LMFDB - Embedded newform 25.34.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,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, 34, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$172.457072203$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 589050 $ x^2 - x - 589050
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-766.996$ 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)

$f(q)$	$=$	$q+171359. q^{2} -5.34420e7 q^{3} +2.07741e10 q^{4} -9.15779e12 q^{6} -5.50153e13 q^{7} +2.08788e15 q^{8} -2.70301e15 q^{9} +O(q^{10})$	\(q+171359. q^{2} -5.34420e7 q^{3} +2.07741e10 q^{4} -9.15779e12 q^{6} -5.50153e13 q^{7} +2.08788e15 q^{8} -2.70301e15 q^{9} -8.18909e16 q^{11} -1.11021e18 q^{12} +1.90399e18 q^{13} -9.42739e18 q^{14} +1.79329e20 q^{16} +3.33893e20 q^{17} -4.63187e20 q^{18} -1.40494e20 q^{19} +2.94013e21 q^{21} -1.40328e22 q^{22} -3.12767e22 q^{23} -1.11580e23 q^{24} +3.26267e23 q^{26} +4.41542e23 q^{27} -1.14289e24 q^{28} -1.50979e24 q^{29} +5.18762e23 q^{31} +1.27950e25 q^{32} +4.37641e24 q^{33} +5.72158e25 q^{34} -5.61527e25 q^{36} +3.01507e25 q^{37} -2.40749e25 q^{38} -1.01753e26 q^{39} -2.18887e26 q^{41} +5.03818e26 q^{42} -1.76701e27 q^{43} -1.70121e27 q^{44} -5.35955e27 q^{46} -3.25654e27 q^{47} -9.58369e27 q^{48} -4.70431e27 q^{49} -1.78439e28 q^{51} +3.95538e28 q^{52} -9.17652e27 q^{53} +7.56623e28 q^{54} -1.14865e29 q^{56} +7.50826e27 q^{57} -2.58716e29 q^{58} -1.18267e29 q^{59} -9.92930e27 q^{61} +8.88948e28 q^{62} +1.48707e29 q^{63} +6.52116e29 q^{64} +7.49940e29 q^{66} -1.11293e30 q^{67} +6.93634e30 q^{68} +1.67149e30 q^{69} +7.58425e29 q^{71} -5.64355e30 q^{72} +6.06835e30 q^{73} +5.16661e30 q^{74} -2.91863e30 q^{76} +4.50525e30 q^{77} -1.74364e31 q^{78} -5.57890e30 q^{79} -8.57067e30 q^{81} -3.75083e31 q^{82} -4.13746e31 q^{83} +6.10785e31 q^{84} -3.02793e32 q^{86} +8.06860e31 q^{87} -1.70978e32 q^{88} +6.21572e31 q^{89} -1.04749e32 q^{91} -6.49745e32 q^{92} -2.77237e31 q^{93} -5.58039e32 q^{94} -6.83789e32 q^{96} -4.04003e32 q^{97} -8.06129e32 q^{98} +2.21352e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 121680 q^{2} - 37919880 q^{3} + 14652233984 q^{4} - 9928922193216 q^{6} + 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 80\!\cdots\!54 q^{9}+O(q^{10}) $ 2 * q + 121680 * q^2 - 37919880 * q^3 + 14652233984 * q^4 - 9928922193216 * q^6 + 67153080066800 * q^7 + 2818750585098240 * q^8 - 8021136954970854 * q^9	$ 2 q + 121680 q^{2} - 37919880 q^{3} + 14652233984 q^{4} - 9928922193216 q^{6} + 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 92\!\cdots\!28 q^{99}+O(q^{100}) $ 2 * q + 121680 * q^2 - 37919880 * q^3 + 14652233984 * q^4 - 9928922193216 * q^6 + 67153080066800 * q^7 + 2818750585098240 * q^8 - 8021136954970854 * q^9 + 133871815441914264 * q^11 - 1205235433330467840 * q^12 + 2981610478259443940 * q^13 - 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 198985322728543319280 * q^18 - 1360696443041697171800 * q^19 + 4836438843082801141824 * q^21 - 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 100235518588319710003200 * q^24 + 272731683634642092710304 * q^26 + 272704742315639906405040 * q^27 - 1890794991723644827125760 * q^28 - 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 7725507376265263259943840 * q^33 + 69860790536166916073075808 * q^34 - 23595755096197135608576768 * q^36 + 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 - 85026272438019668836783248 * q^39 + 277566613022002182732188244 * q^41 + 409610685367579027895216640 * q^42 - 1567661189367072113768291800 * q^43 - 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 - 9331035686759324258712944640 * q^48 + 2489799365888888933444851314 * q^49 - 21794809591439435388668624496 * q^51 + 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 84050074928235529084016073600 * q^54 - 25575237795171758759822131200 * q^56 - 11431882183748158902465090720 * q^57 - 250532370716581201796821222560 * q^58 - 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 - 500999494400792409792776544720 * q^63 + 864365322360380859973709594624 * q^64 + 583558358556830038058269663488 * q^66 - 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1750848530317427976275742443712 * q^69 - 2669761937956104715736810084976 * q^71 - 9530438520123487645446231060480 * q^72 - 946314321191998870965166536340 * q^73 + 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 18267352963262685465124679337600 * q^78 - 8535199972765636469730106191200 * q^79 + 18372400450705101408694430349042 * q^81 - 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 49469534061147727842067908599808 * q^84 - 312696885737578501917214826406336 * q^86 + 78129025791401437906177732680720 * q^87 - 13282372192867492753038509752320 * q^88 + 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 132607664882695458799488635592960 * q^93 - 450506433888867898835049561530112 * q^94 - 793791282556560211499025092837376 * q^96 + 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * q^98 - 926100695332764780030656940070728 * 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 $

$2$	171359.	1.84890	0.924449	−	0.381305i	$-0.124525\pi$
$2$	171359.	1.84890	0.924449	+	0.381305i	$0.124525\pi$
$3$	−5.34420e7	−0.716774	−0.358387	−	0.933573i	$-0.616673\pi$
$3$	−5.34420e7	−0.716774	−0.358387	+	0.933573i	$0.616673\pi$
$4$	2.07741e10	2.41843
$5$	0	0
$5$	0	0
$6$	−9.15779e12	−1.32524
$7$	−5.50153e13	−0.625699	−0.312850	−	0.949803i	$-0.601284\pi$
$7$	−5.50153e13	−0.625699	−0.312850	+	0.949803i	$0.601284\pi$
$8$	2.08788e15	2.62253
$9$	−2.70301e15	−0.486236
$10$	0	0
$11$	−8.18909e16	−0.537349	−0.268674	−	0.963231i	$-0.586586\pi$
$11$	−8.18909e16	−0.537349	−0.268674	+	0.963231i	$0.586586\pi$
$12$	−1.11021e18	−1.73346
$13$	1.90399e18	0.793597	0.396798	−	0.917906i	$-0.370121\pi$
$13$	1.90399e18	0.793597	0.396798	+	0.917906i	$0.370121\pi$
$14$	−9.42739e18	−1.15685
$15$	0	0
$16$	1.79329e20	2.43036
$17$	3.33893e20	1.66418	0.832090	−	0.554640i	$-0.187144\pi$
$17$	3.33893e20	1.66418	0.832090	+	0.554640i	$0.187144\pi$
$18$	−4.63187e20	−0.899000
$19$	−1.40494e20	−0.111743	−0.0558717	−	0.998438i	$-0.517794\pi$
$19$	−1.40494e20	−0.111743	−0.0558717	+	0.998438i	$0.517794\pi$
$20$	0	0
$21$	2.94013e21	0.448485
$22$	−1.40328e22	−0.993503
$23$	−3.12767e22	−1.06344	−0.531718	−	0.846922i	$-0.678453\pi$
