LMFDB - Embedded newform 6014.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.92127 q^{3} +1.00000 q^{4} -1.99624 q^{5} +2.92127 q^{6} -0.468229 q^{7} -1.00000 q^{8} +5.53384 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.92127 q^{3} +1.00000 q^{4} -1.99624 q^{5} +2.92127 q^{6} -0.468229 q^{7} -1.00000 q^{8} +5.53384 q^{9} +1.99624 q^{10} -0.0849659 q^{11} -2.92127 q^{12} -0.396414 q^{13} +0.468229 q^{14} +5.83157 q^{15} +1.00000 q^{16} +3.97814 q^{17} -5.53384 q^{18} -3.68972 q^{19} -1.99624 q^{20} +1.36782 q^{21} +0.0849659 q^{22} -3.79073 q^{23} +2.92127 q^{24} -1.01502 q^{25} +0.396414 q^{26} -7.40204 q^{27} -0.468229 q^{28} -0.172167 q^{29} -5.83157 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.248209 q^{33} -3.97814 q^{34} +0.934698 q^{35} +5.53384 q^{36} +7.23600 q^{37} +3.68972 q^{38} +1.15803 q^{39} +1.99624 q^{40} -8.98181 q^{41} -1.36782 q^{42} +1.52854 q^{43} -0.0849659 q^{44} -11.0469 q^{45} +3.79073 q^{46} +6.18798 q^{47} -2.92127 q^{48} -6.78076 q^{49} +1.01502 q^{50} -11.6212 q^{51} -0.396414 q^{52} -8.56035 q^{53} +7.40204 q^{54} +0.169613 q^{55} +0.468229 q^{56} +10.7787 q^{57} +0.172167 q^{58} +8.03545 q^{59} +5.83157 q^{60} -9.93979 q^{61} -1.00000 q^{62} -2.59110 q^{63} +1.00000 q^{64} +0.791338 q^{65} -0.248209 q^{66} +6.38996 q^{67} +3.97814 q^{68} +11.0738 q^{69} -0.934698 q^{70} +9.62209 q^{71} -5.53384 q^{72} -5.35742 q^{73} -7.23600 q^{74} +2.96515 q^{75} -3.68972 q^{76} +0.0397835 q^{77} -1.15803 q^{78} +1.69251 q^{79} -1.99624 q^{80} +5.02186 q^{81} +8.98181 q^{82} +15.5691 q^{83} +1.36782 q^{84} -7.94134 q^{85} -1.52854 q^{86} +0.502946 q^{87} +0.0849659 q^{88} -0.325466 q^{89} +11.0469 q^{90} +0.185612 q^{91} -3.79073 q^{92} -2.92127 q^{93} -6.18798 q^{94} +7.36557 q^{95} +2.92127 q^{96} +1.00000 q^{97} +6.78076 q^{98} -0.470188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.92127	−1.68660	−0.843299	−	0.537445i	$-0.819390\pi$
$3$	−2.92127	−1.68660	−0.843299	+	0.537445i	$0.819390\pi$
$4$	1.00000	0.500000
$5$	−1.99624	−0.892746	−0.446373	−	0.894847i	$-0.647285\pi$
$5$	−1.99624	−0.892746	−0.446373	+	0.894847i	$0.647285\pi$
$6$	2.92127	1.19260
$7$	−0.468229	−0.176974	−0.0884869	−	0.996077i	$-0.528203\pi$
$7$	−0.468229	−0.176974	−0.0884869	+	0.996077i	$0.528203\pi$
$8$	−1.00000	−0.353553
$9$	5.53384	1.84461
$10$	1.99624	0.631267
$11$	−0.0849659	−0.0256182	−0.0128091	−	0.999918i	$-0.504077\pi$
$11$	−0.0849659	−0.0256182	−0.0128091	+	0.999918i	$0.504077\pi$
$12$	−2.92127	−0.843299
$13$	−0.396414	−0.109945	−0.0549727	−	0.998488i	$-0.517507\pi$
$13$	−0.396414	−0.109945	−0.0549727	+	0.998488i	$0.517507\pi$
$14$	0.468229	0.125139
$15$	5.83157	1.50570
$16$	1.00000	0.250000
$17$	3.97814	0.964842	0.482421	−	0.875940i	$-0.339758\pi$
$17$	3.97814	0.964842	0.482421	+	0.875940i	$0.339758\pi$
$18$	−5.53384	−1.30434
$19$	−3.68972	−0.846479	−0.423240	−	0.906018i	$-0.639107\pi$
$19$	−3.68972	−0.846479	−0.423240	+	0.906018i	$0.639107\pi$
$20$	−1.99624	−0.446373
$21$	1.36782	0.298484
$22$	0.0849659	0.0181148
$23$	−3.79073	−0.790423	−0.395211	−	0.918590i	$-0.629329\pi$
$23$	−3.79073	−0.790423	−0.395211	+	0.918590i	$0.629329\pi$
$24$	2.92127	0.596302
$25$	−1.01502	−0.203004
$26$	0.396414	0.0777432
$27$	−7.40204	−1.42452
$28$	−0.468229	−0.0884869
$29$	−0.172167	−0.0319705	−0.0159853	−	0.999872i	$-0.505088\pi$
$29$	−0.172167	−0.0319705	−0.0159853	+	0.999872i	$0.505088\pi$
$30$	−5.83157	−1.06469
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	0.248209	0.0432076
$34$	−3.97814	−0.682246
$35$	0.934698	0.157993
$36$	5.53384	0.922307
$37$	7.23600	1.18959	0.594795	−	0.803877i	$-0.297233\pi$
$37$	7.23600	1.18959	0.594795	+	0.803877i	$0.297233\pi$
$38$	3.68972	0.598551
$39$	1.15803	0.185434
$40$	1.99624	0.315634
$41$	−8.98181	−1.40272	−0.701361	−	0.712806i	$-0.747424\pi$
$41$	−8.98181	−1.40272	−0.701361	+	0.712806i	$0.747424\pi$
$42$	−1.36782	−0.211060
$43$	1.52854	0.233100	0.116550	−	0.993185i	$-0.462816\pi$
$43$	1.52854	0.233100	0.116550	+	0.993185i	$0.462816\pi$
$44$	−0.0849659	−0.0128091
$45$	−11.0469	−1.64677
$46$	3.79073	0.558913
$47$	6.18798	0.902609	0.451305	−	0.892370i	$-0.350959\pi$
$47$	6.18798	0.902609	0.451305	+	0.892370i	$0.350959\pi$
$48$	−2.92127	−0.421650
$49$	−6.78076	−0.968680
$50$	1.01502	0.143545
$51$	−11.6212	−1.62730
$52$	−0.396414	−0.0549727
$53$	−8.56035	−1.17585	−0.587927	−	0.808914i	$-0.700056\pi$
$53$	−8.56035	−1.17585	−0.587927	+	0.808914i	$0.700056\pi$
$54$	7.40204	1.00729
$55$	0.169613	0.0228706
$56$	0.468229	0.0625697
$57$	10.7787	1.42767
$58$	0.172167	0.0226066
$59$	8.03545	1.04613	0.523063	−	0.852294i	$-0.324789\pi$
$59$	8.03545	1.04613	0.523063	+	0.852294i	$0.324789\pi$
$60$	5.83157	0.752852
$61$	−9.93979	−1.27266	−0.636330	−	0.771417i	$-0.719548\pi$
$61$	−9.93979	−1.27266	−0.636330	+	0.771417i	$0.719548\pi$
$62$	−1.00000	−0.127000
$63$	−2.59110	−0.326448
$64$	1.00000	0.125000
$65$	0.791338	0.0981534
$66$	−0.248209	−0.0305524
$67$	6.38996	0.780658	0.390329	−	0.920676i	$-0.372361\pi$
$67$	6.38996	0.780658	0.390329	+	0.920676i	$0.372361\pi$
$68$	3.97814	0.482421
$69$	11.0738	1.33313
$70$	−0.934698	−0.111718
$71$	9.62209	1.14193	0.570966	−	0.820974i	$-0.306569\pi$
$71$	9.62209	1.14193	0.570966	+	0.820974i	$0.306569\pi$
$72$	−5.53384	−0.652169
$73$	−5.35742	−0.627039	−0.313519	−	0.949582i	$-0.601508\pi$
$73$	−5.35742	−0.627039	−0.313519	+	0.949582i	$0.601508\pi$
$74$	−7.23600	−0.841167
$75$	2.96515	0.342386
$76$	−3.68972	−0.423240
$77$	0.0397835	0.00453375
$78$	−1.15803	−0.131121
$79$	1.69251	0.190422	0.0952111	−	0.995457i	$-0.469647\pi$
