LMFDB - Embedded newform 3850.2.c.z.1849.4

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:	$6$
Coefficient field:	6.0.3182656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 25x^{2} - 10x + 2 $ x^6 - 2x^3 + 25x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.4
Root			$1.46962 + 1.46962i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.z.1849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.93923i q^{3} -1.00000 q^{4} +2.93923 q^{6} +1.00000i q^{7} -1.00000i q^{8} -5.63910 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.93923i q^{3} -1.00000 q^{4} +2.93923 q^{6} +1.00000i q^{7} -1.00000i q^{8} -5.63910 q^{9} +1.00000 q^{11} +2.93923i q^{12} -5.87847i q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.63910i q^{17} -5.63910i q^{18} +5.57834 q^{19} +2.93923 q^{21} +1.00000i q^{22} +5.57834i q^{23} -2.93923 q^{24} +5.87847 q^{26} +7.75694i q^{27} -1.00000i q^{28} +9.45681 q^{29} +6.00000 q^{31} +1.00000i q^{32} -2.93923i q^{33} -4.63910 q^{34} +5.63910 q^{36} -2.30013i q^{37} +5.57834i q^{38} -17.2782 q^{39} -3.06077 q^{41} +2.93923i q^{42} +10.5176i q^{43} -1.00000 q^{44} -5.57834 q^{46} -8.51757i q^{47} -2.93923i q^{48} -1.00000 q^{49} +13.6354 q^{51} +5.87847i q^{52} -9.45681i q^{53} -7.75694 q^{54} +1.00000 q^{56} -16.3960i q^{57} +9.45681i q^{58} -7.23937 q^{59} +14.5176 q^{61} +6.00000i q^{62} -5.63910i q^{63} -1.00000 q^{64} +2.93923 q^{66} -8.00000i q^{67} -4.63910i q^{68} +16.3960 q^{69} -7.15667 q^{71} +5.63910i q^{72} +12.3960i q^{73} +2.30013 q^{74} -5.57834 q^{76} +1.00000i q^{77} -17.2782i q^{78} +10.8565 q^{79} +5.88216 q^{81} -3.06077i q^{82} -13.8785i q^{83} -2.93923 q^{84} -10.5176 q^{86} -27.7958i q^{87} -1.00000i q^{88} -3.87847 q^{89} +5.87847 q^{91} -5.57834i q^{92} -17.6354i q^{93} +8.51757 q^{94} +2.93923 q^{96} -7.57834i q^{97} -1.00000i q^{98} -5.63910 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 22 * q^9	$ 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * 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
$3$	− 2.93923i	− 1.69697i	−0.529221	−	0.848484i	$-0.677516\pi$
$3$	− 2.93923i	− 1.69697i	0.529221	−	0.848484i	$-0.322484\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.93923	1.19994
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−5.63910	−1.87970
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.93923i	0.848484i
$13$	− 5.87847i	− 1.63039i	−0.579184	−	0.815197i	$-0.696629\pi$
$13$	− 5.87847i	− 1.63039i	0.579184	−	0.815197i	$-0.303371\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.63910i	1.12515i	0.826747	+	0.562574i	$0.190189\pi$
$17$	4.63910i	1.12515i	−0.826747	+	0.562574i	$0.809811\pi$
$18$	− 5.63910i	− 1.32915i
$19$	5.57834	1.27976	0.639879	−	0.768476i	$-0.278984\pi$
$19$	5.57834	1.27976	0.639879	+	0.768476i	$0.278984\pi$
$20$	0	0
$21$	2.93923	0.641394
$22$	1.00000i	0.213201i
$23$	5.57834i	1.16316i	0.813488	+	0.581582i	$0.197566\pi$
$23$	5.57834i	1.16316i	−0.813488	+	0.581582i	$0.802434\pi$
$24$	−2.93923	−0.599969
$25$	0	0
$26$	5.87847	1.15286
$27$	7.75694i	1.49282i
$28$	− 1.00000i	− 0.188982i
$29$	9.45681	1.75608	0.878042	−	0.478583i	$-0.158849\pi$
$29$	9.45681	1.75608	0.878042	+	0.478583i	$0.158849\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000i	0.176777i
$33$	− 2.93923i	− 0.511655i
$34$	−4.63910	−0.795599
$35$	0	0
$36$	5.63910	0.939850
$37$	− 2.30013i	− 0.378140i	−0.981964	−	0.189070i	$-0.939453\pi$
$37$	− 2.30013i	− 0.378140i	0.981964	−	0.189070i	$-0.0605472\pi$
$38$	5.57834i	0.904926i
$39$	−17.2782	−2.76673
$40$	0	0
$41$	−3.06077	−0.478011	−0.239006	−	0.971018i	$-0.576821\pi$
$41$	−3.06077	−0.478011	−0.239006	+	0.971018i	$0.576821\pi$
$42$	2.93923i	0.453534i
$43$	10.5176i	1.60391i	0.597381	+	0.801957i	$0.296208\pi$
$43$	10.5176i	1.60391i	−0.597381	+	0.801957i	$0.703792\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−5.57834	−0.822481
$47$	− 8.51757i	− 1.24242i	−0.783646	−	0.621208i	$-0.786642\pi$
$47$	− 8.51757i	− 1.24242i	0.783646	−	0.621208i	$-0.213358\pi$
$48$	− 2.93923i	− 0.424242i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	13.6354	1.90934
$52$	5.87847i	0.815197i
$53$	− 9.45681i	− 1.29899i	−0.760365	−	0.649496i	$-0.774980\pi$
$53$	− 9.45681i	− 1.29899i	0.760365	−	0.649496i	$-0.225020\pi$
$54$	−7.75694	−1.05559
$55$	0	0
$56$	1.00000	0.133631
$57$	− 16.3960i	− 2.17171i
$58$	9.45681i	1.24174i
$59$	−7.23937	−0.942485	−0.471243	−	0.882004i	$-0.656194\pi$
$59$	−7.23937	−0.942485	−0.471243	+	0.882004i	$0.656194\pi$
$60$	0	0
$61$	14.5176	1.85878	0.929392	−	0.369093i	$-0.120332\pi$
$61$	14.5176	1.85878	0.929392	+	0.369093i	$0.120332\pi$
$62$	6.00000i	0.762001i
$63$	− 5.63910i	− 0.710460i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.93923	0.361795
$67$	− 8.00000i	− 0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$	− 8.00000i	− 0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$	− 4.63910i	− 0.562574i
$69$	16.3960	1.97385
$70$	0	0
$71$	−7.15667	−0.849341	−0.424670	−	0.905348i	$-0.639610\pi$
$71$	−7.15667	−0.849341	−0.424670	+	0.905348i	$0.639610\pi$
$72$	5.63910i	0.664574i
$73$	12.3960i	1.45085i	0.688303	+	0.725423i	$0.258356\pi$
$73$	12.3960i	1.45085i	−0.688303	+	0.725423i	$0.741644\pi$
$74$	2.30013	0.267385
$75$	0	0
$76$	−5.57834	−0.639879
$77$	1.00000i	0.113961i
$78$	− 17.2782i	− 1.95637i
$79$	10.8565	1.22146	0.610728	−	0.791840i	$-0.290877\pi$
