LMFDB - Embedded newform 1849.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.381966 q^{2} +2.61803 q^{3} -1.85410 q^{4} -1.23607 q^{5} +1.00000 q^{6} +4.23607 q^{7} -1.47214 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+0.381966 q^{2} +2.61803 q^{3} -1.85410 q^{4} -1.23607 q^{5} +1.00000 q^{6} +4.23607 q^{7} -1.47214 q^{8} +3.85410 q^{9} -0.472136 q^{10} -3.61803 q^{11} -4.85410 q^{12} +1.38197 q^{13} +1.61803 q^{14} -3.23607 q^{15} +3.14590 q^{16} +6.09017 q^{17} +1.47214 q^{18} +1.23607 q^{19} +2.29180 q^{20} +11.0902 q^{21} -1.38197 q^{22} +4.38197 q^{23} -3.85410 q^{24} -3.47214 q^{25} +0.527864 q^{26} +2.23607 q^{27} -7.85410 q^{28} -3.00000 q^{29} -1.23607 q^{30} +4.14590 q^{32} -9.47214 q^{33} +2.32624 q^{34} -5.23607 q^{35} -7.14590 q^{36} +4.85410 q^{37} +0.472136 q^{38} +3.61803 q^{39} +1.81966 q^{40} +9.47214 q^{41} +4.23607 q^{42} +6.70820 q^{44} -4.76393 q^{45} +1.67376 q^{46} +1.14590 q^{47} +8.23607 q^{48} +10.9443 q^{49} -1.32624 q^{50} +15.9443 q^{51} -2.56231 q^{52} -1.38197 q^{53} +0.854102 q^{54} +4.47214 q^{55} -6.23607 q^{56} +3.23607 q^{57} -1.14590 q^{58} +5.09017 q^{59} +6.00000 q^{60} -2.85410 q^{61} +16.3262 q^{63} -4.70820 q^{64} -1.70820 q^{65} -3.61803 q^{66} -3.85410 q^{67} -11.2918 q^{68} +11.4721 q^{69} -2.00000 q^{70} +10.7984 q^{71} -5.67376 q^{72} -1.85410 q^{73} +1.85410 q^{74} -9.09017 q^{75} -2.29180 q^{76} -15.3262 q^{77} +1.38197 q^{78} -1.38197 q^{79} -3.88854 q^{80} -5.70820 q^{81} +3.61803 q^{82} +16.0344 q^{83} -20.5623 q^{84} -7.52786 q^{85} -7.85410 q^{87} +5.32624 q^{88} +1.85410 q^{89} -1.81966 q^{90} +5.85410 q^{91} -8.12461 q^{92} +0.437694 q^{94} -1.52786 q^{95} +10.8541 q^{96} -9.23607 q^{97} +4.18034 q^{98} -13.9443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9} + 8 q^{10} - 5 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 2 q^{15} + 13 q^{16} + q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 11 q^{21} - 5 q^{22} + 11 q^{23} - q^{24} + 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 15 q^{32} - 10 q^{33} - 11 q^{34} - 6 q^{35} - 21 q^{36} + 3 q^{37} - 8 q^{38} + 5 q^{39} + 26 q^{40} + 10 q^{41} + 4 q^{42} - 14 q^{45} + 19 q^{46} + 9 q^{47} + 12 q^{48} + 4 q^{49} + 13 q^{50} + 14 q^{51} + 15 q^{52} - 5 q^{53} - 5 q^{54} - 8 q^{56} + 2 q^{57} - 9 q^{58} - q^{59} + 12 q^{60} + q^{61} + 17 q^{63} + 4 q^{64} + 10 q^{65} - 5 q^{66} - q^{67} - 36 q^{68} + 14 q^{69} - 4 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} - 3 q^{74} - 7 q^{75} - 18 q^{76} - 15 q^{77} + 5 q^{78} - 5 q^{79} + 28 q^{80} + 2 q^{81} + 5 q^{82} + 3 q^{83} - 21 q^{84} - 24 q^{85} - 9 q^{87} - 5 q^{88} - 3 q^{89} - 26 q^{90} + 5 q^{91} + 24 q^{92} + 21 q^{94} - 12 q^{95} + 15 q^{96} - 14 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9 + 8 * q^10 - 5 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 2 * q^15 + 13 * q^16 + q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 11 * q^21 - 5 * q^22 + 11 * q^23 - q^24 + 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 15 * q^32 - 10 * q^33 - 11 * q^34 - 6 * q^35 - 21 * q^36 + 3 * q^37 - 8 * q^38 + 5 * q^39 + 26 * q^40 + 10 * q^41 + 4 * q^42 - 14 * q^45 + 19 * q^46 + 9 * q^47 + 12 * q^48 + 4 * q^49 + 13 * q^50 + 14 * q^51 + 15 * q^52 - 5 * q^53 - 5 * q^54 - 8 * q^56 + 2 * q^57 - 9 * q^58 - q^59 + 12 * q^60 + q^61 + 17 * q^63 + 4 * q^64 + 10 * q^65 - 5 * q^66 - q^67 - 36 * q^68 + 14 * q^69 - 4 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 - 3 * q^74 - 7 * q^75 - 18 * q^76 - 15 * q^77 + 5 * q^78 - 5 * q^79 + 28 * q^80 + 2 * q^81 + 5 * q^82 + 3 * q^83 - 21 * q^84 - 24 * q^85 - 9 * q^87 - 5 * q^88 - 3 * q^89 - 26 * q^90 + 5 * q^91 + 24 * q^92 + 21 * q^94 - 12 * q^95 + 15 * q^96 - 14 * q^97 - 14 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.381966	0.270091	0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966	0.270091	0.135045	+	0.990839i	$0.456882\pi$
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	−1.85410	−0.927051
$5$	−1.23607	−0.552786	−0.276393	−	0.961045i	$-0.589139\pi$
$5$	−1.23607	−0.552786	−0.276393	+	0.961045i	$0.589139\pi$
$6$	1.00000	0.408248
$7$	4.23607	1.60108	0.800542	−	0.599277i	$-0.204545\pi$
$7$	4.23607	1.60108	0.800542	+	0.599277i	$0.204545\pi$
$8$	−1.47214	−0.520479
$9$	3.85410	1.28470
$10$	−0.472136	−0.149302
$11$	−3.61803	−1.09088	−0.545439	−	0.838150i	$-0.683637\pi$
$11$	−3.61803	−1.09088	−0.545439	+	0.838150i	$0.683637\pi$
$12$	−4.85410	−1.40126
$13$	1.38197	0.383288	0.191644	−	0.981464i	$-0.438618\pi$
$13$	1.38197	0.383288	0.191644	+	0.981464i	$0.438618\pi$
$14$	1.61803	0.432438
$15$	−3.23607	−0.835549
$16$	3.14590	0.786475
$17$	6.09017	1.47708	0.738542	−	0.674208i	$-0.235515\pi$
$17$	6.09017	1.47708	0.738542	+	0.674208i	$0.235515\pi$
$18$	1.47214	0.346986
$19$	1.23607	0.283573	0.141787	−	0.989897i	$-0.454715\pi$
$19$	1.23607	0.283573	0.141787	+	0.989897i	$0.454715\pi$
$20$	2.29180	0.512461
$21$	11.0902	2.42007
$22$	−1.38197	−0.294636
$23$	4.38197	0.913703	0.456852	−	0.889543i	$-0.348977\pi$
$23$	4.38197	0.913703	0.456852	+	0.889543i	$0.348977\pi$
$24$	−3.85410	−0.786715
$25$	−3.47214	−0.694427
$26$	0.527864	0.103523
$27$	2.23607	0.430331
$28$	−7.85410	−1.48429
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−1.23607	−0.225674
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	4.14590	0.732898
$33$	−9.47214	−1.64889
$34$	2.32624	0.398947
$35$	−5.23607	−0.885057
$36$	−7.14590	−1.19098
$37$	4.85410	0.798009	0.399005	−	0.916949i	$-0.369356\pi$
$37$	4.85410	0.798009	0.399005	+	0.916949i	$0.369356\pi$
$38$	0.472136	0.0765906
$39$	3.61803	0.579349
$40$	1.81966	0.287714
$41$	9.47214	1.47930	0.739650	−	0.672992i	$-0.234991\pi$
$41$	9.47214	1.47930	0.739650	+	0.672992i	$0.234991\pi$
$42$	4.23607	0.653639
$43$	0	0
$43$	0	0
$44$	6.70820	1.01130
$45$	−4.76393	−0.710165
$46$	1.67376	0.246783
$47$	1.14590	0.167146	0.0835732	−	0.996502i	$-0.473367\pi$
