LMFDB - Embedded newform 6018.2.a.z.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.25177$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25177 q^{5} -1.00000 q^{6} +3.43625 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25177 q^{5} -1.00000 q^{6} +3.43625 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.25177 q^{10} +4.91732 q^{11} -1.00000 q^{12} +2.89360 q^{13} +3.43625 q^{14} -2.25177 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.29000 q^{19} +2.25177 q^{20} -3.43625 q^{21} +4.91732 q^{22} +1.07849 q^{23} -1.00000 q^{24} +0.0704795 q^{25} +2.89360 q^{26} -1.00000 q^{27} +3.43625 q^{28} -8.07398 q^{29} -2.25177 q^{30} +10.0273 q^{31} +1.00000 q^{32} -4.91732 q^{33} -1.00000 q^{34} +7.73765 q^{35} +1.00000 q^{36} +7.39960 q^{37} +1.29000 q^{38} -2.89360 q^{39} +2.25177 q^{40} +1.23543 q^{41} -3.43625 q^{42} -4.17635 q^{43} +4.91732 q^{44} +2.25177 q^{45} +1.07849 q^{46} +3.20590 q^{47} -1.00000 q^{48} +4.80781 q^{49} +0.0704795 q^{50} +1.00000 q^{51} +2.89360 q^{52} -2.85700 q^{53} -1.00000 q^{54} +11.0727 q^{55} +3.43625 q^{56} -1.29000 q^{57} -8.07398 q^{58} -1.00000 q^{59} -2.25177 q^{60} -6.05401 q^{61} +10.0273 q^{62} +3.43625 q^{63} +1.00000 q^{64} +6.51572 q^{65} -4.91732 q^{66} +10.5272 q^{67} -1.00000 q^{68} -1.07849 q^{69} +7.73765 q^{70} -13.1964 q^{71} +1.00000 q^{72} -14.6327 q^{73} +7.39960 q^{74} -0.0704795 q^{75} +1.29000 q^{76} +16.8971 q^{77} -2.89360 q^{78} -5.54705 q^{79} +2.25177 q^{80} +1.00000 q^{81} +1.23543 q^{82} -5.30666 q^{83} -3.43625 q^{84} -2.25177 q^{85} -4.17635 q^{86} +8.07398 q^{87} +4.91732 q^{88} -18.4885 q^{89} +2.25177 q^{90} +9.94312 q^{91} +1.07849 q^{92} -10.0273 q^{93} +3.20590 q^{94} +2.90478 q^{95} -1.00000 q^{96} +3.65116 q^{97} +4.80781 q^{98} +4.91732 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * 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
$5$	2.25177	1.00702	0.503512	−	0.863988i	$-0.332041\pi$
$5$	2.25177	1.00702	0.503512	+	0.863988i	$0.332041\pi$
$6$	−1.00000	−0.408248
$7$	3.43625	1.29878	0.649390	−	0.760455i	$-0.275024\pi$
$7$	3.43625	1.29878	0.649390	+	0.760455i	$0.275024\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.25177	0.712073
$11$	4.91732	1.48263	0.741314	−	0.671158i	$-0.234203\pi$
$11$	4.91732	1.48263	0.741314	+	0.671158i	$0.234203\pi$
$12$	−1.00000	−0.288675
$13$	2.89360	0.802539	0.401270	−	0.915960i	$-0.368569\pi$
$13$	2.89360	0.802539	0.401270	+	0.915960i	$0.368569\pi$
$14$	3.43625	0.918376
$15$	−2.25177	−0.581405
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	1.29000	0.295946	0.147973	−	0.988991i	$-0.452725\pi$
$19$	1.29000	0.295946	0.147973	+	0.988991i	$0.452725\pi$
$20$	2.25177	0.503512
$21$	−3.43625	−0.749851
$22$	4.91732	1.04838
$23$	1.07849	0.224881	0.112440	−	0.993658i	$-0.464133\pi$
$23$	1.07849	0.224881	0.112440	+	0.993658i	$0.464133\pi$
$24$	−1.00000	−0.204124
$25$	0.0704795	0.0140959
$26$	2.89360	0.567481
$27$	−1.00000	−0.192450
$28$	3.43625	0.649390
$29$	−8.07398	−1.49930	−0.749650	−	0.661834i	$-0.769778\pi$
$29$	−8.07398	−1.49930	−0.749650	+	0.661834i	$0.769778\pi$
$30$	−2.25177	−0.411116
$31$	10.0273	1.80096	0.900479	−	0.434900i	$-0.143216\pi$
$31$	10.0273	1.80096	0.900479	+	0.434900i	$0.143216\pi$
$32$	1.00000	0.176777
$33$	−4.91732	−0.855996
$34$	−1.00000	−0.171499
$35$	7.73765	1.30790
$36$	1.00000	0.166667
$37$	7.39960	1.21649	0.608244	−	0.793750i	$-0.291874\pi$
$37$	7.39960	1.21649	0.608244	+	0.793750i	$0.291874\pi$
$38$	1.29000	0.209265
$39$	−2.89360	−0.463346
$40$	2.25177	0.356036
$41$	1.23543	0.192942	0.0964709	−	0.995336i	$-0.469245\pi$
$41$	1.23543	0.192942	0.0964709	+	0.995336i	$0.469245\pi$
$42$	−3.43625	−0.530225
$43$	−4.17635	−0.636887	−0.318443	−	0.947942i	$-0.603160\pi$
$43$	−4.17635	−0.636887	−0.318443	+	0.947942i	$0.603160\pi$
$44$	4.91732	0.741314
$45$	2.25177	0.335674
$46$	1.07849	0.159015
$47$	3.20590	0.467629	0.233815	−	0.972281i	$-0.424879\pi$
$47$	3.20590	0.467629	0.233815	+	0.972281i	$0.424879\pi$
$48$	−1.00000	−0.144338
$49$	4.80781	0.686830
$50$	0.0704795	0.00996731
$51$	1.00000	0.140028
$52$	2.89360	0.401270
$53$	−2.85700	−0.392440	−0.196220	−	0.980560i	$-0.562867\pi$
$53$	−2.85700	−0.392440	−0.196220	+	0.980560i	$0.562867\pi$
$54$	−1.00000	−0.136083
$55$	11.0727	1.49304
$56$	3.43625	0.459188
$57$	−1.29000	−0.170864
$58$	−8.07398	−1.06017
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.25177	−0.290703
$61$	−6.05401	−0.775136	−0.387568	−	0.921841i	$-0.626685\pi$
$61$	−6.05401	−0.775136	−0.387568	+	0.921841i	$0.626685\pi$
$62$	10.0273	1.27347
$63$	3.43625	0.432927
$64$	1.00000	0.125000
$65$	6.51572	0.808176
$66$	−4.91732	−0.605280
$67$	10.5272	1.28611	0.643054	−	0.765821i	$-0.277667\pi$
$67$	10.5272	1.28611	0.643054	+	0.765821i	$0.277667\pi$
$68$	−1.00000	−0.121268
$69$	−1.07849	−0.129835
$70$	7.73765	0.924826
$71$	−13.1964	−1.56612	−0.783062	−	0.621943i	$-0.786343\pi$
$71$	−13.1964	−1.56612	−0.783062	+	0.621943i	$0.786343\pi$
$72$	1.00000	0.117851
$73$	−14.6327	−1.71263	−0.856313	−	0.516458i	$-0.827250\pi$
$73$	−14.6327	−1.71263	−0.856313	+	0.516458i	$0.827250\pi$
$74$	7.39960	0.860186
$75$	−0.0704795	−0.00813827
$76$	1.29000	0.147973
$77$	16.8971	1.92561
$78$	−2.89360	−0.327635
$79$	−5.54705	−0.624092	−0.312046	−	0.950067i	$-0.601014\pi$
$79$	−5.54705	−0.624092	−0.312046	+	0.950067i	$0.601014\pi$
$80$	2.25177	0.251756
$81$	1.00000	0.111111
$82$	1.23543	0.136430
$83$	−5.30666	−0.582482	−0.291241	−	0.956650i	$-0.594068\pi$
