LMFDB - Embedded newform 3362.2.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3362,2,Mod(1,3362)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3362, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3362.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3362 = 2 \cdot 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3362.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,-2,2,1,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$26.8457051596$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{61}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 15 $ x^2 - x - 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.40512$ of defining polynomial
Character	$\chi$	$=$	3362.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.40512 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +3.40512 q^{10} +3.40512 q^{11} -1.00000 q^{12} -5.40512 q^{13} -1.00000 q^{14} +3.40512 q^{15} +1.00000 q^{16} +6.40512 q^{17} +2.00000 q^{18} +1.40512 q^{19} -3.40512 q^{20} -1.00000 q^{21} -3.40512 q^{22} -6.40512 q^{23} +1.00000 q^{24} +6.59488 q^{25} +5.40512 q^{26} +5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} -3.40512 q^{30} -0.594875 q^{31} -1.00000 q^{32} -3.40512 q^{33} -6.40512 q^{34} -3.40512 q^{35} -2.00000 q^{36} +2.00000 q^{37} -1.40512 q^{38} +5.40512 q^{39} +3.40512 q^{40} +1.00000 q^{42} +11.8102 q^{43} +3.40512 q^{44} +6.81025 q^{45} +6.40512 q^{46} +6.40512 q^{47} -1.00000 q^{48} -6.00000 q^{49} -6.59488 q^{50} -6.40512 q^{51} -5.40512 q^{52} +3.81025 q^{53} -5.00000 q^{54} -11.5949 q^{55} -1.00000 q^{56} -1.40512 q^{57} +3.00000 q^{58} +12.4051 q^{59} +3.40512 q^{60} -3.59488 q^{61} +0.594875 q^{62} -2.00000 q^{63} +1.00000 q^{64} +18.4051 q^{65} +3.40512 q^{66} -11.4051 q^{67} +6.40512 q^{68} +6.40512 q^{69} +3.40512 q^{70} +9.81025 q^{71} +2.00000 q^{72} -10.8102 q^{73} -2.00000 q^{74} -6.59488 q^{75} +1.40512 q^{76} +3.40512 q^{77} -5.40512 q^{78} +4.81025 q^{79} -3.40512 q^{80} +1.00000 q^{81} +6.00000 q^{83} -1.00000 q^{84} -21.8102 q^{85} -11.8102 q^{86} +3.00000 q^{87} -3.40512 q^{88} +3.40512 q^{89} -6.81025 q^{90} -5.40512 q^{91} -6.40512 q^{92} +0.594875 q^{93} -6.40512 q^{94} -4.78463 q^{95} +1.00000 q^{96} -5.81025 q^{97} +6.00000 q^{98} -6.81025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - q^{10} - q^{11} - 2 q^{12} - 3 q^{13} - 2 q^{14} - q^{15} + 2 q^{16} + 5 q^{17} + 4 q^{18} - 5 q^{19} + q^{20} - 2 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - q^10 - q^11 - 2 * q^12 - 3 * q^13 - 2 * q^14 - q^15 + 2 * q^16 + 5 * q^17 + 4 * q^18 - 5 * q^19 + q^20 - 2 * q^21 + q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 3 * q^26 + 10 * q^27 + 2 * q^28 - 6 * q^29 + q^30 - 9 * q^31 - 2 * q^32 + q^33 - 5 * q^34 + q^35 - 4 * q^36 + 4 * q^37 + 5 * q^38 + 3 * q^39 - q^40 + 2 * q^42 + 8 * q^43 - q^44 - 2 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 - 12 * q^49 - 21 * q^50 - 5 * q^51 - 3 * q^52 - 8 * q^53 - 10 * q^54 - 31 * q^55 - 2 * q^56 + 5 * q^57 + 6 * q^58 + 17 * q^59 - q^60 - 15 * q^61 + 9 * q^62 - 4 * q^63 + 2 * q^64 + 29 * q^65 - q^66 - 15 * q^67 + 5 * q^68 + 5 * q^69 - q^70 + 4 * q^71 + 4 * q^72 - 6 * q^73 - 4 * q^74 - 21 * q^75 - 5 * q^76 - q^77 - 3 * q^78 - 6 * q^79 + q^80 + 2 * q^81 + 12 * q^83 - 2 * q^84 - 28 * q^85 - 8 * q^86 + 6 * q^87 + q^88 - q^89 + 2 * q^90 - 3 * q^91 - 5 * q^92 + 9 * q^93 - 5 * q^94 - 33 * q^95 + 2 * q^96 + 4 * q^97 + 12 * q^98 + 2 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−3.40512	−1.52282	−0.761409	−	0.648272i	$-0.775492\pi$
$5$	−3.40512	−1.52282	−0.761409	+	0.648272i	$0.775492\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	3.40512	1.07680
$11$	3.40512	1.02668	0.513342	−	0.858184i	$-0.328407\pi$
$11$	3.40512	1.02668	0.513342	+	0.858184i	$0.328407\pi$
$12$	−1.00000	−0.288675
$13$	−5.40512	−1.49911	−0.749556	−	0.661941i	$-0.769733\pi$
$13$	−5.40512	−1.49911	−0.749556	+	0.661941i	$0.769733\pi$
$14$	−1.00000	−0.267261
$15$	3.40512	0.879199
$16$	1.00000	0.250000
$17$	6.40512	1.55347	0.776735	−	0.629827i	$-0.216874\pi$
$17$	6.40512	1.55347	0.776735	+	0.629827i	$0.216874\pi$
$18$	2.00000	0.471405
$19$	1.40512	0.322358	0.161179	−	0.986925i	$-0.448470\pi$
$19$	1.40512	0.322358	0.161179	+	0.986925i	$0.448470\pi$
$20$	−3.40512	−0.761409
$21$	−1.00000	−0.218218
$22$	−3.40512	−0.725975
$23$	−6.40512	−1.33556	−0.667780	−	0.744358i	$-0.732755\pi$
$23$	−6.40512	−1.33556	−0.667780	+	0.744358i	$0.732755\pi$
$24$	1.00000	0.204124
$25$	6.59488	1.31898
$26$	5.40512	1.06003
$27$	5.00000	0.962250
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−3.40512	−0.621688
$31$	−0.594875	−0.106843	−0.0534214	−	0.998572i	$-0.517013\pi$
$31$	−0.594875	−0.106843	−0.0534214	+	0.998572i	$0.517013\pi$
$32$	−1.00000	−0.176777
$33$	−3.40512	−0.592756
$34$	−6.40512	−1.09847
$35$	−3.40512	−0.575571
$36$	−2.00000	−0.333333
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−1.40512	−0.227941
$39$	5.40512	0.865513
$40$	3.40512	0.538398
$41$	0	0
$41$	0	0
$42$	1.00000	0.154303
$43$	11.8102	1.80105	0.900523	−	0.434808i	$-0.143184\pi$
$43$	11.8102	1.80105	0.900523	+	0.434808i	$0.143184\pi$
$44$	3.40512	0.513342
$45$	6.81025	1.01521
$46$	6.40512	0.944384
$47$	6.40512	0.934283	0.467142	−	0.884182i	$-0.345284\pi$
$47$	6.40512	0.934283	0.467142	+	0.884182i	$0.345284\pi$
$48$	−1.00000	−0.144338
$49$	−6.00000	−0.857143
$50$	−6.59488	−0.932656
$51$	−6.40512	−0.896897
$52$	−5.40512	−0.749556
$53$	3.81025	0.523378	0.261689	−	0.965152i	$-0.415721\pi$
$53$	3.81025	0.523378	0.261689	+	0.965152i	$0.415721\pi$
$54$	−5.00000	−0.680414
$55$	−11.5949	−1.56345
$56$	−1.00000	−0.133631
$57$	−1.40512	−0.186113
