LMFDB - Embedded newform 50.26.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(1,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, 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("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 25534923283x^{3} - 31863478542482x^{2} + 141941149085067124800x + 2515032055818200956928000 $ x^5 - 25534923283x^3 - 31863478542482x^2 + 141941149085067124800*x + 2515032055818200956928000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{5}\cdot 5^{12} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-18822.3$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00 q^{2} +43423.8 q^{3} +1.67772e7 q^{4} -1.77864e8 q^{6} +1.17021e10 q^{7} -6.87195e10 q^{8} -8.45403e11 q^{9} +1.64780e13 q^{11} +7.28531e11 q^{12} -1.00150e14 q^{13} -4.79317e13 q^{14} +2.81475e14 q^{16} -4.09920e15 q^{17} +3.46277e15 q^{18} +6.47386e15 q^{19} +5.08149e14 q^{21} -6.74937e16 q^{22} +1.11414e17 q^{23} -2.98406e15 q^{24} +4.10213e17 q^{26} -7.35031e16 q^{27} +1.96328e17 q^{28} -2.49627e18 q^{29} -7.13708e18 q^{31} -1.15292e18 q^{32} +7.15536e17 q^{33} +1.67903e19 q^{34} -1.41835e19 q^{36} +1.51372e19 q^{37} -2.65169e19 q^{38} -4.34889e18 q^{39} +2.55381e20 q^{41} -2.08138e18 q^{42} +1.31517e20 q^{43} +2.76454e20 q^{44} -4.56351e20 q^{46} +5.62025e20 q^{47} +1.22227e19 q^{48} -1.20413e21 q^{49} -1.78003e20 q^{51} -1.68023e21 q^{52} -5.11971e21 q^{53} +3.01069e20 q^{54} -8.04160e20 q^{56} +2.81120e20 q^{57} +1.02247e22 q^{58} +1.95274e22 q^{59} +2.40784e22 q^{61} +2.92335e22 q^{62} -9.89297e21 q^{63} +4.72237e21 q^{64} -2.93083e21 q^{66} -3.73512e22 q^{67} -6.87732e22 q^{68} +4.83801e21 q^{69} -1.22452e23 q^{71} +5.80957e22 q^{72} +1.02009e23 q^{73} -6.20018e22 q^{74} +1.08613e23 q^{76} +1.92826e23 q^{77} +1.78130e22 q^{78} -3.06262e23 q^{79} +7.13109e23 q^{81} -1.04604e24 q^{82} -1.24177e23 q^{83} +8.52532e21 q^{84} -5.38694e23 q^{86} -1.08398e23 q^{87} -1.13236e24 q^{88} +6.70415e23 q^{89} -1.17196e24 q^{91} +1.86921e24 q^{92} -3.09919e23 q^{93} -2.30205e24 q^{94} -5.00642e22 q^{96} -2.48231e24 q^{97} +4.93212e24 q^{98} -1.39305e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) $ 5 * q - 20480 * q^2 - 723995 * q^3 + 83886080 * q^4 + 2965483520 * q^6 - 49218886190 * q^7 - 343597383680 * q^8 + 975375361390 * q^9 - 8837033983815 * q^11 - 12146620497920 * q^12 - 67609989586220 * q^13 + 201600557834240 * q^14 + 1407374883553280 * q^16 - 1543441123223415 * q^17 - 3995137480253440 * q^18 + 6828205451077225 * q^19 - 56457058818760990 * q^21 + 36196491197706240 * q^22 - 175655399207336370 * q^23 + 49752557559480320 * q^24 + 276930517345157120 * q^26 - 1102363638369718625 * q^27 - 825755884889047040 * q^28 + 2616960879251719800 * q^29 + 1381921297247629210 * q^31 - 5764607523034234880 * q^32 - 14683366800887949615 * q^33 + 6321934840723107840 * q^34 + 16364083119118090240 * q^36 - 68054744257794520190 * q^37 - 27968329527612313600 * q^38 - 76418447091053627020 * q^39 + 110646765257217206385 * q^41 + 231248112921645015040 * q^42 + 169174323273383550580 * q^43 - 148260827945804759040 * q^44 + 719484515153249771520 * q^46 + 1653792144435756647460 * q^47 - 203786475763631390720 * q^48 + 4971416583743605737585 * q^49 - 954942568710765966615 * q^51 - 1134307399045763563520 * q^52 - 4245089483221901865570 * q^53 + 4515281462762367488000 * q^54 + 3382296104505536675840 * q^56 + 11353190237350969575425 * q^57 - 10719071761415044300800 * q^58 + 33041536388165595960600 * q^59 - 11589871696744004976590 * q^61 - 5660349633526289244160 * q^62 - 87882675280033083250420 * q^63 + 23611832414348226068480 * q^64 + 60143070416437041623040 * q^66 + 92154529366841541565735 * q^67 - 25894645107601849712640 * q^68 + 67961625053826065275230 * q^69 + 177839620469327433418260 * q^71 - 67027284455907697623040 * q^72 - 192252066408262024306145 * q^73 + 278752232479926354698240 * q^74 + 114558277745100036505600 * q^76 - 420363080385387083988630 * q^77 + 313009959284955656273920 * q^78 - 220198603705551780910250 * q^79 - 1595228143213014227240195 * q^81 - 453209150493561677352960 * q^82 - 1018803599085572371644645 * q^83 - 947192270527057981603840 * q^84 - 692938028127779023175680 * q^86 - 6970820850065961522685800 * q^87 + 607276351266016293027840 * q^88 - 5932331377929555403184925 * q^89 + 3355259607310216720714760 * q^91 - 2947008574067711064145920 * q^92 - 3721806140580454551574390 * q^93 - 6773932623608859227996160 * q^94 + 834709404727834176389120 * q^96 + 377622858226960257754810 * q^97 - 20362922327013809101148160 * q^98 - 23196936518287622996926170 * q^99

Coefficient data

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

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

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

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	43423.8	0.0471750	0.0235875	−	0.999722i	$-0.492491\pi$
$3$	43423.8	0.0471750	0.0235875	+	0.999722i	$0.492491\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−1.77864e8	−0.0333578
$7$	1.17021e10	0.319549	0.159774	−	0.987154i	$-0.448923\pi$
$7$	1.17021e10	0.319549	0.159774	+	0.987154i	$0.448923\pi$
$8$	−6.87195e10	−0.353553
$9$	−8.45403e11	−0.997775
$10$	0	0
$11$	1.64780e13	1.58305	0.791525	−	0.611137i	$-0.209287\pi$
$11$	1.64780e13	1.58305	0.791525	+	0.611137i	$0.209287\pi$
$12$	7.28531e11	0.0235875
$13$	−1.00150e14	−1.19222	−0.596112	−	0.802901i	$-0.703289\pi$
$13$	−1.00150e14	−1.19222	−0.596112	+	0.802901i	$0.703289\pi$
$14$	−4.79317e13	−0.225955
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−4.09920e15	−1.70643	−0.853214	−	0.521561i	$-0.825350\pi$
$17$	−4.09920e15	−1.70643	−0.853214	+	0.521561i	$0.825350\pi$
$18$	3.46277e15	0.705533
$19$	6.47386e15	0.671032	0.335516	−	0.942035i	$-0.391089\pi$
$19$	6.47386e15	0.671032	0.335516	+	0.942035i	$0.391089\pi$
$20$	0	0
$21$	5.08149e14	0.0150747
$22$	−6.74937e16	−1.11939
$23$	1.11414e17	1.06009	0.530043	−	0.847971i	$-0.322176\pi$
$23$	1.11414e17	1.06009	0.530043	+	0.847971i	$0.322176\pi$
$24$	−2.98406e15	−0.0166789
$25$	0	0
$26$	4.10213e17	0.843030
$27$	−7.35031e16	−0.0942451
$28$	1.96328e17	0.159774
$29$	−2.49627e18	−1.31014	−0.655070	−	0.755569i	$-0.727361\pi$
$29$	−2.49627e18	−1.31014	−0.655070	+	0.755569i	$0.727361\pi$
