LMFDB - Embedded newform 5586.2.a.cc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.207085568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 13x^{4} + 28x^{3} + 10x^{2} - 12x + 2 $ x^6 - 2x^5 - 13x^4 + 28x^3 + 10x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.80421$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.909895 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.909895 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.909895 q^{10} -5.25253 q^{11} -1.00000 q^{12} +2.19668 q^{13} -0.909895 q^{15} +1.00000 q^{16} -5.60841 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.909895 q^{20} +5.25253 q^{22} +3.26723 q^{23} +1.00000 q^{24} -4.17209 q^{25} -2.19668 q^{26} -1.00000 q^{27} -6.43684 q^{29} +0.909895 q^{30} +3.73832 q^{31} -1.00000 q^{32} +5.25253 q^{33} +5.60841 q^{34} +1.00000 q^{36} +0.423880 q^{37} -1.00000 q^{38} -2.19668 q^{39} -0.909895 q^{40} -10.0810 q^{41} +4.34366 q^{43} -5.25253 q^{44} +0.909895 q^{45} -3.26723 q^{46} -6.90638 q^{47} -1.00000 q^{48} +4.17209 q^{50} +5.60841 q^{51} +2.19668 q^{52} +11.0366 q^{53} +1.00000 q^{54} -4.77925 q^{55} -1.00000 q^{57} +6.43684 q^{58} +10.0949 q^{59} -0.909895 q^{60} +11.1158 q^{61} -3.73832 q^{62} +1.00000 q^{64} +1.99875 q^{65} -5.25253 q^{66} -6.67896 q^{67} -5.60841 q^{68} -3.26723 q^{69} +2.99136 q^{71} -1.00000 q^{72} -0.424104 q^{73} -0.423880 q^{74} +4.17209 q^{75} +1.00000 q^{76} +2.19668 q^{78} +2.61901 q^{79} +0.909895 q^{80} +1.00000 q^{81} +10.0810 q^{82} -12.2304 q^{83} -5.10306 q^{85} -4.34366 q^{86} +6.43684 q^{87} +5.25253 q^{88} -2.33093 q^{89} -0.909895 q^{90} +3.26723 q^{92} -3.73832 q^{93} +6.90638 q^{94} +0.909895 q^{95} +1.00000 q^{96} +2.52513 q^{97} -5.25253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} - 6 q^{12} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 4 q^{22} + 16 q^{23} + 6 q^{24} + 10 q^{25} - 6 q^{27} + 8 q^{29} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{38} - 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 32 q^{55} - 6 q^{57} - 8 q^{58} - 24 q^{59} + 6 q^{64} + 16 q^{65} + 4 q^{66} - 20 q^{67} - 4 q^{68} - 16 q^{69} + 24 q^{71} - 6 q^{72} + 16 q^{73} - 10 q^{75} + 6 q^{76} + 40 q^{79} + 6 q^{81} + 8 q^{82} - 24 q^{83} + 8 q^{85} - 8 q^{86} - 8 q^{87} - 4 q^{88} - 24 q^{89} + 16 q^{92} + 16 q^{94} + 6 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 - 6 * q^12 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 4 * q^22 + 16 * q^23 + 6 * q^24 + 10 * q^25 - 6 * q^27 + 8 * q^29 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^38 - 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 32 * q^55 - 6 * q^57 - 8 * q^58 - 24 * q^59 + 6 * q^64 + 16 * q^65 + 4 * q^66 - 20 * q^67 - 4 * q^68 - 16 * q^69 + 24 * q^71 - 6 * q^72 + 16 * q^73 - 10 * q^75 + 6 * q^76 + 40 * q^79 + 6 * q^81 + 8 * q^82 - 24 * q^83 + 8 * q^85 - 8 * q^86 - 8 * q^87 - 4 * q^88 - 24 * q^89 + 16 * q^92 + 16 * q^94 + 6 * q^96 + 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.909895	0.406917	0.203459	−	0.979084i	$-0.434782\pi$
$5$	0.909895	0.406917	0.203459	+	0.979084i	$0.434782\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.909895	−0.287734
$11$	−5.25253	−1.58370	−0.791849	−	0.610717i	$-0.790881\pi$
$11$	−5.25253	−1.58370	−0.791849	+	0.610717i	$0.790881\pi$
$12$	−1.00000	−0.288675
$13$	2.19668	0.609249	0.304625	−	0.952472i	$-0.401469\pi$
$13$	2.19668	0.609249	0.304625	+	0.952472i	$0.401469\pi$
$14$	0	0
$15$	−0.909895	−0.234934
$16$	1.00000	0.250000
$17$	−5.60841	−1.36024	−0.680120	−	0.733101i	$-0.738072\pi$
$17$	−5.60841	−1.36024	−0.680120	+	0.733101i	$0.738072\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.909895	0.203459
$21$	0	0
$22$	5.25253	1.11984
$23$	3.26723	0.681264	0.340632	−	0.940197i	$-0.389359\pi$
$23$	3.26723	0.681264	0.340632	+	0.940197i	$0.389359\pi$
$24$	1.00000	0.204124
$25$	−4.17209	−0.834418
$26$	−2.19668	−0.430804
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.43684	−1.19529	−0.597645	−	0.801761i	$-0.703897\pi$
$29$	−6.43684	−1.19529	−0.597645	+	0.801761i	$0.703897\pi$
$30$	0.909895	0.166123
$31$	3.73832	0.671422	0.335711	−	0.941965i	$-0.391023\pi$
$31$	3.73832	0.671422	0.335711	+	0.941965i	$0.391023\pi$
$32$	−1.00000	−0.176777
$33$	5.25253	0.914348
$34$	5.60841	0.961834
$35$	0	0
$36$	1.00000	0.166667
$37$	0.423880	0.0696854	0.0348427	−	0.999393i	$-0.488907\pi$
$37$	0.423880	0.0696854	0.0348427	+	0.999393i	$0.488907\pi$
$38$	−1.00000	−0.162221
$39$	−2.19668	−0.351750
$40$	−0.909895	−0.143867
$41$	−10.0810	−1.57438	−0.787191	−	0.616710i	$-0.788465\pi$
$41$	−10.0810	−1.57438	−0.787191	+	0.616710i	$0.788465\pi$
$42$	0	0
$43$	4.34366	0.662403	0.331201	−	0.943560i	$-0.392546\pi$
$43$	4.34366	0.662403	0.331201	+	0.943560i	$0.392546\pi$
$44$	−5.25253	−0.791849
$45$	0.909895	0.135639
$46$	−3.26723	−0.481727
$47$	−6.90638	−1.00740	−0.503700	−	0.863879i	$-0.668028\pi$
$47$	−6.90638	−1.00740	−0.503700	+	0.863879i	$0.668028\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.17209	0.590023
$51$	5.60841	0.785335
$52$	2.19668	0.304625
$53$	11.0366	1.51600	0.757998	−	0.652257i	$-0.226178\pi$
$53$	11.0366	1.51600	0.757998	+	0.652257i	$0.226178\pi$
$54$	1.00000	0.136083
$55$	−4.77925	−0.644434
$56$	0	0
$57$	−1.00000	−0.132453
$58$	6.43684	0.845198
$59$	10.0949	1.31425	0.657125	−	0.753782i	$-0.271772\pi$
$59$	10.0949	1.31425	0.657125	+	0.753782i	$0.271772\pi$
$60$	−0.909895	−0.117467
$61$	11.1158	1.42323	0.711616	−	0.702569i	$-0.247964\pi$
$61$	11.1158	1.42323	0.711616	+	0.702569i	$0.247964\pi$
