LMFDB - Embedded newform 1050.4.g.n.799.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,4,Mod(799,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.799"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1050.g (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-8,0,12,0,0,-18,0,-16,0,0,28,0,32,0,0,248] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$61.9520055060$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1050.799
Dual form			1050.4.g.n.799.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} -8.00000 q^{11} -12.0000i q^{12} -42.0000i q^{13} +14.0000 q^{14} +16.0000 q^{16} +2.00000i q^{17} +18.0000i q^{18} +124.000 q^{19} -21.0000 q^{21} +16.0000i q^{22} +76.0000i q^{23} -24.0000 q^{24} -84.0000 q^{26} -27.0000i q^{27} -28.0000i q^{28} -254.000 q^{29} -72.0000 q^{31} -32.0000i q^{32} -24.0000i q^{33} +4.00000 q^{34} +36.0000 q^{36} -398.000i q^{37} -248.000i q^{38} +126.000 q^{39} +462.000 q^{41} +42.0000i q^{42} +212.000i q^{43} +32.0000 q^{44} +152.000 q^{46} +264.000i q^{47} +48.0000i q^{48} -49.0000 q^{49} -6.00000 q^{51} +168.000i q^{52} -162.000i q^{53} -54.0000 q^{54} -56.0000 q^{56} +372.000i q^{57} +508.000i q^{58} +772.000 q^{59} +30.0000 q^{61} +144.000i q^{62} -63.0000i q^{63} -64.0000 q^{64} -48.0000 q^{66} +764.000i q^{67} -8.00000i q^{68} -228.000 q^{69} -236.000 q^{71} -72.0000i q^{72} +418.000i q^{73} -796.000 q^{74} -496.000 q^{76} -56.0000i q^{77} -252.000i q^{78} -552.000 q^{79} +81.0000 q^{81} -924.000i q^{82} +1036.00i q^{83} +84.0000 q^{84} +424.000 q^{86} -762.000i q^{87} -64.0000i q^{88} -30.0000 q^{89} +294.000 q^{91} -304.000i q^{92} -216.000i q^{93} +528.000 q^{94} +96.0000 q^{96} +1190.00i q^{97} +98.0000i q^{98} +72.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} - 16 q^{11} + 28 q^{14} + 32 q^{16} + 248 q^{19} - 42 q^{21} - 48 q^{24} - 168 q^{26} - 508 q^{29} - 144 q^{31} + 8 q^{34} + 72 q^{36} + 252 q^{39} + 924 q^{41} + 64 q^{44}+ \cdots + 144 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 - 16 * q^11 + 28 * q^14 + 32 * q^16 + 248 * q^19 - 42 * q^21 - 48 * q^24 - 168 * q^26 - 508 * q^29 - 144 * q^31 + 8 * q^34 + 72 * q^36 + 252 * q^39 + 924 * q^41 + 64 * q^44 + 304 * q^46 - 98 * q^49 - 12 * q^51 - 108 * q^54 - 112 * q^56 + 1544 * q^59 + 60 * q^61 - 128 * q^64 - 96 * q^66 - 456 * q^69 - 472 * q^71 - 1592 * q^74 - 992 * q^76 - 1104 * q^79 + 162 * q^81 + 168 * q^84 + 848 * q^86 - 60 * q^89 + 588 * q^91 + 1056 * q^94 + 192 * q^96 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	8.00000i	0.353553i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−8.00000	−0.219281	−0.109640	−	0.993971i	$-0.534970\pi$
$11$	−8.00000	−0.219281	−0.109640	+	0.993971i	$0.534970\pi$
$12$	− 12.0000i	− 0.288675i
$13$	− 42.0000i	− 0.896054i	−0.894020	−	0.448027i	$-0.852127\pi$
$13$	− 42.0000i	− 0.896054i	0.894020	−	0.448027i	$-0.147873\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	2.00000i	0.0285336i	0.999898	+	0.0142668i	$0.00454142\pi$
$17$	2.00000i	0.0285336i	−0.999898	+	0.0142668i	$0.995459\pi$
$18$	18.0000i	0.235702i
$19$	124.000	1.49724	0.748620	−	0.663000i	$-0.230717\pi$
$19$	124.000	1.49724	0.748620	+	0.663000i	$0.230717\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	16.0000i	0.155055i
$23$	76.0000i	0.689004i	0.938786	+	0.344502i	$0.111952\pi$
$23$	76.0000i	0.689004i	−0.938786	+	0.344502i	$0.888048\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	−84.0000	−0.633606
$27$	− 27.0000i	− 0.192450i
$28$	− 28.0000i	− 0.188982i
$29$	−254.000	−1.62644	−0.813218	−	0.581960i	$-0.802286\pi$
$29$	−254.000	−1.62644	−0.813218	+	0.581960i	$0.802286\pi$
$30$	0	0
$31$	−72.0000	−0.417148	−0.208574	−	0.978007i	$-0.566882\pi$
$31$	−72.0000	−0.417148	−0.208574	+	0.978007i	$0.566882\pi$
$32$	− 32.0000i	− 0.176777i
$33$	− 24.0000i	− 0.126602i
$34$	4.00000	0.0201763
$35$	0	0
$36$	36.0000	0.166667
$37$	− 398.000i	− 1.76840i	−0.467109	−	0.884200i	$-0.654704\pi$
$37$	− 398.000i	− 1.76840i	0.467109	−	0.884200i	$-0.345296\pi$
$38$	− 248.000i	− 1.05871i
$39$	126.000	0.517337
$40$	0	0
$41$	462.000	1.75981	0.879906	−	0.475148i	$-0.157606\pi$
$41$	462.000	1.75981	0.879906	+	0.475148i	$0.157606\pi$
$42$	42.0000i	0.154303i
$43$	212.000i	0.751853i	0.926649	+	0.375927i	$0.122676\pi$
$43$	212.000i	0.751853i	−0.926649	+	0.375927i	$0.877324\pi$
$44$	32.0000	0.109640
$45$	0	0
$46$	152.000	0.487200
$47$	264.000i	0.819327i	0.912237	+	0.409663i	$0.134354\pi$
$47$	264.000i	0.819327i	−0.912237	+	0.409663i	$0.865646\pi$
$48$	48.0000i	0.144338i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−6.00000	−0.0164739
$52$	168.000i	0.448027i
$53$	− 162.000i	− 0.419857i	−0.977717	−	0.209928i	$-0.932677\pi$
$53$	− 162.000i	− 0.419857i	0.977717	−	0.209928i	$-0.0673231\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	−56.0000	−0.133631
$57$	372.000i	0.864432i
$58$	508.000i	1.15006i
$59$	772.000	1.70349	0.851744	−	0.523958i	$-0.175545\pi$
$59$	772.000	1.70349	0.851744	+	0.523958i	$0.175545\pi$
$60$	0	0
$61$	30.0000	0.0629690	0.0314845	−	0.999504i	$-0.489977\pi$
$61$	30.0000	0.0629690	0.0314845	+	0.999504i	$0.489977\pi$
$62$	144.000i	0.294968i
$63$	− 63.0000i	− 0.125988i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	−48.0000	−0.0895211
$67$	764.000i	1.39310i	0.717510	+	0.696548i	$0.245282\pi$
$67$	764.000i	1.39310i	−0.717510	+	0.696548i	$0.754718\pi$
$68$	− 8.00000i	− 0.0142668i
$69$	−228.000	−0.397797
$70$	0	0
$71$	−236.000	−0.394480	−0.197240	−	0.980355i	$-0.563198\pi$
$71$	−236.000	−0.394480	−0.197240	+	0.980355i	$0.563198\pi$
$72$	− 72.0000i	− 0.117851i
$73$	418.000i	0.670181i	0.942186	+	0.335090i	$0.108767\pi$