$30$	0	0
$31$	−7.13708e18	−1.62742	−0.813710	−	0.581271i	$-0.802556\pi$
$31$	−7.13708e18	−1.62742	−0.813710	+	0.581271i	$0.802556\pi$
$32$	−1.15292e18	−0.176777
$33$	7.15536e17	0.0746805
$34$	1.67903e19	1.20663
$35$	0	0
$36$	−1.41835e19	−0.498887
$37$	1.51372e19	0.378027	0.189013	−	0.981974i	$-0.439471\pi$
$37$	1.51372e19	0.378027	0.189013	+	0.981974i	$0.439471\pi$
$38$	−2.65169e19	−0.474491
$39$	−4.34889e18	−0.0562432
$40$	0	0
$41$	2.55381e20	1.76762	0.883811	−	0.467843i	$-0.154969\pi$
$41$	2.55381e20	1.76762	0.883811	+	0.467843i	$0.154969\pi$
$42$	−2.08138e18	−0.0106594
$43$	1.31517e20	0.501911	0.250955	−	0.967999i	$-0.419255\pi$
$43$	1.31517e20	0.501911	0.250955	+	0.967999i	$0.419255\pi$
$44$	2.76454e20	0.791525
$45$	0	0
$46$	−4.56351e20	−0.749594
$47$	5.62025e20	0.705557	0.352778	−	0.935707i	$-0.385237\pi$
$47$	5.62025e20	0.705557	0.352778	+	0.935707i	$0.385237\pi$
$48$	1.22227e19	0.0117938
$49$	−1.20413e21	−0.897889
$50$	0	0
$51$	−1.78003e20	−0.0805008
$52$	−1.68023e21	−0.596112
$53$	−5.11971e21	−1.43152	−0.715759	−	0.698348i	$-0.753919\pi$
$53$	−5.11971e21	−1.43152	−0.715759	+	0.698348i	$0.753919\pi$
$54$	3.01069e20	0.0666413
$55$	0	0
$56$	−8.04160e20	−0.112978
$57$	2.81120e20	0.0316560
$58$	1.02247e22	0.926408
$59$	1.95274e22	1.42888	0.714438	−	0.699699i	$-0.246682\pi$
$59$	1.95274e22	1.42888	0.714438	+	0.699699i	$0.246682\pi$
$60$	0	0
$61$	2.40784e22	1.16146	0.580731	−	0.814096i	$-0.302767\pi$
$61$	2.40784e22	1.16146	0.580731	+	0.814096i	$0.302767\pi$
$62$	2.92335e22	1.15076
$63$	−9.89297e21	−0.318838
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−2.93083e21	−0.0528071
$67$	−3.73512e22	−0.557660	−0.278830	−	0.960340i	$-0.589947\pi$
$67$	−3.73512e22	−0.557660	−0.278830	+	0.960340i	$0.589947\pi$
$68$	−6.87732e22	−0.853214
$69$	4.83801e21	0.0500096
$70$	0	0
$71$	−1.22452e23	−0.885601	−0.442800	−	0.896620i	$-0.646015\pi$
$71$	−1.22452e23	−0.885601	−0.442800	+	0.896620i	$0.646015\pi$
$72$	5.80957e22	0.352767
$73$	1.02009e23	0.521316	0.260658	−	0.965431i	$-0.416060\pi$
$73$	1.02009e23	0.521316	0.260658	+	0.965431i	$0.416060\pi$
$74$	−6.20018e22	−0.267305
$75$	0	0
$76$	1.08613e23	0.335516
$77$	1.92826e23	0.505862
$78$	1.78130e22	0.0397700
$79$	−3.06262e23	−0.583115	−0.291558	−	0.956553i	$-0.594173\pi$
$79$	−3.06262e23	−0.583115	−0.291558	+	0.956553i	$0.594173\pi$
$80$	0	0
$81$	7.13109e23	0.993328
$82$	−1.04604e24	−1.24990
$83$	−1.24177e23	−0.127516	−0.0637581	−	0.997965i	$-0.520309\pi$
$83$	−1.24177e23	−0.127516	−0.0637581	+	0.997965i	$0.520309\pi$
$84$	8.52532e21	0.00753736
$85$	0	0
$86$	−5.38694e23	−0.354905
$87$	−1.08398e23	−0.0618059
$88$	−1.13236e24	−0.559693
$89$	6.70415e23	0.287719	0.143859	−	0.989598i	$-0.454049\pi$
$89$	6.70415e23	0.287719	0.143859	+	0.989598i	$0.454049\pi$
$90$	0	0
$91$	−1.17196e24	−0.380974
$92$	1.86921e24	0.530043
$93$	−3.09919e23	−0.0767736
$94$	−2.30205e24	−0.498904
$95$	0	0
$96$	−5.00642e22	−0.00833945
$97$	−2.48231e24	−0.363253	−0.181626	−	0.983368i	$-0.558136\pi$
$97$	−2.48231e24	−0.363253	−0.181626	+	0.983368i	$0.558136\pi$
$98$	4.93212e24	0.634903
$99$	−1.39305e25	−1.57953
$100$	0	0
$101$	5.99639e24	0.529508	0.264754	−	0.964316i	$-0.414709\pi$
$101$	5.99639e24	0.529508	0.264754	+	0.964316i	$0.414709\pi$
$102$	7.29100e23	0.0569227
$103$	−1.43755e25	−0.993474	−0.496737	−	0.867901i	$-0.665469\pi$
$103$	−1.43755e25	−0.993474	−0.496737	+	0.867901i	$0.665469\pi$
$104$	6.88224e24	0.421515
$105$	0	0
$106$	2.09703e25	1.01224
$107$	−2.52288e25	−1.08293	−0.541463	−	0.840725i	$-0.682129\pi$
$107$	−2.52288e25	−1.08293	−0.541463	+	0.840725i	$0.682129\pi$
$108$	−1.23318e24	−0.0471225
$109$	1.90602e25	0.649078	0.324539	−	0.945872i	$-0.394791\pi$
$109$	1.90602e25	0.649078	0.324539	+	0.945872i	$0.394791\pi$
$110$	0	0
$111$	6.57313e23	0.0178334
$112$	3.29384e24	0.0798872
$113$	−7.00404e25	−1.52009	−0.760043	−	0.649873i	$-0.774822\pi$
$113$	−7.00404e25	−1.52009	−0.760043	+	0.649873i	$0.774822\pi$
$114$	−1.15147e24	−0.0223841
$115$	0	0
$116$	−4.18805e25	−0.655070
$117$	8.46669e25	1.18957
$118$	−7.99843e25	−1.01037
$119$	−4.79692e25	−0.545287
$120$	0	0
$121$	1.63176e26	1.50605
$122$	−9.86252e25	−0.821277
$123$	1.10896e25	0.0833877
$124$	−1.19740e26	−0.813710
$125$	0	0
$126$	4.05216e25	0.225452
$127$	−1.37993e26	−0.695519	−0.347759	−	0.937584i	$-0.613057\pi$
$127$	−1.37993e26	−0.695519	−0.347759	+	0.937584i	$0.613057\pi$
$128$	−1.93428e25	−0.0883883
$129$	5.71097e24	0.0236777
$130$	0	0
$131$	−5.92280e25	−0.202598	−0.101299	−	0.994856i	$-0.532300\pi$
$131$	−5.92280e25	−0.202598	−0.101299	+	0.994856i	$0.532300\pi$
$132$	1.20047e25	0.0373402
$133$	7.57576e25	0.214427
$134$	1.52991e26	0.394325
$135$	0	0
$136$	2.81695e26	0.603313
$137$	−4.40818e26	−0.861494	−0.430747	−	0.902473i	$-0.641750\pi$
$137$	−4.40818e26	−0.861494	−0.430747	+	0.902473i	$0.641750\pi$
$138$	−1.98165e25	−0.0353621
$139$	−8.03278e26	−1.30973	−0.654863	−	0.755747i	$-0.727274\pi$
$139$	−8.03278e26	−1.30973	−0.654863	+	0.755747i	$0.727274\pi$
$140$	0	0
$141$	2.44053e25	0.0332847
$142$	5.01565e26	0.626214
$143$	−1.65026e27	−1.88735
$144$	−2.37960e26	−0.249444
$145$	0	0
$146$	−4.17828e26	−0.368626
$147$	−5.22879e25	−0.0423579
$148$	2.53959e26	0.189013
$149$	1.20493e27	0.824393	0.412197	−	0.911095i	$-0.364762\pi$
$149$	1.20493e27	0.824393	0.412197	+	0.911095i	$0.364762\pi$
$150$	0	0
$151$	1.12194e27	0.649767	0.324884	−	0.945754i	$-0.394675\pi$
$151$	1.12194e27	0.649767	0.324884	+	0.945754i	$0.394675\pi$
$152$	−4.44880e26	−0.237246
$153$	3.46548e27	1.70263
$154$	−7.89816e26	−0.357698
$155$	0	0
$156$	−7.29622e25	−0.0281216
$157$	−7.34635e26	−0.261412	−0.130706	−	0.991421i	$-0.541724\pi$
$157$	−7.34635e26	−0.261412	−0.130706	+	0.991421i	$0.541724\pi$
$158$	1.25445e27	0.412325
$159$	−2.22317e26	−0.0675319
$160$	0	0
$161$	1.30377e27	0.338749
$162$	−2.92089e27	−0.702389
$163$	−3.30397e27	−0.735683	−0.367841	−	0.929889i	$-0.619903\pi$
$163$	−3.30397e27	−0.735683	−0.367841	+	0.929889i	$0.619903\pi$
$164$	4.28457e27	0.883811
$165$	0	0
$166$	5.08629e26	0.0901676
$167$	8.04476e27	1.32299	0.661496	−	0.749949i	$-0.269922\pi$
$167$	8.04476e27	1.32299	0.661496	+	0.749949i	$0.269922\pi$
$168$	−3.49197e25	−0.00532972
$169$	2.97357e27	0.421399
$170$	0	0
