LMFDB - Embedded newform 6026.2.a.h.1.8

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:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.04677 q^{3} +1.00000 q^{4} +3.02542 q^{5} +1.04677 q^{6} -3.14954 q^{7} -1.00000 q^{8} -1.90427 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.04677 q^{3} +1.00000 q^{4} +3.02542 q^{5} +1.04677 q^{6} -3.14954 q^{7} -1.00000 q^{8} -1.90427 q^{9} -3.02542 q^{10} +5.21999 q^{11} -1.04677 q^{12} -5.14076 q^{13} +3.14954 q^{14} -3.16692 q^{15} +1.00000 q^{16} +3.04404 q^{17} +1.90427 q^{18} -1.27389 q^{19} +3.02542 q^{20} +3.29684 q^{21} -5.21999 q^{22} -1.00000 q^{23} +1.04677 q^{24} +4.15319 q^{25} +5.14076 q^{26} +5.13364 q^{27} -3.14954 q^{28} -2.37446 q^{29} +3.16692 q^{30} -3.86161 q^{31} -1.00000 q^{32} -5.46412 q^{33} -3.04404 q^{34} -9.52869 q^{35} -1.90427 q^{36} +10.8947 q^{37} +1.27389 q^{38} +5.38118 q^{39} -3.02542 q^{40} -2.37418 q^{41} -3.29684 q^{42} -9.52894 q^{43} +5.21999 q^{44} -5.76124 q^{45} +1.00000 q^{46} +13.1179 q^{47} -1.04677 q^{48} +2.91960 q^{49} -4.15319 q^{50} -3.18641 q^{51} -5.14076 q^{52} -0.167248 q^{53} -5.13364 q^{54} +15.7927 q^{55} +3.14954 q^{56} +1.33347 q^{57} +2.37446 q^{58} -7.58569 q^{59} -3.16692 q^{60} -0.958220 q^{61} +3.86161 q^{62} +5.99759 q^{63} +1.00000 q^{64} -15.5530 q^{65} +5.46412 q^{66} +13.0601 q^{67} +3.04404 q^{68} +1.04677 q^{69} +9.52869 q^{70} +0.625838 q^{71} +1.90427 q^{72} +6.70674 q^{73} -10.8947 q^{74} -4.34743 q^{75} -1.27389 q^{76} -16.4406 q^{77} -5.38118 q^{78} +1.23334 q^{79} +3.02542 q^{80} +0.339086 q^{81} +2.37418 q^{82} -17.6984 q^{83} +3.29684 q^{84} +9.20952 q^{85} +9.52894 q^{86} +2.48551 q^{87} -5.21999 q^{88} -16.6964 q^{89} +5.76124 q^{90} +16.1910 q^{91} -1.00000 q^{92} +4.04221 q^{93} -13.1179 q^{94} -3.85407 q^{95} +1.04677 q^{96} +18.5688 q^{97} -2.91960 q^{98} -9.94029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−1.04677	−0.604352	−0.302176	−	0.953252i	$-0.597713\pi$
$3$	−1.04677	−0.604352	−0.302176	+	0.953252i	$0.597713\pi$
$4$	1.00000	0.500000
$5$	3.02542	1.35301	0.676505	−	0.736438i	$-0.263494\pi$
$5$	3.02542	1.35301	0.676505	+	0.736438i	$0.263494\pi$
$6$	1.04677	0.427342
$7$	−3.14954	−1.19041	−0.595207	−	0.803572i	$-0.702930\pi$
$7$	−3.14954	−1.19041	−0.595207	+	0.803572i	$0.702930\pi$
$8$	−1.00000	−0.353553
$9$	−1.90427	−0.634758
$10$	−3.02542	−0.956723
$11$	5.21999	1.57389	0.786943	−	0.617026i	$-0.211663\pi$
$11$	5.21999	1.57389	0.786943	+	0.617026i	$0.211663\pi$
$12$	−1.04677	−0.302176
$13$	−5.14076	−1.42579	−0.712895	−	0.701271i	$-0.752616\pi$
$13$	−5.14076	−1.42579	−0.712895	+	0.701271i	$0.752616\pi$
$14$	3.14954	0.841750
$15$	−3.16692	−0.817695
$16$	1.00000	0.250000
$17$	3.04404	0.738289	0.369145	−	0.929372i	$-0.379651\pi$
$17$	3.04404	0.738289	0.369145	+	0.929372i	$0.379651\pi$
$18$	1.90427	0.448842
$19$	−1.27389	−0.292251	−0.146126	−	0.989266i	$-0.546680\pi$
$19$	−1.27389	−0.292251	−0.146126	+	0.989266i	$0.546680\pi$
$20$	3.02542	0.676505
$21$	3.29684	0.719430
$22$	−5.21999	−1.11291
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.04677	0.213671
$25$	4.15319	0.830638
$26$	5.14076	1.00819
$27$	5.13364	0.987970
$28$	−3.14954	−0.595207
$29$	−2.37446	−0.440926	−0.220463	−	0.975395i	$-0.570757\pi$
$29$	−2.37446	−0.440926	−0.220463	+	0.975395i	$0.570757\pi$
$30$	3.16692	0.578198
$31$	−3.86161	−0.693565	−0.346782	−	0.937946i	$-0.612726\pi$
$31$	−3.86161	−0.693565	−0.346782	+	0.937946i	$0.612726\pi$
$32$	−1.00000	−0.176777
$33$	−5.46412	−0.951181
$34$	−3.04404	−0.522049
$35$	−9.52869	−1.61064
$36$	−1.90427	−0.317379
$37$	10.8947	1.79108	0.895540	−	0.444981i	$-0.146790\pi$
$37$	10.8947	1.79108	0.895540	+	0.444981i	$0.146790\pi$
$38$	1.27389	0.206653
$39$	5.38118	0.861679
$40$	−3.02542	−0.478361
$41$	−2.37418	−0.370785	−0.185393	−	0.982665i	$-0.559356\pi$
$41$	−2.37418	−0.370785	−0.185393	+	0.982665i	$0.559356\pi$
$42$	−3.29684	−0.508714
$43$	−9.52894	−1.45315	−0.726575	−	0.687087i	$-0.758889\pi$
$43$	−9.52894	−1.45315	−0.726575	+	0.687087i	$0.758889\pi$
$44$	5.21999	0.786943
$45$	−5.76124	−0.858835
$46$	1.00000	0.147442
$47$	13.1179	1.91345	0.956725	−	0.290995i	$-0.0939863\pi$
$47$	13.1179	1.91345	0.956725	+	0.290995i	$0.0939863\pi$
$48$	−1.04677	−0.151088
$49$	2.91960	0.417086
$50$	−4.15319	−0.587350
$51$	−3.18641	−0.446187
$52$	−5.14076	−0.712895
$53$	−0.167248	−0.0229733	−0.0114867	−	0.999934i	$-0.503656\pi$
$53$	−0.167248	−0.0229733	−0.0114867	+	0.999934i	$0.503656\pi$
$54$	−5.13364	−0.698600
$55$	15.7927	2.12948
$56$	3.14954	0.420875
$57$	1.33347	0.176623
$58$	2.37446	0.311782
$59$	−7.58569	−0.987573	−0.493786	−	0.869583i	$-0.664387\pi$
$59$	−7.58569	−0.987573	−0.493786	+	0.869583i	$0.664387\pi$
$60$	−3.16692	−0.408848
$61$	−0.958220	−0.122687	−0.0613437	−	0.998117i	$-0.519539\pi$
$61$	−0.958220	−0.122687	−0.0613437	+	0.998117i	$0.519539\pi$
$62$	3.86161	0.490424
$63$	5.99759	0.755625
$64$	1.00000	0.125000
$65$	−15.5530	−1.92911
$66$	5.46412	0.672587
$67$	13.0601	1.59555	0.797774	−	0.602956i	$-0.206011\pi$
$67$	13.0601	1.59555	0.797774	+	0.602956i	$0.206011\pi$
$68$	3.04404	0.369145
$69$	1.04677	0.126016
$70$	9.52869	1.13890
$71$	0.625838	0.0742733	0.0371366	−	0.999310i	$-0.488176\pi$
$71$	0.625838	0.0742733	0.0371366	+	0.999310i	$0.488176\pi$
$72$	1.90427	0.224421
$73$	6.70674	0.784964	0.392482	−	0.919760i	$-0.371616\pi$
$73$	6.70674	0.784964	0.392482	+	0.919760i	$0.371616\pi$
$74$	−10.8947	−1.26648
$75$	−4.34743	−0.501998
$76$	−1.27389	−0.146126
$77$	−16.4406	−1.87358
