LMFDB - Embedded newform 4598.2.a.cd.1.3

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
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			1.3
Root			$-1.58152$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.58152 q^{3} +1.00000 q^{4} +2.60241 q^{5} -1.58152 q^{6} +1.55057 q^{7} +1.00000 q^{8} -0.498782 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.58152 q^{3} +1.00000 q^{4} +2.60241 q^{5} -1.58152 q^{6} +1.55057 q^{7} +1.00000 q^{8} -0.498782 q^{9} +2.60241 q^{10} -1.58152 q^{12} -2.29906 q^{13} +1.55057 q^{14} -4.11577 q^{15} +1.00000 q^{16} -0.212293 q^{17} -0.498782 q^{18} +1.00000 q^{19} +2.60241 q^{20} -2.45226 q^{21} -2.47068 q^{23} -1.58152 q^{24} +1.77252 q^{25} -2.29906 q^{26} +5.53341 q^{27} +1.55057 q^{28} +4.68696 q^{29} -4.11577 q^{30} +3.94906 q^{31} +1.00000 q^{32} -0.212293 q^{34} +4.03521 q^{35} -0.498782 q^{36} -2.64942 q^{37} +1.00000 q^{38} +3.63602 q^{39} +2.60241 q^{40} +7.54804 q^{41} -2.45226 q^{42} -5.85824 q^{43} -1.29803 q^{45} -2.47068 q^{46} +12.4845 q^{47} -1.58152 q^{48} -4.59574 q^{49} +1.77252 q^{50} +0.335746 q^{51} -2.29906 q^{52} +7.48676 q^{53} +5.53341 q^{54} +1.55057 q^{56} -1.58152 q^{57} +4.68696 q^{58} +4.18323 q^{59} -4.11577 q^{60} +13.0184 q^{61} +3.94906 q^{62} -0.773395 q^{63} +1.00000 q^{64} -5.98310 q^{65} -8.97065 q^{67} -0.212293 q^{68} +3.90744 q^{69} +4.03521 q^{70} +6.82149 q^{71} -0.498782 q^{72} +8.45234 q^{73} -2.64942 q^{74} -2.80328 q^{75} +1.00000 q^{76} +3.63602 q^{78} -8.98131 q^{79} +2.60241 q^{80} -7.25487 q^{81} +7.54804 q^{82} +16.2968 q^{83} -2.45226 q^{84} -0.552471 q^{85} -5.85824 q^{86} -7.41253 q^{87} -3.58951 q^{89} -1.29803 q^{90} -3.56485 q^{91} -2.47068 q^{92} -6.24554 q^{93} +12.4845 q^{94} +2.60241 q^{95} -1.58152 q^{96} -1.48936 q^{97} -4.59574 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * 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
$3$	−1.58152	−0.913093	−0.456547	−	0.889699i	$-0.650914\pi$
$3$	−1.58152	−0.913093	−0.456547	+	0.889699i	$0.650914\pi$
$4$	1.00000	0.500000
$5$	2.60241	1.16383	0.581916	−	0.813249i	$-0.302303\pi$
$5$	2.60241	1.16383	0.581916	+	0.813249i	$0.302303\pi$
$6$	−1.58152	−0.645654
$7$	1.55057	0.586059	0.293030	−	0.956103i	$-0.405337\pi$
$7$	1.55057	0.586059	0.293030	+	0.956103i	$0.405337\pi$
$8$	1.00000	0.353553
$9$	−0.498782	−0.166261
$10$	2.60241	0.822953
$11$	0	0
$11$	0	0
$12$	−1.58152	−0.456547
$13$	−2.29906	−0.637645	−0.318823	−	0.947814i	$-0.603287\pi$
$13$	−2.29906	−0.637645	−0.318823	+	0.947814i	$0.603287\pi$
$14$	1.55057	0.414407
$15$	−4.11577	−1.06269
$16$	1.00000	0.250000
$17$	−0.212293	−0.0514885	−0.0257443	−	0.999669i	$-0.508196\pi$
$17$	−0.212293	−0.0514885	−0.0257443	+	0.999669i	$0.508196\pi$
$18$	−0.498782	−0.117564
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.60241	0.581916
$21$	−2.45226	−0.535127
$22$	0	0
$23$	−2.47068	−0.515172	−0.257586	−	0.966255i	$-0.582927\pi$
$23$	−2.47068	−0.515172	−0.257586	+	0.966255i	$0.582927\pi$
$24$	−1.58152	−0.322827
$25$	1.77252	0.354504
$26$	−2.29906	−0.450883
$27$	5.53341	1.06490
$28$	1.55057	0.293030
$29$	4.68696	0.870346	0.435173	−	0.900347i	$-0.356687\pi$
$29$	4.68696	0.870346	0.435173	+	0.900347i	$0.356687\pi$
$30$	−4.11577	−0.751433
$31$	3.94906	0.709272	0.354636	−	0.935004i	$-0.384605\pi$
$31$	3.94906	0.709272	0.354636	+	0.935004i	$0.384605\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.212293	−0.0364079
$35$	4.03521	0.682074
$36$	−0.498782	−0.0831303
$37$	−2.64942	−0.435562	−0.217781	−	0.975998i	$-0.569882\pi$
$37$	−2.64942	−0.435562	−0.217781	+	0.975998i	$0.569882\pi$
$38$	1.00000	0.162221
$39$	3.63602	0.582230
$40$	2.60241	0.411477
$41$	7.54804	1.17881	0.589403	−	0.807839i	$-0.299363\pi$
$41$	7.54804	1.17881	0.589403	+	0.807839i	$0.299363\pi$
$42$	−2.45226	−0.378392
$43$	−5.85824	−0.893374	−0.446687	−	0.894690i	$-0.647396\pi$
$43$	−5.85824	−0.893374	−0.446687	+	0.894690i	$0.647396\pi$
$44$	0	0
$45$	−1.29803	−0.193499
$46$	−2.47068	−0.364282
$47$	12.4845	1.82105	0.910525	−	0.413454i	$-0.135678\pi$
$47$	12.4845	1.82105	0.910525	+	0.413454i	$0.135678\pi$
$48$	−1.58152	−0.228273
$49$	−4.59574	−0.656534
$50$	1.77252	0.250672
$51$	0.335746	0.0470138
$52$	−2.29906	−0.318823
$53$	7.48676	1.02839	0.514193	−	0.857675i	$-0.328092\pi$
$53$	7.48676	1.02839	0.514193	+	0.857675i	$0.328092\pi$
$54$	5.53341	0.753001
$55$	0	0
$56$	1.55057	0.207203
$57$	−1.58152	−0.209478
$58$	4.68696	0.615428
$59$	4.18323	0.544611	0.272305	−	0.962211i	$-0.412214\pi$
$59$	4.18323	0.544611	0.272305	+	0.962211i	$0.412214\pi$
$60$	−4.11577	−0.531343
$61$	13.0184	1.66684	0.833421	−	0.552639i	$-0.186379\pi$
$61$	13.0184	1.66684	0.833421	+	0.552639i	$0.186379\pi$
$62$	3.94906	0.501531
$63$	−0.773395	−0.0974386
$64$	1.00000	0.125000
$65$	−5.98310	−0.742112
$66$	0	0
$67$	−8.97065	−1.09594	−0.547970	−	0.836498i	$-0.684599\pi$
$67$	−8.97065	−1.09594	−0.547970	+	0.836498i	$0.684599\pi$
$68$	−0.212293	−0.0257443
$69$	3.90744	0.470400
$70$	4.03521	0.482299
$71$	6.82149	0.809562	0.404781	−	0.914414i	$-0.367348\pi$
$71$	6.82149	0.809562	0.404781	+	0.914414i	$0.367348\pi$
$72$	−0.498782	−0.0587820
$73$	8.45234	0.989271	0.494636	−	0.869100i	$-0.335302\pi$
$73$	8.45234	0.989271	0.494636	+	0.869100i	$0.335302\pi$
$74$	−2.64942	−0.307989
$75$	−2.80328	−0.323695
$76$	1.00000	0.114708
$77$	0	0
$78$	3.63602	0.411699
