LMFDB - Embedded newform 4598.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} +3.23607 q^{6} +3.85410 q^{7} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} +3.23607 q^{6} +3.85410 q^{7} -1.00000 q^{8} +7.47214 q^{9} -3.85410 q^{10} -3.23607 q^{12} +4.00000 q^{13} -3.85410 q^{14} -12.4721 q^{15} +1.00000 q^{16} -1.61803 q^{17} -7.47214 q^{18} -1.00000 q^{19} +3.85410 q^{20} -12.4721 q^{21} +0.854102 q^{23} +3.23607 q^{24} +9.85410 q^{25} -4.00000 q^{26} -14.4721 q^{27} +3.85410 q^{28} +5.70820 q^{29} +12.4721 q^{30} -2.76393 q^{31} -1.00000 q^{32} +1.61803 q^{34} +14.8541 q^{35} +7.47214 q^{36} -3.23607 q^{37} +1.00000 q^{38} -12.9443 q^{39} -3.85410 q^{40} -0.472136 q^{41} +12.4721 q^{42} +7.61803 q^{43} +28.7984 q^{45} -0.854102 q^{46} -0.854102 q^{47} -3.23607 q^{48} +7.85410 q^{49} -9.85410 q^{50} +5.23607 q^{51} +4.00000 q^{52} +11.2361 q^{53} +14.4721 q^{54} -3.85410 q^{56} +3.23607 q^{57} -5.70820 q^{58} +6.94427 q^{59} -12.4721 q^{60} +1.14590 q^{61} +2.76393 q^{62} +28.7984 q^{63} +1.00000 q^{64} +15.4164 q^{65} -9.23607 q^{67} -1.61803 q^{68} -2.76393 q^{69} -14.8541 q^{70} -2.76393 q^{71} -7.47214 q^{72} +10.9443 q^{73} +3.23607 q^{74} -31.8885 q^{75} -1.00000 q^{76} +12.9443 q^{78} +9.23607 q^{79} +3.85410 q^{80} +24.4164 q^{81} +0.472136 q^{82} -2.14590 q^{83} -12.4721 q^{84} -6.23607 q^{85} -7.61803 q^{86} -18.4721 q^{87} -14.1803 q^{89} -28.7984 q^{90} +15.4164 q^{91} +0.854102 q^{92} +8.94427 q^{93} +0.854102 q^{94} -3.85410 q^{95} +3.23607 q^{96} +16.9443 q^{97} -7.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9} - q^{10} - 2 q^{12} + 8 q^{13} - q^{14} - 16 q^{15} + 2 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + q^{20} - 16 q^{21} - 5 q^{23} + 2 q^{24} + 13 q^{25} - 8 q^{26} - 20 q^{27} + q^{28} - 2 q^{29} + 16 q^{30} - 10 q^{31} - 2 q^{32} + q^{34} + 23 q^{35} + 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{39} - q^{40} + 8 q^{41} + 16 q^{42} + 13 q^{43} + 33 q^{45} + 5 q^{46} + 5 q^{47} - 2 q^{48} + 9 q^{49} - 13 q^{50} + 6 q^{51} + 8 q^{52} + 18 q^{53} + 20 q^{54} - q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} - 16 q^{60} + 9 q^{61} + 10 q^{62} + 33 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{67} - q^{68} - 10 q^{69} - 23 q^{70} - 10 q^{71} - 6 q^{72} + 4 q^{73} + 2 q^{74} - 28 q^{75} - 2 q^{76} + 8 q^{78} + 14 q^{79} + q^{80} + 22 q^{81} - 8 q^{82} - 11 q^{83} - 16 q^{84} - 8 q^{85} - 13 q^{86} - 28 q^{87} - 6 q^{89} - 33 q^{90} + 4 q^{91} - 5 q^{92} - 5 q^{94} - q^{95} + 2 q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9 - q^10 - 2 * q^12 + 8 * q^13 - q^14 - 16 * q^15 + 2 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + q^20 - 16 * q^21 - 5 * q^23 + 2 * q^24 + 13 * q^25 - 8 * q^26 - 20 * q^27 + q^28 - 2 * q^29 + 16 * q^30 - 10 * q^31 - 2 * q^32 + q^34 + 23 * q^35 + 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^39 - q^40 + 8 * q^41 + 16 * q^42 + 13 * q^43 + 33 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 + 9 * q^49 - 13 * q^50 + 6 * q^51 + 8 * q^52 + 18 * q^53 + 20 * q^54 - q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 - 16 * q^60 + 9 * q^61 + 10 * q^62 + 33 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^67 - q^68 - 10 * q^69 - 23 * q^70 - 10 * q^71 - 6 * q^72 + 4 * q^73 + 2 * q^74 - 28 * q^75 - 2 * q^76 + 8 * q^78 + 14 * q^79 + q^80 + 22 * q^81 - 8 * q^82 - 11 * q^83 - 16 * q^84 - 8 * q^85 - 13 * q^86 - 28 * q^87 - 6 * q^89 - 33 * q^90 + 4 * q^91 - 5 * q^92 - 5 * q^94 - q^95 + 2 * q^96 + 16 * q^97 - 9 * q^98

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
$3$	−3.23607	−1.86834	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−3.23607	−1.86834	−0.934172	+	0.356822i	$0.883860\pi$
$4$	1.00000	0.500000
$5$	3.85410	1.72361	0.861803	−	0.507242i	$-0.169335\pi$
$5$	3.85410	1.72361	0.861803	+	0.507242i	$0.169335\pi$
$6$	3.23607	1.32112
$7$	3.85410	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$8$	−1.00000	−0.353553
$9$	7.47214	2.49071
$10$	−3.85410	−1.21877
$11$	0	0
$11$	0	0
$12$	−3.23607	−0.934172
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−3.85410	−1.03005
$15$	−12.4721	−3.22029
$16$	1.00000	0.250000
$17$	−1.61803	−0.392431	−0.196215	−	0.980561i	$-0.562865\pi$
$17$	−1.61803	−0.392431	−0.196215	+	0.980561i	$0.562865\pi$
$18$	−7.47214	−1.76120
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.85410	0.861803
$21$	−12.4721	−2.72164
$22$	0	0
$23$	0.854102	0.178093	0.0890463	−	0.996027i	$-0.471618\pi$
$23$	0.854102	0.178093	0.0890463	+	0.996027i	$0.471618\pi$
$24$	3.23607	0.660560
$25$	9.85410	1.97082
$26$	−4.00000	−0.784465
$27$	−14.4721	−2.78516
$28$	3.85410	0.728357
$29$	5.70820	1.05999	0.529993	−	0.848002i	$-0.322194\pi$
$29$	5.70820	1.05999	0.529993	+	0.848002i	$0.322194\pi$
$30$	12.4721	2.27709
$31$	−2.76393	−0.496417	−0.248208	−	0.968707i	$-0.579842\pi$
$31$	−2.76393	−0.496417	−0.248208	+	0.968707i	$0.579842\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.61803	0.277491
$35$	14.8541	2.51080
$36$	7.47214	1.24536
$37$	−3.23607	−0.532006	−0.266003	−	0.963972i	$-0.585703\pi$
$37$	−3.23607	−0.532006	−0.266003	+	0.963972i	$0.585703\pi$
$38$	1.00000	0.162221
$39$	−12.9443	−2.07274
$40$	−3.85410	−0.609387
$41$	−0.472136	−0.0737352	−0.0368676	−	0.999320i	$-0.511738\pi$
$41$	−0.472136	−0.0737352	−0.0368676	+	0.999320i	$0.511738\pi$
$42$	12.4721	1.92449
$43$	7.61803	1.16174	0.580870	−	0.813997i	$-0.302713\pi$
$43$	7.61803	1.16174	0.580870	+	0.813997i	$0.302713\pi$
$44$	0	0
$45$	28.7984	4.29301
$46$	−0.854102	−0.125930
$47$	−0.854102	−0.124584	−0.0622918	−	0.998058i	$-0.519841\pi$
$47$	−0.854102	−0.124584	−0.0622918	+	0.998058i	$0.519841\pi$
$48$	−3.23607	−0.467086
$49$	7.85410	1.12201
$50$	−9.85410	−1.39358
