LMFDB - Embedded newform 245.10.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,10,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.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:	$126.183779860$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 6671 x^{16} + 28472 x^{15} + 18323094 x^{14} - 49525664 x^{13} + \cdots + 24\!\cdots\!76 $ x^18 - 6x^17 - 6671x^16 + 28472x^15 + 18323094x^14 - 49525664x^13 - 26727434016x^12 + 35963326896x^11 + 22243420534040x^10 - 5616028552544x^9 - 10532182760701856x^8 - 5183005906043136x^7 + 2659690061237093664x^6 + 2008343572364565760x^5 - 306799367113693922304x^4 - 73406894211465090304x^3 + 11518524304617146364800x^2 - 25540525208247540535296*x + 244834460756100997376
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4}\cdot 5^{4}\cdot 7^{16} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.00962792$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.40459 q^{2} -144.425 q^{3} -482.790 q^{4} -625.000 q^{5} -780.557 q^{6} -5376.43 q^{8} +1175.54 q^{9} -3377.87 q^{10} -212.237 q^{11} +69727.0 q^{12} -175838. q^{13} +90265.5 q^{15} +218131. q^{16} -66313.9 q^{17} +6353.33 q^{18} +462571. q^{19} +301744. q^{20} -1147.05 q^{22} -27111.1 q^{23} +776490. q^{24} +390625. q^{25} -950330. q^{26} +2.67294e6 q^{27} -1.61946e6 q^{29} +487848. q^{30} +1.01955e6 q^{31} +3.93164e6 q^{32} +30652.3 q^{33} -358399. q^{34} -567542. q^{36} +1.69762e6 q^{37} +2.50000e6 q^{38} +2.53953e7 q^{39} +3.36027e6 q^{40} +502301. q^{41} +1.77723e7 q^{43} +102466. q^{44} -734716. q^{45} -146525. q^{46} +2.60269e7 q^{47} -3.15036e7 q^{48} +2.11117e6 q^{50} +9.57737e6 q^{51} +8.48927e7 q^{52} +7.85456e7 q^{53} +1.44461e7 q^{54} +132648. q^{55} -6.68067e7 q^{57} -8.75253e6 q^{58} +8.18513e7 q^{59} -4.35793e7 q^{60} -1.85662e8 q^{61} +5.51024e6 q^{62} -9.04343e7 q^{64} +1.09899e8 q^{65} +165663. q^{66} +2.72523e8 q^{67} +3.20157e7 q^{68} +3.91552e6 q^{69} +7.23098e7 q^{71} -6.32023e6 q^{72} +1.11403e8 q^{73} +9.17494e6 q^{74} -5.64160e7 q^{75} -2.23325e8 q^{76} +1.37251e8 q^{78} +3.48824e8 q^{79} -1.36332e8 q^{80} -4.09177e8 q^{81} +2.71473e6 q^{82} -4.04010e8 q^{83} +4.14462e7 q^{85} +9.60519e7 q^{86} +2.33891e8 q^{87} +1.14108e6 q^{88} +8.69802e7 q^{89} -3.97083e6 q^{90} +1.30890e7 q^{92} -1.47248e8 q^{93} +1.40664e8 q^{94} -2.89107e8 q^{95} -5.67827e8 q^{96} -1.04518e9 q^{97} -249494. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 66 q^{2} - 112 q^{3} + 4438 q^{4} - 11250 q^{5} - 5184 q^{6} + 58542 q^{8} + 117250 q^{9} - 41250 q^{10} - 50448 q^{11} + 51200 q^{12} - 265416 q^{13} + 70000 q^{15} + 275354 q^{16} - 742108 q^{17}+ \cdots - 3327698948 q^{99}+O(q^{100}) $ 18 * q + 66 * q^2 - 112 * q^3 + 4438 * q^4 - 11250 * q^5 - 5184 * q^6 + 58542 * q^8 + 117250 * q^9 - 41250 * q^10 - 50448 * q^11 + 51200 * q^12 - 265416 * q^13 + 70000 * q^15 + 275354 * q^16 - 742108 * q^17 + 31422 * q^18 - 2003052 * q^19 - 2773750 * q^20 - 898372 * q^22 + 5864112 * q^23 - 7257292 * q^24 + 7031250 * q^25 - 4213696 * q^26 - 12641932 * q^27 + 6575952 * q^29 + 3240000 * q^30 - 15704952 * q^31 + 24442110 * q^32 - 23661356 * q^33 + 7374732 * q^34 + 49561790 * q^36 + 8711420 * q^37 - 8938900 * q^38 + 48598700 * q^39 - 36588750 * q^40 + 5319344 * q^41 + 52311916 * q^43 - 35094960 * q^44 - 73281250 * q^45 + 98407276 * q^46 - 113473964 * q^47 + 50036228 * q^48 + 25781250 * q^50 + 108467832 * q^51 - 193287600 * q^52 + 31548852 * q^53 - 116650276 * q^54 + 31530000 * q^55 + 68889076 * q^57 - 65260756 * q^58 - 267674844 * q^59 - 32000000 * q^60 - 321756900 * q^61 - 651435868 * q^62 - 585550558 * q^64 + 165885000 * q^65 - 865081780 * q^66 - 234918184 * q^67 - 844088700 * q^68 - 380592968 * q^69 - 795896592 * q^71 + 70394666 * q^72 - 617344800 * q^73 - 1029168024 * q^74 - 43750000 * q^75 - 1200935100 * q^76 - 1277509816 * q^78 - 63002188 * q^79 - 172096250 * q^80 + 306235886 * q^81 + 1719855588 * q^82 - 534295300 * q^83 + 463817500 * q^85 + 65726340 * q^86 + 1504843540 * q^87 - 1698935556 * q^88 - 100440944 * q^89 - 19638750 * q^90 + 3229447776 * q^92 - 414903656 * q^93 + 1013675148 * q^94 + 1251907500 * q^95 + 1575858100 * q^96 - 1852351908 * q^97 - 3327698948 * q^99

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 $

$2$	5.40459	0.238851	0.119426	−	0.992843i	$-0.461895\pi$
$2$	5.40459	0.238851	0.119426	+	0.992843i	$0.461895\pi$
$3$	−144.425	−1.02943	−0.514714	−	0.857362i	$-0.672102\pi$
$3$	−144.425	−1.02943	−0.514714	+	0.857362i	$0.672102\pi$
$4$	−482.790	−0.942950
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−780.557	−0.245880
$7$	0	0
$7$	0	0
$8$	−5376.43	−0.464076
$9$	1175.54	0.0597239
$10$	−3377.87	−0.106818
$11$	−212.237	−0.00437073	−0.00218536	−	0.999998i	$-0.500696\pi$
$11$	−212.237	−0.00437073	−0.00218536	+	0.999998i	$0.500696\pi$
$12$	69727.0	0.970700
$13$	−175838.	−1.70752	−0.853762	−	0.520663i	$-0.825685\pi$
$13$	−175838.	−1.70752	−0.853762	+	0.520663i	$0.825685\pi$
$14$	0	0
$15$	90265.5	0.460375
$16$	218131.	0.832105
$17$	−66313.9	−0.192568	−0.0962840	−	0.995354i	$-0.530696\pi$
$17$	−66313.9	−0.192568	−0.0962840	+	0.995354i	$0.530696\pi$
$18$	6353.33	0.0142651
$19$	462571.	0.814305	0.407152	−	0.913360i	$-0.366522\pi$
$19$	462571.	0.814305	0.407152	+	0.913360i	$0.366522\pi$
$20$	301744.	0.421700
$21$	0	0
$22$	−1147.05	−0.00104395
$23$	−27111.1	−0.0202010	−0.0101005	−	0.999949i	$-0.503215\pi$
$23$	−27111.1	−0.0202010	−0.0101005	+	0.999949i	$0.503215\pi$
$24$	776490.	0.477733
$25$	390625.	0.200000
$26$	−950330.	−0.407844
$27$	2.67294e6	0.967947
$28$	0	0
$29$	−1.61946e6	−0.425187	−0.212594	−	0.977141i	$-0.568191\pi$
$29$	−1.61946e6	−0.425187	−0.212594	+	0.977141i	$0.568191\pi$
$30$	487848.	0.109961
$31$	1.01955e6	0.198281	0.0991404	−	0.995073i	$-0.468391\pi$
$31$	1.01955e6	0.198281	0.0991404	+	0.995073i	$0.468391\pi$
$32$	3.93164e6	0.662825
$33$	30652.3	0.00449936
$34$	−358399.	−0.0459951
$35$	0	0
$36$	−567542.	−0.0563166
$37$	1.69762e6	0.148913	0.0744566	−	0.997224i	$-0.476278\pi$
$37$	1.69762e6	0.148913	0.0744566	+	0.997224i	$0.476278\pi$
$38$	2.50000e6	0.194498
$39$	2.53953e7	1.75777
$40$	3.36027e6	0.207541
$41$	502301.	0.0277611	0.0138806	−	0.999904i	$-0.495582\pi$