$79$	10.8565	1.22146	0.610728	+	0.791840i	$0.290877\pi$
$80$	0	0
$81$	5.88216	0.653574
$82$	− 3.06077i	− 0.338005i
$83$	− 13.8785i	− 1.52336i	−0.647953	−	0.761680i	$-0.724375\pi$
$83$	− 13.8785i	− 1.52336i	0.647953	−	0.761680i	$-0.275625\pi$
$84$	−2.93923	−0.320697
$85$	0	0
$86$	−10.5176	−1.13414
$87$	− 27.7958i	− 2.98002i
$88$	− 1.00000i	− 0.106600i
$89$	−3.87847	−0.411117	−0.205558	−	0.978645i	$-0.565901\pi$
$89$	−3.87847	−0.411117	−0.205558	+	0.978645i	$0.565901\pi$
$90$	0	0
$91$	5.87847	0.616231
$92$	− 5.57834i	− 0.581582i
$93$	− 17.6354i	− 1.82871i
$94$	8.51757	0.878520
$95$	0	0
$96$	2.93923	0.299984
$97$	− 7.57834i	− 0.769463i	−0.923028	−	0.384732i	$-0.874294\pi$
$97$	− 7.57834i	− 0.769463i	0.923028	−	0.384732i	$-0.125706\pi$
$98$	− 1.00000i	− 0.101015i
$99$	−5.63910	−0.566751
$100$	0	0
$101$	11.7958	1.17372	0.586862	−	0.809687i	$-0.300363\pi$
$101$	11.7958	1.17372	0.586862	+	0.809687i	$0.300363\pi$
$102$	13.6354i	1.35011i
$103$	17.1178i	1.68667i	0.537388	+	0.843335i	$0.319411\pi$
$103$	17.1178i	1.68667i	−0.537388	+	0.843335i	$0.680589\pi$
$104$	−5.87847	−0.576431
$105$	0	0
$106$	9.45681	0.918526
$107$	− 2.51757i	− 0.243383i	−0.992568	−	0.121691i	$-0.961168\pi$
$107$	− 2.51757i	− 0.243383i	0.992568	−	0.121691i	$-0.0388318\pi$
$108$	− 7.75694i	− 0.746412i
$109$	−10.3001	−0.986574	−0.493287	−	0.869867i	$-0.664205\pi$
$109$	−10.3001	−0.986574	−0.493287	+	0.869867i	$0.664205\pi$
$110$	0	0
$111$	−6.76063	−0.641691
$112$	1.00000i	0.0944911i
$113$	− 14.0000i	− 1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	− 14.0000i	− 1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	16.3960	1.53563
$115$	0	0
$116$	−9.45681	−0.878042
$117$	33.1493i	3.06465i
$118$	− 7.23937i	− 0.666438i
$119$	−4.63910	−0.425266
$120$	0	0
$121$	1.00000	0.0909091
$122$	14.5176i	1.31436i
$123$	8.99631i	0.811170i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	5.63910	0.502371
$127$	− 10.4787i	− 0.929837i	−0.885353	−	0.464919i	$-0.846084\pi$
$127$	− 10.4787i	− 0.929837i	0.885353	−	0.464919i	$-0.153916\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	30.9136	2.72179
$130$	0	0
$131$	−1.57834	−0.137900	−0.0689499	−	0.997620i	$-0.521965\pi$
$131$	−1.57834	−0.137900	−0.0689499	+	0.997620i	$0.521965\pi$
$132$	2.93923i	0.255828i
$133$	5.57834i	0.483703i
$134$	8.00000	0.691095
$135$	0	0
$136$	4.63910	0.397800
$137$	3.27820i	0.280076i	0.990146	+	0.140038i	$0.0447224\pi$
$137$	3.27820i	0.280076i	−0.990146	+	0.140038i	$0.955278\pi$
$138$	16.3960i	1.39572i
$139$	16.0571	1.36194	0.680972	−	0.732310i	$-0.261558\pi$
$139$	16.0571	1.36194	0.680972	+	0.732310i	$0.261558\pi$
$140$	0	0
$141$	−25.0351	−2.10834
$142$	− 7.15667i	− 0.600575i
$143$	− 5.87847i	− 0.491582i
$144$	−5.63910	−0.469925
$145$	0	0
$146$	−12.3960	−1.02590
$147$	2.93923i	0.242424i
$148$	2.30013i	0.189070i
$149$	−10.7350	−0.879446	−0.439723	−	0.898133i	$-0.644923\pi$
$149$	−10.7350	−0.879446	−0.439723	+	0.898133i	$0.644923\pi$
$150$	0	0
$151$	−2.17860	−0.177292	−0.0886461	−	0.996063i	$-0.528254\pi$
$151$	−2.17860	−0.177292	−0.0886461	+	0.996063i	$0.528254\pi$
$152$	− 5.57834i	− 0.452463i
$153$	− 26.1604i	− 2.11494i
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	17.2782	1.38336
$157$	17.1567i	1.36925i	0.728895	+	0.684626i	$0.240034\pi$
$157$	17.1567i	1.36925i	−0.728895	+	0.684626i	$0.759966\pi$
$158$	10.8565i	0.863700i
$159$	−27.7958	−2.20435
$160$	0	0
$161$	−5.57834	−0.439635
$162$	5.88216i	0.462146i
$163$	− 8.00000i	− 0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$	− 8.00000i	− 0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$	3.06077	0.239006
$165$	0	0
$166$	13.8785	1.07718
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	− 2.93923i	− 0.226767i
$169$	−21.5564	−1.65819
$170$	0	0
$171$	−31.4568	−2.40556
$172$	− 10.5176i	− 0.801957i
$173$	− 5.48243i	− 0.416821i	−0.978041	−	0.208411i	$-0.933171\pi$
$173$	− 5.48243i	− 0.416821i	0.978041	−	0.208411i	$-0.0668291\pi$
$174$	27.7958	2.10719
$175$	0	0
$176$	1.00000	0.0753778
$177$	21.2782i	1.59937i
$178$	− 3.87847i	− 0.290704i
$179$	−1.23937	−0.0926347	−0.0463174	−	0.998927i	$-0.514749\pi$
$179$	−1.23937	−0.0926347	−0.0463174	+	0.998927i	$0.514749\pi$
$180$	0	0
$181$	8.55641	0.635993	0.317996	−	0.948092i	$-0.396990\pi$
$181$	8.55641	0.635993	0.317996	+	0.948092i	$0.396990\pi$
$182$	5.87847i	0.435741i
$183$	− 42.6706i	− 3.15430i
$184$	5.57834	0.411240
$185$	0	0
$186$	17.6354	1.29309
$187$	4.63910i	0.339245i
$188$	8.51757i	0.621208i
$189$	−7.75694	−0.564234
$190$	0	0
$191$	−1.27820	−0.0924875	−0.0462438	−	0.998930i	$-0.514725\pi$
$191$	−1.27820	−0.0924875	−0.0462438	+	0.998930i	$0.514725\pi$
$192$	2.93923i	0.212121i
$193$	− 10.6391i	− 0.765819i	−0.923786	−	0.382910i	$-0.874922\pi$
$193$	− 10.6391i	− 0.765819i	0.923786	−	0.382910i	$-0.125078\pi$
$194$	7.57834	0.544093
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 7.87847i	− 0.561318i	−0.959808	−	0.280659i	$-0.909447\pi$
$197$	− 7.87847i	− 0.561318i	0.959808	−	0.280659i	$-0.0905530\pi$
$198$	− 5.63910i	− 0.400754i
$199$	−0.517571	−0.0366897	−0.0183448	−	0.999832i	$-0.505840\pi$
$199$	−0.517571	−0.0366897	−0.0183448	+	0.999832i	$0.505840\pi$
$200$	0	0
$201$	−23.5139	−1.65854
$202$	11.7958i	0.829948i
$203$	9.45681i	0.663738i
$204$	−13.6354	−0.954670
$205$	0	0
$206$	−17.1178	−1.19266
$207$	− 31.4568i	− 2.18640i
$208$	− 5.87847i	− 0.407599i
$209$	5.57834	0.385862