$51$	5.23607	0.733196
$52$	4.00000	0.554700
$53$	11.2361	1.54339	0.771696	−	0.635991i	$-0.219409\pi$
$53$	11.2361	1.54339	0.771696	+	0.635991i	$0.219409\pi$
$54$	14.4721	1.96941
$55$	0	0
$56$	−3.85410	−0.515026
$57$	3.23607	0.428628
$58$	−5.70820	−0.749524
$59$	6.94427	0.904067	0.452034	−	0.892001i	$-0.350699\pi$
$59$	6.94427	0.904067	0.452034	+	0.892001i	$0.350699\pi$
$60$	−12.4721	−1.61015
$61$	1.14590	0.146717	0.0733586	−	0.997306i	$-0.476628\pi$
$61$	1.14590	0.146717	0.0733586	+	0.997306i	$0.476628\pi$
$62$	2.76393	0.351020
$63$	28.7984	3.62825
$64$	1.00000	0.125000
$65$	15.4164	1.91217
$66$	0	0
$67$	−9.23607	−1.12837	−0.564183	−	0.825650i	$-0.690809\pi$
$67$	−9.23607	−1.12837	−0.564183	+	0.825650i	$0.690809\pi$
$68$	−1.61803	−0.196215
$69$	−2.76393	−0.332738
$70$	−14.8541	−1.77540
$71$	−2.76393	−0.328018	−0.164009	−	0.986459i	$-0.552443\pi$
$71$	−2.76393	−0.328018	−0.164009	+	0.986459i	$0.552443\pi$
$72$	−7.47214	−0.880600
$73$	10.9443	1.28093	0.640465	−	0.767987i	$-0.278742\pi$
$73$	10.9443	1.28093	0.640465	+	0.767987i	$0.278742\pi$
$74$	3.23607	0.376185
$75$	−31.8885	−3.68217
$76$	−1.00000	−0.114708
$77$	0	0
$78$	12.9443	1.46565
$79$	9.23607	1.03914	0.519569	−	0.854428i	$-0.326092\pi$
$79$	9.23607	1.03914	0.519569	+	0.854428i	$0.326092\pi$
$80$	3.85410	0.430902
$81$	24.4164	2.71293
$82$	0.472136	0.0521387
$83$	−2.14590	−0.235543	−0.117771	−	0.993041i	$-0.537575\pi$
$83$	−2.14590	−0.235543	−0.117771	+	0.993041i	$0.537575\pi$
$84$	−12.4721	−1.36082
$85$	−6.23607	−0.676397
$86$	−7.61803	−0.821474
$87$	−18.4721	−1.98042
$88$	0	0
$89$	−14.1803	−1.50311	−0.751557	−	0.659669i	$-0.770697\pi$
$89$	−14.1803	−1.50311	−0.751557	+	0.659669i	$0.770697\pi$
$90$	−28.7984	−3.03562
$91$	15.4164	1.61608
$92$	0.854102	0.0890463
$93$	8.94427	0.927478
$94$	0.854102	0.0880939
$95$	−3.85410	−0.395423
$96$	3.23607	0.330280
$97$	16.9443	1.72043	0.860215	−	0.509931i	$-0.170329\pi$
$97$	16.9443	1.72043	0.860215	+	0.509931i	$0.170329\pi$
$98$	−7.85410	−0.793384
$99$	0	0
$100$	9.85410	0.985410
$101$	−3.56231	−0.354463	−0.177231	−	0.984169i	$-0.556714\pi$
$101$	−3.56231	−0.354463	−0.177231	+	0.984169i	$0.556714\pi$
$102$	−5.23607	−0.518448
$103$	−6.94427	−0.684239	−0.342120	−	0.939656i	$-0.611145\pi$
$103$	−6.94427	−0.684239	−0.342120	+	0.939656i	$0.611145\pi$
$104$	−4.00000	−0.392232
$105$	−48.0689	−4.69104
$106$	−11.2361	−1.09134
$107$	2.47214	0.238990	0.119495	−	0.992835i	$-0.461872\pi$
$107$	2.47214	0.238990	0.119495	+	0.992835i	$0.461872\pi$
$108$	−14.4721	−1.39258
$109$	−0.944272	−0.0904448	−0.0452224	−	0.998977i	$-0.514400\pi$
$109$	−0.944272	−0.0904448	−0.0452224	+	0.998977i	$0.514400\pi$
$110$	0	0
$111$	10.4721	0.993971
$112$	3.85410	0.364178
$113$	−7.52786	−0.708162	−0.354081	−	0.935215i	$-0.615206\pi$
$113$	−7.52786	−0.708162	−0.354081	+	0.935215i	$0.615206\pi$
$114$	−3.23607	−0.303086
$115$	3.29180	0.306962
$116$	5.70820	0.529993
$117$	29.8885	2.76320
$118$	−6.94427	−0.639272
$119$	−6.23607	−0.571659
$120$	12.4721	1.13855
$121$	0	0
$122$	−1.14590	−0.103745
$123$	1.52786	0.137763
$124$	−2.76393	−0.248208
$125$	18.7082	1.67331
$126$	−28.7984	−2.56556
$127$	2.29180	0.203364	0.101682	−	0.994817i	$-0.467578\pi$
$127$	2.29180	0.203364	0.101682	+	0.994817i	$0.467578\pi$
$128$	−1.00000	−0.0883883
$129$	−24.6525	−2.17053
$130$	−15.4164	−1.35211
$131$	−13.8541	−1.21044	−0.605219	−	0.796059i	$-0.706915\pi$
$131$	−13.8541	−1.21044	−0.605219	+	0.796059i	$0.706915\pi$
$132$	0	0
$133$	−3.85410	−0.334193
$134$	9.23607	0.797875
$135$	−55.7771	−4.80053
$136$	1.61803	0.138745
$137$	−9.56231	−0.816963	−0.408481	−	0.912767i	$-0.633942\pi$
$137$	−9.56231	−0.816963	−0.408481	+	0.912767i	$0.633942\pi$
$138$	2.76393	0.235282
$139$	−14.0902	−1.19511	−0.597556	−	0.801827i	$-0.703862\pi$
$139$	−14.0902	−1.19511	−0.597556	+	0.801827i	$0.703862\pi$
$140$	14.8541	1.25540
$141$	2.76393	0.232765
$142$	2.76393	0.231944
$143$	0	0
$144$	7.47214	0.622678
$145$	22.0000	1.82700
$146$	−10.9443	−0.905754
$147$	−25.4164	−2.09631
$148$	−3.23607	−0.266003
$149$	3.52786	0.289014	0.144507	−	0.989504i	$-0.453840\pi$
$149$	3.52786	0.289014	0.144507	+	0.989504i	$0.453840\pi$
$150$	31.8885	2.60369
$151$	10.7639	0.875956	0.437978	−	0.898986i	$-0.355695\pi$
$151$	10.7639	0.875956	0.437978	+	0.898986i	$0.355695\pi$
$152$	1.00000	0.0811107
$153$	−12.0902	−0.977432
$154$	0	0
$155$	−10.6525	−0.855627
$156$	−12.9443	−1.03637
$157$	−22.3262	−1.78183	−0.890914	−	0.454172i	$-0.849935\pi$
$157$	−22.3262	−1.78183	−0.890914	+	0.454172i	$0.849935\pi$
$158$	−9.23607	−0.734782
$159$	−36.3607	−2.88359
$160$	−3.85410	−0.304694
$161$	3.29180	0.259430
$162$	−24.4164	−1.91833
$163$	17.2705	1.35273	0.676365	−	0.736566i	$-0.263554\pi$
$163$	17.2705	1.35273	0.676365	+	0.736566i	$0.263554\pi$
$164$	−0.472136	−0.0368676
$165$	0	0
$166$	2.14590	0.166554
$167$	−6.29180	−0.486874	−0.243437	−	0.969917i	$-0.578275\pi$
$167$	−6.29180	−0.486874	−0.243437	+	0.969917i	$0.578275\pi$
$168$	12.4721	0.962246
$169$	3.00000	0.230769
$170$	6.23607	0.478285
$171$	−7.47214	−0.571409
$172$	7.61803	0.580870
$173$	−4.00000	−0.304114	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−4.00000	−0.304114	−0.152057	+	0.988372i	$0.548590\pi$
$174$	18.4721	1.40037
$175$	37.9787	2.87092
$176$	0	0
$177$	−22.4721	−1.68911
$178$	14.1803	1.06286
$179$	−21.1246	−1.57893	−0.789464	−	0.613797i	$-0.789641\pi$
$179$	−21.1246	−1.57893	−0.789464	+	0.613797i	$0.789641\pi$
$180$	28.7984	2.14650
$181$	−5.41641	−0.402598	−0.201299	−	0.979530i	$-0.564516\pi$
$181$	−5.41641	−0.402598	−0.201299	+	0.979530i	$0.564516\pi$
$182$	−15.4164	−1.14274
$183$	−3.70820	−0.274118
$184$	−0.854102	−0.0629652
$185$	−12.4721	−0.916970
$186$	−8.94427	−0.655826
$187$	0	0
$188$	−0.854102	−0.0622918
