LMFDB - Embedded newform 4026.2.a.r.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 4x + 3 $ x^4 - x^3 - 5x^2 + 4x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.491918$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75802 q^{5} -1.00000 q^{6} -2.84864 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75802 q^{5} -1.00000 q^{6} -2.84864 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.75802 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.89322 q^{13} +2.84864 q^{14} +2.75802 q^{15} +1.00000 q^{16} -6.87275 q^{17} -1.00000 q^{18} +2.24993 q^{19} +2.75802 q^{20} -2.84864 q^{21} +1.00000 q^{22} +4.43118 q^{23} -1.00000 q^{24} +2.60665 q^{25} +2.89322 q^{26} +1.00000 q^{27} -2.84864 q^{28} -2.13520 q^{29} -2.75802 q^{30} -5.04028 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.87275 q^{34} -7.85659 q^{35} +1.00000 q^{36} +6.93105 q^{37} -2.24993 q^{38} -2.89322 q^{39} -2.75802 q^{40} +0.372882 q^{41} +2.84864 q^{42} +2.08241 q^{43} -1.00000 q^{44} +2.75802 q^{45} -4.43118 q^{46} +0.528546 q^{47} +1.00000 q^{48} +1.11474 q^{49} -2.60665 q^{50} -6.87275 q^{51} -2.89322 q^{52} -0.0665071 q^{53} -1.00000 q^{54} -2.75802 q^{55} +2.84864 q^{56} +2.24993 q^{57} +2.13520 q^{58} -13.0562 q^{59} +2.75802 q^{60} +1.00000 q^{61} +5.04028 q^{62} -2.84864 q^{63} +1.00000 q^{64} -7.97954 q^{65} +1.00000 q^{66} -1.49192 q^{67} -6.87275 q^{68} +4.43118 q^{69} +7.85659 q^{70} -0.778480 q^{71} -1.00000 q^{72} +6.27551 q^{73} -6.93105 q^{74} +2.60665 q^{75} +2.24993 q^{76} +2.84864 q^{77} +2.89322 q^{78} -14.3201 q^{79} +2.75802 q^{80} +1.00000 q^{81} -0.372882 q^{82} -3.11904 q^{83} -2.84864 q^{84} -18.9552 q^{85} -2.08241 q^{86} -2.13520 q^{87} +1.00000 q^{88} -2.90693 q^{89} -2.75802 q^{90} +8.24172 q^{91} +4.43118 q^{92} -5.04028 q^{93} -0.528546 q^{94} +6.20536 q^{95} -1.00000 q^{96} -18.6729 q^{97} -1.11474 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 4 q^{18} - 4 q^{19} + q^{20} - 4 q^{21} + 4 q^{22} + 10 q^{23} - 4 q^{24} - 7 q^{25} + 3 q^{26} + 4 q^{27} - 4 q^{28} - 10 q^{29} - q^{30} - 9 q^{31} - 4 q^{32} - 4 q^{33} + 3 q^{34} - q^{35} + 4 q^{36} - 6 q^{37} + 4 q^{38} - 3 q^{39} - q^{40} + 3 q^{41} + 4 q^{42} - 18 q^{43} - 4 q^{44} + q^{45} - 10 q^{46} + 21 q^{47} + 4 q^{48} - 10 q^{49} + 7 q^{50} - 3 q^{51} - 3 q^{52} - 20 q^{53} - 4 q^{54} - q^{55} + 4 q^{56} - 4 q^{57} + 10 q^{58} + 5 q^{59} + q^{60} + 4 q^{61} + 9 q^{62} - 4 q^{63} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 3 q^{67} - 3 q^{68} + 10 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} + 6 q^{74} - 7 q^{75} - 4 q^{76} + 4 q^{77} + 3 q^{78} - 31 q^{79} + q^{80} + 4 q^{81} - 3 q^{82} - 8 q^{83} - 4 q^{84} - 25 q^{85} + 18 q^{86} - 10 q^{87} + 4 q^{88} + 5 q^{89} - q^{90} - 9 q^{91} + 10 q^{92} - 9 q^{93} - 21 q^{94} + 13 q^{95} - 4 q^{96} - 25 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 4 * q^18 - 4 * q^19 + q^20 - 4 * q^21 + 4 * q^22 + 10 * q^23 - 4 * q^24 - 7 * q^25 + 3 * q^26 + 4 * q^27 - 4 * q^28 - 10 * q^29 - q^30 - 9 * q^31 - 4 * q^32 - 4 * q^33 + 3 * q^34 - q^35 + 4 * q^36 - 6 * q^37 + 4 * q^38 - 3 * q^39 - q^40 + 3 * q^41 + 4 * q^42 - 18 * q^43 - 4 * q^44 + q^45 - 10 * q^46 + 21 * q^47 + 4 * q^48 - 10 * q^49 + 7 * q^50 - 3 * q^51 - 3 * q^52 - 20 * q^53 - 4 * q^54 - q^55 + 4 * q^56 - 4 * q^57 + 10 * q^58 + 5 * q^59 + q^60 + 4 * q^61 + 9 * q^62 - 4 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 3 * q^67 - 3 * q^68 + 10 * q^69 + q^70 - 9 * q^71 - 4 * q^72 + 6 * q^74 - 7 * q^75 - 4 * q^76 + 4 * q^77 + 3 * q^78 - 31 * q^79 + q^80 + 4 * q^81 - 3 * q^82 - 8 * q^83 - 4 * q^84 - 25 * q^85 + 18 * q^86 - 10 * q^87 + 4 * q^88 + 5 * q^89 - q^90 - 9 * q^91 + 10 * q^92 - 9 * q^93 - 21 * q^94 + 13 * q^95 - 4 * q^96 - 25 * q^97 + 10 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.75802	1.23342	0.616711	−	0.787190i	$-0.288465\pi$
$5$	2.75802	1.23342	0.616711	+	0.787190i	$0.288465\pi$
$6$	−1.00000	−0.408248
$7$	−2.84864	−1.07668	−0.538342	−	0.842727i	$-0.680949\pi$
$7$	−2.84864	−1.07668	−0.538342	+	0.842727i	$0.680949\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.75802	−0.872161
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−2.89322	−0.802434	−0.401217	−	0.915983i	$-0.631413\pi$
$13$	−2.89322	−0.802434	−0.401217	+	0.915983i	$0.631413\pi$
$14$	2.84864	0.761330
$15$	2.75802	0.712117
$16$	1.00000	0.250000
$17$	−6.87275	−1.66689	−0.833444	−	0.552605i	$-0.813634\pi$
$17$	−6.87275	−1.66689	−0.833444	+	0.552605i	$0.813634\pi$
$18$	−1.00000	−0.235702
$19$	2.24993	0.516170	0.258085	−	0.966122i	$-0.416908\pi$
$19$	2.24993	0.516170	0.258085	+	0.966122i	$0.416908\pi$
$20$	2.75802	0.616711
$21$	−2.84864	−0.621624
$22$	1.00000	0.213201
$23$	4.43118	0.923964	0.461982	−	0.886889i	$-0.347138\pi$
$23$	4.43118	0.923964	0.461982	+	0.886889i	$0.347138\pi$
$24$	−1.00000	−0.204124
$25$	2.60665	0.521331
$26$	2.89322	0.567406
$27$	1.00000	0.192450
$28$	−2.84864	−0.538342
$29$	−2.13520	−0.396497	−0.198248	−	0.980152i	$-0.563525\pi$
$29$	−2.13520	−0.396497	−0.198248	+	0.980152i	$0.563525\pi$
$30$	−2.75802	−0.503543
$31$	−5.04028	−0.905261	−0.452630	−	0.891698i	$-0.649514\pi$
$31$	−5.04028	−0.905261	−0.452630	+	0.891698i	$0.649514\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	6.87275	1.17867
$35$	−7.85659	−1.32801
$36$	1.00000	0.166667
$37$	6.93105	1.13946	0.569729	−	0.821833i	$-0.307048\pi$
$37$	6.93105	1.13946	0.569729	+	0.821833i	$0.307048\pi$
$38$	−2.24993	−0.364988
$39$	−2.89322	−0.463285
$40$	−2.75802	−0.436081
$41$	0.372882	0.0582344	0.0291172	−	0.999576i	$-0.490730\pi$
$41$	0.372882	0.0582344	0.0291172	+	0.999576i	$0.490730\pi$
$42$	2.84864	0.439554
$43$	2.08241	0.317564	0.158782	−	0.987314i	$-0.449243\pi$
$43$	2.08241	0.317564	0.158782	+	0.987314i	$0.449243\pi$
$44$	−1.00000	−0.150756
$45$	2.75802	0.411141
$46$	−4.43118	−0.653341
$47$	0.528546	0.0770963	0.0385482	−	0.999257i	$-0.487727\pi$
$47$	0.528546	0.0770963	0.0385482	+	0.999257i	$0.487727\pi$
$48$	1.00000	0.144338