$47$	1.14590	0.167146	0.0835732	+	0.996502i	$0.473367\pi$
$48$	8.23607	1.18877
$49$	10.9443	1.56347
$50$	−1.32624	−0.187558
$51$	15.9443	2.23264
$52$	−2.56231	−0.355328
$53$	−1.38197	−0.189828	−0.0949138	−	0.995485i	$-0.530258\pi$
$53$	−1.38197	−0.189828	−0.0949138	+	0.995485i	$0.530258\pi$
$54$	0.854102	0.116229
$55$	4.47214	0.603023
$56$	−6.23607	−0.833330
$57$	3.23607	0.428628
$58$	−1.14590	−0.150464
$59$	5.09017	0.662684	0.331342	−	0.943511i	$-0.392499\pi$
$59$	5.09017	0.662684	0.331342	+	0.943511i	$0.392499\pi$
$60$	6.00000	0.774597
$61$	−2.85410	−0.365430	−0.182715	−	0.983166i	$-0.558489\pi$
$61$	−2.85410	−0.365430	−0.182715	+	0.983166i	$0.558489\pi$
$62$	0	0
$63$	16.3262	2.05691
$64$	−4.70820	−0.588525
$65$	−1.70820	−0.211877
$66$	−3.61803	−0.445349
$67$	−3.85410	−0.470853	−0.235427	−	0.971892i	$-0.575649\pi$
$67$	−3.85410	−0.470853	−0.235427	+	0.971892i	$0.575649\pi$
$68$	−11.2918	−1.36933
$69$	11.4721	1.38108
$70$	−2.00000	−0.239046
$71$	10.7984	1.28153	0.640766	−	0.767737i	$-0.278617\pi$
$71$	10.7984	1.28153	0.640766	+	0.767737i	$0.278617\pi$
$72$	−5.67376	−0.668659
$73$	−1.85410	−0.217006	−0.108503	−	0.994096i	$-0.534606\pi$
$73$	−1.85410	−0.217006	−0.108503	+	0.994096i	$0.534606\pi$
$74$	1.85410	0.215535
$75$	−9.09017	−1.04964
$76$	−2.29180	−0.262887
$77$	−15.3262	−1.74659
$78$	1.38197	0.156477
$79$	−1.38197	−0.155483	−0.0777417	−	0.996974i	$-0.524771\pi$
$79$	−1.38197	−0.155483	−0.0777417	+	0.996974i	$0.524771\pi$
$80$	−3.88854	−0.434752
$81$	−5.70820	−0.634245
$82$	3.61803	0.399545
$83$	16.0344	1.76001	0.880004	−	0.474966i	$-0.157540\pi$
$83$	16.0344	1.76001	0.880004	+	0.474966i	$0.157540\pi$
$84$	−20.5623	−2.24353
$85$	−7.52786	−0.816511
$86$	0	0
$87$	−7.85410	−0.842048
$88$	5.32624	0.567779
$89$	1.85410	0.196534	0.0982672	−	0.995160i	$-0.468670\pi$
$89$	1.85410	0.196534	0.0982672	+	0.995160i	$0.468670\pi$
$90$	−1.81966	−0.191809
$91$	5.85410	0.613677
$92$	−8.12461	−0.847049
$93$	0	0
$94$	0.437694	0.0451447
$95$	−1.52786	−0.156756
$96$	10.8541	1.10779
$97$	−9.23607	−0.937781	−0.468890	−	0.883256i	$-0.655346\pi$
$97$	−9.23607	−0.937781	−0.468890	+	0.883256i	$0.655346\pi$
$98$	4.18034	0.422278
$99$	−13.9443	−1.40145
$100$	6.43769	0.643769
$101$	3.76393	0.374525	0.187263	−	0.982310i	$-0.440038\pi$
$101$	3.76393	0.374525	0.187263	+	0.982310i	$0.440038\pi$
$102$	6.09017	0.603017
$103$	−16.4164	−1.61756	−0.808778	−	0.588114i	$-0.799871\pi$
$103$	−16.4164	−1.61756	−0.808778	+	0.588114i	$0.799871\pi$
$104$	−2.03444	−0.199493
$105$	−13.7082	−1.33778
$106$	−0.527864	−0.0512707
$107$	7.52786	0.727746	0.363873	−	0.931449i	$-0.381454\pi$
$107$	7.52786	0.727746	0.363873	+	0.931449i	$0.381454\pi$
$108$	−4.14590	−0.398939
$109$	−13.8541	−1.32698	−0.663491	−	0.748184i	$-0.730926\pi$
$109$	−13.8541	−1.32698	−0.663491	+	0.748184i	$0.730926\pi$
$110$	1.70820	0.162871
$111$	12.7082	1.20621
$112$	13.3262	1.25921
$113$	15.6180	1.46922	0.734611	−	0.678489i	$-0.237365\pi$
$113$	15.6180	1.46922	0.734611	+	0.678489i	$0.237365\pi$
$114$	1.23607	0.115768
$115$	−5.41641	−0.505083
$116$	5.56231	0.516447
$117$	5.32624	0.492411
$118$	1.94427	0.178985
$119$	25.7984	2.36493
$120$	4.76393	0.434886
$121$	2.09017	0.190015
$122$	−1.09017	−0.0986993
$123$	24.7984	2.23599
$124$	0	0
$125$	10.4721	0.936656
$126$	6.23607	0.555553
$127$	−14.6525	−1.30020	−0.650098	−	0.759850i	$-0.725272\pi$
$127$	−14.6525	−1.30020	−0.650098	+	0.759850i	$0.725272\pi$
$128$	−10.0902	−0.891853
$129$	0	0
$130$	−0.652476	−0.0572259
$131$	−9.94427	−0.868835	−0.434418	−	0.900712i	$-0.643046\pi$
$131$	−9.94427	−0.868835	−0.434418	+	0.900712i	$0.643046\pi$
$132$	17.5623	1.52860
$133$	5.23607	0.454025
$134$	−1.47214	−0.127173
$135$	−2.76393	−0.237881
$136$	−8.96556	−0.768790
$137$	−3.70820	−0.316813	−0.158407	−	0.987374i	$-0.550636\pi$
$137$	−3.70820	−0.316813	−0.158407	+	0.987374i	$0.550636\pi$
$138$	4.38197	0.373018
$139$	−5.29180	−0.448844	−0.224422	−	0.974492i	$-0.572049\pi$
$139$	−5.29180	−0.448844	−0.224422	+	0.974492i	$0.572049\pi$
$140$	9.70820	0.820493
$141$	3.00000	0.252646
$142$	4.12461	0.346130
$143$	−5.00000	−0.418121
$144$	12.1246	1.01038
$145$	3.70820	0.307950
$146$	−0.708204	−0.0586114
$147$	28.6525	2.36322
$148$	−9.00000	−0.739795
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	−3.47214	−0.283499
$151$	8.85410	0.720537	0.360268	−	0.932849i	$-0.382685\pi$
$151$	8.85410	0.720537	0.360268	+	0.932849i	$0.382685\pi$
$152$	−1.81966	−0.147594
$153$	23.4721	1.89761
$154$	−5.85410	−0.471737
$155$	0	0
$156$	−6.70820	−0.537086
$157$	5.14590	0.410687	0.205344	−	0.978690i	$-0.434169\pi$
$157$	5.14590	0.410687	0.205344	+	0.978690i	$0.434169\pi$
$158$	−0.527864	−0.0419946
$159$	−3.61803	−0.286929
$160$	−5.12461	−0.405136
$161$	18.5623	1.46291
$162$	−2.18034	−0.171304
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	−17.5623	−1.37139
$165$	11.7082	0.911482
$166$	6.12461	0.475362
$167$	14.2361	1.10162	0.550810	−	0.834631i	$-0.314319\pi$
$167$	14.2361	1.10162	0.550810	+	0.834631i	$0.314319\pi$
$168$	−16.3262	−1.25960
$169$	−11.0902	−0.853090
$170$	−2.87539	−0.220532
$171$	4.76393	0.364307
$172$	0	0
$173$	−3.76393	−0.286166	−0.143083	−	0.989711i	$-0.545702\pi$
$173$	−3.76393	−0.286166	−0.143083	+	0.989711i	$0.545702\pi$
$174$	−3.00000	−0.227429
$175$	−14.7082	−1.11184
$176$	−11.3820	−0.857948
$177$	13.3262	1.00166
$178$	0.708204	0.0530821
$179$	−9.65248	−0.721460	−0.360730	−	0.932670i	$-0.617472\pi$
$179$	−9.65248	−0.721460	−0.360730	+	0.932670i	$0.617472\pi$
$180$	8.83282	0.658359
$181$	−19.3820	−1.44065	−0.720325	−	0.693637i	$-0.756007\pi$
$181$	−19.3820	−1.44065	−0.720325	+	0.693637i	$0.756007\pi$
$182$	2.23607	0.165748
$183$	−7.47214	−0.552356
$184$	−6.45085	−0.475563
$185$	−6.00000	−0.441129
$186$	0	0
$187$	−22.0344	−1.61132
$188$	−2.12461	−0.154953
$189$	9.47214	0.688997
$190$	−0.583592	−0.0423382
