LMFDB - Embedded newform 8030.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.3981.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 2x + 1 $ x^4 - x^3 - 4x^2 + 2x + 1
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			1.1
Root			$-1.75080$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.17963 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.17963 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.75080 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.17963 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.17963 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.75080 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.17963 q^{12} -0.321968 q^{13} -3.00000 q^{14} -2.17963 q^{15} +1.00000 q^{16} -1.95844 q^{17} +1.75080 q^{18} -0.00426437 q^{19} +1.00000 q^{20} +6.53890 q^{21} -1.00000 q^{22} -5.48987 q^{23} -2.17963 q^{24} +1.00000 q^{25} -0.321968 q^{26} +2.72280 q^{27} -3.00000 q^{28} +10.4973 q^{29} -2.17963 q^{30} +4.64394 q^{31} +1.00000 q^{32} +2.17963 q^{33} -1.95844 q^{34} -3.00000 q^{35} +1.75080 q^{36} +7.58318 q^{37} -0.00426437 q^{38} +0.701772 q^{39} +1.00000 q^{40} -1.72706 q^{41} +6.53890 q^{42} +5.25240 q^{43} -1.00000 q^{44} +1.75080 q^{45} -5.48987 q^{46} +1.19591 q^{47} -2.17963 q^{48} +2.00000 q^{49} +1.00000 q^{50} +4.26867 q^{51} -0.321968 q^{52} +4.60847 q^{53} +2.72280 q^{54} -1.00000 q^{55} -3.00000 q^{56} +0.00929475 q^{57} +10.4973 q^{58} -13.7865 q^{59} -2.17963 q^{60} +8.27343 q^{61} +4.64394 q^{62} -5.25240 q^{63} +1.00000 q^{64} -0.321968 q^{65} +2.17963 q^{66} -11.4390 q^{67} -1.95844 q^{68} +11.9659 q^{69} -3.00000 q^{70} -1.02983 q^{71} +1.75080 q^{72} -1.00000 q^{73} +7.58318 q^{74} -2.17963 q^{75} -0.00426437 q^{76} +3.00000 q^{77} +0.701772 q^{78} -13.6159 q^{79} +1.00000 q^{80} -11.1871 q^{81} -1.72706 q^{82} -6.57863 q^{83} +6.53890 q^{84} -1.95844 q^{85} +5.25240 q^{86} -22.8803 q^{87} -1.00000 q^{88} +13.7838 q^{89} +1.75080 q^{90} +0.965903 q^{91} -5.48987 q^{92} -10.1221 q^{93} +1.19591 q^{94} -0.00426437 q^{95} -2.17963 q^{96} -19.1575 q^{97} +2.00000 q^{98} -1.75080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} + 4 q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 + 4 * q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + 4 q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} - 4 q^{11} - q^{12} + 7 q^{13} - 12 q^{14} - q^{15} + 4 q^{16} + 4 q^{17} - q^{18} - 19 q^{19} + 4 q^{20} + 3 q^{21} - 4 q^{22} - q^{24} + 4 q^{25} + 7 q^{26} - q^{27} - 12 q^{28} + 7 q^{29} - q^{30} + 2 q^{31} + 4 q^{32} + q^{33} + 4 q^{34} - 12 q^{35} - q^{36} + 9 