LMFDB - Embedded newform 49.26.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 1893235651143 x^{10} + \cdots + 18\!\cdots\!00 $ x^12 - 6x^11 - 1893235651143x^10 - 2806413319284680x^9 + 1366207034897721655024398x^8 + 3312795166707293294503326972x^7 - 472740950482561735952171872520774042x^6 - 1306463460138017667257494385745612412176x^5 + 81582696677278884463837972328572242548650191945x^4 + 210395555452534295320647430642617820851383278332906x^3 - 6559737221151479218960148352096969186826132314084199521375x^2 - 10145823620894406299505180212681539035695843286608488793425800*x + 186490559268947851964754942137649552284372963082878767942887530577000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{48}\cdot 3^{20}\cdot 5^{5}\cdot 7^{15} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-760822.$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5492.18 q^{2} +1.52784e6 q^{3} -3.39037e6 q^{4} -1.00981e9 q^{5} +8.39119e9 q^{6} -2.02908e11 q^{8} +1.48702e12 q^{9} +O(q^{10})$	\(q+5492.18 q^{2} +1.52784e6 q^{3} -3.39037e6 q^{4} -1.00981e9 q^{5} +8.39119e9 q^{6} -2.02908e11 q^{8} +1.48702e12 q^{9} -5.54607e12 q^{10} +1.39326e13 q^{11} -5.17996e12 q^{12} -6.33658e13 q^{13} -1.54283e15 q^{15} -1.00064e15 q^{16} -6.78826e14 q^{17} +8.16696e15 q^{18} -1.52663e16 q^{19} +3.42364e15 q^{20} +7.65203e16 q^{22} +7.85317e16 q^{23} -3.10011e17 q^{24} +7.21696e17 q^{25} -3.48016e17 q^{26} +9.77402e17 q^{27} -1.15188e18 q^{29} -8.47352e18 q^{30} -8.59557e17 q^{31} +1.31273e18 q^{32} +2.12868e19 q^{33} -3.72823e18 q^{34} -5.04154e18 q^{36} +6.89579e19 q^{37} -8.38452e19 q^{38} -9.68129e19 q^{39} +2.04898e20 q^{40} +1.33480e20 q^{41} -1.57196e20 q^{43} -4.72367e19 q^{44} -1.50161e21 q^{45} +4.31311e20 q^{46} +5.03341e20 q^{47} -1.52883e21 q^{48} +3.96369e21 q^{50} -1.03714e21 q^{51} +2.14834e20 q^{52} -5.46318e20 q^{53} +5.36807e21 q^{54} -1.40693e22 q^{55} -2.33245e22 q^{57} -6.32632e21 q^{58} +1.15779e22 q^{59} +5.23078e21 q^{60} -4.67500e21 q^{61} -4.72084e21 q^{62} +4.07858e22 q^{64} +6.39875e22 q^{65} +1.16911e23 q^{66} -8.62714e22 q^{67} +2.30147e21 q^{68} +1.19984e23 q^{69} +1.69430e23 q^{71} -3.01727e23 q^{72} +3.82814e23 q^{73} +3.78729e23 q^{74} +1.10264e24 q^{75} +5.17584e22 q^{76} -5.31714e23 q^{78} +6.19929e23 q^{79} +1.01046e24 q^{80} +2.33385e23 q^{81} +7.33097e23 q^{82} -9.97017e23 q^{83} +6.85486e23 q^{85} -8.63348e23 q^{86} -1.75989e24 q^{87} -2.82703e24 q^{88} +1.70020e24 q^{89} -8.24709e24 q^{90} -2.66252e23 q^{92} -1.31327e24 q^{93} +2.76444e24 q^{94} +1.54161e25 q^{95} +2.00565e24 q^{96} +2.07347e24 q^{97} +2.07180e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9}+O(q^{10}) $ 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9	$ 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9} + 39593455677648 q^{11} + 357546272706144 q^{15} + 18\!\cdots\!56 q^{16}+ \cdots - 14\!\cdots\!88 q^{99}+O(q^{100}) $ 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9 + 39593455677648 * q^11 + 357546272706144 * q^15 + 1897434424858656 * q^16 + 19017456854067300 * q^18 + 85409383356235920 * q^22 + 77196982648366080 * q^23 + 2296738995597808932 * q^25 + 8694499082723336088 * q^29 - 12169958791851770688 * q^30 - 6483391660121958720 * q^32 - 109652263099391094456 * q^36 + 151853425001596848120 * q^37 - 122709680243235084384 * q^39 - 380869142455132177200 * q^43 + 991389584873062609056 * q^44 + 2303857023830118404064 * q^46 + 3165366920999170599036 * q^50 + 1280977431762493664064 * q^51 + 17755418685871290573000 * q^53 - 40456075816140877421280 * q^57 + 90683689500928436394600 * q^58 + 27395532648965383354368 * q^60 - 153351020298413953854336 * q^64 + 200499279532648292123424 * q^65 + 148336212990069406108560 * q^67 + 562419591698095656528384 * q^71 - 554920453414323154337040 * q^72 + 509427689055313155358536 * q^74 - 812506544978626047049920 * q^78 + 1488381592136271978244704 * q^79 - 2624302005301676288302452 * q^81 - 333667887446182173142464 * q^85 - 10612071587035448449112880 * q^86 - 14889193934757325628907840 * q^88 + 8074123164162948551757120 * q^92 + 1647472274074578272984640 * q^93 + 10792312351147270637620128 * q^95 - 148376588023327766946288 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5492.18	0.948134	0.474067	−	0.880489i	$-0.342785\pi$
$2$	5492.18	0.948134	0.474067	+	0.880489i	$0.342785\pi$
$3$	1.52784e6	1.65983	0.829914	−	0.557892i	$-0.188390\pi$
$3$	1.52784e6	1.65983	0.829914	+	0.557892i	$0.188390\pi$
$4$	−3.39037e6	−0.101041
$5$	−1.00981e9	−1.84976	−0.924880	−	0.380260i	$-0.875835\pi$
$5$	−1.00981e9	−1.84976	−0.924880	+	0.380260i	$0.875835\pi$
$6$	8.39119e9	1.57374
$7$	0	0
$7$	0	0
$8$	−2.02908e11	−1.04393
$9$	1.48702e12	1.75503
$10$	−5.54607e12	−1.75382
$11$	1.39326e13	1.33852	0.669258	−	0.743031i	$-0.266612\pi$
$11$	1.39326e13	1.33852	0.669258	+	0.743031i	$0.266612\pi$
$12$	−5.17996e12	−0.167711
$13$	−6.33658e13	−0.754332	−0.377166	−	0.926146i	$-0.623101\pi$
$13$	−6.33658e13	−0.754332	−0.377166	+	0.926146i	$0.623101\pi$
$14$	0	0
$15$	−1.54283e15	−3.07028
$16$	−1.00064e15	−0.888750
$17$	−6.78826e14	−0.282584	−0.141292	−	0.989968i	$-0.545126\pi$
$17$	−6.78826e14	−0.282584	−0.141292	+	0.989968i	$0.545126\pi$
$18$	8.16696e15	1.66400
$19$	−1.52663e16	−1.58239	−0.791195	−	0.611564i	$-0.790541\pi$
$19$	−1.52663e16	−1.58239	−0.791195	+	0.611564i	$0.790541\pi$
$20$	3.42364e15	0.186902
$21$	0	0
$22$	7.65203e16	1.26909
$23$	7.85317e16	0.747218	0.373609	−	0.927586i	$-0.378120\pi$
$23$	7.85317e16	0.747218	0.373609	+	0.927586i	$0.378120\pi$
$24$	−3.10011e17	−1.73275
$25$	7.21696e17	2.42161
$26$	−3.48016e17	−0.715209
$27$	9.77402e17	1.25322
$28$	0	0
$29$	−1.15188e18	−0.604549	−0.302274	−	0.953221i	$-0.597746\pi$
$29$	−1.15188e18	−0.604549	−0.302274	+	0.953221i	$0.597746\pi$
$30$	−8.47352e18	−2.91104
$31$	−8.59557e17	−0.195999	−0.0979995	−	0.995186i	$-0.531244\pi$
$31$	−8.59557e17	−0.195999	−0.0979995	+	0.995186i	$0.531244\pi$
$32$	1.31273e18	0.201281
$33$	2.12868e19	2.22170
$34$	−3.72823e18	−0.267927
$35$	0	0
$36$	−5.04154e18	−0.177330
$37$	6.89579e19	1.72212	0.861058	−	0.508507i	$-0.169802\pi$
$37$	6.89579e19	1.72212	0.861058	+	0.508507i	$0.169802\pi$
