LMFDB - Embedded newform 2550.2.d.b.2449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(2449,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2550.2449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.d (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:	$20.3618525154$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 510)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2449.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.b.2449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -4.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +4.00000 q^{19} +4.00000 q^{21} +4.00000i q^{22} -4.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000i q^{27} -4.00000i q^{28} -2.00000 q^{29} +4.00000 q^{31} -1.00000i q^{32} +4.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} +6.00000i q^{37} -4.00000i q^{38} -2.00000 q^{39} +2.00000 q^{41} -4.00000i q^{42} -12.0000i q^{43} +4.00000 q^{44} -4.00000 q^{46} -8.00000i q^{47} -1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -2.00000i q^{53} +1.00000 q^{54} -4.00000 q^{56} -4.00000i q^{57} +2.00000i q^{58} -12.0000 q^{59} +2.00000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} -4.00000i q^{67} +1.00000i q^{68} -4.00000 q^{69} -4.00000 q^{71} -1.00000i q^{72} -14.0000i q^{73} +6.00000 q^{74} -4.00000 q^{76} -16.0000i q^{77} +2.00000i q^{78} +12.0000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -4.00000i q^{83} -4.00000 q^{84} -12.0000 q^{86} +2.00000i q^{87} -4.00000i q^{88} -10.0000 q^{89} +8.00000 q^{91} +4.00000i q^{92} -4.00000i q^{93} -8.00000 q^{94} -1.00000 q^{96} -18.0000i q^{97} +9.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 8 q^{11} + 8 q^{14} + 2 q^{16} + 8 q^{19} + 8 q^{21} + 2 q^{24} - 4 q^{26} - 4 q^{29} + 8 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} + 4 q^{41} + 8 q^{44} - 8 q^{46} - 18 q^{49} - 2 q^{51} + 2 q^{54} - 8 q^{56} - 24 q^{59} + 4 q^{61} - 2 q^{64} + 8 q^{66} - 8 q^{69} - 8 q^{71} + 12 q^{74} - 8 q^{76} + 24 q^{79} + 2 q^{81} - 8 q^{84} - 24 q^{86} - 20 q^{89} + 16 q^{91} - 16 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 8 * q^11 + 8 * q^14 + 2 * q^16 + 8 * q^19 + 8 * q^21 + 2 * q^24 - 4 * q^26 - 4 * q^29 + 8 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 + 4 * q^41 + 8 * q^44 - 8 * q^46 - 18 * q^49 - 2 * q^51 + 2 * q^54 - 8 * q^56 - 24 * q^59 + 4 * q^61 - 2 * q^64 + 8 * q^66 - 8 * q^69 - 8 * q^71 + 12 * q^74 - 8 * q^76 + 24 * q^79 + 2 * q^81 - 8 * q^84 - 24 * q^86 - 20 * q^89 + 16 * q^91 - 16 * q^94 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2550\mathbb{Z}\right)^\times$.

$n$	$751$	$851$	$1327$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	4.00000i	1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$	4.00000i	1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000i	0.288675i
$13$	− 2.00000i	− 0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$	− 2.00000i	− 0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.00000i	− 0.242536i
$17$	− 1.00000i	− 0.242536i
$18$	1.00000i	0.235702i
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	4.00000i	0.852803i
$23$	− 4.00000i	− 0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$	− 4.00000i	− 0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	1.00000i	0.192450i
$28$	− 4.00000i	− 0.755929i
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	− 1.00000i	− 0.176777i
$33$	4.00000i	0.696311i
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	6.00000i	0.986394i	0.869918	+	0.493197i	$0.164172\pi$
$37$	6.00000i	0.986394i	−0.869918	+	0.493197i	$0.835828\pi$
$38$	− 4.00000i	− 0.648886i
$39$	−2.00000	−0.320256
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	− 4.00000i	− 0.617213i
$43$	− 12.0000i	− 1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	− 12.0000i	− 1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−4.00000	−0.589768
$47$	− 8.00000i	− 1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$	− 8.00000i	− 1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−9.00000	−1.28571
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000i	0.277350i
$53$	− 2.00000i	− 0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$	− 2.00000i	− 0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.00000	−0.534522
$57$	− 4.00000i	− 0.529813i
$58$	2.00000i	0.262613i
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	− 4.00000i	− 0.508001i
$63$	− 4.00000i	− 0.503953i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.00000	0.492366
$67$	− 4.00000i	− 0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$	− 4.00000i	− 0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	1.00000i	0.121268i
$69$	−4.00000	−0.481543
$70$	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
