LMFDB - Embedded newform 7098.2.a.cb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.356896 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.356896 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.356896 q^{10} -3.40581 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.356896 q^{15} +1.00000 q^{16} -2.66487 q^{17} -1.00000 q^{18} -8.63102 q^{19} +0.356896 q^{20} -1.00000 q^{21} +3.40581 q^{22} +8.29590 q^{23} +1.00000 q^{24} -4.87263 q^{25} -1.00000 q^{27} +1.00000 q^{28} +2.21983 q^{29} +0.356896 q^{30} +3.89977 q^{31} -1.00000 q^{32} +3.40581 q^{33} +2.66487 q^{34} +0.356896 q^{35} +1.00000 q^{36} +11.5308 q^{37} +8.63102 q^{38} -0.356896 q^{40} +6.66487 q^{41} +1.00000 q^{42} +5.82371 q^{43} -3.40581 q^{44} +0.356896 q^{45} -8.29590 q^{46} -4.59179 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.87263 q^{50} +2.66487 q^{51} +13.0858 q^{53} +1.00000 q^{54} -1.21552 q^{55} -1.00000 q^{56} +8.63102 q^{57} -2.21983 q^{58} -13.6039 q^{59} -0.356896 q^{60} -13.5254 q^{61} -3.89977 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.40581 q^{66} -3.78017 q^{67} -2.66487 q^{68} -8.29590 q^{69} -0.356896 q^{70} +14.1032 q^{71} -1.00000 q^{72} -1.72587 q^{73} -11.5308 q^{74} +4.87263 q^{75} -8.63102 q^{76} -3.40581 q^{77} +4.49396 q^{79} +0.356896 q^{80} +1.00000 q^{81} -6.66487 q^{82} -10.4940 q^{83} -1.00000 q^{84} -0.951083 q^{85} -5.82371 q^{86} -2.21983 q^{87} +3.40581 q^{88} +13.4330 q^{89} -0.356896 q^{90} +8.29590 q^{92} -3.89977 q^{93} +4.59179 q^{94} -3.08038 q^{95} +1.00000 q^{96} -9.28621 q^{97} -1.00000 q^{98} -3.40581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{15} + 3 q^{16} - 9 q^{17} - 3 q^{18} - 11 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 11 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{27} + 3 q^{28} + 8 q^{29} - 3 q^{30} - 11 q^{31} - 3 q^{32} - 3 q^{33} + 9 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 11 q^{38} + 3 q^{40} + 21 q^{41} + 3 q^{42} + 10 q^{43} + 3 q^{44} - 3 q^{45} - 11 q^{46} + 14 q^{47} - 3 q^{48} + 3 q^{49} - 2 q^{50} + 9 q^{51} + 2 q^{53} + 3 q^{54} - 24 q^{55} - 3 q^{56} + 11 q^{57} - 8 q^{58} - 32 q^{59} + 3 q^{60} - 6 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} + 3 q^{66} - 10 q^{67} - 9 q^{68} - 11 q^{69} + 3 q^{70} + 21 q^{71} - 3 q^{72} - 16 q^{73} + 3 q^{74} - 2 q^{75} - 11 q^{76} + 3 q^{77} + 4 q^{79} - 3 q^{80} + 3 q^{81} - 21 q^{82} - 22 q^{83} - 3 q^{84} - 12 q^{85} - 10 q^{86} - 8 q^{87} - 3 q^{88} + 21 q^{89} + 3 q^{90} + 11 q^{92} + 11 q^{93} - 14 q^{94} + 25 q^{95} + 3 q^{96} - 36 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 + 3 * q^15 + 3 * q^16 - 9 * q^17 - 3 * q^18 - 11 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 11 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^27 + 3 * q^28 + 8 * q^29 - 3 * q^30 - 11 * q^31 - 3 * q^32 - 3 * q^33 + 9 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 11 * q^38 + 3 * q^40 + 21 * q^41 + 3 * q^42 + 10 * q^43 + 3 * q^44 - 3 * q^45 - 11 * q^46 + 14 * q^47 - 3 * q^48 + 3 * q^49 - 2 * q^50 + 9 * q^51 + 2 * q^53 + 3 * q^54 - 24 * q^55 - 3 * q^56 + 11 * q^57 - 8 * q^58 - 32 * q^59 + 3 * q^60 - 6 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 + 3 * q^66 - 10 * q^67 - 9 * q^68 - 11 * q^69 + 3 * q^70 + 21 * q^71 - 3 * q^72 - 16 * q^73 + 3 * q^74 - 2 * q^75 - 11 * q^76 + 3 * q^77 + 4 * q^79 - 3 * q^80 + 3 * q^81 - 21 * q^82 - 22 * q^83 - 3 * q^84 - 12 * q^85 - 10 * q^86 - 8 * q^87 - 3 * q^88 + 21 * q^89 + 3 * q^90 + 11 * q^92 + 11 * q^93 - 14 * q^94 + 25 * q^95 + 3 * q^96 - 36 * q^97 - 3 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

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
$5$	0.356896	0.159609	0.0798043	−	0.996811i	$-0.474570\pi$
$5$	0.356896	0.159609	0.0798043	+	0.996811i	$0.474570\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.356896	−0.112860
$11$	−3.40581	−1.02689	−0.513446	−	0.858122i	$-0.671631\pi$
$11$	−3.40581	−1.02689	−0.513446	+	0.858122i	$0.671631\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.356896	−0.0921501
$16$	1.00000	0.250000
$17$	−2.66487	−0.646327	−0.323163	−	0.946343i	$-0.604746\pi$
$17$	−2.66487	−0.646327	−0.323163	+	0.946343i	$0.604746\pi$
$18$	−1.00000	−0.235702
$19$	−8.63102	−1.98009	−0.990046	−	0.140743i	$-0.955051\pi$
$19$	−8.63102	−1.98009	−0.990046	+	0.140743i	$0.955051\pi$
$20$	0.356896	0.0798043
$21$	−1.00000	−0.218218
$22$	3.40581	0.726122
$23$	8.29590	1.72981	0.864907	−	0.501932i	$-0.167377\pi$
$23$	8.29590	1.72981	0.864907	+	0.501932i	$0.167377\pi$
$24$	1.00000	0.204124
$25$	−4.87263	−0.974525
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	2.21983	0.412213	0.206106	−	0.978530i	$-0.433921\pi$
$29$	2.21983	0.412213	0.206106	+	0.978530i	$0.433921\pi$
$30$	0.356896	0.0651600
$31$	3.89977	0.700420	0.350210	−	0.936671i	$-0.386110\pi$
$31$	3.89977	0.700420	0.350210	+	0.936671i	$0.386110\pi$
$32$	−1.00000	−0.176777
$33$	3.40581	0.592876
$34$	2.66487	0.457022
$35$	0.356896	0.0603264
$36$	1.00000	0.166667
$37$	11.5308	1.89565	0.947826	−	0.318790i	$-0.103276\pi$
$37$	11.5308	1.89565	0.947826	+	0.318790i	$0.103276\pi$
$38$	8.63102	1.40014
$39$	0	0
$40$	−0.356896	−0.0564302
$41$	6.66487	1.04088	0.520439	−	0.853899i	$-0.325768\pi$
$41$	6.66487	1.04088	0.520439	+	0.853899i	$0.325768\pi$
$42$	1.00000	0.154303
$43$	5.82371	0.888107	0.444054	−	0.896000i	$-0.353540\pi$
$43$	5.82371	0.888107	0.444054	+	0.896000i	$0.353540\pi$
$44$	−3.40581	−0.513446
$45$	0.356896	0.0532029
$46$	−8.29590	−1.22316
$47$	−4.59179	−0.669782	−0.334891	−	0.942257i	$-0.608699\pi$
$47$	−4.59179	−0.669782	−0.334891	+	0.942257i	$0.608699\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	4.87263	0.689093
$51$	2.66487	0.373157
$52$	0	0
$53$	13.0858	1.79747	0.898733	−	0.438496i	$-0.144489\pi$