$191$	14.5279	1.05120	0.525600	−	0.850732i	$-0.323841\pi$
$191$	14.5279	1.05120	0.525600	+	0.850732i	$0.323841\pi$
$192$	−12.3262	−0.889570
$193$	2.70820	0.194941	0.0974704	−	0.995238i	$-0.468925\pi$
$193$	2.70820	0.194941	0.0974704	+	0.995238i	$0.468925\pi$
$194$	−3.52786	−0.253286
$195$	−4.47214	−0.320256
$196$	−20.2918	−1.44941
$197$	−2.94427	−0.209771	−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427	−0.209771	−0.104885	+	0.994484i	$0.533448\pi$
$198$	−5.32624	−0.378519
$199$	−1.94427	−0.137826	−0.0689129	−	0.997623i	$-0.521953\pi$
$199$	−1.94427	−0.137826	−0.0689129	+	0.997623i	$0.521953\pi$
$200$	5.11146	0.361435
$201$	−10.0902	−0.711706
$202$	1.43769	0.101156
$203$	−12.7082	−0.891941
$204$	−29.5623	−2.06978
$205$	−11.7082	−0.817736
$206$	−6.27051	−0.436887
$207$	16.8885	1.17383
$208$	4.34752	0.301447
$209$	−4.47214	−0.309344
$210$	−5.23607	−0.361323
$211$	9.23607	0.635837	0.317919	−	0.948118i	$-0.397016\pi$
$211$	9.23607	0.635837	0.317919	+	0.948118i	$0.397016\pi$
$212$	2.56231	0.175980
$213$	28.2705	1.93706
$214$	2.87539	0.196557
$215$	0	0
$216$	−3.29180	−0.223978
$217$	0	0
$218$	−5.29180	−0.358406
$219$	−4.85410	−0.328010
$220$	−8.29180	−0.559033
$221$	8.41641	0.566149
$222$	4.85410	0.325786
$223$	−2.76393	−0.185087	−0.0925433	−	0.995709i	$-0.529500\pi$
$223$	−2.76393	−0.185087	−0.0925433	+	0.995709i	$0.529500\pi$
$224$	17.5623	1.17343
$225$	−13.3820	−0.892131
$226$	5.96556	0.396823
$227$	1.47214	0.0977091	0.0488545	−	0.998806i	$-0.484443\pi$
$227$	1.47214	0.0977091	0.0488545	+	0.998806i	$0.484443\pi$
$228$	−6.00000	−0.397360
$229$	−2.29180	−0.151446	−0.0757231	−	0.997129i	$-0.524126\pi$
$229$	−2.29180	−0.151446	−0.0757231	+	0.997129i	$0.524126\pi$
$230$	−2.06888	−0.136418
$231$	−40.1246	−2.64001
$232$	4.41641	0.289951
$233$	−18.0344	−1.18148	−0.590738	−	0.806864i	$-0.701163\pi$
$233$	−18.0344	−1.18148	−0.590738	+	0.806864i	$0.701163\pi$
$234$	2.03444	0.132996
$235$	−1.41641	−0.0923963
$236$	−9.43769	−0.614342
$237$	−3.61803	−0.235017
$238$	9.85410	0.638747
$239$	−8.29180	−0.536352	−0.268176	−	0.963370i	$-0.586421\pi$
$239$	−8.29180	−0.536352	−0.268176	+	0.963370i	$0.586421\pi$
$240$	−10.1803	−0.657138
$241$	−4.27051	−0.275088	−0.137544	−	0.990496i	$-0.543921\pi$
$241$	−4.27051	−0.275088	−0.137544	+	0.990496i	$0.543921\pi$
$242$	0.798374	0.0513214
$243$	−21.6525	−1.38901
$244$	5.29180	0.338773
$245$	−13.5279	−0.864264
$246$	9.47214	0.603921
$247$	1.70820	0.108690
$248$	0	0
$249$	41.9787	2.66029
$250$	4.00000	0.252982
$251$	−29.1803	−1.84185	−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803	−1.84185	−0.920923	+	0.389744i	$0.872564\pi$
$252$	−30.2705	−1.90686
$253$	−15.8541	−0.996739
$254$	−5.59675	−0.351171
$255$	−19.7082	−1.23418
$256$	5.56231	0.347644
$257$	−3.43769	−0.214437	−0.107219	−	0.994235i	$-0.534195\pi$
$257$	−3.43769	−0.214437	−0.107219	+	0.994235i	$0.534195\pi$
$258$	0	0
$259$	20.5623	1.27768
$260$	3.16718	0.196420
$261$	−11.5623	−0.715689
$262$	−3.79837	−0.234664
$263$	−27.5066	−1.69613	−0.848064	−	0.529894i	$-0.822232\pi$
$263$	−27.5066	−1.69613	−0.848064	+	0.529894i	$0.822232\pi$
$264$	13.9443	0.858211
$265$	1.70820	0.104934
$266$	2.00000	0.122628
$267$	4.85410	0.297066
$268$	7.14590	0.436505
$269$	11.5623	0.704966	0.352483	−	0.935818i	$-0.385337\pi$
$269$	11.5623	0.704966	0.352483	+	0.935818i	$0.385337\pi$
$270$	−1.05573	−0.0642496
$271$	13.8541	0.841577	0.420788	−	0.907159i	$-0.361753\pi$
$271$	13.8541	0.841577	0.420788	+	0.907159i	$0.361753\pi$
$272$	19.1591	1.16169
$273$	15.3262	0.927586
$274$	−1.41641	−0.0855683
$275$	12.5623	0.757536
$276$	−21.2705	−1.28033
$277$	12.4721	0.749378	0.374689	−	0.927151i	$-0.377749\pi$
$277$	12.4721	0.749378	0.374689	+	0.927151i	$0.377749\pi$
$278$	−2.02129	−0.121229
$279$	0	0
$280$	7.70820	0.460653
$281$	7.47214	0.445750	0.222875	−	0.974847i	$-0.428456\pi$
$281$	7.47214	0.445750	0.222875	+	0.974847i	$0.428456\pi$
$282$	1.14590	0.0682372
$283$	10.7639	0.639849	0.319925	−	0.947443i	$-0.396342\pi$
$283$	10.7639	0.639849	0.319925	+	0.947443i	$0.396342\pi$
$284$	−20.0213	−1.18804
$285$	−4.00000	−0.236940
$286$	−1.90983	−0.112931
$287$	40.1246	2.36848
$288$	15.9787	0.941555
$289$	20.0902	1.18177
$290$	1.41641	0.0831743
$291$	−24.1803	−1.41748
$292$	3.43769	0.201176
$293$	−12.0902	−0.706315	−0.353158	−	0.935564i	$-0.614892\pi$
$293$	−12.0902	−0.706315	−0.353158	+	0.935564i	$0.614892\pi$
$294$	10.9443	0.638283
$295$	−6.29180	−0.366323
$296$	−7.14590	−0.415347
$297$	−8.09017	−0.469439
$298$	−3.43769	−0.199140
$299$	6.05573	0.350212
$300$	16.8541	0.973072
$301$	0	0
$302$	3.38197	0.194610
$303$	9.85410	0.566103
$304$	3.88854	0.223023
$305$	3.52786	0.202005
$306$	8.96556	0.512527
$307$	−23.2148	−1.32494	−0.662469	−	0.749090i	$-0.730491\pi$
$307$	−23.2148	−1.32494	−0.662469	+	0.749090i	$0.730491\pi$
$308$	28.4164	1.61918
$309$	−42.9787	−2.44497
$310$	0	0
$311$	−29.8328	−1.69166	−0.845832	−	0.533450i	$-0.820895\pi$
$311$	−29.8328	−1.69166	−0.845832	+	0.533450i	$0.820895\pi$
$312$	−5.32624	−0.301539
$313$	−13.1246	−0.741847	−0.370923	−	0.928663i	$-0.620959\pi$
$313$	−13.1246	−0.741847	−0.370923	+	0.928663i	$0.620959\pi$
$314$	1.96556	0.110923
$315$	−20.1803	−1.13703
$316$	2.56231	0.144141
$317$	33.3050	1.87059	0.935296	−	0.353866i	$-0.115133\pi$
$317$	33.3050	1.87059	0.935296	+	0.353866i	$0.115133\pi$
$318$	−1.38197	−0.0774968
$319$	10.8541	0.607713
$320$	5.81966	0.325329
$321$	19.7082	1.10000
$322$	7.09017	0.395120
$323$	7.52786	0.418862
$324$	10.5836	0.587977
$325$	−4.79837	−0.266166
$326$	−5.34752	−0.296172
$327$	−36.2705	−2.00576
$328$	−13.9443	−0.769944
$329$	4.85410	0.267615
$330$	4.47214	0.246183
$331$	5.47214	0.300776	0.150388	−	0.988627i	$-0.451948\pi$
$331$	5.47214	0.300776	0.150388	+	0.988627i	$0.451948\pi$
$332$	−29.7295	−1.63162
$333$	18.7082	1.02520
$334$	5.43769	0.297537
$335$	4.76393	0.260281
$336$	34.8885	1.90333
