LMFDB - Embedded newform 7098.2.a.cf.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:	$3$
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			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.24698 q^{10} +1.30798 q^{11} +1.00000 q^{12} -1.00000 q^{14} +2.24698 q^{15} +1.00000 q^{16} +4.93900 q^{17} -1.00000 q^{18} +1.08815 q^{19} +2.24698 q^{20} +1.00000 q^{21} -1.30798 q^{22} -4.85086 q^{23} -1.00000 q^{24} +0.0489173 q^{25} +1.00000 q^{27} +1.00000 q^{28} +1.04892 q^{29} -2.24698 q^{30} +5.29590 q^{31} -1.00000 q^{32} +1.30798 q^{33} -4.93900 q^{34} +2.24698 q^{35} +1.00000 q^{36} +0.149145 q^{37} -1.08815 q^{38} -2.24698 q^{40} +4.24698 q^{41} -1.00000 q^{42} +3.07069 q^{43} +1.30798 q^{44} +2.24698 q^{45} +4.85086 q^{46} -3.31767 q^{47} +1.00000 q^{48} +1.00000 q^{49} -0.0489173 q^{50} +4.93900 q^{51} -1.29590 q^{53} -1.00000 q^{54} +2.93900 q^{55} -1.00000 q^{56} +1.08815 q^{57} -1.04892 q^{58} +0.862937 q^{59} +2.24698 q^{60} -1.00000 q^{61} -5.29590 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.30798 q^{66} +3.04892 q^{67} +4.93900 q^{68} -4.85086 q^{69} -2.24698 q^{70} +13.2078 q^{71} -1.00000 q^{72} +0.567040 q^{73} -0.149145 q^{74} +0.0489173 q^{75} +1.08815 q^{76} +1.30798 q^{77} -11.0586 q^{79} +2.24698 q^{80} +1.00000 q^{81} -4.24698 q^{82} +1.35152 q^{83} +1.00000 q^{84} +11.0978 q^{85} -3.07069 q^{86} +1.04892 q^{87} -1.30798 q^{88} +7.66487 q^{89} -2.24698 q^{90} -4.85086 q^{92} +5.29590 q^{93} +3.31767 q^{94} +2.44504 q^{95} -1.00000 q^{96} +9.27844 q^{97} -1.00000 q^{98} +1.30798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * 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} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{10} + 9 q^{11} + 3 q^{12} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 5 q^{17} - 3 q^{18} + 7 q^{19} + 2 q^{20} + 3 q^{21} - 9 q^{22} - q^{23} - 3 q^{24} - 9 q^{25} + 3 q^{27} + 3 q^{28} - 6 q^{29} - 2 q^{30} + 2 q^{31} - 3 q^{32} + 9 q^{33} - 5 q^{34} + 2 q^{35} + 3 q^{36} + 14 q^{37} - 7 q^{38} - 2 q^{40} + 8 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} + 2 q^{45} + q^{46} + 7 q^{47} + 3 q^{48} + 3 q^{49} + 9 q^{50} + 5 q^{51} + 10 q^{53} - 3 q^{54} - q^{55} - 3 q^{56} + 7 q^{57} + 6 q^{58} + 8 q^{59} + 2 q^{60} - 3 q^{61} - 2 q^{62} + 3 q^{63} + 3 q^{64} - 9 q^{66} + 5 q^{68} - q^{69} - 2 q^{70} + 22 q^{71} - 3 q^{72} + 21 q^{73} - 14 q^{74} - 9 q^{75} + 7 q^{76} + 9 q^{77} - 2 q^{79} + 2 q^{80} + 3 q^{81} - 8 q^{82} + 3 q^{83} + 3 q^{84} + 15 q^{85} + 3 q^{86} - 6 q^{87} - 9 q^{88} + 24 q^{89} - 2 q^{90} - q^{92} + 2 q^{93} - 7 q^{94} + 7 q^{95} - 3 q^{96} - 2 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^10 + 9 * q^11 + 3 * q^12 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 5 * q^17 - 3 * q^18 + 7 * q^19 + 2 * q^20 + 3 * q^21 - 9 * q^22 - q^23 - 3 * q^24 - 9 * q^25 + 3 * q^27 + 3 * q^28 - 6 * q^29 - 2 * q^30 + 2 * q^31 - 3 * q^32 + 9 * q^33 - 5 * q^34 + 2 * q^35 + 3 * q^36 + 14 * q^37 - 7 * q^38 - 2 * q^40 + 8 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 + 2 * q^45 + q^46 + 7 * q^47 + 3 * q^48 + 3 * q^49 + 9 * q^50 + 5 * q^51 + 10 * q^53 - 3 * q^54 - q^55 - 3 * q^56 + 7 * q^57 + 6 * q^58 + 8 * q^59 + 2 * q^60 - 3 * q^61 - 2 * q^62 + 3 * q^63 + 3 * q^64 - 9 * q^66 + 5 * q^68 - q^69 - 2 * q^70 + 22 * q^71 - 3 * q^72 + 21 * q^73 - 14 * q^74 - 9 * q^75 + 7 * q^76 + 9 * q^77 - 2 * q^79 + 2 * q^80 + 3 * q^81 - 8 * q^82 + 3 * q^83 + 3 * q^84 + 15 * q^85 + 3 * q^86 - 6 * q^87 - 9 * q^88 + 24 * q^89 - 2 * q^90 - q^92 + 2 * q^93 - 7 * q^94 + 7 * q^95 - 3 * q^96 - 2 * q^97 - 3 * q^98 + 9 * 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
$5$	2.24698	1.00488	0.502440	−	0.864612i	$-0.332436\pi$
$5$	2.24698	1.00488	0.502440	+	0.864612i	$0.332436\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.24698	−0.710557
$11$	1.30798	0.394370	0.197185	−	0.980366i	$-0.436820\pi$
$11$	1.30798	0.394370	0.197185	+	0.980366i	$0.436820\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	2.24698	0.580168
$16$	1.00000	0.250000
$17$	4.93900	1.19788	0.598942	−	0.800793i	$-0.295588\pi$
$17$	4.93900	1.19788	0.598942	+	0.800793i	$0.295588\pi$
$18$	−1.00000	−0.235702
$19$	1.08815	0.249638	0.124819	−	0.992180i	$-0.460165\pi$
$19$	1.08815	0.249638	0.124819	+	0.992180i	$0.460165\pi$
$20$	2.24698	0.502440
$21$	1.00000	0.218218
$22$	−1.30798	−0.278862
$23$	−4.85086	−1.01147	−0.505737	−	0.862688i	$-0.668779\pi$
$23$	−4.85086	−1.01147	−0.505737	+	0.862688i	$0.668779\pi$
$24$	−1.00000	−0.204124
$25$	0.0489173	0.00978347
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	1.04892	0.194779	0.0973895	−	0.995246i	$-0.468951\pi$
$29$	1.04892	0.194779	0.0973895	+	0.995246i	$0.468951\pi$
$30$	−2.24698	−0.410240
$31$	5.29590	0.951171	0.475586	−	0.879669i	$-0.342236\pi$
$31$	5.29590	0.951171	0.475586	+	0.879669i	$0.342236\pi$
$32$	−1.00000	−0.176777
$33$	1.30798	0.227690
$34$	−4.93900	−0.847032
$35$	2.24698	0.379809
$36$	1.00000	0.166667
$37$	0.149145	0.0245193	0.0122596	−	0.999925i	$-0.496098\pi$
$37$	0.149145	0.0245193	0.0122596	+	0.999925i	$0.496098\pi$
$38$	−1.08815	−0.176521
$39$	0	0
$40$	−2.24698	−0.355279
$41$	4.24698	0.663267	0.331633	−	0.943408i	$-0.392400\pi$
$41$	4.24698	0.663267	0.331633	+	0.943408i	$0.392400\pi$
$42$	−1.00000	−0.154303
$43$	3.07069	0.468275	0.234138	−	0.972203i	$-0.424773\pi$
$43$	3.07069	0.468275	0.234138	+	0.972203i	$0.424773\pi$
$44$	1.30798	0.197185
$45$	2.24698	0.334960
$46$	4.85086	0.715220
$47$	−3.31767	−0.483931	−0.241966	−	0.970285i	$-0.577792\pi$
$47$	−3.31767	−0.483931	−0.241966	+	0.970285i	$0.577792\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−0.0489173	−0.00691796
$51$	4.93900	0.691598
$52$	0	0
$53$	−1.29590	−0.178005	−0.0890026	−	0.996031i	$-0.528368\pi$
$53$	−1.29590	−0.178005	−0.0890026	+	0.996031i	$0.528368\pi$
