LMFDB - Embedded newform 6026.2.a.l.1.13

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:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.919839 q^{3} +1.00000 q^{4} -1.90352 q^{5} +0.919839 q^{6} +0.476690 q^{7} -1.00000 q^{8} -2.15390 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.919839 q^{3} +1.00000 q^{4} -1.90352 q^{5} +0.919839 q^{6} +0.476690 q^{7} -1.00000 q^{8} -2.15390 q^{9} +1.90352 q^{10} -5.20961 q^{11} -0.919839 q^{12} -2.74045 q^{13} -0.476690 q^{14} +1.75093 q^{15} +1.00000 q^{16} -3.17734 q^{17} +2.15390 q^{18} +4.26703 q^{19} -1.90352 q^{20} -0.438478 q^{21} +5.20961 q^{22} -1.00000 q^{23} +0.919839 q^{24} -1.37660 q^{25} +2.74045 q^{26} +4.74076 q^{27} +0.476690 q^{28} -3.29515 q^{29} -1.75093 q^{30} -2.27599 q^{31} -1.00000 q^{32} +4.79201 q^{33} +3.17734 q^{34} -0.907391 q^{35} -2.15390 q^{36} -0.550318 q^{37} -4.26703 q^{38} +2.52078 q^{39} +1.90352 q^{40} -4.02329 q^{41} +0.438478 q^{42} -2.72875 q^{43} -5.20961 q^{44} +4.09999 q^{45} +1.00000 q^{46} -12.9871 q^{47} -0.919839 q^{48} -6.77277 q^{49} +1.37660 q^{50} +2.92264 q^{51} -2.74045 q^{52} -10.4452 q^{53} -4.74076 q^{54} +9.91662 q^{55} -0.476690 q^{56} -3.92498 q^{57} +3.29515 q^{58} -13.9157 q^{59} +1.75093 q^{60} +5.22931 q^{61} +2.27599 q^{62} -1.02674 q^{63} +1.00000 q^{64} +5.21651 q^{65} -4.79201 q^{66} -10.1023 q^{67} -3.17734 q^{68} +0.919839 q^{69} +0.907391 q^{70} +0.960006 q^{71} +2.15390 q^{72} +12.0673 q^{73} +0.550318 q^{74} +1.26625 q^{75} +4.26703 q^{76} -2.48337 q^{77} -2.52078 q^{78} -1.09421 q^{79} -1.90352 q^{80} +2.10095 q^{81} +4.02329 q^{82} -8.21284 q^{83} -0.438478 q^{84} +6.04814 q^{85} +2.72875 q^{86} +3.03101 q^{87} +5.20961 q^{88} -9.75306 q^{89} -4.09999 q^{90} -1.30635 q^{91} -1.00000 q^{92} +2.09354 q^{93} +12.9871 q^{94} -8.12239 q^{95} +0.919839 q^{96} +3.85318 q^{97} +6.77277 q^{98} +11.2210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	−0.919839	−0.531069	−0.265535	−	0.964101i	$-0.585548\pi$
$3$	−0.919839	−0.531069	−0.265535	+	0.964101i	$0.585548\pi$
$4$	1.00000	0.500000
$5$	−1.90352	−0.851281	−0.425641	−	0.904892i	$-0.639951\pi$
$5$	−1.90352	−0.851281	−0.425641	+	0.904892i	$0.639951\pi$
$6$	0.919839	0.375523
$7$	0.476690	0.180172	0.0900860	−	0.995934i	$-0.471286\pi$
$7$	0.476690	0.180172	0.0900860	+	0.995934i	$0.471286\pi$
$8$	−1.00000	−0.353553
$9$	−2.15390	−0.717965
$10$	1.90352	0.601947
$11$	−5.20961	−1.57076	−0.785379	−	0.619016i	$-0.787532\pi$
$11$	−5.20961	−1.57076	−0.785379	+	0.619016i	$0.787532\pi$
$12$	−0.919839	−0.265535
$13$	−2.74045	−0.760065	−0.380032	−	0.924973i	$-0.624087\pi$
$13$	−2.74045	−0.760065	−0.380032	+	0.924973i	$0.624087\pi$
$14$	−0.476690	−0.127401
$15$	1.75093	0.452089
$16$	1.00000	0.250000
$17$	−3.17734	−0.770618	−0.385309	−	0.922788i	$-0.625905\pi$
$17$	−3.17734	−0.770618	−0.385309	+	0.922788i	$0.625905\pi$
$18$	2.15390	0.507678
$19$	4.26703	0.978924	0.489462	−	0.872025i	$-0.337193\pi$
$19$	4.26703	0.978924	0.489462	+	0.872025i	$0.337193\pi$
$20$	−1.90352	−0.425641
$21$	−0.438478	−0.0956838
$22$	5.20961	1.11069
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.919839	0.187761
$25$	−1.37660	−0.275320
$26$	2.74045	0.537447
$27$	4.74076	0.912359
$28$	0.476690	0.0900860
$29$	−3.29515	−0.611894	−0.305947	−	0.952049i	$-0.598973\pi$
$29$	−3.29515	−0.611894	−0.305947	+	0.952049i	$0.598973\pi$
$30$	−1.75093	−0.319675
$31$	−2.27599	−0.408779	−0.204390	−	0.978890i	$-0.565521\pi$
$31$	−2.27599	−0.408779	−0.204390	+	0.978890i	$0.565521\pi$
$32$	−1.00000	−0.176777
$33$	4.79201	0.834181
$34$	3.17734	0.544909
$35$	−0.907391	−0.153377
$36$	−2.15390	−0.358983
$37$	−0.550318	−0.0904717	−0.0452358	−	0.998976i	$-0.514404\pi$
$37$	−0.550318	−0.0904717	−0.0452358	+	0.998976i	$0.514404\pi$
$38$	−4.26703	−0.692204
$39$	2.52078	0.403647
$40$	1.90352	0.300973
$41$	−4.02329	−0.628332	−0.314166	−	0.949368i	$-0.601725\pi$
$41$	−4.02329	−0.628332	−0.314166	+	0.949368i	$0.601725\pi$
$42$	0.438478	0.0676587
$43$	−2.72875	−0.416131	−0.208065	−	0.978115i	$-0.566717\pi$
$43$	−2.72875	−0.416131	−0.208065	+	0.978115i	$0.566717\pi$
$44$	−5.20961	−0.785379
$45$	4.09999	0.611190
$46$	1.00000	0.147442
$47$	−12.9871	−1.89437	−0.947185	−	0.320687i	$-0.896086\pi$
$47$	−12.9871	−1.89437	−0.947185	+	0.320687i	$0.896086\pi$
$48$	−0.919839	−0.132767
$49$	−6.77277	−0.967538
$50$	1.37660	0.194681
$51$	2.92264	0.409252
$52$	−2.74045	−0.380032
$53$	−10.4452	−1.43476	−0.717381	−	0.696681i	$-0.754659\pi$
$53$	−10.4452	−1.43476	−0.717381	+	0.696681i	$0.754659\pi$
$54$	−4.74076	−0.645135
$55$	9.91662	1.33716
$56$	−0.476690	−0.0637004
$57$	−3.92498	−0.519877
$58$	3.29515	0.432674
$59$	−13.9157	−1.81167	−0.905836	−	0.423629i	$-0.860756\pi$
$59$	−13.9157	−1.81167	−0.905836	+	0.423629i	$0.860756\pi$
$60$	1.75093	0.226045
$61$	5.22931	0.669545	0.334773	−	0.942299i	$-0.391341\pi$
$61$	5.22931	0.669545	0.334773	+	0.942299i	$0.391341\pi$
$62$	2.27599	0.289050
$63$	−1.02674	−0.129357
$64$	1.00000	0.125000
$65$	5.21651	0.647029
$66$	−4.79201	−0.589855
$67$	−10.1023	−1.23420	−0.617098	−	0.786886i	$-0.711692\pi$
$67$	−10.1023	−1.23420	−0.617098	+	0.786886i	$0.711692\pi$
$68$	−3.17734	−0.385309
$69$	0.919839	0.110736
$70$	0.907391	0.108454
$71$	0.960006	0.113932	0.0569659	−	0.998376i	$-0.481857\pi$
$71$	0.960006	0.113932	0.0569659	+	0.998376i	$0.481857\pi$
$72$	2.15390	0.253839
$73$	12.0673	1.41237	0.706186	−	0.708026i	$-0.250414\pi$
$73$	12.0673	1.41237	0.706186	+	0.708026i	$0.250414\pi$
$74$	0.550318	0.0639731
$75$	1.26625	0.146214
$76$	4.26703	0.489462
