LMFDB - Embedded newform 49.26.a.e.1.4

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			1.4
Root			$-574437.$ 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)

$f(q)$	$=$	$q-7023.80 q^{2} +1.14256e6 q^{3} +1.57794e7 q^{4} -4.38325e8 q^{5} -8.02510e9 q^{6} +1.24848e11 q^{8} +4.58148e11 q^{9} +O(q^{10})$	\(q-7023.80 q^{2} +1.14256e6 q^{3} +1.57794e7 q^{4} -4.38325e8 q^{5} -8.02510e9 q^{6} +1.24848e11 q^{8} +4.58148e11 q^{9} +3.07871e12 q^{10} -1.58272e13 q^{11} +1.80288e13 q^{12} -7.65840e13 q^{13} -5.00811e14 q^{15} -1.40638e15 q^{16} +2.97975e15 q^{17} -3.21794e15 q^{18} -3.40498e15 q^{19} -6.91649e15 q^{20} +1.11167e17 q^{22} -1.02064e17 q^{23} +1.42646e17 q^{24} -1.05895e17 q^{25} +5.37911e17 q^{26} -4.44615e17 q^{27} +4.28121e17 q^{29} +3.51760e18 q^{30} -1.46167e18 q^{31} +5.68891e18 q^{32} -1.80835e19 q^{33} -2.09291e19 q^{34} +7.22929e18 q^{36} +1.41458e18 q^{37} +2.39159e19 q^{38} -8.75016e19 q^{39} -5.47242e19 q^{40} -2.60241e20 q^{41} -2.34818e20 q^{43} -2.49743e20 q^{44} -2.00818e20 q^{45} +7.16881e20 q^{46} +3.59457e20 q^{47} -1.60687e21 q^{48} +7.43783e20 q^{50} +3.40453e21 q^{51} -1.20845e21 q^{52} +1.03311e21 q^{53} +3.12289e21 q^{54} +6.93744e21 q^{55} -3.89038e21 q^{57} -3.00704e21 q^{58} -9.21478e21 q^{59} -7.90249e21 q^{60} +3.55847e22 q^{61} +1.02665e22 q^{62} +7.23246e21 q^{64} +3.35687e22 q^{65} +1.27015e23 q^{66} +5.92207e22 q^{67} +4.70185e22 q^{68} -1.16614e23 q^{69} -1.92146e23 q^{71} +5.71991e22 q^{72} +2.60605e23 q^{73} -9.93575e21 q^{74} -1.20991e23 q^{75} -5.37285e22 q^{76} +6.14594e23 q^{78} -5.22813e23 q^{79} +6.16451e23 q^{80} -8.96182e23 q^{81} +1.82788e24 q^{82} -1.63276e24 q^{83} -1.30610e24 q^{85} +1.64932e24 q^{86} +4.89152e23 q^{87} -1.97600e24 q^{88} +3.17249e24 q^{89} +1.41050e24 q^{90} -1.61051e24 q^{92} -1.67005e24 q^{93} -2.52476e24 q^{94} +1.49249e24 q^{95} +6.49991e24 q^{96} +3.73970e24 q^{97} -7.25119e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7023.80	−1.21254	−0.606272	−	0.795257i	$-0.707336\pi$
$2$	−7023.80	−1.21254	−0.606272	+	0.795257i	$0.707336\pi$
$3$	1.14256e6	1.24126	0.620629	−	0.784104i	$-0.286877\pi$
$3$	1.14256e6	1.24126	0.620629	+	0.784104i	$0.286877\pi$
$4$	1.57794e7	0.470262
$5$	−4.38325e8	−0.802918	−0.401459	−	0.915877i	$-0.631497\pi$
$5$	−4.38325e8	−0.802918	−0.401459	+	0.915877i	$0.631497\pi$
$6$	−8.02510e9	−1.50508
$7$	0	0
$7$	0	0
$8$	1.24848e11	0.642330
$9$	4.58148e11	0.540722
$10$	3.07871e12	0.973573
$11$	−1.58272e13	−1.52053	−0.760265	−	0.649613i	$-0.774931\pi$
$11$	−1.58272e13	−1.52053	−0.760265	+	0.649613i	$0.774931\pi$
$12$	1.80288e13	0.583717
$13$	−7.65840e13	−0.911688	−0.455844	−	0.890060i	$-0.650662\pi$
$13$	−7.65840e13	−0.911688	−0.455844	+	0.890060i	$0.650662\pi$
$14$	0	0
$15$	−5.00811e14	−0.996628
$16$	−1.40638e15	−1.24912
$17$	2.97975e15	1.24042	0.620208	−	0.784437i	$-0.287048\pi$
$17$	2.97975e15	1.24042	0.620208	+	0.784437i	$0.287048\pi$
$18$	−3.21794e15	−0.655650
$19$	−3.40498e15	−0.352935	−0.176467	−	0.984306i	$-0.556467\pi$
$19$	−3.40498e15	−0.352935	−0.176467	+	0.984306i	$0.556467\pi$
$20$	−6.91649e15	−0.377582
$21$	0	0
$22$	1.11167e17	1.84371
$23$	−1.02064e17	−0.971128	−0.485564	−	0.874201i	$-0.661386\pi$
$23$	−1.02064e17	−0.971128	−0.485564	+	0.874201i	$0.661386\pi$
$24$	1.42646e17	0.797298
$25$	−1.05895e17	−0.355323
$26$	5.37911e17	1.10546
$27$	−4.44615e17	−0.570082
$28$	0	0
$29$	4.28121e17	0.224694	0.112347	−	0.993669i	$-0.464163\pi$
$29$	4.28121e17	0.224694	0.112347	+	0.993669i	$0.464163\pi$
$30$	3.51760e18	1.20846
$31$	−1.46167e18	−0.333295	−0.166648	−	0.986016i	$-0.553294\pi$
$31$	−1.46167e18	−0.333295	−0.166648	+	0.986016i	$0.553294\pi$
$32$	5.68891e18	0.872277
$33$	−1.80835e19	−1.88737
$34$	−2.09291e19	−1.50406
$35$	0	0
$36$	7.22929e18	0.254281
$37$	1.41458e18	0.0353270	0.0176635	−	0.999844i	$-0.494377\pi$
$37$	1.41458e18	0.0353270	0.0176635	+	0.999844i	$0.494377\pi$
$38$	2.39159e19	0.427949
$39$	−8.75016e19	−1.13164
$40$	−5.47242e19	−0.515738
$41$	−2.60241e20	−1.80126	−0.900632	−	0.434583i	$-0.856896\pi$
$41$	−2.60241e20	−1.80126	−0.900632	+	0.434583i	$0.856896\pi$
$42$	0	0
$43$	−2.34818e20	−0.896141	−0.448070	−	0.893998i	$-0.647889\pi$
$43$	−2.34818e20	−0.896141	−0.448070	+	0.893998i	$0.647889\pi$
$44$	−2.49743e20	−0.715048
$45$	−2.00818e20	−0.434156
$46$	7.16881e20	1.17754
$47$	3.59457e20	0.451257	0.225628	−	0.974213i	$-0.427556\pi$
$47$	3.59457e20	0.451257	0.225628	+	0.974213i	$0.427556\pi$
$48$	−1.60687e21	−1.55048
$49$	0	0
$50$	7.43783e20	0.430845
$51$	3.40453e21	1.53968
$52$	−1.20845e21	−0.428732
$53$	1.03311e21	0.288867	0.144434	−	0.989514i	$-0.453864\pi$
$53$	1.03311e21	0.288867	0.144434	+	0.989514i	$0.453864\pi$
$54$	3.12289e21	0.691250
$55$	6.93744e21	1.22086
$56$	0	0
$57$	−3.89038e21	−0.438083
$58$	−3.00704e21	−0.272451
$59$	−9.21478e21	−0.674272	−0.337136	−	0.941456i	$-0.609458\pi$
$59$	−9.21478e21	−0.674272	−0.337136	+	0.941456i	$0.609458\pi$
$60$	−7.90249e21	−0.468677
$61$	3.55847e22	1.71649	0.858243	−	0.513244i	$-0.171556\pi$
$61$	3.55847e22	1.71649	0.858243	+	0.513244i	$0.171556\pi$
$62$	1.02665e22	0.404135
$63$	0	0
$64$	7.23246e21	0.191442
$65$	3.35687e22	0.732010
$66$	1.27015e23	2.28852
$67$	5.92207e22	0.884176	0.442088	−	0.896972i	$-0.354238\pi$
$67$	5.92207e22	0.884176	0.442088	+	0.896972i	$0.354238\pi$
$68$	4.70185e22	0.583321
$69$	−1.16614e23	−1.20542
$70$	0	0
$71$	−1.92146e23	−1.38964	−0.694820	−	0.719184i	$-0.744516\pi$
$71$	−1.92146e23	−1.38964	−0.694820	+	0.719184i	$0.744516\pi$
$72$	5.71991e22	0.347322
$73$	2.60605e23	1.33183	0.665913	−	0.746030i	$-0.268042\pi$
$73$	2.60605e23	1.33183	0.665913	+	0.746030i	$0.268042\pi$
$74$	−9.93575e21	−0.0428355