$210$	0	0
$211$	2.72180	0.187376	0.0936881	−	0.995602i	$-0.470134\pi$
$211$	2.72180	0.187376	0.0936881	+	0.995602i	$0.470134\pi$
$212$	9.45681i	0.649496i
$213$	21.0351i	1.44130i
$214$	2.51757	0.172098
$215$	0	0
$216$	7.75694	0.527793
$217$	6.00000i	0.407307i
$218$	− 10.3001i	− 0.697613i
$219$	36.4349	2.46204
$220$	0	0
$221$	27.2708	1.83443
$222$	− 6.76063i	− 0.453744i
$223$	− 22.3960i	− 1.49975i	−0.661580	−	0.749875i	$-0.730114\pi$
$223$	− 22.3960i	− 1.49975i	0.661580	−	0.749875i	$-0.269886\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	14.0000	0.931266
$227$	− 13.0351i	− 0.865173i	−0.901592	−	0.432586i	$-0.857601\pi$
$227$	− 13.0351i	− 0.865173i	0.901592	−	0.432586i	$-0.142399\pi$
$228$	16.3960i	1.08585i
$229$	6.63910	0.438724	0.219362	−	0.975644i	$-0.429602\pi$
$229$	6.63910	0.438724	0.219362	+	0.975644i	$0.429602\pi$
$230$	0	0
$231$	2.93923	0.193387
$232$	− 9.45681i	− 0.620870i
$233$	19.0351i	1.24703i	0.781810	+	0.623517i	$0.214297\pi$
$233$	19.0351i	1.24703i	−0.781810	+	0.623517i	$0.785703\pi$
$234$	−33.1493	−2.16704
$235$	0	0
$236$	7.23937	0.471243
$237$	− 31.9099i	− 2.07277i
$238$	− 4.63910i	− 0.300708i
$239$	−22.6135	−1.46274	−0.731372	−	0.681979i	$-0.761120\pi$
$239$	−22.6135	−1.46274	−0.731372	+	0.681979i	$0.761120\pi$
$240$	0	0
$241$	−17.9744	−1.15783	−0.578916	−	0.815387i	$-0.696524\pi$
$241$	−17.9744	−1.15783	−0.578916	+	0.815387i	$0.696524\pi$
$242$	1.00000i	0.0642824i
$243$	5.98176i	0.383730i
$244$	−14.5176	−0.929392
$245$	0	0
$246$	−8.99631	−0.573584
$247$	− 32.7921i	− 2.08651i
$248$	− 6.00000i	− 0.381000i
$249$	−40.7921	−2.58509
$250$	0	0
$251$	8.76063	0.552966	0.276483	−	0.961019i	$-0.410831\pi$
$251$	8.76063	0.552966	0.276483	+	0.961019i	$0.410831\pi$
$252$	5.63910i	0.355230i
$253$	5.57834i	0.350707i
$254$	10.4787	0.657494
$255$	0	0
$256$	1.00000	0.0625000
$257$	5.09960i	0.318104i	0.987270	+	0.159052i	$0.0508438\pi$
$257$	5.09960i	0.318104i	−0.987270	+	0.159052i	$0.949156\pi$
$258$	30.9136i	1.92460i
$259$	2.30013	0.142923
$260$	0	0
$261$	−53.3279	−3.30091
$262$	− 1.57834i	− 0.0975100i
$263$	− 11.7569i	− 0.724964i	−0.931991	−	0.362482i	$-0.881929\pi$
$263$	− 11.7569i	− 0.724964i	0.931991	−	0.362482i	$-0.118071\pi$
$264$	−2.93923	−0.180897
$265$	0	0
$266$	−5.57834	−0.342030
$267$	11.3997i	0.697652i
$268$	8.00000i	0.488678i
$269$	11.6742	0.711791	0.355896	−	0.934526i	$-0.384176\pi$
$269$	11.6742	0.711791	0.355896	+	0.934526i	$0.384176\pi$
$270$	0	0
$271$	17.6354	1.07127	0.535637	−	0.844448i	$-0.320071\pi$
$271$	17.6354	1.07127	0.535637	+	0.844448i	$0.320071\pi$
$272$	4.63910i	0.281287i
$273$	− 17.2782i	− 1.04572i
$274$	−3.27820	−0.198043
$275$	0	0
$276$	−16.3960	−0.986926
$277$	− 22.0000i	− 1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$	− 22.0000i	− 1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$	16.0571i	0.963039i
$279$	−33.8346	−2.02563
$280$	0	0
$281$	1.15667	0.0690013	0.0345007	−	0.999405i	$-0.489016\pi$
$281$	1.15667	0.0690013	0.0345007	+	0.999405i	$0.489016\pi$
$282$	− 25.0351i	− 1.49082i
$283$	17.2782i	1.02708i	0.858065	+	0.513541i	$0.171667\pi$
$283$	17.2782i	1.02708i	−0.858065	+	0.513541i	$0.828333\pi$
$284$	7.15667	0.424670
$285$	0	0
$286$	5.87847	0.347601
$287$	− 3.06077i	− 0.180671i
$288$	− 5.63910i	− 0.332287i
$289$	−4.52126	−0.265957
$290$	0	0
$291$	−22.2745	−1.30575
$292$	− 12.3960i	− 0.725423i
$293$	1.87847i	0.109741i	0.998493	+	0.0548707i	$0.0174747\pi$
$293$	1.87847i	0.109741i	−0.998493	+	0.0548707i	$0.982525\pi$
$294$	−2.93923	−0.171420
$295$	0	0
$296$	−2.30013	−0.133693
$297$	7.75694i	0.450103i
$298$	− 10.7350i	− 0.621862i
$299$	32.7921	1.89642
$300$	0	0
$301$	−10.5176	−0.606223
$302$	− 2.17860i	− 0.125365i
$303$	− 34.6706i	− 1.99177i
$304$	5.57834	0.319940
$305$	0	0
$306$	26.1604	1.49549
$307$	− 8.60027i	− 0.490843i	−0.969416	−	0.245422i	$-0.921074\pi$
$307$	− 8.60027i	− 0.490843i	0.969416	−	0.245422i	$-0.0789264\pi$
$308$	− 1.00000i	− 0.0569803i
$309$	50.3133	2.86223
$310$	0	0
$311$	13.7569	0.780084	0.390042	−	0.920797i	$-0.372460\pi$
$311$	13.7569	0.780084	0.390042	+	0.920797i	$0.372460\pi$
$312$	17.2782i	0.978186i
$313$	2.90040i	0.163940i	0.996635	+	0.0819701i	$0.0261212\pi$
$313$	2.90040i	0.163940i	−0.996635	+	0.0819701i	$0.973879\pi$
$314$	−17.1567	−0.968207
$315$	0	0
$316$	−10.8565	−0.610728
$317$	− 19.3353i	− 1.08598i	−0.839740	−	0.542989i	$-0.817293\pi$
$317$	− 19.3353i	− 1.08598i	0.839740	−	0.542989i	$-0.182707\pi$
$318$	− 27.7958i	− 1.55871i
$319$	9.45681	0.529479
$320$	0	0
$321$	−7.39973	−0.413013
$322$	− 5.57834i	− 0.310869i
$323$	25.8785i	1.43992i
$324$	−5.88216	−0.326787
$325$	0	0
$326$	8.00000	0.443079
$327$	30.2745i	1.67418i
$328$	3.06077i	0.169002i
$329$	8.51757	0.469589
$330$	0	0
$331$	10.5176	0.578098	0.289049	−	0.957314i	$-0.406661\pi$
$331$	10.5176	0.578098	0.289049	+	0.957314i	$0.406661\pi$
$332$	13.8785i	0.761680i
$333$	12.9707i	0.710789i
$334$	8.00000	0.437741
$335$	0	0
$336$	2.93923	0.160348
$337$	− 7.27820i	− 0.396469i	−0.980155	−	0.198234i	$-0.936479\pi$
$337$	− 7.27820i	− 0.396469i	0.980155	−	0.198234i	$-0.0635208\pi$
$338$	− 21.5564i	− 1.17251i
$339$	−41.1493	−2.23492
$340$	0	0
$341$	6.00000	0.324918
$342$	− 31.4568i	− 1.70099i
$343$	− 1.00000i	− 0.0539949i
$344$	10.5176	0.567069
$345$	0	0
$346$	5.48243	0.294737
$347$	14.2745i	0.766296i	0.923687	+	0.383148i	$0.125160\pi$