q^{37} - 19 q^{38} - 4 q^{39} + 4 q^{40} - 14 q^{41} + 3 q^{42} - 3 q^{43} - 4 q^{44} - q^{45} - 5 q^{47} - q^{48} + 8 q^{49} + 4 q^{50} - 9 q^{51} + 7 q^{52} + 11 q^{53} - q^{54} - 4 q^{55} - 12 q^{56} - 11 q^{57} + 7 q^{58} - 11 q^{59} - q^{60} + 4 q^{61} + 2 q^{62} + 3 q^{63} + 4 q^{64} + 7 q^{65} + q^{66} - 23 q^{67} + 4 q^{68} + 23 q^{69} - 12 q^{70} - 10 q^{71} - q^{72} - 4 q^{73} + 9 q^{74} - q^{75} - 19 q^{76} + 12 q^{77} - 4 q^{78} - 34 q^{79} + 4 q^{80} - 24 q^{81} - 14 q^{82} - 13 q^{83} + 3 q^{84} + 4 q^{85} - 3 q^{86} - 26 q^{87} - 4 q^{88} + 21 q^{89} - q^{90} - 21 q^{91} + 4 q^{93} - 5 q^{94} - 19 q^{95} - q^{96} - 23 q^{97} + 8 q^{98} + q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + 4 * q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 - 4 * q^11 - q^12 + 7 * q^13 - 12 * q^14 - q^15 + 4 * q^16 + 4 * q^17 - q^18 - 19 * q^19 + 4 * q^20 + 3 * q^21 - 4 * q^22 - q^24 + 4 * q^25 + 7 * q^26 - q^27 - 12 * q^28 + 7 * q^29 - q^30 + 2 * q^31 + 4 * q^32 + q^33 + 4 * q^34 - 12 * q^35 - q^36 + 9 * q^37 - 19 * q^38 - 4 * q^39 + 4 * q^40 - 14 * q^41 + 3 * q^42 - 3 * q^43 - 4 * q^44 - q^45 - 5 * q^47 - q^48 + 8 * q^49 + 4 * q^50 - 9 * q^51 + 7 * q^52 + 11 * q^53 - q^54 - 4 * q^55 - 12 * q^56 - 11 * q^57 + 7 * q^58 - 11 * q^59 - q^60 + 4 * q^61 + 2 * q^62 + 3 * q^63 + 4 * q^64 + 7 * q^65 + q^66 - 23 * q^67 + 4 * q^68 + 23 * q^69 - 12 * q^70 - 10 * q^71 - q^72 - 4 * q^73 + 9 * q^74 - q^75 - 19 * q^76 + 12 * q^77 - 4 * q^78 - 34 * q^79 + 4 * q^80 - 24 * q^81 - 14 * q^82 - 13 * q^83 + 3 * q^84 + 4 * q^85 - 3 * q^86 - 26 * q^87 - 4 * q^88 + 21 * q^89 - q^90 - 21 * q^91 + 4 * q^93 - 5 * q^94 - 19 * q^95 - q^96 - 23 * q^97 + 8 * q^98 + 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
$3$	−2.17963	−1.25841	−0.629206	−	0.777239i	$-0.716620\pi$
$3$	−2.17963	−1.25841	−0.629206	+	0.777239i	$0.716620\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.17963	−0.889831
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	1.75080	0.583600
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.17963	−0.629206
$13$	−0.321968	−0.0892978	−0.0446489	−	0.999003i	$-0.514217\pi$
$13$	−0.321968	−0.0892978	−0.0446489	+	0.999003i	$0.514217\pi$
$14$	−3.00000	−0.801784
$15$	−2.17963	−0.562779
$16$	1.00000	0.250000
$17$	−1.95844	−0.474991	−0.237495	−	0.971389i	$-0.576326\pi$
$17$	−1.95844	−0.474991	−0.237495	+	0.971389i	$0.576326\pi$
$18$	1.75080	0.412668
$19$	−0.00426437	−0.000978313 0	−0.000489156	−	1.00000i	$-0.500156\pi$
$19$	−0.00426437	−0.000978313 0	−0.000489156		1.00000i	$0.500156\pi$
$20$	1.00000	0.223607
$21$	6.53890	1.42690
$22$	−1.00000	−0.213201
