LMFDB - Embedded newform 7098.2.a.cu.1.3

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.6148961.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 $ x^6 - 2x^5 - 11x^4 + 12x^3 + 32x^2 - 16*x - 29
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			1.3
Root			$-1.33906$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.404061 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.404061 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.404061 q^{10} -4.72704 q^{11} +1.00000 q^{12} -1.00000 q^{14} +0.404061 q^{15} +1.00000 q^{16} +4.50459 q^{17} +1.00000 q^{18} +4.94294 q^{19} +0.404061 q^{20} -1.00000 q^{21} -4.72704 q^{22} -5.73373 q^{23} +1.00000 q^{24} -4.83673 q^{25} +1.00000 q^{27} -1.00000 q^{28} -0.647042 q^{29} +0.404061 q^{30} +6.14471 q^{31} +1.00000 q^{32} -4.72704 q^{33} +4.50459 q^{34} -0.404061 q^{35} +1.00000 q^{36} +4.41291 q^{37} +4.94294 q^{38} +0.404061 q^{40} +9.13551 q^{41} -1.00000 q^{42} -0.666578 q^{43} -4.72704 q^{44} +0.404061 q^{45} -5.73373 q^{46} +6.47213 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.83673 q^{50} +4.50459 q^{51} -0.811429 q^{53} +1.00000 q^{54} -1.91001 q^{55} -1.00000 q^{56} +4.94294 q^{57} -0.647042 q^{58} +15.0444 q^{59} +0.404061 q^{60} +2.83178 q^{61} +6.14471 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.72704 q^{66} +5.97874 q^{67} +4.50459 q^{68} -5.73373 q^{69} -0.404061 q^{70} +14.3974 q^{71} +1.00000 q^{72} -3.92648 q^{73} +4.41291 q^{74} -4.83673 q^{75} +4.94294 q^{76} +4.72704 q^{77} -8.69273 q^{79} +0.404061 q^{80} +1.00000 q^{81} +9.13551 q^{82} -4.51350 q^{83} -1.00000 q^{84} +1.82013 q^{85} -0.666578 q^{86} -0.647042 q^{87} -4.72704 q^{88} +9.32298 q^{89} +0.404061 q^{90} -5.73373 q^{92} +6.14471 q^{93} +6.47213 q^{94} +1.99725 q^{95} +1.00000 q^{96} +6.19694 q^{97} +1.00000 q^{98} -4.72704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 10 q^{11} + 6 q^{12} - 6 q^{14} + 9 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} + 2 q^{19} + 9 q^{20} - 6 q^{21} + 10 q^{22} + 6 q^{24} + 9 q^{25} + 6 q^{27} - 6 q^{28} - 4 q^{29} + 9 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 4 q^{34} - 9 q^{35} + 6 q^{36} + 9 q^{37} + 2 q^{38} + 9 q^{40} + 25 q^{41} - 6 q^{42} + 19 q^{43} + 10 q^{44} + 9 q^{45} + 21 q^{47} + 6 q^{48} + 6 q^{49} + 9 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 21 q^{55} - 6 q^{56} + 2 q^{57} - 4 q^{58} + 20 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 24 q^{67} + 4 q^{68} - 9 q^{70} + 13 q^{71} + 6 q^{72} - 9 q^{73} + 9 q^{74} + 9 q^{75} + 2 q^{76} - 10 q^{77} + 28 q^{79} + 9 q^{80} + 6 q^{81} + 25 q^{82} + 15 q^{83} - 6 q^{84} + 17 q^{85} + 19 q^{86} - 4 q^{87} + 10 q^{88} + 11 q^{89} + 9 q^{90} + 9 q^{93} + 21 q^{94} + 6 q^{96} + 2 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 10 * q^11 + 6 * q^12 - 6 * q^14 + 9 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 + 2 * q^19 + 9 * q^20 - 6 * q^21 + 10 * q^22 + 6 * q^24 + 9 * q^25 + 6 * q^27 - 6 * q^28 - 4 * q^29 + 9 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 4 * q^34 - 9 * q^35 + 6 * q^36 + 9 * q^37 + 2 * q^38 + 9 * q^40 + 25 * q^41 - 6 * q^42 + 19 * q^43 + 10 * q^44 + 9 * q^45 + 21 * q^47 + 6 * q^48 + 6 * q^49 + 9 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 21 * q^55 - 6 * q^56 + 2 * q^57 - 4 * q^58 + 20 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 24 * q^67 + 4 * q^68 - 9 * q^70 + 13 * q^71 + 6 * q^72 - 9 * q^73 + 9 * q^74 + 9 * q^75 + 2 * q^76 - 10 * q^77 + 28 * q^79 + 9 * q^80 + 6 * q^81 + 25 * q^82 + 15 * q^83 - 6 * q^84 + 17 * q^85 + 19 * q^86 - 4 * q^87 + 10 * q^88 + 11 * q^89 + 9 * q^90 + 9 * q^93 + 21 * q^94 + 6 * q^96 + 2 * q^97 + 6 * q^98 + 10 * 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
$5$	0.404061	0.180701	0.0903507	−	0.995910i	$-0.471201\pi$
$5$	0.404061	0.180701	0.0903507	+	0.995910i	$0.471201\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.404061	0.127775
$11$	−4.72704	−1.42526	−0.712629	−	0.701541i	$-0.752496\pi$
$11$	−4.72704	−1.42526	−0.712629	+	0.701541i	$0.752496\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	0.404061	0.104328
$16$	1.00000	0.250000
$17$	4.50459	1.09252	0.546261	−	0.837615i	$-0.316051\pi$
$17$	4.50459	1.09252	0.546261	+	0.837615i	$0.316051\pi$
$18$	1.00000	0.235702
$19$	4.94294	1.13399	0.566994	−	0.823722i	$-0.308106\pi$
$19$	4.94294	1.13399	0.566994	+	0.823722i	$0.308106\pi$
$20$	0.404061	0.0903507
$21$	−1.00000	−0.218218
$22$	−4.72704	−1.00781
$23$	−5.73373	−1.19557	−0.597783	−	0.801658i	$-0.703952\pi$
$23$	−5.73373	−1.19557	−0.597783	+	0.801658i	$0.703952\pi$
$24$	1.00000	0.204124
$25$	−4.83673	−0.967347
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−0.647042	−0.120153	−0.0600763	−	0.998194i	$-0.519134\pi$
$29$	−0.647042	−0.120153	−0.0600763	+	0.998194i	$0.519134\pi$
$30$	0.404061	0.0737711
$31$	6.14471	1.10362	0.551812	−	0.833969i	$-0.313937\pi$
$31$	6.14471	1.10362	0.551812	+	0.833969i	$0.313937\pi$
$32$	1.00000	0.176777
$33$	−4.72704	−0.822873
$34$	4.50459	0.772530
$35$	−0.404061	−0.0682987
$36$	1.00000	0.166667
$37$	4.41291	0.725478	0.362739	−	0.931891i	$-0.381842\pi$
$37$	4.41291	0.725478	0.362739	+	0.931891i	$0.381842\pi$
$38$	4.94294	0.801851
$39$	0	0
$40$	0.404061	0.0638876
$41$	9.13551	1.42673	0.713363	−	0.700794i	$-0.247171\pi$
$41$	9.13551	1.42673	0.713363	+	0.700794i	$0.247171\pi$
$42$	−1.00000	−0.154303
$43$	−0.666578	−0.101652	−0.0508261	−	0.998708i	$-0.516185\pi$
$43$	−0.666578	−0.101652	−0.0508261	+	0.998708i	$0.516185\pi$
$44$	−4.72704	−0.712629
$45$	0.404061	0.0602338
$46$	−5.73373	−0.845393
$47$	6.47213	0.944057	0.472028	−	0.881583i	$-0.343522\pi$
$47$	6.47213	0.944057	0.472028	+	0.881583i	$0.343522\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−4.83673	−0.684018
$51$	4.50459	0.630768
$52$	0	0
