LMFDB - Embedded newform 2014.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2014,2,Mod(1,2014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2014, 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("2014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2014 = 2 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2014.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:	$16.0818709671$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - x^{5} + 50x^{4} + 21x^{3} - 61x^{2} - 52x - 10 $ x^8 - 13x^6 - x^5 + 50x^4 + 21x^3 - 61x^2 - 52*x - 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.21468$ of defining polynomial
Character	$\chi$	$=$	2014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.21468 q^{3} +1.00000 q^{4} +3.22718 q^{5} -1.21468 q^{6} -1.77598 q^{7} -1.00000 q^{8} -1.52455 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.21468 q^{3} +1.00000 q^{4} +3.22718 q^{5} -1.21468 q^{6} -1.77598 q^{7} -1.00000 q^{8} -1.52455 q^{9} -3.22718 q^{10} -5.04543 q^{11} +1.21468 q^{12} -3.83982 q^{13} +1.77598 q^{14} +3.92000 q^{15} +1.00000 q^{16} +0.609227 q^{17} +1.52455 q^{18} -1.00000 q^{19} +3.22718 q^{20} -2.15725 q^{21} +5.04543 q^{22} +4.07802 q^{23} -1.21468 q^{24} +5.41472 q^{25} +3.83982 q^{26} -5.49589 q^{27} -1.77598 q^{28} -7.78350 q^{29} -3.92000 q^{30} +5.85952 q^{31} -1.00000 q^{32} -6.12859 q^{33} -0.609227 q^{34} -5.73141 q^{35} -1.52455 q^{36} -5.22037 q^{37} +1.00000 q^{38} -4.66415 q^{39} -3.22718 q^{40} +2.17584 q^{41} +2.15725 q^{42} -5.52771 q^{43} -5.04543 q^{44} -4.92000 q^{45} -4.07802 q^{46} -4.41004 q^{47} +1.21468 q^{48} -3.84590 q^{49} -5.41472 q^{50} +0.740017 q^{51} -3.83982 q^{52} -1.00000 q^{53} +5.49589 q^{54} -16.2825 q^{55} +1.77598 q^{56} -1.21468 q^{57} +7.78350 q^{58} +3.10979 q^{59} +3.92000 q^{60} -5.06060 q^{61} -5.85952 q^{62} +2.70756 q^{63} +1.00000 q^{64} -12.3918 q^{65} +6.12859 q^{66} +0.850476 q^{67} +0.609227 q^{68} +4.95350 q^{69} +5.73141 q^{70} -9.72957 q^{71} +1.52455 q^{72} -9.55089 q^{73} +5.22037 q^{74} +6.57716 q^{75} -1.00000 q^{76} +8.96058 q^{77} +4.66415 q^{78} +5.44755 q^{79} +3.22718 q^{80} -2.10210 q^{81} -2.17584 q^{82} +13.5358 q^{83} -2.15725 q^{84} +1.96609 q^{85} +5.52771 q^{86} -9.45447 q^{87} +5.04543 q^{88} -4.97098 q^{89} +4.92000 q^{90} +6.81943 q^{91} +4.07802 q^{92} +7.11745 q^{93} +4.41004 q^{94} -3.22718 q^{95} -1.21468 q^{96} -1.99805 q^{97} +3.84590 q^{98} +7.69201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.21468	0.701297	0.350648	−	0.936507i	$-0.385961\pi$
$3$	1.21468	0.701297	0.350648	+	0.936507i	$0.385961\pi$
$4$	1.00000	0.500000
$5$	3.22718	1.44324	0.721620	−	0.692289i	$-0.243398\pi$
$5$	3.22718	1.44324	0.721620	+	0.692289i	$0.243398\pi$
$6$	−1.21468	−0.495892
$7$	−1.77598	−0.671256	−0.335628	−	0.941995i	$-0.608949\pi$
$7$	−1.77598	−0.671256	−0.335628	+	0.941995i	$0.608949\pi$
$8$	−1.00000	−0.353553
$9$	−1.52455	−0.508183
$10$	−3.22718	−1.02053
$11$	−5.04543	−1.52126	−0.760628	−	0.649188i	$-0.775109\pi$
$11$	−5.04543	−1.52126	−0.760628	+	0.649188i	$0.775109\pi$
$12$	1.21468	0.350648
$13$	−3.83982	−1.06497	−0.532487	−	0.846438i	$-0.678742\pi$
$13$	−3.83982	−1.06497	−0.532487	+	0.846438i	$0.678742\pi$
$14$	1.77598	0.474650
$15$	3.92000	1.01214
$16$	1.00000	0.250000
$17$	0.609227	0.147759	0.0738797	−	0.997267i	$-0.476462\pi$
$17$	0.609227	0.147759	0.0738797	+	0.997267i	$0.476462\pi$
$18$	1.52455	0.359340
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.22718	0.721620
$21$	−2.15725	−0.470750
$22$	5.04543	1.07569
$23$	4.07802	0.850326	0.425163	−	0.905117i	$-0.360217\pi$
$23$	4.07802	0.850326	0.425163	+	0.905117i	$0.360217\pi$
$24$	−1.21468	−0.247946
$25$	5.41472	1.08294
$26$	3.83982	0.753050
$27$	−5.49589	−1.05768
$28$	−1.77598	−0.335628
$29$	−7.78350	−1.44536	−0.722680	−	0.691183i	$-0.757090\pi$
$29$	−7.78350	−1.44536	−0.722680	+	0.691183i	$0.757090\pi$
$30$	−3.92000	−0.715691
$31$	5.85952	1.05240	0.526201	−	0.850360i	$-0.323616\pi$
$31$	5.85952	1.05240	0.526201	+	0.850360i	$0.323616\pi$
$32$	−1.00000	−0.176777
$33$	−6.12859	−1.06685
$34$	−0.609227	−0.104482
$35$	−5.73141	−0.968785
$36$	−1.52455	−0.254092
$37$	−5.22037	−0.858223	−0.429111	−	0.903252i	$-0.641173\pi$
$37$	−5.22037	−0.858223	−0.429111	+	0.903252i	$0.641173\pi$
$38$	1.00000	0.162221
$39$	−4.66415	−0.746862
$40$	−3.22718	−0.510263
$41$	2.17584	0.339809	0.169904	−	0.985461i	$-0.445654\pi$
$41$	2.17584	0.339809	0.169904	+	0.985461i	$0.445654\pi$
$42$	2.15725	0.332870
$43$	−5.52771	−0.842968	−0.421484	−	0.906836i	$-0.638491\pi$
$43$	−5.52771	−0.842968	−0.421484	+	0.906836i	$0.638491\pi$
$44$	−5.04543	−0.760628
$45$	−4.92000	−0.733430
$46$	−4.07802	−0.601271
$47$	−4.41004	−0.643271	−0.321635	−	0.946864i	$-0.604232\pi$
$47$	−4.41004	−0.643271	−0.321635	+	0.946864i	$0.604232\pi$
$48$	1.21468	0.175324
$49$	−3.84590	−0.549415
$50$	−5.41472	−0.765757
$51$	0.740017	0.103623
$52$	−3.83982	−0.532487
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	5.49589	0.747895
$55$	−16.2825	−2.19554
$56$	1.77598	0.237325
$57$	−1.21468	−0.160888
$58$	7.78350	1.02202
$59$	3.10979	0.404860	0.202430	−	0.979297i	$-0.435116\pi$
$59$	3.10979	0.404860	0.202430	+	0.979297i	$0.435116\pi$
$60$	3.92000	0.506070
$61$	−5.06060	−0.647943	−0.323972	−	0.946067i	$-0.605018\pi$
$61$	−5.06060	−0.647943	−0.323972	+	0.946067i	$0.605018\pi$
$62$	−5.85952	−0.744160
$63$	2.70756	0.341121
$64$	1.00000	0.125000
$65$	−12.3918	−1.53701
$66$	6.12859	0.754378
$67$	0.850476	0.103902	0.0519511	−	0.998650i	$-0.483456\pi$
$67$	0.850476	0.103902	0.0519511	+	0.998650i	$0.483456\pi$