$23$	−5.48987	−1.14472	−0.572359	−	0.820003i	$-0.693971\pi$
$23$	−5.48987	−1.14472	−0.572359	+	0.820003i	$0.693971\pi$
$24$	−2.17963	−0.444916
$25$	1.00000	0.200000
$26$	−0.321968	−0.0631431
$27$	2.72280	0.524002
$28$	−3.00000	−0.566947
$29$	10.4973	1.94931	0.974653	−	0.223721i	$-0.0718204\pi$
$29$	10.4973	1.94931	0.974653	+	0.223721i	$0.0718204\pi$
$30$	−2.17963	−0.397945
$31$	4.64394	0.834075	0.417038	−	0.908889i	$-0.363068\pi$
$31$	4.64394	0.834075	0.417038	+	0.908889i	$0.363068\pi$
$32$	1.00000	0.176777
$33$	2.17963	0.379425
$34$	−1.95844	−0.335869
$35$	−3.00000	−0.507093
$36$	1.75080	0.291800
$37$	7.58318	1.24667	0.623333	−	0.781956i	$-0.285778\pi$
$37$	7.58318	1.24667	0.623333	+	0.781956i	$0.285778\pi$
$38$	−0.00426437	−0.000691772 0
$39$	0.701772	0.112373
$40$	1.00000	0.158114
$41$	−1.72706	−0.269722	−0.134861	−	0.990865i	$-0.543059\pi$
$41$	−1.72706	−0.269722	−0.134861	+	0.990865i	$0.543059\pi$
$42$	6.53890	1.00897
$43$	5.25240	0.800984	0.400492	−	0.916300i	$-0.368839\pi$
$43$	5.25240	0.800984	0.400492	+	0.916300i	$0.368839\pi$
$44$	−1.00000	−0.150756
$45$	1.75080	0.260994
$46$	−5.48987	−0.809437
$47$	1.19591	0.174441	0.0872204	−	0.996189i	$-0.472202\pi$
$47$	1.19591	0.174441	0.0872204	+	0.996189i	$0.472202\pi$
$48$	−2.17963	−0.314603
$49$	2.00000	0.285714
$50$	1.00000	0.141421
$51$	4.26867	0.597734
$52$	−0.321968	−0.0446489
$53$	4.60847	0.633021	0.316511	−	0.948589i	$-0.397489\pi$
$53$	4.60847	0.633021	0.316511	+	0.948589i	$0.397489\pi$
$54$	2.72280	0.370526
$55$	−1.00000	−0.134840
$56$	−3.00000	−0.400892
$57$	0.00929475	0.00123112
$58$	10.4973	1.37837
$59$	−13.7865	−1.79486	−0.897428	−	0.441161i	$-0.854567\pi$
$59$	−13.7865	−1.79486	−0.897428	+	0.441161i	$0.854567\pi$
$60$	−2.17963	−0.281389
$61$	8.27343	1.05930	0.529652	−	0.848215i	$-0.322323\pi$
$61$	8.27343	1.05930	0.529652	+	0.848215i	$0.322323\pi$
$62$	4.64394	0.589780
$63$	−5.25240	−0.661740
$64$	1.00000	0.125000
$65$	−0.321968	−0.0399352
$66$	2.17963	0.268294
$67$	−11.4390	−1.39750	−0.698749	−	0.715367i	$-0.746260\pi$
$67$	−11.4390	−1.39750	−0.698749	+	0.715367i	$0.746260\pi$
$68$	−1.95844	−0.237495
$69$	11.9659	1.44053
$70$	−3.00000	−0.358569
$71$	−1.02983	−0.122219	−0.0611093	−	0.998131i	$-0.519464\pi$
$71$	−1.02983	−0.122219	−0.0611093	+	0.998131i	$0.519464\pi$
$72$	1.75080	0.206334
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	7.58318	0.881526
$75$	−2.17963	−0.251682
$76$	−0.00426437	−0.000489156 0
$77$	3.00000	0.341882
$78$	0.701772	0.0794600
$79$	−13.6159	−1.53191	−0.765956	−	0.642893i	$-0.777734\pi$
$79$	−13.6159	−1.53191	−0.765956	+	0.642893i	$0.777734\pi$
