LMFDB - Embedded newform 1254.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1254,2,Mod(1,1254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1254, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1254.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1254 = 2 \cdot 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1254.a (trivial)

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:	yes
Analytic conductor:	$10.0132404135$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	1254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.60388 q^{5} +1.00000 q^{6} +4.49396 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.60388 q^{10} -1.00000 q^{11} -1.00000 q^{12} -5.38404 q^{13} -4.49396 q^{14} +3.60388 q^{15} +1.00000 q^{16} +5.20775 q^{17} -1.00000 q^{18} -1.00000 q^{19} -3.60388 q^{20} -4.49396 q^{21} +1.00000 q^{22} -3.38404 q^{23} +1.00000 q^{24} +7.98792 q^{25} +5.38404 q^{26} -1.00000 q^{27} +4.49396 q^{28} +2.98792 q^{29} -3.60388 q^{30} -0.670251 q^{31} -1.00000 q^{32} +1.00000 q^{33} -5.20775 q^{34} -16.1957 q^{35} +1.00000 q^{36} +4.89008 q^{37} +1.00000 q^{38} +5.38404 q^{39} +3.60388 q^{40} +1.20775 q^{41} +4.49396 q^{42} +12.9879 q^{43} -1.00000 q^{44} -3.60388 q^{45} +3.38404 q^{46} -11.0315 q^{47} -1.00000 q^{48} +13.1957 q^{49} -7.98792 q^{50} -5.20775 q^{51} -5.38404 q^{52} -8.71379 q^{53} +1.00000 q^{54} +3.60388 q^{55} -4.49396 q^{56} +1.00000 q^{57} -2.98792 q^{58} -8.98792 q^{59} +3.60388 q^{60} -13.7017 q^{61} +0.670251 q^{62} +4.49396 q^{63} +1.00000 q^{64} +19.4034 q^{65} -1.00000 q^{66} -14.4155 q^{67} +5.20775 q^{68} +3.38404 q^{69} +16.1957 q^{70} -10.2741 q^{71} -1.00000 q^{72} -14.1957 q^{73} -4.89008 q^{74} -7.98792 q^{75} -1.00000 q^{76} -4.49396 q^{77} -5.38404 q^{78} -5.60388 q^{79} -3.60388 q^{80} +1.00000 q^{81} -1.20775 q^{82} +14.4155 q^{83} -4.49396 q^{84} -18.7681 q^{85} -12.9879 q^{86} -2.98792 q^{87} +1.00000 q^{88} -1.01208 q^{89} +3.60388 q^{90} -24.1957 q^{91} -3.38404 q^{92} +0.670251 q^{93} +11.0315 q^{94} +3.60388 q^{95} +1.00000 q^{96} -1.01208 q^{97} -13.1957 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} - 3 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} - 3 q^{19} - 2 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 - 3 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 - 3 * q^19 - 2 * q^20 - 4 * q^21 + 3 * q^22 + 3 * q^24 + 5 * q^25 + 6 * q^26 - 3 * q^27 + 4 * q^28 - 10 * q^29 - 2 * q^30 - 3 * q^32 + 3 * q^33 + 2 * q^34 - 12 * q^35 + 3 * q^36 + 14 * q^37 + 3 * q^38 + 6 * q^39 + 2 * q^40 - 14 * q^41 + 4 * q^42 + 20 * q^43 - 3 * q^44 - 2 * q^45 - 8 * q^47 - 3 * q^48 + 3 * q^49 - 5 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 3 * q^54 + 2 * q^55 - 4 * q^56 + 3 * q^57 + 10 * q^58 - 8 * q^59 + 2 * q^60 - 14 * q^61 + 4 * q^63 + 3 * q^64 + 4 * q^65 - 3 * q^66 - 8 * q^67 - 2 * q^68 + 12 * q^70 - 20 * q^71 - 3 * q^72 - 6 * q^73 - 14 * q^74 - 5 * q^75 - 3 * q^76 - 4 * q^77 - 6 * q^78 - 8 * q^79 - 2 * q^80 + 3 * q^81 + 14 * q^82 + 8 * q^83 - 4 * q^84 - 36 * q^85 - 20 * q^86 + 10 * q^87 + 3 * q^88 - 22 * q^89 + 2 * q^90 - 36 * q^91 + 8 * q^94 + 2 * q^95 + 3 * q^96 - 22 * q^97 - 3 * q^98 - 3 * 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
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.60388	−1.61170	−0.805851	−	0.592118i	$-0.798292\pi$
$5$	−3.60388	−1.61170	−0.805851	+	0.592118i	$0.798292\pi$
$6$	1.00000	0.408248
$7$	4.49396	1.69856	0.849278	−	0.527945i	$-0.177037\pi$
$7$	4.49396	1.69856	0.849278	+	0.527945i	$0.177037\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.60388	1.13965
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−5.38404	−1.49326	−0.746632	−	0.665237i	$-0.768331\pi$
$13$	−5.38404	−1.49326	−0.746632	+	0.665237i	$0.768331\pi$
$14$	−4.49396	−1.20106
$15$	3.60388	0.930517
$16$	1.00000	0.250000
$17$	5.20775	1.26307	0.631533	−	0.775349i	$-0.282426\pi$
$17$	5.20775	1.26307	0.631533	+	0.775349i	$0.282426\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.60388	−0.805851
$21$	−4.49396	−0.980662
$22$	1.00000	0.213201
$23$	−3.38404	−0.705622	−0.352811	−	0.935695i	$-0.614774\pi$
$23$	−3.38404	−0.705622	−0.352811	+	0.935695i	$0.614774\pi$
$24$	1.00000	0.204124
$25$	7.98792	1.59758
$26$	5.38404	1.05590
$27$	−1.00000	−0.192450
$28$	4.49396	0.849278
$29$	2.98792	0.554843	0.277421	−	0.960748i	$-0.410520\pi$
$29$	2.98792	0.554843	0.277421	+	0.960748i	$0.410520\pi$
$30$	−3.60388	−0.657975
$31$	−0.670251	−0.120381	−0.0601903	−	0.998187i	$-0.519171\pi$
$31$	−0.670251	−0.120381	−0.0601903	+	0.998187i	$0.519171\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−5.20775	−0.893122
$35$	−16.1957	−2.73757
$36$	1.00000	0.166667
$37$	4.89008	0.803925	0.401962	−	0.915656i	$-0.368328\pi$
$37$	4.89008	0.803925	0.401962	+	0.915656i	$0.368328\pi$
$38$	1.00000	0.162221
$39$	5.38404	0.862137
$40$	3.60388	0.569823
$41$	1.20775	0.188619	0.0943095	−	0.995543i	$-0.469936\pi$
$41$	1.20775	0.188619	0.0943095	+	0.995543i	$0.469936\pi$
$42$	4.49396	0.693433
$43$	12.9879	1.98064	0.990319	−	0.138807i	$-0.0443267\pi$
$43$	12.9879	1.98064	0.990319	+	0.138807i	$0.0443267\pi$
$44$	−1.00000	−0.150756
$45$	−3.60388	−0.537234
$46$	3.38404	0.498950
$47$	−11.0315	−1.60910	−0.804552	−	0.593882i	$-0.797594\pi$
$47$	−11.0315	−1.60910	−0.804552	+	0.593882i	$0.797594\pi$
$48$	−1.00000	−0.144338
$49$	13.1957	1.88510
$50$	−7.98792	−1.12966
$51$	−5.20775	−0.729231
$52$	−5.38404	−0.746632
$53$	−8.71379	−1.19693	−0.598466	−	0.801148i	$-0.704223\pi$
$53$	−8.71379	−1.19693	−0.598466	+	0.801148i	$0.704223\pi$
$54$	1.00000	0.136083
$55$	3.60388	0.485946
$56$	−4.49396	−0.600531
$57$	1.00000	0.132453
$58$	−2.98792	−0.392333
$59$	−8.98792	−1.17013	−0.585064	−	0.810987i	$-0.698930\pi$
$59$	−8.98792	−1.17013	−0.585064	+	0.810987i	$0.698930\pi$
$60$	3.60388	0.465258
