LMFDB - Embedded newform 6026.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.34651 q^{3} +1.00000 q^{4} -0.801214 q^{5} +2.34651 q^{6} +2.16934 q^{7} -1.00000 q^{8} +2.50610 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.34651 q^{3} +1.00000 q^{4} -0.801214 q^{5} +2.34651 q^{6} +2.16934 q^{7} -1.00000 q^{8} +2.50610 q^{9} +0.801214 q^{10} +4.95686 q^{11} -2.34651 q^{12} -1.05384 q^{13} -2.16934 q^{14} +1.88006 q^{15} +1.00000 q^{16} -2.72459 q^{17} -2.50610 q^{18} +5.72094 q^{19} -0.801214 q^{20} -5.09038 q^{21} -4.95686 q^{22} +1.00000 q^{23} +2.34651 q^{24} -4.35806 q^{25} +1.05384 q^{26} +1.15893 q^{27} +2.16934 q^{28} -3.63101 q^{29} -1.88006 q^{30} -1.85326 q^{31} -1.00000 q^{32} -11.6313 q^{33} +2.72459 q^{34} -1.73811 q^{35} +2.50610 q^{36} +1.54837 q^{37} -5.72094 q^{38} +2.47285 q^{39} +0.801214 q^{40} -10.7572 q^{41} +5.09038 q^{42} -3.49752 q^{43} +4.95686 q^{44} -2.00793 q^{45} -1.00000 q^{46} +9.13800 q^{47} -2.34651 q^{48} -2.29395 q^{49} +4.35806 q^{50} +6.39327 q^{51} -1.05384 q^{52} +5.24949 q^{53} -1.15893 q^{54} -3.97151 q^{55} -2.16934 q^{56} -13.4242 q^{57} +3.63101 q^{58} -0.391725 q^{59} +1.88006 q^{60} -8.80009 q^{61} +1.85326 q^{62} +5.43660 q^{63} +1.00000 q^{64} +0.844354 q^{65} +11.6313 q^{66} -11.5468 q^{67} -2.72459 q^{68} -2.34651 q^{69} +1.73811 q^{70} -6.56429 q^{71} -2.50610 q^{72} -3.25034 q^{73} -1.54837 q^{74} +10.2262 q^{75} +5.72094 q^{76} +10.7531 q^{77} -2.47285 q^{78} -4.15930 q^{79} -0.801214 q^{80} -10.2378 q^{81} +10.7572 q^{82} -1.60729 q^{83} -5.09038 q^{84} +2.18298 q^{85} +3.49752 q^{86} +8.52020 q^{87} -4.95686 q^{88} -3.89493 q^{89} +2.00793 q^{90} -2.28615 q^{91} +1.00000 q^{92} +4.34870 q^{93} -9.13800 q^{94} -4.58370 q^{95} +2.34651 q^{96} -9.72957 q^{97} +2.29395 q^{98} +12.4224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	−2.34651	−1.35476	−0.677379	−	0.735634i	$-0.736884\pi$
$3$	−2.34651	−1.35476	−0.677379	+	0.735634i	$0.736884\pi$
$4$	1.00000	0.500000
$5$	−0.801214	−0.358314	−0.179157	−	0.983820i	$-0.557337\pi$
$5$	−0.801214	−0.358314	−0.179157	+	0.983820i	$0.557337\pi$
$6$	2.34651	0.957958
$7$	2.16934	0.819935	0.409967	−	0.912100i	$-0.365540\pi$
$7$	2.16934	0.819935	0.409967	+	0.912100i	$0.365540\pi$
$8$	−1.00000	−0.353553
$9$	2.50610	0.835368
$10$	0.801214	0.253366
$11$	4.95686	1.49455	0.747275	−	0.664515i	$-0.231362\pi$
$11$	4.95686	1.49455	0.747275	+	0.664515i	$0.231362\pi$
$12$	−2.34651	−0.677379
$13$	−1.05384	−0.292283	−0.146142	−	0.989264i	$-0.546686\pi$
$13$	−1.05384	−0.292283	−0.146142	+	0.989264i	$0.546686\pi$
$14$	−2.16934	−0.579781
$15$	1.88006	0.485429
$16$	1.00000	0.250000
$17$	−2.72459	−0.660809	−0.330405	−	0.943839i	$-0.607185\pi$
$17$	−2.72459	−0.660809	−0.330405	+	0.943839i	$0.607185\pi$
$18$	−2.50610	−0.590695
$19$	5.72094	1.31247	0.656237	−	0.754555i	$-0.272147\pi$
$19$	5.72094	1.31247	0.656237	+	0.754555i	$0.272147\pi$
$20$	−0.801214	−0.179157
$21$	−5.09038	−1.11081
$22$	−4.95686	−1.05681
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.34651	0.478979
$25$	−4.35806	−0.871611
$26$	1.05384	0.206675
$27$	1.15893	0.223036
$28$	2.16934	0.409967
$29$	−3.63101	−0.674262	−0.337131	−	0.941458i	$-0.609456\pi$
$29$	−3.63101	−0.674262	−0.337131	+	0.941458i	$0.609456\pi$
$30$	−1.88006	−0.343250
$31$	−1.85326	−0.332856	−0.166428	−	0.986054i	$-0.553223\pi$
$31$	−1.85326	−0.332856	−0.166428	+	0.986054i	$0.553223\pi$
$32$	−1.00000	−0.176777
$33$	−11.6313	−2.02475
$34$	2.72459	0.467263
$35$	−1.73811	−0.293794
$36$	2.50610	0.417684
$37$	1.54837	0.254550	0.127275	−	0.991867i	$-0.459377\pi$
$37$	1.54837	0.254550	0.127275	+	0.991867i	$0.459377\pi$
$38$	−5.72094	−0.928060
$39$	2.47285	0.395973
$40$	0.801214	0.126683
$41$	−10.7572	−1.67999	−0.839993	−	0.542597i	$-0.817441\pi$
$41$	−10.7572	−1.67999	−0.839993	+	0.542597i	$0.817441\pi$
$42$	5.09038	0.785463
$43$	−3.49752	−0.533367	−0.266684	−	0.963784i	$-0.585928\pi$
$43$	−3.49752	−0.533367	−0.266684	+	0.963784i	$0.585928\pi$
$44$	4.95686	0.747275
$45$	−2.00793	−0.299324
$46$	−1.00000	−0.147442
$47$	9.13800	1.33291	0.666457	−	0.745543i	$-0.267810\pi$
$47$	9.13800	1.33291	0.666457	+	0.745543i	$0.267810\pi$
$48$	−2.34651	−0.338689
$49$	−2.29395	−0.327707
$50$	4.35806	0.616322
$51$	6.39327	0.895236
$52$	−1.05384	−0.146142
$53$	5.24949	0.721073	0.360536	−	0.932745i	$-0.382594\pi$
$53$	5.24949	0.721073	0.360536	+	0.932745i	$0.382594\pi$
$54$	−1.15893	−0.157710
$55$	−3.97151	−0.535518
$56$	−2.16934	−0.289891
$57$	−13.4242	−1.77808
$58$	3.63101	0.476775
$59$	−0.391725	−0.0509982	−0.0254991	−	0.999675i	$-0.508117\pi$
$59$	−0.391725	−0.0509982	−0.0254991	+	0.999675i	$0.508117\pi$
$60$	1.88006	0.242714
$61$	−8.80009	−1.12674	−0.563368	−	0.826206i	$-0.690495\pi$
$61$	−8.80009	−1.12674	−0.563368	+	0.826206i	$0.690495\pi$
$62$	1.85326	0.235365
$63$	5.43660	0.684947
$64$	1.00000	0.125000
$65$	0.844354	0.104729
$66$	11.6313	1.43172
$67$	−11.5468	−1.41067	−0.705336	−	0.708873i	$-0.749204\pi$
$67$	−11.5468	−1.41067	−0.705336	+	0.708873i	$0.749204\pi$
$68$	−2.72459	−0.330405
$69$	−2.34651	−0.282486
$70$	1.73811	0.207744
$71$	−6.56429	−0.779038	−0.389519	−	0.921018i	$-0.627359\pi$
$71$	−6.56429	−0.779038	−0.389519	+	0.921018i	$0.627359\pi$
$72$	−2.50610	−0.295347
$73$	−3.25034	−0.380423	−0.190212	−	0.981743i	$-0.560917\pi$
$73$	−3.25034	−0.380423	−0.190212	+	0.981743i	$0.560917\pi$
$74$	−1.54837	−0.179994
$75$	10.2262	1.18082
$76$	5.72094	0.656237
$77$	10.7531	1.22543
$78$	−2.47285	−0.279995
$79$	−4.15930	−0.467958	−0.233979	−	0.972242i	$-0.575175\pi$
