LMFDB - Embedded newform 8015.2.a.l.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34348 q^{2} -2.34976 q^{3} -0.195065 q^{4} -1.00000 q^{5} +3.15685 q^{6} -1.00000 q^{7} +2.94902 q^{8} +2.52136 q^{9} +O(q^{10})$	\(q-1.34348 q^{2} -2.34976 q^{3} -0.195065 q^{4} -1.00000 q^{5} +3.15685 q^{6} -1.00000 q^{7} +2.94902 q^{8} +2.52136 q^{9} +1.34348 q^{10} +1.18122 q^{11} +0.458355 q^{12} -0.588443 q^{13} +1.34348 q^{14} +2.34976 q^{15} -3.57182 q^{16} +2.31546 q^{17} -3.38740 q^{18} -8.11161 q^{19} +0.195065 q^{20} +2.34976 q^{21} -1.58694 q^{22} -2.01930 q^{23} -6.92949 q^{24} +1.00000 q^{25} +0.790561 q^{26} +1.12468 q^{27} +0.195065 q^{28} +9.62218 q^{29} -3.15685 q^{30} -1.07051 q^{31} -1.09938 q^{32} -2.77558 q^{33} -3.11078 q^{34} +1.00000 q^{35} -0.491829 q^{36} +2.42896 q^{37} +10.8978 q^{38} +1.38270 q^{39} -2.94902 q^{40} +5.19778 q^{41} -3.15685 q^{42} -7.17480 q^{43} -0.230414 q^{44} -2.52136 q^{45} +2.71289 q^{46} +2.65348 q^{47} +8.39291 q^{48} +1.00000 q^{49} -1.34348 q^{50} -5.44078 q^{51} +0.114785 q^{52} +3.73499 q^{53} -1.51099 q^{54} -1.18122 q^{55} -2.94902 q^{56} +19.0603 q^{57} -12.9272 q^{58} +7.26498 q^{59} -0.458355 q^{60} -8.28356 q^{61} +1.43821 q^{62} -2.52136 q^{63} +8.62064 q^{64} +0.588443 q^{65} +3.72893 q^{66} +2.82605 q^{67} -0.451665 q^{68} +4.74487 q^{69} -1.34348 q^{70} -12.9454 q^{71} +7.43556 q^{72} +0.537958 q^{73} -3.26326 q^{74} -2.34976 q^{75} +1.58229 q^{76} -1.18122 q^{77} -1.85763 q^{78} -6.23859 q^{79} +3.57182 q^{80} -10.2068 q^{81} -6.98310 q^{82} +10.6286 q^{83} -0.458355 q^{84} -2.31546 q^{85} +9.63919 q^{86} -22.6098 q^{87} +3.48344 q^{88} +10.4769 q^{89} +3.38740 q^{90} +0.588443 q^{91} +0.393895 q^{92} +2.51544 q^{93} -3.56490 q^{94} +8.11161 q^{95} +2.58328 q^{96} +11.2081 q^{97} -1.34348 q^{98} +2.97828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.34348	−0.949983	−0.474991	−	0.879990i	$-0.657549\pi$
$2$	−1.34348	−0.949983	−0.474991	+	0.879990i	$0.657549\pi$
$3$	−2.34976	−1.35663	−0.678317	−	0.734770i	$-0.737290\pi$
$3$	−2.34976	−1.35663	−0.678317	+	0.734770i	$0.737290\pi$
$4$	−0.195065	−0.0975324
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.15685	1.28878
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.94902	1.04264
$9$	2.52136	0.840454
$10$	1.34348	0.424845
$11$	1.18122	0.356151	0.178076	−	0.984017i	$-0.443013\pi$
$11$	1.18122	0.356151	0.178076	+	0.984017i	$0.443013\pi$
$12$	0.458355	0.132316
$13$	−0.588443	−0.163205	−0.0816024	−	0.996665i	$-0.526004\pi$
$13$	−0.588443	−0.163205	−0.0816024	+	0.996665i	$0.526004\pi$
$14$	1.34348	0.359060
$15$	2.34976	0.606705
$16$	−3.57182	−0.892955
$17$	2.31546	0.561582	0.280791	−	0.959769i	$-0.409403\pi$
$17$	2.31546	0.561582	0.280791	+	0.959769i	$0.409403\pi$
$18$	−3.38740	−0.798417
$19$	−8.11161	−1.86093	−0.930465	−	0.366381i	$-0.880597\pi$
$19$	−8.11161	−1.86093	−0.930465	+	0.366381i	$0.880597\pi$
$20$	0.195065	0.0436178
$21$	2.34976	0.512759
$22$	−1.58694	−0.338338
$23$	−2.01930	−0.421054	−0.210527	−	0.977588i	$-0.567518\pi$
$23$	−2.01930	−0.421054	−0.210527	+	0.977588i	$0.567518\pi$
$24$	−6.92949	−1.41448
$25$	1.00000	0.200000
$26$	0.790561	0.155042
$27$	1.12468	0.216445
$28$	0.195065	0.0368638
$29$	9.62218	1.78679	0.893397	−	0.449269i	$-0.148315\pi$
$29$	9.62218	1.78679	0.893397	+	0.449269i	$0.148315\pi$
$30$	−3.15685	−0.576359
$31$	−1.07051	−0.192269	−0.0961347	−	0.995368i	$-0.530648\pi$
$31$	−1.07051	−0.192269	−0.0961347	+	0.995368i	$0.530648\pi$
$32$	−1.09938	−0.194345
$33$	−2.77558	−0.483167
$34$	−3.11078	−0.533494
$35$	1.00000	0.169031
$36$	−0.491829	−0.0819715
$37$	2.42896	0.399319	0.199659	−	0.979865i	$-0.436016\pi$
$37$	2.42896	0.399319	0.199659	+	0.979865i	$0.436016\pi$
$38$	10.8978	1.76785
$39$	1.38270	0.221409
$40$	−2.94902	−0.466281
$41$	5.19778	0.811756	0.405878	−	0.913927i	$-0.366966\pi$
$41$	5.19778	0.811756	0.405878	+	0.913927i	$0.366966\pi$
$42$	−3.15685	−0.487113
$43$	−7.17480	−1.09415	−0.547073	−	0.837085i	$-0.684258\pi$
$43$	−7.17480	−1.09415	−0.547073	+	0.837085i	$0.684258\pi$
$44$	−0.230414	−0.0347363
$45$	−2.52136	−0.375863
$46$	2.71289	0.399994
$47$	2.65348	0.387050	0.193525	−	0.981095i	$-0.438008\pi$
$47$	2.65348	0.387050	0.193525	+	0.981095i	$0.438008\pi$
$48$	8.39291	1.21141
$49$	1.00000	0.142857
$50$	−1.34348	−0.189997
$51$	−5.44078	−0.761861
$52$	0.114785	0.0159178
$53$	3.73499	0.513040	0.256520	−	0.966539i	$-0.417424\pi$
$53$	3.73499	0.513040	0.256520	+	0.966539i	$0.417424\pi$
$54$	−1.51099	−0.205619
$55$	−1.18122	−0.159276
$56$	−2.94902	−0.394080
$57$	19.0603	2.52460
$58$	−12.9272	−1.69742
$59$	7.26498	0.945820	0.472910	−	0.881111i	$-0.343204\pi$
$59$	7.26498	0.945820	0.472910	+	0.881111i	$0.343204\pi$
$60$	−0.458355	−0.0591734
$61$	−8.28356	−1.06060	−0.530300	−	0.847810i	$-0.677921\pi$
$61$	−8.28356	−1.06060	−0.530300	+	0.847810i	$0.677921\pi$
$62$	1.43821	0.182653
$63$	−2.52136	−0.317662
$64$	8.62064	1.07758
$65$	0.588443	0.0729874
$66$	3.72893	0.459000
$67$	2.82605	0.345257	0.172629	−	0.984987i	$-0.444774\pi$
$67$	2.82605	0.345257	0.172629	+	0.984987i	$0.444774\pi$
$68$	−0.451665	−0.0547725
$69$	4.74487	0.571216
$70$	−1.34348	−0.160576
$71$	−12.9454	−1.53634	−0.768168	−	0.640249i	$-0.778831\pi$
$71$	−12.9454	−1.53634	−0.768168	+	0.640249i	$0.778831\pi$
$72$	7.43556	0.876289
$73$	0.537958	0.0629632	0.0314816	−	0.999504i	$-0.489977\pi$
$73$	0.537958	0.0629632	0.0314816	+	0.999504i	$0.489977\pi$
$74$	−3.26326	−0.379346
$75$	−2.34976	−0.271327
$76$	1.58229	0.181501
$77$	−1.18122	−0.134612