$61$	−13.7017	−1.75432	−0.877162	−	0.480194i	$-0.840566\pi$
$61$	−13.7017	−1.75432	−0.877162	+	0.480194i	$0.840566\pi$
$62$	0.670251	0.0851220
$63$	4.49396	0.566186
$64$	1.00000	0.125000
$65$	19.4034	2.40670
$66$	−1.00000	−0.123091
$67$	−14.4155	−1.76113	−0.880567	−	0.473922i	$-0.842838\pi$
$67$	−14.4155	−1.76113	−0.880567	+	0.473922i	$0.842838\pi$
$68$	5.20775	0.631533
$69$	3.38404	0.407391
$70$	16.1957	1.93575
$71$	−10.2741	−1.21931	−0.609657	−	0.792665i	$-0.708693\pi$
$71$	−10.2741	−1.21931	−0.609657	+	0.792665i	$0.708693\pi$
$72$	−1.00000	−0.117851
$73$	−14.1957	−1.66148	−0.830739	−	0.556663i	$-0.812082\pi$
$73$	−14.1957	−1.66148	−0.830739	+	0.556663i	$0.812082\pi$
$74$	−4.89008	−0.568461
$75$	−7.98792	−0.922365
$76$	−1.00000	−0.114708
$77$	−4.49396	−0.512134
$78$	−5.38404	−0.609623
$79$	−5.60388	−0.630485	−0.315243	−	0.949011i	$-0.602086\pi$
$79$	−5.60388	−0.630485	−0.315243	+	0.949011i	$0.602086\pi$
$80$	−3.60388	−0.402926
$81$	1.00000	0.111111
$82$	−1.20775	−0.133374
$83$	14.4155	1.58231	0.791153	−	0.611618i	$-0.209481\pi$
$83$	14.4155	1.58231	0.791153	+	0.611618i	$0.209481\pi$
$84$	−4.49396	−0.490331
$85$	−18.7681	−2.03568
$86$	−12.9879	−1.40052
$87$	−2.98792	−0.320338
$88$	1.00000	0.106600
$89$	−1.01208	−0.107280	−0.0536402	−	0.998560i	$-0.517082\pi$
$89$	−1.01208	−0.107280	−0.0536402	+	0.998560i	$0.517082\pi$
$90$	3.60388	0.379882
$91$	−24.1957	−2.53640
$92$	−3.38404	−0.352811
$93$	0.670251	0.0695018
$94$	11.0315	1.13781
$95$	3.60388	0.369750
$96$	1.00000	0.102062
$97$	−1.01208	−0.102761	−0.0513807	−	0.998679i	$-0.516362\pi$
$97$	−1.01208	−0.102761	−0.0513807	+	0.998679i	$0.516362\pi$
$98$	−13.1957	−1.33296
$99$	−1.00000	−0.100504
$100$	7.98792	0.798792
$101$	−3.90217	−0.388280	−0.194140	−	0.980974i	$-0.562192\pi$
$101$	−3.90217	−0.388280	−0.194140	+	0.980974i	$0.562192\pi$
$102$	5.20775	0.515644
$103$	−18.2935	−1.80251	−0.901256	−	0.433286i	$-0.857354\pi$
$103$	−18.2935	−1.80251	−0.901256	+	0.433286i	$0.857354\pi$
$104$	5.38404	0.527949
$105$	16.1957	1.58054
$106$	8.71379	0.846358
$107$	−0.792249	−0.0765896	−0.0382948	−	0.999266i	$-0.512193\pi$
$107$	−0.792249	−0.0765896	−0.0382948	+	0.999266i	$0.512193\pi$
$108$	−1.00000	−0.0962250
$109$	10.3720	0.993454	0.496727	−	0.867907i	$-0.334535\pi$
$109$	10.3720	0.993454	0.496727	+	0.867907i	$0.334535\pi$
$110$	−3.60388	−0.343616
$111$	−4.89008	−0.464146
$112$	4.49396	0.424639
$113$	−5.64742	−0.531264	−0.265632	−	0.964074i	$-0.585581\pi$
$113$	−5.64742	−0.531264	−0.265632	+	0.964074i	$0.585581\pi$
$114$	−1.00000	−0.0936586
$115$	12.1957	1.13725
$116$	2.98792	0.277421
$117$	−5.38404	−0.497755
$118$	8.98792	0.827405
$119$	23.4034	2.14539
$120$	−3.60388	−0.328987
$121$	1.00000	0.0909091
$122$	13.7017	1.24049
$123$	−1.20775	−0.108899
$124$	−0.670251	−0.0601903
$125$	−10.7681	−0.963127
$126$	−4.49396	−0.400354
$127$	14.5918	1.29481	0.647406	−	0.762145i	$-0.275854\pi$
$127$	14.5918	1.29481	0.647406	+	0.762145i	$0.275854\pi$
$128$	−1.00000	−0.0883883
$129$	−12.9879	−1.14352
$130$	−19.4034	−1.70179
$131$	−14.4155	−1.25949	−0.629744	−	0.776803i	$-0.716840\pi$
$131$	−14.4155	−1.25949	−0.629744	+	0.776803i	$0.716840\pi$
$132$	1.00000	0.0870388
$133$	−4.49396	−0.389676
$134$	14.4155	1.24531
$135$	3.60388	0.310172
$136$	−5.20775	−0.446561
$137$	0.219833	0.0187816	0.00939078	−	0.999956i	$-0.497011\pi$
$137$	0.219833	0.0187816	0.00939078	+	0.999956i	$0.497011\pi$
$138$	−3.38404	−0.288069
$139$	−4.43967	−0.376567	−0.188284	−	0.982115i	$-0.560292\pi$
$139$	−4.43967	−0.376567	−0.188284	+	0.982115i	$0.560292\pi$
$140$	−16.1957	−1.36878
$141$	11.0315	0.929016
$142$	10.2741	0.862186
$143$	5.38404	0.450236
$144$	1.00000	0.0833333
$145$	−10.7681	−0.894241
$146$	14.1957	1.17484
$147$	−13.1957	−1.08836
$148$	4.89008	0.401962
$149$	−7.10992	−0.582467	−0.291234	−	0.956652i	$-0.594066\pi$
$149$	−7.10992	−0.582467	−0.291234	+	0.956652i	$0.594066\pi$
$150$	7.98792	0.652211
$151$	−20.0194	−1.62915	−0.814577	−	0.580056i	$-0.803031\pi$
$151$	−20.0194	−1.62915	−0.814577	+	0.580056i	$0.803031\pi$
$152$	1.00000	0.0811107
$153$	5.20775	0.421022
$154$	4.49396	0.362134
$155$	2.41550	0.194018
$156$	5.38404	0.431068
$157$	−12.3284	−0.983915	−0.491958	−	0.870619i	$-0.663718\pi$
$157$	−12.3284	−0.983915	−0.491958	+	0.870619i	$0.663718\pi$
$158$	5.60388	0.445820
$159$	8.71379	0.691049
$160$	3.60388	0.284911
$161$	−15.2078	−1.19854
$162$	−1.00000	−0.0785674
$163$	10.7681	0.843422	0.421711	−	0.906730i	$-0.361430\pi$
$163$	10.7681	0.843422	0.421711	+	0.906730i	$0.361430\pi$
$164$	1.20775	0.0943095
$165$	−3.60388	−0.280561
$166$	−14.4155	−1.11886
$167$	24.7439	1.91474	0.957371	−	0.288861i	$-0.0932765\pi$
$167$	24.7439	1.91474	0.957371	+	0.288861i	$0.0932765\pi$
$168$	4.49396	0.346716
$169$	15.9879	1.22984
$170$	18.7681	1.43945
$171$	−1.00000	−0.0764719
$172$	12.9879	0.990319
$173$	7.18359	0.546158	0.273079	−	0.961992i	$-0.411958\pi$
$173$	7.18359	0.546158	0.273079	+	0.961992i	$0.411958\pi$
$174$	2.98792	0.226514
$175$	35.8974	2.71359
$176$	−1.00000	−0.0753778
$177$	8.98792	0.675573
$178$	1.01208	0.0758587
$179$	11.4034	0.852332	0.426166	−	0.904645i	$-0.359864\pi$
$179$	11.4034	0.852332	0.426166	+	0.904645i	$0.359864\pi$
$180$	−3.60388	−0.268617
$181$	−3.46250	−0.257366	−0.128683	−	0.991686i	$-0.541075\pi$
$181$	−3.46250	−0.257366	−0.128683	+	0.991686i	$0.541075\pi$
$182$	24.1957	1.79350
$183$	13.7017	1.01286
$184$	3.38404	0.249475
$185$	−17.6233	−1.29569
$186$	−0.670251	−0.0491452
$187$	−5.20775	−0.380828
$188$	−11.0315	−0.804552
$189$	−4.49396	−0.326887
$190$	−3.60388	−0.261453
$191$	7.18837	0.520132	0.260066	−	0.965591i	$-0.416256\pi$
$191$	7.18837	0.520132	0.260066	+	0.965591i	$0.416256\pi$
$192$	−1.00000	−0.0721688
$193$	−16.9638	−1.22108	−0.610539	−	0.791986i	$-0.709047\pi$
$193$	−16.9638	−1.22108	−0.610539	+	0.791986i	$0.709047\pi$