$79$	−4.15930	−0.467958	−0.233979	+	0.972242i	$0.575175\pi$
$80$	−0.801214	−0.0895785
$81$	−10.2378	−1.13753
$82$	10.7572	1.18793
$83$	−1.60729	−0.176423	−0.0882113	−	0.996102i	$-0.528115\pi$
$83$	−1.60729	−0.176423	−0.0882113	+	0.996102i	$0.528115\pi$
$84$	−5.09038	−0.555406
$85$	2.18298	0.236777
$86$	3.49752	0.377148
$87$	8.52020	0.913461
$88$	−4.95686	−0.528403
$89$	−3.89493	−0.412862	−0.206431	−	0.978461i	$-0.566185\pi$
$89$	−3.89493	−0.412862	−0.206431	+	0.978461i	$0.566185\pi$
$90$	2.00793	0.211654
$91$	−2.28615	−0.239653
$92$	1.00000	0.104257
$93$	4.34870	0.450939
$94$	−9.13800	−0.942513
$95$	−4.58370	−0.470278
$96$	2.34651	0.239490
$97$	−9.72957	−0.987888	−0.493944	−	0.869494i	$-0.664445\pi$
$97$	−9.72957	−0.987888	−0.493944	+	0.869494i	$0.664445\pi$
$98$	2.29395	0.231724
$99$	12.4224	1.24850
$100$	−4.35806	−0.435806
$101$	2.35792	0.234622	0.117311	−	0.993095i	$-0.462573\pi$
$101$	2.35792	0.234622	0.117311	+	0.993095i	$0.462573\pi$
$102$	−6.39327	−0.633028
$103$	18.5109	1.82393	0.911966	−	0.410265i	$-0.134564\pi$
$103$	18.5109	1.82393	0.911966	+	0.410265i	$0.134564\pi$
$104$	1.05384	0.103338
$105$	4.07849	0.398020
$106$	−5.24949	−0.509876
$107$	17.8100	1.72176	0.860878	−	0.508812i	$-0.169915\pi$
$107$	17.8100	1.72176	0.860878	+	0.508812i	$0.169915\pi$
$108$	1.15893	0.111518
$109$	−4.57649	−0.438348	−0.219174	−	0.975686i	$-0.570336\pi$
$109$	−4.57649	−0.438348	−0.219174	+	0.975686i	$0.570336\pi$
$110$	3.97151	0.378669
$111$	−3.63326	−0.344854
$112$	2.16934	0.204984
$113$	17.0840	1.60713	0.803564	−	0.595219i	$-0.202935\pi$
$113$	17.0840	1.60713	0.803564	+	0.595219i	$0.202935\pi$
$114$	13.4242	1.25730
$115$	−0.801214	−0.0747136
$116$	−3.63101	−0.337131
$117$	−2.64104	−0.244164
$118$	0.391725	0.0360612
$119$	−5.91056	−0.541820
$120$	−1.88006	−0.171625
$121$	13.5705	1.23368
$122$	8.80009	0.796722
$123$	25.2418	2.27597
$124$	−1.85326	−0.166428
$125$	7.49781	0.670624
$126$	−5.43660	−0.484331
$127$	−8.06876	−0.715987	−0.357993	−	0.933724i	$-0.616539\pi$
$127$	−8.06876	−0.715987	−0.357993	+	0.933724i	$0.616539\pi$
$128$	−1.00000	−0.0883883
$129$	8.20697	0.722583
$130$	−0.844354	−0.0740547
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−11.6313	−1.01238
$133$	12.4107	1.07614
$134$	11.5468	0.997496
$135$	−0.928551	−0.0799170
$136$	2.72459	0.233631
$137$	15.0822	1.28856	0.644278	−	0.764792i	$-0.277158\pi$
$137$	15.0822	1.28856	0.644278	+	0.764792i	$0.277158\pi$
$138$	2.34651	0.199748
$139$	−4.84350	−0.410820	−0.205410	−	0.978676i	$-0.565853\pi$
$139$	−4.84350	−0.410820	−0.205410	+	0.978676i	$0.565853\pi$
$140$	−1.73811	−0.146897
$141$	−21.4424	−1.80578
$142$	6.56429	0.550863
$143$	−5.22375	−0.436832
$144$	2.50610	0.208842
$145$	2.90922	0.241597
$146$	3.25034	0.269000
$147$	5.38278	0.443964
$148$	1.54837	0.127275
$149$	−20.2287	−1.65720	−0.828598	−	0.559844i	$-0.810861\pi$
$149$	−20.2287	−1.65720	−0.828598	+	0.559844i	$0.810861\pi$
$150$	−10.2262	−0.834967
$151$	−2.26969	−0.184705	−0.0923524	−	0.995726i	$-0.529439\pi$
$151$	−2.26969	−0.184705	−0.0923524	+	0.995726i	$0.529439\pi$
$152$	−5.72094	−0.464030
$153$	−6.82810	−0.552019
$154$	−10.7531	−0.866513
$155$	1.48486	0.119267
$156$	2.47285	0.197986
$157$	−22.4688	−1.79321	−0.896605	−	0.442832i	$-0.853974\pi$
$157$	−22.4688	−1.79321	−0.896605	+	0.442832i	$0.853974\pi$
$158$	4.15930	0.330896
$159$	−12.3180	−0.976879
$160$	0.801214	0.0633416
$161$	2.16934	0.170968
$162$	10.2378	0.804354
$163$	7.86199	0.615799	0.307899	−	0.951419i	$-0.400374\pi$
$163$	7.86199	0.615799	0.307899	+	0.951419i	$0.400374\pi$
$164$	−10.7572	−0.839993
$165$	9.31919	0.725498
$166$	1.60729	0.124750
$167$	13.9226	1.07736	0.538682	−	0.842509i	$-0.318923\pi$
$167$	13.9226	1.07736	0.538682	+	0.842509i	$0.318923\pi$
$168$	5.09038	0.392732
$169$	−11.8894	−0.914570
$170$	−2.18298	−0.167427
$171$	14.3373	1.09640
$172$	−3.49752	−0.266684
$173$	4.50823	0.342755	0.171377	−	0.985205i	$-0.445178\pi$
$173$	4.50823	0.342755	0.171377	+	0.985205i	$0.445178\pi$
$174$	−8.52020	−0.645914
$175$	−9.45412	−0.714664
$176$	4.95686	0.373638
$177$	0.919185	0.0690902
$178$	3.89493	0.291938
$179$	−10.9819	−0.820828	−0.410414	−	0.911899i	$-0.634616\pi$
$179$	−10.9819	−0.820828	−0.410414	+	0.911899i	$0.634616\pi$
$180$	−2.00793	−0.149662
$181$	23.5272	1.74877	0.874383	−	0.485237i	$-0.161267\pi$
$181$	23.5272	1.74877	0.874383	+	0.485237i	$0.161267\pi$
$182$	2.28615	0.169460
$183$	20.6495	1.52645
$184$	−1.00000	−0.0737210
$185$	−1.24058	−0.0912089
$186$	−4.34870	−0.318862
$187$	−13.5054	−0.987613
$188$	9.13800	0.666457
$189$	2.51412	0.182875
$190$	4.58370	0.332537
$191$	15.6529	1.13261	0.566304	−	0.824197i	$-0.308373\pi$
$191$	15.6529	1.13261	0.566304	+	0.824197i	$0.308373\pi$
$192$	−2.34651	−0.169345
$193$	6.04551	0.435165	0.217583	−	0.976042i	$-0.430183\pi$
$193$	6.04551	0.435165	0.217583	+	0.976042i	$0.430183\pi$
$194$	9.72957	0.698542
$195$	−1.98128	−0.141883
$196$	−2.29395	−0.163854
$197$	−25.0561	−1.78517	−0.892587	−	0.450876i	$-0.851112\pi$
$197$	−25.0561	−1.78517	−0.892587	+	0.450876i	$0.851112\pi$
$198$	−12.4224	−0.882823
$199$	−14.5181	−1.02916	−0.514580	−	0.857443i	$-0.672052\pi$
$199$	−14.5181	−1.02916	−0.514580	+	0.857443i	$0.672052\pi$
$200$	4.35806	0.308161
$201$	27.0948	1.91112
$202$	−2.35792	−0.165903
$203$	−7.87691	−0.552850
$204$	6.39327	0.447618
$205$	8.61879	0.601963
$206$	−18.5109	−1.28972
$207$	2.50610	0.174186
$208$	−1.05384	−0.0730708
$209$	28.3579	1.96156
$210$	−4.07849	−0.281442
