LMFDB - Embedded newform 25.38.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,38,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 38, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 38 $
Character orbit:	$[\chi]$	$=$	25.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:	$216.785095312$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 481549068639 x^{16} + \cdots - 94\!\cdots\!56 $ x^18 - 481549068639x^16 + 93985965632669777852076x^14 - 9628368566809387473030890752468224x^12 + 560141172354070767376864400274123366345670656x^10 - 18546934724816320070044693242782989845297920321809022976x^8 + 324939831814575640345464640472992367787298129881716003189098020864x^6 - 2370422361889416509431397077280114217555992479156444172822242462880734642176x^4 + 1228913418955626210538188759121588894935204618869926387774623804097150250958584807424x^2 - 94567986416239745059180217502439958544533873348778114712636267676791575291958859488355680256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{103}\cdot 3^{40}\cdot 5^{86}\cdot 7^{4}\cdot 11\cdot 29 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$365161.$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+730322. q^{2} -5.29568e8 q^{3} +3.95932e11 q^{4} -3.86755e14 q^{6} +5.41167e15 q^{7} +1.88783e17 q^{8} -1.69842e17 q^{9} +O(q^{10})$	\(q+730322. q^{2} -5.29568e8 q^{3} +3.95932e11 q^{4} -3.86755e14 q^{6} +5.41167e15 q^{7} +1.88783e17 q^{8} -1.69842e17 q^{9} -6.63770e18 q^{11} -2.09673e20 q^{12} +4.65701e20 q^{13} +3.95227e21 q^{14} +8.34562e22 q^{16} +1.91195e22 q^{17} -1.24040e23 q^{18} +1.81662e23 q^{19} -2.86585e24 q^{21} -4.84766e24 q^{22} +1.31296e24 q^{23} -9.99735e25 q^{24} +3.40112e26 q^{26} +3.28399e26 q^{27} +2.14265e27 q^{28} -2.45865e26 q^{29} -5.34172e27 q^{31} +3.50037e28 q^{32} +3.51511e27 q^{33} +1.39634e28 q^{34} -6.72459e28 q^{36} +4.86366e28 q^{37} +1.32672e29 q^{38} -2.46620e29 q^{39} -2.76259e29 q^{41} -2.09299e30 q^{42} -3.62958e29 q^{43} -2.62808e30 q^{44} +9.58886e29 q^{46} +3.33770e30 q^{47} -4.41957e31 q^{48} +1.07241e31 q^{49} -1.01251e31 q^{51} +1.84386e32 q^{52} +1.06131e32 q^{53} +2.39837e32 q^{54} +1.02163e33 q^{56} -9.62025e31 q^{57} -1.79560e32 q^{58} +4.05466e32 q^{59} -6.56338e32 q^{61} -3.90118e33 q^{62} -9.19130e32 q^{63} +1.40939e34 q^{64} +2.56716e33 q^{66} +8.53897e33 q^{67} +7.57003e33 q^{68} -6.95302e32 q^{69} -2.08929e34 q^{71} -3.20633e34 q^{72} +1.73246e34 q^{73} +3.55204e34 q^{74} +7.19259e34 q^{76} -3.59210e34 q^{77} -1.80112e35 q^{78} -9.67376e34 q^{79} -9.74321e34 q^{81} -2.01758e35 q^{82} +2.94893e35 q^{83} -1.13468e36 q^{84} -2.65077e35 q^{86} +1.30202e35 q^{87} -1.25309e36 q^{88} -1.89676e36 q^{89} +2.52022e36 q^{91} +5.19844e35 q^{92} +2.82880e36 q^{93} +2.43760e36 q^{94} -1.85368e37 q^{96} -4.70513e36 q^{97} +7.83203e36 q^{98} +1.12736e36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+O(q^{10}) $ 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9	$ 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+ \cdots + 56\!\cdots\!28 q^{99}+O(q^{100}) $ 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9 + 33986627223034798296 * q^11 + 1891478635206760615032 * q^14 + 156966361562724410096928 * q^16 + 302760323265144477867480 * q^19 - 4075600057180968977719704 * q^21 + 149013794188298144591103840 * q^24 + 740755125071253494506988496 * q^26 + 4979198281142680608411084420 * q^29 - 6151542350452781958579360384 * q^31 - 4353870657762813132282760128 * q^34 + 106785265488844195864724376888 * q^36 - 862865339998466438248367480112 * q^39 - 855196121794787398902389240124 * q^41 + 13806087517221679193940877688352 * q^44 + 21104472252831571358912888976456 * q^46 + 70801883273781655273950124330026 * q^49 - 23706017526907962630925223712384 * q^51 + 523190901027760133510234826308880 * q^54 + 600728793662143364055878849971680 * q^56 + 3947688162499809731531683814232840 * q^59 + 1757475029942100801736311637166796 * q^61 + 35293446897899611856499858227515776 * q^64 + 32483717310049996392729278134533792 * q^66 + 29536156423306266276087371479398168 * q^69 - 15852144098617191882453852538452144 * q^71 - 35174192734582932814586482689499248 * q^74 - 8033980639764558547374281250927840 * q^76 + 81628804120848018323973892688639520 * q^79 - 51387579768336601107744192991686822 * q^81 - 3799290048936464645757894225695060448 * q^84 - 3995229770967016576777180478600492424 * q^86 - 5941001429647591369362270403151043540 * q^89 + 2681006692210129770276250954718747856 * q^91 - 2447341171808746326507906787285919208 * q^94 - 2375166431920457136532866502177021824 * q^96 + 56285732505135601101448147731191891928 * 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 $

$2$	730322.	1.96997	0.984985	−	0.172638i	$-0.0552292\pi$
$2$	730322.	1.96997	0.984985	+	0.172638i	$0.0552292\pi$
$3$	−5.29568e8	−0.789184	−0.394592	−	0.918856i	$-0.629114\pi$
$3$	−5.29568e8	−0.789184	−0.394592	+	0.918856i	$0.629114\pi$
$4$	3.95932e11	2.88078
$5$	0	0
$5$	0	0
$6$	−3.86755e14	−1.55467
$7$	5.41167e15	1.25608	0.628041	−	0.778181i	$-0.283857\pi$
$7$	5.41167e15	1.25608	0.628041	+	0.778181i	$0.283857\pi$
$8$	1.88783e17	3.70509
$9$	−1.69842e17	−0.377189
$10$	0	0
$11$	−6.63770e18	−0.359959	−0.179979	−	0.983670i	$-0.557603\pi$
$11$	−6.63770e18	−0.359959	−0.179979	+	0.983670i	$0.557603\pi$
$12$	−2.09673e20	−2.27347
$13$	4.65701e20	1.14856	0.574282	−	0.818658i	$-0.305281\pi$
$13$	4.65701e20	1.14856	0.574282	+	0.818658i	$0.305281\pi$
$14$	3.95227e21	2.47444
$15$	0	0
$16$	8.34562e22	4.41813
$17$	1.91195e22	0.329740	0.164870	−	0.986315i	$-0.447279\pi$
$17$	1.91195e22	0.329740	0.164870	+	0.986315i	$0.447279\pi$
$18$	−1.24040e23	−0.743051
$19$	1.81662e23	0.400243	0.200121	−	0.979771i	$-0.435866\pi$
$19$	1.81662e23	0.400243	0.200121	+	0.979771i	$0.435866\pi$
$20$	0	0
$21$	−2.86585e24	−0.991279
$22$	−4.84766e24	−0.709108
$23$	1.31296e24	0.0843893	0.0421946	−	0.999109i	$-0.486565\pi$
$23$	1.31296e24	0.0843893	0.0421946	+	0.999109i	$0.486565\pi$
$24$	−9.99735e25	−2.92400
$25$	0	0
$26$	3.40112e26	2.26264
$27$	3.28399e26	1.08686
$28$	2.14265e27	3.61850