$62$	−3.73832	−0.474767
$63$	0	0
$64$	1.00000	0.125000
$65$	1.99875	0.247914
$66$	−5.25253	−0.646542
$67$	−6.67896	−0.815965	−0.407982	−	0.912990i	$-0.633768\pi$
$67$	−6.67896	−0.815965	−0.407982	+	0.912990i	$0.633768\pi$
$68$	−5.60841	−0.680120
$69$	−3.26723	−0.393328
$70$	0	0
$71$	2.99136	0.355009	0.177505	−	0.984120i	$-0.443198\pi$
$71$	2.99136	0.355009	0.177505	+	0.984120i	$0.443198\pi$
$72$	−1.00000	−0.117851
$73$	−0.424104	−0.0496376	−0.0248188	−	0.999692i	$-0.507901\pi$
$73$	−0.424104	−0.0496376	−0.0248188	+	0.999692i	$0.507901\pi$
$74$	−0.423880	−0.0492750
$75$	4.17209	0.481752
$76$	1.00000	0.114708
$77$	0	0
$78$	2.19668	0.248725
$79$	2.61901	0.294662	0.147331	−	0.989087i	$-0.452932\pi$
$79$	2.61901	0.294662	0.147331	+	0.989087i	$0.452932\pi$
$80$	0.909895	0.101729
$81$	1.00000	0.111111
$82$	10.0810	1.11326
$83$	−12.2304	−1.34246	−0.671232	−	0.741248i	$-0.734234\pi$
$83$	−12.2304	−1.34246	−0.671232	+	0.741248i	$0.734234\pi$
$84$	0	0
$85$	−5.10306	−0.553505
$86$	−4.34366	−0.468389
$87$	6.43684	0.690101
$88$	5.25253	0.559922
$89$	−2.33093	−0.247078	−0.123539	−	0.992340i	$-0.539424\pi$
$89$	−2.33093	−0.247078	−0.123539	+	0.992340i	$0.539424\pi$
$90$	−0.909895	−0.0959113
$91$	0	0
$92$	3.26723	0.340632
$93$	−3.73832	−0.387646
$94$	6.90638	0.712339
$95$	0.909895	0.0933532
$96$	1.00000	0.102062
$97$	2.52513	0.256388	0.128194	−	0.991749i	$-0.459082\pi$
$97$	2.52513	0.256388	0.128194	+	0.991749i	$0.459082\pi$
$98$	0	0
$99$	−5.25253	−0.527899
$100$	−4.17209	−0.417209
$101$	7.96378	0.792426	0.396213	−	0.918159i	$-0.370324\pi$
$101$	7.96378	0.792426	0.396213	+	0.918159i	$0.370324\pi$
$102$	−5.60841	−0.555315
$103$	−7.75665	−0.764285	−0.382143	−	0.924103i	$-0.624814\pi$
$103$	−7.75665	−0.764285	−0.382143	+	0.924103i	$0.624814\pi$
$104$	−2.19668	−0.215402
$105$	0	0
$106$	−11.0366	−1.07197
$107$	12.7164	1.22934	0.614672	−	0.788783i	$-0.289288\pi$
$107$	12.7164	1.22934	0.614672	+	0.788783i	$0.289288\pi$
$108$	−1.00000	−0.0962250
$109$	−7.23152	−0.692654	−0.346327	−	0.938114i	$-0.612571\pi$
$109$	−7.23152	−0.692654	−0.346327	+	0.938114i	$0.612571\pi$
$110$	4.77925	0.455684
$111$	−0.423880	−0.0402329
$112$	0	0
$113$	20.5318	1.93147	0.965734	−	0.259535i	$-0.0835692\pi$
$113$	20.5318	1.93147	0.965734	+	0.259535i	$0.0835692\pi$
$114$	1.00000	0.0936586
$115$	2.97283	0.277218
$116$	−6.43684	−0.597645
$117$	2.19668	0.203083
$118$	−10.0949	−0.929315
$119$	0	0
$120$	0.909895	0.0830616
$121$	16.5891	1.50810
$122$	−11.1158	−1.00638
$123$	10.0810	0.908969
$124$	3.73832	0.335711
$125$	−8.34564	−0.746457
$126$	0	0
$127$	18.4820	1.64001	0.820006	−	0.572355i	$-0.193970\pi$
$127$	18.4820	1.64001	0.820006	+	0.572355i	$0.193970\pi$
$128$	−1.00000	−0.0883883
$129$	−4.34366	−0.382438
$130$	−1.99875	−0.175302
$131$	16.0744	1.40442	0.702212	−	0.711968i	$-0.252196\pi$
$131$	16.0744	1.40442	0.702212	+	0.711968i	$0.252196\pi$
$132$	5.25253	0.457174
$133$	0	0
$134$	6.67896	0.576974
$135$	−0.909895	−0.0783113
$136$	5.60841	0.480917
$137$	−2.54882	−0.217761	−0.108880	−	0.994055i	$-0.534727\pi$
$137$	−2.54882	−0.217761	−0.108880	+	0.994055i	$0.534727\pi$
$138$	3.26723	0.278125
$139$	0.805534	0.0683245	0.0341623	−	0.999416i	$-0.489124\pi$
$139$	0.805534	0.0683245	0.0341623	+	0.999416i	$0.489124\pi$
$140$	0	0
$141$	6.90638	0.581622
$142$	−2.99136	−0.251030
$143$	−11.5381	−0.964867
$144$	1.00000	0.0833333
$145$	−5.85684	−0.486384
$146$	0.424104	0.0350991
$147$	0	0
$148$	0.423880	0.0348427
$149$	10.0376	0.822310	0.411155	−	0.911565i	$-0.365125\pi$
$149$	10.0376	0.822310	0.411155	+	0.911565i	$0.365125\pi$
$150$	−4.17209	−0.340650
$151$	10.3688	0.843804	0.421902	−	0.906641i	$-0.361363\pi$
$151$	10.3688	0.843804	0.421902	+	0.906641i	$0.361363\pi$
$152$	−1.00000	−0.0811107
$153$	−5.60841	−0.453413
$154$	0	0
$155$	3.40148	0.273213
$156$	−2.19668	−0.175875
$157$	5.36246	0.427971	0.213985	−	0.976837i	$-0.431355\pi$
$157$	5.36246	0.427971	0.213985	+	0.976837i	$0.431355\pi$
$158$	−2.61901	−0.208357
$159$	−11.0366	−0.875260
$160$	−0.909895	−0.0719335
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	7.51576	0.588679	0.294340	−	0.955701i	$-0.404900\pi$
$163$	7.51576	0.588679	0.294340	+	0.955701i	$0.404900\pi$
$164$	−10.0810	−0.787191
$165$	4.77925	0.372064
$166$	12.2304	0.949265
$167$	−20.4853	−1.58520	−0.792599	−	0.609743i	$-0.791273\pi$
$167$	−20.4853	−1.58520	−0.792599	+	0.609743i	$0.791273\pi$
$168$	0	0
$169$	−8.17460	−0.628815
$170$	5.10306	0.391387
$171$	1.00000	0.0764719
$172$	4.34366	0.331201
$173$	−7.80706	−0.593559	−0.296780	−	0.954946i	$-0.595913\pi$
$173$	−7.80706	−0.593559	−0.296780	+	0.954946i	$0.595913\pi$
$174$	−6.43684	−0.487975
$175$	0	0
$176$	−5.25253	−0.395924
$177$	−10.0949	−0.758782
$178$	2.33093	0.174711
$179$	−14.3548	−1.07293	−0.536463	−	0.843924i	$-0.680240\pi$
$179$	−14.3548	−1.07293	−0.536463	+	0.843924i	$0.680240\pi$
$180$	0.909895	0.0678195
$181$	−10.2728	−0.763570	−0.381785	−	0.924251i	$-0.624690\pi$
$181$	−10.2728	−0.763570	−0.381785	+	0.924251i	$0.624690\pi$
$182$	0	0
$183$	−11.1158	−0.821703
$184$	−3.26723	−0.240863
$185$	0.385686	0.0283562
$186$	3.73832	0.274107
$187$	29.4583	2.15421
$188$	−6.90638	−0.503700
$189$	0	0
$190$	−0.909895	−0.0660107
$191$	21.8896	1.58387	0.791936	−	0.610603i	$-0.209073\pi$
$191$	21.8896	1.58387	0.791936	+	0.610603i	$0.209073\pi$
$192$	−1.00000	−0.0721688
$193$	−17.1533	−1.23472	−0.617360	−	0.786681i	$-0.711798\pi$
$193$	−17.1533	−1.23472	−0.617360	+	0.786681i	$0.711798\pi$
$194$	−2.52513	−0.181294