$49$	1.11474	0.159248
$50$	−2.60665	−0.368637
$51$	−6.87275	−0.962378
$52$	−2.89322	−0.401217
$53$	−0.0665071	−0.00913545	−0.00456773	−	0.999990i	$-0.501454\pi$
$53$	−0.0665071	−0.00913545	−0.00456773	+	0.999990i	$0.501454\pi$
$54$	−1.00000	−0.136083
$55$	−2.75802	−0.371891
$56$	2.84864	0.380665
$57$	2.24993	0.298011
$58$	2.13520	0.280365
$59$	−13.0562	−1.69977	−0.849885	−	0.526968i	$-0.823329\pi$
$59$	−13.0562	−1.69977	−0.849885	+	0.526968i	$0.823329\pi$
$60$	2.75802	0.356058
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	5.04028	0.640116
$63$	−2.84864	−0.358895
$64$	1.00000	0.125000
$65$	−7.97954	−0.989740
$66$	1.00000	0.123091
$67$	−1.49192	−0.182267	−0.0911334	−	0.995839i	$-0.529049\pi$
$67$	−1.49192	−0.182267	−0.0911334	+	0.995839i	$0.529049\pi$
$68$	−6.87275	−0.833444
$69$	4.43118	0.533451
$70$	7.85659	0.939042
$71$	−0.778480	−0.0923886	−0.0461943	−	0.998932i	$-0.514709\pi$
$71$	−0.778480	−0.0923886	−0.0461943	+	0.998932i	$0.514709\pi$
$72$	−1.00000	−0.117851
$73$	6.27551	0.734493	0.367247	−	0.930124i	$-0.380300\pi$
$73$	6.27551	0.734493	0.367247	+	0.930124i	$0.380300\pi$
$74$	−6.93105	−0.805718
$75$	2.60665	0.300990
$76$	2.24993	0.258085
$77$	2.84864	0.324632
$78$	2.89322	0.327592
$79$	−14.3201	−1.61114	−0.805568	−	0.592503i	$-0.798140\pi$
$79$	−14.3201	−1.61114	−0.805568	+	0.592503i	$0.798140\pi$
$80$	2.75802	0.308356
$81$	1.00000	0.111111
$82$	−0.372882	−0.0411779
$83$	−3.11904	−0.342359	−0.171179	−	0.985240i	$-0.554758\pi$
$83$	−3.11904	−0.342359	−0.171179	+	0.985240i	$0.554758\pi$
$84$	−2.84864	−0.310812
$85$	−18.9552	−2.05598
$86$	−2.08241	−0.224552
$87$	−2.13520	−0.228917
$88$	1.00000	0.106600
$89$	−2.90693	−0.308134	−0.154067	−	0.988060i	$-0.549237\pi$
$89$	−2.90693	−0.308134	−0.154067	+	0.988060i	$0.549237\pi$
$90$	−2.75802	−0.290720
$91$	8.24172	0.863967
$92$	4.43118	0.461982
$93$	−5.04028	−0.522652
$94$	−0.528546	−0.0545153
$95$	6.20536	0.636656
$96$	−1.00000	−0.102062
$97$	−18.6729	−1.89595	−0.947973	−	0.318351i	$-0.896871\pi$
$97$	−18.6729	−1.89595	−0.947973	+	0.318351i	$0.896871\pi$
$98$	−1.11474	−0.112605
$99$	−1.00000	−0.100504
$100$	2.60665	0.260665
$101$	−11.8224	−1.17637	−0.588187	−	0.808725i	$-0.700158\pi$
$101$	−11.8224	−1.17637	−0.588187	+	0.808725i	$0.700158\pi$
$102$	6.87275	0.680504
$103$	−11.5880	−1.14180	−0.570902	−	0.821018i	$-0.693406\pi$
$103$	−11.5880	−1.14180	−0.570902	+	0.821018i	$0.693406\pi$
$104$	2.89322	0.283703
$105$	−7.85659	−0.766725
$106$	0.0665071	0.00645974
$107$	−8.35242	−0.807459	−0.403729	−	0.914878i	$-0.632286\pi$
$107$	−8.35242	−0.807459	−0.403729	+	0.914878i	$0.632286\pi$
$108$	1.00000	0.0962250
$109$	−7.07446	−0.677610	−0.338805	−	0.940857i	$-0.610023\pi$
$109$	−7.07446	−0.677610	−0.338805	+	0.940857i	$0.610023\pi$
$110$	2.75802	0.262967
$111$	6.93105	0.657866
$112$	−2.84864	−0.269171
$113$	−5.09857	−0.479633	−0.239817	−	0.970818i	$-0.577087\pi$
$113$	−5.09857	−0.479633	−0.239817	+	0.970818i	$0.577087\pi$
$114$	−2.24993	−0.210726
$115$	12.2213	1.13964
$116$	−2.13520	−0.198248
$117$	−2.89322	−0.267478
$118$	13.0562	1.20192
$119$	19.5780	1.79471
$120$	−2.75802	−0.251771
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	0.372882	0.0336217
$124$	−5.04028	−0.452630
$125$	−6.60089	−0.590401
$126$	2.84864	0.253777
$127$	−9.12725	−0.809912	−0.404956	−	0.914336i	$-0.632713\pi$
$127$	−9.12725	−0.809912	−0.404956	+	0.914336i	$0.632713\pi$
$128$	−1.00000	−0.0883883
$129$	2.08241	0.183346
$130$	7.97954	0.699852
$131$	15.1468	1.32338	0.661691	−	0.749777i	$-0.269839\pi$
$131$	15.1468	1.32338	0.661691	+	0.749777i	$0.269839\pi$
$132$	−1.00000	−0.0870388
$133$	−6.40925	−0.555752
$134$	1.49192	0.128882
$135$	2.75802	0.237372
$136$	6.87275	0.589334
$137$	9.26463	0.791531	0.395766	−	0.918352i	$-0.370479\pi$
$137$	9.26463	0.791531	0.395766	+	0.918352i	$0.370479\pi$
$138$	−4.43118	−0.377207
$139$	−4.12295	−0.349704	−0.174852	−	0.984595i	$-0.555945\pi$
$139$	−4.12295	−0.349704	−0.174852	+	0.984595i	$0.555945\pi$
$140$	−7.85659	−0.664003
$141$	0.528546	0.0445116
$142$	0.778480	0.0653286
$143$	2.89322	0.241943
$144$	1.00000	0.0833333
$145$	−5.88891	−0.489048
$146$	−6.27551	−0.519365
$147$	1.11474	0.0919418
$148$	6.93105	0.569729
$149$	4.30823	0.352944	0.176472	−	0.984306i	$-0.443532\pi$
$149$	4.30823	0.352944	0.176472	+	0.984306i	$0.443532\pi$
$150$	−2.60665	−0.212832
$151$	−21.5025	−1.74985	−0.874926	−	0.484257i	$-0.839090\pi$
$151$	−21.5025	−1.74985	−0.874926	+	0.484257i	$0.839090\pi$
$152$	−2.24993	−0.182494
$153$	−6.87275	−0.555629
$154$	−2.84864	−0.229550
$155$	−13.9012	−1.11657
$156$	−2.89322	−0.231643
$157$	6.69972	0.534696	0.267348	−	0.963600i	$-0.413853\pi$
$157$	6.69972	0.534696	0.267348	+	0.963600i	$0.413853\pi$
$158$	14.3201	1.13925
$159$	−0.0665071	−0.00527435
$160$	−2.75802	−0.218040
$161$	−12.6228	−0.994817
$162$	−1.00000	−0.0785674
$163$	6.21575	0.486855	0.243428	−	0.969919i	$-0.421728\pi$
$163$	6.21575	0.486855	0.243428	+	0.969919i	$0.421728\pi$
$164$	0.372882	0.0291172
$165$	−2.75802	−0.214711
$166$	3.11904	0.242084
$167$	−2.77995	−0.215119	−0.107559	−	0.994199i	$-0.534304\pi$
$167$	−2.77995	−0.215119	−0.107559	+	0.994199i	$0.534304\pi$
$168$	2.84864	0.219777
$169$	−4.62930	−0.356100
$170$	18.9552	1.45379
$171$	2.24993	0.172057
$172$	2.08241	0.158782
$173$	17.2155	1.30887	0.654435	−	0.756118i	$-0.272907\pi$
$173$	17.2155	1.30887	0.654435	+	0.756118i	$0.272907\pi$
$174$	2.13520	0.161869
$175$	−7.42541	−0.561308
$176$	−1.00000	−0.0753778
$177$	−13.0562	−0.981363
$178$	2.90693	0.217884
$179$	10.5927	0.791734	0.395867	−	0.918308i	$-0.370444\pi$
$179$	10.5927	0.791734	0.395867	+	0.918308i	$0.370444\pi$
$180$	2.75802	0.205570
$181$	−9.11375	−0.677420	−0.338710	−	0.940891i	$-0.609991\pi$
$181$	−9.11375	−0.677420	−0.338710	+	0.940891i	$0.609991\pi$
$182$	−8.24172	−0.610917
$183$	1.00000	0.0739221
$184$	−4.43118	−0.326671
$185$	19.1159	1.40543
$186$	5.04028	0.369571
$187$	6.87275	0.502585
$188$	0.528546	0.0385482
$189$	−2.84864	−0.207208
$190$	−6.20536	−0.450184
