LMFDB - Embedded newform 1573.2.a.s.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 19 x^{11} + 169 x^{10} - 136 x^{9} - 649 x^{8} + 455 x^{7} + 1207 x^{6} + \cdots - 29 $ x^14 - x^13 - 21x^12 + 19x^11 + 169x^10 - 136x^9 - 649x^8 + 455x^7 + 1207x^6 - 708x^5 - 1001x^4 + 414x^3 + 343x^2 - 67x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.13331$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13331 q^{2} +0.0976299 q^{3} -0.715602 q^{4} -3.57018 q^{5} +0.110645 q^{6} +0.149191 q^{7} -3.07763 q^{8} -2.99047 q^{9} +O(q^{10})$	\(q+1.13331 q^{2} +0.0976299 q^{3} -0.715602 q^{4} -3.57018 q^{5} +0.110645 q^{6} +0.149191 q^{7} -3.07763 q^{8} -2.99047 q^{9} -4.04613 q^{10} -0.0698641 q^{12} +1.00000 q^{13} +0.169081 q^{14} -0.348556 q^{15} -2.05671 q^{16} +5.85953 q^{17} -3.38914 q^{18} +7.07556 q^{19} +2.55482 q^{20} +0.0145655 q^{21} -1.14805 q^{23} -0.300468 q^{24} +7.74616 q^{25} +1.13331 q^{26} -0.584849 q^{27} -0.106762 q^{28} -3.81648 q^{29} -0.395023 q^{30} -0.0330483 q^{31} +3.82436 q^{32} +6.64068 q^{34} -0.532640 q^{35} +2.13998 q^{36} -7.44531 q^{37} +8.01882 q^{38} +0.0976299 q^{39} +10.9877 q^{40} +8.20506 q^{41} +0.0165073 q^{42} +4.69648 q^{43} +10.6765 q^{45} -1.30110 q^{46} +5.17768 q^{47} -0.200796 q^{48} -6.97774 q^{49} +8.77883 q^{50} +0.572065 q^{51} -0.715602 q^{52} +13.5852 q^{53} -0.662817 q^{54} -0.459155 q^{56} +0.690786 q^{57} -4.32527 q^{58} +12.4659 q^{59} +0.249427 q^{60} +3.09474 q^{61} -0.0374541 q^{62} -0.446152 q^{63} +8.44761 q^{64} -3.57018 q^{65} -6.22640 q^{67} -4.19309 q^{68} -0.112084 q^{69} -0.603648 q^{70} -8.68130 q^{71} +9.20355 q^{72} -3.06171 q^{73} -8.43787 q^{74} +0.756257 q^{75} -5.06328 q^{76} +0.110645 q^{78} -11.1548 q^{79} +7.34282 q^{80} +8.91431 q^{81} +9.29890 q^{82} -5.91734 q^{83} -0.0104231 q^{84} -20.9195 q^{85} +5.32259 q^{86} -0.372603 q^{87} +10.4739 q^{89} +12.0998 q^{90} +0.149191 q^{91} +0.821546 q^{92} -0.00322650 q^{93} +5.86794 q^{94} -25.2610 q^{95} +0.373371 q^{96} +5.32955 q^{97} -7.90797 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

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 $

$2$	1.13331	0.801373	0.400687	−	0.916215i	$-0.368772\pi$
$2$	1.13331	0.801373	0.400687	+	0.916215i	$0.368772\pi$
$3$	0.0976299	0.0563666	0.0281833	−	0.999603i	$-0.491028\pi$
$3$	0.0976299	0.0563666	0.0281833	+	0.999603i	$0.491028\pi$
$4$	−0.715602	−0.357801
$5$	−3.57018	−1.59663	−0.798316	−	0.602239i	$-0.794275\pi$
$5$	−3.57018	−1.59663	−0.798316	+	0.602239i	$0.794275\pi$
$6$	0.110645	0.0451707
$7$	0.149191	0.0563891	0.0281945	−	0.999602i	$-0.491024\pi$
$7$	0.149191	0.0563891	0.0281945	+	0.999602i	$0.491024\pi$
$8$	−3.07763	−1.08811
$9$	−2.99047	−0.996823
$10$	−4.04613	−1.27950
$11$	0	0
$11$	0	0
$12$	−0.0698641	−0.0201680
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.169081	0.0451887
$15$	−0.348556	−0.0899968
$16$	−2.05671	−0.514178
$17$	5.85953	1.42114	0.710572	−	0.703625i	$-0.248436\pi$
$17$	5.85953	1.42114	0.710572	+	0.703625i	$0.248436\pi$
$18$	−3.38914	−0.798827
$19$	7.07556	1.62324	0.811622	−	0.584182i	$-0.198585\pi$
$19$	7.07556	1.62324	0.811622	+	0.584182i	$0.198585\pi$
$20$	2.55482	0.571276
$21$	0.0145655	0.00317846
$22$	0	0
$23$	−1.14805	−0.239385	−0.119692	−	0.992811i	$-0.538191\pi$
$23$	−1.14805	−0.239385	−0.119692	+	0.992811i	$0.538191\pi$
$24$	−0.300468	−0.0613328
$25$	7.74616	1.54923
$26$	1.13331	0.222261
$27$	−0.584849	−0.112554
$28$	−0.106762	−0.0201760
$29$	−3.81648	−0.708703	−0.354351	−	0.935112i	$-0.615298\pi$
$29$	−3.81648	−0.708703	−0.354351	+	0.935112i	$0.615298\pi$
$30$	−0.395023	−0.0721210
$31$	−0.0330483	−0.00593565	−0.00296782	−	0.999996i	$-0.500945\pi$
$31$	−0.0330483	−0.00593565	−0.00296782	+	0.999996i	$0.500945\pi$
$32$	3.82436	0.676057
$33$	0	0
$34$	6.64068	1.13887
$35$	−0.532640	−0.0900326
$36$	2.13998	0.356664
$37$	−7.44531	−1.22400	−0.612001	−	0.790857i	$-0.709635\pi$
$37$	−7.44531	−1.22400	−0.612001	+	0.790857i	$0.709635\pi$
$38$	8.01882	1.30083
$39$	0.0976299	0.0156333
$40$	10.9877	1.73730
$41$	8.20506	1.28141	0.640707	−	0.767785i	$-0.278641\pi$
$41$	8.20506	1.28141	0.640707	+	0.767785i	$0.278641\pi$
$42$	0.0165073	0.00254713
$43$	4.69648	0.716207	0.358104	−	0.933682i	$-0.383423\pi$
$43$	4.69648	0.716207	0.358104	+	0.933682i	$0.383423\pi$
$44$	0	0
$45$	10.6765	1.59156
$46$	−1.30110	−0.191837
$47$	5.17768	0.755243	0.377621	−	0.925960i	$-0.376742\pi$
$47$	5.17768	0.755243	0.377621	+	0.925960i	$0.376742\pi$
$48$	−0.200796	−0.0289825
$49$	−6.97774	−0.996820
$50$	8.77883	1.24151
$51$	0.572065	0.0801051
$52$	−0.715602	−0.0992361
$53$	13.5852	1.86606	0.933032	−	0.359793i	$-0.117153\pi$
$53$	13.5852	1.86606	0.933032	+	0.359793i	$0.117153\pi$
$54$	−0.662817	−0.0901979
$55$	0	0
$56$	−0.459155	−0.0613572
$57$	0.690786	0.0914969
$58$	−4.32527	−0.567935
$59$	12.4659	1.62292	0.811459	−	0.584410i	$-0.198674\pi$
$59$	12.4659	1.62292	0.811459	+	0.584410i	$0.198674\pi$
$60$	0.249427	0.0322009
$61$	3.09474	0.396240	0.198120	−	0.980178i	$-0.436516\pi$
$61$	3.09474	0.396240	0.198120	+	0.980178i	$0.436516\pi$
$62$	−0.0374541	−0.00475667
$63$	−0.446152	−0.0562099
$64$	8.44761	1.05595
$65$	−3.57018	−0.442826
$66$	0	0
$67$	−6.22640	−0.760676	−0.380338	−	0.924848i	$-0.624192\pi$
$67$	−6.22640	−0.760676	−0.380338	+	0.924848i	$0.624192\pi$
$68$	−4.19309	−0.508486
$69$	−0.112084	−0.0134933
$70$	−0.603648	−0.0721497
$71$	−8.68130	−1.03028	−0.515141	−	0.857106i	$-0.672260\pi$
$71$	−8.68130	−1.03028	−0.515141	+	0.857106i	$0.672260\pi$
