LMFDB - Embedded newform 1925.2.b.h.1849.3

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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.3
Root			$1.61803i$ of defining polynomial
Character	$\chi$	$=$	1925.1849
Dual form			1925.2.b.h.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23607i q^{2} +1.23607i q^{3} -3.00000 q^{4} -2.76393 q^{6} +1.00000i q^{7} -2.23607i q^{8} +1.47214 q^{9} +O(q^{10})$	\(q+2.23607i q^{2} +1.23607i q^{3} -3.00000 q^{4} -2.76393 q^{6} +1.00000i q^{7} -2.23607i q^{8} +1.47214 q^{9} -1.00000 q^{11} -3.70820i q^{12} -3.23607i q^{13} -2.23607 q^{14} -1.00000 q^{16} -3.23607i q^{17} +3.29180i q^{18} -6.47214 q^{19} -1.23607 q^{21} -2.23607i q^{22} -2.47214i q^{23} +2.76393 q^{24} +7.23607 q^{26} +5.52786i q^{27} -3.00000i q^{28} -8.47214 q^{29} -2.76393 q^{31} -6.70820i q^{32} -1.23607i q^{33} +7.23607 q^{34} -4.41641 q^{36} -8.47214i q^{37} -14.4721i q^{38} +4.00000 q^{39} -11.2361 q^{41} -2.76393i q^{42} -8.00000i q^{43} +3.00000 q^{44} +5.52786 q^{46} +2.76393i q^{47} -1.23607i q^{48} -1.00000 q^{49} +4.00000 q^{51} +9.70820i q^{52} +0.472136i q^{53} -12.3607 q^{54} +2.23607 q^{56} -8.00000i q^{57} -18.9443i q^{58} +1.23607 q^{59} -7.23607 q^{61} -6.18034i q^{62} +1.47214i q^{63} +13.0000 q^{64} +2.76393 q^{66} +14.4721i q^{67} +9.70820i q^{68} +3.05573 q^{69} -10.4721 q^{71} -3.29180i q^{72} +0.763932i q^{73} +18.9443 q^{74} +19.4164 q^{76} -1.00000i q^{77} +8.94427i q^{78} +8.94427 q^{79} -2.41641 q^{81} -25.1246i q^{82} +11.4164i q^{83} +3.70820 q^{84} +17.8885 q^{86} -10.4721i q^{87} +2.23607i q^{88} -2.00000 q^{89} +3.23607 q^{91} +7.41641i q^{92} -3.41641i q^{93} -6.18034 q^{94} +8.29180 q^{96} +17.4164i q^{97} -2.23607i q^{98} -1.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{4} - 20 q^{6} - 12 q^{9}+O(q^{10}) $ 4 * q - 12 * q^4 - 20 * q^6 - 12 * q^9	$ 4 q - 12 q^{4} - 20 q^{6} - 12 q^{9} - 4 q^{11} - 4 q^{16} - 8 q^{19} + 4 q^{21} + 20 q^{24} + 20 q^{26} - 16 q^{29} - 20 q^{31} + 20 q^{34} + 36 q^{36} + 16 q^{39} - 36 q^{41} + 12 q^{44} + 40 q^{46} - 4 q^{49} + 16 q^{51} + 40 q^{54} - 4 q^{59} - 20 q^{61} + 52 q^{64} + 20 q^{66} + 48 q^{69} - 24 q^{71} + 40 q^{74} + 24 q^{76} + 44 q^{81} - 12 q^{84} - 8 q^{89} + 4 q^{91} + 20 q^{94} + 60 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q - 12 * q^4 - 20 * q^6 - 12 * q^9 - 4 * q^11 - 4 * q^16 - 8 * q^19 + 4 * q^21 + 20 * q^24 + 20 * q^26 - 16 * q^29 - 20 * q^31 + 20 * q^34 + 36 * q^36 + 16 * q^39 - 36 * q^41 + 12 * q^44 + 40 * q^46 - 4 * q^49 + 16 * q^51 + 40 * q^54 - 4 * q^59 - 20 * q^61 + 52 * q^64 + 20 * q^66 + 48 * q^69 - 24 * q^71 + 40 * q^74 + 24 * q^76 + 44 * q^81 - 12 * q^84 - 8 * q^89 + 4 * q^91 + 20 * q^94 + 60 * q^96 + 12 * 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 $

$2$	2.23607i	1.58114i	0.612372	+	0.790569i	$0.290215\pi$
$2$	2.23607i	1.58114i	−0.612372	+	0.790569i	$0.709785\pi$
$3$	1.23607i	0.713644i	0.934172	+	0.356822i	$0.116140\pi$
$3$	1.23607i	0.713644i	−0.934172	+	0.356822i	$0.883860\pi$
$4$	−3.00000	−1.50000
$5$	0	0
$5$	0	0
$6$	−2.76393	−1.12837
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 2.23607i	− 0.790569i
$9$	1.47214	0.490712
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	− 3.70820i	− 1.07047i
$13$	− 3.23607i	− 0.897524i	−0.893651	−	0.448762i	$-0.851865\pi$
$13$	− 3.23607i	− 0.897524i	0.893651	−	0.448762i	$-0.148135\pi$
$14$	−2.23607	−0.597614
$15$	0	0
$16$	−1.00000	−0.250000
$17$	− 3.23607i	− 0.784862i	−0.919781	−	0.392431i	$-0.871634\pi$
$17$	− 3.23607i	− 0.784862i	0.919781	−	0.392431i	$-0.128366\pi$
$18$	3.29180i	0.775884i
$19$	−6.47214	−1.48481	−0.742405	−	0.669951i	$-0.766315\pi$
$19$	−6.47214	−1.48481	−0.742405	+	0.669951i	$0.766315\pi$
$20$	0	0
$21$	−1.23607	−0.269732
$22$	− 2.23607i	− 0.476731i
$23$	− 2.47214i	− 0.515476i	−0.966215	−	0.257738i	$-0.917023\pi$
$23$	− 2.47214i	− 0.515476i	0.966215	−	0.257738i	$-0.0829771\pi$
$24$	2.76393	0.564185
$25$	0	0
$26$	7.23607	1.41911
$27$	5.52786i	1.06384i
$28$	− 3.00000i	− 0.566947i
$29$	−8.47214	−1.57324	−0.786618	−	0.617440i	$-0.788170\pi$
$29$	−8.47214	−1.57324	−0.786618	+	0.617440i	$0.788170\pi$
$30$	0	0
$31$	−2.76393	−0.496417	−0.248208	−	0.968707i	$-0.579842\pi$
$31$	−2.76393	−0.496417	−0.248208	+	0.968707i	$0.579842\pi$
$32$	− 6.70820i	− 1.18585i
$33$	− 1.23607i	− 0.215172i
$34$	7.23607	1.24098
$35$	0	0
$36$	−4.41641	−0.736068
$37$	− 8.47214i	− 1.39281i	−0.717649	−	0.696405i	$-0.754782\pi$
$37$	− 8.47214i	− 1.39281i	0.717649	−	0.696405i	$-0.245218\pi$
$38$	− 14.4721i	− 2.34769i
$39$	4.00000	0.640513
$40$	0	0
$41$	−11.2361	−1.75478	−0.877390	−	0.479779i	$-0.840717\pi$
$41$	−11.2361	−1.75478	−0.877390	+	0.479779i	$0.840717\pi$
$42$	− 2.76393i	− 0.426484i
$43$	− 8.00000i	− 1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$	− 8.00000i	− 1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	5.52786	0.815039
$47$	2.76393i	0.403161i	0.979472	+	0.201580i	$0.0646078\pi$
$47$	2.76393i	0.403161i	−0.979472	+	0.201580i	$0.935392\pi$
$48$	− 1.23607i	− 0.178411i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	9.70820i	1.34629i
$53$	0.472136i	0.0648529i	0.999474	+	0.0324264i	$0.0103235\pi$
$53$	0.472136i	0.0648529i	−0.999474	+	0.0324264i	$0.989677\pi$
$54$	−12.3607	−1.68208
$55$	0	0
$56$	2.23607	0.298807
$57$	− 8.00000i	− 1.05963i
$58$	− 18.9443i	− 2.48750i
$59$	1.23607	0.160922	0.0804612	−	0.996758i	$-0.474361\pi$
$59$	1.23607	0.160922	0.0804612	+	0.996758i	$0.474361\pi$
$60$	0	0
$61$	−7.23607	−0.926484	−0.463242	−	0.886232i	$-0.653314\pi$
$61$	−7.23607	−0.926484	−0.463242	+	0.886232i	$0.653314\pi$
$62$	− 6.18034i	− 0.784904i
$63$	1.47214i	0.185472i
$64$	13.0000	1.62500
$65$	0	0