$54$	−1.00000	−0.136083
$55$	2.93900	0.396295
$56$	−1.00000	−0.133631
$57$	1.08815	0.144128
$58$	−1.04892	−0.137730
$59$	0.862937	0.112345	0.0561724	−	0.998421i	$-0.482110\pi$
$59$	0.862937	0.112345	0.0561724	+	0.998421i	$0.482110\pi$
$60$	2.24698	0.290084
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−5.29590	−0.672580
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.30798	−0.161001
$67$	3.04892	0.372485	0.186242	−	0.982504i	$-0.440369\pi$
$67$	3.04892	0.372485	0.186242	+	0.982504i	$0.440369\pi$
$68$	4.93900	0.598942
$69$	−4.85086	−0.583974
$70$	−2.24698	−0.268565
$71$	13.2078	1.56747	0.783736	−	0.621094i	$-0.213312\pi$
$71$	13.2078	1.56747	0.783736	+	0.621094i	$0.213312\pi$
$72$	−1.00000	−0.117851
$73$	0.567040	0.0663670	0.0331835	−	0.999449i	$-0.489435\pi$
$73$	0.567040	0.0663670	0.0331835	+	0.999449i	$0.489435\pi$
$74$	−0.149145	−0.0173377
$75$	0.0489173	0.00564849
$76$	1.08815	0.124819
$77$	1.30798	0.149058
$78$	0	0
$79$	−11.0586	−1.24419	−0.622095	−	0.782942i	$-0.713718\pi$
$79$	−11.0586	−1.24419	−0.622095	+	0.782942i	$0.713718\pi$
$80$	2.24698	0.251220
$81$	1.00000	0.111111
$82$	−4.24698	−0.469000
$83$	1.35152	0.148348	0.0741742	−	0.997245i	$-0.476368\pi$
$83$	1.35152	0.148348	0.0741742	+	0.997245i	$0.476368\pi$
$84$	1.00000	0.109109
$85$	11.0978	1.20373
$86$	−3.07069	−0.331121
$87$	1.04892	0.112456
$88$	−1.30798	−0.139431
$89$	7.66487	0.812475	0.406238	−	0.913768i	$-0.366841\pi$
$89$	7.66487	0.812475	0.406238	+	0.913768i	$0.366841\pi$
$90$	−2.24698	−0.236852
$91$	0	0
$92$	−4.85086	−0.505737
$93$	5.29590	0.549159
$94$	3.31767	0.342191
$95$	2.44504	0.250856
$96$	−1.00000	−0.102062
$97$	9.27844	0.942083	0.471041	−	0.882111i	$-0.343878\pi$
$97$	9.27844	0.942083	0.471041	+	0.882111i	$0.343878\pi$
$98$	−1.00000	−0.101015
$99$	1.30798	0.131457
$100$	0.0489173	0.00489173
$101$	−18.1468	−1.80567	−0.902835	−	0.429988i	$-0.858518\pi$
$101$	−18.1468	−1.80567	−0.902835	+	0.429988i	$0.858518\pi$
$102$	−4.93900	−0.489034
$103$	0.515729	0.0508163	0.0254082	−	0.999677i	$-0.491911\pi$
$103$	0.515729	0.0508163	0.0254082	+	0.999677i	$0.491911\pi$
$104$	0	0
$105$	2.24698	0.219283
$106$	1.29590	0.125869
$107$	15.3720	1.48606	0.743032	−	0.669256i	$-0.233387\pi$
$107$	15.3720	1.48606	0.743032	+	0.669256i	$0.233387\pi$
$108$	1.00000	0.0962250
$109$	−3.68664	−0.353117	−0.176558	−	0.984290i	$-0.556496\pi$
$109$	−3.68664	−0.353117	−0.176558	+	0.984290i	$0.556496\pi$
$110$	−2.93900	−0.280223
$111$	0.149145	0.0141562
$112$	1.00000	0.0944911
$113$	−3.24698	−0.305450	−0.152725	−	0.988269i	$-0.548805\pi$
$113$	−3.24698	−0.305450	−0.152725	+	0.988269i	$0.548805\pi$
$114$	−1.08815	−0.101914
$115$	−10.8998	−1.01641
$116$	1.04892	0.0973895
$117$	0	0
$118$	−0.862937	−0.0794398
$119$	4.93900	0.452757
$120$	−2.24698	−0.205120
$121$	−9.28919	−0.844472
$122$	1.00000	0.0905357
$123$	4.24698	0.382937
$124$	5.29590	0.475586
$125$	−11.1250	−0.995049
$126$	−1.00000	−0.0890871
$127$	9.70709	0.861365	0.430682	−	0.902504i	$-0.358273\pi$
$127$	9.70709	0.861365	0.430682	+	0.902504i	$0.358273\pi$
$128$	−1.00000	−0.0883883
$129$	3.07069	0.270359
$130$	0	0
$131$	−6.76271	−0.590861	−0.295430	−	0.955364i	$-0.595463\pi$
$131$	−6.76271	−0.590861	−0.295430	+	0.955364i	$0.595463\pi$
$132$	1.30798	0.113845
$133$	1.08815	0.0943542
$134$	−3.04892	−0.263386
$135$	2.24698	0.193389
$136$	−4.93900	−0.423516
$137$	5.30127	0.452918	0.226459	−	0.974021i	$-0.427285\pi$
$137$	5.30127	0.452918	0.226459	+	0.974021i	$0.427285\pi$
$138$	4.85086	0.412932
$139$	13.4373	1.13973	0.569867	−	0.821737i	$-0.306995\pi$
$139$	13.4373	1.13973	0.569867	+	0.821737i	$0.306995\pi$
$140$	2.24698	0.189904
$141$	−3.31767	−0.279398
$142$	−13.2078	−1.10837
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.35690	0.195730
$146$	−0.567040	−0.0469285
$147$	1.00000	0.0824786
$148$	0.149145	0.0122596
$149$	21.6799	1.77609	0.888045	−	0.459757i	$-0.152063\pi$
$149$	21.6799	1.77609	0.888045	+	0.459757i	$0.152063\pi$
$150$	−0.0489173	−0.00399408
$151$	−1.10023	−0.0895353	−0.0447676	−	0.998997i	$-0.514255\pi$
$151$	−1.10023	−0.0895353	−0.0447676	+	0.998997i	$0.514255\pi$
$152$	−1.08815	−0.0882603
$153$	4.93900	0.399295
$154$	−1.30798	−0.105400
$155$	11.8998	0.955813
$156$	0	0
$157$	−1.94571	−0.155284	−0.0776421	−	0.996981i	$-0.524739\pi$
$157$	−1.94571	−0.155284	−0.0776421	+	0.996981i	$0.524739\pi$
$158$	11.0586	0.879775
$159$	−1.29590	−0.102771
$160$	−2.24698	−0.177639
$161$	−4.85086	−0.382301
$162$	−1.00000	−0.0785674
$163$	14.6799	1.14982	0.574911	−	0.818216i	$-0.305037\pi$
$163$	14.6799	1.14982	0.574911	+	0.818216i	$0.305037\pi$
$164$	4.24698	0.331633
$165$	2.93900	0.228801
$166$	−1.35152	−0.104898
$167$	−11.5743	−0.895649	−0.447824	−	0.894121i	$-0.647801\pi$
$167$	−11.5743	−0.895649	−0.447824	+	0.894121i	$0.647801\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−11.0978	−0.851165
$171$	1.08815	0.0832126
$172$	3.07069	0.234138
$173$	−3.65817	−0.278125	−0.139063	−	0.990284i	$-0.544409\pi$
$173$	−3.65817	−0.278125	−0.139063	+	0.990284i	$0.544409\pi$
$174$	−1.04892	−0.0795182
$175$	0.0489173	0.00369780
$176$	1.30798	0.0985926
$177$	0.862937	0.0648623
$178$	−7.66487	−0.574507
$179$	−2.94571	−0.220172	−0.110086	−	0.993922i	$-0.535113\pi$
$179$	−2.94571	−0.220172	−0.110086	+	0.993922i	$0.535113\pi$
$180$	2.24698	0.167480
$181$	−22.5405	−1.67542	−0.837710	−	0.546115i	$-0.816106\pi$
$181$	−22.5405	−1.67542	−0.837710	+	0.546115i	$0.816106\pi$
$182$	0	0
$183$	−1.00000	−0.0739221
$184$	4.85086	0.357610
$185$	0.335126	0.0246389
$186$	−5.29590	−0.388314
$187$	6.46011	0.472410
$188$	−3.31767	−0.241966
$189$	1.00000	0.0727393
$190$	−2.44504	−0.177382
$191$	−11.1153	−0.804274	−0.402137	−	0.915579i	$-0.631733\pi$
$191$	−11.1153	−0.804274	−0.402137	+	0.915579i	$0.631733\pi$
$192$	1.00000	0.0721688