$68$	0.609227	0.0738797
$69$	4.95350	0.596331
$70$	5.73141	0.685034
$71$	−9.72957	−1.15469	−0.577344	−	0.816501i	$-0.695911\pi$
$71$	−9.72957	−1.15469	−0.577344	+	0.816501i	$0.695911\pi$
$72$	1.52455	0.179670
$73$	−9.55089	−1.11785	−0.558923	−	0.829219i	$-0.688785\pi$
$73$	−9.55089	−1.11785	−0.558923	+	0.829219i	$0.688785\pi$
$74$	5.22037	0.606855
$75$	6.57716	0.759465
$76$	−1.00000	−0.114708
$77$	8.96058	1.02115
$78$	4.66415	0.528111
$79$	5.44755	0.612898	0.306449	−	0.951887i	$-0.400859\pi$
$79$	5.44755	0.612898	0.306449	+	0.951887i	$0.400859\pi$
$80$	3.22718	0.360810
$81$	−2.10210	−0.233567
$82$	−2.17584	−0.240281
$83$	13.5358	1.48575	0.742875	−	0.669430i	$-0.233462\pi$
$83$	13.5358	1.48575	0.742875	+	0.669430i	$0.233462\pi$
$84$	−2.15725	−0.235375
$85$	1.96609	0.213252
$86$	5.52771	0.596068
$87$	−9.45447	−1.01363
$88$	5.04543	0.537845
$89$	−4.97098	−0.526923	−0.263462	−	0.964670i	$-0.584864\pi$
$89$	−4.97098	−0.526923	−0.263462	+	0.964670i	$0.584864\pi$
$90$	4.92000	0.518614
$91$	6.81943	0.714870
$92$	4.07802	0.425163
$93$	7.11745	0.738046
$94$	4.41004	0.454861
$95$	−3.22718	−0.331102
$96$	−1.21468	−0.123973
$97$	−1.99805	−0.202871	−0.101436	−	0.994842i	$-0.532344\pi$
$97$	−1.99805	−0.202871	−0.101436	+	0.994842i	$0.532344\pi$
$98$	3.84590	0.388495
$99$	7.69201	0.773076
$100$	5.41472	0.541472
$101$	5.96194	0.593236	0.296618	−	0.954996i	$-0.404141\pi$
$101$	5.96194	0.593236	0.296618	+	0.954996i	$0.404141\pi$
$102$	−0.740017	−0.0732726
$103$	5.60817	0.552589	0.276294	−	0.961073i	$-0.410893\pi$
$103$	5.60817	0.552589	0.276294	+	0.961073i	$0.410893\pi$
$104$	3.83982	0.376525
$105$	−6.96183	−0.679405
$106$	1.00000	0.0971286
$107$	7.66970	0.741458	0.370729	−	0.928741i	$-0.379108\pi$
$107$	7.66970	0.741458	0.370729	+	0.928741i	$0.379108\pi$
$108$	−5.49589	−0.528842
$109$	−3.64338	−0.348972	−0.174486	−	0.984660i	$-0.555826\pi$
$109$	−3.64338	−0.348972	−0.174486	+	0.984660i	$0.555826\pi$
$110$	16.2825	1.55248
$111$	−6.34108	−0.601869
$112$	−1.77598	−0.167814
$113$	−13.9261	−1.31006	−0.655029	−	0.755604i	$-0.727343\pi$
$113$	−13.9261	−1.31006	−0.655029	+	0.755604i	$0.727343\pi$
$114$	1.21468	0.113765
$115$	13.1605	1.22723
$116$	−7.78350	−0.722680
$117$	5.85399	0.541201
$118$	−3.10979	−0.286279
$119$	−1.08197	−0.0991844
$120$	−3.92000	−0.357846
$121$	14.4564	1.31422
$122$	5.06060	0.458165
$123$	2.64295	0.238307
$124$	5.85952	0.526201
$125$	1.33838	0.119708
$126$	−2.70756	−0.241209
$127$	−6.62667	−0.588022	−0.294011	−	0.955802i	$-0.594990\pi$
$127$	−6.62667	−0.588022	−0.294011	+	0.955802i	$0.594990\pi$
$128$	−1.00000	−0.0883883
$129$	−6.71441	−0.591171
$130$	12.3918	1.08683
$131$	−9.57835	−0.836864	−0.418432	−	0.908248i	$-0.637420\pi$
$131$	−9.57835	−0.836864	−0.418432	+	0.908248i	$0.637420\pi$
$132$	−6.12859	−0.533426
$133$	1.77598	0.153997
$134$	−0.850476	−0.0734699
$135$	−17.7362	−1.52649
$136$	−0.609227	−0.0522408
$137$	15.7435	1.34506	0.672529	−	0.740071i	$-0.265208\pi$
$137$	15.7435	1.34506	0.672529	+	0.740071i	$0.265208\pi$
$138$	−4.95350	−0.421670
$139$	0.994763	0.0843747	0.0421873	−	0.999110i	$-0.486567\pi$
$139$	0.994763	0.0843747	0.0421873	+	0.999110i	$0.486567\pi$
$140$	−5.73141	−0.484392
$141$	−5.35679	−0.451123
$142$	9.72957	0.816487
$143$	19.3735	1.62010
$144$	−1.52455	−0.127046
$145$	−25.1188	−2.08600
$146$	9.55089	0.790437
$147$	−4.67155	−0.385303
$148$	−5.22037	−0.429111
$149$	−5.11161	−0.418759	−0.209380	−	0.977834i	$-0.567144\pi$
$149$	−5.11161	−0.418759	−0.209380	+	0.977834i	$0.567144\pi$
$150$	−6.57716	−0.537023
$151$	−7.19586	−0.585591	−0.292795	−	0.956175i	$-0.594585\pi$
$151$	−7.19586	−0.585591	−0.292795	+	0.956175i	$0.594585\pi$
$152$	1.00000	0.0811107
$153$	−0.928797	−0.0750888
$154$	−8.96058	−0.722064
$155$	18.9098	1.51887
$156$	−4.66415	−0.373431
$157$	5.58748	0.445930	0.222965	−	0.974826i	$-0.428426\pi$
$157$	5.58748	0.445930	0.222965	+	0.974826i	$0.428426\pi$
$158$	−5.44755	−0.433384
$159$	−1.21468	−0.0963305
$160$	−3.22718	−0.255131
$161$	−7.24247	−0.570787
$162$	2.10210	0.165157
$163$	15.2566	1.19499	0.597494	−	0.801873i	$-0.296163\pi$
$163$	15.2566	1.19499	0.597494	+	0.801873i	$0.296163\pi$
$164$	2.17584	0.169904
$165$	−19.7781	−1.53972
$166$	−13.5358	−1.05058
$167$	3.69196	0.285692	0.142846	−	0.989745i	$-0.454375\pi$
$167$	3.69196	0.285692	0.142846	+	0.989745i	$0.454375\pi$
$168$	2.15725	0.166435
$169$	1.74419	0.134168
$170$	−1.96609	−0.150792
$171$	1.52455	0.116585
$172$	−5.52771	−0.421484
$173$	−22.6946	−1.72544	−0.862718	−	0.505686i	$-0.831239\pi$
$173$	−22.6946	−1.72544	−0.862718	+	0.505686i	$0.831239\pi$
$174$	9.45447	0.716741
$175$	−9.61642	−0.726933
$176$	−5.04543	−0.380314
$177$	3.77740	0.283927
$178$	4.97098	0.372591
$179$	3.71234	0.277473	0.138737	−	0.990329i	$-0.455696\pi$
$179$	3.71234	0.277473	0.138737	+	0.990329i	$0.455696\pi$
$180$	−4.92000	−0.366715
$181$	12.6829	0.942713	0.471356	−	0.881943i	$-0.343765\pi$
$181$	12.6829	0.942713	0.471356	+	0.881943i	$0.343765\pi$
$182$	−6.81943	−0.505490
$183$	−6.14701	−0.454400
$184$	−4.07802	−0.300636
$185$	−16.8471	−1.23862
$186$	−7.11745	−0.521877
$187$	−3.07382	−0.224780
$188$	−4.41004	−0.321635
$189$	9.76057	0.709977
$190$	3.22718	0.234125
$191$	20.1037	1.45465	0.727325	−	0.686293i	$-0.240763\pi$
$191$	20.1037	1.45465	0.727325	+	0.686293i	$0.240763\pi$
$192$	1.21468	0.0876621
$193$	−8.25427	−0.594155	−0.297078	−	0.954853i	$-0.596012\pi$
$193$	−8.25427	−0.594155	−0.297078	+	0.954853i	$0.596012\pi$
$194$	1.99805	0.143452
$195$	−15.0521	−1.07790
$196$	−3.84590	−0.274707
$197$	−7.26699	−0.517752	−0.258876	−	0.965911i	$-0.583352\pi$
