LMFDB - Embedded newform 6422.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 16x^{5} + 29x^{4} + 60x^{3} - 79x^{2} - 47x - 2 $ x^7 - 2x^6 - 16x^5 + 29x^4 + 60x^3 - 79x^2 - 47x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.29705$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.29705 q^{3} +1.00000 q^{4} -3.53833 q^{5} -3.29705 q^{6} -0.150781 q^{7} +1.00000 q^{8} +7.87054 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.29705 q^{3} +1.00000 q^{4} -3.53833 q^{5} -3.29705 q^{6} -0.150781 q^{7} +1.00000 q^{8} +7.87054 q^{9} -3.53833 q^{10} -2.38888 q^{11} -3.29705 q^{12} -0.150781 q^{14} +11.6661 q^{15} +1.00000 q^{16} +4.64914 q^{17} +7.87054 q^{18} +1.00000 q^{19} -3.53833 q^{20} +0.497134 q^{21} -2.38888 q^{22} -5.53743 q^{23} -3.29705 q^{24} +7.51979 q^{25} -16.0584 q^{27} -0.150781 q^{28} -4.48871 q^{29} +11.6661 q^{30} +5.48738 q^{31} +1.00000 q^{32} +7.87626 q^{33} +4.64914 q^{34} +0.533514 q^{35} +7.87054 q^{36} -10.9060 q^{37} +1.00000 q^{38} -3.53833 q^{40} -1.62883 q^{41} +0.497134 q^{42} +10.5431 q^{43} -2.38888 q^{44} -27.8486 q^{45} -5.53743 q^{46} -7.02837 q^{47} -3.29705 q^{48} -6.97726 q^{49} +7.51979 q^{50} -15.3284 q^{51} +2.39084 q^{53} -16.0584 q^{54} +8.45265 q^{55} -0.150781 q^{56} -3.29705 q^{57} -4.48871 q^{58} -2.86108 q^{59} +11.6661 q^{60} -4.18186 q^{61} +5.48738 q^{62} -1.18673 q^{63} +1.00000 q^{64} +7.87626 q^{66} +9.26189 q^{67} +4.64914 q^{68} +18.2572 q^{69} +0.533514 q^{70} +3.13752 q^{71} +7.87054 q^{72} -2.07937 q^{73} -10.9060 q^{74} -24.7931 q^{75} +1.00000 q^{76} +0.360199 q^{77} -5.29827 q^{79} -3.53833 q^{80} +29.3338 q^{81} -1.62883 q^{82} -12.0013 q^{83} +0.497134 q^{84} -16.4502 q^{85} +10.5431 q^{86} +14.7995 q^{87} -2.38888 q^{88} -18.8413 q^{89} -27.8486 q^{90} -5.53743 q^{92} -18.0922 q^{93} -7.02837 q^{94} -3.53833 q^{95} -3.29705 q^{96} -12.5681 q^{97} -6.97726 q^{98} -18.8018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9} + 2 q^{10} + 5 q^{11} + 2 q^{12} + q^{14} + 13 q^{15} + 7 q^{16} + 16 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} - 3 q^{21} + 5 q^{22} + 3 q^{23} + 2 q^{24} + 7 q^{25} + 5 q^{27} + q^{28} - 7 q^{29} + 13 q^{30} + 11 q^{31} + 7 q^{32} + 6 q^{33} + 16 q^{34} + q^{35} + 15 q^{36} - 3 q^{37} + 7 q^{38} + 2 q^{40} + 15 q^{41} - 3 q^{42} + 23 q^{43} + 5 q^{44} - 38 q^{45} + 3 q^{46} - q^{47} + 2 q^{48} + 14 q^{49} + 7 q^{50} - 16 q^{51} + 21 q^{53} + 5 q^{54} + 8 q^{55} + q^{56} + 2 q^{57} - 7 q^{58} + 8 q^{59} + 13 q^{60} - 6 q^{61} + 11 q^{62} - 22 q^{63} + 7 q^{64} + 6 q^{66} + 28 q^{67} + 16 q^{68} + 48 q^{69} + q^{70} + 4 q^{71} + 15 q^{72} + 12 q^{73} - 3 q^{74} + 5 q^{75} + 7 q^{76} - 26 q^{77} - 4 q^{79} + 2 q^{80} + 51 q^{81} + 15 q^{82} + 13 q^{83} - 3 q^{84} - 39 q^{85} + 23 q^{86} - 16 q^{87} + 5 q^{88} - 15 q^{89} - 38 q^{90} + 3 q^{92} + 6 q^{93} - q^{94} + 2 q^{95} + 2 q^{96} - 37 q^{97} + 14 q^{98} - 15 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9 + 2 * q^10 + 5 * q^11 + 2 * q^12 + q^14 + 13 * q^15 + 7 * q^16 + 16 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 - 3 * q^21 + 5 * q^22 + 3 * q^23 + 2 * q^24 + 7 * q^25 + 5 * q^27 + q^28 - 7 * q^29 + 13 * q^30 + 11 * q^31 + 7 * q^32 + 6 * q^33 + 16 * q^34 + q^35 + 15 * q^36 - 3 * q^37 + 7 * q^38 + 2 * q^40 + 15 * q^41 - 3 * q^42 + 23 * q^43 + 5 * q^44 - 38 * q^45 + 3 * q^46 - q^47 + 2 * q^48 + 14 * q^49 + 7 * q^50 - 16 * q^51 + 21 * q^53 + 5 * q^54 + 8 * q^55 + q^56 + 2 * q^57 - 7 * q^58 + 8 * q^59 + 13 * q^60 - 6 * q^61 + 11 * q^62 - 22 * q^63 + 7 * q^64 + 6 * q^66 + 28 * q^67 + 16 * q^68 + 48 * q^69 + q^70 + 4 * q^71 + 15 * q^72 + 12 * q^73 - 3 * q^74 + 5 * q^75 + 7 * q^76 - 26 * q^77 - 4 * q^79 + 2 * q^80 + 51 * q^81 + 15 * q^82 + 13 * q^83 - 3 * q^84 - 39 * q^85 + 23 * q^86 - 16 * q^87 + 5 * q^88 - 15 * q^89 - 38 * q^90 + 3 * q^92 + 6 * q^93 - q^94 + 2 * q^95 + 2 * q^96 - 37 * q^97 + 14 * q^98 - 15 * 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
$3$	−3.29705	−1.90355	−0.951776	−	0.306792i	$-0.900744\pi$
$3$	−3.29705	−1.90355	−0.951776	+	0.306792i	$0.900744\pi$
$4$	1.00000	0.500000
$5$	−3.53833	−1.58239	−0.791195	−	0.611564i	$-0.790541\pi$
$5$	−3.53833	−1.58239	−0.791195	+	0.611564i	$0.790541\pi$
$6$	−3.29705	−1.34602
$7$	−0.150781	−0.0569900	−0.0284950	−	0.999594i	$-0.509071\pi$
$7$	−0.150781	−0.0569900	−0.0284950	+	0.999594i	$0.509071\pi$
$8$	1.00000	0.353553
$9$	7.87054	2.62351
$10$	−3.53833	−1.11892
$11$	−2.38888	−0.720274	−0.360137	−	0.932899i	$-0.617270\pi$
$11$	−2.38888	−0.720274	−0.360137	+	0.932899i	$0.617270\pi$
$12$	−3.29705	−0.951776
$13$	0	0
$13$	0	0
$14$	−0.150781	−0.0402980
$15$	11.6661	3.01216
$16$	1.00000	0.250000
$17$	4.64914	1.12758	0.563790	−	0.825918i	$-0.309343\pi$
$17$	4.64914	1.12758	0.563790	+	0.825918i	$0.309343\pi$
$18$	7.87054	1.85510
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.53833	−0.791195
$21$	0.497134	0.108483
$22$	−2.38888	−0.509311
$23$	−5.53743	−1.15463	−0.577317	−	0.816520i	$-0.695900\pi$
$23$	−5.53743	−1.15463	−0.577317	+	0.816520i	$0.695900\pi$
$24$	−3.29705	−0.673008
$25$	7.51979	1.50396
$26$	0	0
$27$	−16.0584	−3.09044
$28$	−0.150781	−0.0284950
$29$	−4.48871	−0.833532	−0.416766	−	0.909014i	$-0.636837\pi$
$29$	−4.48871	−0.833532	−0.416766	+	0.909014i	$0.636837\pi$
$30$	11.6661	2.12992
$31$	5.48738	0.985562	0.492781	−	0.870153i	$-0.335980\pi$
$31$	5.48738	0.985562	0.492781	+	0.870153i	$0.335980\pi$
$32$	1.00000	0.176777
$33$	7.87626	1.37108
$34$	4.64914	0.797320
$35$	0.533514	0.0901804
$36$	7.87054	1.31176
$37$	−10.9060	−1.79294	−0.896468	−	0.443108i	$-0.853876\pi$
$37$	−10.9060	−1.79294	−0.896468	+	0.443108i	$0.853876\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−3.53833	−0.559459
$41$	−1.62883	−0.254381	−0.127190	−	0.991878i	$-0.540596\pi$
$41$	−1.62883	−0.254381	−0.127190	+	0.991878i	$0.540596\pi$
$42$	0.497134	0.0767094
$43$	10.5431	1.60781	0.803907	−	0.594754i	$-0.202751\pi$
