LMFDB - Embedded newform 25.24.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,24,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, 24, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 24 $
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:	$83.8010093363$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{144169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 36042 $ x^2 - x - 36042
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-189.348$ 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)

$f(q)$	$=$	$q+4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.56013e9 q^{6} -3.81217e9 q^{7} -2.59512e9 q^{8} +5.67462e10 q^{9} +O(q^{10})$	\(q+4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.56013e9 q^{6} -3.81217e9 q^{7} -2.59512e9 q^{8} +5.67462e10 q^{9} +2.52200e11 q^{11} -3.00752e12 q^{12} +3.59099e12 q^{13} -1.53110e13 q^{14} -7.53715e13 q^{16} -2.34190e14 q^{17} +2.27913e14 q^{18} -6.23086e14 q^{19} +1.48082e15 q^{21} +1.01292e15 q^{22} +3.58786e15 q^{23} +1.00806e15 q^{24} +1.44227e16 q^{26} +1.45267e16 q^{27} -2.95156e16 q^{28} -2.05923e16 q^{29} +1.36357e17 q^{31} -2.80949e17 q^{32} -9.79656e16 q^{33} -9.40588e17 q^{34} +4.39356e17 q^{36} +1.23898e18 q^{37} -2.50253e18 q^{38} -1.39490e18 q^{39} +1.40074e18 q^{41} +5.94748e18 q^{42} -2.18793e17 q^{43} +1.95265e18 q^{44} +1.44101e19 q^{46} +8.67836e18 q^{47} +2.92777e19 q^{48} -1.28361e19 q^{49} +9.09698e19 q^{51} +2.78032e19 q^{52} +7.63436e19 q^{53} +5.83441e19 q^{54} +9.89304e18 q^{56} +2.42034e20 q^{57} -8.27059e19 q^{58} -1.01862e18 q^{59} +2.87337e20 q^{61} +5.47658e20 q^{62} -2.16326e20 q^{63} -4.96127e20 q^{64} -3.93464e20 q^{66} -1.47683e21 q^{67} -1.81321e21 q^{68} -1.39369e21 q^{69} +7.64346e20 q^{71} -1.47263e20 q^{72} +3.49433e21 q^{73} +4.97617e21 q^{74} -4.82422e21 q^{76} -9.61427e20 q^{77} -5.60242e21 q^{78} +1.02350e22 q^{79} -1.09851e22 q^{81} +5.62587e21 q^{82} +7.71597e21 q^{83} +1.14652e22 q^{84} -8.78750e20 q^{86} +7.99897e21 q^{87} -6.54489e20 q^{88} +4.58518e21 q^{89} -1.36895e22 q^{91} +2.77789e22 q^{92} -5.29672e22 q^{93} +3.48553e22 q^{94} +1.09133e23 q^{96} +1.13703e23 q^{97} -5.15544e22 q^{98} +1.43114e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 1809673056 q^{6} + 1359184400 q^{7} - 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) $ 2 * q - 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 1809673056 * q^6 + 1359184400 * q^7 - 49459023360 * q^8 - 34999394166 * q^9	$ 2 q - 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 1809673056 q^{6} + 1359184400 q^{7} - 49459023360 q^{8} - 34999394166 q^{9} + 856801968264 q^{11} - 2146514952960 q^{12} - 4376109322060 q^{13} - 41666034529728 q^{14} + 15956586401792 q^{16} - 254028147597540 q^{17} + 695480683916520 q^{18} + 4260600979960 q^{19} + 17\!\cdots\!44 q^{21}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 1809673056 * q^6 + 1359184400 * q^7 - 49459023360 * q^8 - 34999394166 * q^9 + 856801968264 * q^11 - 2146514952960 * q^12 - 4376109322060 * q^13 - 41666034529728 * q^14 + 15956586401792 * q^16 - 254028147597540 * q^17 + 695480683916520 * q^18 + 4260600979960 * q^19 + 1734031637722944 * q^21 - 2068343882177760 * q^22 + 8144713079008560 * q^23 - 1286622315141120 * q^24 + 55025854658735184 * q^26 + 5424634982716560 * q^27 + 61418438819709440 * q^28 + 20818433601623340 * q^29 + 137714017177000384 * q^31 - 353265663781601280 * q^32 - 68361366766001760 * q^33 - 839483655961325328 * q^34 - 1173916300077574848 * q^36 + 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1785011473665029232 * q^39 - 2294435477168314956 * q^41 + 4657011326437397760 * q^42 + 1750760768619855800 * q^43 + 12584088840033038592 * q^44 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 + 33749519399576616960 * q^48 - 13461981704376200814 * q^49 + 89998362845078292144 * q^51 - 112291883783912022400 * q^52 + 140287253401646796420 * q^53 + 104731223417039799360 * q^54 - 232456712054288117760 * q^56 + 272752401448627175520 * q^57 - 293749486923568689360 * q^58 + 280872989971340771880 * q^59 - 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 690775113933935014320 * q^63 - 893690254469352914944 * q^64 - 544338140913651883392 * q^66 - 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 - 1170560672172404223552 * q^69 + 3055033510194143328624 * q^71 + 4152294352103038548480 * q^72 + 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 + 6207154294513080590080 * q^76 + 2165184764357449665600 * q^77 - 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 - 2793528580929833975598 * q^81 + 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 15917751907190402476032 * q^84 - 10916288812918999243296 * q^86 + 10026640653837674384880 * q^87 - 28988514668199273707520 * q^88 + 6395093086173070004820 * q^89 - 54890178162704560146016 * q^91 + 107907439017191756981760 * q^92 - 52900811441357852079360 * q^93 + 159400518006534931827072 * q^94 + 105592121669584394256384 * q^96 + 31147288846254030500540 * q^97 - 48364767616374671003640 * q^98 - 41158245132312135981912 * 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 $

$2$	4016.35	1.38671	0.693357	−	0.720595i	$-0.256131\pi$
$2$	4016.35	1.38671	0.693357	+	0.720595i	$0.256131\pi$
$3$	−388445.	−1.26600	−0.633002	−	0.774150i	$-0.718177\pi$
$3$	−388445.	−1.26600	−0.633002	+	0.774150i	$0.718177\pi$
$4$	7.74247e6	0.922974
$5$	0	0
$5$	0	0
$6$	−1.56013e9	−1.75558
$7$	−3.81217e9	−0.728693	−0.364346	−	0.931263i	$-0.618708\pi$
$7$	−3.81217e9	−0.728693	−0.364346	+	0.931263i	$0.618708\pi$
$8$	−2.59512e9	−0.106813
$9$	5.67462e10	0.602765
$10$	0	0
$11$	2.52200e11	0.266519	0.133260	−	0.991081i	$-0.457456\pi$
$11$	2.52200e11	0.266519	0.133260	+	0.991081i	$0.457456\pi$
$12$	−3.00752e12	−1.16849
$13$	3.59099e12	0.555733	0.277867	−	0.960620i	$-0.410373\pi$
$13$	3.59099e12	0.555733	0.277867	+	0.960620i	$0.410373\pi$
$14$	−1.53110e13	−1.01049
$15$	0	0
$16$	−7.53715e13	−1.07109
$17$	−2.34190e14	−1.65731	−0.828657	−	0.559756i	$-0.810895\pi$
$17$	−2.34190e14	−1.65731	−0.828657	+	0.559756i	$0.810895\pi$
$18$	2.27913e14	0.835863
$19$	−6.23086e14	−1.22710	−0.613552	−	0.789654i	$-0.710260\pi$
$19$	−6.23086e14	−1.22710	−0.613552	+	0.789654i	$0.710260\pi$
$20$	0	0
$21$	1.48082e15	0.922528
$22$	1.01292e15	0.369586
$23$	3.58786e15	0.785173	0.392587	−	0.919715i	$-0.371580\pi$