$197$	−7.26699	−0.517752	−0.258876	+	0.965911i	$0.583352\pi$
$198$	−7.69201	−0.546647
$199$	12.0396	0.853467	0.426734	−	0.904377i	$-0.359664\pi$
$199$	12.0396	0.853467	0.426734	+	0.904377i	$0.359664\pi$
$200$	−5.41472	−0.382879
$201$	1.03306	0.0728662
$202$	−5.96194	−0.419481
$203$	13.8233	0.970207
$204$	0.740017	0.0518116
$205$	7.02183	0.490426
$206$	−5.60817	−0.390739
$207$	−6.21714	−0.432121
$208$	−3.83982	−0.266243
$209$	5.04543	0.349000
$210$	6.96183	0.480412
$211$	20.3252	1.39924	0.699622	−	0.714513i	$-0.253352\pi$
$211$	20.3252	1.39924	0.699622	+	0.714513i	$0.253352\pi$
$212$	−1.00000	−0.0686803
$213$	−11.8183	−0.809779
$214$	−7.66970	−0.524290
$215$	−17.8389	−1.21661
$216$	5.49589	0.373948
$217$	−10.4064	−0.706431
$218$	3.64338	0.246761
$219$	−11.6013	−0.783942
$220$	−16.2825	−1.09777
$221$	−2.33932	−0.157360
$222$	6.34108	0.425585
$223$	−22.3886	−1.49925	−0.749626	−	0.661862i	$-0.769767\pi$
$223$	−22.3886	−1.49925	−0.749626	+	0.661862i	$0.769767\pi$
$224$	1.77598	0.118662
$225$	−8.25501	−0.550334
$226$	13.9261	0.926350
$227$	15.3494	1.01877	0.509386	−	0.860538i	$-0.329872\pi$
$227$	15.3494	1.01877	0.509386	+	0.860538i	$0.329872\pi$
$228$	−1.21468	−0.0804442
$229$	26.6310	1.75983	0.879913	−	0.475135i	$-0.157601\pi$
$229$	26.6310	1.75983	0.879913	+	0.475135i	$0.157601\pi$
$230$	−13.1605	−0.867779
$231$	10.8842	0.716131
$232$	7.78350	0.511012
$233$	−22.0887	−1.44708	−0.723538	−	0.690284i	$-0.757486\pi$
$233$	−22.0887	−1.44708	−0.723538	+	0.690284i	$0.757486\pi$
$234$	−5.85399	−0.382687
$235$	−14.2320	−0.928394
$236$	3.10979	0.202430
$237$	6.61704	0.429823
$238$	1.08197	0.0701340
$239$	−20.8445	−1.34832	−0.674160	−	0.738586i	$-0.735494\pi$
$239$	−20.8445	−1.34832	−0.674160	+	0.738586i	$0.735494\pi$
$240$	3.92000	0.253035
$241$	−5.08818	−0.327758	−0.163879	−	0.986480i	$-0.552401\pi$
$241$	−5.08818	−0.327758	−0.163879	+	0.986480i	$0.552401\pi$
$242$	−14.4564	−0.929292
$243$	13.9343	0.893884
$244$	−5.06060	−0.323972
$245$	−12.4114	−0.792938
$246$	−2.64295	−0.168508
$247$	3.83982	0.244322
$248$	−5.85952	−0.372080
$249$	16.4417	1.04195
$250$	−1.33838	−0.0846465
$251$	8.44073	0.532774	0.266387	−	0.963866i	$-0.414170\pi$
$251$	8.44073	0.532774	0.266387	+	0.963866i	$0.414170\pi$
$252$	2.70756	0.170561
$253$	−20.5754	−1.29356
$254$	6.62667	0.415794
$255$	2.38817	0.149553
$256$	1.00000	0.0625000
$257$	−20.0559	−1.25105	−0.625525	−	0.780204i	$-0.715115\pi$
$257$	−20.0559	−1.25105	−0.625525	+	0.780204i	$0.715115\pi$
$258$	6.71441	0.418021
$259$	9.27125	0.576088
$260$	−12.3918	−0.768506
$261$	11.8663	0.734507
$262$	9.57835	0.591752
$263$	−12.6770	−0.781695	−0.390847	−	0.920456i	$-0.627818\pi$
$263$	−12.6770	−0.781695	−0.390847	+	0.920456i	$0.627818\pi$
$264$	6.12859	0.377189
$265$	−3.22718	−0.198244
$266$	−1.77598	−0.108892
$267$	−6.03816	−0.369529
$268$	0.850476	0.0519511
$269$	−20.1799	−1.23039	−0.615196	−	0.788374i	$-0.710923\pi$
$269$	−20.1799	−1.23039	−0.615196	+	0.788374i	$0.710923\pi$
$270$	17.7362	1.07939
$271$	−0.467376	−0.0283911	−0.0141955	−	0.999899i	$-0.504519\pi$
$271$	−0.467376	−0.0283911	−0.0141955	+	0.999899i	$0.504519\pi$
$272$	0.609227	0.0369398
$273$	8.28343	0.501336
$274$	−15.7435	−0.951100
$275$	−27.3196	−1.64743
$276$	4.95350	0.298165
$277$	21.7039	1.30406	0.652030	−	0.758193i	$-0.273917\pi$
$277$	21.7039	1.30406	0.652030	+	0.758193i	$0.273917\pi$
$278$	−0.994763	−0.0596619
$279$	−8.93313	−0.534813
$280$	5.73141	0.342517
$281$	13.6640	0.815126	0.407563	−	0.913177i	$-0.366379\pi$
$281$	13.6640	0.815126	0.407563	+	0.913177i	$0.366379\pi$
$282$	5.35679	0.318992
$283$	8.74524	0.519851	0.259925	−	0.965629i	$-0.416302\pi$
$283$	8.74524	0.519851	0.259925	+	0.965629i	$0.416302\pi$
$284$	−9.72957	−0.577344
$285$	−3.92000	−0.232201
$286$	−19.3735	−1.14558
$287$	−3.86424	−0.228099
$288$	1.52455	0.0898349
$289$	−16.6288	−0.978167
$290$	25.1188	1.47503
$291$	−2.42700	−0.142273
$292$	−9.55089	−0.558923
$293$	19.2394	1.12398	0.561989	−	0.827144i	$-0.310036\pi$
$293$	19.2394	1.12398	0.561989	+	0.827144i	$0.310036\pi$
$294$	4.67155	0.272450
$295$	10.0359	0.584310
$296$	5.22037	0.303428
$297$	27.7291	1.60901
$298$	5.11161	0.296107
$299$	−15.6589	−0.905575
$300$	6.57716	0.379733
$301$	9.81709	0.565848
$302$	7.19586	0.414075
$303$	7.24186	0.416034
$304$	−1.00000	−0.0573539
$305$	−16.3315	−0.935138
$306$	0.928797	0.0530958
$307$	−0.987476	−0.0563582	−0.0281791	−	0.999603i	$-0.508971\pi$
$307$	−0.987476	−0.0563582	−0.0281791	+	0.999603i	$0.508971\pi$
$308$	8.96058	0.510576
$309$	6.81213	0.387529
$310$	−18.9098	−1.07400
$311$	−3.92081	−0.222329	−0.111164	−	0.993802i	$-0.535458\pi$
$311$	−3.92081	−0.222329	−0.111164	+	0.993802i	$0.535458\pi$
$312$	4.66415	0.264056
$313$	17.0889	0.965919	0.482960	−	0.875643i	$-0.339562\pi$
$313$	17.0889	0.965919	0.482960	+	0.875643i	$0.339562\pi$
$314$	−5.58748	−0.315320
$315$	8.73781	0.492320
$316$	5.44755	0.306449
$317$	6.12964	0.344275	0.172138	−	0.985073i	$-0.444933\pi$
$317$	6.12964	0.344275	0.172138	+	0.985073i	$0.444933\pi$
$318$	1.21468	0.0681160
$319$	39.2711	2.19876
$320$	3.22718	0.180405
$321$	9.31625	0.519982
$322$	7.24247	0.403607
$323$	−0.609227	−0.0338983
$324$	−2.10210	−0.116784
$325$	−20.7915	−1.15331
$326$	−15.2566	−0.844984
$327$	−4.42554	−0.244733
$328$	−2.17584	−0.120141
$329$	7.83213	0.431799
$330$	19.7781	1.08875
$331$	6.51582	0.358142	0.179071	−	0.983836i	$-0.442691\pi$
$331$	6.51582	0.358142	0.179071	+	0.983836i	$0.442691\pi$
$332$	13.5358	0.742875
$333$	7.95870	0.436134
$334$	−3.69196	−0.202015
$335$	2.74464	0.149956
$336$	−2.15725	−0.117687
$337$	23.6576	1.28871	0.644355	−	0.764727i	$-0.277126\pi$