$41$	502301.	0.0277611	0.0138806	+	0.999904i	$0.495582\pi$
$42$	0	0
$43$	1.77723e7	0.792748	0.396374	−	0.918089i	$-0.370268\pi$
$43$	1.77723e7	0.792748	0.396374	+	0.918089i	$0.370268\pi$
$44$	102466.	0.00412138
$45$	−734716.	−0.0267093
$46$	−146525.	−0.00482503
$47$	2.60269e7	0.778003	0.389002	−	0.921237i	$-0.372820\pi$
$47$	2.60269e7	0.778003	0.389002	+	0.921237i	$0.372820\pi$
$48$	−3.15036e7	−0.856593
$49$	0	0
$50$	2.11117e6	0.0477702
$51$	9.57737e6	0.198235
$52$	8.48927e7	1.61011
$53$	7.85456e7	1.36735	0.683676	−	0.729786i	$-0.260380\pi$
$53$	7.85456e7	1.36735	0.683676	+	0.729786i	$0.260380\pi$
$54$	1.44461e7	0.231195
$55$	132648.	0.00195465
$56$	0	0
$57$	−6.68067e7	−0.838269
$58$	−8.75253e6	−0.101556
$59$	8.18513e7	0.879410	0.439705	−	0.898142i	$-0.355083\pi$
$59$	8.18513e7	0.879410	0.439705	+	0.898142i	$0.355083\pi$
$60$	−4.35793e7	−0.434110
$61$	−1.85662e8	−1.71688	−0.858440	−	0.512914i	$-0.828566\pi$
$61$	−1.85662e8	−1.71688	−0.858440	+	0.512914i	$0.828566\pi$
$62$	5.51024e6	0.0473596
$63$	0	0
$64$	−9.04343e7	−0.673788
$65$	1.09899e8	0.763628
$66$	165663.	0.00107468
$67$	2.72523e8	1.65222	0.826109	−	0.563511i	$-0.190550\pi$
$67$	2.72523e8	1.65222	0.826109	+	0.563511i	$0.190550\pi$
$68$	3.20157e7	0.181582
$69$	3.91552e6	0.0207955
$70$	0	0
$71$	7.23098e7	0.337703	0.168851	−	0.985642i	$-0.445994\pi$
$71$	7.23098e7	0.337703	0.168851	+	0.985642i	$0.445994\pi$
$72$	−6.32023e6	−0.0277164
$73$	1.11403e8	0.459138	0.229569	−	0.973292i	$-0.426268\pi$
$73$	1.11403e8	0.459138	0.229569	+	0.973292i	$0.426268\pi$
$74$	9.17494e6	0.0355681
$75$	−5.64160e7	−0.205886
$76$	−2.23325e8	−0.767849
$77$	0	0
$78$	1.37251e8	0.419847
$79$	3.48824e8	1.00759	0.503796	−	0.863823i	$-0.331936\pi$
$79$	3.48824e8	1.00759	0.503796	+	0.863823i	$0.331936\pi$
$80$	−1.36332e8	−0.372129
$81$	−4.09177e8	−1.05616
$82$	2.71473e6	0.00663078
$83$	−4.04010e8	−0.934417	−0.467209	−	0.884147i	$-0.654740\pi$
$83$	−4.04010e8	−0.934417	−0.467209	+	0.884147i	$0.654740\pi$
$84$	0	0
$85$	4.14462e7	0.0861190
$86$	9.60519e7	0.189349
$87$	2.33891e8	0.437700
$88$	1.14108e6	0.00202835
$89$	8.69802e7	0.146949	0.0734743	−	0.997297i	$-0.476591\pi$
$89$	8.69802e7	0.146949	0.0734743	+	0.997297i	$0.476591\pi$
$90$	−3.97083e6	−0.00637955
$91$	0	0
$92$	1.30890e7	0.0190485
$93$	−1.47248e8	−0.204116
$94$	1.40664e8	0.185827
$95$	−2.89107e8	−0.364168
$96$	−5.67827e8	−0.682331
$97$	−1.04518e9	−1.19873	−0.599363	−	0.800477i	$-0.704579\pi$
$97$	−1.04518e9	−1.19873	−0.599363	+	0.800477i	$0.704579\pi$
$98$	0	0
$99$	−249494.	−0.000261037 0
$100$	−1.88590e8	−0.188590
$101$	−1.57858e9	−1.50946	−0.754729	−	0.656036i	$-0.772232\pi$
$101$	−1.57858e9	−1.50946	−0.754729	+	0.656036i	$0.772232\pi$
$102$	5.17617e7	0.0473487
$103$	−1.42282e9	−1.24561	−0.622806	−	0.782376i	$-0.714007\pi$
$103$	−1.42282e9	−1.24561	−0.622806	+	0.782376i	$0.714007\pi$
$104$	9.45379e8	0.792421
$105$	0	0
$106$	4.24506e8	0.326594
$107$	−8.91273e8	−0.657331	−0.328665	−	0.944446i	$-0.606599\pi$
$107$	−8.91273e8	−0.657331	−0.328665	+	0.944446i	$0.606599\pi$
$108$	−1.29047e9	−0.912726
$109$	5.97559e8	0.405473	0.202736	−	0.979233i	$-0.435017\pi$
$109$	5.97559e8	0.405473	0.202736	+	0.979233i	$0.435017\pi$
$110$	716908.	0.000466870 0
$111$	−2.45179e8	−0.153296
$112$	0	0
$113$	5.05926e7	0.0291900	0.0145950	−	0.999893i	$-0.495354\pi$
$113$	5.05926e7	0.0291900	0.0145950	+	0.999893i	$0.495354\pi$
$114$	−3.61063e8	−0.200222
$115$	1.69445e7	0.00903416
$116$	7.81861e8	0.400930
$117$	−2.06705e8	−0.101980
$118$	4.42372e8	0.210048
$119$	0	0
$120$	−4.85306e8	−0.213649
$121$	−2.35790e9	−0.999981
$122$	−1.00343e9	−0.410079
$123$	−7.25448e7	−0.0285781
$124$	−4.92229e8	−0.186969
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	2.09981e9	0.716249	0.358124	−	0.933674i	$-0.383416\pi$
$127$	2.09981e9	0.716249	0.358124	+	0.933674i	$0.383416\pi$
$128$	−2.50176e9	−0.823760
$129$	−2.56676e9	−0.816078
$130$	5.93956e8	0.182393
$131$	5.52459e9	1.63900	0.819500	−	0.573079i	$-0.194251\pi$
$131$	5.52459e9	1.63900	0.819500	+	0.573079i	$0.194251\pi$
$132$	−1.47986e7	−0.00424267
$133$	0	0
$134$	1.47288e9	0.394634
$135$	−1.67059e9	−0.432879
$136$	3.56532e8	0.0893662
$137$	−2.23235e9	−0.541403	−0.270701	−	0.962663i	$-0.587256\pi$
$137$	−2.23235e9	−0.541403	−0.270701	+	0.962663i	$0.587256\pi$
$138$	2.11618e7	0.00496703
$139$	−5.15166e9	−1.17052	−0.585262	−	0.810844i	$-0.699008\pi$
$139$	−5.15166e9	−1.17052	−0.585262	+	0.810844i	$0.699008\pi$
$140$	0	0
$141$	−3.75893e9	−0.800899
$142$	3.90805e8	0.0806607
$143$	3.73192e7	0.00746313
$144$	2.56423e8	0.0496965
$145$	1.01216e9	0.190149
$146$	6.02086e8	0.109666
$147$	0	0
$148$	−8.19595e8	−0.140418
$149$	−9.71613e9	−1.61494	−0.807468	−	0.589912i	$-0.799163\pi$
$149$	−9.71613e9	−1.61494	−0.807468	+	0.589912i	$0.799163\pi$
$150$	−3.04905e8	−0.0491761
$151$	1.07099e10	1.67645	0.838225	−	0.545325i	$-0.183594\pi$
$151$	1.07099e10	1.67645	0.838225	+	0.545325i	$0.183594\pi$
$152$	−2.48698e9	−0.377899
$153$	−7.79549e7	−0.0115009
$154$	0	0
$155$	−6.37218e8	−0.0886739
$156$	−1.22606e10	−1.65749
$157$	5.89468e9	0.774305	0.387152	−	0.922016i	$-0.373459\pi$
$157$	5.89468e9	0.774305	0.387152	+	0.922016i	$0.373459\pi$
$158$	1.88525e9	0.240664
$159$	−1.13439e10	−1.40759
$160$	−2.45728e9	−0.296424
$161$	0	0
$162$	−2.21143e9	−0.252264
$163$	5.42581e8	0.0602034	0.0301017	−	0.999547i	$-0.490417\pi$
$163$	5.42581e8	0.0602034	0.0301017	+	0.999547i	$0.490417\pi$
$164$	−2.42506e8	−0.0261774
$165$	−1.91577e7	−0.00201217
$166$	−2.18351e9	−0.223187
$167$	−1.64113e10	−1.63275	−0.816373	−	0.577525i	$-0.804019\pi$
$167$	−1.64113e10	−1.63275	−0.816373	+	0.577525i	$0.804019\pi$
$168$	0	0
$169$	2.03144e10	1.91564
$170$	2.23999e8	0.0205696
$171$	5.43773e8	0.0486334
$172$	−8.58029e9	−0.747522
$173$	−1.63721e9	−0.138962	−0.0694809	−	0.997583i	$-0.522134\pi$
$173$	−1.63721e9	−0.138962	−0.0694809	+	0.997583i	$0.522134\pi$
$174$	1.26408e9	0.104545
$175$	0	0
$176$	−4.62955e7	−0.00363691
$177$	−1.18214e10	−0.905290
$178$	4.70092e8	0.0350988
$179$	2.16058e10	1.57301	0.786506	−	0.617583i	$-0.211888\pi$
$179$	2.16058e10	1.57301	0.786506	+	0.617583i	$0.211888\pi$
$180$	3.54714e8	0.0251856