$23$	−3.12767e22	−1.06344	−0.531718	+	0.846922i	$0.678453\pi$
$24$	−1.11580e23	−1.87976
$25$	0	0
$26$	3.26267e23	1.46728
$27$	4.41542e23	1.06529
$28$	−1.14289e24	−1.51321
$29$	−1.50979e24	−1.12034	−0.560168	−	0.828379i	$-0.689264\pi$
$29$	−1.50979e24	−1.12034	−0.560168	+	0.828379i	$0.689264\pi$
$30$	0	0
$31$	5.18762e23	0.128086	0.0640428	−	0.997947i	$-0.479601\pi$
$31$	5.18762e23	0.128086	0.0640428	+	0.997947i	$0.479601\pi$
$32$	1.27950e25	1.87096
$33$	4.37641e24	0.385157
$34$	5.72158e25	3.07690
$35$	0	0
$36$	−5.61527e25	−1.17592
$37$	3.01507e25	0.401762	0.200881	−	0.979616i	$-0.435620\pi$
$37$	3.01507e25	0.401762	0.200881	+	0.979616i	$0.435620\pi$
$38$	−2.40749e25	−0.206602
$39$	−1.01753e26	−0.568829
$40$	0	0
$41$	−2.18887e26	−0.536149	−0.268075	−	0.963398i	$-0.586387\pi$
$41$	−2.18887e26	−0.536149	−0.268075	+	0.963398i	$0.586387\pi$
$42$	5.03818e26	0.829203
$43$	−1.76701e27	−1.97246	−0.986232	−	0.165369i	$-0.947118\pi$
$43$	−1.76701e27	−1.97246	−0.986232	+	0.165369i	$0.947118\pi$
$44$	−1.70121e27	−1.29954
$45$	0	0
$46$	−5.35955e27	−1.96618
$47$	−3.25654e27	−0.837802	−0.418901	−	0.908032i	$-0.637585\pi$
$47$	−3.25654e27	−0.837802	−0.418901	+	0.908032i	$0.637585\pi$
$48$	−9.58369e27	−1.74202
$49$	−4.70431e27	−0.608500
$50$	0	0
$51$	−1.78439e28	−1.19284
$52$	3.95538e28	1.91926
$53$	−9.17652e27	−0.325182	−0.162591	−	0.986694i	$-0.551985\pi$
$53$	−9.17652e27	−0.325182	−0.162591	+	0.986694i	$0.551985\pi$
$54$	7.56623e28	1.96962
$55$	0	0
$56$	−1.14865e29	−1.64091
$57$	7.50826e27	0.0800948
$58$	−2.58716e29	−2.07139
$59$	−1.18267e29	−0.714174	−0.357087	−	0.934071i	$-0.616230\pi$
$59$	−1.18267e29	−0.714174	−0.357087	+	0.934071i	$0.616230\pi$
$60$	0	0
$61$	−9.92930e27	−0.0345920	−0.0172960	−	0.999850i	$-0.505506\pi$
$61$	−9.92930e27	−0.0345920	−0.0172960	+	0.999850i	$0.505506\pi$
$62$	8.88948e28	0.236817
$63$	1.48707e29	0.304237
$64$	6.52116e29	1.02886
$65$	0	0
$66$	7.49940e29	0.712117
$67$	−1.11293e30	−0.824583	−0.412291	−	0.911052i	$-0.635271\pi$
$67$	−1.11293e30	−0.824583	−0.412291	+	0.911052i	$0.635271\pi$
$68$	6.93634e30	4.02470
$69$	1.67149e30	0.762242
$70$	0	0
$71$	7.58425e29	0.215849	0.107924	−	0.994159i	$-0.465580\pi$
$71$	7.58425e29	0.215849	0.107924	+	0.994159i	$0.465580\pi$
$72$	−5.64355e30	−1.27517
$73$	6.06835e30	1.09205	0.546026	−	0.837768i	$-0.316140\pi$
$73$	6.06835e30	1.09205	0.546026	+	0.837768i	$0.316140\pi$
$74$	5.16661e30	0.742818
$75$	0	0
$76$	−2.91863e30	−0.270243
$77$	4.50525e30	0.336219
$78$	−1.74364e31	−1.05171
$79$	−5.57890e30	−0.272711	−0.136355	−	0.990660i	$-0.543539\pi$
$79$	−5.57890e30	−0.272711	−0.136355	+	0.990660i	$0.543539\pi$
$80$	0	0
$81$	−8.57067e30	−0.277339
$82$	−3.75083e31	−0.991286
$83$	−4.13746e31	−0.895252	−0.447626	−	0.894221i	$-0.647730\pi$
$83$	−4.13746e31	−0.895252	−0.447626	+	0.894221i	$0.647730\pi$
$84$	6.10785e31	1.08463
$85$	0	0
$86$	−3.02793e32	−3.64688
$87$	8.06860e31	0.803028
$88$	−1.70978e32	−1.40921
$89$	6.21572e31	0.425164	0.212582	−	0.977143i	$-0.431813\pi$
$89$	6.21572e31	0.425164	0.212582	+	0.977143i	$0.431813\pi$
$90$	0	0
$91$	−1.04749e32	−0.496553
$92$	−6.49745e32	−2.57184
$93$	−2.77237e31	−0.0918084
$94$	−5.58039e32	−1.54901
$95$	0	0
$96$	−6.83789e32	−1.34106
$97$	−4.04003e32	−0.667808	−0.333904	−	0.942607i	$-0.608366\pi$
$97$	−4.04003e32	−0.667808	−0.333904	+	0.942607i	$0.608366\pi$
$98$	−8.06129e32	−1.12506
$99$	2.21352e32	0.261278
$100$	0	0
$101$	−1.20576e33	−1.02319	−0.511596	−	0.859226i	$-0.670946\pi$
$101$	−1.20576e33	−1.02319	−0.511596	+	0.859226i	$0.670946\pi$
$102$	−3.05773e33	−2.20544
$103$	1.69378e33	1.04002	0.520011	−	0.854159i	$-0.325928\pi$
$103$	1.69378e33	1.04002	0.520011	+	0.854159i	$0.325928\pi$
$104$	3.97530e33	2.08123
$105$	0	0
$106$	−1.57248e33	−0.601228
$107$	−7.07121e32	−0.231559	−0.115780	−	0.993275i	$-0.536937\pi$
$107$	−7.07121e32	−0.231559	−0.115780	+	0.993275i	$0.536937\pi$
$108$	9.17264e33	2.57634
$109$	4.42814e33	1.06828	0.534139	−	0.845397i	$-0.320636\pi$
$109$	4.42814e33	1.06828	0.534139	+	0.845397i	$0.320636\pi$
$110$	0	0
$111$	−1.61131e33	−0.287973
$112$	−9.86582e33	−1.52067
$113$	−1.36496e34	−1.81687	−0.908437	−	0.418023i	$-0.862723\pi$
$113$	−1.36496e34	−1.81687	−0.908437	+	0.418023i	$0.862723\pi$
$114$	1.28661e33	0.148087
$115$	0	0
$116$	−3.13645e34	−2.70945
$117$	−5.14652e33	−0.385875
$118$	−2.02661e34	−1.32043
$119$	−1.83692e34	−1.04128
$120$	0	0
$121$	−1.65190e34	−0.711256
$122$	−1.70148e33	−0.0639572
$123$	1.16977e34	0.384298
$124$	1.07768e34	0.309766
$125$	0	0
$126$	2.54823e34	0.562504
$127$	7.12185e34	1.37985	0.689925	−	0.723881i	$-0.257644\pi$
$127$	7.12185e34	1.37985	0.689925	+	0.723881i	$0.257644\pi$
$128$	1.83832e33	0.0312936
$129$	9.44324e34	1.41381
$130$	0	0
$131$	−2.95217e34	−0.342898	−0.171449	−	0.985193i	$-0.554845\pi$
$131$	−2.95217e34	−0.342898	−0.171449	+	0.985193i	$0.554845\pi$
$132$	9.09161e34	0.931475
$133$	7.72929e33	0.0699178
$134$	−1.90711e35	−1.52457
$135$	0	0
$136$	6.97128e35	4.36436
$137$	−8.90834e34	−0.494205	−0.247103	−	0.968989i	$-0.579479\pi$
$137$	−8.90834e34	−0.494205	−0.247103	+	0.968989i	$0.579479\pi$
$138$	2.86425e35	1.40931
$139$	−3.61707e35	−1.57984	−0.789920	−	0.613210i	$-0.789878\pi$
$139$	−3.61707e35	−1.57984	−0.789920	+	0.613210i	$0.789878\pi$
$140$	0	0
$141$	1.74036e35	0.600515
$142$	1.29963e35	0.399083
$143$	−1.55920e35	−0.426438
$144$	−4.84728e35	−1.18173
$145$	0	0
$146$	1.03987e36	2.01909
$147$	2.51408e35	0.436157
$148$	6.26354e35	0.971632
$149$	1.73500e35	0.240839	0.120419	−	0.992723i	$-0.461576\pi$
$149$	1.73500e35	0.240839	0.120419	+	0.992723i	$0.461576\pi$
$150$	0	0
$151$	−1.35744e36	−1.51217	−0.756085	−	0.654473i	$-0.772891\pi$
$151$	−1.35744e36	−1.51217	−0.756085	+	0.654473i	$0.772891\pi$
$152$	−2.93333e35	−0.293050
$153$	−9.02518e35	−0.809184
$154$	7.72017e35	0.621634
$155$	0	0
$156$	−2.11383e36	−1.37567
$157$	2.78049e36	1.62846	0.814229	−	0.580543i	$-0.197160\pi$
$157$	2.78049e36	1.62846	0.814229	+	0.580543i	$0.197160\pi$
$158$	−9.55998e35	−0.504214
$159$	4.90411e35	0.233082
$160$	0	0
$161$	1.72069e36	0.665390
$162$	−1.46866e36	−0.512773
$163$	−2.81381e36	−0.887565	−0.443782	−	0.896135i	$-0.646364\pi$
$163$	−2.81381e36	−0.887565	−0.443782	+	0.896135i	$0.646364\pi$
$164$	−4.54718e36	−1.29664
$165$	0	0
$166$	−7.08993e36	−1.65523