$337$	23.6576	1.28871	0.644355	+	0.764727i	$0.277126\pi$
$338$	−1.74419	−0.0948713
$339$	−16.9158	−0.918739
$340$	1.96609	0.106626
$341$	−29.5638	−1.60097
$342$	−1.52455	−0.0824382
$343$	19.2621	1.04005
$344$	5.52771	0.298034
$345$	15.9858	0.860649
$346$	22.6946	1.22007
$347$	−11.4389	−0.614074	−0.307037	−	0.951698i	$-0.599338\pi$
$347$	−11.4389	−0.614074	−0.307037	+	0.951698i	$0.599338\pi$
$348$	−9.45447	−0.506813
$349$	−28.2305	−1.51115	−0.755573	−	0.655065i	$-0.772641\pi$
$349$	−28.2305	−1.51115	−0.755573	+	0.655065i	$0.772641\pi$
$350$	9.61642	0.514019
$351$	21.1032	1.12640
$352$	5.04543	0.268923
$353$	17.4693	0.929799	0.464899	−	0.885364i	$-0.346091\pi$
$353$	17.4693	0.929799	0.464899	+	0.885364i	$0.346091\pi$
$354$	−3.77740	−0.200766
$355$	−31.3991	−1.66649
$356$	−4.97098	−0.263462
$357$	−1.31425	−0.0695577
$358$	−3.71234	−0.196203
$359$	−23.0863	−1.21845	−0.609225	−	0.792997i	$-0.708519\pi$
$359$	−23.0863	−1.21845	−0.609225	+	0.792997i	$0.708519\pi$
$360$	4.92000	0.259307
$361$	1.00000	0.0526316
$362$	−12.6829	−0.666599
$363$	17.5599	0.921657
$364$	6.81943	0.357435
$365$	−30.8225	−1.61332
$366$	6.14701	0.321310
$367$	16.9973	0.887252	0.443626	−	0.896212i	$-0.353692\pi$
$367$	16.9973	0.887252	0.443626	+	0.896212i	$0.353692\pi$
$368$	4.07802	0.212582
$369$	−3.31717	−0.172685
$370$	16.8471	0.875838
$371$	1.77598	0.0922042
$372$	7.11745	0.369023
$373$	−17.5214	−0.907225	−0.453613	−	0.891199i	$-0.649865\pi$
$373$	−17.5214	−0.907225	−0.453613	+	0.891199i	$0.649865\pi$
$374$	3.07382	0.158943
$375$	1.62570	0.0839510
$376$	4.41004	0.227430
$377$	29.8872	1.53927
$378$	−9.76057	−0.502029
$379$	−9.98468	−0.512879	−0.256439	−	0.966560i	$-0.582549\pi$
$379$	−9.98468	−0.512879	−0.256439	+	0.966560i	$0.582549\pi$
$380$	−3.22718	−0.165551
$381$	−8.04930	−0.412378
$382$	−20.1037	−1.02859
$383$	−23.0803	−1.17935	−0.589675	−	0.807641i	$-0.700744\pi$
$383$	−23.0803	−1.17935	−0.589675	+	0.807641i	$0.700744\pi$
$384$	−1.21468	−0.0619865
$385$	28.9174	1.47377
$386$	8.25427	0.420131
$387$	8.42727	0.428382
$388$	−1.99805	−0.101436
$389$	−16.9665	−0.860233	−0.430117	−	0.902773i	$-0.641528\pi$
$389$	−16.9665	−0.860233	−0.430117	+	0.902773i	$0.641528\pi$
$390$	15.0521	0.762192
$391$	2.48444	0.125644
$392$	3.84590	0.194248
$393$	−11.6346	−0.586890
$394$	7.26699	0.366106
$395$	17.5803	0.884559
$396$	7.69201	0.386538
$397$	21.7663	1.09242	0.546210	−	0.837648i	$-0.316070\pi$
$397$	21.7663	1.09242	0.546210	+	0.837648i	$0.316070\pi$
$398$	−12.0396	−0.603493
$399$	2.15725	0.107997
$400$	5.41472	0.270736
$401$	−14.0561	−0.701928	−0.350964	−	0.936389i	$-0.614146\pi$
$401$	−14.0561	−0.701928	−0.350964	+	0.936389i	$0.614146\pi$
$402$	−1.03306	−0.0515242
$403$	−22.4995	−1.12078
$404$	5.96194	0.296618
$405$	−6.78387	−0.337093
$406$	−13.8233	−0.686040
$407$	26.3390	1.30558
$408$	−0.740017	−0.0366363
$409$	−8.98930	−0.444492	−0.222246	−	0.974991i	$-0.571339\pi$
$409$	−8.98930	−0.444492	−0.222246	+	0.974991i	$0.571339\pi$
$410$	−7.02183	−0.346784
$411$	19.1233	0.943285
$412$	5.60817	0.276294
$413$	−5.52291	−0.271765
$414$	6.21714	0.305556
$415$	43.6826	2.14430
$416$	3.83982	0.188262
$417$	1.20832	0.0591717
$418$	−5.04543	−0.246780
$419$	−32.1878	−1.57247	−0.786237	−	0.617925i	$-0.787974\pi$
$419$	−32.1878	−1.57247	−0.786237	+	0.617925i	$0.787974\pi$
$420$	−6.96183	−0.339703
$421$	11.3911	0.555169	0.277585	−	0.960701i	$-0.410466\pi$
$421$	11.3911	0.555169	0.277585	+	0.960701i	$0.410466\pi$
$422$	−20.3252	−0.989416
$423$	6.72332	0.326899
$424$	1.00000	0.0485643
$425$	3.29880	0.160015
$426$	11.8183	0.572600
$427$	8.98751	0.434936
$428$	7.66970	0.370729
$429$	23.5327	1.13617
$430$	17.8389	0.860270
$431$	−5.67074	−0.273150	−0.136575	−	0.990630i	$-0.543609\pi$
$431$	−5.67074	−0.273150	−0.136575	+	0.990630i	$0.543609\pi$
$432$	−5.49589	−0.264421
$433$	24.9319	1.19815	0.599076	−	0.800692i	$-0.295535\pi$
$433$	24.9319	1.19815	0.599076	+	0.800692i	$0.295535\pi$
$434$	10.4064	0.499522
$435$	−30.5113	−1.46291
$436$	−3.64338	−0.174486
$437$	−4.07802	−0.195078
$438$	11.6013	0.554331
$439$	−7.22356	−0.344762	−0.172381	−	0.985030i	$-0.555146\pi$
$439$	−7.22356	−0.344762	−0.172381	+	0.985030i	$0.555146\pi$
$440$	16.2825	0.776240
$441$	5.86327	0.279203
$442$	2.33932	0.111270
$443$	2.29358	0.108971	0.0544856	−	0.998515i	$-0.482648\pi$
$443$	2.29358	0.108971	0.0544856	+	0.998515i	$0.482648\pi$
$444$	−6.34108	−0.300934
$445$	−16.0423	−0.760477
$446$	22.3886	1.06013
$447$	−6.20897	−0.293674
$448$	−1.77598	−0.0839070
$449$	−26.1364	−1.23345	−0.616727	−	0.787177i	$-0.711542\pi$
$449$	−26.1364	−1.23345	−0.616727	+	0.787177i	$0.711542\pi$
$450$	8.25501	0.389145
$451$	−10.9780	−0.516936
$452$	−13.9261	−0.655029
$453$	−8.74068	−0.410673
$454$	−15.3494	−0.720381
$455$	22.0075	1.03173
$456$	1.21468	0.0568827
$457$	−9.32988	−0.436433	−0.218217	−	0.975900i	$-0.570024\pi$
$457$	−9.32988	−0.436433	−0.218217	+	0.975900i	$0.570024\pi$
$458$	−26.6310	−1.24438
$459$	−3.34824	−0.156283
$460$	13.1605	0.613613
$461$	−4.72952	−0.220276	−0.110138	−	0.993916i	$-0.535129\pi$
$461$	−4.72952	−0.220276	−0.110138	+	0.993916i	$0.535129\pi$
$462$	−10.8842	−0.506381
$463$	27.4663	1.27646	0.638232	−	0.769844i	$-0.279666\pi$
$463$	27.4663	1.27646	0.638232	+	0.769844i	$0.279666\pi$
$464$	−7.78350	−0.361340
$465$	22.9693	1.06518
$466$	22.0887	1.02324
$467$	−0.409855	−0.0189658	−0.00948291	−	0.999955i	$-0.503019\pi$
$467$	−0.409855	−0.0189658	−0.00948291	+	0.999955i	$0.503019\pi$
$468$	5.85399	0.270601
$469$	−1.51043	−0.0697450
$470$	14.2320	0.656474
$471$	6.78701	0.312729
$472$	−3.10979	−0.143139