$189$	−55.7771	−4.05719
$190$	3.85410	0.279606
$191$	−13.3820	−0.968285	−0.484143	−	0.874989i	$-0.660868\pi$
$191$	−13.3820	−0.968285	−0.484143	+	0.874989i	$0.660868\pi$
$192$	−3.23607	−0.233543
$193$	18.4721	1.32965	0.664827	−	0.746998i	$-0.268505\pi$
$193$	18.4721	1.32965	0.664827	+	0.746998i	$0.268505\pi$
$194$	−16.9443	−1.21653
$195$	−49.8885	−3.57259
$196$	7.85410	0.561007
$197$	10.9443	0.779747	0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443	0.779747	0.389874	+	0.920868i	$0.372519\pi$
$198$	0	0
$199$	26.6180	1.88690	0.943451	−	0.331511i	$-0.107559\pi$
$199$	26.6180	1.88690	0.943451	+	0.331511i	$0.107559\pi$
$200$	−9.85410	−0.696790
$201$	29.8885	2.10818
$202$	3.56231	0.250643
$203$	22.0000	1.54410
$204$	5.23607	0.366598
$205$	−1.81966	−0.127091
$206$	6.94427	0.483830
$207$	6.38197	0.443577
$208$	4.00000	0.277350
$209$	0	0
$210$	48.0689	3.31707
$211$	−14.9443	−1.02881	−0.514403	−	0.857549i	$-0.671986\pi$
$211$	−14.9443	−1.02881	−0.514403	+	0.857549i	$0.671986\pi$
$212$	11.2361	0.771696
$213$	8.94427	0.612851
$214$	−2.47214	−0.168992
$215$	29.3607	2.00238
$216$	14.4721	0.984704
$217$	−10.6525	−0.723137
$218$	0.944272	0.0639542
$219$	−35.4164	−2.39322
$220$	0	0
$221$	−6.47214	−0.435363
$222$	−10.4721	−0.702844
$223$	−10.6525	−0.713343	−0.356671	−	0.934230i	$-0.616088\pi$
$223$	−10.6525	−0.713343	−0.356671	+	0.934230i	$0.616088\pi$
$224$	−3.85410	−0.257513
$225$	73.6312	4.90875
$226$	7.52786	0.500746
$227$	26.1803	1.73765	0.868825	−	0.495119i	$-0.164876\pi$
$227$	26.1803	1.73765	0.868825	+	0.495119i	$0.164876\pi$
$228$	3.23607	0.214314
$229$	−10.8541	−0.717259	−0.358630	−	0.933480i	$-0.616756\pi$
$229$	−10.8541	−0.717259	−0.358630	+	0.933480i	$0.616756\pi$
$230$	−3.29180	−0.217055
$231$	0	0
$232$	−5.70820	−0.374762
$233$	0.326238	0.0213726	0.0106863	−	0.999943i	$-0.496598\pi$
$233$	0.326238	0.0213726	0.0106863	+	0.999943i	$0.496598\pi$
$234$	−29.8885	−1.95388
$235$	−3.29180	−0.214733
$236$	6.94427	0.452034
$237$	−29.8885	−1.94147
$238$	6.23607	0.404224
$239$	15.3262	0.991372	0.495686	−	0.868502i	$-0.334917\pi$
$239$	15.3262	0.991372	0.495686	+	0.868502i	$0.334917\pi$
$240$	−12.4721	−0.805073
$241$	19.5279	1.25790	0.628950	−	0.777446i	$-0.283485\pi$
$241$	19.5279	1.25790	0.628950	+	0.777446i	$0.283485\pi$
$242$	0	0
$243$	−35.5967	−2.28353
$244$	1.14590	0.0733586
$245$	30.2705	1.93391
$246$	−1.52786	−0.0974131
$247$	−4.00000	−0.254514
$248$	2.76393	0.175510
$249$	6.94427	0.440075
$250$	−18.7082	−1.18321
$251$	−12.3820	−0.781543	−0.390771	−	0.920488i	$-0.627792\pi$
$251$	−12.3820	−0.781543	−0.390771	+	0.920488i	$0.627792\pi$
$252$	28.7984	1.81413
$253$	0	0
$254$	−2.29180	−0.143800
$255$	20.1803	1.26374
$256$	1.00000	0.0625000
$257$	−18.1803	−1.13406	−0.567029	−	0.823698i	$-0.691907\pi$
$257$	−18.1803	−1.13406	−0.567029	+	0.823698i	$0.691907\pi$
$258$	24.6525	1.53480
$259$	−12.4721	−0.774981
$260$	15.4164	0.956085
$261$	42.6525	2.64012
$262$	13.8541	0.855909
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	43.3050	2.66020
$266$	3.85410	0.236310
$267$	45.8885	2.80833
$268$	−9.23607	−0.564183
$269$	19.7082	1.20163	0.600815	−	0.799388i	$-0.294843\pi$
$269$	19.7082	1.20163	0.600815	+	0.799388i	$0.294843\pi$
$270$	55.7771	3.39449
$271$	−28.0902	−1.70636	−0.853178	−	0.521620i	$-0.825328\pi$
$271$	−28.0902	−1.70636	−0.853178	+	0.521620i	$0.825328\pi$
$272$	−1.61803	−0.0981077
$273$	−49.8885	−3.01939
$274$	9.56231	0.577680
$275$	0	0
$276$	−2.76393	−0.166369
$277$	20.4721	1.23005	0.615026	−	0.788507i	$-0.289146\pi$
$277$	20.4721	1.23005	0.615026	+	0.788507i	$0.289146\pi$
$278$	14.0902	0.845072
$279$	−20.6525	−1.23643
$280$	−14.8541	−0.887702
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	−2.76393	−0.164590
$283$	9.85410	0.585766	0.292883	−	0.956148i	$-0.405385\pi$
$283$	9.85410	0.585766	0.292883	+	0.956148i	$0.405385\pi$
$284$	−2.76393	−0.164009
$285$	12.4721	0.738786
$286$	0	0
$287$	−1.81966	−0.107411
$288$	−7.47214	−0.440300
$289$	−14.3820	−0.845998
$290$	−22.0000	−1.29188
$291$	−54.8328	−3.21436
$292$	10.9443	0.640465
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	25.4164	1.48232
$295$	26.7639	1.55826
$296$	3.23607	0.188093
$297$	0	0
$298$	−3.52786	−0.204364
$299$	3.41641	0.197576
$300$	−31.8885	−1.84109
$301$	29.3607	1.69232
$302$	−10.7639	−0.619395
$303$	11.5279	0.662258
$304$	−1.00000	−0.0573539
$305$	4.41641	0.252883
$306$	12.0902	0.691149
$307$	1.52786	0.0871998	0.0435999	−	0.999049i	$-0.486117\pi$
$307$	1.52786	0.0871998	0.0435999	+	0.999049i	$0.486117\pi$
$308$	0	0
$309$	22.4721	1.27840
$310$	10.6525	0.605020
$311$	5.43769	0.308343	0.154172	−	0.988044i	$-0.450729\pi$
$311$	5.43769	0.308343	0.154172	+	0.988044i	$0.450729\pi$
$312$	12.9443	0.732825
$313$	−15.5066	−0.876484	−0.438242	−	0.898857i	$-0.644399\pi$
$313$	−15.5066	−0.876484	−0.438242	+	0.898857i	$0.644399\pi$
$314$	22.3262	1.25994
$315$	110.992	6.25368
$316$	9.23607	0.519569
$317$	−8.47214	−0.475843	−0.237921	−	0.971284i	$-0.576466\pi$
$317$	−8.47214	−0.475843	−0.237921	+	0.971284i	$0.576466\pi$
$318$	36.3607	2.03901
$319$	0	0
$320$	3.85410	0.215451
$321$	−8.00000	−0.446516
$322$	−3.29180	−0.183445
$323$	1.61803	0.0900298
$324$	24.4164	1.35647
$325$	39.4164	2.18643
$326$	−17.2705	−0.956525
$327$	3.05573	0.168982
$328$	0.472136	0.0260693
$329$	−3.29180	−0.181483
$330$	0	0
$331$	−10.4721	−0.575601	−0.287800	−	0.957690i	$-0.592924\pi$
$331$	−10.4721	−0.575601	−0.287800	+	0.957690i	$0.592924\pi$
$332$	−2.14590	−0.117771
$333$	−24.1803	−1.32507
$334$	6.29180	0.344272
$335$	−35.5967	−1.94486
$336$	−12.4721	−0.680411
$337$	−26.1803	−1.42613	−0.713067	−	0.701096i	$-0.752694\pi$
$337$	−26.1803	−1.42613	−0.713067	+	0.701096i	$0.752694\pi$
$338$	−3.00000	−0.163178
$339$	24.3607	1.32309