$194$	1.01208	0.0726632
$195$	−19.4034	−1.38951
$196$	13.1957	0.942548
$197$	−10.0737	−0.717719	−0.358860	−	0.933392i	$-0.616834\pi$
$197$	−10.0737	−0.717719	−0.358860	+	0.933392i	$0.616834\pi$
$198$	1.00000	0.0710669
$199$	−3.20775	−0.227391	−0.113696	−	0.993516i	$-0.536269\pi$
$199$	−3.20775	−0.227391	−0.113696	+	0.993516i	$0.536269\pi$
$200$	−7.98792	−0.564831
$201$	14.4155	1.01679
$202$	3.90217	0.274555
$203$	13.4276	0.942432
$204$	−5.20775	−0.364615
$205$	−4.35258	−0.303998
$206$	18.2935	1.27457
$207$	−3.38404	−0.235207
$208$	−5.38404	−0.373316
$209$	1.00000	0.0691714
$210$	−16.1957	−1.11761
$211$	−14.4155	−0.992404	−0.496202	−	0.868207i	$-0.665272\pi$
$211$	−14.4155	−0.992404	−0.496202	+	0.868207i	$0.665272\pi$
$212$	−8.71379	−0.598466
$213$	10.2741	0.703972
$214$	0.792249	0.0541570
$215$	−46.8068	−3.19220
$216$	1.00000	0.0680414
$217$	−3.01208	−0.204473
$218$	−10.3720	−0.702478
$219$	14.1957	0.959254
$220$	3.60388	0.242973
$221$	−28.0388	−1.88609
$222$	4.89008	0.328201
$223$	7.32975	0.490836	0.245418	−	0.969417i	$-0.421075\pi$
$223$	7.32975	0.490836	0.245418	+	0.969417i	$0.421075\pi$
$224$	−4.49396	−0.300265
$225$	7.98792	0.532528
$226$	5.64742	0.375661
$227$	−8.19567	−0.543966	−0.271983	−	0.962302i	$-0.587679\pi$
$227$	−8.19567	−0.543966	−0.271983	+	0.962302i	$0.587679\pi$
$228$	1.00000	0.0662266
$229$	−21.8431	−1.44343	−0.721716	−	0.692189i	$-0.756646\pi$
$229$	−21.8431	−1.44343	−0.721716	+	0.692189i	$0.756646\pi$
$230$	−12.1957	−0.804159
$231$	4.49396	0.295681
$232$	−2.98792	−0.196166
$233$	−9.75600	−0.639137	−0.319569	−	0.947563i	$-0.603538\pi$
$233$	−9.75600	−0.639137	−0.319569	+	0.947563i	$0.603538\pi$
$234$	5.38404	0.351966
$235$	39.7560	2.59340
$236$	−8.98792	−0.585064
$237$	5.60388	0.364011
$238$	−23.4034	−1.51702
$239$	−8.31767	−0.538025	−0.269013	−	0.963137i	$-0.586697\pi$
$239$	−8.31767	−0.538025	−0.269013	+	0.963137i	$0.586697\pi$
$240$	3.60388	0.232629
$241$	−5.56033	−0.358173	−0.179086	−	0.983833i	$-0.557314\pi$
$241$	−5.56033	−0.358173	−0.179086	+	0.983833i	$0.557314\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−13.7017	−0.877162
$245$	−47.5555	−3.03821
$246$	1.20775	0.0770034
$247$	5.38404	0.342578
$248$	0.670251	0.0425610
$249$	−14.4155	−0.913545
$250$	10.7681	0.681034
$251$	8.08708	0.510452	0.255226	−	0.966881i	$-0.417850\pi$
$251$	8.08708	0.510452	0.255226	+	0.966881i	$0.417850\pi$
$252$	4.49396	0.283093
$253$	3.38404	0.212753
$254$	−14.5918	−0.915571
$255$	18.7681	1.17530
$256$	1.00000	0.0625000
$257$	19.4276	1.21186	0.605930	−	0.795518i	$-0.292801\pi$
$257$	19.4276	1.21186	0.605930	+	0.795518i	$0.292801\pi$
$258$	12.9879	0.808592
$259$	21.9758	1.36551
$260$	19.4034	1.20335
$261$	2.98792	0.184948
$262$	14.4155	0.890593
$263$	23.0858	1.42353	0.711764	−	0.702418i	$-0.247896\pi$
$263$	23.0858	1.42353	0.711764	+	0.702418i	$0.247896\pi$
$264$	−1.00000	−0.0615457
$265$	31.4034	1.92910
$266$	4.49396	0.275542
$267$	1.01208	0.0619384
$268$	−14.4155	−0.880567
$269$	1.50604	0.0918249	0.0459125	−	0.998945i	$-0.485380\pi$
$269$	1.50604	0.0918249	0.0459125	+	0.998945i	$0.485380\pi$
$270$	−3.60388	−0.219325
$271$	−7.94571	−0.482667	−0.241334	−	0.970442i	$-0.577585\pi$
$271$	−7.94571	−0.482667	−0.241334	+	0.970442i	$0.577585\pi$
$272$	5.20775	0.315766
$273$	24.1957	1.46439
$274$	−0.219833	−0.0132806
$275$	−7.98792	−0.481690
$276$	3.38404	0.203695
$277$	−15.6775	−0.941973	−0.470986	−	0.882141i	$-0.656102\pi$
$277$	−15.6775	−0.941973	−0.470986	+	0.882141i	$0.656102\pi$
$278$	4.43967	0.266273
$279$	−0.670251	−0.0401269
$280$	16.1957	0.967876
$281$	8.96376	0.534733	0.267366	−	0.963595i	$-0.413847\pi$
$281$	8.96376	0.534733	0.267366	+	0.963595i	$0.413847\pi$
$282$	−11.0315	−0.656914
$283$	25.3793	1.50864	0.754320	−	0.656507i	$-0.227967\pi$
$283$	25.3793	1.50864	0.754320	+	0.656507i	$0.227967\pi$
$284$	−10.2741	−0.609657
$285$	−3.60388	−0.213475
$286$	−5.38404	−0.318365
$287$	5.42758	0.320380
$288$	−1.00000	−0.0589256
$289$	10.1207	0.595334
$290$	10.7681	0.632324
$291$	1.01208	0.0593293
$292$	−14.1957	−0.830739
$293$	−3.78017	−0.220840	−0.110420	−	0.993885i	$-0.535220\pi$
$293$	−3.78017	−0.220840	−0.110420	+	0.993885i	$0.535220\pi$
$294$	13.1957	0.769587
$295$	32.3913	1.88590
$296$	−4.89008	−0.284230
$297$	1.00000	0.0580259
$298$	7.10992	0.411866
$299$	18.2198	1.05368
$300$	−7.98792	−0.461183
$301$	58.3672	3.36423
$302$	20.0194	1.15199
$303$	3.90217	0.224174
$304$	−1.00000	−0.0573539
$305$	49.3793	2.82745
$306$	−5.20775	−0.297707
$307$	−21.1836	−1.20901	−0.604506	−	0.796601i	$-0.706629\pi$
$307$	−21.1836	−1.20901	−0.604506	+	0.796601i	$0.706629\pi$
$308$	−4.49396	−0.256067
$309$	18.2935	1.04068
$310$	−2.41550	−0.137191
$311$	20.3720	1.15519	0.577594	−	0.816324i	$-0.303992\pi$
$311$	20.3720	1.15519	0.577594	+	0.816324i	$0.303992\pi$
$312$	−5.38404	−0.304811
$313$	−11.1836	−0.632134	−0.316067	−	0.948737i	$-0.602362\pi$
$313$	−11.1836	−0.632134	−0.316067	+	0.948737i	$0.602362\pi$
$314$	12.3284	0.695733
$315$	−16.1957	−0.912523
$316$	−5.60388	−0.315243
$317$	−0.361208	−0.0202874	−0.0101437	−	0.999949i	$-0.503229\pi$
$317$	−0.361208	−0.0202874	−0.0101437	+	0.999949i	$0.503229\pi$
$318$	−8.71379	−0.488645
$319$	−2.98792	−0.167291
$320$	−3.60388	−0.201463
$321$	0.792249	0.0442190
$322$	15.2078	0.847495
$323$	−5.20775	−0.289767
$324$	1.00000	0.0555556
$325$	−43.0073	−2.38562
$326$	−10.7681	−0.596389
$327$	−10.3720	−0.573571
$328$	−1.20775	−0.0666869
$329$	−49.5749	−2.73315
$330$	3.60388	0.198387
$331$	−3.36467	−0.184939	−0.0924694	−	0.995716i	$-0.529476\pi$
$331$	−3.36467	−0.184939	−0.0924694	+	0.995716i	$0.529476\pi$
$332$	14.4155	0.791153
$333$	4.89008	0.267975
$334$	−24.7439	−1.35393
$335$	51.9517	2.83842
$336$	−4.49396	−0.245166
$337$	23.6233	1.28684	0.643420	−	0.765513i	$-0.277515\pi$