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	−4.23607	−0.230412
$339$	40.8885	2.22076
$340$	13.9574	0.756948
$341$	0	0
$342$	1.81966	0.0983959
$343$	16.7082	0.902158
$344$	0	0
$345$	−14.1803	−0.763444
$346$	−1.43769	−0.0772909
$347$	−10.0902	−0.541669	−0.270834	−	0.962626i	$-0.587300\pi$
$347$	−10.0902	−0.541669	−0.270834	+	0.962626i	$0.587300\pi$
$348$	14.5623	0.780622
$349$	−20.7082	−1.10848	−0.554242	−	0.832355i	$-0.686992\pi$
$349$	−20.7082	−1.10848	−0.554242	+	0.832355i	$0.686992\pi$
$350$	−5.61803	−0.300297
$351$	3.09017	0.164941
$352$	−15.0000	−0.799503
$353$	−17.2361	−0.917383	−0.458692	−	0.888595i	$-0.651682\pi$
$353$	−17.2361	−0.917383	−0.458692	+	0.888595i	$0.651682\pi$
$354$	5.09017	0.270539
$355$	−13.3475	−0.708413
$356$	−3.43769	−0.182197
$357$	67.5410	3.57465
$358$	−3.68692	−0.194860
$359$	−5.34752	−0.282232	−0.141116	−	0.989993i	$-0.545069\pi$
$359$	−5.34752	−0.282232	−0.141116	+	0.989993i	$0.545069\pi$
$360$	7.01316	0.369626
$361$	−17.4721	−0.919586
$362$	−7.40325	−0.389106
$363$	5.47214	0.287213
$364$	−10.8541	−0.568910
$365$	2.29180	0.119958
$366$	−2.85410	−0.149186
$367$	19.1803	1.00121	0.500603	−	0.865677i	$-0.333112\pi$
$367$	19.1803	1.00121	0.500603	+	0.865677i	$0.333112\pi$
$368$	13.7852	0.718604
$369$	36.5066	1.90046
$370$	−2.29180	−0.119145
$371$	−5.85410	−0.303930
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−8.41641	−0.435202
$375$	27.4164	1.41578
$376$	−1.68692	−0.0869961
$377$	−4.14590	−0.213525
$378$	3.61803	0.186092
$379$	−27.3607	−1.40542	−0.702712	−	0.711475i	$-0.748028\pi$
$379$	−27.3607	−1.40542	−0.702712	+	0.711475i	$0.748028\pi$
$380$	2.83282	0.145320
$381$	−38.3607	−1.96528
$382$	5.54915	0.283919
$383$	−38.1246	−1.94808	−0.974038	−	0.226383i	$-0.927310\pi$
$383$	−38.1246	−1.94808	−0.974038	+	0.226383i	$0.927310\pi$
$384$	−26.4164	−1.34806
$385$	18.9443	0.965489
$386$	1.03444	0.0526517
$387$	0	0
$388$	17.1246	0.869370
$389$	35.0689	1.77806	0.889031	−	0.457846i	$-0.151379\pi$
$389$	35.0689	1.77806	0.889031	+	0.457846i	$0.151379\pi$
$390$	−1.70820	−0.0864983
$391$	26.6869	1.34962
$392$	−16.1115	−0.813751
$393$	−26.0344	−1.31326
$394$	−1.12461	−0.0566571
$395$	1.70820	0.0859491
$396$	25.8541	1.29922
$397$	32.4164	1.62693	0.813466	−	0.581612i	$-0.197578\pi$
$397$	32.4164	1.62693	0.813466	+	0.581612i	$0.197578\pi$
$398$	−0.742646	−0.0372255
$399$	13.7082	0.686269
$400$	−10.9230	−0.546149
$401$	−25.4164	−1.26923	−0.634617	−	0.772826i	$-0.718842\pi$
$401$	−25.4164	−1.26923	−0.634617	+	0.772826i	$0.718842\pi$
$402$	−3.85410	−0.192225
$403$	0	0
$404$	−6.97871	−0.347204
$405$	7.05573	0.350602
$406$	−4.85410	−0.240905
$407$	−17.5623	−0.870531
$408$	−23.4721	−1.16204
$409$	−8.90983	−0.440563	−0.220281	−	0.975436i	$-0.570698\pi$
$409$	−8.90983	−0.440563	−0.220281	+	0.975436i	$0.570698\pi$
$410$	−4.47214	−0.220863
$411$	−9.70820	−0.478870
$412$	30.4377	1.49956
$413$	21.5623	1.06101
$414$	6.45085	0.317042
$415$	−19.8197	−0.972909
$416$	5.72949	0.280911
$417$	−13.8541	−0.678438
$418$	−1.70820	−0.0835510
$419$	10.2361	0.500065	0.250032	−	0.968237i	$-0.419559\pi$
$419$	10.2361	0.500065	0.250032	+	0.968237i	$0.419559\pi$
$420$	25.4164	1.24019
$421$	7.65248	0.372959	0.186479	−	0.982459i	$-0.440292\pi$
$421$	7.65248	0.372959	0.186479	+	0.982459i	$0.440292\pi$
$422$	3.52786	0.171734
$423$	4.41641	0.214733
$424$	2.03444	0.0988012
$425$	−21.1459	−1.02573
$426$	10.7984	0.523183
$427$	−12.0902	−0.585084
$428$	−13.9574	−0.674658
$429$	−13.0902	−0.631999
$430$	0	0
$431$	−24.7984	−1.19450	−0.597248	−	0.802057i	$-0.703739\pi$
$431$	−24.7984	−1.19450	−0.597248	+	0.802057i	$0.703739\pi$
$432$	7.03444	0.338445
$433$	34.7082	1.66797	0.833985	−	0.551787i	$-0.186054\pi$
$433$	34.7082	1.66797	0.833985	+	0.551787i	$0.186054\pi$
$434$	0	0
$435$	9.70820	0.465473
$436$	25.6869	1.23018
$437$	5.41641	0.259102
$438$	−1.85410	−0.0885924
$439$	1.14590	0.0546907	0.0273454	−	0.999626i	$-0.491295\pi$
$439$	1.14590	0.0546907	0.0273454	+	0.999626i	$0.491295\pi$
$440$	−6.58359	−0.313860
$441$	42.1803	2.00859
$442$	3.21478	0.152912
$443$	2.47214	0.117455	0.0587274	−	0.998274i	$-0.481296\pi$
$443$	2.47214	0.117455	0.0587274	+	0.998274i	$0.481296\pi$
$444$	−23.5623	−1.11822
$445$	−2.29180	−0.108642
$446$	−1.05573	−0.0499902
$447$	−23.5623	−1.11446
$448$	−19.9443	−0.942278
$449$	32.8328	1.54948	0.774738	−	0.632282i	$-0.217882\pi$
$449$	32.8328	1.54948	0.774738	+	0.632282i	$0.217882\pi$
$450$	−5.11146	−0.240956
$451$	−34.2705	−1.61374
$452$	−28.9574	−1.36204
$453$	23.1803	1.08911
$454$	0.562306	0.0263903
$455$	−7.23607	−0.339232
$456$	−4.76393	−0.223092
$457$	15.7082	0.734799	0.367399	−	0.930063i	$-0.380248\pi$
$457$	15.7082	0.734799	0.367399	+	0.930063i	$0.380248\pi$
$458$	−0.875388	−0.0409042
$459$	13.6180	0.635635
$460$	10.0426	0.468237
$461$	−31.5967	−1.47161	−0.735804	−	0.677195i	$-0.763195\pi$
$461$	−31.5967	−1.47161	−0.735804	+	0.677195i	$0.763195\pi$
$462$	−15.3262	−0.713041
$463$	29.8328	1.38645	0.693224	−	0.720722i	$-0.256190\pi$
$463$	29.8328	1.38645	0.693224	+	0.720722i	$0.256190\pi$
$464$	−9.43769	−0.438134
$465$	0	0
$466$	−6.88854	−0.319106
$467$	15.0557	0.696696	0.348348	−	0.937365i	$-0.386743\pi$
$467$	15.0557	0.696696	0.348348	+	0.937365i	$0.386743\pi$
$468$	−9.87539	−0.456490
$469$	−16.3262	−0.753876
$470$	−0.541020	−0.0249554
$471$	13.4721	0.620763
$472$	−7.49342	−0.344913
$473$	0	0
$474$	−1.38197	−0.0634758
$475$	−4.29180	−0.196921
$476$	−47.8328	−2.19241
$477$	−5.32624	−0.243872
$478$	−3.16718	−0.144864
$479$	−13.8197	−0.631436	−0.315718	−	0.948853i	$-0.602245\pi$
$479$	−13.8197	−0.631436	−0.315718	+	0.948853i	$0.602245\pi$
$480$	−13.4164	−0.612372
$481$	6.70820	0.305868
$482$	−1.63119	−0.0742987
$483$	48.5967	2.21123
$484$	−3.87539	−0.176154
$485$	11.4164	0.518392
$486$	−8.27051	−0.375158
$487$	1.32624	0.0600976	0.0300488	−	0.999548i	$-0.490434\pi$
$487$	1.32624	0.0600976	0.0300488	+	0.999548i	$0.490434\pi$