$43$	10.5431	1.60781	0.803907	+	0.594754i	$0.202751\pi$
$44$	−2.38888	−0.360137
$45$	−27.8486	−4.15142
$46$	−5.53743	−0.816450
$47$	−7.02837	−1.02519	−0.512597	−	0.858630i	$-0.671316\pi$
$47$	−7.02837	−1.02519	−0.512597	+	0.858630i	$0.671316\pi$
$48$	−3.29705	−0.475888
$49$	−6.97726	−0.996752
$50$	7.51979	1.06346
$51$	−15.3284	−2.14641
$52$	0	0
$53$	2.39084	0.328407	0.164204	−	0.986426i	$-0.447495\pi$
$53$	2.39084	0.328407	0.164204	+	0.986426i	$0.447495\pi$
$54$	−16.0584	−2.18527
$55$	8.45265	1.13975
$56$	−0.150781	−0.0201490
$57$	−3.29705	−0.436705
$58$	−4.48871	−0.589396
$59$	−2.86108	−0.372481	−0.186241	−	0.982504i	$-0.559630\pi$
$59$	−2.86108	−0.372481	−0.186241	+	0.982504i	$0.559630\pi$
$60$	11.6661	1.50608
$61$	−4.18186	−0.535432	−0.267716	−	0.963498i	$-0.586269\pi$
$61$	−4.18186	−0.535432	−0.267716	+	0.963498i	$0.586269\pi$
$62$	5.48738	0.696898
$63$	−1.18673	−0.149514
$64$	1.00000	0.125000
$65$	0	0
$66$	7.87626	0.969500
$67$	9.26189	1.13152	0.565760	−	0.824570i	$-0.308583\pi$
$67$	9.26189	1.13152	0.565760	+	0.824570i	$0.308583\pi$
$68$	4.64914	0.563790
$69$	18.2572	2.19791
$70$	0.533514	0.0637672
$71$	3.13752	0.372355	0.186178	−	0.982516i	$-0.440390\pi$
$71$	3.13752	0.372355	0.186178	+	0.982516i	$0.440390\pi$
$72$	7.87054	0.927552
$73$	−2.07937	−0.243372	−0.121686	−	0.992569i	$-0.538830\pi$
$73$	−2.07937	−0.243372	−0.121686	+	0.992569i	$0.538830\pi$
$74$	−10.9060	−1.26780
$75$	−24.7931	−2.86286
$76$	1.00000	0.114708
$77$	0.360199	0.0410484
$78$	0	0
$79$	−5.29827	−0.596102	−0.298051	−	0.954550i	$-0.596337\pi$
$79$	−5.29827	−0.596102	−0.298051	+	0.954550i	$0.596337\pi$
$80$	−3.53833	−0.395597
$81$	29.3338	3.25931
$82$	−1.62883	−0.179874
$83$	−12.0013	−1.31732	−0.658658	−	0.752442i	$-0.728876\pi$
$83$	−12.0013	−1.31732	−0.658658	+	0.752442i	$0.728876\pi$
$84$	0.497134	0.0542417
$85$	−16.4502	−1.78427
$86$	10.5431	1.13690
$87$	14.7995	1.58667
$88$	−2.38888	−0.254655
$89$	−18.8413	−1.99718	−0.998588	−	0.0531164i	$-0.983085\pi$
$89$	−18.8413	−1.99718	−0.998588	+	0.0531164i	$0.983085\pi$
$90$	−27.8486	−2.93550
$91$	0	0
$92$	−5.53743	−0.577317
$93$	−18.0922	−1.87607
$94$	−7.02837	−0.724921
$95$	−3.53833	−0.363025
$96$	−3.29705	−0.336504
$97$	−12.5681	−1.27610	−0.638048	−	0.769997i	$-0.720258\pi$
$97$	−12.5681	−1.27610	−0.638048	+	0.769997i	$0.720258\pi$
$98$	−6.97726	−0.704810
$99$	−18.8018	−1.88965
$100$	7.51979	0.751979
$101$	−8.78739	−0.874378	−0.437189	−	0.899370i	$-0.644026\pi$
$101$	−8.78739	−0.874378	−0.437189	+	0.899370i	$0.644026\pi$
$102$	−15.3284	−1.51774
$103$	12.1560	1.19776	0.598882	−	0.800837i	$-0.295612\pi$
$103$	12.1560	1.19776	0.598882	+	0.800837i	$0.295612\pi$
$104$	0	0
$105$	−1.75902	−0.171663
$106$	2.39084	0.232219
$107$	3.42816	0.331413	0.165706	−	0.986175i	$-0.447010\pi$
$107$	3.42816	0.331413	0.165706	+	0.986175i	$0.447010\pi$
$108$	−16.0584	−1.54522
$109$	−4.98056	−0.477051	−0.238525	−	0.971136i	$-0.576664\pi$
$109$	−4.98056	−0.477051	−0.238525	+	0.971136i	$0.576664\pi$
$110$	8.45265	0.805928
$111$	35.9577	3.41295
$112$	−0.150781	−0.0142475
$113$	4.29254	0.403808	0.201904	−	0.979405i	$-0.435287\pi$
$113$	4.29254	0.403808	0.201904	+	0.979405i	$0.435287\pi$
$114$	−3.29705	−0.308797
$115$	19.5933	1.82708
$116$	−4.48871	−0.416766
$117$	0	0
$118$	−2.86108	−0.263384
$119$	−0.701003	−0.0642608
$120$	11.6661	1.06496
$121$	−5.29325	−0.481205
$122$	−4.18186	−0.378608
$123$	5.37034	0.484227
$124$	5.48738	0.492781
$125$	−8.91584	−0.797457
$126$	−1.18673	−0.105722
$127$	18.5562	1.64659	0.823296	−	0.567612i	$-0.192133\pi$
$127$	18.5562	1.64659	0.823296	+	0.567612i	$0.192133\pi$
$128$	1.00000	0.0883883
$129$	−34.7613	−3.06056
$130$	0	0
$131$	6.91047	0.603770	0.301885	−	0.953344i	$-0.402384\pi$
$131$	6.91047	0.603770	0.301885	+	0.953344i	$0.402384\pi$
$132$	7.87626	0.685540
$133$	−0.150781	−0.0130744
$134$	9.26189	0.800105
$135$	56.8200	4.89029
$136$	4.64914	0.398660
$137$	6.09803	0.520990	0.260495	−	0.965475i	$-0.416114\pi$
$137$	6.09803	0.520990	0.260495	+	0.965475i	$0.416114\pi$
$138$	18.2572	1.55416
$139$	−11.5019	−0.975579	−0.487789	−	0.872961i	$-0.662197\pi$
$139$	−11.5019	−0.975579	−0.487789	+	0.872961i	$0.662197\pi$
$140$	0.533514	0.0450902
$141$	23.1729	1.95151
$142$	3.13752	0.263295
$143$	0	0
$144$	7.87054	0.655879
$145$	15.8825	1.31897
$146$	−2.07937	−0.172090
$147$	23.0044	1.89737
$148$	−10.9060	−0.896468
$149$	2.14754	0.175934	0.0879668	−	0.996123i	$-0.471963\pi$
$149$	2.14754	0.175934	0.0879668	+	0.996123i	$0.471963\pi$
$150$	−24.7931	−2.02435
$151$	11.1518	0.907524	0.453762	−	0.891123i	$-0.350082\pi$
$151$	11.1518	0.907524	0.453762	+	0.891123i	$0.350082\pi$
$152$	1.00000	0.0811107
$153$	36.5912	2.95822
$154$	0.360199	0.0290256
$155$	−19.4162	−1.55954
$156$	0	0
$157$	−13.4492	−1.07336	−0.536680	−	0.843786i	$-0.680322\pi$
$157$	−13.4492	−1.07336	−0.536680	+	0.843786i	$0.680322\pi$
$158$	−5.29827	−0.421508
$159$	−7.88273	−0.625141
$160$	−3.53833	−0.279730
$161$	0.834942	0.0658026
$162$	29.3338	2.30468
$163$	−0.853731	−0.0668694	−0.0334347	−	0.999441i	$-0.510645\pi$
$163$	−0.853731	−0.0668694	−0.0334347	+	0.999441i	$0.510645\pi$
$164$	−1.62883	−0.127190
$165$	−27.8688	−2.16958
$166$	−12.0013	−0.931483
$167$	6.29325	0.486986	0.243493	−	0.969903i	$-0.421707\pi$
$167$	6.29325	0.486986	0.243493	+	0.969903i	$0.421707\pi$
$168$	0.497134	0.0383547
$169$	0	0
$170$	−16.4502	−1.26167
$171$	7.87054	0.601875
$172$	10.5431	0.803907
$173$	−8.41116	−0.639488	−0.319744	−	0.947504i	$-0.603597\pi$
$173$	−8.41116	−0.639488	−0.319744	+	0.947504i	$0.603597\pi$
$174$	14.7995	1.12195
$175$	−1.13384	−0.0857105
$176$	−2.38888	−0.180069
$177$	9.43313	0.709038
$178$	−18.8413	−1.41222
$179$	10.2337	0.764902	0.382451	−	0.923976i	$-0.375080\pi$
$179$	10.2337	0.764902	0.382451	+	0.923976i	$0.375080\pi$
$180$	−27.8486	−2.07571
$181$	14.0040	1.04091	0.520454	−	0.853890i	$-0.325763\pi$
$181$	14.0040	1.04091	0.520454	+	0.853890i	$0.325763\pi$