$171$	−5.47302e27	−0.669539
$172$	2.20649e27	0.250955
$173$	1.78239e28	1.88550	0.942749	−	0.333504i	$-0.108231\pi$
$173$	1.78239e28	1.88550	0.942749	+	0.333504i	$0.108231\pi$
$174$	4.43997e26	0.0437033
$175$	0	0
$176$	4.63813e27	0.395763
$177$	8.47955e26	0.0674073
$178$	−2.74602e27	−0.203448
$179$	2.18421e28	1.50880	0.754399	−	0.656416i	$-0.227928\pi$
$179$	2.18421e28	1.50880	0.754399	+	0.656416i	$0.227928\pi$
$180$	0	0
$181$	3.17113e27	0.190648	0.0953238	−	0.995446i	$-0.469611\pi$
$181$	3.17113e27	0.190648	0.0953238	+	0.995446i	$0.469611\pi$
$182$	4.80035e27	0.269389
$183$	1.04558e27	0.0547920
$184$	−7.65630e27	−0.374797
$185$	0	0
$186$	1.26943e27	0.0542871
$187$	−6.75465e28	−2.70136
$188$	9.42921e27	0.352778
$189$	−8.60139e26	−0.0301159
$190$	0	0
$191$	3.72320e28	1.14288	0.571439	−	0.820645i	$-0.306385\pi$
$191$	3.72320e28	1.14288	0.571439	+	0.820645i	$0.306385\pi$
$192$	2.05063e26	0.00589688
$193$	5.76046e28	1.55235	0.776176	−	0.630516i	$-0.217157\pi$
$193$	5.76046e28	1.55235	0.776176	+	0.630516i	$0.217157\pi$
$194$	1.01675e28	0.256859
$195$	0	0
$196$	−2.02020e28	−0.448944
$197$	7.70781e28	1.60732	0.803662	−	0.595086i	$-0.202882\pi$
$197$	7.70781e28	1.60732	0.803662	+	0.595086i	$0.202882\pi$
$198$	5.70594e28	1.11689
$199$	−3.56814e28	−0.655811	−0.327906	−	0.944711i	$-0.606343\pi$
$199$	−3.56814e28	−0.655811	−0.327906	+	0.944711i	$0.606343\pi$
$200$	0	0
$201$	−1.62193e27	−0.0263076
$202$	−2.45612e28	−0.374419
$203$	−2.92116e28	−0.418653
$204$	−2.98640e27	−0.0402504
$205$	0	0
$206$	5.88819e28	0.702492
$207$	−9.41896e28	−1.05773
$208$	−2.81897e28	−0.298056
$209$	1.06676e29	1.06228
$210$	0	0
$211$	1.75441e29	1.55096	0.775480	−	0.631373i	$-0.217508\pi$
$211$	1.75441e29	1.55096	0.775480	+	0.631373i	$0.217508\pi$
$212$	−8.58944e28	−0.715759
$213$	−5.31735e27	−0.0417783
$214$	1.03337e29	0.765744
$215$	0	0
$216$	5.05110e27	0.0333207
$217$	−8.35187e28	−0.520040
$218$	−7.80707e28	−0.458968
$219$	4.42961e27	0.0245931
$220$	0	0
$221$	4.10534e29	2.03445
$222$	−2.69235e27	−0.0126101
$223$	3.77614e29	1.67200	0.836001	−	0.548728i	$-0.184888\pi$
$223$	3.77614e29	1.67200	0.836001	+	0.548728i	$0.184888\pi$
$224$	−1.34916e28	−0.0564888
$225$	0	0
$226$	2.86886e29	1.07486
$227$	−4.12672e29	−1.46312	−0.731562	−	0.681774i	$-0.761209\pi$
$227$	−4.12672e29	−1.46312	−0.731562	+	0.681774i	$0.761209\pi$
$228$	4.71641e27	0.0158280
$229$	−1.29184e29	−0.410454	−0.205227	−	0.978714i	$-0.565793\pi$
$229$	−1.29184e29	−0.410454	−0.205227	+	0.978714i	$0.565793\pi$
$230$	0	0
$231$	8.37325e27	0.0238641
$232$	1.71543e29	0.463204
$233$	−4.29301e29	−1.09853	−0.549266	−	0.835648i	$-0.685093\pi$
$233$	−4.29301e29	−1.09853	−0.549266	+	0.835648i	$0.685093\pi$
$234$	−3.46796e29	−0.841154
$235$	0	0
$236$	3.27616e29	0.714438
$237$	−1.32991e28	−0.0275085
$238$	1.96482e29	0.385576
$239$	6.70528e29	1.24866	0.624329	−	0.781162i	$-0.285373\pi$
$239$	6.70528e29	1.24866	0.624329	+	0.781162i	$0.285373\pi$
$240$	0	0
$241$	8.94387e29	1.50076	0.750382	−	0.661004i	$-0.229870\pi$
$241$	8.94387e29	1.50076	0.750382	+	0.661004i	$0.229870\pi$
$242$	−6.68368e29	−1.06494
$243$	9.32443e28	0.141105
$244$	4.03969e29	0.580731
$245$	0	0
$246$	−4.54230e28	−0.0589640
$247$	−6.48356e29	−0.800021
$248$	4.90457e29	0.575380
$249$	−5.39224e27	−0.00601558
$250$	0	0
$251$	1.46535e30	1.47917	0.739587	−	0.673061i	$-0.235021\pi$
$251$	1.46535e30	1.47917	0.739587	+	0.673061i	$0.235021\pi$
$252$	−1.65976e29	−0.159419
$253$	1.83587e30	1.67817
$254$	5.65217e29	0.491806
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−1.69807e30	−1.27582	−0.637912	−	0.770110i	$-0.720201\pi$
$257$	−1.69807e30	−1.27582	−0.637912	+	0.770110i	$0.720201\pi$
$258$	−2.33922e28	−0.0167426
$259$	1.77136e29	0.120798
$260$	0	0
$261$	2.11036e30	1.30722
$262$	2.42598e29	0.143259
$263$	2.11180e30	1.18907	0.594534	−	0.804070i	$-0.297336\pi$
$263$	2.11180e30	1.18907	0.594534	+	0.804070i	$0.297336\pi$
$264$	−4.91712e28	−0.0264035
$265$	0	0
$266$	−3.10303e29	−0.151623
$267$	2.91120e28	0.0135731
$268$	−6.26649e29	−0.278830
$269$	−1.68743e30	−0.716676	−0.358338	−	0.933592i	$-0.616656\pi$
$269$	−1.68743e30	−0.716676	−0.358338	+	0.933592i	$0.616656\pi$
$270$	0	0
$271$	−1.00044e30	−0.387324	−0.193662	−	0.981068i	$-0.562036\pi$
$271$	−1.00044e30	−0.387324	−0.193662	+	0.981068i	$0.562036\pi$
$272$	−1.15382e30	−0.426607
$273$	−5.08910e28	−0.0179725
$274$	1.80559e30	0.609168
$275$	0	0
$276$	8.11684e28	0.0250048
$277$	−7.83715e29	−0.230760	−0.115380	−	0.993321i	$-0.536809\pi$
$277$	−7.83715e29	−0.230760	−0.115380	+	0.993321i	$0.536809\pi$
$278$	3.29023e30	0.926117
$279$	6.03371e30	1.62380
$280$	0	0
$281$	1.80627e30	0.444584	0.222292	−	0.974980i	$-0.428646\pi$
$281$	1.80627e30	0.444584	0.222292	+	0.974980i	$0.428646\pi$
$282$	−9.99639e28	−0.0235358
$283$	4.85439e30	1.09346	0.546732	−	0.837308i	$-0.315872\pi$
$283$	4.85439e30	1.09346	0.546732	+	0.837308i	$0.315872\pi$
$284$	−2.05441e30	−0.442800
$285$	0	0
$286$	6.75948e30	1.33456
$287$	2.98848e30	0.564842
$288$	9.74683e29	0.176383
$289$	1.10328e31	1.91190
$290$	0	0
$291$	−1.07791e29	−0.0171365
$292$	1.71142e30	0.260658
$293$	1.46069e30	0.213163	0.106582	−	0.994304i	$-0.466009\pi$
$293$	1.46069e30	0.213163	0.106582	+	0.994304i	$0.466009\pi$
$294$	2.14171e29	0.0299516
$295$	0	0
$296$	−1.04022e30	−0.133653
$297$	−1.21118e30	−0.149195
$298$	−4.93541e30	−0.582934
$299$	−1.11581e31	−1.26386
$300$	0	0
$301$	1.53902e30	0.160385
$302$	−4.59547e30	−0.459455
$303$	2.60386e29	0.0249796
$304$	1.82223e30	0.167758
$305$	0	0
$306$	−1.41946e31	−1.20394
$307$	1.83807e30	0.149669	0.0748345	−	0.997196i	$-0.476157\pi$
$307$	1.83807e30	0.149669	0.0748345	+	0.997196i	$0.476157\pi$
$308$	3.23509e30	0.252931
$309$	−6.24238e29	−0.0468672
$310$	0	0
$311$	−3.33152e30	−0.230748	−0.115374	−	0.993322i	$-0.536807\pi$
$311$	−3.33152e30	−0.230748	−0.115374	+	0.993322i	$0.536807\pi$
$312$	2.98853e29	0.0198850
$313$	−3.48183e30	−0.222589	−0.111294	−	0.993787i	$-0.535500\pi$
$313$	−3.48183e30	−0.222589	−0.111294	+	0.993787i	$0.535500\pi$
$314$	3.00907e30	0.184846
$315$	0	0
$316$	−5.13822e30	−0.291558
$317$	3.11024e30	0.169650	0.0848249	−	0.996396i	$-0.472967\pi$
$317$	3.11024e30	0.169650	0.0848249	+	0.996396i	$0.472967\pi$
$318$	9.10611e29	0.0477523