$340$	−6.23607	−0.338198
$341$	0	0
$342$	7.47214	0.404047
$343$	3.29180	0.177740
$344$	−7.61803	−0.410737
$345$	−10.6525	−0.573510
$346$	4.00000	0.215041
$347$	−3.79837	−0.203907	−0.101954	−	0.994789i	$-0.532509\pi$
$347$	−3.79837	−0.203907	−0.101954	+	0.994789i	$0.532509\pi$
$348$	−18.4721	−0.990210
$349$	−9.67376	−0.517825	−0.258912	−	0.965901i	$-0.583364\pi$
$349$	−9.67376	−0.517825	−0.258912	+	0.965901i	$0.583364\pi$
$350$	−37.9787	−2.03005
$351$	−57.8885	−3.08986
$352$	0	0
$353$	−33.9230	−1.80554	−0.902769	−	0.430125i	$-0.858469\pi$
$353$	−33.9230	−1.80554	−0.902769	+	0.430125i	$0.858469\pi$
$354$	22.4721	1.19438
$355$	−10.6525	−0.565375
$356$	−14.1803	−0.751557
$357$	20.1803	1.06806
$358$	21.1246	1.11647
$359$	2.20163	0.116197	0.0580987	−	0.998311i	$-0.481496\pi$
$359$	2.20163	0.116197	0.0580987	+	0.998311i	$0.481496\pi$
$360$	−28.7984	−1.51781
$361$	1.00000	0.0526316
$362$	5.41641	0.284680
$363$	0	0
$364$	15.4164	0.808039
$365$	42.1803	2.20782
$366$	3.70820	0.193831
$367$	9.09017	0.474503	0.237252	−	0.971448i	$-0.423753\pi$
$367$	9.09017	0.474503	0.237252	+	0.971448i	$0.423753\pi$
$368$	0.854102	0.0445231
$369$	−3.52786	−0.183653
$370$	12.4721	0.648395
$371$	43.3050	2.24828
$372$	8.94427	0.463739
$373$	18.4721	0.956451	0.478225	−	0.878237i	$-0.341280\pi$
$373$	18.4721	0.956451	0.478225	+	0.878237i	$0.341280\pi$
$374$	0	0
$375$	−60.5410	−3.12632
$376$	0.854102	0.0440469
$377$	22.8328	1.17595
$378$	55.7771	2.86886
$379$	7.88854	0.405207	0.202604	−	0.979261i	$-0.435060\pi$
$379$	7.88854	0.405207	0.202604	+	0.979261i	$0.435060\pi$
$380$	−3.85410	−0.197711
$381$	−7.41641	−0.379954
$382$	13.3820	0.684681
$383$	−18.6525	−0.953097	−0.476548	−	0.879148i	$-0.658112\pi$
$383$	−18.6525	−0.953097	−0.476548	+	0.879148i	$0.658112\pi$
$384$	3.23607	0.165140
$385$	0	0
$386$	−18.4721	−0.940207
$387$	56.9230	2.89356
$388$	16.9443	0.860215
$389$	2.27051	0.115119	0.0575597	−	0.998342i	$-0.481668\pi$
$389$	2.27051	0.115119	0.0575597	+	0.998342i	$0.481668\pi$
$390$	49.8885	2.52620
$391$	−1.38197	−0.0698890
$392$	−7.85410	−0.396692
$393$	44.8328	2.26152
$394$	−10.9443	−0.551364
$395$	35.5967	1.79107
$396$	0	0
$397$	16.5623	0.831238	0.415619	−	0.909539i	$-0.363565\pi$
$397$	16.5623	0.831238	0.415619	+	0.909539i	$0.363565\pi$
$398$	−26.6180	−1.33424
$399$	12.4721	0.624388
$400$	9.85410	0.492705
$401$	−19.2361	−0.960603	−0.480302	−	0.877103i	$-0.659473\pi$
$401$	−19.2361	−0.960603	−0.480302	+	0.877103i	$0.659473\pi$
$402$	−29.8885	−1.49071
$403$	−11.0557	−0.550725
$404$	−3.56231	−0.177231
$405$	94.1033	4.67603
$406$	−22.0000	−1.09184
$407$	0	0
$408$	−5.23607	−0.259224
$409$	−29.5279	−1.46006	−0.730029	−	0.683416i	$-0.760494\pi$
$409$	−29.5279	−1.46006	−0.730029	+	0.683416i	$0.760494\pi$
$410$	1.81966	0.0898666
$411$	30.9443	1.52637
$412$	−6.94427	−0.342120
$413$	26.7639	1.31697
$414$	−6.38197	−0.313657
$415$	−8.27051	−0.405983
$416$	−4.00000	−0.196116
$417$	45.5967	2.23288
$418$	0	0
$419$	−28.7426	−1.40417	−0.702085	−	0.712093i	$-0.747747\pi$
$419$	−28.7426	−1.40417	−0.702085	+	0.712093i	$0.747747\pi$
$420$	−48.0689	−2.34552
$421$	24.4721	1.19270	0.596349	−	0.802725i	$-0.296617\pi$
$421$	24.4721	1.19270	0.596349	+	0.802725i	$0.296617\pi$
$422$	14.9443	0.727476
$423$	−6.38197	−0.310302
$424$	−11.2361	−0.545672
$425$	−15.9443	−0.773411
$426$	−8.94427	−0.433351
$427$	4.41641	0.213725
$428$	2.47214	0.119495
$429$	0	0
$430$	−29.3607	−1.41590
$431$	−10.5836	−0.509794	−0.254897	−	0.966968i	$-0.582042\pi$
$431$	−10.5836	−0.509794	−0.254897	+	0.966968i	$0.582042\pi$
$432$	−14.4721	−0.696291
$433$	11.8885	0.571327	0.285663	−	0.958330i	$-0.407786\pi$
$433$	11.8885	0.571327	0.285663	+	0.958330i	$0.407786\pi$
$434$	10.6525	0.511335
$435$	−71.1935	−3.41347
$436$	−0.944272	−0.0452224
$437$	−0.854102	−0.0408572
$438$	35.4164	1.69226
$439$	−18.3607	−0.876307	−0.438154	−	0.898900i	$-0.644367\pi$
$439$	−18.3607	−0.876307	−0.438154	+	0.898900i	$0.644367\pi$
$440$	0	0
$441$	58.6869	2.79462
$442$	6.47214	0.307848
$443$	−21.2705	−1.01059	−0.505296	−	0.862946i	$-0.668617\pi$
$443$	−21.2705	−1.01059	−0.505296	+	0.862946i	$0.668617\pi$
$444$	10.4721	0.496986
$445$	−54.6525	−2.59078
$446$	10.6525	0.504409
$447$	−11.4164	−0.539978
$448$	3.85410	0.182089
$449$	15.7082	0.741316	0.370658	−	0.928769i	$-0.379132\pi$
$449$	15.7082	0.741316	0.370658	+	0.928769i	$0.379132\pi$
$450$	−73.6312	−3.47101
$451$	0	0
$452$	−7.52786	−0.354081
$453$	−34.8328	−1.63659
$454$	−26.1803	−1.22870
$455$	59.4164	2.78548
$456$	−3.23607	−0.151543
$457$	−11.0902	−0.518776	−0.259388	−	0.965773i	$-0.583521\pi$
$457$	−11.0902	−0.518776	−0.259388	+	0.965773i	$0.583521\pi$
$458$	10.8541	0.507179
$459$	23.4164	1.09298
$460$	3.29180	0.153481
$461$	30.6869	1.42923	0.714616	−	0.699517i	$-0.246601\pi$
$461$	30.6869	1.42923	0.714616	+	0.699517i	$0.246601\pi$
$462$	0	0
$463$	−12.2148	−0.567669	−0.283835	−	0.958873i	$-0.591607\pi$
$463$	−12.2148	−0.567669	−0.283835	+	0.958873i	$0.591607\pi$
$464$	5.70820	0.264997
$465$	34.4721	1.59861
$466$	−0.326238	−0.0151127
$467$	9.27051	0.428988	0.214494	−	0.976725i	$-0.431190\pi$
$467$	9.27051	0.428988	0.214494	+	0.976725i	$0.431190\pi$
$468$	29.8885	1.38160
$469$	−35.5967	−1.64371
$470$	3.29180	0.151839
$471$	72.2492	3.32907
$472$	−6.94427	−0.319636
$473$	0	0
$474$	29.8885	1.37283
$475$	−9.85410	−0.452137
$476$	−6.23607	−0.285830
$477$	83.9574	3.84415
$478$	−15.3262	−0.701006
$479$	−19.9098	−0.909703	−0.454852	−	0.890567i	$-0.650308\pi$
$479$	−19.9098	−0.909703	−0.454852	+	0.890567i	$0.650308\pi$
$480$	12.4721	0.569273
$481$	−12.9443	−0.590208
$482$	−19.5279	−0.889470
$483$	−10.6525	−0.484704
$484$	0	0
$485$	65.3050	2.96535
$486$	35.5967	1.61470
$487$	21.4164	0.970470	0.485235	−	0.874384i	$-0.338734\pi$