$80$	1.00000	0.111803
$81$	−11.1871	−1.24301
$82$	−1.72706	−0.190722
$83$	−6.57863	−0.722099	−0.361049	−	0.932547i	$-0.617581\pi$
$83$	−6.57863	−0.722099	−0.361049	+	0.932547i	$0.617581\pi$
$84$	6.53890	0.713452
$85$	−1.95844	−0.212422
$86$	5.25240	0.566381
$87$	−22.8803	−2.45303
$88$	−1.00000	−0.106600
$89$	13.7838	1.46108	0.730542	−	0.682868i	$-0.239268\pi$
$89$	13.7838	1.46108	0.730542	+	0.682868i	$0.239268\pi$
$90$	1.75080	0.184551
$91$	0.965903	0.101254
$92$	−5.48987	−0.572359
$93$	−10.1221	−1.04961
$94$	1.19591	0.123348
$95$	−0.00426437	−0.000437515 0
$96$	−2.17963	−0.222458
$97$	−19.1575	−1.94515	−0.972577	−	0.232581i	$-0.925283\pi$
$97$	−19.1575	−1.94515	−0.972577	+	0.232581i	$0.925283\pi$
$98$	2.00000	0.202031
$99$	−1.75080	−0.175962
$100$	1.00000	0.100000
$101$	−14.3177	−1.42466	−0.712332	−	0.701842i	$-0.752361\pi$
$101$	−14.3177	−1.42466	−0.712332	+	0.701842i	$0.752361\pi$
$102$	4.26867	0.422662
$103$	0.305207	0.0300729	0.0150365	−	0.999887i	$-0.495214\pi$
$103$	0.305207	0.0300729	0.0150365	+	0.999887i	$0.495214\pi$
$104$	−0.321968	−0.0315715
$105$	6.53890	0.638131
$106$	4.60847	0.447614
$107$	8.99467	0.869548	0.434774	−	0.900540i	$-0.356828\pi$
$107$	8.99467	0.869548	0.434774	+	0.900540i	$0.356828\pi$
$108$	2.72280	0.262001
$109$	6.67377	0.639231	0.319616	−	0.947547i	$-0.396446\pi$
$109$	6.67377	0.639231	0.319616	+	0.947547i	$0.396446\pi$
$110$	−1.00000	−0.0953463
$111$	−16.5285	−1.56882
$112$	−3.00000	−0.283473
$113$	−3.64820	−0.343194	−0.171597	−	0.985167i	$-0.554893\pi$
$113$	−3.64820	−0.343194	−0.171597	+	0.985167i	$0.554893\pi$
$114$	0.00929475	0.000870534 0
$115$	−5.48987	−0.511933
$116$	10.4973	0.974653
$117$	−0.563701	−0.0521142
$118$	−13.7865	−1.26915
$119$	5.87531	0.538589
$120$	−2.17963	−0.198972
$121$	1.00000	0.0909091
$122$	8.27343	0.749041
$123$	3.76436	0.339421
$124$	4.64394	0.417038
$125$	1.00000	0.0894427
$126$	−5.25240	−0.467921
$127$	−0.526890	−0.0467540	−0.0233770	−	0.999727i	$-0.507442\pi$
$127$	−0.526890	−0.0467540	−0.0233770	+	0.999727i	$0.507442\pi$
$128$	1.00000	0.0883883
$129$	−11.4483	−1.00797
$130$	−0.321968	−0.0282384
$131$	−0.179146	−0.0156520	−0.00782601	−	0.999969i	$-0.502491\pi$
$131$	−0.179146	−0.0156520	−0.00782601	+	0.999969i	$0.502491\pi$
$132$	2.17963	0.189713
$133$	0.0127931	0.00110930
$134$	−11.4390	−0.988180
$135$	2.72280	0.234341
$136$	−1.95844	−0.167935
$137$	−11.0330	−0.942616	−0.471308	−	0.881969i	$-0.656218\pi$
$137$	−11.0330	−0.942616	−0.471308	+	0.881969i	$0.656218\pi$
$138$	11.9659	1.01861
$139$	−12.1941	−1.03429	−0.517144	−	0.855898i	$-0.673005\pi$
$139$	−12.1941	−1.03429	−0.517144	+	0.855898i	$0.673005\pi$