$319$	−4.11335e31	−2.07402
$320$	0	0
$321$	−1.09553e30	−0.0510871
$322$	−5.34025e30	−0.239532
$323$	−2.65377e31	−1.14507
$324$	1.19640e31	0.496664
$325$	0	0
$326$	1.35330e31	0.520206
$327$	8.27668e29	0.0306203
$328$	−1.75496e31	−0.624949
$329$	6.57685e30	0.225460
$330$	0	0
$331$	2.69668e31	0.856998	0.428499	−	0.903542i	$-0.359043\pi$
$331$	2.69668e31	0.856998	0.428499	+	0.903542i	$0.359043\pi$
$332$	−2.08335e30	−0.0637581
$333$	−1.27970e31	−0.377186
$334$	−3.29513e31	−0.935497
$335$	0	0
$336$	1.43031e29	0.00376868
$337$	4.07016e31	1.03333	0.516664	−	0.856188i	$-0.327174\pi$
$337$	4.07016e31	1.03333	0.516664	+	0.856188i	$0.327174\pi$
$338$	−1.21797e31	−0.297974
$339$	−3.04142e30	−0.0717101
$340$	0	0
$341$	−1.17605e32	−2.57629
$342$	2.24175e31	0.473435
$343$	−2.97841e31	−0.606468
$344$	−9.03779e30	−0.177452
$345$	0	0
$346$	−7.30066e31	−1.33325
$347$	1.58471e31	0.279145	0.139573	−	0.990212i	$-0.455427\pi$
$347$	1.58471e31	0.279145	0.139573	+	0.990212i	$0.455427\pi$
$348$	−1.81861e30	−0.0309029
$349$	−2.28191e30	−0.0374094	−0.0187047	−	0.999825i	$-0.505954\pi$
$349$	−2.28191e30	−0.0374094	−0.0187047	+	0.999825i	$0.505954\pi$
$350$	0	0
$351$	7.36132e30	0.112361
$352$	−1.89978e31	−0.279846
$353$	−8.46470e31	−1.20345	−0.601725	−	0.798704i	$-0.705520\pi$
$353$	−8.46470e31	−1.20345	−0.601725	+	0.798704i	$0.705520\pi$
$354$	−3.47322e30	−0.0476642
$355$	0	0
$356$	1.12477e31	0.143859
$357$	−2.08300e30	−0.0257239
$358$	−8.94652e31	−1.06688
$359$	−2.47468e31	−0.284996	−0.142498	−	0.989795i	$-0.545513\pi$
$359$	−2.47468e31	−0.284996	−0.142498	+	0.989795i	$0.545513\pi$
$360$	0	0
$361$	−5.11656e31	−0.549716
$362$	−1.29889e31	−0.134808
$363$	7.08572e30	0.0710479
$364$	−1.96622e31	−0.190487
$365$	0	0
$366$	−4.28268e30	−0.0387438
$367$	2.15791e32	1.88672	0.943359	−	0.331773i	$-0.107647\pi$
$367$	2.15791e32	1.88672	0.943359	+	0.331773i	$0.107647\pi$
$368$	3.13602e31	0.265022
$369$	−2.15899e32	−1.76369
$370$	0	0
$371$	−5.99112e31	−0.457440
$372$	−5.19958e30	−0.0383868
$373$	1.43569e32	1.02494	0.512471	−	0.858705i	$-0.328730\pi$
$373$	1.43569e32	1.02494	0.512471	+	0.858705i	$0.328730\pi$
$374$	2.76670e32	1.91015
$375$	0	0
$376$	−3.86220e31	−0.249452
$377$	2.50001e32	1.56198
$378$	3.52313e30	0.0212952
$379$	1.53691e32	0.898791	0.449396	−	0.893333i	$-0.351639\pi$
$379$	1.53691e32	0.898791	0.449396	+	0.893333i	$0.351639\pi$
$380$	0	0
$381$	−5.99216e30	−0.0328111
$382$	−1.52502e32	−0.808137
$383$	−2.05714e32	−1.05506	−0.527532	−	0.849535i	$-0.676882\pi$
$383$	−2.05714e32	−1.05506	−0.527532	+	0.849535i	$0.676882\pi$
$384$	−8.39939e29	−0.00416972
$385$	0	0
$386$	−2.35948e32	−1.09768
$387$	−1.11185e32	−0.500794
$388$	−4.16462e31	−0.181626
$389$	−1.97058e32	−0.832192	−0.416096	−	0.909321i	$-0.636602\pi$
$389$	−1.97058e32	−0.832192	−0.416096	+	0.909321i	$0.636602\pi$
$390$	0	0
$391$	−4.56708e32	−1.80896
$392$	8.27472e31	0.317452
$393$	−2.57191e30	−0.00955759
$394$	−3.15712e32	−1.13655
$395$	0	0
$396$	−2.33715e32	−0.789764
$397$	2.04618e31	0.0669980	0.0334990	−	0.999439i	$-0.489335\pi$
$397$	2.04618e31	0.0669980	0.0334990	+	0.999439i	$0.489335\pi$
$398$	1.46151e32	0.463728
$399$	3.28968e30	0.0101156
$400$	0	0
$401$	4.79432e32	1.38491	0.692456	−	0.721460i	$-0.256529\pi$
$401$	4.79432e32	1.38491	0.692456	+	0.721460i	$0.256529\pi$
$402$	6.64343e30	0.0186023
$403$	7.14777e32	1.94025
$404$	1.00603e32	0.264754
$405$	0	0
$406$	1.19651e32	0.296033
$407$	2.49429e32	0.598436
$408$	1.22323e31	0.0284613
$409$	2.61432e32	0.589952	0.294976	−	0.955505i	$-0.404688\pi$
$409$	2.61432e32	0.589952	0.294976	+	0.955505i	$0.404688\pi$
$410$	0	0
$411$	−1.91420e31	−0.0406410
$412$	−2.41180e32	−0.496737
$413$	2.28511e32	0.456596
$414$	3.85801e32	0.747926
$415$	0	0
$416$	1.15465e32	0.210758
$417$	−3.48814e31	−0.0617864
$418$	−4.36945e32	−0.751144
$419$	−2.37687e32	−0.396579	−0.198290	−	0.980143i	$-0.563539\pi$
$419$	−2.37687e32	−0.396579	−0.198290	+	0.980143i	$0.563539\pi$
$420$	0	0
$421$	7.17539e32	1.12803	0.564013	−	0.825766i	$-0.309257\pi$
$421$	7.17539e32	1.12803	0.564013	+	0.825766i	$0.309257\pi$
$422$	−7.18606e32	−1.09669
$423$	−4.75137e32	−0.703987
$424$	3.51824e32	0.506118
$425$	0	0
$426$	2.17799e31	0.0295417
$427$	2.81767e32	0.371144
$428$	−4.23269e32	−0.541463
$429$	−7.16607e31	−0.0890359
$430$	0	0
$431$	4.94839e32	0.580094	0.290047	−	0.957012i	$-0.406329\pi$
$431$	4.94839e32	0.580094	0.290047	+	0.957012i	$0.406329\pi$
$432$	−2.06893e31	−0.0235613
$433$	−1.87459e32	−0.207399	−0.103700	−	0.994609i	$-0.533068\pi$
$433$	−1.87459e32	−0.207399	−0.103700	+	0.994609i	$0.533068\pi$
$434$	3.42092e32	0.367724
$435$	0	0
$436$	3.19778e32	0.324539
$437$	7.21278e32	0.711352
$438$	−1.81437e31	−0.0173900
$439$	−2.54653e32	−0.237215	−0.118607	−	0.992941i	$-0.537843\pi$
$439$	−2.54653e32	−0.237215	−0.118607	+	0.992941i	$0.537843\pi$
$440$	0	0
$441$	1.01798e33	0.895890
$442$	−1.68155e33	−1.43857
$443$	1.63920e33	1.36328	0.681642	−	0.731685i	$-0.261266\pi$
$443$	1.63920e33	1.36328	0.681642	+	0.731685i	$0.261266\pi$
$444$	1.10279e31	0.00891672
$445$	0	0
$446$	−1.54671e33	−1.18228
$447$	5.23228e31	0.0388908
$448$	5.52615e31	0.0399436
$449$	−1.07131e33	−0.753068	−0.376534	−	0.926403i	$-0.622884\pi$
$449$	−1.07131e33	−0.753068	−0.376534	+	0.926403i	$0.622884\pi$
$450$	0	0
$451$	4.20815e33	2.79824
$452$	−1.17508e33	−0.760043
$453$	4.87189e31	0.0306528
$454$	1.69030e33	1.03459
$455$	0	0
$456$	−1.93184e31	−0.0111921
$457$	−1.92628e33	−1.08584	−0.542921	−	0.839784i	$-0.682682\pi$
$457$	−1.92628e33	−1.08584	−0.542921	+	0.839784i	$0.682682\pi$
$458$	5.29137e32	0.290235
$459$	3.01304e32	0.160822
$460$	0	0
$461$	1.76482e33	0.892152	0.446076	−	0.894995i	$-0.352821\pi$
$461$	1.76482e33	0.892152	0.446076	+	0.894995i	$0.352821\pi$
$462$	−3.42968e31	−0.0168744
$463$	−6.39982e32	−0.306482	−0.153241	−	0.988189i	$-0.548971\pi$
$463$	−6.39982e32	−0.306482	−0.153241	+	0.988189i	$0.548971\pi$
$464$	−7.02639e32	−0.327535
$465$	0	0
$466$	1.75842e33	0.776779
$467$	−1.87926e33	−0.808213	−0.404106	−	0.914712i	$-0.632417\pi$
$467$	−1.87926e33	−0.808213	−0.404106	+	0.914712i	$0.632417\pi$
$468$	1.42048e33	0.594786
$469$	−4.37087e32	−0.178200
$470$	0	0
$471$	−3.19007e31	−0.0123321
$472$	−1.34191e33	−0.505184
$473$	2.16713e33	0.794550