$23$	3.58786e15	0.785173	0.392587	+	0.919715i	$0.371580\pi$
$24$	1.00806e15	0.135225
$25$	0	0
$26$	1.44227e16	0.770642
$27$	1.45267e16	0.502901
$28$	−2.95156e16	−0.672565
$29$	−2.05923e16	−0.313421	−0.156710	−	0.987645i	$-0.550089\pi$
$29$	−2.05923e16	−0.313421	−0.156710	+	0.987645i	$0.550089\pi$
$30$	0	0
$31$	1.36357e17	0.963870	0.481935	−	0.876207i	$-0.339934\pi$
$31$	1.36357e17	0.963870	0.481935	+	0.876207i	$0.339934\pi$
$32$	−2.80949e17	−1.37849
$33$	−9.79656e16	−0.337414
$34$	−9.40588e17	−2.29822
$35$	0	0
$36$	4.39356e17	0.556337
$37$	1.23898e18	1.14484	0.572419	−	0.819961i	$-0.306005\pi$
$37$	1.23898e18	1.14484	0.572419	+	0.819961i	$0.306005\pi$
$38$	−2.50253e18	−1.70164
$39$	−1.39490e18	−0.703560
$40$	0	0
$41$	1.40074e18	0.397506	0.198753	−	0.980050i	$-0.436311\pi$
$41$	1.40074e18	0.397506	0.198753	+	0.980050i	$0.436311\pi$
$42$	5.94748e18	1.27928
$43$	−2.18793e17	−0.0359043	−0.0179522	−	0.999839i	$-0.505715\pi$
$43$	−2.18793e17	−0.0359043	−0.0179522	+	0.999839i	$0.505715\pi$
$44$	1.95265e18	0.245990
$45$	0	0
$46$	1.44101e19	1.08881
$47$	8.67836e18	0.512050	0.256025	−	0.966670i	$-0.417587\pi$
$47$	8.67836e18	0.512050	0.256025	+	0.966670i	$0.417587\pi$
$48$	2.92777e19	1.35601
$49$	−1.28361e19	−0.469007
$50$	0	0
$51$	9.09698e19	2.09817
$52$	2.78032e19	0.512927
$53$	7.63436e19	1.13136	0.565679	−	0.824626i	$-0.308614\pi$
$53$	7.63436e19	1.13136	0.565679	+	0.824626i	$0.308614\pi$
$54$	5.83441e19	0.697379
$55$	0	0
$56$	9.89304e18	0.0778337
$57$	2.42034e20	1.55352
$58$	−8.27059e19	−0.434625
$59$	−1.01862e18	−0.00439760	−0.00219880	−	0.999998i	$-0.500700\pi$
$59$	−1.01862e18	−0.00439760	−0.00219880	+	0.999998i	$0.500700\pi$
$60$	0	0
$61$	2.87337e20	0.845472	0.422736	−	0.906253i	$-0.361070\pi$
$61$	2.87337e20	0.845472	0.422736	+	0.906253i	$0.361070\pi$
$62$	5.47658e20	1.33661
$63$	−2.16326e20	−0.439231
$64$	−4.96127e20	−0.840472
$65$	0	0
$66$	−3.93464e20	−0.467897
$67$	−1.47683e21	−1.47730	−0.738652	−	0.674088i	$-0.764537\pi$
$67$	−1.47683e21	−1.47730	−0.738652	+	0.674088i	$0.764537\pi$
$68$	−1.81321e21	−1.52966
$69$	−1.39369e21	−0.994032
$70$	0	0
$71$	7.64346e20	0.392481	0.196241	−	0.980556i	$-0.437127\pi$
$71$	7.64346e20	0.392481	0.196241	+	0.980556i	$0.437127\pi$
$72$	−1.47263e20	−0.0643830
$73$	3.49433e21	1.30362	0.651810	−	0.758382i	$-0.274010\pi$
$73$	3.49433e21	1.30362	0.651810	+	0.758382i	$0.274010\pi$
$74$	4.97617e21	1.58756
$75$	0	0
$76$	−4.82422e21	−1.13259
$77$	−9.61427e20	−0.194211
$78$	−5.60242e21	−0.975636
$79$	1.02350e22	1.53948	0.769742	−	0.638356i	$-0.220385\pi$
$79$	1.02350e22	1.53948	0.769742	+	0.638356i	$0.220385\pi$
$80$	0	0
$81$	−1.09851e22	−1.23944
$82$	5.62587e21	0.551227
$83$	7.71597e21	0.657646	0.328823	−	0.944392i	$-0.393348\pi$
$83$	7.71597e21	0.657646	0.328823	+	0.944392i	$0.393348\pi$
$84$	1.14652e22	0.851469
$85$	0	0
$86$	−8.78750e20	−0.0497890
$87$	7.99897e21	0.396792
$88$	−6.54489e20	−0.0284676
$89$	4.58518e21	0.175134	0.0875672	−	0.996159i	$-0.472091\pi$
$89$	4.58518e21	0.175134	0.0875672	+	0.996159i	$0.472091\pi$
$90$	0	0
$91$	−1.36895e22	−0.404959
$92$	2.77789e22	0.724695
$93$	−5.29672e22	−1.22026
$94$	3.48553e22	0.710067
$95$	0	0
$96$	1.09133e23	1.74517
$97$	1.13703e23	1.61398	0.806991	−	0.590564i	$-0.201095\pi$
$97$	1.13703e23	1.61398	0.806991	+	0.590564i	$0.201095\pi$
$98$	−5.15544e22	−0.650378
$99$	1.43114e22	0.160648
$100$	0	0
$101$	1.36243e23	1.21512	0.607558	−	0.794275i	$-0.292149\pi$
$101$	1.36243e23	1.21512	0.607558	+	0.794275i	$0.292149\pi$
$102$	3.65366e23	2.90956
$103$	−1.41401e22	−0.100653	−0.0503264	−	0.998733i	$-0.516026\pi$
$103$	−1.41401e22	−0.100653	−0.0503264	+	0.998733i	$0.516026\pi$
$104$	−9.31907e21	−0.0593594
$105$	0	0
$106$	3.06623e23	1.56887
$107$	−6.02971e22	−0.276938	−0.138469	−	0.990367i	$-0.544218\pi$
$107$	−6.02971e22	−0.276938	−0.138469	+	0.990367i	$0.544218\pi$
$108$	1.12472e23	0.464164
$109$	−5.58169e22	−0.207186	−0.103593	−	0.994620i	$-0.533034\pi$
$109$	−5.58169e22	−0.207186	−0.103593	+	0.994620i	$0.533034\pi$
$110$	0	0
$111$	−4.81275e23	−1.44937
$112$	2.87329e23	0.780498
$113$	−3.51523e23	−0.862089	−0.431044	−	0.902331i	$-0.641855\pi$
$113$	−3.51523e23	−0.862089	−0.431044	+	0.902331i	$0.641855\pi$
$114$	9.72095e23	2.15428
$115$	0	0
$116$	−1.59435e23	−0.289279
$117$	2.03775e23	0.334976
$118$	−4.09115e21	−0.00609821
$119$	8.92770e23	1.20767
$120$	0	0
$121$	−8.31826e23	−0.928968
$122$	1.15405e24	1.17243
$123$	−5.44111e23	−0.503244
$124$	1.05574e24	0.889627
$125$	0	0
$126$	−8.68842e23	−0.609087
$127$	−2.32044e24	−1.48535	−0.742674	−	0.669653i	$-0.766443\pi$
$127$	−2.32044e24	−1.48535	−0.742674	+	0.669653i	$0.766443\pi$
$128$	3.64148e23	0.212992
$129$	8.49891e22	0.0454550
$130$	0	0
$131$	8.70825e23	0.390221	0.195111	−	0.980781i	$-0.437493\pi$
$131$	8.70825e23	0.390221	0.195111	+	0.980781i	$0.437493\pi$
$132$	−7.58496e23	−0.311425
$133$	2.37531e24	0.894182
$134$	−5.93146e24	−2.04860
$135$	0	0
$136$	6.07751e23	0.177022
$137$	−4.43869e24	−1.18841	−0.594207	−	0.804312i	$-0.702534\pi$
$137$	−4.43869e24	−1.18841	−0.594207	+	0.804312i	$0.702534\pi$
$138$	−5.59753e24	−1.37844
$139$	−4.97229e23	−0.112690	−0.0563452	−	0.998411i	$-0.517945\pi$
$139$	−4.97229e23	−0.112690	−0.0563452	+	0.998411i	$0.517945\pi$
$140$	0	0
$141$	−3.37106e24	−0.648257
$142$	3.06988e24	0.544259
$143$	9.05647e23	0.148114
$144$	−4.27705e24	−0.645617
$145$	0	0
$146$	1.40345e25	1.80775
$147$	4.98613e24	0.593764
$148$	9.59276e24	1.05666
$149$	1.10598e24	0.112748	0.0563738	−	0.998410i	$-0.482046\pi$
$149$	1.10598e24	0.112748	0.0563738	+	0.998410i	$0.482046\pi$
$150$	0	0
$151$	3.76304e24	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$151$	3.76304e24	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$152$	1.61698e24	0.131070
$153$	−1.32894e25	−0.998972
$154$	−3.86143e24	−0.269315
$155$	0	0
$156$	−1.08000e25	−0.649368
$157$	−1.50090e25	−0.838504	−0.419252	−	0.907870i	$-0.637708\pi$
$157$	−1.50090e25	−0.838504	−0.419252	+	0.907870i	$0.637708\pi$
$158$	4.11072e25	2.13482
$159$	−2.96553e25	−1.43230
$160$	0	0
$161$	−1.36775e25	−0.572150
$162$	−4.41199e25	−1.71875
$163$	2.61170e25	0.947907	0.473953	−	0.880550i	$-0.342827\pi$
$163$	2.61170e25	0.947907	0.473953	+	0.880550i	$0.342827\pi$
$164$	1.08452e25	0.366888
$165$	0	0
$166$	3.09900e25	0.911967
$167$	−1.77408e25	−0.487230	−0.243615	−	0.969872i	$-0.578333\pi$