$211$	−4.54692	−0.313023	−0.156512	−	0.987676i	$-0.550025\pi$
$211$	−4.54692	−0.313023	−0.156512	+	0.987676i	$0.550025\pi$
$212$	5.24949	0.360536
$213$	15.4032	1.05541
$214$	−17.8100	−1.21747
$215$	2.80227	0.191113
$216$	−1.15893	−0.0788552
$217$	−4.02036	−0.272920
$218$	4.57649	0.309959
$219$	7.62695	0.515382
$220$	−3.97151	−0.267759
$221$	2.87128	0.193143
$222$	3.63326	0.243849
$223$	10.3638	0.694010	0.347005	−	0.937863i	$-0.387199\pi$
$223$	10.3638	0.694010	0.347005	+	0.937863i	$0.387199\pi$
$224$	−2.16934	−0.144945
$225$	−10.9217	−0.728116
$226$	−17.0840	−1.13641
$227$	−2.15095	−0.142764	−0.0713819	−	0.997449i	$-0.522741\pi$
$227$	−2.15095	−0.142764	−0.0713819	+	0.997449i	$0.522741\pi$
$228$	−13.4242	−0.889042
$229$	−6.99096	−0.461975	−0.230988	−	0.972957i	$-0.574196\pi$
$229$	−6.99096	−0.461975	−0.230988	+	0.972957i	$0.574196\pi$
$230$	0.801214	0.0528305
$231$	−25.2323	−1.66017
$232$	3.63101	0.238387
$233$	−20.8075	−1.36315	−0.681574	−	0.731750i	$-0.738704\pi$
$233$	−20.8075	−1.36315	−0.681574	+	0.731750i	$0.738704\pi$
$234$	2.64104	0.172650
$235$	−7.32150	−0.477602
$236$	−0.391725	−0.0254991
$237$	9.75983	0.633969
$238$	5.91056	0.383125
$239$	−3.34023	−0.216061	−0.108031	−	0.994148i	$-0.534454\pi$
$239$	−3.34023	−0.216061	−0.108031	+	0.994148i	$0.534454\pi$
$240$	1.88006	0.121357
$241$	−0.760361	−0.0489792	−0.0244896	−	0.999700i	$-0.507796\pi$
$241$	−0.760361	−0.0489792	−0.0244896	+	0.999700i	$0.507796\pi$
$242$	−13.5705	−0.872345
$243$	20.5462	1.31804
$244$	−8.80009	−0.563368
$245$	1.83795	0.117422
$246$	−25.2418	−1.60936
$247$	−6.02897	−0.383614
$248$	1.85326	0.117682
$249$	3.77151	0.239010
$250$	−7.49781	−0.474203
$251$	22.7890	1.43843	0.719213	−	0.694789i	$-0.244502\pi$
$251$	22.7890	1.43843	0.719213	+	0.694789i	$0.244502\pi$
$252$	5.43660	0.342474
$253$	4.95686	0.311635
$254$	8.06876	0.506279
$255$	−5.12238	−0.320776
$256$	1.00000	0.0625000
$257$	26.7538	1.66885	0.834427	−	0.551118i	$-0.185799\pi$
$257$	26.7538	1.66885	0.834427	+	0.551118i	$0.185799\pi$
$258$	−8.20697	−0.510943
$259$	3.35894	0.208715
$260$	0.844354	0.0523646
$261$	−9.09969	−0.563257
$262$	−1.00000	−0.0617802
$263$	−26.0349	−1.60538	−0.802689	−	0.596398i	$-0.796598\pi$
$263$	−26.0349	−1.60538	−0.802689	+	0.596398i	$0.796598\pi$
$264$	11.6313	0.715859
$265$	−4.20597	−0.258371
$266$	−12.4107	−0.760948
$267$	9.13949	0.559328
$268$	−11.5468	−0.705336
$269$	−8.46523	−0.516134	−0.258067	−	0.966127i	$-0.583086\pi$
$269$	−8.46523	−0.516134	−0.258067	+	0.966127i	$0.583086\pi$
$270$	0.928551	0.0565098
$271$	1.12438	0.0683014	0.0341507	−	0.999417i	$-0.489127\pi$
$271$	1.12438	0.0683014	0.0341507	+	0.999417i	$0.489127\pi$
$272$	−2.72459	−0.165202
$273$	5.36446	0.324672
$274$	−15.0822	−0.911146
$275$	−21.6023	−1.30267
$276$	−2.34651	−0.141243
$277$	−6.25501	−0.375827	−0.187914	−	0.982186i	$-0.560172\pi$
$277$	−6.25501	−0.375827	−0.187914	+	0.982186i	$0.560172\pi$
$278$	4.84350	0.290494
$279$	−4.64447	−0.278057
$280$	1.73811	0.103872
$281$	3.86835	0.230766	0.115383	−	0.993321i	$-0.463190\pi$
$281$	3.86835	0.230766	0.115383	+	0.993321i	$0.463190\pi$
$282$	21.4424	1.27688
$283$	16.9857	1.00970	0.504848	−	0.863208i	$-0.331548\pi$
$283$	16.9857	1.00970	0.504848	+	0.863208i	$0.331548\pi$
$284$	−6.56429	−0.389519
$285$	10.7557	0.637113
$286$	5.22375	0.308887
$287$	−23.3360	−1.37748
$288$	−2.50610	−0.147674
$289$	−9.57663	−0.563331
$290$	−2.90922	−0.170835
$291$	22.8305	1.33835
$292$	−3.25034	−0.190212
$293$	12.4103	0.725019	0.362509	−	0.931980i	$-0.381920\pi$
$293$	12.4103	0.725019	0.362509	+	0.931980i	$0.381920\pi$
$294$	−5.38278	−0.313930
$295$	0.313855	0.0182734
$296$	−1.54837	−0.0899971
$297$	5.74466	0.333339
$298$	20.2287	1.17181
$299$	−1.05384	−0.0609453
$300$	10.2262	0.590411
$301$	−7.58733	−0.437326
$302$	2.26969	0.130606
$303$	−5.53289	−0.317856
$304$	5.72094	0.328119
$305$	7.05076	0.403725
$306$	6.82810	0.390336
$307$	9.16510	0.523080	0.261540	−	0.965193i	$-0.415770\pi$
$307$	9.16510	0.523080	0.261540	+	0.965193i	$0.415770\pi$
$308$	10.7531	0.612717
$309$	−43.4360	−2.47099
$310$	−1.48486	−0.0843344
$311$	−34.9754	−1.98328	−0.991638	−	0.129052i	$-0.958806\pi$
$311$	−34.9754	−1.98328	−0.991638	+	0.129052i	$0.958806\pi$
$312$	−2.47285	−0.139998
$313$	28.3096	1.60015	0.800076	−	0.599898i	$-0.204792\pi$
$313$	28.3096	1.60015	0.800076	+	0.599898i	$0.204792\pi$
$314$	22.4688	1.26799
$315$	−4.35588	−0.245426
$316$	−4.15930	−0.233979
$317$	21.2570	1.19391	0.596956	−	0.802274i	$-0.296377\pi$
$317$	21.2570	1.19391	0.596956	+	0.802274i	$0.296377\pi$
$318$	12.3180	0.690758
$319$	−17.9984	−1.00772
$320$	−0.801214	−0.0447893
$321$	−41.7913	−2.33256
$322$	−2.16934	−0.120893
$323$	−15.5872	−0.867295
$324$	−10.2378	−0.568764
$325$	4.59270	0.254757
$326$	−7.86199	−0.435435
$327$	10.7388	0.593856
$328$	10.7572	0.593965
$329$	19.8235	1.09290
$330$	−9.31919	−0.513004
$331$	−13.9101	−0.764567	−0.382283	−	0.924045i	$-0.624862\pi$
$331$	−13.9101	−0.764567	−0.382283	+	0.924045i	$0.624862\pi$
$332$	−1.60729	−0.0882113
$333$	3.88037	0.212643
$334$	−13.9226	−0.761811
$335$	9.25150	0.505463
$336$	−5.09038	−0.277703
$337$	−32.6134	−1.77657	−0.888284	−	0.459295i	$-0.848102\pi$
$337$	−32.6134	−1.77657	−0.888284	+	0.459295i	$0.848102\pi$
$338$	11.8894	0.646699
$339$	−40.0878	−2.17727
$340$	2.18298	0.118389
$341$	−9.18637	−0.497470
$342$	−14.3373	−0.775272
$343$	−20.1618	−1.08863
$344$	3.49752	0.188574
$345$	1.88006	0.101219
$346$	−4.50823	−0.242364
$347$	13.6324	0.731827	0.365914	−	0.930649i	$-0.380757\pi$