$79$	−8.98131	−1.01048	−0.505238	−	0.862980i	$-0.668595\pi$
$79$	−8.98131	−1.01048	−0.505238	+	0.862980i	$0.668595\pi$
$80$	2.60241	0.290958
$81$	−7.25487	−0.806097
$82$	7.54804	0.833541
$83$	16.2968	1.78881	0.894403	−	0.447262i	$-0.147601\pi$
$83$	16.2968	1.78881	0.894403	+	0.447262i	$0.147601\pi$
$84$	−2.45226	−0.267563
$85$	−0.552471	−0.0599239
$86$	−5.85824	−0.631711
$87$	−7.41253	−0.794707
$88$	0	0
$89$	−3.58951	−0.380487	−0.190244	−	0.981737i	$-0.560928\pi$
$89$	−3.58951	−0.380487	−0.190244	+	0.981737i	$0.560928\pi$
$90$	−1.29803	−0.136825
$91$	−3.56485	−0.373698
$92$	−2.47068	−0.257586
$93$	−6.24554	−0.647632
$94$	12.4845	1.28768
$95$	2.60241	0.267001
$96$	−1.58152	−0.161414
$97$	−1.48936	−0.151222	−0.0756109	−	0.997137i	$-0.524091\pi$
$97$	−1.48936	−0.151222	−0.0756109	+	0.997137i	$0.524091\pi$
$98$	−4.59574	−0.464240
$99$	0	0
$100$	1.77252	0.177252
$101$	2.51305	0.250058	0.125029	−	0.992153i	$-0.460098\pi$
$101$	2.51305	0.250058	0.125029	+	0.992153i	$0.460098\pi$
$102$	0.335746	0.0332438
$103$	6.77320	0.667384	0.333692	−	0.942682i	$-0.391706\pi$
$103$	6.77320	0.667384	0.333692	+	0.942682i	$0.391706\pi$
$104$	−2.29906	−0.225442
$105$	−6.38177	−0.622797
$106$	7.48676	0.727178
$107$	13.1359	1.26990	0.634949	−	0.772554i	$-0.281021\pi$
$107$	13.1359	1.26990	0.634949	+	0.772554i	$0.281021\pi$
$108$	5.53341	0.532452
$109$	2.72603	0.261106	0.130553	−	0.991441i	$-0.458325\pi$
$109$	2.72603	0.261106	0.130553	+	0.991441i	$0.458325\pi$
$110$	0	0
$111$	4.19012	0.397709
$112$	1.55057	0.146515
$113$	−8.85491	−0.833000	−0.416500	−	0.909136i	$-0.636743\pi$
$113$	−8.85491	−0.833000	−0.416500	+	0.909136i	$0.636743\pi$
$114$	−1.58152	−0.148123
$115$	−6.42971	−0.599573
$116$	4.68696	0.435173
$117$	1.14673	0.106015
$118$	4.18323	0.385098
$119$	−0.329174	−0.0301753
$120$	−4.11577	−0.375716
$121$	0	0
$122$	13.0184	1.17864
$123$	−11.9374	−1.07636
$124$	3.94906	0.354636
$125$	−8.39922	−0.751249
$126$	−0.773395	−0.0688995
$127$	9.25283	0.821056	0.410528	−	0.911848i	$-0.365344\pi$
$127$	9.25283	0.821056	0.410528	+	0.911848i	$0.365344\pi$
$128$	1.00000	0.0883883
$129$	9.26495	0.815733
$130$	−5.98310	−0.524752
$131$	−12.1117	−1.05821	−0.529103	−	0.848558i	$-0.677472\pi$
$131$	−12.1117	−1.05821	−0.529103	+	0.848558i	$0.677472\pi$
$132$	0	0
$133$	1.55057	0.134451
$134$	−8.97065	−0.774946
$135$	14.4002	1.23937
$136$	−0.212293	−0.0182039
$137$	−9.74968	−0.832971	−0.416486	−	0.909142i	$-0.636738\pi$
$137$	−9.74968	−0.832971	−0.416486	+	0.909142i	$0.636738\pi$
$138$	3.90744	0.332623
$139$	−12.7167	−1.07862	−0.539309	−	0.842108i	$-0.681315\pi$
$139$	−12.7167	−1.07862	−0.539309	+	0.842108i	$0.681315\pi$
$140$	4.03521	0.341037
$141$	−19.7445	−1.66279
$142$	6.82149	0.572447
$143$	0	0
$144$	−0.498782	−0.0415652
$145$	12.1974	1.01294
$146$	8.45234	0.699520
$147$	7.26827	0.599477
$148$	−2.64942	−0.217781
$149$	−13.5641	−1.11121	−0.555607	−	0.831445i	$-0.687514\pi$
$149$	−13.5641	−1.11121	−0.555607	+	0.831445i	$0.687514\pi$
$150$	−2.80328	−0.228887
$151$	−10.8519	−0.883115	−0.441557	−	0.897233i	$-0.645574\pi$
$151$	−10.8519	−0.883115	−0.441557	+	0.897233i	$0.645574\pi$
$152$	1.00000	0.0811107
$153$	0.105888	0.00856051
$154$	0	0
$155$	10.2771	0.825474
$156$	3.63602	0.291115
$157$	5.17350	0.412890	0.206445	−	0.978458i	$-0.433810\pi$
$157$	5.17350	0.412890	0.206445	+	0.978458i	$0.433810\pi$
$158$	−8.98131	−0.714514
$159$	−11.8405	−0.939012
$160$	2.60241	0.205738
$161$	−3.83095	−0.301921
$162$	−7.25487	−0.569996
$163$	−1.20001	−0.0939919	−0.0469959	−	0.998895i	$-0.514965\pi$
$163$	−1.20001	−0.0939919	−0.0469959	+	0.998895i	$0.514965\pi$
$164$	7.54804	0.589403
$165$	0	0
$166$	16.2968	1.26488
$167$	7.82624	0.605613	0.302806	−	0.953052i	$-0.402076\pi$
$167$	7.82624	0.605613	0.302806	+	0.953052i	$0.402076\pi$
$168$	−2.45226	−0.189196
$169$	−7.71431	−0.593408
$170$	−0.552471	−0.0423726
$171$	−0.498782	−0.0381428
$172$	−5.85824	−0.446687
$173$	−4.91882	−0.373971	−0.186986	−	0.982363i	$-0.559872\pi$
$173$	−4.91882	−0.373971	−0.186986	+	0.982363i	$0.559872\pi$
$174$	−7.41253	−0.561943
$175$	2.74841	0.207760
$176$	0	0
$177$	−6.61589	−0.497280
$178$	−3.58951	−0.269045
$179$	9.53506	0.712684	0.356342	−	0.934356i	$-0.384024\pi$
$179$	9.53506	0.712684	0.356342	+	0.934356i	$0.384024\pi$
$180$	−1.29803	−0.0967497
$181$	19.3338	1.43707	0.718534	−	0.695492i	$-0.244814\pi$
$181$	19.3338	1.43707	0.718534	+	0.695492i	$0.244814\pi$
$182$	−3.56485	−0.264244
$183$	−20.5890	−1.52198
$184$	−2.47068	−0.182141
$185$	−6.89487	−0.506921
$186$	−6.24554	−0.457945
$187$	0	0
$188$	12.4845	0.910525
$189$	8.57992	0.624097
$190$	2.60241	0.188798
$191$	−2.08916	−0.151166	−0.0755831	−	0.997140i	$-0.524082\pi$
$191$	−2.08916	−0.151166	−0.0755831	+	0.997140i	$0.524082\pi$
$192$	−1.58152	−0.114137
$193$	7.56792	0.544751	0.272376	−	0.962191i	$-0.412191\pi$
$193$	7.56792	0.544751	0.272376	+	0.962191i	$0.412191\pi$
$194$	−1.48936	−0.106930
$195$	9.46241	0.677617
$196$	−4.59574	−0.328267
$197$	−1.65699	−0.118055	−0.0590277	−	0.998256i	$-0.518800\pi$
$197$	−1.65699	−0.118055	−0.0590277	+	0.998256i	$0.518800\pi$
$198$	0	0
$199$	−3.68327	−0.261100	−0.130550	−	0.991442i	$-0.541674\pi$
$199$	−3.68327	−0.261100	−0.130550	+	0.991442i	$0.541674\pi$
$200$	1.77252	0.125336
$201$	14.1873	1.00069
$202$	2.51305	0.176818
$203$	7.26744	0.510074
$204$	0.335746	0.0235069
$205$	19.6431	1.37193
$206$	6.77320	0.471911
