LMFDB - Embedded newform 3850.2.c.x.1849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, 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("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.x.1849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.73205i q^{3} -1.00000 q^{4} +2.73205 q^{6} -1.00000i q^{7} +1.00000i q^{8} -4.46410 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.73205i q^{3} -1.00000 q^{4} +2.73205 q^{6} -1.00000i q^{7} +1.00000i q^{8} -4.46410 q^{9} +1.00000 q^{11} -2.73205i q^{12} -1.46410i q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.46410i q^{17} +4.46410i q^{18} -6.73205 q^{19} +2.73205 q^{21} -1.00000i q^{22} -8.19615i q^{23} -2.73205 q^{24} -1.46410 q^{26} -4.00000i q^{27} +1.00000i q^{28} +4.73205 q^{29} +2.00000 q^{31} -1.00000i q^{32} +2.73205i q^{33} +3.46410 q^{34} +4.46410 q^{36} -0.732051i q^{37} +6.73205i q^{38} +4.00000 q^{39} -2.19615 q^{41} -2.73205i q^{42} +2.00000i q^{43} -1.00000 q^{44} -8.19615 q^{46} -6.92820i q^{47} +2.73205i q^{48} -1.00000 q^{49} -9.46410 q^{51} +1.46410i q^{52} -7.26795i q^{53} -4.00000 q^{54} +1.00000 q^{56} -18.3923i q^{57} -4.73205i q^{58} -6.92820 q^{59} -4.92820 q^{61} -2.00000i q^{62} +4.46410i q^{63} -1.00000 q^{64} +2.73205 q^{66} +4.00000i q^{67} -3.46410i q^{68} +22.3923 q^{69} +9.46410 q^{71} -4.46410i q^{72} -14.3923i q^{73} -0.732051 q^{74} +6.73205 q^{76} -1.00000i q^{77} -4.00000i q^{78} +12.1962 q^{79} -2.46410 q^{81} +2.19615i q^{82} -16.3923i q^{83} -2.73205 q^{84} +2.00000 q^{86} +12.9282i q^{87} +1.00000i q^{88} -3.46410 q^{89} -1.46410 q^{91} +8.19615i q^{92} +5.46410i q^{93} -6.92820 q^{94} +2.73205 q^{96} -14.5885i q^{97} +1.00000i q^{98} -4.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 4 q^{14} + 4 q^{16} - 20 q^{19} + 4 q^{21} - 4 q^{24} + 8 q^{26} + 12 q^{29} + 8 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 4 q^{44} - 12 q^{46} - 4 q^{49} - 24 q^{51} - 16 q^{54} + 4 q^{56} + 8 q^{61} - 4 q^{64} + 4 q^{66} + 48 q^{69} + 24 q^{71} + 4 q^{74} + 20 q^{76} + 28 q^{79} + 4 q^{81} - 4 q^{84} + 8 q^{86} + 8 q^{91} + 4 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 4 * q^14 + 4 * q^16 - 20 * q^19 + 4 * q^21 - 4 * q^24 + 8 * q^26 + 12 * q^29 + 8 * q^31 + 4 * q^36 + 16 * q^39 + 12 * q^41 - 4 * q^44 - 12 * q^46 - 4 * q^49 - 24 * q^51 - 16 * q^54 + 4 * q^56 + 8 * q^61 - 4 * q^64 + 4 * q^66 + 48 * q^69 + 24 * q^71 + 4 * q^74 + 20 * q^76 + 28 * q^79 + 4 * q^81 - 4 * q^84 + 8 * q^86 + 8 * q^91 + 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	2.73205i	1.57735i	0.614810	+	0.788675i	$0.289233\pi$
$3$	2.73205i	1.57735i	−0.614810	+	0.788675i	$0.710767\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.73205	1.11536
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	1.00000i	0.353553i
$9$	−4.46410	−1.48803
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	− 2.73205i	− 0.788675i
$13$	− 1.46410i	− 0.406069i	−0.979172	−	0.203034i	$-0.934920\pi$
$13$	− 1.46410i	− 0.406069i	0.979172	−	0.203034i	$-0.0650803\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	3.46410i	0.840168i	0.907485	+	0.420084i	$0.137999\pi$
$17$	3.46410i	0.840168i	−0.907485	+	0.420084i	$0.862001\pi$
$18$	4.46410i	1.05220i
$19$	−6.73205	−1.54444	−0.772219	−	0.635356i	$-0.780853\pi$
$19$	−6.73205	−1.54444	−0.772219	+	0.635356i	$0.780853\pi$
$20$	0	0
$21$	2.73205	0.596182
$22$	− 1.00000i	− 0.213201i
$23$	− 8.19615i	− 1.70902i	−0.519438	−	0.854508i	$-0.673859\pi$
$23$	− 8.19615i	− 1.70902i	0.519438	−	0.854508i	$-0.326141\pi$
$24$	−2.73205	−0.557678
$25$	0	0
$26$	−1.46410	−0.287134
$27$	− 4.00000i	− 0.769800i
$28$	1.00000i	0.188982i
$29$	4.73205	0.878720	0.439360	−	0.898311i	$-0.355205\pi$
$29$	4.73205	0.878720	0.439360	+	0.898311i	$0.355205\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	− 1.00000i	− 0.176777i
$33$	2.73205i	0.475589i
$34$	3.46410	0.594089
$35$	0	0
$36$	4.46410	0.744017
$37$	− 0.732051i	− 0.120348i	−0.998188	−	0.0601742i	$-0.980834\pi$
$37$	− 0.732051i	− 0.120348i	0.998188	−	0.0601742i	$-0.0191656\pi$
$38$	6.73205i	1.09208i
$39$	4.00000	0.640513
$40$	0	0
$41$	−2.19615	−0.342981	−0.171491	−	0.985186i	$-0.554858\pi$
$41$	−2.19615	−0.342981	−0.171491	+	0.985186i	$0.554858\pi$
$42$	− 2.73205i	− 0.421565i
$43$	2.00000i	0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$	2.00000i	0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−8.19615	−1.20846
$47$	− 6.92820i	− 1.01058i	−0.862949	−	0.505291i	$-0.831385\pi$
$47$	− 6.92820i	− 1.01058i	0.862949	−	0.505291i	$-0.168615\pi$
$48$	2.73205i	0.394338i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−9.46410	−1.32524
$52$	1.46410i	0.203034i
$53$	− 7.26795i	− 0.998330i	−0.866507	−	0.499165i	$-0.833640\pi$
$53$	− 7.26795i	− 0.998330i	0.866507	−	0.499165i	$-0.166360\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	− 18.3923i	− 2.43612i
$58$	− 4.73205i	− 0.621349i
$59$	−6.92820	−0.901975	−0.450988	−	0.892530i	$-0.648928\pi$
$59$	−6.92820	−0.901975	−0.450988	+	0.892530i	$0.648928\pi$
$60$	0	0
$61$	−4.92820	−0.630992	−0.315496	−	0.948927i	$-0.602171\pi$
$61$	−4.92820	−0.630992	−0.315496	+	0.948927i	$0.602171\pi$
$62$	− 2.00000i	− 0.254000i
$63$	4.46410i	0.562424i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.73205	0.336292
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	− 3.46410i	− 0.420084i
$69$	22.3923	2.69572
$70$	0	0
$71$	9.46410	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$72$	− 4.46410i	− 0.526099i