$58$	3.00000	0.393919
$59$	12.4051	1.61501	0.807505	−	0.589861i	$-0.200817\pi$
$59$	12.4051	1.61501	0.807505	+	0.589861i	$0.200817\pi$
$60$	3.40512	0.439600
$61$	−3.59488	−0.460277	−0.230138	−	0.973158i	$-0.573918\pi$
$61$	−3.59488	−0.460277	−0.230138	+	0.973158i	$0.573918\pi$
$62$	0.594875	0.0755492
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	18.4051	2.28287
$66$	3.40512	0.419142
$67$	−11.4051	−1.39336	−0.696679	−	0.717383i	$-0.745340\pi$
$67$	−11.4051	−1.39336	−0.696679	+	0.717383i	$0.745340\pi$
$68$	6.40512	0.776735
$69$	6.40512	0.771086
$70$	3.40512	0.406990
$71$	9.81025	1.16426	0.582131	−	0.813095i	$-0.302219\pi$
$71$	9.81025	1.16426	0.582131	+	0.813095i	$0.302219\pi$
$72$	2.00000	0.235702
$73$	−10.8102	−1.26524	−0.632622	−	0.774461i	$-0.718021\pi$
$73$	−10.8102	−1.26524	−0.632622	+	0.774461i	$0.718021\pi$
$74$	−2.00000	−0.232495
$75$	−6.59488	−0.761511
$76$	1.40512	0.161179
$77$	3.40512	0.388050
$78$	−5.40512	−0.612010
$79$	4.81025	0.541195	0.270598	−	0.962693i	$-0.412779\pi$
$79$	4.81025	0.541195	0.270598	+	0.962693i	$0.412779\pi$
$80$	−3.40512	−0.380705
$81$	1.00000	0.111111
$82$	0	0
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	−0.109109
$85$	−21.8102	−2.36565
$86$	−11.8102	−1.27353
$87$	3.00000	0.321634
$88$	−3.40512	−0.362988
$89$	3.40512	0.360943	0.180471	−	0.983580i	$-0.442238\pi$
$89$	3.40512	0.360943	0.180471	+	0.983580i	$0.442238\pi$
$90$	−6.81025	−0.717863
$91$	−5.40512	−0.566611
$92$	−6.40512	−0.667780
$93$	0.594875	0.0616857
$94$	−6.40512	−0.660638
$95$	−4.78463	−0.490892
$96$	1.00000	0.102062
$97$	−5.81025	−0.589941	−0.294971	−	0.955506i	$-0.595310\pi$
$97$	−5.81025	−0.589941	−0.294971	+	0.955506i	$0.595310\pi$
$98$	6.00000	0.606092
$99$	−6.81025	−0.684456
$100$	6.59488	0.659488
$101$	−19.2154	−1.91200	−0.956001	−	0.293365i	$-0.905225\pi$
$101$	−19.2154	−1.91200	−0.956001	+	0.293365i	$0.905225\pi$
$102$	6.40512	0.634202
$103$	2.81025	0.276902	0.138451	−	0.990369i	$-0.455788\pi$
$103$	2.81025	0.276902	0.138451	+	0.990369i	$0.455788\pi$
$104$	5.40512	0.530016
$105$	3.40512	0.332306
$106$	−3.81025	−0.370084
$107$	18.4051	1.77929	0.889645	−	0.456652i	$-0.150952\pi$
$107$	18.4051	1.77929	0.889645	+	0.456652i	$0.150952\pi$
$108$	5.00000	0.481125
$109$	−5.81025	−0.556521	−0.278260	−	0.960506i	$-0.589758\pi$
$109$	−5.81025	−0.556521	−0.278260	+	0.960506i	$0.589758\pi$
$110$	11.5949	1.10553
$111$	−2.00000	−0.189832
$112$	1.00000	0.0944911
$113$	−12.8102	−1.20509	−0.602543	−	0.798086i	$-0.705846\pi$
$113$	−12.8102	−1.20509	−0.602543	+	0.798086i	$0.705846\pi$
$114$	1.40512	0.131602
$115$	21.8102	2.03382
$116$	−3.00000	−0.278543
$117$	10.8102	0.999408
$118$	−12.4051	−1.14198
$119$	6.40512	0.587157
$120$	−3.40512	−0.310844
$121$	0.594875	0.0540796
$122$	3.59488	0.325465
$123$	0	0
$124$	−0.594875	−0.0534214
$125$	−5.43075	−0.485741
$126$	2.00000	0.178174
$127$	−13.8102	−1.22546	−0.612731	−	0.790292i	$-0.709929\pi$
$127$	−13.8102	−1.22546	−0.612731	+	0.790292i	$0.709929\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8102	−1.03983
$130$	−18.4051	−1.61424
$131$	13.2154	1.15463	0.577316	−	0.816521i	$-0.304100\pi$
$131$	13.2154	1.15463	0.577316	+	0.816521i	$0.304100\pi$
$132$	−3.40512	−0.296378
$133$	1.40512	0.121840
$134$	11.4051	0.985253
$135$	−17.0256	−1.46533
$136$	−6.40512	−0.549235
$137$	−22.2154	−1.89799	−0.948994	−	0.315295i	$-0.897897\pi$
$137$	−22.2154	−1.89799	−0.948994	+	0.315295i	$0.897897\pi$
$138$	−6.40512	−0.545240
$139$	6.21537	0.527181	0.263591	−	0.964635i	$-0.415093\pi$
$139$	6.21537	0.527181	0.263591	+	0.964635i	$0.415093\pi$
$140$	−3.40512	−0.287786
$141$	−6.40512	−0.539409
$142$	−9.81025	−0.823258
$143$	−18.4051	−1.53911
$144$	−2.00000	−0.166667
$145$	10.2154	0.848341
$146$	10.8102	0.894663
$147$	6.00000	0.494872
$148$	2.00000	0.164399
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	6.59488	0.538469
$151$	3.59488	0.292547	0.146273	−	0.989244i	$-0.453272\pi$
$151$	3.59488	0.292547	0.146273	+	0.989244i	$0.453272\pi$
$152$	−1.40512	−0.113971
$153$	−12.8102	−1.03565
$154$	−3.40512	−0.274393
$155$	2.02562	0.162702
$156$	5.40512	0.432756
$157$	−1.18975	−0.0949524	−0.0474762	−	0.998872i	$-0.515118\pi$
$157$	−1.18975	−0.0949524	−0.0474762	+	0.998872i	$0.515118\pi$
$158$	−4.81025	−0.382683
$159$	−3.81025	−0.302172
$160$	3.40512	0.269199
$161$	−6.40512	−0.504795
$162$	−1.00000	−0.0785674
$163$	−20.6205	−1.61512	−0.807561	−	0.589784i	$-0.799213\pi$
$163$	−20.6205	−1.61512	−0.807561	+	0.589784i	$0.799213\pi$
$164$	0	0
$165$	11.5949	0.902660
$166$	−6.00000	−0.465690
$167$	−8.18975	−0.633742	−0.316871	−	0.948469i	$-0.602632\pi$
$167$	−8.18975	−0.633742	−0.316871	+	0.948469i	$0.602632\pi$
$168$	1.00000	0.0771517
$169$	16.2154	1.24734
$170$	21.8102	1.67277
$171$	−2.81025	−0.214905
$172$	11.8102	0.900523
$173$	−3.00000	−0.228086	−0.114043	−	0.993476i	$-0.536380\pi$
$173$	−3.00000	−0.228086	−0.114043	+	0.993476i	$0.536380\pi$
$174$	−3.00000	−0.227429
$175$	6.59488	0.498526
$176$	3.40512	0.256671
$177$	−12.4051	−0.932426
$178$	−3.40512	−0.255225
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	6.81025	0.507606
$181$	−11.0000	−0.817624	−0.408812	−	0.912619i	$-0.634057\pi$
$181$	−11.0000	−0.817624	−0.408812	+	0.912619i	$0.634057\pi$
$182$	5.40512	0.400655
$183$	3.59488	0.265741
$184$	6.40512	0.472192
$185$	−6.81025	−0.500700
$186$	−0.594875	−0.0436184
$187$	21.8102	1.59492
$188$	6.40512	0.467142
$189$	5.00000	0.363696
$190$	4.78463	0.347113
$191$	−1.78463	−0.129131	−0.0645655	−	0.997913i	$-0.520566\pi$
$191$	−1.78463	−0.129131	−0.0645655	+	0.997913i	$0.520566\pi$
$192$	−1.00000	−0.0721688
$193$	−13.0256	−0.937605	−0.468802	−	0.883303i	$-0.655314\pi$
