LMFDB - Embedded newform 3850.2.c.y.1849.1

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:	$\Q(i, \sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
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			1849.1
Root			$3.37228i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.y.1849.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.00000 q^{11} -2.00000i q^{12} -4.74456i q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.74456i q^{17} +1.00000i q^{18} -4.74456 q^{19} +2.00000 q^{21} +1.00000i q^{22} +4.74456i q^{23} -2.00000 q^{24} -4.74456 q^{26} +4.00000i q^{27} +1.00000i q^{28} +2.74456 q^{29} -6.74456 q^{31} -1.00000i q^{32} -2.00000i q^{33} -4.74456 q^{34} +1.00000 q^{36} +10.7446i q^{37} +4.74456i q^{38} +9.48913 q^{39} -4.00000 q^{41} -2.00000i q^{42} +4.00000i q^{43} +1.00000 q^{44} +4.74456 q^{46} +6.74456i q^{47} +2.00000i q^{48} -1.00000 q^{49} +9.48913 q^{51} +4.74456i q^{52} -1.25544i q^{53} +4.00000 q^{54} +1.00000 q^{56} -9.48913i q^{57} -2.74456i q^{58} -2.74456 q^{59} +12.7446 q^{61} +6.74456i q^{62} +1.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +4.00000i q^{67} +4.74456i q^{68} -9.48913 q^{69} -4.00000 q^{71} -1.00000i q^{72} -0.744563i q^{73} +10.7446 q^{74} +4.74456 q^{76} +1.00000i q^{77} -9.48913i q^{78} +4.74456 q^{79} -11.0000 q^{81} +4.00000i q^{82} +8.00000i q^{83} -2.00000 q^{84} +4.00000 q^{86} +5.48913i q^{87} -1.00000i q^{88} +7.48913 q^{89} -4.74456 q^{91} -4.74456i q^{92} -13.4891i q^{93} +6.74456 q^{94} +2.00000 q^{96} +5.25544i q^{97} +1.00000i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9} - 4 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 8 q^{21} - 8 q^{24} + 4 q^{26} - 12 q^{29} - 4 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 4 q^{46} - 4 q^{49} - 8 q^{51} + 16 q^{54} + 4 q^{56} + 12 q^{59} + 28 q^{61} - 4 q^{64} - 8 q^{66} + 8 q^{69} - 16 q^{71} + 20 q^{74} - 4 q^{76} - 4 q^{79} - 44 q^{81} - 8 q^{84} + 16 q^{86} - 16 q^{89} + 4 q^{91} + 4 q^{94} + 8 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9 - 4 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 8 * q^21 - 8 * q^24 + 4 * q^26 - 12 * q^29 - 4 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 4 * q^46 - 4 * q^49 - 8 * q^51 + 16 * q^54 + 4 * q^56 + 12 * q^59 + 28 * q^61 - 4 * q^64 - 8 * q^66 + 8 * q^69 - 16 * q^71 + 20 * q^74 - 4 * q^76 - 4 * q^79 - 44 * q^81 - 8 * q^84 + 16 * q^86 - 16 * q^89 + 4 * q^91 + 4 * q^94 + 8 * 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
$3$	2.00000i	1.15470i	0.816497	+	0.577350i	$0.195913\pi$
$3$	2.00000i	1.15470i	−0.816497	+	0.577350i	$0.804087\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	− 2.00000i	− 0.577350i
$13$	− 4.74456i	− 1.31590i	−0.753059	−	0.657952i	$-0.771423\pi$
$13$	− 4.74456i	− 1.31590i	0.753059	−	0.657952i	$-0.228577\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.74456i	− 1.15073i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	− 4.74456i	− 1.15073i	0.817898	−	0.575363i	$-0.195139\pi$
$18$	1.00000i	0.235702i
$19$	−4.74456	−1.08848	−0.544239	−	0.838930i	$-0.683181\pi$
$19$	−4.74456	−1.08848	−0.544239	+	0.838930i	$0.683181\pi$
$20$	0	0
$21$	2.00000	0.436436
$22$	1.00000i	0.213201i
$23$	4.74456i	0.989310i	0.869090	+	0.494655i	$0.164706\pi$
$23$	4.74456i	0.989310i	−0.869090	+	0.494655i	$0.835294\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	−4.74456	−0.930485
$27$	4.00000i	0.769800i
$28$	1.00000i	0.188982i
$29$	2.74456	0.509652	0.254826	−	0.966987i	$-0.417982\pi$
$29$	2.74456	0.509652	0.254826	+	0.966987i	$0.417982\pi$
$30$	0	0
$31$	−6.74456	−1.21136	−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456	−1.21136	−0.605680	+	0.795709i	$0.707099\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 2.00000i	− 0.348155i
$34$	−4.74456	−0.813686
$35$	0	0
$36$	1.00000	0.166667
$37$	10.7446i	1.76640i	0.469001	+	0.883198i	$0.344614\pi$
$37$	10.7446i	1.76640i	−0.469001	+	0.883198i	$0.655386\pi$
$38$	4.74456i	0.769670i
$39$	9.48913	1.51948
$40$	0	0
$41$	−4.00000	−0.624695	−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000	−0.624695	−0.312348	+	0.949968i	$0.601115\pi$
$42$	− 2.00000i	− 0.308607i
$43$	4.00000i	0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$	4.00000i	0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	4.74456	0.699548
$47$	6.74456i	0.983796i	0.870653	+	0.491898i	$0.163697\pi$
$47$	6.74456i	0.983796i	−0.870653	+	0.491898i	$0.836303\pi$
$48$	2.00000i	0.288675i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	9.48913	1.32874
$52$	4.74456i	0.657952i
$53$	− 1.25544i	− 0.172448i	−0.996276	−	0.0862238i	$-0.972520\pi$
$53$	− 1.25544i	− 0.172448i	0.996276	−	0.0862238i	$-0.0274800\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	− 9.48913i	− 1.25687i
$58$	− 2.74456i	− 0.360379i
$59$	−2.74456	−0.357312	−0.178656	−	0.983912i	$-0.557175\pi$
$59$	−2.74456	−0.357312	−0.178656	+	0.983912i	$0.557175\pi$
$60$	0	0
$61$	12.7446	1.63177	0.815887	−	0.578211i	$-0.196249\pi$
$61$	12.7446	1.63177	0.815887	+	0.578211i	$0.196249\pi$
$62$	6.74456i	0.856560i
$63$	1.00000i	0.125988i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	4.74456i	0.575363i
$69$	−9.48913	−1.14236
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 0.744563i	− 0.0871445i	−0.999050	−	0.0435722i	$-0.986126\pi$
$73$	− 0.744563i	− 0.0871445i	0.999050	−	0.0435722i	$-0.0138739\pi$