$473$	27.8897	1.28237
$474$	−6.61704	−0.303931
$475$	−5.41472	−0.248444
$476$	−1.08197	−0.0495922
$477$	1.52455	0.0698043
$478$	20.8445	0.953406
$479$	−8.49426	−0.388112	−0.194056	−	0.980990i	$-0.562164\pi$
$479$	−8.49426	−0.388112	−0.194056	+	0.980990i	$0.562164\pi$
$480$	−3.92000	−0.178923
$481$	20.0452	0.913984
$482$	5.08818	0.231760
$483$	−8.79730	−0.400291
$484$	14.4564	0.657109
$485$	−6.44808	−0.292792
$486$	−13.9343	−0.632071
$487$	−10.5754	−0.479216	−0.239608	−	0.970870i	$-0.577019\pi$
$487$	−10.5754	−0.479216	−0.239608	+	0.970870i	$0.577019\pi$
$488$	5.06060	0.229082
$489$	18.5319	0.838041
$490$	12.4114	0.560692
$491$	−25.9327	−1.17033	−0.585163	−	0.810916i	$-0.698969\pi$
$491$	−25.9327	−1.17033	−0.585163	+	0.810916i	$0.698969\pi$
$492$	2.64295	0.119153
$493$	−4.74192	−0.213565
$494$	−3.83982	−0.172761
$495$	24.8235	1.11574
$496$	5.85952	0.263100
$497$	17.2795	0.775091
$498$	−16.4417	−0.736771
$499$	36.7310	1.64431	0.822154	−	0.569266i	$-0.192772\pi$
$499$	36.7310	1.64431	0.822154	+	0.569266i	$0.192772\pi$
$500$	1.33838	0.0598541
$501$	4.48455	0.200355
$502$	−8.44073	−0.376728
$503$	18.9137	0.843320	0.421660	−	0.906754i	$-0.361448\pi$
$503$	18.9137	0.843320	0.421660	+	0.906754i	$0.361448\pi$
$504$	−2.70756	−0.120605
$505$	19.2403	0.856182
$506$	20.5754	0.914687
$507$	2.11863	0.0940917
$508$	−6.62667	−0.294011
$509$	3.11619	0.138123	0.0690614	−	0.997612i	$-0.478000\pi$
$509$	3.11619	0.138123	0.0690614	+	0.997612i	$0.478000\pi$
$510$	−2.38817	−0.105750
$511$	16.9622	0.750362
$512$	−1.00000	−0.0441942
$513$	5.49589	0.242649
$514$	20.0559	0.884626
$515$	18.0986	0.797519
$516$	−6.71441	−0.295585
$517$	22.2506	0.978579
$518$	−9.27125	−0.407355
$519$	−27.5667	−1.21004
$520$	12.3918	0.543416
$521$	43.9330	1.92474	0.962370	−	0.271742i	$-0.0875997\pi$
$521$	43.9330	1.92474	0.962370	+	0.271742i	$0.0875997\pi$
$522$	−11.8663	−0.519375
$523$	−35.0395	−1.53217	−0.766084	−	0.642740i	$-0.777798\pi$
$523$	−35.0395	−1.53217	−0.766084	+	0.642740i	$0.777798\pi$
$524$	−9.57835	−0.418432
$525$	−11.6809	−0.509796
$526$	12.6770	0.552742
$527$	3.56978	0.155502
$528$	−6.12859	−0.266713
$529$	−6.36974	−0.276945
$530$	3.22718	0.140180
$531$	−4.74102	−0.205743
$532$	1.77598	0.0769984
$533$	−8.35482	−0.361887
$534$	6.03816	0.261297
$535$	24.7516	1.07010
$536$	−0.850476	−0.0367350
$537$	4.50931	0.194591
$538$	20.1799	0.870018
$539$	19.4043	0.835800
$540$	−17.7362	−0.763246
$541$	19.0502	0.819030	0.409515	−	0.912303i	$-0.365698\pi$
$541$	19.0502	0.819030	0.409515	+	0.912303i	$0.365698\pi$
$542$	0.467376	0.0200755
$543$	15.4057	0.661121
$544$	−0.609227	−0.0261204
$545$	−11.7579	−0.503651
$546$	−8.28343	−0.354498
$547$	−8.56110	−0.366046	−0.183023	−	0.983109i	$-0.558588\pi$
$547$	−8.56110	−0.366046	−0.183023	+	0.983109i	$0.558588\pi$
$548$	15.7435	0.672529
$549$	7.71513	0.329274
$550$	27.3196	1.16491
$551$	7.78350	0.331588
$552$	−4.95350	−0.210835
$553$	−9.67473	−0.411411
$554$	−21.7039	−0.922110
$555$	−20.4638	−0.868642
$556$	0.994763	0.0421873
$557$	12.6983	0.538045	0.269023	−	0.963134i	$-0.413299\pi$
$557$	12.6983	0.538045	0.269023	+	0.963134i	$0.413299\pi$
$558$	8.93313	0.378170
$559$	21.2254	0.897738
$560$	−5.73141	−0.242196
$561$	−3.73371	−0.157637
$562$	−13.6640	−0.576381
$563$	17.3271	0.730249	0.365125	−	0.930959i	$-0.381026\pi$
$563$	17.3271	0.730249	0.365125	+	0.930959i	$0.381026\pi$
$564$	−5.35679	−0.225562
$565$	−44.9421	−1.89073
$566$	−8.74524	−0.367590
$567$	3.73329	0.156783
$568$	9.72957	0.408244
$569$	−4.16816	−0.174738	−0.0873691	−	0.996176i	$-0.527846\pi$
$569$	−4.16816	−0.174738	−0.0873691	+	0.996176i	$0.527846\pi$
$570$	3.92000	0.164191
$571$	39.6088	1.65758	0.828789	−	0.559561i	$-0.189030\pi$
$571$	39.6088	1.65758	0.828789	+	0.559561i	$0.189030\pi$
$572$	19.3735	0.810048
$573$	24.4195	1.02014
$574$	3.86424	0.161290
$575$	22.0813	0.920856
$576$	−1.52455	−0.0635229
$577$	−30.1601	−1.25558	−0.627792	−	0.778381i	$-0.716041\pi$
$577$	−30.1601	−1.25558	−0.627792	+	0.778381i	$0.716041\pi$
$578$	16.6288	0.691669
$579$	−10.0263	−0.416679
$580$	−25.1188	−1.04300
$581$	−24.0393	−0.997319
$582$	2.42700	0.100602
$583$	5.04543	0.208961
$584$	9.55089	0.395219
$585$	18.8919	0.781084
$586$	−19.2394	−0.794773
$587$	11.2710	0.465205	0.232602	−	0.972572i	$-0.425276\pi$
$587$	11.2710	0.465205	0.232602	+	0.972572i	$0.425276\pi$
$588$	−4.67155	−0.192651
$589$	−5.85952	−0.241437
$590$	−10.0359	−0.413169
$591$	−8.82708	−0.363098
$592$	−5.22037	−0.214556
$593$	−16.8110	−0.690346	−0.345173	−	0.938539i	$-0.612180\pi$
$593$	−16.8110	−0.690346	−0.345173	+	0.938539i	$0.612180\pi$
$594$	−27.7291	−1.13774
$595$	−3.49173	−0.143147
$596$	−5.11161	−0.209380
$597$	14.6243	0.598534
$598$	15.6589	0.640338
$599$	14.4156	0.589006	0.294503	−	0.955651i	$-0.404846\pi$
$599$	14.4156	0.589006	0.294503	+	0.955651i	$0.404846\pi$
$600$	−6.57716	−0.268511
$601$	−29.2911	−1.19481	−0.597403	−	0.801941i	$-0.703801\pi$
$601$	−29.2911	−1.19481	−0.597403	+	0.801941i	$0.703801\pi$
$602$	−9.81709	−0.400115
$603$	−1.29659	−0.0528013
$604$	−7.19586	−0.292795
$605$	46.6535	1.89673
$606$	−7.24186	−0.294181
$607$	−39.2338	−1.59245	−0.796226	−	0.605000i	$-0.793173\pi$
$607$	−39.2338	−1.59245	−0.796226	+	0.605000i	$0.793173\pi$
$608$	1.00000	0.0405554
$609$	16.7909	0.680403
$610$	16.3315	0.661242
$611$	16.9337	0.685066
$612$	−0.928797	−0.0375444
$613$	41.2794	1.66726	0.833630	−	0.552324i	$-0.186259\pi$
$613$	41.2794	1.66726	0.833630	+	0.552324i	$0.186259\pi$
$614$	0.987476	0.0398513
$615$	8.52929	0.343934
$616$	−8.96058	−0.361032
$617$	−23.0541	−0.928122	−0.464061	−	0.885803i	$-0.653608\pi$