$193$	−13.0256	−0.937605	−0.468802	+	0.883303i	$0.655314\pi$
$194$	5.81025	0.417152
$195$	−18.4051	−1.31802
$196$	−6.00000	−0.428571
$197$	18.4051	1.31131	0.655655	−	0.755060i	$-0.272392\pi$
$197$	18.4051	1.31131	0.655655	+	0.755060i	$0.272392\pi$
$198$	6.81025	0.483983
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	−6.59488	−0.466328
$201$	11.4051	0.804455
$202$	19.2154	1.35199
$203$	−3.00000	−0.210559
$204$	−6.40512	−0.448448
$205$	0	0
$206$	−2.81025	−0.195799
$207$	12.8102	0.890374
$208$	−5.40512	−0.374778
$209$	4.78463	0.330959
$210$	−3.40512	−0.234976
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	3.81025	0.261689
$213$	−9.81025	−0.672187
$214$	−18.4051	−1.25815
$215$	−40.2154	−2.74267
$216$	−5.00000	−0.340207
$217$	−0.594875	−0.0403828
$218$	5.81025	0.393520
$219$	10.8102	0.730489
$220$	−11.5949	−0.781726
$221$	−34.6205	−2.32883
$222$	2.00000	0.134231
$223$	−17.6205	−1.17996	−0.589978	−	0.807419i	$-0.700864\pi$
$223$	−17.6205	−1.17996	−0.589978	+	0.807419i	$0.700864\pi$
$224$	−1.00000	−0.0668153
$225$	−13.1898	−0.879317
$226$	12.8102	0.852125
$227$	−7.21537	−0.478901	−0.239451	−	0.970909i	$-0.576967\pi$
$227$	−7.21537	−0.478901	−0.239451	+	0.970909i	$0.576967\pi$
$228$	−1.40512	−0.0930567
$229$	0.594875	0.0393105	0.0196552	−	0.999807i	$-0.493743\pi$
$229$	0.594875	0.0393105	0.0196552	+	0.999807i	$0.493743\pi$
$230$	−21.8102	−1.43813
$231$	−3.40512	−0.224041
$232$	3.00000	0.196960
$233$	−6.81025	−0.446154	−0.223077	−	0.974801i	$-0.571610\pi$
$233$	−6.81025	−0.446154	−0.223077	+	0.974801i	$0.571610\pi$
$234$	−10.8102	−0.706688
$235$	−21.8102	−1.42274
$236$	12.4051	0.807505
$237$	−4.81025	−0.312459
$238$	−6.40512	−0.415183
$239$	−20.4307	−1.32156	−0.660778	−	0.750582i	$-0.729773\pi$
$239$	−20.4307	−1.32156	−0.660778	+	0.750582i	$0.729773\pi$
$240$	3.40512	0.219800
$241$	−3.59488	−0.231566	−0.115783	−	0.993275i	$-0.536938\pi$
$241$	−3.59488	−0.231566	−0.115783	+	0.993275i	$0.536938\pi$
$242$	−0.594875	−0.0382400
$243$	−16.0000	−1.02640
$244$	−3.59488	−0.230138
$245$	20.4307	1.30527
$246$	0	0
$247$	−7.59488	−0.483250
$248$	0.594875	0.0377746
$249$	−6.00000	−0.380235
$250$	5.43075	0.343471
$251$	−15.0000	−0.946792	−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000	−0.946792	−0.473396	+	0.880850i	$0.656972\pi$
$252$	−2.00000	−0.125988
$253$	−21.8102	−1.37120
$254$	13.8102	0.866532
$255$	21.8102	1.36581
$256$	1.00000	0.0625000
$257$	2.59488	0.161864	0.0809319	−	0.996720i	$-0.474210\pi$
$257$	2.59488	0.161864	0.0809319	+	0.996720i	$0.474210\pi$
$258$	11.8102	0.735274
$259$	2.00000	0.124274
$260$	18.4051	1.14144
$261$	6.00000	0.371391
$262$	−13.2154	−0.816449
$263$	−5.18975	−0.320014	−0.160007	−	0.987116i	$-0.551152\pi$
$263$	−5.18975	−0.320014	−0.160007	+	0.987116i	$0.551152\pi$
$264$	3.40512	0.209571
$265$	−12.9744	−0.797010
$266$	−1.40512	−0.0861537
$267$	−3.40512	−0.208390
$268$	−11.4051	−0.696679
$269$	−15.0000	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$270$	17.0256	1.03615
$271$	21.2154	1.28874	0.644371	−	0.764713i	$-0.277119\pi$
$271$	21.2154	1.28874	0.644371	+	0.764713i	$0.277119\pi$
$272$	6.40512	0.388368
$273$	5.40512	0.327133
$274$	22.2154	1.34208
$275$	22.4564	1.35417
$276$	6.40512	0.385543
$277$	2.81025	0.168852	0.0844258	−	0.996430i	$-0.473094\pi$
$277$	2.81025	0.168852	0.0844258	+	0.996430i	$0.473094\pi$
$278$	−6.21537	−0.372773
$279$	1.18975	0.0712285
$280$	3.40512	0.203495
$281$	−0.810250	−0.0483354	−0.0241677	−	0.999708i	$-0.507694\pi$
$281$	−0.810250	−0.0483354	−0.0241677	+	0.999708i	$0.507694\pi$
$282$	6.40512	0.381420
$283$	−27.4307	−1.63059	−0.815294	−	0.579047i	$-0.803425\pi$
$283$	−27.4307	−1.63059	−0.815294	+	0.579047i	$0.803425\pi$
$284$	9.81025	0.582131
$285$	4.78463	0.283417
$286$	18.4051	1.08832
$287$	0	0
$288$	2.00000	0.117851
$289$	24.0256	1.41327
$290$	−10.2154	−0.599867
$291$	5.81025	0.340603
$292$	−10.8102	−0.632622
$293$	−21.4051	−1.25050	−0.625250	−	0.780424i	$-0.715003\pi$
$293$	−21.4051	−1.25050	−0.625250	+	0.780424i	$0.715003\pi$
$294$	−6.00000	−0.349927
$295$	−42.2410	−2.45937
$296$	−2.00000	−0.116248
$297$	17.0256	0.987927
$298$	0	0
$299$	34.6205	2.00216
$300$	−6.59488	−0.380755
$301$	11.8102	0.680731
$302$	−3.59488	−0.206862
$303$	19.2154	1.10389
$304$	1.40512	0.0805894
$305$	12.2410	0.700918
$306$	12.8102	0.732313
$307$	−15.0256	−0.857558	−0.428779	−	0.903409i	$-0.641056\pi$
$307$	−15.0256	−0.857558	−0.428779	+	0.903409i	$0.641056\pi$
$308$	3.40512	0.194025
$309$	−2.81025	−0.159870
$310$	−2.02562	−0.115048
$311$	−28.6205	−1.62292	−0.811460	−	0.584408i	$-0.801327\pi$
$311$	−28.6205	−1.62292	−0.811460	+	0.584408i	$0.801327\pi$
$312$	−5.40512	−0.306005
$313$	30.4307	1.72005	0.860024	−	0.510254i	$-0.170449\pi$
$313$	30.4307	1.72005	0.860024	+	0.510254i	$0.170449\pi$
$314$	1.18975	0.0671415
$315$	6.81025	0.383714
$316$	4.81025	0.270598
$317$	3.40512	0.191251	0.0956254	−	0.995417i	$-0.469515\pi$
$317$	3.40512	0.191251	0.0956254	+	0.995417i	$0.469515\pi$
$318$	3.81025	0.213668
$319$	−10.2154	−0.571951
$320$	−3.40512	−0.190352
$321$	−18.4051	−1.02727
$322$	6.40512	0.356944
$323$	9.00000	0.500773
$324$	1.00000	0.0555556
$325$	−35.6461	−1.97729
$326$	20.6205	1.14206
$327$	5.81025	0.321308
$328$	0	0
$329$	6.40512	0.353126
$330$	−11.5949	−0.638277
$331$	23.6205	1.29830	0.649150	−	0.760660i	$-0.275125\pi$
$331$	23.6205	1.29830	0.649150	+	0.760660i	$0.275125\pi$
$332$	6.00000	0.329293
$333$	−4.00000	−0.219199
$334$	8.18975	0.448123
$335$	38.8359	2.12183
$336$	−1.00000	−0.0545545
$337$	11.8102	0.643345	0.321673	−	0.946851i	$-0.395755\pi$
$337$	11.8102	0.643345	0.321673	+	0.946851i	$0.395755\pi$
$338$	−16.2154	−0.882000