$77$	−2.48337	−0.283006
$78$	−2.52078	−0.285422
$79$	−1.09421	−0.123108	−0.0615542	−	0.998104i	$-0.519606\pi$
$79$	−1.09421	−0.123108	−0.0615542	+	0.998104i	$0.519606\pi$
$80$	−1.90352	−0.212820
$81$	2.10095	0.233439
$82$	4.02329	0.444298
$83$	−8.21284	−0.901476	−0.450738	−	0.892656i	$-0.648839\pi$
$83$	−8.21284	−0.901476	−0.450738	+	0.892656i	$0.648839\pi$
$84$	−0.438478	−0.0478419
$85$	6.04814	0.656013
$86$	2.72875	0.294249
$87$	3.03101	0.324958
$88$	5.20961	0.555347
$89$	−9.75306	−1.03382	−0.516911	−	0.856039i	$-0.672918\pi$
$89$	−9.75306	−1.03382	−0.516911	+	0.856039i	$0.672918\pi$
$90$	−4.09999	−0.432177
$91$	−1.30635	−0.136942
$92$	−1.00000	−0.104257
$93$	2.09354	0.217090
$94$	12.9871	1.33952
$95$	−8.12239	−0.833340
$96$	0.919839	0.0938807
$97$	3.85318	0.391231	0.195616	−	0.980681i	$-0.437330\pi$
$97$	3.85318	0.391231	0.195616	+	0.980681i	$0.437330\pi$
$98$	6.77277	0.684153
$99$	11.2210	1.12775
$100$	−1.37660	−0.137660
$101$	3.32087	0.330439	0.165219	−	0.986257i	$-0.447167\pi$
$101$	3.32087	0.330439	0.165219	+	0.986257i	$0.447167\pi$
$102$	−2.92264	−0.289385
$103$	−19.1907	−1.89091	−0.945457	−	0.325748i	$-0.894384\pi$
$103$	−19.1907	−1.89091	−0.945457	+	0.325748i	$0.894384\pi$
$104$	2.74045	0.268723
$105$	0.834653	0.0814538
$106$	10.4452	1.01453
$107$	−0.196213	−0.0189687	−0.00948433	−	0.999955i	$-0.503019\pi$
$107$	−0.196213	−0.0189687	−0.00948433	+	0.999955i	$0.503019\pi$
$108$	4.74076	0.456179
$109$	−2.78582	−0.266833	−0.133416	−	0.991060i	$-0.542595\pi$
$109$	−2.78582	−0.266833	−0.133416	+	0.991060i	$0.542595\pi$
$110$	−9.91662	−0.945512
$111$	0.506204	0.0480467
$112$	0.476690	0.0450430
$113$	19.3073	1.81627	0.908137	−	0.418673i	$-0.137505\pi$
$113$	19.3073	1.81627	0.908137	+	0.418673i	$0.137505\pi$
$114$	3.92498	0.367608
$115$	1.90352	0.177504
$116$	−3.29515	−0.305947
$117$	5.90265	0.545700
$118$	13.9157	1.28105
$119$	−1.51461	−0.138844
$120$	−1.75093	−0.159838
$121$	16.1401	1.46728
$122$	−5.22931	−0.473440
$123$	3.70078	0.333688
$124$	−2.27599	−0.204390
$125$	12.1380	1.08566
$126$	1.02674	0.0914694
$127$	−15.1447	−1.34387	−0.671936	−	0.740609i	$-0.734537\pi$
$127$	−15.1447	−1.34387	−0.671936	+	0.740609i	$0.734537\pi$
$128$	−1.00000	−0.0883883
$129$	2.51001	0.220994
$130$	−5.21651	−0.457518
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.79201	0.417091
$133$	2.03405	0.176375
$134$	10.1023	0.872708
$135$	−9.02413	−0.776674
$136$	3.17734	0.272455
$137$	2.55382	0.218188	0.109094	−	0.994031i	$-0.465205\pi$
$137$	2.55382	0.218188	0.109094	+	0.994031i	$0.465205\pi$
$138$	−0.919839	−0.0783019
$139$	16.1427	1.36921	0.684605	−	0.728914i	$-0.259975\pi$
$139$	16.1427	1.36921	0.684605	+	0.728914i	$0.259975\pi$
$140$	−0.907391	−0.0766885
$141$	11.9461	1.00604
$142$	−0.960006	−0.0805620
$143$	14.2767	1.19388
$144$	−2.15390	−0.179491
$145$	6.27239	0.520894
$146$	−12.0673	−0.998698
$147$	6.22986	0.513830
$148$	−0.550318	−0.0452358
$149$	1.79194	0.146801	0.0734006	−	0.997303i	$-0.476615\pi$
$149$	1.79194	0.146801	0.0734006	+	0.997303i	$0.476615\pi$
$150$	−1.26625	−0.103389
$151$	−15.3123	−1.24610	−0.623048	−	0.782183i	$-0.714106\pi$
$151$	−15.3123	−1.24610	−0.623048	+	0.782183i	$0.714106\pi$
$152$	−4.26703	−0.346102
$153$	6.84366	0.553277
$154$	2.48337	0.200116
$155$	4.33239	0.347986
$156$	2.52078	0.201824
$157$	−13.2876	−1.06047	−0.530234	−	0.847851i	$-0.677896\pi$
$157$	−13.2876	−1.06047	−0.530234	+	0.847851i	$0.677896\pi$
$158$	1.09421	0.0870508
$159$	9.60793	0.761959
$160$	1.90352	0.150487
$161$	−0.476690	−0.0375685
$162$	−2.10095	−0.165067
$163$	18.8424	1.47585	0.737927	−	0.674881i	$-0.235805\pi$
$163$	18.8424	1.47585	0.737927	+	0.674881i	$0.235805\pi$
$164$	−4.02329	−0.314166
$165$	−9.12169	−0.710123
$166$	8.21284	0.637440
$167$	−8.13949	−0.629853	−0.314926	−	0.949116i	$-0.601980\pi$
$167$	−8.13949	−0.629853	−0.314926	+	0.949116i	$0.601980\pi$
$168$	0.438478	0.0338293
$169$	−5.48992	−0.422302
$170$	−6.04814	−0.463871
$171$	−9.19074	−0.702833
$172$	−2.72875	−0.208065
$173$	−9.28616	−0.706014	−0.353007	−	0.935621i	$-0.614841\pi$
$173$	−9.28616	−0.706014	−0.353007	+	0.935621i	$0.614841\pi$
$174$	−3.03101	−0.229780
$175$	−0.656213	−0.0496050
$176$	−5.20961	−0.392689
$177$	12.8002	0.962123
$178$	9.75306	0.731023
$179$	−4.23775	−0.316744	−0.158372	−	0.987380i	$-0.550625\pi$
$179$	−4.23775	−0.316744	−0.158372	+	0.987380i	$0.550625\pi$
$180$	4.09999	0.305595
$181$	−21.8840	−1.62662	−0.813312	−	0.581827i	$-0.802338\pi$
$181$	−21.8840	−1.62662	−0.813312	+	0.581827i	$0.802338\pi$
$182$	1.30635	0.0968329
$183$	−4.81013	−0.355575
$184$	1.00000	0.0737210
$185$	1.04754	0.0770168
$186$	−2.09354	−0.153506
$187$	16.5527	1.21045
$188$	−12.9871	−0.947185
$189$	2.25987	0.164381
$190$	8.12239	0.589260
$191$	8.24355	0.596482	0.298241	−	0.954491i	$-0.403600\pi$
$191$	8.24355	0.596482	0.298241	+	0.954491i	$0.403600\pi$
$192$	−0.919839	−0.0663837
$193$	−19.5193	−1.40503	−0.702517	−	0.711667i	$-0.747940\pi$
$193$	−19.5193	−1.40503	−0.702517	+	0.711667i	$0.747940\pi$
$194$	−3.85318	−0.276642
$195$	−4.79835	−0.343617
$196$	−6.77277	−0.483769
$197$	15.7331	1.12094	0.560468	−	0.828176i	$-0.310621\pi$
$197$	15.7331	1.12094	0.560468	+	0.828176i	$0.310621\pi$
$198$	−11.2210	−0.797439
$199$	10.5512	0.747952	0.373976	−	0.927438i	$-0.377994\pi$
$199$	10.5512	0.747952	0.373976	+	0.927438i	$0.377994\pi$
$200$	1.37660	0.0973405
$201$	9.29252	0.655444
$202$	−3.32087	−0.233655
$203$	−1.57077	−0.110246
$204$	2.92264	0.204626
$205$	7.65843	0.534888
$206$	19.1907	1.33708
$207$	2.15390	0.149706
