LMFDB - Embedded newform 5290.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} -3.85410 q^{11} -0.618034 q^{12} +4.09017 q^{13} -1.61803 q^{14} +0.618034 q^{15} +1.00000 q^{16} +5.09017 q^{17} -2.61803 q^{18} +4.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} -3.85410 q^{22} -0.618034 q^{24} +1.00000 q^{25} +4.09017 q^{26} +3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} +0.618034 q^{30} -2.09017 q^{31} +1.00000 q^{32} +2.38197 q^{33} +5.09017 q^{34} +1.61803 q^{35} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -1.00000 q^{40} -12.3262 q^{41} +1.00000 q^{42} -3.85410 q^{44} +2.61803 q^{45} +9.70820 q^{47} -0.618034 q^{48} -4.38197 q^{49} +1.00000 q^{50} -3.14590 q^{51} +4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +3.85410 q^{55} -1.61803 q^{56} -3.00000 q^{57} -4.76393 q^{58} -11.7082 q^{59} +0.618034 q^{60} -6.32624 q^{61} -2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -4.09017 q^{65} +2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} +1.61803 q^{70} +7.09017 q^{71} -2.61803 q^{72} -1.23607 q^{73} +2.47214 q^{74} -0.618034 q^{75} +4.85410 q^{76} +6.23607 q^{77} -2.52786 q^{78} -10.4721 q^{79} -1.00000 q^{80} +5.70820 q^{81} -12.3262 q^{82} -10.9443 q^{83} +1.00000 q^{84} -5.09017 q^{85} +2.94427 q^{87} -3.85410 q^{88} +1.52786 q^{89} +2.61803 q^{90} -6.61803 q^{91} +1.29180 q^{93} +9.70820 q^{94} -4.85410 q^{95} -0.618034 q^{96} -14.6180 q^{97} -4.38197 q^{98} +10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21} - q^{22} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - q^{28} - 14 q^{29} - q^{30} + 7 q^{31} + 2 q^{32} + 7 q^{33} - q^{34} + q^{35} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 2 q^{40} - 9 q^{41} + 2 q^{42} - q^{44} + 3 q^{45} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 13 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{55} - q^{56} - 6 q^{57} - 14 q^{58} - 10 q^{59} - q^{60} + 3 q^{61} + 7 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{65} + 7 q^{66} - 20 q^{67} - q^{68} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} - 4 q^{74} + q^{75} + 3 q^{76} + 8 q^{77} - 14 q^{78} - 12 q^{79} - 2 q^{80} - 2 q^{81} - 9 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 12 q^{87} - q^{88} + 12 q^{89} + 3 q^{90} - 11 q^{91} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} - 27 q^{97} - 11 q^{98} + 9 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + q^12 - 3 * q^13 - q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 + 3 * q^19 - 2 * q^20 + 2 * q^21 - q^22 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - q^28 - 14 * q^29 - q^30 + 7 * q^31 + 2 * q^32 + 7 * q^33 - q^34 + q^35 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - q^44 + 3 * q^45 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 13 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 + q^55 - q^56 - 6 * q^57 - 14 * q^58 - 10 * q^59 - q^60 + 3 * q^61 + 7 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^65 + 7 * q^66 - 20 * q^67 - q^68 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 - 4 * q^74 + q^75 + 3 * q^76 + 8 * q^77 - 14 * q^78 - 12 * q^79 - 2 * q^80 - 2 * q^81 - 9 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 12 * q^87 - q^88 + 12 * q^89 + 3 * q^90 - 11 * q^91 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 - 27 * q^97 - 11 * 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
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.618034	−0.252311
$7$	−1.61803	−0.611559	−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803	−0.611559	−0.305780	+	0.952102i	$0.598917\pi$
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	−1.00000	−0.316228
$11$	−3.85410	−1.16206	−0.581028	−	0.813884i	$-0.697349\pi$
$11$	−3.85410	−1.16206	−0.581028	+	0.813884i	$0.697349\pi$
$12$	−0.618034	−0.178411
$13$	4.09017	1.13441	0.567205	−	0.823577i	$-0.308025\pi$
$13$	4.09017	1.13441	0.567205	+	0.823577i	$0.308025\pi$
$14$	−1.61803	−0.432438
$15$	0.618034	0.159576
$16$	1.00000	0.250000
$17$	5.09017	1.23455	0.617274	−	0.786748i	$-0.288237\pi$
$17$	5.09017	1.23455	0.617274	+	0.786748i	$0.288237\pi$
$18$	−2.61803	−0.617077
$19$	4.85410	1.11361	0.556804	−	0.830644i	$-0.312028\pi$
$19$	4.85410	1.11361	0.556804	+	0.830644i	$0.312028\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	−3.85410	−0.821697
$23$	0	0
$23$	0	0
$24$	−0.618034	−0.126156
$25$	1.00000	0.200000
$26$	4.09017	0.802148
$27$	3.47214	0.668213
$28$	−1.61803	−0.305780
$29$	−4.76393	−0.884640	−0.442320	−	0.896857i	$-0.645844\pi$
$29$	−4.76393	−0.884640	−0.442320	+	0.896857i	$0.645844\pi$
$30$	0.618034	0.112837
$31$	−2.09017	−0.375406	−0.187703	−	0.982226i	$-0.560104\pi$
$31$	−2.09017	−0.375406	−0.187703	+	0.982226i	$0.560104\pi$
$32$	1.00000	0.176777
$33$	2.38197	0.414647
$34$	5.09017	0.872957
$35$	1.61803	0.273498
$36$	−2.61803	−0.436339
$37$	2.47214	0.406417	0.203208	−	0.979136i	$-0.434863\pi$
$37$	2.47214	0.406417	0.203208	+	0.979136i	$0.434863\pi$
$38$	4.85410	0.787439
$39$	−2.52786	−0.404782
$40$	−1.00000	−0.158114
$41$	−12.3262	−1.92503	−0.962517	−	0.271220i	$-0.912573\pi$
$41$	−12.3262	−1.92503	−0.962517	+	0.271220i	$0.912573\pi$
$42$	1.00000	0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−3.85410	−0.581028
$45$	2.61803	0.390273
$46$	0	0
$47$	9.70820	1.41609	0.708044	−	0.706169i	$-0.249578\pi$
$47$	9.70820	1.41609	0.708044	+	0.706169i	$0.249578\pi$
$48$	−0.618034	−0.0892055
$49$	−4.38197	−0.625995
$50$	1.00000	0.141421
$51$	−3.14590	−0.440514
$52$	4.09017	0.567205
$53$	8.47214	1.16374	0.581869	−	0.813283i	$-0.302322\pi$
$53$	8.47214	1.16374	0.581869	+	0.813283i	$0.302322\pi$
$54$	3.47214	0.472498
$55$	3.85410	0.519687
$56$	−1.61803	−0.216219
$57$	−3.00000	−0.397360
$58$	−4.76393	−0.625535