$72$	9.20355	1.08465
$73$	−3.06171	−0.358346	−0.179173	−	0.983818i	$-0.557342\pi$
$73$	−3.06171	−0.358346	−0.179173	+	0.983818i	$0.557342\pi$
$74$	−8.43787	−0.980882
$75$	0.756257	0.0873250
$76$	−5.06328	−0.580798
$77$	0	0
$78$	0.110645	0.0125281
$79$	−11.1548	−1.25501	−0.627504	−	0.778613i	$-0.715923\pi$
$79$	−11.1548	−1.25501	−0.627504	+	0.778613i	$0.715923\pi$
$80$	7.34282	0.820953
$81$	8.91431	0.990479
$82$	9.29890	1.02689
$83$	−5.91734	−0.649512	−0.324756	−	0.945798i	$-0.605282\pi$
$83$	−5.91734	−0.649512	−0.324756	+	0.945798i	$0.605282\pi$
$84$	−0.0104231	−0.00113726
$85$	−20.9195	−2.26904
$86$	5.32259	0.573949
$87$	−0.372603	−0.0399472
$88$	0	0
$89$	10.4739	1.11024	0.555118	−	0.831772i	$-0.312673\pi$
$89$	10.4739	1.11024	0.555118	+	0.831772i	$0.312673\pi$
$90$	12.0998	1.27543
$91$	0.149191	0.0156395
$92$	0.821546	0.0856521
$93$	−0.00322650	−0.000334573 0
$94$	5.86794	0.605231
$95$	−25.2610	−2.59172
$96$	0.373371	0.0381071
$97$	5.32955	0.541134	0.270567	−	0.962701i	$-0.412789\pi$
$97$	5.32955	0.541134	0.270567	+	0.962701i	$0.412789\pi$
$98$	−7.90797	−0.798825
$99$	0	0
$100$	−5.54317	−0.554317
$101$	0.906457	0.0901958	0.0450979	−	0.998983i	$-0.485640\pi$
$101$	0.906457	0.0901958	0.0450979	+	0.998983i	$0.485640\pi$
$102$	0.648329	0.0641941
$103$	−2.92340	−0.288051	−0.144025	−	0.989574i	$-0.546005\pi$
$103$	−2.92340	−0.288051	−0.144025	+	0.989574i	$0.546005\pi$
$104$	−3.07763	−0.301786
$105$	−0.0520016	−0.00507483
$106$	15.3962	1.49541
$107$	7.63312	0.737922	0.368961	−	0.929445i	$-0.379714\pi$
$107$	7.63312	0.737922	0.368961	+	0.929445i	$0.379714\pi$
$108$	0.418519	0.0402720
$109$	−7.35693	−0.704666	−0.352333	−	0.935875i	$-0.614612\pi$
$109$	−7.35693	−0.704666	−0.352333	+	0.935875i	$0.614612\pi$
$110$	0	0
$111$	−0.726885	−0.0689929
$112$	−0.306844	−0.0289940
$113$	−7.01588	−0.659999	−0.329999	−	0.943981i	$-0.607049\pi$
$113$	−7.01588	−0.659999	−0.329999	+	0.943981i	$0.607049\pi$
$114$	0.782877	0.0733231
$115$	4.09874	0.382210
$116$	2.73108	0.253574
$117$	−2.99047	−0.276469
$118$	14.1277	1.30056
$119$	0.874191	0.0801370
$120$	1.07273	0.0979260
$121$	0	0
$122$	3.50730	0.317536
$123$	0.801059	0.0722290
$124$	0.0236494	0.00212378
$125$	−9.80429	−0.876922
$126$	−0.505630	−0.0450451
$127$	−1.16225	−0.103133	−0.0515667	−	0.998670i	$-0.516421\pi$
$127$	−1.16225	−0.103133	−0.0515667	+	0.998670i	$0.516421\pi$
$128$	1.92508	0.170155
$129$	0.458517	0.0403702
$130$	−4.04613	−0.354869
$131$	4.61701	0.403390	0.201695	−	0.979448i	$-0.435355\pi$
$131$	4.61701	0.403390	0.201695	+	0.979448i	$0.435355\pi$
$132$	0	0
$133$	1.05561	0.0915332
$134$	−7.05646	−0.609586
$135$	2.08801	0.179708
$136$	−18.0334	−1.54635
$137$	18.8126	1.60727	0.803633	−	0.595125i	$-0.202897\pi$
$137$	18.8126	1.60727	0.803633	+	0.595125i	$0.202897\pi$
$138$	−0.127026	−0.0108132
$139$	−2.77033	−0.234976	−0.117488	−	0.993074i	$-0.537484\pi$
$139$	−2.77033	−0.234976	−0.117488	+	0.993074i	$0.537484\pi$
$140$	0.381158	0.0322137
$141$	0.505497	0.0425705
$142$	−9.83864	−0.825640
$143$	0	0
$144$	6.15053	0.512544
$145$	13.6255	1.13154
$146$	−3.46988	−0.287169
$147$	−0.681236	−0.0561874
$148$	5.32788	0.437949
$149$	1.42558	0.116788	0.0583942	−	0.998294i	$-0.481402\pi$
$149$	1.42558	0.116788	0.0583942	+	0.998294i	$0.481402\pi$
$150$	0.857076	0.0699800
$151$	15.2881	1.24413	0.622065	−	0.782966i	$-0.286294\pi$
$151$	15.2881	1.24413	0.622065	+	0.782966i	$0.286294\pi$
$152$	−21.7759	−1.76626
$153$	−17.5227	−1.41663
$154$	0	0
$155$	0.117988	0.00947705
$156$	−0.0698641	−0.00559360
$157$	8.67074	0.692000	0.346000	−	0.938234i	$-0.387540\pi$
$157$	8.67074	0.692000	0.346000	+	0.938234i	$0.387540\pi$
$158$	−12.6418	−1.00573
$159$	1.32632	0.105184
$160$	−13.6536	−1.07941
$161$	−0.171279	−0.0134987
$162$	10.1027	0.793743
$163$	−12.7209	−0.996377	−0.498188	−	0.867069i	$-0.666001\pi$
$163$	−12.7209	−0.996377	−0.498188	+	0.867069i	$0.666001\pi$
$164$	−5.87155	−0.458491
$165$	0	0
$166$	−6.70620	−0.520502
$167$	14.1574	1.09553	0.547767	−	0.836631i	$-0.315478\pi$
$167$	14.1574	1.09553	0.547767	+	0.836631i	$0.315478\pi$
$168$	−0.0448273	−0.00345850
$169$	1.00000	0.0769231
$170$	−23.7084	−1.81835
$171$	−21.1592	−1.61809
$172$	−3.36081	−0.256259
$173$	−5.31160	−0.403833	−0.201917	−	0.979403i	$-0.564717\pi$
$173$	−5.31160	−0.403833	−0.201917	+	0.979403i	$0.564717\pi$
$174$	−0.422275	−0.0320126
$175$	1.15566	0.0873598
$176$	0	0
$177$	1.21704	0.0914784
$178$	11.8703	0.889713
$179$	9.16847	0.685284	0.342642	−	0.939466i	$-0.388678\pi$
$179$	9.16847	0.685284	0.342642	+	0.939466i	$0.388678\pi$
$180$	−7.64012	−0.569461
$181$	4.29644	0.319352	0.159676	−	0.987169i	$-0.448955\pi$
$181$	4.29644	0.319352	0.159676	+	0.987169i	$0.448955\pi$
$182$	0.169081	0.0125331
$183$	0.302139	0.0223347
$184$	3.53327	0.260476
$185$	26.5811	1.95428
$186$	−0.00365664	−0.000268118 0
$187$	0	0
$188$	−3.70516	−0.270226
$189$	−0.0872544	−0.00634682
$190$	−28.6286	−2.07694
$191$	24.2892	1.75750	0.878751	−	0.477280i	$-0.158377\pi$
$191$	24.2892	1.75750	0.878751	+	0.477280i	$0.158377\pi$
$192$	0.824740	0.0595205
$193$	6.20132	0.446381	0.223190	−	0.974775i	$-0.428353\pi$
$193$	6.20132	0.446381	0.223190	+	0.974775i	$0.428353\pi$
$194$	6.04005	0.433650
$195$	−0.348556	−0.0249606
$196$	4.99328	0.356663
$197$	20.1208	1.43355	0.716773	−	0.697306i	$-0.245618\pi$
$197$	20.1208	1.43355	0.716773	+	0.697306i	$0.245618\pi$
$198$	0	0
$199$	−6.04104	−0.428238	−0.214119	−	0.976808i	$-0.568688\pi$
