LMFDB - Embedded newform 1925.2.b.m.1849.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1849,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1925.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 385)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.5
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1925.1849
Dual form			1925.2.b.m.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.53919i q^{2} -3.17009i q^{3} -0.369102 q^{4} +4.87936 q^{6} -1.00000i q^{7} +2.51026i q^{8} -7.04945 q^{9} +O(q^{10})$	\(q+1.53919i q^{2} -3.17009i q^{3} -0.369102 q^{4} +4.87936 q^{6} -1.00000i q^{7} +2.51026i q^{8} -7.04945 q^{9} +1.00000 q^{11} +1.17009i q^{12} -0.829914i q^{13} +1.53919 q^{14} -4.60197 q^{16} +2.82991i q^{17} -10.8504i q^{18} -6.49693 q^{19} -3.17009 q^{21} +1.53919i q^{22} -6.97107i q^{23} +7.95774 q^{24} +1.27739 q^{26} +12.8371i q^{27} +0.369102i q^{28} -3.26180 q^{29} -10.2979 q^{31} -2.06278i q^{32} -3.17009i q^{33} -4.35577 q^{34} +2.60197 q^{36} -11.3112i q^{37} -10.0000i q^{38} -2.63090 q^{39} -0.199016 q^{41} -4.87936i q^{42} -0.447480i q^{43} -0.369102 q^{44} +10.7298 q^{46} +6.82991i q^{47} +14.5886i q^{48} -1.00000 q^{49} +8.97107 q^{51} +0.306323i q^{52} -7.31124i q^{53} -19.7587 q^{54} +2.51026 q^{56} +20.5958i q^{57} -5.02052i q^{58} +7.95774 q^{59} -6.87936 q^{61} -15.8504i q^{62} +7.04945i q^{63} -6.02893 q^{64} +4.87936 q^{66} -6.20620i q^{67} -1.04453i q^{68} -22.0989 q^{69} -11.4186 q^{71} -17.6959i q^{72} +5.66701i q^{73} +17.4101 q^{74} +2.39803 q^{76} -1.00000i q^{77} -4.04945i q^{78} +14.5464 q^{79} +19.5464 q^{81} -0.306323i q^{82} +2.89496i q^{83} +1.17009 q^{84} +0.688756 q^{86} +10.3402i q^{87} +2.51026i q^{88} +0.581449 q^{89} -0.829914 q^{91} +2.57304i q^{92} +32.6453i q^{93} -10.5125 q^{94} -6.53919 q^{96} +2.15676i q^{97} -1.53919i q^{98} -7.04945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 6 q^{11} + 6 q^{14} + 10 q^{16} - 4 q^{19} - 8 q^{21} + 16 q^{24} + 20 q^{26} - 4 q^{29} - 8 q^{31} - 32 q^{34} - 22 q^{36} - 8 q^{39} - 20 q^{41} - 10 q^{44} - 16 q^{46} - 6 q^{49} + 24 q^{51} - 68 q^{54} - 18 q^{56} + 16 q^{59} - 16 q^{61} - 66 q^{64} + 4 q^{66} - 60 q^{69} - 40 q^{71} - 20 q^{74} + 52 q^{76} + 16 q^{79} + 46 q^{81} - 4 q^{84} + 56 q^{86} + 32 q^{89} - 16 q^{91} - 56 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 6 * q^11 + 6 * q^14 + 10 * q^16 - 4 * q^19 - 8 * q^21 + 16 * q^24 + 20 * q^26 - 4 * q^29 - 8 * q^31 - 32 * q^34 - 22 * q^36 - 8 * q^39 - 20 * q^41 - 10 * q^44 - 16 * q^46 - 6 * q^49 + 24 * q^51 - 68 * q^54 - 18 * q^56 + 16 * q^59 - 16 * q^61 - 66 * q^64 + 4 * q^66 - 60 * q^69 - 40 * q^71 - 20 * q^74 + 52 * q^76 + 16 * q^79 + 46 * q^81 - 4 * q^84 + 56 * q^86 + 32 * q^89 - 16 * q^91 - 56 * q^94 - 36 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times$.

$n$	$276$	$1002$	$1751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.53919i	1.08837i	0.838965	+	0.544185i	$0.183161\pi$
$2$	1.53919i	1.08837i	−0.838965	+	0.544185i	$0.816839\pi$
$3$	− 3.17009i	− 1.83025i	−0.403170	−	0.915125i	$-0.632092\pi$
$3$	− 3.17009i	− 1.83025i	0.403170	−	0.915125i	$-0.367908\pi$
$4$	−0.369102	−0.184551
$5$	0	0
$5$	0	0
$6$	4.87936	1.99199
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	2.51026i	0.887511i
$9$	−7.04945	−2.34982
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.17009i	0.337775i
$13$	− 0.829914i	− 0.230177i	−0.993355	−	0.115088i	$-0.963285\pi$
$13$	− 0.829914i	− 0.230177i	0.993355	−	0.115088i	$-0.0367151\pi$
$14$	1.53919	0.411366
$15$	0	0
$16$	−4.60197	−1.15049
$17$	2.82991i	0.686355i	0.939271	+	0.343177i	$0.111503\pi$
$17$	2.82991i	0.686355i	−0.939271	+	0.343177i	$0.888497\pi$
$18$	− 10.8504i	− 2.55747i
$19$	−6.49693	−1.49050	−0.745249	−	0.666786i	$-0.767669\pi$
$19$	−6.49693	−1.49050	−0.745249	+	0.666786i	$0.767669\pi$
$20$	0	0
$21$	−3.17009	−0.691770
$22$	1.53919i	0.328156i
$23$	− 6.97107i	− 1.45357i	−0.686866	−	0.726784i	$-0.741014\pi$
$23$	− 6.97107i	− 1.45357i	0.686866	−	0.726784i	$-0.258986\pi$
$24$	7.95774	1.62437
$25$	0	0
$26$	1.27739	0.250518
$27$	12.8371i	2.47050i
$28$	0.369102i	0.0697538i
$29$	−3.26180	−0.605700	−0.302850	−	0.953038i	$-0.597938\pi$
$29$	−3.26180	−0.605700	−0.302850	+	0.953038i	$0.597938\pi$
$30$	0	0
$31$	−10.2979	−1.84956	−0.924780	−	0.380503i	$-0.875751\pi$
$31$	−10.2979	−1.84956	−0.924780	+	0.380503i	$0.875751\pi$
$32$	− 2.06278i	− 0.364651i
$33$	− 3.17009i	− 0.551841i
$34$	−4.35577	−0.747009
$35$	0	0
$36$	2.60197	0.433661
$37$	− 11.3112i	− 1.85956i	−0.368119	−	0.929778i	$-0.619998\pi$
$37$	− 11.3112i	− 1.85956i	0.368119	−	0.929778i	$-0.380002\pi$
$38$	− 10.0000i	− 1.62221i
$39$	−2.63090	−0.421281
$40$	0	0
$41$	−0.199016	−0.0310811	−0.0155405	−	0.999879i	$-0.504947\pi$
$41$	−0.199016	−0.0310811	−0.0155405	+	0.999879i	$0.504947\pi$
$42$	− 4.87936i	− 0.752902i
$43$	− 0.447480i	− 0.0682401i	−0.999418	−	0.0341200i	$-0.989137\pi$
$43$	− 0.447480i	− 0.0682401i	0.999418	−	0.0341200i	$-0.0108629\pi$
$44$	−0.369102	−0.0556443
$45$	0	0
$46$	10.7298	1.58202
$47$	6.82991i	0.996245i	0.867107	+	0.498123i	$0.165977\pi$
$47$	6.82991i	0.996245i	−0.867107	+	0.498123i	$0.834023\pi$
$48$	14.5886i	2.10569i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	8.97107	1.25620
$52$	0.306323i	0.0424794i
$53$	− 7.31124i	− 1.00428i	−0.864787	−	0.502138i	$-0.832547\pi$
$53$	− 7.31124i	− 1.00428i	0.864787	−	0.502138i	$-0.167453\pi$
$54$	−19.7587	−2.68882
$55$	0	0
$56$	2.51026	0.335448
$57$	20.5958i	2.72798i
$58$	− 5.02052i	− 0.659226i
$59$	7.95774	1.03601	0.518005	−	0.855378i	$-0.326675\pi$
$59$	7.95774	1.03601	0.518005	+	0.855378i	$0.326675\pi$