$181$	−1.49930e10	−1.03833	−0.519163	−	0.854675i	$-0.673756\pi$
$181$	−1.49930e10	−1.03833	−0.519163	+	0.854675i	$0.673756\pi$
$182$	0	0
$183$	2.68143e10	1.76741
$184$	1.45761e8	0.00937479
$185$	−1.06101e9	−0.0665960
$186$	−7.95816e8	−0.0487533
$187$	1.40743e7	0.000841663 0
$188$	−1.25655e10	−0.733618
$189$	0	0
$190$	−1.56250e9	−0.0869820
$191$	1.53348e10	0.833734	0.416867	−	0.908967i	$-0.363128\pi$
$191$	1.53348e10	0.833734	0.416867	+	0.908967i	$0.363128\pi$
$192$	1.30610e10	0.693617
$193$	1.71662e9	0.0890569	0.0445284	−	0.999008i	$-0.485821\pi$
$193$	1.71662e9	0.0890569	0.0445284	+	0.999008i	$0.485821\pi$
$194$	−5.64879e9	−0.286317
$195$	−1.58721e10	−0.786101
$196$	0	0
$197$	1.68528e10	0.797215	0.398607	−	0.917122i	$-0.369494\pi$
$197$	1.68528e10	0.797215	0.398607	+	0.917122i	$0.369494\pi$
$198$	−1.34841e6	−6.23490e−5 0
$199$	1.92812e9	0.0871558	0.0435779	−	0.999050i	$-0.486124\pi$
$199$	1.92812e9	0.0871558	0.0435779	+	0.999050i	$0.486124\pi$
$200$	−2.10017e9	−0.0928152
$201$	−3.93592e10	−1.70084
$202$	−8.53159e9	−0.360536
$203$	0	0
$204$	−4.62386e9	−0.186926
$205$	−3.13938e8	−0.0124152
$206$	−7.68976e9	−0.297516
$207$	−3.18704e7	−0.00120648
$208$	−3.83557e10	−1.42084
$209$	−9.81746e7	−0.00355911
$210$	0	0
$211$	8.00175e9	0.277916	0.138958	−	0.990298i	$-0.455625\pi$
$211$	8.00175e9	0.277916	0.138958	+	0.990298i	$0.455625\pi$
$212$	−3.79211e10	−1.28934
$213$	−1.04433e10	−0.347641
$214$	−4.81696e9	−0.157004
$215$	−1.11077e10	−0.354528
$216$	−1.43709e10	−0.449201
$217$	0	0
$218$	3.22956e9	0.0968477
$219$	−1.60893e10	−0.472650
$220$	−6.40412e7	−0.00184314
$221$	1.16605e10	0.328815
$222$	−1.32509e9	−0.0366148
$223$	4.99695e9	0.135311	0.0676554	−	0.997709i	$-0.478448\pi$
$223$	4.99695e9	0.135311	0.0676554	+	0.997709i	$0.478448\pi$
$224$	0	0
$225$	4.59197e8	0.0119448
$226$	2.73432e8	0.00697206
$227$	4.53936e10	1.13469	0.567346	−	0.823480i	$-0.307970\pi$
$227$	4.53936e10	1.13469	0.567346	+	0.823480i	$0.307970\pi$
$228$	3.22536e10	0.790446
$229$	9.09334e9	0.218506	0.109253	−	0.994014i	$-0.465154\pi$
$229$	9.09334e9	0.218506	0.109253	+	0.994014i	$0.465154\pi$
$230$	9.15778e7	0.00215782
$231$	0	0
$232$	8.70693e9	0.197319
$233$	−4.15098e10	−0.922675	−0.461338	−	0.887225i	$-0.652630\pi$
$233$	−4.15098e10	−0.922675	−0.461338	+	0.887225i	$0.652630\pi$
$234$	−1.11716e9	−0.0243580
$235$	−1.62668e10	−0.347934
$236$	−3.95170e10	−0.829240
$237$	−5.03789e10	−1.03724
$238$	0	0
$239$	6.96132e10	1.38007	0.690035	−	0.723776i	$-0.257595\pi$
$239$	6.96132e10	1.38007	0.690035	+	0.723776i	$0.257595\pi$
$240$	1.96897e10	0.383080
$241$	−8.75274e10	−1.67135	−0.835675	−	0.549224i	$-0.814923\pi$
$241$	−8.75274e10	−1.67135	−0.835675	+	0.549224i	$0.814923\pi$
$242$	−1.27435e10	−0.238847
$243$	6.48390e9	0.119291
$244$	8.96361e10	1.61893
$245$	0	0
$246$	−3.92075e8	−0.00682591
$247$	−8.13374e10	−1.39044
$248$	−5.48154e9	−0.0920173
$249$	5.83491e10	0.961916
$250$	−1.31948e9	−0.0213635
$251$	−9.14565e10	−1.45440	−0.727198	−	0.686428i	$-0.759178\pi$
$251$	−9.14565e10	−1.45440	−0.727198	+	0.686428i	$0.759178\pi$
$252$	0	0
$253$	5.75399e6	8.82931e−5 0
$254$	1.13486e10	0.171077
$255$	−5.98586e9	−0.0886534
$256$	3.27814e10	0.477032
$257$	1.24795e11	1.78442	0.892209	−	0.451623i	$-0.149155\pi$
$257$	1.24795e11	1.78442	0.892209	+	0.451623i	$0.149155\pi$
$258$	−1.38723e10	−0.194921
$259$	0	0
$260$	−5.30580e10	−0.720063
$261$	−1.90375e9	−0.0253938
$262$	2.98581e10	0.391477
$263$	4.16951e10	0.537384	0.268692	−	0.963226i	$-0.413409\pi$
$263$	4.16951e10	0.537384	0.268692	+	0.963226i	$0.413409\pi$
$264$	−1.64800e8	−0.00208804
$265$	−4.90910e10	−0.611498
$266$	0	0
$267$	−1.25621e10	−0.151273
$268$	−1.31572e11	−1.55796
$269$	−9.09454e10	−1.05900	−0.529499	−	0.848310i	$-0.677620\pi$
$269$	−9.09454e10	−1.05900	−0.529499	+	0.848310i	$0.677620\pi$
$270$	−9.02882e9	−0.103394
$271$	6.77697e10	0.763262	0.381631	−	0.924315i	$-0.375362\pi$
$271$	6.77697e10	0.763262	0.381631	+	0.924315i	$0.375362\pi$
$272$	−1.44651e10	−0.160237
$273$	0	0
$274$	−1.20649e10	−0.129315
$275$	−8.29051e7	−0.000874146 0
$276$	−1.89038e9	−0.0196091
$277$	−1.87907e11	−1.91771	−0.958856	−	0.283894i	$-0.908373\pi$
$277$	−1.87907e11	−1.91771	−0.958856	+	0.283894i	$0.908373\pi$
$278$	−2.78426e10	−0.279581
$279$	1.19853e9	0.0118421
$280$	0	0
$281$	−1.60407e11	−1.53478	−0.767389	−	0.641181i	$-0.778445\pi$
$281$	−1.60407e11	−1.53478	−0.767389	+	0.641181i	$0.778445\pi$
$282$	−2.03154e10	−0.191296
$283$	2.58420e10	0.239490	0.119745	−	0.992805i	$-0.461792\pi$
$283$	2.58420e10	0.239490	0.119745	+	0.992805i	$0.461792\pi$
$284$	−3.49105e10	−0.318437
$285$	4.17542e10	0.374885
$286$	2.01695e8	0.00178258
$287$	0	0
$288$	4.62182e9	0.0395865
$289$	−1.14190e11	−0.962918
$290$	5.47033e9	0.0454174
$291$	1.50951e11	1.23400
$292$	−5.37842e10	−0.432944
$293$	1.10643e11	0.877040	0.438520	−	0.898721i	$-0.355503\pi$
$293$	1.10643e11	0.877040	0.438520	+	0.898721i	$0.355503\pi$
$294$	0	0
$295$	−5.11570e10	−0.393284
$296$	−9.12714e9	−0.0691070
$297$	−5.67296e8	−0.00423064
$298$	−5.25117e10	−0.385729
$299$	4.76716e9	0.0344937
$300$	2.72371e10	0.194140
$301$	0	0
$302$	5.78827e10	0.400422
$303$	2.27987e11	1.55388
$304$	1.00901e11	0.677587
$305$	1.16039e11	0.767812
$306$	−4.21314e8	−0.00274701
$307$	1.08905e11	0.699722	0.349861	−	0.936802i	$-0.386229\pi$
$307$	1.08905e11	0.699722	0.349861	+	0.936802i	$0.386229\pi$
$308$	0	0
$309$	2.05491e11	1.28227
$310$	−3.44390e9	−0.0211799
$311$	−1.97229e11	−1.19550	−0.597749	−	0.801683i	$-0.703938\pi$
$311$	−1.97229e11	−1.19550	−0.597749	+	0.801683i	$0.703938\pi$
$312$	−1.36536e11	−0.815741
$313$	7.57585e10	0.446151	0.223076	−	0.974801i	$-0.428390\pi$
$313$	7.57585e10	0.446151	0.223076	+	0.974801i	$0.428390\pi$
$314$	3.18583e10	0.184944
$315$	0	0
$316$	−1.68409e11	−0.950108
$317$	1.87336e11	1.04197	0.520984	−	0.853566i	$-0.325565\pi$
$317$	1.87336e11	1.04197	0.520984	+	0.853566i	$0.325565\pi$
$318$	−6.13093e10	−0.336205
$319$	3.43710e8	0.00185838
$320$	5.65215e10	0.301327
$321$	1.28722e11	0.676675
$322$	0	0
$323$	−3.06749e10	−0.156809
$324$	1.97547e11	0.995903
$325$	−6.86866e10	−0.341505
$326$	2.93243e9	0.0143796
$327$	−8.63024e10	−0.417406