$79$	1.69251	0.190422	0.0952111	+	0.995457i	$0.469647\pi$
$80$	−1.99624	−0.223187
$81$	5.02186	0.557984
$82$	8.98181	0.991875
$83$	15.5691	1.70893	0.854463	−	0.519512i	$-0.173886\pi$
$83$	15.5691	1.70893	0.854463	+	0.519512i	$0.173886\pi$
$84$	1.36782	0.149242
$85$	−7.94134	−0.861359
$86$	−1.52854	−0.164827
$87$	0.502946	0.0539214
$88$	0.0849659	0.00905740
$89$	−0.325466	−0.0344993	−0.0172497	−	0.999851i	$-0.505491\pi$
$89$	−0.325466	−0.0344993	−0.0172497	+	0.999851i	$0.505491\pi$
$90$	11.0469	1.16444
$91$	0.185612	0.0194575
$92$	−3.79073	−0.395211
$93$	−2.92127	−0.302922
$94$	−6.18798	−0.638241
$95$	7.36557	0.755691
$96$	2.92127	0.298151
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.78076	0.684960
$99$	−0.470188	−0.0472557
$100$	−1.01502	−0.101502
$101$	4.55936	0.453673	0.226837	−	0.973933i	$-0.427162\pi$
$101$	4.55936	0.453673	0.226837	+	0.973933i	$0.427162\pi$
$102$	11.6212	1.15067
$103$	−6.72330	−0.662467	−0.331233	−	0.943549i	$-0.607465\pi$
$103$	−6.72330	−0.662467	−0.331233	+	0.943549i	$0.607465\pi$
$104$	0.396414	0.0388716
$105$	−2.73051	−0.266470
$106$	8.56035	0.831454
$107$	12.3849	1.19729	0.598645	−	0.801015i	$-0.295706\pi$
$107$	12.3849	1.19729	0.598645	+	0.801015i	$0.295706\pi$
$108$	−7.40204	−0.712261
$109$	19.1525	1.83448	0.917241	−	0.398334i	$-0.130411\pi$
$109$	19.1525	1.83448	0.917241	+	0.398334i	$0.130411\pi$
$110$	−0.169613	−0.0161719
$111$	−21.1383	−2.00636
$112$	−0.468229	−0.0442435
$113$	−7.69368	−0.723760	−0.361880	−	0.932225i	$-0.617865\pi$
$113$	−7.69368	−0.723760	−0.361880	+	0.932225i	$0.617865\pi$
$114$	−10.7787	−1.00952
$115$	7.56722	0.705647
$116$	−0.172167	−0.0159853
$117$	−2.19369	−0.202807
$118$	−8.03545	−0.739723
$119$	−1.86268	−0.170752
$120$	−5.83157	−0.532347
$121$	−10.9928	−0.999344
$122$	9.93979	0.899906
$123$	26.2383	2.36583
$124$	1.00000	0.0898027
$125$	12.0074	1.07398
$126$	2.59110	0.230834
$127$	0.270686	0.0240195	0.0120097	−	0.999928i	$-0.496177\pi$
$127$	0.270686	0.0240195	0.0120097	+	0.999928i	$0.496177\pi$
$128$	−1.00000	−0.0883883
$129$	−4.46528	−0.393146
$130$	−0.791338	−0.0694049
$131$	−3.86697	−0.337859	−0.168929	−	0.985628i	$-0.554031\pi$
$131$	−3.86697	−0.337859	−0.168929	+	0.985628i	$0.554031\pi$
$132$	0.248209	0.0216038
$133$	1.72763	0.149805
$134$	−6.38996	−0.552008
$135$	14.7763	1.27174
$136$	−3.97814	−0.341123
$137$	14.9196	1.27467	0.637334	−	0.770588i	$-0.280037\pi$
$137$	14.9196	1.27467	0.637334	+	0.770588i	$0.280037\pi$
$138$	−11.0738	−0.942662
$139$	3.43811	0.291617	0.145808	−	0.989313i	$-0.453422\pi$
$139$	3.43811	0.291617	0.145808	+	0.989313i	$0.453422\pi$
$140$	0.934698	0.0789964
$141$	−18.0768	−1.52234
$142$	−9.62209	−0.807468
$143$	0.0336817	0.00281660
$144$	5.53384	0.461153
$145$	0.343686	0.0285416
$146$	5.35742	0.443383
$147$	19.8085	1.63377
$148$	7.23600	0.594795
$149$	7.66609	0.628030	0.314015	−	0.949418i	$-0.398326\pi$
$149$	7.66609	0.628030	0.314015	+	0.949418i	$0.398326\pi$
$150$	−2.96515	−0.242103
$151$	−1.79104	−0.145753	−0.0728765	−	0.997341i	$-0.523218\pi$
$151$	−1.79104	−0.145753	−0.0728765	+	0.997341i	$0.523218\pi$
$152$	3.68972	0.299276
$153$	22.0144	1.77976
$154$	−0.0397835	−0.00320585
$155$	−1.99624	−0.160342
$156$	1.15803	0.0927169
$157$	8.43250	0.672987	0.336494	−	0.941686i	$-0.390759\pi$
$157$	8.43250	0.672987	0.336494	+	0.941686i	$0.390759\pi$
$158$	−1.69251	−0.134649
$159$	25.0071	1.98319
$160$	1.99624	0.157817
$161$	1.77493	0.139884
$162$	−5.02186	−0.394555
$163$	10.2132	0.799959	0.399979	−	0.916524i	$-0.369017\pi$
$163$	10.2132	0.799959	0.399979	+	0.916524i	$0.369017\pi$
$164$	−8.98181	−0.701361
$165$	−0.495485	−0.0385734
$166$	−15.5691	−1.20839
$167$	−7.31129	−0.565764	−0.282882	−	0.959155i	$-0.591291\pi$
$167$	−7.31129	−0.565764	−0.282882	+	0.959155i	$0.591291\pi$
$168$	−1.36782	−0.105530
$169$	−12.8429	−0.987912
$170$	7.94134	0.609073
$171$	−20.4183	−1.56143
$172$	1.52854	0.116550
$173$	−4.44011	−0.337575	−0.168787	−	0.985652i	$-0.553985\pi$
$173$	−4.44011	−0.337575	−0.168787	+	0.985652i	$0.553985\pi$
$174$	−0.502946	−0.0381282
$175$	0.475261	0.0359264
$176$	−0.0849659	−0.00640455
$177$	−23.4738	−1.76440
$178$	0.325466	0.0243947
$179$	10.2195	0.763844	0.381922	−	0.924195i	$-0.375262\pi$
$179$	10.2195	0.763844	0.381922	+	0.924195i	$0.375262\pi$
$180$	−11.0469	−0.823386
$181$	17.5727	1.30617	0.653084	−	0.757285i	$-0.273475\pi$
$181$	17.5727	1.30617	0.653084	+	0.757285i	$0.273475\pi$
$182$	−0.185612	−0.0137585
$183$	29.0368	2.14647
$184$	3.79073	0.279457
$185$	−14.4448	−1.06200
$186$	2.92127	0.214198
$187$	−0.338007	−0.0247175
$188$	6.18798	0.451305
$189$	3.46585	0.252103
$190$	−7.36557	−0.534354
$191$	19.3244	1.39826	0.699131	−	0.714993i	$-0.253570\pi$
$191$	19.3244	1.39826	0.699131	+	0.714993i	$0.253570\pi$
$192$	−2.92127	−0.210825
$193$	−13.6411	−0.981906	−0.490953	−	0.871186i	$-0.663351\pi$
$193$	−13.6411	−0.981906	−0.490953	+	0.871186i	$0.663351\pi$
$194$	−1.00000	−0.0717958
$195$	−2.31171	−0.165545
$196$	−6.78076	−0.484340
$197$	13.9451	0.993547	0.496773	−	0.867880i	$-0.334518\pi$
$197$	13.9451	0.993547	0.496773	+	0.867880i	$0.334518\pi$
$198$	0.470188	0.0334148
$199$	0.543977	0.0385615	0.0192807	−	0.999814i	$-0.493862\pi$
$199$	0.543977	0.0385615	0.0192807	+	0.999814i	$0.493862\pi$
$200$	1.01502	0.0717727
$201$	−18.6668	−1.31666
$202$	−4.55936	−0.320795
$203$	0.0806133	0.00565795
$204$	−11.6212	−0.813650
$205$	17.9299	1.25228
$206$	6.72330	0.468435
$207$	−20.9773	−1.45802
$208$	−0.396414	−0.0274864
$209$	0.313500	0.0216853
$210$	2.73051	0.188423
