LMFDB - Embedded newform 6422.2.a.bm.1.5

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:	$14$
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} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
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			1.5
Root			$-1.17869$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.17869 q^{3} +1.00000 q^{4} +0.970755 q^{5} +1.17869 q^{6} +1.94107 q^{7} -1.00000 q^{8} -1.61069 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.17869 q^{3} +1.00000 q^{4} +0.970755 q^{5} +1.17869 q^{6} +1.94107 q^{7} -1.00000 q^{8} -1.61069 q^{9} -0.970755 q^{10} +3.59911 q^{11} -1.17869 q^{12} -1.94107 q^{14} -1.14422 q^{15} +1.00000 q^{16} -3.06452 q^{17} +1.61069 q^{18} -1.00000 q^{19} +0.970755 q^{20} -2.28792 q^{21} -3.59911 q^{22} -5.40100 q^{23} +1.17869 q^{24} -4.05763 q^{25} +5.43457 q^{27} +1.94107 q^{28} -5.32430 q^{29} +1.14422 q^{30} -3.17085 q^{31} -1.00000 q^{32} -4.24223 q^{33} +3.06452 q^{34} +1.88431 q^{35} -1.61069 q^{36} -10.2477 q^{37} +1.00000 q^{38} -0.970755 q^{40} +11.4845 q^{41} +2.28792 q^{42} +7.67163 q^{43} +3.59911 q^{44} -1.56359 q^{45} +5.40100 q^{46} +6.73338 q^{47} -1.17869 q^{48} -3.23223 q^{49} +4.05763 q^{50} +3.61212 q^{51} +7.89427 q^{53} -5.43457 q^{54} +3.49386 q^{55} -1.94107 q^{56} +1.17869 q^{57} +5.32430 q^{58} +6.56597 q^{59} -1.14422 q^{60} +12.7232 q^{61} +3.17085 q^{62} -3.12647 q^{63} +1.00000 q^{64} +4.24223 q^{66} -5.66912 q^{67} -3.06452 q^{68} +6.36610 q^{69} -1.88431 q^{70} -3.18208 q^{71} +1.61069 q^{72} -1.81384 q^{73} +10.2477 q^{74} +4.78269 q^{75} -1.00000 q^{76} +6.98614 q^{77} -0.937757 q^{79} +0.970755 q^{80} -1.57359 q^{81} -11.4845 q^{82} +12.7952 q^{83} -2.28792 q^{84} -2.97490 q^{85} -7.67163 q^{86} +6.27570 q^{87} -3.59911 q^{88} -11.6203 q^{89} +1.56359 q^{90} -5.40100 q^{92} +3.73745 q^{93} -6.73338 q^{94} -0.970755 q^{95} +1.17869 q^{96} +17.7433 q^{97} +3.23223 q^{98} -5.79706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.17869	−0.680516	−0.340258	−	0.940332i	$-0.610514\pi$
$3$	−1.17869	−0.680516	−0.340258	+	0.940332i	$0.610514\pi$
$4$	1.00000	0.500000
$5$	0.970755	0.434135	0.217067	−	0.976157i	$-0.430351\pi$
$5$	0.970755	0.434135	0.217067	+	0.976157i	$0.430351\pi$
$6$	1.17869	0.481198
$7$	1.94107	0.733657	0.366828	−	0.930289i	$-0.380444\pi$
$7$	1.94107	0.733657	0.366828	+	0.930289i	$0.380444\pi$
$8$	−1.00000	−0.353553
$9$	−1.61069	−0.536897
$10$	−0.970755	−0.306980
$11$	3.59911	1.08517	0.542587	−	0.840000i	$-0.317445\pi$
$11$	3.59911	1.08517	0.542587	+	0.840000i	$0.317445\pi$
$12$	−1.17869	−0.340258
$13$	0	0
$13$	0	0
$14$	−1.94107	−0.518774
$15$	−1.14422	−0.295436
$16$	1.00000	0.250000
$17$	−3.06452	−0.743256	−0.371628	−	0.928382i	$-0.621200\pi$
$17$	−3.06452	−0.743256	−0.371628	+	0.928382i	$0.621200\pi$
$18$	1.61069	0.379644
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.970755	0.217067
$21$	−2.28792	−0.499265
$22$	−3.59911	−0.767333
$23$	−5.40100	−1.12619	−0.563093	−	0.826393i	$-0.690389\pi$
$23$	−5.40100	−1.12619	−0.563093	+	0.826393i	$0.690389\pi$
$24$	1.17869	0.240599
$25$	−4.05763	−0.811527
$26$	0	0
$27$	5.43457	1.04588
$28$	1.94107	0.366828
$29$	−5.32430	−0.988699	−0.494349	−	0.869263i	$-0.664594\pi$
$29$	−5.32430	−0.988699	−0.494349	+	0.869263i	$0.664594\pi$
$30$	1.14422	0.208905
$31$	−3.17085	−0.569502	−0.284751	−	0.958602i	$-0.591911\pi$
$31$	−3.17085	−0.569502	−0.284751	+	0.958602i	$0.591911\pi$
$32$	−1.00000	−0.176777
$33$	−4.24223	−0.738478
$34$	3.06452	0.525561
$35$	1.88431	0.318506
$36$	−1.61069	−0.268449
$37$	−10.2477	−1.68471	−0.842354	−	0.538925i	$-0.818831\pi$
$37$	−10.2477	−1.68471	−0.842354	+	0.538925i	$0.818831\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−0.970755	−0.153490
$41$	11.4845	1.79357	0.896786	−	0.442465i	$-0.145896\pi$
$41$	11.4845	1.79357	0.896786	+	0.442465i	$0.145896\pi$
$42$	2.28792	0.353034
$43$	7.67163	1.16991	0.584956	−	0.811065i	$-0.301112\pi$
$43$	7.67163	1.16991	0.584956	+	0.811065i	$0.301112\pi$
$44$	3.59911	0.542587
$45$	−1.56359	−0.233086
$46$	5.40100	0.796334
$47$	6.73338	0.982165	0.491082	−	0.871113i	$-0.336601\pi$
$47$	6.73338	0.982165	0.491082	+	0.871113i	$0.336601\pi$
$48$	−1.17869	−0.170129
$49$	−3.23223	−0.461748
$50$	4.05763	0.573836
$51$	3.61212	0.505798
$52$	0	0
$53$	7.89427	1.08436	0.542181	−	0.840262i	$-0.317599\pi$
$53$	7.89427	1.08436	0.542181	+	0.840262i	$0.317599\pi$
$54$	−5.43457	−0.739552
$55$	3.49386	0.471112
$56$	−1.94107	−0.259387
$57$	1.17869	0.156121
$58$	5.32430	0.699115
$59$	6.56597	0.854817	0.427408	−	0.904059i	$-0.359427\pi$
$59$	6.56597	0.854817	0.427408	+	0.904059i	$0.359427\pi$
$60$	−1.14422	−0.147718
$61$	12.7232	1.62904	0.814518	−	0.580138i	$-0.197001\pi$
$61$	12.7232	1.62904	0.814518	+	0.580138i	$0.197001\pi$
$62$	3.17085	0.402698
$63$	−3.12647	−0.393898
$64$	1.00000	0.125000
$65$	0	0
$66$	4.24223	0.522183
$67$	−5.66912	−0.692593	−0.346296	−	0.938125i	$-0.612561\pi$
$67$	−5.66912	−0.692593	−0.346296	+	0.938125i	$0.612561\pi$
$68$	−3.06452	−0.371628
$69$	6.36610	0.766388
$70$	−1.88431	−0.225218
$71$	−3.18208	−0.377643	−0.188822	−	0.982011i	$-0.560467\pi$
$71$	−3.18208	−0.377643	−0.188822	+	0.982011i	$0.560467\pi$
$72$	1.61069	0.189822
$73$	−1.81384	−0.212293	−0.106147	−	0.994350i	$-0.533851\pi$
$73$	−1.81384	−0.212293	−0.106147	+	0.994350i	$0.533851\pi$
$74$	10.2477	1.19127
$75$	4.78269	0.552257
$76$	−1.00000	−0.114708
