LMFDB - Embedded newform 8017.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62968 q^{2} -1.21671 q^{3} +4.91523 q^{4} +1.08723 q^{5} +3.19957 q^{6} +0.844404 q^{7} -7.66614 q^{8} -1.51960 q^{9} +O(q^{10})$	\(q-2.62968 q^{2} -1.21671 q^{3} +4.91523 q^{4} +1.08723 q^{5} +3.19957 q^{6} +0.844404 q^{7} -7.66614 q^{8} -1.51960 q^{9} -2.85908 q^{10} -0.776704 q^{11} -5.98044 q^{12} +2.97138 q^{13} -2.22051 q^{14} -1.32285 q^{15} +10.3291 q^{16} -5.91869 q^{17} +3.99608 q^{18} -3.62786 q^{19} +5.34400 q^{20} -1.02740 q^{21} +2.04248 q^{22} +7.06955 q^{23} +9.32751 q^{24} -3.81793 q^{25} -7.81379 q^{26} +5.49907 q^{27} +4.15044 q^{28} +8.31647 q^{29} +3.47868 q^{30} +2.72622 q^{31} -11.8299 q^{32} +0.945027 q^{33} +15.5643 q^{34} +0.918063 q^{35} -7.46921 q^{36} +2.48715 q^{37} +9.54013 q^{38} -3.61532 q^{39} -8.33487 q^{40} +4.04189 q^{41} +2.70173 q^{42} -4.63925 q^{43} -3.81768 q^{44} -1.65216 q^{45} -18.5907 q^{46} -9.43445 q^{47} -12.5675 q^{48} -6.28698 q^{49} +10.0399 q^{50} +7.20136 q^{51} +14.6050 q^{52} +13.0469 q^{53} -14.4608 q^{54} -0.844457 q^{55} -6.47332 q^{56} +4.41407 q^{57} -21.8697 q^{58} -0.0533537 q^{59} -6.50212 q^{60} -4.29445 q^{61} -7.16909 q^{62} -1.28316 q^{63} +10.4507 q^{64} +3.23058 q^{65} -2.48512 q^{66} +5.74666 q^{67} -29.0918 q^{68} -8.60162 q^{69} -2.41421 q^{70} +8.37613 q^{71} +11.6495 q^{72} -10.6024 q^{73} -6.54040 q^{74} +4.64533 q^{75} -17.8318 q^{76} -0.655852 q^{77} +9.50715 q^{78} -5.37953 q^{79} +11.2301 q^{80} -2.13199 q^{81} -10.6289 q^{82} -9.17947 q^{83} -5.04990 q^{84} -6.43499 q^{85} +12.1997 q^{86} -10.1188 q^{87} +5.95432 q^{88} -5.14223 q^{89} +4.34467 q^{90} +2.50904 q^{91} +34.7485 q^{92} -3.31703 q^{93} +24.8096 q^{94} -3.94433 q^{95} +14.3936 q^{96} -7.00826 q^{97} +16.5328 q^{98} +1.18028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.62968	−1.85947	−0.929733	−	0.368233i	$-0.879963\pi$
$2$	−2.62968	−1.85947	−0.929733	+	0.368233i	$0.879963\pi$
$3$	−1.21671	−0.702471	−0.351235	−	0.936287i	$-0.614238\pi$
$3$	−1.21671	−0.702471	−0.351235	+	0.936287i	$0.614238\pi$
$4$	4.91523	2.45762
$5$	1.08723	0.486225	0.243112	−	0.969998i	$-0.421832\pi$
$5$	1.08723	0.486225	0.243112	+	0.969998i	$0.421832\pi$
$6$	3.19957	1.30622
$7$	0.844404	0.319155	0.159577	−	0.987185i	$-0.448987\pi$
$7$	0.844404	0.319155	0.159577	+	0.987185i	$0.448987\pi$
$8$	−7.66614	−2.71039
$9$	−1.51960	−0.506535
$10$	−2.85908	−0.904119
$11$	−0.776704	−0.234185	−0.117093	−	0.993121i	$-0.537357\pi$
$11$	−0.776704	−0.234185	−0.117093	+	0.993121i	$0.537357\pi$
$12$	−5.98044	−1.72640
$13$	2.97138	0.824112	0.412056	−	0.911158i	$-0.364811\pi$
$13$	2.97138	0.824112	0.412056	+	0.911158i	$0.364811\pi$
$14$	−2.22051	−0.593457
$15$	−1.32285	−0.341559
$16$	10.3291	2.58226
$17$	−5.91869	−1.43549	−0.717747	−	0.696304i	$-0.754827\pi$
$17$	−5.91869	−1.43549	−0.717747	+	0.696304i	$0.754827\pi$
$18$	3.99608	0.941885
$19$	−3.62786	−0.832288	−0.416144	−	0.909299i	$-0.636619\pi$
$19$	−3.62786	−0.832288	−0.416144	+	0.909299i	$0.636619\pi$
$20$	5.34400	1.19495
$21$	−1.02740	−0.224197
$22$	2.04248	0.435459
$23$	7.06955	1.47410	0.737051	−	0.675837i	$-0.236218\pi$
$23$	7.06955	1.47410	0.737051	+	0.675837i	$0.236218\pi$
$24$	9.32751	1.90397
$25$	−3.81793	−0.763585
$26$	−7.81379	−1.53241
$27$	5.49907	1.05830
$28$	4.15044	0.784360
$29$	8.31647	1.54433	0.772165	−	0.635422i	$-0.219174\pi$
$29$	8.31647	1.54433	0.772165	+	0.635422i	$0.219174\pi$
$30$	3.47868	0.635117
$31$	2.72622	0.489643	0.244822	−	0.969568i	$-0.421271\pi$
$31$	2.72622	0.489643	0.244822	+	0.969568i	$0.421271\pi$
$32$	−11.8299	−2.09124
$33$	0.945027	0.164508
$34$	15.5643	2.66925
$35$	0.918063	0.155181
$36$	−7.46921	−1.24487
$37$	2.48715	0.408884	0.204442	−	0.978879i	$-0.434462\pi$
$37$	2.48715	0.408884	0.204442	+	0.978879i	$0.434462\pi$
$38$	9.54013	1.54761
$39$	−3.61532	−0.578915
$40$	−8.33487	−1.31786
$41$	4.04189	0.631237	0.315618	−	0.948886i	$-0.397788\pi$
$41$	4.04189	0.631237	0.315618	+	0.948886i	$0.397788\pi$
$42$	2.70173	0.416886
$43$	−4.63925	−0.707478	−0.353739	−	0.935344i	$-0.615090\pi$
$43$	−4.63925	−0.707478	−0.353739	+	0.935344i	$0.615090\pi$
$44$	−3.81768	−0.575537
$45$	−1.65216	−0.246290
$46$	−18.5907	−2.74104
$47$	−9.43445	−1.37616	−0.688078	−	0.725637i	$-0.741545\pi$
$47$	−9.43445	−1.37616	−0.688078	+	0.725637i	$0.741545\pi$
$48$	−12.5675	−1.81396
$49$	−6.28698	−0.898140
$50$	10.0399	1.41986
$51$	7.20136	1.00839
$52$	14.6050	2.02535
$53$	13.0469	1.79213	0.896063	−	0.443927i	$-0.146415\pi$
$53$	13.0469	1.79213	0.896063	+	0.443927i	$0.146415\pi$
$54$	−14.4608	−1.96787
$55$	−0.844457	−0.113867
$56$	−6.47332	−0.865033
$57$	4.41407	0.584658
$58$	−21.8697	−2.87163
$59$	−0.0533537	−0.00694606	−0.00347303	−	0.999994i	$-0.501106\pi$
$59$	−0.0533537	−0.00694606	−0.00347303	+	0.999994i	$0.501106\pi$
$60$	−6.50212	−0.839420
$61$	−4.29445	−0.549848	−0.274924	−	0.961466i	$-0.588653\pi$
$61$	−4.29445	−0.549848	−0.274924	+	0.961466i	$0.588653\pi$
$62$	−7.16909	−0.910476
$63$	−1.28316	−0.161663
$64$	10.4507	1.30633
$65$	3.23058	0.400704
$66$	−2.48512	−0.305897
$67$	5.74666	0.702066	0.351033	−	0.936363i	$-0.385830\pi$
$67$	5.74666	0.702066	0.351033	+	0.936363i	$0.385830\pi$
$68$	−29.0918	−3.52789
$69$	−8.60162	−1.03551
$70$	−2.41421	−0.288554
$71$	8.37613	0.994064	0.497032	−	0.867732i	$-0.334423\pi$
$71$	8.37613	0.994064	0.497032	+	0.867732i	$0.334423\pi$
$72$	11.6495	1.37291
$73$	−10.6024	−1.24091	−0.620457	−	0.784240i	$-0.713053\pi$