$66$	2.76393	0.340217
$67$	14.4721i	1.76805i	0.467437	+	0.884026i	$0.345177\pi$
$67$	14.4721i	1.76805i	−0.467437	+	0.884026i	$0.654823\pi$
$68$	9.70820i	1.17729i
$69$	3.05573	0.367866
$70$	0	0
$71$	−10.4721	−1.24281	−0.621407	−	0.783488i	$-0.713439\pi$
$71$	−10.4721	−1.24281	−0.621407	+	0.783488i	$0.713439\pi$
$72$	− 3.29180i	− 0.387942i
$73$	0.763932i	0.0894115i	0.999000	+	0.0447057i	$0.0142350\pi$
$73$	0.763932i	0.0894115i	−0.999000	+	0.0447057i	$0.985765\pi$
$74$	18.9443	2.20223
$75$	0	0
$76$	19.4164	2.22721
$77$	− 1.00000i	− 0.113961i
$78$	8.94427i	1.01274i
$79$	8.94427	1.00631	0.503155	−	0.864196i	$-0.332173\pi$
$79$	8.94427	1.00631	0.503155	+	0.864196i	$0.332173\pi$
$80$	0	0
$81$	−2.41641	−0.268490
$82$	− 25.1246i	− 2.77455i
$83$	11.4164i	1.25311i	0.779376	+	0.626557i	$0.215536\pi$
$83$	11.4164i	1.25311i	−0.779376	+	0.626557i	$0.784464\pi$
$84$	3.70820	0.404598
$85$	0	0
$86$	17.8885	1.92897
$87$	− 10.4721i	− 1.12273i
$88$	2.23607i	0.238366i
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	3.23607	0.339232
$92$	7.41641i	0.773214i
$93$	− 3.41641i	− 0.354265i
$94$	−6.18034	−0.637453
$95$	0	0
$96$	8.29180	0.846278
$97$	17.4164i	1.76837i	0.467139	+	0.884184i	$0.345285\pi$
$97$	17.4164i	1.76837i	−0.467139	+	0.884184i	$0.654715\pi$
$98$	− 2.23607i	− 0.225877i
$99$	−1.47214	−0.147955
$100$	0	0
$101$	−4.76393	−0.474029	−0.237014	−	0.971506i	$-0.576169\pi$
$101$	−4.76393	−0.474029	−0.237014	+	0.971506i	$0.576169\pi$
$102$	8.94427i	0.885615i
$103$	− 7.70820i	− 0.759512i	−0.925087	−	0.379756i	$-0.876008\pi$
$103$	− 7.70820i	− 0.759512i	0.925087	−	0.379756i	$-0.123992\pi$
$104$	−7.23607	−0.709555
$105$	0	0
$106$	−1.05573	−0.102541
$107$	− 4.00000i	− 0.386695i	−0.981130	−	0.193347i	$-0.938066\pi$
$107$	− 4.00000i	− 0.386695i	0.981130	−	0.193347i	$-0.0619344\pi$
$108$	− 16.5836i	− 1.59576i
$109$	4.47214	0.428353	0.214176	−	0.976795i	$-0.431293\pi$
$109$	4.47214	0.428353	0.214176	+	0.976795i	$0.431293\pi$
$110$	0	0
$111$	10.4721	0.993971
$112$	− 1.00000i	− 0.0944911i
$113$	− 2.00000i	− 0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$	− 2.00000i	− 0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$	17.8885	1.67542
$115$	0	0
$116$	25.4164	2.35985
$117$	− 4.76393i	− 0.440426i
$118$	2.76393i	0.254441i
$119$	3.23607	0.296650
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 16.1803i	− 1.46490i
$123$	− 13.8885i	− 1.25229i
$124$	8.29180	0.744625
$125$	0	0
$126$	−3.29180	−0.293257
$127$	3.05573i	0.271152i	0.990767	+	0.135576i	$0.0432885\pi$
$127$	3.05573i	0.271152i	−0.990767	+	0.135576i	$0.956712\pi$
$128$	15.6525i	1.38350i
$129$	9.88854	0.870638
$130$	0	0
$131$	21.8885	1.91241	0.956205	−	0.292696i	$-0.0945525\pi$
$131$	21.8885	1.91241	0.956205	+	0.292696i	$0.0945525\pi$
$132$	3.70820i	0.322758i
$133$	− 6.47214i	− 0.561205i
$134$	−32.3607	−2.79554
$135$	0	0
$136$	−7.23607	−0.620488
$137$	16.4721i	1.40731i	0.710542	+	0.703655i	$0.248450\pi$
$137$	16.4721i	1.40731i	−0.710542	+	0.703655i	$0.751550\pi$
$138$	6.83282i	0.581648i
$139$	1.52786	0.129592	0.0647959	−	0.997899i	$-0.479360\pi$
$139$	1.52786	0.129592	0.0647959	+	0.997899i	$0.479360\pi$
$140$	0	0
$141$	−3.41641	−0.287713
$142$	− 23.4164i	− 1.96506i
$143$	3.23607i	0.270614i
$144$	−1.47214	−0.122678
$145$	0	0
$146$	−1.70820	−0.141372
$147$	− 1.23607i	− 0.101949i
$148$	25.4164i	2.08922i
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	8.94427	0.727875	0.363937	−	0.931423i	$-0.381432\pi$
$151$	8.94427	0.727875	0.363937	+	0.931423i	$0.381432\pi$
$152$	14.4721i	1.17385i
$153$	− 4.76393i	− 0.385141i
$154$	2.23607	0.180187
$155$	0	0
$156$	−12.0000	−0.960769
$157$	10.9443i	0.873448i	0.899596	+	0.436724i	$0.143861\pi$
$157$	10.9443i	0.873448i	−0.899596	+	0.436724i	$0.856139\pi$
$158$	20.0000i	1.59111i
$159$	−0.583592	−0.0462819
$160$	0	0
$161$	2.47214	0.194832
$162$	− 5.40325i	− 0.424520i
$163$	3.41641i	0.267594i	0.991009	+	0.133797i	$0.0427170\pi$
$163$	3.41641i	0.267594i	−0.991009	+	0.133797i	$0.957283\pi$
$164$	33.7082	2.63217
$165$	0	0
$166$	−25.5279	−1.98135
$167$	4.94427i	0.382599i	0.981532	+	0.191300i	$0.0612702\pi$
$167$	4.94427i	0.382599i	−0.981532	+	0.191300i	$0.938730\pi$
$168$	2.76393i	0.213242i
$169$	2.52786	0.194451
$170$	0	0
$171$	−9.52786	−0.728614
$172$	24.0000i	1.82998i
$173$	12.7639i	0.970424i	0.874397	+	0.485212i	$0.161258\pi$
$173$	12.7639i	0.970424i	−0.874397	+	0.485212i	$0.838742\pi$
$174$	23.4164	1.77519
$175$	0	0
$176$	1.00000	0.0753778
$177$	1.52786i	0.114841i
$178$	− 4.47214i	− 0.335201i
$179$	8.94427	0.668526	0.334263	−	0.942480i	$-0.391513\pi$
$179$	8.94427	0.668526	0.334263	+	0.942480i	$0.391513\pi$
$180$	0	0
$181$	−25.4164	−1.88919	−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164	−1.88919	−0.944593	+	0.328243i	$0.893544\pi$
$182$	7.23607i	0.536373i
$183$	− 8.94427i	− 0.661180i
$184$	−5.52786	−0.407520
$185$	0	0
$186$	7.63932	0.560142
$187$	3.23607i	0.236645i
$188$	− 8.29180i	− 0.604741i
$189$	−5.52786	−0.402093
$190$	0	0
$191$	−3.05573	−0.221105	−0.110552	−	0.993870i	$-0.535262\pi$
$191$	−3.05573	−0.221105	−0.110552	+	0.993870i	$0.535262\pi$
$192$	16.0689i	1.15967i
$193$	− 11.8885i	− 0.855756i	−0.903836	−	0.427878i	$-0.859261\pi$
$193$	− 11.8885i	− 0.855756i	0.903836	−	0.427878i	$-0.140739\pi$
$194$	−38.9443	−2.79604
$195$	0	0
$196$	3.00000	0.214286
$197$	− 2.00000i	− 0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$	− 2.00000i	− 0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	− 3.29180i	− 0.233938i
$199$	2.18034	0.154560	0.0772801	−	0.997009i	$-0.475376\pi$
$199$	2.18034	0.154560	0.0772801	+	0.997009i	$0.475376\pi$
$200$	0	0
$201$	−17.8885	−1.26176
$202$	− 10.6525i	− 0.749506i
$203$	− 8.47214i	− 0.594627i