$73$	− 14.3923i	− 1.68449i	−0.539093	−	0.842246i	$-0.681233\pi$
$73$	− 14.3923i	− 1.68449i	0.539093	−	0.842246i	$-0.318767\pi$
$74$	−0.732051	−0.0850992
$75$	0	0
$76$	6.73205	0.772219
$77$	− 1.00000i	− 0.113961i
$78$	− 4.00000i	− 0.452911i
$79$	12.1962	1.37217	0.686087	−	0.727519i	$-0.259327\pi$
$79$	12.1962	1.37217	0.686087	+	0.727519i	$0.259327\pi$
$80$	0	0
$81$	−2.46410	−0.273789
$82$	2.19615i	0.242524i
$83$	− 16.3923i	− 1.79929i	−0.436623	−	0.899645i	$-0.643826\pi$
$83$	− 16.3923i	− 1.79929i	0.436623	−	0.899645i	$-0.356174\pi$
$84$	−2.73205	−0.298091
$85$	0	0
$86$	2.00000	0.215666
$87$	12.9282i	1.38605i
$88$	1.00000i	0.106600i
$89$	−3.46410	−0.367194	−0.183597	−	0.983002i	$-0.558774\pi$
$89$	−3.46410	−0.367194	−0.183597	+	0.983002i	$0.558774\pi$
$90$	0	0
$91$	−1.46410	−0.153480
$92$	8.19615i	0.854508i
$93$	5.46410i	0.566601i
$94$	−6.92820	−0.714590
$95$	0	0
$96$	2.73205	0.278839
$97$	− 14.5885i	− 1.48123i	−0.671928	−	0.740617i	$-0.734533\pi$
$97$	− 14.5885i	− 1.48123i	0.671928	−	0.740617i	$-0.265467\pi$
$98$	1.00000i	0.101015i
$99$	−4.46410	−0.448659
$100$	0	0
$101$	−7.85641	−0.781742	−0.390871	−	0.920446i	$-0.627826\pi$
$101$	−7.85641	−0.781742	−0.390871	+	0.920446i	$0.627826\pi$
$102$	9.46410i	0.937086i
$103$	12.3923i	1.22105i	0.791997	+	0.610525i	$0.209042\pi$
$103$	12.3923i	1.22105i	−0.791997	+	0.610525i	$0.790958\pi$
$104$	1.46410	0.143567
$105$	0	0
$106$	−7.26795	−0.705926
$107$	− 7.85641i	− 0.759507i	−0.925088	−	0.379754i	$-0.876009\pi$
$107$	− 7.85641i	− 0.759507i	0.925088	−	0.379754i	$-0.123991\pi$
$108$	4.00000i	0.384900i
$109$	15.6603	1.49998	0.749990	−	0.661449i	$-0.230058\pi$
$109$	15.6603	1.49998	0.749990	+	0.661449i	$0.230058\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	− 1.00000i	− 0.0944911i
$113$	7.85641i	0.739069i	0.929217	+	0.369534i	$0.120483\pi$
$113$	7.85641i	0.739069i	−0.929217	+	0.369534i	$0.879517\pi$
$114$	−18.3923	−1.72260
$115$	0	0
$116$	−4.73205	−0.439360
$117$	6.53590i	0.604244i
$118$	6.92820i	0.637793i
$119$	3.46410	0.317554
$120$	0	0
$121$	1.00000	0.0909091
$122$	4.92820i	0.446179i
$123$	− 6.00000i	− 0.541002i
$124$	−2.00000	−0.179605
$125$	0	0
$126$	4.46410	0.397694
$127$	− 1.07180i	− 0.0951066i	−0.998869	−	0.0475533i	$-0.984858\pi$
$127$	− 1.07180i	− 0.0951066i	0.998869	−	0.0475533i	$-0.0151424\pi$
$128$	1.00000i	0.0883883i
$129$	−5.46410	−0.481087
$130$	0	0
$131$	5.66025	0.494539	0.247269	−	0.968947i	$-0.420467\pi$
$131$	5.66025	0.494539	0.247269	+	0.968947i	$0.420467\pi$
$132$	− 2.73205i	− 0.237795i
$133$	6.73205i	0.583743i
$134$	4.00000	0.345547
$135$	0	0
$136$	−3.46410	−0.297044
$137$	0.928203i	0.0793018i	0.999214	+	0.0396509i	$0.0126246\pi$
$137$	0.928203i	0.0793018i	−0.999214	+	0.0396509i	$0.987375\pi$
$138$	− 22.3923i	− 1.90616i
$139$	−13.6603	−1.15865	−0.579324	−	0.815097i	$-0.696683\pi$
$139$	−13.6603	−1.15865	−0.579324	+	0.815097i	$0.696683\pi$
$140$	0	0
$141$	18.9282	1.59404
$142$	− 9.46410i	− 0.794210i
$143$	− 1.46410i	− 0.122434i
$144$	−4.46410	−0.372008
$145$	0	0
$146$	−14.3923	−1.19112
$147$	− 2.73205i	− 0.225336i
$148$	0.732051i	0.0601742i
$149$	7.26795	0.595414	0.297707	−	0.954657i	$-0.403778\pi$
$149$	7.26795	0.595414	0.297707	+	0.954657i	$0.403778\pi$
$150$	0	0
$151$	11.1244	0.905287	0.452644	−	0.891692i	$-0.350481\pi$
$151$	11.1244	0.905287	0.452644	+	0.891692i	$0.350481\pi$
$152$	− 6.73205i	− 0.546041i
$153$	− 15.4641i	− 1.25020i
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−4.00000	−0.320256
$157$	− 4.53590i	− 0.362004i	−0.983483	−	0.181002i	$-0.942066\pi$
$157$	− 4.53590i	− 0.362004i	0.983483	−	0.181002i	$-0.0579341\pi$
$158$	− 12.1962i	− 0.970274i
$159$	19.8564	1.57472
$160$	0	0
$161$	−8.19615	−0.645947
$162$	2.46410i	0.193598i
$163$	− 4.00000i	− 0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$	− 4.00000i	− 0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	2.19615	0.171491
$165$	0	0
$166$	−16.3923	−1.27229
$167$	− 13.8564i	− 1.07224i	−0.844141	−	0.536120i	$-0.819889\pi$
$167$	− 13.8564i	− 1.07224i	0.844141	−	0.536120i	$-0.180111\pi$
$168$	2.73205i	0.210782i
$169$	10.8564	0.835108
$170$	0	0
$171$	30.0526	2.29818
$172$	− 2.00000i	− 0.152499i
$173$	0.928203i	0.0705700i	0.999377	+	0.0352850i	$0.0112339\pi$
$173$	0.928203i	0.0705700i	−0.999377	+	0.0352850i	$0.988766\pi$
$174$	12.9282	0.980085
$175$	0	0
$176$	1.00000	0.0753778
$177$	− 18.9282i	− 1.42273i
$178$	3.46410i	0.259645i
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	1.46410i	0.108526i
$183$	− 13.4641i	− 0.995295i
$184$	8.19615	0.604228
$185$	0	0
$186$	5.46410	0.400647
$187$	3.46410i	0.253320i
$188$	6.92820i	0.505291i
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	− 2.73205i	− 0.197169i
$193$	12.3923i	0.892018i	0.895029	+	0.446009i	$0.147155\pi$
$193$	12.3923i	0.892018i	−0.895029	+	0.446009i	$0.852845\pi$
$194$	−14.5885	−1.04739
$195$	0	0
$196$	1.00000	0.0714286
$197$	24.2487i	1.72765i	0.503793	+	0.863825i	$0.331938\pi$
$197$	24.2487i	1.72765i	−0.503793	+	0.863825i	$0.668062\pi$
$198$	4.46410i	0.317250i
$199$	−2.92820	−0.207575	−0.103787	−	0.994600i	$-0.533096\pi$
$199$	−2.92820	−0.207575	−0.103787	+	0.994600i	$0.533096\pi$
$200$	0	0
$201$	−10.9282	−0.770816
$202$	7.85641i	0.552775i
$203$	− 4.73205i	− 0.332125i
$204$	9.46410	0.662620
$205$	0	0
$206$	12.3923	0.863413
$207$	36.5885i	2.54307i
$208$	− 1.46410i	− 0.101517i
$209$	−6.73205	−0.465666
$210$	0	0