$167$	−1.77408e25	−0.487230	−0.243615	+	0.969872i	$0.578333\pi$
$168$	−3.84290e24	−0.0985377
$169$	−2.88587e25	−0.691161
$170$	0	0
$171$	−3.53578e25	−0.739656
$172$	−1.69400e24	−0.0331387
$173$	−1.04109e26	−1.90528	−0.952640	−	0.304100i	$-0.901644\pi$
$173$	−1.04109e26	−1.90528	−0.952640	+	0.304100i	$0.901644\pi$
$174$	3.21267e25	0.550237
$175$	0	0
$176$	−1.90087e25	−0.285467
$177$	3.95679e23	0.00556737
$178$	1.84157e25	0.242861
$179$	−1.00142e25	−0.123824	−0.0619122	−	0.998082i	$-0.519720\pi$
$179$	−1.00142e25	−0.123824	−0.0619122	+	0.998082i	$0.519720\pi$
$180$	0	0
$181$	−5.17169e25	−0.562768	−0.281384	−	0.959595i	$-0.590793\pi$
$181$	−5.17169e25	−0.562768	−0.281384	+	0.959595i	$0.590793\pi$
$182$	−5.49817e25	−0.561562
$183$	−1.11615e26	−1.07037
$184$	−9.31094e24	−0.0838665
$185$	0	0
$186$	−2.12735e26	−1.69216
$187$	−5.90625e25	−0.441706
$188$	6.71919e25	0.472609
$189$	−5.53780e25	−0.366460
$190$	0	0
$191$	3.10126e26	1.81825	0.909127	−	0.416520i	$-0.136750\pi$
$191$	3.10126e26	1.81825	0.909127	+	0.416520i	$0.136750\pi$
$192$	1.92718e26	1.06404
$193$	1.28183e26	0.666687	0.333344	−	0.942805i	$-0.391823\pi$
$193$	1.28183e26	0.666687	0.333344	+	0.942805i	$0.391823\pi$
$194$	4.56673e26	2.23813
$195$	0	0
$196$	−9.93833e25	−0.432881
$197$	3.89967e26	1.60201	0.801007	−	0.598655i	$-0.204298\pi$
$197$	3.89967e26	1.60201	0.801007	+	0.598655i	$0.204298\pi$
$198$	5.74795e25	0.222773
$199$	−1.25611e26	−0.459426	−0.229713	−	0.973258i	$-0.573779\pi$
$199$	−1.25611e26	−0.459426	−0.229713	+	0.973258i	$0.573779\pi$
$200$	0	0
$201$	5.73666e26	1.87027
$202$	5.47199e26	1.68502
$203$	7.85013e25	0.228387
$204$	7.04330e26	1.93655
$205$	0	0
$206$	−5.67918e25	−0.139577
$207$	2.03598e26	0.473275
$208$	−2.70658e26	−0.595242
$209$	−1.57142e26	−0.327047
$210$	0	0
$211$	5.88286e26	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$211$	5.88286e26	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$212$	5.91088e26	1.04421
$213$	−2.96906e26	−0.496883
$214$	−2.42174e26	−0.384034
$215$	0	0
$216$	−3.76984e25	−0.0537162
$217$	−5.19817e26	−0.702365
$218$	−2.24180e26	−0.287308
$219$	−1.35735e27	−1.65039
$220$	0	0
$221$	−8.40974e26	−0.921025
$222$	−1.93297e27	−2.00986
$223$	−1.38821e27	−1.37072	−0.685361	−	0.728203i	$-0.740356\pi$
$223$	−1.38821e27	−1.37072	−0.685361	+	0.728203i	$0.740356\pi$
$224$	1.07102e27	1.00449
$225$	0	0
$226$	−1.41184e27	−1.19547
$227$	2.14958e27	1.73004	0.865022	−	0.501734i	$-0.167304\pi$
$227$	2.14958e27	1.73004	0.865022	+	0.501734i	$0.167304\pi$
$228$	1.87394e27	1.43386
$229$	−6.39851e26	−0.465554	−0.232777	−	0.972530i	$-0.574781\pi$
$229$	−6.39851e26	−0.465554	−0.232777	+	0.972530i	$0.574781\pi$
$230$	0	0
$231$	3.73461e26	0.245871
$232$	5.34395e25	0.0334773
$233$	−2.19149e27	−1.30661	−0.653306	−	0.757094i	$-0.726619\pi$
$233$	−2.19149e27	−1.30661	−0.653306	+	0.757094i	$0.726619\pi$
$234$	8.18434e26	0.464516
$235$	0	0
$236$	−7.88666e24	−0.00405887
$237$	−3.97572e27	−1.94899
$238$	3.58568e27	1.67470
$239$	1.09944e27	0.489322	0.244661	−	0.969609i	$-0.421323\pi$
$239$	1.09944e27	0.489322	0.244661	+	0.969609i	$0.421323\pi$
$240$	0	0
$241$	−1.44651e27	−0.584961	−0.292480	−	0.956272i	$-0.594481\pi$
$241$	−1.44651e27	−0.584961	−0.292480	+	0.956272i	$0.594481\pi$
$242$	−3.34090e27	−1.28821
$243$	2.89951e27	1.06623
$244$	2.22470e27	0.780349
$245$	0	0
$246$	−2.18534e27	−0.697855
$247$	−2.23750e27	−0.681942
$248$	−3.53864e26	−0.102954
$249$	−2.99723e27	−0.832582
$250$	0	0
$251$	2.24453e26	0.0568693	0.0284346	−	0.999596i	$-0.490948\pi$
$251$	2.24453e26	0.0568693	0.0284346	+	0.999596i	$0.490948\pi$
$252$	−1.67490e27	−0.405399
$253$	9.04857e26	0.209264
$254$	−9.31972e27	−2.05975
$255$	0	0
$256$	5.62436e27	1.13583
$257$	3.95005e27	0.762732	0.381366	−	0.924424i	$-0.375454\pi$
$257$	3.95005e27	0.762732	0.381366	+	0.924424i	$0.375454\pi$
$258$	3.41346e26	0.0630330
$259$	−4.72320e27	−0.834236
$260$	0	0
$261$	−1.16853e27	−0.188919
$262$	3.49754e27	0.541125
$263$	−2.01521e27	−0.298420	−0.149210	−	0.988805i	$-0.547673\pi$
$263$	−2.01521e27	−0.298420	−0.149210	+	0.988805i	$0.547673\pi$
$264$	2.54233e26	0.0360401
$265$	0	0
$266$	9.54007e27	1.23997
$267$	−1.78109e27	−0.221721
$268$	−1.14343e28	−1.36351
$269$	5.72063e27	0.653571	0.326785	−	0.945099i	$-0.394035\pi$
$269$	5.72063e27	0.653571	0.326785	+	0.945099i	$0.394035\pi$
$270$	0	0
$271$	5.18050e27	0.543531	0.271766	−	0.962363i	$-0.412392\pi$
$271$	5.18050e27	0.543531	0.271766	+	0.962363i	$0.412392\pi$
$272$	1.76512e28	1.77514
$273$	5.31761e27	0.512679
$274$	−1.78273e28	−1.64799
$275$	0	0
$276$	−1.07906e28	−0.917466
$277$	−1.29611e28	−1.05712	−0.528560	−	0.848896i	$-0.677268\pi$
$277$	−1.29611e28	−1.05712	−0.528560	+	0.848896i	$0.677268\pi$
$278$	−1.99705e27	−0.156269
$279$	7.73776e27	0.580987
$280$	0	0
$281$	1.24154e28	0.858691	0.429346	−	0.903140i	$-0.358744\pi$
$281$	1.24154e28	0.858691	0.429346	+	0.903140i	$0.358744\pi$
$282$	−1.35394e28	−0.898947
$283$	2.15031e28	1.37074	0.685372	−	0.728193i	$-0.259640\pi$
$283$	2.15031e28	1.37074	0.685372	+	0.728193i	$0.259640\pi$
$284$	5.91792e27	0.362250
$285$	0	0
$286$	3.63740e27	0.205391
$287$	−5.33986e27	−0.289660
$288$	−1.59428e28	−0.830903
$289$	3.48772e28	1.74669
$290$	0	0
$291$	−4.41675e28	−2.04331
$292$	2.70547e28	1.20321
$293$	1.20307e28	0.514416	0.257208	−	0.966356i	$-0.417197\pi$
$293$	1.20307e28	0.514416	0.257208	+	0.966356i	$0.417197\pi$
$294$	2.00260e28	0.823380
$295$	0	0
$296$	−3.21530e27	−0.122283
$297$	3.66362e27	0.134033
$298$	4.44202e27	0.156349
$299$	1.28840e28	0.436347
$300$	0	0
$301$	8.34076e26	0.0261632
$302$	1.51137e28	0.456342
$303$	−5.29228e28	−1.53834
$304$	4.69629e28	1.31434
$305$	0	0
$306$	−5.33748e28	−1.38529
$307$	4.70428e28	1.17598	0.587992	−	0.808867i	$-0.299919\pi$
$307$	4.70428e28	1.17598	0.587992	+	0.808867i	$0.299919\pi$
$308$	−7.44382e27	−0.179251
$309$	5.49267e27	0.127427
$310$	0	0
$311$	−8.99672e26	−0.0193794	−0.00968968	−	0.999953i	$-0.503084\pi$
$311$	−8.99672e26	−0.0193794	−0.00968968	+	0.999953i	$0.503084\pi$
$312$	3.61994e27	0.0751492
$313$	1.13525e28	0.227159	0.113579	−	0.993529i	$-0.463768\pi$
$313$	1.13525e28	0.227159	0.113579	+	0.993529i	$0.463768\pi$
$314$	−6.02814e28	−1.16277
$315$	0	0
$316$	7.92439e28	1.42090
$317$	−1.37896e28	−0.238436	−0.119218	−	0.992868i	$-0.538039\pi$
$317$	−1.37896e28	−0.238436	−0.119218	+	0.992868i	$0.538039\pi$