$53$	−0.811429	−0.111458	−0.0557291	−	0.998446i	$-0.517748\pi$
$53$	−0.811429	−0.111458	−0.0557291	+	0.998446i	$0.517748\pi$
$54$	1.00000	0.136083
$55$	−1.91001	−0.257546
$56$	−1.00000	−0.133631
$57$	4.94294	0.654708
$58$	−0.647042	−0.0849607
$59$	15.0444	1.95861	0.979305	−	0.202388i	$-0.0648702\pi$
$59$	15.0444	1.95861	0.979305	+	0.202388i	$0.0648702\pi$
$60$	0.404061	0.0521640
$61$	2.83178	0.362572	0.181286	−	0.983430i	$-0.441974\pi$
$61$	2.83178	0.362572	0.181286	+	0.983430i	$0.441974\pi$
$62$	6.14471	0.780379
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.72704	−0.581859
$67$	5.97874	0.730419	0.365209	−	0.930925i	$-0.380997\pi$
$67$	5.97874	0.730419	0.365209	+	0.930925i	$0.380997\pi$
$68$	4.50459	0.546261
$69$	−5.73373	−0.690260
$70$	−0.404061	−0.0482945
$71$	14.3974	1.70866	0.854331	−	0.519729i	$-0.173967\pi$
$71$	14.3974	1.70866	0.854331	+	0.519729i	$0.173967\pi$
$72$	1.00000	0.117851
$73$	−3.92648	−0.459560	−0.229780	−	0.973243i	$-0.573801\pi$
$73$	−3.92648	−0.459560	−0.229780	+	0.973243i	$0.573801\pi$
$74$	4.41291	0.512990
$75$	−4.83673	−0.558498
$76$	4.94294	0.566994
$77$	4.72704	0.538697
$78$	0	0
$79$	−8.69273	−0.978008	−0.489004	−	0.872282i	$-0.662640\pi$
$79$	−8.69273	−0.978008	−0.489004	+	0.872282i	$0.662640\pi$
$80$	0.404061	0.0451754
$81$	1.00000	0.111111
$82$	9.13551	1.00885
$83$	−4.51350	−0.495420	−0.247710	−	0.968834i	$-0.579678\pi$
$83$	−4.51350	−0.495420	−0.247710	+	0.968834i	$0.579678\pi$
$84$	−1.00000	−0.109109
$85$	1.82013	0.197420
$86$	−0.666578	−0.0718789
$87$	−0.647042	−0.0693702
$88$	−4.72704	−0.503905
$89$	9.32298	0.988234	0.494117	−	0.869395i	$-0.335491\pi$
$89$	9.32298	0.988234	0.494117	+	0.869395i	$0.335491\pi$
$90$	0.404061	0.0425918
$91$	0	0
$92$	−5.73373	−0.597783
$93$	6.14471	0.637177
$94$	6.47213	0.667549
$95$	1.99725	0.204913
$96$	1.00000	0.102062
$97$	6.19694	0.629204	0.314602	−	0.949224i	$-0.398129\pi$
$97$	6.19694	0.629204	0.314602	+	0.949224i	$0.398129\pi$
$98$	1.00000	0.101015
$99$	−4.72704	−0.475086
$100$	−4.83673	−0.483673
$101$	10.7135	1.06603	0.533015	−	0.846106i	$-0.321059\pi$
$101$	10.7135	1.06603	0.533015	+	0.846106i	$0.321059\pi$
$102$	4.50459	0.446021
$103$	−1.21750	−0.119964	−0.0599818	−	0.998199i	$-0.519104\pi$
$103$	−1.21750	−0.119964	−0.0599818	+	0.998199i	$0.519104\pi$
$104$	0	0
$105$	−0.404061	−0.0394323
$106$	−0.811429	−0.0788129
$107$	13.5610	1.31100	0.655498	−	0.755197i	$-0.272459\pi$
$107$	13.5610	1.31100	0.655498	+	0.755197i	$0.272459\pi$
$108$	1.00000	0.0962250
$109$	−12.5344	−1.20058	−0.600289	−	0.799783i	$-0.704948\pi$
$109$	−12.5344	−1.20058	−0.600289	+	0.799783i	$0.704948\pi$
$110$	−1.91001	−0.182113
$111$	4.41291	0.418855
$112$	−1.00000	−0.0944911
$113$	−18.1761	−1.70987	−0.854933	−	0.518739i	$-0.826402\pi$
$113$	−18.1761	−1.70987	−0.854933	+	0.518739i	$0.826402\pi$
$114$	4.94294	0.462949
$115$	−2.31678	−0.216041
$116$	−0.647042	−0.0600763
$117$	0	0
$118$	15.0444	1.38495
$119$	−4.50459	−0.412935
$120$	0.404061	0.0368855
$121$	11.3449	1.03136
$122$	2.83178	0.256377
$123$	9.13551	0.823721
$124$	6.14471	0.551812
$125$	−3.97464	−0.355503
$126$	−1.00000	−0.0890871
$127$	11.2447	0.997803	0.498902	−	0.866659i	$-0.333737\pi$
$127$	11.2447	0.997803	0.498902	+	0.866659i	$0.333737\pi$
$128$	1.00000	0.0883883
$129$	−0.666578	−0.0586889
$130$	0	0
$131$	−3.57875	−0.312677	−0.156338	−	0.987704i	$-0.549969\pi$
$131$	−3.57875	−0.312677	−0.156338	+	0.987704i	$0.549969\pi$
$132$	−4.72704	−0.411436
$133$	−4.94294	−0.428607
$134$	5.97874	0.516484
$135$	0.404061	0.0347760
$136$	4.50459	0.386265
$137$	−3.27155	−0.279507	−0.139754	−	0.990186i	$-0.544631\pi$
$137$	−3.27155	−0.279507	−0.139754	+	0.990186i	$0.544631\pi$
$138$	−5.73373	−0.488088
$139$	−10.7168	−0.908984	−0.454492	−	0.890751i	$-0.650179\pi$
$139$	−10.7168	−0.908984	−0.454492	+	0.890751i	$0.650179\pi$
$140$	−0.404061	−0.0341494
$141$	6.47213	0.545051
$142$	14.3974	1.20821
$143$	0	0
$144$	1.00000	0.0833333
$145$	−0.261444	−0.0217118
$146$	−3.92648	−0.324958
$147$	1.00000	0.0824786
$148$	4.41291	0.362739
$149$	1.18034	0.0966972	0.0483486	−	0.998831i	$-0.484604\pi$
$149$	1.18034	0.0966972	0.0483486	+	0.998831i	$0.484604\pi$
$150$	−4.83673	−0.394918
$151$	−20.7040	−1.68487	−0.842434	−	0.538799i	$-0.818878\pi$
$151$	−20.7040	−1.68487	−0.842434	+	0.538799i	$0.818878\pi$
$152$	4.94294	0.400925
$153$	4.50459	0.364174
$154$	4.72704	0.380916
$155$	2.48284	0.199426
$156$	0	0
$157$	12.8774	1.02772	0.513862	−	0.857873i	$-0.328214\pi$
$157$	12.8774	1.02772	0.513862	+	0.857873i	$0.328214\pi$
$158$	−8.69273	−0.691556
$159$	−0.811429	−0.0643505
$160$	0.404061	0.0319438
$161$	5.73373	0.451881
$162$	1.00000	0.0785674
$163$	−21.0202	−1.64643	−0.823215	−	0.567729i	$-0.807822\pi$
$163$	−21.0202	−1.64643	−0.823215	+	0.567729i	$0.807822\pi$
$164$	9.13551	0.713363
$165$	−1.91001	−0.148694
$166$	−4.51350	−0.350315
$167$	13.8944	1.07518	0.537592	−	0.843205i	$-0.319334\pi$
$167$	13.8944	1.07518	0.537592	+	0.843205i	$0.319334\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	1.82013	0.139597
$171$	4.94294	0.377996
$172$	−0.666578	−0.0508261
$173$	8.88152	0.675250	0.337625	−	0.941281i	$-0.390376\pi$
$173$	8.88152	0.675250	0.337625	+	0.941281i	$0.390376\pi$
$174$	−0.647042	−0.0490521
$175$	4.83673	0.365623
$176$	−4.72704	−0.356314
$177$	15.0444	1.13080
$178$	9.32298	0.698787
$179$	−17.7757	−1.32862	−0.664308	−	0.747459i	$-0.731274\pi$
$179$	−17.7757	−1.32862	−0.664308	+	0.747459i	$0.731274\pi$
$180$	0.404061	0.0301169
$181$	20.2125	1.50239	0.751193	−	0.660082i	$-0.229479\pi$
$181$	20.2125	1.50239	0.751193	+	0.660082i	$0.229479\pi$
$182$	0	0
$183$	2.83178	0.209331
$184$	−5.73373	−0.422696
$185$	1.78308	0.131095
$186$	6.14471	0.450552
$187$	−21.2934	−1.55713
$188$	6.47213	0.472028
$189$	−1.00000	−0.0727393
$190$	1.99725	0.144896
$191$	−17.5158	−1.26740	−0.633698	−	0.773580i	$-0.718464\pi$
