LMFDB - Embedded newform 4598.2.a.bv.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.258228.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 12x^{2} + 6x + 24 $ x^4 - 2x^3 - 12x^2 + 6*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48761$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +1.48761 q^{10} +2.48761 q^{12} -3.09144 q^{13} +4.90325 q^{14} +3.70058 q^{15} +1.00000 q^{16} -5.90325 q^{17} +3.18819 q^{18} +1.00000 q^{19} +1.48761 q^{20} +12.1974 q^{21} +2.09144 q^{23} +2.48761 q^{24} -2.78703 q^{25} -3.09144 q^{26} +0.468133 q^{27} +4.90325 q^{28} -0.700580 q^{29} +3.70058 q^{30} +4.97521 q^{31} +1.00000 q^{32} -5.90325 q^{34} +7.29411 q^{35} +3.18819 q^{36} +9.31889 q^{37} +1.00000 q^{38} -7.69028 q^{39} +1.48761 q^{40} -6.48229 q^{41} +12.1974 q^{42} +0.792340 q^{43} +4.74277 q^{45} +2.09144 q^{46} -2.18819 q^{47} +2.48761 q^{48} +17.0419 q^{49} -2.78703 q^{50} -14.6850 q^{51} -3.09144 q^{52} -5.29942 q^{53} +0.468133 q^{54} +4.90325 q^{56} +2.48761 q^{57} -0.700580 q^{58} -0.603830 q^{59} +3.70058 q^{60} +5.11123 q^{61} +4.97521 q^{62} +15.6325 q^{63} +1.00000 q^{64} -4.59884 q^{65} -11.8731 q^{67} -5.90325 q^{68} +5.20267 q^{69} +7.29411 q^{70} +9.45751 q^{71} +3.18819 q^{72} +1.90325 q^{73} +9.31889 q^{74} -6.93303 q^{75} +1.00000 q^{76} -7.69028 q^{78} +14.4823 q^{79} +1.48761 q^{80} -8.40003 q^{81} -6.48229 q^{82} -7.48761 q^{83} +12.1974 q^{84} -8.78171 q^{85} +0.792340 q^{86} -1.74277 q^{87} +3.50708 q^{89} +4.74277 q^{90} -15.1581 q^{91} +2.09144 q^{92} +12.3764 q^{93} -2.18819 q^{94} +1.48761 q^{95} +2.48761 q^{96} -10.0000 q^{97} +17.0419 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9 - 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 + 26 * q^15 + 4 * q^16 - 7 * q^17 + 16 * q^18 + 4 * q^19 - 2 * q^20 - 9 * q^21 - 5 * q^23 + 2 * q^24 + 8 * q^25 + q^26 + 8 * q^27 + 3 * q^28 - 14 * q^29 + 26 * q^30 + 4 * q^31 + 4 * q^32 - 7 * q^34 - 12 * q^35 + 16 * q^36 + 12 * q^37 + 4 * q^38 + 5 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 14 * q^43 - 2 * q^45 - 5 * q^46 - 12 * q^47 + 2 * q^48 + 23 * q^49 + 8 * q^50 + 7 * q^51 + q^52 - 10 * q^53 + 8 * q^54 + 3 * q^56 + 2 * q^57 - 14 * q^58 + 3 * q^59 + 26 * q^60 + 6 * q^61 + 4 * q^62 - 18 * q^63 + 4 * q^64 + 4 * q^65 + 15 * q^67 - 7 * q^68 - 7 * q^69 - 12 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 - 44 * q^75 + 4 * q^76 + 5 * q^78 + 20 * q^79 - 2 * q^80 + 52 * q^81 + 12 * q^82 - 22 * q^83 - 9 * q^84 + 14 * q^85 + 14 * q^86 + 14 * q^87 - 8 * q^89 - 2 * q^90 - 18 * q^91 - 5 * q^92 + 56 * q^93 - 12 * q^94 - 2 * q^95 + 2 * q^96 - 40 * q^97 + 23 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.48761	1.43622	0.718110	−	0.695929i	$-0.245007\pi$
$3$	2.48761	1.43622	0.718110	+	0.695929i	$0.245007\pi$
$4$	1.00000	0.500000
$5$	1.48761	0.665278	0.332639	−	0.943054i	$-0.392061\pi$
$5$	1.48761	0.665278	0.332639	+	0.943054i	$0.392061\pi$
$6$	2.48761	1.01556
$7$	4.90325	1.85325	0.926627	−	0.375981i	$-0.122694\pi$
$7$	4.90325	1.85325	0.926627	+	0.375981i	$0.122694\pi$
$8$	1.00000	0.353553
$9$	3.18819	1.06273
$10$	1.48761	0.470422
$11$	0	0
$11$	0	0
$12$	2.48761	0.718110
$13$	−3.09144	−0.857410	−0.428705	−	0.903444i	$-0.641030\pi$
$13$	−3.09144	−0.857410	−0.428705	+	0.903444i	$0.641030\pi$
$14$	4.90325	1.31045
$15$	3.70058	0.955486
$16$	1.00000	0.250000
$17$	−5.90325	−1.43175	−0.715874	−	0.698229i	$-0.753972\pi$
$17$	−5.90325	−1.43175	−0.715874	+	0.698229i	$0.753972\pi$
$18$	3.18819	0.751463
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.48761	0.332639
$21$	12.1974	2.66168
$22$	0	0
$23$	2.09144	0.436095	0.218047	−	0.975938i	$-0.430031\pi$
$23$	2.09144	0.436095	0.218047	+	0.975938i	$0.430031\pi$
$24$	2.48761	0.507781
$25$	−2.78703	−0.557405
$26$	−3.09144	−0.606281
$27$	0.468133	0.0900922
$28$	4.90325	0.926627
$29$	−0.700580	−0.130094	−0.0650472	−	0.997882i	$-0.520720\pi$
$29$	−0.700580	−0.130094	−0.0650472	+	0.997882i	$0.520720\pi$
$30$	3.70058	0.675630
$31$	4.97521	0.893575	0.446787	−	0.894640i	$-0.352568\pi$
$31$	4.97521	0.893575	0.446787	+	0.894640i	$0.352568\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−5.90325	−1.01240
$35$	7.29411	1.23293
$36$	3.18819	0.531364
$37$	9.31889	1.53202	0.766008	−	0.642831i	$-0.222240\pi$
$37$	9.31889	1.53202	0.766008	+	0.642831i	$0.222240\pi$
$38$	1.00000	0.162221
$39$	−7.69028	−1.23143
$40$	1.48761	0.235211
$41$	−6.48229	−1.01236	−0.506182	−	0.862427i	$-0.668944\pi$
$41$	−6.48229	−1.01236	−0.506182	+	0.862427i	$0.668944\pi$
$42$	12.1974	1.88209
$43$	0.792340	0.120831	0.0604154	−	0.998173i	$-0.480757\pi$
$43$	0.792340	0.120831	0.0604154	+	0.998173i	$0.480757\pi$
$44$	0	0
$45$	4.74277	0.707010
$46$	2.09144	0.308365
$47$	−2.18819	−0.319180	−0.159590	−	0.987183i	$-0.551017\pi$
$47$	−2.18819	−0.319180	−0.159590	+	0.987183i	$0.551017\pi$
$48$	2.48761	0.359055
$49$	17.0419	2.43455
$50$	−2.78703	−0.394145
$51$	−14.6850	−2.05631
$52$	−3.09144	−0.428705
$53$	−5.29942	−0.727931	−0.363966	−	0.931412i	$-0.618577\pi$
$53$	−5.29942	−0.727931	−0.363966	+	0.931412i	$0.618577\pi$
$54$	0.468133	0.0637048
$55$	0	0
$56$	4.90325	0.655224
$57$	2.48761	0.329492
$58$	−0.700580	−0.0919906
$59$	−0.603830	−0.0786119	−0.0393060	−	0.999227i	$-0.512515\pi$
$59$	−0.603830	−0.0786119	−0.0393060	+	0.999227i	$0.512515\pi$
$60$	3.70058	0.477743
$61$	5.11123	0.654426	0.327213	−	0.944951i	$-0.393890\pi$
$61$	5.11123	0.654426	0.327213	+	0.944951i	$0.393890\pi$
$62$	4.97521	0.631853
$63$	15.6325	1.96951
$64$	1.00000	0.125000
$65$	−4.59884	−0.570416
$66$	0	0
$67$	−11.8731	−1.45054	−0.725268	−	0.688467i	$-0.758284\pi$
$67$	−11.8731	−1.45054	−0.725268	+	0.688467i	$0.758284\pi$
