LMFDB - Embedded newform 983.2.a.b.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.898401 q^{2} -0.781362 q^{3} -1.19287 q^{4} -3.58725 q^{5} -0.701977 q^{6} +3.40057 q^{7} -2.86848 q^{8} -2.38947 q^{9} +O(q^{10})$	\(q+0.898401 q^{2} -0.781362 q^{3} -1.19287 q^{4} -3.58725 q^{5} -0.701977 q^{6} +3.40057 q^{7} -2.86848 q^{8} -2.38947 q^{9} -3.22279 q^{10} -4.53556 q^{11} +0.932067 q^{12} +5.29057 q^{13} +3.05508 q^{14} +2.80294 q^{15} -0.191299 q^{16} +5.37759 q^{17} -2.14671 q^{18} -1.95510 q^{19} +4.27914 q^{20} -2.65708 q^{21} -4.07475 q^{22} +4.00980 q^{23} +2.24132 q^{24} +7.86836 q^{25} +4.75305 q^{26} +4.21113 q^{27} -4.05646 q^{28} -1.90764 q^{29} +2.51817 q^{30} +9.80574 q^{31} +5.56510 q^{32} +3.54391 q^{33} +4.83123 q^{34} -12.1987 q^{35} +2.85034 q^{36} -2.35246 q^{37} -1.75646 q^{38} -4.13385 q^{39} +10.2900 q^{40} +5.57023 q^{41} -2.38712 q^{42} -12.2485 q^{43} +5.41035 q^{44} +8.57164 q^{45} +3.60241 q^{46} -0.987801 q^{47} +0.149474 q^{48} +4.56390 q^{49} +7.06895 q^{50} -4.20184 q^{51} -6.31098 q^{52} -0.820026 q^{53} +3.78328 q^{54} +16.2702 q^{55} -9.75449 q^{56} +1.52764 q^{57} -1.71383 q^{58} -4.90054 q^{59} -3.34356 q^{60} +6.79892 q^{61} +8.80949 q^{62} -8.12558 q^{63} +5.38229 q^{64} -18.9786 q^{65} +3.18386 q^{66} +9.06048 q^{67} -6.41479 q^{68} -3.13310 q^{69} -10.9593 q^{70} +5.91614 q^{71} +6.85417 q^{72} +0.630227 q^{73} -2.11345 q^{74} -6.14804 q^{75} +2.33219 q^{76} -15.4235 q^{77} -3.71385 q^{78} +7.92488 q^{79} +0.686239 q^{80} +3.87801 q^{81} +5.00430 q^{82} +10.6870 q^{83} +3.16956 q^{84} -19.2907 q^{85} -11.0041 q^{86} +1.49056 q^{87} +13.0102 q^{88} -6.34809 q^{89} +7.70077 q^{90} +17.9910 q^{91} -4.78319 q^{92} -7.66183 q^{93} -0.887442 q^{94} +7.01342 q^{95} -4.34836 q^{96} +1.78591 q^{97} +4.10021 q^{98} +10.8376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	0.898401	0.635266	0.317633	−	0.948214i	$-0.397112\pi$
$2$	0.898401	0.635266	0.317633	+	0.948214i	$0.397112\pi$
$3$	−0.781362	−0.451119	−0.225560	−	0.974229i	$-0.572421\pi$
$3$	−0.781362	−0.451119	−0.225560	+	0.974229i	$0.572421\pi$
$4$	−1.19287	−0.596437
$5$	−3.58725	−1.60427	−0.802133	−	0.597145i	$-0.796302\pi$
$5$	−3.58725	−1.60427	−0.802133	+	0.597145i	$0.796302\pi$
$6$	−0.701977	−0.286581
$7$	3.40057	1.28530	0.642648	−	0.766162i	$-0.277836\pi$
$7$	3.40057	1.28530	0.642648	+	0.766162i	$0.277836\pi$
$8$	−2.86848	−1.01416
$9$	−2.38947	−0.796491
$10$	−3.22279	−1.01914
$11$	−4.53556	−1.36752	−0.683761	−	0.729706i	$-0.739657\pi$
$11$	−4.53556	−1.36752	−0.683761	+	0.729706i	$0.739657\pi$
$12$	0.932067	0.269065
$13$	5.29057	1.46734	0.733670	−	0.679506i	$-0.237806\pi$
$13$	5.29057	1.46734	0.733670	+	0.679506i	$0.237806\pi$
$14$	3.05508	0.816504
$15$	2.80294	0.723716
$16$	−0.191299	−0.0478249
$17$	5.37759	1.30426	0.652128	−	0.758109i	$-0.273876\pi$
$17$	5.37759	1.30426	0.652128	+	0.758109i	$0.273876\pi$
$18$	−2.14671	−0.505984
$19$	−1.95510	−0.448530	−0.224265	−	0.974528i	$-0.571998\pi$
$19$	−1.95510	−0.448530	−0.224265	+	0.974528i	$0.571998\pi$
$20$	4.27914	0.956845
$21$	−2.65708	−0.579822
$22$	−4.07475	−0.868740
$23$	4.00980	0.836100	0.418050	−	0.908424i	$-0.362714\pi$
$23$	4.00980	0.836100	0.418050	+	0.908424i	$0.362714\pi$
$24$	2.24132	0.457508
$25$	7.86836	1.57367
$26$	4.75305	0.932150
$27$	4.21113	0.810432
$28$	−4.05646	−0.766599
$29$	−1.90764	−0.354240	−0.177120	−	0.984189i	$-0.556678\pi$
$29$	−1.90764	−0.354240	−0.177120	+	0.984189i	$0.556678\pi$
$30$	2.51817	0.459752
$31$	9.80574	1.76116	0.880581	−	0.473895i	$-0.157152\pi$
$31$	9.80574	1.76116	0.880581	+	0.473895i	$0.157152\pi$
$32$	5.56510	0.983780
$33$	3.54391	0.616916
$34$	4.83123	0.828549
$35$	−12.1987	−2.06196
$36$	2.85034	0.475057
$37$	−2.35246	−0.386742	−0.193371	−	0.981126i	$-0.561942\pi$
$37$	−2.35246	−0.386742	−0.193371	+	0.981126i	$0.561942\pi$
$38$	−1.75646	−0.284936
$39$	−4.13385	−0.661945
$40$	10.2900	1.62699
$41$	5.57023	0.869924	0.434962	−	0.900449i	$-0.356762\pi$
$41$	5.57023	0.869924	0.434962	+	0.900449i	$0.356762\pi$
$42$	−2.38712	−0.368341
$43$	−12.2485	−1.86788	−0.933942	−	0.357424i	$-0.883655\pi$
$43$	−12.2485	−1.86788	−0.933942	+	0.357424i	$0.883655\pi$
$44$	5.41035	0.815642
$45$	8.57164	1.27778
$46$	3.60241	0.531146
$47$	−0.987801	−0.144086	−0.0720428	−	0.997402i	$-0.522952\pi$
$47$	−0.987801	−0.144086	−0.0720428	+	0.997402i	$0.522952\pi$
$48$	0.149474	0.0215747
$49$	4.56390	0.651985
$50$	7.06895	0.999700
$51$	−4.20184	−0.588375
$52$	−6.31098	−0.875176
$53$	−0.820026	−0.112639	−0.0563196	−	0.998413i	$-0.517937\pi$
$53$	−0.820026	−0.112639	−0.0563196	+	0.998413i	$0.517937\pi$
$54$	3.78328	0.514840
$55$	16.2702	2.19387
$56$	−9.75449	−1.30350
$57$	1.52764	0.202341
$58$	−1.71383	−0.225036
$59$	−4.90054	−0.637996	−0.318998	−	0.947755i	$-0.603346\pi$
$59$	−4.90054	−0.637996	−0.318998	+	0.947755i	$0.603346\pi$
$60$	−3.34356	−0.431651
$61$	6.79892	0.870513	0.435257	−	0.900306i	$-0.356658\pi$
$61$	6.79892	0.870513	0.435257	+	0.900306i	$0.356658\pi$
$62$	8.80949	1.11881
$63$	−8.12558	−1.02373
$64$	5.38229	0.672787
$65$	−18.9786	−2.35400
$66$	3.18386	0.391906
$67$	9.06048	1.10691	0.553457	−	0.832878i	$-0.313308\pi$
$67$	9.06048	1.10691	0.553457	+	0.832878i	$0.313308\pi$
$68$	−6.41479	−0.777907
$69$	−3.13310	−0.377181
$70$	−10.9593	−1.30989
$71$	5.91614	0.702117	0.351058	−	0.936354i	$-0.385822\pi$
$71$	5.91614	0.702117	0.351058	+	0.936354i	$0.385822\pi$
$72$	6.85417	0.807771
$73$	0.630227	0.0737625	0.0368812	−	0.999320i	$-0.488258\pi$
$73$	0.630227	0.0737625	0.0368812	+	0.999320i	$0.488258\pi$