$199$	−6.04104	−0.428238	−0.214119	+	0.976808i	$0.568688\pi$
$200$	−23.8398	−1.68573
$201$	−0.607883	−0.0428768
$202$	1.02730	0.0722805
$203$	−0.569386	−0.0399631
$204$	−0.409370	−0.0286617
$205$	−29.2935	−2.04595
$206$	−3.31312	−0.230836
$207$	3.43321	0.238624
$208$	−2.05671	−0.142607
$209$	0	0
$210$	−0.0589340	−0.00406684
$211$	6.58234	0.453147	0.226573	−	0.973994i	$-0.427248\pi$
$211$	6.58234	0.453147	0.226573	+	0.973994i	$0.427248\pi$
$212$	−9.72156	−0.667679
$213$	−0.847555	−0.0580735
$214$	8.65071	0.591351
$215$	−16.7673	−1.14352
$216$	1.79995	0.122471
$217$	−0.00493052	−0.000334706 0
$218$	−8.33770	−0.564700
$219$	−0.298914	−0.0201988
$220$	0	0
$221$	5.85953	0.394154
$222$	−0.823788	−0.0552890
$223$	−21.8046	−1.46015	−0.730073	−	0.683369i	$-0.760514\pi$
$223$	−21.8046	−1.46015	−0.730073	+	0.683369i	$0.760514\pi$
$224$	0.570561	0.0381222
$225$	−23.1647	−1.54431
$226$	−7.95119	−0.528906
$227$	25.4436	1.68875	0.844377	−	0.535749i	$-0.179971\pi$
$227$	25.4436	1.68875	0.844377	+	0.535749i	$0.179971\pi$
$228$	−0.494328	−0.0327376
$229$	−4.56244	−0.301495	−0.150747	−	0.988572i	$-0.548168\pi$
$229$	−4.56244	−0.301495	−0.150747	+	0.988572i	$0.548168\pi$
$230$	4.64516	0.306293
$231$	0	0
$232$	11.7457	0.771143
$233$	−8.02590	−0.525794	−0.262897	−	0.964824i	$-0.584678\pi$
$233$	−8.02590	−0.525794	−0.262897	+	0.964824i	$0.584678\pi$
$234$	−3.38914	−0.221555
$235$	−18.4852	−1.20584
$236$	−8.92059	−0.580681
$237$	−1.08904	−0.0707406
$238$	0.990732	0.0642196
$239$	−18.4414	−1.19288	−0.596439	−	0.802659i	$-0.703418\pi$
$239$	−18.4414	−1.19288	−0.596439	+	0.802659i	$0.703418\pi$
$240$	0.716879	0.0462743
$241$	3.06708	0.197568	0.0987839	−	0.995109i	$-0.468505\pi$
$241$	3.06708	0.197568	0.0987839	+	0.995109i	$0.468505\pi$
$242$	0	0
$243$	2.62485	0.168384
$244$	−2.21460	−0.141775
$245$	24.9118	1.59155
$246$	0.907850	0.0578824
$247$	7.07556	0.450207
$248$	0.101710	0.00645861
$249$	−0.577709	−0.0366108
$250$	−11.1113	−0.702742
$251$	−6.29670	−0.397444	−0.198722	−	0.980056i	$-0.563679\pi$
$251$	−6.29670	−0.397444	−0.198722	+	0.980056i	$0.563679\pi$
$252$	0.319267	0.0201119
$253$	0	0
$254$	−1.31720	−0.0826483
$255$	−2.04237	−0.127898
$256$	−14.7135	−0.919594
$257$	15.5469	0.969792	0.484896	−	0.874572i	$-0.338857\pi$
$257$	15.5469	0.969792	0.484896	+	0.874572i	$0.338857\pi$
$258$	0.519644	0.0323516
$259$	−1.11078	−0.0690203
$260$	2.55482	0.158443
$261$	11.4131	0.706451
$262$	5.23252	0.323266
$263$	−18.0189	−1.11110	−0.555548	−	0.831485i	$-0.687491\pi$
$263$	−18.0189	−1.11110	−0.555548	+	0.831485i	$0.687491\pi$
$264$	0	0
$265$	−48.5014	−2.97942
$266$	1.19634	0.0733523
$267$	1.02257	0.0625802
$268$	4.45562	0.272171
$269$	14.3998	0.877969	0.438984	−	0.898495i	$-0.355338\pi$
$269$	14.3998	0.877969	0.438984	+	0.898495i	$0.355338\pi$
$270$	2.36637	0.144013
$271$	16.1364	0.980216	0.490108	−	0.871662i	$-0.336957\pi$
$271$	16.1364	0.980216	0.490108	+	0.871662i	$0.336957\pi$
$272$	−12.0514	−0.730721
$273$	0.0145655	0.000881547 0
$274$	21.3205	1.28802
$275$	0	0
$276$	0.0802075	0.00482792
$277$	−6.44263	−0.387100	−0.193550	−	0.981090i	$-0.562000\pi$
$277$	−6.44263	−0.387100	−0.193550	+	0.981090i	$0.562000\pi$
$278$	−3.13965	−0.188304
$279$	0.0988299	0.00591679
$280$	1.63927	0.0979649
$281$	7.84066	0.467735	0.233867	−	0.972269i	$-0.424862\pi$
$281$	7.84066	0.467735	0.233867	+	0.972269i	$0.424862\pi$
$282$	0.572886	0.0341149
$283$	−14.3522	−0.853147	−0.426574	−	0.904453i	$-0.640279\pi$
$283$	−14.3522	−0.853147	−0.426574	+	0.904453i	$0.640279\pi$
$284$	6.21235	0.368635
$285$	−2.46623	−0.146087
$286$	0	0
$287$	1.22412	0.0722577
$288$	−11.4366	−0.673909
$289$	17.3341	1.01965
$290$	15.4420	0.906784
$291$	0.520323	0.0305019
$292$	2.19096	0.128217
$293$	2.66117	0.155467	0.0777337	−	0.996974i	$-0.475232\pi$
$293$	2.66117	0.155467	0.0777337	+	0.996974i	$0.475232\pi$
$294$	−0.772054	−0.0450271
$295$	−44.5053	−2.59120
$296$	22.9139	1.33184
$297$	0	0
$298$	1.61563	0.0935911
$299$	−1.14805	−0.0663934
$300$	−0.541179	−0.0312450
$301$	0.700675	0.0403862
$302$	17.3262	0.997012
$303$	0.0884973	0.00508403
$304$	−14.5524	−0.834637
$305$	−11.0488	−0.632650
$306$	−19.8587	−1.13525
$307$	22.6933	1.29517	0.647587	−	0.761992i	$-0.275778\pi$
$307$	22.6933	1.29517	0.647587	+	0.761992i	$0.275778\pi$
$308$	0	0
$309$	−0.285411	−0.0162365
$310$	0.133718	0.00759465
$311$	−26.4203	−1.49816	−0.749078	−	0.662482i	$-0.769503\pi$
$311$	−26.4203	−1.49816	−0.749078	+	0.662482i	$0.769503\pi$
$312$	−0.300468	−0.0170107
$313$	5.24753	0.296608	0.148304	−	0.988942i	$-0.452619\pi$
$313$	5.24753	0.296608	0.148304	+	0.988942i	$0.452619\pi$
$314$	9.82666	0.554551
$315$	1.59284	0.0897465
$316$	7.98236	0.449043
$317$	12.6753	0.711916	0.355958	−	0.934502i	$-0.384155\pi$
$317$	12.6753	0.711916	0.355958	+	0.934502i	$0.384155\pi$
$318$	1.50313	0.0842915
$319$	0	0
$320$	−30.1595	−1.68597
$321$	0.745221	0.0415942
$322$	−0.194113	−0.0108175
$323$	41.4594	2.30686
$324$	−6.37909	−0.354394
$325$	7.74616	0.429680
$326$	−14.4168	−0.798470
$327$	−0.718256	−0.0397196
$328$	−25.2521	−1.39431
$329$	0.772466	0.0425874
$330$	0	0
$331$	18.9859	1.04356	0.521780	−	0.853080i	$-0.325268\pi$
$331$	18.9859	1.04356	0.521780	+	0.853080i	$0.325268\pi$
$332$	4.23446	0.232396
$333$	22.2650	1.22011
$334$	16.0448	0.877932
$335$	22.2294	1.21452
$336$	−0.0299571	−0.00163429
$337$	−18.3191	−0.997907	−0.498954	−	0.866629i	$-0.666282\pi$
$337$	−18.3191	−0.997907	−0.498954	+	0.866629i	$0.666282\pi$
$338$	1.13331	0.0616441
