LMFDB - Embedded newform 325.10.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, 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("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.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:	$167.386646753$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 4134 x^{8} - 3624 x^{7} + 5679966 x^{6} + 22403396 x^{5} - 2851482688 x^{4} + \cdots - 12862990590450 $ x^10 - 2x^9 - 4134x^8 - 3624x^7 + 5679966x^6 + 22403396x^5 - 2851482688x^4 - 21022962952x^3 + 366083359993x^2 + 2279190669294*x - 12862990590450
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-12.5874$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-13.5874 q^{2} +160.949 q^{3} -327.382 q^{4} -2186.88 q^{6} +8291.63 q^{7} +11405.0 q^{8} +6221.59 q^{9} -75684.8 q^{11} -52691.8 q^{12} -28561.0 q^{13} -112662. q^{14} +12654.5 q^{16} +316428. q^{17} -84535.3 q^{18} -187425. q^{19} +1.33453e6 q^{21} +1.02836e6 q^{22} +1.56452e6 q^{23} +1.83563e6 q^{24} +388070. q^{26} -2.16660e6 q^{27} -2.71453e6 q^{28} -4.30603e6 q^{29} +7.76007e6 q^{31} -6.01132e6 q^{32} -1.21814e7 q^{33} -4.29944e6 q^{34} -2.03684e6 q^{36} -412536. q^{37} +2.54663e6 q^{38} -4.59687e6 q^{39} -3.08779e7 q^{41} -1.81328e7 q^{42} -2.15517e7 q^{43} +2.47778e7 q^{44} -2.12578e7 q^{46} +2.01133e7 q^{47} +2.03674e6 q^{48} +2.83975e7 q^{49} +5.09287e7 q^{51} +9.35036e6 q^{52} +4.89511e7 q^{53} +2.94385e7 q^{54} +9.45663e7 q^{56} -3.01659e7 q^{57} +5.85079e7 q^{58} -1.02147e8 q^{59} -1.41547e8 q^{61} -1.05439e8 q^{62} +5.15871e7 q^{63} +7.51992e7 q^{64} +1.65514e8 q^{66} -1.07231e8 q^{67} -1.03593e8 q^{68} +2.51808e8 q^{69} +3.31935e8 q^{71} +7.09574e7 q^{72} +3.81069e8 q^{73} +5.60530e6 q^{74} +6.13597e7 q^{76} -6.27550e8 q^{77} +6.24595e7 q^{78} +1.61165e7 q^{79} -4.71172e8 q^{81} +4.19551e8 q^{82} +5.16835e8 q^{83} -4.36901e8 q^{84} +2.92832e8 q^{86} -6.93052e8 q^{87} -8.63187e8 q^{88} -9.01566e8 q^{89} -2.36817e8 q^{91} -5.12195e8 q^{92} +1.24898e9 q^{93} -2.73288e8 q^{94} -9.67516e8 q^{96} -3.05437e8 q^{97} -3.85848e8 q^{98} -4.70879e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{2} - 170 q^{3} + 3158 q^{4} - 3306 q^{6} - 4796 q^{7} + 19056 q^{8} + 92810 q^{9} - 74950 q^{11} + 51834 q^{12} - 285610 q^{13} + 60672 q^{14} + 1368530 q^{16} - 1066000 q^{17} - 1679076 q^{18}+ \cdots - 2805512690 q^{99}+O(q^{100}) $ 10 * q - 8 * q^2 - 170 * q^3 + 3158 * q^4 - 3306 * q^6 - 4796 * q^7 + 19056 * q^8 + 92810 * q^9 - 74950 * q^11 + 51834 * q^12 - 285610 * q^13 + 60672 * q^14 + 1368530 * q^16 - 1066000 * q^17 - 1679076 * q^18 + 1130702 * q^19 + 317220 * q^21 - 92986 * q^22 - 1639630 * q^23 - 6364494 * q^24 + 228488 * q^26 + 1067896 * q^27 - 4816012 * q^28 - 11823692 * q^29 + 17332410 * q^31 - 8813936 * q^32 - 12030884 * q^33 + 7284340 * q^34 + 81850198 * q^36 - 27892424 * q^37 - 72453870 * q^38 + 4855370 * q^39 - 3891824 * q^41 - 165021660 * q^42 - 84011234 * q^43 + 46801070 * q^44 + 173504026 * q^46 - 79184500 * q^47 - 204770370 * q^48 + 171631330 * q^49 + 111905236 * q^51 - 90195638 * q^52 + 51026128 * q^53 + 70324704 * q^54 + 80292608 * q^56 + 156021572 * q^57 - 170753836 * q^58 - 55847702 * q^59 - 34702428 * q^61 - 123241794 * q^62 - 791924972 * q^63 + 176769142 * q^64 + 943669416 * q^66 - 558023952 * q^67 - 1103318464 * q^68 + 595498384 * q^69 + 400978870 * q^71 + 227926092 * q^72 - 479660152 * q^73 - 1842717232 * q^74 + 667629178 * q^76 + 35600172 * q^77 + 94422666 * q^78 + 811405652 * q^79 - 172430134 * q^81 + 728501492 * q^82 + 873577748 * q^83 - 3454865492 * q^84 - 4017148098 * q^86 + 14661024 * q^87 - 266182958 * q^88 - 798868188 * q^89 + 136978556 * q^91 + 547168398 * q^92 + 1978869188 * q^93 + 212588928 * q^94 - 6199507594 * q^96 - 588759252 * q^97 + 3898704088 * q^98 - 2805512690 * 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 $

$2$	−13.5874	−0.600485	−0.300242	−	0.953863i	$-0.597068\pi$
$2$	−13.5874	−0.600485	−0.300242	+	0.953863i	$0.597068\pi$
$3$	160.949	1.14721	0.573605	−	0.819132i	$-0.305545\pi$
$3$	160.949	1.14721	0.573605	+	0.819132i	$0.305545\pi$
$4$	−327.382	−0.639418
$5$	0	0
$5$	0	0
$6$	−2186.88	−0.688882
$7$	8291.63	1.30526	0.652632	−	0.757675i	$-0.273665\pi$
$7$	8291.63	1.30526	0.652632	+	0.757675i	$0.273665\pi$
$8$	11405.0	0.984446
$9$	6221.59	0.316089
$10$	0	0
$11$	−75684.8	−1.55862	−0.779312	−	0.626636i	$-0.784431\pi$
$11$	−75684.8	−1.55862	−0.779312	+	0.626636i	$0.784431\pi$
$12$	−52691.8	−0.733546
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−112662.	−0.783792
$15$	0	0
$16$	12654.5	0.0482732
$17$	316428.	0.918871	0.459435	−	0.888211i	$-0.348052\pi$
$17$	316428.	0.918871	0.459435	+	0.888211i	$0.348052\pi$
$18$	−84535.3	−0.189807
$19$	−187425.	−0.329942	−0.164971	−	0.986298i	$-0.552753\pi$
$19$	−187425.	−0.329942	−0.164971	+	0.986298i	$0.552753\pi$
$20$	0	0
$21$	1.33453e6	1.49741
$22$	1.02836e6	0.935930
$23$	1.56452e6	1.16575	0.582875	−	0.812562i	$-0.301928\pi$
$23$	1.56452e6	1.16575	0.582875	+	0.812562i	$0.301928\pi$
$24$	1.83563e6	1.12937
$25$	0	0
$26$	388070.	0.166545
$27$	−2.16660e6	−0.784589
$28$	−2.71453e6	−0.834610
$29$	−4.30603e6	−1.13054	−0.565271	−	0.824905i	$-0.691228\pi$
$29$	−4.30603e6	−1.13054	−0.565271	+	0.824905i	$0.691228\pi$
$30$	0	0
$31$	7.76007e6	1.50917	0.754584	−	0.656203i	$-0.227839\pi$
$31$	7.76007e6	1.50917	0.754584	+	0.656203i	$0.227839\pi$
$32$	−6.01132e6	−1.01343
$33$	−1.21814e7	−1.78807
$34$	−4.29944e6	−0.551768
$35$	0	0
$36$	−2.03684e6	−0.202113
$37$	−412536.	−0.0361871	−0.0180936	−	0.999836i	$-0.505760\pi$
$37$	−412536.	−0.0361871	−0.0180936	+	0.999836i	$0.505760\pi$
$38$	2.54663e6	0.198125
$39$	−4.59687e6	−0.318179
$40$	0	0
$41$	−3.08779e7	−1.70655	−0.853277	−	0.521458i	$-0.825388\pi$
$41$	−3.08779e7	−1.70655	−0.853277	+	0.521458i	$0.825388\pi$
$42$	−1.81328e7	−0.899173
$43$	−2.15517e7	−0.961332	−0.480666	−	0.876904i	$-0.659605\pi$
$43$	−2.15517e7	−0.961332	−0.480666	+	0.876904i	$0.659605\pi$