$195$	−1.99875	−0.143133
$196$	0	0
$197$	10.2387	0.729477	0.364739	−	0.931110i	$-0.381158\pi$
$197$	10.2387	0.729477	0.364739	+	0.931110i	$0.381158\pi$
$198$	5.25253	0.373281
$199$	−25.6583	−1.81887	−0.909436	−	0.415845i	$-0.863486\pi$
$199$	−25.6583	−1.81887	−0.909436	+	0.415845i	$0.863486\pi$
$200$	4.17209	0.295011
$201$	6.67896	0.471097
$202$	−7.96378	−0.560330
$203$	0	0
$204$	5.60841	0.392667
$205$	−9.17261	−0.640643
$206$	7.75665	0.540431
$207$	3.26723	0.227088
$208$	2.19668	0.152312
$209$	−5.25253	−0.363325
$210$	0	0
$211$	24.8257	1.70907	0.854534	−	0.519395i	$-0.173843\pi$
$211$	24.8257	1.70907	0.854534	+	0.519395i	$0.173843\pi$
$212$	11.0366	0.757998
$213$	−2.99136	−0.204965
$214$	−12.7164	−0.869278
$215$	3.95228	0.269543
$216$	1.00000	0.0680414
$217$	0	0
$218$	7.23152	0.489780
$219$	0.424104	0.0286583
$220$	−4.77925	−0.322217
$221$	−12.3199	−0.828725
$222$	0.423880	0.0284489
$223$	12.5148	0.838053	0.419026	−	0.907974i	$-0.362372\pi$
$223$	12.5148	0.838053	0.419026	+	0.907974i	$0.362372\pi$
$224$	0	0
$225$	−4.17209	−0.278139
$226$	−20.5318	−1.36575
$227$	−10.8546	−0.720447	−0.360224	−	0.932866i	$-0.617300\pi$
$227$	−10.8546	−0.720447	−0.360224	+	0.932866i	$0.617300\pi$
$228$	−1.00000	−0.0662266
$229$	−12.4812	−0.824780	−0.412390	−	0.911007i	$-0.635306\pi$
$229$	−12.4812	−0.824780	−0.412390	+	0.911007i	$0.635306\pi$
$230$	−2.97283	−0.196023
$231$	0	0
$232$	6.43684	0.422599
$233$	−8.60154	−0.563506	−0.281753	−	0.959487i	$-0.590916\pi$
$233$	−8.60154	−0.563506	−0.281753	+	0.959487i	$0.590916\pi$
$234$	−2.19668	−0.143601
$235$	−6.28408	−0.409928
$236$	10.0949	0.657125
$237$	−2.61901	−0.170123
$238$	0	0
$239$	−17.0673	−1.10399	−0.551995	−	0.833847i	$-0.686133\pi$
$239$	−17.0673	−1.10399	−0.551995	+	0.833847i	$0.686133\pi$
$240$	−0.909895	−0.0587335
$241$	6.26777	0.403742	0.201871	−	0.979412i	$-0.435298\pi$
$241$	6.26777	0.403742	0.201871	+	0.979412i	$0.435298\pi$
$242$	−16.5891	−1.06639
$243$	−1.00000	−0.0641500
$244$	11.1158	0.711616
$245$	0	0
$246$	−10.0810	−0.642738
$247$	2.19668	0.139771
$248$	−3.73832	−0.237384
$249$	12.2304	0.775072
$250$	8.34564	0.527824
$251$	6.91849	0.436691	0.218346	−	0.975872i	$-0.429934\pi$
$251$	6.91849	0.436691	0.218346	+	0.975872i	$0.429934\pi$
$252$	0	0
$253$	−17.1612	−1.07892
$254$	−18.4820	−1.15966
$255$	5.10306	0.319566
$256$	1.00000	0.0625000
$257$	18.2194	1.13649	0.568247	−	0.822858i	$-0.307622\pi$
$257$	18.2194	1.13649	0.568247	+	0.822858i	$0.307622\pi$
$258$	4.34366	0.270425
$259$	0	0
$260$	1.99875	0.123957
$261$	−6.43684	−0.398430
$262$	−16.0744	−0.993077
$263$	21.1288	1.30285	0.651427	−	0.758711i	$-0.274170\pi$
$263$	21.1288	1.30285	0.651427	+	0.758711i	$0.274170\pi$
$264$	−5.25253	−0.323271
$265$	10.0422	0.616885
$266$	0	0
$267$	2.33093	0.142651
$268$	−6.67896	−0.407982
$269$	−29.9548	−1.82638	−0.913188	−	0.407539i	$-0.866387\pi$
$269$	−29.9548	−1.82638	−0.913188	+	0.407539i	$0.866387\pi$
$270$	0.909895	0.0553744
$271$	16.1310	0.979890	0.489945	−	0.871753i	$-0.337017\pi$
$271$	16.1310	0.979890	0.489945	+	0.871753i	$0.337017\pi$
$272$	−5.60841	−0.340060
$273$	0	0
$274$	2.54882	0.153980
$275$	21.9140	1.32147
$276$	−3.26723	−0.196664
$277$	13.9595	0.838743	0.419371	−	0.907815i	$-0.362251\pi$
$277$	13.9595	0.838743	0.419371	+	0.907815i	$0.362251\pi$
$278$	−0.805534	−0.0483127
$279$	3.73832	0.223807
$280$	0	0
$281$	−15.9320	−0.950424	−0.475212	−	0.879871i	$-0.657629\pi$
$281$	−15.9320	−0.950424	−0.475212	+	0.879871i	$0.657629\pi$
$282$	−6.90638	−0.411269
$283$	25.1782	1.49669	0.748345	−	0.663310i	$-0.230849\pi$
$283$	25.1782	1.49669	0.748345	+	0.663310i	$0.230849\pi$
$284$	2.99136	0.177505
$285$	−0.909895	−0.0538975
$286$	11.5381	0.682264
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	14.4543	0.850251
$290$	5.85684	0.343926
$291$	−2.52513	−0.148026
$292$	−0.424104	−0.0248188
$293$	19.5096	1.13976	0.569882	−	0.821727i	$-0.306989\pi$
$293$	19.5096	1.13976	0.569882	+	0.821727i	$0.306989\pi$
$294$	0	0
$295$	9.18534	0.534791
$296$	−0.423880	−0.0246375
$297$	5.25253	0.304783
$298$	−10.0376	−0.581461
$299$	7.17706	0.415060
$300$	4.17209	0.240876
$301$	0	0
$302$	−10.3688	−0.596660
$303$	−7.96378	−0.457507
$304$	1.00000	0.0573539
$305$	10.1142	0.579138
$306$	5.60841	0.320611
$307$	−16.8281	−0.960433	−0.480216	−	0.877150i	$-0.659442\pi$
$307$	−16.8281	−0.960433	−0.480216	+	0.877150i	$0.659442\pi$
$308$	0	0
$309$	7.75665	0.441260
$310$	−3.40148	−0.193191
$311$	14.7944	0.838913	0.419457	−	0.907775i	$-0.362221\pi$
$311$	14.7944	0.838913	0.419457	+	0.907775i	$0.362221\pi$
$312$	2.19668	0.124363
$313$	7.94059	0.448829	0.224414	−	0.974494i	$-0.427953\pi$
$313$	7.94059	0.448829	0.224414	+	0.974494i	$0.427953\pi$
$314$	−5.36246	−0.302621
$315$	0	0
$316$	2.61901	0.147331
$317$	−22.3068	−1.25288	−0.626439	−	0.779471i	$-0.715488\pi$
$317$	−22.3068	−1.25288	−0.626439	+	0.779471i	$0.715488\pi$
$318$	11.0366	0.618902
$319$	33.8097	1.89298
$320$	0.909895	0.0508647
$321$	−12.7164	−0.709762
$322$	0	0
$323$	−5.60841	−0.312060
$324$	1.00000	0.0555556
$325$	−9.16475	−0.508369
$326$	−7.51576	−0.416259
$327$	7.23152	0.399904
$328$	10.0810	0.556628
$329$	0	0
$330$	−4.77925	−0.263089
$331$	−14.1885	−0.779873	−0.389936	−	0.920842i	$-0.627503\pi$
$331$	−14.1885	−0.779873	−0.389936	+	0.920842i	$0.627503\pi$
$332$	−12.2304	−0.671232
$333$	0.423880	0.0232285
$334$	20.4853	1.12090
$335$	−6.07715	−0.332030
$336$	0	0
$337$	28.8873	1.57359	0.786795	−	0.617214i	$-0.211739\pi$
$337$	28.8873	1.57359	0.786795	+	0.617214i	$0.211739\pi$