$487$	21.4164	0.970470	0.485235	+	0.874384i	$0.338734\pi$
$488$	−1.14590	−0.0518724
$489$	−55.8885	−2.52737
$490$	−30.2705	−1.36748
$491$	23.7426	1.07149	0.535745	−	0.844380i	$-0.320031\pi$
$491$	23.7426	1.07149	0.535745	+	0.844380i	$0.320031\pi$
$492$	1.52786	0.0688814
$493$	−9.23607	−0.415972
$494$	4.00000	0.179969
$495$	0	0
$496$	−2.76393	−0.124104
$497$	−10.6525	−0.477829
$498$	−6.94427	−0.311180
$499$	−20.0344	−0.896865	−0.448432	−	0.893817i	$-0.648018\pi$
$499$	−20.0344	−0.896865	−0.448432	+	0.893817i	$0.648018\pi$
$500$	18.7082	0.836656
$501$	20.3607	0.909648
$502$	12.3820	0.552634
$503$	−24.9443	−1.11221	−0.556105	−	0.831112i	$-0.687705\pi$
$503$	−24.9443	−1.11221	−0.556105	+	0.831112i	$0.687705\pi$
$504$	−28.7984	−1.28278
$505$	−13.7295	−0.610954
$506$	0	0
$507$	−9.70820	−0.431156
$508$	2.29180	0.101682
$509$	23.2361	1.02992	0.514960	−	0.857214i	$-0.327807\pi$
$509$	23.2361	1.02992	0.514960	+	0.857214i	$0.327807\pi$
$510$	−20.1803	−0.893600
$511$	42.1803	1.86595
$512$	−1.00000	−0.0441942
$513$	14.4721	0.638960
$514$	18.1803	0.801900
$515$	−26.7639	−1.17936
$516$	−24.6525	−1.08526
$517$	0	0
$518$	12.4721	0.547994
$519$	12.9443	0.568190
$520$	−15.4164	−0.676054
$521$	−23.4164	−1.02589	−0.512946	−	0.858421i	$-0.671446\pi$
$521$	−23.4164	−1.02589	−0.512946	+	0.858421i	$0.671446\pi$
$522$	−42.6525	−1.86685
$523$	29.4164	1.28629	0.643145	−	0.765745i	$-0.277629\pi$
$523$	29.4164	1.28629	0.643145	+	0.765745i	$0.277629\pi$
$524$	−13.8541	−0.605219
$525$	−122.902	−5.36387
$526$	−16.0000	−0.697633
$527$	4.47214	0.194809
$528$	0	0
$529$	−22.2705	−0.968283
$530$	−43.3050	−1.88105
$531$	51.8885	2.25177
$532$	−3.85410	−0.167097
$533$	−1.88854	−0.0818019
$534$	−45.8885	−1.98579
$535$	9.52786	0.411925
$536$	9.23607	0.398937
$537$	68.3607	2.94998
$538$	−19.7082	−0.849681
$539$	0	0
$540$	−55.7771	−2.40026
$541$	−14.8541	−0.638628	−0.319314	−	0.947649i	$-0.603452\pi$
$541$	−14.8541	−0.638628	−0.319314	+	0.947649i	$0.603452\pi$
$542$	28.0902	1.20658
$543$	17.5279	0.752193
$544$	1.61803	0.0693726
$545$	−3.63932	−0.155891
$546$	49.8885	2.13503
$547$	43.3050	1.85159	0.925793	−	0.378031i	$-0.123399\pi$
$547$	43.3050	1.85159	0.925793	+	0.378031i	$0.123399\pi$
$548$	−9.56231	−0.408481
$549$	8.56231	0.365430
$550$	0	0
$551$	−5.70820	−0.243178
$552$	2.76393	0.117641
$553$	35.5967	1.51373
$554$	−20.4721	−0.869778
$555$	40.3607	1.71322
$556$	−14.0902	−0.597556
$557$	−28.1459	−1.19258	−0.596290	−	0.802769i	$-0.703359\pi$
$557$	−28.1459	−1.19258	−0.596290	+	0.802769i	$0.703359\pi$
$558$	20.6525	0.874289
$559$	30.4721	1.28883
$560$	14.8541	0.627700
$561$	0	0
$562$	−4.00000	−0.168730
$563$	−32.9443	−1.38844	−0.694218	−	0.719765i	$-0.744250\pi$
$563$	−32.9443	−1.38844	−0.694218	+	0.719765i	$0.744250\pi$
$564$	2.76393	0.116383
$565$	−29.0132	−1.22059
$566$	−9.85410	−0.414199
$567$	94.1033	3.95197
$568$	2.76393	0.115972
$569$	−14.1803	−0.594471	−0.297235	−	0.954804i	$-0.596065\pi$
$569$	−14.1803	−0.594471	−0.297235	+	0.954804i	$0.596065\pi$
$570$	−12.4721	−0.522400
$571$	−14.2148	−0.594870	−0.297435	−	0.954742i	$-0.596131\pi$
$571$	−14.2148	−0.594870	−0.297435	+	0.954742i	$0.596131\pi$
$572$	0	0
$573$	43.3050	1.80909
$574$	1.81966	0.0759511
$575$	8.41641	0.350988
$576$	7.47214	0.311339
$577$	39.3050	1.63629	0.818143	−	0.575014i	$-0.195004\pi$
$577$	39.3050	1.63629	0.818143	+	0.575014i	$0.195004\pi$
$578$	14.3820	0.598211
$579$	−59.7771	−2.48425
$580$	22.0000	0.913500
$581$	−8.27051	−0.343119
$582$	54.8328	2.27289
$583$	0	0
$584$	−10.9443	−0.452877
$585$	115.193	4.76266
$586$	−24.0000	−0.991431
$587$	33.5279	1.38384	0.691922	−	0.721973i	$-0.256764\pi$
$587$	33.5279	1.38384	0.691922	+	0.721973i	$0.256764\pi$
$588$	−25.4164	−1.04815
$589$	2.76393	0.113886
$590$	−26.7639	−1.10185
$591$	−35.4164	−1.45684
$592$	−3.23607	−0.133002
$593$	−10.7426	−0.441148	−0.220574	−	0.975370i	$-0.570793\pi$
$593$	−10.7426	−0.441148	−0.220574	+	0.975370i	$0.570793\pi$
$594$	0	0
$595$	−24.0344	−0.985316
$596$	3.52786	0.144507
$597$	−86.1378	−3.52538
$598$	−3.41641	−0.139707
$599$	29.4164	1.20192	0.600961	−	0.799278i	$-0.294785\pi$
$599$	29.4164	1.20192	0.600961	+	0.799278i	$0.294785\pi$
$600$	31.8885	1.30184
$601$	−29.3050	−1.19537	−0.597687	−	0.801730i	$-0.703913\pi$
$601$	−29.3050	−1.19537	−0.597687	+	0.801730i	$0.703913\pi$
$602$	−29.3607	−1.19665
$603$	−69.0132	−2.81043
$604$	10.7639	0.437978
$605$	0	0
$606$	−11.5279	−0.468287
$607$	9.23607	0.374880	0.187440	−	0.982276i	$-0.439981\pi$
$607$	9.23607	0.374880	0.187440	+	0.982276i	$0.439981\pi$
$608$	1.00000	0.0405554
$609$	−71.1935	−2.88491
$610$	−4.41641	−0.178815
$611$	−3.41641	−0.138213
$612$	−12.0902	−0.488716
$613$	2.27051	0.0917050	0.0458525	−	0.998948i	$-0.485400\pi$
$613$	2.27051	0.0917050	0.0458525	+	0.998948i	$0.485400\pi$
$614$	−1.52786	−0.0616596
$615$	5.88854	0.237449
$616$	0	0
$617$	2.36068	0.0950374	0.0475187	−	0.998870i	$-0.484869\pi$
$617$	2.36068	0.0950374	0.0475187	+	0.998870i	$0.484869\pi$
$618$	−22.4721	−0.903962
$619$	34.2705	1.37745	0.688724	−	0.725024i	$-0.258171\pi$
$619$	34.2705	1.37745	0.688724	+	0.725024i	$0.258171\pi$
$620$	−10.6525	−0.427814
$621$	−12.3607	−0.496017
$622$	−5.43769	−0.218032
$623$	−54.6525	−2.18961
$624$	−12.9443	−0.518186
$625$	22.8328	0.913313
$626$	15.5066	0.619767
$627$	0	0
$628$	−22.3262	−0.890914
$629$	5.23607	0.208776
$630$	−110.992	−4.42202
$631$	−13.5279	−0.538536	−0.269268	−	0.963065i	$-0.586782\pi$
$631$	−13.5279	−0.538536	−0.269268	+	0.963065i	$0.586782\pi$
$632$	−9.23607	−0.367391
$633$	48.3607	1.92216
$634$	8.47214	0.336472
$635$	8.83282	0.350520
$636$	−36.3607	−1.44179
$637$	31.4164	1.24476
$638$	0	0
$639$	−20.6525	−0.816999
$640$	−3.85410	−0.152347
$641$	2.11146	0.0833975	0.0416988	−	0.999130i	$-0.486723\pi$