$191$	−8.76313	−0.634078	−0.317039	−	0.948413i	$-0.602689\pi$
$191$	−8.76313	−0.634078	−0.317039	+	0.948413i	$0.602689\pi$
$192$	1.00000	0.0721688
$193$	20.6479	1.48627	0.743133	−	0.669143i	$-0.233339\pi$
$193$	20.6479	1.48627	0.743133	+	0.669143i	$0.233339\pi$
$194$	18.6729	1.34064
$195$	−7.97954	−0.571426
$196$	1.11474	0.0796239
$197$	−17.9081	−1.27590	−0.637951	−	0.770077i	$-0.720218\pi$
$197$	−17.9081	−1.27590	−0.637951	+	0.770077i	$0.720218\pi$
$198$	1.00000	0.0710669
$199$	5.39944	0.382756	0.191378	−	0.981516i	$-0.438704\pi$
$199$	5.39944	0.382756	0.191378	+	0.981516i	$0.438704\pi$
$200$	−2.60665	−0.184318
$201$	−1.49192	−0.105232
$202$	11.8224	0.831822
$203$	6.08241	0.426901
$204$	−6.87275	−0.481189
$205$	1.02842	0.0718276
$206$	11.5880	0.807377
$207$	4.43118	0.307988
$208$	−2.89322	−0.200608
$209$	−2.24993	−0.155631
$210$	7.85659	0.542156
$211$	−13.8756	−0.955235	−0.477617	−	0.878568i	$-0.658499\pi$
$211$	−13.8756	−0.955235	−0.477617	+	0.878568i	$0.658499\pi$
$212$	−0.0665071	−0.00456773
$213$	−0.778480	−0.0533406
$214$	8.35242	0.570960
$215$	5.74332	0.391691
$216$	−1.00000	−0.0680414
$217$	14.3579	0.974679
$218$	7.07446	0.479143
$219$	6.27551	0.424060
$220$	−2.75802	−0.185945
$221$	19.8844	1.33757
$222$	−6.93105	−0.465181
$223$	−8.55485	−0.572875	−0.286437	−	0.958099i	$-0.592471\pi$
$223$	−8.55485	−0.572875	−0.286437	+	0.958099i	$0.592471\pi$
$224$	2.84864	0.190333
$225$	2.60665	0.173777
$226$	5.09857	0.339152
$227$	6.33234	0.420292	0.210146	−	0.977670i	$-0.432606\pi$
$227$	6.33234	0.420292	0.210146	+	0.977670i	$0.432606\pi$
$228$	2.24993	0.149006
$229$	6.09613	0.402843	0.201422	−	0.979505i	$-0.435444\pi$
$229$	6.09613	0.402843	0.201422	+	0.979505i	$0.435444\pi$
$230$	−12.2213	−0.805846
$231$	2.84864	0.187427
$232$	2.13520	0.140183
$233$	1.40804	0.0922441	0.0461220	−	0.998936i	$-0.485314\pi$
$233$	1.40804	0.0922441	0.0461220	+	0.998936i	$0.485314\pi$
$234$	2.89322	0.189135
$235$	1.45774	0.0950923
$236$	−13.0562	−0.849885
$237$	−14.3201	−0.930190
$238$	−19.5780	−1.26905
$239$	11.2694	0.728958	0.364479	−	0.931212i	$-0.381247\pi$
$239$	11.2694	0.728958	0.364479	+	0.931212i	$0.381247\pi$
$240$	2.75802	0.178029
$241$	−8.35792	−0.538381	−0.269191	−	0.963087i	$-0.586756\pi$
$241$	−8.35792	−0.538381	−0.269191	+	0.963087i	$0.586756\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	3.07446	0.196420
$246$	−0.372882	−0.0237741
$247$	−6.50955	−0.414193
$248$	5.04028	0.320058
$249$	−3.11904	−0.197661
$250$	6.60089	0.417477
$251$	−21.3436	−1.34720	−0.673598	−	0.739097i	$-0.735252\pi$
$251$	−21.3436	−1.34720	−0.673598	+	0.739097i	$0.735252\pi$
$252$	−2.84864	−0.179447
$253$	−4.43118	−0.278586
$254$	9.12725	0.572695
$255$	−18.9552	−1.18702
$256$	1.00000	0.0625000
$257$	23.0354	1.43691	0.718454	−	0.695575i	$-0.244850\pi$
$257$	23.0354	1.43691	0.718454	+	0.695575i	$0.244850\pi$
$258$	−2.08241	−0.129645
$259$	−19.7440	−1.22683
$260$	−7.97954	−0.494870
$261$	−2.13520	−0.132166
$262$	−15.1468	−0.935772
$263$	28.5295	1.75920	0.879602	−	0.475711i	$-0.157809\pi$
$263$	28.5295	1.75920	0.879602	+	0.475711i	$0.157809\pi$
$264$	1.00000	0.0615457
$265$	−0.183428	−0.0112679
$266$	6.40925	0.392976
$267$	−2.90693	−0.177901
$268$	−1.49192	−0.0911334
$269$	−3.41355	−0.208128	−0.104064	−	0.994571i	$-0.533185\pi$
$269$	−3.41355	−0.208128	−0.104064	+	0.994571i	$0.533185\pi$
$270$	−2.75802	−0.167848
$271$	−20.5600	−1.24893	−0.624464	−	0.781053i	$-0.714683\pi$
$271$	−20.5600	−1.24893	−0.624464	+	0.781053i	$0.714683\pi$
$272$	−6.87275	−0.416722
$273$	8.24172	0.498812
$274$	−9.26463	−0.559697
$275$	−2.60665	−0.157187
$276$	4.43118	0.266726
$277$	16.0333	0.963346	0.481673	−	0.876351i	$-0.340029\pi$
$277$	16.0333	0.963346	0.481673	+	0.876351i	$0.340029\pi$
$278$	4.12295	0.247278
$279$	−5.04028	−0.301754
$280$	7.85659	0.469521
$281$	20.2268	1.20663	0.603314	−	0.797504i	$-0.293847\pi$
$281$	20.2268	1.20663	0.603314	+	0.797504i	$0.293847\pi$
$282$	−0.528546	−0.0314744
$283$	1.43362	0.0852201	0.0426100	−	0.999092i	$-0.486433\pi$
$283$	1.43362	0.0852201	0.0426100	+	0.999092i	$0.486433\pi$
$284$	−0.778480	−0.0461943
$285$	6.20536	0.367574
$286$	−2.89322	−0.171079
$287$	−1.06221	−0.0627000
$288$	−1.00000	−0.0589256
$289$	30.2347	1.77851
$290$	5.88891	0.345809
$291$	−18.6729	−1.09462
$292$	6.27551	0.367247
$293$	29.1382	1.70227	0.851136	−	0.524945i	$-0.175914\pi$
$293$	29.1382	1.70227	0.851136	+	0.524945i	$0.175914\pi$
$294$	−1.11474	−0.0650127
$295$	−36.0092	−2.09653
$296$	−6.93105	−0.402859
$297$	−1.00000	−0.0580259
$298$	−4.30823	−0.249569
$299$	−12.8204	−0.741420
$300$	2.60665	0.150495
$301$	−5.93203	−0.341916
$302$	21.5025	1.23733
$303$	−11.8224	−0.679180
$304$	2.24993	0.129043
$305$	2.75802	0.157924
$306$	6.87275	0.392889
$307$	−33.9545	−1.93789	−0.968943	−	0.247284i	$-0.920462\pi$
$307$	−33.9545	−1.93789	−0.968943	+	0.247284i	$0.920462\pi$
$308$	2.84864	0.162316
$309$	−11.5880	−0.659221
$310$	13.9012	0.789533
$311$	−12.0797	−0.684977	−0.342489	−	0.939522i	$-0.611270\pi$
$311$	−12.0797	−0.684977	−0.342489	+	0.939522i	$0.611270\pi$
$312$	2.89322	0.163796
$313$	7.02020	0.396805	0.198403	−	0.980121i	$-0.436425\pi$
$313$	7.02020	0.396805	0.198403	+	0.980121i	$0.436425\pi$
$314$	−6.69972	−0.378087
$315$	−7.85659	−0.442669
$316$	−14.3201	−0.805568
$317$	20.3119	1.14083	0.570414	−	0.821357i	$-0.306783\pi$
$317$	20.3119	1.14083	0.570414	+	0.821357i	$0.306783\pi$
$318$	0.0665071	0.00372953
$319$	2.13520	0.119548
$320$	2.75802	0.154178
$321$	−8.35242	−0.466187
$322$	12.6228	0.703442
$323$	−15.4632	−0.860398
$324$	1.00000	0.0555556
$325$	−7.54161	−0.418333
$326$	−6.21575	−0.344259
$327$	−7.07446	−0.391218
$328$	−0.372882	−0.0205890
$329$	−1.50564	−0.0830083
$330$	2.75802	0.151824
$331$	−4.45125	−0.244663	−0.122331	−	0.992489i	$-0.539037\pi$
$331$	−4.45125	−0.244663	−0.122331	+	0.992489i	$0.539037\pi$
$332$	−3.11904	−0.171179
$333$	6.93105	0.379819
$334$	2.77995	0.152112
$335$	−4.11474	−0.224812
$336$	−2.84864	−0.155406