$347$	13.6324	0.731827	0.365914	+	0.930649i	$0.380757\pi$
$348$	8.52020	0.456730
$349$	−31.6422	−1.69377	−0.846883	−	0.531779i	$-0.821524\pi$
$349$	−31.6422	−1.69377	−0.846883	+	0.531779i	$0.821524\pi$
$350$	9.45412	0.505344
$351$	−1.22133	−0.0651897
$352$	−4.95686	−0.264202
$353$	2.99798	0.159566	0.0797832	−	0.996812i	$-0.474577\pi$
$353$	2.99798	0.159566	0.0797832	+	0.996812i	$0.474577\pi$
$354$	−0.919185	−0.0488541
$355$	5.25941	0.279140
$356$	−3.89493	−0.206431
$357$	13.8692	0.734035
$358$	10.9819	0.580413
$359$	−9.88532	−0.521727	−0.260864	−	0.965376i	$-0.584007\pi$
$359$	−9.88532	−0.521727	−0.260864	+	0.965376i	$0.584007\pi$
$360$	2.00793	0.105827
$361$	13.7292	0.722589
$362$	−23.5272	−1.23656
$363$	−31.8433	−1.67134
$364$	−2.28615	−0.119827
$365$	2.60422	0.136311
$366$	−20.6495	−1.07937
$367$	7.10593	0.370927	0.185463	−	0.982651i	$-0.440621\pi$
$367$	7.10593	0.370927	0.185463	+	0.982651i	$0.440621\pi$
$368$	1.00000	0.0521286
$369$	−26.9586	−1.40341
$370$	1.24058	0.0644944
$371$	11.3879	0.591233
$372$	4.34870	0.225469
$373$	−2.94518	−0.152496	−0.0762479	−	0.997089i	$-0.524294\pi$
$373$	−2.94518	−0.152496	−0.0762479	+	0.997089i	$0.524294\pi$
$374$	13.5054	0.698348
$375$	−17.5937	−0.908534
$376$	−9.13800	−0.471256
$377$	3.82651	0.197075
$378$	−2.51412	−0.129312
$379$	−27.5028	−1.41272	−0.706362	−	0.707851i	$-0.749665\pi$
$379$	−27.5028	−1.41272	−0.706362	+	0.707851i	$0.749665\pi$
$380$	−4.58370	−0.235139
$381$	18.9334	0.969988
$382$	−15.6529	−0.800874
$383$	−29.9652	−1.53115	−0.765575	−	0.643347i	$-0.777545\pi$
$383$	−29.9652	−1.53115	−0.765575	+	0.643347i	$0.777545\pi$
$384$	2.34651	0.119745
$385$	−8.61557	−0.439090
$386$	−6.04551	−0.307708
$387$	−8.76516	−0.445558
$388$	−9.72957	−0.493944
$389$	−19.3084	−0.978975	−0.489487	−	0.872010i	$-0.662816\pi$
$389$	−19.3084	−0.978975	−0.489487	+	0.872010i	$0.662816\pi$
$390$	1.98128	0.100326
$391$	−2.72459	−0.137788
$392$	2.29395	0.115862
$393$	−2.34651	−0.118366
$394$	25.0561	1.26231
$395$	3.33249	0.167676
$396$	12.4224	0.624250
$397$	14.7981	0.742697	0.371349	−	0.928493i	$-0.378895\pi$
$397$	14.7981	0.742697	0.371349	+	0.928493i	$0.378895\pi$
$398$	14.5181	0.727726
$399$	−29.1218	−1.45791
$400$	−4.35806	−0.217903
$401$	−19.7159	−0.984567	−0.492283	−	0.870435i	$-0.663838\pi$
$401$	−19.7159	−0.984567	−0.492283	+	0.870435i	$0.663838\pi$
$402$	−27.0948	−1.35136
$403$	1.95305	0.0972882
$404$	2.35792	0.117311
$405$	8.20264	0.407592
$406$	7.87691	0.390924
$407$	7.67505	0.380438
$408$	−6.39327	−0.316514
$409$	7.73328	0.382386	0.191193	−	0.981552i	$-0.438764\pi$
$409$	7.73328	0.382386	0.191193	+	0.981552i	$0.438764\pi$
$410$	−8.61879	−0.425652
$411$	−35.3904	−1.74568
$412$	18.5109	0.911966
$413$	−0.849785	−0.0418152
$414$	−2.50610	−0.123168
$415$	1.28778	0.0632147
$416$	1.05384	0.0516689
$417$	11.3653	0.556562
$418$	−28.3579	−1.38703
$419$	0.0658483	0.00321690	0.00160845	−	0.999999i	$-0.499488\pi$
$419$	0.0658483	0.00321690	0.00160845	+	0.999999i	$0.499488\pi$
$420$	4.07849	0.199010
$421$	29.7977	1.45225	0.726125	−	0.687563i	$-0.241319\pi$
$421$	29.7977	1.45225	0.726125	+	0.687563i	$0.241319\pi$
$422$	4.54692	0.221341
$423$	22.9008	1.11347
$424$	−5.24949	−0.254938
$425$	11.8739	0.575969
$426$	−15.4032	−0.746286
$427$	−19.0904	−0.923850
$428$	17.8100	0.860878
$429$	12.2576	0.591802
$430$	−2.80227	−0.135137
$431$	−35.7277	−1.72094	−0.860472	−	0.509498i	$-0.829831\pi$
$431$	−35.7277	−1.72094	−0.860472	+	0.509498i	$0.829831\pi$
$432$	1.15893	0.0557590
$433$	−3.20078	−0.153819	−0.0769097	−	0.997038i	$-0.524505\pi$
$433$	−3.20078	−0.153819	−0.0769097	+	0.997038i	$0.524505\pi$
$434$	4.02036	0.192984
$435$	−6.82651	−0.327306
$436$	−4.57649	−0.219174
$437$	5.72094	0.273670
$438$	−7.62695	−0.364430
$439$	1.11275	0.0531086	0.0265543	−	0.999647i	$-0.491547\pi$
$439$	1.11275	0.0531086	0.0265543	+	0.999647i	$0.491547\pi$
$440$	3.97151	0.189334
$441$	−5.74888	−0.273756
$442$	−2.87128	−0.136573
$443$	−36.2757	−1.72351	−0.861755	−	0.507325i	$-0.830634\pi$
$443$	−36.2757	−1.72351	−0.861755	+	0.507325i	$0.830634\pi$
$444$	−3.63326	−0.172427
$445$	3.12068	0.147934
$446$	−10.3638	−0.490739
$447$	47.4667	2.24510
$448$	2.16934	0.102492
$449$	−22.3452	−1.05454	−0.527268	−	0.849699i	$-0.676784\pi$
$449$	−22.3452	−1.05454	−0.527268	+	0.849699i	$0.676784\pi$
$450$	10.9217	0.514856
$451$	−53.3218	−2.51082
$452$	17.0840	0.803564
$453$	5.32585	0.250230
$454$	2.15095	0.100949
$455$	1.83169	0.0858711
$456$	13.4242	0.628648
$457$	−33.7980	−1.58100	−0.790502	−	0.612460i	$-0.790180\pi$
$457$	−33.7980	−1.58100	−0.790502	+	0.612460i	$0.790180\pi$
$458$	6.99096	0.326666
$459$	−3.15760	−0.147384
$460$	−0.801214	−0.0373568
$461$	−32.0441	−1.49244	−0.746221	−	0.665698i	$-0.768134\pi$
$461$	−32.0441	−1.49244	−0.746221	+	0.665698i	$0.768134\pi$
$462$	25.2323	1.17391
$463$	38.1770	1.77424	0.887118	−	0.461543i	$-0.152704\pi$
$463$	38.1770	1.77424	0.887118	+	0.461543i	$0.152704\pi$
$464$	−3.63101	−0.168565
$465$	−3.48424	−0.161578
$466$	20.8075	0.963891
$467$	−28.3122	−1.31013	−0.655067	−	0.755571i	$-0.727360\pi$
$467$	−28.3122	−1.31013	−0.655067	+	0.755571i	$0.727360\pi$
$468$	−2.64104	−0.122082
$469$	−25.0491	−1.15666
$470$	7.32150	0.337715
$471$	52.7234	2.42936
$472$	0.391725	0.0180306
$473$	−17.3367	−0.797144
$474$	−9.75983	−0.448284
$475$	−24.9322	−1.14397
$476$	−5.91056	−0.270910
$477$	13.1558	0.602362
$478$	3.34023	0.152778
$479$	13.2565	0.605704	0.302852	−	0.953038i	$-0.402061\pi$
$479$	13.2565	0.605704	0.302852	+	0.953038i	$0.402061\pi$