$73$	−10.6024	−1.24091	−0.620457	+	0.784240i	$0.713053\pi$
$74$	−6.54040	−0.760307
$75$	4.64533	0.536396
$76$	−17.8318	−2.04545
$77$	−0.655852	−0.0747412
$78$	9.50715	1.07647
$79$	−5.37953	−0.605244	−0.302622	−	0.953111i	$-0.597862\pi$
$79$	−5.37953	−0.605244	−0.302622	+	0.953111i	$0.597862\pi$
$80$	11.2301	1.25556
$81$	−2.13199	−0.236887
$82$	−10.6289	−1.17376
$83$	−9.17947	−1.00758	−0.503789	−	0.863827i	$-0.668061\pi$
$83$	−9.17947	−1.00758	−0.503789	+	0.863827i	$0.668061\pi$
$84$	−5.04990	−0.550990
$85$	−6.43499	−0.697973
$86$	12.1997	1.31553
$87$	−10.1188	−1.08485
$88$	5.95432	0.634733
$89$	−5.14223	−0.545076	−0.272538	−	0.962145i	$-0.587863\pi$
$89$	−5.14223	−0.545076	−0.272538	+	0.962145i	$0.587863\pi$
$90$	4.34467	0.457968
$91$	2.50904	0.263019
$92$	34.7485	3.62278
$93$	−3.31703	−0.343960
$94$	24.8096	2.55892
$95$	−3.94433	−0.404679
$96$	14.3936	1.46904
$97$	−7.00826	−0.711581	−0.355791	−	0.934566i	$-0.615788\pi$
$97$	−7.00826	−0.711581	−0.355791	+	0.934566i	$0.615788\pi$
$98$	16.5328	1.67006
$99$	1.18028	0.118623
$100$	−18.7660	−1.87660
$101$	16.9544	1.68702	0.843511	−	0.537111i	$-0.180484\pi$
$101$	16.9544	1.68702	0.843511	+	0.537111i	$0.180484\pi$
$102$	−18.9373	−1.87507
$103$	5.43093	0.535125	0.267563	−	0.963540i	$-0.413782\pi$
$103$	5.43093	0.535125	0.267563	+	0.963540i	$0.413782\pi$
$104$	−22.7790	−2.23367
$105$	−1.11702	−0.109010
$106$	−34.3091	−3.33240
$107$	10.2999	0.995732	0.497866	−	0.867254i	$-0.334117\pi$
$107$	10.2999	0.995732	0.497866	+	0.867254i	$0.334117\pi$
$108$	27.0292	2.60089
$109$	−3.54915	−0.339947	−0.169973	−	0.985449i	$-0.554368\pi$
$109$	−3.54915	−0.339947	−0.169973	+	0.985449i	$0.554368\pi$
$110$	2.22065	0.211731
$111$	−3.02615	−0.287229
$112$	8.72189	0.824141
$113$	4.88766	0.459793	0.229896	−	0.973215i	$-0.426161\pi$
$113$	4.88766	0.459793	0.229896	+	0.973215i	$0.426161\pi$
$114$	−11.6076	−1.08715
$115$	7.68624	0.716745
$116$	40.8774	3.79537
$117$	−4.51532	−0.417442
$118$	0.140303	0.0129160
$119$	−4.99777	−0.458145
$120$	10.1412	0.925757
$121$	−10.3967	−0.945157
$122$	11.2930	1.02242
$123$	−4.91782	−0.443425
$124$	13.4000	1.20336
$125$	−9.58713	−0.857499
$126$	3.37430	0.300607
$127$	−8.07761	−0.716772	−0.358386	−	0.933574i	$-0.616673\pi$
$127$	−8.07761	−0.716772	−0.358386	+	0.933574i	$0.616673\pi$
$128$	−3.82223	−0.337840
$129$	5.64464	0.496983
$130$	−8.49540	−0.745096
$131$	−10.5383	−0.920733	−0.460366	−	0.887729i	$-0.652282\pi$
$131$	−10.5383	−0.920733	−0.460366	+	0.887729i	$0.652282\pi$
$132$	4.64503	0.404298
$133$	−3.06338	−0.265629
$134$	−15.1119	−1.30547
$135$	5.97877	0.514570
$136$	45.3735	3.89075
$137$	−6.59895	−0.563786	−0.281893	−	0.959446i	$-0.590962\pi$
$137$	−6.59895	−0.563786	−0.281893	+	0.959446i	$0.590962\pi$
$138$	22.6195	1.92550
$139$	11.8541	1.00545	0.502727	−	0.864445i	$-0.332330\pi$
$139$	11.8541	1.00545	0.502727	+	0.864445i	$0.332330\pi$
$140$	4.51249	0.381375
$141$	11.4790	0.966709
$142$	−22.0266	−1.84843
$143$	−2.30788	−0.192995
$144$	−15.6961	−1.30801
$145$	9.04193	0.750892
$146$	27.8809	2.30744
$147$	7.64947	0.630917
$148$	12.2249	1.00488
$149$	−1.58273	−0.129662	−0.0648312	−	0.997896i	$-0.520651\pi$
$149$	−1.58273	−0.129662	−0.0648312	+	0.997896i	$0.520651\pi$
$150$	−12.2157	−0.997411
$151$	−0.437278	−0.0355852	−0.0177926	−	0.999842i	$-0.505664\pi$
$151$	−0.437278	−0.0355852	−0.0177926	+	0.999842i	$0.505664\pi$
$152$	27.8117	2.25583
$153$	8.99408	0.727128
$154$	1.72468	0.138979
$155$	2.96403	0.238077
$156$	−17.7701	−1.42275
$157$	21.9677	1.75321	0.876606	−	0.481210i	$-0.159802\pi$
$157$	21.9677	1.75321	0.876606	+	0.481210i	$0.159802\pi$
$158$	14.1465	1.12543
$159$	−15.8743	−1.25892
$160$	−12.8618	−1.01681
$161$	5.96955	0.470467
$162$	5.60645	0.440484
$163$	−23.6228	−1.85028	−0.925142	−	0.379622i	$-0.876054\pi$
$163$	−23.6228	−1.85028	−0.925142	+	0.379622i	$0.876054\pi$
$164$	19.8668	1.55134
$165$	1.02746	0.0799879
$166$	24.1391	1.87356
$167$	19.4842	1.50773	0.753867	−	0.657027i	$-0.228186\pi$
$167$	19.4842	1.50773	0.753867	+	0.657027i	$0.228186\pi$
$168$	7.87618	0.607661
$169$	−4.17091	−0.320839
$170$	16.9220	1.29786
$171$	5.51292	0.421583
$172$	−22.8030	−1.73871
$173$	9.35504	0.711251	0.355625	−	0.934629i	$-0.384268\pi$
$173$	9.35504	0.711251	0.355625	+	0.934629i	$0.384268\pi$
$174$	26.6092	2.01724
$175$	−3.22387	−0.243702
$176$	−8.02261	−0.604727
$177$	0.0649162	0.00487940
$178$	13.5224	1.01355
$179$	11.9463	0.892911	0.446456	−	0.894806i	$-0.352686\pi$
$179$	11.9463	0.892911	0.446456	+	0.894806i	$0.352686\pi$
$180$	−8.12077	−0.605286
$181$	−7.11932	−0.529175	−0.264587	−	0.964362i	$-0.585236\pi$
$181$	−7.11932	−0.529175	−0.264587	+	0.964362i	$0.585236\pi$
$182$	−6.59799	−0.489075
$183$	5.22512	0.386252
$184$	−54.1961	−3.99539
$185$	2.70410	0.198810
$186$	8.72274	0.639582
$187$	4.59707	0.336171
$188$	−46.3725	−3.38206
$189$	4.64344	0.337760
$190$	10.3723	0.752488
$191$	−22.5126	−1.62896	−0.814478	−	0.580194i	$-0.802977\pi$
$191$	−22.5126	−1.62896	−0.814478	+	0.580194i	$0.802977\pi$
$192$	−12.7155	−0.917661
$193$	−10.5007	−0.755859	−0.377929	−	0.925834i	$-0.623364\pi$
$193$	−10.5007	−0.755859	−0.377929	+	0.925834i	$0.623364\pi$
$194$	18.4295	1.32316
$195$	−3.93069	−0.281483
$196$	−30.9020	−2.20728
$197$	23.5532	1.67810	0.839049	−	0.544056i	$-0.183112\pi$
$197$	23.5532	1.67810	0.839049	+	0.544056i	$0.183112\pi$
$198$	−3.10377	−0.220575
$199$	4.91104	0.348134	0.174067	−	0.984734i	$-0.444309\pi$
$199$	4.91104	0.348134	0.174067	+	0.984734i	$0.444309\pi$
$200$	29.2688	2.06961