$140$	−3.00000	−0.253546
$141$	−2.60664	−0.219518
$142$	−1.02983	−0.0864216
$143$	0.321968	0.0269243
$144$	1.75080	0.145900
$145$	10.4973	0.871756
$146$	−1.00000	−0.0827606
$147$	−4.35927	−0.359546
$148$	7.58318	0.623333
$149$	23.2396	1.90386	0.951931	−	0.306311i	$-0.0990948\pi$
$149$	23.2396	1.90386	0.951931	+	0.306311i	$0.0990948\pi$
$150$	−2.17963	−0.177966
$151$	−14.2929	−1.16314	−0.581570	−	0.813496i	$-0.697561\pi$
$151$	−14.2929	−1.16314	−0.581570	+	0.813496i	$0.697561\pi$
$152$	−0.00426437	−0.000345886 0
$153$	−3.42883	−0.277205
$154$	3.00000	0.241747
$155$	4.64394	0.373010
$156$	0.701772	0.0561867
$157$	−18.7423	−1.49580	−0.747898	−	0.663814i	$-0.768937\pi$
$157$	−18.7423	−1.49580	−0.747898	+	0.663814i	$0.768937\pi$
$158$	−13.6159	−1.08323
$159$	−10.0448	−0.796602
$160$	1.00000	0.0790569
$161$	16.4696	1.29799
$162$	−11.1871	−0.878942
$163$	−2.46885	−0.193375	−0.0966874	−	0.995315i	$-0.530825\pi$
$163$	−2.46885	−0.193375	−0.0966874	+	0.995315i	$0.530825\pi$
$164$	−1.72706	−0.134861
$165$	2.17963	0.169684
$166$	−6.57863	−0.510601
$167$	17.1930	1.33044	0.665218	−	0.746649i	$-0.268339\pi$
$167$	17.1930	1.33044	0.665218	+	0.746649i	$0.268339\pi$
$168$	6.53890	0.504487
$169$	−12.8963	−0.992026
$170$	−1.95844	−0.150205
$171$	−0.00746605	−0.000570943 0
$172$	5.25240	0.400492
$173$	−21.2766	−1.61763	−0.808816	−	0.588062i	$-0.799891\pi$
$173$	−21.2766	−1.61763	−0.808816	+	0.588062i	$0.799891\pi$
$174$	−22.8803	−1.73455
$175$	−3.00000	−0.226779
$176$	−1.00000	−0.0753778
$177$	30.0496	2.25867
$178$	13.7838	1.03314
$179$	6.32971	0.473105	0.236552	−	0.971619i	$-0.423982\pi$
$179$	6.32971	0.473105	0.236552	+	0.971619i	$0.423982\pi$
$180$	1.75080	0.130497
$181$	21.7855	1.61930	0.809651	−	0.586911i	$-0.199656\pi$
$181$	21.7855	1.61930	0.809651	+	0.586911i	$0.199656\pi$
$182$	0.965903	0.0715975
$183$	−18.0330	−1.33304
$184$	−5.48987	−0.404719
$185$	7.58318	0.557526
$186$	−10.1221	−0.742187
$187$	1.95844	0.143215
$188$	1.19591	0.0872204
$189$	−8.16839	−0.594163
$190$	−0.00426437	−0.000309370 0
$191$	14.0227	1.01465	0.507323	−	0.861756i	$-0.330635\pi$
$191$	14.0227	1.01465	0.507323	+	0.861756i	$0.330635\pi$
$192$	−2.17963	−0.157301
$193$	−17.0690	−1.22865	−0.614326	−	0.789052i	$-0.710572\pi$
$193$	−17.0690	−1.22865	−0.614326	+	0.789052i	$0.710572\pi$
$194$	−19.1575	−1.37543
$195$	0.701772	0.0502549
$196$	2.00000	0.142857
$197$	−5.21693	−0.371691	−0.185845	−	0.982579i	$-0.559502\pi$
$197$	−5.21693	−0.371691	−0.185845	+	0.982579i	$0.559502\pi$
$198$	−1.75080	−0.124424
$199$	8.19911	0.581219	0.290610	−	0.956842i	$-0.406142\pi$