$74$	−2.11345	−0.245684
$75$	−6.14804	−0.709914
$76$	2.33219	0.267520
$77$	−15.4235	−1.75767
$78$	−3.71385	−0.420511
$79$	7.92488	0.891618	0.445809	−	0.895128i	$-0.352916\pi$
$79$	7.92488	0.891618	0.445809	+	0.895128i	$0.352916\pi$
$80$	0.686239	0.0767238
$81$	3.87801	0.430890
$82$	5.00430	0.552633
$83$	10.6870	1.17305	0.586525	−	0.809931i	$-0.300496\pi$
$83$	10.6870	1.17305	0.586525	+	0.809931i	$0.300496\pi$
$84$	3.16956	0.345828
$85$	−19.2907	−2.09237
$86$	−11.0041	−1.18660
$87$	1.49056	0.159805
$88$	13.0102	1.38689
$89$	−6.34809	−0.672896	−0.336448	−	0.941702i	$-0.609226\pi$
$89$	−6.34809	−0.672896	−0.336448	+	0.941702i	$0.609226\pi$
$90$	7.70077	0.811733
$91$	17.9910	1.88596
$92$	−4.78319	−0.498682
$93$	−7.66183	−0.794495
$94$	−0.887442	−0.0915326
$95$	7.01342	0.719562
$96$	−4.34836	−0.443803
$97$	1.78591	0.181332	0.0906658	−	0.995881i	$-0.471100\pi$
$97$	1.78591	0.181332	0.0906658	+	0.995881i	$0.471100\pi$
$98$	4.10021	0.414184
$99$	10.8376	1.08922
$100$	−9.38597	−0.938597
$101$	16.8946	1.68108	0.840538	−	0.541752i	$-0.182239\pi$
$101$	16.8946	1.68108	0.840538	+	0.541752i	$0.182239\pi$
$102$	−3.77494	−0.373775
$103$	14.0678	1.38614	0.693071	−	0.720870i	$-0.256257\pi$
$103$	14.0678	1.38614	0.693071	+	0.720870i	$0.256257\pi$
$104$	−15.1759	−1.48812
$105$	9.53160	0.930189
$106$	−0.736712	−0.0715558
$107$	−5.77544	−0.558333	−0.279167	−	0.960243i	$-0.590058\pi$
$107$	−5.77544	−0.558333	−0.279167	+	0.960243i	$0.590058\pi$
$108$	−5.02335	−0.483372
$109$	2.15817	0.206715	0.103358	−	0.994644i	$-0.467041\pi$
$109$	2.15817	0.206715	0.103358	+	0.994644i	$0.467041\pi$
$110$	14.6172	1.39369
$111$	1.83812	0.174467
$112$	−0.650528	−0.0614691
$113$	−20.8503	−1.96143	−0.980717	−	0.195434i	$-0.937389\pi$
$113$	−20.8503	−1.96143	−0.980717	+	0.195434i	$0.937389\pi$
$114$	1.37243	0.128540
$115$	−14.3841	−1.34133
$116$	2.27558	0.211282
$117$	−12.6417	−1.16872
$118$	−4.40265	−0.405297
$119$	18.2869	1.67635
$120$	−8.04019	−0.733965
$121$	9.57129	0.870117
$122$	6.10816	0.553007
$123$	−4.35237	−0.392440
$124$	−11.6970	−1.05042
$125$	−10.2895	−0.920323
$126$	−7.30003	−0.650339
$127$	8.47454	0.751993	0.375997	−	0.926621i	$-0.377300\pi$
$127$	8.47454	0.751993	0.375997	+	0.926621i	$0.377300\pi$
$128$	−6.29474	−0.556382
$129$	9.57054	0.842639
$130$	−17.0504	−1.49542
$131$	−13.3117	−1.16305	−0.581523	−	0.813530i	$-0.697543\pi$
$131$	−13.3117	−1.16305	−0.581523	+	0.813530i	$0.697543\pi$
$132$	−4.22744	−0.367952
$133$	−6.64845	−0.576494
$134$	8.13995	0.703185
$135$	−15.1064	−1.30015
$136$	−15.4255	−1.32273
$137$	−19.8147	−1.69288	−0.846440	−	0.532484i	$-0.821259\pi$
$137$	−19.8147	−1.69288	−0.846440	+	0.532484i	$0.821259\pi$
$138$	−2.81478	−0.239610
$139$	−14.7062	−1.24736	−0.623681	−	0.781679i	$-0.714364\pi$
$139$	−14.7062	−1.24736	−0.623681	+	0.781679i	$0.714364\pi$
$140$	14.5515	1.22983
$141$	0.771830	0.0649998
$142$	5.31507	0.446031
$143$	−23.9957	−2.00662
$144$	0.457105	0.0380921
$145$	6.84318	0.568295
$146$	0.566197	0.0468588
$147$	−3.56605	−0.294123
$148$	2.80619	0.230668
$149$	10.2691	0.841276	0.420638	−	0.907229i	$-0.361806\pi$
$149$	10.2691	0.841276	0.420638	+	0.907229i	$0.361806\pi$
$150$	−5.52340	−0.450984
$151$	13.9037	1.13147	0.565735	−	0.824587i	$-0.308592\pi$
$151$	13.9037	1.13147	0.565735	+	0.824587i	$0.308592\pi$
$152$	5.60816	0.454882
$153$	−12.8496	−1.03883
$154$	−13.8565	−1.11659
$155$	−35.1756	−2.82537
$156$	4.93116	0.394809
$157$	3.88201	0.309818	0.154909	−	0.987929i	$-0.450492\pi$
$157$	3.88201	0.309818	0.154909	+	0.987929i	$0.450492\pi$
$158$	7.11972	0.566414
$159$	0.640737	0.0508137
$160$	−19.9634	−1.57825
$161$	13.6356	1.07464
$162$	3.48401	0.273729
$163$	−11.1232	−0.871238	−0.435619	−	0.900131i	$-0.643471\pi$
$163$	−11.1232	−0.871238	−0.435619	+	0.900131i	$0.643471\pi$
$164$	−6.64459	−0.518855
$165$	−12.7129	−0.989698
$166$	9.60121	0.745198
$167$	−19.2973	−1.49327	−0.746635	−	0.665234i	$-0.768332\pi$
$167$	−19.2973	−1.49327	−0.746635	+	0.665234i	$0.768332\pi$
$168$	7.62178	0.588033
$169$	14.9901	1.15308
$170$	−17.3308	−1.32921
$171$	4.67165	0.357250
$172$	14.6110	1.11408
$173$	6.25571	0.475613	0.237806	−	0.971313i	$-0.423572\pi$
$173$	6.25571	0.475613	0.237806	+	0.971313i	$0.423572\pi$
$174$	1.33912	0.101518
$175$	26.7569	2.02263
$176$	0.867650	0.0654016
$177$	3.82909	0.287812
$178$	−5.70313	−0.427468
$179$	23.6094	1.76465	0.882324	−	0.470643i	$-0.155978\pi$
$179$	23.6094	1.76465	0.882324	+	0.470643i	$0.155978\pi$
$180$	−10.2249	−0.762119
$181$	−11.0413	−0.820694	−0.410347	−	0.911929i	$-0.634592\pi$
$181$	−11.0413	−0.820694	−0.410347	+	0.911929i	$0.634592\pi$
$182$	16.1631	1.19809
$183$	−5.31242	−0.392705
$184$	−11.5020	−0.847941
$185$	8.43887	0.620438
$186$	−6.88340	−0.504715
$187$	−24.3904	−1.78360
$188$	1.17832	0.0859380
$189$	14.3203	1.04164
$190$	6.30087	0.457113
$191$	10.1266	0.732737	0.366368	−	0.930470i	$-0.380601\pi$
$191$	10.1266	0.732737	0.366368	+	0.930470i	$0.380601\pi$
$192$	−4.20552	−0.303507
$193$	21.1509	1.52248	0.761238	−	0.648472i	$-0.224592\pi$
$193$	21.1509	1.52248	0.761238	+	0.648472i	$0.224592\pi$
$194$	1.60446	0.115194
$195$	14.8291	1.06194
$196$	−5.44416	−0.388868
$197$	19.0154	1.35479	0.677397	−	0.735618i	$-0.263108\pi$
$197$	19.0154	1.35479	0.677397	+	0.735618i	$0.263108\pi$
$198$	9.73651	0.691944
$199$	−12.0656	−0.855308	−0.427654	−	0.903942i	$-0.640660\pi$
$199$	−12.0656	−0.855308	−0.427654	+	0.903942i	$0.640660\pi$
$200$	−22.5703	−1.59596
$201$	−7.07951	−0.499350
$202$	15.1781	1.06793