$167$	−6.77893e36	−1.43331	−0.716653	−	0.697430i	$-0.754327\pi$
$167$	−6.77893e36	−1.43331	−0.716653	+	0.697430i	$0.754327\pi$
$168$	6.13862e36	1.17616
$169$	−2.13094e36	−0.370204
$170$	0	0
$171$	3.79756e35	0.0543336
$172$	−3.67080e37	−4.77026
$173$	1.42570e37	1.68370	0.841852	−	0.539708i	$-0.181465\pi$
$173$	1.42570e37	1.68370	0.841852	+	0.539708i	$0.181465\pi$
$174$	1.38263e37	1.48472
$175$	0	0
$176$	−1.46854e37	−1.30595
$177$	6.32040e36	0.511901
$178$	1.06512e37	0.786085
$179$	7.37934e36	0.496527	0.248263	−	0.968693i	$-0.420140\pi$
$179$	7.37934e36	0.496527	0.248263	+	0.968693i	$0.420140\pi$
$180$	0	0
$181$	2.39313e36	0.134051	0.0670254	−	0.997751i	$-0.478649\pi$
$181$	2.39313e36	0.134051	0.0670254	+	0.997751i	$0.478649\pi$
$182$	−1.79497e37	−0.918076
$183$	5.30642e35	0.0247947
$184$	−6.53018e37	−2.78889
$185$	0	0
$186$	−4.75072e36	−0.169744
$187$	−2.73428e37	−0.894245
$188$	−6.76517e37	−2.02616
$189$	−2.42915e37	−0.666554
$190$	0	0
$191$	−6.98026e35	−0.0160998	−0.00804991	−	0.999968i	$-0.502562\pi$
$191$	−6.98026e35	−0.0160998	−0.00804991	+	0.999968i	$0.502562\pi$
$192$	−3.48504e37	−0.737458
$193$	−6.67098e36	−0.129567	−0.0647835	−	0.997899i	$-0.520636\pi$
$193$	−6.67098e36	−0.129567	−0.0647835	+	0.997899i	$0.520636\pi$
$194$	−6.92298e37	−1.23471
$195$	0	0
$196$	−9.77280e37	−1.47161
$197$	8.89563e37	1.23164	0.615821	−	0.787886i	$-0.288825\pi$
$197$	8.89563e37	1.23164	0.615821	+	0.787886i	$0.288825\pi$
$198$	3.79308e37	0.483077
$199$	1.05106e38	1.23183	0.615916	−	0.787812i	$-0.288786\pi$
$199$	1.05106e38	1.23183	0.615916	+	0.787812i	$0.288786\pi$
$200$	0	0
$201$	5.94773e37	0.591039
$202$	−2.06618e38	−1.89178
$203$	8.30613e37	0.700994
$204$	−3.70692e38	−2.88480
$205$	0	0
$206$	2.90245e38	1.92290
$207$	8.45412e37	0.517080
$208$	3.41441e38	1.92873
$209$	1.15051e37	0.0600452
$210$	0	0
$211$	−5.59870e37	−0.249705	−0.124852	−	0.992175i	$-0.539846\pi$
$211$	−5.59870e37	−0.249705	−0.124852	+	0.992175i	$0.539846\pi$
$212$	−1.90634e38	−0.786428
$213$	−4.05318e37	−0.154715
$214$	−1.21172e38	−0.428129
$215$	0	0
$216$	9.21884e38	2.79376
$217$	−2.85398e37	−0.0801431
$218$	7.58804e38	1.97514
$219$	−3.24305e38	−0.782755
$220$	0	0
$221$	6.35730e38	1.32069
$222$	−2.76114e38	−0.532432
$223$	−4.65676e38	−0.833784	−0.416892	−	0.908956i	$-0.636881\pi$
$223$	−4.65676e38	−0.833784	−0.416892	+	0.908956i	$0.636881\pi$
$224$	−7.03919e38	−1.17066
$225$	0	0
$226$	−2.33898e39	−3.35921
$227$	2.61802e38	0.349580	0.174790	−	0.984606i	$-0.444075\pi$
$227$	2.61802e38	0.349580	0.174790	+	0.984606i	$0.444075\pi$
$228$	1.55977e38	0.193703
$229$	9.20963e38	1.06404	0.532018	−	0.846733i	$-0.321434\pi$
$229$	9.20963e38	1.06404	0.532018	+	0.846733i	$0.321434\pi$
$230$	0	0
$231$	−2.40770e38	−0.240993
$232$	−3.15225e39	−2.93811
$233$	−7.13755e37	−0.0619693	−0.0309847	−	0.999520i	$-0.509864\pi$
$233$	−7.13755e37	−0.0619693	−0.0309847	+	0.999520i	$0.509864\pi$
$234$	−8.81904e38	−0.713444
$235$	0	0
$236$	−2.45688e39	−1.72718
$237$	2.98148e38	0.195472
$238$	−3.14774e39	−1.92522
$239$	−1.83178e39	−1.04546	−0.522731	−	0.852498i	$-0.675087\pi$
$239$	−1.83178e39	−1.04546	−0.522731	+	0.852498i	$0.675087\pi$
$240$	0	0
$241$	−3.05313e39	−1.51867	−0.759336	−	0.650698i	$-0.774476\pi$
$241$	−3.05313e39	−1.51867	−0.759336	+	0.650698i	$0.774476\pi$
$242$	−2.83069e39	−1.31504
$243$	−1.99652e39	−0.866505
$244$	−2.06272e38	−0.0836583
$245$	0	0
$246$	2.00452e39	0.710527
$247$	−2.67499e38	−0.0886793
$248$	1.08311e39	0.335908
$249$	2.21114e39	0.641693
$250$	0	0
$251$	3.03407e39	0.771631	0.385815	−	0.922576i	$-0.373920\pi$
$251$	3.03407e39	0.771631	0.385815	+	0.922576i	$0.373920\pi$
$252$	3.08926e39	0.735775
$253$	2.56127e39	0.571435
$254$	1.22040e40	2.55120
$255$	0	0
$256$	−5.28662e39	−0.970999
$257$	2.91186e39	0.501503	0.250752	−	0.968051i	$-0.419322\pi$
$257$	2.91186e39	0.501503	0.250752	+	0.968051i	$0.419322\pi$
$258$	1.61819e40	2.61399
$259$	−1.65875e39	−0.251382
$260$	0	0
$261$	4.08097e39	0.544748
$262$	−5.05883e39	−0.633984
$263$	5.62907e39	0.662471	0.331236	−	0.943548i	$-0.392534\pi$
$263$	5.62907e39	0.662471	0.331236	+	0.943548i	$0.392534\pi$
$264$	9.13740e39	1.01009
$265$	0	0
$266$	1.32449e39	0.129271
$267$	−3.32180e39	−0.304746
$268$	−2.31202e40	−1.99419
$269$	−9.77080e39	−0.792533	−0.396266	−	0.918136i	$-0.629694\pi$
$269$	−9.77080e39	−0.792533	−0.396266	+	0.918136i	$0.629694\pi$
$270$	0	0
$271$	2.38779e40	1.71397	0.856985	−	0.515342i	$-0.172335\pi$
$271$	2.38779e40	1.71397	0.856985	+	0.515342i	$0.172335\pi$
$272$	5.98767e40	4.04456
$273$	5.59798e39	0.355916
$274$	−1.52653e40	−0.913736
$275$	0	0
$276$	3.47237e40	1.84343
$277$	1.39835e40	0.699358	0.349679	−	0.936870i	$-0.386291\pi$
$277$	1.39835e40	0.699358	0.349679	+	0.936870i	$0.386291\pi$
$278$	−6.19820e40	−2.92096
$279$	−1.40222e39	−0.0622798
$280$	0	0
$281$	−2.89927e40	−1.14455	−0.572274	−	0.820062i	$-0.693939\pi$
$281$	−2.89927e40	−1.14455	−0.572274	+	0.820062i	$0.693939\pi$
$282$	2.98227e40	1.11029
$283$	1.50945e40	0.530081	0.265040	−	0.964237i	$-0.414615\pi$
$283$	1.50945e40	0.530081	0.265040	+	0.964237i	$0.414615\pi$
$284$	1.57556e40	0.522015
$285$	0	0
$286$	−2.67183e40	−0.788441
$287$	1.20421e40	0.335468
$288$	−3.45850e40	−0.909728
$289$	7.12303e40	1.76950
$290$	0	0
$291$	2.15907e40	0.478667
$292$	1.26065e41	2.64105
$293$	1.40305e40	0.277816	0.138908	−	0.990305i	$-0.455641\pi$
$293$	1.40305e40	0.277816	0.138908	+	0.990305i	$0.455641\pi$
$294$	4.30811e40	0.806410
$295$	0	0
$296$	6.29509e40	1.05363
$297$	−3.61582e40	−0.572435
$298$	2.97309e40	0.445286
$299$	−5.95505e40	−0.843939
$300$	0	0
$301$	9.72124e40	1.23417
$302$	−2.32610e41	−2.79585
$303$	6.44381e40	0.733398
$304$	−2.51945e40	−0.271577
$305$	0	0
$306$	−1.54655e41	−1.49610
$307$	2.92194e40	0.267848	0.133924	−	0.990992i	$-0.457242\pi$
$307$	2.92194e40	0.267848	0.133924	+	0.990992i	$0.457242\pi$
$308$	9.35926e40	0.813120
$309$	−9.05190e40	−0.745461
$310$	0	0
$311$	−2.24927e41	−1.66531	−0.832653	−	0.553794i	$-0.813179\pi$
$311$	−2.24927e41	−1.66531	−0.832653	+	0.553794i	$0.813179\pi$
$312$	−2.12448e41	−1.49177
$313$	−1.17836e41	−0.784868	−0.392434	−	0.919780i	$-0.628367\pi$
$313$	−1.17836e41	−0.784868	−0.392434	+	0.919780i	$0.628367\pi$
$314$	4.76463e41	3.01086
$315$	0	0
$316$	−1.15897e41	−0.659530
$317$	9.02704e40	0.487604	0.243802	−	0.969825i	$-0.421605\pi$
