LMFDB - Embedded newform 5054.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} +0.236068 q^{5} -2.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} +0.236068 q^{5} -2.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +3.85410 q^{9} -0.236068 q^{10} +3.00000 q^{11} +2.61803 q^{12} +2.85410 q^{13} +1.00000 q^{14} +0.618034 q^{15} +1.00000 q^{16} -4.85410 q^{17} -3.85410 q^{18} +0.236068 q^{20} -2.61803 q^{21} -3.00000 q^{22} +6.70820 q^{23} -2.61803 q^{24} -4.94427 q^{25} -2.85410 q^{26} +2.23607 q^{27} -1.00000 q^{28} -3.76393 q^{29} -0.618034 q^{30} +5.00000 q^{31} -1.00000 q^{32} +7.85410 q^{33} +4.85410 q^{34} -0.236068 q^{35} +3.85410 q^{36} -5.00000 q^{37} +7.47214 q^{39} -0.236068 q^{40} +7.09017 q^{41} +2.61803 q^{42} +8.56231 q^{43} +3.00000 q^{44} +0.909830 q^{45} -6.70820 q^{46} -1.76393 q^{47} +2.61803 q^{48} +1.00000 q^{49} +4.94427 q^{50} -12.7082 q^{51} +2.85410 q^{52} +0.708204 q^{53} -2.23607 q^{54} +0.708204 q^{55} +1.00000 q^{56} +3.76393 q^{58} +5.76393 q^{59} +0.618034 q^{60} +6.70820 q^{61} -5.00000 q^{62} -3.85410 q^{63} +1.00000 q^{64} +0.673762 q^{65} -7.85410 q^{66} +15.5623 q^{67} -4.85410 q^{68} +17.5623 q^{69} +0.236068 q^{70} +12.4721 q^{71} -3.85410 q^{72} +2.09017 q^{73} +5.00000 q^{74} -12.9443 q^{75} -3.00000 q^{77} -7.47214 q^{78} +16.8541 q^{79} +0.236068 q^{80} -5.70820 q^{81} -7.09017 q^{82} +2.47214 q^{83} -2.61803 q^{84} -1.14590 q^{85} -8.56231 q^{86} -9.85410 q^{87} -3.00000 q^{88} -3.61803 q^{89} -0.909830 q^{90} -2.85410 q^{91} +6.70820 q^{92} +13.0902 q^{93} +1.76393 q^{94} -2.61803 q^{96} -18.7082 q^{97} -1.00000 q^{98} +11.5623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 4 q^{5} - 3 q^{6} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 4 * q^5 - 3 * q^6 - 2 * q^7 - 2 * q^8 + q^9	$ 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 4 q^{5} - 3 q^{6} - 2 q^{7} - 2 q^{8} + q^{9} + 4 q^{10} + 6 q^{11} + 3 q^{12} - q^{13} + 2 q^{14} - q^{15} + 2 q^{16} - 3 q^{17} - q^{18} - 4 q^{20} - 3 q^{21} - 6 q^{22} - 3 q^{24} + 8 q^{25} + q^{26} - 2 q^{28} - 12 q^{29} + q^{30} + 10 q^{31} - 2 q^{32} + 9 q^{33} + 3 q^{34} + 4 q^{35} + q^{36} - 10 q^{37} + 6 q^{39} + 4 q^{40} + 3 q^{41} + 3 q^{42} - 3 q^{43} + 6 q^{44} + 13 q^{45} - 8 q^{47} + 3 q^{48} + 2 q^{49} - 8 q^{50} - 12 q^{51} - q^{52} - 12 q^{53} - 12 q^{55} + 2 q^{56} + 12 q^{58} + 16 q^{59} - q^{60} - 10 q^{62} - q^{63} + 2 q^{64} + 17 q^{65} - 9 q^{66} + 11 q^{67} - 3 q^{68} + 15 q^{69} - 4 q^{70} + 16 q^{71} - q^{72} - 7 q^{73} + 10 q^{74} - 8 q^{75} - 6 q^{77} - 6 q^{78} + 27 q^{79} - 4 q^{80} + 2 q^{81} - 3 q^{82} - 4 q^{83} - 3 q^{84} - 9 q^{85} + 3 q^{86} - 13 q^{87} - 6 q^{88} - 5 q^{89} - 13 q^{90} + q^{91} + 15 q^{93} + 8 q^{94} - 3 q^{96} - 24 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 4 * q^5 - 3 * q^6 - 2 * q^7 - 2 * q^8 + q^9 + 4 * q^10 + 6 * q^11 + 3 * q^12 - q^13 + 2 * q^14 - q^15 + 2 * q^16 - 3 * q^17 - q^18 - 4 * q^20 - 3 * q^21 - 6 * q^22 - 3 * q^24 + 8 * q^25 + q^26 - 2 * q^28 - 12 * q^29 + q^30 + 10 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 + 4 * q^35 + q^36 - 10 * q^37 + 6 * q^39 + 4 * q^40 + 3 * q^41 + 3 * q^42 - 3 * q^43 + 6 * q^44 + 13 * q^45 - 8 * q^47 + 3 * q^48 + 2 * q^49 - 8 * q^50 - 12 * q^51 - q^52 - 12 * q^53 - 12 * q^55 + 2 * q^56 + 12 * q^58 + 16 * q^59 - q^60 - 10 * q^62 - q^63 + 2 * q^64 + 17 * q^65 - 9 * q^66 + 11 * q^67 - 3 * q^68 + 15 * q^69 - 4 * q^70 + 16 * q^71 - q^72 - 7 * q^73 + 10 * q^74 - 8 * q^75 - 6 * q^77 - 6 * q^78 + 27 * q^79 - 4 * q^80 + 2 * q^81 - 3 * q^82 - 4 * q^83 - 3 * q^84 - 9 * q^85 + 3 * q^86 - 13 * q^87 - 6 * q^88 - 5 * q^89 - 13 * q^90 + q^91 + 15 * q^93 + 8 * q^94 - 3 * q^96 - 24 * q^97 - 2 * q^98 + 3 * 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
$3$	2.61803	1.51152	0.755761	−	0.654847i	$-0.227267\pi$
$3$	2.61803	1.51152	0.755761	+	0.654847i	$0.227267\pi$
$4$	1.00000	0.500000
$5$	0.236068	0.105573	0.0527864	−	0.998606i	$-0.483190\pi$
$5$	0.236068	0.105573	0.0527864	+	0.998606i	$0.483190\pi$
$6$	−2.61803	−1.06881
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	3.85410	1.28470
$10$	−0.236068	−0.0746512
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	2.61803	0.755761
$13$	2.85410	0.791585	0.395793	−	0.918340i	$-0.370470\pi$
$13$	2.85410	0.791585	0.395793	+	0.918340i	$0.370470\pi$
$14$	1.00000	0.267261
$15$	0.618034	0.159576
$16$	1.00000	0.250000
$17$	−4.85410	−1.17729	−0.588646	−	0.808391i	$-0.700339\pi$
$17$	−4.85410	−1.17729	−0.588646	+	0.808391i	$0.700339\pi$
$18$	−3.85410	−0.908421
$19$	0	0
$19$	0	0
$20$	0.236068	0.0527864
$21$	−2.61803	−0.571302
$22$	−3.00000	−0.639602
$23$	6.70820	1.39876	0.699379	−	0.714751i	$-0.253460\pi$
$23$	6.70820	1.39876	0.699379	+	0.714751i	$0.253460\pi$
$24$	−2.61803	−0.534404
$25$	−4.94427	−0.988854
$26$	−2.85410	−0.559735
$27$	2.23607	0.430331
$28$	−1.00000	−0.188982
$29$	−3.76393	−0.698945	−0.349472	−	0.936947i	$-0.613639\pi$
$29$	−3.76393	−0.698945	−0.349472	+	0.936947i	$0.613639\pi$
$30$	−0.618034	−0.112837
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−1.00000	−0.176777
$33$	7.85410	1.36722
$34$	4.85410	0.832472
$35$	−0.236068	−0.0399028
$36$	3.85410	0.642350
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	0	0
$39$	7.47214	1.19650
$40$	−0.236068	−0.0373256
$41$	7.09017	1.10730	0.553649	−	0.832750i	$-0.313235\pi$
$41$	7.09017	1.10730	0.553649	+	0.832750i	$0.313235\pi$
$42$	2.61803	0.403971
$43$	8.56231	1.30574	0.652870	−	0.757470i	$-0.273565\pi$
$43$	8.56231	1.30574	0.652870	+	0.757470i	$0.273565\pi$
$44$	3.00000	0.452267
$45$	0.909830	0.135629
$46$	−6.70820	−0.989071
$47$	−1.76393	−0.257296	−0.128648	−	0.991690i	$-0.541064\pi$
$47$	−1.76393	−0.257296	−0.128648	+	0.991690i	$0.541064\pi$
$48$	2.61803	0.377881
$49$	1.00000	0.142857
$50$	4.94427	0.699226
$51$	−12.7082	−1.77950
$52$	2.85410	0.395793