$318$	−1.19106e29	−1.98619
$319$	−5.19337e27	−0.0835326
$320$	0	0
$321$	2.34221e28	0.350605
$322$	−5.49338e28	−0.793408
$323$	1.45920e29	2.03370
$324$	−8.50516e28	−1.14397
$325$	0	0
$326$	1.04895e29	1.31448
$327$	2.16818e28	0.262298
$328$	−3.63510e27	−0.0424587
$329$	−3.30834e28	−0.373127
$330$	0	0
$331$	1.62668e29	1.71112	0.855559	−	0.517706i	$-0.173214\pi$
$331$	1.62668e29	1.71112	0.855559	+	0.517706i	$0.173214\pi$
$332$	5.97406e28	0.606990
$333$	7.03074e28	0.690069
$334$	−7.12534e28	−0.675649
$335$	0	0
$336$	−1.11611e29	−0.988113
$337$	1.64138e29	1.40432	0.702160	−	0.712019i	$-0.252219\pi$
$337$	1.64138e29	1.40432	0.702160	+	0.712019i	$0.252219\pi$
$338$	−1.15907e29	−0.958442
$339$	1.36547e29	1.09141
$340$	0	0
$341$	3.43892e28	0.256890
$342$	−1.42009e29	−1.02569
$343$	1.53268e29	1.07045
$344$	5.67795e26	0.00383504
$345$	0	0
$346$	−4.18139e29	−2.64208
$347$	−1.45586e29	−0.889876	−0.444938	−	0.895561i	$-0.646774\pi$
$347$	−1.45586e29	−0.889876	−0.444938	+	0.895561i	$0.646774\pi$
$348$	6.19318e28	0.366229
$349$	2.22110e28	0.127080	0.0635398	−	0.997979i	$-0.479761\pi$
$349$	2.22110e28	0.127080	0.0635398	+	0.997979i	$0.479761\pi$
$350$	0	0
$351$	5.21651e28	0.279479
$352$	−7.08552e28	−0.367393
$353$	−2.57166e28	−0.129064	−0.0645320	−	0.997916i	$-0.520555\pi$
$353$	−2.57166e28	−0.129064	−0.0645320	+	0.997916i	$0.520555\pi$
$354$	1.58919e27	0.00772035
$355$	0	0
$356$	3.55006e28	0.161644
$357$	−3.46792e29	−1.52892
$358$	−4.02205e28	−0.171709
$359$	−3.34157e29	−1.38154	−0.690771	−	0.723074i	$-0.742729\pi$
$359$	−3.34157e29	−1.38154	−0.690771	+	0.723074i	$0.742729\pi$
$360$	0	0
$361$	1.30406e29	0.505785
$362$	−2.07713e29	−0.780398
$363$	3.23118e29	1.17608
$364$	−1.05990e29	−0.373766
$365$	0	0
$366$	−4.48284e29	−1.48430
$367$	−1.62664e29	−0.521954	−0.260977	−	0.965345i	$-0.584045\pi$
$367$	−1.62664e29	−0.521954	−0.260977	+	0.965345i	$0.584045\pi$
$368$	−2.70422e29	−0.840994
$369$	7.94868e28	0.239603
$370$	0	0
$371$	−2.91034e29	−0.824412
$372$	−4.10097e29	−1.12627
$373$	−1.03540e29	−0.275712	−0.137856	−	0.990452i	$-0.544021\pi$
$373$	−1.03540e29	−0.275712	−0.137856	+	0.990452i	$0.544021\pi$
$374$	−2.37216e29	−0.612520
$375$	0	0
$376$	−2.25214e28	−0.0546935
$377$	−7.39468e28	−0.174178
$378$	−2.22418e29	−0.508175
$379$	6.62210e29	1.46772	0.733862	−	0.679298i	$-0.237716\pi$
$379$	6.62210e29	1.46772	0.733862	+	0.679298i	$0.237716\pi$
$380$	0	0
$381$	9.01364e29	1.88046
$382$	1.24557e30	2.52140
$383$	−2.96585e29	−0.582591	−0.291295	−	0.956633i	$-0.594086\pi$
$383$	−2.96585e29	−0.582591	−0.291295	+	0.956633i	$0.594086\pi$
$384$	−1.41451e29	−0.269648
$385$	0	0
$386$	5.14829e29	0.924504
$387$	−1.24157e28	−0.0216419
$388$	8.80345e29	1.48966
$389$	−1.06609e30	−1.75134	−0.875672	−	0.482906i	$-0.839581\pi$
$389$	−1.06609e30	−1.75134	−0.875672	+	0.482906i	$0.839581\pi$
$390$	0	0
$391$	−8.40240e29	−1.30128
$392$	3.33113e28	0.0500959
$393$	−3.38267e29	−0.494021
$394$	1.56624e30	2.22153
$395$	0	0
$396$	1.10805e29	0.148274
$397$	−1.67462e28	−0.0217683	−0.0108842	−	0.999941i	$-0.503465\pi$
$397$	−1.67462e28	−0.0217683	−0.0108842	+	0.999941i	$0.503465\pi$
$398$	−5.04496e29	−0.637093
$399$	−9.22676e29	−1.13204
$400$	0	0
$401$	3.87121e29	0.448421	0.224211	−	0.974541i	$-0.428020\pi$
$401$	3.87121e29	0.448421	0.224211	+	0.974541i	$0.428020\pi$
$402$	2.30404e30	2.59353
$403$	4.89658e29	0.535654
$404$	1.05486e30	1.12152
$405$	0	0
$406$	3.15289e29	0.316708
$407$	3.12470e29	0.305121
$408$	−2.36078e29	−0.224111
$409$	5.00511e29	0.461950	0.230975	−	0.972960i	$-0.425808\pi$
$409$	5.00511e29	0.461950	0.230975	+	0.972960i	$0.425808\pi$
$410$	0	0
$411$	1.72418e30	1.50454
$412$	−1.09480e29	−0.0928999
$413$	3.88316e27	0.00320450
$414$	8.17719e29	0.656297
$415$	0	0
$416$	−1.00889e30	−0.766070
$417$	1.93146e29	0.142666
$418$	−6.31137e29	−0.453520
$419$	1.70760e30	1.19378	0.596891	−	0.802322i	$-0.296402\pi$
$419$	1.70760e30	1.19378	0.596891	+	0.802322i	$0.296402\pi$
$420$	0	0
$421$	−5.97218e29	−0.395265	−0.197633	−	0.980276i	$-0.563325\pi$
$421$	−5.97218e29	−0.395265	−0.197633	+	0.980276i	$0.563325\pi$
$422$	2.36276e30	1.52169
$423$	4.92464e29	0.308646
$424$	−1.98121e29	−0.120843
$425$	0	0
$426$	−1.19248e30	−0.689034
$427$	−1.09538e30	−0.616089
$428$	−4.66848e29	−0.255607
$429$	−3.51794e29	−0.187512
$430$	0	0
$431$	1.91854e30	0.969353	0.484676	−	0.874694i	$-0.338937\pi$
$431$	1.91854e30	0.969353	0.484676	+	0.874694i	$0.338937\pi$
$432$	−1.09490e30	−0.538653
$433$	2.68456e30	1.28606	0.643032	−	0.765839i	$-0.277676\pi$
$433$	2.68456e30	1.28606	0.643032	+	0.765839i	$0.277676\pi$
$434$	−2.08777e30	−0.973980
$435$	0	0
$436$	−4.32160e29	−0.191228
$437$	−2.23555e30	−0.963489
$438$	−5.45161e30	−2.28862
$439$	2.11168e29	0.0863549	0.0431775	−	0.999067i	$-0.486252\pi$
$439$	2.11168e29	0.0863549	0.0431775	+	0.999067i	$0.486252\pi$
$440$	0	0
$441$	−7.28401e29	−0.282701
$442$	−3.37765e30	−1.27720
$443$	8.12623e29	0.299396	0.149698	−	0.988732i	$-0.452170\pi$
$443$	8.12623e29	0.299396	0.149698	+	0.988732i	$0.452170\pi$
$444$	−3.72626e30	−1.33773
$445$	0	0
$446$	−5.57554e30	−1.90080
$447$	−4.29614e29	−0.142739
$448$	1.89132e30	0.612446
$449$	−3.76596e30	−1.18862	−0.594310	−	0.804236i	$-0.702575\pi$
$449$	−3.76596e30	−1.18862	−0.594310	+	0.804236i	$0.702575\pi$
$450$	0	0
$451$	3.53267e29	0.105943
$452$	−2.72166e30	−0.795686
$453$	−1.46173e30	−0.416619
$454$	8.63348e30	2.39907
$455$	0	0
$456$	−6.28109e29	−0.165936
$457$	−2.14090e30	−0.551518	−0.275759	−	0.961227i	$-0.588929\pi$
$457$	−2.14090e30	−0.551518	−0.275759	+	0.961227i	$0.588929\pi$
$458$	−2.56986e30	−0.645591
$459$	−3.40199e30	−0.833465
$460$	0	0
$461$	4.76379e30	1.11018	0.555088	−	0.831792i	$-0.312685\pi$
$461$	4.76379e30	1.11018	0.555088	+	0.831792i	$0.312685\pi$
$462$	1.49995e30	0.340953
$463$	7.67574e30	1.70192	0.850959	−	0.525232i	$-0.176021\pi$
$463$	7.67574e30	1.70192	0.850959	+	0.525232i	$0.176021\pi$
$464$	1.55207e30	0.335703
$465$	0	0
$466$	−8.80180e30	−1.81190
$467$	2.87884e30	0.578194	0.289097	−	0.957300i	$-0.406645\pi$
$467$	2.87884e30	0.578194	0.289097	+	0.957300i	$0.406645\pi$
$468$	1.57772e30	0.309175
$469$	5.62992e30	1.07650
$470$	0	0
$471$	5.83016e30	1.06155
$472$	2.64345e27	0.000469719 0
$473$	−5.51796e28	−0.00956919
$474$	−1.59679e31	−2.70269
$475$	0	0
$476$	6.91225e30	1.11465
$477$	4.33221e30	0.681943
$478$	4.41573e30	0.678549