$78$	−1.85763	−0.210335
$79$	−6.23859	−0.701897	−0.350948	−	0.936395i	$-0.614141\pi$
$79$	−6.23859	−0.701897	−0.350948	+	0.936395i	$0.614141\pi$
$80$	3.57182	0.399342
$81$	−10.2068	−1.13409
$82$	−6.98310	−0.771155
$83$	10.6286	1.16665	0.583323	−	0.812240i	$-0.301752\pi$
$83$	10.6286	1.16665	0.583323	+	0.812240i	$0.301752\pi$
$84$	−0.458355	−0.0500106
$85$	−2.31546	−0.251147
$86$	9.63919	1.03942
$87$	−22.6098	−2.42402
$88$	3.48344	0.371336
$89$	10.4769	1.11054	0.555272	−	0.831669i	$-0.312614\pi$
$89$	10.4769	1.11054	0.555272	+	0.831669i	$0.312614\pi$
$90$	3.38740	0.357063
$91$	0.588443	0.0616856
$92$	0.393895	0.0410664
$93$	2.51544	0.260839
$94$	−3.56490	−0.367691
$95$	8.11161	0.832233
$96$	2.58328	0.263655
$97$	11.2081	1.13801	0.569006	−	0.822333i	$-0.307328\pi$
$97$	11.2081	1.13801	0.569006	+	0.822333i	$0.307328\pi$
$98$	−1.34348	−0.135712
$99$	2.97828	0.299329
$100$	−0.195065	−0.0195065
$101$	6.15885	0.612829	0.306414	−	0.951898i	$-0.400871\pi$
$101$	6.15885	0.612829	0.306414	+	0.951898i	$0.400871\pi$
$102$	7.30957	0.723755
$103$	9.84805	0.970357	0.485178	−	0.874415i	$-0.338755\pi$
$103$	9.84805	0.970357	0.485178	+	0.874415i	$0.338755\pi$
$104$	−1.73533	−0.170163
$105$	−2.34976	−0.229313
$106$	−5.01788	−0.487379
$107$	−3.80353	−0.367701	−0.183850	−	0.982954i	$-0.558856\pi$
$107$	−3.80353	−0.367701	−0.183850	+	0.982954i	$0.558856\pi$
$108$	−0.219386	−0.0211104
$109$	4.95785	0.474875	0.237438	−	0.971403i	$-0.423692\pi$
$109$	4.95785	0.474875	0.237438	+	0.971403i	$0.423692\pi$
$110$	1.58694	0.151309
$111$	−5.70747	−0.541729
$112$	3.57182	0.337505
$113$	−2.87330	−0.270297	−0.135149	−	0.990825i	$-0.543151\pi$
$113$	−2.87330	−0.270297	−0.135149	+	0.990825i	$0.543151\pi$
$114$	−25.6071	−2.39833
$115$	2.01930	0.188301
$116$	−1.87695	−0.174270
$117$	−1.48368	−0.137166
$118$	−9.76035	−0.898513
$119$	−2.31546	−0.212258
$120$	6.92949	0.632573
$121$	−9.60472	−0.873156
$122$	11.1288	1.00755
$123$	−12.2135	−1.10126
$124$	0.208819	0.0187525
$125$	−1.00000	−0.0894427
$126$	3.38740	0.301773
$127$	−19.7529	−1.75279	−0.876395	−	0.481593i	$-0.840058\pi$
$127$	−19.7529	−1.75279	−0.876395	+	0.481593i	$0.840058\pi$
$128$	−9.38288	−0.829337
$129$	16.8590	1.48436
$130$	−0.790561	−0.0693368
$131$	−1.68532	−0.147247	−0.0736234	−	0.997286i	$-0.523456\pi$
$131$	−1.68532	−0.147247	−0.0736234	+	0.997286i	$0.523456\pi$
$132$	0.541418	0.0471244
$133$	8.11161	0.703365
$134$	−3.79674	−0.327988
$135$	−1.12468	−0.0967971
$136$	6.82835	0.585527
$137$	−2.67251	−0.228328	−0.114164	−	0.993462i	$-0.536419\pi$
$137$	−2.67251	−0.228328	−0.114164	+	0.993462i	$0.536419\pi$
$138$	−6.37464	−0.542645
$139$	−10.7562	−0.912325	−0.456162	−	0.889897i	$-0.650776\pi$
$139$	−10.7562	−0.912325	−0.456162	+	0.889897i	$0.650776\pi$
$140$	−0.195065	−0.0164860
$141$	−6.23504	−0.525085
$142$	17.3919	1.45949
$143$	−0.695081	−0.0581256
$144$	−9.00586	−0.750488
$145$	−9.62218	−0.799078
$146$	−0.722735	−0.0598140
$147$	−2.34976	−0.193805
$148$	−0.473805	−0.0389465
$149$	3.31814	0.271832	0.135916	−	0.990720i	$-0.456602\pi$
$149$	3.31814	0.271832	0.135916	+	0.990720i	$0.456602\pi$
$150$	3.15685	0.257756
$151$	−17.1574	−1.39625	−0.698126	−	0.715975i	$-0.745982\pi$
$151$	−17.1574	−1.39625	−0.698126	+	0.715975i	$0.745982\pi$
$152$	−23.9213	−1.94027
$153$	5.83812	0.471984
$154$	1.58694	0.127880
$155$	1.07051	0.0859855
$156$	−0.269716	−0.0215946
$157$	22.5011	1.79578	0.897891	−	0.440217i	$-0.145099\pi$
$157$	22.5011	1.79578	0.897891	+	0.440217i	$0.145099\pi$
$158$	8.38142	0.666790
$159$	−8.77632	−0.696007
$160$	1.09938	0.0869137
$161$	2.01930	0.159143
$162$	13.7126	1.07737
$163$	−18.8319	−1.47503	−0.737513	−	0.675333i	$-0.764000\pi$
$163$	−18.8319	−1.47503	−0.737513	+	0.675333i	$0.764000\pi$
$164$	−1.01390	−0.0791725
$165$	2.77558	0.216079
$166$	−14.2794	−1.10829
$167$	11.4516	0.886155	0.443077	−	0.896483i	$-0.353887\pi$
$167$	11.4516	0.886155	0.443077	+	0.896483i	$0.353887\pi$
$168$	6.92949	0.534622
$169$	−12.6537	−0.973364
$170$	3.11078	0.238586
$171$	−20.4523	−1.56403
$172$	1.39955	0.106715
$173$	−4.05375	−0.308201	−0.154100	−	0.988055i	$-0.549248\pi$
$173$	−4.05375	−0.308201	−0.154100	+	0.988055i	$0.549248\pi$
$174$	30.3758	2.30278
$175$	−1.00000	−0.0755929
$176$	−4.21910	−0.318027
$177$	−17.0709	−1.28313
$178$	−14.0754	−1.05500
$179$	16.2202	1.21235	0.606177	−	0.795330i	$-0.292702\pi$
$179$	16.2202	1.21235	0.606177	+	0.795330i	$0.292702\pi$
$180$	0.491829	0.0366588
$181$	−16.2703	−1.20936	−0.604682	−	0.796467i	$-0.706700\pi$
$181$	−16.2703	−1.20936	−0.604682	+	0.796467i	$0.706700\pi$
$182$	−0.790561	−0.0586003
$183$	19.4644	1.43885
$184$	−5.95497	−0.439006
$185$	−2.42896	−0.178581
$186$	−3.37944	−0.247793
$187$	2.73507	0.200008
$188$	−0.517601	−0.0377499
$189$	−1.12468	−0.0818085
$190$	−10.8978	−0.790607
$191$	−24.7749	−1.79265	−0.896324	−	0.443399i	$-0.853773\pi$
$191$	−24.7749	−1.79265	−0.896324	+	0.443399i	$0.853773\pi$
$192$	−20.2564	−1.46188
$193$	−13.6464	−0.982290	−0.491145	−	0.871078i	$-0.663421\pi$
$193$	−13.6464	−0.982290	−0.491145	+	0.871078i	$0.663421\pi$
$194$	−15.0579	−1.08109
$195$	−1.38270	−0.0990171
$196$	−0.195065	−0.0139332
$197$	−5.53232	−0.394162	−0.197081	−	0.980387i	$-0.563146\pi$
$197$	−5.53232	−0.394162	−0.197081	+	0.980387i	$0.563146\pi$
$198$	−4.00126	−0.284357
$199$	−12.9874	−0.920649	−0.460325	−	0.887751i	$-0.652267\pi$
$199$	−12.9874	−0.920649	−0.460325	+	0.887751i	$0.652267\pi$
$200$	2.94902	0.208527
$201$	−6.64054	−0.468388
$202$	−8.27429	−0.582177
$203$	−9.62218	−0.675344