$182$	0	0
$183$	13.7878	1.01922
$184$	−5.53743	−0.408225
$185$	38.5891	2.83712
$186$	−18.0922	−1.32658
$187$	−11.1062	−0.812168
$188$	−7.02837	−0.512597
$189$	2.42131	0.176124
$190$	−3.53833	−0.256698
$191$	5.05349	0.365658	0.182829	−	0.983145i	$-0.441475\pi$
$191$	5.05349	0.365658	0.182829	+	0.983145i	$0.441475\pi$
$192$	−3.29705	−0.237944
$193$	12.1526	0.874764	0.437382	−	0.899276i	$-0.355906\pi$
$193$	12.1526	0.874764	0.437382	+	0.899276i	$0.355906\pi$
$194$	−12.5681	−0.902336
$195$	0	0
$196$	−6.97726	−0.498376
$197$	8.00854	0.570585	0.285293	−	0.958440i	$-0.407909\pi$
$197$	8.00854	0.570585	0.285293	+	0.958440i	$0.407909\pi$
$198$	−18.8018	−1.33618
$199$	17.3501	1.22991	0.614957	−	0.788561i	$-0.289173\pi$
$199$	17.3501	1.22991	0.614957	+	0.788561i	$0.289173\pi$
$200$	7.51979	0.531729
$201$	−30.5369	−2.15391
$202$	−8.78739	−0.618279
$203$	0.676814	0.0475030
$204$	−15.3284	−1.07321
$205$	5.76334	0.402529
$206$	12.1560	0.846948
$207$	−43.5826	−3.02920
$208$	0	0
$209$	−2.38888	−0.165242
$210$	−1.75902	−0.121384
$211$	−7.54866	−0.519671	−0.259836	−	0.965653i	$-0.583668\pi$
$211$	−7.54866	−0.519671	−0.259836	+	0.965653i	$0.583668\pi$
$212$	2.39084	0.164204
$213$	−10.3446	−0.708798
$214$	3.42816	0.234344
$215$	−37.3051	−2.54419
$216$	−16.0584	−1.09264
$217$	−0.827394	−0.0561672
$218$	−4.98056	−0.337326
$219$	6.85579	0.463272
$220$	8.45265	0.569877
$221$	0	0
$222$	35.9577	2.41332
$223$	28.7643	1.92620	0.963099	−	0.269146i	$-0.0867415\pi$
$223$	28.7643	1.92620	0.963099	+	0.269146i	$0.0867415\pi$
$224$	−0.150781	−0.0100745
$225$	59.1848	3.94565
$226$	4.29254	0.285535
$227$	−1.92833	−0.127988	−0.0639939	−	0.997950i	$-0.520384\pi$
$227$	−1.92833	−0.127988	−0.0639939	+	0.997950i	$0.520384\pi$
$228$	−3.29705	−0.218353
$229$	17.3072	1.14369	0.571845	−	0.820361i	$-0.306228\pi$
$229$	17.3072	1.14369	0.571845	+	0.820361i	$0.306228\pi$
$230$	19.5933	1.29194
$231$	−1.18759	−0.0781379
$232$	−4.48871	−0.294698
$233$	23.2739	1.52472	0.762362	−	0.647150i	$-0.224039\pi$
$233$	23.2739	1.52472	0.762362	+	0.647150i	$0.224039\pi$
$234$	0	0
$235$	24.8687	1.62226
$236$	−2.86108	−0.186241
$237$	17.4687	1.13471
$238$	−0.701003	−0.0454393
$239$	14.6296	0.946313	0.473156	−	0.880978i	$-0.343115\pi$
$239$	14.6296	0.946313	0.473156	+	0.880978i	$0.343115\pi$
$240$	11.6661	0.753041
$241$	14.5700	0.938534	0.469267	−	0.883056i	$-0.344518\pi$
$241$	14.5700	0.938534	0.469267	+	0.883056i	$0.344518\pi$
$242$	−5.29325	−0.340263
$243$	−48.5398	−3.11383
$244$	−4.18186	−0.267716
$245$	24.6879	1.57725
$246$	5.37034	0.342400
$247$	0	0
$248$	5.48738	0.348449
$249$	39.5690	2.50758
$250$	−8.91584	−0.563887
$251$	−22.4809	−1.41898	−0.709491	−	0.704715i	$-0.751075\pi$
$251$	−22.4809	−1.41898	−0.709491	+	0.704715i	$0.751075\pi$
$252$	−1.18673	−0.0747570
$253$	13.2283	0.831654
$254$	18.5562	1.16432
$255$	54.2371	3.39646
$256$	1.00000	0.0625000
$257$	6.16163	0.384352	0.192176	−	0.981360i	$-0.438446\pi$
$257$	6.16163	0.384352	0.192176	+	0.981360i	$0.438446\pi$
$258$	−34.7613	−2.16414
$259$	1.64442	0.102179
$260$	0	0
$261$	−35.3286	−2.18678
$262$	6.91047	0.426930
$263$	−11.3849	−0.702021	−0.351011	−	0.936372i	$-0.614162\pi$
$263$	−11.3849	−0.702021	−0.351011	+	0.936372i	$0.614162\pi$
$264$	7.87626	0.484750
$265$	−8.45959	−0.519668
$266$	−0.150781	−0.00924500
$267$	62.1208	3.80173
$268$	9.26189	0.565760
$269$	1.99978	0.121929	0.0609644	−	0.998140i	$-0.480582\pi$
$269$	1.99978	0.121929	0.0609644	+	0.998140i	$0.480582\pi$
$270$	56.8200	3.45796
$271$	−23.7845	−1.44480	−0.722401	−	0.691474i	$-0.756962\pi$
$271$	−23.7845	−1.44480	−0.722401	+	0.691474i	$0.756962\pi$
$272$	4.64914	0.281895
$273$	0	0
$274$	6.09803	0.368395
$275$	−17.9639	−1.08326
$276$	18.2572	1.09895
$277$	1.25069	0.0751465	0.0375733	−	0.999294i	$-0.488037\pi$
$277$	1.25069	0.0751465	0.0375733	+	0.999294i	$0.488037\pi$
$278$	−11.5019	−0.689839
$279$	43.1886	2.58564
$280$	0.533514	0.0318836
$281$	−27.4423	−1.63707	−0.818536	−	0.574455i	$-0.805214\pi$
$281$	−27.4423	−1.63707	−0.818536	+	0.574455i	$0.805214\pi$
$282$	23.1729	1.37993
$283$	20.5950	1.22424	0.612122	−	0.790764i	$-0.290316\pi$
$283$	20.5950	1.22424	0.612122	+	0.790764i	$0.290316\pi$
$284$	3.13752	0.186178
$285$	11.6661	0.691038
$286$	0	0
$287$	0.245597	0.0144971
$288$	7.87054	0.463776
$289$	4.61446	0.271439
$290$	15.8825	0.932655
$291$	41.4376	2.42911
$292$	−2.07937	−0.121686
$293$	−9.00761	−0.526230	−0.263115	−	0.964764i	$-0.584750\pi$
$293$	−9.00761	−0.526230	−0.263115	+	0.964764i	$0.584750\pi$
$294$	23.0044	1.34164
$295$	10.1235	0.589410
$296$	−10.9060	−0.633899
$297$	38.3616	2.22597
$298$	2.14754	0.124404
$299$	0	0
$300$	−24.7931	−1.43143
$301$	−1.58971	−0.0916294
$302$	11.1518	0.641716
$303$	28.9725	1.66443
$304$	1.00000	0.0573539
$305$	14.7968	0.847263
$306$	36.5912	2.09178
$307$	5.40794	0.308647	0.154324	−	0.988020i	$-0.450680\pi$
$307$	5.40794	0.308647	0.154324	+	0.988020i	$0.450680\pi$
$308$	0.360199	0.0205242
$309$	−40.0789	−2.28001
$310$	−19.4162	−1.10276
$311$	9.55248	0.541672	0.270836	−	0.962626i	$-0.412700\pi$
$311$	9.55248	0.541672	0.270836	+	0.962626i	$0.412700\pi$
$312$	0	0
$313$	15.7527	0.890397	0.445198	−	0.895432i	$-0.353133\pi$
$313$	15.7527	0.890397	0.445198	+	0.895432i	$0.353133\pi$
$314$	−13.4492	−0.758980
$315$	4.19905	0.236590
$316$	−5.29827	−0.298051
$317$	−3.14485	−0.176632	−0.0883161	−	0.996092i	$-0.528149\pi$
$317$	−3.14485	−0.176632	−0.0883161	+	0.996092i	$0.528149\pi$
$318$	−7.88273	−0.442041
$319$	10.7230	0.600372
$320$	−3.53833	−0.197799
$321$	−11.3028	−0.630862
$322$	0.834942	0.0465295
$323$	4.64914	0.258685
$324$	29.3338	1.62966
$325$	0	0
$326$	−0.853731	−0.0472838
$327$	16.4211	0.908092
$328$	−1.62883	−0.0899371
$329$	1.05975	0.0584258
$330$	−27.8688	−1.53413
$331$	−0.269421	−0.0148087	−0.00740436	−	0.999973i	$-0.502357\pi$
$331$	−0.269421	−0.0148087	−0.00740436	+	0.999973i	$0.502357\pi$