$77$	6.98614	0.796145
$78$	0	0
$79$	−0.937757	−0.105506	−0.0527530	−	0.998608i	$-0.516800\pi$
$79$	−0.937757	−0.105506	−0.0527530	+	0.998608i	$0.516800\pi$
$80$	0.970755	0.108534
$81$	−1.57359	−0.174844
$82$	−11.4845	−1.26825
$83$	12.7952	1.40446	0.702228	−	0.711952i	$-0.252189\pi$
$83$	12.7952	1.40446	0.702228	+	0.711952i	$0.252189\pi$
$84$	−2.28792	−0.249633
$85$	−2.97490	−0.322673
$86$	−7.67163	−0.827253
$87$	6.27570	0.672826
$88$	−3.59911	−0.383667
$89$	−11.6203	−1.23175	−0.615874	−	0.787845i	$-0.711197\pi$
$89$	−11.6203	−1.23175	−0.615874	+	0.787845i	$0.711197\pi$
$90$	1.56359	0.164817
$91$	0	0
$92$	−5.40100	−0.563093
$93$	3.73745	0.387555
$94$	−6.73338	−0.694495
$95$	−0.970755	−0.0995974
$96$	1.17869	0.120299
$97$	17.7433	1.80156	0.900782	−	0.434272i	$-0.142994\pi$
$97$	17.7433	1.80156	0.900782	+	0.434272i	$0.142994\pi$
$98$	3.23223	0.326505
$99$	−5.79706	−0.582627
$100$	−4.05763	−0.405763
$101$	0.407791	0.0405767	0.0202884	−	0.999794i	$-0.493542\pi$
$101$	0.407791	0.0405767	0.0202884	+	0.999794i	$0.493542\pi$
$102$	−3.61212	−0.357653
$103$	15.0680	1.48470	0.742349	−	0.670013i	$-0.233711\pi$
$103$	15.0680	1.48470	0.742349	+	0.670013i	$0.233711\pi$
$104$	0	0
$105$	−2.22101	−0.216749
$106$	−7.89427	−0.766760
$107$	−15.3417	−1.48314	−0.741571	−	0.670874i	$-0.765919\pi$
$107$	−15.3417	−1.48314	−0.741571	+	0.670874i	$0.765919\pi$
$108$	5.43457	0.522942
$109$	−14.2569	−1.36557	−0.682783	−	0.730621i	$-0.739231\pi$
$109$	−14.2569	−1.36557	−0.682783	+	0.730621i	$0.739231\pi$
$110$	−3.49386	−0.333126
$111$	12.0788	1.14647
$112$	1.94107	0.183414
$113$	0.452190	0.0425385	0.0212692	−	0.999774i	$-0.493229\pi$
$113$	0.452190	0.0425385	0.0212692	+	0.999774i	$0.493229\pi$
$114$	−1.17869	−0.110394
$115$	−5.24305	−0.488917
$116$	−5.32430	−0.494349
$117$	0	0
$118$	−6.56597	−0.604447
$119$	−5.94846	−0.545295
$120$	1.14422	0.104452
$121$	1.95361	0.177601
$122$	−12.7232	−1.15190
$123$	−13.5366	−1.22055
$124$	−3.17085	−0.284751
$125$	−8.79274	−0.786447
$126$	3.12647	0.278528
$127$	10.1514	0.900792	0.450396	−	0.892829i	$-0.351283\pi$
$127$	10.1514	0.900792	0.450396	+	0.892829i	$0.351283\pi$
$128$	−1.00000	−0.0883883
$129$	−9.04247	−0.796145
$130$	0	0
$131$	13.0826	1.14303	0.571514	−	0.820592i	$-0.306356\pi$
$131$	13.0826	1.14303	0.571514	+	0.820592i	$0.306356\pi$
$132$	−4.24223	−0.369239
$133$	−1.94107	−0.168312
$134$	5.66912	0.489737
$135$	5.27564	0.454055
$136$	3.06452	0.262781
$137$	16.7054	1.42724	0.713621	−	0.700532i	$-0.247054\pi$
$137$	16.7054	1.42724	0.713621	+	0.700532i	$0.247054\pi$
$138$	−6.36610	−0.541918
$139$	18.0537	1.53130	0.765648	−	0.643259i	$-0.222418\pi$
$139$	18.0537	1.53130	0.765648	+	0.643259i	$0.222418\pi$
$140$	1.88431	0.159253
$141$	−7.93656	−0.668379
$142$	3.18208	0.267034
$143$	0	0
$144$	−1.61069	−0.134224
$145$	−5.16860	−0.429229
$146$	1.81384	0.150114
$147$	3.80980	0.314227
$148$	−10.2477	−0.842354
$149$	−13.5277	−1.10823	−0.554116	−	0.832439i	$-0.686944\pi$
$149$	−13.5277	−1.10823	−0.554116	+	0.832439i	$0.686944\pi$
$150$	−4.78269	−0.390505
$151$	12.4811	1.01570	0.507850	−	0.861446i	$-0.330441\pi$
$151$	12.4811	1.01570	0.507850	+	0.861446i	$0.330441\pi$
$152$	1.00000	0.0811107
$153$	4.93600	0.399052
$154$	−6.98614	−0.562959
$155$	−3.07812	−0.247240
$156$	0	0
$157$	22.8574	1.82422	0.912110	−	0.409947i	$-0.134453\pi$
$157$	22.8574	1.82422	0.912110	+	0.409947i	$0.134453\pi$
$158$	0.937757	0.0746040
$159$	−9.30489	−0.737926
$160$	−0.970755	−0.0767449
$161$	−10.4837	−0.826234
$162$	1.57359	0.123633
$163$	−5.91844	−0.463568	−0.231784	−	0.972767i	$-0.574456\pi$
$163$	−5.91844	−0.463568	−0.231784	+	0.972767i	$0.574456\pi$
$164$	11.4845	0.896786
$165$	−4.11817	−0.320599
$166$	−12.7952	−0.993100
$167$	10.5932	0.819728	0.409864	−	0.912147i	$-0.365576\pi$
$167$	10.5932	0.819728	0.409864	+	0.912147i	$0.365576\pi$
$168$	2.28792	0.176517
$169$	0	0
$170$	2.97490	0.228164
$171$	1.61069	0.123173
$172$	7.67163	0.584956
$173$	−7.50724	−0.570765	−0.285382	−	0.958414i	$-0.592121\pi$
$173$	−7.50724	−0.570765	−0.285382	+	0.958414i	$0.592121\pi$
$174$	−6.27570	−0.475760
$175$	−7.87617	−0.595382
$176$	3.59911	0.271293
$177$	−7.73924	−0.581717
$178$	11.6203	0.870977
$179$	−20.3989	−1.52469	−0.762343	−	0.647173i	$-0.775951\pi$
$179$	−20.3989	−1.52469	−0.762343	+	0.647173i	$0.775951\pi$
$180$	−1.56359	−0.116543
$181$	−0.989512	−0.0735498	−0.0367749	−	0.999324i	$-0.511708\pi$
$181$	−0.989512	−0.0735498	−0.0367749	+	0.999324i	$0.511708\pi$
$182$	0	0
$183$	−14.9967	−1.10859
$184$	5.40100	0.398167
$185$	−9.94798	−0.731390
$186$	−3.73745	−0.274043
$187$	−11.0296	−0.806561
$188$	6.73338	0.491082
$189$	10.5489	0.767320
$190$	0.970755	0.0704260
$191$	3.07075	0.222192	0.111096	−	0.993810i	$-0.464564\pi$
$191$	3.07075	0.222192	0.111096	+	0.993810i	$0.464564\pi$
$192$	−1.17869	−0.0850646
$193$	26.8452	1.93236	0.966180	−	0.257870i	$-0.0830206\pi$
$193$	26.8452	1.93236	0.966180	+	0.257870i	$0.0830206\pi$
$194$	−17.7433	−1.27390
$195$	0	0
$196$	−3.23223	−0.230874
$197$	−11.6680	−0.831313	−0.415657	−	0.909522i	$-0.636448\pi$
$197$	−11.6680	−0.831313	−0.415657	+	0.909522i	$0.636448\pi$
$198$	5.79706	0.411979
$199$	23.5055	1.66626	0.833129	−	0.553078i	$-0.186547\pi$
$199$	23.5055	1.66626	0.833129	+	0.553078i	$0.186547\pi$
$200$	4.05763	0.286918
$201$	6.68212	0.471321
$202$	−0.407791	−0.0286921
$203$	−10.3349	−0.725365
$204$	3.61212	0.252899
$205$	11.1486	0.778652