$201$	−6.99205	−0.493181
$202$	−44.5846	−3.13696
$203$	7.02246	0.492880
$204$	35.3964	2.47824
$205$	4.39447	0.306923
$206$	−14.2816	−0.995048
$207$	−10.7429	−0.746684
$208$	30.6915	2.12807
$209$	2.81777	0.194909
$210$	2.93741	0.202701
$211$	4.50960	0.310454	0.155227	−	0.987879i	$-0.450389\pi$
$211$	4.50960	0.310454	0.155227	+	0.987879i	$0.450389\pi$
$212$	64.1284	4.40436
$213$	−10.1914	−0.698301
$214$	−27.0856	−1.85153
$215$	−5.04394	−0.343994
$216$	−42.1566	−2.86840
$217$	2.30203	0.156272
$218$	9.33314	0.632120
$219$	12.9001	0.871706
$220$	−4.15070	−0.279840
$221$	−17.5867	−1.18301
$222$	7.95781	0.534093
$223$	−7.91572	−0.530076	−0.265038	−	0.964238i	$-0.585384\pi$
$223$	−7.91572	−0.530076	−0.265038	+	0.964238i	$0.585384\pi$
$224$	−9.98917	−0.667430
$225$	5.80174	0.386783
$226$	−12.8530	−0.854969
$227$	21.2670	1.41154	0.705771	−	0.708440i	$-0.250601\pi$
$227$	21.2670	1.41154	0.705771	+	0.708440i	$0.250601\pi$
$228$	21.6962	1.43687
$229$	22.8841	1.51222	0.756111	−	0.654443i	$-0.227097\pi$
$229$	22.8841	1.51222	0.756111	+	0.654443i	$0.227097\pi$
$230$	−20.2124	−1.33276
$231$	0.797984	0.0525035
$232$	−63.7552	−4.18574
$233$	27.3632	1.79262	0.896312	−	0.443424i	$-0.146236\pi$
$233$	27.3632	1.79262	0.896312	+	0.443424i	$0.146236\pi$
$234$	11.8739	0.776219
$235$	−10.2574	−0.669121
$236$	−0.262246	−0.0170708
$237$	6.54535	0.425166
$238$	13.1425	0.851905
$239$	−4.75908	−0.307839	−0.153920	−	0.988083i	$-0.549190\pi$
$239$	−4.75908	−0.307839	−0.153920	+	0.988083i	$0.549190\pi$
$240$	−13.6638	−0.881995
$241$	6.74662	0.434588	0.217294	−	0.976106i	$-0.430277\pi$
$241$	6.74662	0.434588	0.217294	+	0.976106i	$0.430277\pi$
$242$	27.3401	1.75749
$243$	−13.9032	−0.891890
$244$	−21.1082	−1.35131
$245$	−6.83541	−0.436698
$246$	12.9323	0.824535
$247$	−10.7798	−0.685899
$248$	−20.8996	−1.32712
$249$	11.1688	0.707794
$250$	25.2111	1.59449
$251$	−26.1801	−1.65248	−0.826238	−	0.563322i	$-0.809523\pi$
$251$	−26.1801	−1.65248	−0.826238	+	0.563322i	$0.809523\pi$
$252$	−6.30703	−0.397306
$253$	−5.49094	−0.345213
$254$	21.2415	1.33281
$255$	7.82955	0.490306
$256$	−10.8501	−0.678130
$257$	−23.9643	−1.49485	−0.747425	−	0.664346i	$-0.768710\pi$
$257$	−23.9643	−1.49485	−0.747425	+	0.664346i	$0.768710\pi$
$258$	−14.8436	−0.924123
$259$	2.10015	0.130497
$260$	15.8790	0.984777
$261$	−12.6377	−0.782257
$262$	27.7123	1.71207
$263$	19.4974	1.20226	0.601129	−	0.799152i	$-0.294718\pi$
$263$	19.4974	1.20226	0.601129	+	0.799152i	$0.294718\pi$
$264$	−7.24471	−0.445881
$265$	14.1850	0.871376
$266$	8.05572	0.493928
$267$	6.25663	0.382900
$268$	28.2462	1.72541
$269$	−4.44888	−0.271253	−0.135627	−	0.990760i	$-0.543305\pi$
$269$	−4.44888	−0.271253	−0.135627	+	0.990760i	$0.543305\pi$
$270$	−15.7223	−0.956826
$271$	25.4171	1.54398	0.771988	−	0.635637i	$-0.219262\pi$
$271$	25.4171	1.54398	0.771988	+	0.635637i	$0.219262\pi$
$272$	−61.1345	−3.70682
$273$	−3.05279	−0.184763
$274$	17.3531	1.04834
$275$	2.96540	0.178820
$276$	−42.2790	−2.54490
$277$	28.7215	1.72571	0.862855	−	0.505452i	$-0.168674\pi$
$277$	28.7215	1.72571	0.862855	+	0.505452i	$0.168674\pi$
$278$	−31.1726	−1.86961
$279$	−4.14278	−0.248021
$280$	−7.03800	−0.420601
$281$	−22.8554	−1.36344	−0.681720	−	0.731614i	$-0.738768\pi$
$281$	−22.8554	−1.36344	−0.681720	+	0.731614i	$0.738768\pi$
$282$	−30.1862	−1.79756
$283$	8.33120	0.495239	0.247619	−	0.968857i	$-0.420352\pi$
$283$	8.33120	0.495239	0.247619	+	0.968857i	$0.420352\pi$
$284$	41.1706	2.44303
$285$	4.79912	0.284275
$286$	6.06900	0.358867
$287$	3.41298	0.201462
$288$	17.9767	1.05929
$289$	18.0309	1.06064
$290$	−23.7774	−1.39626
$291$	8.52706	0.499865
$292$	−52.1132	−3.04969
$293$	2.15971	0.126172	0.0630858	−	0.998008i	$-0.479906\pi$
$293$	2.15971	0.126172	0.0630858	+	0.998008i	$0.479906\pi$
$294$	−20.1157	−1.17317
$295$	−0.0580079	−0.00337735
$296$	−19.0668	−1.10824
$297$	−4.27115	−0.247837
$298$	4.16208	0.241103
$299$	21.0063	1.21483
$300$	22.8329	1.31826
$301$	−3.91740	−0.225795
$302$	1.14990	0.0661695
$303$	−20.6286	−1.18508
$304$	−37.4724	−2.14919
$305$	−4.66906	−0.267350
$306$	−23.6516	−1.35207
$307$	24.4366	1.39467	0.697334	−	0.716746i	$-0.254369\pi$
$307$	24.4366	1.39467	0.697334	+	0.716746i	$0.254369\pi$
$308$	−3.22366	−0.183685
$309$	−6.60789	−0.375910
$310$	−7.79447	−0.442696
$311$	19.7101	1.11766	0.558828	−	0.829284i	$-0.311251\pi$
$311$	19.7101	1.11766	0.558828	+	0.829284i	$0.311251\pi$
$312$	27.7156	1.56908
$313$	−29.4913	−1.66695	−0.833474	−	0.552559i	$-0.813651\pi$
$313$	−29.4913	−1.66695	−0.833474	+	0.552559i	$0.813651\pi$
$314$	−57.7680	−3.26004
$315$	−1.39509	−0.0786046
$316$	−26.4416	−1.48746
$317$	20.5576	1.15463	0.577314	−	0.816522i	$-0.304101\pi$
$317$	20.5576	1.15463	0.577314	+	0.816522i	$0.304101\pi$
$318$	41.7444	2.34091
$319$	−6.45943	−0.361659
$320$	11.3623	0.635172
$321$	−12.5321	−0.699473
$322$	−15.6980	−0.874817
$323$	21.4722	1.19475
$324$	−10.4792	−0.582178
$325$	−11.3445	−0.629280
$326$	62.1206	3.44054
$327$	4.31830	0.238803
$328$	−30.9857	−1.71090
$329$	−7.96648	−0.439206
$330$	−2.70190	−0.148735
$331$	−15.9173	−0.874893	−0.437447	−	0.899244i	$-0.644117\pi$
$331$	−15.9173	−0.874893	−0.437447	+	0.899244i	$0.644117\pi$
$332$	−45.1193	−2.47624
$333$	−3.77948	−0.207114
$334$	−51.2373	−2.80358
$335$	6.24795	0.341362
$336$	−10.6121	−0.578935
$337$	1.04219	0.0567719	0.0283859	−	0.999597i	$-0.490963\pi$
$337$	1.04219	0.0567719	0.0283859	+	0.999597i	$0.490963\pi$
$338$	10.9682	0.596589
$339$	−5.94689	−0.322991
$340$	−31.6295	−1.71535