$488$	4.20163	0.190199
$489$	−36.6525	−1.65748
$490$	−5.16718	−0.233430
$491$	−21.6525	−0.977163	−0.488581	−	0.872518i	$-0.662485\pi$
$491$	−21.6525	−0.977163	−0.488581	+	0.872518i	$0.662485\pi$
$492$	−45.9787	−2.07288
$493$	−18.2705	−0.822862
$494$	0.652476	0.0293563
$495$	17.2361	0.774704
$496$	0	0
$497$	45.7426	2.05184
$498$	16.0344	0.718521
$499$	−13.8541	−0.620195	−0.310097	−	0.950705i	$-0.600362\pi$
$499$	−13.8541	−0.620195	−0.310097	+	0.950705i	$0.600362\pi$
$500$	−19.4164	−0.868328
$501$	37.2705	1.66512
$502$	−11.1459	−0.497466
$503$	13.4721	0.600693	0.300346	−	0.953830i	$-0.402898\pi$
$503$	13.4721	0.600693	0.300346	+	0.953830i	$0.402898\pi$
$504$	−24.0344	−1.07058
$505$	−4.65248	−0.207032
$506$	−6.05573	−0.269210
$507$	−29.0344	−1.28946
$508$	27.1672	1.20535
$509$	18.7082	0.829227	0.414613	−	0.909998i	$-0.363917\pi$
$509$	18.7082	0.829227	0.414613	+	0.909998i	$0.363917\pi$
$510$	−7.52786	−0.333339
$511$	−7.85410	−0.347445
$512$	22.3050	0.985749
$513$	2.76393	0.122031
$514$	−1.31308	−0.0579176
$515$	20.2918	0.894163
$516$	0	0
$517$	−4.14590	−0.182336
$518$	7.85410	0.345089
$519$	−9.85410	−0.432547
$520$	2.51471	0.110277
$521$	22.0344	0.965346	0.482673	−	0.875801i	$-0.339666\pi$
$521$	22.0344	0.965346	0.482673	+	0.875801i	$0.339666\pi$
$522$	−4.41641	−0.193301
$523$	−35.8328	−1.56686	−0.783430	−	0.621480i	$-0.786532\pi$
$523$	−35.8328	−1.56686	−0.783430	+	0.621480i	$0.786532\pi$
$524$	18.4377	0.805454
$525$	−38.5066	−1.68056
$526$	−10.5066	−0.458109
$527$	0	0
$528$	−29.7984	−1.29681
$529$	−3.79837	−0.165147
$530$	0.652476	0.0283417
$531$	19.6180	0.851350
$532$	−9.70820	−0.420904
$533$	13.0902	0.566998
$534$	1.85410	0.0802348
$535$	−9.30495	−0.402288
$536$	5.67376	0.245069
$537$	−25.2705	−1.09050
$538$	4.41641	0.190405
$539$	−39.5967	−1.70555
$540$	5.12461	0.220528
$541$	−37.9443	−1.63135	−0.815676	−	0.578509i	$-0.803635\pi$
$541$	−37.9443	−1.63135	−0.815676	+	0.578509i	$0.803635\pi$
$542$	5.29180	0.227302
$543$	−50.7426	−2.17758
$544$	25.2492	1.08255
$545$	17.1246	0.733538
$546$	5.85410	0.250532
$547$	21.0000	0.897895	0.448948	−	0.893558i	$-0.351799\pi$
$547$	21.0000	0.897895	0.448948	+	0.893558i	$0.351799\pi$
$548$	6.87539	0.293702
$549$	−11.0000	−0.469469
$550$	4.79837	0.204603
$551$	−3.70820	−0.157975
$552$	−16.8885	−0.718824
$553$	−5.85410	−0.248942
$554$	4.76393	0.202400
$555$	−15.7082	−0.666776
$556$	9.81153	0.416102
$557$	−38.5623	−1.63394	−0.816969	−	0.576682i	$-0.804347\pi$
$557$	−38.5623	−1.63394	−0.816969	+	0.576682i	$0.804347\pi$
$558$	0	0
$559$	0	0
$560$	−16.4721	−0.696075
$561$	−57.6869	−2.43554
$562$	2.85410	0.120393
$563$	−1.32624	−0.0558943	−0.0279471	−	0.999609i	$-0.508897\pi$
$563$	−1.32624	−0.0558943	−0.0279471	+	0.999609i	$0.508897\pi$
$564$	−5.56231	−0.234215
$565$	−19.3050	−0.812165
$566$	4.11146	0.172817
$567$	−24.1803	−1.01548
$568$	−15.8967	−0.667010
$569$	−25.9443	−1.08764	−0.543820	−	0.839202i	$-0.683023\pi$
$569$	−25.9443	−1.08764	−0.543820	+	0.839202i	$0.683023\pi$
$570$	−1.52786	−0.0639952
$571$	43.1803	1.80704	0.903520	−	0.428545i	$-0.140974\pi$
$571$	43.1803	1.80704	0.903520	+	0.428545i	$0.140974\pi$
$572$	9.27051	0.387619
$573$	38.0344	1.58891
$574$	15.3262	0.639705
$575$	−15.2148	−0.634500
$576$	−18.1459	−0.756079
$577$	28.2148	1.17460	0.587298	−	0.809371i	$-0.300192\pi$
$577$	28.2148	1.17460	0.587298	+	0.809371i	$0.300192\pi$
$578$	7.67376	0.319186
$579$	7.09017	0.294657
$580$	−6.87539	−0.285485
$581$	67.9230	2.81792
$582$	−9.23607	−0.382847
$583$	5.00000	0.207079
$584$	2.72949	0.112947
$585$	−6.58359	−0.272198
$586$	−4.61803	−0.190769
$587$	−15.7426	−0.649769	−0.324884	−	0.945754i	$-0.605325\pi$
$587$	−15.7426	−0.649769	−0.324884	+	0.945754i	$0.605325\pi$
$588$	−53.1246	−2.19082
$589$	0	0
$590$	−2.40325	−0.0989403
$591$	−7.70820	−0.317073
$592$	15.2705	0.627614
$593$	30.4721	1.25134	0.625670	−	0.780088i	$-0.284826\pi$
$593$	30.4721	1.25134	0.625670	+	0.780088i	$0.284826\pi$
$594$	−3.09017	−0.126791
$595$	−31.8885	−1.30730
$596$	16.6869	0.683523
$597$	−5.09017	−0.208327
$598$	2.31308	0.0945890
$599$	36.2361	1.48057	0.740283	−	0.672296i	$-0.234692\pi$
$599$	36.2361	1.48057	0.740283	+	0.672296i	$0.234692\pi$
$600$	13.3820	0.546316
$601$	−29.4164	−1.19992	−0.599960	−	0.800030i	$-0.704817\pi$
$601$	−29.4164	−1.19992	−0.599960	+	0.800030i	$0.704817\pi$
$602$	0	0
$603$	−14.8541	−0.604906
$604$	−16.4164	−0.667974
$605$	−2.58359	−0.105038
$606$	3.76393	0.152899
$607$	23.8541	0.968208	0.484104	−	0.875010i	$-0.339146\pi$
$607$	23.8541	0.968208	0.484104	+	0.875010i	$0.339146\pi$
$608$	5.12461	0.207830
$609$	−33.2705	−1.34819
$610$	1.34752	0.0545597
$611$	1.58359	0.0640653
$612$	−43.5197	−1.75918
$613$	5.20163	0.210092	0.105046	−	0.994467i	$-0.466501\pi$
$613$	5.20163	0.210092	0.105046	+	0.994467i	$0.466501\pi$
$614$	−8.86726	−0.357853
$615$	−30.6525	−1.23603
$616$	22.5623	0.909061
$617$	9.70820	0.390838	0.195419	−	0.980720i	$-0.437393\pi$
$617$	9.70820	0.390838	0.195419	+	0.980720i	$0.437393\pi$
$618$	−16.4164	−0.660365
$619$	−30.2705	−1.21667	−0.608337	−	0.793679i	$-0.708163\pi$
$619$	−30.2705	−1.21667	−0.608337	+	0.793679i	$0.708163\pi$
$620$	0	0
$621$	9.79837	0.393195
$622$	−11.3951	−0.456903
$623$	7.85410	0.314668
$624$	11.3820	0.455643
$625$	4.41641	0.176656
$626$	−5.01316	−0.200366
$627$	−11.7082	−0.467581
$628$	−9.54102	−0.380728
$629$	29.5623	1.17873
$630$	−7.70820	−0.307102
$631$	27.0902	1.07844	0.539221	−	0.842164i	$-0.318719\pi$
$631$	27.0902	1.07844	0.539221	+	0.842164i	$0.318719\pi$
$632$	2.03444	0.0809258
$633$	24.1803	0.961082
$634$	12.7214	0.505230
$635$	18.1115	0.718731
$636$	6.70820	0.265998
$637$	15.1246	0.599259
$638$	4.14590	0.164138
$639$	41.6180	1.64638
$640$	12.4721	0.493004
$641$	−10.8197	−0.427351	−0.213675	−	0.976905i	$-0.568543\pi$
$641$	−10.8197	−0.427351	−0.213675	+	0.976905i	$0.568543\pi$
$642$	7.52786	0.297101