$203$	−6.48707	−0.455303
$204$	5.01227	0.350929
$205$	−19.9818	−1.39559
$206$	12.6385	0.880568
$207$	−9.58130	−0.665947
$208$	−1.01208	−0.0701753
$209$	8.86746	0.613375
$210$	8.56320	0.590917
$211$	20.9269	1.44067	0.720334	−	0.693627i	$-0.243988\pi$
$211$	20.9269	1.44067	0.720334	+	0.693627i	$0.243988\pi$
$212$	0.978188	0.0671822
$213$	−4.62265	−0.316739
$214$	−5.18867	−0.354690
$215$	43.9386	2.99658
$216$	−12.0796	−0.821909
$217$	33.3451	2.26361
$218$	1.93890	0.131319
$219$	−0.492435	−0.0332757
$220$	−19.4083	−1.30851
$221$	28.4505	1.91379
$222$	1.65137	0.110833
$223$	4.53442	0.303647	0.151824	−	0.988408i	$-0.451485\pi$
$223$	4.53442	0.303647	0.151824	+	0.988408i	$0.451485\pi$
$224$	18.9245	1.26445
$225$	−18.8012	−1.25342
$226$	−18.7320	−1.24603
$227$	11.7280	0.778415	0.389207	−	0.921150i	$-0.372749\pi$
$227$	11.7280	0.778415	0.389207	+	0.921150i	$0.372749\pi$
$228$	−1.82228	−0.120684
$229$	−8.55588	−0.565389	−0.282694	−	0.959210i	$-0.591228\pi$
$229$	−8.55588	−0.565389	−0.282694	+	0.959210i	$0.591228\pi$
$230$	−12.9227	−0.852100
$231$	12.0513	0.792919
$232$	5.47203	0.359257
$233$	2.04275	0.133825	0.0669124	−	0.997759i	$-0.478685\pi$
$233$	2.04275	0.133825	0.0669124	+	0.997759i	$0.478685\pi$
$234$	−11.3573	−0.742450
$235$	3.54349	0.231152
$236$	5.84573	0.380525
$237$	−6.19220	−0.402226
$238$	16.4290	1.06493
$239$	−13.1833	−0.852755	−0.426378	−	0.904545i	$-0.640211\pi$
$239$	−13.1833	−0.852755	−0.426378	+	0.904545i	$0.640211\pi$
$240$	−0.536201	−0.0346116
$241$	10.7477	0.692320	0.346160	−	0.938176i	$-0.387485\pi$
$241$	10.7477	0.692320	0.346160	+	0.938176i	$0.387485\pi$
$242$	8.59886	0.552756
$243$	−15.6635	−1.00481
$244$	−8.11027	−0.519207
$245$	−16.3718	−1.04596
$246$	−3.91017	−0.249303
$247$	−10.3436	−0.658146
$248$	−28.1276	−1.78610
$249$	−8.35041	−0.529185
$250$	−9.24412	−0.584650
$251$	19.6311	1.23910	0.619552	−	0.784956i	$-0.287314\pi$
$251$	19.6311	1.23910	0.619552	+	0.784956i	$0.287314\pi$
$252$	9.69280	0.610589
$253$	−18.1867	−1.14339
$254$	7.61353	0.477716
$255$	15.0730	0.943911
$256$	−16.4198	−1.02624
$257$	7.86175	0.490402	0.245201	−	0.969472i	$-0.421146\pi$
$257$	7.86175	0.490402	0.245201	+	0.969472i	$0.421146\pi$
$258$	8.59818	0.535300
$259$	−7.99972	−0.497078
$260$	22.6391	1.40402
$261$	4.55826	0.282149
$262$	−11.9592	−0.738843
$263$	19.9159	1.22807	0.614033	−	0.789280i	$-0.289546\pi$
$263$	19.9159	1.22807	0.614033	+	0.789280i	$0.289546\pi$
$264$	−10.1657	−0.625653
$265$	2.94164	0.180703
$266$	−5.97298	−0.366227
$267$	4.96015	0.303556
$268$	−10.8080	−0.660205
$269$	−2.42874	−0.148083	−0.0740414	−	0.997255i	$-0.523590\pi$
$269$	−2.42874	−0.148083	−0.0740414	+	0.997255i	$0.523590\pi$
$270$	−13.5716	−0.825940
$271$	−4.02477	−0.244487	−0.122244	−	0.992500i	$-0.539009\pi$
$271$	−4.02477	−0.244487	−0.122244	+	0.992500i	$0.539009\pi$
$272$	−1.02873	−0.0623759
$273$	−14.0574	−0.850795
$274$	−17.8015	−1.07543
$275$	−35.6874	−2.15203
$276$	3.73740	0.224965
$277$	15.0580	0.904747	0.452374	−	0.891828i	$-0.350577\pi$
$277$	15.0580	0.904747	0.452374	+	0.891828i	$0.350577\pi$
$278$	−13.2121	−0.792406
$279$	−23.4306	−1.40275
$280$	34.9918	2.09116
$281$	−26.1830	−1.56195	−0.780975	−	0.624563i	$-0.785277\pi$
$281$	−26.1830	−1.56195	−0.780975	+	0.624563i	$0.785277\pi$
$282$	0.693413	0.0412921
$283$	−20.9787	−1.24705	−0.623526	−	0.781802i	$-0.714301\pi$
$283$	−20.9787	−1.24705	−0.623526	+	0.781802i	$0.714301\pi$
$284$	−7.05722	−0.418769
$285$	−5.48002	−0.324608
$286$	−21.5577	−1.27474
$287$	18.9420	1.11811
$288$	−13.2977	−0.783573
$289$	11.9184	0.701084
$290$	6.14792	0.361019
$291$	−1.39544	−0.0818022
$292$	−0.751782	−0.0439947
$293$	24.5222	1.43260	0.716300	−	0.697792i	$-0.245834\pi$
$293$	24.5222	1.43260	0.716300	+	0.697792i	$0.245834\pi$
$294$	−3.20375	−0.186846
$295$	17.5795	1.02352
$296$	6.74800	0.392219
$297$	−19.0998	−1.10828
$298$	9.22576	0.534434
$299$	21.2141	1.22684
$300$	7.33384	0.423419
$301$	−41.6520	−2.40078
$302$	12.4911	0.718784
$303$	−13.2008	−0.758366
$304$	0.374009	0.0214509
$305$	−24.3894	−1.39654
$306$	−11.5441	−0.659932
$307$	25.8319	1.47430	0.737152	−	0.675727i	$-0.236170\pi$
$307$	25.8319	1.47430	0.737152	+	0.675727i	$0.236170\pi$
$308$	18.3983	1.04834
$309$	−10.9920	−0.625315
$310$	−31.6018	−1.79486
$311$	1.59379	0.0903757	0.0451879	−	0.998979i	$-0.485611\pi$
$311$	1.59379	0.0903757	0.0451879	+	0.998979i	$0.485611\pi$
$312$	11.8579	0.671320
$313$	−4.87848	−0.275748	−0.137874	−	0.990450i	$-0.544027\pi$
$313$	−4.87848	−0.275748	−0.137874	+	0.990450i	$0.544027\pi$
$314$	3.48760	0.196817
$315$	29.1485	1.64233
$316$	−9.45339	−0.531795
$317$	24.3537	1.36784	0.683921	−	0.729556i	$-0.260273\pi$
$317$	24.3537	1.36784	0.683921	+	0.729556i	$0.260273\pi$
$318$	0.575639	0.0322802
$319$	8.65221	0.484431
$320$	−19.3076	−1.07933
$321$	4.51271	0.251875
$322$	12.2502	0.682680
$323$	−10.5137	−0.584998
$324$	−4.62598	−0.256999
$325$	41.6281	2.30911
$326$	−9.99312	−0.553468
$327$	−1.68631	−0.0932533
$328$	−15.9781	−0.882244
$329$	−3.35909	−0.185193
$330$	−11.4213	−0.628721
$331$	−27.7648	−1.52609	−0.763047	−	0.646343i	$-0.776297\pi$
$331$	−27.7648	−1.52609	−0.763047	+	0.646343i	$0.776297\pi$
$332$	−12.7482	−0.699651
$333$	5.62115	0.308037
$334$	−17.3367	−0.948623
$335$	−32.5022	−1.77579
$336$	0.508297	0.0277299
$337$	5.18979	0.282706	0.141353	−	0.989959i	$-0.454855\pi$
$337$	5.18979	0.282706	0.141353	+	0.989959i	$0.454855\pi$
$338$	13.4671	0.732515
$339$	16.2916	0.884841
$340$	23.0114	1.24797
$341$	−44.4745	−2.40843
$342$	4.19702	0.226949
$343$	−8.28415	−0.447302