$73$	418.000i	0.670181i	−0.942186	+	0.335090i	$0.891233\pi$
$74$	−796.000	−1.25045
$75$	0	0
$76$	−496.000	−0.748620
$77$	− 56.0000i	− 0.0828804i
$78$	− 252.000i	− 0.365813i
$79$	−552.000	−0.786137	−0.393069	−	0.919509i	$-0.628587\pi$
$79$	−552.000	−0.786137	−0.393069	+	0.919509i	$0.628587\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 924.000i	− 1.24437i
$83$	1036.00i	1.37007i	0.728510	+	0.685035i	$0.240213\pi$
$83$	1036.00i	1.37007i	−0.728510	+	0.685035i	$0.759787\pi$
$84$	84.0000	0.109109
$85$	0	0
$86$	424.000	0.531641
$87$	− 762.000i	− 0.939023i
$88$	− 64.0000i	− 0.0775275i
$89$	−30.0000	−0.0357303	−0.0178651	−	0.999840i	$-0.505687\pi$
$89$	−30.0000	−0.0357303	−0.0178651	+	0.999840i	$0.505687\pi$
$90$	0	0
$91$	294.000	0.338677
$92$	− 304.000i	− 0.344502i
$93$	− 216.000i	− 0.240840i
$94$	528.000	0.579352
$95$	0	0
$96$	96.0000	0.102062
$97$	1190.00i	1.24563i	0.782369	+	0.622815i	$0.214011\pi$
$97$	1190.00i	1.24563i	−0.782369	+	0.622815i	$0.785989\pi$
$98$	98.0000i	0.101015i
$99$	72.0000	0.0730937
$100$	0	0
$101$	1370.00	1.34970	0.674852	−	0.737953i	$-0.264207\pi$
$101$	1370.00	1.34970	0.674852	+	0.737953i	$0.264207\pi$
$102$	12.0000i	0.0116488i
$103$	464.000i	0.443876i	0.975061	+	0.221938i	$0.0712383\pi$
$103$	464.000i	0.443876i	−0.975061	+	0.221938i	$0.928762\pi$
$104$	336.000	0.316803
$105$	0	0
$106$	−324.000	−0.296884
$107$	2136.00i	1.92986i	0.262509	+	0.964930i	$0.415450\pi$
$107$	2136.00i	1.92986i	−0.262509	+	0.964930i	$0.584550\pi$
$108$	108.000i	0.0962250i
$109$	1226.00	1.07733	0.538667	−	0.842518i	$-0.318928\pi$
$109$	1226.00	1.07733	0.538667	+	0.842518i	$0.318928\pi$
$110$	0	0
$111$	1194.00	1.02099
$112$	112.000i	0.0944911i
$113$	338.000i	0.281384i	0.990053	+	0.140692i	$0.0449327\pi$
$113$	338.000i	0.281384i	−0.990053	+	0.140692i	$0.955067\pi$
$114$	744.000	0.611245
$115$	0	0
$116$	1016.00	0.813218
$117$	378.000i	0.298685i
$118$	− 1544.00i	− 1.20455i
$119$	−14.0000	−0.0107847
$120$	0	0
$121$	−1267.00	−0.951916
$122$	− 60.0000i	− 0.0445258i
$123$	1386.00i	1.01603i
$124$	288.000	0.208574
$125$	0	0
$126$	−126.000	−0.0890871
$127$	− 2088.00i	− 1.45890i	−0.684035	−	0.729449i	$-0.739777\pi$
$127$	− 2088.00i	− 1.45890i	0.684035	−	0.729449i	$-0.260223\pi$
$128$	128.000i	0.0883883i
$129$	−636.000	−0.434083
$130$	0	0
$131$	−292.000	−0.194749	−0.0973747	−	0.995248i	$-0.531045\pi$
$131$	−292.000	−0.194749	−0.0973747	+	0.995248i	$0.531045\pi$
$132$	96.0000i	0.0633010i
$133$	868.000i	0.565903i
$134$	1528.00	0.985068
$135$	0	0
$136$	−16.0000	−0.0100882
$137$	− 818.000i	− 0.510120i	−0.966925	−	0.255060i	$-0.917905\pi$
$137$	− 818.000i	− 0.510120i	0.966925	−	0.255060i	$-0.0820952\pi$
$138$	456.000i	0.281285i
$139$	2156.00	1.31561	0.657804	−	0.753189i	$-0.271485\pi$
$139$	2156.00	1.31561	0.657804	+	0.753189i	$0.271485\pi$
$140$	0	0
$141$	−792.000	−0.473039
$142$	472.000i	0.278939i
$143$	336.000i	0.196488i
$144$	−144.000	−0.0833333
$145$	0	0
$146$	836.000	0.473889
$147$	− 147.000i	− 0.0824786i
$148$	1592.00i	0.884200i
$149$	2850.00	1.56699	0.783494	−	0.621400i	$-0.213436\pi$
$149$	2850.00	1.56699	0.783494	+	0.621400i	$0.213436\pi$
$150$	0	0
$151$	1672.00	0.901096	0.450548	−	0.892752i	$-0.351229\pi$
$151$	1672.00	0.901096	0.450548	+	0.892752i	$0.351229\pi$
$152$	992.000i	0.529354i
$153$	− 18.0000i	− 0.00951120i
$154$	−112.000	−0.0586053
$155$	0	0
$156$	−504.000	−0.258669
$157$	− 446.000i	− 0.226718i	−0.993554	−	0.113359i	$-0.963839\pi$
$157$	− 446.000i	− 0.226718i	0.993554	−	0.113359i	$-0.0361610\pi$
$158$	1104.00i	0.555883i
$159$	486.000	0.242404
$160$	0	0
$161$	−532.000	−0.260419
$162$	− 162.000i	− 0.0785674i
$163$	2708.00i	1.30127i	0.759391	+	0.650635i	$0.225497\pi$
$163$	2708.00i	1.30127i	−0.759391	+	0.650635i	$0.774503\pi$
$164$	−1848.00	−0.879906
$165$	0	0
$166$	2072.00	0.968785
$167$	− 896.000i	− 0.415177i	−0.978216	−	0.207589i	$-0.933439\pi$
$167$	− 896.000i	− 0.415177i	0.978216	−	0.207589i	$-0.0665615\pi$
$168$	− 168.000i	− 0.0771517i
$169$	433.000	0.197087
$170$	0	0
$171$	−1116.00	−0.499080
$172$	− 848.000i	− 0.375927i
$173$	4034.00i	1.77283i	0.462893	+	0.886414i	$0.346811\pi$
$173$	4034.00i	1.77283i	−0.462893	+	0.886414i	$0.653189\pi$
$174$	−1524.00	−0.663989
$175$	0	0
$176$	−128.000	−0.0548202
$177$	2316.00i	0.983510i
$178$	60.0000i	0.0252651i
$179$	3480.00	1.45311	0.726557	−	0.687106i	$-0.241119\pi$
$179$	3480.00	1.45311	0.726557	+	0.687106i	$0.241119\pi$
$180$	0	0
$181$	−2898.00	−1.19009	−0.595046	−	0.803692i	$-0.702866\pi$
$181$	−2898.00	−1.19009	−0.595046	+	0.803692i	$0.702866\pi$
$182$	− 588.000i	− 0.239481i
$183$	90.0000i	0.0363551i
$184$	−608.000	−0.243600
$185$	0	0
$186$	−432.000	−0.170300
$187$	− 16.0000i	− 0.00625688i
$188$	− 1056.00i	− 0.409663i
$189$	189.000	0.0727393
$190$	0	0
$191$	2652.00	1.00467	0.502335	−	0.864673i	$-0.332474\pi$
$191$	2652.00	1.00467	0.502335	+	0.864673i	$0.332474\pi$
$192$	− 192.000i	− 0.0721688i
$193$	146.000i	0.0544524i	0.999629	+	0.0272262i	$0.00866744\pi$
$193$	146.000i	0.0544524i	−0.999629	+	0.0272262i	$0.991333\pi$
$194$	2380.00	0.880794
$195$	0	0
$196$	196.000	0.0714286
$197$	2546.00i	0.920787i	0.887715	+	0.460393i	$0.152292\pi$
$197$	2546.00i	0.920787i	−0.887715	+	0.460393i	$0.847708\pi$
$198$	− 144.000i	− 0.0516850i
$199$	2536.00	0.903378	0.451689	−	0.892175i	$-0.350822\pi$
$199$	2536.00	0.903378	0.451689	+	0.892175i	$0.350822\pi$
$200$	0	0
$201$	−2292.00	−0.804305
$202$	− 2740.00i	− 0.954385i
$203$	− 1778.00i	− 0.614735i
$204$	24.0000	0.00823694
$205$	0	0
$206$	928.000	0.313868
$207$	− 684.000i	− 0.229668i
$208$	− 672.000i	− 0.224014i
$209$	−992.000	−0.328316
$210$	0	0
