	0.836211i	$-0.315234\pi$
$829$	2.17030e7	1.09682	0.548408	+	0.836211i	$0.315234\pi$
$830$	0	0
$831$	−1.02277e7	−0.513780
$832$	−3.31413e6	−0.165982
$833$	−2.17026e7	−1.08367
$834$	1.23952e7	0.617075
$835$	0	0
$836$	3.72991e7	1.84579
$837$	2.01049e7	0.991949
$838$	2.37320e7	1.16741
$839$	−1.01238e7	−0.496520	−0.248260	−	0.968693i	$-0.579859\pi$
$839$	−1.01238e7	−0.496520	−0.248260	+	0.968693i	$0.579859\pi$
$840$	0	0
$841$	−1.87181e7	−0.912584
$842$	4.54914e7	2.21131
$843$	−500784.	−0.0242707
$844$	−3.37799e7	−1.63231
$845$	0	0
$846$	−1.95230e6	−0.0937825
$847$	5.18837e6	0.248498
$848$	−3.87409e7	−1.85003
$849$	5.13366e6	0.244432
$850$	0	0
$851$	−1.35354e6	−0.0640691
$852$	2.08200e7	0.982613
$853$	1.46326e7	0.688573	0.344286	−	0.938865i	$-0.388121\pi$
$853$	1.46326e7	0.688573	0.344286	+	0.938865i	$0.388121\pi$
$854$	−1.96159e7	−0.920371
$855$	0	0
$856$	2.87797e7	1.34246
$857$	−5.52218e6	−0.256838	−0.128419	−	0.991720i	$-0.540990\pi$
$857$	−5.52218e6	−0.256838	−0.128419	+	0.991720i	$0.540990\pi$
$858$	−1.18051e7	−0.547458
$859$	−3.02260e6	−0.139765	−0.0698824	−	0.997555i	$-0.522262\pi$
$859$	−3.02260e6	−0.139765	−0.0698824	+	0.997555i	$0.522262\pi$
$860$	0	0
$861$	−4.10313e6	−0.188628
$862$	6.13672e7	2.81299
$863$	−3.06818e7	−1.40234	−0.701172	−	0.712992i	$-0.747339\pi$
$863$	−3.06818e7	−1.40234	−0.701172	+	0.712992i	$0.747339\pi$
$864$	1.76243e7	0.803207
$865$	0	0
$866$	2.11829e7	0.959820
$867$	−1.00676e7	−0.454860
$868$	4.03900e7	1.81959
$869$	3.02633e6	0.135946
$870$	0	0
$871$	3.30686e6	0.147697
$872$	−9.29649e7	−4.14026
$873$	3.14514e7	1.39671
$874$	−7.37741e6	−0.326682
$875$	0	0
$876$	1.77286e7	0.780573
$877$	−5.17607e6	−0.227249	−0.113624	−	0.993524i	$-0.536246\pi$
$877$	−5.17607e6	−0.227249	−0.113624	+	0.993524i	$0.536246\pi$
$878$	−4.19871e7	−1.83815
$879$	−1.50662e7	−0.657707
$880$	0	0
$881$	−4.25937e7	−1.84887	−0.924433	−	0.381345i	$-0.875461\pi$
$881$	−4.25937e7	−1.84887	−0.924433	+	0.381345i	$0.875461\pi$
$882$	2.62811e7	1.13756
$883$	−1.72076e7	−0.742709	−0.371354	−	0.928491i	$-0.621107\pi$
$883$	−1.72076e7	−0.742709	−0.371354	+	0.928491i	$0.621107\pi$
$884$	−5.65496e7	−2.43388
$885$	0	0
$886$	2.83051e7	1.21138
$887$	2.53773e6	0.108302	0.0541510	−	0.998533i	$-0.482755\pi$
$887$	2.53773e6	0.108302	0.0541510	+	0.998533i	$0.482755\pi$
$888$	4.61499e6	0.196398
$889$	1.11220e7	0.471984
$890$	0	0
$891$	−1.83425e7	−0.774043
$892$	−7.93941e7	−3.34100
$893$	−937108.	−0.0393243
$894$	2.19615e6	0.0919007
$895$	0	0
$896$	−9.98078e6	−0.415331
$897$	1.62543e6	0.0674508
$898$	−3.86519e7	−1.59949
$899$	−1.06993e7	−0.441525
$900$	0	0
$901$	−3.48012e7	−1.42818
$902$	−5.37364e7	−2.19913
$903$	−5.72026e6	−0.233452
$904$	−3.42468e7	−1.39380
$905$	0	0
$906$	8.78377e6	0.355517