$339$	−0.684960	−0.0372019
$340$	14.9701	0.811865
$341$	0	0
$342$	−23.9800	−1.29669
$343$	−2.08536	−0.112599
$344$	−14.4540	−0.779309
$345$	0.400160	0.0215439
$346$	−6.01971	−0.323621
$347$	−26.6296	−1.42955	−0.714775	−	0.699355i	$-0.753471\pi$
$347$	−26.6296	−1.42955	−0.714775	+	0.699355i	$0.753471\pi$
$348$	0.266635	0.0142931
$349$	12.6854	0.679032	0.339516	−	0.940600i	$-0.389737\pi$
$349$	12.6854	0.679032	0.339516	+	0.940600i	$0.389737\pi$
$350$	1.30973	0.0700078
$351$	−0.584849	−0.0312169
$352$	0	0
$353$	−6.01788	−0.320300	−0.160150	−	0.987093i	$-0.551198\pi$
$353$	−6.01788	−0.320300	−0.160150	+	0.987093i	$0.551198\pi$
$354$	1.37929	0.0733083
$355$	30.9938	1.64498
$356$	−7.49517	−0.397243
$357$	0.0853472	0.00451705
$358$	10.3907	0.549168
$359$	23.5768	1.24434	0.622169	−	0.782883i	$-0.286252\pi$
$359$	23.5768	1.24434	0.622169	+	0.782883i	$0.286252\pi$
$360$	−32.8583	−1.73178
$361$	31.0636	1.63492
$362$	4.86921	0.255920
$363$	0	0
$364$	−0.106762	−0.00559583
$365$	10.9308	0.572147
$366$	0.342418	0.0178985
$367$	−33.9521	−1.77228	−0.886142	−	0.463414i	$-0.846624\pi$
$367$	−33.9521	−1.77228	−0.886142	+	0.463414i	$0.846624\pi$
$368$	2.36121	0.123086
$369$	−24.5370	−1.27734
$370$	30.1247	1.56611
$371$	2.02679	0.105226
$372$	0.00230889	0.000119710 0
$373$	19.4008	1.00453	0.502267	−	0.864712i	$-0.332499\pi$
$373$	19.4008	1.00453	0.502267	+	0.864712i	$0.332499\pi$
$374$	0	0
$375$	−0.957192	−0.0494292
$376$	−15.9350	−0.821784
$377$	−3.81648	−0.196559
$378$	−0.0988866	−0.00508618
$379$	9.36259	0.480924	0.240462	−	0.970659i	$-0.422701\pi$
$379$	9.36259	0.480924	0.240462	+	0.970659i	$0.422701\pi$
$380$	18.0768	0.927321
$381$	−0.113471	−0.00581328
$382$	27.5272	1.40842
$383$	−13.8571	−0.708063	−0.354032	−	0.935233i	$-0.615189\pi$
$383$	−13.8571	−0.708063	−0.354032	+	0.935233i	$0.615189\pi$
$384$	0.187945	0.00959105
$385$	0	0
$386$	7.02804	0.357718
$387$	−14.0447	−0.713932
$388$	−3.81383	−0.193618
$389$	−3.40195	−0.172486	−0.0862429	−	0.996274i	$-0.527486\pi$
$389$	−3.40195	−0.172486	−0.0862429	+	0.996274i	$0.527486\pi$
$390$	−0.395023	−0.0200028
$391$	−6.72703	−0.340200
$392$	21.4749	1.08465
$393$	0.450758	0.0227377
$394$	22.8031	1.14881
$395$	39.8245	2.00379
$396$	0	0
$397$	−3.16677	−0.158936	−0.0794678	−	0.996837i	$-0.525322\pi$
$397$	−3.16677	−0.158936	−0.0794678	+	0.996837i	$0.525322\pi$
$398$	−6.84639	−0.343178
$399$	0.103059	0.00515942
$400$	−15.9316	−0.796581
$401$	−29.6819	−1.48224	−0.741121	−	0.671371i	$-0.765706\pi$
$401$	−29.6819	−1.48224	−0.741121	+	0.671371i	$0.765706\pi$
$402$	−0.688922	−0.0343603
$403$	−0.0330483	−0.00164625
$404$	−0.648662	−0.0322721
$405$	−31.8257	−1.58143
$406$	−0.645293	−0.0320253
$407$	0	0
$408$	−1.76060	−0.0871628
$409$	33.3435	1.64873	0.824364	−	0.566060i	$-0.191533\pi$
$409$	33.3435	1.64873	0.824364	+	0.566060i	$0.191533\pi$
$410$	−33.1987	−1.63957
$411$	1.83667	0.0905962
$412$	2.09199	0.103065
$413$	1.85980	0.0915148
$414$	3.89090	0.191227
$415$	21.1259	1.03703
$416$	3.82436	0.187504
$417$	−0.270467	−0.0132448
$418$	0	0
$419$	23.7908	1.16226	0.581128	−	0.813812i	$-0.302611\pi$
$419$	23.7908	1.16226	0.581128	+	0.813812i	$0.302611\pi$
$420$	0.0372124	0.00181578
$421$	−0.976467	−0.0475901	−0.0237951	−	0.999717i	$-0.507575\pi$
$421$	−0.976467	−0.0475901	−0.0237951	+	0.999717i	$0.507575\pi$
$422$	7.45985	0.363140
$423$	−15.4837	−0.752843
$424$	−41.8100	−2.03047
$425$	45.3889	2.20168
$426$	−0.960545	−0.0465385
$427$	0.461708	0.0223436
$428$	−5.46227	−0.264029
$429$	0	0
$430$	−19.0026	−0.916386
$431$	−24.8849	−1.19866	−0.599332	−	0.800501i	$-0.704567\pi$
$431$	−24.8849	−1.19866	−0.599332	+	0.800501i	$0.704567\pi$
$432$	1.20287	0.0578729
$433$	14.6313	0.703137	0.351568	−	0.936162i	$-0.385648\pi$
$433$	14.6313	0.703137	0.351568	+	0.936162i	$0.385648\pi$
$434$	−0.00558783	−0.000268224 0
$435$	1.33026	0.0637809
$436$	5.26463	0.252130
$437$	−8.12310	−0.388580
$438$	−0.338764	−0.0161868
$439$	10.5309	0.502612	0.251306	−	0.967908i	$-0.419140\pi$
$439$	10.5309	0.502612	0.251306	+	0.967908i	$0.419140\pi$
$440$	0	0
$441$	20.8667	0.993653
$442$	6.64068	0.315865
$443$	12.2074	0.579993	0.289997	−	0.957028i	$-0.406346\pi$
$443$	12.2074	0.579993	0.289997	+	0.957028i	$0.406346\pi$
$444$	0.520160	0.0246857
$445$	−37.3938	−1.77264
$446$	−24.7115	−1.17012
$447$	0.139180	0.00658297
$448$	1.26031	0.0595441
$449$	−39.6131	−1.86946	−0.934730	−	0.355359i	$-0.884359\pi$
$449$	−39.6131	−1.86946	−0.934730	+	0.355359i	$0.884359\pi$
$450$	−26.2528	−1.23757
$451$	0	0
$452$	5.02058	0.236148
$453$	1.49258	0.0701274
$454$	28.8356	1.35332
$455$	−0.532640	−0.0249705
$456$	−2.12598	−0.0995582
$457$	10.2979	0.481714	0.240857	−	0.970561i	$-0.422572\pi$
$457$	10.2979	0.481714	0.240857	+	0.970561i	$0.422572\pi$
$458$	−5.17068	−0.241610
$459$	−3.42694	−0.159956
$460$	−2.93307	−0.136755
$461$	−11.1823	−0.520810	−0.260405	−	0.965500i	$-0.583856\pi$
$461$	−11.1823	−0.520810	−0.260405	+	0.965500i	$0.583856\pi$
$462$	0	0
$463$	17.1035	0.794868	0.397434	−	0.917631i	$-0.369901\pi$
$463$	17.1035	0.794868	0.397434	+	0.917631i	$0.369901\pi$
$464$	7.84940	0.364399
$465$	0.0115192	0.000534189 0
$466$	−9.09586	−0.421358
$467$	−14.5587	−0.673697	−0.336848	−	0.941559i	$-0.609361\pi$
$467$	−14.5587	−0.673697	−0.336848	+	0.941559i	$0.609361\pi$
$468$	2.13998	0.0989208
$469$	−0.928926	−0.0428938
$470$	−20.9496	−0.966332
$471$	0.846523	0.0390057
$472$	−38.3653	−1.76590
$473$	0	0
$474$	−1.23422	−0.0566896
$475$	54.8084	2.51478