$29$	−2.45865e26	−0.216937	−0.108468	−	0.994100i	$-0.534595\pi$
$29$	−2.45865e26	−0.216937	−0.108468	+	0.994100i	$0.534595\pi$
$30$	0	0
$31$	−5.34172e27	−1.37243	−0.686214	−	0.727399i	$-0.740729\pi$
$31$	−5.34172e27	−1.37243	−0.686214	+	0.727399i	$0.740729\pi$
$32$	3.50037e28	4.99850
$33$	3.51511e27	0.284074
$34$	1.39634e28	0.649579
$35$	0	0
$36$	−6.72459e28	−1.08660
$37$	4.86366e28	0.473403	0.236701	−	0.971582i	$-0.423934\pi$
$37$	4.86366e28	0.473403	0.236701	+	0.971582i	$0.423934\pi$
$38$	1.32672e29	0.788466
$39$	−2.46620e29	−0.906428
$40$	0	0
$41$	−2.76259e29	−0.402545	−0.201272	−	0.979535i	$-0.564508\pi$
$41$	−2.76259e29	−0.402545	−0.201272	+	0.979535i	$0.564508\pi$
$42$	−2.09299e30	−1.95279
$43$	−3.62958e29	−0.219124	−0.109562	−	0.993980i	$-0.534945\pi$
$43$	−3.62958e29	−0.219124	−0.109562	+	0.993980i	$0.534945\pi$
$44$	−2.62808e30	−1.03696
$45$	0	0
$46$	9.58886e29	0.166244
$47$	3.33770e30	0.388720	0.194360	−	0.980930i	$-0.437737\pi$
$47$	3.33770e30	0.388720	0.194360	+	0.980930i	$0.437737\pi$
$48$	−4.41957e31	−3.48672
$49$	1.07241e31	0.577740
$50$	0	0
$51$	−1.01251e31	−0.260226
$52$	1.84386e32	3.30876
$53$	1.06131e32	1.33887	0.669433	−	0.742872i	$-0.266537\pi$
$53$	1.06131e32	1.33887	0.669433	+	0.742872i	$0.266537\pi$
$54$	2.39837e32	2.14107
$55$	0	0
$56$	1.02163e33	4.65389
$57$	−9.62025e31	−0.315865
$58$	−1.79560e32	−0.427359
$59$	4.05466e32	0.703384	0.351692	−	0.936116i	$-0.385606\pi$
$59$	4.05466e32	0.703384	0.351692	+	0.936116i	$0.385606\pi$
$60$	0	0
$61$	−6.56338e32	−0.614505	−0.307253	−	0.951628i	$-0.599410\pi$
$61$	−6.56338e32	−0.614505	−0.307253	+	0.951628i	$0.599410\pi$
$62$	−3.90118e33	−2.70364
$63$	−9.19130e32	−0.473780
$64$	1.40939e34	5.42877
$65$	0	0
$66$	2.56716e33	0.559617
$67$	8.53897e33	1.40936	0.704679	−	0.709526i	$-0.251091\pi$
$67$	8.53897e33	1.40936	0.704679	+	0.709526i	$0.251091\pi$
$68$	7.57003e33	0.949911
$69$	−6.95302e32	−0.0665986
$70$	0	0
$71$	−2.08929e34	−1.17956	−0.589780	−	0.807564i	$-0.700786\pi$
$71$	−2.08929e34	−1.17956	−0.589780	+	0.807564i	$0.700786\pi$
$72$	−3.20633e34	−1.39752
$73$	1.73246e34	0.585048	0.292524	−	0.956258i	$-0.405505\pi$
$73$	1.73246e34	0.585048	0.292524	+	0.956258i	$0.405505\pi$
$74$	3.55204e34	0.932590
$75$	0	0
$76$	7.19259e34	1.15301
$77$	−3.59210e34	−0.452137
$78$	−1.80112e35	−1.78564
$79$	−9.67376e34	−0.757694	−0.378847	−	0.925459i	$-0.623679\pi$
$79$	−9.67376e34	−0.757694	−0.378847	+	0.925459i	$0.623679\pi$
$80$	0	0
$81$	−9.74321e34	−0.480540
$82$	−2.01758e35	−0.793002
$83$	2.94893e35	0.926232	0.463116	−	0.886298i	$-0.346731\pi$
$83$	2.94893e35	0.926232	0.463116	+	0.886298i	$0.346731\pi$
$84$	−1.13468e36	−2.85566
$85$	0	0
$86$	−2.65077e35	−0.431668
$87$	1.30202e35	0.171203
$88$	−1.25309e36	−1.33368
$89$	−1.89676e36	−1.63794	−0.818968	−	0.573839i	$-0.805454\pi$
$89$	−1.89676e36	−1.63794	−0.818968	+	0.573839i	$0.805454\pi$
$90$	0	0
$91$	2.52022e36	1.44269
$92$	5.19844e35	0.243107
$93$	2.82880e36	1.08310
$94$	2.43760e36	0.765767
$95$	0	0
$96$	−1.85368e37	−3.94474
$97$	−4.70513e36	−0.826599	−0.413300	−	0.910595i	$-0.635624\pi$
$97$	−4.70513e36	−0.826599	−0.413300	+	0.910595i	$0.635624\pi$
$98$	7.83203e36	1.13813
$99$	1.12736e36	0.135772
$100$	0	0
$101$	1.94654e37	1.61927	0.809634	−	0.586934i	$-0.199665\pi$
$101$	1.94654e37	1.61927	0.809634	+	0.586934i	$0.199665\pi$
$102$	−7.39457e36	−0.512637
$103$	2.41093e35	0.0139539	0.00697697	−	0.999976i	$-0.497779\pi$
$103$	2.41093e35	0.0139539	0.00697697	+	0.999976i	$0.497779\pi$
$104$	8.79165e37	4.25553
$105$	0	0
$106$	7.75096e37	2.63753
$107$	−1.00863e37	−0.288490	−0.144245	−	0.989542i	$-0.546075\pi$
$107$	−1.00863e37	−0.288490	−0.144245	+	0.989542i	$0.546075\pi$
$108$	1.30024e38	3.13100
$109$	−5.75568e37	−1.16871	−0.584354	−	0.811499i	$-0.698652\pi$
$109$	−5.75568e37	−1.16871	−0.584354	+	0.811499i	$0.698652\pi$
$110$	0	0
$111$	−2.57563e37	−0.373602
$112$	4.51637e38	5.54953
$113$	2.64864e37	0.276103	0.138052	−	0.990425i	$-0.455916\pi$
$113$	2.64864e37	0.276103	0.138052	+	0.990425i	$0.455916\pi$
$114$	−7.02588e37	−0.622245
$115$	0	0
$116$	−9.73457e37	−0.624948
$117$	−7.90956e37	−0.433225
$118$	2.96121e38	1.38565
$119$	1.03469e38	0.414181
$120$	0	0
$121$	−2.95980e38	−0.870430
$122$	−4.79338e38	−1.21056
$123$	1.46298e38	0.317682
$124$	−2.11496e39	−3.95367
$125$	0	0
$126$	−6.71261e38	−0.933332
$127$	8.79854e38	1.05692	0.528459	−	0.848959i	$-0.322770\pi$
$127$	8.79854e38	1.05692	0.528459	+	0.848959i	$0.322770\pi$
$128$	5.48221e39	5.69601
$129$	1.92211e38	0.172929
$130$	0	0
$131$	4.64114e38	0.314127	0.157064	−	0.987588i	$-0.449797\pi$
$131$	4.64114e38	0.314127	0.157064	+	0.987588i	$0.449797\pi$
$132$	1.39174e39	0.818355
$133$	9.83097e38	0.502737
$134$	6.23620e39	2.77639
$135$	0	0
$136$	3.60945e39	1.22172
$137$	5.79508e39	1.71289	0.856444	−	0.516240i	$-0.172669\pi$
$137$	5.79508e39	1.71289	0.856444	+	0.516240i	$0.172669\pi$
$138$	−5.07795e38	−0.131197
$139$	5.40197e39	1.22118	0.610588	−	0.791948i	$-0.290933\pi$
$139$	5.40197e39	1.22118	0.610588	+	0.791948i	$0.290933\pi$
$140$	0	0
$141$	−1.76754e39	−0.306771
$142$	−1.52586e40	−2.32370
$143$	−3.09118e39	−0.413435
$144$	−1.41744e40	−1.66647
$145$	0	0
$146$	1.26526e40	1.15253
$147$	−5.67912e39	−0.455943
$148$	1.92568e40	1.36377
$149$	3.02036e40	1.88848	0.944240	−	0.329258i	$-0.106799\pi$
$149$	3.02036e40	1.88848	0.944240	+	0.329258i	$0.106799\pi$
$150$	0	0
$151$	7.70161e39	0.376277	0.188139	−	0.982142i	$-0.439755\pi$
$151$	7.70161e39	0.376277	0.188139	+	0.982142i	$0.439755\pi$
$152$	3.42948e40	1.48293
$153$	−3.24730e39	−0.124374
$154$	−2.62339e40	−0.890697
$155$	0	0
$156$	−9.76447e40	−2.61122
$157$	4.07873e40	0.969128	0.484564	−	0.874756i	$-0.338978\pi$
$157$	4.07873e40	0.969128	0.484564	+	0.874756i	$0.338978\pi$
$158$	−7.06496e40	−1.49264
$159$	−5.62033e40	−1.05661
$160$	0	0
$161$	7.10532e39	0.106000
$162$	−7.11568e40	−0.946649
$163$	1.00098e41	1.18837	0.594186	−	0.804327i	$-0.297474\pi$
$163$	1.00098e41	1.18837	0.594186	+	0.804327i	$0.297474\pi$
$164$	−1.09380e41	−1.15965
$165$	0	0
$166$	2.15367e41	1.82465
$167$	−1.82115e41	−1.38067	−0.690336	−	0.723489i	$-0.742537\pi$