$204$	−12.0000	−0.840168
$205$	0	0
$206$	17.2361	1.20089
$207$	− 3.63932i	− 0.252950i
$208$	3.23607i	0.224381i
$209$	6.47214	0.447687
$210$	0	0
$211$	−13.8885	−0.956127	−0.478063	−	0.878325i	$-0.658661\pi$
$211$	−13.8885	−0.956127	−0.478063	+	0.878325i	$0.658661\pi$
$212$	− 1.41641i	− 0.0972793i
$213$	− 12.9443i	− 0.886927i
$214$	8.94427	0.611418
$215$	0	0
$216$	12.3607	0.841038
$217$	− 2.76393i	− 0.187628i
$218$	10.0000i	0.677285i
$219$	−0.944272	−0.0638080
$220$	0	0
$221$	−10.4721	−0.704432
$222$	23.4164i	1.57161i
$223$	10.1803i	0.681726i	0.940113	+	0.340863i	$0.110719\pi$
$223$	10.1803i	0.681726i	−0.940113	+	0.340863i	$0.889281\pi$
$224$	6.70820	0.448211
$225$	0	0
$226$	4.47214	0.297482
$227$	5.88854i	0.390836i	0.980720	+	0.195418i	$0.0626064\pi$
$227$	5.88854i	0.390836i	−0.980720	+	0.195418i	$0.937394\pi$
$228$	24.0000i	1.58944i
$229$	4.47214	0.295527	0.147764	−	0.989023i	$-0.452793\pi$
$229$	4.47214	0.295527	0.147764	+	0.989023i	$0.452793\pi$
$230$	0	0
$231$	1.23607	0.0813273
$232$	18.9443i	1.24375i
$233$	− 9.41641i	− 0.616889i	−0.951242	−	0.308445i	$-0.900192\pi$
$233$	− 9.41641i	− 0.616889i	0.951242	−	0.308445i	$-0.0998085\pi$
$234$	10.6525	0.696374
$235$	0	0
$236$	−3.70820	−0.241384
$237$	11.0557i	0.718147i
$238$	7.23607i	0.469045i
$239$	9.88854	0.639637	0.319818	−	0.947479i	$-0.396378\pi$
$239$	9.88854	0.639637	0.319818	+	0.947479i	$0.396378\pi$
$240$	0	0
$241$	−13.1246	−0.845431	−0.422715	−	0.906263i	$-0.638923\pi$
$241$	−13.1246	−0.845431	−0.422715	+	0.906263i	$0.638923\pi$
$242$	2.23607i	0.143740i
$243$	13.5967i	0.872232i
$244$	21.7082	1.38973
$245$	0	0
$246$	31.0557	1.98004
$247$	20.9443i	1.33265i
$248$	6.18034i	0.392452i
$249$	−14.1115	−0.894277
$250$	0	0
$251$	4.29180	0.270896	0.135448	−	0.990784i	$-0.456753\pi$
$251$	4.29180	0.270896	0.135448	+	0.990784i	$0.456753\pi$
$252$	− 4.41641i	− 0.278208i
$253$	2.47214i	0.155422i
$254$	−6.83282	−0.428729
$255$	0	0
$256$	−9.00000	−0.562500
$257$	− 6.00000i	− 0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$	− 6.00000i	− 0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$	22.1115i	1.37660i
$259$	8.47214	0.526433
$260$	0	0
$261$	−12.4721	−0.772006
$262$	48.9443i	3.02379i
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	−2.76393	−0.170108
$265$	0	0
$266$	14.4721	0.887344
$267$	− 2.47214i	− 0.151292i
$268$	− 43.4164i	− 2.65208i
$269$	−13.4164	−0.818013	−0.409006	−	0.912532i	$-0.634125\pi$
$269$	−13.4164	−0.818013	−0.409006	+	0.912532i	$0.634125\pi$
$270$	0	0
$271$	−10.4721	−0.636137	−0.318068	−	0.948068i	$-0.603034\pi$
$271$	−10.4721	−0.636137	−0.318068	+	0.948068i	$0.603034\pi$
$272$	3.23607i	0.196215i
$273$	4.00000i	0.242091i
$274$	−36.8328	−2.22515
$275$	0	0
$276$	−9.16718	−0.551800
$277$	− 19.8885i	− 1.19499i	−0.801874	−	0.597493i	$-0.796163\pi$
$277$	− 19.8885i	− 1.19499i	0.801874	−	0.597493i	$-0.203837\pi$
$278$	3.41641i	0.204903i
$279$	−4.06888	−0.243598
$280$	0	0
$281$	−3.52786	−0.210455	−0.105227	−	0.994448i	$-0.533557\pi$
$281$	−3.52786	−0.210455	−0.105227	+	0.994448i	$0.533557\pi$
$282$	− 7.63932i	− 0.454915i
$283$	− 29.8885i	− 1.77669i	−0.459177	−	0.888345i	$-0.651856\pi$
$283$	− 29.8885i	− 1.77669i	0.459177	−	0.888345i	$-0.348144\pi$
$284$	31.4164	1.86422
$285$	0	0
$286$	−7.23607	−0.427878
$287$	− 11.2361i	− 0.663244i
$288$	− 9.87539i	− 0.581913i
$289$	6.52786	0.383992
$290$	0	0
$291$	−21.5279	−1.26199
$292$	− 2.29180i	− 0.134117i
$293$	25.1246i	1.46780i	0.679260	+	0.733898i	$0.262301\pi$
$293$	25.1246i	1.46780i	−0.679260	+	0.733898i	$0.737699\pi$
$294$	2.76393	0.161196
$295$	0	0
$296$	−18.9443	−1.10111
$297$	− 5.52786i	− 0.320759i
$298$	− 31.3050i	− 1.81345i
$299$	−8.00000	−0.462652
$300$	0	0
$301$	8.00000	0.461112
$302$	20.0000i	1.15087i
$303$	− 5.88854i	− 0.338288i
$304$	6.47214	0.371202
$305$	0	0
$306$	10.6525	0.608962
$307$	− 8.94427i	− 0.510477i	−0.966878	−	0.255238i	$-0.917846\pi$
$307$	− 8.94427i	− 0.510477i	0.966878	−	0.255238i	$-0.0821539\pi$
$308$	3.00000i	0.170941i
$309$	9.52786	0.542021
$310$	0	0
$311$	−8.29180	−0.470185	−0.235092	−	0.971973i	$-0.575539\pi$
$311$	−8.29180	−0.470185	−0.235092	+	0.971973i	$0.575539\pi$
$312$	− 8.94427i	− 0.506370i
$313$	− 14.9443i	− 0.844700i	−0.906433	−	0.422350i	$-0.861205\pi$
$313$	− 14.9443i	− 0.844700i	0.906433	−	0.422350i	$-0.138795\pi$
$314$	−24.4721	−1.38104
$315$	0	0
$316$	−26.8328	−1.50946
$317$	14.0000i	0.786318i	0.919470	+	0.393159i	$0.128618\pi$
$317$	14.0000i	0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$	− 1.30495i	− 0.0731781i
$319$	8.47214	0.474349
$320$	0	0
$321$	4.94427	0.275962
$322$	5.52786i	0.308056i
$323$	20.9443i	1.16537i
$324$	7.24922	0.402735
$325$	0	0
$326$	−7.63932	−0.423103
$327$	5.52786i	0.305692i
$328$	25.1246i	1.38727i
$329$	−2.76393	−0.152381
$330$	0	0
$331$	−13.8885	−0.763383	−0.381692	−	0.924290i	$-0.624658\pi$
$331$	−13.8885	−0.763383	−0.381692	+	0.924290i	$0.624658\pi$
$332$	− 34.2492i	− 1.87967i
$333$	− 12.4721i	− 0.683469i
$334$	−11.0557	−0.604943
$335$	0	0
$336$	1.23607	0.0674330
$337$	− 11.5279i	− 0.627963i	−0.949429	−	0.313981i	$-0.898337\pi$
$337$	− 11.5279i	− 0.627963i	0.949429	−	0.313981i	$-0.101663\pi$
$338$	5.65248i	0.307454i
$339$	2.47214	0.134268
$340$	0	0
$341$	2.76393	0.149675
$342$	− 21.3050i	− 1.15204i
$343$	− 1.00000i	− 0.0539949i
$344$	−17.8885	−0.964486
$345$	0	0
$346$	−28.5410	−1.53437
$347$	20.9443i	1.12435i	0.827019	+	0.562174i	$0.190035\pi$
$347$	20.9443i	1.12435i	−0.827019	+	0.562174i	$0.809965\pi$
$348$	31.4164i	1.68410i
$349$	7.23607	0.387338	0.193669	−	0.981067i	$-0.437961\pi$
$349$	7.23607	0.387338	0.193669	+	0.981067i	$0.437961\pi$
$350$	0	0
$351$	17.8885	0.954820
$352$	6.70820i	0.357548i