$73$	− 14.0000i	− 1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$	− 14.0000i	− 1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$	6.00000	0.697486
$75$	0	0
$76$	−4.00000	−0.458831
$77$	− 16.0000i	− 1.82337i
$78$	2.00000i	0.226455i
$79$	12.0000	1.35011	0.675053	−	0.737769i	$-0.264121\pi$
$79$	12.0000	1.35011	0.675053	+	0.737769i	$0.264121\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 2.00000i	− 0.220863i
$83$	− 4.00000i	− 0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$	− 4.00000i	− 0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	−12.0000	−1.29399
$87$	2.00000i	0.214423i
$88$	− 4.00000i	− 0.426401i
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	4.00000i	0.417029i
$93$	− 4.00000i	− 0.414781i
$94$	−8.00000	−0.825137
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 18.0000i	− 1.82762i	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	− 18.0000i	− 1.82762i	0.406138	−	0.913812i	$-0.366875\pi$
$98$	9.00000i	0.909137i
$99$	4.00000	0.402015
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	1.00000i	0.0990148i
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−2.00000	−0.194257
$107$	− 12.0000i	− 1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$	− 12.0000i	− 1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	4.00000i	0.377964i
$113$	− 6.00000i	− 0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$	− 6.00000i	− 0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	2.00000	0.185695
$117$	2.00000i	0.184900i
$118$	12.0000i	1.10469i
$119$	4.00000	0.366679
$120$	0	0
$121$	5.00000	0.454545
$122$	− 2.00000i	− 0.181071i
$123$	− 2.00000i	− 0.180334i
$124$	−4.00000	−0.359211
$125$	0	0
$126$	−4.00000	−0.356348
$127$	16.0000i	1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$	16.0000i	1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	1.00000i	0.0883883i
$129$	−12.0000	−1.05654
$130$	0	0
$131$	20.0000	1.74741	0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000	1.74741	0.873704	+	0.486458i	$0.161711\pi$
$132$	− 4.00000i	− 0.348155i
$133$	16.0000i	1.38738i
$134$	−4.00000	−0.345547
$135$	0	0
$136$	1.00000	0.0857493
$137$	6.00000i	0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$	6.00000i	0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$	4.00000i	0.340503i
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	4.00000i	0.335673i
$143$	8.00000i	0.668994i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−14.0000	−1.15865
$147$	9.00000i	0.742307i
$148$	− 6.00000i	− 0.493197i
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	4.00000i	0.324443i
$153$	1.00000i	0.0808452i
$154$	−16.0000	−1.28932
$155$	0	0
$156$	2.00000	0.160128
$157$	10.0000i	0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$	10.0000i	0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$	− 12.0000i	− 0.954669i
$159$	−2.00000	−0.158610
$160$	0	0
$161$	16.0000	1.26098
$162$	− 1.00000i	− 0.0785674i
$163$	− 20.0000i	− 1.56652i	−0.621694	−	0.783260i	$-0.713555\pi$
$163$	− 20.0000i	− 1.56652i	0.621694	−	0.783260i	$-0.286445\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	−4.00000	−0.310460
$167$	− 12.0000i	− 0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$	− 12.0000i	− 0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	4.00000i	0.308607i
$169$	9.00000	0.692308
$170$	0	0
$171$	−4.00000	−0.305888
$172$	12.0000i	0.914991i
$173$	− 14.0000i	− 1.06440i	−0.846619	−	0.532200i	$-0.821365\pi$
$173$	− 14.0000i	− 1.06440i	0.846619	−	0.532200i	$-0.178635\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−4.00000	−0.301511
$177$	12.0000i	0.901975i
$178$	10.0000i	0.749532i
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	− 8.00000i	− 0.592999i
$183$	− 2.00000i	− 0.147844i
$184$	4.00000	0.294884
$185$	0	0
$186$	−4.00000	−0.293294
$187$	4.00000i	0.292509i
$188$	8.00000i	0.583460i
$189$	−4.00000	−0.290957
$190$	0	0
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	1.00000i	0.0721688i
$193$	18.0000i	1.29567i	0.761781	+	0.647834i	$0.224325\pi$
$193$	18.0000i	1.29567i	−0.761781	+	0.647834i	$0.775675\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	9.00000	0.642857
$197$	14.0000i	0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$	14.0000i	0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$	− 4.00000i	− 0.284268i
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	10.0000i	0.703598i
$203$	− 8.00000i	− 0.561490i
$204$	1.00000	0.0700140
$205$	0	0
$206$	0	0
$207$	4.00000i	0.278019i
$208$	− 2.00000i	− 0.138675i
$209$	−16.0000	−1.10674
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	2.00000i	0.137361i
$213$	4.00000i	0.274075i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	16.0000i	1.08615i
$218$	10.0000i	0.677285i