$60$	0	0
$61$	−6.87936	−0.880812	−0.440406	−	0.897799i	$-0.645165\pi$
$61$	−6.87936	−0.880812	−0.440406	+	0.897799i	$0.645165\pi$
$62$	− 15.8504i	− 2.01301i
$63$	7.04945i	0.888147i
$64$	−6.02893	−0.753616
$65$	0	0
$66$	4.87936	0.600608
$67$	− 6.20620i	− 0.758208i	−0.925354	−	0.379104i	$-0.876232\pi$
$67$	− 6.20620i	− 0.758208i	0.925354	−	0.379104i	$-0.123768\pi$
$68$	− 1.04453i	− 0.126668i
$69$	−22.0989	−2.66039
$70$	0	0
$71$	−11.4186	−1.35513	−0.677566	−	0.735462i	$-0.736965\pi$
$71$	−11.4186	−1.35513	−0.677566	+	0.735462i	$0.736965\pi$
$72$	− 17.6959i	− 2.08549i
$73$	5.66701i	0.663274i	0.943407	+	0.331637i	$0.107601\pi$
$73$	5.66701i	0.663274i	−0.943407	+	0.331637i	$0.892399\pi$
$74$	17.4101	2.02389
$75$	0	0
$76$	2.39803	0.275073
$77$	− 1.00000i	− 0.113961i
$78$	− 4.04945i	− 0.458510i
$79$	14.5464	1.63660	0.818298	−	0.574795i	$-0.194918\pi$
$79$	14.5464	1.63660	0.818298	+	0.574795i	$0.194918\pi$
$80$	0	0
$81$	19.5464	2.17182
$82$	− 0.306323i	− 0.0338277i
$83$	2.89496i	0.317763i	0.987298	+	0.158882i	$0.0507888\pi$
$83$	2.89496i	0.317763i	−0.987298	+	0.158882i	$0.949211\pi$
$84$	1.17009	0.127667
$85$	0	0
$86$	0.688756	0.0742705
$87$	10.3402i	1.10858i
$88$	2.51026i	0.267595i
$89$	0.581449	0.0616335	0.0308168	−	0.999525i	$-0.490189\pi$
$89$	0.581449	0.0616335	0.0308168	+	0.999525i	$0.490189\pi$
$90$	0	0
$91$	−0.829914	−0.0869986
$92$	2.57304i	0.268258i
$93$	32.6453i	3.38516i
$94$	−10.5125	−1.08428
$95$	0	0
$96$	−6.53919	−0.667403
$97$	2.15676i	0.218985i	0.993988	+	0.109493i	$0.0349226\pi$
$97$	2.15676i	0.218985i	−0.993988	+	0.109493i	$0.965077\pi$
$98$	− 1.53919i	− 0.155482i
$99$	−7.04945	−0.708496
$100$	0	0
$101$	−7.21953	−0.718371	−0.359185	−	0.933266i	$-0.616945\pi$
$101$	−7.21953	−0.718371	−0.359185	+	0.933266i	$0.616945\pi$
$102$	13.8082i	1.36721i
$103$	3.66701i	0.361322i	0.983545	+	0.180661i	$0.0578236\pi$
$103$	3.66701i	0.361322i	−0.983545	+	0.180661i	$0.942176\pi$
$104$	2.08330	0.204284
$105$	0	0
$106$	11.2534	1.09303
$107$	9.26180i	0.895372i	0.894191	+	0.447686i	$0.147752\pi$
$107$	9.26180i	0.895372i	−0.894191	+	0.447686i	$0.852248\pi$
$108$	− 4.73820i	− 0.455934i
$109$	−6.86376	−0.657429	−0.328715	−	0.944429i	$-0.606615\pi$
$109$	−6.86376	−0.657429	−0.328715	+	0.944429i	$0.606615\pi$
$110$	0	0
$111$	−35.8576	−3.40345
$112$	4.60197i	0.434845i
$113$	− 3.75872i	− 0.353591i	−0.984248	−	0.176795i	$-0.943427\pi$
$113$	− 3.75872i	− 0.353591i	0.984248	−	0.176795i	$-0.0565731\pi$
$114$	−31.7009	−2.96906
$115$	0	0
$116$	1.20394	0.111783
$117$	5.85043i	0.540873i
$118$	12.2485i	1.12756i
$119$	2.82991	0.259418
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 10.5886i	− 0.958650i
$123$	0.630898i	0.0568861i
$124$	3.80098	0.341338
$125$	0	0
$126$	−10.8504	−0.966633
$127$	21.5441i	1.91173i	0.293805	+	0.955865i	$0.405078\pi$
$127$	21.5441i	1.91173i	−0.293805	+	0.955865i	$0.594922\pi$
$128$	− 13.4052i	− 1.18487i
$129$	−1.41855	−0.124896
$130$	0	0
$131$	−12.6803	−1.10789	−0.553943	−	0.832554i	$-0.686878\pi$
$131$	−12.6803	−1.10789	−0.553943	+	0.832554i	$0.686878\pi$
$132$	1.17009i	0.101843i
$133$	6.49693i	0.563355i
$134$	9.55252	0.825212
$135$	0	0
$136$	−7.10382	−0.609147
$137$	− 19.6248i	− 1.67666i	−0.545166	−	0.838328i	$-0.683533\pi$
$137$	− 19.6248i	− 1.67666i	0.545166	−	0.838328i	$-0.316467\pi$
$138$	− 34.0144i	− 2.89550i
$139$	0.496928	0.0421489	0.0210745	−	0.999778i	$-0.493291\pi$
$139$	0.496928	0.0421489	0.0210745	+	0.999778i	$0.493291\pi$
$140$	0	0
$141$	21.6514	1.82338
$142$	− 17.5753i	− 1.47489i
$143$	− 0.829914i	− 0.0694009i
$144$	32.4413	2.70344
$145$	0	0
$146$	−8.72261	−0.721888
$147$	3.17009i	0.261464i
$148$	4.17501i	0.343183i
$149$	13.3340	1.09237	0.546183	−	0.837666i	$-0.316080\pi$
$149$	13.3340	1.09237	0.546183	+	0.837666i	$0.316080\pi$
$150$	0	0
$151$	−1.05559	−0.0859028	−0.0429514	−	0.999077i	$-0.513676\pi$
$151$	−1.05559	−0.0859028	−0.0429514	+	0.999077i	$0.513676\pi$
$152$	− 16.3090i	− 1.32283i
$153$	− 19.9493i	− 1.61281i
$154$	1.53919	0.124031
$155$	0	0
$156$	0.971071	0.0777479
$157$	0.496928i	0.0396592i	0.999803	+	0.0198296i	$0.00631237\pi$
$157$	0.496928i	0.0396592i	−0.999803	+	0.0198296i	$0.993688\pi$
$158$	22.3896i	1.78122i
$159$	−23.1773	−1.83808
$160$	0	0
$161$	−6.97107	−0.549397
$162$	30.0856i	2.36375i
$163$	1.31124i	0.102705i	0.998681	+	0.0513523i	$0.0163531\pi$
$163$	1.31124i	0.102705i	−0.998681	+	0.0513523i	$0.983647\pi$
$164$	0.0734572	0.00573605
$165$	0	0
$166$	−4.45589	−0.345844
$167$	− 3.17727i	− 0.245865i	−0.992415	−	0.122932i	$-0.960770\pi$
$167$	− 3.17727i	− 0.245865i	0.992415	−	0.122932i	$-0.0392298\pi$
$168$	− 7.95774i	− 0.613953i
$169$	12.3112	0.947019
$170$	0	0
$171$	45.7998	3.50240
$172$	0.165166i	0.0125938i
$173$	− 17.9493i	− 1.36466i	−0.731043	−	0.682331i	$-0.760966\pi$
$173$	− 17.9493i	− 1.36466i	0.731043	−	0.682331i	$-0.239034\pi$
$174$	−15.9155	−1.20655
$175$	0	0
$176$	−4.60197	−0.346886
$177$	− 25.2267i	− 1.89616i
$178$	0.894960i	0.0670801i
$179$	−15.7321	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$179$	−15.7321	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$180$	0	0
$181$	−16.8104	−1.24951	−0.624755	−	0.780821i	$-0.714801\pi$
$181$	−16.8104	−1.24951	−0.624755	+	0.780821i	$0.714801\pi$
$182$	− 1.27739i	− 0.0946867i
$183$	21.8082i	1.61211i
$184$	17.4992	1.29006
$185$	0	0
$186$	−50.2472	−3.68431
$187$	2.82991i	0.206944i
$188$	− 2.52094i	− 0.183858i
$189$	12.8371	0.933762
$190$	0	0
$191$	−2.92162	−0.211401	−0.105701	−	0.994398i	$-0.533709\pi$
$191$	−2.92162	−0.211401	−0.105701	+	0.994398i	$0.533709\pi$
$192$	19.1122i	1.37931i
$193$	− 22.8287i	− 1.64325i	−0.570032	−	0.821623i	$-0.693069\pi$