$193$	−24.9245	−1.79411	−0.897053	−	0.441922i	$-0.854297\pi$
$193$	−24.9245	−1.79411	−0.897053	+	0.441922i	$0.854297\pi$
$194$	−9.27844	−0.666153
$195$	0	0
$196$	1.00000	0.0714286
$197$	27.9269	1.98971	0.994855	−	0.101306i	$-0.0323021\pi$
$197$	27.9269	1.98971	0.994855	+	0.101306i	$0.0323021\pi$
$198$	−1.30798	−0.0929540
$199$	20.2174	1.43318	0.716588	−	0.697497i	$-0.245703\pi$
$199$	20.2174	1.43318	0.716588	+	0.697497i	$0.245703\pi$
$200$	−0.0489173	−0.00345898
$201$	3.04892	0.215054
$202$	18.1468	1.27680
$203$	1.04892	0.0736196
$204$	4.93900	0.345799
$205$	9.54288	0.666503
$206$	−0.515729	−0.0359326
$207$	−4.85086	−0.337158
$208$	0	0
$209$	1.42327	0.0984498
$210$	−2.24698	−0.155056
$211$	−15.3002	−1.05331	−0.526655	−	0.850079i	$-0.676554\pi$
$211$	−15.3002	−1.05331	−0.526655	+	0.850079i	$0.676554\pi$
$212$	−1.29590	−0.0890026
$213$	13.2078	0.904980
$214$	−15.3720	−1.05081
$215$	6.89977	0.470561
$216$	−1.00000	−0.0680414
$217$	5.29590	0.359509
$218$	3.68664	0.249691
$219$	0.567040	0.0383170
$220$	2.93900	0.198147
$221$	0	0
$222$	−0.149145	−0.0100100
$223$	−3.05131	−0.204331	−0.102165	−	0.994767i	$-0.532577\pi$
$223$	−3.05131	−0.204331	−0.102165	+	0.994767i	$0.532577\pi$
$224$	−1.00000	−0.0668153
$225$	0.0489173	0.00326116
$226$	3.24698	0.215986
$227$	19.6843	1.30649	0.653245	−	0.757147i	$-0.273407\pi$
$227$	19.6843	1.30649	0.653245	+	0.757147i	$0.273407\pi$
$228$	1.08815	0.0720642
$229$	20.9909	1.38712	0.693559	−	0.720400i	$-0.256042\pi$
$229$	20.9909	1.38712	0.693559	+	0.720400i	$0.256042\pi$
$230$	10.8998	0.718710
$231$	1.30798	0.0860587
$232$	−1.04892	−0.0688648
$233$	20.2054	1.32370	0.661849	−	0.749638i	$-0.269772\pi$
$233$	20.2054	1.32370	0.661849	+	0.749638i	$0.269772\pi$
$234$	0	0
$235$	−7.45473	−0.486293
$236$	0.862937	0.0561724
$237$	−11.0586	−0.718334
$238$	−4.93900	−0.320148
$239$	5.40821	0.349828	0.174914	−	0.984584i	$-0.444035\pi$
$239$	5.40821	0.349828	0.174914	+	0.984584i	$0.444035\pi$
$240$	2.24698	0.145042
$241$	−13.5405	−0.872219	−0.436110	−	0.899894i	$-0.643644\pi$
$241$	−13.5405	−0.872219	−0.436110	+	0.899894i	$0.643644\pi$
$242$	9.28919	0.597132
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	2.24698	0.143554
$246$	−4.24698	−0.270778
$247$	0	0
$248$	−5.29590	−0.336290
$249$	1.35152	0.0856490
$250$	11.1250	0.703606
$251$	2.61058	0.164778	0.0823892	−	0.996600i	$-0.473745\pi$
$251$	2.61058	0.164778	0.0823892	+	0.996600i	$0.473745\pi$
$252$	1.00000	0.0629941
$253$	−6.34481	−0.398895
$254$	−9.70709	−0.609077
$255$	11.0978	0.694973
$256$	1.00000	0.0625000
$257$	1.53989	0.0960559	0.0480279	−	0.998846i	$-0.484706\pi$
$257$	1.53989	0.0960559	0.0480279	+	0.998846i	$0.484706\pi$
$258$	−3.07069	−0.191173
$259$	0.149145	0.00926741
$260$	0	0
$261$	1.04892	0.0649264
$262$	6.76271	0.417802
$263$	4.06100	0.250412	0.125206	−	0.992131i	$-0.460041\pi$
$263$	4.06100	0.250412	0.125206	+	0.992131i	$0.460041\pi$
$264$	−1.30798	−0.0805005
$265$	−2.91185	−0.178874
$266$	−1.08815	−0.0667185
$267$	7.66487	0.469083
$268$	3.04892	0.186242
$269$	−8.03684	−0.490015	−0.245007	−	0.969521i	$-0.578790\pi$
$269$	−8.03684	−0.490015	−0.245007	+	0.969521i	$0.578790\pi$
$270$	−2.24698	−0.136747
$271$	−16.0543	−0.975229	−0.487614	−	0.873059i	$-0.662133\pi$
$271$	−16.0543	−0.975229	−0.487614	+	0.873059i	$0.662133\pi$
$272$	4.93900	0.299471
$273$	0	0
$274$	−5.30127	−0.320262
$275$	0.0639828	0.00385831
$276$	−4.85086	−0.291987
$277$	−5.83877	−0.350818	−0.175409	−	0.984496i	$-0.556125\pi$
$277$	−5.83877	−0.350818	−0.175409	+	0.984496i	$0.556125\pi$
$278$	−13.4373	−0.805914
$279$	5.29590	0.317057
$280$	−2.24698	−0.134283
$281$	23.0218	1.37336	0.686682	−	0.726958i	$-0.259067\pi$
$281$	23.0218	1.37336	0.686682	+	0.726958i	$0.259067\pi$
$282$	3.31767	0.197564
$283$	4.42327	0.262936	0.131468	−	0.991320i	$-0.458031\pi$
$283$	4.42327	0.262936	0.131468	+	0.991320i	$0.458031\pi$
$284$	13.2078	0.783736
$285$	2.44504	0.144832
$286$	0	0
$287$	4.24698	0.250691
$288$	−1.00000	−0.0589256
$289$	7.39373	0.434925
$290$	−2.35690	−0.138402
$291$	9.27844	0.543912
$292$	0.567040	0.0331835
$293$	−14.4577	−0.844629	−0.422314	−	0.906449i	$-0.638782\pi$
$293$	−14.4577	−0.844629	−0.422314	+	0.906449i	$0.638782\pi$
$294$	−1.00000	−0.0583212
$295$	1.93900	0.112893
$296$	−0.149145	−0.00866887
$297$	1.30798	0.0758966
$298$	−21.6799	−1.25589
$299$	0	0
$300$	0.0489173	0.00282424
$301$	3.07069	0.176991
$302$	1.10023	0.0633110
$303$	−18.1468	−1.04250
$304$	1.08815	0.0624095
$305$	−2.24698	−0.128662
$306$	−4.93900	−0.282344
$307$	−26.1390	−1.49183	−0.745915	−	0.666041i	$-0.767988\pi$
$307$	−26.1390	−1.49183	−0.745915	+	0.666041i	$0.767988\pi$
$308$	1.30798	0.0745290
$309$	0.515729	0.0293388
$310$	−11.8998	−0.675862
$311$	−23.2379	−1.31770	−0.658850	−	0.752275i	$-0.728957\pi$
$311$	−23.2379	−1.31770	−0.658850	+	0.752275i	$0.728957\pi$
$312$	0	0
$313$	−14.7657	−0.834606	−0.417303	−	0.908767i	$-0.637025\pi$
$313$	−14.7657	−0.834606	−0.417303	+	0.908767i	$0.637025\pi$
$314$	1.94571	0.109803
$315$	2.24698	0.126603
$316$	−11.0586	−0.622095
$317$	8.17821	0.459334	0.229667	−	0.973269i	$-0.426236\pi$
$317$	8.17821	0.459334	0.229667	+	0.973269i	$0.426236\pi$
$318$	1.29590	0.0726703
$319$	1.37196	0.0768151
$320$	2.24698	0.125610
$321$	15.3720	0.857979
$322$	4.85086	0.270328
$323$	5.37435	0.299037
$324$	1.00000	0.0555556
$325$	0	0
$326$	−14.6799	−0.813047
$327$	−3.68664	−0.203872
$328$	−4.24698	−0.234500
$329$	−3.31767	−0.182909
$330$	−2.93900	−0.161787
$331$	16.1497	0.887670	0.443835	−	0.896109i	$-0.353618\pi$
$331$	16.1497	0.887670	0.443835	+	0.896109i	$0.353618\pi$
$332$	1.35152	0.0741742
$333$	0.149145	0.00817309
$334$	11.5743	0.633319
$335$	6.85086	0.374302
$336$	1.00000	0.0545545
$337$	−16.9715	−0.924498	−0.462249	−	0.886750i	$-0.652957\pi$
$337$	−16.9715	−0.924498	−0.462249	+	0.886750i	$0.652957\pi$