$53$	13.0858	1.79747	0.898733	+	0.438496i	$0.144489\pi$
$54$	1.00000	0.136083
$55$	−1.21552	−0.163901
$56$	−1.00000	−0.133631
$57$	8.63102	1.14321
$58$	−2.21983	−0.291478
$59$	−13.6039	−1.77107	−0.885537	−	0.464569i	$-0.846209\pi$
$59$	−13.6039	−1.77107	−0.885537	+	0.464569i	$0.846209\pi$
$60$	−0.356896	−0.0460751
$61$	−13.5254	−1.73175	−0.865876	−	0.500258i	$-0.833238\pi$
$61$	−13.5254	−1.73175	−0.865876	+	0.500258i	$0.833238\pi$
$62$	−3.89977	−0.495272
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.40581	−0.419227
$67$	−3.78017	−0.461821	−0.230910	−	0.972975i	$-0.574170\pi$
$67$	−3.78017	−0.461821	−0.230910	+	0.972975i	$0.574170\pi$
$68$	−2.66487	−0.323163
$69$	−8.29590	−0.998709
$70$	−0.356896	−0.0426572
$71$	14.1032	1.67374	0.836872	−	0.547399i	$-0.184382\pi$
$71$	14.1032	1.67374	0.836872	+	0.547399i	$0.184382\pi$
$72$	−1.00000	−0.117851
$73$	−1.72587	−0.201998	−0.100999	−	0.994887i	$-0.532204\pi$
$73$	−1.72587	−0.201998	−0.100999	+	0.994887i	$0.532204\pi$
$74$	−11.5308	−1.34043
$75$	4.87263	0.562642
$76$	−8.63102	−0.990046
$77$	−3.40581	−0.388128
$78$	0	0
$79$	4.49396	0.505610	0.252805	−	0.967517i	$-0.418647\pi$
$79$	4.49396	0.505610	0.252805	+	0.967517i	$0.418647\pi$
$80$	0.356896	0.0399022
$81$	1.00000	0.111111
$82$	−6.66487	−0.736012
$83$	−10.4940	−1.15186	−0.575931	−	0.817498i	$-0.695360\pi$
$83$	−10.4940	−1.15186	−0.575931	+	0.817498i	$0.695360\pi$
$84$	−1.00000	−0.109109
$85$	−0.951083	−0.103159
$86$	−5.82371	−0.627987
$87$	−2.21983	−0.237991
$88$	3.40581	0.363061
$89$	13.4330	1.42389	0.711945	−	0.702235i	$-0.247814\pi$
$89$	13.4330	1.42389	0.711945	+	0.702235i	$0.247814\pi$
$90$	−0.356896	−0.0376201
$91$	0	0
$92$	8.29590	0.864907
$93$	−3.89977	−0.404388
$94$	4.59179	0.473607
$95$	−3.08038	−0.316040
$96$	1.00000	0.102062
$97$	−9.28621	−0.942872	−0.471436	−	0.881900i	$-0.656264\pi$
$97$	−9.28621	−0.942872	−0.471436	+	0.881900i	$0.656264\pi$
$98$	−1.00000	−0.101015
$99$	−3.40581	−0.342297
$100$	−4.87263	−0.487263
$101$	−6.33273	−0.630130	−0.315065	−	0.949070i	$-0.602026\pi$
$101$	−6.33273	−0.630130	−0.315065	+	0.949070i	$0.602026\pi$
$102$	−2.66487	−0.263862
$103$	−11.9433	−1.17681	−0.588405	−	0.808567i	$-0.700244\pi$
$103$	−11.9433	−1.17681	−0.588405	+	0.808567i	$0.700244\pi$
$104$	0	0
$105$	−0.356896	−0.0348295
$106$	−13.0858	−1.27100
$107$	−0.356896	−0.0345024	−0.0172512	−	0.999851i	$-0.505492\pi$
$107$	−0.356896	−0.0345024	−0.0172512	+	0.999851i	$0.505492\pi$
$108$	−1.00000	−0.0962250
$109$	−18.5429	−1.77609	−0.888043	−	0.459761i	$-0.847935\pi$
$109$	−18.5429	−1.77609	−0.888043	+	0.459761i	$0.847935\pi$
$110$	1.21552	0.115895
$111$	−11.5308	−1.09445
$112$	1.00000	0.0944911
$113$	−0.274127	−0.0257877	−0.0128938	−	0.999917i	$-0.504104\pi$
$113$	−0.274127	−0.0257877	−0.0128938	+	0.999917i	$0.504104\pi$
$114$	−8.63102	−0.808369
$115$	2.96077	0.276093
$116$	2.21983	0.206106
$117$	0	0
$118$	13.6039	1.25234
$119$	−2.66487	−0.244289
$120$	0.356896	0.0325800
$121$	0.599564	0.0545058
$122$	13.5254	1.22453
$123$	−6.66487	−0.600951
$124$	3.89977	0.350210
$125$	−3.52350	−0.315151
$126$	−1.00000	−0.0890871
$127$	5.42758	0.481620	0.240810	−	0.970572i	$-0.422587\pi$
$127$	5.42758	0.481620	0.240810	+	0.970572i	$0.422587\pi$
$128$	−1.00000	−0.0883883
$129$	−5.82371	−0.512749
$130$	0	0
$131$	−5.78017	−0.505016	−0.252508	−	0.967595i	$-0.581255\pi$
$131$	−5.78017	−0.505016	−0.252508	+	0.967595i	$0.581255\pi$
$132$	3.40581	0.296438
$133$	−8.63102	−0.748405
$134$	3.78017	0.326557
$135$	−0.356896	−0.0307167
$136$	2.66487	0.228511
$137$	18.1957	1.55456	0.777280	−	0.629154i	$-0.216599\pi$
$137$	18.1957	1.55456	0.777280	+	0.629154i	$0.216599\pi$
$138$	8.29590	0.706194
$139$	3.21014	0.272281	0.136140	−	0.990690i	$-0.456530\pi$
$139$	3.21014	0.272281	0.136140	+	0.990690i	$0.456530\pi$
$140$	0.356896	0.0301632
$141$	4.59179	0.386699
$142$	−14.1032	−1.18352
$143$	0	0
$144$	1.00000	0.0833333
$145$	0.792249	0.0657927
$146$	1.72587	0.142834
$147$	−1.00000	−0.0824786
$148$	11.5308	0.947826
$149$	−18.4698	−1.51310	−0.756552	−	0.653933i	$-0.773118\pi$
$149$	−18.4698	−1.51310	−0.756552	+	0.653933i	$0.773118\pi$
$150$	−4.87263	−0.397848
$151$	−19.2814	−1.56910	−0.784550	−	0.620066i	$-0.787106\pi$
$151$	−19.2814	−1.56910	−0.784550	+	0.620066i	$0.787106\pi$
$152$	8.63102	0.700068
$153$	−2.66487	−0.215442
$154$	3.40581	0.274448
$155$	1.39181	0.111793
$156$	0	0
$157$	16.7681	1.33824	0.669119	−	0.743155i	$-0.266671\pi$
$157$	16.7681	1.33824	0.669119	+	0.743155i	$0.266671\pi$
$158$	−4.49396	−0.357520
$159$	−13.0858	−1.03777
$160$	−0.356896	−0.0282151
$161$	8.29590	0.653808
$162$	−1.00000	−0.0785674
$163$	−5.15346	−0.403650	−0.201825	−	0.979422i	$-0.564687\pi$
$163$	−5.15346	−0.403650	−0.201825	+	0.979422i	$0.564687\pi$
$164$	6.66487	0.520439
$165$	1.21552	0.0946282
$166$	10.4940	0.814489
$167$	13.3599	1.03382	0.516909	−	0.856040i	$-0.327082\pi$
$167$	13.3599	1.03382	0.516909	+	0.856040i	$0.327082\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	0.951083	0.0729447
$171$	−8.63102	−0.660031
$172$	5.82371	0.444054
$173$	14.8509	1.12909	0.564545	−	0.825402i	$-0.309052\pi$
$173$	14.8509	1.12909	0.564545	+	0.825402i	$0.309052\pi$
$174$	2.21983	0.168285
$175$	−4.87263	−0.368336
$176$	−3.40581	−0.256723
$177$	13.6039	1.02253
$178$	−13.4330	−1.00684
$179$	2.21983	0.165918	0.0829590	−	0.996553i	$-0.473563\pi$
$179$	2.21983	0.165918	0.0829590	+	0.996553i	$0.473563\pi$
$180$	0.356896	0.0266014
$181$	17.2271	1.28048	0.640241	−	0.768174i	$-0.278834\pi$
$181$	17.2271	1.28048	0.640241	+	0.768174i	$0.278834\pi$
$182$	0	0
$183$	13.5254	0.999828
$184$	−8.29590	−0.611582
$185$	4.11529	0.302562
$186$	3.89977	0.285945
$187$	9.07606	0.663708
$188$	−4.59179	−0.334891
$189$	−1.00000	−0.0727393
$190$	3.08038	0.223474
$191$	6.58748	0.476653	0.238327	−	0.971185i	$-0.423401\pi$