$347$	14.2745i	0.766296i	−0.923687	+	0.383148i	$0.874840\pi$
$348$	27.7958i	1.49001i
$349$	−0.396041	−0.0211996	−0.0105998	−	0.999944i	$-0.503374\pi$
$349$	−0.396041	−0.0211996	−0.0105998	+	0.999944i	$0.503374\pi$
$350$	0	0
$351$	45.5989	2.43389
$352$	1.00000i	0.0533002i
$353$	− 5.09960i	− 0.271424i	−0.990748	−	0.135712i	$-0.956668\pi$
$353$	− 5.09960i	− 0.271424i	0.990748	−	0.135712i	$-0.0433322\pi$
$354$	−21.2782	−1.13092
$355$	0	0
$356$	3.87847	0.205558
$357$	13.6354i	0.721662i
$358$	− 1.23937i	− 0.0655026i
$359$	18.3704	0.969554	0.484777	−	0.874638i	$-0.338901\pi$
$359$	18.3704	0.969554	0.484777	+	0.874638i	$0.338901\pi$
$360$	0	0
$361$	12.1178	0.637781
$362$	8.55641i	0.449715i
$363$	− 2.93923i	− 0.154270i
$364$	−5.87847	−0.308116
$365$	0	0
$366$	42.6706	2.23043
$367$	− 17.1178i	− 0.893544i	−0.894648	−	0.446772i	$-0.852574\pi$
$367$	− 17.1178i	− 0.893544i	0.894648	−	0.446772i	$-0.147426\pi$
$368$	5.57834i	0.290791i
$369$	17.2600	0.898518
$370$	0	0
$371$	9.45681	0.490973
$372$	17.6354i	0.914353i
$373$	− 6.35721i	− 0.329164i	−0.986363	−	0.164582i	$-0.947373\pi$
$373$	− 6.35721i	− 0.329164i	0.986363	−	0.164582i	$-0.0526275\pi$
$374$	−4.63910	−0.239882
$375$	0	0
$376$	−8.51757	−0.439260
$377$	− 55.5915i	− 2.86311i
$378$	− 7.75694i	− 0.398974i
$379$	5.03514	0.258638	0.129319	−	0.991603i	$-0.458721\pi$
$379$	5.03514	0.258638	0.129319	+	0.991603i	$0.458721\pi$
$380$	0	0
$381$	−30.7995	−1.57790
$382$	− 1.27820i	− 0.0653986i
$383$	− 7.43118i	− 0.379716i	−0.981812	−	0.189858i	$-0.939197\pi$
$383$	− 7.43118i	− 0.379716i	0.981812	−	0.189858i	$-0.0608027\pi$
$384$	−2.93923	−0.149992
$385$	0	0
$386$	10.6391	0.541516
$387$	− 59.3097i	− 3.01488i
$388$	7.57834i	0.384732i
$389$	5.15667	0.261454	0.130727	−	0.991418i	$-0.458269\pi$
$389$	5.15667	0.261454	0.130727	+	0.991418i	$0.458269\pi$
$390$	0	0
$391$	−25.8785	−1.30873
$392$	1.00000i	0.0505076i
$393$	4.63910i	0.234012i
$394$	7.87847	0.396912
$395$	0	0
$396$	5.63910	0.283376
$397$	19.6354i	0.985473i	0.870179	+	0.492736i	$0.164003\pi$
$397$	19.6354i	0.985473i	−0.870179	+	0.492736i	$0.835997\pi$
$398$	− 0.517571i	− 0.0259435i
$399$	16.3960	0.820829
$400$	0	0
$401$	−5.11784	−0.255573	−0.127786	−	0.991802i	$-0.540787\pi$
$401$	−5.11784	−0.255573	−0.127786	+	0.991802i	$0.540787\pi$
$402$	− 23.5139i	− 1.17277i
$403$	− 35.2708i	− 1.75696i
$404$	−11.7958	−0.586862
$405$	0	0
$406$	−9.45681	−0.469333
$407$	− 2.30013i	− 0.114013i
$408$	− 13.6354i	− 0.675053i
$409$	−2.21744	−0.109645	−0.0548226	−	0.998496i	$-0.517459\pi$
$409$	−2.21744	−0.109645	−0.0548226	+	0.998496i	$0.517459\pi$
$410$	0	0
$411$	9.63541	0.475280
$412$	− 17.1178i	− 0.843335i
$413$	− 7.23937i	− 0.356226i
$414$	31.4568	1.54602
$415$	0	0
$416$	5.87847	0.288216
$417$	− 47.1955i	− 2.31117i
$418$	5.57834i	0.272845i
$419$	4.51757	0.220698	0.110349	−	0.993893i	$-0.464803\pi$
$419$	4.51757	0.220698	0.110349	+	0.993893i	$0.464803\pi$
$420$	0	0
$421$	−12.3133	−0.600116	−0.300058	−	0.953921i	$-0.597006\pi$
$421$	−12.3133	−0.600116	−0.300058	+	0.953921i	$0.597006\pi$
$422$	2.72180i	0.132495i
$423$	48.0315i	2.33537i
$424$	−9.45681	−0.459263
$425$	0	0
$426$	−21.0351	−1.01916
$427$	14.5176i	0.702555i
$428$	2.51757i	0.121691i
$429$	−17.2782	−0.834200
$430$	0	0
$431$	−2.17860	−0.104940	−0.0524698	−	0.998623i	$-0.516709\pi$
$431$	−2.17860	−0.104940	−0.0524698	+	0.998623i	$0.516709\pi$
$432$	7.75694i	0.373206i
$433$	5.02193i	0.241339i	0.992693	+	0.120669i	$0.0385041\pi$
$433$	5.02193i	0.241339i	−0.992693	+	0.120669i	$0.961496\pi$
$434$	−6.00000	−0.288009
$435$	0	0
$436$	10.3001	0.493287
$437$	31.1178i	1.48857i
$438$	36.4349i	1.74093i
$439$	−7.15667	−0.341569	−0.170785	−	0.985308i	$-0.554630\pi$
$439$	−7.15667	−0.341569	−0.170785	+	0.985308i	$0.554630\pi$
$440$	0	0
$441$	5.63910	0.268529
$442$	27.2708i	1.29714i
$443$	− 19.5139i	− 0.927132i	−0.886062	−	0.463566i	$-0.846570\pi$
$443$	− 19.5139i	− 0.927132i	0.886062	−	0.463566i	$-0.153430\pi$
$444$	6.76063	0.320845
$445$	0	0
$446$	22.3960	1.06048
$447$	31.5527i	1.49239i
$448$	− 1.00000i	− 0.0472456i
$449$	−1.36090	−0.0642248	−0.0321124	−	0.999484i	$-0.510223\pi$
$449$	−1.36090	−0.0642248	−0.0321124	+	0.999484i	$0.510223\pi$
$450$	0	0
$451$	−3.06077	−0.144126
$452$	14.0000i	0.658505i
$453$	6.40343i	0.300859i
$454$	13.0351	0.611770
$455$	0	0
$456$	−16.3960	−0.767815
$457$	− 4.47874i	− 0.209506i	−0.994498	−	0.104753i	$-0.966595\pi$
$457$	− 4.47874i	− 0.209506i	0.994498	−	0.104753i	$-0.0334053\pi$
$458$	6.63910i	0.310225i
$459$	−35.9852	−1.67965
$460$	0	0
$461$	−36.1530	−1.68381	−0.841906	−	0.539624i	$-0.818566\pi$
$461$	−36.1530	−1.68381	−0.841906	+	0.539624i	$0.818566\pi$
$462$	2.93923i	0.136746i
$463$	21.0922i	0.980238i	0.871655	+	0.490119i	$0.163047\pi$
$463$	21.0922i	0.980238i	−0.871655	+	0.490119i	$0.836953\pi$
$464$	9.45681	0.439021
$465$	0	0
$466$	−19.0351	−0.881786
$467$	− 19.1311i	− 0.885279i	−0.896700	−	0.442640i	$-0.854042\pi$
$467$	− 19.1311i	− 0.885279i	0.896700	−	0.442640i	$-0.145958\pi$
$468$	− 33.1493i	− 1.53233i
$469$	8.00000	0.369406
$470$	0	0
$471$	50.4275	2.32358
$472$	7.23937i	0.333219i
$473$	10.5176i	0.483598i
$474$	31.9099	1.46567
$475$	0	0
$476$	4.63910	0.212633
$477$	53.3279i	2.44172i
$478$	− 22.6135i	− 1.03432i
$479$	−5.27820	−0.241167	−0.120584	−	0.992703i	$-0.538477\pi$
$479$	−5.27820	−0.241167	−0.120584	+	0.992703i	$0.538477\pi$
$480$	0	0
$481$	−13.5213	−0.616517
$482$	− 17.9744i	− 0.818710i