$211$	26.9282	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$211$	26.9282	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$212$	7.26795i	0.499165i
$213$	25.8564i	1.77165i
$214$	−7.85641	−0.537053
$215$	0	0
$216$	4.00000	0.272166
$217$	− 2.00000i	− 0.135769i
$218$	− 15.6603i	− 1.06065i
$219$	39.3205	2.65703
$220$	0	0
$221$	5.07180	0.341166
$222$	− 2.00000i	− 0.134231i
$223$	− 25.4641i	− 1.70520i	−0.522562	−	0.852601i	$-0.675024\pi$
$223$	− 25.4641i	− 1.70520i	0.522562	−	0.852601i	$-0.324976\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	7.85641	0.522600
$227$	− 6.92820i	− 0.459841i	−0.973209	−	0.229920i	$-0.926153\pi$
$227$	− 6.92820i	− 0.459841i	0.973209	−	0.229920i	$-0.0738466\pi$
$228$	18.3923i	1.21806i
$229$	−24.3923	−1.61189	−0.805944	−	0.591991i	$-0.798342\pi$
$229$	−24.3923	−1.61189	−0.805944	+	0.591991i	$0.798342\pi$
$230$	0	0
$231$	2.73205	0.179756
$232$	4.73205i	0.310674i
$233$	− 7.85641i	− 0.514690i	−0.966320	−	0.257345i	$-0.917152\pi$
$233$	− 7.85641i	− 0.514690i	0.966320	−	0.257345i	$-0.0828477\pi$
$234$	6.53590	0.427265
$235$	0	0
$236$	6.92820	0.450988
$237$	33.3205i	2.16440i
$238$	− 3.46410i	− 0.224544i
$239$	−1.26795	−0.0820168	−0.0410084	−	0.999159i	$-0.513057\pi$
$239$	−1.26795	−0.0820168	−0.0410084	+	0.999159i	$0.513057\pi$
$240$	0	0
$241$	3.26795	0.210507	0.105254	−	0.994445i	$-0.466435\pi$
$241$	3.26795	0.210507	0.105254	+	0.994445i	$0.466435\pi$
$242$	− 1.00000i	− 0.0642824i
$243$	− 18.7321i	− 1.20166i
$244$	4.92820	0.315496
$245$	0	0
$246$	−6.00000	−0.382546
$247$	9.85641i	0.627148i
$248$	2.00000i	0.127000i
$249$	44.7846	2.83811
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	− 4.46410i	− 0.281212i
$253$	− 8.19615i	− 0.515288i
$254$	−1.07180	−0.0672505
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.6603i	1.47589i	0.674863	+	0.737943i	$0.264203\pi$
$257$	23.6603i	1.47589i	−0.674863	+	0.737943i	$0.735797\pi$
$258$	5.46410i	0.340180i
$259$	−0.732051	−0.0454874
$260$	0	0
$261$	−21.1244	−1.30756
$262$	− 5.66025i	− 0.349692i
$263$	− 24.0000i	− 1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$	− 24.0000i	− 1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$	−2.73205	−0.168146
$265$	0	0
$266$	6.73205	0.412769
$267$	− 9.46410i	− 0.579194i
$268$	− 4.00000i	− 0.244339i
$269$	−28.3923	−1.73111	−0.865555	−	0.500814i	$-0.833034\pi$
$269$	−28.3923	−1.73111	−0.865555	+	0.500814i	$0.833034\pi$
$270$	0	0
$271$	0.392305	0.0238308	0.0119154	−	0.999929i	$-0.496207\pi$
$271$	0.392305	0.0238308	0.0119154	+	0.999929i	$0.496207\pi$
$272$	3.46410i	0.210042i
$273$	− 4.00000i	− 0.242091i
$274$	0.928203	0.0560748
$275$	0	0
$276$	−22.3923	−1.34786
$277$	− 7.07180i	− 0.424903i	−0.977172	−	0.212452i	$-0.931855\pi$
$277$	− 7.07180i	− 0.424903i	0.977172	−	0.212452i	$-0.0681448\pi$
$278$	13.6603i	0.819288i
$279$	−8.92820	−0.534518
$280$	0	0
$281$	22.3923	1.33581	0.667906	−	0.744245i	$-0.267191\pi$
$281$	22.3923	1.33581	0.667906	+	0.744245i	$0.267191\pi$
$282$	− 18.9282i	− 1.12716i
$283$	− 31.7128i	− 1.88513i	−0.334021	−	0.942566i	$-0.608406\pi$
$283$	− 31.7128i	− 1.88513i	0.334021	−	0.942566i	$-0.391594\pi$
$284$	−9.46410	−0.561591
$285$	0	0
$286$	−1.46410	−0.0865741
$287$	2.19615i	0.129635i
$288$	4.46410i	0.263050i
$289$	5.00000	0.294118
$290$	0	0
$291$	39.8564	2.33642
$292$	14.3923i	0.842246i
$293$	21.4641i	1.25395i	0.779041	+	0.626973i	$0.215706\pi$
$293$	21.4641i	1.25395i	−0.779041	+	0.626973i	$0.784294\pi$
$294$	−2.73205	−0.159336
$295$	0	0
$296$	0.732051	0.0425496
$297$	− 4.00000i	− 0.232104i
$298$	− 7.26795i	− 0.421021i
$299$	−12.0000	−0.693978
$300$	0	0
$301$	2.00000	0.115278
$302$	− 11.1244i	− 0.640135i
$303$	− 21.4641i	− 1.23308i
$304$	−6.73205	−0.386110
$305$	0	0
$306$	−15.4641	−0.884024
$307$	− 24.3923i	− 1.39214i	−0.717973	−	0.696071i	$-0.754930\pi$
$307$	− 24.3923i	− 1.39214i	0.717973	−	0.696071i	$-0.245070\pi$
$308$	1.00000i	0.0569803i
$309$	−33.8564	−1.92602
$310$	0	0
$311$	24.9282	1.41355	0.706774	−	0.707439i	$-0.250150\pi$
$311$	24.9282	1.41355	0.706774	+	0.707439i	$0.250150\pi$
$312$	4.00000i	0.226455i
$313$	22.1962i	1.25460i	0.778777	+	0.627300i	$0.215840\pi$
$313$	22.1962i	1.25460i	−0.778777	+	0.627300i	$0.784160\pi$
$314$	−4.53590	−0.255976
$315$	0	0
$316$	−12.1962	−0.686087
$317$	− 30.5885i	− 1.71802i	−0.511960	−	0.859009i	$-0.671080\pi$
$317$	− 30.5885i	− 1.71802i	0.511960	−	0.859009i	$-0.328920\pi$
$318$	− 19.8564i	− 1.11349i
$319$	4.73205	0.264944
$320$	0	0
$321$	21.4641	1.19801
$322$	8.19615i	0.456754i
$323$	− 23.3205i	− 1.29759i
$324$	2.46410	0.136895
$325$	0	0
$326$	−4.00000	−0.221540
$327$	42.7846i	2.36599i
$328$	− 2.19615i	− 0.121262i
$329$	−6.92820	−0.381964
$330$	0	0
$331$	−18.7846	−1.03250	−0.516248	−	0.856439i	$-0.672672\pi$
$331$	−18.7846	−1.03250	−0.516248	+	0.856439i	$0.672672\pi$
$332$	16.3923i	0.899645i
$333$	3.26795i	0.179083i
$334$	−13.8564	−0.758189
$335$	0	0
$336$	2.73205	0.149046
$337$	− 22.7846i	− 1.24116i	−0.784144	−	0.620578i	$-0.786898\pi$
$337$	− 22.7846i	− 1.24116i	0.784144	−	0.620578i	$-0.213102\pi$
$338$	− 10.8564i	− 0.590511i
$339$	−21.4641	−1.16577
$340$	0	0
$341$	2.00000	0.108306
$342$	− 30.0526i	− 1.62506i
$343$	1.00000i	0.0539949i
$344$	−2.00000	−0.107833
$345$	0	0
$346$	0.928203	0.0499005
$347$	23.0718i	1.23856i	0.785171	+	0.619279i	$0.212575\pi$
$347$	23.0718i	1.23856i	−0.785171	+	0.619279i	$0.787425\pi$
$348$	− 12.9282i	− 0.693024i
$349$	5.60770	0.300173	0.150087	−	0.988673i	$-0.452045\pi$
$349$	5.60770	0.300173	0.150087	+	0.988673i	$0.452045\pi$