$75$	−1.20991e23	−0.441048
$76$	−5.37285e22	−0.165972
$77$	0	0
$78$	6.14594e23	1.37216
$79$	−5.22813e23	−0.995424	−0.497712	−	0.867342i	$-0.665826\pi$
$79$	−5.22813e23	−0.995424	−0.497712	+	0.867342i	$0.665826\pi$
$80$	6.16451e23	1.00294
$81$	−8.96182e23	−1.24834
$82$	1.82788e24	2.18411
$83$	−1.63276e24	−1.67666	−0.838330	−	0.545163i	$-0.816468\pi$
$83$	−1.63276e24	−1.67666	−0.838330	+	0.545163i	$0.816468\pi$
$84$	0	0
$85$	−1.30610e24	−0.995952
$86$	1.64932e24	1.08661
$87$	4.89152e23	0.278903
$88$	−1.97600e24	−0.976682
$89$	3.17249e24	1.36152	0.680762	−	0.732505i	$-0.261649\pi$
$89$	3.17249e24	1.36152	0.680762	+	0.732505i	$0.261649\pi$
$90$	1.41050e24	0.526433
$91$	0	0
$92$	−1.61051e24	−0.456685
$93$	−1.67005e24	−0.413706
$94$	−2.52476e24	−0.547169
$95$	1.49249e24	0.283378
$96$	6.49991e24	1.08272
$97$	3.73970e24	0.547255	0.273628	−	0.961836i	$-0.411776\pi$
$97$	3.73970e24	0.547255	0.273628	+	0.961836i	$0.411776\pi$
$98$	0	0
$99$	−7.25119e24	−0.822184
$100$	−1.67095e24	−0.167095
$101$	2.25425e24	0.199061	0.0995303	−	0.995035i	$-0.468266\pi$
$101$	2.25425e24	0.199061	0.0995303	+	0.995035i	$0.468266\pi$
$102$	−2.39127e25	−1.86693
$103$	−2.52879e25	−1.74762	−0.873809	−	0.486269i	$-0.838358\pi$
$103$	−2.52879e25	−1.74762	−0.873809	+	0.486269i	$0.838358\pi$
$104$	−9.56139e24	−0.585605
$105$	0	0
$106$	−7.25636e24	−0.350264
$107$	4.03080e25	1.73019	0.865095	−	0.501608i	$-0.167258\pi$
$107$	4.03080e25	1.73019	0.865095	+	0.501608i	$0.167258\pi$
$108$	−7.01576e24	−0.268088
$109$	−3.74126e25	−1.27405	−0.637026	−	0.770842i	$-0.719836\pi$
$109$	−3.74126e25	−1.27405	−0.637026	+	0.770842i	$0.719836\pi$
$110$	−4.87272e25	−1.48035
$111$	1.61624e24	0.0438499
$112$	0	0
$113$	−8.92415e25	−1.93681	−0.968403	−	0.249390i	$-0.919770\pi$
$113$	−8.92415e25	−1.93681	−0.968403	+	0.249390i	$0.919770\pi$
$114$	2.73253e25	0.531195
$115$	4.47374e25	0.779736
$116$	6.75548e24	0.105665
$117$	−3.50868e25	−0.492970
$118$	6.47228e25	0.817584
$119$	0	0
$120$	−6.25255e25	−0.640165
$121$	1.42153e26	1.31201
$122$	−2.49940e26	−2.08131
$123$	−2.97340e26	−2.23583
$124$	−2.30643e25	−0.156736
$125$	1.77047e26	1.08821
$126$	0	0
$127$	−1.08673e26	−0.547739	−0.273869	−	0.961767i	$-0.588304\pi$
$127$	−1.08673e26	−0.547739	−0.273869	+	0.961767i	$0.588304\pi$
$128$	−2.41688e26	−1.10441
$129$	−2.68293e26	−1.11234
$130$	−2.35780e26	−0.887594
$131$	2.59375e24	0.00887232	0.00443616	−	0.999990i	$-0.498588\pi$
$131$	2.59375e24	0.00887232	0.00443616	+	0.999990i	$0.498588\pi$
$132$	−2.85346e26	−0.887559
$133$	0	0
$134$	−4.15955e26	−1.07210
$135$	1.94886e26	0.457729
$136$	3.72017e26	0.796757
$137$	−3.28329e26	−0.641656	−0.320828	−	0.947137i	$-0.603961\pi$
$137$	−3.28329e26	−0.641656	−0.320828	+	0.947137i	$0.603961\pi$
$138$	8.19077e26	1.46163
$139$	7.74537e25	0.126287	0.0631433	−	0.998004i	$-0.479887\pi$
$139$	7.74537e25	0.126287	0.0631433	+	0.998004i	$0.479887\pi$
$140$	0	0
$141$	4.10700e26	0.560127
$142$	1.34960e27	1.68500
$143$	1.21211e27	1.38625
$144$	−6.44330e26	−0.675425
$145$	−1.87656e26	−0.180411
$146$	−1.83044e27	−1.61490
$147$	0	0
$148$	2.23212e25	0.0166130
$149$	−1.63940e27	−1.12165	−0.560823	−	0.827936i	$-0.689515\pi$
$149$	−1.63940e27	−1.12165	−0.560823	+	0.827936i	$0.689515\pi$
$150$	8.49814e26	0.534790
$151$	−9.50626e25	−0.0550551	−0.0275276	−	0.999621i	$-0.508763\pi$
$151$	−9.50626e25	−0.0550551	−0.0275276	+	0.999621i	$0.508763\pi$
$152$	−4.25106e26	−0.226701
$153$	1.36516e27	0.670721
$154$	0	0
$155$	6.40688e26	0.267609
$156$	−1.38072e27	−0.532167
$157$	2.91092e27	1.03582	0.517910	−	0.855435i	$-0.326710\pi$
$157$	2.91092e27	1.03582	0.517910	+	0.855435i	$0.326710\pi$
$158$	3.67214e27	1.20699
$159$	1.18039e27	0.358559
$160$	−2.49359e27	−0.700367
$161$	0	0
$162$	6.29461e27	1.51367
$163$	2.61641e27	0.582586	0.291293	−	0.956634i	$-0.405915\pi$
$163$	2.61641e27	0.582586	0.291293	+	0.956634i	$0.405915\pi$
$164$	−4.10644e27	−0.847066
$165$	7.92643e27	1.51540
$166$	1.14682e28	2.03302
$167$	1.17878e28	1.93856	0.969279	−	0.245965i	$-0.0791049\pi$
$167$	1.17878e28	1.93856	0.969279	+	0.245965i	$0.0791049\pi$
$168$	0	0
$169$	−1.19130e27	−0.168826
$170$	9.17376e27	1.20764
$171$	−1.55998e27	−0.190840
$172$	−3.70529e27	−0.421421
$173$	−1.59890e28	−1.69139	−0.845696	−	0.533664i	$-0.820815\pi$
$173$	−1.59890e28	−1.69139	−0.845696	+	0.533664i	$0.820815\pi$
$174$	−3.43571e27	−0.338182
$175$	0	0
$176$	2.22590e28	1.89932
$177$	−1.05284e28	−0.836946
$178$	−2.22830e28	−1.65091
$179$	1.37684e28	0.951091	0.475545	−	0.879691i	$-0.342251\pi$
$179$	1.37684e28	0.951091	0.475545	+	0.879691i	$0.342251\pi$
$180$	−3.16878e27	−0.204167
$181$	−1.90638e28	−1.14611	−0.573057	−	0.819516i	$-0.694242\pi$
$181$	−1.90638e28	−1.14611	−0.573057	+	0.819516i	$0.694242\pi$
$182$	0	0
$183$	4.06575e28	2.13060
$184$	−1.27426e28	−0.623785
$185$	−6.20047e26	−0.0283647
$186$	1.17301e28	0.501636
$187$	−4.71610e28	−1.88609
$188$	5.67201e27	0.212209
$189$	0	0
$190$	−1.04829e28	−0.343608
$191$	8.74441e27	0.268419	0.134210	−	0.990953i	$-0.457150\pi$
$191$	8.74441e27	0.268419	0.134210	+	0.990953i	$0.457150\pi$
$192$	8.26350e27	0.237629
$193$	−2.94270e28	−0.793011	−0.396505	−	0.918032i	$-0.629777\pi$
$193$	−2.94270e28	−0.793011	−0.396505	+	0.918032i	$0.629777\pi$
$194$	−2.62669e28	−0.663571
$195$	3.83541e28	0.908614
$196$	0	0
$197$	5.53491e28	1.15420	0.577102	−	0.816672i	$-0.304183\pi$
$197$	5.53491e28	1.15420	0.577102	+	0.816672i	$0.304183\pi$
$198$	5.09309e28	0.996935
$199$	−9.01973e27	−0.165779	−0.0828896	−	0.996559i	$-0.526415\pi$
$199$	−9.01973e27	−0.165779	−0.0828896	+	0.996559i	$0.526415\pi$
$200$	−1.32208e28	−0.228235
$201$	6.76630e28	1.09749
$202$	−1.58334e28	−0.241370