$483$	16.3960i	0.746046i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	−5.98176	−0.271338
$487$	19.8140i	0.897859i	0.893567	+	0.448929i	$0.148194\pi$
$487$	19.8140i	0.897859i	−0.893567	+	0.448929i	$0.851806\pi$
$488$	− 14.5176i	− 0.657180i
$489$	−23.5139	−1.06333
$490$	0	0
$491$	−6.47874	−0.292381	−0.146191	−	0.989256i	$-0.546701\pi$
$491$	−6.47874	−0.292381	−0.146191	+	0.989256i	$0.546701\pi$
$492$	− 8.99631i	− 0.405585i
$493$	43.8711i	1.97585i
$494$	32.7921	1.47539
$495$	0	0
$496$	6.00000	0.269408
$497$	− 7.15667i	− 0.321021i
$498$	− 40.7921i	− 1.82794i
$499$	21.2394	0.950805	0.475402	−	0.879768i	$-0.342302\pi$
$499$	21.2394	0.950805	0.475402	+	0.879768i	$0.342302\pi$
$500$	0	0
$501$	−23.5139	−1.05052
$502$	8.76063i	0.391006i
$503$	42.2357i	1.88320i	0.336739	+	0.941598i	$0.390676\pi$
$503$	42.2357i	1.88320i	−0.336739	+	0.941598i	$0.609324\pi$
$504$	−5.63910	−0.251186
$505$	0	0
$506$	−5.57834	−0.247987
$507$	63.3593i	2.81389i
$508$	10.4787i	0.464919i
$509$	−38.8698	−1.72287	−0.861436	−	0.507867i	$-0.830434\pi$
$509$	−38.8698	−1.72287	−0.861436	+	0.507867i	$0.830434\pi$
$510$	0	0
$511$	−12.3960	−0.548369
$512$	1.00000i	0.0441942i
$513$	43.2708i	1.91045i
$514$	−5.09960	−0.224934
$515$	0	0
$516$	−30.9136	−1.36090
$517$	− 8.51757i	− 0.374602i
$518$	2.30013i	0.101062i
$519$	−16.1141	−0.707332
$520$	0	0
$521$	25.9488	1.13684	0.568418	−	0.822740i	$-0.307556\pi$
$521$	25.9488	1.13684	0.568418	+	0.822740i	$0.307556\pi$
$522$	− 53.3279i	− 2.33410i
$523$	42.7482i	1.86925i	0.355636	+	0.934625i	$0.384264\pi$
$523$	42.7482i	1.86925i	−0.355636	+	0.934625i	$0.615736\pi$
$524$	1.57834	0.0689499
$525$	0	0
$526$	11.7569	0.512627
$527$	27.8346i	1.21249i
$528$	− 2.93923i	− 0.127914i
$529$	−8.11784	−0.352949
$530$	0	0
$531$	40.8235	1.77159
$532$	− 5.57834i	− 0.241852i
$533$	17.9926i	0.779347i
$534$	−11.3997	−0.493315
$535$	0	0
$536$	−8.00000	−0.345547
$537$	3.64279i	0.157198i
$538$	11.6742i	0.503312i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−6.73501	−0.289561	−0.144780	−	0.989464i	$-0.546248\pi$
$541$	−6.73501	−0.289561	−0.144780	+	0.989464i	$0.546248\pi$
$542$	17.6354i	0.757506i
$543$	− 25.1493i	− 1.07926i
$544$	−4.63910	−0.198900
$545$	0	0
$546$	17.2782	0.739439
$547$	− 23.7569i	− 1.01577i	−0.861424	−	0.507887i	$-0.830427\pi$
$547$	− 23.7569i	− 1.01577i	0.861424	−	0.507887i	$-0.169573\pi$
$548$	− 3.27820i	− 0.140038i
$549$	−81.8661	−3.49396
$550$	0	0
$551$	52.7532	2.24736
$552$	− 16.3960i	− 0.697862i
$553$	10.8565i	0.461667i
$554$	22.0000	0.934690
$555$	0	0
$556$	−16.0571	−0.680972
$557$	34.1918i	1.44875i	0.689404	+	0.724377i	$0.257872\pi$
$557$	34.1918i	1.44875i	−0.689404	+	0.724377i	$0.742128\pi$
$558$	− 33.8346i	− 1.43233i
$559$	61.8272	2.61501
$560$	0	0
$561$	13.6354	0.575687
$562$	1.15667i	0.0487913i
$563$	− 31.3485i	− 1.32118i	−0.750746	−	0.660591i	$-0.770306\pi$
$563$	− 31.3485i	− 1.32118i	0.750746	−	0.660591i	$-0.229694\pi$
$564$	25.0351	1.05417
$565$	0	0
$566$	−17.2782	−0.726257
$567$	5.88216i	0.247028i
$568$	7.15667i	0.300287i
$569$	38.5490	1.61606	0.808030	−	0.589142i	$-0.200534\pi$
$569$	38.5490	1.61606	0.808030	+	0.589142i	$0.200534\pi$
$570$	0	0
$571$	26.9136	1.12630	0.563150	−	0.826355i	$-0.309589\pi$
$571$	26.9136	1.12630	0.563150	+	0.826355i	$0.309589\pi$
$572$	5.87847i	0.245791i
$573$	3.75694i	0.156948i
$574$	3.06077	0.127754
$575$	0	0
$576$	5.63910	0.234963
$577$	15.3353i	0.638416i	0.947685	+	0.319208i	$0.103417\pi$
$577$	15.3353i	0.638416i	−0.947685	+	0.319208i	$0.896583\pi$
$578$	− 4.52126i	− 0.188060i
$579$	−31.2708	−1.29957
$580$	0	0
$581$	13.8785	0.575776
$582$	− 22.2745i	− 0.923308i
$583$	− 9.45681i	− 0.391661i
$584$	12.3960	0.512952
$585$	0	0
$586$	−1.87847	−0.0775989
$587$	21.2526i	0.877188i	0.898685	+	0.438594i	$0.144523\pi$
$587$	21.2526i	0.877188i	−0.898685	+	0.438594i	$0.855477\pi$
$588$	− 2.93923i	− 0.121212i
$589$	33.4700	1.37911
$590$	0	0
$591$	−23.1567	−0.952538
$592$	− 2.30013i	− 0.0945349i
$593$	19.1955i	0.788265i	0.919054	+	0.394133i	$0.128955\pi$
$593$	19.1955i	0.788265i	−0.919054	+	0.394133i	$0.871045\pi$
$594$	−7.75694	−0.318271
$595$	0	0
$596$	10.7350	0.439723
$597$	1.52126i	0.0622612i
$598$	32.7921i	1.34097i
$599$	−3.39973	−0.138909	−0.0694547	−	0.997585i	$-0.522126\pi$
$599$	−3.39973	−0.138909	−0.0694547	+	0.997585i	$0.522126\pi$
$600$	0	0
$601$	−7.90409	−0.322415	−0.161207	−	0.986921i	$-0.551539\pi$
$601$	−7.90409	−0.322415	−0.161207	+	0.986921i	$0.551539\pi$
$602$	− 10.5176i	− 0.428664i
$603$	45.1128i	1.83714i
$604$	2.17860	0.0886461
$605$	0	0
$606$	34.6706	1.40839
$607$	23.7181i	0.962688i	0.876532	+	0.481344i	$0.159851\pi$
$607$	23.7181i	0.962688i	−0.876532	+	0.481344i	$0.840149\pi$
$608$	5.57834i	0.226231i
$609$	27.7958	1.12634
$610$	0	0
$611$	−50.0703	−2.02563
$612$	26.1604i	1.05747i
$613$	40.9136i	1.65249i	0.563314	+	0.826243i	$0.309526\pi$
$613$	40.9136i	1.65249i	−0.563314	+	0.826243i	$0.690474\pi$
$614$	8.60027	0.347079
$615$	0	0
$616$	1.00000	0.0402911
$617$	30.3572i	1.22214i	0.791578	+	0.611068i	$0.209260\pi$
$617$	30.3572i	1.22214i	−0.791578	+	0.611068i	$0.790740\pi$
$618$	50.3133i	2.02390i
$619$	34.9963	1.40662	0.703310	−	0.710883i	$-0.251705\pi$
$619$	34.9963	1.40662	0.703310	+	0.710883i	$0.251705\pi$
$620$	0	0
$621$	−43.2708	−1.73640
$622$	13.7569i	0.551603i
$623$	− 3.87847i	− 0.155388i
$624$	−17.2782	−0.691682
$625$	0	0