$167$	−1.82115e41	−1.38067	−0.690336	+	0.723489i	$0.742537\pi$
$168$	−5.41024e41	−3.67278
$169$	5.24764e40	0.319198
$170$	0	0
$171$	−3.08539e40	−0.150967
$172$	−1.43707e41	−0.631249
$173$	9.37891e40	0.370083	0.185042	−	0.982731i	$-0.440758\pi$
$173$	9.37891e40	0.370083	0.185042	+	0.982731i	$0.440758\pi$
$174$	9.50894e40	0.337265
$175$	0	0
$176$	−5.53957e41	−1.59035
$177$	−2.14722e41	−0.555099
$178$	−1.38525e42	−3.22669
$179$	7.17809e41	1.50740	0.753699	−	0.657220i	$-0.228268\pi$
$179$	7.17809e41	1.50740	0.753699	+	0.657220i	$0.228268\pi$
$180$	0	0
$181$	8.45661e41	1.44591	0.722957	−	0.690893i	$-0.242782\pi$
$181$	8.45661e41	1.44591	0.722957	+	0.690893i	$0.242782\pi$
$182$	1.84057e42	2.84205
$183$	3.47575e41	0.484958
$184$	2.47865e41	0.312670
$185$	0	0
$186$	2.06594e42	2.13367
$187$	−1.26910e41	−0.118693
$188$	1.32150e42	1.11982
$189$	1.77719e42	1.36518
$190$	0	0
$191$	−2.73270e42	−1.72772	−0.863861	−	0.503730i	$-0.831961\pi$
$191$	−2.73270e42	−1.72772	−0.863861	+	0.503730i	$0.831961\pi$
$192$	−7.46367e42	−4.28430
$193$	−9.14022e41	−0.476591	−0.238296	−	0.971193i	$-0.576589\pi$
$193$	−9.14022e41	−0.476591	−0.238296	+	0.971193i	$0.576589\pi$
$194$	−3.43626e42	−1.62838
$195$	0	0
$196$	4.24600e42	1.66434
$197$	−1.95353e42	−0.696941	−0.348470	−	0.937320i	$-0.613299\pi$
$197$	−1.95353e42	−0.696941	−0.348470	+	0.937320i	$0.613299\pi$
$198$	8.23336e41	0.267468
$199$	−5.09535e40	−0.0150797	−0.00753984	−	0.999972i	$-0.502400\pi$
$199$	−5.09535e40	−0.0150797	−0.00753984	+	0.999972i	$0.502400\pi$
$200$	0	0
$201$	−4.52196e42	−1.11224
$202$	1.42161e43	3.18991
$203$	−1.33054e42	−0.272490
$204$	−4.00884e42	−0.749654
$205$	0	0
$206$	1.76076e41	0.0274888
$207$	−2.22996e41	−0.0318307
$208$	3.88656e43	5.07451
$209$	−1.20582e42	−0.144071
$210$	0	0
$211$	−1.03253e43	−1.03437	−0.517185	−	0.855874i	$-0.673020\pi$
$211$	−1.03253e43	−1.03437	−0.517185	+	0.855874i	$0.673020\pi$
$212$	4.20205e43	3.85698
$213$	1.10642e43	0.930890
$214$	−7.36622e42	−0.568316
$215$	0	0
$216$	6.19962e43	4.02690
$217$	−2.89076e43	−1.72388
$218$	−4.20350e43	−2.30232
$219$	−9.17457e42	−0.461710
$220$	0	0
$221$	8.90398e42	0.378728
$222$	−1.88104e43	−0.735985
$223$	2.90981e43	1.04767	0.523835	−	0.851820i	$-0.324501\pi$
$223$	2.90981e43	1.04767	0.523835	+	0.851820i	$0.324501\pi$
$224$	1.89429e44	6.27853
$225$	0	0
$226$	1.93436e43	0.543915
$227$	1.39725e43	0.362073	0.181036	−	0.983476i	$-0.442055\pi$
$227$	1.39725e43	0.362073	0.181036	+	0.983476i	$0.442055\pi$
$228$	−3.80896e43	−0.909939
$229$	−3.10603e43	−0.684304	−0.342152	−	0.939645i	$-0.611156\pi$
$229$	−3.10603e43	−0.684304	−0.342152	+	0.939645i	$0.611156\pi$
$230$	0	0
$231$	1.90226e43	0.356819
$232$	−4.64151e43	−0.803770
$233$	1.27462e43	0.203844	0.101922	−	0.994792i	$-0.467501\pi$
$233$	1.27462e43	0.203844	0.101922	+	0.994792i	$0.467501\pi$
$234$	−5.77653e43	−0.853441
$235$	0	0
$236$	1.60537e44	2.02630
$237$	5.12291e43	0.597960
$238$	7.55654e43	0.815924
$239$	−3.18573e43	−0.318308	−0.159154	−	0.987254i	$-0.550877\pi$
$239$	−3.18573e43	−0.318308	−0.159154	+	0.987254i	$0.550877\pi$
$240$	0	0
$241$	−8.49950e43	−0.727911	−0.363955	−	0.931416i	$-0.618574\pi$
$241$	−8.49950e43	−0.727911	−0.363955	+	0.931416i	$0.618574\pi$
$242$	−2.16161e44	−1.71472
$243$	−9.62757e43	−0.707621
$244$	−2.59865e44	−1.77026
$245$	0	0
$246$	1.06844e44	0.625824
$247$	8.46003e43	0.459704
$248$	−1.00843e45	−5.08497
$249$	−1.56166e44	−0.730968
$250$	0	0
$251$	−4.90186e44	−1.97878	−0.989389	−	0.145288i	$-0.953589\pi$
$251$	−4.90186e44	−1.97878	−0.989389	+	0.145288i	$0.953589\pi$
$252$	−3.63913e44	−1.36486
$253$	−8.71504e42	−0.0303766
$254$	6.42577e44	2.08210
$255$	0	0
$256$	2.06673e45	5.79221
$257$	−1.54143e44	−0.401941	−0.200970	−	0.979597i	$-0.564410\pi$
$257$	−1.54143e44	−0.401941	−0.200970	+	0.979597i	$0.564410\pi$
$258$	1.40376e44	0.340665
$259$	2.63205e44	0.594633
$260$	0	0
$261$	4.17582e43	0.0818261
$262$	3.38953e44	0.618821
$263$	−5.54952e44	−0.944223	−0.472111	−	0.881539i	$-0.656508\pi$
$263$	−5.54952e44	−0.944223	−0.472111	+	0.881539i	$0.656508\pi$
$264$	6.63593e44	1.05252
$265$	0	0
$266$	7.17978e44	0.990378
$267$	1.00446e45	1.29263
$268$	3.38085e45	4.06006
$269$	−6.11950e43	−0.0685960	−0.0342980	−	0.999412i	$-0.510920\pi$
$269$	−6.11950e43	−0.0685960	−0.0342980	+	0.999412i	$0.510920\pi$
$270$	0	0
$271$	6.79672e44	0.664305	0.332153	−	0.943226i	$-0.392225\pi$
$271$	6.79672e44	0.664305	0.332153	+	0.943226i	$0.392225\pi$
$272$	1.59564e45	1.45684
$273$	−1.33463e45	−1.13855
$274$	4.23228e45	3.37434
$275$	0	0
$276$	−2.75292e44	−0.191856
$277$	−1.23953e45	−0.807942	−0.403971	−	0.914772i	$-0.632370\pi$
$277$	−1.23953e45	−0.807942	−0.403971	+	0.914772i	$0.632370\pi$
$278$	3.94518e45	2.40568
$279$	9.07249e44	0.517665
$280$	0	0
$281$	9.16351e44	0.458137	0.229068	−	0.973410i	$-0.426432\pi$
$281$	9.16351e44	0.458137	0.229068	+	0.973410i	$0.426432\pi$
$282$	−1.29087e45	−0.604331
$283$	2.02108e45	0.886207	0.443103	−	0.896471i	$-0.353877\pi$
$283$	2.02108e45	0.886207	0.443103	+	0.896471i	$0.353877\pi$
$284$	−8.27218e45	−3.39806
$285$	0	0
$286$	−2.25756e45	−0.814455
$287$	−1.49502e45	−0.505629
$288$	−5.94511e45	−1.88538
$289$	−2.99654e45	−0.891271
$290$	0	0
$291$	2.49169e45	0.652339
$292$	6.85938e45	1.68540
$293$	−1.51569e45	−0.349591	−0.174796	−	0.984605i	$-0.555927\pi$
$293$	−1.51569e45	−0.349591	−0.174796	+	0.984605i	$0.555927\pi$
$294$	−4.14759e45	−0.898194
$295$	0	0
$296$	9.18177e45	1.75400
$297$	−2.17981e45	−0.391223
$298$	2.20583e46	3.72025
$299$	6.11447e44	0.0969264
$300$	0	0
$301$	−1.96421e45	−0.275238
$302$	5.62466e45	0.741255
$303$	−1.03083e46	−1.27790
$304$	1.51608e46	1.76833
$305$	0	0
$306$	−2.37158e45	−0.245014
$307$	1.10982e46	1.07943	0.539713	−	0.841849i	$-0.318533\pi$
$307$	1.10982e46	1.07943	0.539713	+	0.841849i	$0.318533\pi$
$308$	−1.42223e46	−1.30251
$309$	−1.27675e44	−0.0110122
$310$	0	0
$311$	−9.07246e45	−0.694477	−0.347239	−	0.937777i	$-0.612881\pi$
$311$	−9.07246e45	−0.694477	−0.347239	+	0.937777i	$0.612881\pi$
$312$	−4.65577e46	−3.35839
$313$	2.30774e45	0.156898	0.0784490	−	0.996918i	$-0.475003\pi$
$313$	2.30774e45	0.156898	0.0784490	+	0.996918i	$0.475003\pi$