$59$	−11.7082	−1.52428	−0.762139	−	0.647413i	$-0.775851\pi$
$59$	−11.7082	−1.52428	−0.762139	+	0.647413i	$0.775851\pi$
$60$	0.618034	0.0797878
$61$	−6.32624	−0.809992	−0.404996	−	0.914319i	$-0.632727\pi$
$61$	−6.32624	−0.809992	−0.404996	+	0.914319i	$0.632727\pi$
$62$	−2.09017	−0.265452
$63$	4.23607	0.533694
$64$	1.00000	0.125000
$65$	−4.09017	−0.507323
$66$	2.38197	0.293200
$67$	−5.52786	−0.675336	−0.337668	−	0.941265i	$-0.609638\pi$
$67$	−5.52786	−0.675336	−0.337668	+	0.941265i	$0.609638\pi$
$68$	5.09017	0.617274
$69$	0	0
$70$	1.61803	0.193392
$71$	7.09017	0.841448	0.420724	−	0.907189i	$-0.361776\pi$
$71$	7.09017	0.841448	0.420724	+	0.907189i	$0.361776\pi$
$72$	−2.61803	−0.308538
$73$	−1.23607	−0.144671	−0.0723354	−	0.997380i	$-0.523045\pi$
$73$	−1.23607	−0.144671	−0.0723354	+	0.997380i	$0.523045\pi$
$74$	2.47214	0.287380
$75$	−0.618034	−0.0713644
$76$	4.85410	0.556804
$77$	6.23607	0.710666
$78$	−2.52786	−0.286224
$79$	−10.4721	−1.17821	−0.589104	−	0.808057i	$-0.700519\pi$
$79$	−10.4721	−1.17821	−0.589104	+	0.808057i	$0.700519\pi$
$80$	−1.00000	−0.111803
$81$	5.70820	0.634245
$82$	−12.3262	−1.36121
$83$	−10.9443	−1.20129	−0.600645	−	0.799516i	$-0.705089\pi$
$83$	−10.9443	−1.20129	−0.600645	+	0.799516i	$0.705089\pi$
$84$	1.00000	0.109109
$85$	−5.09017	−0.552106
$86$	0	0
$87$	2.94427	0.315659
$88$	−3.85410	−0.410849
$89$	1.52786	0.161953	0.0809766	−	0.996716i	$-0.474196\pi$
$89$	1.52786	0.161953	0.0809766	+	0.996716i	$0.474196\pi$
$90$	2.61803	0.275965
$91$	−6.61803	−0.693758
$92$	0	0
$93$	1.29180	0.133953
$94$	9.70820	1.00132
$95$	−4.85410	−0.498020
$96$	−0.618034	−0.0630778
$97$	−14.6180	−1.48424	−0.742118	−	0.670269i	$-0.766179\pi$
$97$	−14.6180	−1.48424	−0.742118	+	0.670269i	$0.766179\pi$
$98$	−4.38197	−0.442645
$99$	10.0902	1.01410
$100$	1.00000	0.100000
$101$	−13.7082	−1.36402	−0.682009	−	0.731344i	$-0.738893\pi$
$101$	−13.7082	−1.36402	−0.682009	+	0.731344i	$0.738893\pi$
$102$	−3.14590	−0.311490
$103$	3.56231	0.351004	0.175502	−	0.984479i	$-0.443845\pi$
$103$	3.56231	0.351004	0.175502	+	0.984479i	$0.443845\pi$
$104$	4.09017	0.401074
$105$	−1.00000	−0.0975900
$106$	8.47214	0.822887
$107$	4.18034	0.404129	0.202064	−	0.979372i	$-0.435235\pi$
$107$	4.18034	0.404129	0.202064	+	0.979372i	$0.435235\pi$
$108$	3.47214	0.334106
$109$	−8.56231	−0.820120	−0.410060	−	0.912059i	$-0.634492\pi$
$109$	−8.56231	−0.820120	−0.410060	+	0.912059i	$0.634492\pi$
$110$	3.85410	0.367474
$111$	−1.52786	−0.145018
$112$	−1.61803	−0.152890
$113$	−18.9443	−1.78213	−0.891064	−	0.453878i	$-0.850040\pi$
$113$	−18.9443	−1.78213	−0.891064	+	0.453878i	$0.850040\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	−4.76393	−0.442320
$117$	−10.7082	−0.989974
$118$	−11.7082	−1.07783
$119$	−8.23607	−0.754999
$120$	0.618034	0.0564185
$121$	3.85410	0.350373
$122$	−6.32624	−0.572751
$123$	7.61803	0.686895
$124$	−2.09017	−0.187703
$125$	−1.00000	−0.0894427
$126$	4.23607	0.377379
$127$	−6.18034	−0.548416	−0.274208	−	0.961670i	$-0.588416\pi$
$127$	−6.18034	−0.548416	−0.274208	+	0.961670i	$0.588416\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−4.09017	−0.358732
$131$	−14.9443	−1.30569	−0.652844	−	0.757493i	$-0.726424\pi$
$131$	−14.9443	−1.30569	−0.652844	+	0.757493i	$0.726424\pi$
$132$	2.38197	0.207324
$133$	−7.85410	−0.681037
$134$	−5.52786	−0.477535
$135$	−3.47214	−0.298834
$136$	5.09017	0.436478
$137$	−5.32624	−0.455051	−0.227526	−	0.973772i	$-0.573064\pi$
$137$	−5.32624	−0.455051	−0.227526	+	0.973772i	$0.573064\pi$
$138$	0	0
$139$	17.2361	1.46194	0.730972	−	0.682407i	$-0.239067\pi$
$139$	17.2361	1.46194	0.730972	+	0.682407i	$0.239067\pi$
$140$	1.61803	0.136749
$141$	−6.00000	−0.505291
$142$	7.09017	0.594994
$143$	−15.7639	−1.31825
$144$	−2.61803	−0.218169
$145$	4.76393	0.395623
$146$	−1.23607	−0.102298
$147$	2.70820	0.223369
$148$	2.47214	0.203208
$149$	1.14590	0.0938756	0.0469378	−	0.998898i	$-0.485054\pi$
$149$	1.14590	0.0938756	0.0469378	+	0.998898i	$0.485054\pi$
$150$	−0.618034	−0.0504623
$151$	17.5623	1.42920	0.714600	−	0.699533i	$-0.246609\pi$
$151$	17.5623	1.42920	0.714600	+	0.699533i	$0.246609\pi$
$152$	4.85410	0.393720
$153$	−13.3262	−1.07736
$154$	6.23607	0.502517
$155$	2.09017	0.167886
$156$	−2.52786	−0.202391
$157$	−9.70820	−0.774799	−0.387400	−	0.921912i	$-0.626627\pi$
$157$	−9.70820	−0.774799	−0.387400	+	0.921912i	$0.626627\pi$
$158$	−10.4721	−0.833118
$159$	−5.23607	−0.415247
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	5.70820	0.448479
$163$	3.61803	0.283386	0.141693	−	0.989911i	$-0.454745\pi$
$163$	3.61803	0.283386	0.141693	+	0.989911i	$0.454745\pi$
$164$	−12.3262	−0.962517
$165$	−2.38197	−0.185436
$166$	−10.9443	−0.849440
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	1.00000	0.0771517
$169$	3.72949	0.286884
$170$	−5.09017	−0.390398
$171$	−12.7082	−0.971821
$172$	0	0
$173$	−21.5623	−1.63935	−0.819676	−	0.572828i	$-0.805846\pi$
$173$	−21.5623	−1.63935	−0.819676	+	0.572828i	$0.805846\pi$
$174$	2.94427	0.223205
$175$	−1.61803	−0.122312
$176$	−3.85410	−0.290514
$177$	7.23607	0.543896
$178$	1.52786	0.114518
$179$	−20.1803	−1.50835	−0.754175	−	0.656674i	$-0.771963\pi$
$179$	−20.1803	−1.50835	−0.754175	+	0.656674i	$0.771963\pi$
$180$	2.61803	0.195137
$181$	18.8541	1.40141	0.700707	−	0.713449i	$-0.252868\pi$
$181$	18.8541	1.40141	0.700707	+	0.713449i	$0.252868\pi$
$182$	−6.61803	−0.490561
$183$	3.90983	0.289023
$184$	0	0
$185$	−2.47214	−0.181755
$186$	1.29180	0.0947191
$187$	−19.6180	−1.43461
$188$	9.70820	0.708044
$189$	−5.61803	−0.408652
$190$	−4.85410	−0.352154
$191$	0.291796	0.0211136	0.0105568	−	0.999944i	$-0.496640\pi$
$191$	0.291796	0.0211136	0.0105568	+	0.999944i	$0.496640\pi$
$192$	−0.618034	−0.0446028
$193$	5.23607	0.376900	0.188450	−	0.982083i	$-0.439654\pi$