$907$	2.60899e7	1.05306	0.526531	−	0.850156i	$-0.323492\pi$
$907$	2.60899e7	1.05306	0.526531	+	0.850156i	$0.323492\pi$
$908$	3.02186e7	1.21635
$909$	−3.15487e7	−1.26640
$910$	0	0
$911$	1.44818e7	0.578130	0.289065	−	0.957309i	$-0.406656\pi$
$911$	1.44818e7	0.578130	0.289065	+	0.957309i	$0.406656\pi$
$912$	1.15897e7	0.461409
$913$	−2.57392e7	−1.02192
$914$	4.93200e6	0.195280
$915$	0	0
$916$	−3.17553e7	−1.25048
$917$	−1.33081e7	−0.522627
$918$	4.64947e7	1.82095
$919$	4.61041e7	1.80074	0.900369	−	0.435127i	$-0.143296\pi$
$919$	4.61041e7	1.80074	0.900369	+	0.435127i	$0.143296\pi$
$920$	0	0
$921$	1.26861e7	0.492811
$922$	4.64374e7	1.79904
$923$	2.20234e7	0.850903
$924$	1.35740e7	0.523031
$925$	0	0
$926$	7.59369e7	2.91022
$927$	−4.00301e7	−1.52998
$928$	−9.37914e6	−0.357514
$929$	−1.81557e7	−0.690197	−0.345098	−	0.938567i	$-0.612154\pi$
$929$	−1.81557e7	−0.690197	−0.345098	+	0.938567i	$0.612154\pi$
$930$	0	0
$931$	1.26150e7	0.476993
$932$	5.57230e7	2.10133
$933$	−5.44047e6	−0.204612
$934$	1.89552e7	0.710987
$935$	0	0
$936$	3.85884e7	1.43968
$937$	1.78946e7	0.665844	0.332922	−	0.942954i	$-0.391965\pi$
$937$	1.78946e7	0.665844	0.332922	+	0.942954i	$0.391965\pi$
$938$	−5.46210e6	−0.202700
$939$	−1.14157e7	−0.422512
$940$	0	0
$941$	−3.04463e6	−0.112088	−0.0560441	−	0.998428i	$-0.517849\pi$
$941$	−3.04463e6	−0.112088	−0.0560441	+	0.998428i	$0.517849\pi$
$942$	1.95262e7	0.716954
$943$	7.39891e6	0.270950
$944$	4.24825e7	1.55160
$945$	0	0
$946$	−7.49151e7	−2.72171
$947$	3.17110e7	1.14904	0.574519	−	0.818491i	$-0.305189\pi$
$947$	3.17110e7	1.14904	0.574519	+	0.818491i	$0.305189\pi$
$948$	2.52127e6	0.0911169
$949$	1.87532e7	0.675944
$950$	0	0
$951$	−6.31686e6	−0.226491
$952$	5.26342e7	1.88224
$953$	1.01913e7	0.363494	0.181747	−	0.983345i	$-0.441825\pi$
$953$	1.01913e7	0.363494	0.181747	+	0.983345i	$0.441825\pi$
$954$	4.21432e7	1.49919
$955$	0	0
$956$	−7.24764e7	−2.56479
$957$	−3.59574e6	−0.126914
$958$	−3.13084e7	−1.10216
$959$	1.72613e7	0.606077
$960$	0	0
$961$	3.52157e7	1.23006
$962$	8.66322e6	0.301816
$963$	−1.44250e7	−0.501246
$964$	−2.63095e7	−0.911844
$965$	0	0
$966$	−2.68481e6	−0.0925699
$967$	−3.21125e7	−1.10435	−0.552177	−	0.833727i	$-0.686203\pi$
$967$	−3.21125e7	−1.10435	−0.552177	+	0.833727i	$0.686203\pi$
$968$	3.18993e7	1.09419
$969$	1.04111e7	0.356196
$970$	0	0
$971$	2.29867e7	0.782399	0.391200	−	0.920306i	$-0.372060\pi$
$971$	2.29867e7	0.782399	0.391200	+	0.920306i	$0.372060\pi$
$972$	−6.01055e7	−2.04056
$973$	−1.50763e7	−0.510519
$974$	7.47219e7	2.52378
$975$	0	0
$976$	−5.55687e7	−1.86726
$977$	−2.47331e7	−0.828978	−0.414489	−	0.910054i	$-0.636040\pi$
$977$	−2.47331e7	−0.828978	−0.414489	+	0.910054i	$0.636040\pi$
$978$	−2.07599e7	−0.694029
$979$	−2.16954e7	−0.723455
$980$	0	0
$981$	4.65960e7	1.54588