$219$	−14.0000	−0.946032
$220$	0	0
$221$	−2.00000	−0.134535
$222$	− 6.00000i	− 0.402694i
$223$	− 8.00000i	− 0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$	− 8.00000i	− 0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	−6.00000	−0.399114
$227$	20.0000i	1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$227$	20.0000i	1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$228$	4.00000i	0.264906i
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	−16.0000	−1.05272
$232$	− 2.00000i	− 0.131306i
$233$	18.0000i	1.17922i	0.807688	+	0.589610i	$0.200718\pi$
$233$	18.0000i	1.17922i	−0.807688	+	0.589610i	$0.799282\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	12.0000	0.781133
$237$	− 12.0000i	− 0.779484i
$238$	− 4.00000i	− 0.259281i
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	− 5.00000i	− 0.321412i
$243$	− 1.00000i	− 0.0641500i
$244$	−2.00000	−0.128037
$245$	0	0
$246$	−2.00000	−0.127515
$247$	− 8.00000i	− 0.509028i
$248$	4.00000i	0.254000i
$249$	−4.00000	−0.253490
$250$	0	0
$251$	−28.0000	−1.76734	−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000	−1.76734	−0.883672	+	0.468106i	$0.844936\pi$
$252$	4.00000i	0.251976i
$253$	16.0000i	1.00591i
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 18.0000i	− 1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$	− 18.0000i	− 1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$	12.0000i	0.747087i
$259$	−24.0000	−1.49129
$260$	0	0
$261$	2.00000	0.123797
$262$	− 20.0000i	− 1.23560i
$263$	− 16.0000i	− 0.986602i	−0.869859	−	0.493301i	$-0.835790\pi$
$263$	− 16.0000i	− 0.986602i	0.869859	−	0.493301i	$-0.164210\pi$
$264$	−4.00000	−0.246183
$265$	0	0
$266$	16.0000	0.981023
$267$	10.0000i	0.611990i
$268$	4.00000i	0.244339i
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	− 1.00000i	− 0.0606339i
$273$	− 8.00000i	− 0.484182i
$274$	6.00000	0.362473
$275$	0	0
$276$	4.00000	0.240772
$277$	− 2.00000i	− 0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$	− 2.00000i	− 0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$	− 20.0000i	− 1.19952i
$279$	−4.00000	−0.239474
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	8.00000i	0.476393i
$283$	− 20.0000i	− 1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$	− 20.0000i	− 1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	4.00000	0.237356
$285$	0	0
$286$	8.00000	0.473050
$287$	8.00000i	0.472225i
$288$	1.00000i	0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−18.0000	−1.05518
$292$	14.0000i	0.819288i
$293$	− 26.0000i	− 1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$	− 26.0000i	− 1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−6.00000	−0.348743
$297$	− 4.00000i	− 0.232104i
$298$	− 2.00000i	− 0.115857i
$299$	−8.00000	−0.462652
$300$	0	0
$301$	48.0000	2.76667
$302$	8.00000i	0.460348i
$303$	10.0000i	0.574485i
$304$	4.00000	0.229416
$305$	0	0
$306$	1.00000	0.0571662
$307$	4.00000i	0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$	4.00000i	0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$	16.0000i	0.911685i
$309$	0	0
$310$	0	0
$311$	20.0000	1.13410	0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000	1.13410	0.567048	+	0.823685i	$0.308085\pi$
$312$	− 2.00000i	− 0.113228i
$313$	10.0000i	0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$	10.0000i	0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$	10.0000	0.564333
$315$	0	0
$316$	−12.0000	−0.675053
$317$	− 10.0000i	− 0.561656i	−0.959758	−	0.280828i	$-0.909391\pi$
$317$	− 10.0000i	− 0.561656i	0.959758	−	0.280828i	$-0.0906090\pi$
$318$	2.00000i	0.112154i
$319$	8.00000	0.447914
$320$	0	0
$321$	−12.0000	−0.669775
$322$	− 16.0000i	− 0.891645i
$323$	− 4.00000i	− 0.222566i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−20.0000	−1.10770
$327$	10.0000i	0.553001i
$328$	2.00000i	0.110432i
$329$	32.0000	1.76422
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	4.00000i	0.219529i
$333$	− 6.00000i	− 0.328798i
$334$	−12.0000	−0.656611
$335$	0	0
$336$	4.00000	0.218218
$337$	22.0000i	1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$	22.0000i	1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$	− 9.00000i	− 0.489535i
$339$	−6.00000	−0.325875
$340$	0	0
$341$	−16.0000	−0.866449
$342$	4.00000i	0.216295i
$343$	− 8.00000i	− 0.431959i
$344$	12.0000	0.646997
$345$	0	0
$346$	−14.0000	−0.752645
$347$	− 20.0000i	− 1.07366i	−0.843692	−	0.536828i	$-0.819622\pi$
$347$	− 20.0000i	− 1.07366i	0.843692	−	0.536828i	$-0.180378\pi$
$348$	− 2.00000i	− 0.107211i
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	4.00000i	0.213201i
$353$	2.00000i	0.106449i	0.998583	+	0.0532246i	$0.0169499\pi$
$353$	2.00000i	0.106449i	−0.998583	+	0.0532246i	$0.983050\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	10.0000	0.529999