$626$	−2.90040	−0.115923
$627$	− 16.3960i	− 0.654795i
$628$	− 17.1567i	− 0.684626i
$629$	10.6706	0.425463
$630$	0	0
$631$	38.2357	1.52214	0.761069	−	0.648671i	$-0.224675\pi$
$631$	38.2357	1.52214	0.761069	+	0.648671i	$0.224675\pi$
$632$	− 10.8565i	− 0.431850i
$633$	− 8.00000i	− 0.317971i
$634$	19.3353	0.767902
$635$	0	0
$636$	27.7958	1.10217
$637$	5.87847i	0.232913i
$638$	9.45681i	0.374399i
$639$	40.3572	1.59651
$640$	0	0
$641$	−25.5139	−1.00774	−0.503869	−	0.863780i	$-0.668091\pi$
$641$	−25.5139	−1.00774	−0.503869	+	0.863780i	$0.668091\pi$
$642$	− 7.39973i	− 0.292044i
$643$	− 37.8528i	− 1.49277i	−0.665514	−	0.746385i	$-0.731788\pi$
$643$	− 37.8528i	− 1.49277i	0.665514	−	0.746385i	$-0.268212\pi$
$644$	5.57834	0.219817
$645$	0	0
$646$	−25.8785	−1.01817
$647$	24.7094i	0.971426i	0.874118	+	0.485713i	$0.161440\pi$
$647$	24.7094i	0.971426i	−0.874118	+	0.485713i	$0.838560\pi$
$648$	− 5.88216i	− 0.231073i
$649$	−7.23937	−0.284170
$650$	0	0
$651$	17.6354	0.691186
$652$	8.00000i	0.313304i
$653$	16.7789i	0.656608i	0.944572	+	0.328304i	$0.106477\pi$
$653$	16.7789i	0.656608i	−0.944572	+	0.328304i	$0.893523\pi$
$654$	−30.2745	−1.18383
$655$	0	0
$656$	−3.06077	−0.119503
$657$	− 69.9025i	− 2.72716i
$658$	8.51757i	0.332050i
$659$	−10.1215	−0.394279	−0.197139	−	0.980375i	$-0.563165\pi$
$659$	−10.1215	−0.394279	−0.197139	+	0.980375i	$0.563165\pi$
$660$	0	0
$661$	23.1128	0.898984	0.449492	−	0.893284i	$-0.351605\pi$
$661$	23.1128	0.898984	0.449492	+	0.893284i	$0.351605\pi$
$662$	10.5176i	0.408777i
$663$	− 80.1553i	− 3.11298i
$664$	−13.8785	−0.538589
$665$	0	0
$666$	−12.9707	−0.502604
$667$	52.7532i	2.04261i
$668$	8.00000i	0.309529i
$669$	−65.8272	−2.54503
$670$	0	0
$671$	14.5176	0.560445
$672$	2.93923i	0.113383i
$673$	38.0000i	1.46479i	0.680879	+	0.732396i	$0.261598\pi$
$673$	38.0000i	1.46479i	−0.680879	+	0.732396i	$0.738402\pi$
$674$	7.27820	0.280346
$675$	0	0
$676$	21.5564	0.829093
$677$	− 8.83092i	− 0.339400i	−0.985496	−	0.169700i	$-0.945720\pi$
$677$	− 8.83092i	− 0.339400i	0.985496	−	0.169700i	$-0.0542798\pi$
$678$	− 41.1493i	− 1.58033i
$679$	7.57834	0.290830
$680$	0	0
$681$	−38.3133	−1.46817
$682$	6.00000i	0.229752i
$683$	11.3997i	0.436199i	0.975927	+	0.218099i	$0.0699857\pi$
$683$	11.3997i	0.436199i	−0.975927	+	0.218099i	$0.930014\pi$
$684$	31.4568	1.20278
$685$	0	0
$686$	1.00000	0.0381802
$687$	− 19.5139i	− 0.744501i
$688$	10.5176i	0.400979i
$689$	−55.5915	−2.11787
$690$	0	0
$691$	−0.0826952	−0.00314587	−0.00157294	−	0.999999i	$-0.500501\pi$
$691$	−0.0826952	−0.00314587	−0.00157294	+	0.999999i	$0.500501\pi$
$692$	5.48243i	0.208411i
$693$	− 5.63910i	− 0.214212i
$694$	−14.2745	−0.541853
$695$	0	0
$696$	−27.7958	−1.05360
$697$	− 14.1992i	− 0.537833i
$698$	− 0.396041i	− 0.0149904i
$699$	55.9488	2.11618
$700$	0	0
$701$	38.0571	1.43740	0.718698	−	0.695322i	$-0.244738\pi$
$701$	38.0571	1.43740	0.718698	+	0.695322i	$0.244738\pi$
$702$	45.5989i	1.72102i
$703$	− 12.8309i	− 0.483927i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	5.09960	0.191926
$707$	11.7958i	0.443626i
$708$	− 21.2782i	− 0.799684i
$709$	−36.4275	−1.36806	−0.684032	−	0.729452i	$-0.739775\pi$
$709$	−36.4275	−1.36806	−0.684032	+	0.729452i	$0.739775\pi$
$710$	0	0
$711$	−61.2211	−2.29597
$712$	3.87847i	0.145352i
$713$	33.4700i	1.25346i
$714$	−13.6354	−0.510292
$715$	0	0
$716$	1.23937	0.0463174
$717$	66.4663i	2.48223i
$718$	18.3704i	0.685578i
$719$	−37.3097	−1.39142	−0.695708	−	0.718325i	$-0.744909\pi$
$719$	−37.3097	−1.39142	−0.695708	+	0.718325i	$0.744909\pi$
$720$	0	0
$721$	−17.1178	−0.637502
$722$	12.1178i	0.450979i
$723$	52.8309i	1.96480i
$724$	−8.55641	−0.317996
$725$	0	0
$726$	2.93923	0.109085
$727$	− 3.23937i	− 0.120142i	−0.998194	−	0.0600708i	$-0.980867\pi$
$727$	− 3.23937i	− 0.120142i	0.998194	−	0.0600708i	$-0.0191326\pi$
$728$	− 5.87847i	− 0.217871i
$729$	35.2283	1.30475
$730$	0	0
$731$	−48.7921	−1.80464
$732$	42.6706i	1.57715i
$733$	− 26.3522i	− 0.973340i	−0.873586	−	0.486670i	$-0.838211\pi$
$733$	− 26.3522i	− 0.973340i	0.873586	−	0.486670i	$-0.161789\pi$
$734$	17.1178	0.631831
$735$	0	0
$736$	−5.57834	−0.205620
$737$	− 8.00000i	− 0.294684i
$738$	17.2600i	0.635348i
$739$	11.9223	0.438570	0.219285	−	0.975661i	$-0.429628\pi$
$739$	11.9223	0.438570	0.219285	+	0.975661i	$0.429628\pi$
$740$	0	0
$741$	−96.3836	−3.54074
$742$	9.45681i	0.347170i
$743$	− 26.0703i	− 0.956426i	−0.878244	−	0.478213i	$-0.841285\pi$
$743$	− 26.0703i	− 0.956426i	0.878244	−	0.478213i	$-0.158715\pi$
$744$	−17.6354	−0.646545
$745$	0	0
$746$	6.35721	0.232754
$747$	78.2621i	2.86346i
$748$	− 4.63910i	− 0.169622i
$749$	2.51757	0.0919901
$750$	0	0
$751$	36.6003	1.33556	0.667781	−	0.744357i	$-0.267244\pi$
$751$	36.6003	1.33556	0.667781	+	0.744357i	$0.267244\pi$
$752$	− 8.51757i	− 0.310604i
$753$	− 25.7496i	− 0.938366i
$754$	55.5915	2.02452
$755$	0	0
$756$	7.75694	0.282117
$757$	43.0922i	1.56621i	0.621887	+	0.783107i	$0.286366\pi$
$757$	43.0922i	1.56621i	−0.621887	+	0.783107i	$0.713634\pi$
$758$	5.03514i	0.182885i
$759$	16.3960	0.595139
$760$	0	0
$761$	−44.0959	−1.59848	−0.799238	−	0.601015i	$-0.794763\pi$
$761$	−44.0959	−1.59848	−0.799238	+	0.601015i	$0.794763\pi$
$762$	− 30.7995i	− 1.11575i
$763$	− 10.3001i	− 0.372890i
$764$	1.27820	0.0462438
$765$	0	0
$766$	7.43118	0.268500
$767$	42.5564i	1.53662i
$768$	− 2.93923i	− 0.106061i
$769$	8.33897	0.300711	0.150355	−	0.988632i	$-0.451958\pi$