$199$	8.19911	0.581219	0.290610	+	0.956842i	$0.406142\pi$
$200$	1.00000	0.0707107
$201$	24.9329	1.75863
$202$	−14.3177	−1.00739
$203$	−31.4920	−2.21031
$204$	4.26867	0.298867
$205$	−1.72706	−0.120623
$206$	0.305207	0.0212648
$207$	−9.61167	−0.668057
$208$	−0.321968	−0.0223244
$209$	0.00426437	0.000294972 0
$210$	6.53890	0.451227
$211$	10.0947	0.694946	0.347473	−	0.937690i	$-0.387040\pi$
$211$	10.0947	0.694946	0.347473	+	0.937690i	$0.387040\pi$
$212$	4.60847	0.316511
$213$	2.24466	0.153801
$214$	8.99467	0.614863
$215$	5.25240	0.358211
$216$	2.72280	0.185263
$217$	−13.9318	−0.945753
$218$	6.67377	0.452005
$219$	2.17963	0.147286
$220$	−1.00000	−0.0674200
$221$	0.630554	0.0424156
$222$	−16.5285	−1.10932
$223$	−19.5629	−1.31003	−0.655015	−	0.755616i	$-0.727338\pi$
$223$	−19.5629	−1.31003	−0.655015	+	0.755616i	$0.727338\pi$
$224$	−3.00000	−0.200446
$225$	1.75080	0.116720
$226$	−3.64820	−0.242675
$227$	−17.0265	−1.13009	−0.565043	−	0.825062i	$-0.691140\pi$
$227$	−17.0265	−1.13009	−0.565043	+	0.825062i	$0.691140\pi$
$228$	0.00929475	0.000615560 0
$229$	−9.88750	−0.653384	−0.326692	−	0.945131i	$-0.605934\pi$
$229$	−9.88750	−0.653384	−0.326692	+	0.945131i	$0.605934\pi$
$230$	−5.48987	−0.361991
$231$	−6.53890	−0.430228
$232$	10.4973	0.689184
$233$	−24.4701	−1.60309	−0.801545	−	0.597935i	$-0.795988\pi$
$233$	−24.4701	−1.60309	−0.801545	+	0.597935i	$0.795988\pi$
$234$	−0.563701	−0.0368503
$235$	1.19591	0.0780123
$236$	−13.7865	−0.897428
$237$	29.6777	1.92778
$238$	5.87531	0.380840
$239$	1.90913	0.123491	0.0617457	−	0.998092i	$-0.480333\pi$
$239$	1.90913	0.123491	0.0617457	+	0.998092i	$0.480333\pi$
$240$	−2.17963	−0.140695
$241$	11.5445	0.743649	0.371824	−	0.928303i	$-0.378732\pi$
$241$	11.5445	0.743649	0.371824	+	0.928303i	$0.378732\pi$
$242$	1.00000	0.0642824
$243$	16.2154	1.04022
$244$	8.27343	0.529652
$245$	2.00000	0.127775
$246$	3.76436	0.240007
$247$	0.00137299	8.73612e−5 0
$248$	4.64394	0.294890
$249$	14.3390	0.908698
$250$	1.00000	0.0632456
$251$	1.51312	0.0955074	0.0477537	−	0.998859i	$-0.484794\pi$
$251$	1.51312	0.0955074	0.0477537	+	0.998859i	$0.484794\pi$
$252$	−5.25240	−0.330870
$253$	5.48987	0.345145
$254$	−0.526890	−0.0330600
$255$	4.26867	0.267315
$256$	1.00000	0.0625000
$257$	−18.5098	−1.15461	−0.577306	−	0.816528i	$-0.695896\pi$
$257$	−18.5098	−1.15461	−0.577306	+	0.816528i	$0.695896\pi$
$258$	−11.4483	−0.712741
$259$	−22.7495	−1.41359
$260$	−0.321968	−0.0199676
$261$	18.3787	1.13762
$262$	−0.179146	−0.0110676
$263$	6.86066	0.423046	0.211523	−	0.977373i	$-0.432158\pi$
$263$	6.86066	0.423046	0.211523	+	0.977373i	$0.432158\pi$
$264$	2.17963	0.134147