$344$	35.1347	1.89434
$345$	11.2392	0.605099
$346$	5.62014	0.302140
$347$	−15.5931	−0.837080	−0.418540	−	0.908198i	$-0.637458\pi$
$347$	−15.5931	−0.837080	−0.418540	+	0.908198i	$0.637458\pi$
$348$	−1.77805	−0.0953134
$349$	20.7329	1.10981	0.554904	−	0.831914i	$-0.312755\pi$
$349$	20.7329	1.10981	0.554904	+	0.831914i	$0.312755\pi$
$350$	24.0385	1.28491
$351$	22.2793	1.18918
$352$	−25.2408	−1.34534
$353$	30.5927	1.62829	0.814143	−	0.580664i	$-0.197207\pi$
$353$	30.5927	1.62829	0.814143	+	0.580664i	$0.197207\pi$
$354$	3.44006	0.182837
$355$	−21.2227	−1.12638
$356$	7.57247	0.401340
$357$	−14.2887	−0.756236
$358$	21.2107	1.12102
$359$	16.2202	0.856068	0.428034	−	0.903763i	$-0.359206\pi$
$359$	16.2202	0.856068	0.428034	+	0.903763i	$0.359206\pi$
$360$	−24.5876	−1.29588
$361$	−15.1776	−0.798821
$362$	−9.91952	−0.521359
$363$	−7.47864	−0.392527
$364$	−21.4610	−1.12486
$365$	−2.26078	−0.118335
$366$	−4.77269	−0.249472
$367$	19.6476	1.02560	0.512798	−	0.858509i	$-0.328609\pi$
$367$	19.6476	1.02560	0.512798	+	0.858509i	$0.328609\pi$
$368$	−0.767072	−0.0399864
$369$	−13.3099	−0.692887
$370$	7.58149	0.394143
$371$	−2.78856	−0.144775
$372$	9.13960	0.473866
$373$	1.83549	0.0950381	0.0475190	−	0.998870i	$-0.484869\pi$
$373$	1.83549	0.0950381	0.0475190	+	0.998870i	$0.484869\pi$
$374$	−21.9123	−1.13306
$375$	8.03984	0.415176
$376$	2.83349	0.146126
$377$	−10.0925	−0.519790
$378$	12.8653	0.661721
$379$	−7.15906	−0.367736	−0.183868	−	0.982951i	$-0.558862\pi$
$379$	−7.15906	−0.367736	−0.183868	+	0.982951i	$0.558862\pi$
$380$	−8.36614	−0.429174
$381$	−6.62168	−0.339239
$382$	9.09778	0.465483
$383$	−33.1995	−1.69641	−0.848207	−	0.529665i	$-0.822318\pi$
$383$	−33.1995	−1.69641	−0.848207	+	0.529665i	$0.822318\pi$
$384$	4.91847	0.250995
$385$	55.3279	2.81977
$386$	19.0020	0.967177
$387$	29.2676	1.48775
$388$	−2.13037	−0.108153
$389$	27.9105	1.41512	0.707559	−	0.706654i	$-0.249796\pi$
$389$	27.9105	1.41512	0.707559	+	0.706654i	$0.249796\pi$
$390$	13.3225	0.674612
$391$	21.5630	1.09049
$392$	−13.0915	−0.661219
$393$	10.4012	0.524672
$394$	17.0835	0.860654
$395$	−28.4285	−1.43039
$396$	−12.9279	−0.649651
$397$	32.9900	1.65572	0.827861	−	0.560934i	$-0.189558\pi$
$397$	32.9900	1.65572	0.827861	+	0.560934i	$0.189558\pi$
$398$	−10.8398	−0.543348
$399$	5.19485	0.260068
$400$	−1.50521	−0.0752606
$401$	−20.1734	−1.00741	−0.503706	−	0.863875i	$-0.668031\pi$
$401$	−20.1734	−1.00741	−0.503706	+	0.863875i	$0.668031\pi$
$402$	−6.36025	−0.317220
$403$	51.8779	2.58422
$404$	−20.1532	−1.00266
$405$	−13.9114	−0.691262
$406$	−5.82799	−0.289238
$407$	10.6697	0.528879
$408$	12.0529	0.596708
$409$	13.4111	0.663137	0.331568	−	0.943431i	$-0.392422\pi$
$409$	13.4111	0.663137	0.331568	+	0.943431i	$0.392422\pi$
$410$	−17.9517	−0.886570
$411$	15.4824	0.763691
$412$	−16.7811	−0.826746
$413$	−16.6646	−0.820013
$414$	−8.60786	−0.423053
$415$	−38.3369	−1.88188
$416$	29.4425	1.44354
$417$	11.4908	0.562709
$418$	7.96654	0.389656
$419$	23.0975	1.12839	0.564194	−	0.825642i	$-0.309187\pi$
$419$	23.0975	1.12839	0.564194	+	0.825642i	$0.309187\pi$
$420$	−11.3700	−0.554800
$421$	20.2734	0.988064	0.494032	−	0.869444i	$-0.335523\pi$
$421$	20.2734	0.988064	0.494032	+	0.869444i	$0.335523\pi$
$422$	18.8008	0.915208
$423$	2.36032	0.114763
$424$	2.35223	0.114234
$425$	42.3128	2.05247
$426$	−4.15299	−0.201213
$427$	23.1202	1.11887
$428$	6.88938	0.333011
$429$	18.7493	0.905225
$430$	39.4745	1.90363
$431$	−37.2526	−1.79440	−0.897198	−	0.441628i	$-0.854401\pi$
$431$	−37.2526	−1.79440	−0.897198	+	0.441628i	$0.854401\pi$
$432$	−0.805586	−0.0387588
$433$	−8.12606	−0.390513	−0.195257	−	0.980752i	$-0.562554\pi$
$433$	−8.12606	−0.390513	−0.195257	+	0.980752i	$0.562554\pi$
$434$	29.9573	1.43800
$435$	−5.34700	−0.256369
$436$	−2.57443	−0.123293
$437$	−7.83954	−0.375016
$438$	−0.442404	−0.0211389
$439$	3.55073	0.169467	0.0847335	−	0.996404i	$-0.472996\pi$
$439$	3.55073	0.169467	0.0847335	+	0.996404i	$0.472996\pi$
$440$	−46.6707	−2.22494
$441$	−10.9053	−0.519300
$442$	25.5599	1.21576
$443$	−11.8997	−0.565372	−0.282686	−	0.959213i	$-0.591225\pi$
$443$	−11.8997	−0.565372	−0.282686	+	0.959213i	$0.591225\pi$
$444$	−2.19265	−0.104059
$445$	22.7722	1.07950
$446$	4.07373	0.192897
$447$	−8.02387	−0.379516
$448$	18.3029	0.864730
$449$	17.5584	0.828632	0.414316	−	0.910133i	$-0.364021\pi$
$449$	17.5584	0.828632	0.414316	+	0.910133i	$0.364021\pi$
$450$	−16.8911	−0.796252
$451$	−25.2641	−1.18964
$452$	24.8718	1.16987
$453$	−10.8639	−0.510428
$454$	10.5365	0.494500
$455$	−64.5381	−3.02559
$456$	−4.38201	−0.205206
$457$	−22.8485	−1.06881	−0.534405	−	0.845229i	$-0.679464\pi$
$457$	−22.8485	−1.06881	−0.534405	+	0.845229i	$0.679464\pi$
$458$	−7.68662	−0.359172
$459$	22.6457	1.05701
$460$	17.1585	0.800018
$461$	−32.8679	−1.53081	−0.765406	−	0.643548i	$-0.777462\pi$
$461$	−32.8679	−1.53081	−0.765406	+	0.643548i	$0.777462\pi$
$462$	10.8269	0.503715
$463$	−29.8280	−1.38623	−0.693113	−	0.720829i	$-0.743761\pi$
$463$	−29.8280	−1.38623	−0.693113	+	0.720829i	$0.743761\pi$
$464$	0.364930	0.0169415
$465$	27.4849	1.27458
$466$	1.83521	0.0850142
$467$	−30.9753	−1.43337	−0.716684	−	0.697398i	$-0.754341\pi$
$467$	−30.9753	−1.43337	−0.716684	+	0.697398i	$0.754341\pi$
$468$	15.0799	0.697070
$469$	30.8108	1.42271
$470$	3.18347	0.146843
$471$	−3.03325	−0.139765
$472$	14.0571	0.647031
$473$	55.5539	2.55437
$474$	−5.56308	−0.255521
$475$	−15.3834	−0.705839
$476$	−21.8140	−0.999841
$477$	1.95943	0.0897161
$478$	−11.8439	−0.541726
$479$	−27.5378	−1.25823	−0.629117	−	0.777310i	$-0.716584\pi$