$68$	−5.90325	−0.715874
$69$	5.20267	0.626328
$70$	7.29411	0.871813
$71$	9.45751	1.12240	0.561200	−	0.827680i	$-0.310340\pi$
$71$	9.45751	1.12240	0.561200	+	0.827680i	$0.310340\pi$
$72$	3.18819	0.375731
$73$	1.90325	0.222759	0.111379	−	0.993778i	$-0.464473\pi$
$73$	1.90325	0.222759	0.111379	+	0.993778i	$0.464473\pi$
$74$	9.31889	1.08330
$75$	−6.93303	−0.800557
$76$	1.00000	0.114708
$77$	0	0
$78$	−7.69028	−0.870752
$79$	14.4823	1.62939	0.814693	−	0.579893i	$-0.196906\pi$
$79$	14.4823	1.62939	0.814693	+	0.579893i	$0.196906\pi$
$80$	1.48761	0.166319
$81$	−8.40003	−0.933336
$82$	−6.48229	−0.715850
$83$	−7.48761	−0.821872	−0.410936	−	0.911664i	$-0.634798\pi$
$83$	−7.48761	−0.821872	−0.410936	+	0.911664i	$0.634798\pi$
$84$	12.1974	1.33084
$85$	−8.78171	−0.952511
$86$	0.792340	0.0854403
$87$	−1.74277	−0.186844
$88$	0	0
$89$	3.50708	0.371750	0.185875	−	0.982573i	$-0.440488\pi$
$89$	3.50708	0.371750	0.185875	+	0.982573i	$0.440488\pi$
$90$	4.74277	0.499931
$91$	−15.1581	−1.58900
$92$	2.09144	0.218047
$93$	12.3764	1.28337
$94$	−2.18819	−0.225694
$95$	1.48761	0.152625
$96$	2.48761	0.253890
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	17.0419	1.72149
$99$	0	0
$100$	−2.78703	−0.278703
$101$	−6.08645	−0.605624	−0.302812	−	0.953050i	$-0.597925\pi$
$101$	−6.08645	−0.605624	−0.302812	+	0.953050i	$0.597925\pi$
$102$	−14.6850	−1.45403
$103$	17.5071	1.72502	0.862512	−	0.506037i	$-0.168890\pi$
$103$	17.5071	1.72502	0.862512	+	0.506037i	$0.168890\pi$
$104$	−3.09144	−0.303140
$105$	18.1449	1.77076
$106$	−5.29942	−0.514725
$107$	−11.7424	−1.13518	−0.567592	−	0.823310i	$-0.692125\pi$
$107$	−11.7424	−1.13518	−0.567592	+	0.823310i	$0.692125\pi$
$108$	0.468133	0.0450461
$109$	2.60383	0.249402	0.124701	−	0.992194i	$-0.460203\pi$
$109$	2.60383	0.249402	0.124701	+	0.992194i	$0.460203\pi$
$110$	0	0
$111$	23.1817	2.20031
$112$	4.90325	0.463314
$113$	12.4823	1.17424	0.587118	−	0.809502i	$-0.300263\pi$
$113$	12.4823	1.17424	0.587118	+	0.809502i	$0.300263\pi$
$114$	2.48761	0.232986
$115$	3.11123	0.290124
$116$	−0.700580	−0.0650472
$117$	−9.85607	−0.911194
$118$	−0.603830	−0.0555870
$119$	−28.9451	−2.65339
$120$	3.70058	0.337815
$121$	0	0
$122$	5.11123	0.462749
$123$	−16.1254	−1.45398
$124$	4.97521	0.446787
$125$	−11.5840	−1.03611
$126$	15.6325	1.39265
$127$	−18.7817	−1.66661	−0.833304	−	0.552815i	$-0.813553\pi$
$127$	−18.7817	−1.66661	−0.833304	+	0.552815i	$0.813553\pi$
$128$	1.00000	0.0883883
$129$	1.97103	0.173540
$130$	−4.59884	−0.403345
$131$	−9.98937	−0.872776	−0.436388	−	0.899759i	$-0.643742\pi$
$131$	−9.98937	−0.872776	−0.436388	+	0.899759i	$0.643742\pi$
$132$	0	0
$133$	4.90325	0.425166
$134$	−11.8731	−1.02568
$135$	0.696398	0.0599364
$136$	−5.90325	−0.506200
$137$	10.6956	0.913786	0.456893	−	0.889522i	$-0.348962\pi$
$137$	10.6956	0.913786	0.456893	+	0.889522i	$0.348962\pi$
$138$	5.20267	0.442881
$139$	−8.32680	−0.706270	−0.353135	−	0.935572i	$-0.614884\pi$
$139$	−8.32680	−0.706270	−0.353135	+	0.935572i	$0.614884\pi$
$140$	7.29411	0.616465
$141$	−5.44335	−0.458412
$142$	9.45751	0.793656
$143$	0	0
$144$	3.18819	0.265682
$145$	−1.04219	−0.0865489
$146$	1.90325	0.157514
$147$	42.3934	3.49655
$148$	9.31889	0.766008
$149$	−23.3410	−1.91217	−0.956083	−	0.293096i	$-0.905314\pi$
$149$	−23.3410	−1.91217	−0.956083	+	0.293096i	$0.905314\pi$
$150$	−6.93303	−0.566079
$151$	−3.32421	−0.270520	−0.135260	−	0.990810i	$-0.543187\pi$
$151$	−3.32421	−0.270520	−0.135260	+	0.990810i	$0.543187\pi$
$152$	1.00000	0.0811107
$153$	−18.8207	−1.52156
$154$	0	0
$155$	7.40116	0.594475
$156$	−7.69028	−0.615715
$157$	22.9177	1.82903	0.914517	−	0.404547i	$-0.132571\pi$
$157$	22.9177	1.82903	0.914517	+	0.404547i	$0.132571\pi$
$158$	14.4823	1.15215
$159$	−13.1829	−1.04547
$160$	1.48761	0.117606
$161$	10.2548	0.808194
$162$	−8.40003	−0.659968
$163$	−20.4053	−1.59827	−0.799135	−	0.601152i	$-0.794709\pi$
$163$	−20.4053	−1.59827	−0.799135	+	0.601152i	$0.794709\pi$
$164$	−6.48229	−0.506182
$165$	0	0
$166$	−7.48761	−0.581151
$167$	−14.7817	−1.14384	−0.571922	−	0.820308i	$-0.693802\pi$
$167$	−14.7817	−1.14384	−0.571922	+	0.820308i	$0.693802\pi$
$168$	12.1974	0.941047
$169$	−3.44302	−0.264848
$170$	−8.78171	−0.673527
$171$	3.18819	0.243807
$172$	0.792340	0.0604154
$173$	−18.2640	−1.38859	−0.694293	−	0.719692i	$-0.744283\pi$
$173$	−18.2640	−1.38859	−0.694293	+	0.719692i	$0.744283\pi$
$174$	−1.74277	−0.132119
$175$	−13.6655	−1.03301
$176$	0	0
$177$	−1.50209	−0.112904
$178$	3.50708	0.262867
$179$	−15.6262	−1.16796	−0.583979	−	0.811769i	$-0.698505\pi$
$179$	−15.6262	−1.16796	−0.583979	+	0.811769i	$0.698505\pi$
$180$	4.74277	0.353505
$181$	22.6378	1.68265	0.841327	−	0.540527i	$-0.181775\pi$
$181$	22.6378	1.68265	0.841327	+	0.540527i	$0.181775\pi$
$182$	−15.1581	−1.12359
$183$	12.7147	0.939901
$184$	2.09144	0.154183
$185$	13.8628	1.01922
$186$	12.3764	0.907480
$187$	0	0
$188$	−2.18819	−0.159590
$189$	2.29537	0.166964
$190$	1.48761	0.107922
$191$	13.5021	0.976977	0.488489	−	0.872570i	$-0.337548\pi$
$191$	13.5021	0.976977	0.488489	+	0.872570i	$0.337548\pi$
$192$	2.48761	0.179528
$193$	8.00000	0.575853	0.287926	−	0.957653i	$-0.407034\pi$
$193$	8.00000	0.575853	0.287926	+	0.957653i	$0.407034\pi$
$194$	−10.0000	−0.717958
$195$	−11.4401	−0.819243
$196$	17.0419	1.21728
$197$	13.3806	0.953325	0.476663	−	0.879086i	$-0.341846\pi$
$197$	13.3806	0.953325	0.476663	+	0.879086i	$0.341846\pi$
$198$	0	0
$199$	−24.6354	−1.74636	−0.873178	−	0.487401i	$-0.837945\pi$
$199$	−24.6354	−1.74636	−0.873178	+	0.487401i	$0.837945\pi$
$200$	−2.78703	−0.197073
$201$	−29.5357	−2.08329
$202$	−6.08645	−0.428241
$203$	−3.43512	−0.241098
$204$	−14.6850	−1.02815