$204$	1.06130	0.0743062
$205$	−5.19778	−0.363028
$206$	−13.2306	−0.921823
$207$	−5.09140	−0.353877
$208$	2.10181	0.145735
$209$	−9.58159	−0.662772
$210$	3.15685	0.217843
$211$	−22.8288	−1.57160	−0.785799	−	0.618482i	$-0.787748\pi$
$211$	−22.8288	−1.57160	−0.785799	+	0.618482i	$0.787748\pi$
$212$	−0.728564	−0.0500380
$213$	30.4185	2.08424
$214$	5.10996	0.349309
$215$	7.17480	0.489317
$216$	3.31671	0.225674
$217$	1.07051	0.0726710
$218$	−6.66076	−0.451124
$219$	−1.26407	−0.0854180
$220$	0.230414	0.0155345
$221$	−1.36252	−0.0916529
$222$	7.66787	0.514634
$223$	5.16394	0.345803	0.172902	−	0.984939i	$-0.444686\pi$
$223$	5.16394	0.345803	0.172902	+	0.984939i	$0.444686\pi$
$224$	1.09938	0.0734555
$225$	2.52136	0.168091
$226$	3.86022	0.256778
$227$	−5.88901	−0.390868	−0.195434	−	0.980717i	$-0.562611\pi$
$227$	−5.88901	−0.390868	−0.195434	+	0.980717i	$0.562611\pi$
$228$	−3.71800	−0.246230
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−2.71289	−0.178883
$231$	2.77558	0.182620
$232$	28.3760	1.86298
$233$	1.35253	0.0886071	0.0443036	−	0.999018i	$-0.485893\pi$
$233$	1.35253	0.0886071	0.0443036	+	0.999018i	$0.485893\pi$
$234$	1.99329	0.130305
$235$	−2.65348	−0.173094
$236$	−1.41714	−0.0922481
$237$	14.6592	0.952216
$238$	3.11078	0.201642
$239$	2.06443	0.133537	0.0667684	−	0.997769i	$-0.478731\pi$
$239$	2.06443	0.133537	0.0667684	+	0.997769i	$0.478731\pi$
$240$	−8.39291	−0.541760
$241$	−16.7076	−1.07623	−0.538115	−	0.842871i	$-0.680863\pi$
$241$	−16.7076	−1.07623	−0.538115	+	0.842871i	$0.680863\pi$
$242$	12.9037	0.829484
$243$	20.6095	1.32210
$244$	1.61583	0.103443
$245$	−1.00000	−0.0638877
$246$	16.4086	1.04617
$247$	4.77322	0.303713
$248$	−3.15696	−0.200467
$249$	−24.9747	−1.58271
$250$	1.34348	0.0849691
$251$	12.5260	0.790631	0.395316	−	0.918545i	$-0.370635\pi$
$251$	12.5260	0.790631	0.395316	+	0.918545i	$0.370635\pi$
$252$	0.491829	0.0309823
$253$	−2.38524	−0.149959
$254$	26.5377	1.66512
$255$	5.44078	0.340715
$256$	−4.63557	−0.289723
$257$	−10.0770	−0.628583	−0.314292	−	0.949326i	$-0.601767\pi$
$257$	−10.0770	−0.628583	−0.314292	+	0.949326i	$0.601767\pi$
$258$	−22.6498	−1.41011
$259$	−2.42896	−0.150928
$260$	−0.114785	−0.00711864
$261$	24.2610	1.50172
$262$	2.26419	0.139882
$263$	25.1696	1.55202	0.776011	−	0.630720i	$-0.217240\pi$
$263$	25.1696	1.55202	0.776011	+	0.630720i	$0.217240\pi$
$264$	−8.18525	−0.503767
$265$	−3.73499	−0.229438
$266$	−10.8978	−0.668185
$267$	−24.6181	−1.50660
$268$	−0.551263	−0.0336738
$269$	−13.3627	−0.814735	−0.407368	−	0.913264i	$-0.633553\pi$
$269$	−13.3627	−0.814735	−0.407368	+	0.913264i	$0.633553\pi$
$270$	1.51099	0.0919556
$271$	13.8615	0.842026	0.421013	−	0.907055i	$-0.361675\pi$
$271$	13.8615	0.842026	0.421013	+	0.907055i	$0.361675\pi$
$272$	−8.27042	−0.501468
$273$	−1.38270	−0.0836847
$274$	3.59046	0.216907
$275$	1.18122	0.0712302
$276$	−0.925558	−0.0557120
$277$	−4.75479	−0.285688	−0.142844	−	0.989745i	$-0.545625\pi$
$277$	−4.75479	−0.285688	−0.142844	+	0.989745i	$0.545625\pi$
$278$	14.4507	0.866693
$279$	−2.69915	−0.161594
$280$	2.94902	0.176238
$281$	2.02237	0.120644	0.0603222	−	0.998179i	$-0.480787\pi$
$281$	2.02237	0.120644	0.0603222	+	0.998179i	$0.480787\pi$
$282$	8.37664	0.498822
$283$	18.0658	1.07390	0.536949	−	0.843615i	$-0.319577\pi$
$283$	18.0658	1.07390	0.536949	+	0.843615i	$0.319577\pi$
$284$	2.52519	0.149842
$285$	−19.0603	−1.12904
$286$	0.933826	0.0552183
$287$	−5.19778	−0.306815
$288$	−2.77194	−0.163338
$289$	−11.6386	−0.684625
$290$	12.9272	0.759111
$291$	−26.3364	−1.54387
$292$	−0.104937	−0.00614096
$293$	−19.4223	−1.13466	−0.567331	−	0.823490i	$-0.692024\pi$
$293$	−19.4223	−1.13466	−0.567331	+	0.823490i	$0.692024\pi$
$294$	3.15685	0.184111
$295$	−7.26498	−0.422984
$296$	7.16306	0.416345
$297$	1.32850	0.0770871
$298$	−4.45785	−0.258236
$299$	1.18825	0.0687180
$300$	0.458355	0.0264631
$301$	7.17480	0.413549
$302$	23.0506	1.32642
$303$	−14.4718	−0.831384
$304$	28.9732	1.66173
$305$	8.28356	0.474315
$306$	−7.84340	−0.448377
$307$	−9.47889	−0.540989	−0.270494	−	0.962722i	$-0.587187\pi$
$307$	−9.47889	−0.540989	−0.270494	+	0.962722i	$0.587187\pi$
$308$	0.230414	0.0131291
$309$	−23.1405	−1.31642
$310$	−1.43821	−0.0816848
$311$	−14.6059	−0.828222	−0.414111	−	0.910226i	$-0.635908\pi$
$311$	−14.6059	−0.828222	−0.414111	+	0.910226i	$0.635908\pi$
$312$	4.07761	0.230849
$313$	30.4330	1.72017	0.860086	−	0.510149i	$-0.170410\pi$
$313$	30.4330	1.72017	0.860086	+	0.510149i	$0.170410\pi$
$314$	−30.2297	−1.70596
$315$	2.52136	0.142063
$316$	1.21693	0.0684577
$317$	−20.0525	−1.12626	−0.563132	−	0.826367i	$-0.690404\pi$
$317$	−20.0525	−1.12626	−0.563132	+	0.826367i	$0.690404\pi$
$318$	11.7908	0.661195
$319$	11.3659	0.636369
$320$	−8.62064	−0.481908
$321$	8.93737	0.498835
$322$	−2.71289	−0.151184
$323$	−18.7821	−1.04507
$324$	1.99099	0.110611
$325$	−0.588443	−0.0326410
$326$	25.3002	1.40125
$327$	−11.6497	−0.644232
$328$	15.3284	0.846367
$329$	−2.65348	−0.146291
$330$	−3.72893	−0.205271
$331$	3.04507	0.167372	0.0836860	−	0.996492i	$-0.473331\pi$
$331$	3.04507	0.167372	0.0836860	+	0.996492i	$0.473331\pi$
$332$	−2.07327	−0.113786
$333$	6.12429	0.335609
$334$	−15.3850	−0.841832
$335$	−2.82605	−0.154404
$336$	−8.39291	−0.457871
$337$	27.0603	1.47407	0.737035	−	0.675854i	$-0.236225\pi$
$337$	27.0603	1.47407	0.737035	+	0.675854i	$0.236225\pi$
$338$	17.0000	0.924679
$339$	6.75156	0.366694
$340$	0.451665	0.0244950
$341$	−1.26451	−0.0684770
$342$	27.4772	1.48580
$343$	−1.00000	−0.0539949
$344$	−21.1587	−1.14080