$474$	5.44729e31	0.0194514
$475$	0	0
$476$	−8.04789e32	−0.272643
$477$	4.32821e33	1.42833
$478$	−2.74648e33	−0.882934
$479$	−4.49267e32	−0.140705	−0.0703527	−	0.997522i	$-0.522412\pi$
$479$	−4.49267e32	−0.140705	−0.0703527	+	0.997522i	$0.522412\pi$
$480$	0	0
$481$	−1.51598e33	−0.450693
$482$	−3.66341e33	−1.06120
$483$	5.66148e31	0.0159805
$484$	2.73764e33	0.753024
$485$	0	0
$486$	−3.81928e32	−0.0997766
$487$	4.38487e33	1.11646	0.558232	−	0.829685i	$-0.311480\pi$
$487$	4.38487e33	1.11646	0.558232	+	0.829685i	$0.311480\pi$
$488$	−1.65466e33	−0.410639
$489$	−1.43471e32	−0.0347059
$490$	0	0
$491$	8.31613e33	1.91162	0.955812	−	0.293978i	$-0.0949794\pi$
$491$	8.31613e33	1.91162	0.955812	+	0.293978i	$0.0949794\pi$
$492$	1.86053e32	0.0416938
$493$	1.02327e34	2.23566
$494$	2.65566e33	0.565700
$495$	0	0
$496$	−2.00891e33	−0.406855
$497$	−1.43295e33	−0.282993
$498$	2.20866e31	0.00425366
$499$	−5.09164e33	−0.956315	−0.478158	−	0.878274i	$-0.658695\pi$
$499$	−5.09164e33	−0.956315	−0.478158	+	0.878274i	$0.658695\pi$
$500$	0	0
$501$	3.49334e32	0.0624122
$502$	−6.00207e33	−1.04593
$503$	1.81699e33	0.308853	0.154427	−	0.988004i	$-0.450647\pi$
$503$	1.81699e33	0.308853	0.154427	+	0.988004i	$0.450647\pi$
$504$	6.79839e32	0.112726
$505$	0	0
$506$	−7.51973e33	−1.18665
$507$	1.29124e32	0.0198795
$508$	−2.31513e33	−0.347759
$509$	5.80999e33	0.851537	0.425768	−	0.904832i	$-0.360004\pi$
$509$	5.80999e33	0.851537	0.425768	+	0.904832i	$0.360004\pi$
$510$	0	0
$511$	1.19371e33	0.166586
$512$	−3.24519e32	−0.0441942
$513$	−4.75849e32	−0.0632415
$514$	6.95528e33	0.902143
$515$	0	0
$516$	9.58143e31	0.0118388
$517$	9.26101e33	1.11693
$518$	−7.25549e32	−0.0854171
$519$	7.73981e32	0.0889484
$520$	0	0
$521$	−5.31585e33	−0.582238	−0.291119	−	0.956687i	$-0.594028\pi$
$521$	−5.31585e33	−0.582238	−0.291119	+	0.956687i	$0.594028\pi$
$522$	−8.64403e33	−0.924347
$523$	6.52606e33	0.681365	0.340682	−	0.940178i	$-0.389342\pi$
$523$	6.52606e33	0.681365	0.340682	+	0.940178i	$0.389342\pi$
$524$	−9.93681e32	−0.101299
$525$	0	0
$526$	−8.64995e33	−0.840798
$527$	2.92564e34	2.77707
$528$	2.01405e32	0.0186701
$529$	1.36728e33	0.123783
$530$	0	0
$531$	−1.65085e34	−1.42570
$532$	1.27100e33	0.107214
$533$	−2.55763e34	−2.10740
$534$	−1.19243e32	−0.00959767
$535$	0	0
$536$	2.56676e33	0.197163
$537$	9.48467e32	0.0711776
$538$	6.91172e33	0.506766
$539$	−1.98416e34	−1.42140
$540$	0	0
$541$	1.24335e34	0.850410	0.425205	−	0.905097i	$-0.360202\pi$
$541$	1.24335e34	0.850410	0.425205	+	0.905097i	$0.360202\pi$
$542$	4.09779e33	0.273879
$543$	1.37702e32	0.00899381
$544$	4.72606e33	0.301657
$545$	0	0
$546$	2.08449e32	0.0127084
$547$	−1.77086e34	−1.05522	−0.527610	−	0.849487i	$-0.676912\pi$
$547$	−1.77086e34	−1.05522	−0.527610	+	0.849487i	$0.676912\pi$
$548$	−7.39570e33	−0.430747
$549$	−2.03560e34	−1.15888
$550$	0	0
$551$	−1.61605e34	−0.879145
$552$	−3.32466e32	−0.0176811
$553$	−3.58390e33	−0.186334
$554$	3.21010e33	0.163172
$555$	0	0
$556$	−1.34768e34	−0.654863
$557$	8.12072e33	0.385838	0.192919	−	0.981215i	$-0.438205\pi$
$557$	8.12072e33	0.385838	0.192919	+	0.981215i	$0.438205\pi$
$558$	−2.47141e34	−1.14820
$559$	−1.31714e34	−0.598390
$560$	0	0
$561$	−2.93313e33	−0.127437
$562$	−7.39849e33	−0.314369
$563$	1.21025e34	0.502946	0.251473	−	0.967864i	$-0.419085\pi$
$563$	1.21025e34	0.502946	0.251473	+	0.967864i	$0.419085\pi$
$564$	4.09452e32	0.0166423
$565$	0	0
$566$	−1.98836e34	−0.773195
$567$	8.34485e33	0.317417
$568$	8.41487e33	0.313107
$569$	−9.61211e33	−0.349877	−0.174938	−	0.984579i	$-0.555973\pi$
$569$	−9.61211e33	−0.349877	−0.174938	+	0.984579i	$0.555973\pi$
$570$	0	0
$571$	−1.48318e34	−0.516704	−0.258352	−	0.966051i	$-0.583179\pi$
$571$	−1.48318e34	−0.516704	−0.258352	+	0.966051i	$0.583179\pi$
$572$	−2.76868e34	−0.943676
$573$	1.61676e33	0.0539153
$574$	−1.22408e34	−0.399403
$575$	0	0
$576$	−3.99230e33	−0.124722
$577$	4.94604e34	1.51203	0.756014	−	0.654556i	$-0.227144\pi$
$577$	4.94604e34	1.51203	0.756014	+	0.654556i	$0.227144\pi$
$578$	−4.51905e34	−1.35191
$579$	2.50141e33	0.0732323
$580$	0	0
$581$	−1.45313e33	−0.0407477
$582$	4.41513e32	0.0121173
$583$	−8.43623e34	−2.26616
$584$	−7.00998e33	−0.184313
$585$	0	0
$586$	−5.98297e33	−0.150729
$587$	5.81688e34	1.43454	0.717272	−	0.696793i	$-0.245390\pi$
$587$	5.81688e34	1.43454	0.717272	+	0.696793i	$0.245390\pi$
$588$	−8.77246e32	−0.0211790
$589$	−4.62045e34	−1.09205
$590$	0	0
$591$	3.34703e33	0.0758256
$592$	4.26073e33	0.0945067
$593$	−1.10616e34	−0.240234	−0.120117	−	0.992760i	$-0.538327\pi$
$593$	−1.10616e34	−0.240234	−0.120117	+	0.992760i	$0.538327\pi$
$594$	4.96100e33	0.105497
$595$	0	0
$596$	2.02154e34	0.412197
$597$	−1.54942e33	−0.0309379
$598$	4.57035e34	0.893685
$599$	7.59828e34	1.45506	0.727529	−	0.686077i	$-0.240669\pi$
$599$	7.59828e34	1.45506	0.727529	+	0.686077i	$0.240669\pi$
$600$	0	0
$601$	3.55188e34	0.652421	0.326210	−	0.945297i	$-0.394228\pi$
$601$	3.55188e34	0.652421	0.326210	+	0.945297i	$0.394228\pi$
$602$	−6.30384e33	−0.113409
$603$	3.15768e34	0.556419
$604$	1.88230e34	0.324884
$605$	0	0
$606$	−1.06654e33	−0.0176632
$607$	−7.28541e34	−1.18194	−0.590970	−	0.806694i	$-0.701255\pi$
$607$	−7.28541e34	−1.18194	−0.590970	+	0.806694i	$0.701255\pi$
$608$	−7.46385e33	−0.118623
$609$	−1.26848e33	−0.0197500
$610$	0	0
$611$	−5.62866e34	−0.841182
$612$	5.81411e34	0.851315
$613$	1.55275e34	0.222765	0.111382	−	0.993778i	$-0.464472\pi$
$613$	1.55275e34	0.222765	0.111382	+	0.993778i	$0.464472\pi$
$614$	−7.52872e33	−0.105832
$615$	0	0
$616$	−1.32509e34	−0.178849
$617$	−1.18825e35	−1.57160	−0.785800	−	0.618481i	$-0.787748\pi$
$617$	−1.18825e35	−1.57160	−0.785800	+	0.618481i	$0.787748\pi$
$618$	2.55688e33	0.0331401
$619$	−1.31383e34	−0.166881	−0.0834406	−	0.996513i	$-0.526591\pi$
$619$	−1.31383e34	−0.166881	−0.0834406	+	0.996513i	$0.526591\pi$
$620$	0	0
$621$	−8.18927e33	−0.0999079
$622$	1.36459e34	0.163163
$623$	7.84524e33	0.0919402
$624$	−1.22410e33	−0.0140608
$625$	0	0
$626$	1.42616e34	0.157394
$627$	4.63228e33	0.0501130
$628$	−1.23251e34	−0.130706
$629$	−6.20503e34	−0.645076
$630$	0	0
$631$	1.62969e35	1.62831	0.814154	−	0.580649i	$-0.197201\pi$
$631$	1.62969e35	1.62831	0.814154	+	0.580649i	$0.197201\pi$
$632$	2.10462e34	0.206162
$633$	7.61832e33	0.0731666