$353$	− 19.8885i	− 1.05856i	−0.848447	−	0.529280i	$-0.822462\pi$
$353$	− 19.8885i	− 1.05856i	0.848447	−	0.529280i	$-0.177538\pi$
$354$	−3.41641	−0.181580
$355$	0	0
$356$	6.00000	0.317999
$357$	4.00000i	0.211702i
$358$	20.0000i	1.05703i
$359$	24.9443	1.31651	0.658254	−	0.752796i	$-0.271295\pi$
$359$	24.9443	1.31651	0.658254	+	0.752796i	$0.271295\pi$
$360$	0	0
$361$	22.8885	1.20466
$362$	− 56.8328i	− 2.98707i
$363$	1.23607i	0.0648767i
$364$	−9.70820	−0.508848
$365$	0	0
$366$	20.0000	1.04542
$367$	− 23.1246i	− 1.20709i	−0.797327	−	0.603547i	$-0.793753\pi$
$367$	− 23.1246i	− 1.20709i	0.797327	−	0.603547i	$-0.206247\pi$
$368$	2.47214i	0.128869i
$369$	−16.5410	−0.861091
$370$	0	0
$371$	−0.472136	−0.0245121
$372$	10.2492i	0.531397i
$373$	− 6.00000i	− 0.310668i	−0.987862	−	0.155334i	$-0.950355\pi$
$373$	− 6.00000i	− 0.310668i	0.987862	−	0.155334i	$-0.0496454\pi$
$374$	−7.23607	−0.374168
$375$	0	0
$376$	6.18034	0.318727
$377$	27.4164i	1.41202i
$378$	− 12.3607i	− 0.635765i
$379$	−37.3050	−1.91623	−0.958113	−	0.286389i	$-0.907545\pi$
$379$	−37.3050	−1.91623	−0.958113	+	0.286389i	$0.907545\pi$
$380$	0	0
$381$	−3.77709	−0.193506
$382$	− 6.83282i	− 0.349597i
$383$	4.65248i	0.237730i	0.992910	+	0.118865i	$0.0379256\pi$
$383$	4.65248i	0.237730i	−0.992910	+	0.118865i	$0.962074\pi$
$384$	−19.3475	−0.987324
$385$	0	0
$386$	26.5836	1.35307
$387$	− 11.7771i	− 0.598663i
$388$	− 52.2492i	− 2.65255i
$389$	−15.8885	−0.805581	−0.402791	−	0.915292i	$-0.631960\pi$
$389$	−15.8885	−0.805581	−0.402791	+	0.915292i	$0.631960\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	2.23607i	0.112938i
$393$	27.0557i	1.36478i
$394$	4.47214	0.225303
$395$	0	0
$396$	4.41641	0.221933
$397$	− 35.8885i	− 1.80119i	−0.434655	−	0.900597i	$-0.643130\pi$
$397$	− 35.8885i	− 1.80119i	0.434655	−	0.900597i	$-0.356870\pi$
$398$	4.87539i	0.244381i
$399$	8.00000	0.400501
$400$	0	0
$401$	22.9443	1.14578	0.572891	−	0.819631i	$-0.305822\pi$
$401$	22.9443	1.14578	0.572891	+	0.819631i	$0.305822\pi$
$402$	− 40.0000i	− 1.99502i
$403$	8.94427i	0.445546i
$404$	14.2918	0.711043
$405$	0	0
$406$	18.9443	0.940188
$407$	8.47214i	0.419948i
$408$	− 8.94427i	− 0.442807i
$409$	−9.12461	−0.451183	−0.225592	−	0.974222i	$-0.572431\pi$
$409$	−9.12461	−0.451183	−0.225592	+	0.974222i	$0.572431\pi$
$410$	0	0
$411$	−20.3607	−1.00432
$412$	23.1246i	1.13927i
$413$	1.23607i	0.0608229i
$414$	8.13777	0.399949
$415$	0	0
$416$	−21.7082	−1.06433
$417$	1.88854i	0.0924824i
$418$	14.4721i	0.707855i
$419$	−24.6525	−1.20435	−0.602176	−	0.798363i	$-0.705700\pi$
$419$	−24.6525	−1.20435	−0.602176	+	0.798363i	$0.705700\pi$
$420$	0	0
$421$	22.3607	1.08979	0.544896	−	0.838503i	$-0.316569\pi$
$421$	22.3607	1.08979	0.544896	+	0.838503i	$0.316569\pi$
$422$	− 31.0557i	− 1.51177i
$423$	4.06888i	0.197836i
$424$	1.05573	0.0512707
$425$	0	0
$426$	28.9443	1.40235
$427$	− 7.23607i	− 0.350178i
$428$	12.0000i	0.580042i
$429$	−4.00000	−0.193122
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	− 5.52786i	− 0.265959i
$433$	8.47214i	0.407145i	0.979060	+	0.203572i	$0.0652552\pi$
$433$	8.47214i	0.407145i	−0.979060	+	0.203572i	$0.934745\pi$
$434$	6.18034	0.296666
$435$	0	0
$436$	−13.4164	−0.642529
$437$	16.0000i	0.765384i
$438$	− 2.11146i	− 0.100889i
$439$	−10.4721	−0.499808	−0.249904	−	0.968271i	$-0.580399\pi$
$439$	−10.4721	−0.499808	−0.249904	+	0.968271i	$0.580399\pi$
$440$	0	0
$441$	−1.47214	−0.0701017
$442$	− 23.4164i	− 1.11380i
$443$	24.9443i	1.18514i	0.805520	+	0.592569i	$0.201886\pi$
$443$	24.9443i	1.18514i	−0.805520	+	0.592569i	$0.798114\pi$
$444$	−31.4164	−1.49096
$445$	0	0
$446$	−22.7639	−1.07790
$447$	− 17.3050i	− 0.818496i
$448$	13.0000i	0.614192i
$449$	28.4721	1.34368	0.671842	−	0.740695i	$-0.265504\pi$
$449$	28.4721	1.34368	0.671842	+	0.740695i	$0.265504\pi$
$450$	0	0
$451$	11.2361	0.529086
$452$	6.00000i	0.282216i
$453$	11.0557i	0.519443i
$454$	−13.1672	−0.617967
$455$	0	0
$456$	−17.8885	−0.837708
$457$	− 28.8328i	− 1.34874i	−0.738393	−	0.674371i	$-0.764415\pi$
$457$	− 28.8328i	− 1.34874i	0.738393	−	0.674371i	$-0.235585\pi$
$458$	10.0000i	0.467269i
$459$	17.8885	0.834966
$460$	0	0
$461$	−12.1803	−0.567295	−0.283647	−	0.958929i	$-0.591545\pi$
$461$	−12.1803	−0.567295	−0.283647	+	0.958929i	$0.591545\pi$
$462$	2.76393i	0.128590i
$463$	5.52786i	0.256902i	0.991716	+	0.128451i	$0.0410004\pi$
$463$	5.52786i	0.256902i	−0.991716	+	0.128451i	$0.959000\pi$
$464$	8.47214	0.393309
$465$	0	0
$466$	21.0557	0.975388
$467$	24.0689i	1.11378i	0.830588	+	0.556888i	$0.188005\pi$
$467$	24.0689i	1.11378i	−0.830588	+	0.556888i	$0.811995\pi$
$468$	14.2918i	0.660639i
$469$	−14.4721	−0.668261
$470$	0	0
$471$	−13.5279	−0.623331
$472$	− 2.76393i	− 0.127220i
$473$	8.00000i	0.367840i
$474$	−24.7214	−1.13549
$475$	0	0
$476$	−9.70820	−0.444975
$477$	0.695048i	0.0318241i
$478$	22.1115i	1.01135i
$479$	−13.5279	−0.618104	−0.309052	−	0.951045i	$-0.600012\pi$
$479$	−13.5279	−0.618104	−0.309052	+	0.951045i	$0.600012\pi$
$480$	0	0
$481$	−27.4164	−1.25008
$482$	− 29.3475i	− 1.33674i
$483$	3.05573i	0.139040i
$484$	−3.00000	−0.136364
$485$	0	0
$486$	−30.4033	−1.37912
$487$	− 36.3607i	− 1.64766i	−0.566837	−	0.823830i	$-0.691833\pi$
$487$	− 36.3607i	− 1.64766i	0.566837	−	0.823830i	$-0.308167\pi$
$488$	16.1803i	0.732450i
$489$	−4.22291	−0.190967
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	41.6656i	1.87843i
$493$	27.4164i	1.23477i
$494$	−46.8328	−2.10711
$495$	0	0
$496$	2.76393	0.124104
$497$	− 10.4721i	− 0.469739i
$498$	− 31.5542i	− 1.41398i
$499$	−1.52786	−0.0683966	−0.0341983	−	0.999415i	$-0.510888\pi$
$499$	−1.52786	−0.0683966	−0.0341983	+	0.999415i	$0.510888\pi$
$500$	0	0
$501$	−6.11146	−0.273040
$502$	9.59675i	0.428324i