$191$	−17.5158	−1.26740	−0.633698	+	0.773580i	$0.718464\pi$
$192$	1.00000	0.0721688
$193$	19.7673	1.42288	0.711441	−	0.702746i	$-0.248043\pi$
$193$	19.7673	1.42288	0.711441	+	0.702746i	$0.248043\pi$
$194$	6.19694	0.444915
$195$	0	0
$196$	1.00000	0.0714286
$197$	9.54410	0.679989	0.339994	−	0.940427i	$-0.389575\pi$
$197$	9.54410	0.679989	0.339994	+	0.940427i	$0.389575\pi$
$198$	−4.72704	−0.335936
$199$	5.57473	0.395182	0.197591	−	0.980285i	$-0.436688\pi$
$199$	5.57473	0.395182	0.197591	+	0.980285i	$0.436688\pi$
$200$	−4.83673	−0.342009
$201$	5.97874	0.421707
$202$	10.7135	0.753797
$203$	0.647042	0.0454134
$204$	4.50459	0.315384
$205$	3.69130	0.257812
$206$	−1.21750	−0.0848271
$207$	−5.73373	−0.398522
$208$	0	0
$209$	−23.3655	−1.61622
$210$	−0.404061	−0.0278828
$211$	15.1334	1.04183	0.520914	−	0.853609i	$-0.325591\pi$
$211$	15.1334	1.04183	0.520914	+	0.853609i	$0.325591\pi$
$212$	−0.811429	−0.0557291
$213$	14.3974	0.986497
$214$	13.5610	0.927014
$215$	−0.269338	−0.0183687
$216$	1.00000	0.0680414
$217$	−6.14471	−0.417130
$218$	−12.5344	−0.848936
$219$	−3.92648	−0.265327
$220$	−1.91001	−0.128773
$221$	0	0
$222$	4.41291	0.296175
$223$	7.60285	0.509124	0.254562	−	0.967056i	$-0.418069\pi$
$223$	7.60285	0.509124	0.254562	+	0.967056i	$0.418069\pi$
$224$	−1.00000	−0.0668153
$225$	−4.83673	−0.322449
$226$	−18.1761	−1.20906
$227$	0.478747	0.0317756	0.0158878	−	0.999874i	$-0.494943\pi$
$227$	0.478747	0.0317756	0.0158878	+	0.999874i	$0.494943\pi$
$228$	4.94294	0.327354
$229$	−20.0110	−1.32237	−0.661183	−	0.750224i	$-0.729945\pi$
$229$	−20.0110	−1.32237	−0.661183	+	0.750224i	$0.729945\pi$
$230$	−2.31678	−0.152764
$231$	4.72704	0.311017
$232$	−0.647042	−0.0424804
$233$	5.45868	0.357610	0.178805	−	0.983885i	$-0.442777\pi$
$233$	5.45868	0.357610	0.178805	+	0.983885i	$0.442777\pi$
$234$	0	0
$235$	2.61513	0.170592
$236$	15.0444	0.979305
$237$	−8.69273	−0.564653
$238$	−4.50459	−0.291989
$239$	6.30483	0.407826	0.203913	−	0.978989i	$-0.434634\pi$
$239$	6.30483	0.407826	0.203913	+	0.978989i	$0.434634\pi$
$240$	0.404061	0.0260820
$241$	−2.62771	−0.169265	−0.0846327	−	0.996412i	$-0.526972\pi$
$241$	−2.62771	−0.169265	−0.0846327	+	0.996412i	$0.526972\pi$
$242$	11.3449	0.729280
$243$	1.00000	0.0641500
$244$	2.83178	0.181286
$245$	0.404061	0.0258145
$246$	9.13551	0.582459
$247$	0	0
$248$	6.14471	0.390190
$249$	−4.51350	−0.286031
$250$	−3.97464	−0.251378
$251$	−25.4341	−1.60538	−0.802692	−	0.596394i	$-0.796599\pi$
$251$	−25.4341	−1.60538	−0.802692	+	0.596394i	$0.796599\pi$
$252$	−1.00000	−0.0629941
$253$	27.1036	1.70399
$254$	11.2447	0.705553
$255$	1.82013	0.113981
$256$	1.00000	0.0625000
$257$	0.822060	0.0512787	0.0256393	−	0.999671i	$-0.491838\pi$
$257$	0.822060	0.0512787	0.0256393	+	0.999671i	$0.491838\pi$
$258$	−0.666578	−0.0414993
$259$	−4.41291	−0.274205
$260$	0	0
$261$	−0.647042	−0.0400509
$262$	−3.57875	−0.221096
$263$	23.7426	1.46403	0.732015	−	0.681288i	$-0.238580\pi$
$263$	23.7426	1.46403	0.732015	+	0.681288i	$0.238580\pi$
$264$	−4.72704	−0.290929
$265$	−0.327867	−0.0201407
$266$	−4.94294	−0.303071
$267$	9.32298	0.570557
$268$	5.97874	0.365209
$269$	−6.81198	−0.415334	−0.207667	−	0.978200i	$-0.566587\pi$
$269$	−6.81198	−0.415334	−0.207667	+	0.978200i	$0.566587\pi$
$270$	0.404061	0.0245904
$271$	−13.3555	−0.811288	−0.405644	−	0.914031i	$-0.632953\pi$
$271$	−13.3555	−0.811288	−0.405644	+	0.914031i	$0.632953\pi$
$272$	4.50459	0.273131
$273$	0	0
$274$	−3.27155	−0.197642
$275$	22.8635	1.37872
$276$	−5.73373	−0.345130
$277$	23.3676	1.40402	0.702012	−	0.712166i	$-0.252285\pi$
$277$	23.3676	1.40402	0.702012	+	0.712166i	$0.252285\pi$
$278$	−10.7168	−0.642749
$279$	6.14471	0.367874
$280$	−0.404061	−0.0241473
$281$	1.31057	0.0781820	0.0390910	−	0.999236i	$-0.487554\pi$
$281$	1.31057	0.0781820	0.0390910	+	0.999236i	$0.487554\pi$
$282$	6.47213	0.385410
$283$	−27.0743	−1.60940	−0.804699	−	0.593683i	$-0.797673\pi$
$283$	−27.0743	−1.60940	−0.804699	+	0.593683i	$0.797673\pi$
$284$	14.3974	0.854331
$285$	1.99725	0.118307
$286$	0	0
$287$	−9.13551	−0.539252
$288$	1.00000	0.0589256
$289$	3.29130	0.193606
$290$	−0.261444	−0.0153525
$291$	6.19694	0.363271
$292$	−3.92648	−0.229780
$293$	17.1700	1.00308	0.501541	−	0.865134i	$-0.332767\pi$
$293$	17.1700	1.00308	0.501541	+	0.865134i	$0.332767\pi$
$294$	1.00000	0.0583212
$295$	6.07884	0.353924
$296$	4.41291	0.256495
$297$	−4.72704	−0.274291
$298$	1.18034	0.0683753
$299$	0	0
$300$	−4.83673	−0.279249
$301$	0.666578	0.0384209
$302$	−20.7040	−1.19138
$303$	10.7135	0.615473
$304$	4.94294	0.283497
$305$	1.14421	0.0655173
$306$	4.50459	0.257510
$307$	−20.6481	−1.17845	−0.589225	−	0.807969i	$-0.700567\pi$
$307$	−20.6481	−1.17845	−0.589225	+	0.807969i	$0.700567\pi$
$308$	4.72704	0.269348
$309$	−1.21750	−0.0692610
$310$	2.48284	0.141016
$311$	31.1584	1.76683	0.883415	−	0.468591i	$-0.155238\pi$
$311$	31.1584	1.76683	0.883415	+	0.468591i	$0.155238\pi$
$312$	0	0
$313$	−21.2384	−1.20046	−0.600232	−	0.799826i	$-0.704925\pi$
$313$	−21.2384	−1.20046	−0.600232	+	0.799826i	$0.704925\pi$
$314$	12.8774	0.726711
$315$	−0.404061	−0.0227662
$316$	−8.69273	−0.489004
$317$	3.67433	0.206371	0.103185	−	0.994662i	$-0.467097\pi$
$317$	3.67433	0.206371	0.103185	+	0.994662i	$0.467097\pi$
$318$	−0.811429	−0.0455027
$319$	3.05859	0.171248
$320$	0.404061	0.0225877
$321$	13.5610	0.756903
$322$	5.73373	0.319528
$323$	22.2659	1.23891
$324$	1.00000	0.0555556
$325$	0	0
$326$	−21.0202	−1.16420
$327$	−12.5344	−0.693154
$328$	9.13551	0.504424
$329$	−6.47213	−0.356820
$330$	−1.91001	−0.105143
$331$	25.6685	1.41087	0.705434	−	0.708776i	$-0.250752\pi$
$331$	25.6685	1.41087	0.705434	+	0.708776i	$0.250752\pi$
$332$	−4.51350	−0.247710
$333$	4.41291	0.241826
$334$	13.8944	0.760270
$335$	2.41577	0.131988
$336$	−1.00000	−0.0545545
$337$	−19.8182	−1.07956	−0.539782	−	0.841805i	$-0.681493\pi$