$634$	−1.27395e34	−0.119961
$635$	0	0
$636$	−3.72986e33	−0.0337659
$637$	1.20593e35	1.07048
$638$	1.68483e35	1.46655
$639$	1.03522e35	0.883630
$640$	0	0
$641$	−2.15302e35	−1.76735	−0.883675	−	0.468100i	$-0.844939\pi$
$641$	−2.15302e35	−1.76735	−0.883675	+	0.468100i	$0.844939\pi$
$642$	4.48729e33	0.0361240
$643$	9.81888e34	0.775220	0.387610	−	0.921823i	$-0.373301\pi$
$643$	9.81888e34	0.775220	0.387610	+	0.921823i	$0.373301\pi$
$644$	2.18737e34	0.169375
$645$	0	0
$646$	1.08698e35	0.809685
$647$	−9.66650e34	−0.706262	−0.353131	−	0.935574i	$-0.614883\pi$
$647$	−9.66650e34	−0.706262	−0.353131	+	0.935574i	$0.614883\pi$
$648$	−4.90044e34	−0.351195
$649$	3.21772e35	2.26198
$650$	0	0
$651$	−3.62670e33	−0.0245329
$652$	−5.54314e34	−0.367841
$653$	2.65692e35	1.72967	0.864835	−	0.502056i	$-0.167423\pi$
$653$	2.65692e35	1.72967	0.864835	+	0.502056i	$0.167423\pi$
$654$	−3.39013e33	−0.0216518
$655$	0	0
$656$	7.18832e34	0.441906
$657$	−8.62384e34	−0.520156
$658$	−2.69388e34	−0.159424
$659$	−1.12403e35	−0.652697	−0.326348	−	0.945250i	$-0.605818\pi$
$659$	−1.12403e35	−0.652697	−0.326348	+	0.945250i	$0.605818\pi$
$660$	0	0
$661$	1.74137e35	0.973582	0.486791	−	0.873518i	$-0.338167\pi$
$661$	1.74137e35	0.973582	0.486791	+	0.873518i	$0.338167\pi$
$662$	−1.10456e35	−0.605989
$663$	1.78270e34	0.0959750
$664$	8.53339e33	0.0450838
$665$	0	0
$666$	5.24165e34	0.266711
$667$	−2.78120e35	−1.38886
$668$	1.34969e35	0.661496
$669$	1.63974e34	0.0788768
$670$	0	0
$671$	3.96763e35	1.83865
$672$	−5.85855e32	−0.00266486
$673$	7.64859e34	0.341502	0.170751	−	0.985314i	$-0.445381\pi$
$673$	7.64859e34	0.341502	0.170751	+	0.985314i	$0.445381\pi$
$674$	−1.66714e35	−0.730673
$675$	0	0
$676$	4.98882e34	0.210700
$677$	−3.11236e34	−0.129042	−0.0645211	−	0.997916i	$-0.520552\pi$
$677$	−3.11236e34	−0.129042	−0.0645211	+	0.997916i	$0.520552\pi$
$678$	1.24577e34	0.0507067
$679$	−2.90481e34	−0.116077
$680$	0	0
$681$	−1.79198e34	−0.0690230
$682$	4.81708e35	1.82171
$683$	−1.85231e35	−0.687790	−0.343895	−	0.939008i	$-0.611746\pi$
$683$	−1.85231e35	−0.687790	−0.343895	+	0.939008i	$0.611746\pi$
$684$	−9.18220e34	−0.334769
$685$	0	0
$686$	1.21996e35	0.428838
$687$	−5.60966e33	−0.0193632
$688$	3.70188e34	0.125478
$689$	5.12737e35	1.70669
$690$	0	0
$691$	−4.90286e35	−1.57389	−0.786944	−	0.617024i	$-0.788338\pi$
$691$	−4.90286e35	−1.57389	−0.786944	+	0.617024i	$0.788338\pi$
$692$	2.99035e35	0.942749
$693$	−1.63016e35	−0.504736
$694$	−6.49096e34	−0.197386
$695$	0	0
$696$	7.44904e33	0.0218517
$697$	−1.04686e36	−3.01632
$698$	9.34669e33	0.0264524
$699$	−1.86419e34	−0.0518233
$700$	0	0
$701$	4.65445e35	1.24851	0.624257	−	0.781219i	$-0.285402\pi$
$701$	4.65445e35	1.24851	0.624257	+	0.781219i	$0.285402\pi$
$702$	−3.01520e34	−0.0794514
$703$	9.79958e34	0.253668
$704$	7.78149e34	0.197881
$705$	0	0
$706$	3.46714e35	0.850967
$707$	7.01702e34	0.169204
$708$	1.42263e34	0.0337036
$709$	−1.61968e35	−0.377009	−0.188504	−	0.982072i	$-0.560364\pi$
$709$	−1.61968e35	−0.377009	−0.188504	+	0.982072i	$0.560364\pi$
$710$	0	0
$711$	2.58915e35	0.581817
$712$	−4.60705e34	−0.101724
$713$	−7.95170e35	−1.72521
$714$	8.53198e33	0.0181896
$715$	0	0
$716$	3.66449e35	0.754399
$717$	2.91169e34	0.0589055
$718$	1.01363e35	0.201523
$719$	3.86289e35	0.754747	0.377374	−	0.926061i	$-0.376827\pi$
$719$	3.86289e35	0.754747	0.377374	+	0.926061i	$0.376827\pi$
$720$	0	0
$721$	−1.68223e35	−0.317464
$722$	2.09574e35	0.388708
$723$	3.88377e34	0.0707986
$724$	5.32027e34	0.0953238
$725$	0	0
$726$	−2.90231e34	−0.0502384
$727$	3.11776e35	0.530471	0.265236	−	0.964184i	$-0.414550\pi$
$727$	3.11776e35	0.530471	0.265236	+	0.964184i	$0.414550\pi$
$728$	8.05365e34	0.134695
$729$	−6.00160e35	−0.986672
$730$	0	0
$731$	−5.39115e35	−0.856474
$732$	1.75419e34	0.0273960
$733$	2.23983e35	0.343886	0.171943	−	0.985107i	$-0.444995\pi$
$733$	2.23983e35	0.343886	0.171943	+	0.985107i	$0.444995\pi$
$734$	−8.83879e35	−1.33411
$735$	0	0
$736$	−1.28451e35	−0.187399
$737$	−6.15471e35	−0.882804
$738$	8.84324e35	1.24712
$739$	5.23044e34	0.0725241	0.0362621	−	0.999342i	$-0.488455\pi$
$739$	5.23044e34	0.0725241	0.0362621	+	0.999342i	$0.488455\pi$
$740$	0	0
$741$	−2.81541e34	−0.0377410
$742$	2.45396e35	0.323459
$743$	−7.47724e35	−0.969127	−0.484564	−	0.874756i	$-0.661022\pi$
$743$	−7.47724e35	−0.969127	−0.484564	+	0.874756i	$0.661022\pi$
$744$	2.12975e34	0.0271436
$745$	0	0
$746$	−5.88057e35	−0.724743
$747$	1.04980e35	0.127232
$748$	−1.13324e36	−1.35068
$749$	−2.95229e35	−0.346048
$750$	0	0
$751$	−1.40867e36	−1.59702	−0.798510	−	0.601982i	$-0.794378\pi$
$751$	−1.40867e36	−1.59702	−0.798510	+	0.601982i	$0.794378\pi$
$752$	1.58196e35	0.176389
$753$	6.36310e34	0.0697801
$754$	−1.02401e36	−1.10449
$755$	0	0
$756$	−1.44307e34	−0.0150580
$757$	1.39455e36	1.43132	0.715658	−	0.698451i	$-0.246127\pi$
$757$	1.39455e36	1.43132	0.715658	+	0.698451i	$0.246127\pi$
$758$	−6.29519e35	−0.635541
$759$	7.97206e34	0.0791677
$760$	0	0
$761$	−1.19222e36	−1.14564	−0.572818	−	0.819682i	$-0.694150\pi$
$761$	−1.19222e36	−1.14564	−0.572818	+	0.819682i	$0.694150\pi$
$762$	2.45439e34	0.0232010
$763$	2.23044e35	0.207412
$764$	6.24650e35	0.571439
$765$	0	0
$766$	8.42603e35	0.746042
$767$	−1.95567e36	−1.70354
$768$	3.44039e33	0.00294844
$769$	4.70446e35	0.396671	0.198336	−	0.980134i	$-0.436446\pi$
$769$	4.70446e35	0.396671	0.198336	+	0.980134i	$0.436446\pi$
$770$	0	0
$771$	−7.37365e34	−0.0601870
$772$	9.66444e35	0.776176
$773$	−4.82216e35	−0.381064	−0.190532	−	0.981681i	$-0.561021\pi$
$773$	−4.82216e35	−0.381064	−0.190532	+	0.981681i	$0.561021\pi$
$774$	4.55414e35	0.354115
$775$	0	0
$776$	1.70583e35	0.128429
$777$	7.69192e33	0.00569865
$778$	8.07148e35	0.588448
$779$	1.65330e36	1.18613
$780$	0	0
$781$	−2.01777e36	−1.40195
$782$	1.87068e36	1.27913
$783$	1.83484e35	0.123474
$784$	−3.38933e35	−0.224472
$785$	0	0
$786$	1.05345e34	0.00675824
$787$	1.69806e36	1.07219	0.536093	−	0.844159i	$-0.319900\pi$
$787$	1.69806e36	1.07219	0.536093	+	0.844159i	$0.319900\pi$
$788$	1.29316e36	0.803662
$789$	9.17026e34	0.0560944
$790$	0	0
$791$	−8.19618e35	−0.485742
$792$	9.57297e35	0.558447
$793$	−2.41145e36	−1.38472
$794$	−8.38114e34	−0.0473747
$795$	0	0
$796$	−5.98635e35	−0.327906
$797$	2.41463e36	1.30203	0.651017	−	0.759063i	$-0.274343\pi$