$191$	6.58748	0.476653	0.238327	+	0.971185i	$0.423401\pi$
$192$	−1.00000	−0.0721688
$193$	−22.4373	−1.61507	−0.807535	−	0.589820i	$-0.799199\pi$
$193$	−22.4373	−1.61507	−0.807535	+	0.589820i	$0.799199\pi$
$194$	9.28621	0.666711
$195$	0	0
$196$	1.00000	0.0714286
$197$	−22.8659	−1.62913	−0.814565	−	0.580073i	$-0.803024\pi$
$197$	−22.8659	−1.62913	−0.814565	+	0.580073i	$0.803024\pi$
$198$	3.40581	0.242041
$199$	−11.2373	−0.796590	−0.398295	−	0.917257i	$-0.630398\pi$
$199$	−11.2373	−0.796590	−0.398295	+	0.917257i	$0.630398\pi$
$200$	4.87263	0.344547
$201$	3.78017	0.266632
$202$	6.33273	0.445570
$203$	2.21983	0.155802
$204$	2.66487	0.186579
$205$	2.37867	0.166133
$206$	11.9433	0.832130
$207$	8.29590	0.576605
$208$	0	0
$209$	29.3957	2.03334
$210$	0.356896	0.0246282
$211$	−0.219833	−0.0151339	−0.00756695	−	0.999971i	$-0.502409\pi$
$211$	−0.219833	−0.0151339	−0.00756695	+	0.999971i	$0.502409\pi$
$212$	13.0858	0.898733
$213$	−14.1032	−0.966336
$214$	0.356896	0.0243969
$215$	2.07846	0.141750
$216$	1.00000	0.0680414
$217$	3.89977	0.264734
$218$	18.5429	1.25588
$219$	1.72587	0.116624
$220$	−1.21552	−0.0819504
$221$	0	0
$222$	11.5308	0.773896
$223$	−19.8562	−1.32967	−0.664836	−	0.746990i	$-0.731499\pi$
$223$	−19.8562	−1.32967	−0.664836	+	0.746990i	$0.731499\pi$
$224$	−1.00000	−0.0668153
$225$	−4.87263	−0.324842
$226$	0.274127	0.0182346
$227$	−0.537500	−0.0356751	−0.0178376	−	0.999841i	$-0.505678\pi$
$227$	−0.537500	−0.0356751	−0.0178376	+	0.999841i	$0.505678\pi$
$228$	8.63102	0.571603
$229$	−16.2741	−1.07542	−0.537712	−	0.843128i	$-0.680711\pi$
$229$	−16.2741	−1.07542	−0.537712	+	0.843128i	$0.680711\pi$
$230$	−2.96077	−0.195227
$231$	3.40581	0.224086
$232$	−2.21983	−0.145739
$233$	5.43834	0.356277	0.178139	−	0.984005i	$-0.442992\pi$
$233$	5.43834	0.356277	0.178139	+	0.984005i	$0.442992\pi$
$234$	0	0
$235$	−1.63879	−0.106903
$236$	−13.6039	−0.885537
$237$	−4.49396	−0.291914
$238$	2.66487	0.172738
$239$	−24.1323	−1.56099	−0.780494	−	0.625164i	$-0.785032\pi$
$239$	−24.1323	−1.56099	−0.780494	+	0.625164i	$0.785032\pi$
$240$	−0.356896	−0.0230375
$241$	16.9095	1.08923	0.544617	−	0.838685i	$-0.316675\pi$
$241$	16.9095	1.08923	0.544617	+	0.838685i	$0.316675\pi$
$242$	−0.599564	−0.0385414
$243$	−1.00000	−0.0641500
$244$	−13.5254	−0.865876
$245$	0.356896	0.0228012
$246$	6.66487	0.424937
$247$	0	0
$248$	−3.89977	−0.247636
$249$	10.4940	0.665028
$250$	3.52350	0.222846
$251$	−5.62804	−0.355239	−0.177619	−	0.984099i	$-0.556840\pi$
$251$	−5.62804	−0.355239	−0.177619	+	0.984099i	$0.556840\pi$
$252$	1.00000	0.0629941
$253$	−28.2543	−1.77633
$254$	−5.42758	−0.340557
$255$	0.951083	0.0595591
$256$	1.00000	0.0625000
$257$	−5.56033	−0.346844	−0.173422	−	0.984848i	$-0.555482\pi$
$257$	−5.56033	−0.346844	−0.173422	+	0.984848i	$0.555482\pi$
$258$	5.82371	0.362568
$259$	11.5308	0.716489
$260$	0	0
$261$	2.21983	0.137404
$262$	5.78017	0.357100
$263$	−3.50365	−0.216044	−0.108022	−	0.994148i	$-0.534452\pi$
$263$	−3.50365	−0.216044	−0.108022	+	0.994148i	$0.534452\pi$
$264$	−3.40581	−0.209613
$265$	4.67025	0.286891
$266$	8.63102	0.529202
$267$	−13.4330	−0.822084
$268$	−3.78017	−0.230910
$269$	−2.54288	−0.155042	−0.0775210	−	0.996991i	$-0.524700\pi$
$269$	−2.54288	−0.155042	−0.0775210	+	0.996991i	$0.524700\pi$
$270$	0.356896	0.0217200
$271$	−2.83148	−0.172000	−0.0860000	−	0.996295i	$-0.527409\pi$
$271$	−2.83148	−0.172000	−0.0860000	+	0.996295i	$0.527409\pi$
$272$	−2.66487	−0.161582
$273$	0	0
$274$	−18.1957	−1.09924
$275$	16.5953	1.00073
$276$	−8.29590	−0.499354
$277$	−12.4655	−0.748978	−0.374489	−	0.927231i	$-0.622182\pi$
$277$	−12.4655	−0.748978	−0.374489	+	0.927231i	$0.622182\pi$
$278$	−3.21014	−0.192532
$279$	3.89977	0.233473
$280$	−0.356896	−0.0213286
$281$	0.493959	0.0294671	0.0147336	−	0.999891i	$-0.495310\pi$
$281$	0.493959	0.0294671	0.0147336	+	0.999891i	$0.495310\pi$
$282$	−4.59179	−0.273437
$283$	−15.4058	−0.915781	−0.457890	−	0.889009i	$-0.651395\pi$
$283$	−15.4058	−0.915781	−0.457890	+	0.889009i	$0.651395\pi$
$284$	14.1032	0.836872
$285$	3.08038	0.182466
$286$	0	0
$287$	6.66487	0.393415
$288$	−1.00000	−0.0589256
$289$	−9.89844	−0.582261
$290$	−0.792249	−0.0465225
$291$	9.28621	0.544367
$292$	−1.72587	−0.100999
$293$	−22.4450	−1.31125	−0.655627	−	0.755085i	$-0.727595\pi$
$293$	−22.4450	−1.31125	−0.655627	+	0.755085i	$0.727595\pi$
$294$	1.00000	0.0583212
$295$	−4.85517	−0.282679
$296$	−11.5308	−0.670214
$297$	3.40581	0.197625
$298$	18.4698	1.06993
$299$	0	0
$300$	4.87263	0.281321
$301$	5.82371	0.335673
$302$	19.2814	1.10952
$303$	6.33273	0.363806
$304$	−8.63102	−0.495023
$305$	−4.82717	−0.276403
$306$	2.66487	0.152341
$307$	25.7265	1.46829	0.734143	−	0.678994i	$-0.237584\pi$
$307$	25.7265	1.46829	0.734143	+	0.678994i	$0.237584\pi$
$308$	−3.40581	−0.194064
$309$	11.9433	0.679431
$310$	−1.39181	−0.0790496
$311$	9.70171	0.550134	0.275067	−	0.961425i	$-0.411300\pi$
$311$	9.70171	0.550134	0.275067	+	0.961425i	$0.411300\pi$
$312$	0	0
$313$	−8.74392	−0.494236	−0.247118	−	0.968985i	$-0.579483\pi$
$313$	−8.74392	−0.494236	−0.247118	+	0.968985i	$0.579483\pi$
$314$	−16.7681	−0.946278
$315$	0.356896	0.0201088
$316$	4.49396	0.252805
$317$	1.10992	0.0623391	0.0311696	−	0.999514i	$-0.490077\pi$
$317$	1.10992	0.0623391	0.0311696	+	0.999514i	$0.490077\pi$
$318$	13.0858	0.733813
$319$	−7.56033	−0.423297
$320$	0.356896	0.0199511
$321$	0.356896	0.0199200
$322$	−8.29590	−0.462312
$323$	23.0006	1.27979
$324$	1.00000	0.0555556
$325$	0	0
$326$	5.15346	0.285424
$327$	18.5429	1.02542
$328$	−6.66487	−0.368006
$329$	−4.59179	−0.253154
$330$	−1.21552	−0.0669122
$331$	−17.0073	−0.934806	−0.467403	−	0.884044i	$-0.654810\pi$
$331$	−17.0073	−0.934806	−0.467403	+	0.884044i	$0.654810\pi$
$332$	−10.4940	−0.575931
$333$	11.5308	0.631884
$334$	−13.3599	−0.731020
$335$	−1.34913	−0.0737106
$336$	−1.00000	−0.0545545