$44$	2.47778e7	0.996612
$45$	0	0
$46$	−2.12578e7	−0.700015
$47$	2.01133e7	0.601233	0.300616	−	0.953745i	$-0.402808\pi$
$47$	2.01133e7	0.601233	0.300616	+	0.953745i	$0.402808\pi$
$48$	2.03674e6	0.0553795
$49$	2.83975e7	0.703715
$50$	0	0
$51$	5.09287e7	1.05414
$52$	9.35036e6	0.177343
$53$	4.89511e7	0.852159	0.426080	−	0.904686i	$-0.359894\pi$
$53$	4.89511e7	0.852159	0.426080	+	0.904686i	$0.359894\pi$
$54$	2.94385e7	0.471134
$55$	0	0
$56$	9.45663e7	1.28496
$57$	−3.01659e7	−0.378512
$58$	5.85079e7	0.678873
$59$	−1.02147e8	−1.09746	−0.548732	−	0.835998i	$-0.684889\pi$
$59$	−1.02147e8	−1.09746	−0.548732	+	0.835998i	$0.684889\pi$
$60$	0	0
$61$	−1.41547e8	−1.30893	−0.654464	−	0.756093i	$-0.727106\pi$
$61$	−1.41547e8	−1.30893	−0.654464	+	0.756093i	$0.727106\pi$
$62$	−1.05439e8	−0.906233
$63$	5.15871e7	0.412580
$64$	7.51992e7	0.560278
$65$	0	0
$66$	1.65514e8	1.07371
$67$	−1.07231e8	−0.650108	−0.325054	−	0.945695i	$-0.605382\pi$
$67$	−1.07231e8	−0.650108	−0.325054	+	0.945695i	$0.605382\pi$
$68$	−1.03593e8	−0.587542
$69$	2.51808e8	1.33736
$70$	0	0
$71$	3.31935e8	1.55021	0.775105	−	0.631832i	$-0.217697\pi$
$71$	3.31935e8	1.55021	0.775105	+	0.631832i	$0.217697\pi$
$72$	7.09574e7	0.311173
$73$	3.81069e8	1.57055	0.785274	−	0.619148i	$-0.212522\pi$
$73$	3.81069e8	1.57055	0.785274	+	0.619148i	$0.212522\pi$
$74$	5.60530e6	0.0217298
$75$	0	0
$76$	6.13597e7	0.210971
$77$	−6.27550e8	−2.03442
$78$	6.24595e7	0.191061
$79$	1.61165e7	0.0465532	0.0232766	−	0.999729i	$-0.492590\pi$
$79$	1.61165e7	0.0465532	0.0232766	+	0.999729i	$0.492590\pi$
$80$	0	0
$81$	−4.71172e8	−1.21618
$82$	4.19551e8	1.02476
$83$	5.16835e8	1.19536	0.597682	−	0.801733i	$-0.296089\pi$
$83$	5.16835e8	1.19536	0.597682	+	0.801733i	$0.296089\pi$
$84$	−4.36901e8	−0.957472
$85$	0	0
$86$	2.92832e8	0.577265
$87$	−6.93052e8	−1.29697
$88$	−8.63187e8	−1.53438
$89$	−9.01566e8	−1.52315	−0.761574	−	0.648077i	$-0.775573\pi$
$89$	−9.01566e8	−1.52315	−0.761574	+	0.648077i	$0.775573\pi$
$90$	0	0
$91$	−2.36817e8	−0.362015
$92$	−5.12195e8	−0.745401
$93$	1.24898e9	1.73133
$94$	−2.73288e8	−0.361031
$95$	0	0
$96$	−9.67516e8	−1.16262
$97$	−3.05437e8	−0.350307	−0.175153	−	0.984541i	$-0.556042\pi$
$97$	−3.05437e8	−0.350307	−0.175153	+	0.984541i	$0.556042\pi$
$98$	−3.85848e8	−0.422570
$99$	−4.70879e8	−0.492665
$100$	0	0
$101$	−1.91803e9	−1.83404	−0.917020	−	0.398841i	$-0.869413\pi$
$101$	−1.91803e9	−1.83404	−0.917020	+	0.398841i	$0.869413\pi$
$102$	−6.91990e8	−0.632993
$103$	1.00361e9	0.878610	0.439305	−	0.898338i	$-0.355225\pi$
$103$	1.00361e9	0.878610	0.439305	+	0.898338i	$0.355225\pi$
$104$	−3.25739e8	−0.273036
$105$	0	0
$106$	−6.65119e8	−0.511709
$107$	−1.83445e8	−0.135294	−0.0676471	−	0.997709i	$-0.521549\pi$
$107$	−1.83445e8	−0.135294	−0.0676471	+	0.997709i	$0.521549\pi$
$108$	7.09306e8	0.501680
$109$	−9.57254e8	−0.649543	−0.324771	−	0.945793i	$-0.605287\pi$
$109$	−9.57254e8	−0.649543	−0.324771	+	0.945793i	$0.605287\pi$
$110$	0	0
$111$	−6.63972e7	−0.0415142
$112$	1.04927e8	0.0630093
$113$	1.10637e9	0.638334	0.319167	−	0.947698i	$-0.396597\pi$
$113$	1.10637e9	0.638334	0.319167	+	0.947698i	$0.396597\pi$
$114$	4.09877e8	0.227291
$115$	0	0
$116$	1.40972e9	0.722888
$117$	−1.77695e8	−0.0876674
$118$	1.38791e9	0.659010
$119$	2.62370e9	1.19937
$120$	0	0
$121$	3.37024e9	1.42931
$122$	1.92326e9	0.785992
$123$	−4.96976e9	−1.95777
$124$	−2.54051e9	−0.964990
$125$	0	0
$126$	−7.00935e8	−0.247748
$127$	1.21998e9	0.416136	0.208068	−	0.978114i	$-0.433282\pi$
$127$	1.21998e9	0.416136	0.208068	+	0.978114i	$0.433282\pi$
$128$	2.05603e9	0.676995
$129$	−3.46872e9	−1.10285
$130$	0	0
$131$	5.25104e9	1.55784	0.778922	−	0.627120i	$-0.215767\pi$
$131$	5.25104e9	1.55784	0.778922	+	0.627120i	$0.215767\pi$
$132$	3.98797e9	1.14332
$133$	−1.55406e9	−0.430661
$134$	1.45700e9	0.390380
$135$	0	0
$136$	3.60887e9	0.904578
$137$	−6.07545e9	−1.47345	−0.736726	−	0.676192i	$-0.763629\pi$
$137$	−6.07545e9	−1.47345	−0.736726	+	0.676192i	$0.763629\pi$
$138$	−3.42141e9	−0.803063
$139$	4.17680e9	0.949024	0.474512	−	0.880249i	$-0.342625\pi$
$139$	4.17680e9	0.949024	0.474512	+	0.880249i	$0.342625\pi$
$140$	0	0
$141$	3.23721e9	0.689740
$142$	−4.51014e9	−0.930878
$143$	2.16163e9	0.432285
$144$	7.87313e7	0.0152587
$145$	0	0
$146$	−5.17775e9	−0.943090
$147$	4.57054e9	0.807309
$148$	1.35057e8	0.0231387
$149$	2.90520e8	0.0482878	0.0241439	−	0.999708i	$-0.492314\pi$
$149$	2.90520e8	0.0482878	0.0241439	+	0.999708i	$0.492314\pi$
$150$	0	0
$151$	−1.03439e10	−1.61915	−0.809577	−	0.587013i	$-0.800304\pi$
$151$	−1.03439e10	−1.61915	−0.809577	+	0.587013i	$0.800304\pi$
$152$	−2.13759e9	−0.324810
$153$	1.96868e9	0.290445
$154$	8.52678e9	1.22164
$155$	0	0
$156$	1.50493e9	0.203449
$157$	−9.50868e9	−1.24903	−0.624514	−	0.781014i	$-0.714703\pi$
$157$	−9.50868e9	−1.24903	−0.624514	+	0.781014i	$0.714703\pi$
$158$	−2.18982e8	−0.0279545
$159$	7.87863e9	0.977605
$160$	0	0
$161$	1.29724e10	1.52161
$162$	6.40201e9	0.730296
$163$	2.22995e9	0.247429	0.123715	−	0.992318i	$-0.460519\pi$
$163$	2.22995e9	0.247429	0.123715	+	0.992318i	$0.460519\pi$
$164$	1.01089e10	1.09120
$165$	0	0
$166$	−7.02245e9	−0.717798
$167$	−7.50737e9	−0.746902	−0.373451	−	0.927650i	$-0.621826\pi$
$167$	−7.50737e9	−0.746902	−0.373451	+	0.927650i	$0.621826\pi$
$168$	1.52204e10	1.47412
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−1.16608e9	−0.104291
$172$	7.05563e9	0.614693
$173$	−1.58812e10	−1.34795	−0.673977	−	0.738753i	$-0.735415\pi$
$173$	−1.58812e10	−1.34795	−0.673977	+	0.738753i	$0.735415\pi$
$174$	9.41679e9	0.778809
$175$	0	0
$176$	−9.57756e8	−0.0752398
$177$	−1.64404e10	−1.25902
$178$	1.22500e10	0.914628
$179$	−1.14604e10	−0.834372	−0.417186	−	0.908821i	$-0.636984\pi$
$179$	−1.14604e10	−0.834372	−0.417186	+	0.908821i	$0.636984\pi$
$180$	0	0
$181$	−2.40713e9	−0.166704	−0.0833518	−	0.996520i	$-0.526563\pi$
$181$	−2.40713e9	−0.166704	−0.0833518	+	0.996520i	$0.526563\pi$