$338$	8.17460	0.444639
$339$	−20.5318	−1.11513
$340$	−5.10306	−0.276752
$341$	−19.6357	−1.06333
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−4.34366	−0.234195
$345$	−2.97283	−0.160052
$346$	7.80706	0.419710
$347$	27.5555	1.47926	0.739630	−	0.673014i	$-0.235001\pi$
$347$	27.5555	1.47926	0.739630	+	0.673014i	$0.235001\pi$
$348$	6.43684	0.345051
$349$	−2.01524	−0.107873	−0.0539366	−	0.998544i	$-0.517177\pi$
$349$	−2.01524	−0.107873	−0.0539366	+	0.998544i	$0.517177\pi$
$350$	0	0
$351$	−2.19668	−0.117250
$352$	5.25253	0.279961
$353$	−26.8368	−1.42838	−0.714189	−	0.699953i	$-0.753204\pi$
$353$	−26.8368	−1.42838	−0.714189	+	0.699953i	$0.753204\pi$
$354$	10.0949	0.536540
$355$	2.72182	0.144459
$356$	−2.33093	−0.123539
$357$	0	0
$358$	14.3548	0.758673
$359$	28.3197	1.49465	0.747327	−	0.664456i	$-0.231337\pi$
$359$	28.3197	1.49465	0.747327	+	0.664456i	$0.231337\pi$
$360$	−0.909895	−0.0479557
$361$	1.00000	0.0526316
$362$	10.2728	0.539925
$363$	−16.5891	−0.870701
$364$	0	0
$365$	−0.385890	−0.0201984
$366$	11.1158	0.581032
$367$	0.545730	0.0284869	0.0142434	−	0.999899i	$-0.495466\pi$
$367$	0.545730	0.0284869	0.0142434	+	0.999899i	$0.495466\pi$
$368$	3.26723	0.170316
$369$	−10.0810	−0.524794
$370$	−0.385686	−0.0200509
$371$	0	0
$372$	−3.73832	−0.193823
$373$	−15.5751	−0.806448	−0.403224	−	0.915101i	$-0.632110\pi$
$373$	−15.5751	−0.806448	−0.403224	+	0.915101i	$0.632110\pi$
$374$	−29.4583	−1.52325
$375$	8.34564	0.430967
$376$	6.90638	0.356170
$377$	−14.1397	−0.728230
$378$	0	0
$379$	28.7592	1.47726	0.738631	−	0.674110i	$-0.235473\pi$
$379$	28.7592	1.47726	0.738631	+	0.674110i	$0.235473\pi$
$380$	0.909895	0.0466766
$381$	−18.4820	−0.946861
$382$	−21.8896	−1.11997
$383$	6.34418	0.324173	0.162086	−	0.986777i	$-0.448178\pi$
$383$	6.34418	0.324173	0.162086	+	0.986777i	$0.448178\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	17.1533	0.873079
$387$	4.34366	0.220801
$388$	2.52513	0.128194
$389$	−5.81268	−0.294715	−0.147357	−	0.989083i	$-0.547077\pi$
$389$	−5.81268	−0.294715	−0.147357	+	0.989083i	$0.547077\pi$
$390$	1.99875	0.101211
$391$	−18.3240	−0.926683
$392$	0	0
$393$	−16.0744	−0.810844
$394$	−10.2387	−0.515818
$395$	2.38303	0.119903
$396$	−5.25253	−0.263950
$397$	−2.79095	−0.140074	−0.0700368	−	0.997544i	$-0.522312\pi$
$397$	−2.79095	−0.140074	−0.0700368	+	0.997544i	$0.522312\pi$
$398$	25.6583	1.28614
$399$	0	0
$400$	−4.17209	−0.208605
$401$	27.1083	1.35372	0.676861	−	0.736111i	$-0.263340\pi$
$401$	27.1083	1.35372	0.676861	+	0.736111i	$0.263340\pi$
$402$	−6.67896	−0.333116
$403$	8.21190	0.409064
$404$	7.96378	0.396213
$405$	0.909895	0.0452130
$406$	0	0
$407$	−2.22644	−0.110361
$408$	−5.60841	−0.277658
$409$	22.3511	1.10519	0.552594	−	0.833450i	$-0.313638\pi$
$409$	22.3511	1.10519	0.552594	+	0.833450i	$0.313638\pi$
$410$	9.17261	0.453003
$411$	2.54882	0.125724
$412$	−7.75665	−0.382143
$413$	0	0
$414$	−3.26723	−0.160576
$415$	−11.1284	−0.546272
$416$	−2.19668	−0.107701
$417$	−0.805534	−0.0394472
$418$	5.25253	0.256910
$419$	29.7948	1.45557	0.727785	−	0.685806i	$-0.240550\pi$
$419$	29.7948	1.45557	0.727785	+	0.685806i	$0.240550\pi$
$420$	0	0
$421$	−14.7934	−0.720986	−0.360493	−	0.932762i	$-0.617391\pi$
$421$	−14.7934	−0.720986	−0.360493	+	0.932762i	$0.617391\pi$
$422$	−24.8257	−1.20849
$423$	−6.90638	−0.335800
$424$	−11.0366	−0.535985
$425$	23.3988	1.13501
$426$	2.99136	0.144932
$427$	0	0
$428$	12.7164	0.614672
$429$	11.5381	0.557066
$430$	−3.95228	−0.190596
$431$	−12.8741	−0.620125	−0.310062	−	0.950716i	$-0.600350\pi$
$431$	−12.8741	−0.620125	−0.310062	+	0.950716i	$0.600350\pi$
$432$	−1.00000	−0.0481125
$433$	−21.0627	−1.01221	−0.506104	−	0.862473i	$-0.668915\pi$
$433$	−21.0627	−1.01221	−0.506104	+	0.862473i	$0.668915\pi$
$434$	0	0
$435$	5.85684	0.280814
$436$	−7.23152	−0.346327
$437$	3.26723	0.156293
$438$	−0.424104	−0.0202645
$439$	−4.82968	−0.230508	−0.115254	−	0.993336i	$-0.536768\pi$
$439$	−4.82968	−0.230508	−0.115254	+	0.993336i	$0.536768\pi$
$440$	4.77925	0.227842
$441$	0	0
$442$	12.3199	0.585997
$443$	29.9867	1.42471	0.712355	−	0.701819i	$-0.247629\pi$
$443$	29.9867	1.42471	0.712355	+	0.701819i	$0.247629\pi$
$444$	−0.423880	−0.0201164
$445$	−2.12090	−0.100540
$446$	−12.5148	−0.592593
$447$	−10.0376	−0.474761
$448$	0	0
$449$	2.81963	0.133067	0.0665333	−	0.997784i	$-0.478806\pi$
$449$	2.81963	0.133067	0.0665333	+	0.997784i	$0.478806\pi$
$450$	4.17209	0.196674
$451$	52.9505	2.49334
$452$	20.5318	0.965734
$453$	−10.3688	−0.487171
$454$	10.8546	0.509433
$455$	0	0
$456$	1.00000	0.0468293
$457$	9.65685	0.451729	0.225864	−	0.974159i	$-0.427479\pi$
$457$	9.65685	0.451729	0.225864	+	0.974159i	$0.427479\pi$
$458$	12.4812	0.583208
$459$	5.60841	0.261778
$460$	2.97283	0.138609
$461$	17.9124	0.834265	0.417132	−	0.908846i	$-0.363035\pi$
$461$	17.9124	0.834265	0.417132	+	0.908846i	$0.363035\pi$
$462$	0	0
$463$	29.5269	1.37223	0.686115	−	0.727493i	$-0.259315\pi$
$463$	29.5269	1.37223	0.686115	+	0.727493i	$0.259315\pi$
$464$	−6.43684	−0.298823
$465$	−3.40148	−0.157740
$466$	8.60154	0.398459
$467$	−1.24653	−0.0576827	−0.0288413	−	0.999584i	$-0.509182\pi$
$467$	−1.24653	−0.0576827	−0.0288413	+	0.999584i	$0.509182\pi$
$468$	2.19668	0.101542
$469$	0	0
$470$	6.28408	0.289863
$471$	−5.36246	−0.247089
$472$	−10.0949	−0.464657
$473$	−22.8152	−1.04905
$474$	2.61901	0.120295
$475$	−4.17209	−0.191429
$476$	0	0
$477$	11.0366	0.505332
$478$	17.0673	0.780639
$479$	36.5072	1.66806	0.834028	−	0.551722i	$-0.186029\pi$
$479$	36.5072	1.66806	0.834028	+	0.551722i	$0.186029\pi$