$193$	− 22.8287i	− 1.64325i	0.570032	−	0.821623i	$-0.306931\pi$
$194$	−3.31965	−0.238337
$195$	0	0
$196$	0.369102	0.0263645
$197$	− 19.7237i	− 1.40525i	−0.711559	−	0.702626i	$-0.752011\pi$
$197$	− 19.7237i	− 1.40525i	0.711559	−	0.702626i	$-0.247989\pi$
$198$	− 10.8504i	− 0.771107i
$199$	10.6381	0.754114	0.377057	−	0.926190i	$-0.376936\pi$
$199$	10.6381	0.754114	0.377057	+	0.926190i	$0.376936\pi$
$200$	0	0
$201$	−19.6742	−1.38771
$202$	− 11.1122i	− 0.781854i
$203$	3.26180i	0.228933i
$204$	−3.31124	−0.231833
$205$	0	0
$206$	−5.64423	−0.393252
$207$	49.1422i	3.41562i
$208$	3.81924i	0.264816i
$209$	−6.49693	−0.449402
$210$	0	0
$211$	7.50307	0.516533	0.258266	−	0.966074i	$-0.416849\pi$
$211$	7.50307	0.516533	0.258266	+	0.966074i	$0.416849\pi$
$212$	2.69860i	0.185340i
$213$	36.1978i	2.48023i
$214$	−14.2557	−0.974496
$215$	0	0
$216$	−32.2245	−2.19260
$217$	10.2979i	0.699068i
$218$	− 10.5646i	− 0.715527i
$219$	17.9649	1.21396
$220$	0	0
$221$	2.34858	0.157983
$222$	− 55.1917i	− 3.70422i
$223$	24.0338i	1.60943i	0.593664	+	0.804713i	$0.297681\pi$
$223$	24.0338i	1.60943i	−0.593664	+	0.804713i	$0.702319\pi$
$224$	−2.06278	−0.137825
$225$	0	0
$226$	5.78539	0.384838
$227$	− 1.47641i	− 0.0979927i	−0.998799	−	0.0489964i	$-0.984398\pi$
$227$	− 1.47641i	− 0.0979927i	0.998799	−	0.0489964i	$-0.0156023\pi$
$228$	− 7.60197i	− 0.503453i
$229$	−8.07223	−0.533428	−0.266714	−	0.963776i	$-0.585938\pi$
$229$	−8.07223	−0.533428	−0.266714	+	0.963776i	$0.585938\pi$
$230$	0	0
$231$	−3.17009	−0.208576
$232$	− 8.18795i	− 0.537565i
$233$	− 6.44748i	− 0.422388i	−0.977444	−	0.211194i	$-0.932265\pi$
$233$	− 6.44748i	− 0.422388i	0.977444	−	0.211194i	$-0.0677353\pi$
$234$	−9.00492	−0.588670
$235$	0	0
$236$	−2.93722	−0.191197
$237$	− 46.1133i	− 2.99538i
$238$	4.35577i	0.282343i
$239$	8.18342	0.529341	0.264671	−	0.964339i	$-0.414737\pi$
$239$	8.18342	0.529341	0.264671	+	0.964339i	$0.414737\pi$
$240$	0	0
$241$	10.9060	0.702519	0.351259	−	0.936278i	$-0.385754\pi$
$241$	10.9060	0.702519	0.351259	+	0.936278i	$0.385754\pi$
$242$	1.53919i	0.0989428i
$243$	− 23.4524i	− 1.50447i
$244$	2.53919	0.162555
$245$	0	0
$246$	−0.971071	−0.0619132
$247$	5.39189i	0.343078i
$248$	− 25.8504i	− 1.64150i
$249$	9.17727	0.581586
$250$	0	0
$251$	18.7948	1.18632	0.593160	−	0.805085i	$-0.297880\pi$
$251$	18.7948	1.18632	0.593160	+	0.805085i	$0.297880\pi$
$252$	− 2.60197i	− 0.163909i
$253$	− 6.97107i	− 0.438267i
$254$	−33.1605	−2.08067
$255$	0	0
$256$	8.57531	0.535957
$257$	13.0784i	0.815807i	0.913025	+	0.407903i	$0.133740\pi$
$257$	13.0784i	0.815807i	−0.913025	+	0.407903i	$0.866260\pi$
$258$	− 2.18342i	− 0.135934i
$259$	−11.3112	−0.702846
$260$	0	0
$261$	22.9939	1.42328
$262$	− 19.5174i	− 1.20579i
$263$	− 10.0267i	− 0.618270i	−0.951018	−	0.309135i	$-0.899960\pi$
$263$	− 10.0267i	− 0.618270i	0.951018	−	0.309135i	$-0.100040\pi$
$264$	7.95774	0.489765
$265$	0	0
$266$	−10.0000	−0.613139
$267$	− 1.84324i	− 0.112805i
$268$	2.29072i	0.139928i
$269$	11.9155	0.726500	0.363250	−	0.931692i	$-0.381667\pi$
$269$	11.9155	0.726500	0.363250	+	0.931692i	$0.381667\pi$
$270$	0	0
$271$	25.1773	1.52941	0.764705	−	0.644380i	$-0.222885\pi$
$271$	25.1773	1.52941	0.764705	+	0.644380i	$0.222885\pi$
$272$	− 13.0232i	− 0.789646i
$273$	2.63090i	0.159229i
$274$	30.2062	1.82482
$275$	0	0
$276$	8.15676	0.490979
$277$	5.33791i	0.320724i	0.987058	+	0.160362i	$0.0512661\pi$
$277$	5.33791i	0.320724i	−0.987058	+	0.160362i	$0.948734\pi$
$278$	0.764867i	0.0458737i
$279$	72.5946	4.34613
$280$	0	0
$281$	16.4703	0.982534	0.491267	−	0.871009i	$-0.336534\pi$
$281$	16.4703	0.982534	0.491267	+	0.871009i	$0.336534\pi$
$282$	33.3256i	1.98451i
$283$	− 0.948284i	− 0.0563696i	−0.999603	−	0.0281848i	$-0.991027\pi$
$283$	− 0.948284i	− 0.0563696i	0.999603	−	0.0281848i	$-0.00897270\pi$
$284$	4.21461	0.250091
$285$	0	0
$286$	1.27739	0.0755339
$287$	0.199016i	0.0117475i
$288$	14.5415i	0.856864i
$289$	8.99159	0.528917
$290$	0	0
$291$	6.83710	0.400798
$292$	− 2.09171i	− 0.122408i
$293$	− 7.72487i	− 0.451292i	−0.974209	−	0.225646i	$-0.927551\pi$
$293$	− 7.72487i	− 0.451292i	0.974209	−	0.225646i	$-0.0724493\pi$
$294$	−4.87936	−0.284570
$295$	0	0
$296$	28.3942	1.65038
$297$	12.8371i	0.744884i
$298$	20.5236i	1.18890i
$299$	−5.78539	−0.334577
$300$	0	0
$301$	−0.447480	−0.0257923
$302$	− 1.62475i	− 0.0934941i
$303$	22.8865i	1.31480i
$304$	29.8987	1.71481
$305$	0	0
$306$	30.7058	1.75533
$307$	32.7526i	1.86929i	0.355584	+	0.934644i	$0.384282\pi$
$307$	32.7526i	1.86929i	−0.355584	+	0.934644i	$0.615718\pi$
$308$	0.369102i	0.0210316i
$309$	11.6248	0.661309
$310$	0	0
$311$	22.9204	1.29970	0.649848	−	0.760064i	$-0.274832\pi$
$311$	22.9204	1.29970	0.649848	+	0.760064i	$0.274832\pi$
$312$	− 6.60424i	− 0.373891i
$313$	− 11.5753i	− 0.654275i	−0.944977	−	0.327137i	$-0.893916\pi$
$313$	− 11.5753i	− 0.654275i	0.944977	−	0.327137i	$-0.106084\pi$
$314$	−0.764867	−0.0431639
$315$	0	0
$316$	−5.36910	−0.302036
$317$	− 12.5236i	− 0.703395i	−0.936114	−	0.351697i	$-0.885605\pi$
$317$	− 12.5236i	− 0.703395i	0.936114	−	0.351697i	$-0.114395\pi$
$318$	− 35.6742i	− 2.00051i
$319$	−3.26180	−0.182625
$320$	0	0
$321$	29.3607	1.63875
$322$	− 10.7298i	− 0.597948i
$323$	− 18.3857i	− 1.02301i
$324$	−7.21461	−0.400812
$325$	0	0
$326$	−2.01825	−0.111781
$327$	21.7587i	1.20326i
$328$	− 0.499582i	− 0.0275848i
$329$	6.82991	0.376545
$330$	0	0
$331$	−18.1711	−0.998776	−0.499388	−	0.866379i	$-0.666442\pi$
$331$	−18.1711	−0.998776	−0.499388	+	0.866379i	$0.666442\pi$
$332$	− 1.06854i	− 0.0586436i
$333$	79.7380i	4.36962i
$334$	4.89043	0.267592
$335$	0	0
$336$	14.5886	0.795875
$337$	− 28.0905i	− 1.53019i	−0.643920	−	0.765093i	$-0.722693\pi$
