LMFDB - Embedded newform 6010.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.00989 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00989 q^{6} -0.566476 q^{7} -1.00000 q^{8} +1.03966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.00989 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00989 q^{6} -0.566476 q^{7} -1.00000 q^{8} +1.03966 q^{9} -1.00000 q^{10} -3.22347 q^{11} -2.00989 q^{12} +1.91368 q^{13} +0.566476 q^{14} -2.00989 q^{15} +1.00000 q^{16} +6.98779 q^{17} -1.03966 q^{18} +7.08539 q^{19} +1.00000 q^{20} +1.13856 q^{21} +3.22347 q^{22} +5.48539 q^{23} +2.00989 q^{24} +1.00000 q^{25} -1.91368 q^{26} +3.94006 q^{27} -0.566476 q^{28} +3.17044 q^{29} +2.00989 q^{30} +7.24049 q^{31} -1.00000 q^{32} +6.47882 q^{33} -6.98779 q^{34} -0.566476 q^{35} +1.03966 q^{36} -10.8293 q^{37} -7.08539 q^{38} -3.84629 q^{39} -1.00000 q^{40} -2.88732 q^{41} -1.13856 q^{42} +2.55329 q^{43} -3.22347 q^{44} +1.03966 q^{45} -5.48539 q^{46} +0.387208 q^{47} -2.00989 q^{48} -6.67910 q^{49} -1.00000 q^{50} -14.0447 q^{51} +1.91368 q^{52} -2.94317 q^{53} -3.94006 q^{54} -3.22347 q^{55} +0.566476 q^{56} -14.2409 q^{57} -3.17044 q^{58} +0.646086 q^{59} -2.00989 q^{60} +15.3973 q^{61} -7.24049 q^{62} -0.588945 q^{63} +1.00000 q^{64} +1.91368 q^{65} -6.47882 q^{66} +1.36036 q^{67} +6.98779 q^{68} -11.0250 q^{69} +0.566476 q^{70} +11.3277 q^{71} -1.03966 q^{72} -13.9379 q^{73} +10.8293 q^{74} -2.00989 q^{75} +7.08539 q^{76} +1.82602 q^{77} +3.84629 q^{78} -6.99325 q^{79} +1.00000 q^{80} -11.0381 q^{81} +2.88732 q^{82} -15.6119 q^{83} +1.13856 q^{84} +6.98779 q^{85} -2.55329 q^{86} -6.37224 q^{87} +3.22347 q^{88} -0.856725 q^{89} -1.03966 q^{90} -1.08405 q^{91} +5.48539 q^{92} -14.5526 q^{93} -0.387208 q^{94} +7.08539 q^{95} +2.00989 q^{96} -10.0439 q^{97} +6.67910 q^{98} -3.35133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.00989	−1.16041	−0.580206	−	0.814470i	$-0.697028\pi$
$3$	−2.00989	−1.16041	−0.580206	+	0.814470i	$0.697028\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00989	0.820535
$7$	−0.566476	−0.214108	−0.107054	−	0.994253i	$-0.534142\pi$
$7$	−0.566476	−0.214108	−0.107054	+	0.994253i	$0.534142\pi$
$8$	−1.00000	−0.353553
$9$	1.03966	0.346555
$10$	−1.00000	−0.316228
$11$	−3.22347	−0.971913	−0.485956	−	0.873983i	$-0.661529\pi$
$11$	−3.22347	−0.971913	−0.485956	+	0.873983i	$0.661529\pi$
$12$	−2.00989	−0.580206
$13$	1.91368	0.530760	0.265380	−	0.964144i	$-0.414503\pi$
$13$	1.91368	0.530760	0.265380	+	0.964144i	$0.414503\pi$
$14$	0.566476	0.151397
$15$	−2.00989	−0.518952
$16$	1.00000	0.250000
$17$	6.98779	1.69479	0.847394	−	0.530964i	$-0.178170\pi$
$17$	6.98779	1.69479	0.847394	+	0.530964i	$0.178170\pi$
$18$	−1.03966	−0.245051
$19$	7.08539	1.62550	0.812750	−	0.582612i	$-0.197969\pi$
$19$	7.08539	1.62550	0.812750	+	0.582612i	$0.197969\pi$
$20$	1.00000	0.223607
$21$	1.13856	0.248453
$22$	3.22347	0.687246
$23$	5.48539	1.14378	0.571892	−	0.820329i	$-0.306210\pi$
$23$	5.48539	1.14378	0.571892	+	0.820329i	$0.306210\pi$
$24$	2.00989	0.410267
$25$	1.00000	0.200000
$26$	−1.91368	−0.375304
$27$	3.94006	0.758265
$28$	−0.566476	−0.107054
$29$	3.17044	0.588736	0.294368	−	0.955692i	$-0.404891\pi$
$29$	3.17044	0.588736	0.294368	+	0.955692i	$0.404891\pi$
$30$	2.00989	0.366954
$31$	7.24049	1.30043	0.650216	−	0.759750i	$-0.274679\pi$
$31$	7.24049	1.30043	0.650216	+	0.759750i	$0.274679\pi$
$32$	−1.00000	−0.176777
$33$	6.47882	1.12782
$34$	−6.98779	−1.19840
$35$	−0.566476	−0.0957519
$36$	1.03966	0.173277
$37$	−10.8293	−1.78033	−0.890163	−	0.455643i	$-0.849409\pi$
$37$	−10.8293	−1.78033	−0.890163	+	0.455643i	$0.849409\pi$
$38$	−7.08539	−1.14940
$39$	−3.84629	−0.615900
$40$	−1.00000	−0.158114
$41$	−2.88732	−0.450923	−0.225462	−	0.974252i	$-0.572389\pi$
$41$	−2.88732	−0.450923	−0.225462	+	0.974252i	$0.572389\pi$
$42$	−1.13856	−0.175683
$43$	2.55329	0.389373	0.194686	−	0.980866i	$-0.437631\pi$
$43$	2.55329	0.389373	0.194686	+	0.980866i	$0.437631\pi$
$44$	−3.22347	−0.485956
$45$	1.03966	0.154984
$46$	−5.48539	−0.808777
$47$	0.387208	0.0564801	0.0282401	−	0.999601i	$-0.491010\pi$
$47$	0.387208	0.0564801	0.0282401	+	0.999601i	$0.491010\pi$
$48$	−2.00989	−0.290103
$49$	−6.67910	−0.954158
$50$	−1.00000	−0.141421
$51$	−14.0447	−1.96665
$52$	1.91368	0.265380
$53$	−2.94317	−0.404276	−0.202138	−	0.979357i	$-0.564789\pi$
$53$	−2.94317	−0.404276	−0.202138	+	0.979357i	$0.564789\pi$
$54$	−3.94006	−0.536175
$55$	−3.22347	−0.434653
$56$	0.566476	0.0756985
$57$	−14.2409	−1.88625
$58$	−3.17044	−0.416299
$59$	0.646086	0.0841132	0.0420566	−	0.999115i	$-0.486609\pi$
$59$	0.646086	0.0841132	0.0420566	+	0.999115i	$0.486609\pi$
$60$	−2.00989	−0.259476
$61$	15.3973	1.97142	0.985710	−	0.168449i	$-0.0538759\pi$
$61$	15.3973	1.97142	0.985710	+	0.168449i	$0.0538759\pi$
$62$	−7.24049	−0.919544
$63$	−0.588945	−0.0742001
$64$	1.00000	0.125000
$65$	1.91368	0.237363
$66$	−6.47882	−0.797488
$67$	1.36036	0.166195	0.0830973	−	0.996541i	$-0.473519\pi$
$67$	1.36036	0.166195	0.0830973	+	0.996541i	$0.473519\pi$
$68$	6.98779	0.847394
$69$	−11.0250	−1.32726
$70$	0.566476	0.0677068
$71$	11.3277	1.34435	0.672177	−	0.740390i	$-0.265359\pi$
$71$	11.3277	1.34435	0.672177	+	0.740390i	$0.265359\pi$
$72$	−1.03966	−0.122526
$73$	−13.9379	−1.63131	−0.815655	−	0.578538i	$-0.803623\pi$
$73$	−13.9379	−1.63131	−0.815655	+	0.578538i	$0.803623\pi$
$74$	10.8293	1.25888
$75$	−2.00989	−0.232082
$76$	7.08539	0.812750
$77$	1.82602	0.208094
$78$	3.84629	0.435507
$79$	−6.99325	−0.786802	−0.393401	−	0.919367i	$-0.628702\pi$