$206$	−15.0680	−1.04984
$207$	8.69935	0.604646
$208$	0	0
$209$	−3.59911	−0.248956
$210$	2.22101	0.153264
$211$	13.5513	0.932912	0.466456	−	0.884544i	$-0.345531\pi$
$211$	13.5513	0.932912	0.466456	+	0.884544i	$0.345531\pi$
$212$	7.89427	0.542181
$213$	3.75068	0.256993
$214$	15.3417	1.04874
$215$	7.44727	0.507900
$216$	−5.43457	−0.369776
$217$	−6.15485	−0.417819
$218$	14.2569	0.965601
$219$	2.13795	0.144469
$220$	3.49386	0.235556
$221$	0	0
$222$	−12.0788	−0.810678
$223$	4.42238	0.296144	0.148072	−	0.988977i	$-0.452693\pi$
$223$	4.42238	0.296144	0.148072	+	0.988977i	$0.452693\pi$
$224$	−1.94107	−0.129693
$225$	6.53560	0.435707
$226$	−0.452190	−0.0300793
$227$	−24.7294	−1.64135	−0.820674	−	0.571397i	$-0.806402\pi$
$227$	−24.7294	−1.64135	−0.820674	+	0.571397i	$0.806402\pi$
$228$	1.17869	0.0780606
$229$	2.25971	0.149326	0.0746629	−	0.997209i	$-0.476212\pi$
$229$	2.25971	0.149326	0.0746629	+	0.997209i	$0.476212\pi$
$230$	5.24305	0.345716
$231$	−8.23449	−0.541790
$232$	5.32430	0.349558
$233$	−8.56423	−0.561061	−0.280531	−	0.959845i	$-0.590510\pi$
$233$	−8.56423	−0.561061	−0.280531	+	0.959845i	$0.590510\pi$
$234$	0	0
$235$	6.53646	0.426392
$236$	6.56597	0.427408
$237$	1.10532	0.0717985
$238$	5.94846	0.385581
$239$	1.40430	0.0908368	0.0454184	−	0.998968i	$-0.485538\pi$
$239$	1.40430	0.0908368	0.0454184	+	0.998968i	$0.485538\pi$
$240$	−1.14422	−0.0738590
$241$	−2.35360	−0.151609	−0.0758044	−	0.997123i	$-0.524152\pi$
$241$	−2.35360	−0.151609	−0.0758044	+	0.997123i	$0.524152\pi$
$242$	−1.95361	−0.125583
$243$	−14.4489	−0.926900
$244$	12.7232	0.814518
$245$	−3.13771	−0.200461
$246$	13.5366	0.863063
$247$	0	0
$248$	3.17085	0.201349
$249$	−15.0816	−0.955755
$250$	8.79274	0.556102
$251$	−4.32039	−0.272701	−0.136350	−	0.990661i	$-0.543537\pi$
$251$	−4.32039	−0.272701	−0.136350	+	0.990661i	$0.543537\pi$
$252$	−3.12647	−0.196949
$253$	−19.4388	−1.22211
$254$	−10.1514	−0.636956
$255$	3.50648	0.219584
$256$	1.00000	0.0625000
$257$	8.66479	0.540495	0.270247	−	0.962791i	$-0.412895\pi$
$257$	8.66479	0.540495	0.270247	+	0.962791i	$0.412895\pi$
$258$	9.04247	0.562959
$259$	−19.8915	−1.23600
$260$	0	0
$261$	8.57582	0.530830
$262$	−13.0826	−0.808243
$263$	22.9985	1.41815	0.709074	−	0.705135i	$-0.249113\pi$
$263$	22.9985	1.41815	0.709074	+	0.705135i	$0.249113\pi$
$264$	4.24223	0.261092
$265$	7.66341	0.470759
$266$	1.94107	0.119015
$267$	13.6967	0.838224
$268$	−5.66912	−0.346296
$269$	0.248941	0.0151782	0.00758912	−	0.999971i	$-0.497584\pi$
$269$	0.248941	0.0151782	0.00758912	+	0.999971i	$0.497584\pi$
$270$	−5.27564	−0.321065
$271$	−7.43286	−0.451514	−0.225757	−	0.974184i	$-0.572486\pi$
$271$	−7.43286	−0.451514	−0.225757	+	0.974184i	$0.572486\pi$
$272$	−3.06452	−0.185814
$273$	0	0
$274$	−16.7054	−1.00921
$275$	−14.6039	−0.880647
$276$	6.36610	0.383194
$277$	−20.5065	−1.23212	−0.616059	−	0.787700i	$-0.711272\pi$
$277$	−20.5065	−1.23212	−0.616059	+	0.787700i	$0.711272\pi$
$278$	−18.0537	−1.08279
$279$	5.10726	0.305764
$280$	−1.88431	−0.112609
$281$	−27.6720	−1.65077	−0.825386	−	0.564568i	$-0.809043\pi$
$281$	−27.6720	−1.65077	−0.825386	+	0.564568i	$0.809043\pi$
$282$	7.93656	0.472615
$283$	−11.7343	−0.697534	−0.348767	−	0.937209i	$-0.613400\pi$
$283$	−11.7343	−0.697534	−0.348767	+	0.937209i	$0.613400\pi$
$284$	−3.18208	−0.188822
$285$	1.14422	0.0677776
$286$	0	0
$287$	22.2922	1.31587
$288$	1.61069	0.0949109
$289$	−7.60871	−0.447571
$290$	5.16860	0.303510
$291$	−20.9139	−1.22599
$292$	−1.81384	−0.106147
$293$	7.32628	0.428006	0.214003	−	0.976833i	$-0.431350\pi$
$293$	7.32628	0.428006	0.214003	+	0.976833i	$0.431350\pi$
$294$	−3.80980	−0.222192
$295$	6.37395	0.371106
$296$	10.2477	0.595634
$297$	19.5596	1.13497
$298$	13.5277	0.783639
$299$	0	0
$300$	4.78269	0.276129
$301$	14.8912	0.858314
$302$	−12.4811	−0.718208
$303$	−0.480659	−0.0276131
$304$	−1.00000	−0.0573539
$305$	12.3511	0.707221
$306$	−4.93600	−0.282172
$307$	9.32280	0.532080	0.266040	−	0.963962i	$-0.414285\pi$
$307$	9.32280	0.532080	0.266040	+	0.963962i	$0.414285\pi$
$308$	6.98614	0.398072
$309$	−17.7605	−1.01036
$310$	3.07812	0.174825
$311$	16.5415	0.937981	0.468991	−	0.883203i	$-0.344618\pi$
$311$	16.5415	0.937981	0.468991	+	0.883203i	$0.344618\pi$
$312$	0	0
$313$	16.0695	0.908304	0.454152	−	0.890924i	$-0.349942\pi$
$313$	16.0695	0.908304	0.454152	+	0.890924i	$0.349942\pi$
$314$	−22.8574	−1.28992
$315$	−3.03504	−0.171005
$316$	−0.937757	−0.0527530
$317$	2.65400	0.149064	0.0745319	−	0.997219i	$-0.476254\pi$
$317$	2.65400	0.149064	0.0745319	+	0.997219i	$0.476254\pi$
$318$	9.30489	0.521793
$319$	−19.1628	−1.07291
$320$	0.970755	0.0542669
$321$	18.0831	1.00930
$322$	10.4837	0.584236
$323$	3.06452	0.170515
$324$	−1.57359	−0.0874219
$325$	0	0
$326$	5.91844	0.327792
$327$	16.8045	0.929290
$328$	−11.4845	−0.634123
$329$	13.0700	0.720572
$330$	4.11817	0.226698
$331$	−27.4776	−1.51031	−0.755153	−	0.655548i	$-0.772438\pi$
$331$	−27.4776	−1.51031	−0.755153	+	0.655548i	$0.772438\pi$
$332$	12.7952	0.702228
$333$	16.5059	0.904515
$334$	−10.5932	−0.579635
$335$	−5.50332	−0.300679
$336$	−2.28792	−0.124816
$337$	−5.64382	−0.307439	−0.153719	−	0.988115i	$-0.549125\pi$
$337$	−5.64382	−0.307439	−0.153719	+	0.988115i	$0.549125\pi$
$338$	0	0
$339$	−0.532992	−0.0289481
$340$	−2.97490	−0.161337
$341$	−11.4122	−0.618008
$342$	−1.61069	−0.0870963
$343$	−19.8615	−1.07242
$344$	−7.67163	−0.413627
$345$	6.17992	0.332716
$346$	7.50724	0.403592