$83$	−5.30666	−0.582482	−0.291241	+	0.956650i	$0.594068\pi$
$84$	−3.43625	−0.374926
$85$	−2.25177	−0.244239
$86$	−4.17635	−0.450347
$87$	8.07398	0.865621
$88$	4.91732	0.524188
$89$	−18.4885	−1.95978	−0.979889	−	0.199542i	$-0.936054\pi$
$89$	−18.4885	−1.95978	−0.979889	+	0.199542i	$0.936054\pi$
$90$	2.25177	0.237358
$91$	9.94312	1.04232
$92$	1.07849	0.112440
$93$	−10.0273	−1.03978
$94$	3.20590	0.330664
$95$	2.90478	0.298024
$96$	−1.00000	−0.102062
$97$	3.65116	0.370719	0.185360	−	0.982671i	$-0.440655\pi$
$97$	3.65116	0.370719	0.185360	+	0.982671i	$0.440655\pi$
$98$	4.80781	0.485662
$99$	4.91732	0.494209
$100$	0.0704795	0.00704795
$101$	12.0938	1.20338	0.601690	−	0.798730i	$-0.294494\pi$
$101$	12.0938	1.20338	0.601690	+	0.798730i	$0.294494\pi$
$102$	1.00000	0.0990148
$103$	−10.6829	−1.05262	−0.526311	−	0.850292i	$-0.676425\pi$
$103$	−10.6829	−1.05262	−0.526311	+	0.850292i	$0.676425\pi$
$104$	2.89360	0.283741
$105$	−7.73765	−0.755118
$106$	−2.85700	−0.277497
$107$	−15.5802	−1.50620	−0.753099	−	0.657908i	$-0.771442\pi$
$107$	−15.5802	−1.50620	−0.753099	+	0.657908i	$0.771442\pi$
$108$	−1.00000	−0.0962250
$109$	−8.68560	−0.831930	−0.415965	−	0.909381i	$-0.636556\pi$
$109$	−8.68560	−0.831930	−0.415965	+	0.909381i	$0.636556\pi$
$110$	11.0727	1.05574
$111$	−7.39960	−0.702339
$112$	3.43625	0.324695
$113$	4.52074	0.425276	0.212638	−	0.977131i	$-0.431795\pi$
$113$	4.52074	0.425276	0.212638	+	0.977131i	$0.431795\pi$
$114$	−1.29000	−0.120819
$115$	2.42852	0.226460
$116$	−8.07398	−0.749650
$117$	2.89360	0.267513
$118$	−1.00000	−0.0920575
$119$	−3.43625	−0.315000
$120$	−2.25177	−0.205558
$121$	13.1800	1.19819
$122$	−6.05401	−0.548104
$123$	−1.23543	−0.111395
$124$	10.0273	0.900479
$125$	−11.1002	−0.992828
$126$	3.43625	0.306125
$127$	−9.37239	−0.831666	−0.415833	−	0.909441i	$-0.636510\pi$
$127$	−9.37239	−0.831666	−0.415833	+	0.909441i	$0.636510\pi$
$128$	1.00000	0.0883883
$129$	4.17635	0.367707
$130$	6.51572	0.571467
$131$	−0.789909	−0.0690147	−0.0345073	−	0.999404i	$-0.510986\pi$
$131$	−0.789909	−0.0690147	−0.0345073	+	0.999404i	$0.510986\pi$
$132$	−4.91732	−0.427998
$133$	4.43275	0.384368
$134$	10.5272	0.909415
$135$	−2.25177	−0.193802
$136$	−1.00000	−0.0857493
$137$	3.05258	0.260800	0.130400	−	0.991461i	$-0.458374\pi$
$137$	3.05258	0.260800	0.130400	+	0.991461i	$0.458374\pi$
$138$	−1.07849	−0.0918073
$139$	−21.5220	−1.82547	−0.912737	−	0.408547i	$-0.866036\pi$
$139$	−21.5220	−1.82547	−0.912737	+	0.408547i	$0.866036\pi$
$140$	7.73765	0.653951
$141$	−3.20590	−0.269986
$142$	−13.1964	−1.10742
$143$	14.2287	1.18987
$144$	1.00000	0.0833333
$145$	−18.1808	−1.50983
$146$	−14.6327	−1.21101
$147$	−4.80781	−0.396542
$148$	7.39960	0.608244
$149$	−7.84479	−0.642671	−0.321335	−	0.946965i	$-0.604132\pi$
$149$	−7.84479	−0.642671	−0.321335	+	0.946965i	$0.604132\pi$
$150$	−0.0704795	−0.00575463
$151$	17.9093	1.45744	0.728719	−	0.684813i	$-0.240116\pi$
$151$	17.9093	1.45744	0.728719	+	0.684813i	$0.240116\pi$
$152$	1.29000	0.104633
$153$	−1.00000	−0.0808452
$154$	16.8971	1.36161
$155$	22.5792	1.81361
$156$	−2.89360	−0.231673
$157$	−4.20712	−0.335764	−0.167882	−	0.985807i	$-0.553693\pi$
$157$	−4.20712	−0.335764	−0.167882	+	0.985807i	$0.553693\pi$
$158$	−5.54705	−0.441300
$159$	2.85700	0.226575
$160$	2.25177	0.178018
$161$	3.70596	0.292071
$162$	1.00000	0.0785674
$163$	−23.3656	−1.83014	−0.915069	−	0.403297i	$-0.867864\pi$
$163$	−23.3656	−1.83014	−0.915069	+	0.403297i	$0.867864\pi$
$164$	1.23543	0.0964709
$165$	−11.0727	−0.862008
$166$	−5.30666	−0.411877
$167$	6.58591	0.509633	0.254817	−	0.966989i	$-0.417985\pi$
$167$	6.58591	0.509633	0.254817	+	0.966989i	$0.417985\pi$
$168$	−3.43625	−0.265112
$169$	−4.62710	−0.355931
$170$	−2.25177	−0.172703
$171$	1.29000	0.0986486
$172$	−4.17635	−0.318443
$173$	−4.65230	−0.353708	−0.176854	−	0.984237i	$-0.556592\pi$
$173$	−4.65230	−0.353708	−0.176854	+	0.984237i	$0.556592\pi$
$174$	8.07398	0.612087
$175$	0.242185	0.0183075
$176$	4.91732	0.370657
$177$	1.00000	0.0751646
$178$	−18.4885	−1.38577
$179$	17.8952	1.33755	0.668775	−	0.743465i	$-0.266819\pi$
$179$	17.8952	1.33755	0.668775	+	0.743465i	$0.266819\pi$
$180$	2.25177	0.167837
$181$	19.4991	1.44935	0.724677	−	0.689089i	$-0.241989\pi$
$181$	19.4991	1.44935	0.724677	+	0.689089i	$0.241989\pi$
$182$	9.94312	0.737033
$183$	6.05401	0.447525
$184$	1.07849	0.0795074
$185$	16.6622	1.22503
$186$	−10.0273	−0.735238
$187$	−4.91732	−0.359590
$188$	3.20590	0.233815
$189$	−3.43625	−0.249950
$190$	2.90478	0.210735
$191$	1.52133	0.110080	0.0550398	−	0.998484i	$-0.482471\pi$
$191$	1.52133	0.110080	0.0550398	+	0.998484i	$0.482471\pi$
$192$	−1.00000	−0.0721688
$193$	−5.82567	−0.419341	−0.209670	−	0.977772i	$-0.567239\pi$
$193$	−5.82567	−0.419341	−0.209670	+	0.977772i	$0.567239\pi$
$194$	3.65116	0.262138
$195$	−6.51572	−0.466601
$196$	4.80781	0.343415
$197$	−0.559432	−0.0398579	−0.0199289	−	0.999801i	$-0.506344\pi$
$197$	−0.559432	−0.0398579	−0.0199289	+	0.999801i	$0.506344\pi$
$198$	4.91732	0.349459
$199$	4.53257	0.321305	0.160653	−	0.987011i	$-0.448640\pi$
$199$	4.53257	0.321305	0.160653	+	0.987011i	$0.448640\pi$
$200$	0.0704795	0.00498365
$201$	−10.5272	−0.742535
$202$	12.0938	0.850918
$203$	−27.7442	−1.94726
$204$	1.00000	0.0700140
$205$	2.78191	0.194297
$206$	−10.6829	−0.744316
$207$	1.07849	0.0749603
$208$	2.89360	0.200635
$209$	6.34333	0.438777
$210$	−7.73765	−0.533949
$211$	7.51348	0.517249	0.258625	−	0.965978i	$-0.416731\pi$