$203$	0	0
$204$	5.37213e28	0.724052
$205$	1.14070e29	1.44627
$206$	1.77617e29	2.11906
$207$	−4.67606e28	−0.525111
$208$	1.07706e29	1.13880
$209$	5.38912e28	0.536648
$210$	0	0
$211$	−4.74410e28	−0.419395	−0.209698	−	0.977766i	$-0.567248\pi$
$211$	−4.74410e28	−0.419395	−0.209698	+	0.977766i	$0.567248\pi$
$212$	1.63018e28	0.135843
$213$	−2.19538e29	−1.72490
$214$	−2.83115e29	−2.09793
$215$	1.02927e29	0.719527
$216$	−5.55096e28	−0.366181
$217$	0	0
$218$	2.62779e29	1.54484
$219$	2.97756e29	1.65314
$220$	1.09469e29	0.574124
$221$	−2.28201e29	−1.13087
$222$	−1.13522e28	−0.0531700
$223$	−6.22526e28	−0.275643	−0.137821	−	0.990457i	$-0.544010\pi$
$223$	−6.22526e28	−0.275643	−0.137821	+	0.990457i	$0.544010\pi$
$224$	0	0
$225$	−4.85154e28	−0.192131
$226$	6.26814e29	2.34846
$227$	1.39856e29	0.495857	0.247928	−	0.968778i	$-0.420250\pi$
$227$	1.39856e29	0.495857	0.247928	+	0.968778i	$0.420250\pi$
$228$	−6.13878e28	−0.206014
$229$	2.11577e29	0.672240	0.336120	−	0.941819i	$-0.390885\pi$
$229$	2.11577e29	0.672240	0.336120	+	0.941819i	$0.390885\pi$
$230$	−3.14227e29	−0.945464
$231$	0	0
$232$	5.34502e28	0.144328
$233$	−4.24353e28	−0.108587	−0.0542936	−	0.998525i	$-0.517291\pi$
$233$	−4.24353e28	−0.108587	−0.0542936	+	0.998525i	$0.517291\pi$
$234$	2.46443e29	0.597748
$235$	−1.57559e29	−0.362322
$236$	−1.45404e29	−0.317085
$237$	−5.97344e29	−1.23558
$238$	0	0
$239$	−3.58388e28	−0.0667391	−0.0333695	−	0.999443i	$-0.510624\pi$
$239$	−3.58388e28	−0.0667391	−0.0333695	+	0.999443i	$0.510624\pi$
$240$	7.04330e29	1.24490
$241$	−3.25555e29	−0.546275	−0.273137	−	0.961975i	$-0.588061\pi$
$241$	−3.25555e29	−0.546275	−0.273137	+	0.961975i	$0.588061\pi$
$242$	−9.98451e29	−1.59087
$243$	−6.47221e29	−0.979432
$244$	5.61504e29	0.807198
$245$	0	0
$246$	2.08846e30	2.71105
$247$	2.60767e29	0.321766
$248$	−1.82488e29	−0.214086
$249$	−1.86552e30	−2.08117
$250$	−1.24354e30	−1.31951
$251$	1.80638e30	1.82343	0.911714	−	0.410825i	$-0.134759\pi$
$251$	1.80638e30	1.82343	0.911714	+	0.410825i	$0.134759\pi$
$252$	0	0
$253$	1.61539e30	1.47663
$254$	7.63295e29	0.664157
$255$	−1.49229e30	−1.23623
$256$	1.45488e30	1.14770
$257$	1.60964e30	1.20939	0.604694	−	0.796458i	$-0.293295\pi$
$257$	1.60964e30	1.20939	0.604694	+	0.796458i	$0.293295\pi$
$258$	1.88444e30	1.34876
$259$	0	0
$260$	5.29693e29	0.344237
$261$	1.96143e29	0.121497
$262$	−1.82180e28	−0.0107581
$263$	3.36538e30	1.89490	0.947452	−	0.319897i	$-0.103648\pi$
$263$	3.36538e30	1.89490	0.947452	+	0.319897i	$0.103648\pi$
$264$	−2.25769e30	−1.21232
$265$	−4.52838e29	−0.231937
$266$	0	0
$267$	3.62475e30	1.69000
$268$	9.34466e29	0.415794
$269$	1.10931e30	0.471137	0.235569	−	0.971858i	$-0.424305\pi$
$269$	1.10931e30	0.471137	0.235569	+	0.971858i	$0.424305\pi$
$270$	−1.36884e30	−0.555016
$271$	1.57252e30	0.608807	0.304404	−	0.952543i	$-0.401543\pi$
$271$	1.57252e30	0.608807	0.304404	+	0.952543i	$0.401543\pi$
$272$	−4.19065e30	−1.54942
$273$	0	0
$274$	2.30612e30	0.778036
$275$	1.67601e30	0.540280
$276$	−1.84010e30	−0.566864
$277$	3.23071e30	0.951262	0.475631	−	0.879645i	$-0.342220\pi$
$277$	3.23071e30	0.951262	0.475631	+	0.879645i	$0.342220\pi$
$278$	−5.44019e29	−0.153128
$279$	−6.69663e29	−0.180220
$280$	0	0
$281$	2.34681e30	0.577629	0.288814	−	0.957385i	$-0.406739\pi$
$281$	2.34681e30	0.577629	0.288814	+	0.957385i	$0.406739\pi$
$282$	−2.88468e30	−0.679178
$283$	2.80519e30	0.631877	0.315938	−	0.948780i	$-0.397681\pi$
$283$	2.80519e30	0.631877	0.315938	+	0.948780i	$0.397681\pi$
$284$	−3.03195e30	−0.653495
$285$	1.70525e30	0.351745
$286$	−8.51361e30	−1.68089
$287$	0	0
$288$	2.60636e30	0.471660
$289$	3.10825e30	0.538633
$290$	1.31806e30	0.218756
$291$	4.27282e30	0.679285
$292$	4.11219e30	0.626307
$293$	7.77455e30	1.13457	0.567283	−	0.823523i	$-0.307994\pi$
$293$	7.77455e30	1.13457	0.567283	+	0.823523i	$0.307994\pi$
$294$	0	0
$295$	4.03907e30	0.541385
$296$	1.76608e29	0.0226916
$297$	7.03701e30	0.866827
$298$	1.15148e31	1.36004
$299$	7.81650e30	0.885365
$300$	−1.90916e30	−0.207408
$301$	0	0
$302$	6.67701e29	0.0667567
$303$	2.57561e30	0.247086
$304$	4.78869e30	0.440856
$305$	−1.55976e31	−1.37820
$306$	−9.58864e30	−0.813279
$307$	1.69626e31	1.38122	0.690609	−	0.723228i	$-0.257343\pi$
$307$	1.69626e31	1.38122	0.690609	+	0.723228i	$0.257343\pi$
$308$	0	0
$309$	−2.88928e31	−2.16925
$310$	−4.50007e30	−0.324487
$311$	−4.38595e30	−0.303780	−0.151890	−	0.988397i	$-0.548536\pi$
$311$	−4.38595e30	−0.303780	−0.151890	+	0.988397i	$0.548536\pi$
$312$	−1.09244e31	−0.726887
$313$	2.45460e31	1.56919	0.784597	−	0.620007i	$-0.212870\pi$
$313$	2.45460e31	1.56919	0.784597	+	0.620007i	$0.212870\pi$
$314$	−2.04457e31	−1.25598
$315$	0	0
$316$	−8.24967e30	−0.468110
$317$	−1.77996e31	−0.970889	−0.485445	−	0.874267i	$-0.661342\pi$
$317$	−1.77996e31	−0.970889	−0.485445	+	0.874267i	$0.661342\pi$
$318$	−8.29081e30	−0.434768
$319$	−6.77594e30	−0.341654
$320$	−3.17017e30	−0.153712
$321$	4.60542e31	2.14761
$322$	0	0
$323$	−1.01460e31	−0.437786
$324$	−1.41412e31	−0.587048
$325$	8.10983e30	0.323944
$326$	−1.83771e31	−0.706411
$327$	−4.27461e31	−1.58143
$328$	−3.24907e31	−1.15701
$329$	0	0
$330$	−5.56737e31	−1.83749
$331$	−7.91448e30	−0.251520	−0.125760	−	0.992061i	$-0.540137\pi$
$331$	−7.91448e30	−0.251520	−0.125760	+	0.992061i	$0.540137\pi$
$332$	−2.57639e31	−0.788470
$333$	6.48088e29	0.0191021
$334$	−8.27955e31	−2.35059
$335$	−2.59579e31	−0.709920
$336$	0	0
$337$	−7.30067e31	−1.85349	−0.926743	−	0.375697i	$-0.877403\pi$
$337$	−7.30067e31	−1.85349	−0.926743	+	0.375697i	$0.877403\pi$
$338$	8.36748e30	0.204708
$339$	−1.01963e32	−2.40408
$340$	−2.06094e31	−0.468359
$341$	2.31342e31	0.506786
$342$	1.09570e31	0.231401
$343$	0	0