$341$	−2.11746	−0.114667
$342$	−14.4972	−0.783920
$343$	−11.2196	−0.605800
$344$	35.5651	1.91754
$345$	−9.35196	−0.503493
$346$	−24.6008	−1.32255
$347$	8.06798	0.433112	0.216556	−	0.976270i	$-0.430518\pi$
$347$	8.06798	0.433112	0.216556	+	0.976270i	$0.430518\pi$
$348$	−49.7361	−2.66614
$349$	−15.4972	−0.829547	−0.414773	−	0.909925i	$-0.636139\pi$
$349$	−15.4972	−0.829547	−0.414773	+	0.909925i	$0.636139\pi$
$350$	8.47776	0.453155
$351$	16.3398	0.872155
$352$	9.18829	0.489738
$353$	−29.6315	−1.57713	−0.788564	−	0.614953i	$-0.789175\pi$
$353$	−29.6315	−1.57713	−0.788564	+	0.614953i	$0.789175\pi$
$354$	−0.170709	−0.00907309
$355$	9.10680	0.483339
$356$	−25.2753	−1.33959
$357$	6.08086	0.321833
$358$	−31.4151	−1.66034
$359$	−17.1042	−0.902725	−0.451362	−	0.892341i	$-0.649062\pi$
$359$	−17.1042	−0.902725	−0.451362	+	0.892341i	$0.649062\pi$
$360$	12.6657	0.667542
$361$	−5.83862	−0.307296
$362$	18.7215	0.983983
$363$	12.6499	0.663945
$364$	12.3325	0.646400
$365$	−11.5272	−0.603363
$366$	−13.7404	−0.718223
$367$	25.5039	1.33129	0.665645	−	0.746268i	$-0.268156\pi$
$367$	25.5039	1.33129	0.665645	+	0.746268i	$0.268156\pi$
$368$	73.0217	3.80652
$369$	−6.14207	−0.319743
$370$	−7.11094	−0.369680
$371$	11.0168	0.571965
$372$	−16.3040	−0.845322
$373$	−21.2022	−1.09781	−0.548904	−	0.835885i	$-0.684955\pi$
$373$	−21.2022	−1.09781	−0.548904	+	0.835885i	$0.684955\pi$
$374$	−12.0888	−0.625099
$375$	11.6648	0.602368
$376$	72.3258	3.72992
$377$	24.7114	1.27270
$378$	−12.2108	−0.628054
$379$	21.5841	1.10870	0.554352	−	0.832283i	$-0.312966\pi$
$379$	21.5841	1.10870	0.554352	+	0.832283i	$0.312966\pi$
$380$	−19.3873	−0.994547
$381$	9.82815	0.503511
$382$	59.2011	3.02899
$383$	−29.3511	−1.49977	−0.749885	−	0.661568i	$-0.769891\pi$
$383$	−29.3511	−1.49977	−0.749885	+	0.661568i	$0.769891\pi$
$384$	4.65056	0.237323
$385$	−0.713063	−0.0363410
$386$	27.6136	1.40549
$387$	7.04982	0.358362
$388$	−34.4472	−1.74879
$389$	−0.982373	−0.0498083	−0.0249041	−	0.999690i	$-0.507928\pi$
$389$	−0.982373	−0.0498083	−0.0249041	+	0.999690i	$0.507928\pi$
$390$	10.3365	0.523408
$391$	−41.8425	−2.11607
$392$	48.1969	2.43431
$393$	12.8221	0.646788
$394$	−61.9375	−3.12037
$395$	−5.84880	−0.294285
$396$	5.80137	0.291530
$397$	−4.53106	−0.227407	−0.113704	−	0.993515i	$-0.536271\pi$
$397$	−4.53106	−0.227407	−0.113704	+	0.993515i	$0.536271\pi$
$398$	−12.9145	−0.647344
$399$	3.72726	0.186596
$400$	−39.4356	−1.97178
$401$	−13.2445	−0.661401	−0.330701	−	0.943736i	$-0.607285\pi$
$401$	−13.2445	−0.661401	−0.330701	+	0.943736i	$0.607285\pi$
$402$	18.3869	0.917054
$403$	8.10063	0.403521
$404$	83.3347	4.14606
$405$	−2.31796	−0.115181
$406$	−18.4668	−0.916494
$407$	−1.93178	−0.0957546
$408$	−55.2067	−2.73314
$409$	−17.9480	−0.887471	−0.443735	−	0.896158i	$-0.646347\pi$
$409$	−17.9480	−0.887471	−0.443735	+	0.896158i	$0.646347\pi$
$410$	−11.5561	−0.570713
$411$	8.02904	0.396043
$412$	26.6943	1.31513
$413$	−0.0450521	−0.00221687
$414$	28.2505	1.38843
$415$	−9.98022	−0.489910
$416$	−35.1510	−1.72342
$417$	−14.4231	−0.706302
$418$	−7.40985	−0.362428
$419$	−34.3690	−1.67903	−0.839517	−	0.543333i	$-0.817162\pi$
$419$	−34.3690	−1.67903	−0.839517	+	0.543333i	$0.817162\pi$
$420$	−5.49042	−0.267905
$421$	7.95782	0.387840	0.193920	−	0.981017i	$-0.437880\pi$
$421$	7.95782	0.387840	0.193920	+	0.981017i	$0.437880\pi$
$422$	−11.8588	−0.577278
$423$	14.3366	0.697071
$424$	−100.019	−4.85736
$425$	22.5971	1.09612
$426$	26.8001	1.29847
$427$	−3.62625	−0.175486
$428$	50.6266	2.44713
$429$	2.80803	0.135573
$430$	13.2640	0.639645
$431$	−30.4994	−1.46910	−0.734551	−	0.678553i	$-0.762607\pi$
$431$	−30.4994	−1.46910	−0.734551	+	0.678553i	$0.762607\pi$
$432$	56.8002	2.73280
$433$	−20.5864	−0.989318	−0.494659	−	0.869087i	$-0.664707\pi$
$433$	−20.5864	−0.989318	−0.494659	+	0.869087i	$0.664707\pi$
$434$	−6.05361	−0.290582
$435$	−11.0015	−0.527479
$436$	−17.4449	−0.835459
$437$	−25.6473	−1.22688
$438$	−33.9231	−1.62091
$439$	35.2540	1.68258	0.841291	−	0.540582i	$-0.181796\pi$
$439$	35.2540	1.68258	0.841291	+	0.540582i	$0.181796\pi$
$440$	6.47373	0.308623
$441$	9.55373	0.454939
$442$	46.2474	2.19976
$443$	36.6309	1.74038	0.870192	−	0.492713i	$-0.163995\pi$
$443$	36.6309	1.74038	0.870192	+	0.492713i	$0.163995\pi$
$444$	−14.8742	−0.705899
$445$	−5.59080	−0.265029
$446$	20.8158	0.985658
$447$	1.92573	0.0910840
$448$	8.82458	0.416922
$449$	5.94181	0.280411	0.140206	−	0.990122i	$-0.455224\pi$
$449$	5.94181	0.280411	0.140206	+	0.990122i	$0.455224\pi$
$450$	−15.2567	−0.719210
$451$	−3.13935	−0.147826
$452$	24.0240	1.12999
$453$	0.532043	0.0249975
$454$	−55.9255	−2.62471
$455$	2.72791	0.127886
$456$	−33.8389	−1.58465
$457$	34.3471	1.60669	0.803344	−	0.595515i	$-0.203052\pi$
$457$	34.3471	1.60669	0.803344	+	0.595515i	$0.203052\pi$
$458$	−60.1779	−2.81193
$459$	−32.5473	−1.51918
$460$	37.7797	1.76149
$461$	25.3894	1.18250	0.591251	−	0.806488i	$-0.298634\pi$
$461$	25.3894	1.18250	0.591251	+	0.806488i	$0.298634\pi$
$462$	−2.09845	−0.0976285
$463$	−11.4430	−0.531801	−0.265901	−	0.964000i	$-0.585669\pi$
$463$	−11.4430	−0.531801	−0.265901	+	0.964000i	$0.585669\pi$
$464$	85.9013	3.98787
$465$	−3.60638	−0.167242
$466$	−71.9566	−3.33332
$467$	−10.6432	−0.492507	−0.246254	−	0.969205i	$-0.579200\pi$
$467$	−10.6432	−0.492507	−0.246254	+	0.969205i	$0.579200\pi$
$468$	−22.1939	−1.02591
$469$	4.85250	0.224068
$470$	26.9738	1.24421
$471$	−26.7284	−1.23158
$472$	0.409017	0.0188265
$473$	3.60332	0.165681
$474$	−17.2122	−0.790583