$337$	−8.72886	−0.475491	−0.237746	−	0.971327i	$-0.576408\pi$
$337$	−8.72886	−0.475491	−0.237746	+	0.971327i	$0.576408\pi$
$338$	0	0
$339$	0.274127	0.0148885
$340$	−0.951083	−0.0515797
$341$	−13.2819	−0.719255
$342$	8.63102	0.466712
$343$	1.00000	0.0539949
$344$	−5.82371	−0.313993
$345$	−2.96077	−0.159403
$346$	−14.8509	−0.798387
$347$	−11.7560	−0.631095	−0.315548	−	0.948910i	$-0.602188\pi$
$347$	−11.7560	−0.631095	−0.315548	+	0.948910i	$0.602188\pi$
$348$	−2.21983	−0.118996
$349$	23.9758	1.28340	0.641699	−	0.766957i	$-0.278230\pi$
$349$	23.9758	1.28340	0.641699	+	0.766957i	$0.278230\pi$
$350$	4.87263	0.260453
$351$	0	0
$352$	3.40581	0.181530
$353$	−17.8019	−0.947502	−0.473751	−	0.880659i	$-0.657100\pi$
$353$	−17.8019	−0.947502	−0.473751	+	0.880659i	$0.657100\pi$
$354$	−13.6039	−0.723038
$355$	5.03338	0.267144
$356$	13.4330	0.711945
$357$	2.66487	0.141040
$358$	−2.21983	−0.117322
$359$	4.93123	0.260260	0.130130	−	0.991497i	$-0.458460\pi$
$359$	4.93123	0.260260	0.130130	+	0.991497i	$0.458460\pi$
$360$	−0.356896	−0.0188101
$361$	55.4946	2.92077
$362$	−17.2271	−0.905438
$363$	−0.599564	−0.0314689
$364$	0	0
$365$	−0.615957	−0.0322407
$366$	−13.5254	−0.706985
$367$	−26.0694	−1.36081	−0.680405	−	0.732837i	$-0.738196\pi$
$367$	−26.0694	−1.36081	−0.680405	+	0.732837i	$0.738196\pi$
$368$	8.29590	0.432454
$369$	6.66487	0.346960
$370$	−4.11529	−0.213944
$371$	13.0858	0.679378
$372$	−3.89977	−0.202194
$373$	−17.7506	−0.919093	−0.459546	−	0.888154i	$-0.651988\pi$
$373$	−17.7506	−0.919093	−0.459546	+	0.888154i	$0.651988\pi$
$374$	−9.07606	−0.469312
$375$	3.52350	0.181953
$376$	4.59179	0.236804
$377$	0	0
$378$	1.00000	0.0514344
$379$	4.85517	0.249393	0.124697	−	0.992195i	$-0.460204\pi$
$379$	4.85517	0.249393	0.124697	+	0.992195i	$0.460204\pi$
$380$	−3.08038	−0.158020
$381$	−5.42758	−0.278064
$382$	−6.58748	−0.337045
$383$	−9.20775	−0.470494	−0.235247	−	0.971936i	$-0.575590\pi$
$383$	−9.20775	−0.470494	−0.235247	+	0.971936i	$0.575590\pi$
$384$	1.00000	0.0510310
$385$	−1.21552	−0.0619487
$386$	22.4373	1.14203
$387$	5.82371	0.296036
$388$	−9.28621	−0.471436
$389$	11.7802	0.597278	0.298639	−	0.954366i	$-0.403467\pi$
$389$	11.7802	0.597278	0.298639	+	0.954366i	$0.403467\pi$
$390$	0	0
$391$	−22.1075	−1.11803
$392$	−1.00000	−0.0505076
$393$	5.78017	0.291571
$394$	22.8659	1.15197
$395$	1.60388	0.0806997
$396$	−3.40581	−0.171149
$397$	−5.12929	−0.257432	−0.128716	−	0.991682i	$-0.541086\pi$
$397$	−5.12929	−0.257432	−0.128716	+	0.991682i	$0.541086\pi$
$398$	11.2373	0.563274
$399$	8.63102	0.432092
$400$	−4.87263	−0.243631
$401$	26.8611	1.34138	0.670691	−	0.741737i	$-0.265998\pi$
$401$	26.8611	1.34138	0.670691	+	0.741737i	$0.265998\pi$
$402$	−3.78017	−0.188538
$403$	0	0
$404$	−6.33273	−0.315065
$405$	0.356896	0.0177343
$406$	−2.21983	−0.110168
$407$	−39.2717	−1.94663
$408$	−2.66487	−0.131931
$409$	−27.2513	−1.34749	−0.673745	−	0.738964i	$-0.735315\pi$
$409$	−27.2513	−1.34749	−0.673745	+	0.738964i	$0.735315\pi$
$410$	−2.37867	−0.117474
$411$	−18.1957	−0.897526
$412$	−11.9433	−0.588405
$413$	−13.6039	−0.669403
$414$	−8.29590	−0.407721
$415$	−3.74525	−0.183847
$416$	0	0
$417$	−3.21014	−0.157201
$418$	−29.3957	−1.43779
$419$	−28.8418	−1.40901	−0.704506	−	0.709698i	$-0.748831\pi$
$419$	−28.8418	−1.40901	−0.704506	+	0.709698i	$0.748831\pi$
$420$	−0.356896	−0.0174147
$421$	−15.2121	−0.741391	−0.370695	−	0.928755i	$-0.620881\pi$
$421$	−15.2121	−0.741391	−0.370695	+	0.928755i	$0.620881\pi$
$422$	0.219833	0.0107013
$423$	−4.59179	−0.223261
$424$	−13.0858	−0.635500
$425$	12.9849	0.629862
$426$	14.1032	0.683303
$427$	−13.5254	−0.654541
$428$	−0.356896	−0.0172512
$429$	0	0
$430$	−2.07846	−0.100232
$431$	−4.45473	−0.214577	−0.107288	−	0.994228i	$-0.534217\pi$
$431$	−4.45473	−0.214577	−0.107288	+	0.994228i	$0.534217\pi$
$432$	−1.00000	−0.0481125
$433$	36.6655	1.76203	0.881015	−	0.473089i	$-0.156861\pi$
$433$	36.6655	1.76203	0.881015	+	0.473089i	$0.156861\pi$
$434$	−3.89977	−0.187195
$435$	−0.792249	−0.0379854
$436$	−18.5429	−0.888043
$437$	−71.6021	−3.42519
$438$	−1.72587	−0.0824654
$439$	7.41849	0.354065	0.177033	−	0.984205i	$-0.443350\pi$
$439$	7.41849	0.354065	0.177033	+	0.984205i	$0.443350\pi$
$440$	1.21552	0.0579477
$441$	1.00000	0.0476190
$442$	0	0
$443$	34.2747	1.62844	0.814220	−	0.580556i	$-0.197165\pi$
$443$	34.2747	1.62844	0.814220	+	0.580556i	$0.197165\pi$
$444$	−11.5308	−0.547227
$445$	4.79417	0.227265
$446$	19.8562	0.940220
$447$	18.4698	0.873591
$448$	1.00000	0.0472456
$449$	9.70171	0.457852	0.228926	−	0.973444i	$-0.426479\pi$
$449$	9.70171	0.457852	0.228926	+	0.973444i	$0.426479\pi$
$450$	4.87263	0.229698
$451$	−22.6993	−1.06887
$452$	−0.274127	−0.0128938
$453$	19.2814	0.905920
$454$	0.537500	0.0252261
$455$	0	0
$456$	−8.63102	−0.404185
$457$	7.58402	0.354766	0.177383	−	0.984142i	$-0.443237\pi$
$457$	7.58402	0.354766	0.177383	+	0.984142i	$0.443237\pi$
$458$	16.2741	0.760440
$459$	2.66487	0.124386
$460$	2.96077	0.138047
$461$	4.51573	0.210318	0.105159	−	0.994455i	$-0.466465\pi$
$461$	4.51573	0.210318	0.105159	+	0.994455i	$0.466465\pi$
$462$	−3.40581	−0.158453
$463$	−13.0556	−0.606746	−0.303373	−	0.952872i	$-0.598113\pi$
$463$	−13.0556	−0.606746	−0.303373	+	0.952872i	$0.598113\pi$
$464$	2.21983	0.103053
$465$	−1.39181	−0.0645438
$466$	−5.43834	−0.251926
$467$	23.9711	1.10925	0.554624	−	0.832101i	$-0.312862\pi$
$467$	23.9711	1.10925	0.554624	+	0.832101i	$0.312862\pi$
$468$	0	0
$469$	−3.78017	−0.174552
$470$	1.63879	0.0755919
$471$	−16.7681	−0.772633
$472$	13.6039	0.626169
$473$	−19.8345	−0.911990
$474$	4.49396	0.206414
$475$	42.0557	1.92965
$476$	−2.66487	−0.122144
$477$	13.0858	0.599155
$478$	24.1323	1.10378
$479$	2.84654	0.130062	0.0650309	−	0.997883i	$-0.479285\pi$
$479$	2.84654	0.130062	0.0650309	+	0.997883i	$0.479285\pi$
$480$	0.356896	0.0162900
$481$	0	0