$337$	−19.8182	−1.07956	−0.539782	+	0.841805i	$0.681493\pi$
$338$	0	0
$339$	−18.1761	−0.987192
$340$	1.82013	0.0987102
$341$	−29.0463	−1.57295
$342$	4.94294	0.267284
$343$	−1.00000	−0.0539949
$344$	−0.666578	−0.0359395
$345$	−2.31678	−0.124731
$346$	8.88152	0.477474
$347$	−7.05961	−0.378980	−0.189490	−	0.981883i	$-0.560683\pi$
$347$	−7.05961	−0.378980	−0.189490	+	0.981883i	$0.560683\pi$
$348$	−0.647042	−0.0346851
$349$	−8.96825	−0.480059	−0.240030	−	0.970766i	$-0.577157\pi$
$349$	−8.96825	−0.480059	−0.240030	+	0.970766i	$0.577157\pi$
$350$	4.83673	0.258534
$351$	0	0
$352$	−4.72704	−0.251952
$353$	−19.6812	−1.04753	−0.523763	−	0.851864i	$-0.675472\pi$
$353$	−19.6812	−1.04753	−0.523763	+	0.851864i	$0.675472\pi$
$354$	15.0444	0.799600
$355$	5.81744	0.308758
$356$	9.32298	0.494117
$357$	−4.50459	−0.238408
$358$	−17.7757	−0.939473
$359$	−32.8782	−1.73524	−0.867622	−	0.497224i	$-0.834353\pi$
$359$	−32.8782	−1.73524	−0.867622	+	0.497224i	$0.834353\pi$
$360$	0.404061	0.0212959
$361$	5.43264	0.285929
$362$	20.2125	1.06235
$363$	11.3449	0.595455
$364$	0	0
$365$	−1.58654	−0.0830431
$366$	2.83178	0.148019
$367$	−25.2819	−1.31970	−0.659852	−	0.751395i	$-0.729381\pi$
$367$	−25.2819	−1.31970	−0.659852	+	0.751395i	$0.729381\pi$
$368$	−5.73373	−0.298892
$369$	9.13551	0.475576
$370$	1.78308	0.0926981
$371$	0.811429	0.0421273
$372$	6.14471	0.318589
$373$	11.3971	0.590118	0.295059	−	0.955479i	$-0.404661\pi$
$373$	11.3971	0.590118	0.295059	+	0.955479i	$0.404661\pi$
$374$	−21.2934	−1.10105
$375$	−3.97464	−0.205249
$376$	6.47213	0.333775
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−19.2765	−0.990168	−0.495084	−	0.868845i	$-0.664863\pi$
$379$	−19.2765	−0.990168	−0.495084	+	0.868845i	$0.664863\pi$
$380$	1.99725	0.102457
$381$	11.2447	0.576082
$382$	−17.5158	−0.896184
$383$	−14.4663	−0.739192	−0.369596	−	0.929193i	$-0.620504\pi$
$383$	−14.4663	−0.739192	−0.369596	+	0.929193i	$0.620504\pi$
$384$	1.00000	0.0510310
$385$	1.91001	0.0973433
$386$	19.7673	1.00613
$387$	−0.666578	−0.0338840
$388$	6.19694	0.314602
$389$	−0.913387	−0.0463106	−0.0231553	−	0.999732i	$-0.507371\pi$
$389$	−0.913387	−0.0463106	−0.0231553	+	0.999732i	$0.507371\pi$
$390$	0	0
$391$	−25.8281	−1.30618
$392$	1.00000	0.0505076
$393$	−3.57875	−0.180524
$394$	9.54410	0.480825
$395$	−3.51239	−0.176728
$396$	−4.72704	−0.237543
$397$	33.5036	1.68150	0.840748	−	0.541427i	$-0.182116\pi$
$397$	33.5036	1.68150	0.840748	+	0.541427i	$0.182116\pi$
$398$	5.57473	0.279436
$399$	−4.94294	−0.247456
$400$	−4.83673	−0.241837
$401$	−20.0314	−1.00032	−0.500160	−	0.865933i	$-0.666725\pi$
$401$	−20.0314	−1.00032	−0.500160	+	0.865933i	$0.666725\pi$
$402$	5.97874	0.298192
$403$	0	0
$404$	10.7135	0.533015
$405$	0.404061	0.0200779
$406$	0.647042	0.0321121
$407$	−20.8600	−1.03399
$408$	4.50459	0.223010
$409$	12.2787	0.607142	0.303571	−	0.952809i	$-0.401821\pi$
$409$	12.2787	0.607142	0.303571	+	0.952809i	$0.401821\pi$
$410$	3.69130	0.182300
$411$	−3.27155	−0.161374
$412$	−1.21750	−0.0599818
$413$	−15.0444	−0.740285
$414$	−5.73373	−0.281798
$415$	−1.82373	−0.0895232
$416$	0	0
$417$	−10.7168	−0.524802
$418$	−23.3655	−1.14284
$419$	−9.98508	−0.487803	−0.243902	−	0.969800i	$-0.578427\pi$
$419$	−9.98508	−0.487803	−0.243902	+	0.969800i	$0.578427\pi$
$420$	−0.404061	−0.0197161
$421$	−12.1776	−0.593498	−0.296749	−	0.954956i	$-0.595902\pi$
$421$	−12.1776	−0.593498	−0.296749	+	0.954956i	$0.595902\pi$
$422$	15.1334	0.736684
$423$	6.47213	0.314686
$424$	−0.811429	−0.0394065
$425$	−21.7875	−1.05685
$426$	14.3974	0.697558
$427$	−2.83178	−0.137039
$428$	13.5610	0.655498
$429$	0	0
$430$	−0.269338	−0.0129886
$431$	−30.1287	−1.45125	−0.725623	−	0.688092i	$-0.758448\pi$
$431$	−30.1287	−1.45125	−0.725623	+	0.688092i	$0.758448\pi$
$432$	1.00000	0.0481125
$433$	26.4737	1.27225	0.636123	−	0.771588i	$-0.280537\pi$
$433$	26.4737	1.27225	0.636123	+	0.771588i	$0.280537\pi$
$434$	−6.14471	−0.294956
$435$	−0.261444	−0.0125353
$436$	−12.5344	−0.600289
$437$	−28.3415	−1.35576
$438$	−3.92648	−0.187614
$439$	−34.7765	−1.65979	−0.829896	−	0.557918i	$-0.811600\pi$
$439$	−34.7765	−1.65979	−0.829896	+	0.557918i	$0.811600\pi$
$440$	−1.91001	−0.0910563
$441$	1.00000	0.0476190
$442$	0	0
$443$	−8.91795	−0.423704	−0.211852	−	0.977302i	$-0.567950\pi$
$443$	−8.91795	−0.423704	−0.211852	+	0.977302i	$0.567950\pi$
$444$	4.41291	0.209427
$445$	3.76705	0.178575
$446$	7.60285	0.360005
$447$	1.18034	0.0558282
$448$	−1.00000	−0.0472456
$449$	18.0313	0.850949	0.425475	−	0.904970i	$-0.360107\pi$
$449$	18.0313	0.850949	0.425475	+	0.904970i	$0.360107\pi$
$450$	−4.83673	−0.228006
$451$	−43.1839	−2.03345
$452$	−18.1761	−0.854933
$453$	−20.7040	−0.972760
$454$	0.478747	0.0224687
$455$	0	0
$456$	4.94294	0.231474
$457$	18.9373	0.885849	0.442925	−	0.896559i	$-0.353941\pi$
$457$	18.9373	0.885849	0.442925	+	0.896559i	$0.353941\pi$
$458$	−20.0110	−0.935054
$459$	4.50459	0.210256
$460$	−2.31678	−0.108020
$461$	6.51876	0.303609	0.151804	−	0.988411i	$-0.451492\pi$
$461$	6.51876	0.303609	0.151804	+	0.988411i	$0.451492\pi$
$462$	4.72704	0.219922
$463$	13.1560	0.611409	0.305705	−	0.952126i	$-0.401108\pi$
$463$	13.1560	0.611409	0.305705	+	0.952126i	$0.401108\pi$
$464$	−0.647042	−0.0300382
$465$	2.48284	0.115139
$466$	5.45868	0.252869
$467$	2.00592	0.0928230	0.0464115	−	0.998922i	$-0.485221\pi$
$467$	2.00592	0.0928230	0.0464115	+	0.998922i	$0.485221\pi$
$468$	0	0
$469$	−5.97874	−0.276072
$470$	2.61513	0.120627
$471$	12.8774	0.593357
$472$	15.0444	0.692474
$473$	3.15094	0.144880
$474$	−8.69273	−0.399270
$475$	−23.9077	−1.09696
$476$	−4.50459	−0.206467
$477$	−0.811429	−0.0371528
$478$	6.30483	0.288376
$479$	12.1195	0.553756	0.276878	−	0.960905i	$-0.410700\pi$
$479$	12.1195	0.553756	0.276878	+	0.960905i	$0.410700\pi$
$480$	0.404061	0.0184428
$481$	0	0
$482$	−2.62771	−0.119689