$480$	−1.88006	−0.0858125
$481$	−1.63174	−0.0744008
$482$	0.760361	0.0346335
$483$	−5.09038	−0.231620
$484$	13.5705	0.616841
$485$	7.79547	0.353974
$486$	−20.5462	−0.931994
$487$	3.81113	0.172699	0.0863493	−	0.996265i	$-0.472480\pi$
$487$	3.81113	0.172699	0.0863493	+	0.996265i	$0.472480\pi$
$488$	8.80009	0.398361
$489$	−18.4482	−0.834258
$490$	−1.83795	−0.0830299
$491$	30.2940	1.36715	0.683575	−	0.729880i	$-0.260424\pi$
$491$	30.2940	1.36715	0.683575	+	0.729880i	$0.260424\pi$
$492$	25.2418	1.13799
$493$	9.89300	0.445558
$494$	6.02897	0.271256
$495$	−9.95302	−0.447355
$496$	−1.85326	−0.0832140
$497$	−14.2402	−0.638760
$498$	−3.77151	−0.169005
$499$	9.88708	0.442606	0.221303	−	0.975205i	$-0.428969\pi$
$499$	9.88708	0.442606	0.221303	+	0.975205i	$0.428969\pi$
$500$	7.49781	0.335312
$501$	−32.6695	−1.45957
$502$	−22.7890	−1.01712
$503$	−8.28046	−0.369208	−0.184604	−	0.982813i	$-0.559100\pi$
$503$	−8.28046	−0.369208	−0.184604	+	0.982813i	$0.559100\pi$
$504$	−5.43660	−0.242165
$505$	−1.88920	−0.0840684
$506$	−4.95686	−0.220359
$507$	27.8986	1.23902
$508$	−8.06876	−0.357993
$509$	−13.9904	−0.620114	−0.310057	−	0.950718i	$-0.600348\pi$
$509$	−13.9904	−0.620114	−0.310057	+	0.950718i	$0.600348\pi$
$510$	5.12238	0.226823
$511$	−7.05110	−0.311922
$512$	−1.00000	−0.0441942
$513$	6.63017	0.292729
$514$	−26.7538	−1.18006
$515$	−14.8312	−0.653541
$516$	8.20697	0.361292
$517$	45.2958	1.99211
$518$	−3.35894	−0.147583
$519$	−10.5786	−0.464349
$520$	−0.844354	−0.0370274
$521$	40.6942	1.78285	0.891424	−	0.453171i	$-0.149707\pi$
$521$	40.6942	1.78285	0.891424	+	0.453171i	$0.149707\pi$
$522$	9.09969	0.398283
$523$	−27.2572	−1.19187	−0.595937	−	0.803032i	$-0.703219\pi$
$523$	−27.2572	−1.19187	−0.595937	+	0.803032i	$0.703219\pi$
$524$	1.00000	0.0436852
$525$	22.1842	0.968197
$526$	26.0349	1.13517
$527$	5.04937	0.219954
$528$	−11.6313	−0.506188
$529$	1.00000	0.0434783
$530$	4.20597	0.182696
$531$	−0.981703	−0.0426023
$532$	12.4107	0.538072
$533$	11.3364	0.491032
$534$	−9.13949	−0.395505
$535$	−14.2696	−0.616929
$536$	11.5468	0.498748
$537$	25.7692	1.11202
$538$	8.46523	0.364962
$539$	−11.3708	−0.489775
$540$	−0.928551	−0.0399585
$541$	−42.8788	−1.84350	−0.921751	−	0.387782i	$-0.873241\pi$
$541$	−42.8788	−1.84350	−0.921751	+	0.387782i	$0.873241\pi$
$542$	−1.12438	−0.0482963
$543$	−55.2069	−2.36915
$544$	2.72459	0.116816
$545$	3.66675	0.157066
$546$	−5.36446	−0.229578
$547$	−37.9295	−1.62175	−0.810875	−	0.585219i	$-0.801008\pi$
$547$	−37.9295	−1.62175	−0.810875	+	0.585219i	$0.801008\pi$
$548$	15.0822	0.644278
$549$	−22.0539	−0.941239
$550$	21.6023	0.921125
$551$	−20.7728	−0.884951
$552$	2.34651	0.0998741
$553$	−9.02295	−0.383695
$554$	6.25501	0.265750
$555$	2.91102	0.123566
$556$	−4.84350	−0.205410
$557$	18.1271	0.768070	0.384035	−	0.923319i	$-0.374534\pi$
$557$	18.1271	0.768070	0.384035	+	0.923319i	$0.374534\pi$
$558$	4.64447	0.196616
$559$	3.68584	0.155894
$560$	−1.73811	−0.0734485
$561$	31.6905	1.33798
$562$	−3.86835	−0.163176
$563$	−1.00248	−0.0422495	−0.0211247	−	0.999777i	$-0.506725\pi$
$563$	−1.00248	−0.0422495	−0.0211247	+	0.999777i	$0.506725\pi$
$564$	−21.4424	−0.902888
$565$	−13.6880	−0.575856
$566$	−16.9857	−0.713963
$567$	−22.2092	−0.932699
$568$	6.56429	0.275432
$569$	40.4471	1.69563	0.847815	−	0.530292i	$-0.177918\pi$
$569$	40.4471	1.69563	0.847815	+	0.530292i	$0.177918\pi$
$570$	−10.7557	−0.450507
$571$	10.8177	0.452708	0.226354	−	0.974045i	$-0.427319\pi$
$571$	10.8177	0.452708	0.226354	+	0.974045i	$0.427319\pi$
$572$	−5.22375	−0.218416
$573$	−36.7298	−1.53441
$574$	23.3360	0.974025
$575$	−4.35806	−0.181743
$576$	2.50610	0.104421
$577$	−1.81018	−0.0753589	−0.0376794	−	0.999290i	$-0.511997\pi$
$577$	−1.81018	−0.0753589	−0.0376794	+	0.999290i	$0.511997\pi$
$578$	9.57663	0.398335
$579$	−14.1858	−0.589544
$580$	2.90922	0.120799
$581$	−3.48676	−0.144655
$582$	−22.8305	−0.946355
$583$	26.0210	1.07768
$584$	3.25034	0.134500
$585$	2.11604	0.0874874
$586$	−12.4103	−0.512666
$587$	9.46704	0.390746	0.195373	−	0.980729i	$-0.437408\pi$
$587$	9.46704	0.390746	0.195373	+	0.980729i	$0.437408\pi$
$588$	5.38278	0.221982
$589$	−10.6024	−0.436865
$590$	−0.313855	−0.0129212
$591$	58.7944	2.41848
$592$	1.54837	0.0636376
$593$	17.2800	0.709604	0.354802	−	0.934941i	$-0.384548\pi$
$593$	17.2800	0.709604	0.354802	+	0.934941i	$0.384548\pi$
$594$	−5.74466	−0.235706
$595$	4.73563	0.194142
$596$	−20.2287	−0.828598
$597$	34.0668	1.39426
$598$	1.05384	0.0430948
$599$	45.2397	1.84844	0.924221	−	0.381858i	$-0.124716\pi$
$599$	45.2397	1.84844	0.924221	+	0.381858i	$0.124716\pi$
$600$	−10.2262	−0.417484
$601$	−27.4082	−1.11800	−0.559002	−	0.829167i	$-0.688815\pi$
$601$	−27.4082	−1.11800	−0.559002	+	0.829167i	$0.688815\pi$
$602$	7.58733	0.309236
$603$	−28.9376	−1.17843
$604$	−2.26969	−0.0923524
$605$	−10.8729	−0.442045
$606$	5.53289	0.224758
$607$	−23.8072	−0.966304	−0.483152	−	0.875537i	$-0.660508\pi$
$607$	−23.8072	−0.966304	−0.483152	+	0.875537i	$0.660508\pi$
$608$	−5.72094	−0.232015
$609$	18.4832	0.748978
$610$	−7.05076	−0.285477
$611$	−9.63001	−0.389589
$612$	−6.82810	−0.276010
$613$	−34.8656	−1.40821	−0.704104	−	0.710097i	$-0.748651\pi$
$613$	−34.8656	−1.40821	−0.704104	+	0.710097i	$0.748651\pi$
$614$	−9.16510	−0.369873
$615$	−20.2241	−0.815514
$616$	−10.7531	−0.433256
$617$	−18.4346	−0.742150	−0.371075	−	0.928603i	$-0.621011\pi$
$617$	−18.4346	−0.742150	−0.371075	+	0.928603i	$0.621011\pi$
$618$	43.4360	1.74725
$619$	10.1319	0.407235	0.203617	−	0.979051i	$-0.434730\pi$