$79$	−6.99325	−0.786802	−0.393401	+	0.919367i	$0.628702\pi$
$80$	1.00000	0.111803
$81$	−11.0381	−1.22645
$82$	2.88732	0.318851
$83$	−15.6119	−1.71363	−0.856815	−	0.515624i	$-0.827560\pi$
$83$	−15.6119	−1.71363	−0.856815	+	0.515624i	$0.827560\pi$
$84$	1.13856	0.124227
$85$	6.98779	0.757932
$86$	−2.55329	−0.275328
$87$	−6.37224	−0.683176
$88$	3.22347	0.343623
$89$	−0.856725	−0.0908127	−0.0454063	−	0.998969i	$-0.514458\pi$
$89$	−0.856725	−0.0908127	−0.0454063	+	0.998969i	$0.514458\pi$
$90$	−1.03966	−0.109590
$91$	−1.08405	−0.113640
$92$	5.48539	0.571892
$93$	−14.5526	−1.50904
$94$	−0.387208	−0.0399375
$95$	7.08539	0.726946
$96$	2.00989	0.205134
$97$	−10.0439	−1.01980	−0.509900	−	0.860234i	$-0.670318\pi$
$97$	−10.0439	−1.01980	−0.509900	+	0.860234i	$0.670318\pi$
$98$	6.67910	0.674691
$99$	−3.35133	−0.336821
$100$	1.00000	0.100000
$101$	4.00313	0.398326	0.199163	−	0.979966i	$-0.436178\pi$
$101$	4.00313	0.398326	0.199163	+	0.979966i	$0.436178\pi$
$102$	14.0447	1.39063
$103$	1.20199	0.118435	0.0592176	−	0.998245i	$-0.481139\pi$
$103$	1.20199	0.118435	0.0592176	+	0.998245i	$0.481139\pi$
$104$	−1.91368	−0.187652
$105$	1.13856	0.111112
$106$	2.94317	0.285866
$107$	9.35534	0.904415	0.452207	−	0.891913i	$-0.350637\pi$
$107$	9.35534	0.904415	0.452207	+	0.891913i	$0.350637\pi$
$108$	3.94006	0.379133
$109$	6.13328	0.587462	0.293731	−	0.955888i	$-0.405103\pi$
$109$	6.13328	0.587462	0.293731	+	0.955888i	$0.405103\pi$
$110$	3.22347	0.307346
$111$	21.7657	2.06591
$112$	−0.566476	−0.0535270
$113$	11.8653	1.11620	0.558098	−	0.829775i	$-0.311531\pi$
$113$	11.8653	1.11620	0.558098	+	0.829775i	$0.311531\pi$
$114$	14.2409	1.33378
$115$	5.48539	0.511516
$116$	3.17044	0.294368
$117$	1.98959	0.183937
$118$	−0.646086	−0.0594770
$119$	−3.95842	−0.362867
$120$	2.00989	0.183477
$121$	−0.609245	−0.0553859
$122$	−15.3973	−1.39400
$123$	5.80319	0.523256
$124$	7.24049	0.650216
$125$	1.00000	0.0894427
$126$	0.588945	0.0524674
$127$	0.720232	0.0639103	0.0319551	−	0.999489i	$-0.489827\pi$
$127$	0.720232	0.0639103	0.0319551	+	0.999489i	$0.489827\pi$
$128$	−1.00000	−0.0883883
$129$	−5.13183	−0.451832
$130$	−1.91368	−0.167841
$131$	−2.50921	−0.219231	−0.109616	−	0.993974i	$-0.534962\pi$
$131$	−2.50921	−0.219231	−0.109616	+	0.993974i	$0.534962\pi$
$132$	6.47882	0.563909
$133$	−4.01370	−0.348032
$134$	−1.36036	−0.117517
$135$	3.94006	0.339107
$136$	−6.98779	−0.599198
$137$	2.22822	0.190370	0.0951848	−	0.995460i	$-0.469656\pi$
$137$	2.22822	0.190370	0.0951848	+	0.995460i	$0.469656\pi$
$138$	11.0250	0.938514
$139$	2.75665	0.233816	0.116908	−	0.993143i	$-0.462702\pi$
$139$	2.75665	0.233816	0.116908	+	0.993143i	$0.462702\pi$
$140$	−0.566476	−0.0478760
$141$	−0.778247	−0.0655402
$142$	−11.3277	−0.950602
$143$	−6.16869	−0.515852
$144$	1.03966	0.0866387
$145$	3.17044	0.263291
$146$	13.9379	1.15351
$147$	13.4243	1.10722
$148$	−10.8293	−0.890163
$149$	7.91218	0.648191	0.324095	−	0.946024i	$-0.394940\pi$
$149$	7.91218	0.648191	0.324095	+	0.946024i	$0.394940\pi$
$150$	2.00989	0.164107
$151$	6.99670	0.569383	0.284692	−	0.958619i	$-0.408109\pi$
$151$	6.99670	0.569383	0.284692	+	0.958619i	$0.408109\pi$
$152$	−7.08539	−0.574701
$153$	7.26496	0.587337
$154$	−1.82602	−0.147145
$155$	7.24049	0.581570
$156$	−3.84629	−0.307950
$157$	−2.61815	−0.208951	−0.104476	−	0.994527i	$-0.533316\pi$
$157$	−2.61815	−0.208951	−0.104476	+	0.994527i	$0.533316\pi$
$158$	6.99325	0.556353
$159$	5.91546	0.469126
$160$	−1.00000	−0.0790569
$161$	−3.10734	−0.244893
$162$	11.0381	0.867234
$163$	5.98741	0.468970	0.234485	−	0.972120i	$-0.424660\pi$
$163$	5.98741	0.468970	0.234485	+	0.972120i	$0.424660\pi$
$164$	−2.88732	−0.225462
$165$	6.47882	0.504376
$166$	15.6119	1.21172
$167$	12.5414	0.970482	0.485241	−	0.874380i	$-0.338732\pi$
$167$	12.5414	0.970482	0.485241	+	0.874380i	$0.338732\pi$
$168$	−1.13856	−0.0878415
$169$	−9.33782	−0.718294
$170$	−6.98779	−0.535939
$171$	7.36643	0.563325
$172$	2.55329	0.194686
$173$	−14.6774	−1.11590	−0.557951	−	0.829874i	$-0.688412\pi$
$173$	−14.6774	−1.11590	−0.557951	+	0.829874i	$0.688412\pi$
$174$	6.37224	0.483078
$175$	−0.566476	−0.0428216
$176$	−3.22347	−0.242978
$177$	−1.29856	−0.0976059
$178$	0.856725	0.0642143
$179$	10.8029	0.807449	0.403725	−	0.914881i	$-0.367715\pi$
$179$	10.8029	0.807449	0.403725	+	0.914881i	$0.367715\pi$
$180$	1.03966	0.0774920
$181$	18.0114	1.33878	0.669389	−	0.742912i	$-0.266556\pi$
$181$	18.0114	1.33878	0.669389	+	0.742912i	$0.266556\pi$
$182$	1.08405	0.0803555
$183$	−30.9469	−2.28766
$184$	−5.48539	−0.404389
$185$	−10.8293	−0.796186
$186$	14.5526	1.06705
$187$	−22.5249	−1.64719
$188$	0.387208	0.0282401
$189$	−2.23195	−0.162351
$190$	−7.08539	−0.514028
$191$	10.0434	0.726713	0.363356	−	0.931650i	$-0.381631\pi$
$191$	10.0434	0.726713	0.363356	+	0.931650i	$0.381631\pi$
$192$	−2.00989	−0.145051
$193$	−6.77332	−0.487554	−0.243777	−	0.969831i	$-0.578387\pi$
$193$	−6.77332	−0.487554	−0.243777	+	0.969831i	$0.578387\pi$
$194$	10.0439	0.721108
$195$	−3.84629	−0.275439
$196$	−6.67910	−0.477079
$197$	−15.6507	−1.11506	−0.557532	−	0.830155i	$-0.688252\pi$
$197$	−15.6507	−1.11506	−0.557532	+	0.830155i	$0.688252\pi$
$198$	3.35133	0.238168
$199$	13.0829	0.927424	0.463712	−	0.885986i	$-0.346517\pi$
$199$	13.0829	0.927424	0.463712	+	0.885986i	$0.346517\pi$
$200$	−1.00000	−0.0707107
$201$	−2.73418	−0.192854
$202$	−4.00313	−0.281659
$203$	−1.79598	−0.126053
$204$	−14.0447	−0.983326
$205$	−2.88732	−0.201659
$206$	−1.20199	−0.0837464
$207$	5.70297	0.396384
$208$	1.91368	0.132690