$38$	−8.38452e19	−1.50032
$39$	−9.68129e19	−1.25206
$40$	2.04898e20	1.93103
$41$	1.33480e20	0.923886	0.461943	−	0.886910i	$-0.347152\pi$
$41$	1.33480e20	0.923886	0.461943	+	0.886910i	$0.347152\pi$
$42$	0	0
$43$	−1.57196e20	−0.599909	−0.299954	−	0.953954i	$-0.596971\pi$
$43$	−1.57196e20	−0.599909	−0.299954	+	0.953954i	$0.596971\pi$
$44$	−4.72367e19	−0.135245
$45$	−1.50161e21	−3.24638
$46$	4.31311e20	0.708463
$47$	5.03341e20	0.631887	0.315943	−	0.948778i	$-0.397679\pi$
$47$	5.03341e20	0.631887	0.315943	+	0.948778i	$0.397679\pi$
$48$	−1.52883e21	−1.47517
$49$	0	0
$50$	3.96369e21	2.29601
$51$	−1.03714e21	−0.469040
$52$	2.14834e20	0.0762185
$53$	−5.46318e20	−0.152755	−0.0763777	−	0.997079i	$-0.524335\pi$
$53$	−5.46318e20	−0.152755	−0.0763777	+	0.997079i	$0.524335\pi$
$54$	5.36807e21	1.18822
$55$	−1.40693e22	−2.47593
$56$	0	0
$57$	−2.33245e22	−2.62649
$58$	−6.32632e21	−0.573194
$59$	1.15779e22	0.847188	0.423594	−	0.905852i	$-0.360768\pi$
$59$	1.15779e22	0.847188	0.423594	+	0.905852i	$0.360768\pi$
$60$	5.23078e21	0.310224
$61$	−4.67500e21	−0.225506	−0.112753	−	0.993623i	$-0.535967\pi$
$61$	−4.67500e21	−0.225506	−0.112753	+	0.993623i	$0.535967\pi$
$62$	−4.72084e21	−0.185833
$63$	0	0
$64$	4.07858e22	1.07959
$65$	6.39875e22	1.39533
$66$	1.16911e23	2.10647
$67$	−8.62714e22	−1.28805	−0.644024	−	0.765005i	$-0.722736\pi$
$67$	−8.62714e22	−1.28805	−0.644024	+	0.765005i	$0.722736\pi$
$68$	2.30147e21	0.0285525
$69$	1.19984e23	1.24025
$70$	0	0
$71$	1.69430e23	1.22535	0.612675	−	0.790335i	$-0.290093\pi$
$71$	1.69430e23	1.22535	0.612675	+	0.790335i	$0.290093\pi$
$72$	−3.01727e23	−1.83214
$73$	3.82814e23	1.95637	0.978187	−	0.207725i	$-0.0666060\pi$
$73$	3.82814e23	1.95637	0.978187	+	0.207725i	$0.0666060\pi$
$74$	3.78729e23	1.63280
$75$	1.10264e24	4.01946
$76$	5.17584e22	0.159886
$77$	0	0
$78$	−5.31714e23	−1.18712
$79$	6.19929e23	1.18033	0.590165	−	0.807283i	$-0.299063\pi$
$79$	6.19929e23	1.18033	0.590165	+	0.807283i	$0.299063\pi$
$80$	1.01046e24	1.64397
$81$	2.33385e23	0.325095
$82$	7.33097e23	0.875968
$83$	−9.97017e23	−1.02383	−0.511913	−	0.859037i	$-0.671063\pi$
$83$	−9.97017e23	−1.02383	−0.511913	+	0.859037i	$0.671063\pi$
$84$	0	0
$85$	6.85486e23	0.522712
$86$	−8.63348e23	−0.568794
$87$	−1.75989e24	−1.00345
$88$	−2.82703e24	−1.39732
$89$	1.70020e24	0.729668	0.364834	−	0.931073i	$-0.381126\pi$
$89$	1.70020e24	0.729668	0.364834	+	0.931073i	$0.381126\pi$
$90$	−8.24709e24	−3.07800
$91$	0	0
$92$	−2.66252e23	−0.0754997
$93$	−1.31327e24	−0.325324
$94$	2.76444e24	0.599114
$95$	1.54161e25	2.92704
$96$	2.00565e24	0.334091
$97$	2.07347e24	0.303425	0.151713	−	0.988425i	$-0.451521\pi$
$97$	2.07347e24	0.303425	0.151713	+	0.988425i	$0.451521\pi$
$98$	0	0
$99$	2.07180e25	2.34913
$100$	−2.44682e24	−0.244682
$101$	2.79079e24	0.246439	0.123220	−	0.992379i	$-0.460678\pi$
$101$	2.79079e24	0.246439	0.123220	+	0.992379i	$0.460678\pi$
$102$	−5.69616e24	−0.444713
$103$	5.59369e24	0.386575	0.193287	−	0.981142i	$-0.438085\pi$
$103$	5.59369e24	0.386575	0.193287	+	0.981142i	$0.438085\pi$
$104$	1.28574e25	0.787474
$105$	0	0
$106$	−3.00047e24	−0.144833
$107$	1.13578e25	0.487527	0.243763	−	0.969835i	$-0.421618\pi$
$107$	1.13578e25	0.487527	0.243763	+	0.969835i	$0.421618\pi$
$108$	−3.31376e24	−0.126626
$109$	4.18305e25	1.42450	0.712249	−	0.701927i	$-0.247677\pi$
$109$	4.18305e25	1.42450	0.712249	+	0.701927i	$0.247677\pi$
$110$	−7.72711e25	−2.34752
$111$	1.05357e26	2.85842
$112$	0	0
$113$	−5.09057e25	−1.10481	−0.552403	−	0.833577i	$-0.686289\pi$
$113$	−5.09057e25	−1.10481	−0.552403	+	0.833577i	$0.686289\pi$
$114$	−1.28102e26	−2.49027
$115$	−7.93023e25	−1.38217
$116$	3.90530e24	0.0610842
$117$	−9.42259e25	−1.32387
$118$	6.35879e25	0.803248
$119$	0	0
$120$	3.13053e26	3.20517
$121$	8.57700e25	0.791623
$122$	−2.56759e25	−0.213810
$123$	2.03937e26	1.53349
$124$	2.91422e24	0.0198039
$125$	−4.27830e26	−2.62964
$126$	0	0
$127$	2.13306e26	1.07512	0.537560	−	0.843225i	$-0.319346\pi$
$127$	2.13306e26	1.07512	0.537560	+	0.843225i	$0.319346\pi$
$128$	1.79955e26	0.822317
$129$	−2.40171e26	−0.995745
$130$	3.51431e26	1.32296
$131$	−2.00314e26	−0.685205	−0.342602	−	0.939481i	$-0.611308\pi$
$131$	−2.00314e26	−0.685205	−0.342602	+	0.939481i	$0.611308\pi$
$132$	−7.21702e25	−0.224483
$133$	0	0
$134$	−4.73818e26	−1.22124
$135$	−9.86992e26	−2.31815
$136$	1.37739e26	0.294999
$137$	1.30513e26	0.255062	0.127531	−	0.991835i	$-0.459295\pi$
$137$	1.30513e26	0.255062	0.127531	+	0.991835i	$0.459295\pi$
$138$	6.58975e26	1.17593
$139$	−3.20692e26	−0.522881	−0.261441	−	0.965220i	$-0.584198\pi$
$139$	−3.20692e26	−0.522881	−0.261441	+	0.965220i	$0.584198\pi$
$140$	0	0
$141$	7.69026e26	1.04882
$142$	9.30539e26	1.16180
$143$	−8.82849e26	−1.00969
$144$	−1.48797e27	−1.55978
$145$	1.16318e27	1.11827
$146$	2.10248e27	1.85491
$147$	0	0
$148$	−2.33793e26	−0.174004
$149$	3.46606e26	0.237141	0.118571	−	0.992946i	$-0.462169\pi$
$149$	3.46606e26	0.237141	0.118571	+	0.992946i	$0.462169\pi$
$150$	6.05589e27	3.81099
$151$	2.02021e27	1.17000	0.584999	−	0.811034i	$-0.301095\pi$
$151$	2.02021e27	1.17000	0.584999	+	0.811034i	$0.301095\pi$
$152$	3.09764e27	1.65191
$153$	−1.00942e27	−0.495942
$154$	0	0
$155$	8.67991e26	0.362551
$156$	3.28232e26	0.126510
$157$	2.55981e27	0.910882	0.455441	−	0.890266i	$-0.349482\pi$
$157$	2.55981e27	0.910882	0.455441	+	0.890266i	$0.349482\pi$
$158$	3.40476e27	1.11911
$159$	−8.34687e26	−0.253548
$160$	−1.32561e27	−0.372321
$161$	0	0
$162$	1.28179e27	0.308234
$163$	2.23307e27	0.497230	0.248615	−	0.968602i	$-0.420025\pi$
$163$	2.23307e27	0.497230	0.248615	+	0.968602i	$0.420025\pi$
$164$	−4.52548e26	−0.0933504
$165$	−2.14957e28	−4.10962
$166$	−5.47580e27	−0.970725
$167$	−2.89018e27	−0.475301	−0.237650	−	0.971351i	$-0.576377\pi$
$167$	−2.89018e27	−0.475301	−0.237650	+	0.971351i	$0.576377\pi$
$168$	0	0
$169$	−3.04119e27	−0.430983
$170$	3.76481e27	0.495601
$171$	−2.27012e28	−2.77714
$172$	5.32953e26	0.0606154
$173$	−1.01579e28	−1.07455	−0.537275	−	0.843407i	$-0.680546\pi$
$173$	−1.01579e28	−1.07455	−0.537275	+	0.843407i	$0.680546\pi$
$174$	−9.66563e27	−0.951403
$175$	0	0
$176$	−1.39416e28	−1.18960