$350$	0	0
$351$	−5.85641	−0.312592
$352$	− 1.00000i	− 0.0533002i
$353$	14.1962i	0.755585i	0.925890	+	0.377792i	$0.123317\pi$
$353$	14.1962i	0.755585i	−0.925890	+	0.377792i	$0.876683\pi$
$354$	−18.9282	−1.00602
$355$	0	0
$356$	3.46410	0.183597
$357$	9.46410i	0.500893i
$358$	− 6.00000i	− 0.317110i
$359$	34.0526	1.79723	0.898613	−	0.438743i	$-0.144576\pi$
$359$	34.0526	1.79723	0.898613	+	0.438743i	$0.144576\pi$
$360$	0	0
$361$	26.3205	1.38529
$362$	− 14.0000i	− 0.735824i
$363$	2.73205i	0.143395i
$364$	1.46410	0.0767398
$365$	0	0
$366$	−13.4641	−0.703780
$367$	− 12.3923i	− 0.646873i	−0.946250	−	0.323437i	$-0.895162\pi$
$367$	− 12.3923i	− 0.646873i	0.946250	−	0.323437i	$-0.104838\pi$
$368$	− 8.19615i	− 0.427254i
$369$	9.80385	0.510368
$370$	0	0
$371$	−7.26795	−0.377333
$372$	− 5.46410i	− 0.283300i
$373$	18.3923i	0.952317i	0.879359	+	0.476159i	$0.157971\pi$
$373$	18.3923i	0.952317i	−0.879359	+	0.476159i	$0.842029\pi$
$374$	3.46410	0.179124
$375$	0	0
$376$	6.92820	0.357295
$377$	− 6.92820i	− 0.356821i
$378$	4.00000i	0.205738i
$379$	−6.14359	−0.315575	−0.157788	−	0.987473i	$-0.550436\pi$
$379$	−6.14359	−0.315575	−0.157788	+	0.987473i	$0.550436\pi$
$380$	0	0
$381$	2.92820	0.150016
$382$	12.0000i	0.613973i
$383$	− 33.4641i	− 1.70994i	−0.518681	−	0.854968i	$-0.673577\pi$
$383$	− 33.4641i	− 1.70994i	0.518681	−	0.854968i	$-0.326423\pi$
$384$	−2.73205	−0.139419
$385$	0	0
$386$	12.3923	0.630752
$387$	− 8.92820i	− 0.453846i
$388$	14.5885i	0.740617i
$389$	1.60770	0.0815134	0.0407567	−	0.999169i	$-0.487023\pi$
$389$	1.60770	0.0815134	0.0407567	+	0.999169i	$0.487023\pi$
$390$	0	0
$391$	28.3923	1.43586
$392$	− 1.00000i	− 0.0505076i
$393$	15.4641i	0.780061i
$394$	24.2487	1.22163
$395$	0	0
$396$	4.46410	0.224330
$397$	− 30.3923i	− 1.52535i	−0.646784	−	0.762673i	$-0.723887\pi$
$397$	− 30.3923i	− 1.52535i	0.646784	−	0.762673i	$-0.276113\pi$
$398$	2.92820i	0.146778i
$399$	−18.3923	−0.920767
$400$	0	0
$401$	2.53590	0.126637	0.0633184	−	0.997993i	$-0.479832\pi$
$401$	2.53590	0.126637	0.0633184	+	0.997993i	$0.479832\pi$
$402$	10.9282i	0.545049i
$403$	− 2.92820i	− 0.145864i
$404$	7.85641	0.390871
$405$	0	0
$406$	−4.73205	−0.234848
$407$	− 0.732051i	− 0.0362864i
$408$	− 9.46410i	− 0.468543i
$409$	−10.8756	−0.537766	−0.268883	−	0.963173i	$-0.586654\pi$
$409$	−10.8756	−0.537766	−0.268883	+	0.963173i	$0.586654\pi$
$410$	0	0
$411$	−2.53590	−0.125087
$412$	− 12.3923i	− 0.610525i
$413$	6.92820i	0.340915i
$414$	36.5885	1.79822
$415$	0	0
$416$	−1.46410	−0.0717835
$417$	− 37.3205i	− 1.82759i
$418$	6.73205i	0.329275i
$419$	−30.9282	−1.51094	−0.755471	−	0.655182i	$-0.772592\pi$
$419$	−30.9282	−1.51094	−0.755471	+	0.655182i	$0.772592\pi$
$420$	0	0
$421$	−35.8564	−1.74753	−0.873767	−	0.486344i	$-0.838330\pi$
$421$	−35.8564	−1.74753	−0.873767	+	0.486344i	$0.838330\pi$
$422$	− 26.9282i	− 1.31084i
$423$	30.9282i	1.50378i
$424$	7.26795	0.352963
$425$	0	0
$426$	25.8564	1.25275
$427$	4.92820i	0.238492i
$428$	7.85641i	0.379754i
$429$	4.00000	0.193122
$430$	0	0
$431$	3.12436	0.150495	0.0752475	−	0.997165i	$-0.476025\pi$
$431$	3.12436	0.150495	0.0752475	+	0.997165i	$0.476025\pi$
$432$	− 4.00000i	− 0.192450i
$433$	− 18.1962i	− 0.874451i	−0.899352	−	0.437226i	$-0.855961\pi$
$433$	− 18.1962i	− 0.874451i	0.899352	−	0.437226i	$-0.144039\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	−15.6603	−0.749990
$437$	55.1769i	2.63947i
$438$	− 39.3205i	− 1.87881i
$439$	−26.2487	−1.25278	−0.626391	−	0.779509i	$-0.715469\pi$
$439$	−26.2487	−1.25278	−0.626391	+	0.779509i	$0.715469\pi$
$440$	0	0
$441$	4.46410	0.212576
$442$	− 5.07180i	− 0.241241i
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−25.4641	−1.20576
$447$	19.8564i	0.939176i
$448$	1.00000i	0.0472456i
$449$	−40.3923	−1.90623	−0.953115	−	0.302607i	$-0.902143\pi$
$449$	−40.3923	−1.90623	−0.953115	+	0.302607i	$0.902143\pi$
$450$	0	0
$451$	−2.19615	−0.103413
$452$	− 7.85641i	− 0.369534i
$453$	30.3923i	1.42796i
$454$	−6.92820	−0.325157
$455$	0	0
$456$	18.3923	0.861299
$457$	− 2.00000i	− 0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$	− 2.00000i	− 0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$	24.3923i	1.13978i
$459$	13.8564	0.646762
$460$	0	0
$461$	22.3923	1.04291	0.521457	−	0.853278i	$-0.325389\pi$
$461$	22.3923	1.04291	0.521457	+	0.853278i	$0.325389\pi$
$462$	− 2.73205i	− 0.127107i
$463$	27.5167i	1.27881i	0.768871	+	0.639404i	$0.220819\pi$
$463$	27.5167i	1.27881i	−0.768871	+	0.639404i	$0.779181\pi$
$464$	4.73205	0.219680
$465$	0	0
$466$	−7.85641	−0.363941
$467$	34.0526i	1.57576i	0.615826	+	0.787882i	$0.288822\pi$
$467$	34.0526i	1.57576i	−0.615826	+	0.787882i	$0.711178\pi$
$468$	− 6.53590i	− 0.302122i
$469$	4.00000	0.184703
$470$	0	0
$471$	12.3923	0.571007
$472$	− 6.92820i	− 0.318896i
$473$	2.00000i	0.0919601i
$474$	33.3205	1.53046
$475$	0	0
$476$	−3.46410	−0.158777
$477$	32.4449i	1.48555i
$478$	1.26795i	0.0579946i
$479$	32.7846	1.49797	0.748984	−	0.662589i	$-0.230542\pi$
$479$	32.7846	1.49797	0.748984	+	0.662589i	$0.230542\pi$
$480$	0	0
$481$	−1.07180	−0.0488697
$482$	− 3.26795i	− 0.148851i
$483$	− 22.3923i	− 1.01889i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	−18.7321	−0.849703
$487$	− 4.19615i	− 0.190146i	−0.995470	−	0.0950729i	$-0.969692\pi$
$487$	− 4.19615i	− 0.190146i	0.995470	−	0.0950729i	$-0.0303084\pi$
$488$	− 4.92820i	− 0.223089i
$489$	10.9282	0.494190
$490$	0	0
$491$	−27.7128	−1.25066	−0.625331	−	0.780360i	$-0.715036\pi$