$211$	21.8556	1.50460	0.752301	−	0.658820i	$-0.228944\pi$
$211$	21.8556	1.50460	0.752301	+	0.658820i	$0.228944\pi$
$212$	−8.56035	−0.587927
$213$	−28.1088	−1.92598
$214$	−12.3849	−0.846612
$215$	−3.05133	−0.208099
$216$	7.40204	0.503645
$217$	−0.468229	−0.0317854
$218$	−19.1525	−1.29717
$219$	15.6505	1.05756
$220$	0.169613	0.0114353
$221$	−1.57699	−0.106080
$222$	21.1383	1.41871
$223$	−11.0128	−0.737474	−0.368737	−	0.929534i	$-0.620210\pi$
$223$	−11.0128	−0.737474	−0.368737	+	0.929534i	$0.620210\pi$
$224$	0.468229	0.0312849
$225$	−5.61695	−0.374464
$226$	7.69368	0.511776
$227$	−14.7376	−0.978169	−0.489085	−	0.872236i	$-0.662669\pi$
$227$	−14.7376	−0.978169	−0.489085	+	0.872236i	$0.662669\pi$
$228$	10.7787	0.713835
$229$	−20.7359	−1.37027	−0.685133	−	0.728418i	$-0.740256\pi$
$229$	−20.7359	−1.37027	−0.685133	+	0.728418i	$0.740256\pi$
$230$	−7.56722	−0.498968
$231$	−0.116219	−0.00764662
$232$	0.172167	0.0113033
$233$	2.42846	0.159094	0.0795470	−	0.996831i	$-0.474653\pi$
$233$	2.42846	0.159094	0.0795470	+	0.996831i	$0.474653\pi$
$234$	2.19369	0.143406
$235$	−12.3527	−0.805801
$236$	8.03545	0.523063
$237$	−4.94428	−0.321166
$238$	1.86268	0.120740
$239$	−7.00797	−0.453308	−0.226654	−	0.973975i	$-0.572779\pi$
$239$	−7.00797	−0.453308	−0.226654	+	0.973975i	$0.572779\pi$
$240$	5.83157	0.376426
$241$	−27.1283	−1.74749	−0.873745	−	0.486385i	$-0.838315\pi$
$241$	−27.1283	−1.74749	−0.873745	+	0.486385i	$0.838315\pi$
$242$	10.9928	0.706643
$243$	7.53589	0.483427
$244$	−9.93979	−0.636330
$245$	13.5360	0.864786
$246$	−26.2383	−1.67289
$247$	1.46266	0.0930665
$248$	−1.00000	−0.0635001
$249$	−45.4815	−2.88227
$250$	−12.0074	−0.759417
$251$	5.25225	0.331519	0.165759	−	0.986166i	$-0.446992\pi$
$251$	5.25225	0.331519	0.165759	+	0.986166i	$0.446992\pi$
$252$	−2.59110	−0.163224
$253$	0.322083	0.0202492
$254$	−0.270686	−0.0169843
$255$	23.1988	1.45277
$256$	1.00000	0.0625000
$257$	16.6418	1.03809	0.519045	−	0.854747i	$-0.326288\pi$
$257$	16.6418	1.03809	0.519045	+	0.854747i	$0.326288\pi$
$258$	4.46528	0.277996
$259$	−3.38810	−0.210526
$260$	0.791338	0.0490767
$261$	−0.952742	−0.0589732
$262$	3.86697	0.238902
$263$	−12.7333	−0.785167	−0.392584	−	0.919716i	$-0.628419\pi$
$263$	−12.7333	−0.785167	−0.392584	+	0.919716i	$0.628419\pi$
$264$	−0.248209	−0.0152762
$265$	17.0885	1.04974
$266$	−1.72763	−0.105928
$267$	0.950775	0.0581865
$268$	6.38996	0.390329
$269$	−4.23603	−0.258275	−0.129138	−	0.991627i	$-0.541221\pi$
$269$	−4.23603	−0.258275	−0.129138	+	0.991627i	$0.541221\pi$
$270$	−14.7763	−0.899254
$271$	−29.2995	−1.77982	−0.889908	−	0.456141i	$-0.849231\pi$
$271$	−29.2995	−1.77982	−0.889908	+	0.456141i	$0.849231\pi$
$272$	3.97814	0.241210
$273$	−0.542225	−0.0328169
$274$	−14.9196	−0.901326
$275$	0.0862421	0.00520059
$276$	11.0738	0.666563
$277$	−3.64054	−0.218739	−0.109369	−	0.994001i	$-0.534883\pi$
$277$	−3.64054	−0.218739	−0.109369	+	0.994001i	$0.534883\pi$
$278$	−3.43811	−0.206204
$279$	5.53384	0.331302
$280$	−0.934698	−0.0558589
$281$	−17.3694	−1.03617	−0.518086	−	0.855328i	$-0.673355\pi$
$281$	−17.3694	−1.03617	−0.518086	+	0.855328i	$0.673355\pi$
$282$	18.0768	1.07646
$283$	16.9746	1.00903	0.504517	−	0.863402i	$-0.331671\pi$
$283$	16.9746	1.00903	0.504517	+	0.863402i	$0.331671\pi$
$284$	9.62209	0.570966
$285$	−21.5168	−1.27455
$286$	−0.0336817	−0.00199164
$287$	4.20554	0.248245
$288$	−5.53384	−0.326085
$289$	−1.17437	−0.0690805
$290$	−0.343686	−0.0201819
$291$	−2.92127	−0.171248
$292$	−5.35742	−0.313519
$293$	−10.2074	−0.596322	−0.298161	−	0.954516i	$-0.596373\pi$
$293$	−10.2074	−0.596322	−0.298161	+	0.954516i	$0.596373\pi$
$294$	−19.8085	−1.15525
$295$	−16.0407	−0.933926
$296$	−7.23600	−0.420584
$297$	0.628921	0.0364937
$298$	−7.66609	−0.444084
$299$	1.50270	0.0869034
$300$	2.96515	0.171193
$301$	−0.715706	−0.0412526
$302$	1.79104	0.103063
$303$	−13.3191	−0.765164
$304$	−3.68972	−0.211620
$305$	19.8422	1.13616
$306$	−22.0144	−1.25848
$307$	5.64876	0.322392	0.161196	−	0.986922i	$-0.448465\pi$
$307$	5.64876	0.322392	0.161196	+	0.986922i	$0.448465\pi$
$308$	0.0397835	0.00226688
$309$	19.6406	1.11732
$310$	1.99624	0.113379
$311$	−23.1664	−1.31365	−0.656823	−	0.754045i	$-0.728100\pi$
$311$	−23.1664	−1.31365	−0.656823	+	0.754045i	$0.728100\pi$
$312$	−1.15803	−0.0655607
$313$	5.75552	0.325321	0.162660	−	0.986682i	$-0.447992\pi$
$313$	5.75552	0.325321	0.162660	+	0.986682i	$0.447992\pi$
$314$	−8.43250	−0.475874
$315$	5.17247	0.291436
$316$	1.69251	0.0952111
$317$	−24.5769	−1.38038	−0.690189	−	0.723629i	$-0.742473\pi$
$317$	−24.5769	−1.38038	−0.690189	+	0.723629i	$0.742473\pi$
$318$	−25.0071	−1.40233
$319$	0.0146283	0.000819027 0
$320$	−1.99624	−0.111593
$321$	−36.1796	−2.01935
$322$	−1.77493	−0.0989130
$323$	−14.6782	−0.816718
$324$	5.02186	0.278992
$325$	0.402368	0.0223193
$326$	−10.2132	−0.565656
$327$	−55.9498	−3.09403
$328$	8.98181	0.495937
$329$	−2.89739	−0.159738
$330$	0.495485	0.0272755
$331$	6.61568	0.363631	0.181815	−	0.983333i	$-0.441803\pi$
$331$	6.61568	0.363631	0.181815	+	0.983333i	$0.441803\pi$
$332$	15.5691	0.854463
$333$	40.0428	2.19433
$334$	7.31129	0.400056
$335$	−12.7559	−0.696929
$336$	1.36782	0.0746209
$337$	25.3359	1.38014	0.690068	−	0.723745i	$-0.257581\pi$
$337$	25.3359	1.38014	0.690068	+	0.723745i	$0.257581\pi$
$338$	12.8429	0.698559
$339$	22.4753	1.22069
$340$	−7.94134	−0.430679
$341$	−0.0849659	−0.00460116
$342$	20.4183	1.10410
$343$	6.45255	0.348405
$344$	−1.52854	−0.0824133
$345$	−22.1059	−1.19014
$346$	4.44011	0.238702
$347$	27.8465	1.49488	0.747440	−	0.664329i	$-0.231283\pi$