$476$	−0.625572	−0.0286731
$477$	−40.6260	−1.86014
$478$	−20.8999	−0.955940
$479$	37.0768	1.69408	0.847042	−	0.531526i	$-0.178381\pi$
$479$	37.0768	1.69408	0.847042	+	0.531526i	$0.178381\pi$
$480$	−1.33300	−0.0608429
$481$	−7.44531	−0.339477
$482$	3.47596	0.158326
$483$	−0.0167220	−0.000760876 0
$484$	0	0
$485$	−19.0274	−0.863991
$486$	2.97478	0.134939
$487$	11.5598	0.523824	0.261912	−	0.965092i	$-0.415647\pi$
$487$	11.5598	0.523824	0.261912	+	0.965092i	$0.415647\pi$
$488$	−9.52444	−0.431151
$489$	−1.24194	−0.0561624
$490$	28.2328	1.27543
$491$	−30.8957	−1.39430	−0.697151	−	0.716924i	$-0.745549\pi$
$491$	−30.8957	−1.39430	−0.697151	+	0.716924i	$0.745549\pi$
$492$	−0.573239	−0.0258436
$493$	−22.3628	−1.00717
$494$	8.01882	0.360784
$495$	0	0
$496$	0.0679708	0.00305198
$497$	−1.29518	−0.0580966
$498$	−0.654725	−0.0293389
$499$	27.7333	1.24151	0.620757	−	0.784003i	$-0.286825\pi$
$499$	27.7333	1.24151	0.620757	+	0.784003i	$0.286825\pi$
$500$	7.01597	0.313764
$501$	1.38219	0.0617516
$502$	−7.13613	−0.318501
$503$	−15.0272	−0.670031	−0.335016	−	0.942213i	$-0.608742\pi$
$503$	−15.0272	−0.670031	−0.335016	+	0.942213i	$0.608742\pi$
$504$	1.37309	0.0611623
$505$	−3.23621	−0.144009
$506$	0	0
$507$	0.0976299	0.00433590
$508$	0.831710	0.0369012
$509$	−23.3318	−1.03416	−0.517081	−	0.855936i	$-0.672981\pi$
$509$	−23.3318	−1.03416	−0.517081	+	0.855936i	$0.672981\pi$
$510$	−2.31465	−0.102494
$511$	−0.456781	−0.0202068
$512$	−20.5252	−0.907093
$513$	−4.13813	−0.182703
$514$	17.6196	0.777165
$515$	10.4370	0.459911
$516$	−0.328116	−0.0144445
$517$	0	0
$518$	−1.25886	−0.0553110
$519$	−0.518571	−0.0227627
$520$	10.9877	0.481841
$521$	−18.9947	−0.832175	−0.416087	−	0.909325i	$-0.636599\pi$
$521$	−18.9947	−0.832175	−0.416087	+	0.909325i	$0.636599\pi$
$522$	12.9346	0.566131
$523$	−12.4401	−0.543967	−0.271984	−	0.962302i	$-0.587680\pi$
$523$	−12.4401	−0.543967	−0.271984	+	0.962302i	$0.587680\pi$
$524$	−3.30394	−0.144333
$525$	0.112827	0.00492418
$526$	−20.4211	−0.890403
$527$	−0.193647	−0.00843541
$528$	0	0
$529$	−21.6820	−0.942695
$530$	−54.9673	−2.38763
$531$	−37.2788	−1.61776
$532$	−0.755398	−0.0327507
$533$	8.20506	0.355400
$534$	1.15889	0.0501501
$535$	−27.2516	−1.17819
$536$	19.1625	0.827696
$537$	0.895117	0.0386271
$538$	16.3194	0.703581
$539$	0	0
$540$	−1.49419	−0.0642995
$541$	24.0772	1.03516	0.517580	−	0.855635i	$-0.326833\pi$
$541$	24.0772	1.03516	0.517580	+	0.855635i	$0.326833\pi$
$542$	18.2876	0.785519
$543$	0.419461	0.0180008
$544$	22.4089	0.960774
$545$	26.2655	1.12509
$546$	0.0165073	0.000706448 0
$547$	−13.4013	−0.572998	−0.286499	−	0.958081i	$-0.592491\pi$
$547$	−13.4013	−0.572998	−0.286499	+	0.958081i	$0.592491\pi$
$548$	−13.4623	−0.575081
$549$	−9.25471	−0.394981
$550$	0	0
$551$	−27.0037	−1.15040
$552$	0.344953	0.0146822
$553$	−1.66419	−0.0707687
$554$	−7.30152	−0.310212
$555$	2.59511	0.110156
$556$	1.98245	0.0840746
$557$	5.97478	0.253160	0.126580	−	0.991956i	$-0.459600\pi$
$557$	5.97478	0.253160	0.126580	+	0.991956i	$0.459600\pi$
$558$	0.112005	0.00474156
$559$	4.69648	0.198640
$560$	1.09549	0.0462927
$561$	0	0
$562$	8.88592	0.374830
$563$	−37.2986	−1.57195	−0.785975	−	0.618258i	$-0.787839\pi$
$563$	−37.2986	−1.57195	−0.785975	+	0.618258i	$0.787839\pi$
$564$	−0.361734	−0.0152318
$565$	25.0479	1.05378
$566$	−16.2655	−0.683689
$567$	1.32994	0.0558521
$568$	26.7178	1.12105
$569$	26.4005	1.10677	0.553383	−	0.832927i	$-0.313337\pi$
$569$	26.4005	1.10677	0.553383	+	0.832927i	$0.313337\pi$
$570$	−2.79501	−0.117070
$571$	−1.77330	−0.0742105	−0.0371052	−	0.999311i	$-0.511814\pi$
$571$	−1.77330	−0.0742105	−0.0371052	+	0.999311i	$0.511814\pi$
$572$	0	0
$573$	2.37135	0.0990645
$574$	1.38732	0.0579054
$575$	−8.89298	−0.370863
$576$	−25.2623	−1.05260
$577$	−18.4767	−0.769195	−0.384597	−	0.923084i	$-0.625660\pi$
$577$	−18.4767	−0.769195	−0.384597	+	0.923084i	$0.625660\pi$
$578$	19.6449	0.817120
$579$	0.605434	0.0251610
$580$	−9.75044	−0.404865
$581$	−0.882816	−0.0366254
$582$	0.589689	0.0244434
$583$	0	0
$584$	9.42280	0.389918
$585$	10.6765	0.441419
$586$	3.01594	0.124587
$587$	38.6600	1.59567	0.797834	−	0.602877i	$-0.205979\pi$
$587$	38.6600	1.59567	0.797834	+	0.602877i	$0.205979\pi$
$588$	0.487494	0.0201039
$589$	−0.233835	−0.00963501
$590$	−50.4385	−2.07652
$591$	1.96439	0.0808042
$592$	15.3129	0.629355
$593$	9.13044	0.374942	0.187471	−	0.982270i	$-0.439971\pi$
$593$	9.13044	0.374942	0.187471	+	0.982270i	$0.439971\pi$
$594$	0	0
$595$	−3.12102	−0.127949
$596$	−1.02015	−0.0417870
$597$	−0.589786	−0.0241383
$598$	−1.30110	−0.0532059
$599$	38.6846	1.58061	0.790305	−	0.612714i	$-0.209922\pi$
$599$	38.6846	1.58061	0.790305	+	0.612714i	$0.209922\pi$
$600$	−2.32748	−0.0950188
$601$	−30.5525	−1.24626	−0.623132	−	0.782117i	$-0.714140\pi$
$601$	−30.5525	−1.24626	−0.623132	+	0.782117i	$0.714140\pi$
$602$	0.794084	0.0323645
$603$	18.6199	0.758259
$604$	−10.9402	−0.445150
$605$	0	0
$606$	0.100295	0.00407421
$607$	17.0424	0.691728	0.345864	−	0.938285i	$-0.387586\pi$
$607$	17.0424	0.691728	0.345864	+	0.938285i	$0.387586\pi$
$608$	27.0595	1.09741
$609$	−0.0555891	−0.00225258
$610$	−12.5217	−0.506989
$611$	5.17768	0.209467
$612$	12.5393	0.506871
$613$	−20.4127	−0.824461	−0.412231	−	0.911079i	$-0.635250\pi$
$613$	−20.4127	−0.824461	−0.412231	+	0.911079i	$0.635250\pi$
$614$	25.7186	1.03792
$615$	−2.85992	−0.115323
$616$	0	0
$617$	−11.0257	−0.443877	−0.221939	−	0.975061i	$-0.571238\pi$
$617$	−11.0257	−0.443877	−0.221939	+	0.975061i	$0.571238\pi$