$337$	− 28.0905i	− 1.53019i	0.643920	−	0.765093i	$-0.277307\pi$
$338$	18.9493i	1.03071i
$339$	−11.9155	−0.647160
$340$	0	0
$341$	−10.2979	−0.557663
$342$	70.4945i	3.81191i
$343$	1.00000i	0.0539949i
$344$	1.12329	0.0605638
$345$	0	0
$346$	27.6274	1.48526
$347$	− 22.0761i	− 1.18511i	−0.805531	−	0.592554i	$-0.798120\pi$
$347$	− 22.0761i	− 1.18511i	0.805531	−	0.592554i	$-0.201880\pi$
$348$	− 3.81658i	− 0.204590i
$349$	−18.2134	−0.974941	−0.487470	−	0.873140i	$-0.662080\pi$
$349$	−18.2134	−0.974941	−0.487470	+	0.873140i	$0.662080\pi$
$350$	0	0
$351$	10.6537	0.568652
$352$	− 2.06278i	− 0.109947i
$353$	− 1.41855i	− 0.0755018i	−0.999287	−	0.0377509i	$-0.987981\pi$
$353$	− 1.41855i	− 0.0755018i	0.999287	−	0.0377509i	$-0.0120193\pi$
$354$	38.8287	2.06372
$355$	0	0
$356$	−0.214614	−0.0113745
$357$	− 8.97107i	− 0.474799i
$358$	− 24.2146i	− 1.27978i
$359$	−13.0700	−0.689806	−0.344903	−	0.938638i	$-0.612088\pi$
$359$	−13.0700	−0.689806	−0.344903	+	0.938638i	$0.612088\pi$
$360$	0	0
$361$	23.2101	1.22158
$362$	− 25.8744i	− 1.35993i
$363$	− 3.17009i	− 0.166386i
$364$	0.306323	0.0160557
$365$	0	0
$366$	−33.5669	−1.75457
$367$	− 19.7926i	− 1.03316i	−0.856238	−	0.516582i	$-0.827204\pi$
$367$	− 19.7926i	− 1.03316i	0.856238	−	0.516582i	$-0.172796\pi$
$368$	32.0806i	1.67232i
$369$	1.40295	0.0730348
$370$	0	0
$371$	−7.31124	−0.379581
$372$	− 12.0494i	− 0.624735i
$373$	− 31.4101i	− 1.62636i	−0.582015	−	0.813178i	$-0.697736\pi$
$373$	− 31.4101i	− 1.62636i	0.582015	−	0.813178i	$-0.302264\pi$
$374$	−4.35577	−0.225232
$375$	0	0
$376$	−17.1449	−0.884178
$377$	2.70701i	0.139418i
$378$	19.7587i	1.01628i
$379$	−21.9421	−1.12709	−0.563546	−	0.826085i	$-0.690563\pi$
$379$	−21.9421	−1.12709	−0.563546	+	0.826085i	$0.690563\pi$
$380$	0	0
$381$	68.2967	3.49895
$382$	− 4.49693i	− 0.230083i
$383$	6.95547i	0.355408i	0.984084	+	0.177704i	$0.0568670\pi$
$383$	6.95547i	0.355408i	−0.984084	+	0.177704i	$0.943133\pi$
$384$	−42.4957	−2.16860
$385$	0	0
$386$	35.1377	1.78846
$387$	3.15449i	0.160352i
$388$	− 0.796064i	− 0.0404140i
$389$	−2.76487	−0.140184	−0.0700922	−	0.997541i	$-0.522329\pi$
$389$	−2.76487	−0.140184	−0.0700922	+	0.997541i	$0.522329\pi$
$390$	0	0
$391$	19.7275	0.997664
$392$	− 2.51026i	− 0.126787i
$393$	40.1978i	2.02771i
$394$	30.3584	1.52944
$395$	0	0
$396$	2.60197	0.130754
$397$	− 6.92162i	− 0.347386i	−0.984800	−	0.173693i	$-0.944430\pi$
$397$	− 6.92162i	− 0.347386i	0.984800	−	0.173693i	$-0.0555701\pi$
$398$	16.3740i	0.820756i
$399$	20.5958	1.03108
$400$	0	0
$401$	−6.68035	−0.333601	−0.166800	−	0.985991i	$-0.553344\pi$
$401$	−6.68035	−0.333601	−0.166800	+	0.985991i	$0.553344\pi$
$402$	− 30.2823i	− 1.51034i
$403$	8.54638i	0.425725i
$404$	2.66475	0.132576
$405$	0	0
$406$	−5.02052	−0.249164
$407$	− 11.3112i	− 0.560678i
$408$	22.5197i	1.11489i
$409$	−15.0772	−0.745517	−0.372759	−	0.927928i	$-0.621588\pi$
$409$	−15.0772	−0.745517	−0.372759	+	0.927928i	$0.621588\pi$
$410$	0	0
$411$	−62.2122	−3.06870
$412$	− 1.35350i	− 0.0666824i
$413$	− 7.95774i	− 0.391575i
$414$	−75.6391	−3.71746
$415$	0	0
$416$	−1.71193	−0.0839342
$417$	− 1.57531i	− 0.0771431i
$418$	− 10.0000i	− 0.489116i
$419$	9.54533	0.466320	0.233160	−	0.972438i	$-0.425093\pi$
$419$	9.54533	0.466320	0.233160	+	0.972438i	$0.425093\pi$
$420$	0	0
$421$	−32.7442	−1.59585	−0.797927	−	0.602755i	$-0.794070\pi$
$421$	−32.7442	−1.59585	−0.797927	+	0.602755i	$0.794070\pi$
$422$	11.5486i	0.562179i
$423$	− 48.1471i	− 2.34099i
$424$	18.3531	0.891306
$425$	0	0
$426$	−55.7152	−2.69941
$427$	6.87936i	0.332916i
$428$	− 3.41855i	− 0.165242i
$429$	−2.63090	−0.127021
$430$	0	0
$431$	−23.0289	−1.10926	−0.554632	−	0.832096i	$-0.687141\pi$
$431$	−23.0289	−1.10926	−0.554632	+	0.832096i	$0.687141\pi$
$432$	− 59.0759i	− 2.84229i
$433$	− 34.3279i	− 1.64969i	−0.565357	−	0.824846i	$-0.691262\pi$
$433$	− 34.3279i	− 1.64969i	0.565357	−	0.824846i	$-0.308738\pi$
$434$	−15.8504	−0.760845
$435$	0	0
$436$	2.53343	0.121329
$437$	45.2905i	2.16654i
$438$	27.6514i	1.32124i
$439$	16.5958	0.792076	0.396038	−	0.918234i	$-0.370385\pi$
$439$	16.5958	0.792076	0.396038	+	0.918234i	$0.370385\pi$
$440$	0	0
$441$	7.04945	0.335688
$442$	3.61491i	0.171944i
$443$	10.9177i	0.518718i	0.965781	+	0.259359i	$0.0835112\pi$
$443$	10.9177i	0.518718i	−0.965781	+	0.259359i	$0.916489\pi$
$444$	13.2351	0.628112
$445$	0	0
$446$	−36.9926	−1.75165
$447$	− 42.2700i	− 1.99930i
$448$	6.02893i	0.284840i
$449$	24.5997	1.16093	0.580466	−	0.814285i	$-0.302870\pi$
$449$	24.5997	1.16093	0.580466	+	0.814285i	$0.302870\pi$
$450$	0	0
$451$	−0.199016	−0.00937129
$452$	1.38735i	0.0652556i
$453$	3.34632i	0.157224i
$454$	2.27247	0.106652
$455$	0	0
$456$	−51.7009	−2.42111
$457$	36.9854i	1.73011i	0.501680	+	0.865053i	$0.332715\pi$
$457$	36.9854i	1.73011i	−0.501680	+	0.865053i	$0.667285\pi$
$458$	− 12.4247i	− 0.580568i
$459$	−36.3279	−1.69564
$460$	0	0
$461$	37.3595	1.74000	0.870002	−	0.493048i	$-0.164117\pi$
$461$	37.3595	1.74000	0.870002	+	0.493048i	$0.164117\pi$
$462$	− 4.87936i	− 0.227008i
$463$	7.05559i	0.327901i	0.986469	+	0.163951i	$0.0524238\pi$
$463$	7.05559i	0.327901i	−0.986469	+	0.163951i	$0.947576\pi$
$464$	15.0107	0.696853
$465$	0	0
$466$	9.92389	0.459715
$467$	19.8648i	0.919234i	0.888117	+	0.459617i	$0.152013\pi$
$467$	19.8648i	0.919234i	−0.888117	+	0.459617i	$0.847987\pi$
$468$	− 2.15941i	− 0.0998187i
$469$	−6.20620	−0.286576
$470$	0	0
$471$	1.57531	0.0725863
$472$	19.9760i	0.919470i
$473$	− 0.447480i	− 0.0205752i
$474$	70.9770	3.26008
$475$	0	0
$476$	−1.04453	−0.0478759
$477$	51.5402i	2.35987i
$478$	12.5958i	0.576120i
$479$	−6.39803	−0.292334	−0.146167	−	0.989260i	$-0.546694\pi$