$491$	−27.7128	−1.25066	−0.625331	+	0.780360i	$0.715036\pi$
$492$	6.00000i	0.270501i
$493$	16.3923i	0.738272i
$494$	9.85641	0.443461
$495$	0	0
$496$	2.00000	0.0898027
$497$	− 9.46410i	− 0.424523i
$498$	− 44.7846i	− 2.00685i
$499$	−12.1436	−0.543622	−0.271811	−	0.962351i	$-0.587623\pi$
$499$	−12.1436	−0.543622	−0.271811	+	0.962351i	$0.587623\pi$
$500$	0	0
$501$	37.8564	1.69130
$502$	− 12.0000i	− 0.535586i
$503$	8.78461i	0.391686i	0.980635	+	0.195843i	$0.0627444\pi$
$503$	8.78461i	0.391686i	−0.980635	+	0.195843i	$0.937256\pi$
$504$	−4.46410	−0.198847
$505$	0	0
$506$	−8.19615	−0.364363
$507$	29.6603i	1.31726i
$508$	1.07180i	0.0475533i
$509$	−11.0718	−0.490749	−0.245374	−	0.969428i	$-0.578911\pi$
$509$	−11.0718	−0.490749	−0.245374	+	0.969428i	$0.578911\pi$
$510$	0	0
$511$	−14.3923	−0.636678
$512$	− 1.00000i	− 0.0441942i
$513$	26.9282i	1.18891i
$514$	23.6603	1.04361
$515$	0	0
$516$	5.46410	0.240544
$517$	− 6.92820i	− 0.304702i
$518$	0.732051i	0.0321645i
$519$	−2.53590	−0.111314
$520$	0	0
$521$	10.3923	0.455295	0.227648	−	0.973744i	$-0.426897\pi$
$521$	10.3923	0.455295	0.227648	+	0.973744i	$0.426897\pi$
$522$	21.1244i	0.924588i
$523$	− 29.1769i	− 1.27582i	−0.770112	−	0.637909i	$-0.779800\pi$
$523$	− 29.1769i	− 1.27582i	0.770112	−	0.637909i	$-0.220200\pi$
$524$	−5.66025	−0.247269
$525$	0	0
$526$	−24.0000	−1.04645
$527$	6.92820i	0.301797i
$528$	2.73205i	0.118897i
$529$	−44.1769	−1.92074
$530$	0	0
$531$	30.9282	1.34217
$532$	− 6.73205i	− 0.291871i
$533$	3.21539i	0.139274i
$534$	−9.46410	−0.409552
$535$	0	0
$536$	−4.00000	−0.172774
$537$	16.3923i	0.707380i
$538$	28.3923i	1.22408i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−20.7321	−0.891340	−0.445670	−	0.895197i	$-0.647035\pi$
$541$	−20.7321	−0.891340	−0.445670	+	0.895197i	$0.647035\pi$
$542$	− 0.392305i	− 0.0168509i
$543$	38.2487i	1.64141i
$544$	3.46410	0.148522
$545$	0	0
$546$	−4.00000	−0.171184
$547$	− 28.7846i	− 1.23074i	−0.788238	−	0.615371i	$-0.789006\pi$
$547$	− 28.7846i	− 1.23074i	0.788238	−	0.615371i	$-0.210994\pi$
$548$	− 0.928203i	− 0.0396509i
$549$	22.0000	0.938937
$550$	0	0
$551$	−31.8564	−1.35713
$552$	22.3923i	0.953080i
$553$	− 12.1962i	− 0.518633i
$554$	−7.07180	−0.300452
$555$	0	0
$556$	13.6603	0.579324
$557$	25.6077i	1.08503i	0.840045	+	0.542516i	$0.182528\pi$
$557$	25.6077i	1.08503i	−0.840045	+	0.542516i	$0.817472\pi$
$558$	8.92820i	0.377961i
$559$	2.92820	0.123850
$560$	0	0
$561$	−9.46410	−0.399575
$562$	− 22.3923i	− 0.944562i
$563$	5.07180i	0.213751i	0.994272	+	0.106875i	$0.0340846\pi$
$563$	5.07180i	0.213751i	−0.994272	+	0.106875i	$0.965915\pi$
$564$	−18.9282	−0.797021
$565$	0	0
$566$	−31.7128	−1.33299
$567$	2.46410i	0.103483i
$568$	9.46410i	0.397105i
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	3.60770	0.150977	0.0754887	−	0.997147i	$-0.475948\pi$
$571$	3.60770	0.150977	0.0754887	+	0.997147i	$0.475948\pi$
$572$	1.46410i	0.0612172i
$573$	− 32.7846i	− 1.36960i
$574$	2.19615	0.0916656
$575$	0	0
$576$	4.46410	0.186004
$577$	34.5885i	1.43994i	0.694007	+	0.719968i	$0.255844\pi$
$577$	34.5885i	1.43994i	−0.694007	+	0.719968i	$0.744156\pi$
$578$	− 5.00000i	− 0.207973i
$579$	−33.8564	−1.40702
$580$	0	0
$581$	−16.3923	−0.680067
$582$	− 39.8564i	− 1.65210i
$583$	− 7.26795i	− 0.301008i
$584$	14.3923	0.595558
$585$	0	0
$586$	21.4641	0.886674
$587$	11.4115i	0.471005i	0.971874	+	0.235502i	$0.0756735\pi$
$587$	11.4115i	0.471005i	−0.971874	+	0.235502i	$0.924326\pi$
$588$	2.73205i	0.112668i
$589$	−13.4641	−0.554779
$590$	0	0
$591$	−66.2487	−2.72511
$592$	− 0.732051i	− 0.0300871i
$593$	0.248711i	0.0102133i	0.999987	+	0.00510667i	$0.00162551\pi$
$593$	0.248711i	0.0102133i	−0.999987	+	0.00510667i	$0.998374\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−7.26795	−0.297707
$597$	− 8.00000i	− 0.327418i
$598$	12.0000i	0.490716i
$599$	−37.1769	−1.51901	−0.759504	−	0.650503i	$-0.774558\pi$
$599$	−37.1769	−1.51901	−0.759504	+	0.650503i	$0.774558\pi$
$600$	0	0
$601$	−5.51666	−0.225029	−0.112515	−	0.993650i	$-0.535891\pi$
$601$	−5.51666	−0.225029	−0.112515	+	0.993650i	$0.535891\pi$
$602$	− 2.00000i	− 0.0815139i
$603$	− 17.8564i	− 0.727169i
$604$	−11.1244	−0.452644
$605$	0	0
$606$	−21.4641	−0.871920
$607$	− 20.9282i	− 0.849450i	−0.905323	−	0.424725i	$-0.860371\pi$
$607$	− 20.9282i	− 0.849450i	0.905323	−	0.424725i	$-0.139629\pi$
$608$	6.73205i	0.273021i
$609$	12.9282	0.523877
$610$	0	0
$611$	−10.1436	−0.410366
$612$	15.4641i	0.625099i
$613$	− 35.1769i	− 1.42078i	−0.703807	−	0.710391i	$-0.748518\pi$
$613$	− 35.1769i	− 1.42078i	0.703807	−	0.710391i	$-0.251482\pi$
$614$	−24.3923	−0.984393
$615$	0	0
$616$	1.00000	0.0402911
$617$	− 17.3205i	− 0.697297i	−0.937253	−	0.348649i	$-0.886641\pi$
$617$	− 17.3205i	− 0.697297i	0.937253	−	0.348649i	$-0.113359\pi$
$618$	33.8564i	1.36190i
$619$	−28.7846	−1.15695	−0.578476	−	0.815700i	$-0.696352\pi$
$619$	−28.7846	−1.15695	−0.578476	+	0.815700i	$0.696352\pi$
$620$	0	0
$621$	−32.7846	−1.31560
$622$	− 24.9282i	− 0.999530i
$623$	3.46410i	0.138786i
$624$	4.00000	0.160128
$625$	0	0
$626$	22.1962	0.887137
$627$	− 18.3923i	− 0.734518i
$628$	4.53590i	0.181002i
$629$	2.53590	0.101113
$630$	0	0
$631$	−46.9282	−1.86818	−0.934091	−	0.357035i	$-0.883788\pi$
$631$	−46.9282	−1.86818	−0.934091	+	0.357035i	$0.883788\pi$
$632$	12.1962i	0.485137i
$633$	73.5692i	2.92411i
$634$	−30.5885	−1.21482
$635$	0	0
$636$	−19.8564	−0.787358
$637$	1.46410i	0.0580098i
$638$	− 4.73205i	− 0.187344i
$639$	−42.2487	−1.67133
$640$	0	0