$619$	10.1319	0.407235	0.203617	+	0.979051i	$0.434730\pi$
$620$	1.48486	0.0596334
$621$	1.15893	0.0465062
$622$	34.9754	1.40239
$623$	−8.44944	−0.338520
$624$	2.47285	0.0989932
$625$	15.7829	0.631317
$626$	−28.3096	−1.13148
$627$	−66.5422	−2.65744
$628$	−22.4688	−0.896605
$629$	−4.21866	−0.168209
$630$	4.35588	0.173543
$631$	−26.1719	−1.04189	−0.520944	−	0.853591i	$-0.674420\pi$
$631$	−26.1719	−1.04189	−0.520944	+	0.853591i	$0.674420\pi$
$632$	4.15930	0.165448
$633$	10.6694	0.424070
$634$	−21.2570	−0.844223
$635$	6.46481	0.256548
$636$	−12.3180	−0.488440
$637$	2.41746	0.0957833
$638$	17.9984	0.712564
$639$	−16.4508	−0.650784
$640$	0.801214	0.0316708
$641$	17.9495	0.708964	0.354482	−	0.935063i	$-0.384657\pi$
$641$	17.9495	0.708964	0.354482	+	0.935063i	$0.384657\pi$
$642$	41.7913	1.64937
$643$	−46.2363	−1.82338	−0.911692	−	0.410875i	$-0.865223\pi$
$643$	−46.2363	−1.82338	−0.911692	+	0.410875i	$0.865223\pi$
$644$	2.16934	0.0854841
$645$	−6.57554	−0.258912
$646$	15.5872	0.613270
$647$	23.2982	0.915947	0.457973	−	0.888966i	$-0.348575\pi$
$647$	23.2982	0.915947	0.457973	+	0.888966i	$0.348575\pi$
$648$	10.2378	0.402177
$649$	−1.94173	−0.0762194
$650$	−4.59270	−0.180141
$651$	9.43382	0.369740
$652$	7.86199	0.307899
$653$	−1.63158	−0.0638485	−0.0319242	−	0.999490i	$-0.510164\pi$
$653$	−1.63158	−0.0638485	−0.0319242	+	0.999490i	$0.510164\pi$
$654$	−10.7388	−0.419919
$655$	−0.801214	−0.0313060
$656$	−10.7572	−0.419997
$657$	−8.14569	−0.317794
$658$	−19.8235	−0.772799
$659$	−11.8686	−0.462334	−0.231167	−	0.972914i	$-0.574254\pi$
$659$	−11.8686	−0.462334	−0.231167	+	0.972914i	$0.574254\pi$
$660$	9.31919	0.362749
$661$	26.1156	1.01578	0.507890	−	0.861422i	$-0.330426\pi$
$661$	26.1156	1.01578	0.507890	+	0.861422i	$0.330426\pi$
$662$	13.9101	0.540630
$663$	−6.73749	−0.261663
$664$	1.60729	0.0623748
$665$	−9.94362	−0.385597
$666$	−3.88037	−0.150361
$667$	−3.63101	−0.140593
$668$	13.9226	0.538682
$669$	−24.3187	−0.940216
$670$	−9.25150	−0.357417
$671$	−43.6208	−1.68396
$672$	5.09038	0.196366
$673$	26.5063	1.02174	0.510872	−	0.859657i	$-0.329323\pi$
$673$	26.5063	1.02174	0.510872	+	0.859657i	$0.329323\pi$
$674$	32.6134	1.25622
$675$	−5.05068	−0.194401
$676$	−11.8894	−0.457285
$677$	−22.5908	−0.868236	−0.434118	−	0.900856i	$-0.642940\pi$
$677$	−22.5908	−0.868236	−0.434118	+	0.900856i	$0.642940\pi$
$678$	40.0878	1.53956
$679$	−21.1068	−0.810003
$680$	−2.18298	−0.0837134
$681$	5.04723	0.193410
$682$	9.18637	0.351764
$683$	−46.4146	−1.77600	−0.888002	−	0.459839i	$-0.847907\pi$
$683$	−46.4146	−1.77600	−0.888002	+	0.459839i	$0.847907\pi$
$684$	14.3373	0.548200
$685$	−12.0840	−0.461707
$686$	20.1618	0.769780
$687$	16.4043	0.625865
$688$	−3.49752	−0.133342
$689$	−5.53214	−0.210758
$690$	−1.88006	−0.0715725
$691$	−13.3213	−0.506766	−0.253383	−	0.967366i	$-0.581543\pi$
$691$	−13.3213	−0.506766	−0.253383	+	0.967366i	$0.581543\pi$
$692$	4.50823	0.171377
$693$	26.9485	1.02369
$694$	−13.6324	−0.517480
$695$	3.88068	0.147203
$696$	−8.52020	−0.322957
$697$	29.3088	1.11015
$698$	31.6422	1.19767
$699$	48.8251	1.84673
$700$	−9.45412	−0.357332
$701$	−2.54850	−0.0962557	−0.0481279	−	0.998841i	$-0.515325\pi$
$701$	−2.54850	−0.0962557	−0.0481279	+	0.998841i	$0.515325\pi$
$702$	1.22133	0.0460961
$703$	8.85813	0.334091
$704$	4.95686	0.186819
$705$	17.1800	0.647035
$706$	−2.99798	−0.112830
$707$	5.11514	0.192375
$708$	0.919185	0.0345451
$709$	7.95334	0.298694	0.149347	−	0.988785i	$-0.452283\pi$
$709$	7.95334	0.298694	0.149347	+	0.988785i	$0.452283\pi$
$710$	−5.25941	−0.197382
$711$	−10.4236	−0.390917
$712$	3.89493	0.145969
$713$	−1.85326	−0.0694052
$714$	−13.8692	−0.519041
$715$	4.18535	0.156523
$716$	−10.9819	−0.410414
$717$	7.83787	0.292711
$718$	9.88532	0.368917
$719$	23.0187	0.858453	0.429226	−	0.903197i	$-0.358786\pi$
$719$	23.0187	0.858453	0.429226	+	0.903197i	$0.358786\pi$
$720$	−2.00793	−0.0748310
$721$	40.1565	1.49551
$722$	−13.7292	−0.510948
$723$	1.78419	0.0663549
$724$	23.5272	0.874383
$725$	15.8241	0.587694
$726$	31.8433	1.18182
$727$	11.8822	0.440687	0.220344	−	0.975422i	$-0.429282\pi$
$727$	11.8822	0.440687	0.220344	+	0.975422i	$0.429282\pi$
$728$	2.28615	0.0847302
$729$	−17.4986	−0.648095
$730$	−2.60422	−0.0963865
$731$	9.52930	0.352454
$732$	20.6495	0.763227
$733$	−39.1487	−1.44599	−0.722996	−	0.690852i	$-0.757235\pi$
$733$	−39.1487	−1.44599	−0.722996	+	0.690852i	$0.757235\pi$
$734$	−7.10593	−0.262285
$735$	−4.31276	−0.159078
$736$	−1.00000	−0.0368605
$737$	−57.2361	−2.10832
$738$	26.9586	0.992359
$739$	42.4684	1.56223	0.781113	−	0.624389i	$-0.214652\pi$
$739$	42.4684	1.56223	0.781113	+	0.624389i	$0.214652\pi$
$740$	−1.24058	−0.0456045
$741$	14.1470	0.519704
$742$	−11.3879	−0.418065
$743$	12.9776	0.476103	0.238051	−	0.971253i	$-0.423491\pi$
$743$	12.9776	0.476103	0.238051	+	0.971253i	$0.423491\pi$
$744$	−4.34870	−0.159431
$745$	16.2075	0.593796
$746$	2.94518	0.107831
$747$	−4.02803	−0.147378
$748$	−13.5054	−0.493806
$749$	38.6360	1.41173
$750$	17.5937	0.642430
$751$	−36.1688	−1.31982	−0.659909	−	0.751345i	$-0.729405\pi$
$751$	−36.1688	−1.31982	−0.659909	+	0.751345i	$0.729405\pi$
$752$	9.13800	0.333229
$753$	−53.4745	−1.94872
$754$	−3.82651	−0.139353
$755$	1.81851	0.0661823
$756$	2.51412	0.0914375
$757$	2.30039	0.0836090	0.0418045	−	0.999126i	$-0.486689\pi$
$757$	2.30039	0.0836090	0.0418045	+	0.999126i	$0.486689\pi$
$758$	27.5028	0.998947
$759$	−11.6313	−0.422190
$760$	4.58370	0.166268
$761$	−7.05622	−0.255788	−0.127894	−	0.991788i	$-0.540822\pi$
$761$	−7.05622	−0.255788	−0.127894	+	0.991788i	$0.540822\pi$