$339$	12.8102	0.695757
$340$	−21.8102	−1.18283
$341$	−2.02562	−0.109694
$342$	2.81025	0.151961
$343$	−13.0000	−0.701934
$344$	−11.8102	−0.636766
$345$	−21.8102	−1.17422
$346$	3.00000	0.161281
$347$	6.81025	0.365593	0.182797	−	0.983151i	$-0.441485\pi$
$347$	6.81025	0.365593	0.182797	+	0.983151i	$0.441485\pi$
$348$	3.00000	0.160817
$349$	−11.2154	−0.600345	−0.300173	−	0.953885i	$-0.597044\pi$
$349$	−11.2154	−0.600345	−0.300173	+	0.953885i	$0.597044\pi$
$350$	−6.59488	−0.352511
$351$	−27.0256	−1.44252
$352$	−3.40512	−0.181494
$353$	−21.8102	−1.16084	−0.580421	−	0.814316i	$-0.697112\pi$
$353$	−21.8102	−1.16084	−0.580421	+	0.814316i	$0.697112\pi$
$354$	12.4051	0.659325
$355$	−33.4051	−1.77296
$356$	3.40512	0.180471
$357$	−6.40512	−0.338995
$358$	−9.00000	−0.475665
$359$	25.2154	1.33082	0.665408	−	0.746480i	$-0.268257\pi$
$359$	25.2154	1.33082	0.665408	+	0.746480i	$0.268257\pi$
$360$	−6.81025	−0.358932
$361$	−17.0256	−0.896085
$362$	11.0000	0.578147
$363$	−0.594875	−0.0312228
$364$	−5.40512	−0.283306
$365$	36.8102	1.92674
$366$	−3.59488	−0.187907
$367$	3.21537	0.167841	0.0839206	−	0.996472i	$-0.473256\pi$
$367$	3.21537	0.167841	0.0839206	+	0.996472i	$0.473256\pi$
$368$	−6.40512	−0.333890
$369$	0	0
$370$	6.81025	0.354048
$371$	3.81025	0.197818
$372$	0.594875	0.0308428
$373$	−13.0000	−0.673114	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	−13.0000	−0.673114	−0.336557	+	0.941663i	$0.609263\pi$
$374$	−21.8102	−1.12778
$375$	5.43075	0.280443
$376$	−6.40512	−0.330319
$377$	16.2154	0.835134
$378$	−5.00000	−0.257172
$379$	18.6205	0.956471	0.478235	−	0.878232i	$-0.341277\pi$
$379$	18.6205	0.956471	0.478235	+	0.878232i	$0.341277\pi$
$380$	−4.78463	−0.245446
$381$	13.8102	0.707521
$382$	1.78463	0.0913094
$383$	−12.4051	−0.633872	−0.316936	−	0.948447i	$-0.602654\pi$
$383$	−12.4051	−0.633872	−0.316936	+	0.948447i	$0.602654\pi$
$384$	1.00000	0.0510310
$385$	−11.5949	−0.590930
$386$	13.0256	0.662987
$387$	−23.6205	−1.20070
$388$	−5.81025	−0.294971
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	18.4051	0.931980
$391$	−41.0256	−2.07475
$392$	6.00000	0.303046
$393$	−13.2154	−0.666627
$394$	−18.4051	−0.927237
$395$	−16.3795	−0.824142
$396$	−6.81025	−0.342228
$397$	−26.0000	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$397$	−26.0000	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$398$	11.0000	0.551380
$399$	−1.40512	−0.0703442
$400$	6.59488	0.329744
$401$	−5.59488	−0.279395	−0.139697	−	0.990194i	$-0.544613\pi$
$401$	−5.59488	−0.279395	−0.139697	+	0.990194i	$0.544613\pi$
$402$	−11.4051	−0.568836
$403$	3.21537	0.160169
$404$	−19.2154	−0.956001
$405$	−3.40512	−0.169202
$406$	3.00000	0.148888
$407$	6.81025	0.337572
$408$	6.40512	0.317101
$409$	−15.5949	−0.771117	−0.385558	−	0.922683i	$-0.625991\pi$
$409$	−15.5949	−0.771117	−0.385558	+	0.922683i	$0.625991\pi$
$410$	0	0
$411$	22.2154	1.09580
$412$	2.81025	0.138451
$413$	12.4051	0.610416
$414$	−12.8102	−0.629589
$415$	−20.4307	−1.00291
$416$	5.40512	0.265008
$417$	−6.21537	−0.304368
$418$	−4.78463	−0.234024
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	3.40512	0.166153
$421$	5.62050	0.273926	0.136963	−	0.990576i	$-0.456266\pi$
$421$	5.62050	0.273926	0.136963	+	0.990576i	$0.456266\pi$
$422$	−13.0000	−0.632830
$423$	−12.8102	−0.622856
$424$	−3.81025	−0.185042
$425$	42.2410	2.04899
$426$	9.81025	0.475308
$427$	−3.59488	−0.173968
$428$	18.4051	0.889645
$429$	18.4051	0.888608
$430$	40.2154	1.93936
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	5.00000	0.240563
$433$	−10.0000	−0.480569	−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000	−0.480569	−0.240285	+	0.970702i	$0.577241\pi$
$434$	0.594875	0.0285549
$435$	−10.2154	−0.489790
$436$	−5.81025	−0.278260
$437$	−9.00000	−0.430528
$438$	−10.8102	−0.516534
$439$	−25.4307	−1.21374	−0.606872	−	0.794800i	$-0.707576\pi$
$439$	−25.4307	−1.21374	−0.606872	+	0.794800i	$0.707576\pi$
$440$	11.5949	0.552764
$441$	12.0000	0.571429
$442$	34.6205	1.64673
$443$	17.4307	0.828160	0.414080	−	0.910241i	$-0.364103\pi$
$443$	17.4307	0.828160	0.414080	+	0.910241i	$0.364103\pi$
$444$	−2.00000	−0.0949158
$445$	−11.5949	−0.549650
$446$	17.6205	0.834355
$447$	0	0
$448$	1.00000	0.0472456
$449$	24.0000	1.13263	0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000	1.13263	0.566315	+	0.824189i	$0.308369\pi$
$450$	13.1898	0.621771
$451$	0	0
$452$	−12.8102	−0.602543
$453$	−3.59488	−0.168902
$454$	7.21537	0.338634
$455$	18.4051	0.862846
$456$	1.40512	0.0658010
$457$	−5.00000	−0.233890	−0.116945	−	0.993138i	$-0.537310\pi$
$457$	−5.00000	−0.233890	−0.116945	+	0.993138i	$0.537310\pi$
$458$	−0.594875	−0.0277967
$459$	32.0256	1.49483
$460$	21.8102	1.01691
$461$	12.4051	0.577764	0.288882	−	0.957365i	$-0.406716\pi$
$461$	12.4051	0.577764	0.288882	+	0.957365i	$0.406716\pi$
$462$	3.40512	0.158421
$463$	−12.6205	−0.586524	−0.293262	−	0.956032i	$-0.594741\pi$
$463$	−12.6205	−0.586524	−0.293262	+	0.956032i	$0.594741\pi$
$464$	−3.00000	−0.139272
$465$	−2.02562	−0.0939361
$466$	6.81025	0.315479
$467$	11.1898	0.517800	0.258900	−	0.965904i	$-0.416640\pi$
$467$	11.1898	0.517800	0.258900	+	0.965904i	$0.416640\pi$
$468$	10.8102	0.499704
$469$	−11.4051	−0.526640
$470$	21.8102	1.00603
$471$	1.18975	0.0548208
$472$	−12.4051	−0.570992
$473$	40.2154	1.84910
$474$	4.81025	0.220942
$475$	9.26662	0.425182
$476$	6.40512	0.293578
$477$	−7.62050	−0.348919
$478$	20.4307	0.934481
$479$	9.00000	0.411220	0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000	0.411220	0.205610	+	0.978634i	$0.434082\pi$
$480$	−3.40512	−0.155422
$481$	−10.8102	−0.492905
$482$	3.59488	0.163742
$483$	6.40512	0.291443
$484$	0.594875	0.0270398