$205$	−9.64310	−0.673503
$206$	17.5071	1.21978
$207$	6.66789	0.463450
$208$	−3.09144	−0.214353
$209$	0	0
$210$	18.1449	1.25211
$211$	−21.4522	−1.47683	−0.738415	−	0.674347i	$-0.764425\pi$
$211$	−21.4522	−1.47683	−0.738415	+	0.674347i	$0.764425\pi$
$212$	−5.29942	−0.363966
$213$	23.5266	1.61201
$214$	−11.7424	−0.802697
$215$	1.17869	0.0803860
$216$	0.468133	0.0318524
$217$	24.3947	1.65602
$218$	2.60383	0.176354
$219$	4.73454	0.319930
$220$	0	0
$221$	18.2495	1.22760
$222$	23.1817	1.55586
$223$	−7.26401	−0.486434	−0.243217	−	0.969972i	$-0.578203\pi$
$223$	−7.26401	−0.486434	−0.243217	+	0.969972i	$0.578203\pi$
$224$	4.90325	0.327612
$225$	−8.88556	−0.592371
$226$	12.4823	0.830310
$227$	6.44302	0.427638	0.213819	−	0.976873i	$-0.431410\pi$
$227$	6.44302	0.427638	0.213819	+	0.976873i	$0.431410\pi$
$228$	2.48761	0.164746
$229$	−14.1333	−0.933955	−0.466977	−	0.884269i	$-0.654657\pi$
$229$	−14.1333	−0.933955	−0.466977	+	0.884269i	$0.654657\pi$
$230$	3.11123	0.205149
$231$	0	0
$232$	−0.700580	−0.0459953
$233$	−24.1776	−1.58392	−0.791962	−	0.610570i	$-0.790940\pi$
$233$	−24.1776	−1.58392	−0.791962	+	0.610570i	$0.790940\pi$
$234$	−9.85607	−0.644312
$235$	−3.25516	−0.212343
$236$	−0.603830	−0.0393060
$237$	36.0262	2.34016
$238$	−28.9451	−1.87623
$239$	28.1581	1.82140	0.910698	−	0.413074i	$-0.135545\pi$
$239$	28.1581	1.82140	0.910698	+	0.413074i	$0.135545\pi$
$240$	3.70058	0.238871
$241$	−17.7843	−1.14559	−0.572794	−	0.819699i	$-0.694140\pi$
$241$	−17.7843	−1.14559	−0.572794	+	0.819699i	$0.694140\pi$
$242$	0	0
$243$	−22.3004	−1.43057
$244$	5.11123	0.327213
$245$	25.3516	1.61965
$246$	−16.1254	−1.02812
$247$	−3.09144	−0.196703
$248$	4.97521	0.315926
$249$	−18.6262	−1.18039
$250$	−11.5840	−0.732639
$251$	1.20766	0.0762268	0.0381134	−	0.999273i	$-0.487865\pi$
$251$	1.20766	0.0762268	0.0381134	+	0.999273i	$0.487865\pi$
$252$	15.6325	0.984753
$253$	0	0
$254$	−18.7817	−1.17847
$255$	−21.8454	−1.36801
$256$	1.00000	0.0625000
$257$	−16.4053	−1.02334	−0.511669	−	0.859183i	$-0.670972\pi$
$257$	−16.4053	−1.02334	−0.511669	+	0.859183i	$0.670972\pi$
$258$	1.97103	0.122711
$259$	45.6929	2.83922
$260$	−4.59884	−0.285208
$261$	−2.23358	−0.138255
$262$	−9.98937	−0.617146
$263$	27.1776	1.67584	0.837920	−	0.545793i	$-0.183772\pi$
$263$	27.1776	1.67584	0.837920	+	0.545793i	$0.183772\pi$
$264$	0	0
$265$	−7.88345	−0.484277
$266$	4.90325	0.300638
$267$	8.72423	0.533915
$268$	−11.8731	−0.725268
$269$	9.23922	0.563325	0.281663	−	0.959514i	$-0.409114\pi$
$269$	9.23922	0.563325	0.281663	+	0.959514i	$0.409114\pi$
$270$	0.696398	0.0423814
$271$	−17.0613	−1.03640	−0.518201	−	0.855259i	$-0.673398\pi$
$271$	−17.0613	−1.03640	−0.518201	+	0.855259i	$0.673398\pi$
$272$	−5.90325	−0.357937
$273$	−37.7074	−2.28215
$274$	10.6956	0.646144
$275$	0	0
$276$	5.20267	0.313164
$277$	−21.6705	−1.30205	−0.651026	−	0.759055i	$-0.725661\pi$
$277$	−21.6705	−1.30205	−0.651026	+	0.759055i	$0.725661\pi$
$278$	−8.32680	−0.499408
$279$	15.8619	0.949627
$280$	7.29411	0.435906
$281$	0.675793	0.0403144	0.0201572	−	0.999797i	$-0.493583\pi$
$281$	0.675793	0.0403144	0.0201572	+	0.999797i	$0.493583\pi$
$282$	−5.44335	−0.324147
$283$	−2.64841	−0.157432	−0.0787160	−	0.996897i	$-0.525082\pi$
$283$	−2.64841	−0.157432	−0.0787160	+	0.996897i	$0.525082\pi$
$284$	9.45751	0.561200
$285$	3.70058	0.219203
$286$	0	0
$287$	−31.7843	−1.87617
$288$	3.18819	0.187866
$289$	17.8484	1.04990
$290$	−1.04219	−0.0611993
$291$	−24.8761	−1.45826
$292$	1.90325	0.111379
$293$	1.70589	0.0996593	0.0498297	−	0.998758i	$-0.484132\pi$
$293$	1.70589	0.0996593	0.0498297	+	0.998758i	$0.484132\pi$
$294$	42.3934	2.47244
$295$	−0.898261	−0.0522988
$296$	9.31889	0.541650
$297$	0	0
$298$	−23.3410	−1.35211
$299$	−6.46554	−0.373912
$300$	−6.93303	−0.400278
$301$	3.88504	0.223930
$302$	−3.32421	−0.191287
$303$	−15.1407	−0.869810
$304$	1.00000	0.0573539
$305$	7.60351	0.435375
$306$	−18.8207	−1.07591
$307$	14.3136	0.816919	0.408460	−	0.912776i	$-0.366066\pi$
$307$	14.3136	0.816919	0.408460	+	0.912776i	$0.366066\pi$
$308$	0	0
$309$	43.5507	2.47751
$310$	7.40116	0.420358
$311$	22.1805	1.25774	0.628870	−	0.777511i	$-0.283518\pi$
$311$	22.1805	1.25774	0.628870	+	0.777511i	$0.283518\pi$
$312$	−7.69028	−0.435376
$313$	10.4873	0.592776	0.296388	−	0.955068i	$-0.404218\pi$
$313$	10.4873	0.592776	0.296388	+	0.955068i	$0.404218\pi$
$314$	22.9177	1.29332
$315$	23.2550	1.31027
$316$	14.4823	0.814693
$317$	30.2785	1.70061	0.850305	−	0.526291i	$-0.176418\pi$
$317$	30.2785	1.70061	0.850305	+	0.526291i	$0.176418\pi$
$318$	−13.1829	−0.739259
$319$	0	0
$320$	1.48761	0.0831597
$321$	−29.2106	−1.63038
$322$	10.2548	0.571480
$323$	−5.90325	−0.328466
$324$	−8.40003	−0.466668
$325$	8.61592	0.477925
$326$	−20.4053	−1.13015
$327$	6.47730	0.358196
$328$	−6.48229	−0.357925
$329$	−10.7292	−0.591521
$330$	0	0
$331$	4.62330	0.254120	0.127060	−	0.991895i	$-0.459446\pi$
$331$	4.62330	0.254120	0.127060	+	0.991895i	$0.459446\pi$
$332$	−7.48761	−0.410936
$333$	29.7104	1.62812
$334$	−14.7817	−0.808819
$335$	−17.6626	−0.965010
$336$	12.1974	0.665420
$337$	25.8728	1.40938	0.704691	−	0.709514i	$-0.251086\pi$
$337$	25.8728	1.40938	0.704691	+	0.709514i	$0.251086\pi$
$338$	−3.44302	−0.187276
$339$	31.0510	1.68646
$340$	−8.78171	−0.476255
$341$	0	0
$342$	3.18819	0.172397
$343$	49.2378	2.65859
$344$	0.792340	0.0427201
$345$	7.73953	0.416682
$346$	−18.2640	−0.981879
$347$	30.4911	1.63685	0.818425	−	0.574613i	$-0.194848\pi$
$347$	30.4911	1.63685	0.818425	+	0.574613i	$0.194848\pi$
$348$	−1.74277	−0.0934221
$349$	29.6967	1.58963	0.794815	−	0.606852i	$-0.207568\pi$
$349$	29.6967	1.58963	0.794815	+	0.606852i	$0.207568\pi$