$317$	9.02704e40	0.487604	0.243802	+	0.969825i	$0.421605\pi$
$318$	8.40366e40	0.430944
$319$	1.23638e41	0.602012
$320$	0	0
$321$	3.77900e40	0.165975
$322$	2.94857e41	1.23024
$323$	−4.69099e40	−0.185961
$324$	−1.78048e41	−0.670725
$325$	0	0
$326$	−4.82174e41	−1.64102
$327$	−2.36649e41	−0.765714
$328$	−4.57008e41	−1.40607
$329$	1.79159e41	0.524212
$330$	0	0
$331$	−2.91394e41	−0.771469	−0.385734	−	0.922610i	$-0.626052\pi$
$331$	−2.91394e41	−0.771469	−0.385734	+	0.922610i	$0.626052\pi$
$332$	−8.59521e41	−2.16510
$333$	−8.14977e40	−0.195351
$334$	−1.16163e42	−2.65004
$335$	0	0
$336$	5.27249e41	1.08998
$337$	5.69474e41	1.12094	0.560468	−	0.828176i	$-0.310621\pi$
$337$	5.69474e41	1.12094	0.560468	+	0.828176i	$0.310621\pi$
$338$	−3.65157e41	−0.684470
$339$	7.29460e41	1.30229
$340$	0	0
$341$	−4.24819e40	−0.0688266
$342$	6.50748e40	0.100457
$343$	6.84132e41	1.00644
$344$	−3.68929e42	−5.17284
$345$	0	0
$346$	2.44306e42	3.11300
$347$	−4.85020e41	−0.589283	−0.294641	−	0.955608i	$-0.595200\pi$
$347$	−4.85020e41	−0.589283	−0.294641	+	0.955608i	$0.595200\pi$
$348$	1.67618e42	1.94206
$349$	5.38533e41	0.595104	0.297552	−	0.954706i	$-0.403830\pi$
$349$	5.38533e41	0.595104	0.297552	+	0.954706i	$0.403830\pi$
$350$	0	0
$351$	8.40692e41	0.845414
$352$	−1.04779e42	−1.00536
$353$	9.77578e41	0.895094	0.447547	−	0.894260i	$-0.352298\pi$
$353$	9.77578e41	0.895094	0.447547	+	0.894260i	$0.352298\pi$
$354$	1.08306e42	0.946453
$355$	0	0
$356$	1.29126e42	1.02823
$357$	9.81689e41	0.746360
$358$	1.26452e42	0.918027
$359$	1.18143e42	0.819124	0.409562	−	0.912282i	$-0.365682\pi$
$359$	1.18143e42	0.819124	0.409562	+	0.912282i	$0.365682\pi$
$360$	0	0
$361$	−1.56103e42	−0.987513
$362$	4.10085e41	0.247846
$363$	8.82811e41	0.509810
$364$	−2.17606e42	−1.20088
$365$	0	0
$366$	9.09304e40	0.0458428
$367$	−7.16875e41	−0.345504	−0.172752	−	0.984965i	$-0.555266\pi$
$367$	−7.16875e41	−0.345504	−0.172752	+	0.984965i	$0.555266\pi$
$368$	−5.60881e42	−2.58453
$369$	5.91654e41	0.260695
$370$	0	0
$371$	5.04849e41	0.203466
$372$	−5.75935e41	−0.222032
$373$	6.80691e41	0.251047	0.125523	−	0.992091i	$-0.459939\pi$
$373$	6.80691e41	0.251047	0.125523	+	0.992091i	$0.459939\pi$
$374$	−4.68545e42	−1.65337
$375$	0	0
$376$	−6.79925e42	−2.19716
$377$	−2.87462e42	−0.889096
$378$	−4.16258e42	−1.23239
$379$	5.14200e42	1.45742	0.728711	−	0.684821i	$-0.240120\pi$
$379$	5.14200e42	1.45742	0.728711	+	0.684821i	$0.240120\pi$
$380$	0	0
$381$	−3.80606e42	−0.989040
$382$	−1.19613e41	−0.0297669
$383$	6.82496e42	1.62675	0.813375	−	0.581740i	$-0.197628\pi$
$383$	6.82496e42	1.62675	0.813375	+	0.581740i	$0.197628\pi$
$384$	−9.82434e40	−0.0224305
$385$	0	0
$386$	−1.14314e42	−0.239556
$387$	4.77624e42	0.959082
$388$	−8.39281e42	−1.61504
$389$	3.03602e42	0.559933	0.279966	−	0.960010i	$-0.409677\pi$
$389$	3.03602e42	0.559933	0.279966	+	0.960010i	$0.409677\pi$
$390$	0	0
$391$	−1.04431e43	−1.76975
$392$	−9.82202e42	−1.59581
$393$	1.57770e42	0.245781
$394$	1.52435e43	2.27718
$395$	0	0
$396$	4.59839e42	0.631882
$397$	−8.54761e42	−1.12668	−0.563341	−	0.826225i	$-0.690484\pi$
$397$	−8.54761e42	−1.12668	−0.563341	+	0.826225i	$0.690484\pi$
$398$	1.80109e43	2.27753
$399$	−4.13069e41	−0.0501152
$400$	0	0
$401$	4.64638e42	0.519078	0.259539	−	0.965733i	$-0.416429\pi$
$401$	4.64638e42	0.519078	0.259539	+	0.965733i	$0.416429\pi$
$402$	1.01920e43	1.09277
$403$	9.87719e41	0.101648
$404$	−2.50486e43	−2.47452
$405$	0	0
$406$	1.42333e43	1.29607
$407$	−2.46907e42	−0.215886
$408$	−3.72559e43	−3.12826
$409$	1.73477e43	1.39897	0.699483	−	0.714649i	$-0.253414\pi$
$409$	1.73477e43	1.39897	0.699483	+	0.714649i	$0.253414\pi$
$410$	0	0
$411$	4.76080e42	0.354233
$412$	3.51868e43	2.51522
$413$	6.50647e42	0.446858
$414$	1.44869e43	0.956028
$415$	0	0
$416$	2.43615e43	1.48479
$417$	1.93304e43	1.13239
$418$	1.97151e42	0.111017
$419$	1.59552e43	0.863717	0.431858	−	0.901941i	$-0.357858\pi$
$419$	1.59552e43	0.863717	0.431858	+	0.901941i	$0.357858\pi$
$420$	0	0
$421$	−2.07154e43	−1.03667	−0.518333	−	0.855179i	$-0.673447\pi$
$421$	−2.07154e43	−1.03667	−0.518333	+	0.855179i	$0.673447\pi$
$422$	−9.59390e42	−0.461679
$423$	8.80247e42	0.407369
$424$	−1.91594e43	−0.852797
$425$	0	0
$426$	−6.94550e42	−0.286052
$427$	5.46263e41	0.0216442
$428$	−1.46898e43	−0.560008
$429$	8.33266e42	0.305660
$430$	0	0
$431$	−2.15255e43	−0.731272	−0.365636	−	0.930758i	$-0.619149\pi$
$431$	−2.15255e43	−0.731272	−0.365636	+	0.930758i	$0.619149\pi$
$432$	7.91812e43	2.58905
$433$	2.62411e43	0.825908	0.412954	−	0.910752i	$-0.364497\pi$
$433$	2.62411e43	0.825908	0.412954	+	0.910752i	$0.364497\pi$
$434$	−4.89057e42	−0.148176
$435$	0	0
$436$	9.19908e43	2.58355
$437$	4.39417e42	0.118832
$438$	−5.55727e43	−1.44723
$439$	1.50091e43	0.376434	0.188217	−	0.982127i	$-0.439729\pi$
$439$	1.50091e43	0.376434	0.188217	+	0.982127i	$0.439729\pi$
$440$	0	0
$441$	1.27158e43	0.295875
$442$	1.08938e44	2.44182
$443$	−1.03686e43	−0.223902	−0.111951	−	0.993714i	$-0.535710\pi$
$443$	−1.03686e43	−0.223902	−0.111951	+	0.993714i	$0.535710\pi$
$444$	−3.34736e43	−0.696440
$445$	0	0
$446$	−7.97979e43	−1.54158
$447$	−9.27219e42	−0.172627
$448$	−3.58764e43	−0.643756
$449$	−3.05007e42	−0.0527528	−0.0263764	−	0.999652i	$-0.508397\pi$
$449$	−3.05007e42	−0.0527528	−0.0263764	+	0.999652i	$0.508397\pi$
$450$	0	0
$451$	1.79248e43	0.288099
$452$	−2.83558e44	−4.39397
$453$	7.25443e43	1.08388
$454$	4.48623e43	0.646338
$455$	0	0
$456$	1.56763e43	0.210051
$457$	8.15124e43	1.05343	0.526716	−	0.850042i	$-0.323423\pi$
$457$	8.15124e43	1.05343	0.526716	+	0.850042i	$0.323423\pi$
$458$	1.57816e44	1.96730
$459$	1.47428e44	1.77284
$460$	0	0
$461$	9.49311e43	1.06253	0.531267	−	0.847204i	$-0.321716\pi$
$461$	9.49311e43	1.06253	0.531267	+	0.847204i	$0.321716\pi$
$462$	−4.12581e43	−0.445571
$463$	6.84730e43	0.713564	0.356782	−	0.934188i	$-0.383874\pi$
$463$	6.84730e43	0.713564	0.356782	+	0.934188i	$0.383874\pi$
$464$	−2.70748e44	−2.72282
$465$	0	0
$466$	−1.22309e43	−0.114575
$467$	−1.13867e44	−1.02961	−0.514803	−	0.857308i	$-0.672135\pi$
$467$	−1.13867e44	−1.02961	−0.514803	+	0.857308i	$0.672135\pi$
$468$	−1.06914e44	−0.933210
$469$	6.12282e43	0.515941
$470$	0	0
$471$	−1.48595e44	−1.16724
$472$	−2.46926e44	−1.87294
$473$	1.44702e44	1.05990
$474$	5.10904e43	0.361407
$475$	0	0
$476$	−3.81605e44	−2.51825
$477$	2.48042e43	0.158115
$478$	−3.13893e44	−1.93295