$338$	0	0
$339$	−3.24698	−0.176352
$340$	11.0978	0.601865
$341$	6.92692	0.375114
$342$	−1.08815	−0.0588402
$343$	1.00000	0.0539949
$344$	−3.07069	−0.165560
$345$	−10.8998	−0.586824
$346$	3.65817	0.196664
$347$	27.1118	1.45544	0.727720	−	0.685875i	$-0.240580\pi$
$347$	27.1118	1.45544	0.727720	+	0.685875i	$0.240580\pi$
$348$	1.04892	0.0562279
$349$	−35.2529	−1.88705	−0.943524	−	0.331306i	$-0.892511\pi$
$349$	−35.2529	−1.88705	−0.943524	+	0.331306i	$0.892511\pi$
$350$	−0.0489173	−0.00261474
$351$	0	0
$352$	−1.30798	−0.0697155
$353$	17.3163	0.921656	0.460828	−	0.887490i	$-0.347553\pi$
$353$	17.3163	0.921656	0.460828	+	0.887490i	$0.347553\pi$
$354$	−0.862937	−0.0458646
$355$	29.6775	1.57512
$356$	7.66487	0.406238
$357$	4.93900	0.261400
$358$	2.94571	0.155685
$359$	−7.06531	−0.372893	−0.186446	−	0.982465i	$-0.559697\pi$
$359$	−7.06531	−0.372893	−0.186446	+	0.982465i	$0.559697\pi$
$360$	−2.24698	−0.118426
$361$	−17.8159	−0.937681
$362$	22.5405	1.18470
$363$	−9.28919	−0.487556
$364$	0	0
$365$	1.27413	0.0666908
$366$	1.00000	0.0522708
$367$	19.8237	1.03479	0.517395	−	0.855747i	$-0.326902\pi$
$367$	19.8237	1.03479	0.517395	+	0.855747i	$0.326902\pi$
$368$	−4.85086	−0.252868
$369$	4.24698	0.221089
$370$	−0.335126	−0.0174224
$371$	−1.29590	−0.0672796
$372$	5.29590	0.274579
$373$	−23.7627	−1.23039	−0.615193	−	0.788376i	$-0.710922\pi$
$373$	−23.7627	−1.23039	−0.615193	+	0.788376i	$0.710922\pi$
$374$	−6.46011	−0.334044
$375$	−11.1250	−0.574492
$376$	3.31767	0.171096
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−6.13706	−0.315240	−0.157620	−	0.987500i	$-0.550382\pi$
$379$	−6.13706	−0.315240	−0.157620	+	0.987500i	$0.550382\pi$
$380$	2.44504	0.125428
$381$	9.70709	0.497309
$382$	11.1153	0.568708
$383$	19.2121	0.981691	0.490845	−	0.871247i	$-0.336688\pi$
$383$	19.2121	0.981691	0.490845	+	0.871247i	$0.336688\pi$
$384$	−1.00000	−0.0510310
$385$	2.93900	0.149785
$386$	24.9245	1.26863
$387$	3.07069	0.156092
$388$	9.27844	0.471041
$389$	−15.5066	−0.786217	−0.393109	−	0.919492i	$-0.628600\pi$
$389$	−15.5066	−0.786217	−0.393109	+	0.919492i	$0.628600\pi$
$390$	0	0
$391$	−23.9584	−1.21163
$392$	−1.00000	−0.0505076
$393$	−6.76271	−0.341134
$394$	−27.9269	−1.40694
$395$	−24.8485	−1.25026
$396$	1.30798	0.0657284
$397$	−36.7211	−1.84298	−0.921489	−	0.388404i	$-0.873027\pi$
$397$	−36.7211	−1.84298	−0.921489	+	0.388404i	$0.873027\pi$
$398$	−20.2174	−1.01341
$399$	1.08815	0.0544754
$400$	0.0489173	0.00244587
$401$	−24.3424	−1.21560	−0.607801	−	0.794089i	$-0.707948\pi$
$401$	−24.3424	−1.21560	−0.607801	+	0.794089i	$0.707948\pi$
$402$	−3.04892	−0.152066
$403$	0	0
$404$	−18.1468	−0.902835
$405$	2.24698	0.111653
$406$	−1.04892	−0.0520569
$407$	0.195078	0.00966968
$408$	−4.93900	−0.244517
$409$	−14.2946	−0.706821	−0.353410	−	0.935468i	$-0.614978\pi$
$409$	−14.2946	−0.706821	−0.353410	+	0.935468i	$0.614978\pi$
$410$	−9.54288	−0.471289
$411$	5.30127	0.261493
$412$	0.515729	0.0254082
$413$	0.862937	0.0424623
$414$	4.85086	0.238407
$415$	3.03684	0.149072
$416$	0	0
$417$	13.4373	0.658026
$418$	−1.42327	−0.0696145
$419$	18.3405	0.895992	0.447996	−	0.894036i	$-0.352138\pi$
$419$	18.3405	0.895992	0.447996	+	0.894036i	$0.352138\pi$
$420$	2.24698	0.109641
$421$	4.78986	0.233443	0.116722	−	0.993165i	$-0.462761\pi$
$421$	4.78986	0.233443	0.116722	+	0.993165i	$0.462761\pi$
$422$	15.3002	0.744803
$423$	−3.31767	−0.161310
$424$	1.29590	0.0629343
$425$	0.241603	0.0117195
$426$	−13.2078	−0.639918
$427$	−1.00000	−0.0483934
$428$	15.3720	0.743032
$429$	0	0
$430$	−6.89977	−0.332737
$431$	−32.5297	−1.56690	−0.783451	−	0.621454i	$-0.786542\pi$
$431$	−32.5297	−1.56690	−0.783451	+	0.621454i	$0.786542\pi$
$432$	1.00000	0.0481125
$433$	25.5230	1.22656	0.613279	−	0.789866i	$-0.289850\pi$
$433$	25.5230	1.22656	0.613279	+	0.789866i	$0.289850\pi$
$434$	−5.29590	−0.254211
$435$	2.35690	0.113005
$436$	−3.68664	−0.176558
$437$	−5.27844	−0.252502
$438$	−0.567040	−0.0270942
$439$	27.8267	1.32810	0.664048	−	0.747690i	$-0.268837\pi$
$439$	27.8267	1.32810	0.664048	+	0.747690i	$0.268837\pi$
$440$	−2.93900	−0.140111
$441$	1.00000	0.0476190
$442$	0	0
$443$	−24.0237	−1.14140	−0.570700	−	0.821159i	$-0.693328\pi$
$443$	−24.0237	−1.14140	−0.570700	+	0.821159i	$0.693328\pi$
$444$	0.149145	0.00707810
$445$	17.2228	0.816440
$446$	3.05131	0.144484
$447$	21.6799	1.02543
$448$	1.00000	0.0472456
$449$	16.8465	0.795038	0.397519	−	0.917594i	$-0.369871\pi$
$449$	16.8465	0.795038	0.397519	+	0.917594i	$0.369871\pi$
$450$	−0.0489173	−0.00230599
$451$	5.55496	0.261573
$452$	−3.24698	−0.152725
$453$	−1.10023	−0.0516932
$454$	−19.6843	−0.923828
$455$	0	0
$456$	−1.08815	−0.0509571
$457$	5.88231	0.275163	0.137582	−	0.990490i	$-0.456067\pi$
$457$	5.88231	0.275163	0.137582	+	0.990490i	$0.456067\pi$
$458$	−20.9909	−0.980840
$459$	4.93900	0.230533
$460$	−10.8998	−0.508205
$461$	29.4282	1.37061	0.685303	−	0.728258i	$-0.259670\pi$
$461$	29.4282	1.37061	0.685303	+	0.728258i	$0.259670\pi$
$462$	−1.30798	−0.0608527
$463$	31.3467	1.45681	0.728403	−	0.685149i	$-0.240263\pi$
$463$	31.3467	1.45681	0.728403	+	0.685149i	$0.240263\pi$
$464$	1.04892	0.0486948
$465$	11.8998	0.551839
$466$	−20.2054	−0.935995
$467$	−32.4010	−1.49934	−0.749670	−	0.661811i	$-0.769788\pi$
$467$	−32.4010	−1.49934	−0.749670	+	0.661811i	$0.769788\pi$
$468$	0	0
$469$	3.04892	0.140786
$470$	7.45473	0.343861
$471$	−1.94571	−0.0896534
$472$	−0.862937	−0.0397199
$473$	4.01639	0.184674
$474$	11.0586	0.507939
$475$	0.0532292	0.00244232
$476$	4.93900	0.226379
$477$	−1.29590	−0.0593350
$478$	−5.40821	−0.247366
$479$	3.92692	0.179426	0.0897128	−	0.995968i	$-0.471405\pi$
$479$	3.92692	0.179426	0.0897128	+	0.995968i	$0.471405\pi$
$480$	−2.24698	−0.102560
$481$	0	0
$482$	13.5405	0.616752
$483$	−4.85086	−0.220722
$484$	−9.28919	−0.422236