$617$	−23.0541	−0.928122	−0.464061	+	0.885803i	$0.653608\pi$
$618$	−6.81213	−0.274024
$619$	26.1910	1.05270	0.526352	−	0.850267i	$-0.323559\pi$
$619$	26.1910	1.05270	0.526352	+	0.850267i	$0.323559\pi$
$620$	18.9098	0.759434
$621$	−22.4123	−0.899376
$622$	3.92081	0.157210
$623$	8.82835	0.353701
$624$	−4.66415	−0.186716
$625$	−22.7544	−0.910176
$626$	−17.0889	−0.683008
$627$	6.12859	0.244752
$628$	5.58748	0.222965
$629$	−3.18039	−0.126810
$630$	−8.73781	−0.348123
$631$	−29.0549	−1.15666	−0.578329	−	0.815804i	$-0.696295\pi$
$631$	−29.0549	−1.15666	−0.578329	+	0.815804i	$0.696295\pi$
$632$	−5.44755	−0.216692
$633$	24.6887	0.981286
$634$	−6.12964	−0.243439
$635$	−21.3855	−0.848658
$636$	−1.21468	−0.0481653
$637$	14.7676	0.585112
$638$	−39.2711	−1.55476
$639$	14.8332	0.586793
$640$	−3.22718	−0.127566
$641$	−21.2945	−0.841084	−0.420542	−	0.907273i	$-0.638160\pi$
$641$	−21.2945	−0.841084	−0.420542	+	0.907273i	$0.638160\pi$
$642$	−9.31625	−0.367683
$643$	−19.7951	−0.780641	−0.390320	−	0.920679i	$-0.627636\pi$
$643$	−19.7951	−0.780641	−0.390320	+	0.920679i	$0.627636\pi$
$644$	−7.24247	−0.285393
$645$	−21.6686	−0.853202
$646$	0.609227	0.0239697
$647$	9.45168	0.371584	0.185792	−	0.982589i	$-0.440515\pi$
$647$	9.45168	0.371584	0.185792	+	0.982589i	$0.440515\pi$
$648$	2.10210	0.0825784
$649$	−15.6902	−0.615895
$650$	20.7915	0.815511
$651$	−12.6404	−0.495418
$652$	15.2566	0.597494
$653$	27.6776	1.08311	0.541553	−	0.840666i	$-0.317836\pi$
$653$	27.6776	1.08311	0.541553	+	0.840666i	$0.317836\pi$
$654$	4.42554	0.173052
$655$	−30.9111	−1.20780
$656$	2.17584	0.0849522
$657$	14.5608	0.568071
$658$	−7.83213	−0.305328
$659$	−31.8529	−1.24081	−0.620406	−	0.784281i	$-0.713032\pi$
$659$	−31.8529	−1.24081	−0.620406	+	0.784281i	$0.713032\pi$
$660$	−19.7781	−0.769862
$661$	−5.68019	−0.220934	−0.110467	−	0.993880i	$-0.535235\pi$
$661$	−5.68019	−0.220934	−0.110467	+	0.993880i	$0.535235\pi$
$662$	−6.51582	−0.253245
$663$	−2.84153	−0.110356
$664$	−13.5358	−0.525292
$665$	5.73141	0.222254
$666$	−7.95870	−0.308393
$667$	−31.7413	−1.22903
$668$	3.69196	0.142846
$669$	−27.1950	−1.05142
$670$	−2.74464	−0.106035
$671$	25.5329	0.985687
$672$	2.15725	0.0832176
$673$	7.74219	0.298440	0.149220	−	0.988804i	$-0.452324\pi$
$673$	7.74219	0.298440	0.149220	+	0.988804i	$0.452324\pi$
$674$	−23.6576	−0.911255
$675$	−29.7587	−1.14541
$676$	1.74419	0.0670841
$677$	−44.3474	−1.70441	−0.852205	−	0.523208i	$-0.824735\pi$
$677$	−44.3474	−1.70441	−0.852205	+	0.523208i	$0.824735\pi$
$678$	16.9158	0.649646
$679$	3.54849	0.136179
$680$	−1.96609	−0.0753961
$681$	18.6446	0.714462
$682$	29.5638	1.13206
$683$	42.1371	1.61233	0.806166	−	0.591689i	$-0.201539\pi$
$683$	42.1371	1.61233	0.806166	+	0.591689i	$0.201539\pi$
$684$	1.52455	0.0582926
$685$	50.8072	1.94124
$686$	−19.2621	−0.735430
$687$	32.3482	1.23416
$688$	−5.52771	−0.210742
$689$	3.83982	0.146285
$690$	−15.9858	−0.608571
$691$	−43.7347	−1.66375	−0.831874	−	0.554965i	$-0.812732\pi$
$691$	−43.7347	−1.66375	−0.831874	+	0.554965i	$0.812732\pi$
$692$	−22.6946	−0.862718
$693$	−13.6608	−0.518932
$694$	11.4389	0.434216
$695$	3.21028	0.121773
$696$	9.45447	0.358371
$697$	1.32558	0.0502099
$698$	28.2305	1.06854
$699$	−26.8307	−1.01483
$700$	−9.61642	−0.363467
$701$	−21.4172	−0.808917	−0.404458	−	0.914556i	$-0.632540\pi$
$701$	−21.4172	−0.808917	−0.404458	+	0.914556i	$0.632540\pi$
$702$	−21.1032	−0.796489
$703$	5.22037	0.196890
$704$	−5.04543	−0.190157
$705$	−17.2874	−0.651080
$706$	−17.4693	−0.657467
$707$	−10.5883	−0.398213
$708$	3.77740	0.141963
$709$	33.8315	1.27057	0.635284	−	0.772279i	$-0.280883\pi$
$709$	33.8315	1.27057	0.635284	+	0.772279i	$0.280883\pi$
$710$	31.3991	1.17839
$711$	−8.30506	−0.311464
$712$	4.97098	0.186295
$713$	23.8953	0.894885
$714$	1.31425	0.0491847
$715$	62.5220	2.33819
$716$	3.71234	0.138737
$717$	−25.3194	−0.945572
$718$	23.0863	0.861574
$719$	−5.97336	−0.222769	−0.111384	−	0.993777i	$-0.535528\pi$
$719$	−5.97336	−0.222769	−0.111384	+	0.993777i	$0.535528\pi$
$720$	−4.92000	−0.183358
$721$	−9.95998	−0.370929
$722$	−1.00000	−0.0372161
$723$	−6.18052	−0.229856
$724$	12.6829	0.471356
$725$	−42.1455	−1.56524
$726$	−17.5599	−0.651710
$727$	6.31979	0.234388	0.117194	−	0.993109i	$-0.462610\pi$
$727$	6.31979	0.234388	0.117194	+	0.993109i	$0.462610\pi$
$728$	−6.81943	−0.252745
$729$	23.2320	0.860445
$730$	30.8225	1.14079
$731$	−3.36763	−0.124556
$732$	−6.14701	−0.227200
$733$	33.9005	1.25214	0.626071	−	0.779766i	$-0.284662\pi$
$733$	33.9005	1.25214	0.626071	+	0.779766i	$0.284662\pi$
$734$	−16.9973	−0.627382
$735$	−15.0759	−0.556085
$736$	−4.07802	−0.150318
$737$	−4.29102	−0.158062
$738$	3.31717	0.122107
$739$	2.61206	0.0960861	0.0480431	−	0.998845i	$-0.484702\pi$
$739$	2.61206	0.0960861	0.0480431	+	0.998845i	$0.484702\pi$
$740$	−16.8471	−0.619311
$741$	4.66415	0.171342
$742$	−1.77598	−0.0651982
$743$	−17.7888	−0.652609	−0.326305	−	0.945265i	$-0.605804\pi$
$743$	−17.7888	−0.652609	−0.326305	+	0.945265i	$0.605804\pi$
$744$	−7.11745	−0.260939
$745$	−16.4961	−0.604370
$746$	17.5214	0.641505
$747$	−20.6360	−0.755033
$748$	−3.07382	−0.112390
$749$	−13.6212	−0.497709
$750$	−1.62570	−0.0593623
$751$	−33.3327	−1.21633	−0.608163	−	0.793812i	$-0.708093\pi$
$751$	−33.3327	−1.21633	−0.608163	+	0.793812i	$0.708093\pi$
$752$	−4.41004	−0.160818
$753$	10.2528	0.373633
$754$	−29.8872	−1.08843
$755$	−23.2224	−0.845149
$756$	9.76057	0.354988
$757$	49.7954	1.80984	0.904922	−	0.425577i	$-0.139929\pi$
$757$	49.7954	1.80984	0.904922	+	0.425577i	$0.139929\pi$
$758$	9.98468	0.362660
$759$	−24.9925	−0.907172
$760$	3.22718	0.117062