$74$	10.7446	1.24903
$75$	0	0
$76$	4.74456	0.544239
$77$	1.00000i	0.113961i
$78$	− 9.48913i	− 1.07443i
$79$	4.74456	0.533805	0.266903	−	0.963724i	$-0.414000\pi$
$79$	4.74456	0.533805	0.266903	+	0.963724i	$0.414000\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	4.00000i	0.441726i
$83$	8.00000i	0.878114i	0.898459	+	0.439057i	$0.144687\pi$
$83$	8.00000i	0.878114i	−0.898459	+	0.439057i	$0.855313\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	4.00000	0.431331
$87$	5.48913i	0.588496i
$88$	− 1.00000i	− 0.106600i
$89$	7.48913	0.793846	0.396923	−	0.917852i	$-0.370078\pi$
$89$	7.48913	0.793846	0.396923	+	0.917852i	$0.370078\pi$
$90$	0	0
$91$	−4.74456	−0.497365
$92$	− 4.74456i	− 0.494655i
$93$	− 13.4891i	− 1.39876i
$94$	6.74456	0.695649
$95$	0	0
$96$	2.00000	0.204124
$97$	5.25544i	0.533609i	0.963751	+	0.266804i	$0.0859678\pi$
$97$	5.25544i	0.533609i	−0.963751	+	0.266804i	$0.914032\pi$
$98$	1.00000i	0.101015i
$99$	1.00000	0.100504
$100$	0	0
$101$	−8.74456	−0.870117	−0.435058	−	0.900402i	$-0.643272\pi$
$101$	−8.74456	−0.870117	−0.435058	+	0.900402i	$0.643272\pi$
$102$	− 9.48913i	− 0.939563i
$103$	10.7446i	1.05869i	0.848406	+	0.529347i	$0.177563\pi$
$103$	10.7446i	1.05869i	−0.848406	+	0.529347i	$0.822437\pi$
$104$	4.74456	0.465243
$105$	0	0
$106$	−1.25544	−0.121939
$107$	12.0000i	1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$	12.0000i	1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	− 4.00000i	− 0.384900i
$109$	−16.2337	−1.55491	−0.777453	−	0.628941i	$-0.783489\pi$
$109$	−16.2337	−1.55491	−0.777453	+	0.628941i	$0.783489\pi$
$110$	0	0
$111$	−21.4891	−2.03966
$112$	− 1.00000i	− 0.0944911i
$113$	10.0000i	0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$	10.0000i	0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$	−9.48913	−0.888738
$115$	0	0
$116$	−2.74456	−0.254826
$117$	4.74456i	0.438635i
$118$	2.74456i	0.252657i
$119$	−4.74456	−0.434933
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 12.7446i	− 1.15384i
$123$	− 8.00000i	− 0.721336i
$124$	6.74456	0.605680
$125$	0	0
$126$	1.00000	0.0890871
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	1.00000i	0.0883883i
$129$	−8.00000	−0.704361
$130$	0	0
$131$	8.74456	0.764016	0.382008	−	0.924159i	$-0.375233\pi$
$131$	8.74456	0.764016	0.382008	+	0.924159i	$0.375233\pi$
$132$	2.00000i	0.174078i
$133$	4.74456i	0.411406i
$134$	4.00000	0.345547
$135$	0	0
$136$	4.74456	0.406843
$137$	19.4891i	1.66507i	0.553974	+	0.832534i	$0.313111\pi$
$137$	19.4891i	1.66507i	−0.553974	+	0.832534i	$0.686889\pi$
$138$	9.48913i	0.807768i
$139$	−3.25544	−0.276123	−0.138061	−	0.990424i	$-0.544087\pi$
$139$	−3.25544	−0.276123	−0.138061	+	0.990424i	$0.544087\pi$
$140$	0	0
$141$	−13.4891	−1.13599
$142$	4.00000i	0.335673i
$143$	4.74456i	0.396760i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−0.744563	−0.0616204
$147$	− 2.00000i	− 0.164957i
$148$	− 10.7446i	− 0.883198i
$149$	−10.7446	−0.880229	−0.440114	−	0.897942i	$-0.645062\pi$
$149$	−10.7446	−0.880229	−0.440114	+	0.897942i	$0.645062\pi$
$150$	0	0
$151$	−20.7446	−1.68817	−0.844084	−	0.536211i	$-0.819855\pi$
$151$	−20.7446	−1.68817	−0.844084	+	0.536211i	$0.819855\pi$
$152$	− 4.74456i	− 0.384835i
$153$	4.74456i	0.383575i
$154$	1.00000	0.0805823
$155$	0	0
$156$	−9.48913	−0.759738
$157$	− 23.4891i	− 1.87464i	−0.348475	−	0.937318i	$-0.613300\pi$
$157$	− 23.4891i	− 1.87464i	0.348475	−	0.937318i	$-0.386700\pi$
$158$	− 4.74456i	− 0.377457i
$159$	2.51087	0.199125
$160$	0	0
$161$	4.74456	0.373924
$162$	11.0000i	0.864242i
$163$	− 4.00000i	− 0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$	− 4.00000i	− 0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	8.00000	0.620920
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	2.00000i	0.154303i
$169$	−9.51087	−0.731606
$170$	0	0
$171$	4.74456	0.362826
$172$	− 4.00000i	− 0.304997i
$173$	− 14.2337i	− 1.08217i	−0.840969	−	0.541084i	$-0.818014\pi$
$173$	− 14.2337i	− 1.08217i	0.840969	−	0.541084i	$-0.181986\pi$
$174$	5.48913	0.416130
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	− 5.48913i	− 0.412588i
$178$	− 7.48913i	− 0.561334i
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	0	0
$181$	3.48913	0.259345	0.129672	−	0.991557i	$-0.458607\pi$
$181$	3.48913	0.259345	0.129672	+	0.991557i	$0.458607\pi$
$182$	4.74456i	0.351690i
$183$	25.4891i	1.88421i
$184$	−4.74456	−0.349774
$185$	0	0
$186$	−13.4891	−0.989071
$187$	4.74456i	0.346957i
$188$	− 6.74456i	− 0.491898i
$189$	4.00000	0.290957
$190$	0	0
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	− 2.00000i	− 0.144338i
$193$	− 2.00000i	− 0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$	− 2.00000i	− 0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	5.25544	0.377318
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 10.0000i	− 0.712470i	−0.934396	−	0.356235i	$-0.884060\pi$
$197$	− 10.0000i	− 0.712470i	0.934396	−	0.356235i	$-0.115940\pi$
$198$	− 1.00000i	− 0.0710669i
$199$	−14.7446	−1.04521	−0.522607	−	0.852574i	$-0.675041\pi$
$199$	−14.7446	−1.04521	−0.522607	+	0.852574i	$0.675041\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	8.74456i	0.615265i
$203$	− 2.74456i	− 0.192631i
$204$	−9.48913	−0.664372
$205$	0	0
$206$	10.7446	0.748609
$207$	− 4.74456i	− 0.329770i
$208$	− 4.74456i	− 0.328976i
$209$	4.74456	0.328188
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	1.25544i	0.0862238i