$193$	5.23607	0.376900	0.188450	+	0.982083i	$0.439654\pi$
$194$	−14.6180	−1.04951
$195$	2.52786	0.181024
$196$	−4.38197	−0.312998
$197$	−2.43769	−0.173679	−0.0868393	−	0.996222i	$-0.527677\pi$
$197$	−2.43769	−0.173679	−0.0868393	+	0.996222i	$0.527677\pi$
$198$	10.0902	0.717077
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	1.00000	0.0707107
$201$	3.41641	0.240975
$202$	−13.7082	−0.964506
$203$	7.70820	0.541010
$204$	−3.14590	−0.220257
$205$	12.3262	0.860902
$206$	3.56231	0.248198
$207$	0	0
$208$	4.09017	0.283602
$209$	−18.7082	−1.29407
$210$	−1.00000	−0.0690066
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	8.47214	0.581869
$213$	−4.38197	−0.300247
$214$	4.18034	0.285762
$215$	0	0
$216$	3.47214	0.236249
$217$	3.38197	0.229583
$218$	−8.56231	−0.579913
$219$	0.763932	0.0516217
$220$	3.85410	0.259844
$221$	20.8197	1.40048
$222$	−1.52786	−0.102544
$223$	−3.05573	−0.204627	−0.102313	−	0.994752i	$-0.532624\pi$
$223$	−3.05573	−0.204627	−0.102313	+	0.994752i	$0.532624\pi$
$224$	−1.61803	−0.108109
$225$	−2.61803	−0.174536
$226$	−18.9443	−1.26015
$227$	23.2361	1.54223	0.771116	−	0.636695i	$-0.219699\pi$
$227$	23.2361	1.54223	0.771116	+	0.636695i	$0.219699\pi$
$228$	−3.00000	−0.198680
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	−3.85410	−0.253581
$232$	−4.76393	−0.312767
$233$	19.7082	1.29113	0.645564	−	0.763706i	$-0.276622\pi$
$233$	19.7082	1.29113	0.645564	+	0.763706i	$0.276622\pi$
$234$	−10.7082	−0.700017
$235$	−9.70820	−0.633293
$236$	−11.7082	−0.762139
$237$	6.47214	0.420410
$238$	−8.23607	−0.533865
$239$	24.3607	1.57576	0.787881	−	0.615828i	$-0.211178\pi$
$239$	24.3607	1.57576	0.787881	+	0.615828i	$0.211178\pi$
$240$	0.618034	0.0398939
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	3.85410	0.247751
$243$	−13.9443	−0.894525
$244$	−6.32624	−0.404996
$245$	4.38197	0.279954
$246$	7.61803	0.485708
$247$	19.8541	1.26329
$248$	−2.09017	−0.132726
$249$	6.76393	0.428647
$250$	−1.00000	−0.0632456
$251$	−12.8541	−0.811344	−0.405672	−	0.914019i	$-0.632962\pi$
$251$	−12.8541	−0.811344	−0.405672	+	0.914019i	$0.632962\pi$
$252$	4.23607	0.266847
$253$	0	0
$254$	−6.18034	−0.387789
$255$	3.14590	0.197004
$256$	1.00000	0.0625000
$257$	−30.1803	−1.88260	−0.941299	−	0.337574i	$-0.890394\pi$
$257$	−30.1803	−1.88260	−0.941299	+	0.337574i	$0.890394\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	−4.09017	−0.253662
$261$	12.4721	0.772006
$262$	−14.9443	−0.923260
$263$	21.7426	1.34071	0.670354	−	0.742041i	$-0.266142\pi$
$263$	21.7426	1.34071	0.670354	+	0.742041i	$0.266142\pi$
$264$	2.38197	0.146600
$265$	−8.47214	−0.520439
$266$	−7.85410	−0.481566
$267$	−0.944272	−0.0577885
$268$	−5.52786	−0.337668
$269$	8.18034	0.498764	0.249382	−	0.968405i	$-0.419773\pi$
$269$	8.18034	0.498764	0.249382	+	0.968405i	$0.419773\pi$
$270$	−3.47214	−0.211307
$271$	−14.6738	−0.891368	−0.445684	−	0.895190i	$-0.647039\pi$
$271$	−14.6738	−0.891368	−0.445684	+	0.895190i	$0.647039\pi$
$272$	5.09017	0.308637
$273$	4.09017	0.247548
$274$	−5.32624	−0.321770
$275$	−3.85410	−0.232411
$276$	0	0
$277$	2.58359	0.155233	0.0776165	−	0.996983i	$-0.475269\pi$
$277$	2.58359	0.155233	0.0776165	+	0.996983i	$0.475269\pi$
$278$	17.2361	1.03375
$279$	5.47214	0.327608
$280$	1.61803	0.0966960
$281$	−27.2361	−1.62477	−0.812384	−	0.583123i	$-0.801831\pi$
$281$	−27.2361	−1.62477	−0.812384	+	0.583123i	$0.801831\pi$
$282$	−6.00000	−0.357295
$283$	9.05573	0.538307	0.269154	−	0.963097i	$-0.413256\pi$
$283$	9.05573	0.538307	0.269154	+	0.963097i	$0.413256\pi$
$284$	7.09017	0.420724
$285$	3.00000	0.177705
$286$	−15.7639	−0.932141
$287$	19.9443	1.17727
$288$	−2.61803	−0.154269
$289$	8.90983	0.524108
$290$	4.76393	0.279748
$291$	9.03444	0.529608
$292$	−1.23607	−0.0723354
$293$	−15.8885	−0.928219	−0.464109	−	0.885778i	$-0.653626\pi$
$293$	−15.8885	−0.928219	−0.464109	+	0.885778i	$0.653626\pi$
$294$	2.70820	0.157946
$295$	11.7082	0.681678
$296$	2.47214	0.143690
$297$	−13.3820	−0.776500
$298$	1.14590	0.0663801
$299$	0	0
$300$	−0.618034	−0.0356822
$301$	0	0
$302$	17.5623	1.01060
$303$	8.47214	0.486711
$304$	4.85410	0.278402
$305$	6.32624	0.362239
$306$	−13.3262	−0.761810
$307$	27.4508	1.56670	0.783351	−	0.621579i	$-0.213509\pi$
$307$	27.4508	1.56670	0.783351	+	0.621579i	$0.213509\pi$
$308$	6.23607	0.355333
$309$	−2.20163	−0.125246
$310$	2.09017	0.118714
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−2.52786	−0.143112
$313$	11.7984	0.666884	0.333442	−	0.942771i	$-0.391790\pi$
$313$	11.7984	0.666884	0.333442	+	0.942771i	$0.391790\pi$
$314$	−9.70820	−0.547866
$315$	−4.23607	−0.238675
$316$	−10.4721	−0.589104
$317$	0.0901699	0.00506445	0.00253222	−	0.999997i	$-0.499194\pi$
$317$	0.0901699	0.00506445	0.00253222	+	0.999997i	$0.499194\pi$
$318$	−5.23607	−0.293624
$319$	18.3607	1.02800
$320$	−1.00000	−0.0559017
$321$	−2.58359	−0.144202
$322$	0	0
$323$	24.7082	1.37480
$324$	5.70820	0.317122
$325$	4.09017	0.226882
$326$	3.61803	0.200384
$327$	5.29180	0.292637
$328$	−12.3262	−0.680603
$329$	−15.7082	−0.866021
$330$	−2.38197	−0.131123
$331$	14.7639	0.811499	0.405750	−	0.913984i	$-0.367011\pi$
$331$	14.7639	0.811499	0.405750	+	0.913984i	$0.367011\pi$
$332$	−10.9443	−0.600645
$333$	−6.47214	−0.354671
$334$	−8.00000	−0.437741
$335$	5.52786	0.302019
$336$	1.00000	0.0545545
$337$	−29.3262	−1.59750	−0.798751	−	0.601662i	$-0.794506\pi$
$337$	−29.3262	−1.59750	−0.798751	+	0.601662i	$0.794506\pi$
$338$	3.72949	0.202858
$339$	11.7082	0.635902
$340$	−5.09017	−0.276053
$341$	8.05573	0.436242
$342$	−12.7082	−0.687181
$343$	18.4164	0.994393
$344$	0	0
$345$	0	0
$346$	−21.5623	−1.15920
$347$	−8.61803	−0.462640	−0.231320	−	0.972878i	$-0.574304\pi$
$347$	−8.61803	−0.462640	−0.231320	+	0.972878i	$0.574304\pi$
$348$	2.94427	0.157830
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−1.61803	−0.0864876