$208$	−2.74045	−0.190016
$209$	−22.2296	−1.53765
$210$	−0.834653	−0.0575966
$211$	−10.4261	−0.717764	−0.358882	−	0.933383i	$-0.616842\pi$
$211$	−10.4261	−0.717764	−0.358882	+	0.933383i	$0.616842\pi$
$212$	−10.4452	−0.717381
$213$	−0.883052	−0.0605057
$214$	0.196213	0.0134129
$215$	5.19424	0.354244
$216$	−4.74076	−0.322568
$217$	−1.08494	−0.0736505
$218$	2.78582	0.188679
$219$	−11.1000	−0.750068
$220$	9.91662	0.668578
$221$	8.70735	0.585720
$222$	−0.506204	−0.0339742
$223$	14.8190	0.992350	0.496175	−	0.868222i	$-0.334737\pi$
$223$	14.8190	0.992350	0.496175	+	0.868222i	$0.334737\pi$
$224$	−0.476690	−0.0318502
$225$	2.96506	0.197670
$226$	−19.3073	−1.28430
$227$	−3.07690	−0.204221	−0.102111	−	0.994773i	$-0.532560\pi$
$227$	−3.07690	−0.204221	−0.102111	+	0.994773i	$0.532560\pi$
$228$	−3.92498	−0.259938
$229$	26.3227	1.73946	0.869728	−	0.493532i	$-0.164294\pi$
$229$	26.3227	1.73946	0.869728	+	0.493532i	$0.164294\pi$
$230$	−1.90352	−0.125515
$231$	2.28430	0.150296
$232$	3.29515	0.216337
$233$	−2.89421	−0.189606	−0.0948029	−	0.995496i	$-0.530222\pi$
$233$	−2.89421	−0.189606	−0.0948029	+	0.995496i	$0.530222\pi$
$234$	−5.90265	−0.385868
$235$	24.7213	1.61264
$236$	−13.9157	−0.905836
$237$	1.00650	0.0653791
$238$	1.51461	0.0981774
$239$	3.88797	0.251492	0.125746	−	0.992062i	$-0.459868\pi$
$239$	3.88797	0.251492	0.125746	+	0.992062i	$0.459868\pi$
$240$	1.75093	0.113022
$241$	−26.5153	−1.70800	−0.854000	−	0.520274i	$-0.825830\pi$
$241$	−26.5153	−1.70800	−0.854000	+	0.520274i	$0.825830\pi$
$242$	−16.1401	−1.03752
$243$	−16.1548	−1.03633
$244$	5.22931	0.334773
$245$	12.8921	0.823647
$246$	−3.70078	−0.235953
$247$	−11.6936	−0.744046
$248$	2.27599	0.144525
$249$	7.55449	0.478746
$250$	−12.1380	−0.767675
$251$	0.354503	0.0223760	0.0111880	−	0.999937i	$-0.496439\pi$
$251$	0.354503	0.0223760	0.0111880	+	0.999937i	$0.496439\pi$
$252$	−1.02674	−0.0646786
$253$	5.20961	0.327526
$254$	15.1447	0.950261
$255$	−5.56332	−0.348388
$256$	1.00000	0.0625000
$257$	19.1170	1.19248	0.596242	−	0.802805i	$-0.296660\pi$
$257$	19.1170	1.19248	0.596242	+	0.802805i	$0.296660\pi$
$258$	−2.51001	−0.156267
$259$	−0.262331	−0.0163005
$260$	5.21651	0.323514
$261$	7.09741	0.439318
$262$	−1.00000	−0.0617802
$263$	8.46808	0.522164	0.261082	−	0.965317i	$-0.415921\pi$
$263$	8.46808	0.522164	0.261082	+	0.965317i	$0.415921\pi$
$264$	−4.79201	−0.294928
$265$	19.8827	1.22139
$266$	−2.03405	−0.124716
$267$	8.97125	0.549032
$268$	−10.1023	−0.617098
$269$	−12.8112	−0.781116	−0.390558	−	0.920578i	$-0.627718\pi$
$269$	−12.8112	−0.781116	−0.390558	+	0.920578i	$0.627718\pi$
$270$	9.02413	0.549191
$271$	17.9969	1.09323	0.546616	−	0.837384i	$-0.315916\pi$
$271$	17.9969	1.09323	0.546616	+	0.837384i	$0.315916\pi$
$272$	−3.17734	−0.192655
$273$	1.20163	0.0727259
$274$	−2.55382	−0.154282
$275$	7.17156	0.432462
$276$	0.919839	0.0553678
$277$	11.1982	0.672837	0.336418	−	0.941713i	$-0.390784\pi$
$277$	11.1982	0.672837	0.336418	+	0.941713i	$0.390784\pi$
$278$	−16.1427	−0.968178
$279$	4.90224	0.293489
$280$	0.907391	0.0542270
$281$	−31.8752	−1.90151	−0.950757	−	0.309938i	$-0.899692\pi$
$281$	−31.8752	−1.90151	−0.950757	+	0.309938i	$0.899692\pi$
$282$	−11.9461	−0.711379
$283$	−18.3717	−1.09209	−0.546044	−	0.837757i	$-0.683867\pi$
$283$	−18.3717	−1.09209	−0.546044	+	0.837757i	$0.683867\pi$
$284$	0.960006	0.0569659
$285$	7.47129	0.442561
$286$	−14.2767	−0.844199
$287$	−1.91786	−0.113208
$288$	2.15390	0.126920
$289$	−6.90450	−0.406147
$290$	−6.27239	−0.368327
$291$	−3.54431	−0.207771
$292$	12.0673	0.706186
$293$	−6.32632	−0.369587	−0.184794	−	0.982777i	$-0.559162\pi$
$293$	−6.32632	−0.369587	−0.184794	+	0.982777i	$0.559162\pi$
$294$	−6.22986	−0.363333
$295$	26.4889	1.54224
$296$	0.550318	0.0319866
$297$	−24.6975	−1.43309
$298$	−1.79194	−0.103804
$299$	2.74045	0.158484
$300$	1.26625	0.0731071
$301$	−1.30077	−0.0749751
$302$	15.3123	0.881123
$303$	−3.05466	−0.175486
$304$	4.26703	0.244731
$305$	−9.95412	−0.569971
$306$	−6.84366	−0.391226
$307$	26.4027	1.50688	0.753441	−	0.657515i	$-0.228392\pi$
$307$	26.4027	1.50688	0.753441	+	0.657515i	$0.228392\pi$
$308$	−2.48337	−0.141503
$309$	17.6523	1.00421
$310$	−4.33239	−0.246063
$311$	24.6589	1.39828	0.699138	−	0.714986i	$-0.253567\pi$
$311$	24.6589	1.39828	0.699138	+	0.714986i	$0.253567\pi$
$312$	−2.52078	−0.142711
$313$	−14.7925	−0.836121	−0.418060	−	0.908419i	$-0.637290\pi$
$313$	−14.7925	−0.836121	−0.418060	+	0.908419i	$0.637290\pi$
$314$	13.2876	0.749865
$315$	1.95442	0.110119
$316$	−1.09421	−0.0615542
$317$	−4.66150	−0.261816	−0.130908	−	0.991395i	$-0.541789\pi$
$317$	−4.66150	−0.261816	−0.130908	+	0.991395i	$0.541789\pi$
$318$	−9.60793	−0.538786
$319$	17.1664	0.961137
$320$	−1.90352	−0.106410
$321$	0.180485	0.0100737
$322$	0.476690	0.0265649
$323$	−13.5578	−0.754377
$324$	2.10095	0.116720
$325$	3.77251	0.209261
$326$	−18.8424	−1.04359
$327$	2.56250	0.141707
$328$	4.02329	0.222149
$329$	−6.19085	−0.341312
$330$	9.12169	0.502133
$331$	10.8221	0.594834	0.297417	−	0.954748i	$-0.403875\pi$
$331$	10.8221	0.594834	0.297417	+	0.954748i	$0.403875\pi$
$332$	−8.21284	−0.450738
$333$	1.18533	0.0649555
$334$	8.13949	0.445373
$335$	19.2300	1.05065
$336$	−0.438478	−0.0239210
$337$	−24.9035	−1.35658	−0.678290	−	0.734794i	$-0.737279\pi$
$337$	−24.9035	−1.35658	−0.678290	+	0.734794i	$0.737279\pi$
$338$	5.48992	0.298612
$339$	−17.7596	−0.964567
$340$	6.04814	0.328006
$341$	11.8570	0.642093
$342$	9.19074	0.496978
$343$	−6.56534	−0.354495
$344$	2.72875	0.147124
$345$	−1.75093	−0.0942672
$346$	9.28616	0.499227