$177$	1.76892e28	1.40619
$178$	9.33782e27	0.691823
$179$	−6.60799e27	−0.456464	−0.228232	−	0.973607i	$-0.573295\pi$
$179$	−6.60799e27	−0.456464	−0.228232	+	0.973607i	$0.573295\pi$
$180$	5.09100e27	0.328018
$181$	1.88503e28	1.13327	0.566637	−	0.823967i	$-0.308244\pi$
$181$	1.88503e28	1.13327	0.566637	+	0.823967i	$0.308244\pi$
$182$	0	0
$183$	−7.14266e27	−0.374301
$184$	−1.59347e28	−0.780047
$185$	−6.96345e28	−3.18550
$186$	−7.21271e27	−0.308451
$187$	−9.45780e27	−0.378242
$188$	−1.70652e27	−0.0638465
$189$	0	0
$190$	8.46679e28	2.77523
$191$	4.75772e28	1.46043	0.730217	−	0.683215i	$-0.239419\pi$
$191$	4.75772e28	1.46043	0.730217	+	0.683215i	$0.239419\pi$
$192$	6.23143e28	1.79193
$193$	6.33149e27	0.170624	0.0853119	−	0.996354i	$-0.472811\pi$
$193$	6.33149e27	0.170624	0.0853119	+	0.996354i	$0.472811\pi$
$194$	1.13879e28	0.287688
$195$	9.77628e28	2.31601
$196$	0	0
$197$	2.19691e28	0.458126	0.229063	−	0.973412i	$-0.426434\pi$
$197$	2.19691e28	0.458126	0.229063	+	0.973412i	$0.426434\pi$
$198$	1.13787e29	2.22729
$199$	1.54099e28	0.283228	0.141614	−	0.989922i	$-0.454771\pi$
$199$	1.54099e28	0.283228	0.141614	+	0.989922i	$0.454771\pi$
$200$	−1.46438e29	−2.52800
$201$	−1.31809e29	−2.13794
$202$	1.53275e28	0.233657
$203$	0	0
$204$	3.51629e27	0.0473923
$205$	−1.34790e29	−1.70897
$206$	3.07216e28	0.366525
$207$	1.16778e29	1.31139
$208$	6.34065e28	0.670413
$209$	−2.12699e29	−2.11805
$210$	0	0
$211$	7.16594e28	0.633494	0.316747	−	0.948510i	$-0.397409\pi$
$211$	7.16594e28	0.633494	0.316747	+	0.948510i	$0.397409\pi$
$212$	1.85222e27	0.0154346
$213$	2.58862e29	2.03387
$214$	6.23793e28	0.462241
$215$	1.58738e29	1.10969
$216$	−1.98322e29	−1.30828
$217$	0	0
$218$	2.29741e29	1.35062
$219$	5.84880e29	3.24724
$220$	4.77002e28	0.250171
$221$	4.30143e28	0.213162
$222$	5.78639e29	2.71016
$223$	1.34109e29	0.593810	0.296905	−	0.954907i	$-0.404045\pi$
$223$	1.34109e29	0.593810	0.296905	+	0.954907i	$0.404045\pi$
$224$	0	0
$225$	1.07317e30	4.24999
$226$	−2.79583e29	−1.04750
$227$	−4.32992e29	−1.53517	−0.767585	−	0.640947i	$-0.778542\pi$
$227$	−4.32992e29	−1.53517	−0.767585	+	0.640947i	$0.778542\pi$
$228$	7.90787e28	0.265384
$229$	−5.73658e28	−0.182268	−0.0911339	−	0.995839i	$-0.529049\pi$
$229$	−5.73658e28	−0.182268	−0.0911339	+	0.995839i	$0.529049\pi$
$230$	−4.35542e29	−1.31049
$231$	0	0
$232$	2.33725e29	0.631110
$233$	−3.56166e29	−0.911387	−0.455694	−	0.890137i	$-0.650609\pi$
$233$	−3.56166e29	−0.911387	−0.455694	+	0.890137i	$0.650609\pi$
$234$	−5.17506e29	−1.25521
$235$	−5.08280e29	−1.16884
$236$	−3.92534e28	−0.0856007
$237$	9.47154e29	1.95914
$238$	0	0
$239$	−1.92099e29	−0.357727	−0.178864	−	0.983874i	$-0.557242\pi$
$239$	−1.92099e29	−0.357727	−0.178864	+	0.983874i	$0.557242\pi$
$240$	1.54383e30	2.72871
$241$	4.98946e29	0.837222	0.418611	−	0.908166i	$-0.362517\pi$
$241$	4.98946e29	0.837222	0.418611	+	0.908166i	$0.362517\pi$
$242$	4.71064e29	0.750565
$243$	−4.71565e29	−0.713614
$244$	1.58500e28	0.0227854
$245$	0	0
$246$	1.12006e30	1.45396
$247$	9.67360e29	1.19365
$248$	1.74411e29	0.204610
$249$	−1.52329e30	−1.69938
$250$	−2.34972e30	−2.49325
$251$	1.12391e30	1.13452	0.567259	−	0.823539i	$-0.308004\pi$
$251$	1.12391e30	1.13452	0.567259	+	0.823539i	$0.308004\pi$
$252$	0	0
$253$	1.09415e30	1.00016
$254$	1.17152e30	1.01936
$255$	1.04732e30	0.867611
$256$	−3.80199e29	−0.299924
$257$	1.04993e30	0.788852	0.394426	−	0.918928i	$-0.370943\pi$
$257$	1.04993e30	0.788852	0.394426	+	0.918928i	$0.370943\pi$
$258$	−1.31906e30	−0.944101
$259$	0	0
$260$	−2.16942e29	−0.140986
$261$	−1.71286e30	−1.06100
$262$	−1.10016e30	−0.649666
$263$	1.70785e30	0.961618	0.480809	−	0.876825i	$-0.340343\pi$
$263$	1.70785e30	0.961618	0.480809	+	0.876825i	$0.340343\pi$
$264$	−4.31925e30	−2.31931
$265$	5.51678e29	0.282561
$266$	0	0
$267$	2.59764e30	1.21112
$268$	2.92492e29	0.130146
$269$	−3.07069e30	−1.30417	−0.652083	−	0.758148i	$-0.726105\pi$
$269$	−3.07069e30	−1.30417	−0.652083	+	0.758148i	$0.726105\pi$
$270$	−5.42074e30	−2.19792
$271$	2.16910e30	0.839778	0.419889	−	0.907576i	$-0.362069\pi$
$271$	2.16910e30	0.839778	0.419889	+	0.907576i	$0.362069\pi$
$272$	6.79262e29	0.251146
$273$	0	0
$274$	7.16799e29	0.241833
$275$	1.00551e31	3.24136
$276$	−4.06791e29	−0.125316
$277$	−6.74020e30	−1.98461	−0.992307	−	0.123804i	$-0.960491\pi$
$277$	−6.74020e30	−1.98461	−0.992307	+	0.123804i	$0.960491\pi$
$278$	−1.76130e30	−0.495762
$279$	−1.27817e30	−0.343984
$280$	0	0
$281$	−3.41415e30	−0.840337	−0.420169	−	0.907446i	$-0.638029\pi$
$281$	−3.41415e30	−0.840337	−0.420169	+	0.907446i	$0.638029\pi$
$282$	4.22363e30	0.994426
$283$	−4.09634e30	−0.922710	−0.461355	−	0.887216i	$-0.652636\pi$
$283$	−4.09634e30	−0.922710	−0.461355	+	0.887216i	$0.652636\pi$
$284$	−5.74430e29	−0.123811
$285$	2.35533e31	4.85838
$286$	−4.84877e30	−0.957318
$287$	0	0
$288$	1.95206e30	0.353253
$289$	−5.30982e30	−0.920147
$290$	6.38839e30	1.06027
$291$	3.16794e30	0.503634
$292$	−1.29788e30	−0.197674
$293$	2.09673e30	0.305982	0.152991	−	0.988228i	$-0.451109\pi$
$293$	2.09673e30	0.305982	0.152991	+	0.988228i	$0.451109\pi$
$294$	0	0
$295$	−1.16915e31	−1.56709
$296$	−1.39921e31	−1.79778
$297$	1.36177e31	1.67745
$298$	1.90362e30	0.224842
$299$	−4.97622e30	−0.563651
$300$	−3.73836e30	−0.406130
$301$	0	0
$302$	1.10954e31	1.10932
$303$	4.26389e30	0.409047
$304$	1.52761e31	1.40635
$305$	4.72087e30	0.417132
$306$	−5.54394e30	−0.470220
$307$	−5.92149e30	−0.482171	−0.241086	−	0.970504i	$-0.577503\pi$
$307$	−5.92149e30	−0.482171	−0.241086	+	0.970504i	$0.577503\pi$
$308$	0	0
$309$	8.54628e30	0.641647
$310$	4.76716e30	0.343747
$311$	2.92810e29	0.0202806	0.0101403	−	0.999949i	$-0.496772\pi$
$311$	2.92810e29	0.0202806	0.0101403	+	0.999949i	$0.496772\pi$
$312$	1.96441e31	1.30707
$313$	−1.62619e31	−1.03960	−0.519801	−	0.854287i	$-0.673994\pi$
$313$	−1.62619e31	−1.03960	−0.519801	+	0.854287i	$0.673994\pi$
$314$	1.40589e31	0.863639
$315$	0	0
$316$	−2.10179e30	−0.119262
$317$	−9.06205e30	−0.494294	−0.247147	−	0.968978i	$-0.579493\pi$
$317$	−9.06205e30	−0.494294	−0.247147	+	0.968978i	$0.579493\pi$
$318$	−4.58425e30	−0.240397
$319$	−1.60486e31	−0.809198