$475$	13.8509	0.635523
$476$	−24.5652	−1.12594
$477$	−19.8261	−0.907774
$478$	12.5149	0.572417
$479$	16.0927	0.735293	0.367647	−	0.929966i	$-0.380164\pi$
$479$	16.0927	0.735293	0.367647	+	0.929966i	$0.380164\pi$
$480$	15.6491	0.714282
$481$	7.39025	0.336966
$482$	−17.7415	−0.808101
$483$	−7.26324	−0.330489
$484$	−51.1024	−2.32283
$485$	−7.61961	−0.345989
$486$	36.5610	1.65844
$487$	34.9145	1.58213	0.791064	−	0.611733i	$-0.209527\pi$
$487$	34.9145	1.58213	0.791064	+	0.611733i	$0.209527\pi$
$488$	32.9218	1.49030
$489$	28.7423	1.29977
$490$	17.9750	0.812026
$491$	−37.6206	−1.69779	−0.848896	−	0.528560i	$-0.822732\pi$
$491$	−37.6206	−1.69779	−0.848896	+	0.528560i	$0.822732\pi$
$492$	−24.1723	−1.08977
$493$	−49.2226	−2.21688
$494$	28.3473	1.27541
$495$	1.28324	0.0576774
$496$	28.1593	1.26439
$497$	7.07284	0.317260
$498$	−29.3704	−1.31612
$499$	−28.0727	−1.25671	−0.628354	−	0.777927i	$-0.716271\pi$
$499$	−28.0727	−1.25671	−0.628354	+	0.777927i	$0.716271\pi$
$500$	−47.1230	−2.10740
$501$	−23.7067	−1.05914
$502$	68.8455	3.07272
$503$	0.729557	0.0325293	0.0162647	−	0.999868i	$-0.494823\pi$
$503$	0.729557	0.0325293	0.0162647	+	0.999868i	$0.494823\pi$
$504$	9.83688	0.438170
$505$	18.4333	0.820273
$506$	14.4394	0.641912
$507$	5.07480	0.225380
$508$	−39.7033	−1.76155
$509$	9.23175	0.409190	0.204595	−	0.978847i	$-0.434412\pi$
$509$	9.23175	0.409190	0.204595	+	0.978847i	$0.434412\pi$
$510$	−20.5892	−0.911707
$511$	−8.95269	−0.396043
$512$	36.1767	1.59880
$513$	−19.9499	−0.880808
$514$	63.0184	2.77962
$515$	5.90468	0.260191
$516$	27.7447	1.22139
$517$	7.32777	0.322275
$518$	−5.52274	−0.242655
$519$	−11.3824	−0.499633
$520$	−24.7661	−1.08606
$521$	10.6330	0.465842	0.232921	−	0.972496i	$-0.425172\pi$
$521$	10.6330	0.465842	0.232921	+	0.972496i	$0.425172\pi$
$522$	33.2333	1.45458
$523$	34.2650	1.49830	0.749151	−	0.662399i	$-0.230462\pi$
$523$	34.2650	1.49830	0.749151	+	0.662399i	$0.230462\pi$
$524$	−51.7981	−2.26281
$525$	3.92253	0.171193
$526$	−51.2719	−2.23556
$527$	−16.1357	−0.702880
$528$	9.76123	0.424803
$529$	26.9785	1.17298
$530$	−37.3020	−1.62030
$531$	0.0810766	0.00351842
$532$	−15.0572	−0.652813
$533$	12.0100	0.520210
$534$	−16.4530	−0.711989
$535$	11.1984	0.484150
$536$	−44.0547	−1.90287
$537$	−14.5353	−0.627244
$538$	11.6992	0.504386
$539$	4.88312	0.210331
$540$	29.3870	1.26462
$541$	−27.9530	−1.20179	−0.600897	−	0.799326i	$-0.705190\pi$
$541$	−27.9530	−1.20179	−0.600897	+	0.799326i	$0.705190\pi$
$542$	−66.8388	−2.87097
$543$	8.66218	0.371730
$544$	70.0173	3.00197
$545$	−3.85875	−0.165291
$546$	8.02787	0.343561
$547$	−6.20287	−0.265216	−0.132608	−	0.991169i	$-0.542335\pi$
$547$	−6.20287	−0.265216	−0.132608	+	0.991169i	$0.542335\pi$
$548$	−32.4354	−1.38557
$549$	6.52586	0.278517
$550$	−7.79806	−0.332510
$551$	−30.1710	−1.28533
$552$	65.9412	2.80665
$553$	−4.54249	−0.193166
$554$	−75.5285	−3.20890
$555$	−3.29012	−0.139658
$556$	58.2658	2.47102
$557$	−26.9862	−1.14344	−0.571722	−	0.820448i	$-0.693724\pi$
$557$	−26.9862	−1.14344	−0.571722	+	0.820448i	$0.693724\pi$
$558$	10.8942	0.461188
$559$	−13.7850	−0.583041
$560$	9.48272	0.400718
$561$	−5.59333	−0.236150
$562$	60.1025	2.53527
$563$	28.7612	1.21214	0.606070	−	0.795412i	$-0.292745\pi$
$563$	28.7612	1.21214	0.606070	+	0.795412i	$0.292745\pi$
$564$	56.4221	2.37580
$565$	5.31402	0.223563
$566$	−21.9084	−0.920880
$567$	−1.80026	−0.0756037
$568$	−64.2126	−2.69430
$569$	15.3103	0.641841	0.320921	−	0.947106i	$-0.396008\pi$
$569$	15.3103	0.641841	0.320921	+	0.947106i	$0.396008\pi$
$570$	−12.6202	−0.528601
$571$	−13.8583	−0.579952	−0.289976	−	0.957034i	$-0.593647\pi$
$571$	−13.8583	−0.579952	−0.289976	+	0.957034i	$0.593647\pi$
$572$	−11.3438	−0.474307
$573$	27.3914	1.14429
$574$	−8.97507	−0.374612
$575$	−26.9910	−1.12560
$576$	−15.8809	−0.661703
$577$	4.76663	0.198438	0.0992188	−	0.995066i	$-0.468366\pi$
$577$	4.76663	0.198438	0.0992188	+	0.995066i	$0.468366\pi$
$578$	−47.4157	−1.97223
$579$	12.7764	0.530968
$580$	44.4432	1.84540
$581$	−7.75118	−0.321573
$582$	−22.4235	−0.929482
$583$	−10.1336	−0.419689
$584$	81.2793	3.36336
$585$	−4.90920	−0.202971
$586$	−5.67936	−0.234612
$587$	32.4754	1.34040	0.670202	−	0.742178i	$-0.266207\pi$
$587$	32.4754	1.34040	0.670202	+	0.742178i	$0.266207\pi$
$588$	37.5989	1.55055
$589$	−9.89034	−0.407525
$590$	0.152542	0.00628007
$591$	−28.6576	−1.17881
$592$	25.6899	1.05585
$593$	18.7599	0.770377	0.385188	−	0.922838i	$-0.374136\pi$
$593$	18.7599	0.770377	0.385188	+	0.922838i	$0.374136\pi$
$594$	11.2318	0.460845
$595$	−5.43373	−0.222761
$596$	−7.77949	−0.318660
$597$	−5.97533	−0.244554
$598$	−55.2399	−2.25893
$599$	17.6358	0.720580	0.360290	−	0.932840i	$-0.382678\pi$
$599$	17.6358	0.720580	0.360290	+	0.932840i	$0.382678\pi$
$600$	−35.6117	−1.45384
$601$	3.31036	0.135033	0.0675163	−	0.997718i	$-0.478493\pi$
$601$	3.31036	0.135033	0.0675163	+	0.997718i	$0.478493\pi$
$602$	10.3015	0.419858
$603$	−8.73265	−0.355621
$604$	−2.14932	−0.0874547
$605$	−11.3037	−0.459559
$606$	54.2468	2.20362
$607$	25.1774	1.02192	0.510959	−	0.859605i	$-0.329290\pi$
$607$	25.1774	1.02192	0.510959	+	0.859605i	$0.329290\pi$
$608$	42.9171	1.74052
$609$	−8.54433	−0.346234
$610$	12.2782	0.497128
$611$	−28.0333	−1.13411
$612$	44.2080	1.78700
$613$	31.9001	1.28843	0.644216	−	0.764844i	$-0.277184\pi$
$613$	31.9001	1.28843	0.644216	+	0.764844i	$0.277184\pi$
$614$	−64.2604	−2.59334
$615$	−5.34682	−0.215604
$616$	5.02785	0.202578
$617$	−33.7534	−1.35886	−0.679430	−	0.733740i	$-0.737773\pi$