$345$	−4.74487	−0.255455
$346$	5.44613	0.292786
$347$	−3.17128	−0.170243	−0.0851215	−	0.996371i	$-0.527128\pi$
$347$	−3.17128	−0.170243	−0.0851215	+	0.996371i	$0.527128\pi$
$348$	4.41037	0.236421
$349$	−3.71195	−0.198696	−0.0993481	−	0.995053i	$-0.531676\pi$
$349$	−3.71195	−0.198696	−0.0993481	+	0.995053i	$0.531676\pi$
$350$	1.34348	0.0718120
$351$	−0.661811	−0.0353249
$352$	−1.29861	−0.0692162
$353$	29.2773	1.55827	0.779136	−	0.626856i	$-0.215658\pi$
$353$	29.2773	1.55827	0.779136	+	0.626856i	$0.215658\pi$
$354$	22.9345	1.21895
$355$	12.9454	0.687070
$356$	−2.04367	−0.108314
$357$	5.44078	0.287957
$358$	−21.7915	−1.15172
$359$	−13.6382	−0.719799	−0.359900	−	0.932991i	$-0.617189\pi$
$359$	−13.6382	−0.719799	−0.359900	+	0.932991i	$0.617189\pi$
$360$	−7.43556	−0.391888
$361$	46.7981	2.46306
$362$	21.8589	1.14888
$363$	22.5688	1.18455
$364$	−0.114785	−0.00601634
$365$	−0.537958	−0.0281580
$366$	−26.1499	−1.36688
$367$	31.5700	1.64794	0.823972	−	0.566631i	$-0.191754\pi$
$367$	31.5700	1.64794	0.823972	+	0.566631i	$0.191754\pi$
$368$	7.21259	0.375982
$369$	13.1055	0.682244
$370$	3.26326	0.169649
$371$	−3.73499	−0.193911
$372$	−0.490674	−0.0254403
$373$	−6.90853	−0.357710	−0.178855	−	0.983875i	$-0.557239\pi$
$373$	−6.90853	−0.357710	−0.178855	+	0.983875i	$0.557239\pi$
$374$	−3.67451	−0.190004
$375$	2.34976	0.121341
$376$	7.82518	0.403553
$377$	−5.66210	−0.291613
$378$	1.51099	0.0777167
$379$	21.7233	1.11585	0.557925	−	0.829892i	$-0.311598\pi$
$379$	21.7233	1.11585	0.557925	+	0.829892i	$0.311598\pi$
$380$	−1.58229	−0.0811697
$381$	46.4146	2.37789
$382$	33.2846	1.70299
$383$	16.8599	0.861501	0.430750	−	0.902471i	$-0.358249\pi$
$383$	16.8599	0.861501	0.430750	+	0.902471i	$0.358249\pi$
$384$	22.0475	1.12511
$385$	1.18122	0.0602005
$386$	18.3337	0.933158
$387$	−18.0903	−0.919580
$388$	−2.18631	−0.110993
$389$	3.02442	0.153344	0.0766720	−	0.997056i	$-0.475571\pi$
$389$	3.02442	0.153344	0.0766720	+	0.997056i	$0.475571\pi$
$390$	1.85763	0.0940646
$391$	−4.67562	−0.236456
$392$	2.94902	0.148948
$393$	3.96008	0.199760
$394$	7.43256	0.374447
$395$	6.23859	0.313898
$396$	−0.580958	−0.0291943
$397$	−31.2074	−1.56625	−0.783127	−	0.621862i	$-0.786376\pi$
$397$	−31.2074	−1.56625	−0.783127	+	0.621862i	$0.786376\pi$
$398$	17.4482	0.874601
$399$	−19.0603	−0.954209
$400$	−3.57182	−0.178591
$401$	−4.46073	−0.222758	−0.111379	−	0.993778i	$-0.535527\pi$
$401$	−4.46073	−0.222758	−0.111379	+	0.993778i	$0.535527\pi$
$402$	8.92142	0.444960
$403$	0.629935	0.0313793
$404$	−1.20138	−0.0597707
$405$	10.2068	0.507181
$406$	12.9272	0.641566
$407$	2.86914	0.142218
$408$	−16.0450	−0.794345
$409$	−18.5904	−0.919235	−0.459618	−	0.888117i	$-0.652014\pi$
$409$	−18.5904	−0.919235	−0.459618	+	0.888117i	$0.652014\pi$
$410$	6.98310	0.344871
$411$	6.27974	0.309757
$412$	−1.92101	−0.0946412
$413$	−7.26498	−0.357486
$414$	6.84018	0.336177
$415$	−10.6286	−0.521740
$416$	0.646923	0.0317180
$417$	25.2744	1.23769
$418$	12.8727	0.629622
$419$	−3.55784	−0.173812	−0.0869060	−	0.996217i	$-0.527698\pi$
$419$	−3.55784	−0.173812	−0.0869060	+	0.996217i	$0.527698\pi$
$420$	0.458355	0.0223654
$421$	1.69987	0.0828466	0.0414233	−	0.999142i	$-0.486811\pi$
$421$	1.69987	0.0828466	0.0414233	+	0.999142i	$0.486811\pi$
$422$	30.6700	1.49299
$423$	6.69039	0.325298
$424$	11.0146	0.534914
$425$	2.31546	0.112316
$426$	−40.8667	−1.98000
$427$	8.28356	0.400869
$428$	0.741934	0.0358627
$429$	1.63327	0.0788551
$430$	−9.63919	−0.464843
$431$	−12.6235	−0.608053	−0.304027	−	0.952664i	$-0.598331\pi$
$431$	−12.6235	−0.608053	−0.304027	+	0.952664i	$0.598331\pi$
$432$	−4.01716	−0.193276
$433$	25.7484	1.23739	0.618696	−	0.785631i	$-0.287661\pi$
$433$	25.7484	1.23739	0.618696	+	0.785631i	$0.287661\pi$
$434$	−1.43821	−0.0690362
$435$	22.6098	1.08406
$436$	−0.967101	−0.0463157
$437$	16.3798	0.783552
$438$	1.69825	0.0811457
$439$	26.7028	1.27445	0.637227	−	0.770676i	$-0.280081\pi$
$439$	26.7028	1.27445	0.637227	+	0.770676i	$0.280081\pi$
$440$	−3.48344	−0.166067
$441$	2.52136	0.120065
$442$	1.83051	0.0870687
$443$	−8.34285	−0.396381	−0.198190	−	0.980164i	$-0.563506\pi$
$443$	−8.34285	−0.396381	−0.198190	+	0.980164i	$0.563506\pi$
$444$	1.11333	0.0528362
$445$	−10.4769	−0.496651
$446$	−6.93764	−0.328507
$447$	−7.79682	−0.368777
$448$	−8.62064	−0.407287
$449$	29.4222	1.38852	0.694259	−	0.719725i	$-0.255732\pi$
$449$	29.4222	1.38852	0.694259	+	0.719725i	$0.255732\pi$
$450$	−3.38740	−0.159683
$451$	6.13971	0.289108
$452$	0.560479	0.0263627
$453$	40.3158	1.89420
$454$	7.91177	0.371318
$455$	−0.588443	−0.0275866
$456$	56.2093	2.63224
$457$	28.1428	1.31646	0.658232	−	0.752816i	$-0.271305\pi$
$457$	28.1428	1.31646	0.658232	+	0.752816i	$0.271305\pi$
$458$	−1.34348	−0.0627766
$459$	2.60416	0.121552
$460$	−0.393895	−0.0183655
$461$	−32.8624	−1.53055	−0.765276	−	0.643702i	$-0.777398\pi$
$461$	−32.8624	−1.53055	−0.765276	+	0.643702i	$0.777398\pi$
$462$	−3.72893	−0.173486
$463$	−9.16872	−0.426107	−0.213053	−	0.977041i	$-0.568341\pi$
$463$	−9.16872	−0.426107	−0.213053	+	0.977041i	$0.568341\pi$
$464$	−34.3687	−1.59553
$465$	−2.51544	−0.116651
$466$	−1.81709	−0.0841753
$467$	20.3466	0.941530	0.470765	−	0.882259i	$-0.343978\pi$
$467$	20.3466	0.941530	0.470765	+	0.882259i	$0.343978\pi$
$468$	0.289413	0.0133781
$469$	−2.82605	−0.130495
$470$	3.56490	0.164436
$471$	−52.8721	−2.43622
$472$	21.4246	0.986147
$473$	−8.47502	−0.389682
$474$	−19.6943	−0.904589
$475$	−8.11161	−0.372186
$476$	0.451665	0.0207021
$477$	9.41726	0.431187
$478$	−2.77351	−0.126858