$344$	−2.93167e31	−0.575618
$345$	5.11150e31	0.967854
$346$	1.12303e32	2.05089
$347$	8.66708e31	1.52670	0.763351	−	0.645984i	$-0.223553\pi$
$347$	8.66708e31	1.52670	0.763351	+	0.645984i	$0.223553\pi$
$348$	7.71852e30	0.131158
$349$	−5.67518e31	−0.930383	−0.465191	−	0.885210i	$-0.654015\pi$
$349$	−5.67518e31	−0.930383	−0.465191	+	0.885210i	$0.654015\pi$
$350$	0	0
$351$	3.40504e31	0.519737
$352$	−9.00394e31	−1.32632
$353$	−1.78722e31	−0.254094	−0.127047	−	0.991897i	$-0.540550\pi$
$353$	−1.78722e31	−0.254094	−0.127047	+	0.991897i	$0.540550\pi$
$354$	7.39495e31	1.01483
$355$	8.42224e31	1.11577
$356$	5.00599e31	0.640273
$357$	0	0
$358$	−9.67068e31	−1.15324
$359$	−9.54631e31	−1.09940	−0.549699	−	0.835363i	$-0.685258\pi$
$359$	−9.54631e31	−1.09940	−0.549699	+	0.835363i	$0.685258\pi$
$360$	−2.50718e31	−0.278871
$361$	−8.14826e31	−0.875437
$362$	1.33900e32	1.38971
$363$	1.62417e32	1.62854
$364$	0	0
$365$	−1.14230e32	−1.06935
$366$	−2.85570e32	−2.58345
$367$	3.46459e30	0.0302918	0.0151459	−	0.999885i	$-0.495179\pi$
$367$	3.46459e30	0.0302918	0.0151459	+	0.999885i	$0.495179\pi$
$368$	1.43541e32	1.21305
$369$	−1.19229e32	−0.973984
$370$	4.35509e30	0.0343934
$371$	0	0
$372$	−2.63523e31	−0.194550
$373$	1.55221e32	1.10813	0.554066	−	0.832473i	$-0.313076\pi$
$373$	1.55221e32	1.10813	0.554066	+	0.832473i	$0.313076\pi$
$374$	3.31249e32	2.28697
$375$	2.02287e32	1.35075
$376$	4.48777e31	0.289856
$377$	−3.27872e31	−0.204851
$378$	0	0
$379$	1.93491e32	1.13154	0.565772	−	0.824562i	$-0.308578\pi$
$379$	1.93491e32	1.13154	0.565772	+	0.824562i	$0.308578\pi$
$380$	2.35505e31	0.133262
$381$	−1.24165e32	−0.679886
$382$	−6.14190e31	−0.325470
$383$	2.43299e32	1.24783	0.623916	−	0.781492i	$-0.285541\pi$
$383$	2.43299e32	1.24783	0.623916	+	0.781492i	$0.285541\pi$
$384$	−2.76142e32	−1.37086
$385$	0	0
$386$	2.06689e32	0.961560
$387$	−1.07582e32	−0.484563
$388$	5.90101e31	0.257353
$389$	4.24287e32	1.79180	0.895901	−	0.444254i	$-0.146531\pi$
$389$	4.24287e32	1.79180	0.895901	+	0.444254i	$0.146531\pi$
$390$	−2.69392e32	−1.10173
$391$	−3.04126e32	−1.20460
$392$	0	0
$393$	2.96351e30	0.0110128
$394$	−3.88761e32	−1.39952
$395$	2.29162e32	0.799243
$396$	−1.14419e32	−0.386642
$397$	1.05092e32	0.344103	0.172052	−	0.985088i	$-0.444960\pi$
$397$	1.05092e32	0.344103	0.172052	+	0.985088i	$0.444960\pi$
$398$	6.33528e31	0.201015
$399$	0	0
$400$	1.48928e32	0.443840
$401$	−1.79668e32	−0.519000	−0.259500	−	0.965743i	$-0.583558\pi$
$401$	−1.79668e32	−0.519000	−0.259500	+	0.965743i	$0.583558\pi$
$402$	−4.75252e32	−1.33076
$403$	1.11941e32	0.303861
$404$	3.55707e31	0.0936106
$405$	3.92819e32	1.00232
$406$	0	0
$407$	−2.23889e31	−0.0537158
$408$	4.25050e32	0.988982
$409$	−2.65670e32	−0.599518	−0.299759	−	0.954015i	$-0.596906\pi$
$409$	−2.65670e32	−0.599518	−0.299759	+	0.954015i	$0.596906\pi$
$410$	−8.01205e32	−1.75366
$411$	−3.75135e32	−0.796461
$412$	−3.99027e32	−0.821839
$413$	0	0
$414$	3.28437e32	0.636720
$415$	7.15677e32	1.34622
$416$	−4.35679e32	−0.795244
$417$	8.84952e31	0.156754
$418$	−3.78521e32	−0.650709
$419$	5.58069e32	0.931134	0.465567	−	0.885013i	$-0.345850\pi$
$419$	5.58069e32	0.931134	0.465567	+	0.885013i	$0.345850\pi$
$420$	0	0
$421$	−8.32404e32	−1.30860	−0.654302	−	0.756234i	$-0.727037\pi$
$421$	−8.32404e32	−1.30860	−0.654302	+	0.756234i	$0.727037\pi$
$422$	3.33217e32	0.508535
$423$	1.64685e32	0.244005
$424$	1.28982e32	0.185548
$425$	−3.15539e32	−0.440749
$426$	1.54199e33	2.09152
$427$	0	0
$428$	6.36035e32	0.813643
$429$	1.38490e33	1.72069
$430$	−7.22937e32	−0.872458
$431$	−2.48538e32	−0.291358	−0.145679	−	0.989332i	$-0.546537\pi$
$431$	−2.48538e32	−0.291358	−0.145679	+	0.989332i	$0.546537\pi$
$432$	6.25298e32	0.712099
$433$	−7.47589e32	−0.827111	−0.413556	−	0.910479i	$-0.635713\pi$
$433$	−7.47589e32	−0.827111	−0.413556	+	0.910479i	$0.635713\pi$
$434$	0	0
$435$	−2.14408e32	−0.223936
$436$	−5.90348e32	−0.599138
$437$	3.47527e32	0.342745
$438$	−2.09138e33	−2.00450
$439$	−6.75382e32	−0.629134	−0.314567	−	0.949235i	$-0.601859\pi$
$439$	−6.75382e32	−0.629134	−0.314567	+	0.949235i	$0.601859\pi$
$440$	8.66129e32	0.784195
$441$	0	0
$442$	1.60284e33	1.37123
$443$	2.35864e33	1.96162	0.980810	−	0.194964i	$-0.0624591\pi$
$443$	2.35864e33	1.96162	0.980810	+	0.194964i	$0.0624591\pi$
$444$	2.55033e31	0.0206210
$445$	−1.39058e33	−1.09319
$446$	4.37250e32	0.334229
$447$	−1.87310e33	−1.39225
$448$	0	0
$449$	7.14928e32	0.502554	0.251277	−	0.967915i	$-0.419149\pi$
$449$	7.14928e32	0.502554	0.251277	+	0.967915i	$0.419149\pi$
$450$	3.40762e32	0.232968
$451$	4.11888e33	2.73887
$452$	−1.40817e33	−0.910807
$453$	−1.08614e32	−0.0683376
$454$	−9.82318e32	−0.601248
$455$	0	0
$456$	−4.85708e32	−0.281394
$457$	2.37004e31	0.0133599	0.00667995	−	0.999978i	$-0.497874\pi$
$457$	2.37004e31	0.0133599	0.00667995	+	0.999978i	$0.497874\pi$
$458$	−1.48607e33	−0.815121
$459$	−1.32484e33	−0.707139
$460$	7.05928e32	0.366680
$461$	−1.75850e33	−0.888958	−0.444479	−	0.895789i	$-0.646611\pi$
$461$	−1.75850e33	−0.888958	−0.444479	+	0.895789i	$0.646611\pi$
$462$	0	0
$463$	1.53968e33	0.737342	0.368671	−	0.929560i	$-0.379813\pi$
$463$	1.53968e33	0.737342	0.368671	+	0.929560i	$0.379813\pi$
$464$	−6.02100e32	−0.280669
$465$	7.32023e32	0.332172
$466$	2.98057e32	0.131667
$467$	−2.17229e32	−0.0934235	−0.0467117	−	0.998908i	$-0.514874\pi$
$467$	−2.17229e32	−0.0934235	−0.0467117	+	0.998908i	$0.514874\pi$
$468$	−5.53648e32	−0.231825
$469$	0	0
$470$	1.10666e33	0.439331
$471$	3.32589e33	1.28572
$472$	−1.15045e33	−0.433105
$473$	3.71651e33	1.36261
$474$	4.19563e33	1.49819
$475$	3.60569e32	0.125406
$476$	0	0
$477$	4.73317e32	0.156197
$478$	2.51725e32	0.0809241