$78$	−5.38118	−0.609299
$79$	1.23334	0.138762	0.0693809	−	0.997590i	$-0.477898\pi$
$79$	1.23334	0.138762	0.0693809	+	0.997590i	$0.477898\pi$
$80$	3.02542	0.338253
$81$	0.339086	0.0376762
$82$	2.37418	0.262185
$83$	−17.6984	−1.94265	−0.971325	−	0.237757i	$-0.923588\pi$
$83$	−17.6984	−1.94265	−0.971325	+	0.237757i	$0.923588\pi$
$84$	3.29684	0.359715
$85$	9.20952	0.998913
$86$	9.52894	1.02753
$87$	2.48551	0.266474
$88$	−5.21999	−0.556453
$89$	−16.6964	−1.76982	−0.884908	−	0.465766i	$-0.845779\pi$
$89$	−16.6964	−1.76982	−0.884908	+	0.465766i	$0.845779\pi$
$90$	5.76124	0.607288
$91$	16.1910	1.69728
$92$	−1.00000	−0.104257
$93$	4.04221	0.419158
$94$	−13.1179	−1.35301
$95$	−3.85407	−0.395419
$96$	1.04677	0.106835
$97$	18.5688	1.88537	0.942686	−	0.333682i	$-0.108291\pi$
$97$	18.5688	1.88537	0.942686	+	0.333682i	$0.108291\pi$
$98$	−2.91960	−0.294924
$99$	−9.94029	−0.999037
$100$	4.15319	0.415319
$101$	−4.09930	−0.407895	−0.203948	−	0.978982i	$-0.565377\pi$
$101$	−4.09930	−0.407895	−0.203948	+	0.978982i	$0.565377\pi$
$102$	3.18641	0.315502
$103$	2.13595	0.210461	0.105230	−	0.994448i	$-0.466442\pi$
$103$	2.13595	0.210461	0.105230	+	0.994448i	$0.466442\pi$
$104$	5.14076	0.504093
$105$	9.97434	0.973396
$106$	0.167248	0.0162446
$107$	−10.9910	−1.06254	−0.531271	−	0.847202i	$-0.678285\pi$
$107$	−10.9910	−1.06254	−0.531271	+	0.847202i	$0.678285\pi$
$108$	5.13364	0.493985
$109$	−18.2661	−1.74958	−0.874789	−	0.484503i	$-0.839000\pi$
$109$	−18.2661	−1.74958	−0.874789	+	0.484503i	$0.839000\pi$
$110$	−15.7927	−1.50577
$111$	−11.4043	−1.08244
$112$	−3.14954	−0.297604
$113$	7.36243	0.692600	0.346300	−	0.938124i	$-0.387438\pi$
$113$	7.36243	0.692600	0.346300	+	0.938124i	$0.387438\pi$
$114$	−1.33347	−0.124891
$115$	−3.02542	−0.282122
$116$	−2.37446	−0.220463
$117$	9.78941	0.905031
$118$	7.58569	0.698319
$119$	−9.58734	−0.878870
$120$	3.16692	0.289099
$121$	16.2483	1.47712
$122$	0.958220	0.0867531
$123$	2.48522	0.224085
$124$	−3.86161	−0.346782
$125$	−2.56196	−0.229149
$126$	−5.99759	−0.534308
$127$	−8.81708	−0.782389	−0.391195	−	0.920308i	$-0.627938\pi$
$127$	−8.81708	−0.782389	−0.391195	+	0.920308i	$0.627938\pi$
$128$	−1.00000	−0.0883883
$129$	9.97460	0.878214
$130$	15.5530	1.36409
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−5.46412	−0.475591
$133$	4.01218	0.347900
$134$	−13.0601	−1.12822
$135$	15.5314	1.33673
$136$	−3.04404	−0.261025
$137$	−9.26831	−0.791845	−0.395923	−	0.918284i	$-0.629575\pi$
$137$	−9.26831	−0.791845	−0.395923	+	0.918284i	$0.629575\pi$
$138$	−1.04677	−0.0891069
$139$	2.50308	0.212308	0.106154	−	0.994350i	$-0.466146\pi$
$139$	2.50308	0.212308	0.106154	+	0.994350i	$0.466146\pi$
$140$	−9.52869	−0.805321
$141$	−13.7315	−1.15640
$142$	−0.625838	−0.0525191
$143$	−26.8347	−2.24403
$144$	−1.90427	−0.158690
$145$	−7.18374	−0.596577
$146$	−6.70674	−0.555054
$147$	−3.05615	−0.252067
$148$	10.8947	0.895540
$149$	−4.75376	−0.389443	−0.194722	−	0.980859i	$-0.562380\pi$
$149$	−4.75376	−0.389443	−0.194722	+	0.980859i	$0.562380\pi$
$150$	4.34743	0.354966
$151$	−12.1325	−0.987328	−0.493664	−	0.869653i	$-0.664343\pi$
$151$	−12.1325	−0.987328	−0.493664	+	0.869653i	$0.664343\pi$
$152$	1.27389	0.103326
$153$	−5.79670	−0.468635
$154$	16.4406	1.32482
$155$	−11.6830	−0.938400
$156$	5.38118	0.430840
$157$	−10.9164	−0.871223	−0.435612	−	0.900135i	$-0.643468\pi$
$157$	−10.9164	−0.871223	−0.435612	+	0.900135i	$0.643468\pi$
$158$	−1.23334	−0.0981194
$159$	0.175070	0.0138840
$160$	−3.02542	−0.239181
$161$	3.14954	0.248219
$162$	−0.339086	−0.0266411
$163$	−13.2609	−1.03867	−0.519336	−	0.854570i	$-0.673821\pi$
$163$	−13.2609	−1.03867	−0.519336	+	0.854570i	$0.673821\pi$
$164$	−2.37418	−0.185393
$165$	−16.5313	−1.28696
$166$	17.6984	1.37366
$167$	−23.6252	−1.82818	−0.914088	−	0.405516i	$-0.867092\pi$
$167$	−23.6252	−1.82818	−0.914088	+	0.405516i	$0.867092\pi$
$168$	−3.29684	−0.254357
$169$	13.4274	1.03288
$170$	−9.20952	−0.706338
$171$	2.42584	0.185509
$172$	−9.52894	−0.726575
$173$	19.8326	1.50784	0.753921	−	0.656965i	$-0.228160\pi$
$173$	19.8326	1.50784	0.753921	+	0.656965i	$0.228160\pi$
$174$	−2.48551	−0.188426
$175$	−13.0806	−0.988803
$176$	5.21999	0.393471
$177$	7.94046	0.596842
$178$	16.6964	1.25145
$179$	−16.7626	−1.25289	−0.626447	−	0.779464i	$-0.715491\pi$
$179$	−16.7626	−1.25289	−0.626447	+	0.779464i	$0.715491\pi$
$180$	−5.76124	−0.429417
$181$	7.59423	0.564475	0.282237	−	0.959345i	$-0.408923\pi$
$181$	7.59423	0.564475	0.282237	+	0.959345i	$0.408923\pi$
$182$	−16.1910	−1.20016
$183$	1.00303	0.0741465
$184$	1.00000	0.0737210
$185$	32.9611	2.42335
$186$	−4.04221	−0.296389
$187$	15.8899	1.16198
$188$	13.1179	0.956725
$189$	−16.1686	−1.17609
$190$	3.85407	0.279603
$191$	22.6661	1.64006	0.820029	−	0.572321i	$-0.193957\pi$
$191$	22.6661	1.64006	0.820029	+	0.572321i	$0.193957\pi$
$192$	−1.04677	−0.0755440
$193$	−7.92638	−0.570553	−0.285277	−	0.958445i	$-0.592085\pi$
$193$	−7.92638	−0.570553	−0.285277	+	0.958445i	$0.592085\pi$
$194$	−18.5688	−1.33316
$195$	16.2804	1.16586
$196$	2.91960	0.208543
$197$	15.4109	1.09798	0.548991	−	0.835829i	$-0.315012\pi$
$197$	15.4109	1.09798	0.548991	+	0.835829i	$0.315012\pi$
$198$	9.94029	0.706426
$199$	−20.8953	−1.48123	−0.740613	−	0.671932i	$-0.765465\pi$
$199$	−20.8953	−1.48123	−0.740613	+	0.671932i	$0.765465\pi$
$200$	−4.15319	−0.293675
$201$	−13.6709	−0.964273
$202$	4.09930	0.288426
$203$	7.47845	0.524884
$204$	−3.18641	−0.223093
$205$	−7.18291	−0.501676
$206$	−2.13595	−0.148818
$207$	1.90427	0.132356
$208$	−5.14076	−0.356447