$182$	3.21773e9	0.217385
$183$	−2.27818e10	−1.50162
$184$	1.78434e10	1.14762
$185$	0	0
$186$	−1.69704e10	−1.03964
$187$	−2.39488e10	−1.43217
$188$	−6.58473e9	−0.384439
$189$	−1.79646e10	−1.02410
$190$	0	0
$191$	−1.95693e10	−1.06396	−0.531980	−	0.846757i	$-0.678552\pi$
$191$	−1.95693e10	−1.06396	−0.531980	+	0.846757i	$0.678552\pi$
$192$	1.21032e10	0.642756
$193$	1.30616e10	0.677626	0.338813	−	0.940854i	$-0.389975\pi$
$193$	1.30616e10	0.677626	0.338813	+	0.940854i	$0.389975\pi$
$194$	4.15010e9	0.210354
$195$	0	0
$196$	−9.29681e9	−0.449968
$197$	5.02009e8	0.0237472	0.0118736	−	0.999930i	$-0.496220\pi$
$197$	5.02009e8	0.0237472	0.0118736	+	0.999930i	$0.496220\pi$
$198$	6.39804e9	0.295838
$199$	1.40039e10	0.633012	0.316506	−	0.948591i	$-0.397490\pi$
$199$	1.40039e10	0.633012	0.316506	+	0.948591i	$0.397490\pi$
$200$	0	0
$201$	−1.72588e10	−0.745810
$202$	2.60611e10	1.10131
$203$	−3.57040e10	−1.47566
$204$	−1.66732e10	−0.674034
$205$	0	0
$206$	−1.36364e10	−0.527592
$207$	9.73378e9	0.368481
$208$	−3.61426e8	−0.0133886
$209$	1.41853e10	0.514255
$210$	0	0
$211$	−7.33497e9	−0.254758	−0.127379	−	0.991854i	$-0.540656\pi$
$211$	−7.33497e9	−0.254758	−0.127379	+	0.991854i	$0.540656\pi$
$212$	−1.60257e10	−0.544886
$213$	5.34246e10	1.77842
$214$	2.49255e9	0.0812421
$215$	0	0
$216$	−2.47102e10	−0.772385
$217$	6.43436e10	1.96986
$218$	1.30066e10	0.390041
$219$	6.13328e10	1.80175
$220$	0	0
$221$	−9.03749e9	−0.254849
$222$	9.02167e8	0.0249286
$223$	−3.50187e10	−0.948261	−0.474130	−	0.880455i	$-0.657237\pi$
$223$	−3.50187e10	−0.948261	−0.474130	+	0.880455i	$0.657237\pi$
$224$	−4.98436e10	−1.32280
$225$	0	0
$226$	−1.50327e10	−0.383310
$227$	−7.31720e10	−1.82906	−0.914531	−	0.404515i	$-0.867440\pi$
$227$	−7.31720e10	−1.82906	−0.914531	+	0.404515i	$0.867440\pi$
$228$	9.87579e9	0.242028
$229$	−3.39268e10	−0.815235	−0.407618	−	0.913153i	$-0.633640\pi$
$229$	−3.39268e10	−0.815235	−0.407618	+	0.913153i	$0.633640\pi$
$230$	0	0
$231$	−1.01004e11	−2.33390
$232$	−4.91105e10	−1.11296
$233$	−2.11791e10	−0.470767	−0.235383	−	0.971903i	$-0.575635\pi$
$233$	−2.11791e10	−0.470767	−0.235383	+	0.971903i	$0.575635\pi$
$234$	2.41441e9	0.0526430
$235$	0	0
$236$	3.34410e10	0.701738
$237$	2.59394e9	0.0534062
$238$	−3.56493e10	−0.720203
$239$	−5.47243e10	−1.08490	−0.542450	−	0.840088i	$-0.682503\pi$
$239$	−5.47243e10	−1.08490	−0.542450	+	0.840088i	$0.682503\pi$
$240$	0	0
$241$	−4.62069e9	−0.0882328	−0.0441164	−	0.999026i	$-0.514047\pi$
$241$	−4.62069e9	−0.0882328	−0.0441164	+	0.999026i	$0.514047\pi$
$242$	−4.57928e10	−0.858278
$243$	−3.31894e10	−0.610621
$244$	4.63399e10	0.836953
$245$	0	0
$246$	6.75263e10	1.17561
$247$	5.35306e9	0.0915094
$248$	8.85038e10	1.48569
$249$	8.31840e10	1.37133
$250$	0	0
$251$	−7.06512e10	−1.12354	−0.561769	−	0.827294i	$-0.689879\pi$
$251$	−7.06512e10	−1.12354	−0.561769	+	0.827294i	$0.689879\pi$
$252$	−1.68887e10	−0.263811
$253$	−1.18410e11	−1.81696
$254$	−1.65764e10	−0.249884
$255$	0	0
$256$	−6.64382e10	−0.966803
$257$	−7.82149e10	−1.11838	−0.559191	−	0.829039i	$-0.688888\pi$
$257$	−7.82149e10	−1.11838	−0.559191	+	0.829039i	$0.688888\pi$
$258$	4.71310e10	0.662244
$259$	−3.42059e9	−0.0472337
$260$	0	0
$261$	−2.67904e10	−0.357352
$262$	−7.13480e10	−0.935462
$263$	−2.65738e10	−0.342494	−0.171247	−	0.985228i	$-0.554780\pi$
$263$	−2.65738e10	−0.342494	−0.171247	+	0.985228i	$0.554780\pi$
$264$	−1.38929e11	−1.76026
$265$	0	0
$266$	2.11157e10	0.258606
$267$	−1.45106e11	−1.74737
$268$	3.51056e10	0.415691
$269$	−4.78271e10	−0.556915	−0.278458	−	0.960449i	$-0.589823\pi$
$269$	−4.78271e10	−0.556915	−0.278458	+	0.960449i	$0.589823\pi$
$270$	0	0
$271$	1.60370e10	0.180618	0.0903092	−	0.995914i	$-0.471214\pi$
$271$	1.60370e10	0.180618	0.0903092	+	0.995914i	$0.471214\pi$
$272$	4.00425e9	0.0443569
$273$	−3.81155e10	−0.415307
$274$	8.25497e10	0.884785
$275$	0	0
$276$	−8.24372e10	−0.855131
$277$	1.13361e10	0.115692	0.0578462	−	0.998326i	$-0.481577\pi$
$277$	1.13361e10	0.115692	0.0578462	+	0.998326i	$0.481577\pi$
$278$	−5.67520e10	−0.569875
$279$	4.82799e10	0.477032
$280$	0	0
$281$	1.04524e10	0.100009	0.0500044	−	0.998749i	$-0.484076\pi$
$281$	1.04524e10	0.100009	0.0500044	+	0.998749i	$0.484076\pi$
$282$	−4.39854e10	−0.414178
$283$	8.30382e10	0.769554	0.384777	−	0.923010i	$-0.374278\pi$
$283$	8.30382e10	0.769554	0.384777	+	0.923010i	$0.374278\pi$
$284$	−1.08670e11	−0.991232
$285$	0	0
$286$	−2.93710e10	−0.259580
$287$	−2.56028e11	−2.22750
$288$	−3.74000e10	−0.320335
$289$	−1.84614e10	−0.155677
$290$	0	0
$291$	−4.91597e10	−0.401875
$292$	−1.24755e11	−1.00424
$293$	1.54023e11	1.22090	0.610450	−	0.792055i	$-0.290989\pi$
$293$	1.54023e11	1.22090	0.610450	+	0.792055i	$0.290989\pi$
$294$	−6.21019e10	−0.484777
$295$	0	0
$296$	−4.70499e9	−0.0356242
$297$	1.63979e11	1.22288
$298$	−3.94741e9	−0.0289961
$299$	−4.46842e10	−0.323321
$300$	0	0
$301$	−1.78699e11	−1.25479
$302$	1.40547e11	0.972278
$303$	−3.08705e11	−2.10403
$304$	−2.37178e9	−0.0159274
$305$	0	0
$306$	−2.67493e10	−0.174408
$307$	1.27480e11	0.819070	0.409535	−	0.912294i	$-0.365691\pi$
$307$	1.27480e11	0.819070	0.409535	+	0.912294i	$0.365691\pi$
$308$	2.05448e11	1.30084
$309$	1.61530e11	1.00795
$310$	0	0
$311$	9.31763e10	0.564785	0.282393	−	0.959299i	$-0.408872\pi$
$311$	9.31763e10	0.564785	0.282393	+	0.959299i	$0.408872\pi$
$312$	−5.24274e10	−0.313230
$313$	−2.16180e11	−1.27311	−0.636556	−	0.771231i	$-0.719641\pi$
$313$	−2.16180e11	−1.27311	−0.636556	+	0.771231i	$0.719641\pi$
$314$	1.29198e11	0.750022
$315$	0	0
$316$	−5.27626e9	−0.0297669
$317$	6.07946e10	0.338141	0.169071	−	0.985604i	$-0.445923\pi$
$317$	6.07946e10	0.338141	0.169071	+	0.985604i	$0.445923\pi$
$318$	−1.07050e11	−0.587037
$319$	3.25901e11	1.76209
$320$	0	0
$321$	−2.95253e10	−0.155211
$322$	−1.76261e11	−0.913704
$323$	−5.93066e10	−0.303174
$324$	1.54253e11	0.777645
$325$	0	0
$326$	−3.02993e10	−0.148577
$327$	−1.54069e11	−0.745162
$328$	−3.52163e11	−1.68001