$347$	27.8465	1.49488	0.747440	+	0.664329i	$0.231283\pi$
$348$	0.502946	0.0269607
$349$	11.7825	0.630702	0.315351	−	0.948975i	$-0.397878\pi$
$349$	11.7825	0.630702	0.315351	+	0.948975i	$0.397878\pi$
$350$	−0.475261	−0.0254038
$351$	2.93427	0.156620
$352$	0.0849659	0.00452870
$353$	26.9008	1.43178	0.715891	−	0.698212i	$-0.246021\pi$
$353$	26.9008	1.43178	0.715891	+	0.698212i	$0.246021\pi$
$354$	23.4738	1.24762
$355$	−19.2080	−1.01946
$356$	−0.325466	−0.0172497
$357$	5.44140	0.287990
$358$	−10.2195	−0.540119
$359$	11.1578	0.588884	0.294442	−	0.955669i	$-0.404866\pi$
$359$	11.1578	0.588884	0.294442	+	0.955669i	$0.404866\pi$
$360$	11.0469	0.582222
$361$	−5.38599	−0.283473
$362$	−17.5727	−0.923601
$363$	32.1129	1.68549
$364$	0.185612	0.00972874
$365$	10.6947	0.559787
$366$	−29.0368	−1.51778
$367$	20.2667	1.05791	0.528956	−	0.848649i	$-0.322584\pi$
$367$	20.2667	1.05791	0.528956	+	0.848649i	$0.322584\pi$
$368$	−3.79073	−0.197606
$369$	−49.7039	−2.58748
$370$	14.4448	0.750949
$371$	4.00820	0.208095
$372$	−2.92127	−0.151461
$373$	3.98873	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$373$	3.98873	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$374$	0.338007	0.0174779
$375$	−35.0770	−1.81137
$376$	−6.18798	−0.319121
$377$	0.0682492	0.00351501
$378$	−3.46585	−0.178264
$379$	−19.3272	−0.992771	−0.496386	−	0.868102i	$-0.665340\pi$
$379$	−19.3272	−0.992771	−0.496386	+	0.868102i	$0.665340\pi$
$380$	7.36557	0.377846
$381$	−0.790747	−0.0405112
$382$	−19.3244	−0.988721
$383$	16.0305	0.819121	0.409560	−	0.912283i	$-0.365682\pi$
$383$	16.0305	0.819121	0.409560	+	0.912283i	$0.365682\pi$
$384$	2.92127	0.149076
$385$	−0.0794175	−0.00404749
$386$	13.6411	0.694312
$387$	8.45869	0.429979
$388$	1.00000	0.0507673
$389$	−25.3891	−1.28728	−0.643638	−	0.765330i	$-0.722576\pi$
$389$	−25.3891	−1.28728	−0.643638	+	0.765330i	$0.722576\pi$
$390$	2.31171	0.117058
$391$	−15.0801	−0.762633
$392$	6.78076	0.342480
$393$	11.2965	0.569832
$394$	−13.9451	−0.702544
$395$	−3.37866	−0.169999
$396$	−0.470188	−0.0236278
$397$	15.4473	0.775280	0.387640	−	0.921811i	$-0.373290\pi$
$397$	15.4473	0.775280	0.387640	+	0.921811i	$0.373290\pi$
$398$	−0.543977	−0.0272671
$399$	−5.04689	−0.252660
$400$	−1.01502	−0.0507510
$401$	−9.29739	−0.464290	−0.232145	−	0.972681i	$-0.574574\pi$
$401$	−9.29739	−0.464290	−0.232145	+	0.972681i	$0.574574\pi$
$402$	18.6668	0.931016
$403$	−0.396414	−0.0197468
$404$	4.55936	0.226837
$405$	−10.0248	−0.498139
$406$	−0.0806133	−0.00400077
$407$	−0.614813	−0.0304752
$408$	11.6212	0.575337
$409$	23.4727	1.16065	0.580326	−	0.814384i	$-0.302925\pi$
$409$	23.4727	1.16065	0.580326	+	0.814384i	$0.302925\pi$
$410$	−17.9299	−0.885492
$411$	−43.5842	−2.14985
$412$	−6.72330	−0.331233
$413$	−3.76243	−0.185137
$414$	20.9773	1.03098
$415$	−31.0796	−1.52564
$416$	0.396414	0.0194358
$417$	−10.0437	−0.491841
$418$	−0.313500	−0.0153338
$419$	−21.7775	−1.06390	−0.531950	−	0.846776i	$-0.678541\pi$
$419$	−21.7775	−1.06390	−0.531950	+	0.846776i	$0.678541\pi$
$420$	−2.73051	−0.133235
$421$	−20.3011	−0.989415	−0.494708	−	0.869059i	$-0.664725\pi$
$421$	−20.3011	−0.989415	−0.494708	+	0.869059i	$0.664725\pi$
$422$	−21.8556	−1.06391
$423$	34.2433	1.66496
$424$	8.56035	0.415727
$425$	−4.03789	−0.195867
$426$	28.1088	1.36187
$427$	4.65410	0.225227
$428$	12.3849	0.598645
$429$	−0.0983934	−0.00475048
$430$	3.05133	0.147148
$431$	17.0570	0.821608	0.410804	−	0.911724i	$-0.365248\pi$
$431$	17.0570	0.821608	0.410804	+	0.911724i	$0.365248\pi$
$432$	−7.40204	−0.356131
$433$	−34.1333	−1.64034	−0.820171	−	0.572119i	$-0.806122\pi$
$433$	−34.1333	−1.64034	−0.820171	+	0.572119i	$0.806122\pi$
$434$	0.468229	0.0224757
$435$	−1.00400	−0.0481382
$436$	19.1525	0.917241
$437$	13.9867	0.669076
$438$	−15.6505	−0.747810
$439$	−34.8188	−1.66181	−0.830904	−	0.556415i	$-0.812176\pi$
$439$	−34.8188	−1.66181	−0.830904	+	0.556415i	$0.812176\pi$
$440$	−0.169613	−0.00808596
$441$	−37.5236	−1.78684
$442$	1.57699	0.0750099
$443$	24.9406	1.18496	0.592481	−	0.805584i	$-0.298148\pi$
$443$	24.9406	1.18496	0.592481	+	0.805584i	$0.298148\pi$
$444$	−21.1383	−1.00318
$445$	0.649708	0.0307991
$446$	11.0128	0.521473
$447$	−22.3947	−1.05923
$448$	−0.468229	−0.0221217
$449$	−5.36337	−0.253113	−0.126557	−	0.991959i	$-0.540393\pi$
$449$	−5.36337	−0.253113	−0.126557	+	0.991959i	$0.540393\pi$
$450$	5.61695	0.264786
$451$	0.763148	0.0359352
$452$	−7.69368	−0.361880
$453$	5.23212	0.245827
$454$	14.7376	0.691670
$455$	−0.370527	−0.0173706
$456$	−10.7787	−0.504758
$457$	−7.93729	−0.371291	−0.185645	−	0.982617i	$-0.559438\pi$
$457$	−7.93729	−0.371291	−0.185645	+	0.982617i	$0.559438\pi$
$458$	20.7359	0.968925
$459$	−29.4464	−1.37444
$460$	7.56722	0.352824
$461$	−28.1909	−1.31298	−0.656491	−	0.754334i	$-0.727960\pi$
$461$	−28.1909	−1.31298	−0.656491	+	0.754334i	$0.727960\pi$
$462$	0.116219	0.00540697
$463$	−23.2480	−1.08042	−0.540212	−	0.841529i	$-0.681656\pi$
$463$	−23.2480	−1.08042	−0.540212	+	0.841529i	$0.681656\pi$
$464$	−0.172167	−0.00799263
$465$	5.83157	0.270432
$466$	−2.42846	−0.112496
$467$	−26.4583	−1.22435	−0.612173	−	0.790724i	$-0.709704\pi$
$467$	−26.4583	−1.22435	−0.612173	+	0.790724i	$0.709704\pi$
$468$	−2.19369	−0.101403
$469$	−2.99196	−0.138156
$470$	12.3527	0.569787
$471$	−24.6337	−1.13506
$472$	−8.03545	−0.369862
$473$	−0.129874	−0.00597160
$474$	4.94428	0.227098
$475$	3.74513	0.171839
$476$	−1.86268	−0.0853759
$477$	−47.3716	−2.16900
$478$	7.00797	0.320537
$479$	5.69701	0.260303	0.130152	−	0.991494i	$-0.458454\pi$