$479$	−5.19832e33	−1.62806	−0.814028	−	0.580825i	$-0.802730\pi$
$479$	−5.19832e33	−1.62806	−0.814028	+	0.580825i	$0.802730\pi$
$480$	−2.84907e33	−0.869336
$481$	−1.08334e32	−0.0322072
$482$	2.28663e33	0.662382
$483$	0	0
$484$	2.24308e33	0.616989
$485$	−1.63920e33	−0.439401
$486$	4.54596e33	1.18760
$487$	3.77714e33	0.961726	0.480863	−	0.876796i	$-0.340323\pi$
$487$	3.77714e33	0.961726	0.480863	+	0.876796i	$0.340323\pi$
$488$	4.44269e33	1.10255
$489$	2.98939e33	0.723140
$490$	0	0
$491$	−1.89820e32	−0.0436339	−0.0218170	−	0.999762i	$-0.506945\pi$
$491$	−1.89820e32	−0.0436339	−0.0218170	+	0.999762i	$0.506945\pi$
$492$	−4.69184e33	−1.05143
$493$	1.27569e33	0.278714
$494$	−1.83158e33	−0.390156
$495$	3.17838e33	0.660146
$496$	2.05567e33	0.416325
$497$	0	0
$498$	1.31030e34	2.52351
$499$	6.65166e33	1.24932	0.624660	−	0.780897i	$-0.285238\pi$
$499$	6.65166e33	1.24932	0.624660	+	0.780897i	$0.285238\pi$
$500$	2.79369e33	0.511745
$501$	1.34683e34	2.40625
$502$	−1.26877e34	−2.21099
$503$	−6.30623e33	−1.07194	−0.535969	−	0.844238i	$-0.680054\pi$
$503$	−6.30623e33	−1.07194	−0.535969	+	0.844238i	$0.680054\pi$
$504$	0	0
$505$	−9.88094e32	−0.159829
$506$	−1.13462e34	−1.79048
$507$	−1.36113e33	−0.209556
$508$	−1.71479e33	−0.257581
$509$	−1.06547e34	−1.56159	−0.780795	−	0.624787i	$-0.785186\pi$
$509$	−1.06547e34	−1.56159	−0.780795	+	0.624787i	$0.785186\pi$
$510$	1.04815e34	1.49899
$511$	0	0
$512$	−2.10914e33	−0.287230
$513$	1.51391e33	0.201202
$514$	−1.13058e34	−1.46644
$515$	1.10843e34	1.40319
$516$	−4.23350e33	−0.523092
$517$	−5.68919e33	−0.686150
$518$	0	0
$519$	−1.82683e34	−2.09946
$520$	4.19100e33	0.470192
$521$	−8.18647e33	−0.896654	−0.448327	−	0.893870i	$-0.647980\pi$
$521$	−8.18647e33	−0.896654	−0.448327	+	0.893870i	$0.647980\pi$
$522$	−1.37767e33	−0.147320
$523$	−9.37733e33	−0.979058	−0.489529	−	0.871987i	$-0.662831\pi$
$523$	−9.37733e33	−0.979058	−0.489529	+	0.871987i	$0.662831\pi$
$524$	4.09278e31	0.00417231
$525$	0	0
$526$	−2.36378e34	−2.29765
$527$	−4.35542e33	−0.413425
$528$	2.54322e34	2.35754
$529$	−6.28618e32	−0.0569103
$530$	3.18064e33	0.281233
$531$	−4.22173e33	−0.364594
$532$	0	0
$533$	1.99303e34	1.64219
$534$	−2.54595e34	−2.04920
$535$	−1.76680e34	−1.38920
$536$	7.39362e33	0.567933
$537$	1.57312e34	1.18055
$538$	−7.79154e33	−0.571275
$539$	0	0
$540$	3.07518e33	0.215253
$541$	−5.05256e33	−0.345578	−0.172789	−	0.984959i	$-0.555278\pi$
$541$	−5.05256e33	−0.345578	−0.172789	+	0.984959i	$0.555278\pi$
$542$	−1.10451e34	−0.738206
$543$	−2.17815e34	−1.42262
$544$	1.69515e34	1.08199
$545$	1.63989e34	1.02296
$546$	0	0
$547$	−1.91091e34	−1.13867	−0.569335	−	0.822106i	$-0.692799\pi$
$547$	−1.91091e34	−1.13867	−0.569335	+	0.822106i	$0.692799\pi$
$548$	−5.18083e33	−0.301747
$549$	1.63030e34	0.928142
$550$	−1.17720e34	−0.655113
$551$	−1.45774e33	−0.0793023
$552$	−1.45591e34	−0.774278
$553$	0	0
$554$	−2.26918e34	−1.15345
$555$	−7.08439e32	−0.0352079
$556$	1.22217e33	0.0593878
$557$	6.09278e33	0.289485	0.144742	−	0.989469i	$-0.453765\pi$
$557$	6.09278e33	0.289485	0.144742	+	0.989469i	$0.453765\pi$
$558$	4.70358e33	0.218525
$559$	1.79833e34	0.817000
$560$	0	0
$561$	−5.38841e34	−2.34113
$562$	−1.64835e34	−0.700400
$563$	1.23197e34	0.511971	0.255985	−	0.966681i	$-0.417600\pi$
$563$	1.23197e34	0.511971	0.255985	+	0.966681i	$0.417600\pi$
$564$	6.48060e33	0.263406
$565$	3.91167e34	1.55510
$566$	−1.97031e34	−0.766178
$567$	0	0
$568$	−2.39892e34	−0.892608
$569$	4.23478e34	1.54144	0.770722	−	0.637171i	$-0.219896\pi$
$569$	4.23478e34	1.54144	0.770722	+	0.637171i	$0.219896\pi$
$570$	−1.19773e34	−0.426506
$571$	−1.75220e34	−0.610424	−0.305212	−	0.952284i	$-0.598727\pi$
$571$	−1.75220e34	−0.610424	−0.305212	+	0.952284i	$0.598727\pi$
$572$	1.91263e34	0.651900
$573$	9.99099e33	0.333178
$574$	0	0
$575$	1.08081e34	0.345064
$576$	3.31354e33	0.103517
$577$	1.88819e34	0.577230	0.288615	−	0.957445i	$-0.406805\pi$
$577$	1.88819e34	0.577230	0.288615	+	0.957445i	$0.406805\pi$
$578$	−2.18318e34	−0.653117
$579$	−3.36220e34	−0.984331
$580$	−2.96109e33	−0.0848403
$581$	0	0
$582$	−3.00114e34	−0.823663
$583$	−1.63512e34	−0.439231
$584$	3.25362e34	0.855472
$585$	1.53794e34	0.395814
$586$	−5.46069e34	−1.37571
$587$	−5.78399e33	−0.142643	−0.0713216	−	0.997453i	$-0.522722\pi$
$587$	−5.78399e33	−0.142643	−0.0713216	+	0.997453i	$0.522722\pi$
$588$	0	0
$589$	4.97697e33	0.117632
$590$	−2.83696e34	−0.656453
$591$	6.32395e34	1.43267
$592$	−1.98944e33	−0.0441275
$593$	−2.12568e34	−0.461651	−0.230826	−	0.972995i	$-0.574143\pi$
$593$	−2.12568e34	−0.461651	−0.230826	+	0.972995i	$0.574143\pi$
$594$	−4.94266e34	−1.05107
$595$	0	0
$596$	−2.58687e34	−0.527467
$597$	−1.03056e34	−0.205775
$598$	−5.49016e34	−1.07354
$599$	6.52058e34	1.24868	0.624339	−	0.781153i	$-0.285368\pi$
$599$	6.52058e34	1.24868	0.624339	+	0.781153i	$0.285368\pi$
$600$	−1.51055e34	−0.283298
$601$	1.92233e34	0.353100	0.176550	−	0.984292i	$-0.443506\pi$
$601$	1.92233e34	0.353100	0.176550	+	0.984292i	$0.443506\pi$
$602$	0	0
$603$	2.71318e34	0.478094
$604$	−1.50003e33	−0.0258903
$605$	−6.23090e34	−1.05344
$606$	−1.80906e34	−0.299602
$607$	7.67940e34	1.24586	0.622929	−	0.782279i	$-0.285943\pi$
$607$	7.67940e34	1.24586	0.622929	+	0.782279i	$0.285943\pi$
$608$	−1.93706e34	−0.307857
$609$	0	0
$610$	1.09555e35	1.67112
$611$	−2.75287e34	−0.411405
$612$	2.15414e34	0.315415
$613$	1.14226e33	0.0163874	0.00819369	−	0.999966i	$-0.497392\pi$
$613$	1.14226e33	0.0163874	0.00819369	+	0.999966i	$0.497392\pi$
$614$	−1.19142e35	−1.67479
$615$	1.30332e35	1.79519
$616$	0	0
$617$	4.45099e34	0.588698	0.294349	−	0.955698i	$-0.404897\pi$
$617$	4.45099e34	0.588698	0.294349	+	0.955698i	$0.404897\pi$
$618$	2.02937e35	2.63031