$329$	1.66772e11	0.784768
$330$	0	0
$331$	−4.08289e11	−1.86957	−0.934786	−	0.355212i	$-0.884409\pi$
$331$	−4.08289e11	−1.86957	−0.934786	+	0.355212i	$0.884409\pi$
$332$	−1.69202e11	−0.764337
$333$	−2.56663e9	−0.0114384
$334$	1.02006e11	0.448503
$335$	0	0
$336$	1.68879e10	0.0722849
$337$	−1.75555e10	−0.0741443	−0.0370721	−	0.999313i	$-0.511803\pi$
$337$	−1.75555e10	−0.0741443	−0.0370721	+	0.999313i	$0.511803\pi$
$338$	−1.10837e10	−0.0461911
$339$	1.78069e11	0.732303
$340$	0	0
$341$	−5.87319e11	−2.35223
$342$	1.58441e10	0.0626252
$343$	−9.91360e10	−0.386730
$344$	−2.45798e11	−0.946379
$345$	0	0
$346$	2.15784e11	0.809425
$347$	1.95585e11	0.724190	0.362095	−	0.932141i	$-0.382062\pi$
$347$	1.95585e11	0.724190	0.362095	+	0.932141i	$0.382062\pi$
$348$	2.26893e11	0.829304
$349$	−2.28568e11	−0.824708	−0.412354	−	0.911024i	$-0.635293\pi$
$349$	−2.28568e11	−0.824708	−0.412354	+	0.911024i	$0.635293\pi$
$350$	0	0
$351$	6.18803e10	0.217606
$352$	4.54965e11	1.57956
$353$	5.20913e11	1.78558	0.892790	−	0.450474i	$-0.148745\pi$
$353$	5.20913e11	1.78558	0.892790	+	0.450474i	$0.148745\pi$
$354$	2.23383e11	0.756023
$355$	0	0
$356$	2.95156e11	0.973929
$357$	4.22282e11	1.37593
$358$	1.55717e11	0.501028
$359$	−4.53052e11	−1.43954	−0.719770	−	0.694213i	$-0.755753\pi$
$359$	−4.53052e11	−1.43954	−0.719770	+	0.694213i	$0.755753\pi$
$360$	0	0
$361$	−2.87559e11	−0.891138
$362$	3.27066e10	0.100103
$363$	5.42436e11	1.63972
$364$	7.75297e10	0.231479
$365$	0	0
$366$	3.09546e11	0.901697
$367$	3.57014e11	1.02728	0.513639	−	0.858007i	$-0.328297\pi$
$367$	3.57014e11	1.02728	0.513639	+	0.858007i	$0.328297\pi$
$368$	1.97982e10	0.0562745
$369$	−1.92109e11	−0.539424
$370$	0	0
$371$	4.05884e11	1.11229
$372$	−4.08892e11	−1.10705
$373$	8.64026e10	0.231120	0.115560	−	0.993301i	$-0.463134\pi$
$373$	8.64026e10	0.231120	0.115560	+	0.993301i	$0.463134\pi$
$374$	3.25402e11	0.859999
$375$	0	0
$376$	2.29393e11	0.591881
$377$	1.22985e11	0.313556
$378$	2.44093e11	0.614954
$379$	2.85135e11	0.709862	0.354931	−	0.934892i	$-0.384504\pi$
$379$	2.85135e11	0.709862	0.354931	+	0.934892i	$0.384504\pi$
$380$	0	0
$381$	1.96354e11	0.477396
$382$	2.65896e11	0.638892
$383$	−7.39172e10	−0.175530	−0.0877650	−	0.996141i	$-0.527972\pi$
$383$	−7.39172e10	−0.175530	−0.0877650	+	0.996141i	$0.527972\pi$
$384$	3.30916e11	0.776655
$385$	0	0
$386$	−1.77474e11	−0.406904
$387$	−1.34086e11	−0.303867
$388$	9.99945e10	0.223992
$389$	−7.20854e11	−1.59615	−0.798075	−	0.602558i	$-0.794148\pi$
$389$	−7.20854e11	−1.59615	−0.798075	+	0.602558i	$0.794148\pi$
$390$	0	0
$391$	4.95057e11	1.07117
$392$	3.23874e11	0.692769
$393$	8.45149e11	1.78717
$394$	−6.82100e9	−0.0142599
$395$	0	0
$396$	1.54157e11	0.315019
$397$	−7.41808e11	−1.49877	−0.749383	−	0.662136i	$-0.769650\pi$
$397$	−7.41808e11	−1.49877	−0.749383	+	0.662136i	$0.769650\pi$
$398$	−1.90278e11	−0.380114
$399$	−2.50125e11	−0.494059
$400$	0	0
$401$	3.16583e11	0.611417	0.305708	−	0.952125i	$-0.401107\pi$
$401$	3.16583e11	0.611417	0.305708	+	0.952125i	$0.401107\pi$
$402$	2.34502e11	0.447847
$403$	−2.21635e11	−0.418568
$404$	6.27928e11	1.17272
$405$	0	0
$406$	4.85126e11	0.886109
$407$	3.12227e10	0.0564021
$408$	5.80844e11	1.03774
$409$	−8.53891e11	−1.50885	−0.754427	−	0.656383i	$-0.772085\pi$
$409$	−8.53891e11	−1.50885	−0.754427	+	0.656383i	$0.772085\pi$
$410$	0	0
$411$	−9.77838e11	−1.69036
$412$	−3.28563e11	−0.561799
$413$	−8.46962e11	−1.43248
$414$	−1.32257e11	−0.221267
$415$	0	0
$416$	1.71689e11	0.281076
$417$	6.72252e11	1.08873
$418$	−1.92741e11	−0.308803
$419$	7.64667e11	1.21202	0.606009	−	0.795458i	$-0.292769\pi$
$419$	7.64667e11	1.21202	0.606009	+	0.795458i	$0.292769\pi$
$420$	0	0
$421$	3.19607e11	0.495846	0.247923	−	0.968780i	$-0.420252\pi$
$421$	3.19607e11	0.495846	0.247923	+	0.968780i	$0.420252\pi$
$422$	9.96634e10	0.152978
$423$	1.25137e11	0.190043
$424$	5.58289e11	0.838905
$425$	0	0
$426$	−7.25903e11	−1.06791
$427$	−1.17365e12	−1.70850
$428$	6.00566e10	0.0865095
$429$	3.47913e11	0.495921
$430$	0	0
$431$	6.33999e10	0.0884996	0.0442498	−	0.999020i	$-0.485910\pi$
$431$	6.33999e10	0.0884996	0.0442498	+	0.999020i	$0.485910\pi$
$432$	−2.74173e10	−0.0378746
$433$	−1.44375e12	−1.97377	−0.986886	−	0.161422i	$-0.948392\pi$
$433$	−1.44375e12	−1.97377	−0.986886	+	0.161422i	$0.948392\pi$
$434$	−8.74263e11	−1.18287
$435$	0	0
$436$	3.13388e11	0.415329
$437$	−2.93230e11	−0.384629
$438$	−8.33354e11	−1.08192
$439$	−3.23421e11	−0.415602	−0.207801	−	0.978171i	$-0.566631\pi$
$439$	−3.23421e11	−0.415602	−0.207801	+	0.978171i	$0.566631\pi$
$440$	0	0
$441$	1.76677e11	0.222437
$442$	1.22796e11	0.153033
$443$	1.00232e12	1.23649	0.618246	−	0.785985i	$-0.287844\pi$
$443$	1.00232e12	1.23649	0.618246	+	0.785985i	$0.287844\pi$
$444$	2.17373e10	0.0265449
$445$	0	0
$446$	4.75813e11	0.569416
$447$	4.67589e10	0.0553962
$448$	6.23524e11	0.731311
$449$	−4.59898e11	−0.534014	−0.267007	−	0.963695i	$-0.586035\pi$
$449$	−4.59898e11	−0.534014	−0.267007	+	0.963695i	$0.586035\pi$
$450$	0	0
$451$	2.33698e12	2.65988
$452$	−3.62206e11	−0.408162
$453$	−1.66484e12	−1.85751
$454$	9.94219e11	1.09832
$455$	0	0
$456$	−3.44044e11	−0.372625
$457$	−7.20432e11	−0.772628	−0.386314	−	0.922367i	$-0.626252\pi$
$457$	−7.20432e11	−0.772628	−0.386314	+	0.922367i	$0.626252\pi$
$458$	4.60977e11	0.489536
$459$	−6.85573e11	−0.720936
$460$	0	0
$461$	3.61758e11	0.373047	0.186524	−	0.982450i	$-0.440278\pi$
$461$	3.61758e11	0.373047	0.186524	+	0.982450i	$0.440278\pi$
$462$	1.37238e12	1.40147
$463$	−1.63053e12	−1.64898	−0.824490	−	0.565876i	$-0.808538\pi$
$463$	−1.63053e12	−1.64898	−0.824490	+	0.565876i	$0.808538\pi$
$464$	−5.44909e10	−0.0545749
$465$	0	0
$466$	2.87769e11	0.282688
$467$	−7.48072e11	−0.727809	−0.363904	−	0.931436i	$-0.618556\pi$
$467$	−7.48072e11	−0.727809	−0.363904	+	0.931436i	$0.618556\pi$
$468$	5.81741e10	0.0560561
$469$	−8.89123e11	−0.848563
$470$	0	0
$471$	−1.53041e12	−1.43290
$472$	−1.16499e12	−1.08039
$473$	1.63113e12	1.49835