$479$	5.69701	0.260303	0.130152	+	0.991494i	$0.458454\pi$
$480$	−5.83157	−0.266173
$481$	−2.86845	−0.130790
$482$	27.1283	1.23566
$483$	−5.18506	−0.235928
$484$	−10.9928	−0.499672
$485$	−1.99624	−0.0906447
$486$	−7.53589	−0.341835
$487$	−39.5339	−1.79145	−0.895726	−	0.444607i	$-0.853343\pi$
$487$	−39.5339	−1.79145	−0.895726	+	0.444607i	$0.853343\pi$
$488$	9.93979	0.449953
$489$	−29.8355	−1.34921
$490$	−13.5360	−0.611496
$491$	−29.1963	−1.31761	−0.658805	−	0.752314i	$-0.728938\pi$
$491$	−29.1963	−1.31761	−0.658805	+	0.752314i	$0.728938\pi$
$492$	26.2383	1.18291
$493$	−0.684903	−0.0308465
$494$	−1.46266	−0.0658080
$495$	0.938609	0.0421873
$496$	1.00000	0.0449013
$497$	−4.50534	−0.202092
$498$	45.4815	2.03807
$499$	−20.6060	−0.922453	−0.461227	−	0.887282i	$-0.652590\pi$
$499$	−20.6060	−0.922453	−0.461227	+	0.887282i	$0.652590\pi$
$500$	12.0074	0.536989
$501$	21.3583	0.954217
$502$	−5.25225	−0.234419
$503$	13.0632	0.582457	0.291229	−	0.956653i	$-0.405936\pi$
$503$	13.0632	0.582457	0.291229	+	0.956653i	$0.405936\pi$
$504$	2.59110	0.115417
$505$	−9.10158	−0.405015
$506$	−0.322083	−0.0143184
$507$	37.5175	1.66621
$508$	0.270686	0.0120097
$509$	−37.2177	−1.64965	−0.824824	−	0.565390i	$-0.808726\pi$
$509$	−37.2177	−1.64965	−0.824824	+	0.565390i	$0.808726\pi$
$510$	−23.1988	−1.02726
$511$	2.50850	0.110969
$512$	−1.00000	−0.0441942
$513$	27.3114	1.20583
$514$	−16.6418	−0.734040
$515$	13.4213	0.591415
$516$	−4.46528	−0.196573
$517$	−0.525767	−0.0231232
$518$	3.38810	0.148865
$519$	12.9708	0.569353
$520$	−0.791338	−0.0347025
$521$	3.72349	0.163129	0.0815646	−	0.996668i	$-0.474008\pi$
$521$	3.72349	0.163129	0.0815646	+	0.996668i	$0.474008\pi$
$522$	0.952742	0.0417004
$523$	−39.4224	−1.72382	−0.861910	−	0.507061i	$-0.830732\pi$
$523$	−39.4224	−1.72382	−0.861910	+	0.507061i	$0.830732\pi$
$524$	−3.86697	−0.168929
$525$	−1.38837	−0.0605934
$526$	12.7333	0.555197
$527$	3.97814	0.173291
$528$	0.248209	0.0108019
$529$	−8.63033	−0.375232
$530$	−17.0885	−0.742278
$531$	44.4669	1.92970
$532$	1.72763	0.0749023
$533$	3.56051	0.154223
$534$	−0.950775	−0.0411440
$535$	−24.7232	−1.06888
$536$	−6.38996	−0.276004
$537$	−29.8541	−1.28830
$538$	4.23603	0.182628
$539$	0.576134	0.0248158
$540$	14.7763	0.635869
$541$	35.8167	1.53988	0.769939	−	0.638117i	$-0.220287\pi$
$541$	35.8167	1.53988	0.769939	+	0.638117i	$0.220287\pi$
$542$	29.2995	1.25852
$543$	−51.3347	−2.20298
$544$	−3.97814	−0.170562
$545$	−38.2331	−1.63773
$546$	0.542225	0.0232051
$547$	−27.2147	−1.16362	−0.581808	−	0.813326i	$-0.697654\pi$
$547$	−27.2147	−1.16362	−0.581808	+	0.813326i	$0.697654\pi$
$548$	14.9196	0.637334
$549$	−55.0052	−2.34756
$550$	−0.0862421	−0.00367737
$551$	0.635246	0.0270624
$552$	−11.0738	−0.471331
$553$	−0.792482	−0.0336998
$554$	3.64054	0.154672
$555$	42.1972	1.79117
$556$	3.43811	0.145808
$557$	15.0839	0.639125	0.319562	−	0.947565i	$-0.396464\pi$
$557$	15.0839	0.639125	0.319562	+	0.947565i	$0.396464\pi$
$558$	−5.53384	−0.234266
$559$	−0.605934	−0.0256283
$560$	0.934698	0.0394982
$561$	0.987410	0.0416885
$562$	17.3694	0.732685
$563$	−2.37625	−0.100147	−0.0500736	−	0.998746i	$-0.515946\pi$
$563$	−2.37625	−0.100147	−0.0500736	+	0.998746i	$0.515946\pi$
$564$	−18.0768	−0.761169
$565$	15.3584	0.646134
$566$	−16.9746	−0.713494
$567$	−2.35138	−0.0987487
$568$	−9.62209	−0.403734
$569$	−5.45044	−0.228494	−0.114247	−	0.993452i	$-0.536446\pi$
$569$	−5.45044	−0.228494	−0.114247	+	0.993452i	$0.536446\pi$
$570$	21.5168	0.901241
$571$	−21.9619	−0.919075	−0.459538	−	0.888158i	$-0.651985\pi$
$571$	−21.9619	−0.919075	−0.459538	+	0.888158i	$0.651985\pi$
$572$	0.0336817	0.00140830
$573$	−56.4518	−2.35831
$574$	−4.20554	−0.175536
$575$	3.84767	0.160459
$576$	5.53384	0.230577
$577$	1.93450	0.0805343	0.0402672	−	0.999189i	$-0.487179\pi$
$577$	1.93450	0.0805343	0.0402672	+	0.999189i	$0.487179\pi$
$578$	1.17437	0.0488473
$579$	39.8493	1.65608
$580$	0.343686	0.0142708
$581$	−7.28988	−0.302435
$582$	2.92127	0.121091
$583$	0.727338	0.0301233
$584$	5.35742	0.221692
$585$	4.37914	0.181055
$586$	10.2074	0.421663
$587$	42.3287	1.74709	0.873547	−	0.486740i	$-0.161814\pi$
$587$	42.3287	1.74709	0.873547	+	0.486740i	$0.161814\pi$
$588$	19.8085	0.816887
$589$	−3.68972	−0.152032
$590$	16.0407	0.660385
$591$	−40.7374	−1.67571
$592$	7.23600	0.297398
$593$	22.0936	0.907276	0.453638	−	0.891186i	$-0.350126\pi$
$593$	22.0936	0.907276	0.453638	+	0.891186i	$0.350126\pi$
$594$	−0.628921	−0.0258049
$595$	3.71836	0.152438
$596$	7.66609	0.314015
$597$	−1.58910	−0.0650377
$598$	−1.50270	−0.0614500
$599$	−17.3410	−0.708534	−0.354267	−	0.935144i	$-0.615270\pi$
$599$	−17.3410	−0.708534	−0.354267	+	0.935144i	$0.615270\pi$
$600$	−2.96515	−0.121052
$601$	11.2720	0.459793	0.229897	−	0.973215i	$-0.426161\pi$
$601$	11.2720	0.459793	0.229897	+	0.973215i	$0.426161\pi$
$602$	0.715706	0.0291700
$603$	35.3610	1.44001
$604$	−1.79104	−0.0728765
$605$	21.9442	0.892161
$606$	13.3191	0.541053
$607$	−13.2615	−0.538266	−0.269133	−	0.963103i	$-0.586737\pi$
$607$	−13.2615	−0.538266	−0.269133	+	0.963103i	$0.586737\pi$
$608$	3.68972	0.149638
$609$	−0.235494	−0.00954268
$610$	−19.8422	−0.803388
$611$	−2.45300	−0.0992378
$612$	22.0144	0.889880
$613$	−5.91746	−0.239004	−0.119502	−	0.992834i	$-0.538130\pi$
$613$	−5.91746	−0.239004	−0.119502	+	0.992834i	$0.538130\pi$
$614$	−5.64876	−0.227966
$615$	−52.3780	−2.11209
$616$	−0.0397835	−0.00160292
$617$	29.9097	1.20412	0.602059	−	0.798452i	$-0.294347\pi$
$617$	29.9097	1.20412	0.602059	+	0.798452i	$0.294347\pi$
$618$	−19.6406	−0.790061
$619$	−6.73659	−0.270766	−0.135383	−	0.990793i	$-0.543227\pi$