$485$	20.8485	0.946680
$486$	−1.00000	−0.0453609
$487$	−36.6631	−1.66136	−0.830681	−	0.556748i	$-0.812049\pi$
$487$	−36.6631	−1.66136	−0.830681	+	0.556748i	$0.812049\pi$
$488$	1.00000	0.0452679
$489$	14.6799	0.663850
$490$	−2.24698	−0.101508
$491$	−19.4416	−0.877386	−0.438693	−	0.898637i	$-0.644559\pi$
$491$	−19.4416	−0.877386	−0.438693	+	0.898637i	$0.644559\pi$
$492$	4.24698	0.191469
$493$	5.18060	0.233323
$494$	0	0
$495$	2.93900	0.132098
$496$	5.29590	0.237793
$497$	13.2078	0.592449
$498$	−1.35152	−0.0605630
$499$	−21.4222	−0.958990	−0.479495	−	0.877545i	$-0.659180\pi$
$499$	−21.4222	−0.958990	−0.479495	+	0.877545i	$0.659180\pi$
$500$	−11.1250	−0.497524
$501$	−11.5743	−0.517103
$502$	−2.61058	−0.116516
$503$	16.5593	0.738341	0.369171	−	0.929362i	$-0.379642\pi$
$503$	16.5593	0.738341	0.369171	+	0.929362i	$0.379642\pi$
$504$	−1.00000	−0.0445435
$505$	−40.7754	−1.81448
$506$	6.34481	0.282061
$507$	0	0
$508$	9.70709	0.430682
$509$	0.287536	0.0127448	0.00637241	−	0.999980i	$-0.497972\pi$
$509$	0.287536	0.0127448	0.00637241	+	0.999980i	$0.497972\pi$
$510$	−11.0978	−0.491420
$511$	0.567040	0.0250844
$512$	−1.00000	−0.0441942
$513$	1.08815	0.0480428
$514$	−1.53989	−0.0679218
$515$	1.15883	0.0510643
$516$	3.07069	0.135179
$517$	−4.33944	−0.190848
$518$	−0.149145	−0.00655305
$519$	−3.65817	−0.160576
$520$	0	0
$521$	35.1497	1.53994	0.769969	−	0.638081i	$-0.220272\pi$
$521$	35.1497	1.53994	0.769969	+	0.638081i	$0.220272\pi$
$522$	−1.04892	−0.0459099
$523$	33.6775	1.47262	0.736308	−	0.676646i	$-0.236567\pi$
$523$	33.6775	1.47262	0.736308	+	0.676646i	$0.236567\pi$
$524$	−6.76271	−0.295430
$525$	0.0489173	0.00213493
$526$	−4.06100	−0.177068
$527$	26.1564	1.13939
$528$	1.30798	0.0569225
$529$	0.530795	0.0230780
$530$	2.91185	0.126483
$531$	0.862937	0.0374483
$532$	1.08815	0.0471771
$533$	0	0
$534$	−7.66487	−0.331692
$535$	34.5405	1.49332
$536$	−3.04892	−0.131693
$537$	−2.94571	−0.127117
$538$	8.03684	0.346493
$539$	1.30798	0.0563386
$540$	2.24698	0.0966946
$541$	−4.48965	−0.193025	−0.0965125	−	0.995332i	$-0.530769\pi$
$541$	−4.48965	−0.193025	−0.0965125	+	0.995332i	$0.530769\pi$
$542$	16.0543	0.689591
$543$	−22.5405	−0.967305
$544$	−4.93900	−0.211758
$545$	−8.28382	−0.354840
$546$	0	0
$547$	−23.8611	−1.02023	−0.510114	−	0.860107i	$-0.670397\pi$
$547$	−23.8611	−1.02023	−0.510114	+	0.860107i	$0.670397\pi$
$548$	5.30127	0.226459
$549$	−1.00000	−0.0426790
$550$	−0.0639828	−0.00272824
$551$	1.14138	0.0486242
$552$	4.85086	0.206466
$553$	−11.0586	−0.470260
$554$	5.83877	0.248066
$555$	0.335126	0.0142253
$556$	13.4373	0.569867
$557$	21.8340	0.925136	0.462568	−	0.886584i	$-0.346928\pi$
$557$	21.8340	0.925136	0.462568	+	0.886584i	$0.346928\pi$
$558$	−5.29590	−0.224193
$559$	0	0
$560$	2.24698	0.0949522
$561$	6.46011	0.272746
$562$	−23.0218	−0.971115
$563$	39.6340	1.67037	0.835187	−	0.549966i	$-0.185359\pi$
$563$	39.6340	1.67037	0.835187	+	0.549966i	$0.185359\pi$
$564$	−3.31767	−0.139699
$565$	−7.29590	−0.306941
$566$	−4.42327	−0.185924
$567$	1.00000	0.0419961
$568$	−13.2078	−0.554185
$569$	−10.8629	−0.455398	−0.227699	−	0.973732i	$-0.573120\pi$
$569$	−10.8629	−0.455398	−0.227699	+	0.973732i	$0.573120\pi$
$570$	−2.44504	−0.102412
$571$	33.3347	1.39501	0.697506	−	0.716579i	$-0.254293\pi$
$571$	33.3347	1.39501	0.697506	+	0.716579i	$0.254293\pi$
$572$	0	0
$573$	−11.1153	−0.464348
$574$	−4.24698	−0.177266
$575$	−0.237291	−0.00989572
$576$	1.00000	0.0416667
$577$	−28.0358	−1.16714	−0.583572	−	0.812061i	$-0.698345\pi$
$577$	−28.0358	−1.16714	−0.583572	+	0.812061i	$0.698345\pi$
$578$	−7.39373	−0.307539
$579$	−24.9245	−1.03583
$580$	2.35690	0.0978648
$581$	1.35152	0.0560705
$582$	−9.27844	−0.384604
$583$	−1.69501	−0.0701999
$584$	−0.567040	−0.0234643
$585$	0	0
$586$	14.4577	0.597243
$587$	−22.1444	−0.913996	−0.456998	−	0.889468i	$-0.651075\pi$
$587$	−22.1444	−0.913996	−0.456998	+	0.889468i	$0.651075\pi$
$588$	1.00000	0.0412393
$589$	5.76271	0.237448
$590$	−1.93900	−0.0798274
$591$	27.9269	1.14876
$592$	0.149145	0.00612982
$593$	19.8804	0.816390	0.408195	−	0.912895i	$-0.366158\pi$
$593$	19.8804	0.816390	0.408195	+	0.912895i	$0.366158\pi$
$594$	−1.30798	−0.0536670
$595$	11.0978	0.454967
$596$	21.6799	0.888045
$597$	20.2174	0.827445
$598$	0	0
$599$	1.89200	0.0773051	0.0386526	−	0.999253i	$-0.487693\pi$
$599$	1.89200	0.0773051	0.0386526	+	0.999253i	$0.487693\pi$
$600$	−0.0489173	−0.00199704
$601$	33.3894	1.36198	0.680991	−	0.732291i	$-0.261549\pi$
$601$	33.3894	1.36198	0.680991	+	0.732291i	$0.261549\pi$
$602$	−3.07069	−0.125152
$603$	3.04892	0.124162
$604$	−1.10023	−0.0447676
$605$	−20.8726	−0.848593
$606$	18.1468	0.737161
$607$	−45.3430	−1.84042	−0.920208	−	0.391430i	$-0.871981\pi$
$607$	−45.3430	−1.84042	−0.920208	+	0.391430i	$0.871981\pi$
$608$	−1.08815	−0.0441301
$609$	1.04892	0.0425043
$610$	2.24698	0.0909775
$611$	0	0
$612$	4.93900	0.199647
$613$	−19.4359	−0.785010	−0.392505	−	0.919750i	$-0.628392\pi$
$613$	−19.4359	−0.785010	−0.392505	+	0.919750i	$0.628392\pi$
$614$	26.1390	1.05488
$615$	9.54288	0.384806
$616$	−1.30798	−0.0527000
$617$	11.8086	0.475398	0.237699	−	0.971339i	$-0.423607\pi$
$617$	11.8086	0.475398	0.237699	+	0.971339i	$0.423607\pi$
$618$	−0.515729	−0.0207457
$619$	−2.94869	−0.118518	−0.0592589	−	0.998243i	$-0.518874\pi$
$619$	−2.94869	−0.118518	−0.0592589	+	0.998243i	$0.518874\pi$
$620$	11.8998	0.477906
$621$	−4.85086	−0.194658
$622$	23.2379	0.931754
$623$	7.66487	0.307087
$624$	0	0
$625$	−25.2422	−1.00969
$626$	14.7657	0.590156
$627$	1.42327	0.0568400
$628$	−1.94571	−0.0776421
$629$	0.736627	0.0293712
$630$	−2.24698	−0.0895218
$631$	49.6467	1.97640	0.988202	−	0.153159i	$-0.0489447\pi$
$631$	49.6467	1.97640	0.988202	+	0.153159i	$0.0489447\pi$
$632$	11.0586	0.439888
$633$	−15.3002	−0.608129
$634$	−8.17821	−0.324798
$635$	21.8116	0.865568