$474$	−3.52449e10	−0.0320696
$475$	0	0
$476$	−8.58952e11	−0.766898
$477$	3.04553e11	0.269359
$478$	7.43562e11	0.651466
$479$	−1.90591e12	−1.65421	−0.827107	−	0.562045i	$-0.810015\pi$
$479$	−1.90591e12	−1.65421	−0.827107	+	0.562045i	$0.810015\pi$
$480$	0	0
$481$	1.17824e10	0.0100365
$482$	6.27832e10	0.0529824
$483$	2.08789e12	1.74561
$484$	−1.10335e12	−0.913926
$485$	0	0
$486$	4.50959e11	0.366669
$487$	4.13291e11	0.332947	0.166474	−	0.986046i	$-0.446762\pi$
$487$	4.13291e11	0.332947	0.166474	+	0.986046i	$0.446762\pi$
$488$	−1.61435e12	−1.28857
$489$	3.58908e11	0.283853
$490$	0	0
$491$	−5.57466e11	−0.432864	−0.216432	−	0.976298i	$-0.569442\pi$
$491$	−5.57466e11	−0.432864	−0.216432	+	0.976298i	$0.569442\pi$
$492$	1.62701e12	1.25184
$493$	−1.36255e12	−1.03882
$494$	−7.27343e10	−0.0549500
$495$	0	0
$496$	9.82001e10	0.0728525
$497$	2.75228e12	2.02343
$498$	−1.13026e12	−0.823465
$499$	7.42448e11	0.536060	0.268030	−	0.963411i	$-0.413627\pi$
$499$	7.42448e11	0.536060	0.268030	+	0.963411i	$0.413627\pi$
$500$	0	0
$501$	−1.20830e12	−0.856853
$502$	9.59967e11	0.674667
$503$	1.36593e12	0.951422	0.475711	−	0.879602i	$-0.342191\pi$
$503$	1.36593e12	0.951422	0.475711	+	0.879602i	$0.342191\pi$
$504$	5.88352e11	0.406163
$505$	0	0
$506$	1.60889e12	1.09106
$507$	1.31291e11	0.0882469
$508$	−3.99399e11	−0.266085
$509$	−6.51348e11	−0.430113	−0.215057	−	0.976602i	$-0.568994\pi$
$509$	−6.51348e11	−0.430113	−0.215057	+	0.976602i	$0.568994\pi$
$510$	0	0
$511$	3.15969e12	2.04998
$512$	−1.49965e11	−0.0964441
$513$	4.06076e11	0.258869
$514$	1.06274e12	0.671572
$515$	0	0
$516$	1.13560e12	0.705181
$517$	−1.52227e12	−0.937096
$518$	4.64770e10	0.0283631
$519$	−2.55606e12	−1.54638
$520$	0	0
$521$	1.00231e12	0.595982	0.297991	−	0.954569i	$-0.403683\pi$
$521$	1.00231e12	0.595982	0.297991	+	0.954569i	$0.403683\pi$
$522$	3.64012e11	0.214585
$523$	1.77614e12	1.03805	0.519027	−	0.854758i	$-0.326294\pi$
$523$	1.77614e12	1.03805	0.519027	+	0.854758i	$0.326294\pi$
$524$	−1.71909e12	−0.996114
$525$	0	0
$526$	3.61069e11	0.205662
$527$	2.45550e12	1.38673
$528$	−1.54150e11	−0.0863158
$529$	6.46562e11	0.358971
$530$	0	0
$531$	−6.35515e11	−0.346897
$532$	5.08772e11	0.275373
$533$	8.81903e11	0.473313
$534$	1.97162e12	1.04927
$535$	0	0
$536$	−1.22298e12	−0.639996
$537$	−1.84453e12	−0.957199
$538$	6.49848e11	0.334419
$539$	−2.14925e12	−1.09683
$540$	0	0
$541$	3.32080e12	1.66669	0.833346	−	0.552751i	$-0.186422\pi$
$541$	3.32080e12	1.66669	0.833346	+	0.552751i	$0.186422\pi$
$542$	−2.17902e11	−0.108459
$543$	−3.87424e11	−0.191244
$544$	−1.90215e12	−0.931214
$545$	0	0
$546$	5.17891e11	0.249386
$547$	−6.94762e11	−0.331813	−0.165906	−	0.986142i	$-0.553055\pi$
$547$	−6.94762e11	−0.331813	−0.165906	+	0.986142i	$0.553055\pi$
$548$	1.98899e12	0.942151
$549$	−8.80646e11	−0.413739
$550$	0	0
$551$	8.07060e11	0.373013
$552$	2.87187e12	1.31656
$553$	1.33632e11	0.0607642
$554$	−1.54028e11	−0.0694716
$555$	0	0
$556$	−1.36741e12	−0.606823
$557$	3.92680e12	1.72858	0.864291	−	0.502992i	$-0.167767\pi$
$557$	3.92680e12	1.72858	0.864291	+	0.502992i	$0.167767\pi$
$558$	−6.56000e11	−0.286451
$559$	6.15538e11	0.266625
$560$	0	0
$561$	−3.85453e12	−1.64300
$562$	−1.42021e11	−0.0600538
$563$	1.77824e10	0.00745938	0.00372969	−	0.999993i	$-0.498813\pi$
$563$	1.77824e10	0.00745938	0.00372969	+	0.999993i	$0.498813\pi$
$564$	−1.05981e12	−0.441032
$565$	0	0
$566$	−1.12828e12	−0.462105
$567$	−3.90678e12	−1.58743
$568$	3.78573e12	1.52610
$569$	2.82415e12	1.12949	0.564746	−	0.825265i	$-0.308974\pi$
$569$	2.82415e12	1.12949	0.564746	+	0.825265i	$0.308974\pi$
$570$	0	0
$571$	−1.89626e12	−0.746509	−0.373255	−	0.927729i	$-0.621758\pi$
$571$	−1.89626e12	−0.746509	−0.373255	+	0.927729i	$0.621758\pi$
$572$	−7.07680e11	−0.276410
$573$	−3.14966e12	−1.22059
$574$	3.47876e12	1.33758
$575$	0	0
$576$	4.67859e11	0.177098
$577$	4.58042e12	1.72034	0.860169	−	0.510009i	$-0.170358\pi$
$577$	4.58042e12	1.72034	0.860169	+	0.510009i	$0.170358\pi$
$578$	2.50842e11	0.0934814
$579$	2.10226e12	0.777379
$580$	0	0
$581$	4.28540e12	1.56027
$582$	6.67954e11	0.241320
$583$	−3.70485e12	−1.32820
$584$	4.34611e12	1.54612
$585$	0	0
$586$	−2.09277e12	−0.733132
$587$	2.85381e11	0.0992097	0.0496049	−	0.998769i	$-0.484204\pi$
$587$	2.85381e11	0.0992097	0.0496049	+	0.998769i	$0.484204\pi$
$588$	−1.49631e12	−0.516208
$589$	−1.45443e12	−0.497938
$590$	0	0
$591$	8.07978e10	0.0272431
$592$	−5.22045e9	−0.00174687
$593$	−1.06834e12	−0.354783	−0.177391	−	0.984140i	$-0.556766\pi$
$593$	−1.06834e12	−0.354783	−0.177391	+	0.984140i	$0.556766\pi$
$594$	−2.22805e12	−0.734320
$595$	0	0
$596$	−9.51109e10	−0.0308761
$597$	2.25392e12	0.726197
$598$	6.07143e11	0.194149
$599$	2.46712e12	0.783013	0.391507	−	0.920175i	$-0.371954\pi$
$599$	2.46712e12	0.783013	0.391507	+	0.920175i	$0.371954\pi$
$600$	0	0
$601$	7.90173e11	0.247051	0.123526	−	0.992341i	$-0.460580\pi$
$601$	7.90173e11	0.247051	0.123526	+	0.992341i	$0.460580\pi$
$602$	2.42805e12	0.753484
$603$	−6.67150e11	−0.205492
$604$	3.38641e12	1.03532
$605$	0	0
$606$	4.19450e12	1.26344
$607$	2.41014e12	0.720598	0.360299	−	0.932837i	$-0.382675\pi$
$607$	2.41014e12	0.720598	0.360299	+	0.932837i	$0.382675\pi$
$608$	1.12667e12	0.334374
$609$	−5.74653e12	−1.69289
$610$	0	0
$611$	−5.74456e11	−0.166752
$612$	−6.44511e11	−0.185716
$613$	4.34443e11	0.124268	0.0621342	−	0.998068i	$-0.480209\pi$
$613$	4.34443e11	0.124268	0.0621342	+	0.998068i	$0.480209\pi$
$614$	−1.73213e12	−0.491839
$615$	0	0
$616$	−7.15723e12	−2.00277
$617$	−4.77599e12	−1.32672	−0.663361	−	0.748299i	$-0.730871\pi$
$617$	−4.77599e12	−1.32672	−0.663361	+	0.748299i	$0.730871\pi$
$618$	−2.19477e12	−0.605258
$619$	3.28418e12	0.899122	0.449561	−	0.893250i	$-0.351580\pi$
$619$	3.28418e12	0.899122	0.449561	+	0.893250i	$0.351580\pi$
$620$	0	0
$621$	−3.38968e12	−0.914634
$622$	−1.26603e12	−0.339145
$623$	−7.47545e12	−1.98811
$624$	−5.81712e10	−0.0153595
$625$	0	0