$209$	−22.8395	−1.57984
$210$	−1.13856	−0.0785678
$211$	−19.2673	−1.32641	−0.663207	−	0.748436i	$-0.730805\pi$
$211$	−19.2673	−1.32641	−0.663207	+	0.748436i	$0.730805\pi$
$212$	−2.94317	−0.202138
$213$	−22.7675	−1.56000
$214$	−9.35534	−0.639518
$215$	2.55329	0.174133
$216$	−3.94006	−0.268087
$217$	−4.10157	−0.278432
$218$	−6.13328	−0.415398
$219$	28.0137	1.89299
$220$	−3.22347	−0.217326
$221$	13.3724	0.899526
$222$	−21.7657	−1.46082
$223$	−15.8084	−1.05861	−0.529304	−	0.848432i	$-0.677547\pi$
$223$	−15.8084	−1.05861	−0.529304	+	0.848432i	$0.677547\pi$
$224$	0.566476	0.0378493
$225$	1.03966	0.0693109
$226$	−11.8653	−0.789270
$227$	8.30977	0.551539	0.275769	−	0.961224i	$-0.411067\pi$
$227$	8.30977	0.551539	0.275769	+	0.961224i	$0.411067\pi$
$228$	−14.2409	−0.943125
$229$	−17.0421	−1.12617	−0.563087	−	0.826398i	$-0.690386\pi$
$229$	−17.0421	−1.12617	−0.563087	+	0.826398i	$0.690386\pi$
$230$	−5.48539	−0.361696
$231$	−3.67010	−0.241475
$232$	−3.17044	−0.208150
$233$	−5.11095	−0.334830	−0.167415	−	0.985887i	$-0.553542\pi$
$233$	−5.11095	−0.334830	−0.167415	+	0.985887i	$0.553542\pi$
$234$	−1.98959	−0.130063
$235$	0.387208	0.0252587
$236$	0.646086	0.0420566
$237$	14.0557	0.913014
$238$	3.95842	0.256586
$239$	14.8031	0.957530	0.478765	−	0.877943i	$-0.341085\pi$
$239$	14.8031	0.957530	0.478765	+	0.877943i	$0.341085\pi$
$240$	−2.00989	−0.129738
$241$	5.14459	0.331392	0.165696	−	0.986177i	$-0.447013\pi$
$241$	5.14459	0.331392	0.165696	+	0.986177i	$0.447013\pi$
$242$	0.609245	0.0391638
$243$	10.3652	0.664926
$244$	15.3973	0.985710
$245$	−6.67910	−0.426712
$246$	−5.80319	−0.369998
$247$	13.5592	0.862750
$248$	−7.24049	−0.459772
$249$	31.3782	1.98852
$250$	−1.00000	−0.0632456
$251$	−0.917455	−0.0579093	−0.0289546	−	0.999581i	$-0.509218\pi$
$251$	−0.917455	−0.0579093	−0.0289546	+	0.999581i	$0.509218\pi$
$252$	−0.588945	−0.0371000
$253$	−17.6820	−1.11166
$254$	−0.720232	−0.0451914
$255$	−14.0447	−0.879514
$256$	1.00000	0.0625000
$257$	−25.3957	−1.58414	−0.792069	−	0.610432i	$-0.790996\pi$
$257$	−25.3957	−1.58414	−0.792069	+	0.610432i	$0.790996\pi$
$258$	5.13183	0.319494
$259$	6.13454	0.381182
$260$	1.91368	0.118681
$261$	3.29619	0.204029
$262$	2.50921	0.155020
$263$	28.2031	1.73907	0.869537	−	0.493867i	$-0.164417\pi$
$263$	28.2031	1.73907	0.869537	+	0.493867i	$0.164417\pi$
$264$	−6.47882	−0.398744
$265$	−2.94317	−0.180798
$266$	4.01370	0.246096
$267$	1.72192	0.105380
$268$	1.36036	0.0830973
$269$	29.6271	1.80639	0.903197	−	0.429227i	$-0.141214\pi$
$269$	29.6271	1.80639	0.903197	+	0.429227i	$0.141214\pi$
$270$	−3.94006	−0.239785
$271$	18.5310	1.12568	0.562840	−	0.826566i	$-0.309709\pi$
$271$	18.5310	1.12568	0.562840	+	0.826566i	$0.309709\pi$
$272$	6.98779	0.423697
$273$	2.17883	0.131869
$274$	−2.22822	−0.134612
$275$	−3.22347	−0.194383
$276$	−11.0250	−0.663630
$277$	9.03968	0.543142	0.271571	−	0.962418i	$-0.412457\pi$
$277$	9.03968	0.543142	0.271571	+	0.962418i	$0.412457\pi$
$278$	−2.75665	−0.165333
$279$	7.52768	0.450670
$280$	0.566476	0.0338534
$281$	−18.1260	−1.08131	−0.540653	−	0.841246i	$-0.681823\pi$
$281$	−18.1260	−1.08131	−0.540653	+	0.841246i	$0.681823\pi$
$282$	0.778247	0.0463439
$283$	−23.6388	−1.40518	−0.702590	−	0.711594i	$-0.747973\pi$
$283$	−23.6388	−1.40518	−0.702590	+	0.711594i	$0.747973\pi$
$284$	11.3277	0.672177
$285$	−14.2409	−0.843556
$286$	6.16869	0.364762
$287$	1.63560	0.0965462
$288$	−1.03966	−0.0612628
$289$	31.8292	1.87231
$290$	−3.17044	−0.186175
$291$	20.1871	1.18339
$292$	−13.9379	−0.815655
$293$	2.54620	0.148751	0.0743754	−	0.997230i	$-0.476304\pi$
$293$	2.54620	0.148751	0.0743754	+	0.997230i	$0.476304\pi$
$294$	−13.4243	−0.782920
$295$	0.646086	0.0376166
$296$	10.8293	0.629440
$297$	−12.7007	−0.736968
$298$	−7.91218	−0.458340
$299$	10.4973	0.607074
$300$	−2.00989	−0.116041
$301$	−1.44638	−0.0833677
$302$	−6.99670	−0.402615
$303$	−8.04585	−0.462222
$304$	7.08539	0.406375
$305$	15.3973	0.881646
$306$	−7.26496	−0.415310
$307$	16.9252	0.965974	0.482987	−	0.875628i	$-0.339552\pi$
$307$	16.9252	0.965974	0.482987	+	0.875628i	$0.339552\pi$
$308$	1.82602	0.104047
$309$	−2.41586	−0.137434
$310$	−7.24049	−0.411232
$311$	−24.4768	−1.38795	−0.693977	−	0.719998i	$-0.744143\pi$
$311$	−24.4768	−1.38795	−0.693977	+	0.719998i	$0.744143\pi$
$312$	3.84629	0.217753
$313$	15.1203	0.854648	0.427324	−	0.904098i	$-0.359456\pi$
$313$	15.1203	0.854648	0.427324	+	0.904098i	$0.359456\pi$
$314$	2.61815	0.147751
$315$	−0.588945	−0.0331833
$316$	−6.99325	−0.393401
$317$	−10.6423	−0.597729	−0.298865	−	0.954295i	$-0.596608\pi$
$317$	−10.6423	−0.597729	−0.298865	+	0.954295i	$0.596608\pi$
$318$	−5.91546	−0.331722
$319$	−10.2198	−0.572200
$320$	1.00000	0.0559017
$321$	−18.8032	−1.04949
$322$	3.10734	0.173166
$323$	49.5112	2.75488
$324$	−11.0381	−0.613227
$325$	1.91368	0.106152
$326$	−5.98741	−0.331612
$327$	−12.3272	−0.681697
$328$	2.88732	0.159425
$329$	−0.219344	−0.0120928
$330$	−6.47882	−0.356648
$331$	−1.20204	−0.0660701	−0.0330350	−	0.999454i	$-0.510517\pi$
$331$	−1.20204	−0.0660701	−0.0330350	+	0.999454i	$0.510517\pi$
$332$	−15.6119	−0.856815
$333$	−11.2588	−0.616980
$334$	−12.5414	−0.686234
$335$	1.36036	0.0743245
$336$	1.13856	0.0621133
$337$	−14.3636	−0.782436	−0.391218	−	0.920298i	$-0.627946\pi$
$337$	−14.3636	−0.782436	−0.391218	+	0.920298i	$0.627946\pi$
$338$	9.33782	0.507911
$339$	−23.8480	−1.29525
$340$	6.98779	0.378966
$341$	−23.3395	−1.26391
$342$	−7.36643	−0.398331
$343$	7.74889	0.418400
$344$	−2.55329	−0.137664
$345$	−11.0250	−0.593568
$346$	14.6774	0.789062