$479$	−6.39803	−0.292334	−0.146167	+	0.989260i	$0.546694\pi$
$480$	0	0
$481$	−9.38735	−0.428026
$482$	16.7864i	0.764601i
$483$	22.0989i	1.00553i
$484$	−0.369102	−0.0167774
$485$	0	0
$486$	36.0977	1.63742
$487$	25.8082i	1.16948i	0.811221	+	0.584740i	$0.198803\pi$
$487$	25.8082i	1.16948i	−0.811221	+	0.584740i	$0.801197\pi$
$488$	− 17.2690i	− 0.781730i
$489$	4.15676	0.187975
$490$	0	0
$491$	−17.1689	−0.774820	−0.387410	−	0.921908i	$-0.626630\pi$
$491$	−17.1689	−0.774820	−0.387410	+	0.921908i	$0.626630\pi$
$492$	− 0.232866i	− 0.0104984i
$493$	− 9.23060i	− 0.415725i
$494$	−8.29914	−0.373396
$495$	0	0
$496$	47.3907	2.12790
$497$	11.4186i	0.512192i
$498$	14.1256i	0.632981i
$499$	13.1629	0.589252	0.294626	−	0.955613i	$-0.404805\pi$
$499$	13.1629	0.589252	0.294626	+	0.955613i	$0.404805\pi$
$500$	0	0
$501$	−10.0722	−0.449994
$502$	28.9288i	1.29116i
$503$	− 30.7259i	− 1.37000i	−0.728543	−	0.685000i	$-0.759802\pi$
$503$	− 30.7259i	− 1.37000i	0.728543	−	0.685000i	$-0.240198\pi$
$504$	−17.6959	−0.788240
$505$	0	0
$506$	10.7298	0.476998
$507$	− 39.0277i	− 1.73328i
$508$	− 7.95198i	− 0.352812i
$509$	−25.2183	−1.11778	−0.558891	−	0.829241i	$-0.688773\pi$
$509$	−25.2183	−1.11778	−0.558891	+	0.829241i	$0.688773\pi$
$510$	0	0
$511$	5.66701	0.250694
$512$	− 13.6114i	− 0.601546i
$513$	− 83.4017i	− 3.68228i
$514$	−20.1301	−0.887900
$515$	0	0
$516$	0.523590	0.0230498
$517$	6.82991i	0.300379i
$518$	− 17.4101i	− 0.764958i
$519$	−56.9009	−2.49767
$520$	0	0
$521$	0.183417	0.00803567	0.00401783	−	0.999992i	$-0.498721\pi$
$521$	0.183417	0.00803567	0.00401783	+	0.999992i	$0.498721\pi$
$522$	35.3919i	1.54906i
$523$	− 4.86830i	− 0.212876i	−0.994319	−	0.106438i	$-0.966055\pi$
$523$	− 4.86830i	− 0.212876i	0.994319	−	0.106438i	$-0.0339445\pi$
$524$	4.68035	0.204462
$525$	0	0
$526$	15.4329	0.672908
$527$	− 29.1422i	− 1.26945i
$528$	14.5886i	0.634889i
$529$	−25.5958	−1.11286
$530$	0	0
$531$	−56.0977	−2.43443
$532$	− 2.39803i	− 0.103968i
$533$	0.165166i	0.00715413i
$534$	2.83710	0.122773
$535$	0	0
$536$	15.5792	0.672918
$537$	49.8720i	2.15214i
$538$	18.3402i	0.790701i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−45.7009	−1.96483	−0.982417	−	0.186701i	$-0.940221\pi$
$541$	−45.7009	−1.96483	−0.982417	+	0.186701i	$0.940221\pi$
$542$	38.7526i	1.66457i
$543$	53.2905i	2.28692i
$544$	5.83749	0.250280
$545$	0	0
$546$	−4.04945	−0.173300
$547$	24.5958i	1.05164i	0.850595	+	0.525821i	$0.176242\pi$
$547$	24.5958i	1.05164i	−0.850595	+	0.525821i	$0.823758\pi$
$548$	7.24354i	0.309429i
$549$	48.4957	2.06975
$550$	0	0
$551$	21.1917	0.902795
$552$	− 55.4740i	− 2.36113i
$553$	− 14.5464i	− 0.618575i
$554$	−8.21604	−0.349066
$555$	0	0
$556$	−0.183417	−0.00777863
$557$	− 33.6514i	− 1.42586i	−0.701237	−	0.712928i	$-0.747369\pi$
$557$	− 33.6514i	− 1.42586i	0.701237	−	0.712928i	$-0.252631\pi$
$558$	111.737i	4.73020i
$559$	−0.371370	−0.0157073
$560$	0	0
$561$	8.97107	0.378759
$562$	25.3509i	1.06936i
$563$	− 32.2290i	− 1.35829i	−0.734004	−	0.679145i	$-0.762351\pi$
$563$	− 32.2290i	− 1.35829i	0.734004	−	0.679145i	$-0.237649\pi$
$564$	−7.99159	−0.336507
$565$	0	0
$566$	1.45959	0.0613511
$567$	− 19.5464i	− 0.820871i
$568$	− 28.6635i	− 1.20269i
$569$	−5.33403	−0.223614	−0.111807	−	0.993730i	$-0.535664\pi$
$569$	−5.33403	−0.223614	−0.111807	+	0.993730i	$0.535664\pi$
$570$	0	0
$571$	−29.5441	−1.23638	−0.618191	−	0.786028i	$-0.712134\pi$
$571$	−29.5441	−1.23638	−0.618191	+	0.786028i	$0.712134\pi$
$572$	0.306323i	0.0128080i
$573$	9.26180i	0.386917i
$574$	−0.306323	−0.0127857
$575$	0	0
$576$	42.5006	1.77086
$577$	− 3.78539i	− 0.157588i	−0.996891	−	0.0787938i	$-0.974893\pi$
$577$	− 3.78539i	− 0.157588i	0.996891	−	0.0787938i	$-0.0251069\pi$
$578$	13.8398i	0.575658i
$579$	−72.3689	−3.00755
$580$	0	0
$581$	2.89496	0.120103
$582$	10.5236i	0.436217i
$583$	− 7.31124i	− 0.302801i
$584$	−14.2257	−0.588663
$585$	0	0
$586$	11.8900	0.491173
$587$	− 14.5353i	− 0.599937i	−0.953949	−	0.299968i	$-0.903024\pi$
$587$	− 14.5353i	− 0.599937i	0.953949	−	0.299968i	$-0.0969761\pi$
$588$	− 1.17009i	− 0.0482536i
$589$	66.9048	2.75676
$590$	0	0
$591$	−62.5257	−2.57196
$592$	52.0540i	2.13941i
$593$	43.6814i	1.79378i	0.442254	+	0.896890i	$0.354179\pi$
$593$	43.6814i	1.79378i	−0.442254	+	0.896890i	$0.645821\pi$
$594$	−19.7587	−0.810710
$595$	0	0
$596$	−4.92162	−0.201598
$597$	− 33.7237i	− 1.38022i
$598$	− 8.90480i	− 0.364144i
$599$	22.8371	0.933099	0.466549	−	0.884495i	$-0.345497\pi$
$599$	22.8371	0.933099	0.466549	+	0.884495i	$0.345497\pi$
$600$	0	0
$601$	−27.8687	−1.13679	−0.568394	−	0.822757i	$-0.692435\pi$
$601$	−27.8687	−1.13679	−0.568394	+	0.822757i	$0.692435\pi$
$602$	− 0.688756i	− 0.0280716i
$603$	43.7503i	1.78165i
$604$	0.389621	0.0158535
$605$	0	0
$606$	−35.2267	−1.43099
$607$	− 29.8987i	− 1.21355i	−0.794874	−	0.606775i	$-0.792463\pi$
$607$	− 29.8987i	− 1.21355i	0.794874	−	0.606775i	$-0.207537\pi$
$608$	13.4017i	0.543512i
$609$	10.3402	0.419005
$610$	0	0
$611$	5.66824	0.229312
$612$	7.36334i	0.297646i
$613$	21.0700i	0.851008i	0.904957	+	0.425504i	$0.139903\pi$
$613$	21.0700i	0.851008i	−0.904957	+	0.425504i	$0.860097\pi$
$614$	−50.4124	−2.03448
$615$	0	0
$616$	2.51026	0.101141
$617$	− 4.10731i	− 0.165354i	−0.996576	−	0.0826770i	$-0.973653\pi$
$617$	− 4.10731i	− 0.165354i	0.996576	−	0.0826770i	$-0.0263470\pi$
$618$	17.8927i	0.719750i
$619$	14.5536	0.584957	0.292479	−	0.956272i	$-0.405520\pi$
$619$	14.5536	0.584957	0.292479	+	0.956272i	$0.405520\pi$
$620$	0	0
$621$	89.4883	3.59104
$622$	35.2788i	1.41455i
$623$	− 0.581449i	− 0.0232953i
$624$	12.1073	0.484680
$625$	0	0
$626$	17.8166	0.712094
$627$	20.5958i	0.822518i