$332$	−12.0013	−0.658658
$333$	−85.8362	−4.70379
$334$	6.29325	0.344351
$335$	−32.7716	−1.79051
$336$	0.497134	0.0271209
$337$	2.80206	0.152638	0.0763191	−	0.997083i	$-0.475683\pi$
$337$	2.80206	0.152638	0.0763191	+	0.997083i	$0.475683\pi$
$338$	0	0
$339$	−14.1527	−0.768670
$340$	−16.4502	−0.892136
$341$	−13.1087	−0.709875
$342$	7.87054	0.425590
$343$	2.10751	0.113795
$344$	10.5431	0.568448
$345$	−64.6000	−3.47795
$346$	−8.41116	−0.452187
$347$	26.5610	1.42587	0.712935	−	0.701231i	$-0.247366\pi$
$347$	26.5610	1.42587	0.712935	+	0.701231i	$0.247366\pi$
$348$	14.7995	0.793336
$349$	−12.9895	−0.695311	−0.347656	−	0.937622i	$-0.613022\pi$
$349$	−12.9895	−0.695311	−0.347656	+	0.937622i	$0.613022\pi$
$350$	−1.13384	−0.0606065
$351$	0	0
$352$	−2.38888	−0.127328
$353$	−12.7132	−0.676656	−0.338328	−	0.941028i	$-0.609861\pi$
$353$	−12.7132	−0.676656	−0.338328	+	0.941028i	$0.609861\pi$
$354$	9.43313	0.501365
$355$	−11.1016	−0.589211
$356$	−18.8413	−0.998588
$357$	2.31124	0.122324
$358$	10.2337	0.540868
$359$	−1.98013	−0.104507	−0.0522535	−	0.998634i	$-0.516640\pi$
$359$	−1.98013	−0.104507	−0.0522535	+	0.998634i	$0.516640\pi$
$360$	−27.8486	−1.46775
$361$	1.00000	0.0526316
$362$	14.0040	0.736033
$363$	17.4521	0.915999
$364$	0	0
$365$	7.35751	0.385109
$366$	13.7878	0.720700
$367$	−30.9704	−1.61664	−0.808321	−	0.588742i	$-0.799623\pi$
$367$	−30.9704	−1.61664	−0.808321	+	0.588742i	$0.799623\pi$
$368$	−5.53743	−0.288659
$369$	−12.8198	−0.667371
$370$	38.5891	2.00615
$371$	−0.360494	−0.0187159
$372$	−18.0922	−0.938035
$373$	18.5731	0.961681	0.480840	−	0.876808i	$-0.340332\pi$
$373$	18.5731	0.961681	0.480840	+	0.876808i	$0.340332\pi$
$374$	−11.1062	−0.574289
$375$	29.3960	1.51800
$376$	−7.02837	−0.362460
$377$	0	0
$378$	2.42131	0.124539
$379$	19.3298	0.992903	0.496451	−	0.868064i	$-0.334636\pi$
$379$	19.3298	0.992903	0.496451	+	0.868064i	$0.334636\pi$
$380$	−3.53833	−0.181513
$381$	−61.1806	−3.13438
$382$	5.05349	0.258559
$383$	−18.9244	−0.966991	−0.483496	−	0.875347i	$-0.660633\pi$
$383$	−18.9244	−0.966991	−0.483496	+	0.875347i	$0.660633\pi$
$384$	−3.29705	−0.168252
$385$	−1.27450	−0.0649546
$386$	12.1526	0.618552
$387$	82.9803	4.21813
$388$	−12.5681	−0.638048
$389$	30.1046	1.52636	0.763181	−	0.646185i	$-0.223637\pi$
$389$	30.1046	1.52636	0.763181	+	0.646185i	$0.223637\pi$
$390$	0	0
$391$	−25.7443	−1.30194
$392$	−6.97726	−0.352405
$393$	−22.7842	−1.14931
$394$	8.00854	0.403465
$395$	18.7470	0.943266
$396$	−18.8018	−0.944825
$397$	−19.7312	−0.990279	−0.495140	−	0.868813i	$-0.664883\pi$
$397$	−19.7312	−0.990279	−0.495140	+	0.868813i	$0.664883\pi$
$398$	17.3501	0.869680
$399$	0.497134	0.0248878
$400$	7.51979	0.375989
$401$	38.5836	1.92677	0.963386	−	0.268119i	$-0.0864021\pi$
$401$	38.5836	1.92677	0.963386	+	0.268119i	$0.0864021\pi$
$402$	−30.5369	−1.52304
$403$	0	0
$404$	−8.78739	−0.437189
$405$	−103.793	−5.15750
$406$	0.676814	0.0335897
$407$	26.0531	1.29141
$408$	−15.3284	−0.758871
$409$	2.63015	0.130052	0.0650262	−	0.997884i	$-0.479287\pi$
$409$	2.63015	0.130052	0.0650262	+	0.997884i	$0.479287\pi$
$410$	5.76334	0.284631
$411$	−20.1055	−0.991732
$412$	12.1560	0.598882
$413$	0.431398	0.0212277
$414$	−43.5826	−2.14197
$415$	42.4647	2.08451
$416$	0	0
$417$	37.9224	1.85707
$418$	−2.38888	−0.116844
$419$	−21.0823	−1.02994	−0.514970	−	0.857208i	$-0.672197\pi$
$419$	−21.0823	−1.02994	−0.514970	+	0.857208i	$0.672197\pi$
$420$	−1.75902	−0.0858316
$421$	−29.9487	−1.45961	−0.729806	−	0.683654i	$-0.760390\pi$
$421$	−29.9487	−1.45961	−0.729806	+	0.683654i	$0.760390\pi$
$422$	−7.54866	−0.367463
$423$	−55.3171	−2.68961
$424$	2.39084	0.116110
$425$	34.9605	1.69583
$426$	−10.3446	−0.501196
$427$	0.630547	0.0305143
$428$	3.42816	0.165706
$429$	0	0
$430$	−37.3051	−1.79901
$431$	−28.3577	−1.36594	−0.682971	−	0.730446i	$-0.739312\pi$
$431$	−28.3577	−1.36594	−0.682971	+	0.730446i	$0.739312\pi$
$432$	−16.0584	−0.772611
$433$	−26.4624	−1.27170	−0.635851	−	0.771812i	$-0.719351\pi$
$433$	−26.4624	−1.27170	−0.635851	+	0.771812i	$0.719351\pi$
$434$	−0.827394	−0.0397162
$435$	−52.3655	−2.51073
$436$	−4.98056	−0.238525
$437$	−5.53743	−0.264891
$438$	6.85579	0.327582
$439$	2.22341	0.106117	0.0530587	−	0.998591i	$-0.483103\pi$
$439$	2.22341	0.106117	0.0530587	+	0.998591i	$0.483103\pi$
$440$	8.45265	0.402964
$441$	−54.9149	−2.61499
$442$	0	0
$443$	17.6039	0.836387	0.418194	−	0.908358i	$-0.362663\pi$
$443$	17.6039	0.836387	0.418194	+	0.908358i	$0.362663\pi$
$444$	35.9577	1.70647
$445$	66.6669	3.16031
$446$	28.7643	1.36203
$447$	−7.08056	−0.334899
$448$	−0.150781	−0.00712375
$449$	27.8127	1.31256	0.656282	−	0.754516i	$-0.272128\pi$
$449$	27.8127	1.31256	0.656282	+	0.754516i	$0.272128\pi$
$450$	59.1848	2.79000
$451$	3.89108	0.183224
$452$	4.29254	0.201904
$453$	−36.7682	−1.72752
$454$	−1.92833	−0.0905010
$455$	0	0
$456$	−3.29705	−0.154399
$457$	33.2600	1.55584	0.777918	−	0.628366i	$-0.216276\pi$
$457$	33.2600	1.55584	0.777918	+	0.628366i	$0.216276\pi$
$458$	17.3072	0.808711
$459$	−74.6578	−3.48473
$460$	19.5933	0.913541
$461$	19.6577	0.915553	0.457776	−	0.889067i	$-0.348646\pi$
$461$	19.6577	0.915553	0.457776	+	0.889067i	$0.348646\pi$
$462$	−1.18759	−0.0552518
$463$	−9.51924	−0.442396	−0.221198	−	0.975229i	$-0.570997\pi$
$463$	−9.51924	−0.442396	−0.221198	+	0.975229i	$0.570997\pi$
$464$	−4.48871	−0.208383
$465$	64.0161	2.96867
$466$	23.2739	1.07814
$467$	−3.59653	−0.166428	−0.0832138	−	0.996532i	$-0.526518\pi$
$467$	−3.59653	−0.166428	−0.0832138	+	0.996532i	$0.526518\pi$
$468$	0	0
$469$	−1.39652	−0.0644853
$470$	24.8687	1.14711
$471$	44.3425	2.04320
$472$	−2.86108	−0.131692
$473$	−25.1863	−1.15807
$474$	17.4687	0.802362
$475$	7.51979	0.345032
$476$	−0.701003	−0.0321304
$477$	18.8172	0.861581
$478$	14.6296	0.669144
$479$	28.3976	1.29752	0.648759	−	0.760994i	$-0.275288\pi$
$479$	28.3976	1.29752	0.648759	+	0.760994i	$0.275288\pi$
$480$	11.6661	0.532480
$481$	0	0
$482$	14.5700	0.663644