$480$	0.909895	0.0415308
$481$	0.931128	0.0424558
$482$	−6.26777	−0.285489
$483$	0	0
$484$	16.5891	0.754049
$485$	2.29760	0.104329
$486$	1.00000	0.0453609
$487$	23.4927	1.06456	0.532278	−	0.846570i	$-0.321336\pi$
$487$	23.4927	1.06456	0.532278	+	0.846570i	$0.321336\pi$
$488$	−11.1158	−0.503189
$489$	−7.51576	−0.339874
$490$	0	0
$491$	21.1246	0.953339	0.476670	−	0.879082i	$-0.341844\pi$
$491$	21.1246	0.953339	0.476670	+	0.879082i	$0.341844\pi$
$492$	10.0810	0.454485
$493$	36.1004	1.62588
$494$	−2.19668	−0.0988333
$495$	−4.77925	−0.214811
$496$	3.73832	0.167856
$497$	0	0
$498$	−12.2304	−0.548058
$499$	7.59400	0.339954	0.169977	−	0.985448i	$-0.445631\pi$
$499$	7.59400	0.339954	0.169977	+	0.985448i	$0.445631\pi$
$500$	−8.34564	−0.373228
$501$	20.4853	0.915215
$502$	−6.91849	−0.308787
$503$	20.8787	0.930935	0.465467	−	0.885065i	$-0.345886\pi$
$503$	20.8787	0.930935	0.465467	+	0.885065i	$0.345886\pi$
$504$	0	0
$505$	7.24620	0.322452
$506$	17.1612	0.762909
$507$	8.17460	0.363047
$508$	18.4820	0.820006
$509$	−23.2748	−1.03164	−0.515819	−	0.856698i	$-0.672512\pi$
$509$	−23.2748	−1.03164	−0.515819	+	0.856698i	$0.672512\pi$
$510$	−5.10306	−0.225967
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−18.2194	−0.803622
$515$	−7.05773	−0.311001
$516$	−4.34366	−0.191219
$517$	36.2760	1.59542
$518$	0	0
$519$	7.80706	0.342692
$520$	−1.99875	−0.0876509
$521$	24.1137	1.05644	0.528220	−	0.849108i	$-0.322860\pi$
$521$	24.1137	1.05644	0.528220	+	0.849108i	$0.322860\pi$
$522$	6.43684	0.281733
$523$	−6.71147	−0.293472	−0.146736	−	0.989176i	$-0.546877\pi$
$523$	−6.71147	−0.293472	−0.146736	+	0.989176i	$0.546877\pi$
$524$	16.0744	0.702212
$525$	0	0
$526$	−21.1288	−0.921258
$527$	−20.9660	−0.913295
$528$	5.25253	0.228587
$529$	−12.3252	−0.535879
$530$	−10.0422	−0.436203
$531$	10.0949	0.438083
$532$	0	0
$533$	−22.1446	−0.959191
$534$	−2.33093	−0.100869
$535$	11.5706	0.500242
$536$	6.67896	0.288487
$537$	14.3548	0.619454
$538$	29.9548	1.29144
$539$	0	0
$540$	−0.909895	−0.0391556
$541$	23.9857	1.03122	0.515612	−	0.856822i	$-0.327565\pi$
$541$	23.9857	1.03122	0.515612	+	0.856822i	$0.327565\pi$
$542$	−16.1310	−0.692887
$543$	10.2728	0.440847
$544$	5.60841	0.240459
$545$	−6.57992	−0.281853
$546$	0	0
$547$	3.53710	0.151235	0.0756177	−	0.997137i	$-0.475907\pi$
$547$	3.53710	0.151235	0.0756177	+	0.997137i	$0.475907\pi$
$548$	−2.54882	−0.108880
$549$	11.1158	0.474411
$550$	−21.9140	−0.934418
$551$	−6.43684	−0.274219
$552$	3.26723	0.139063
$553$	0	0
$554$	−13.9595	−0.593081
$555$	−0.385686	−0.0163715
$556$	0.805534	0.0341623
$557$	−16.3370	−0.692223	−0.346111	−	0.938193i	$-0.612498\pi$
$557$	−16.3370	−0.692223	−0.346111	+	0.938193i	$0.612498\pi$
$558$	−3.73832	−0.158256
$559$	9.54164	0.403568
$560$	0	0
$561$	−29.4583	−1.24373
$562$	15.9320	0.672051
$563$	−9.30822	−0.392295	−0.196147	−	0.980574i	$-0.562843\pi$
$563$	−9.30822	−0.392295	−0.196147	+	0.980574i	$0.562843\pi$
$564$	6.90638	0.290811
$565$	18.6818	0.785948
$566$	−25.1782	−1.05832
$567$	0	0
$568$	−2.99136	−0.125515
$569$	35.5994	1.49241	0.746203	−	0.665718i	$-0.231875\pi$
$569$	35.5994	1.49241	0.746203	+	0.665718i	$0.231875\pi$
$570$	0.909895	0.0381113
$571$	11.0381	0.461932	0.230966	−	0.972962i	$-0.425811\pi$
$571$	11.0381	0.461932	0.230966	+	0.972962i	$0.425811\pi$
$572$	−11.5381	−0.482433
$573$	−21.8896	−0.914449
$574$	0	0
$575$	−13.6312	−0.568459
$576$	1.00000	0.0416667
$577$	−7.94371	−0.330701	−0.165350	−	0.986235i	$-0.552876\pi$
$577$	−7.94371	−0.330701	−0.165350	+	0.986235i	$0.552876\pi$
$578$	−14.4543	−0.601218
$579$	17.1533	0.712866
$580$	−5.85684	−0.243192
$581$	0	0
$582$	2.52513	0.104670
$583$	−57.9701	−2.40088
$584$	0.424104	0.0175495
$585$	1.99875	0.0826380
$586$	−19.5096	−0.805934
$587$	−16.0857	−0.663930	−0.331965	−	0.943292i	$-0.607712\pi$
$587$	−16.0857	−0.663930	−0.331965	+	0.943292i	$0.607712\pi$
$588$	0	0
$589$	3.73832	0.154035
$590$	−9.18534	−0.378154
$591$	−10.2387	−0.421164
$592$	0.423880	0.0174214
$593$	−39.0374	−1.60307	−0.801536	−	0.597946i	$-0.795984\pi$
$593$	−39.0374	−1.60307	−0.801536	+	0.597946i	$0.795984\pi$
$594$	−5.25253	−0.215514
$595$	0	0
$596$	10.0376	0.411155
$597$	25.6583	1.05013
$598$	−7.17706	−0.293492
$599$	3.26654	0.133467	0.0667335	−	0.997771i	$-0.478742\pi$
$599$	3.26654	0.133467	0.0667335	+	0.997771i	$0.478742\pi$
$600$	−4.17209	−0.170325
$601$	32.0779	1.30848	0.654242	−	0.756285i	$-0.272988\pi$
$601$	32.0779	1.30848	0.654242	+	0.756285i	$0.272988\pi$
$602$	0	0
$603$	−6.67896	−0.271988
$604$	10.3688	0.421902
$605$	15.0943	0.613671
$606$	7.96378	0.323506
$607$	29.9235	1.21456	0.607279	−	0.794488i	$-0.292261\pi$
$607$	29.9235	1.21456	0.607279	+	0.794488i	$0.292261\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−10.1142	−0.409512
$611$	−15.1711	−0.613758
$612$	−5.60841	−0.226707
$613$	−8.45912	−0.341661	−0.170830	−	0.985300i	$-0.554645\pi$
$613$	−8.45912	−0.341661	−0.170830	+	0.985300i	$0.554645\pi$
$614$	16.8281	0.679129
$615$	9.17261	0.369875
$616$	0	0
$617$	−5.92608	−0.238575	−0.119287	−	0.992860i	$-0.538061\pi$
$617$	−5.92608	−0.238575	−0.119287	+	0.992860i	$0.538061\pi$
$618$	−7.75665	−0.312018
$619$	15.1281	0.608049	0.304025	−	0.952664i	$-0.401669\pi$
$619$	15.1281	0.608049	0.304025	+	0.952664i	$0.401669\pi$
$620$	3.40148	0.136607
$621$	−3.26723	−0.131109
$622$	−14.7944	−0.593201
$623$	0	0
$624$	−2.19668	−0.0879376
$625$	13.2668	0.530672
$626$	−7.94059	−0.317370
$627$	5.25253	0.209766
$628$	5.36246	0.213985
$629$	−2.37729	−0.0947888
$630$	0	0