$479$	−27.5378	−1.25823	−0.629117	+	0.777310i	$0.716584\pi$
$480$	15.5986	0.711978
$481$	−12.4459	−0.567482
$482$	9.65574	0.439807
$483$	−10.6543	−0.484789
$484$	−11.4174	−0.518971
$485$	−6.40650	−0.290904
$486$	−14.0721	−0.638324
$487$	17.1784	0.778425	0.389213	−	0.921148i	$-0.372747\pi$
$487$	17.1784	0.778425	0.389213	+	0.921148i	$0.372747\pi$
$488$	−19.5026	−0.882841
$489$	8.69126	0.393032
$490$	−14.7085	−0.664461
$491$	−4.43143	−0.199987	−0.0999937	−	0.994988i	$-0.531882\pi$
$491$	−4.43143	−0.199987	−0.0999937	+	0.994988i	$0.531882\pi$
$492$	5.19183	0.234066
$493$	−10.2585	−0.462020
$494$	−9.29268	−0.418097
$495$	−38.8772	−1.74740
$496$	−1.87583	−0.0842273
$497$	20.1183	0.902428
$498$	−7.50202	−0.336173
$499$	−11.9861	−0.536570	−0.268285	−	0.963340i	$-0.586457\pi$
$499$	−11.9861	−0.536570	−0.268285	+	0.963340i	$0.586457\pi$
$500$	12.2741	0.548915
$501$	15.0782	0.673643
$502$	17.6366	0.787160
$503$	−11.1904	−0.498955	−0.249478	−	0.968381i	$-0.580259\pi$
$503$	−11.1904	−0.498955	−0.249478	+	0.968381i	$0.580259\pi$
$504$	23.3081	1.03822
$505$	−60.6052	−2.69690
$506$	−16.3389	−0.726354
$507$	−11.7127	−0.520179
$508$	−10.1091	−0.448517
$509$	9.21741	0.408555	0.204277	−	0.978913i	$-0.434516\pi$
$509$	9.21741	0.408555	0.204277	+	0.978913i	$0.434516\pi$
$510$	13.5416	0.599634
$511$	2.14313	0.0948066
$512$	−2.16208	−0.0955513
$513$	−8.23317	−0.363503
$514$	7.06300	0.311536
$515$	−50.4647	−2.22374
$516$	−11.4165	−0.502581
$517$	4.48023	0.197040
$518$	−7.18696	−0.315777
$519$	−4.88797	−0.214558
$520$	54.4397	2.38734
$521$	43.2288	1.89389	0.946943	−	0.321401i	$-0.104154\pi$
$521$	43.2288	1.89389	0.946943	+	0.321401i	$0.104154\pi$
$522$	4.09514	0.179240
$523$	−18.6763	−0.816657	−0.408328	−	0.912835i	$-0.633888\pi$
$523$	−18.6763	−0.816657	−0.408328	+	0.912835i	$0.633888\pi$
$524$	15.8791	0.693684
$525$	−20.9068	−0.912450
$526$	17.8925	0.780148
$527$	52.7312	2.29701
$528$	−0.677948	−0.0295039
$529$	−6.92153	−0.300936
$530$	2.64277	0.114795
$531$	11.7097	0.508158
$532$	7.93077	0.343843
$533$	29.4697	1.27647
$534$	4.45621	0.192839
$535$	20.7180	0.895716
$536$	−25.9898	−1.12259
$537$	−18.4475	−0.796067
$538$	−2.18198	−0.0940719
$539$	−20.6998	−0.891604
$540$	18.0200	0.775458
$541$	37.0724	1.59386	0.796932	−	0.604068i	$-0.206455\pi$
$541$	37.0724	1.59386	0.796932	+	0.604068i	$0.206455\pi$
$542$	−3.61586	−0.155314
$543$	8.62725	0.370231
$544$	29.9268	1.28310
$545$	−7.74190	−0.331627
$546$	−12.6292	−0.540481
$547$	6.27110	0.268133	0.134066	−	0.990972i	$-0.457196\pi$
$547$	6.27110	0.268133	0.134066	+	0.990972i	$0.457196\pi$
$548$	23.6364	1.00970
$549$	−16.2459	−0.693356
$550$	−32.0616	−1.36711
$551$	3.72962	0.158887
$552$	8.98725	0.382523
$553$	26.9491	1.14599
$554$	13.5281	0.574755
$555$	−6.59381	−0.279892
$556$	17.5426	0.743973
$557$	0.179898	0.00762253	0.00381127	−	0.999993i	$-0.498787\pi$
$557$	0.179898	0.00762253	0.00381127	+	0.999993i	$0.498787\pi$
$558$	−21.0500	−0.891119
$559$	−64.8017	−2.74082
$560$	2.33360	0.0986128
$561$	19.0577	0.804616
$562$	−23.5229	−0.992253
$563$	21.0421	0.886820	0.443410	−	0.896319i	$-0.353769\pi$
$563$	21.0421	0.886820	0.443410	+	0.896319i	$0.353769\pi$
$564$	−0.920696	−0.0387683
$565$	74.7953	3.14666
$566$	−18.8473	−0.792210
$567$	13.1874	0.553821
$568$	−16.9704	−0.712060
$569$	5.68707	0.238415	0.119207	−	0.992869i	$-0.461965\pi$
$569$	5.68707	0.238415	0.119207	+	0.992869i	$0.461965\pi$
$570$	−4.92326	−0.206213
$571$	−13.8286	−0.578710	−0.289355	−	0.957222i	$-0.593441\pi$
$571$	−13.8286	−0.578710	−0.289355	+	0.957222i	$0.593441\pi$
$572$	28.6238	1.19682
$573$	−7.91256	−0.330552
$574$	17.0175	0.710297
$575$	31.5505	1.31575
$576$	−12.8609	−0.535869
$577$	−25.4339	−1.05883	−0.529413	−	0.848364i	$-0.677588\pi$
$577$	−25.4339	−1.05883	−0.529413	+	0.848364i	$0.677588\pi$
$578$	10.7075	0.445375
$579$	−16.5265	−0.686819
$580$	−8.16306	−0.338953
$581$	36.3419	1.50772
$582$	−1.25367	−0.0519661
$583$	3.71927	0.154037
$584$	−1.80779	−0.0748071
$585$	45.3488	1.87494
$586$	22.0308	0.910082
$587$	−17.6916	−0.730212	−0.365106	−	0.930966i	$-0.618967\pi$
$587$	−17.6916	−0.730212	−0.365106	+	0.930966i	$0.618967\pi$
$588$	4.25386	0.175426
$589$	−19.1712	−0.789935
$590$	15.7934	0.650204
$591$	−14.8579	−0.611174
$592$	0.450025	0.0184959
$593$	−15.8841	−0.652282	−0.326141	−	0.945321i	$-0.605748\pi$
$593$	−15.8841	−0.652282	−0.326141	+	0.945321i	$0.605748\pi$
$594$	−17.1593	−0.704055
$595$	−65.5996	−2.68932
$596$	−12.2497	−0.501768
$597$	9.42760	0.385846
$598$	19.0588	0.779371
$599$	−23.0643	−0.942382	−0.471191	−	0.882031i	$-0.656176\pi$
$599$	−23.0643	−0.942382	−0.471191	+	0.882031i	$0.656176\pi$
$600$	17.6355	0.719968
$601$	−20.4736	−0.835137	−0.417569	−	0.908645i	$-0.637118\pi$
$601$	−20.4736	−0.835137	−0.417569	+	0.908645i	$0.637118\pi$
$602$	−37.4202	−1.52514
$603$	−21.6498	−0.881647
$604$	−16.5854	−0.674851
$605$	−34.3346	−1.39590
$606$	−11.8596	−0.481764
$607$	−27.7140	−1.12488	−0.562438	−	0.826839i	$-0.690137\pi$
$607$	−27.7140	−1.12488	−0.562438	+	0.826839i	$0.690137\pi$
$608$	−10.8803	−0.441255
$609$	5.06875	0.205396
$610$	−21.9115	−0.887171
$611$	−5.22603	−0.211422
$612$	15.3280	0.619596
$613$	5.48639	0.221593	0.110797	−	0.993843i	$-0.464660\pi$
$613$	5.48639	0.221593	0.110797	+	0.993843i	$0.464660\pi$
$614$	23.2074	0.936575
$615$	15.6130	0.629578
$616$	44.2420	1.78256
$617$	−24.6321	−0.991653	−0.495826	−	0.868422i	$-0.665135\pi$
$617$	−24.6321	−0.991653	−0.495826	+	0.868422i	$0.665135\pi$
$618$	−9.87526	−0.397241