$213$	− 8.00000i	− 0.548151i
$214$	12.0000	0.820303
$215$	0	0
$216$	−4.00000	−0.272166
$217$	6.74456i	0.457851i
$218$	16.2337i	1.09948i
$219$	1.48913	0.100626
$220$	0	0
$221$	−22.5109	−1.51425
$222$	21.4891i	1.44226i
$223$	26.7446i	1.79095i	0.445113	+	0.895474i	$0.353163\pi$
$223$	26.7446i	1.79095i	−0.445113	+	0.895474i	$0.646837\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	10.0000	0.665190
$227$	− 20.0000i	− 1.32745i	−0.747978	−	0.663723i	$-0.768975\pi$
$227$	− 20.0000i	− 1.32745i	0.747978	−	0.663723i	$-0.231025\pi$
$228$	9.48913i	0.628433i
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	2.74456i	0.180189i
$233$	20.9783i	1.37433i	0.726501	+	0.687165i	$0.241145\pi$
$233$	20.9783i	1.37433i	−0.726501	+	0.687165i	$0.758855\pi$
$234$	4.74456	0.310162
$235$	0	0
$236$	2.74456	0.178656
$237$	9.48913i	0.616385i
$238$	4.74456i	0.307544i
$239$	3.25544	0.210577	0.105288	−	0.994442i	$-0.466423\pi$
$239$	3.25544	0.210577	0.105288	+	0.994442i	$0.466423\pi$
$240$	0	0
$241$	20.0000	1.28831	0.644157	−	0.764894i	$-0.277208\pi$
$241$	20.0000	1.28831	0.644157	+	0.764894i	$0.277208\pi$
$242$	− 1.00000i	− 0.0642824i
$243$	− 10.0000i	− 0.641500i
$244$	−12.7446	−0.815887
$245$	0	0
$246$	−8.00000	−0.510061
$247$	22.5109i	1.43233i
$248$	− 6.74456i	− 0.428280i
$249$	−16.0000	−1.01396
$250$	0	0
$251$	8.23369	0.519706	0.259853	−	0.965648i	$-0.416326\pi$
$251$	8.23369	0.519706	0.259853	+	0.965648i	$0.416326\pi$
$252$	− 1.00000i	− 0.0629941i
$253$	− 4.74456i	− 0.298288i
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 24.2337i	− 1.51166i	−0.654770	−	0.755828i	$-0.727235\pi$
$257$	− 24.2337i	− 1.51166i	0.654770	−	0.755828i	$-0.272765\pi$
$258$	8.00000i	0.498058i
$259$	10.7446	0.667635
$260$	0	0
$261$	−2.74456	−0.169884
$262$	− 8.74456i	− 0.540241i
$263$	− 18.9783i	− 1.17025i	−0.810943	−	0.585125i	$-0.801046\pi$
$263$	− 18.9783i	− 1.17025i	0.810943	−	0.585125i	$-0.198954\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	4.74456	0.290908
$267$	14.9783i	0.916654i
$268$	− 4.00000i	− 0.244339i
$269$	24.9783	1.52295	0.761475	−	0.648194i	$-0.224475\pi$
$269$	24.9783	1.52295	0.761475	+	0.648194i	$0.224475\pi$
$270$	0	0
$271$	−30.9783	−1.88179	−0.940897	−	0.338692i	$-0.890016\pi$
$271$	−30.9783	−1.88179	−0.940897	+	0.338692i	$0.890016\pi$
$272$	− 4.74456i	− 0.287681i
$273$	− 9.48913i	− 0.574308i
$274$	19.4891	1.17738
$275$	0	0
$276$	9.48913	0.571178
$277$	7.48913i	0.449978i	0.974361	+	0.224989i	$0.0722346\pi$
$277$	7.48913i	0.449978i	−0.974361	+	0.224989i	$0.927765\pi$
$278$	3.25544i	0.195248i
$279$	6.74456	0.403786
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	13.4891i	0.803266i
$283$	28.0000i	1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$	28.0000i	1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$	4.00000	0.237356
$285$	0	0
$286$	4.74456	0.280552
$287$	4.00000i	0.236113i
$288$	1.00000i	0.0589256i
$289$	−5.51087	−0.324169
$290$	0	0
$291$	−10.5109	−0.616158
$292$	0.744563i	0.0435722i
$293$	24.7446i	1.44559i	0.691061	+	0.722796i	$0.257144\pi$
$293$	24.7446i	1.44559i	−0.691061	+	0.722796i	$0.742856\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−10.7446	−0.624515
$297$	− 4.00000i	− 0.232104i
$298$	10.7446i	0.622416i
$299$	22.5109	1.30184
$300$	0	0
$301$	4.00000	0.230556
$302$	20.7446i	1.19372i
$303$	− 17.4891i	− 1.00472i
$304$	−4.74456	−0.272119
$305$	0	0
$306$	4.74456	0.271229
$307$	− 21.4891i	− 1.22645i	−0.789909	−	0.613225i	$-0.789872\pi$
$307$	− 21.4891i	− 1.22645i	0.789909	−	0.613225i	$-0.210128\pi$
$308$	− 1.00000i	− 0.0569803i
$309$	−21.4891	−1.22247
$310$	0	0
$311$	−9.25544	−0.524828	−0.262414	−	0.964955i	$-0.584519\pi$
$311$	−9.25544	−0.524828	−0.262414	+	0.964955i	$0.584519\pi$
$312$	9.48913i	0.537216i
$313$	32.2337i	1.82196i	0.412455	+	0.910978i	$0.364671\pi$
$313$	32.2337i	1.82196i	−0.412455	+	0.910978i	$0.635329\pi$
$314$	−23.4891	−1.32557
$315$	0	0
$316$	−4.74456	−0.266903
$317$	32.2337i	1.81042i	0.424960	+	0.905212i	$0.360288\pi$
$317$	32.2337i	1.81042i	−0.424960	+	0.905212i	$0.639712\pi$
$318$	− 2.51087i	− 0.140803i
$319$	−2.74456	−0.153666
$320$	0	0
$321$	−24.0000	−1.33955
$322$	− 4.74456i	− 0.264404i
$323$	22.5109i	1.25254i
$324$	11.0000	0.611111
$325$	0	0
$326$	−4.00000	−0.221540
$327$	− 32.4674i	− 1.79545i
$328$	− 4.00000i	− 0.220863i
$329$	6.74456	0.371840
$330$	0	0
$331$	−30.9783	−1.70272	−0.851359	−	0.524583i	$-0.824221\pi$
$331$	−30.9783	−1.70272	−0.851359	+	0.524583i	$0.824221\pi$
$332$	− 8.00000i	− 0.439057i
$333$	− 10.7446i	− 0.588798i
$334$	0	0
$335$	0	0
$336$	2.00000	0.109109
$337$	− 26.0000i	− 1.41631i	−0.706057	−	0.708155i	$-0.749528\pi$
$337$	− 26.0000i	− 1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$338$	9.51087i	0.517323i
$339$	−20.0000	−1.08625
$340$	0	0
$341$	6.74456	0.365239
$342$	− 4.74456i	− 0.256557i
$343$	1.00000i	0.0539949i
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−14.2337	−0.765208
$347$	− 22.9783i	− 1.23354i	−0.787145	−	0.616769i	$-0.788441\pi$
$347$	− 22.9783i	− 1.23354i	0.787145	−	0.616769i	$-0.211559\pi$
$348$	− 5.48913i	− 0.294248i
$349$	−19.2554	−1.03072	−0.515360	−	0.856974i	$-0.672342\pi$
$349$	−19.2554	−1.03072	−0.515360	+	0.856974i	$0.672342\pi$
$350$	0	0
$351$	18.9783	1.01298
$352$	1.00000i	0.0533002i
$353$	− 2.74456i	− 0.146078i	−0.997329	−	0.0730392i	$-0.976730\pi$