$337$	23.6233	1.28684	0.643420	+	0.765513i	$0.277515\pi$
$338$	−15.9879	−0.869628
$339$	5.64742	0.306726
$340$	−18.7681	−1.01784
$341$	0.670251	0.0362961
$342$	1.00000	0.0540738
$343$	27.8431	1.50339
$344$	−12.9879	−0.700262
$345$	−12.1957	−0.656593
$346$	−7.18359	−0.386192
$347$	13.0750	0.701903	0.350951	−	0.936394i	$-0.385858\pi$
$347$	13.0750	0.701903	0.350951	+	0.936394i	$0.385858\pi$
$348$	−2.98792	−0.160169
$349$	−3.37329	−0.180568	−0.0902840	−	0.995916i	$-0.528777\pi$
$349$	−3.37329	−0.180568	−0.0902840	+	0.995916i	$0.528777\pi$
$350$	−35.8974	−1.91880
$351$	5.38404	0.287379
$352$	1.00000	0.0533002
$353$	7.86725	0.418731	0.209366	−	0.977837i	$-0.432860\pi$
$353$	7.86725	0.418731	0.209366	+	0.977837i	$0.432860\pi$
$354$	−8.98792	−0.477702
$355$	37.0267	1.96517
$356$	−1.01208	−0.0536402
$357$	−23.4034	−1.23864
$358$	−11.4034	−0.602689
$359$	−17.6582	−0.931963	−0.465981	−	0.884795i	$-0.654299\pi$
$359$	−17.6582	−0.931963	−0.465981	+	0.884795i	$0.654299\pi$
$360$	3.60388	0.189941
$361$	1.00000	0.0526316
$362$	3.46250	0.181985
$363$	−1.00000	−0.0524864
$364$	−24.1957	−1.26820
$365$	51.1594	2.67781
$366$	−13.7017	−0.716200
$367$	21.0750	1.10011	0.550053	−	0.835130i	$-0.314608\pi$
$367$	21.0750	1.10011	0.550053	+	0.835130i	$0.314608\pi$
$368$	−3.38404	−0.176405
$369$	1.20775	0.0628730
$370$	17.6233	0.916189
$371$	−39.1594	−2.03306
$372$	0.670251	0.0347509
$373$	28.9831	1.50069	0.750345	−	0.661047i	$-0.229887\pi$
$373$	28.9831	1.50069	0.750345	+	0.661047i	$0.229887\pi$
$374$	5.20775	0.269286
$375$	10.7681	0.556062
$376$	11.0315	0.568904
$377$	−16.0871	−0.828527
$378$	4.49396	0.231144
$379$	−29.7318	−1.52722	−0.763611	−	0.645677i	$-0.776575\pi$
$379$	−29.7318	−1.52722	−0.763611	+	0.645677i	$0.776575\pi$
$380$	3.60388	0.184875
$381$	−14.5918	−0.747560
$382$	−7.18837	−0.367789
$383$	22.8224	1.16617	0.583085	−	0.812411i	$-0.301846\pi$
$383$	22.8224	1.16617	0.583085	+	0.812411i	$0.301846\pi$
$384$	1.00000	0.0510310
$385$	16.1957	0.825408
$386$	16.9638	0.863432
$387$	12.9879	0.660213
$388$	−1.01208	−0.0513807
$389$	−10.7245	−0.543756	−0.271878	−	0.962332i	$-0.587645\pi$
$389$	−10.7245	−0.543756	−0.271878	+	0.962332i	$0.587645\pi$
$390$	19.4034	0.982530
$391$	−17.6233	−0.891246
$392$	−13.1957	−0.666482
$393$	14.4155	0.727166
$394$	10.0737	0.507504
$395$	20.1957	1.01615
$396$	−1.00000	−0.0502519
$397$	14.7439	0.739976	0.369988	−	0.929036i	$-0.379362\pi$
$397$	14.7439	0.739976	0.369988	+	0.929036i	$0.379362\pi$
$398$	3.20775	0.160790
$399$	4.49396	0.224979
$400$	7.98792	0.399396
$401$	−22.6353	−1.13035	−0.565177	−	0.824969i	$-0.691192\pi$
$401$	−22.6353	−1.13035	−0.565177	+	0.824969i	$0.691192\pi$
$402$	−14.4155	−0.718980
$403$	3.60866	0.179760
$404$	−3.90217	−0.194140
$405$	−3.60388	−0.179078
$406$	−13.4276	−0.666400
$407$	−4.89008	−0.242392
$408$	5.20775	0.257822
$409$	−2.87933	−0.142374	−0.0711869	−	0.997463i	$-0.522679\pi$
$409$	−2.87933	−0.142374	−0.0711869	+	0.997463i	$0.522679\pi$
$410$	4.35258	0.214959
$411$	−0.219833	−0.0108435
$412$	−18.2935	−0.901256
$413$	−40.3913	−1.98753
$414$	3.38404	0.166317
$415$	−51.9517	−2.55021
$416$	5.38404	0.263974
$417$	4.43967	0.217411
$418$	−1.00000	−0.0489116
$419$	15.1207	0.738693	0.369347	−	0.929292i	$-0.379582\pi$
$419$	15.1207	0.738693	0.369347	+	0.929292i	$0.379582\pi$
$420$	16.1957	0.790268
$421$	−13.9651	−0.680617	−0.340308	−	0.940314i	$-0.610531\pi$
$421$	−13.9651	−0.680617	−0.340308	+	0.940314i	$0.610531\pi$
$422$	14.4155	0.701736
$423$	−11.0315	−0.536368
$424$	8.71379	0.423179
$425$	41.5991	2.01785
$426$	−10.2741	−0.497783
$427$	−61.5749	−2.97982
$428$	−0.792249	−0.0382948
$429$	−5.38404	−0.259944
$430$	46.8068	2.25723
$431$	7.36467	0.354743	0.177372	−	0.984144i	$-0.443241\pi$
$431$	7.36467	0.354743	0.177372	+	0.984144i	$0.443241\pi$
$432$	−1.00000	−0.0481125
$433$	−10.1957	−0.489973	−0.244986	−	0.969527i	$-0.578783\pi$
$433$	−10.1957	−0.489973	−0.244986	+	0.969527i	$0.578783\pi$
$434$	3.01208	0.144585
$435$	10.7681	0.516290
$436$	10.3720	0.496727
$437$	3.38404	0.161881
$438$	−14.1957	−0.678295
$439$	14.9831	0.715106	0.357553	−	0.933893i	$-0.383611\pi$
$439$	14.9831	0.715106	0.357553	+	0.933893i	$0.383611\pi$
$440$	−3.60388	−0.171808
$441$	13.1957	0.628365
$442$	28.0388	1.33367
$443$	−21.5362	−1.02321	−0.511607	−	0.859219i	$-0.670950\pi$
$443$	−21.5362	−1.02321	−0.511607	+	0.859219i	$0.670950\pi$
$444$	−4.89008	−0.232073
$445$	3.64742	0.172904
$446$	−7.32975	−0.347074
$447$	7.10992	0.336287
$448$	4.49396	0.212320
$449$	2.43967	0.115135	0.0575675	−	0.998342i	$-0.481666\pi$
$449$	2.43967	0.115135	0.0575675	+	0.998342i	$0.481666\pi$
$450$	−7.98792	−0.376554
$451$	−1.20775	−0.0568708
$452$	−5.64742	−0.265632
$453$	20.0194	0.940592
$454$	8.19567	0.384642
$455$	87.1982	4.08791
$456$	−1.00000	−0.0468293
$457$	−22.1086	−1.03420	−0.517098	−	0.855926i	$-0.672988\pi$
$457$	−22.1086	−1.03420	−0.517098	+	0.855926i	$0.672988\pi$
$458$	21.8431	1.02066
$459$	−5.20775	−0.243077
$460$	12.1957	0.568626
$461$	−27.9409	−1.30134	−0.650669	−	0.759361i	$-0.725512\pi$
$461$	−27.9409	−1.30134	−0.650669	+	0.759361i	$0.725512\pi$
$462$	−4.49396	−0.209078
$463$	4.79225	0.222715	0.111357	−	0.993780i	$-0.464480\pi$
$463$	4.79225	0.222715	0.111357	+	0.993780i	$0.464480\pi$
$464$	2.98792	0.138711
$465$	−2.41550	−0.112016
$466$	9.75600	0.451938
$467$	36.3043	1.67996	0.839980	−	0.542617i	$-0.182566\pi$
$467$	36.3043	1.67996	0.839980	+	0.542617i	$0.182566\pi$
$468$	−5.38404	−0.248877
$469$	−64.7827	−2.99139
$470$	−39.7560	−1.83381
$471$	12.3284	0.568064
$472$	8.98792	0.413702
$473$	−12.9879	−0.597185
$474$	−5.60388	−0.257395
$475$	−7.98792	−0.366511
$476$	23.4034	1.07269
$477$	−8.71379	−0.398977
$478$	8.31767	0.380441
$479$	−11.5254	−0.526610	−0.263305	−	0.964713i	$-0.584813\pi$
$479$	−11.5254	−0.526610	−0.263305	+	0.964713i	$0.584813\pi$
$480$	−3.60388	−0.164494