$328$	−2.70059e9	−0.0128833
$329$	0	0
$330$	−1.03539e8	−0.000480610 0
$331$	2.31201e11	1.05868	0.529340	−	0.848410i	$-0.322440\pi$
$331$	2.31201e11	1.05868	0.529340	+	0.848410i	$0.322440\pi$
$332$	1.95052e11	0.881109
$333$	1.99563e9	0.00889367
$334$	−8.86963e10	−0.389983
$335$	−1.70327e11	−0.738894
$336$	0	0
$337$	2.37206e11	1.00182	0.500911	−	0.865499i	$-0.332998\pi$
$337$	2.37206e11	1.00182	0.500911	+	0.865499i	$0.332998\pi$
$338$	1.09791e11	0.457552
$339$	−7.30682e9	−0.0300490
$340$	−2.00098e10	−0.0812060
$341$	−2.16386e8	−0.000866632 0
$342$	2.93887e9	0.0116162
$343$	0	0
$344$	−9.55515e10	−0.367895
$345$	−2.44720e9	−0.00930002
$346$	−8.84842e9	−0.0331912
$347$	−2.06749e11	−0.765527	−0.382763	−	0.923846i	$-0.625028\pi$
$347$	−2.06749e11	−0.765527	−0.382763	+	0.923846i	$0.625028\pi$
$348$	−1.12920e11	−0.412729
$349$	3.78449e10	0.136550	0.0682752	−	0.997667i	$-0.478250\pi$
$349$	3.78449e10	0.136550	0.0682752	+	0.997667i	$0.478250\pi$
$350$	0	0
$351$	−4.70003e11	−1.65279
$352$	−8.34440e8	−0.00289703
$353$	2.35080e11	0.805804	0.402902	−	0.915243i	$-0.368002\pi$
$353$	2.35080e11	0.805804	0.402902	+	0.915243i	$0.368002\pi$
$354$	−6.38895e10	−0.216230
$355$	−4.51936e10	−0.151025
$356$	−4.19932e10	−0.138565
$357$	0	0
$358$	1.16770e11	0.375716
$359$	2.05933e11	0.654336	0.327168	−	0.944966i	$-0.393906\pi$
$359$	2.05933e11	0.654336	0.327168	+	0.944966i	$0.393906\pi$
$360$	3.95015e9	0.0123952
$361$	−1.08716e11	−0.336908
$362$	−8.10307e10	−0.248005
$363$	3.40540e11	1.02941
$364$	0	0
$365$	−6.96267e10	−0.205333
$366$	1.44920e11	0.422147
$367$	5.67758e11	1.63368	0.816838	−	0.576868i	$-0.195725\pi$
$367$	5.67758e11	1.63368	0.816838	+	0.576868i	$0.195725\pi$
$368$	−5.91379e9	−0.0168093
$369$	5.90478e8	0.00165800
$370$	−5.73434e9	−0.0159065
$371$	0	0
$372$	7.10901e10	0.192471
$373$	4.13421e11	1.10587	0.552933	−	0.833226i	$-0.313509\pi$
$373$	4.13421e11	1.10587	0.552933	+	0.833226i	$0.313509\pi$
$374$	7.60655e7	0.000201032 0
$375$	3.52600e10	0.0920749
$376$	−1.39932e11	−0.361053
$377$	2.84763e11	0.726017
$378$	0	0
$379$	2.48740e11	0.619255	0.309627	−	0.950858i	$-0.399796\pi$
$379$	2.48740e11	0.619255	0.309627	+	0.950858i	$0.399796\pi$
$380$	1.39578e11	0.343392
$381$	−3.03265e11	−0.737327
$382$	8.28782e10	0.199138
$383$	3.56848e11	0.847399	0.423700	−	0.905803i	$-0.360731\pi$
$383$	3.56848e11	0.847399	0.423700	+	0.905803i	$0.360731\pi$
$384$	3.61316e11	0.848003
$385$	0	0
$386$	9.27764e9	0.0212713
$387$	2.08921e10	0.0473460
$388$	5.04605e11	1.13034
$389$	−1.54494e11	−0.342089	−0.171045	−	0.985263i	$-0.554714\pi$
$389$	−1.54494e11	−0.342089	−0.171045	+	0.985263i	$0.554714\pi$
$390$	−8.57820e10	−0.187761
$391$	1.79784e9	0.00389006
$392$	0	0
$393$	−7.97888e11	−1.68723
$394$	9.10826e10	0.190416
$395$	−2.18015e11	−0.450609
$396$	1.20453e8	0.000246145 0
$397$	6.14418e11	1.24139	0.620693	−	0.784054i	$-0.286851\pi$
$397$	6.14418e11	1.24139	0.620693	+	0.784054i	$0.286851\pi$
$398$	1.04207e10	0.0208173
$399$	0	0
$400$	8.52076e10	0.166421
$401$	4.70986e11	0.909616	0.454808	−	0.890589i	$-0.349708\pi$
$401$	4.70986e11	0.909616	0.454808	+	0.890589i	$0.349708\pi$
$402$	−2.12720e11	−0.406248
$403$	−1.79275e11	−0.338569
$404$	7.62125e11	1.42334
$405$	2.55736e11	0.472328
$406$	0	0
$407$	−3.60298e8	−0.000650859 0
$408$	−5.14921e10	−0.0919961
$409$	9.40676e11	1.66221	0.831103	−	0.556118i	$-0.187710\pi$
$409$	9.40676e11	1.66221	0.831103	+	0.556118i	$0.187710\pi$
$410$	−1.69671e9	−0.00296537
$411$	3.22407e11	0.557336
$412$	6.86925e11	1.17455
$413$	0	0
$414$	−1.72246e8	−0.000288169 0
$415$	2.52506e11	0.417884
$416$	−6.91331e11	−1.13179
$417$	7.44028e11	1.20497
$418$	−5.30593e8	−0.000850097 0
$419$	−4.87630e11	−0.772907	−0.386453	−	0.922309i	$-0.626300\pi$
$419$	−4.87630e11	−0.772907	−0.386453	+	0.922309i	$0.626300\pi$
$420$	0	0
$421$	−3.86173e11	−0.599118	−0.299559	−	0.954078i	$-0.596840\pi$
$421$	−3.86173e11	−0.599118	−0.299559	+	0.954078i	$0.596840\pi$
$422$	4.32461e10	0.0663806
$423$	3.05957e10	0.0464654
$424$	−4.22295e11	−0.634555
$425$	−2.59039e10	−0.0385136
$426$	−5.64419e10	−0.0830345
$427$	0	0
$428$	4.30298e11	0.619830
$429$	−5.38983e9	−0.00768276
$430$	−6.00324e10	−0.0846794
$431$	−7.19033e11	−1.00369	−0.501847	−	0.864957i	$-0.667346\pi$
$431$	−7.19033e11	−1.00369	−0.501847	+	0.864957i	$0.667346\pi$
$432$	5.83051e11	0.805434
$433$	−2.33884e11	−0.319746	−0.159873	−	0.987138i	$-0.551109\pi$
$433$	−2.33884e11	−0.319746	−0.159873	+	0.987138i	$0.551109\pi$
$434$	0	0
$435$	−1.46182e11	−0.195745
$436$	−2.88496e11	−0.382341
$437$	−1.25408e10	−0.0164498
$438$	−8.69562e10	−0.112893
$439$	1.29065e12	1.65851	0.829254	−	0.558872i	$-0.188766\pi$
$439$	1.29065e12	1.65851	0.829254	+	0.558872i	$0.188766\pi$
$440$	−7.13173e8	−0.000907106 0
$441$	0	0
$442$	6.30200e10	0.0785377
$443$	−9.64626e11	−1.18999	−0.594994	−	0.803730i	$-0.702845\pi$
$443$	−9.64626e11	−1.18999	−0.594994	+	0.803730i	$0.702845\pi$
$444$	1.18370e11	0.144550
$445$	−5.43626e10	−0.0657174
$446$	2.70064e10	0.0323192
$447$	1.40325e12	1.66246
$448$	0	0
$449$	−1.25561e12	−1.45796	−0.728978	−	0.684537i	$-0.760005\pi$
$449$	−1.25561e12	−1.45796	−0.728978	+	0.684537i	$0.760005\pi$
$450$	2.48177e9	0.00285302
$451$	−1.06607e8	−0.000121336 0
$452$	−2.44256e10	−0.0275247
$453$	−1.54678e12	−1.72579
$454$	2.45333e11	0.271022
$455$	0	0
$456$	3.59182e11	0.389020
$457$	−4.67060e11	−0.500898	−0.250449	−	0.968130i	$-0.580578\pi$
$457$	−4.67060e11	−0.500898	−0.250449	+	0.968130i	$0.580578\pi$
$458$	4.91458e10	0.0521905
$459$	−1.77253e11	−0.186396
$460$	−8.18063e9	−0.00851876
$461$	1.84971e11	0.190744	0.0953718	−	0.995442i	$-0.469596\pi$
$461$	1.84971e11	0.190744	0.0953718	+	0.995442i	$0.469596\pi$
$462$	0	0
$463$	−2.46173e11	−0.248958	−0.124479	−	0.992222i	$-0.539726\pi$
$463$	−2.46173e11	−0.248958	−0.124479	+	0.992222i	$0.539726\pi$
$464$	−3.53256e11	−0.353800
$465$	9.20302e10	0.0912834
$466$	−2.24343e11	−0.220382
$467$	−7.93271e11	−0.771784	−0.385892	−	0.922544i	$-0.626106\pi$
$467$	−7.93271e11	−0.771784	−0.385892	+	0.922544i	$0.626106\pi$
$468$	9.97952e10	0.0961620
$469$	0	0
$470$	−8.79153e10	−0.0831044
$471$	−8.51339e11	−0.797092
$472$	−4.40068e11	−0.408113