$353$	− 2.74456i	− 0.146078i	0.997329	−	0.0730392i	$-0.0232698\pi$
$354$	−5.48913	−0.291744
$355$	0	0
$356$	−7.48913	−0.396923
$357$	− 9.48913i	− 0.502218i
$358$	− 4.00000i	− 0.211407i
$359$	12.7446	0.672632	0.336316	−	0.941749i	$-0.390819\pi$
$359$	12.7446	0.672632	0.336316	+	0.941749i	$0.390819\pi$
$360$	0	0
$361$	3.51087	0.184783
$362$	− 3.48913i	− 0.183384i
$363$	2.00000i	0.104973i
$364$	4.74456	0.248683
$365$	0	0
$366$	25.4891	1.33234
$367$	− 2.74456i	− 0.143265i	−0.997431	−	0.0716325i	$-0.977179\pi$
$367$	− 2.74456i	− 0.143265i	0.997431	−	0.0716325i	$-0.0228209\pi$
$368$	4.74456i	0.247327i
$369$	4.00000	0.208232
$370$	0	0
$371$	−1.25544	−0.0651791
$372$	13.4891i	0.699379i
$373$	28.9783i	1.50044i	0.661190	+	0.750218i	$0.270052\pi$
$373$	28.9783i	1.50044i	−0.661190	+	0.750218i	$0.729948\pi$
$374$	4.74456	0.245335
$375$	0	0
$376$	−6.74456	−0.347824
$377$	− 13.0217i	− 0.670654i
$378$	− 4.00000i	− 0.205738i
$379$	14.5109	0.745374	0.372687	−	0.927957i	$-0.378437\pi$
$379$	14.5109	0.745374	0.372687	+	0.927957i	$0.378437\pi$
$380$	0	0
$381$	0	0
$382$	16.0000i	0.818631i
$383$	− 37.7228i	− 1.92755i	−0.266724	−	0.963773i	$-0.585941\pi$
$383$	− 37.7228i	− 1.92755i	0.266724	−	0.963773i	$-0.414059\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−2.00000	−0.101797
$387$	− 4.00000i	− 0.203331i
$388$	− 5.25544i	− 0.266804i
$389$	−15.4891	−0.785330	−0.392665	−	0.919682i	$-0.628447\pi$
$389$	−15.4891	−0.785330	−0.392665	+	0.919682i	$0.628447\pi$
$390$	0	0
$391$	22.5109	1.13842
$392$	− 1.00000i	− 0.0505076i
$393$	17.4891i	0.882210i
$394$	−10.0000	−0.503793
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	− 12.5109i	− 0.627903i	−0.949439	−	0.313951i	$-0.898347\pi$
$397$	− 12.5109i	− 0.627903i	0.949439	−	0.313951i	$-0.101653\pi$
$398$	14.7446i	0.739078i
$399$	−9.48913	−0.475050
$400$	0	0
$401$	0.510875	0.0255119	0.0127559	−	0.999919i	$-0.495940\pi$
$401$	0.510875	0.0255119	0.0127559	+	0.999919i	$0.495940\pi$
$402$	8.00000i	0.399004i
$403$	32.0000i	1.59403i
$404$	8.74456	0.435058
$405$	0	0
$406$	−2.74456	−0.136210
$407$	− 10.7446i	− 0.532588i
$408$	9.48913i	0.469782i
$409$	−1.48913	−0.0736325	−0.0368163	−	0.999322i	$-0.511722\pi$
$409$	−1.48913	−0.0736325	−0.0368163	+	0.999322i	$0.511722\pi$
$410$	0	0
$411$	−38.9783	−1.92266
$412$	− 10.7446i	− 0.529347i
$413$	2.74456i	0.135051i
$414$	−4.74456	−0.233183
$415$	0	0
$416$	−4.74456	−0.232621
$417$	− 6.51087i	− 0.318839i
$418$	− 4.74456i	− 0.232064i
$419$	−10.7446	−0.524906	−0.262453	−	0.964945i	$-0.584532\pi$
$419$	−10.7446	−0.524906	−0.262453	+	0.964945i	$0.584532\pi$
$420$	0	0
$421$	27.4891	1.33974	0.669869	−	0.742479i	$-0.266350\pi$
$421$	27.4891	1.33974	0.669869	+	0.742479i	$0.266350\pi$
$422$	12.0000i	0.584151i
$423$	− 6.74456i	− 0.327932i
$424$	1.25544	0.0609694
$425$	0	0
$426$	−8.00000	−0.387601
$427$	− 12.7446i	− 0.616753i
$428$	− 12.0000i	− 0.580042i
$429$	−9.48913	−0.458139
$430$	0	0
$431$	−28.7446	−1.38458	−0.692288	−	0.721621i	$-0.743397\pi$
$431$	−28.7446	−1.38458	−0.692288	+	0.721621i	$0.743397\pi$
$432$	4.00000i	0.192450i
$433$	25.2554i	1.21370i	0.794817	+	0.606849i	$0.207567\pi$
$433$	25.2554i	1.21370i	−0.794817	+	0.606849i	$0.792433\pi$
$434$	6.74456	0.323749
$435$	0	0
$436$	16.2337	0.777453
$437$	− 22.5109i	− 1.07684i
$438$	− 1.48913i	− 0.0711532i
$439$	30.9783	1.47851	0.739256	−	0.673425i	$-0.235178\pi$
$439$	30.9783	1.47851	0.739256	+	0.673425i	$0.235178\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	22.5109i	1.07073i
$443$	− 6.51087i	− 0.309341i	−0.987966	−	0.154670i	$-0.950568\pi$
$443$	− 6.51087i	− 0.309341i	0.987966	−	0.154670i	$-0.0494316\pi$
$444$	21.4891	1.01983
$445$	0	0
$446$	26.7446	1.26639
$447$	− 21.4891i	− 1.01640i
$448$	1.00000i	0.0472456i
$449$	−40.9783	−1.93388	−0.966942	−	0.254998i	$-0.917925\pi$
$449$	−40.9783	−1.93388	−0.966942	+	0.254998i	$0.917925\pi$
$450$	0	0
$451$	4.00000	0.188353
$452$	− 10.0000i	− 0.470360i
$453$	− 41.4891i	− 1.94933i
$454$	−20.0000	−0.938647
$455$	0	0
$456$	9.48913	0.444369
$457$	19.4891i	0.911663i	0.890066	+	0.455831i	$0.150658\pi$
$457$	19.4891i	0.911663i	−0.890066	+	0.455831i	$0.849342\pi$
$458$	− 6.00000i	− 0.280362i
$459$	18.9783	0.885829
$460$	0	0
$461$	−23.7228	−1.10488	−0.552441	−	0.833552i	$-0.686303\pi$
$461$	−23.7228	−1.10488	−0.552441	+	0.833552i	$0.686303\pi$
$462$	2.00000i	0.0930484i
$463$	12.7446i	0.592290i	0.955143	+	0.296145i	$0.0957012\pi$
$463$	12.7446i	0.592290i	−0.955143	+	0.296145i	$0.904299\pi$
$464$	2.74456	0.127413
$465$	0	0
$466$	20.9783	0.971799
$467$	28.9783i	1.34095i	0.741931	+	0.670477i	$0.233910\pi$
$467$	28.9783i	1.34095i	−0.741931	+	0.670477i	$0.766090\pi$
$468$	− 4.74456i	− 0.219317i
$469$	4.00000	0.184703
$470$	0	0
$471$	46.9783	2.16464
$472$	− 2.74456i	− 0.126329i
$473$	− 4.00000i	− 0.183920i
$474$	9.48913	0.435850
$475$	0	0
$476$	4.74456	0.217467
$477$	1.25544i	0.0574825i
$478$	− 3.25544i	− 0.148900i
$479$	18.5109	0.845783	0.422892	−	0.906180i	$-0.361015\pi$
$479$	18.5109	0.845783	0.422892	+	0.906180i	$0.361015\pi$
$480$	0	0
$481$	50.9783	2.32441
$482$	− 20.0000i	− 0.910975i
$483$	9.48913i	0.431770i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	−10.0000	−0.453609
$487$	− 20.7446i	− 0.940026i	−0.882660	−	0.470013i	$-0.844249\pi$
$487$	− 20.7446i	− 0.940026i	0.882660	−	0.470013i	$-0.155751\pi$
$488$	12.7446i	0.576919i
$489$	8.00000	0.361773
$490$	0	0