$797$	2.41463e36	1.30203	0.651017	+	0.759063i	$0.274343\pi$
$798$	−1.34745e34	−0.00715283
$799$	−2.30385e36	−1.20398
$800$	0	0
$801$	−5.66770e35	−0.287079
$802$	−1.96375e36	−0.979281
$803$	1.68089e36	0.825270
$804$	−2.72115e34	−0.0131538
$805$	0	0
$806$	−2.92773e36	−1.37196
$807$	−7.32747e34	−0.0338092
$808$	−4.12069e35	−0.187209
$809$	−4.34243e35	−0.194257	−0.0971283	−	0.995272i	$-0.530966\pi$
$809$	−4.34243e35	−0.194257	−0.0971283	+	0.995272i	$0.530966\pi$
$810$	0	0
$811$	−1.52344e35	−0.0660792	−0.0330396	−	0.999454i	$-0.510519\pi$
$811$	−1.52344e35	−0.0660792	−0.0330396	+	0.999454i	$0.510519\pi$
$812$	−4.90089e35	−0.209327
$813$	−4.34428e34	−0.0182720
$814$	−1.02166e36	−0.423158
$815$	0	0
$816$	−5.01034e34	−0.0201252
$817$	8.51423e35	0.336798
$818$	−1.07082e36	−0.417159
$819$	9.90778e35	0.380126
$820$	0	0
$821$	1.12855e36	0.419983	0.209992	−	0.977703i	$-0.432656\pi$
$821$	1.12855e36	0.419983	0.209992	+	0.977703i	$0.432656\pi$
$822$	7.84056e34	0.0287375
$823$	−3.43120e36	−1.23865	−0.619325	−	0.785135i	$-0.712594\pi$
$823$	−3.43120e36	−1.23865	−0.619325	+	0.785135i	$0.712594\pi$
$824$	9.87875e35	0.351246
$825$	0	0
$826$	−9.35982e35	−0.322862
$827$	−2.18743e36	−0.743216	−0.371608	−	0.928390i	$-0.621193\pi$
$827$	−2.18743e36	−0.743216	−0.371608	+	0.928390i	$0.621193\pi$
$828$	−1.58024e36	−0.528864
$829$	2.16830e36	0.714804	0.357402	−	0.933951i	$-0.383663\pi$
$829$	2.16830e36	0.714804	0.357402	+	0.933951i	$0.383663\pi$
$830$	0	0
$831$	−3.40319e34	−0.0108861
$832$	−4.72944e35	−0.149028
$833$	4.93597e36	1.53218
$834$	1.42874e35	0.0436896
$835$	0	0
$836$	1.78973e36	0.531139
$837$	5.24598e35	0.153376
$838$	9.73566e35	0.280424
$839$	−6.23659e36	−1.76980	−0.884898	−	0.465786i	$-0.845772\pi$
$839$	−6.23659e36	−1.76980	−0.884898	+	0.465786i	$0.845772\pi$
$840$	0	0
$841$	2.60103e36	0.716465
$842$	−2.93904e36	−0.797635
$843$	7.84352e34	0.0209733
$844$	2.94341e36	0.775480
$845$	0	0
$846$	1.94616e36	0.497794
$847$	1.90950e36	0.481256
$848$	−1.44107e36	−0.357879
$849$	2.10796e35	0.0515842
$850$	0	0
$851$	1.68649e36	0.400741
$852$	−8.92103e34	−0.0208891
$853$	1.57022e36	0.362325	0.181163	−	0.983453i	$-0.442014\pi$
$853$	1.57022e36	0.362325	0.181163	+	0.983453i	$0.442014\pi$
$854$	−1.15412e36	−0.262438
$855$	0	0
$856$	1.73371e36	0.382872
$857$	−1.90353e36	−0.414284	−0.207142	−	0.978311i	$-0.566416\pi$
$857$	−1.90353e36	−0.414284	−0.207142	+	0.978311i	$0.566416\pi$
$858$	2.93522e35	0.0629579
$859$	1.49712e36	0.316476	0.158238	−	0.987401i	$-0.449419\pi$
$859$	1.49712e36	0.316476	0.158238	+	0.987401i	$0.449419\pi$
$860$	0	0
$861$	1.29771e35	0.0266464
$862$	−2.02686e36	−0.410188
$863$	−6.49700e36	−1.29592	−0.647960	−	0.761675i	$-0.724378\pi$
$863$	−6.49700e36	−1.29592	−0.647960	+	0.761675i	$0.724378\pi$
$864$	8.47433e34	0.0166603
$865$	0	0
$866$	7.67830e35	0.146653
$867$	4.79088e35	0.0901937
$868$	−1.40121e36	−0.260020
$869$	−5.04657e36	−0.923101
$870$	0	0
$871$	3.74072e36	0.664856
$872$	−1.30981e36	−0.229484
$873$	2.09855e36	0.362444
$874$	−2.95435e36	−0.503002
$875$	0	0
$876$	7.43165e34	0.0122966
$877$	−4.25958e36	−0.694819	−0.347410	−	0.937713i	$-0.612939\pi$
$877$	−4.25958e36	−0.694819	−0.347410	+	0.937713i	$0.612939\pi$
$878$	1.04306e36	0.167736
$879$	6.34286e34	0.0100560
$880$	0	0
$881$	1.17230e36	0.180652	0.0903258	−	0.995912i	$-0.471209\pi$
$881$	1.17230e36	0.180652	0.0903258	+	0.995912i	$0.471209\pi$
$882$	−4.16963e36	−0.633490
$883$	8.13959e36	1.21925	0.609626	−	0.792689i	$-0.291320\pi$
$883$	8.13959e36	1.21925	0.609626	+	0.792689i	$0.291320\pi$
$884$	6.88762e36	1.01722
$885$	0	0
$886$	−6.71418e36	−0.963988
$887$	−3.20938e36	−0.454335	−0.227168	−	0.973856i	$-0.572947\pi$
$887$	−3.20938e36	−0.454335	−0.227168	+	0.973856i	$0.572947\pi$
$888$	−4.51702e34	−0.00630507
$889$	−1.61480e36	−0.222252
$890$	0	0
$891$	1.17506e37	1.57249
$892$	6.33530e36	0.836001
$893$	3.63847e36	0.473451
$894$	−2.14314e35	−0.0274999
$895$	0	0
$896$	−2.26351e35	−0.0282444
$897$	−4.84526e35	−0.0596227
$898$	4.38807e36	0.532499
$899$	1.78161e37	2.13215
$900$	0	0
$901$	2.09867e37	2.44278
$902$	−1.72366e37	−1.97865
$903$	6.68302e34	0.00756617
$904$	4.81314e36	0.537432
$905$	0	0
$906$	−1.99553e35	−0.0216748
$907$	1.37794e37	1.47618	0.738091	−	0.674702i	$-0.235728\pi$
$907$	1.37794e37	1.47618	0.738091	+	0.674702i	$0.235728\pi$
$908$	−6.92348e36	−0.731562
$909$	−5.06937e36	−0.528330
$910$	0	0
$911$	1.00864e37	1.02272	0.511359	−	0.859367i	$-0.329142\pi$
$911$	1.00864e37	1.02272	0.511359	+	0.859367i	$0.329142\pi$
$912$	7.91282e34	0.00791399
$913$	−2.04618e36	−0.201865
$914$	7.89003e36	0.767806
$915$	0	0
$916$	−2.16735e36	−0.205227
$917$	−6.93090e35	−0.0647401
$918$	−1.23414e36	−0.113719
$919$	−1.70873e37	−1.55321	−0.776603	−	0.629991i	$-0.783059\pi$
$919$	−1.70873e37	−1.55321	−0.776603	+	0.629991i	$0.783059\pi$
$920$	0	0
$921$	7.98159e34	0.00706064
$922$	−7.22870e36	−0.630846
$923$	1.22636e37	1.05584
$924$	1.40480e35	0.0119320
$925$	0	0
$926$	2.62137e36	0.216716
$927$	1.21531e37	0.991263
$928$	2.87801e36	0.231602
$929$	1.39851e37	1.11037	0.555185	−	0.831727i	$-0.312647\pi$
$929$	1.39851e37	1.11037	0.555185	+	0.831727i	$0.312647\pi$
$930$	0	0
$931$	−7.79537e36	−0.602512
$932$	−7.20247e36	−0.549266
$933$	−1.44667e35	−0.0108855
$934$	7.69744e36	0.571493
$935$	0	0
$936$	−5.81827e36	−0.420577
$937$	−5.96148e36	−0.425216	−0.212608	−	0.977138i	$-0.568196\pi$
$937$	−5.96148e36	−0.425216	−0.212608	+	0.977138i	$0.568196\pi$
$938$	1.79031e36	0.126006
$939$	−1.51194e35	−0.0105006
$940$	0	0
$941$	−2.77897e37	−1.87937	−0.939686	−	0.342038i	$-0.888883\pi$
$941$	−2.77897e37	−1.87937	−0.939686	+	0.342038i	$0.888883\pi$
$942$	1.30665e35	0.00872014
$943$	2.84529e37	1.87383
$944$	5.49648e36	0.357219
$945$	0	0
$946$	−8.87658e36	−0.561832
$947$	3.29072e36	0.205549	0.102775	−	0.994705i	$-0.467228\pi$
$947$	3.29072e36	0.205549	0.102775	+	0.994705i	$0.467228\pi$
$948$	−2.23121e35	−0.0137542
$949$	−1.02161e37	−0.621526
$950$	0	0
$951$	1.35059e35	0.00800324
$952$	3.29642e36	0.192788
$953$	−3.30322e36	−0.190667	−0.0953337	−	0.995445i	$-0.530392\pi$
$953$	−3.30322e36	−0.190667	−0.0953337	+	0.995445i	$0.530392\pi$
$954$	−1.77284e37	−1.00998
$955$	0	0
$956$	1.12496e37	0.624329
$957$	−1.78617e36	−0.0978418