$479$	−32.6342	−1.49109	−0.745547	−	0.666453i	$-0.767812\pi$
$479$	−32.6342	−1.49109	−0.745547	+	0.666453i	$0.767812\pi$
$480$	−2.58328	−0.117910
$481$	−1.42931	−0.0651707
$482$	22.4463	1.02240
$483$	−4.74487	−0.215899
$484$	1.87354	0.0851610
$485$	−11.2081	−0.508935
$486$	−27.6884	−1.25597
$487$	21.5038	0.974428	0.487214	−	0.873283i	$-0.338013\pi$
$487$	21.5038	0.974428	0.487214	+	0.873283i	$0.338013\pi$
$488$	−24.4284	−1.10582
$489$	44.2503	2.00107
$490$	1.34348	0.0606922
$491$	40.5459	1.82981	0.914906	−	0.403667i	$-0.132265\pi$
$491$	40.5459	1.82981	0.914906	+	0.403667i	$0.132265\pi$
$492$	2.38243	0.107408
$493$	22.2798	1.00343
$494$	−6.41272	−0.288522
$495$	−2.97828	−0.133864
$496$	3.82367	0.171688
$497$	12.9454	0.580680
$498$	33.5530	1.50355
$499$	34.7688	1.55646	0.778232	−	0.627976i	$-0.216117\pi$
$499$	34.7688	1.55646	0.778232	+	0.627976i	$0.216117\pi$
$500$	0.195065	0.00872356
$501$	−26.9086	−1.20219
$502$	−16.8284	−0.751086
$503$	23.0853	1.02932	0.514661	−	0.857394i	$-0.327918\pi$
$503$	23.0853	1.02932	0.514661	+	0.857394i	$0.327918\pi$
$504$	−7.43556	−0.331206
$505$	−6.15885	−0.274065
$506$	3.20452	0.142458
$507$	29.7332	1.32050
$508$	3.85310	0.170954
$509$	21.8248	0.967369	0.483684	−	0.875242i	$-0.339298\pi$
$509$	21.8248	0.967369	0.483684	+	0.875242i	$0.339298\pi$
$510$	−7.30957	−0.323673
$511$	−0.537958	−0.0237979
$512$	24.9936	1.10457
$513$	−9.12297	−0.402789
$514$	13.5382	0.597143
$515$	−9.84805	−0.433957
$516$	−3.28861	−0.144773
$517$	3.13434	0.137848
$518$	3.26326	0.143379
$519$	9.52533	0.418116
$520$	1.73533	0.0760994
$521$	6.09504	0.267029	0.133514	−	0.991047i	$-0.457374\pi$
$521$	6.09504	0.267029	0.133514	+	0.991047i	$0.457374\pi$
$522$	−32.5941	−1.42661
$523$	−35.0802	−1.53395	−0.766976	−	0.641676i	$-0.778239\pi$
$523$	−35.0802	−1.53395	−0.766976	+	0.641676i	$0.778239\pi$
$524$	0.328746	0.0143613
$525$	2.34976	0.102552
$526$	−33.8148	−1.47439
$527$	−2.47873	−0.107975
$528$	9.91387	0.431446
$529$	−18.9224	−0.822714
$530$	5.01788	0.217963
$531$	18.3177	0.794918
$532$	−1.58229	−0.0686009
$533$	−3.05860	−0.132482
$534$	33.0739	1.43125
$535$	3.80353	0.164441
$536$	8.33409	0.359978
$537$	−38.1135	−1.64472
$538$	17.9524	0.773985
$539$	1.18122	0.0508787
$540$	0.219386	0.00944086
$541$	6.81669	0.293072	0.146536	−	0.989205i	$-0.453188\pi$
$541$	6.81669	0.293072	0.146536	+	0.989205i	$0.453188\pi$
$542$	−18.6226	−0.799911
$543$	38.2314	1.64067
$544$	−2.54558	−0.109141
$545$	−4.95785	−0.212371
$546$	1.85763	0.0794991
$547$	−39.6774	−1.69648	−0.848242	−	0.529609i	$-0.822339\pi$
$547$	−39.6774	−1.69648	−0.848242	+	0.529609i	$0.822339\pi$
$548$	0.521312	0.0222693
$549$	−20.8859	−0.891387
$550$	−1.58694	−0.0676675
$551$	−78.0513	−3.32510
$552$	13.9927	0.595571
$553$	6.23859	0.265292
$554$	6.38796	0.271398
$555$	5.70747	0.242269
$556$	2.09815	0.0889812
$557$	1.03626	0.0439079	0.0219540	−	0.999759i	$-0.493011\pi$
$557$	1.03626	0.0439079	0.0219540	+	0.999759i	$0.493011\pi$
$558$	3.62625	0.153511
$559$	4.22196	0.178570
$560$	−3.57182	−0.150937
$561$	−6.42676	−0.271338
$562$	−2.71701	−0.114610
$563$	−33.0047	−1.39098	−0.695491	−	0.718535i	$-0.744813\pi$
$563$	−33.0047	−1.39098	−0.695491	+	0.718535i	$0.744813\pi$
$564$	1.21624	0.0512128
$565$	2.87330	0.120881
$566$	−24.2710	−1.02018
$567$	10.2068	0.428646
$568$	−38.1763	−1.60184
$569$	−39.3399	−1.64921	−0.824607	−	0.565707i	$-0.808604\pi$
$569$	−39.3399	−1.64921	−0.824607	+	0.565707i	$0.808604\pi$
$570$	25.6071	1.07256
$571$	−39.7548	−1.66369	−0.831843	−	0.555011i	$-0.812714\pi$
$571$	−39.7548	−1.66369	−0.831843	+	0.555011i	$0.812714\pi$
$572$	0.135586	0.00566913
$573$	58.2150	2.43197
$574$	6.98310	0.291469
$575$	−2.01930	−0.0842108
$576$	21.7358	0.905656
$577$	45.2193	1.88251	0.941253	−	0.337703i	$-0.109650\pi$
$577$	45.2193	1.88251	0.941253	+	0.337703i	$0.109650\pi$
$578$	15.6363	0.650382
$579$	32.0657	1.33261
$580$	1.87695	0.0779360
$581$	−10.6286	−0.440951
$582$	35.3824	1.46665
$583$	4.41184	0.182720
$584$	1.58645	0.0656478
$585$	1.48368	0.0613426
$586$	26.0934	1.07791
$587$	−17.2896	−0.713617	−0.356808	−	0.934178i	$-0.616135\pi$
$587$	−17.2896	−0.713617	−0.356808	+	0.934178i	$0.616135\pi$
$588$	0.458355	0.0189022
$589$	8.68356	0.357800
$590$	9.76035	0.401827
$591$	12.9996	0.534733
$592$	−8.67581	−0.356574
$593$	20.1371	0.826933	0.413466	−	0.910519i	$-0.364318\pi$
$593$	20.1371	0.826933	0.413466	+	0.910519i	$0.364318\pi$
$594$	−1.78481	−0.0732315
$595$	2.31546	0.0949247
$596$	−0.647252	−0.0265125
$597$	30.5172	1.24898
$598$	−1.59638	−0.0652809
$599$	25.3359	1.03520	0.517598	−	0.855624i	$-0.326826\pi$
$599$	25.3359	1.03520	0.517598	+	0.855624i	$0.326826\pi$
$600$	−6.92949	−0.282895
$601$	−21.9537	−0.895509	−0.447755	−	0.894156i	$-0.647776\pi$
$601$	−21.9537	−0.895509	−0.447755	+	0.894156i	$0.647776\pi$
$602$	−9.63919	−0.392864
$603$	7.12550	0.290173
$604$	3.34681	0.136180
$605$	9.60472	0.390487
$606$	19.4426	0.789801
$607$	2.43986	0.0990310	0.0495155	−	0.998773i	$-0.484232\pi$
$607$	2.43986	0.0990310	0.0495155	+	0.998773i	$0.484232\pi$
$608$	8.91775	0.361662
$609$	22.6098	0.916195
$610$	−11.1288	−0.450591
$611$	−1.56142	−0.0631684
$612$	−1.13881	−0.0460338
$613$	13.1917	0.532809	0.266405	−	0.963861i	$-0.414164\pi$
$613$	13.1917	0.532809	0.266405	+	0.963861i	$0.414164\pi$
$614$	12.7347	0.513930
$615$	12.2135	0.492496
$616$	−3.48344	−0.140352
$617$	−19.3368	−0.778470	−0.389235	−	0.921138i	$-0.627261\pi$
$617$	−19.3368	−0.778470	−0.389235	+	0.921138i	$0.627261\pi$
$618$	31.0888	1.25058