$357$	− 4.00000i	− 0.211702i
$358$	12.0000i	0.634220i
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	22.0000i	1.15629i
$363$	− 5.00000i	− 0.262432i
$364$	−8.00000	−0.419314
$365$	0	0
$366$	−2.00000	−0.104542
$367$	− 28.0000i	− 1.46159i	−0.682598	−	0.730794i	$-0.739150\pi$
$367$	− 28.0000i	− 1.46159i	0.682598	−	0.730794i	$-0.260850\pi$
$368$	− 4.00000i	− 0.208514i
$369$	−2.00000	−0.104116
$370$	0	0
$371$	8.00000	0.415339
$372$	4.00000i	0.207390i
$373$	38.0000i	1.96757i	0.179364	+	0.983783i	$0.442596\pi$
$373$	38.0000i	1.96757i	−0.179364	+	0.983783i	$0.557404\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	8.00000	0.412568
$377$	4.00000i	0.206010i
$378$	4.00000i	0.205738i
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	8.00000i	0.409316i
$383$	8.00000i	0.408781i	0.978889	+	0.204390i	$0.0655212\pi$
$383$	8.00000i	0.408781i	−0.978889	+	0.204390i	$0.934479\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	18.0000	0.916176
$387$	12.0000i	0.609994i
$388$	18.0000i	0.913812i
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−4.00000	−0.202289
$392$	− 9.00000i	− 0.454569i
$393$	− 20.0000i	− 1.00887i
$394$	14.0000	0.705310
$395$	0	0
$396$	−4.00000	−0.201008
$397$	30.0000i	1.50566i	0.658217	+	0.752828i	$0.271311\pi$
$397$	30.0000i	1.50566i	−0.658217	+	0.752828i	$0.728689\pi$
$398$	4.00000i	0.200502i
$399$	16.0000	0.801002
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	4.00000i	0.199502i
$403$	− 8.00000i	− 0.398508i
$404$	10.0000	0.497519
$405$	0	0
$406$	−8.00000	−0.397033
$407$	− 24.0000i	− 1.18964i
$408$	− 1.00000i	− 0.0495074i
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	0	0
$413$	− 48.0000i	− 2.36193i
$414$	4.00000	0.196589
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	− 20.0000i	− 0.979404i
$418$	16.0000i	0.782586i
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	− 4.00000i	− 0.194717i
$423$	8.00000i	0.388973i
$424$	2.00000	0.0971286
$425$	0	0
$426$	4.00000	0.193801
$427$	8.00000i	0.387147i
$428$	12.0000i	0.580042i
$429$	8.00000	0.386244
$430$	0	0
$431$	−4.00000	−0.192673	−0.0963366	−	0.995349i	$-0.530713\pi$
$431$	−4.00000	−0.192673	−0.0963366	+	0.995349i	$0.530713\pi$
$432$	1.00000i	0.0481125i
$433$	− 14.0000i	− 0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$	− 14.0000i	− 0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	16.0000	0.768025
$435$	0	0
$436$	10.0000	0.478913
$437$	− 16.0000i	− 0.765384i
$438$	14.0000i	0.668946i
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	2.00000i	0.0951303i
$443$	− 36.0000i	− 1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$	− 36.0000i	− 1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	−6.00000	−0.284747
$445$	0	0
$446$	−8.00000	−0.378811
$447$	− 2.00000i	− 0.0945968i
$448$	− 4.00000i	− 0.188982i
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	−8.00000	−0.376705
$452$	6.00000i	0.282216i
$453$	8.00000i	0.375873i
$454$	20.0000	0.938647
$455$	0	0
$456$	4.00000	0.187317
$457$	− 10.0000i	− 0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$	− 10.0000i	− 0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	6.00000i	0.280362i
$459$	1.00000	0.0466760
$460$	0	0
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	16.0000i	0.744387i
$463$	40.0000i	1.85896i	0.368875	+	0.929479i	$0.379743\pi$
$463$	40.0000i	1.85896i	−0.368875	+	0.929479i	$0.620257\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	18.0000	0.833834
$467$	− 36.0000i	− 1.66588i	−0.553362	−	0.832941i	$-0.686655\pi$
$467$	− 36.0000i	− 1.66588i	0.553362	−	0.832941i	$-0.313345\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	16.0000	0.738811
$470$	0	0
$471$	10.0000	0.460776
$472$	− 12.0000i	− 0.552345i
$473$	48.0000i	2.20704i
$474$	−12.0000	−0.551178
$475$	0	0
$476$	−4.00000	−0.183340
$477$	2.00000i	0.0915737i
$478$	− 24.0000i	− 1.09773i
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	0	0
$481$	12.0000	0.547153
$482$	− 10.0000i	− 0.455488i
$483$	− 16.0000i	− 0.728025i
$484$	−5.00000	−0.227273
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	− 20.0000i	− 0.906287i	−0.891438	−	0.453143i	$-0.850303\pi$
$487$	− 20.0000i	− 0.906287i	0.891438	−	0.453143i	$-0.149697\pi$
$488$	2.00000i	0.0905357i
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	2.00000i	0.0901670i
$493$	2.00000i	0.0900755i
$494$	−8.00000	−0.359937
$495$	0	0
$496$	4.00000	0.179605
$497$	− 16.0000i	− 0.717698i
$498$	4.00000i	0.179244i
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	28.0000i	1.24970i
$503$	44.0000i	1.96186i	0.194354	+	0.980932i	$0.437739\pi$
$503$	44.0000i	1.96186i	−0.194354	+	0.980932i	$0.562261\pi$
$504$	4.00000	0.178174
$505$	0	0
$506$	16.0000	0.711287
$507$	− 9.00000i	− 0.399704i