$485$	19.7846	0.898374
$486$	16.0000	0.725775
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	3.59488	0.162732
$489$	20.6205	0.932491
$490$	−20.4307	−0.922967
$491$	1.37950	0.0622560	0.0311280	−	0.999515i	$-0.490090\pi$
$491$	1.37950	0.0622560	0.0311280	+	0.999515i	$0.490090\pi$
$492$	0	0
$493$	−19.2154	−0.865417
$494$	7.59488	0.341710
$495$	23.1898	1.04230
$496$	−0.594875	−0.0267107
$497$	9.81025	0.440050
$498$	6.00000	0.268866
$499$	−3.21537	−0.143940	−0.0719700	−	0.997407i	$-0.522929\pi$
$499$	−3.21537	−0.143940	−0.0719700	+	0.997407i	$0.522929\pi$
$500$	−5.43075	−0.242870
$501$	8.18975	0.365891
$502$	15.0000	0.669483
$503$	−32.4307	−1.44602	−0.723008	−	0.690840i	$-0.757241\pi$
$503$	−32.4307	−1.44602	−0.723008	+	0.690840i	$0.757241\pi$
$504$	2.00000	0.0890871
$505$	65.4307	2.91163
$506$	21.8102	0.969584
$507$	−16.2154	−0.720150
$508$	−13.8102	−0.612731
$509$	42.8102	1.89753	0.948765	−	0.315981i	$-0.102334\pi$
$509$	42.8102	1.89753	0.948765	+	0.315981i	$0.102334\pi$
$510$	−21.8102	−0.965774
$511$	−10.8102	−0.478217
$512$	−1.00000	−0.0441942
$513$	7.02562	0.310189
$514$	−2.59488	−0.114455
$515$	−9.56925	−0.421672
$516$	−11.8102	−0.519917
$517$	21.8102	0.959214
$518$	−2.00000	−0.0878750
$519$	3.00000	0.131685
$520$	−18.4051	−0.807118
$521$	−7.62050	−0.333860	−0.166930	−	0.985969i	$-0.553385\pi$
$521$	−7.62050	−0.333860	−0.166930	+	0.985969i	$0.553385\pi$
$522$	−6.00000	−0.262613
$523$	−35.2154	−1.53986	−0.769930	−	0.638128i	$-0.779709\pi$
$523$	−35.2154	−1.53986	−0.769930	+	0.638128i	$0.779709\pi$
$524$	13.2154	0.577316
$525$	−6.59488	−0.287824
$526$	5.18975	0.226284
$527$	−3.81025	−0.165977
$528$	−3.40512	−0.148189
$529$	18.0256	0.783723
$530$	12.9744	0.563571
$531$	−24.8102	−1.07667
$532$	1.40512	0.0609199
$533$	0	0
$534$	3.40512	0.147354
$535$	−62.6717	−2.70954
$536$	11.4051	0.492626
$537$	−9.00000	−0.388379
$538$	15.0000	0.646696
$539$	−20.4307	−0.880015
$540$	−17.0256	−0.732666
$541$	−25.0000	−1.07483	−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000	−1.07483	−0.537417	+	0.843317i	$0.680600\pi$
$542$	−21.2154	−0.911278
$543$	11.0000	0.472055
$544$	−6.40512	−0.274617
$545$	19.7846	0.847480
$546$	−5.40512	−0.231318
$547$	14.6205	0.625127	0.312564	−	0.949897i	$-0.398812\pi$
$547$	14.6205	0.625127	0.312564	+	0.949897i	$0.398812\pi$
$548$	−22.2154	−0.948994
$549$	7.18975	0.306851
$550$	−22.4564	−0.957543
$551$	−4.21537	−0.179581
$552$	−6.40512	−0.272620
$553$	4.81025	0.204553
$554$	−2.81025	−0.119396
$555$	6.81025	0.289079
$556$	6.21537	0.263591
$557$	1.78463	0.0756170	0.0378085	−	0.999285i	$-0.487962\pi$
$557$	1.78463	0.0756170	0.0378085	+	0.999285i	$0.487962\pi$
$558$	−1.18975	−0.0503661
$559$	−63.8359	−2.69997
$560$	−3.40512	−0.143893
$561$	−21.8102	−0.920829
$562$	0.810250	0.0341783
$563$	−5.18975	−0.218722	−0.109361	−	0.994002i	$-0.534880\pi$
$563$	−5.18975	−0.218722	−0.109361	+	0.994002i	$0.534880\pi$
$564$	−6.40512	−0.269704
$565$	43.6205	1.83513
$566$	27.4307	1.15300
$567$	1.00000	0.0419961
$568$	−9.81025	−0.411629
$569$	3.00000	0.125767	0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000	0.125767	0.0628833	+	0.998021i	$0.479970\pi$
$570$	−4.78463	−0.200406
$571$	8.62050	0.360757	0.180378	−	0.983597i	$-0.442268\pi$
$571$	8.62050	0.360757	0.180378	+	0.983597i	$0.442268\pi$
$572$	−18.4051	−0.769557
$573$	1.78463	0.0745538
$574$	0	0
$575$	−42.2410	−1.76157
$576$	−2.00000	−0.0833333
$577$	−9.62050	−0.400507	−0.200253	−	0.979744i	$-0.564177\pi$
$577$	−9.62050	−0.400507	−0.200253	+	0.979744i	$0.564177\pi$
$578$	−24.0256	−0.999334
$579$	13.0256	0.541326
$580$	10.2154	0.424170
$581$	6.00000	0.248922
$582$	−5.81025	−0.240843
$583$	12.9744	0.537344
$584$	10.8102	0.447331
$585$	−36.8102	−1.52192
$586$	21.4051	0.884238
$587$	9.81025	0.404912	0.202456	−	0.979291i	$-0.435108\pi$
$587$	9.81025	0.404912	0.202456	+	0.979291i	$0.435108\pi$
$588$	6.00000	0.247436
$589$	−0.835874	−0.0344416
$590$	42.2410	1.73903
$591$	−18.4051	−0.757086
$592$	2.00000	0.0821995
$593$	−2.43075	−0.0998189	−0.0499094	−	0.998754i	$-0.515893\pi$
$593$	−2.43075	−0.0998189	−0.0499094	+	0.998754i	$0.515893\pi$
$594$	−17.0256	−0.698570
$595$	−21.8102	−0.894133
$596$	0	0
$597$	11.0000	0.450200
$598$	−34.6205	−1.41574
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	6.59488	0.269235
$601$	−29.4051	−1.19946	−0.599730	−	0.800202i	$-0.704725\pi$
$601$	−29.4051	−1.19946	−0.599730	+	0.800202i	$0.704725\pi$
$602$	−11.8102	−0.481350
$603$	22.8102	0.928905
$604$	3.59488	0.146273
$605$	−2.02562	−0.0823533
$606$	−19.2154	−0.780571
$607$	−25.8102	−1.04761	−0.523803	−	0.851840i	$-0.675487\pi$
$607$	−25.8102	−1.04761	−0.523803	+	0.851840i	$0.675487\pi$
$608$	−1.40512	−0.0569853
$609$	3.00000	0.121566
$610$	−12.2410	−0.495624
$611$	−34.6205	−1.40060
$612$	−12.8102	−0.517824
$613$	8.40512	0.339480	0.169740	−	0.985489i	$-0.445707\pi$
$613$	8.40512	0.339480	0.169740	+	0.985489i	$0.445707\pi$
$614$	15.0256	0.606385
$615$	0	0
$616$	−3.40512	−0.137196
$617$	−26.1898	−1.05436	−0.527180	−	0.849754i	$-0.676751\pi$
$617$	−26.1898	−1.05436	−0.527180	+	0.849754i	$0.676751\pi$
$618$	2.81025	0.113045
$619$	31.5949	1.26991	0.634953	−	0.772551i	$-0.281020\pi$
$619$	31.5949	1.26991	0.634953	+	0.772551i	$0.281020\pi$
$620$	2.02562	0.0813510
$621$	−32.0256	−1.28514
$622$	28.6205	1.14758
$623$	3.40512	0.136423
$624$	5.40512	0.216378
$625$	−14.4820	−0.579280
$626$	−30.4307	−1.21626
$627$	−4.78463	−0.191080
$628$	−1.18975	−0.0474762
$629$	12.8102	0.510778
$630$	−6.81025	−0.271327
$631$	−0.594875	−0.0236816	−0.0118408	−	0.999930i	$-0.503769\pi$
$631$	−0.594875	−0.0236816	−0.0118408	+	0.999930i	$0.503769\pi$
$632$	−4.81025	−0.191341