$483$	−2.75284	−0.125259
$484$	−5.29325	−0.240602
$485$	44.4700	2.01928
$486$	−48.5398	−2.20181
$487$	−32.9147	−1.49151	−0.745754	−	0.666222i	$-0.767910\pi$
$487$	−32.9147	−1.49151	−0.745754	+	0.666222i	$0.767910\pi$
$488$	−4.18186	−0.189304
$489$	2.81479	0.127289
$490$	24.6879	1.11528
$491$	0.282195	0.0127353	0.00636764	−	0.999980i	$-0.497973\pi$
$491$	0.282195	0.0127353	0.00636764	+	0.999980i	$0.497973\pi$
$492$	5.37034	0.242113
$493$	−20.8686	−0.939875
$494$	0	0
$495$	66.5269	2.99016
$496$	5.48738	0.246391
$497$	−0.473080	−0.0212205
$498$	39.5690	1.77313
$499$	−29.4739	−1.31944	−0.659718	−	0.751514i	$-0.729324\pi$
$499$	−29.4739	−1.31944	−0.659718	+	0.751514i	$0.729324\pi$
$500$	−8.91584	−0.398729
$501$	−20.7492	−0.927005
$502$	−22.4809	−1.00337
$503$	−0.929384	−0.0414392	−0.0207196	−	0.999785i	$-0.506596\pi$
$503$	−0.929384	−0.0414392	−0.0207196	+	0.999785i	$0.506596\pi$
$504$	−1.18673	−0.0528612
$505$	31.0927	1.38361
$506$	13.2283	0.588068
$507$	0	0
$508$	18.5562	0.823296
$509$	−10.8326	−0.480145	−0.240072	−	0.970755i	$-0.577171\pi$
$509$	−10.8326	−0.480145	−0.240072	+	0.970755i	$0.577171\pi$
$510$	54.2371	2.40166
$511$	0.313531	0.0138698
$512$	1.00000	0.0441942
$513$	−16.0584	−0.708997
$514$	6.16163	0.271778
$515$	−43.0119	−1.89533
$516$	−34.7613	−1.53028
$517$	16.7899	0.738420
$518$	1.64442	0.0722518
$519$	27.7320	1.21730
$520$	0	0
$521$	−14.6684	−0.642634	−0.321317	−	0.946972i	$-0.604126\pi$
$521$	−14.6684	−0.642634	−0.321317	+	0.946972i	$0.604126\pi$
$522$	−35.3286	−1.54629
$523$	44.7432	1.95648	0.978241	−	0.207471i	$-0.0665234\pi$
$523$	44.7432	1.95648	0.978241	+	0.207471i	$0.0665234\pi$
$524$	6.91047	0.301885
$525$	3.73834	0.163155
$526$	−11.3849	−0.496404
$527$	25.5116	1.11130
$528$	7.87626	0.342770
$529$	7.66315	0.333181
$530$	−8.45959	−0.367461
$531$	−22.5183	−0.977209
$532$	−0.150781	−0.00653720
$533$	0	0
$534$	62.1208	2.68823
$535$	−12.1300	−0.524424
$536$	9.26189	0.400053
$537$	−33.7410	−1.45603
$538$	1.99978	0.0862166
$539$	16.6678	0.717935
$540$	56.8200	2.44514
$541$	3.61109	0.155253	0.0776265	−	0.996983i	$-0.475266\pi$
$541$	3.61109	0.155253	0.0776265	+	0.996983i	$0.475266\pi$
$542$	−23.7845	−1.02163
$543$	−46.1718	−1.98142
$544$	4.64914	0.199330
$545$	17.6229	0.754880
$546$	0	0
$547$	24.1186	1.03124	0.515618	−	0.856819i	$-0.327563\pi$
$547$	24.1186	1.03124	0.515618	+	0.856819i	$0.327563\pi$
$548$	6.09803	0.260495
$549$	−32.9135	−1.40471
$550$	−17.9639	−0.765982
$551$	−4.48871	−0.191225
$552$	18.2572	0.777078
$553$	0.798880	0.0339719
$554$	1.25069	0.0531366
$555$	−127.230	−5.40062
$556$	−11.5019	−0.487789
$557$	0.381806	0.0161777	0.00808883	−	0.999967i	$-0.497425\pi$
$557$	0.381806	0.0161777	0.00808883	+	0.999967i	$0.497425\pi$
$558$	43.1886	1.82832
$559$	0	0
$560$	0.533514	0.0225451
$561$	36.6178	1.54600
$562$	−27.4423	−1.15758
$563$	13.4387	0.566372	0.283186	−	0.959065i	$-0.408609\pi$
$563$	13.4387	0.566372	0.283186	+	0.959065i	$0.408609\pi$
$564$	23.1729	0.975755
$565$	−15.1884	−0.638982
$566$	20.5950	0.865671
$567$	−4.42299	−0.185748
$568$	3.13752	0.131648
$569$	26.7295	1.12056	0.560278	−	0.828304i	$-0.310694\pi$
$569$	26.7295	1.12056	0.560278	+	0.828304i	$0.310694\pi$
$570$	11.6661	0.488637
$571$	23.7707	0.994774	0.497387	−	0.867529i	$-0.334293\pi$
$571$	23.7707	0.994774	0.497387	+	0.867529i	$0.334293\pi$
$572$	0	0
$573$	−16.6616	−0.696049
$574$	0.245597	0.0102510
$575$	−41.6403	−1.73652
$576$	7.87054	0.327939
$577$	43.6306	1.81636	0.908182	−	0.418575i	$-0.137470\pi$
$577$	43.6306	1.81636	0.908182	+	0.418575i	$0.137470\pi$
$578$	4.61446	0.191936
$579$	−40.0678	−1.66516
$580$	15.8825	0.659486
$581$	1.80958	0.0750739
$582$	41.4376	1.71764
$583$	−5.71143	−0.236543
$584$	−2.07937	−0.0860450
$585$	0	0
$586$	−9.00761	−0.372101
$587$	4.46031	0.184097	0.0920483	−	0.995755i	$-0.470659\pi$
$587$	4.46031	0.184097	0.0920483	+	0.995755i	$0.470659\pi$
$588$	23.0044	0.948685
$589$	5.48738	0.226103
$590$	10.1235	0.416776
$591$	−26.4046	−1.08614
$592$	−10.9060	−0.448234
$593$	−13.3387	−0.547753	−0.273877	−	0.961765i	$-0.588306\pi$
$593$	−13.3387	−0.547753	−0.273877	+	0.961765i	$0.588306\pi$
$594$	38.3616	1.57400
$595$	2.48038	0.101686
$596$	2.14754	0.0879668
$597$	−57.2041	−2.34121
$598$	0	0
$599$	37.0831	1.51517	0.757587	−	0.652734i	$-0.226378\pi$
$599$	37.0831	1.51517	0.757587	+	0.652734i	$0.226378\pi$
$600$	−24.7931	−1.01217
$601$	−10.1680	−0.414761	−0.207381	−	0.978260i	$-0.566494\pi$
$601$	−10.1680	−0.414761	−0.207381	+	0.978260i	$0.566494\pi$
$602$	−1.58971	−0.0647918
$603$	72.8961	2.96856
$604$	11.1518	0.453762
$605$	18.7293	0.761453
$606$	28.9725	1.17693
$607$	22.2624	0.903601	0.451800	−	0.892119i	$-0.350782\pi$
$607$	22.2624	0.903601	0.451800	+	0.892119i	$0.350782\pi$
$608$	1.00000	0.0405554
$609$	−2.23149	−0.0904245
$610$	14.7968	0.599105
$611$	0	0
$612$	36.5912	1.47911
$613$	−27.2117	−1.09907	−0.549535	−	0.835471i	$-0.685195\pi$
$613$	−27.2117	−1.09907	−0.549535	+	0.835471i	$0.685195\pi$
$614$	5.40794	0.218247
$615$	−19.0020	−0.766236
$616$	0.360199	0.0145128
$617$	40.4879	1.62998	0.814992	−	0.579473i	$-0.196741\pi$
$617$	40.4879	1.62998	0.814992	+	0.579473i	$0.196741\pi$
$618$	−40.0789	−1.61221
$619$	−1.63008	−0.0655183	−0.0327591	−	0.999463i	$-0.510429\pi$
$619$	−1.63008	−0.0655183	−0.0327591	+	0.999463i	$0.510429\pi$
$620$	−19.4162	−0.779772
$621$	88.9224	3.56833
$622$	9.55248	0.383020
$623$	2.84092	0.113819
$624$	0	0
$625$	−6.05173	−0.242069
$626$	15.7527	0.629605
$627$	7.87626	0.314547
$628$	−13.4492	−0.536680
$629$	−50.7035	−2.02168
$630$	4.19905	0.167294
$631$	1.05111	0.0418439	0.0209220	−	0.999781i	$-0.493340\pi$
$631$	1.05111	0.0418439	0.0209220	+	0.999781i	$0.493340\pi$
$632$	−5.29827	−0.210754
$633$	24.8883	0.989222
$634$	−3.14485	−0.124898
$635$	−65.6578	−2.60555
$636$	−7.88273	−0.312570
$637$	0	0
$638$	10.7230	0.424527
$639$	24.6940	0.976880
$640$	−3.53833	−0.139865