$481$	−26.3284	−1.20047
$482$	5.56033	0.253266
$483$	15.2078	0.691977
$484$	1.00000	0.0454545
$485$	3.64742	0.165621
$486$	1.00000	0.0453609
$487$	14.4892	0.656567	0.328284	−	0.944579i	$-0.393530\pi$
$487$	14.4892	0.656567	0.328284	+	0.944579i	$0.393530\pi$
$488$	13.7017	0.620247
$489$	−10.7681	−0.486950
$490$	47.5555	2.14834
$491$	13.5147	0.609908	0.304954	−	0.952367i	$-0.401359\pi$
$491$	13.5147	0.609908	0.304954	+	0.952367i	$0.401359\pi$
$492$	−1.20775	−0.0544496
$493$	15.5603	0.700802
$494$	−5.38404	−0.242240
$495$	3.60388	0.161982
$496$	−0.670251	−0.0300952
$497$	−46.1715	−2.07108
$498$	14.4155	0.645974
$499$	20.6353	0.923764	0.461882	−	0.886941i	$-0.347174\pi$
$499$	20.6353	0.923764	0.461882	+	0.886941i	$0.347174\pi$
$500$	−10.7681	−0.481563
$501$	−24.7439	−1.10548
$502$	−8.08708	−0.360944
$503$	−23.4383	−1.04506	−0.522532	−	0.852620i	$-0.675012\pi$
$503$	−23.4383	−1.04506	−0.522532	+	0.852620i	$0.675012\pi$
$504$	−4.49396	−0.200177
$505$	14.0629	0.625792
$506$	−3.38404	−0.150439
$507$	−15.9879	−0.710048
$508$	14.5918	0.647406
$509$	−36.0301	−1.59701	−0.798504	−	0.601990i	$-0.794375\pi$
$509$	−36.0301	−1.59701	−0.798504	+	0.601990i	$0.794375\pi$
$510$	−18.7681	−0.831065
$511$	−63.7948	−2.82211
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−19.4276	−0.856914
$515$	65.9275	2.90511
$516$	−12.9879	−0.571761
$517$	11.0315	0.485163
$518$	−21.9758	−0.965563
$519$	−7.18359	−0.315325
$520$	−19.4034	−0.850896
$521$	0.681005	0.0298354	0.0149177	−	0.999889i	$-0.495251\pi$
$521$	0.681005	0.0298354	0.0149177	+	0.999889i	$0.495251\pi$
$522$	−2.98792	−0.130778
$523$	22.7198	0.993466	0.496733	−	0.867903i	$-0.334533\pi$
$523$	22.7198	0.993466	0.496733	+	0.867903i	$0.334533\pi$
$524$	−14.4155	−0.629744
$525$	−35.8974	−1.56669
$526$	−23.0858	−1.00659
$527$	−3.49050	−0.152049
$528$	1.00000	0.0435194
$529$	−11.5483	−0.502098
$530$	−31.4034	−1.36408
$531$	−8.98792	−0.390042
$532$	−4.49396	−0.194838
$533$	−6.50258	−0.281658
$534$	−1.01208	−0.0437971
$535$	2.85517	0.123440
$536$	14.4155	0.622655
$537$	−11.4034	−0.492094
$538$	−1.50604	−0.0649300
$539$	−13.1957	−0.568378
$540$	3.60388	0.155086
$541$	32.5784	1.40065	0.700327	−	0.713822i	$-0.253037\pi$
$541$	32.5784	1.40065	0.700327	+	0.713822i	$0.253037\pi$
$542$	7.94571	0.341297
$543$	3.46250	0.148590
$544$	−5.20775	−0.223280
$545$	−37.3793	−1.60115
$546$	−24.1957	−1.03548
$547$	−41.6233	−1.77968	−0.889841	−	0.456271i	$-0.849185\pi$
$547$	−41.6233	−1.77968	−0.889841	+	0.456271i	$0.849185\pi$
$548$	0.219833	0.00939078
$549$	−13.7017	−0.584775
$550$	7.98792	0.340606
$551$	−2.98792	−0.127290
$552$	−3.38404	−0.144034
$553$	−25.1836	−1.07092
$554$	15.6775	0.666075
$555$	17.6233	0.748065
$556$	−4.43967	−0.188284
$557$	19.2573	0.815956	0.407978	−	0.912992i	$-0.366234\pi$
$557$	19.2573	0.815956	0.407978	+	0.912992i	$0.366234\pi$
$558$	0.670251	0.0283740
$559$	−69.9275	−2.95762
$560$	−16.1957	−0.684392
$561$	5.20775	0.219871
$562$	−8.96376	−0.378113
$563$	−28.0388	−1.18169	−0.590846	−	0.806784i	$-0.701206\pi$
$563$	−28.0388	−1.18169	−0.590846	+	0.806784i	$0.701206\pi$
$564$	11.0315	0.464508
$565$	20.3526	0.856240
$566$	−25.3793	−1.06677
$567$	4.49396	0.188729
$568$	10.2741	0.431093
$569$	−27.0267	−1.13302	−0.566509	−	0.824056i	$-0.691706\pi$
$569$	−27.0267	−1.13302	−0.566509	+	0.824056i	$0.691706\pi$
$570$	3.60388	0.150950
$571$	2.41550	0.101086	0.0505428	−	0.998722i	$-0.483905\pi$
$571$	2.41550	0.101086	0.0505428	+	0.998722i	$0.483905\pi$
$572$	5.38404	0.225118
$573$	−7.18837	−0.300299
$574$	−5.42758	−0.226543
$575$	−27.0315	−1.12729
$576$	1.00000	0.0416667
$577$	10.6353	0.442755	0.221377	−	0.975188i	$-0.428945\pi$
$577$	10.6353	0.442755	0.221377	+	0.975188i	$0.428945\pi$
$578$	−10.1207	−0.420964
$579$	16.9638	0.704990
$580$	−10.7681	−0.447120
$581$	64.7827	2.68764
$582$	−1.01208	−0.0419521
$583$	8.71379	0.360888
$584$	14.1957	0.587421
$585$	19.4034	0.802233
$586$	3.78017	0.156157
$587$	−12.4397	−0.513440	−0.256720	−	0.966486i	$-0.582642\pi$
$587$	−12.4397	−0.513440	−0.256720	+	0.966486i	$0.582642\pi$
$588$	−13.1957	−0.544180
$589$	0.670251	0.0276172
$590$	−32.3913	−1.33353
$591$	10.0737	0.414375
$592$	4.89008	0.200981
$593$	9.01208	0.370082	0.185041	−	0.982731i	$-0.440758\pi$
$593$	9.01208	0.370082	0.185041	+	0.982731i	$0.440758\pi$
$594$	−1.00000	−0.0410305
$595$	−84.3430	−3.45773
$596$	−7.10992	−0.291234
$597$	3.20775	0.131285
$598$	−18.2198	−0.745064
$599$	3.11470	0.127263	0.0636316	−	0.997973i	$-0.479732\pi$
$599$	3.11470	0.127263	0.0636316	+	0.997973i	$0.479732\pi$
$600$	7.98792	0.326105
$601$	−31.1836	−1.27201	−0.636003	−	0.771687i	$-0.719413\pi$
$601$	−31.1836	−1.27201	−0.636003	+	0.771687i	$0.719413\pi$
$602$	−58.3672	−2.37887
$603$	−14.4155	−0.587045
$604$	−20.0194	−0.814577
$605$	−3.60388	−0.146518
$606$	−3.90217	−0.158515
$607$	−28.0194	−1.13727	−0.568636	−	0.822589i	$-0.692529\pi$
$607$	−28.0194	−1.13727	−0.568636	+	0.822589i	$0.692529\pi$
$608$	1.00000	0.0405554
$609$	−13.4276	−0.544113
$610$	−49.3793	−1.99931
$611$	59.3938	2.40282
$612$	5.20775	0.210511
$613$	17.3491	0.700725	0.350362	−	0.936614i	$-0.386058\pi$
$613$	17.3491	0.700725	0.350362	+	0.936614i	$0.386058\pi$
$614$	21.1836	0.854900
$615$	4.35258	0.175513
$616$	4.49396	0.181067
$617$	23.3793	0.941213	0.470607	−	0.882343i	$-0.344035\pi$
$617$	23.3793	0.941213	0.470607	+	0.882343i	$0.344035\pi$
$618$	−18.2935	−0.735873
$619$	29.8672	1.20047	0.600233	−	0.799825i	$-0.295075\pi$
$619$	29.8672	1.20047	0.600233	+	0.799825i	$0.295075\pi$
$620$	2.41550	0.0970089
$621$	3.38404	0.135797
$622$	−20.3720	−0.816841
$623$	−4.54825	−0.182222
$624$	5.38404	0.215534
$625$	−1.13275	−0.0453101
$626$	11.1836	0.446986
$627$	−1.00000	−0.0399362
$628$	−12.3284	−0.491958
$629$	25.4663	1.01541
$630$	16.1957	0.645251
$631$	5.14483	0.204813	0.102406	−	0.994743i	$-0.467346\pi$