$491$	−14.9783	−0.675959	−0.337979	−	0.941153i	$-0.609743\pi$
$491$	−14.9783	−0.675959	−0.337979	+	0.941153i	$0.609743\pi$
$492$	8.00000i	0.360668i
$493$	− 13.0217i	− 0.586470i
$494$	22.5109	1.01281
$495$	0	0
$496$	−6.74456	−0.302840
$497$	4.00000i	0.179425i
$498$	16.0000i	0.716977i
$499$	−9.48913	−0.424792	−0.212396	−	0.977184i	$-0.568127\pi$
$499$	−9.48913	−0.424792	−0.212396	+	0.977184i	$0.568127\pi$
$500$	0	0
$501$	0	0
$502$	− 8.23369i	− 0.367487i
$503$	29.4891i	1.31486i	0.753518	+	0.657428i	$0.228355\pi$
$503$	29.4891i	1.31486i	−0.753518	+	0.657428i	$0.771645\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	−4.74456	−0.210922
$507$	− 19.0217i	− 0.844786i
$508$	0	0
$509$	12.5109	0.554535	0.277267	−	0.960793i	$-0.410571\pi$
$509$	12.5109	0.554535	0.277267	+	0.960793i	$0.410571\pi$
$510$	0	0
$511$	−0.744563	−0.0329375
$512$	− 1.00000i	− 0.0441942i
$513$	− 18.9783i	− 0.837910i
$514$	−24.2337	−1.06890
$515$	0	0
$516$	8.00000	0.352180
$517$	− 6.74456i	− 0.296626i
$518$	− 10.7446i	− 0.472089i
$519$	28.4674	1.24958
$520$	0	0
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	2.74456i	0.120126i
$523$	5.48913i	0.240023i	0.992773	+	0.120011i	$0.0382931\pi$
$523$	5.48913i	0.240023i	−0.992773	+	0.120011i	$0.961707\pi$
$524$	−8.74456	−0.382008
$525$	0	0
$526$	−18.9783	−0.827491
$527$	32.0000i	1.39394i
$528$	− 2.00000i	− 0.0870388i
$529$	0.489125	0.0212663
$530$	0	0
$531$	2.74456	0.119104
$532$	− 4.74456i	− 0.205703i
$533$	18.9783i	0.822039i
$534$	14.9783	0.648172
$535$	0	0
$536$	−4.00000	−0.172774
$537$	8.00000i	0.345225i
$538$	− 24.9783i	− 1.07689i
$539$	1.00000	0.0430730
$540$	0	0
$541$	36.2337	1.55781	0.778904	−	0.627143i	$-0.215776\pi$
$541$	36.2337	1.55781	0.778904	+	0.627143i	$0.215776\pi$
$542$	30.9783i	1.33063i
$543$	6.97825i	0.299465i
$544$	−4.74456	−0.203421
$545$	0	0
$546$	−9.48913	−0.406097
$547$	30.9783i	1.32453i	0.749268	+	0.662267i	$0.230406\pi$
$547$	30.9783i	1.32453i	−0.749268	+	0.662267i	$0.769594\pi$
$548$	− 19.4891i	− 0.832534i
$549$	−12.7446	−0.543925
$550$	0	0
$551$	−13.0217	−0.554745
$552$	− 9.48913i	− 0.403884i
$553$	− 4.74456i	− 0.201759i
$554$	7.48913	0.318182
$555$	0	0
$556$	3.25544	0.138061
$557$	− 44.9783i	− 1.90579i	−0.303301	−	0.952895i	$-0.598089\pi$
$557$	− 44.9783i	− 1.90579i	0.303301	−	0.952895i	$-0.401911\pi$
$558$	− 6.74456i	− 0.285520i
$559$	18.9783	0.802694
$560$	0	0
$561$	−9.48913	−0.400631
$562$	− 14.0000i	− 0.590554i
$563$	− 17.4891i	− 0.737079i	−0.929612	−	0.368539i	$-0.879858\pi$
$563$	− 17.4891i	− 0.737079i	0.929612	−	0.368539i	$-0.120142\pi$
$564$	13.4891	0.567995
$565$	0	0
$566$	28.0000	1.17693
$567$	11.0000i	0.461957i
$568$	− 4.00000i	− 0.167836i
$569$	−39.4891	−1.65547	−0.827735	−	0.561119i	$-0.810371\pi$
$569$	−39.4891	−1.65547	−0.827735	+	0.561119i	$0.810371\pi$
$570$	0	0
$571$	5.48913	0.229713	0.114856	−	0.993382i	$-0.463359\pi$
$571$	5.48913	0.229713	0.114856	+	0.993382i	$0.463359\pi$
$572$	− 4.74456i	− 0.198380i
$573$	− 32.0000i	− 1.33682i
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 2.74456i	− 0.114258i	−0.998367	−	0.0571288i	$-0.981805\pi$
$577$	− 2.74456i	− 0.114258i	0.998367	−	0.0571288i	$-0.0181946\pi$
$578$	5.51087i	0.229222i
$579$	4.00000	0.166234
$580$	0	0
$581$	8.00000	0.331896
$582$	10.5109i	0.435690i
$583$	1.25544i	0.0519949i
$584$	0.744563	0.0308102
$585$	0	0
$586$	24.7446	1.02219
$587$	− 40.9783i	− 1.69135i	−0.533696	−	0.845677i	$-0.679197\pi$
$587$	− 40.9783i	− 1.69135i	0.533696	−	0.845677i	$-0.320803\pi$
$588$	2.00000i	0.0824786i
$589$	32.0000	1.31854
$590$	0	0
$591$	20.0000	0.822690
$592$	10.7446i	0.441599i
$593$	− 5.76631i	− 0.236794i	−0.992966	−	0.118397i	$-0.962224\pi$
$593$	− 5.76631i	− 0.236794i	0.992966	−	0.118397i	$-0.0377756\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	10.7446	0.440114
$597$	− 29.4891i	− 1.20691i
$598$	− 22.5109i	− 0.920538i
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−10.5109	−0.428748	−0.214374	−	0.976752i	$-0.568771\pi$
$601$	−10.5109	−0.428748	−0.214374	+	0.976752i	$0.568771\pi$
$602$	− 4.00000i	− 0.163028i
$603$	− 4.00000i	− 0.162893i
$604$	20.7446	0.844084
$605$	0	0
$606$	−17.4891	−0.710447
$607$	− 8.00000i	− 0.324710i	−0.986732	−	0.162355i	$-0.948091\pi$
$607$	− 8.00000i	− 0.324710i	0.986732	−	0.162355i	$-0.0519090\pi$
$608$	4.74456i	0.192417i
$609$	5.48913	0.222431
$610$	0	0
$611$	32.0000	1.29458
$612$	− 4.74456i	− 0.191788i
$613$	− 11.4891i	− 0.464041i	−0.972711	−	0.232021i	$-0.925466\pi$
$613$	− 11.4891i	− 0.464041i	0.972711	−	0.232021i	$-0.0745337\pi$
$614$	−21.4891	−0.867231
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	10.0000i	0.402585i	0.979531	+	0.201292i	$0.0645141\pi$
$617$	10.0000i	0.402585i	−0.979531	+	0.201292i	$0.935486\pi$
$618$	21.4891i	0.864419i
$619$	10.7446	0.431860	0.215930	−	0.976409i	$-0.430722\pi$
$619$	10.7446	0.431860	0.215930	+	0.976409i	$0.430722\pi$
$620$	0	0
$621$	−18.9783	−0.761571
$622$	9.25544i	0.371109i
$623$	− 7.48913i	− 0.300045i
$624$	9.48913	0.379869
$625$	0	0
$626$	32.2337	1.28832
$627$	9.48913i	0.378959i
$628$	23.4891i	0.937318i
$629$	50.9783	2.03264
$630$	0	0
$631$	42.9783	1.71094	0.855469	−	0.517855i	$-0.173269\pi$
$631$	42.9783	1.71094	0.855469	+	0.517855i	$0.173269\pi$
$632$	4.74456i	0.188729i
$633$	− 24.0000i	− 0.953914i
$634$	32.2337	1.28016
$635$	0	0
$636$	−2.51087	−0.0995627
$637$	4.74456i	0.187986i