$641$	2.11146	0.0833975	0.0416988	+	0.999130i	$0.486723\pi$
$642$	8.00000	0.315735
$643$	29.3262	1.15651	0.578257	−	0.815855i	$-0.303733\pi$
$643$	29.3262	1.15651	0.578257	+	0.815855i	$0.303733\pi$
$644$	3.29180	0.129715
$645$	−95.0132	−3.74114
$646$	−1.61803	−0.0636607
$647$	−33.3050	−1.30935	−0.654676	−	0.755909i	$-0.727195\pi$
$647$	−33.3050	−1.30935	−0.654676	+	0.755909i	$0.727195\pi$
$648$	−24.4164	−0.959167
$649$	0	0
$650$	−39.4164	−1.54604
$651$	34.4721	1.35107
$652$	17.2705	0.676365
$653$	27.6180	1.08078	0.540389	−	0.841416i	$-0.318277\pi$
$653$	27.6180	1.08078	0.540389	+	0.841416i	$0.318277\pi$
$654$	−3.05573	−0.119488
$655$	−53.3951	−2.08632
$656$	−0.472136	−0.0184338
$657$	81.7771	3.19043
$658$	3.29180	0.128328
$659$	−29.4164	−1.14590	−0.572950	−	0.819590i	$-0.694201\pi$
$659$	−29.4164	−1.14590	−0.572950	+	0.819590i	$0.694201\pi$
$660$	0	0
$661$	−19.4164	−0.755211	−0.377605	−	0.925967i	$-0.623252\pi$
$661$	−19.4164	−0.755211	−0.377605	+	0.925967i	$0.623252\pi$
$662$	10.4721	0.407011
$663$	20.9443	0.813408
$664$	2.14590	0.0832770
$665$	−14.8541	−0.576017
$666$	24.1803	0.936969
$667$	4.87539	0.188776
$668$	−6.29180	−0.243437
$669$	34.4721	1.33277
$670$	35.5967	1.37522
$671$	0	0
$672$	12.4721	0.481123
$673$	24.6525	0.950283	0.475142	−	0.879909i	$-0.342397\pi$
$673$	24.6525	0.950283	0.475142	+	0.879909i	$0.342397\pi$
$674$	26.1803	1.00843
$675$	−142.610	−5.48906
$676$	3.00000	0.115385
$677$	17.4164	0.669367	0.334683	−	0.942331i	$-0.391371\pi$
$677$	17.4164	0.669367	0.334683	+	0.942331i	$0.391371\pi$
$678$	−24.3607	−0.935566
$679$	65.3050	2.50617
$680$	6.23607	0.239142
$681$	−84.7214	−3.24653
$682$	0	0
$683$	−9.70820	−0.371474	−0.185737	−	0.982599i	$-0.559467\pi$
$683$	−9.70820	−0.371474	−0.185737	+	0.982599i	$0.559467\pi$
$684$	−7.47214	−0.285704
$685$	−36.8541	−1.40812
$686$	−3.29180	−0.125681
$687$	35.1246	1.34009
$688$	7.61803	0.290435
$689$	44.9443	1.71224
$690$	10.6525	0.405533
$691$	14.2148	0.540756	0.270378	−	0.962754i	$-0.412851\pi$
$691$	14.2148	0.540756	0.270378	+	0.962754i	$0.412851\pi$
$692$	−4.00000	−0.152057
$693$	0	0
$694$	3.79837	0.144184
$695$	−54.3050	−2.05990
$696$	18.4721	0.700185
$697$	0.763932	0.0289360
$698$	9.67376	0.366157
$699$	−1.05573	−0.0399313
$700$	37.9787	1.43546
$701$	−42.0902	−1.58972	−0.794862	−	0.606790i	$-0.792457\pi$
$701$	−42.0902	−1.58972	−0.794862	+	0.606790i	$0.792457\pi$
$702$	57.8885	2.18486
$703$	3.23607	0.122051
$704$	0	0
$705$	10.6525	0.401195
$706$	33.9230	1.27671
$707$	−13.7295	−0.516351
$708$	−22.4721	−0.844555
$709$	46.0344	1.72886	0.864430	−	0.502753i	$-0.167680\pi$
$709$	46.0344	1.72886	0.864430	+	0.502753i	$0.167680\pi$
$710$	10.6525	0.399780
$711$	69.0132	2.58820
$712$	14.1803	0.531431
$713$	−2.36068	−0.0884082
$714$	−20.1803	−0.755230
$715$	0	0
$716$	−21.1246	−0.789464
$717$	−49.5967	−1.85222
$718$	−2.20163	−0.0821640
$719$	−8.72949	−0.325555	−0.162778	−	0.986663i	$-0.552045\pi$
$719$	−8.72949	−0.325555	−0.162778	+	0.986663i	$0.552045\pi$
$720$	28.7984	1.07325
$721$	−26.7639	−0.996741
$722$	−1.00000	−0.0372161
$723$	−63.1935	−2.35019
$724$	−5.41641	−0.201299
$725$	56.2492	2.08904
$726$	0	0
$727$	34.1591	1.26689	0.633445	−	0.773788i	$-0.281640\pi$
$727$	34.1591	1.26689	0.633445	+	0.773788i	$0.281640\pi$
$728$	−15.4164	−0.571370
$729$	41.9443	1.55349
$730$	−42.1803	−1.56116
$731$	−12.3262	−0.455902
$732$	−3.70820	−0.137059
$733$	−20.7984	−0.768205	−0.384103	−	0.923290i	$-0.625489\pi$
$733$	−20.7984	−0.768205	−0.384103	+	0.923290i	$0.625489\pi$
$734$	−9.09017	−0.335524
$735$	−97.9574	−3.61321
$736$	−0.854102	−0.0314826
$737$	0	0
$738$	3.52786	0.129862
$739$	46.2148	1.70004	0.850019	−	0.526752i	$-0.176590\pi$
$739$	46.2148	1.70004	0.850019	+	0.526752i	$0.176590\pi$
$740$	−12.4721	−0.458485
$741$	12.9443	0.475520
$742$	−43.3050	−1.58977
$743$	−3.41641	−0.125336	−0.0626679	−	0.998034i	$-0.519961\pi$
$743$	−3.41641	−0.125336	−0.0626679	+	0.998034i	$0.519961\pi$
$744$	−8.94427	−0.327913
$745$	13.5967	0.498146
$746$	−18.4721	−0.676313
$747$	−16.0344	−0.586670
$748$	0	0
$749$	9.52786	0.348141
$750$	60.5410	2.21065
$751$	−37.8885	−1.38257	−0.691286	−	0.722581i	$-0.742956\pi$
$751$	−37.8885	−1.38257	−0.691286	+	0.722581i	$0.742956\pi$
$752$	−0.854102	−0.0311459
$753$	40.0689	1.46019
$754$	−22.8328	−0.831522
$755$	41.4853	1.50980
$756$	−55.7771	−2.02859
$757$	30.3607	1.10348	0.551739	−	0.834017i	$-0.313965\pi$
$757$	30.3607	1.10348	0.551739	+	0.834017i	$0.313965\pi$
$758$	−7.88854	−0.286525
$759$	0	0
$760$	3.85410	0.139803
$761$	31.5279	1.14288	0.571442	−	0.820642i	$-0.306384\pi$
$761$	31.5279	1.14288	0.571442	+	0.820642i	$0.306384\pi$
$762$	7.41641	0.268668
$763$	−3.63932	−0.131752
$764$	−13.3820	−0.484143
$765$	−46.5967	−1.68471
$766$	18.6525	0.673941
$767$	27.7771	1.00297
$768$	−3.23607	−0.116772
$769$	13.2705	0.478547	0.239273	−	0.970952i	$-0.423091\pi$
$769$	13.2705	0.478547	0.239273	+	0.970952i	$0.423091\pi$
$770$	0	0
$771$	58.8328	2.11881
$772$	18.4721	0.664827
$773$	14.3607	0.516518	0.258259	−	0.966076i	$-0.416851\pi$
$773$	14.3607	0.516518	0.258259	+	0.966076i	$0.416851\pi$
$774$	−56.9230	−2.04605
$775$	−27.2361	−0.978348
$776$	−16.9443	−0.608264
$777$	40.3607	1.44793
$778$	−2.27051	−0.0814017
$779$	0.472136	0.0169160
$780$	−49.8885	−1.78630
$781$	0	0
$782$	1.38197	0.0494190
$783$	−82.6099	−2.95224
$784$	7.85410	0.280504
$785$	−86.0476	−3.07117
$786$	−44.8328	−1.59913
$787$	−17.4164	−0.620828	−0.310414	−	0.950601i	$-0.600468\pi$
$787$	−17.4164	−0.620828	−0.310414	+	0.950601i	$0.600468\pi$
$788$	10.9443	0.389874
$789$	−51.7771	−1.84331
$790$	−35.5967	−1.26648
$791$	−29.0132	−1.03159
$792$	0	0
$793$	4.58359	0.162768
$794$	−16.5623	−0.587774
$795$	−140.138	−4.97017