$53$	0.708204	0.0972793	0.0486396	−	0.998816i	$-0.484511\pi$
$53$	0.708204	0.0972793	0.0486396	+	0.998816i	$0.484511\pi$
$54$	−2.23607	−0.304290
$55$	0.708204	0.0954942
$56$	1.00000	0.133631
$57$	0	0
$58$	3.76393	0.494228
$59$	5.76393	0.750400	0.375200	−	0.926944i	$-0.377574\pi$
$59$	5.76393	0.750400	0.375200	+	0.926944i	$0.377574\pi$
$60$	0.618034	0.0797878
$61$	6.70820	0.858898	0.429449	−	0.903091i	$-0.358708\pi$
$61$	6.70820	0.858898	0.429449	+	0.903091i	$0.358708\pi$
$62$	−5.00000	−0.635001
$63$	−3.85410	−0.485571
$64$	1.00000	0.125000
$65$	0.673762	0.0835699
$66$	−7.85410	−0.966773
$67$	15.5623	1.90124	0.950619	−	0.310360i	$-0.100450\pi$
$67$	15.5623	1.90124	0.950619	+	0.310360i	$0.100450\pi$
$68$	−4.85410	−0.588646
$69$	17.5623	2.11425
$70$	0.236068	0.0282155
$71$	12.4721	1.48017	0.740085	−	0.672513i	$-0.234785\pi$
$71$	12.4721	1.48017	0.740085	+	0.672513i	$0.234785\pi$
$72$	−3.85410	−0.454210
$73$	2.09017	0.244636	0.122318	−	0.992491i	$-0.460967\pi$
$73$	2.09017	0.244636	0.122318	+	0.992491i	$0.460967\pi$
$74$	5.00000	0.581238
$75$	−12.9443	−1.49468
$76$	0	0
$77$	−3.00000	−0.341882
$78$	−7.47214	−0.846053
$79$	16.8541	1.89623	0.948117	−	0.317921i	$-0.102985\pi$
$79$	16.8541	1.89623	0.948117	+	0.317921i	$0.102985\pi$
$80$	0.236068	0.0263932
$81$	−5.70820	−0.634245
$82$	−7.09017	−0.782978
$83$	2.47214	0.271352	0.135676	−	0.990753i	$-0.456679\pi$
$83$	2.47214	0.271352	0.135676	+	0.990753i	$0.456679\pi$
$84$	−2.61803	−0.285651
$85$	−1.14590	−0.124290
$86$	−8.56231	−0.923297
$87$	−9.85410	−1.05647
$88$	−3.00000	−0.319801
$89$	−3.61803	−0.383511	−0.191755	−	0.981443i	$-0.561418\pi$
$89$	−3.61803	−0.383511	−0.191755	+	0.981443i	$0.561418\pi$
$90$	−0.909830	−0.0959045
$91$	−2.85410	−0.299191
$92$	6.70820	0.699379
$93$	13.0902	1.35739
$94$	1.76393	0.181936
$95$	0	0
$96$	−2.61803	−0.267202
$97$	−18.7082	−1.89953	−0.949765	−	0.312963i	$-0.898678\pi$
$97$	−18.7082	−1.89953	−0.949765	+	0.312963i	$0.898678\pi$
$98$	−1.00000	−0.101015
$99$	11.5623	1.16206
$100$	−4.94427	−0.494427
$101$	3.09017	0.307483	0.153742	−	0.988111i	$-0.450868\pi$
$101$	3.09017	0.307483	0.153742	+	0.988111i	$0.450868\pi$
$102$	12.7082	1.25830
$103$	0.145898	0.0143758	0.00718788	−	0.999974i	$-0.497712\pi$
$103$	0.145898	0.0143758	0.00718788	+	0.999974i	$0.497712\pi$
$104$	−2.85410	−0.279868
$105$	−0.618034	−0.0603139
$106$	−0.708204	−0.0687868
$107$	−4.52786	−0.437725	−0.218863	−	0.975756i	$-0.570235\pi$
$107$	−4.52786	−0.437725	−0.218863	+	0.975756i	$0.570235\pi$
$108$	2.23607	0.215166
$109$	−1.85410	−0.177591	−0.0887954	−	0.996050i	$-0.528302\pi$
$109$	−1.85410	−0.177591	−0.0887954	+	0.996050i	$0.528302\pi$
$110$	−0.708204	−0.0675246
$111$	−13.0902	−1.24246
$112$	−1.00000	−0.0944911
$113$	−12.7984	−1.20397	−0.601985	−	0.798507i	$-0.705623\pi$
$113$	−12.7984	−1.20397	−0.601985	+	0.798507i	$0.705623\pi$
$114$	0	0
$115$	1.58359	0.147671
$116$	−3.76393	−0.349472
$117$	11.0000	1.01695
$118$	−5.76393	−0.530613
$119$	4.85410	0.444975
$120$	−0.618034	−0.0564185
$121$	−2.00000	−0.181818
$122$	−6.70820	−0.607332
$123$	18.5623	1.67371
$124$	5.00000	0.449013
$125$	−2.34752	−0.209969
$126$	3.85410	0.343351
$127$	−9.03444	−0.801677	−0.400839	−	0.916149i	$-0.631281\pi$
$127$	−9.03444	−0.801677	−0.400839	+	0.916149i	$0.631281\pi$
$128$	−1.00000	−0.0883883
$129$	22.4164	1.97365
$130$	−0.673762	−0.0590928
$131$	−5.61803	−0.490850	−0.245425	−	0.969416i	$-0.578927\pi$
$131$	−5.61803	−0.490850	−0.245425	+	0.969416i	$0.578927\pi$
$132$	7.85410	0.683612
$133$	0	0
$134$	−15.5623	−1.34438
$135$	0.527864	0.0454313
$136$	4.85410	0.416236
$137$	4.76393	0.407010	0.203505	−	0.979074i	$-0.434767\pi$
$137$	4.76393	0.407010	0.203505	+	0.979074i	$0.434767\pi$
$138$	−17.5623	−1.49500
$139$	19.0000	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$139$	19.0000	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$140$	−0.236068	−0.0199514
$141$	−4.61803	−0.388909
$142$	−12.4721	−1.04664
$143$	8.56231	0.716016
$144$	3.85410	0.321175
$145$	−0.888544	−0.0737895
$146$	−2.09017	−0.172984
$147$	2.61803	0.215932
$148$	−5.00000	−0.410997
$149$	−13.0902	−1.07239	−0.536194	−	0.844095i	$-0.680139\pi$
$149$	−13.0902	−1.07239	−0.536194	+	0.844095i	$0.680139\pi$
$150$	12.9443	1.05690
$151$	−4.23607	−0.344726	−0.172363	−	0.985033i	$-0.555140\pi$
$151$	−4.23607	−0.344726	−0.172363	+	0.985033i	$0.555140\pi$
$152$	0	0
$153$	−18.7082	−1.51247
$154$	3.00000	0.241747
$155$	1.18034	0.0948072
$156$	7.47214	0.598250
$157$	−12.6180	−1.00703	−0.503514	−	0.863987i	$-0.667960\pi$
$157$	−12.6180	−1.00703	−0.503514	+	0.863987i	$0.667960\pi$
$158$	−16.8541	−1.34084
$159$	1.85410	0.147040
$160$	−0.236068	−0.0186628
$161$	−6.70820	−0.528681
$162$	5.70820	0.448479
$163$	−12.4721	−0.976893	−0.488447	−	0.872594i	$-0.662436\pi$
$163$	−12.4721	−0.976893	−0.488447	+	0.872594i	$0.662436\pi$
$164$	7.09017	0.553649
$165$	1.85410	0.144342
$166$	−2.47214	−0.191875
$167$	17.2361	1.33377	0.666883	−	0.745162i	$-0.267628\pi$
$167$	17.2361	1.33377	0.666883	+	0.745162i	$0.267628\pi$
$168$	2.61803	0.201986
$169$	−4.85410	−0.373392
$170$	1.14590	0.0878864
$171$	0	0
$172$	8.56231	0.652870
$173$	22.4164	1.70429	0.852144	−	0.523307i	$-0.175302\pi$
$173$	22.4164	1.70429	0.852144	+	0.523307i	$0.175302\pi$
$174$	9.85410	0.747038
$175$	4.94427	0.373752
$176$	3.00000	0.226134
$177$	15.0902	1.13425
$178$	3.61803	0.271183
$179$	19.3262	1.44451	0.722255	−	0.691626i	$-0.243106\pi$
$179$	19.3262	1.44451	0.722255	+	0.691626i	$0.243106\pi$
$180$	0.909830	0.0678147
$181$	−1.94427	−0.144517	−0.0722583	−	0.997386i	$-0.523021\pi$
$181$	−1.94427	−0.144517	−0.0722583	+	0.997386i	$0.523021\pi$
$182$	2.85410	0.211560
$183$	17.5623	1.29824
$184$	−6.70820	−0.494535
$185$	−1.18034	−0.0867803
$186$	−13.0902	−0.959818
$187$	−14.5623	−1.06490
$188$	−1.76393	−0.128648
$189$	−2.23607	−0.162650
$190$	0	0
$191$	−12.2361	−0.885371	−0.442685	−	0.896677i	$-0.645974\pi$