$347$	−5.27665	−0.283265	−0.141633	−	0.989919i	$-0.545235\pi$
$347$	−5.27665	−0.283265	−0.141633	+	0.989919i	$0.545235\pi$
$348$	6.27570	0.336413
$349$	24.6953	1.32191	0.660955	−	0.750426i	$-0.270152\pi$
$349$	24.6953	1.32191	0.660955	+	0.750426i	$0.270152\pi$
$350$	7.87617	0.420999
$351$	0	0
$352$	−3.59911	−0.191833
$353$	3.69376	0.196599	0.0982995	−	0.995157i	$-0.468660\pi$
$353$	3.69376	0.196599	0.0982995	+	0.995157i	$0.468660\pi$
$354$	7.73924	0.411336
$355$	−3.08902	−0.163948
$356$	−11.6203	−0.615874
$357$	7.01139	0.371082
$358$	20.3989	1.07812
$359$	−9.64429	−0.509006	−0.254503	−	0.967072i	$-0.581912\pi$
$359$	−9.64429	−0.509006	−0.254503	+	0.967072i	$0.581912\pi$
$360$	1.56359	0.0824083
$361$	1.00000	0.0526316
$362$	0.989512	0.0520076
$363$	−2.30270	−0.120861
$364$	0	0
$365$	−1.76079	−0.0921640
$366$	14.9967	0.783889
$367$	−10.5757	−0.552048	−0.276024	−	0.961151i	$-0.589017\pi$
$367$	−10.5757	−0.552048	−0.276024	+	0.961151i	$0.589017\pi$
$368$	−5.40100	−0.281547
$369$	−18.4979	−0.962964
$370$	9.94798	0.517171
$371$	15.3234	0.795549
$372$	3.73745	0.193778
$373$	18.9556	0.981486	0.490743	−	0.871304i	$-0.336725\pi$
$373$	18.9556	0.981486	0.490743	+	0.871304i	$0.336725\pi$
$374$	11.0296	0.570325
$375$	10.3639	0.535190
$376$	−6.73338	−0.347248
$377$	0	0
$378$	−10.5489	−0.542577
$379$	2.56971	0.131997	0.0659986	−	0.997820i	$-0.478977\pi$
$379$	2.56971	0.131997	0.0659986	+	0.997820i	$0.478977\pi$
$380$	−0.970755	−0.0497987
$381$	−11.9654	−0.613004
$382$	−3.07075	−0.157113
$383$	−8.43886	−0.431206	−0.215603	−	0.976481i	$-0.569172\pi$
$383$	−8.43886	−0.431206	−0.215603	+	0.976481i	$0.569172\pi$
$384$	1.17869	0.0601497
$385$	6.78183	0.345634
$386$	−26.8452	−1.36638
$387$	−12.3566	−0.628123
$388$	17.7433	0.900782
$389$	15.2162	0.771492	0.385746	−	0.922605i	$-0.373944\pi$
$389$	15.2162	0.771492	0.385746	+	0.922605i	$0.373944\pi$
$390$	0	0
$391$	16.5515	0.837044
$392$	3.23223	0.163252
$393$	−15.4203	−0.777850
$394$	11.6680	0.587827
$395$	−0.910333	−0.0458038
$396$	−5.79706	−0.291313
$397$	37.6901	1.89161	0.945806	−	0.324732i	$-0.105274\pi$
$397$	37.6901	1.89161	0.945806	+	0.324732i	$0.105274\pi$
$398$	−23.5055	−1.17822
$399$	2.28792	0.114539
$400$	−4.05763	−0.202882
$401$	29.6777	1.48204	0.741018	−	0.671485i	$-0.234343\pi$
$401$	29.6777	1.48204	0.741018	+	0.671485i	$0.234343\pi$
$402$	−6.68212	−0.333274
$403$	0	0
$404$	0.407791	0.0202884
$405$	−1.52757	−0.0759058
$406$	10.3349	0.512911
$407$	−36.8825	−1.82820
$408$	−3.61212	−0.178826
$409$	2.49931	0.123583	0.0617915	−	0.998089i	$-0.480319\pi$
$409$	2.49931	0.123583	0.0617915	+	0.998089i	$0.480319\pi$
$410$	−11.1486	−0.550590
$411$	−19.6905	−0.971262
$412$	15.0680	0.742349
$413$	12.7450	0.627142
$414$	−8.69935	−0.427550
$415$	12.4210	0.609723
$416$	0	0
$417$	−21.2797	−1.04207
$418$	3.59911	0.176038
$419$	12.3287	0.602298	0.301149	−	0.953577i	$-0.402630\pi$
$419$	12.3287	0.602298	0.301149	+	0.953577i	$0.402630\pi$
$420$	−2.22101	−0.108374
$421$	16.6136	0.809699	0.404850	−	0.914383i	$-0.367324\pi$
$421$	16.6136	0.809699	0.404850	+	0.914383i	$0.367324\pi$
$422$	−13.5513	−0.659668
$423$	−10.8454	−0.527322
$424$	−7.89427	−0.383380
$425$	12.4347	0.603172
$426$	−3.75068	−0.181721
$427$	24.6966	1.19515
$428$	−15.3417	−0.741571
$429$	0	0
$430$	−7.44727	−0.359139
$431$	−15.1325	−0.728905	−0.364452	−	0.931222i	$-0.618744\pi$
$431$	−15.1325	−0.728905	−0.364452	+	0.931222i	$0.618744\pi$
$432$	5.43457	0.261471
$433$	37.4863	1.80148	0.900739	−	0.434360i	$-0.143025\pi$
$433$	37.4863	1.80148	0.900739	+	0.434360i	$0.143025\pi$
$434$	6.15485	0.295442
$435$	6.09217	0.292097
$436$	−14.2569	−0.682783
$437$	5.40100	0.258365
$438$	−2.13795	−0.102155
$439$	3.02450	0.144352	0.0721758	−	0.997392i	$-0.477006\pi$
$439$	3.02450	0.144352	0.0721758	+	0.997392i	$0.477006\pi$
$440$	−3.49386	−0.166563
$441$	5.20613	0.247911
$442$	0	0
$443$	23.0034	1.09292	0.546461	−	0.837484i	$-0.315975\pi$
$443$	23.0034	1.09292	0.546461	+	0.837484i	$0.315975\pi$
$444$	12.0788	0.573236
$445$	−11.2804	−0.534744
$446$	−4.42238	−0.209406
$447$	15.9450	0.754171
$448$	1.94107	0.0917071
$449$	21.4024	1.01004	0.505021	−	0.863107i	$-0.331485\pi$
$449$	21.4024	1.01004	0.505021	+	0.863107i	$0.331485\pi$
$450$	−6.53560	−0.308091
$451$	41.3339	1.94634
$452$	0.452190	0.0212692
$453$	−14.7114	−0.691200
$454$	24.7294	1.16061
$455$	0	0
$456$	−1.17869	−0.0551972
$457$	20.0766	0.939144	0.469572	−	0.882894i	$-0.344408\pi$
$457$	20.0766	0.939144	0.469572	+	0.882894i	$0.344408\pi$
$458$	−2.25971	−0.105589
$459$	−16.6544	−0.777359
$460$	−5.24305	−0.244458
$461$	11.9850	0.558197	0.279099	−	0.960262i	$-0.409964\pi$
$461$	11.9850	0.558197	0.279099	+	0.960262i	$0.409964\pi$
$462$	8.23449	0.383103
$463$	17.9959	0.836342	0.418171	−	0.908368i	$-0.362671\pi$
$463$	17.9959	0.836342	0.418171	+	0.908368i	$0.362671\pi$
$464$	−5.32430	−0.247175
$465$	3.62815	0.168251
$466$	8.56423	0.396730
$467$	25.7659	1.19230	0.596151	−	0.802872i	$-0.296696\pi$
$467$	25.7659	1.19230	0.596151	+	0.802872i	$0.296696\pi$
$468$	0	0
$469$	−11.0042	−0.508125
$470$	−6.53646	−0.301505
$471$	−26.9418	−1.24141
$472$	−6.56597	−0.302223
$473$	27.6111	1.26956
$474$	−1.10532	−0.0507692
$475$	4.05763	0.186177
$476$	−5.94846	−0.272647
$477$	−12.7152	−0.582191
$478$	−1.40430	−0.0642313
$479$	−0.727532	−0.0332418	−0.0166209	−	0.999862i	$-0.505291\pi$
$479$	−0.727532	−0.0332418	−0.0166209	+	0.999862i	$0.505291\pi$