$211$	7.51348	0.517249	0.258625	+	0.965978i	$0.416731\pi$
$212$	−2.85700	−0.196220
$213$	13.1964	0.904202
$214$	−15.5802	−1.06504
$215$	−9.40418	−0.641360
$216$	−1.00000	−0.0680414
$217$	34.4563	2.33905
$218$	−8.68560	−0.588263
$219$	14.6327	0.988785
$220$	11.0727	0.746520
$221$	−2.89360	−0.194644
$222$	−7.39960	−0.496629
$223$	−14.5486	−0.974244	−0.487122	−	0.873334i	$-0.661953\pi$
$223$	−14.5486	−0.974244	−0.487122	+	0.873334i	$0.661953\pi$
$224$	3.43625	0.229594
$225$	0.0704795	0.00469863
$226$	4.52074	0.300715
$227$	−9.87142	−0.655189	−0.327595	−	0.944818i	$-0.606238\pi$
$227$	−9.87142	−0.655189	−0.327595	+	0.944818i	$0.606238\pi$
$228$	−1.29000	−0.0854322
$229$	13.5895	0.898020	0.449010	−	0.893527i	$-0.351777\pi$
$229$	13.5895	0.898020	0.449010	+	0.893527i	$0.351777\pi$
$230$	2.42852	0.160132
$231$	−16.8971	−1.11175
$232$	−8.07398	−0.530083
$233$	5.12489	0.335743	0.167871	−	0.985809i	$-0.446311\pi$
$233$	5.12489	0.335743	0.167871	+	0.985809i	$0.446311\pi$
$234$	2.89360	0.189160
$235$	7.21897	0.470913
$236$	−1.00000	−0.0650945
$237$	5.54705	0.360320
$238$	−3.43625	−0.222739
$239$	10.2564	0.663434	0.331717	−	0.943379i	$-0.392372\pi$
$239$	10.2564	0.663434	0.331717	+	0.943379i	$0.392372\pi$
$240$	−2.25177	−0.145351
$241$	25.0013	1.61047	0.805237	−	0.592953i	$-0.202038\pi$
$241$	25.0013	1.61047	0.805237	+	0.592953i	$0.202038\pi$
$242$	13.1800	0.847245
$243$	−1.00000	−0.0641500
$244$	−6.05401	−0.387568
$245$	10.8261	0.691654
$246$	−1.23543	−0.0787682
$247$	3.73273	0.237508
$248$	10.0273	0.636735
$249$	5.30666	0.336296
$250$	−11.1002	−0.702036
$251$	−25.0032	−1.57819	−0.789095	−	0.614271i	$-0.789450\pi$
$251$	−25.0032	−1.57819	−0.789095	+	0.614271i	$0.789450\pi$
$252$	3.43625	0.216463
$253$	5.30329	0.333415
$254$	−9.37239	−0.588076
$255$	2.25177	0.141011
$256$	1.00000	0.0625000
$257$	−8.89567	−0.554897	−0.277448	−	0.960741i	$-0.589489\pi$
$257$	−8.89567	−0.554897	−0.277448	+	0.960741i	$0.589489\pi$
$258$	4.17635	0.260008
$259$	25.4269	1.57995
$260$	6.51572	0.404088
$261$	−8.07398	−0.499767
$262$	−0.789909	−0.0488007
$263$	4.79106	0.295429	0.147715	−	0.989030i	$-0.452808\pi$
$263$	4.79106	0.295429	0.147715	+	0.989030i	$0.452808\pi$
$264$	−4.91732	−0.302640
$265$	−6.43332	−0.395196
$266$	4.43275	0.271790
$267$	18.4885	1.13148
$268$	10.5272	0.643054
$269$	7.99401	0.487403	0.243702	−	0.969850i	$-0.421638\pi$
$269$	7.99401	0.487403	0.243702	+	0.969850i	$0.421638\pi$
$270$	−2.25177	−0.137039
$271$	5.33695	0.324197	0.162098	−	0.986775i	$-0.448174\pi$
$271$	5.33695	0.324197	0.162098	+	0.986775i	$0.448174\pi$
$272$	−1.00000	−0.0606339
$273$	−9.94312	−0.601785
$274$	3.05258	0.184413
$275$	0.346570	0.0208990
$276$	−1.07849	−0.0649175
$277$	−4.66444	−0.280259	−0.140130	−	0.990133i	$-0.544752\pi$
$277$	−4.66444	−0.280259	−0.140130	+	0.990133i	$0.544752\pi$
$278$	−21.5220	−1.29081
$279$	10.0273	0.600319
$280$	7.73765	0.462413
$281$	10.8964	0.650023	0.325011	−	0.945710i	$-0.394632\pi$
$281$	10.8964	0.650023	0.325011	+	0.945710i	$0.394632\pi$
$282$	−3.20590	−0.190909
$283$	27.3503	1.62581	0.812903	−	0.582400i	$-0.197886\pi$
$283$	27.3503	1.62581	0.812903	+	0.582400i	$0.197886\pi$
$284$	−13.1964	−0.783062
$285$	−2.90478	−0.172064
$286$	14.2287	0.841363
$287$	4.24525	0.250589
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−18.1808	−1.06761
$291$	−3.65116	−0.214035
$292$	−14.6327	−0.856313
$293$	−1.19975	−0.0700902	−0.0350451	−	0.999386i	$-0.511157\pi$
$293$	−1.19975	−0.0700902	−0.0350451	+	0.999386i	$0.511157\pi$
$294$	−4.80781	−0.280397
$295$	−2.25177	−0.131103
$296$	7.39960	0.430093
$297$	−4.91732	−0.285332
$298$	−7.84479	−0.454437
$299$	3.12072	0.180476
$300$	−0.0704795	−0.00406914
$301$	−14.3510	−0.827176
$302$	17.9093	1.03056
$303$	−12.0938	−0.694772
$304$	1.29000	0.0739864
$305$	−13.6322	−0.780580
$306$	−1.00000	−0.0571662
$307$	−14.9413	−0.852747	−0.426374	−	0.904547i	$-0.640209\pi$
$307$	−14.9413	−0.852747	−0.426374	+	0.904547i	$0.640209\pi$
$308$	16.8971	0.962804
$309$	10.6829	0.607731
$310$	22.5792	1.28241
$311$	17.4896	0.991743	0.495871	−	0.868396i	$-0.334849\pi$
$311$	17.4896	0.991743	0.495871	+	0.868396i	$0.334849\pi$
$312$	−2.89360	−0.163818
$313$	10.8682	0.614308	0.307154	−	0.951660i	$-0.400623\pi$
$313$	10.8682	0.614308	0.307154	+	0.951660i	$0.400623\pi$
$314$	−4.20712	−0.237421
$315$	7.73765	0.435967
$316$	−5.54705	−0.312046
$317$	21.5281	1.20914	0.604570	−	0.796552i	$-0.293345\pi$
$317$	21.5281	1.20914	0.604570	+	0.796552i	$0.293345\pi$
$318$	2.85700	0.160213
$319$	−39.7023	−2.22290
$320$	2.25177	0.125878
$321$	15.5802	0.869603
$322$	3.70596	0.206525
$323$	−1.29000	−0.0717774
$324$	1.00000	0.0555556
$325$	0.203939	0.0113125
$326$	−23.3656	−1.29410
$327$	8.68560	0.480315
$328$	1.23543	0.0682152
$329$	11.0163	0.607347
$330$	−11.0727	−0.609531
$331$	28.7881	1.58234	0.791168	−	0.611599i	$-0.209473\pi$
$331$	28.7881	1.58234	0.791168	+	0.611599i	$0.209473\pi$
$332$	−5.30666	−0.291241
$333$	7.39960	0.405496
$334$	6.58591	0.360365
$335$	23.7050	1.29514
$336$	−3.43625	−0.187463
$337$	8.50860	0.463493	0.231747	−	0.972776i	$-0.425556\pi$
$337$	8.50860	0.463493	0.231747	+	0.972776i	$0.425556\pi$
$338$	−4.62710	−0.251681
$339$	−4.52074	−0.245533
$340$	−2.25177	−0.122120
$341$	49.3075	2.67015
$342$	1.29000	0.0697551
$343$	−7.53291	−0.406739
$344$	−4.17635	−0.225174
$345$	−2.42852	−0.130747
$346$	−4.65230	−0.250109
$347$	−6.07353	−0.326044	−0.163022	−	0.986622i	$-0.552124\pi$
$347$	−6.07353	−0.326044	−0.163022	+	0.986622i	$0.552124\pi$