$347$	35.4858	1.90498	0.952489	−	0.304573i	$-0.0985137\pi$
$347$	35.4858	1.90498	0.952489	+	0.304573i	$0.0985137\pi$
$348$	−6.37224	−0.341588
$349$	−6.93174	−0.371047	−0.185524	−	0.982640i	$-0.559398\pi$
$349$	−6.93174	−0.371047	−0.185524	+	0.982640i	$0.559398\pi$
$350$	0.566476	0.0302794
$351$	7.54002	0.402457
$352$	3.22347	0.171811
$353$	−2.01575	−0.107288	−0.0536438	−	0.998560i	$-0.517084\pi$
$353$	−2.01575	−0.107288	−0.0536438	+	0.998560i	$0.517084\pi$
$354$	1.29856	0.0690178
$355$	11.3277	0.601214
$356$	−0.856725	−0.0454063
$357$	7.95599	0.421076
$358$	−10.8029	−0.570953
$359$	31.5718	1.66629	0.833147	−	0.553052i	$-0.186537\pi$
$359$	31.5718	1.66629	0.833147	+	0.553052i	$0.186537\pi$
$360$	−1.03966	−0.0547951
$361$	31.2028	1.64225
$362$	−18.0114	−0.946658
$363$	1.22452	0.0642705
$364$	−1.08405	−0.0568199
$365$	−13.9379	−0.729544
$366$	30.9469	1.61762
$367$	−32.2113	−1.68142	−0.840708	−	0.541489i	$-0.817861\pi$
$367$	−32.2113	−1.68142	−0.840708	+	0.541489i	$0.817861\pi$
$368$	5.48539	0.285946
$369$	−3.00184	−0.156270
$370$	10.8293	0.562988
$371$	1.66724	0.0865586
$372$	−14.5526	−0.754518
$373$	−14.8983	−0.771405	−0.385703	−	0.922623i	$-0.626041\pi$
$373$	−14.8983	−0.771405	−0.385703	+	0.922623i	$0.626041\pi$
$374$	22.5249	1.16474
$375$	−2.00989	−0.103790
$376$	−0.387208	−0.0199687
$377$	6.06721	0.312477
$378$	2.23195	0.114799
$379$	17.8909	0.918992	0.459496	−	0.888180i	$-0.348030\pi$
$379$	17.8909	0.918992	0.459496	+	0.888180i	$0.348030\pi$
$380$	7.08539	0.363473
$381$	−1.44759	−0.0741622
$382$	−10.0434	−0.513863
$383$	−18.4425	−0.942366	−0.471183	−	0.882035i	$-0.656173\pi$
$383$	−18.4425	−0.942366	−0.471183	+	0.882035i	$0.656173\pi$
$384$	2.00989	0.102567
$385$	1.82602	0.0930625
$386$	6.77332	0.344753
$387$	2.65456	0.134939
$388$	−10.0439	−0.509900
$389$	16.0270	0.812601	0.406300	−	0.913740i	$-0.366819\pi$
$389$	16.0270	0.812601	0.406300	+	0.913740i	$0.366819\pi$
$390$	3.84629	0.194765
$391$	38.3308	1.93847
$392$	6.67910	0.337346
$393$	5.04325	0.254398
$394$	15.6507	0.788470
$395$	−6.99325	−0.351868
$396$	−3.35133	−0.168410
$397$	39.1527	1.96502	0.982508	−	0.186221i	$-0.0596241\pi$
$397$	39.1527	1.96502	0.982508	+	0.186221i	$0.0596241\pi$
$398$	−13.0829	−0.655788
$399$	8.06711	0.403861
$400$	1.00000	0.0500000
$401$	−33.0160	−1.64874	−0.824370	−	0.566051i	$-0.808470\pi$
$401$	−33.0160	−1.64874	−0.824370	+	0.566051i	$0.808470\pi$
$402$	2.73418	0.136369
$403$	13.8560	0.690216
$404$	4.00313	0.199163
$405$	−11.0381	−0.548487
$406$	1.79598	0.0891329
$407$	34.9079	1.73032
$408$	14.0447	0.695316
$409$	30.7026	1.51815	0.759074	−	0.651005i	$-0.225652\pi$
$409$	30.7026	1.51815	0.759074	+	0.651005i	$0.225652\pi$
$410$	2.88732	0.142594
$411$	−4.47848	−0.220907
$412$	1.20199	0.0592176
$413$	−0.365992	−0.0180093
$414$	−5.70297	−0.280286
$415$	−15.6119	−0.766358
$416$	−1.91368	−0.0938260
$417$	−5.54057	−0.271323
$418$	22.8395	1.11712
$419$	30.4158	1.48591	0.742955	−	0.669341i	$-0.233424\pi$
$419$	30.4158	1.48591	0.742955	+	0.669341i	$0.233424\pi$
$420$	1.13856	0.0555558
$421$	−18.9211	−0.922158	−0.461079	−	0.887359i	$-0.652538\pi$
$421$	−18.9211	−0.922158	−0.461079	+	0.887359i	$0.652538\pi$
$422$	19.2673	0.937917
$423$	0.402566	0.0195735
$424$	2.94317	0.142933
$425$	6.98779	0.338958
$426$	22.7675	1.10309
$427$	−8.72219	−0.422097
$428$	9.35534	0.452207
$429$	12.3984	0.598601
$430$	−2.55329	−0.123130
$431$	−34.2619	−1.65034	−0.825168	−	0.564887i	$-0.808920\pi$
$431$	−34.2619	−1.65034	−0.825168	+	0.564887i	$0.808920\pi$
$432$	3.94006	0.189566
$433$	14.7822	0.710385	0.355193	−	0.934793i	$-0.384415\pi$
$433$	14.7822	0.710385	0.355193	+	0.934793i	$0.384415\pi$
$434$	4.10157	0.196881
$435$	−6.37224	−0.305525
$436$	6.13328	0.293731
$437$	38.8662	1.85922
$438$	−28.0137	−1.33855
$439$	0.0249332	0.00118999	0.000594997	−	1.00000i	$-0.499811\pi$
$439$	0.0249332	0.00118999	0.000594997		1.00000i	$0.499811\pi$
$440$	3.22347	0.153673
$441$	−6.94403	−0.330668
$442$	−13.3724	−0.636061
$443$	17.2837	0.821173	0.410586	−	0.911822i	$-0.365324\pi$
$443$	17.2837	0.821173	0.410586	+	0.911822i	$0.365324\pi$
$444$	21.7657	1.03295
$445$	−0.856725	−0.0406127
$446$	15.8084	0.748549
$447$	−15.9026	−0.752168
$448$	−0.566476	−0.0267635
$449$	22.6851	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$449$	22.6851	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$450$	−1.03966	−0.0490102
$451$	9.30718	0.438258
$452$	11.8653	0.558098
$453$	−14.0626	−0.660719
$454$	−8.30977	−0.389997
$455$	−1.08405	−0.0508213
$456$	14.2409	0.666890
$457$	−30.5022	−1.42683	−0.713417	−	0.700740i	$-0.752853\pi$
$457$	−30.5022	−1.42683	−0.713417	+	0.700740i	$0.752853\pi$
$458$	17.0421	0.796325
$459$	27.5323	1.28510
$460$	5.48539	0.255758
$461$	10.9970	0.512180	0.256090	−	0.966653i	$-0.417566\pi$
$461$	10.9970	0.512180	0.256090	+	0.966653i	$0.417566\pi$
$462$	3.67010	0.170748
$463$	0.772330	0.0358932	0.0179466	−	0.999839i	$-0.494287\pi$
$463$	0.772330	0.0358932	0.0179466	+	0.999839i	$0.494287\pi$
$464$	3.17044	0.147184
$465$	−14.5526	−0.674861
$466$	5.11095	0.236760
$467$	11.6025	0.536898	0.268449	−	0.963294i	$-0.413489\pi$
$467$	11.6025	0.536898	0.268449	+	0.963294i	$0.413489\pi$
$468$	1.98959	0.0919686
$469$	−0.770613	−0.0355836
$470$	−0.387208	−0.0178606
$471$	5.26220	0.242469
$472$	−0.646086	−0.0297385
$473$	−8.23044	−0.378436
$474$	−14.0557	−0.645598
$475$	7.08539	0.325100
$476$	−3.95842	−0.181434
$477$	−3.05991	−0.140104
$478$	−14.8031	−0.677076
$479$	3.22761	0.147473	0.0737366	−	0.997278i	$-0.476508\pi$