$191$	−12.2361	−0.885371	−0.442685	+	0.896677i	$0.645974\pi$
$192$	2.61803	0.188940
$193$	18.1803	1.30865	0.654325	−	0.756214i	$-0.272953\pi$
$193$	18.1803	1.30865	0.654325	+	0.756214i	$0.272953\pi$
$194$	18.7082	1.34317
$195$	1.76393	0.126318
$196$	1.00000	0.0714286
$197$	−10.0344	−0.714924	−0.357462	−	0.933928i	$-0.616358\pi$
$197$	−10.0344	−0.714924	−0.357462	+	0.933928i	$0.616358\pi$
$198$	−11.5623	−0.821697
$199$	−8.79837	−0.623700	−0.311850	−	0.950131i	$-0.600949\pi$
$199$	−8.79837	−0.623700	−0.311850	+	0.950131i	$0.600949\pi$
$200$	4.94427	0.349613
$201$	40.7426	2.87376
$202$	−3.09017	−0.217424
$203$	3.76393	0.264176
$204$	−12.7082	−0.889752
$205$	1.67376	0.116901
$206$	−0.145898	−0.0101652
$207$	25.8541	1.79698
$208$	2.85410	0.197896
$209$	0	0
$210$	0.618034	0.0426484
$211$	21.0000	1.44570	0.722850	−	0.691005i	$-0.242832\pi$
$211$	21.0000	1.44570	0.722850	+	0.691005i	$0.242832\pi$
$212$	0.708204	0.0486396
$213$	32.6525	2.23731
$214$	4.52786	0.309518
$215$	2.02129	0.137851
$216$	−2.23607	−0.152145
$217$	−5.00000	−0.339422
$218$	1.85410	0.125576
$219$	5.47214	0.369773
$220$	0.708204	0.0477471
$221$	−13.8541	−0.931928
$222$	13.0902	0.878555
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	1.00000	0.0668153
$225$	−19.0557	−1.27038
$226$	12.7984	0.851335
$227$	27.0000	1.79205	0.896026	−	0.444001i	$-0.146441\pi$
$227$	27.0000	1.79205	0.896026	+	0.444001i	$0.146441\pi$
$228$	0	0
$229$	2.56231	0.169322	0.0846610	−	0.996410i	$-0.473019\pi$
$229$	2.56231	0.169322	0.0846610	+	0.996410i	$0.473019\pi$
$230$	−1.58359	−0.104419
$231$	−7.85410	−0.516762
$232$	3.76393	0.247114
$233$	7.79837	0.510888	0.255444	−	0.966824i	$-0.417778\pi$
$233$	7.79837	0.510888	0.255444	+	0.966824i	$0.417778\pi$
$234$	−11.0000	−0.719092
$235$	−0.416408	−0.0271635
$236$	5.76393	0.375200
$237$	44.1246	2.86620
$238$	−4.85410	−0.314645
$239$	−25.0344	−1.61934	−0.809672	−	0.586883i	$-0.800355\pi$
$239$	−25.0344	−1.61934	−0.809672	+	0.586883i	$0.800355\pi$
$240$	0.618034	0.0398939
$241$	26.8541	1.72982	0.864912	−	0.501923i	$-0.167374\pi$
$241$	26.8541	1.72982	0.864912	+	0.501923i	$0.167374\pi$
$242$	2.00000	0.128565
$243$	−21.6525	−1.38901
$244$	6.70820	0.429449
$245$	0.236068	0.0150818
$246$	−18.5623	−1.18349
$247$	0	0
$248$	−5.00000	−0.317500
$249$	6.47214	0.410155
$250$	2.34752	0.148470
$251$	−28.3607	−1.79011	−0.895055	−	0.445956i	$-0.852864\pi$
$251$	−28.3607	−1.79011	−0.895055	+	0.445956i	$0.852864\pi$
$252$	−3.85410	−0.242786
$253$	20.1246	1.26522
$254$	9.03444	0.566871
$255$	−3.00000	−0.187867
$256$	1.00000	0.0625000
$257$	12.7082	0.792716	0.396358	−	0.918096i	$-0.370274\pi$
$257$	12.7082	0.792716	0.396358	+	0.918096i	$0.370274\pi$
$258$	−22.4164	−1.39558
$259$	5.00000	0.310685
$260$	0.673762	0.0417850
$261$	−14.5066	−0.897935
$262$	5.61803	0.347083
$263$	−18.7082	−1.15360	−0.576799	−	0.816886i	$-0.695698\pi$
$263$	−18.7082	−1.15360	−0.576799	+	0.816886i	$0.695698\pi$
$264$	−7.85410	−0.483387
$265$	0.167184	0.0102700
$266$	0	0
$267$	−9.47214	−0.579685
$268$	15.5623	0.950619
$269$	−22.5279	−1.37355	−0.686774	−	0.726871i	$-0.740974\pi$
$269$	−22.5279	−1.37355	−0.686774	+	0.726871i	$0.740974\pi$
$270$	−0.527864	−0.0321248
$271$	30.4164	1.84767	0.923833	−	0.382797i	$-0.125039\pi$
$271$	30.4164	1.84767	0.923833	+	0.382797i	$0.125039\pi$
$272$	−4.85410	−0.294323
$273$	−7.47214	−0.452234
$274$	−4.76393	−0.287800
$275$	−14.8328	−0.894452
$276$	17.5623	1.05713
$277$	−9.52786	−0.572474	−0.286237	−	0.958159i	$-0.592404\pi$
$277$	−9.52786	−0.572474	−0.286237	+	0.958159i	$0.592404\pi$
$278$	−19.0000	−1.13954
$279$	19.2705	1.15370
$280$	0.236068	0.0141078
$281$	15.6525	0.933748	0.466874	−	0.884324i	$-0.345380\pi$
$281$	15.6525	0.933748	0.466874	+	0.884324i	$0.345380\pi$
$282$	4.61803	0.275000
$283$	−14.0344	−0.834261	−0.417130	−	0.908847i	$-0.636964\pi$
$283$	−14.0344	−0.834261	−0.417130	+	0.908847i	$0.636964\pi$
$284$	12.4721	0.740085
$285$	0	0
$286$	−8.56231	−0.506300
$287$	−7.09017	−0.418519
$288$	−3.85410	−0.227105
$289$	6.56231	0.386018
$290$	0.888544	0.0521771
$291$	−48.9787	−2.87118
$292$	2.09017	0.122318
$293$	−28.4164	−1.66010	−0.830052	−	0.557686i	$-0.811689\pi$
$293$	−28.4164	−1.66010	−0.830052	+	0.557686i	$0.811689\pi$
$294$	−2.61803	−0.152687
$295$	1.36068	0.0792218
$296$	5.00000	0.290619
$297$	6.70820	0.389249
$298$	13.0902	0.758293
$299$	19.1459	1.10724
$300$	−12.9443	−0.747338
$301$	−8.56231	−0.493523
$302$	4.23607	0.243758
$303$	8.09017	0.464768
$304$	0	0
$305$	1.58359	0.0906762
$306$	18.7082	1.06948
$307$	−26.8328	−1.53143	−0.765715	−	0.643180i	$-0.777615\pi$
$307$	−26.8328	−1.53143	−0.765715	+	0.643180i	$0.777615\pi$
$308$	−3.00000	−0.170941
$309$	0.381966	0.0217293
$310$	−1.18034	−0.0670388
$311$	−16.0557	−0.910437	−0.455218	−	0.890380i	$-0.650439\pi$
$311$	−16.0557	−0.910437	−0.455218	+	0.890380i	$0.650439\pi$
$312$	−7.47214	−0.423026
$313$	29.2705	1.65447	0.827234	−	0.561858i	$-0.189913\pi$
$313$	29.2705	1.65447	0.827234	+	0.561858i	$0.189913\pi$
$314$	12.6180	0.712077
$315$	−0.909830	−0.0512631
$316$	16.8541	0.948117
$317$	−27.4721	−1.54299	−0.771494	−	0.636236i	$-0.780490\pi$
$317$	−27.4721	−1.54299	−0.771494	+	0.636236i	$0.780490\pi$
$318$	−1.85410	−0.103973
$319$	−11.2918	−0.632219
$320$	0.236068	0.0131966
$321$	−11.8541	−0.661631
$322$	6.70820	0.373834
$323$	0	0
$324$	−5.70820	−0.317122
$325$	−14.1115	−0.782763
$326$	12.4721	0.690768
$327$	−4.85410	−0.268432
$328$	−7.09017	−0.391489
$329$	1.76393	0.0972487
$330$	−1.85410	−0.102065
$331$	8.47214	0.465671	0.232835	−	0.972516i	$-0.425200\pi$
$331$	8.47214	0.465671	0.232835	+	0.972516i	$0.425200\pi$
$332$	2.47214	0.135676
$333$	−19.2705	−1.05602
$334$	−17.2361	−0.943116
$335$	3.67376	0.200719
$336$	−2.61803	−0.142825
$337$	11.5623	0.629839	0.314919	−	0.949118i	$-0.398022\pi$
$337$	11.5623	0.629839	0.314919	+	0.949118i	$0.398022\pi$