$473$	−3.77194e9	−0.00346489
$474$	−2.72277e11	−0.247747
$475$	1.80692e11	0.162861
$476$	0	0
$477$	9.23339e10	0.0816636
$478$	3.76231e11	0.329631
$479$	−1.94824e12	−1.69095	−0.845477	−	0.534012i	$-0.820684\pi$
$479$	−1.94824e12	−1.69095	−0.845477	+	0.534012i	$0.820684\pi$
$480$	3.54892e11	0.305148
$481$	−2.98506e11	−0.254273
$482$	−4.73049e11	−0.399204
$483$	0	0
$484$	1.13837e12	0.942932
$485$	6.53240e11	0.536087
$486$	3.50428e10	0.0284928
$487$	−5.77223e11	−0.465011	−0.232505	−	0.972595i	$-0.574692\pi$
$487$	−5.77223e11	−0.465011	−0.232505	+	0.972595i	$0.574692\pi$
$488$	9.98201e11	0.796763
$489$	−7.83623e10	−0.0619751
$490$	0	0
$491$	−6.72723e11	−0.522359	−0.261180	−	0.965290i	$-0.584112\pi$
$491$	−6.72723e11	−0.522359	−0.261180	+	0.965290i	$0.584112\pi$
$492$	3.50239e10	0.0269477
$493$	1.07393e11	0.0818774
$494$	−4.39595e11	−0.332109
$495$	1.55934e8	0.000116739 0
$496$	2.22396e11	0.164990
$497$	0	0
$498$	3.15353e11	0.229755
$499$	5.98672e11	0.432251	0.216126	−	0.976366i	$-0.430658\pi$
$499$	5.98672e11	0.432251	0.216126	+	0.976366i	$0.430658\pi$
$500$	1.17869e11	0.0843400
$501$	2.37020e12	1.68080
$502$	−4.94284e11	−0.347384
$503$	−1.47666e12	−1.02855	−0.514274	−	0.857626i	$-0.671939\pi$
$503$	−1.47666e12	−1.02855	−0.514274	+	0.857626i	$0.671939\pi$
$504$	0	0
$505$	9.86614e11	0.675050
$506$	3.10979e7	2.10889e−5 0
$507$	−2.93390e12	−1.97201
$508$	−1.01377e12	−0.675387
$509$	−8.53091e11	−0.563333	−0.281666	−	0.959512i	$-0.590887\pi$
$509$	−8.53091e11	−0.563333	−0.281666	+	0.959512i	$0.590887\pi$
$510$	−3.23511e10	−0.0211750
$511$	0	0
$512$	1.45807e12	0.937700
$513$	1.23642e12	0.788204
$514$	6.74463e11	0.426210
$515$	8.89263e11	0.557055
$516$	1.23921e12	0.769521
$517$	−5.52386e9	−0.00340044
$518$	0	0
$519$	2.36453e11	0.143051
$520$	−5.90862e11	−0.354381
$521$	1.21815e12	0.724321	0.362160	−	0.932116i	$-0.382039\pi$
$521$	1.21815e12	0.724321	0.362160	+	0.932116i	$0.382039\pi$
$522$	−1.02890e10	−0.00606534
$523$	−1.44018e12	−0.841702	−0.420851	−	0.907130i	$-0.638268\pi$
$523$	−1.44018e12	−0.841702	−0.420851	+	0.907130i	$0.638268\pi$
$524$	−2.66722e12	−1.54550
$525$	0	0
$526$	2.25345e11	0.128355
$527$	−6.76102e10	−0.0381825
$528$	6.68623e9	0.00374394
$529$	−1.80042e12	−0.999592
$530$	−2.65316e11	−0.146057
$531$	9.62198e10	0.0525218
$532$	0	0
$533$	−8.83235e10	−0.0474028
$534$	−6.78930e10	−0.0361318
$535$	5.57046e11	0.293967
$536$	−1.46520e12	−0.766754
$537$	−3.12042e12	−1.61930
$538$	−4.91522e11	−0.252943
$539$	0	0
$540$	8.06543e11	0.408184
$541$	−3.26999e12	−1.64119	−0.820594	−	0.571512i	$-0.806357\pi$
$541$	−3.26999e12	−1.64119	−0.820594	+	0.571512i	$0.806357\pi$
$542$	3.66267e11	0.182306
$543$	2.16536e12	1.06888
$544$	−2.60722e11	−0.127639
$545$	−3.73475e11	−0.181333
$546$	0	0
$547$	−1.33103e12	−0.635690	−0.317845	−	0.948143i	$-0.602959\pi$
$547$	−1.33103e12	−0.635690	−0.317845	+	0.948143i	$0.602959\pi$
$548$	1.07776e12	0.510516
$549$	−2.18255e11	−0.102539
$550$	−4.48067e8	−0.000208791 0
$551$	−7.49116e11	−0.346232
$552$	−2.10515e10	−0.00965068
$553$	0	0
$554$	−1.01556e12	−0.458048
$555$	1.53237e11	0.0685558
$556$	2.48717e12	1.10375
$557$	3.21451e12	1.41503	0.707516	−	0.706697i	$-0.249816\pi$
$557$	3.21451e12	1.41503	0.707516	+	0.706697i	$0.249816\pi$
$558$	6.47754e9	0.00282850
$559$	−3.12504e12	−1.35364
$560$	0	0
$561$	−2.03267e9	−0.000866432 0
$562$	−8.66935e11	−0.366584
$563$	4.13522e12	1.73465	0.867323	−	0.497746i	$-0.165839\pi$
$563$	4.13522e12	1.73465	0.867323	+	0.497746i	$0.165839\pi$
$564$	1.81477e12	0.755208
$565$	−3.16203e10	−0.0130541
$566$	1.39665e11	0.0572024
$567$	0	0
$568$	−3.88769e11	−0.156720
$569$	−2.84974e11	−0.113972	−0.0569862	−	0.998375i	$-0.518149\pi$
$569$	−2.84974e11	−0.113972	−0.0569862	+	0.998375i	$0.518149\pi$
$570$	2.25664e11	0.0895418
$571$	−9.60485e11	−0.378118	−0.189059	−	0.981966i	$-0.560544\pi$
$571$	−9.60485e11	−0.378118	−0.189059	+	0.981966i	$0.560544\pi$
$572$	−1.80174e10	−0.00703735
$573$	−2.21472e12	−0.858270
$574$	0	0
$575$	−1.05903e10	−0.00404020
$576$	−1.06310e11	−0.0402412
$577$	−2.71877e12	−1.02113	−0.510566	−	0.859838i	$-0.670564\pi$
$577$	−2.71877e12	−1.02113	−0.510566	+	0.859838i	$0.670564\pi$
$578$	−6.17152e11	−0.229994
$579$	−2.47923e11	−0.0916777
$580$	−4.88663e11	−0.179301
$581$	0	0
$582$	8.15826e11	0.294743
$583$	−1.66703e10	−0.00597633
$584$	−5.98949e11	−0.213075
$585$	1.29191e11	0.0456068
$586$	5.97979e11	0.209482
$587$	−4.24800e12	−1.47677	−0.738385	−	0.674379i	$-0.764411\pi$
$587$	−4.24800e12	−1.47677	−0.738385	+	0.674379i	$0.764411\pi$
$588$	0	0
$589$	4.71614e11	0.161461
$590$	−2.76483e11	−0.0939364
$591$	−2.43397e12	−0.820676
$592$	3.70304e11	0.123911
$593$	−2.98332e12	−0.990727	−0.495364	−	0.868686i	$-0.664965\pi$
$593$	−2.98332e12	−0.990727	−0.495364	+	0.868686i	$0.664965\pi$
$594$	−3.06600e9	−0.00101049
$595$	0	0
$596$	4.69086e12	1.52280
$597$	−2.78469e11	−0.0897207
$598$	2.57645e10	0.00823886
$599$	5.02044e12	1.59339	0.796693	−	0.604385i	$-0.206581\pi$
$599$	5.02044e12	1.59339	0.796693	+	0.604385i	$0.206581\pi$
$600$	3.03317e11	0.0955466
$601$	−6.50005e11	−0.203227	−0.101613	−	0.994824i	$-0.532400\pi$
$601$	−6.50005e11	−0.203227	−0.101613	+	0.994824i	$0.532400\pi$
$602$	0	0
$603$	3.20363e11	0.0986768
$604$	−5.17065e12	−1.58081
$605$	1.47369e12	0.447205
$606$	1.23217e12	0.371146
$607$	3.78352e12	1.13122	0.565610	−	0.824673i	$-0.308641\pi$
$607$	3.78352e12	1.13122	0.565610	+	0.824673i	$0.308641\pi$
$608$	1.81866e12	0.539742
$609$	0	0
$610$	6.27143e11	0.183393
$611$	−4.57650e12	−1.32846
$612$	3.76359e10	0.0108448
$613$	5.13548e12	1.46896	0.734478	−	0.678632i	$-0.237427\pi$
$613$	5.13548e12	1.46896	0.734478	+	0.678632i	$0.237427\pi$
$614$	5.88587e11	0.167129
$615$	4.53405e10	0.0127805
$616$	0	0
$617$	−6.73391e12	−1.87061	−0.935307	−	0.353837i	$-0.884877\pi$
$617$	−6.73391e12	−1.87061	−0.935307	+	0.353837i	$0.884877\pi$
$618$	1.11059e12	0.306272
$619$	−1.11783e11	−0.0306032	−0.0153016	−	0.999883i	$-0.504871\pi$
$619$	−1.11783e11	−0.0306032	−0.0153016	+	0.999883i	$0.504871\pi$
$620$	3.07643e11	0.0836150
$621$	−7.24664e10	−0.0195535
$622$	−1.06594e12	−0.285546
$623$	0	0
$624$	5.53952e12	1.46265
$625$	1.52588e11	0.0400000