$483$	5.73373	0.260894
$484$	11.3449	0.515679
$485$	2.50394	0.113698
$486$	1.00000	0.0453609
$487$	−43.1568	−1.95562	−0.977810	−	0.209492i	$-0.932819\pi$
$487$	−43.1568	−1.95562	−0.977810	+	0.209492i	$0.932819\pi$
$488$	2.83178	0.128188
$489$	−21.0202	−0.950567
$490$	0.404061	0.0182536
$491$	16.5276	0.745880	0.372940	−	0.927856i	$-0.378350\pi$
$491$	16.5276	0.745880	0.372940	+	0.927856i	$0.378350\pi$
$492$	9.13551	0.411861
$493$	−2.91466	−0.131269
$494$	0	0
$495$	−1.91001	−0.0858487
$496$	6.14471	0.275906
$497$	−14.3974	−0.645814
$498$	−4.51350	−0.202255
$499$	−15.6585	−0.700972	−0.350486	−	0.936568i	$-0.613984\pi$
$499$	−15.6585	−0.700972	−0.350486	+	0.936568i	$0.613984\pi$
$500$	−3.97464	−0.177751
$501$	13.8944	0.620758
$502$	−25.4341	−1.13518
$503$	−5.85397	−0.261016	−0.130508	−	0.991447i	$-0.541661\pi$
$503$	−5.85397	−0.261016	−0.130508	+	0.991447i	$0.541661\pi$
$504$	−1.00000	−0.0445435
$505$	4.32890	0.192633
$506$	27.1036	1.20490
$507$	0	0
$508$	11.2447	0.498902
$509$	23.1149	1.02455	0.512274	−	0.858822i	$-0.328803\pi$
$509$	23.1149	1.02455	0.512274	+	0.858822i	$0.328803\pi$
$510$	1.82013	0.0805966
$511$	3.92648	0.173697
$512$	1.00000	0.0441942
$513$	4.94294	0.218236
$514$	0.822060	0.0362595
$515$	−0.491943	−0.0216776
$516$	−0.666578	−0.0293444
$517$	−30.5940	−1.34552
$518$	−4.41291	−0.193892
$519$	8.88152	0.389856
$520$	0	0
$521$	33.4240	1.46433	0.732167	−	0.681125i	$-0.238509\pi$
$521$	33.4240	1.46433	0.732167	+	0.681125i	$0.238509\pi$
$522$	−0.647042	−0.0283202
$523$	6.05442	0.264741	0.132371	−	0.991200i	$-0.457741\pi$
$523$	6.05442	0.264741	0.132371	+	0.991200i	$0.457741\pi$
$524$	−3.57875	−0.156338
$525$	4.83673	0.211092
$526$	23.7426	1.03523
$527$	27.6794	1.20573
$528$	−4.72704	−0.205718
$529$	9.87570	0.429378
$530$	−0.327867	−0.0142416
$531$	15.0444	0.652870
$532$	−4.94294	−0.214304
$533$	0	0
$534$	9.32298	0.403445
$535$	5.47948	0.236899
$536$	5.97874	0.258242
$537$	−17.7757	−0.767077
$538$	−6.81198	−0.293685
$539$	−4.72704	−0.203608
$540$	0.404061	0.0173880
$541$	−31.8120	−1.36770	−0.683851	−	0.729621i	$-0.739696\pi$
$541$	−31.8120	−1.36770	−0.683851	+	0.729621i	$0.739696\pi$
$542$	−13.3555	−0.573667
$543$	20.2125	0.867403
$544$	4.50459	0.193133
$545$	−5.06466	−0.216946
$546$	0	0
$547$	25.5362	1.09185	0.545926	−	0.837834i	$-0.316178\pi$
$547$	25.5362	1.09185	0.545926	+	0.837834i	$0.316178\pi$
$548$	−3.27155	−0.139754
$549$	2.83178	0.120857
$550$	22.8635	0.974901
$551$	−3.19829	−0.136252
$552$	−5.73373	−0.244044
$553$	8.69273	0.369652
$554$	23.3676	0.992794
$555$	1.78308	0.0756877
$556$	−10.7168	−0.454492
$557$	−8.41516	−0.356562	−0.178281	−	0.983980i	$-0.557054\pi$
$557$	−8.41516	−0.356562	−0.178281	+	0.983980i	$0.557054\pi$
$558$	6.14471	0.260126
$559$	0	0
$560$	−0.404061	−0.0170747
$561$	−21.2934	−0.899007
$562$	1.31057	0.0552830
$563$	−4.82618	−0.203399	−0.101700	−	0.994815i	$-0.532428\pi$
$563$	−4.82618	−0.203399	−0.101700	+	0.994815i	$0.532428\pi$
$564$	6.47213	0.272526
$565$	−7.34426	−0.308975
$566$	−27.0743	−1.13802
$567$	−1.00000	−0.0419961
$568$	14.3974	0.604103
$569$	17.8366	0.747751	0.373876	−	0.927479i	$-0.378029\pi$
$569$	17.8366	0.747751	0.373876	+	0.927479i	$0.378029\pi$
$570$	1.99725	0.0836555
$571$	−3.04959	−0.127621	−0.0638107	−	0.997962i	$-0.520325\pi$
$571$	−3.04959	−0.127621	−0.0638107	+	0.997962i	$0.520325\pi$
$572$	0	0
$573$	−17.5158	−0.731732
$574$	−9.13551	−0.381309
$575$	27.7325	1.15653
$576$	1.00000	0.0416667
$577$	39.2941	1.63583	0.817917	−	0.575336i	$-0.195129\pi$
$577$	39.2941	1.63583	0.817917	+	0.575336i	$0.195129\pi$
$578$	3.29130	0.136900
$579$	19.7673	0.821501
$580$	−0.261444	−0.0108559
$581$	4.51350	0.187251
$582$	6.19694	0.256872
$583$	3.83566	0.158857
$584$	−3.92648	−0.162479
$585$	0	0
$586$	17.1700	0.709286
$587$	1.76826	0.0729840	0.0364920	−	0.999334i	$-0.488382\pi$
$587$	1.76826	0.0729840	0.0364920	+	0.999334i	$0.488382\pi$
$588$	1.00000	0.0412393
$589$	30.3729	1.25150
$590$	6.07884	0.250262
$591$	9.54410	0.392592
$592$	4.41291	0.181369
$593$	23.0287	0.945673	0.472837	−	0.881150i	$-0.343230\pi$
$593$	23.0287	0.945673	0.472837	+	0.881150i	$0.343230\pi$
$594$	−4.72704	−0.193953
$595$	−1.82013	−0.0746179
$596$	1.18034	0.0483486
$597$	5.57473	0.228158
$598$	0	0
$599$	9.68489	0.395714	0.197857	−	0.980231i	$-0.436602\pi$
$599$	9.68489	0.395714	0.197857	+	0.980231i	$0.436602\pi$
$600$	−4.83673	−0.197459
$601$	25.4886	1.03970	0.519850	−	0.854257i	$-0.325988\pi$
$601$	25.4886	1.03970	0.519850	+	0.854257i	$0.325988\pi$
$602$	0.666578	0.0271677
$603$	5.97874	0.243473
$604$	−20.7040	−0.842434
$605$	4.58405	0.186368
$606$	10.7135	0.435205
$607$	15.3612	0.623493	0.311747	−	0.950165i	$-0.399086\pi$
$607$	15.3612	0.623493	0.311747	+	0.950165i	$0.399086\pi$
$608$	4.94294	0.200463
$609$	0.647042	0.0262195
$610$	1.14421	0.0463277
$611$	0	0
$612$	4.50459	0.182087
$613$	−28.4105	−1.14749	−0.573744	−	0.819035i	$-0.694509\pi$
$613$	−28.4105	−1.14749	−0.573744	+	0.819035i	$0.694509\pi$
$614$	−20.6481	−0.833290
$615$	3.69130	0.148848
$616$	4.72704	0.190458
$617$	21.9379	0.883186	0.441593	−	0.897216i	$-0.354414\pi$
$617$	21.9379	0.883186	0.441593	+	0.897216i	$0.354414\pi$
$618$	−1.21750	−0.0489750
$619$	−15.4136	−0.619526	−0.309763	−	0.950814i	$-0.600250\pi$
$619$	−15.4136	−0.619526	−0.309763	+	0.950814i	$0.600250\pi$
$620$	2.48284	0.0997132
$621$	−5.73373	−0.230087
$622$	31.1584	1.24934
$623$	−9.32298	−0.373517
$624$	0	0
$625$	22.5777	0.903107
$626$	−21.2384	−0.848856
$627$	−23.3655	−0.933128
$628$	12.8774	0.513862
$629$	19.8783	0.792601
$630$	−0.404061	−0.0160982
$631$	24.4822	0.974623	0.487311	−	0.873228i	$-0.337978\pi$
$631$	24.4822	0.974623	0.487311	+	0.873228i	$0.337978\pi$
$632$	−8.69273	−0.345778
$633$	15.1334	0.601500
$634$	3.67433	0.145926
$635$	4.54353	0.180305
$636$	−0.811429	−0.0321752
$637$	0	0