$337$	5.63752	0.307095	0.153548	−	0.988141i	$-0.450930\pi$
$337$	5.63752	0.307095	0.153548	+	0.988141i	$0.450930\pi$
$338$	4.62930	0.251801
$339$	−5.09857	−0.276916
$340$	−18.9552	−1.02799
$341$	5.04028	0.272946
$342$	−2.24993	−0.121663
$343$	16.7650	0.905224
$344$	−2.08241	−0.112276
$345$	12.2213	0.657970
$346$	−17.2155	−0.925511
$347$	14.1410	0.759131	0.379565	−	0.925165i	$-0.376074\pi$
$347$	14.1410	0.759131	0.379565	+	0.925165i	$0.376074\pi$
$348$	−2.13520	−0.114459
$349$	15.4105	0.824903	0.412451	−	0.910980i	$-0.364673\pi$
$349$	15.4105	0.824903	0.412451	+	0.910980i	$0.364673\pi$
$350$	7.42541	0.396905
$351$	−2.89322	−0.154428
$352$	1.00000	0.0533002
$353$	−4.73080	−0.251795	−0.125898	−	0.992043i	$-0.540181\pi$
$353$	−4.73080	−0.251795	−0.125898	+	0.992043i	$0.540181\pi$
$354$	13.0562	0.693928
$355$	−2.14706	−0.113954
$356$	−2.90693	−0.154067
$357$	19.5780	1.03618
$358$	−10.5927	−0.559840
$359$	−6.90215	−0.364281	−0.182141	−	0.983272i	$-0.558303\pi$
$359$	−6.90215	−0.364281	−0.182141	+	0.983272i	$0.558303\pi$
$360$	−2.75802	−0.145360
$361$	−13.9378	−0.733568
$362$	9.11375	0.479008
$363$	1.00000	0.0524864
$364$	8.24172	0.431984
$365$	17.3080	0.905940
$366$	−1.00000	−0.0522708
$367$	−1.93714	−0.101118	−0.0505590	−	0.998721i	$-0.516100\pi$
$367$	−1.93714	−0.101118	−0.0505590	+	0.998721i	$0.516100\pi$
$368$	4.43118	0.230991
$369$	0.372882	0.0194115
$370$	−19.1159	−0.993790
$371$	0.189455	0.00983599
$372$	−5.04028	−0.261326
$373$	15.1757	0.785768	0.392884	−	0.919588i	$-0.371477\pi$
$373$	15.1757	0.785768	0.392884	+	0.919588i	$0.371477\pi$
$374$	−6.87275	−0.355382
$375$	−6.60089	−0.340868
$376$	−0.528546	−0.0272577
$377$	6.17759	0.318162
$378$	2.84864	0.146518
$379$	25.2878	1.29895	0.649474	−	0.760383i	$-0.274989\pi$
$379$	25.2878	1.29895	0.649474	+	0.760383i	$0.274989\pi$
$380$	6.20536	0.318328
$381$	−9.12725	−0.467603
$382$	8.76313	0.448361
$383$	28.5286	1.45774	0.728871	−	0.684651i	$-0.240045\pi$
$383$	28.5286	1.45774	0.728871	+	0.684651i	$0.240045\pi$
$384$	−1.00000	−0.0510310
$385$	7.85659	0.400409
$386$	−20.6479	−1.05095
$387$	2.08241	0.105855
$388$	−18.6729	−0.947973
$389$	−3.52975	−0.178965	−0.0894827	−	0.995988i	$-0.528521\pi$
$389$	−3.52975	−0.178965	−0.0894827	+	0.995988i	$0.528521\pi$
$390$	7.97954	0.404060
$391$	−30.4544	−1.54014
$392$	−1.11474	−0.0563026
$393$	15.1468	0.764055
$394$	17.9081	0.902199
$395$	−39.4950	−1.98721
$396$	−1.00000	−0.0502519
$397$	−13.9344	−0.699349	−0.349675	−	0.936871i	$-0.613708\pi$
$397$	−13.9344	−0.699349	−0.349675	+	0.936871i	$0.613708\pi$
$398$	−5.39944	−0.270650
$399$	−6.40925	−0.320864
$400$	2.60665	0.130333
$401$	−15.6003	−0.779042	−0.389521	−	0.921018i	$-0.627359\pi$
$401$	−15.6003	−0.779042	−0.389521	+	0.921018i	$0.627359\pi$
$402$	1.49192	0.0744101
$403$	14.5826	0.726412
$404$	−11.8224	−0.588187
$405$	2.75802	0.137047
$406$	−6.08241	−0.301865
$407$	−6.93105	−0.343559
$408$	6.87275	0.340252
$409$	−7.64083	−0.377815	−0.188907	−	0.981995i	$-0.560495\pi$
$409$	−7.64083	−0.377815	−0.188907	+	0.981995i	$0.560495\pi$
$410$	−1.02842	−0.0507898
$411$	9.26463	0.456991
$412$	−11.5880	−0.570902
$413$	37.1923	1.83011
$414$	−4.43118	−0.217780
$415$	−8.60235	−0.422273
$416$	2.89322	0.141852
$417$	−4.12295	−0.201902
$418$	2.24993	0.110048
$419$	8.42808	0.411739	0.205869	−	0.978579i	$-0.433998\pi$
$419$	8.42808	0.411739	0.205869	+	0.978579i	$0.433998\pi$
$420$	−7.85659	−0.383362
$421$	−20.4032	−0.994392	−0.497196	−	0.867638i	$-0.665637\pi$
$421$	−20.4032	−0.994392	−0.497196	+	0.867638i	$0.665637\pi$
$422$	13.8756	0.675453
$423$	0.528546	0.0256988
$424$	0.0665071	0.00322987
$425$	−17.9149	−0.868999
$426$	0.778480	0.0377175
$427$	−2.84864	−0.137855
$428$	−8.35242	−0.403729
$429$	2.89322	0.139686
$430$	−5.74332	−0.276967
$431$	−0.0951834	−0.00458482	−0.00229241	−	0.999997i	$-0.500730\pi$
$431$	−0.0951834	−0.00458482	−0.00229241	+	0.999997i	$0.500730\pi$
$432$	1.00000	0.0481125
$433$	−23.0613	−1.10826	−0.554128	−	0.832432i	$-0.686948\pi$
$433$	−23.0613	−1.10826	−0.554128	+	0.832432i	$0.686948\pi$
$434$	−14.3579	−0.689202
$435$	−5.88891	−0.282352
$436$	−7.07446	−0.338805
$437$	9.96986	0.476923
$438$	−6.27551	−0.299856
$439$	−17.9735	−0.857829	−0.428914	−	0.903345i	$-0.641104\pi$
$439$	−17.9735	−0.857829	−0.428914	+	0.903345i	$0.641104\pi$
$440$	2.75802	0.131483
$441$	1.11474	0.0530826
$442$	−19.8844	−0.945802
$443$	20.1358	0.956681	0.478341	−	0.878174i	$-0.341238\pi$
$443$	20.1358	0.956681	0.478341	+	0.878174i	$0.341238\pi$
$444$	6.93105	0.328933
$445$	−8.01737	−0.380060
$446$	8.55485	0.405084
$447$	4.30823	0.203772
$448$	−2.84864	−0.134585
$449$	−15.1157	−0.713355	−0.356677	−	0.934228i	$-0.616090\pi$
$449$	−15.1157	−0.713355	−0.356677	+	0.934228i	$0.616090\pi$
$450$	−2.60665	−0.122879
$451$	−0.372882	−0.0175583
$452$	−5.09857	−0.239817
$453$	−21.5025	−1.01028
$454$	−6.33234	−0.297192
$455$	22.7308	1.06564
$456$	−2.24993	−0.105363
$457$	−6.89507	−0.322538	−0.161269	−	0.986911i	$-0.551559\pi$
$457$	−6.89507	−0.322538	−0.161269	+	0.986911i	$0.551559\pi$
$458$	−6.09613	−0.284853
$459$	−6.87275	−0.320793
$460$	12.2213	0.569819
$461$	31.8133	1.48170	0.740848	−	0.671673i	$-0.234424\pi$
$461$	31.8133	1.48170	0.740848	+	0.671673i	$0.234424\pi$
$462$	−2.84864	−0.132531
$463$	−33.9923	−1.57976	−0.789879	−	0.613263i	$-0.789857\pi$
$463$	−33.9923	−1.57976	−0.789879	+	0.613263i	$0.789857\pi$
$464$	−2.13520	−0.0991241
$465$	−13.9012	−0.644651
$466$	−1.40804	−0.0652264
$467$	−25.5409	−1.18189	−0.590945	−	0.806712i	$-0.701245\pi$
$467$	−25.5409	−1.18189	−0.590945	+	0.806712i	$0.701245\pi$
$468$	−2.89322	−0.133739
$469$	4.24993	0.196244
$470$	−1.45774	−0.0672404
$471$	6.69972	0.308707
$472$	13.0562	0.600959
$473$	−2.08241	−0.0957493
$474$	14.3201	0.657744
$475$	5.86480	0.269096
$476$	19.5780	0.897355
$477$	−0.0665071	−0.00304515
$478$	−11.2694	−0.515451
$479$	−32.4034	−1.48055	−0.740276	−	0.672304i	$-0.765305\pi$
$479$	−32.4034	−1.48055	−0.740276	+	0.672304i	$0.765305\pi$
$480$	−2.75802	−0.125886
$481$	−20.0530	−0.914339