$351$	14.2016	0.758027
$352$	−3.85410	−0.205424
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	7.23607	0.384593
$355$	−7.09017	−0.376307
$356$	1.52786	0.0809766
$357$	5.09017	0.269400
$358$	−20.1803	−1.06656
$359$	18.3607	0.969040	0.484520	−	0.874780i	$-0.338994\pi$
$359$	18.3607	0.969040	0.484520	+	0.874780i	$0.338994\pi$
$360$	2.61803	0.137983
$361$	4.56231	0.240121
$362$	18.8541	0.990950
$363$	−2.38197	−0.125021
$364$	−6.61803	−0.346879
$365$	1.23607	0.0646988
$366$	3.90983	0.204370
$367$	2.47214	0.129044	0.0645222	−	0.997916i	$-0.479448\pi$
$367$	2.47214	0.129044	0.0645222	+	0.997916i	$0.479448\pi$
$368$	0	0
$369$	32.2705	1.67994
$370$	−2.47214	−0.128520
$371$	−13.7082	−0.711694
$372$	1.29180	0.0669765
$373$	2.18034	0.112894	0.0564469	−	0.998406i	$-0.482023\pi$
$373$	2.18034	0.112894	0.0564469	+	0.998406i	$0.482023\pi$
$374$	−19.6180	−1.01442
$375$	0.618034	0.0319151
$376$	9.70820	0.500662
$377$	−19.4853	−1.00354
$378$	−5.61803	−0.288960
$379$	−33.4508	−1.71825	−0.859127	−	0.511762i	$-0.828993\pi$
$379$	−33.4508	−1.71825	−0.859127	+	0.511762i	$0.828993\pi$
$380$	−4.85410	−0.249010
$381$	3.81966	0.195687
$382$	0.291796	0.0149296
$383$	−17.8885	−0.914062	−0.457031	−	0.889451i	$-0.651087\pi$
$383$	−17.8885	−0.914062	−0.457031	+	0.889451i	$0.651087\pi$
$384$	−0.618034	−0.0315389
$385$	−6.23607	−0.317819
$386$	5.23607	0.266509
$387$	0	0
$388$	−14.6180	−0.742118
$389$	−5.67376	−0.287671	−0.143836	−	0.989602i	$-0.545944\pi$
$389$	−5.67376	−0.287671	−0.143836	+	0.989602i	$0.545944\pi$
$390$	2.52786	0.128003
$391$	0	0
$392$	−4.38197	−0.221323
$393$	9.23607	0.465898
$394$	−2.43769	−0.122809
$395$	10.4721	0.526910
$396$	10.0902	0.507050
$397$	−8.32624	−0.417882	−0.208941	−	0.977928i	$-0.567002\pi$
$397$	−8.32624	−0.417882	−0.208941	+	0.977928i	$0.567002\pi$
$398$	−2.00000	−0.100251
$399$	4.85410	0.243009
$400$	1.00000	0.0500000
$401$	−11.7082	−0.584680	−0.292340	−	0.956314i	$-0.594434\pi$
$401$	−11.7082	−0.584680	−0.292340	+	0.956314i	$0.594434\pi$
$402$	3.41641	0.170395
$403$	−8.54915	−0.425864
$404$	−13.7082	−0.682009
$405$	−5.70820	−0.283643
$406$	7.70820	0.382552
$407$	−9.52786	−0.472279
$408$	−3.14590	−0.155745
$409$	21.2148	1.04900	0.524502	−	0.851409i	$-0.324252\pi$
$409$	21.2148	1.04900	0.524502	+	0.851409i	$0.324252\pi$
$410$	12.3262	0.608750
$411$	3.29180	0.162372
$412$	3.56231	0.175502
$413$	18.9443	0.932187
$414$	0	0
$415$	10.9443	0.537233
$416$	4.09017	0.200537
$417$	−10.6525	−0.521654
$418$	−18.7082	−0.915048
$419$	−5.52786	−0.270054	−0.135027	−	0.990842i	$-0.543112\pi$
$419$	−5.52786	−0.270054	−0.135027	+	0.990842i	$0.543112\pi$
$420$	−1.00000	−0.0487950
$421$	28.7426	1.40083	0.700415	−	0.713735i	$-0.252998\pi$
$421$	28.7426	1.40083	0.700415	+	0.713735i	$0.252998\pi$
$422$	14.0000	0.681509
$423$	−25.4164	−1.23579
$424$	8.47214	0.411443
$425$	5.09017	0.246910
$426$	−4.38197	−0.212307
$427$	10.2361	0.495358
$428$	4.18034	0.202064
$429$	9.74265	0.470379
$430$	0	0
$431$	−34.6525	−1.66915	−0.834576	−	0.550894i	$-0.814287\pi$
$431$	−34.6525	−1.66915	−0.834576	+	0.550894i	$0.814287\pi$
$432$	3.47214	0.167053
$433$	29.5066	1.41800	0.708998	−	0.705211i	$-0.249148\pi$
$433$	29.5066	1.41800	0.708998	+	0.705211i	$0.249148\pi$
$434$	3.38197	0.162340
$435$	−2.94427	−0.141167
$436$	−8.56231	−0.410060
$437$	0	0
$438$	0.763932	0.0365021
$439$	−15.6180	−0.745408	−0.372704	−	0.927950i	$-0.621569\pi$
$439$	−15.6180	−0.745408	−0.372704	+	0.927950i	$0.621569\pi$
$440$	3.85410	0.183737
$441$	11.4721	0.546292
$442$	20.8197	0.990290
$443$	13.9098	0.660876	0.330438	−	0.943828i	$-0.392804\pi$
$443$	13.9098	0.660876	0.330438	+	0.943828i	$0.392804\pi$
$444$	−1.52786	−0.0725092
$445$	−1.52786	−0.0724277
$446$	−3.05573	−0.144693
$447$	−0.708204	−0.0334969
$448$	−1.61803	−0.0764449
$449$	18.5623	0.876009	0.438005	−	0.898973i	$-0.355685\pi$
$449$	18.5623	0.876009	0.438005	+	0.898973i	$0.355685\pi$
$450$	−2.61803	−0.123415
$451$	47.5066	2.23700
$452$	−18.9443	−0.891064
$453$	−10.8541	−0.509970
$454$	23.2361	1.09052
$455$	6.61803	0.310258
$456$	−3.00000	−0.140488
$457$	−33.7771	−1.58003	−0.790013	−	0.613090i	$-0.789926\pi$
$457$	−33.7771	−1.58003	−0.790013	+	0.613090i	$0.789926\pi$
$458$	−10.0000	−0.467269
$459$	17.6738	0.824941
$460$	0	0
$461$	−34.7639	−1.61912	−0.809559	−	0.587039i	$-0.800294\pi$
$461$	−34.7639	−1.61912	−0.809559	+	0.587039i	$0.800294\pi$
$462$	−3.85410	−0.179309
$463$	2.00000	0.0929479	0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000	0.0929479	0.0464739	+	0.998920i	$0.485202\pi$
$464$	−4.76393	−0.221160
$465$	−1.29180	−0.0599056
$466$	19.7082	0.912965
$467$	−23.1246	−1.07008	−0.535040	−	0.844827i	$-0.679703\pi$
$467$	−23.1246	−1.07008	−0.535040	+	0.844827i	$0.679703\pi$
$468$	−10.7082	−0.494987
$469$	8.94427	0.413008
$470$	−9.70820	−0.447806
$471$	6.00000	0.276465
$472$	−11.7082	−0.538914
$473$	0	0
$474$	6.47214	0.297275
$475$	4.85410	0.222721
$476$	−8.23607	−0.377500
$477$	−22.1803	−1.01557
$478$	24.3607	1.11423
$479$	−3.88854	−0.177672	−0.0888361	−	0.996046i	$-0.528315\pi$
$479$	−3.88854	−0.177672	−0.0888361	+	0.996046i	$0.528315\pi$
$480$	0.618034	0.0282093
$481$	10.1115	0.461043
$482$	0	0
$483$	0	0
$484$	3.85410	0.175186
$485$	14.6180	0.663771
$486$	−13.9443	−0.632525
$487$	−42.1803	−1.91137	−0.955687	−	0.294385i	$-0.904885\pi$
$487$	−42.1803	−1.91137	−0.955687	+	0.294385i	$0.904885\pi$
$488$	−6.32624	−0.286375
$489$	−2.23607	−0.101118
$490$	4.38197	0.197957
$491$	−16.1803	−0.730209	−0.365104	−	0.930967i	$-0.618967\pi$
$491$	−16.1803	−0.730209	−0.365104	+	0.930967i	$0.618967\pi$
$492$	7.61803	0.343447
$493$	−24.2492	−1.09213
$494$	19.8541	0.893278
$495$	−10.0902	−0.453519
$496$	−2.09017	−0.0938514
$497$	−11.4721	−0.514596