$479$	3.22761	0.147473	0.0737366	+	0.997278i	$0.476508\pi$
$480$	2.00989	0.0917386
$481$	−20.7238	−0.944925
$482$	−5.14459	−0.234330
$483$	6.24542	0.284177
$484$	−0.609245	−0.0276930
$485$	−10.0439	−0.456069
$486$	−10.3652	−0.470174
$487$	12.3978	0.561797	0.280899	−	0.959737i	$-0.409368\pi$
$487$	12.3978	0.561797	0.280899	+	0.959737i	$0.409368\pi$
$488$	−15.3973	−0.697002
$489$	−12.0341	−0.544199
$490$	6.67910	0.301731
$491$	15.6333	0.705520	0.352760	−	0.935714i	$-0.385243\pi$
$491$	15.6333	0.705520	0.352760	+	0.935714i	$0.385243\pi$
$492$	5.80319	0.261628
$493$	22.1544	0.997782
$494$	−13.5592	−0.610056
$495$	−3.35133	−0.150631
$496$	7.24049	0.325108
$497$	−6.41689	−0.287837
$498$	−31.3782	−1.40609
$499$	−24.1541	−1.08129	−0.540644	−	0.841252i	$-0.681819\pi$
$499$	−24.1541	−1.08129	−0.540644	+	0.841252i	$0.681819\pi$
$500$	1.00000	0.0447214
$501$	−25.2068	−1.12616
$502$	0.917455	0.0409480
$503$	−27.5234	−1.22721	−0.613605	−	0.789613i	$-0.710281\pi$
$503$	−27.5234	−1.22721	−0.613605	+	0.789613i	$0.710281\pi$
$504$	0.588945	0.0262337
$505$	4.00313	0.178137
$506$	17.6820	0.786061
$507$	18.7680	0.833517
$508$	0.720232	0.0319551
$509$	21.1030	0.935376	0.467688	−	0.883894i	$-0.345087\pi$
$509$	21.1030	0.935376	0.467688	+	0.883894i	$0.345087\pi$
$510$	14.0447	0.621910
$511$	7.89550	0.349276
$512$	−1.00000	−0.0441942
$513$	27.9169	1.23256
$514$	25.3957	1.12015
$515$	1.20199	0.0529659
$516$	−5.13183	−0.225916
$517$	−1.24815	−0.0548937
$518$	−6.13454	−0.269536
$519$	29.5000	1.29490
$520$	−1.91368	−0.0839205
$521$	11.3168	0.495798	0.247899	−	0.968786i	$-0.420260\pi$
$521$	11.3168	0.495798	0.247899	+	0.968786i	$0.420260\pi$
$522$	−3.29619	−0.144270
$523$	20.0706	0.877628	0.438814	−	0.898578i	$-0.355399\pi$
$523$	20.0706	0.877628	0.438814	+	0.898578i	$0.355399\pi$
$524$	−2.50921	−0.109616
$525$	1.13856	0.0496906
$526$	−28.2031	−1.22971
$527$	50.5951	2.20396
$528$	6.47882	0.281955
$529$	7.08954	0.308241
$530$	2.94317	0.127843
$531$	0.671712	0.0291498
$532$	−4.01370	−0.174016
$533$	−5.52540	−0.239332
$534$	−1.72192	−0.0745150
$535$	9.35534	0.404467
$536$	−1.36036	−0.0587587
$537$	−21.7127	−0.936973
$538$	−29.6271	−1.27731
$539$	21.5299	0.927358
$540$	3.94006	0.169553
$541$	21.8208	0.938152	0.469076	−	0.883158i	$-0.344587\pi$
$541$	21.8208	0.938152	0.469076	+	0.883158i	$0.344587\pi$
$542$	−18.5310	−0.795976
$543$	−36.2010	−1.55353
$544$	−6.98779	−0.299599
$545$	6.13328	0.262721
$546$	−2.17883	−0.0932454
$547$	17.8867	0.764779	0.382389	−	0.924001i	$-0.375101\pi$
$547$	17.8867	0.764779	0.382389	+	0.924001i	$0.375101\pi$
$548$	2.22822	0.0951848
$549$	16.0080	0.683205
$550$	3.22347	0.137449
$551$	22.4638	0.956990
$552$	11.0250	0.469257
$553$	3.96151	0.168460
$554$	−9.03968	−0.384059
$555$	21.7657	0.923903
$556$	2.75665	0.116908
$557$	13.0662	0.553631	0.276816	−	0.960923i	$-0.410721\pi$
$557$	13.0662	0.553631	0.276816	+	0.960923i	$0.410721\pi$
$558$	−7.52768	−0.318672
$559$	4.88618	0.206663
$560$	−0.566476	−0.0239380
$561$	45.2727	1.91141
$562$	18.1260	0.764598
$563$	−4.20830	−0.177359	−0.0886793	−	0.996060i	$-0.528265\pi$
$563$	−4.20830	−0.177359	−0.0886793	+	0.996060i	$0.528265\pi$
$564$	−0.778247	−0.0327701
$565$	11.8653	0.499178
$566$	23.6388	0.993613
$567$	6.25281	0.262594
$568$	−11.3277	−0.475301
$569$	−14.1577	−0.593523	−0.296762	−	0.954952i	$-0.595907\pi$
$569$	−14.1577	−0.593523	−0.296762	+	0.954952i	$0.595907\pi$
$570$	14.2409	0.596484
$571$	−11.5294	−0.482489	−0.241245	−	0.970464i	$-0.577556\pi$
$571$	−11.5294	−0.482489	−0.241245	+	0.970464i	$0.577556\pi$
$572$	−6.16869	−0.257926
$573$	−20.1861	−0.843286
$574$	−1.63560	−0.0682684
$575$	5.48539	0.228757
$576$	1.03966	0.0433193
$577$	−17.2315	−0.717356	−0.358678	−	0.933461i	$-0.616772\pi$
$577$	−17.2315	−0.717356	−0.358678	+	0.933461i	$0.616772\pi$
$578$	−31.8292	−1.32392
$579$	13.6136	0.565764
$580$	3.17044	0.131645
$581$	8.84377	0.366901
$582$	−20.1871	−0.836782
$583$	9.48723	0.392921
$584$	13.9379	0.576755
$585$	1.98959	0.0822593
$586$	−2.54620	−0.105183
$587$	−12.9043	−0.532617	−0.266309	−	0.963888i	$-0.585804\pi$
$587$	−12.9043	−0.532617	−0.266309	+	0.963888i	$0.585804\pi$
$588$	13.4243	0.553608
$589$	51.3017	2.11385
$590$	−0.646086	−0.0265989
$591$	31.4562	1.29393
$592$	−10.8293	−0.445081
$593$	12.4784	0.512428	0.256214	−	0.966620i	$-0.417525\pi$
$593$	12.4784	0.512428	0.256214	+	0.966620i	$0.417525\pi$
$594$	12.7007	0.521115
$595$	−3.95842	−0.162279
$596$	7.91218	0.324095
$597$	−26.2953	−1.07619
$598$	−10.4973	−0.429266
$599$	33.4749	1.36775	0.683873	−	0.729601i	$-0.260294\pi$
$599$	33.4749	1.36775	0.683873	+	0.729601i	$0.260294\pi$
$600$	2.00989	0.0820535
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	1.44638	0.0589499
$603$	1.41432	0.0575956
$604$	6.99670	0.284692
$605$	−0.609245	−0.0247693
$606$	8.04585	0.326840
$607$	−20.1378	−0.817366	−0.408683	−	0.912676i	$-0.634012\pi$
$607$	−20.1378	−0.817366	−0.408683	+	0.912676i	$0.634012\pi$
$608$	−7.08539	−0.287351
$609$	3.60972	0.146273
$610$	−15.3973	−0.623418
$611$	0.740993	0.0299774
$612$	7.26496	0.293668
$613$	−16.2153	−0.654930	−0.327465	−	0.944863i	$-0.606194\pi$
$613$	−16.2153	−0.654930	−0.327465	+	0.944863i	$0.606194\pi$
$614$	−16.9252	−0.683047
$615$	5.80319	0.234007
$616$	−1.82602	−0.0735724
$617$	31.7773	1.27930	0.639652	−	0.768665i	$-0.279078\pi$
$617$	31.7773	1.27930	0.639652	+	0.768665i	$0.279078\pi$
$618$	2.41586	0.0971803
$619$	−31.0470	−1.24788	−0.623942	−	0.781470i	$-0.714470\pi$
$619$	−31.0470	−1.24788	−0.623942	+	0.781470i	$0.714470\pi$