$631$	15.7132	0.625534	0.312767	−	0.949830i	$-0.398744\pi$
$631$	15.7132	0.625534	0.312767	+	0.949830i	$0.398744\pi$
$632$	−2.61901	−0.104179
$633$	−24.8257	−0.986731
$634$	22.3068	0.885918
$635$	16.8167	0.667349
$636$	−11.0366	−0.437630
$637$	0	0
$638$	−33.8097	−1.33854
$639$	2.99136	0.118336
$640$	−0.909895	−0.0359667
$641$	−1.89621	−0.0748956	−0.0374478	−	0.999299i	$-0.511923\pi$
$641$	−1.89621	−0.0748956	−0.0374478	+	0.999299i	$0.511923\pi$
$642$	12.7164	0.501878
$643$	7.53707	0.297233	0.148617	−	0.988895i	$-0.452518\pi$
$643$	7.53707	0.297233	0.148617	+	0.988895i	$0.452518\pi$
$644$	0	0
$645$	−3.95228	−0.155621
$646$	5.60841	0.220660
$647$	−32.8775	−1.29255	−0.646275	−	0.763105i	$-0.723674\pi$
$647$	−32.8775	−1.29255	−0.646275	+	0.763105i	$0.723674\pi$
$648$	−1.00000	−0.0392837
$649$	−53.0240	−2.08137
$650$	9.16475	0.359471
$651$	0	0
$652$	7.51576	0.294340
$653$	−34.9655	−1.36831	−0.684154	−	0.729338i	$-0.739828\pi$
$653$	−34.9655	−1.36831	−0.684154	+	0.729338i	$0.739828\pi$
$654$	−7.23152	−0.282775
$655$	14.6260	0.571484
$656$	−10.0810	−0.393595
$657$	−0.424104	−0.0165459
$658$	0	0
$659$	3.66251	0.142671	0.0713355	−	0.997452i	$-0.477274\pi$
$659$	3.66251	0.142671	0.0713355	+	0.997452i	$0.477274\pi$
$660$	4.77925	0.186032
$661$	−12.8830	−0.501091	−0.250545	−	0.968105i	$-0.580610\pi$
$661$	−12.8830	−0.501091	−0.250545	+	0.968105i	$0.580610\pi$
$662$	14.1885	0.551453
$663$	12.3199	0.478465
$664$	12.2304	0.474633
$665$	0	0
$666$	−0.423880	−0.0164250
$667$	−21.0306	−0.814309
$668$	−20.4853	−0.792599
$669$	−12.5148	−0.483850
$670$	6.07715	0.234781
$671$	−58.3861	−2.25397
$672$	0	0
$673$	51.1559	1.97191	0.985957	−	0.166998i	$-0.0534072\pi$
$673$	51.1559	1.97191	0.985957	+	0.166998i	$0.0534072\pi$
$674$	−28.8873	−1.11270
$675$	4.17209	0.160584
$676$	−8.17460	−0.314408
$677$	−26.9589	−1.03611	−0.518057	−	0.855346i	$-0.673344\pi$
$677$	−26.9589	−1.03611	−0.518057	+	0.855346i	$0.673344\pi$
$678$	20.5318	0.788518
$679$	0	0
$680$	5.10306	0.195694
$681$	10.8546	0.415950
$682$	19.6357	0.751888
$683$	−38.8806	−1.48773	−0.743863	−	0.668332i	$-0.767009\pi$
$683$	−38.8806	−1.48773	−0.743863	+	0.668332i	$0.767009\pi$
$684$	1.00000	0.0382360
$685$	−2.31916	−0.0886106
$686$	0	0
$687$	12.4812	0.476187
$688$	4.34366	0.165601
$689$	24.2439	0.923619
$690$	2.97283	0.113174
$691$	40.5900	1.54412	0.772058	−	0.635552i	$-0.219228\pi$
$691$	40.5900	1.54412	0.772058	+	0.635552i	$0.219228\pi$
$692$	−7.80706	−0.296780
$693$	0	0
$694$	−27.5555	−1.04599
$695$	0.732952	0.0278024
$696$	−6.43684	−0.243988
$697$	56.5382	2.14154
$698$	2.01524	0.0762779
$699$	8.60154	0.325340
$700$	0	0
$701$	27.4695	1.03751	0.518755	−	0.854923i	$-0.326396\pi$
$701$	27.4695	1.03751	0.518755	+	0.854923i	$0.326396\pi$
$702$	2.19668	0.0829084
$703$	0.423880	0.0159869
$704$	−5.25253	−0.197962
$705$	6.28408	0.236672
$706$	26.8368	1.01002
$707$	0	0
$708$	−10.0949	−0.379391
$709$	−33.1779	−1.24602	−0.623011	−	0.782213i	$-0.714091\pi$
$709$	−33.1779	−1.24602	−0.623011	+	0.782213i	$0.714091\pi$
$710$	−2.72182	−0.102148
$711$	2.61901	0.0982207
$712$	2.33093	0.0873553
$713$	12.2140	0.457416
$714$	0	0
$715$	−10.4985	−0.392621
$716$	−14.3548	−0.536463
$717$	17.0673	0.637389
$718$	−28.3197	−1.05688
$719$	−10.0340	−0.374205	−0.187102	−	0.982340i	$-0.559910\pi$
$719$	−10.0340	−0.374205	−0.187102	+	0.982340i	$0.559910\pi$
$720$	0.909895	0.0339098
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−6.26777	−0.233101
$724$	−10.2728	−0.381785
$725$	26.8551	0.997373
$726$	16.5891	0.615678
$727$	−0.934714	−0.0346666	−0.0173333	−	0.999850i	$-0.505518\pi$
$727$	−0.934714	−0.0346666	−0.0173333	+	0.999850i	$0.505518\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.385890	0.0142824
$731$	−24.3611	−0.901026
$732$	−11.1158	−0.410852
$733$	−7.71908	−0.285111	−0.142555	−	0.989787i	$-0.545532\pi$
$733$	−7.71908	−0.285111	−0.142555	+	0.989787i	$0.545532\pi$
$734$	−0.545730	−0.0201433
$735$	0	0
$736$	−3.26723	−0.120432
$737$	35.0814	1.29224
$738$	10.0810	0.371085
$739$	11.9693	0.440297	0.220149	−	0.975466i	$-0.429346\pi$
$739$	11.9693	0.440297	0.220149	+	0.975466i	$0.429346\pi$
$740$	0.385686	0.0141781
$741$	−2.19668	−0.0806971
$742$	0	0
$743$	27.7326	1.01741	0.508705	−	0.860941i	$-0.330124\pi$
$743$	27.7326	1.01741	0.508705	+	0.860941i	$0.330124\pi$
$744$	3.73832	0.137054
$745$	9.13313	0.334612
$746$	15.5751	0.570245
$747$	−12.2304	−0.447488
$748$	29.4583	1.07710
$749$	0	0
$750$	−8.34564	−0.304740
$751$	37.8231	1.38018	0.690092	−	0.723721i	$-0.257570\pi$
$751$	37.8231	1.38018	0.690092	+	0.723721i	$0.257570\pi$
$752$	−6.90638	−0.251850
$753$	−6.91849	−0.252124
$754$	14.1397	0.514937
$755$	9.43455	0.343358
$756$	0	0
$757$	4.14650	0.150707	0.0753536	−	0.997157i	$-0.475991\pi$
$757$	4.14650	0.150707	0.0753536	+	0.997157i	$0.475991\pi$
$758$	−28.7592	−1.04458
$759$	17.1612	0.622913
$760$	−0.909895	−0.0330054
$761$	5.94400	0.215470	0.107735	−	0.994180i	$-0.465640\pi$
$761$	5.94400	0.215470	0.107735	+	0.994180i	$0.465640\pi$
$762$	18.4820	0.669532
$763$	0	0
$764$	21.8896	0.791936
$765$	−5.10306	−0.184502
$766$	−6.34418	−0.229225
$767$	22.1754	0.800706
$768$	−1.00000	−0.0360844
$769$	12.6072	0.454628	0.227314	−	0.973822i	$-0.427006\pi$
$769$	12.6072	0.454628	0.227314	+	0.973822i	$0.427006\pi$
$770$	0	0
$771$	−18.2194	−0.656155
$772$	−17.1533	−0.617360
$773$	−7.89710	−0.284039	−0.142020	−	0.989864i	$-0.545360\pi$
$773$	−7.89710	−0.284039	−0.142020	+	0.989864i	$0.545360\pi$
$774$	−4.34366	−0.156130
$775$	−15.5966	−0.560247
$776$	−2.52513	−0.0906468