$982$	−6.77785e7	−2.24292
$983$	5.57031e7	1.83863	0.919317	−	0.393518i	$-0.128742\pi$
$983$	5.57031e7	1.83863	0.919317	+	0.393518i	$0.128742\pi$
$984$	−2.52270e7	−0.830574
$985$	0	0
$986$	−2.47431e7	−0.810518
$987$	−341035.	−0.0111431
$988$	3.28704e7	1.07130
$989$	1.03150e7	0.335335
$990$	0	0
$991$	−6.86029e6	−0.221901	−0.110950	−	0.993826i	$-0.535389\pi$
$991$	−6.86029e6	−0.221901	−0.110950	+	0.993826i	$0.535389\pi$
$992$	5.59673e7	1.80574
$993$	−1.13373e6	−0.0364868
$994$	−3.63772e7	−1.16778
$995$	0	0
$996$	−2.14436e7	−0.684936
$997$	6.03725e7	1.92354	0.961771	−	0.273856i	$-0.0882993\pi$
$997$	6.03725e7	1.92354	0.961771	+	0.273856i	$0.0882993\pi$
$998$	4.99770e7	1.58834
$999$	−4.95847e6	−0.157193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.6.a.d.1.2	yes	2
3.2	odd	2		225.6.a.l.1.1		2
4.3	odd	2		400.6.a.o.1.2		2
5.2	odd	4		25.6.b.b.24.4		4
5.3	odd	4		25.6.b.b.24.1		4
5.4	even	2		25.6.a.b.1.1	✓	2
15.2	even	4		225.6.b.i.199.1		4
15.8	even	4		225.6.b.i.199.4		4
15.14	odd	2		225.6.a.s.1.2		2
20.3	even	4		400.6.c.n.49.3		4
20.7	even	4		400.6.c.n.49.2		4
20.19	odd	2		400.6.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.6.a.b.1.1	✓	2	5.4	even	2
25.6.a.d.1.2	yes	2	1.1	even	1	trivial
25.6.b.b.24.1		4	5.3	odd	4
25.6.b.b.24.4		4	5.2	odd	4
225.6.a.l.1.1		2	3.2	odd	2
225.6.a.s.1.2		2	15.14	odd	2
225.6.b.i.199.1		4	15.2	even	4
225.6.b.i.199.4		4	15.8	even	4
400.6.a.o.1.2		2	4.3	odd	2
400.6.a.w.1.1		2	20.19	odd	2
400.6.c.n.49.2		4	20.7	even	4
400.6.c.n.49.3		4	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+10.2621 q^{2} -5.52417 q^{3} +73.3104 q^{4} -56.6896 q^{6} +68.9517 q^{7} +423.931 q^{8} -212.483 q^{9} +O(q^{10})\)	\(q+10.2621 q^{2} -5.52417 q^{3} +73.3104 q^{4} -56.6896 q^{6} +68.9517 q^{7} +423.931 q^{8} -212.483 q^{9} -486.104 q^{11} -404.980 q^{12} -428.387 q^{13} +707.588 q^{14} +2004.49 q^{16} +1800.64 q^{17} -2180.52 q^{18} -1046.65 q^{19} -380.901 q^{21} -4988.45 q^{22} +686.855 q^{23} -2341.87 q^{24} -4396.14 q^{26} +2516.17 q^{27} +5054.88 q^{28} -1339.03 q^{29} +7990.30 q^{31} +7004.41 q^{32} +2685.33 q^{33} +18478.4 q^{34} -15577.3 q^{36} -1970.64 q^{37} -10740.9 q^{38} +2366.48 q^{39} +10772.2 q^{41} -3908.84 q^{42} +15017.7 q^{43} -35636.5 q^{44} +7048.57 q^{46} +895.337 q^{47} -11073.1 q^{48} -12052.7 q^{49} -9947.07 q^{51} -31405.2 q^{52} -19327.1 q^{53} +25821.2 q^{54} +29230.8 q^{56} +5781.90 q^{57} -13741.3 q^{58} +21193.7 q^{59} -27722.2 q^{61} +81997.1 q^{62} -14651.1 q^{63} +7736.31 q^{64} +27557.0 q^{66} -7719.33 q^{67} +132006. q^{68} -3794.31 q^{69} -51410.1 q^{71} -90078.4 q^{72} -43776.4 q^{73} -20222.9 q^{74} -76730.7 q^{76} -33517.7 q^{77} +24285.1 q^{78} -6225.68 q^{79} +37733.7 q^{81} +110545. q^{82} +52949.9 q^{83} -27924.0 q^{84} +154113. q^{86} +7397.05 q^{87} -206075. q^{88} +44631.2 q^{89} -29538.0 q^{91} +50353.6 q^{92} -44139.8 q^{93} +9188.03 q^{94} -38693.6 q^{96} -148018. q^{97} -123686. q^{98} +103289. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} + 20 q^{3} + 69 q^{4} - 191 q^{6} + 200 q^{7} + 615 q^{8} + 196 q^{9}+O(q^{10}) \) 2 * q + 5 * q^2 + 20 * q^3 + 69 * q^4 - 191 * q^6 + 200 * q^7 + 615 * q^8 + 196 * q^9	\( 2 q + 5 q^{2} + 20 q^{3} + 69 q^{4} - 191 q^{6} + 200 q^{7} + 615 q^{8} + 196 q^{9} - 196 q^{11} - 515 q^{12} - 360 q^{13} + 18 q^{14} + 1137 q^{16} + 1490 q^{17} - 4330 q^{18} - 3180 q^{19} + 2964 q^{21} - 6515 q^{22} + 1560 q^{23} + 2535 q^{24} - 4756 q^{26} + 6740 q^{27} + 4490 q^{28} - 3920 q^{29} - 1096 q^{31} + 5455 q^{32} + 10090 q^{33} + 20113 q^{34} - 17338 q^{36} + 2020 q^{37} + 485 q^{38} + 4112 q^{39} + 27754 q^{41} - 21510 q^{42} - 3000 q^{43} - 36887 q^{44} + 2454 q^{46} + 25760 q^{47} - 33215 q^{48} - 11686 q^{49} - 17876 q^{51} - 31700 q^{52} - 26980 q^{53} + 3595 q^{54} + 54270 q^{56} - 48670 q^{57} - 160 q^{58} + 11960 q^{59} - 24396 q^{61} + 129810 q^{62} + 38880 q^{63} + 43649 q^{64} - 11407 q^{66} - 40060 q^{67} + 133345 q^{68} + 18492 q^{69} - 87296 q^{71} - 12030 q^{72} - 70290 q^{73} - 41222 q^{74} - 67535 q^{76} + 4500 q^{77} + 15100 q^{78} + 65480 q^{79} + 46282 q^{81} + 21185 q^{82} + 92580 q^{83} - 42342 q^{84} + 248924 q^{86} - 58480 q^{87} - 150645 q^{88} - 72810 q^{89} - 20576 q^{91} + 46590 q^{92} - 276060 q^{93} - 121652 q^{94} - 78241 q^{96} - 126140 q^{97} - 125615 q^{98} + 221792 q^{99}+O(q^{100}) \) 2 * q + 5 * q^2 + 20 * q^3 + 69 * q^4 - 191 * q^6 + 200 * q^7 + 615 * q^8 + 196 * q^9 - 196 * q^11 - 515 * q^12 - 360 * q^13 + 18 * q^14 + 1137 * q^16 + 1490 * q^17 - 4330 * q^18 - 3180 * q^19 + 2964 * q^21 - 6515 * q^22 + 1560 * q^23 + 2535 * q^24 - 4756 * q^26 + 6740 * q^27 + 4490 * q^28 - 3920 * q^29 - 1096 * q^31 + 5455 * q^32 + 10090 * q^33 + 20113 * q^34 - 17338 * q^36 + 2020 * q^37 + 485 * q^38 + 4112 * q^39 + 27754 * q^41 - 21510 * q^42 - 3000 * q^43 - 36887 * q^44 + 2454 * q^46 + 25760 * q^47 - 33215 * q^48 - 11686 * q^49 - 17876 * q^51 - 31700 * q^52 - 26980 * q^53 + 3595 * q^54 + 54270 * q^56 - 48670 * q^57 - 160 * q^58 + 11960 * q^59 - 24396 * q^61 + 129810 * q^62 + 38880 * q^63 + 43649 * q^64 - 11407 * q^66 - 40060 * q^67 + 133345 * q^68 + 18492 * q^69 - 87296 * q^71 - 12030 * q^72 - 70290 * q^73 - 41222 * q^74 - 67535 * q^76 + 4500 * q^77 + 15100 * q^78 + 65480 * q^79 + 46282 * q^81 + 21185 * q^82 + 92580 * q^83 - 42342 * q^84 + 248924 * q^86 - 58480 * q^87 - 150645 * q^88 - 72810 * q^89 - 20576 * q^91 + 46590 * q^92 - 276060 * q^93 - 121652 * q^94 - 78241 * q^96 - 126140 * q^97 - 125615 * q^98 + 221792 * q^99

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