$482$	−16.9095	−0.770205
$483$	−8.29590	−0.377476
$484$	0.599564	0.0272529
$485$	−3.31421	−0.150490
$486$	1.00000	0.0453609
$487$	−13.7694	−0.623952	−0.311976	−	0.950090i	$-0.600991\pi$
$487$	−13.7694	−0.623952	−0.311976	+	0.950090i	$0.600991\pi$
$488$	13.5254	0.612267
$489$	5.15346	0.233047
$490$	−0.356896	−0.0161229
$491$	−38.2825	−1.72766	−0.863832	−	0.503780i	$-0.831942\pi$
$491$	−38.2825	−1.72766	−0.863832	+	0.503780i	$0.831942\pi$
$492$	−6.66487	−0.300476
$493$	−5.91557	−0.266424
$494$	0	0
$495$	−1.21552	−0.0546336
$496$	3.89977	0.175105
$497$	14.1032	0.632615
$498$	−10.4940	−0.470246
$499$	−32.2828	−1.44517	−0.722587	−	0.691280i	$-0.757047\pi$
$499$	−32.2828	−1.44517	−0.722587	+	0.691280i	$0.757047\pi$
$500$	−3.52350	−0.157576
$501$	−13.3599	−0.596875
$502$	5.62804	0.251192
$503$	−3.47112	−0.154770	−0.0773849	−	0.997001i	$-0.524657\pi$
$503$	−3.47112	−0.154770	−0.0773849	+	0.997001i	$0.524657\pi$
$504$	−1.00000	−0.0445435
$505$	−2.26013	−0.100574
$506$	28.2543	1.25606
$507$	0	0
$508$	5.42758	0.240810
$509$	6.25236	0.277131	0.138565	−	0.990353i	$-0.455751\pi$
$509$	6.25236	0.277131	0.138565	+	0.990353i	$0.455751\pi$
$510$	−0.951083	−0.0421146
$511$	−1.72587	−0.0763481
$512$	−1.00000	−0.0441942
$513$	8.63102	0.381069
$514$	5.56033	0.245256
$515$	−4.26252	−0.187829
$516$	−5.82371	−0.256374
$517$	15.6388	0.687793
$518$	−11.5308	−0.506634
$519$	−14.8509	−0.651880
$520$	0	0
$521$	−28.2174	−1.23623	−0.618114	−	0.786088i	$-0.712103\pi$
$521$	−28.2174	−1.23623	−0.618114	+	0.786088i	$0.712103\pi$
$522$	−2.21983	−0.0971594
$523$	−4.27844	−0.187083	−0.0935415	−	0.995615i	$-0.529819\pi$
$523$	−4.27844	−0.187083	−0.0935415	+	0.995615i	$0.529819\pi$
$524$	−5.78017	−0.252508
$525$	4.87263	0.212659
$526$	3.50365	0.152766
$527$	−10.3924	−0.452700
$528$	3.40581	0.148219
$529$	45.8219	1.99226
$530$	−4.67025	−0.202863
$531$	−13.6039	−0.590358
$532$	−8.63102	−0.374202
$533$	0	0
$534$	13.4330	0.581301
$535$	−0.127375	−0.00550689
$536$	3.78017	0.163278
$537$	−2.21983	−0.0957928
$538$	2.54288	0.109631
$539$	−3.40581	−0.146699
$540$	−0.356896	−0.0153584
$541$	10.3026	0.442943	0.221472	−	0.975167i	$-0.428914\pi$
$541$	10.3026	0.442943	0.221472	+	0.975167i	$0.428914\pi$
$542$	2.83148	0.121622
$543$	−17.2271	−0.739287
$544$	2.66487	0.114256
$545$	−6.61788	−0.283479
$546$	0	0
$547$	29.4276	1.25823	0.629116	−	0.777311i	$-0.283417\pi$
$547$	29.4276	1.25823	0.629116	+	0.777311i	$0.283417\pi$
$548$	18.1957	0.777280
$549$	−13.5254	−0.577251
$550$	−16.5953	−0.707624
$551$	−19.1594	−0.816219
$552$	8.29590	0.353097
$553$	4.49396	0.191103
$554$	12.4655	0.529608
$555$	−4.11529	−0.174684
$556$	3.21014	0.136140
$557$	11.7802	0.499142	0.249571	−	0.968357i	$-0.419710\pi$
$557$	11.7802	0.499142	0.249571	+	0.968357i	$0.419710\pi$
$558$	−3.89977	−0.165091
$559$	0	0
$560$	0.356896	0.0150816
$561$	−9.07606	−0.383192
$562$	−0.493959	−0.0208364
$563$	−21.3163	−0.898377	−0.449188	−	0.893437i	$-0.648287\pi$
$563$	−21.3163	−0.898377	−0.449188	+	0.893437i	$0.648287\pi$
$564$	4.59179	0.193349
$565$	−0.0978347	−0.00411594
$566$	15.4058	0.647555
$567$	1.00000	0.0419961
$568$	−14.1032	−0.591758
$569$	−39.1159	−1.63982	−0.819912	−	0.572490i	$-0.805977\pi$
$569$	−39.1159	−1.63982	−0.819912	+	0.572490i	$0.805977\pi$
$570$	−3.08038	−0.129023
$571$	−22.0629	−0.923304	−0.461652	−	0.887061i	$-0.652743\pi$
$571$	−22.0629	−0.923304	−0.461652	+	0.887061i	$0.652743\pi$
$572$	0	0
$573$	−6.58748	−0.275196
$574$	−6.66487	−0.278186
$575$	−40.4228	−1.68575
$576$	1.00000	0.0416667
$577$	−23.2078	−0.966151	−0.483076	−	0.875579i	$-0.660480\pi$
$577$	−23.2078	−0.966151	−0.483076	+	0.875579i	$0.660480\pi$
$578$	9.89844	0.411721
$579$	22.4373	0.932461
$580$	0.792249	0.0328964
$581$	−10.4940	−0.435363
$582$	−9.28621	−0.384926
$583$	−44.5676	−1.84580
$584$	1.72587	0.0714171
$585$	0	0
$586$	22.4450	0.927196
$587$	−41.7754	−1.72425	−0.862127	−	0.506692i	$-0.830868\pi$
$587$	−41.7754	−1.72425	−0.862127	+	0.506692i	$0.830868\pi$
$588$	−1.00000	−0.0412393
$589$	−33.6590	−1.38690
$590$	4.85517	0.199884
$591$	22.8659	0.940578
$592$	11.5308	0.473913
$593$	14.4397	0.592966	0.296483	−	0.955038i	$-0.404186\pi$
$593$	14.4397	0.592966	0.296483	+	0.955038i	$0.404186\pi$
$594$	−3.40581	−0.139742
$595$	−0.951083	−0.0389906
$596$	−18.4698	−0.756552
$597$	11.2373	0.459912
$598$	0	0
$599$	−6.85517	−0.280095	−0.140047	−	0.990145i	$-0.544725\pi$
$599$	−6.85517	−0.280095	−0.140047	+	0.990145i	$0.544725\pi$
$600$	−4.87263	−0.198924
$601$	0.914247	0.0372929	0.0186465	−	0.999826i	$-0.494064\pi$
$601$	0.914247	0.0372929	0.0186465	+	0.999826i	$0.494064\pi$
$602$	−5.82371	−0.237357
$603$	−3.78017	−0.153940
$604$	−19.2814	−0.784550
$605$	0.213982	0.00869960
$606$	−6.33273	−0.257250
$607$	−19.5791	−0.794692	−0.397346	−	0.917669i	$-0.630069\pi$
$607$	−19.5791	−0.794692	−0.397346	+	0.917669i	$0.630069\pi$
$608$	8.63102	0.350034
$609$	−2.21983	−0.0899522
$610$	4.82717	0.195446
$611$	0	0
$612$	−2.66487	−0.107721
$613$	−26.3394	−1.06384	−0.531920	−	0.846795i	$-0.678529\pi$
$613$	−26.3394	−1.06384	−0.531920	+	0.846795i	$0.678529\pi$
$614$	−25.7265	−1.03824
$615$	−2.37867	−0.0959171
$616$	3.40581	0.137224
$617$	6.24400	0.251374	0.125687	−	0.992070i	$-0.459887\pi$
$617$	6.24400	0.251374	0.125687	+	0.992070i	$0.459887\pi$
$618$	−11.9433	−0.480431
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	1.39181	0.0558965
$621$	−8.29590	−0.332903
$622$	−9.70171	−0.389003
$623$	13.4330	0.538180
$624$	0	0
$625$	23.1056	0.924224
$626$	8.74392	0.349477
$627$	−29.3957	−1.17395
$628$	16.7681	0.669119
$629$	−30.7281	−1.22521
$630$	−0.356896	−0.0142191
$631$	−20.0629	−0.798692	−0.399346	−	0.916800i	$-0.630763\pi$
$631$	−20.0629	−0.798692	−0.399346	+	0.916800i	$0.630763\pi$
$632$	−4.49396	−0.178760
$633$	0.219833	0.00873756
$634$	−1.10992	−0.0440804
$635$	1.93708	0.0768708