$482$	8.35792	0.380693
$483$	−12.6228	−0.574358
$484$	1.00000	0.0454545
$485$	−51.5002	−2.33850
$486$	−1.00000	−0.0453609
$487$	−4.32994	−0.196208	−0.0981041	−	0.995176i	$-0.531278\pi$
$487$	−4.32994	−0.196208	−0.0981041	+	0.995176i	$0.531278\pi$
$488$	−1.00000	−0.0452679
$489$	6.21575	0.281086
$490$	−3.07446	−0.138890
$491$	11.8005	0.532548	0.266274	−	0.963897i	$-0.414207\pi$
$491$	11.8005	0.532548	0.266274	+	0.963897i	$0.414207\pi$
$492$	0.372882	0.0168108
$493$	14.6747	0.660915
$494$	6.50955	0.292878
$495$	−2.75802	−0.123964
$496$	−5.04028	−0.226315
$497$	2.21761	0.0994733
$498$	3.11904	0.139767
$499$	1.21237	0.0542729	0.0271365	−	0.999632i	$-0.491361\pi$
$499$	1.21237	0.0542729	0.0271365	+	0.999632i	$0.491361\pi$
$500$	−6.60089	−0.295201
$501$	−2.77995	−0.124199
$502$	21.3436	0.952612
$503$	−4.87057	−0.217168	−0.108584	−	0.994087i	$-0.534632\pi$
$503$	−4.87057	−0.217168	−0.108584	+	0.994087i	$0.534632\pi$
$504$	2.84864	0.126888
$505$	−32.6064	−1.45097
$506$	4.43118	0.196990
$507$	−4.62930	−0.205595
$508$	−9.12725	−0.404956
$509$	2.84385	0.126052	0.0630258	−	0.998012i	$-0.479925\pi$
$509$	2.84385	0.126052	0.0630258	+	0.998012i	$0.479925\pi$
$510$	18.9552	0.839349
$511$	−17.8767	−0.790817
$512$	−1.00000	−0.0441942
$513$	2.24993	0.0993370
$514$	−23.0354	−1.01605
$515$	−31.9600	−1.40833
$516$	2.08241	0.0916729
$517$	−0.528546	−0.0232454
$518$	19.7440	0.867503
$519$	17.2155	0.755676
$520$	7.97954	0.349926
$521$	2.35978	0.103384	0.0516919	−	0.998663i	$-0.483539\pi$
$521$	2.35978	0.103384	0.0516919	+	0.998663i	$0.483539\pi$
$522$	2.13520	0.0934551
$523$	−38.2300	−1.67168	−0.835841	−	0.548971i	$-0.815020\pi$
$523$	−38.2300	−1.67168	−0.835841	+	0.548971i	$0.815020\pi$
$524$	15.1468	0.661691
$525$	−7.42541	−0.324072
$526$	−28.5295	−1.24394
$527$	34.6406	1.50897
$528$	−1.00000	−0.0435194
$529$	−3.36467	−0.146290
$530$	0.183428	0.00796759
$531$	−13.0562	−0.566590
$532$	−6.40925	−0.277876
$533$	−1.07883	−0.0467293
$534$	2.90693	0.125795
$535$	−23.0361	−0.995938
$536$	1.49192	0.0644411
$537$	10.5927	0.457108
$538$	3.41355	0.147169
$539$	−1.11474	−0.0480150
$540$	2.75802	0.118686
$541$	−13.7040	−0.589182	−0.294591	−	0.955623i	$-0.595183\pi$
$541$	−13.7040	−0.589182	−0.294591	+	0.955623i	$0.595183\pi$
$542$	20.5600	0.883126
$543$	−9.11375	−0.391109
$544$	6.87275	0.294667
$545$	−19.5115	−0.835780
$546$	−8.24172	−0.352713
$547$	5.06096	0.216391	0.108196	−	0.994130i	$-0.465493\pi$
$547$	5.06096	0.216391	0.108196	+	0.994130i	$0.465493\pi$
$548$	9.26463	0.395766
$549$	1.00000	0.0426790
$550$	2.60665	0.111148
$551$	−4.80406	−0.204660
$552$	−4.43118	−0.188603
$553$	40.7927	1.73468
$554$	−16.0333	−0.681188
$555$	19.1159	0.811426
$556$	−4.12295	−0.174852
$557$	43.0427	1.82378	0.911889	−	0.410438i	$-0.134624\pi$
$557$	43.0427	1.82378	0.911889	+	0.410438i	$0.134624\pi$
$558$	5.04028	0.213372
$559$	−6.02486	−0.254824
$560$	−7.85659	−0.332001
$561$	6.87275	0.290168
$562$	−20.2268	−0.853214
$563$	−5.23231	−0.220515	−0.110258	−	0.993903i	$-0.535168\pi$
$563$	−5.23231	−0.220515	−0.110258	+	0.993903i	$0.535168\pi$
$564$	0.528546	0.0222558
$565$	−14.0619	−0.591590
$566$	−1.43362	−0.0602597
$567$	−2.84864	−0.119632
$568$	0.778480	0.0326643
$569$	−4.78949	−0.200786	−0.100393	−	0.994948i	$-0.532010\pi$
$569$	−4.78949	−0.200786	−0.100393	+	0.994948i	$0.532010\pi$
$570$	−6.20536	−0.259914
$571$	−29.1773	−1.22103	−0.610517	−	0.792003i	$-0.709038\pi$
$571$	−29.1773	−1.22103	−0.610517	+	0.792003i	$0.709038\pi$
$572$	2.89322	0.120971
$573$	−8.76313	−0.366085
$574$	1.06221	0.0443356
$575$	11.5505	0.481691
$576$	1.00000	0.0416667
$577$	9.82280	0.408928	0.204464	−	0.978874i	$-0.434455\pi$
$577$	9.82280	0.408928	0.204464	+	0.978874i	$0.434455\pi$
$578$	−30.2347	−1.25760
$579$	20.6479	0.858096
$580$	−5.88891	−0.244524
$581$	8.88500	0.368612
$582$	18.6729	0.774017
$583$	0.0665071	0.00275444
$584$	−6.27551	−0.259683
$585$	−7.97954	−0.329913
$586$	−29.1382	−1.20369
$587$	−3.37904	−0.139468	−0.0697339	−	0.997566i	$-0.522215\pi$
$587$	−3.37904	−0.139468	−0.0697339	+	0.997566i	$0.522215\pi$
$588$	1.11474	0.0459709
$589$	−11.3403	−0.467269
$590$	36.0092	1.48247
$591$	−17.9081	−0.736642
$592$	6.93105	0.284864
$593$	2.11766	0.0869621	0.0434810	−	0.999054i	$-0.486155\pi$
$593$	2.11766	0.0869621	0.0434810	+	0.999054i	$0.486155\pi$
$594$	1.00000	0.0410305
$595$	53.9964	2.21364
$596$	4.30823	0.176472
$597$	5.39944	0.220984
$598$	12.8204	0.524263
$599$	−38.6460	−1.57903	−0.789517	−	0.613729i	$-0.789669\pi$
$599$	−38.6460	−1.57903	−0.789517	+	0.613729i	$0.789669\pi$
$600$	−2.60665	−0.106416
$601$	21.7101	0.885573	0.442786	−	0.896627i	$-0.353990\pi$
$601$	21.7101	0.885573	0.442786	+	0.896627i	$0.353990\pi$
$602$	5.93203	0.241771
$603$	−1.49192	−0.0607556
$604$	−21.5025	−0.874926
$605$	2.75802	0.112129
$606$	11.8224	0.480252
$607$	7.41169	0.300831	0.150416	−	0.988623i	$-0.451939\pi$
$607$	7.41169	0.300831	0.150416	+	0.988623i	$0.451939\pi$
$608$	−2.24993	−0.0912469
$609$	6.08241	0.246472
$610$	−2.75802	−0.111669
$611$	−1.52920	−0.0618647
$612$	−6.87275	−0.277815
$613$	45.9288	1.85505	0.927524	−	0.373764i	$-0.121933\pi$
$613$	45.9288	1.85505	0.927524	+	0.373764i	$0.121933\pi$
$614$	33.9545	1.37029
$615$	1.02842	0.0414697
$616$	−2.84864	−0.114775
$617$	11.0708	0.445694	0.222847	−	0.974853i	$-0.428465\pi$
$617$	11.0708	0.445694	0.222847	+	0.974853i	$0.428465\pi$
$618$	11.5880	0.466139
$619$	−4.19349	−0.168551	−0.0842754	−	0.996443i	$-0.526858\pi$
$619$	−4.19349	−0.168551	−0.0842754	+	0.996443i	$0.526858\pi$
$620$	−13.9012	−0.558284
$621$	4.43118	0.177817
$622$	12.0797	0.484352
$623$	8.28080	0.331763
$624$	−2.89322	−0.115821
$625$	−31.2386	−1.24954
$626$	−7.02020	−0.280584
$627$	−2.24993	−0.0898537
$628$	6.69972	0.267348
$629$	−47.6354	−1.89935
$630$	7.85659	0.313014
$631$	18.0155	0.717186	0.358593	−	0.933494i	$-0.383257\pi$
$631$	18.0155	0.717186	0.358593	+	0.933494i	$0.383257\pi$
$632$	14.3201	0.569623
$633$	−13.8756	−0.551505
$634$	−20.3119	−0.806688