$638$	2.74456i	0.108658i
$639$	4.00000	0.158238
$640$	0	0
$641$	−11.4891	−0.453793	−0.226897	−	0.973919i	$-0.572858\pi$
$641$	−11.4891	−0.453793	−0.226897	+	0.973919i	$0.572858\pi$
$642$	24.0000i	0.947204i
$643$	− 22.4674i	− 0.886027i	−0.896515	−	0.443013i	$-0.853909\pi$
$643$	− 22.4674i	− 0.886027i	0.896515	−	0.443013i	$-0.146091\pi$
$644$	−4.74456	−0.186962
$645$	0	0
$646$	22.5109	0.885679
$647$	2.74456i	0.107900i	0.998544	+	0.0539499i	$0.0171811\pi$
$647$	2.74456i	0.107900i	−0.998544	+	0.0539499i	$0.982819\pi$
$648$	− 11.0000i	− 0.432121i
$649$	2.74456	0.107734
$650$	0	0
$651$	−13.4891	−0.528681
$652$	4.00000i	0.156652i
$653$	− 41.7228i	− 1.63274i	−0.577529	−	0.816370i	$-0.695983\pi$
$653$	− 41.7228i	− 1.63274i	0.577529	−	0.816370i	$-0.304017\pi$
$654$	−32.4674	−1.26957
$655$	0	0
$656$	−4.00000	−0.156174
$657$	0.744563i	0.0290482i
$658$	− 6.74456i	− 0.262930i
$659$	18.5109	0.721081	0.360541	−	0.932744i	$-0.382592\pi$
$659$	18.5109	0.721081	0.360541	+	0.932744i	$0.382592\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	30.9783i	1.20400i
$663$	− 45.0217i	− 1.74850i
$664$	−8.00000	−0.310460
$665$	0	0
$666$	−10.7446	−0.416343
$667$	13.0217i	0.504204i
$668$	0	0
$669$	−53.4891	−2.06801
$670$	0	0
$671$	−12.7446	−0.491998
$672$	− 2.00000i	− 0.0771517i
$673$	− 24.9783i	− 0.962841i	−0.876490	−	0.481420i	$-0.840121\pi$
$673$	− 24.9783i	− 0.962841i	0.876490	−	0.481420i	$-0.159879\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	9.51087	0.365803
$677$	− 1.76631i	− 0.0678849i	−0.999424	−	0.0339424i	$-0.989194\pi$
$677$	− 1.76631i	− 0.0678849i	0.999424	−	0.0339424i	$-0.0108063\pi$
$678$	20.0000i	0.768095i
$679$	5.25544	0.201685
$680$	0	0
$681$	40.0000	1.53280
$682$	− 6.74456i	− 0.258263i
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	−4.74456	−0.181413
$685$	0	0
$686$	1.00000	0.0381802
$687$	12.0000i	0.457829i
$688$	4.00000i	0.152499i
$689$	−5.95650	−0.226925
$690$	0	0
$691$	36.2337	1.37839	0.689197	−	0.724574i	$-0.257963\pi$
$691$	36.2337	1.37839	0.689197	+	0.724574i	$0.257963\pi$
$692$	14.2337i	0.541084i
$693$	− 1.00000i	− 0.0379869i
$694$	−22.9783	−0.872242
$695$	0	0
$696$	−5.48913	−0.208065
$697$	18.9783i	0.718853i
$698$	19.2554i	0.728829i
$699$	−41.9565	−1.58694
$700$	0	0
$701$	−12.2337	−0.462060	−0.231030	−	0.972947i	$-0.574210\pi$
$701$	−12.2337	−0.462060	−0.231030	+	0.972947i	$0.574210\pi$
$702$	− 18.9783i	− 0.716288i
$703$	− 50.9783i	− 1.92268i
$704$	1.00000	0.0376889
$705$	0	0
$706$	−2.74456	−0.103293
$707$	8.74456i	0.328873i
$708$	5.48913i	0.206294i
$709$	−23.4891	−0.882153	−0.441076	−	0.897470i	$-0.645403\pi$
$709$	−23.4891	−0.882153	−0.441076	+	0.897470i	$0.645403\pi$
$710$	0	0
$711$	−4.74456	−0.177935
$712$	7.48913i	0.280667i
$713$	− 32.0000i	− 1.19841i
$714$	−9.48913	−0.355122
$715$	0	0
$716$	−4.00000	−0.149487
$717$	6.51087i	0.243153i
$718$	− 12.7446i	− 0.475623i
$719$	49.7228	1.85435	0.927174	−	0.374631i	$-0.122231\pi$
$719$	49.7228	1.85435	0.927174	+	0.374631i	$0.122231\pi$
$720$	0	0
$721$	10.7446	0.400148
$722$	− 3.51087i	− 0.130661i
$723$	40.0000i	1.48762i
$724$	−3.48913	−0.129672
$725$	0	0
$726$	2.00000	0.0742270
$727$	20.2337i	0.750426i	0.926939	+	0.375213i	$0.122430\pi$
$727$	20.2337i	0.750426i	−0.926939	+	0.375213i	$0.877570\pi$
$728$	− 4.74456i	− 0.175845i
$729$	−13.0000	−0.481481
$730$	0	0
$731$	18.9783	0.701936
$732$	− 25.4891i	− 0.942105i
$733$	18.2337i	0.673477i	0.941598	+	0.336738i	$0.109324\pi$
$733$	18.2337i	0.673477i	−0.941598	+	0.336738i	$0.890676\pi$
$734$	−2.74456	−0.101304
$735$	0	0
$736$	4.74456	0.174887
$737$	− 4.00000i	− 0.147342i
$738$	− 4.00000i	− 0.147242i
$739$	−14.9783	−0.550984	−0.275492	−	0.961303i	$-0.588841\pi$
$739$	−14.9783	−0.550984	−0.275492	+	0.961303i	$0.588841\pi$
$740$	0	0
$741$	−45.0217	−1.65392
$742$	1.25544i	0.0460886i
$743$	− 18.9783i	− 0.696244i	−0.937449	−	0.348122i	$-0.886819\pi$
$743$	− 18.9783i	− 0.696244i	0.937449	−	0.348122i	$-0.113181\pi$
$744$	13.4891	0.494535
$745$	0	0
$746$	28.9783	1.06097
$747$	− 8.00000i	− 0.292705i
$748$	− 4.74456i	− 0.173478i
$749$	12.0000	0.438470
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	6.74456i	0.245949i
$753$	16.4674i	0.600105i
$754$	−13.0217	−0.474224
$755$	0	0
$756$	−4.00000	−0.145479
$757$	30.7446i	1.11743i	0.829360	+	0.558715i	$0.188705\pi$
$757$	30.7446i	1.11743i	−0.829360	+	0.558715i	$0.811295\pi$
$758$	− 14.5109i	− 0.527059i
$759$	9.48913	0.344433
$760$	0	0
$761$	−6.51087	−0.236019	−0.118010	−	0.993012i	$-0.537651\pi$
$761$	−6.51087	−0.236019	−0.118010	+	0.993012i	$0.537651\pi$
$762$	0	0
$763$	16.2337i	0.587699i
$764$	16.0000	0.578860
$765$	0	0
$766$	−37.7228	−1.36298
$767$	13.0217i	0.470188i
$768$	2.00000i	0.0721688i
$769$	8.00000	0.288487	0.144244	−	0.989542i	$-0.453925\pi$
$769$	8.00000	0.288487	0.144244	+	0.989542i	$0.453925\pi$
$770$	0	0
$771$	48.4674	1.74551
$772$	2.00000i	0.0719816i
$773$	− 28.5109i	− 1.02546i	−0.858548	−	0.512732i	$-0.828633\pi$
$773$	− 28.5109i	− 1.02546i	0.858548	−	0.512732i	$-0.171367\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	−5.25544	−0.188659
$777$	21.4891i	0.770918i
$778$	15.4891i	0.555312i
$779$	18.9783	0.679966
$780$	0	0
$781$	4.00000	0.143131
$782$	− 22.5109i	− 0.804987i
$783$	10.9783i	0.392331i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	17.4891	0.623816
$787$	17.4891i	0.623420i	0.950177	+	0.311710i	$0.100902\pi$