$508$	− 16.0000i	− 0.709885i
$509$	−38.0000	−1.68432	−0.842160	−	0.539227i	$-0.818716\pi$
$509$	−38.0000	−1.68432	−0.842160	+	0.539227i	$0.818716\pi$
$510$	0	0
$511$	56.0000	2.47729
$512$	− 1.00000i	− 0.0441942i
$513$	4.00000i	0.176604i
$514$	−18.0000	−0.793946
$515$	0	0
$516$	12.0000	0.528271
$517$	32.0000i	1.40736i
$518$	24.0000i	1.05450i
$519$	−14.0000	−0.614532
$520$	0	0
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	− 2.00000i	− 0.0875376i
$523$	28.0000i	1.22435i	0.790721	+	0.612177i	$0.209706\pi$
$523$	28.0000i	1.22435i	−0.790721	+	0.612177i	$0.790294\pi$
$524$	−20.0000	−0.873704
$525$	0	0
$526$	−16.0000	−0.697633
$527$	− 4.00000i	− 0.174243i
$528$	4.00000i	0.174078i
$529$	7.00000	0.304348
$530$	0	0
$531$	12.0000	0.520756
$532$	− 16.0000i	− 0.693688i
$533$	− 4.00000i	− 0.173259i
$534$	10.0000	0.432742
$535$	0	0
$536$	4.00000	0.172774
$537$	12.0000i	0.517838i
$538$	− 30.0000i	− 1.29339i
$539$	36.0000	1.55063
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	0	0
$543$	22.0000i	0.944110i
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−8.00000	−0.342368
$547$	− 20.0000i	− 0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$	− 20.0000i	− 0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$	− 6.00000i	− 0.256307i
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	−8.00000	−0.340811
$552$	− 4.00000i	− 0.170251i
$553$	48.0000i	2.04117i
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	−20.0000	−0.848189
$557$	26.0000i	1.10166i	0.834619	+	0.550828i	$0.185688\pi$
$557$	26.0000i	1.10166i	−0.834619	+	0.550828i	$0.814312\pi$
$558$	4.00000i	0.169334i
$559$	−24.0000	−1.01509
$560$	0	0
$561$	4.00000	0.168880
$562$	− 10.0000i	− 0.421825i
$563$	− 36.0000i	− 1.51722i	−0.651546	−	0.758610i	$-0.725879\pi$
$563$	− 36.0000i	− 1.51722i	0.651546	−	0.758610i	$-0.274121\pi$
$564$	8.00000	0.336861
$565$	0	0
$566$	−20.0000	−0.840663
$567$	4.00000i	0.167984i
$568$	− 4.00000i	− 0.167836i
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	− 8.00000i	− 0.334497i
$573$	8.00000i	0.334205i
$574$	8.00000	0.333914
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 18.0000i	− 0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$	− 18.0000i	− 0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	1.00000i	0.0415945i
$579$	18.0000	0.748054
$580$	0	0
$581$	16.0000	0.663792
$582$	18.0000i	0.746124i
$583$	8.00000i	0.331326i
$584$	14.0000	0.579324
$585$	0	0
$586$	−26.0000	−1.07405
$587$	− 44.0000i	− 1.81607i	−0.418890	−	0.908037i	$-0.637581\pi$
$587$	− 44.0000i	− 1.81607i	0.418890	−	0.908037i	$-0.362419\pi$
$588$	− 9.00000i	− 0.371154i
$589$	16.0000	0.659269
$590$	0	0
$591$	14.0000	0.575883
$592$	6.00000i	0.246598i
$593$	18.0000i	0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$	18.0000i	0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	4.00000i	0.163709i
$598$	8.00000i	0.327144i
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−6.00000	−0.244745	−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000	−0.244745	−0.122373	+	0.992484i	$0.539050\pi$
$602$	− 48.0000i	− 1.95633i
$603$	4.00000i	0.162893i
$604$	8.00000	0.325515
$605$	0	0
$606$	10.0000	0.406222
$607$	− 28.0000i	− 1.13648i	−0.822861	−	0.568242i	$-0.807624\pi$
$607$	− 28.0000i	− 1.13648i	0.822861	−	0.568242i	$-0.192376\pi$
$608$	− 4.00000i	− 0.162221i
$609$	−8.00000	−0.324176
$610$	0	0
$611$	−16.0000	−0.647291
$612$	− 1.00000i	− 0.0404226i
$613$	− 2.00000i	− 0.0807792i	−0.999184	−	0.0403896i	$-0.987140\pi$
$613$	− 2.00000i	− 0.0807792i	0.999184	−	0.0403896i	$-0.0128599\pi$
$614$	4.00000	0.161427
$615$	0	0
$616$	16.0000	0.644658
$617$	30.0000i	1.20775i	0.797077	+	0.603877i	$0.206378\pi$
$617$	30.0000i	1.20775i	−0.797077	+	0.603877i	$0.793622\pi$
$618$	0	0
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	− 20.0000i	− 0.801927i
$623$	− 40.0000i	− 1.60257i
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	10.0000	0.399680
$627$	16.0000i	0.638978i
$628$	− 10.0000i	− 0.399043i
$629$	6.00000	0.239236
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	12.0000i	0.477334i
$633$	− 4.00000i	− 0.158986i
$634$	−10.0000	−0.397151
$635$	0	0
$636$	2.00000	0.0793052
$637$	18.0000i	0.713186i
$638$	− 8.00000i	− 0.316723i
$639$	4.00000	0.158238
$640$	0	0
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	12.0000i	0.473602i
$643$	28.0000i	1.10421i	0.833774	+	0.552106i	$0.186176\pi$
$643$	28.0000i	1.10421i	−0.833774	+	0.552106i	$0.813824\pi$
$644$	−16.0000	−0.630488
$645$	0	0
$646$	−4.00000	−0.157378
$647$	16.0000i	0.629025i	0.949253	+	0.314512i	$0.101841\pi$
$647$	16.0000i	0.629025i	−0.949253	+	0.314512i	$0.898159\pi$
$648$	1.00000i	0.0392837i
$649$	48.0000	1.88416
$650$	0	0
$651$	16.0000	0.627089
$652$	20.0000i	0.783260i