$631$	5.14483	0.204813	0.102406	+	0.994743i	$0.467346\pi$
$632$	5.60388	0.222910
$633$	14.4155	0.572965
$634$	0.361208	0.0143454
$635$	−52.5870	−2.08685
$636$	8.71379	0.345524
$637$	−71.0461	−2.81495
$638$	2.98792	0.118293
$639$	−10.2741	−0.406438
$640$	3.60388	0.142456
$641$	23.9758	0.946989	0.473494	−	0.880797i	$-0.342992\pi$
$641$	23.9758	0.946989	0.473494	+	0.880797i	$0.342992\pi$
$642$	−0.792249	−0.0312676
$643$	3.12067	0.123067	0.0615336	−	0.998105i	$-0.480401\pi$
$643$	3.12067	0.123067	0.0615336	+	0.998105i	$0.480401\pi$
$644$	−15.2078	−0.599269
$645$	46.8068	1.84302
$646$	5.20775	0.204896
$647$	15.4711	0.608233	0.304116	−	0.952635i	$-0.401639\pi$
$647$	15.4711	0.608233	0.304116	+	0.952635i	$0.401639\pi$
$648$	−1.00000	−0.0392837
$649$	8.98792	0.352807
$650$	43.0073	1.68688
$651$	3.01208	0.118053
$652$	10.7681	0.421711
$653$	−4.34780	−0.170142	−0.0850712	−	0.996375i	$-0.527112\pi$
$653$	−4.34780	−0.170142	−0.0850712	+	0.996375i	$0.527112\pi$
$654$	10.3720	0.405576
$655$	51.9517	2.02992
$656$	1.20775	0.0471548
$657$	−14.1957	−0.553826
$658$	49.5749	1.93263
$659$	12.6353	0.492203	0.246101	−	0.969244i	$-0.420850\pi$
$659$	12.6353	0.492203	0.246101	+	0.969244i	$0.420850\pi$
$660$	−3.60388	−0.140281
$661$	5.17283	0.201200	0.100600	−	0.994927i	$-0.467924\pi$
$661$	5.17283	0.201200	0.100600	+	0.994927i	$0.467924\pi$
$662$	3.36467	0.130771
$663$	28.0388	1.08894
$664$	−14.4155	−0.559430
$665$	16.1957	0.628041
$666$	−4.89008	−0.189487
$667$	−10.1112	−0.391509
$668$	24.7439	0.957371
$669$	−7.32975	−0.283384
$670$	−51.9517	−2.00707
$671$	13.7017	0.528949
$672$	4.49396	0.173358
$673$	−1.84309	−0.0710457	−0.0355229	−	0.999369i	$-0.511310\pi$
$673$	−1.84309	−0.0710457	−0.0355229	+	0.999369i	$0.511310\pi$
$674$	−23.6233	−0.909934
$675$	−7.98792	−0.307455
$676$	15.9879	0.614920
$677$	−43.4276	−1.66906	−0.834529	−	0.550964i	$-0.814260\pi$
$677$	−43.4276	−1.66906	−0.834529	+	0.550964i	$0.814260\pi$
$678$	−5.64742	−0.216888
$679$	−4.54825	−0.174546
$680$	18.7681	0.719723
$681$	8.19567	0.314059
$682$	−0.670251	−0.0256652
$683$	20.9879	0.803080	0.401540	−	0.915841i	$-0.368475\pi$
$683$	20.9879	0.803080	0.401540	+	0.915841i	$0.368475\pi$
$684$	−1.00000	−0.0382360
$685$	−0.792249	−0.0302703
$686$	−27.8431	−1.06305
$687$	21.8431	0.833366
$688$	12.9879	0.495160
$689$	46.9154	1.78734
$690$	12.1957	0.464281
$691$	−30.0844	−1.14447	−0.572233	−	0.820091i	$-0.693923\pi$
$691$	−30.0844	−1.14447	−0.572233	+	0.820091i	$0.693923\pi$
$692$	7.18359	0.273079
$693$	−4.49396	−0.170711
$694$	−13.0750	−0.496320
$695$	16.0000	0.606915
$696$	2.98792	0.113257
$697$	6.28967	0.238238
$698$	3.37329	0.127681
$699$	9.75600	0.369006
$700$	35.8974	1.35679
$701$	−34.4263	−1.30026	−0.650131	−	0.759822i	$-0.725286\pi$
$701$	−34.4263	−1.30026	−0.650131	+	0.759822i	$0.725286\pi$
$702$	−5.38404	−0.203208
$703$	−4.89008	−0.184433
$704$	−1.00000	−0.0376889
$705$	−39.7560	−1.49730
$706$	−7.86725	−0.296088
$707$	−17.5362	−0.659516
$708$	8.98792	0.337787
$709$	38.4999	1.44590	0.722948	−	0.690903i	$-0.242787\pi$
$709$	38.4999	1.44590	0.722948	+	0.690903i	$0.242787\pi$
$710$	−37.0267	−1.38959
$711$	−5.60388	−0.210162
$712$	1.01208	0.0379294
$713$	2.26816	0.0849432
$714$	23.4034	0.875851
$715$	−19.4034	−0.725647
$716$	11.4034	0.426166
$717$	8.31767	0.310629
$718$	17.6582	0.658997
$719$	−43.1400	−1.60885	−0.804426	−	0.594053i	$-0.797527\pi$
$719$	−43.1400	−1.60885	−0.804426	+	0.594053i	$0.797527\pi$
$720$	−3.60388	−0.134309
$721$	−82.2103	−3.06167
$722$	−1.00000	−0.0372161
$723$	5.56033	0.206791
$724$	−3.46250	−0.128683
$725$	23.8672	0.886407
$726$	1.00000	0.0371135
$727$	33.3793	1.23797	0.618984	−	0.785404i	$-0.287545\pi$
$727$	33.3793	1.23797	0.618984	+	0.785404i	$0.287545\pi$
$728$	24.1957	0.896751
$729$	1.00000	0.0370370
$730$	−51.1594	−1.89350
$731$	67.6378	2.50168
$732$	13.7017	0.506430
$733$	44.1387	1.63030	0.815150	−	0.579249i	$-0.196654\pi$
$733$	44.1387	1.63030	0.815150	+	0.579249i	$0.196654\pi$
$734$	−21.0750	−0.777892
$735$	47.5555	1.75411
$736$	3.38404	0.124737
$737$	14.4155	0.531002
$738$	−1.20775	−0.0444579
$739$	13.8189	0.508337	0.254169	−	0.967160i	$-0.418198\pi$
$739$	13.8189	0.508337	0.254169	+	0.967160i	$0.418198\pi$
$740$	−17.6233	−0.647844
$741$	−5.38404	−0.197788
$742$	39.1594	1.43759
$743$	−34.7198	−1.27374	−0.636872	−	0.770969i	$-0.719772\pi$
$743$	−34.7198	−1.27374	−0.636872	+	0.770969i	$0.719772\pi$
$744$	−0.670251	−0.0245726
$745$	25.6233	0.938763
$746$	−28.9831	−1.06115
$747$	14.4155	0.527436
$748$	−5.20775	−0.190414
$749$	−3.56033	−0.130092
$750$	−10.7681	−0.393195
$751$	−10.8901	−0.397385	−0.198692	−	0.980062i	$-0.563669\pi$
$751$	−10.8901	−0.397385	−0.198692	+	0.980062i	$0.563669\pi$
$752$	−11.0315	−0.402276
$753$	−8.08708	−0.294710
$754$	16.0871	0.585857
$755$	72.1473	2.62571
$756$	−4.49396	−0.163444
$757$	41.0025	1.49026	0.745131	−	0.666918i	$-0.232387\pi$
$757$	41.0025	1.49026	0.745131	+	0.666918i	$0.232387\pi$
$758$	29.7318	1.07991
$759$	−3.38404	−0.122833
$760$	−3.60388	−0.130726
$761$	15.6716	0.568094	0.284047	−	0.958810i	$-0.408323\pi$
$761$	15.6716	0.568094	0.284047	+	0.958810i	$0.408323\pi$
$762$	14.5918	0.528605
$763$	46.6112	1.68744
$764$	7.18837	0.260066
$765$	−18.7681	−0.678562
$766$	−22.8224	−0.824606
$767$	48.3913	1.74731
$768$	−1.00000	−0.0360844
$769$	−0.0629179	−0.00226888	−0.00113444	−	0.999999i	$-0.500361\pi$
$769$	−0.0629179	−0.00226888	−0.00113444	+	0.999999i	$0.500361\pi$
$770$	−16.1957	−0.583651
$771$	−19.4276	−0.699667
$772$	−16.9638	−0.610539
$773$	−26.9336	−0.968735	−0.484368	−	0.874865i	$-0.660950\pi$
$773$	−26.9336	−0.968735	−0.484368	+	0.874865i	$0.660950\pi$
$774$	−12.9879	−0.466841
$775$	−5.35391	−0.192318
$776$	1.01208	0.0363316
$777$	−21.9758	−0.788379
$778$	10.7245	0.384494
$779$	−1.20775	−0.0432722