$636$	−13.0858	−0.518884
$637$	0	0
$638$	7.56033	0.299317
$639$	14.1032	0.557914
$640$	−0.356896	−0.0141075
$641$	−13.1535	−0.519530	−0.259765	−	0.965672i	$-0.583645\pi$
$641$	−13.1535	−0.519530	−0.259765	+	0.965672i	$0.583645\pi$
$642$	−0.356896	−0.0140856
$643$	−43.2006	−1.70366	−0.851832	−	0.523815i	$-0.824508\pi$
$643$	−43.2006	−1.70366	−0.851832	+	0.523815i	$0.824508\pi$
$644$	8.29590	0.326904
$645$	−2.07846	−0.0818392
$646$	−23.0006	−0.904946
$647$	7.10513	0.279332	0.139666	−	0.990199i	$-0.455397\pi$
$647$	7.10513	0.279332	0.139666	+	0.990199i	$0.455397\pi$
$648$	−1.00000	−0.0392837
$649$	46.3323	1.81870
$650$	0	0
$651$	−3.89977	−0.152844
$652$	−5.15346	−0.201825
$653$	18.9422	0.741267	0.370634	−	0.928779i	$-0.379141\pi$
$653$	18.9422	0.741267	0.370634	+	0.928779i	$0.379141\pi$
$654$	−18.5429	−0.725084
$655$	−2.06292	−0.0806049
$656$	6.66487	0.260220
$657$	−1.72587	−0.0673327
$658$	4.59179	0.179007
$659$	20.8286	0.811367	0.405684	−	0.914014i	$-0.367033\pi$
$659$	20.8286	0.811367	0.405684	+	0.914014i	$0.367033\pi$
$660$	1.21552	0.0473141
$661$	33.7995	1.31465	0.657325	−	0.753607i	$-0.271688\pi$
$661$	33.7995	1.31465	0.657325	+	0.753607i	$0.271688\pi$
$662$	17.0073	0.661007
$663$	0	0
$664$	10.4940	0.407245
$665$	−3.08038	−0.119452
$666$	−11.5308	−0.446809
$667$	18.4155	0.713051
$668$	13.3599	0.516909
$669$	19.8562	0.767686
$670$	1.34913	0.0521213
$671$	46.0650	1.77832
$672$	1.00000	0.0385758
$673$	18.3521	0.707422	0.353711	−	0.935355i	$-0.384920\pi$
$673$	18.3521	0.707422	0.353711	+	0.935355i	$0.384920\pi$
$674$	8.72886	0.336223
$675$	4.87263	0.187547
$676$	0	0
$677$	−11.0750	−0.425647	−0.212823	−	0.977091i	$-0.568266\pi$
$677$	−11.0750	−0.425647	−0.212823	+	0.977091i	$0.568266\pi$
$678$	−0.274127	−0.0105278
$679$	−9.28621	−0.356372
$680$	0.951083	0.0364724
$681$	0.537500	0.0205970
$682$	13.2819	0.508590
$683$	26.8015	1.02553	0.512765	−	0.858529i	$-0.328621\pi$
$683$	26.8015	1.02553	0.512765	+	0.858529i	$0.328621\pi$
$684$	−8.63102	−0.330015
$685$	6.49396	0.248121
$686$	−1.00000	−0.0381802
$687$	16.2741	0.620897
$688$	5.82371	0.222027
$689$	0	0
$690$	2.96077	0.112715
$691$	21.5338	0.819184	0.409592	−	0.912269i	$-0.365671\pi$
$691$	21.5338	0.819184	0.409592	+	0.912269i	$0.365671\pi$
$692$	14.8509	0.564545
$693$	−3.40581	−0.129376
$694$	11.7560	0.446252
$695$	1.14569	0.0434584
$696$	2.21983	0.0841425
$697$	−17.7611	−0.672748
$698$	−23.9758	−0.907499
$699$	−5.43834	−0.205697
$700$	−4.87263	−0.184168
$701$	−28.9724	−1.09427	−0.547136	−	0.837044i	$-0.684282\pi$
$701$	−28.9724	−1.09427	−0.547136	+	0.837044i	$0.684282\pi$
$702$	0	0
$703$	−99.5226	−3.75356
$704$	−3.40581	−0.128361
$705$	1.63879	0.0617205
$706$	17.8019	0.669985
$707$	−6.33273	−0.238167
$708$	13.6039	0.511265
$709$	−34.6069	−1.29969	−0.649844	−	0.760068i	$-0.725166\pi$
$709$	−34.6069	−1.29969	−0.649844	+	0.760068i	$0.725166\pi$
$710$	−5.03338	−0.188899
$711$	4.49396	0.168537
$712$	−13.4330	−0.503421
$713$	32.3521	1.21160
$714$	−2.66487	−0.0997304
$715$	0	0
$716$	2.21983	0.0829590
$717$	24.1323	0.901236
$718$	−4.93123	−0.184032
$719$	−5.78017	−0.215564	−0.107782	−	0.994175i	$-0.534375\pi$
$719$	−5.78017	−0.215564	−0.107782	+	0.994175i	$0.534375\pi$
$720$	0.356896	0.0133007
$721$	−11.9433	−0.444792
$722$	−55.4946	−2.06529
$723$	−16.9095	−0.628870
$724$	17.2271	0.640241
$725$	−10.8164	−0.401711
$726$	0.599564	0.0222519
$727$	−19.4668	−0.721984	−0.360992	−	0.932569i	$-0.617562\pi$
$727$	−19.4668	−0.721984	−0.360992	+	0.932569i	$0.617562\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.615957	0.0227976
$731$	−15.5195	−0.574008
$732$	13.5254	0.499914
$733$	13.3948	0.494748	0.247374	−	0.968920i	$-0.420432\pi$
$733$	13.3948	0.494748	0.247374	+	0.968920i	$0.420432\pi$
$734$	26.0694	0.962238
$735$	−0.356896	−0.0131643
$736$	−8.29590	−0.305791
$737$	12.8745	0.474240
$738$	−6.66487	−0.245337
$739$	19.2814	0.709279	0.354639	−	0.935003i	$-0.384604\pi$
$739$	19.2814	0.709279	0.354639	+	0.935003i	$0.384604\pi$
$740$	4.11529	0.151281
$741$	0	0
$742$	−13.0858	−0.480393
$743$	−21.9842	−0.806522	−0.403261	−	0.915085i	$-0.632123\pi$
$743$	−21.9842	−0.806522	−0.403261	+	0.915085i	$0.632123\pi$
$744$	3.89977	0.142973
$745$	−6.59179	−0.241505
$746$	17.7506	0.649897
$747$	−10.4940	−0.383954
$748$	9.07606	0.331854
$749$	−0.356896	−0.0130407
$750$	−3.52350	−0.128660
$751$	10.8659	0.396503	0.198252	−	0.980151i	$-0.436474\pi$
$751$	10.8659	0.396503	0.198252	+	0.980151i	$0.436474\pi$
$752$	−4.59179	−0.167445
$753$	5.62804	0.205097
$754$	0	0
$755$	−6.88146	−0.250442
$756$	−1.00000	−0.0363696
$757$	31.0320	1.12788	0.563940	−	0.825816i	$-0.309285\pi$
$757$	31.0320	1.12788	0.563940	+	0.825816i	$0.309285\pi$
$758$	−4.85517	−0.176348
$759$	28.2543	1.02557
$760$	3.08038	0.111737
$761$	25.5211	0.925139	0.462570	−	0.886583i	$-0.346928\pi$
$761$	25.5211	0.925139	0.462570	+	0.886583i	$0.346928\pi$
$762$	5.42758	0.196621
$763$	−18.5429	−0.671297
$764$	6.58748	0.238327
$765$	−0.951083	−0.0343865
$766$	9.20775	0.332690
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	17.8780	0.644697	0.322349	−	0.946621i	$-0.395528\pi$
$769$	17.8780	0.644697	0.322349	+	0.946621i	$0.395528\pi$
$770$	1.21552	0.0438043
$771$	5.56033	0.200251
$772$	−22.4373	−0.807535
$773$	42.5870	1.53175	0.765874	−	0.642991i	$-0.222307\pi$
$773$	42.5870	1.53175	0.765874	+	0.642991i	$0.222307\pi$
$774$	−5.82371	−0.209329
$775$	−19.0021	−0.682577
$776$	9.28621	0.333355
$777$	−11.5308	−0.413665
$778$	−11.7802	−0.422339
$779$	−57.5247	−2.06104
$780$	0	0
$781$	−48.0329	−1.71875
$782$	22.1075	0.790563
$783$	−2.21983	−0.0793303
$784$	1.00000	0.0357143
$785$	5.98446	0.213595
$786$	−5.78017	−0.206172
$787$	−41.4902	−1.47897	−0.739484	−	0.673175i	$-0.764930\pi$
$787$	−41.4902	−1.47897	−0.739484	+	0.673175i	$0.764930\pi$
$788$	−22.8659	−0.814565