$641$	−35.5692	−1.40490	−0.702450	−	0.711733i	$-0.747910\pi$
$641$	−35.5692	−1.40490	−0.702450	+	0.711733i	$0.747910\pi$
$642$	− 21.4641i	− 0.847121i
$643$	33.2679i	1.31196i	0.754778	+	0.655980i	$0.227744\pi$
$643$	33.2679i	1.31196i	−0.754778	+	0.655980i	$0.772256\pi$
$644$	8.19615	0.322974
$645$	0	0
$646$	−23.3205	−0.917533
$647$	26.5359i	1.04323i	0.853180	+	0.521617i	$0.174671\pi$
$647$	26.5359i	1.04323i	−0.853180	+	0.521617i	$0.825329\pi$
$648$	− 2.46410i	− 0.0967991i
$649$	−6.92820	−0.271956
$650$	0	0
$651$	5.46410	0.214155
$652$	4.00000i	0.156652i
$653$	11.6603i	0.456301i	0.973626	+	0.228151i	$0.0732678\pi$
$653$	11.6603i	0.456301i	−0.973626	+	0.228151i	$0.926732\pi$
$654$	42.7846	1.67301
$655$	0	0
$656$	−2.19615	−0.0857453
$657$	64.2487i	2.50658i
$658$	6.92820i	0.270089i
$659$	−30.2487	−1.17832	−0.589161	−	0.808015i	$-0.700542\pi$
$659$	−30.2487	−1.17832	−0.589161	+	0.808015i	$0.700542\pi$
$660$	0	0
$661$	−46.0000	−1.78919	−0.894596	−	0.446875i	$-0.852537\pi$
$661$	−46.0000	−1.78919	−0.894596	+	0.446875i	$0.852537\pi$
$662$	18.7846i	0.730085i
$663$	13.8564i	0.538138i
$664$	16.3923	0.636145
$665$	0	0
$666$	3.26795	0.126630
$667$	− 38.7846i	− 1.50175i
$668$	13.8564i	0.536120i
$669$	69.5692	2.68970
$670$	0	0
$671$	−4.92820	−0.190251
$672$	− 2.73205i	− 0.105391i
$673$	2.00000i	0.0770943i	0.999257	+	0.0385472i	$0.0122730\pi$
$673$	2.00000i	0.0770943i	−0.999257	+	0.0385472i	$0.987727\pi$
$674$	−22.7846	−0.877630
$675$	0	0
$676$	−10.8564	−0.417554
$677$	4.14359i	0.159251i	0.996825	+	0.0796256i	$0.0253725\pi$
$677$	4.14359i	0.159251i	−0.996825	+	0.0796256i	$0.974628\pi$
$678$	21.4641i	0.824324i
$679$	−14.5885	−0.559854
$680$	0	0
$681$	18.9282	0.725330
$682$	− 2.00000i	− 0.0765840i
$683$	6.24871i	0.239100i	0.992828	+	0.119550i	$0.0381452\pi$
$683$	6.24871i	0.239100i	−0.992828	+	0.119550i	$0.961855\pi$
$684$	−30.0526	−1.14909
$685$	0	0
$686$	1.00000	0.0381802
$687$	− 66.6410i	− 2.54251i
$688$	2.00000i	0.0762493i
$689$	−10.6410	−0.405390
$690$	0	0
$691$	−13.4641	−0.512199	−0.256099	−	0.966650i	$-0.582437\pi$
$691$	−13.4641	−0.512199	−0.256099	+	0.966650i	$0.582437\pi$
$692$	− 0.928203i	− 0.0352850i
$693$	4.46410i	0.169577i
$694$	23.0718	0.875793
$695$	0	0
$696$	−12.9282	−0.490042
$697$	− 7.60770i	− 0.288162i
$698$	− 5.60770i	− 0.212254i
$699$	21.4641	0.811847
$700$	0	0
$701$	41.9090	1.58288	0.791440	−	0.611247i	$-0.209332\pi$
$701$	41.9090	1.58288	0.791440	+	0.611247i	$0.209332\pi$
$702$	5.85641i	0.221036i
$703$	4.92820i	0.185871i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	14.1962	0.534279
$707$	7.85641i	0.295471i
$708$	18.9282i	0.711365i
$709$	−25.3205	−0.950932	−0.475466	−	0.879734i	$-0.657720\pi$
$709$	−25.3205	−0.950932	−0.475466	+	0.879734i	$0.657720\pi$
$710$	0	0
$711$	−54.4449	−2.04184
$712$	− 3.46410i	− 0.129823i
$713$	− 16.3923i	− 0.613897i
$714$	9.46410	0.354185
$715$	0	0
$716$	−6.00000	−0.224231
$717$	− 3.46410i	− 0.129369i
$718$	− 34.0526i	− 1.27083i
$719$	27.7128	1.03351	0.516757	−	0.856132i	$-0.327139\pi$
$719$	27.7128	1.03351	0.516757	+	0.856132i	$0.327139\pi$
$720$	0	0
$721$	12.3923	0.461514
$722$	− 26.3205i	− 0.979548i
$723$	8.92820i	0.332043i
$724$	−14.0000	−0.520306
$725$	0	0
$726$	2.73205	0.101396
$727$	4.00000i	0.148352i	0.997245	+	0.0741759i	$0.0236326\pi$
$727$	4.00000i	0.148352i	−0.997245	+	0.0741759i	$0.976367\pi$
$728$	− 1.46410i	− 0.0542632i
$729$	43.7846	1.62165
$730$	0	0
$731$	−6.92820	−0.256249
$732$	13.4641i	0.497648i
$733$	26.0000i	0.960332i	0.877178	+	0.480166i	$0.159424\pi$
$733$	26.0000i	0.960332i	−0.877178	+	0.480166i	$0.840576\pi$
$734$	−12.3923	−0.457408
$735$	0	0
$736$	−8.19615	−0.302114
$737$	4.00000i	0.147342i
$738$	− 9.80385i	− 0.360885i
$739$	−11.7128	−0.430863	−0.215431	−	0.976519i	$-0.569116\pi$
$739$	−11.7128	−0.430863	−0.215431	+	0.976519i	$0.569116\pi$
$740$	0	0
$741$	−26.9282	−0.989232
$742$	7.26795i	0.266815i
$743$	− 32.7846i	− 1.20275i	−0.798967	−	0.601375i	$-0.794620\pi$
$743$	− 32.7846i	− 1.20275i	0.798967	−	0.601375i	$-0.205380\pi$
$744$	−5.46410	−0.200324
$745$	0	0
$746$	18.3923	0.673390
$747$	73.1769i	2.67740i
$748$	− 3.46410i	− 0.126660i
$749$	−7.85641	−0.287067
$750$	0	0
$751$	−11.6077	−0.423571	−0.211785	−	0.977316i	$-0.567928\pi$
$751$	−11.6077	−0.423571	−0.211785	+	0.977316i	$0.567928\pi$
$752$	− 6.92820i	− 0.252646i
$753$	32.7846i	1.19474i
$754$	−6.92820	−0.252310
$755$	0	0
$756$	4.00000	0.145479
$757$	43.3731i	1.57642i	0.615406	+	0.788210i	$0.288992\pi$
$757$	43.3731i	1.57642i	−0.615406	+	0.788210i	$0.711008\pi$
$758$	6.14359i	0.223145i
$759$	22.3923	0.812789
$760$	0	0
$761$	−12.3397	−0.447315	−0.223658	−	0.974668i	$-0.571800\pi$
$761$	−12.3397	−0.447315	−0.223658	+	0.974668i	$0.571800\pi$
$762$	− 2.92820i	− 0.106078i
$763$	− 15.6603i	− 0.566939i
$764$	12.0000	0.434145
$765$	0	0
$766$	−33.4641	−1.20911
$767$	10.1436i	0.366264i
$768$	2.73205i	0.0985844i
$769$	18.1962	0.656170	0.328085	−	0.944648i	$-0.393597\pi$
$769$	18.1962	0.656170	0.328085	+	0.944648i	$0.393597\pi$
$770$	0	0
$771$	−64.6410	−2.32799
$772$	− 12.3923i	− 0.446009i
$773$	− 0.928203i	− 0.0333851i	−0.999861	−	0.0166926i	$-0.994686\pi$
$773$	− 0.928203i	− 0.0333851i	0.999861	−	0.0166926i	$-0.00531366\pi$
$774$	−8.92820	−0.320918
$775$	0	0
$776$	14.5885	0.523695
$777$	− 2.00000i	− 0.0717496i
$778$	− 1.60770i	− 0.0576387i
$779$	14.7846	0.529714
$780$	0	0
$781$	9.46410	0.338652
$782$	− 28.3923i	− 1.01531i
$783$	− 18.9282i	− 0.676439i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	15.4641	0.551586