$347$	19.6680	1.05583	0.527916	−	0.849297i	$-0.322974\pi$
$347$	19.6680	1.05583	0.527916	+	0.849297i	$0.322974\pi$
$348$	3.03101	0.162479
$349$	−8.32179	−0.445455	−0.222728	−	0.974881i	$-0.571496\pi$
$349$	−8.32179	−0.445455	−0.222728	+	0.974881i	$0.571496\pi$
$350$	0.656213	0.0350760
$351$	−12.9918	−0.693452
$352$	5.20961	0.277673
$353$	2.67587	0.142422	0.0712112	−	0.997461i	$-0.477314\pi$
$353$	2.67587	0.142422	0.0712112	+	0.997461i	$0.477314\pi$
$354$	−12.8002	−0.680324
$355$	−1.82739	−0.0969880
$356$	−9.75306	−0.516911
$357$	1.39320	0.0737357
$358$	4.23775	0.223972
$359$	−13.5980	−0.717674	−0.358837	−	0.933400i	$-0.616827\pi$
$359$	−13.5980	−0.717674	−0.358837	+	0.933400i	$0.616827\pi$
$360$	−4.09999	−0.216088
$361$	−0.792448	−0.0417078
$362$	21.8840	1.15020
$363$	−14.8463	−0.779227
$364$	−1.30635	−0.0684712
$365$	−22.9704	−1.20233
$366$	4.81013	0.251429
$367$	10.9177	0.569897	0.284949	−	0.958543i	$-0.408023\pi$
$367$	10.9177	0.569897	0.284949	+	0.958543i	$0.408023\pi$
$368$	−1.00000	−0.0521286
$369$	8.66575	0.451121
$370$	−1.04754	−0.0544591
$371$	−4.97914	−0.258504
$372$	2.09354	0.108545
$373$	6.35513	0.329056	0.164528	−	0.986372i	$-0.447390\pi$
$373$	6.35513	0.329056	0.164528	+	0.986372i	$0.447390\pi$
$374$	−16.5527	−0.855921
$375$	−11.1650	−0.576559
$376$	12.9871	0.669761
$377$	9.03020	0.465079
$378$	−2.25987	−0.116235
$379$	18.3951	0.944894	0.472447	−	0.881359i	$-0.343371\pi$
$379$	18.3951	0.944894	0.472447	+	0.881359i	$0.343371\pi$
$380$	−8.12239	−0.416670
$381$	13.9307	0.713689
$382$	−8.24355	−0.421777
$383$	−28.1149	−1.43660	−0.718302	−	0.695732i	$-0.755080\pi$
$383$	−28.1149	−1.43660	−0.718302	+	0.695732i	$0.755080\pi$
$384$	0.919839	0.0469403
$385$	4.72715	0.240918
$386$	19.5193	0.993509
$387$	5.87745	0.298767
$388$	3.85318	0.195616
$389$	−15.4953	−0.785641	−0.392820	−	0.919615i	$-0.628501\pi$
$389$	−15.4953	−0.785641	−0.392820	+	0.919615i	$0.628501\pi$
$390$	4.79835	0.242974
$391$	3.17734	0.160685
$392$	6.77277	0.342076
$393$	−0.919839	−0.0463998
$394$	−15.7331	−0.792621
$395$	2.08286	0.104800
$396$	11.2210	0.563875
$397$	36.8869	1.85130	0.925650	−	0.378381i	$-0.123519\pi$
$397$	36.8869	1.85130	0.925650	+	0.378381i	$0.123519\pi$
$398$	−10.5512	−0.528882
$399$	−1.87100	−0.0936672
$400$	−1.37660	−0.0688301
$401$	33.9375	1.69476	0.847380	−	0.530988i	$-0.178179\pi$
$401$	33.9375	1.69476	0.847380	+	0.530988i	$0.178179\pi$
$402$	−9.29252	−0.463469
$403$	6.23723	0.310699
$404$	3.32087	0.165219
$405$	−3.99921	−0.198723
$406$	1.57077	0.0779558
$407$	2.86694	0.142109
$408$	−2.92264	−0.144692
$409$	30.8015	1.52304	0.761518	−	0.648144i	$-0.224455\pi$
$409$	30.8015	1.52304	0.761518	+	0.648144i	$0.224455\pi$
$410$	−7.65843	−0.378223
$411$	−2.34910	−0.115873
$412$	−19.1907	−0.945457
$413$	−6.63349	−0.326412
$414$	−2.15390	−0.105858
$415$	15.6333	0.767410
$416$	2.74045	0.134362
$417$	−14.8487	−0.727146
$418$	22.2296	1.08728
$419$	24.0157	1.17324	0.586622	−	0.809861i	$-0.300457\pi$
$419$	24.0157	1.17324	0.586622	+	0.809861i	$0.300457\pi$
$420$	0.834653	0.0407269
$421$	14.8510	0.723796	0.361898	−	0.932218i	$-0.382129\pi$
$421$	14.8510	0.723796	0.361898	+	0.932218i	$0.382129\pi$
$422$	10.4261	0.507536
$423$	27.9730	1.36009
$424$	10.4452	0.507265
$425$	4.37393	0.212167
$426$	0.883052	0.0427840
$427$	2.49276	0.120633
$428$	−0.196213	−0.00948433
$429$	−13.1323	−0.634032
$430$	−5.19424	−0.250489
$431$	−30.8184	−1.48447	−0.742234	−	0.670140i	$-0.766234\pi$
$431$	−30.8184	−1.48447	−0.742234	+	0.670140i	$0.766234\pi$
$432$	4.74076	0.228090
$433$	32.7567	1.57419	0.787093	−	0.616834i	$-0.211585\pi$
$433$	32.7567	1.57419	0.787093	+	0.616834i	$0.211585\pi$
$434$	1.08494	0.0520788
$435$	−5.76959	−0.276631
$436$	−2.78582	−0.133416
$437$	−4.26703	−0.204120
$438$	11.1000	0.530378
$439$	2.75765	0.131615	0.0658077	−	0.997832i	$-0.479038\pi$
$439$	2.75765	0.131615	0.0658077	+	0.997832i	$0.479038\pi$
$440$	−9.91662	−0.472756
$441$	14.5878	0.694659
$442$	−8.70735	−0.414166
$443$	−13.0481	−0.619934	−0.309967	−	0.950747i	$-0.600318\pi$
$443$	−13.0481	−0.619934	−0.309967	+	0.950747i	$0.600318\pi$
$444$	0.506204	0.0240234
$445$	18.5652	0.880074
$446$	−14.8190	−0.701698
$447$	−1.64829	−0.0779616
$448$	0.476690	0.0225215
$449$	−5.65400	−0.266829	−0.133414	−	0.991060i	$-0.542594\pi$
$449$	−5.65400	−0.266829	−0.133414	+	0.991060i	$0.542594\pi$
$450$	−2.96506	−0.139774
$451$	20.9598	0.986958
$452$	19.3073	0.908137
$453$	14.0848	0.661764
$454$	3.07690	0.144406
$455$	2.48666	0.116576
$456$	3.92498	0.183804
$457$	−23.5489	−1.10157	−0.550785	−	0.834647i	$-0.685672\pi$
$457$	−23.5489	−1.10157	−0.550785	+	0.834647i	$0.685672\pi$
$458$	−26.3227	−1.22998
$459$	−15.0630	−0.703080
$460$	1.90352	0.0887522
$461$	−9.94663	−0.463261	−0.231630	−	0.972804i	$-0.574406\pi$
$461$	−9.94663	−0.463261	−0.231630	+	0.972804i	$0.574406\pi$
$462$	−2.28430	−0.106275
$463$	6.14787	0.285716	0.142858	−	0.989743i	$-0.454371\pi$
$463$	6.14787	0.285716	0.142858	+	0.989743i	$0.454371\pi$
$464$	−3.29515	−0.152973
$465$	−3.98510	−0.184805
$466$	2.89421	0.134071
$467$	27.6815	1.28095	0.640474	−	0.767980i	$-0.278738\pi$
$467$	27.6815	1.28095	0.640474	+	0.767980i	$0.278738\pi$
$468$	5.90265	0.272850
$469$	−4.81568	−0.222367
$470$	−24.7213	−1.14031
$471$	12.2225	0.563183
$472$	13.9157	0.640523
$473$	14.2157	0.653641
$474$	−1.00650	−0.0462300
$475$	−5.87400	−0.269518
$476$	−1.51461	−0.0694219
$477$	22.4979	1.03011
$478$	−3.88797	−0.177832
$479$	20.8140	0.951014	0.475507	−	0.879712i	$-0.342265\pi$