$636$	−1.29590	−0.0513857
$637$	0	0
$638$	−1.37196	−0.0543165
$639$	13.2078	0.522491
$640$	−2.24698	−0.0888197
$641$	18.9963	0.750308	0.375154	−	0.926963i	$-0.377590\pi$
$641$	18.9963	0.750308	0.375154	+	0.926963i	$0.377590\pi$
$642$	−15.3720	−0.606683
$643$	−25.4959	−1.00546	−0.502730	−	0.864444i	$-0.667671\pi$
$643$	−25.4959	−1.00546	−0.502730	+	0.864444i	$0.667671\pi$
$644$	−4.85086	−0.191150
$645$	6.89977	0.271678
$646$	−5.37435	−0.211451
$647$	−26.8896	−1.05714	−0.528570	−	0.848890i	$-0.677272\pi$
$647$	−26.8896	−1.05714	−0.528570	+	0.848890i	$0.677272\pi$
$648$	−1.00000	−0.0392837
$649$	1.12870	0.0443055
$650$	0	0
$651$	5.29590	0.207563
$652$	14.6799	0.574911
$653$	10.8984	0.426489	0.213245	−	0.976999i	$-0.431597\pi$
$653$	10.8984	0.426489	0.213245	+	0.976999i	$0.431597\pi$
$654$	3.68664	0.144159
$655$	−15.1957	−0.593744
$656$	4.24698	0.165817
$657$	0.567040	0.0221223
$658$	3.31767	0.129336
$659$	−0.768086	−0.0299204	−0.0149602	−	0.999888i	$-0.504762\pi$
$659$	−0.768086	−0.0299204	−0.0149602	+	0.999888i	$0.504762\pi$
$660$	2.93900	0.114400
$661$	8.76164	0.340788	0.170394	−	0.985376i	$-0.445496\pi$
$661$	8.76164	0.340788	0.170394	+	0.985376i	$0.445496\pi$
$662$	−16.1497	−0.627677
$663$	0	0
$664$	−1.35152	−0.0524491
$665$	2.44504	0.0948147
$666$	−0.149145	−0.00577925
$667$	−5.08815	−0.197014
$668$	−11.5743	−0.447824
$669$	−3.05131	−0.117970
$670$	−6.85086	−0.264672
$671$	−1.30798	−0.0504940
$672$	−1.00000	−0.0385758
$673$	16.2553	0.626597	0.313299	−	0.949655i	$-0.398566\pi$
$673$	16.2553	0.626597	0.313299	+	0.949655i	$0.398566\pi$
$674$	16.9715	0.653719
$675$	0.0489173	0.00188283
$676$	0	0
$677$	34.0417	1.30833	0.654165	−	0.756352i	$-0.273020\pi$
$677$	34.0417	1.30833	0.654165	+	0.756352i	$0.273020\pi$
$678$	3.24698	0.124700
$679$	9.27844	0.356074
$680$	−11.0978	−0.425583
$681$	19.6843	0.754302
$682$	−6.92692	−0.265245
$683$	15.4077	0.589560	0.294780	−	0.955565i	$-0.404754\pi$
$683$	15.4077	0.589560	0.294780	+	0.955565i	$0.404754\pi$
$684$	1.08815	0.0416063
$685$	11.9119	0.455129
$686$	−1.00000	−0.0381802
$687$	20.9909	0.800853
$688$	3.07069	0.117069
$689$	0	0
$690$	10.8998	0.414947
$691$	−8.10454	−0.308311	−0.154156	−	0.988047i	$-0.549266\pi$
$691$	−8.10454	−0.308311	−0.154156	+	0.988047i	$0.549266\pi$
$692$	−3.65817	−0.139063
$693$	1.30798	0.0496860
$694$	−27.1118	−1.02915
$695$	30.1933	1.14530
$696$	−1.04892	−0.0397591
$697$	20.9758	0.794516
$698$	35.2529	1.33434
$699$	20.2054	0.764237
$700$	0.0489173	0.00184890
$701$	18.6993	0.706263	0.353132	−	0.935574i	$-0.385117\pi$
$701$	18.6993	0.706263	0.353132	+	0.935574i	$0.385117\pi$
$702$	0	0
$703$	0.162291	0.00612094
$704$	1.30798	0.0492963
$705$	−7.45473	−0.280761
$706$	−17.3163	−0.651709
$707$	−18.1468	−0.682479
$708$	0.862937	0.0324311
$709$	−0.575400	−0.0216096	−0.0108048	−	0.999942i	$-0.503439\pi$
$709$	−0.575400	−0.0216096	−0.0108048	+	0.999942i	$0.503439\pi$
$710$	−29.6775	−1.11378
$711$	−11.0586	−0.414730
$712$	−7.66487	−0.287253
$713$	−25.6896	−0.962084
$714$	−4.93900	−0.184837
$715$	0	0
$716$	−2.94571	−0.110086
$717$	5.40821	0.201973
$718$	7.06531	0.263675
$719$	−17.2687	−0.644016	−0.322008	−	0.946737i	$-0.604358\pi$
$719$	−17.2687	−0.644016	−0.322008	+	0.946737i	$0.604358\pi$
$720$	2.24698	0.0837400
$721$	0.515729	0.0192068
$722$	17.8159	0.663041
$723$	−13.5405	−0.503576
$724$	−22.5405	−0.837710
$725$	0.0513102	0.00190561
$726$	9.28919	0.344754
$727$	11.4480	0.424584	0.212292	−	0.977206i	$-0.431907\pi$
$727$	11.4480	0.424584	0.212292	+	0.977206i	$0.431907\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.27413	−0.0471575
$731$	15.1661	0.560940
$732$	−1.00000	−0.0369611
$733$	10.7222	0.396032	0.198016	−	0.980199i	$-0.436550\pi$
$733$	10.7222	0.396032	0.198016	+	0.980199i	$0.436550\pi$
$734$	−19.8237	−0.731706
$735$	2.24698	0.0828811
$736$	4.85086	0.178805
$737$	3.98792	0.146897
$738$	−4.24698	−0.156333
$739$	38.0417	1.39939	0.699694	−	0.714443i	$-0.253320\pi$
$739$	38.0417	1.39939	0.699694	+	0.714443i	$0.253320\pi$
$740$	0.335126	0.0123195
$741$	0	0
$742$	1.29590	0.0475739
$743$	−1.47411	−0.0540798	−0.0270399	−	0.999634i	$-0.508608\pi$
$743$	−1.47411	−0.0540798	−0.0270399	+	0.999634i	$0.508608\pi$
$744$	−5.29590	−0.194157
$745$	48.7144	1.78476
$746$	23.7627	0.870015
$747$	1.35152	0.0494495
$748$	6.46011	0.236205
$749$	15.3720	0.561679
$750$	11.1250	0.406227
$751$	−5.93708	−0.216647	−0.108324	−	0.994116i	$-0.534548\pi$
$751$	−5.93708	−0.216647	−0.108324	+	0.994116i	$0.534548\pi$
$752$	−3.31767	−0.120983
$753$	2.61058	0.0951348
$754$	0	0
$755$	−2.47219	−0.0899722
$756$	1.00000	0.0363696
$757$	19.3123	0.701917	0.350959	−	0.936391i	$-0.385856\pi$
$757$	19.3123	0.701917	0.350959	+	0.936391i	$0.385856\pi$
$758$	6.13706	0.222908
$759$	−6.34481	−0.230302
$760$	−2.44504	−0.0886910
$761$	−15.7060	−0.569343	−0.284671	−	0.958625i	$-0.591884\pi$
$761$	−15.7060	−0.569343	−0.284671	+	0.958625i	$0.591884\pi$
$762$	−9.70709	−0.351651
$763$	−3.68664	−0.133465
$764$	−11.1153	−0.402137
$765$	11.0978	0.401243
$766$	−19.2121	−0.694160
$767$	0	0
$768$	1.00000	0.0360844
$769$	−18.7627	−0.676601	−0.338300	−	0.941038i	$-0.609852\pi$
$769$	−18.7627	−0.676601	−0.338300	+	0.941038i	$0.609852\pi$
$770$	−2.93900	−0.105914
$771$	1.53989	0.0554579
$772$	−24.9245	−0.897053
$773$	−39.9407	−1.43657	−0.718283	−	0.695751i	$-0.755072\pi$
$773$	−39.9407	−1.43657	−0.718283	+	0.695751i	$0.755072\pi$
$774$	−3.07069	−0.110374
$775$	0.259061	0.00930575
$776$	−9.27844	−0.333077
$777$	0.149145	0.00535054
$778$	15.5066	0.555940
$779$	4.62133	0.165576
$780$	0	0
$781$	17.2755	0.618164
$782$	23.9584	0.856750
$783$	1.04892	0.0374852
$784$	1.00000	0.0357143
$785$	−4.37196	−0.156042
$786$	6.76271	0.241218
$787$	9.68724	0.345313	0.172656	−	0.984982i	$-0.444765\pi$
$787$	9.68724	0.345313	0.172656	+	0.984982i	$0.444765\pi$