$787$	− 18.1436i	− 0.646749i	−0.946271	−	0.323375i	$-0.895183\pi$
$787$	− 18.1436i	− 0.646749i	0.946271	−	0.323375i	$-0.104817\pi$
$788$	− 24.2487i	− 0.863825i
$789$	65.5692	2.33433
$790$	0	0
$791$	7.85641	0.279342
$792$	− 4.46410i	− 0.158625i
$793$	7.21539i	0.256226i
$794$	−30.3923	−1.07858
$795$	0	0
$796$	2.92820	0.103787
$797$	25.6077i	0.907071i	0.891238	+	0.453536i	$0.149837\pi$
$797$	25.6077i	0.907071i	−0.891238	+	0.453536i	$0.850163\pi$
$798$	18.3923i	0.651081i
$799$	24.0000	0.849059
$800$	0	0
$801$	15.4641	0.546397
$802$	− 2.53590i	− 0.0895457i
$803$	− 14.3923i	− 0.507893i
$804$	10.9282	0.385408
$805$	0	0
$806$	−2.92820	−0.103142
$807$	− 77.5692i	− 2.73057i
$808$	− 7.85641i	− 0.276387i
$809$	31.1769	1.09612	0.548061	−	0.836438i	$-0.315366\pi$
$809$	31.1769	1.09612	0.548061	+	0.836438i	$0.315366\pi$
$810$	0	0
$811$	−43.1244	−1.51430	−0.757150	−	0.653241i	$-0.773409\pi$
$811$	−43.1244	−1.51430	−0.757150	+	0.653241i	$0.773409\pi$
$812$	4.73205i	0.166062i
$813$	1.07180i	0.0375896i
$814$	−0.732051	−0.0256584
$815$	0	0
$816$	−9.46410	−0.331310
$817$	− 13.4641i	− 0.471049i
$818$	10.8756i	0.380258i
$819$	6.53590	0.228383
$820$	0	0
$821$	17.9090	0.625027	0.312514	−	0.949913i	$-0.398829\pi$
$821$	17.9090	0.625027	0.312514	+	0.949913i	$0.398829\pi$
$822$	2.53590i	0.0884496i
$823$	− 0.875644i	− 0.0305230i	−0.999884	−	0.0152615i	$-0.995142\pi$
$823$	− 0.875644i	− 0.0305230i	0.999884	−	0.0152615i	$-0.00485808\pi$
$824$	−12.3923	−0.431706
$825$	0	0
$826$	6.92820	0.241063
$827$	25.8564i	0.899115i	0.893251	+	0.449558i	$0.148418\pi$
$827$	25.8564i	0.899115i	−0.893251	+	0.449558i	$0.851582\pi$
$828$	− 36.5885i	− 1.27154i
$829$	−2.24871	−0.0781010	−0.0390505	−	0.999237i	$-0.512433\pi$
$829$	−2.24871	−0.0781010	−0.0390505	+	0.999237i	$0.512433\pi$
$830$	0	0
$831$	19.3205	0.670221
$832$	1.46410i	0.0507586i
$833$	− 3.46410i	− 0.120024i
$834$	−37.3205	−1.29230
$835$	0	0
$836$	6.73205	0.232833
$837$	− 8.00000i	− 0.276520i
$838$	30.9282i	1.06840i
$839$	31.8564	1.09981	0.549903	−	0.835229i	$-0.314665\pi$
$839$	31.8564	1.09981	0.549903	+	0.835229i	$0.314665\pi$
$840$	0	0
$841$	−6.60770	−0.227852
$842$	35.8564i	1.23569i
$843$	61.1769i	2.10704i
$844$	−26.9282	−0.926907
$845$	0	0
$846$	30.9282	1.06333
$847$	− 1.00000i	− 0.0343604i
$848$	− 7.26795i	− 0.249582i
$849$	86.6410	2.97351
$850$	0	0
$851$	−6.00000	−0.205677
$852$	− 25.8564i	− 0.885826i
$853$	− 54.7846i	− 1.87579i	−0.346920	−	0.937895i	$-0.612773\pi$
$853$	− 54.7846i	− 1.87579i	0.346920	−	0.937895i	$-0.387227\pi$
$854$	4.92820	0.168640
$855$	0	0
$856$	7.85641	0.268526
$857$	27.4641i	0.938156i	0.883157	+	0.469078i	$0.155414\pi$
$857$	27.4641i	0.938156i	−0.883157	+	0.469078i	$0.844586\pi$
$858$	− 4.00000i	− 0.136558i
$859$	12.7846	0.436205	0.218103	−	0.975926i	$-0.430013\pi$
$859$	12.7846	0.436205	0.218103	+	0.975926i	$0.430013\pi$
$860$	0	0
$861$	−6.00000	−0.204479
$862$	− 3.12436i	− 0.106416i
$863$	− 7.51666i	− 0.255870i	−0.991783	−	0.127935i	$-0.959165\pi$
$863$	− 7.51666i	− 0.255870i	0.991783	−	0.127935i	$-0.0408349\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	−18.1962	−0.618330
$867$	13.6603i	0.463927i
$868$	2.00000i	0.0678844i
$869$	12.1962	0.413726
$870$	0	0
$871$	5.85641	0.198437
$872$	15.6603i	0.530323i
$873$	65.1244i	2.20413i
$874$	55.1769	1.86639
$875$	0	0
$876$	−39.3205	−1.32852
$877$	21.3205i	0.719942i	0.932963	+	0.359971i	$0.117213\pi$
$877$	21.3205i	0.719942i	−0.932963	+	0.359971i	$0.882787\pi$
$878$	26.2487i	0.885851i
$879$	−58.6410	−1.97791
$880$	0	0
$881$	11.0718	0.373018	0.186509	−	0.982453i	$-0.440283\pi$
$881$	11.0718	0.373018	0.186509	+	0.982453i	$0.440283\pi$
$882$	− 4.46410i	− 0.150314i
$883$	− 35.6077i	− 1.19829i	−0.800639	−	0.599147i	$-0.795506\pi$
$883$	− 35.6077i	− 1.19829i	0.800639	−	0.599147i	$-0.204494\pi$
$884$	−5.07180	−0.170583
$885$	0	0
$886$	0	0
$887$	− 13.8564i	− 0.465253i	−0.972566	−	0.232626i	$-0.925268\pi$
$887$	− 13.8564i	− 0.465253i	0.972566	−	0.232626i	$-0.0747319\pi$
$888$	2.00000i	0.0671156i
$889$	−1.07180	−0.0359469
$890$	0	0
$891$	−2.46410	−0.0825505
$892$	25.4641i	0.852601i
$893$	46.6410i	1.56078i
$894$	19.8564	0.664098
$895$	0	0
$896$	1.00000	0.0334077
$897$	− 32.7846i	− 1.09465i
$898$	40.3923i	1.34791i
$899$	9.46410	0.315645
$900$	0	0
$901$	25.1769	0.838765
$902$	2.19615i	0.0731239i
$903$	5.46410i	0.181834i
$904$	−7.85641	−0.261300
$905$	0	0
$906$	30.3923	1.00972
$907$	31.0333i	1.03044i	0.857057	+	0.515222i	$0.172291\pi$
$907$	31.0333i	1.03044i	−0.857057	+	0.515222i	$0.827709\pi$
$908$	6.92820i	0.229920i
$909$	35.0718	1.16326
$910$	0	0
$911$	9.46410	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$911$	9.46410	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$912$	− 18.3923i	− 0.609030i
$913$	− 16.3923i	− 0.542506i
$914$	−2.00000	−0.0661541
$915$	0	0
$916$	24.3923	0.805944
$917$	− 5.66025i	− 0.186918i
$918$	− 13.8564i	− 0.457330i
$919$	25.3731	0.836980	0.418490	−	0.908221i	$-0.362559\pi$
$919$	25.3731	0.836980	0.418490	+	0.908221i	$0.362559\pi$
$920$	0	0
$921$	66.6410	2.19590
$922$	− 22.3923i	− 0.737451i
$923$	− 13.8564i	− 0.456089i
$924$	−2.73205	−0.0898779
$925$	0	0
$926$	27.5167	0.904254
$927$	− 55.3205i	− 1.81696i
$928$	− 4.73205i	− 0.155337i
$929$	25.6077	0.840161	0.420081	−	0.907487i	$-0.362002\pi$
$929$	25.6077	0.840161	0.420081	+	0.907487i	$0.362002\pi$
$930$	0	0
$931$	6.73205	0.220634
$932$	7.85641i	0.257345i
$933$	68.1051i	2.22966i