$479$	20.8140	0.951014	0.475507	+	0.879712i	$0.342265\pi$
$480$	−1.75093	−0.0799189
$481$	1.50812	0.0687643
$482$	26.5153	1.20774
$483$	0.438478	0.0199515
$484$	16.1401	0.733640
$485$	−7.33462	−0.333048
$486$	16.1548	0.732797
$487$	12.2134	0.553440	0.276720	−	0.960951i	$-0.410753\pi$
$487$	12.2134	0.553440	0.276720	+	0.960951i	$0.410753\pi$
$488$	−5.22931	−0.236720
$489$	−17.3320	−0.783781
$490$	−12.8921	−0.582406
$491$	−24.5751	−1.10906	−0.554529	−	0.832164i	$-0.687102\pi$
$491$	−24.5751	−1.10906	−0.554529	+	0.832164i	$0.687102\pi$
$492$	3.70078	0.166844
$493$	10.4698	0.471537
$494$	11.6936	0.526120
$495$	−21.3594	−0.960032
$496$	−2.27599	−0.102195
$497$	0.457626	0.0205273
$498$	−7.55449	−0.338525
$499$	−14.6798	−0.657158	−0.328579	−	0.944476i	$-0.606570\pi$
$499$	−14.6798	−0.657158	−0.328579	+	0.944476i	$0.606570\pi$
$500$	12.1380	0.542828
$501$	7.48702	0.334496
$502$	−0.354503	−0.0158222
$503$	42.3295	1.88738	0.943689	−	0.330833i	$-0.107330\pi$
$503$	42.3295	1.88738	0.943689	+	0.330833i	$0.107330\pi$
$504$	1.02674	0.0457347
$505$	−6.32135	−0.281296
$506$	−5.20961	−0.231596
$507$	5.04984	0.224271
$508$	−15.1447	−0.671936
$509$	−22.2934	−0.988136	−0.494068	−	0.869423i	$-0.664491\pi$
$509$	−22.2934	−0.988136	−0.494068	+	0.869423i	$0.664491\pi$
$510$	5.56332	0.246348
$511$	5.75237	0.254470
$512$	−1.00000	−0.0441942
$513$	20.2289	0.893130
$514$	−19.1170	−0.843214
$515$	36.5299	1.60970
$516$	2.51001	0.110497
$517$	67.6580	2.97560
$518$	0.262331	0.0115262
$519$	8.54177	0.374942
$520$	−5.21651	−0.228759
$521$	−25.1249	−1.10074	−0.550372	−	0.834920i	$-0.685514\pi$
$521$	−25.1249	−1.10074	−0.550372	+	0.834920i	$0.685514\pi$
$522$	−7.09741	−0.310645
$523$	−29.1935	−1.27654	−0.638271	−	0.769812i	$-0.720350\pi$
$523$	−29.1935	−1.27654	−0.638271	+	0.769812i	$0.720350\pi$
$524$	1.00000	0.0436852
$525$	0.603610	0.0263437
$526$	−8.46808	−0.369226
$527$	7.23158	0.315013
$528$	4.79201	0.208545
$529$	1.00000	0.0434783
$530$	−19.8827	−0.863651
$531$	29.9730	1.30072
$532$	2.03405	0.0881873
$533$	11.0256	0.477573
$534$	−8.97125	−0.388224
$535$	0.373497	0.0161477
$536$	10.1023	0.436354
$537$	3.89805	0.168213
$538$	12.8112	0.552332
$539$	35.2835	1.51977
$540$	−9.02413	−0.388337
$541$	−2.12323	−0.0912846	−0.0456423	−	0.998958i	$-0.514533\pi$
$541$	−2.12323	−0.0912846	−0.0456423	+	0.998958i	$0.514533\pi$
$542$	−17.9969	−0.773031
$543$	20.1298	0.863851
$544$	3.17734	0.136227
$545$	5.30286	0.227150
$546$	−1.20163	−0.0514250
$547$	−18.0646	−0.772386	−0.386193	−	0.922418i	$-0.626210\pi$
$547$	−18.0646	−0.772386	−0.386193	+	0.922418i	$0.626210\pi$
$548$	2.55382	0.109094
$549$	−11.2634	−0.480710
$550$	−7.17156	−0.305796
$551$	−14.0605	−0.598997
$552$	−0.919839	−0.0391510
$553$	−0.521600	−0.0221807
$554$	−11.1982	−0.475767
$555$	−0.963570	−0.0409013
$556$	16.1427	0.684605
$557$	16.6772	0.706636	0.353318	−	0.935503i	$-0.385053\pi$
$557$	16.6772	0.706636	0.353318	+	0.935503i	$0.385053\pi$
$558$	−4.90224	−0.207528
$559$	7.47802	0.316286
$560$	−0.907391	−0.0383443
$561$	−15.2258	−0.642835
$562$	31.8752	1.34457
$563$	−45.4108	−1.91384	−0.956919	−	0.290355i	$-0.906227\pi$
$563$	−45.4108	−1.91384	−0.956919	+	0.290355i	$0.906227\pi$
$564$	11.9461	0.503021
$565$	−36.7518	−1.54616
$566$	18.3717	0.772222
$567$	1.00150	0.0420592
$568$	−0.960006	−0.0402810
$569$	9.48614	0.397680	0.198840	−	0.980032i	$-0.436283\pi$
$569$	9.48614	0.397680	0.198840	+	0.980032i	$0.436283\pi$
$570$	−7.47129	−0.312938
$571$	12.9530	0.542067	0.271034	−	0.962570i	$-0.412635\pi$
$571$	12.9530	0.542067	0.271034	+	0.962570i	$0.412635\pi$
$572$	14.2767	0.596939
$573$	−7.58274	−0.316774
$574$	1.91786	0.0800501
$575$	1.37660	0.0574083
$576$	−2.15390	−0.0897457
$577$	−31.9710	−1.33097	−0.665485	−	0.746411i	$-0.731775\pi$
$577$	−31.9710	−1.33097	−0.665485	+	0.746411i	$0.731775\pi$
$578$	6.90450	0.287190
$579$	17.9547	0.746170
$580$	6.27239	0.260447
$581$	−3.91498	−0.162421
$582$	3.54431	0.146916
$583$	54.4156	2.25366
$584$	−12.0673	−0.499349
$585$	−11.2358	−0.464544
$586$	6.32632	0.261338
$587$	−10.4311	−0.430540	−0.215270	−	0.976555i	$-0.569063\pi$
$587$	−10.4311	−0.430540	−0.215270	+	0.976555i	$0.569063\pi$
$588$	6.22986	0.256915
$589$	−9.71170	−0.400164
$590$	−26.4889	−1.09053
$591$	−14.4719	−0.595295
$592$	−0.550318	−0.0226179
$593$	1.01616	0.0417288	0.0208644	−	0.999782i	$-0.493358\pi$
$593$	1.01616	0.0417288	0.0208644	+	0.999782i	$0.493358\pi$
$594$	24.6975	1.01335
$595$	2.88309	0.118195
$596$	1.79194	0.0734006
$597$	−9.70537	−0.397214
$598$	−2.74045	−0.112065
$599$	37.4306	1.52937	0.764687	−	0.644402i	$-0.222894\pi$
$599$	37.4306	1.52937	0.764687	+	0.644402i	$0.222894\pi$
$600$	−1.26625	−0.0516945
$601$	7.38783	0.301356	0.150678	−	0.988583i	$-0.451854\pi$
$601$	7.38783	0.301356	0.150678	+	0.988583i	$0.451854\pi$
$602$	1.30077	0.0530154
$603$	21.7594	0.886110
$604$	−15.3123	−0.623048
$605$	−30.7230	−1.24907
$606$	3.05466	0.124087
$607$	−41.7898	−1.69620	−0.848098	−	0.529839i	$-0.822252\pi$
$607$	−41.7898	−1.69620	−0.848098	+	0.529839i	$0.822252\pi$
$608$	−4.26703	−0.173051
$609$	1.44485	0.0585483
$610$	9.95412	0.403030
$611$	35.5907	1.43984
$612$	6.84366	0.276639
$613$	−21.3451	−0.862119	−0.431059	−	0.902324i	$-0.641860\pi$
$613$	−21.3451	−0.862119	−0.431059	+	0.902324i	$0.641860\pi$
$614$	−26.4027	−1.06553
$615$	−7.04452	−0.284062
$616$	2.48337	0.100058
$617$	−34.1244	−1.37380	−0.686899	−	0.726753i	$-0.741028\pi$
$617$	−34.1244	−1.37380	−0.686899	+	0.726753i	$0.741028\pi$
$618$	−17.6523	−0.710081
$619$	35.4935	1.42660	0.713302	−	0.700857i	$-0.247199\pi$