$211$	−1300.00	−0.424150	−0.212075	−	0.977253i	$-0.568022\pi$
$211$	−1300.00	−0.424150	−0.212075	+	0.977253i	$0.568022\pi$
$212$	648.000i	0.209928i
$213$	− 708.000i	− 0.227753i
$214$	4272.00	1.36462
$215$	0	0
$216$	216.000	0.0680414
$217$	− 504.000i	− 0.157667i
$218$	− 2452.00i	− 0.761791i
$219$	−1254.00	−0.386929
$220$	0	0
$221$	84.0000	0.0255677
$222$	− 2388.00i	− 0.721946i
$223$	2576.00i	0.773550i	0.922174	+	0.386775i	$0.126411\pi$
$223$	2576.00i	0.773550i	−0.922174	+	0.386775i	$0.873589\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	676.000	0.198968
$227$	1836.00i	0.536826i	0.963304	+	0.268413i	$0.0864993\pi$
$227$	1836.00i	0.536826i	−0.963304	+	0.268413i	$0.913501\pi$
$228$	− 1488.00i	− 0.432216i
$229$	1874.00	0.540775	0.270387	−	0.962752i	$-0.412848\pi$
$229$	1874.00	0.540775	0.270387	+	0.962752i	$0.412848\pi$
$230$	0	0
$231$	168.000	0.0478510
$232$	− 2032.00i	− 0.575032i
$233$	3730.00i	1.04876i	0.851485	+	0.524379i	$0.175702\pi$
$233$	3730.00i	1.04876i	−0.851485	+	0.524379i	$0.824298\pi$
$234$	756.000	0.211202
$235$	0	0
$236$	−3088.00	−0.851744
$237$	− 1656.00i	− 0.453877i
$238$	28.0000i	0.00762593i
$239$	−2004.00	−0.542377	−0.271188	−	0.962526i	$-0.587417\pi$
$239$	−2004.00	−0.542377	−0.271188	+	0.962526i	$0.587417\pi$
$240$	0	0
$241$	−646.000	−0.172666	−0.0863330	−	0.996266i	$-0.527515\pi$
$241$	−646.000	−0.172666	−0.0863330	+	0.996266i	$0.527515\pi$
$242$	2534.00i	0.673106i
$243$	243.000i	0.0641500i
$244$	−120.000	−0.0314845
$245$	0	0
$246$	2772.00	0.718440
$247$	− 5208.00i	− 1.34161i
$248$	− 576.000i	− 0.147484i
$249$	−3108.00	−0.791010
$250$	0	0
$251$	1260.00	0.316855	0.158427	−	0.987371i	$-0.449358\pi$
$251$	1260.00	0.316855	0.158427	+	0.987371i	$0.449358\pi$
$252$	252.000i	0.0629941i
$253$	− 608.000i	− 0.151086i
$254$	−4176.00	−1.03160
$255$	0	0
$256$	256.000	0.0625000
$257$	− 5910.00i	− 1.43446i	−0.696838	−	0.717229i	$-0.745410\pi$
$257$	− 5910.00i	− 1.43446i	0.696838	−	0.717229i	$-0.254590\pi$
$258$	1272.00i	0.306943i
$259$	2786.00	0.668392
$260$	0	0
$261$	2286.00	0.542145
$262$	584.000i	0.137709i
$263$	2988.00i	0.700563i	0.936645	+	0.350281i	$0.113914\pi$
$263$	2988.00i	0.700563i	−0.936645	+	0.350281i	$0.886086\pi$
$264$	192.000	0.0447605
$265$	0	0
$266$	1736.00	0.400154
$267$	− 90.0000i	− 0.0206289i
$268$	− 3056.00i	− 0.696548i
$269$	1318.00	0.298736	0.149368	−	0.988782i	$-0.452276\pi$
$269$	1318.00	0.298736	0.149368	+	0.988782i	$0.452276\pi$
$270$	0	0
$271$	−5640.00	−1.26423	−0.632114	−	0.774876i	$-0.717812\pi$
$271$	−5640.00	−1.26423	−0.632114	+	0.774876i	$0.717812\pi$
$272$	32.0000i	0.00713340i
$273$	882.000i	0.195535i
$274$	−1636.00	−0.360709
$275$	0	0
$276$	912.000	0.198898
$277$	− 6446.00i	− 1.39820i	−0.715022	−	0.699102i	$-0.753583\pi$
$277$	− 6446.00i	− 1.39820i	0.715022	−	0.699102i	$-0.246417\pi$
$278$	− 4312.00i	− 0.930275i
$279$	648.000	0.139049
$280$	0	0
$281$	4930.00	1.04662	0.523308	−	0.852144i	$-0.324698\pi$
$281$	4930.00	1.04662	0.523308	+	0.852144i	$0.324698\pi$
$282$	1584.00i	0.334489i
$283$	− 6260.00i	− 1.31491i	−0.753496	−	0.657453i	$-0.771634\pi$
$283$	− 6260.00i	− 1.31491i	0.753496	−	0.657453i	$-0.228366\pi$
$284$	944.000	0.197240
$285$	0	0
$286$	672.000	0.138938
$287$	3234.00i	0.665146i
$288$	288.000i	0.0589256i
$289$	4909.00	0.999186
$290$	0	0
$291$	−3570.00	−0.719165
$292$	− 1672.00i	− 0.335090i
$293$	− 2310.00i	− 0.460586i	−0.973121	−	0.230293i	$-0.926032\pi$
$293$	− 2310.00i	− 0.460586i	0.973121	−	0.230293i	$-0.0739684\pi$
$294$	−294.000	−0.0583212
$295$	0	0
$296$	3184.00	0.625224
$297$	216.000i	0.0422006i
$298$	− 5700.00i	− 1.10803i
$299$	3192.00	0.617385
$300$	0	0
$301$	−1484.00	−0.284174
$302$	− 3344.00i	− 0.637171i
$303$	4110.00i	0.779252i
$304$	1984.00	0.374310
$305$	0	0
$306$	−36.0000	−0.00672543
$307$	− 196.000i	− 0.0364375i	−0.999834	−	0.0182187i	$-0.994200\pi$
$307$	− 196.000i	− 0.0364375i	0.999834	−	0.0182187i	$-0.00579953\pi$
$308$	224.000i	0.0414402i
$309$	−1392.00	−0.256272
$310$	0	0
$311$	−6736.00	−1.22818	−0.614089	−	0.789237i	$-0.710477\pi$
$311$	−6736.00	−1.22818	−0.614089	+	0.789237i	$0.710477\pi$
$312$	1008.00i	0.182906i
$313$	394.000i	0.0711508i	0.999367	+	0.0355754i	$0.0113264\pi$
$313$	394.000i	0.0711508i	−0.999367	+	0.0355754i	$0.988674\pi$
$314$	−892.000	−0.160314
$315$	0	0
$316$	2208.00	0.393069
$317$	6714.00i	1.18958i	0.803882	+	0.594788i	$0.202764\pi$
$317$	6714.00i	1.18958i	−0.803882	+	0.594788i	$0.797236\pi$
$318$	− 972.000i	− 0.171406i
$319$	2032.00	0.356646
$320$	0	0
$321$	−6408.00	−1.11420
$322$	1064.00i	0.184144i
$323$	248.000i	0.0427216i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	5416.00	0.920136
$327$	3678.00i	0.622000i
$328$	3696.00i	0.622187i
$329$	−1848.00	−0.309676
$330$	0	0
$331$	692.000	0.114912	0.0574558	−	0.998348i	$-0.481701\pi$
$331$	692.000	0.114912	0.0574558	+	0.998348i	$0.481701\pi$
$332$	− 4144.00i	− 0.685035i
$333$	3582.00i	0.589467i
$334$	−1792.00	−0.293574
$335$	0	0
$336$	−336.000	−0.0545545
$337$	1566.00i	0.253132i	0.991958	+	0.126566i	$0.0403955\pi$
$337$	1566.00i	0.253132i	−0.991958	+	0.126566i	$0.959604\pi$
$338$	− 866.000i	− 0.139362i
$339$	−1014.00	−0.162457
$340$	0	0
$341$	576.000	0.0914726
$342$	2232.00i	0.352903i
$343$	− 343.000i	− 0.0539949i
$344$	−1696.00	−0.265820
$345$	0	0
$346$	8068.00	1.25358
$347$	5328.00i	0.824271i	0.911123	+	0.412135i	$0.135217\pi$
$347$	5328.00i	0.824271i	−0.911123	+	0.412135i	$0.864783\pi$
$348$	3048.00i	0.469511i
$349$	−11326.0	−1.73715	−0.868577	−	0.495554i	$-0.834965\pi$
$349$	−11326.0	−1.73715	−0.868577	+	0.495554i	$0.834965\pi$
$350$	0	0
$351$	−1134.00	−0.172446
$352$	256.000i	0.0387638i