$320$	−4.11860e31	−1.99698
$321$	1.73530e31	0.809211
$322$	0	0
$323$	1.03631e31	0.447157
$324$	−7.91263e29	−0.0328480
$325$	−4.57308e31	−1.82670
$326$	1.22644e31	0.471441
$327$	6.39104e31	2.36442
$328$	−2.70841e31	−0.964477
$329$	0	0
$330$	−1.18058e32	−3.89647
$331$	−6.00073e31	−1.90701	−0.953507	−	0.301371i	$-0.902556\pi$
$331$	−6.00073e31	−1.90701	−0.953507	+	0.301371i	$0.902556\pi$
$332$	3.38026e30	0.103449
$333$	1.02541e32	3.02236
$334$	−1.58734e31	−0.450649
$335$	8.71179e31	2.38258
$336$	0	0
$337$	5.36431e31	1.36188	0.680942	−	0.732337i	$-0.261570\pi$
$337$	5.36431e31	1.36188	0.680942	+	0.732337i	$0.261570\pi$
$338$	−1.67028e31	−0.408629
$339$	−7.77759e31	−1.83379
$340$	−2.32405e30	−0.0528153
$341$	−1.19759e31	−0.262348
$342$	−1.24679e32	−2.63310
$343$	0	0
$344$	3.18962e31	0.626266
$345$	−1.21161e32	−2.29417
$346$	−5.57889e31	−1.01882
$347$	−6.60299e31	−1.16311	−0.581557	−	0.813506i	$-0.697556\pi$
$347$	−6.60299e31	−1.16311	−0.581557	+	0.813506i	$0.697556\pi$
$348$	5.96668e30	0.101389
$349$	5.89789e31	0.966894	0.483447	−	0.875374i	$-0.339385\pi$
$349$	5.89789e31	0.966894	0.483447	+	0.875374i	$0.339385\pi$
$350$	0	0
$351$	−6.19338e31	−0.945342
$352$	1.82898e31	0.269417
$353$	−7.60190e31	−1.08078	−0.540391	−	0.841414i	$-0.681724\pi$
$353$	−7.60190e31	−1.08078	−0.540391	+	0.841414i	$0.681724\pi$
$354$	9.71524e31	1.33325
$355$	−1.71092e32	−2.26660
$356$	−5.76432e30	−0.0737264
$357$	0	0
$358$	−3.62923e31	−0.432789
$359$	2.33915e31	0.269388	0.134694	−	0.990887i	$-0.456995\pi$
$359$	2.33915e31	0.269388	0.134694	+	0.990887i	$0.456995\pi$
$360$	3.04687e32	3.38901
$361$	1.39983e32	1.50396
$362$	1.03529e32	1.07450
$363$	1.31043e32	1.31396
$364$	0	0
$365$	−3.86570e32	−3.61882
$366$	−3.92288e31	−0.354888
$367$	2.09629e32	1.83285	0.916423	−	0.400212i	$-0.131063\pi$
$367$	2.09629e32	1.83285	0.916423	+	0.400212i	$0.131063\pi$
$368$	−7.85823e31	−0.664090
$369$	1.98487e32	1.62145
$370$	−3.82445e32	−3.02028
$371$	0	0
$372$	4.45247e30	0.0328711
$373$	7.35783e31	0.525278	0.262639	−	0.964894i	$-0.415407\pi$
$373$	7.35783e31	0.525278	0.262639	+	0.964894i	$0.415407\pi$
$374$	−5.19440e31	−0.358625
$375$	−6.53657e32	−4.36475
$376$	−1.02132e32	−0.659649
$377$	7.29896e31	0.456031
$378$	0	0
$379$	7.43959e31	0.435070	0.217535	−	0.976053i	$-0.430198\pi$
$379$	7.43959e31	0.435070	0.217535	+	0.976053i	$0.430198\pi$
$380$	−5.22663e31	−0.295751
$381$	3.25899e32	1.78451
$382$	2.61303e32	1.38469
$383$	2.11635e32	1.08543	0.542717	−	0.839916i	$-0.317396\pi$
$383$	2.11635e32	1.08543	0.542717	+	0.839916i	$0.317396\pi$
$384$	2.74943e32	1.36490
$385$	0	0
$386$	3.47737e31	0.161774
$387$	−2.33753e32	−1.05286
$388$	−7.02985e30	−0.0306584
$389$	4.20416e32	1.77545	0.887726	−	0.460372i	$-0.152284\pi$
$389$	4.20416e32	1.77545	0.887726	+	0.460372i	$0.152284\pi$
$390$	5.36931e32	2.19589
$391$	−5.33094e31	−0.211151
$392$	0	0
$393$	−3.06048e32	−1.13732
$394$	1.20659e32	0.434365
$395$	−6.26011e32	−2.18333
$396$	−7.02417e31	−0.237359
$397$	−5.74443e32	−1.88090	−0.940450	−	0.339931i	$-0.889596\pi$
$397$	−5.74443e32	−1.88090	−0.940450	+	0.339931i	$0.889596\pi$
$398$	8.46340e31	0.268538
$399$	0	0
$400$	−7.22160e32	−2.15221
$401$	−2.54153e31	−0.0734160	−0.0367080	−	0.999326i	$-0.511687\pi$
$401$	−2.54153e31	−0.0734160	−0.0367080	+	0.999326i	$0.511687\pi$
$402$	−7.23920e32	−2.02705
$403$	5.44665e31	0.147848
$404$	−9.46182e30	−0.0249005
$405$	−2.35675e32	−0.601348
$406$	0	0
$407$	9.60762e32	2.30508
$408$	2.10443e32	0.489647
$409$	−4.54825e31	−0.102637	−0.0513184	−	0.998682i	$-0.516342\pi$
$409$	−4.54825e31	−0.102637	−0.0513184	+	0.998682i	$0.516342\pi$
$410$	−7.40290e32	−1.62033
$411$	1.99403e32	0.423359
$412$	−1.89647e31	−0.0390599
$413$	0	0
$414$	6.41365e32	1.24337
$415$	1.00680e33	1.89383
$416$	−8.31824e31	−0.151833
$417$	−4.89967e32	−0.867893
$418$	−1.16818e33	−2.00820
$419$	−8.93992e32	−1.49162	−0.745810	−	0.666158i	$-0.767938\pi$
$419$	−8.93992e32	−1.49162	−0.745810	+	0.666158i	$0.767938\pi$
$420$	0	0
$421$	6.33666e32	0.996172	0.498086	−	0.867128i	$-0.334036\pi$
$421$	6.33666e32	0.996172	0.498086	+	0.867128i	$0.334036\pi$
$422$	3.93566e32	0.600637
$423$	7.48476e32	1.10898
$424$	1.10852e32	0.159467
$425$	−4.89906e32	−0.684307
$426$	1.42172e33	1.92838
$427$	0	0
$428$	−3.85073e31	−0.0492602
$429$	−1.34885e33	−1.67590
$430$	8.71819e32	1.05213
$431$	2.50138e32	0.293234	0.146617	−	0.989193i	$-0.453162\pi$
$431$	2.50138e32	0.293234	0.146617	+	0.989193i	$0.453162\pi$
$432$	−9.78030e32	−1.11380
$433$	−8.22225e32	−0.909687	−0.454843	−	0.890571i	$-0.650305\pi$
$433$	−8.22225e32	−0.909687	−0.454843	+	0.890571i	$0.650305\pi$
$434$	0	0
$435$	1.77716e33	1.85614
$436$	−1.41821e32	−0.143933
$437$	−1.19889e33	−1.18239
$438$	3.21226e33	3.07882
$439$	−3.33247e32	−0.310427	−0.155214	−	0.987881i	$-0.549607\pi$
$439$	−3.33247e32	−0.310427	−0.155214	+	0.987881i	$0.549607\pi$
$440$	2.85477e33	2.58471
$441$	0	0
$442$	2.36242e32	0.202106
$443$	−8.60451e32	−0.715615	−0.357808	−	0.933795i	$-0.616476\pi$
$443$	−8.60451e32	−0.715615	−0.357808	+	0.933795i	$0.616476\pi$
$444$	−3.57199e32	−0.288817
$445$	−1.71688e33	−1.34971
$446$	7.36552e32	0.563012
$447$	5.29559e32	0.393614
$448$	0	0
$449$	5.65798e32	0.397725	0.198862	−	0.980027i	$-0.436275\pi$
$449$	5.65798e32	0.397725	0.198862	+	0.980027i	$0.436275\pi$
$450$	5.89406e33	4.02957
$451$	1.85972e33	1.23664
$452$	1.72589e32	0.111631
$453$	3.08657e33	1.94199
$454$	−2.37807e33	−1.45555
$455$	0	0
$456$	4.73271e33	2.74189
$457$	−2.65715e33	−1.49783	−0.748916	−	0.662664i	$-0.769426\pi$
$457$	−2.65715e33	−1.49783	−0.748916	+	0.662664i	$0.769426\pi$
$458$	−3.15064e32	−0.172814
$459$	−6.63486e32	−0.354138
$460$	2.68864e32	0.139656
$461$	−1.06789e32	−0.0539839	−0.0269920	−	0.999636i	$-0.508593\pi$
$461$	−1.06789e32	−0.0539839	−0.0269920	+	0.999636i	$0.508593\pi$
$462$	0	0
$463$	1.00652e33	0.482013	0.241007	−	0.970523i	$-0.422522\pi$
$463$	1.00652e33	0.482013	0.241007	+	0.970523i	$0.422522\pi$
$464$	1.15262e33	0.537293
$465$	1.32615e33	0.601772
$466$	−1.95613e33	−0.864118
$467$	3.97005e33	1.70740	0.853698	−	0.520768i	$-0.174354\pi$
$467$	3.97005e33	1.70740	0.853698	+	0.520768i	$0.174354\pi$