$338$	4.85410	0.264028
$339$	−33.5066	−1.81983
$340$	−1.14590	−0.0621450
$341$	15.0000	0.812296
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−8.56231	−0.461649
$345$	4.14590	0.223208
$346$	−22.4164	−1.20511
$347$	−4.47214	−0.240077	−0.120038	−	0.992769i	$-0.538302\pi$
$347$	−4.47214	−0.240077	−0.120038	+	0.992769i	$0.538302\pi$
$348$	−9.85410	−0.528235
$349$	−31.8328	−1.70397	−0.851986	−	0.523565i	$-0.824602\pi$
$349$	−31.8328	−1.70397	−0.851986	+	0.523565i	$0.824602\pi$
$350$	−4.94427	−0.264282
$351$	6.38197	0.340644
$352$	−3.00000	−0.159901
$353$	1.20163	0.0639561	0.0319781	−	0.999489i	$-0.489819\pi$
$353$	1.20163	0.0639561	0.0319781	+	0.999489i	$0.489819\pi$
$354$	−15.0902	−0.802033
$355$	2.94427	0.156266
$356$	−3.61803	−0.191755
$357$	12.7082	0.672589
$358$	−19.3262	−1.02142
$359$	15.9443	0.841506	0.420753	−	0.907175i	$-0.361766\pi$
$359$	15.9443	0.841506	0.420753	+	0.907175i	$0.361766\pi$
$360$	−0.909830	−0.0479523
$361$	0	0
$362$	1.94427	0.102189
$363$	−5.23607	−0.274822
$364$	−2.85410	−0.149596
$365$	0.493422	0.0258269
$366$	−17.5623	−0.917996
$367$	21.5623	1.12554	0.562772	−	0.826612i	$-0.309735\pi$
$367$	21.5623	1.12554	0.562772	+	0.826612i	$0.309735\pi$
$368$	6.70820	0.349689
$369$	27.3262	1.42255
$370$	1.18034	0.0613629
$371$	−0.708204	−0.0367681
$372$	13.0902	0.678694
$373$	−5.14590	−0.266445	−0.133222	−	0.991086i	$-0.542532\pi$
$373$	−5.14590	−0.266445	−0.133222	+	0.991086i	$0.542532\pi$
$374$	14.5623	0.752999
$375$	−6.14590	−0.317373
$376$	1.76393	0.0909678
$377$	−10.7426	−0.553274
$378$	2.23607	0.115011
$379$	21.2705	1.09259	0.546296	−	0.837592i	$-0.316037\pi$
$379$	21.2705	1.09259	0.546296	+	0.837592i	$0.316037\pi$
$380$	0	0
$381$	−23.6525	−1.21175
$382$	12.2361	0.626052
$383$	12.7082	0.649359	0.324679	−	0.945824i	$-0.394744\pi$
$383$	12.7082	0.649359	0.324679	+	0.945824i	$0.394744\pi$
$384$	−2.61803	−0.133601
$385$	−0.708204	−0.0360934
$386$	−18.1803	−0.925355
$387$	33.0000	1.67748
$388$	−18.7082	−0.949765
$389$	34.7984	1.76435	0.882174	−	0.470924i	$-0.156079\pi$
$389$	34.7984	1.76435	0.882174	+	0.470924i	$0.156079\pi$
$390$	−1.76393	−0.0893202
$391$	−32.5623	−1.64675
$392$	−1.00000	−0.0505076
$393$	−14.7082	−0.741931
$394$	10.0344	0.505528
$395$	3.97871	0.200191
$396$	11.5623	0.581028
$397$	1.32624	0.0665620	0.0332810	−	0.999446i	$-0.489404\pi$
$397$	1.32624	0.0665620	0.0332810	+	0.999446i	$0.489404\pi$
$398$	8.79837	0.441023
$399$	0	0
$400$	−4.94427	−0.247214
$401$	−15.5279	−0.775425	−0.387712	−	0.921780i	$-0.626735\pi$
$401$	−15.5279	−0.775425	−0.387712	+	0.921780i	$0.626735\pi$
$402$	−40.7426	−2.03206
$403$	14.2705	0.710865
$404$	3.09017	0.153742
$405$	−1.34752	−0.0669590
$406$	−3.76393	−0.186801
$407$	−15.0000	−0.743522
$408$	12.7082	0.629150
$409$	22.8541	1.13006	0.565031	−	0.825069i	$-0.308864\pi$
$409$	22.8541	1.13006	0.565031	+	0.825069i	$0.308864\pi$
$410$	−1.67376	−0.0826612
$411$	12.4721	0.615205
$412$	0.145898	0.00718788
$413$	−5.76393	−0.283625
$414$	−25.8541	−1.27066
$415$	0.583592	0.0286474
$416$	−2.85410	−0.139934
$417$	49.7426	2.43591
$418$	0	0
$419$	−16.9098	−0.826099	−0.413050	−	0.910709i	$-0.635536\pi$
$419$	−16.9098	−0.826099	−0.413050	+	0.910709i	$0.635536\pi$
$420$	−0.618034	−0.0301570
$421$	18.8885	0.920571	0.460286	−	0.887771i	$-0.347747\pi$
$421$	18.8885	0.920571	0.460286	+	0.887771i	$0.347747\pi$
$422$	−21.0000	−1.02226
$423$	−6.79837	−0.330548
$424$	−0.708204	−0.0343934
$425$	24.0000	1.16417
$426$	−32.6525	−1.58202
$427$	−6.70820	−0.324633
$428$	−4.52786	−0.218863
$429$	22.4164	1.08227
$430$	−2.02129	−0.0974751
$431$	−22.3607	−1.07708	−0.538538	−	0.842601i	$-0.681023\pi$
$431$	−22.3607	−1.07708	−0.538538	+	0.842601i	$0.681023\pi$
$432$	2.23607	0.107583
$433$	−19.1459	−0.920093	−0.460047	−	0.887895i	$-0.652167\pi$
$433$	−19.1459	−0.920093	−0.460047	+	0.887895i	$0.652167\pi$
$434$	5.00000	0.240008
$435$	−2.32624	−0.111535
$436$	−1.85410	−0.0887954
$437$	0	0
$438$	−5.47214	−0.261469
$439$	18.2361	0.870360	0.435180	−	0.900343i	$-0.356685\pi$
$439$	18.2361	0.870360	0.435180	+	0.900343i	$0.356685\pi$
$440$	−0.708204	−0.0337623
$441$	3.85410	0.183529
$442$	13.8541	0.658972
$443$	−11.5066	−0.546694	−0.273347	−	0.961915i	$-0.588131\pi$
$443$	−11.5066	−0.546694	−0.273347	+	0.961915i	$0.588131\pi$
$444$	−13.0902	−0.621232
$445$	−0.854102	−0.0404883
$446$	−9.00000	−0.426162
$447$	−34.2705	−1.62094
$448$	−1.00000	−0.0472456
$449$	−33.2361	−1.56851	−0.784254	−	0.620441i	$-0.786954\pi$
$449$	−33.2361	−1.56851	−0.784254	+	0.620441i	$0.786954\pi$
$450$	19.0557	0.898296
$451$	21.2705	1.00159
$452$	−12.7984	−0.601985
$453$	−11.0902	−0.521062
$454$	−27.0000	−1.26717
$455$	−0.673762	−0.0315865
$456$	0	0
$457$	−2.11146	−0.0987698	−0.0493849	−	0.998780i	$-0.515726\pi$
$457$	−2.11146	−0.0987698	−0.0493849	+	0.998780i	$0.515726\pi$
$458$	−2.56231	−0.119729
$459$	−10.8541	−0.506626
$460$	1.58359	0.0738354
$461$	−8.29180	−0.386187	−0.193094	−	0.981180i	$-0.561852\pi$
$461$	−8.29180	−0.386187	−0.193094	+	0.981180i	$0.561852\pi$
$462$	7.85410	0.365406
$463$	−12.9787	−0.603172	−0.301586	−	0.953439i	$-0.597516\pi$
$463$	−12.9787	−0.603172	−0.301586	+	0.953439i	$0.597516\pi$
$464$	−3.76393	−0.174736
$465$	3.09017	0.143303
$466$	−7.79837	−0.361253
$467$	−2.12461	−0.0983153	−0.0491577	−	0.998791i	$-0.515654\pi$
$467$	−2.12461	−0.0983153	−0.0491577	+	0.998791i	$0.515654\pi$
$468$	11.0000	0.508475
$469$	−15.5623	−0.718601
$470$	0.416408	0.0192075
$471$	−33.0344	−1.52215
$472$	−5.76393	−0.265306
$473$	25.6869	1.18109
$474$	−44.1246	−2.02671
$475$	0	0
$476$	4.85410	0.222487
$477$	2.72949	0.124975
$478$	25.0344	1.14505
$479$	−14.2918	−0.653009	−0.326504	−	0.945196i	$-0.605871\pi$
$479$	−14.2918	−0.653009	−0.326504	+	0.945196i	$0.605871\pi$
$480$	−0.618034	−0.0282093
$481$	−14.2705	−0.650679
$482$	−26.8541	−1.22317
$483$	−17.5623	−0.799113
$484$	−2.00000	−0.0909091
$485$	−4.41641	−0.200539