$479$	−2.43710e44	−1.44990	−0.724948	−	0.688804i	$-0.758136\pi$
$479$	−2.43710e44	−1.44990	−0.724948	+	0.688804i	$0.758136\pi$
$480$	0	0
$481$	5.74067e43	0.318837
$482$	−5.23183e44	−2.80787
$483$	−9.19573e43	−0.476934
$484$	−3.43169e44	−1.72012
$485$	0	0
$486$	−3.42123e44	−1.60208
$487$	1.55812e44	0.705300	0.352650	−	0.935755i	$-0.385281\pi$
$487$	1.55812e44	0.705300	0.352650	+	0.935755i	$0.385281\pi$
$488$	−2.07311e43	−0.0907185
$489$	1.50376e44	0.636183
$490$	0	0
$491$	−2.64492e43	−0.104609	−0.0523044	−	0.998631i	$-0.516657\pi$
$491$	−2.64492e43	−0.104609	−0.0523044	+	0.998631i	$0.516657\pi$
$492$	2.43010e44	0.929396
$493$	−5.04108e44	−1.86444
$494$	−4.58384e43	−0.163959
$495$	0	0
$496$	9.30290e43	0.311294
$497$	−4.17250e43	−0.135057
$498$	3.78900e44	1.18643
$499$	3.31565e44	1.00441	0.502203	−	0.864750i	$-0.332523\pi$
$499$	3.31565e44	1.00441	0.502203	+	0.864750i	$0.332523\pi$
$500$	0	0
$501$	3.62279e44	1.02736
$502$	5.19917e44	1.42667
$503$	4.39485e44	1.16700	0.583502	−	0.812112i	$-0.301682\pi$
$503$	4.39485e44	1.16700	0.583502	+	0.812112i	$0.301682\pi$
$504$	3.10482e44	0.797870
$505$	0	0
$506$	4.38898e44	1.05653
$507$	1.13882e44	0.265352
$508$	1.47950e45	3.33706
$509$	−7.37330e44	−1.60997	−0.804986	−	0.593294i	$-0.797827\pi$
$509$	−7.37330e44	−1.60997	−0.804986	+	0.593294i	$0.797827\pi$
$510$	0	0
$511$	−3.33852e44	−0.683296
$512$	−9.21704e44	−1.82657
$513$	−6.20338e43	−0.119040
$514$	4.98975e44	0.927229
$515$	0	0
$516$	1.96175e45	3.41919
$517$	2.66681e44	0.450192
$518$	−2.84242e44	−0.464780
$519$	−7.61920e44	−1.20684
$520$	0	0
$521$	1.67201e43	0.0248552	0.0124276	−	0.999923i	$-0.496044\pi$
$521$	1.67201e43	0.0248552	0.0124276	+	0.999923i	$0.496044\pi$
$522$	6.99313e44	1.00718
$523$	−1.06261e45	−1.48284	−0.741420	−	0.671041i	$-0.765847\pi$
$523$	−1.06261e45	−1.48284	−0.741420	+	0.671041i	$0.765847\pi$
$524$	−6.13288e44	−0.829275
$525$	0	0
$526$	9.64595e44	1.22484
$527$	1.73211e44	0.213158
$528$	7.84817e44	0.936071
$529$	1.13224e44	0.130894
$530$	0	0
$531$	3.19676e44	0.347257
$532$	1.60569e44	0.169091
$533$	−4.16759e44	−0.425486
$534$	−5.69223e44	−0.563445
$535$	0	0
$536$	−2.32366e45	−2.16249
$537$	−3.94367e44	−0.355897
$538$	−1.67432e45	−1.46531
$539$	3.85240e44	0.326977
$540$	0	0
$541$	−1.73107e45	−1.38217	−0.691084	−	0.722774i	$-0.742867\pi$
$541$	−1.73107e45	−1.38217	−0.691084	+	0.722774i	$0.742867\pi$
$542$	4.09171e45	3.16896
$543$	−1.27894e44	−0.0960841
$544$	4.27216e45	3.11362
$545$	0	0
$546$	9.59267e44	0.658053
$547$	−1.88809e45	−1.25670	−0.628350	−	0.777931i	$-0.716269\pi$
$547$	−1.88809e45	−1.25670	−0.628350	+	0.777931i	$0.716269\pi$
$548$	−1.85063e45	−1.19520
$549$	2.68390e43	0.0168199
$550$	0	0
$551$	2.12115e44	0.125190
$552$	3.48986e45	1.99900
$553$	3.06925e44	0.170635
$554$	2.39620e45	1.29304
$555$	0	0
$556$	−7.51415e45	−3.82073
$557$	−1.82254e45	−0.899636	−0.449818	−	0.893120i	$-0.648511\pi$
$557$	−1.82254e45	−0.899636	−0.449818	+	0.893120i	$0.648511\pi$
$558$	−2.40284e44	−0.115149
$559$	−3.36437e45	−1.56534
$560$	0	0
$561$	1.46125e45	0.640972
$562$	−4.96817e45	−2.11615
$563$	−3.54966e45	−1.46824	−0.734122	−	0.679018i	$-0.762406\pi$
$563$	−3.54966e45	−1.46824	−0.734122	+	0.679018i	$0.762406\pi$
$564$	3.61544e45	1.45230
$565$	0	0
$566$	2.58658e45	0.980066
$567$	4.71517e44	0.173531
$568$	1.58350e45	0.566070
$569$	−3.23817e45	−1.12447	−0.562234	−	0.826978i	$-0.690058\pi$
$569$	−3.23817e45	−1.12447	−0.562234	+	0.826978i	$0.690058\pi$
$570$	0	0
$571$	1.75221e45	0.574237	0.287118	−	0.957895i	$-0.407303\pi$
$571$	1.75221e45	0.574237	0.287118	+	0.957895i	$0.407303\pi$
$572$	−3.23909e45	−1.03131
$573$	3.73039e43	0.0115399
$574$	2.06353e45	0.620247
$575$	0	0
$576$	−1.76268e45	−0.500267
$577$	2.22828e45	0.614566	0.307283	−	0.951618i	$-0.400580\pi$
$577$	2.22828e45	0.614566	0.307283	+	0.951618i	$0.400580\pi$
$578$	1.22060e46	3.27162
$579$	3.56511e44	0.0928702
$580$	0	0
$581$	2.27624e45	0.560159
$582$	3.69978e45	0.885006
$583$	7.51473e44	0.174736
$584$	1.26700e46	2.86394
$585$	0	0
$586$	2.40426e45	0.513654
$587$	−1.91072e45	−0.396889	−0.198444	−	0.980112i	$-0.563589\pi$
$587$	−1.91072e45	−0.396889	−0.198444	+	0.980112i	$0.563589\pi$
$588$	5.22278e45	1.05481
$589$	−7.28827e43	−0.0143127
$590$	0	0
$591$	−4.75400e45	−0.882808
$592$	5.40689e45	0.976426
$593$	−8.87275e45	−1.55832	−0.779158	−	0.626827i	$-0.784353\pi$
$593$	−8.87275e45	−1.55832	−0.779158	+	0.626827i	$0.784353\pi$
$594$	−6.19606e45	−1.05837
$595$	0	0
$596$	3.60431e45	0.582451
$597$	−5.61707e45	−0.882945
$598$	−1.02045e46	−1.56036
$599$	−1.96939e45	−0.292947	−0.146474	−	0.989215i	$-0.546792\pi$
$599$	−1.96939e45	−0.292947	−0.146474	+	0.989215i	$0.546792\pi$
$600$	0	0
$601$	6.49113e45	0.913885	0.456942	−	0.889496i	$-0.348945\pi$
$601$	6.49113e45	0.913885	0.456942	+	0.889496i	$0.348945\pi$
$602$	1.66583e46	2.28185
$603$	3.00827e45	0.400941
$604$	−2.81996e46	−3.65707
$605$	0	0
$606$	1.10421e46	1.35598
$607$	1.08656e46	1.29849	0.649247	−	0.760577i	$-0.275084\pi$
$607$	1.08656e46	1.29849	0.649247	+	0.760577i	$0.275084\pi$
$608$	−1.79761e45	−0.209068
$609$	−4.43896e45	−0.502454
$610$	0	0
$611$	−6.20043e45	−0.664877
$612$	−1.87490e46	−1.95695
$613$	−8.70542e45	−0.884488	−0.442244	−	0.896895i	$-0.645818\pi$
$613$	−8.70542e45	−0.884488	−0.442244	+	0.896895i	$0.645818\pi$
$614$	5.00703e45	0.495224
$615$	0	0
$616$	9.40640e45	0.881742
$617$	1.12685e46	1.02840	0.514199	−	0.857671i	$-0.328089\pi$
$617$	1.12685e46	1.02840	0.514199	+	0.857671i	$0.328089\pi$
$618$	−1.55113e46	−1.37828
$619$	−1.07685e46	−0.931663	−0.465831	−	0.884874i	$-0.654245\pi$
$619$	−1.07685e46	−0.931663	−0.465831	+	0.884874i	$0.654245\pi$
$620$	0	0
$621$	−1.38099e46	−1.13287
$622$	−3.85433e46	−3.07898
$623$	−3.41959e45	−0.266025
$624$	−1.82473e46	−1.38246
$625$	0	0
$626$	−2.01923e46	−1.45114
$627$	−6.14858e44	−0.0430388
$628$	5.77622e46	3.93831
$629$	1.00671e46	0.668605
$630$	0	0
$631$	2.47581e46	1.56039	0.780196	−	0.625535i	$-0.215119\pi$
$631$	2.47581e46	1.56039	0.780196	+	0.625535i	$0.215119\pi$
$632$	−1.16481e46	−0.715190
$633$	2.99206e45	0.178982
$634$	1.54687e46	0.901531
$635$	0	0
$636$	1.01879e46	0.563691
$637$	−8.95698e45	−0.482904
$638$	2.11865e46	1.11306
$639$	−2.05003e45	−0.104953
$640$	0	0
$641$	−6.66844e45	−0.324240	−0.162120	−	0.986771i	$-0.551833\pi$
$641$	−6.66844e45	−0.324240	−0.162120	+	0.986771i	$0.551833\pi$