$468$	3.19461e32	0.133766
$469$	0	0
$470$	−2.79157e33	−1.10822
$471$	3.91099e33	1.51191
$472$	−2.34924e33	−0.884409
$473$	−2.19014e33	−0.802987
$474$	5.20194e33	1.85753
$475$	−1.10176e34	−3.83193
$476$	0	0
$477$	−8.12382e32	−0.268090
$478$	−1.05504e33	−0.339173
$479$	3.32812e33	1.04233	0.521165	−	0.853456i	$-0.325498\pi$
$479$	3.32812e33	1.04233	0.521165	+	0.853456i	$0.325498\pi$
$480$	−2.02533e33	−0.617989
$481$	−4.36957e33	−1.29905
$482$	2.74030e33	0.793799
$483$	0	0
$484$	−2.90792e32	−0.0799864
$485$	−2.09382e33	−0.561264
$486$	−2.58992e33	−0.676602
$487$	−3.17453e31	−0.00808290	−0.00404145	−	0.999992i	$-0.501286\pi$
$487$	−3.17453e31	−0.00808290	−0.00404145	+	0.999992i	$0.501286\pi$
$488$	9.48592e32	0.235414
$489$	3.41178e33	0.825316
$490$	0	0
$491$	6.41678e33	1.47502	0.737511	−	0.675335i	$-0.236001\pi$
$491$	6.41678e33	1.47502	0.737511	+	0.675335i	$0.236001\pi$
$492$	−6.91422e32	−0.154946
$493$	7.81925e32	0.170836
$494$	5.31292e33	1.13174
$495$	−2.09212e34	−4.34533
$496$	8.60110e32	0.174194
$497$	0	0
$498$	−8.36616e33	−1.61124
$499$	6.97277e33	1.30963	0.654815	−	0.755790i	$-0.272747\pi$
$499$	6.97277e33	1.30963	0.654815	+	0.755790i	$0.272747\pi$
$500$	1.45050e33	0.265701
$501$	−4.41573e33	−0.788917
$502$	6.17274e33	1.07568
$503$	5.93402e33	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$503$	5.93402e33	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$504$	0	0
$505$	−2.81817e33	−0.455853
$506$	6.00927e33	0.948289
$507$	−4.64646e33	−0.715357
$508$	−7.23188e32	−0.108631
$509$	−7.61674e32	−0.111634	−0.0558171	−	0.998441i	$-0.517776\pi$
$509$	−7.61674e32	−0.111634	−0.0558171	+	0.998441i	$0.517776\pi$
$510$	5.75205e33	0.822612
$511$	0	0
$512$	−8.12641e33	−1.10669
$513$	−1.49213e34	−1.98308
$514$	5.76639e33	0.747938
$515$	−5.64858e33	−0.715070
$516$	8.14268e32	0.100611
$517$	7.01285e33	0.845790
$518$	0	0
$519$	−1.55196e34	−1.78357
$520$	−1.29835e34	−1.45664
$521$	1.65582e33	0.181360	0.0906801	−	0.995880i	$-0.471096\pi$
$521$	1.65582e33	0.181360	0.0906801	+	0.995880i	$0.471096\pi$
$522$	−9.40734e33	−1.00597
$523$	−3.99380e31	−0.00416980	−0.00208490	−	0.999998i	$-0.500664\pi$
$523$	−3.99380e31	−0.00416980	−0.00208490	+	0.999998i	$0.500664\pi$
$524$	6.79140e32	0.0692338
$525$	0	0
$526$	9.37982e33	0.911743
$527$	5.83490e32	0.0553861
$528$	−2.13005e34	−1.97454
$529$	−4.87853e33	−0.441665
$530$	3.02991e33	0.267906
$531$	1.72165e34	1.48684
$532$	0	0
$533$	−8.45807e33	−0.696917
$534$	1.42667e34	1.14831
$535$	−1.14693e34	−0.901807
$536$	1.75051e34	1.34464
$537$	−1.00960e34	−0.757652
$538$	−1.68648e34	−1.23652
$539$	0	0
$540$	3.34627e33	0.234228
$541$	4.40867e33	0.301538	0.150769	−	0.988569i	$-0.451825\pi$
$541$	4.40867e33	0.301538	0.150769	+	0.988569i	$0.451825\pi$
$542$	1.19131e34	0.796222
$543$	2.88002e34	1.88104
$544$	−8.91118e32	−0.0568786
$545$	−4.22409e34	−2.63498
$546$	0	0
$547$	1.16307e34	0.693049	0.346524	−	0.938041i	$-0.387362\pi$
$547$	1.16307e34	0.693049	0.346524	+	0.938041i	$0.387362\pi$
$548$	−4.42487e32	−0.0257717
$549$	−6.95179e33	−0.395770
$550$	5.52244e34	3.07325
$551$	1.75849e34	0.956632
$552$	−2.43457e34	−1.29474
$553$	0	0
$554$	−3.70184e34	−1.88168
$555$	−1.06391e35	−5.28738
$556$	1.08727e33	0.0528325
$557$	−2.01122e34	−0.955587	−0.477794	−	0.878472i	$-0.658563\pi$
$557$	−2.01122e34	−0.955587	−0.477794	+	0.878472i	$0.658563\pi$
$558$	−7.01997e33	−0.326143
$559$	9.96083e33	0.452531
$560$	0	0
$561$	−1.44500e34	−0.627817
$562$	−1.87511e34	−0.796753
$563$	7.23217e32	0.0300548	0.0150274	−	0.999887i	$-0.495216\pi$
$563$	7.23217e32	0.0300548	0.0150274	+	0.999887i	$0.495216\pi$
$564$	−2.60729e33	−0.105974
$565$	5.14052e34	2.04362
$566$	−2.24978e34	−0.874853
$567$	0	0
$568$	−3.43786e34	−1.27919
$569$	3.04611e34	1.10877	0.554386	−	0.832260i	$-0.312953\pi$
$569$	3.04611e34	1.10877	0.554386	+	0.832260i	$0.312953\pi$
$570$	1.29359e35	4.60640
$571$	−5.58165e33	−0.194452	−0.0972258	−	0.995262i	$-0.530997\pi$
$571$	−5.58165e33	−0.194452	−0.0972258	+	0.995262i	$0.530997\pi$
$572$	2.99319e33	0.102020
$573$	7.26906e34	2.42407
$574$	0	0
$575$	5.66761e34	1.80947
$576$	6.06491e34	1.89471
$577$	1.14576e33	0.0350263	0.0175132	−	0.999847i	$-0.494425\pi$
$577$	1.14576e33	0.0350263	0.0175132	+	0.999847i	$0.494425\pi$
$578$	−2.91625e34	−0.872423
$579$	9.67352e33	0.283206
$580$	−3.94361e33	−0.112991
$581$	0	0
$582$	1.73989e34	0.477513
$583$	−7.61162e33	−0.204465
$584$	−7.76758e34	−2.04233
$585$	9.51504e34	2.44885
$586$	1.15156e34	0.290112
$587$	−1.99725e34	−0.492555	−0.246278	−	0.969199i	$-0.579208\pi$
$587$	−1.99725e34	−0.492555	−0.246278	+	0.969199i	$0.579208\pi$
$588$	0	0
$589$	1.31222e34	0.310147
$590$	−6.42118e34	−1.48582
$591$	3.35654e34	0.760411
$592$	−6.90022e34	−1.53053
$593$	3.93780e34	0.855204	0.427602	−	0.903967i	$-0.359359\pi$
$593$	3.93780e34	0.855204	0.427602	+	0.903967i	$0.359359\pi$
$594$	7.47911e34	1.59045
$595$	0	0
$596$	−1.17512e33	−0.0239610
$597$	2.35439e34	0.470110
$598$	−2.73303e34	−0.534417
$599$	3.55934e34	0.681608	0.340804	−	0.940134i	$-0.389301\pi$
$599$	3.55934e34	0.681608	0.340804	+	0.940134i	$0.389301\pi$
$600$	−2.23734e35	−4.19605
$601$	9.07531e34	1.66698	0.833491	−	0.552534i	$-0.186339\pi$
$601$	9.07531e34	1.66698	0.833491	+	0.552534i	$0.186339\pi$
$602$	0	0
$603$	−1.28287e35	−2.26056
$604$	−6.84927e33	−0.118218
$605$	−8.66115e34	−1.46431
$606$	2.34180e34	0.387831
$607$	3.62504e34	0.588104	0.294052	−	0.955789i	$-0.404996\pi$
$607$	3.62504e34	0.588104	0.294052	+	0.955789i	$0.404996\pi$
$608$	−2.00406e34	−0.318505
$609$	0	0
$610$	2.59279e34	0.395497
$611$	−3.18946e34	−0.476653
$612$	3.42233e33	0.0501105
$613$	−3.27762e34	−0.470222	−0.235111	−	0.971968i	$-0.575545\pi$
$613$	−3.27762e34	−0.470222	−0.235111	+	0.971968i	$0.575545\pi$
$614$	−3.25219e34	−0.457163
$615$	−2.05938e35	−2.83659
$616$	0	0
$617$	9.84958e34	1.30273	0.651363	−	0.758766i	$-0.274197\pi$
$617$	9.84958e34	1.30273	0.651363	+	0.758766i	$0.274197\pi$
$618$	4.69377e34	0.608368
$619$	−8.99878e34	−1.14301	−0.571506	−	0.820598i	$-0.693640\pi$
$619$	−8.99878e34	−1.14301	−0.571506	+	0.820598i	$0.693640\pi$
$620$	−2.94281e33	−0.0366325