$314$	2.97879e46	1.90915
$315$	0	0
$316$	−3.83015e46	−2.18275
$317$	−2.73266e46	−1.46889	−0.734444	−	0.678670i	$-0.762557\pi$
$317$	−2.73266e46	−1.46889	−0.734444	+	0.678670i	$0.762557\pi$
$318$	−4.10466e46	−2.08149
$319$	1.63197e45	0.0780883
$320$	0	0
$321$	5.34135e45	0.227671
$322$	5.18917e45	0.208816
$323$	3.47330e45	0.131976
$324$	−3.85765e46	−1.38433
$325$	0	0
$326$	7.31035e46	2.34106
$327$	3.04802e46	0.922326
$328$	−5.21530e46	−1.49146
$329$	1.80625e46	0.488264
$330$	0	0
$331$	−4.17667e46	−1.00928	−0.504641	−	0.863329i	$-0.668375\pi$
$331$	−4.17667e46	−1.00928	−0.504641	+	0.863329i	$0.668375\pi$
$332$	1.16758e47	2.66828
$333$	−8.26054e45	−0.178562
$334$	−1.33003e47	−2.71988
$335$	0	0
$336$	−2.39173e47	−4.37960
$337$	−8.64709e45	−0.149871	−0.0749353	−	0.997188i	$-0.523875\pi$
$337$	−8.64709e45	−0.149871	−0.0749353	+	0.997188i	$0.523875\pi$
$338$	3.83247e46	0.628810
$339$	−1.40263e46	−0.217896
$340$	0	0
$341$	3.54567e46	0.494018
$342$	−2.25333e46	−0.297401
$343$	−4.24169e46	−0.530393
$344$	−6.85204e46	−0.811874
$345$	0	0
$346$	6.84963e46	0.729053
$347$	−1.39433e47	−1.40692	−0.703461	−	0.710734i	$-0.748363\pi$
$347$	−1.39433e47	−1.40692	−0.703461	+	0.710734i	$0.748363\pi$
$348$	5.15511e46	0.493199
$349$	2.67356e46	0.242560	0.121280	−	0.992618i	$-0.461300\pi$
$349$	2.67356e46	0.242560	0.121280	+	0.992618i	$0.461300\pi$
$350$	0	0
$351$	1.52935e47	1.24832
$352$	−2.32344e47	−1.79925
$353$	1.62902e45	0.0119700	0.00598502	−	0.999982i	$-0.498095\pi$
$353$	1.62902e45	0.0119700	0.00598502	+	0.999982i	$0.498095\pi$
$354$	−1.56816e47	−1.09353
$355$	0	0
$356$	−7.50988e47	−4.71854
$357$	−5.47936e46	−0.326865
$358$	5.24232e47	2.96953
$359$	−8.84787e46	−0.475983	−0.237991	−	0.971267i	$-0.576489\pi$
$359$	−8.84787e46	−0.475983	−0.237991	+	0.971267i	$0.576489\pi$
$360$	0	0
$361$	−1.73006e47	−0.839806
$362$	6.17605e47	2.84841
$363$	1.56742e47	0.686929
$364$	9.97835e47	4.15607
$365$	0	0
$366$	2.53842e47	0.955352
$367$	−2.31824e47	−0.829537	−0.414768	−	0.909927i	$-0.636137\pi$
$367$	−2.31824e47	−0.829537	−0.414768	+	0.909927i	$0.636137\pi$
$368$	1.09575e47	0.372843
$369$	4.69203e46	0.151835
$370$	0	0
$371$	5.74344e47	1.68172
$372$	1.12001e48	3.12017
$373$	−7.43690e47	−1.97142	−0.985709	−	0.168456i	$-0.946122\pi$
$373$	−7.43690e47	−1.97142	−0.985709	+	0.168456i	$0.946122\pi$
$374$	−9.26849e46	−0.233821
$375$	0	0
$376$	6.30102e47	1.44024
$377$	−1.14499e47	−0.249166
$378$	1.29792e48	2.68936
$379$	2.42162e47	0.477837	0.238919	−	0.971040i	$-0.423207\pi$
$379$	2.42162e47	0.477837	0.238919	+	0.971040i	$0.423207\pi$
$380$	0	0
$381$	−4.65942e47	−0.834103
$382$	−1.99575e48	−3.40356
$383$	5.76836e45	0.00937293	0.00468646	−	0.999989i	$-0.498508\pi$
$383$	5.76836e45	0.00937293	0.00468646	+	0.999989i	$0.498508\pi$
$384$	−2.90320e48	−4.49520
$385$	0	0
$386$	−6.67531e47	−0.938871
$387$	6.16456e46	0.0826512
$388$	−1.86291e48	−2.38125
$389$	1.08737e48	1.32529	0.662644	−	0.748935i	$-0.269434\pi$
$389$	1.08737e48	1.32529	0.662644	+	0.748935i	$0.269434\pi$
$390$	0	0
$391$	2.51032e46	0.0278265
$392$	2.02453e48	2.14058
$393$	−2.45780e47	−0.247904
$394$	−1.42671e48	−1.37295
$395$	0	0
$396$	4.46358e47	0.391131
$397$	1.15144e48	0.962976	0.481488	−	0.876453i	$-0.340096\pi$
$397$	1.15144e48	0.962976	0.481488	+	0.876453i	$0.340096\pi$
$398$	−3.72125e46	−0.0297065
$399$	−5.20616e47	−0.396752
$400$	0	0
$401$	3.98114e47	0.276590	0.138295	−	0.990391i	$-0.455838\pi$
$401$	3.98114e47	0.276590	0.138295	+	0.990391i	$0.455838\pi$
$402$	−3.30249e48	−2.19109
$403$	−2.48764e48	−1.57632
$404$	7.70699e48	4.66476
$405$	0	0
$406$	−9.71722e47	−0.536798
$407$	−3.22835e47	−0.170405
$408$	−1.91145e48	−0.964160
$409$	−3.71385e48	−1.79037	−0.895186	−	0.445694i	$-0.852957\pi$
$409$	−3.71385e48	−1.79037	−0.895186	+	0.445694i	$0.852957\pi$
$410$	0	0
$411$	−3.06889e48	−1.35178
$412$	9.54566e46	0.0401983
$413$	2.19425e48	0.883507
$414$	−1.62859e47	−0.0627055
$415$	0	0
$416$	1.63013e49	5.74110
$417$	−2.86071e48	−0.963733
$418$	−8.80637e47	−0.283815
$419$	−7.48923e47	−0.230929	−0.115464	−	0.993312i	$-0.536836\pi$
$419$	−7.48923e47	−0.230929	−0.115464	+	0.993312i	$0.536836\pi$
$420$	0	0
$421$	2.40487e48	0.679005	0.339502	−	0.940605i	$-0.389741\pi$
$421$	2.40487e48	0.679005	0.339502	+	0.940605i	$0.389741\pi$
$422$	−7.54077e48	−2.03768
$423$	−5.66882e47	−0.146621
$424$	2.00357e49	4.96062
$425$	0	0
$426$	8.08045e48	1.83383
$427$	−3.55189e48	−0.771869
$428$	−3.99347e48	−0.831076
$429$	1.63699e48	0.326276
$430$	0	0
$431$	−1.72112e48	−0.314761	−0.157381	−	0.987538i	$-0.550305\pi$
$431$	−1.72112e48	−0.314761	−0.157381	+	0.987538i	$0.550305\pi$
$432$	2.74069e49	4.80187
$433$	7.37887e48	1.23869	0.619347	−	0.785117i	$-0.287397\pi$
$433$	7.37887e48	1.23869	0.619347	+	0.785117i	$0.287397\pi$
$434$	−2.11119e49	−3.39600
$435$	0	0
$436$	−2.27886e49	−3.36680
$437$	2.38516e47	0.0337762
$438$	−6.70039e48	−0.909555
$439$	−4.18564e48	−0.544713	−0.272357	−	0.962196i	$-0.587803\pi$
$439$	−4.18564e48	−0.544713	−0.272357	+	0.962196i	$0.587803\pi$
$440$	0	0
$441$	−1.82140e48	−0.217917
$442$	6.50277e48	0.746082
$443$	−9.57544e47	−0.105363	−0.0526817	−	0.998611i	$-0.516777\pi$
$443$	−9.57544e47	−0.105363	−0.0526817	+	0.998611i	$0.516777\pi$
$444$	−1.01978e49	−1.07627
$445$	0	0
$446$	2.12510e49	2.06388
$447$	−1.59948e49	−1.49036
$448$	7.62715e49	6.81898
$449$	−3.83089e48	−0.328656	−0.164328	−	0.986406i	$-0.552546\pi$
$449$	−3.83089e48	−0.328656	−0.164328	+	0.986406i	$0.552546\pi$
$450$	0	0
$451$	1.83372e48	0.144900
$452$	1.04868e49	0.795394
$453$	−4.07852e48	−0.296952
$454$	1.02044e49	0.713273
$455$	0	0
$456$	−1.81614e49	−1.17031
$457$	−1.64838e49	−1.02002	−0.510010	−	0.860168i	$-0.670358\pi$
$457$	−1.64838e49	−1.02002	−0.510010	+	0.860168i	$0.670358\pi$
$458$	−2.26840e49	−1.34806
$459$	6.27883e48	0.358380
$460$	0	0
$461$	−9.74478e48	−0.513221	−0.256611	−	0.966515i	$-0.582606\pi$
$461$	−9.74478e48	−0.513221	−0.256611	+	0.966515i	$0.582606\pi$
$462$	1.38926e49	0.702924
$463$	−6.82466e48	−0.331767	−0.165883	−	0.986145i	$-0.553048\pi$
$463$	−6.82466e48	−0.331767	−0.165883	+	0.986145i	$0.553048\pi$