$209$	−6.64971	−0.459970
$210$	−9.97434	−0.688295
$211$	5.23930	0.360689	0.180344	−	0.983604i	$-0.442279\pi$
$211$	5.23930	0.360689	0.180344	+	0.983604i	$0.442279\pi$
$212$	−0.167248	−0.0114867
$213$	−0.655107	−0.0448872
$214$	10.9910	0.751330
$215$	−28.8291	−1.96613
$216$	−5.13364	−0.349300
$217$	12.1623	0.825629
$218$	18.2661	1.23714
$219$	−7.02041	−0.474395
$220$	15.7927	1.06474
$221$	−15.6487	−1.05264
$222$	11.4043	0.765403
$223$	14.0674	0.942023	0.471012	−	0.882127i	$-0.343889\pi$
$223$	14.0674	0.942023	0.471012	+	0.882127i	$0.343889\pi$
$224$	3.14954	0.210437
$225$	−7.90881	−0.527254
$226$	−7.36243	−0.489742
$227$	8.01412	0.531916	0.265958	−	0.963985i	$-0.414312\pi$
$227$	8.01412	0.531916	0.265958	+	0.963985i	$0.414312\pi$
$228$	1.33347	0.0883114
$229$	1.99324	0.131717	0.0658584	−	0.997829i	$-0.479021\pi$
$229$	1.99324	0.131717	0.0658584	+	0.997829i	$0.479021\pi$
$230$	3.02542	0.199491
$231$	17.2095	1.13230
$232$	2.37446	0.155891
$233$	22.3493	1.46415	0.732075	−	0.681224i	$-0.238552\pi$
$233$	22.3493	1.46415	0.732075	+	0.681224i	$0.238552\pi$
$234$	−9.78941	−0.639954
$235$	39.6873	2.58892
$236$	−7.58569	−0.493786
$237$	−1.29102	−0.0838610
$238$	9.58734	0.621455
$239$	−20.8519	−1.34880	−0.674400	−	0.738366i	$-0.735598\pi$
$239$	−20.8519	−1.34880	−0.674400	+	0.738366i	$0.735598\pi$
$240$	−3.16692	−0.204424
$241$	23.7143	1.52757	0.763786	−	0.645469i	$-0.223338\pi$
$241$	23.7143	1.52757	0.763786	+	0.645469i	$0.223338\pi$
$242$	−16.2483	−1.04448
$243$	−15.7559	−1.01074
$244$	−0.958220	−0.0613437
$245$	8.83303	0.564322
$246$	−2.48522	−0.158452
$247$	6.54878	0.416689
$248$	3.86161	0.245212
$249$	18.5261	1.17404
$250$	2.56196	0.162033
$251$	−4.83713	−0.305317	−0.152658	−	0.988279i	$-0.548783\pi$
$251$	−4.83713	−0.305317	−0.152658	+	0.988279i	$0.548783\pi$
$252$	5.99759	0.377813
$253$	−5.21999	−0.328178
$254$	8.81708	0.553233
$255$	−9.64024	−0.603696
$256$	1.00000	0.0625000
$257$	−14.7777	−0.921809	−0.460904	−	0.887450i	$-0.652475\pi$
$257$	−14.7777	−0.921809	−0.460904	+	0.887450i	$0.652475\pi$
$258$	−9.97460	−0.620991
$259$	−34.3133	−2.13213
$260$	−15.5530	−0.964554
$261$	4.52162	0.279881
$262$	1.00000	0.0617802
$263$	8.81903	0.543805	0.271902	−	0.962325i	$-0.412347\pi$
$263$	8.81903	0.543805	0.271902	+	0.962325i	$0.412347\pi$
$264$	5.46412	0.336293
$265$	−0.505997	−0.0310832
$266$	−4.01218	−0.246002
$267$	17.4773	1.06959
$268$	13.0601	0.797774
$269$	30.6979	1.87168	0.935841	−	0.352421i	$-0.114642\pi$
$269$	30.6979	1.87168	0.935841	+	0.352421i	$0.114642\pi$
$270$	−15.5314	−0.945214
$271$	−30.0589	−1.82595	−0.912975	−	0.408016i	$-0.866221\pi$
$271$	−30.0589	−1.82595	−0.912975	+	0.408016i	$0.866221\pi$
$272$	3.04404	0.184572
$273$	−16.9483	−1.02576
$274$	9.26831	0.559919
$275$	21.6796	1.30733
$276$	1.04677	0.0630081
$277$	−30.1294	−1.81030	−0.905150	−	0.425093i	$-0.860241\pi$
$277$	−30.1294	−1.81030	−0.905150	+	0.425093i	$0.860241\pi$
$278$	−2.50308	−0.150125
$279$	7.35356	0.440246
$280$	9.52869	0.569448
$281$	0.152255	0.00908275	0.00454137	−	0.999990i	$-0.498554\pi$
$281$	0.152255	0.00908275	0.00454137	+	0.999990i	$0.498554\pi$
$282$	13.7315	0.817697
$283$	−14.5431	−0.864499	−0.432250	−	0.901754i	$-0.642280\pi$
$283$	−14.5431	−0.864499	−0.432250	+	0.901754i	$0.642280\pi$
$284$	0.625838	0.0371366
$285$	4.03432	0.238972
$286$	26.8347	1.58677
$287$	7.47758	0.441388
$288$	1.90427	0.112210
$289$	−7.73379	−0.454929
$290$	7.18374	0.421844
$291$	−19.4372	−1.13943
$292$	6.70674	0.392482
$293$	26.8655	1.56950	0.784750	−	0.619813i	$-0.212791\pi$
$293$	26.8655	1.56950	0.784750	+	0.619813i	$0.212791\pi$
$294$	3.05615	0.178238
$295$	−22.9499	−1.33620
$296$	−10.8947	−0.633242
$297$	26.7976	1.55495
$298$	4.75376	0.275378
$299$	5.14076	0.297298
$300$	−4.34743	−0.250999
$301$	30.0118	1.72985
$302$	12.1325	0.698147
$303$	4.29102	0.246513
$304$	−1.27389	−0.0730628
$305$	−2.89902	−0.165997
$306$	5.79670	0.331375
$307$	−7.51874	−0.429117	−0.214559	−	0.976711i	$-0.568831\pi$
$307$	−7.51874	−0.429117	−0.214559	+	0.976711i	$0.568831\pi$
$308$	−16.4406	−0.936788
$309$	−2.23584	−0.127193
$310$	11.6830	0.663549
$311$	−16.2277	−0.920189	−0.460094	−	0.887870i	$-0.652184\pi$
$311$	−16.2277	−0.920189	−0.460094	+	0.887870i	$0.652184\pi$
$312$	−5.38118	−0.304650
$313$	−18.0804	−1.02196	−0.510981	−	0.859592i	$-0.670718\pi$
$313$	−18.0804	−1.02196	−0.510981	+	0.859592i	$0.670718\pi$
$314$	10.9164	0.616048
$315$	18.1452	1.02237
$316$	1.23334	0.0693809
$317$	−10.9186	−0.613249	−0.306625	−	0.951831i	$-0.599200\pi$
$317$	−10.9186	−0.613249	−0.306625	+	0.951831i	$0.599200\pi$
$318$	−0.175070	−0.00981746
$319$	−12.3946	−0.693966
$320$	3.02542	0.169126
$321$	11.5051	0.642149
$322$	−3.14954	−0.175517
$323$	−3.87779	−0.215766
$324$	0.339086	0.0188381
$325$	−21.3505	−1.18431
$326$	13.2609	0.734451
$327$	19.1204	1.05736
$328$	2.37418	0.131092
$329$	−41.3155	−2.27780
$330$	16.5313	0.910017
$331$	7.35143	0.404071	0.202036	−	0.979378i	$-0.435244\pi$
$331$	7.35143	0.404071	0.202036	+	0.979378i	$0.435244\pi$
$332$	−17.6984	−0.971325
$333$	−20.7465	−1.13690
$334$	23.6252	1.29272
$335$	39.5124	2.15879
$336$	3.29684	0.179857
$337$	−24.7369	−1.34751	−0.673753	−	0.738957i	$-0.735319\pi$
$337$	−24.7369	−1.34751	−0.673753	+	0.738957i	$0.735319\pi$
$338$	−13.4274	−0.730353
$339$	−7.70677	−0.418574
$340$	9.20952	0.499457
$341$	−20.1575	−1.09159
$342$	−2.42584	−0.131175
$343$	12.8514	0.693909
$344$	9.52894	0.513766
$345$	3.16692	0.170501
$346$	−19.8326	−1.06621