$480$	1.14422	0.0522262
$481$	0	0
$482$	2.35360	0.107204
$483$	12.3571	0.562266
$484$	1.95361	0.0888006
$485$	17.2244	0.782121
$486$	14.4489	0.655417
$487$	−15.2154	−0.689476	−0.344738	−	0.938699i	$-0.612032\pi$
$487$	−15.2154	−0.689476	−0.344738	+	0.938699i	$0.612032\pi$
$488$	−12.7232	−0.575951
$489$	6.97600	0.315466
$490$	3.13771	0.141747
$491$	13.1303	0.592560	0.296280	−	0.955101i	$-0.404254\pi$
$491$	13.1303	0.592560	0.296280	+	0.955101i	$0.404254\pi$
$492$	−13.5366	−0.610277
$493$	16.3164	0.734856
$494$	0	0
$495$	−5.62753	−0.252939
$496$	−3.17085	−0.142375
$497$	−6.17665	−0.277061
$498$	15.0816	0.675821
$499$	−33.1393	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$499$	−33.1393	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$500$	−8.79274	−0.393223
$501$	−12.4861	−0.557838
$502$	4.32039	0.192828
$503$	−7.77469	−0.346656	−0.173328	−	0.984864i	$-0.555452\pi$
$503$	−7.77469	−0.346656	−0.173328	+	0.984864i	$0.555452\pi$
$504$	3.12647	0.139264
$505$	0.395865	0.0176158
$506$	19.4388	0.864160
$507$	0	0
$508$	10.1514	0.450396
$509$	22.7437	1.00810	0.504049	−	0.863675i	$-0.331843\pi$
$509$	22.7437	1.00810	0.504049	+	0.863675i	$0.331843\pi$
$510$	−3.50648	−0.155270
$511$	−3.52079	−0.155751
$512$	−1.00000	−0.0441942
$513$	−5.43457	−0.239942
$514$	−8.66479	−0.382188
$515$	14.6274	0.644559
$516$	−9.04247	−0.398072
$517$	24.2342	1.06582
$518$	19.8915	0.873982
$519$	8.84870	0.388415
$520$	0	0
$521$	−37.5941	−1.64703	−0.823515	−	0.567295i	$-0.807990\pi$
$521$	−37.5941	−1.64703	−0.823515	+	0.567295i	$0.807990\pi$
$522$	−8.57582	−0.375353
$523$	−30.4011	−1.32935	−0.664673	−	0.747134i	$-0.731429\pi$
$523$	−30.4011	−1.32935	−0.664673	+	0.747134i	$0.731429\pi$
$524$	13.0826	0.571514
$525$	9.28355	0.405167
$526$	−22.9985	−1.00278
$527$	9.71714	0.423285
$528$	−4.24223	−0.184620
$529$	6.17080	0.268295
$530$	−7.66341	−0.332877
$531$	−10.5758	−0.458949
$532$	−1.94107	−0.0841562
$533$	0	0
$534$	−13.6967	−0.592714
$535$	−14.8931	−0.643884
$536$	5.66912	0.244869
$537$	24.0440	1.03757
$538$	−0.248941	−0.0107326
$539$	−11.6332	−0.501076
$540$	5.27564	0.227027
$541$	−7.03358	−0.302397	−0.151199	−	0.988503i	$-0.548313\pi$
$541$	−7.03358	−0.302397	−0.151199	+	0.988503i	$0.548313\pi$
$542$	7.43286	0.319269
$543$	1.16633	0.0500519
$544$	3.06452	0.131390
$545$	−13.8400	−0.592840
$546$	0	0
$547$	−19.7878	−0.846067	−0.423033	−	0.906114i	$-0.639035\pi$
$547$	−19.7878	−0.846067	−0.423033	+	0.906114i	$0.639035\pi$
$548$	16.7054	0.713621
$549$	−20.4931	−0.874625
$550$	14.6039	0.622712
$551$	5.32430	0.226823
$552$	−6.36610	−0.270959
$553$	−1.82026	−0.0774052
$554$	20.5065	0.871239
$555$	11.7256	0.497723
$556$	18.0537	0.765648
$557$	−18.6812	−0.791546	−0.395773	−	0.918348i	$-0.629523\pi$
$557$	−18.6812	−0.791546	−0.395773	+	0.918348i	$0.629523\pi$
$558$	−5.10726	−0.216208
$559$	0	0
$560$	1.88431	0.0796265
$561$	13.0004	0.548878
$562$	27.6720	1.16727
$563$	27.5811	1.16241	0.581203	−	0.813759i	$-0.302582\pi$
$563$	27.5811	1.16241	0.581203	+	0.813759i	$0.302582\pi$
$564$	−7.93656	−0.334190
$565$	0.438966	0.0184674
$566$	11.7343	0.493231
$567$	−3.05446	−0.128275
$568$	3.18208	0.133517
$569$	−4.49725	−0.188535	−0.0942673	−	0.995547i	$-0.530051\pi$
$569$	−4.49725	−0.188535	−0.0942673	+	0.995547i	$0.530051\pi$
$570$	−1.14422	−0.0479260
$571$	12.2003	0.510566	0.255283	−	0.966866i	$-0.417831\pi$
$571$	12.2003	0.510566	0.255283	+	0.966866i	$0.417831\pi$
$572$	0	0
$573$	−3.61946	−0.151205
$574$	−22.2922	−0.930458
$575$	21.9153	0.913930
$576$	−1.61069	−0.0671122
$577$	−29.4126	−1.22446	−0.612231	−	0.790679i	$-0.709728\pi$
$577$	−29.4126	−1.22446	−0.612231	+	0.790679i	$0.709728\pi$
$578$	7.60871	0.316481
$579$	−31.6421	−1.31500
$580$	−5.16860	−0.214614
$581$	24.8364	1.03039
$582$	20.9139	0.866908
$583$	28.4124	1.17672
$584$	1.81384	0.0750571
$585$	0	0
$586$	−7.32628	−0.302646
$587$	−7.56769	−0.312352	−0.156176	−	0.987729i	$-0.549917\pi$
$587$	−7.56769	−0.312352	−0.156176	+	0.987729i	$0.549917\pi$
$588$	3.80980	0.157113
$589$	3.17085	0.130653
$590$	−6.37395	−0.262411
$591$	13.7530	0.565722
$592$	−10.2477	−0.421177
$593$	4.88324	0.200530	0.100265	−	0.994961i	$-0.468031\pi$
$593$	4.88324	0.200530	0.100265	+	0.994961i	$0.468031\pi$
$594$	−19.5596	−0.802542
$595$	−5.77450	−0.236731
$596$	−13.5277	−0.554116
$597$	−27.7056	−1.13392
$598$	0	0
$599$	41.4750	1.69462	0.847312	−	0.531096i	$-0.178220\pi$
$599$	41.4750	1.69462	0.847312	+	0.531096i	$0.178220\pi$
$600$	−4.78269	−0.195252
$601$	−8.43952	−0.344255	−0.172128	−	0.985075i	$-0.555064\pi$
$601$	−8.43952	−0.344255	−0.172128	+	0.985075i	$0.555064\pi$
$602$	−14.8912	−0.606920
$603$	9.13120	0.371851
$604$	12.4811	0.507850
$605$	1.89648	0.0771029
$606$	0.480659	0.0195254
$607$	3.55656	0.144356	0.0721782	−	0.997392i	$-0.477005\pi$
$607$	3.55656	0.144356	0.0721782	+	0.997392i	$0.477005\pi$
$608$	1.00000	0.0405554
$609$	12.1816	0.493623
$610$	−12.3511	−0.500081
$611$	0	0
$612$	4.93600	0.199526
$613$	26.3218	1.06313	0.531564	−	0.847018i	$-0.321604\pi$
$613$	26.3218	1.06313	0.531564	+	0.847018i	$0.321604\pi$
$614$	−9.32280	−0.376238
$615$	−13.1407	−0.529885
$616$	−6.98614	−0.281480
$617$	−13.6283	−0.548656	−0.274328	−	0.961636i	$-0.588455\pi$
$617$	−13.6283	−0.548656	−0.274328	+	0.961636i	$0.588455\pi$
$618$	17.7605	0.714434
$619$	5.19617	0.208852	0.104426	−	0.994533i	$-0.466699\pi$
$619$	5.19617	0.208852	0.104426	+	0.994533i	$0.466699\pi$