$620$	7.24049	0.290785
$621$	21.6128	0.867291
$622$	24.4768	0.981431
$623$	0.485314	0.0194437
$624$	−3.84629	−0.153975
$625$	1.00000	0.0400000
$626$	−15.1203	−0.604328
$627$	45.9050	1.83327
$628$	−2.61815	−0.104476
$629$	−75.6729	−3.01727
$630$	0.588945	0.0234641
$631$	4.51453	0.179721	0.0898603	−	0.995954i	$-0.471358\pi$
$631$	4.51453	0.179721	0.0898603	+	0.995954i	$0.471358\pi$
$632$	6.99325	0.278176
$633$	38.7252	1.53919
$634$	10.6423	0.422659
$635$	0.720232	0.0285816
$636$	5.91546	0.234563
$637$	−12.7817	−0.506429
$638$	10.2198	0.404606
$639$	11.7770	0.465892
$640$	−1.00000	−0.0395285
$641$	1.21985	0.0481811	0.0240905	−	0.999710i	$-0.492331\pi$
$641$	1.21985	0.0481811	0.0240905	+	0.999710i	$0.492331\pi$
$642$	18.8032	0.742104
$643$	−30.9799	−1.22173	−0.610864	−	0.791735i	$-0.709178\pi$
$643$	−30.9799	−1.22173	−0.610864	+	0.791735i	$0.709178\pi$
$644$	−3.10734	−0.122447
$645$	−5.13183	−0.202066
$646$	−49.5112	−1.94799
$647$	−24.2273	−0.952473	−0.476237	−	0.879317i	$-0.657999\pi$
$647$	−24.2273	−0.952473	−0.476237	+	0.879317i	$0.657999\pi$
$648$	11.0381	0.433617
$649$	−2.08264	−0.0817507
$650$	−1.91368	−0.0750608
$651$	8.24370	0.323096
$652$	5.98741	0.234485
$653$	19.1665	0.750044	0.375022	−	0.927016i	$-0.377635\pi$
$653$	19.1665	0.750044	0.375022	+	0.927016i	$0.377635\pi$
$654$	12.3272	0.482033
$655$	−2.50921	−0.0980431
$656$	−2.88732	−0.112731
$657$	−14.4908	−0.565338
$658$	0.219344	0.00855093
$659$	−6.56372	−0.255686	−0.127843	−	0.991794i	$-0.540805\pi$
$659$	−6.56372	−0.255686	−0.127843	+	0.991794i	$0.540805\pi$
$660$	6.47882	0.252188
$661$	−17.0035	−0.661358	−0.330679	−	0.943743i	$-0.607278\pi$
$661$	−17.0035	−0.661358	−0.330679	+	0.943743i	$0.607278\pi$
$662$	1.20204	0.0467186
$663$	−26.8771	−1.04382
$664$	15.6119	0.605860
$665$	−4.01370	−0.155645
$666$	11.2588	0.436271
$667$	17.3911	0.673386
$668$	12.5414	0.485241
$669$	31.7731	1.22842
$670$	−1.36036	−0.0525554
$671$	−49.6327	−1.91605
$672$	−1.13856	−0.0439207
$673$	31.8462	1.22758	0.613791	−	0.789468i	$-0.289644\pi$
$673$	31.8462	1.22758	0.613791	+	0.789468i	$0.289644\pi$
$674$	14.3636	0.553266
$675$	3.94006	0.151653
$676$	−9.33782	−0.359147
$677$	−2.47794	−0.0952349	−0.0476175	−	0.998866i	$-0.515163\pi$
$677$	−2.47794	−0.0952349	−0.0476175	+	0.998866i	$0.515163\pi$
$678$	23.8480	0.915878
$679$	5.68961	0.218347
$680$	−6.98779	−0.267970
$681$	−16.7017	−0.640012
$682$	23.3395	0.893716
$683$	8.94358	0.342216	0.171108	−	0.985252i	$-0.445265\pi$
$683$	8.94358	0.342216	0.171108	+	0.985252i	$0.445265\pi$
$684$	7.36643	0.281662
$685$	2.22822	0.0851359
$686$	−7.74889	−0.295854
$687$	34.2528	1.30683
$688$	2.55329	0.0973431
$689$	−5.63230	−0.214573
$690$	11.0250	0.419716
$691$	13.1782	0.501321	0.250660	−	0.968075i	$-0.419352\pi$
$691$	13.1782	0.501321	0.250660	+	0.968075i	$0.419352\pi$
$692$	−14.6774	−0.557951
$693$	1.89845	0.0721160
$694$	−35.4858	−1.34702
$695$	2.75665	0.104566
$696$	6.37224	0.241539
$697$	−20.1760	−0.764219
$698$	6.93174	0.262370
$699$	10.2725	0.388540
$700$	−0.566476	−0.0214108
$701$	15.9431	0.602163	0.301081	−	0.953598i	$-0.402652\pi$
$701$	15.9431	0.602163	0.301081	+	0.953598i	$0.402652\pi$
$702$	−7.54002	−0.284580
$703$	−76.7298	−2.89392
$704$	−3.22347	−0.121489
$705$	−0.778247	−0.0293105
$706$	2.01575	0.0758638
$707$	−2.26768	−0.0852847
$708$	−1.29856	−0.0488029
$709$	21.3881	0.803248	0.401624	−	0.915805i	$-0.368446\pi$
$709$	21.3881	0.803248	0.401624	+	0.915805i	$0.368446\pi$
$710$	−11.3277	−0.425122
$711$	−7.27063	−0.272670
$712$	0.856725	0.0321071
$713$	39.7170	1.48741
$714$	−7.95599	−0.297745
$715$	−6.16869	−0.230696
$716$	10.8029	0.403725
$717$	−29.7525	−1.11113
$718$	−31.5718	−1.17825
$719$	−6.18643	−0.230715	−0.115357	−	0.993324i	$-0.536801\pi$
$719$	−6.18643	−0.230715	−0.115357	+	0.993324i	$0.536801\pi$
$720$	1.03966	0.0387460
$721$	−0.680897	−0.0253579
$722$	−31.2028	−1.16125
$723$	−10.3401	−0.384551
$724$	18.0114	0.669389
$725$	3.17044	0.117747
$726$	−1.22452	−0.0454461
$727$	−42.8530	−1.58933	−0.794665	−	0.607048i	$-0.792353\pi$
$727$	−42.8530	−1.58933	−0.794665	+	0.607048i	$0.792353\pi$
$728$	1.08405	0.0401777
$729$	12.2814	0.454866
$730$	13.9379	0.515866
$731$	17.8418	0.659904
$732$	−30.9469	−1.14383
$733$	−7.78891	−0.287690	−0.143845	−	0.989600i	$-0.545947\pi$
$733$	−7.78891	−0.287690	−0.143845	+	0.989600i	$0.545947\pi$
$734$	32.2113	1.18894
$735$	13.4243	0.495162
$736$	−5.48539	−0.202194
$737$	−4.38509	−0.161527
$738$	3.00184	0.110499
$739$	−39.8782	−1.46694	−0.733472	−	0.679720i	$-0.762101\pi$
$739$	−39.8782	−1.46694	−0.733472	+	0.679720i	$0.762101\pi$
$740$	−10.8293	−0.398093
$741$	−27.2525	−1.00115
$742$	−1.66724	−0.0612062
$743$	0.543482	0.0199384	0.00996921	−	0.999950i	$-0.496827\pi$
$743$	0.543482	0.0199384	0.00996921	+	0.999950i	$0.496827\pi$
$744$	14.5526	0.533524
$745$	7.91218	0.289880
$746$	14.8983	0.545466
$747$	−16.2311	−0.593866
$748$	−22.5249	−0.823593
$749$	−5.29958	−0.193642
$750$	2.00989	0.0733909
$751$	18.8421	0.687557	0.343779	−	0.939051i	$-0.388293\pi$
$751$	18.8421	0.687557	0.343779	+	0.939051i	$0.388293\pi$
$752$	0.387208	0.0141200
$753$	1.84399	0.0671986
$754$	−6.06721	−0.220955
$755$	6.99670	0.254636
$756$	−2.23195	−0.0811753
$757$	22.6638	0.823730	0.411865	−	0.911245i	$-0.364877\pi$
$757$	22.6638	0.823730	0.411865	+	0.911245i	$0.364877\pi$
$758$	−17.8909	−0.649825
$759$	35.5389	1.28998
$760$	−7.08539	−0.257014
$761$	−14.2544	−0.516721	−0.258360	−	0.966049i	$-0.583182\pi$
$761$	−14.2544	−0.516721	−0.258360	+	0.966049i	$0.583182\pi$