$787$	17.4891i	0.623420i	−0.950177	+	0.311710i	$0.899098\pi$
$788$	10.0000i	0.356235i
$789$	37.9565	1.35129
$790$	0	0
$791$	10.0000	0.355559
$792$	1.00000i	0.0355335i
$793$	− 60.4674i	− 2.14726i
$794$	−12.5109	−0.443994
$795$	0	0
$796$	14.7446	0.522607
$797$	− 26.4674i	− 0.937523i	−0.883325	−	0.468761i	$-0.844700\pi$
$797$	− 26.4674i	− 0.937523i	0.883325	−	0.468761i	$-0.155300\pi$
$798$	9.48913i	0.335911i
$799$	32.0000	1.13208
$800$	0	0
$801$	−7.48913	−0.264615
$802$	− 0.510875i	− 0.0180396i
$803$	0.744563i	0.0262750i
$804$	8.00000	0.282138
$805$	0	0
$806$	32.0000	1.12715
$807$	49.9565i	1.75855i
$808$	− 8.74456i	− 0.307633i
$809$	34.4674	1.21181	0.605904	−	0.795538i	$-0.292811\pi$
$809$	34.4674	1.21181	0.605904	+	0.795538i	$0.292811\pi$
$810$	0	0
$811$	−7.25544	−0.254773	−0.127386	−	0.991853i	$-0.540659\pi$
$811$	−7.25544	−0.254773	−0.127386	+	0.991853i	$0.540659\pi$
$812$	2.74456i	0.0963153i
$813$	− 61.9565i	− 2.17291i
$814$	−10.7446	−0.376597
$815$	0	0
$816$	9.48913	0.332186
$817$	− 18.9783i	− 0.663965i
$818$	1.48913i	0.0520660i
$819$	4.74456	0.165788
$820$	0	0
$821$	−49.7228	−1.73534	−0.867669	−	0.497142i	$-0.834383\pi$
$821$	−49.7228	−1.73534	−0.867669	+	0.497142i	$0.834383\pi$
$822$	38.9783i	1.35952i
$823$	42.2337i	1.47217i	0.676887	+	0.736087i	$0.263329\pi$
$823$	42.2337i	1.47217i	−0.676887	+	0.736087i	$0.736671\pi$
$824$	−10.7446	−0.374305
$825$	0	0
$826$	2.74456	0.0954955
$827$	− 4.00000i	− 0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$	− 4.00000i	− 0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$	4.74456i	0.164885i
$829$	54.4674	1.89173	0.945865	−	0.324560i	$-0.105216\pi$
$829$	54.4674	1.89173	0.945865	+	0.324560i	$0.105216\pi$
$830$	0	0
$831$	−14.9783	−0.519590
$832$	4.74456i	0.164488i
$833$	4.74456i	0.164389i
$834$	−6.51087	−0.225453
$835$	0	0
$836$	−4.74456	−0.164094
$837$	− 26.9783i	− 0.932505i
$838$	10.7446i	0.371165i
$839$	14.7446	0.509039	0.254519	−	0.967068i	$-0.418083\pi$
$839$	14.7446	0.509039	0.254519	+	0.967068i	$0.418083\pi$
$840$	0	0
$841$	−21.4674	−0.740254
$842$	− 27.4891i	− 0.947338i
$843$	28.0000i	0.964371i
$844$	12.0000	0.413057
$845$	0	0
$846$	−6.74456	−0.231883
$847$	− 1.00000i	− 0.0343604i
$848$	− 1.25544i	− 0.0431119i
$849$	−56.0000	−1.92192
$850$	0	0
$851$	−50.9783	−1.74751
$852$	8.00000i	0.274075i
$853$	− 11.2554i	− 0.385379i	−0.981260	−	0.192689i	$-0.938279\pi$
$853$	− 11.2554i	− 0.385379i	0.981260	−	0.192689i	$-0.0617210\pi$
$854$	−12.7446	−0.436110
$855$	0	0
$856$	−12.0000	−0.410152
$857$	− 37.2119i	− 1.27114i	−0.772045	−	0.635568i	$-0.780766\pi$
$857$	− 37.2119i	− 1.27114i	0.772045	−	0.635568i	$-0.219234\pi$
$858$	9.48913i	0.323953i
$859$	−51.2119	−1.74733	−0.873664	−	0.486529i	$-0.838263\pi$
$859$	−51.2119	−1.74733	−0.873664	+	0.486529i	$0.838263\pi$
$860$	0	0
$861$	−8.00000	−0.272639
$862$	28.7446i	0.979044i
$863$	− 5.76631i	− 0.196288i	−0.995172	−	0.0981438i	$-0.968709\pi$
$863$	− 5.76631i	− 0.196288i	0.995172	−	0.0981438i	$-0.0312905\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	25.2554	0.858215
$867$	− 11.0217i	− 0.374318i
$868$	− 6.74456i	− 0.228925i
$869$	−4.74456	−0.160948
$870$	0	0
$871$	18.9783	0.643053
$872$	− 16.2337i	− 0.549742i
$873$	− 5.25544i	− 0.177870i
$874$	−22.5109	−0.761442
$875$	0	0
$876$	−1.48913	−0.0503129
$877$	− 42.4674i	− 1.43402i	−0.697062	−	0.717011i	$-0.745510\pi$
$877$	− 42.4674i	− 1.43402i	0.697062	−	0.717011i	$-0.254490\pi$
$878$	− 30.9783i	− 1.04547i
$879$	−49.4891	−1.66923
$880$	0	0
$881$	−32.5109	−1.09532	−0.547660	−	0.836701i	$-0.684481\pi$
$881$	−32.5109	−1.09532	−0.547660	+	0.836701i	$0.684481\pi$
$882$	− 1.00000i	− 0.0336718i
$883$	− 8.00000i	− 0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$	− 8.00000i	− 0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	22.5109	0.757123
$885$	0	0
$886$	−6.51087	−0.218737
$887$	18.5109i	0.621534i	0.950486	+	0.310767i	$0.100586\pi$
$887$	18.5109i	0.621534i	−0.950486	+	0.310767i	$0.899414\pi$
$888$	− 21.4891i	− 0.721128i
$889$	0	0
$890$	0	0
$891$	11.0000	0.368514
$892$	− 26.7446i	− 0.895474i
$893$	− 32.0000i	− 1.07084i
$894$	−21.4891	−0.718704
$895$	0	0
$896$	1.00000	0.0334077
$897$	45.0217i	1.50323i
$898$	40.9783i	1.36746i
$899$	−18.5109	−0.617372
$900$	0	0
$901$	−5.95650	−0.198440
$902$	− 4.00000i	− 0.133185i
$903$	8.00000i	0.266223i
$904$	−10.0000	−0.332595
$905$	0	0
$906$	−41.4891	−1.37838
$907$	37.4891i	1.24481i	0.782697	+	0.622403i	$0.213843\pi$
$907$	37.4891i	1.24481i	−0.782697	+	0.622403i	$0.786157\pi$
$908$	20.0000i	0.663723i
$909$	8.74456	0.290039
$910$	0	0
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	− 9.48913i	− 0.314216i
$913$	− 8.00000i	− 0.264761i
$914$	19.4891	0.644643
$915$	0	0
$916$	−6.00000	−0.198246
$917$	− 8.74456i	− 0.288771i
$918$	− 18.9783i	− 0.626376i
$919$	−25.2119	−0.831665	−0.415833	−	0.909441i	$-0.636510\pi$
$919$	−25.2119	−0.831665	−0.415833	+	0.909441i	$0.636510\pi$
$920$	0	0
$921$	42.9783	1.41618
$922$	23.7228i	0.781269i
$923$	18.9783i	0.624677i
$924$	2.00000	0.0657952
$925$	0	0
$926$	12.7446	0.418812
$927$	− 10.7446i	− 0.352898i
$928$	− 2.74456i	− 0.0900947i
$929$	−16.9783	−0.557038	−0.278519	−	0.960431i	$-0.589844\pi$
$929$	−16.9783	−0.557038	−0.278519	+	0.960431i	$0.589844\pi$
$930$	0	0
$931$	4.74456	0.155497
$932$	− 20.9783i	− 0.687165i
$933$	− 18.5109i	− 0.606019i
$934$	28.9783	0.948197
$935$	0	0