$503$	− 23.4164i	− 1.04409i	−0.852919	−	0.522043i	$-0.825170\pi$
$503$	− 23.4164i	− 1.04409i	0.852919	−	0.522043i	$-0.174830\pi$
$504$	3.29180	0.146628
$505$	0	0
$506$	−5.52786	−0.245744
$507$	3.12461i	0.138769i
$508$	− 9.16718i	− 0.406728i
$509$	−40.4721	−1.79390	−0.896948	−	0.442136i	$-0.854221\pi$
$509$	−40.4721	−1.79390	−0.896948	+	0.442136i	$0.854221\pi$
$510$	0	0
$511$	−0.763932	−0.0337944
$512$	11.1803i	0.494106i
$513$	− 35.7771i	− 1.57960i
$514$	13.4164	0.591772
$515$	0	0
$516$	−29.6656	−1.30596
$517$	− 2.76393i	− 0.121558i
$518$	18.9443i	0.832364i
$519$	−15.7771	−0.692537
$520$	0	0
$521$	30.3607	1.33013	0.665063	−	0.746787i	$-0.268405\pi$
$521$	30.3607	1.33013	0.665063	+	0.746787i	$0.268405\pi$
$522$	− 27.8885i	− 1.22065i
$523$	− 44.0000i	− 1.92399i	−0.273075	−	0.961993i	$-0.588041\pi$
$523$	− 44.0000i	− 1.92399i	0.273075	−	0.961993i	$-0.411959\pi$
$524$	−65.6656	−2.86862
$525$	0	0
$526$	0	0
$527$	8.94427i	0.389619i
$528$	1.23607i	0.0537930i
$529$	16.8885	0.734285
$530$	0	0
$531$	1.81966	0.0789665
$532$	19.4164i	0.841808i
$533$	36.3607i	1.57496i
$534$	5.52786	0.239214
$535$	0	0
$536$	32.3607	1.39777
$537$	11.0557i	0.477090i
$538$	− 30.0000i	− 1.29339i
$539$	1.00000	0.0430730
$540$	0	0
$541$	20.8328	0.895673	0.447836	−	0.894116i	$-0.352195\pi$
$541$	20.8328	0.895673	0.447836	+	0.894116i	$0.352195\pi$
$542$	− 23.4164i	− 1.00582i
$543$	− 31.4164i	− 1.34821i
$544$	−21.7082	−0.930732
$545$	0	0
$546$	−8.94427	−0.382780
$547$	28.0000i	1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$	28.0000i	1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	− 49.4164i	− 2.11096i
$549$	−10.6525	−0.454637
$550$	0	0
$551$	54.8328	2.33596
$552$	− 6.83282i	− 0.290824i
$553$	8.94427i	0.380349i
$554$	44.4721	1.88944
$555$	0	0
$556$	−4.58359	−0.194388
$557$	− 38.9443i	− 1.65012i	−0.565044	−	0.825061i	$-0.691141\pi$
$557$	− 38.9443i	− 1.65012i	0.565044	−	0.825061i	$-0.308859\pi$
$558$	− 9.09830i	− 0.385162i
$559$	−25.8885	−1.09497
$560$	0	0
$561$	−4.00000	−0.168880
$562$	− 7.88854i	− 0.332758i
$563$	− 12.5836i	− 0.530335i	−0.964202	−	0.265168i	$-0.914573\pi$
$563$	− 12.5836i	− 0.530335i	0.964202	−	0.265168i	$-0.0854273\pi$
$564$	10.2492	0.431570
$565$	0	0
$566$	66.8328	2.80919
$567$	− 2.41641i	− 0.101480i
$568$	23.4164i	0.982531i
$569$	−7.52786	−0.315584	−0.157792	−	0.987472i	$-0.550438\pi$
$569$	−7.52786	−0.315584	−0.157792	+	0.987472i	$0.550438\pi$
$570$	0	0
$571$	−15.0557	−0.630063	−0.315031	−	0.949081i	$-0.602015\pi$
$571$	−15.0557	−0.630063	−0.315031	+	0.949081i	$0.602015\pi$
$572$	− 9.70820i	− 0.405920i
$573$	− 3.77709i	− 0.157790i
$574$	25.1246	1.04868
$575$	0	0
$576$	19.1378	0.797407
$577$	− 19.5279i	− 0.812956i	−0.913661	−	0.406478i	$-0.866757\pi$
$577$	− 19.5279i	− 0.812956i	0.913661	−	0.406478i	$-0.133243\pi$
$578$	14.5967i	0.607145i
$579$	14.6950	0.610705
$580$	0	0
$581$	−11.4164	−0.473632
$582$	− 48.1378i	− 1.99537i
$583$	− 0.472136i	− 0.0195539i
$584$	1.70820	0.0706860
$585$	0	0
$586$	−56.1803	−2.32079
$587$	27.1246i	1.11955i	0.828644	+	0.559776i	$0.189113\pi$
$587$	27.1246i	1.11955i	−0.828644	+	0.559776i	$0.810887\pi$
$588$	3.70820i	0.152924i
$589$	17.8885	0.737085
$590$	0	0
$591$	2.47214	0.101690
$592$	8.47214i	0.348203i
$593$	45.7082i	1.87701i	0.345264	+	0.938505i	$0.387789\pi$
$593$	45.7082i	1.87701i	−0.345264	+	0.938505i	$0.612211\pi$
$594$	12.3607	0.507165
$595$	0	0
$596$	42.0000	1.72039
$597$	2.69505i	0.110301i
$598$	− 17.8885i	− 0.731517i
$599$	23.4164	0.956768	0.478384	−	0.878151i	$-0.341223\pi$
$599$	23.4164	0.956768	0.478384	+	0.878151i	$0.341223\pi$
$600$	0	0
$601$	−37.1246	−1.51434	−0.757172	−	0.653215i	$-0.773420\pi$
$601$	−37.1246	−1.51434	−0.757172	+	0.653215i	$0.773420\pi$
$602$	17.8885i	0.729083i
$603$	21.3050i	0.867605i
$604$	−26.8328	−1.09181
$605$	0	0
$606$	13.1672	0.534880
$607$	12.9443i	0.525392i	0.964879	+	0.262696i	$0.0846116\pi$
$607$	12.9443i	0.525392i	−0.964879	+	0.262696i	$0.915388\pi$
$608$	43.4164i	1.76077i
$609$	10.4721	0.424352
$610$	0	0
$611$	8.94427	0.361847
$612$	14.2918i	0.577712i
$613$	− 15.3050i	− 0.618161i	−0.951036	−	0.309081i	$-0.899979\pi$
$613$	− 15.3050i	− 0.618161i	0.951036	−	0.309081i	$-0.100021\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	−2.23607	−0.0900937
$617$	6.58359i	0.265045i	0.991180	+	0.132523i	$0.0423078\pi$
$617$	6.58359i	0.265045i	−0.991180	+	0.132523i	$0.957692\pi$
$618$	21.3050i	0.857011i
$619$	−11.1246	−0.447136	−0.223568	−	0.974688i	$-0.571770\pi$
$619$	−11.1246	−0.447136	−0.223568	+	0.974688i	$0.571770\pi$
$620$	0	0
$621$	13.6656	0.548383
$622$	− 18.5410i	− 0.743427i
$623$	− 2.00000i	− 0.0801283i
$624$	−4.00000	−0.160128
$625$	0	0
$626$	33.4164	1.33559
$627$	8.00000i	0.319489i
$628$	− 32.8328i	− 1.31017i
$629$	−27.4164	−1.09316
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	− 20.0000i	− 0.795557i
$633$	− 17.1672i	− 0.682334i
$634$	−31.3050	−1.24328
$635$	0	0
$636$	1.75078	0.0694228
$637$	3.23607i	0.128218i
$638$	18.9443i	0.750011i
$639$	−15.4164	−0.609864
$640$	0	0
$641$	−15.5279	−0.613314	−0.306657	−	0.951820i	$-0.599210\pi$
$641$	−15.5279	−0.613314	−0.306657	+	0.951820i	$0.599210\pi$
$642$	11.0557i	0.436335i
$643$	− 11.1246i	− 0.438712i	−0.975645	−	0.219356i	$-0.929604\pi$
$643$	− 11.1246i	− 0.438712i	0.975645	−	0.219356i	$-0.0703956\pi$
$644$	−7.41641	−0.292247
$645$	0	0
$646$	−46.8328	−1.84261
$647$	36.0689i	1.41801i	0.705201	+	0.709007i	$0.250857\pi$
$647$	36.0689i	1.41801i	−0.705201	+	0.709007i	$0.749143\pi$
$648$	5.40325i	0.212260i
$649$	−1.23607	−0.0485199
$650$	0	0
$651$	3.41641	0.133900
$652$	− 10.2492i	− 0.401391i
$653$	− 25.0557i	− 0.980506i	−0.871580	−	0.490253i	$-0.836904\pi$
$653$	− 25.0557i	− 0.980506i	0.871580	−	0.490253i	$-0.163096\pi$