$626$	4.09443e11	0.106564
$627$	1.41789e10	0.00366385
$628$	−2.84590e12	−0.730131
$629$	−1.12576e11	−0.0286759
$630$	0	0
$631$	3.95171e12	0.992322	0.496161	−	0.868231i	$-0.334743\pi$
$631$	3.95171e12	0.992322	0.496161	+	0.868231i	$0.334743\pi$
$632$	−1.87543e12	−0.467599
$633$	−1.15565e12	−0.286095
$634$	1.01247e12	0.248876
$635$	−1.31238e12	−0.320316
$636$	5.47674e12	1.32729
$637$	0	0
$638$	1.85761e9	0.000443876 0
$639$	8.50034e10	0.0201689
$640$	1.56360e12	0.368397
$641$	−8.34229e12	−1.95175	−0.975875	−	0.218332i	$-0.929939\pi$
$641$	−8.34229e12	−1.95175	−0.975875	+	0.218332i	$0.929939\pi$
$642$	6.95689e11	0.161625
$643$	−3.74487e12	−0.863948	−0.431974	−	0.901886i	$-0.642183\pi$
$643$	−3.74487e12	−0.863948	−0.431974	+	0.901886i	$0.642183\pi$
$644$	0	0
$645$	1.60423e12	0.364961
$646$	−1.65785e11	−0.0374540
$647$	−2.12177e11	−0.0476024	−0.0238012	−	0.999717i	$-0.507577\pi$
$647$	−2.12177e11	−0.0476024	−0.0238012	+	0.999717i	$0.507577\pi$
$648$	2.19991e12	0.490137
$649$	−1.73719e10	−0.00384366
$650$	−3.71223e11	−0.0815688
$651$	0	0
$652$	−2.61953e11	−0.0567688
$653$	−5.52575e12	−1.18927	−0.594637	−	0.803994i	$-0.702704\pi$
$653$	−5.52575e12	−1.18927	−0.594637	+	0.803994i	$0.702704\pi$
$654$	−4.66429e11	−0.0996978
$655$	−3.45287e12	−0.732983
$656$	1.09568e11	0.0231002
$657$	1.30959e11	0.0274215
$658$	0	0
$659$	−7.16711e12	−1.48033	−0.740167	−	0.672423i	$-0.765254\pi$
$659$	−7.16711e12	−1.48033	−0.740167	+	0.672423i	$0.765254\pi$
$660$	9.24915e9	0.00189738
$661$	−8.03527e12	−1.63717	−0.818586	−	0.574384i	$-0.805241\pi$
$661$	−8.03527e12	−1.63717	−0.818586	+	0.574384i	$0.805241\pi$
$662$	1.24955e12	0.252867
$663$	−1.68406e12	−0.338491
$664$	2.17213e12	0.433641
$665$	0	0
$666$	1.07856e10	0.00212426
$667$	4.39055e10	0.00858920
$668$	7.92322e12	1.53960
$669$	−7.21683e11	−0.139293
$670$	−9.20547e11	−0.176486
$671$	3.94044e10	0.00750402
$672$	0	0
$673$	−1.07643e12	−0.202264	−0.101132	−	0.994873i	$-0.532247\pi$
$673$	−1.07643e12	−0.202264	−0.101132	+	0.994873i	$0.532247\pi$
$674$	1.28200e12	0.239287
$675$	1.04412e12	0.193589
$676$	−9.80759e12	−1.80635
$677$	2.34762e12	0.429516	0.214758	−	0.976667i	$-0.431104\pi$
$677$	2.34762e12	0.429516	0.214758	+	0.976667i	$0.431104\pi$
$678$	−3.94904e10	−0.00717724
$679$	0	0
$680$	−2.22832e11	−0.0399658
$681$	−6.55596e12	−1.16808
$682$	−1.16948e9	−0.000206996 0
$683$	9.76504e11	0.171704	0.0858521	−	0.996308i	$-0.472639\pi$
$683$	9.76504e11	0.171704	0.0858521	+	0.996308i	$0.472639\pi$
$684$	−2.62528e11	−0.0458589
$685$	1.39522e12	0.242123
$686$	0	0
$687$	−1.31330e12	−0.224937
$688$	3.87669e12	0.659650
$689$	−1.38113e13	−2.33479
$690$	−1.32261e10	−0.00222132
$691$	1.66239e12	0.277383	0.138692	−	0.990336i	$-0.455710\pi$
$691$	1.66239e12	0.277383	0.138692	+	0.990336i	$0.455710\pi$
$692$	7.90427e11	0.131034
$693$	0	0
$694$	−1.11739e12	−0.182847
$695$	3.21979e12	0.523475
$696$	−1.25750e12	−0.203126
$697$	−3.33095e10	−0.00534590
$698$	2.04536e11	0.0326152
$699$	5.99505e12	0.949828
$700$	0	0
$701$	7.09258e12	1.10936	0.554681	−	0.832063i	$-0.312840\pi$
$701$	7.09258e12	1.10936	0.554681	+	0.832063i	$0.312840\pi$
$702$	−2.54017e12	−0.394772
$703$	7.85270e11	0.121261
$704$	1.91935e10	0.00294495
$705$	2.34933e12	0.358173
$706$	1.27051e12	0.192467
$707$	0	0
$708$	5.70724e12	0.853643
$709$	1.05215e13	1.56377	0.781883	−	0.623426i	$-0.214260\pi$
$709$	1.05215e13	1.56377	0.781883	+	0.623426i	$0.214260\pi$
$710$	−2.44253e11	−0.0360726
$711$	4.10058e11	0.0601773
$712$	−4.67643e11	−0.0681953
$713$	−2.76412e10	−0.00400547
$714$	0	0
$715$	−2.33245e10	−0.00333761
$716$	−1.04311e13	−1.48327
$717$	−1.00539e13	−1.42068
$718$	1.11298e12	0.156289
$719$	−3.31659e11	−0.0462819	−0.0231410	−	0.999732i	$-0.507367\pi$
$719$	−3.31659e11	−0.0462819	−0.0231410	+	0.999732i	$0.507367\pi$
$720$	−1.60264e11	−0.0222250
$721$	0	0
$722$	−5.87565e11	−0.0804708
$723$	1.26411e13	1.72054
$724$	7.23846e12	0.979090
$725$	−6.32603e11	−0.0850374
$726$	1.84048e12	0.245876
$727$	−1.15087e13	−1.52799	−0.763996	−	0.645221i	$-0.776765\pi$
$727$	−1.15087e13	−1.52799	−0.763996	+	0.645221i	$0.776765\pi$
$728$	0	0
$729$	7.11739e12	0.933355
$730$	−3.76304e11	−0.0490440
$731$	−1.17855e12	−0.152658
$732$	−1.29457e13	−1.66658
$733$	−1.93503e12	−0.247582	−0.123791	−	0.992308i	$-0.539505\pi$
$733$	−1.93503e12	−0.247582	−0.123791	+	0.992308i	$0.539505\pi$
$734$	3.06850e12	0.390205
$735$	0	0
$736$	−1.06591e11	−0.0133897
$737$	−5.78395e10	−0.00722139
$738$	3.19129e9	0.000396016 0
$739$	−4.05351e12	−0.499955	−0.249977	−	0.968252i	$-0.580423\pi$
$739$	−4.05351e12	−0.499955	−0.249977	+	0.968252i	$0.580423\pi$
$740$	5.12247e11	0.0627967
$741$	1.17471e13	1.43136
$742$	0	0
$743$	3.85392e12	0.463930	0.231965	−	0.972724i	$-0.425485\pi$
$743$	3.85392e12	0.463930	0.231965	+	0.972724i	$0.425485\pi$
$744$	7.91670e11	0.0947253
$745$	6.07258e12	0.722221
$746$	2.23437e12	0.264137
$747$	−4.74932e11	−0.0558070
$748$	−6.79491e9	−0.000793646 0
$749$	0	0
$750$	1.90566e11	0.0219922
$751$	5.30260e12	0.608288	0.304144	−	0.952626i	$-0.401630\pi$
$751$	5.30260e12	0.608288	0.304144	+	0.952626i	$0.401630\pi$
$752$	5.67727e12	0.647380
$753$	1.32086e13	1.49720
$754$	1.53902e12	0.173410
$755$	−6.69371e12	−0.749731
$756$	0	0
$757$	−1.33892e13	−1.48192	−0.740959	−	0.671550i	$-0.765629\pi$
$757$	−1.33892e13	−1.48192	−0.740959	+	0.671550i	$0.765629\pi$
$758$	1.34434e12	0.147910
$759$	−8.31019e8	−9.08914e−5 0
$760$	1.55436e12	0.169002
$761$	1.10632e13	1.19578	0.597890	−	0.801578i	$-0.296006\pi$
$761$	1.10632e13	1.19578	0.597890	+	0.801578i	$0.296006\pi$
$762$	−1.63902e12	−0.176111
$763$	0	0
$764$	−7.40349e12	−0.786170
$765$	4.87218e10	0.00514336
$766$	1.92861e12	0.202402
$767$	−1.43925e13	−1.50161
$768$	−4.73445e12	−0.491071
$769$	2.71361e12	0.279820	0.139910	−	0.990164i	$-0.455319\pi$
$769$	2.71361e12	0.279820	0.139910	+	0.990164i	$0.455319\pi$
$770$	0	0
$771$	−1.80234e13	−1.83693
$772$	−8.28770e11	−0.0839762
$773$	1.18476e13	1.19350	0.596749	−	0.802428i	$-0.296459\pi$
$773$	1.18476e13	1.19350	0.596749	+	0.802428i	$0.296459\pi$
$774$	1.12913e11	0.0113086
$775$	3.98261e11	0.0396562
$776$	5.61936e12	0.556300
$777$	0	0
$778$	−8.34978e11	−0.0817084