$620$	−3.07812	−0.123620
$621$	−29.3521	−1.17786
$622$	−16.5415	−0.663253
$623$	−22.5558	−0.903680
$624$	0	0
$625$	11.7526	0.470103
$626$	−16.0695	−0.642268
$627$	4.24223	0.169419
$628$	22.8574	0.912110
$629$	31.4042	1.25217
$630$	3.03504	0.120919
$631$	21.8238	0.868791	0.434396	−	0.900722i	$-0.356962\pi$
$631$	21.8238	0.868791	0.434396	+	0.900722i	$0.356962\pi$
$632$	0.937757	0.0373020
$633$	−15.9728	−0.634862
$634$	−2.65400	−0.105404
$635$	9.85454	0.391065
$636$	−9.30489	−0.368963
$637$	0	0
$638$	19.1628	0.758662
$639$	5.12535	0.202756
$640$	−0.970755	−0.0383725
$641$	−2.14943	−0.0848974	−0.0424487	−	0.999099i	$-0.513516\pi$
$641$	−2.14943	−0.0848974	−0.0424487	+	0.999099i	$0.513516\pi$
$642$	−18.0831	−0.713685
$643$	38.7222	1.52706	0.763528	−	0.645775i	$-0.223466\pi$
$643$	38.7222	1.52706	0.763528	+	0.645775i	$0.223466\pi$
$644$	−10.4837	−0.413117
$645$	−8.77802	−0.345634
$646$	−3.06452	−0.120572
$647$	6.23082	0.244959	0.122479	−	0.992471i	$-0.460915\pi$
$647$	6.23082	0.244959	0.122479	+	0.992471i	$0.460915\pi$
$648$	1.57359	0.0618166
$649$	23.6317	0.927624
$650$	0	0
$651$	7.25466	0.284332
$652$	−5.91844	−0.231784
$653$	33.6675	1.31751	0.658755	−	0.752357i	$-0.271083\pi$
$653$	33.6675	1.31751	0.658755	+	0.752357i	$0.271083\pi$
$654$	−16.8045	−0.657108
$655$	12.7000	0.496229
$656$	11.4845	0.448393
$657$	2.92153	0.113980
$658$	−13.0700	−0.509521
$659$	3.76905	0.146821	0.0734106	−	0.997302i	$-0.476612\pi$
$659$	3.76905	0.146821	0.0734106	+	0.997302i	$0.476612\pi$
$660$	−4.11817	−0.160300
$661$	8.71680	0.339044	0.169522	−	0.985526i	$-0.445778\pi$
$661$	8.71680	0.339044	0.169522	+	0.985526i	$0.445778\pi$
$662$	27.4776	1.06795
$663$	0	0
$664$	−12.7952	−0.496550
$665$	−1.88431	−0.0730703
$666$	−16.5059	−0.639589
$667$	28.7566	1.11346
$668$	10.5932	0.409864
$669$	−5.21261	−0.201531
$670$	5.50332	0.212612
$671$	45.7922	1.76779
$672$	2.28792	0.0882585
$673$	20.2033	0.778782	0.389391	−	0.921073i	$-0.372686\pi$
$673$	20.2033	0.778782	0.389391	+	0.921073i	$0.372686\pi$
$674$	5.64382	0.217392
$675$	−22.0515	−0.848763
$676$	0	0
$677$	10.1661	0.390715	0.195358	−	0.980732i	$-0.437413\pi$
$677$	10.1661	0.390715	0.195358	+	0.980732i	$0.437413\pi$
$678$	0.532992	0.0204694
$679$	34.4411	1.32173
$680$	2.97490	0.114082
$681$	29.1483	1.11696
$682$	11.4122	0.436998
$683$	−24.1394	−0.923667	−0.461834	−	0.886967i	$-0.652808\pi$
$683$	−24.1394	−0.923667	−0.461834	+	0.886967i	$0.652808\pi$
$684$	1.61069	0.0615864
$685$	16.2169	0.619616
$686$	19.8615	0.758316
$687$	−2.66349	−0.101619
$688$	7.67163	0.292478
$689$	0	0
$690$	−6.17992	−0.235266
$691$	12.8027	0.487038	0.243519	−	0.969896i	$-0.421698\pi$
$691$	12.8027	0.487038	0.243519	+	0.969896i	$0.421698\pi$
$692$	−7.50724	−0.285382
$693$	−11.2525	−0.427448
$694$	5.27665	0.200299
$695$	17.5257	0.664789
$696$	−6.27570	−0.237880
$697$	−35.1944	−1.33308
$698$	−24.6953	−0.934731
$699$	10.0946	0.381812
$700$	−7.87617	−0.297691
$701$	34.3805	1.29854	0.649268	−	0.760560i	$-0.275075\pi$
$701$	34.3805	1.29854	0.649268	+	0.760560i	$0.275075\pi$
$702$	0	0
$703$	10.2477	0.386498
$704$	3.59911	0.135647
$705$	−7.70446	−0.290167
$706$	−3.69376	−0.139017
$707$	0.791552	0.0297694
$708$	−7.73924	−0.290858
$709$	28.6414	1.07565	0.537825	−	0.843057i	$-0.319246\pi$
$709$	28.6414	1.07565	0.537825	+	0.843057i	$0.319246\pi$
$710$	3.08902	0.115929
$711$	1.51044	0.0566459
$712$	11.6203	0.435488
$713$	17.1258	0.641365
$714$	−7.01139	−0.262395
$715$	0	0
$716$	−20.3989	−0.762343
$717$	−1.65524	−0.0618159
$718$	9.64429	0.359922
$719$	−46.5414	−1.73570	−0.867851	−	0.496825i	$-0.834499\pi$
$719$	−46.5414	−1.73570	−0.867851	+	0.496825i	$0.834499\pi$
$720$	−1.56359	−0.0582715
$721$	29.2482	1.08926
$722$	−1.00000	−0.0372161
$723$	2.77417	0.103172
$724$	−0.989512	−0.0367749
$725$	21.6041	0.802356
$726$	2.30270	0.0854613
$727$	−22.4850	−0.833923	−0.416961	−	0.908924i	$-0.636905\pi$
$727$	−22.4850	−0.833923	−0.416961	+	0.908924i	$0.636905\pi$
$728$	0	0
$729$	21.7516	0.805614
$730$	1.76079	0.0651698
$731$	−23.5099	−0.869544
$732$	−14.9967	−0.554293
$733$	40.8505	1.50885	0.754424	−	0.656387i	$-0.227916\pi$
$733$	40.8505	1.50885	0.754424	+	0.656387i	$0.227916\pi$
$734$	10.5757	0.390357
$735$	3.69838	0.136417
$736$	5.40100	0.199083
$737$	−20.4038	−0.751583
$738$	18.4979	0.680918
$739$	8.01992	0.295017	0.147509	−	0.989061i	$-0.452875\pi$
$739$	8.01992	0.295017	0.147509	+	0.989061i	$0.452875\pi$
$740$	−9.94798	−0.365695
$741$	0	0
$742$	−15.3234	−0.562538
$743$	−48.0548	−1.76296	−0.881481	−	0.472220i	$-0.843453\pi$
$743$	−48.0548	−1.76296	−0.881481	+	0.472220i	$0.843453\pi$
$744$	−3.73745	−0.137021
$745$	−13.1321	−0.481123
$746$	−18.9556	−0.694015
$747$	−20.6091	−0.754049
$748$	−11.0296	−0.403281
$749$	−29.7795	−1.08812
$750$	−10.3639	−0.378437
$751$	−12.7846	−0.466516	−0.233258	−	0.972415i	$-0.574939\pi$
$751$	−12.7846	−0.466516	−0.233258	+	0.972415i	$0.574939\pi$
$752$	6.73338	0.245541
$753$	5.09240	0.185577
$754$	0	0
$755$	12.1161	0.440950
$756$	10.5489	0.383660
$757$	43.6342	1.58591	0.792956	−	0.609279i	$-0.208541\pi$
$757$	43.6342	1.58591	0.792956	+	0.609279i	$0.208541\pi$
$758$	−2.56971	−0.0933362
$759$	22.9123	0.831664
$760$	0.970755	0.0352130
$761$	−1.38883	−0.0503450	−0.0251725	−	0.999683i	$-0.508013\pi$
$761$	−1.38883	−0.0503450	−0.0251725	+	0.999683i	$0.508013\pi$
$762$	11.9654	0.433459
$763$	−27.6738	−1.00186
$764$	3.07075	0.111096