$617$	−33.7534	−1.35886	−0.679430	+	0.733740i	$0.737773\pi$
$618$	17.3767	0.698992
$619$	12.3280	0.495505	0.247753	−	0.968823i	$-0.420308\pi$
$619$	12.3280	0.495505	0.247753	+	0.968823i	$0.420308\pi$
$620$	14.5689	0.585102
$621$	38.8759	1.56004
$622$	−51.8312	−2.07824
$623$	−4.34212	−0.173963
$624$	−37.3428	−1.49491
$625$	8.66620	0.346648
$626$	77.5528	3.09963
$627$	−3.42843	−0.136918
$628$	107.976	4.30872
$629$	−14.7207	−0.586951
$630$	3.66865	0.146163
$631$	0.789279	0.0314207	0.0157103	−	0.999877i	$-0.494999\pi$
$631$	0.789279	0.0314207	0.0157103	+	0.999877i	$0.494999\pi$
$632$	41.2402	1.64045
$633$	−5.48690	−0.218085
$634$	−54.0599	−2.14699
$635$	−8.78223	−0.348512
$636$	−78.0260	−3.09393
$637$	−18.6810	−0.740168
$638$	16.9863	0.672493
$639$	−12.7284	−0.503528
$640$	−4.15565	−0.164266
$641$	24.9752	0.986462	0.493231	−	0.869898i	$-0.335816\pi$
$641$	24.9752	0.986462	0.493231	+	0.869898i	$0.335816\pi$
$642$	32.9554	1.30065
$643$	−33.4658	−1.31976	−0.659881	−	0.751371i	$-0.729393\pi$
$643$	−33.4658	−1.31976	−0.659881	+	0.751371i	$0.729393\pi$
$644$	29.3417	1.15623
$645$	6.13703	0.241645
$646$	−56.4651	−2.22159
$647$	26.9818	1.06077	0.530383	−	0.847758i	$-0.322048\pi$
$647$	26.9818	1.06077	0.530383	+	0.847758i	$0.322048\pi$
$648$	16.3441	0.642057
$649$	0.0414400	0.00162666
$650$	29.8325	1.17013
$651$	−2.80091	−0.109776
$652$	−116.112	−4.54729
$653$	17.9686	0.703166	0.351583	−	0.936157i	$-0.385643\pi$
$653$	17.9686	0.703166	0.351583	+	0.936157i	$0.385643\pi$
$654$	−11.3558	−0.444046
$655$	−11.4575	−0.447683
$656$	41.7489	1.63002
$657$	16.1114	0.628566
$658$	20.9493	0.816690
$659$	−45.0287	−1.75407	−0.877035	−	0.480427i	$-0.840482\pi$
$659$	−45.0287	−1.75407	−0.877035	+	0.480427i	$0.840482\pi$
$660$	5.05022	0.196580
$661$	4.38076	0.170392	0.0851958	−	0.996364i	$-0.472848\pi$
$661$	4.38076	0.170392	0.0851958	+	0.996364i	$0.472848\pi$
$662$	41.8574	1.62683
$663$	21.3980	0.831029
$664$	70.3711	2.73093
$665$	−3.33060	−0.129155
$666$	9.93883	0.385122
$667$	58.7937	2.27650
$668$	95.7695	3.70543
$669$	9.63117	0.372363
$670$	−16.4301	−0.634752
$671$	3.33551	0.128766
$672$	12.1540	0.468850
$673$	5.71984	0.220484	0.110242	−	0.993905i	$-0.464837\pi$
$673$	5.71984	0.220484	0.110242	+	0.993905i	$0.464837\pi$
$674$	−2.74064	−0.105565
$675$	−20.9950	−0.808100
$676$	−20.5010	−0.788499
$677$	46.0374	1.76936	0.884681	−	0.466197i	$-0.154376\pi$
$677$	46.0374	1.76936	0.884681	+	0.466197i	$0.154376\pi$
$678$	15.6384	0.600591
$679$	−5.91780	−0.227104
$680$	49.3316	1.89178
$681$	−25.8759	−0.991567
$682$	5.56826	0.213220
$683$	32.1238	1.22918	0.614591	−	0.788846i	$-0.289321\pi$
$683$	32.1238	1.22918	0.614591	+	0.788846i	$0.289321\pi$
$684$	27.0973	1.03609
$685$	−7.17459	−0.274127
$686$	29.5039	1.12647
$687$	−27.8434	−1.06229
$688$	−47.9190	−1.82689
$689$	38.7672	1.47691
$690$	24.5927	0.936228
$691$	35.4587	1.34891	0.674456	−	0.738315i	$-0.264378\pi$
$691$	35.4587	1.34891	0.674456	+	0.738315i	$0.264378\pi$
$692$	45.9822	1.74798
$693$	0.996635	0.0378590
$694$	−21.2162	−0.805357
$695$	12.8882	0.488877
$696$	77.5719	2.94036
$697$	−23.9227	−0.906137
$698$	40.7528	1.54251
$699$	−33.2932	−1.25927
$700$	−15.8461	−0.598926
$701$	37.4373	1.41399	0.706994	−	0.707219i	$-0.250051\pi$
$701$	37.4373	1.41399	0.706994	+	0.707219i	$0.250051\pi$
$702$	−42.9686	−1.62174
$703$	−9.02302	−0.340310
$704$	−8.11707	−0.305924
$705$	12.4804	0.470038
$706$	77.9215	2.93262
$707$	14.3163	0.538421
$708$	0.319079	0.0119917
$709$	41.0409	1.54132	0.770662	−	0.637244i	$-0.219926\pi$
$709$	41.0409	1.54132	0.770662	+	0.637244i	$0.219926\pi$
$710$	−23.9480	−0.898752
$711$	8.17476	0.306577
$712$	39.4211	1.47737
$713$	19.2731	0.721784
$714$	−15.9907	−0.598438
$715$	−2.50920	−0.0938388
$716$	58.7190	2.19443
$717$	5.79045	0.216248
$718$	44.9786	1.67859
$719$	28.0823	1.04729	0.523647	−	0.851935i	$-0.324571\pi$
$719$	28.0823	1.04729	0.523647	+	0.851935i	$0.324571\pi$
$720$	−17.0653	−0.635985
$721$	4.58590	0.170788
$722$	15.3537	0.571407
$723$	−8.20871	−0.305285
$724$	−34.9931	−1.30051
$725$	−31.7517	−1.17923
$726$	−33.2651	−1.23458
$727$	35.8444	1.32939	0.664697	−	0.747113i	$-0.268561\pi$
$727$	35.8444	1.32939	0.664697	+	0.747113i	$0.268561\pi$
$728$	−19.2347	−0.712885
$729$	23.3122	0.863414
$730$	30.3130	1.12193
$731$	27.4583	1.01558
$732$	25.6827	0.949259
$733$	16.7669	0.619298	0.309649	−	0.950851i	$-0.399788\pi$
$733$	16.7669	0.619298	0.309649	+	0.950851i	$0.399788\pi$
$734$	−67.0671	−2.47549
$735$	8.31674	0.306768
$736$	−83.6317	−3.08271
$737$	−4.46345	−0.164413
$738$	16.1517	0.594552
$739$	19.8617	0.730625	0.365313	−	0.930885i	$-0.380962\pi$
$739$	19.8617	0.730625	0.365313	+	0.930885i	$0.380962\pi$
$740$	13.2913	0.488598
$741$	13.1159	0.481824
$742$	−28.9708	−1.06355
$743$	−9.42843	−0.345896	−0.172948	−	0.984931i	$-0.555329\pi$
$743$	−9.42843	−0.345896	−0.172948	+	0.984931i	$0.555329\pi$
$744$	25.4288	0.932266
$745$	−1.72079	−0.0630450
$746$	55.7551	2.04134
$747$	13.9492	0.510374
$748$	22.5957	0.826180
$749$	8.69730	0.317792
$750$	−30.6747	−1.12008
$751$	−7.93899	−0.289698	−0.144849	−	0.989454i	$-0.546270\pi$
$751$	−7.93899	−0.289698	−0.144849	+	0.989454i	$0.546270\pi$
$752$	−97.4489	−3.55360
$753$	31.8538	1.16082
$754$	−64.9831	−2.36655
$755$	−0.475423	−0.0173024
$756$	22.8236	0.830085
$757$	0.812023	0.0295135	0.0147567	−	0.999891i	$-0.495303\pi$
$757$	0.812023	0.0295135	0.0147567	+	0.999891i	$0.495303\pi$
$758$	−56.7595	−2.06160
$759$	6.68091	0.242502
$760$	30.2378	1.09684