$621$	7.67571e34	0.936426
$622$	1.60817e33	0.0192288
$623$	0	0
$624$	9.68752e34	1.11277
$625$	2.16945e35	2.44259
$626$	−8.93133e34	−0.985683
$627$	−3.24970e35	−3.51560
$628$	−8.67872e33	−0.0920365
$629$	−4.68104e34	−0.486642
$630$	0	0
$631$	−1.32495e35	−1.32383	−0.661913	−	0.749581i	$-0.730255\pi$
$631$	−1.32495e35	−1.32383	−0.661913	+	0.749581i	$0.730255\pi$
$632$	−1.25788e35	−1.23219
$633$	1.09484e35	1.05149
$634$	−4.97704e34	−0.468658
$635$	−2.15399e35	−1.98871
$636$	2.82990e33	0.0256187
$637$	0	0
$638$	−8.81421e34	−0.767228
$639$	2.51945e35	2.15052
$640$	−1.81721e35	−1.52109
$641$	1.61443e34	0.132523	0.0662617	−	0.997802i	$-0.478893\pi$
$641$	1.61443e34	0.132523	0.0662617	+	0.997802i	$0.478893\pi$
$642$	9.53058e34	0.767240
$643$	8.49674e34	0.670834	0.335417	−	0.942070i	$-0.391123\pi$
$643$	8.49674e34	0.670834	0.335417	+	0.942070i	$0.391123\pi$
$644$	0	0
$645$	2.42527e35	1.84189
$646$	5.69163e34	0.423965
$647$	1.68218e35	1.22905	0.614525	−	0.788898i	$-0.289348\pi$
$647$	1.68218e35	1.22905	0.614525	+	0.788898i	$0.289348\pi$
$648$	−4.73556e34	−0.339378
$649$	1.61310e35	1.13397
$650$	−2.51162e35	−1.73196
$651$	0	0
$652$	−7.57095e33	−0.0502406
$653$	9.55504e34	0.622039	0.311020	−	0.950403i	$-0.399330\pi$
$653$	9.55504e34	0.622039	0.311020	+	0.950403i	$0.399330\pi$
$654$	3.51008e35	2.24179
$655$	2.02279e35	1.26746
$656$	−1.33566e35	−0.821104
$657$	5.69250e35	3.43349
$658$	0	0
$659$	−6.84681e34	−0.397576	−0.198788	−	0.980042i	$-0.563701\pi$
$659$	−6.84681e34	−0.397576	−0.198788	+	0.980042i	$0.563701\pi$
$660$	7.28783e34	0.415240
$661$	−2.34472e35	−1.31091	−0.655454	−	0.755235i	$-0.727523\pi$
$661$	−2.34472e35	−1.31091	−0.655454	+	0.755235i	$0.727523\pi$
$662$	−3.29571e35	−1.80811
$663$	6.57191e34	0.353812
$664$	2.02302e35	1.06881
$665$	0	0
$666$	5.63176e35	2.86560
$667$	−9.04590e34	−0.451730
$668$	9.79878e33	0.0480249
$669$	2.04898e35	0.985623
$670$	4.78467e35	2.25900
$671$	−6.51348e34	−0.301843
$672$	0	0
$673$	4.11166e35	1.83581	0.917906	−	0.396797i	$-0.129878\pi$
$673$	4.11166e35	1.83581	0.917906	+	0.396797i	$0.129878\pi$
$674$	2.94618e35	1.29125
$675$	7.05387e35	3.03480
$676$	1.03108e34	0.0435469
$677$	1.98211e35	0.821806	0.410903	−	0.911679i	$-0.365213\pi$
$677$	1.98211e35	0.821806	0.410903	+	0.911679i	$0.365213\pi$
$678$	−4.27159e35	−1.73868
$679$	0	0
$680$	−1.39090e35	−0.545677
$681$	−6.61543e35	−2.54812
$682$	−6.57736e34	−0.248741
$683$	4.20284e35	1.56057	0.780286	−	0.625422i	$-0.215073\pi$
$683$	4.20284e35	1.56057	0.780286	+	0.625422i	$0.215073\pi$
$684$	7.69656e34	0.280605
$685$	−1.31793e35	−0.471803
$686$	0	0
$687$	−8.76460e34	−0.302533
$688$	1.57297e35	0.533169
$689$	3.46178e34	0.115228
$690$	−6.65440e35	−2.17518
$691$	−3.40612e35	−1.09341	−0.546707	−	0.837324i	$-0.684119\pi$
$691$	−3.40612e35	−1.09341	−0.546707	+	0.837324i	$0.684119\pi$
$692$	3.44390e34	0.108574
$693$	0	0
$694$	−3.62648e35	−1.10279
$695$	3.23839e35	0.967205
$696$	3.57095e35	1.04753
$697$	−9.06098e34	−0.261075
$698$	3.23923e35	0.916746
$699$	−5.44165e35	−1.51275
$700$	0	0
$701$	1.07240e35	0.287661	0.143831	−	0.989602i	$-0.454058\pi$
$701$	1.07240e35	0.287661	0.143831	+	0.989602i	$0.454058\pi$
$702$	−3.40152e35	−0.896311
$703$	−1.05273e36	−2.72506
$704$	5.68252e35	1.44505
$705$	−7.76572e35	−1.94007
$706$	−4.17510e35	−1.02473
$707$	0	0
$708$	−5.99731e34	−0.142082
$709$	3.85500e35	0.897318	0.448659	−	0.893703i	$-0.351902\pi$
$709$	3.85500e35	0.897318	0.448659	+	0.893703i	$0.351902\pi$
$710$	−9.39669e35	−2.14904
$711$	9.21844e35	2.07151
$712$	−3.44984e35	−0.761726
$713$	−6.75025e34	−0.146454
$714$	0	0
$715$	8.91511e35	1.86768
$716$	2.24036e34	0.0461216
$717$	−2.93497e35	−0.593765
$718$	1.28470e35	0.255416
$719$	−6.76617e35	−1.32200	−0.661000	−	0.750386i	$-0.729868\pi$
$719$	−6.76617e35	−1.32200	−0.661000	+	0.750386i	$0.729868\pi$
$720$	1.50257e36	2.88522
$721$	0	0
$722$	7.68812e35	1.42595
$723$	7.62312e35	1.38964
$724$	−6.39094e34	−0.114507
$725$	−8.31306e35	−1.46398
$726$	7.19712e35	1.24581
$727$	−8.27129e35	−1.40732	−0.703661	−	0.710536i	$-0.748453\pi$
$727$	−8.27129e35	−1.40732	−0.703661	+	0.710536i	$0.748453\pi$
$728$	0	0
$729$	−9.18222e35	−1.50957
$730$	−2.12311e36	−3.43113
$731$	1.06709e35	0.169524
$732$	2.42163e34	0.0378198
$733$	−2.49214e34	−0.0382624	−0.0191312	−	0.999817i	$-0.506090\pi$
$733$	−2.49214e34	−0.0382624	−0.0191312	+	0.999817i	$0.506090\pi$
$734$	1.15132e36	1.73778
$735$	0	0
$736$	1.03091e35	0.150401
$737$	−1.20198e36	−1.72407
$738$	1.09013e36	1.53735
$739$	4.02152e35	0.557615	0.278807	−	0.960347i	$-0.410061\pi$
$739$	4.02152e35	0.557615	0.278807	+	0.960347i	$0.410061\pi$
$740$	2.36087e35	0.321866
$741$	1.47797e36	1.98125
$742$	0	0
$743$	−1.03295e36	−1.33880	−0.669402	−	0.742900i	$-0.733450\pi$
$743$	−1.03295e36	−1.33880	−0.669402	+	0.742900i	$0.733450\pi$
$744$	2.66472e35	0.339618
$745$	−3.50006e35	−0.438655
$746$	4.04105e35	0.498034
$747$	−1.48258e36	−1.79684
$748$	3.20655e34	0.0382180
$749$	0	0
$750$	−3.59000e36	−4.13837
$751$	3.34126e35	0.378800	0.189400	−	0.981900i	$-0.439346\pi$
$751$	3.34126e35	0.378800	0.189400	+	0.981900i	$0.439346\pi$
$752$	−5.03665e35	−0.561589
$753$	1.71716e36	1.88310
$754$	4.00872e35	0.432379
$755$	−2.04003e36	−2.16421
$756$	0	0
$757$	−1.37258e36	−1.40877	−0.704385	−	0.709818i	$-0.748777\pi$
$757$	−1.37258e36	−1.40877	−0.704385	+	0.709818i	$0.748777\pi$
$758$	4.08596e35	0.412504
$759$	1.67169e36	1.66010
$760$	−3.12804e36	−3.05564
$761$	1.66890e36	1.60370	0.801849	−	0.597527i	$-0.203850\pi$
$761$	1.66890e36	1.60370	0.801849	+	0.597527i	$0.203850\pi$
$762$	1.78989e36	1.69196
$763$	0	0
$764$	−1.61305e35	−0.147564
$765$	1.01933e36	0.917374
$766$	1.16234e36	1.02914
$767$	−7.33643e35	−0.639061
$768$	−5.80884e35	−0.497822
$769$	−1.07167e36	−0.903614	−0.451807	−	0.892116i	$-0.649220\pi$
$769$	−1.07167e36	−0.903614	−0.451807	+	0.892116i	$0.649220\pi$
$770$	0	0
$771$	1.60412e36	1.30936
$772$	−2.14661e34	−0.0172400
$773$	−1.02735e36	−0.811844	−0.405922	−	0.913908i	$-0.633050\pi$
$773$	−1.02735e36	−0.811844	−0.405922	+	0.913908i	$0.633050\pi$
$774$	−1.28381e36	−0.998250
$775$	−6.20339e35	−0.474633
$776$	−4.20723e35	−0.316756