$653$	− 30.0000i	− 1.17399i	−0.809590	−	0.586995i	$-0.800311\pi$
$653$	− 30.0000i	− 1.17399i	0.809590	−	0.586995i	$-0.199689\pi$
$654$	10.0000	0.391031
$655$	0	0
$656$	2.00000	0.0780869
$657$	14.0000i	0.546192i
$658$	− 32.0000i	− 1.24749i
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	− 28.0000i	− 1.08825i
$663$	2.00000i	0.0776736i
$664$	4.00000	0.155230
$665$	0	0
$666$	−6.00000	−0.232495
$667$	8.00000i	0.309761i
$668$	12.0000i	0.464294i
$669$	−8.00000	−0.309298
$670$	0	0
$671$	−8.00000	−0.308837
$672$	− 4.00000i	− 0.154303i
$673$	34.0000i	1.31060i	0.755367	+	0.655302i	$0.227459\pi$
$673$	34.0000i	1.31060i	−0.755367	+	0.655302i	$0.772541\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	−9.00000	−0.346154
$677$	− 18.0000i	− 0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$	− 18.0000i	− 0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	6.00000i	0.230429i
$679$	72.0000	2.76311
$680$	0	0
$681$	20.0000	0.766402
$682$	16.0000i	0.612672i
$683$	36.0000i	1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$	36.0000i	1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	4.00000	0.152944
$685$	0	0
$686$	−8.00000	−0.305441
$687$	6.00000i	0.228914i
$688$	− 12.0000i	− 0.457496i
$689$	−4.00000	−0.152388
$690$	0	0
$691$	−44.0000	−1.67384	−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000	−1.67384	−0.836919	+	0.547326i	$0.815646\pi$
$692$	14.0000i	0.532200i
$693$	16.0000i	0.607790i
$694$	−20.0000	−0.759190
$695$	0	0
$696$	−2.00000	−0.0758098
$697$	− 2.00000i	− 0.0757554i
$698$	22.0000i	0.832712i
$699$	18.0000	0.680823
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	− 2.00000i	− 0.0754851i
$703$	24.0000i	0.905177i
$704$	4.00000	0.150756
$705$	0	0
$706$	2.00000	0.0752710
$707$	− 40.0000i	− 1.50435i
$708$	− 12.0000i	− 0.450988i
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	−12.0000	−0.450035
$712$	− 10.0000i	− 0.374766i
$713$	− 16.0000i	− 0.599205i
$714$	−4.00000	−0.149696
$715$	0	0
$716$	12.0000	0.448461
$717$	− 24.0000i	− 0.896296i
$718$	− 24.0000i	− 0.895672i
$719$	44.0000	1.64092	0.820462	−	0.571702i	$-0.193717\pi$
$719$	44.0000	1.64092	0.820462	+	0.571702i	$0.193717\pi$
$720$	0	0
$721$	0	0
$722$	3.00000i	0.111648i
$723$	− 10.0000i	− 0.371904i
$724$	22.0000	0.817624
$725$	0	0
$726$	−5.00000	−0.185567
$727$	− 8.00000i	− 0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$	− 8.00000i	− 0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$	8.00000i	0.296500i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−12.0000	−0.443836
$732$	2.00000i	0.0739221i
$733$	− 18.0000i	− 0.664845i	−0.943131	−	0.332423i	$-0.892134\pi$
$733$	− 18.0000i	− 0.664845i	0.943131	−	0.332423i	$-0.107866\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	−4.00000	−0.147442
$737$	16.0000i	0.589368i
$738$	2.00000i	0.0736210i
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	− 8.00000i	− 0.293689i
$743$	28.0000i	1.02722i	0.858024	+	0.513610i	$0.171692\pi$
$743$	28.0000i	1.02722i	−0.858024	+	0.513610i	$0.828308\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	38.0000	1.39128
$747$	4.00000i	0.146352i
$748$	− 4.00000i	− 0.146254i
$749$	48.0000	1.75388
$750$	0	0
$751$	12.0000	0.437886	0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000	0.437886	0.218943	+	0.975738i	$0.429739\pi$
$752$	− 8.00000i	− 0.291730i
$753$	28.0000i	1.02038i
$754$	4.00000	0.145671
$755$	0	0
$756$	4.00000	0.145479
$757$	34.0000i	1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$	34.0000i	1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$	20.0000i	0.726433i
$759$	16.0000	0.580763
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	− 16.0000i	− 0.579619i
$763$	− 40.0000i	− 1.44810i
$764$	8.00000	0.289430
$765$	0	0
$766$	8.00000	0.289052
$767$	24.0000i	0.866590i
$768$	− 1.00000i	− 0.0360844i
$769$	46.0000	1.65880	0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000	1.65880	0.829401	+	0.558653i	$0.188682\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	− 18.0000i	− 0.647834i
$773$	6.00000i	0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$	6.00000i	0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	18.0000	0.646162
$777$	24.0000i	0.860995i
$778$	− 18.0000i	− 0.645331i
$779$	8.00000	0.286630
$780$	0	0
$781$	16.0000	0.572525
$782$	4.00000i	0.143040i
$783$	− 2.00000i	− 0.0714742i
$784$	−9.00000	−0.321429
$785$	0	0
$786$	−20.0000	−0.713376
$787$	− 36.0000i	− 1.28326i	−0.767014	−	0.641631i	$-0.778258\pi$
$787$	− 36.0000i	− 1.28326i	0.767014	−	0.641631i	$-0.221742\pi$
$788$	− 14.0000i	− 0.498729i
$789$	−16.0000	−0.569615
$790$	0	0
$791$	24.0000	0.853342
$792$	4.00000i	0.142134i
$793$	− 4.00000i	− 0.142044i
$794$	30.0000	1.06466
$795$	0	0
$796$	4.00000	0.141776