$626$	2.93733e12	0.764484
$627$	2.28310e12	0.589959
$628$	3.11297e12	0.798650
$629$	−1.30538e11	−0.0332513
$630$	0	0
$631$	3.55254e12	0.892087	0.446044	−	0.895011i	$-0.352833\pi$
$631$	3.55254e12	0.892087	0.446044	+	0.895011i	$0.352833\pi$
$632$	1.83809e11	0.0458291
$633$	−1.18056e12	−0.292261
$634$	−8.26042e11	−0.203049
$635$	0	0
$636$	−2.57932e12	−0.625098
$637$	−8.11060e11	−0.195176
$638$	−4.42816e12	−1.05811
$639$	2.06516e12	0.490005
$640$	0	0
$641$	−1.09653e12	−0.256543	−0.128271	−	0.991739i	$-0.540943\pi$
$641$	−1.09653e12	−0.256543	−0.128271	+	0.991739i	$0.540943\pi$
$642$	4.01173e11	0.0932017
$643$	6.94265e12	1.60168	0.800840	−	0.598878i	$-0.204386\pi$
$643$	6.94265e12	1.60168	0.800840	+	0.598878i	$0.204386\pi$
$644$	−4.24693e12	−0.972945
$645$	0	0
$646$	8.05824e11	0.182051
$647$	2.69988e12	0.605725	0.302862	−	0.953034i	$-0.402058\pi$
$647$	2.69988e12	0.605725	0.302862	+	0.953034i	$0.402058\pi$
$648$	−5.37373e12	−1.19726
$649$	7.73095e12	1.71053
$650$	0	0
$651$	1.03560e13	2.25985
$652$	−7.30045e11	−0.158211
$653$	−2.74009e12	−0.589734	−0.294867	−	0.955538i	$-0.595275\pi$
$653$	−2.74009e12	−0.589734	−0.294867	+	0.955538i	$0.595275\pi$
$654$	2.09340e12	0.447458
$655$	0	0
$656$	−3.90745e11	−0.0823809
$657$	2.37086e12	0.496434
$658$	−2.26600e12	−0.471241
$659$	9.28259e11	0.191728	0.0958638	−	0.995394i	$-0.469439\pi$
$659$	9.28259e11	0.191728	0.0958638	+	0.995394i	$0.469439\pi$
$660$	0	0
$661$	−4.04087e12	−0.823319	−0.411659	−	0.911338i	$-0.635051\pi$
$661$	−4.04087e12	−0.823319	−0.411659	+	0.911338i	$0.635051\pi$
$662$	5.54760e12	1.12265
$663$	−1.45458e12	−0.292365
$664$	5.89452e12	1.17677
$665$	0	0
$666$	3.48738e10	0.00686856
$667$	−6.73686e12	−1.31793
$668$	2.45778e12	0.477583
$669$	−5.63622e12	−1.08785
$670$	0	0
$671$	1.07129e13	2.04013
$672$	−8.02228e12	−1.51753
$673$	8.50021e12	1.59721	0.798604	−	0.601856i	$-0.205572\pi$
$673$	8.50021e12	1.59721	0.798604	+	0.601856i	$0.205572\pi$
$674$	2.38533e11	0.0445225
$675$	0	0
$676$	−2.67056e11	−0.0491860
$677$	−5.00631e12	−0.915944	−0.457972	−	0.888967i	$-0.651424\pi$
$677$	−5.00631e12	−0.915944	−0.457972	+	0.888967i	$0.651424\pi$
$678$	−2.41950e12	−0.439737
$679$	−2.53257e12	−0.457243
$680$	0	0
$681$	−1.17770e13	−2.09832
$682$	7.98015e12	1.41248
$683$	2.20816e12	0.388274	0.194137	−	0.980974i	$-0.437809\pi$
$683$	2.20816e12	0.388274	0.194137	+	0.980974i	$0.437809\pi$
$684$	3.81755e11	0.0666856
$685$	0	0
$686$	1.34700e12	0.232225
$687$	−5.46048e12	−0.935245
$688$	−2.72727e11	−0.0464066
$689$	−1.39809e12	−0.236346
$690$	0	0
$691$	1.06597e13	1.77866	0.889329	−	0.457268i	$-0.151172\pi$
$691$	1.06597e13	1.77866	0.889329	+	0.457268i	$0.151172\pi$
$692$	5.19921e12	0.861905
$693$	−3.90436e12	−0.643057
$694$	−2.65749e12	−0.434865
$695$	0	0
$696$	−7.90428e12	−1.27679
$697$	−9.77061e12	−1.56810
$698$	3.10564e12	0.495225
$699$	−3.40875e12	−0.540068
$700$	0	0
$701$	−3.70907e12	−0.580141	−0.290071	−	0.957005i	$-0.593679\pi$
$701$	−3.70907e12	−0.580141	−0.290071	+	0.957005i	$0.593679\pi$
$702$	−8.40794e11	−0.130669
$703$	7.73197e10	0.0119396
$704$	−5.69144e12	−0.873263
$705$	0	0
$706$	−7.07787e12	−1.07221
$707$	−1.59036e13	−2.39391
$708$	5.38229e12	0.805041
$709$	−1.01872e13	−1.51407	−0.757035	−	0.653375i	$-0.773353\pi$
$709$	−1.01872e13	−1.51407	−0.757035	+	0.653375i	$0.773353\pi$
$710$	0	0
$711$	1.00270e11	0.0147150
$712$	−1.02824e13	−1.49946
$713$	1.21408e13	1.75931
$714$	−5.73772e12	−0.826224
$715$	0	0
$716$	3.75191e12	0.533512
$717$	−8.80782e12	−1.24461
$718$	6.15581e12	0.864421
$719$	1.21879e13	1.70078	0.850391	−	0.526151i	$-0.176365\pi$
$719$	1.21879e13	1.70078	0.850391	+	0.526151i	$0.176365\pi$
$720$	0	0
$721$	8.32153e12	1.14682
$722$	3.90719e12	0.535115
$723$	−7.43695e11	−0.101221
$724$	7.88049e11	0.106593
$725$	0	0
$726$	−7.37031e12	−0.984625
$727$	−1.01425e13	−1.34661	−0.673305	−	0.739364i	$-0.735126\pi$
$727$	−1.01425e13	−1.34661	−0.673305	+	0.739364i	$0.735126\pi$
$728$	−2.70091e12	−0.356384
$729$	3.93227e12	0.515667
$730$	0	0
$731$	−6.81955e12	−0.883340
$732$	7.45836e12	0.960160
$733$	7.07904e12	0.905745	0.452873	−	0.891575i	$-0.350399\pi$
$733$	7.07904e12	0.905745	0.452873	+	0.891575i	$0.350399\pi$
$734$	−4.85090e12	−0.616865
$735$	0	0
$736$	−9.40482e12	−1.18141
$737$	8.11578e12	1.01327
$738$	2.61027e12	0.323916
$739$	−2.44746e12	−0.301867	−0.150934	−	0.988544i	$-0.548228\pi$
$739$	−2.44746e12	−0.301867	−0.150934	+	0.988544i	$0.548228\pi$
$740$	0	0
$741$	8.61570e11	0.104980
$742$	−5.51492e12	−0.667915
$743$	1.41311e13	1.70109	0.850545	−	0.525902i	$-0.176272\pi$
$743$	1.41311e13	1.70109	0.850545	+	0.525902i	$0.176272\pi$
$744$	1.42446e13	1.70440
$745$	0	0
$746$	−1.17399e12	−0.138784
$747$	3.21553e12	0.377842
$748$	7.84039e12	0.915758
$749$	−1.52106e12	−0.176595
$750$	0	0
$751$	4.52777e12	0.519403	0.259701	−	0.965689i	$-0.416376\pi$
$751$	4.52777e12	0.519403	0.259701	+	0.965689i	$0.416376\pi$
$752$	2.54524e11	0.0290235
$753$	−1.13712e13	−1.28893
$754$	−1.67104e12	−0.188285
$755$	0	0
$756$	5.88130e12	0.654825
$757$	1.57044e12	0.173817	0.0869083	−	0.996216i	$-0.472301\pi$
$757$	1.57044e12	0.173817	0.0869083	+	0.996216i	$0.472301\pi$
$758$	−3.87425e12	−0.426262
$759$	−1.90580e13	−2.08444
$760$	0	0
$761$	6.80692e12	0.735732	0.367866	−	0.929879i	$-0.380089\pi$
$761$	6.80692e12	0.735732	0.367866	+	0.929879i	$0.380089\pi$
$762$	−2.66795e12	−0.286669
$763$	−7.93719e12	−0.847825
$764$	6.40664e12	0.680315
$765$	0	0
$766$	1.00434e12	0.105403
$767$	2.91741e12	0.304382
$768$	−1.06932e13	−1.10913
$769$	3.96959e12	0.409333	0.204667	−	0.978832i	$-0.434389\pi$
$769$	3.96959e12	0.409333	0.204667	+	0.978832i	$0.434389\pi$
$770$	0	0
$771$	−1.25886e13	−1.28302
$772$	−4.27615e12	−0.433286
$773$	4.26504e11	0.0429650	0.0214825	−	0.999769i	$-0.493161\pi$
$773$	4.26504e11	0.0429650	0.0214825	+	0.999769i	$0.493161\pi$
$774$	1.82188e12	0.182467
$775$	0	0
$776$	−3.48352e12	−0.344858
$777$	−5.50541e11	−0.0541870