$207$	1.23233	0.0856529
$208$	−2.29906	−0.159411
$209$	0	0
$210$	−6.38177	−0.440384
$211$	2.08891	0.143806	0.0719031	−	0.997412i	$-0.477093\pi$
$211$	2.08891	0.143806	0.0719031	+	0.997412i	$0.477093\pi$
$212$	7.48676	0.514193
$213$	−10.7884	−0.739206
$214$	13.1359	0.897954
$215$	−15.2455	−1.03974
$216$	5.53341	0.376501
$217$	6.12329	0.415676
$218$	2.72603	0.184630
$219$	−13.3676	−0.903297
$220$	0	0
$221$	0.488074	0.0328314
$222$	4.19012	0.281223
$223$	23.1754	1.55194	0.775971	−	0.630768i	$-0.217260\pi$
$223$	23.1754	1.55194	0.775971	+	0.630768i	$0.217260\pi$
$224$	1.55057	0.103602
$225$	−0.884100	−0.0589400
$226$	−8.85491	−0.589020
$227$	−9.22043	−0.611981	−0.305991	−	0.952035i	$-0.598988\pi$
$227$	−9.22043	−0.611981	−0.305991	+	0.952035i	$0.598988\pi$
$228$	−1.58152	−0.104739
$229$	−16.2844	−1.07611	−0.538053	−	0.842911i	$-0.680840\pi$
$229$	−16.2844	−1.07611	−0.538053	+	0.842911i	$0.680840\pi$
$230$	−6.42971	−0.423962
$231$	0	0
$232$	4.68696	0.307714
$233$	15.6828	1.02741	0.513706	−	0.857966i	$-0.328272\pi$
$233$	15.6828	1.02741	0.513706	+	0.857966i	$0.328272\pi$
$234$	1.14673	0.0749642
$235$	32.4897	2.11940
$236$	4.18323	0.272305
$237$	14.2041	0.922659
$238$	−0.329174	−0.0213372
$239$	23.9513	1.54928	0.774640	−	0.632402i	$-0.217931\pi$
$239$	23.9513	1.54928	0.774640	+	0.632402i	$0.217931\pi$
$240$	−4.11577	−0.265672
$241$	3.80838	0.245320	0.122660	−	0.992449i	$-0.460858\pi$
$241$	3.80838	0.245320	0.122660	+	0.992449i	$0.460858\pi$
$242$	0	0
$243$	−5.12647	−0.328863
$244$	13.0184	0.833421
$245$	−11.9600	−0.764095
$246$	−11.9374	−0.761101
$247$	−2.29906	−0.146286
$248$	3.94906	0.250766
$249$	−25.7738	−1.63335
$250$	−8.39922	−0.531213
$251$	4.63462	0.292534	0.146267	−	0.989245i	$-0.453274\pi$
$251$	4.63462	0.292534	0.146267	+	0.989245i	$0.453274\pi$
$252$	−0.773395	−0.0487193
$253$	0	0
$254$	9.25283	0.580574
$255$	0.873747	0.0547161
$256$	1.00000	0.0625000
$257$	−25.7043	−1.60339	−0.801695	−	0.597734i	$-0.796068\pi$
$257$	−25.7043	−1.60339	−0.801695	+	0.597734i	$0.796068\pi$
$258$	9.26495	0.576811
$259$	−4.10810	−0.255265
$260$	−5.98310	−0.371056
$261$	−2.33777	−0.144704
$262$	−12.1117	−0.748265
$263$	21.8725	1.34872	0.674358	−	0.738405i	$-0.264421\pi$
$263$	21.8725	1.34872	0.674358	+	0.738405i	$0.264421\pi$
$264$	0	0
$265$	19.4836	1.19687
$266$	1.55057	0.0950714
$267$	5.67690	0.347420
$268$	−8.97065	−0.547970
$269$	−20.5982	−1.25590	−0.627948	−	0.778255i	$-0.716105\pi$
$269$	−20.5982	−1.25590	−0.627948	+	0.778255i	$0.716105\pi$
$270$	14.4002	0.876367
$271$	22.1499	1.34551	0.672756	−	0.739864i	$-0.265110\pi$
$271$	22.1499	1.34551	0.672756	+	0.739864i	$0.265110\pi$
$272$	−0.212293	−0.0128721
$273$	5.63790	0.341221
$274$	−9.74968	−0.588999
$275$	0	0
$276$	3.90744	0.235200
$277$	8.79403	0.528382	0.264191	−	0.964470i	$-0.414895\pi$
$277$	8.79403	0.528382	0.264191	+	0.964470i	$0.414895\pi$
$278$	−12.7167	−0.762698
$279$	−1.96972	−0.117924
$280$	4.03521	0.241150
$281$	−17.0989	−1.02004	−0.510019	−	0.860163i	$-0.670362\pi$
$281$	−17.0989	−1.02004	−0.510019	+	0.860163i	$0.670362\pi$
$282$	−19.7445	−1.17577
$283$	24.1009	1.43265	0.716324	−	0.697768i	$-0.245823\pi$
$283$	24.1009	1.43265	0.716324	+	0.697768i	$0.245823\pi$
$284$	6.82149	0.404781
$285$	−4.11577	−0.243797
$286$	0	0
$287$	11.7037	0.690850
$288$	−0.498782	−0.0293910
$289$	−16.9549	−0.997349
$290$	12.1974	0.716254
$291$	2.35546	0.138080
$292$	8.45234	0.494636
$293$	2.55321	0.149160	0.0745800	−	0.997215i	$-0.476238\pi$
$293$	2.55321	0.149160	0.0745800	+	0.997215i	$0.476238\pi$
$294$	7.26827	0.423894
$295$	10.8865	0.633835
$296$	−2.64942	−0.153994
$297$	0	0
$298$	−13.5641	−0.785747
$299$	5.68024	0.328497
$300$	−2.80328	−0.161847
$301$	−9.08360	−0.523570
$302$	−10.8519	−0.624457
$303$	−3.97445	−0.228326
$304$	1.00000	0.0573539
$305$	33.8793	1.93992
$306$	0.105888	0.00605320
$307$	18.9304	1.08041	0.540207	−	0.841532i	$-0.318346\pi$
$307$	18.9304	1.08041	0.540207	+	0.841532i	$0.318346\pi$
$308$	0	0
$309$	−10.7120	−0.609383
$310$	10.2771	0.583698
$311$	16.8210	0.953831	0.476916	−	0.878949i	$-0.341755\pi$
$311$	16.8210	0.953831	0.476916	+	0.878949i	$0.341755\pi$
$312$	3.63602	0.205849
$313$	−24.6812	−1.39507	−0.697533	−	0.716553i	$-0.745719\pi$
$313$	−24.6812	−1.39507	−0.697533	+	0.716553i	$0.745719\pi$
$314$	5.17350	0.291958
$315$	−2.01269	−0.113402
$316$	−8.98131	−0.505238
$317$	23.4588	1.31758	0.658788	−	0.752328i	$-0.271069\pi$
$317$	23.4588	1.31758	0.658788	+	0.752328i	$0.271069\pi$
$318$	−11.8405	−0.663982
$319$	0	0
$320$	2.60241	0.145479
$321$	−20.7748	−1.15954
$322$	−3.83095	−0.213491
$323$	−0.212293	−0.0118123
$324$	−7.25487	−0.403048
$325$	−4.07513	−0.226048
$326$	−1.20001	−0.0664623
$327$	−4.31128	−0.238414
$328$	7.54804	0.416771
$329$	19.3580	1.06724
$330$	0	0
$331$	16.6549	0.915436	0.457718	−	0.889097i	$-0.348667\pi$
$331$	16.6549	0.915436	0.457718	+	0.889097i	$0.348667\pi$
$332$	16.2968	0.894403
$333$	1.32148	0.0724168
$334$	7.82624	0.428233
$335$	−23.3453	−1.27549
$336$	−2.45226	−0.133782
$337$	22.4034	1.22039	0.610195	−	0.792251i	$-0.291091\pi$
$337$	22.4034	1.22039	0.610195	+	0.792251i	$0.291091\pi$
$338$	−7.71431	−0.419603
$339$	14.0043	0.760607
$340$	−0.552471	−0.0299620
$341$	0	0
$342$	−0.498782	−0.0269710
$343$	−17.9800	−0.970827
$344$	−5.85824	−0.315855
$345$	10.1687	0.547466
$346$	−4.91882	−0.264438
$347$	10.0811	0.541183	0.270591	−	0.962694i	$-0.412781\pi$