$642$	6.47567e45	0.306872
$643$	8.88748e42	0.000410485 0	0.000205243	−	1.00000i	$-0.499935\pi$
$643$	8.88748e42	0.000410485 0	0.000205243		1.00000i	$0.499935\pi$
$644$	3.57459e46	1.60920
$645$	0	0
$646$	−8.03845e45	−0.343824
$647$	1.36920e46	0.570884	0.285442	−	0.958396i	$-0.407860\pi$
$647$	1.36920e46	0.570884	0.285442	+	0.958396i	$0.407860\pi$
$648$	−1.78945e46	−0.727330
$649$	9.68495e45	0.383760
$650$	0	0
$651$	1.52523e45	0.0574444
$652$	−5.84545e46	−2.14651
$653$	1.32140e46	0.473115	0.236557	−	0.971618i	$-0.423981\pi$
$653$	1.32140e46	0.473115	0.236557	+	0.971618i	$0.423981\pi$
$654$	−4.05520e46	−1.41573
$655$	0	0
$656$	−3.92527e46	−1.30304
$657$	−1.64028e46	−0.530995
$658$	3.07007e46	0.969215
$659$	3.14029e46	0.966852	0.483426	−	0.875385i	$-0.339392\pi$
$659$	3.14029e46	0.966852	0.483426	+	0.875385i	$0.339392\pi$
$660$	0	0
$661$	−5.62366e46	−1.64701	−0.823503	−	0.567313i	$-0.807983\pi$
$661$	−5.62366e46	−1.64701	−0.823503	+	0.567313i	$0.807983\pi$
$662$	−4.99331e46	−1.42637
$663$	−3.39747e46	−0.946635
$664$	−8.63851e46	−2.34782
$665$	0	0
$666$	−1.39654e46	−0.361184
$667$	4.72211e46	1.19141
$668$	−1.40826e47	−3.46635
$669$	2.48866e46	0.597634
$670$	0	0
$671$	8.13119e44	0.0185880
$672$	3.76188e46	0.839097
$673$	−1.86687e45	−0.0406317	−0.0203159	−	0.999794i	$-0.506467\pi$
$673$	−1.86687e45	−0.0406317	−0.0203159	+	0.999794i	$0.506467\pi$
$674$	9.75848e46	2.07250
$675$	0	0
$676$	−4.42685e46	−0.895311
$677$	3.19535e46	0.630674	0.315337	−	0.948980i	$-0.397882\pi$
$677$	3.19535e46	0.630674	0.315337	+	0.948980i	$0.397882\pi$
$678$	1.25000e47	2.40780
$679$	2.22264e46	0.417847
$680$	0	0
$681$	−1.39912e46	−0.250570
$682$	−7.27967e45	−0.127253
$683$	9.67204e46	1.65035	0.825176	−	0.564876i	$-0.191076\pi$
$683$	9.67204e46	1.65035	0.825176	+	0.564876i	$0.191076\pi$
$684$	7.88910e45	0.131402
$685$	0	0
$686$	1.17232e47	1.86080
$687$	−4.92181e46	−0.762673
$688$	−3.16875e47	−4.79379
$689$	−1.74720e46	−0.258063
$690$	0	0
$691$	−4.21417e46	−0.593368	−0.296684	−	0.954976i	$-0.595881\pi$
$691$	−4.21417e46	−0.593368	−0.296684	+	0.954976i	$0.595881\pi$
$692$	2.96176e47	4.07192
$693$	−1.21777e46	−0.163481
$694$	−8.31128e46	−1.08952
$695$	0	0
$696$	1.68462e47	2.10596
$697$	−7.30848e46	−0.892249
$698$	9.22827e46	1.10029
$699$	3.81445e45	0.0444180
$700$	0	0
$701$	1.07382e47	1.19284	0.596422	−	0.802671i	$-0.296589\pi$
$701$	1.07382e47	1.19284	0.596422	+	0.802671i	$0.296589\pi$
$702$	1.44061e47	1.56309
$703$	−4.23598e45	−0.0448943
$704$	−5.34024e46	−0.552856
$705$	0	0
$706$	1.67517e47	1.65494
$707$	6.63351e46	0.640211
$708$	1.31301e47	1.23799
$709$	9.99645e46	0.920837	0.460419	−	0.887702i	$-0.347699\pi$
$709$	9.99645e46	0.920837	0.460419	+	0.887702i	$0.347699\pi$
$710$	0	0
$711$	1.50798e46	0.132602
$712$	1.29776e47	1.11500
$713$	−1.62251e46	−0.136211
$714$	1.68222e47	1.37994
$715$	0	0
$716$	1.53299e47	1.20081
$717$	9.78940e46	0.749359
$718$	2.02449e47	1.51448
$719$	−7.93598e46	−0.580195	−0.290097	−	0.956997i	$-0.593688\pi$
$719$	−7.93598e46	−0.580195	−0.290097	+	0.956997i	$0.593688\pi$
$720$	0	0
$721$	−9.31838e46	−0.650741
$722$	−2.67498e47	−1.82581
$723$	1.63165e47	1.08854
$724$	4.97151e46	0.324192
$725$	0	0
$726$	1.51278e47	0.942587
$727$	−1.33485e47	−0.813046	−0.406523	−	0.913641i	$-0.633259\pi$
$727$	−1.33485e47	−0.813046	−0.406523	+	0.913641i	$0.633259\pi$
$728$	−2.18702e47	−1.30222
$729$	1.54343e47	0.898427
$730$	0	0
$731$	−5.89992e47	−3.28254
$732$	1.10236e46	0.0599641
$733$	−8.41792e46	−0.447702	−0.223851	−	0.974623i	$-0.571863\pi$
$733$	−8.41792e46	−0.447702	−0.223851	+	0.974623i	$0.571863\pi$
$734$	−1.22843e47	−0.638802
$735$	0	0
$736$	−4.00184e47	−1.98965
$737$	9.11389e46	0.443088
$738$	1.01385e47	0.481998
$739$	2.39720e47	1.11448	0.557239	−	0.830352i	$-0.311861\pi$
$739$	2.39720e47	1.11448	0.557239	+	0.830352i	$0.311861\pi$
$740$	0	0
$741$	1.42957e46	0.0635630
$742$	8.65106e46	0.376188
$743$	−4.51636e47	−1.92076	−0.960380	−	0.278695i	$-0.910098\pi$
$743$	−4.51636e47	−1.92076	−0.960380	+	0.278695i	$0.910098\pi$
$744$	−5.78836e46	−0.240770
$745$	0	0
$746$	1.16643e47	0.464160
$747$	1.11836e47	0.435304
$748$	−5.68023e47	−2.16267
$749$	3.89025e46	0.144886
$750$	0	0
$751$	−2.31769e46	−0.0826030	−0.0413015	−	0.999147i	$-0.513150\pi$
$751$	−2.31769e46	−0.0826030	−0.0413015	+	0.999147i	$0.513150\pi$
$752$	−5.83991e47	−2.03616
$753$	−1.62147e47	−0.553085
$754$	−4.92594e47	−1.64385
$755$	0	0
$756$	−5.04635e47	−1.61201
$757$	6.14297e46	0.191998	0.0959989	−	0.995381i	$-0.469395\pi$
$757$	6.14297e46	0.191998	0.0959989	+	0.995381i	$0.469395\pi$
$758$	8.81131e47	2.69463
$759$	−1.36880e47	−0.409590
$760$	0	0
$761$	−4.18126e47	−1.19801	−0.599004	−	0.800746i	$-0.704437\pi$
$761$	−4.18126e47	−1.19801	−0.599004	+	0.800746i	$0.704437\pi$
$762$	−6.52205e47	−1.82863
$763$	−2.43616e47	−0.668421
$764$	−1.45009e46	−0.0389362
$765$	0	0
$766$	1.16952e48	3.00769
$767$	−2.25179e47	−0.566766
$768$	2.82528e47	0.695987
$769$	−2.07493e47	−0.500286	−0.250143	−	0.968209i	$-0.580478\pi$
$769$	−2.07493e47	−0.500286	−0.250143	+	0.968209i	$0.580478\pi$
$770$	0	0
$771$	−1.55616e47	−0.359464
$772$	−1.38584e47	−0.313348
$773$	3.82656e47	0.846930	0.423465	−	0.905912i	$-0.360814\pi$
$773$	3.82656e47	0.846930	0.423465	+	0.905912i	$0.360814\pi$
$774$	8.18455e47	1.77324
$775$	0	0
$776$	−8.43509e47	−1.75134
$777$	8.86469e46	0.180184
$778$	5.20250e47	1.03526
$779$	3.07522e46	0.0599112
$780$	0	0
$781$	−6.21081e46	−0.115986
$782$	−1.78952e48	−3.27209
$783$	−6.66634e47	−1.19349
$784$	−8.43619e47	−1.47887
$785$	0	0
$786$	2.70354e47	0.454423
$787$	6.26036e47	1.03043	0.515213	−	0.857062i	$-0.327713\pi$
$787$	6.26036e47	1.03043	0.515213	+	0.857062i	$0.327713\pi$
$788$	1.84799e48	2.97863
$789$	−3.00829e47	−0.474842
$790$	0	0
$791$	7.50935e47	1.13682
$792$	4.62156e47	0.685208
$793$	−1.89053e46	−0.0274521
$794$	−1.46471e48	−2.08312
$795$	0	0
$796$	2.18348e48	2.97910
$797$	−1.56391e47	−0.209002	−0.104501	−	0.994525i	$-0.533325\pi$
$797$	−1.56391e47	−0.209002	−0.104501	+	0.994525i	$0.533325\pi$
$798$	−7.07833e46	−0.0926580
$799$	−1.08734e48	−1.39425
$800$	0	0
$801$	−1.68012e47	−0.206730
$802$	7.96201e47	0.959722
$803$	−4.96943e47	−0.586813
$804$	1.23559e48	1.42938
$805$	0	0
$806$	1.69255e47	0.187937
$807$	5.22171e47	0.568067
$808$	−2.51747e48	−2.68335