$498$	6.76393	0.303099
$499$	−32.3607	−1.44866	−0.724331	−	0.689452i	$-0.757851\pi$
$499$	−32.3607	−1.44866	−0.724331	+	0.689452i	$0.757851\pi$
$500$	−1.00000	−0.0447214
$501$	4.94427	0.220894
$502$	−12.8541	−0.573707
$503$	−20.6738	−0.921797	−0.460899	−	0.887453i	$-0.652473\pi$
$503$	−20.6738	−0.921797	−0.460899	+	0.887453i	$0.652473\pi$
$504$	4.23607	0.188689
$505$	13.7082	0.610007
$506$	0	0
$507$	−2.30495	−0.102366
$508$	−6.18034	−0.274208
$509$	5.34752	0.237025	0.118512	−	0.992953i	$-0.462187\pi$
$509$	5.34752	0.237025	0.118512	+	0.992953i	$0.462187\pi$
$510$	3.14590	0.139303
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	16.8541	0.744127
$514$	−30.1803	−1.33120
$515$	−3.56231	−0.156974
$516$	0	0
$517$	−37.4164	−1.64557
$518$	−4.00000	−0.175750
$519$	13.3262	0.584957
$520$	−4.09017	−0.179366
$521$	24.4721	1.07214	0.536072	−	0.844172i	$-0.319908\pi$
$521$	24.4721	1.07214	0.536072	+	0.844172i	$0.319908\pi$
$522$	12.4721	0.545891
$523$	26.0000	1.13690	0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000	1.13690	0.568450	+	0.822718i	$0.307543\pi$
$524$	−14.9443	−0.652844
$525$	1.00000	0.0436436
$526$	21.7426	0.948024
$527$	−10.6393	−0.463456
$528$	2.38197	0.103662
$529$	0	0
$530$	−8.47214	−0.368006
$531$	30.6525	1.33020
$532$	−7.85410	−0.340519
$533$	−50.4164	−2.18378
$534$	−0.944272	−0.0408626
$535$	−4.18034	−0.180732
$536$	−5.52786	−0.238767
$537$	12.4721	0.538212
$538$	8.18034	0.352679
$539$	16.8885	0.727441
$540$	−3.47214	−0.149417
$541$	−30.8328	−1.32561	−0.662803	−	0.748794i	$-0.730633\pi$
$541$	−30.8328	−1.32561	−0.662803	+	0.748794i	$0.730633\pi$
$542$	−14.6738	−0.630292
$543$	−11.6525	−0.500056
$544$	5.09017	0.218239
$545$	8.56231	0.366769
$546$	4.09017	0.175043
$547$	−36.9230	−1.57871	−0.789356	−	0.613935i	$-0.789586\pi$
$547$	−36.9230	−1.57871	−0.789356	+	0.613935i	$0.789586\pi$
$548$	−5.32624	−0.227526
$549$	16.5623	0.706862
$550$	−3.85410	−0.164339
$551$	−23.1246	−0.985142
$552$	0	0
$553$	16.9443	0.720544
$554$	2.58359	0.109766
$555$	1.52786	0.0648542
$556$	17.2361	0.730972
$557$	−30.8328	−1.30643	−0.653214	−	0.757173i	$-0.726580\pi$
$557$	−30.8328	−1.30643	−0.653214	+	0.757173i	$0.726580\pi$
$558$	5.47214	0.231654
$559$	0	0
$560$	1.61803	0.0683744
$561$	12.1246	0.511902
$562$	−27.2361	−1.14888
$563$	−21.8885	−0.922492	−0.461246	−	0.887272i	$-0.652597\pi$
$563$	−21.8885	−0.922492	−0.461246	+	0.887272i	$0.652597\pi$
$564$	−6.00000	−0.252646
$565$	18.9443	0.796992
$566$	9.05573	0.380641
$567$	−9.23607	−0.387878
$568$	7.09017	0.297497
$569$	2.00000	0.0838444	0.0419222	−	0.999121i	$-0.486652\pi$
$569$	2.00000	0.0838444	0.0419222	+	0.999121i	$0.486652\pi$
$570$	3.00000	0.125656
$571$	30.9787	1.29642	0.648209	−	0.761462i	$-0.275518\pi$
$571$	30.9787	1.29642	0.648209	+	0.761462i	$0.275518\pi$
$572$	−15.7639	−0.659123
$573$	−0.180340	−0.00753381
$574$	19.9443	0.832458
$575$	0	0
$576$	−2.61803	−0.109085
$577$	−12.4721	−0.519222	−0.259611	−	0.965713i	$-0.583594\pi$
$577$	−12.4721	−0.519222	−0.259611	+	0.965713i	$0.583594\pi$
$578$	8.90983	0.370600
$579$	−3.23607	−0.134486
$580$	4.76393	0.197812
$581$	17.7082	0.734660
$582$	9.03444	0.374490
$583$	−32.6525	−1.35233
$584$	−1.23607	−0.0511489
$585$	10.7082	0.442730
$586$	−15.8885	−0.656350
$587$	11.3820	0.469784	0.234892	−	0.972021i	$-0.424526\pi$
$587$	11.3820	0.469784	0.234892	+	0.972021i	$0.424526\pi$
$588$	2.70820	0.111684
$589$	−10.1459	−0.418054
$590$	11.7082	0.482019
$591$	1.50658	0.0619723
$592$	2.47214	0.101604
$593$	34.7639	1.42758	0.713792	−	0.700358i	$-0.246976\pi$
$593$	34.7639	1.42758	0.713792	+	0.700358i	$0.246976\pi$
$594$	−13.3820	−0.549069
$595$	8.23607	0.337646
$596$	1.14590	0.0469378
$597$	1.23607	0.0505889
$598$	0	0
$599$	−20.6180	−0.842430	−0.421215	−	0.906961i	$-0.638396\pi$
$599$	−20.6180	−0.842430	−0.421215	+	0.906961i	$0.638396\pi$
$600$	−0.618034	−0.0252311
$601$	0.270510	0.0110343	0.00551716	−	0.999985i	$-0.498244\pi$
$601$	0.270510	0.0110343	0.00551716	+	0.999985i	$0.498244\pi$
$602$	0	0
$603$	14.4721	0.589351
$604$	17.5623	0.714600
$605$	−3.85410	−0.156692
$606$	8.47214	0.344157
$607$	17.5279	0.711434	0.355717	−	0.934594i	$-0.384237\pi$
$607$	17.5279	0.711434	0.355717	+	0.934594i	$0.384237\pi$
$608$	4.85410	0.196860
$609$	−4.76393	−0.193044
$610$	6.32624	0.256142
$611$	39.7082	1.60642
$612$	−13.3262	−0.538681
$613$	43.3050	1.74907	0.874535	−	0.484962i	$-0.161167\pi$
$613$	43.3050	1.74907	0.874535	+	0.484962i	$0.161167\pi$
$614$	27.4508	1.10783
$615$	−7.61803	−0.307189
$616$	6.23607	0.251258
$617$	−22.9098	−0.922315	−0.461158	−	0.887318i	$-0.652566\pi$
$617$	−22.9098	−0.922315	−0.461158	+	0.887318i	$0.652566\pi$
$618$	−2.20163	−0.0885624
$619$	−21.7984	−0.876151	−0.438075	−	0.898938i	$-0.644340\pi$
$619$	−21.7984	−0.876151	−0.438075	+	0.898938i	$0.644340\pi$
$620$	2.09017	0.0839432
$621$	0	0
$622$	4.00000	0.160385
$623$	−2.47214	−0.0990440
$624$	−2.52786	−0.101196
$625$	1.00000	0.0400000
$626$	11.7984	0.471558
$627$	11.5623	0.461754
$628$	−9.70820	−0.387400
$629$	12.5836	0.501741
$630$	−4.23607	−0.168769
$631$	16.0689	0.639692	0.319846	−	0.947470i	$-0.396369\pi$
$631$	16.0689	0.639692	0.319846	+	0.947470i	$0.396369\pi$
$632$	−10.4721	−0.416559
$633$	−8.65248	−0.343905
$634$	0.0901699	0.00358111
$635$	6.18034	0.245259
$636$	−5.23607	−0.207624
$637$	−17.9230	−0.710135
$638$	18.3607	0.726906
$639$	−18.5623	−0.734313
$640$	−1.00000	−0.0395285
$641$	44.3607	1.75214	0.876071	−	0.482183i	$-0.160156\pi$
$641$	44.3607	1.75214	0.876071	+	0.482183i	$0.160156\pi$
$642$	−2.58359	−0.101966
$643$	21.7082	0.856088	0.428044	−	0.903758i	$-0.359203\pi$
$643$	21.7082	0.856088	0.428044	+	0.903758i	$0.359203\pi$
$644$	0	0
$645$	0	0
$646$	24.7082	0.972131
$647$	44.2492	1.73962	0.869808	−	0.493390i	$-0.164242\pi$