$353$	− 2130.00i	− 0.321157i	−0.987023	−	0.160579i	$-0.948664\pi$
$353$	− 2130.00i	− 0.321157i	0.987023	−	0.160579i	$-0.0513360\pi$
$354$	4632.00	0.695446
$355$	0	0
$356$	120.000	0.0178651
$357$	− 42.0000i	− 0.00622654i
$358$	− 6960.00i	− 1.02751i
$359$	−3044.00	−0.447510	−0.223755	−	0.974645i	$-0.571832\pi$
$359$	−3044.00	−0.447510	−0.223755	+	0.974645i	$0.571832\pi$
$360$	0	0
$361$	8517.00	1.24173
$362$	5796.00i	0.841522i
$363$	− 3801.00i	− 0.549589i
$364$	−1176.00	−0.169338
$365$	0	0
$366$	180.000	0.0257070
$367$	− 12416.0i	− 1.76597i	−0.469404	−	0.882984i	$-0.655531\pi$
$367$	− 12416.0i	− 1.76597i	0.469404	−	0.882984i	$-0.344469\pi$
$368$	1216.00i	0.172251i
$369$	−4158.00	−0.586604
$370$	0	0
$371$	1134.00	0.158691
$372$	864.000i	0.120420i
$373$	− 7442.00i	− 1.03306i	−0.856268	−	0.516531i	$-0.827223\pi$
$373$	− 7442.00i	− 1.03306i	0.856268	−	0.516531i	$-0.172777\pi$
$374$	−32.0000	−0.00442428
$375$	0	0
$376$	−2112.00	−0.289676
$377$	10668.0i	1.45737i
$378$	− 378.000i	− 0.0514344i
$379$	−100.000	−0.0135532	−0.00677659	−	0.999977i	$-0.502157\pi$
$379$	−100.000	−0.0135532	−0.00677659	+	0.999977i	$0.502157\pi$
$380$	0	0
$381$	6264.00	0.842295
$382$	− 5304.00i	− 0.710409i
$383$	8080.00i	1.07799i	0.842310	+	0.538993i	$0.181195\pi$
$383$	8080.00i	1.07799i	−0.842310	+	0.538993i	$0.818805\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	292.000	0.0385036
$387$	− 1908.00i	− 0.250618i
$388$	− 4760.00i	− 0.622815i
$389$	5482.00	0.714520	0.357260	−	0.934005i	$-0.383711\pi$
$389$	5482.00	0.714520	0.357260	+	0.934005i	$0.383711\pi$
$390$	0	0
$391$	−152.000	−0.0196598
$392$	− 392.000i	− 0.0505076i
$393$	− 876.000i	− 0.112439i
$394$	5092.00	0.651095
$395$	0	0
$396$	−288.000	−0.0365468
$397$	− 10446.0i	− 1.32058i	−0.751011	−	0.660289i	$-0.770434\pi$
$397$	− 10446.0i	− 1.32058i	0.751011	−	0.660289i	$-0.229566\pi$
$398$	− 5072.00i	− 0.638785i
$399$	−2604.00	−0.326724
$400$	0	0
$401$	−11334.0	−1.41145	−0.705727	−	0.708484i	$-0.749379\pi$
$401$	−11334.0	−1.41145	−0.705727	+	0.708484i	$0.749379\pi$
$402$	4584.00i	0.568729i
$403$	3024.00i	0.373787i
$404$	−5480.00	−0.674852
$405$	0	0
$406$	−3556.00	−0.434683
$407$	3184.00i	0.387776i
$408$	− 48.0000i	− 0.00582440i
$409$	−8594.00	−1.03899	−0.519494	−	0.854474i	$-0.673879\pi$
$409$	−8594.00	−1.03899	−0.519494	+	0.854474i	$0.673879\pi$
$410$	0	0
$411$	2454.00	0.294518
$412$	− 1856.00i	− 0.221938i
$413$	5404.00i	0.643858i
$414$	−1368.00	−0.162400
$415$	0	0
$416$	−1344.00	−0.158401
$417$	6468.00i	0.759567i
$418$	1984.00i	0.232155i
$419$	−10500.0	−1.22424	−0.612122	−	0.790763i	$-0.709684\pi$
$419$	−10500.0	−1.22424	−0.612122	+	0.790763i	$0.709684\pi$
$420$	0	0
$421$	−12066.0	−1.39682	−0.698410	−	0.715698i	$-0.746109\pi$
$421$	−12066.0	−1.39682	−0.698410	+	0.715698i	$0.746109\pi$
$422$	2600.00i	0.299919i
$423$	− 2376.00i	− 0.273109i
$424$	1296.00	0.148442
$425$	0	0
$426$	−1416.00	−0.161046
$427$	210.000i	0.0238000i
$428$	− 8544.00i	− 0.964930i
$429$	−1008.00	−0.113442
$430$	0	0
$431$	4332.00	0.484142	0.242071	−	0.970259i	$-0.422173\pi$
$431$	4332.00	0.484142	0.242071	+	0.970259i	$0.422173\pi$
$432$	− 432.000i	− 0.0481125i
$433$	− 1918.00i	− 0.212871i	−0.994320	−	0.106436i	$-0.966056\pi$
$433$	− 1918.00i	− 0.212871i	0.994320	−	0.106436i	$-0.0339438\pi$
$434$	−1008.00	−0.111487
$435$	0	0
$436$	−4904.00	−0.538667
$437$	9424.00i	1.03160i
$438$	2508.00i	0.273600i
$439$	7992.00	0.868878	0.434439	−	0.900701i	$-0.356947\pi$
$439$	7992.00	0.868878	0.434439	+	0.900701i	$0.356947\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 168.000i	− 0.0180791i
$443$	3184.00i	0.341482i	0.985316	+	0.170741i	$0.0546161\pi$
$443$	3184.00i	0.341482i	−0.985316	+	0.170741i	$0.945384\pi$
$444$	−4776.00	−0.510493
$445$	0	0
$446$	5152.00	0.546983
$447$	8550.00i	0.904700i
$448$	− 448.000i	− 0.0472456i
$449$	−11426.0	−1.20095	−0.600475	−	0.799644i	$-0.705022\pi$
$449$	−11426.0	−1.20095	−0.600475	+	0.799644i	$0.705022\pi$
$450$	0	0
$451$	−3696.00	−0.385893
$452$	− 1352.00i	− 0.140692i
$453$	5016.00i	0.520248i
$454$	3672.00	0.379594
$455$	0	0
$456$	−2976.00	−0.305623
$457$	16934.0i	1.73335i	0.498877	+	0.866673i	$0.333746\pi$
$457$	16934.0i	1.73335i	−0.498877	+	0.866673i	$0.666254\pi$
$458$	− 3748.00i	− 0.382385i
$459$	54.0000	0.00549129
$460$	0	0
$461$	−17038.0	−1.72134	−0.860671	−	0.509161i	$-0.829956\pi$
$461$	−17038.0	−1.72134	−0.860671	+	0.509161i	$0.829956\pi$
$462$	− 336.000i	− 0.0338358i
$463$	− 13592.0i	− 1.36431i	−0.731209	−	0.682153i	$-0.761044\pi$
$463$	− 13592.0i	− 1.36431i	0.731209	−	0.682153i	$-0.238956\pi$
$464$	−4064.00	−0.406609
$465$	0	0
$466$	7460.00	0.741583
$467$	− 8612.00i	− 0.853353i	−0.904404	−	0.426676i	$-0.859684\pi$
$467$	− 8612.00i	− 0.853353i	0.904404	−	0.426676i	$-0.140316\pi$
$468$	− 1512.00i	− 0.149342i
$469$	−5348.00	−0.526541
$470$	0	0
$471$	1338.00	0.130896
$472$	6176.00i	0.602274i
$473$	− 1696.00i	− 0.164867i
$474$	−3312.00	−0.320939
$475$	0	0
$476$	56.0000	0.00539234
$477$	1458.00i	0.139952i
$478$	4008.00i	0.383518i
$479$	−7432.00	−0.708928	−0.354464	−	0.935070i	$-0.615337\pi$
$479$	−7432.00	−0.708928	−0.354464	+	0.935070i	$0.615337\pi$
$480$	0	0
$481$	−16716.0	−1.58458
$482$	1292.00i	0.122093i
$483$	− 1596.00i	− 0.150353i
$484$	5068.00	0.475958
$485$	0	0
$486$	486.000	0.0453609
$487$	6616.00i	0.615605i	0.951450	+	0.307802i	$0.0995936\pi$
$487$	6616.00i	0.615605i	−0.951450	+	0.307802i	$0.900406\pi$
$488$	240.000i	0.0222629i
$489$	−8124.00	−0.751288
$490$	0	0
$491$	17040.0	1.56620	0.783100	−	0.621896i	$-0.213637\pi$
$491$	17040.0	1.56620	0.783100	+	0.621896i	$0.213637\pi$
$492$	− 5544.00i	− 0.508014i