$654$	−12.3607	−0.483341
$655$	0	0
$656$	11.2361	0.438695
$657$	1.12461i	0.0438753i
$658$	− 6.18034i	− 0.240935i
$659$	17.8885	0.696839	0.348419	−	0.937339i	$-0.386719\pi$
$659$	17.8885	0.696839	0.348419	+	0.937339i	$0.386719\pi$
$660$	0	0
$661$	−40.8328	−1.58821	−0.794106	−	0.607779i	$-0.792061\pi$
$661$	−40.8328	−1.58821	−0.794106	+	0.607779i	$0.792061\pi$
$662$	− 31.0557i	− 1.20702i
$663$	− 12.9443i	− 0.502714i
$664$	25.5279	0.990673
$665$	0	0
$666$	27.8885	1.08066
$667$	20.9443i	0.810965i
$668$	− 14.8328i	− 0.573899i
$669$	−12.5836	−0.486510
$670$	0	0
$671$	7.23607	0.279345
$672$	8.29180i	0.319863i
$673$	21.4164i	0.825542i	0.910835	+	0.412771i	$0.135439\pi$
$673$	21.4164i	0.825542i	−0.910835	+	0.412771i	$0.864561\pi$
$674$	25.7771	0.992896
$675$	0	0
$676$	−7.58359	−0.291677
$677$	− 9.70820i	− 0.373117i	−0.982444	−	0.186558i	$-0.940267\pi$
$677$	− 9.70820i	− 0.373117i	0.982444	−	0.186558i	$-0.0597333\pi$
$678$	5.52786i	0.212296i
$679$	−17.4164	−0.668380
$680$	0	0
$681$	−7.27864	−0.278918
$682$	6.18034i	0.236657i
$683$	5.88854i	0.225319i	0.993634	+	0.112659i	$0.0359369\pi$
$683$	5.88854i	0.225319i	−0.993634	+	0.112659i	$0.964063\pi$
$684$	28.5836	1.09292
$685$	0	0
$686$	2.23607	0.0853735
$687$	5.52786i	0.210901i
$688$	8.00000i	0.304997i
$689$	1.52786	0.0582070
$690$	0	0
$691$	18.5410	0.705334	0.352667	−	0.935749i	$-0.385275\pi$
$691$	18.5410	0.705334	0.352667	+	0.935749i	$0.385275\pi$
$692$	− 38.2918i	− 1.45564i
$693$	− 1.47214i	− 0.0559218i
$694$	−46.8328	−1.77775
$695$	0	0
$696$	−23.4164	−0.887597
$697$	36.3607i	1.37726i
$698$	16.1803i	0.612435i
$699$	11.6393	0.440240
$700$	0	0
$701$	−15.5279	−0.586479	−0.293240	−	0.956039i	$-0.594733\pi$
$701$	−15.5279	−0.586479	−0.293240	+	0.956039i	$0.594733\pi$
$702$	40.0000i	1.50970i
$703$	54.8328i	2.06806i
$704$	−13.0000	−0.489956
$705$	0	0
$706$	44.4721	1.67373
$707$	− 4.76393i	− 0.179166i
$708$	− 4.58359i	− 0.172262i
$709$	14.9443	0.561244	0.280622	−	0.959818i	$-0.409459\pi$
$709$	14.9443	0.561244	0.280622	+	0.959818i	$0.409459\pi$
$710$	0	0
$711$	13.1672	0.493808
$712$	4.47214i	0.167600i
$713$	6.83282i	0.255891i
$714$	−8.94427	−0.334731
$715$	0	0
$716$	−26.8328	−1.00279
$717$	12.2229i	0.456473i
$718$	55.7771i	2.08158i
$719$	51.4853	1.92008	0.960039	−	0.279867i	$-0.0902905\pi$
$719$	51.4853	1.92008	0.960039	+	0.279867i	$0.0902905\pi$
$720$	0	0
$721$	7.70820	0.287069
$722$	51.1803i	1.90474i
$723$	− 16.2229i	− 0.603337i
$724$	76.2492	2.83378
$725$	0	0
$726$	−2.76393	−0.102579
$727$	25.0132i	0.927687i	0.885917	+	0.463843i	$0.153530\pi$
$727$	25.0132i	0.927687i	−0.885917	+	0.463843i	$0.846470\pi$
$728$	− 7.23607i	− 0.268187i
$729$	−24.0557	−0.890953
$730$	0	0
$731$	−25.8885	−0.957522
$732$	26.8328i	0.991769i
$733$	− 8.76393i	− 0.323703i	−0.986815	−	0.161852i	$-0.948253\pi$
$733$	− 8.76393i	− 0.323703i	0.986815	−	0.161852i	$-0.0517466\pi$
$734$	51.7082	1.90858
$735$	0	0
$736$	−16.5836	−0.611279
$737$	− 14.4721i	− 0.533088i
$738$	− 36.9868i	− 1.36150i
$739$	−24.9443	−0.917590	−0.458795	−	0.888542i	$-0.651719\pi$
$739$	−24.9443	−0.917590	−0.458795	+	0.888542i	$0.651719\pi$
$740$	0	0
$741$	−25.8885	−0.951039
$742$	− 1.05573i	− 0.0387570i
$743$	− 1.88854i	− 0.0692840i	−0.999400	−	0.0346420i	$-0.988971\pi$
$743$	− 1.88854i	− 0.0692840i	0.999400	−	0.0346420i	$-0.0110291\pi$
$744$	−7.63932	−0.280071
$745$	0	0
$746$	13.4164	0.491210
$747$	16.8065i	0.614918i
$748$	− 9.70820i	− 0.354967i
$749$	4.00000	0.146157
$750$	0	0
$751$	29.5279	1.07749	0.538744	−	0.842470i	$-0.318899\pi$
$751$	29.5279	1.07749	0.538744	+	0.842470i	$0.318899\pi$
$752$	− 2.76393i	− 0.100790i
$753$	5.30495i	0.193323i
$754$	−61.3050	−2.23259
$755$	0	0
$756$	16.5836	0.603139
$757$	15.8885i	0.577479i	0.957408	+	0.288739i	$0.0932361\pi$
$757$	15.8885i	0.577479i	−0.957408	+	0.288739i	$0.906764\pi$
$758$	− 83.4164i	− 3.02982i
$759$	−3.05573	−0.110916
$760$	0	0
$761$	−31.5967	−1.14538	−0.572691	−	0.819772i	$-0.694100\pi$
$761$	−31.5967	−1.14538	−0.572691	+	0.819772i	$0.694100\pi$
$762$	− 8.44582i	− 0.305960i
$763$	4.47214i	0.161902i
$764$	9.16718	0.331657
$765$	0	0
$766$	−10.4033	−0.375885
$767$	− 4.00000i	− 0.144432i
$768$	− 11.1246i	− 0.401425i
$769$	−18.2918	−0.659619	−0.329810	−	0.944047i	$-0.606985\pi$
$769$	−18.2918	−0.659619	−0.329810	+	0.944047i	$0.606985\pi$
$770$	0	0
$771$	7.41641	0.267095
$772$	35.6656i	1.28363i
$773$	38.3607i	1.37974i	0.723934	+	0.689869i	$0.242332\pi$
$773$	38.3607i	1.37974i	−0.723934	+	0.689869i	$0.757668\pi$
$774$	26.3344	0.946569
$775$	0	0
$776$	38.9443	1.39802
$777$	10.4721i	0.375686i
$778$	− 35.5279i	− 1.27374i
$779$	72.7214	2.60551
$780$	0	0
$781$	10.4721	0.374722
$782$	− 17.8885i	− 0.639693i
$783$	− 46.8328i	− 1.67367i
$784$	1.00000	0.0357143
$785$	0	0
$786$	−60.4984	−2.15791
$787$	− 43.4164i	− 1.54763i	−0.633413	−	0.773814i	$-0.718347\pi$
$787$	− 43.4164i	− 1.54763i	0.633413	−	0.773814i	$-0.281653\pi$
$788$	6.00000i	0.213741i
$789$	0	0
$790$	0	0
$791$	2.00000	0.0711118
$792$	3.29180i	0.116969i
$793$	23.4164i	0.831541i
$794$	80.2492	2.84794
$795$	0	0
$796$	−6.54102	−0.231840
$797$	− 14.9443i	− 0.529353i	−0.964337	−	0.264677i	$-0.914735\pi$
$797$	− 14.9443i	− 0.529353i	0.964337	−	0.264677i	$-0.0852652\pi$
$798$	17.8885i	0.633248i
$799$	8.94427	0.316426
$800$	0	0
$801$	−2.94427	−0.104031
$802$	51.3050i	1.81164i
$803$	− 0.763932i	− 0.0269586i
$804$	53.6656	1.89264
$805$	0	0
$806$	−20.0000	−0.704470
$807$	− 16.5836i	− 0.583770i
$808$	10.6525i	0.374753i
$809$	−21.0557	−0.740280	−0.370140	−	0.928976i	$-0.620690\pi$
$809$	−21.0557	−0.740280	−0.370140	+	0.928976i	$0.620690\pi$
$810$	0	0
$811$	−34.8328	−1.22315	−0.611573	−	0.791188i	$-0.709463\pi$