$618$	−0.323460	−0.0130115
$619$	12.0272	0.483413	0.241706	−	0.970349i	$-0.422293\pi$
$619$	12.0272	0.483413	0.241706	+	0.970349i	$0.422293\pi$
$620$	−0.0844326	−0.00339089
$621$	0.671436	0.0269438
$622$	−29.9424	−1.20058
$623$	1.56262	0.0626051
$624$	−0.200796	−0.00803829
$625$	−3.72776	−0.149111
$626$	5.94709	0.237694
$627$	0	0
$628$	−6.20479	−0.247598
$629$	−43.6260	−1.73948
$630$	1.80519	0.0719205
$631$	−16.8622	−0.671274	−0.335637	−	0.941991i	$-0.608952\pi$
$631$	−16.8622	−0.671274	−0.335637	+	0.941991i	$0.608952\pi$
$632$	34.3302	1.36558
$633$	0.642633	0.0255424
$634$	14.3651	0.570511
$635$	4.14945	0.164666
$636$	−0.949115	−0.0376348
$637$	−6.97774	−0.276468
$638$	0	0
$639$	25.9612	1.02701
$640$	−6.87288	−0.271674
$641$	21.1307	0.834614	0.417307	−	0.908765i	$-0.362974\pi$
$641$	21.1307	0.834614	0.417307	+	0.908765i	$0.362974\pi$
$642$	0.844568	0.0333325
$643$	28.8342	1.13711	0.568554	−	0.822646i	$-0.307503\pi$
$643$	28.8342	1.13711	0.568554	+	0.822646i	$0.307503\pi$
$644$	0.122568	0.00482984
$645$	−1.63699	−0.0644563
$646$	46.9865	1.84866
$647$	46.8132	1.84042	0.920209	−	0.391428i	$-0.128019\pi$
$647$	46.8132	1.84042	0.920209	+	0.391428i	$0.128019\pi$
$648$	−27.4349	−1.07774
$649$	0	0
$650$	8.77883	0.344334
$651$	−0.000481366 0	−1.88662e−5 0
$652$	9.10309	0.356504
$653$	20.9489	0.819793	0.409896	−	0.912132i	$-0.365565\pi$
$653$	20.9489	0.819793	0.409896	+	0.912132i	$0.365565\pi$
$654$	−0.814009	−0.0318303
$655$	−16.4835	−0.644065
$656$	−16.8754	−0.658875
$657$	9.15595	0.357208
$658$	0.875446	0.0341284
$659$	23.8282	0.928215	0.464107	−	0.885779i	$-0.346375\pi$
$659$	23.8282	0.928215	0.464107	+	0.885779i	$0.346375\pi$
$660$	0	0
$661$	41.5729	1.61700	0.808499	−	0.588497i	$-0.200280\pi$
$661$	41.5729	1.61700	0.808499	+	0.588497i	$0.200280\pi$
$662$	21.5170	0.836280
$663$	0.572065	0.0222172
$664$	18.2114	0.706738
$665$	−3.76872	−0.146145
$666$	25.2332	0.977766
$667$	4.38151	0.169653
$668$	−10.1311	−0.391983
$669$	−2.12878	−0.0823035
$670$	25.1928	0.973284
$671$	0	0
$672$	0.0557038	0.00214882
$673$	31.5279	1.21531	0.607655	−	0.794201i	$-0.292110\pi$
$673$	31.5279	1.21531	0.607655	+	0.794201i	$0.292110\pi$
$674$	−20.7613	−0.799696
$675$	−4.53033	−0.174373
$676$	−0.715602	−0.0275231
$677$	−7.53267	−0.289504	−0.144752	−	0.989468i	$-0.546238\pi$
$677$	−7.53267	−0.289504	−0.144752	+	0.989468i	$0.546238\pi$
$678$	−0.776274	−0.0298126
$679$	0.795123	0.0305140
$680$	64.3826	2.46896
$681$	2.48406	0.0951894
$682$	0	0
$683$	42.6535	1.63209	0.816045	−	0.577989i	$-0.196162\pi$
$683$	42.6535	1.63209	0.816045	+	0.577989i	$0.196162\pi$
$684$	15.1416	0.578953
$685$	−67.1642	−2.56621
$686$	−2.36336	−0.0902337
$687$	−0.445431	−0.0169942
$688$	−9.65931	−0.368258
$689$	13.5852	0.517553
$690$	0.453506	0.0172647
$691$	−20.4111	−0.776476	−0.388238	−	0.921559i	$-0.626916\pi$
$691$	−20.4111	−0.776476	−0.388238	+	0.921559i	$0.626916\pi$
$692$	3.80099	0.144492
$693$	0	0
$694$	−30.1796	−1.14560
$695$	9.89056	0.375170
$696$	1.14673	0.0434667
$697$	48.0777	1.82107
$698$	14.3765	0.544158
$699$	−0.783568	−0.0296373
$700$	−0.826993	−0.0312574
$701$	7.94334	0.300016	0.150008	−	0.988685i	$-0.452070\pi$
$701$	7.94334	0.300016	0.150008	+	0.988685i	$0.452070\pi$
$702$	−0.662817	−0.0250164
$703$	−52.6798	−1.98685
$704$	0	0
$705$	−1.80471	−0.0679694
$706$	−6.82015	−0.256680
$707$	0.135236	0.00508606
$708$	−0.870916	−0.0327310
$709$	−1.37991	−0.0518236	−0.0259118	−	0.999664i	$-0.508249\pi$
$709$	−1.37991	−0.0518236	−0.0259118	+	0.999664i	$0.508249\pi$
$710$	35.1257	1.31824
$711$	33.3580	1.25102
$712$	−32.2349	−1.20805
$713$	0.0379411	0.00142091
$714$	0.0967251	0.00361984
$715$	0	0
$716$	−6.56097	−0.245195
$717$	−1.80044	−0.0672385
$718$	26.7199	0.997180
$719$	−23.9083	−0.891630	−0.445815	−	0.895125i	$-0.647086\pi$
$719$	−23.9083	−0.891630	−0.445815	+	0.895125i	$0.647086\pi$
$720$	−21.9585	−0.818344
$721$	−0.436146	−0.0162429
$722$	35.2047	1.31018
$723$	0.299438	0.0111362
$724$	−3.07454	−0.114264
$725$	−29.5631	−1.09795
$726$	0	0
$727$	16.9242	0.627686	0.313843	−	0.949475i	$-0.398383\pi$
$727$	16.9242	0.627686	0.313843	+	0.949475i	$0.398383\pi$
$728$	−0.459155	−0.0170174
$729$	−26.4867	−0.980987
$730$	12.3881	0.458503
$731$	27.5192	1.01783
$732$	−0.216211	−0.00799138
$733$	−41.7076	−1.54051	−0.770253	−	0.637738i	$-0.779870\pi$
$733$	−41.7076	−1.54051	−0.770253	+	0.637738i	$0.779870\pi$
$734$	−38.4783	−1.42026
$735$	2.43213	0.0897106
$736$	−4.39055	−0.161838
$737$	0	0
$738$	−27.8081	−1.02363
$739$	−6.98409	−0.256914	−0.128457	−	0.991715i	$-0.541002\pi$
$739$	−6.98409	−0.256914	−0.128457	+	0.991715i	$0.541002\pi$
$740$	−19.0215	−0.699243
$741$	0.690786	0.0253767
$742$	2.29699	0.0843250
$743$	−39.7470	−1.45818	−0.729088	−	0.684420i	$-0.760055\pi$
$743$	−39.7470	−1.45818	−0.729088	+	0.684420i	$0.760055\pi$
$744$	0.00992997	0.000364050 0
$745$	−5.08959	−0.186468
$746$	21.9872	0.805007
$747$	17.6956	0.647448
$748$	0	0
$749$	1.13880	0.0416107
$750$	−1.08480	−0.0396112
$751$	−1.90449	−0.0694959	−0.0347480	−	0.999396i	$-0.511063\pi$
$751$	−1.90449	−0.0694959	−0.0347480	+	0.999396i	$0.511063\pi$
$752$	−10.6490	−0.388329
$753$	−0.614746	−0.0224026
$754$	−4.32527	−0.157517
$755$	−54.5813	−1.98642
$756$	0.0624394	0.00227090
$757$	25.9063	0.941581	0.470791	−	0.882245i	$-0.343969\pi$
$757$	25.9063	0.941581	0.470791	+	0.882245i	$0.343969\pi$
$758$	10.6107	0.385400
$759$	0	0
$760$	77.7439	2.82007
$761$	−51.8254	−1.87867	−0.939334	−	0.343003i	$-0.888556\pi$