$619$	−6.70331	−0.269429	−0.134714	−	0.990884i	$-0.543012\pi$
$619$	−6.70331	−0.269429	−0.134714	+	0.990884i	$0.543012\pi$
$620$	41.9601	1.68516
$621$	16.8858	0.677603
$622$	1.43187	0.0574126
$623$	−21.5871	−0.864870
$624$	0.790802	0.0316574
$625$	−2.43071	−0.0972282
$626$	−4.38283	−0.175173
$627$	−6.92869	−0.276705
$628$	−4.63075	−0.184787
$629$	−12.6506	−0.504411
$630$	26.1870	1.04332
$631$	−8.80286	−0.350436	−0.175218	−	0.984530i	$-0.556063\pi$
$631$	−8.80286	−0.350436	−0.175218	+	0.984530i	$0.556063\pi$
$632$	−22.7324	−0.904245
$633$	−16.3515	−0.649914
$634$	21.8794	0.868943
$635$	−30.4003	−1.20640
$636$	−0.764319	−0.0303072
$637$	24.1456	0.956683
$638$	7.77316	0.307742
$639$	−14.1365	−0.559230
$640$	22.5808	0.892585
$641$	15.7225	0.621000	0.310500	−	0.950573i	$-0.399504\pi$
$641$	15.7225	0.621000	0.310500	+	0.950573i	$0.399504\pi$
$642$	4.05423	0.160008
$643$	−37.6633	−1.48530	−0.742649	−	0.669681i	$-0.766431\pi$
$643$	−37.6633	−1.48530	−0.742649	+	0.669681i	$0.766431\pi$
$644$	−16.2656	−0.640953
$645$	−34.3319	−1.35182
$646$	−9.44553	−0.371629
$647$	19.1987	0.754778	0.377389	−	0.926055i	$-0.376822\pi$
$647$	19.1987	0.754778	0.377389	+	0.926055i	$0.376822\pi$
$648$	−11.1240	−0.436992
$649$	22.2267	0.872474
$650$	37.3987	1.46690
$651$	−26.0546	−1.02116
$652$	13.2686	0.519639
$653$	−6.98296	−0.273264	−0.136632	−	0.990622i	$-0.543628\pi$
$653$	−6.98296	−0.273264	−0.136632	+	0.990622i	$0.543628\pi$
$654$	−1.51499	−0.0592406
$655$	47.7522	1.86583
$656$	−1.06558	−0.0416040
$657$	−1.50591	−0.0587511
$658$	−3.01781	−0.117646
$659$	30.5273	1.18918	0.594588	−	0.804031i	$-0.297315\pi$
$659$	30.5273	1.18918	0.594588	+	0.804031i	$0.297315\pi$
$660$	15.1649	0.590293
$661$	17.0745	0.664122	0.332061	−	0.943258i	$-0.392256\pi$
$661$	17.0745	0.664122	0.332061	+	0.943258i	$0.392256\pi$
$662$	−24.9440	−0.969475
$663$	−22.2301	−0.863346
$664$	−30.6555	−1.18966
$665$	23.8497	0.924850
$666$	5.05004	0.195685
$667$	−7.64925	−0.296180
$668$	23.0193	0.890642
$669$	−3.54302	−0.136981
$670$	−29.2000	−1.12810
$671$	−30.8369	−1.19045
$672$	−14.7869	−0.570417
$673$	7.17742	0.276669	0.138335	−	0.990386i	$-0.455825\pi$
$673$	7.17742	0.276669	0.138335	+	0.990386i	$0.455825\pi$
$674$	4.66251	0.179593
$675$	33.1347	1.27535
$676$	−17.8813	−0.687743
$677$	−9.38224	−0.360589	−0.180294	−	0.983613i	$-0.557705\pi$
$677$	−9.38224	−0.360589	−0.180294	+	0.983613i	$0.557705\pi$
$678$	14.6364	0.562109
$679$	6.07311	0.233065
$680$	55.3352	2.12201
$681$	−9.16381	−0.351158
$682$	−39.9560	−1.52999
$683$	39.4998	1.51142	0.755709	−	0.654907i	$-0.227292\pi$
$683$	39.4998	1.51142	0.755709	+	0.654907i	$0.227292\pi$
$684$	−5.57270	−0.213077
$685$	71.0801	2.71583
$686$	−7.44249	−0.284156
$687$	6.68524	0.255058
$688$	2.34314	0.0893313
$689$	−4.33840	−0.165280
$690$	10.0973	0.384399
$691$	15.1766	0.577346	0.288673	−	0.957428i	$-0.406786\pi$
$691$	15.1766	0.577346	0.288673	+	0.957428i	$0.406786\pi$
$692$	−7.46228	−0.283673
$693$	36.8540	1.39997
$694$	−14.0088	−0.531768
$695$	52.7547	2.00110
$696$	−4.27564	−0.162068
$697$	29.9544	1.13460
$698$	18.6265	0.705023
$699$	−1.59612	−0.0603709
$700$	−31.9177	−1.20637
$701$	−45.9551	−1.73570	−0.867849	−	0.496828i	$-0.834498\pi$
$701$	−45.9551	−1.73570	−0.867849	+	0.496828i	$0.834498\pi$
$702$	20.0157	0.755445
$703$	4.59929	0.173466
$704$	−24.4117	−0.920051
$705$	−2.76875	−0.104277
$706$	27.4846	1.03439
$707$	57.4514	2.16068
$708$	−4.56763	−0.171662
$709$	17.2364	0.647327	0.323664	−	0.946172i	$-0.395085\pi$
$709$	17.2364	0.647327	0.323664	+	0.946172i	$0.395085\pi$
$710$	−19.0665	−0.715552
$711$	−18.9363	−0.710166
$712$	18.2094	0.682425
$713$	39.3190	1.47251
$714$	−12.8370	−0.480411
$715$	86.0785	3.21915
$716$	−28.1630	−1.05250
$717$	10.3009	0.384694
$718$	14.5722	0.543830
$719$	8.19421	0.305592	0.152796	−	0.988258i	$-0.451172\pi$
$719$	8.19421	0.305592	0.152796	+	0.988258i	$0.451172\pi$
$720$	−1.63975	−0.0611099
$721$	47.8386	1.78160
$722$	−13.6356	−0.507463
$723$	−8.39784	−0.312319
$724$	13.1709	0.489493
$725$	−15.0100	−0.557457
$726$	−6.71882	−0.249359
$727$	−18.3999	−0.682415	−0.341208	−	0.939988i	$-0.610836\pi$
$727$	−18.3999	−0.682415	−0.341208	+	0.939988i	$0.610836\pi$
$728$	−51.6068	−1.91267
$729$	0.604853	0.0224019
$730$	−2.03109	−0.0751740
$731$	−65.8676	−2.43620
$732$	6.33705	0.234224
$733$	43.7528	1.61605	0.808023	−	0.589151i	$-0.200538\pi$
$733$	43.7528	1.61605	0.808023	+	0.589151i	$0.200538\pi$
$734$	17.6514	0.651526
$735$	12.7923	0.471852
$736$	22.3149	0.822539
$737$	−41.0943	−1.51373
$738$	−11.9576	−0.440167
$739$	−29.3853	−1.08096	−0.540478	−	0.841358i	$-0.681757\pi$
$739$	−29.3853	−1.08096	−0.540478	+	0.841358i	$0.681757\pi$
$740$	−10.0665	−0.370052
$741$	8.08207	0.296902
$742$	−2.50524	−0.0919704
$743$	40.9598	1.50267	0.751334	−	0.659922i	$-0.229411\pi$
$743$	40.9598	1.50267	0.751334	+	0.659922i	$0.229411\pi$
$744$	21.9778	0.805746
$745$	−36.8378	−1.34963
$746$	1.64901	0.0603744
$747$	−25.5363	−0.934324
$748$	29.0946	1.06381
$749$	−19.6398	−0.717623
$750$	7.22301	0.263747
$751$	1.63042	0.0594950	0.0297475	−	0.999557i	$-0.490530\pi$
$751$	1.63042	0.0594950	0.0297475	+	0.999557i	$0.490530\pi$
$752$	0.188966	0.00689087
$753$	−15.3390	−0.558983
$754$	−9.06711	−0.330205
$755$	−49.8762	−1.81518
$756$	−17.0823	−0.621276
$757$	−15.8143	−0.574780	−0.287390	−	0.957814i	$-0.592788\pi$
$757$	−15.8143	−0.574780	−0.287390	+	0.957814i	$0.592788\pi$
$758$	−6.43171	−0.233610
$759$	14.2104	0.515804
$760$	−20.1179	−0.729752
$761$	12.3961	0.449359	0.224680	−	0.974433i	$-0.427866\pi$