$493$	− 508.000i	− 0.0464081i
$494$	−10416.0	−0.948660
$495$	0	0
$496$	−1152.00	−0.104287
$497$	− 1652.00i	− 0.149099i
$498$	6216.00i	0.559329i
$499$	2948.00	0.264470	0.132235	−	0.991218i	$-0.457785\pi$
$499$	2948.00	0.264470	0.132235	+	0.991218i	$0.457785\pi$
$500$	0	0
$501$	2688.00	0.239703
$502$	− 2520.00i	− 0.224050i
$503$	17304.0i	1.53389i	0.641712	+	0.766946i	$0.278224\pi$
$503$	17304.0i	1.53389i	−0.641712	+	0.766946i	$0.721776\pi$
$504$	504.000	0.0445435
$505$	0	0
$506$	−1216.00	−0.106834
$507$	1299.00i	0.113788i
$508$	8352.00i	0.729449i
$509$	−4650.00	−0.404927	−0.202463	−	0.979290i	$-0.564895\pi$
$509$	−4650.00	−0.404927	−0.202463	+	0.979290i	$0.564895\pi$
$510$	0	0
$511$	−2926.00	−0.253305
$512$	− 512.000i	− 0.0441942i
$513$	− 3348.00i	− 0.288144i
$514$	−11820.0	−1.01431
$515$	0	0
$516$	2544.00	0.217041
$517$	− 2112.00i	− 0.179663i
$518$	− 5572.00i	− 0.472625i
$519$	−12102.0	−1.02354
$520$	0	0
$521$	16854.0	1.41725	0.708625	−	0.705585i	$-0.249316\pi$
$521$	16854.0	1.41725	0.708625	+	0.705585i	$0.249316\pi$
$522$	− 4572.00i	− 0.383354i
$523$	− 124.000i	− 0.0103674i	−0.999987	−	0.00518369i	$-0.998350\pi$
$523$	− 124.000i	− 0.0103674i	0.999987	−	0.00518369i	$-0.00165003\pi$
$524$	1168.00	0.0973747
$525$	0	0
$526$	5976.00	0.495373
$527$	− 144.000i	− 0.0119027i
$528$	− 384.000i	− 0.0316505i
$529$	6391.00	0.525273
$530$	0	0
$531$	−6948.00	−0.567830
$532$	− 3472.00i	− 0.282952i
$533$	− 19404.0i	− 1.57689i
$534$	−180.000	−0.0145868
$535$	0	0
$536$	−6112.00	−0.492534
$537$	10440.0i	0.838956i
$538$	− 2636.00i	− 0.211238i
$539$	392.000	0.0313259
$540$	0	0
$541$	5382.00	0.427708	0.213854	−	0.976866i	$-0.431398\pi$
$541$	5382.00	0.427708	0.213854	+	0.976866i	$0.431398\pi$
$542$	11280.0i	0.893944i
$543$	− 8694.00i	− 0.687100i
$544$	64.0000	0.00504408
$545$	0	0
$546$	1764.00	0.138264
$547$	− 17460.0i	− 1.36478i	−0.730987	−	0.682391i	$-0.760940\pi$
$547$	− 17460.0i	− 1.36478i	0.730987	−	0.682391i	$-0.239060\pi$
$548$	3272.00i	0.255060i
$549$	−270.000	−0.0209897
$550$	0	0
$551$	−31496.0	−2.43516
$552$	− 1824.00i	− 0.140642i
$553$	− 3864.00i	− 0.297132i
$554$	−12892.0	−0.988680
$555$	0	0
$556$	−8624.00	−0.657804
$557$	9514.00i	0.723736i	0.932229	+	0.361868i	$0.117861\pi$
$557$	9514.00i	0.723736i	−0.932229	+	0.361868i	$0.882139\pi$
$558$	− 1296.00i	− 0.0983227i
$559$	8904.00	0.673701
$560$	0	0
$561$	48.0000	0.00361241
$562$	− 9860.00i	− 0.740069i
$563$	3988.00i	0.298533i	0.988797	+	0.149267i	$0.0476913\pi$
$563$	3988.00i	0.298533i	−0.988797	+	0.149267i	$0.952309\pi$
$564$	3168.00	0.236519
$565$	0	0
$566$	−12520.0	−0.929779
$567$	567.000i	0.0419961i
$568$	− 1888.00i	− 0.139470i
$569$	−11346.0	−0.835939	−0.417969	−	0.908461i	$-0.637258\pi$
$569$	−11346.0	−0.835939	−0.417969	+	0.908461i	$0.637258\pi$
$570$	0	0
$571$	−8436.00	−0.618276	−0.309138	−	0.951017i	$-0.600041\pi$
$571$	−8436.00	−0.618276	−0.309138	+	0.951017i	$0.600041\pi$
$572$	− 1344.00i	− 0.0982438i
$573$	7956.00i	0.580047i
$574$	6468.00	0.470329
$575$	0	0
$576$	576.000	0.0416667
$577$	− 2098.00i	− 0.151371i	−0.997132	−	0.0756853i	$-0.975886\pi$
$577$	− 2098.00i	− 0.151371i	0.997132	−	0.0756853i	$-0.0241145\pi$
$578$	− 9818.00i	− 0.706531i
$579$	−438.000	−0.0314381
$580$	0	0
$581$	−7252.00	−0.517838
$582$	7140.00i	0.508527i
$583$	1296.00i	0.0920666i
$584$	−3344.00	−0.236945
$585$	0	0
$586$	−4620.00	−0.325683
$587$	− 9436.00i	− 0.663484i	−0.943370	−	0.331742i	$-0.892364\pi$
$587$	− 9436.00i	− 0.663484i	0.943370	−	0.331742i	$-0.107636\pi$
$588$	588.000i	0.0412393i
$589$	−8928.00	−0.624570
$590$	0	0
$591$	−7638.00	−0.531616
$592$	− 6368.00i	− 0.442100i
$593$	− 1314.00i	− 0.0909941i	−0.998964	−	0.0454971i	$-0.985513\pi$
$593$	− 1314.00i	− 0.0909941i	0.998964	−	0.0454971i	$-0.0144872\pi$
$594$	432.000	0.0298404
$595$	0	0
$596$	−11400.0	−0.783494
$597$	7608.00i	0.521566i
$598$	− 6384.00i	− 0.436557i
$599$	8940.00	0.609814	0.304907	−	0.952382i	$-0.401375\pi$
$599$	8940.00	0.609814	0.304907	+	0.952382i	$0.401375\pi$
$600$	0	0
$601$	16058.0	1.08988	0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0	1.08988	0.544941	+	0.838474i	$0.316552\pi$
$602$	2968.00i	0.200941i
$603$	− 6876.00i	− 0.464365i
$604$	−6688.00	−0.450548
$605$	0	0
$606$	8220.00	0.551014
$607$	− 3936.00i	− 0.263192i	−0.991303	−	0.131596i	$-0.957990\pi$
$607$	− 3936.00i	− 0.263192i	0.991303	−	0.131596i	$-0.0420101\pi$
$608$	− 3968.00i	− 0.264677i
$609$	5334.00	0.354917
$610$	0	0
$611$	11088.0	0.734161
$612$	72.0000i	0.00475560i
$613$	174.000i	0.0114646i	0.999984	+	0.00573230i	$0.00182466\pi$
$613$	174.000i	0.0114646i	−0.999984	+	0.00573230i	$0.998175\pi$
$614$	−392.000	−0.0257652
$615$	0	0
$616$	448.000	0.0293027
$617$	− 16018.0i	− 1.04515i	−0.852592	−	0.522577i	$-0.824971\pi$
$617$	− 16018.0i	− 1.04515i	0.852592	−	0.522577i	$-0.175029\pi$
$618$	2784.00i	0.181212i
$619$	3068.00	0.199214	0.0996069	−	0.995027i	$-0.468241\pi$
$619$	3068.00	0.199214	0.0996069	+	0.995027i	$0.468241\pi$
$620$	0	0
$621$	2052.00	0.132599
$622$	13472.0i	0.868453i
$623$	− 210.000i	− 0.0135048i
$624$	2016.00	0.129334
$625$	0	0
$626$	788.000	0.0503112
$627$	− 2976.00i	− 0.189553i
$628$	1784.00i	0.113359i
$629$	796.000	0.0504588
$630$	0	0
$631$	24656.0	1.55553	0.777765	−	0.628555i	$-0.216353\pi$
$631$	24656.0	1.55553	0.777765	+	0.628555i	$0.216353\pi$
$632$	− 4416.00i	− 0.277942i
$633$	− 3900.00i	− 0.244883i
$634$	13428.0	0.841158
$635$	0	0
$636$	−1944.00	−0.121202
$637$	2058.00i	0.128008i
$638$	− 4064.00i	− 0.252187i
$639$	2124.00	0.131493
$640$	0	0
$641$	7594.00	0.467933	0.233966	−	0.972245i	$-0.424829\pi$
$641$	7594.00	0.467933	0.233966	+	0.972245i	$0.424829\pi$