$761$	−12.3447	−0.447496	−0.223748	−	0.974647i	$-0.571829\pi$
$761$	−12.3447	−0.447496	−0.223748	+	0.974647i	$0.571829\pi$
$762$	−25.8449	−0.936262
$763$	−2.99691	−0.108496
$764$	−110.655	−4.00335
$765$	9.77865	0.353548
$766$	77.1841	2.78877
$767$	−0.158534	−0.00572433
$768$	13.2015	0.476367
$769$	−49.2492	−1.77597	−0.887987	−	0.459869i	$-0.847896\pi$
$769$	−49.2492	−1.77597	−0.887987	+	0.459869i	$0.847896\pi$
$770$	1.87513	0.0675750
$771$	29.1577	1.05009
$772$	−51.6135	−1.85761
$773$	1.26771	0.0455963	0.0227981	−	0.999740i	$-0.492743\pi$
$773$	1.26771	0.0455963	0.0227981	+	0.999740i	$0.492743\pi$
$774$	−18.5388	−0.666363
$775$	−10.4085	−0.373884
$776$	53.7263	1.92866
$777$	−2.55529	−0.0916705
$778$	2.58333	0.0926168
$779$	−14.6634	−0.525371
$780$	−19.3203	−0.691777
$781$	−6.50577	−0.232795
$782$	110.032	3.93475
$783$	45.7329	1.63436
$784$	−64.9386	−2.31923
$785$	23.8840	0.852455
$786$	−33.7180	−1.20268
$787$	31.0935	1.10836	0.554182	−	0.832396i	$-0.313031\pi$
$787$	31.0935	1.10836	0.554182	+	0.832396i	$0.313031\pi$
$788$	115.770	4.12412
$789$	−23.7227	−0.844551
$790$	15.3805	0.547213
$791$	4.12716	0.146745
$792$	−9.04821	−0.321514
$793$	−12.7604	−0.453136
$794$	11.9152	0.422856
$795$	−17.2591	−0.612116
$796$	24.1389	0.855581
$797$	−1.64133	−0.0581390	−0.0290695	−	0.999577i	$-0.509254\pi$
$797$	−1.64133	−0.0581390	−0.0290695	+	0.999577i	$0.509254\pi$
$798$	−9.80151	−0.346970
$799$	55.8396	1.97546
$800$	45.1655	1.59684
$801$	7.81416	0.276100
$802$	34.8290	1.22985
$803$	8.23491	0.290604
$804$	−34.3675	−1.21205
$805$	6.49029	0.228753
$806$	−21.3021	−0.750334
$807$	5.41302	0.190547
$808$	−129.975	−4.57249
$809$	−24.5371	−0.862679	−0.431340	−	0.902190i	$-0.641959\pi$
$809$	−24.5371	−0.862679	−0.431340	+	0.902190i	$0.641959\pi$
$810$	6.09551	0.214174
$811$	54.8019	1.92436	0.962178	−	0.272421i	$-0.0878243\pi$
$811$	54.8019	1.92436	0.962178	+	0.272421i	$0.0878243\pi$
$812$	34.5170	1.21131
$813$	−30.9253	−1.08460
$814$	5.07996	0.178052
$815$	−25.6835	−0.899654
$816$	74.3833	2.60394
$817$	16.8305	0.588826
$818$	47.1975	1.65022
$819$	−3.81275	−0.133228
$820$	21.5998	0.754299
$821$	7.24751	0.252940	0.126470	−	0.991970i	$-0.459635\pi$
$821$	7.24751	0.252940	0.126470	+	0.991970i	$0.459635\pi$
$822$	−21.1138	−0.736429
$823$	−34.5726	−1.20513	−0.602563	−	0.798072i	$-0.705854\pi$
$823$	−34.5726	−1.20513	−0.602563	+	0.798072i	$0.705854\pi$
$824$	−41.6343	−1.45040
$825$	−3.60804	−0.125616
$826$	0.118473	0.00412219
$827$	17.2218	0.598861	0.299431	−	0.954118i	$-0.403203\pi$
$827$	17.2218	0.598861	0.299431	+	0.954118i	$0.403203\pi$
$828$	−52.8040	−1.83506
$829$	45.4385	1.57815	0.789073	−	0.614300i	$-0.210561\pi$
$829$	45.4385	1.57815	0.789073	+	0.614300i	$0.210561\pi$
$830$	26.2448	0.910971
$831$	−34.9459	−1.21226
$832$	31.0529	1.07656
$833$	37.2107	1.28928
$834$	37.9282	1.31335
$835$	21.1839	0.733098
$836$	13.8500	0.479013
$837$	14.9917	0.518188
$838$	90.3795	3.12211
$839$	26.2738	0.907073	0.453537	−	0.891238i	$-0.350162\pi$
$839$	26.2738	0.907073	0.453537	+	0.891238i	$0.350162\pi$
$840$	8.56324	0.295460
$841$	40.1637	1.38495
$842$	−20.9265	−0.721176
$843$	27.8085	0.957776
$844$	22.1657	0.762976
$845$	−4.53474	−0.156000
$846$	−37.7008	−1.29618
$847$	−8.77904	−0.301651
$848$	134.762	4.62774
$849$	−10.1367	−0.347891
$850$	−59.4233	−2.03820
$851$	17.5830	0.602737
$852$	−50.0929	−1.71616
$853$	10.1536	0.347654	0.173827	−	0.984776i	$-0.444387\pi$
$853$	10.1536	0.347654	0.173827	+	0.984776i	$0.444387\pi$
$854$	9.53588	0.326311
$855$	5.99382	0.204984
$856$	−78.9607	−2.69882
$857$	6.45529	0.220509	0.110254	−	0.993903i	$-0.464833\pi$
$857$	6.45529	0.220509	0.110254	+	0.993903i	$0.464833\pi$
$858$	−7.38424	−0.252094
$859$	38.0037	1.29667	0.648334	−	0.761356i	$-0.275466\pi$
$859$	38.0037	1.29667	0.648334	+	0.761356i	$0.275466\pi$
$860$	−24.7921	−0.845404
$861$	−4.15263	−0.141521
$862$	80.2037	2.73175
$863$	−14.2776	−0.486015	−0.243007	−	0.970024i	$-0.578134\pi$
$863$	−14.2776	−0.486015	−0.243007	+	0.970024i	$0.578134\pi$
$864$	−65.0532	−2.21315
$865$	10.1711	0.345828
$866$	54.1357	1.83960
$867$	−21.9385	−0.745071
$868$	11.3150	0.384056
$869$	4.17830	0.141739
$870$	28.9303	0.980830
$871$	17.0755	0.578581
$872$	27.2083	0.921388
$873$	10.6498	0.360441
$874$	67.4444	2.28134
$875$	−8.09541	−0.273675
$876$	63.4068	2.14232
$877$	−2.15824	−0.0728787	−0.0364394	−	0.999336i	$-0.511602\pi$
$877$	−2.15824	−0.0728787	−0.0364394	+	0.999336i	$0.511602\pi$
$878$	−92.7069	−3.12871
$879$	−2.62775	−0.0886319
$880$	−8.72244	−0.294033
$881$	15.8890	0.535316	0.267658	−	0.963514i	$-0.413750\pi$
$881$	15.8890	0.535316	0.267658	+	0.963514i	$0.413750\pi$
$882$	−25.1233	−0.845945
$883$	30.0292	1.01056	0.505282	−	0.862954i	$-0.331389\pi$
$883$	30.0292	1.01056	0.505282	+	0.862954i	$0.331389\pi$
$884$	−86.4427	−2.90738
$885$	0.0705790	0.00237249
$886$	−96.3275	−3.23619
$887$	10.7576	0.361205	0.180603	−	0.983556i	$-0.442195\pi$
$887$	10.7576	0.361205	0.180603	+	0.983556i	$0.442195\pi$
$888$	23.1989	0.778503
$889$	−6.82076	−0.228761
$890$	14.7020	0.492813
$891$	1.65592	0.0554755
$892$	−38.9076	−1.30272
$893$	34.2269	1.14536
$894$	−5.06406	−0.169368
$895$	12.9884	0.434156
$896$	−3.22750	−0.107823
$897$	−25.5587	−0.853380
$898$	−15.6251	−0.521416
$899$	22.6725	0.756171
$900$	28.5169	0.950564
$901$	−77.2205	−2.57259
$902$	8.25549	0.274878
$903$	4.76635	0.158614
$904$	−37.4695	−1.24622
$905$	−7.74035	−0.257298
$906$	−1.39910	−0.0464821
$907$	6.97258	0.231521	0.115760	−	0.993277i	$-0.463070\pi$