$796$	26.6180	0.943451
$797$	34.0000	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$798$	−12.4721	−0.441509
$799$	1.38197	0.0488904
$800$	−9.85410	−0.348395
$801$	−105.957	−3.74382
$802$	19.2361	0.679249
$803$	0	0
$804$	29.8885	1.05409
$805$	12.6869	0.447155
$806$	11.0557	0.389421
$807$	−63.7771	−2.24506
$808$	3.56231	0.125321
$809$	−35.0902	−1.23370	−0.616852	−	0.787079i	$-0.711592\pi$
$809$	−35.0902	−1.23370	−0.616852	+	0.787079i	$0.711592\pi$
$810$	−94.1033	−3.30645
$811$	12.7639	0.448202	0.224101	−	0.974566i	$-0.428055\pi$
$811$	12.7639	0.448202	0.224101	+	0.974566i	$0.428055\pi$
$812$	22.0000	0.772049
$813$	90.9017	3.18806
$814$	0	0
$815$	66.5623	2.33158
$816$	5.23607	0.183299
$817$	−7.61803	−0.266521
$818$	29.5279	1.03242
$819$	115.193	4.02519
$820$	−1.81966	−0.0635453
$821$	−47.6180	−1.66188	−0.830940	−	0.556361i	$-0.812197\pi$
$821$	−47.6180	−1.66188	−0.830940	+	0.556361i	$0.812197\pi$
$822$	−30.9443	−1.07931
$823$	−1.74265	−0.0607448	−0.0303724	−	0.999539i	$-0.509669\pi$
$823$	−1.74265	−0.0607448	−0.0303724	+	0.999539i	$0.509669\pi$
$824$	6.94427	0.241915
$825$	0	0
$826$	−26.7639	−0.931236
$827$	12.0689	0.419676	0.209838	−	0.977736i	$-0.432706\pi$
$827$	12.0689	0.419676	0.209838	+	0.977736i	$0.432706\pi$
$828$	6.38197	0.221789
$829$	42.3607	1.47125	0.735624	−	0.677391i	$-0.236889\pi$
$829$	42.3607	1.47125	0.735624	+	0.677391i	$0.236889\pi$
$830$	8.27051	0.287074
$831$	−66.2492	−2.29816
$832$	4.00000	0.138675
$833$	−12.7082	−0.440313
$834$	−45.5967	−1.57889
$835$	−24.2492	−0.839179
$836$	0	0
$837$	40.0000	1.38260
$838$	28.7426	0.992898
$839$	23.0132	0.794502	0.397251	−	0.917710i	$-0.369964\pi$
$839$	23.0132	0.794502	0.397251	+	0.917710i	$0.369964\pi$
$840$	48.0689	1.65853
$841$	3.58359	0.123572
$842$	−24.4721	−0.843365
$843$	−12.9443	−0.445824
$844$	−14.9443	−0.514403
$845$	11.5623	0.397755
$846$	6.38197	0.219417
$847$	0	0
$848$	11.2361	0.385848
$849$	−31.8885	−1.09441
$850$	15.9443	0.546884
$851$	−2.76393	−0.0947464
$852$	8.94427	0.306426
$853$	−6.85410	−0.234680	−0.117340	−	0.993092i	$-0.537437\pi$
$853$	−6.85410	−0.234680	−0.117340	+	0.993092i	$0.537437\pi$
$854$	−4.41641	−0.151126
$855$	−28.7984	−0.984884
$856$	−2.47214	−0.0844959
$857$	−26.8328	−0.916592	−0.458296	−	0.888800i	$-0.651540\pi$
$857$	−26.8328	−0.916592	−0.458296	+	0.888800i	$0.651540\pi$
$858$	0	0
$859$	7.03444	0.240012	0.120006	−	0.992773i	$-0.461709\pi$
$859$	7.03444	0.240012	0.120006	+	0.992773i	$0.461709\pi$
$860$	29.3607	1.00119
$861$	5.88854	0.200681
$862$	10.5836	0.360479
$863$	−18.7639	−0.638732	−0.319366	−	0.947632i	$-0.603470\pi$
$863$	−18.7639	−0.638732	−0.319366	+	0.947632i	$0.603470\pi$
$864$	14.4721	0.492352
$865$	−15.4164	−0.524174
$866$	−11.8885	−0.403989
$867$	46.5410	1.58062
$868$	−10.6525	−0.361569
$869$	0	0
$870$	71.1935	2.41369
$871$	−36.9443	−1.25181
$872$	0.944272	0.0319771
$873$	126.610	4.28510
$874$	0.854102	0.0288904
$875$	72.1033	2.43754
$876$	−35.4164	−1.19661
$877$	−32.6525	−1.10260	−0.551298	−	0.834308i	$-0.685867\pi$
$877$	−32.6525	−1.10260	−0.551298	+	0.834308i	$0.685867\pi$
$878$	18.3607	0.619643
$879$	−77.6656	−2.61960
$880$	0	0
$881$	5.41641	0.182483	0.0912417	−	0.995829i	$-0.470916\pi$
$881$	5.41641	0.182483	0.0912417	+	0.995829i	$0.470916\pi$
$882$	−58.6869	−1.97609
$883$	28.0344	0.943434	0.471717	−	0.881750i	$-0.343634\pi$
$883$	28.0344	0.943434	0.471717	+	0.881750i	$0.343634\pi$
$884$	−6.47214	−0.217681
$885$	−86.6099	−2.91136
$886$	21.2705	0.714597
$887$	35.3050	1.18542	0.592712	−	0.805414i	$-0.298057\pi$
$887$	35.3050	1.18542	0.592712	+	0.805414i	$0.298057\pi$
$888$	−10.4721	−0.351422
$889$	8.83282	0.296243
$890$	54.6525	1.83196
$891$	0	0
$892$	−10.6525	−0.356671
$893$	0.854102	0.0285814
$894$	11.4164	0.381822
$895$	−81.4164	−2.72145
$896$	−3.85410	−0.128757
$897$	−11.0557	−0.369140
$898$	−15.7082	−0.524190
$899$	−15.7771	−0.526195
$900$	73.6312	2.45437
$901$	−18.1803	−0.605675
$902$	0	0
$903$	−95.0132	−3.16184
$904$	7.52786	0.250373
$905$	−20.8754	−0.693921
$906$	34.8328	1.15724
$907$	17.3475	0.576015	0.288008	−	0.957628i	$-0.407007\pi$
$907$	17.3475	0.576015	0.288008	+	0.957628i	$0.407007\pi$
$908$	26.1803	0.868825
$909$	−26.6180	−0.882864
$910$	−59.4164	−1.96963
$911$	23.5967	0.781795	0.390898	−	0.920434i	$-0.372165\pi$
$911$	23.5967	0.781795	0.390898	+	0.920434i	$0.372165\pi$
$912$	3.23607	0.107157
$913$	0	0
$914$	11.0902	0.366830
$915$	−14.2918	−0.472472
$916$	−10.8541	−0.358630
$917$	−53.3951	−1.76326
$918$	−23.4164	−0.772857
$919$	−39.6312	−1.30731	−0.653656	−	0.756792i	$-0.726766\pi$
$919$	−39.6312	−1.30731	−0.653656	+	0.756792i	$0.726766\pi$
$920$	−3.29180	−0.108527
$921$	−4.94427	−0.162919
$922$	−30.6869	−1.01062
$923$	−11.0557	−0.363904
$924$	0	0
$925$	−31.8885	−1.04849
$926$	12.2148	0.401403
$927$	−51.8885	−1.70424
$928$	−5.70820	−0.187381
$929$	−49.6180	−1.62791	−0.813957	−	0.580925i	$-0.802691\pi$
$929$	−49.6180	−1.62791	−0.813957	+	0.580925i	$0.802691\pi$
$930$	−34.4721	−1.13039
$931$	−7.85410	−0.257408
$932$	0.326238	0.0106863
$933$	−17.5967	−0.576092
$934$	−9.27051	−0.303340
$935$	0	0
$936$	−29.8885	−0.976938
$937$	8.49342	0.277468	0.138734	−	0.990330i	$-0.455697\pi$
$937$	8.49342	0.277468	0.138734	+	0.990330i	$0.455697\pi$
$938$	35.5967	1.16228
$939$	50.1803	1.63757
$940$	−3.29180	−0.107367
$941$	−20.7639	−0.676885	−0.338442	−	0.940987i	$-0.609900\pi$
$941$	−20.7639	−0.676885	−0.338442	+	0.940987i	$0.609900\pi$
$942$	−72.2492	−2.35401
$943$	−0.403252	−0.0131317
$944$	6.94427	0.226017
$945$	−214.971	−6.99299
$946$	0	0
$947$	−1.49342	−0.0485297	−0.0242649	−	0.999706i	$-0.507724\pi$
$947$	−1.49342	−0.0485297	−0.0242649	+	0.999706i	$0.507724\pi$
$948$	−29.8885	−0.970735
$949$	43.7771	1.42106
$950$	9.85410	0.319709