$619$	−1.08369e35	−1.37649	−0.688246	−	0.725478i	$-0.741619\pi$
$619$	−1.08369e35	−1.37649	−0.688246	+	0.725478i	$0.741619\pi$
$620$	1.01097e34	0.125846
$621$	4.53794e34	0.553623
$622$	3.08061e34	0.368346
$623$	0	0
$624$	1.23060e35	1.41355
$625$	−4.60451e34	−0.518422
$626$	−1.72406e35	−1.90272
$627$	6.15738e34	0.666119
$628$	4.59325e34	0.487107
$629$	4.21510e33	0.0438202
$630$	0	0
$631$	8.89890e34	0.889139	0.444569	−	0.895744i	$-0.353357\pi$
$631$	8.89890e34	0.889139	0.444569	+	0.895744i	$0.353357\pi$
$632$	−6.52725e34	−0.639391
$633$	−5.42041e34	−0.520578
$634$	1.25021e35	1.17725
$635$	4.76339e34	0.439789
$636$	1.86258e34	0.168617
$637$	0	0
$638$	4.75929e34	0.414270
$639$	−8.80314e34	−0.751410
$640$	1.05938e35	0.886749
$641$	−1.43907e35	−1.18129	−0.590647	−	0.806930i	$-0.701127\pi$
$641$	−1.43907e35	−1.18129	−0.590647	+	0.806930i	$0.701127\pi$
$642$	−3.23475e35	−2.60408
$643$	−1.02120e35	−0.806260	−0.403130	−	0.915143i	$-0.632078\pi$
$643$	−1.02120e35	−0.806260	−0.403130	+	0.915143i	$0.632078\pi$
$644$	0	0
$645$	1.17600e35	0.893119
$646$	7.12633e34	0.530835
$647$	1.70970e35	1.24916	0.624578	−	0.780963i	$-0.285271\pi$
$647$	1.70970e35	1.24916	0.624578	+	0.780963i	$0.285271\pi$
$648$	−1.11887e35	−0.801848
$649$	1.45844e35	1.02525
$650$	−5.69618e34	−0.392796
$651$	0	0
$652$	4.12853e34	0.273968
$653$	5.70017e34	0.371085	0.185542	−	0.982636i	$-0.440596\pi$
$653$	5.70017e34	0.371085	0.185542	+	0.982636i	$0.440596\pi$
$654$	3.00240e35	1.91755
$655$	−1.13691e33	−0.00712374
$656$	3.65997e35	2.24999
$657$	1.19396e35	0.720148
$658$	0	0
$659$	1.98836e35	1.15459	0.577295	−	0.816535i	$-0.304108\pi$
$659$	1.98836e35	1.15459	0.577295	+	0.816535i	$0.304108\pi$
$660$	1.25074e35	0.712637
$661$	−8.91095e34	−0.498203	−0.249101	−	0.968477i	$-0.580135\pi$
$661$	−8.91095e34	−0.498203	−0.249101	+	0.968477i	$0.580135\pi$
$662$	5.55897e34	0.304979
$663$	−2.60732e35	−1.40371
$664$	−2.03847e35	−1.07697
$665$	0	0
$666$	−4.55204e33	−0.0231621
$667$	−4.36959e34	−0.218207
$668$	1.86005e35	0.911630
$669$	−7.11272e34	−0.342144
$670$	1.82323e35	0.860809
$671$	−5.63205e35	−2.60997
$672$	0	0
$673$	1.24182e35	0.554460	0.277230	−	0.960804i	$-0.410584\pi$
$673$	1.24182e35	0.554460	0.277230	+	0.960804i	$0.410584\pi$
$674$	5.12785e35	2.24743
$675$	4.70824e34	0.202563
$676$	−1.87980e34	−0.0793923
$677$	−6.16839e34	−0.255749	−0.127874	−	0.991790i	$-0.540815\pi$
$677$	−6.16839e34	−0.255749	−0.127874	+	0.991790i	$0.540815\pi$
$678$	7.16171e35	2.91505
$679$	0	0
$680$	−1.63064e35	−0.639730
$681$	1.59793e35	0.615487
$682$	−1.62490e35	−0.614500
$683$	7.53579e34	0.279814	0.139907	−	0.990165i	$-0.455320\pi$
$683$	7.53579e34	0.279814	0.139907	+	0.990165i	$0.455320\pi$
$684$	−2.46156e34	−0.0897447
$685$	1.43915e35	0.515197
$686$	0	0
$687$	2.41739e35	0.834424
$688$	3.30244e35	1.11938
$689$	−7.91197e34	−0.263357
$690$	−3.59022e35	−1.17356
$691$	6.92967e34	0.222452	0.111226	−	0.993795i	$-0.464522\pi$
$691$	6.92967e34	0.222452	0.111226	+	0.993795i	$0.464522\pi$
$692$	−2.52296e35	−0.795398
$693$	0	0
$694$	−6.08759e35	−1.85119
$695$	−3.39499e34	−0.101398
$696$	6.10699e34	0.179148
$697$	−7.75451e35	−2.23432
$698$	3.98613e35	1.12813
$699$	−4.84848e34	−0.134785
$700$	0	0
$701$	−1.33800e35	−0.358906	−0.179453	−	0.983767i	$-0.557433\pi$
$701$	−1.33800e35	−0.358906	−0.179453	+	0.983767i	$0.557433\pi$
$702$	−2.39163e35	−0.630204
$703$	−4.81662e33	−0.0124681
$704$	−1.14469e35	−0.291093
$705$	−1.80020e35	−0.449735
$706$	1.25531e35	0.308100
$707$	0	0
$708$	−1.66132e35	−0.393584
$709$	−5.50973e35	−1.28249	−0.641243	−	0.767338i	$-0.721581\pi$
$709$	−5.50973e35	−1.28249	−0.641243	+	0.767338i	$0.721581\pi$
$710$	−5.91562e35	−1.35292
$711$	−2.39526e35	−0.538248
$712$	3.96081e35	0.874548
$713$	1.49185e35	0.323673
$714$	0	0
$715$	−5.31297e35	−1.11304
$716$	2.17257e35	0.447262
$717$	−4.09479e34	−0.0828404
$718$	6.70514e35	1.33307
$719$	−1.11117e35	−0.217105	−0.108552	−	0.994091i	$-0.534621\pi$
$719$	−1.11117e35	−0.217105	−0.108552	+	0.994091i	$0.534621\pi$
$720$	2.82426e35	0.542311
$721$	0	0
$722$	5.72318e35	1.06151
$723$	−3.71965e35	−0.678068
$724$	−3.00815e35	−0.538974
$725$	−4.53357e34	−0.0798390
$726$	−1.14079e36	−1.97468
$727$	−3.82152e35	−0.650214	−0.325107	−	0.945677i	$-0.605400\pi$
$727$	−3.82152e35	−0.650214	−0.325107	+	0.945677i	$0.605400\pi$
$728$	0	0
$729$	1.98374e34	0.0326130
$730$	8.02327e35	1.29663
$731$	−6.99699e35	−1.11159
$732$	6.41551e35	1.00194
$733$	−8.81403e35	−1.35324	−0.676620	−	0.736332i	$-0.736556\pi$
$733$	−8.81403e35	−1.35324	−0.676620	+	0.736332i	$0.736556\pi$
$734$	−2.43346e34	−0.0367302
$735$	0	0
$736$	−5.80636e35	−0.847093
$737$	−9.37297e35	−1.34442
$738$	8.37440e35	1.18100
$739$	1.33078e35	0.184524	0.0922618	−	0.995735i	$-0.470590\pi$
$739$	1.33078e35	0.184524	0.0922618	+	0.995735i	$0.470590\pi$
$740$	−9.78395e33	−0.0133388
$741$	2.97941e35	0.399395
$742$	0	0
$743$	−4.56621e35	−0.591828	−0.295914	−	0.955215i	$-0.595624\pi$
$743$	−4.56621e35	−0.591828	−0.295914	+	0.955215i	$0.595624\pi$
$744$	−2.08503e35	−0.265736
$745$	7.18588e35	0.900589
$746$	−1.09024e36	−1.34366
$747$	−7.48044e35	−0.906608
$748$	−7.44171e35	−0.886957
$749$	0	0
$750$	−1.42082e36	−1.63785
$751$	−9.09846e35	−1.03150	−0.515749	−	0.856740i	$-0.672486\pi$
$751$	−9.09846e35	−1.03150	−0.515749	+	0.856740i	$0.672486\pi$
$752$	−5.05533e35	−0.563672
$753$	2.06390e36	2.26335
$754$	2.30291e35	0.248390
$755$	4.16683e34	0.0442047
$756$	0	0
$757$	1.37686e36	1.41316	0.706581	−	0.707632i	$-0.250236\pi$
$757$	1.37686e36	1.41316	0.706581	+	0.707632i	$0.250236\pi$
$758$	−1.35904e36	−1.37205
$759$	1.84568e36	1.83288
$760$	1.86335e35	0.182022
$761$	3.76000e35	0.361310	0.180655	−	0.983547i	$-0.442178\pi$