$642$	12816.0i	0.787862i
$643$	− 3724.00i	− 0.228398i	−0.993458	−	0.114199i	$-0.963570\pi$
$643$	− 3724.00i	− 0.228398i	0.993458	−	0.114199i	$-0.0364302\pi$
$644$	2128.00	0.130210
$645$	0	0
$646$	496.000	0.0302088
$647$	− 3792.00i	− 0.230416i	−0.993341	−	0.115208i	$-0.963247\pi$
$647$	− 3792.00i	− 0.230416i	0.993341	−	0.115208i	$-0.0367534\pi$
$648$	648.000i	0.0392837i
$649$	−6176.00	−0.373543
$650$	0	0
$651$	1512.00	0.0910291
$652$	− 10832.0i	− 0.650635i
$653$	24702.0i	1.48034i	0.672418	+	0.740171i	$0.265256\pi$
$653$	24702.0i	1.48034i	−0.672418	+	0.740171i	$0.734744\pi$
$654$	7356.00	0.439820
$655$	0	0
$656$	7392.00	0.439953
$657$	− 3762.00i	− 0.223394i
$658$	3696.00i	0.218974i
$659$	20144.0	1.19074	0.595371	−	0.803451i	$-0.297005\pi$
$659$	20144.0	1.19074	0.595371	+	0.803451i	$0.297005\pi$
$660$	0	0
$661$	−2522.00	−0.148403	−0.0742015	−	0.997243i	$-0.523641\pi$
$661$	−2522.00	−0.148403	−0.0742015	+	0.997243i	$0.523641\pi$
$662$	− 1384.00i	− 0.0812548i
$663$	252.000i	0.0147615i
$664$	−8288.00	−0.484393
$665$	0	0
$666$	7164.00	0.416816
$667$	− 19304.0i	− 1.12062i
$668$	3584.00i	0.207589i
$669$	−7728.00	−0.446609
$670$	0	0
$671$	−240.000	−0.0138079
$672$	672.000i	0.0385758i
$673$	− 10414.0i	− 0.596479i	−0.954491	−	0.298239i	$-0.903601\pi$
$673$	− 10414.0i	− 0.596479i	0.954491	−	0.298239i	$-0.0963994\pi$
$674$	3132.00	0.178991
$675$	0	0
$676$	−1732.00	−0.0985435
$677$	22230.0i	1.26199i	0.775786	+	0.630996i	$0.217353\pi$
$677$	22230.0i	1.26199i	−0.775786	+	0.630996i	$0.782647\pi$
$678$	2028.00i	0.114874i
$679$	−8330.00	−0.470804
$680$	0	0
$681$	−5508.00	−0.309937
$682$	− 1152.00i	− 0.0646809i
$683$	18192.0i	1.01918i	0.860418	+	0.509588i	$0.170202\pi$
$683$	18192.0i	1.01918i	−0.860418	+	0.509588i	$0.829798\pi$
$684$	4464.00	0.249540
$685$	0	0
$686$	−686.000	−0.0381802
$687$	5622.00i	0.312216i
$688$	3392.00i	0.187963i
$689$	−6804.00	−0.376214
$690$	0	0
$691$	8108.00	0.446372	0.223186	−	0.974776i	$-0.428354\pi$
$691$	8108.00	0.446372	0.223186	+	0.974776i	$0.428354\pi$
$692$	− 16136.0i	− 0.886414i
$693$	504.000i	0.0276268i
$694$	10656.0	0.582848
$695$	0	0
$696$	6096.00	0.331995
$697$	924.000i	0.0502138i
$698$	22652.0i	1.22835i
$699$	−11190.0	−0.605500
$700$	0	0
$701$	−5794.00	−0.312177	−0.156089	−	0.987743i	$-0.549889\pi$
$701$	−5794.00	−0.312177	−0.156089	+	0.987743i	$0.549889\pi$
$702$	2268.00i	0.121938i
$703$	− 49352.0i	− 2.64772i
$704$	512.000	0.0274101
$705$	0	0
$706$	−4260.00	−0.227092
$707$	9590.00i	0.510140i
$708$	− 9264.00i	− 0.491755i
$709$	1954.00	0.103504	0.0517518	−	0.998660i	$-0.483520\pi$
$709$	1954.00	0.103504	0.0517518	+	0.998660i	$0.483520\pi$
$710$	0	0
$711$	4968.00	0.262046
$712$	− 240.000i	− 0.0126326i
$713$	− 5472.00i	− 0.287417i
$714$	−84.0000	−0.00440283
$715$	0	0
$716$	−13920.0	−0.726557
$717$	− 6012.00i	− 0.313141i
$718$	6088.00i	0.316438i
$719$	32016.0	1.66063	0.830317	−	0.557292i	$-0.188160\pi$
$719$	32016.0	1.66063	0.830317	+	0.557292i	$0.188160\pi$
$720$	0	0
$721$	−3248.00	−0.167770
$722$	− 17034.0i	− 0.878033i
$723$	− 1938.00i	− 0.0996888i
$724$	11592.0	0.595046
$725$	0	0
$726$	−7602.00	−0.388618
$727$	23072.0i	1.17702i	0.808490	+	0.588510i	$0.200285\pi$
$727$	23072.0i	1.17702i	−0.808490	+	0.588510i	$0.799715\pi$
$728$	2352.00i	0.119740i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−424.000	−0.0214531
$732$	− 360.000i	− 0.0181776i
$733$	31782.0i	1.60149i	0.599003	+	0.800747i	$0.295564\pi$
$733$	31782.0i	1.60149i	−0.599003	+	0.800747i	$0.704436\pi$
$734$	−24832.0	−1.24873
$735$	0	0
$736$	2432.00	0.121800
$737$	− 6112.00i	− 0.305480i
$738$	8316.00i	0.414792i
$739$	24396.0	1.21437	0.607186	−	0.794559i	$-0.292298\pi$
$739$	24396.0	1.21437	0.607186	+	0.794559i	$0.292298\pi$
$740$	0	0
$741$	15624.0	0.774578
$742$	− 2268.00i	− 0.112211i
$743$	− 32604.0i	− 1.60986i	−0.593371	−	0.804929i	$-0.702203\pi$
$743$	− 32604.0i	− 1.60986i	0.593371	−	0.804929i	$-0.297797\pi$
$744$	1728.00	0.0851499
$745$	0	0
$746$	−14884.0	−0.730485
$747$	− 9324.00i	− 0.456690i
$748$	64.0000i	0.00312844i
$749$	−14952.0	−0.729418
$750$	0	0
$751$	−7680.00	−0.373165	−0.186583	−	0.982439i	$-0.559741\pi$
$751$	−7680.00	−0.373165	−0.186583	+	0.982439i	$0.559741\pi$
$752$	4224.00i	0.204832i
$753$	3780.00i	0.182936i
$754$	21336.0	1.03052
$755$	0	0
$756$	−756.000	−0.0363696
$757$	− 366.000i	− 0.0175727i	−0.999961	−	0.00878633i	$-0.997203\pi$
$757$	− 366.000i	− 0.0175727i	0.999961	−	0.00878633i	$-0.00279681\pi$
$758$	200.000i	0.00958355i
$759$	1824.00	0.0872293
$760$	0	0
$761$	29374.0	1.39922	0.699610	−	0.714525i	$-0.253357\pi$
$761$	29374.0	1.39922	0.699610	+	0.714525i	$0.253357\pi$
$762$	− 12528.0i	− 0.595593i
$763$	8582.00i	0.407194i
$764$	−10608.0	−0.502335
$765$	0	0
$766$	16160.0	0.762251
$767$	− 32424.0i	− 1.52642i
$768$	768.000i	0.0360844i
$769$	38990.0	1.82837	0.914184	−	0.405299i	$-0.132833\pi$
$769$	38990.0	1.82837	0.914184	+	0.405299i	$0.132833\pi$
$770$	0	0
$771$	17730.0	0.828185
$772$	− 584.000i	− 0.0272262i
$773$	− 20470.0i	− 0.952464i	−0.879320	−	0.476232i	$-0.842002\pi$
$773$	− 20470.0i	− 0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$774$	−3816.00	−0.177214
$775$	0	0
$776$	−9520.00	−0.440397
$777$	8358.00i	0.385896i
$778$	− 10964.0i	− 0.505242i
$779$	57288.0	2.63486
$780$	0	0
$781$	1888.00	0.0865019
$782$	304.000i	0.0139016i
$783$	6858.00i	0.313008i
$784$	−784.000	−0.0357143
$785$	0	0
$786$	−1752.00	−0.0795061
$787$	− 29916.0i	− 1.35501i	−0.735520	−	0.677503i	$-0.763062\pi$
$787$	− 29916.0i	− 1.35501i	0.735520	−	0.677503i	$-0.236938\pi$
$788$	− 10184.0i	− 0.460393i
$789$	−8964.00	−0.404470
$790$	0	0
$791$	−2366.00	−0.106353