$762$	−18.9334	−0.685885
$763$	−9.92798	−0.359417
$764$	15.6529	0.566304
$765$	5.47077	0.197796
$766$	29.9652	1.08269
$767$	0.412816	0.0149059
$768$	−2.34651	−0.0846724
$769$	−53.9520	−1.94556	−0.972780	−	0.231731i	$-0.925561\pi$
$769$	−53.9520	−1.94556	−0.972780	+	0.231731i	$0.925561\pi$
$770$	8.61557	0.310484
$771$	−62.7780	−2.26089
$772$	6.04551	0.217583
$773$	−37.7566	−1.35801	−0.679005	−	0.734134i	$-0.737588\pi$
$773$	−37.7566	−1.35801	−0.679005	+	0.734134i	$0.737588\pi$
$774$	8.76516	0.315057
$775$	8.07662	0.290121
$776$	9.72957	0.349271
$777$	−7.88179	−0.282758
$778$	19.3084	0.692240
$779$	−61.5411	−2.20494
$780$	−1.98128	−0.0709413
$781$	−32.5383	−1.16431
$782$	2.72459	0.0974310
$783$	−4.20808	−0.150385
$784$	−2.29395	−0.0819268
$785$	18.0024	0.642532
$786$	2.34651	0.0836972
$787$	−44.1385	−1.57337	−0.786683	−	0.617357i	$-0.788203\pi$
$787$	−44.1385	−1.57337	−0.786683	+	0.617357i	$0.788203\pi$
$788$	−25.0561	−0.892587
$789$	61.0910	2.17490
$790$	−3.33249	−0.118565
$791$	37.0611	1.31774
$792$	−12.4224	−0.441411
$793$	9.27390	0.329326
$794$	−14.7981	−0.525166
$795$	9.86934	0.350029
$796$	−14.5181	−0.514580
$797$	−19.8010	−0.701386	−0.350693	−	0.936490i	$-0.614054\pi$
$797$	−19.8010	−0.701386	−0.350693	+	0.936490i	$0.614054\pi$
$798$	29.1218	1.03090
$799$	−24.8973	−0.880802
$800$	4.35806	0.154081
$801$	−9.76111	−0.344892
$802$	19.7159	0.696194
$803$	−16.1115	−0.568562
$804$	27.0948	0.955559
$805$	−1.73811	−0.0612603
$806$	−1.95305	−0.0687931
$807$	19.8637	0.699237
$808$	−2.35792	−0.0829514
$809$	−6.78896	−0.238687	−0.119344	−	0.992853i	$-0.538079\pi$
$809$	−6.78896	−0.238687	−0.119344	+	0.992853i	$0.538079\pi$
$810$	−8.20264	−0.288211
$811$	42.9659	1.50874	0.754368	−	0.656452i	$-0.227943\pi$
$811$	42.9659	1.50874	0.754368	+	0.656452i	$0.227943\pi$
$812$	−7.87691	−0.276425
$813$	−2.63837	−0.0925318
$814$	−7.67505	−0.269010
$815$	−6.29914	−0.220649
$816$	6.39327	0.223809
$817$	−20.0091	−0.700031
$818$	−7.73328	−0.270388
$819$	−5.72932	−0.200199
$820$	8.61879	0.300981
$821$	46.9328	1.63797	0.818983	−	0.573817i	$-0.194538\pi$
$821$	46.9328	1.63797	0.818983	+	0.573817i	$0.194538\pi$
$822$	35.3904	1.23438
$823$	16.3680	0.570554	0.285277	−	0.958445i	$-0.407914\pi$
$823$	16.3680	0.570554	0.285277	+	0.958445i	$0.407914\pi$
$824$	−18.5109	−0.644858
$825$	50.6900	1.76480
$826$	0.849785	0.0295678
$827$	1.97138	0.0685517	0.0342758	−	0.999412i	$-0.489088\pi$
$827$	1.97138	0.0685517	0.0342758	+	0.999412i	$0.489088\pi$
$828$	2.50610	0.0870932
$829$	46.0931	1.60088	0.800439	−	0.599414i	$-0.204600\pi$
$829$	46.0931	1.60088	0.800439	+	0.599414i	$0.204600\pi$
$830$	−1.28778	−0.0446995
$831$	14.6774	0.509155
$832$	−1.05384	−0.0365354
$833$	6.25007	0.216552
$834$	−11.3653	−0.393549
$835$	−11.1550	−0.386034
$836$	28.3579	0.980780
$837$	−2.14780	−0.0742389
$838$	−0.0658483	−0.00227469
$839$	56.0780	1.93603	0.968014	−	0.250896i	$-0.0807253\pi$
$839$	56.0780	1.93603	0.968014	+	0.250896i	$0.0807253\pi$
$840$	−4.07849	−0.140721
$841$	−15.8158	−0.545371
$842$	−29.7977	−1.02690
$843$	−9.07712	−0.312633
$844$	−4.54692	−0.156512
$845$	9.52597	0.327703
$846$	−22.9008	−0.787345
$847$	29.4391	1.01154
$848$	5.24949	0.180268
$849$	−39.8572	−1.36789
$850$	−11.8739	−0.407271
$851$	1.54837	0.0530774
$852$	15.4032	0.527704
$853$	−17.6307	−0.603662	−0.301831	−	0.953361i	$-0.597598\pi$
$853$	−17.6307	−0.603662	−0.301831	+	0.953361i	$0.597598\pi$
$854$	19.0904	0.653260
$855$	−11.4872	−0.392855
$856$	−17.8100	−0.608733
$857$	25.5825	0.873883	0.436941	−	0.899490i	$-0.356062\pi$
$857$	25.5825	0.873883	0.436941	+	0.899490i	$0.356062\pi$
$858$	−12.2576	−0.418467
$859$	−23.8615	−0.814145	−0.407072	−	0.913396i	$-0.633450\pi$
$859$	−23.8615	−0.814145	−0.407072	+	0.913396i	$0.633450\pi$
$860$	2.80227	0.0955565
$861$	54.7581	1.86615
$862$	35.7277	1.21689
$863$	41.8838	1.42574	0.712871	−	0.701295i	$-0.247394\pi$
$863$	41.8838	1.42574	0.712871	+	0.701295i	$0.247394\pi$
$864$	−1.15893	−0.0394276
$865$	−3.61206	−0.122814
$866$	3.20078	0.108767
$867$	22.4717	0.763177
$868$	−4.02036	−0.136460
$869$	−20.6171	−0.699386
$870$	6.82651	0.231440
$871$	12.1686	0.412316
$872$	4.57649	0.154980
$873$	−24.3833	−0.825250
$874$	−5.72094	−0.193514
$875$	16.2653	0.549868
$876$	7.62695	0.257691
$877$	−2.29207	−0.0773977	−0.0386989	−	0.999251i	$-0.512321\pi$
$877$	−2.29207	−0.0773977	−0.0386989	+	0.999251i	$0.512321\pi$
$878$	−1.11275	−0.0375534
$879$	−29.1209	−0.982225
$880$	−3.97151	−0.133880
$881$	38.3660	1.29258	0.646291	−	0.763091i	$-0.276319\pi$
$881$	38.3660	1.29258	0.646291	+	0.763091i	$0.276319\pi$
$882$	5.74888	0.193575
$883$	−22.7495	−0.765581	−0.382791	−	0.923835i	$-0.625037\pi$
$883$	−22.7495	−0.765581	−0.382791	+	0.923835i	$0.625037\pi$
$884$	2.87128	0.0965717
$885$	−0.736464	−0.0247560
$886$	36.2757	1.21871
$887$	−33.8641	−1.13704	−0.568522	−	0.822668i	$-0.692485\pi$
$887$	−33.8641	−1.13704	−0.568522	+	0.822668i	$0.692485\pi$
$888$	3.63326	0.121924
$889$	−17.5039	−0.587062
$890$	−3.12068	−0.104605
$891$	−50.7471	−1.70009
$892$	10.3638	0.347005
$893$	52.2780	1.74942
$894$	−47.4667	−1.58752
$895$	8.79888	0.294114
$896$	−2.16934	−0.0724727
$897$	2.47285	0.0825661
$898$	22.3452	0.745670
$899$	6.72921	0.224432
$900$	−10.9217	−0.364058
$901$	−14.3027	−0.476492
$902$	53.3218	1.77542
$903$	17.8037	0.592471
$904$	−17.0840	−0.568205
$905$	−18.8504	−0.626607
$906$	−5.32585	−0.176940
$907$	20.2556	0.672575	0.336287	−	0.941759i	$-0.390829\pi$
$907$	20.2556	0.672575	0.336287	+	0.941759i	$0.390829\pi$