$628$	− 0.183417i	− 0.00731915i
$629$	32.0098	1.27632
$630$	0	0
$631$	12.9939	0.517277	0.258639	−	0.965974i	$-0.416726\pi$
$631$	12.9939	0.517277	0.258639	+	0.965974i	$0.416726\pi$
$632$	36.5152i	1.45250i
$633$	− 23.7854i	− 0.945384i
$634$	19.2762	0.765555
$635$	0	0
$636$	8.55479	0.339219
$637$	0.829914i	0.0328824i
$638$	− 5.02052i	− 0.198764i
$639$	80.4945	3.18431
$640$	0	0
$641$	8.54638	0.337562	0.168781	−	0.985654i	$-0.446017\pi$
$641$	8.54638	0.337562	0.168781	+	0.985654i	$0.446017\pi$
$642$	45.1917i	1.78357i
$643$	17.7659i	0.700619i	0.936634	+	0.350310i	$0.113924\pi$
$643$	17.7659i	0.700619i	−0.936634	+	0.350310i	$0.886076\pi$
$644$	2.57304	0.101392
$645$	0	0
$646$	28.2991	1.11341
$647$	− 44.9698i	− 1.76795i	−0.467537	−	0.883974i	$-0.654858\pi$
$647$	− 44.9698i	− 1.76795i	0.467537	−	0.883974i	$-0.345142\pi$
$648$	49.0665i	1.92751i
$649$	7.95774	0.312369
$650$	0	0
$651$	32.6453	1.27947
$652$	− 0.483983i	− 0.0189542i
$653$	− 4.75258i	− 0.185983i	−0.995667	−	0.0929914i	$-0.970357\pi$
$653$	− 4.75258i	− 0.185983i	0.995667	−	0.0929914i	$-0.0296429\pi$
$654$	−33.4908	−1.30959
$655$	0	0
$656$	0.915865	0.0357585
$657$	− 39.9493i	− 1.55857i
$658$	10.5125i	0.409821i
$659$	17.2990	0.673872	0.336936	−	0.941528i	$-0.390609\pi$
$659$	17.2990	0.673872	0.336936	+	0.941528i	$0.390609\pi$
$660$	0	0
$661$	29.1629	1.13431	0.567153	−	0.823613i	$-0.308045\pi$
$661$	29.1629	1.13431	0.567153	+	0.823613i	$0.308045\pi$
$662$	− 27.9688i	− 1.08704i
$663$	− 7.44521i	− 0.289148i
$664$	−7.26710	−0.282018
$665$	0	0
$666$	−122.732	−4.75576
$667$	22.7382i	0.880427i
$668$	1.17274i	0.0453747i
$669$	76.1894	2.94565
$670$	0	0
$671$	−6.87936	−0.265575
$672$	6.53919i	0.252255i
$673$	36.0905i	1.39119i	0.718436	+	0.695593i	$0.244858\pi$
$673$	36.0905i	1.39119i	−0.718436	+	0.695593i	$0.755142\pi$
$674$	43.2366	1.66541
$675$	0	0
$676$	−4.54411	−0.174773
$677$	12.7310i	0.489293i	0.969612	+	0.244646i	$0.0786719\pi$
$677$	12.7310i	0.489293i	−0.969612	+	0.244646i	$0.921328\pi$
$678$	− 18.3402i	− 0.704350i
$679$	2.15676	0.0827687
$680$	0	0
$681$	−4.68035	−0.179351
$682$	− 15.8504i	− 0.606944i
$683$	− 5.47253i	− 0.209401i	−0.994504	−	0.104700i	$-0.966612\pi$
$683$	− 5.47253i	− 0.209401i	0.994504	−	0.104700i	$-0.0333883\pi$
$684$	−16.9048	−0.646371
$685$	0	0
$686$	−1.53919	−0.0587665
$687$	25.5897i	0.976307i
$688$	2.05929i	0.0785097i
$689$	−6.06770	−0.231161
$690$	0	0
$691$	30.7226	1.16874	0.584372	−	0.811486i	$-0.301341\pi$
$691$	30.7226	1.16874	0.584372	+	0.811486i	$0.301341\pi$
$692$	6.62514i	0.251850i
$693$	7.04945i	0.267786i
$694$	33.9793	1.28984
$695$	0	0
$696$	−25.9565	−0.983879
$697$	− 0.563198i	− 0.0213326i
$698$	− 28.0338i	− 1.06110i
$699$	−20.4391	−0.773077
$700$	0	0
$701$	−14.7649	−0.557661	−0.278831	−	0.960340i	$-0.589947\pi$
$701$	−14.7649	−0.557661	−0.278831	+	0.960340i	$0.589947\pi$
$702$	16.3980i	0.618904i
$703$	73.4883i	2.77167i
$704$	−6.02893	−0.227224
$705$	0	0
$706$	2.18342	0.0821740
$707$	7.21953i	0.271519i
$708$	9.31124i	0.349938i
$709$	5.63317	0.211558	0.105779	−	0.994390i	$-0.466266\pi$
$709$	5.63317	0.211558	0.105779	+	0.994390i	$0.466266\pi$
$710$	0	0
$711$	−102.544	−3.84570
$712$	1.45959i	0.0547004i
$713$	71.7875i	2.68846i
$714$	13.8082	0.516758
$715$	0	0
$716$	5.80674	0.217008
$717$	− 25.9421i	− 0.968827i
$718$	− 20.1171i	− 0.750765i
$719$	−35.0505	−1.30716	−0.653581	−	0.756856i	$-0.726734\pi$
$719$	−35.0505	−1.30716	−0.653581	+	0.756856i	$0.726734\pi$
$720$	0	0
$721$	3.66701	0.136567
$722$	35.7247i	1.32954i
$723$	− 34.5730i	− 1.28579i
$724$	6.20477	0.230599
$725$	0	0
$726$	4.87936	0.181090
$727$	1.80486i	0.0669385i	0.999440	+	0.0334693i	$0.0106556\pi$
$727$	1.80486i	0.0669385i	−0.999440	+	0.0334693i	$0.989344\pi$
$728$	− 2.08330i	− 0.0772122i
$729$	−15.7070	−0.581741
$730$	0	0
$731$	1.26633	0.0468369
$732$	− 8.04945i	− 0.297516i
$733$	− 34.0338i	− 1.25707i	−0.777782	−	0.628534i	$-0.783655\pi$
$733$	− 34.0338i	− 1.25707i	0.777782	−	0.628534i	$-0.216345\pi$
$734$	30.4645	1.12447
$735$	0	0
$736$	−14.3798	−0.530046
$737$	− 6.20620i	− 0.228608i
$738$	2.15941i	0.0794889i
$739$	14.1568	0.520765	0.260382	−	0.965506i	$-0.416151\pi$
$739$	14.1568	0.520765	0.260382	+	0.965506i	$0.416151\pi$
$740$	0	0
$741$	17.0928	0.627918
$742$	− 11.2534i	− 0.413125i
$743$	6.62249i	0.242955i	0.992594	+	0.121478i	$0.0387633\pi$
$743$	6.62249i	0.242955i	−0.992594	+	0.121478i	$0.961237\pi$
$744$	−81.9481	−3.00436
$745$	0	0
$746$	48.3461	1.77008
$747$	− 20.4079i	− 0.746685i
$748$	− 1.04453i	− 0.0381917i
$749$	9.26180	0.338419
$750$	0	0
$751$	28.6947	1.04709	0.523543	−	0.851999i	$-0.324610\pi$
$751$	28.6947	1.04709	0.523543	+	0.851999i	$0.324610\pi$
$752$	− 31.4310i	− 1.14617i
$753$	− 59.5813i	− 2.17126i
$754$	−4.16660	−0.151738
$755$	0	0
$756$	−4.73820	−0.172327
$757$	− 13.3874i	− 0.486572i	−0.969955	−	0.243286i	$-0.921775\pi$
$757$	− 13.3874i	− 0.486572i	0.969955	−	0.243286i	$-0.0782253\pi$
$758$	− 33.7731i	− 1.22669i
$759$	−22.0989	−0.802139
$760$	0	0
$761$	37.3041	1.35227	0.676135	−	0.736777i	$-0.263653\pi$
$761$	37.3041	1.35227	0.676135	+	0.736777i	$0.263653\pi$
$762$	105.122i	3.80815i
$763$	6.86376i	0.248485i
$764$	1.07838	0.0390143
$765$	0	0
$766$	−10.7058	−0.386816
$767$	− 6.60424i	− 0.238465i
$768$	− 27.1845i	− 0.980935i
$769$	12.0156	0.433294	0.216647	−	0.976250i	$-0.430488\pi$
$769$	12.0156	0.433294	0.216647	+	0.976250i	$0.430488\pi$
$770$	0	0
$771$	41.4596	1.49313
$772$	8.42612i	0.303263i
$773$	3.20394i	0.115238i	0.998339	+	0.0576188i	$0.0183508\pi$
$773$	3.20394i	0.115238i	−0.998339	+	0.0576188i	$0.981649\pi$
$774$	−4.85535	−0.174522
$775$	0	0
$776$	−5.41402	−0.194352
$777$	35.8576i	1.28638i