$792$	576.000i	0.0258425i
$793$	− 1260.00i	− 0.0564236i
$794$	−20892.0	−0.933790
$795$	0	0
$796$	−10144.0	−0.451689
$797$	− 4914.00i	− 0.218398i	−0.994020	−	0.109199i	$-0.965172\pi$
$797$	− 4914.00i	− 0.218398i	0.994020	−	0.109199i	$-0.0348285\pi$
$798$	5208.00i	0.231029i
$799$	−528.000	−0.0233783
$800$	0	0
$801$	270.000	0.0119101
$802$	22668.0i	0.998049i
$803$	− 3344.00i	− 0.146958i
$804$	9168.00	0.402152
$805$	0	0
$806$	6048.00	0.264307
$807$	3954.00i	0.172475i
$808$	10960.0i	0.477192i
$809$	−34250.0	−1.48846	−0.744231	−	0.667922i	$-0.767184\pi$
$809$	−34250.0	−1.48846	−0.744231	+	0.667922i	$0.767184\pi$
$810$	0	0
$811$	−41804.0	−1.81003	−0.905017	−	0.425376i	$-0.860142\pi$
$811$	−41804.0	−1.81003	−0.905017	+	0.425376i	$0.860142\pi$
$812$	7112.00i	0.307367i
$813$	− 16920.0i	− 0.729902i
$814$	6368.00	0.274199
$815$	0	0
$816$	−96.0000	−0.00411847
$817$	26288.0i	1.12570i
$818$	17188.0i	0.734675i
$819$	−2646.00	−0.112892
$820$	0	0
$821$	30862.0	1.31193	0.655963	−	0.754793i	$-0.272263\pi$
$821$	30862.0	1.31193	0.655963	+	0.754793i	$0.272263\pi$
$822$	− 4908.00i	− 0.208256i
$823$	10576.0i	0.447942i	0.974596	+	0.223971i	$0.0719021\pi$
$823$	10576.0i	0.447942i	−0.974596	+	0.223971i	$0.928098\pi$
$824$	−3712.00	−0.156934
$825$	0	0
$826$	10808.0	0.455277
$827$	10680.0i	0.449069i	0.974466	+	0.224534i	$0.0720861\pi$
$827$	10680.0i	0.449069i	−0.974466	+	0.224534i	$0.927914\pi$
$828$	2736.00i	0.114834i
$829$	1178.00	0.0493530	0.0246765	−	0.999695i	$-0.492144\pi$
$829$	1178.00	0.0493530	0.0246765	+	0.999695i	$0.492144\pi$
$830$	0	0
$831$	19338.0	0.807254
$832$	2688.00i	0.112007i
$833$	− 98.0000i	− 0.00407623i
$834$	12936.0	0.537095
$835$	0	0
$836$	3968.00	0.164158
$837$	1944.00i	0.0802801i
$838$	21000.0i	0.865672i
$839$	5600.00	0.230433	0.115217	−	0.993340i	$-0.463244\pi$
$839$	5600.00	0.230433	0.115217	+	0.993340i	$0.463244\pi$
$840$	0	0
$841$	40127.0	1.64529
$842$	24132.0i	0.987700i
$843$	14790.0i	0.604264i
$844$	5200.00	0.212075
$845$	0	0
$846$	−4752.00	−0.193117
$847$	− 8869.00i	− 0.359790i
$848$	− 2592.00i	− 0.104964i
$849$	18780.0	0.759161
$850$	0	0
$851$	30248.0	1.21843
$852$	2832.00i	0.113876i
$853$	− 826.000i	− 0.0331556i	−0.999863	−	0.0165778i	$-0.994723\pi$
$853$	− 826.000i	− 0.0331556i	0.999863	−	0.0165778i	$-0.00527711\pi$
$854$	420.000	0.0168292
$855$	0	0
$856$	−17088.0	−0.682308
$857$	− 45918.0i	− 1.83026i	−0.403164	−	0.915128i	$-0.632090\pi$
$857$	− 45918.0i	− 1.83026i	0.403164	−	0.915128i	$-0.367910\pi$
$858$	2016.00i	0.0802157i
$859$	−42380.0	−1.68334	−0.841669	−	0.539994i	$-0.818426\pi$
$859$	−42380.0	−1.68334	−0.841669	+	0.539994i	$0.818426\pi$
$860$	0	0
$861$	−9702.00	−0.384022
$862$	− 8664.00i	− 0.342340i
$863$	− 26524.0i	− 1.04622i	−0.852265	−	0.523110i	$-0.824772\pi$
$863$	− 26524.0i	− 1.04622i	0.852265	−	0.523110i	$-0.175228\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	−3836.00	−0.150523
$867$	14727.0i	0.576880i
$868$	2016.00i	0.0788335i
$869$	4416.00	0.172385
$870$	0	0
$871$	32088.0	1.24829
$872$	9808.00i	0.380895i
$873$	− 10710.0i	− 0.415210i
$874$	18848.0	0.729454
$875$	0	0
$876$	5016.00	0.193465
$877$	− 20614.0i	− 0.793712i	−0.917881	−	0.396856i	$-0.870101\pi$
$877$	− 20614.0i	− 0.793712i	0.917881	−	0.396856i	$-0.129899\pi$
$878$	− 15984.0i	− 0.614389i
$879$	6930.00	0.265919
$880$	0	0
$881$	−23730.0	−0.907473	−0.453737	−	0.891136i	$-0.649909\pi$
$881$	−23730.0	−0.907473	−0.453737	+	0.891136i	$0.649909\pi$
$882$	− 882.000i	− 0.0336718i
$883$	− 9028.00i	− 0.344073i	−0.985091	−	0.172036i	$-0.944965\pi$
$883$	− 9028.00i	− 0.344073i	0.985091	−	0.172036i	$-0.0550347\pi$
$884$	−336.000	−0.0127838
$885$	0	0
$886$	6368.00	0.241464
$887$	− 37200.0i	− 1.40818i	−0.710112	−	0.704089i	$-0.751356\pi$
$887$	− 37200.0i	− 1.40818i	0.710112	−	0.704089i	$-0.248644\pi$
$888$	9552.00i	0.360973i
$889$	14616.0	0.551412
$890$	0	0
$891$	−648.000	−0.0243646
$892$	− 10304.0i	− 0.386775i
$893$	32736.0i	1.22673i
$894$	17100.0	0.639720
$895$	0	0
$896$	−896.000	−0.0334077
$897$	9576.00i	0.356447i
$898$	22852.0i	0.849199i
$899$	18288.0	0.678464
$900$	0	0
$901$	324.000	0.0119800
$902$	7392.00i	0.272868i
$903$	− 4452.00i	− 0.164068i
$904$	−2704.00	−0.0994842
$905$	0	0
$906$	10032.0	0.367871
$907$	− 23988.0i	− 0.878179i	−0.898443	−	0.439090i	$-0.855301\pi$
$907$	− 23988.0i	− 0.878179i	0.898443	−	0.439090i	$-0.144699\pi$
$908$	− 7344.00i	− 0.268413i
$909$	−12330.0	−0.449901
$910$	0	0
$911$	15276.0	0.555561	0.277781	−	0.960645i	$-0.410401\pi$
$911$	15276.0	0.555561	0.277781	+	0.960645i	$0.410401\pi$
$912$	5952.00i	0.216108i
$913$	− 8288.00i	− 0.300430i
$914$	33868.0	1.22566
$915$	0	0
$916$	−7496.00	−0.270387
$917$	− 2044.00i	− 0.0736083i
$918$	− 108.000i	− 0.00388293i
$919$	10760.0	0.386224	0.193112	−	0.981177i	$-0.438142\pi$
$919$	10760.0	0.386224	0.193112	+	0.981177i	$0.438142\pi$
$920$	0	0
$921$	588.000	0.0210372
$922$	34076.0i	1.21717i
$923$	9912.00i	0.353475i
$924$	−672.000	−0.0239255
$925$	0	0
$926$	−27184.0	−0.964710
$927$	− 4176.00i	− 0.147959i
$928$	8128.00i	0.287516i
$929$	52890.0	1.86788	0.933942	−	0.357424i	$-0.116345\pi$
$929$	52890.0	1.86788	0.933942	+	0.357424i	$0.116345\pi$
$930$	0	0
$931$	−6076.00	−0.213891
$932$	− 14920.0i	− 0.524379i
$933$	− 20208.0i	− 0.709089i
$934$	−17224.0	−0.603412
$935$	0	0
$936$	−3024.00	−0.105601
$937$	6118.00i	0.213305i	0.994296	+	0.106652i	$0.0340132\pi$
$937$	6118.00i	0.213305i	−0.994296	+	0.106652i	$0.965987\pi$
$938$	10696.0i	0.372321i
$939$	−1182.00	−0.0410789
$940$	0	0
$941$	−32230.0	−1.11654	−0.558272	−	0.829658i	$-0.688535\pi$
$941$	−32230.0	−1.11654	−0.558272	+	0.829658i	$0.688535\pi$