$777$	0	0
$778$	5.81268	0.208395
$779$	−10.0810	−0.361188
$780$	−1.99875	−0.0715666
$781$	−15.7122	−0.562228
$782$	18.3240	0.655264
$783$	6.43684	0.230034
$784$	0	0
$785$	4.87927	0.174149
$786$	16.0744	0.573353
$787$	−12.7246	−0.453584	−0.226792	−	0.973943i	$-0.572824\pi$
$787$	−12.7246	−0.453584	−0.226792	+	0.973943i	$0.572824\pi$
$788$	10.2387	0.364739
$789$	−21.1288	−0.752204
$790$	−2.38303	−0.0847843
$791$	0	0
$792$	5.25253	0.186641
$793$	24.4179	0.867103
$794$	2.79095	0.0990470
$795$	−10.0422	−0.356158
$796$	−25.6583	−0.909436
$797$	−24.3533	−0.862636	−0.431318	−	0.902200i	$-0.641951\pi$
$797$	−24.3533	−0.862636	−0.431318	+	0.902200i	$0.641951\pi$
$798$	0	0
$799$	38.7338	1.37030
$800$	4.17209	0.147506
$801$	−2.33093	−0.0823594
$802$	−27.1083	−0.957226
$803$	2.22762	0.0786109
$804$	6.67896	0.235549
$805$	0	0
$806$	−8.21190	−0.289252
$807$	29.9548	1.05446
$808$	−7.96378	−0.280165
$809$	0.769615	0.0270582	0.0135291	−	0.999908i	$-0.495693\pi$
$809$	0.769615	0.0270582	0.0135291	+	0.999908i	$0.495693\pi$
$810$	−0.909895	−0.0319704
$811$	16.7505	0.588191	0.294096	−	0.955776i	$-0.404982\pi$
$811$	16.7505	0.588191	0.294096	+	0.955776i	$0.404982\pi$
$812$	0	0
$813$	−16.1310	−0.565740
$814$	2.22644	0.0780367
$815$	6.83855	0.239544
$816$	5.60841	0.196334
$817$	4.34366	0.151966
$818$	−22.3511	−0.781486
$819$	0	0
$820$	−9.17261	−0.320321
$821$	52.0925	1.81804	0.909020	−	0.416753i	$-0.136832\pi$
$821$	52.0925	1.81804	0.909020	+	0.416753i	$0.136832\pi$
$822$	−2.54882	−0.0889005
$823$	−25.0076	−0.871711	−0.435855	−	0.900017i	$-0.643554\pi$
$823$	−25.0076	−0.871711	−0.435855	+	0.900017i	$0.643554\pi$
$824$	7.75665	0.270216
$825$	−21.9140	−0.762949
$826$	0	0
$827$	−54.7275	−1.90306	−0.951530	−	0.307556i	$-0.900489\pi$
$827$	−54.7275	−1.90306	−0.951530	+	0.307556i	$0.900489\pi$
$828$	3.26723	0.113544
$829$	33.2824	1.15594	0.577972	−	0.816056i	$-0.303844\pi$
$829$	33.2824	1.15594	0.577972	+	0.816056i	$0.303844\pi$
$830$	11.1284	0.386272
$831$	−13.9595	−0.484248
$832$	2.19668	0.0761562
$833$	0	0
$834$	0.805534	0.0278934
$835$	−18.6394	−0.645045
$836$	−5.25253	−0.181663
$837$	−3.73832	−0.129215
$838$	−29.7948	−1.02924
$839$	44.3112	1.52979	0.764896	−	0.644153i	$-0.222790\pi$
$839$	44.3112	1.52979	0.764896	+	0.644153i	$0.222790\pi$
$840$	0	0
$841$	12.4329	0.428720
$842$	14.7934	0.509814
$843$	15.9320	0.548728
$844$	24.8257	0.854534
$845$	−7.43802	−0.255876
$846$	6.90638	0.237446
$847$	0	0
$848$	11.0366	0.378999
$849$	−25.1782	−0.864115
$850$	−23.3988	−0.802572
$851$	1.38491	0.0474742
$852$	−2.99136	−0.102482
$853$	−15.4067	−0.527514	−0.263757	−	0.964589i	$-0.584962\pi$
$853$	−15.4067	−0.527514	−0.263757	+	0.964589i	$0.584962\pi$
$854$	0	0
$855$	0.909895	0.0311177
$856$	−12.7164	−0.434639
$857$	−40.0528	−1.36818	−0.684089	−	0.729399i	$-0.739800\pi$
$857$	−40.0528	−1.36818	−0.684089	+	0.729399i	$0.739800\pi$
$858$	−11.5381	−0.393905
$859$	5.91862	0.201941	0.100970	−	0.994889i	$-0.467805\pi$
$859$	5.91862	0.201941	0.100970	+	0.994889i	$0.467805\pi$
$860$	3.95228	0.134772
$861$	0	0
$862$	12.8741	0.438494
$863$	5.65144	0.192377	0.0961886	−	0.995363i	$-0.469335\pi$
$863$	5.65144	0.192377	0.0961886	+	0.995363i	$0.469335\pi$
$864$	1.00000	0.0340207
$865$	−7.10360	−0.241530
$866$	21.0627	0.715739
$867$	−14.4543	−0.490893
$868$	0	0
$869$	−13.7564	−0.466655
$870$	−5.85684	−0.198566
$871$	−14.6715	−0.497126
$872$	7.23152	0.244890
$873$	2.52513	0.0854626
$874$	−3.26723	−0.110516
$875$	0	0
$876$	0.424104	0.0143291
$877$	−4.60919	−0.155641	−0.0778206	−	0.996967i	$-0.524796\pi$
$877$	−4.60919	−0.155641	−0.0778206	+	0.996967i	$0.524796\pi$
$878$	4.82968	0.162994
$879$	−19.5096	−0.658043
$880$	−4.77925	−0.161108
$881$	39.1928	1.32044	0.660220	−	0.751072i	$-0.270463\pi$
$881$	39.1928	1.32044	0.660220	+	0.751072i	$0.270463\pi$
$882$	0	0
$883$	−31.4595	−1.05870	−0.529348	−	0.848405i	$-0.677563\pi$
$883$	−31.4595	−1.05870	−0.529348	+	0.848405i	$0.677563\pi$
$884$	−12.3199	−0.414363
$885$	−9.18534	−0.308762
$886$	−29.9867	−1.00742
$887$	−8.75629	−0.294007	−0.147004	−	0.989136i	$-0.546963\pi$
$887$	−8.75629	−0.294007	−0.147004	+	0.989136i	$0.546963\pi$
$888$	0.423880	0.0142245
$889$	0	0
$890$	2.12090	0.0710928
$891$	−5.25253	−0.175966
$892$	12.5148	0.419026
$893$	−6.90638	−0.231113
$894$	10.0376	0.335707
$895$	−13.0613	−0.436592
$896$	0	0
$897$	−7.17706	−0.239635
$898$	−2.81963	−0.0940924
$899$	−24.0630	−0.802545
$900$	−4.17209	−0.139070
$901$	−61.8978	−2.06212
$902$	−52.9505	−1.76306
$903$	0	0
$904$	−20.5318	−0.682877
$905$	−9.34715	−0.310710
$906$	10.3688	0.344482
$907$	−43.2363	−1.43564	−0.717819	−	0.696230i	$-0.754859\pi$
$907$	−43.2363	−1.43564	−0.717819	+	0.696230i	$0.754859\pi$
$908$	−10.8546	−0.360224
$909$	7.96378	0.264142
$910$	0	0
$911$	13.3300	0.441642	0.220821	−	0.975314i	$-0.429126\pi$
$911$	13.3300	0.441642	0.220821	+	0.975314i	$0.429126\pi$
$912$	−1.00000	−0.0331133
$913$	64.2407	2.12606
$914$	−9.65685	−0.319420
$915$	−10.1142	−0.334365
$916$	−12.4812	−0.412390
$917$	0	0
$918$	−5.60841	−0.185105
$919$	−20.3356	−0.670811	−0.335405	−	0.942074i	$-0.608873\pi$
$919$	−20.3356	−0.670811	−0.335405	+	0.942074i	$0.608873\pi$
$920$	−2.97283	−0.0980115
$921$	16.8281	0.554506
$922$	−17.9124	−0.589914
$923$	6.57107	0.216289
$924$	0	0
$925$	−1.76847	−0.0581468
$926$	−29.5269	−0.970313
$927$	−7.75665	−0.254762
$928$	6.43684	0.211300
$929$	−33.9022	−1.11230	−0.556148	−	0.831083i	$-0.687721\pi$
$929$	−33.9022	−1.11230	−0.556148	+	0.831083i	$0.687721\pi$
$930$	3.40148	0.111539