$761$	−51.8254	−1.87867	−0.939334	+	0.343003i	$0.888556\pi$
$762$	−0.128598	−0.00465861
$763$	−1.09759	−0.0397354
$764$	−17.3814	−0.628836
$765$	62.5592	2.26183
$766$	−15.7044	−0.567423
$767$	12.4659	0.450116
$768$	−1.43648	−0.0518344
$769$	−43.9447	−1.58469	−0.792343	−	0.610075i	$-0.791139\pi$
$769$	−43.9447	−1.58469	−0.792343	+	0.610075i	$0.791139\pi$
$770$	0	0
$771$	1.51785	0.0546639
$772$	−4.43768	−0.159715
$773$	−10.0136	−0.360165	−0.180083	−	0.983651i	$-0.557636\pi$
$773$	−10.0136	−0.360165	−0.180083	+	0.983651i	$0.557636\pi$
$774$	−15.9170	−0.572126
$775$	−0.255998	−0.00919570
$776$	−16.4024	−0.588810
$777$	−0.108445	−0.00389044
$778$	−3.85548	−0.138226
$779$	58.0554	2.08005
$780$	0.249427	0.00893093
$781$	0	0
$782$	−7.62383	−0.272628
$783$	2.23206	0.0797675
$784$	14.3512	0.512543
$785$	−30.9561	−1.10487
$786$	0.510850	0.0182214
$787$	−8.91326	−0.317724	−0.158862	−	0.987301i	$-0.550782\pi$
$787$	−8.91326	−0.317724	−0.158862	+	0.987301i	$0.550782\pi$
$788$	−14.3985	−0.512924
$789$	−1.75919	−0.0626287
$790$	45.1336	1.60578
$791$	−1.04671	−0.0372167
$792$	0	0
$793$	3.09474	0.109897
$794$	−3.58894	−0.127367
$795$	−4.73519	−0.167940
$796$	4.32298	0.153224
$797$	−22.4672	−0.795829	−0.397914	−	0.917423i	$-0.630266\pi$
$797$	−22.4672	−0.795829	−0.397914	+	0.917423i	$0.630266\pi$
$798$	0.116799	0.00413462
$799$	30.3388	1.07331
$800$	29.6241	1.04737
$801$	−31.3220	−1.10671
$802$	−33.6389	−1.18783
$803$	0	0
$804$	0.435002	0.0153413
$805$	0.611497	0.0215524
$806$	−0.0374541	−0.00131926
$807$	1.40585	0.0494882
$808$	−2.78974	−0.0981425
$809$	−7.71621	−0.271287	−0.135644	−	0.990758i	$-0.543310\pi$
$809$	−7.71621	−0.271287	−0.135644	+	0.990758i	$0.543310\pi$
$810$	−36.0684	−1.26732
$811$	52.2857	1.83600	0.918000	−	0.396581i	$-0.129804\pi$
$811$	52.2857	1.83600	0.918000	+	0.396581i	$0.129804\pi$
$812$	0.407454	0.0142988
$813$	1.57539	0.0552515
$814$	0	0
$815$	45.4158	1.59085
$816$	−1.17657	−0.0411883
$817$	33.2303	1.16258
$818$	37.7886	1.32125
$819$	−0.446152	−0.0155898
$820$	20.9625	0.732041
$821$	13.7171	0.478729	0.239364	−	0.970930i	$-0.423061\pi$
$821$	13.7171	0.478729	0.239364	+	0.970930i	$0.423061\pi$
$822$	2.08152	0.0726014
$823$	13.9555	0.486458	0.243229	−	0.969969i	$-0.421793\pi$
$823$	13.9555	0.486458	0.243229	+	0.969969i	$0.421793\pi$
$824$	8.99712	0.313430
$825$	0	0
$826$	2.10774	0.0733375
$827$	−14.0156	−0.487372	−0.243686	−	0.969854i	$-0.578357\pi$
$827$	−14.0156	−0.487372	−0.243686	+	0.969854i	$0.578357\pi$
$828$	−2.45681	−0.0853800
$829$	−53.1330	−1.84539	−0.922693	−	0.385536i	$-0.874016\pi$
$829$	−53.1330	−1.84539	−0.922693	+	0.385536i	$0.874016\pi$
$830$	23.9423	0.831050
$831$	−0.628994	−0.0218195
$832$	8.44761	0.292868
$833$	−40.8863	−1.41663
$834$	−0.306523	−0.0106140
$835$	−50.5445	−1.74916
$836$	0	0
$837$	0.0193283	0.000668082 0
$838$	26.9624	0.931401
$839$	24.3369	0.840204	0.420102	−	0.907477i	$-0.361994\pi$
$839$	24.3369	0.840204	0.420102	+	0.907477i	$0.361994\pi$
$840$	0.160041	0.00552195
$841$	−14.4345	−0.497740
$842$	−1.10664	−0.0381374
$843$	0.765483	0.0263646
$844$	−4.71033	−0.162136
$845$	−3.57018	−0.122818
$846$	−17.5479	−0.603308
$847$	0	0
$848$	−27.9407	−0.959489
$849$	−1.40120	−0.0480890
$850$	51.4398	1.76437
$851$	8.54759	0.293008
$852$	0.606511	0.0207787
$853$	35.7734	1.22486	0.612428	−	0.790526i	$-0.290193\pi$
$853$	35.7734	1.22486	0.612428	+	0.790526i	$0.290193\pi$
$854$	0.523260	0.0179056
$855$	75.5422	2.58349
$856$	−23.4919	−0.802936
$857$	−21.8355	−0.745885	−0.372942	−	0.927854i	$-0.621651\pi$
$857$	−21.8355	−0.745885	−0.372942	+	0.927854i	$0.621651\pi$
$858$	0	0
$859$	−43.8802	−1.49717	−0.748586	−	0.663038i	$-0.769267\pi$
$859$	−43.8802	−1.49717	−0.748586	+	0.663038i	$0.769267\pi$
$860$	11.9987	0.409152
$861$	0.119511	0.00407293
$862$	−28.2024	−0.960577
$863$	18.6086	0.633446	0.316723	−	0.948518i	$-0.397417\pi$
$863$	18.6086	0.633446	0.316723	+	0.948518i	$0.397417\pi$
$864$	−2.23667	−0.0760930
$865$	18.9634	0.644773
$866$	16.5819	0.563475
$867$	1.69232	0.0574742
$868$	0.00352829	0.000119758 0
$869$	0	0
$870$	1.50760	0.0511124
$871$	−6.22640	−0.210974
$872$	22.6419	0.766751
$873$	−15.9378	−0.539414
$874$	−9.20601	−0.311398
$875$	−1.46272	−0.0494488
$876$	0.213904	0.00722713
$877$	−32.2364	−1.08854	−0.544272	−	0.838908i	$-0.683194\pi$
$877$	−32.2364	−1.08854	−0.544272	+	0.838908i	$0.683194\pi$
$878$	11.9348	0.402779
$879$	0.259810	0.00876318
$880$	0	0
$881$	−6.18418	−0.208350	−0.104175	−	0.994559i	$-0.533220\pi$
$881$	−6.18418	−0.208350	−0.104175	+	0.994559i	$0.533220\pi$
$882$	23.6485	0.796287
$883$	16.5636	0.557410	0.278705	−	0.960377i	$-0.410095\pi$
$883$	16.5636	0.557410	0.278705	+	0.960377i	$0.410095\pi$
$884$	−4.19309	−0.141029
$885$	−4.34505	−0.146057
$886$	13.8349	0.464791
$887$	38.4843	1.29217	0.646087	−	0.763263i	$-0.276404\pi$
$887$	38.4843	1.29217	0.646087	+	0.763263i	$0.276404\pi$
$888$	2.23708	0.0750715
$889$	−0.173398	−0.00581559
$890$	−42.3789	−1.42054
$891$	0	0
$892$	15.6034	0.522441
$893$	36.6350	1.22594
$894$	0.157734	0.00527542
$895$	−32.7331	−1.09415
$896$	0.287206	0.00959487
$897$	−0.112084	−0.00374238
$898$	−44.8941	−1.49814
$899$	0.126128	0.00420661
$900$	16.5767	0.552555
$901$	79.6026	2.65195
$902$	0	0
$903$	0.0684068	0.00227644
$904$	21.5923	0.718148
$905$	−15.3390	−0.509887
$906$	1.69156	0.0561982
$907$	−19.3324	−0.641922	−0.320961	−	0.947092i	$-0.604006\pi$
$907$	−19.3324	−0.641922	−0.320961	+	0.947092i	$0.604006\pi$
$908$	−18.2075	−0.604237