$761$	12.3961	0.449359	0.224680	+	0.974433i	$0.427866\pi$
$762$	−5.94892	−0.215507
$763$	7.33902	0.265690
$764$	−12.0798	−0.437032
$765$	46.0947	1.66656
$766$	−29.8264	−1.07767
$767$	−25.9266	−0.936156
$768$	12.8298	0.462956
$769$	28.4483	1.02587	0.512935	−	0.858427i	$-0.328558\pi$
$769$	28.4483	1.02587	0.512935	+	0.858427i	$0.328558\pi$
$770$	49.7067	1.79130
$771$	−6.14287	−0.221230
$772$	−25.2304	−0.908062
$773$	−52.5310	−1.88941	−0.944704	−	0.327925i	$-0.893651\pi$
$773$	−52.5310	−1.88941	−0.944704	+	0.327925i	$0.893651\pi$
$774$	26.2940	0.945119
$775$	77.1551	2.77149
$776$	−5.12285	−0.183900
$777$	6.25067	0.224242
$778$	25.0748	0.898976
$779$	−10.8903	−0.390187
$780$	−17.6893	−0.633379
$781$	−26.8330	−0.960160
$782$	19.3723	0.692750
$783$	−8.03332	−0.287087
$784$	−0.873071	−0.0311811
$785$	−13.9257	−0.497031
$786$	9.34447	0.333306
$787$	−54.7313	−1.95096	−0.975480	−	0.220087i	$-0.929366\pi$
$787$	−54.7313	−1.95096	−0.975480	+	0.220087i	$0.929366\pi$
$788$	−22.6830	−0.808049
$789$	−15.5615	−0.554005
$790$	−25.5402	−0.908680
$791$	−70.9031	−2.52102
$792$	−31.0875	−1.10465
$793$	35.9702	1.27734
$794$	29.6383	1.05182
$795$	−2.29848	−0.0815188
$796$	14.3928	0.510138
$797$	9.85119	0.348947	0.174473	−	0.984662i	$-0.444178\pi$
$797$	9.85119	0.348947	0.174473	+	0.984662i	$0.444178\pi$
$798$	4.66706	0.165212
$799$	−5.31198	−0.187924
$800$	43.7882	1.54815
$801$	15.1686	0.535956
$802$	−18.1238	−0.639975
$803$	−2.85843	−0.100872
$804$	8.44498	0.297831
$805$	−48.9143	−1.72400
$806$	46.6072	1.64167
$807$	1.89772	0.0668030
$808$	−48.4619	−1.70488
$809$	30.5587	1.07439	0.537193	−	0.843459i	$-0.319485\pi$
$809$	30.5587	1.07439	0.537193	+	0.843459i	$0.319485\pi$
$810$	−12.4980	−0.439135
$811$	50.9983	1.79079	0.895396	−	0.445270i	$-0.146892\pi$
$811$	50.9983	1.79079	0.895396	+	0.445270i	$0.146892\pi$
$812$	7.73826	0.271560
$813$	3.14480	0.110293
$814$	9.58570	0.335979
$815$	39.9018	1.39770
$816$	0.803810	0.0281390
$817$	23.9471	0.837802
$818$	12.0486	0.421268
$819$	−42.9889	−1.50215
$820$	23.8358	0.832382
$821$	17.0582	0.595336	0.297668	−	0.954669i	$-0.403791\pi$
$821$	17.0582	0.595336	0.297668	+	0.954669i	$0.403791\pi$
$822$	13.9094	0.485147
$823$	−1.03825	−0.0361910	−0.0180955	−	0.999836i	$-0.505760\pi$
$823$	−1.03825	−0.0361910	−0.0180955	+	0.999836i	$0.505760\pi$
$824$	−40.3532	−1.40577
$825$	27.8848	0.970823
$826$	−14.9715	−0.520926
$827$	−5.28537	−0.183790	−0.0918951	−	0.995769i	$-0.529292\pi$
$827$	−5.28537	−0.183790	−0.0918951	+	0.995769i	$0.529292\pi$
$828$	11.4293	0.397196
$829$	−5.76581	−0.200255	−0.100127	−	0.994975i	$-0.531925\pi$
$829$	−5.76581	−0.200255	−0.100127	+	0.994975i	$0.531925\pi$
$830$	−34.4419	−1.19550
$831$	−11.7657	−0.408149
$832$	28.4754	0.987207
$833$	24.5427	0.850356
$834$	10.3234	0.357470
$835$	69.2242	2.39560
$836$	−10.5778	−0.365840
$837$	41.2932	1.42730
$838$	20.7509	0.716827
$839$	28.4081	0.980758	0.490379	−	0.871509i	$-0.336858\pi$
$839$	28.4081	0.980758	0.490379	+	0.871509i	$0.336858\pi$
$840$	−27.3412	−0.943362
$841$	−25.3609	−0.874514
$842$	18.2136	0.627683
$843$	20.4584	0.704626
$844$	−24.9632	−0.859269
$845$	−53.7732	−1.84985
$846$	2.12052	0.0729049
$847$	32.5479	1.11836
$848$	0.156870	0.00538695
$849$	16.3919	0.562570
$850$	38.0139	1.30386
$851$	−9.43289	−0.323355
$852$	5.51424	0.188915
$853$	−31.7011	−1.08542	−0.542712	−	0.839919i	$-0.682602\pi$
$853$	−31.7011	−1.08542	−0.542712	+	0.839919i	$0.682602\pi$
$854$	20.7713	0.710778
$855$	−16.7584	−0.573125
$856$	16.5668	0.566240
$857$	−45.2300	−1.54503	−0.772513	−	0.634999i	$-0.781001\pi$
$857$	−45.2300	−1.54503	−0.772513	+	0.634999i	$0.781001\pi$
$858$	16.8444	0.575058
$859$	−31.1787	−1.06380	−0.531901	−	0.846806i	$-0.678522\pi$
$859$	−31.1787	−1.06380	−0.531901	+	0.846806i	$0.678522\pi$
$860$	−52.4132	−1.78728
$861$	−14.8005	−0.504401
$862$	−33.4678	−1.13992
$863$	−20.8640	−0.710220	−0.355110	−	0.934825i	$-0.615557\pi$
$863$	−20.8640	−0.710220	−0.355110	+	0.934825i	$0.615557\pi$
$864$	23.4354	0.797287
$865$	−22.4408	−0.763010
$866$	−7.30046	−0.248080
$867$	−9.31261	−0.316273
$868$	−39.7766	−1.35010
$869$	−35.9437	−1.21931
$870$	−4.80375	−0.162862
$871$	47.9351	1.62422
$872$	−6.19068	−0.209643
$873$	−4.26738	−0.144429
$874$	−7.04306	−0.238235
$875$	−34.9903	−1.18289
$876$	0.587413	0.0198469
$877$	−7.68643	−0.259552	−0.129776	−	0.991543i	$-0.541426\pi$
$877$	−7.68643	−0.259552	−0.129776	+	0.991543i	$0.541426\pi$
$878$	3.18998	0.107657
$879$	−19.1607	−0.646274
$880$	−3.11248	−0.104922
$881$	−40.6984	−1.37116	−0.685581	−	0.727996i	$-0.740452\pi$
$881$	−40.6984	−1.37116	−0.685581	+	0.727996i	$0.740452\pi$
$882$	−9.79735	−0.329894
$883$	−30.7314	−1.03419	−0.517097	−	0.855927i	$-0.672987\pi$
$883$	−30.7314	−1.03419	−0.517097	+	0.855927i	$0.672987\pi$
$884$	−33.9379	−1.14145
$885$	−13.7359	−0.461728
$886$	−10.6907	−0.359161
$887$	23.5448	0.790556	0.395278	−	0.918562i	$-0.370648\pi$
$887$	23.5448	0.790556	0.395278	+	0.918562i	$0.370648\pi$
$888$	−5.27263	−0.176938
$889$	28.8183	0.966534
$890$	20.4585	0.685772
$891$	−17.5889	−0.589251
$892$	−5.40900	−0.181107
$893$	1.93125	0.0646267
$894$	−7.20865	−0.241093
$895$	−84.6927	−2.83097
$896$	−21.4057	−0.715116
$897$	−16.5759	−0.553453
$898$	15.7745	0.526402
$899$	−18.7058	−0.623874
$900$	22.4275	0.747584
$901$	−4.40976	−0.146910
$902$	−22.6973	−0.755738
$903$	32.5453	1.08304
$904$	59.8088	1.98921
$905$	39.6079	1.31661
$906$	−9.76010	−0.324258
$907$	25.8525	0.858419	0.429210	−	0.903205i	$-0.358792\pi$