$638$	3.05859	0.121091
$639$	14.3974	0.569554
$640$	0.404061	0.0159719
$641$	−17.5668	−0.693848	−0.346924	−	0.937893i	$-0.612774\pi$
$641$	−17.5668	−0.693848	−0.346924	+	0.937893i	$0.612774\pi$
$642$	13.5610	0.535211
$643$	7.41189	0.292297	0.146148	−	0.989263i	$-0.453312\pi$
$643$	7.41189	0.292297	0.146148	+	0.989263i	$0.453312\pi$
$644$	5.73373	0.225941
$645$	−0.269338	−0.0106052
$646$	22.2659	0.876040
$647$	−15.3162	−0.602143	−0.301071	−	0.953602i	$-0.597344\pi$
$647$	−15.3162	−0.602143	−0.301071	+	0.953602i	$0.597344\pi$
$648$	1.00000	0.0392837
$649$	−71.1154	−2.79152
$650$	0	0
$651$	−6.14471	−0.240830
$652$	−21.0202	−0.823215
$653$	1.48147	0.0579746	0.0289873	−	0.999580i	$-0.490772\pi$
$653$	1.48147	0.0579746	0.0289873	+	0.999580i	$0.490772\pi$
$654$	−12.5344	−0.490134
$655$	−1.44603	−0.0565012
$656$	9.13551	0.356682
$657$	−3.92648	−0.153187
$658$	−6.47213	−0.252310
$659$	−31.9552	−1.24480	−0.622399	−	0.782700i	$-0.713842\pi$
$659$	−31.9552	−1.24480	−0.622399	+	0.782700i	$0.713842\pi$
$660$	−1.91001	−0.0743472
$661$	33.7430	1.31245	0.656226	−	0.754564i	$-0.272152\pi$
$661$	33.7430	1.31245	0.656226	+	0.754564i	$0.272152\pi$
$662$	25.6685	0.997634
$663$	0	0
$664$	−4.51350	−0.175158
$665$	−1.99725	−0.0774500
$666$	4.41291	0.170997
$667$	3.70996	0.143650
$668$	13.8944	0.537592
$669$	7.60285	0.293943
$670$	2.41577	0.0933294
$671$	−13.3859	−0.516758
$672$	−1.00000	−0.0385758
$673$	−37.5539	−1.44760	−0.723798	−	0.690011i	$-0.757605\pi$
$673$	−37.5539	−1.44760	−0.723798	+	0.690011i	$0.757605\pi$
$674$	−19.8182	−0.763367
$675$	−4.83673	−0.186166
$676$	0	0
$677$	4.53554	0.174315	0.0871574	−	0.996195i	$-0.472222\pi$
$677$	4.53554	0.174315	0.0871574	+	0.996195i	$0.472222\pi$
$678$	−18.1761	−0.698050
$679$	−6.19694	−0.237817
$680$	1.82013	0.0697987
$681$	0.478747	0.0183456
$682$	−29.0463	−1.11224
$683$	43.7634	1.67456	0.837281	−	0.546773i	$-0.184144\pi$
$683$	43.7634	1.67456	0.837281	+	0.546773i	$0.184144\pi$
$684$	4.94294	0.188998
$685$	−1.32191	−0.0505074
$686$	−1.00000	−0.0381802
$687$	−20.0110	−0.763469
$688$	−0.666578	−0.0254130
$689$	0	0
$690$	−2.31678	−0.0881982
$691$	25.7358	0.979037	0.489518	−	0.871993i	$-0.337173\pi$
$691$	25.7358	0.979037	0.489518	+	0.871993i	$0.337173\pi$
$692$	8.88152	0.337625
$693$	4.72704	0.179566
$694$	−7.05961	−0.267979
$695$	−4.33023	−0.164255
$696$	−0.647042	−0.0245261
$697$	41.1517	1.55873
$698$	−8.96825	−0.339453
$699$	5.45868	0.206466
$700$	4.83673	0.182811
$701$	−10.6876	−0.403664	−0.201832	−	0.979420i	$-0.564689\pi$
$701$	−10.6876	−0.403664	−0.201832	+	0.979420i	$0.564689\pi$
$702$	0	0
$703$	21.8127	0.822683
$704$	−4.72704	−0.178157
$705$	2.61513	0.0984916
$706$	−19.6812	−0.740712
$707$	−10.7135	−0.402922
$708$	15.0444	0.565402
$709$	−33.5571	−1.26026	−0.630132	−	0.776488i	$-0.716999\pi$
$709$	−33.5571	−1.26026	−0.630132	+	0.776488i	$0.716999\pi$
$710$	5.81744	0.218325
$711$	−8.69273	−0.326003
$712$	9.32298	0.349394
$713$	−35.2321	−1.31945
$714$	−4.50459	−0.168580
$715$	0	0
$716$	−17.7757	−0.664308
$717$	6.30483	0.235458
$718$	−32.8782	−1.22700
$719$	34.1548	1.27376	0.636879	−	0.770964i	$-0.280225\pi$
$719$	34.1548	1.27376	0.636879	+	0.770964i	$0.280225\pi$
$720$	0.404061	0.0150585
$721$	1.21750	0.0453420
$722$	5.43264	0.202182
$723$	−2.62771	−0.0977254
$724$	20.2125	0.751193
$725$	3.12957	0.116229
$726$	11.3449	0.421050
$727$	−21.3381	−0.791388	−0.395694	−	0.918383i	$-0.629496\pi$
$727$	−21.3381	−0.791388	−0.395694	+	0.918383i	$0.629496\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.58654	−0.0587204
$731$	−3.00266	−0.111057
$732$	2.83178	0.104665
$733$	27.5592	1.01792	0.508961	−	0.860790i	$-0.330030\pi$
$733$	27.5592	1.01792	0.508961	+	0.860790i	$0.330030\pi$
$734$	−25.2819	−0.933172
$735$	0.404061	0.0149040
$736$	−5.73373	−0.211348
$737$	−28.2617	−1.04103
$738$	9.13551	0.336283
$739$	−31.3875	−1.15461	−0.577304	−	0.816529i	$-0.695895\pi$
$739$	−31.3875	−1.15461	−0.577304	+	0.816529i	$0.695895\pi$
$740$	1.78308	0.0655475
$741$	0	0
$742$	0.811429	0.0297885
$743$	22.8912	0.839797	0.419899	−	0.907571i	$-0.362066\pi$
$743$	22.8912	0.839797	0.419899	+	0.907571i	$0.362066\pi$
$744$	6.14471	0.225276
$745$	0.476929	0.0174733
$746$	11.3971	0.417276
$747$	−4.51350	−0.165140
$748$	−21.2934	−0.778563
$749$	−13.5610	−0.495510
$750$	−3.97464	−0.145133
$751$	18.3810	0.670733	0.335366	−	0.942088i	$-0.391140\pi$
$751$	18.3810	0.670733	0.335366	+	0.942088i	$0.391140\pi$
$752$	6.47213	0.236014
$753$	−25.4341	−0.926868
$754$	0	0
$755$	−8.36568	−0.304458
$756$	−1.00000	−0.0363696
$757$	2.10502	0.0765083	0.0382541	−	0.999268i	$-0.487820\pi$
$757$	2.10502	0.0765083	0.0382541	+	0.999268i	$0.487820\pi$
$758$	−19.2765	−0.700155
$759$	27.1036	0.983799
$760$	1.99725	0.0724478
$761$	29.8044	1.08041	0.540204	−	0.841534i	$-0.318347\pi$
$761$	29.8044	1.08041	0.540204	+	0.841534i	$0.318347\pi$
$762$	11.2447	0.407351
$763$	12.5344	0.453776
$764$	−17.5158	−0.633698
$765$	1.82013	0.0658068
$766$	−14.4663	−0.522688
$767$	0	0
$768$	1.00000	0.0360844
$769$	−8.71023	−0.314099	−0.157049	−	0.987591i	$-0.550198\pi$
$769$	−8.71023	−0.314099	−0.157049	+	0.987591i	$0.550198\pi$
$770$	1.91001	0.0688321
$771$	0.822060	0.0296058
$772$	19.7673	0.711441
$773$	−42.0212	−1.51140	−0.755699	−	0.654920i	$-0.772702\pi$
$773$	−42.0212	−1.51140	−0.755699	+	0.654920i	$0.772702\pi$
$774$	−0.666578	−0.0239596
$775$	−29.7203	−1.06759
$776$	6.19694	0.222457
$777$	−4.41291	−0.158312
$778$	−0.913387	−0.0327465
$779$	45.1563	1.61789
$780$	0	0
$781$	−68.0573	−2.43528
$782$	−25.8281	−0.923611
$783$	−0.647042	−0.0231234
$784$	1.00000	0.0357143
$785$	5.20323	0.185711
$786$	−3.57875	−0.127650
$787$	−33.7001	−1.20128	−0.600639	−	0.799520i	$-0.705087\pi$
$787$	−33.7001	−1.20128	−0.600639	+	0.799520i	$0.705087\pi$
$788$	9.54410	0.339994
$789$	23.7426	0.845258
$790$	−3.51239	−0.124965