$619$	−30.6643	−1.23250	−0.616252	−	0.787549i	$-0.711350\pi$
$619$	−30.6643	−1.23250	−0.616252	+	0.787549i	$0.711350\pi$
$620$	−0.208819	−0.00838637
$621$	−2.27107	−0.0911350
$622$	19.6227	0.786797
$623$	−10.4769	−0.419746
$624$	−4.93875	−0.197708
$625$	1.00000	0.0400000
$626$	−40.8860	−1.63413
$627$	22.5144	0.899139
$628$	−4.38917	−0.175147
$629$	5.62417	0.224250
$630$	−3.38740	−0.134957
$631$	19.5300	0.777478	0.388739	−	0.921348i	$-0.372911\pi$
$631$	19.5300	0.777478	0.388739	+	0.921348i	$0.372911\pi$
$632$	−18.3978	−0.731823
$633$	53.6421	2.13208
$634$	26.9402	1.06993
$635$	19.7529	0.783871
$636$	1.71195	0.0678832
$637$	−0.588443	−0.0233150
$638$	−15.2699	−0.604539
$639$	−32.6400	−1.29122
$640$	9.38288	0.370891
$641$	46.7753	1.84751	0.923757	−	0.382978i	$-0.125102\pi$
$641$	46.7753	1.84751	0.923757	+	0.382978i	$0.125102\pi$
$642$	−12.0072	−0.473885
$643$	11.3562	0.447843	0.223922	−	0.974607i	$-0.428114\pi$
$643$	11.3562	0.447843	0.223922	+	0.974607i	$0.428114\pi$
$644$	−0.393895	−0.0155216
$645$	−16.8590	−0.663824
$646$	25.2334	0.992794
$647$	24.9919	0.982533	0.491267	−	0.871009i	$-0.336534\pi$
$647$	24.9919	0.982533	0.491267	+	0.871009i	$0.336534\pi$
$648$	−30.1001	−1.18245
$649$	8.58154	0.336855
$650$	0.790561	0.0310083
$651$	−2.51544	−0.0985879
$652$	3.67343	0.143863
$653$	4.83804	0.189327	0.0946636	−	0.995509i	$-0.469822\pi$
$653$	4.83804	0.189327	0.0946636	+	0.995509i	$0.469822\pi$
$654$	15.6512	0.612009
$655$	1.68532	0.0658507
$656$	−18.5655	−0.724862
$657$	1.35639	0.0529177
$658$	3.56490	0.138974
$659$	4.31741	0.168182	0.0840912	−	0.996458i	$-0.473201\pi$
$659$	4.31741	0.168182	0.0840912	+	0.996458i	$0.473201\pi$
$660$	−0.541418	−0.0210747
$661$	−38.7835	−1.50850	−0.754251	−	0.656587i	$-0.772000\pi$
$661$	−38.7835	−1.50850	−0.754251	+	0.656587i	$0.772000\pi$
$662$	−4.09098	−0.159000
$663$	3.20159	0.124339
$664$	31.3441	1.21639
$665$	−8.11161	−0.314555
$666$	−8.22786	−0.318823
$667$	−19.4301	−0.752336
$668$	−2.23381	−0.0864288
$669$	−12.1340	−0.469128
$670$	3.79674	0.146681
$671$	−9.78470	−0.377734
$672$	−2.58328	−0.0996522
$673$	11.4099	0.439820	0.219910	−	0.975520i	$-0.429424\pi$
$673$	11.4099	0.439820	0.219910	+	0.975520i	$0.429424\pi$
$674$	−36.3550	−1.40034
$675$	1.12468	0.0432890
$676$	2.46830	0.0949345
$677$	−11.4807	−0.441239	−0.220619	−	0.975360i	$-0.570808\pi$
$677$	−11.4807	−0.441239	−0.220619	+	0.975360i	$0.570808\pi$
$678$	−9.07057	−0.348353
$679$	−11.2081	−0.430128
$680$	−6.82835	−0.261855
$681$	13.8378	0.530264
$682$	1.69884	0.0650520
$683$	9.22267	0.352896	0.176448	−	0.984310i	$-0.443539\pi$
$683$	9.22267	0.352896	0.176448	+	0.984310i	$0.443539\pi$
$684$	3.98952	0.152543
$685$	2.67251	0.102111
$686$	1.34348	0.0512943
$687$	−2.34976	−0.0896489
$688$	25.6271	0.977024
$689$	−2.19783	−0.0837306
$690$	6.37464	0.242678
$691$	24.7109	0.940049	0.470024	−	0.882653i	$-0.344245\pi$
$691$	24.7109	0.940049	0.470024	+	0.882653i	$0.344245\pi$
$692$	0.790744	0.0300596
$693$	−2.97828	−0.113136
$694$	4.26054	0.161728
$695$	10.7562	0.408004
$696$	−66.6768	−2.52738
$697$	12.0353	0.455868
$698$	4.98693	0.188758
$699$	−3.17812	−0.120207
$700$	0.195065	0.00737276
$701$	47.2226	1.78357	0.891786	−	0.452457i	$-0.149453\pi$
$701$	47.2226	1.78357	0.891786	+	0.452457i	$0.149453\pi$
$702$	0.889129	0.0335580
$703$	−19.7028	−0.743104
$704$	10.1829	0.383781
$705$	6.23504	0.234825
$706$	−39.3334	−1.48033
$707$	−6.15885	−0.231628
$708$	3.32994	0.125147
$709$	7.22005	0.271155	0.135577	−	0.990767i	$-0.456711\pi$
$709$	7.22005	0.271155	0.135577	+	0.990767i	$0.456711\pi$
$710$	−17.3919	−0.652705
$711$	−15.7298	−0.589912
$712$	30.8965	1.15790
$713$	2.16169	0.0809558
$714$	−7.30957	−0.273554
$715$	0.695081	0.0259945
$716$	−3.16399	−0.118244
$717$	−4.85091	−0.181160
$718$	18.3227	0.683797
$719$	43.8422	1.63504	0.817518	−	0.575902i	$-0.195349\pi$
$719$	43.8422	1.63504	0.817518	+	0.575902i	$0.195349\pi$
$720$	9.00586	0.335628
$721$	−9.84805	−0.366760
$722$	−62.8723	−2.33987
$723$	39.2588	1.46005
$724$	3.17377	0.117952
$725$	9.62218	0.357359
$726$	−30.3207	−1.12531
$727$	31.0870	1.15295	0.576476	−	0.817114i	$-0.304428\pi$
$727$	31.0870	1.15295	0.576476	+	0.817114i	$0.304428\pi$
$728$	1.73533	0.0643157
$729$	−17.8069	−0.659515
$730$	0.722735	0.0267496
$731$	−16.6130	−0.614454
$732$	−3.79681	−0.140334
$733$	−13.6443	−0.503965	−0.251982	−	0.967732i	$-0.581082\pi$
$733$	−13.6443	−0.503965	−0.251982	+	0.967732i	$0.581082\pi$
$734$	−42.4137	−1.56552
$735$	2.34976	0.0866721
$736$	2.21998	0.0818297
$737$	3.33819	0.122964
$738$	−17.6069	−0.648120
$739$	−44.5250	−1.63788	−0.818940	−	0.573879i	$-0.805438\pi$
$739$	−44.5250	−1.63788	−0.818940	+	0.573879i	$0.805438\pi$
$740$	0.473805	0.0174174
$741$	−11.2159	−0.412027
$742$	5.01788	0.184212
$743$	38.0854	1.39722	0.698609	−	0.715503i	$-0.253803\pi$
$743$	38.0854	1.39722	0.698609	+	0.715503i	$0.253803\pi$
$744$	7.41810	0.271961
$745$	−3.31814	−0.121567
$746$	9.28147	0.339819
$747$	26.7987	0.980512
$748$	−0.533516	−0.0195073
$749$	3.80353	0.138978
$750$	−3.15685	−0.115272
$751$	−42.4382	−1.54859	−0.774297	−	0.632823i	$-0.781896\pi$
$751$	−42.4382	−1.54859	−0.774297	+	0.632823i	$0.781896\pi$
$752$	−9.47776	−0.345618
$753$	−29.4330	−1.07260
$754$	7.60692	0.277028
$755$	17.1574	0.624423
$756$	0.219386	0.00797898
$757$	44.3242	1.61099	0.805496	−	0.592602i	$-0.201899\pi$
$757$	44.3242	1.61099	0.805496	+	0.592602i	$0.201899\pi$
$758$	−29.1848	−1.06004
$759$	5.60474	0.203439
$760$	23.9213	0.867717
$761$	−17.8626	−0.647518	−0.323759	−	0.946140i	$-0.604947\pi$