$619$	−6.73659	−0.270766	−0.135383	+	0.990793i	$0.543227\pi$
$620$	−1.99624	−0.0801710
$621$	28.0592	1.12598
$622$	23.1664	0.928888
$623$	0.152392	0.00610547
$624$	1.15803	0.0463584
$625$	−18.8946	−0.755786
$626$	−5.75552	−0.230037
$627$	−0.915820	−0.0365743
$628$	8.43250	0.336494
$629$	28.7858	1.14777
$630$	−5.17247	−0.206076
$631$	−1.06323	−0.0423266	−0.0211633	−	0.999776i	$-0.506737\pi$
$631$	−1.06323	−0.0423266	−0.0211633	+	0.999776i	$0.506737\pi$
$632$	−1.69251	−0.0673244
$633$	−63.8462	−2.53766
$634$	24.5769	0.976075
$635$	−0.540354	−0.0214433
$636$	25.0071	0.991596
$637$	2.68799	0.106502
$638$	−0.0146283	−0.000579140 0
$639$	53.2471	2.10642
$640$	1.99624	0.0789084
$641$	26.2560	1.03705	0.518525	−	0.855063i	$-0.326481\pi$
$641$	26.2560	1.03705	0.518525	+	0.855063i	$0.326481\pi$
$642$	36.1796	1.42789
$643$	27.2158	1.07329	0.536643	−	0.843809i	$-0.319692\pi$
$643$	27.2158	1.07329	0.536643	+	0.843809i	$0.319692\pi$
$644$	1.77493	0.0699421
$645$	8.91378	0.350980
$646$	14.6782	0.577507
$647$	−14.4520	−0.568165	−0.284082	−	0.958800i	$-0.591689\pi$
$647$	−14.4520	−0.568165	−0.284082	+	0.958800i	$0.591689\pi$
$648$	−5.02186	−0.197277
$649$	−0.682740	−0.0267999
$650$	−0.402368	−0.0157822
$651$	1.36782	0.0536093
$652$	10.2132	0.399979
$653$	−19.9226	−0.779634	−0.389817	−	0.920892i	$-0.627462\pi$
$653$	−19.9226	−0.779634	−0.389817	+	0.920892i	$0.627462\pi$
$654$	55.9498	2.18781
$655$	7.71941	0.301622
$656$	−8.98181	−0.350681
$657$	−29.6471	−1.15664
$658$	2.89739	0.112952
$659$	−23.6160	−0.919949	−0.459974	−	0.887932i	$-0.652141\pi$
$659$	−23.6160	−0.919949	−0.459974	+	0.887932i	$0.652141\pi$
$660$	−0.495485	−0.0192867
$661$	−26.3228	−1.02384	−0.511919	−	0.859034i	$-0.671065\pi$
$661$	−26.3228	−1.02384	−0.511919	+	0.859034i	$0.671065\pi$
$662$	−6.61568	−0.257126
$663$	4.60682	0.178914
$664$	−15.5691	−0.604196
$665$	−3.44877	−0.133738
$666$	−40.0428	−1.55163
$667$	0.652638	0.0252702
$668$	−7.31129	−0.282882
$669$	32.1715	1.24382
$670$	12.7559	0.492803
$671$	0.844544	0.0326032
$672$	−1.36782	−0.0527650
$673$	−6.53181	−0.251783	−0.125891	−	0.992044i	$-0.540179\pi$
$673$	−6.53181	−0.251783	−0.125891	+	0.992044i	$0.540179\pi$
$674$	−25.3359	−0.975903
$675$	7.51321	0.289184
$676$	−12.8429	−0.493956
$677$	32.5912	1.25258	0.626291	−	0.779590i	$-0.284572\pi$
$677$	32.5912	1.25258	0.626291	+	0.779590i	$0.284572\pi$
$678$	−22.4753	−0.863160
$679$	−0.468229	−0.0179690
$680$	7.94134	0.304536
$681$	43.0526	1.64978
$682$	0.0849659	0.00325351
$683$	8.72032	0.333674	0.166837	−	0.985985i	$-0.446645\pi$
$683$	8.72032	0.333674	0.166837	+	0.985985i	$0.446645\pi$
$684$	−20.4183	−0.780713
$685$	−29.7831	−1.13795
$686$	−6.45255	−0.246360
$687$	60.5752	2.31109
$688$	1.52854	0.0582750
$689$	3.39344	0.129280
$690$	22.1059	0.841558
$691$	−46.3005	−1.76136	−0.880678	−	0.473716i	$-0.842912\pi$
$691$	−46.3005	−1.76136	−0.880678	+	0.473716i	$0.842912\pi$
$692$	−4.44011	−0.168787
$693$	0.220156	0.00836302
$694$	−27.8465	−1.05704
$695$	−6.86330	−0.260340
$696$	−0.502946	−0.0190641
$697$	−35.7309	−1.35341
$698$	−11.7825	−0.445973
$699$	−7.09421	−0.268328
$700$	0.475261	0.0179632
$701$	−38.9691	−1.47184	−0.735922	−	0.677066i	$-0.763251\pi$
$701$	−38.9691	−1.47184	−0.735922	+	0.677066i	$0.763251\pi$
$702$	−2.93427	−0.110747
$703$	−26.6988	−1.00696
$704$	−0.0849659	−0.00320227
$705$	36.0856	1.35906
$706$	−26.9008	−1.01242
$707$	−2.13482	−0.0802883
$708$	−23.4738	−0.882198
$709$	27.4755	1.03187	0.515933	−	0.856629i	$-0.327445\pi$
$709$	27.4755	1.03187	0.515933	+	0.856629i	$0.327445\pi$
$710$	19.2080	0.720864
$711$	9.36608	0.351255
$712$	0.325466	0.0121973
$713$	−3.79073	−0.141964
$714$	−5.44140	−0.203639
$715$	−0.0672368	−0.00251451
$716$	10.2195	0.381922
$717$	20.4722	0.764549
$718$	−11.1578	−0.416404
$719$	−8.49354	−0.316756	−0.158378	−	0.987379i	$-0.550626\pi$
$719$	−8.49354	−0.316756	−0.158378	+	0.987379i	$0.550626\pi$
$720$	−11.0469	−0.411693
$721$	3.14804	0.117239
$722$	5.38599	0.200446
$723$	79.2493	2.94731
$724$	17.5727	0.653084
$725$	0.174752	0.00649014
$726$	−32.1129	−1.19182
$727$	−11.8032	−0.437756	−0.218878	−	0.975752i	$-0.570240\pi$
$727$	−11.8032	−0.437756	−0.218878	+	0.975752i	$0.570240\pi$
$728$	−0.185612	−0.00687925
$729$	−37.0800	−1.37333
$730$	−10.6947	−0.395829
$731$	6.08075	0.224905
$732$	29.0368	1.07323
$733$	−29.0763	−1.07396	−0.536979	−	0.843596i	$-0.680434\pi$
$733$	−29.0763	−1.07396	−0.536979	+	0.843596i	$0.680434\pi$
$734$	−20.2667	−0.748057
$735$	−39.5425	−1.45855
$736$	3.79073	0.139728
$737$	−0.542929	−0.0199990
$738$	49.7039	1.82962
$739$	28.8934	1.06286	0.531431	−	0.847102i	$-0.321654\pi$
$739$	28.8934	1.06286	0.531431	+	0.847102i	$0.321654\pi$
$740$	−14.4448	−0.531001
$741$	−4.27282	−0.156966
$742$	−4.00820	−0.147146
$743$	29.3208	1.07568	0.537838	−	0.843048i	$-0.319241\pi$
$743$	29.3208	1.07568	0.537838	+	0.843048i	$0.319241\pi$
$744$	2.92127	0.107099
$745$	−15.3034	−0.560672
$746$	−3.98873	−0.146038
$747$	86.1566	3.15231
$748$	−0.338007	−0.0123588
$749$	−5.79895	−0.211889
$750$	35.0770	1.28083
$751$	12.8675	0.469542	0.234771	−	0.972051i	$-0.424566\pi$
$751$	12.8675	0.469542	0.234771	+	0.972051i	$0.424566\pi$
$752$	6.18798	0.225652
$753$	−15.3433	−0.559139
$754$	−0.0682492	−0.00248549
$755$	3.57535	0.130120
$756$	3.46585	0.126052
$757$	−17.4847	−0.635492	−0.317746	−	0.948176i	$-0.602926\pi$
$757$	−17.4847	−0.635492	−0.317746	+	0.948176i	$0.602926\pi$
$758$	19.3272	0.701995
$759$	−0.940894	−0.0341523
$760$	−7.36557	−0.267177
$761$	26.0632	0.944791	0.472395	−	0.881387i	$-0.343389\pi$