$769$	8.33897	0.300711	0.150355	+	0.988632i	$0.451958\pi$
$770$	0	0
$771$	14.9889	0.539813
$772$	10.6391i	0.382910i
$773$	− 19.2782i	− 0.693389i	−0.937978	−	0.346694i	$-0.887304\pi$
$773$	− 19.2782i	− 0.693389i	0.937978	−	0.346694i	$-0.112696\pi$
$774$	59.3097	2.13184
$775$	0	0
$776$	−7.57834	−0.272046
$777$	− 6.76063i	− 0.242536i
$778$	5.15667i	0.184876i
$779$	−17.0740	−0.611739
$780$	0	0
$781$	−7.15667	−0.256086
$782$	− 25.8785i	− 0.925412i
$783$	73.3559i	2.62153i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−4.63910	−0.165471
$787$	− 43.5915i	− 1.55387i	−0.629580	−	0.776935i	$-0.716773\pi$
$787$	− 43.5915i	− 1.55387i	0.629580	−	0.776935i	$-0.283227\pi$
$788$	7.87847i	0.280659i
$789$	−34.5564	−1.23024
$790$	0	0
$791$	14.0000	0.497783
$792$	5.63910i	0.200377i
$793$	− 85.3411i	− 3.03055i
$794$	−19.6354	−0.696835
$795$	0	0
$796$	0.517571	0.0183448
$797$	51.1493i	1.81180i	0.423491	+	0.905900i	$0.360805\pi$
$797$	51.1493i	1.81180i	−0.423491	+	0.905900i	$0.639195\pi$
$798$	16.3960i	0.580414i
$799$	39.5139	1.39790
$800$	0	0
$801$	21.8711	0.772777
$802$	− 5.11784i	− 0.180717i
$803$	12.3960i	0.437447i
$804$	23.5139	0.829271
$805$	0	0
$806$	35.2708	1.24236
$807$	− 34.3133i	− 1.20789i
$808$	− 11.7958i	− 0.414974i
$809$	−45.1567	−1.58762	−0.793812	−	0.608163i	$-0.791907\pi$
$809$	−45.1567	−1.58762	−0.793812	+	0.608163i	$0.791907\pi$
$810$	0	0
$811$	39.2914	1.37971	0.689854	−	0.723948i	$-0.257675\pi$
$811$	39.2914	1.37971	0.689854	+	0.723948i	$0.257675\pi$
$812$	− 9.45681i	− 0.331869i
$813$	− 51.8346i	− 1.81792i
$814$	2.30013	0.0806196
$815$	0	0
$816$	13.6354	0.477335
$817$	58.6706i	2.05262i
$818$	− 2.21744i	− 0.0775309i
$819$	−33.1493	−1.15833
$820$	0	0
$821$	25.6486	0.895143	0.447572	−	0.894248i	$-0.352289\pi$
$821$	25.6486	0.895143	0.447572	+	0.894248i	$0.352289\pi$
$822$	9.63541i	0.336073i
$823$	− 51.6486i	− 1.80036i	−0.435520	−	0.900179i	$-0.643436\pi$
$823$	− 51.6486i	− 1.80036i	0.435520	−	0.900179i	$-0.356564\pi$
$824$	17.1178	0.596328
$825$	0	0
$826$	7.23937	0.251890
$827$	− 12.0000i	− 0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$	− 12.0000i	− 0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	31.4568i	1.09320i
$829$	−5.36090	−0.186192	−0.0930958	−	0.995657i	$-0.529676\pi$
$829$	−5.36090	−0.186192	−0.0930958	+	0.995657i	$0.529676\pi$
$830$	0	0
$831$	−64.6632	−2.24314
$832$	5.87847i	0.203799i
$833$	− 4.63910i	− 0.160735i
$834$	47.1955	1.63425
$835$	0	0
$836$	−5.57834	−0.192931
$837$	46.5416i	1.60871i
$838$	4.51757i	0.156057i
$839$	−16.9649	−0.585692	−0.292846	−	0.956160i	$-0.594602\pi$
$839$	−16.9649	−0.585692	−0.292846	+	0.956160i	$0.594602\pi$
$840$	0	0
$841$	60.4312	2.08383
$842$	− 12.3133i	− 0.424346i
$843$	− 3.39973i	− 0.117093i
$844$	−2.72180	−0.0936881
$845$	0	0
$846$	−48.0315	−1.65136
$847$	1.00000i	0.0343604i
$848$	− 9.45681i	− 0.324748i
$849$	50.7847	1.74293
$850$	0	0
$851$	12.8309	0.439838
$852$	− 21.0351i	− 0.720652i
$853$	31.0666i	1.06370i	0.846839	+	0.531850i	$0.178503\pi$
$853$	31.0666i	1.06370i	−0.846839	+	0.531850i	$0.821497\pi$
$854$	−14.5176	−0.496781
$855$	0	0
$856$	−2.51757	−0.0860488
$857$	− 37.5966i	− 1.28427i	−0.766590	−	0.642137i	$-0.778048\pi$
$857$	− 37.5966i	− 1.28427i	0.766590	−	0.642137i	$-0.221952\pi$
$858$	− 17.2782i	− 0.589868i
$859$	14.0388	0.478999	0.239499	−	0.970897i	$-0.423017\pi$
$859$	14.0388	0.478999	0.239499	+	0.970897i	$0.423017\pi$
$860$	0	0
$861$	−8.99631	−0.306593
$862$	− 2.17860i	− 0.0742035i
$863$	38.8053i	1.32095i	0.750849	+	0.660474i	$0.229645\pi$
$863$	38.8053i	1.32095i	−0.750849	+	0.660474i	$0.770355\pi$
$864$	−7.75694	−0.263896
$865$	0	0
$866$	−5.02193	−0.170652
$867$	13.2891i	0.451320i
$868$	− 6.00000i	− 0.203653i
$869$	10.8565	0.368283
$870$	0	0
$871$	−47.0278	−1.59347
$872$	10.3001i	0.348807i
$873$	42.7350i	1.44636i
$874$	−31.1178	−1.05258
$875$	0	0
$876$	−36.4349	−1.23102
$877$	− 31.7131i	− 1.07087i	−0.844575	−	0.535437i	$-0.820147\pi$
$877$	− 31.7131i	− 1.07087i	0.844575	−	0.535437i	$-0.179853\pi$
$878$	− 7.15667i	− 0.241526i
$879$	5.52126	0.186228
$880$	0	0
$881$	2.24306	0.0755706	0.0377853	−	0.999286i	$-0.487970\pi$
$881$	2.24306	0.0755706	0.0377853	+	0.999286i	$0.487970\pi$
$882$	5.63910i	0.189878i
$883$	24.4349i	0.822299i	0.911568	+	0.411150i	$0.134873\pi$
$883$	24.4349i	0.822299i	−0.911568	+	0.411150i	$0.865127\pi$
$884$	−27.2708	−0.917217
$885$	0	0
$886$	19.5139	0.655582
$887$	− 35.5915i	− 1.19505i	−0.801851	−	0.597524i	$-0.796151\pi$
$887$	− 35.5915i	− 1.19505i	0.801851	−	0.597524i	$-0.203849\pi$
$888$	6.76063i	0.226872i
$889$	10.4787	0.351446
$890$	0	0
$891$	5.88216	0.197060
$892$	22.3960i	0.749875i
$893$	− 47.5139i	− 1.58999i
$894$	−31.5527	−1.05528
$895$	0	0
$896$	1.00000	0.0334077
$897$	− 96.3836i	− 3.21816i
$898$	− 1.36090i	− 0.0454138i
$899$	56.7408	1.89241
$900$	0	0
$901$	43.8711	1.46156
$902$	− 3.06077i	− 0.101912i
$903$	30.9136i	1.02874i
$904$	−14.0000	−0.465633
$905$	0	0
$906$	−6.40343	−0.212740
$907$	− 17.3923i	− 0.577503i	−0.957404	−	0.288752i	$-0.906760\pi$
$907$	− 17.3923i	− 0.577503i	0.957404	−	0.288752i	$-0.0932402\pi$
$908$	13.0351i	0.432586i
$909$	−66.5176	−2.20625
$910$	0	0
$911$	52.1141	1.72662	0.863309	−	0.504675i	$-0.168388\pi$
$911$	52.1141	1.72662	0.863309	+	0.504675i	$0.168388\pi$
$912$	− 16.3960i	− 0.542927i
$913$	− 13.8785i	− 0.459310i
$914$	4.47874	0.148143
$915$	0	0
$916$	−6.63910	−0.219362