$350$	−13.6655	−0.730451
$351$	−1.44720	−0.0772460
$352$	0	0
$353$	−9.53977	−0.507751	−0.253875	−	0.967237i	$-0.581705\pi$
$353$	−9.53977	−0.507751	−0.253875	+	0.967237i	$0.581705\pi$
$354$	−1.50209	−0.0798352
$355$	14.0690	0.746708
$356$	3.50708	0.185875
$357$	−72.0041	−3.81086
$358$	−15.6262	−0.825871
$359$	16.6956	0.881160	0.440580	−	0.897713i	$-0.354773\pi$
$359$	16.6956	0.881160	0.440580	+	0.897713i	$0.354773\pi$
$360$	4.74277	0.249966
$361$	1.00000	0.0526316
$362$	22.6378	1.18982
$363$	0	0
$364$	−15.1581	−0.794500
$365$	2.83129	0.148196
$366$	12.7147	0.664610
$367$	0.198813	0.0103780	0.00518898	−	0.999987i	$-0.498348\pi$
$367$	0.198813	0.0103780	0.00518898	+	0.999987i	$0.498348\pi$
$368$	2.09144	0.109024
$369$	−20.6668	−1.07587
$370$	13.8628	0.720695
$371$	−25.9844	−1.34904
$372$	12.3764	0.641685
$373$	15.4427	0.799593	0.399796	−	0.916604i	$-0.369081\pi$
$373$	15.4427	0.799593	0.399796	+	0.916604i	$0.369081\pi$
$374$	0	0
$375$	−28.8165	−1.48808
$376$	−2.18819	−0.112847
$377$	2.16580	0.111544
$378$	2.29537	0.118061
$379$	20.9791	1.07762	0.538811	−	0.842427i	$-0.318874\pi$
$379$	20.9791	1.07762	0.538811	+	0.842427i	$0.318874\pi$
$380$	1.48761	0.0763126
$381$	−46.7215	−2.39362
$382$	13.5021	0.690827
$383$	−25.3310	−1.29435	−0.647176	−	0.762340i	$-0.724050\pi$
$383$	−25.3310	−1.29435	−0.647176	+	0.762340i	$0.724050\pi$
$384$	2.48761	0.126945
$385$	0	0
$386$	8.00000	0.407189
$387$	2.52613	0.128410
$388$	−10.0000	−0.507673
$389$	−4.46282	−0.226274	−0.113137	−	0.993579i	$-0.536090\pi$
$389$	−4.46282	−0.226274	−0.113137	+	0.993579i	$0.536090\pi$
$390$	−11.4401	−0.579292
$391$	−12.3463	−0.624378
$392$	17.0419	0.860744
$393$	−24.8496	−1.25350
$394$	13.3806	0.674103
$395$	21.5440	1.08399
$396$	0	0
$397$	29.9398	1.50264	0.751318	−	0.659941i	$-0.229419\pi$
$397$	29.9398	1.50264	0.751318	+	0.659941i	$0.229419\pi$
$398$	−24.6354	−1.23486
$399$	12.1974	0.610632
$400$	−2.78703	−0.139351
$401$	−18.2888	−0.913299	−0.456649	−	0.889647i	$-0.650951\pi$
$401$	−18.2888	−0.913299	−0.456649	+	0.889647i	$0.650951\pi$
$402$	−29.5357	−1.47311
$403$	−15.3806	−0.766160
$404$	−6.08645	−0.302812
$405$	−12.4959	−0.620928
$406$	−3.43512	−0.170482
$407$	0	0
$408$	−14.6850	−0.727014
$409$	25.5634	1.26403	0.632015	−	0.774956i	$-0.282228\pi$
$409$	25.5634	1.26403	0.632015	+	0.774956i	$0.282228\pi$
$410$	−9.64310	−0.476239
$411$	26.6064	1.31240
$412$	17.5071	0.862512
$413$	−2.96073	−0.145688
$414$	6.66789	0.327709
$415$	−11.1386	−0.546773
$416$	−3.09144	−0.151570
$417$	−20.7138	−1.01436
$418$	0	0
$419$	−27.6103	−1.34885	−0.674425	−	0.738343i	$-0.735608\pi$
$419$	−27.6103	−1.34885	−0.674425	+	0.738343i	$0.735608\pi$
$420$	18.1449	0.885379
$421$	−18.5242	−0.902812	−0.451406	−	0.892319i	$-0.649077\pi$
$421$	−18.5242	−0.902812	−0.451406	+	0.892319i	$0.649077\pi$
$422$	−21.4522	−1.04428
$423$	−6.97634	−0.339201
$424$	−5.29942	−0.257363
$425$	16.4525	0.798064
$426$	23.5266	1.13987
$427$	25.0617	1.21282
$428$	−11.7424	−0.567592
$429$	0	0
$430$	1.17869	0.0568415
$431$	13.8835	0.668742	0.334371	−	0.942441i	$-0.391476\pi$
$431$	13.8835	0.668742	0.334371	+	0.942441i	$0.391476\pi$
$432$	0.468133	0.0225231
$433$	5.02479	0.241476	0.120738	−	0.992684i	$-0.461474\pi$
$433$	5.02479	0.241476	0.120738	+	0.992684i	$0.461474\pi$
$434$	24.3947	1.17098
$435$	−2.59255	−0.124303
$436$	2.60383	0.124701
$437$	2.09144	0.100047
$438$	4.73454	0.226225
$439$	−8.23245	−0.392913	−0.196457	−	0.980513i	$-0.562943\pi$
$439$	−8.23245	−0.392913	−0.196457	+	0.980513i	$0.562943\pi$
$440$	0	0
$441$	54.3326	2.58727
$442$	18.2495	0.868041
$443$	−20.1722	−0.958412	−0.479206	−	0.877702i	$-0.659075\pi$
$443$	−20.1722	−0.958412	−0.479206	+	0.877702i	$0.659075\pi$
$444$	23.1817	1.10016
$445$	5.21715	0.247317
$446$	−7.26401	−0.343961
$447$	−58.0631	−2.74629
$448$	4.90325	0.231657
$449$	−10.7923	−0.509322	−0.254661	−	0.967030i	$-0.581964\pi$
$449$	−10.7923	−0.509322	−0.254661	+	0.967030i	$0.581964\pi$
$450$	−8.88556	−0.418869
$451$	0	0
$452$	12.4823	0.587118
$453$	−8.26932	−0.388527
$454$	6.44302	0.302386
$455$	−22.5493	−1.05713
$456$	2.48761	0.116493
$457$	8.27431	0.387056	0.193528	−	0.981095i	$-0.438007\pi$
$457$	8.27431	0.387056	0.193528	+	0.981095i	$0.438007\pi$
$458$	−14.1333	−0.660406
$459$	−2.76351	−0.128989
$460$	3.11123	0.145062
$461$	17.6209	0.820687	0.410344	−	0.911931i	$-0.365409\pi$
$461$	17.6209	0.820687	0.410344	+	0.911931i	$0.365409\pi$
$462$	0	0
$463$	2.53977	0.118033	0.0590166	−	0.998257i	$-0.481204\pi$
$463$	2.53977	0.118033	0.0590166	+	0.998257i	$0.481204\pi$
$464$	−0.700580	−0.0325236
$465$	18.4112	0.853798
$466$	−24.1776	−1.12000
$467$	−10.8213	−0.500750	−0.250375	−	0.968149i	$-0.580554\pi$
$467$	−10.8213	−0.500750	−0.250375	+	0.968149i	$0.580554\pi$
$468$	−9.85607	−0.455597
$469$	−58.2170	−2.68821
$470$	−3.25516	−0.150149
$471$	57.0103	2.62690
$472$	−0.603830	−0.0277935
$473$	0	0
$474$	36.0262	1.65474
$475$	−2.78703	−0.127878
$476$	−28.9451	−1.32670
$477$	−16.8955	−0.773594
$478$	28.1581	1.28792
$479$	9.96459	0.455294	0.227647	−	0.973744i	$-0.426897\pi$
$479$	9.96459	0.455294	0.227647	+	0.973744i	$0.426897\pi$
$480$	3.70058	0.168908
$481$	−28.8088	−1.31357
$482$	−17.7843	−0.810053
$483$	25.5100	1.16074
$484$	0	0
$485$	−14.8761	−0.675487
$486$	−22.3004	−1.01156
$487$	8.36639	0.379118	0.189559	−	0.981869i	$-0.439294\pi$
$487$	8.36639	0.379118	0.189559	+	0.981869i	$0.439294\pi$
$488$	5.11123	0.231375
$489$	−50.7605	−2.29547
$490$	25.3516	1.14527
$491$	−4.27722	−0.193028	−0.0965142	−	0.995332i	$-0.530769\pi$
$491$	−4.27722	−0.193028	−0.0965142	+	0.995332i	$0.530769\pi$
$492$	−16.1254	−0.726989
$493$	4.13570	0.186262
$494$	−3.09144	−0.139090