$347$	2.02795	0.108866	0.0544330	−	0.998517i	$-0.482665\pi$
$347$	2.02795	0.108866	0.0544330	+	0.998517i	$0.482665\pi$
$348$	2.48551	0.133237
$349$	−29.6327	−1.58620	−0.793101	−	0.609090i	$-0.791535\pi$
$349$	−29.6327	−1.58620	−0.793101	+	0.609090i	$0.791535\pi$
$350$	13.0806	0.699189
$351$	−26.3908	−1.40864
$352$	−5.21999	−0.278226
$353$	−0.0127493	−0.000678578 0	−0.000339289	−	1.00000i	$-0.500108\pi$
$353$	−0.0127493	−0.000678578 0	−0.000339289		1.00000i	$0.500108\pi$
$354$	−7.94046	−0.422031
$355$	1.89342	0.100493
$356$	−16.6964	−0.884908
$357$	10.0357	0.531147
$358$	16.7626	0.885929
$359$	−8.48428	−0.447783	−0.223892	−	0.974614i	$-0.571876\pi$
$359$	−8.48428	−0.447783	−0.223892	+	0.974614i	$0.571876\pi$
$360$	5.76124	0.303644
$361$	−17.3772	−0.914589
$362$	−7.59423	−0.399144
$363$	−17.0082	−0.892698
$364$	16.1910	0.848640
$365$	20.2907	1.06207
$366$	−1.00303	−0.0524295
$367$	13.2569	0.692007	0.346003	−	0.938233i	$-0.387539\pi$
$367$	13.2569	0.692007	0.346003	+	0.938233i	$0.387539\pi$
$368$	−1.00000	−0.0521286
$369$	4.52110	0.235359
$370$	−32.9611	−1.71357
$371$	0.526755	0.0273478
$372$	4.04221	0.209579
$373$	20.5034	1.06163	0.530813	−	0.847489i	$-0.321887\pi$
$373$	20.5034	1.06163	0.530813	+	0.847489i	$0.321887\pi$
$374$	−15.8899	−0.821646
$375$	2.68178	0.138487
$376$	−13.1179	−0.676506
$377$	12.2065	0.628667
$378$	16.1686	0.831624
$379$	8.74897	0.449405	0.224702	−	0.974427i	$-0.427859\pi$
$379$	8.74897	0.449405	0.224702	+	0.974427i	$0.427859\pi$
$380$	−3.85407	−0.197710
$381$	9.22945	0.472839
$382$	−22.6661	−1.15970
$383$	9.41680	0.481176	0.240588	−	0.970627i	$-0.422660\pi$
$383$	9.41680	0.481176	0.240588	+	0.970627i	$0.422660\pi$
$384$	1.04677	0.0534177
$385$	−49.7397	−2.53497
$386$	7.92638	0.403442
$387$	18.1457	0.922399
$388$	18.5688	0.942686
$389$	−18.5320	−0.939612	−0.469806	−	0.882770i	$-0.655676\pi$
$389$	−18.5320	−0.939612	−0.469806	+	0.882770i	$0.655676\pi$
$390$	−16.2804	−0.824388
$391$	−3.04404	−0.153944
$392$	−2.91960	−0.147462
$393$	1.04677	0.0528025
$394$	−15.4109	−0.776390
$395$	3.73138	0.187746
$396$	−9.94029	−0.499518
$397$	8.99391	0.451392	0.225696	−	0.974198i	$-0.427534\pi$
$397$	8.99391	0.451392	0.225696	+	0.974198i	$0.427534\pi$
$398$	20.8953	1.04739
$399$	−4.19982	−0.210254
$400$	4.15319	0.207659
$401$	6.04775	0.302010	0.151005	−	0.988533i	$-0.451749\pi$
$401$	6.04775	0.302010	0.151005	+	0.988533i	$0.451749\pi$
$402$	13.6709	0.681844
$403$	19.8516	0.988877
$404$	−4.09930	−0.203948
$405$	1.02588	0.0509763
$406$	−7.47845	−0.371149
$407$	56.8703	2.81896
$408$	3.18641	0.157751
$409$	4.90714	0.242642	0.121321	−	0.992613i	$-0.461287\pi$
$409$	4.90714	0.242642	0.121321	+	0.992613i	$0.461287\pi$
$410$	7.18291	0.354739
$411$	9.70178	0.478553
$412$	2.13595	0.105230
$413$	23.8914	1.17562
$414$	−1.90427	−0.0935900
$415$	−53.5451	−2.62843
$416$	5.14076	0.252046
$417$	−2.62014	−0.128309
$418$	6.64971	0.325248
$419$	−25.7798	−1.25942	−0.629712	−	0.776828i	$-0.716827\pi$
$419$	−25.7798	−1.25942	−0.629712	+	0.776828i	$0.716827\pi$
$420$	9.97434	0.486698
$421$	−20.2967	−0.989201	−0.494600	−	0.869120i	$-0.664686\pi$
$421$	−20.2967	−0.989201	−0.494600	+	0.869120i	$0.664686\pi$
$422$	−5.23930	−0.255045
$423$	−24.9802	−1.21458
$424$	0.167248	0.00812230
$425$	12.6425	0.613251
$426$	0.655107	0.0317401
$427$	3.01795	0.146049
$428$	−10.9910	−0.531271
$429$	28.0897	1.35618
$430$	28.8291	1.39026
$431$	−23.0821	−1.11183	−0.555914	−	0.831240i	$-0.687632\pi$
$431$	−23.0821	−1.11183	−0.555914	+	0.831240i	$0.687632\pi$
$432$	5.13364	0.246993
$433$	36.2582	1.74246	0.871229	−	0.490876i	$-0.163323\pi$
$433$	36.2582	1.74246	0.871229	+	0.490876i	$0.163323\pi$
$434$	−12.1623	−0.583808
$435$	7.51972	0.360543
$436$	−18.2661	−0.874789
$437$	1.27389	0.0609386
$438$	7.02041	0.335448
$439$	−14.4607	−0.690169	−0.345085	−	0.938572i	$-0.612150\pi$
$439$	−14.4607	−0.690169	−0.345085	+	0.938572i	$0.612150\pi$
$440$	−15.7927	−0.752886
$441$	−5.55972	−0.264749
$442$	15.6487	0.744332
$443$	−22.1585	−1.05278	−0.526391	−	0.850242i	$-0.676455\pi$
$443$	−22.1585	−1.05278	−0.526391	+	0.850242i	$0.676455\pi$
$444$	−11.4043	−0.541222
$445$	−50.5137	−2.39458
$446$	−14.0674	−0.666111
$447$	4.97609	0.235361
$448$	−3.14954	−0.148802
$449$	−31.8227	−1.50181	−0.750904	−	0.660412i	$-0.770382\pi$
$449$	−31.8227	−1.50181	−0.750904	+	0.660412i	$0.770382\pi$
$450$	7.90881	0.372825
$451$	−12.3932	−0.583573
$452$	7.36243	0.346300
$453$	12.6999	0.596694
$454$	−8.01412	−0.376121
$455$	48.9847	2.29644
$456$	−1.33347	−0.0624456
$457$	16.0212	0.749441	0.374720	−	0.927138i	$-0.377739\pi$
$457$	16.0212	0.749441	0.374720	+	0.927138i	$0.377739\pi$
$458$	−1.99324	−0.0931379
$459$	15.6270	0.729408
$460$	−3.02542	−0.141061
$461$	−19.3391	−0.900712	−0.450356	−	0.892849i	$-0.648703\pi$
$461$	−19.3391	−0.900712	−0.450356	+	0.892849i	$0.648703\pi$
$462$	−17.2095	−0.800657
$463$	−9.86263	−0.458355	−0.229178	−	0.973385i	$-0.573604\pi$
$463$	−9.86263	−0.458355	−0.229178	+	0.973385i	$0.573604\pi$
$464$	−2.37446	−0.110231
$465$	12.2294	0.567125
$466$	−22.3493	−1.03531
$467$	−36.7936	−1.70260	−0.851302	−	0.524675i	$-0.824187\pi$
$467$	−36.7936	−1.70260	−0.851302	+	0.524675i	$0.824187\pi$
$468$	9.78941	0.452516
$469$	−41.1334	−1.89936
$470$	−39.6873	−1.83064
$471$	11.4269	0.526526
$472$	7.58569	0.349160
$473$	−49.7410	−2.28709
$474$	1.29102	0.0592987
$475$	−5.29072	−0.242755
$476$	−9.58734	−0.439435
$477$	0.318487	0.0145825
$478$	20.8519	0.953746
$479$	−8.67563	−0.396400	−0.198200	−	0.980162i	$-0.563510\pi$