$958$	1.84020e36	0.0994938
$959$	−5.15848e36	−0.275289
$960$	0	0
$961$	3.17052e37	1.64850
$962$	6.20947e36	0.318688
$963$	2.13285e37	1.08052
$964$	1.50053e37	0.750382
$965$	0	0
$966$	−2.31894e35	−0.0112999
$967$	−1.07284e37	−0.516064	−0.258032	−	0.966136i	$-0.583074\pi$
$967$	−1.07284e37	−0.516064	−0.258032	+	0.966136i	$0.583074\pi$
$968$	−1.12134e37	−0.532468
$969$	−1.15237e36	−0.0540186
$970$	0	0
$971$	−3.81170e36	−0.174132	−0.0870659	−	0.996203i	$-0.527749\pi$
$971$	−3.81170e36	−0.174132	−0.0870659	+	0.996203i	$0.527749\pi$
$972$	1.56438e36	0.0705527
$973$	−9.40001e36	−0.418522
$974$	−1.79604e37	−0.789459
$975$	0	0
$976$	6.77747e36	0.290365
$977$	4.24334e37	1.79484	0.897420	−	0.441178i	$-0.145439\pi$
$977$	4.24334e37	1.79484	0.897420	+	0.441178i	$0.145439\pi$
$978$	5.87657e35	0.0245408
$979$	1.10471e37	0.455473
$980$	0	0
$981$	−1.61136e37	−0.647634
$982$	−3.40629e37	−1.35172
$983$	−2.83202e37	−1.10963	−0.554814	−	0.831974i	$-0.687211\pi$
$983$	−2.83202e37	−1.10963	−0.554814	+	0.831974i	$0.687211\pi$
$984$	−7.62071e35	−0.0294820
$985$	0	0
$986$	−4.19133e37	−1.58085
$987$	2.85592e35	0.0106361
$988$	−1.08776e37	−0.400010
$989$	1.46528e37	0.532069
$990$	0	0
$991$	−2.64697e37	−0.937193	−0.468596	−	0.883412i	$-0.655240\pi$
$991$	−2.64697e37	−0.937193	−0.468596	+	0.883412i	$0.655240\pi$
$992$	8.22850e36	0.287690
$993$	1.17100e36	0.0404289
$994$	5.86935e36	0.200106
$995$	0	0
$996$	−9.04668e34	−0.00300779
$997$	2.72983e37	0.896287	0.448143	−	0.893962i	$-0.352085\pi$
$997$	2.72983e37	0.896287	0.448143	+	0.893962i	$0.352085\pi$
$998$	2.08554e37	0.676217
$999$	−1.11263e36	−0.0356272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.i.1.3	✓	5
5.2	odd	4		50.26.b.h.49.3		10
5.3	odd	4		50.26.b.h.49.8		10
5.4	even	2		50.26.a.j.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.26.a.i.1.3	✓	5	1.1	even	1	trivial
50.26.a.j.1.3	yes	5	5.4	even	2
50.26.b.h.49.3		10	5.2	odd	4
50.26.b.h.49.8		10	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +43423.8 q^{3} +1.67772e7 q^{4} -1.77864e8 q^{6} +1.17021e10 q^{7} -6.87195e10 q^{8} -8.45403e11 q^{9} +1.64780e13 q^{11} +7.28531e11 q^{12} -1.00150e14 q^{13} -4.79317e13 q^{14} +2.81475e14 q^{16} -4.09920e15 q^{17} +3.46277e15 q^{18} +6.47386e15 q^{19} +5.08149e14 q^{21} -6.74937e16 q^{22} +1.11414e17 q^{23} -2.98406e15 q^{24} +4.10213e17 q^{26} -7.35031e16 q^{27} +1.96328e17 q^{28} -2.49627e18 q^{29} -7.13708e18 q^{31} -1.15292e18 q^{32} +7.15536e17 q^{33} +1.67903e19 q^{34} -1.41835e19 q^{36} +1.51372e19 q^{37} -2.65169e19 q^{38} -4.34889e18 q^{39} +2.55381e20 q^{41} -2.08138e18 q^{42} +1.31517e20 q^{43} +2.76454e20 q^{44} -4.56351e20 q^{46} +5.62025e20 q^{47} +1.22227e19 q^{48} -1.20413e21 q^{49} -1.78003e20 q^{51} -1.68023e21 q^{52} -5.11971e21 q^{53} +3.01069e20 q^{54} -8.04160e20 q^{56} +2.81120e20 q^{57} +1.02247e22 q^{58} +1.95274e22 q^{59} +2.40784e22 q^{61} +2.92335e22 q^{62} -9.89297e21 q^{63} +4.72237e21 q^{64} -2.93083e21 q^{66} -3.73512e22 q^{67} -6.87732e22 q^{68} +4.83801e21 q^{69} -1.22452e23 q^{71} +5.80957e22 q^{72} +1.02009e23 q^{73} -6.20018e22 q^{74} +1.08613e23 q^{76} +1.92826e23 q^{77} +1.78130e22 q^{78} -3.06262e23 q^{79} +7.13109e23 q^{81} -1.04604e24 q^{82} -1.24177e23 q^{83} +8.52532e21 q^{84} -5.38694e23 q^{86} -1.08398e23 q^{87} -1.13236e24 q^{88} +6.70415e23 q^{89} -1.17196e24 q^{91} +1.86921e24 q^{92} -3.09919e23 q^{93} -2.30205e24 q^{94} -5.00642e22 q^{96} -2.48231e24 q^{97} +4.93212e24 q^{98} -1.39305e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20480 q^{2} - 723995 q^{3} + 83886080 q^{4} + 2965483520 q^{6} - 49218886190 q^{7} - 343597383680 q^{8} + 975375361390 q^{9} - 8837033983815 q^{11} - 12146620497920 q^{12} - 67609989586220 q^{13}+ \cdots - 23\!\cdots\!70 q^{99}+O(q^{100}) \) 5 * q - 20480 * q^2 - 723995 * q^3 + 83886080 * q^4 + 2965483520 * q^6 - 49218886190 * q^7 - 343597383680 * q^8 + 975375361390 * q^9 - 8837033983815 * q^11 - 12146620497920 * q^12 - 67609989586220 * q^13 + 201600557834240 * q^14 + 1407374883553280 * q^16 - 1543441123223415 * q^17 - 3995137480253440 * q^18 + 6828205451077225 * q^19 - 56457058818760990 * q^21 + 36196491197706240 * q^22 - 175655399207336370 * q^23 + 49752557559480320 * q^24 + 276930517345157120 * q^26 - 1102363638369718625 * q^27 - 825755884889047040 * q^28 + 2616960879251719800 * q^29 + 1381921297247629210 * q^31 - 5764607523034234880 * q^32 - 14683366800887949615 * q^33 + 6321934840723107840 * q^34 + 16364083119118090240 * q^36 - 68054744257794520190 * q^37 - 27968329527612313600 * q^38 - 76418447091053627020 * q^39 + 110646765257217206385 * q^41 + 231248112921645015040 * q^42 + 169174323273383550580 * q^43 - 148260827945804759040 * q^44 + 719484515153249771520 * q^46 + 1653792144435756647460 * q^47 - 203786475763631390720 * q^48 + 4971416583743605737585 * q^49 - 954942568710765966615 * q^51 - 1134307399045763563520 * q^52 - 4245089483221901865570 * q^53 + 4515281462762367488000 * q^54 + 3382296104505536675840 * q^56 + 11353190237350969575425 * q^57 - 10719071761415044300800 * q^58 + 33041536388165595960600 * q^59 - 11589871696744004976590 * q^61 - 5660349633526289244160 * q^62 - 87882675280033083250420 * q^63 + 23611832414348226068480 * q^64 + 60143070416437041623040 * q^66 + 92154529366841541565735 * q^67 - 25894645107601849712640 * q^68 + 67961625053826065275230 * q^69 + 177839620469327433418260 * q^71 - 67027284455907697623040 * q^72 - 192252066408262024306145 * q^73 + 278752232479926354698240 * q^74 + 114558277745100036505600 * q^76 - 420363080385387083988630 * q^77 + 313009959284955656273920 * q^78 - 220198603705551780910250 * q^79 - 1595228143213014227240195 * q^81 - 453209150493561677352960 * q^82 - 1018803599085572371644645 * q^83 - 947192270527057981603840 * q^84 - 692938028127779023175680 * q^86 - 6970820850065961522685800 * q^87 + 607276351266016293027840 * q^88 - 5932331377929555403184925 * q^89 + 3355259607310216720714760 * q^91 - 2947008574067711064145920 * q^92 - 3721806140580454551574390 * q^93 - 6773932623608859227996160 * q^94 + 834709404727834176389120 * q^96 + 377622858226960257754810 * q^97 - 20362922327013809101148160 * q^98 - 23196936518287622996926170 * q^99

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