$348$	8.07398	0.432811
$349$	14.2666	0.763675	0.381838	−	0.924229i	$-0.375291\pi$
$349$	14.2666	0.763675	0.381838	+	0.924229i	$0.375291\pi$
$350$	0.242185	0.0129453
$351$	−2.89360	−0.154449
$352$	4.91732	0.262094
$353$	11.9338	0.635172	0.317586	−	0.948229i	$-0.397128\pi$
$353$	11.9338	0.635172	0.317586	+	0.948229i	$0.397128\pi$
$354$	1.00000	0.0531494
$355$	−29.7153	−1.57712
$356$	−18.4885	−0.979889
$357$	3.43625	0.181866
$358$	17.8952	0.945791
$359$	−30.9383	−1.63286	−0.816430	−	0.577445i	$-0.804050\pi$
$359$	−30.9383	−1.63286	−0.816430	+	0.577445i	$0.804050\pi$
$360$	2.25177	0.118679
$361$	−17.3359	−0.912416
$362$	19.4991	1.02485
$363$	−13.1800	−0.691773
$364$	9.94312	0.521161
$365$	−32.9495	−1.72465
$366$	6.05401	0.316448
$367$	7.43176	0.387935	0.193967	−	0.981008i	$-0.437864\pi$
$367$	7.43176	0.387935	0.193967	+	0.981008i	$0.437864\pi$
$368$	1.07849	0.0562202
$369$	1.23543	0.0643139
$370$	16.6622	0.866228
$371$	−9.81738	−0.509693
$372$	−10.0273	−0.519892
$373$	32.9334	1.70523	0.852613	−	0.522544i	$-0.175017\pi$
$373$	32.9334	1.70523	0.852613	+	0.522544i	$0.175017\pi$
$374$	−4.91732	−0.254269
$375$	11.1002	0.573210
$376$	3.20590	0.165332
$377$	−23.3628	−1.20325
$378$	−3.43625	−0.176742
$379$	−35.6006	−1.82868	−0.914339	−	0.404950i	$-0.867289\pi$
$379$	−35.6006	−1.82868	−0.914339	+	0.404950i	$0.867289\pi$
$380$	2.90478	0.149012
$381$	9.37239	0.480162
$382$	1.52133	0.0778381
$383$	−5.07334	−0.259236	−0.129618	−	0.991564i	$-0.541375\pi$
$383$	−5.07334	−0.259236	−0.129618	+	0.991564i	$0.541375\pi$
$384$	−1.00000	−0.0510310
$385$	38.0485	1.93913
$386$	−5.82567	−0.296519
$387$	−4.17635	−0.212296
$388$	3.65116	0.185360
$389$	−26.7190	−1.35470	−0.677352	−	0.735659i	$-0.736873\pi$
$389$	−26.7190	−1.35470	−0.677352	+	0.735659i	$0.736873\pi$
$390$	−6.51572	−0.329936
$391$	−1.07849	−0.0545416
$392$	4.80781	0.242831
$393$	0.789909	0.0398456
$394$	−0.559432	−0.0281838
$395$	−12.4907	−0.628475
$396$	4.91732	0.247105
$397$	27.1614	1.36319	0.681596	−	0.731728i	$-0.261286\pi$
$397$	27.1614	1.36319	0.681596	+	0.731728i	$0.261286\pi$
$398$	4.53257	0.227197
$399$	−4.43275	−0.221915
$400$	0.0704795	0.00352397
$401$	0.0278209	0.00138931	0.000694654	−	1.00000i	$-0.499779\pi$
$401$	0.0278209	0.00138931	0.000694654		1.00000i	$0.499779\pi$
$402$	−10.5272	−0.525051
$403$	29.0150	1.44534
$404$	12.0938	0.601690
$405$	2.25177	0.111891
$406$	−27.7442	−1.37692
$407$	36.3862	1.80360
$408$	1.00000	0.0495074
$409$	7.43141	0.367459	0.183730	−	0.982977i	$-0.441183\pi$
$409$	7.43141	0.367459	0.183730	+	0.982977i	$0.441183\pi$
$410$	2.78191	0.137389
$411$	−3.05258	−0.150573
$412$	−10.6829	−0.526311
$413$	−3.43625	−0.169087
$414$	1.07849	0.0530050
$415$	−11.9494	−0.586573
$416$	2.89360	0.141870
$417$	21.5220	1.05394
$418$	6.34333	0.310262
$419$	33.1844	1.62116	0.810582	−	0.585625i	$-0.199151\pi$
$419$	33.1844	1.62116	0.810582	+	0.585625i	$0.199151\pi$
$420$	−7.73765	−0.377559
$421$	−25.0292	−1.21985	−0.609924	−	0.792460i	$-0.708800\pi$
$421$	−25.0292	−1.21985	−0.609924	+	0.792460i	$0.708800\pi$
$422$	7.51348	0.365750
$423$	3.20590	0.155876
$424$	−2.85700	−0.138748
$425$	−0.0704795	−0.00341876
$426$	13.1964	0.639368
$427$	−20.8031	−1.00673
$428$	−15.5802	−0.753099
$429$	−14.2287	−0.686970
$430$	−9.40418	−0.453510
$431$	−35.2078	−1.69590	−0.847950	−	0.530076i	$-0.822163\pi$
$431$	−35.2078	−1.69590	−0.847950	+	0.530076i	$0.822163\pi$
$432$	−1.00000	−0.0481125
$433$	18.5971	0.893721	0.446860	−	0.894604i	$-0.352542\pi$
$433$	18.5971	0.893721	0.446860	+	0.894604i	$0.352542\pi$
$434$	34.4563	1.65396
$435$	18.1808	0.871701
$436$	−8.68560	−0.415965
$437$	1.39125	0.0665526
$438$	14.6327	0.699176
$439$	−12.8152	−0.611637	−0.305819	−	0.952090i	$-0.598930\pi$
$439$	−12.8152	−0.611637	−0.305819	+	0.952090i	$0.598930\pi$
$440$	11.0727	0.527870
$441$	4.80781	0.228943
$442$	−2.89360	−0.137634
$443$	15.7072	0.746270	0.373135	−	0.927777i	$-0.378283\pi$
$443$	15.7072	0.746270	0.373135	+	0.927777i	$0.378283\pi$
$444$	−7.39960	−0.351170
$445$	−41.6319	−1.97354
$446$	−14.5486	−0.688895
$447$	7.84479	0.371046
$448$	3.43625	0.162348
$449$	−26.9384	−1.27130	−0.635651	−	0.771977i	$-0.719268\pi$
$449$	−26.9384	−1.27130	−0.635651	+	0.771977i	$0.719268\pi$
$450$	0.0704795	0.00332244
$451$	6.07501	0.286061
$452$	4.52074	0.212638
$453$	−17.9093	−0.841452
$454$	−9.87142	−0.463289
$455$	22.3896	1.04964
$456$	−1.29000	−0.0604097
$457$	22.6635	1.06015	0.530077	−	0.847949i	$-0.322163\pi$
$457$	22.6635	1.06015	0.530077	+	0.847949i	$0.322163\pi$
$458$	13.5895	0.634996
$459$	1.00000	0.0466760
$460$	2.42852	0.113230
$461$	2.26106	0.105308	0.0526539	−	0.998613i	$-0.483232\pi$
$461$	2.26106	0.105308	0.0526539	+	0.998613i	$0.483232\pi$
$462$	−16.8971	−0.786126
$463$	31.6292	1.46994	0.734968	−	0.678102i	$-0.237197\pi$
$463$	31.6292	1.46994	0.734968	+	0.678102i	$0.237197\pi$
$464$	−8.07398	−0.374825
$465$	−22.5792	−1.04709
$466$	5.12489	0.237406
$467$	−35.0545	−1.62213	−0.811064	−	0.584958i	$-0.801111\pi$
$467$	−35.0545	−1.62213	−0.811064	+	0.584958i	$0.801111\pi$
$468$	2.89360	0.133757
$469$	36.1742	1.67037
$470$	7.21897	0.332986
$471$	4.20712	0.193854
$472$	−1.00000	−0.0460287
$473$	−20.5364	−0.944266
$474$	5.54705	0.254784
$475$	0.0909184	0.00417162
$476$	−3.43625	−0.157500
$477$	−2.85700	−0.130813
$478$	10.2564	0.469119
$479$	16.8806	0.771296	0.385648	−	0.922646i	$-0.373978\pi$
$479$	16.8806	0.771296	0.385648	+	0.922646i	$0.373978\pi$
$480$	−2.25177	−0.102779