$479$	6.82143e30	1.02333	0.511666	−	0.859184i	$-0.329028\pi$
$479$	6.82143e30	1.02333	0.511666	+	0.859184i	$0.329028\pi$
$480$	0	0
$481$	4.44917e30	0.636224
$482$	−5.80971e30	−0.811173
$483$	5.31297e30	0.724344
$484$	−6.44038e30	−0.857413
$485$	0	0
$486$	1.16455e31	1.47856
$487$	−8.59361e29	−0.106560	−0.0532798	−	0.998580i	$-0.516968\pi$
$487$	−8.59361e29	−0.106560	−0.0532798	+	0.998580i	$0.516968\pi$
$488$	−7.45676e29	−0.0903071
$489$	−1.01450e31	−1.20005
$490$	0	0
$491$	−7.15140e30	−0.807149	−0.403575	−	0.914947i	$-0.632232\pi$
$491$	−7.15140e30	−0.807149	−0.403575	+	0.914947i	$0.632232\pi$
$492$	−4.21276e30	−0.464481
$493$	4.82250e30	0.519437
$494$	−8.98658e30	−0.945659
$495$	0	0
$496$	−1.02774e31	−1.03239
$497$	−2.91382e30	−0.285998
$498$	−1.20379e31	−1.15455
$499$	1.77913e31	1.66744	0.833722	−	0.552185i	$-0.186206\pi$
$499$	1.77913e31	1.66744	0.833722	+	0.552185i	$0.186206\pi$
$500$	0	0
$501$	6.89133e30	0.616835
$502$	9.01483e29	0.0788614
$503$	−6.56155e30	−0.561015	−0.280507	−	0.959852i	$-0.590503\pi$
$503$	−6.56155e30	−0.561015	−0.280507	+	0.959852i	$0.590503\pi$
$504$	5.61393e29	0.0469154
$505$	0	0
$506$	3.63422e30	0.290189
$507$	1.12100e31	0.875012
$508$	−1.79660e31	−1.37094
$509$	−1.19826e31	−0.893917	−0.446959	−	0.894555i	$-0.647493\pi$
$509$	−1.19826e31	−0.893917	−0.446959	+	0.894555i	$0.647493\pi$
$510$	0	0
$511$	−1.33210e31	−0.949939
$512$	1.95347e31	1.36208
$513$	−9.05135e30	−0.617112
$514$	1.58648e31	1.05769
$515$	0	0
$516$	6.58025e29	0.0419538
$517$	2.18868e30	0.136471
$518$	−1.89700e31	−1.15685
$519$	4.04407e31	2.41209
$520$	0	0
$521$	−2.26240e31	−1.29103	−0.645514	−	0.763749i	$-0.723357\pi$
$521$	−2.26240e31	−1.29103	−0.645514	+	0.763749i	$0.723357\pi$
$522$	−4.69325e30	−0.261977
$523$	3.41914e31	1.86702	0.933508	−	0.358557i	$-0.116731\pi$
$523$	3.41914e31	1.86702	0.933508	+	0.358557i	$0.116731\pi$
$524$	6.74233e30	0.360164
$525$	0	0
$526$	−8.09378e30	−0.413824
$527$	−3.19334e31	−1.59744
$528$	7.38381e30	0.361402
$529$	−8.00772e30	−0.383503
$530$	0	0
$531$	−5.78030e28	−0.00265072
$532$	1.83907e31	0.825307
$533$	5.03006e30	0.220907
$534$	−7.15348e30	−0.307463
$535$	0	0
$536$	3.83255e30	0.157795
$537$	3.88996e30	0.156762
$538$	2.29761e31	0.906315
$539$	−3.23726e30	−0.124999
$540$	0	0
$541$	−2.75024e30	−0.101766	−0.0508829	−	0.998705i	$-0.516204\pi$
$541$	−2.75024e30	−0.101766	−0.0508829	+	0.998705i	$0.516204\pi$
$542$	2.08067e31	0.753722
$543$	2.00892e31	0.712466
$544$	6.57953e31	2.28459
$545$	0	0
$546$	2.13574e31	0.710939
$547$	1.03197e31	0.336367	0.168184	−	0.985756i	$-0.446210\pi$
$547$	1.03197e31	0.336367	0.168184	+	0.985756i	$0.446210\pi$
$548$	−3.43664e31	−1.09688
$549$	1.63053e31	0.509621
$550$	0	0
$551$	1.28308e31	0.384600
$552$	3.61679e30	0.106175
$553$	−3.90174e31	−1.12181
$554$	−5.20563e31	−1.46592
$555$	0	0
$556$	−3.84978e30	−0.104010
$557$	−1.36262e31	−0.360613	−0.180307	−	0.983610i	$-0.557709\pi$
$557$	−1.36262e31	−0.360613	−0.180307	+	0.983610i	$0.557709\pi$
$558$	3.10775e31	0.805663
$559$	−7.85685e29	−0.0199532
$560$	0	0
$561$	2.29425e31	0.559202
$562$	4.98645e31	1.19076
$563$	−3.09091e31	−0.723169	−0.361585	−	0.932339i	$-0.617764\pi$
$563$	−3.09091e31	−0.723169	−0.361585	+	0.932339i	$0.617764\pi$
$564$	−2.61004e31	−0.598325
$565$	0	0
$566$	8.63638e31	1.90083
$567$	4.18769e31	0.903171
$568$	−1.98357e30	−0.0419220
$569$	−6.93051e31	−1.43540	−0.717702	−	0.696350i	$-0.754806\pi$
$569$	−6.93051e31	−1.43540	−0.717702	+	0.696350i	$0.754806\pi$
$570$	0	0
$571$	−6.24961e30	−0.124319	−0.0621595	−	0.998066i	$-0.519799\pi$
$571$	−6.24961e30	−0.124319	−0.0621595	+	0.998066i	$0.519799\pi$
$572$	7.01195e30	0.136705
$573$	−1.20467e32	−2.30192
$574$	−2.14468e31	−0.401675
$575$	0	0
$576$	−2.81534e31	−0.506607
$577$	1.59740e31	0.281768	0.140884	−	0.990026i	$-0.455006\pi$
$577$	1.59740e31	0.281768	0.140884	+	0.990026i	$0.455006\pi$
$578$	1.40079e32	2.42216
$579$	−4.97921e31	−0.844029
$580$	0	0
$581$	−2.94146e31	−0.479222
$582$	−1.77392e32	−2.83348
$583$	1.92538e31	0.301529
$584$	−9.06822e30	−0.139243
$585$	0	0
$586$	4.83197e31	0.713348
$587$	−8.16635e31	−1.18220	−0.591099	−	0.806599i	$-0.701306\pi$
$587$	−8.16635e31	−1.18220	−0.591099	+	0.806599i	$0.701306\pi$
$588$	3.86049e31	0.548029
$589$	−8.49622e31	−1.18277
$590$	0	0
$591$	−1.51481e32	−2.02816
$592$	−9.33837e31	−1.22623
$593$	5.61370e30	0.0722970	0.0361485	−	0.999346i	$-0.488491\pi$
$593$	5.61370e30	0.0722970	0.0361485	+	0.999346i	$0.488491\pi$
$594$	1.47144e31	0.185865
$595$	0	0
$596$	8.56305e30	0.104063
$597$	4.87928e31	0.581635
$598$	5.17466e31	0.605088
$599$	1.60231e32	1.83797	0.918985	−	0.394293i	$-0.129010\pi$
$599$	1.60231e32	1.83797	0.918985	+	0.394293i	$0.129010\pi$
$600$	0	0
$601$	8.47641e31	0.935741	0.467870	−	0.883797i	$-0.345021\pi$
$601$	8.47641e31	0.935741	0.467870	+	0.883797i	$0.345021\pi$
$602$	3.34994e30	0.0362809
$603$	−8.38044e31	−0.890467
$604$	2.91352e31	0.303734
$605$	0	0
$606$	−2.12557e32	−2.13324
$607$	1.63793e31	0.161296	0.0806481	−	0.996743i	$-0.474301\pi$
$607$	1.63793e31	0.161296	0.0806481	+	0.996743i	$0.474301\pi$
$608$	1.75055e32	1.69155
$609$	−3.04934e31	−0.289139
$610$	0	0
$611$	3.11639e31	0.284563
$612$	−1.02893e32	−0.922025
$613$	−1.93558e31	−0.170222	−0.0851110	−	0.996371i	$-0.527124\pi$
$613$	−1.93558e31	−0.170222	−0.0851110	+	0.996371i	$0.527124\pi$
$614$	1.88940e32	1.63075
$615$	0	0
$616$	2.49502e30	0.0207442
$617$	−5.25618e31	−0.428934	−0.214467	−	0.976731i	$-0.568801\pi$
$617$	−5.25618e31	−0.428934	−0.214467	+	0.976731i	$0.568801\pi$
$618$	2.20605e31	0.176704
$619$	−9.42009e31	−0.740650	−0.370325	−	0.928902i	$-0.620754\pi$
$619$	−9.42009e31	−0.740650	−0.370325	+	0.928902i	$0.620754\pi$
$620$	0	0
$621$	5.21196e31	0.394864
$622$	−3.61340e30	−0.0268736
$623$	−1.74795e31	−0.127619
$624$	1.05136e32	0.753578
$625$	0	0
$626$	4.55954e31	0.315004
$627$	6.10410e31	0.414042
$628$	−1.16207e32	−0.773918
$629$	−2.90156e32	−1.89736
$630$	0	0
$631$	−2.22784e32	−1.40458	−0.702288	−	0.711892i	$-0.747838\pi$
$631$	−2.22784e32	−1.40458	−0.702288	+	0.711892i	$0.747838\pi$
$632$	−2.65610e31	−0.164436
$633$	−2.28517e32	−1.38923
$634$	−5.53840e31	−0.330642
$635$	0	0
$636$	−2.29605e32	−1.32198
$637$	−4.60944e31	−0.260642
$638$	−2.08584e31	−0.115836
$639$	4.33738e31	0.236574
$640$	0	0
$641$	1.38602e32	0.729295	0.364648	−	0.931146i	$-0.381189\pi$