$951$	27.4164	0.889038
$952$	6.23607	0.202112
$953$	−23.0132	−0.745469	−0.372735	−	0.927938i	$-0.621580\pi$
$953$	−23.0132	−0.745469	−0.372735	+	0.927938i	$0.621580\pi$
$954$	−83.9574	−2.71822
$955$	−51.5755	−1.66894
$956$	15.3262	0.495686
$957$	0	0
$958$	19.9098	0.643257
$959$	−36.8541	−1.19008
$960$	−12.4721	−0.402536
$961$	−23.3607	−0.753570
$962$	12.9443	0.417340
$963$	18.4721	0.595256
$964$	19.5279	0.628950
$965$	71.1935	2.29180
$966$	10.6525	0.342738
$967$	48.8541	1.57104	0.785521	−	0.618835i	$-0.212395\pi$
$967$	48.8541	1.57104	0.785521	+	0.618835i	$0.212395\pi$
$968$	0	0
$969$	−5.23607	−0.168207
$970$	−65.3050	−2.09682
$971$	−32.9443	−1.05723	−0.528616	−	0.848861i	$-0.677289\pi$
$971$	−32.9443	−1.05723	−0.528616	+	0.848861i	$0.677289\pi$
$972$	−35.5967	−1.14177
$973$	−54.3050	−1.74094
$974$	−21.4164	−0.686226
$975$	−127.554	−4.08500
$976$	1.14590	0.0366793
$977$	6.83282	0.218601	0.109301	−	0.994009i	$-0.465139\pi$
$977$	6.83282	0.218601	0.109301	+	0.994009i	$0.465139\pi$
$978$	55.8885	1.78712
$979$	0	0
$980$	30.2705	0.966956
$981$	−7.05573	−0.225272
$982$	−23.7426	−0.757658
$983$	0.583592	0.0186137	0.00930685	−	0.999957i	$-0.497037\pi$
$983$	0.583592	0.0186137	0.00930685	+	0.999957i	$0.497037\pi$
$984$	−1.52786	−0.0487065
$985$	42.1803	1.34398
$986$	9.23607	0.294136
$987$	10.6525	0.339072
$988$	−4.00000	−0.127257
$989$	6.50658	0.206897
$990$	0	0
$991$	12.9443	0.411188	0.205594	−	0.978637i	$-0.434087\pi$
$991$	12.9443	0.411188	0.205594	+	0.978637i	$0.434087\pi$
$992$	2.76393	0.0877549
$993$	33.8885	1.07542
$994$	10.6525	0.337876
$995$	102.589	3.25228
$996$	6.94427	0.220038
$997$	−39.9230	−1.26437	−0.632187	−	0.774816i	$-0.717842\pi$
$997$	−39.9230	−1.26437	−0.632187	+	0.774816i	$0.717842\pi$
$998$	20.0344	0.634179
$999$	46.8328	1.48172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.v.1.1		2
11.2	odd	10		418.2.f.a.191.1	✓	4
11.6	odd	10		418.2.f.a.267.1	yes	4
11.10	odd	2		4598.2.a.be.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.a.191.1	✓	4	11.2	odd	10
418.2.f.a.267.1	yes	4	11.6	odd	10
4598.2.a.v.1.1		2	1.1	even	1	trivial
4598.2.a.be.1.1		2	11.10	odd	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} +3.23607 q^{6} +3.85410 q^{7} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.23607 q^{3} +1.00000 q^{4} +3.85410 q^{5} +3.23607 q^{6} +3.85410 q^{7} -1.00000 q^{8} +7.47214 q^{9} -3.85410 q^{10} -3.23607 q^{12} +4.00000 q^{13} -3.85410 q^{14} -12.4721 q^{15} +1.00000 q^{16} -1.61803 q^{17} -7.47214 q^{18} -1.00000 q^{19} +3.85410 q^{20} -12.4721 q^{21} +0.854102 q^{23} +3.23607 q^{24} +9.85410 q^{25} -4.00000 q^{26} -14.4721 q^{27} +3.85410 q^{28} +5.70820 q^{29} +12.4721 q^{30} -2.76393 q^{31} -1.00000 q^{32} +1.61803 q^{34} +14.8541 q^{35} +7.47214 q^{36} -3.23607 q^{37} +1.00000 q^{38} -12.9443 q^{39} -3.85410 q^{40} -0.472136 q^{41} +12.4721 q^{42} +7.61803 q^{43} +28.7984 q^{45} -0.854102 q^{46} -0.854102 q^{47} -3.23607 q^{48} +7.85410 q^{49} -9.85410 q^{50} +5.23607 q^{51} +4.00000 q^{52} +11.2361 q^{53} +14.4721 q^{54} -3.85410 q^{56} +3.23607 q^{57} -5.70820 q^{58} +6.94427 q^{59} -12.4721 q^{60} +1.14590 q^{61} +2.76393 q^{62} +28.7984 q^{63} +1.00000 q^{64} +15.4164 q^{65} -9.23607 q^{67} -1.61803 q^{68} -2.76393 q^{69} -14.8541 q^{70} -2.76393 q^{71} -7.47214 q^{72} +10.9443 q^{73} +3.23607 q^{74} -31.8885 q^{75} -1.00000 q^{76} +12.9443 q^{78} +9.23607 q^{79} +3.85410 q^{80} +24.4164 q^{81} +0.472136 q^{82} -2.14590 q^{83} -12.4721 q^{84} -6.23607 q^{85} -7.61803 q^{86} -18.4721 q^{87} -14.1803 q^{89} -28.7984 q^{90} +15.4164 q^{91} +0.854102 q^{92} +8.94427 q^{93} +0.854102 q^{94} -3.85410 q^{95} +3.23607 q^{96} +16.9443 q^{97} -7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} + q^{7} - 2 q^{8} + 6 q^{9} - q^{10} - 2 q^{12} + 8 q^{13} - q^{14} - 16 q^{15} + 2 q^{16} - q^{17} - 6 q^{18} - 2 q^{19} + q^{20} - 16 q^{21} - 5 q^{23} + 2 q^{24} + 13 q^{25} - 8 q^{26} - 20 q^{27} + q^{28} - 2 q^{29} + 16 q^{30} - 10 q^{31} - 2 q^{32} + q^{34} + 23 q^{35} + 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{39} - q^{40} + 8 q^{41} + 16 q^{42} + 13 q^{43} + 33 q^{45} + 5 q^{46} + 5 q^{47} - 2 q^{48} + 9 q^{49} - 13 q^{50} + 6 q^{51} + 8 q^{52} + 18 q^{53} + 20 q^{54} - q^{56} + 2 q^{57} + 2 q^{58} - 4 q^{59} - 16 q^{60} + 9 q^{61} + 10 q^{62} + 33 q^{63} + 2 q^{64} + 4 q^{65} - 14 q^{67} - q^{68} - 10 q^{69} - 23 q^{70} - 10 q^{71} - 6 q^{72} + 4 q^{73} + 2 q^{74} - 28 q^{75} - 2 q^{76} + 8 q^{78} + 14 q^{79} + q^{80} + 22 q^{81} - 8 q^{82} - 11 q^{83} - 16 q^{84} - 8 q^{85} - 13 q^{86} - 28 q^{87} - 6 q^{89} - 33 q^{90} + 4 q^{91} - 5 q^{92} - 5 q^{94} - q^{95} + 2 q^{96} + 16 q^{97} - 9 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 + q^7 - 2 * q^8 + 6 * q^9 - q^10 - 2 * q^12 + 8 * q^13 - q^14 - 16 * q^15 + 2 * q^16 - q^17 - 6 * q^18 - 2 * q^19 + q^20 - 16 * q^21 - 5 * q^23 + 2 * q^24 + 13 * q^25 - 8 * q^26 - 20 * q^27 + q^28 - 2 * q^29 + 16 * q^30 - 10 * q^31 - 2 * q^32 + q^34 + 23 * q^35 + 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^39 - q^40 + 8 * q^41 + 16 * q^42 + 13 * q^43 + 33 * q^45 + 5 * q^46 + 5 * q^47 - 2 * q^48 + 9 * q^49 - 13 * q^50 + 6 * q^51 + 8 * q^52 + 18 * q^53 + 20 * q^54 - q^56 + 2 * q^57 + 2 * q^58 - 4 * q^59 - 16 * q^60 + 9 * q^61 + 10 * q^62 + 33 * q^63 + 2 * q^64 + 4 * q^65 - 14 * q^67 - q^68 - 10 * q^69 - 23 * q^70 - 10 * q^71 - 6 * q^72 + 4 * q^73 + 2 * q^74 - 28 * q^75 - 2 * q^76 + 8 * q^78 + 14 * q^79 + q^80 + 22 * q^81 - 8 * q^82 - 11 * q^83 - 16 * q^84 - 8 * q^85 - 13 * q^86 - 28 * q^87 - 6 * q^89 - 33 * q^90 + 4 * q^91 - 5 * q^92 - 5 * q^94 - q^95 + 2 * q^96 + 16 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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