$635$	−25.1731	−0.998964
$636$	−0.0665071	−0.00263718
$637$	−3.22517	−0.127786
$638$	−2.13520	−0.0845334
$639$	−0.778480	−0.0307962
$640$	−2.75802	−0.109020
$641$	−2.62428	−0.103653	−0.0518264	−	0.998656i	$-0.516504\pi$
$641$	−2.62428	−0.103653	−0.0518264	+	0.998656i	$0.516504\pi$
$642$	8.35242	0.329644
$643$	3.76068	0.148307	0.0741535	−	0.997247i	$-0.476375\pi$
$643$	3.76068	0.148307	0.0741535	+	0.997247i	$0.476375\pi$
$644$	−12.6228	−0.497409
$645$	5.74332	0.226143
$646$	15.4632	0.608393
$647$	−19.4862	−0.766082	−0.383041	−	0.923731i	$-0.625123\pi$
$647$	−19.4862	−0.766082	−0.383041	+	0.923731i	$0.625123\pi$
$648$	−1.00000	−0.0392837
$649$	13.0562	0.512500
$650$	7.54161	0.295806
$651$	14.3579	0.562731
$652$	6.21575	0.243428
$653$	40.4766	1.58397	0.791987	−	0.610538i	$-0.209047\pi$
$653$	40.4766	1.58397	0.791987	+	0.610538i	$0.209047\pi$
$654$	7.07446	0.276633
$655$	41.7751	1.63229
$656$	0.372882	0.0145586
$657$	6.27551	0.244831
$658$	1.50564	0.0586958
$659$	20.3289	0.791900	0.395950	−	0.918272i	$-0.370415\pi$
$659$	20.3289	0.791900	0.395950	+	0.918272i	$0.370415\pi$
$660$	−2.75802	−0.107356
$661$	21.5115	0.836699	0.418350	−	0.908286i	$-0.362609\pi$
$661$	21.5115	0.836699	0.418350	+	0.908286i	$0.362609\pi$
$662$	4.45125	0.173003
$663$	19.8844	0.772244
$664$	3.11904	0.121042
$665$	−17.6768	−0.685477
$666$	−6.93105	−0.268573
$667$	−9.46145	−0.366349
$668$	−2.77995	−0.107559
$669$	−8.55485	−0.330749
$670$	4.11474	0.158966
$671$	−1.00000	−0.0386046
$672$	2.84864	0.109889
$673$	18.8227	0.725561	0.362780	−	0.931875i	$-0.381828\pi$
$673$	18.8227	0.725561	0.362780	+	0.931875i	$0.381828\pi$
$674$	−5.63752	−0.217149
$675$	2.60665	0.100330
$676$	−4.62930	−0.178050
$677$	8.23019	0.316312	0.158156	−	0.987414i	$-0.449445\pi$
$677$	8.23019	0.316312	0.158156	+	0.987414i	$0.449445\pi$
$678$	5.09857	0.195809
$679$	53.1923	2.04133
$680$	18.9552	0.726897
$681$	6.33234	0.242656
$682$	−5.04028	−0.193002
$683$	−6.37468	−0.243920	−0.121960	−	0.992535i	$-0.538918\pi$
$683$	−6.37468	−0.243920	−0.121960	+	0.992535i	$0.538918\pi$
$684$	2.24993	0.0860284
$685$	25.5520	0.976292
$686$	−16.7650	−0.640090
$687$	6.09613	0.232582
$688$	2.08241	0.0793911
$689$	0.192419	0.00733059
$690$	−12.2213	−0.465255
$691$	6.70816	0.255190	0.127595	−	0.991826i	$-0.459274\pi$
$691$	6.70816	0.255190	0.127595	+	0.991826i	$0.459274\pi$
$692$	17.2155	0.654435
$693$	2.84864	0.108211
$694$	−14.1410	−0.536786
$695$	−11.3712	−0.431333
$696$	2.13520	0.0809345
$697$	−2.56273	−0.0970702
$698$	−15.4105	−0.583294
$699$	1.40804	0.0532571
$700$	−7.42541	−0.280654
$701$	13.2136	0.499072	0.249536	−	0.968365i	$-0.419722\pi$
$701$	13.2136	0.499072	0.249536	+	0.968365i	$0.419722\pi$
$702$	2.89322	0.109197
$703$	15.5944	0.588154
$704$	−1.00000	−0.0376889
$705$	1.45774	0.0549016
$706$	4.73080	0.178046
$707$	33.6778	1.26658
$708$	−13.0562	−0.490681
$709$	12.1281	0.455481	0.227741	−	0.973722i	$-0.426866\pi$
$709$	12.1281	0.455481	0.227741	+	0.973722i	$0.426866\pi$
$710$	2.14706	0.0805778
$711$	−14.3201	−0.537045
$712$	2.90693	0.108942
$713$	−22.3344	−0.836428
$714$	−19.5780	−0.732687
$715$	7.97954	0.298418
$716$	10.5927	0.395867
$717$	11.2694	0.420864
$718$	6.90215	0.257586
$719$	25.4962	0.950847	0.475424	−	0.879757i	$-0.342295\pi$
$719$	25.4962	0.950847	0.475424	+	0.879757i	$0.342295\pi$
$720$	2.75802	0.102785
$721$	33.0101	1.22936
$722$	13.9378	0.518711
$723$	−8.35792	−0.310834
$724$	−9.11375	−0.338710
$725$	−5.56573	−0.206706
$726$	−1.00000	−0.0371135
$727$	50.6851	1.87981	0.939903	−	0.341442i	$-0.110915\pi$
$727$	50.6851	1.87981	0.939903	+	0.341442i	$0.110915\pi$
$728$	−8.24172	−0.305459
$729$	1.00000	0.0370370
$730$	−17.3080	−0.640597
$731$	−14.3119	−0.529344
$732$	1.00000	0.0369611
$733$	4.67049	0.172509	0.0862543	−	0.996273i	$-0.472510\pi$
$733$	4.67049	0.172509	0.0862543	+	0.996273i	$0.472510\pi$
$734$	1.93714	0.0715012
$735$	3.07446	0.113403
$736$	−4.43118	−0.163335
$737$	1.49192	0.0549555
$738$	−0.372882	−0.0137260
$739$	34.0333	1.25193	0.625967	−	0.779850i	$-0.284704\pi$
$739$	34.0333	1.25193	0.625967	+	0.779850i	$0.284704\pi$
$740$	19.1159	0.702716
$741$	−6.50955	−0.239134
$742$	−0.189455	−0.00695510
$743$	−38.9473	−1.42884	−0.714419	−	0.699719i	$-0.753309\pi$
$743$	−38.9473	−1.42884	−0.714419	+	0.699719i	$0.753309\pi$
$744$	5.04028	0.184786
$745$	11.8822	0.435329
$746$	−15.1757	−0.555622
$747$	−3.11904	−0.114120
$748$	6.87275	0.251293
$749$	23.7930	0.869378
$750$	6.60089	0.241030
$751$	42.4462	1.54888	0.774441	−	0.632646i	$-0.218031\pi$
$751$	42.4462	1.54888	0.774441	+	0.632646i	$0.218031\pi$
$752$	0.528546	0.0192741
$753$	−21.3436	−0.777805
$754$	−6.17759	−0.224975
$755$	−59.3043	−2.15831
$756$	−2.84864	−0.103604
$757$	−47.2960	−1.71900	−0.859502	−	0.511132i	$-0.829226\pi$
$757$	−47.2960	−1.71900	−0.859502	+	0.511132i	$0.829226\pi$
$758$	−25.2878	−0.918496
$759$	−4.43118	−0.160842
$760$	−6.20536	−0.225092
$761$	−42.9005	−1.55514	−0.777571	−	0.628795i	$-0.783549\pi$
$761$	−42.9005	−1.55514	−0.777571	+	0.628795i	$0.783549\pi$
$762$	9.12725	0.330645
$763$	20.1526	0.729572
$764$	−8.76313	−0.317039
$765$	−18.9552	−0.685325
$766$	−28.5286	−1.03078
$767$	37.7743	1.36395
$768$	1.00000	0.0360844
$769$	23.3596	0.842370	0.421185	−	0.906975i	$-0.361614\pi$
$769$	23.3596	0.842370	0.421185	+	0.906975i	$0.361614\pi$
$770$	−7.85659	−0.283132
$771$	23.0354	0.829599
$772$	20.6479	0.743133
$773$	0.753424	0.0270988	0.0135494	−	0.999908i	$-0.495687\pi$
$773$	0.753424	0.0270988	0.0135494	+	0.999908i	$0.495687\pi$
$774$	−2.08241	−0.0748506
$775$	−13.1383	−0.471940
$776$	18.6729	0.670318
$777$	−19.7440	−0.708313
$778$	3.52975	0.126548
$779$	0.838961	0.0300589
$780$	−7.97954	−0.285713
$781$	0.778480	0.0278562
$782$	30.4544	1.08905
$783$	−2.13520	−0.0763058
$784$	1.11474	0.0398120
$785$	18.4779	0.659506
$786$	−15.1468	−0.540268
$787$	−30.5199	−1.08792	−0.543959	−	0.839112i	$-0.683075\pi$
$787$	−30.5199	−1.08792	−0.543959	+	0.839112i	$0.683075\pi$
$788$	−17.9081	−0.637951
$789$	28.5295	1.01568