$777$	0	0
$778$	2.30900e36	1.68337
$779$	−2.03775e36	−1.46195
$780$	−3.31453e35	−0.234012
$781$	2.36059e36	1.64015
$782$	−2.92785e35	−0.200200
$783$	−1.12585e36	−0.757631
$784$	0	0
$785$	−2.58493e36	−1.68491
$786$	−1.68087e36	−1.07833
$787$	2.14239e36	1.35274	0.676371	−	0.736561i	$-0.263552\pi$
$787$	2.14239e36	1.35274	0.676371	+	0.736561i	$0.263552\pi$
$788$	−7.44836e34	−0.0462896
$789$	2.60933e36	1.59612
$790$	−3.43817e36	−2.07009
$791$	0	0
$792$	−4.20383e36	−2.45234
$793$	2.96235e35	0.170107
$794$	−3.15495e36	−1.78335
$795$	8.42877e35	0.469002
$796$	−5.22453e34	−0.0286177
$797$	−1.28498e36	−0.692898	−0.346449	−	0.938069i	$-0.612613\pi$
$797$	−1.28498e36	−0.692898	−0.346449	+	0.938069i	$0.612613\pi$
$798$	0	0
$799$	−3.41681e35	−0.178561
$800$	9.47396e35	0.487424
$801$	2.52823e36	1.28059
$802$	−1.39586e35	−0.0696083
$803$	5.33359e36	2.61864
$804$	4.46882e35	0.216019
$805$	0	0
$806$	2.99140e35	0.140180
$807$	−4.69154e36	−2.16469
$808$	−5.66272e35	−0.257266
$809$	5.74652e35	0.257068	0.128534	−	0.991705i	$-0.458973\pi$
$809$	5.74652e35	0.257068	0.128534	+	0.991705i	$0.458973\pi$
$810$	−1.29437e36	−0.570159
$811$	−9.68492e35	−0.420083	−0.210042	−	0.977692i	$-0.567360\pi$
$811$	−9.68492e35	−0.420083	−0.210042	+	0.977692i	$0.567360\pi$
$812$	0	0
$813$	3.31405e36	1.39389
$814$	5.27668e36	2.18552
$815$	−2.25498e36	−0.919756
$816$	1.03781e36	0.416859
$817$	2.39980e36	0.949289
$818$	−2.49798e35	−0.0973136
$819$	0	0
$820$	4.56988e35	0.172676
$821$	−6.55167e35	−0.243816	−0.121908	−	0.992541i	$-0.538901\pi$
$821$	−6.55167e35	−0.243816	−0.121908	+	0.992541i	$0.538901\pi$
$822$	1.09516e36	0.401401
$823$	−4.45924e36	−1.60977	−0.804884	−	0.593433i	$-0.797772\pi$
$823$	−4.45924e36	−1.60977	−0.804884	+	0.593433i	$0.797772\pi$
$824$	−1.13500e36	−0.403559
$825$	1.53626e37	5.38010
$826$	0	0
$827$	2.46287e36	0.836802	0.418401	−	0.908262i	$-0.362591\pi$
$827$	2.46287e36	0.836802	0.418401	+	0.908262i	$0.362591\pi$
$828$	−3.95921e35	−0.132504
$829$	−2.38637e35	−0.0786696	−0.0393348	−	0.999226i	$-0.512524\pi$
$829$	−2.38637e35	−0.0786696	−0.0393348	+	0.999226i	$0.512524\pi$
$830$	5.52953e36	1.79561
$831$	−1.02980e37	−3.29412
$832$	−2.58442e36	−0.814370
$833$	0	0
$834$	−2.69099e36	−0.822879
$835$	2.91853e36	0.879192
$836$	7.21129e35	0.214010
$837$	−8.40133e35	−0.245629
$838$	−4.90997e36	−1.41426
$839$	−7.93842e35	−0.225273	−0.112637	−	0.993636i	$-0.535930\pi$
$839$	−7.93842e35	−0.225273	−0.112637	+	0.993636i	$0.535930\pi$
$840$	0	0
$841$	−2.30354e36	−0.634521
$842$	3.48021e36	0.944505
$843$	−5.21629e36	−1.39482
$844$	−2.42952e35	−0.0640089
$845$	3.07103e36	0.797214
$846$	4.11077e36	1.05146
$847$	0	0
$848$	5.46669e35	0.135761
$849$	−6.25856e36	−1.53154
$850$	−2.69065e36	−0.648815
$851$	5.41538e36	1.28680
$852$	−8.77639e35	−0.205504
$853$	−2.99916e36	−0.692048	−0.346024	−	0.938226i	$-0.612468\pi$
$853$	−2.99916e36	−0.692048	−0.346024	+	0.938226i	$0.612468\pi$
$854$	0	0
$855$	2.29239e37	5.13704
$856$	−2.30459e36	−0.508946
$857$	6.63842e36	1.44479	0.722394	−	0.691481i	$-0.243042\pi$
$857$	6.63842e36	1.44479	0.722394	+	0.691481i	$0.243042\pi$
$858$	−7.40816e36	−1.58898
$859$	−8.18612e36	−1.73047	−0.865234	−	0.501368i	$-0.832830\pi$
$859$	−8.18612e36	−1.73047	−0.865234	+	0.501368i	$0.832830\pi$
$860$	−5.38182e35	−0.112124
$861$	0	0
$862$	1.37380e36	0.278025
$863$	−1.33712e36	−0.266708	−0.133354	−	0.991068i	$-0.542575\pi$
$863$	−1.33712e36	−0.266708	−0.133354	+	0.991068i	$0.542575\pi$
$864$	1.28307e36	0.252248
$865$	1.02575e37	1.98766
$866$	−4.51581e36	−0.862505
$867$	−8.11258e36	−1.52728
$868$	0	0
$869$	8.63721e36	1.57989
$870$	9.76046e36	1.75987
$871$	5.46666e36	0.971616
$872$	−8.48772e36	−1.48708
$873$	3.08329e36	0.532520
$874$	−6.58451e36	−1.12106
$875$	0	0
$876$	−1.98296e36	−0.328105
$877$	1.07210e37	1.74881	0.874404	−	0.485199i	$-0.161253\pi$
$877$	1.07210e37	1.74881	0.874404	+	0.485199i	$0.161253\pi$
$878$	−1.83025e36	−0.294327
$879$	3.20347e36	0.507878
$880$	1.40783e37	2.20048
$881$	1.11812e37	1.72301	0.861507	−	0.507746i	$-0.169521\pi$
$881$	1.11812e37	1.72301	0.861507	+	0.507746i	$0.169521\pi$
$882$	0	0
$883$	−1.46714e36	−0.219767	−0.109884	−	0.993944i	$-0.535048\pi$
$883$	−1.46714e36	−0.219767	−0.109884	+	0.993944i	$0.535048\pi$
$884$	−1.45835e35	−0.0215381
$885$	−1.78628e37	−2.60111
$886$	−4.72575e36	−0.678499
$887$	1.10635e37	1.56621	0.783103	−	0.621892i	$-0.213636\pi$
$887$	1.10635e37	1.56621	0.783103	+	0.621892i	$0.213636\pi$
$888$	−2.13777e37	−2.98400
$889$	0	0
$890$	−9.42943e36	−1.27971
$891$	3.25166e36	0.435145
$892$	−4.54680e35	−0.0599992
$893$	−7.68415e36	−0.999891
$894$	2.90843e36	0.373199
$895$	6.67283e36	0.844349
$896$	0	0
$897$	−7.60289e36	−0.935563
$898$	3.10747e36	0.377096
$899$	9.90105e35	0.118491
$900$	−3.63846e36	−0.429424
$901$	3.70854e35	0.0431662
$902$	1.02139e37	1.17250
$903$	0	0
$904$	1.03292e37	1.15334
$905$	−1.90352e37	−2.09629
$906$	1.69520e37	1.84127
$907$	5.49114e35	0.0588263	0.0294132	−	0.999567i	$-0.490636\pi$
$907$	5.49114e35	0.0588263	0.0294132	+	0.999567i	$0.490636\pi$
$908$	1.46800e36	0.155115
$909$	4.14994e36	0.432508
$910$	0	0
$911$	−1.23647e37	−1.25372	−0.626862	−	0.779130i	$-0.715661\pi$
$911$	−1.23647e37	−1.25372	−0.626862	+	0.779130i	$0.715661\pi$
$912$	2.33395e37	2.33430
$913$	−1.38910e37	−1.37041
$914$	−1.45935e37	−1.42015
$915$	7.21274e36	0.692368
$916$	1.94492e35	0.0184165
$917$	0	0
$918$	−3.64398e36	−0.335771
$919$	−2.32782e36	−0.211595	−0.105797	−	0.994388i	$-0.533739\pi$
$919$	−2.32782e36	−0.211595	−0.105797	+	0.994388i	$0.533739\pi$
$920$	1.60910e37	1.44290
$921$	−9.04711e36	−0.800321
$922$	−5.86504e35	−0.0511840
$923$	−1.07360e37	−0.924322
$924$	0	0
$925$	4.97666e37	4.17029
$926$	5.52797e36	0.457013
$927$	8.31791e36	0.678449
$928$	−1.51211e36	−0.121684
$929$	−6.43944e36	−0.511272	−0.255636	−	0.966773i	$-0.582285\pi$
$929$	−6.43944e36	−0.511272	−0.255636	+	0.966773i	$0.582285\pi$
$930$	7.28348e36	0.570561
$931$	0	0
$932$	1.20753e36	0.0920875
$933$	4.47368e35	0.0336623
$934$	2.18042e37	1.61884
$935$	9.55060e36	0.699657
$936$	1.91191e37	1.38204
$937$	1.33966e37	0.955544	0.477772	−	0.878484i	$-0.341445\pi$