$619$	35.4935	1.42660	0.713302	+	0.700857i	$0.247199\pi$
$620$	4.33239	0.173993
$621$	−4.74076	−0.190240
$622$	−24.6589	−0.988731
$623$	−4.64919	−0.186266
$624$	2.52078	0.100912
$625$	−16.2220	−0.648878
$626$	14.7925	0.591227
$627$	20.4476	0.816600
$628$	−13.2876	−0.530234
$629$	1.74855	0.0697191
$630$	−1.95442	−0.0778662
$631$	16.0555	0.639160	0.319580	−	0.947559i	$-0.396458\pi$
$631$	16.0555	0.639160	0.319580	+	0.947559i	$0.396458\pi$
$632$	1.09421	0.0435254
$633$	9.59036	0.381183
$634$	4.66150	0.185132
$635$	28.8282	1.14401
$636$	9.60793	0.380979
$637$	18.5604	0.735392
$638$	−17.1664	−0.679626
$639$	−2.06775	−0.0817991
$640$	1.90352	0.0752433
$641$	16.7002	0.659618	0.329809	−	0.944048i	$-0.393016\pi$
$641$	16.7002	0.659618	0.329809	+	0.944048i	$0.393016\pi$
$642$	−0.180485	−0.00712317
$643$	−11.5623	−0.455972	−0.227986	−	0.973664i	$-0.573214\pi$
$643$	−11.5623	−0.455972	−0.227986	+	0.973664i	$0.573214\pi$
$644$	−0.476690	−0.0187842
$645$	−4.77787	−0.188128
$646$	13.5578	0.533425
$647$	−42.9881	−1.69004	−0.845018	−	0.534738i	$-0.820410\pi$
$647$	−42.9881	−1.69004	−0.845018	+	0.534738i	$0.820410\pi$
$648$	−2.10095	−0.0825333
$649$	72.4955	2.84570
$650$	−3.77251	−0.147970
$651$	0.997970	0.0391135
$652$	18.8424	0.737927
$653$	−37.5639	−1.46999	−0.734995	−	0.678073i	$-0.762816\pi$
$653$	−37.5639	−1.46999	−0.734995	+	0.678073i	$0.762816\pi$
$654$	−2.56250	−0.100202
$655$	−1.90352	−0.0743768
$656$	−4.02329	−0.157083
$657$	−25.9917	−1.01403
$658$	6.19085	0.241344
$659$	0.581869	0.0226664	0.0113332	−	0.999936i	$-0.496392\pi$
$659$	0.581869	0.0226664	0.0113332	+	0.999936i	$0.496392\pi$
$660$	−9.12169	−0.355061
$661$	3.00487	0.116876	0.0584379	−	0.998291i	$-0.481388\pi$
$661$	3.00487	0.116876	0.0584379	+	0.998291i	$0.481388\pi$
$662$	−10.8221	−0.420611
$663$	−8.00936	−0.311058
$664$	8.21284	0.318720
$665$	−3.87186	−0.150144
$666$	−1.18533	−0.0459305
$667$	3.29515	0.127589
$668$	−8.13949	−0.314926
$669$	−13.6311	−0.527007
$670$	−19.2300	−0.742920
$671$	−27.2427	−1.05169
$672$	0.438478	0.0169147
$673$	−37.9804	−1.46404	−0.732019	−	0.681284i	$-0.761422\pi$
$673$	−37.9804	−1.46404	−0.732019	+	0.681284i	$0.761422\pi$
$674$	24.9035	0.959247
$675$	−6.52613	−0.251191
$676$	−5.48992	−0.211151
$677$	−3.16151	−0.121507	−0.0607533	−	0.998153i	$-0.519350\pi$
$677$	−3.16151	−0.121507	−0.0607533	+	0.998153i	$0.519350\pi$
$678$	17.7596	0.682052
$679$	1.83677	0.0704889
$680$	−6.04814	−0.231936
$681$	2.83026	0.108456
$682$	−11.8570	−0.454028
$683$	50.5640	1.93478	0.967389	−	0.253296i	$-0.0815146\pi$
$683$	50.5640	1.93478	0.967389	+	0.253296i	$0.0815146\pi$
$684$	−9.19074	−0.351417
$685$	−4.86126	−0.185739
$686$	6.56534	0.250666
$687$	−24.2127	−0.923771
$688$	−2.72875	−0.104033
$689$	28.6247	1.09051
$690$	1.75093	0.0666569
$691$	27.8254	1.05853	0.529265	−	0.848457i	$-0.322468\pi$
$691$	27.8254	1.05853	0.529265	+	0.848457i	$0.322468\pi$
$692$	−9.28616	−0.353007
$693$	5.34892	0.203189
$694$	−19.6680	−0.746586
$695$	−30.7281	−1.16558
$696$	−3.03101	−0.114890
$697$	12.7834	0.484205
$698$	8.32179	0.314985
$699$	2.66220	0.100694
$700$	−0.656213	−0.0248025
$701$	−1.82789	−0.0690385	−0.0345193	−	0.999404i	$-0.510990\pi$
$701$	−1.82789	−0.0690385	−0.0345193	+	0.999404i	$0.510990\pi$
$702$	12.9918	0.490344
$703$	−2.34822	−0.0885649
$704$	−5.20961	−0.196345
$705$	−22.7396	−0.856425
$706$	−2.67587	−0.100708
$707$	1.58303	0.0595358
$708$	12.8002	0.481062
$709$	−21.8811	−0.821762	−0.410881	−	0.911689i	$-0.634779\pi$
$709$	−21.8811	−0.821762	−0.410881	+	0.911689i	$0.634779\pi$
$710$	1.82739	0.0685809
$711$	2.35682	0.0883876
$712$	9.75306	0.365511
$713$	2.27599	0.0852363
$714$	−1.39320	−0.0521390
$715$	−27.1760	−1.01633
$716$	−4.23775	−0.158372
$717$	−3.57631	−0.133560
$718$	13.5980	0.507472
$719$	−24.9257	−0.929572	−0.464786	−	0.885423i	$-0.653869\pi$
$719$	−24.9257	−0.929572	−0.464786	+	0.885423i	$0.653869\pi$
$720$	4.09999	0.152798
$721$	−9.14801	−0.340690
$722$	0.792448	0.0294918
$723$	24.3898	0.907066
$724$	−21.8840	−0.813312
$725$	4.53611	0.168467
$726$	14.8463	0.550997
$727$	10.1997	0.378286	0.189143	−	0.981950i	$-0.439429\pi$
$727$	10.1997	0.378286	0.189143	+	0.981950i	$0.439429\pi$
$728$	1.30635	0.0484164
$729$	8.55696	0.316924
$730$	22.9704	0.850173
$731$	8.67018	0.320678
$732$	−4.81013	−0.177787
$733$	−12.2132	−0.451104	−0.225552	−	0.974231i	$-0.572419\pi$
$733$	−12.2132	−0.451104	−0.225552	+	0.974231i	$0.572419\pi$
$734$	−10.9177	−0.402978
$735$	−11.8587	−0.437414
$736$	1.00000	0.0368605
$737$	52.6292	1.93862
$738$	−8.66575	−0.318991
$739$	−0.905165	−0.0332970	−0.0166485	−	0.999861i	$-0.505300\pi$
$739$	−0.905165	−0.0332970	−0.0166485	+	0.999861i	$0.505300\pi$
$740$	1.04754	0.0385084
$741$	10.7562	0.395140
$742$	4.97914	0.182790
$743$	−26.8042	−0.983351	−0.491676	−	0.870778i	$-0.663615\pi$
$743$	−26.8042	−0.983351	−0.491676	+	0.870778i	$0.663615\pi$
$744$	−2.09354	−0.0767529
$745$	−3.41099	−0.124969
$746$	−6.35513	−0.232678
$747$	17.6896	0.647229
$748$	16.5527	0.605227
$749$	−0.0935330	−0.00341762
$750$	11.1650	0.407689
$751$	−21.6256	−0.789131	−0.394565	−	0.918868i	$-0.629105\pi$
$751$	−21.6256	−0.789131	−0.394565	+	0.918868i	$0.629105\pi$
$752$	−12.9871	−0.473593
$753$	−0.326086	−0.0118832
$754$	−9.03020	−0.328860
$755$	29.1473	1.06078
$756$	2.25987	0.0821907
$757$	−20.9802	−0.762538	−0.381269	−	0.924464i	$-0.624513\pi$
$757$	−20.9802	−0.762538	−0.381269	+	0.924464i	$0.624513\pi$
$758$	−18.3951	−0.668141
$759$	−4.79201	−0.173939
$760$	8.12239	0.294630