$790$	39.4950	1.40517
$791$	14.5240	0.516413
$792$	1.00000	0.0355335
$793$	−2.89322	−0.102741
$794$	13.9344	0.494515
$795$	−0.183428	−0.00650551
$796$	5.39944	0.191378
$797$	−13.3473	−0.472784	−0.236392	−	0.971658i	$-0.575965\pi$
$797$	−13.3473	−0.472784	−0.236392	+	0.971658i	$0.575965\pi$
$798$	6.40925	0.226885
$799$	−3.63256	−0.128511
$800$	−2.60665	−0.0921591
$801$	−2.90693	−0.102711
$802$	15.6003	0.550866
$803$	−6.27551	−0.221458
$804$	−1.49192	−0.0526159
$805$	−34.8139	−1.22703
$806$	−14.5826	−0.513650
$807$	−3.41355	−0.120163
$808$	11.8224	0.415911
$809$	31.4129	1.10442	0.552209	−	0.833706i	$-0.313785\pi$
$809$	31.4129	1.10442	0.552209	+	0.833706i	$0.313785\pi$
$810$	−2.75802	−0.0969068
$811$	−27.6127	−0.969613	−0.484807	−	0.874621i	$-0.661110\pi$
$811$	−27.6127	−0.969613	−0.484807	+	0.874621i	$0.661110\pi$
$812$	6.08241	0.213451
$813$	−20.5600	−0.721069
$814$	6.93105	0.242933
$815$	17.1432	0.600498
$816$	−6.87275	−0.240594
$817$	4.68528	0.163917
$818$	7.64083	0.267156
$819$	8.24172	0.287989
$820$	1.02842	0.0359138
$821$	51.9927	1.81456	0.907278	−	0.420531i	$-0.138156\pi$
$821$	51.9927	1.81456	0.907278	+	0.420531i	$0.138156\pi$
$822$	−9.26463	−0.323141
$823$	−5.64899	−0.196911	−0.0984557	−	0.995141i	$-0.531390\pi$
$823$	−5.64899	−0.196911	−0.0984557	+	0.995141i	$0.531390\pi$
$824$	11.5880	0.403689
$825$	−2.60665	−0.0907520
$826$	−37.1923	−1.29409
$827$	−31.1488	−1.08315	−0.541575	−	0.840652i	$-0.682172\pi$
$827$	−31.1488	−1.08315	−0.541575	+	0.840652i	$0.682172\pi$
$828$	4.43118	0.153994
$829$	−5.65303	−0.196338	−0.0981689	−	0.995170i	$-0.531299\pi$
$829$	−5.65303	−0.196338	−0.0981689	+	0.995170i	$0.531299\pi$
$830$	8.60235	0.298592
$831$	16.0333	0.556188
$832$	−2.89322	−0.100304
$833$	−7.66130	−0.265448
$834$	4.12295	0.142766
$835$	−7.66713	−0.265332
$836$	−2.24993	−0.0778156
$837$	−5.04028	−0.174217
$838$	−8.42808	−0.291143
$839$	18.3272	0.632726	0.316363	−	0.948638i	$-0.397538\pi$
$839$	18.3272	0.632726	0.316363	+	0.948638i	$0.397538\pi$
$840$	7.85659	0.271078
$841$	−24.4409	−0.842790
$842$	20.4032	0.703141
$843$	20.2268	0.696647
$844$	−13.8756	−0.477617
$845$	−12.7677	−0.439222
$846$	−0.528546	−0.0181718
$847$	−2.84864	−0.0978803
$848$	−0.0665071	−0.00228386
$849$	1.43362	0.0492018
$850$	17.9149	0.614475
$851$	30.7127	1.05282
$852$	−0.778480	−0.0266703
$853$	−20.3897	−0.698131	−0.349065	−	0.937098i	$-0.613501\pi$
$853$	−20.3897	−0.698131	−0.349065	+	0.937098i	$0.613501\pi$
$854$	2.84864	0.0974784
$855$	6.20536	0.212219
$856$	8.35242	0.285480
$857$	0.597569	0.0204126	0.0102063	−	0.999948i	$-0.496751\pi$
$857$	0.597569	0.0204126	0.0102063	+	0.999948i	$0.496751\pi$
$858$	−2.89322	−0.0987728
$859$	24.2096	0.826022	0.413011	−	0.910726i	$-0.364477\pi$
$859$	24.2096	0.826022	0.413011	+	0.910726i	$0.364477\pi$
$860$	5.74332	0.195846
$861$	−1.06221	−0.0361999
$862$	0.0951834	0.00324196
$863$	11.9194	0.405741	0.202870	−	0.979206i	$-0.434973\pi$
$863$	11.9194	0.405741	0.202870	+	0.979206i	$0.434973\pi$
$864$	−1.00000	−0.0340207
$865$	47.4806	1.61439
$866$	23.0613	0.783655
$867$	30.2347	1.02682
$868$	14.3579	0.487340
$869$	14.3201	0.485776
$870$	5.88891	0.199653
$871$	4.31644	0.146257
$872$	7.07446	0.239571
$873$	−18.6729	−0.631982
$874$	−9.96986	−0.337236
$875$	18.8035	0.635676
$876$	6.27551	0.212030
$877$	31.5393	1.06501	0.532503	−	0.846428i	$-0.321251\pi$
$877$	31.5393	1.06501	0.532503	+	0.846428i	$0.321251\pi$
$878$	17.9735	0.606577
$879$	29.1382	0.982807
$880$	−2.75802	−0.0929727
$881$	5.10460	0.171978	0.0859892	−	0.996296i	$-0.472595\pi$
$881$	5.10460	0.171978	0.0859892	+	0.996296i	$0.472595\pi$
$882$	−1.11474	−0.0375351
$883$	43.0520	1.44882	0.724408	−	0.689372i	$-0.242113\pi$
$883$	43.0520	1.44882	0.724408	+	0.689372i	$0.242113\pi$
$884$	19.8844	0.668783
$885$	−36.0092	−1.21043
$886$	−20.1358	−0.676476
$887$	−43.1050	−1.44732	−0.723661	−	0.690155i	$-0.757542\pi$
$887$	−43.1050	−1.44732	−0.723661	+	0.690155i	$0.757542\pi$
$888$	−6.93105	−0.232591
$889$	26.0002	0.872019
$890$	8.01737	0.268743
$891$	−1.00000	−0.0335013
$892$	−8.55485	−0.286437
$893$	1.18919	0.0397948
$894$	−4.30823	−0.144089
$895$	29.2148	0.976542
$896$	2.84864	0.0951663
$897$	−12.8204	−0.428059
$898$	15.1157	0.504418
$899$	10.7620	0.358933
$900$	2.60665	0.0868885
$901$	0.457087	0.0152278
$902$	0.372882	0.0124156
$903$	−5.93203	−0.197406
$904$	5.09857	0.169576
$905$	−25.1359	−0.835545
$906$	21.5025	0.714374
$907$	−14.3360	−0.476019	−0.238009	−	0.971263i	$-0.576495\pi$
$907$	−14.3360	−0.476019	−0.238009	+	0.971263i	$0.576495\pi$
$908$	6.33234	0.210146
$909$	−11.8224	−0.392125
$910$	−22.7308	−0.753519
$911$	18.3802	0.608965	0.304482	−	0.952518i	$-0.401517\pi$
$911$	18.3802	0.608965	0.304482	+	0.952518i	$0.401517\pi$
$912$	2.24993	0.0745028
$913$	3.11904	0.103225
$914$	6.89507	0.228069
$915$	2.75802	0.0911772
$916$	6.09613	0.201422
$917$	−43.1477	−1.42486
$918$	6.87275	0.226835
$919$	−0.218683	−0.00721370	−0.00360685	−	0.999993i	$-0.501148\pi$
$919$	−0.218683	−0.00721370	−0.00360685	+	0.999993i	$0.501148\pi$
$920$	−12.2213	−0.402923
$921$	−33.9545	−1.11884
$922$	−31.8133	−1.04772
$923$	2.25231	0.0741357
$924$	2.84864	0.0937133
$925$	18.0668	0.594034
$926$	33.9923	1.11706
$927$	−11.5880	−0.380601
$928$	2.13520	0.0700914
$929$	3.37633	0.110774	0.0553869	−	0.998465i	$-0.482361\pi$
$929$	3.37633	0.110774	0.0553869	+	0.998465i	$0.482361\pi$
$930$	13.9012	0.455837
$931$	2.50808	0.0821991
$932$	1.40804	0.0461220
$933$	−12.0797	−0.395472
$934$	25.5409	0.835723
$935$	18.9552	0.619900
$936$	2.89322	0.0945677
$937$	−44.8821	−1.46624	−0.733118	−	0.680102i	$-0.761936\pi$
$937$	−44.8821	−1.46624	−0.733118	+	0.680102i	$0.761936\pi$
$938$	−4.24993	−0.138765
$939$	7.02020	0.229096
$940$	1.45774	0.0475462
$941$	−10.8135	−0.352510	−0.176255	−	0.984344i	$-0.556398\pi$
$941$	−10.8135	−0.352510	−0.176255	+	0.984344i	$0.556398\pi$
$942$	−6.69972	−0.218289
$943$	1.65231	0.0538065
$944$	−13.0562	−0.424942
$945$	−7.85659	−0.255575
$946$	2.08241	0.0677050