$761$	−9.44662	−0.342440	−0.171220	−	0.985233i	$-0.554771\pi$
$761$	−9.44662	−0.342440	−0.171220	+	0.985233i	$0.554771\pi$
$762$	8.04930	0.291595
$763$	6.47056	0.234250
$764$	20.1037	0.727325
$765$	−2.99740	−0.108371
$766$	23.0803	0.833926
$767$	−11.9410	−0.431165
$768$	1.21468	0.0438310
$769$	43.4361	1.56635	0.783173	−	0.621804i	$-0.213600\pi$
$769$	43.4361	1.56635	0.783173	+	0.621804i	$0.213600\pi$
$770$	−28.9174	−1.04211
$771$	−24.3615	−0.877357
$772$	−8.25427	−0.297078
$773$	−35.7849	−1.28709	−0.643547	−	0.765406i	$-0.722538\pi$
$773$	−35.7849	−1.28709	−0.643547	+	0.765406i	$0.722538\pi$
$774$	−8.42727	−0.302912
$775$	31.7277	1.13969
$776$	1.99805	0.0717259
$777$	11.2616	0.404008
$778$	16.9665	0.608277
$779$	−2.17584	−0.0779575
$780$	−15.0521	−0.538951
$781$	49.0899	1.75657
$782$	−2.48444	−0.0888435
$783$	42.7772	1.52873
$784$	−3.84590	−0.137354
$785$	18.0318	0.643584
$786$	11.6346	0.414994
$787$	52.0232	1.85443	0.927213	−	0.374534i	$-0.122197\pi$
$787$	52.0232	1.85443	0.927213	+	0.374534i	$0.122197\pi$
$788$	−7.26699	−0.258876
$789$	−15.3985	−0.548200
$790$	−17.5803	−0.625478
$791$	24.7324	0.879384
$792$	−7.69201	−0.273324
$793$	19.4318	0.690042
$794$	−21.7663	−0.772457
$795$	−3.92000	−0.139028
$796$	12.0396	0.426734
$797$	−13.8346	−0.490046	−0.245023	−	0.969517i	$-0.578796\pi$
$797$	−13.8346	−0.490046	−0.245023	+	0.969517i	$0.578796\pi$
$798$	−2.15725	−0.0763657
$799$	−2.68672	−0.0950492
$800$	−5.41472	−0.191439
$801$	7.57851	0.267773
$802$	14.0561	0.496338
$803$	48.1884	1.70053
$804$	1.03306	0.0364331
$805$	−23.3728	−0.823783
$806$	22.4995	0.792511
$807$	−24.5122	−0.862869
$808$	−5.96194	−0.209740
$809$	−52.4870	−1.84534	−0.922672	−	0.385585i	$-0.874000\pi$
$809$	−52.4870	−1.84534	−0.922672	+	0.385585i	$0.874000\pi$
$810$	6.78387	0.238361
$811$	−45.7008	−1.60477	−0.802387	−	0.596805i	$-0.796437\pi$
$811$	−45.7008	−1.60477	−0.802387	+	0.596805i	$0.796437\pi$
$812$	13.8233	0.485103
$813$	−0.567713	−0.0199106
$814$	−26.3390	−0.923182
$815$	49.2358	1.72466
$816$	0.740017	0.0259058
$817$	5.52771	0.193390
$818$	8.98930	0.314303
$819$	−10.3966	−0.363285
$820$	7.02183	0.245213
$821$	36.6529	1.27919	0.639597	−	0.768710i	$-0.279101\pi$
$821$	36.6529	1.27919	0.639597	+	0.768710i	$0.279101\pi$
$822$	−19.1233	−0.667003
$823$	2.35606	0.0821272	0.0410636	−	0.999157i	$-0.486925\pi$
$823$	2.35606	0.0821272	0.0410636	+	0.999157i	$0.486925\pi$
$824$	−5.60817	−0.195370
$825$	−33.1846	−1.15534
$826$	5.52291	0.192167
$827$	−51.4829	−1.79024	−0.895118	−	0.445830i	$-0.852909\pi$
$827$	−51.4829	−1.79024	−0.895118	+	0.445830i	$0.852909\pi$
$828$	−6.21714	−0.216061
$829$	−16.1593	−0.561236	−0.280618	−	0.959820i	$-0.590539\pi$
$829$	−16.1593	−0.561236	−0.280618	+	0.959820i	$0.590539\pi$
$830$	−43.6826	−1.51625
$831$	26.3633	0.914533
$832$	−3.83982	−0.133122
$833$	−2.34303	−0.0811812
$834$	−1.20832	−0.0418407
$835$	11.9146	0.412323
$836$	5.04543	0.174500
$837$	−32.2033	−1.11311
$838$	32.1878	1.11191
$839$	24.8079	0.856463	0.428231	−	0.903669i	$-0.359137\pi$
$839$	24.8079	0.856463	0.428231	+	0.903669i	$0.359137\pi$
$840$	6.96183	0.240206
$841$	31.5828	1.08906
$842$	−11.3911	−0.392564
$843$	16.5974	0.571645
$844$	20.3252	0.699622
$845$	5.62881	0.193637
$846$	−6.72332	−0.231153
$847$	−25.6742	−0.882177
$848$	−1.00000	−0.0343401
$849$	10.6227	0.364570
$850$	−3.29880	−0.113148
$851$	−21.2888	−0.729769
$852$	−11.8183	−0.404889
$853$	11.7845	0.403492	0.201746	−	0.979438i	$-0.435338\pi$
$853$	11.7845	0.403492	0.201746	+	0.979438i	$0.435338\pi$
$854$	−8.98751	−0.307546
$855$	4.92000	0.168260
$856$	−7.66970	−0.262145
$857$	−35.0208	−1.19629	−0.598143	−	0.801389i	$-0.704095\pi$
$857$	−35.0208	−1.19629	−0.598143	+	0.801389i	$0.704095\pi$
$858$	−23.5327	−0.803392
$859$	11.9600	0.408069	0.204034	−	0.978964i	$-0.434595\pi$
$859$	11.9600	0.408069	0.204034	+	0.978964i	$0.434595\pi$
$860$	−17.8389	−0.608303
$861$	−4.69382	−0.159965
$862$	5.67074	0.193146
$863$	1.31694	0.0448291	0.0224145	−	0.999749i	$-0.492865\pi$
$863$	1.31694	0.0448291	0.0224145	+	0.999749i	$0.492865\pi$
$864$	5.49589	0.186974
$865$	−73.2395	−2.49022
$866$	−24.9319	−0.847221
$867$	−20.1987	−0.685985
$868$	−10.4064	−0.353216
$869$	−27.4853	−0.932374
$870$	30.5113	1.03443
$871$	−3.26567	−0.110653
$872$	3.64338	0.123380
$873$	3.04613	0.103096
$874$	4.07802	0.137941
$875$	−2.37693	−0.0803549
$876$	−11.6013	−0.391971
$877$	3.62080	0.122266	0.0611329	−	0.998130i	$-0.480529\pi$
$877$	3.62080	0.122266	0.0611329	+	0.998130i	$0.480529\pi$
$878$	7.22356	0.243783
$879$	23.3698	0.788243
$880$	−16.2825	−0.548884
$881$	17.6507	0.594666	0.297333	−	0.954774i	$-0.403903\pi$
$881$	17.6507	0.594666	0.297333	+	0.954774i	$0.403903\pi$
$882$	−5.86327	−0.197427
$883$	−6.02314	−0.202695	−0.101347	−	0.994851i	$-0.532315\pi$
$883$	−6.02314	−0.202695	−0.101347	+	0.994851i	$0.532315\pi$
$884$	−2.33932	−0.0786799
$885$	12.1904	0.409774
$886$	−2.29358	−0.0770542
$887$	8.92210	0.299575	0.149787	−	0.988718i	$-0.452141\pi$
$887$	8.92210	0.299575	0.149787	+	0.988718i	$0.452141\pi$
$888$	6.34108	0.212793
$889$	11.7688	0.394714
$890$	16.0423	0.537738
$891$	10.6060	0.355315
$892$	−22.3886	−0.749626
$893$	4.41004	0.147576
$894$	6.20897	0.207659
$895$	11.9804	0.400461
$896$	1.77598	0.0593312
$897$	−19.0205	−0.635077
$898$	26.1364	0.872183
$899$	−45.6076	−1.52110
$900$	−8.25501	−0.275167
$901$	−0.609227	−0.0202963
$902$	10.9780	0.365529
$903$	11.9246	0.396827
$904$	13.9261	0.463175
$905$	40.9301	1.36056
$906$	8.74068	0.290390
$907$	−0.237277	−0.00787866	−0.00393933	−	0.999992i	$-0.501254\pi$
$907$	−0.237277	−0.00787866	−0.00393933	+	0.999992i	$0.501254\pi$