$791$	18.1761	0.646269
$792$	−4.72704	−0.167968
$793$	0	0
$794$	33.5036	1.18900
$795$	−0.327867	−0.0116282
$796$	5.57473	0.197591
$797$	19.1578	0.678603	0.339301	−	0.940678i	$-0.389809\pi$
$797$	19.1578	0.678603	0.339301	+	0.940678i	$0.389809\pi$
$798$	−4.94294	−0.174978
$799$	29.1543	1.03140
$800$	−4.83673	−0.171004
$801$	9.32298	0.329411
$802$	−20.0314	−0.707333
$803$	18.5606	0.654991
$804$	5.97874	0.210854
$805$	2.31678	0.0816557
$806$	0	0
$807$	−6.81198	−0.239793
$808$	10.7135	0.376899
$809$	−3.88293	−0.136516	−0.0682582	−	0.997668i	$-0.521744\pi$
$809$	−3.88293	−0.136516	−0.0682582	+	0.997668i	$0.521744\pi$
$810$	0.404061	0.0141973
$811$	−55.8930	−1.96267	−0.981334	−	0.192311i	$-0.938402\pi$
$811$	−55.8930	−1.96267	−0.981334	+	0.192311i	$0.938402\pi$
$812$	0.647042	0.0227067
$813$	−13.3555	−0.468397
$814$	−20.8600	−0.731143
$815$	−8.49345	−0.297513
$816$	4.50459	0.157692
$817$	−3.29485	−0.115272
$818$	12.2787	0.429314
$819$	0	0
$820$	3.69130	0.128906
$821$	−12.0332	−0.419963	−0.209982	−	0.977705i	$-0.567340\pi$
$821$	−12.0332	−0.419963	−0.209982	+	0.977705i	$0.567340\pi$
$822$	−3.27155	−0.114108
$823$	−18.6745	−0.650954	−0.325477	−	0.945550i	$-0.605525\pi$
$823$	−18.6745	−0.650954	−0.325477	+	0.945550i	$0.605525\pi$
$824$	−1.21750	−0.0424136
$825$	22.8635	0.796003
$826$	−15.0444	−0.523461
$827$	55.3970	1.92634	0.963172	−	0.268888i	$-0.0866560\pi$
$827$	55.3970	1.92634	0.963172	+	0.268888i	$0.0866560\pi$
$828$	−5.73373	−0.199261
$829$	−35.7473	−1.24155	−0.620777	−	0.783987i	$-0.713183\pi$
$829$	−35.7473	−1.24155	−0.620777	+	0.783987i	$0.713183\pi$
$830$	−1.82373	−0.0633025
$831$	23.3676	0.810613
$832$	0	0
$833$	4.50459	0.156075
$834$	−10.7168	−0.371091
$835$	5.61420	0.194287
$836$	−23.3655	−0.808112
$837$	6.14471	0.212392
$838$	−9.98508	−0.344929
$839$	−0.500765	−0.0172883	−0.00864417	−	0.999963i	$-0.502752\pi$
$839$	−0.500765	−0.0172883	−0.00864417	+	0.999963i	$0.502752\pi$
$840$	−0.404061	−0.0139414
$841$	−28.5813	−0.985563
$842$	−12.1776	−0.419666
$843$	1.31057	0.0451384
$844$	15.1334	0.520914
$845$	0	0
$846$	6.47213	0.222516
$847$	−11.3449	−0.389817
$848$	−0.811429	−0.0278646
$849$	−27.0743	−0.929187
$850$	−21.7875	−0.747305
$851$	−25.3024	−0.867356
$852$	14.3974	0.493248
$853$	−24.2025	−0.828677	−0.414338	−	0.910123i	$-0.635987\pi$
$853$	−24.2025	−0.828677	−0.414338	+	0.910123i	$0.635987\pi$
$854$	−2.83178	−0.0969014
$855$	1.99725	0.0683044
$856$	13.5610	0.463507
$857$	−41.5477	−1.41924	−0.709621	−	0.704583i	$-0.751134\pi$
$857$	−41.5477	−1.41924	−0.709621	+	0.704583i	$0.751134\pi$
$858$	0	0
$859$	4.09866	0.139845	0.0699223	−	0.997552i	$-0.477725\pi$
$859$	4.09866	0.139845	0.0699223	+	0.997552i	$0.477725\pi$
$860$	−0.269338	−0.00918435
$861$	−9.13551	−0.311337
$862$	−30.1287	−1.02619
$863$	−40.4001	−1.37523	−0.687617	−	0.726074i	$-0.741343\pi$
$863$	−40.4001	−1.37523	−0.687617	+	0.726074i	$0.741343\pi$
$864$	1.00000	0.0340207
$865$	3.58868	0.122019
$866$	26.4737	0.899614
$867$	3.29130	0.111778
$868$	−6.14471	−0.208565
$869$	41.0909	1.39391
$870$	−0.261444	−0.00886379
$871$	0	0
$872$	−12.5344	−0.424468
$873$	6.19694	0.209735
$874$	−28.3415	−0.958665
$875$	3.97464	0.134367
$876$	−3.92648	−0.132663
$877$	38.1960	1.28979	0.644893	−	0.764273i	$-0.276902\pi$
$877$	38.1960	1.28979	0.644893	+	0.764273i	$0.276902\pi$
$878$	−34.7765	−1.17365
$879$	17.1700	0.579130
$880$	−1.91001	−0.0643865
$881$	27.4214	0.923850	0.461925	−	0.886919i	$-0.347159\pi$
$881$	27.4214	0.923850	0.461925	+	0.886919i	$0.347159\pi$
$882$	1.00000	0.0336718
$883$	−32.2272	−1.08453	−0.542266	−	0.840207i	$-0.682433\pi$
$883$	−32.2272	−1.08453	−0.542266	+	0.840207i	$0.682433\pi$
$884$	0	0
$885$	6.07884	0.204338
$886$	−8.91795	−0.299604
$887$	−53.7465	−1.80463	−0.902316	−	0.431075i	$-0.858134\pi$
$887$	−53.7465	−1.80463	−0.902316	+	0.431075i	$0.858134\pi$
$888$	4.41291	0.148088
$889$	−11.2447	−0.377134
$890$	3.76705	0.126272
$891$	−4.72704	−0.158362
$892$	7.60285	0.254562
$893$	31.9913	1.07055
$894$	1.18034	0.0394765
$895$	−7.18245	−0.240083
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0313	0.601712
$899$	−3.97589	−0.132603
$900$	−4.83673	−0.161224
$901$	−3.65515	−0.121771
$902$	−43.1839	−1.43787
$903$	0.666578	0.0221823
$904$	−18.1761	−0.604529
$905$	8.16710	0.271483
$906$	−20.7040	−0.687845
$907$	−41.6640	−1.38343	−0.691715	−	0.722171i	$-0.743145\pi$
$907$	−41.6640	−1.38343	−0.691715	+	0.722171i	$0.743145\pi$
$908$	0.478747	0.0158878
$909$	10.7135	0.355343
$910$	0	0
$911$	−4.42098	−0.146474	−0.0732368	−	0.997315i	$-0.523333\pi$
$911$	−4.42098	−0.146474	−0.0732368	+	0.997315i	$0.523333\pi$
$912$	4.94294	0.163677
$913$	21.3355	0.706102
$914$	18.9373	0.626390
$915$	1.14421	0.0378264
$916$	−20.0110	−0.661183
$917$	3.57875	0.118181
$918$	4.50459	0.148674
$919$	48.0655	1.58553	0.792767	−	0.609525i	$-0.208640\pi$
$919$	48.0655	1.58553	0.792767	+	0.609525i	$0.208640\pi$
$920$	−2.31678	−0.0763819
$921$	−20.6481	−0.680379
$922$	6.51876	0.214684
$923$	0	0
$924$	4.72704	0.155508
$925$	−21.3441	−0.701789
$926$	13.1560	0.432332
$927$	−1.21750	−0.0399879
$928$	−0.647042	−0.0212402
$929$	−43.3028	−1.42072	−0.710359	−	0.703840i	$-0.751467\pi$
$929$	−43.3028	−1.42072	−0.710359	+	0.703840i	$0.751467\pi$
$930$	2.48284	0.0814155
$931$	4.94294	0.161998
$932$	5.45868	0.178805
$933$	31.1584	1.02008
$934$	2.00592	0.0656358
$935$	−8.60382	−0.281375
$936$	0	0
$937$	24.1899	0.790249	0.395124	−	0.918628i	$-0.370701\pi$
$937$	24.1899	0.790249	0.395124	+	0.918628i	$0.370701\pi$
$938$	−5.97874	−0.195213
$939$	−21.2384	−0.693088
$940$	2.61513	0.0852962
$941$	41.3649	1.34846	0.674228	−	0.738523i	$-0.264476\pi$
$941$	41.3649	1.34846	0.674228	+	0.738523i	$0.264476\pi$
$942$	12.8774	0.419567
$943$	−52.3806	−1.70575
$944$	15.0444	0.489653
$945$	−0.404061	−0.0131441
$946$	3.15094	0.102446