$347$	10.0811	0.541183	0.270591	+	0.962694i	$0.412781\pi$
$348$	−7.41253	−0.397354
$349$	−25.6119	−1.37098	−0.685488	−	0.728084i	$-0.740411\pi$
$349$	−25.6119	−1.37098	−0.685488	+	0.728084i	$0.740411\pi$
$350$	2.74841	0.146909
$351$	−12.7217	−0.679032
$352$	0	0
$353$	−6.10891	−0.325144	−0.162572	−	0.986697i	$-0.551979\pi$
$353$	−6.10891	−0.325144	−0.162572	+	0.986697i	$0.551979\pi$
$354$	−6.61589	−0.351630
$355$	17.7523	0.942194
$356$	−3.58951	−0.190244
$357$	0.520596	0.0275529
$358$	9.53506	0.503944
$359$	25.8236	1.36292	0.681458	−	0.731857i	$-0.261346\pi$
$359$	25.8236	1.36292	0.681458	+	0.731857i	$0.261346\pi$
$360$	−1.29803	−0.0684124
$361$	1.00000	0.0526316
$362$	19.3338	1.01616
$363$	0	0
$364$	−3.56485	−0.186849
$365$	21.9964	1.15134
$366$	−20.5890	−1.07620
$367$	−24.3799	−1.27262	−0.636309	−	0.771434i	$-0.719540\pi$
$367$	−24.3799	−1.27262	−0.636309	+	0.771434i	$0.719540\pi$
$368$	−2.47068	−0.128793
$369$	−3.76482	−0.195989
$370$	−6.89487	−0.358447
$371$	11.6087	0.602695
$372$	−6.24554	−0.323816
$373$	−4.33069	−0.224234	−0.112117	−	0.993695i	$-0.535763\pi$
$373$	−4.33069	−0.224234	−0.112117	+	0.993695i	$0.535763\pi$
$374$	0	0
$375$	13.2836	0.685960
$376$	12.4845	0.643838
$377$	−10.7756	−0.554972
$378$	8.57992	0.441303
$379$	−2.46844	−0.126795	−0.0633976	−	0.997988i	$-0.520194\pi$
$379$	−2.46844	−0.126795	−0.0633976	+	0.997988i	$0.520194\pi$
$380$	2.60241	0.133501
$381$	−14.6336	−0.749701
$382$	−2.08916	−0.106891
$383$	−21.4383	−1.09545	−0.547723	−	0.836660i	$-0.684505\pi$
$383$	−21.4383	−1.09545	−0.547723	+	0.836660i	$0.684505\pi$
$384$	−1.58152	−0.0807068
$385$	0	0
$386$	7.56792	0.385197
$387$	2.92199	0.148533
$388$	−1.48936	−0.0756109
$389$	−5.90159	−0.299222	−0.149611	−	0.988745i	$-0.547802\pi$
$389$	−5.90159	−0.299222	−0.149611	+	0.988745i	$0.547802\pi$
$390$	9.46241	0.479148
$391$	0.524507	0.0265254
$392$	−4.59574	−0.232120
$393$	19.1550	0.966241
$394$	−1.65699	−0.0834778
$395$	−23.3730	−1.17602
$396$	0	0
$397$	11.4881	0.576571	0.288286	−	0.957544i	$-0.406915\pi$
$397$	11.4881	0.576571	0.288286	+	0.957544i	$0.406915\pi$
$398$	−3.68327	−0.184626
$399$	−2.45226	−0.122767
$400$	1.77252	0.0886259
$401$	28.0949	1.40299	0.701496	−	0.712673i	$-0.252516\pi$
$401$	28.0949	1.40299	0.701496	+	0.712673i	$0.252516\pi$
$402$	14.1873	0.707598
$403$	−9.07914	−0.452264
$404$	2.51305	0.125029
$405$	−18.8801	−0.938161
$406$	7.26744	0.360677
$407$	0	0
$408$	0.335746	0.0166219
$409$	−30.5782	−1.51200	−0.755999	−	0.654573i	$-0.772848\pi$
$409$	−30.5782	−1.51200	−0.755999	+	0.654573i	$0.772848\pi$
$410$	19.6431	0.970101
$411$	15.4193	0.760580
$412$	6.77320	0.333692
$413$	6.48639	0.319174
$414$	1.23233	0.0605657
$415$	42.4109	2.08187
$416$	−2.29906	−0.112721
$417$	20.1118	0.984879
$418$	0	0
$419$	−29.3802	−1.43532	−0.717658	−	0.696395i	$-0.754786\pi$
$419$	−29.3802	−1.43532	−0.717658	+	0.696395i	$0.754786\pi$
$420$	−6.38177	−0.311399
$421$	−13.1995	−0.643304	−0.321652	−	0.946858i	$-0.604238\pi$
$421$	−13.1995	−0.643304	−0.321652	+	0.946858i	$0.604238\pi$
$422$	2.08891	0.101686
$423$	−6.22704	−0.302769
$424$	7.48676	0.363589
$425$	−0.376292	−0.0182529
$426$	−10.7884	−0.522697
$427$	20.1860	0.976868
$428$	13.1359	0.634949
$429$	0	0
$430$	−15.2455	−0.735205
$431$	33.7059	1.62356	0.811778	−	0.583966i	$-0.198500\pi$
$431$	33.7059	1.62356	0.811778	+	0.583966i	$0.198500\pi$
$432$	5.53341	0.266226
$433$	−36.3076	−1.74483	−0.872416	−	0.488765i	$-0.837448\pi$
$433$	−36.3076	−1.74483	−0.872416	+	0.488765i	$0.837448\pi$
$434$	6.12329	0.293927
$435$	−19.2904	−0.924905
$436$	2.72603	0.130553
$437$	−2.47068	−0.118189
$438$	−13.3676	−0.638727
$439$	15.5926	0.744196	0.372098	−	0.928194i	$-0.378639\pi$
$439$	15.5926	0.744196	0.372098	+	0.928194i	$0.378639\pi$
$440$	0	0
$441$	2.29227	0.109156
$442$	0.488074	0.0232153
$443$	−7.15831	−0.340101	−0.170051	−	0.985435i	$-0.554393\pi$
$443$	−7.15831	−0.340101	−0.170051	+	0.985435i	$0.554393\pi$
$444$	4.19012	0.198854
$445$	−9.34136	−0.442823
$446$	23.1754	1.09739
$447$	21.4519	1.01464
$448$	1.55057	0.0732574
$449$	14.5393	0.686150	0.343075	−	0.939308i	$-0.388532\pi$
$449$	14.5393	0.686150	0.343075	+	0.939308i	$0.388532\pi$
$450$	−0.884100	−0.0416769
$451$	0	0
$452$	−8.85491	−0.416500
$453$	17.1625	0.806366
$454$	−9.22043	−0.432736
$455$	−9.27719	−0.434921
$456$	−1.58152	−0.0740616
$457$	2.89135	0.135252	0.0676258	−	0.997711i	$-0.478458\pi$
$457$	2.89135	0.135252	0.0676258	+	0.997711i	$0.478458\pi$
$458$	−16.2844	−0.760922
$459$	−1.17470	−0.0548304
$460$	−6.42971	−0.299787
$461$	22.8907	1.06612	0.533062	−	0.846076i	$-0.321041\pi$
$461$	22.8907	1.06612	0.533062	+	0.846076i	$0.321041\pi$
$462$	0	0
$463$	−39.1694	−1.82036	−0.910178	−	0.414218i	$-0.864055\pi$
$463$	−39.1694	−1.82036	−0.910178	+	0.414218i	$0.864055\pi$
$464$	4.68696	0.217586
$465$	−16.2534	−0.753734
$466$	15.6828	0.726491
$467$	−27.7227	−1.28285	−0.641427	−	0.767184i	$-0.721657\pi$
$467$	−27.7227	−1.28285	−0.641427	+	0.767184i	$0.721657\pi$
$468$	1.14673	0.0530077
$469$	−13.9096	−0.642285
$470$	32.4897	1.49864
$471$	−8.18202	−0.377007
$472$	4.18323	0.192549
$473$	0	0
$474$	14.2041	0.652418
$475$	1.77252	0.0813287
$476$	−0.329174	−0.0150877
$477$	−3.73426	−0.170980
$478$	23.9513	1.09551
$479$	−16.8581	−0.770265	−0.385132	−	0.922861i	$-0.625844\pi$
$479$	−16.8581	−0.770265	−0.385132	+	0.922861i	$0.625844\pi$