$908$	15.3494	0.509386
$909$	−9.08928	−0.301472
$910$	−22.0075	−0.729543
$911$	12.1493	0.402523	0.201261	−	0.979538i	$-0.435496\pi$
$911$	12.1493	0.402523	0.201261	+	0.979538i	$0.435496\pi$
$912$	−1.21468	−0.0402221
$913$	−68.2941	−2.26021
$914$	9.32988	0.308605
$915$	−19.8375	−0.655809
$916$	26.6310	0.879913
$917$	17.0109	0.561750
$918$	3.34824	0.110509
$919$	−17.1760	−0.566583	−0.283292	−	0.959034i	$-0.591426\pi$
$919$	−17.1760	−0.566583	−0.283292	+	0.959034i	$0.591426\pi$
$920$	−13.1605	−0.433890
$921$	−1.19947	−0.0395238
$922$	4.72952	0.155759
$923$	37.3598	1.22971
$924$	10.8842	0.358065
$925$	−28.2668	−0.929407
$926$	−27.4663	−0.902597
$927$	−8.54992	−0.280816
$928$	7.78350	0.255506
$929$	−36.7549	−1.20589	−0.602944	−	0.797783i	$-0.706006\pi$
$929$	−36.7549	−1.20589	−0.602944	+	0.797783i	$0.706006\pi$
$930$	−22.9693	−0.753194
$931$	3.84590	0.126044
$932$	−22.0887	−0.723538
$933$	−4.76253	−0.155918
$934$	0.409855	0.0134109
$935$	−9.91977	−0.324411
$936$	−5.85399	−0.191344
$937$	−37.6490	−1.22994	−0.614970	−	0.788550i	$-0.710832\pi$
$937$	−37.6490	−1.22994	−0.614970	+	0.788550i	$0.710832\pi$
$938$	1.51043	0.0493172
$939$	20.7575	0.677396
$940$	−14.2320	−0.464197
$941$	−20.6982	−0.674741	−0.337370	−	0.941372i	$-0.609537\pi$
$941$	−20.6982	−0.674741	−0.337370	+	0.941372i	$0.609537\pi$
$942$	−6.78701	−0.221133
$943$	8.87311	0.288948
$944$	3.10979	0.101215
$945$	31.4992	1.02467
$946$	−27.8897	−0.906772
$947$	50.2159	1.63180	0.815899	−	0.578194i	$-0.196242\pi$
$947$	50.2159	1.63180	0.815899	+	0.578194i	$0.196242\pi$
$948$	6.61704	0.214912
$949$	36.6737	1.19048
$950$	5.41472	0.175677
$951$	7.44556	0.241439
$952$	1.08197	0.0350670
$953$	−27.9057	−0.903955	−0.451977	−	0.892029i	$-0.649281\pi$
$953$	−27.9057	−0.903955	−0.451977	+	0.892029i	$0.649281\pi$
$954$	−1.52455	−0.0493591
$955$	64.8782	2.09941
$956$	−20.8445	−0.674160
$957$	47.7019	1.54198
$958$	8.49426	0.274437
$959$	−27.9601	−0.902879
$960$	3.92000	0.126517
$961$	3.33401	0.107549
$962$	−20.0452	−0.646285
$963$	−11.6928	−0.376797
$964$	−5.08818	−0.163879
$965$	−26.6381	−0.857509
$966$	8.79730	0.283048
$967$	37.6452	1.21059	0.605294	−	0.796002i	$-0.293055\pi$
$967$	37.6452	1.21059	0.605294	+	0.796002i	$0.293055\pi$
$968$	−14.4564	−0.464646
$969$	−0.740017	−0.0237728
$970$	6.44808	0.207035
$971$	−34.1587	−1.09620	−0.548102	−	0.836411i	$-0.684650\pi$
$971$	−34.1587	−1.09620	−0.548102	+	0.836411i	$0.684650\pi$
$972$	13.9343	0.446942
$973$	−1.76668	−0.0566370
$974$	10.5754	0.338857
$975$	−25.2551	−0.808810
$976$	−5.06060	−0.161986
$977$	−57.0333	−1.82466	−0.912329	−	0.409459i	$-0.865718\pi$
$977$	−57.0333	−1.82466	−0.912329	+	0.409459i	$0.865718\pi$
$978$	−18.5319	−0.592584
$979$	25.0808	0.801585
$980$	−12.4114	−0.396469
$981$	5.55451	0.177342
$982$	25.9327	0.827545
$983$	15.7367	0.501924	0.250962	−	0.967997i	$-0.419253\pi$
$983$	15.7367	0.501924	0.250962	+	0.967997i	$0.419253\pi$
$984$	−2.64295	−0.0842542
$985$	−23.4519	−0.747240
$986$	4.74192	0.151013
$987$	9.51355	0.302820
$988$	3.83982	0.122161
$989$	−22.5421	−0.716798
$990$	−24.8235	−0.788944
$991$	17.8055	0.565611	0.282805	−	0.959177i	$-0.408735\pi$
$991$	17.8055	0.565611	0.282805	+	0.959177i	$0.408735\pi$
$992$	−5.85952	−0.186040
$993$	7.91465	0.251164
$994$	−17.2795	−0.548072
$995$	38.8541	1.23176
$996$	16.4417	0.520976
$997$	−32.5257	−1.03010	−0.515050	−	0.857160i	$-0.672227\pi$
$997$	−32.5257	−1.03010	−0.515050	+	0.857160i	$0.672227\pi$
$998$	−36.7310	−1.16270
$999$	28.6905	0.907728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2014.2.a.g.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2014.2.a.g.1.6	✓	8	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:	\( N \)	\(=\)	\( 2014 = 2 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.21468 q^{3} +1.00000 q^{4} +3.22718 q^{5} -1.21468 q^{6} -1.77598 q^{7} -1.00000 q^{8} -1.52455 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.21468 q^{3} +1.00000 q^{4} +3.22718 q^{5} -1.21468 q^{6} -1.77598 q^{7} -1.00000 q^{8} -1.52455 q^{9} -3.22718 q^{10} -5.04543 q^{11} +1.21468 q^{12} -3.83982 q^{13} +1.77598 q^{14} +3.92000 q^{15} +1.00000 q^{16} +0.609227 q^{17} +1.52455 q^{18} -1.00000 q^{19} +3.22718 q^{20} -2.15725 q^{21} +5.04543 q^{22} +4.07802 q^{23} -1.21468 q^{24} +5.41472 q^{25} +3.83982 q^{26} -5.49589 q^{27} -1.77598 q^{28} -7.78350 q^{29} -3.92000 q^{30} +5.85952 q^{31} -1.00000 q^{32} -6.12859 q^{33} -0.609227 q^{34} -5.73141 q^{35} -1.52455 q^{36} -5.22037 q^{37} +1.00000 q^{38} -4.66415 q^{39} -3.22718 q^{40} +2.17584 q^{41} +2.15725 q^{42} -5.52771 q^{43} -5.04543 q^{44} -4.92000 q^{45} -4.07802 q^{46} -4.41004 q^{47} +1.21468 q^{48} -3.84590 q^{49} -5.41472 q^{50} +0.740017 q^{51} -3.83982 q^{52} -1.00000 q^{53} +5.49589 q^{54} -16.2825 q^{55} +1.77598 q^{56} -1.21468 q^{57} +7.78350 q^{58} +3.10979 q^{59} +3.92000 q^{60} -5.06060 q^{61} -5.85952 q^{62} +2.70756 q^{63} +1.00000 q^{64} -12.3918 q^{65} +6.12859 q^{66} +0.850476 q^{67} +0.609227 q^{68} +4.95350 q^{69} +5.73141 q^{70} -9.72957 q^{71} +1.52455 q^{72} -9.55089 q^{73} +5.22037 q^{74} +6.57716 q^{75} -1.00000 q^{76} +8.96058 q^{77} +4.66415 q^{78} +5.44755 q^{79} +3.22718 q^{80} -2.10210 q^{81} -2.17584 q^{82} +13.5358 q^{83} -2.15725 q^{84} +1.96609 q^{85} +5.52771 q^{86} -9.45447 q^{87} +5.04543 q^{88} -4.97098 q^{89} +4.92000 q^{90} +6.81943 q^{91} +4.07802 q^{92} +7.11745 q^{93} +4.41004 q^{94} -3.22718 q^{95} -1.21468 q^{96} -1.99805 q^{97} +3.84590 q^{98} +7.69201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

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