$908$	−2.15095	−0.0713819
$909$	5.90920	0.195996
$910$	−1.83169	−0.0607200
$911$	18.5546	0.614741	0.307370	−	0.951590i	$-0.400551\pi$
$911$	18.5546	0.614741	0.307370	+	0.951590i	$0.400551\pi$
$912$	−13.4242	−0.444521
$913$	−7.96710	−0.263672
$914$	33.7980	1.11794
$915$	−16.5447	−0.546950
$916$	−6.99096	−0.230988
$917$	2.16934	0.0716380
$918$	3.15760	0.104216
$919$	−11.0170	−0.363419	−0.181709	−	0.983352i	$-0.558163\pi$
$919$	−11.0170	−0.363419	−0.181709	+	0.983352i	$0.558163\pi$
$920$	0.801214	0.0264153
$921$	−21.5060	−0.708646
$922$	32.0441	1.05532
$923$	6.91773	0.227700
$924$	−25.2323	−0.830083
$925$	−6.74788	−0.221869
$926$	−38.1770	−1.25457
$927$	46.3902	1.52366
$928$	3.63101	0.119194
$929$	23.4114	0.768104	0.384052	−	0.923312i	$-0.374528\pi$
$929$	23.4114	0.768104	0.384052	+	0.923312i	$0.374528\pi$
$930$	3.48424	0.114253
$931$	−13.1236	−0.430107
$932$	−20.8075	−0.681574
$933$	82.0702	2.68686
$934$	28.3122	0.926405
$935$	10.8207	0.353876
$936$	2.64104	0.0863251
$937$	−11.8029	−0.385583	−0.192791	−	0.981240i	$-0.561754\pi$
$937$	−11.8029	−0.385583	−0.192791	+	0.981240i	$0.561754\pi$
$938$	25.0491	0.817881
$939$	−66.4287	−2.16782
$940$	−7.32150	−0.238801
$941$	34.6407	1.12925	0.564627	−	0.825346i	$-0.309020\pi$
$941$	34.6407	1.12925	0.564627	+	0.825346i	$0.309020\pi$
$942$	−52.7234	−1.71782
$943$	−10.7572	−0.350301
$944$	−0.391725	−0.0127495
$945$	−2.01435	−0.0655267
$946$	17.3367	0.563666
$947$	5.24140	0.170323	0.0851613	−	0.996367i	$-0.472859\pi$
$947$	5.24140	0.170323	0.0851613	+	0.996367i	$0.472859\pi$
$948$	9.75983	0.316985
$949$	3.42535	0.111191
$950$	24.9322	0.808907
$951$	−49.8797	−1.61746
$952$	5.91056	0.191562
$953$	−46.1346	−1.49445	−0.747223	−	0.664573i	$-0.768614\pi$
$953$	−46.1346	−1.49445	−0.747223	+	0.664573i	$0.768614\pi$
$954$	−13.1558	−0.425934
$955$	−12.5414	−0.405829
$956$	−3.34023	−0.108031
$957$	42.2335	1.36521
$958$	−13.2565	−0.428297
$959$	32.7184	1.05653
$960$	1.88006	0.0606786
$961$	−27.5654	−0.889207
$962$	1.63174	0.0526093
$963$	44.6337	1.43830
$964$	−0.760361	−0.0244896
$965$	−4.84375	−0.155926
$966$	5.09038	0.163780
$967$	−56.9759	−1.83222	−0.916111	−	0.400925i	$-0.868689\pi$
$967$	−56.9759	−1.83222	−0.916111	+	0.400925i	$0.868689\pi$
$968$	−13.5705	−0.436172
$969$	36.5755	1.17497
$970$	−7.79547	−0.250297
$971$	−32.3179	−1.03713	−0.518566	−	0.855038i	$-0.673534\pi$
$971$	−32.3179	−1.03713	−0.518566	+	0.855038i	$0.673534\pi$
$972$	20.5462	0.659019
$973$	−10.5072	−0.336846
$974$	−3.81113	−0.122116
$975$	−10.7768	−0.345134
$976$	−8.80009	−0.281684
$977$	33.7699	1.08040	0.540198	−	0.841538i	$-0.318349\pi$
$977$	33.7699	1.08040	0.540198	+	0.841538i	$0.318349\pi$
$978$	18.4482	0.589909
$979$	−19.3066	−0.617043
$980$	1.83795	0.0587110
$981$	−11.4692	−0.366182
$982$	−30.2940	−0.966721
$983$	24.1219	0.769370	0.384685	−	0.923048i	$-0.374310\pi$
$983$	24.1219	0.769370	0.384685	+	0.923048i	$0.374310\pi$
$984$	−25.2418	−0.804679
$985$	20.0753	0.639653
$986$	−9.89300	−0.315057
$987$	−46.5159	−1.48062
$988$	−6.02897	−0.191807
$989$	−3.49752	−0.111215
$990$	9.95302	0.316328
$991$	−5.22611	−0.166013	−0.0830064	−	0.996549i	$-0.526452\pi$
$991$	−5.22611	−0.166013	−0.0830064	+	0.996549i	$0.526452\pi$
$992$	1.85326	0.0588411
$993$	32.6401	1.03580
$994$	14.2402	0.451672
$995$	11.6321	0.368762
$996$	3.77151	0.119505
$997$	−16.2074	−0.513295	−0.256647	−	0.966505i	$-0.582618\pi$
$997$	−16.2074	−0.513295	−0.256647	+	0.966505i	$0.582618\pi$
$998$	−9.88708	−0.312970
$999$	1.79445	0.0567739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.6	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.6	✓	25	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.34651 q^{3} +1.00000 q^{4} -0.801214 q^{5} +2.34651 q^{6} +2.16934 q^{7} -1.00000 q^{8} +2.50610 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.34651 q^{3} +1.00000 q^{4} -0.801214 q^{5} +2.34651 q^{6} +2.16934 q^{7} -1.00000 q^{8} +2.50610 q^{9} +0.801214 q^{10} +4.95686 q^{11} -2.34651 q^{12} -1.05384 q^{13} -2.16934 q^{14} +1.88006 q^{15} +1.00000 q^{16} -2.72459 q^{17} -2.50610 q^{18} +5.72094 q^{19} -0.801214 q^{20} -5.09038 q^{21} -4.95686 q^{22} +1.00000 q^{23} +2.34651 q^{24} -4.35806 q^{25} +1.05384 q^{26} +1.15893 q^{27} +2.16934 q^{28} -3.63101 q^{29} -1.88006 q^{30} -1.85326 q^{31} -1.00000 q^{32} -11.6313 q^{33} +2.72459 q^{34} -1.73811 q^{35} +2.50610 q^{36} +1.54837 q^{37} -5.72094 q^{38} +2.47285 q^{39} +0.801214 q^{40} -10.7572 q^{41} +5.09038 q^{42} -3.49752 q^{43} +4.95686 q^{44} -2.00793 q^{45} -1.00000 q^{46} +9.13800 q^{47} -2.34651 q^{48} -2.29395 q^{49} +4.35806 q^{50} +6.39327 q^{51} -1.05384 q^{52} +5.24949 q^{53} -1.15893 q^{54} -3.97151 q^{55} -2.16934 q^{56} -13.4242 q^{57} +3.63101 q^{58} -0.391725 q^{59} +1.88006 q^{60} -8.80009 q^{61} +1.85326 q^{62} +5.43660 q^{63} +1.00000 q^{64} +0.844354 q^{65} +11.6313 q^{66} -11.5468 q^{67} -2.72459 q^{68} -2.34651 q^{69} +1.73811 q^{70} -6.56429 q^{71} -2.50610 q^{72} -3.25034 q^{73} -1.54837 q^{74} +10.2262 q^{75} +5.72094 q^{76} +10.7531 q^{77} -2.47285 q^{78} -4.15930 q^{79} -0.801214 q^{80} -10.2378 q^{81} +10.7572 q^{82} -1.60729 q^{83} -5.09038 q^{84} +2.18298 q^{85} +3.49752 q^{86} +8.52020 q^{87} -4.95686 q^{88} -3.89493 q^{89} +2.00793 q^{90} -2.28615 q^{91} +1.00000 q^{92} +4.34870 q^{93} -9.13800 q^{94} -4.58370 q^{95} +2.34651 q^{96} -9.72957 q^{97} +2.29395 q^{98} +12.4224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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