$643$	9.43769	0.372186	0.186093	−	0.982532i	$-0.440417\pi$
$643$	9.43769	0.372186	0.186093	+	0.982532i	$0.440417\pi$
$644$	−34.4164	−1.35620
$645$	0	0
$646$	2.87539	0.113131
$647$	21.6738	0.852084	0.426042	−	0.904703i	$-0.359908\pi$
$647$	21.6738	0.852084	0.426042	+	0.904703i	$0.359908\pi$
$648$	8.40325	0.330111
$649$	−18.4164	−0.722907
$650$	−1.83282	−0.0718889
$651$	0	0
$652$	25.9574	1.01657
$653$	32.8885	1.28703	0.643514	−	0.765434i	$-0.277476\pi$
$653$	32.8885	1.28703	0.643514	+	0.765434i	$0.277476\pi$
$654$	−13.8541	−0.541738
$655$	12.2918	0.480280
$656$	29.7984	1.16343
$657$	−7.14590	−0.278788
$658$	1.85410	0.0722804
$659$	−29.3607	−1.14373	−0.571865	−	0.820348i	$-0.693780\pi$
$659$	−29.3607	−1.14373	−0.571865	+	0.820348i	$0.693780\pi$
$660$	−21.7082	−0.844991
$661$	−43.3951	−1.68787	−0.843937	−	0.536442i	$-0.819768\pi$
$661$	−43.3951	−1.68787	−0.843937	+	0.536442i	$0.819768\pi$
$662$	2.09017	0.0812368
$663$	22.0344	0.855747
$664$	−23.6049	−0.916047
$665$	−6.47214	−0.250979
$666$	7.14590	0.276898
$667$	−13.1459	−0.509011
$668$	−26.3951	−1.02126
$669$	−7.23607	−0.279763
$670$	1.81966	0.0702996
$671$	10.3262	0.398640
$672$	45.9787	1.77367
$673$	−13.8328	−0.533216	−0.266608	−	0.963805i	$-0.585903\pi$
$673$	−13.8328	−0.533216	−0.266608	+	0.963805i	$0.585903\pi$
$674$	10.6950	0.411958
$675$	−7.76393	−0.298834
$676$	20.5623	0.790858
$677$	31.7639	1.22079	0.610394	−	0.792098i	$-0.291011\pi$
$677$	31.7639	1.22079	0.610394	+	0.792098i	$0.291011\pi$
$678$	15.6180	0.599807
$679$	−39.1246	−1.50146
$680$	11.0820	0.424977
$681$	3.85410	0.147690
$682$	0	0
$683$	−11.1246	−0.425671	−0.212836	−	0.977088i	$-0.568270\pi$
$683$	−11.1246	−0.425671	−0.212836	+	0.977088i	$0.568270\pi$
$684$	−8.83282	−0.337731
$685$	4.58359	0.175130
$686$	6.38197	0.243665
$687$	−6.00000	−0.228914
$688$	0	0
$689$	−1.90983	−0.0727587
$690$	−5.41641	−0.206199
$691$	−15.7295	−0.598378	−0.299189	−	0.954194i	$-0.596716\pi$
$691$	−15.7295	−0.598378	−0.299189	+	0.954194i	$0.596716\pi$
$692$	6.97871	0.265291
$693$	−59.0689	−2.24384
$694$	−3.85410	−0.146300
$695$	6.54102	0.248115
$696$	11.5623	0.438268
$697$	57.6869	2.18505
$698$	−7.90983	−0.299391
$699$	−47.2148	−1.78583
$700$	27.2705	1.03073
$701$	−14.5066	−0.547906	−0.273953	−	0.961743i	$-0.588331\pi$
$701$	−14.5066	−0.547906	−0.273953	+	0.961743i	$0.588331\pi$
$702$	1.18034	0.0445491
$703$	6.00000	0.226294
$704$	17.0344	0.642010
$705$	−3.70820	−0.139659
$706$	−6.58359	−0.247777
$707$	15.9443	0.599646
$708$	−24.7082	−0.928591
$709$	28.8885	1.08493	0.542466	−	0.840078i	$-0.317491\pi$
$709$	28.8885	1.08493	0.542466	+	0.840078i	$0.317491\pi$
$710$	−5.09830	−0.191336
$711$	−5.32624	−0.199750
$712$	−2.72949	−0.102292
$713$	0	0
$714$	25.7984	0.965480
$715$	6.18034	0.231132
$716$	17.8967	0.668830
$717$	−21.7082	−0.810708
$718$	−2.04257	−0.0762281
$719$	−10.7984	−0.402711	−0.201356	−	0.979518i	$-0.564535\pi$
$719$	−10.7984	−0.402711	−0.201356	+	0.979518i	$0.564535\pi$
$720$	−14.9868	−0.558527
$721$	−69.5410	−2.58984
$722$	−6.67376	−0.248372
$723$	−11.1803	−0.415801
$724$	35.9361	1.33556
$725$	10.4164	0.386856
$726$	2.09017	0.0775735
$727$	17.9787	0.666794	0.333397	−	0.942787i	$-0.391805\pi$
$727$	17.9787	0.666794	0.333397	+	0.942787i	$0.391805\pi$
$728$	−8.61803	−0.319406
$729$	−39.5623	−1.46527
$730$	0.875388	0.0323996
$731$	0	0
$732$	13.8541	0.512062
$733$	−24.5410	−0.906443	−0.453222	−	0.891398i	$-0.649725\pi$
$733$	−24.5410	−0.906443	−0.453222	+	0.891398i	$0.649725\pi$
$734$	7.32624	0.270416
$735$	−35.4164	−1.30635
$736$	18.1672	0.669651
$737$	13.9443	0.513644
$738$	13.9443	0.513296
$739$	−49.5410	−1.82240	−0.911198	−	0.411969i	$-0.864841\pi$
$739$	−49.5410	−1.82240	−0.911198	+	0.411969i	$0.864841\pi$
$740$	11.1246	0.408949
$741$	4.47214	0.164288
$742$	−2.23607	−0.0820886
$743$	−33.3607	−1.22388	−0.611942	−	0.790902i	$-0.709612\pi$
$743$	−33.3607	−1.22388	−0.611942	+	0.790902i	$0.709612\pi$
$744$	0	0
$745$	11.1246	0.407574
$746$	−2.29180	−0.0839086
$747$	61.7984	2.26108
$748$	40.8541	1.49377
$749$	31.8885	1.16518
$750$	10.4721	0.382388
$751$	37.9787	1.38586	0.692931	−	0.721003i	$-0.256319\pi$
$751$	37.9787	1.38586	0.692931	+	0.721003i	$0.256319\pi$
$752$	3.60488	0.131456
$753$	−76.3951	−2.78399
$754$	−1.58359	−0.0576710
$755$	−10.9443	−0.398303
$756$	−17.5623	−0.638735
$757$	30.9787	1.12594	0.562970	−	0.826477i	$-0.309659\pi$
$757$	30.9787	1.12594	0.562970	+	0.826477i	$0.309659\pi$
$758$	−10.4508	−0.379592
$759$	−41.5066	−1.50659
$760$	2.24922	0.0815879
$761$	−1.09017	−0.0395186	−0.0197593	−	0.999805i	$-0.506290\pi$
$761$	−1.09017	−0.0395186	−0.0197593	+	0.999805i	$0.506290\pi$
$762$	−14.6525	−0.530803
$763$	−58.6869	−2.12461
$764$	−26.9361	−0.974515
$765$	−29.0132	−1.04897
$766$	−14.5623	−0.526157
$767$	7.03444	0.253999
$768$	14.5623	0.525472
$769$	19.8885	0.717199	0.358600	−	0.933491i	$-0.383254\pi$
$769$	19.8885	0.717199	0.358600	+	0.933491i	$0.383254\pi$
$770$	7.23607	0.260770
$771$	−9.00000	−0.324127
$772$	−5.02129	−0.180720
$773$	−15.5967	−0.560976	−0.280488	−	0.959858i	$-0.590496\pi$
$773$	−15.5967	−0.560976	−0.280488	+	0.959858i	$0.590496\pi$
$774$	0	0
$775$	0	0
$776$	13.5967	0.488095
$777$	53.8328	1.93124
$778$	13.3951	0.480238
$779$	11.7082	0.419490
$780$	8.29180	0.296894
$781$	−39.0689	−1.39799
$782$	10.1935	0.364519
$783$	−6.70820	−0.239732
$784$	34.4296	1.22963
$785$	−6.36068	−0.227022
$786$	−9.94427	−0.354700
$787$	10.4508	0.372533	0.186266	−	0.982499i	$-0.440361\pi$
$787$	10.4508	0.372533	0.186266	+	0.982499i	$0.440361\pi$
$788$	5.45898	0.194468
$789$	−72.0132	−2.56374
$790$	0.652476	0.0232140
$791$	66.1591	2.35235
$792$	20.5279	0.729426
$793$	−3.94427	−0.140065
$794$	12.3820	0.439420
$795$	4.47214	0.158610
$796$	3.60488	0.127772
$797$	−8.23607	−0.291736	−0.145868	−	0.989304i	$-0.546598\pi$
$797$	−8.23607	−0.291736	−0.145868	+	0.989304i	$0.546598\pi$
$798$	5.23607	0.185355
$799$	6.97871	0.246889