$761$	3.76000e35	0.361310	0.180655	+	0.983547i	$0.442178\pi$
$762$	8.72108e35	0.824391
$763$	0	0
$764$	1.37981e35	0.126227
$765$	−5.98385e35	−0.538534
$766$	−1.70889e36	−1.51305
$767$	7.05705e35	0.614725
$768$	1.66229e36	1.42459
$769$	1.81672e35	0.153182	0.0765910	−	0.997063i	$-0.475596\pi$
$769$	1.81672e35	0.153182	0.0765910	+	0.997063i	$0.475596\pi$
$770$	0	0
$771$	1.83911e36	1.50116
$772$	−4.64339e35	−0.372923
$773$	6.01833e35	0.475590	0.237795	−	0.971315i	$-0.423575\pi$
$773$	6.01833e35	0.475590	0.237795	+	0.971315i	$0.423575\pi$
$774$	7.55631e35	0.587554
$775$	1.54783e35	0.118428
$776$	4.66896e35	0.351519
$777$	0	0
$778$	−2.98011e36	−2.17264
$779$	8.86115e35	0.635728
$780$	6.05204e35	0.427287
$781$	3.04113e36	2.11299
$782$	2.13612e36	1.46063
$783$	−1.90349e35	−0.128094
$784$	0	0
$785$	−1.27593e36	−0.831678
$786$	−2.08151e34	−0.0133535
$787$	−6.00622e35	−0.379243	−0.189621	−	0.981857i	$-0.560726\pi$
$787$	−6.00622e35	−0.379243	−0.189621	+	0.981857i	$0.560726\pi$
$788$	8.73374e35	0.542778
$789$	3.84514e36	2.35207
$790$	−1.60959e36	−0.969118
$791$	0	0
$792$	−9.05300e35	−0.528114
$793$	−2.72522e36	−1.56490
$794$	−7.38146e35	−0.417240
$795$	−5.17393e35	−0.287893
$796$	−1.42326e35	−0.0779597
$797$	−7.30543e35	−0.393928	−0.196964	−	0.980411i	$-0.563108\pi$
$797$	−7.30543e35	−0.393928	−0.196964	+	0.980411i	$0.563108\pi$
$798$	0	0
$799$	1.07109e36	0.559747
$800$	−6.02425e35	−0.309940
$801$	1.45347e36	0.736207
$802$	1.26196e36	0.629310
$803$	−4.12464e36	−2.02508
$804$	1.06768e36	0.516108
$805$	0	0
$806$	−7.86250e35	−0.368445
$807$	1.26744e36	0.584803
$808$	2.81440e35	0.127863
$809$	−1.63779e35	−0.0732657	−0.0366328	−	0.999329i	$-0.511663\pi$
$809$	−1.63779e35	−0.0732657	−0.0366328	+	0.999329i	$0.511663\pi$
$810$	−2.75908e36	−1.21535
$811$	−4.03019e36	−1.74809	−0.874046	−	0.485842i	$-0.838513\pi$
$811$	−4.03019e36	−1.74809	−0.874046	+	0.485842i	$0.838513\pi$
$812$	0	0
$813$	1.79669e36	0.755687
$814$	1.57255e35	0.0651327
$815$	−1.14684e36	−0.467769
$816$	−4.78806e36	−1.92324
$817$	7.99551e35	0.316279
$818$	1.86602e36	0.726941
$819$	0	0
$820$	1.79995e36	0.680124
$821$	3.38683e36	1.26039	0.630193	−	0.776438i	$-0.282976\pi$
$821$	3.38683e36	1.26039	0.630193	+	0.776438i	$0.282976\pi$
$822$	2.63487e36	0.965744
$823$	−1.93589e36	−0.698849	−0.349425	−	0.936964i	$-0.613623\pi$
$823$	−1.93589e36	−0.698849	−0.349425	+	0.936964i	$0.613623\pi$
$824$	−3.15715e36	−1.12255
$825$	1.91494e36	0.670627
$826$	0	0
$827$	−1.06636e36	−0.362313	−0.181156	−	0.983454i	$-0.557984\pi$
$827$	−1.06636e36	−0.362313	−0.181156	+	0.983454i	$0.557984\pi$
$828$	−7.37853e35	−0.246940
$829$	−4.29035e36	−1.41436	−0.707181	−	0.707032i	$-0.750033\pi$
$829$	−4.29035e36	−1.41436	−0.707181	+	0.707032i	$0.750033\pi$
$830$	−5.02678e36	−1.63235
$831$	3.69127e36	1.18076
$832$	−5.53891e35	−0.174535
$833$	0	0
$834$	−6.21573e35	−0.190071
$835$	−5.16691e36	−1.55650
$836$	8.50370e35	0.252365
$837$	6.49883e35	0.190006
$838$	−3.91976e36	−1.12904
$839$	8.30998e35	0.235817	0.117909	−	0.993024i	$-0.462381\pi$
$839$	8.30998e35	0.235817	0.117909	+	0.993024i	$0.462381\pi$
$840$	0	0
$841$	−3.44707e36	−0.949513
$842$	5.84664e36	1.58674
$843$	2.68136e36	0.716987
$844$	−7.48590e35	−0.197226
$845$	5.22178e35	0.135553
$846$	−1.15671e36	−0.295866
$847$	0	0
$848$	−1.45294e36	−0.360829
$849$	3.20509e36	0.784323
$850$	2.21628e36	0.534427
$851$	−1.44379e35	−0.0343070
$852$	−3.46417e36	−0.811156
$853$	6.27219e36	1.44729	0.723646	−	0.690171i	$-0.242465\pi$
$853$	6.27219e36	1.44729	0.723646	+	0.690171i	$0.242465\pi$
$854$	0	0
$855$	6.83780e35	0.153229
$856$	5.03239e36	1.11135
$857$	−9.09012e36	−1.97838	−0.989189	−	0.146646i	$-0.953152\pi$
$857$	−9.09012e36	−1.97838	−0.989189	+	0.146646i	$0.953152\pi$
$858$	−9.72729e36	−2.08641
$859$	−2.05086e36	−0.433533	−0.216766	−	0.976223i	$-0.569551\pi$
$859$	−2.05086e36	−0.433533	−0.216766	+	0.976223i	$0.569551\pi$
$860$	1.62412e36	0.338366
$861$	0	0
$862$	1.74568e36	0.353285
$863$	5.40543e36	1.07819	0.539095	−	0.842245i	$-0.318766\pi$
$863$	5.40543e36	1.07819	0.539095	+	0.842245i	$0.318766\pi$
$864$	−2.52938e36	−0.497270
$865$	7.00837e36	1.35805
$866$	5.25091e36	1.00291
$867$	3.55136e36	0.668583
$868$	0	0
$869$	8.27466e36	1.51357
$870$	1.50596e36	0.271533
$871$	−4.53536e36	−0.806092
$872$	−4.67091e36	−0.818362
$873$	1.71334e36	0.295913
$874$	−2.44096e36	−0.415593
$875$	0	0
$876$	4.69841e36	0.777409
$877$	−1.06058e36	−0.173001	−0.0865006	−	0.996252i	$-0.527568\pi$
$877$	−1.06058e36	−0.173001	−0.0865006	+	0.996252i	$0.527568\pi$
$878$	4.74375e36	0.762852
$879$	8.88287e36	1.40829
$880$	−9.75668e36	−1.52500
$881$	4.88397e35	0.0752618	0.0376309	−	0.999292i	$-0.488019\pi$
$881$	4.88397e35	0.0752618	0.0376309	+	0.999292i	$0.488019\pi$
$882$	0	0
$883$	−2.95127e36	−0.442080	−0.221040	−	0.975265i	$-0.570945\pi$
$883$	−2.95127e36	−0.442080	−0.221040	+	0.975265i	$0.570945\pi$
$884$	−3.60087e36	−0.531807
$885$	4.61487e36	0.671998
$886$	−1.65666e37	−2.37855
$887$	9.80313e36	1.38778	0.693888	−	0.720083i	$-0.255896\pi$
$887$	9.80313e36	1.38778	0.693888	+	0.720083i	$0.255896\pi$
$888$	2.01785e35	0.0281661
$889$	0	0
$890$	9.76717e36	1.32554
$891$	1.41840e37	1.89814
$892$	−9.82308e35	−0.129624
$893$	−1.22394e36	−0.159264
$894$	1.31563e37	1.68817
$895$	−6.03505e36	−0.763647
$896$	0	0
$897$	8.93080e36	1.09897
$898$	−5.02151e36	−0.609369
$899$	−6.25773e35	−0.0748895
$900$	−7.65543e35	−0.0903520
$901$	3.07840e36	0.358316
$902$	−2.89302e37	−3.32101
$903$	0	0
$904$	−1.11417e37	−1.24407
$905$	8.35614e36	0.920234
$906$	7.62886e35	0.0828624
$907$	1.64190e37	1.75896	0.879478	−	0.475939i	$-0.157892\pi$
$907$	1.64190e37	1.75896	0.879478	+	0.475939i	$0.157892\pi$