$641$	−18.0793	−0.714091	−0.357045	−	0.934087i	$-0.616216\pi$
$641$	−18.0793	−0.714091	−0.357045	+	0.934087i	$0.616216\pi$
$642$	−11.3028	−0.446087
$643$	10.2623	0.404705	0.202352	−	0.979313i	$-0.435141\pi$
$643$	10.2623	0.404705	0.202352	+	0.979313i	$0.435141\pi$
$644$	0.834942	0.0329013
$645$	122.997	4.84300
$646$	4.64914	0.182918
$647$	−3.53071	−0.138807	−0.0694033	−	0.997589i	$-0.522110\pi$
$647$	−3.53071	−0.138807	−0.0694033	+	0.997589i	$0.522110\pi$
$648$	29.3338	1.15234
$649$	6.83478	0.268289
$650$	0	0
$651$	2.72796	0.106917
$652$	−0.853731	−0.0334347
$653$	−10.1156	−0.395855	−0.197928	−	0.980217i	$-0.563421\pi$
$653$	−10.1156	−0.395855	−0.197928	+	0.980217i	$0.563421\pi$
$654$	16.4211	0.642118
$655$	−24.4515	−0.955400
$656$	−1.62883	−0.0635951
$657$	−16.3658	−0.638490
$658$	1.05975	0.0413132
$659$	−17.5458	−0.683486	−0.341743	−	0.939794i	$-0.611017\pi$
$659$	−17.5458	−0.683486	−0.341743	+	0.939794i	$0.611017\pi$
$660$	−27.8688	−1.08479
$661$	−14.0163	−0.545171	−0.272586	−	0.962132i	$-0.587879\pi$
$661$	−14.0163	−0.545171	−0.272586	+	0.962132i	$0.587879\pi$
$662$	−0.269421	−0.0104714
$663$	0	0
$664$	−12.0013	−0.465742
$665$	0.533514	0.0206888
$666$	−85.8362	−3.32608
$667$	24.8559	0.962425
$668$	6.29325	0.243493
$669$	−94.8373	−3.66662
$670$	−32.7716	−1.26608
$671$	9.98996	0.385658
$672$	0.497134	0.0191774
$673$	31.1907	1.20231	0.601157	−	0.799131i	$-0.294707\pi$
$673$	31.1907	1.20231	0.601157	+	0.799131i	$0.294707\pi$
$674$	2.80206	0.107931
$675$	−120.756	−4.64790
$676$	0	0
$677$	13.2383	0.508789	0.254394	−	0.967101i	$-0.418124\pi$
$677$	13.2383	0.508789	0.254394	+	0.967101i	$0.418124\pi$
$678$	−14.1527	−0.543532
$679$	1.89503	0.0727247
$680$	−16.4502	−0.630836
$681$	6.35780	0.243632
$682$	−13.1087	−0.501958
$683$	−11.3659	−0.434905	−0.217453	−	0.976071i	$-0.569775\pi$
$683$	−11.3659	−0.434905	−0.217453	+	0.976071i	$0.569775\pi$
$684$	7.87054	0.300938
$685$	−21.5768	−0.824409
$686$	2.10751	0.0804651
$687$	−57.0626	−2.17708
$688$	10.5431	0.401954
$689$	0	0
$690$	−64.6000	−2.45928
$691$	37.7882	1.43753	0.718765	−	0.695253i	$-0.244708\pi$
$691$	37.7882	1.43753	0.718765	+	0.695253i	$0.244708\pi$
$692$	−8.41116	−0.319744
$693$	2.83496	0.107691
$694$	26.5610	1.00824
$695$	40.6976	1.54375
$696$	14.7995	0.560974
$697$	−7.57265	−0.286835
$698$	−12.9895	−0.491659
$699$	−76.7353	−2.90239
$700$	−1.13384	−0.0428553
$701$	−29.1278	−1.10014	−0.550070	−	0.835118i	$-0.685399\pi$
$701$	−29.1278	−1.10014	−0.550070	+	0.835118i	$0.685399\pi$
$702$	0	0
$703$	−10.9060	−0.411328
$704$	−2.38888	−0.0900343
$705$	−81.9934	−3.08805
$706$	−12.7132	−0.478468
$707$	1.32498	0.0498308
$708$	9.43313	0.354519
$709$	−45.5773	−1.71169	−0.855846	−	0.517230i	$-0.826963\pi$
$709$	−45.5773	−1.71169	−0.855846	+	0.517230i	$0.826963\pi$
$710$	−11.1016	−0.416635
$711$	−41.7003	−1.56388
$712$	−18.8413	−0.706109
$713$	−30.3860	−1.13796
$714$	2.31124	0.0864961
$715$	0	0
$716$	10.2337	0.382451
$717$	−48.2347	−1.80136
$718$	−1.98013	−0.0738976
$719$	1.91188	0.0713012	0.0356506	−	0.999364i	$-0.488650\pi$
$719$	1.91188	0.0713012	0.0356506	+	0.999364i	$0.488650\pi$
$720$	−27.8486	−1.03786
$721$	−1.83290	−0.0682606
$722$	1.00000	0.0372161
$723$	−48.0379	−1.78655
$724$	14.0040	0.520454
$725$	−33.7541	−1.25360
$726$	17.4521	0.647709
$727$	27.5738	1.02265	0.511327	−	0.859386i	$-0.329154\pi$
$727$	27.5738	1.02265	0.511327	+	0.859386i	$0.329154\pi$
$728$	0	0
$729$	72.0367	2.66802
$730$	7.35751	0.272314
$731$	49.0165	1.81294
$732$	13.7878	0.509612
$733$	47.5901	1.75778	0.878890	−	0.477025i	$-0.158285\pi$
$733$	47.5901	1.75778	0.878890	+	0.477025i	$0.158285\pi$
$734$	−30.9704	−1.14314
$735$	−81.3972	−3.00238
$736$	−5.53743	−0.204112
$737$	−22.1255	−0.815005
$738$	−12.8198	−0.471903
$739$	−12.4006	−0.456162	−0.228081	−	0.973642i	$-0.573245\pi$
$739$	−12.4006	−0.456162	−0.228081	+	0.973642i	$0.573245\pi$
$740$	38.5891	1.41856
$741$	0	0
$742$	−0.360494	−0.0132342
$743$	1.90025	0.0697135	0.0348568	−	0.999392i	$-0.488902\pi$
$743$	1.90025	0.0697135	0.0348568	+	0.999392i	$0.488902\pi$
$744$	−18.0922	−0.663291
$745$	−7.59872	−0.278395
$746$	18.5731	0.680011
$747$	−94.4569	−3.45600
$748$	−11.1062	−0.406084
$749$	−0.516903	−0.0188872
$750$	29.3960	1.07339
$751$	44.9955	1.64191	0.820955	−	0.570993i	$-0.193442\pi$
$751$	44.9955	1.64191	0.820955	+	0.570993i	$0.193442\pi$
$752$	−7.02837	−0.256298
$753$	74.1206	2.70111
$754$	0	0
$755$	−39.4589	−1.43606
$756$	2.42131	0.0880622
$757$	9.53993	0.346735	0.173367	−	0.984857i	$-0.444535\pi$
$757$	9.53993	0.346735	0.173367	+	0.984857i	$0.444535\pi$
$758$	19.3298	0.702088
$759$	−43.6142	−1.58310
$760$	−3.53833	−0.128349
$761$	23.0991	0.837343	0.418671	−	0.908138i	$-0.362496\pi$
$761$	23.0991	0.837343	0.418671	+	0.908138i	$0.362496\pi$
$762$	−61.1806	−2.21634
$763$	0.750975	0.0271871
$764$	5.05349	0.182829
$765$	−129.472	−4.68106
$766$	−18.9244	−0.683766
$767$	0	0
$768$	−3.29705	−0.118972
$769$	−33.4512	−1.20628	−0.603141	−	0.797634i	$-0.706084\pi$
$769$	−33.4512	−1.20628	−0.603141	+	0.797634i	$0.706084\pi$
$770$	−1.27450	−0.0459299
$771$	−20.3152	−0.731634
$772$	12.1526	0.437382
$773$	14.1395	0.508564	0.254282	−	0.967130i	$-0.418161\pi$
$773$	14.1395	0.508564	0.254282	+	0.967130i	$0.418161\pi$
$774$	82.9803	2.98266
$775$	41.2639	1.48224
$776$	−12.5681	−0.451168
$777$	−5.42174	−0.194504
$778$	30.1046	1.07930
$779$	−1.62883	−0.0583589
$780$	0	0
$781$	−7.49517	−0.268198
$782$	−25.7443	−0.920613
$783$	72.0816	2.57599
$784$	−6.97726	−0.249188
$785$	47.5876	1.69847
$786$	−22.7842	−0.812684
$787$	44.7650	1.59570	0.797851	−	0.602855i	$-0.205970\pi$
$787$	44.7650	1.59570	0.797851	+	0.602855i	$0.205970\pi$
$788$	8.00854	0.285293
$789$	37.5365	1.33633
$790$	18.7470	0.666990
$791$	−0.647235	−0.0230130
$792$	−18.8018	−0.668092
$793$	0	0
$794$	−19.7312	−0.700233
$795$	27.8917	0.989216
$796$	17.3501	0.614957
$797$	8.86399	0.313979	0.156989	−	0.987600i	$-0.449821\pi$