$479$	−8.67563	−0.396400	−0.198200	+	0.980162i	$0.563510\pi$
$480$	3.16692	0.144549
$481$	−56.0071	−2.55370
$482$	−23.7143	−1.08016
$483$	−3.29684	−0.150011
$484$	16.2483	0.738558
$485$	56.1783	2.55093
$486$	15.7559	0.714701
$487$	22.9577	1.04031	0.520156	−	0.854071i	$-0.325874\pi$
$487$	22.9577	1.04031	0.520156	+	0.854071i	$0.325874\pi$
$488$	0.958220	0.0433766
$489$	13.8811	0.627723
$490$	−8.83303	−0.399036
$491$	18.4917	0.834518	0.417259	−	0.908788i	$-0.362991\pi$
$491$	18.4917	0.834518	0.417259	+	0.908788i	$0.362991\pi$
$492$	2.48522	0.112042
$493$	−7.22795	−0.325531
$494$	−6.54878	−0.294643
$495$	−30.0736	−1.35171
$496$	−3.86161	−0.173391
$497$	−1.97110	−0.0884159
$498$	−18.5261	−0.830175
$499$	24.6607	1.10396	0.551982	−	0.833856i	$-0.313872\pi$
$499$	24.6607	1.10396	0.551982	+	0.833856i	$0.313872\pi$
$500$	−2.56196	−0.114575
$501$	24.7302	1.10486
$502$	4.83713	0.215892
$503$	−28.3611	−1.26456	−0.632280	−	0.774740i	$-0.717881\pi$
$503$	−28.3611	−1.26456	−0.632280	+	0.774740i	$0.717881\pi$
$504$	−5.99759	−0.267154
$505$	−12.4021	−0.551887
$506$	5.21999	0.232057
$507$	−14.0554	−0.624221
$508$	−8.81708	−0.391195
$509$	14.8103	0.656456	0.328228	−	0.944598i	$-0.393549\pi$
$509$	14.8103	0.656456	0.328228	+	0.944598i	$0.393549\pi$
$510$	9.64024	0.426877
$511$	−21.1231	−0.934433
$512$	−1.00000	−0.0441942
$513$	−6.53972	−0.288735
$514$	14.7777	0.651817
$515$	6.46214	0.284756
$516$	9.97460	0.439107
$517$	68.4755	3.01155
$518$	34.3133	1.50764
$519$	−20.7601	−0.911268
$520$	15.5530	0.682043
$521$	18.7169	0.820001	0.410000	−	0.912085i	$-0.365529\pi$
$521$	18.7169	0.820001	0.410000	+	0.912085i	$0.365529\pi$
$522$	−4.52162	−0.197906
$523$	−32.1793	−1.40710	−0.703550	−	0.710645i	$-0.748403\pi$
$523$	−32.1793	−1.40710	−0.703550	+	0.710645i	$0.748403\pi$
$524$	−1.00000	−0.0436852
$525$	13.6924	0.597585
$526$	−8.81903	−0.384528
$527$	−11.7549	−0.512051
$528$	−5.46412	−0.237795
$529$	1.00000	0.0434783
$530$	0.505997	0.0219791
$531$	14.4452	0.626870
$532$	4.01218	0.173950
$533$	12.2051	0.528661
$534$	−17.4773	−0.756316
$535$	−33.2525	−1.43763
$536$	−13.0601	−0.564111
$537$	17.5465	0.757189
$538$	−30.6979	−1.32348
$539$	15.2403	0.656445
$540$	15.5314	0.668367
$541$	−7.02657	−0.302096	−0.151048	−	0.988526i	$-0.548265\pi$
$541$	−7.02657	−0.302096	−0.151048	+	0.988526i	$0.548265\pi$
$542$	30.0589	1.29114
$543$	−7.94941	−0.341142
$544$	−3.04404	−0.130512
$545$	−55.2628	−2.36720
$546$	16.9483	0.725318
$547$	21.4386	0.916647	0.458324	−	0.888785i	$-0.348450\pi$
$547$	21.4386	0.916647	0.458324	+	0.888785i	$0.348450\pi$
$548$	−9.26831	−0.395923
$549$	1.82471	0.0778769
$550$	−21.6796	−0.924421
$551$	3.02481	0.128861
$552$	−1.04677	−0.0445534
$553$	−3.88446	−0.165184
$554$	30.1294	1.28008
$555$	−34.5027	−1.46456
$556$	2.50308	0.106154
$557$	−4.96603	−0.210417	−0.105209	−	0.994450i	$-0.533551\pi$
$557$	−4.96603	−0.210417	−0.105209	+	0.994450i	$0.533551\pi$
$558$	−7.35356	−0.311301
$559$	48.9860	2.07189
$560$	−9.52869	−0.402661
$561$	−16.6330	−0.702247
$562$	−0.152255	−0.00642247
$563$	10.1665	0.428466	0.214233	−	0.976783i	$-0.431275\pi$
$563$	10.1665	0.428466	0.214233	+	0.976783i	$0.431275\pi$
$564$	−13.7315	−0.578199
$565$	22.2745	0.937095
$566$	14.5431	0.611293
$567$	−1.06796	−0.0448503
$568$	−0.625838	−0.0262596
$569$	46.9043	1.96633	0.983166	−	0.182716i	$-0.0584888\pi$
$569$	46.9043	1.96633	0.983166	+	0.182716i	$0.0584888\pi$
$570$	−4.03432	−0.168979
$571$	−25.9001	−1.08389	−0.541943	−	0.840415i	$-0.682311\pi$
$571$	−25.9001	−1.08389	−0.541943	+	0.840415i	$0.682311\pi$
$572$	−26.8347	−1.12201
$573$	−23.7261	−0.991173
$574$	−7.47758	−0.312108
$575$	−4.15319	−0.173200
$576$	−1.90427	−0.0793448
$577$	−35.1868	−1.46484	−0.732422	−	0.680851i	$-0.761610\pi$
$577$	−35.1868	−1.46484	−0.732422	+	0.680851i	$0.761610\pi$
$578$	7.73379	0.321683
$579$	8.29709	0.344815
$580$	−7.18374	−0.298289
$581$	55.7417	2.31256
$582$	19.4372	0.805698
$583$	−0.873034	−0.0361574
$584$	−6.70674	−0.277527
$585$	29.6171	1.22452
$586$	−26.8655	−1.10980
$587$	−16.0124	−0.660901	−0.330451	−	0.943823i	$-0.607201\pi$
$587$	−16.0124	−0.660901	−0.330451	+	0.943823i	$0.607201\pi$
$588$	−3.05615	−0.126033
$589$	4.91927	0.202695
$590$	22.9499	0.944833
$591$	−16.1317	−0.663567
$592$	10.8947	0.447770
$593$	−7.64727	−0.314036	−0.157018	−	0.987596i	$-0.550188\pi$
$593$	−7.64727	−0.314036	−0.157018	+	0.987596i	$0.550188\pi$
$594$	−26.7976	−1.09952
$595$	−29.0058	−1.18912
$596$	−4.75376	−0.194722
$597$	21.8725	0.895183
$598$	−5.14076	−0.210221
$599$	−37.1777	−1.51904	−0.759519	−	0.650485i	$-0.774566\pi$
$599$	−37.1777	−1.51904	−0.759519	+	0.650485i	$0.774566\pi$
$600$	4.34743	0.177483
$601$	−6.46405	−0.263674	−0.131837	−	0.991271i	$-0.542088\pi$
$601$	−6.46405	−0.263674	−0.131837	+	0.991271i	$0.542088\pi$
$602$	−30.0118	−1.22319
$603$	−24.8701	−1.01279
$604$	−12.1325	−0.493664
$605$	49.1579	1.99855
$606$	−4.29102	−0.174311
$607$	25.0979	1.01869	0.509346	−	0.860562i	$-0.329887\pi$
$607$	25.0979	1.01869	0.509346	+	0.860562i	$0.329887\pi$
$608$	1.27389	0.0516632
$609$	−7.82821	−0.317215
$610$	2.89902	0.117378
$611$	−67.4362	−2.72818
$612$	−5.79670	−0.234318
$613$	22.4318	0.906010	0.453005	−	0.891508i	$-0.350352\pi$
$613$	22.4318	0.906010	0.453005	+	0.891508i	$0.350352\pi$
$614$	7.51874	0.303432
$615$	7.51885	0.303189
$616$	16.4406	0.662409
$617$	2.35749	0.0949090	0.0474545	−	0.998873i	$-0.484889\pi$
$617$	2.35749	0.0949090	0.0474545	+	0.998873i	$0.484889\pi$
$618$	2.23584	0.0899388
$619$	−6.32247	−0.254122	−0.127061	−	0.991895i	$-0.540554\pi$