$908$	2.20683e36	0.233183
$909$	1.03278e36	0.107637
$910$	0	0
$911$	1.60189e37	1.62425	0.812124	−	0.583485i	$-0.198311\pi$
$911$	1.60189e37	1.62425	0.812124	+	0.583485i	$0.198311\pi$
$912$	5.47135e36	0.547217
$913$	2.58419e37	2.54941
$914$	−1.66467e35	−0.0161995
$915$	−1.78212e37	−1.71070
$916$	3.33855e36	0.316129
$917$	0	0
$918$	9.30542e36	0.857437
$919$	−1.12179e37	−1.01969	−0.509844	−	0.860267i	$-0.670297\pi$
$919$	−1.12179e37	−1.01969	−0.509844	+	0.860267i	$0.670297\pi$
$920$	5.58539e36	0.500848
$921$	1.93807e37	1.71445
$922$	1.23514e37	1.07790
$923$	1.47153e37	1.26692
$924$	0	0
$925$	−1.49797e35	−0.0125525
$926$	−1.08144e37	−0.894059
$927$	−1.15856e37	−0.944976
$928$	2.43554e36	0.195995
$929$	−1.47705e37	−1.17273	−0.586367	−	0.810045i	$-0.699442\pi$
$929$	−1.47705e37	−1.17273	−0.586367	+	0.810045i	$0.699442\pi$
$930$	−5.14158e36	−0.402773
$931$	0	0
$932$	−6.69603e35	−0.0510644
$933$	−5.01120e36	−0.377069
$934$	1.52577e36	0.113280
$935$	2.06718e37	1.51438
$936$	−4.38053e36	−0.316650
$937$	1.83686e37	1.31018	0.655089	−	0.755552i	$-0.272631\pi$
$937$	1.83686e37	1.31018	0.655089	+	0.755552i	$0.272631\pi$
$938$	0	0
$939$	2.80452e37	1.94777
$940$	−2.48618e36	−0.170386
$941$	−6.27684e36	−0.424493	−0.212246	−	0.977216i	$-0.568078\pi$
$941$	−6.27684e36	−0.424493	−0.212246	+	0.977216i	$0.568078\pi$
$942$	−2.33604e37	−1.55899
$943$	2.65613e37	1.74926
$944$	1.29595e37	0.842244
$945$	0	0
$946$	−2.61040e37	−1.65222
$947$	−1.59483e37	−0.996183	−0.498091	−	0.867125i	$-0.665966\pi$
$947$	−1.59483e37	−0.996183	−0.498091	+	0.867125i	$0.665966\pi$
$948$	−9.42572e36	−0.581046
$949$	−1.99582e37	−1.21421
$950$	−2.53256e36	−0.152060
$951$	−2.03371e37	−1.20512
$952$	0	0
$953$	7.71711e36	0.445445	0.222722	−	0.974882i	$-0.428506\pi$
$953$	7.71711e36	0.445445	0.222722	+	0.974882i	$0.428506\pi$
$954$	−3.32449e36	−0.189396
$955$	−3.83289e36	−0.215518
$956$	−5.65515e35	−0.0313849
$957$	−7.74190e36	−0.424081
$958$	3.65120e37	1.97409
$959$	0	0
$960$	−3.62210e36	−0.190796
$961$	−1.70963e37	−0.888914
$962$	7.60919e35	0.0390526
$963$	1.84670e37	0.935553
$964$	−5.13705e36	−0.256892
$965$	1.28986e37	0.636722
$966$	0	0
$967$	−3.32956e37	−1.60160	−0.800802	−	0.598929i	$-0.795593\pi$
$967$	−3.32956e37	−1.60160	−0.800802	+	0.598929i	$0.795593\pi$
$968$	1.77475e37	0.842744
$969$	−1.15923e37	−0.543406
$970$	1.15134e37	0.532793
$971$	−3.98138e36	−0.181883	−0.0909417	−	0.995856i	$-0.528988\pi$
$971$	−3.98138e36	−0.181883	−0.0909417	+	0.995856i	$0.528988\pi$
$972$	−1.02128e37	−0.460590
$973$	0	0
$974$	−2.65299e37	−1.16613
$975$	9.26594e36	0.402098
$976$	−5.00456e37	−2.14409
$977$	2.10349e37	0.889732	0.444866	−	0.895597i	$-0.353251\pi$
$977$	2.10349e37	0.889732	0.444866	+	0.895597i	$0.353251\pi$
$978$	−2.09969e37	−0.876839
$979$	−5.02116e37	−2.07024
$980$	0	0
$981$	−1.71405e37	−0.688908
$982$	1.33326e36	0.0529081
$983$	4.04322e37	1.58419	0.792096	−	0.610396i	$-0.208990\pi$
$983$	4.04322e37	1.58419	0.792096	+	0.610396i	$0.208990\pi$
$984$	−3.71224e37	−1.43614
$985$	−2.42609e37	−0.926731
$986$	−8.96020e36	−0.337953
$987$	0	0
$988$	4.11474e36	0.151314
$989$	2.39666e37	0.870267
$990$	−2.23243e37	−0.800456
$991$	4.02410e37	1.42478	0.712390	−	0.701784i	$-0.247613\pi$
$991$	4.02410e37	1.42478	0.712390	+	0.701784i	$0.247613\pi$
$992$	−8.31533e36	−0.290726
$993$	−9.04274e36	−0.312201
$994$	0	0
$995$	3.95357e36	0.133107
$996$	−2.94367e37	−0.978695
$997$	2.58476e37	0.848654	0.424327	−	0.905509i	$-0.360511\pi$
$997$	2.58476e37	0.848654	0.424327	+	0.905509i	$0.360511\pi$
$998$	−4.67200e37	−1.51485
$999$	−6.28945e35	−0.0201393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.e.1.4	yes	12
7.6	odd	2	inner	49.26.a.e.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.26.a.e.1.3	✓	12	7.6	odd	2	inner
49.26.a.e.1.4	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)

\(f(q)\)	\(=\)	\(q-7023.80 q^{2} +1.14256e6 q^{3} +1.57794e7 q^{4} -4.38325e8 q^{5} -8.02510e9 q^{6} +1.24848e11 q^{8} +4.58148e11 q^{9} +O(q^{10})\)	\(q-7023.80 q^{2} +1.14256e6 q^{3} +1.57794e7 q^{4} -4.38325e8 q^{5} -8.02510e9 q^{6} +1.24848e11 q^{8} +4.58148e11 q^{9} +3.07871e12 q^{10} -1.58272e13 q^{11} +1.80288e13 q^{12} -7.65840e13 q^{13} -5.00811e14 q^{15} -1.40638e15 q^{16} +2.97975e15 q^{17} -3.21794e15 q^{18} -3.40498e15 q^{19} -6.91649e15 q^{20} +1.11167e17 q^{22} -1.02064e17 q^{23} +1.42646e17 q^{24} -1.05895e17 q^{25} +5.37911e17 q^{26} -4.44615e17 q^{27} +4.28121e17 q^{29} +3.51760e18 q^{30} -1.46167e18 q^{31} +5.68891e18 q^{32} -1.80835e19 q^{33} -2.09291e19 q^{34} +7.22929e18 q^{36} +1.41458e18 q^{37} +2.39159e19 q^{38} -8.75016e19 q^{39} -5.47242e19 q^{40} -2.60241e20 q^{41} -2.34818e20 q^{43} -2.49743e20 q^{44} -2.00818e20 q^{45} +7.16881e20 q^{46} +3.59457e20 q^{47} -1.60687e21 q^{48} +7.43783e20 q^{50} +3.40453e21 q^{51} -1.20845e21 q^{52} +1.03311e21 q^{53} +3.12289e21 q^{54} +6.93744e21 q^{55} -3.89038e21 q^{57} -3.00704e21 q^{58} -9.21478e21 q^{59} -7.90249e21 q^{60} +3.55847e22 q^{61} +1.02665e22 q^{62} +7.23246e21 q^{64} +3.35687e22 q^{65} +1.27015e23 q^{66} +5.92207e22 q^{67} +4.70185e22 q^{68} -1.16614e23 q^{69} -1.92146e23 q^{71} +5.71991e22 q^{72} +2.60605e23 q^{73} -9.93575e21 q^{74} -1.20991e23 q^{75} -5.37285e22 q^{76} +6.14594e23 q^{78} -5.22813e23 q^{79} +6.16451e23 q^{80} -8.96182e23 q^{81} +1.82788e24 q^{82} -1.63276e24 q^{83} -1.30610e24 q^{85} +1.64932e24 q^{86} +4.89152e23 q^{87} -1.97600e24 q^{88} +3.17249e24 q^{89} +1.41050e24 q^{90} -1.61051e24 q^{92} -1.67005e24 q^{93} -2.52476e24 q^{94} +1.49249e24 q^{95} +6.49991e24 q^{96} +3.73970e24 q^{97} -7.25119e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more