$464$	−2.05189e49	−0.958455
$465$	0	0
$466$	9.30886e48	0.401566
$467$	−2.51643e49	−1.04333	−0.521665	−	0.853150i	$-0.674689\pi$
$467$	−2.51643e49	−1.04333	−0.521665	+	0.853150i	$0.674689\pi$
$468$	−3.13165e49	−1.24803
$469$	4.62101e49	1.77027
$470$	0	0
$471$	−2.15996e49	−0.764820
$472$	7.65452e49	2.60610
$473$	2.40921e48	0.0788756
$474$	3.74138e49	1.17796
$475$	0	0
$476$	4.09665e49	1.19316
$477$	−1.80254e49	−0.505005
$478$	−2.32661e49	−0.627057
$479$	3.51529e49	0.911494	0.455747	−	0.890109i	$-0.349372\pi$
$479$	3.51529e49	0.911494	0.455747	+	0.890109i	$0.349372\pi$
$480$	0	0
$481$	2.26501e49	0.543733
$482$	−6.20737e49	−1.43396
$483$	−3.76275e48	−0.0836533
$484$	−1.17188e50	−2.50752
$485$	0	0
$486$	−7.03123e49	−1.39399
$487$	−2.53562e49	−0.483948	−0.241974	−	0.970283i	$-0.577795\pi$
$487$	−2.53562e49	−0.483948	−0.241974	+	0.970283i	$0.577795\pi$
$488$	−1.23906e50	−2.27680
$489$	−5.30084e49	−0.937844
$490$	0	0
$491$	3.84129e49	0.630188	0.315094	−	0.949061i	$-0.397964\pi$
$491$	3.84129e49	0.630188	0.315094	+	0.949061i	$0.397964\pi$
$492$	5.79239e49	0.915173
$493$	−4.70081e48	−0.0715328
$494$	6.17855e49	0.905603
$495$	0	0
$496$	−4.45800e50	−6.06357
$497$	−1.13066e50	−1.48162
$498$	−1.14051e50	−1.43998
$499$	−9.72020e49	−1.18254	−0.591269	−	0.806474i	$-0.701373\pi$
$499$	−9.72020e49	−1.18254	−0.591269	+	0.806474i	$0.701373\pi$
$500$	0	0
$501$	9.64421e49	1.08960
$502$	−3.57994e50	−3.89814
$503$	−1.21991e50	−1.28033	−0.640163	−	0.768239i	$-0.721133\pi$
$503$	−1.21991e50	−1.28033	−0.640163	+	0.768239i	$0.721133\pi$
$504$	−1.73516e50	−1.75540
$505$	0	0
$506$	−6.36479e48	−0.0598411
$507$	−2.77898e49	−0.251906
$508$	3.48362e50	3.04475
$509$	1.45251e50	1.22416	0.612081	−	0.790795i	$-0.290333\pi$
$509$	1.45251e50	1.22416	0.612081	+	0.790795i	$0.290333\pi$
$510$	0	0
$511$	9.37553e49	0.734867
$512$	7.55910e50	5.71447
$513$	5.96577e49	0.435006
$514$	−1.12574e50	−0.791812
$515$	0	0
$516$	7.61024e49	0.498172
$517$	−2.21546e49	−0.139923
$518$	1.92225e50	1.17141
$519$	−4.96677e49	−0.292064
$520$	0	0
$521$	5.28610e49	0.289493	0.144746	−	0.989469i	$-0.453763\pi$
$521$	5.28610e49	0.289493	0.144746	+	0.989469i	$0.453763\pi$
$522$	3.04969e49	0.161195
$523$	−1.30446e50	−0.665503	−0.332751	−	0.943015i	$-0.607977\pi$
$523$	−1.30446e50	−0.665503	−0.332751	+	0.943015i	$0.607977\pi$
$524$	1.83757e50	0.904932
$525$	0	0
$526$	−4.05294e50	−1.86009
$527$	−1.02131e50	−0.452545
$528$	2.93357e50	1.25507
$529$	−2.40340e50	−0.992878
$530$	0	0
$531$	−6.88652e49	−0.265309
$532$	3.89240e50	1.44828
$533$	−1.28654e50	−0.462348
$534$	7.33581e50	2.54645
$535$	0	0
$536$	1.61201e51	5.22180
$537$	−3.80128e50	−1.18961
$538$	−4.46921e49	−0.135132
$539$	−7.11831e49	−0.207963
$540$	0	0
$541$	−7.19988e50	−1.96416	−0.982078	−	0.188476i	$-0.939645\pi$
$541$	−7.19988e50	−1.96416	−0.982078	+	0.188476i	$0.939645\pi$
$542$	4.96380e50	1.30866
$543$	−4.47835e50	−1.14109
$544$	6.69255e50	1.64821
$545$	0	0
$546$	−9.74708e50	−2.24290
$547$	−7.37481e50	−1.64053	−0.820267	−	0.571981i	$-0.806175\pi$
$547$	−7.37481e50	−1.64053	−0.820267	+	0.571981i	$0.806175\pi$
$548$	2.29446e51	4.93446
$549$	1.11474e50	0.231785
$550$	0	0
$551$	−4.46643e49	−0.0868273
$552$	−1.31261e50	−0.246754
$553$	−5.23512e50	−0.951726
$554$	−9.05254e50	−1.59162
$555$	0	0
$556$	2.13881e51	3.51795
$557$	8.54456e49	0.135947	0.0679734	−	0.997687i	$-0.478347\pi$
$557$	8.54456e49	0.135947	0.0679734	+	0.997687i	$0.478347\pi$
$558$	6.62584e50	1.01978
$559$	−1.69030e50	−0.251678
$560$	0	0
$561$	6.72072e49	0.0936705
$562$	6.69232e50	0.902516
$563$	−6.17813e50	−0.806217	−0.403108	−	0.915152i	$-0.632070\pi$
$563$	−6.17813e50	−0.806217	−0.403108	+	0.915152i	$0.632070\pi$
$564$	−6.99824e50	−0.883742
$565$	0	0
$566$	1.47604e51	1.74580
$567$	−5.27271e50	−0.603597
$568$	−3.94424e51	−4.37038
$569$	3.82112e50	0.409840	0.204920	−	0.978779i	$-0.434307\pi$
$569$	3.82112e50	0.409840	0.204920	+	0.978779i	$0.434307\pi$
$570$	0	0
$571$	−7.91655e50	−0.795734	−0.397867	−	0.917443i	$-0.630250\pi$
$571$	−7.91655e50	−0.795734	−0.397867	+	0.917443i	$0.630250\pi$
$572$	−1.22390e51	−1.19102
$573$	1.44715e51	1.36349
$574$	−1.09185e51	−0.996075
$575$	0	0
$576$	−2.39374e51	−2.04767
$577$	−1.32127e51	−1.09456	−0.547280	−	0.836950i	$-0.684337\pi$
$577$	−1.32127e51	−1.09456	−0.547280	+	0.836950i	$0.684337\pi$
$578$	−2.18844e51	−1.75578
$579$	4.84036e50	0.376118
$580$	0	0
$581$	1.59586e51	1.16342
$582$	1.81973e51	1.28509
$583$	−7.04463e50	−0.481936
$584$	3.27060e51	2.16765
$585$	0	0
$586$	−1.10695e51	−0.688685
$587$	−2.53870e51	−1.53040	−0.765202	−	0.643790i	$-0.777361\pi$
$587$	−2.53870e51	−1.53040	−0.765202	+	0.643790i	$0.777361\pi$
$588$	−2.24855e51	−1.31347
$589$	−9.70390e50	−0.549305
$590$	0	0
$591$	1.03453e51	0.550014
$592$	4.05902e51	2.09156
$593$	2.11775e51	1.05770	0.528851	−	0.848714i	$-0.322623\pi$
$593$	2.11775e51	1.05770	0.528851	+	0.848714i	$0.322623\pi$
$594$	−1.59196e51	−0.770698
$595$	0	0
$596$	1.19586e52	5.44030
$597$	2.69833e49	0.0119006
$598$	4.46554e50	0.190942
$599$	2.99089e51	1.23995	0.619976	−	0.784621i	$-0.287142\pi$
$599$	2.99089e51	1.23995	0.619976	+	0.784621i	$0.287142\pi$
$600$	0	0
$601$	−3.17455e51	−1.23738	−0.618692	−	0.785634i	$-0.712337\pi$
$601$	−3.17455e51	−1.23738	−0.618692	+	0.785634i	$0.712337\pi$
$602$	−1.43451e51	−0.542210
$603$	−1.45028e51	−0.531594
$604$	3.04931e51	1.08397
$605$	0	0
$606$	−7.52836e51	−2.51743
$607$	2.97302e51	0.964289	0.482144	−	0.876092i	$-0.339858\pi$
$607$	2.97302e51	0.964289	0.482144	+	0.876092i	$0.339858\pi$
$608$	6.35886e51	2.00061
$609$	7.04610e50	0.215045
$610$	0	0
$611$	1.55437e51	0.446469
$612$	−1.28571e51	−0.358296
$613$	3.37890e51	0.913601	0.456800	−	0.889569i	$-0.348995\pi$
$613$	3.37890e51	0.913601	0.456800	+	0.889569i	$0.348995\pi$
$614$	8.10527e51	2.12644
$615$	0	0
$616$	−6.78129e51	−1.67521
$617$	6.44825e51	1.54585	0.772924	−	0.634499i	$-0.218794\pi$
$617$	6.44825e51	1.54585	0.772924	+	0.634499i	$0.218794\pi$
$618$	−9.32441e49	−0.0216938
$619$	−3.50311e51	−0.791001	−0.395501	−	0.918466i	$-0.629429\pi$
$619$	−3.50311e51	−0.791001	−0.395501	+	0.918466i	$0.629429\pi$