$761$	−17.8626	−0.647518	−0.323759	+	0.946140i	$0.604947\pi$
$762$	−62.3571	−2.25896
$763$	−4.95785	−0.179486
$764$	4.83271	0.174841
$765$	−5.83812	−0.211078
$766$	−22.6509	−0.818411
$767$	−4.27503	−0.154362
$768$	10.8925	0.393048
$769$	−1.26385	−0.0455757	−0.0227878	−	0.999740i	$-0.507254\pi$
$769$	−1.26385	−0.0455757	−0.0227878	+	0.999740i	$0.507254\pi$
$770$	−1.58694	−0.0571895
$771$	23.6784	0.852757
$772$	2.66193	0.0958051
$773$	−33.9385	−1.22068	−0.610341	−	0.792139i	$-0.708967\pi$
$773$	−33.9385	−1.22068	−0.610341	+	0.792139i	$0.708967\pi$
$774$	24.3039	0.873586
$775$	−1.07051	−0.0384539
$776$	33.0530	1.18653
$777$	5.70747	0.204754
$778$	−4.06324	−0.145674
$779$	−42.1623	−1.51062
$780$	0.269716	0.00965738
$781$	−15.2914	−0.547168
$782$	6.28160	0.224630
$783$	10.8219	0.386743
$784$	−3.57182	−0.127565
$785$	−22.5011	−0.803098
$786$	−5.32029	−0.189768
$787$	33.3308	1.18812	0.594058	−	0.804422i	$-0.297525\pi$
$787$	33.3308	1.18812	0.594058	+	0.804422i	$0.297525\pi$
$788$	1.07916	0.0384435
$789$	−59.1424	−2.10552
$790$	−8.38142	−0.298197
$791$	2.87330	0.102163
$792$	8.78303	0.312091
$793$	4.87440	0.173095
$794$	41.9265	1.48791
$795$	8.77632	0.311264
$796$	2.53338	0.0897932
$797$	−41.2385	−1.46074	−0.730371	−	0.683051i	$-0.760653\pi$
$797$	−41.2385	−1.46074	−0.730371	+	0.683051i	$0.760653\pi$
$798$	25.6071	0.906482
$799$	6.14404	0.217360
$800$	−1.09938	−0.0388690
$801$	26.4160	0.933362
$802$	5.99289	0.211616
$803$	0.635447	0.0224244
$804$	1.29534	0.0456830
$805$	−2.01930	−0.0711711
$806$	−0.846304	−0.0298098
$807$	31.3990	1.10530
$808$	18.1626	0.638958
$809$	55.1572	1.93922	0.969612	−	0.244647i	$-0.0786721\pi$
$809$	55.1572	1.93922	0.969612	+	0.244647i	$0.0786721\pi$
$810$	−13.7126	−0.481813
$811$	−2.84299	−0.0998307	−0.0499154	−	0.998753i	$-0.515895\pi$
$811$	−2.84299	−0.0998307	−0.0499154	+	0.998753i	$0.515895\pi$
$812$	1.87695	0.0658680
$813$	−32.5712	−1.14232
$814$	−3.85462	−0.135105
$815$	18.8319	0.659652
$816$	19.4335	0.680308
$817$	58.1992	2.03613
$818$	24.9758	0.873258
$819$	1.48368	0.0518439
$820$	1.01390	0.0354070
$821$	−45.9213	−1.60267	−0.801333	−	0.598219i	$-0.795875\pi$
$821$	−45.9213	−1.60267	−0.801333	+	0.598219i	$0.795875\pi$
$822$	−8.43670	−0.294264
$823$	42.5417	1.48291	0.741456	−	0.671002i	$-0.234136\pi$
$823$	42.5417	1.48291	0.741456	+	0.671002i	$0.234136\pi$
$824$	29.0421	1.01173
$825$	−2.77558	−0.0966333
$826$	9.76035	0.339606
$827$	52.1980	1.81510	0.907552	−	0.419940i	$-0.137949\pi$
$827$	52.1980	1.81510	0.907552	+	0.419940i	$0.137949\pi$
$828$	0.993152	0.0345144
$829$	9.43933	0.327841	0.163921	−	0.986474i	$-0.447586\pi$
$829$	9.43933	0.327841	0.163921	+	0.986474i	$0.447586\pi$
$830$	14.2794	0.495644
$831$	11.1726	0.387574
$832$	−5.07275	−0.175866
$833$	2.31546	0.0802261
$834$	−33.9556	−1.17578
$835$	−11.4516	−0.396300
$836$	1.86903	0.0646418
$837$	−1.20398	−0.0416158
$838$	4.77989	0.165118
$839$	9.69987	0.334877	0.167438	−	0.985883i	$-0.446450\pi$
$839$	9.69987	0.334877	0.167438	+	0.985883i	$0.446450\pi$
$840$	−6.92949	−0.239090
$841$	63.5863	2.19263
$842$	−2.28374	−0.0787028
$843$	−4.75208	−0.163670
$844$	4.45309	0.153282
$845$	12.6537	0.435302
$846$	−8.98840	−0.309027
$847$	9.60472	0.330022
$848$	−13.3407	−0.458122
$849$	−42.4502	−1.45689
$850$	−3.11078	−0.106699
$851$	−4.90481	−0.168135
$852$	−5.93359	−0.203281
$853$	−30.7939	−1.05436	−0.527182	−	0.849752i	$-0.676751\pi$
$853$	−30.7939	−1.05436	−0.527182	+	0.849752i	$0.676751\pi$
$854$	−11.1288	−0.380819
$855$	20.4523	0.699454
$856$	−11.2167	−0.383378
$857$	38.3000	1.30830	0.654151	−	0.756364i	$-0.273026\pi$
$857$	38.3000	1.30830	0.654151	+	0.756364i	$0.273026\pi$
$858$	−2.19427	−0.0749110
$859$	47.2572	1.61240	0.806198	−	0.591646i	$-0.201522\pi$
$859$	47.2572	1.61240	0.806198	+	0.591646i	$0.201522\pi$
$860$	−1.39955	−0.0477243
$861$	12.2135	0.416235
$862$	16.9594	0.577640
$863$	−42.3782	−1.44257	−0.721286	−	0.692637i	$-0.756449\pi$
$863$	−42.3782	−1.44257	−0.721286	+	0.692637i	$0.756449\pi$
$864$	−1.23645	−0.0420650
$865$	4.05375	0.137832
$866$	−34.5925	−1.17550
$867$	27.3480	0.928785
$868$	−0.208819	−0.00708778
$869$	−7.36915	−0.249981
$870$	−30.3758	−1.02984
$871$	−1.66297	−0.0563476
$872$	14.6208	0.495123
$873$	28.2597	0.956448
$874$	−22.0059	−0.744361
$875$	1.00000	0.0338062
$876$	0.246576	0.00833103
$877$	18.9651	0.640406	0.320203	−	0.947349i	$-0.396249\pi$
$877$	18.9651	0.640406	0.320203	+	0.947349i	$0.396249\pi$
$878$	−35.8746	−1.21071
$879$	45.6376	1.53932
$880$	4.21910	0.142226
$881$	9.04517	0.304739	0.152370	−	0.988324i	$-0.451310\pi$
$881$	9.04517	0.304739	0.152370	+	0.988324i	$0.451310\pi$
$882$	−3.38740	−0.114060
$883$	−54.5193	−1.83472	−0.917360	−	0.398059i	$-0.869684\pi$
$883$	−54.5193	−1.83472	−0.917360	+	0.398059i	$0.869684\pi$
$884$	0.265779	0.00893913
$885$	17.0709	0.573834
$886$	11.2084	0.376555
$887$	−1.38125	−0.0463777	−0.0231888	−	0.999731i	$-0.507382\pi$
$887$	−1.38125	−0.0463777	−0.0231888	+	0.999731i	$0.507382\pi$
$888$	−16.8315	−0.564827
$889$	19.7529	0.662492
$890$	14.0754	0.471810
$891$	−12.0565	−0.403908
$892$	−1.00730	−0.0337270
$893$	−21.5240	−0.720273
$894$	10.4749	0.350332
$895$	−16.2202	−0.542181
$896$	9.38288	0.313460
$897$	−2.79209	−0.0932251
$898$	−39.5281	−1.31907
$899$	−10.3006	−0.343546
$900$	−0.491829	−0.0163943
$901$	8.64823	0.288114
$902$	−8.24858	−0.274648
$903$	−16.8590	−0.561034
$904$	−8.47342	−0.281822
$905$	16.2703	0.540844
$906$	−54.1634	−1.79946
$907$	12.0485	0.400065	0.200033	−	0.979789i	$-0.435895\pi$