$761$	26.0632	0.944791	0.472395	+	0.881387i	$0.343389\pi$
$762$	0.790747	0.0286458
$763$	−8.96777	−0.324655
$764$	19.3244	0.699131
$765$	−43.9461	−1.58887
$766$	−16.0305	−0.579206
$767$	−3.18536	−0.115017
$768$	−2.92127	−0.105412
$769$	−31.5119	−1.13635	−0.568175	−	0.822908i	$-0.692350\pi$
$769$	−31.5119	−1.13635	−0.568175	+	0.822908i	$0.692350\pi$
$770$	0.0794175	0.00286201
$771$	−48.6154	−1.75084
$772$	−13.6411	−0.490953
$773$	20.2957	0.729987	0.364993	−	0.931010i	$-0.381071\pi$
$773$	20.2957	0.729987	0.364993	+	0.931010i	$0.381071\pi$
$774$	−8.45869	−0.304041
$775$	−1.01502	−0.0364606
$776$	−1.00000	−0.0358979
$777$	9.89757	0.355073
$778$	25.3891	0.910242
$779$	33.1403	1.18738
$780$	−2.31171	−0.0827727
$781$	−0.817550	−0.0292543
$782$	15.0801	0.539263
$783$	1.27438	0.0455427
$784$	−6.78076	−0.242170
$785$	−16.8333	−0.600807
$786$	−11.2965	−0.402932
$787$	−29.4188	−1.04867	−0.524334	−	0.851513i	$-0.675686\pi$
$787$	−29.4188	−1.04867	−0.524334	+	0.851513i	$0.675686\pi$
$788$	13.9451	0.496773
$789$	37.1974	1.32426
$790$	3.37866	0.120207
$791$	3.60240	0.128087
$792$	0.470188	0.0167074
$793$	3.94027	0.139923
$794$	−15.4473	−0.548206
$795$	−49.9202	−1.77049
$796$	0.543977	0.0192807
$797$	−28.9104	−1.02406	−0.512029	−	0.858968i	$-0.671106\pi$
$797$	−28.9104	−1.02406	−0.512029	+	0.858968i	$0.671106\pi$
$798$	5.04689	0.178658
$799$	24.6167	0.870875
$800$	1.01502	0.0358863
$801$	−1.80108	−0.0636379
$802$	9.29739	0.328302
$803$	0.455198	0.0160636
$804$	−18.6668	−0.658328
$805$	−3.54319	−0.124881
$806$	0.396414	0.0139631
$807$	12.3746	0.435607
$808$	−4.55936	−0.160398
$809$	4.59685	0.161617	0.0808083	−	0.996730i	$-0.474250\pi$
$809$	4.59685	0.161617	0.0808083	+	0.996730i	$0.474250\pi$
$810$	10.0248	0.352237
$811$	−18.7328	−0.657797	−0.328898	−	0.944365i	$-0.606677\pi$
$811$	−18.7328	−0.657797	−0.328898	+	0.944365i	$0.606677\pi$
$812$	0.0806133	0.00282897
$813$	85.5917	3.00183
$814$	0.614813	0.0215492
$815$	−20.3880	−0.714160
$816$	−11.6212	−0.406825
$817$	−5.63988	−0.197314
$818$	−23.4727	−0.820705
$819$	1.02715	0.0358915
$820$	17.9299	0.626138
$821$	3.82725	0.133572	0.0667860	−	0.997767i	$-0.478726\pi$
$821$	3.82725	0.133572	0.0667860	+	0.997767i	$0.478726\pi$
$822$	43.5842	1.52017
$823$	37.0023	1.28982	0.644910	−	0.764259i	$-0.276895\pi$
$823$	37.0023	1.28982	0.644910	+	0.764259i	$0.276895\pi$
$824$	6.72330	0.234217
$825$	−0.251937	−0.00877131
$826$	3.76243	0.130912
$827$	−13.0629	−0.454243	−0.227121	−	0.973866i	$-0.572931\pi$
$827$	−13.0629	−0.454243	−0.227121	+	0.973866i	$0.572931\pi$
$828$	−20.9773	−0.729012
$829$	6.21879	0.215987	0.107994	−	0.994152i	$-0.465557\pi$
$829$	6.21879	0.215987	0.107994	+	0.994152i	$0.465557\pi$
$830$	31.0796	1.07879
$831$	10.6350	0.368924
$832$	−0.396414	−0.0137432
$833$	−26.9748	−0.934623
$834$	10.0437	0.347784
$835$	14.5951	0.505084
$836$	0.313500	0.0108426
$837$	−7.40204	−0.255852
$838$	21.7775	0.752291
$839$	−1.43443	−0.0495221	−0.0247611	−	0.999693i	$-0.507882\pi$
$839$	−1.43443	−0.0495221	−0.0247611	+	0.999693i	$0.507882\pi$
$840$	2.73051	0.0942115
$841$	−28.9704	−0.998978
$842$	20.3011	0.699622
$843$	50.7408	1.74761
$844$	21.8556	0.752301
$845$	25.6374	0.881955
$846$	−34.2433	−1.17731
$847$	5.14714	0.176858
$848$	−8.56035	−0.293963
$849$	−49.5874	−1.70183
$850$	4.03789	0.138499
$851$	−27.4297	−0.940279
$852$	−28.1088	−0.962991
$853$	−56.1716	−1.92328	−0.961640	−	0.274314i	$-0.911549\pi$
$853$	−56.1716	−1.92328	−0.961640	+	0.274314i	$0.911549\pi$
$854$	−4.65410	−0.159260
$855$	40.7599	1.39396
$856$	−12.3849	−0.423306
$857$	40.5459	1.38502	0.692511	−	0.721408i	$-0.256505\pi$
$857$	40.5459	1.38502	0.692511	+	0.721408i	$0.256505\pi$
$858$	0.0983934	0.00335910
$859$	−33.3359	−1.13741	−0.568703	−	0.822543i	$-0.692555\pi$
$859$	−33.3359	−1.13741	−0.568703	+	0.822543i	$0.692555\pi$
$860$	−3.05133	−0.104050
$861$	−12.2855	−0.418690
$862$	−17.0570	−0.580964
$863$	24.2134	0.824232	0.412116	−	0.911131i	$-0.364790\pi$
$863$	24.2134	0.824232	0.412116	+	0.911131i	$0.364790\pi$
$864$	7.40204	0.251822
$865$	8.86352	0.301369
$866$	34.1333	1.15990
$867$	3.43065	0.116511
$868$	−0.468229	−0.0158927
$869$	−0.143806	−0.00487827
$870$	1.00400	0.0340388
$871$	−2.53307	−0.0858298
$872$	−19.1525	−0.648587
$873$	5.53384	0.187292
$874$	−13.9867	−0.473108
$875$	−5.62223	−0.190066
$876$	15.6505	0.528781
$877$	−49.3255	−1.66560	−0.832801	−	0.553572i	$-0.813264\pi$
$877$	−49.3255	−1.66560	−0.832801	+	0.553572i	$0.813264\pi$
$878$	34.8188	1.17508
$879$	29.8185	1.00575
$880$	0.169613	0.00571764
$881$	−30.2194	−1.01812	−0.509058	−	0.860732i	$-0.670006\pi$
$881$	−30.2194	−1.01812	−0.509058	+	0.860732i	$0.670006\pi$
$882$	37.5236	1.26349
$883$	−36.4417	−1.22636	−0.613181	−	0.789943i	$-0.710110\pi$
$883$	−36.4417	−1.22636	−0.613181	+	0.789943i	$0.710110\pi$
$884$	−1.57699	−0.0530400
$885$	46.8593	1.57516
$886$	−24.9406	−0.837895
$887$	33.8620	1.13698	0.568488	−	0.822692i	$-0.307529\pi$
$887$	33.8620	1.13698	0.568488	+	0.822692i	$0.307529\pi$
$888$	21.1383	0.709356
$889$	−0.126743	−0.00425082
$890$	−0.649708	−0.0217783
$891$	−0.426687	−0.0142946
$892$	−11.0128	−0.368737
$893$	−22.8319	−0.764040
$894$	22.3947	0.748992
$895$	−20.4007	−0.681919
$896$	0.468229	0.0156424
$897$	−4.38980	−0.146571
$898$	5.36337	0.178978
$899$	−0.172167	−0.00574208
$900$	−5.61695	−0.187232
$901$	−34.0543	−1.13451
$902$	−0.763148	−0.0254100
$903$	2.09077	0.0695766
$904$	7.69368	0.255888
$905$	−35.0794	−1.16608
$906$	−5.23212	−0.173826
$907$	5.74377	0.190719	0.0953594	−	0.995443i	$-0.469600\pi$