$797$	26.0000i	0.920967i	0.887668	+	0.460484i	$0.152324\pi$
$797$	26.0000i	0.920967i	−0.887668	+	0.460484i	$0.847676\pi$
$798$	− 16.0000i	− 0.566394i
$799$	−8.00000	−0.283020
$800$	0	0
$801$	10.0000	0.353333
$802$	6.00000i	0.211867i
$803$	56.0000i	1.97620i
$804$	4.00000	0.141069
$805$	0	0
$806$	−8.00000	−0.281788
$807$	− 30.0000i	− 1.05605i
$808$	− 10.0000i	− 0.351799i
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	8.00000i	0.280745i
$813$	0	0
$814$	−24.0000	−0.841200
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	− 48.0000i	− 1.67931i
$818$	10.0000i	0.349642i
$819$	−8.00000	−0.279543
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	− 6.00000i	− 0.209274i
$823$	− 28.0000i	− 0.976019i	−0.872838	−	0.488009i	$-0.837723\pi$
$823$	− 28.0000i	− 0.976019i	0.872838	−	0.488009i	$-0.162277\pi$
$824$	0	0
$825$	0	0
$826$	−48.0000	−1.67013
$827$	− 44.0000i	− 1.53003i	−0.644013	−	0.765015i	$-0.722732\pi$
$827$	− 44.0000i	− 1.53003i	0.644013	−	0.765015i	$-0.277268\pi$
$828$	− 4.00000i	− 0.139010i
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	0	0
$831$	−2.00000	−0.0693792
$832$	2.00000i	0.0693375i
$833$	9.00000i	0.311832i
$834$	−20.0000	−0.692543
$835$	0	0
$836$	16.0000	0.553372
$837$	4.00000i	0.138260i
$838$	12.0000i	0.414533i
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	18.0000i	0.620321i
$843$	− 10.0000i	− 0.344418i
$844$	−4.00000	−0.137686
$845$	0	0
$846$	8.00000	0.275046
$847$	20.0000i	0.687208i
$848$	− 2.00000i	− 0.0686803i
$849$	−20.0000	−0.686398
$850$	0	0
$851$	24.0000	0.822709
$852$	− 4.00000i	− 0.137038i
$853$	− 46.0000i	− 1.57501i	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	− 46.0000i	− 1.57501i	0.616308	−	0.787505i	$-0.288628\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	12.0000	0.410152
$857$	22.0000i	0.751506i	0.926720	+	0.375753i	$0.122616\pi$
$857$	22.0000i	0.751506i	−0.926720	+	0.375753i	$0.877384\pi$
$858$	− 8.00000i	− 0.273115i
$859$	−28.0000	−0.955348	−0.477674	−	0.878537i	$-0.658520\pi$
$859$	−28.0000	−0.955348	−0.477674	+	0.878537i	$0.658520\pi$
$860$	0	0
$861$	8.00000	0.272639
$862$	4.00000i	0.136241i
$863$	32.0000i	1.08929i	0.838666	+	0.544646i	$0.183336\pi$
$863$	32.0000i	1.08929i	−0.838666	+	0.544646i	$0.816664\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−14.0000	−0.475739
$867$	1.00000i	0.0339618i
$868$	− 16.0000i	− 0.543075i
$869$	−48.0000	−1.62829
$870$	0	0
$871$	−8.00000	−0.271070
$872$	− 10.0000i	− 0.338643i
$873$	18.0000i	0.609208i
$874$	−16.0000	−0.541208
$875$	0	0
$876$	14.0000	0.473016
$877$	22.0000i	0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$	22.0000i	0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$	− 12.0000i	− 0.404980i
$879$	−26.0000	−0.876958
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	− 9.00000i	− 0.303046i
$883$	− 28.0000i	− 0.942275i	−0.882060	−	0.471138i	$-0.843844\pi$
$883$	− 28.0000i	− 0.942275i	0.882060	−	0.471138i	$-0.156156\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	−36.0000	−1.20944
$887$	12.0000i	0.402921i	0.979497	+	0.201460i	$0.0645687\pi$
$887$	12.0000i	0.402921i	−0.979497	+	0.201460i	$0.935431\pi$
$888$	6.00000i	0.201347i
$889$	−64.0000	−2.14649
$890$	0	0
$891$	−4.00000	−0.134005
$892$	8.00000i	0.267860i
$893$	− 32.0000i	− 1.07084i
$894$	−2.00000	−0.0668900
$895$	0	0
$896$	−4.00000	−0.133631
$897$	8.00000i	0.267112i
$898$	− 6.00000i	− 0.200223i
$899$	−8.00000	−0.266815
$900$	0	0
$901$	−2.00000	−0.0666297
$902$	8.00000i	0.266371i
$903$	− 48.0000i	− 1.59734i
$904$	6.00000	0.199557
$905$	0	0
$906$	8.00000	0.265782
$907$	− 28.0000i	− 0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$	− 28.0000i	− 0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$	− 20.0000i	− 0.663723i
$909$	10.0000	0.331679
$910$	0	0
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	− 4.00000i	− 0.132453i
$913$	16.0000i	0.529523i
$914$	−10.0000	−0.330771
$915$	0	0
$916$	6.00000	0.198246
$917$	80.0000i	2.64183i
$918$	− 1.00000i	− 0.0330049i
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	0	0
$921$	4.00000	0.131804
$922$	− 14.0000i	− 0.461065i
$923$	8.00000i	0.263323i
$924$	16.0000	0.526361
$925$	0	0
$926$	40.0000	1.31448
$927$	0	0
$928$	2.00000i	0.0656532i
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	−36.0000	−1.17985
$932$	− 18.0000i	− 0.589610i
$933$	− 20.0000i	− 0.654771i
$934$	−36.0000	−1.17796
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	22.0000i	0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$	22.0000i	0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$	− 16.0000i	− 0.522419i
$939$	10.0000	0.326338
$940$	0	0
$941$	10.0000	0.325991	0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000	0.325991	0.162995	+	0.986627i	$0.447884\pi$
$942$	− 10.0000i	− 0.325818i