$761$	43.9504	1.59320	0.796600	−	0.604506i	$-0.206630\pi$
$761$	43.9504	1.59320	0.796600	+	0.604506i	$0.206630\pi$
$762$	−13.9307	−0.504654
$763$	−1.32797	−0.0480758
$764$	8.24355	0.298241
$765$	−13.0271	−0.470995
$766$	28.1149	1.01583
$767$	38.1354	1.37699
$768$	−0.919839	−0.0331918
$769$	−42.3697	−1.52789	−0.763945	−	0.645282i	$-0.776740\pi$
$769$	−42.3697	−1.52789	−0.763945	+	0.645282i	$0.776740\pi$
$770$	−4.72715	−0.170355
$771$	−17.5845	−0.633292
$772$	−19.5193	−0.702517
$773$	25.9093	0.931892	0.465946	−	0.884813i	$-0.345714\pi$
$773$	25.9093	0.931892	0.465946	+	0.884813i	$0.345714\pi$
$774$	−5.87745	−0.211261
$775$	3.13313	0.112545
$776$	−3.85318	−0.138321
$777$	0.241302	0.00865668
$778$	15.4953	0.555532
$779$	−17.1675	−0.615090
$780$	−4.79835	−0.171809
$781$	−5.00126	−0.178959
$782$	−3.17734	−0.113621
$783$	−15.6215	−0.558267
$784$	−6.77277	−0.241885
$785$	25.2933	0.902757
$786$	0.919839	0.0328096
$787$	17.8321	0.635647	0.317823	−	0.948150i	$-0.397048\pi$
$787$	17.8321	0.635647	0.317823	+	0.948150i	$0.397048\pi$
$788$	15.7331	0.560468
$789$	−7.78927	−0.277306
$790$	−2.08286	−0.0741047
$791$	9.20358	0.327242
$792$	−11.2210	−0.398720
$793$	−14.3307	−0.508898
$794$	−36.8869	−1.30907
$795$	−18.2889	−0.648641
$796$	10.5512	0.373976
$797$	20.6565	0.731692	0.365846	−	0.930675i	$-0.380780\pi$
$797$	20.6565	0.731692	0.365846	+	0.930675i	$0.380780\pi$
$798$	1.87100	0.0662327
$799$	41.2646	1.45984
$800$	1.37660	0.0486702
$801$	21.0071	0.742249
$802$	−33.9375	−1.19838
$803$	−62.8660	−2.21849
$804$	9.29252	0.327722
$805$	0.907391	0.0319813
$806$	−6.23723	−0.219697
$807$	11.7843	0.414827
$808$	−3.32087	−0.116828
$809$	21.8616	0.768612	0.384306	−	0.923206i	$-0.374441\pi$
$809$	21.8616	0.768612	0.384306	+	0.923206i	$0.374441\pi$
$810$	3.99921	0.140518
$811$	−21.8666	−0.767840	−0.383920	−	0.923366i	$-0.625426\pi$
$811$	−21.8666	−0.767840	−0.383920	+	0.923366i	$0.625426\pi$
$812$	−1.57077	−0.0551231
$813$	−16.5542	−0.580582
$814$	−2.86694	−0.100486
$815$	−35.8670	−1.25637
$816$	2.92264	0.102313
$817$	−11.6437	−0.407360
$818$	−30.8015	−1.07695
$819$	2.81374	0.0983199
$820$	7.65843	0.267444
$821$	8.55956	0.298731	0.149365	−	0.988782i	$-0.452277\pi$
$821$	8.55956	0.298731	0.149365	+	0.988782i	$0.452277\pi$
$822$	2.34910	0.0819344
$823$	−48.1971	−1.68004	−0.840022	−	0.542553i	$-0.817458\pi$
$823$	−48.1971	−1.68004	−0.840022	+	0.542553i	$0.817458\pi$
$824$	19.1907	0.668539
$825$	−6.59669	−0.229667
$826$	6.63349	0.230808
$827$	−3.82244	−0.132919	−0.0664597	−	0.997789i	$-0.521170\pi$
$827$	−3.82244	−0.132919	−0.0664597	+	0.997789i	$0.521170\pi$
$828$	2.15390	0.0748531
$829$	6.65210	0.231037	0.115518	−	0.993305i	$-0.463147\pi$
$829$	6.65210	0.231037	0.115518	+	0.993305i	$0.463147\pi$
$830$	−15.6333	−0.542641
$831$	−10.3006	−0.357323
$832$	−2.74045	−0.0950081
$833$	21.5194	0.745603
$834$	14.8487	0.514170
$835$	15.4937	0.536182
$836$	−22.2296	−0.768826
$837$	−10.7899	−0.372953
$838$	−24.0157	−0.829609
$839$	24.5745	0.848404	0.424202	−	0.905567i	$-0.360555\pi$
$839$	24.5745	0.848404	0.424202	+	0.905567i	$0.360555\pi$
$840$	−0.834653	−0.0287983
$841$	−18.1420	−0.625586
$842$	−14.8510	−0.511801
$843$	29.3200	1.00984
$844$	−10.4261	−0.358882
$845$	10.4502	0.359497
$846$	−27.9730	−0.961730
$847$	7.69381	0.264363
$848$	−10.4452	−0.358691
$849$	16.8991	0.579974
$850$	−4.37393	−0.150025
$851$	0.550318	0.0188646
$852$	−0.883052	−0.0302528
$853$	31.8719	1.09127	0.545637	−	0.838021i	$-0.316288\pi$
$853$	31.8719	1.09127	0.545637	+	0.838021i	$0.316288\pi$
$854$	−2.49276	−0.0853006
$855$	17.4948	0.598309
$856$	0.196213	0.00670643
$857$	−24.9736	−0.853082	−0.426541	−	0.904468i	$-0.640268\pi$
$857$	−24.9736	−0.853082	−0.426541	+	0.904468i	$0.640268\pi$
$858$	13.1323	0.448328
$859$	32.3987	1.10543	0.552715	−	0.833370i	$-0.313592\pi$
$859$	32.3987	1.10543	0.552715	+	0.833370i	$0.313592\pi$
$860$	5.19424	0.177122
$861$	1.76413	0.0601213
$862$	30.8184	1.04968
$863$	−48.8593	−1.66319	−0.831595	−	0.555383i	$-0.812572\pi$
$863$	−48.8593	−1.66319	−0.831595	+	0.555383i	$0.812572\pi$
$864$	−4.74076	−0.161284
$865$	17.6764	0.601016
$866$	−32.7567	−1.11312
$867$	6.35103	0.215692
$868$	−1.08494	−0.0368253
$869$	5.70042	0.193374
$870$	5.76959	0.195607
$871$	27.6849	0.938069
$872$	2.78582	0.0943396
$873$	−8.29935	−0.280890
$874$	4.26703	0.144334
$875$	5.78607	0.195605
$876$	−11.1000	−0.375034
$877$	−10.8443	−0.366185	−0.183092	−	0.983096i	$-0.558611\pi$
$877$	−10.8443	−0.366185	−0.183092	+	0.983096i	$0.558611\pi$
$878$	−2.75765	−0.0930662
$879$	5.81919	0.196277
$880$	9.91662	0.334289
$881$	44.7607	1.50802	0.754012	−	0.656860i	$-0.228116\pi$
$881$	44.7607	1.50802	0.754012	+	0.656860i	$0.228116\pi$
$882$	−14.5878	−0.491198
$883$	−13.0964	−0.440728	−0.220364	−	0.975418i	$-0.570725\pi$
$883$	−13.0964	−0.440728	−0.220364	+	0.975418i	$0.570725\pi$
$884$	8.70735	0.292860
$885$	−24.3655	−0.819038
$886$	13.0481	0.438360
$887$	25.0946	0.842594	0.421297	−	0.906923i	$-0.361575\pi$
$887$	25.0946	0.842594	0.421297	+	0.906923i	$0.361575\pi$
$888$	−0.506204	−0.0169871
$889$	−7.21931	−0.242128
$890$	−18.5652	−0.622306
$891$	−10.9452	−0.366677
$892$	14.8190	0.496175
$893$	−55.4166	−1.85444
$894$	1.64829	0.0551272
$895$	8.06665	0.269638
$896$	−0.476690	−0.0159251
$897$	−2.52078	−0.0841662
$898$	5.65400	0.188676
$899$	7.49971	0.250129
$900$	2.96506	0.0988352
$901$	33.1881	1.10565
$902$	−20.9598	−0.697885
$903$	1.19650	0.0398170
$904$	−19.3073	−0.642150
$905$	41.6567	1.38472
$906$	−14.0848	−0.467938
$907$	−35.3915	−1.17515	−0.587577	−	0.809168i	$-0.699918\pi$