$641$	1.38602e32	0.729295	0.364648	+	0.931146i	$0.381189\pi$
$642$	9.40714e31	0.486188
$643$	−3.71401e31	−0.188546	−0.0942729	−	0.995546i	$-0.530053\pi$
$643$	−3.71401e31	−0.188546	−0.0942729	+	0.995546i	$0.530053\pi$
$644$	−1.05898e32	−0.528080
$645$	0	0
$646$	5.86067e32	2.82016
$647$	3.77554e32	1.78476	0.892379	−	0.451286i	$-0.149035\pi$
$647$	3.77554e32	1.78476	0.892379	+	0.451286i	$0.149035\pi$
$648$	2.85076e31	0.132388
$649$	−2.56896e29	−0.00117204
$650$	0	0
$651$	2.01920e32	0.889197
$652$	2.02210e32	0.874893
$653$	8.58042e31	0.364760	0.182380	−	0.983228i	$-0.441620\pi$
$653$	8.58042e31	0.364760	0.182380	+	0.983228i	$0.441620\pi$
$654$	8.70816e31	0.363733
$655$	0	0
$656$	−1.05576e32	−0.425766
$657$	1.98290e32	0.785777
$658$	−1.32874e32	−0.517421
$659$	1.46687e32	0.561319	0.280660	−	0.959807i	$-0.409447\pi$
$659$	1.46687e32	0.561319	0.280660	+	0.959807i	$0.409447\pi$
$660$	0	0
$661$	2.02066e32	0.746752	0.373376	−	0.927680i	$-0.378200\pi$
$661$	2.02066e32	0.746752	0.373376	+	0.927680i	$0.378200\pi$
$662$	6.53331e32	2.37283
$663$	3.26672e32	1.16602
$664$	−2.00239e31	−0.0702450
$665$	0	0
$666$	2.82379e32	0.956927
$667$	−7.38823e31	−0.246090
$668$	−1.37358e32	−0.449701
$669$	5.39243e32	1.73534
$670$	0	0
$671$	7.24664e31	0.225334
$672$	−4.16034e32	−1.27169
$673$	−5.34692e32	−1.60668	−0.803341	−	0.595519i	$-0.796947\pi$
$673$	−5.34692e32	−1.60668	−0.803341	+	0.595519i	$0.796947\pi$
$674$	6.59237e32	1.94739
$675$	0	0
$676$	−2.23437e32	−0.637924
$677$	−1.10049e32	−0.308899	−0.154449	−	0.988001i	$-0.549360\pi$
$677$	−1.10049e32	−0.308899	−0.154449	+	0.988001i	$0.549360\pi$
$678$	5.48422e32	1.51347
$679$	−4.33457e32	−1.17610
$680$	0	0
$681$	−8.34995e32	−2.19024
$682$	1.38119e32	0.356233
$683$	2.97297e32	0.753967	0.376983	−	0.926220i	$-0.376961\pi$
$683$	2.97297e32	0.753967	0.376983	+	0.926220i	$0.376961\pi$
$684$	−2.73756e32	−0.682683
$685$	0	0
$686$	6.15577e32	1.48441
$687$	2.48547e32	0.589394
$688$	1.64908e31	0.0384568
$689$	2.74149e32	0.628733
$690$	0	0
$691$	−7.18838e32	−1.59453	−0.797266	−	0.603628i	$-0.793721\pi$
$691$	−7.18838e32	−1.59453	−0.797266	+	0.603628i	$0.793721\pi$
$692$	−8.06062e32	−1.75852
$693$	−5.45574e31	−0.117063
$694$	−5.84723e32	−1.23400
$695$	0	0
$696$	−2.07583e31	−0.0423824
$697$	−3.28039e32	−0.658793
$698$	8.92072e31	0.176223
$699$	8.51274e32	1.65418
$700$	0	0
$701$	−1.02832e33	−1.93362	−0.966810	−	0.255497i	$-0.917761\pi$
$701$	−1.02832e33	−1.93362	−0.966810	+	0.255497i	$0.917761\pi$
$702$	2.09513e32	0.387557
$703$	−7.71990e32	−1.40484
$704$	−1.25123e32	−0.224002
$705$	0	0
$706$	−1.03287e32	−0.178975
$707$	−5.19380e32	−0.885446
$708$	3.06353e30	0.00513854
$709$	−2.50942e32	−0.414134	−0.207067	−	0.978327i	$-0.566392\pi$
$709$	−2.50942e32	−0.414134	−0.207067	+	0.978327i	$0.566392\pi$
$710$	0	0
$711$	5.80796e32	0.927947
$712$	−1.18991e31	−0.0187066
$713$	4.89231e32	0.756805
$714$	−1.39284e33	−2.12017
$715$	0	0
$716$	−7.75346e31	−0.114287
$717$	−4.27071e32	−0.619483
$718$	−1.34209e33	−1.91580
$719$	7.09247e32	0.996358	0.498179	−	0.867074i	$-0.334002\pi$
$719$	7.09247e32	0.996358	0.498179	+	0.867074i	$0.334002\pi$
$720$	0	0
$721$	5.39046e31	0.0733450
$722$	5.23757e32	0.701378
$723$	5.61891e32	0.740562
$724$	−4.00417e32	−0.519420
$725$	0	0
$726$	1.29776e33	1.63088
$727$	−4.63712e32	−0.573591	−0.286795	−	0.957992i	$-0.592590\pi$
$727$	−4.63712e32	−0.573591	−0.286795	+	0.957992i	$0.592590\pi$
$728$	3.55259e31	0.0432547
$729$	−9.21300e31	−0.110417
$730$	0	0
$731$	5.12391e31	0.0595047
$732$	−8.64174e32	−0.987924
$733$	1.54780e33	1.74188	0.870941	−	0.491387i	$-0.163510\pi$
$733$	1.54780e33	1.74188	0.870941	+	0.491387i	$0.163510\pi$
$734$	−6.53317e32	−0.723801
$735$	0	0
$736$	−1.00801e33	−1.08235
$737$	−3.72455e32	−0.393730
$738$	3.19247e32	0.332260
$739$	−1.49249e33	−1.52932	−0.764662	−	0.644431i	$-0.777094\pi$
$739$	−1.49249e33	−1.52932	−0.764662	+	0.644431i	$0.777094\pi$
$740$	0	0
$741$	8.69144e32	0.863341
$742$	−1.16890e33	−1.14322
$743$	−1.19934e32	−0.115497	−0.0577487	−	0.998331i	$-0.518392\pi$
$743$	−1.19934e32	−0.115497	−0.0577487	+	0.998331i	$0.518392\pi$
$744$	1.37456e32	0.130340
$745$	0	0
$746$	−4.15852e32	−0.382334
$747$	4.37852e32	0.396406
$748$	−4.57290e32	−0.407683
$749$	2.29863e32	0.201803
$750$	0	0
$751$	1.42812e33	1.21592	0.607959	−	0.793969i	$-0.291989\pi$
$751$	1.42812e33	1.21592	0.607959	+	0.793969i	$0.291989\pi$
$752$	−6.54101e32	−0.548453
$753$	−8.71877e31	−0.0719967
$754$	−2.96996e32	−0.241535
$755$	0	0
$756$	−4.28763e32	−0.338233
$757$	1.56208e33	1.21367	0.606835	−	0.794828i	$-0.292439\pi$
$757$	1.56208e33	1.21367	0.606835	+	0.794828i	$0.292439\pi$
$758$	2.65967e33	2.03531
$759$	−3.51487e32	−0.264929
$760$	0	0
$761$	1.92115e33	1.40488	0.702439	−	0.711744i	$-0.252094\pi$
$761$	1.92115e33	1.40488	0.702439	+	0.711744i	$0.252094\pi$
$762$	3.62020e33	2.60765
$763$	2.12783e32	0.150975
$764$	2.40114e33	1.67820
$765$	0	0
$766$	−1.19119e33	−0.807886
$767$	−3.65787e30	−0.00244389
$768$	−2.18475e33	−1.43797
$769$	1.22615e33	0.795044	0.397522	−	0.917593i	$-0.369870\pi$
$769$	1.22615e33	0.795044	0.397522	+	0.917593i	$0.369870\pi$
$770$	0	0
$771$	−1.53438e33	−0.965621
$772$	9.92455e32	0.615335
$773$	8.43914e32	0.515507	0.257753	−	0.966211i	$-0.417018\pi$
$773$	8.43914e32	0.515507	0.257753	+	0.966211i	$0.417018\pi$
$774$	−4.98658e31	−0.0300111
$775$	0	0
$776$	−2.95074e32	−0.172394
$777$	1.83470e33	1.05615
$778$	−4.28177e33	−2.42861
$779$	−8.72782e32	−0.487781
$780$	0	0
$781$	1.92768e32	0.104604
$782$	−3.37470e33	−1.80450
$783$	−2.99137e32	−0.157620
$784$	9.67477e32	0.502350
$785$	0	0
$786$	−1.35860e33	−0.685066
$787$	−1.37027e33	−0.680919	−0.340460	−	0.940259i	$-0.610583\pi$
$787$	−1.37027e33	−0.680919	−0.340460	+	0.940259i	$0.610583\pi$
$788$	3.01931e33	1.47862
$789$	7.82797e32	0.377801
$790$	0	0
$791$	1.34007e33	0.628198
$792$	−3.71398e31	−0.0171593
$793$	1.03183e33	0.469857
$794$	−6.72586e31	−0.0301865
$795$	0	0
$796$	−9.72536e32	−0.424039
$797$	−1.57462e33	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$797$	−1.57462e33	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$798$	−3.70579e33	−1.56981
$799$	−2.03238e33	−0.848628
$800$	0	0
$801$	2.60192e32	0.105565
$802$	1.55481e33	0.621832
$803$	8.81269e32	0.347440
$804$	4.44159e33	1.72621
$805$	0	0
$806$	1.96664e33	0.742799
$807$	−2.22215e33	−0.827423
$808$	−3.53567e32	−0.129790