$907$	12.0485	0.400065	0.200033	+	0.979789i	$0.435895\pi$
$908$	1.14874	0.0381223
$909$	15.5287	0.515055
$910$	0.790561	0.0262068
$911$	35.4322	1.17392	0.586961	−	0.809615i	$-0.300324\pi$
$911$	35.4322	1.17392	0.586961	+	0.809615i	$0.300324\pi$
$912$	−68.0800	−2.25435
$913$	12.5548	0.415502
$914$	−37.8092	−1.25062
$915$	−19.4644	−0.643472
$916$	−0.195065	−0.00644512
$917$	1.68532	0.0556540
$918$	−3.49863	−0.115472
$919$	43.6474	1.43980	0.719898	−	0.694080i	$-0.244189\pi$
$919$	43.6474	1.43980	0.719898	+	0.694080i	$0.244189\pi$
$920$	5.95497	0.196330
$921$	22.2731	0.733924
$922$	44.1499	1.45400
$923$	7.61763	0.250737
$924$	−0.541418	−0.0178113
$925$	2.42896	0.0798638
$926$	12.3180	0.404794
$927$	24.8305	0.815541
$928$	−10.5784	−0.347254
$929$	30.4460	0.998901	0.499451	−	0.866342i	$-0.333535\pi$
$929$	30.4460	0.998901	0.499451	+	0.866342i	$0.333535\pi$
$930$	3.37944	0.110816
$931$	−8.11161	−0.265847
$932$	−0.263831	−0.00864207
$933$	34.3202	1.12359
$934$	−27.3353	−0.894437
$935$	−2.73507	−0.0894464
$936$	−4.37540	−0.143015
$937$	−18.3231	−0.598590	−0.299295	−	0.954161i	$-0.596751\pi$
$937$	−18.3231	−0.598590	−0.299295	+	0.954161i	$0.596751\pi$
$938$	3.79674	0.123968
$939$	−71.5101	−2.33364
$940$	0.517601	0.0168823
$941$	−15.7355	−0.512963	−0.256481	−	0.966549i	$-0.582563\pi$
$941$	−15.7355	−0.512963	−0.256481	+	0.966549i	$0.582563\pi$
$942$	71.0326	2.31437
$943$	−10.4959	−0.341793
$944$	−25.9492	−0.844575
$945$	1.12468	0.0365859
$946$	11.3860	0.370191
$947$	−37.8295	−1.22929	−0.614647	−	0.788802i	$-0.710702\pi$
$947$	−37.8295	−1.22929	−0.614647	+	0.788802i	$0.710702\pi$
$948$	−2.85949	−0.0928719
$949$	−0.316558	−0.0102759
$950$	10.8978	0.353570
$951$	47.1186	1.52793
$952$	−6.82835	−0.221308
$953$	−43.7274	−1.41647	−0.708235	−	0.705977i	$-0.750508\pi$
$953$	−43.7274	−1.41647	−0.708235	+	0.705977i	$0.750508\pi$
$954$	−12.6519	−0.409620
$955$	24.7749	0.801697
$956$	−0.402697	−0.0130242
$957$	−26.7071	−0.863319
$958$	43.8433	1.41651
$959$	2.67251	0.0862997
$960$	20.2564	0.653773
$961$	−29.8540	−0.963032
$962$	1.92024	0.0619111
$963$	−9.59007	−0.309036
$964$	3.25906	0.104967
$965$	13.6464	0.439293
$966$	6.37464	0.205101
$967$	−11.1226	−0.357678	−0.178839	−	0.983878i	$-0.557234\pi$
$967$	−11.1226	−0.357678	−0.178839	+	0.983878i	$0.557234\pi$
$968$	−28.3245	−0.910385
$969$	44.1335	1.41777
$970$	15.0579	0.483479
$971$	28.8786	0.926759	0.463380	−	0.886160i	$-0.346637\pi$
$971$	28.8786	0.926759	0.463380	+	0.886160i	$0.346637\pi$
$972$	−4.02019	−0.128948
$973$	10.7562	0.344826
$974$	−28.8898	−0.925690
$975$	1.38270	0.0442818
$976$	29.5874	0.947069
$977$	23.7443	0.759649	0.379824	−	0.925059i	$-0.375984\pi$
$977$	23.7443	0.759649	0.379824	+	0.925059i	$0.375984\pi$
$978$	−59.4494	−1.90098
$979$	12.3755	0.395522
$980$	0.195065	0.00623112
$981$	12.5005	0.399111
$982$	−54.4726	−1.73829
$983$	24.8690	0.793197	0.396599	−	0.917992i	$-0.370190\pi$
$983$	24.8690	0.793197	0.396599	+	0.917992i	$0.370190\pi$
$984$	−36.0179	−1.14821
$985$	5.53232	0.176274
$986$	−29.9324	−0.953243
$987$	6.23504	0.198463
$988$	−0.931087	−0.0296218
$989$	14.4881	0.460695
$990$	4.00126	0.127168
$991$	−41.2045	−1.30890	−0.654452	−	0.756103i	$-0.727101\pi$
$991$	−41.2045	−1.30890	−0.654452	+	0.756103i	$0.727101\pi$
$992$	1.17690	0.0373666
$993$	−7.15517	−0.227062
$994$	−17.3919	−0.551636
$995$	12.9874	0.411727
$996$	4.87169	0.154366
$997$	12.4015	0.392760	0.196380	−	0.980528i	$-0.437081\pi$
$997$	12.4015	0.392760	0.196380	+	0.980528i	$0.437081\pi$
$998$	−46.7111	−1.47861
$999$	2.73181	0.0864306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.18	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.18	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.34348 q^{2} -2.34976 q^{3} -0.195065 q^{4} -1.00000 q^{5} +3.15685 q^{6} -1.00000 q^{7} +2.94902 q^{8} +2.52136 q^{9} +O(q^{10})\)	\(q-1.34348 q^{2} -2.34976 q^{3} -0.195065 q^{4} -1.00000 q^{5} +3.15685 q^{6} -1.00000 q^{7} +2.94902 q^{8} +2.52136 q^{9} +1.34348 q^{10} +1.18122 q^{11} +0.458355 q^{12} -0.588443 q^{13} +1.34348 q^{14} +2.34976 q^{15} -3.57182 q^{16} +2.31546 q^{17} -3.38740 q^{18} -8.11161 q^{19} +0.195065 q^{20} +2.34976 q^{21} -1.58694 q^{22} -2.01930 q^{23} -6.92949 q^{24} +1.00000 q^{25} +0.790561 q^{26} +1.12468 q^{27} +0.195065 q^{28} +9.62218 q^{29} -3.15685 q^{30} -1.07051 q^{31} -1.09938 q^{32} -2.77558 q^{33} -3.11078 q^{34} +1.00000 q^{35} -0.491829 q^{36} +2.42896 q^{37} +10.8978 q^{38} +1.38270 q^{39} -2.94902 q^{40} +5.19778 q^{41} -3.15685 q^{42} -7.17480 q^{43} -0.230414 q^{44} -2.52136 q^{45} +2.71289 q^{46} +2.65348 q^{47} +8.39291 q^{48} +1.00000 q^{49} -1.34348 q^{50} -5.44078 q^{51} +0.114785 q^{52} +3.73499 q^{53} -1.51099 q^{54} -1.18122 q^{55} -2.94902 q^{56} +19.0603 q^{57} -12.9272 q^{58} +7.26498 q^{59} -0.458355 q^{60} -8.28356 q^{61} +1.43821 q^{62} -2.52136 q^{63} +8.62064 q^{64} +0.588443 q^{65} +3.72893 q^{66} +2.82605 q^{67} -0.451665 q^{68} +4.74487 q^{69} -1.34348 q^{70} -12.9454 q^{71} +7.43556 q^{72} +0.537958 q^{73} -3.26326 q^{74} -2.34976 q^{75} +1.58229 q^{76} -1.18122 q^{77} -1.85763 q^{78} -6.23859 q^{79} +3.57182 q^{80} -10.2068 q^{81} -6.98310 q^{82} +10.6286 q^{83} -0.458355 q^{84} -2.31546 q^{85} +9.63919 q^{86} -22.6098 q^{87} +3.48344 q^{88} +10.4769 q^{89} +3.38740 q^{90} +0.588443 q^{91} +0.393895 q^{92} +2.51544 q^{93} -3.56490 q^{94} +8.11161 q^{95} +2.58328 q^{96} +11.2081 q^{97} -1.34348 q^{98} +2.97828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more