$907$	6.97258	0.231521	0.115760	+	0.993277i	$0.463070\pi$
$908$	104.532	3.46903
$909$	−25.7639	−0.854536
$910$	−7.17354	−0.237801
$911$	−16.7829	−0.556043	−0.278022	−	0.960575i	$-0.589679\pi$
$911$	−16.7829	−0.556043	−0.278022	+	0.960575i	$0.589679\pi$
$912$	45.5932	1.50974
$913$	7.12973	0.235960
$914$	−90.3219	−2.98758
$915$	5.68092	0.187805
$916$	112.481	3.71646
$917$	−8.89855	−0.293856
$918$	85.5891	2.82486
$919$	−49.7363	−1.64065	−0.820325	−	0.571898i	$-0.806207\pi$
$919$	−49.7363	−1.64065	−0.820325	+	0.571898i	$0.806207\pi$
$920$	−58.9238	−1.94266
$921$	−29.7323	−0.979714
$922$	−66.7661	−2.19882
$923$	24.8887	0.819220
$924$	3.92228	0.129034
$925$	−9.49574	−0.312218
$926$	30.0915	0.988867
$927$	−8.25287	−0.271060
$928$	−98.3826	−3.22957
$929$	−3.60434	−0.118255	−0.0591273	−	0.998250i	$-0.518832\pi$
$929$	−3.60434	−0.118255	−0.0591273	+	0.998250i	$0.518832\pi$
$930$	9.48364	0.310981
$931$	22.8083	0.747512
$932$	134.497	4.40558
$933$	−23.9815	−0.785120
$934$	27.9882	0.915801
$935$	4.99808	0.163455
$936$	34.6151	1.13143
$937$	32.5079	1.06199	0.530993	−	0.847376i	$-0.321819\pi$
$937$	32.5079	1.06199	0.530993	+	0.847376i	$0.321819\pi$
$938$	−12.7605	−0.416646
$939$	35.8825	1.17098
$940$	−50.4177	−1.64444
$941$	4.12934	0.134613	0.0673064	−	0.997732i	$-0.478560\pi$
$941$	4.12934	0.134613	0.0673064	+	0.997732i	$0.478560\pi$
$942$	70.2872	2.29008
$943$	28.5743	0.930508
$944$	−0.551093	−0.0179366
$945$	5.04849	0.164227
$946$	−9.47559	−0.308078
$947$	−52.4637	−1.70484	−0.852421	−	0.522856i	$-0.824866\pi$
$947$	−52.4637	−1.70484	−0.852421	+	0.522856i	$0.824866\pi$
$948$	32.1719	1.04490
$949$	−31.5037	−1.02265
$950$	−36.4235	−1.18173
$951$	−25.0127	−0.811093
$952$	38.3136	1.24175
$953$	44.5297	1.44246	0.721229	−	0.692697i	$-0.243578\pi$
$953$	44.5297	1.44246	0.721229	+	0.692697i	$0.243578\pi$
$954$	52.1363	1.68798
$955$	−24.4764	−0.792039
$956$	−23.3920	−0.756551
$957$	7.85929	0.254055
$958$	−42.3187	−1.36725
$959$	−5.57218	−0.179935
$960$	−13.8247	−0.446189
$961$	−23.5677	−0.760249
$962$	−19.4340	−0.626578
$963$	−15.6518	−0.504373
$964$	33.1612	1.06805
$965$	−11.4167	−0.367517
$966$	19.1000	0.614533
$967$	2.83741	0.0912451	0.0456226	−	0.998959i	$-0.485473\pi$
$967$	2.83741	0.0912451	0.0456226	+	0.998959i	$0.485473\pi$
$968$	79.7028	2.56174
$969$	−26.1255	−0.839274
$970$	20.0372	0.643354
$971$	52.7952	1.69428	0.847139	−	0.531372i	$-0.178323\pi$
$971$	52.7952	1.69428	0.847139	+	0.531372i	$0.178323\pi$
$972$	−68.3374	−2.19192
$973$	10.0097	0.320895
$974$	−91.8142	−2.94192
$975$	13.8030	0.442051
$976$	−44.3576	−1.41985
$977$	33.0650	1.05784	0.528921	−	0.848671i	$-0.322597\pi$
$977$	33.0650	1.05784	0.528921	+	0.848671i	$0.322597\pi$
$978$	−75.5830	−2.41688
$979$	3.99399	0.127649
$980$	−33.5976	−1.07324
$981$	5.39330	0.172195
$982$	98.9301	3.15699
$983$	25.9688	0.828275	0.414137	−	0.910214i	$-0.364083\pi$
$983$	25.9688	0.828275	0.414137	+	0.910214i	$0.364083\pi$
$984$	37.7007	1.20186
$985$	25.6078	0.815933
$986$	129.440	4.12221
$987$	9.69294	0.308530
$988$	−52.9850	−1.68568
$989$	−32.7974	−1.04290
$990$	−3.37452	−0.107249
$991$	23.7032	0.752955	0.376478	−	0.926426i	$-0.377135\pi$
$991$	23.7032	0.752955	0.376478	+	0.926426i	$0.377135\pi$
$992$	−32.2508	−1.02396
$993$	19.3668	0.614587
$994$	−18.5993	−0.589935
$995$	5.33944	0.169272
$996$	54.8973	1.73949
$997$	−25.6524	−0.812420	−0.406210	−	0.913780i	$-0.633150\pi$
$997$	−25.6524	−0.812420	−0.406210	+	0.913780i	$0.633150\pi$
$998$	73.8224	2.33681
$999$	13.6770	0.432721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.12	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.12	✓	340	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62968 q^{2} -1.21671 q^{3} +4.91523 q^{4} +1.08723 q^{5} +3.19957 q^{6} +0.844404 q^{7} -7.66614 q^{8} -1.51960 q^{9} +O(q^{10})\)	\(q-2.62968 q^{2} -1.21671 q^{3} +4.91523 q^{4} +1.08723 q^{5} +3.19957 q^{6} +0.844404 q^{7} -7.66614 q^{8} -1.51960 q^{9} -2.85908 q^{10} -0.776704 q^{11} -5.98044 q^{12} +2.97138 q^{13} -2.22051 q^{14} -1.32285 q^{15} +10.3291 q^{16} -5.91869 q^{17} +3.99608 q^{18} -3.62786 q^{19} +5.34400 q^{20} -1.02740 q^{21} +2.04248 q^{22} +7.06955 q^{23} +9.32751 q^{24} -3.81793 q^{25} -7.81379 q^{26} +5.49907 q^{27} +4.15044 q^{28} +8.31647 q^{29} +3.47868 q^{30} +2.72622 q^{31} -11.8299 q^{32} +0.945027 q^{33} +15.5643 q^{34} +0.918063 q^{35} -7.46921 q^{36} +2.48715 q^{37} +9.54013 q^{38} -3.61532 q^{39} -8.33487 q^{40} +4.04189 q^{41} +2.70173 q^{42} -4.63925 q^{43} -3.81768 q^{44} -1.65216 q^{45} -18.5907 q^{46} -9.43445 q^{47} -12.5675 q^{48} -6.28698 q^{49} +10.0399 q^{50} +7.20136 q^{51} +14.6050 q^{52} +13.0469 q^{53} -14.4608 q^{54} -0.844457 q^{55} -6.47332 q^{56} +4.41407 q^{57} -21.8697 q^{58} -0.0533537 q^{59} -6.50212 q^{60} -4.29445 q^{61} -7.16909 q^{62} -1.28316 q^{63} +10.4507 q^{64} +3.23058 q^{65} -2.48512 q^{66} +5.74666 q^{67} -29.0918 q^{68} -8.60162 q^{69} -2.41421 q^{70} +8.37613 q^{71} +11.6495 q^{72} -10.6024 q^{73} -6.54040 q^{74} +4.64533 q^{75} -17.8318 q^{76} -0.655852 q^{77} +9.50715 q^{78} -5.37953 q^{79} +11.2301 q^{80} -2.13199 q^{81} -10.6289 q^{82} -9.17947 q^{83} -5.04990 q^{84} -6.43499 q^{85} +12.1997 q^{86} -10.1188 q^{87} +5.95432 q^{88} -5.14223 q^{89} +4.34467 q^{90} +2.50904 q^{91} +34.7485 q^{92} -3.31703 q^{93} +24.8096 q^{94} -3.94433 q^{95} +14.3936 q^{96} -7.00826 q^{97} +16.5328 q^{98} +1.18028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more