$480$	−4.11577	−0.187858
$481$	6.09118	0.277734
$482$	3.80838	0.173467
$483$	6.05874	0.275682
$484$	0	0
$485$	−3.87592	−0.175997
$486$	−5.12647	−0.232541
$487$	−27.5472	−1.24828	−0.624142	−	0.781311i	$-0.714551\pi$
$487$	−27.5472	−1.24828	−0.624142	+	0.781311i	$0.714551\pi$
$488$	13.0184	0.589318
$489$	1.89784	0.0858233
$490$	−11.9600	−0.540297
$491$	−20.0830	−0.906333	−0.453167	−	0.891426i	$-0.649706\pi$
$491$	−20.0830	−0.906333	−0.453167	+	0.891426i	$0.649706\pi$
$492$	−11.9374	−0.538179
$493$	−0.995006	−0.0448128
$494$	−2.29906	−0.103440
$495$	0	0
$496$	3.94906	0.177318
$497$	10.5772	0.474451
$498$	−25.7738	−1.15495
$499$	−16.6068	−0.743422	−0.371711	−	0.928349i	$-0.621229\pi$
$499$	−16.6068	−0.743422	−0.371711	+	0.928349i	$0.621229\pi$
$500$	−8.39922	−0.375624
$501$	−12.3774	−0.552981
$502$	4.63462	0.206853
$503$	−22.9249	−1.02217	−0.511086	−	0.859530i	$-0.670757\pi$
$503$	−22.9249	−1.02217	−0.511086	+	0.859530i	$0.670757\pi$
$504$	−0.773395	−0.0344498
$505$	6.53998	0.291025
$506$	0	0
$507$	12.2004	0.541837
$508$	9.25283	0.410528
$509$	−35.6597	−1.58059	−0.790295	−	0.612726i	$-0.790073\pi$
$509$	−35.6597	−1.58059	−0.790295	+	0.612726i	$0.790073\pi$
$510$	0.873747	0.0386902
$511$	13.1059	0.579772
$512$	1.00000	0.0441942
$513$	5.53341	0.244306
$514$	−25.7043	−1.13377
$515$	17.6266	0.776722
$516$	9.26495	0.407867
$517$	0	0
$518$	−4.10810	−0.180500
$519$	7.77924	0.341471
$520$	−5.98310	−0.262376
$521$	16.3671	0.717056	0.358528	−	0.933519i	$-0.383279\pi$
$521$	16.3671	0.717056	0.358528	+	0.933519i	$0.383279\pi$
$522$	−2.33777	−0.102321
$523$	35.3902	1.54750	0.773752	−	0.633489i	$-0.218378\pi$
$523$	35.3902	1.54750	0.773752	+	0.633489i	$0.218378\pi$
$524$	−12.1117	−0.529103
$525$	−4.34667	−0.189704
$526$	21.8725	0.953686
$527$	−0.838356	−0.0365194
$528$	0	0
$529$	−16.8957	−0.734598
$530$	19.4836	0.846313
$531$	−2.08652	−0.0905474
$532$	1.55057	0.0672256
$533$	−17.3534	−0.751660
$534$	5.67690	0.245663
$535$	34.1850	1.47795
$536$	−8.97065	−0.387473
$537$	−15.0799	−0.650747
$538$	−20.5982	−0.888053
$539$	0	0
$540$	14.4002	0.619685
$541$	−36.5921	−1.57322	−0.786609	−	0.617451i	$-0.788165\pi$
$541$	−36.5921	−1.57322	−0.786609	+	0.617451i	$0.788165\pi$
$542$	22.1499	0.951421
$543$	−30.5768	−1.31218
$544$	−0.212293	−0.00910197
$545$	7.09423	0.303883
$546$	5.63790	0.241280
$547$	−14.2523	−0.609383	−0.304691	−	0.952451i	$-0.598553\pi$
$547$	−14.2523	−0.609383	−0.304691	+	0.952451i	$0.598553\pi$
$548$	−9.74968	−0.416486
$549$	−6.49337	−0.277130
$550$	0	0
$551$	4.68696	0.199671
$552$	3.90744	0.166312
$553$	−13.9261	−0.592199
$554$	8.79403	0.373623
$555$	10.9044	0.462866
$556$	−12.7167	−0.539309
$557$	−32.7611	−1.38813	−0.694067	−	0.719911i	$-0.744183\pi$
$557$	−32.7611	−1.38813	−0.694067	+	0.719911i	$0.744183\pi$
$558$	−1.96972	−0.0833849
$559$	13.4685	0.569656
$560$	4.03521	0.170519
$561$	0	0
$562$	−17.0989	−0.721275
$563$	−10.0804	−0.424836	−0.212418	−	0.977179i	$-0.568134\pi$
$563$	−10.0804	−0.424836	−0.212418	+	0.977179i	$0.568134\pi$
$564$	−19.7445	−0.831394
$565$	−23.0441	−0.969471
$566$	24.1009	1.01304
$567$	−11.2492	−0.472420
$568$	6.82149	0.286223
$569$	−40.8655	−1.71317	−0.856585	−	0.516005i	$-0.827418\pi$
$569$	−40.8655	−1.71317	−0.856585	+	0.516005i	$0.827418\pi$
$570$	−4.11577	−0.172391
$571$	28.0002	1.17177	0.585886	−	0.810393i	$-0.300747\pi$
$571$	28.0002	1.17177	0.585886	+	0.810393i	$0.300747\pi$
$572$	0	0
$573$	3.30405	0.138029
$574$	11.7037	0.488505
$575$	−4.37932	−0.182630
$576$	−0.498782	−0.0207826
$577$	−28.2778	−1.17722	−0.588610	−	0.808417i	$-0.700325\pi$
$577$	−28.2778	−1.17722	−0.588610	+	0.808417i	$0.700325\pi$
$578$	−16.9549	−0.705232
$579$	−11.9689	−0.497408
$580$	12.1974	0.506468
$581$	25.2693	1.04835
$582$	2.35546	0.0976370
$583$	0	0
$584$	8.45234	0.349760
$585$	2.98426	0.123384
$586$	2.55321	0.105472
$587$	−12.7652	−0.526874	−0.263437	−	0.964677i	$-0.584856\pi$
$587$	−12.7652	−0.526874	−0.263437	+	0.964677i	$0.584856\pi$
$588$	7.26827	0.299739
$589$	3.94906	0.162718
$590$	10.8865	0.448189
$591$	2.62056	0.107796
$592$	−2.64942	−0.108891
$593$	25.1426	1.03248	0.516242	−	0.856443i	$-0.327331\pi$
$593$	25.1426	1.03248	0.516242	+	0.856443i	$0.327331\pi$
$594$	0	0
$595$	−0.856644	−0.0351190
$596$	−13.5641	−0.555607
$597$	5.82518	0.238409
$598$	5.68024	0.232282
$599$	47.4222	1.93762	0.968808	−	0.247811i	$-0.0797111\pi$
$599$	47.4222	1.93762	0.968808	+	0.247811i	$0.0797111\pi$
$600$	−2.80328	−0.114443
$601$	23.8388	0.972405	0.486202	−	0.873846i	$-0.338382\pi$
$601$	23.8388	0.972405	0.486202	+	0.873846i	$0.338382\pi$
$602$	−9.08360	−0.370220
$603$	4.47440	0.182212
$604$	−10.8519	−0.441557
$605$	0	0
$606$	−3.97445	−0.161451
$607$	2.93319	0.119054	0.0595272	−	0.998227i	$-0.481041\pi$
$607$	2.93319	0.119054	0.0595272	+	0.998227i	$0.481041\pi$
$608$	1.00000	0.0405554
$609$	−11.4936	−0.465745
$610$	33.8793	1.37173
$611$	−28.7026	−1.16118
$612$	0.105888	0.00428026
$613$	−6.10807	−0.246703	−0.123351	−	0.992363i	$-0.539364\pi$
$613$	−6.10807	−0.246703	−0.123351	+	0.992363i	$0.539364\pi$
$614$	18.9304	0.763969
$615$	−31.0660	−1.25270
$616$	0	0
$617$	−21.6728	−0.872513	−0.436257	−	0.899822i	$-0.643696\pi$
$617$	−21.6728	−0.872513	−0.436257	+	0.899822i	$0.643696\pi$
$618$	−10.7120	−0.430899
$619$	8.12535	0.326586	0.163293	−	0.986578i	$-0.447788\pi$
$619$	8.12535	0.326586	0.163293	+	0.986578i	$0.447788\pi$