$788$	27.9269	0.994855
$789$	4.06100	0.144575
$790$	24.8485	0.884069
$791$	−3.24698	−0.115449
$792$	−1.30798	−0.0464770
$793$	0	0
$794$	36.7211	1.30318
$795$	−2.91185	−0.103273
$796$	20.2174	0.716588
$797$	−3.33214	−0.118031	−0.0590153	−	0.998257i	$-0.518796\pi$
$797$	−3.33214	−0.118031	−0.0590153	+	0.998257i	$0.518796\pi$
$798$	−1.08815	−0.0385200
$799$	−16.3860	−0.579694
$800$	−0.0489173	−0.00172949
$801$	7.66487	0.270825
$802$	24.3424	0.859561
$803$	0.741676	0.0261732
$804$	3.04892	0.107527
$805$	−10.8998	−0.384166
$806$	0	0
$807$	−8.03684	−0.282910
$808$	18.1468	0.638401
$809$	6.52243	0.229317	0.114658	−	0.993405i	$-0.463423\pi$
$809$	6.52243	0.229317	0.114658	+	0.993405i	$0.463423\pi$
$810$	−2.24698	−0.0789508
$811$	−25.9051	−0.909653	−0.454826	−	0.890580i	$-0.650299\pi$
$811$	−25.9051	−0.909653	−0.454826	+	0.890580i	$0.650299\pi$
$812$	1.04892	0.0368098
$813$	−16.0543	−0.563049
$814$	−0.195078	−0.00683749
$815$	32.9855	1.15543
$816$	4.93900	0.172900
$817$	3.34136	0.116899
$818$	14.2946	0.499798
$819$	0	0
$820$	9.54288	0.333252
$821$	−26.2610	−0.916515	−0.458257	−	0.888820i	$-0.651526\pi$
$821$	−26.2610	−0.916515	−0.458257	+	0.888820i	$0.651526\pi$
$822$	−5.30127	−0.184903
$823$	13.0747	0.455757	0.227878	−	0.973690i	$-0.426821\pi$
$823$	13.0747	0.455757	0.227878	+	0.973690i	$0.426821\pi$
$824$	−0.515729	−0.0179663
$825$	0.0639828	0.00222760
$826$	−0.862937	−0.0300254
$827$	16.1185	0.560497	0.280248	−	0.959928i	$-0.409583\pi$
$827$	16.1185	0.560497	0.280248	+	0.959928i	$0.409583\pi$
$828$	−4.85086	−0.168579
$829$	39.2355	1.36270	0.681352	−	0.731956i	$-0.261392\pi$
$829$	39.2355	1.36270	0.681352	+	0.731956i	$0.261392\pi$
$830$	−3.03684	−0.105410
$831$	−5.83877	−0.202545
$832$	0	0
$833$	4.93900	0.171126
$834$	−13.4373	−0.465295
$835$	−26.0073	−0.900020
$836$	1.42327	0.0492249
$837$	5.29590	0.183053
$838$	−18.3405	−0.633562
$839$	10.4601	0.361123	0.180562	−	0.983564i	$-0.442209\pi$
$839$	10.4601	0.361123	0.180562	+	0.983564i	$0.442209\pi$
$840$	−2.24698	−0.0775282
$841$	−27.8998	−0.962061
$842$	−4.78986	−0.165069
$843$	23.0218	0.792912
$844$	−15.3002	−0.526655
$845$	0	0
$846$	3.31767	0.114064
$847$	−9.28919	−0.319180
$848$	−1.29590	−0.0445013
$849$	4.42327	0.151806
$850$	−0.241603	−0.00828691
$851$	−0.723480	−0.0248006
$852$	13.2078	0.452490
$853$	−31.3244	−1.07253	−0.536263	−	0.844051i	$-0.680164\pi$
$853$	−31.3244	−1.07253	−0.536263	+	0.844051i	$0.680164\pi$
$854$	1.00000	0.0342193
$855$	2.44504	0.0836187
$856$	−15.3720	−0.525403
$857$	−1.94438	−0.0664187	−0.0332093	−	0.999448i	$-0.510573\pi$
$857$	−1.94438	−0.0664187	−0.0332093	+	0.999448i	$0.510573\pi$
$858$	0	0
$859$	−9.65040	−0.329267	−0.164634	−	0.986355i	$-0.552644\pi$
$859$	−9.65040	−0.329267	−0.164634	+	0.986355i	$0.552644\pi$
$860$	6.89977	0.235280
$861$	4.24698	0.144737
$862$	32.5297	1.10797
$863$	−8.75707	−0.298094	−0.149047	−	0.988830i	$-0.547621\pi$
$863$	−8.75707	−0.298094	−0.149047	+	0.988830i	$0.547621\pi$
$864$	−1.00000	−0.0340207
$865$	−8.21983	−0.279483
$866$	−25.5230	−0.867308
$867$	7.39373	0.251104
$868$	5.29590	0.179754
$869$	−14.4644	−0.490672
$870$	−2.35690	−0.0799063
$871$	0	0
$872$	3.68664	0.124846
$873$	9.27844	0.314028
$874$	5.27844	0.178546
$875$	−11.1250	−0.376093
$876$	0.567040	0.0191585
$877$	−20.0019	−0.675417	−0.337708	−	0.941251i	$-0.609652\pi$
$877$	−20.0019	−0.675417	−0.337708	+	0.941251i	$0.609652\pi$
$878$	−27.8267	−0.939105
$879$	−14.4577	−0.487647
$880$	2.93900	0.0990737
$881$	−19.7138	−0.664175	−0.332087	−	0.943249i	$-0.607753\pi$
$881$	−19.7138	−0.664175	−0.332087	+	0.943249i	$0.607753\pi$
$882$	−1.00000	−0.0336718
$883$	41.6805	1.40266	0.701331	−	0.712836i	$-0.252590\pi$
$883$	41.6805	1.40266	0.701331	+	0.712836i	$0.252590\pi$
$884$	0	0
$885$	1.93900	0.0651788
$886$	24.0237	0.807092
$887$	10.3696	0.348176	0.174088	−	0.984730i	$-0.444302\pi$
$887$	10.3696	0.348176	0.174088	+	0.984730i	$0.444302\pi$
$888$	−0.149145	−0.00500498
$889$	9.70709	0.325565
$890$	−17.2228	−0.577310
$891$	1.30798	0.0438189
$892$	−3.05131	−0.102165
$893$	−3.61011	−0.120808
$894$	−21.6799	−0.725086
$895$	−6.61894	−0.221247
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−16.8465	−0.562176
$899$	5.55496	0.185268
$900$	0.0489173	0.00163058
$901$	−6.40044	−0.213229
$902$	−5.55496	−0.184960
$903$	3.07069	0.102186
$904$	3.24698	0.107993
$905$	−50.6480	−1.68360
$906$	1.10023	0.0365526
$907$	−7.84713	−0.260560	−0.130280	−	0.991477i	$-0.541588\pi$
$907$	−7.84713	−0.260560	−0.130280	+	0.991477i	$0.541588\pi$
$908$	19.6843	0.653245
$909$	−18.1468	−0.601890
$910$	0	0
$911$	53.4523	1.77095	0.885477	−	0.464682i	$-0.153831\pi$
$911$	53.4523	1.77095	0.885477	+	0.464682i	$0.153831\pi$
$912$	1.08815	0.0360321
$913$	1.76776	0.0585042
$914$	−5.88231	−0.194570
$915$	−2.24698	−0.0742829
$916$	20.9909	0.693559
$917$	−6.76271	−0.223324
$918$	−4.93900	−0.163011
$919$	−47.7590	−1.57542	−0.787712	−	0.616044i	$-0.788734\pi$
$919$	−47.7590	−1.57542	−0.787712	+	0.616044i	$0.788734\pi$
$920$	10.8998	0.359355
$921$	−26.1390	−0.861309
$922$	−29.4282	−0.969165
$923$	0	0
$924$	1.30798	0.0430293
$925$	0.00729577	0.000239884 0
$926$	−31.3467	−1.03012
$927$	0.515729	0.0169388
$928$	−1.04892	−0.0344324
$929$	−4.38596	−0.143899	−0.0719494	−	0.997408i	$-0.522922\pi$
$929$	−4.38596	−0.143899	−0.0719494	+	0.997408i	$0.522922\pi$
$930$	−11.8998	−0.390209
$931$	1.08815	0.0356625
$932$	20.2054	0.661849
$933$	−23.2379	−0.760774
$934$	32.4010	1.06019
$935$	14.5157	0.474715
$936$	0	0
$937$	−11.2030	−0.365985	−0.182992	−	0.983114i	$-0.558578\pi$
$937$	−11.2030	−0.365985	−0.182992	+	0.983114i	$0.558578\pi$
$938$	−3.04892	−0.0995507
$939$	−14.7657	−0.481860
$940$	−7.45473	−0.243147
$941$	−4.96987	−0.162013	−0.0810065	−	0.996714i	$-0.525813\pi$
$941$	−4.96987	−0.162013	−0.0810065	+	0.996714i	$0.525813\pi$