$619$	−6.32247	−0.254122	−0.127061	+	0.991895i	$0.540554\pi$
$620$	−11.6830	−0.469200
$621$	−5.13364	−0.206006
$622$	16.2277	0.650672
$623$	52.5860	2.10681
$624$	5.38118	0.215420
$625$	−28.5170	−1.14068
$626$	18.0804	0.722637
$627$	6.96071	0.277984
$628$	−10.9164	−0.435612
$629$	33.1640	1.32234
$630$	−18.1452	−0.722924
$631$	6.31491	0.251393	0.125696	−	0.992069i	$-0.459884\pi$
$631$	6.31491	0.251393	0.125696	+	0.992069i	$0.459884\pi$
$632$	−1.23334	−0.0490597
$633$	−5.48434	−0.217983
$634$	10.9186	0.433633
$635$	−26.6754	−1.05858
$636$	0.175070	0.00694199
$637$	−15.0090	−0.594677
$638$	12.3946	0.490708
$639$	−1.19177	−0.0471456
$640$	−3.02542	−0.119590
$641$	−43.8331	−1.73130	−0.865652	−	0.500647i	$-0.833096\pi$
$641$	−43.8331	−1.73130	−0.865652	+	0.500647i	$0.833096\pi$
$642$	−11.5051	−0.454068
$643$	28.1706	1.11094	0.555471	−	0.831536i	$-0.312538\pi$
$643$	28.1706	1.11094	0.555471	+	0.831536i	$0.312538\pi$
$644$	3.14954	0.124109
$645$	30.1774	1.18823
$646$	3.87779	0.152570
$647$	−42.6719	−1.67761	−0.838803	−	0.544435i	$-0.816744\pi$
$647$	−42.6719	−1.67761	−0.838803	+	0.544435i	$0.816744\pi$
$648$	−0.339086	−0.0133205
$649$	−39.5972	−1.55433
$650$	21.3505	0.837437
$651$	−12.7311	−0.498971
$652$	−13.2609	−0.519336
$653$	−46.2071	−1.80822	−0.904112	−	0.427297i	$-0.859466\pi$
$653$	−46.2071	−1.80822	−0.904112	+	0.427297i	$0.859466\pi$
$654$	−19.1204	−0.747668
$655$	−3.02542	−0.118213
$656$	−2.37418	−0.0926963
$657$	−12.7715	−0.498263
$658$	41.3155	1.61065
$659$	−32.6540	−1.27202	−0.636010	−	0.771681i	$-0.719416\pi$
$659$	−32.6540	−1.27202	−0.636010	+	0.771681i	$0.719416\pi$
$660$	−16.5313	−0.643479
$661$	−0.184289	−0.00716800	−0.00358400	−	0.999994i	$-0.501141\pi$
$661$	−0.184289	−0.00716800	−0.00358400	+	0.999994i	$0.501141\pi$
$662$	−7.35143	−0.285722
$663$	16.3806	0.636168
$664$	17.6984	0.686830
$665$	12.1385	0.470712
$666$	20.7465	0.803912
$667$	2.37446	0.0919394
$668$	−23.6252	−0.914088
$669$	−14.7253	−0.569314
$670$	−39.5124	−1.52650
$671$	−5.00190	−0.193096
$672$	−3.29684	−0.127178
$673$	−48.7096	−1.87762	−0.938808	−	0.344441i	$-0.888069\pi$
$673$	−48.7096	−1.87762	−0.938808	+	0.344441i	$0.888069\pi$
$674$	24.7369	0.952830
$675$	21.3210	0.820645
$676$	13.4274	0.516438
$677$	−10.1269	−0.389207	−0.194604	−	0.980882i	$-0.562342\pi$
$677$	−10.1269	−0.389207	−0.194604	+	0.980882i	$0.562342\pi$
$678$	7.70677	0.295977
$679$	−58.4830	−2.24437
$680$	−9.20952	−0.353169
$681$	−8.38893	−0.321465
$682$	20.1575	0.771872
$683$	−47.3889	−1.81329	−0.906643	−	0.421899i	$-0.861364\pi$
$683$	−47.3889	−1.81329	−0.906643	+	0.421899i	$0.861364\pi$
$684$	2.42584	0.0927544
$685$	−28.0406	−1.07137
$686$	−12.8514	−0.490668
$687$	−2.08646	−0.0796034
$688$	−9.52894	−0.363287
$689$	0.859783	0.0327551
$690$	−3.16692	−0.120563
$691$	−22.1019	−0.840797	−0.420399	−	0.907339i	$-0.638110\pi$
$691$	−22.1019	−0.840797	−0.420399	+	0.907339i	$0.638110\pi$
$692$	19.8326	0.753921
$693$	31.3073	1.18927
$694$	−2.02795	−0.0769799
$695$	7.57287	0.287255
$696$	−2.48551	−0.0942129
$697$	−7.22712	−0.273747
$698$	29.6327	1.12161
$699$	−23.3945	−0.884863
$700$	−13.0806	−0.494401
$701$	−1.60571	−0.0606467	−0.0303234	−	0.999540i	$-0.509654\pi$
$701$	−1.60571	−0.0606467	−0.0303234	+	0.999540i	$0.509654\pi$
$702$	26.3908	0.996057
$703$	−13.8787	−0.523445
$704$	5.21999	0.196736
$705$	−41.5435	−1.56462
$706$	0.0127493	0.000479827 0
$707$	12.9109	0.485564
$708$	7.94046	0.298421
$709$	11.3865	0.427628	0.213814	−	0.976874i	$-0.431411\pi$
$709$	11.3865	0.427628	0.213814	+	0.976874i	$0.431411\pi$
$710$	−1.89342	−0.0710589
$711$	−2.34862	−0.0880802
$712$	16.6964	0.625725
$713$	3.86161	0.144618
$714$	−10.0357	−0.375578
$715$	−81.1863	−3.03620
$716$	−16.7626	−0.626447
$717$	21.8272	0.815150
$718$	8.48428	0.316631
$719$	−29.0379	−1.08293	−0.541466	−	0.840722i	$-0.682131\pi$
$719$	−29.0379	−1.08293	−0.541466	+	0.840722i	$0.682131\pi$
$720$	−5.76124	−0.214709
$721$	−6.72725	−0.250536
$722$	17.3772	0.646712
$723$	−24.8234	−0.923192
$724$	7.59423	0.282237
$725$	−9.86157	−0.366249
$726$	17.0082	0.631233
$727$	8.16869	0.302960	0.151480	−	0.988460i	$-0.451596\pi$
$727$	8.16869	0.302960	0.151480	+	0.988460i	$0.451596\pi$
$728$	−16.1910	−0.600079
$729$	15.4755	0.573167
$730$	−20.2907	−0.750993
$731$	−29.0065	−1.07284
$732$	1.00303	0.0370732
$733$	−25.4395	−0.939629	−0.469814	−	0.882765i	$-0.655679\pi$
$733$	−25.4395	−0.939629	−0.469814	+	0.882765i	$0.655679\pi$
$734$	−13.2569	−0.489323
$735$	−9.24614	−0.341049
$736$	1.00000	0.0368605
$737$	68.1737	2.51121
$738$	−4.52110	−0.166424
$739$	−49.7902	−1.83156	−0.915781	−	0.401677i	$-0.868427\pi$
$739$	−49.7902	−1.83156	−0.915781	+	0.401677i	$0.868427\pi$
$740$	32.9611	1.21168
$741$	−6.85506	−0.251827
$742$	−0.526755	−0.0193378
$743$	−1.10791	−0.0406453	−0.0203226	−	0.999793i	$-0.506469\pi$
$743$	−1.10791	−0.0406453	−0.0203226	+	0.999793i	$0.506469\pi$
$744$	−4.04221	−0.148195
$745$	−14.3821	−0.526921
$746$	−20.5034	−0.750683
$747$	33.7026	1.23311
$748$	15.8899	0.580991
$749$	34.6166	1.26486
$750$	−2.68178	−0.0979249
$751$	32.3284	1.17968	0.589840	−	0.807520i	$-0.299191\pi$
$751$	32.3284	1.17968	0.589840	+	0.807520i	$0.299191\pi$
$752$	13.1179	0.478362
$753$	5.06335	0.184519
$754$	−12.2065	−0.444535
$755$	−36.7059	−1.33587
$756$	−16.1686	−0.588047
$757$	50.0016	1.81734	0.908669	−	0.417516i	$-0.137099\pi$
$757$	50.0016	1.81734	0.908669	+	0.417516i	$0.137099\pi$
$758$	−8.74897	−0.317777
$759$	5.46412	0.198335
$760$	3.85407	0.139802