$765$	4.79165	0.173242
$766$	8.43886	0.304908
$767$	0	0
$768$	−1.17869	−0.0425323
$769$	−34.0111	−1.22647	−0.613236	−	0.789900i	$-0.710132\pi$
$769$	−34.0111	−1.22647	−0.613236	+	0.789900i	$0.710132\pi$
$770$	−6.78183	−0.244400
$771$	−10.2131	−0.367816
$772$	26.8452	0.966180
$773$	5.12201	0.184226	0.0921129	−	0.995749i	$-0.470638\pi$
$773$	5.12201	0.184226	0.0921129	+	0.995749i	$0.470638\pi$
$774$	12.3566	0.444150
$775$	12.8662	0.462166
$776$	−17.7433	−0.636949
$777$	23.4459	0.841116
$778$	−15.2162	−0.545527
$779$	−11.4845	−0.411473
$780$	0	0
$781$	−11.4527	−0.409809
$782$	−16.5515	−0.591880
$783$	−28.9353	−1.03406
$784$	−3.23223	−0.115437
$785$	22.1889	0.791957
$786$	15.4203	0.550023
$787$	−7.20142	−0.256703	−0.128351	−	0.991729i	$-0.540969\pi$
$787$	−7.20142	−0.256703	−0.128351	+	0.991729i	$0.540969\pi$
$788$	−11.6680	−0.415657
$789$	−27.1081	−0.965072
$790$	0.910333	0.0323882
$791$	0.877735	0.0312087
$792$	5.79706	0.205990
$793$	0	0
$794$	−37.6901	−1.33757
$795$	−9.03277	−0.320359
$796$	23.5055	0.833129
$797$	15.1807	0.537729	0.268864	−	0.963178i	$-0.413352\pi$
$797$	15.1807	0.537729	0.268864	+	0.963178i	$0.413352\pi$
$798$	−2.28792	−0.0809916
$799$	−20.6346	−0.729999
$800$	4.05763	0.143459
$801$	18.7167	0.661322
$802$	−29.6777	−1.04796
$803$	−6.52820	−0.230375
$804$	6.68212	0.235660
$805$	−10.1771	−0.358697
$806$	0	0
$807$	−0.293425	−0.0103290
$808$	−0.407791	−0.0143460
$809$	−12.6699	−0.445449	−0.222725	−	0.974881i	$-0.571495\pi$
$809$	−12.6699	−0.445449	−0.222725	+	0.974881i	$0.571495\pi$
$810$	1.52757	0.0536735
$811$	21.8463	0.767126	0.383563	−	0.923515i	$-0.374697\pi$
$811$	21.8463	0.767126	0.383563	+	0.923515i	$0.374697\pi$
$812$	−10.3349	−0.362683
$813$	8.76103	0.307263
$814$	36.8825	1.29273
$815$	−5.74535	−0.201251
$816$	3.61212	0.126449
$817$	−7.67163	−0.268396
$818$	−2.49931	−0.0873864
$819$	0	0
$820$	11.1486	0.389326
$821$	30.7503	1.07319	0.536597	−	0.843839i	$-0.319710\pi$
$821$	30.7503	1.07319	0.536597	+	0.843839i	$0.319710\pi$
$822$	19.6905	0.686786
$823$	30.5272	1.06411	0.532056	−	0.846709i	$-0.321420\pi$
$823$	30.5272	1.06411	0.532056	+	0.846709i	$0.321420\pi$
$824$	−15.0680	−0.524920
$825$	17.2134	0.599295
$826$	−12.7450	−0.443456
$827$	−35.7462	−1.24302	−0.621509	−	0.783407i	$-0.713480\pi$
$827$	−35.7462	−1.24302	−0.621509	+	0.783407i	$0.713480\pi$
$828$	8.69935	0.302323
$829$	−29.9714	−1.04095	−0.520476	−	0.853877i	$-0.674245\pi$
$829$	−29.9714	−1.04095	−0.520476	+	0.853877i	$0.674245\pi$
$830$	−12.4210	−0.431139
$831$	24.1708	0.838476
$832$	0	0
$833$	9.90525	0.343197
$834$	21.2797	0.736856
$835$	10.2834	0.355872
$836$	−3.59911	−0.124478
$837$	−17.2322	−0.595633
$838$	−12.3287	−0.425889
$839$	−1.27944	−0.0441713	−0.0220857	−	0.999756i	$-0.507031\pi$
$839$	−1.27944	−0.0441713	−0.0220857	+	0.999756i	$0.507031\pi$
$840$	2.22101	0.0766322
$841$	−0.651779	−0.0224751
$842$	−16.6136	−0.572544
$843$	32.6167	1.12338
$844$	13.5513	0.466456
$845$	0	0
$846$	10.8454	0.372873
$847$	3.79211	0.130298
$848$	7.89427	0.271090
$849$	13.8311	0.474683
$850$	−12.4347	−0.426507
$851$	55.3477	1.89729
$852$	3.75068	0.128496
$853$	−24.0984	−0.825112	−0.412556	−	0.910932i	$-0.635364\pi$
$853$	−24.0984	−0.825112	−0.412556	+	0.910932i	$0.635364\pi$
$854$	−24.6966	−0.845101
$855$	1.56359	0.0534736
$856$	15.3417	0.524370
$857$	−19.3996	−0.662679	−0.331340	−	0.943512i	$-0.607501\pi$
$857$	−19.3996	−0.662679	−0.331340	+	0.943512i	$0.607501\pi$
$858$	0	0
$859$	−7.37594	−0.251664	−0.125832	−	0.992052i	$-0.540160\pi$
$859$	−7.37594	−0.251664	−0.125832	+	0.992052i	$0.540160\pi$
$860$	7.44727	0.253950
$861$	−26.2755	−0.895468
$862$	15.1325	0.515413
$863$	18.4934	0.629523	0.314761	−	0.949171i	$-0.398075\pi$
$863$	18.4934	0.629523	0.314761	+	0.949171i	$0.398075\pi$
$864$	−5.43457	−0.184888
$865$	−7.28769	−0.247789
$866$	−37.4863	−1.27384
$867$	8.96830	0.304579
$868$	−6.15485	−0.208909
$869$	−3.37510	−0.114492
$870$	−6.09217	−0.206544
$871$	0	0
$872$	14.2569	0.482801
$873$	−28.5791	−0.967255
$874$	−5.40100	−0.182692
$875$	−17.0674	−0.576982
$876$	2.13795	0.0722346
$877$	3.23154	0.109121	0.0545607	−	0.998510i	$-0.482624\pi$
$877$	3.23154	0.109121	0.0545607	+	0.998510i	$0.482624\pi$
$878$	−3.02450	−0.102072
$879$	−8.63541	−0.291265
$880$	3.49386	0.117778
$881$	29.5593	0.995879	0.497940	−	0.867212i	$-0.334090\pi$
$881$	29.5593	0.995879	0.497940	+	0.867212i	$0.334090\pi$
$882$	−5.20613	−0.175300
$883$	29.6333	0.997241	0.498620	−	0.866821i	$-0.333840\pi$
$883$	29.6333	0.997241	0.498620	+	0.866821i	$0.333840\pi$
$884$	0	0
$885$	−7.51290	−0.252543
$886$	−23.0034	−0.772813
$887$	23.5828	0.791832	0.395916	−	0.918287i	$-0.370427\pi$
$887$	23.5828	0.791832	0.395916	+	0.918287i	$0.370427\pi$
$888$	−12.0788	−0.405339
$889$	19.7046	0.660872
$890$	11.2804	0.378121
$891$	−5.66354	−0.189736
$892$	4.42238	0.148072
$893$	−6.73338	−0.225324
$894$	−15.9450	−0.533279
$895$	−19.8024	−0.661920
$896$	−1.94107	−0.0648467
$897$	0	0
$898$	−21.4024	−0.714207
$899$	16.8826	0.563065
$900$	6.53560	0.217853
$901$	−24.1922	−0.805958
$902$	−41.3339	−1.37627
$903$	−17.5521	−0.584097
$904$	−0.452190	−0.0150396
$905$	−0.960573	−0.0319305
$906$	14.7114	0.488752
$907$	−22.1769	−0.736371	−0.368185	−	0.929752i	$-0.620021\pi$
$907$	−22.1769	−0.736371	−0.368185	+	0.929752i	$0.620021\pi$
$908$	−24.7294	−0.820674
$909$	−0.656826	−0.0217855
$910$	0	0
$911$	−52.9368	−1.75388	−0.876938	−	0.480604i	$-0.840417\pi$