$789$	3.50365	0.124733
$790$	−1.60388	−0.0570633
$791$	−0.274127	−0.00974682
$792$	3.40581	0.121020
$793$	0	0
$794$	5.12929	0.182032
$795$	−4.67025	−0.165637
$796$	−11.2373	−0.398295
$797$	16.1661	0.572634	0.286317	−	0.958135i	$-0.407569\pi$
$797$	16.1661	0.572634	0.286317	+	0.958135i	$0.407569\pi$
$798$	−8.63102	−0.305535
$799$	12.2366	0.432898
$800$	4.87263	0.172273
$801$	13.4330	0.474630
$802$	−26.8611	−0.948500
$803$	5.87800	0.207430
$804$	3.78017	0.133316
$805$	2.96077	0.104353
$806$	0	0
$807$	2.54288	0.0895135
$808$	6.33273	0.222785
$809$	−15.0905	−0.530555	−0.265278	−	0.964172i	$-0.585464\pi$
$809$	−15.0905	−0.530555	−0.265278	+	0.964172i	$0.585464\pi$
$810$	−0.356896	−0.0125400
$811$	9.42221	0.330858	0.165429	−	0.986222i	$-0.447099\pi$
$811$	9.42221	0.330858	0.165429	+	0.986222i	$0.447099\pi$
$812$	2.21983	0.0779009
$813$	2.83148	0.0993043
$814$	39.2717	1.37647
$815$	−1.83925	−0.0644260
$816$	2.66487	0.0932893
$817$	−50.2646	−1.75853
$818$	27.2513	0.952819
$819$	0	0
$820$	2.37867	0.0830666
$821$	0.640120	0.0223403	0.0111702	−	0.999938i	$-0.496444\pi$
$821$	0.640120	0.0223403	0.0111702	+	0.999938i	$0.496444\pi$
$822$	18.1957	0.634647
$823$	−32.1715	−1.12143	−0.560714	−	0.828009i	$-0.689473\pi$
$823$	−32.1715	−1.12143	−0.560714	+	0.828009i	$0.689473\pi$
$824$	11.9433	0.416065
$825$	−16.5953	−0.577773
$826$	13.6039	0.473339
$827$	−15.3002	−0.532040	−0.266020	−	0.963967i	$-0.585709\pi$
$827$	−15.3002	−0.532040	−0.266020	+	0.963967i	$0.585709\pi$
$828$	8.29590	0.288302
$829$	17.3491	0.602560	0.301280	−	0.953536i	$-0.402586\pi$
$829$	17.3491	0.602560	0.301280	+	0.953536i	$0.402586\pi$
$830$	3.74525	0.130000
$831$	12.4655	0.432423
$832$	0	0
$833$	−2.66487	−0.0923324
$834$	3.21014	0.111158
$835$	4.76809	0.165006
$836$	29.3957	1.01667
$837$	−3.89977	−0.134796
$838$	28.8418	0.996322
$839$	3.10992	0.107366	0.0536831	−	0.998558i	$-0.482904\pi$
$839$	3.10992	0.107366	0.0536831	+	0.998558i	$0.482904\pi$
$840$	0.356896	0.0123141
$841$	−24.0723	−0.830081
$842$	15.2121	0.524242
$843$	−0.493959	−0.0170129
$844$	−0.219833	−0.00756695
$845$	0	0
$846$	4.59179	0.157869
$847$	0.599564	0.0206012
$848$	13.0858	0.449367
$849$	15.4058	0.528726
$850$	−12.9849	−0.445380
$851$	95.6583	3.27912
$852$	−14.1032	−0.483168
$853$	−42.3961	−1.45162	−0.725808	−	0.687898i	$-0.758534\pi$
$853$	−42.3961	−1.45162	−0.725808	+	0.687898i	$0.758534\pi$
$854$	13.5254	0.462830
$855$	−3.08038	−0.105347
$856$	0.356896	0.0121984
$857$	−10.3918	−0.354978	−0.177489	−	0.984123i	$-0.556797\pi$
$857$	−10.3918	−0.354978	−0.177489	+	0.984123i	$0.556797\pi$
$858$	0	0
$859$	−47.4862	−1.62021	−0.810104	−	0.586286i	$-0.800589\pi$
$859$	−47.4862	−1.62021	−0.810104	+	0.586286i	$0.800589\pi$
$860$	2.07846	0.0708748
$861$	−6.66487	−0.227138
$862$	4.45473	0.151729
$863$	22.8364	0.777359	0.388680	−	0.921373i	$-0.372931\pi$
$863$	22.8364	0.777359	0.388680	+	0.921373i	$0.372931\pi$
$864$	1.00000	0.0340207
$865$	5.30021	0.180213
$866$	−36.6655	−1.24594
$867$	9.89844	0.336169
$868$	3.89977	0.132367
$869$	−15.3056	−0.519206
$870$	0.792249	0.0268598
$871$	0	0
$872$	18.5429	0.627941
$873$	−9.28621	−0.314291
$874$	71.6021	2.42198
$875$	−3.52350	−0.119116
$876$	1.72587	0.0583119
$877$	−52.8122	−1.78334	−0.891671	−	0.452684i	$-0.850467\pi$
$877$	−52.8122	−1.78334	−0.891671	+	0.452684i	$0.850467\pi$
$878$	−7.41849	−0.250362
$879$	22.4450	0.757052
$880$	−1.21552	−0.0409752
$881$	−14.1564	−0.476943	−0.238471	−	0.971150i	$-0.576646\pi$
$881$	−14.1564	−0.476943	−0.238471	+	0.971150i	$0.576646\pi$
$882$	−1.00000	−0.0336718
$883$	−22.0785	−0.742999	−0.371500	−	0.928433i	$-0.621156\pi$
$883$	−22.0785	−0.742999	−0.371500	+	0.928433i	$0.621156\pi$
$884$	0	0
$885$	4.85517	0.163205
$886$	−34.2747	−1.15148
$887$	−28.4397	−0.954910	−0.477455	−	0.878656i	$-0.658441\pi$
$887$	−28.4397	−0.954910	−0.477455	+	0.878656i	$0.658441\pi$
$888$	11.5308	0.386948
$889$	5.42758	0.182035
$890$	−4.79417	−0.160701
$891$	−3.40581	−0.114099
$892$	−19.8562	−0.664836
$893$	39.6319	1.32623
$894$	−18.4698	−0.617722
$895$	0.792249	0.0264820
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−9.70171	−0.323750
$899$	8.65684	0.288722
$900$	−4.87263	−0.162421
$901$	−34.8719	−1.16175
$902$	22.6993	0.755805
$903$	−5.82371	−0.193801
$904$	0.274127	0.00911732
$905$	6.14829	0.204376
$906$	−19.2814	−0.640582
$907$	−30.2828	−1.00552	−0.502761	−	0.864425i	$-0.667682\pi$
$907$	−30.2828	−1.00552	−0.502761	+	0.864425i	$0.667682\pi$
$908$	−0.537500	−0.0178376
$909$	−6.33273	−0.210043
$910$	0	0
$911$	−14.0392	−0.465140	−0.232570	−	0.972580i	$-0.574714\pi$
$911$	−14.0392	−0.465140	−0.232570	+	0.972580i	$0.574714\pi$
$912$	8.63102	0.285802
$913$	35.7405	1.18284
$914$	−7.58402	−0.250857
$915$	4.82717	0.159581
$916$	−16.2741	−0.537712
$917$	−5.78017	−0.190878
$918$	−2.66487	−0.0879540
$919$	−5.06425	−0.167054	−0.0835270	−	0.996506i	$-0.526618\pi$
$919$	−5.06425	−0.167054	−0.0835270	+	0.996506i	$0.526618\pi$
$920$	−2.96077	−0.0976137
$921$	−25.7265	−0.847716
$922$	−4.51573	−0.148718
$923$	0	0
$924$	3.40581	0.112043
$925$	−56.1852	−1.84736
$926$	13.0556	0.429034
$927$	−11.9433	−0.392270
$928$	−2.21983	−0.0728696
$929$	34.1957	1.12192	0.560962	−	0.827842i	$-0.310431\pi$
$929$	34.1957	1.12192	0.560962	+	0.827842i	$0.310431\pi$
$930$	1.39181	0.0456393
$931$	−8.63102	−0.282870
$932$	5.43834	0.178139
$933$	−9.70171	−0.317620
$934$	−23.9711	−0.784357
$935$	3.23921	0.105933
$936$	0	0
$937$	10.6052	0.346457	0.173228	−	0.984882i	$-0.444580\pi$
$937$	10.6052	0.346457	0.173228	+	0.984882i	$0.444580\pi$
$938$	3.78017	0.123427
$939$	8.74392	0.285347
$940$	−1.63879	−0.0534515
$941$	5.10082	0.166282	0.0831410	−	0.996538i	$-0.473505\pi$
$941$	5.10082	0.166282	0.0831410	+	0.996538i	$0.473505\pi$
$942$	16.7681	0.546334
$943$	55.2911	1.80053
$944$	−13.6039	−0.442768