$907$	−35.3915	−1.17515	−0.587577	+	0.809168i	$0.699918\pi$
$908$	−3.07690	−0.102111
$909$	−7.15280	−0.237243
$910$	−2.48666	−0.0824320
$911$	−37.5397	−1.24374	−0.621872	−	0.783119i	$-0.713628\pi$
$911$	−37.5397	−1.24374	−0.621872	+	0.783119i	$0.713628\pi$
$912$	−3.92498	−0.129969
$913$	42.7857	1.41600
$914$	23.5489	0.778927
$915$	9.15619	0.302694
$916$	26.3227	0.869728
$917$	0.476690	0.0157417
$918$	15.0630	0.497153
$919$	50.7504	1.67410	0.837050	−	0.547126i	$-0.184278\pi$
$919$	50.7504	1.67410	0.837050	+	0.547126i	$0.184278\pi$
$920$	−1.90352	−0.0627573
$921$	−24.2863	−0.800259
$922$	9.94663	0.327575
$923$	−2.63085	−0.0865955
$924$	2.28430	0.0751480
$925$	0.757568	0.0249087
$926$	−6.14787	−0.202032
$927$	41.3347	1.35761
$928$	3.29515	0.108169
$929$	−46.1700	−1.51479	−0.757395	−	0.652957i	$-0.773528\pi$
$929$	−46.1700	−1.51479	−0.757395	+	0.652957i	$0.773528\pi$
$930$	3.98510	0.130677
$931$	−28.8996	−0.947146
$932$	−2.89421	−0.0948029
$933$	−22.6822	−0.742582
$934$	−27.6815	−0.905767
$935$	−31.5085	−1.03044
$936$	−5.90265	−0.192934
$937$	−27.8323	−0.909242	−0.454621	−	0.890685i	$-0.650225\pi$
$937$	−27.8323	−0.909242	−0.454621	+	0.890685i	$0.650225\pi$
$938$	4.81568	0.157238
$939$	13.6067	0.444038
$940$	24.7213	0.806321
$941$	−48.8855	−1.59362	−0.796810	−	0.604230i	$-0.793481\pi$
$941$	−48.8855	−1.59362	−0.796810	+	0.604230i	$0.793481\pi$
$942$	−12.2225	−0.398230
$943$	4.02329	0.131016
$944$	−13.9157	−0.452918
$945$	−4.30172	−0.139935
$946$	−14.2157	−0.462194
$947$	2.94993	0.0958598	0.0479299	−	0.998851i	$-0.484738\pi$
$947$	2.94993	0.0958598	0.0479299	+	0.998851i	$0.484738\pi$
$948$	1.00650	0.0326896
$949$	−33.0699	−1.07349
$950$	5.87400	0.190578
$951$	4.28783	0.139042
$952$	1.51461	0.0490887
$953$	−23.2883	−0.754383	−0.377192	−	0.926135i	$-0.623110\pi$
$953$	−23.2883	−0.754383	−0.377192	+	0.926135i	$0.623110\pi$
$954$	−22.4979	−0.728398
$955$	−15.6918	−0.507774
$956$	3.88797	0.125746
$957$	−15.7904	−0.510430
$958$	−20.8140	−0.672468
$959$	1.21738	0.0393113
$960$	1.75093	0.0565112
$961$	−25.8199	−0.832900
$962$	−1.50812	−0.0486237
$963$	0.422623	0.0136188
$964$	−26.5153	−0.854000
$965$	37.1555	1.19608
$966$	−0.438478	−0.0141078
$967$	3.25403	0.104642	0.0523212	−	0.998630i	$-0.483338\pi$
$967$	3.25403	0.104642	0.0523212	+	0.998630i	$0.483338\pi$
$968$	−16.1401	−0.518762
$969$	12.4710	0.400626
$970$	7.33462	0.235500
$971$	7.13533	0.228984	0.114492	−	0.993424i	$-0.463476\pi$
$971$	7.13533	0.228984	0.114492	+	0.993424i	$0.463476\pi$
$972$	−16.1548	−0.518166
$973$	7.69509	0.246693
$974$	−12.2134	−0.391341
$975$	−3.47010	−0.111132
$976$	5.22931	0.167386
$977$	8.57851	0.274451	0.137225	−	0.990540i	$-0.456182\pi$
$977$	8.57851	0.274451	0.137225	+	0.990540i	$0.456182\pi$
$978$	17.3320	0.554217
$979$	50.8097	1.62388
$980$	12.8921	0.411823
$981$	6.00036	0.191577
$982$	24.5751	0.784223
$983$	54.8251	1.74865	0.874325	−	0.485340i	$-0.161304\pi$
$983$	54.8251	1.74865	0.874325	+	0.485340i	$0.161304\pi$
$984$	−3.70078	−0.117977
$985$	−29.9483	−0.954231
$986$	−10.4698	−0.333427
$987$	5.69458	0.181261
$988$	−11.6936	−0.372023
$989$	2.72875	0.0867693
$990$	21.3594	0.678845
$991$	−44.4343	−1.41150	−0.705752	−	0.708459i	$-0.749391\pi$
$991$	−44.4343	−1.41150	−0.705752	+	0.708459i	$0.749391\pi$
$992$	2.27599	0.0722626
$993$	−9.95455	−0.315898
$994$	−0.457626	−0.0145150
$995$	−20.0844	−0.636718
$996$	7.55449	0.239373
$997$	−19.5805	−0.620121	−0.310060	−	0.950717i	$-0.600349\pi$
$997$	−19.5805	−0.620121	−0.310060	+	0.950717i	$0.600349\pi$
$998$	14.6798	0.464681
$999$	−2.60892	−0.0825426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.13	✓	36	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.919839 q^{3} +1.00000 q^{4} -1.90352 q^{5} +0.919839 q^{6} +0.476690 q^{7} -1.00000 q^{8} -2.15390 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.919839 q^{3} +1.00000 q^{4} -1.90352 q^{5} +0.919839 q^{6} +0.476690 q^{7} -1.00000 q^{8} -2.15390 q^{9} +1.90352 q^{10} -5.20961 q^{11} -0.919839 q^{12} -2.74045 q^{13} -0.476690 q^{14} +1.75093 q^{15} +1.00000 q^{16} -3.17734 q^{17} +2.15390 q^{18} +4.26703 q^{19} -1.90352 q^{20} -0.438478 q^{21} +5.20961 q^{22} -1.00000 q^{23} +0.919839 q^{24} -1.37660 q^{25} +2.74045 q^{26} +4.74076 q^{27} +0.476690 q^{28} -3.29515 q^{29} -1.75093 q^{30} -2.27599 q^{31} -1.00000 q^{32} +4.79201 q^{33} +3.17734 q^{34} -0.907391 q^{35} -2.15390 q^{36} -0.550318 q^{37} -4.26703 q^{38} +2.52078 q^{39} +1.90352 q^{40} -4.02329 q^{41} +0.438478 q^{42} -2.72875 q^{43} -5.20961 q^{44} +4.09999 q^{45} +1.00000 q^{46} -12.9871 q^{47} -0.919839 q^{48} -6.77277 q^{49} +1.37660 q^{50} +2.92264 q^{51} -2.74045 q^{52} -10.4452 q^{53} -4.74076 q^{54} +9.91662 q^{55} -0.476690 q^{56} -3.92498 q^{57} +3.29515 q^{58} -13.9157 q^{59} +1.75093 q^{60} +5.22931 q^{61} +2.27599 q^{62} -1.02674 q^{63} +1.00000 q^{64} +5.21651 q^{65} -4.79201 q^{66} -10.1023 q^{67} -3.17734 q^{68} +0.919839 q^{69} +0.907391 q^{70} +0.960006 q^{71} +2.15390 q^{72} +12.0673 q^{73} +0.550318 q^{74} +1.26625 q^{75} +4.26703 q^{76} -2.48337 q^{77} -2.52078 q^{78} -1.09421 q^{79} -1.90352 q^{80} +2.10095 q^{81} +4.02329 q^{82} -8.21284 q^{83} -0.438478 q^{84} +6.04814 q^{85} +2.72875 q^{86} +3.03101 q^{87} +5.20961 q^{88} -9.75306 q^{89} -4.09999 q^{90} -1.30635 q^{91} -1.00000 q^{92} +2.09354 q^{93} +12.9871 q^{94} -8.12239 q^{95} +0.919839 q^{96} +3.85318 q^{97} +6.77277 q^{98} +11.2210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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