$797$	8.86399	0.313979	0.156989	+	0.987600i	$0.449821\pi$
$798$	0.497134	0.0175983
$799$	−32.6758	−1.15599
$800$	7.51979	0.265865
$801$	−148.291	−5.23962
$802$	38.5836	1.36243
$803$	4.96737	0.175295
$804$	−30.5369	−1.07695
$805$	−2.95430	−0.104125
$806$	0	0
$807$	−6.59338	−0.232098
$808$	−8.78739	−0.309139
$809$	−11.5701	−0.406783	−0.203392	−	0.979097i	$-0.565196\pi$
$809$	−11.5701	−0.406783	−0.203392	+	0.979097i	$0.565196\pi$
$810$	−103.793	−3.64690
$811$	−42.2403	−1.48326	−0.741629	−	0.670811i	$-0.765946\pi$
$811$	−42.2403	−1.48326	−0.741629	+	0.670811i	$0.765946\pi$
$812$	0.676814	0.0237515
$813$	78.4186	2.75026
$814$	26.0531	0.913162
$815$	3.02078	0.105813
$816$	−15.3284	−0.536603
$817$	10.5431	0.368858
$818$	2.63015	0.0919609
$819$	0	0
$820$	5.76334	0.201265
$821$	−54.5203	−1.90277	−0.951386	−	0.308001i	$-0.900340\pi$
$821$	−54.5203	−1.90277	−0.951386	+	0.308001i	$0.900340\pi$
$822$	−20.1055	−0.701260
$823$	10.0705	0.351034	0.175517	−	0.984476i	$-0.443840\pi$
$823$	10.0705	0.351034	0.175517	+	0.984476i	$0.443840\pi$
$824$	12.1560	0.423474
$825$	59.2278	2.06205
$826$	0.431398	0.0150102
$827$	10.9110	0.379411	0.189706	−	0.981841i	$-0.439247\pi$
$827$	10.9110	0.379411	0.189706	+	0.981841i	$0.439247\pi$
$828$	−43.5826	−1.51460
$829$	53.0765	1.84342	0.921711	−	0.387877i	$-0.126791\pi$
$829$	53.0765	1.84342	0.921711	+	0.387877i	$0.126791\pi$
$830$	42.4647	1.47397
$831$	−4.12358	−0.143045
$832$	0	0
$833$	−32.4382	−1.12392
$834$	37.9224	1.31314
$835$	−22.2676	−0.770602
$836$	−2.38888	−0.0826211
$837$	−88.1186	−3.04583
$838$	−21.0823	−0.728277
$839$	16.1528	0.557658	0.278829	−	0.960341i	$-0.410054\pi$
$839$	16.1528	0.557658	0.278829	+	0.960341i	$0.410054\pi$
$840$	−1.75902	−0.0606921
$841$	−8.85150	−0.305224
$842$	−29.9487	−1.03210
$843$	90.4787	3.11625
$844$	−7.54866	−0.259836
$845$	0	0
$846$	−55.3171	−1.90184
$847$	0.798124	0.0274239
$848$	2.39084	0.0821018
$849$	−67.9026	−2.33041
$850$	34.9605	1.19914
$851$	60.3913	2.07019
$852$	−10.3446	−0.354399
$853$	−32.2364	−1.10375	−0.551877	−	0.833926i	$-0.686088\pi$
$853$	−32.2364	−1.10375	−0.551877	+	0.833926i	$0.686088\pi$
$854$	0.630547	0.0215769
$855$	−27.8486	−0.952401
$856$	3.42816	0.117172
$857$	−14.4059	−0.492095	−0.246048	−	0.969258i	$-0.579132\pi$
$857$	−14.4059	−0.492095	−0.246048	+	0.969258i	$0.579132\pi$
$858$	0	0
$859$	14.0342	0.478842	0.239421	−	0.970916i	$-0.423042\pi$
$859$	14.0342	0.478842	0.239421	+	0.970916i	$0.423042\pi$
$860$	−37.3051	−1.27210
$861$	−0.809747	−0.0275961
$862$	−28.3577	−0.965866
$863$	2.54991	0.0868000	0.0434000	−	0.999058i	$-0.486181\pi$
$863$	2.54991	0.0868000	0.0434000	+	0.999058i	$0.486181\pi$
$864$	−16.0584	−0.546319
$865$	29.7615	1.01192
$866$	−26.4624	−0.899229
$867$	−15.2141	−0.516698
$868$	−0.827394	−0.0280836
$869$	12.6569	0.429357
$870$	−52.3655	−1.77536
$871$	0	0
$872$	−4.98056	−0.168663
$873$	−98.9176	−3.34785
$874$	−5.53743	−0.187306
$875$	1.34434	0.0454471
$876$	6.85579	0.231636
$877$	47.0463	1.58864	0.794320	−	0.607499i	$-0.207827\pi$
$877$	47.0463	1.58864	0.794320	+	0.607499i	$0.207827\pi$
$878$	2.22341	0.0750364
$879$	29.6985	1.00171
$880$	8.45265	0.284939
$881$	−45.2418	−1.52423	−0.762117	−	0.647440i	$-0.775840\pi$
$881$	−45.2418	−1.52423	−0.762117	+	0.647440i	$0.775840\pi$
$882$	−54.9149	−1.84908
$883$	−6.45909	−0.217366	−0.108683	−	0.994076i	$-0.534663\pi$
$883$	−6.45909	−0.217366	−0.108683	+	0.994076i	$0.534663\pi$
$884$	0	0
$885$	−33.3775	−1.12197
$886$	17.6039	0.591415
$887$	−27.7245	−0.930899	−0.465449	−	0.885074i	$-0.654107\pi$
$887$	−27.7245	−0.930899	−0.465449	+	0.885074i	$0.654107\pi$
$888$	35.9577	1.20666
$889$	−2.79792	−0.0938393
$890$	66.6669	2.23468
$891$	−70.0749	−2.34760
$892$	28.7643	0.963099
$893$	−7.02837	−0.235195
$894$	−7.08056	−0.236809
$895$	−36.2102	−1.21037
$896$	−0.150781	−0.00503725
$897$	0	0
$898$	27.8127	0.928123
$899$	−24.6312	−0.821498
$900$	59.1848	1.97283
$901$	11.1153	0.370306
$902$	3.89108	0.129559
$903$	5.24135	0.174421
$904$	4.29254	0.142768
$905$	−49.5507	−1.64712
$906$	−36.7682	−1.22154
$907$	−20.0680	−0.666348	−0.333174	−	0.942865i	$-0.608120\pi$
$907$	−20.0680	−0.666348	−0.333174	+	0.942865i	$0.608120\pi$
$908$	−1.92833	−0.0639939
$909$	−69.1616	−2.29394
$910$	0	0
$911$	−57.8610	−1.91702	−0.958510	−	0.285059i	$-0.907987\pi$
$911$	−57.8610	−1.91702	−0.958510	+	0.285059i	$0.907987\pi$
$912$	−3.29705	−0.109176
$913$	28.6697	0.948829
$914$	33.2600	1.10014
$915$	−48.7858	−1.61281
$916$	17.3072	0.571845
$917$	−1.04197	−0.0344089
$918$	−74.6578	−2.46407
$919$	33.5024	1.10514	0.552572	−	0.833465i	$-0.313646\pi$
$919$	33.5024	1.10514	0.552572	+	0.833465i	$0.313646\pi$
$920$	19.5933	0.645971
$921$	−17.8302	−0.587526
$922$	19.6577	0.647393
$923$	0	0
$924$	−1.18759	−0.0390689
$925$	−82.0109	−2.69650
$926$	−9.51924	−0.312822
$927$	95.6742	3.14235
$928$	−4.48871	−0.147349
$929$	44.0193	1.44423	0.722113	−	0.691775i	$-0.243171\pi$
$929$	44.0193	1.44423	0.722113	+	0.691775i	$0.243171\pi$
$930$	64.0161	2.09917
$931$	−6.97726	−0.228671
$932$	23.2739	0.762362
$933$	−31.4950	−1.03110
$934$	−3.59653	−0.117682
$935$	39.2975	1.28517
$936$	0	0
$937$	23.9226	0.781519	0.390759	−	0.920493i	$-0.372212\pi$
$937$	23.9226	0.781519	0.390759	+	0.920493i	$0.372212\pi$
$938$	−1.39652	−0.0455980
$939$	−51.9375	−1.69492
$940$	24.8687	0.811128
$941$	−11.9315	−0.388955	−0.194478	−	0.980907i	$-0.562301\pi$
$941$	−11.9315	−0.388955	−0.194478	+	0.980907i	$0.562301\pi$
$942$	44.3425	1.44476
$943$	9.01954	0.293717
$944$	−2.86108	−0.0931203
$945$	−8.56740	−0.278698
$946$	−25.1863	−0.818878
$947$	44.4175	1.44338	0.721688	−	0.692219i	$-0.243367\pi$
$947$	44.4175	1.44338	0.721688	+	0.692219i	$0.243367\pi$
$948$	17.4687	0.567356
$949$	0	0
$950$	7.51979	0.243974
$951$	10.3687	0.336229
$952$	−0.701003	−0.0227196
$953$	19.1284	0.619631	0.309816	−	0.950797i	$-0.399733\pi$
$953$	19.1284	0.619631	0.309816	+	0.950797i	$0.399733\pi$