$943$	− 8.00000i	− 0.260516i
$944$	−12.0000	−0.390567
$945$	0	0
$946$	48.0000	1.56061
$947$	28.0000i	0.909878i	0.890523	+	0.454939i	$0.150339\pi$
$947$	28.0000i	0.909878i	−0.890523	+	0.454939i	$0.849661\pi$
$948$	12.0000i	0.389742i
$949$	−28.0000	−0.908918
$950$	0	0
$951$	−10.0000	−0.324272
$952$	4.00000i	0.129641i
$953$	− 6.00000i	− 0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$	− 6.00000i	− 0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	2.00000	0.0647524
$955$	0	0
$956$	−24.0000	−0.776215
$957$	− 8.00000i	− 0.258603i
$958$	20.0000i	0.646171i
$959$	−24.0000	−0.775000
$960$	0	0
$961$	−15.0000	−0.483871
$962$	− 12.0000i	− 0.386896i
$963$	12.0000i	0.386695i
$964$	−10.0000	−0.322078
$965$	0	0
$966$	−16.0000	−0.514792
$967$	16.0000i	0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$967$	16.0000i	0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$968$	5.00000i	0.160706i
$969$	−4.00000	−0.128499
$970$	0	0
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	1.00000i	0.0320750i
$973$	80.0000i	2.56468i
$974$	−20.0000	−0.640841
$975$	0	0
$976$	2.00000	0.0640184
$977$	30.0000i	0.959785i	0.877327	+	0.479893i	$0.159324\pi$
$977$	30.0000i	0.959785i	−0.877327	+	0.479893i	$0.840676\pi$
$978$	20.0000i	0.639529i
$979$	40.0000	1.27841
$980$	0	0
$981$	10.0000	0.319275
$982$	12.0000i	0.382935i
$983$	− 28.0000i	− 0.893061i	−0.894768	−	0.446531i	$-0.852659\pi$
$983$	− 28.0000i	− 0.893061i	0.894768	−	0.446531i	$-0.147341\pi$
$984$	2.00000	0.0637577
$985$	0	0
$986$	2.00000	0.0636930
$987$	− 32.0000i	− 1.01857i
$988$	8.00000i	0.254514i
$989$	−48.0000	−1.52631
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	− 4.00000i	− 0.127000i
$993$	− 28.0000i	− 0.888553i
$994$	−16.0000	−0.507489
$995$	0	0
$996$	4.00000	0.126745
$997$	38.0000i	1.20347i	0.798695	+	0.601736i	$0.205524\pi$
$997$	38.0000i	1.20347i	−0.798695	+	0.601736i	$0.794476\pi$
$998$	4.00000i	0.126618i
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.b.2449.1		2
5.2	odd	4		510.2.a.c.1.1	✓	1
5.3	odd	4		2550.2.a.n.1.1		1
5.4	even	2	inner	2550.2.d.b.2449.2		2
15.2	even	4		1530.2.a.d.1.1		1
15.8	even	4		7650.2.a.cn.1.1		1
20.7	even	4		4080.2.a.x.1.1		1
85.67	odd	4		8670.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.a.c.1.1	✓	1	5.2	odd	4
1530.2.a.d.1.1		1	15.2	even	4
2550.2.a.n.1.1		1	5.3	odd	4
2550.2.d.b.2449.1		2	1.1	even	1	trivial
2550.2.d.b.2449.2		2	5.4	even	2	inner
4080.2.a.x.1.1		1	20.7	even	4
7650.2.a.cn.1.1		1	15.8	even	4
8670.2.a.bb.1.1		1	85.67	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -4.00000 q^{11} +1.00000i q^{12} -2.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} +4.00000 q^{19} +4.00000 q^{21} +4.00000i q^{22} -4.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} +1.00000i q^{27} -4.00000i q^{28} -2.00000 q^{29} +4.00000 q^{31} -1.00000i q^{32} +4.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} +6.00000i q^{37} -4.00000i q^{38} -2.00000 q^{39} +2.00000 q^{41} -4.00000i q^{42} -12.0000i q^{43} +4.00000 q^{44} -4.00000 q^{46} -8.00000i q^{47} -1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -2.00000i q^{53} +1.00000 q^{54} -4.00000 q^{56} -4.00000i q^{57} +2.00000i q^{58} -12.0000 q^{59} +2.00000 q^{61} -4.00000i q^{62} -4.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} -4.00000i q^{67} +1.00000i q^{68} -4.00000 q^{69} -4.00000 q^{71} -1.00000i q^{72} -14.0000i q^{73} +6.00000 q^{74} -4.00000 q^{76} -16.0000i q^{77} +2.00000i q^{78} +12.0000 q^{79} +1.00000 q^{81} -2.00000i q^{82} -4.00000i q^{83} -4.00000 q^{84} -12.0000 q^{86} +2.00000i q^{87} -4.00000i q^{88} -10.0000 q^{89} +8.00000 q^{91} +4.00000i q^{92} -4.00000i q^{93} -8.00000 q^{94} -1.00000 q^{96} -18.0000i q^{97} +9.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 8 q^{11} + 8 q^{14} + 2 q^{16} + 8 q^{19} + 8 q^{21} + 2 q^{24} - 4 q^{26} - 4 q^{29} + 8 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} + 4 q^{41} + 8 q^{44} - 8 q^{46} - 18 q^{49} - 2 q^{51} + 2 q^{54} - 8 q^{56} - 24 q^{59} + 4 q^{61} - 2 q^{64} + 8 q^{66} - 8 q^{69} - 8 q^{71} + 12 q^{74} - 8 q^{76} + 24 q^{79} + 2 q^{81} - 8 q^{84} - 24 q^{86} - 20 q^{89} + 16 q^{91} - 16 q^{94} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 8 * q^11 + 8 * q^14 + 2 * q^16 + 8 * q^19 + 8 * q^21 + 2 * q^24 - 4 * q^26 - 4 * q^29 + 8 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 + 4 * q^41 + 8 * q^44 - 8 * q^46 - 18 * q^49 - 2 * q^51 + 2 * q^54 - 8 * q^56 - 24 * q^59 + 4 * q^61 - 2 * q^64 + 8 * q^66 - 8 * q^69 - 8 * q^71 + 12 * q^74 - 8 * q^76 + 24 * q^79 + 2 * q^81 - 8 * q^84 - 24 * q^86 - 20 * q^89 + 16 * q^91 - 16 * q^94 - 2 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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