$778$	9.79454e12	0.958464
$779$	5.78730e12	0.563063
$780$	0	0
$781$	−2.51224e13	−2.41620
$782$	−6.72654e12	−0.643223
$783$	9.32946e12	0.887010
$784$	3.59357e11	0.0339706
$785$	0	0
$786$	−1.14834e13	−1.07317
$787$	1.98338e13	1.84298	0.921489	−	0.388404i	$-0.126974\pi$
$787$	1.98338e13	1.84298	0.921489	+	0.388404i	$0.126974\pi$
$788$	−1.64349e11	−0.0151844
$789$	−4.27702e12	−0.392912
$790$	0	0
$791$	9.17362e12	0.833195
$792$	−5.37040e12	−0.485001
$793$	4.04272e12	0.363032
$794$	1.00793e13	0.899987
$795$	0	0
$796$	−4.58464e12	−0.404759
$797$	−1.39367e13	−1.22348	−0.611742	−	0.791057i	$-0.709531\pi$
$797$	−1.39367e13	−1.22348	−0.611742	+	0.791057i	$0.709531\pi$
$798$	3.39855e12	0.296675
$799$	6.36440e12	0.552455
$800$	0	0
$801$	−5.60917e12	−0.481451
$802$	−4.30154e12	−0.367146
$803$	−2.88412e13	−2.44789
$804$	5.65022e12	0.476884
$805$	0	0
$806$	3.01145e12	0.251344
$807$	−7.69773e12	−0.638898
$808$	−2.18752e13	−1.80551
$809$	−1.07051e13	−0.878661	−0.439330	−	0.898326i	$-0.644784\pi$
$809$	−1.07051e13	−0.878661	−0.439330	+	0.898326i	$0.644784\pi$
$810$	0	0
$811$	−8.79121e12	−0.713600	−0.356800	−	0.934181i	$-0.616132\pi$
$811$	−8.79121e12	−0.713600	−0.356800	+	0.934181i	$0.616132\pi$
$812$	1.16889e13	0.943561
$813$	2.58114e12	0.207207
$814$	−4.24236e11	−0.0338686
$815$	0	0
$816$	6.44480e11	0.0508866
$817$	4.03934e12	0.317184
$818$	1.16022e13	0.906045
$819$	−1.47338e12	−0.114429
$820$	0	0
$821$	−1.68572e13	−1.29491	−0.647456	−	0.762103i	$-0.724167\pi$
$821$	−1.68572e13	−1.29491	−0.647456	+	0.762103i	$0.724167\pi$
$822$	1.32863e13	1.01503
$823$	7.63277e11	0.0579940	0.0289970	−	0.999579i	$-0.490769\pi$
$823$	7.63277e11	0.0579940	0.0289970	+	0.999579i	$0.490769\pi$
$824$	1.14462e13	0.864944
$825$	0	0
$826$	1.15080e13	0.860183
$827$	−2.54768e12	−0.189396	−0.0946979	−	0.995506i	$-0.530189\pi$
$827$	−2.54768e12	−0.189396	−0.0946979	+	0.995506i	$0.530189\pi$
$828$	−3.18666e12	−0.235613
$829$	−2.61115e13	−1.92016	−0.960079	−	0.279728i	$-0.909756\pi$
$829$	−2.61115e13	−1.92016	−0.960079	+	0.279728i	$0.909756\pi$
$830$	0	0
$831$	1.82454e12	0.132723
$832$	−2.14777e12	−0.155393
$833$	8.98574e12	0.646623
$834$	−9.13417e12	−0.653766
$835$	0	0
$836$	−4.64400e12	−0.328824
$837$	−1.68130e13	−1.18408
$838$	−1.03899e13	−0.727799
$839$	2.02768e13	1.41277	0.706385	−	0.707828i	$-0.250325\pi$
$839$	2.02768e13	1.41277	0.706385	+	0.707828i	$0.250325\pi$
$840$	0	0
$841$	4.03478e12	0.278124
$842$	−4.34263e12	−0.297748
$843$	1.68231e12	0.114731
$844$	2.40134e12	0.162897
$845$	0	0
$846$	−1.70028e12	−0.114118
$847$	2.79447e13	1.86563
$848$	6.19453e11	0.0411365
$849$	1.33649e13	0.882839
$850$	0	0
$851$	−6.45419e11	−0.0421851
$852$	−1.74903e13	−1.13715
$853$	−5.68425e12	−0.367623	−0.183811	−	0.982962i	$-0.558844\pi$
$853$	−5.68425e12	−0.367623	−0.183811	+	0.982962i	$0.558844\pi$
$854$	1.59469e13	1.02593
$855$	0	0
$856$	−2.09220e12	−0.133190
$857$	−2.21261e13	−1.40117	−0.700586	−	0.713568i	$-0.747078\pi$
$857$	−2.21261e13	−1.40117	−0.700586	+	0.713568i	$0.747078\pi$
$858$	−4.72724e12	−0.297793
$859$	5.39127e12	0.337848	0.168924	−	0.985629i	$-0.445971\pi$
$859$	5.39127e12	0.337848	0.168924	+	0.985629i	$0.445971\pi$
$860$	0	0
$861$	−4.12074e13	−2.55541
$862$	−8.61442e11	−0.0531427
$863$	2.64450e12	0.162291	0.0811457	−	0.996702i	$-0.474142\pi$
$863$	2.64450e12	0.162291	0.0811457	+	0.996702i	$0.474142\pi$
$864$	1.30241e13	0.795128
$865$	0	0
$866$	1.96169e13	1.18522
$867$	−2.97134e12	−0.178594
$868$	−2.10649e13	−1.25957
$869$	−1.21977e12	−0.0725589
$870$	0	0
$871$	3.06264e12	0.180307
$872$	−1.09175e13	−0.639440
$873$	−1.90030e12	−0.110728
$874$	3.98424e12	0.230964
$875$	0	0
$876$	−2.00792e13	−1.15207
$877$	1.72860e13	0.986723	0.493362	−	0.869824i	$-0.335768\pi$
$877$	1.72860e13	0.986723	0.493362	+	0.869824i	$0.335768\pi$
$878$	4.39445e12	0.249563
$879$	2.47898e13	1.40063
$880$	0	0
$881$	−5.09524e12	−0.284953	−0.142477	−	0.989798i	$-0.545507\pi$
$881$	−5.09524e12	−0.284953	−0.142477	+	0.989798i	$0.545507\pi$
$882$	−2.40059e12	−0.133570
$883$	5.94406e12	0.329048	0.164524	−	0.986373i	$-0.447391\pi$
$883$	5.94406e12	0.329048	0.164524	+	0.986373i	$0.447391\pi$
$884$	2.95871e12	0.162955
$885$	0	0
$886$	−1.36190e13	−0.742495
$887$	−9.01179e12	−0.488826	−0.244413	−	0.969671i	$-0.578595\pi$
$887$	−9.01179e12	−0.488826	−0.244413	+	0.969671i	$0.578595\pi$
$888$	−7.57263e11	−0.0408685
$889$	1.01156e13	0.543168
$890$	0	0
$891$	3.56605e13	1.89556
$892$	1.14645e13	0.606335
$893$	−3.76974e12	−0.198372
$894$	−6.35332e11	−0.0332646
$895$	0	0
$896$	1.70479e13	0.883657
$897$	−7.19187e12	−0.370916
$898$	6.24883e12	0.320667
$899$	−3.34151e13	−1.70618
$900$	0	0
$901$	1.54895e13	0.783024
$902$	−3.17536e13	−1.59721
$903$	−2.87614e13	−1.43951
$904$	1.26182e13	0.628405
$905$	0	0
$906$	2.26209e13	1.11541
$907$	−1.80291e13	−0.884589	−0.442295	−	0.896870i	$-0.645835\pi$
$907$	−1.80291e13	−0.884589	−0.442295	+	0.896870i	$0.645835\pi$
$908$	2.39552e13	1.16954
$909$	−1.19332e13	−0.579721
$910$	0	0
$911$	−8.74176e12	−0.420500	−0.210250	−	0.977648i	$-0.567428\pi$
$911$	−8.74176e12	−0.420500	−0.210250	+	0.977648i	$0.567428\pi$
$912$	−3.81736e11	−0.0182720
$913$	−3.91165e13	−1.86312
$914$	9.78882e12	0.463951
$915$	0	0
$916$	1.11070e13	0.521276
$917$	4.35396e13	2.03340
$918$	9.31517e12	0.432911
$919$	4.88737e12	0.226025	0.113012	−	0.993594i	$-0.463950\pi$
$919$	4.88737e12	0.226025	0.113012	+	0.993594i	$0.463950\pi$
$920$	0	0
$921$	2.05179e13	0.939645
$922$	−4.91536e12	−0.224009
$923$	−9.48040e12	−0.429951
$924$	3.30667e13	1.49234
$925$	0	0
$926$	2.21548e13	0.990188
$927$	6.24403e12	0.277719
$928$	2.58850e13	1.14573
$929$	−3.90471e13	−1.71996	−0.859979	−	0.510329i	$-0.829524\pi$
$929$	−3.90471e13	−1.71996	−0.859979	+	0.510329i	$0.829524\pi$
$930$	0	0
$931$	−5.32241e12	−0.232185
$932$	6.93365e12	0.301017
$933$	1.49966e13	0.647927
$934$	1.01644e13	0.437038
$935$	0	0
$936$	−2.02662e12	−0.0863038