$495$	0	0
$496$	4.97521	0.223394
$497$	46.3725	2.08009
$498$	−18.6262	−0.834661
$499$	2.08645	0.0934022	0.0467011	−	0.998909i	$-0.485129\pi$
$499$	2.08645	0.0934022	0.0467011	+	0.998909i	$0.485129\pi$
$500$	−11.5840	−0.518054
$501$	−36.7711	−1.64281
$502$	1.20766	0.0539005
$503$	7.55166	0.336712	0.168356	−	0.985726i	$-0.446154\pi$
$503$	7.55166	0.336712	0.168356	+	0.985726i	$0.446154\pi$
$504$	15.6325	0.696326
$505$	−9.05424	−0.402908
$506$	0	0
$507$	−8.56488	−0.380380
$508$	−18.7817	−0.833304
$509$	−23.3578	−1.03532	−0.517659	−	0.855587i	$-0.673196\pi$
$509$	−23.3578	−1.03532	−0.517659	+	0.855587i	$0.673196\pi$
$510$	−21.8454	−0.967333
$511$	9.33211	0.412828
$512$	1.00000	0.0441942
$513$	0.468133	0.0206686
$514$	−16.4053	−0.723609
$515$	26.0436	1.14762
$516$	1.97103	0.0867698
$517$	0	0
$518$	45.6929	2.00763
$519$	−45.4337	−1.99432
$520$	−4.59884	−0.201673
$521$	−15.0538	−0.659517	−0.329759	−	0.944065i	$-0.606967\pi$
$521$	−15.0538	−0.659517	−0.329759	+	0.944065i	$0.606967\pi$
$522$	−2.23358	−0.0977611
$523$	−18.6027	−0.813439	−0.406720	−	0.913553i	$-0.633327\pi$
$523$	−18.6027	−0.813439	−0.406720	+	0.913553i	$0.633327\pi$
$524$	−9.98937	−0.436388
$525$	−33.9944	−1.48364
$526$	27.1776	1.18500
$527$	−29.3699	−1.27937
$528$	0	0
$529$	−18.6259	−0.809821
$530$	−7.88345	−0.342435
$531$	−1.92512	−0.0835432
$532$	4.90325	0.212583
$533$	20.0396	0.868011
$534$	8.72423	0.377535
$535$	−17.4681	−0.755213
$536$	−11.8731	−0.512842
$537$	−38.8719	−1.67745
$538$	9.23922	0.398331
$539$	0	0
$540$	0.696398	0.0299682
$541$	0.549267	0.0236148	0.0118074	−	0.999930i	$-0.496241\pi$
$541$	0.549267	0.0236148	0.0118074	+	0.999930i	$0.496241\pi$
$542$	−17.0613	−0.732847
$543$	56.3139	2.41666
$544$	−5.90325	−0.253100
$545$	3.87347	0.165921
$546$	−37.7074	−1.61373
$547$	40.5059	1.73191	0.865955	−	0.500123i	$-0.166712\pi$
$547$	40.5059	1.73191	0.865955	+	0.500123i	$0.166712\pi$
$548$	10.6956	0.456893
$549$	16.2956	0.695478
$550$	0	0
$551$	−0.700580	−0.0298457
$552$	5.20267	0.221440
$553$	71.0103	3.01967
$554$	−21.6705	−0.920690
$555$	34.4853	1.46382
$556$	−8.32680	−0.353135
$557$	41.5924	1.76233	0.881163	−	0.472812i	$-0.156761\pi$
$557$	41.5924	1.76233	0.881163	+	0.472812i	$0.156761\pi$
$558$	15.8619	0.671488
$559$	−2.44947	−0.103602
$560$	7.29411	0.308232
$561$	0	0
$562$	0.675793	0.0285066
$563$	7.87879	0.332051	0.166026	−	0.986121i	$-0.446907\pi$
$563$	7.87879	0.332051	0.166026	+	0.986121i	$0.446907\pi$
$564$	−5.44335	−0.229206
$565$	18.5687	0.781193
$566$	−2.64841	−0.111321
$567$	−41.1874	−1.72971
$568$	9.45751	0.396828
$569$	7.38055	0.309409	0.154704	−	0.987961i	$-0.450557\pi$
$569$	7.38055	0.309409	0.154704	+	0.987961i	$0.450557\pi$
$570$	3.70058	0.155000
$571$	2.68464	0.112349	0.0561743	−	0.998421i	$-0.482110\pi$
$571$	2.68464	0.112349	0.0561743	+	0.998421i	$0.482110\pi$
$572$	0	0
$573$	33.5879	1.40315
$574$	−31.7843	−1.32665
$575$	−5.82889	−0.243081
$576$	3.18819	0.132841
$577$	6.42355	0.267416	0.133708	−	0.991021i	$-0.457312\pi$
$577$	6.42355	0.267416	0.133708	+	0.991021i	$0.457312\pi$
$578$	17.8484	0.742394
$579$	19.9009	0.827051
$580$	−1.04219	−0.0432745
$581$	−36.7136	−1.52314
$582$	−24.8761	−1.03115
$583$	0	0
$584$	1.90325	0.0787571
$585$	−14.6620	−0.606197
$586$	1.70589	0.0704698
$587$	−20.8392	−0.860125	−0.430063	−	0.902799i	$-0.641509\pi$
$587$	−20.8392	−0.860125	−0.430063	+	0.902799i	$0.641509\pi$
$588$	42.3934	1.74828
$589$	4.97521	0.205000
$590$	−0.898261	−0.0369808
$591$	33.2856	1.36918
$592$	9.31889	0.383004
$593$	5.11383	0.210000	0.105000	−	0.994472i	$-0.466516\pi$
$593$	5.11383	0.210000	0.105000	+	0.994472i	$0.466516\pi$
$594$	0	0
$595$	−43.0589	−1.76524
$596$	−23.3410	−0.956083
$597$	−61.2832	−2.50815
$598$	−6.46554	−0.264396
$599$	−19.4797	−0.795919	−0.397960	−	0.917403i	$-0.630282\pi$
$599$	−19.4797	−0.795919	−0.397960	+	0.917403i	$0.630282\pi$
$600$	−6.93303	−0.283040
$601$	33.3020	1.35842	0.679209	−	0.733945i	$-0.262323\pi$
$601$	33.3020	1.35842	0.679209	+	0.733945i	$0.262323\pi$
$602$	3.88504	0.158343
$603$	−37.8538	−1.54153
$604$	−3.32421	−0.135260
$605$	0	0
$606$	−15.1407	−0.615048
$607$	−7.07051	−0.286983	−0.143492	−	0.989652i	$-0.545833\pi$
$607$	−7.07051	−0.286983	−0.143492	+	0.989652i	$0.545833\pi$
$608$	1.00000	0.0405554
$609$	−8.54522	−0.346270
$610$	7.60351	0.307857
$611$	6.76464	0.273668
$612$	−18.8207	−0.760780
$613$	−31.2552	−1.26238	−0.631192	−	0.775627i	$-0.717434\pi$
$613$	−31.2552	−1.26238	−0.631192	+	0.775627i	$0.717434\pi$
$614$	14.3136	0.577649
$615$	−23.9882	−0.967299
$616$	0	0
$617$	41.7410	1.68043	0.840214	−	0.542254i	$-0.182429\pi$
$617$	41.7410	1.68043	0.840214	+	0.542254i	$0.182429\pi$
$618$	43.5507	1.75187
$619$	−8.82131	−0.354558	−0.177279	−	0.984161i	$-0.556730\pi$
$619$	−8.82131	−0.354558	−0.177279	+	0.984161i	$0.556730\pi$
$620$	7.40116	0.297238
$621$	0.979070	0.0392887
$622$	22.1805	0.889356
$623$	17.1961	0.688947
$624$	−7.69028	−0.307857
$625$	−3.29735	−0.131894
$626$	10.4873	0.419156
$627$	0	0
$628$	22.9177	0.914517
$629$	−55.0118	−2.19346
$630$	23.2550	0.926500
$631$	−29.1623	−1.16093	−0.580466	−	0.814285i	$-0.697129\pi$
$631$	−29.1623	−1.16093	−0.580466	+	0.814285i	$0.697129\pi$
$632$	14.4823	0.576075
$633$	−53.3646	−2.12105
$634$	30.2785	1.20251
$635$	−27.9398	−1.10876
$636$	−13.1829	−0.522735
$637$	−52.6838	−2.08741
$638$	0	0
$639$	30.1523	1.19281
$640$	1.48761	0.0588028
$641$	−39.8735	−1.57491	−0.787454	−	0.616374i	$-0.788601\pi$
$641$	−39.8735	−1.57491	−0.787454	+	0.616374i	$0.788601\pi$
$642$	−29.2106	−1.15285
$643$	−11.2366	−0.443129	−0.221565	−	0.975146i	$-0.571116\pi$
$643$	−11.2366	−0.443129	−0.221565	+	0.975146i	$0.571116\pi$