$620$	10.2771	0.412737
$621$	−13.6713	−0.548609
$622$	16.8210	0.674460
$623$	−5.56578	−0.222988
$624$	3.63602	0.145557
$625$	−30.7208	−1.22883
$626$	−24.6812	−0.986461
$627$	0	0
$628$	5.17350	0.206445
$629$	0.562452	0.0224264
$630$	−2.01269	−0.0801874
$631$	−43.3278	−1.72485	−0.862427	−	0.506181i	$-0.831057\pi$
$631$	−43.3278	−1.72485	−0.862427	+	0.506181i	$0.831057\pi$
$632$	−8.98131	−0.357257
$633$	−3.30366	−0.131309
$634$	23.4588	0.931667
$635$	24.0796	0.955571
$636$	−11.8405	−0.469506
$637$	10.5659	0.418636
$638$	0	0
$639$	−3.40244	−0.134598
$640$	2.60241	0.102869
$641$	36.8966	1.45733	0.728665	−	0.684871i	$-0.240141\pi$
$641$	36.8966	1.45733	0.728665	+	0.684871i	$0.240141\pi$
$642$	−20.7748	−0.819915
$643$	26.6605	1.05139	0.525694	−	0.850674i	$-0.323806\pi$
$643$	26.6605	1.05139	0.525694	+	0.850674i	$0.323806\pi$
$644$	−3.83095	−0.150961
$645$	24.1112	0.949376
$646$	−0.212293	−0.00835254
$647$	14.7156	0.578531	0.289265	−	0.957249i	$-0.406589\pi$
$647$	14.7156	0.578531	0.289265	+	0.957249i	$0.406589\pi$
$648$	−7.25487	−0.284998
$649$	0	0
$650$	−4.07513	−0.159840
$651$	−9.68412	−0.379551
$652$	−1.20001	−0.0469959
$653$	36.3529	1.42260	0.711299	−	0.702889i	$-0.248107\pi$
$653$	36.3529	1.42260	0.711299	+	0.702889i	$0.248107\pi$
$654$	−4.31128	−0.168584
$655$	−31.5196	−1.23157
$656$	7.54804	0.294701
$657$	−4.21587	−0.164477
$658$	19.3580	0.754655
$659$	−12.1432	−0.473030	−0.236515	−	0.971628i	$-0.576005\pi$
$659$	−12.1432	−0.473030	−0.236515	+	0.971628i	$0.576005\pi$
$660$	0	0
$661$	−6.74774	−0.262457	−0.131228	−	0.991352i	$-0.541892\pi$
$661$	−6.74774	−0.262457	−0.131228	+	0.991352i	$0.541892\pi$
$662$	16.6549	0.647311
$663$	−0.771901	−0.0299781
$664$	16.2968	0.632439
$665$	4.03521	0.156479
$666$	1.32148	0.0512064
$667$	−11.5800	−0.448378
$668$	7.82624	0.302806
$669$	−36.6525	−1.41707
$670$	−23.3453	−0.901907
$671$	0	0
$672$	−2.45226	−0.0945980
$673$	8.80261	0.339316	0.169658	−	0.985503i	$-0.445734\pi$
$673$	8.80261	0.339316	0.169658	+	0.985503i	$0.445734\pi$
$674$	22.4034	0.862947
$675$	9.80807	0.377513
$676$	−7.71431	−0.296704
$677$	6.40711	0.246245	0.123123	−	0.992391i	$-0.460709\pi$
$677$	6.40711	0.246245	0.123123	+	0.992391i	$0.460709\pi$
$678$	14.0043	0.537830
$679$	−2.30935	−0.0886249
$680$	−0.552471	−0.0211863
$681$	14.5823	0.558796
$682$	0	0
$683$	−33.6400	−1.28720	−0.643600	−	0.765362i	$-0.722560\pi$
$683$	−33.6400	−1.28720	−0.643600	+	0.765362i	$0.722560\pi$
$684$	−0.498782	−0.0190714
$685$	−25.3726	−0.969438
$686$	−17.9800	−0.686479
$687$	25.7542	0.982585
$688$	−5.85824	−0.223343
$689$	−17.2125	−0.655745
$690$	10.1687	0.387117
$691$	−23.5678	−0.896563	−0.448281	−	0.893893i	$-0.647964\pi$
$691$	−23.5678	−0.896563	−0.448281	+	0.893893i	$0.647964\pi$
$692$	−4.91882	−0.186986
$693$	0	0
$694$	10.0811	0.382674
$695$	−33.0941	−1.25533
$696$	−7.41253	−0.280971
$697$	−1.60239	−0.0606949
$698$	−25.6119	−0.969426
$699$	−24.8027	−0.938124
$700$	2.74841	0.103880
$701$	−48.8414	−1.84472	−0.922358	−	0.386337i	$-0.873740\pi$
$701$	−48.8414	−1.84472	−0.922358	+	0.386337i	$0.873740\pi$
$702$	−12.7217	−0.480148
$703$	−2.64942	−0.0999248
$704$	0	0
$705$	−51.3833	−1.93521
$706$	−6.10891	−0.229912
$707$	3.89666	0.146549
$708$	−6.61589	−0.248640
$709$	4.53204	0.170204	0.0851021	−	0.996372i	$-0.472878\pi$
$709$	4.53204	0.170204	0.0851021	+	0.996372i	$0.472878\pi$
$710$	17.7523	0.666232
$711$	4.47971	0.168002
$712$	−3.58951	−0.134523
$713$	−9.75686	−0.365397
$714$	0.520596	0.0194828
$715$	0	0
$716$	9.53506	0.356342
$717$	−37.8796	−1.41464
$718$	25.8236	0.963727
$719$	41.9588	1.56480	0.782400	−	0.622776i	$-0.213995\pi$
$719$	41.9588	1.56480	0.782400	+	0.622776i	$0.213995\pi$
$720$	−1.29803	−0.0483749
$721$	10.5023	0.391126
$722$	1.00000	0.0372161
$723$	−6.02305	−0.224000
$724$	19.3338	0.718534
$725$	8.30772	0.308541
$726$	0	0
$727$	−25.2797	−0.937572	−0.468786	−	0.883312i	$-0.655308\pi$
$727$	−25.2797	−0.937572	−0.468786	+	0.883312i	$0.655308\pi$
$728$	−3.56485	−0.132122
$729$	29.8722	1.10638
$730$	21.9964	0.814124
$731$	1.24366	0.0459985
$732$	−20.5890	−0.760991
$733$	31.0149	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$733$	31.0149	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$734$	−24.3799	−0.899877
$735$	18.9150	0.697690
$736$	−2.47068	−0.0910704
$737$	0	0
$738$	−3.76482	−0.138585
$739$	34.6559	1.27484	0.637419	−	0.770517i	$-0.280002\pi$
$739$	34.6559	1.27484	0.637419	+	0.770517i	$0.280002\pi$
$740$	−6.89487	−0.253460
$741$	3.63602	0.133573
$742$	11.6087	0.426170
$743$	−8.96117	−0.328753	−0.164377	−	0.986398i	$-0.552561\pi$
$743$	−8.96117	−0.328753	−0.164377	+	0.986398i	$0.552561\pi$
$744$	−6.24554	−0.228972
$745$	−35.2993	−1.29327
$746$	−4.33069	−0.158558
$747$	−8.12855	−0.297408
$748$	0	0
$749$	20.3681	0.744236
$750$	13.2836	0.485047
$751$	9.15499	0.334070	0.167035	−	0.985951i	$-0.446581\pi$
$751$	9.15499	0.334070	0.167035	+	0.985951i	$0.446581\pi$
$752$	12.4845	0.455263
$753$	−7.32976	−0.267111
$754$	−10.7756	−0.392424
$755$	−28.2410	−1.02780
$756$	8.57992	0.312049
$757$	22.9591	0.834463	0.417232	−	0.908800i	$-0.363000\pi$
$757$	22.9591	0.834463	0.417232	+	0.908800i	$0.363000\pi$
$758$	−2.46844	−0.0896578
$759$	0	0
$760$	2.60241	0.0943992
$761$	−33.4081	−1.21104	−0.605521	−	0.795829i	$-0.707035\pi$
$761$	−33.4081	−1.21104	−0.605521	+	0.795829i	$0.707035\pi$
$762$	−14.6336	−0.530118
$763$	4.22689	0.153024