$931$	0	0
$932$	−8.60154	−0.281753
$933$	−14.7944	−0.484347
$934$	1.24653	0.0407878
$935$	26.8040	0.876584
$936$	−2.19668	−0.0718007
$937$	50.8001	1.65957	0.829784	−	0.558084i	$-0.188463\pi$
$937$	50.8001	1.65957	0.829784	+	0.558084i	$0.188463\pi$
$938$	0	0
$939$	−7.94059	−0.259131
$940$	−6.28408	−0.204964
$941$	−7.65365	−0.249502	−0.124751	−	0.992188i	$-0.539813\pi$
$941$	−7.65365	−0.249502	−0.124751	+	0.992188i	$0.539813\pi$
$942$	5.36246	0.174718
$943$	−32.9368	−1.07257
$944$	10.0949	0.328562
$945$	0	0
$946$	22.8152	0.741787
$947$	8.55863	0.278118	0.139059	−	0.990284i	$-0.455592\pi$
$947$	8.55863	0.278118	0.139059	+	0.990284i	$0.455592\pi$
$948$	−2.61901	−0.0850616
$949$	−0.931620	−0.0302417
$950$	4.17209	0.135361
$951$	22.3068	0.723349
$952$	0	0
$953$	21.5013	0.696496	0.348248	−	0.937403i	$-0.386777\pi$
$953$	21.5013	0.696496	0.348248	+	0.937403i	$0.386777\pi$
$954$	−11.0366	−0.357323
$955$	19.9172	0.644505
$956$	−17.0673	−0.551995
$957$	−33.8097	−1.09291
$958$	−36.5072	−1.17949
$959$	0	0
$960$	−0.909895	−0.0293667
$961$	−17.0249	−0.549192
$962$	−0.931128	−0.0300208
$963$	12.7164	0.409782
$964$	6.26777	0.201871
$965$	−15.6077	−0.502429
$966$	0	0
$967$	0.185899	0.00597811	0.00298906	−	0.999996i	$-0.499049\pi$
$967$	0.185899	0.00597811	0.00298906	+	0.999996i	$0.499049\pi$
$968$	−16.5891	−0.533193
$969$	5.60841	0.180168
$970$	−2.29760	−0.0737715
$971$	−52.8131	−1.69485	−0.847427	−	0.530912i	$-0.821849\pi$
$971$	−52.8131	−1.69485	−0.847427	+	0.530912i	$0.821849\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−23.4927	−0.752754
$975$	9.16475	0.293507
$976$	11.1158	0.355808
$977$	−45.0473	−1.44119	−0.720596	−	0.693356i	$-0.756132\pi$
$977$	−45.0473	−1.44119	−0.720596	+	0.693356i	$0.756132\pi$
$978$	7.51576	0.240327
$979$	12.2433	0.391297
$980$	0	0
$981$	−7.23152	−0.230885
$982$	−21.1246	−0.674113
$983$	−44.0214	−1.40407	−0.702033	−	0.712145i	$-0.747724\pi$
$983$	−44.0214	−1.40407	−0.702033	+	0.712145i	$0.747724\pi$
$984$	−10.0810	−0.321369
$985$	9.31614	0.296837
$986$	−36.1004	−1.14967
$987$	0	0
$988$	2.19668	0.0698857
$989$	14.1917	0.451271
$990$	4.77925	0.151895
$991$	−22.0880	−0.701649	−0.350824	−	0.936441i	$-0.614099\pi$
$991$	−22.0880	−0.701649	−0.350824	+	0.936441i	$0.614099\pi$
$992$	−3.73832	−0.118692
$993$	14.1885	0.450260
$994$	0	0
$995$	−23.3464	−0.740130
$996$	12.2304	0.387536
$997$	46.3022	1.46641	0.733203	−	0.680010i	$-0.238025\pi$
$997$	46.3022	1.46641	0.733203	+	0.680010i	$0.238025\pi$
$998$	−7.59400	−0.240384
$999$	−0.423880	−0.0134110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.cc.1.4	✓	6
7.6	odd	2		5586.2.a.cd.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.cc.1.4	✓	6	1.1	even	1	trivial
5586.2.a.cd.1.3	yes	6	7.6	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.909895 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.909895 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.909895 q^{10} -5.25253 q^{11} -1.00000 q^{12} +2.19668 q^{13} -0.909895 q^{15} +1.00000 q^{16} -5.60841 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.909895 q^{20} +5.25253 q^{22} +3.26723 q^{23} +1.00000 q^{24} -4.17209 q^{25} -2.19668 q^{26} -1.00000 q^{27} -6.43684 q^{29} +0.909895 q^{30} +3.73832 q^{31} -1.00000 q^{32} +5.25253 q^{33} +5.60841 q^{34} +1.00000 q^{36} +0.423880 q^{37} -1.00000 q^{38} -2.19668 q^{39} -0.909895 q^{40} -10.0810 q^{41} +4.34366 q^{43} -5.25253 q^{44} +0.909895 q^{45} -3.26723 q^{46} -6.90638 q^{47} -1.00000 q^{48} +4.17209 q^{50} +5.60841 q^{51} +2.19668 q^{52} +11.0366 q^{53} +1.00000 q^{54} -4.77925 q^{55} -1.00000 q^{57} +6.43684 q^{58} +10.0949 q^{59} -0.909895 q^{60} +11.1158 q^{61} -3.73832 q^{62} +1.00000 q^{64} +1.99875 q^{65} -5.25253 q^{66} -6.67896 q^{67} -5.60841 q^{68} -3.26723 q^{69} +2.99136 q^{71} -1.00000 q^{72} -0.424104 q^{73} -0.423880 q^{74} +4.17209 q^{75} +1.00000 q^{76} +2.19668 q^{78} +2.61901 q^{79} +0.909895 q^{80} +1.00000 q^{81} +10.0810 q^{82} -12.2304 q^{83} -5.10306 q^{85} -4.34366 q^{86} +6.43684 q^{87} +5.25253 q^{88} -2.33093 q^{89} -0.909895 q^{90} +3.26723 q^{92} -3.73832 q^{93} +6.90638 q^{94} +0.909895 q^{95} +1.00000 q^{96} +2.52513 q^{97} -5.25253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} - 6 q^{12} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 4 q^{22} + 16 q^{23} + 6 q^{24} + 10 q^{25} - 6 q^{27} + 8 q^{29} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{38} - 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 32 q^{55} - 6 q^{57} - 8 q^{58} - 24 q^{59} + 6 q^{64} + 16 q^{65} + 4 q^{66} - 20 q^{67} - 4 q^{68} - 16 q^{69} + 24 q^{71} - 6 q^{72} + 16 q^{73} - 10 q^{75} + 6 q^{76} + 40 q^{79} + 6 q^{81} + 8 q^{82} - 24 q^{83} + 8 q^{85} - 8 q^{86} - 8 q^{87} - 4 q^{88} - 24 q^{89} + 16 q^{92} + 16 q^{94} + 6 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 - 6 * q^12 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 4 * q^22 + 16 * q^23 + 6 * q^24 + 10 * q^25 - 6 * q^27 + 8 * q^29 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^38 - 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 32 * q^55 - 6 * q^57 - 8 * q^58 - 24 * q^59 + 6 * q^64 + 16 * q^65 + 4 * q^66 - 20 * q^67 - 4 * q^68 - 16 * q^69 + 24 * q^71 - 6 * q^72 + 16 * q^73 - 10 * q^75 + 6 * q^76 + 40 * q^79 + 6 * q^81 + 8 * q^82 - 24 * q^83 + 8 * q^85 - 8 * q^86 - 8 * q^87 - 4 * q^88 - 24 * q^89 + 16 * q^92 + 16 * q^94 + 6 * q^96 + 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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