$620$	0	0
$621$	4.31175e50	0.0917189
$622$	−6.62582e51	−1.36810
$623$	−1.02646e52	−2.05738
$624$	−2.05820e52	−4.00472
$625$	0	0
$626$	1.68540e51	0.309084
$627$	6.38563e50	0.113698
$628$	1.61490e52	2.79185
$629$	9.29908e50	0.156100
$630$	0	0
$631$	−1.83210e51	−0.290006	−0.145003	−	0.989431i	$-0.546319\pi$
$631$	−1.83210e51	−0.290006	−0.145003	+	0.989431i	$0.546319\pi$
$632$	−1.82624e52	−2.80733
$633$	5.46793e51	0.816308
$634$	−1.99572e52	−2.89367
$635$	0	0
$636$	−2.22527e52	−3.04387
$637$	4.99421e51	0.663571
$638$	1.19187e51	0.153832
$639$	3.54850e51	0.444917
$640$	0	0
$641$	−2.29605e51	−0.271711	−0.135855	−	0.990729i	$-0.543378\pi$
$641$	−2.29605e51	−0.271711	−0.135855	+	0.990729i	$0.543378\pi$
$642$	3.90091e51	0.448506
$643$	4.26413e51	0.476351	0.238176	−	0.971222i	$-0.423451\pi$
$643$	4.26413e51	0.476351	0.238176	+	0.971222i	$0.423451\pi$
$644$	2.81322e51	0.305362
$645$	0	0
$646$	2.53663e51	0.259989
$647$	1.70676e52	1.69998	0.849988	−	0.526802i	$-0.176609\pi$
$647$	1.70676e52	1.69998	0.849988	+	0.526802i	$0.176609\pi$
$648$	−1.83935e52	−1.78044
$649$	−2.69136e51	−0.253189
$650$	0	0
$651$	1.53085e52	1.36046
$652$	3.96318e52	3.42344
$653$	1.58855e52	1.33385	0.666923	−	0.745126i	$-0.267611\pi$
$653$	1.58855e52	1.33385	0.666923	+	0.745126i	$0.267611\pi$
$654$	2.22604e52	1.81696
$655$	0	0
$656$	−2.30555e52	−1.77850
$657$	−2.94245e51	−0.220674
$658$	1.31915e52	0.961865
$659$	−5.74463e51	−0.407269	−0.203635	−	0.979047i	$-0.565275\pi$
$659$	−5.74463e51	−0.407269	−0.203635	+	0.979047i	$0.565275\pi$
$660$	0	0
$661$	9.96822e51	0.668175	0.334088	−	0.942542i	$-0.391572\pi$
$661$	9.96822e51	0.668175	0.334088	+	0.942542i	$0.391572\pi$
$662$	−3.05032e52	−1.98825
$663$	−4.71526e51	−0.298886
$664$	5.56709e52	3.43177
$665$	0	0
$666$	−6.03285e51	−0.351763
$667$	−3.22811e50	−0.0183071
$668$	−7.21051e52	−3.97742
$669$	−1.54094e52	−0.826804
$670$	0	0
$671$	4.35657e51	0.221196
$672$	−1.00315e53	−4.95491
$673$	−3.94681e51	−0.189657	−0.0948283	−	0.995494i	$-0.530230\pi$
$673$	−3.94681e51	−0.189657	−0.0948283	+	0.995494i	$0.530230\pi$
$674$	−6.31516e51	−0.295241
$675$	0	0
$676$	2.07771e52	0.919539
$677$	1.53461e52	0.660856	0.330428	−	0.943831i	$-0.392807\pi$
$677$	1.53461e52	0.660856	0.330428	+	0.943831i	$0.392807\pi$
$678$	−1.02437e52	−0.429249
$679$	−2.54626e52	−1.03828
$680$	0	0
$681$	−7.39939e51	−0.285742
$682$	2.58948e52	0.973200
$683$	3.42386e52	1.25237	0.626185	−	0.779674i	$-0.284615\pi$
$683$	3.42386e52	1.25237	0.626185	+	0.779674i	$0.284615\pi$
$684$	−1.22161e52	−0.434904
$685$	0	0
$686$	−3.09780e52	−1.04486
$687$	1.64485e52	0.540042
$688$	−3.02911e52	−0.968120
$689$	4.94251e52	1.53777
$690$	0	0
$691$	−1.84197e52	−0.543174	−0.271587	−	0.962414i	$-0.587548\pi$
$691$	−1.84197e52	−0.543174	−0.271587	+	0.962414i	$0.587548\pi$
$692$	3.71341e52	1.06613
$693$	6.10090e51	0.170541
$694$	−1.01831e53	−2.77159
$695$	0	0
$696$	2.45799e52	0.634322
$697$	−5.28193e51	−0.132735
$698$	1.95256e52	0.477837
$699$	−6.74999e51	−0.160870
$700$	0	0
$701$	−4.28495e52	−0.968641	−0.484320	−	0.874891i	$-0.660933\pi$
$701$	−4.28495e52	−0.968641	−0.484320	+	0.874891i	$0.660933\pi$
$702$	1.11692e53	2.45916
$703$	8.83543e51	0.189476
$704$	−9.35510e52	−1.95413
$705$	0	0
$706$	1.18971e51	0.0235806
$707$	1.05341e53	2.03393
$708$	−8.50152e52	−1.59912
$709$	6.56896e52	1.20376	0.601882	−	0.798585i	$-0.294418\pi$
$709$	6.56896e52	1.20376	0.601882	+	0.798585i	$0.294418\pi$
$710$	0	0
$711$	1.64301e52	0.285794
$712$	−3.58076e53	−6.06870
$713$	−7.01348e51	−0.115818
$714$	−4.00170e52	−0.643914
$715$	0	0
$716$	2.84204e53	4.34249
$717$	1.68706e52	0.251203
$718$	−6.46180e52	−0.937672
$719$	9.11736e52	1.28939	0.644695	−	0.764440i	$-0.276984\pi$
$719$	9.11736e52	1.28939	0.644695	+	0.764440i	$0.276984\pi$
$720$	0	0
$721$	1.30472e51	0.0175273
$722$	−1.26350e53	−1.65439
$723$	4.50106e52	0.574455
$724$	3.34824e53	4.16537
$725$	0	0
$726$	1.14472e53	1.35323
$727$	9.81175e52	1.13073	0.565366	−	0.824840i	$-0.308735\pi$
$727$	9.81175e52	1.13073	0.565366	+	0.824840i	$0.308735\pi$
$728$	4.75775e53	5.34529
$729$	9.48566e52	1.03898
$730$	0	0
$731$	−6.93959e51	−0.0722541
$732$	1.37616e53	1.39706
$733$	3.22518e52	0.319250	0.159625	−	0.987178i	$-0.448972\pi$
$733$	3.22518e52	0.319250	0.159625	+	0.987178i	$0.448972\pi$
$734$	−1.69306e53	−1.63416
$735$	0	0
$736$	4.59586e52	0.421820
$737$	−5.66791e52	−0.507311
$738$	3.42670e52	0.299111
$739$	−2.08463e53	−1.77463	−0.887313	−	0.461167i	$-0.847431\pi$
$739$	−2.08463e53	−1.77463	−0.887313	+	0.461167i	$0.847431\pi$
$740$	0	0
$741$	−4.48016e52	−0.362791
$742$	4.19456e53	3.31295
$743$	−1.12118e53	−0.863735	−0.431868	−	0.901937i	$-0.642145\pi$
$743$	−1.12118e53	−0.863735	−0.431868	+	0.901937i	$0.642145\pi$
$744$	5.34030e53	4.01298
$745$	0	0
$746$	−5.43134e53	−3.88364
$747$	−5.00853e52	−0.349365
$748$	−5.02476e52	−0.341929
$749$	−5.45835e52	−0.362366
$750$	0	0
$751$	8.16188e52	0.515765	0.257882	−	0.966176i	$-0.416975\pi$
$751$	8.16188e52	0.515765	0.257882	+	0.966176i	$0.416975\pi$
$752$	2.78552e53	1.71742
$753$	2.59587e53	1.56162
$754$	−8.36214e52	−0.490849
$755$	0	0
$756$	7.03645e53	3.93278
$757$	−2.67813e53	−1.46069	−0.730344	−	0.683080i	$-0.760640\pi$
$757$	−2.67813e53	−1.46069	−0.730344	+	0.683080i	$0.760640\pi$
$758$	1.76856e53	0.941325
$759$	4.61520e51	0.0239728
$760$	0	0
$761$	−1.07572e53	−0.532208	−0.266104	−	0.963944i	$-0.585736\pi$
$761$	−1.07572e53	−0.532208	−0.266104	+	0.963944i	$0.585736\pi$
$762$	−3.40288e53	−1.64316
$763$	−3.11478e53	−1.46799
$764$	−1.08196e54	−4.97719
$765$	0	0
$766$	4.21277e51	0.0184644
$767$	1.88826e53	0.807881
$768$	−1.09447e54	−4.57112
$769$	−2.61837e53	−1.06757	−0.533783	−	0.845622i	$-0.679230\pi$
$769$	−2.61837e53	−1.06757	−0.533783	+	0.845622i	$0.679230\pi$
$770$	0	0
$771$	8.16294e52	0.317205
$772$	−3.61890e53	−1.37296
$773$	−2.80792e53	−1.04007	−0.520036	−	0.854144i	$-0.674082\pi$
$773$	−2.80792e53	−1.04007	−0.520036	+	0.854144i	$0.674082\pi$
$774$	4.50212e52	0.162820
$775$	0	0
$776$	−8.88250e53	−3.06262
$777$	−1.39385e53	−0.469274
$778$	7.94131e53	2.61078
$779$	−5.01858e52	−0.161116
$780$	0	0