$937$	3.22449e13	1.36657	0.683286	−	0.730151i	$-0.260550\pi$
$937$	3.22449e13	1.36657	0.683286	+	0.730151i	$0.260550\pi$
$938$	1.20809e13	0.509549
$939$	−3.47940e13	−1.46053
$940$	0	0
$941$	−3.12301e13	−1.29843	−0.649217	−	0.760604i	$-0.724903\pi$
$941$	−3.12301e13	−1.29843	−0.649217	+	0.760604i	$0.724903\pi$
$942$	2.07944e13	0.860432
$943$	−4.83090e13	−1.98941
$944$	−1.29262e12	−0.0529781
$945$	0	0
$946$	−2.21629e13	−0.899739
$947$	−3.13952e12	−0.126849	−0.0634247	−	0.997987i	$-0.520202\pi$
$947$	−3.13952e12	−0.126849	−0.0634247	+	0.997987i	$0.520202\pi$
$948$	−8.49208e11	−0.0341489
$949$	−1.08837e13	−0.435592
$950$	0	0
$951$	9.78483e12	0.387919
$952$	2.99234e13	1.18071
$953$	−2.60434e13	−1.02277	−0.511387	−	0.859351i	$-0.670868\pi$
$953$	−2.60434e13	−1.02277	−0.511387	+	0.859351i	$0.670868\pi$
$954$	−4.13810e12	−0.161746
$955$	0	0
$956$	1.79158e13	0.693705
$957$	5.24535e13	2.02148
$958$	2.58963e13	0.993330
$959$	−5.03754e13	−1.92324
$960$	0	0
$961$	3.37790e13	1.27759
$962$	−1.60093e11	−0.00602676
$963$	−1.14132e12	−0.0427651
$964$	1.51273e12	0.0564176
$965$	0	0
$966$	−2.83691e13	−1.04821
$967$	4.11231e13	1.51240	0.756200	−	0.654341i	$-0.227054\pi$
$967$	4.11231e13	1.51240	0.756200	+	0.654341i	$0.227054\pi$
$968$	3.84377e13	1.40708
$969$	−9.54534e12	−0.347804
$970$	0	0
$971$	−1.83064e13	−0.660870	−0.330435	−	0.943829i	$-0.607195\pi$
$971$	−1.83064e13	−0.660870	−0.330435	+	0.943829i	$0.607195\pi$
$972$	1.08656e13	0.390442
$973$	3.46325e13	1.23873
$974$	−5.61555e12	−0.199930
$975$	0	0
$976$	−1.79121e12	−0.0631862
$977$	−3.09720e13	−1.08753	−0.543767	−	0.839236i	$-0.683003\pi$
$977$	−3.09720e13	−1.08753	−0.543767	+	0.839236i	$0.683003\pi$
$978$	−4.87664e12	−0.170449
$979$	6.82348e13	2.37402
$980$	0	0
$981$	−5.95564e12	−0.205314
$982$	7.57452e12	0.259928
$983$	−8.41222e12	−0.287356	−0.143678	−	0.989625i	$-0.545893\pi$
$983$	−8.41222e12	−0.287356	−0.143678	+	0.989625i	$0.545893\pi$
$984$	−5.66803e13	−1.92732
$985$	0	0
$986$	1.85135e13	0.623797
$987$	2.68418e13	0.900293
$988$	−1.75250e12	−0.0585128
$989$	−3.37180e13	−1.12067
$990$	0	0
$991$	1.06870e13	0.351986	0.175993	−	0.984391i	$-0.443686\pi$
$991$	1.06870e13	0.351986	0.175993	+	0.984391i	$0.443686\pi$
$992$	−4.66483e13	−1.52944
$993$	−6.57138e13	−2.14479
$994$	−3.73964e13	−1.21504
$995$	0	0
$996$	−2.72330e13	−0.876855
$997$	5.74730e13	1.84219	0.921097	−	0.389333i	$-0.127295\pi$
$997$	5.74730e13	1.84219	0.921097	+	0.389333i	$0.127295\pi$
$998$	−1.00880e13	−0.321896
$999$	8.93800e11	0.0283920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.f.1.5		10
5.4	even	2		65.10.a.c.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.a.c.1.6	✓	10	5.4	even	2
325.10.a.f.1.5		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-13.5874 q^{2} +160.949 q^{3} -327.382 q^{4} -2186.88 q^{6} +8291.63 q^{7} +11405.0 q^{8} +6221.59 q^{9} -75684.8 q^{11} -52691.8 q^{12} -28561.0 q^{13} -112662. q^{14} +12654.5 q^{16} +316428. q^{17} -84535.3 q^{18} -187425. q^{19} +1.33453e6 q^{21} +1.02836e6 q^{22} +1.56452e6 q^{23} +1.83563e6 q^{24} +388070. q^{26} -2.16660e6 q^{27} -2.71453e6 q^{28} -4.30603e6 q^{29} +7.76007e6 q^{31} -6.01132e6 q^{32} -1.21814e7 q^{33} -4.29944e6 q^{34} -2.03684e6 q^{36} -412536. q^{37} +2.54663e6 q^{38} -4.59687e6 q^{39} -3.08779e7 q^{41} -1.81328e7 q^{42} -2.15517e7 q^{43} +2.47778e7 q^{44} -2.12578e7 q^{46} +2.01133e7 q^{47} +2.03674e6 q^{48} +2.83975e7 q^{49} +5.09287e7 q^{51} +9.35036e6 q^{52} +4.89511e7 q^{53} +2.94385e7 q^{54} +9.45663e7 q^{56} -3.01659e7 q^{57} +5.85079e7 q^{58} -1.02147e8 q^{59} -1.41547e8 q^{61} -1.05439e8 q^{62} +5.15871e7 q^{63} +7.51992e7 q^{64} +1.65514e8 q^{66} -1.07231e8 q^{67} -1.03593e8 q^{68} +2.51808e8 q^{69} +3.31935e8 q^{71} +7.09574e7 q^{72} +3.81069e8 q^{73} +5.60530e6 q^{74} +6.13597e7 q^{76} -6.27550e8 q^{77} +6.24595e7 q^{78} +1.61165e7 q^{79} -4.71172e8 q^{81} +4.19551e8 q^{82} +5.16835e8 q^{83} -4.36901e8 q^{84} +2.92832e8 q^{86} -6.93052e8 q^{87} -8.63187e8 q^{88} -9.01566e8 q^{89} -2.36817e8 q^{91} -5.12195e8 q^{92} +1.24898e9 q^{93} -2.73288e8 q^{94} -9.67516e8 q^{96} -3.05437e8 q^{97} -3.85848e8 q^{98} -4.70879e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{2} - 170 q^{3} + 3158 q^{4} - 3306 q^{6} - 4796 q^{7} + 19056 q^{8} + 92810 q^{9} - 74950 q^{11} + 51834 q^{12} - 285610 q^{13} + 60672 q^{14} + 1368530 q^{16} - 1066000 q^{17} - 1679076 q^{18}+ \cdots - 2805512690 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 170 * q^3 + 3158 * q^4 - 3306 * q^6 - 4796 * q^7 + 19056 * q^8 + 92810 * q^9 - 74950 * q^11 + 51834 * q^12 - 285610 * q^13 + 60672 * q^14 + 1368530 * q^16 - 1066000 * q^17 - 1679076 * q^18 + 1130702 * q^19 + 317220 * q^21 - 92986 * q^22 - 1639630 * q^23 - 6364494 * q^24 + 228488 * q^26 + 1067896 * q^27 - 4816012 * q^28 - 11823692 * q^29 + 17332410 * q^31 - 8813936 * q^32 - 12030884 * q^33 + 7284340 * q^34 + 81850198 * q^36 - 27892424 * q^37 - 72453870 * q^38 + 4855370 * q^39 - 3891824 * q^41 - 165021660 * q^42 - 84011234 * q^43 + 46801070 * q^44 + 173504026 * q^46 - 79184500 * q^47 - 204770370 * q^48 + 171631330 * q^49 + 111905236 * q^51 - 90195638 * q^52 + 51026128 * q^53 + 70324704 * q^54 + 80292608 * q^56 + 156021572 * q^57 - 170753836 * q^58 - 55847702 * q^59 - 34702428 * q^61 - 123241794 * q^62 - 791924972 * q^63 + 176769142 * q^64 + 943669416 * q^66 - 558023952 * q^67 - 1103318464 * q^68 + 595498384 * q^69 + 400978870 * q^71 + 227926092 * q^72 - 479660152 * q^73 - 1842717232 * q^74 + 667629178 * q^76 + 35600172 * q^77 + 94422666 * q^78 + 811405652 * q^79 - 172430134 * q^81 + 728501492 * q^82 + 873577748 * q^83 - 3454865492 * q^84 - 4017148098 * q^86 + 14661024 * q^87 - 266182958 * q^88 - 798868188 * q^89 + 136978556 * q^91 + 547168398 * q^92 + 1978869188 * q^93 + 212588928 * q^94 - 6199507594 * q^96 - 588759252 * q^97 + 3898704088 * q^98 - 2805512690 * q^99

Introduction

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