$947$	27.3363	0.888309	0.444154	−	0.895950i	$-0.353504\pi$
$947$	27.3363	0.888309	0.444154	+	0.895950i	$0.353504\pi$
$948$	−14.3201	−0.465095
$949$	−18.1564	−0.589382
$950$	−5.86480	−0.190279
$951$	20.3119	0.658658
$952$	−19.5780	−0.634526
$953$	−16.9183	−0.548037	−0.274018	−	0.961724i	$-0.588353\pi$
$953$	−16.9183	−0.548037	−0.274018	+	0.961724i	$0.588353\pi$
$954$	0.0665071	0.00215325
$955$	−24.1689	−0.782086
$956$	11.2694	0.364479
$957$	2.13520	0.0690212
$958$	32.4034	1.04691
$959$	−26.3916	−0.852229
$960$	2.75802	0.0890146
$961$	−5.59561	−0.180503
$962$	20.0530	0.646535
$963$	−8.35242	−0.269153
$964$	−8.35792	−0.269191
$965$	56.9472	1.83319
$966$	12.6228	0.406132
$967$	−17.8239	−0.573177	−0.286589	−	0.958054i	$-0.592521\pi$
$967$	−17.8239	−0.573177	−0.286589	+	0.958054i	$0.592521\pi$
$968$	−1.00000	−0.0321412
$969$	−15.4632	−0.496751
$970$	51.5002	1.65357
$971$	35.6202	1.14311	0.571553	−	0.820565i	$-0.306341\pi$
$971$	35.6202	1.14311	0.571553	+	0.820565i	$0.306341\pi$
$972$	1.00000	0.0320750
$973$	11.7448	0.376520
$974$	4.32994	0.138740
$975$	−7.54161	−0.241525
$976$	1.00000	0.0320092
$977$	4.29125	0.137289	0.0686447	−	0.997641i	$-0.478133\pi$
$977$	4.29125	0.137289	0.0686447	+	0.997641i	$0.478133\pi$
$978$	−6.21575	−0.198758
$979$	2.90693	0.0929060
$980$	3.07446	0.0982100
$981$	−7.07446	−0.225870
$982$	−11.8005	−0.376568
$983$	−29.4486	−0.939265	−0.469632	−	0.882862i	$-0.655614\pi$
$983$	−29.4486	−0.939265	−0.469632	+	0.882862i	$0.655614\pi$
$984$	−0.372882	−0.0118870
$985$	−49.3909	−1.57373
$986$	−14.6747	−0.467337
$987$	−1.50564	−0.0479249
$988$	−6.50955	−0.207096
$989$	9.22752	0.293418
$990$	2.75802	0.0876555
$991$	−28.1310	−0.893612	−0.446806	−	0.894631i	$-0.647438\pi$
$991$	−28.1310	−0.893612	−0.446806	+	0.894631i	$0.647438\pi$
$992$	5.04028	0.160029
$993$	−4.45125	−0.141256
$994$	−2.21761	−0.0703383
$995$	14.8918	0.472100
$996$	−3.11904	−0.0988304
$997$	47.7618	1.51263	0.756316	−	0.654207i	$-0.226997\pi$
$997$	47.7618	1.51263	0.756316	+	0.654207i	$0.226997\pi$
$998$	−1.21237	−0.0383767
$999$	6.93105	0.219289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.r.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.r.1.4	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75802 q^{5} -1.00000 q^{6} -2.84864 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.75802 q^{5} -1.00000 q^{6} -2.84864 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.75802 q^{10} -1.00000 q^{11} +1.00000 q^{12} -2.89322 q^{13} +2.84864 q^{14} +2.75802 q^{15} +1.00000 q^{16} -6.87275 q^{17} -1.00000 q^{18} +2.24993 q^{19} +2.75802 q^{20} -2.84864 q^{21} +1.00000 q^{22} +4.43118 q^{23} -1.00000 q^{24} +2.60665 q^{25} +2.89322 q^{26} +1.00000 q^{27} -2.84864 q^{28} -2.13520 q^{29} -2.75802 q^{30} -5.04028 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.87275 q^{34} -7.85659 q^{35} +1.00000 q^{36} +6.93105 q^{37} -2.24993 q^{38} -2.89322 q^{39} -2.75802 q^{40} +0.372882 q^{41} +2.84864 q^{42} +2.08241 q^{43} -1.00000 q^{44} +2.75802 q^{45} -4.43118 q^{46} +0.528546 q^{47} +1.00000 q^{48} +1.11474 q^{49} -2.60665 q^{50} -6.87275 q^{51} -2.89322 q^{52} -0.0665071 q^{53} -1.00000 q^{54} -2.75802 q^{55} +2.84864 q^{56} +2.24993 q^{57} +2.13520 q^{58} -13.0562 q^{59} +2.75802 q^{60} +1.00000 q^{61} +5.04028 q^{62} -2.84864 q^{63} +1.00000 q^{64} -7.97954 q^{65} +1.00000 q^{66} -1.49192 q^{67} -6.87275 q^{68} +4.43118 q^{69} +7.85659 q^{70} -0.778480 q^{71} -1.00000 q^{72} +6.27551 q^{73} -6.93105 q^{74} +2.60665 q^{75} +2.24993 q^{76} +2.84864 q^{77} +2.89322 q^{78} -14.3201 q^{79} +2.75802 q^{80} +1.00000 q^{81} -0.372882 q^{82} -3.11904 q^{83} -2.84864 q^{84} -18.9552 q^{85} -2.08241 q^{86} -2.13520 q^{87} +1.00000 q^{88} -2.90693 q^{89} -2.75802 q^{90} +8.24172 q^{91} +4.43118 q^{92} -5.04028 q^{93} -0.528546 q^{94} +6.20536 q^{95} -1.00000 q^{96} -18.6729 q^{97} -1.11474 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 4 q^{12} - 3 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 3 q^{17} - 4 q^{18} - 4 q^{19} + q^{20} - 4 q^{21} + 4 q^{22} + 10 q^{23} - 4 q^{24} - 7 q^{25} + 3 q^{26} + 4 q^{27} - 4 q^{28} - 10 q^{29} - q^{30} - 9 q^{31} - 4 q^{32} - 4 q^{33} + 3 q^{34} - q^{35} + 4 q^{36} - 6 q^{37} + 4 q^{38} - 3 q^{39} - q^{40} + 3 q^{41} + 4 q^{42} - 18 q^{43} - 4 q^{44} + q^{45} - 10 q^{46} + 21 q^{47} + 4 q^{48} - 10 q^{49} + 7 q^{50} - 3 q^{51} - 3 q^{52} - 20 q^{53} - 4 q^{54} - q^{55} + 4 q^{56} - 4 q^{57} + 10 q^{58} + 5 q^{59} + q^{60} + 4 q^{61} + 9 q^{62} - 4 q^{63} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 3 q^{67} - 3 q^{68} + 10 q^{69} + q^{70} - 9 q^{71} - 4 q^{72} + 6 q^{74} - 7 q^{75} - 4 q^{76} + 4 q^{77} + 3 q^{78} - 31 q^{79} + q^{80} + 4 q^{81} - 3 q^{82} - 8 q^{83} - 4 q^{84} - 25 q^{85} + 18 q^{86} - 10 q^{87} + 4 q^{88} + 5 q^{89} - q^{90} - 9 q^{91} + 10 q^{92} - 9 q^{93} - 21 q^{94} + 13 q^{95} - 4 q^{96} - 25 q^{97} + 10 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 4 * q^12 - 3 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 3 * q^17 - 4 * q^18 - 4 * q^19 + q^20 - 4 * q^21 + 4 * q^22 + 10 * q^23 - 4 * q^24 - 7 * q^25 + 3 * q^26 + 4 * q^27 - 4 * q^28 - 10 * q^29 - q^30 - 9 * q^31 - 4 * q^32 - 4 * q^33 + 3 * q^34 - q^35 + 4 * q^36 - 6 * q^37 + 4 * q^38 - 3 * q^39 - q^40 + 3 * q^41 + 4 * q^42 - 18 * q^43 - 4 * q^44 + q^45 - 10 * q^46 + 21 * q^47 + 4 * q^48 - 10 * q^49 + 7 * q^50 - 3 * q^51 - 3 * q^52 - 20 * q^53 - 4 * q^54 - q^55 + 4 * q^56 - 4 * q^57 + 10 * q^58 + 5 * q^59 + q^60 + 4 * q^61 + 9 * q^62 - 4 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 3 * q^67 - 3 * q^68 + 10 * q^69 + q^70 - 9 * q^71 - 4 * q^72 + 6 * q^74 - 7 * q^75 - 4 * q^76 + 4 * q^77 + 3 * q^78 - 31 * q^79 + q^80 + 4 * q^81 - 3 * q^82 - 8 * q^83 - 4 * q^84 - 25 * q^85 + 18 * q^86 - 10 * q^87 + 4 * q^88 + 5 * q^89 - q^90 - 9 * q^91 + 10 * q^92 - 9 * q^93 - 21 * q^94 + 13 * q^95 - 4 * q^96 - 25 * q^97 + 10 * q^98 - 4 * q^99

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