$486$	21.6525	0.982176
$487$	−41.6525	−1.88745	−0.943727	−	0.330726i	$-0.892707\pi$
$487$	−41.6525	−1.88745	−0.943727	+	0.330726i	$0.892707\pi$
$488$	−6.70820	−0.303666
$489$	−32.6525	−1.47660
$490$	−0.236068	−0.0106645
$491$	34.0689	1.53751	0.768754	−	0.639545i	$-0.220877\pi$
$491$	34.0689	1.53751	0.768754	+	0.639545i	$0.220877\pi$
$492$	18.5623	0.836853
$493$	18.2705	0.822862
$494$	0	0
$495$	2.72949	0.122681
$496$	5.00000	0.224507
$497$	−12.4721	−0.559452
$498$	−6.47214	−0.290023
$499$	−3.00000	−0.134298	−0.0671492	−	0.997743i	$-0.521390\pi$
$499$	−3.00000	−0.134298	−0.0671492	+	0.997743i	$0.521390\pi$
$500$	−2.34752	−0.104984
$501$	45.1246	2.01602
$502$	28.3607	1.26580
$503$	4.94427	0.220454	0.110227	−	0.993906i	$-0.464842\pi$
$503$	4.94427	0.220454	0.110227	+	0.993906i	$0.464842\pi$
$504$	3.85410	0.171675
$505$	0.729490	0.0324619
$506$	−20.1246	−0.894648
$507$	−12.7082	−0.564391
$508$	−9.03444	−0.400839
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	3.00000	0.132842
$511$	−2.09017	−0.0924637
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−12.7082	−0.560535
$515$	0.0344419	0.00151769
$516$	22.4164	0.986827
$517$	−5.29180	−0.232733
$518$	−5.00000	−0.219687
$519$	58.6869	2.57607
$520$	−0.673762	−0.0295464
$521$	−24.8885	−1.09039	−0.545193	−	0.838310i	$-0.683544\pi$
$521$	−24.8885	−1.09039	−0.545193	+	0.838310i	$0.683544\pi$
$522$	14.5066	0.634936
$523$	18.9098	0.826869	0.413435	−	0.910534i	$-0.364329\pi$
$523$	18.9098	0.826869	0.413435	+	0.910534i	$0.364329\pi$
$524$	−5.61803	−0.245425
$525$	12.9443	0.564934
$526$	18.7082	0.815716
$527$	−24.2705	−1.05724
$528$	7.85410	0.341806
$529$	22.0000	0.956522
$530$	−0.167184	−0.00726202
$531$	22.2148	0.964039
$532$	0	0
$533$	20.2361	0.876521
$534$	9.47214	0.409899
$535$	−1.06888	−0.0462119
$536$	−15.5623	−0.672189
$537$	50.5967	2.18341
$538$	22.5279	0.971245
$539$	3.00000	0.129219
$540$	0.527864	0.0227157
$541$	5.47214	0.235266	0.117633	−	0.993057i	$-0.462469\pi$
$541$	5.47214	0.235266	0.117633	+	0.993057i	$0.462469\pi$
$542$	−30.4164	−1.30650
$543$	−5.09017	−0.218440
$544$	4.85410	0.208118
$545$	−0.437694	−0.0187488
$546$	7.47214	0.319778
$547$	−1.18034	−0.0504677	−0.0252338	−	0.999682i	$-0.508033\pi$
$547$	−1.18034	−0.0504677	−0.0252338	+	0.999682i	$0.508033\pi$
$548$	4.76393	0.203505
$549$	25.8541	1.10343
$550$	14.8328	0.632473
$551$	0	0
$552$	−17.5623	−0.747501
$553$	−16.8541	−0.716709
$554$	9.52786	0.404800
$555$	−3.09017	−0.131170
$556$	19.0000	0.805779
$557$	−42.2361	−1.78960	−0.894800	−	0.446468i	$-0.852682\pi$
$557$	−42.2361	−1.78960	−0.894800	+	0.446468i	$0.852682\pi$
$558$	−19.2705	−0.815786
$559$	24.4377	1.03360
$560$	−0.236068	−0.00997569
$561$	−38.1246	−1.60962
$562$	−15.6525	−0.660260
$563$	10.1803	0.429050	0.214525	−	0.976718i	$-0.431180\pi$
$563$	10.1803	0.429050	0.214525	+	0.976718i	$0.431180\pi$
$564$	−4.61803	−0.194454
$565$	−3.02129	−0.127106
$566$	14.0344	0.589912
$567$	5.70820	0.239722
$568$	−12.4721	−0.523319
$569$	−23.6180	−0.990119	−0.495060	−	0.868859i	$-0.664854\pi$
$569$	−23.6180	−0.990119	−0.495060	+	0.868859i	$0.664854\pi$
$570$	0	0
$571$	38.6525	1.61756	0.808778	−	0.588114i	$-0.200129\pi$
$571$	38.6525	1.61756	0.808778	+	0.588114i	$0.200129\pi$
$572$	8.56231	0.358008
$573$	−32.0344	−1.33826
$574$	7.09017	0.295938
$575$	−33.1672	−1.38317
$576$	3.85410	0.160588
$577$	11.5836	0.482231	0.241116	−	0.970496i	$-0.422487\pi$
$577$	11.5836	0.482231	0.241116	+	0.970496i	$0.422487\pi$
$578$	−6.56231	−0.272956
$579$	47.5967	1.97805
$580$	−0.888544	−0.0368948
$581$	−2.47214	−0.102561
$582$	48.9787	2.03023
$583$	2.12461	0.0879924
$584$	−2.09017	−0.0864918
$585$	2.59675	0.107362
$586$	28.4164	1.17387
$587$	25.6525	1.05879	0.529395	−	0.848375i	$-0.322419\pi$
$587$	25.6525	1.05879	0.529395	+	0.848375i	$0.322419\pi$
$588$	2.61803	0.107966
$589$	0	0
$590$	−1.36068	−0.0560183
$591$	−26.2705	−1.08062
$592$	−5.00000	−0.205499
$593$	−21.3262	−0.875764	−0.437882	−	0.899033i	$-0.644271\pi$
$593$	−21.3262	−0.875764	−0.437882	+	0.899033i	$0.644271\pi$
$594$	−6.70820	−0.275241
$595$	1.14590	0.0469772
$596$	−13.0902	−0.536194
$597$	−23.0344	−0.942737
$598$	−19.1459	−0.782934
$599$	4.52786	0.185004	0.0925018	−	0.995713i	$-0.470514\pi$
$599$	4.52786	0.185004	0.0925018	+	0.995713i	$0.470514\pi$
$600$	12.9443	0.528448
$601$	−15.8328	−0.645834	−0.322917	−	0.946427i	$-0.604663\pi$
$601$	−15.8328	−0.645834	−0.322917	+	0.946427i	$0.604663\pi$
$602$	8.56231	0.348974
$603$	59.9787	2.44252
$604$	−4.23607	−0.172363
$605$	−0.472136	−0.0191951
$606$	−8.09017	−0.328641
$607$	−22.8328	−0.926755	−0.463378	−	0.886161i	$-0.653363\pi$
$607$	−22.8328	−0.926755	−0.463378	+	0.886161i	$0.653363\pi$
$608$	0	0
$609$	9.85410	0.399308
$610$	−1.58359	−0.0641178
$611$	−5.03444	−0.203672
$612$	−18.7082	−0.756234
$613$	4.18034	0.168842	0.0844212	−	0.996430i	$-0.473096\pi$
$613$	4.18034	0.168842	0.0844212	+	0.996430i	$0.473096\pi$
$614$	26.8328	1.08288
$615$	4.38197	0.176698
$616$	3.00000	0.120873
$617$	−10.7984	−0.434726	−0.217363	−	0.976091i	$-0.569746\pi$
$617$	−10.7984	−0.434726	−0.217363	+	0.976091i	$0.569746\pi$
$618$	−0.381966	−0.0153649
$619$	0.145898	0.00586414	0.00293207	−	0.999996i	$-0.499067\pi$
$619$	0.145898	0.00586414	0.00293207	+	0.999996i	$0.499067\pi$
$620$	1.18034	0.0474036
$621$	15.0000	0.601929
$622$	16.0557	0.643776
$623$	3.61803	0.144953
$624$	7.47214	0.299125
$625$	24.1672	0.966687
$626$	−29.2705	−1.16988
$627$	0	0
$628$	−12.6180	−0.503514
$629$	24.2705	0.967729
$630$	0.909830	0.0362485
$631$	−38.8328	−1.54591	−0.772955	−	0.634461i	$-0.781222\pi$
$631$	−38.8328	−1.54591	−0.772955	+	0.634461i	$0.781222\pi$
$632$	−16.8541	−0.670420
$633$	54.9787	2.18521
$634$	27.4721	1.09106
$635$	−2.13274	−0.0846353
$636$	1.85410	0.0735199
$637$	2.85410	0.113084
$638$	11.2918	0.447046
$639$	48.0689	1.90158
$640$	−0.236068	−0.00933141