$934$	34.0526	1.11423
$935$	0	0
$936$	−6.53590	−0.213633
$937$	1.21539i	0.0397051i	0.999803	+	0.0198525i	$0.00631967\pi$
$937$	1.21539i	0.0397051i	−0.999803	+	0.0198525i	$0.993680\pi$
$938$	− 4.00000i	− 0.130605i
$939$	−60.6410	−1.97894
$940$	0	0
$941$	−14.7846	−0.481965	−0.240982	−	0.970530i	$-0.577470\pi$
$941$	−14.7846	−0.481965	−0.240982	+	0.970530i	$0.577470\pi$
$942$	− 12.3923i	− 0.403763i
$943$	18.0000i	0.586161i
$944$	−6.92820	−0.225494
$945$	0	0
$946$	2.00000	0.0650256
$947$	− 47.3205i	− 1.53771i	−0.639423	−	0.768855i	$-0.720827\pi$
$947$	− 47.3205i	− 1.53771i	0.639423	−	0.768855i	$-0.279173\pi$
$948$	− 33.3205i	− 1.08220i
$949$	−21.0718	−0.684019
$950$	0	0
$951$	83.5692	2.70992
$952$	3.46410i	0.112272i
$953$	26.5359i	0.859582i	0.902928	+	0.429791i	$0.141413\pi$
$953$	26.5359i	0.859582i	−0.902928	+	0.429791i	$0.858587\pi$
$954$	32.4449	1.05044
$955$	0	0
$956$	1.26795	0.0410084
$957$	12.9282i	0.417909i
$958$	− 32.7846i	− 1.05922i
$959$	0.928203	0.0299732
$960$	0	0
$961$	−27.0000	−0.870968
$962$	1.07180i	0.0345561i
$963$	35.0718i	1.13017i
$964$	−3.26795	−0.105254
$965$	0	0
$966$	−22.3923	−0.720461
$967$	− 26.9282i	− 0.865953i	−0.901405	−	0.432976i	$-0.857463\pi$
$967$	− 26.9282i	− 0.865953i	0.901405	−	0.432976i	$-0.142537\pi$
$968$	1.00000i	0.0321412i
$969$	63.7128	2.04675
$970$	0	0
$971$	42.9282	1.37763	0.688816	−	0.724936i	$-0.258131\pi$
$971$	42.9282	1.37763	0.688816	+	0.724936i	$0.258131\pi$
$972$	18.7321i	0.600831i
$973$	13.6603i	0.437928i
$974$	−4.19615	−0.134453
$975$	0	0
$976$	−4.92820	−0.157748
$977$	33.7128i	1.07857i	0.842124	+	0.539284i	$0.181305\pi$
$977$	33.7128i	1.07857i	−0.842124	+	0.539284i	$0.818695\pi$
$978$	− 10.9282i	− 0.349445i
$979$	−3.46410	−0.110713
$980$	0	0
$981$	−69.9090	−2.23202
$982$	27.7128i	0.884351i
$983$	− 37.1769i	− 1.18576i	−0.805291	−	0.592880i	$-0.797991\pi$
$983$	− 37.1769i	− 1.18576i	0.805291	−	0.592880i	$-0.202009\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	16.3923	0.522037
$987$	− 18.9282i	− 0.602491i
$988$	− 9.85641i	− 0.313574i
$989$	16.3923	0.521245
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	− 2.00000i	− 0.0635001i
$993$	− 51.3205i	− 1.62861i
$994$	−9.46410	−0.300183
$995$	0	0
$996$	−44.7846	−1.41905
$997$	− 17.7128i	− 0.560970i	−0.959858	−	0.280485i	$-0.909505\pi$
$997$	− 17.7128i	− 0.560970i	0.959858	−	0.280485i	$-0.0904954\pi$
$998$	12.1436i	0.384399i
$999$	−2.92820	−0.0926443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.x.1849.2		4
5.2	odd	4		770.2.a.j.1.2	✓	2
5.3	odd	4		3850.2.a.bd.1.1		2
5.4	even	2	inner	3850.2.c.x.1849.3		4
15.2	even	4		6930.2.a.bv.1.1		2
20.7	even	4		6160.2.a.t.1.1		2
35.27	even	4		5390.2.a.bs.1.1		2
55.32	even	4		8470.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.j.1.2	✓	2	5.2	odd	4
3850.2.a.bd.1.1		2	5.3	odd	4
3850.2.c.x.1849.2		4	1.1	even	1	trivial
3850.2.c.x.1849.3		4	5.4	even	2	inner
5390.2.a.bs.1.1		2	35.27	even	4
6160.2.a.t.1.1		2	20.7	even	4
6930.2.a.bv.1.1		2	15.2	even	4
8470.2.a.br.1.2		2	55.32	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.73205i q^{3} -1.00000 q^{4} +2.73205 q^{6} -1.00000i q^{7} +1.00000i q^{8} -4.46410 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.73205i q^{3} -1.00000 q^{4} +2.73205 q^{6} -1.00000i q^{7} +1.00000i q^{8} -4.46410 q^{9} +1.00000 q^{11} -2.73205i q^{12} -1.46410i q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.46410i q^{17} +4.46410i q^{18} -6.73205 q^{19} +2.73205 q^{21} -1.00000i q^{22} -8.19615i q^{23} -2.73205 q^{24} -1.46410 q^{26} -4.00000i q^{27} +1.00000i q^{28} +4.73205 q^{29} +2.00000 q^{31} -1.00000i q^{32} +2.73205i q^{33} +3.46410 q^{34} +4.46410 q^{36} -0.732051i q^{37} +6.73205i q^{38} +4.00000 q^{39} -2.19615 q^{41} -2.73205i q^{42} +2.00000i q^{43} -1.00000 q^{44} -8.19615 q^{46} -6.92820i q^{47} +2.73205i q^{48} -1.00000 q^{49} -9.46410 q^{51} +1.46410i q^{52} -7.26795i q^{53} -4.00000 q^{54} +1.00000 q^{56} -18.3923i q^{57} -4.73205i q^{58} -6.92820 q^{59} -4.92820 q^{61} -2.00000i q^{62} +4.46410i q^{63} -1.00000 q^{64} +2.73205 q^{66} +4.00000i q^{67} -3.46410i q^{68} +22.3923 q^{69} +9.46410 q^{71} -4.46410i q^{72} -14.3923i q^{73} -0.732051 q^{74} +6.73205 q^{76} -1.00000i q^{77} -4.00000i q^{78} +12.1962 q^{79} -2.46410 q^{81} +2.19615i q^{82} -16.3923i q^{83} -2.73205 q^{84} +2.00000 q^{86} +12.9282i q^{87} +1.00000i q^{88} -3.46410 q^{89} -1.46410 q^{91} +8.19615i q^{92} +5.46410i q^{93} -6.92820 q^{94} +2.73205 q^{96} -14.5885i q^{97} +1.00000i q^{98} -4.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 4 q^{14} + 4 q^{16} - 20 q^{19} + 4 q^{21} - 4 q^{24} + 8 q^{26} + 12 q^{29} + 8 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 4 q^{44} - 12 q^{46} - 4 q^{49} - 24 q^{51} - 16 q^{54} + 4 q^{56} + 8 q^{61} - 4 q^{64} + 4 q^{66} + 48 q^{69} + 24 q^{71} + 4 q^{74} + 20 q^{76} + 28 q^{79} + 4 q^{81} - 4 q^{84} + 8 q^{86} + 8 q^{91} + 4 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 4 * q^14 + 4 * q^16 - 20 * q^19 + 4 * q^21 - 4 * q^24 + 8 * q^26 + 12 * q^29 + 8 * q^31 + 4 * q^36 + 16 * q^39 + 12 * q^41 - 4 * q^44 - 12 * q^46 - 4 * q^49 - 24 * q^51 - 16 * q^54 + 4 * q^56 + 8 * q^61 - 4 * q^64 + 4 * q^66 + 48 * q^69 + 24 * q^71 + 4 * q^74 + 20 * q^76 + 28 * q^79 + 4 * q^81 - 4 * q^84 + 8 * q^86 + 8 * q^91 + 4 * q^96 - 4 * q^99

Introduction

L-functions

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Database

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