$481$	21.4115	0.976279
$482$	25.0013	1.13878
$483$	−3.70596	−0.168627
$484$	13.1800	0.599093
$485$	8.22158	0.373323
$486$	−1.00000	−0.0453609
$487$	−26.0721	−1.18144	−0.590721	−	0.806876i	$-0.701156\pi$
$487$	−26.0721	−1.18144	−0.590721	+	0.806876i	$0.701156\pi$
$488$	−6.05401	−0.274052
$489$	23.3656	1.05663
$490$	10.8261	0.489073
$491$	3.17302	0.143197	0.0715983	−	0.997434i	$-0.477190\pi$
$491$	3.17302	0.143197	0.0715983	+	0.997434i	$0.477190\pi$
$492$	−1.23543	−0.0556975
$493$	8.07398	0.363634
$494$	3.73273	0.167944
$495$	11.0727	0.497680
$496$	10.0273	0.450239
$497$	−45.3461	−2.03405
$498$	5.30666	0.237797
$499$	−1.41281	−0.0632462	−0.0316231	−	0.999500i	$-0.510068\pi$
$499$	−1.41281	−0.0632462	−0.0316231	+	0.999500i	$0.510068\pi$
$500$	−11.1002	−0.496414
$501$	−6.58591	−0.294237
$502$	−25.0032	−1.11595
$503$	18.2015	0.811566	0.405783	−	0.913969i	$-0.366999\pi$
$503$	18.2015	0.811566	0.405783	+	0.913969i	$0.366999\pi$
$504$	3.43625	0.153063
$505$	27.2325	1.21183
$506$	5.30329	0.235760
$507$	4.62710	0.205497
$508$	−9.37239	−0.415833
$509$	−24.8016	−1.09931	−0.549656	−	0.835391i	$-0.685241\pi$
$509$	−24.8016	−1.09931	−0.549656	+	0.835391i	$0.685241\pi$
$510$	2.25177	0.0997102
$511$	−50.2815	−2.22432
$512$	1.00000	0.0441942
$513$	−1.29000	−0.0569548
$514$	−8.89567	−0.392371
$515$	−24.0556	−1.06001
$516$	4.17635	0.183853
$517$	15.7645	0.693320
$518$	25.4269	1.11719
$519$	4.65230	0.204213
$520$	6.51572	0.285733
$521$	6.55840	0.287329	0.143664	−	0.989626i	$-0.454111\pi$
$521$	6.55840	0.287329	0.143664	+	0.989626i	$0.454111\pi$
$522$	−8.07398	−0.353388
$523$	18.1916	0.795463	0.397731	−	0.917502i	$-0.369798\pi$
$523$	18.1916	0.795463	0.397731	+	0.917502i	$0.369798\pi$
$524$	−0.789909	−0.0345073
$525$	−0.242185	−0.0105698
$526$	4.79106	0.208900
$527$	−10.0273	−0.436796
$528$	−4.91732	−0.213999
$529$	−21.8369	−0.949429
$530$	−6.43332	−0.279446
$531$	−1.00000	−0.0433963
$532$	4.43275	0.192184
$533$	3.57484	0.154843
$534$	18.4885	0.800076
$535$	−35.0831	−1.51678
$536$	10.5272	0.454708
$537$	−17.8952	−0.772235
$538$	7.99401	0.344646
$539$	23.6415	1.01831
$540$	−2.25177	−0.0969009
$541$	−2.80222	−0.120477	−0.0602385	−	0.998184i	$-0.519186\pi$
$541$	−2.80222	−0.120477	−0.0602385	+	0.998184i	$0.519186\pi$
$542$	5.33695	0.229242
$543$	−19.4991	−0.836785
$544$	−1.00000	−0.0428746
$545$	−19.5580	−0.837773
$546$	−9.94312	−0.425526
$547$	−3.07377	−0.131425	−0.0657126	−	0.997839i	$-0.520932\pi$
$547$	−3.07377	−0.131425	−0.0657126	+	0.997839i	$0.520932\pi$
$548$	3.05258	0.130400
$549$	−6.05401	−0.258379
$550$	0.346570	0.0147778
$551$	−10.4154	−0.443712
$552$	−1.07849	−0.0459036
$553$	−19.0610	−0.810558
$554$	−4.66444	−0.198173
$555$	−16.6622	−0.707272
$556$	−21.5220	−0.912737
$557$	28.1076	1.19096	0.595478	−	0.803371i	$-0.296963\pi$
$557$	28.1076	1.19096	0.595478	+	0.803371i	$0.296963\pi$
$558$	10.0273	0.424490
$559$	−12.0847	−0.511127
$560$	7.73765	0.326975
$561$	4.91732	0.207609
$562$	10.8964	0.459635
$563$	−1.45374	−0.0612677	−0.0306338	−	0.999531i	$-0.509753\pi$
$563$	−1.45374	−0.0612677	−0.0306338	+	0.999531i	$0.509753\pi$
$564$	−3.20590	−0.134993
$565$	10.1797	0.428262
$566$	27.3503	1.14962
$567$	3.43625	0.144309
$568$	−13.1964	−0.553709
$569$	19.6298	0.822923	0.411461	−	0.911427i	$-0.365019\pi$
$569$	19.6298	0.822923	0.411461	+	0.911427i	$0.365019\pi$
$570$	−2.90478	−0.121668
$571$	31.0296	1.29855	0.649274	−	0.760555i	$-0.275073\pi$
$571$	31.0296	1.29855	0.649274	+	0.760555i	$0.275073\pi$
$572$	14.2287	0.594934
$573$	−1.52133	−0.0635545
$574$	4.24525	0.177193
$575$	0.0760115	0.00316990
$576$	1.00000	0.0416667
$577$	−26.1699	−1.08947	−0.544733	−	0.838609i	$-0.683369\pi$
$577$	−26.1699	−1.08947	−0.544733	+	0.838609i	$0.683369\pi$
$578$	1.00000	0.0415945
$579$	5.82567	0.242106
$580$	−18.1808	−0.754915
$581$	−18.2350	−0.756516
$582$	−3.65116	−0.151345
$583$	−14.0488	−0.581842
$584$	−14.6327	−0.605504
$585$	6.51572	0.269392
$586$	−1.19975	−0.0495613
$587$	−36.8379	−1.52046	−0.760231	−	0.649653i	$-0.774914\pi$
$587$	−36.8379	−1.52046	−0.760231	+	0.649653i	$0.774914\pi$
$588$	−4.80781	−0.198271
$589$	12.9352	0.532986
$590$	−2.25177	−0.0927040
$591$	0.559432	0.0230120
$592$	7.39960	0.304122
$593$	17.4327	0.715877	0.357938	−	0.933745i	$-0.383480\pi$
$593$	17.4327	0.715877	0.357938	+	0.933745i	$0.383480\pi$
$594$	−4.91732	−0.201760
$595$	−7.73765	−0.317213
$596$	−7.84479	−0.321335
$597$	−4.53257	−0.185506
$598$	3.12072	0.127616
$599$	43.2265	1.76619	0.883093	−	0.469197i	$-0.155457\pi$
$599$	43.2265	1.76619	0.883093	+	0.469197i	$0.155457\pi$
$600$	−0.0704795	−0.00287731
$601$	−25.6587	−1.04664	−0.523321	−	0.852136i	$-0.675307\pi$
$601$	−25.6587	−1.04664	−0.523321	+	0.852136i	$0.675307\pi$
$602$	−14.3510	−0.584902
$603$	10.5272	0.428703
$604$	17.9093	0.728719
$605$	29.6785	1.20660
$606$	−12.0938	−0.491278
$607$	8.24092	0.334488	0.167244	−	0.985915i	$-0.446513\pi$
$607$	8.24092	0.334488	0.167244	+	0.985915i	$0.446513\pi$
$608$	1.29000	0.0523163
$609$	27.7442	1.12425
$610$	−13.6322	−0.551954
$611$	9.27659	0.375291
$612$	−1.00000	−0.0404226
$613$	21.7479	0.878388	0.439194	−	0.898392i	$-0.355264\pi$
$613$	21.7479	0.878388	0.439194	+	0.898392i	$0.355264\pi$
$614$	−14.9413	−0.602983
$615$	−2.78191	−0.112177
$616$	16.8971	0.680805
$617$	−11.8356	−0.476483	−0.238241	−	0.971206i	$-0.576571\pi$
$617$	−11.8356	−0.476483	−0.238241	+	0.971206i	$0.576571\pi$
$618$	10.6829	0.429731
$619$	−38.5631	−1.54998	−0.774990	−	0.631974i	$-0.782245\pi$