$809$	4.01144e47	0.418938	0.209469	−	0.977815i	$-0.432826\pi$
$809$	4.01144e47	0.418938	0.209469	+	0.977815i	$0.432826\pi$
$810$	0	0
$811$	2.34209e47	0.234833	0.117417	−	0.993083i	$-0.462539\pi$
$811$	2.34209e47	0.234833	0.117417	+	0.993083i	$0.462539\pi$
$812$	1.72553e48	1.69530
$813$	−1.27608e48	−1.22853
$814$	−4.23098e47	−0.399152
$815$	0	0
$816$	−3.19993e48	−2.89903
$817$	2.48253e47	0.220410
$818$	2.97269e48	2.58655
$819$	2.83137e47	0.241442
$820$	0	0
$821$	4.03504e47	0.330510	0.165255	−	0.986251i	$-0.447155\pi$
$821$	4.03504e47	0.330510	0.165255	+	0.986251i	$0.447155\pi$
$822$	8.15807e47	0.654942
$823$	−1.82505e48	−1.43608	−0.718039	−	0.696002i	$-0.754960\pi$
$823$	−1.82505e48	−1.43608	−0.718039	+	0.696002i	$0.754960\pi$
$824$	3.53640e48	2.72749
$825$	0	0
$826$	1.11494e48	0.826195
$827$	−7.52706e47	−0.546744	−0.273372	−	0.961908i	$-0.588139\pi$
$827$	−7.52706e47	−0.546744	−0.273372	+	0.961908i	$0.588139\pi$
$828$	1.75627e48	1.25052
$829$	−2.19354e48	−1.53107	−0.765537	−	0.643392i	$-0.777526\pi$
$829$	−2.19354e48	−1.53107	−0.765537	+	0.643392i	$0.777526\pi$
$830$	0	0
$831$	−7.47306e47	−0.501281
$832$	1.24162e48	0.816499
$833$	−1.57074e48	−1.01265
$834$	3.31244e48	2.09367
$835$	0	0
$836$	2.39009e47	0.145215
$837$	2.29055e47	0.136449
$838$	2.73408e48	1.59693
$839$	−2.86394e48	−1.64018	−0.820091	−	0.572233i	$-0.806077\pi$
$839$	−2.86394e48	−1.64018	−0.820091	+	0.572233i	$0.806077\pi$
$840$	0	0
$841$	4.63381e47	0.255155
$842$	−3.54978e48	−1.91669
$843$	1.54943e48	0.820382
$844$	−1.16308e48	−0.603892
$845$	0	0
$846$	1.50839e48	0.753185
$847$	9.08800e47	0.445033
$848$	−1.64561e48	−0.790308
$849$	−8.06680e47	−0.379948
$850$	0	0
$851$	−9.43013e47	−0.427248
$852$	−8.42012e47	−0.374166
$853$	−4.28657e48	−1.86832	−0.934158	−	0.356859i	$-0.883848\pi$
$853$	−4.28657e48	−1.86832	−0.934158	+	0.356859i	$0.883848\pi$
$854$	9.36073e46	0.0400180
$855$	0	0
$856$	−1.47638e48	−0.607270
$857$	8.64522e47	0.348813	0.174406	−	0.984674i	$-0.444199\pi$
$857$	8.64522e47	0.348813	0.174406	+	0.984674i	$0.444199\pi$
$858$	1.42788e48	0.565134
$859$	2.35883e48	0.915817	0.457909	−	0.888999i	$-0.348599\pi$
$859$	2.35883e48	0.915817	0.457909	+	0.888999i	$0.348599\pi$
$860$	0	0
$861$	−6.43555e47	−0.240455
$862$	−3.68860e48	−1.35205
$863$	6.27316e46	0.0225584	0.0112792	−	0.999936i	$-0.496410\pi$
$863$	6.27316e46	0.0225584	0.0112792	+	0.999936i	$0.496410\pi$
$864$	5.64951e48	1.99312
$865$	0	0
$866$	4.49666e48	1.52702
$867$	−3.80669e48	−1.26833
$868$	−5.92890e47	−0.193820
$869$	4.56861e47	0.146541
$870$	0	0
$871$	−2.11901e48	−0.654386
$872$	9.24541e48	2.80159
$873$	1.09203e48	0.324712
$874$	7.52982e47	0.219708
$875$	0	0
$876$	−6.73715e48	−1.89303
$877$	2.00783e48	0.553647	0.276823	−	0.960921i	$-0.410718\pi$
$877$	2.00783e48	0.553647	0.276823	+	0.960921i	$0.410718\pi$
$878$	2.57194e48	0.695988
$879$	−7.49818e47	−0.199131
$880$	0	0
$881$	−4.20296e48	−1.07511	−0.537555	−	0.843229i	$-0.680652\pi$
$881$	−4.20296e48	−1.07511	−0.537555	+	0.843229i	$0.680652\pi$
$882$	2.17898e48	0.547042
$883$	−7.94997e48	−1.95891	−0.979453	−	0.201672i	$-0.935362\pi$
$883$	−7.94997e48	−1.95891	−0.979453	+	0.201672i	$0.935362\pi$
$884$	1.32067e49	3.19399
$885$	0	0
$886$	−1.77675e48	−0.413971
$887$	7.43922e48	1.70133	0.850664	−	0.525710i	$-0.176200\pi$
$887$	7.43922e48	1.70133	0.850664	+	0.525710i	$0.176200\pi$
$888$	−3.36422e48	−0.755216
$889$	−3.91811e48	−0.863371
$890$	0	0
$891$	7.01859e47	0.149028
$892$	−9.67400e48	−2.01644
$893$	4.57523e47	0.0936189
$894$	−1.58888e48	−0.319170
$895$	0	0
$896$	−1.01136e47	−0.0195804
$897$	3.18250e48	0.604913
$898$	−5.22659e47	−0.0975345
$899$	−7.83220e47	−0.143499
$900$	0	0
$901$	−3.06398e48	−0.541161
$902$	3.07159e48	0.532666
$903$	−5.19523e48	−0.884620
$904$	−2.84986e49	−4.76480
$905$	0	0
$906$	1.24311e49	2.00399
$907$	−8.96944e48	−1.41986	−0.709929	−	0.704273i	$-0.751273\pi$
$907$	−8.96944e48	−1.41986	−0.709929	+	0.704273i	$0.751273\pi$
$908$	5.43871e48	0.845433
$909$	3.25918e48	0.497513
$910$	0	0
$911$	2.25421e48	0.331850	0.165925	−	0.986138i	$-0.446939\pi$
$911$	2.25421e48	0.331850	0.165925	+	0.986138i	$0.446939\pi$
$912$	1.34645e48	0.194659
$913$	3.38820e48	0.481063
$914$	1.39679e49	1.94769
$915$	0	0
$916$	1.91322e49	2.57329
$917$	1.62415e48	0.214551
$918$	2.52632e49	3.27781
$919$	−7.04277e48	−0.897507	−0.448754	−	0.893656i	$-0.648132\pi$
$919$	−7.04277e48	−0.897507	−0.448754	+	0.893656i	$0.648132\pi$
$920$	0	0
$921$	−1.56155e48	−0.191987
$922$	1.62673e49	1.96452
$923$	1.44404e48	0.171297
$924$	−5.00178e48	−0.582823
$925$	0	0
$926$	1.17335e49	1.31931
$927$	−4.57831e48	−0.505696
$928$	−1.93177e49	−2.09611
$929$	1.56732e49	1.67070	0.835348	−	0.549721i	$-0.185266\pi$
$929$	1.56732e49	1.67070	0.835348	+	0.549721i	$0.185266\pi$
$930$	0	0
$931$	6.60926e47	0.0679959
$932$	−1.48276e48	−0.149868
$933$	1.20205e49	1.19365
$934$	−1.95123e49	−1.90364
$935$	0	0
$936$	−1.07453e49	−1.01197
$937$	−4.17295e48	−0.386136	−0.193068	−	0.981185i	$-0.561844\pi$
$937$	−4.17295e48	−0.386136	−0.193068	+	0.981185i	$0.561844\pi$
$938$	1.04920e49	0.953922
$939$	6.29740e48	0.562573
$940$	0	0
$941$	−5.21719e48	−0.449995	−0.224998	−	0.974359i	$-0.572237\pi$
$941$	−5.21719e48	−0.449995	−0.224998	+	0.974359i	$0.572237\pi$
$942$	−2.54631e49	−2.15810
$943$	6.84604e48	0.570160
$944$	−2.12086e49	−1.73570
$945$	0	0
$946$	2.47960e49	1.95965
$947$	1.05918e49	0.822616	0.411308	−	0.911496i	$-0.365072\pi$
$947$	1.05918e49	0.822616	0.411308	+	0.911496i	$0.365072\pi$
$948$	6.19376e48	0.472734
$949$	1.15541e49	0.866650
$950$	0	0
$951$	−4.82423e48	−0.349502
$952$	−3.83527e49	−2.73078
$953$	−1.49599e49	−1.04688	−0.523438	−	0.852064i	$-0.675351\pi$
$953$	−1.49599e49	−1.04688	−0.523438	+	0.852064i	$0.675351\pi$
$954$	4.25044e48	0.292338
$955$	0	0
$956$	−3.80536e49	−2.52837
$957$	−6.60745e48	−0.431506
$958$	−4.17619e49	−2.68071
$959$	4.90095e48	0.309224
$960$	0	0
$961$	−1.61344e49	−0.983594
$962$	9.83718e48	0.589498
$963$	1.91136e48	0.112592
$964$	−6.34261e49	−3.67280
$965$	0	0
$966$	−1.57578e49	−0.881803
$967$	2.39619e49	1.31821	0.659106	−	0.752050i	$-0.270935\pi$
$967$	2.39619e49	1.31821	0.659106	+	0.752050i	$0.270935\pi$
$968$	−3.44897e49	−1.86529
$969$	2.50696e48	0.133292
$970$	0	0
$971$	−1.35152e47	−0.00694552	−0.00347276	−	0.999994i	$-0.501105\pi$
$971$	−1.35152e47	−0.00694552	−0.00347276	+	0.999994i	$0.501105\pi$