$764$	−2.08916	−0.0755831
$765$	0.275563	0.00996299
$766$	−21.4383	−0.774598
$767$	−9.61752	−0.347269
$768$	−1.58152	−0.0570683
$769$	−16.2969	−0.587681	−0.293841	−	0.955854i	$-0.594934\pi$
$769$	−16.2969	−0.587681	−0.293841	+	0.955854i	$0.594934\pi$
$770$	0	0
$771$	40.6519	1.46404
$772$	7.56792	0.272376
$773$	39.8057	1.43171	0.715856	−	0.698248i	$-0.246037\pi$
$773$	39.8057	1.43171	0.715856	+	0.698248i	$0.246037\pi$
$774$	2.92199	0.105029
$775$	6.99978	0.251440
$776$	−1.48936	−0.0534649
$777$	6.49707	0.233081
$778$	−5.90159	−0.211582
$779$	7.54804	0.270436
$780$	9.46241	0.338809
$781$	0	0
$782$	0.524507	0.0187563
$783$	25.9348	0.926836
$784$	−4.59574	−0.164134
$785$	13.4636	0.480535
$786$	19.1550	0.683236
$787$	36.9437	1.31690	0.658450	−	0.752624i	$-0.271212\pi$
$787$	36.9437	1.31690	0.658450	+	0.752624i	$0.271212\pi$
$788$	−1.65699	−0.0590277
$789$	−34.5919	−1.23150
$790$	−23.3730	−0.831574
$791$	−13.7301	−0.488187
$792$	0	0
$793$	−29.9302	−1.06285
$794$	11.4881	0.407697
$795$	−30.8138	−1.09285
$796$	−3.68327	−0.130550
$797$	−51.3632	−1.81938	−0.909688	−	0.415291i	$-0.863680\pi$
$797$	−51.3632	−1.81938	−0.909688	+	0.415291i	$0.863680\pi$
$798$	−2.45226	−0.0868090
$799$	−2.65036	−0.0937631
$800$	1.77252	0.0626680
$801$	1.79038	0.0632601
$802$	28.0949	0.992066
$803$	0	0
$804$	14.1873	0.500347
$805$	−9.96970	−0.351386
$806$	−9.07914	−0.319799
$807$	32.5766	1.14675
$808$	2.51305	0.0884088
$809$	−8.79840	−0.309335	−0.154668	−	0.987967i	$-0.549431\pi$
$809$	−8.79840	−0.309335	−0.154668	+	0.987967i	$0.549431\pi$
$810$	−18.8801	−0.663380
$811$	34.2586	1.20298	0.601491	−	0.798880i	$-0.294574\pi$
$811$	34.2586	1.20298	0.601491	+	0.798880i	$0.294574\pi$
$812$	7.26744	0.255037
$813$	−35.0306	−1.22858
$814$	0	0
$815$	−3.12291	−0.109391
$816$	0.335746	0.0117535
$817$	−5.85824	−0.204954
$818$	−30.5782	−1.06914
$819$	1.77808	0.0621313
$820$	19.6431	0.685965
$821$	−28.0298	−0.978247	−0.489124	−	0.872214i	$-0.662683\pi$
$821$	−28.0298	−0.978247	−0.489124	+	0.872214i	$0.662683\pi$
$822$	15.4193	0.537811
$823$	27.5653	0.960865	0.480433	−	0.877032i	$-0.340480\pi$
$823$	27.5653	0.960865	0.480433	+	0.877032i	$0.340480\pi$
$824$	6.77320	0.235956
$825$	0	0
$826$	6.48639	0.225690
$827$	−40.9679	−1.42459	−0.712296	−	0.701879i	$-0.752345\pi$
$827$	−40.9679	−1.42459	−0.712296	+	0.701879i	$0.752345\pi$
$828$	1.23233	0.0428264
$829$	−12.7706	−0.443542	−0.221771	−	0.975099i	$-0.571184\pi$
$829$	−12.7706	−0.443542	−0.221771	+	0.975099i	$0.571184\pi$
$830$	42.4109	1.47210
$831$	−13.9080	−0.482462
$832$	−2.29906	−0.0797057
$833$	0.975642	0.0338040
$834$	20.1118	0.696415
$835$	20.3671	0.704831
$836$	0	0
$837$	21.8518	0.755308
$838$	−29.3802	−1.01492
$839$	5.27149	0.181992	0.0909960	−	0.995851i	$-0.470995\pi$
$839$	5.27149	0.181992	0.0909960	+	0.995851i	$0.470995\pi$
$840$	−6.38177	−0.220192
$841$	−7.03244	−0.242498
$842$	−13.1995	−0.454884
$843$	27.0424	0.931389
$844$	2.08891	0.0719031
$845$	−20.0758	−0.690627
$846$	−6.22704	−0.214090
$847$	0	0
$848$	7.48676	0.257096
$849$	−38.1161	−1.30814
$850$	−0.376292	−0.0129067
$851$	6.54587	0.224389
$852$	−10.7884	−0.369603
$853$	2.71843	0.0930774	0.0465387	−	0.998916i	$-0.485181\pi$
$853$	2.71843	0.0930774	0.0465387	+	0.998916i	$0.485181\pi$
$854$	20.1860	0.690750
$855$	−1.29803	−0.0443918
$856$	13.1359	0.448977
$857$	−51.9734	−1.77538	−0.887689	−	0.460443i	$-0.847691\pi$
$857$	−51.9734	−1.77538	−0.887689	+	0.460443i	$0.847691\pi$
$858$	0	0
$859$	−44.7212	−1.52587	−0.762933	−	0.646477i	$-0.776242\pi$
$859$	−44.7212	−1.52587	−0.762933	+	0.646477i	$0.776242\pi$
$860$	−15.2455	−0.519868
$861$	−18.5097	−0.630810
$862$	33.7059	1.14803
$863$	39.8913	1.35792	0.678958	−	0.734177i	$-0.262432\pi$
$863$	39.8913	1.35792	0.678958	+	0.734177i	$0.262432\pi$
$864$	5.53341	0.188250
$865$	−12.8008	−0.435239
$866$	−36.3076	−1.23378
$867$	26.8146	0.910673
$868$	6.12329	0.207838
$869$	0	0
$870$	−19.2904	−0.654007
$871$	20.6241	0.698821
$872$	2.72603	0.0923149
$873$	0.742867	0.0251422
$874$	−2.47068	−0.0835719
$875$	−13.0236	−0.440276
$876$	−13.3676	−0.451648
$877$	−2.99612	−0.101172	−0.0505859	−	0.998720i	$-0.516109\pi$
$877$	−2.99612	−0.101172	−0.0505859	+	0.998720i	$0.516109\pi$
$878$	15.5926	0.526226
$879$	−4.03796	−0.136197
$880$	0	0
$881$	20.5582	0.692625	0.346312	−	0.938119i	$-0.387434\pi$
$881$	20.5582	0.692625	0.346312	+	0.938119i	$0.387434\pi$
$882$	2.29227	0.0771849
$883$	−20.5953	−0.693089	−0.346544	−	0.938034i	$-0.612645\pi$
$883$	−20.5953	−0.693089	−0.346544	+	0.938034i	$0.612645\pi$
$884$	0.488074	0.0164157
$885$	−17.2172	−0.578751
$886$	−7.15831	−0.240488
$887$	−42.7076	−1.43398	−0.716990	−	0.697083i	$-0.754481\pi$
$887$	−42.7076	−1.43398	−0.716990	+	0.697083i	$0.754481\pi$
$888$	4.19012	0.140611
$889$	14.3471	0.481188
$890$	−9.34136	−0.313123
$891$	0	0
$892$	23.1754	0.775971
$893$	12.4845	0.417778
$894$	21.4519	0.717460
$895$	24.8141	0.829444
$896$	1.55057	0.0518008
$897$	−8.98344	−0.299948
$898$	14.5393	0.485181
$899$	18.5091	0.617312
$900$	−0.884100	−0.0294700
$901$	−1.58938	−0.0529500
$902$	0	0
$903$	14.3659	0.478068
$904$	−8.85491	−0.294510
$905$	50.3143	1.67250
$906$	17.1625	0.570187
$907$	8.59910	0.285528	0.142764	−	0.989757i	$-0.454401\pi$
$907$	8.59910	0.285528	0.142764	+	0.989757i	$0.454401\pi$
$908$	−9.22043	−0.305991
$909$	−1.25347	−0.0415748
$910$	−9.27719	−0.307536