$954$	18.8172	0.609230
$955$	−17.8809	−0.578613
$956$	14.6296	0.473156
$957$	−35.3542	−1.14284
$958$	28.3976	0.917484
$959$	−0.919469	−0.0296912
$960$	11.6661	0.376520
$961$	−0.888682	−0.0286672
$962$	0	0
$963$	26.9815	0.869466
$964$	14.5700	0.469267
$965$	−43.0000	−1.38422
$966$	−2.75284	−0.0885713
$967$	−25.1740	−0.809543	−0.404771	−	0.914418i	$-0.632649\pi$
$967$	−25.1740	−0.809543	−0.404771	+	0.914418i	$0.632649\pi$
$968$	−5.29325	−0.170132
$969$	−15.3284	−0.492420
$970$	44.4700	1.42785
$971$	−36.4759	−1.17057	−0.585284	−	0.810828i	$-0.699017\pi$
$971$	−36.4759	−1.17057	−0.585284	+	0.810828i	$0.699017\pi$
$972$	−48.5398	−1.55691
$973$	1.73427	0.0555982
$974$	−32.9147	−1.05465
$975$	0	0
$976$	−4.18186	−0.133858
$977$	3.72604	0.119206	0.0596032	−	0.998222i	$-0.481016\pi$
$977$	3.72604	0.119206	0.0596032	+	0.998222i	$0.481016\pi$
$978$	2.81479	0.0900072
$979$	45.0097	1.43852
$980$	24.6879	0.788625
$981$	−39.1997	−1.25155
$982$	0.282195	0.00900521
$983$	−2.94137	−0.0938151	−0.0469075	−	0.998899i	$-0.514937\pi$
$983$	−2.94137	−0.0938151	−0.0469075	+	0.998899i	$0.514937\pi$
$984$	5.37034	0.171200
$985$	−28.3369	−0.902888
$986$	−20.8686	−0.664592
$987$	−3.49404	−0.111217
$988$	0	0
$989$	−58.3820	−1.85644
$990$	66.5269	2.11436
$991$	−0.474014	−0.0150575	−0.00752877	−	0.999972i	$-0.502397\pi$
$991$	−0.474014	−0.0150575	−0.00752877	+	0.999972i	$0.502397\pi$
$992$	5.48738	0.174224
$993$	0.888295	0.0281892
$994$	−0.473080	−0.0150052
$995$	−61.3903	−1.94620
$996$	39.5690	1.25379
$997$	−27.5785	−0.873421	−0.436711	−	0.899602i	$-0.643857\pi$
$997$	−27.5785	−0.873421	−0.436711	+	0.899602i	$0.643857\pi$
$998$	−29.4739	−0.932981
$999$	175.133	5.54097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bf.1.1		7
13.5	odd	4		494.2.d.c.77.1	✓	14
13.8	odd	4		494.2.d.c.77.8	yes	14
13.12	even	2		6422.2.a.be.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.c.77.1	✓	14	13.5	odd	4
494.2.d.c.77.8	yes	14	13.8	odd	4
6422.2.a.be.1.1		7	13.12	even	2
6422.2.a.bf.1.1		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.29705 q^{3} +1.00000 q^{4} -3.53833 q^{5} -3.29705 q^{6} -0.150781 q^{7} +1.00000 q^{8} +7.87054 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.29705 q^{3} +1.00000 q^{4} -3.53833 q^{5} -3.29705 q^{6} -0.150781 q^{7} +1.00000 q^{8} +7.87054 q^{9} -3.53833 q^{10} -2.38888 q^{11} -3.29705 q^{12} -0.150781 q^{14} +11.6661 q^{15} +1.00000 q^{16} +4.64914 q^{17} +7.87054 q^{18} +1.00000 q^{19} -3.53833 q^{20} +0.497134 q^{21} -2.38888 q^{22} -5.53743 q^{23} -3.29705 q^{24} +7.51979 q^{25} -16.0584 q^{27} -0.150781 q^{28} -4.48871 q^{29} +11.6661 q^{30} +5.48738 q^{31} +1.00000 q^{32} +7.87626 q^{33} +4.64914 q^{34} +0.533514 q^{35} +7.87054 q^{36} -10.9060 q^{37} +1.00000 q^{38} -3.53833 q^{40} -1.62883 q^{41} +0.497134 q^{42} +10.5431 q^{43} -2.38888 q^{44} -27.8486 q^{45} -5.53743 q^{46} -7.02837 q^{47} -3.29705 q^{48} -6.97726 q^{49} +7.51979 q^{50} -15.3284 q^{51} +2.39084 q^{53} -16.0584 q^{54} +8.45265 q^{55} -0.150781 q^{56} -3.29705 q^{57} -4.48871 q^{58} -2.86108 q^{59} +11.6661 q^{60} -4.18186 q^{61} +5.48738 q^{62} -1.18673 q^{63} +1.00000 q^{64} +7.87626 q^{66} +9.26189 q^{67} +4.64914 q^{68} +18.2572 q^{69} +0.533514 q^{70} +3.13752 q^{71} +7.87054 q^{72} -2.07937 q^{73} -10.9060 q^{74} -24.7931 q^{75} +1.00000 q^{76} +0.360199 q^{77} -5.29827 q^{79} -3.53833 q^{80} +29.3338 q^{81} -1.62883 q^{82} -12.0013 q^{83} +0.497134 q^{84} -16.4502 q^{85} +10.5431 q^{86} +14.7995 q^{87} -2.38888 q^{88} -18.8413 q^{89} -27.8486 q^{90} -5.53743 q^{92} -18.0922 q^{93} -7.02837 q^{94} -3.53833 q^{95} -3.29705 q^{96} -12.5681 q^{97} -6.97726 q^{98} -18.8018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9	\( 7 q + 7 q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} + 2 q^{6} + q^{7} + 7 q^{8} + 15 q^{9} + 2 q^{10} + 5 q^{11} + 2 q^{12} + q^{14} + 13 q^{15} + 7 q^{16} + 16 q^{17} + 15 q^{18} + 7 q^{19} + 2 q^{20} - 3 q^{21} + 5 q^{22} + 3 q^{23} + 2 q^{24} + 7 q^{25} + 5 q^{27} + q^{28} - 7 q^{29} + 13 q^{30} + 11 q^{31} + 7 q^{32} + 6 q^{33} + 16 q^{34} + q^{35} + 15 q^{36} - 3 q^{37} + 7 q^{38} + 2 q^{40} + 15 q^{41} - 3 q^{42} + 23 q^{43} + 5 q^{44} - 38 q^{45} + 3 q^{46} - q^{47} + 2 q^{48} + 14 q^{49} + 7 q^{50} - 16 q^{51} + 21 q^{53} + 5 q^{54} + 8 q^{55} + q^{56} + 2 q^{57} - 7 q^{58} + 8 q^{59} + 13 q^{60} - 6 q^{61} + 11 q^{62} - 22 q^{63} + 7 q^{64} + 6 q^{66} + 28 q^{67} + 16 q^{68} + 48 q^{69} + q^{70} + 4 q^{71} + 15 q^{72} + 12 q^{73} - 3 q^{74} + 5 q^{75} + 7 q^{76} - 26 q^{77} - 4 q^{79} + 2 q^{80} + 51 q^{81} + 15 q^{82} + 13 q^{83} - 3 q^{84} - 39 q^{85} + 23 q^{86} - 16 q^{87} + 5 q^{88} - 15 q^{89} - 38 q^{90} + 3 q^{92} + 6 q^{93} - q^{94} + 2 q^{95} + 2 q^{96} - 37 q^{97} + 14 q^{98} - 15 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 2 * q^3 + 7 * q^4 + 2 * q^5 + 2 * q^6 + q^7 + 7 * q^8 + 15 * q^9 + 2 * q^10 + 5 * q^11 + 2 * q^12 + q^14 + 13 * q^15 + 7 * q^16 + 16 * q^17 + 15 * q^18 + 7 * q^19 + 2 * q^20 - 3 * q^21 + 5 * q^22 + 3 * q^23 + 2 * q^24 + 7 * q^25 + 5 * q^27 + q^28 - 7 * q^29 + 13 * q^30 + 11 * q^31 + 7 * q^32 + 6 * q^33 + 16 * q^34 + q^35 + 15 * q^36 - 3 * q^37 + 7 * q^38 + 2 * q^40 + 15 * q^41 - 3 * q^42 + 23 * q^43 + 5 * q^44 - 38 * q^45 + 3 * q^46 - q^47 + 2 * q^48 + 14 * q^49 + 7 * q^50 - 16 * q^51 + 21 * q^53 + 5 * q^54 + 8 * q^55 + q^56 + 2 * q^57 - 7 * q^58 + 8 * q^59 + 13 * q^60 - 6 * q^61 + 11 * q^62 - 22 * q^63 + 7 * q^64 + 6 * q^66 + 28 * q^67 + 16 * q^68 + 48 * q^69 + q^70 + 4 * q^71 + 15 * q^72 + 12 * q^73 - 3 * q^74 + 5 * q^75 + 7 * q^76 - 26 * q^77 - 4 * q^79 + 2 * q^80 + 51 * q^81 + 15 * q^82 + 13 * q^83 - 3 * q^84 - 39 * q^85 + 23 * q^86 - 16 * q^87 + 5 * q^88 - 15 * q^89 - 38 * q^90 + 3 * q^92 + 6 * q^93 - q^94 + 2 * q^95 + 2 * q^96 - 37 * q^97 + 14 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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