$942$	− 2676.00i	− 0.0925571i
$943$	35112.0i	1.21252i
$944$	12352.0	0.425872
$945$	0	0
$946$	−3392.00	−0.116579
$947$	18544.0i	0.636324i	0.948036	+	0.318162i	$0.103066\pi$
$947$	18544.0i	0.636324i	−0.948036	+	0.318162i	$0.896934\pi$
$948$	6624.00i	0.226938i
$949$	17556.0	0.600518
$950$	0	0
$951$	−20142.0	−0.686802
$952$	− 112.000i	− 0.00381296i
$953$	25930.0i	0.881380i	0.897659	+	0.440690i	$0.145266\pi$
$953$	25930.0i	0.881380i	−0.897659	+	0.440690i	$0.854734\pi$
$954$	2916.00	0.0989612
$955$	0	0
$956$	8016.00	0.271188
$957$	6096.00i	0.205910i
$958$	14864.0i	0.501288i
$959$	5726.00	0.192807
$960$	0	0
$961$	−24607.0	−0.825988
$962$	33432.0i	1.12047i
$963$	− 19224.0i	− 0.643286i
$964$	2584.00	0.0863330
$965$	0	0
$966$	−3192.00	−0.106316
$967$	− 8192.00i	− 0.272427i	−0.990680	−	0.136214i	$-0.956507\pi$
$967$	− 8192.00i	− 0.272427i	0.990680	−	0.136214i	$-0.0434933\pi$
$968$	− 10136.0i	− 0.336553i
$969$	−744.000	−0.0246653
$970$	0	0
$971$	−54444.0	−1.79937	−0.899686	−	0.436537i	$-0.856205\pi$
$971$	−54444.0	−1.79937	−0.899686	+	0.436537i	$0.856205\pi$
$972$	− 972.000i	− 0.0320750i
$973$	15092.0i	0.497253i
$974$	13232.0	0.435298
$975$	0	0
$976$	480.000	0.0157422
$977$	25446.0i	0.833255i	0.909077	+	0.416627i	$0.136788\pi$
$977$	25446.0i	0.833255i	−0.909077	+	0.416627i	$0.863212\pi$
$978$	16248.0i	0.531241i
$979$	240.000	0.00783497
$980$	0	0
$981$	−11034.0	−0.359112
$982$	− 34080.0i	− 1.10747i
$983$	33192.0i	1.07697i	0.842635	+	0.538484i	$0.181003\pi$
$983$	33192.0i	1.07697i	−0.842635	+	0.538484i	$0.818997\pi$
$984$	−11088.0	−0.359220
$985$	0	0
$986$	−1016.00	−0.0328154
$987$	− 5544.00i	− 0.178792i
$988$	20832.0i	0.670804i
$989$	−16112.0	−0.518030
$990$	0	0
$991$	11024.0	0.353369	0.176685	−	0.984268i	$-0.443463\pi$
$991$	11024.0	0.353369	0.176685	+	0.984268i	$0.443463\pi$
$992$	2304.00i	0.0737420i
$993$	2076.00i	0.0663443i
$994$	−3304.00	−0.105429
$995$	0	0
$996$	12432.0	0.395505
$997$	40714.0i	1.29331i	0.762785	+	0.646653i	$0.223832\pi$
$997$	40714.0i	1.29331i	−0.762785	+	0.646653i	$0.776168\pi$
$998$	− 5896.00i	− 0.187009i
$999$	−10746.0	−0.340329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.4.g.n.799.1		2
5.2	odd	4		42.4.a.b.1.1	✓	1
5.3	odd	4		1050.4.a.d.1.1		1
5.4	even	2	inner	1050.4.g.n.799.2		2
15.2	even	4		126.4.a.c.1.1		1
20.7	even	4		336.4.a.d.1.1		1
35.2	odd	12		294.4.e.a.67.1		2
35.12	even	12		294.4.e.d.67.1		2
35.17	even	12		294.4.e.d.79.1		2
35.27	even	4		294.4.a.h.1.1		1
35.32	odd	12		294.4.e.a.79.1		2
40.27	even	4		1344.4.a.t.1.1		1
40.37	odd	4		1344.4.a.f.1.1		1
60.47	odd	4		1008.4.a.j.1.1		1
105.2	even	12		882.4.g.s.361.1		2
105.17	odd	12		882.4.g.r.667.1		2
105.32	even	12		882.4.g.s.667.1		2
105.47	odd	12		882.4.g.r.361.1		2
105.62	odd	4		882.4.a.d.1.1		1
140.27	odd	4		2352.4.a.ba.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.b.1.1	✓	1	5.2	odd	4
126.4.a.c.1.1		1	15.2	even	4
294.4.a.h.1.1		1	35.27	even	4
294.4.e.a.67.1		2	35.2	odd	12
294.4.e.a.79.1		2	35.32	odd	12
294.4.e.d.67.1		2	35.12	even	12
294.4.e.d.79.1		2	35.17	even	12
336.4.a.d.1.1		1	20.7	even	4
882.4.a.d.1.1		1	105.62	odd	4
882.4.g.r.361.1		2	105.47	odd	12
882.4.g.r.667.1		2	105.17	odd	12
882.4.g.s.361.1		2	105.2	even	12
882.4.g.s.667.1		2	105.32	even	12
1008.4.a.j.1.1		1	60.47	odd	4
1050.4.a.d.1.1		1	5.3	odd	4
1050.4.g.n.799.1		2	1.1	even	1	trivial
1050.4.g.n.799.2		2	5.4	even	2	inner
1344.4.a.f.1.1		1	40.37	odd	4
1344.4.a.t.1.1		1	40.27	even	4
2352.4.a.ba.1.1		1	140.27	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} -8.00000 q^{11} -12.0000i q^{12} -42.0000i q^{13} +14.0000 q^{14} +16.0000 q^{16} +2.00000i q^{17} +18.0000i q^{18} +124.000 q^{19} -21.0000 q^{21} +16.0000i q^{22} +76.0000i q^{23} -24.0000 q^{24} -84.0000 q^{26} -27.0000i q^{27} -28.0000i q^{28} -254.000 q^{29} -72.0000 q^{31} -32.0000i q^{32} -24.0000i q^{33} +4.00000 q^{34} +36.0000 q^{36} -398.000i q^{37} -248.000i q^{38} +126.000 q^{39} +462.000 q^{41} +42.0000i q^{42} +212.000i q^{43} +32.0000 q^{44} +152.000 q^{46} +264.000i q^{47} +48.0000i q^{48} -49.0000 q^{49} -6.00000 q^{51} +168.000i q^{52} -162.000i q^{53} -54.0000 q^{54} -56.0000 q^{56} +372.000i q^{57} +508.000i q^{58} +772.000 q^{59} +30.0000 q^{61} +144.000i q^{62} -63.0000i q^{63} -64.0000 q^{64} -48.0000 q^{66} +764.000i q^{67} -8.00000i q^{68} -228.000 q^{69} -236.000 q^{71} -72.0000i q^{72} +418.000i q^{73} -796.000 q^{74} -496.000 q^{76} -56.0000i q^{77} -252.000i q^{78} -552.000 q^{79} +81.0000 q^{81} -924.000i q^{82} +1036.00i q^{83} +84.0000 q^{84} +424.000 q^{86} -762.000i q^{87} -64.0000i q^{88} -30.0000 q^{89} +294.000 q^{91} -304.000i q^{92} -216.000i q^{93} +528.000 q^{94} +96.0000 q^{96} +1190.00i q^{97} +98.0000i q^{98} +72.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 12 q^{6} - 18 q^{9} - 16 q^{11} + 28 q^{14} + 32 q^{16} + 248 q^{19} - 42 q^{21} - 48 q^{24} - 168 q^{26} - 508 q^{29} - 144 q^{31} + 8 q^{34} + 72 q^{36} + 252 q^{39} + 924 q^{41} + 64 q^{44}+ \cdots + 144 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 + 12 * q^6 - 18 * q^9 - 16 * q^11 + 28 * q^14 + 32 * q^16 + 248 * q^19 - 42 * q^21 - 48 * q^24 - 168 * q^26 - 508 * q^29 - 144 * q^31 + 8 * q^34 + 72 * q^36 + 252 * q^39 + 924 * q^41 + 64 * q^44 + 304 * q^46 - 98 * q^49 - 12 * q^51 - 108 * q^54 - 112 * q^56 + 1544 * q^59 + 60 * q^61 - 128 * q^64 - 96 * q^66 - 456 * q^69 - 472 * q^71 - 1592 * q^74 - 992 * q^76 - 1104 * q^79 + 162 * q^81 + 168 * q^84 + 848 * q^86 - 60 * q^89 + 588 * q^91 + 1056 * q^94 + 192 * q^96 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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