$633$	−13.0000	−0.516704
$634$	−3.40512	−0.135235
$635$	47.0256	1.86615
$636$	−3.81025	−0.151086
$637$	32.4307	1.28495
$638$	10.2154	0.404431
$639$	−19.6205	−0.776175
$640$	3.40512	0.134599
$641$	4.78463	0.188981	0.0944907	−	0.995526i	$-0.469878\pi$
$641$	4.78463	0.188981	0.0944907	+	0.995526i	$0.469878\pi$
$642$	18.4051	0.726392
$643$	−16.1898	−0.638461	−0.319231	−	0.947677i	$-0.603424\pi$
$643$	−16.1898	−0.638461	−0.319231	+	0.947677i	$0.603424\pi$
$644$	−6.40512	−0.252397
$645$	40.2154	1.58348
$646$	−9.00000	−0.354100
$647$	−10.6205	−0.417535	−0.208767	−	0.977965i	$-0.566945\pi$
$647$	−10.6205	−0.417535	−0.208767	+	0.977965i	$0.566945\pi$
$648$	−1.00000	−0.0392837
$649$	42.2410	1.65810
$650$	35.6461	1.39816
$651$	0.594875	0.0233150
$652$	−20.6205	−0.807561
$653$	33.6461	1.31667	0.658337	−	0.752723i	$-0.271260\pi$
$653$	33.6461	1.31667	0.658337	+	0.752723i	$0.271260\pi$
$654$	−5.81025	−0.227199
$655$	−45.0000	−1.75830
$656$	0	0
$657$	21.6205	0.843496
$658$	−6.40512	−0.249698
$659$	−23.4307	−0.912732	−0.456366	−	0.889792i	$-0.650849\pi$
$659$	−23.4307	−0.912732	−0.456366	+	0.889792i	$0.650849\pi$
$660$	11.5949	0.451330
$661$	45.2154	1.75867	0.879337	−	0.476200i	$-0.157986\pi$
$661$	45.2154	1.75867	0.879337	+	0.476200i	$0.157986\pi$
$662$	−23.6205	−0.918037
$663$	34.6205	1.34455
$664$	−6.00000	−0.232845
$665$	−4.78463	−0.185540
$666$	4.00000	0.154997
$667$	19.2154	0.744022
$668$	−8.18975	−0.316871
$669$	17.6205	0.681248
$670$	−38.8359	−1.50036
$671$	−12.2410	−0.472559
$672$	1.00000	0.0385758
$673$	30.5949	1.17935	0.589673	−	0.807642i	$-0.299257\pi$
$673$	30.5949	1.17935	0.589673	+	0.807642i	$0.299257\pi$
$674$	−11.8102	−0.454914
$675$	32.9744	1.26918
$676$	16.2154	0.623668
$677$	29.4307	1.13112	0.565558	−	0.824709i	$-0.308661\pi$
$677$	29.4307	1.13112	0.565558	+	0.824709i	$0.308661\pi$
$678$	−12.8102	−0.491975
$679$	−5.81025	−0.222977
$680$	21.8102	0.836385
$681$	7.21537	0.276494
$682$	2.02562	0.0775652
$683$	−11.0256	−0.421884	−0.210942	−	0.977499i	$-0.567653\pi$
$683$	−11.0256	−0.421884	−0.210942	+	0.977499i	$0.567653\pi$
$684$	−2.81025	−0.107453
$685$	75.6461	2.89029
$686$	13.0000	0.496342
$687$	−0.594875	−0.0226959
$688$	11.8102	0.450262
$689$	−20.5949	−0.784602
$690$	21.8102	0.830302
$691$	0.0256242	0.000974790 0	0.000487395	−	1.00000i	$-0.499845\pi$
$691$	0.0256242	0.000974790 0	0.000487395		1.00000i	$0.499845\pi$
$692$	−3.00000	−0.114043
$693$	−6.81025	−0.258700
$694$	−6.81025	−0.258514
$695$	−21.1641	−0.802801
$696$	−3.00000	−0.113715
$697$	0	0
$698$	11.2154	0.424508
$699$	6.81025	0.257587
$700$	6.59488	0.249263
$701$	15.4051	0.581844	0.290922	−	0.956747i	$-0.406038\pi$
$701$	15.4051	0.581844	0.290922	+	0.956747i	$0.406038\pi$
$702$	27.0256	1.02002
$703$	2.81025	0.105991
$704$	3.40512	0.128335
$705$	21.8102	0.821422
$706$	21.8102	0.820840
$707$	−19.2154	−0.722669
$708$	−12.4051	−0.466213
$709$	−24.6205	−0.924642	−0.462321	−	0.886713i	$-0.652983\pi$
$709$	−24.6205	−0.924642	−0.462321	+	0.886713i	$0.652983\pi$
$710$	33.4051	1.25367
$711$	−9.62050	−0.360797
$712$	−3.40512	−0.127612
$713$	3.81025	0.142695
$714$	6.40512	0.239706
$715$	62.6717	2.34379
$716$	9.00000	0.336346
$717$	20.4307	0.763000
$718$	−25.2154	−0.941029
$719$	27.2410	1.01592	0.507959	−	0.861381i	$-0.330400\pi$
$719$	27.2410	1.01592	0.507959	+	0.861381i	$0.330400\pi$
$720$	6.81025	0.253803
$721$	2.81025	0.104659
$722$	17.0256	0.633628
$723$	3.59488	0.133695
$724$	−11.0000	−0.408812
$725$	−19.7846	−0.734783
$726$	0.594875	0.0220779
$727$	15.0256	0.557270	0.278635	−	0.960397i	$-0.410118\pi$
$727$	15.0256	0.557270	0.278635	+	0.960397i	$0.410118\pi$
$728$	5.40512	0.200327
$729$	13.0000	0.481481
$730$	−36.8102	−1.36241
$731$	75.6461	2.79787
$732$	3.59488	0.132870
$733$	31.4307	1.16092	0.580461	−	0.814288i	$-0.302873\pi$
$733$	31.4307	1.16092	0.580461	+	0.814288i	$0.302873\pi$
$734$	−3.21537	−0.118682
$735$	−20.4307	−0.753600
$736$	6.40512	0.236096
$737$	−38.8359	−1.43054
$738$	0	0
$739$	−11.3795	−0.418602	−0.209301	−	0.977851i	$-0.567119\pi$
$739$	−11.3795	−0.418602	−0.209301	+	0.977851i	$0.567119\pi$
$740$	−6.81025	−0.250350
$741$	7.59488	0.279005
$742$	−3.81025	−0.139879
$743$	−9.40512	−0.345041	−0.172520	−	0.985006i	$-0.555191\pi$
$743$	−9.40512	−0.345041	−0.172520	+	0.985006i	$0.555191\pi$
$744$	−0.594875	−0.0218092
$745$	0	0
$746$	13.0000	0.475964
$747$	−12.0000	−0.439057
$748$	21.8102	0.797462
$749$	18.4051	0.672509
$750$	−5.43075	−0.198303
$751$	36.0256	1.31459	0.657297	−	0.753632i	$-0.271700\pi$
$751$	36.0256	1.31459	0.657297	+	0.753632i	$0.271700\pi$
$752$	6.40512	0.233571
$753$	15.0000	0.546630
$754$	−16.2154	−0.590529
$755$	−12.2410	−0.445496
$756$	5.00000	0.181848
$757$	−53.8102	−1.95577	−0.977883	−	0.209151i	$-0.932930\pi$
$757$	−53.8102	−1.95577	−0.977883	+	0.209151i	$0.932930\pi$
$758$	−18.6205	−0.676327
$759$	21.8102	0.791662
$760$	4.78463	0.173557
$761$	5.18975	0.188128	0.0940642	−	0.995566i	$-0.470014\pi$
$761$	5.18975	0.188128	0.0940642	+	0.995566i	$0.470014\pi$
$762$	−13.8102	−0.500293
$763$	−5.81025	−0.210345
$764$	−1.78463	−0.0645655
$765$	43.6205	1.57710
$766$	12.4051	0.448215
$767$	−67.0512	−2.42108
$768$	−1.00000	−0.0360844
$769$	39.6205	1.42875	0.714376	−	0.699762i	$-0.246711\pi$
$769$	39.6205	1.42875	0.714376	+	0.699762i	$0.246711\pi$
$770$	11.5949	0.417850
$771$	−2.59488	−0.0934521
$772$	−13.0256	−0.468802
$773$	33.0000	1.18693	0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000	1.18693	0.593464	+	0.804861i	$0.297760\pi$
$774$	23.6205	0.849021
$775$	−3.92313	−0.140923
$776$	5.81025	0.208576
$777$	−2.00000	−0.0717496
$778$	0	0
$779$	0	0
$780$	−18.4051	−0.659009