$937$	1.33966e37	0.955544	0.477772	+	0.878484i	$0.341445\pi$
$938$	0	0
$939$	−2.48456e37	−1.72556
$940$	1.72326e36	0.118101
$941$	2.03098e37	1.37352	0.686762	−	0.726883i	$-0.259032\pi$
$941$	2.03098e37	1.37352	0.686762	+	0.726883i	$0.259032\pi$
$942$	2.14799e37	1.43349
$943$	1.04824e37	0.690344
$944$	−1.15853e37	−0.752938
$945$	0	0
$946$	−1.20287e37	−0.761340
$947$	1.56403e37	0.976943	0.488471	−	0.872580i	$-0.337555\pi$
$947$	1.56403e37	0.976943	0.488471	+	0.872580i	$0.337555\pi$
$948$	−3.21121e36	−0.197954
$949$	−2.42573e37	−1.47576
$950$	−6.05108e37	−3.63319
$951$	−1.38454e37	−0.820443
$952$	0	0
$953$	−1.44281e37	−0.832815	−0.416407	−	0.909178i	$-0.636711\pi$
$953$	−1.44281e37	−0.832815	−0.416407	+	0.909178i	$0.636711\pi$
$954$	−4.46175e36	−0.254185
$955$	−4.80441e37	−2.70145
$956$	6.51288e35	0.0361451
$957$	−2.45198e37	−1.34313
$958$	1.82786e37	0.988269
$959$	0	0
$960$	−6.29257e37	−3.31465
$961$	−1.84940e37	−0.961584
$962$	−2.39985e37	−1.23167
$963$	1.68893e37	0.855623
$964$	−1.69161e36	−0.0845938
$965$	−6.39361e36	−0.315613
$966$	0	0
$967$	−6.53810e35	−0.0314500	−0.0157250	−	0.999876i	$-0.505006\pi$
$967$	−6.53810e35	−0.0314500	−0.0157250	+	0.999876i	$0.505006\pi$
$968$	−1.74034e37	−0.826403
$969$	1.58333e37	0.742204
$970$	−1.14996e37	−0.532154
$971$	−1.41134e37	−0.644750	−0.322375	−	0.946612i	$-0.604481\pi$
$971$	−1.41134e37	−0.644750	−0.322375	+	0.946612i	$0.604481\pi$
$972$	1.59878e36	0.0721043
$973$	0	0
$974$	−1.74351e35	−0.00766368
$975$	−6.98695e37	−3.03201
$976$	4.67800e36	0.200419
$977$	3.75740e37	1.58930	0.794650	−	0.607068i	$-0.207655\pi$
$977$	3.75740e37	1.58930	0.794650	+	0.607068i	$0.207655\pi$
$978$	1.87381e37	0.782511
$979$	2.36882e37	0.976672
$980$	0	0
$981$	6.22026e37	2.50003
$982$	3.52421e37	1.39852
$983$	−4.57677e37	−1.79325	−0.896624	−	0.442794i	$-0.853987\pi$
$983$	−4.57677e37	−1.79325	−0.896624	+	0.442794i	$0.853987\pi$
$984$	−4.13803e37	−1.60087
$985$	−2.21847e37	−0.847424
$986$	4.29447e36	0.161975
$987$	0	0
$988$	−3.27971e36	−0.120607
$989$	−1.23449e37	−0.448263
$990$	−1.14903e38	−4.11996
$991$	1.20105e36	0.0425245	0.0212623	−	0.999774i	$-0.493232\pi$
$991$	1.20105e36	0.0425245	0.0212623	+	0.999774i	$0.493232\pi$
$992$	−1.12837e36	−0.0394508
$993$	−9.16817e37	−3.16531
$994$	0	0
$995$	−1.55611e37	−0.523904
$996$	5.16451e36	0.171707
$997$	5.60137e37	1.83910	0.919548	−	0.392977i	$-0.128555\pi$
$997$	5.60137e37	1.83910	0.919548	+	0.392977i	$0.128555\pi$
$998$	3.82957e37	1.24170
$999$	6.73995e37	2.15818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.e.1.10	yes	12
7.6	odd	2	inner	49.26.a.e.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.26.a.e.1.9	✓	12	7.6	odd	2	inner
49.26.a.e.1.10	yes	12	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+5492.18 q^{2} +1.52784e6 q^{3} -3.39037e6 q^{4} -1.00981e9 q^{5} +8.39119e9 q^{6} -2.02908e11 q^{8} +1.48702e12 q^{9} +O(q^{10})\)	\(q+5492.18 q^{2} +1.52784e6 q^{3} -3.39037e6 q^{4} -1.00981e9 q^{5} +8.39119e9 q^{6} -2.02908e11 q^{8} +1.48702e12 q^{9} -5.54607e12 q^{10} +1.39326e13 q^{11} -5.17996e12 q^{12} -6.33658e13 q^{13} -1.54283e15 q^{15} -1.00064e15 q^{16} -6.78826e14 q^{17} +8.16696e15 q^{18} -1.52663e16 q^{19} +3.42364e15 q^{20} +7.65203e16 q^{22} +7.85317e16 q^{23} -3.10011e17 q^{24} +7.21696e17 q^{25} -3.48016e17 q^{26} +9.77402e17 q^{27} -1.15188e18 q^{29} -8.47352e18 q^{30} -8.59557e17 q^{31} +1.31273e18 q^{32} +2.12868e19 q^{33} -3.72823e18 q^{34} -5.04154e18 q^{36} +6.89579e19 q^{37} -8.38452e19 q^{38} -9.68129e19 q^{39} +2.04898e20 q^{40} +1.33480e20 q^{41} -1.57196e20 q^{43} -4.72367e19 q^{44} -1.50161e21 q^{45} +4.31311e20 q^{46} +5.03341e20 q^{47} -1.52883e21 q^{48} +3.96369e21 q^{50} -1.03714e21 q^{51} +2.14834e20 q^{52} -5.46318e20 q^{53} +5.36807e21 q^{54} -1.40693e22 q^{55} -2.33245e22 q^{57} -6.32632e21 q^{58} +1.15779e22 q^{59} +5.23078e21 q^{60} -4.67500e21 q^{61} -4.72084e21 q^{62} +4.07858e22 q^{64} +6.39875e22 q^{65} +1.16911e23 q^{66} -8.62714e22 q^{67} +2.30147e21 q^{68} +1.19984e23 q^{69} +1.69430e23 q^{71} -3.01727e23 q^{72} +3.82814e23 q^{73} +3.78729e23 q^{74} +1.10264e24 q^{75} +5.17584e22 q^{76} -5.31714e23 q^{78} +6.19929e23 q^{79} +1.01046e24 q^{80} +2.33385e23 q^{81} +7.33097e23 q^{82} -9.97017e23 q^{83} +6.85486e23 q^{85} -8.63348e23 q^{86} -1.75989e24 q^{87} -2.82703e24 q^{88} +1.70020e24 q^{89} -8.24709e24 q^{90} -2.66252e23 q^{92} -1.31327e24 q^{93} +2.76444e24 q^{94} +1.54161e25 q^{95} +2.00565e24 q^{96} +2.07347e24 q^{97} +2.07180e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9}+O(q^{10}) \) 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9	\( 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9} + 39593455677648 q^{11} + 357546272706144 q^{15} + 18\!\cdots\!56 q^{16}+ \cdots - 14\!\cdots\!88 q^{99}+O(q^{100}) \) 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9 + 39593455677648 * q^11 + 357546272706144 * q^15 + 1897434424858656 * q^16 + 19017456854067300 * q^18 + 85409383356235920 * q^22 + 77196982648366080 * q^23 + 2296738995597808932 * q^25 + 8694499082723336088 * q^29 - 12169958791851770688 * q^30 - 6483391660121958720 * q^32 - 109652263099391094456 * q^36 + 151853425001596848120 * q^37 - 122709680243235084384 * q^39 - 380869142455132177200 * q^43 + 991389584873062609056 * q^44 + 2303857023830118404064 * q^46 + 3165366920999170599036 * q^50 + 1280977431762493664064 * q^51 + 17755418685871290573000 * q^53 - 40456075816140877421280 * q^57 + 90683689500928436394600 * q^58 + 27395532648965383354368 * q^60 - 153351020298413953854336 * q^64 + 200499279532648292123424 * q^65 + 148336212990069406108560 * q^67 + 562419591698095656528384 * q^71 - 554920453414323154337040 * q^72 + 509427689055313155358536 * q^74 - 812506544978626047049920 * q^78 + 1488381592136271978244704 * q^79 - 2624302005301676288302452 * q^81 - 333667887446182173142464 * q^85 - 10612071587035448449112880 * q^86 - 14889193934757325628907840 * q^88 + 8074123164162948551757120 * q^92 + 1647472274074578272984640 * q^93 + 10792312351147270637620128 * q^95 - 148376588023327766946288 * q^99

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