$911$	−52.9368	−1.75388	−0.876938	+	0.480604i	$0.840417\pi$
$912$	1.17869	0.0390303
$913$	46.0514	1.52408
$914$	−20.0766	−0.664075
$915$	−14.5581	−0.481276
$916$	2.25971	0.0746629
$917$	25.3942	0.838591
$918$	16.6544	0.549676
$919$	−18.0662	−0.595950	−0.297975	−	0.954574i	$-0.596311\pi$
$919$	−18.0662	−0.595950	−0.297975	+	0.954574i	$0.596311\pi$
$920$	5.24305	0.172858
$921$	−10.9887	−0.362089
$922$	−11.9850	−0.394705
$923$	0	0
$924$	−8.23449	−0.270895
$925$	41.5813	1.36719
$926$	−17.9959	−0.591383
$927$	−24.2700	−0.797131
$928$	5.32430	0.174779
$929$	−7.71778	−0.253212	−0.126606	−	0.991953i	$-0.540408\pi$
$929$	−7.71778	−0.253212	−0.126606	+	0.991953i	$0.540408\pi$
$930$	−3.62815	−0.118972
$931$	3.23223	0.105932
$932$	−8.56423	−0.280531
$933$	−19.4973	−0.638312
$934$	−25.7659	−0.843085
$935$	−10.7070	−0.350156
$936$	0	0
$937$	5.07374	0.165752	0.0828759	−	0.996560i	$-0.473590\pi$
$937$	5.07374	0.165752	0.0828759	+	0.996560i	$0.473590\pi$
$938$	11.0042	0.359299
$939$	−18.9410	−0.618116
$940$	6.53646	0.213196
$941$	−46.8028	−1.52573	−0.762864	−	0.646558i	$-0.776208\pi$
$941$	−46.8028	−1.52573	−0.762864	+	0.646558i	$0.776208\pi$
$942$	26.9418	0.877810
$943$	−62.0276	−2.01990
$944$	6.56597	0.213704
$945$	10.2404	0.333120
$946$	−27.6111	−0.897713
$947$	−15.2549	−0.495719	−0.247860	−	0.968796i	$-0.579727\pi$
$947$	−15.2549	−0.495719	−0.247860	+	0.968796i	$0.579727\pi$
$948$	1.10532	0.0358993
$949$	0	0
$950$	−4.05763	−0.131647
$951$	−3.12825	−0.101440
$952$	5.94846	0.192791
$953$	−49.1548	−1.59228	−0.796139	−	0.605113i	$-0.793128\pi$
$953$	−49.1548	−1.59228	−0.796139	+	0.605113i	$0.793128\pi$
$954$	12.7152	0.411671
$955$	2.98094	0.0964611
$956$	1.40430	0.0454184
$957$	22.5870	0.730132
$958$	0.727532	0.0235055
$959$	32.4265	1.04711
$960$	−1.14422	−0.0369295
$961$	−20.9457	−0.675668
$962$	0	0
$963$	24.7108	0.796295
$964$	−2.35360	−0.0758044
$965$	26.0601	0.838904
$966$	−12.3571	−0.397582
$967$	−24.3319	−0.782462	−0.391231	−	0.920292i	$-0.627951\pi$
$967$	−24.3319	−0.782462	−0.391231	+	0.920292i	$0.627951\pi$
$968$	−1.95361	−0.0627915
$969$	−3.61212	−0.116038
$970$	−17.2244	−0.553043
$971$	36.8460	1.18244	0.591222	−	0.806509i	$-0.298646\pi$
$971$	36.8460	1.18244	0.591222	+	0.806509i	$0.298646\pi$
$972$	−14.4489	−0.463450
$973$	35.0436	1.12345
$974$	15.2154	0.487533
$975$	0	0
$976$	12.7232	0.407259
$977$	−16.2629	−0.520295	−0.260148	−	0.965569i	$-0.583771\pi$
$977$	−16.2629	−0.520295	−0.260148	+	0.965569i	$0.583771\pi$
$978$	−6.97600	−0.223068
$979$	−41.8227	−1.33666
$980$	−3.13771	−0.100230
$981$	22.9635	0.733169
$982$	−13.1303	−0.419003
$983$	−51.6233	−1.64653	−0.823263	−	0.567660i	$-0.807849\pi$
$983$	−51.6233	−1.64653	−0.823263	+	0.567660i	$0.807849\pi$
$984$	13.5366	0.431531
$985$	−11.3268	−0.360902
$986$	−16.3164	−0.519622
$987$	−15.4054	−0.490361
$988$	0	0
$989$	−41.4345	−1.31754
$990$	5.62753	0.178855
$991$	14.7639	0.468990	0.234495	−	0.972117i	$-0.424656\pi$
$991$	14.7639	0.468990	0.234495	+	0.972117i	$0.424656\pi$
$992$	3.17085	0.100675
$993$	32.3876	1.02779
$994$	6.17665	0.195911
$995$	22.8181	0.723381
$996$	−15.0816	−0.477878
$997$	−17.3203	−0.548539	−0.274270	−	0.961653i	$-0.588436\pi$
$997$	−17.3203	−0.548539	−0.274270	+	0.961653i	$0.588436\pi$
$998$	33.1393	1.04901
$999$	−55.6917	−1.76201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bm.1.5		14
13.6	odd	12		494.2.m.b.153.12	✓	28
13.11	odd	12		494.2.m.b.381.12	yes	28
13.12	even	2		6422.2.a.bn.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.12	✓	28	13.6	odd	12
494.2.m.b.381.12	yes	28	13.11	odd	12
6422.2.a.bm.1.5		14	1.1	even	1	trivial
6422.2.a.bn.1.5		14	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.17869 q^{3} +1.00000 q^{4} +0.970755 q^{5} +1.17869 q^{6} +1.94107 q^{7} -1.00000 q^{8} -1.61069 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.17869 q^{3} +1.00000 q^{4} +0.970755 q^{5} +1.17869 q^{6} +1.94107 q^{7} -1.00000 q^{8} -1.61069 q^{9} -0.970755 q^{10} +3.59911 q^{11} -1.17869 q^{12} -1.94107 q^{14} -1.14422 q^{15} +1.00000 q^{16} -3.06452 q^{17} +1.61069 q^{18} -1.00000 q^{19} +0.970755 q^{20} -2.28792 q^{21} -3.59911 q^{22} -5.40100 q^{23} +1.17869 q^{24} -4.05763 q^{25} +5.43457 q^{27} +1.94107 q^{28} -5.32430 q^{29} +1.14422 q^{30} -3.17085 q^{31} -1.00000 q^{32} -4.24223 q^{33} +3.06452 q^{34} +1.88431 q^{35} -1.61069 q^{36} -10.2477 q^{37} +1.00000 q^{38} -0.970755 q^{40} +11.4845 q^{41} +2.28792 q^{42} +7.67163 q^{43} +3.59911 q^{44} -1.56359 q^{45} +5.40100 q^{46} +6.73338 q^{47} -1.17869 q^{48} -3.23223 q^{49} +4.05763 q^{50} +3.61212 q^{51} +7.89427 q^{53} -5.43457 q^{54} +3.49386 q^{55} -1.94107 q^{56} +1.17869 q^{57} +5.32430 q^{58} +6.56597 q^{59} -1.14422 q^{60} +12.7232 q^{61} +3.17085 q^{62} -3.12647 q^{63} +1.00000 q^{64} +4.24223 q^{66} -5.66912 q^{67} -3.06452 q^{68} +6.36610 q^{69} -1.88431 q^{70} -3.18208 q^{71} +1.61069 q^{72} -1.81384 q^{73} +10.2477 q^{74} +4.78269 q^{75} -1.00000 q^{76} +6.98614 q^{77} -0.937757 q^{79} +0.970755 q^{80} -1.57359 q^{81} -11.4845 q^{82} +12.7952 q^{83} -2.28792 q^{84} -2.97490 q^{85} -7.67163 q^{86} +6.27570 q^{87} -3.59911 q^{88} -11.6203 q^{89} +1.56359 q^{90} -5.40100 q^{92} +3.73745 q^{93} -6.73338 q^{94} -0.970755 q^{95} +1.17869 q^{96} +17.7433 q^{97} +3.23223 q^{98} -5.79706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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