$917$	− 1.57834i	− 0.0521213i
$918$	− 35.9852i	− 1.18769i
$919$	−12.1347	−0.400288	−0.200144	−	0.979766i	$-0.564141\pi$
$919$	−12.1347	−0.400288	−0.200144	+	0.979766i	$0.564141\pi$
$920$	0	0
$921$	−25.2782	−0.832945
$922$	− 36.1530i	− 1.19064i
$923$	42.0703i	1.38476i
$924$	−2.93923	−0.0966937
$925$	0	0
$926$	−21.0922	−0.693133
$927$	− 96.5292i	− 3.17044i
$928$	9.45681i	0.310435i
$929$	−23.8008	−0.780879	−0.390439	−	0.920629i	$-0.627677\pi$
$929$	−23.8008	−0.780879	−0.390439	+	0.920629i	$0.627677\pi$
$930$	0	0
$931$	−5.57834	−0.182823
$932$	− 19.0351i	− 0.623517i
$933$	− 40.4349i	− 1.32378i
$934$	19.1311	0.625987
$935$	0	0
$936$	33.1493	1.08352
$937$	− 9.16170i	− 0.299300i	−0.988739	−	0.149650i	$-0.952185\pi$
$937$	− 9.16170i	− 0.299300i	0.988739	−	0.149650i	$-0.0478146\pi$
$938$	8.00000i	0.261209i
$939$	8.52496	0.278201
$940$	0	0
$941$	0.996308	0.0324787	0.0162393	−	0.999868i	$-0.494831\pi$
$941$	0.996308	0.0324787	0.0162393	+	0.999868i	$0.494831\pi$
$942$	50.4275i	1.64302i
$943$	− 17.0740i	− 0.556005i
$944$	−7.23937	−0.235621
$945$	0	0
$946$	−10.5176	−0.341956
$947$	18.8359i	0.612086i	0.952018	+	0.306043i	$0.0990051\pi$
$947$	18.8359i	0.612086i	−0.952018	+	0.306043i	$0.900995\pi$
$948$	31.9099i	1.03639i
$949$	72.8698	2.36545
$950$	0	0
$951$	−56.8309	−1.84287
$952$	4.63910i	0.150354i
$953$	21.4386i	0.694463i	0.937779	+	0.347232i	$0.112878\pi$
$953$	21.4386i	0.694463i	−0.937779	+	0.347232i	$0.887122\pi$
$954$	−53.3279	−1.72655
$955$	0	0
$956$	22.6135	0.731372
$957$	− 27.7958i	− 0.898510i
$958$	− 5.27820i	− 0.170531i
$959$	−3.27820	−0.105859
$960$	0	0
$961$	5.00000	0.161290
$962$	− 13.5213i	− 0.435943i
$963$	14.1968i	0.457487i
$964$	17.9744	0.578916
$965$	0	0
$966$	−16.3960	−0.527534
$967$	− 31.5139i	− 1.01342i	−0.862117	−	0.506709i	$-0.830862\pi$
$967$	− 31.5139i	− 1.01342i	0.862117	−	0.506709i	$-0.169138\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	76.0629	2.44349
$970$	0	0
$971$	16.1968	0.519781	0.259891	−	0.965638i	$-0.416313\pi$
$971$	16.1968	0.519781	0.259891	+	0.965638i	$0.416313\pi$
$972$	− 5.98176i	− 0.191865i
$973$	16.0571i	0.514766i
$974$	−19.8140	−0.634882
$975$	0	0
$976$	14.5176	0.464696
$977$	− 17.5139i	− 0.560319i	−0.959954	−	0.280159i	$-0.909613\pi$
$977$	− 17.5139i	− 0.560319i	0.959954	−	0.280159i	$-0.0903873\pi$
$978$	− 23.5139i	− 0.751891i
$979$	−3.87847	−0.123956
$980$	0	0
$981$	58.0835	1.85446
$982$	− 6.47874i	− 0.206745i
$983$	41.1178i	1.31146i	0.754997	+	0.655728i	$0.227638\pi$
$983$	41.1178i	1.31146i	−0.754997	+	0.655728i	$0.772362\pi$
$984$	8.99631	0.286792
$985$	0	0
$986$	−43.8711	−1.39714
$987$	− 25.0351i	− 0.796877i
$988$	32.7921i	1.04326i
$989$	−58.6706	−1.86562
$990$	0	0
$991$	−2.79947	−0.0889280	−0.0444640	−	0.999011i	$-0.514158\pi$
$991$	−2.79947	−0.0889280	−0.0444640	+	0.999011i	$0.514158\pi$
$992$	6.00000i	0.190500i
$993$	− 30.9136i	− 0.981014i
$994$	7.15667	0.226996
$995$	0	0
$996$	40.7921	1.29255
$997$	− 11.7181i	− 0.371116i	−0.982633	−	0.185558i	$-0.940591\pi$
$997$	− 11.7181i	− 0.371116i	0.982633	−	0.185558i	$-0.0594093\pi$
$998$	21.2394i	0.672320i
$999$	17.8420	0.564496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.z.1849.4		6
5.2	odd	4		770.2.a.l.1.1	✓	3
5.3	odd	4		3850.2.a.bu.1.3		3
5.4	even	2	inner	3850.2.c.z.1849.3		6
15.2	even	4		6930.2.a.cl.1.1		3
20.7	even	4		6160.2.a.bi.1.3		3
35.27	even	4		5390.2.a.bz.1.3		3
55.32	even	4		8470.2.a.cl.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.l.1.1	✓	3	5.2	odd	4
3850.2.a.bu.1.3		3	5.3	odd	4
3850.2.c.z.1849.3		6	5.4	even	2	inner
3850.2.c.z.1849.4		6	1.1	even	1	trivial
5390.2.a.bz.1.3		3	35.27	even	4
6160.2.a.bi.1.3		3	20.7	even	4
6930.2.a.cl.1.1		3	15.2	even	4
8470.2.a.cl.1.1		3	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.93923i q^{3} -1.00000 q^{4} +2.93923 q^{6} +1.00000i q^{7} -1.00000i q^{8} -5.63910 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.93923i q^{3} -1.00000 q^{4} +2.93923 q^{6} +1.00000i q^{7} -1.00000i q^{8} -5.63910 q^{9} +1.00000 q^{11} +2.93923i q^{12} -5.87847i q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.63910i q^{17} -5.63910i q^{18} +5.57834 q^{19} +2.93923 q^{21} +1.00000i q^{22} +5.57834i q^{23} -2.93923 q^{24} +5.87847 q^{26} +7.75694i q^{27} -1.00000i q^{28} +9.45681 q^{29} +6.00000 q^{31} +1.00000i q^{32} -2.93923i q^{33} -4.63910 q^{34} +5.63910 q^{36} -2.30013i q^{37} +5.57834i q^{38} -17.2782 q^{39} -3.06077 q^{41} +2.93923i q^{42} +10.5176i q^{43} -1.00000 q^{44} -5.57834 q^{46} -8.51757i q^{47} -2.93923i q^{48} -1.00000 q^{49} +13.6354 q^{51} +5.87847i q^{52} -9.45681i q^{53} -7.75694 q^{54} +1.00000 q^{56} -16.3960i q^{57} +9.45681i q^{58} -7.23937 q^{59} +14.5176 q^{61} +6.00000i q^{62} -5.63910i q^{63} -1.00000 q^{64} +2.93923 q^{66} -8.00000i q^{67} -4.63910i q^{68} +16.3960 q^{69} -7.15667 q^{71} +5.63910i q^{72} +12.3960i q^{73} +2.30013 q^{74} -5.57834 q^{76} +1.00000i q^{77} -17.2782i q^{78} +10.8565 q^{79} +5.88216 q^{81} -3.06077i q^{82} -13.8785i q^{83} -2.93923 q^{84} -10.5176 q^{86} -27.7958i q^{87} -1.00000i q^{88} -3.87847 q^{89} +5.87847 q^{91} -5.57834i q^{92} -17.6354i q^{93} +8.51757 q^{94} +2.93923 q^{96} -7.57834i q^{97} -1.00000i q^{98} -5.63910 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 22 * q^9	\( 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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