$619$	−38.5631	−1.54998	−0.774990	+	0.631974i	$0.782245\pi$
$620$	22.5792	0.906803
$621$	−1.07849	−0.0432784
$622$	17.4896	0.701268
$623$	−63.5311	−2.54532
$624$	−2.89360	−0.115837
$625$	−25.3474	−1.01390
$626$	10.8682	0.434381
$627$	−6.34333	−0.253328
$628$	−4.20712	−0.167882
$629$	−7.39960	−0.295042
$630$	7.73765	0.308275
$631$	−20.1736	−0.803098	−0.401549	−	0.915837i	$-0.631528\pi$
$631$	−20.1736	−0.803098	−0.401549	+	0.915837i	$0.631528\pi$
$632$	−5.54705	−0.220650
$633$	−7.51348	−0.298634
$634$	21.5281	0.854991
$635$	−21.1045	−0.837507
$636$	2.85700	0.113288
$637$	13.9119	0.551208
$638$	−39.7023	−1.57183
$639$	−13.1964	−0.522041
$640$	2.25177	0.0890091
$641$	6.16002	0.243306	0.121653	−	0.992573i	$-0.461180\pi$
$641$	6.16002	0.243306	0.121653	+	0.992573i	$0.461180\pi$
$642$	15.5802	0.614902
$643$	1.87896	0.0740991	0.0370496	−	0.999313i	$-0.488204\pi$
$643$	1.87896	0.0740991	0.0370496	+	0.999313i	$0.488204\pi$
$644$	3.70596	0.146035
$645$	9.40418	0.370289
$646$	−1.29000	−0.0507543
$647$	−14.7884	−0.581392	−0.290696	−	0.956816i	$-0.593887\pi$
$647$	−14.7884	−0.581392	−0.290696	+	0.956816i	$0.593887\pi$
$648$	1.00000	0.0392837
$649$	−4.91732	−0.193022
$650$	0.203939	0.00799916
$651$	−34.4563	−1.35045
$652$	−23.3656	−0.915069
$653$	46.8140	1.83197	0.915987	−	0.401207i	$-0.131409\pi$
$653$	46.8140	1.83197	0.915987	+	0.401207i	$0.131409\pi$
$654$	8.68560	0.339634
$655$	−1.77870	−0.0694994
$656$	1.23543	0.0482355
$657$	−14.6327	−0.570875
$658$	11.0163	0.429459
$659$	−14.0808	−0.548508	−0.274254	−	0.961657i	$-0.588431\pi$
$659$	−14.0808	−0.548508	−0.274254	+	0.961657i	$0.588431\pi$
$660$	−11.0727	−0.431004
$661$	5.63291	0.219095	0.109547	−	0.993982i	$-0.465060\pi$
$661$	5.63291	0.219095	0.109547	+	0.993982i	$0.465060\pi$
$662$	28.7881	1.11888
$663$	2.89360	0.112378
$664$	−5.30666	−0.205938
$665$	9.98155	0.387068
$666$	7.39960	0.286729
$667$	−8.70772	−0.337164
$668$	6.58591	0.254817
$669$	14.5486	0.562480
$670$	23.7050	0.915803
$671$	−29.7695	−1.14924
$672$	−3.43625	−0.132556
$673$	42.8894	1.65326	0.826632	−	0.562743i	$-0.190254\pi$
$673$	42.8894	1.65326	0.826632	+	0.562743i	$0.190254\pi$
$674$	8.50860	0.327739
$675$	−0.0704795	−0.00271276
$676$	−4.62710	−0.177965
$677$	−34.5792	−1.32899	−0.664493	−	0.747295i	$-0.731352\pi$
$677$	−34.5792	−1.32899	−0.664493	+	0.747295i	$0.731352\pi$
$678$	−4.52074	−0.173618
$679$	12.5463	0.481483
$680$	−2.25177	−0.0863515
$681$	9.87142	0.378274
$682$	49.3075	1.88808
$683$	−39.2853	−1.50321	−0.751606	−	0.659613i	$-0.770720\pi$
$683$	−39.2853	−1.50321	−0.751606	+	0.659613i	$0.770720\pi$
$684$	1.29000	0.0493243
$685$	6.87373	0.262632
$686$	−7.53291	−0.287608
$687$	−13.5895	−0.518472
$688$	−4.17635	−0.159222
$689$	−8.26702	−0.314948
$690$	−2.42852	−0.0924521
$691$	−0.755003	−0.0287216	−0.0143608	−	0.999897i	$-0.504571\pi$
$691$	−0.755003	−0.0287216	−0.0143608	+	0.999897i	$0.504571\pi$
$692$	−4.65230	−0.176854
$693$	16.8971	0.641869
$694$	−6.07353	−0.230548
$695$	−48.4627	−1.83830
$696$	8.07398	0.306043
$697$	−1.23543	−0.0467953
$698$	14.2666	0.540000
$699$	−5.12489	−0.193841
$700$	0.242185	0.00915374
$701$	22.6023	0.853676	0.426838	−	0.904328i	$-0.359627\pi$
$701$	22.6023	0.853676	0.426838	+	0.904328i	$0.359627\pi$
$702$	−2.89360	−0.109212
$703$	9.54547	0.360014
$704$	4.91732	0.185328
$705$	−7.21897	−0.271882
$706$	11.9338	0.449135
$707$	41.5574	1.56293
$708$	1.00000	0.0375823
$709$	17.9184	0.672940	0.336470	−	0.941694i	$-0.390767\pi$
$709$	17.9184	0.672940	0.336470	+	0.941694i	$0.390767\pi$
$710$	−29.7153	−1.11519
$711$	−5.54705	−0.208031
$712$	−18.4885	−0.692886
$713$	10.8144	0.405001
$714$	3.43625	0.128598
$715$	32.0399	1.19822
$716$	17.8952	0.668775
$717$	−10.2564	−0.383034
$718$	−30.9383	−1.15461
$719$	1.41152	0.0526407	0.0263204	−	0.999654i	$-0.491621\pi$
$719$	1.41152	0.0526407	0.0263204	+	0.999654i	$0.491621\pi$
$720$	2.25177	0.0839186
$721$	−36.7093	−1.36712
$722$	−17.3359	−0.645176
$723$	−25.0013	−0.929808
$724$	19.4991	0.724677
$725$	−0.569050	−0.0211340
$726$	−13.1800	−0.489157
$727$	−23.2806	−0.863430	−0.431715	−	0.902010i	$-0.642091\pi$
$727$	−23.2806	−0.863430	−0.431715	+	0.902010i	$0.642091\pi$
$728$	9.94312	0.368517
$729$	1.00000	0.0370370
$730$	−32.9495	−1.21951
$731$	4.17635	0.154468
$732$	6.05401	0.223763
$733$	−1.61062	−0.0594895	−0.0297448	−	0.999558i	$-0.509469\pi$
$733$	−1.61062	−0.0594895	−0.0297448	+	0.999558i	$0.509469\pi$
$734$	7.43176	0.274311
$735$	−10.8261	−0.399327
$736$	1.07849	0.0397537
$737$	51.7658	1.90682
$738$	1.23543	0.0454768
$739$	33.4590	1.23081	0.615405	−	0.788211i	$-0.288993\pi$
$739$	33.4590	1.23081	0.615405	+	0.788211i	$0.288993\pi$
$740$	16.6622	0.612516
$741$	−3.73273	−0.137125
$742$	−9.81738	−0.360407
$743$	7.37439	0.270540	0.135270	−	0.990809i	$-0.456810\pi$
$743$	7.37439	0.270540	0.135270	+	0.990809i	$0.456810\pi$
$744$	−10.0273	−0.367619
$745$	−17.6647	−0.647184
$746$	32.9334	1.20578
$747$	−5.30666	−0.194161
$748$	−4.91732	−0.179795
$749$	−53.5375	−1.95622
$750$	11.1002	0.405320
$751$	−6.77314	−0.247155	−0.123578	−	0.992335i	$-0.539437\pi$
$751$	−6.77314	−0.247155	−0.123578	+	0.992335i	$0.539437\pi$
$752$	3.20590	0.116907
$753$	25.0032	0.911169
$754$	−23.3628	−0.850824
$755$	40.3277	1.46767
$756$	−3.43625	−0.124975
$757$	25.1356	0.913570	0.456785	−	0.889577i	$-0.349001\pi$
$757$	25.1356	0.913570	0.456785	+	0.889577i	$0.349001\pi$
$758$	−35.6006	−1.29307
$759$	−5.30329	−0.192497
$760$	2.90478	0.105367