$972$	−4.14760e49	−2.09558
$973$	1.98994e49	0.988505
$974$	2.66999e49	1.30403
$975$	0	0
$976$	−1.78061e48	−0.0840711
$977$	−1.84460e48	−0.0856333	−0.0428166	−	0.999083i	$-0.513633\pi$
$977$	−1.84460e48	−0.0856333	−0.0428166	+	0.999083i	$0.513633\pi$
$978$	2.57683e49	1.17624
$979$	−5.09011e48	−0.228461
$980$	0	0
$981$	−1.19693e49	−0.519435
$982$	−4.53233e48	−0.193411
$983$	6.69809e48	0.281072	0.140536	−	0.990076i	$-0.455117\pi$
$983$	6.69809e48	0.281072	0.140536	+	0.990076i	$0.455117\pi$
$984$	2.44234e49	1.00783
$985$	0	0
$986$	−8.63836e49	−3.44717
$987$	−9.57464e48	−0.375742
$988$	−5.55705e48	−0.214464
$989$	5.52661e49	2.09759
$990$	0	0
$991$	1.17168e49	0.430123	0.215062	−	0.976600i	$-0.431005\pi$
$991$	1.17168e49	0.430123	0.215062	+	0.976600i	$0.431005\pi$
$992$	6.63755e48	0.239643
$993$	1.55727e49	0.552969
$994$	−7.14997e48	−0.249706
$995$	0	0
$996$	4.59345e49	1.55189
$997$	−2.44007e49	−0.810834	−0.405417	−	0.914132i	$-0.632874\pi$
$997$	−2.44007e49	−0.810834	−0.405417	+	0.914132i	$0.632874\pi$
$998$	5.68168e49	1.85705
$999$	1.33128e49	0.427995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.a.1.2		2
5.2	odd	4		25.34.b.a.24.4		4
5.3	odd	4		25.34.b.a.24.1		4
5.4	even	2		1.34.a.a.1.1	✓	2
15.14	odd	2		9.34.a.b.1.2		2
20.19	odd	2		16.34.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.34.a.a.1.1	✓	2	5.4	even	2
9.34.a.b.1.2		2	15.14	odd	2
16.34.a.b.1.1		2	20.19	odd	2
25.34.a.a.1.2		2	1.1	even	1	trivial
25.34.b.a.24.1		4	5.3	odd	4
25.34.b.a.24.4		4	5.2	odd	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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+171359. q^{2} -5.34420e7 q^{3} +2.07741e10 q^{4} -9.15779e12 q^{6} -5.50153e13 q^{7} +2.08788e15 q^{8} -2.70301e15 q^{9} +O(q^{10})\)	\(q+171359. q^{2} -5.34420e7 q^{3} +2.07741e10 q^{4} -9.15779e12 q^{6} -5.50153e13 q^{7} +2.08788e15 q^{8} -2.70301e15 q^{9} -8.18909e16 q^{11} -1.11021e18 q^{12} +1.90399e18 q^{13} -9.42739e18 q^{14} +1.79329e20 q^{16} +3.33893e20 q^{17} -4.63187e20 q^{18} -1.40494e20 q^{19} +2.94013e21 q^{21} -1.40328e22 q^{22} -3.12767e22 q^{23} -1.11580e23 q^{24} +3.26267e23 q^{26} +4.41542e23 q^{27} -1.14289e24 q^{28} -1.50979e24 q^{29} +5.18762e23 q^{31} +1.27950e25 q^{32} +4.37641e24 q^{33} +5.72158e25 q^{34} -5.61527e25 q^{36} +3.01507e25 q^{37} -2.40749e25 q^{38} -1.01753e26 q^{39} -2.18887e26 q^{41} +5.03818e26 q^{42} -1.76701e27 q^{43} -1.70121e27 q^{44} -5.35955e27 q^{46} -3.25654e27 q^{47} -9.58369e27 q^{48} -4.70431e27 q^{49} -1.78439e28 q^{51} +3.95538e28 q^{52} -9.17652e27 q^{53} +7.56623e28 q^{54} -1.14865e29 q^{56} +7.50826e27 q^{57} -2.58716e29 q^{58} -1.18267e29 q^{59} -9.92930e27 q^{61} +8.88948e28 q^{62} +1.48707e29 q^{63} +6.52116e29 q^{64} +7.49940e29 q^{66} -1.11293e30 q^{67} +6.93634e30 q^{68} +1.67149e30 q^{69} +7.58425e29 q^{71} -5.64355e30 q^{72} +6.06835e30 q^{73} +5.16661e30 q^{74} -2.91863e30 q^{76} +4.50525e30 q^{77} -1.74364e31 q^{78} -5.57890e30 q^{79} -8.57067e30 q^{81} -3.75083e31 q^{82} -4.13746e31 q^{83} +6.10785e31 q^{84} -3.02793e32 q^{86} +8.06860e31 q^{87} -1.70978e32 q^{88} +6.21572e31 q^{89} -1.04749e32 q^{91} -6.49745e32 q^{92} -2.77237e31 q^{93} -5.58039e32 q^{94} -6.83789e32 q^{96} -4.04003e32 q^{97} -8.06129e32 q^{98} +2.21352e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 121680 q^{2} - 37919880 q^{3} + 14652233984 q^{4} - 9928922193216 q^{6} + 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 80\!\cdots\!54 q^{9}+O(q^{10}) \) 2 * q + 121680 * q^2 - 37919880 * q^3 + 14652233984 * q^4 - 9928922193216 * q^6 + 67153080066800 * q^7 + 2818750585098240 * q^8 - 8021136954970854 * q^9	\( 2 q + 121680 q^{2} - 37919880 q^{3} + 14652233984 q^{4} - 9928922193216 q^{6} + 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 92\!\cdots\!28 q^{99}+O(q^{100}) \) 2 * q + 121680 * q^2 - 37919880 * q^3 + 14652233984 * q^4 - 9928922193216 * q^6 + 67153080066800 * q^7 + 2818750585098240 * q^8 - 8021136954970854 * q^9 + 133871815441914264 * q^11 - 1205235433330467840 * q^12 + 2981610478259443940 * q^13 - 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 198985322728543319280 * q^18 - 1360696443041697171800 * q^19 + 4836438843082801141824 * q^21 - 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 100235518588319710003200 * q^24 + 272731683634642092710304 * q^26 + 272704742315639906405040 * q^27 - 1890794991723644827125760 * q^28 - 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 7725507376265263259943840 * q^33 + 69860790536166916073075808 * q^34 - 23595755096197135608576768 * q^36 + 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 - 85026272438019668836783248 * q^39 + 277566613022002182732188244 * q^41 + 409610685367579027895216640 * q^42 - 1567661189367072113768291800 * q^43 - 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 - 9331035686759324258712944640 * q^48 + 2489799365888888933444851314 * q^49 - 21794809591439435388668624496 * q^51 + 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 84050074928235529084016073600 * q^54 - 25575237795171758759822131200 * q^56 - 11431882183748158902465090720 * q^57 - 250532370716581201796821222560 * q^58 - 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 - 500999494400792409792776544720 * q^63 + 864365322360380859973709594624 * q^64 + 583558358556830038058269663488 * q^66 - 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1750848530317427976275742443712 * q^69 - 2669761937956104715736810084976 * q^71 - 9530438520123487645446231060480 * q^72 - 946314321191998870965166536340 * q^73 + 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 18267352963262685465124679337600 * q^78 - 8535199972765636469730106191200 * q^79 + 18372400450705101408694430349042 * q^81 - 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 49469534061147727842067908599808 * q^84 - 312696885737578501917214826406336 * q^86 + 78129025791401437906177732680720 * q^87 - 13282372192867492753038509752320 * q^88 + 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 132607664882695458799488635592960 * q^93 - 450506433888867898835049561530112 * q^94 - 793791282556560211499025092837376 * q^96 + 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * q^98 - 926100695332764780030656940070728 * q^99

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