$809$	−2.56942e33	−0.929882	−0.464941	−	0.885342i	$-0.653924\pi$
$809$	−2.56942e33	−0.929882	−0.464941	+	0.885342i	$0.653924\pi$
$810$	0	0
$811$	1.25770e33	0.442423	0.221212	−	0.975226i	$-0.428999\pi$
$811$	1.25770e33	0.442423	0.221212	+	0.975226i	$0.428999\pi$
$812$	6.07794e32	0.210796
$813$	−2.01234e33	−0.688112
$814$	1.25499e33	0.423116
$815$	0	0
$816$	−6.85652e33	−2.24733
$817$	1.36327e32	0.0440583
$818$	2.01023e33	0.640593
$819$	−7.76826e32	−0.244095
$820$	0	0
$821$	−2.38117e32	−0.0727519	−0.0363759	−	0.999338i	$-0.511581\pi$
$821$	−2.38117e32	−0.0727519	−0.0363759	+	0.999338i	$0.511581\pi$
$822$	6.92493e33	2.08636
$823$	−5.82453e33	−1.73047	−0.865233	−	0.501370i	$-0.832830\pi$
$823$	−5.82453e33	−1.73047	−0.865233	+	0.501370i	$0.832830\pi$
$824$	3.66954e31	0.0107510
$825$	0	0
$826$	1.55961e31	0.00444372
$827$	3.61128e33	1.01472	0.507362	−	0.861733i	$-0.330621\pi$
$827$	3.61128e33	1.01472	0.507362	+	0.861733i	$0.330621\pi$
$828$	1.57635e33	0.436821
$829$	6.27935e33	1.71608	0.858040	−	0.513584i	$-0.171682\pi$
$829$	6.27935e33	1.71608	0.858040	+	0.513584i	$0.171682\pi$
$830$	0	0
$831$	5.03467e33	1.33832
$832$	−1.78159e33	−0.467078
$833$	3.00609e33	0.777292
$834$	7.75743e32	0.197837
$835$	0	0
$836$	−1.21667e33	−0.301856
$837$	1.98081e33	0.484731
$838$	6.85832e33	1.65543
$839$	7.51696e32	0.178970	0.0894849	−	0.995988i	$-0.471478\pi$
$839$	7.51696e32	0.178970	0.0894849	+	0.995988i	$0.471478\pi$
$840$	0	0
$841$	−3.89268e33	−0.901767
$842$	−2.39864e33	−0.548120
$843$	−4.82269e33	−1.08711
$844$	4.55478e33	1.01281
$845$	0	0
$846$	1.97791e33	0.428003
$847$	3.17106e33	0.676932
$848$	−5.75412e33	−1.21179
$849$	−8.35275e33	−1.73537
$850$	0	0
$851$	4.44528e33	0.898896
$852$	−2.29879e33	−0.458610
$853$	9.11290e33	1.79367	0.896836	−	0.442364i	$-0.145860\pi$
$853$	9.11290e33	1.79367	0.896836	+	0.442364i	$0.145860\pi$
$854$	−4.39943e33	−0.854339
$855$	0	0
$856$	1.56478e32	0.0295805
$857$	−6.17423e33	−1.15160	−0.575802	−	0.817589i	$-0.695310\pi$
$857$	−6.17423e33	−1.15160	−0.575802	+	0.817589i	$0.695310\pi$
$858$	−1.41293e33	−0.260026
$859$	−1.86175e33	−0.338065	−0.169033	−	0.985610i	$-0.554064\pi$
$859$	−1.86175e33	−0.338065	−0.169033	+	0.985610i	$0.554064\pi$
$860$	0	0
$861$	2.07424e33	0.366710
$862$	7.70552e33	1.34421
$863$	5.22144e33	0.898806	0.449403	−	0.893329i	$-0.351637\pi$
$863$	5.22144e33	0.898806	0.449403	+	0.893329i	$0.351637\pi$
$864$	−4.08125e33	−0.693242
$865$	0	0
$866$	1.07821e34	1.78340
$867$	−1.35479e34	−2.21132
$868$	−4.02466e33	−0.648265
$869$	2.58126e33	0.410302
$870$	0	0
$871$	−5.30328e33	−0.820986
$872$	1.44852e32	0.0221301
$873$	6.45224e33	0.972852
$874$	−8.97874e33	−1.33608
$875$	0	0
$876$	−1.05093e34	−1.52327
$877$	6.73800e32	0.0963908	0.0481954	−	0.998838i	$-0.484653\pi$
$877$	6.73800e32	0.0963908	0.0481954	+	0.998838i	$0.484653\pi$
$878$	8.48127e32	0.119750
$879$	−4.67328e33	−0.651253
$880$	0	0
$881$	1.36978e34	1.85963	0.929815	−	0.368028i	$-0.119967\pi$
$881$	1.36978e34	1.85963	0.929815	+	0.368028i	$0.119967\pi$
$882$	−2.92552e33	−0.392025
$883$	−1.49590e33	−0.197859	−0.0989294	−	0.995094i	$-0.531542\pi$
$883$	−1.49590e33	−0.197859	−0.0989294	+	0.995094i	$0.531542\pi$
$884$	−6.51121e33	−0.850082
$885$	0	0
$886$	3.26378e33	0.415177
$887$	6.44904e33	0.809792	0.404896	−	0.914363i	$-0.367308\pi$
$887$	6.44904e33	0.809792	0.404896	+	0.914363i	$0.367308\pi$
$888$	1.24897e33	0.154811
$889$	8.84592e33	1.08236
$890$	0	0
$891$	−2.77043e33	−0.330334
$892$	−1.07482e34	−1.26514
$893$	−5.40736e33	−0.628339
$894$	−1.72548e33	−0.197938
$895$	0	0
$896$	−1.38819e33	−0.155206
$897$	−5.00472e33	−0.552417
$898$	−1.51254e34	−1.64827
$899$	−2.80791e33	−0.302097
$900$	0	0
$901$	−1.78789e34	−1.87502
$902$	1.41884e33	0.146913
$903$	−3.23993e32	−0.0331227
$904$	9.12246e32	0.0920820
$905$	0	0
$906$	−5.87083e33	−0.577731
$907$	−6.42282e33	−0.624083	−0.312041	−	0.950069i	$-0.601013\pi$
$907$	−6.42282e33	−0.624083	−0.312041	+	0.950069i	$0.601013\pi$
$908$	1.66431e34	1.59679
$909$	7.73126e33	0.732430
$910$	0	0
$911$	−1.48932e34	−1.37571	−0.687855	−	0.725848i	$-0.741447\pi$
$911$	−1.48932e34	−1.37571	−0.687855	+	0.725848i	$0.741447\pi$
$912$	−1.82425e34	−1.66396
$913$	1.94596e33	0.175275
$914$	−8.59859e33	−0.764797
$915$	0	0
$916$	−4.95402e33	−0.429695
$917$	−3.31973e33	−0.284351
$918$	−1.36636e34	−1.15578
$919$	3.10701e33	0.259546	0.129773	−	0.991544i	$-0.458575\pi$
$919$	3.10701e33	0.259546	0.129773	+	0.991544i	$0.458575\pi$
$920$	0	0
$921$	−1.82735e34	−1.48880
$922$	1.91330e34	1.53950
$923$	2.74476e33	0.218115
$924$	2.89151e33	0.226933
$925$	0	0
$926$	3.08285e34	2.36007
$927$	−8.02400e32	−0.0606700
$928$	5.78538e33	0.432046
$929$	1.72846e34	1.27490	0.637452	−	0.770490i	$-0.279988\pi$
$929$	1.72846e34	1.27490	0.637452	+	0.770490i	$0.279988\pi$
$930$	0	0
$931$	7.99801e33	0.575520
$932$	−1.69676e34	−1.20597
$933$	3.49473e32	0.0245343
$934$	1.15624e34	0.801790
$935$	0	0
$936$	−5.28822e32	−0.0357797
$937$	1.61548e34	1.07969	0.539843	−	0.841766i	$-0.318484\pi$
$937$	1.61548e34	1.07969	0.539843	+	0.841766i	$0.318484\pi$
$938$	2.26117e34	1.49280
$939$	−4.40980e33	−0.287584
$940$	0	0
$941$	7.69275e33	0.489554	0.244777	−	0.969579i	$-0.421285\pi$
$941$	7.69275e33	0.489554	0.244777	+	0.969579i	$0.421285\pi$
$942$	2.34160e34	1.47206
$943$	5.02567e33	0.312111
$944$	7.67751e31	0.00471023
$945$	0	0
$946$	−2.21620e32	−0.0132697
$947$	2.94332e34	1.74106	0.870528	−	0.492119i	$-0.163778\pi$
$947$	2.94332e34	1.74106	0.870528	+	0.492119i	$0.163778\pi$
$948$	−3.07819e34	−1.79887
$949$	1.25481e34	0.724465
$950$	0	0
$951$	5.35651e33	0.301860
$952$	−2.31685e33	−0.128995
$953$	−1.97292e34	−1.08528	−0.542641	−	0.839965i	$-0.682575\pi$
$953$	−1.97292e34	−1.08528	−0.542641	+	0.839965i	$0.682575\pi$
$954$	1.73997e34	0.945659
$955$	0	0
$956$	8.51236e33	0.451632
$957$	2.01734e33	0.105753
$958$	2.73973e34	1.41907
$959$	1.69210e34	0.865989
$960$	0	0
$961$	−1.42003e33	−0.0709542
$962$	1.78694e34	0.882261
$963$	−3.42163e33	−0.166929
$964$	−1.11996e34	−0.539904
$965$	0	0
$966$	2.13387e34	1.00446
$967$	2.03266e34	0.945496	0.472748	−	0.881198i	$-0.343262\pi$
$967$	2.03266e34	0.945496	0.472748	+	0.881198i	$0.343262\pi$
$968$	2.15869e33	0.0992255
$969$	−5.66820e34	−2.57467
$970$	0	0
$971$	3.40470e34	1.51028	0.755141	−	0.655563i	$-0.227569\pi$
$971$	3.40470e34	1.51028	0.755141	+	0.655563i	$0.227569\pi$