$641$	−0.798374	−0.0315339	−0.0157669	−	0.999876i	$-0.505019\pi$
$641$	−0.798374	−0.0315339	−0.0157669	+	0.999876i	$0.505019\pi$
$642$	11.8541	0.467844
$643$	−43.5967	−1.71929	−0.859644	−	0.510894i	$-0.829315\pi$
$643$	−43.5967	−1.71929	−0.859644	+	0.510894i	$0.829315\pi$
$644$	−6.70820	−0.264340
$645$	5.29180	0.208364
$646$	0	0
$647$	17.7984	0.699726	0.349863	−	0.936801i	$-0.386228\pi$
$647$	17.7984	0.699726	0.349863	+	0.936801i	$0.386228\pi$
$648$	5.70820	0.224239
$649$	17.2918	0.678762
$650$	14.1115	0.553497
$651$	−13.0902	−0.513044
$652$	−12.4721	−0.488447
$653$	23.3262	0.912826	0.456413	−	0.889768i	$-0.349134\pi$
$653$	23.3262	0.912826	0.456413	+	0.889768i	$0.349134\pi$
$654$	4.85410	0.189810
$655$	−1.32624	−0.0518204
$656$	7.09017	0.276825
$657$	8.05573	0.314284
$658$	−1.76393	−0.0687652
$659$	33.6525	1.31091	0.655457	−	0.755232i	$-0.272476\pi$
$659$	33.6525	1.31091	0.655457	+	0.755232i	$0.272476\pi$
$660$	1.85410	0.0721708
$661$	−24.7082	−0.961038	−0.480519	−	0.876984i	$-0.659552\pi$
$661$	−24.7082	−0.961038	−0.480519	+	0.876984i	$0.659552\pi$
$662$	−8.47214	−0.329279
$663$	−36.2705	−1.40863
$664$	−2.47214	−0.0959375
$665$	0	0
$666$	19.2705	0.746717
$667$	−25.2492	−0.977654
$668$	17.2361	0.666883
$669$	23.5623	0.910971
$670$	−3.67376	−0.141930
$671$	20.1246	0.776902
$672$	2.61803	0.100993
$673$	−7.38197	−0.284554	−0.142277	−	0.989827i	$-0.545442\pi$
$673$	−7.38197	−0.284554	−0.142277	+	0.989827i	$0.545442\pi$
$674$	−11.5623	−0.445363
$675$	−11.0557	−0.425535
$676$	−4.85410	−0.186696
$677$	−24.0689	−0.925042	−0.462521	−	0.886608i	$-0.653055\pi$
$677$	−24.0689	−0.925042	−0.462521	+	0.886608i	$0.653055\pi$
$678$	33.5066	1.28681
$679$	18.7082	0.717955
$680$	1.14590	0.0439432
$681$	70.6869	2.70873
$682$	−15.0000	−0.574380
$683$	−1.25735	−0.0481113	−0.0240557	−	0.999711i	$-0.507658\pi$
$683$	−1.25735	−0.0481113	−0.0240557	+	0.999711i	$0.507658\pi$
$684$	0	0
$685$	1.12461	0.0429692
$686$	1.00000	0.0381802
$687$	6.70820	0.255934
$688$	8.56231	0.326435
$689$	2.02129	0.0770049
$690$	−4.14590	−0.157832
$691$	8.12461	0.309075	0.154537	−	0.987987i	$-0.450611\pi$
$691$	8.12461	0.309075	0.154537	+	0.987987i	$0.450611\pi$
$692$	22.4164	0.852144
$693$	−11.5623	−0.439216
$694$	4.47214	0.169760
$695$	4.48529	0.170137
$696$	9.85410	0.373519
$697$	−34.4164	−1.30361
$698$	31.8328	1.20489
$699$	20.4164	0.772219
$700$	4.94427	0.186876
$701$	−43.2148	−1.63220	−0.816100	−	0.577911i	$-0.803868\pi$
$701$	−43.2148	−1.63220	−0.816100	+	0.577911i	$0.803868\pi$
$702$	−6.38197	−0.240872
$703$	0	0
$704$	3.00000	0.113067
$705$	−1.09017	−0.0410582
$706$	−1.20163	−0.0452238
$707$	−3.09017	−0.116218
$708$	15.0902	0.567123
$709$	−31.7639	−1.19292	−0.596460	−	0.802643i	$-0.703426\pi$
$709$	−31.7639	−1.19292	−0.596460	+	0.802643i	$0.703426\pi$
$710$	−2.94427	−0.110497
$711$	64.9574	2.43609
$712$	3.61803	0.135592
$713$	33.5410	1.25612
$714$	−12.7082	−0.475593
$715$	2.02129	0.0755918
$716$	19.3262	0.722255
$717$	−65.5410	−2.44767
$718$	−15.9443	−0.595035
$719$	−17.0689	−0.636562	−0.318281	−	0.947996i	$-0.603106\pi$
$719$	−17.0689	−0.636562	−0.318281	+	0.947996i	$0.603106\pi$
$720$	0.909830	0.0339074
$721$	−0.145898	−0.00543353
$722$	0	0
$723$	70.3050	2.61467
$724$	−1.94427	−0.0722583
$725$	18.6099	0.691154
$726$	5.23607	0.194329
$727$	45.3607	1.68233	0.841167	−	0.540775i	$-0.181869\pi$
$727$	45.3607	1.68233	0.841167	+	0.540775i	$0.181869\pi$
$728$	2.85410	0.105780
$729$	−39.5623	−1.46527
$730$	−0.493422	−0.0182624
$731$	−41.5623	−1.53724
$732$	17.5623	0.649122
$733$	31.0000	1.14501	0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000	1.14501	0.572506	+	0.819901i	$0.305971\pi$
$734$	−21.5623	−0.795879
$735$	0.618034	0.0227965
$736$	−6.70820	−0.247268
$737$	46.6869	1.71973
$738$	−27.3262	−1.00589
$739$	38.8328	1.42849	0.714244	−	0.699897i	$-0.246771\pi$
$739$	38.8328	1.42849	0.714244	+	0.699897i	$0.246771\pi$
$740$	−1.18034	−0.0433902
$741$	0	0
$742$	0.708204	0.0259990
$743$	−13.8541	−0.508258	−0.254129	−	0.967170i	$-0.581789\pi$
$743$	−13.8541	−0.508258	−0.254129	+	0.967170i	$0.581789\pi$
$744$	−13.0902	−0.479909
$745$	−3.09017	−0.113215
$746$	5.14590	0.188405
$747$	9.52786	0.348606
$748$	−14.5623	−0.532451
$749$	4.52786	0.165445
$750$	6.14590	0.224416
$751$	25.1246	0.916810	0.458405	−	0.888743i	$-0.348421\pi$
$751$	25.1246	0.916810	0.458405	+	0.888743i	$0.348421\pi$
$752$	−1.76393	−0.0643240
$753$	−74.2492	−2.70579
$754$	10.7426	0.391224
$755$	−1.00000	−0.0363937
$756$	−2.23607	−0.0813250
$757$	0.583592	0.0212110	0.0106055	−	0.999944i	$-0.496624\pi$
$757$	0.583592	0.0212110	0.0106055	+	0.999944i	$0.496624\pi$
$758$	−21.2705	−0.772580
$759$	52.6869	1.91241
$760$	0	0
$761$	20.1246	0.729517	0.364758	−	0.931102i	$-0.381152\pi$
$761$	20.1246	0.729517	0.364758	+	0.931102i	$0.381152\pi$
$762$	23.6525	0.856839
$763$	1.85410	0.0671230
$764$	−12.2361	−0.442685
$765$	−4.41641	−0.159676
$766$	−12.7082	−0.459166
$767$	16.4508	0.594006
$768$	2.61803	0.0944702
$769$	−50.2492	−1.81203	−0.906017	−	0.423242i	$-0.860892\pi$
$769$	−50.2492	−1.81203	−0.906017	+	0.423242i	$0.860892\pi$
$770$	0.708204	0.0255219
$771$	33.2705	1.19821
$772$	18.1803	0.654325
$773$	−34.2148	−1.23062	−0.615310	−	0.788285i	$-0.710969\pi$
$773$	−34.2148	−1.23062	−0.615310	+	0.788285i	$0.710969\pi$
$774$	−33.0000	−1.18616
$775$	−24.7214	−0.888017
$776$	18.7082	0.671585
$777$	13.0902	0.469607
$778$	−34.7984	−1.24758
$779$	0	0
$780$	1.76393	0.0631589
$781$	37.4164	1.33886
$782$	32.5623	1.16443
$783$	−8.41641	−0.300778
$784$	1.00000	0.0357143
$785$	−2.97871	−0.106315
$786$	14.7082	0.524624
$787$	27.9098	0.994878	0.497439	−	0.867499i	$-0.334274\pi$
$787$	27.9098	0.994878	0.497439	+	0.867499i	$0.334274\pi$
$788$	−10.0344	−0.357462
$789$	−48.9787	−1.74369
$790$	−3.97871	−0.141556
$791$	12.7984	0.455058
$792$	−11.5623	−0.410849
$793$	19.1459	0.679891
$794$	−1.32624	−0.0470664
$795$	0.437694	0.0155234