$647$	44.2492	1.73962	0.869808	+	0.493390i	$0.164242\pi$
$648$	5.70820	0.224239
$649$	45.1246	1.77130
$650$	4.09017	0.160430
$651$	−2.09017	−0.0819202
$652$	3.61803	0.141693
$653$	21.0344	0.823141	0.411571	−	0.911378i	$-0.364980\pi$
$653$	21.0344	0.823141	0.411571	+	0.911378i	$0.364980\pi$
$654$	5.29180	0.206926
$655$	14.9443	0.583921
$656$	−12.3262	−0.481259
$657$	3.23607	0.126251
$658$	−15.7082	−0.612370
$659$	−34.2492	−1.33416	−0.667080	−	0.744986i	$-0.732456\pi$
$659$	−34.2492	−1.33416	−0.667080	+	0.744986i	$0.732456\pi$
$660$	−2.38197	−0.0927179
$661$	−34.3262	−1.33514	−0.667568	−	0.744549i	$-0.732665\pi$
$661$	−34.3262	−1.33514	−0.667568	+	0.744549i	$0.732665\pi$
$662$	14.7639	0.573817
$663$	−12.8673	−0.499723
$664$	−10.9443	−0.424720
$665$	7.85410	0.304569
$666$	−6.47214	−0.250790
$667$	0	0
$668$	−8.00000	−0.309529
$669$	1.88854	0.0730153
$670$	5.52786	0.213560
$671$	24.3820	0.941255
$672$	1.00000	0.0385758
$673$	6.94427	0.267682	0.133841	−	0.991003i	$-0.457269\pi$
$673$	6.94427	0.267682	0.133841	+	0.991003i	$0.457269\pi$
$674$	−29.3262	−1.12960
$675$	3.47214	0.133643
$676$	3.72949	0.143442
$677$	33.0557	1.27043	0.635217	−	0.772333i	$-0.280910\pi$
$677$	33.0557	1.27043	0.635217	+	0.772333i	$0.280910\pi$
$678$	11.7082	0.449651
$679$	23.6525	0.907699
$680$	−5.09017	−0.195199
$681$	−14.3607	−0.550302
$682$	8.05573	0.308470
$683$	−11.4377	−0.437651	−0.218826	−	0.975764i	$-0.570223\pi$
$683$	−11.4377	−0.437651	−0.218826	+	0.975764i	$0.570223\pi$
$684$	−12.7082	−0.485910
$685$	5.32624	0.203505
$686$	18.4164	0.703142
$687$	6.18034	0.235795
$688$	0	0
$689$	34.6525	1.32015
$690$	0	0
$691$	−24.7639	−0.942064	−0.471032	−	0.882116i	$-0.656118\pi$
$691$	−24.7639	−0.942064	−0.471032	+	0.882116i	$0.656118\pi$
$692$	−21.5623	−0.819676
$693$	−16.3262	−0.620182
$694$	−8.61803	−0.327136
$695$	−17.2361	−0.653801
$696$	2.94427	0.111602
$697$	−62.7426	−2.37655
$698$	−2.00000	−0.0757011
$699$	−12.1803	−0.460703
$700$	−1.61803	−0.0611559
$701$	48.3394	1.82575	0.912877	−	0.408235i	$-0.133856\pi$
$701$	48.3394	1.82575	0.912877	+	0.408235i	$0.133856\pi$
$702$	14.2016	0.536006
$703$	12.0000	0.452589
$704$	−3.85410	−0.145257
$705$	6.00000	0.225973
$706$	24.0000	0.903252
$707$	22.1803	0.834178
$708$	7.23607	0.271948
$709$	14.9098	0.559950	0.279975	−	0.960007i	$-0.409674\pi$
$709$	14.9098	0.559950	0.279975	+	0.960007i	$0.409674\pi$
$710$	−7.09017	−0.266089
$711$	27.4164	1.02820
$712$	1.52786	0.0572591
$713$	0	0
$714$	5.09017	0.190495
$715$	15.7639	0.589538
$716$	−20.1803	−0.754175
$717$	−15.0557	−0.562266
$718$	18.3607	0.685214
$719$	1.72949	0.0644991	0.0322495	−	0.999480i	$-0.489733\pi$
$719$	1.72949	0.0644991	0.0322495	+	0.999480i	$0.489733\pi$
$720$	2.61803	0.0975684
$721$	−5.76393	−0.214660
$722$	4.56231	0.169791
$723$	0	0
$724$	18.8541	0.700707
$725$	−4.76393	−0.176928
$726$	−2.38197	−0.0884031
$727$	−52.7984	−1.95818	−0.979092	−	0.203420i	$-0.934794\pi$
$727$	−52.7984	−1.95818	−0.979092	+	0.203420i	$0.934794\pi$
$728$	−6.61803	−0.245281
$729$	−8.50658	−0.315058
$730$	1.23607	0.0457489
$731$	0	0
$732$	3.90983	0.144511
$733$	2.58359	0.0954272	0.0477136	−	0.998861i	$-0.484807\pi$
$733$	2.58359	0.0954272	0.0477136	+	0.998861i	$0.484807\pi$
$734$	2.47214	0.0912482
$735$	−2.70820	−0.0998936
$736$	0	0
$737$	21.3050	0.784778
$738$	32.2705	1.18789
$739$	21.8885	0.805183	0.402592	−	0.915380i	$-0.368110\pi$
$739$	21.8885	0.805183	0.402592	+	0.915380i	$0.368110\pi$
$740$	−2.47214	−0.0908775
$741$	−12.2705	−0.450768
$742$	−13.7082	−0.503244
$743$	44.6312	1.63736	0.818680	−	0.574250i	$-0.194706\pi$
$743$	44.6312	1.63736	0.818680	+	0.574250i	$0.194706\pi$
$744$	1.29180	0.0473595
$745$	−1.14590	−0.0419825
$746$	2.18034	0.0798279
$747$	28.6525	1.04834
$748$	−19.6180	−0.717306
$749$	−6.76393	−0.247149
$750$	0.618034	0.0225674
$751$	−29.0132	−1.05871	−0.529353	−	0.848402i	$-0.677565\pi$
$751$	−29.0132	−1.05871	−0.529353	+	0.848402i	$0.677565\pi$
$752$	9.70820	0.354022
$753$	7.94427	0.289505
$754$	−19.4853	−0.709612
$755$	−17.5623	−0.639158
$756$	−5.61803	−0.204326
$757$	−17.8885	−0.650170	−0.325085	−	0.945685i	$-0.605393\pi$
$757$	−17.8885	−0.650170	−0.325085	+	0.945685i	$0.605393\pi$
$758$	−33.4508	−1.21499
$759$	0	0
$760$	−4.85410	−0.176077
$761$	−35.8673	−1.30019	−0.650094	−	0.759854i	$-0.725270\pi$
$761$	−35.8673	−1.30019	−0.650094	+	0.759854i	$0.725270\pi$
$762$	3.81966	0.138372
$763$	13.8541	0.501552
$764$	0.291796	0.0105568
$765$	13.3262	0.481811
$766$	−17.8885	−0.646339
$767$	−47.8885	−1.72916
$768$	−0.618034	−0.0223014
$769$	33.4164	1.20503	0.602513	−	0.798109i	$-0.294166\pi$
$769$	33.4164	1.20503	0.602513	+	0.798109i	$0.294166\pi$
$770$	−6.23607	−0.224732
$771$	18.6525	0.671753
$772$	5.23607	0.188450
$773$	−11.0557	−0.397647	−0.198823	−	0.980035i	$-0.563712\pi$
$773$	−11.0557	−0.397647	−0.198823	+	0.980035i	$0.563712\pi$
$774$	0	0
$775$	−2.09017	−0.0750811
$776$	−14.6180	−0.524757
$777$	2.47214	0.0886874
$778$	−5.67376	−0.203414
$779$	−59.8328	−2.14373
$780$	2.52786	0.0905121
$781$	−27.3262	−0.977810
$782$	0	0
$783$	−16.5410	−0.591128
$784$	−4.38197	−0.156499
$785$	9.70820	0.346501
$786$	9.23607	0.329440
$787$	43.1246	1.53723	0.768613	−	0.639714i	$-0.220947\pi$
$787$	43.1246	1.53723	0.768613	+	0.639714i	$0.220947\pi$
$788$	−2.43769	−0.0868393
$789$	−13.4377	−0.478395
$790$	10.4721	0.372582
$791$	30.6525	1.08988
$792$	10.0902	0.358539
$793$	−25.8754	−0.918862
$794$	−8.32624	−0.295487
$795$	5.23607	0.185704
$796$	−2.00000	−0.0708881
$797$	−0.291796	−0.0103359	−0.00516797	−	0.999987i	$-0.501645\pi$
$797$	−0.291796	−0.0103359	−0.00516797	+	0.999987i	$0.501645\pi$
$798$	4.85410	0.171833
$799$	49.4164	1.74823
$800$	1.00000	0.0353553
$801$	−4.00000	−0.141333
$802$	−11.7082	−0.413431
$803$	4.76393	0.168116