$907$	25.8525	0.858419	0.429210	+	0.903205i	$0.358792\pi$
$908$	−13.9900	−0.464276
$909$	−40.3692	−1.33896
$910$	−57.9811	−1.92205
$911$	−8.22106	−0.272376	−0.136188	−	0.990683i	$-0.543485\pi$
$911$	−8.22106	−0.272376	−0.136188	+	0.990683i	$0.543485\pi$
$912$	−0.292236	−0.00967691
$913$	−48.4715	−1.60417
$914$	−20.5272	−0.678978
$915$	19.0570	0.630004
$916$	10.2061	0.337219
$917$	−45.2673	−1.49486
$918$	20.3449	0.671483
$919$	0.773421	0.0255128	0.0127564	−	0.999919i	$-0.495939\pi$
$919$	0.773421	0.0255128	0.0127564	+	0.999919i	$0.495939\pi$
$920$	41.2607	1.36032
$921$	−20.1841	−0.665087
$922$	−29.5286	−0.972473
$923$	31.2997	1.03024
$924$	−14.3757	−0.472927
$925$	−18.5100	−0.608606
$926$	−26.7975	−0.880622
$927$	−33.6146	−1.10405
$928$	−10.6162	−0.348494
$929$	31.3632	1.02899	0.514497	−	0.857492i	$-0.327979\pi$
$929$	31.3632	1.02899	0.514497	+	0.857492i	$0.327979\pi$
$930$	24.6925	0.809698
$931$	−8.92286	−0.292435
$932$	−2.43674	−0.0798181
$933$	−1.24533	−0.0407703
$934$	−27.8283	−0.910569
$935$	87.4943	2.86137
$936$	36.2624	1.18527
$937$	−23.7210	−0.774930	−0.387465	−	0.921884i	$-0.626649\pi$
$937$	−23.7210	−0.774930	−0.387465	+	0.921884i	$0.626649\pi$
$938$	27.6805	0.903800
$939$	3.81186	0.124395
$940$	−4.22694	−0.137868
$941$	−4.48127	−0.146085	−0.0730426	−	0.997329i	$-0.523271\pi$
$941$	−4.48127	−0.146085	−0.0730426	+	0.997329i	$0.523271\pi$
$942$	−2.72508	−0.0887879
$943$	22.3355	0.727344
$944$	0.937470	0.0305121
$945$	−51.3703	−1.67108
$946$	49.9097	1.62271
$947$	24.6069	0.799617	0.399809	−	0.916599i	$-0.369077\pi$
$947$	24.6069	0.799617	0.399809	+	0.916599i	$0.369077\pi$
$948$	7.38651	0.239903
$949$	3.33426	0.108235
$950$	−13.8205	−0.448396
$951$	−19.0291	−0.617060
$952$	−52.4556	−1.70010
$953$	−17.3064	−0.560609	−0.280304	−	0.959911i	$-0.590435\pi$
$953$	−17.3064	−0.560609	−0.280304	+	0.959911i	$0.590435\pi$
$954$	1.76035	0.0569936
$955$	−36.3267	−1.17551
$956$	15.7260	0.508615
$957$	−6.76051	−0.218536
$958$	−24.7400	−0.799313
$959$	−67.3812	−2.17585
$960$	15.0862	0.486907
$961$	65.1525	2.10169
$962$	−11.1814	−0.360502
$963$	13.8003	0.444708
$964$	−12.8207	−0.412925
$965$	−75.8736	−2.44246
$966$	−9.57188	−0.307970
$967$	−29.3825	−0.944877	−0.472439	−	0.881364i	$-0.656626\pi$
$967$	−29.3825	−0.944877	−0.472439	+	0.881364i	$0.656626\pi$
$968$	−27.4551	−0.882440
$969$	8.21501	0.263904
$970$	−5.75561	−0.184801
$971$	−18.7262	−0.600954	−0.300477	−	0.953789i	$-0.597146\pi$
$971$	−18.7262	−0.600954	−0.300477	+	0.953789i	$0.597146\pi$
$972$	18.6846	0.599309
$973$	−50.0094	−1.60323
$974$	15.4331	0.494507
$975$	−32.5266	−1.04168
$976$	−1.30063	−0.0416322
$977$	30.1648	0.965057	0.482529	−	0.875880i	$-0.339718\pi$
$977$	30.1648	0.965057	0.482529	+	0.875880i	$0.339718\pi$
$978$	7.80824	0.249680
$979$	28.7921	0.920200
$980$	19.5296	0.623849
$981$	−5.15690	−0.164647
$982$	−3.98120	−0.127045
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	12.4847	0.397997
$985$	−68.2131	−2.17345
$986$	−9.21625	−0.293505
$987$	2.62466	0.0835440
$988$	12.3386	0.392543
$989$	−49.1141	−1.56174
$990$	−34.9273	−1.11006
$991$	−15.7780	−0.501204	−0.250602	−	0.968090i	$-0.580629\pi$
$991$	−15.7780	−0.501204	−0.250602	+	0.968090i	$0.580629\pi$
$992$	54.5699	1.73260
$993$	21.6944	0.688450
$994$	18.0743	0.573281
$995$	43.2823	1.37214
$996$	9.96099	0.315626
$997$	−46.2633	−1.46517	−0.732587	−	0.680674i	$-0.761687\pi$
$997$	−46.2633	−1.46517	−0.732587	+	0.680674i	$0.761687\pi$
$998$	−10.7683	−0.340864
$999$	−9.90652	−0.313428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.32	✓	54
3.2	odd	2		8847.2.a.g.1.23		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.32	✓	54	1.1	even	1	trivial
8847.2.a.g.1.23		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q+0.898401 q^{2} -0.781362 q^{3} -1.19287 q^{4} -3.58725 q^{5} -0.701977 q^{6} +3.40057 q^{7} -2.86848 q^{8} -2.38947 q^{9} +O(q^{10})\)	\(q+0.898401 q^{2} -0.781362 q^{3} -1.19287 q^{4} -3.58725 q^{5} -0.701977 q^{6} +3.40057 q^{7} -2.86848 q^{8} -2.38947 q^{9} -3.22279 q^{10} -4.53556 q^{11} +0.932067 q^{12} +5.29057 q^{13} +3.05508 q^{14} +2.80294 q^{15} -0.191299 q^{16} +5.37759 q^{17} -2.14671 q^{18} -1.95510 q^{19} +4.27914 q^{20} -2.65708 q^{21} -4.07475 q^{22} +4.00980 q^{23} +2.24132 q^{24} +7.86836 q^{25} +4.75305 q^{26} +4.21113 q^{27} -4.05646 q^{28} -1.90764 q^{29} +2.51817 q^{30} +9.80574 q^{31} +5.56510 q^{32} +3.54391 q^{33} +4.83123 q^{34} -12.1987 q^{35} +2.85034 q^{36} -2.35246 q^{37} -1.75646 q^{38} -4.13385 q^{39} +10.2900 q^{40} +5.57023 q^{41} -2.38712 q^{42} -12.2485 q^{43} +5.41035 q^{44} +8.57164 q^{45} +3.60241 q^{46} -0.987801 q^{47} +0.149474 q^{48} +4.56390 q^{49} +7.06895 q^{50} -4.20184 q^{51} -6.31098 q^{52} -0.820026 q^{53} +3.78328 q^{54} +16.2702 q^{55} -9.75449 q^{56} +1.52764 q^{57} -1.71383 q^{58} -4.90054 q^{59} -3.34356 q^{60} +6.79892 q^{61} +8.80949 q^{62} -8.12558 q^{63} +5.38229 q^{64} -18.9786 q^{65} +3.18386 q^{66} +9.06048 q^{67} -6.41479 q^{68} -3.13310 q^{69} -10.9593 q^{70} +5.91614 q^{71} +6.85417 q^{72} +0.630227 q^{73} -2.11345 q^{74} -6.14804 q^{75} +2.33219 q^{76} -15.4235 q^{77} -3.71385 q^{78} +7.92488 q^{79} +0.686239 q^{80} +3.87801 q^{81} +5.00430 q^{82} +10.6870 q^{83} +3.16956 q^{84} -19.2907 q^{85} -11.0041 q^{86} +1.49056 q^{87} +13.0102 q^{88} -6.34809 q^{89} +7.70077 q^{90} +17.9910 q^{91} -4.78319 q^{92} -7.66183 q^{93} -0.887442 q^{94} +7.01342 q^{95} -4.34836 q^{96} +1.78591 q^{97} +4.10021 q^{98} +10.8376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more