$644$	10.2548	0.404097
$645$	2.93212	0.115452
$646$	−5.90325	−0.232260
$647$	−10.7022	−0.420746	−0.210373	−	0.977621i	$-0.567468\pi$
$647$	−10.7022	−0.420746	−0.210373	+	0.977621i	$0.567468\pi$
$648$	−8.40003	−0.329984
$649$	0	0
$650$	8.61592	0.337944
$651$	60.6844	2.37841
$652$	−20.4053	−0.799135
$653$	−33.6024	−1.31496	−0.657481	−	0.753471i	$-0.728378\pi$
$653$	−33.6024	−1.31496	−0.657481	+	0.753471i	$0.728378\pi$
$654$	6.47730	0.253283
$655$	−14.8603	−0.580638
$656$	−6.48229	−0.253091
$657$	6.06792	0.236732
$658$	−10.7292	−0.418269
$659$	6.17529	0.240555	0.120278	−	0.992740i	$-0.461622\pi$
$659$	6.17529	0.240555	0.120278	+	0.992740i	$0.461622\pi$
$660$	0	0
$661$	22.0114	0.856146	0.428073	−	0.903744i	$-0.359193\pi$
$661$	22.0114	0.856146	0.428073	+	0.903744i	$0.359193\pi$
$662$	4.62330	0.179690
$663$	45.3976	1.76310
$664$	−7.48761	−0.290575
$665$	7.29411	0.282853
$666$	29.7104	1.15125
$667$	−1.46522	−0.0567335
$668$	−14.7817	−0.571922
$669$	−18.0700	−0.698626
$670$	−17.6626	−0.682365
$671$	0	0
$672$	12.1974	0.470523
$673$	6.63620	0.255807	0.127903	−	0.991787i	$-0.459175\pi$
$673$	6.63620	0.255807	0.127903	+	0.991787i	$0.459175\pi$
$674$	25.8728	0.996584
$675$	−1.30470	−0.0502179
$676$	−3.44302	−0.132424
$677$	26.2521	1.00895	0.504475	−	0.863426i	$-0.331686\pi$
$677$	26.2521	1.00895	0.504475	+	0.863426i	$0.331686\pi$
$678$	31.0510	1.19251
$679$	−49.0325	−1.88169
$680$	−8.78171	−0.336763
$681$	16.0277	0.614183
$682$	0	0
$683$	36.5776	1.39960	0.699801	−	0.714338i	$-0.253272\pi$
$683$	36.5776	1.39960	0.699801	+	0.714338i	$0.253272\pi$
$684$	3.18819	0.121903
$685$	15.9108	0.607922
$686$	49.2378	1.87991
$687$	−35.1581	−1.34136
$688$	0.792340	0.0302077
$689$	16.3828	0.624136
$690$	7.73953	0.294639
$691$	−17.1660	−0.653025	−0.326513	−	0.945193i	$-0.605874\pi$
$691$	−17.1660	−0.653025	−0.326513	+	0.945193i	$0.605874\pi$
$692$	−18.2640	−0.694293
$693$	0	0
$694$	30.4911	1.15743
$695$	−12.3870	−0.469866
$696$	−1.74277	−0.0660594
$697$	38.2666	1.44945
$698$	29.6967	1.12404
$699$	−60.1443	−2.27486
$700$	−13.6655	−0.516507
$701$	5.67838	0.214470	0.107235	−	0.994234i	$-0.465800\pi$
$701$	5.67838	0.214470	0.107235	+	0.994234i	$0.465800\pi$
$702$	−1.44720	−0.0546212
$703$	9.31889	0.351469
$704$	0	0
$705$	−8.09756	−0.304972
$706$	−9.53977	−0.359034
$707$	−29.8434	−1.12238
$708$	−1.50209	−0.0564520
$709$	5.39118	0.202470	0.101235	−	0.994863i	$-0.467721\pi$
$709$	5.39118	0.202470	0.101235	+	0.994863i	$0.467721\pi$
$710$	14.0690	0.528002
$711$	46.1722	1.73159
$712$	3.50708	0.131433
$713$	10.4053	0.389683
$714$	−72.0041	−2.69468
$715$	0	0
$716$	−15.6262	−0.583979
$717$	70.0462	2.61592
$718$	16.6956	0.623074
$719$	−44.4507	−1.65773	−0.828866	−	0.559447i	$-0.811014\pi$
$719$	−44.4507	−1.65773	−0.828866	+	0.559447i	$0.811014\pi$
$720$	4.74277	0.176752
$721$	85.8416	3.19691
$722$	1.00000	0.0372161
$723$	−44.2404	−1.64532
$724$	22.6378	0.841327
$725$	1.95253	0.0725153
$726$	0	0
$727$	−9.35690	−0.347028	−0.173514	−	0.984831i	$-0.555512\pi$
$727$	−9.35690	−0.347028	−0.173514	+	0.984831i	$0.555512\pi$
$728$	−15.1581	−0.561796
$729$	−30.2744	−1.12128
$730$	2.83129	0.104791
$731$	−4.67738	−0.172999
$732$	12.7147	0.469950
$733$	5.76690	0.213005	0.106503	−	0.994312i	$-0.466035\pi$
$733$	5.76690	0.213005	0.106503	+	0.994312i	$0.466035\pi$
$734$	0.198813	0.00733833
$735$	63.0648	2.32618
$736$	2.09144	0.0770914
$737$	0	0
$738$	−20.6668	−0.760754
$739$	−21.1843	−0.779278	−0.389639	−	0.920968i	$-0.627400\pi$
$739$	−21.1843	−0.779278	−0.389639	+	0.920968i	$0.627400\pi$
$740$	13.8628	0.509608
$741$	−7.69028	−0.282509
$742$	−25.9844	−0.953917
$743$	−21.8117	−0.800193	−0.400097	−	0.916473i	$-0.631023\pi$
$743$	−21.8117	−0.800193	−0.400097	+	0.916473i	$0.631023\pi$
$744$	12.3764	0.453740
$745$	−34.7222	−1.27212
$746$	15.4427	0.565397
$747$	−23.8719	−0.873427
$748$	0	0
$749$	−57.5761	−2.10379
$750$	−28.8165	−1.05223
$751$	−0.530276	−0.0193500	−0.00967502	−	0.999953i	$-0.503080\pi$
$751$	−0.530276	−0.0193500	−0.00967502	+	0.999953i	$0.503080\pi$
$752$	−2.18819	−0.0797949
$753$	3.00418	0.109478
$754$	2.16580	0.0788737
$755$	−4.94511	−0.179971
$756$	2.29537	0.0834819
$757$	6.70589	0.243730	0.121865	−	0.992547i	$-0.461113\pi$
$757$	6.70589	0.243730	0.121865	+	0.992547i	$0.461113\pi$
$758$	20.9791	0.761994
$759$	0	0
$760$	1.48761	0.0539612
$761$	−46.5357	−1.68692	−0.843459	−	0.537193i	$-0.819485\pi$
$761$	−46.5357	−1.68692	−0.843459	+	0.537193i	$0.819485\pi$
$762$	−46.7215	−1.69254
$763$	12.7672	0.462205
$764$	13.5021	0.488489
$765$	−27.9977	−1.01226
$766$	−25.3310	−0.915246
$767$	1.86670	0.0674027
$768$	2.48761	0.0897638
$769$	19.5882	0.706369	0.353185	−	0.935554i	$-0.385099\pi$
$769$	19.5882	0.706369	0.353185	+	0.935554i	$0.385099\pi$
$770$	0	0
$771$	−40.8100	−1.46974
$772$	8.00000	0.287926
$773$	28.5348	1.02632	0.513162	−	0.858292i	$-0.328474\pi$
$773$	28.5348	1.02632	0.513162	+	0.858292i	$0.328474\pi$
$774$	2.52613	0.0907998
$775$	−13.8661	−0.498083
$776$	−10.0000	−0.358979
$777$	113.666	4.07774
$778$	−4.46282	−0.160000
$779$	−6.48229	−0.232252
$780$	−11.4401	−0.409622
$781$	0	0
$782$	−12.3463	−0.441502
$783$	−0.327964	−0.0117205
$784$	17.0419	0.608638
$785$	34.0926	1.21682
$786$	−24.8496	−0.886357
$787$	22.0811	0.787107	0.393554	−	0.919302i	$-0.371246\pi$
$787$	22.0811	0.787107	0.393554	+	0.919302i	$0.371246\pi$
$788$	13.3806	0.476663
$789$	67.6071	2.40688
$790$	21.5440	0.766499
$791$	61.2038	2.17616
$792$	0	0
$793$	−15.8011	−0.561112
$794$	29.9398	1.06252
$795$	−19.6109	−0.695528
$796$	−24.6354	−0.873178
$797$	40.8484	1.44692	0.723462	−	0.690365i	$-0.242550\pi$