$804$	3.41641	0.120487
$805$	0	0
$806$	−8.54915	−0.301131
$807$	−5.05573	−0.177970
$808$	−13.7082	−0.482253
$809$	−4.25735	−0.149681	−0.0748403	−	0.997196i	$-0.523845\pi$
$809$	−4.25735	−0.149681	−0.0748403	+	0.997196i	$0.523845\pi$
$810$	−5.70820	−0.200566
$811$	44.1803	1.55138	0.775691	−	0.631113i	$-0.217402\pi$
$811$	44.1803	1.55138	0.775691	+	0.631113i	$0.217402\pi$
$812$	7.70820	0.270505
$813$	9.06888	0.318060
$814$	−9.52786	−0.333951
$815$	−3.61803	−0.126734
$816$	−3.14590	−0.110128
$817$	0	0
$818$	21.2148	0.741757
$819$	17.3262	0.605428
$820$	12.3262	0.430451
$821$	−50.9443	−1.77797	−0.888984	−	0.457939i	$-0.848588\pi$
$821$	−50.9443	−1.77797	−0.888984	+	0.457939i	$0.848588\pi$
$822$	3.29180	0.114815
$823$	−1.41641	−0.0493729	−0.0246864	−	0.999695i	$-0.507859\pi$
$823$	−1.41641	−0.0493729	−0.0246864	+	0.999695i	$0.507859\pi$
$824$	3.56231	0.124099
$825$	2.38197	0.0829294
$826$	18.9443	0.659156
$827$	−8.29180	−0.288334	−0.144167	−	0.989553i	$-0.546050\pi$
$827$	−8.29180	−0.288334	−0.144167	+	0.989553i	$0.546050\pi$
$828$	0	0
$829$	1.05573	0.0366670	0.0183335	−	0.999832i	$-0.494164\pi$
$829$	1.05573	0.0366670	0.0183335	+	0.999832i	$0.494164\pi$
$830$	10.9443	0.379881
$831$	−1.59675	−0.0553906
$832$	4.09017	0.141801
$833$	−22.3050	−0.772821
$834$	−10.6525	−0.368865
$835$	8.00000	0.276851
$836$	−18.7082	−0.647037
$837$	−7.25735	−0.250851
$838$	−5.52786	−0.190957
$839$	43.0132	1.48498	0.742490	−	0.669858i	$-0.233645\pi$
$839$	43.0132	1.48498	0.742490	+	0.669858i	$0.233645\pi$
$840$	−1.00000	−0.0345033
$841$	−6.30495	−0.217412
$842$	28.7426	0.990537
$843$	16.8328	0.579753
$844$	14.0000	0.481900
$845$	−3.72949	−0.128298
$846$	−25.4164	−0.873834
$847$	−6.23607	−0.214274
$848$	8.47214	0.290934
$849$	−5.59675	−0.192080
$850$	5.09017	0.174591
$851$	0	0
$852$	−4.38197	−0.150124
$853$	13.7984	0.472447	0.236224	−	0.971699i	$-0.424090\pi$
$853$	13.7984	0.472447	0.236224	+	0.971699i	$0.424090\pi$
$854$	10.2361	0.350271
$855$	12.7082	0.434611
$856$	4.18034	0.142881
$857$	−33.4164	−1.14148	−0.570741	−	0.821130i	$-0.693344\pi$
$857$	−33.4164	−1.14148	−0.570741	+	0.821130i	$0.693344\pi$
$858$	9.74265	0.332608
$859$	34.0689	1.16242	0.581208	−	0.813755i	$-0.302580\pi$
$859$	34.0689	1.16242	0.581208	+	0.813755i	$0.302580\pi$
$860$	0	0
$861$	−12.3262	−0.420077
$862$	−34.6525	−1.18027
$863$	37.2361	1.26753	0.633765	−	0.773525i	$-0.281509\pi$
$863$	37.2361	1.26753	0.633765	+	0.773525i	$0.281509\pi$
$864$	3.47214	0.118124
$865$	21.5623	0.733140
$866$	29.5066	1.00267
$867$	−5.50658	−0.187013
$868$	3.38197	0.114791
$869$	40.3607	1.36914
$870$	−2.94427	−0.0998202
$871$	−22.6099	−0.766107
$872$	−8.56231	−0.289956
$873$	38.2705	1.29526
$874$	0	0
$875$	1.61803	0.0546995
$876$	0.763932	0.0258109
$877$	−23.7426	−0.801732	−0.400866	−	0.916137i	$-0.631291\pi$
$877$	−23.7426	−0.801732	−0.400866	+	0.916137i	$0.631291\pi$
$878$	−15.6180	−0.527083
$879$	9.81966	0.331209
$880$	3.85410	0.129922
$881$	−35.4164	−1.19321	−0.596605	−	0.802535i	$-0.703484\pi$
$881$	−35.4164	−1.19321	−0.596605	+	0.802535i	$0.703484\pi$
$882$	11.4721	0.386287
$883$	−4.56231	−0.153534	−0.0767669	−	0.997049i	$-0.524460\pi$
$883$	−4.56231	−0.153534	−0.0767669	+	0.997049i	$0.524460\pi$
$884$	20.8197	0.700241
$885$	−7.23607	−0.243238
$886$	13.9098	0.467310
$887$	−58.8328	−1.97541	−0.987706	−	0.156321i	$-0.950037\pi$
$887$	−58.8328	−1.97541	−0.987706	+	0.156321i	$0.950037\pi$
$888$	−1.52786	−0.0512718
$889$	10.0000	0.335389
$890$	−1.52786	−0.0512141
$891$	−22.0000	−0.737028
$892$	−3.05573	−0.102313
$893$	47.1246	1.57697
$894$	−0.708204	−0.0236859
$895$	20.1803	0.674554
$896$	−1.61803	−0.0540547
$897$	0	0
$898$	18.5623	0.619432
$899$	9.95743	0.332099
$900$	−2.61803	−0.0872678
$901$	43.1246	1.43669
$902$	47.5066	1.58180
$903$	0	0
$904$	−18.9443	−0.630077
$905$	−18.8541	−0.626732
$906$	−10.8541	−0.360603
$907$	33.1246	1.09988	0.549942	−	0.835203i	$-0.314650\pi$
$907$	33.1246	1.09988	0.549942	+	0.835203i	$0.314650\pi$
$908$	23.2361	0.771116
$909$	35.8885	1.19035
$910$	6.61803	0.219386
$911$	22.0689	0.731175	0.365587	−	0.930777i	$-0.380868\pi$
$911$	22.0689	0.731175	0.365587	+	0.930777i	$0.380868\pi$
$912$	−3.00000	−0.0993399
$913$	42.1803	1.39597
$914$	−33.7771	−1.11725
$915$	−3.90983	−0.129255
$916$	−10.0000	−0.330409
$917$	24.1803	0.798505
$918$	17.6738	0.583321
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	−16.9656	−0.559034
$922$	−34.7639	−1.14489
$923$	29.0000	0.954547
$924$	−3.85410	−0.126791
$925$	2.47214	0.0812833
$926$	2.00000	0.0657241
$927$	−9.32624	−0.306314
$928$	−4.76393	−0.156384
$929$	−12.4721	−0.409198	−0.204599	−	0.978846i	$-0.565589\pi$
$929$	−12.4721	−0.409198	−0.204599	+	0.978846i	$0.565589\pi$
$930$	−1.29180	−0.0423597
$931$	−21.2705	−0.697113
$932$	19.7082	0.645564
$933$	−2.47214	−0.0809341
$934$	−23.1246	−0.756660
$935$	19.6180	0.641578
$936$	−10.7082	−0.350009
$937$	12.2016	0.398610	0.199305	−	0.979938i	$-0.436132\pi$
$937$	12.2016	0.398610	0.199305	+	0.979938i	$0.436132\pi$
$938$	8.94427	0.292041
$939$	−7.29180	−0.237959
$940$	−9.70820	−0.316647
$941$	60.5066	1.97246	0.986229	−	0.165385i	$-0.0528868\pi$
$941$	60.5066	1.97246	0.986229	+	0.165385i	$0.0528868\pi$
$942$	6.00000	0.195491
$943$	0	0
$944$	−11.7082	−0.381070
$945$	5.61803	0.182755
$946$	0	0
$947$	5.68692	0.184800	0.0924000	−	0.995722i	$-0.470546\pi$
$947$	5.68692	0.184800	0.0924000	+	0.995722i	$0.470546\pi$
$948$	6.47214	0.210205
$949$	−5.05573	−0.164116
$950$	4.85410	0.157488
$951$	−0.0557281	−0.00180711
$952$	−8.23607	−0.266932
$953$	20.7984	0.673725	0.336863	−	0.941554i	$-0.390634\pi$
$953$	20.7984	0.673725	0.336863	+	0.941554i	$0.390634\pi$
$954$	−22.1803	−0.718115
$955$	−0.291796	−0.00944230
$956$	24.3607	0.787881
$957$	−11.3475	−0.366813