$800$	−14.3951	−0.508944
$801$	7.14590	0.252488
$802$	−9.70820	−0.342809
$803$	6.70820	0.236727
$804$	18.7082	0.659787
$805$	−22.9443	−0.808679
$806$	0	0
$807$	30.2705	1.06557
$808$	−5.54102	−0.194932
$809$	4.74265	0.166743	0.0833713	−	0.996519i	$-0.473431\pi$
$809$	4.74265	0.166743	0.0833713	+	0.996519i	$0.473431\pi$
$810$	2.69505	0.0946943
$811$	−47.3951	−1.66427	−0.832134	−	0.554575i	$-0.812881\pi$
$811$	−47.3951	−1.66427	−0.832134	+	0.554575i	$0.812881\pi$
$812$	23.5623	0.826875
$813$	36.2705	1.27206
$814$	−6.70820	−0.235122
$815$	17.3050	0.606166
$816$	50.1591	1.75592
$817$	0	0
$818$	−3.40325	−0.118992
$819$	22.5623	0.788391
$820$	21.7082	0.758083
$821$	0.326238	0.0113858	0.00569289	−	0.999984i	$-0.498188\pi$
$821$	0.326238	0.0113858	0.00569289	+	0.999984i	$0.498188\pi$
$822$	−3.70820	−0.129338
$823$	52.0132	1.81306	0.906532	−	0.422136i	$-0.138720\pi$
$823$	52.0132	1.81306	0.906532	+	0.422136i	$0.138720\pi$
$824$	24.1672	0.841904
$825$	32.8885	1.14503
$826$	8.23607	0.286569
$827$	9.18034	0.319232	0.159616	−	0.987179i	$-0.448974\pi$
$827$	9.18034	0.319232	0.159616	+	0.987179i	$0.448974\pi$
$828$	−31.3131	−1.08820
$829$	−28.1591	−0.978004	−0.489002	−	0.872283i	$-0.662639\pi$
$829$	−28.1591	−0.978004	−0.489002	+	0.872283i	$0.662639\pi$
$830$	−7.57044	−0.262774
$831$	32.6525	1.13270
$832$	−6.50658	−0.225575
$833$	66.6525	2.30937
$834$	−5.29180	−0.183240
$835$	−17.5967	−0.608961
$836$	8.29180	0.286778
$837$	0	0
$838$	3.90983	0.135063
$839$	−25.8885	−0.893772	−0.446886	−	0.894591i	$-0.647467\pi$
$839$	−25.8885	−0.893772	−0.446886	+	0.894591i	$0.647467\pi$
$840$	20.1803	0.696288
$841$	−20.0000	−0.689655
$842$	2.92299	0.100733
$843$	19.5623	0.673762
$844$	−17.1246	−0.589453
$845$	13.7082	0.471577
$846$	1.68692	0.0579974
$847$	8.85410	0.304231
$848$	−4.34752	−0.149295
$849$	28.1803	0.967147
$850$	−8.07701	−0.277039
$851$	21.2705	0.729144
$852$	−52.4164	−1.79576
$853$	11.2574	0.385444	0.192722	−	0.981253i	$-0.438268\pi$
$853$	11.2574	0.385444	0.192722	+	0.981253i	$0.438268\pi$
$854$	−4.61803	−0.158026
$855$	−5.88854	−0.201384
$856$	−11.0820	−0.378776
$857$	−36.1803	−1.23590	−0.617948	−	0.786219i	$-0.712036\pi$
$857$	−36.1803	−1.23590	−0.617948	+	0.786219i	$0.712036\pi$
$858$	−5.00000	−0.170697
$859$	49.4164	1.68607	0.843033	−	0.537862i	$-0.180768\pi$
$859$	49.4164	1.68607	0.843033	+	0.537862i	$0.180768\pi$
$860$	0	0
$861$	105.048	3.58001
$862$	−9.47214	−0.322622
$863$	−9.50658	−0.323608	−0.161804	−	0.986823i	$-0.551731\pi$
$863$	−9.50658	−0.323608	−0.161804	+	0.986823i	$0.551731\pi$
$864$	9.27051	0.315389
$865$	4.65248	0.158189
$866$	13.2574	0.450503
$867$	52.5967	1.78628
$868$	0	0
$869$	5.00000	0.169613
$870$	3.70820	0.125720
$871$	−5.32624	−0.180473
$872$	20.3951	0.690666
$873$	−35.5967	−1.20477
$874$	2.06888	0.0699810
$875$	44.3607	1.49966
$876$	9.00000	0.304082
$877$	−7.65248	−0.258406	−0.129203	−	0.991618i	$-0.541242\pi$
$877$	−7.65248	−0.258406	−0.129203	+	0.991618i	$0.541242\pi$
$878$	0.437694	0.0147715
$879$	−31.6525	−1.06761
$880$	14.0689	0.474262
$881$	33.7639	1.13754	0.568768	−	0.822498i	$-0.307420\pi$
$881$	33.7639	1.13754	0.568768	+	0.822498i	$0.307420\pi$
$882$	16.1115	0.542501
$883$	13.1246	0.441678	0.220839	−	0.975310i	$-0.429120\pi$
$883$	13.1246	0.441678	0.220839	+	0.975310i	$0.429120\pi$
$884$	−15.6049	−0.524849
$885$	−16.4721	−0.553705
$886$	0.944272	0.0317234
$887$	52.9574	1.77814	0.889068	−	0.457775i	$-0.151353\pi$
$887$	52.9574	1.77814	0.889068	+	0.457775i	$0.151353\pi$
$888$	−18.7082	−0.627806
$889$	−62.0689	−2.08172
$890$	−0.875388	−0.0293431
$891$	20.6525	0.691884
$892$	5.12461	0.171585
$893$	1.41641	0.0473983
$894$	−9.00000	−0.301005
$895$	11.9311	0.398813
$896$	−42.7426	−1.42793
$897$	15.8541	0.529353
$898$	12.5410	0.418499
$899$	0	0
$900$	24.8115	0.827051
$901$	−8.41641	−0.280391
$902$	−13.0902	−0.435855
$903$	0	0
$904$	−22.9919	−0.764698
$905$	23.9574	0.796372
$906$	8.85410	0.294158
$907$	−21.7082	−0.720809	−0.360405	−	0.932796i	$-0.617361\pi$
$907$	−21.7082	−0.720809	−0.360405	+	0.932796i	$0.617361\pi$
$908$	−2.72949	−0.0905813
$909$	14.5066	0.481153
$910$	−2.76393	−0.0916235
$911$	42.9787	1.42395	0.711974	−	0.702206i	$-0.247801\pi$
$911$	42.9787	1.42395	0.711974	+	0.702206i	$0.247801\pi$
$912$	10.1803	0.337105
$913$	−58.0132	−1.91996
$914$	6.00000	0.198462
$915$	9.23607	0.305335
$916$	4.24922	0.140398
$917$	−42.1246	−1.39108
$918$	5.20163	0.171679
$919$	29.3951	0.969656	0.484828	−	0.874610i	$-0.338882\pi$
$919$	29.3951	0.969656	0.484828	+	0.874610i	$0.338882\pi$
$920$	7.97369	0.262885
$921$	−60.7771	−2.00267
$922$	−12.0689	−0.397468
$923$	14.9230	0.491196
$924$	74.3951	2.44742
$925$	−16.8541	−0.554159
$926$	11.3951	0.374467
$927$	−63.2705	−2.07808
$928$	−12.4377	−0.408287
$929$	−35.2361	−1.15606	−0.578029	−	0.816016i	$-0.696178\pi$
$929$	−35.2361	−1.15606	−0.578029	+	0.816016i	$0.696178\pi$
$930$	0	0
$931$	13.5279	0.443358
$932$	33.4377	1.09529
$933$	−78.1033	−2.55699
$934$	5.75078	0.188171
$935$	27.2361	0.890715
$936$	−7.84095	−0.256289
$937$	55.3262	1.80743	0.903715	−	0.428135i	$-0.140829\pi$
$937$	55.3262	1.80743	0.903715	+	0.428135i	$0.140829\pi$
$938$	−6.23607	−0.203615
$939$	−34.3607	−1.12132
$940$	2.62616	0.0856560
$941$	−26.2361	−0.855271	−0.427636	−	0.903951i	$-0.640653\pi$
$941$	−26.2361	−0.855271	−0.427636	+	0.903951i	$0.640653\pi$
$942$	5.14590	0.167662
$943$	41.5066	1.35164
$944$	16.0132	0.521184
$945$	−11.7082	−0.380868
$946$	0	0
$947$	25.3607	0.824111	0.412056	−	0.911159i	$-0.364811\pi$
$947$	25.3607	0.824111	0.412056	+	0.911159i	$0.364811\pi$
$948$	6.70820	0.217872
$949$	−2.56231	−0.0831760
$950$	−1.63932	−0.0531866
$951$	87.1935	2.82744
$952$	−37.9787	−1.23090
$953$	38.8885	1.25972	0.629862	−	0.776707i	$-0.283112\pi$
$953$	38.8885	1.25972	0.629862	+	0.776707i	$0.283112\pi$
$954$	−2.03444	−0.0658675
$955$	−17.9574	−0.581089
$956$	15.3738	0.497225
$957$	28.4164	0.918572