$797$	40.8484	1.44692	0.723462	+	0.690365i	$0.242550\pi$
$798$	12.1974	0.431782
$799$	12.9174	0.456985
$800$	−2.78703	−0.0985363
$801$	11.1812	0.395069
$802$	−18.2888	−0.645800
$803$	0	0
$804$	−29.5357	−1.04164
$805$	15.2552	0.537674
$806$	−15.3806	−0.541757
$807$	22.9835	0.809059
$808$	−6.08645	−0.214120
$809$	5.16340	0.181535	0.0907677	−	0.995872i	$-0.471068\pi$
$809$	5.16340	0.181535	0.0907677	+	0.995872i	$0.471068\pi$
$810$	−12.4959	−0.439062
$811$	−33.6162	−1.18043	−0.590213	−	0.807248i	$-0.700956\pi$
$811$	−33.6162	−1.18043	−0.590213	+	0.807248i	$0.700956\pi$
$812$	−3.43512	−0.120549
$813$	−42.4419	−1.48850
$814$	0	0
$815$	−30.3551	−1.06329
$816$	−14.6850	−0.514077
$817$	0.792340	0.0277205
$818$	25.5634	0.893804
$819$	−48.3268	−1.68867
$820$	−9.64310	−0.336752
$821$	38.4026	1.34026	0.670130	−	0.742243i	$-0.266238\pi$
$821$	38.4026	1.34026	0.670130	+	0.742243i	$0.266238\pi$
$822$	26.6064	0.928005
$823$	42.0589	1.46608	0.733041	−	0.680184i	$-0.238100\pi$
$823$	42.0589	1.46608	0.733041	+	0.680184i	$0.238100\pi$
$824$	17.5071	0.609888
$825$	0	0
$826$	−2.96073	−0.103017
$827$	46.2094	1.60686	0.803430	−	0.595399i	$-0.203006\pi$
$827$	46.2094	1.60686	0.803430	+	0.595399i	$0.203006\pi$
$828$	6.66789	0.231725
$829$	−20.8484	−0.724094	−0.362047	−	0.932160i	$-0.617922\pi$
$829$	−20.8484	−0.724094	−0.362047	+	0.932160i	$0.617922\pi$
$830$	−11.1386	−0.386627
$831$	−53.9076	−1.87003
$832$	−3.09144	−0.107176
$833$	−100.602	−3.48567
$834$	−20.7138	−0.717260
$835$	−21.9894	−0.760974
$836$	0	0
$837$	2.32906	0.0805041
$838$	−27.6103	−0.953781
$839$	53.8522	1.85919	0.929593	−	0.368589i	$-0.120159\pi$
$839$	53.8522	1.85919	0.929593	+	0.368589i	$0.120159\pi$
$840$	18.1449	0.626057
$841$	−28.5092	−0.983075
$842$	−18.5242	−0.638385
$843$	1.68111	0.0579004
$844$	−21.4522	−0.738415
$845$	−5.12186	−0.176197
$846$	−6.97634	−0.239852
$847$	0	0
$848$	−5.29942	−0.181983
$849$	−6.58821	−0.226107
$850$	16.4525	0.564317
$851$	19.4899	0.668104
$852$	23.5266	0.806006
$853$	7.61300	0.260664	0.130332	−	0.991470i	$-0.458396\pi$
$853$	7.61300	0.260664	0.130332	+	0.991470i	$0.458396\pi$
$854$	25.0617	0.857592
$855$	4.74277	0.162199
$856$	−11.7424	−0.401348
$857$	−45.9688	−1.57026	−0.785132	−	0.619329i	$-0.787405\pi$
$857$	−45.9688	−1.57026	−0.785132	+	0.619329i	$0.787405\pi$
$858$	0	0
$859$	35.5813	1.21402	0.607009	−	0.794695i	$-0.292369\pi$
$859$	35.5813	1.21402	0.607009	+	0.794695i	$0.292369\pi$
$860$	1.17869	0.0401930
$861$	−79.0668	−2.69459
$862$	13.8835	0.472872
$863$	4.29783	0.146300	0.0731499	−	0.997321i	$-0.476695\pi$
$863$	4.29783	0.146300	0.0731499	+	0.997321i	$0.476695\pi$
$864$	0.468133	0.0159262
$865$	−27.1697	−0.923796
$866$	5.02479	0.170749
$867$	44.3997	1.50789
$868$	24.3947	0.828011
$869$	0	0
$870$	−2.59255	−0.0878957
$871$	36.7051	1.24370
$872$	2.60383	0.0881768
$873$	−31.8819	−1.07904
$874$	2.09144	0.0707439
$875$	−56.7994	−1.92017
$876$	4.73454	0.159965
$877$	−7.43836	−0.251175	−0.125588	−	0.992083i	$-0.540082\pi$
$877$	−7.43836	−0.251175	−0.125588	+	0.992083i	$0.540082\pi$
$878$	−8.23245	−0.277832
$879$	4.24359	0.143133
$880$	0	0
$881$	1.71380	0.0577393	0.0288697	−	0.999583i	$-0.490809\pi$
$881$	1.71380	0.0577393	0.0288697	+	0.999583i	$0.490809\pi$
$882$	54.3326	1.82947
$883$	9.92418	0.333975	0.166988	−	0.985959i	$-0.446596\pi$
$883$	9.92418	0.333975	0.166988	+	0.985959i	$0.446596\pi$
$884$	18.2495	0.613798
$885$	−2.23452	−0.0751126
$886$	−20.1722	−0.677700
$887$	−7.22441	−0.242572	−0.121286	−	0.992618i	$-0.538702\pi$
$887$	−7.22441	−0.242572	−0.121286	+	0.992618i	$0.538702\pi$
$888$	23.1817	0.777928
$889$	−92.0914	−3.08865
$890$	5.21715	0.174879
$891$	0	0
$892$	−7.26401	−0.243217
$893$	−2.18819	−0.0732249
$894$	−58.0631	−1.94192
$895$	−23.2457	−0.777017
$896$	4.90325	0.163806
$897$	−16.0837	−0.537020
$898$	−10.7923	−0.360145
$899$	−3.48553	−0.116249
$900$	−8.88556	−0.296185
$901$	31.2838	1.04221
$902$	0	0
$903$	9.66446	0.321613
$904$	12.4823	0.415155
$905$	33.6761	1.11943
$906$	−8.26932	−0.274730
$907$	26.1673	0.868869	0.434435	−	0.900703i	$-0.356948\pi$
$907$	26.1673	0.868869	0.434435	+	0.900703i	$0.356948\pi$
$908$	6.44302	0.213819
$909$	−19.4047	−0.643614
$910$	−22.5493	−0.747501
$911$	45.0705	1.49325	0.746626	−	0.665244i	$-0.231672\pi$
$911$	45.0705	1.49325	0.746626	+	0.665244i	$0.231672\pi$
$912$	2.48761	0.0823729
$913$	0	0
$914$	8.27431	0.273690
$915$	18.9145	0.625295
$916$	−14.1333	−0.466977
$917$	−48.9804	−1.61748
$918$	−2.76351	−0.0912093
$919$	−25.4024	−0.837949	−0.418974	−	0.907998i	$-0.637610\pi$
$919$	−25.4024	−0.837949	−0.418974	+	0.907998i	$0.637610\pi$
$920$	3.11123	0.102574
$921$	35.6066	1.17328
$922$	17.6209	0.580314
$923$	−29.2373	−0.962357
$924$	0	0
$925$	−25.9720	−0.853954
$926$	2.53977	0.0834621
$927$	55.8158	1.83323
$928$	−0.700580	−0.0229977
$929$	24.9398	0.818248	0.409124	−	0.912479i	$-0.365834\pi$
$929$	24.9398	0.818248	0.409124	+	0.912479i	$0.365834\pi$
$930$	18.4112	0.603726
$931$	17.0419	0.558524
$932$	−24.1776	−0.791962
$933$	55.1763	1.80639
$934$	−10.8213	−0.354084
$935$	0	0
$936$	−9.85607	−0.322156
$937$	−16.0288	−0.523639	−0.261820	−	0.965117i	$-0.584323\pi$
$937$	−16.0288	−0.523639	−0.261820	+	0.965117i	$0.584323\pi$
$938$	−58.2170	−1.90085
$939$	26.0882	0.851357
$940$	−3.25516	−0.106172
$941$	−35.9569	−1.17216	−0.586080	−	0.810253i	$-0.699330\pi$
$941$	−35.9569	−1.17216	−0.586080	+	0.810253i	$0.699330\pi$
$942$	57.0103	1.85750
$943$	−13.5573	−0.441487
$944$	−0.603830	−0.0196530
$945$	3.41461	0.111077
$946$	0	0
$947$	−39.1771	−1.27308	−0.636542	−	0.771242i	$-0.719636\pi$
$947$	−39.1771	−1.27308	−0.636542	+	0.771242i	$0.719636\pi$
$948$	36.0262	1.17008
$949$	−5.88378	−0.190995