$781$	1.38681e53	0.424593
$782$	1.83334e52	0.0548175
$783$	−8.07416e52	−0.235779
$784$	8.94990e53	2.55253
$785$	0	0
$786$	−1.79498e53	−0.488364
$787$	−7.41111e52	−0.196948	−0.0984738	−	0.995140i	$-0.531396\pi$
$787$	−7.41111e52	−0.196948	−0.0984738	+	0.995140i	$0.531396\pi$
$788$	−7.73467e53	−2.00774
$789$	2.93885e53	0.745165
$790$	0	0
$791$	1.43336e53	0.346808
$792$	2.12827e53	0.503049
$793$	−3.05657e53	−0.705798
$794$	8.40920e53	1.89704
$795$	0	0
$796$	−2.01741e52	−0.0434413
$797$	−3.42260e53	−0.720075	−0.360037	−	0.932938i	$-0.617236\pi$
$797$	−3.42260e53	−0.720075	−0.360037	+	0.932938i	$0.617236\pi$
$798$	−3.80218e53	−0.781590
$799$	6.38152e52	0.128177
$800$	0	0
$801$	3.22150e53	0.617812
$802$	2.90751e53	0.544874
$803$	−1.14996e53	−0.210593
$804$	−1.79039e54	−3.20413
$805$	0	0
$806$	−1.81678e54	−3.10531
$807$	3.24069e52	0.0541349
$808$	3.67475e54	5.99954
$809$	9.57955e53	1.52861	0.764306	−	0.644853i	$-0.223082\pi$
$809$	9.57955e53	1.52861	0.764306	+	0.644853i	$0.223082\pi$
$810$	0	0
$811$	4.43318e53	0.675818	0.337909	−	0.941179i	$-0.390280\pi$
$811$	4.43318e53	0.675818	0.337909	+	0.941179i	$0.390280\pi$
$812$	−5.26803e53	−0.784985
$813$	−3.59932e53	−0.524259
$814$	−2.35773e53	−0.335694
$815$	0	0
$816$	−8.45000e53	−1.14971
$817$	−6.59358e52	−0.0877028
$818$	−2.71231e54	−3.52698
$819$	−4.28039e53	−0.544166
$820$	0	0
$821$	−6.24147e53	−0.758470	−0.379235	−	0.925300i	$-0.623813\pi$
$821$	−6.24147e53	−0.758470	−0.379235	+	0.925300i	$0.623813\pi$
$822$	−2.24128e54	−2.66297
$823$	7.86676e53	0.913901	0.456950	−	0.889492i	$-0.348942\pi$
$823$	7.86676e53	0.913901	0.456950	+	0.889492i	$0.348942\pi$
$824$	4.55144e52	0.0517006
$825$	0	0
$826$	1.60251e54	1.74048
$827$	2.10023e53	0.223056	0.111528	−	0.993761i	$-0.464425\pi$
$827$	2.10023e53	0.223056	0.111528	+	0.993761i	$0.464425\pi$
$828$	−8.82913e52	−0.0916974
$829$	1.58193e54	1.60667	0.803337	−	0.595524i	$-0.203056\pi$
$829$	1.58193e54	1.60667	0.803337	+	0.595524i	$0.203056\pi$
$830$	0	0
$831$	6.56413e53	0.637614
$832$	6.56354e54	6.23529
$833$	2.05039e53	0.190504
$834$	−2.08924e54	−1.89853
$835$	0	0
$836$	−4.77422e53	−0.415037
$837$	−1.75421e54	−1.49163
$838$	−5.46956e53	−0.454923
$839$	4.44903e53	0.361967	0.180984	−	0.983486i	$-0.442072\pi$
$839$	4.44903e53	0.361967	0.180984	+	0.983486i	$0.442072\pi$
$840$	0	0
$841$	−1.22403e54	−0.952938
$842$	1.75633e54	1.33762
$843$	−4.85270e53	−0.361554
$844$	−4.08810e54	−2.97980
$845$	0	0
$846$	−4.14007e53	−0.288839
$847$	−1.60175e54	−1.09333
$848$	8.85726e54	5.91529
$849$	−1.07030e54	−0.699380
$850$	0	0
$851$	6.38580e52	0.0399501
$852$	4.38068e54	2.68169
$853$	2.64856e54	1.58654	0.793272	−	0.608867i	$-0.208376\pi$
$853$	2.64856e54	1.58654	0.793272	+	0.608867i	$0.208376\pi$
$854$	−2.59402e54	−1.52056
$855$	0	0
$856$	−1.90412e54	−1.06888
$857$	−2.09455e54	−1.15066	−0.575328	−	0.817923i	$-0.695126\pi$
$857$	−2.09455e54	−1.15066	−0.575328	+	0.817923i	$0.695126\pi$
$858$	1.19553e54	0.642755
$859$	7.66702e53	0.403416	0.201708	−	0.979446i	$-0.435351\pi$
$859$	7.66702e53	0.403416	0.201708	+	0.979446i	$0.435351\pi$
$860$	0	0
$861$	7.91714e53	0.399034
$862$	−1.25697e54	−0.620071
$863$	−1.89461e54	−0.914789	−0.457394	−	0.889264i	$-0.651217\pi$
$863$	−1.89461e54	−0.914789	−0.457394	+	0.889264i	$0.651217\pi$
$864$	1.14952e55	5.43265
$865$	0	0
$866$	5.38896e54	2.44019
$867$	1.58687e54	0.703377
$868$	−1.14455e55	−4.96613
$869$	6.42115e53	0.272739
$870$	0	0
$871$	3.97660e54	1.61874
$872$	−1.08658e55	−4.33017
$873$	7.99130e53	0.311784
$874$	1.74193e53	0.0665381
$875$	0	0
$876$	−3.63250e54	−1.33009
$877$	−4.21262e54	−1.51029	−0.755144	−	0.655559i	$-0.772433\pi$
$877$	−4.21262e54	−1.51029	−0.755144	+	0.655559i	$0.772433\pi$
$878$	−3.05687e54	−1.07307
$879$	8.02663e53	0.275892
$880$	0	0
$881$	−4.71460e54	−1.55378	−0.776892	−	0.629634i	$-0.783205\pi$
$881$	−4.71460e54	−1.55378	−0.776892	+	0.629634i	$0.783205\pi$
$882$	−1.33021e54	−0.429290
$883$	−1.30813e54	−0.413408	−0.206704	−	0.978404i	$-0.566274\pi$
$883$	−1.30813e54	−0.413408	−0.206704	+	0.978404i	$0.566274\pi$
$884$	3.52537e54	1.09103
$885$	0	0
$886$	−6.99316e53	−0.207563
$887$	2.57424e54	0.748277	0.374139	−	0.927373i	$-0.377938\pi$
$887$	2.57424e54	0.748277	0.374139	+	0.927373i	$0.377938\pi$
$888$	−4.86237e54	−1.38423
$889$	4.76148e54	1.32758
$890$	0	0
$891$	6.46725e53	0.172974
$892$	1.15209e55	3.01811
$893$	6.06334e53	0.155582
$894$	−1.16814e55	−2.93596
$895$	0	0
$896$	2.96679e55	7.15466
$897$	−3.23803e53	−0.0764927
$898$	−2.79778e54	−0.647443
$899$	1.31334e54	0.297730
$900$	0	0
$901$	2.02917e54	0.441478
$902$	1.33921e54	0.285448
$903$	1.04018e54	0.217213
$904$	5.00019e54	1.02299
$905$	0	0
$906$	−2.97864e54	−0.584987
$907$	1.32610e53	0.0255176	0.0127588	−	0.999919i	$-0.495939\pi$
$907$	1.32610e53	0.0255176	0.0127588	+	0.999919i	$0.495939\pi$
$908$	5.53216e54	1.04305
$909$	−3.30605e54	−0.610770
$910$	0	0
$911$	−6.58063e54	−1.16729	−0.583644	−	0.812010i	$-0.698373\pi$
$911$	−6.58063e54	−1.16729	−0.583644	+	0.812010i	$0.698373\pi$
$912$	−8.02869e54	−1.39553
$913$	−1.95741e54	−0.333405
$914$	−1.20385e55	−2.00941
$915$	0	0
$916$	−1.22978e55	−1.97133
$917$	2.51163e54	0.394569
$918$	4.58557e54	0.705998
$919$	−8.05673e54	−1.21569	−0.607844	−	0.794057i	$-0.707965\pi$
$919$	−8.05673e54	−1.21569	−0.607844	+	0.794057i	$0.707965\pi$
$920$	0	0
$921$	−5.87725e54	−0.851865
$922$	−7.11683e54	−1.01103
$923$	−9.72986e54	−1.35480
$924$	7.53166e54	1.02792
$925$	0	0
$926$	−4.98420e54	−0.653571
$927$	−4.09478e52	−0.00526327
$928$	−8.60618e54	−1.08436
$929$	8.99993e54	1.11160	0.555800	−	0.831316i	$-0.312412\pi$
$929$	8.99993e54	1.11160	0.555800	+	0.831316i	$0.312412\pi$
$930$	0	0
$931$	1.94816e54	0.231236
$932$	5.04664e54	0.587229
$933$	4.80448e54	0.548070
$934$	−1.83780e55	−2.05533
$935$	0	0
$936$	−1.49319e55	−1.60514
$937$	9.02057e54	0.950718	0.475359	−	0.879792i	$-0.342318\pi$
$937$	9.02057e54	0.950718	0.475359	+	0.879792i	$0.342318\pi$
$938$	3.37483e55	3.48738
$939$	−1.22211e54	−0.123821
$940$	0	0
$941$	1.87997e55	1.83123	0.915616	−	0.402054i	$-0.131703\pi$
$941$	1.87997e55	1.83123	0.915616	+	0.402054i	$0.131703\pi$