$779$	2.32350e11	0.0226060
$780$	7.66289e12	0.741254
$781$	−1.53468e10	−0.00147601
$782$	9.71661e9	0.000929147 0
$783$	−4.32872e12	−0.411559
$784$	0	0
$785$	−3.68418e12	−0.346280
$786$	−4.31225e12	−0.402998
$787$	−2.03165e12	−0.188783	−0.0943914	−	0.995535i	$-0.530091\pi$
$787$	−2.03165e12	−0.188783	−0.0943914	+	0.995535i	$0.530091\pi$
$788$	−8.13639e12	−0.751734
$789$	−6.02181e12	−0.553198
$790$	−1.17828e12	−0.107628
$791$	0	0
$792$	1.34139e9	0.000121141 0
$793$	3.26465e13	2.93161
$794$	3.32067e12	0.296506
$795$	7.08996e12	0.629494
$796$	−9.30880e11	−0.0821835
$797$	5.21189e12	0.457543	0.228772	−	0.973480i	$-0.426529\pi$
$797$	5.21189e12	0.457543	0.228772	+	0.973480i	$0.426529\pi$
$798$	0	0
$799$	−1.72594e12	−0.149819
$800$	1.53580e12	0.132565
$801$	1.02249e11	0.00877634
$802$	2.54548e12	0.217263
$803$	−2.36438e10	−0.00200677
$804$	1.90022e13	1.60381
$805$	0	0
$806$	−9.68908e11	−0.0808677
$807$	1.31348e13	1.09016
$808$	8.48714e12	0.700504
$809$	1.34215e13	1.10162	0.550812	−	0.834630i	$-0.314318\pi$
$809$	1.34215e13	1.10162	0.550812	+	0.834630i	$0.314318\pi$
$810$	1.38214e12	0.112816
$811$	1.86464e12	0.151356	0.0756782	−	0.997132i	$-0.475888\pi$
$811$	1.86464e12	0.151356	0.0756782	+	0.997132i	$0.475888\pi$
$812$	0	0
$813$	−9.78763e12	−0.785724
$814$	−1.94726e9	−0.000155458 0
$815$	−3.39113e11	−0.0269238
$816$	2.08912e12	0.164952
$817$	8.22094e12	0.645539
$818$	5.08396e12	0.397020
$819$	0	0
$820$	1.51566e11	0.0117069
$821$	2.27753e12	0.174952	0.0874762	−	0.996167i	$-0.472120\pi$
$821$	2.27753e12	0.174952	0.0874762	+	0.996167i	$0.472120\pi$
$822$	1.74248e12	0.133120
$823$	1.31485e13	0.999023	0.499511	−	0.866307i	$-0.333513\pi$
$823$	1.31485e13	0.999023	0.499511	+	0.866307i	$0.333513\pi$
$824$	7.64970e12	0.578059
$825$	1.19736e10	0.000899871 0
$826$	0	0
$827$	6.06740e12	0.451053	0.225527	−	0.974237i	$-0.427590\pi$
$827$	6.06740e12	0.451053	0.225527	+	0.974237i	$0.427590\pi$
$828$	1.53867e10	0.00113765
$829$	−1.08516e13	−0.797991	−0.398995	−	0.916953i	$-0.630641\pi$
$829$	−1.08516e13	−0.797991	−0.398995	+	0.916953i	$0.630641\pi$
$830$	1.36469e12	0.0998121
$831$	2.71384e13	1.97415
$832$	1.59018e13	1.15051
$833$	0	0
$834$	4.02116e12	0.287809
$835$	1.02571e13	0.730187
$836$	4.73978e10	0.00335606
$837$	2.72519e12	0.191925
$838$	−2.63544e12	−0.184610
$839$	−1.44757e13	−1.00858	−0.504289	−	0.863535i	$-0.668245\pi$
$839$	−1.44757e13	−1.00858	−0.504289	+	0.863535i	$0.668245\pi$
$840$	0	0
$841$	−1.18845e13	−0.819216
$842$	−2.08711e12	−0.143100
$843$	2.31668e13	1.57995
$844$	−3.86317e12	−0.262061
$845$	−1.26965e13	−0.856699
$846$	1.65357e11	0.0110983
$847$	0	0
$848$	1.71333e13	1.13778
$849$	−3.73223e12	−0.246538
$850$	−1.40000e11	−0.00919902
$851$	−4.60245e10	−0.00300819
$852$	5.04194e12	0.327808
$853$	−4.07815e12	−0.263750	−0.131875	−	0.991266i	$-0.542100\pi$
$853$	−4.07815e12	−0.263750	−0.131875	+	0.991266i	$0.542100\pi$
$854$	0	0
$855$	−3.39858e11	−0.0217495
$856$	4.79187e12	0.305051
$857$	−5.88651e12	−0.372773	−0.186386	−	0.982477i	$-0.559678\pi$
$857$	−5.88651e12	−0.372773	−0.186386	+	0.982477i	$0.559678\pi$
$858$	−2.91298e10	−0.00183504
$859$	−8.19019e12	−0.513245	−0.256623	−	0.966512i	$-0.582610\pi$
$859$	−8.19019e12	−0.513245	−0.256623	+	0.966512i	$0.582610\pi$
$860$	5.36268e12	0.334302
$861$	0	0
$862$	−3.88607e12	−0.239733
$863$	2.82802e13	1.73554	0.867768	−	0.496970i	$-0.165554\pi$
$863$	2.82802e13	1.73554	0.867768	+	0.496970i	$0.165554\pi$
$864$	1.05090e13	0.641580
$865$	1.02325e12	0.0621456
$866$	−1.26405e12	−0.0763718
$867$	1.64919e13	0.991255
$868$	0	0
$869$	−7.40333e10	−0.00440391
$870$	−7.90052e11	−0.0467540
$871$	−4.79199e13	−2.82120
$872$	−3.21274e12	−0.188170
$873$	−1.22866e12	−0.0715926
$874$	−6.77780e10	−0.00392905
$875$	0	0
$876$	7.76778e12	0.445685
$877$	−7.31598e12	−0.417614	−0.208807	−	0.977957i	$-0.566958\pi$
$877$	−7.31598e12	−0.417614	−0.208807	+	0.977957i	$0.566958\pi$
$878$	6.97542e12	0.396137
$879$	−1.59796e13	−0.902851
$880$	2.89347e10	0.00162647
$881$	9.97541e12	0.557878	0.278939	−	0.960309i	$-0.410017\pi$
$881$	9.97541e12	0.557878	0.278939	+	0.960309i	$0.410017\pi$
$882$	0	0
$883$	−2.04212e13	−1.13047	−0.565233	−	0.824931i	$-0.691214\pi$
$883$	−2.04212e13	−1.13047	−0.565233	+	0.824931i	$0.691214\pi$
$884$	−5.62957e12	−0.310056
$885$	7.38835e12	0.404858
$886$	−5.21341e12	−0.284230
$887$	2.97743e13	1.61505	0.807524	−	0.589835i	$-0.200807\pi$
$887$	2.97743e13	1.61505	0.807524	+	0.589835i	$0.200807\pi$
$888$	1.31819e12	0.0711408
$889$	0	0
$890$	−2.93807e11	−0.0156967
$891$	8.68424e10	0.00461618
$892$	−2.41248e12	−0.127591
$893$	1.20393e13	0.633532
$894$	7.58399e12	0.397081
$895$	−1.35036e13	−0.703472
$896$	0	0
$897$	−6.88497e11	−0.0355088
$898$	−6.78603e12	−0.348235
$899$	−1.65112e12	−0.0843064
$900$	−2.21696e11	−0.0112633
$901$	−5.20866e12	−0.263308
$902$	−5.76166e8	−2.89813e−5 0
$903$	0	0
$904$	−2.72007e11	−0.0135464
$905$	9.37060e12	0.464354
$906$	−8.35971e12	−0.412206
$907$	−2.06267e13	−1.01204	−0.506019	−	0.862523i	$-0.668883\pi$
$907$	−2.06267e13	−1.01204	−0.506019	+	0.862523i	$0.668883\pi$
$908$	−2.19156e13	−1.06996
$909$	−1.85570e12	−0.0901507
$910$	0	0
$911$	−2.52587e13	−1.21500	−0.607502	−	0.794318i	$-0.707828\pi$
$911$	−2.52587e13	−1.21500	−0.607502	+	0.794318i	$0.707828\pi$
$912$	−1.45726e13	−0.697528
$913$	8.57459e10	0.00408408
$914$	−2.52426e12	−0.119640
$915$	−1.67589e13	−0.790408
$916$	−4.39018e12	−0.206041
$917$	0	0
$918$	−9.57978e11	−0.0445208
$919$	−2.09741e13	−0.969981	−0.484991	−	0.874519i	$-0.661177\pi$
$919$	−2.09741e13	−0.969981	−0.484991	+	0.874519i	$0.661177\pi$
$920$	−9.11007e10	−0.00419254
$921$	−1.57286e13	−0.720314
$922$	9.99692e11	0.0455593
$923$	−1.27148e13	−0.576636
$924$	0	0
$925$	6.63133e11	0.0297826
$926$	−1.33046e12	−0.0594640
$927$	−1.67259e12	−0.0743928
$928$	−6.36715e12	−0.281825
$929$	−1.64770e13	−0.725786	−0.362893	−	0.931831i	$-0.618211\pi$
$929$	−1.64770e13	−0.725786	−0.362893	+	0.931831i	$0.618211\pi$
$930$	4.97385e11	0.0218032
$931$	0	0
$932$	2.00405e13	0.870037
$933$	2.84848e13	1.23068
$934$	−4.28730e12	−0.184341
$935$	−8.79641e9	−0.000376403 0
$936$	1.11134e12	0.0473264