$778$	− 4.25565i	− 0.152573i
$779$	1.29299	0.0463262
$780$	0	0
$781$	−11.4186	−0.408588
$782$	30.3644i	1.08583i
$783$	− 41.8720i	− 1.49638i
$784$	4.60197	0.164356
$785$	0	0
$786$	−61.8720	−2.20690
$787$	5.13170i	0.182925i	0.995809	+	0.0914627i	$0.0291542\pi$
$787$	5.13170i	0.182925i	−0.995809	+	0.0914627i	$0.970846\pi$
$788$	7.28005i	0.259341i
$789$	−31.7854	−1.13159
$790$	0	0
$791$	−3.75872	−0.133645
$792$	− 17.6959i	− 0.628798i
$793$	5.70928i	0.202742i
$794$	10.6537	0.378085
$795$	0	0
$796$	−3.92654	−0.139173
$797$	− 8.86376i	− 0.313971i	−0.987601	−	0.156985i	$-0.949822\pi$
$797$	− 8.86376i	− 0.313971i	0.987601	−	0.156985i	$-0.0501775\pi$
$798$	31.7009i	1.12220i
$799$	−19.3281	−0.683778
$800$	0	0
$801$	−4.09890	−0.144827
$802$	− 10.2823i	− 0.363081i
$803$	5.66701i	0.199985i
$804$	7.26180	0.256104
$805$	0	0
$806$	−13.1545	−0.463347
$807$	− 37.7731i	− 1.32968i
$808$	− 18.1229i	− 0.637562i
$809$	−16.7915	−0.590359	−0.295179	−	0.955442i	$-0.595379\pi$
$809$	−16.7915	−0.590359	−0.295179	+	0.955442i	$0.595379\pi$
$810$	0	0
$811$	23.9421	0.840722	0.420361	−	0.907357i	$-0.361903\pi$
$811$	23.9421	0.840722	0.420361	+	0.907357i	$0.361903\pi$
$812$	− 1.20394i	− 0.0422499i
$813$	− 79.8141i	− 2.79920i
$814$	17.4101	0.610225
$815$	0	0
$816$	−41.2846	−1.44525
$817$	2.90725i	0.101712i
$818$	− 23.2066i	− 0.811399i
$819$	5.85043	0.204431
$820$	0	0
$821$	15.7054	0.548122	0.274061	−	0.961712i	$-0.411633\pi$
$821$	15.7054	0.548122	0.274061	+	0.961712i	$0.411633\pi$
$822$	− 95.7563i	− 3.33988i
$823$	− 40.5152i	− 1.41227i	−0.708077	−	0.706135i	$-0.750437\pi$
$823$	− 40.5152i	− 1.41227i	0.708077	−	0.706135i	$-0.249563\pi$
$824$	−9.20516	−0.320677
$825$	0	0
$826$	12.2485	0.426179
$827$	− 29.6391i	− 1.03065i	−0.856994	−	0.515327i	$-0.827671\pi$
$827$	− 29.6391i	− 1.03065i	0.856994	−	0.515327i	$-0.172329\pi$
$828$	− 18.1385i	− 0.630357i
$829$	−28.7838	−0.999702	−0.499851	−	0.866111i	$-0.666612\pi$
$829$	−28.7838	−0.999702	−0.499851	+	0.866111i	$0.666612\pi$
$830$	0	0
$831$	16.9216	0.587005
$832$	5.00349i	0.173465i
$833$	− 2.82991i	− 0.0980507i
$834$	2.42469	0.0839603
$835$	0	0
$836$	2.39803	0.0829377
$837$	− 132.195i	− 4.56934i
$838$	14.6921i	0.507529i
$839$	11.1350	0.384423	0.192212	−	0.981353i	$-0.438434\pi$
$839$	11.1350	0.384423	0.192212	+	0.981353i	$0.438434\pi$
$840$	0	0
$841$	−18.3607	−0.633127
$842$	− 50.3995i	− 1.73688i
$843$	− 52.2122i	− 1.79828i
$844$	−2.76940	−0.0953267
$845$	0	0
$846$	74.1075	2.54787
$847$	− 1.00000i	− 0.0343604i
$848$	33.6461i	1.15541i
$849$	−3.00614	−0.103171
$850$	0	0
$851$	−78.8515	−2.70299
$852$	− 13.3607i	− 0.457730i
$853$	2.00719i	0.0687248i	0.999409	+	0.0343624i	$0.0109400\pi$
$853$	2.00719i	0.0687248i	−0.999409	+	0.0343624i	$0.989060\pi$
$854$	−10.5886	−0.362336
$855$	0	0
$856$	−23.2495	−0.794652
$857$	− 21.2013i	− 0.724222i	−0.932135	−	0.362111i	$-0.882056\pi$
$857$	− 21.2013i	− 0.724222i	0.932135	−	0.362111i	$-0.117944\pi$
$858$	− 4.04945i	− 0.138246i
$859$	−38.6959	−1.32029	−0.660144	−	0.751139i	$-0.729505\pi$
$859$	−38.6959	−1.32029	−0.660144	+	0.751139i	$0.729505\pi$
$860$	0	0
$861$	0.630898	0.0215009
$862$	− 35.4459i	− 1.20729i
$863$	38.3728i	1.30623i	0.757261	+	0.653113i	$0.226537\pi$
$863$	38.3728i	1.30623i	−0.757261	+	0.653113i	$0.773463\pi$
$864$	26.4801	0.900872
$865$	0	0
$866$	52.8371	1.79548
$867$	− 28.5041i	− 0.968051i
$868$	− 3.80098i	− 0.129014i
$869$	14.5464	0.493452
$870$	0	0
$871$	−5.15061	−0.174522
$872$	− 17.2298i	− 0.583476i
$873$	− 15.2039i	− 0.514575i
$874$	−69.7107	−2.35800
$875$	0	0
$876$	−6.63090	−0.224037
$877$	32.3195i	1.09135i	0.837997	+	0.545676i	$0.183727\pi$
$877$	32.3195i	1.09135i	−0.837997	+	0.545676i	$0.816273\pi$
$878$	25.5441i	0.862072i
$879$	−24.4885	−0.825977
$880$	0	0
$881$	−45.3217	−1.52693	−0.763464	−	0.645850i	$-0.776503\pi$
$881$	−45.3217	−1.52693	−0.763464	+	0.645850i	$0.776503\pi$
$882$	10.8504i	0.365353i
$883$	42.5197i	1.43090i	0.698663	+	0.715451i	$0.253779\pi$
$883$	42.5197i	1.43090i	−0.698663	+	0.715451i	$0.746221\pi$
$884$	−0.866868	−0.0291559
$885$	0	0
$886$	−16.8045	−0.564557
$887$	44.6947i	1.50070i	0.661040	+	0.750351i	$0.270115\pi$
$887$	44.6947i	1.50070i	−0.661040	+	0.750351i	$0.729885\pi$
$888$	− 90.0119i	− 3.02060i
$889$	21.5441	0.722566
$890$	0	0
$891$	19.5464	0.654828
$892$	− 8.87095i	− 0.297021i
$893$	− 44.3735i	− 1.48490i
$894$	65.0616	2.17598
$895$	0	0
$896$	−13.4052	−0.447837
$897$	18.3402i	0.612361i
$898$	37.8636i	1.26352i
$899$	33.5897	1.12028
$900$	0	0
$901$	20.6902	0.689290
$902$	− 0.306323i	− 0.0101994i
$903$	1.41855i	0.0472064i
$904$	9.43537	0.313816
$905$	0	0
$906$	−5.15061	−0.171118
$907$	− 5.28912i	− 0.175622i	−0.996137	−	0.0878111i	$-0.972013\pi$
$907$	− 5.28912i	− 0.175622i	0.996137	−	0.0878111i	$-0.0279872\pi$
$908$	0.544946i	0.0180847i
$909$	50.8937	1.68804
$910$	0	0
$911$	−47.7321	−1.58143	−0.790717	−	0.612182i	$-0.790292\pi$
$911$	−47.7321	−1.58143	−0.790717	+	0.612182i	$0.790292\pi$
$912$	− 94.7813i	− 3.13852i
$913$	2.89496i	0.0958092i
$914$	−56.9276	−1.88300
$915$	0	0
$916$	2.97948	0.0984448
$917$	12.6803i	0.418742i
$918$	− 55.9155i	− 1.84549i
$919$	−45.6886	−1.50713	−0.753564	−	0.657375i	$-0.771667\pi$
$919$	−45.6886	−1.50713	−0.753564	+	0.657375i	$0.771667\pi$
$920$	0	0
$921$	103.829	3.42127
$922$	57.5033i	1.89377i
$923$	9.47641i	0.311920i
$924$	1.17009	0.0384930
$925$	0	0
$926$	−10.8599	−0.356878
$927$	− 25.8504i	− 0.849040i
$928$	6.72836i	0.220869i
$929$	−35.3874	−1.16102	−0.580511	−	0.814253i	$-0.697147\pi$
$929$	−35.3874	−1.16102	−0.580511	+	0.814253i	$0.697147\pi$
$930$	0	0
$931$	6.49693	0.212928
$932$	2.37978i	0.0779523i