$945$	−0.356896	−0.0116098
$946$	19.8345	0.644874
$947$	41.6577	1.35369	0.676847	−	0.736124i	$-0.263346\pi$
$947$	41.6577	1.35369	0.676847	+	0.736124i	$0.263346\pi$
$948$	−4.49396	−0.145957
$949$	0	0
$950$	−42.0557	−1.36447
$951$	−1.10992	−0.0359915
$952$	2.66487	0.0863691
$953$	−6.55901	−0.212467	−0.106234	−	0.994341i	$-0.533879\pi$
$953$	−6.55901	−0.212467	−0.106234	+	0.994341i	$0.533879\pi$
$954$	−13.0858	−0.423667
$955$	2.35105	0.0760780
$956$	−24.1323	−0.780494
$957$	7.56033	0.244391
$958$	−2.84654	−0.0919676
$959$	18.1957	0.587569
$960$	−0.356896	−0.0115188
$961$	−15.7918	−0.509412
$962$	0	0
$963$	−0.356896	−0.0115008
$964$	16.9095	0.544617
$965$	−8.00777	−0.257779
$966$	8.29590	0.266916
$967$	36.7042	1.18033	0.590164	−	0.807283i	$-0.299063\pi$
$967$	36.7042	1.18033	0.590164	+	0.807283i	$0.299063\pi$
$968$	−0.599564	−0.0192707
$969$	−23.0006	−0.738885
$970$	3.31421	0.106413
$971$	34.8853	1.11952	0.559761	−	0.828654i	$-0.310893\pi$
$971$	34.8853	1.11952	0.559761	+	0.828654i	$0.310893\pi$
$972$	−1.00000	−0.0320750
$973$	3.21014	0.102912
$974$	13.7694	0.441200
$975$	0	0
$976$	−13.5254	−0.432938
$977$	43.0461	1.37717	0.688583	−	0.725158i	$-0.258233\pi$
$977$	43.0461	1.37717	0.688583	+	0.725158i	$0.258233\pi$
$978$	−5.15346	−0.164789
$979$	−45.7502	−1.46218
$980$	0.356896	0.0114006
$981$	−18.5429	−0.592028
$982$	38.2825	1.22164
$983$	−36.9724	−1.17924	−0.589618	−	0.807682i	$-0.700722\pi$
$983$	−36.9724	−1.17924	−0.589618	+	0.807682i	$0.700722\pi$
$984$	6.66487	0.212468
$985$	−8.16075	−0.260023
$986$	5.91557	0.188390
$987$	4.59179	0.146158
$988$	0	0
$989$	48.3129	1.53626
$990$	1.21552	0.0386318
$991$	−6.03875	−0.191827	−0.0959137	−	0.995390i	$-0.530577\pi$
$991$	−6.03875	−0.191827	−0.0959137	+	0.995390i	$0.530577\pi$
$992$	−3.89977	−0.123818
$993$	17.0073	0.539710
$994$	−14.1032	−0.447327
$995$	−4.01054	−0.127143
$996$	10.4940	0.332514
$997$	−49.9866	−1.58309	−0.791546	−	0.611110i	$-0.790723\pi$
$997$	−49.9866	−1.58309	−0.791546	+	0.611110i	$0.790723\pi$
$998$	32.2828	1.02189
$999$	−11.5308	−0.364818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cb.1.2	✓	3
13.12	even	2		7098.2.a.ck.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cb.1.2	✓	3	1.1	even	1	trivial
7098.2.a.ck.1.2	yes	3	13.12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.356896 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.356896 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.356896 q^{10} -3.40581 q^{11} -1.00000 q^{12} -1.00000 q^{14} -0.356896 q^{15} +1.00000 q^{16} -2.66487 q^{17} -1.00000 q^{18} -8.63102 q^{19} +0.356896 q^{20} -1.00000 q^{21} +3.40581 q^{22} +8.29590 q^{23} +1.00000 q^{24} -4.87263 q^{25} -1.00000 q^{27} +1.00000 q^{28} +2.21983 q^{29} +0.356896 q^{30} +3.89977 q^{31} -1.00000 q^{32} +3.40581 q^{33} +2.66487 q^{34} +0.356896 q^{35} +1.00000 q^{36} +11.5308 q^{37} +8.63102 q^{38} -0.356896 q^{40} +6.66487 q^{41} +1.00000 q^{42} +5.82371 q^{43} -3.40581 q^{44} +0.356896 q^{45} -8.29590 q^{46} -4.59179 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.87263 q^{50} +2.66487 q^{51} +13.0858 q^{53} +1.00000 q^{54} -1.21552 q^{55} -1.00000 q^{56} +8.63102 q^{57} -2.21983 q^{58} -13.6039 q^{59} -0.356896 q^{60} -13.5254 q^{61} -3.89977 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.40581 q^{66} -3.78017 q^{67} -2.66487 q^{68} -8.29590 q^{69} -0.356896 q^{70} +14.1032 q^{71} -1.00000 q^{72} -1.72587 q^{73} -11.5308 q^{74} +4.87263 q^{75} -8.63102 q^{76} -3.40581 q^{77} +4.49396 q^{79} +0.356896 q^{80} +1.00000 q^{81} -6.66487 q^{82} -10.4940 q^{83} -1.00000 q^{84} -0.951083 q^{85} -5.82371 q^{86} -2.21983 q^{87} +3.40581 q^{88} +13.4330 q^{89} -0.356896 q^{90} +8.29590 q^{92} -3.89977 q^{93} +4.59179 q^{94} -3.08038 q^{95} +1.00000 q^{96} -9.28621 q^{97} -1.00000 q^{98} -3.40581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{15} + 3 q^{16} - 9 q^{17} - 3 q^{18} - 11 q^{19} - 3 q^{20} - 3 q^{21} - 3 q^{22} + 11 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{27} + 3 q^{28} + 8 q^{29} - 3 q^{30} - 11 q^{31} - 3 q^{32} - 3 q^{33} + 9 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 11 q^{38} + 3 q^{40} + 21 q^{41} + 3 q^{42} + 10 q^{43} + 3 q^{44} - 3 q^{45} - 11 q^{46} + 14 q^{47} - 3 q^{48} + 3 q^{49} - 2 q^{50} + 9 q^{51} + 2 q^{53} + 3 q^{54} - 24 q^{55} - 3 q^{56} + 11 q^{57} - 8 q^{58} - 32 q^{59} + 3 q^{60} - 6 q^{61} + 11 q^{62} + 3 q^{63} + 3 q^{64} + 3 q^{66} - 10 q^{67} - 9 q^{68} - 11 q^{69} + 3 q^{70} + 21 q^{71} - 3 q^{72} - 16 q^{73} + 3 q^{74} - 2 q^{75} - 11 q^{76} + 3 q^{77} + 4 q^{79} - 3 q^{80} + 3 q^{81} - 21 q^{82} - 22 q^{83} - 3 q^{84} - 12 q^{85} - 10 q^{86} - 8 q^{87} - 3 q^{88} + 21 q^{89} + 3 q^{90} + 11 q^{92} + 11 q^{93} - 14 q^{94} + 25 q^{95} + 3 q^{96} - 36 q^{97} - 3 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^14 + 3 * q^15 + 3 * q^16 - 9 * q^17 - 3 * q^18 - 11 * q^19 - 3 * q^20 - 3 * q^21 - 3 * q^22 + 11 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^27 + 3 * q^28 + 8 * q^29 - 3 * q^30 - 11 * q^31 - 3 * q^32 - 3 * q^33 + 9 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 11 * q^38 + 3 * q^40 + 21 * q^41 + 3 * q^42 + 10 * q^43 + 3 * q^44 - 3 * q^45 - 11 * q^46 + 14 * q^47 - 3 * q^48 + 3 * q^49 - 2 * q^50 + 9 * q^51 + 2 * q^53 + 3 * q^54 - 24 * q^55 - 3 * q^56 + 11 * q^57 - 8 * q^58 - 32 * q^59 + 3 * q^60 - 6 * q^61 + 11 * q^62 + 3 * q^63 + 3 * q^64 + 3 * q^66 - 10 * q^67 - 9 * q^68 - 11 * q^69 + 3 * q^70 + 21 * q^71 - 3 * q^72 - 16 * q^73 + 3 * q^74 - 2 * q^75 - 11 * q^76 + 3 * q^77 + 4 * q^79 - 3 * q^80 + 3 * q^81 - 21 * q^82 - 22 * q^83 - 3 * q^84 - 12 * q^85 - 10 * q^86 - 8 * q^87 - 3 * q^88 + 21 * q^89 + 3 * q^90 + 11 * q^92 + 11 * q^93 - 14 * q^94 + 25 * q^95 + 3 * q^96 - 36 * q^97 - 3 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more