$958$	−5.27864	−0.170545
$959$	−15.7082	−0.507244
$960$	15.2361	0.491742
$961$	−31.0000	−1.00000
$962$	2.56231	0.0826121
$963$	29.0132	0.934936
$964$	7.91796	0.255020
$965$	−3.34752	−0.107761
$966$	18.5623	0.597232
$967$	38.1033	1.22532	0.612660	−	0.790346i	$-0.290099\pi$
$967$	38.1033	1.22532	0.612660	+	0.790346i	$0.290099\pi$
$968$	−3.07701	−0.0988990
$969$	19.7082	0.633119
$970$	4.36068	0.140013
$971$	−17.3607	−0.557131	−0.278565	−	0.960417i	$-0.589859\pi$
$971$	−17.3607	−0.557131	−0.278565	+	0.960417i	$0.589859\pi$
$972$	40.1459	1.28768
$973$	−22.4164	−0.718637
$974$	0.506578	0.0162318
$975$	−12.5623	−0.402316
$976$	−8.97871	−0.287402
$977$	41.2361	1.31926	0.659629	−	0.751591i	$-0.270713\pi$
$977$	41.2361	1.31926	0.659629	+	0.751591i	$0.270713\pi$
$978$	−14.0000	−0.447671
$979$	−6.70820	−0.214395
$980$	25.0820	0.801216
$981$	−53.3951	−1.70478
$982$	−8.27051	−0.263923
$983$	10.4721	0.334009	0.167005	−	0.985956i	$-0.446591\pi$
$983$	10.4721	0.334009	0.167005	+	0.985956i	$0.446591\pi$
$984$	−36.5066	−1.16379
$985$	3.63932	0.115958
$986$	−6.97871	−0.222248
$987$	12.7082	0.404507
$988$	−3.16718	−0.100762
$989$	0	0
$990$	6.58359	0.209240
$991$	10.8197	0.343698	0.171849	−	0.985123i	$-0.445026\pi$
$991$	10.8197	0.343698	0.171849	+	0.985123i	$0.445026\pi$
$992$	0	0
$993$	14.3262	0.454629
$994$	17.4721	0.554183
$995$	2.40325	0.0761882
$996$	−77.8328	−2.46623
$997$	19.4508	0.616015	0.308007	−	0.951384i	$-0.400338\pi$
$997$	19.4508	0.616015	0.308007	+	0.951384i	$0.400338\pi$
$998$	−5.29180	−0.167509
$999$	10.8541	0.343409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.h.1.1		2
43.7	odd	6		43.2.c.b.6.2	✓	4
43.37	odd	6		43.2.c.b.36.2	yes	4
43.42	odd	2		1849.2.a.e.1.2		2
129.50	even	6		387.2.h.d.307.1		4
129.80	even	6		387.2.h.d.208.1		4
172.7	even	6		688.2.i.e.49.1		4
172.123	even	6		688.2.i.e.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.2	✓	4	43.7	odd	6
43.2.c.b.36.2	yes	4	43.37	odd	6
387.2.h.d.208.1		4	129.80	even	6
387.2.h.d.307.1		4	129.50	even	6
688.2.i.e.49.1		4	172.7	even	6
688.2.i.e.337.1		4	172.123	even	6
1849.2.a.e.1.2		2	43.42	odd	2
1849.2.a.h.1.1		2	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} +2.61803 q^{3} -1.85410 q^{4} -1.23607 q^{5} +1.00000 q^{6} +4.23607 q^{7} -1.47214 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+0.381966 q^{2} +2.61803 q^{3} -1.85410 q^{4} -1.23607 q^{5} +1.00000 q^{6} +4.23607 q^{7} -1.47214 q^{8} +3.85410 q^{9} -0.472136 q^{10} -3.61803 q^{11} -4.85410 q^{12} +1.38197 q^{13} +1.61803 q^{14} -3.23607 q^{15} +3.14590 q^{16} +6.09017 q^{17} +1.47214 q^{18} +1.23607 q^{19} +2.29180 q^{20} +11.0902 q^{21} -1.38197 q^{22} +4.38197 q^{23} -3.85410 q^{24} -3.47214 q^{25} +0.527864 q^{26} +2.23607 q^{27} -7.85410 q^{28} -3.00000 q^{29} -1.23607 q^{30} +4.14590 q^{32} -9.47214 q^{33} +2.32624 q^{34} -5.23607 q^{35} -7.14590 q^{36} +4.85410 q^{37} +0.472136 q^{38} +3.61803 q^{39} +1.81966 q^{40} +9.47214 q^{41} +4.23607 q^{42} +6.70820 q^{44} -4.76393 q^{45} +1.67376 q^{46} +1.14590 q^{47} +8.23607 q^{48} +10.9443 q^{49} -1.32624 q^{50} +15.9443 q^{51} -2.56231 q^{52} -1.38197 q^{53} +0.854102 q^{54} +4.47214 q^{55} -6.23607 q^{56} +3.23607 q^{57} -1.14590 q^{58} +5.09017 q^{59} +6.00000 q^{60} -2.85410 q^{61} +16.3262 q^{63} -4.70820 q^{64} -1.70820 q^{65} -3.61803 q^{66} -3.85410 q^{67} -11.2918 q^{68} +11.4721 q^{69} -2.00000 q^{70} +10.7984 q^{71} -5.67376 q^{72} -1.85410 q^{73} +1.85410 q^{74} -9.09017 q^{75} -2.29180 q^{76} -15.3262 q^{77} +1.38197 q^{78} -1.38197 q^{79} -3.88854 q^{80} -5.70820 q^{81} +3.61803 q^{82} +16.0344 q^{83} -20.5623 q^{84} -7.52786 q^{85} -7.85410 q^{87} +5.32624 q^{88} +1.85410 q^{89} -1.81966 q^{90} +5.85410 q^{91} -8.12461 q^{92} +0.437694 q^{94} -1.52786 q^{95} +10.8541 q^{96} -9.23607 q^{97} +4.18034 q^{98} -13.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9} + 8 q^{10} - 5 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 2 q^{15} + 13 q^{16} + q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 11 q^{21} - 5 q^{22} + 11 q^{23} - q^{24} + 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 15 q^{32} - 10 q^{33} - 11 q^{34} - 6 q^{35} - 21 q^{36} + 3 q^{37} - 8 q^{38} + 5 q^{39} + 26 q^{40} + 10 q^{41} + 4 q^{42} - 14 q^{45} + 19 q^{46} + 9 q^{47} + 12 q^{48} + 4 q^{49} + 13 q^{50} + 14 q^{51} + 15 q^{52} - 5 q^{53} - 5 q^{54} - 8 q^{56} + 2 q^{57} - 9 q^{58} - q^{59} + 12 q^{60} + q^{61} + 17 q^{63} + 4 q^{64} + 10 q^{65} - 5 q^{66} - q^{67} - 36 q^{68} + 14 q^{69} - 4 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} - 3 q^{74} - 7 q^{75} - 18 q^{76} - 15 q^{77} + 5 q^{78} - 5 q^{79} + 28 q^{80} + 2 q^{81} + 5 q^{82} + 3 q^{83} - 21 q^{84} - 24 q^{85} - 9 q^{87} - 5 q^{88} - 3 q^{89} - 26 q^{90} + 5 q^{91} + 24 q^{92} + 21 q^{94} - 12 q^{95} + 15 q^{96} - 14 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9 + 8 * q^10 - 5 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 2 * q^15 + 13 * q^16 + q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 11 * q^21 - 5 * q^22 + 11 * q^23 - q^24 + 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 15 * q^32 - 10 * q^33 - 11 * q^34 - 6 * q^35 - 21 * q^36 + 3 * q^37 - 8 * q^38 + 5 * q^39 + 26 * q^40 + 10 * q^41 + 4 * q^42 - 14 * q^45 + 19 * q^46 + 9 * q^47 + 12 * q^48 + 4 * q^49 + 13 * q^50 + 14 * q^51 + 15 * q^52 - 5 * q^53 - 5 * q^54 - 8 * q^56 + 2 * q^57 - 9 * q^58 - q^59 + 12 * q^60 + q^61 + 17 * q^63 + 4 * q^64 + 10 * q^65 - 5 * q^66 - q^67 - 36 * q^68 + 14 * q^69 - 4 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 - 3 * q^74 - 7 * q^75 - 18 * q^76 - 15 * q^77 + 5 * q^78 - 5 * q^79 + 28 * q^80 + 2 * q^81 + 5 * q^82 + 3 * q^83 - 21 * q^84 - 24 * q^85 - 9 * q^87 - 5 * q^88 - 3 * q^89 - 26 * q^90 + 5 * q^91 + 24 * q^92 + 21 * q^94 - 12 * q^95 + 15 * q^96 - 14 * q^97 - 14 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more