$761$	−24.6887	−0.894965	−0.447482	−	0.894293i	$-0.647679\pi$
$761$	−24.6887	−0.894965	−0.447482	+	0.894293i	$0.647679\pi$
$762$	9.37239	0.339526
$763$	−29.8459	−1.08049
$764$	1.52133	0.0550398
$765$	−2.25177	−0.0814130
$766$	−5.07334	−0.183307
$767$	−2.89360	−0.104482
$768$	−1.00000	−0.0360844
$769$	−27.6938	−0.998665	−0.499333	−	0.866410i	$-0.666421\pi$
$769$	−27.6938	−0.998665	−0.499333	+	0.866410i	$0.666421\pi$
$770$	38.0485	1.37117
$771$	8.89567	0.320370
$772$	−5.82567	−0.209670
$773$	32.3971	1.16524	0.582622	−	0.812744i	$-0.302027\pi$
$773$	32.3971	1.16524	0.582622	+	0.812744i	$0.302027\pi$
$774$	−4.17635	−0.150116
$775$	0.706719	0.0253861
$776$	3.65116	0.131069
$777$	−25.4269	−0.912184
$778$	−26.7190	−0.957921
$779$	1.59370	0.0571003
$780$	−6.51572	−0.233300
$781$	−64.8909	−2.32198
$782$	−1.07849	−0.0385668
$783$	8.07398	0.288540
$784$	4.80781	0.171708
$785$	−9.47347	−0.338123
$786$	0.789909	0.0281751
$787$	40.4300	1.44117	0.720587	−	0.693365i	$-0.243873\pi$
$787$	40.4300	1.44117	0.720587	+	0.693365i	$0.243873\pi$
$788$	−0.559432	−0.0199289
$789$	−4.79106	−0.170566
$790$	−12.4907	−0.444399
$791$	15.5344	0.552340
$792$	4.91732	0.174729
$793$	−17.5179	−0.622077
$794$	27.1614	0.963923
$795$	6.43332	0.228166
$796$	4.53257	0.160653
$797$	6.17488	0.218726	0.109363	−	0.994002i	$-0.465119\pi$
$797$	6.17488	0.218726	0.109363	+	0.994002i	$0.465119\pi$
$798$	−4.43275	−0.156918
$799$	−3.20590	−0.113417
$800$	0.0704795	0.00249183
$801$	−18.4885	−0.653259
$802$	0.0278209	0.000982389 0
$803$	−71.9536	−2.53919
$804$	−10.5272	−0.371267
$805$	8.34499	0.294122
$806$	29.0150	1.02201
$807$	−7.99401	−0.281402
$808$	12.0938	0.425459
$809$	37.9093	1.33282	0.666410	−	0.745586i	$-0.267830\pi$
$809$	37.9093	1.33282	0.666410	+	0.745586i	$0.267830\pi$
$810$	2.25177	0.0791192
$811$	−12.8510	−0.451261	−0.225631	−	0.974213i	$-0.572444\pi$
$811$	−12.8510	−0.451261	−0.225631	+	0.974213i	$0.572444\pi$
$812$	−27.7442	−0.973631
$813$	−5.33695	−0.187175
$814$	36.3862	1.27534
$815$	−52.6141	−1.84299
$816$	1.00000	0.0350070
$817$	−5.38748	−0.188484
$818$	7.43141	0.259833
$819$	9.94312	0.347441
$820$	2.78191	0.0971484
$821$	−32.3825	−1.13016	−0.565078	−	0.825037i	$-0.691154\pi$
$821$	−32.3825	−1.13016	−0.565078	+	0.825037i	$0.691154\pi$
$822$	−3.05258	−0.106471
$823$	39.6974	1.38376	0.691882	−	0.722010i	$-0.256782\pi$
$823$	39.6974	1.38376	0.691882	+	0.722010i	$0.256782\pi$
$824$	−10.6829	−0.372158
$825$	−0.346570	−0.0120660
$826$	−3.43625	−0.119562
$827$	31.7995	1.10578	0.552888	−	0.833256i	$-0.313526\pi$
$827$	31.7995	1.10578	0.552888	+	0.833256i	$0.313526\pi$
$828$	1.07849	0.0374802
$829$	−37.4949	−1.30225	−0.651126	−	0.758969i	$-0.725703\pi$
$829$	−37.4949	−1.30225	−0.651126	+	0.758969i	$0.725703\pi$
$830$	−11.9494	−0.414769
$831$	4.66444	0.161808
$832$	2.89360	0.100317
$833$	−4.80781	−0.166581
$834$	21.5220	0.745247
$835$	14.8300	0.513213
$836$	6.34333	0.219389
$837$	−10.0273	−0.346594
$838$	33.1844	1.14634
$839$	28.6386	0.988713	0.494357	−	0.869259i	$-0.335404\pi$
$839$	28.6386	0.988713	0.494357	+	0.869259i	$0.335404\pi$
$840$	−7.73765	−0.266974
$841$	36.1891	1.24790
$842$	−25.0292	−0.862562
$843$	−10.8964	−0.375291
$844$	7.51348	0.258625
$845$	−10.4192	−0.358430
$846$	3.20590	0.110221
$847$	45.2899	1.55618
$848$	−2.85700	−0.0981099
$849$	−27.3503	−0.938659
$850$	−0.0704795	−0.00241743
$851$	7.98041	0.273565
$852$	13.1964	0.452101
$853$	11.6026	0.397266	0.198633	−	0.980074i	$-0.436350\pi$
$853$	11.6026	0.397266	0.198633	+	0.980074i	$0.436350\pi$
$854$	−20.8031	−0.711867
$855$	2.90478	0.0993414
$856$	−15.5802	−0.532521
$857$	49.8696	1.70351	0.851757	−	0.523937i	$-0.175537\pi$
$857$	49.8696	1.70351	0.851757	+	0.523937i	$0.175537\pi$
$858$	−14.2287	−0.485761
$859$	51.3518	1.75210	0.876050	−	0.482220i	$-0.160169\pi$
$859$	51.3518	1.75210	0.876050	+	0.482220i	$0.160169\pi$
$860$	−9.40418	−0.320680
$861$	−4.24525	−0.144678
$862$	−35.2078	−1.19918
$863$	41.6611	1.41816	0.709079	−	0.705129i	$-0.249111\pi$
$863$	41.6611	1.41816	0.709079	+	0.705129i	$0.249111\pi$
$864$	−1.00000	−0.0340207
$865$	−10.4759	−0.356192
$866$	18.5971	0.631956
$867$	−1.00000	−0.0339618
$868$	34.4563	1.16952
$869$	−27.2766	−0.925296
$870$	18.1808	0.616386
$871$	30.4616	1.03215
$872$	−8.68560	−0.294132
$873$	3.65116	0.123573
$874$	1.39125	0.0470598
$875$	−38.1429	−1.28947
$876$	14.6327	0.494392
$877$	−8.93878	−0.301841	−0.150920	−	0.988546i	$-0.548224\pi$
$877$	−8.93878	−0.301841	−0.150920	+	0.988546i	$0.548224\pi$
$878$	−12.8152	−0.432493
$879$	1.19975	0.0404666
$880$	11.0727	0.373260
$881$	−19.9516	−0.672186	−0.336093	−	0.941829i	$-0.609106\pi$
$881$	−19.9516	−0.672186	−0.336093	+	0.941829i	$0.609106\pi$
$882$	4.80781	0.161887
$883$	53.5546	1.80226	0.901128	−	0.433553i	$-0.142740\pi$
$883$	53.5546	1.80226	0.901128	+	0.433553i	$0.142740\pi$
$884$	−2.89360	−0.0973222
$885$	2.25177	0.0756925
$886$	15.7072	0.527693
$887$	−4.41181	−0.148134	−0.0740671	−	0.997253i	$-0.523598\pi$
$887$	−4.41181	−0.148134	−0.0740671	+	0.997253i	$0.523598\pi$
$888$	−7.39960	−0.248314
$889$	−32.2059	−1.08015
$890$	−41.6319	−1.39551
$891$	4.91732	0.164736
$892$	−14.5486	−0.487122
$893$	4.13561	0.138393
$894$	7.84479	0.262369
$895$	40.2959	1.34694
$896$	3.43625	0.114797
$897$	−3.12072	−0.104198
$898$	−26.9384	−0.898946
$899$	−80.9603	−2.70018
$900$	0.0704795	0.00234932
$901$	2.85700	0.0951806
$902$	6.07501	0.202276
$903$	14.3510	0.477570
$904$	4.52074	0.150358
$905$	43.9075	1.45953