$958$	−3.88854	−0.125633
$959$	8.61803	0.278291
$960$	0.618034	0.0199470
$961$	−26.6312	−0.859071
$962$	10.1115	0.326006
$963$	−10.9443	−0.352674
$964$	0	0
$965$	−5.23607	−0.168555
$966$	0	0
$967$	50.5410	1.62529	0.812645	−	0.582759i	$-0.198027\pi$
$967$	50.5410	1.62529	0.812645	+	0.582759i	$0.198027\pi$
$968$	3.85410	0.123876
$969$	−15.2705	−0.490559
$970$	14.6180	0.469357
$971$	−0.729490	−0.0234105	−0.0117052	−	0.999931i	$-0.503726\pi$
$971$	−0.729490	−0.0234105	−0.0117052	+	0.999931i	$0.503726\pi$
$972$	−13.9443	−0.447263
$973$	−27.8885	−0.894066
$974$	−42.1803	−1.35155
$975$	−2.52786	−0.0809564
$976$	−6.32624	−0.202498
$977$	3.43769	0.109982	0.0549908	−	0.998487i	$-0.482487\pi$
$977$	3.43769	0.109982	0.0549908	+	0.998487i	$0.482487\pi$
$978$	−2.23607	−0.0715016
$979$	−5.88854	−0.188199
$980$	4.38197	0.139977
$981$	22.4164	0.715701
$982$	−16.1803	−0.516335
$983$	−19.2705	−0.614634	−0.307317	−	0.951607i	$-0.599431\pi$
$983$	−19.2705	−0.614634	−0.307317	+	0.951607i	$0.599431\pi$
$984$	7.61803	0.242854
$985$	2.43769	0.0776714
$986$	−24.2492	−0.772253
$987$	9.70820	0.309016
$988$	19.8541	0.631643
$989$	0	0
$990$	−10.0902	−0.320687
$991$	−10.5066	−0.333752	−0.166876	−	0.985978i	$-0.553368\pi$
$991$	−10.5066	−0.333752	−0.166876	+	0.985978i	$0.553368\pi$
$992$	−2.09017	−0.0663630
$993$	−9.12461	−0.289561
$994$	−11.4721	−0.363874
$995$	2.00000	0.0634043
$996$	6.76393	0.214323
$997$	−41.1935	−1.30461	−0.652306	−	0.757956i	$-0.726198\pi$
$997$	−41.1935	−1.30461	−0.652306	+	0.757956i	$0.726198\pi$
$998$	−32.3607	−1.02436
$999$	8.58359	0.271573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.o.1.1		2
23.22	odd	2		230.2.a.c.1.1	✓	2
69.68	even	2		2070.2.a.u.1.2		2
92.91	even	2		1840.2.a.l.1.2		2
115.22	even	4		1150.2.b.i.599.4		4
115.68	even	4		1150.2.b.i.599.1		4
115.114	odd	2		1150.2.a.j.1.2		2
184.45	odd	2		7360.2.a.bh.1.2		2
184.91	even	2		7360.2.a.bn.1.1		2
460.459	even	2		9200.2.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.c.1.1	✓	2	23.22	odd	2
1150.2.a.j.1.2		2	115.114	odd	2
1150.2.b.i.599.1		4	115.68	even	4
1150.2.b.i.599.4		4	115.22	even	4
1840.2.a.l.1.2		2	92.91	even	2
2070.2.a.u.1.2		2	69.68	even	2
5290.2.a.o.1.1		2	1.1	even	1	trivial
7360.2.a.bh.1.2		2	184.45	odd	2
7360.2.a.bn.1.1		2	184.91	even	2
9200.2.a.bu.1.1		2	460.459	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} -3.85410 q^{11} -0.618034 q^{12} +4.09017 q^{13} -1.61803 q^{14} +0.618034 q^{15} +1.00000 q^{16} +5.09017 q^{17} -2.61803 q^{18} +4.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} -3.85410 q^{22} -0.618034 q^{24} +1.00000 q^{25} +4.09017 q^{26} +3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} +0.618034 q^{30} -2.09017 q^{31} +1.00000 q^{32} +2.38197 q^{33} +5.09017 q^{34} +1.61803 q^{35} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -1.00000 q^{40} -12.3262 q^{41} +1.00000 q^{42} -3.85410 q^{44} +2.61803 q^{45} +9.70820 q^{47} -0.618034 q^{48} -4.38197 q^{49} +1.00000 q^{50} -3.14590 q^{51} +4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +3.85410 q^{55} -1.61803 q^{56} -3.00000 q^{57} -4.76393 q^{58} -11.7082 q^{59} +0.618034 q^{60} -6.32624 q^{61} -2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -4.09017 q^{65} +2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} +1.61803 q^{70} +7.09017 q^{71} -2.61803 q^{72} -1.23607 q^{73} +2.47214 q^{74} -0.618034 q^{75} +4.85410 q^{76} +6.23607 q^{77} -2.52786 q^{78} -10.4721 q^{79} -1.00000 q^{80} +5.70820 q^{81} -12.3262 q^{82} -10.9443 q^{83} +1.00000 q^{84} -5.09017 q^{85} +2.94427 q^{87} -3.85410 q^{88} +1.52786 q^{89} +2.61803 q^{90} -6.61803 q^{91} +1.29180 q^{93} +9.70820 q^{94} -4.85410 q^{95} -0.618034 q^{96} -14.6180 q^{97} -4.38197 q^{98} +10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21} - q^{22} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - q^{28} - 14 q^{29} - q^{30} + 7 q^{31} + 2 q^{32} + 7 q^{33} - q^{34} + q^{35} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 2 q^{40} - 9 q^{41} + 2 q^{42} - q^{44} + 3 q^{45} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 13 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{55} - q^{56} - 6 q^{57} - 14 q^{58} - 10 q^{59} - q^{60} + 3 q^{61} + 7 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{65} + 7 q^{66} - 20 q^{67} - q^{68} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} - 4 q^{74} + q^{75} + 3 q^{76} + 8 q^{77} - 14 q^{78} - 12 q^{79} - 2 q^{80} - 2 q^{81} - 9 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 12 q^{87} - q^{88} + 12 q^{89} + 3 q^{90} - 11 q^{91} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} - 27 q^{97} - 11 q^{98} + 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 + q^6 - q^7 + 2 * q^8 - 3 * q^9 - 2 * q^10 - q^11 + q^12 - 3 * q^13 - q^14 - q^15 + 2 * q^16 - q^17 - 3 * q^18 + 3 * q^19 - 2 * q^20 + 2 * q^21 - q^22 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - q^28 - 14 * q^29 - q^30 + 7 * q^31 + 2 * q^32 + 7 * q^33 - q^34 + q^35 - 3 * q^36 - 4 * q^37 + 3 * q^38 - 14 * q^39 - 2 * q^40 - 9 * q^41 + 2 * q^42 - q^44 + 3 * q^45 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 - 13 * q^51 - 3 * q^52 + 8 * q^53 - 2 * q^54 + q^55 - q^56 - 6 * q^57 - 14 * q^58 - 10 * q^59 - q^60 + 3 * q^61 + 7 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^65 + 7 * q^66 - 20 * q^67 - q^68 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 - 4 * q^74 + q^75 + 3 * q^76 + 8 * q^77 - 14 * q^78 - 12 * q^79 - 2 * q^80 - 2 * q^81 - 9 * q^82 - 4 * q^83 + 2 * q^84 + q^85 - 12 * q^87 - q^88 + 12 * q^89 + 3 * q^90 - 11 * q^91 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 - 27 * q^97 - 11 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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