$781$	33.4051	1.19533
$782$	41.0256	1.46707
$783$	−15.0000	−0.536056
$784$	−6.00000	−0.214286
$785$	4.05125	0.144595
$786$	13.2154	0.471377
$787$	11.8102	0.420990	0.210495	−	0.977595i	$-0.432492\pi$
$787$	11.8102	0.420990	0.210495	+	0.977595i	$0.432492\pi$
$788$	18.4051	0.655655
$789$	5.18975	0.184760
$790$	16.3795	0.582756
$791$	−12.8102	−0.455480
$792$	6.81025	0.241992
$793$	19.4307	0.690006
$794$	26.0000	0.922705
$795$	12.9744	0.460154
$796$	−11.0000	−0.389885
$797$	−45.2410	−1.60252	−0.801259	−	0.598317i	$-0.795836\pi$
$797$	−45.2410	−1.60252	−0.801259	+	0.598317i	$0.795836\pi$
$798$	1.40512	0.0497409
$799$	41.0256	1.45138
$800$	−6.59488	−0.233164
$801$	−6.81025	−0.240628
$802$	5.59488	0.197562
$803$	−36.8102	−1.29901
$804$	11.4051	0.402228
$805$	21.8102	0.768710
$806$	−3.21537	−0.113257
$807$	15.0000	0.528025
$808$	19.2154	0.675995
$809$	45.4051	1.59636	0.798180	−	0.602420i	$-0.205797\pi$
$809$	45.4051	1.59636	0.798180	+	0.602420i	$0.205797\pi$
$810$	3.40512	0.119644
$811$	−5.62050	−0.197362	−0.0986812	−	0.995119i	$-0.531462\pi$
$811$	−5.62050	−0.197362	−0.0986812	+	0.995119i	$0.531462\pi$
$812$	−3.00000	−0.105279
$813$	−21.2154	−0.744056
$814$	−6.81025	−0.238699
$815$	70.2154	2.45954
$816$	−6.40512	−0.224224
$817$	16.5949	0.580581
$818$	15.5949	0.545262
$819$	10.8102	0.377741
$820$	0	0
$821$	5.43075	0.189534	0.0947672	−	0.995499i	$-0.469789\pi$
$821$	5.43075	0.189534	0.0947672	+	0.995499i	$0.469789\pi$
$822$	−22.2154	−0.774850
$823$	31.0000	1.08059	0.540296	−	0.841475i	$-0.318312\pi$
$823$	31.0000	1.08059	0.540296	+	0.841475i	$0.318312\pi$
$824$	−2.81025	−0.0978997
$825$	−22.4564	−0.781831
$826$	−12.4051	−0.431629
$827$	−15.2410	−0.529981	−0.264991	−	0.964251i	$-0.585369\pi$
$827$	−15.2410	−0.529981	−0.264991	+	0.964251i	$0.585369\pi$
$828$	12.8102	0.445187
$829$	16.5949	0.576364	0.288182	−	0.957576i	$-0.406949\pi$
$829$	16.5949	0.576364	0.288182	+	0.957576i	$0.406949\pi$
$830$	20.4307	0.709162
$831$	−2.81025	−0.0974865
$832$	−5.40512	−0.187389
$833$	−38.4307	−1.33155
$834$	6.21537	0.215221
$835$	27.8871	0.965074
$836$	4.78463	0.165480
$837$	−2.97438	−0.102809
$838$	0	0
$839$	34.2154	1.18125	0.590623	−	0.806948i	$-0.298882\pi$
$839$	34.2154	1.18125	0.590623	+	0.806948i	$0.298882\pi$
$840$	−3.40512	−0.117488
$841$	−20.0000	−0.689655
$842$	−5.62050	−0.193695
$843$	0.810250	0.0279065
$844$	13.0000	0.447478
$845$	−55.2154	−1.89947
$846$	12.8102	0.440425
$847$	0.594875	0.0204402
$848$	3.81025	0.130845
$849$	27.4307	0.941421
$850$	−42.2410	−1.44885
$851$	−12.8102	−0.439130
$852$	−9.81025	−0.336094
$853$	−11.3795	−0.389627	−0.194813	−	0.980840i	$-0.562410\pi$
$853$	−11.3795	−0.389627	−0.194813	+	0.980840i	$0.562410\pi$
$854$	3.59488	0.123014
$855$	9.56925	0.327261
$856$	−18.4051	−0.629074
$857$	−23.4307	−0.800379	−0.400190	−	0.916432i	$-0.631056\pi$
$857$	−23.4307	−0.800379	−0.400190	+	0.916432i	$0.631056\pi$
$858$	−18.4051	−0.628341
$859$	−29.0512	−0.991216	−0.495608	−	0.868546i	$-0.665055\pi$
$859$	−29.0512	−0.991216	−0.495608	+	0.868546i	$0.665055\pi$
$860$	−40.2154	−1.37133
$861$	0	0
$862$	−15.0000	−0.510902
$863$	25.0512	0.852754	0.426377	−	0.904545i	$-0.359790\pi$
$863$	25.0512	0.852754	0.426377	+	0.904545i	$0.359790\pi$
$864$	−5.00000	−0.170103
$865$	10.2154	0.347333
$866$	10.0000	0.339814
$867$	−24.0256	−0.815953
$868$	−0.594875	−0.0201914
$869$	16.3795	0.555637
$870$	10.2154	0.346334
$871$	61.6461	2.08880
$872$	5.81025	0.196760
$873$	11.6205	0.393294
$874$	9.00000	0.304430
$875$	−5.43075	−0.183593
$876$	10.8102	0.365244
$877$	36.0512	1.21736	0.608682	−	0.793414i	$-0.291699\pi$
$877$	36.0512	1.21736	0.608682	+	0.793414i	$0.291699\pi$
$878$	25.4307	0.858246
$879$	21.4051	0.721977
$880$	−11.5949	−0.390863
$881$	−23.4307	−0.789402	−0.394701	−	0.918810i	$-0.629152\pi$
$881$	−23.4307	−0.789402	−0.394701	+	0.918810i	$0.629152\pi$
$882$	−12.0000	−0.404061
$883$	−39.2154	−1.31970	−0.659851	−	0.751396i	$-0.729381\pi$
$883$	−39.2154	−1.31970	−0.659851	+	0.751396i	$0.729381\pi$
$884$	−34.6205	−1.16441
$885$	42.2410	1.41992
$886$	−17.4307	−0.585597
$887$	−23.5949	−0.792238	−0.396119	−	0.918199i	$-0.629643\pi$
$887$	−23.5949	−0.792238	−0.396119	+	0.918199i	$0.629643\pi$
$888$	2.00000	0.0671156
$889$	−13.8102	−0.463181
$890$	11.5949	0.388661
$891$	3.40512	0.114076
$892$	−17.6205	−0.589978
$893$	9.00000	0.301174
$894$	0	0
$895$	−30.6461	−1.02439
$896$	−1.00000	−0.0334077
$897$	−34.6205	−1.15594
$898$	−24.0000	−0.800890
$899$	1.78463	0.0595206
$900$	−13.1898	−0.439658
$901$	24.4051	0.813053
$902$	0	0
$903$	−11.8102	−0.393020
$904$	12.8102	0.426063
$905$	37.4564	1.24509
$906$	3.59488	0.119432
$907$	41.8102	1.38829	0.694143	−	0.719837i	$-0.255783\pi$
$907$	41.8102	1.38829	0.694143	+	0.719837i	$0.255783\pi$
$908$	−7.21537	−0.239451
$909$	38.4307	1.27467
$910$	−18.4051	−0.610124
$911$	−22.6205	−0.749451	−0.374725	−	0.927136i	$-0.622263\pi$
$911$	−22.6205	−0.749451	−0.374725	+	0.927136i	$0.622263\pi$
$912$	−1.40512	−0.0465283
$913$	20.4307	0.676159
$914$	5.00000	0.165385
$915$	−12.2410	−0.404675
$916$	0.594875	0.0196552
$917$	13.2154	0.436410
$918$	−32.0256	−1.05700
$919$	43.2410	1.42639	0.713194	−	0.700966i	$-0.247248\pi$
$919$	43.2410	1.42639	0.713194	+	0.700966i	$0.247248\pi$
$920$	−21.8102	−0.719063
$921$	15.0256	0.495111
$922$	−12.4051	−0.408541
$923$	−53.0256	−1.74536
$924$	−3.40512	−0.112020
$925$	13.1898	0.433676
$926$	12.6205	0.414735
$927$	−5.62050	−0.184601
$928$	3.00000	0.0984798
$929$	24.8102	0.813998	0.406999	−	0.913429i	$-0.366575\pi$
$929$	24.8102	0.813998	0.406999	+	0.913429i	$0.366575\pi$
$930$	2.02562	0.0664228
$931$	−8.43075	−0.276307
$932$	−6.81025	−0.223077
$933$	28.6205	0.936993