$762$	1.44759	0.0524406
$763$	−3.47436	−0.125780
$764$	10.0434	0.363356
$765$	7.26496	0.262665
$766$	18.4425	0.666353
$767$	1.23640	0.0446439
$768$	−2.00989	−0.0725257
$769$	−28.1755	−1.01604	−0.508018	−	0.861346i	$-0.669622\pi$
$769$	−28.1755	−1.01604	−0.508018	+	0.861346i	$0.669622\pi$
$770$	−1.82602	−0.0658051
$771$	51.0425	1.83825
$772$	−6.77332	−0.243777
$773$	−8.54786	−0.307445	−0.153723	−	0.988114i	$-0.549126\pi$
$773$	−8.54786	−0.307445	−0.153723	+	0.988114i	$0.549126\pi$
$774$	−2.65456	−0.0954162
$775$	7.24049	0.260086
$776$	10.0439	0.360554
$777$	−12.3298	−0.442327
$778$	−16.0270	−0.574596
$779$	−20.4578	−0.732976
$780$	−3.84629	−0.137719
$781$	−36.5146	−1.30660
$782$	−38.3308	−1.37071
$783$	12.4917	0.446418
$784$	−6.67910	−0.238539
$785$	−2.61815	−0.0934458
$786$	−5.04325	−0.179887
$787$	3.09434	0.110301	0.0551507	−	0.998478i	$-0.482436\pi$
$787$	3.09434	0.110301	0.0551507	+	0.998478i	$0.482436\pi$
$788$	−15.6507	−0.557532
$789$	−56.6851	−2.01804
$790$	6.99325	0.248809
$791$	−6.72143	−0.238986
$792$	3.35133	0.119084
$793$	29.4655	1.04635
$794$	−39.1527	−1.38948
$795$	5.91546	0.209800
$796$	13.0829	0.463712
$797$	45.7848	1.62178	0.810890	−	0.585198i	$-0.198983\pi$
$797$	45.7848	1.62178	0.810890	+	0.585198i	$0.198983\pi$
$798$	−8.06711	−0.285573
$799$	2.70573	0.0957219
$800$	−1.00000	−0.0353553
$801$	−0.890706	−0.0314716
$802$	33.0160	1.16584
$803$	44.9285	1.58549
$804$	−2.73418	−0.0964271
$805$	−3.10734	−0.109519
$806$	−13.8560	−0.488057
$807$	−59.5472	−2.09616
$808$	−4.00313	−0.140830
$809$	−8.77241	−0.308421	−0.154211	−	0.988038i	$-0.549283\pi$
$809$	−8.77241	−0.308421	−0.154211	+	0.988038i	$0.549283\pi$
$810$	11.0381	0.387839
$811$	31.6894	1.11276	0.556382	−	0.830927i	$-0.312189\pi$
$811$	31.6894	1.11276	0.556382	+	0.830927i	$0.312189\pi$
$812$	−1.79598	−0.0630265
$813$	−37.2454	−1.30625
$814$	−34.9079	−1.22352
$815$	5.98741	0.209730
$816$	−14.0447	−0.491663
$817$	18.0910	0.632925
$818$	−30.7026	−1.07349
$819$	−1.12705	−0.0393824
$820$	−2.88732	−0.100829
$821$	3.96515	0.138385	0.0691924	−	0.997603i	$-0.477958\pi$
$821$	3.96515	0.138385	0.0691924	+	0.997603i	$0.477958\pi$
$822$	4.47848	0.156205
$823$	−15.9422	−0.555712	−0.277856	−	0.960623i	$-0.589624\pi$
$823$	−15.9422	−0.555712	−0.277856	+	0.960623i	$0.589624\pi$
$824$	−1.20199	−0.0418732
$825$	6.47882	0.225564
$826$	0.365992	0.0127345
$827$	−35.9612	−1.25050	−0.625248	−	0.780426i	$-0.715002\pi$
$827$	−35.9612	−1.25050	−0.625248	+	0.780426i	$0.715002\pi$
$828$	5.70297	0.198192
$829$	26.8759	0.933439	0.466720	−	0.884405i	$-0.345436\pi$
$829$	26.8759	0.933439	0.466720	+	0.884405i	$0.345436\pi$
$830$	15.6119	0.541897
$831$	−18.1688	−0.630268
$832$	1.91368	0.0663450
$833$	−46.6722	−1.61710
$834$	5.54057	0.191854
$835$	12.5414	0.434013
$836$	−22.8395	−0.789922
$837$	28.5280	0.986072
$838$	−30.4158	−1.05070
$839$	−33.4188	−1.15375	−0.576873	−	0.816834i	$-0.695727\pi$
$839$	−33.4188	−1.15375	−0.576873	+	0.816834i	$0.695727\pi$
$840$	−1.13856	−0.0392839
$841$	−18.9483	−0.653390
$842$	18.9211	0.652064
$843$	36.4313	1.25476
$844$	−19.2673	−0.663207
$845$	−9.33782	−0.321231
$846$	−0.402566	−0.0138405
$847$	0.345123	0.0118586
$848$	−2.94317	−0.101069
$849$	47.5114	1.63059
$850$	−6.98779	−0.239679
$851$	−59.4029	−2.03631
$852$	−22.7675	−0.780002
$853$	−37.0935	−1.27006	−0.635029	−	0.772488i	$-0.719012\pi$
$853$	−37.0935	−1.27006	−0.635029	+	0.772488i	$0.719012\pi$
$854$	8.72219	0.298467
$855$	7.36643	0.251926
$856$	−9.35534	−0.319759
$857$	5.05964	0.172834	0.0864171	−	0.996259i	$-0.472458\pi$
$857$	5.05964	0.172834	0.0864171	+	0.996259i	$0.472458\pi$
$858$	−12.3984	−0.423275
$859$	47.4353	1.61847	0.809235	−	0.587485i	$-0.199882\pi$
$859$	47.4353	1.61847	0.809235	+	0.587485i	$0.199882\pi$
$860$	2.55329	0.0870663
$861$	−3.28737	−0.112033
$862$	34.2619	1.16696
$863$	29.9415	1.01922	0.509610	−	0.860405i	$-0.329790\pi$
$863$	29.9415	1.01922	0.509610	+	0.860405i	$0.329790\pi$
$864$	−3.94006	−0.134044
$865$	−14.6774	−0.499046
$866$	−14.7822	−0.502318
$867$	−63.9733	−2.17265
$868$	−4.10157	−0.139216
$869$	22.5425	0.764702
$870$	6.37224	0.216039
$871$	2.60330	0.0882095
$872$	−6.13328	−0.207699
$873$	−10.4422	−0.353417
$874$	−38.8662	−1.31467
$875$	−0.566476	−0.0191504
$876$	28.0137	0.946496
$877$	7.64520	0.258160	0.129080	−	0.991634i	$-0.458798\pi$
$877$	7.64520	0.258160	0.129080	+	0.991634i	$0.458798\pi$
$878$	−0.0249332	−0.000841453 0
$879$	−5.11760	−0.172612
$880$	−3.22347	−0.108663
$881$	5.35788	0.180511	0.0902557	−	0.995919i	$-0.471232\pi$
$881$	5.35788	0.180511	0.0902557	+	0.995919i	$0.471232\pi$
$882$	6.94403	0.233817
$883$	−23.2834	−0.783550	−0.391775	−	0.920061i	$-0.628139\pi$
$883$	−23.2834	−0.783550	−0.391775	+	0.920061i	$0.628139\pi$
$884$	13.3724	0.449763
$885$	−1.29856	−0.0436507
$886$	−17.2837	−0.580657
$887$	−9.70677	−0.325921	−0.162961	−	0.986633i	$-0.552104\pi$
$887$	−9.70677	−0.325921	−0.162961	+	0.986633i	$0.552104\pi$
$888$	−21.7657	−0.730409
$889$	−0.407994	−0.0136837
$890$	0.856725	0.0287175
$891$	35.5809	1.19201
$892$	−15.8084	−0.529304
$893$	2.74352	0.0918085
$894$	15.9026	0.531863
$895$	10.8029	0.361102
$896$	0.566476	0.0189246
$897$	−21.0984	−0.704456
$898$	−22.6851	−0.757012
$899$	22.9555	0.765610
$900$	1.03966	0.0346555
$901$	−20.5663	−0.685162
$902$	−9.30718	−0.309895
$903$	2.90706	0.0967408
$904$	−11.8653	−0.394635
$905$	18.0114	0.598719
$906$	14.0626	0.467199
$907$	51.2448	1.70156	0.850779	−	0.525524i	$-0.176131\pi$
$907$	51.2448	1.70156	0.850779	+	0.525524i	$0.176131\pi$