$811$	−34.8328	−1.22315	−0.611573	+	0.791188i	$0.709463\pi$
$812$	25.4164i	0.891941i
$813$	− 12.9443i	− 0.453975i
$814$	−18.9443	−0.663996
$815$	0	0
$816$	−4.00000	−0.140028
$817$	51.7771i	1.81145i
$818$	− 20.4033i	− 0.713383i
$819$	4.76393	0.166465
$820$	0	0
$821$	44.8328	1.56468	0.782338	−	0.622854i	$-0.214027\pi$
$821$	44.8328	1.56468	0.782338	+	0.622854i	$0.214027\pi$
$822$	− 45.5279i	− 1.58797i
$823$	14.1115i	0.491894i	0.969283	+	0.245947i	$0.0790990\pi$
$823$	14.1115i	0.491894i	−0.969283	+	0.245947i	$0.920901\pi$
$824$	−17.2361	−0.600447
$825$	0	0
$826$	−2.76393	−0.0961695
$827$	− 12.9443i	− 0.450116i	−0.974345	−	0.225058i	$-0.927743\pi$
$827$	− 12.9443i	− 0.450116i	0.974345	−	0.225058i	$-0.0722572\pi$
$828$	10.9180i	0.379425i
$829$	−36.8328	−1.27926	−0.639628	−	0.768684i	$-0.720912\pi$
$829$	−36.8328	−1.27926	−0.639628	+	0.768684i	$0.720912\pi$
$830$	0	0
$831$	24.5836	0.852795
$832$	− 42.0689i	− 1.45848i
$833$	3.23607i	0.112123i
$834$	−4.22291	−0.146227
$835$	0	0
$836$	−19.4164	−0.671531
$837$	− 15.2786i	− 0.528107i
$838$	− 55.1246i	− 1.90425i
$839$	−44.0689	−1.52143	−0.760713	−	0.649088i	$-0.775151\pi$
$839$	−44.0689	−1.52143	−0.760713	+	0.649088i	$0.775151\pi$
$840$	0	0
$841$	42.7771	1.47507
$842$	50.0000i	1.72311i
$843$	− 4.36068i	− 0.150190i
$844$	41.6656	1.43419
$845$	0	0
$846$	−9.09830	−0.312806
$847$	1.00000i	0.0343604i
$848$	− 0.472136i	− 0.0162132i
$849$	36.9443	1.26792
$850$	0	0
$851$	−20.9443	−0.717960
$852$	38.8328i	1.33039i
$853$	30.6525i	1.04952i	0.851250	+	0.524760i	$0.175845\pi$
$853$	30.6525i	1.04952i	−0.851250	+	0.524760i	$0.824155\pi$
$854$	16.1803	0.553680
$855$	0	0
$856$	−8.94427	−0.305709
$857$	15.2361i	0.520454i	0.965547	+	0.260227i	$0.0837974\pi$
$857$	15.2361i	0.520454i	−0.965547	+	0.260227i	$0.916203\pi$
$858$	− 8.94427i	− 0.305352i
$859$	26.5410	0.905568	0.452784	−	0.891620i	$-0.350431\pi$
$859$	26.5410	0.905568	0.452784	+	0.891620i	$0.350431\pi$
$860$	0	0
$861$	13.8885	0.473320
$862$	26.8328i	0.913929i
$863$	3.05573i	0.104018i	0.998647	+	0.0520091i	$0.0165625\pi$
$863$	3.05573i	0.104018i	−0.998647	+	0.0520091i	$0.983438\pi$
$864$	37.0820	1.26156
$865$	0	0
$866$	−18.9443	−0.643753
$867$	8.06888i	0.274034i
$868$	8.29180i	0.281442i
$869$	−8.94427	−0.303414
$870$	0	0
$871$	46.8328	1.58687
$872$	− 10.0000i	− 0.338643i
$873$	25.6393i	0.867760i
$874$	−35.7771	−1.21018
$875$	0	0
$876$	2.83282	0.0957120
$877$	14.5836i	0.492453i	0.969212	+	0.246226i	$0.0791907\pi$
$877$	14.5836i	0.492453i	−0.969212	+	0.246226i	$0.920809\pi$
$878$	− 23.4164i	− 0.790265i
$879$	−31.0557	−1.04748
$880$	0	0
$881$	2.58359	0.0870434	0.0435217	−	0.999052i	$-0.486142\pi$
$881$	2.58359	0.0870434	0.0435217	+	0.999052i	$0.486142\pi$
$882$	− 3.29180i	− 0.110841i
$883$	8.94427i	0.300999i	0.988610	+	0.150499i	$0.0480881\pi$
$883$	8.94427i	0.300999i	−0.988610	+	0.150499i	$0.951912\pi$
$884$	31.4164	1.05665
$885$	0	0
$886$	−55.7771	−1.87387
$887$	− 4.36068i	− 0.146417i	−0.997317	−	0.0732086i	$-0.976676\pi$
$887$	− 4.36068i	− 0.146417i	0.997317	−	0.0732086i	$-0.0233239\pi$
$888$	− 23.4164i	− 0.785803i
$889$	−3.05573	−0.102486
$890$	0	0
$891$	2.41641	0.0809527
$892$	− 30.5410i	− 1.02259i
$893$	− 17.8885i	− 0.598617i
$894$	38.6950	1.29416
$895$	0	0
$896$	−15.6525	−0.522913
$897$	− 9.88854i	− 0.330169i
$898$	63.6656i	2.12455i
$899$	23.4164	0.780981
$900$	0	0
$901$	1.52786	0.0509005
$902$	25.1246i	0.836558i
$903$	9.88854i	0.329070i
$904$	−4.47214	−0.148741
$905$	0	0
$906$	−24.7214	−0.821312
$907$	22.4721i	0.746175i	0.927796	+	0.373088i	$0.121701\pi$
$907$	22.4721i	0.746175i	−0.927796	+	0.373088i	$0.878299\pi$
$908$	− 17.6656i	− 0.586255i
$909$	−7.01316	−0.232612
$910$	0	0
$911$	42.4721	1.40716	0.703582	−	0.710614i	$-0.251583\pi$
$911$	42.4721	1.40716	0.703582	+	0.710614i	$0.251583\pi$
$912$	8.00000i	0.264906i
$913$	− 11.4164i	− 0.377828i
$914$	64.4721	2.13255
$915$	0	0
$916$	−13.4164	−0.443291
$917$	21.8885i	0.722823i
$918$	40.0000i	1.32020i
$919$	−41.8885	−1.38178	−0.690888	−	0.722962i	$-0.742780\pi$
$919$	−41.8885	−1.38178	−0.690888	+	0.722962i	$0.742780\pi$
$920$	0	0
$921$	11.0557	0.364299
$922$	− 27.2361i	− 0.896972i
$923$	33.8885i	1.11546i
$924$	−3.70820	−0.121991
$925$	0	0
$926$	−12.3607	−0.406197
$927$	− 11.3475i	− 0.372702i
$928$	56.8328i	1.86563i
$929$	52.2492	1.71424	0.857121	−	0.515116i	$-0.172251\pi$
$929$	52.2492	1.71424	0.857121	+	0.515116i	$0.172251\pi$
$930$	0	0
$931$	6.47214	0.212116
$932$	28.2492i	0.925334i
$933$	− 10.2492i	− 0.335545i
$934$	−53.8197	−1.76103
$935$	0	0
$936$	−10.6525	−0.348187
$937$	− 10.6525i	− 0.348001i	−0.984746	−	0.174001i	$-0.944331\pi$
$937$	− 10.6525i	− 0.348001i	0.984746	−	0.174001i	$-0.0556695\pi$
$938$	− 32.3607i	− 1.05661i
$939$	18.4721	0.602815
$940$	0	0
$941$	7.59675	0.247647	0.123823	−	0.992304i	$-0.460484\pi$
$941$	7.59675	0.247647	0.123823	+	0.992304i	$0.460484\pi$
$942$	− 30.2492i	− 0.985573i
$943$	27.7771i	0.904546i
$944$	−1.23607	−0.0402306
$945$	0	0
$946$	−17.8885	−0.581607
$947$	− 5.16718i	− 0.167911i	−0.996470	−	0.0839555i	$-0.973245\pi$
$947$	− 5.16718i	− 0.167911i	0.996470	−	0.0839555i	$-0.0267553\pi$
$948$	− 33.1672i	− 1.07722i
$949$	2.47214	0.0802489
$950$	0	0
$951$	−17.3050	−0.561152
$952$	− 7.23607i	− 0.234522i
$953$	− 22.9443i	− 0.743238i	−0.928385	−	0.371619i	$-0.878803\pi$
$953$	− 22.9443i	− 0.743238i	0.928385	−	0.371619i	$-0.121197\pi$
$954$	−1.55418	−0.0503183
$955$	0	0
$956$	−29.6656	−0.959455
$957$	10.4721i	0.338516i
$958$	− 30.2492i	− 0.977308i
$959$	−16.4721	−0.531913
$960$	0	0
$961$	−23.3607	−0.753570
$962$	− 61.3050i	− 1.97655i
$963$	− 5.88854i	− 0.189756i
$964$	39.3738	1.26815
$965$	0	0
$966$	−6.83282	−0.219842