$761$	10.9462	0.396799	0.198400	−	0.980121i	$-0.436426\pi$
$761$	10.9462	0.396799	0.198400	+	0.980121i	$0.436426\pi$
$762$	−9.22945	−0.334348
$763$	57.5299	2.08272
$764$	22.6661	0.820029
$765$	−17.5375	−0.634068
$766$	−9.41680	−0.340243
$767$	38.9962	1.40807
$768$	−1.04677	−0.0377720
$769$	0.585405	0.0211102	0.0105551	−	0.999944i	$-0.496640\pi$
$769$	0.585405	0.0211102	0.0105551	+	0.999944i	$0.496640\pi$
$770$	49.7397	1.79249
$771$	15.4689	0.557097
$772$	−7.92638	−0.285277
$773$	−13.5638	−0.487856	−0.243928	−	0.969793i	$-0.578436\pi$
$773$	−13.5638	−0.487856	−0.243928	+	0.969793i	$0.578436\pi$
$774$	−18.1457	−0.652234
$775$	−16.0380	−0.576101
$776$	−18.5688	−0.666579
$777$	35.9181	1.28856
$778$	18.5320	0.664406
$779$	3.02446	0.108362
$780$	16.2804	0.582931
$781$	3.26686	0.116898
$782$	3.04404	0.108855
$783$	−12.1896	−0.435621
$784$	2.91960	0.104271
$785$	−33.0267	−1.17877
$786$	−1.04677	−0.0373370
$787$	55.7855	1.98854	0.994269	−	0.106907i	$-0.0340947\pi$
$787$	55.7855	1.98854	0.994269	+	0.106907i	$0.0340947\pi$
$788$	15.4109	0.548991
$789$	−9.23149	−0.328650
$790$	−3.73138	−0.132757
$791$	−23.1883	−0.824480
$792$	9.94029	0.353213
$793$	4.92597	0.174926
$794$	−8.99391	−0.319182
$795$	0.529662	0.0187852
$796$	−20.8953	−0.740613
$797$	53.7424	1.90365	0.951826	−	0.306637i	$-0.0992039\pi$
$797$	53.7424	1.90365	0.951826	+	0.306637i	$0.0992039\pi$
$798$	4.19982	0.148672
$799$	39.9316	1.41268
$800$	−4.15319	−0.146837
$801$	31.7946	1.12341
$802$	−6.04775	−0.213553
$803$	35.0091	1.23544
$804$	−13.6709	−0.482137
$805$	9.52869	0.335842
$806$	−19.8516	−0.699242
$807$	−32.1336	−1.13116
$808$	4.09930	0.144213
$809$	−47.9366	−1.68536	−0.842681	−	0.538413i	$-0.819024\pi$
$809$	−47.9366	−1.68536	−0.842681	+	0.538413i	$0.819024\pi$
$810$	−1.02588	−0.0360457
$811$	14.8844	0.522660	0.261330	−	0.965249i	$-0.415839\pi$
$811$	14.8844	0.522660	0.261330	+	0.965249i	$0.415839\pi$
$812$	7.47845	0.262442
$813$	31.4647	1.10352
$814$	−56.8703	−1.99330
$815$	−40.1197	−1.40533
$816$	−3.18641	−0.111547
$817$	12.1389	0.424685
$818$	−4.90714	−0.171574
$819$	−30.8321	−1.07736
$820$	−7.18291	−0.250838
$821$	45.3610	1.58311	0.791555	−	0.611097i	$-0.209272\pi$
$821$	45.3610	1.58311	0.791555	+	0.611097i	$0.209272\pi$
$822$	−9.70178	−0.338388
$823$	−10.9617	−0.382099	−0.191050	−	0.981580i	$-0.561189\pi$
$823$	−10.9617	−0.382099	−0.191050	+	0.981580i	$0.561189\pi$
$824$	−2.13595	−0.0744092
$825$	−22.6935	−0.790087
$826$	−23.8914	−0.831289
$827$	−24.6882	−0.858491	−0.429246	−	0.903188i	$-0.641221\pi$
$827$	−24.6882	−0.858491	−0.429246	+	0.903188i	$0.641221\pi$
$828$	1.90427	0.0661781
$829$	21.5198	0.747413	0.373707	−	0.927547i	$-0.378087\pi$
$829$	21.5198	0.747413	0.373707	+	0.927547i	$0.378087\pi$
$830$	53.5451	1.85858
$831$	31.5385	1.09406
$832$	−5.14076	−0.178224
$833$	8.88739	0.307930
$834$	2.62014	0.0907282
$835$	−71.4764	−2.47354
$836$	−6.64971	−0.229985
$837$	−19.8241	−0.685221
$838$	25.7798	0.890548
$839$	40.8920	1.41175	0.705874	−	0.708338i	$-0.250555\pi$
$839$	40.8920	1.41175	0.705874	+	0.708338i	$0.250555\pi$
$840$	−9.97434	−0.344147
$841$	−23.3620	−0.805585
$842$	20.2967	0.699471
$843$	−0.159375	−0.00548918
$844$	5.23930	0.180344
$845$	40.6235	1.39749
$846$	24.9802	0.858836
$847$	−51.1746	−1.75838
$848$	−0.167248	−0.00574333
$849$	15.2233	0.522462
$850$	−12.6425	−0.433634
$851$	−10.8947	−0.373466
$852$	−0.655107	−0.0224436
$853$	49.4139	1.69190	0.845951	−	0.533261i	$-0.179034\pi$
$853$	49.4139	1.69190	0.845951	+	0.533261i	$0.179034\pi$
$854$	−3.01795	−0.103272
$855$	7.33920	0.250995
$856$	10.9910	0.375665
$857$	−32.6474	−1.11521	−0.557607	−	0.830105i	$-0.688280\pi$
$857$	−32.6474	−1.11521	−0.557607	+	0.830105i	$0.688280\pi$
$858$	−28.0897	−0.958967
$859$	3.49690	0.119313	0.0596564	−	0.998219i	$-0.480999\pi$
$859$	3.49690	0.119313	0.0596564	+	0.998219i	$0.480999\pi$
$860$	−28.8291	−0.983063
$861$	−7.82730	−0.266754
$862$	23.0821	0.786181
$863$	18.0762	0.615322	0.307661	−	0.951496i	$-0.400454\pi$
$863$	18.0762	0.615322	0.307661	+	0.951496i	$0.400454\pi$
$864$	−5.13364	−0.174650
$865$	60.0019	2.04013
$866$	−36.2582	−1.23210
$867$	8.09550	0.274937
$868$	12.1623	0.412815
$869$	6.43803	0.218395
$870$	−7.51972	−0.254942
$871$	−67.1389	−2.27492
$872$	18.2661	0.618570
$873$	−35.3600	−1.19675
$874$	−1.27389	−0.0430901
$875$	8.06901	0.272782
$876$	−7.02041	−0.237198
$877$	−22.0629	−0.745012	−0.372506	−	0.928030i	$-0.621501\pi$
$877$	−22.0629	−0.745012	−0.372506	+	0.928030i	$0.621501\pi$
$878$	14.4607	0.488023
$879$	−28.1220	−0.948531
$880$	15.7927	0.532371
$881$	47.7843	1.60989	0.804947	−	0.593347i	$-0.202194\pi$
$881$	47.7843	1.60989	0.804947	+	0.593347i	$0.202194\pi$
$882$	5.55972	0.187206
$883$	−51.2459	−1.72456	−0.862282	−	0.506429i	$-0.830965\pi$
$883$	−51.2459	−1.72456	−0.862282	+	0.506429i	$0.830965\pi$
$884$	−15.6487	−0.526322
$885$	24.0233	0.807533
$886$	22.1585	0.744430
$887$	−35.8793	−1.20471	−0.602355	−	0.798229i	$-0.705771\pi$
$887$	−35.8793	−1.20471	−0.602355	+	0.798229i	$0.705771\pi$
$888$	11.4043	0.382702
$889$	27.7697	0.931367
$890$	50.5137	1.69322
$891$	1.77002	0.0592980
$892$	14.0674	0.471012
$893$	−16.7109	−0.559208
$894$	−4.97609	−0.166425
$895$	−50.7139	−1.69518
$896$	3.14954	0.105219
$897$	−5.38118	−0.179673
$898$	31.8227	1.06194
$899$	9.16922	0.305810
$900$	−7.90881	−0.263627
$901$	−0.509111	−0.0169610
$902$	12.3932	0.412649
$903$	−31.4154	−1.04544
$904$	−7.36243	−0.244871
$905$	22.9758	0.763741
$906$	−12.6999	−0.421927