$934$	−11.1898	−0.366140
$935$	−74.2666	−2.42878
$936$	−10.8102	−0.353344
$937$	−31.4307	−1.02680	−0.513399	−	0.858150i	$-0.671614\pi$
$937$	−31.4307	−1.02680	−0.513399	+	0.858150i	$0.671614\pi$
$938$	11.4051	0.372391
$939$	−30.4307	−0.993070
$940$	−21.8102	−0.711372
$941$	−36.8102	−1.19998	−0.599990	−	0.800008i	$-0.704829\pi$
$941$	−36.8102	−1.19998	−0.599990	+	0.800008i	$0.704829\pi$
$942$	−1.18975	−0.0387642
$943$	0	0
$944$	12.4051	0.403752
$945$	−17.0256	−0.553844
$946$	−40.2154	−1.30751
$947$	38.4307	1.24883	0.624416	−	0.781092i	$-0.285337\pi$
$947$	38.4307	1.24883	0.624416	+	0.781092i	$0.285337\pi$
$948$	−4.81025	−0.156230
$949$	58.4307	1.89674
$950$	−9.26662	−0.300649
$951$	−3.40512	−0.110419
$952$	−6.40512	−0.207591
$953$	58.0512	1.88046	0.940232	−	0.340534i	$-0.110608\pi$
$953$	58.0512	1.88046	0.940232	+	0.340534i	$0.110608\pi$
$954$	7.62050	0.246723
$955$	6.07687	0.196643
$956$	−20.4307	−0.660778
$957$	10.2154	0.330216
$958$	−9.00000	−0.290777
$959$	−22.2154	−0.717372
$960$	3.40512	0.109900
$961$	−30.6461	−0.988585
$962$	10.8102	0.348536
$963$	−36.8102	−1.18619
$964$	−3.59488	−0.115783
$965$	44.3539	1.42780
$966$	−6.40512	−0.206082
$967$	−25.4307	−0.817798	−0.408899	−	0.912580i	$-0.634087\pi$
$967$	−25.4307	−0.817798	−0.408899	+	0.912580i	$0.634087\pi$
$968$	−0.594875	−0.0191200
$969$	−9.00000	−0.289122
$970$	−19.7846	−0.635246
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−16.0000	−0.513200
$973$	6.21537	0.199256
$974$	7.00000	0.224294
$975$	35.6461	1.14159
$976$	−3.59488	−0.115069
$977$	−1.21537	−0.0388833	−0.0194416	−	0.999811i	$-0.506189\pi$
$977$	−1.21537	−0.0388833	−0.0194416	+	0.999811i	$0.506189\pi$
$978$	−20.6205	−0.659371
$979$	11.5949	0.370574
$980$	20.4307	0.652636
$981$	11.6205	0.371014
$982$	−1.37950	−0.0440216
$983$	46.8615	1.49465	0.747325	−	0.664459i	$-0.231338\pi$
$983$	46.8615	1.49465	0.747325	+	0.664459i	$0.231338\pi$
$984$	0	0
$985$	−62.6717	−1.99689
$986$	19.2154	0.611942
$987$	−6.40512	−0.203877
$988$	−7.59488	−0.241625
$989$	−75.6461	−2.40541
$990$	−23.1898	−0.737019
$991$	−0.784625	−0.0249244	−0.0124622	−	0.999922i	$-0.503967\pi$
$991$	−0.784625	−0.0249244	−0.0124622	+	0.999922i	$0.503967\pi$
$992$	0.594875	0.0188873
$993$	−23.6205	−0.749574
$994$	−9.81025	−0.311162
$995$	37.4564	1.18745
$996$	−6.00000	−0.190117
$997$	−4.83587	−0.153154	−0.0765768	−	0.997064i	$-0.524399\pi$
$997$	−4.83587	−0.153154	−0.0765768	+	0.997064i	$0.524399\pi$
$998$	3.21537	0.101781
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3362.2.a.d.1.1	✓	2
41.40	even	2		3362.2.a.i.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3362.2.a.d.1.1	✓	2	1.1	even	1	trivial
3362.2.a.i.1.1	yes	2	41.40	even	2

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:	\( N \)	\(=\)	\( 3362 = 2 \cdot 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3362.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.40512 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +3.40512 q^{10} +3.40512 q^{11} -1.00000 q^{12} -5.40512 q^{13} -1.00000 q^{14} +3.40512 q^{15} +1.00000 q^{16} +6.40512 q^{17} +2.00000 q^{18} +1.40512 q^{19} -3.40512 q^{20} -1.00000 q^{21} -3.40512 q^{22} -6.40512 q^{23} +1.00000 q^{24} +6.59488 q^{25} +5.40512 q^{26} +5.00000 q^{27} +1.00000 q^{28} -3.00000 q^{29} -3.40512 q^{30} -0.594875 q^{31} -1.00000 q^{32} -3.40512 q^{33} -6.40512 q^{34} -3.40512 q^{35} -2.00000 q^{36} +2.00000 q^{37} -1.40512 q^{38} +5.40512 q^{39} +3.40512 q^{40} +1.00000 q^{42} +11.8102 q^{43} +3.40512 q^{44} +6.81025 q^{45} +6.40512 q^{46} +6.40512 q^{47} -1.00000 q^{48} -6.00000 q^{49} -6.59488 q^{50} -6.40512 q^{51} -5.40512 q^{52} +3.81025 q^{53} -5.00000 q^{54} -11.5949 q^{55} -1.00000 q^{56} -1.40512 q^{57} +3.00000 q^{58} +12.4051 q^{59} +3.40512 q^{60} -3.59488 q^{61} +0.594875 q^{62} -2.00000 q^{63} +1.00000 q^{64} +18.4051 q^{65} +3.40512 q^{66} -11.4051 q^{67} +6.40512 q^{68} +6.40512 q^{69} +3.40512 q^{70} +9.81025 q^{71} +2.00000 q^{72} -10.8102 q^{73} -2.00000 q^{74} -6.59488 q^{75} +1.40512 q^{76} +3.40512 q^{77} -5.40512 q^{78} +4.81025 q^{79} -3.40512 q^{80} +1.00000 q^{81} +6.00000 q^{83} -1.00000 q^{84} -21.8102 q^{85} -11.8102 q^{86} +3.00000 q^{87} -3.40512 q^{88} +3.40512 q^{89} -6.81025 q^{90} -5.40512 q^{91} -6.40512 q^{92} +0.594875 q^{93} -6.40512 q^{94} -4.78463 q^{95} +1.00000 q^{96} -5.81025 q^{97} +6.00000 q^{98} -6.81025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - q^{10} - q^{11} - 2 q^{12} - 3 q^{13} - 2 q^{14} - q^{15} + 2 q^{16} + 5 q^{17} + 4 q^{18} - 5 q^{19} + q^{20} - 2 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - q^10 - q^11 - 2 * q^12 - 3 * q^13 - 2 * q^14 - q^15 + 2 * q^16 + 5 * q^17 + 4 * q^18 - 5 * q^19 + q^20 - 2 * q^21 + q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 3 * q^26 + 10 * q^27 + 2 * q^28 - 6 * q^29 + q^30 - 9 * q^31 - 2 * q^32 + q^33 - 5 * q^34 + q^35 - 4 * q^36 + 4 * q^37 + 5 * q^38 + 3 * q^39 - q^40 + 2 * q^42 + 8 * q^43 - q^44 - 2 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 - 12 * q^49 - 21 * q^50 - 5 * q^51 - 3 * q^52 - 8 * q^53 - 10 * q^54 - 31 * q^55 - 2 * q^56 + 5 * q^57 + 6 * q^58 + 17 * q^59 - q^60 - 15 * q^61 + 9 * q^62 - 4 * q^63 + 2 * q^64 + 29 * q^65 - q^66 - 15 * q^67 + 5 * q^68 + 5 * q^69 - q^70 + 4 * q^71 + 4 * q^72 - 6 * q^73 - 4 * q^74 - 21 * q^75 - 5 * q^76 - q^77 - 3 * q^78 - 6 * q^79 + q^80 + 2 * q^81 + 12 * q^83 - 2 * q^84 - 28 * q^85 - 8 * q^86 + 6 * q^87 + q^88 - q^89 + 2 * q^90 - 3 * q^91 - 5 * q^92 + 9 * q^93 - 5 * q^94 - 33 * q^95 + 2 * q^96 + 4 * q^97 + 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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