$967$	− 13.8885i	− 0.446625i	−0.974747	−	0.223313i	$-0.928313\pi$
$967$	− 13.8885i	− 0.446625i	0.974747	−	0.223313i	$-0.0716871\pi$
$968$	− 2.23607i	− 0.0718699i
$969$	−25.8885	−0.831660
$970$	0	0
$971$	11.1246	0.357006	0.178503	−	0.983939i	$-0.442875\pi$
$971$	11.1246	0.357006	0.178503	+	0.983939i	$0.442875\pi$
$972$	− 40.7902i	− 1.30835i
$973$	1.52786i	0.0489811i
$974$	81.3050	2.60518
$975$	0	0
$976$	7.23607	0.231621
$977$	22.9443i	0.734052i	0.930211	+	0.367026i	$0.119624\pi$
$977$	22.9443i	0.734052i	−0.930211	+	0.367026i	$0.880376\pi$
$978$	− 9.44272i	− 0.301945i
$979$	2.00000	0.0639203
$980$	0	0
$981$	6.58359	0.210198
$982$	0	0
$983$	− 21.8197i	− 0.695939i	−0.937506	−	0.347970i	$-0.886871\pi$
$983$	− 21.8197i	− 0.695939i	0.937506	−	0.347970i	$-0.113129\pi$
$984$	−31.0557	−0.990020
$985$	0	0
$986$	−61.3050	−1.95235
$987$	− 3.41641i	− 0.108745i
$988$	− 62.8328i	− 1.99898i
$989$	−19.7771	−0.628875
$990$	0	0
$991$	54.2492	1.72328	0.861642	−	0.507517i	$-0.169437\pi$
$991$	54.2492	1.72328	0.861642	+	0.507517i	$0.169437\pi$
$992$	18.5410i	0.588678i
$993$	− 17.1672i	− 0.544784i
$994$	23.4164	0.742723
$995$	0	0
$996$	42.3344	1.34142
$997$	1.34752i	0.0426765i	0.999772	+	0.0213383i	$0.00679269\pi$
$997$	1.34752i	0.0426765i	−0.999772	+	0.0213383i	$0.993207\pi$
$998$	− 3.41641i	− 0.108145i
$999$	46.8328	1.48172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.b.h.1849.3		4
5.2	odd	4		1925.2.a.r.1.1		2
5.3	odd	4		77.2.a.d.1.2	✓	2
5.4	even	2	inner	1925.2.b.h.1849.2		4
15.8	even	4		693.2.a.h.1.1		2
20.3	even	4		1232.2.a.m.1.2		2
35.3	even	12		539.2.e.j.177.1		4
35.13	even	4		539.2.a.f.1.2		2
35.18	odd	12		539.2.e.i.177.1		4
35.23	odd	12		539.2.e.i.67.1		4
35.33	even	12		539.2.e.j.67.1		4
40.3	even	4		4928.2.a.bv.1.1		2
40.13	odd	4		4928.2.a.bm.1.2		2
55.3	odd	20		847.2.f.n.372.1		4
55.8	even	20		847.2.f.b.372.1		4
55.13	even	20		847.2.f.m.323.1		4
55.18	even	20		847.2.f.b.148.1		4
55.28	even	20		847.2.f.m.729.1		4
55.38	odd	20		847.2.f.a.729.1		4
55.43	even	4		847.2.a.f.1.1		2
55.48	odd	20		847.2.f.n.148.1		4
55.53	odd	20		847.2.f.a.323.1		4
105.83	odd	4		4851.2.a.y.1.1		2
140.83	odd	4		8624.2.a.ce.1.1		2
165.98	odd	4		7623.2.a.bl.1.2		2
385.153	odd	4		5929.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.2	✓	2	5.3	odd	4
539.2.a.f.1.2		2	35.13	even	4
539.2.e.i.67.1		4	35.23	odd	12
539.2.e.i.177.1		4	35.18	odd	12
539.2.e.j.67.1		4	35.33	even	12
539.2.e.j.177.1		4	35.3	even	12
693.2.a.h.1.1		2	15.8	even	4
847.2.a.f.1.1		2	55.43	even	4
847.2.f.a.323.1		4	55.53	odd	20
847.2.f.a.729.1		4	55.38	odd	20
847.2.f.b.148.1		4	55.18	even	20
847.2.f.b.372.1		4	55.8	even	20
847.2.f.m.323.1		4	55.13	even	20
847.2.f.m.729.1		4	55.28	even	20
847.2.f.n.148.1		4	55.48	odd	20
847.2.f.n.372.1		4	55.3	odd	20
1232.2.a.m.1.2		2	20.3	even	4
1925.2.a.r.1.1		2	5.2	odd	4
1925.2.b.h.1849.2		4	5.4	even	2	inner
1925.2.b.h.1849.3		4	1.1	even	1	trivial
4851.2.a.y.1.1		2	105.83	odd	4
4928.2.a.bm.1.2		2	40.13	odd	4
4928.2.a.bv.1.1		2	40.3	even	4
5929.2.a.m.1.1		2	385.153	odd	4
7623.2.a.bl.1.2		2	165.98	odd	4
8624.2.a.ce.1.1		2	140.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.23607i q^{2} +1.23607i q^{3} -3.00000 q^{4} -2.76393 q^{6} +1.00000i q^{7} -2.23607i q^{8} +1.47214 q^{9} +O(q^{10})\)	\(q+2.23607i q^{2} +1.23607i q^{3} -3.00000 q^{4} -2.76393 q^{6} +1.00000i q^{7} -2.23607i q^{8} +1.47214 q^{9} -1.00000 q^{11} -3.70820i q^{12} -3.23607i q^{13} -2.23607 q^{14} -1.00000 q^{16} -3.23607i q^{17} +3.29180i q^{18} -6.47214 q^{19} -1.23607 q^{21} -2.23607i q^{22} -2.47214i q^{23} +2.76393 q^{24} +7.23607 q^{26} +5.52786i q^{27} -3.00000i q^{28} -8.47214 q^{29} -2.76393 q^{31} -6.70820i q^{32} -1.23607i q^{33} +7.23607 q^{34} -4.41641 q^{36} -8.47214i q^{37} -14.4721i q^{38} +4.00000 q^{39} -11.2361 q^{41} -2.76393i q^{42} -8.00000i q^{43} +3.00000 q^{44} +5.52786 q^{46} +2.76393i q^{47} -1.23607i q^{48} -1.00000 q^{49} +4.00000 q^{51} +9.70820i q^{52} +0.472136i q^{53} -12.3607 q^{54} +2.23607 q^{56} -8.00000i q^{57} -18.9443i q^{58} +1.23607 q^{59} -7.23607 q^{61} -6.18034i q^{62} +1.47214i q^{63} +13.0000 q^{64} +2.76393 q^{66} +14.4721i q^{67} +9.70820i q^{68} +3.05573 q^{69} -10.4721 q^{71} -3.29180i q^{72} +0.763932i q^{73} +18.9443 q^{74} +19.4164 q^{76} -1.00000i q^{77} +8.94427i q^{78} +8.94427 q^{79} -2.41641 q^{81} -25.1246i q^{82} +11.4164i q^{83} +3.70820 q^{84} +17.8885 q^{86} -10.4721i q^{87} +2.23607i q^{88} -2.00000 q^{89} +3.23607 q^{91} +7.41641i q^{92} -3.41641i q^{93} -6.18034 q^{94} +8.29180 q^{96} +17.4164i q^{97} -2.23607i q^{98} -1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{4} - 20 q^{6} - 12 q^{9}+O(q^{10}) \) 4 * q - 12 * q^4 - 20 * q^6 - 12 * q^9	\( 4 q - 12 q^{4} - 20 q^{6} - 12 q^{9} - 4 q^{11} - 4 q^{16} - 8 q^{19} + 4 q^{21} + 20 q^{24} + 20 q^{26} - 16 q^{29} - 20 q^{31} + 20 q^{34} + 36 q^{36} + 16 q^{39} - 36 q^{41} + 12 q^{44} + 40 q^{46} - 4 q^{49} + 16 q^{51} + 40 q^{54} - 4 q^{59} - 20 q^{61} + 52 q^{64} + 20 q^{66} + 48 q^{69} - 24 q^{71} + 40 q^{74} + 24 q^{76} + 44 q^{81} - 12 q^{84} - 8 q^{89} + 4 q^{91} + 20 q^{94} + 60 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q - 12 * q^4 - 20 * q^6 - 12 * q^9 - 4 * q^11 - 4 * q^16 - 8 * q^19 + 4 * q^21 + 20 * q^24 + 20 * q^26 - 16 * q^29 - 20 * q^31 + 20 * q^34 + 36 * q^36 + 16 * q^39 - 36 * q^41 + 12 * q^44 + 40 * q^46 - 4 * q^49 + 16 * q^51 + 40 * q^54 - 4 * q^59 - 20 * q^61 + 52 * q^64 + 20 * q^66 + 48 * q^69 - 24 * q^71 + 40 * q^74 + 24 * q^76 + 44 * q^81 - 12 * q^84 - 8 * q^89 + 4 * q^91 + 20 * q^94 + 60 * q^96 + 12 * q^99

Introduction

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Database

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