$796$	−8.79837	−0.311850
$797$	−10.7984	−0.382498	−0.191249	−	0.981542i	$-0.561254\pi$
$797$	−10.7984	−0.382498	−0.191249	+	0.981542i	$0.561254\pi$
$798$	0	0
$799$	8.56231	0.302913
$800$	4.94427	0.174806
$801$	−13.9443	−0.492697
$802$	15.5279	0.548308
$803$	6.27051	0.221281
$804$	40.7426	1.43688
$805$	−1.58359	−0.0558143
$806$	−14.2705	−0.502657
$807$	−58.9787	−2.07615
$808$	−3.09017	−0.108712
$809$	45.2705	1.59163	0.795813	−	0.605542i	$-0.207044\pi$
$809$	45.2705	1.59163	0.795813	+	0.605542i	$0.207044\pi$
$810$	1.34752	0.0473472
$811$	−3.23607	−0.113634	−0.0568169	−	0.998385i	$-0.518095\pi$
$811$	−3.23607	−0.113634	−0.0568169	+	0.998385i	$0.518095\pi$
$812$	3.76393	0.132088
$813$	79.6312	2.79279
$814$	15.0000	0.525750
$815$	−2.94427	−0.103133
$816$	−12.7082	−0.444876
$817$	0	0
$818$	−22.8541	−0.799075
$819$	−11.0000	−0.384371
$820$	1.67376	0.0584503
$821$	9.18034	0.320396	0.160198	−	0.987085i	$-0.448787\pi$
$821$	9.18034	0.320396	0.160198	+	0.987085i	$0.448787\pi$
$822$	−12.4721	−0.435016
$823$	25.0689	0.873846	0.436923	−	0.899499i	$-0.356068\pi$
$823$	25.0689	0.873846	0.436923	+	0.899499i	$0.356068\pi$
$824$	−0.145898	−0.00508260
$825$	−38.8328	−1.35199
$826$	5.76393	0.200553
$827$	−5.38197	−0.187149	−0.0935746	−	0.995612i	$-0.529829\pi$
$827$	−5.38197	−0.187149	−0.0935746	+	0.995612i	$0.529829\pi$
$828$	25.8541	0.898492
$829$	13.8754	0.481912	0.240956	−	0.970536i	$-0.422539\pi$
$829$	13.8754	0.481912	0.240956	+	0.970536i	$0.422539\pi$
$830$	−0.583592	−0.0202568
$831$	−24.9443	−0.865307
$832$	2.85410	0.0989482
$833$	−4.85410	−0.168185
$834$	−49.7426	−1.72245
$835$	4.06888	0.140810
$836$	0	0
$837$	11.1803	0.386449
$838$	16.9098	0.584140
$839$	−42.5279	−1.46822	−0.734112	−	0.679028i	$-0.762402\pi$
$839$	−42.5279	−1.46822	−0.734112	+	0.679028i	$0.762402\pi$
$840$	0.618034	0.0213242
$841$	−14.8328	−0.511476
$842$	−18.8885	−0.650942
$843$	40.9787	1.41138
$844$	21.0000	0.722850
$845$	−1.14590	−0.0394201
$846$	6.79837	0.233733
$847$	2.00000	0.0687208
$848$	0.708204	0.0243198
$849$	−36.7426	−1.26100
$850$	−24.0000	−0.823193
$851$	−33.5410	−1.14977
$852$	32.6525	1.11866
$853$	−41.0000	−1.40381	−0.701907	−	0.712269i	$-0.747668\pi$
$853$	−41.0000	−1.40381	−0.701907	+	0.712269i	$0.747668\pi$
$854$	6.70820	0.229550
$855$	0	0
$856$	4.52786	0.154759
$857$	−34.7984	−1.18869	−0.594345	−	0.804210i	$-0.702589\pi$
$857$	−34.7984	−1.18869	−0.594345	+	0.804210i	$0.702589\pi$
$858$	−22.4164	−0.765284
$859$	−8.30495	−0.283361	−0.141681	−	0.989912i	$-0.545251\pi$
$859$	−8.30495	−0.283361	−0.141681	+	0.989912i	$0.545251\pi$
$860$	2.02129	0.0689253
$861$	−18.5623	−0.632602
$862$	22.3607	0.761608
$863$	−20.3475	−0.692638	−0.346319	−	0.938117i	$-0.612568\pi$
$863$	−20.3475	−0.692638	−0.346319	+	0.938117i	$0.612568\pi$
$864$	−2.23607	−0.0760726
$865$	5.29180	0.179926
$866$	19.1459	0.650604
$867$	17.1803	0.583475
$868$	−5.00000	−0.169711
$869$	50.5623	1.71521
$870$	2.32624	0.0788669
$871$	44.4164	1.50499
$872$	1.85410	0.0627878
$873$	−72.1033	−2.44033
$874$	0	0
$875$	2.34752	0.0793608
$876$	5.47214	0.184886
$877$	−13.3262	−0.449995	−0.224998	−	0.974359i	$-0.572237\pi$
$877$	−13.3262	−0.449995	−0.224998	+	0.974359i	$0.572237\pi$
$878$	−18.2361	−0.615437
$879$	−74.3951	−2.50929
$880$	0.708204	0.0238735
$881$	−37.7426	−1.27158	−0.635791	−	0.771861i	$-0.719326\pi$
$881$	−37.7426	−1.27158	−0.635791	+	0.771861i	$0.719326\pi$
$882$	−3.85410	−0.129774
$883$	−44.1033	−1.48420	−0.742098	−	0.670292i	$-0.766169\pi$
$883$	−44.1033	−1.48420	−0.742098	+	0.670292i	$0.766169\pi$
$884$	−13.8541	−0.465964
$885$	3.56231	0.119746
$886$	11.5066	0.386571
$887$	−29.7771	−0.999817	−0.499908	−	0.866078i	$-0.666633\pi$
$887$	−29.7771	−0.999817	−0.499908	+	0.866078i	$0.666633\pi$
$888$	13.0902	0.439277
$889$	9.03444	0.303005
$890$	0.854102	0.0286296
$891$	−17.1246	−0.573696
$892$	9.00000	0.301342
$893$	0	0
$894$	34.2705	1.14618
$895$	4.56231	0.152501
$896$	1.00000	0.0334077
$897$	50.1246	1.67361
$898$	33.2361	1.10910
$899$	−18.8197	−0.627671
$900$	−19.0557	−0.635191
$901$	−3.43769	−0.114526
$902$	−21.2705	−0.708231
$903$	−22.4164	−0.745971
$904$	12.7984	0.425668
$905$	−0.458980	−0.0152570
$906$	11.0902	0.368446
$907$	28.8541	0.958085	0.479042	−	0.877792i	$-0.340984\pi$
$907$	28.8541	0.958085	0.479042	+	0.877792i	$0.340984\pi$
$908$	27.0000	0.896026
$909$	11.9098	0.395024
$910$	0.673762	0.0223350
$911$	−34.7426	−1.15108	−0.575538	−	0.817775i	$-0.695207\pi$
$911$	−34.7426	−1.15108	−0.575538	+	0.817775i	$0.695207\pi$
$912$	0	0
$913$	7.41641	0.245447
$914$	2.11146	0.0698408
$915$	4.14590	0.137059
$916$	2.56231	0.0846610
$917$	5.61803	0.185524
$918$	10.8541	0.358239
$919$	38.3951	1.26654	0.633269	−	0.773932i	$-0.281713\pi$
$919$	38.3951	1.26654	0.633269	+	0.773932i	$0.281713\pi$
$920$	−1.58359	−0.0522095
$921$	−70.2492	−2.31479
$922$	8.29180	0.273076
$923$	35.5967	1.17168
$924$	−7.85410	−0.258381
$925$	24.7214	0.812833
$926$	12.9787	0.426507
$927$	0.562306	0.0184685
$928$	3.76393	0.123557
$929$	−27.0689	−0.888101	−0.444051	−	0.896002i	$-0.646459\pi$
$929$	−27.0689	−0.888101	−0.444051	+	0.896002i	$0.646459\pi$
$930$	−3.09017	−0.101331
$931$	0	0
$932$	7.79837	0.255444
$933$	−42.0344	−1.37615
$934$	2.12461	0.0695194
$935$	−3.43769	−0.112425
$936$	−11.0000	−0.359546
$937$	−9.96556	−0.325561	−0.162780	−	0.986662i	$-0.552046\pi$
$937$	−9.96556	−0.325561	−0.162780	+	0.986662i	$0.552046\pi$
$938$	15.5623	0.508127
$939$	76.6312	2.50076
$940$	−0.416408	−0.0135817
$941$	6.38197	0.208046	0.104023	−	0.994575i	$-0.466828\pi$
$941$	6.38197	0.208046	0.104023	+	0.994575i	$0.466828\pi$
$942$	33.0344	1.07632
$943$	47.5623	1.54884
$944$	5.76393	0.187600
$945$	−0.527864	−0.0171714
$946$	−25.6869	−0.835154
$947$	−46.4721	−1.51014	−0.755071	−	0.655643i	$-0.772398\pi$
$947$	−46.4721	−1.51014	−0.755071	+	0.655643i	$0.772398\pi$
$948$	44.1246	1.43310
$949$	5.96556	0.193650