$947$	−36.8712	−1.19815	−0.599076	−	0.800692i	$-0.704465\pi$
$947$	−36.8712	−1.19815	−0.599076	+	0.800692i	$0.704465\pi$
$948$	−8.69273	−0.282327
$949$	0	0
$950$	−23.9077	−0.775668
$951$	3.67433	0.119148
$952$	−4.50459	−0.145994
$953$	−4.43358	−0.143618	−0.0718089	−	0.997418i	$-0.522877\pi$
$953$	−4.43358	−0.143618	−0.0718089	+	0.997418i	$0.522877\pi$
$954$	−0.811429	−0.0262710
$955$	−7.07743	−0.229020
$956$	6.30483	0.203913
$957$	3.05859	0.0988703
$958$	12.1195	0.391564
$959$	3.27155	0.105644
$960$	0.404061	0.0130410
$961$	6.75750	0.217984
$962$	0	0
$963$	13.5610	0.436998
$964$	−2.62771	−0.0846327
$965$	7.98719	0.257117
$966$	5.73373	0.184480
$967$	−20.5363	−0.660403	−0.330201	−	0.943911i	$-0.607117\pi$
$967$	−20.5363	−0.660403	−0.330201	+	0.943911i	$0.607117\pi$
$968$	11.3449	0.364640
$969$	22.2659	0.715284
$970$	2.50394	0.0803967
$971$	−18.4314	−0.591492	−0.295746	−	0.955267i	$-0.595568\pi$
$971$	−18.4314	−0.591492	−0.295746	+	0.955267i	$0.595568\pi$
$972$	1.00000	0.0320750
$973$	10.7168	0.343564
$974$	−43.1568	−1.38283
$975$	0	0
$976$	2.83178	0.0906429
$977$	−33.6168	−1.07550	−0.537749	−	0.843105i	$-0.680725\pi$
$977$	−33.6168	−1.07550	−0.537749	+	0.843105i	$0.680725\pi$
$978$	−21.0202	−0.672153
$979$	−44.0701	−1.40849
$980$	0.404061	0.0129072
$981$	−12.5344	−0.400193
$982$	16.5276	0.527417
$983$	7.35152	0.234477	0.117239	−	0.993104i	$-0.462596\pi$
$983$	7.35152	0.234477	0.117239	+	0.993104i	$0.462596\pi$
$984$	9.13551	0.291229
$985$	3.85640	0.122875
$986$	−2.91466	−0.0928215
$987$	−6.47213	−0.206010
$988$	0	0
$989$	3.82198	0.121532
$990$	−1.91001	−0.0607042
$991$	34.1050	1.08338	0.541691	−	0.840578i	$-0.317784\pi$
$991$	34.1050	1.08338	0.541691	+	0.840578i	$0.317784\pi$
$992$	6.14471	0.195095
$993$	25.6685	0.814565
$994$	−14.3974	−0.456659
$995$	2.25253	0.0714100
$996$	−4.51350	−0.143016
$997$	3.62122	0.114685	0.0573425	−	0.998355i	$-0.481737\pi$
$997$	3.62122	0.114685	0.0573425	+	0.998355i	$0.481737\pi$
$998$	−15.6585	−0.495662
$999$	4.41291	0.139618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cu.1.3	yes	6
13.12	even	2		7098.2.a.cq.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cq.1.4	✓	6	13.12	even	2
7098.2.a.cu.1.3	yes	6	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.404061 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.404061 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.404061 q^{10} -4.72704 q^{11} +1.00000 q^{12} -1.00000 q^{14} +0.404061 q^{15} +1.00000 q^{16} +4.50459 q^{17} +1.00000 q^{18} +4.94294 q^{19} +0.404061 q^{20} -1.00000 q^{21} -4.72704 q^{22} -5.73373 q^{23} +1.00000 q^{24} -4.83673 q^{25} +1.00000 q^{27} -1.00000 q^{28} -0.647042 q^{29} +0.404061 q^{30} +6.14471 q^{31} +1.00000 q^{32} -4.72704 q^{33} +4.50459 q^{34} -0.404061 q^{35} +1.00000 q^{36} +4.41291 q^{37} +4.94294 q^{38} +0.404061 q^{40} +9.13551 q^{41} -1.00000 q^{42} -0.666578 q^{43} -4.72704 q^{44} +0.404061 q^{45} -5.73373 q^{46} +6.47213 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.83673 q^{50} +4.50459 q^{51} -0.811429 q^{53} +1.00000 q^{54} -1.91001 q^{55} -1.00000 q^{56} +4.94294 q^{57} -0.647042 q^{58} +15.0444 q^{59} +0.404061 q^{60} +2.83178 q^{61} +6.14471 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.72704 q^{66} +5.97874 q^{67} +4.50459 q^{68} -5.73373 q^{69} -0.404061 q^{70} +14.3974 q^{71} +1.00000 q^{72} -3.92648 q^{73} +4.41291 q^{74} -4.83673 q^{75} +4.94294 q^{76} +4.72704 q^{77} -8.69273 q^{79} +0.404061 q^{80} +1.00000 q^{81} +9.13551 q^{82} -4.51350 q^{83} -1.00000 q^{84} +1.82013 q^{85} -0.666578 q^{86} -0.647042 q^{87} -4.72704 q^{88} +9.32298 q^{89} +0.404061 q^{90} -5.73373 q^{92} +6.14471 q^{93} +6.47213 q^{94} +1.99725 q^{95} +1.00000 q^{96} +6.19694 q^{97} +1.00000 q^{98} -4.72704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 10 q^{11} + 6 q^{12} - 6 q^{14} + 9 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} + 2 q^{19} + 9 q^{20} - 6 q^{21} + 10 q^{22} + 6 q^{24} + 9 q^{25} + 6 q^{27} - 6 q^{28} - 4 q^{29} + 9 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 4 q^{34} - 9 q^{35} + 6 q^{36} + 9 q^{37} + 2 q^{38} + 9 q^{40} + 25 q^{41} - 6 q^{42} + 19 q^{43} + 10 q^{44} + 9 q^{45} + 21 q^{47} + 6 q^{48} + 6 q^{49} + 9 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 21 q^{55} - 6 q^{56} + 2 q^{57} - 4 q^{58} + 20 q^{59} + 9 q^{60} + 3 q^{61} + 9 q^{62} - 6 q^{63} + 6 q^{64} + 10 q^{66} + 24 q^{67} + 4 q^{68} - 9 q^{70} + 13 q^{71} + 6 q^{72} - 9 q^{73} + 9 q^{74} + 9 q^{75} + 2 q^{76} - 10 q^{77} + 28 q^{79} + 9 q^{80} + 6 q^{81} + 25 q^{82} + 15 q^{83} - 6 q^{84} + 17 q^{85} + 19 q^{86} - 4 q^{87} + 10 q^{88} + 11 q^{89} + 9 q^{90} + 9 q^{93} + 21 q^{94} + 6 q^{96} + 2 q^{97} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 9 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 10 * q^11 + 6 * q^12 - 6 * q^14 + 9 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 + 2 * q^19 + 9 * q^20 - 6 * q^21 + 10 * q^22 + 6 * q^24 + 9 * q^25 + 6 * q^27 - 6 * q^28 - 4 * q^29 + 9 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 4 * q^34 - 9 * q^35 + 6 * q^36 + 9 * q^37 + 2 * q^38 + 9 * q^40 + 25 * q^41 - 6 * q^42 + 19 * q^43 + 10 * q^44 + 9 * q^45 + 21 * q^47 + 6 * q^48 + 6 * q^49 + 9 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 21 * q^55 - 6 * q^56 + 2 * q^57 - 4 * q^58 + 20 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 6 * q^63 + 6 * q^64 + 10 * q^66 + 24 * q^67 + 4 * q^68 - 9 * q^70 + 13 * q^71 + 6 * q^72 - 9 * q^73 + 9 * q^74 + 9 * q^75 + 2 * q^76 - 10 * q^77 + 28 * q^79 + 9 * q^80 + 6 * q^81 + 25 * q^82 + 15 * q^83 - 6 * q^84 + 17 * q^85 + 19 * q^86 - 4 * q^87 + 10 * q^88 + 11 * q^89 + 9 * q^90 + 9 * q^93 + 21 * q^94 + 6 * q^96 + 2 * q^97 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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