$933$	− 72.6596i	− 2.37877i
$934$	−30.5757	−1.00047
$935$	0	0
$936$	−14.6861	−0.480030
$937$	23.2378i	0.759145i	0.925162	+	0.379573i	$0.123929\pi$
$937$	23.2378i	0.759145i	−0.925162	+	0.379573i	$0.876071\pi$
$938$	− 9.55252i	− 0.311901i
$939$	−36.6947	−1.19749
$940$	0	0
$941$	29.2651	0.954015	0.477008	−	0.878899i	$-0.341721\pi$
$941$	29.2651	0.954015	0.477008	+	0.878899i	$0.341721\pi$
$942$	2.42469i	0.0790008i
$943$	1.38735i	0.0451785i
$944$	−36.6213	−1.19192
$945$	0	0
$946$	0.688756	0.0223934
$947$	5.55705i	0.180580i	0.995916	+	0.0902900i	$0.0287794\pi$
$947$	5.55705i	0.180580i	−0.995916	+	0.0902900i	$0.971221\pi$
$948$	17.0205i	0.552801i
$949$	4.70313	0.152670
$950$	0	0
$951$	−39.7009	−1.28739
$952$	7.10382i	0.230236i
$953$	− 11.7548i	− 0.380777i	−0.981709	−	0.190388i	$-0.939025\pi$
$953$	− 11.7548i	− 0.380777i	0.981709	−	0.190388i	$-0.0609747\pi$
$954$	−79.3302	−2.56841
$955$	0	0
$956$	−3.02052	−0.0976906
$957$	10.3402i	0.334250i
$958$	− 9.84778i	− 0.318167i
$959$	−19.6248	−0.633716
$960$	0	0
$961$	75.0470	2.42087
$962$	− 14.4489i	− 0.465852i
$963$	− 65.2905i	− 2.10396i
$964$	−4.02544	−0.129651
$965$	0	0
$966$	−34.0144	−1.09439
$967$	− 33.2267i	− 1.06850i	−0.845327	−	0.534250i	$-0.820594\pi$
$967$	− 33.2267i	− 1.06850i	0.845327	−	0.534250i	$-0.179406\pi$
$968$	2.51026i	0.0806828i
$969$	−58.2844	−1.87236
$970$	0	0
$971$	3.16621	0.101609	0.0508043	−	0.998709i	$-0.483822\pi$
$971$	3.16621	0.101609	0.0508043	+	0.998709i	$0.483822\pi$
$972$	8.65634i	0.277652i
$973$	− 0.496928i	− 0.0159308i
$974$	−39.7237	−1.27283
$975$	0	0
$976$	31.6586	1.01337
$977$	32.4391i	1.03782i	0.854830	+	0.518909i	$0.173662\pi$
$977$	32.4391i	1.03782i	−0.854830	+	0.518909i	$0.826338\pi$
$978$	6.39803i	0.204586i
$979$	0.581449	0.0185832
$980$	0	0
$981$	48.3857	1.54484
$982$	− 26.4261i	− 0.843292i
$983$	− 30.1496i	− 0.961622i	−0.876824	−	0.480811i	$-0.840342\pi$
$983$	− 30.1496i	− 0.961622i	0.876824	−	0.480811i	$-0.159658\pi$
$984$	−1.58372	−0.0504870
$985$	0	0
$986$	14.2076	0.452463
$987$	− 21.6514i	− 0.689172i
$988$	− 1.99016i	− 0.0633154i
$989$	−3.11942	−0.0991916
$990$	0	0
$991$	−21.4452	−0.681230	−0.340615	−	0.940203i	$-0.610635\pi$
$991$	−21.4452	−0.681230	−0.340615	+	0.940203i	$0.610635\pi$
$992$	21.2423i	0.674444i
$993$	57.6041i	1.82801i
$994$	−17.5753	−0.557455
$995$	0	0
$996$	−3.38735	−0.107332
$997$	− 39.6547i	− 1.25588i	−0.778263	−	0.627939i	$-0.783899\pi$
$997$	− 39.6547i	− 1.25588i	0.778263	−	0.627939i	$-0.216101\pi$
$998$	20.2602i	0.641325i
$999$	145.204	4.59404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.b.m.1849.5		6
5.2	odd	4		385.2.a.e.1.2	✓	3
5.3	odd	4		1925.2.a.w.1.2		3
5.4	even	2	inner	1925.2.b.m.1849.2		6
15.2	even	4		3465.2.a.bi.1.2		3
20.7	even	4		6160.2.a.bo.1.3		3
35.27	even	4		2695.2.a.h.1.2		3
55.32	even	4		4235.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.e.1.2	✓	3	5.2	odd	4
1925.2.a.w.1.2		3	5.3	odd	4
1925.2.b.m.1849.2		6	5.4	even	2	inner
1925.2.b.m.1849.5		6	1.1	even	1	trivial
2695.2.a.h.1.2		3	35.27	even	4
3465.2.a.bi.1.2		3	15.2	even	4
4235.2.a.p.1.2		3	55.32	even	4
6160.2.a.bo.1.3		3	20.7	even	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.53919i q^{2} -3.17009i q^{3} -0.369102 q^{4} +4.87936 q^{6} -1.00000i q^{7} +2.51026i q^{8} -7.04945 q^{9} +O(q^{10})\)	\(q+1.53919i q^{2} -3.17009i q^{3} -0.369102 q^{4} +4.87936 q^{6} -1.00000i q^{7} +2.51026i q^{8} -7.04945 q^{9} +1.00000 q^{11} +1.17009i q^{12} -0.829914i q^{13} +1.53919 q^{14} -4.60197 q^{16} +2.82991i q^{17} -10.8504i q^{18} -6.49693 q^{19} -3.17009 q^{21} +1.53919i q^{22} -6.97107i q^{23} +7.95774 q^{24} +1.27739 q^{26} +12.8371i q^{27} +0.369102i q^{28} -3.26180 q^{29} -10.2979 q^{31} -2.06278i q^{32} -3.17009i q^{33} -4.35577 q^{34} +2.60197 q^{36} -11.3112i q^{37} -10.0000i q^{38} -2.63090 q^{39} -0.199016 q^{41} -4.87936i q^{42} -0.447480i q^{43} -0.369102 q^{44} +10.7298 q^{46} +6.82991i q^{47} +14.5886i q^{48} -1.00000 q^{49} +8.97107 q^{51} +0.306323i q^{52} -7.31124i q^{53} -19.7587 q^{54} +2.51026 q^{56} +20.5958i q^{57} -5.02052i q^{58} +7.95774 q^{59} -6.87936 q^{61} -15.8504i q^{62} +7.04945i q^{63} -6.02893 q^{64} +4.87936 q^{66} -6.20620i q^{67} -1.04453i q^{68} -22.0989 q^{69} -11.4186 q^{71} -17.6959i q^{72} +5.66701i q^{73} +17.4101 q^{74} +2.39803 q^{76} -1.00000i q^{77} -4.04945i q^{78} +14.5464 q^{79} +19.5464 q^{81} -0.306323i q^{82} +2.89496i q^{83} +1.17009 q^{84} +0.688756 q^{86} +10.3402i q^{87} +2.51026i q^{88} +0.581449 q^{89} -0.829914 q^{91} +2.57304i q^{92} +32.6453i q^{93} -10.5125 q^{94} -6.53919 q^{96} +2.15676i q^{97} -1.53919i q^{98} -7.04945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 6 q^{11} + 6 q^{14} + 10 q^{16} - 4 q^{19} - 8 q^{21} + 16 q^{24} + 20 q^{26} - 4 q^{29} - 8 q^{31} - 32 q^{34} - 22 q^{36} - 8 q^{39} - 20 q^{41} - 10 q^{44} - 16 q^{46} - 6 q^{49} + 24 q^{51} - 68 q^{54} - 18 q^{56} + 16 q^{59} - 16 q^{61} - 66 q^{64} + 4 q^{66} - 60 q^{69} - 40 q^{71} - 20 q^{74} + 52 q^{76} + 16 q^{79} + 46 q^{81} - 4 q^{84} + 56 q^{86} + 32 q^{89} - 16 q^{91} - 56 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 6 * q^11 + 6 * q^14 + 10 * q^16 - 4 * q^19 - 8 * q^21 + 16 * q^24 + 20 * q^26 - 4 * q^29 - 8 * q^31 - 32 * q^34 - 22 * q^36 - 8 * q^39 - 20 * q^41 - 10 * q^44 - 16 * q^46 - 6 * q^49 + 24 * q^51 - 68 * q^54 - 18 * q^56 + 16 * q^59 - 16 * q^61 - 66 * q^64 + 4 * q^66 - 60 * q^69 - 40 * q^71 - 20 * q^74 + 52 * q^76 + 16 * q^79 + 46 * q^81 - 4 * q^84 + 56 * q^86 + 32 * q^89 - 16 * q^91 - 56 * q^94 - 36 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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