$936$	−4.74456	−0.155081
$937$	7.25544i	0.237025i	0.992953	+	0.118512i	$0.0378125\pi$
$937$	7.25544i	0.237025i	−0.992953	+	0.118512i	$0.962187\pi$
$938$	− 4.00000i	− 0.130605i
$939$	−64.4674	−2.10381
$940$	0	0
$941$	−22.2337	−0.724798	−0.362399	−	0.932023i	$-0.618042\pi$
$941$	−22.2337	−0.724798	−0.362399	+	0.932023i	$0.618042\pi$
$942$	− 46.9783i	− 1.53063i
$943$	− 18.9783i	− 0.618017i
$944$	−2.74456	−0.0893279
$945$	0	0
$946$	−4.00000	−0.130051
$947$	8.00000i	0.259965i	0.991516	+	0.129983i	$0.0414921\pi$
$947$	8.00000i	0.259965i	−0.991516	+	0.129983i	$0.958508\pi$
$948$	− 9.48913i	− 0.308192i
$949$	−3.53262	−0.114674
$950$	0	0
$951$	−64.4674	−2.09050
$952$	− 4.74456i	− 0.153772i
$953$	6.00000i	0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$	6.00000i	0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	1.25544	0.0406463
$955$	0	0
$956$	−3.25544	−0.105288
$957$	− 5.48913i	− 0.177438i
$958$	− 18.5109i	− 0.598059i
$959$	19.4891	0.629337
$960$	0	0
$961$	14.4891	0.467391
$962$	− 50.9783i	− 1.64360i
$963$	− 12.0000i	− 0.386695i
$964$	−20.0000	−0.644157
$965$	0	0
$966$	9.48913	0.305308
$967$	5.02175i	0.161489i	0.996735	+	0.0807443i	$0.0257297\pi$
$967$	5.02175i	0.161489i	−0.996735	+	0.0807443i	$0.974270\pi$
$968$	1.00000i	0.0321412i
$969$	−45.0217	−1.44631
$970$	0	0
$971$	−37.7228	−1.21058	−0.605291	−	0.796004i	$-0.706943\pi$
$971$	−37.7228	−1.21058	−0.605291	+	0.796004i	$0.706943\pi$
$972$	10.0000i	0.320750i
$973$	3.25544i	0.104365i
$974$	−20.7446	−0.664699
$975$	0	0
$976$	12.7446	0.407944
$977$	32.9783i	1.05507i	0.849534	+	0.527534i	$0.176883\pi$
$977$	32.9783i	1.05507i	−0.849534	+	0.527534i	$0.823117\pi$
$978$	− 8.00000i	− 0.255812i
$979$	−7.48913	−0.239353
$980$	0	0
$981$	16.2337	0.518302
$982$	14.9783i	0.477975i
$983$	− 32.2337i	− 1.02809i	−0.857762	−	0.514047i	$-0.828146\pi$
$983$	− 32.2337i	− 1.02809i	0.857762	−	0.514047i	$-0.171854\pi$
$984$	8.00000	0.255031
$985$	0	0
$986$	−13.0217	−0.414697
$987$	13.4891i	0.429364i
$988$	− 22.5109i	− 0.716166i
$989$	−18.9783	−0.603473
$990$	0	0
$991$	−21.4891	−0.682625	−0.341312	−	0.939950i	$-0.610871\pi$
$991$	−21.4891	−0.682625	−0.341312	+	0.939950i	$0.610871\pi$
$992$	6.74456i	0.214140i
$993$	− 61.9565i	− 1.96613i
$994$	4.00000	0.126872
$995$	0	0
$996$	16.0000	0.506979
$997$	41.2119i	1.30520i	0.757705	+	0.652598i	$0.226321\pi$
$997$	41.2119i	1.30520i	−0.757705	+	0.652598i	$0.773679\pi$
$998$	9.48913i	0.300373i
$999$	−42.9783	−1.35977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.y.1849.1		4
5.2	odd	4		770.2.a.k.1.1	✓	2
5.3	odd	4		3850.2.a.bc.1.2		2
5.4	even	2	inner	3850.2.c.y.1849.4		4
15.2	even	4		6930.2.a.bo.1.1		2
20.7	even	4		6160.2.a.r.1.1		2
35.27	even	4		5390.2.a.bq.1.2		2
55.32	even	4		8470.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.k.1.1	✓	2	5.2	odd	4
3850.2.a.bc.1.2		2	5.3	odd	4
3850.2.c.y.1849.1		4	1.1	even	1	trivial
3850.2.c.y.1849.4		4	5.4	even	2	inner
5390.2.a.bq.1.2		2	35.27	even	4
6160.2.a.r.1.1		2	20.7	even	4
6930.2.a.bo.1.1		2	15.2	even	4
8470.2.a.bu.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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.00000 q^{11} -2.00000i q^{12} -4.74456i q^{13} -1.00000 q^{14} +1.00000 q^{16} -4.74456i q^{17} +1.00000i q^{18} -4.74456 q^{19} +2.00000 q^{21} +1.00000i q^{22} +4.74456i q^{23} -2.00000 q^{24} -4.74456 q^{26} +4.00000i q^{27} +1.00000i q^{28} +2.74456 q^{29} -6.74456 q^{31} -1.00000i q^{32} -2.00000i q^{33} -4.74456 q^{34} +1.00000 q^{36} +10.7446i q^{37} +4.74456i q^{38} +9.48913 q^{39} -4.00000 q^{41} -2.00000i q^{42} +4.00000i q^{43} +1.00000 q^{44} +4.74456 q^{46} +6.74456i q^{47} +2.00000i q^{48} -1.00000 q^{49} +9.48913 q^{51} +4.74456i q^{52} -1.25544i q^{53} +4.00000 q^{54} +1.00000 q^{56} -9.48913i q^{57} -2.74456i q^{58} -2.74456 q^{59} +12.7446 q^{61} +6.74456i q^{62} +1.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +4.00000i q^{67} +4.74456i q^{68} -9.48913 q^{69} -4.00000 q^{71} -1.00000i q^{72} -0.744563i q^{73} +10.7446 q^{74} +4.74456 q^{76} +1.00000i q^{77} -9.48913i q^{78} +4.74456 q^{79} -11.0000 q^{81} +4.00000i q^{82} +8.00000i q^{83} -2.00000 q^{84} +4.00000 q^{86} +5.48913i q^{87} -1.00000i q^{88} +7.48913 q^{89} -4.74456 q^{91} -4.74456i q^{92} -13.4891i q^{93} +6.74456 q^{94} +2.00000 q^{96} +5.25544i q^{97} +1.00000i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9} - 4 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 8 q^{21} - 8 q^{24} + 4 q^{26} - 12 q^{29} - 4 q^{31} + 4 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 4 q^{46} - 4 q^{49} - 8 q^{51} + 16 q^{54} + 4 q^{56} + 12 q^{59} + 28 q^{61} - 4 q^{64} - 8 q^{66} + 8 q^{69} - 16 q^{71} + 20 q^{74} - 4 q^{76} - 4 q^{79} - 44 q^{81} - 8 q^{84} + 16 q^{86} - 16 q^{89} + 4 q^{91} + 4 q^{94} + 8 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9 - 4 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 8 * q^21 - 8 * q^24 + 4 * q^26 - 12 * q^29 - 4 * q^31 + 4 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 4 * q^46 - 4 * q^49 - 8 * q^51 + 16 * q^54 + 4 * q^56 + 12 * q^59 + 28 * q^61 - 4 * q^64 - 8 * q^66 + 8 * q^69 - 16 * q^71 + 20 * q^74 - 4 * q^76 - 4 * q^79 - 44 * q^81 - 8 * q^84 + 16 * q^86 - 16 * q^89 + 4 * q^91 + 4 * q^94 + 8 * q^96 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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