$909$	−2.71073	−0.0899092
$910$	−0.603648	−0.0200107
$911$	−2.89909	−0.0960511	−0.0480255	−	0.998846i	$-0.515293\pi$
$911$	−2.89909	−0.0960511	−0.0480255	+	0.998846i	$0.515293\pi$
$912$	−1.42075	−0.0470457
$913$	0	0
$914$	11.6707	0.386033
$915$	−1.07869	−0.0356603
$916$	3.26489	0.107875
$917$	0.688818	0.0227468
$918$	−3.88379	−0.128184
$919$	52.1651	1.72077	0.860384	−	0.509647i	$-0.170224\pi$
$919$	52.1651	1.72077	0.860384	+	0.509647i	$0.170224\pi$
$920$	−12.6144	−0.415884
$921$	2.21554	0.0730046
$922$	−12.6730	−0.417363
$923$	−8.68130	−0.285749
$924$	0	0
$925$	−57.6726	−1.89626
$926$	19.3836	0.636986
$927$	8.74232	0.287136
$928$	−14.5956	−0.479123
$929$	16.1243	0.529022	0.264511	−	0.964383i	$-0.414789\pi$
$929$	16.1243	0.529022	0.264511	+	0.964383i	$0.414789\pi$
$930$	0.0130548	0.000428085 0
$931$	−49.3714	−1.61808
$932$	5.74335	0.188130
$933$	−2.57941	−0.0844460
$934$	−16.4996	−0.539882
$935$	0	0
$936$	9.20355	0.300827
$937$	−52.3732	−1.71096	−0.855478	−	0.517839i	$-0.826737\pi$
$937$	−52.3732	−1.71096	−0.855478	+	0.517839i	$0.826737\pi$
$938$	−1.05276	−0.0343740
$939$	0.512316	0.0167188
$940$	13.2281	0.431452
$941$	8.19184	0.267046	0.133523	−	0.991046i	$-0.457371\pi$
$941$	8.19184	0.267046	0.133523	+	0.991046i	$0.457371\pi$
$942$	0.959376	0.0312581
$943$	−9.41981	−0.306751
$944$	−25.6387	−0.834468
$945$	0.311514	0.0101335
$946$	0	0
$947$	41.8680	1.36053	0.680264	−	0.732968i	$-0.261865\pi$
$947$	41.8680	1.36053	0.680264	+	0.732968i	$0.261865\pi$
$948$	0.779317	0.0253110
$949$	−3.06171	−0.0993873
$950$	62.1151	2.01528
$951$	1.23749	0.0401283
$952$	−2.69043	−0.0871975
$953$	−19.3249	−0.625995	−0.312998	−	0.949754i	$-0.601333\pi$
$953$	−19.3249	−0.625995	−0.312998	+	0.949754i	$0.601333\pi$
$954$	−46.0419	−1.49066
$955$	−86.7166	−2.80608
$956$	13.1967	0.426812
$957$	0	0
$958$	42.0197	1.35759
$959$	2.80668	0.0906323
$960$	−2.94447	−0.0950322
$961$	−30.9989	−0.999965
$962$	−8.43787	−0.272048
$963$	−22.8266	−0.735577
$964$	−2.19480	−0.0706899
$965$	−22.1398	−0.712706
$966$	−0.0189512	−0.000609746 0
$967$	−57.9531	−1.86365	−0.931823	−	0.362913i	$-0.881782\pi$
$967$	−57.9531	−1.86365	−0.931823	+	0.362913i	$0.881782\pi$
$968$	0	0
$969$	4.04768	0.130030
$970$	−21.5640	−0.692379
$971$	17.8596	0.573143	0.286571	−	0.958059i	$-0.407484\pi$
$971$	17.8596	0.573143	0.286571	+	0.958059i	$0.407484\pi$
$972$	−1.87835	−0.0602480
$973$	−0.413309	−0.0132501
$974$	13.1008	0.419778
$975$	0.756257	0.0242196
$976$	−6.36498	−0.203738
$977$	−2.24573	−0.0718472	−0.0359236	−	0.999355i	$-0.511437\pi$
$977$	−2.24573	−0.0718472	−0.0359236	+	0.999355i	$0.511437\pi$
$978$	−1.40751	−0.0450071
$979$	0	0
$980$	−17.8269	−0.569460
$981$	22.0007	0.702427
$982$	−35.0145	−1.11736
$983$	−30.9131	−0.985975	−0.492987	−	0.870036i	$-0.664095\pi$
$983$	−30.9131	−0.985975	−0.492987	+	0.870036i	$0.664095\pi$
$984$	−2.46536	−0.0785928
$985$	−71.8348	−2.28885
$986$	−25.3440	−0.807118
$987$	0.0754158	0.00240051
$988$	−5.06328	−0.161084
$989$	−5.39180	−0.171449
$990$	0	0
$991$	27.5241	0.874331	0.437166	−	0.899381i	$-0.355982\pi$
$991$	27.5241	0.874331	0.437166	+	0.899381i	$0.355982\pi$
$992$	−0.126388	−0.00401284
$993$	1.85359	0.0588219
$994$	−1.46784	−0.0465571
$995$	21.5676	0.683738
$996$	0.413409	0.0130994
$997$	49.5572	1.56949	0.784747	−	0.619816i	$-0.212793\pi$
$997$	49.5572	1.56949	0.784747	+	0.619816i	$0.212793\pi$
$998$	31.4305	0.994916
$999$	4.35438	0.137767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.s.1.10		14
11.3	even	5		143.2.h.c.53.5	yes	28
11.4	even	5		143.2.h.c.27.5	✓	28
11.10	odd	2		1573.2.a.r.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.27.5	✓	28	11.4	even	5
143.2.h.c.53.5	yes	28	11.3	even	5
1573.2.a.r.1.5		14	11.10	odd	2
1573.2.a.s.1.10		14	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+1.13331 q^{2} +0.0976299 q^{3} -0.715602 q^{4} -3.57018 q^{5} +0.110645 q^{6} +0.149191 q^{7} -3.07763 q^{8} -2.99047 q^{9} +O(q^{10})\)	\(q+1.13331 q^{2} +0.0976299 q^{3} -0.715602 q^{4} -3.57018 q^{5} +0.110645 q^{6} +0.149191 q^{7} -3.07763 q^{8} -2.99047 q^{9} -4.04613 q^{10} -0.0698641 q^{12} +1.00000 q^{13} +0.169081 q^{14} -0.348556 q^{15} -2.05671 q^{16} +5.85953 q^{17} -3.38914 q^{18} +7.07556 q^{19} +2.55482 q^{20} +0.0145655 q^{21} -1.14805 q^{23} -0.300468 q^{24} +7.74616 q^{25} +1.13331 q^{26} -0.584849 q^{27} -0.106762 q^{28} -3.81648 q^{29} -0.395023 q^{30} -0.0330483 q^{31} +3.82436 q^{32} +6.64068 q^{34} -0.532640 q^{35} +2.13998 q^{36} -7.44531 q^{37} +8.01882 q^{38} +0.0976299 q^{39} +10.9877 q^{40} +8.20506 q^{41} +0.0165073 q^{42} +4.69648 q^{43} +10.6765 q^{45} -1.30110 q^{46} +5.17768 q^{47} -0.200796 q^{48} -6.97774 q^{49} +8.77883 q^{50} +0.572065 q^{51} -0.715602 q^{52} +13.5852 q^{53} -0.662817 q^{54} -0.459155 q^{56} +0.690786 q^{57} -4.32527 q^{58} +12.4659 q^{59} +0.249427 q^{60} +3.09474 q^{61} -0.0374541 q^{62} -0.446152 q^{63} +8.44761 q^{64} -3.57018 q^{65} -6.22640 q^{67} -4.19309 q^{68} -0.112084 q^{69} -0.603648 q^{70} -8.68130 q^{71} +9.20355 q^{72} -3.06171 q^{73} -8.43787 q^{74} +0.756257 q^{75} -5.06328 q^{76} +0.110645 q^{78} -11.1548 q^{79} +7.34282 q^{80} +8.91431 q^{81} +9.29890 q^{82} -5.91734 q^{83} -0.0104231 q^{84} -20.9195 q^{85} +5.32259 q^{86} -0.372603 q^{87} +10.4739 q^{89} +12.0998 q^{90} +0.149191 q^{91} +0.821546 q^{92} -0.00322650 q^{93} +5.86794 q^{94} -25.2610 q^{95} +0.373371 q^{96} +5.32955 q^{97} -7.90797 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more