$950$	0	0
$951$	−71.9230	−2.33226
$952$	−4.85410	−0.157322
$953$	7.58359	0.245657	0.122828	−	0.992428i	$-0.460804\pi$
$953$	7.58359	0.245657	0.122828	+	0.992428i	$0.460804\pi$
$954$	−2.72949	−0.0883705
$955$	−2.88854	−0.0934711
$956$	−25.0344	−0.809672
$957$	−29.5623	−0.955614
$958$	14.2918	0.461747
$959$	−4.76393	−0.153835
$960$	0.618034	0.0199470
$961$	−6.00000	−0.193548
$962$	14.2705	0.460100
$963$	−17.4508	−0.562346
$964$	26.8541	0.864912
$965$	4.29180	0.138158
$966$	17.5623	0.565058
$967$	11.5623	0.371819	0.185909	−	0.982567i	$-0.440477\pi$
$967$	11.5623	0.371819	0.185909	+	0.982567i	$0.440477\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	4.41641	0.141802
$971$	15.7639	0.505889	0.252944	−	0.967481i	$-0.418601\pi$
$971$	15.7639	0.505889	0.252944	+	0.967481i	$0.418601\pi$
$972$	−21.6525	−0.694503
$973$	−19.0000	−0.609112
$974$	41.6525	1.33463
$975$	−36.9443	−1.18316
$976$	6.70820	0.214724
$977$	−41.4721	−1.32681	−0.663406	−	0.748260i	$-0.730890\pi$
$977$	−41.4721	−1.32681	−0.663406	+	0.748260i	$0.730890\pi$
$978$	32.6525	1.04411
$979$	−10.8541	−0.346899
$980$	0.236068	0.00754091
$981$	−7.14590	−0.228151
$982$	−34.0689	−1.08718
$983$	−0.798374	−0.0254642	−0.0127321	−	0.999919i	$-0.504053\pi$
$983$	−0.798374	−0.0254642	−0.0127321	+	0.999919i	$0.504053\pi$
$984$	−18.5623	−0.591745
$985$	−2.36881	−0.0754766
$986$	−18.2705	−0.581852
$987$	4.61803	0.146994
$988$	0	0
$989$	57.4377	1.82641
$990$	−2.72949	−0.0867489
$991$	−13.4164	−0.426186	−0.213093	−	0.977032i	$-0.568354\pi$
$991$	−13.4164	−0.426186	−0.213093	+	0.977032i	$0.568354\pi$
$992$	−5.00000	−0.158750
$993$	22.1803	0.703872
$994$	12.4721	0.395592
$995$	−2.07701	−0.0658458
$996$	6.47214	0.205077
$997$	−45.0344	−1.42626	−0.713128	−	0.701034i	$-0.752722\pi$
$997$	−45.0344	−1.42626	−0.713128	+	0.701034i	$0.752722\pi$
$998$	3.00000	0.0949633
$999$	−11.1803	−0.353730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.i.1.2	✓	2
19.18	odd	2		5054.2.a.j.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.i.1.2	✓	2	1.1	even	1	trivial
5054.2.a.j.1.1	yes	2	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} +0.236068 q^{5} -2.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.61803 q^{3} +1.00000 q^{4} +0.236068 q^{5} -2.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} +3.85410 q^{9} -0.236068 q^{10} +3.00000 q^{11} +2.61803 q^{12} +2.85410 q^{13} +1.00000 q^{14} +0.618034 q^{15} +1.00000 q^{16} -4.85410 q^{17} -3.85410 q^{18} +0.236068 q^{20} -2.61803 q^{21} -3.00000 q^{22} +6.70820 q^{23} -2.61803 q^{24} -4.94427 q^{25} -2.85410 q^{26} +2.23607 q^{27} -1.00000 q^{28} -3.76393 q^{29} -0.618034 q^{30} +5.00000 q^{31} -1.00000 q^{32} +7.85410 q^{33} +4.85410 q^{34} -0.236068 q^{35} +3.85410 q^{36} -5.00000 q^{37} +7.47214 q^{39} -0.236068 q^{40} +7.09017 q^{41} +2.61803 q^{42} +8.56231 q^{43} +3.00000 q^{44} +0.909830 q^{45} -6.70820 q^{46} -1.76393 q^{47} +2.61803 q^{48} +1.00000 q^{49} +4.94427 q^{50} -12.7082 q^{51} +2.85410 q^{52} +0.708204 q^{53} -2.23607 q^{54} +0.708204 q^{55} +1.00000 q^{56} +3.76393 q^{58} +5.76393 q^{59} +0.618034 q^{60} +6.70820 q^{61} -5.00000 q^{62} -3.85410 q^{63} +1.00000 q^{64} +0.673762 q^{65} -7.85410 q^{66} +15.5623 q^{67} -4.85410 q^{68} +17.5623 q^{69} +0.236068 q^{70} +12.4721 q^{71} -3.85410 q^{72} +2.09017 q^{73} +5.00000 q^{74} -12.9443 q^{75} -3.00000 q^{77} -7.47214 q^{78} +16.8541 q^{79} +0.236068 q^{80} -5.70820 q^{81} -7.09017 q^{82} +2.47214 q^{83} -2.61803 q^{84} -1.14590 q^{85} -8.56231 q^{86} -9.85410 q^{87} -3.00000 q^{88} -3.61803 q^{89} -0.909830 q^{90} -2.85410 q^{91} +6.70820 q^{92} +13.0902 q^{93} +1.76393 q^{94} -2.61803 q^{96} -18.7082 q^{97} -1.00000 q^{98} +11.5623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 4 q^{5} - 3 q^{6} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 4 * q^5 - 3 * q^6 - 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - 4 q^{5} - 3 q^{6} - 2 q^{7} - 2 q^{8} + q^{9} + 4 q^{10} + 6 q^{11} + 3 q^{12} - q^{13} + 2 q^{14} - q^{15} + 2 q^{16} - 3 q^{17} - q^{18} - 4 q^{20} - 3 q^{21} - 6 q^{22} - 3 q^{24} + 8 q^{25} + q^{26} - 2 q^{28} - 12 q^{29} + q^{30} + 10 q^{31} - 2 q^{32} + 9 q^{33} + 3 q^{34} + 4 q^{35} + q^{36} - 10 q^{37} + 6 q^{39} + 4 q^{40} + 3 q^{41} + 3 q^{42} - 3 q^{43} + 6 q^{44} + 13 q^{45} - 8 q^{47} + 3 q^{48} + 2 q^{49} - 8 q^{50} - 12 q^{51} - q^{52} - 12 q^{53} - 12 q^{55} + 2 q^{56} + 12 q^{58} + 16 q^{59} - q^{60} - 10 q^{62} - q^{63} + 2 q^{64} + 17 q^{65} - 9 q^{66} + 11 q^{67} - 3 q^{68} + 15 q^{69} - 4 q^{70} + 16 q^{71} - q^{72} - 7 q^{73} + 10 q^{74} - 8 q^{75} - 6 q^{77} - 6 q^{78} + 27 q^{79} - 4 q^{80} + 2 q^{81} - 3 q^{82} - 4 q^{83} - 3 q^{84} - 9 q^{85} + 3 q^{86} - 13 q^{87} - 6 q^{88} - 5 q^{89} - 13 q^{90} + q^{91} + 15 q^{93} + 8 q^{94} - 3 q^{96} - 24 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - 4 * q^5 - 3 * q^6 - 2 * q^7 - 2 * q^8 + q^9 + 4 * q^10 + 6 * q^11 + 3 * q^12 - q^13 + 2 * q^14 - q^15 + 2 * q^16 - 3 * q^17 - q^18 - 4 * q^20 - 3 * q^21 - 6 * q^22 - 3 * q^24 + 8 * q^25 + q^26 - 2 * q^28 - 12 * q^29 + q^30 + 10 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 + 4 * q^35 + q^36 - 10 * q^37 + 6 * q^39 + 4 * q^40 + 3 * q^41 + 3 * q^42 - 3 * q^43 + 6 * q^44 + 13 * q^45 - 8 * q^47 + 3 * q^48 + 2 * q^49 - 8 * q^50 - 12 * q^51 - q^52 - 12 * q^53 - 12 * q^55 + 2 * q^56 + 12 * q^58 + 16 * q^59 - q^60 - 10 * q^62 - q^63 + 2 * q^64 + 17 * q^65 - 9 * q^66 + 11 * q^67 - 3 * q^68 + 15 * q^69 - 4 * q^70 + 16 * q^71 - q^72 - 7 * q^73 + 10 * q^74 - 8 * q^75 - 6 * q^77 - 6 * q^78 + 27 * q^79 - 4 * q^80 + 2 * q^81 - 3 * q^82 - 4 * q^83 - 3 * q^84 - 9 * q^85 + 3 * q^86 - 13 * q^87 - 6 * q^88 - 5 * q^89 - 13 * q^90 + q^91 + 15 * q^93 + 8 * q^94 - 3 * q^96 - 24 * q^97 - 2 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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