$907$	5.74377	0.190719	0.0953594	+	0.995443i	$0.469600\pi$
$908$	−14.7376	−0.489085
$909$	25.2308	0.836851
$910$	0.370527	0.0122829
$911$	38.5064	1.27577	0.637887	−	0.770130i	$-0.279809\pi$
$911$	38.5064	1.27577	0.637887	+	0.770130i	$0.279809\pi$
$912$	10.7787	0.356918
$913$	−1.32284	−0.0437796
$914$	7.93729	0.262542
$915$	−57.9646	−1.91625
$916$	−20.7359	−0.685133
$917$	1.81063	0.0597922
$918$	29.4464	0.971875
$919$	20.5788	0.678832	0.339416	−	0.940636i	$-0.389771\pi$
$919$	20.5788	0.678832	0.339416	+	0.940636i	$0.389771\pi$
$920$	−7.56722	−0.249484
$921$	−16.5016	−0.543746
$922$	28.1909	0.928418
$923$	−3.81433	−0.125550
$924$	−0.116219	−0.00382331
$925$	−7.34467	−0.241491
$926$	23.2480	0.763976
$927$	−37.2057	−1.22199
$928$	0.172167	0.00565164
$929$	27.2030	0.892500	0.446250	−	0.894908i	$-0.352759\pi$
$929$	27.2030	0.892500	0.446250	+	0.894908i	$0.352759\pi$
$930$	−5.83157	−0.191225
$931$	25.0191	0.819968
$932$	2.42846	0.0795470
$933$	67.6754	2.21559
$934$	26.4583	0.865744
$935$	0.674743	0.0220665
$936$	2.19369	0.0717030
$937$	45.2494	1.47823	0.739116	−	0.673578i	$-0.235243\pi$
$937$	45.2494	1.47823	0.739116	+	0.673578i	$0.235243\pi$
$938$	2.99196	0.0976910
$939$	−16.8134	−0.548686
$940$	−12.3527	−0.402901
$941$	38.6705	1.26062	0.630312	−	0.776342i	$-0.282927\pi$
$941$	38.6705	1.26062	0.630312	+	0.776342i	$0.282927\pi$
$942$	24.6337	0.802608
$943$	34.0476	1.10874
$944$	8.03545	0.261532
$945$	−6.91867	−0.225064
$946$	0.129874	0.00422256
$947$	16.7083	0.542947	0.271473	−	0.962446i	$-0.412489\pi$
$947$	16.7083	0.542947	0.271473	+	0.962446i	$0.412489\pi$
$948$	−4.94428	−0.160583
$949$	2.12376	0.0689401
$950$	−3.74513	−0.121508
$951$	71.7960	2.32814
$952$	1.86268	0.0603699
$953$	−35.3231	−1.14423	−0.572113	−	0.820175i	$-0.693876\pi$
$953$	−35.3231	−1.14423	−0.572113	+	0.820175i	$0.693876\pi$
$954$	47.3716	1.53371
$955$	−38.5761	−1.24829
$956$	−7.00797	−0.226654
$957$	−0.0427332	−0.00138137
$958$	−5.69701	−0.184062
$959$	−6.98578	−0.225583
$960$	5.83157	0.188213
$961$	1.00000	0.0322581
$962$	2.86845	0.0924825
$963$	68.5358	2.20854
$964$	−27.1283	−0.873745
$965$	27.2309	0.876593
$966$	5.18506	0.166827
$967$	35.2306	1.13294	0.566469	−	0.824083i	$-0.308309\pi$
$967$	35.2306	1.13294	0.566469	+	0.824083i	$0.308309\pi$
$968$	10.9928	0.353321
$969$	42.8791	1.37748
$970$	1.99624	0.0640955
$971$	−15.8072	−0.507279	−0.253639	−	0.967299i	$-0.581628\pi$
$971$	−15.8072	−0.507279	−0.253639	+	0.967299i	$0.581628\pi$
$972$	7.53589	0.241714
$973$	−1.60982	−0.0516086
$974$	39.5339	1.26675
$975$	−1.17543	−0.0376438
$976$	−9.93979	−0.318165
$977$	−3.47503	−0.111176	−0.0555881	−	0.998454i	$-0.517703\pi$
$977$	−3.47503	−0.111176	−0.0555881	+	0.998454i	$0.517703\pi$
$978$	29.8355	0.954035
$979$	0.0276535	0.000883810 0
$980$	13.5360	0.432393
$981$	105.987	3.38391
$982$	29.1963	0.931691
$983$	−10.9288	−0.348575	−0.174288	−	0.984695i	$-0.555762\pi$
$983$	−10.9288	−0.348575	−0.174288	+	0.984695i	$0.555762\pi$
$984$	−26.2383	−0.836447
$985$	−27.8378	−0.886985
$986$	0.684903	0.0218118
$987$	8.46407	0.269414
$988$	1.46266	0.0465333
$989$	−5.79428	−0.184248
$990$	−0.938609	−0.0298309
$991$	51.9909	1.65155	0.825773	−	0.564003i	$-0.190739\pi$
$991$	51.9909	1.65155	0.825773	+	0.564003i	$0.190739\pi$
$992$	−1.00000	−0.0317500
$993$	−19.3262	−0.613299
$994$	4.50534	0.142901
$995$	−1.08591	−0.0344256
$996$	−45.4815	−1.44114
$997$	3.04816	0.0965362	0.0482681	−	0.998834i	$-0.484630\pi$
$997$	3.04816	0.0965362	0.0482681	+	0.998834i	$0.484630\pi$
$998$	20.6060	0.652273
$999$	−53.5611	−1.69460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.1	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.1	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.92127 q^{3} +1.00000 q^{4} -1.99624 q^{5} +2.92127 q^{6} -0.468229 q^{7} -1.00000 q^{8} +5.53384 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.92127 q^{3} +1.00000 q^{4} -1.99624 q^{5} +2.92127 q^{6} -0.468229 q^{7} -1.00000 q^{8} +5.53384 q^{9} +1.99624 q^{10} -0.0849659 q^{11} -2.92127 q^{12} -0.396414 q^{13} +0.468229 q^{14} +5.83157 q^{15} +1.00000 q^{16} +3.97814 q^{17} -5.53384 q^{18} -3.68972 q^{19} -1.99624 q^{20} +1.36782 q^{21} +0.0849659 q^{22} -3.79073 q^{23} +2.92127 q^{24} -1.01502 q^{25} +0.396414 q^{26} -7.40204 q^{27} -0.468229 q^{28} -0.172167 q^{29} -5.83157 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.248209 q^{33} -3.97814 q^{34} +0.934698 q^{35} +5.53384 q^{36} +7.23600 q^{37} +3.68972 q^{38} +1.15803 q^{39} +1.99624 q^{40} -8.98181 q^{41} -1.36782 q^{42} +1.52854 q^{43} -0.0849659 q^{44} -11.0469 q^{45} +3.79073 q^{46} +6.18798 q^{47} -2.92127 q^{48} -6.78076 q^{49} +1.01502 q^{50} -11.6212 q^{51} -0.396414 q^{52} -8.56035 q^{53} +7.40204 q^{54} +0.169613 q^{55} +0.468229 q^{56} +10.7787 q^{57} +0.172167 q^{58} +8.03545 q^{59} +5.83157 q^{60} -9.93979 q^{61} -1.00000 q^{62} -2.59110 q^{63} +1.00000 q^{64} +0.791338 q^{65} -0.248209 q^{66} +6.38996 q^{67} +3.97814 q^{68} +11.0738 q^{69} -0.934698 q^{70} +9.62209 q^{71} -5.53384 q^{72} -5.35742 q^{73} -7.23600 q^{74} +2.96515 q^{75} -3.68972 q^{76} +0.0397835 q^{77} -1.15803 q^{78} +1.69251 q^{79} -1.99624 q^{80} +5.02186 q^{81} +8.98181 q^{82} +15.5691 q^{83} +1.36782 q^{84} -7.94134 q^{85} -1.52854 q^{86} +0.502946 q^{87} +0.0849659 q^{88} -0.325466 q^{89} +11.0469 q^{90} +0.185612 q^{91} -3.79073 q^{92} -2.92127 q^{93} -6.18798 q^{94} +7.36557 q^{95} +2.92127 q^{96} +1.00000 q^{97} +6.78076 q^{98} -0.470188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more