$942$	1.94571	0.0633945
$943$	−20.6015	−0.670877
$944$	0.862937	0.0280862
$945$	2.24698	0.0730943
$946$	−4.01639	−0.130584
$947$	7.48965	0.243381	0.121690	−	0.992568i	$-0.461168\pi$
$947$	7.48965	0.243381	0.121690	+	0.992568i	$0.461168\pi$
$948$	−11.0586	−0.359167
$949$	0	0
$950$	−0.0532292	−0.00172698
$951$	8.17821	0.265197
$952$	−4.93900	−0.160074
$953$	4.58019	0.148367	0.0741834	−	0.997245i	$-0.476365\pi$
$953$	4.58019	0.148367	0.0741834	+	0.997245i	$0.476365\pi$
$954$	1.29590	0.0419562
$955$	−24.9758	−0.808199
$956$	5.40821	0.174914
$957$	1.37196	0.0443492
$958$	−3.92692	−0.126873
$959$	5.30127	0.171187
$960$	2.24698	0.0725210
$961$	−2.95348	−0.0952734
$962$	0	0
$963$	15.3720	0.495355
$964$	−13.5405	−0.436110
$965$	−56.0049	−1.80286
$966$	4.85086	0.156074
$967$	46.6069	1.49878	0.749388	−	0.662131i	$-0.230348\pi$
$967$	46.6069	1.49878	0.749388	+	0.662131i	$0.230348\pi$
$968$	9.28919	0.298566
$969$	5.37435	0.172649
$970$	−20.8485	−0.669404
$971$	15.7493	0.505419	0.252710	−	0.967542i	$-0.418678\pi$
$971$	15.7493	0.505419	0.252710	+	0.967542i	$0.418678\pi$
$972$	1.00000	0.0320750
$973$	13.4373	0.430779
$974$	36.6631	1.17476
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	−50.7488	−1.62360	−0.811799	−	0.583936i	$-0.801512\pi$
$977$	−50.7488	−1.62360	−0.811799	+	0.583936i	$0.801512\pi$
$978$	−14.6799	−0.469413
$979$	10.0255	0.320416
$980$	2.24698	0.0717771
$981$	−3.68664	−0.117706
$982$	19.4416	0.620406
$983$	−5.93123	−0.189177	−0.0945885	−	0.995516i	$-0.530154\pi$
$983$	−5.93123	−0.189177	−0.0945885	+	0.995516i	$0.530154\pi$
$984$	−4.24698	−0.135389
$985$	62.7512	1.99942
$986$	−5.18060	−0.164984
$987$	−3.31767	−0.105603
$988$	0	0
$989$	−14.8955	−0.473648
$990$	−2.93900	−0.0934076
$991$	42.0484	1.33571	0.667856	−	0.744290i	$-0.267212\pi$
$991$	42.0484	1.33571	0.667856	+	0.744290i	$0.267212\pi$
$992$	−5.29590	−0.168145
$993$	16.1497	0.512496
$994$	−13.2078	−0.418924
$995$	45.4282	1.44017
$996$	1.35152	0.0428245
$997$	−6.53511	−0.206969	−0.103484	−	0.994631i	$-0.532999\pi$
$997$	−6.53511	−0.206969	−0.103484	+	0.994631i	$0.532999\pi$
$998$	21.4222	0.678108
$999$	0.149145	0.00471874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cf.1.3	✓	3
13.12	even	2		7098.2.a.cm.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cf.1.3	✓	3	1.1	even	1	trivial
7098.2.a.cm.1.1	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.24698 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.24698 q^{10} +1.30798 q^{11} +1.00000 q^{12} -1.00000 q^{14} +2.24698 q^{15} +1.00000 q^{16} +4.93900 q^{17} -1.00000 q^{18} +1.08815 q^{19} +2.24698 q^{20} +1.00000 q^{21} -1.30798 q^{22} -4.85086 q^{23} -1.00000 q^{24} +0.0489173 q^{25} +1.00000 q^{27} +1.00000 q^{28} +1.04892 q^{29} -2.24698 q^{30} +5.29590 q^{31} -1.00000 q^{32} +1.30798 q^{33} -4.93900 q^{34} +2.24698 q^{35} +1.00000 q^{36} +0.149145 q^{37} -1.08815 q^{38} -2.24698 q^{40} +4.24698 q^{41} -1.00000 q^{42} +3.07069 q^{43} +1.30798 q^{44} +2.24698 q^{45} +4.85086 q^{46} -3.31767 q^{47} +1.00000 q^{48} +1.00000 q^{49} -0.0489173 q^{50} +4.93900 q^{51} -1.29590 q^{53} -1.00000 q^{54} +2.93900 q^{55} -1.00000 q^{56} +1.08815 q^{57} -1.04892 q^{58} +0.862937 q^{59} +2.24698 q^{60} -1.00000 q^{61} -5.29590 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.30798 q^{66} +3.04892 q^{67} +4.93900 q^{68} -4.85086 q^{69} -2.24698 q^{70} +13.2078 q^{71} -1.00000 q^{72} +0.567040 q^{73} -0.149145 q^{74} +0.0489173 q^{75} +1.08815 q^{76} +1.30798 q^{77} -11.0586 q^{79} +2.24698 q^{80} +1.00000 q^{81} -4.24698 q^{82} +1.35152 q^{83} +1.00000 q^{84} +11.0978 q^{85} -3.07069 q^{86} +1.04892 q^{87} -1.30798 q^{88} +7.66487 q^{89} -2.24698 q^{90} -4.85086 q^{92} +5.29590 q^{93} +3.31767 q^{94} +2.44504 q^{95} -1.00000 q^{96} +9.27844 q^{97} -1.00000 q^{98} +1.30798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{10} + 9 q^{11} + 3 q^{12} - 3 q^{14} + 2 q^{15} + 3 q^{16} + 5 q^{17} - 3 q^{18} + 7 q^{19} + 2 q^{20} + 3 q^{21} - 9 q^{22} - q^{23} - 3 q^{24} - 9 q^{25} + 3 q^{27} + 3 q^{28} - 6 q^{29} - 2 q^{30} + 2 q^{31} - 3 q^{32} + 9 q^{33} - 5 q^{34} + 2 q^{35} + 3 q^{36} + 14 q^{37} - 7 q^{38} - 2 q^{40} + 8 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} + 2 q^{45} + q^{46} + 7 q^{47} + 3 q^{48} + 3 q^{49} + 9 q^{50} + 5 q^{51} + 10 q^{53} - 3 q^{54} - q^{55} - 3 q^{56} + 7 q^{57} + 6 q^{58} + 8 q^{59} + 2 q^{60} - 3 q^{61} - 2 q^{62} + 3 q^{63} + 3 q^{64} - 9 q^{66} + 5 q^{68} - q^{69} - 2 q^{70} + 22 q^{71} - 3 q^{72} + 21 q^{73} - 14 q^{74} - 9 q^{75} + 7 q^{76} + 9 q^{77} - 2 q^{79} + 2 q^{80} + 3 q^{81} - 8 q^{82} + 3 q^{83} + 3 q^{84} + 15 q^{85} + 3 q^{86} - 6 q^{87} - 9 q^{88} + 24 q^{89} - 2 q^{90} - q^{92} + 2 q^{93} - 7 q^{94} + 7 q^{95} - 3 q^{96} - 2 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^10 + 9 * q^11 + 3 * q^12 - 3 * q^14 + 2 * q^15 + 3 * q^16 + 5 * q^17 - 3 * q^18 + 7 * q^19 + 2 * q^20 + 3 * q^21 - 9 * q^22 - q^23 - 3 * q^24 - 9 * q^25 + 3 * q^27 + 3 * q^28 - 6 * q^29 - 2 * q^30 + 2 * q^31 - 3 * q^32 + 9 * q^33 - 5 * q^34 + 2 * q^35 + 3 * q^36 + 14 * q^37 - 7 * q^38 - 2 * q^40 + 8 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 + 2 * q^45 + q^46 + 7 * q^47 + 3 * q^48 + 3 * q^49 + 9 * q^50 + 5 * q^51 + 10 * q^53 - 3 * q^54 - q^55 - 3 * q^56 + 7 * q^57 + 6 * q^58 + 8 * q^59 + 2 * q^60 - 3 * q^61 - 2 * q^62 + 3 * q^63 + 3 * q^64 - 9 * q^66 + 5 * q^68 - q^69 - 2 * q^70 + 22 * q^71 - 3 * q^72 + 21 * q^73 - 14 * q^74 - 9 * q^75 + 7 * q^76 + 9 * q^77 - 2 * q^79 + 2 * q^80 + 3 * q^81 - 8 * q^82 + 3 * q^83 + 3 * q^84 + 15 * q^85 + 3 * q^86 - 6 * q^87 - 9 * q^88 + 24 * q^89 - 2 * q^90 - q^92 + 2 * q^93 - 7 * q^94 + 7 * q^95 - 3 * q^96 - 2 * q^97 - 3 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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