$972$	2.24494e34	0.984106
$973$	1.89552e33	0.0821166
$974$	−3.45150e33	−0.147768
$975$	0	0
$976$	−2.16570e34	−0.905579
$977$	3.68167e32	0.0152145	0.00760725	−	0.999971i	$-0.497579\pi$
$977$	3.68167e32	0.0152145	0.00760725	+	0.999971i	$0.497579\pi$
$978$	−4.07459e34	−1.66413
$979$	1.15638e33	0.0466767
$980$	0	0
$981$	−3.16740e33	−0.124885
$982$	−2.87225e34	−1.11928
$983$	8.23724e33	0.317261	0.158630	−	0.987338i	$-0.449292\pi$
$983$	8.23724e33	0.317261	0.158630	+	0.987338i	$0.449292\pi$
$984$	1.41203e33	0.0537529
$985$	0	0
$986$	1.93689e34	0.720310
$987$	1.28511e34	0.472380
$988$	−1.73238e34	−0.629415
$989$	−7.85000e32	−0.0281911
$990$	0	0
$991$	2.70349e33	0.0948590	0.0474295	−	0.998875i	$-0.484897\pi$
$991$	2.70349e33	0.0948590	0.0474295	+	0.998875i	$0.484897\pi$
$992$	−3.83094e34	−1.32868
$993$	−6.31875e34	−2.16628
$994$	−1.17029e34	−0.396598
$995$	0	0
$996$	−2.32059e34	−0.768452
$997$	4.64692e33	0.152115	0.0760573	−	0.997103i	$-0.475767\pi$
$997$	4.64692e33	0.152115	0.0760573	+	0.997103i	$0.475767\pi$
$998$	7.14561e34	2.31227
$999$	1.79982e34	0.575740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.24.a.a.1.2		2
5.2	odd	4		25.24.b.a.24.3		4
5.3	odd	4		25.24.b.a.24.2		4
5.4	even	2		1.24.a.a.1.1	✓	2
15.14	odd	2		9.24.a.b.1.2		2
20.19	odd	2		16.24.a.b.1.1		2
35.34	odd	2		49.24.a.b.1.1		2
40.19	odd	2		64.24.a.g.1.2		2
40.29	even	2		64.24.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.24.a.a.1.1	✓	2	5.4	even	2
9.24.a.b.1.2		2	15.14	odd	2
16.24.a.b.1.1		2	20.19	odd	2
25.24.a.a.1.2		2	1.1	even	1	trivial
25.24.b.a.24.2		4	5.3	odd	4
25.24.b.a.24.3		4	5.2	odd	4
49.24.a.b.1.1		2	35.34	odd	2
64.24.a.d.1.1		2	40.29	even	2
64.24.a.g.1.2		2	40.19	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.56013e9 q^{6} -3.81217e9 q^{7} -2.59512e9 q^{8} +5.67462e10 q^{9} +O(q^{10})\)	\(q+4016.35 q^{2} -388445. q^{3} +7.74247e6 q^{4} -1.56013e9 q^{6} -3.81217e9 q^{7} -2.59512e9 q^{8} +5.67462e10 q^{9} +2.52200e11 q^{11} -3.00752e12 q^{12} +3.59099e12 q^{13} -1.53110e13 q^{14} -7.53715e13 q^{16} -2.34190e14 q^{17} +2.27913e14 q^{18} -6.23086e14 q^{19} +1.48082e15 q^{21} +1.01292e15 q^{22} +3.58786e15 q^{23} +1.00806e15 q^{24} +1.44227e16 q^{26} +1.45267e16 q^{27} -2.95156e16 q^{28} -2.05923e16 q^{29} +1.36357e17 q^{31} -2.80949e17 q^{32} -9.79656e16 q^{33} -9.40588e17 q^{34} +4.39356e17 q^{36} +1.23898e18 q^{37} -2.50253e18 q^{38} -1.39490e18 q^{39} +1.40074e18 q^{41} +5.94748e18 q^{42} -2.18793e17 q^{43} +1.95265e18 q^{44} +1.44101e19 q^{46} +8.67836e18 q^{47} +2.92777e19 q^{48} -1.28361e19 q^{49} +9.09698e19 q^{51} +2.78032e19 q^{52} +7.63436e19 q^{53} +5.83441e19 q^{54} +9.89304e18 q^{56} +2.42034e20 q^{57} -8.27059e19 q^{58} -1.01862e18 q^{59} +2.87337e20 q^{61} +5.47658e20 q^{62} -2.16326e20 q^{63} -4.96127e20 q^{64} -3.93464e20 q^{66} -1.47683e21 q^{67} -1.81321e21 q^{68} -1.39369e21 q^{69} +7.64346e20 q^{71} -1.47263e20 q^{72} +3.49433e21 q^{73} +4.97617e21 q^{74} -4.82422e21 q^{76} -9.61427e20 q^{77} -5.60242e21 q^{78} +1.02350e22 q^{79} -1.09851e22 q^{81} +5.62587e21 q^{82} +7.71597e21 q^{83} +1.14652e22 q^{84} -8.78750e20 q^{86} +7.99897e21 q^{87} -6.54489e20 q^{88} +4.58518e21 q^{89} -1.36895e22 q^{91} +2.77789e22 q^{92} -5.29672e22 q^{93} +3.48553e22 q^{94} +1.09133e23 q^{96} +1.13703e23 q^{97} -5.15544e22 q^{98} +1.43114e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 1809673056 q^{6} + 1359184400 q^{7} - 49459023360 q^{8} - 34999394166 q^{9}+O(q^{10}) \) 2 * q - 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 1809673056 * q^6 + 1359184400 * q^7 - 49459023360 * q^8 - 34999394166 * q^9	\( 2 q - 1080 q^{2} - 339480 q^{3} + 25326656 q^{4} - 1809673056 q^{6} + 1359184400 q^{7} - 49459023360 q^{8} - 34999394166 q^{9} + 856801968264 q^{11} - 2146514952960 q^{12} - 4376109322060 q^{13} - 41666034529728 q^{14} + 15956586401792 q^{16} - 254028147597540 q^{17} + 695480683916520 q^{18} + 4260600979960 q^{19} + 17\!\cdots\!44 q^{21}+ \cdots - 41\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 1080 * q^2 - 339480 * q^3 + 25326656 * q^4 - 1809673056 * q^6 + 1359184400 * q^7 - 49459023360 * q^8 - 34999394166 * q^9 + 856801968264 * q^11 - 2146514952960 * q^12 - 4376109322060 * q^13 - 41666034529728 * q^14 + 15956586401792 * q^16 - 254028147597540 * q^17 + 695480683916520 * q^18 + 4260600979960 * q^19 + 1734031637722944 * q^21 - 2068343882177760 * q^22 + 8144713079008560 * q^23 - 1286622315141120 * q^24 + 55025854658735184 * q^26 + 5424634982716560 * q^27 + 61418438819709440 * q^28 + 20818433601623340 * q^29 + 137714017177000384 * q^31 - 353265663781601280 * q^32 - 68361366766001760 * q^33 - 839483655961325328 * q^34 - 1173916300077574848 * q^36 + 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1785011473665029232 * q^39 - 2294435477168314956 * q^41 + 4657011326437397760 * q^42 + 1750760768619855800 * q^43 + 12584088840033038592 * q^44 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 + 33749519399576616960 * q^48 - 13461981704376200814 * q^49 + 89998362845078292144 * q^51 - 112291883783912022400 * q^52 + 140287253401646796420 * q^53 + 104731223417039799360 * q^54 - 232456712054288117760 * q^56 + 272752401448627175520 * q^57 - 293749486923568689360 * q^58 + 280872989971340771880 * q^59 - 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 690775113933935014320 * q^63 - 893690254469352914944 * q^64 - 544338140913651883392 * q^66 - 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 - 1170560672172404223552 * q^69 + 3055033510194143328624 * q^71 + 4152294352103038548480 * q^72 + 8063408253877606149260 * q^73 + 6715344283148807757072 * q^74 + 6207154294513080590080 * q^76 + 2165184764357449665600 * q^77 - 3614293948840808587200 * q^78 + 6244916814559639980640 * q^79 - 2793528580929833975598 * q^81 + 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 15917751907190402476032 * q^84 - 10916288812918999243296 * q^86 + 10026640653837674384880 * q^87 - 28988514668199273707520 * q^88 + 6395093086173070004820 * q^89 - 54890178162704560146016 * q^91 + 107907439017191756981760 * q^92 - 52900811441357852079360 * q^93 + 159400518006534931827072 * q^94 + 105592121669584394256384 * q^96 + 31147288846254030500540 * q^97 - 48364767616374671003640 * q^98 - 41158245132312135981912 * q^99

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