$780$	−19.4034	−0.694754
$781$	10.2741	0.367637
$782$	17.6233	0.630206
$783$	−2.98792	−0.106779
$784$	13.1957	0.471274
$785$	44.4301	1.58578
$786$	−14.4155	−0.514184
$787$	−29.7103	−1.05906	−0.529530	−	0.848292i	$-0.677632\pi$
$787$	−29.7103	−1.05906	−0.529530	+	0.848292i	$0.677632\pi$
$788$	−10.0737	−0.358860
$789$	−23.0858	−0.821875
$790$	−20.1957	−0.718530
$791$	−25.3793	−0.902382
$792$	1.00000	0.0355335
$793$	73.7706	2.61967
$794$	−14.7439	−0.523242
$795$	−31.4034	−1.11376
$796$	−3.20775	−0.113696
$797$	20.3612	0.721231	0.360615	−	0.932715i	$-0.382567\pi$
$797$	20.3612	0.721231	0.360615	+	0.932715i	$0.382567\pi$
$798$	−4.49396	−0.159084
$799$	−57.4491	−2.03240
$800$	−7.98792	−0.282416
$801$	−1.01208	−0.0357601
$802$	22.6353	0.799281
$803$	14.1957	0.500954
$804$	14.4155	0.508396
$805$	54.8068	1.93169
$806$	−3.60866	−0.127110
$807$	−1.50604	−0.0530151
$808$	3.90217	0.137278
$809$	−10.0000	−0.351581	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000	−0.351581	−0.175791	+	0.984428i	$0.556248\pi$
$810$	3.60388	0.126627
$811$	14.3284	0.503139	0.251569	−	0.967839i	$-0.419053\pi$
$811$	14.3284	0.503139	0.251569	+	0.967839i	$0.419053\pi$
$812$	13.4276	0.471216
$813$	7.94571	0.278668
$814$	4.89008	0.171397
$815$	−38.8068	−1.35934
$816$	−5.20775	−0.182308
$817$	−12.9879	−0.454390
$818$	2.87933	0.100673
$819$	−24.1957	−0.845465
$820$	−4.35258	−0.151999
$821$	−25.6125	−0.893882	−0.446941	−	0.894563i	$-0.647487\pi$
$821$	−25.6125	−0.893882	−0.446941	+	0.894563i	$0.647487\pi$
$822$	0.219833	0.00766754
$823$	−27.2465	−0.949753	−0.474877	−	0.880052i	$-0.657507\pi$
$823$	−27.2465	−0.949753	−0.474877	+	0.880052i	$0.657507\pi$
$824$	18.2935	0.637284
$825$	7.98792	0.278104
$826$	40.3913	1.40539
$827$	23.8431	0.829105	0.414553	−	0.910025i	$-0.363938\pi$
$827$	23.8431	0.829105	0.414553	+	0.910025i	$0.363938\pi$
$828$	−3.38404	−0.117604
$829$	−4.45042	−0.154569	−0.0772847	−	0.997009i	$-0.524625\pi$
$829$	−4.45042	−0.154569	−0.0772847	+	0.997009i	$0.524625\pi$
$830$	51.9517	1.80327
$831$	15.6775	0.543848
$832$	−5.38404	−0.186658
$833$	68.7198	2.38100
$834$	−4.43967	−0.153733
$835$	−89.1740	−3.08599
$836$	1.00000	0.0345857
$837$	0.670251	0.0231673
$838$	−15.1207	−0.522335
$839$	−9.92154	−0.342530	−0.171265	−	0.985225i	$-0.554785\pi$
$839$	−9.92154	−0.342530	−0.171265	+	0.985225i	$0.554785\pi$
$840$	−16.1957	−0.558804
$841$	−20.0723	−0.692150
$842$	13.9651	0.481269
$843$	−8.96376	−0.308728
$844$	−14.4155	−0.496202
$845$	−57.6185	−1.98214
$846$	11.0315	0.379269
$847$	4.49396	0.154414
$848$	−8.71379	−0.299233
$849$	−25.3793	−0.871014
$850$	−41.5991	−1.42684
$851$	−16.5483	−0.567267
$852$	10.2741	0.351986
$853$	−1.75004	−0.0599201	−0.0299601	−	0.999551i	$-0.509538\pi$
$853$	−1.75004	−0.0599201	−0.0299601	+	0.999551i	$0.509538\pi$
$854$	61.5749	2.10705
$855$	3.60388	0.123250
$856$	0.792249	0.0270785
$857$	−1.12067	−0.0382814	−0.0191407	−	0.999817i	$-0.506093\pi$
$857$	−1.12067	−0.0382814	−0.0191407	+	0.999817i	$0.506093\pi$
$858$	5.38404	0.183808
$859$	7.31634	0.249630	0.124815	−	0.992180i	$-0.460166\pi$
$859$	7.31634	0.249630	0.124815	+	0.992180i	$0.460166\pi$
$860$	−46.8068	−1.59610
$861$	−5.42758	−0.184972
$862$	−7.36467	−0.250842
$863$	−29.8732	−1.01690	−0.508448	−	0.861093i	$-0.669781\pi$
$863$	−29.8732	−1.01690	−0.508448	+	0.861093i	$0.669781\pi$
$864$	1.00000	0.0340207
$865$	−25.8888	−0.880244
$866$	10.1957	0.346463
$867$	−10.1207	−0.343716
$868$	−3.01208	−0.102237
$869$	5.60388	0.190098
$870$	−10.7681	−0.365072
$871$	77.6137	2.62984
$872$	−10.3720	−0.351239
$873$	−1.01208	−0.0342538
$874$	−3.38404	−0.114467
$875$	−48.3913	−1.63593
$876$	14.1957	0.479627
$877$	48.5435	1.63920	0.819598	−	0.572939i	$-0.194197\pi$
$877$	48.5435	1.63920	0.819598	+	0.572939i	$0.194197\pi$
$878$	−14.9831	−0.505656
$879$	3.78017	0.127502
$880$	3.60388	0.121487
$881$	−3.37926	−0.113850	−0.0569250	−	0.998378i	$-0.518130\pi$
$881$	−3.37926	−0.113850	−0.0569250	+	0.998378i	$0.518130\pi$
$882$	−13.1957	−0.444321
$883$	−14.9638	−0.503570	−0.251785	−	0.967783i	$-0.581018\pi$
$883$	−14.9638	−0.503570	−0.251785	+	0.967783i	$0.581018\pi$
$884$	−28.0388	−0.943045
$885$	−32.3913	−1.08882
$886$	21.5362	0.723522
$887$	−26.7198	−0.897162	−0.448581	−	0.893742i	$-0.648070\pi$
$887$	−26.7198	−0.897162	−0.448581	+	0.893742i	$0.648070\pi$
$888$	4.89008	0.164100
$889$	65.5749	2.19931
$890$	−3.64742	−0.122262
$891$	−1.00000	−0.0335013
$892$	7.32975	0.245418
$893$	11.0315	0.369154
$894$	−7.10992	−0.237791
$895$	−41.0965	−1.37370
$896$	−4.49396	−0.150133
$897$	−18.2198	−0.608343
$898$	−2.43967	−0.0814127
$899$	−2.00266	−0.0667923
$900$	7.98792	0.266264
$901$	−45.3793	−1.51180
$902$	1.20775	0.0402137
$903$	−58.3672	−1.94234
$904$	5.64742	0.187830
$905$	12.4784	0.414797
$906$	−20.0194	−0.665099
$907$	49.9758	1.65942	0.829710	−	0.558194i	$-0.188506\pi$
$907$	49.9758	1.65942	0.829710	+	0.558194i	$0.188506\pi$
$908$	−8.19567	−0.271983
$909$	−3.90217	−0.129427
$910$	−87.1982	−2.89059
$911$	35.0180	1.16020	0.580100	−	0.814545i	$-0.303014\pi$
$911$	35.0180	1.16020	0.580100	+	0.814545i	$0.303014\pi$
$912$	1.00000	0.0331133
$913$	−14.4155	−0.477083
$914$	22.1086	0.731287
$915$	−49.3793	−1.63243
$916$	−21.8431	−0.721716
$917$	−64.7827	−2.13931
$918$	5.20775	0.171881
$919$	−18.3827	−0.606390	−0.303195	−	0.952929i	$-0.598053\pi$
$919$	−18.3827	−0.606390	−0.303195	+	0.952929i	$0.598053\pi$
$920$	−12.1957	−0.402079
$921$	21.1836	0.698023
$922$	27.9409	0.920185
$923$	55.3163	1.82076
$924$	4.49396	0.147840
$925$	39.0616	1.28434
$926$	−4.79225	−0.157483
$927$	−18.2935	−0.600838
$928$	−2.98792	−0.0980832
$929$	−12.9250	−0.424056	−0.212028	−	0.977264i	$-0.568007\pi$
$929$	−12.9250	−0.424056	−0.212028	+	0.977264i	$0.568007\pi$
$930$	2.41550	0.0792074
$931$	−13.1957	−0.432471
$932$	−9.75600	−0.319569
$933$	−20.3720	−0.666948