$911$	−29.7933	−0.987097	−0.493548	−	0.869718i	$-0.664300\pi$
$911$	−29.7933	−0.987097	−0.493548	+	0.869718i	$0.664300\pi$
$912$	−1.58152	−0.0523695
$913$	0	0
$914$	2.89135	0.0956373
$915$	−53.5809	−1.77133
$916$	−16.2844	−0.538053
$917$	−18.7800	−0.620172
$918$	−1.17470	−0.0387709
$919$	−42.0481	−1.38704	−0.693520	−	0.720438i	$-0.743941\pi$
$919$	−42.0481	−1.38704	−0.693520	+	0.720438i	$0.743941\pi$
$920$	−6.42971	−0.211981
$921$	−29.9389	−0.986520
$922$	22.8907	0.753864
$923$	−15.6830	−0.516214
$924$	0	0
$925$	−4.69615	−0.154408
$926$	−39.1694	−1.28719
$927$	−3.37835	−0.110960
$928$	4.68696	0.153857
$929$	−54.4126	−1.78522	−0.892609	−	0.450831i	$-0.851128\pi$
$929$	−54.4126	−1.78522	−0.892609	+	0.450831i	$0.851128\pi$
$930$	−16.2534	−0.532971
$931$	−4.59574	−0.150619
$932$	15.6828	0.513706
$933$	−26.6028	−0.870937
$934$	−27.7227	−0.907115
$935$	0	0
$936$	1.14673	0.0374821
$937$	−34.8887	−1.13977	−0.569883	−	0.821726i	$-0.693011\pi$
$937$	−34.8887	−1.13977	−0.569883	+	0.821726i	$0.693011\pi$
$938$	−13.9096	−0.454164
$939$	39.0340	1.27383
$940$	32.4897	1.05970
$941$	12.7763	0.416496	0.208248	−	0.978076i	$-0.433224\pi$
$941$	12.7763	0.416496	0.208248	+	0.978076i	$0.433224\pi$
$942$	−8.18202	−0.266585
$943$	−18.6488	−0.607287
$944$	4.18323	0.136153
$945$	22.3284	0.726344
$946$	0	0
$947$	2.31945	0.0753720	0.0376860	−	0.999290i	$-0.488001\pi$
$947$	2.31945	0.0753720	0.0376860	+	0.999290i	$0.488001\pi$
$948$	14.2041	0.461329
$949$	−19.4325	−0.630804
$950$	1.77252	0.0575081
$951$	−37.1006	−1.20307
$952$	−0.329174	−0.0106686
$953$	7.12896	0.230930	0.115465	−	0.993312i	$-0.463164\pi$
$953$	7.12896	0.230930	0.115465	+	0.993312i	$0.463164\pi$
$954$	−3.73426	−0.120901
$955$	−5.43684	−0.175932
$956$	23.9513	0.774640
$957$	0	0
$958$	−16.8581	−0.544660
$959$	−15.1175	−0.488170
$960$	−4.11577	−0.132836
$961$	−15.4049	−0.496933
$962$	6.09118	0.196388
$963$	−6.55197	−0.211134
$964$	3.80838	0.122660
$965$	19.6948	0.633998
$966$	6.05874	0.194937
$967$	14.9561	0.480957	0.240478	−	0.970654i	$-0.422696\pi$
$967$	14.9561	0.480957	0.240478	+	0.970654i	$0.422696\pi$
$968$	0	0
$969$	0.335746	0.0107857
$970$	−3.87592	−0.124448
$971$	−44.7106	−1.43483	−0.717415	−	0.696646i	$-0.754675\pi$
$971$	−44.7106	−1.43483	−0.717415	+	0.696646i	$0.754675\pi$
$972$	−5.12647	−0.164432
$973$	−19.7181	−0.632134
$974$	−27.5472	−0.882670
$975$	6.44492	0.206403
$976$	13.0184	0.416710
$977$	−43.3812	−1.38789	−0.693943	−	0.720030i	$-0.744128\pi$
$977$	−43.3812	−1.38789	−0.693943	+	0.720030i	$0.744128\pi$
$978$	1.89784	0.0606863
$979$	0	0
$980$	−11.9600	−0.382048
$981$	−1.35969	−0.0434117
$982$	−20.0830	−0.640875
$983$	42.1394	1.34404	0.672020	−	0.740533i	$-0.265427\pi$
$983$	42.1394	1.34404	0.672020	+	0.740533i	$0.265427\pi$
$984$	−11.9374	−0.380550
$985$	−4.31215	−0.137397
$986$	−0.995006	−0.0316874
$987$	−30.6152	−0.974493
$988$	−2.29906	−0.0731429
$989$	14.4738	0.460241
$990$	0	0
$991$	55.5865	1.76576	0.882881	−	0.469596i	$-0.155600\pi$
$991$	55.5865	1.76576	0.882881	+	0.469596i	$0.155600\pi$
$992$	3.94906	0.125383
$993$	−26.3401	−0.835878
$994$	10.5772	0.335488
$995$	−9.58537	−0.303877
$996$	−25.7738	−0.816674
$997$	3.77748	0.119634	0.0598170	−	0.998209i	$-0.480948\pi$
$997$	3.77748	0.119634	0.0598170	+	0.998209i	$0.480948\pi$
$998$	−16.6068	−0.525678
$999$	−14.6603	−0.463832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.3		10
11.7	odd	10		418.2.f.h.115.4	✓	20
11.8	odd	10		418.2.f.h.229.4	yes	20
11.10	odd	2		4598.2.a.cc.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.4	✓	20	11.7	odd	10
418.2.f.h.229.4	yes	20	11.8	odd	10
4598.2.a.cc.1.3		10	11.10	odd	2
4598.2.a.cd.1.3		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.58152 q^{3} +1.00000 q^{4} +2.60241 q^{5} -1.58152 q^{6} +1.55057 q^{7} +1.00000 q^{8} -0.498782 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.58152 q^{3} +1.00000 q^{4} +2.60241 q^{5} -1.58152 q^{6} +1.55057 q^{7} +1.00000 q^{8} -0.498782 q^{9} +2.60241 q^{10} -1.58152 q^{12} -2.29906 q^{13} +1.55057 q^{14} -4.11577 q^{15} +1.00000 q^{16} -0.212293 q^{17} -0.498782 q^{18} +1.00000 q^{19} +2.60241 q^{20} -2.45226 q^{21} -2.47068 q^{23} -1.58152 q^{24} +1.77252 q^{25} -2.29906 q^{26} +5.53341 q^{27} +1.55057 q^{28} +4.68696 q^{29} -4.11577 q^{30} +3.94906 q^{31} +1.00000 q^{32} -0.212293 q^{34} +4.03521 q^{35} -0.498782 q^{36} -2.64942 q^{37} +1.00000 q^{38} +3.63602 q^{39} +2.60241 q^{40} +7.54804 q^{41} -2.45226 q^{42} -5.85824 q^{43} -1.29803 q^{45} -2.47068 q^{46} +12.4845 q^{47} -1.58152 q^{48} -4.59574 q^{49} +1.77252 q^{50} +0.335746 q^{51} -2.29906 q^{52} +7.48676 q^{53} +5.53341 q^{54} +1.55057 q^{56} -1.58152 q^{57} +4.68696 q^{58} +4.18323 q^{59} -4.11577 q^{60} +13.0184 q^{61} +3.94906 q^{62} -0.773395 q^{63} +1.00000 q^{64} -5.98310 q^{65} -8.97065 q^{67} -0.212293 q^{68} +3.90744 q^{69} +4.03521 q^{70} +6.82149 q^{71} -0.498782 q^{72} +8.45234 q^{73} -2.64942 q^{74} -2.80328 q^{75} +1.00000 q^{76} +3.63602 q^{78} -8.98131 q^{79} +2.60241 q^{80} -7.25487 q^{81} +7.54804 q^{82} +16.2968 q^{83} -2.45226 q^{84} -0.552471 q^{85} -5.85824 q^{86} -7.41253 q^{87} -3.58951 q^{89} -1.29803 q^{90} -3.56485 q^{91} -2.47068 q^{92} -6.24554 q^{93} +12.4845 q^{94} +2.60241 q^{95} -1.58152 q^{96} -1.48936 q^{97} -4.59574 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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