$908$	8.30977	0.275769
$909$	4.16191	0.138042
$910$	1.08405	0.0359361
$911$	18.9861	0.629039	0.314520	−	0.949251i	$-0.398157\pi$
$911$	18.9861	0.629039	0.314520	+	0.949251i	$0.398157\pi$
$912$	−14.2409	−0.471562
$913$	50.3245	1.66550
$914$	30.5022	1.00892
$915$	−30.9469	−1.02307
$916$	−17.0421	−0.563087
$917$	1.42141	0.0469391
$918$	−27.5323	−0.908703
$919$	−29.2594	−0.965178	−0.482589	−	0.875847i	$-0.660304\pi$
$919$	−29.2594	−0.965178	−0.482589	+	0.875847i	$0.660304\pi$
$920$	−5.48539	−0.180848
$921$	−34.0179	−1.12093
$922$	−10.9970	−0.362166
$923$	21.6777	0.713529
$924$	−3.67010	−0.120737
$925$	−10.8293	−0.356065
$926$	−0.772330	−0.0253803
$927$	1.24966	0.0410443
$928$	−3.17044	−0.104075
$929$	−23.1882	−0.760782	−0.380391	−	0.924826i	$-0.624211\pi$
$929$	−23.1882	−0.760782	−0.380391	+	0.924826i	$0.624211\pi$
$930$	14.5526	0.477199
$931$	−47.3241	−1.55098
$932$	−5.11095	−0.167415
$933$	49.1958	1.61060
$934$	−11.6025	−0.379645
$935$	−22.5249	−0.736644
$936$	−1.98959	−0.0650316
$937$	27.2115	0.888962	0.444481	−	0.895788i	$-0.353388\pi$
$937$	27.2115	0.888962	0.444481	+	0.895788i	$0.353388\pi$
$938$	0.770613	0.0251614
$939$	−30.3901	−0.991744
$940$	0.387208	0.0126293
$941$	21.1494	0.689452	0.344726	−	0.938703i	$-0.387972\pi$
$941$	21.1494	0.689452	0.344726	+	0.938703i	$0.387972\pi$
$942$	−5.26220	−0.171452
$943$	−15.8381	−0.515758
$944$	0.646086	0.0210283
$945$	−2.23195	−0.0726054
$946$	8.23044	0.267595
$947$	15.2074	0.494173	0.247087	−	0.968993i	$-0.420527\pi$
$947$	15.2074	0.494173	0.247087	+	0.968993i	$0.420527\pi$
$948$	14.0557	0.456507
$949$	−26.6727	−0.865834
$950$	−7.08539	−0.229880
$951$	21.3898	0.693612
$952$	3.95842	0.128293
$953$	−4.60836	−0.149279	−0.0746397	−	0.997211i	$-0.523781\pi$
$953$	−4.60836	−0.149279	−0.0746397	+	0.997211i	$0.523781\pi$
$954$	3.05991	0.0990683
$955$	10.0434	0.324996
$956$	14.8031	0.478765
$957$	20.5407	0.663987
$958$	−3.22761	−0.104279
$959$	−1.26223	−0.0407596
$960$	−2.00989	−0.0648690
$961$	21.4248	0.691121
$962$	20.7238	0.668163
$963$	9.72641	0.313429
$964$	5.14459	0.165696
$965$	−6.77332	−0.218041
$966$	−6.24542	−0.200943
$967$	29.7237	0.955848	0.477924	−	0.878401i	$-0.341389\pi$
$967$	29.7237	0.955848	0.477924	+	0.878401i	$0.341389\pi$
$968$	0.609245	0.0195819
$969$	−99.5122	−3.19679
$970$	10.0439	0.322489
$971$	1.61237	0.0517434	0.0258717	−	0.999665i	$-0.491764\pi$
$971$	1.61237	0.0517434	0.0258717	+	0.999665i	$0.491764\pi$
$972$	10.3652	0.332463
$973$	−1.56158	−0.0500618
$974$	−12.3978	−0.397251
$975$	−3.84629	−0.123180
$976$	15.3973	0.492855
$977$	20.0328	0.640907	0.320453	−	0.947264i	$-0.396165\pi$
$977$	20.0328	0.640907	0.320453	+	0.947264i	$0.396165\pi$
$978$	12.0341	0.384807
$979$	2.76163	0.0882620
$980$	−6.67910	−0.213356
$981$	6.37655	0.203588
$982$	−15.6333	−0.498878
$983$	23.0399	0.734858	0.367429	−	0.930051i	$-0.380238\pi$
$983$	23.0399	0.734858	0.367429	+	0.930051i	$0.380238\pi$
$984$	−5.80319	−0.184999
$985$	−15.6507	−0.498672
$986$	−22.1544	−0.705539
$987$	0.440858	0.0140327
$988$	13.5592	0.431375
$989$	14.0058	0.445358
$990$	3.35133	0.106512
$991$	41.8899	1.33068	0.665338	−	0.746543i	$-0.268288\pi$
$991$	41.8899	1.33068	0.665338	+	0.746543i	$0.268288\pi$
$992$	−7.24049	−0.229886
$993$	2.41597	0.0766685
$994$	6.41689	0.203531
$995$	13.0829	0.414757
$996$	31.3782	0.994258
$997$	2.39130	0.0757334	0.0378667	−	0.999283i	$-0.487944\pi$
$997$	2.39130	0.0757334	0.0378667	+	0.999283i	$0.487944\pi$
$998$	24.1541	0.764586
$999$	−42.6681	−1.34996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.6	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.6	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.00989 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00989 q^{6} -0.566476 q^{7} -1.00000 q^{8} +1.03966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.00989 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.00989 q^{6} -0.566476 q^{7} -1.00000 q^{8} +1.03966 q^{9} -1.00000 q^{10} -3.22347 q^{11} -2.00989 q^{12} +1.91368 q^{13} +0.566476 q^{14} -2.00989 q^{15} +1.00000 q^{16} +6.98779 q^{17} -1.03966 q^{18} +7.08539 q^{19} +1.00000 q^{20} +1.13856 q^{21} +3.22347 q^{22} +5.48539 q^{23} +2.00989 q^{24} +1.00000 q^{25} -1.91368 q^{26} +3.94006 q^{27} -0.566476 q^{28} +3.17044 q^{29} +2.00989 q^{30} +7.24049 q^{31} -1.00000 q^{32} +6.47882 q^{33} -6.98779 q^{34} -0.566476 q^{35} +1.03966 q^{36} -10.8293 q^{37} -7.08539 q^{38} -3.84629 q^{39} -1.00000 q^{40} -2.88732 q^{41} -1.13856 q^{42} +2.55329 q^{43} -3.22347 q^{44} +1.03966 q^{45} -5.48539 q^{46} +0.387208 q^{47} -2.00989 q^{48} -6.67910 q^{49} -1.00000 q^{50} -14.0447 q^{51} +1.91368 q^{52} -2.94317 q^{53} -3.94006 q^{54} -3.22347 q^{55} +0.566476 q^{56} -14.2409 q^{57} -3.17044 q^{58} +0.646086 q^{59} -2.00989 q^{60} +15.3973 q^{61} -7.24049 q^{62} -0.588945 q^{63} +1.00000 q^{64} +1.91368 q^{65} -6.47882 q^{66} +1.36036 q^{67} +6.98779 q^{68} -11.0250 q^{69} +0.566476 q^{70} +11.3277 q^{71} -1.03966 q^{72} -13.9379 q^{73} +10.8293 q^{74} -2.00989 q^{75} +7.08539 q^{76} +1.82602 q^{77} +3.84629 q^{78} -6.99325 q^{79} +1.00000 q^{80} -11.0381 q^{81} +2.88732 q^{82} -15.6119 q^{83} +1.13856 q^{84} +6.98779 q^{85} -2.55329 q^{86} -6.37224 q^{87} +3.22347 q^{88} -0.856725 q^{89} -1.03966 q^{90} -1.08405 q^{91} +5.48539 q^{92} -14.5526 q^{93} -0.387208 q^{94} +7.08539 q^{95} +2.00989 q^{96} -10.0439 q^{97} +6.67910 q^{98} -3.35133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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