$906$	−17.9093	−0.594997
$907$	−21.0686	−0.699572	−0.349786	−	0.936830i	$-0.613746\pi$
$907$	−21.0686	−0.699572	−0.349786	+	0.936830i	$0.613746\pi$
$908$	−9.87142	−0.327595
$909$	12.0938	0.401127
$910$	22.3896	0.742210
$911$	56.3606	1.86731	0.933655	−	0.358173i	$-0.116600\pi$
$911$	56.3606	1.86731	0.933655	+	0.358173i	$0.116600\pi$
$912$	−1.29000	−0.0427161
$913$	−26.0945	−0.863604
$914$	22.6635	0.749643
$915$	13.6322	0.450668
$916$	13.5895	0.449010
$917$	−2.71432	−0.0896349
$918$	1.00000	0.0330049
$919$	17.2665	0.569571	0.284785	−	0.958591i	$-0.408078\pi$
$919$	17.2665	0.569571	0.284785	+	0.958591i	$0.408078\pi$
$920$	2.42852	0.0800658
$921$	14.9413	0.492334
$922$	2.26106	0.0744639
$923$	−38.1851	−1.25688
$924$	−16.8971	−0.555875
$925$	0.521520	0.0171475
$926$	31.6292	1.03940
$927$	−10.6829	−0.350874
$928$	−8.07398	−0.265041
$929$	−11.5225	−0.378039	−0.189020	−	0.981973i	$-0.560531\pi$
$929$	−11.5225	−0.378039	−0.189020	+	0.981973i	$0.560531\pi$
$930$	−22.5792	−0.740402
$931$	6.20206	0.203264
$932$	5.12489	0.167871
$933$	−17.4896	−0.572583
$934$	−35.0545	−1.14702
$935$	−11.0727	−0.362116
$936$	2.89360	0.0945802
$937$	−31.7763	−1.03809	−0.519043	−	0.854748i	$-0.673712\pi$
$937$	−31.7763	−1.03809	−0.519043	+	0.854748i	$0.673712\pi$
$938$	36.1742	1.18113
$939$	−10.8682	−0.354671
$940$	7.21897	0.235457
$941$	−37.6547	−1.22751	−0.613755	−	0.789497i	$-0.710342\pi$
$941$	−37.6547	−1.22751	−0.613755	+	0.789497i	$0.710342\pi$
$942$	4.20712	0.137075
$943$	1.33240	0.0433889
$944$	−1.00000	−0.0325472
$945$	−7.73765	−0.251706
$946$	−20.5364	−0.667697
$947$	−29.1994	−0.948853	−0.474426	−	0.880295i	$-0.657345\pi$
$947$	−29.1994	−0.948853	−0.474426	+	0.880295i	$0.657345\pi$
$948$	5.54705	0.180160
$949$	−42.3411	−1.37445
$950$	0.0909184	0.00294978
$951$	−21.5281	−0.698097
$952$	−3.43625	−0.111369
$953$	−41.1917	−1.33433	−0.667164	−	0.744911i	$-0.732492\pi$
$953$	−41.1917	−1.33433	−0.667164	+	0.744911i	$0.732492\pi$
$954$	−2.85700	−0.0924989
$955$	3.42569	0.110853
$956$	10.2564	0.331717
$957$	39.7023	1.28339
$958$	16.8806	0.545389
$959$	10.4894	0.338722
$960$	−2.25177	−0.0726756
$961$	69.5469	2.24345
$962$	21.4115	0.690333
$963$	−15.5802	−0.502066
$964$	25.0013	0.805237
$965$	−13.1181	−0.422286
$966$	−3.70596	−0.119237
$967$	−1.19017	−0.0382733	−0.0191367	−	0.999817i	$-0.506092\pi$
$967$	−1.19017	−0.0382733	−0.0191367	+	0.999817i	$0.506092\pi$
$968$	13.1800	0.423623
$969$	1.29000	0.0414407
$970$	8.22158	0.263979
$971$	−49.6905	−1.59464	−0.797321	−	0.603555i	$-0.793750\pi$
$971$	−49.6905	−1.59464	−0.797321	+	0.603555i	$0.793750\pi$
$972$	−1.00000	−0.0320750
$973$	−73.9551	−2.37089
$974$	−26.0721	−0.835405
$975$	−0.203939	−0.00653128
$976$	−6.05401	−0.193784
$977$	−58.3111	−1.86554	−0.932769	−	0.360475i	$-0.882615\pi$
$977$	−58.3111	−1.86554	−0.932769	+	0.360475i	$0.882615\pi$
$978$	23.3656	0.747151
$979$	−90.9139	−2.90562
$980$	10.8261	0.345827
$981$	−8.68560	−0.277310
$982$	3.17302	0.101255
$983$	−48.8470	−1.55798	−0.778989	−	0.627038i	$-0.784267\pi$
$983$	−48.8470	−1.55798	−0.778989	+	0.627038i	$0.784267\pi$
$984$	−1.23543	−0.0393841
$985$	−1.25971	−0.0401378
$986$	8.07398	0.257128
$987$	−11.0163	−0.350652
$988$	3.73273	0.118754
$989$	−4.50415	−0.143224
$990$	11.0727	0.351913
$991$	46.5472	1.47862	0.739311	−	0.673364i	$-0.235151\pi$
$991$	46.5472	1.47862	0.739311	+	0.673364i	$0.235151\pi$
$992$	10.0273	0.318367
$993$	−28.7881	−0.913562
$994$	−45.3461	−1.43829
$995$	10.2063	0.323562
$996$	5.30666	0.168148
$997$	44.5202	1.40997	0.704985	−	0.709222i	$-0.250954\pi$
$997$	44.5202	1.40997	0.704985	+	0.709222i	$0.250954\pi$
$998$	−1.41281	−0.0447218
$999$	−7.39960	−0.234113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.8	✓	11	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25177 q^{5} -1.00000 q^{6} +3.43625 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.25177 q^{5} -1.00000 q^{6} +3.43625 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.25177 q^{10} +4.91732 q^{11} -1.00000 q^{12} +2.89360 q^{13} +3.43625 q^{14} -2.25177 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.29000 q^{19} +2.25177 q^{20} -3.43625 q^{21} +4.91732 q^{22} +1.07849 q^{23} -1.00000 q^{24} +0.0704795 q^{25} +2.89360 q^{26} -1.00000 q^{27} +3.43625 q^{28} -8.07398 q^{29} -2.25177 q^{30} +10.0273 q^{31} +1.00000 q^{32} -4.91732 q^{33} -1.00000 q^{34} +7.73765 q^{35} +1.00000 q^{36} +7.39960 q^{37} +1.29000 q^{38} -2.89360 q^{39} +2.25177 q^{40} +1.23543 q^{41} -3.43625 q^{42} -4.17635 q^{43} +4.91732 q^{44} +2.25177 q^{45} +1.07849 q^{46} +3.20590 q^{47} -1.00000 q^{48} +4.80781 q^{49} +0.0704795 q^{50} +1.00000 q^{51} +2.89360 q^{52} -2.85700 q^{53} -1.00000 q^{54} +11.0727 q^{55} +3.43625 q^{56} -1.29000 q^{57} -8.07398 q^{58} -1.00000 q^{59} -2.25177 q^{60} -6.05401 q^{61} +10.0273 q^{62} +3.43625 q^{63} +1.00000 q^{64} +6.51572 q^{65} -4.91732 q^{66} +10.5272 q^{67} -1.00000 q^{68} -1.07849 q^{69} +7.73765 q^{70} -13.1964 q^{71} +1.00000 q^{72} -14.6327 q^{73} +7.39960 q^{74} -0.0704795 q^{75} +1.29000 q^{76} +16.8971 q^{77} -2.89360 q^{78} -5.54705 q^{79} +2.25177 q^{80} +1.00000 q^{81} +1.23543 q^{82} -5.30666 q^{83} -3.43625 q^{84} -2.25177 q^{85} -4.17635 q^{86} +8.07398 q^{87} +4.91732 q^{88} -18.4885 q^{89} +2.25177 q^{90} +9.94312 q^{91} +1.07849 q^{92} -10.0273 q^{93} +3.20590 q^{94} +2.90478 q^{95} -1.00000 q^{96} +3.65116 q^{97} +4.80781 q^{98} +4.91732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more