$934$	−36.3043	−1.18791
$935$	18.7681	0.613782
$936$	5.38404	0.175983
$937$	−14.1957	−0.463752	−0.231876	−	0.972745i	$-0.574486\pi$
$937$	−14.1957	−0.463752	−0.231876	+	0.972745i	$0.574486\pi$
$938$	64.7827	2.11523
$939$	11.1836	0.364963
$940$	39.7560	1.29670
$941$	23.1836	0.755763	0.377882	−	0.925854i	$-0.376653\pi$
$941$	23.1836	0.755763	0.377882	+	0.925854i	$0.376653\pi$
$942$	−12.3284	−0.401682
$943$	−4.08708	−0.133094
$944$	−8.98792	−0.292532
$945$	16.1957	0.526845
$946$	12.9879	0.422274
$947$	−17.2319	−0.559962	−0.279981	−	0.960006i	$-0.590328\pi$
$947$	−17.2319	−0.559962	−0.279981	+	0.960006i	$0.590328\pi$
$948$	5.60388	0.182005
$949$	76.4301	2.48103
$950$	7.98792	0.259162
$951$	0.361208	0.0117130
$952$	−23.4034	−0.758509
$953$	11.8888	0.385115	0.192557	−	0.981286i	$-0.438322\pi$
$953$	11.8888	0.385115	0.192557	+	0.981286i	$0.438322\pi$
$954$	8.71379	0.282119
$955$	−25.9060	−0.838299
$956$	−8.31767	−0.269013
$957$	2.98792	0.0965857
$958$	11.5254	0.372369
$959$	0.987918	0.0319015
$960$	3.60388	0.116315
$961$	−30.5508	−0.985508
$962$	26.3284	0.848862
$963$	−0.792249	−0.0255299
$964$	−5.56033	−0.179086
$965$	61.1353	1.96801
$966$	−15.2078	−0.489301
$967$	9.04221	0.290778	0.145389	−	0.989375i	$-0.453557\pi$
$967$	9.04221	0.290778	0.145389	+	0.989375i	$0.453557\pi$
$968$	−1.00000	−0.0321412
$969$	5.20775	0.167297
$970$	−3.64742	−0.117111
$971$	−46.2586	−1.48451	−0.742254	−	0.670118i	$-0.766243\pi$
$971$	−46.2586	−1.48451	−0.742254	+	0.670118i	$0.766243\pi$
$972$	−1.00000	−0.0320750
$973$	−19.9517	−0.639621
$974$	−14.4892	−0.464263
$975$	43.0073	1.37734
$976$	−13.7017	−0.438581
$977$	53.7077	1.71826	0.859130	−	0.511757i	$-0.171005\pi$
$977$	53.7077	1.71826	0.859130	+	0.511757i	$0.171005\pi$
$978$	10.7681	0.344325
$979$	1.01208	0.0323463
$980$	−47.5555	−1.51911
$981$	10.3720	0.331151
$982$	−13.5147	−0.431270
$983$	0.406878	0.0129774	0.00648870	−	0.999979i	$-0.497935\pi$
$983$	0.406878	0.0129774	0.00648870	+	0.999979i	$0.497935\pi$
$984$	1.20775	0.0385017
$985$	36.3043	1.15675
$986$	−15.5603	−0.495542
$987$	49.5749	1.57799
$988$	5.38404	0.171289
$989$	−43.9517	−1.39758
$990$	−3.60388	−0.114539
$991$	−51.0374	−1.62126	−0.810629	−	0.585561i	$-0.800874\pi$
$991$	−51.0374	−1.62126	−0.810629	+	0.585561i	$0.800874\pi$
$992$	0.670251	0.0212805
$993$	3.36467	0.106774
$994$	46.1715	1.46447
$995$	11.5603	0.366487
$996$	−14.4155	−0.456773
$997$	−40.9095	−1.29562	−0.647808	−	0.761804i	$-0.724314\pi$
$997$	−40.9095	−1.29562	−0.647808	+	0.761804i	$0.724314\pi$
$998$	−20.6353	−0.653200
$999$	−4.89008	−0.154715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1254.2.a.p.1.1	✓	3
3.2	odd	2		3762.2.a.bf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1254.2.a.p.1.1	✓	3	1.1	even	1	trivial
3762.2.a.bf.1.3		3	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1254.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.60388 q^{5} +1.00000 q^{6} +4.49396 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.60388 q^{10} -1.00000 q^{11} -1.00000 q^{12} -5.38404 q^{13} -4.49396 q^{14} +3.60388 q^{15} +1.00000 q^{16} +5.20775 q^{17} -1.00000 q^{18} -1.00000 q^{19} -3.60388 q^{20} -4.49396 q^{21} +1.00000 q^{22} -3.38404 q^{23} +1.00000 q^{24} +7.98792 q^{25} +5.38404 q^{26} -1.00000 q^{27} +4.49396 q^{28} +2.98792 q^{29} -3.60388 q^{30} -0.670251 q^{31} -1.00000 q^{32} +1.00000 q^{33} -5.20775 q^{34} -16.1957 q^{35} +1.00000 q^{36} +4.89008 q^{37} +1.00000 q^{38} +5.38404 q^{39} +3.60388 q^{40} +1.20775 q^{41} +4.49396 q^{42} +12.9879 q^{43} -1.00000 q^{44} -3.60388 q^{45} +3.38404 q^{46} -11.0315 q^{47} -1.00000 q^{48} +13.1957 q^{49} -7.98792 q^{50} -5.20775 q^{51} -5.38404 q^{52} -8.71379 q^{53} +1.00000 q^{54} +3.60388 q^{55} -4.49396 q^{56} +1.00000 q^{57} -2.98792 q^{58} -8.98792 q^{59} +3.60388 q^{60} -13.7017 q^{61} +0.670251 q^{62} +4.49396 q^{63} +1.00000 q^{64} +19.4034 q^{65} -1.00000 q^{66} -14.4155 q^{67} +5.20775 q^{68} +3.38404 q^{69} +16.1957 q^{70} -10.2741 q^{71} -1.00000 q^{72} -14.1957 q^{73} -4.89008 q^{74} -7.98792 q^{75} -1.00000 q^{76} -4.49396 q^{77} -5.38404 q^{78} -5.60388 q^{79} -3.60388 q^{80} +1.00000 q^{81} -1.20775 q^{82} +14.4155 q^{83} -4.49396 q^{84} -18.7681 q^{85} -12.9879 q^{86} -2.98792 q^{87} +1.00000 q^{88} -1.01208 q^{89} +3.60388 q^{90} -24.1957 q^{91} -3.38404 q^{92} +0.670251 q^{93} +11.0315 q^{94} +3.60388 q^{95} +1.00000 q^{96} -1.01208 q^{97} -13.1957 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 2 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} - 3 q^{12} - 6 q^{13} - 4 q^{14} + 2 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} - 3 q^{19} - 2 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 2 * q^5 + 3 * q^6 + 4 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 - 3 * q^12 - 6 * q^13 - 4 * q^14 + 2 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 - 3 * q^19 - 2 * q^20 - 4 * q^21 + 3 * q^22 + 3 * q^24 + 5 * q^25 + 6 * q^26 - 3 * q^27 + 4 * q^28 - 10 * q^29 - 2 * q^30 - 3 * q^32 + 3 * q^33 + 2 * q^34 - 12 * q^35 + 3 * q^36 + 14 * q^37 + 3 * q^38 + 6 * q^39 + 2 * q^40 - 14 * q^41 + 4 * q^42 + 20 * q^43 - 3 * q^44 - 2 * q^45 - 8 * q^47 - 3 * q^48 + 3 * q^49 - 5 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 3 * q^54 + 2 * q^55 - 4 * q^56 + 3 * q^57 + 10 * q^58 - 8 * q^59 + 2 * q^60 - 14 * q^61 + 4 * q^63 + 3 * q^64 + 4 * q^65 - 3 * q^66 - 8 * q^67 - 2 * q^68 + 12 * q^70 - 20 * q^71 - 3 * q^72 - 6 * q^73 - 14 * q^74 - 5 * q^75 - 3 * q^76 - 4 * q^77 - 6 * q^78 - 8 * q^79 - 2 * q^80 + 3 * q^81 + 14 * q^82 + 8 * q^83 - 4 * q^84 - 36 * q^85 - 20 * q^86 + 10 * q^87 + 3 * q^88 - 22 * q^89 + 2 * q^90 - 36 * q^91 + 8 * q^94 + 2 * q^95 + 3 * q^96 - 22 * q^97 - 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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