$942$	−1.57747e55	−1.50667
$943$	−3.62717e53	−0.0339705
$944$	3.38387e55	3.10764
$945$	0	0
$946$	1.75950e54	0.155383
$947$	1.51134e55	1.30884	0.654420	−	0.756131i	$-0.272913\pi$
$947$	1.51134e55	1.30884	0.654420	+	0.756131i	$0.272913\pi$
$948$	2.02832e55	1.72259
$949$	8.06810e54	0.671964
$950$	0	0
$951$	1.44713e55	1.15922
$952$	1.95331e55	1.53458
$953$	5.13084e53	0.0395339	0.0197669	−	0.999805i	$-0.493708\pi$
$953$	5.13084e53	0.0395339	0.0197669	+	0.999805i	$0.493708\pi$
$954$	−1.31644e55	−0.994846
$955$	0	0
$956$	−1.26133e55	−0.916976
$957$	−8.64241e53	−0.0616260
$958$	2.56729e55	1.79562
$959$	3.13611e55	2.15153
$960$	0	0
$961$	1.33850e55	0.883561
$962$	1.65419e55	1.07114
$963$	1.71307e54	0.108815
$964$	−3.36522e55	−2.09695
$965$	0	0
$966$	−2.74802e54	−0.164795
$967$	3.56316e54	0.209626	0.104813	−	0.994492i	$-0.466576\pi$
$967$	3.56316e54	0.209626	0.104813	+	0.994492i	$0.466576\pi$
$968$	−5.58762e55	−3.22502
$969$	−1.83935e54	−0.104153
$970$	0	0
$971$	−2.53392e54	−0.138114	−0.0690570	−	0.997613i	$-0.521999\pi$
$971$	−2.53392e54	−0.138114	−0.0690570	+	0.997613i	$0.521999\pi$
$972$	−3.81186e55	−2.03850
$973$	2.92337e55	1.53390
$974$	−1.85182e55	−0.953363
$975$	0	0
$976$	−5.47755e55	−2.71497
$977$	9.38989e54	0.456679	0.228340	−	0.973582i	$-0.426670\pi$
$977$	9.38989e54	0.456679	0.228340	+	0.973582i	$0.426670\pi$
$978$	−3.87132e55	−1.84753
$979$	1.25901e55	0.589589
$980$	0	0
$981$	9.77557e54	0.440824
$982$	2.80538e55	1.24145
$983$	−2.38999e55	−1.03790	−0.518950	−	0.854805i	$-0.673677\pi$
$983$	−2.38999e55	−1.03790	−0.518950	+	0.854805i	$0.673677\pi$
$984$	2.76185e55	1.17704
$985$	0	0
$986$	−3.43311e54	−0.140917
$987$	−9.56533e54	−0.385330
$988$	3.34960e55	1.32431
$989$	−4.76550e53	−0.0184917
$990$	0	0
$991$	−6.28338e54	−0.234872	−0.117436	−	0.993080i	$-0.537467\pi$
$991$	−6.28338e54	−0.234872	−0.117436	+	0.993080i	$0.537467\pi$
$992$	−1.86980e56	−6.86009
$993$	2.21183e55	0.796509
$994$	−8.25745e55	−2.91876
$995$	0	0
$996$	−6.18310e55	−2.10576
$997$	5.02299e55	1.67920	0.839599	−	0.543206i	$-0.182790\pi$
$997$	5.02299e55	1.67920	0.839599	+	0.543206i	$0.182790\pi$
$998$	−7.09888e55	−2.32957
$999$	1.59722e55	0.514520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.38.a.f.1.18		18
5.2	odd	4		5.38.b.a.4.18	yes	18
5.3	odd	4		5.38.b.a.4.1	✓	18
5.4	even	2	inner	25.38.a.f.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.38.b.a.4.1	✓	18	5.3	odd	4
5.38.b.a.4.18	yes	18	5.2	odd	4
25.38.a.f.1.1		18	5.4	even	2	inner
25.38.a.f.1.18		18	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+730322. q^{2} -5.29568e8 q^{3} +3.95932e11 q^{4} -3.86755e14 q^{6} +5.41167e15 q^{7} +1.88783e17 q^{8} -1.69842e17 q^{9} +O(q^{10})\)	\(q+730322. q^{2} -5.29568e8 q^{3} +3.95932e11 q^{4} -3.86755e14 q^{6} +5.41167e15 q^{7} +1.88783e17 q^{8} -1.69842e17 q^{9} -6.63770e18 q^{11} -2.09673e20 q^{12} +4.65701e20 q^{13} +3.95227e21 q^{14} +8.34562e22 q^{16} +1.91195e22 q^{17} -1.24040e23 q^{18} +1.81662e23 q^{19} -2.86585e24 q^{21} -4.84766e24 q^{22} +1.31296e24 q^{23} -9.99735e25 q^{24} +3.40112e26 q^{26} +3.28399e26 q^{27} +2.14265e27 q^{28} -2.45865e26 q^{29} -5.34172e27 q^{31} +3.50037e28 q^{32} +3.51511e27 q^{33} +1.39634e28 q^{34} -6.72459e28 q^{36} +4.86366e28 q^{37} +1.32672e29 q^{38} -2.46620e29 q^{39} -2.76259e29 q^{41} -2.09299e30 q^{42} -3.62958e29 q^{43} -2.62808e30 q^{44} +9.58886e29 q^{46} +3.33770e30 q^{47} -4.41957e31 q^{48} +1.07241e31 q^{49} -1.01251e31 q^{51} +1.84386e32 q^{52} +1.06131e32 q^{53} +2.39837e32 q^{54} +1.02163e33 q^{56} -9.62025e31 q^{57} -1.79560e32 q^{58} +4.05466e32 q^{59} -6.56338e32 q^{61} -3.90118e33 q^{62} -9.19130e32 q^{63} +1.40939e34 q^{64} +2.56716e33 q^{66} +8.53897e33 q^{67} +7.57003e33 q^{68} -6.95302e32 q^{69} -2.08929e34 q^{71} -3.20633e34 q^{72} +1.73246e34 q^{73} +3.55204e34 q^{74} +7.19259e34 q^{76} -3.59210e34 q^{77} -1.80112e35 q^{78} -9.67376e34 q^{79} -9.74321e34 q^{81} -2.01758e35 q^{82} +2.94893e35 q^{83} -1.13468e36 q^{84} -2.65077e35 q^{86} +1.30202e35 q^{87} -1.25309e36 q^{88} -1.89676e36 q^{89} +2.52022e36 q^{91} +5.19844e35 q^{92} +2.82880e36 q^{93} +2.43760e36 q^{94} -1.85368e37 q^{96} -4.70513e36 q^{97} +7.83203e36 q^{98} +1.12736e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+O(q^{10}) \) 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9	\( 18 q + 1378491386616 q^{4} + 235050070586136 q^{6} + 26\!\cdots\!74 q^{9}+ \cdots + 56\!\cdots\!28 q^{99}+O(q^{100}) \) 18 * q + 1378491386616 * q^4 + 235050070586136 * q^6 + 2687284960012241874 * q^9 + 33986627223034798296 * q^11 + 1891478635206760615032 * q^14 + 156966361562724410096928 * q^16 + 302760323265144477867480 * q^19 - 4075600057180968977719704 * q^21 + 149013794188298144591103840 * q^24 + 740755125071253494506988496 * q^26 + 4979198281142680608411084420 * q^29 - 6151542350452781958579360384 * q^31 - 4353870657762813132282760128 * q^34 + 106785265488844195864724376888 * q^36 - 862865339998466438248367480112 * q^39 - 855196121794787398902389240124 * q^41 + 13806087517221679193940877688352 * q^44 + 21104472252831571358912888976456 * q^46 + 70801883273781655273950124330026 * q^49 - 23706017526907962630925223712384 * q^51 + 523190901027760133510234826308880 * q^54 + 600728793662143364055878849971680 * q^56 + 3947688162499809731531683814232840 * q^59 + 1757475029942100801736311637166796 * q^61 + 35293446897899611856499858227515776 * q^64 + 32483717310049996392729278134533792 * q^66 + 29536156423306266276087371479398168 * q^69 - 15852144098617191882453852538452144 * q^71 - 35174192734582932814586482689499248 * q^74 - 8033980639764558547374281250927840 * q^76 + 81628804120848018323973892688639520 * q^79 - 51387579768336601107744192991686822 * q^81 - 3799290048936464645757894225695060448 * q^84 - 3995229770967016576777180478600492424 * q^86 - 5941001429647591369362270403151043540 * q^89 + 2681006692210129770276250954718747856 * q^91 - 2447341171808746326507906787285919208 * q^94 - 2375166431920457136532866502177021824 * q^96 + 56285732505135601101448147731191891928 * q^99

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