$937$	2.36772e13	1.00346	0.501732	−	0.865023i	$-0.332696\pi$
$937$	2.36772e13	1.00346	0.501732	+	0.865023i	$0.332696\pi$
$938$	0	0
$939$	−1.09414e13	−0.459281
$940$	7.85345e12	0.328084
$941$	−4.05889e13	−1.68754	−0.843770	−	0.536706i	$-0.819669\pi$
$941$	−4.05889e13	−1.68754	−0.843770	+	0.536706i	$0.819669\pi$
$942$	−4.60113e12	−0.190386
$943$	−1.36180e10	−0.000560802 0
$944$	1.78543e13	0.731761
$945$	0	0
$946$	−2.03858e10	−0.000827593 0
$947$	−4.78061e13	−1.93156	−0.965780	−	0.259364i	$-0.916487\pi$
$947$	−4.78061e13	−1.93156	−0.965780	+	0.259364i	$0.916487\pi$
$948$	2.43224e13	0.978069
$949$	−1.95888e13	−0.783989
$950$	9.76564e11	0.0388995
$951$	−2.70560e13	−1.07263
$952$	0	0
$953$	2.83337e13	1.11272	0.556358	−	0.830943i	$-0.312198\pi$
$953$	2.83337e13	1.11272	0.556358	+	0.830943i	$0.312198\pi$
$954$	4.99026e11	0.0195054
$955$	−9.58424e12	−0.372857
$956$	−3.36086e13	−1.30134
$957$	−4.96403e10	−0.00191307
$958$	−1.05294e13	−0.403886
$959$	0	0
$960$	−8.16311e12	−0.310195
$961$	−2.54001e13	−0.960685
$962$	−1.61330e12	−0.0607334
$963$	−1.04773e12	−0.0392583
$964$	4.22574e13	1.57600
$965$	−1.07289e12	−0.0398274
$966$	0	0
$967$	2.91402e13	1.07170	0.535850	−	0.844313i	$-0.319991\pi$
$967$	2.91402e13	1.07170	0.535850	+	0.844313i	$0.319991\pi$
$968$	1.26771e13	0.464067
$969$	4.43021e12	0.161424
$970$	3.53049e12	0.128045
$971$	4.08627e12	0.147517	0.0737583	−	0.997276i	$-0.476501\pi$
$971$	4.08627e12	0.147517	0.0737583	+	0.997276i	$0.476501\pi$
$972$	−3.13036e12	−0.112485
$973$	0	0
$974$	−3.11965e12	−0.111068
$975$	9.92005e12	0.351555
$976$	−4.04988e13	−1.42862
$977$	4.35920e13	1.53067	0.765335	−	0.643632i	$-0.222573\pi$
$977$	4.35920e13	1.53067	0.765335	+	0.643632i	$0.222573\pi$
$978$	−4.23515e11	−0.0148028
$979$	−1.84604e10	−0.000642272 0
$980$	0	0
$981$	7.02458e11	0.0242164
$982$	−3.63579e12	−0.124766
$983$	3.75023e13	1.28105	0.640526	−	0.767937i	$-0.278717\pi$
$983$	3.75023e13	1.28105	0.640526	+	0.767937i	$0.278717\pi$
$984$	3.90032e11	0.0132624
$985$	−1.05330e13	−0.356525
$986$	5.80414e11	0.0195565
$987$	0	0
$988$	3.92689e13	1.31112
$989$	−4.81827e11	−0.0160143
$990$	8.42757e8	2.78833e−5 0
$991$	−2.18234e12	−0.0718772	−0.0359386	−	0.999354i	$-0.511442\pi$
$991$	−2.18234e12	−0.0718772	−0.0359386	+	0.999354i	$0.511442\pi$
$992$	4.00850e12	0.131425
$993$	−3.33912e13	−1.08984
$994$	0	0
$995$	−1.20508e12	−0.0389772
$996$	−2.81704e13	−0.907039
$997$	−2.40921e13	−0.772230	−0.386115	−	0.922451i	$-0.626183\pi$
$997$	−2.40921e13	−0.772230	−0.386115	+	0.922451i	$0.626183\pi$
$998$	3.23557e12	0.103244
$999$	4.53763e12	0.144140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.n.1.10	✓	18
7.6	odd	2		245.10.a.o.1.10	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.10.a.n.1.10	✓	18	1.1	even	1	trivial
245.10.a.o.1.10	yes	18	7.6	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+5.40459 q^{2} -144.425 q^{3} -482.790 q^{4} -625.000 q^{5} -780.557 q^{6} -5376.43 q^{8} +1175.54 q^{9} -3377.87 q^{10} -212.237 q^{11} +69727.0 q^{12} -175838. q^{13} +90265.5 q^{15} +218131. q^{16} -66313.9 q^{17} +6353.33 q^{18} +462571. q^{19} +301744. q^{20} -1147.05 q^{22} -27111.1 q^{23} +776490. q^{24} +390625. q^{25} -950330. q^{26} +2.67294e6 q^{27} -1.61946e6 q^{29} +487848. q^{30} +1.01955e6 q^{31} +3.93164e6 q^{32} +30652.3 q^{33} -358399. q^{34} -567542. q^{36} +1.69762e6 q^{37} +2.50000e6 q^{38} +2.53953e7 q^{39} +3.36027e6 q^{40} +502301. q^{41} +1.77723e7 q^{43} +102466. q^{44} -734716. q^{45} -146525. q^{46} +2.60269e7 q^{47} -3.15036e7 q^{48} +2.11117e6 q^{50} +9.57737e6 q^{51} +8.48927e7 q^{52} +7.85456e7 q^{53} +1.44461e7 q^{54} +132648. q^{55} -6.68067e7 q^{57} -8.75253e6 q^{58} +8.18513e7 q^{59} -4.35793e7 q^{60} -1.85662e8 q^{61} +5.51024e6 q^{62} -9.04343e7 q^{64} +1.09899e8 q^{65} +165663. q^{66} +2.72523e8 q^{67} +3.20157e7 q^{68} +3.91552e6 q^{69} +7.23098e7 q^{71} -6.32023e6 q^{72} +1.11403e8 q^{73} +9.17494e6 q^{74} -5.64160e7 q^{75} -2.23325e8 q^{76} +1.37251e8 q^{78} +3.48824e8 q^{79} -1.36332e8 q^{80} -4.09177e8 q^{81} +2.71473e6 q^{82} -4.04010e8 q^{83} +4.14462e7 q^{85} +9.60519e7 q^{86} +2.33891e8 q^{87} +1.14108e6 q^{88} +8.69802e7 q^{89} -3.97083e6 q^{90} +1.30890e7 q^{92} -1.47248e8 q^{93} +1.40664e8 q^{94} -2.89107e8 q^{95} -5.67827e8 q^{96} -1.04518e9 q^{97} -249494. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 66 q^{2} - 112 q^{3} + 4438 q^{4} - 11250 q^{5} - 5184 q^{6} + 58542 q^{8} + 117250 q^{9} - 41250 q^{10} - 50448 q^{11} + 51200 q^{12} - 265416 q^{13} + 70000 q^{15} + 275354 q^{16} - 742108 q^{17}+ \cdots - 3327698948 q^{99}+O(q^{100}) \) 18 * q + 66 * q^2 - 112 * q^3 + 4438 * q^4 - 11250 * q^5 - 5184 * q^6 + 58542 * q^8 + 117250 * q^9 - 41250 * q^10 - 50448 * q^11 + 51200 * q^12 - 265416 * q^13 + 70000 * q^15 + 275354 * q^16 - 742108 * q^17 + 31422 * q^18 - 2003052 * q^19 - 2773750 * q^20 - 898372 * q^22 + 5864112 * q^23 - 7257292 * q^24 + 7031250 * q^25 - 4213696 * q^26 - 12641932 * q^27 + 6575952 * q^29 + 3240000 * q^30 - 15704952 * q^31 + 24442110 * q^32 - 23661356 * q^33 + 7374732 * q^34 + 49561790 * q^36 + 8711420 * q^37 - 8938900 * q^38 + 48598700 * q^39 - 36588750 * q^40 + 5319344 * q^41 + 52311916 * q^43 - 35094960 * q^44 - 73281250 * q^45 + 98407276 * q^46 - 113473964 * q^47 + 50036228 * q^48 + 25781250 * q^50 + 108467832 * q^51 - 193287600 * q^52 + 31548852 * q^53 - 116650276 * q^54 + 31530000 * q^55 + 68889076 * q^57 - 65260756 * q^58 - 267674844 * q^59 - 32000000 * q^60 - 321756900 * q^61 - 651435868 * q^62 - 585550558 * q^64 + 165885000 * q^65 - 865081780 * q^66 - 234918184 * q^67 - 844088700 * q^68 - 380592968 * q^69 - 795896592 * q^71 + 70394666 * q^72 - 617344800 * q^73 - 1029168024 * q^74 - 43750000 * q^75 - 1200935100 * q^76 - 1277509816 * q^78 - 63002188 * q^79 - 172096250 * q^80 + 306235886 * q^81 + 1719855588 * q^82 - 534295300 * q^83 + 463817500 * q^85 + 65726340 * q^86 + 1504843540 * q^87 - 1698935556 * q^88 - 100440944 * q^89 - 19638750 * q^90 + 3229447776 * q^92 - 414903656 * q^93 + 1013675148 * q^94 + 1251907500 * q^95 + 1575858100 * q^96 - 1852351908 * q^97 - 3327698948 * q^99

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