$907$	−19.8016	−0.657501	−0.328750	−	0.944417i	$-0.606627\pi$
$907$	−19.8016	−0.657501	−0.328750	+	0.944417i	$0.606627\pi$
$908$	8.01412	0.265958
$909$	7.80619	0.258915
$910$	−48.9847	−1.62383
$911$	13.0534	0.432480	0.216240	−	0.976340i	$-0.430621\pi$
$911$	13.0534	0.432480	0.216240	+	0.976340i	$0.430621\pi$
$912$	1.33347	0.0441557
$913$	−92.3853	−3.05751
$914$	−16.0212	−0.529935
$915$	3.03460	0.100321
$916$	1.99324	0.0658584
$917$	3.14954	0.104007
$918$	−15.6270	−0.515769
$919$	−5.96660	−0.196820	−0.0984099	−	0.995146i	$-0.531376\pi$
$919$	−5.96660	−0.196820	−0.0984099	+	0.995146i	$0.531376\pi$
$920$	3.02542	0.0997453
$921$	7.87039	0.259338
$922$	19.3391	0.636900
$923$	−3.21728	−0.105898
$924$	17.2095	0.566150
$925$	45.2478	1.48774
$926$	9.86263	0.324106
$927$	−4.06743	−0.133592
$928$	2.37446	0.0779454
$929$	33.0383	1.08395	0.541976	−	0.840394i	$-0.317676\pi$
$929$	33.0383	1.08395	0.541976	+	0.840394i	$0.317676\pi$
$930$	−12.2294	−0.401018
$931$	−3.71926	−0.121894
$932$	22.3493	0.732075
$933$	16.9867	0.556118
$934$	36.7936	1.20392
$935$	48.0736	1.57217
$936$	−9.78941	−0.319977
$937$	43.3951	1.41766	0.708828	−	0.705382i	$-0.249224\pi$
$937$	43.3951	1.41766	0.708828	+	0.705382i	$0.249224\pi$
$938$	41.1334	1.34305
$939$	18.9260	0.617626
$940$	39.6873	1.29446
$941$	−8.46701	−0.276017	−0.138008	−	0.990431i	$-0.544070\pi$
$941$	−8.46701	−0.276017	−0.138008	+	0.990431i	$0.544070\pi$
$942$	−11.4269	−0.372310
$943$	2.37418	0.0773140
$944$	−7.58569	−0.246893
$945$	−48.9169	−1.59127
$946$	49.7410	1.61722
$947$	30.9014	1.00416	0.502080	−	0.864821i	$-0.332568\pi$
$947$	30.9014	1.00416	0.502080	+	0.864821i	$0.332568\pi$
$948$	−1.29102	−0.0419305
$949$	−34.4777	−1.11919
$950$	5.29072	0.171654
$951$	11.4292	0.370619
$952$	9.58734	0.310727
$953$	28.7499	0.931299	0.465650	−	0.884969i	$-0.345821\pi$
$953$	28.7499	0.931299	0.465650	+	0.884969i	$0.345821\pi$
$954$	−0.318487	−0.0103114
$955$	68.5744	2.21902
$956$	−20.8519	−0.674400
$957$	12.9743	0.419400
$958$	8.67563	0.280297
$959$	29.1909	0.942624
$960$	−3.16692	−0.102212
$961$	−16.0880	−0.518968
$962$	56.0071	1.80574
$963$	20.9299	0.674457
$964$	23.7143	0.763786
$965$	−23.9807	−0.771965
$966$	3.29684	0.106074
$967$	−24.7389	−0.795548	−0.397774	−	0.917483i	$-0.630217\pi$
$967$	−24.7389	−0.795548	−0.397774	+	0.917483i	$0.630217\pi$
$968$	−16.2483	−0.522239
$969$	4.05915	0.130399
$970$	−56.1783	−1.80378
$971$	−7.37370	−0.236633	−0.118317	−	0.992976i	$-0.537750\pi$
$971$	−7.37370	−0.236633	−0.118317	+	0.992976i	$0.537750\pi$
$972$	−15.7559	−0.505370
$973$	−7.88354	−0.252735
$974$	−22.9577	−0.735612
$975$	22.3491	0.715743
$976$	−0.958220	−0.0306719
$977$	7.63827	0.244370	0.122185	−	0.992507i	$-0.461010\pi$
$977$	7.63827	0.244370	0.122185	+	0.992507i	$0.461010\pi$
$978$	−13.8811	−0.443867
$979$	−87.1551	−2.78549
$980$	8.83303	0.282161
$981$	34.7837	1.11056
$982$	−18.4917	−0.590093
$983$	−30.9979	−0.988678	−0.494339	−	0.869269i	$-0.664590\pi$
$983$	−30.9979	−0.988678	−0.494339	+	0.869269i	$0.664590\pi$
$984$	−2.48522	−0.0792260
$985$	46.6245	1.48558
$986$	7.22795	0.230185
$987$	43.2478	1.37659
$988$	6.54878	0.208344
$989$	9.52894	0.303003
$990$	30.0736	0.955801
$991$	49.4681	1.57141	0.785703	−	0.618604i	$-0.212301\pi$
$991$	49.4681	1.57141	0.785703	+	0.618604i	$0.212301\pi$
$992$	3.86161	0.122606
$993$	−7.69525	−0.244202
$994$	1.97110	0.0625195
$995$	−63.2170	−2.00411
$996$	18.5261	0.587022
$997$	−31.5266	−0.998458	−0.499229	−	0.866470i	$-0.666383\pi$
$997$	−31.5266	−0.998458	−0.499229	+	0.866470i	$0.666383\pi$
$998$	−24.6607	−0.780620
$999$	55.9296	1.76953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.8	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.04677 q^{3} +1.00000 q^{4} +3.02542 q^{5} +1.04677 q^{6} -3.14954 q^{7} -1.00000 q^{8} -1.90427 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.04677 q^{3} +1.00000 q^{4} +3.02542 q^{5} +1.04677 q^{6} -3.14954 q^{7} -1.00000 q^{8} -1.90427 q^{9} -3.02542 q^{10} +5.21999 q^{11} -1.04677 q^{12} -5.14076 q^{13} +3.14954 q^{14} -3.16692 q^{15} +1.00000 q^{16} +3.04404 q^{17} +1.90427 q^{18} -1.27389 q^{19} +3.02542 q^{20} +3.29684 q^{21} -5.21999 q^{22} -1.00000 q^{23} +1.04677 q^{24} +4.15319 q^{25} +5.14076 q^{26} +5.13364 q^{27} -3.14954 q^{28} -2.37446 q^{29} +3.16692 q^{30} -3.86161 q^{31} -1.00000 q^{32} -5.46412 q^{33} -3.04404 q^{34} -9.52869 q^{35} -1.90427 q^{36} +10.8947 q^{37} +1.27389 q^{38} +5.38118 q^{39} -3.02542 q^{40} -2.37418 q^{41} -3.29684 q^{42} -9.52894 q^{43} +5.21999 q^{44} -5.76124 q^{45} +1.00000 q^{46} +13.1179 q^{47} -1.04677 q^{48} +2.91960 q^{49} -4.15319 q^{50} -3.18641 q^{51} -5.14076 q^{52} -0.167248 q^{53} -5.13364 q^{54} +15.7927 q^{55} +3.14954 q^{56} +1.33347 q^{57} +2.37446 q^{58} -7.58569 q^{59} -3.16692 q^{60} -0.958220 q^{61} +3.86161 q^{62} +5.99759 q^{63} +1.00000 q^{64} -15.5530 q^{65} +5.46412 q^{66} +13.0601 q^{67} +3.04404 q^{68} +1.04677 q^{69} +9.52869 q^{70} +0.625838 q^{71} +1.90427 q^{72} +6.70674 q^{73} -10.8947 q^{74} -4.34743 q^{75} -1.27389 q^{76} -16.4406 q^{77} -5.38118 q^{78} +1.23334 q^{79} +3.02542 q^{80} +0.339086 q^{81} +2.37418 q^{82} -17.6984 q^{83} +3.29684 q^{84} +9.20952 q^{85} +9.52894 q^{86} +2.48551 q^{87} -5.21999 q^{88} -16.6964 q^{89} +5.76124 q^{90} +16.1910 q^{91} -1.00000 q^{92} +4.04221 q^{93} -13.1179 q^{94} -3.85407 q^{95} +1.04677 q^{96} +18.5688 q^{97} -2.91960 q^{98} -9.94029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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