$950$	−2.78703	−0.0904231
$951$	75.3210	2.44245
$952$	−28.9451	−0.938116
$953$	34.0670	1.10354	0.551769	−	0.833997i	$-0.313953\pi$
$953$	34.0670	1.10354	0.551769	+	0.833997i	$0.313953\pi$
$954$	−16.8955	−0.547013
$955$	20.0858	0.649961
$956$	28.1581	0.910698
$957$	0	0
$958$	9.96459	0.321941
$959$	52.4432	1.69348
$960$	3.70058	0.119436
$961$	−6.24726	−0.201524
$962$	−28.8088	−0.928832
$963$	−37.4371	−1.20639
$964$	−17.7843	−0.572794
$965$	11.9009	0.383102
$966$	25.5100	0.820771
$967$	4.50980	0.145025	0.0725127	−	0.997367i	$-0.476898\pi$
$967$	4.50980	0.145025	0.0725127	+	0.997367i	$0.476898\pi$
$968$	0	0
$969$	−14.6850	−0.471749
$970$	−14.8761	−0.477642
$971$	−1.82970	−0.0587178	−0.0293589	−	0.999569i	$-0.509347\pi$
$971$	−1.82970	−0.0587178	−0.0293589	+	0.999569i	$0.509347\pi$
$972$	−22.3004	−0.715284
$973$	−40.8284	−1.30890
$974$	8.36639	0.268077
$975$	21.4330	0.686406
$976$	5.11123	0.163607
$977$	−27.8902	−0.892287	−0.446144	−	0.894961i	$-0.647203\pi$
$977$	−27.8902	−0.892287	−0.446144	+	0.894961i	$0.647203\pi$
$978$	−50.7605	−1.62314
$979$	0	0
$980$	25.3516	0.809827
$981$	8.30149	0.265046
$982$	−4.27722	−0.136492
$983$	46.1790	1.47288	0.736441	−	0.676502i	$-0.236505\pi$
$983$	46.1790	1.47288	0.736441	+	0.676502i	$0.236505\pi$
$984$	−16.1254	−0.514059
$985$	19.9050	0.634226
$986$	4.13570	0.131707
$987$	−26.6901	−0.849555
$988$	−3.09144	−0.0983517
$989$	1.65713	0.0526937
$990$	0	0
$991$	36.2782	1.15241	0.576207	−	0.817304i	$-0.304532\pi$
$991$	36.2782	1.15241	0.576207	+	0.817304i	$0.304532\pi$
$992$	4.97521	0.157963
$993$	11.5010	0.364972
$994$	46.3725	1.47085
$995$	−36.6478	−1.16181
$996$	−18.6262	−0.590194
$997$	−44.0469	−1.39498	−0.697489	−	0.716596i	$-0.745699\pi$
$997$	−44.0469	−1.39498	−0.697489	+	0.716596i	$0.745699\pi$
$998$	2.08645	0.0660453
$999$	4.36248	0.138023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bv.1.3	yes	4
11.10	odd	2		4598.2.a.bs.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bs.1.3	✓	4	11.10	odd	2
4598.2.a.bv.1.3	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.48761 q^{3} +1.00000 q^{4} +1.48761 q^{5} +2.48761 q^{6} +4.90325 q^{7} +1.00000 q^{8} +3.18819 q^{9} +1.48761 q^{10} +2.48761 q^{12} -3.09144 q^{13} +4.90325 q^{14} +3.70058 q^{15} +1.00000 q^{16} -5.90325 q^{17} +3.18819 q^{18} +1.00000 q^{19} +1.48761 q^{20} +12.1974 q^{21} +2.09144 q^{23} +2.48761 q^{24} -2.78703 q^{25} -3.09144 q^{26} +0.468133 q^{27} +4.90325 q^{28} -0.700580 q^{29} +3.70058 q^{30} +4.97521 q^{31} +1.00000 q^{32} -5.90325 q^{34} +7.29411 q^{35} +3.18819 q^{36} +9.31889 q^{37} +1.00000 q^{38} -7.69028 q^{39} +1.48761 q^{40} -6.48229 q^{41} +12.1974 q^{42} +0.792340 q^{43} +4.74277 q^{45} +2.09144 q^{46} -2.18819 q^{47} +2.48761 q^{48} +17.0419 q^{49} -2.78703 q^{50} -14.6850 q^{51} -3.09144 q^{52} -5.29942 q^{53} +0.468133 q^{54} +4.90325 q^{56} +2.48761 q^{57} -0.700580 q^{58} -0.603830 q^{59} +3.70058 q^{60} +5.11123 q^{61} +4.97521 q^{62} +15.6325 q^{63} +1.00000 q^{64} -4.59884 q^{65} -11.8731 q^{67} -5.90325 q^{68} +5.20267 q^{69} +7.29411 q^{70} +9.45751 q^{71} +3.18819 q^{72} +1.90325 q^{73} +9.31889 q^{74} -6.93303 q^{75} +1.00000 q^{76} -7.69028 q^{78} +14.4823 q^{79} +1.48761 q^{80} -8.40003 q^{81} -6.48229 q^{82} -7.48761 q^{83} +12.1974 q^{84} -8.78171 q^{85} +0.792340 q^{86} -1.74277 q^{87} +3.50708 q^{89} +4.74277 q^{90} -15.1581 q^{91} +2.09144 q^{92} +12.3764 q^{93} -2.18819 q^{94} +1.48761 q^{95} +2.48761 q^{96} -10.0000 q^{97} +17.0419 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} + 3 q^{7} + 4 q^{8} + 16 q^{9} - 2 q^{10} + 2 q^{12} + q^{13} + 3 q^{14} + 26 q^{15} + 4 q^{16} - 7 q^{17} + 16 q^{18} + 4 q^{19} - 2 q^{20} - 9 q^{21} - 5 q^{23} + 2 q^{24} + 8 q^{25} + q^{26} + 8 q^{27} + 3 q^{28} - 14 q^{29} + 26 q^{30} + 4 q^{31} + 4 q^{32} - 7 q^{34} - 12 q^{35} + 16 q^{36} + 12 q^{37} + 4 q^{38} + 5 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} + 14 q^{43} - 2 q^{45} - 5 q^{46} - 12 q^{47} + 2 q^{48} + 23 q^{49} + 8 q^{50} + 7 q^{51} + q^{52} - 10 q^{53} + 8 q^{54} + 3 q^{56} + 2 q^{57} - 14 q^{58} + 3 q^{59} + 26 q^{60} + 6 q^{61} + 4 q^{62} - 18 q^{63} + 4 q^{64} + 4 q^{65} + 15 q^{67} - 7 q^{68} - 7 q^{69} - 12 q^{70} - 16 q^{71} + 16 q^{72} - 9 q^{73} + 12 q^{74} - 44 q^{75} + 4 q^{76} + 5 q^{78} + 20 q^{79} - 2 q^{80} + 52 q^{81} + 12 q^{82} - 22 q^{83} - 9 q^{84} + 14 q^{85} + 14 q^{86} + 14 q^{87} - 8 q^{89} - 2 q^{90} - 18 q^{91} - 5 q^{92} + 56 q^{93} - 12 q^{94} - 2 q^{95} + 2 q^{96} - 40 q^{97} + 23 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 + 3 * q^7 + 4 * q^8 + 16 * q^9 - 2 * q^10 + 2 * q^12 + q^13 + 3 * q^14 + 26 * q^15 + 4 * q^16 - 7 * q^17 + 16 * q^18 + 4 * q^19 - 2 * q^20 - 9 * q^21 - 5 * q^23 + 2 * q^24 + 8 * q^25 + q^26 + 8 * q^27 + 3 * q^28 - 14 * q^29 + 26 * q^30 + 4 * q^31 + 4 * q^32 - 7 * q^34 - 12 * q^35 + 16 * q^36 + 12 * q^37 + 4 * q^38 + 5 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 14 * q^43 - 2 * q^45 - 5 * q^46 - 12 * q^47 + 2 * q^48 + 23 * q^49 + 8 * q^50 + 7 * q^51 + q^52 - 10 * q^53 + 8 * q^54 + 3 * q^56 + 2 * q^57 - 14 * q^58 + 3 * q^59 + 26 * q^60 + 6 * q^61 + 4 * q^62 - 18 * q^63 + 4 * q^64 + 4 * q^65 + 15 * q^67 - 7 * q^68 - 7 * q^69 - 12 * q^70 - 16 * q^71 + 16 * q^72 - 9 * q^73 + 12 * q^74 - 44 * q^75 + 4 * q^76 + 5 * q^78 + 20 * q^79 - 2 * q^80 + 52 * q^81 + 12 * q^82 - 22 * q^83 - 9 * q^84 + 14 * q^85 + 14 * q^86 + 14 * q^87 - 8 * q^89 - 2 * q^90 - 18 * q^91 - 5 * q^92 + 56 * q^93 - 12 * q^94 - 2 * q^95 + 2 * q^96 - 40 * q^97 + 23 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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