$265$	4.60847	0.283096
$266$	0.0127931	0.000784395 0
$267$	−30.0437	−1.83864
$268$	−11.4390	−0.698749
$269$	28.2705	1.72368	0.861842	−	0.507176i	$-0.169311\pi$
$269$	28.2705	1.72368	0.861842	+	0.507176i	$0.169311\pi$
$270$	2.72280	0.165704
$271$	9.79374	0.594927	0.297464	−	0.954733i	$-0.403859\pi$
$271$	9.79374	0.594927	0.297464	+	0.954733i	$0.403859\pi$
$272$	−1.95844	−0.118748
$273$	−2.10531	−0.127419
$274$	−11.0330	−0.666530
$275$	−1.00000	−0.0603023
$276$	11.9659	0.720263
$277$	9.76756	0.586876	0.293438	−	0.955978i	$-0.405201\pi$
$277$	9.76756	0.586876	0.293438	+	0.955978i	$0.405201\pi$
$278$	−12.1941	−0.731352
$279$	8.13060	0.486767
$280$	−3.00000	−0.179284
$281$	−29.2814	−1.74678	−0.873392	−	0.487017i	$-0.838085\pi$
$281$	−29.2814	−1.74678	−0.873392	+	0.487017i	$0.838085\pi$
$282$	−2.60664	−0.155223
$283$	5.50480	0.327227	0.163613	−	0.986525i	$-0.447685\pi$
$283$	5.50480	0.327227	0.163613	+	0.986525i	$0.447685\pi$
$284$	−1.02983	−0.0611093
$285$	0.00929475	0.000550574 0
$286$	0.321968	0.0190384
$287$	5.18118	0.305836
$288$	1.75080	0.103167
$289$	−13.1645	−0.774384
$290$	10.4973	0.616425
$291$	41.7564	2.44780
$292$	−1.00000	−0.0585206
$293$	−18.2151	−1.06414	−0.532069	−	0.846701i	$-0.678585\pi$
$293$	−18.2151	−1.06414	−0.532069	+	0.846701i	$0.678585\pi$
$294$	−4.35927	−0.254238
$295$	−13.7865	−0.802684
$296$	7.58318	0.440763
$297$	−2.72280	−0.157993
$298$	23.2396	1.34623
$299$	1.76756	0.102221
$300$	−2.17963	−0.125841
$301$	−15.7572	−0.908230
$302$	−14.2929	−0.822464
$303$	31.2073	1.79281
$304$	−0.00426437	−0.000244578 0
$305$	8.27343	0.473735
$306$	−3.42883	−0.196013
$307$	9.34251	0.533205	0.266602	−	0.963807i	$-0.414099\pi$
$307$	9.34251	0.533205	0.266602	+	0.963807i	$0.414099\pi$
$308$	3.00000	0.170941
$309$	−0.665239	−0.0378441
$310$	4.64394	0.263758
$311$	−24.8968	−1.41177	−0.705885	−	0.708327i	$-0.749450\pi$
$311$	−24.8968	−1.41177	−0.705885	+	0.708327i	$0.749450\pi$
$312$	0.701772	0.0397300
$313$	−32.9496	−1.86242	−0.931211	−	0.364480i	$-0.881247\pi$
$313$	−32.9496	−1.86242	−0.931211	+	0.364480i	$0.881247\pi$
$314$	−18.7423	−1.05769
$315$	−5.25240	−0.295939
$316$	−13.6159	−0.765956
$317$	17.0997	0.960415	0.480208	−	0.877155i	$-0.340561\pi$
$317$	17.0997	0.960415	0.480208	+	0.877155i	$0.340561\pi$
$318$	−10.0448	−0.563282
$319$	−10.4973	−0.587738
$320$	1.00000	0.0559017
$321$	−19.6051	−1.09425
$322$	16.4696	0.917816
$323$	0.00835149	0.000464690 0
$324$	−11.1871	−0.621506
$325$	−0.321968	−0.0178596
$326$	−2.46885	−0.136737
$327$	−14.5464	−0.804416
$328$	−1.72706	−0.0953610
$329$	−3.58772	−0.197797
$330$	2.17963	0.119985
$331$	9.06713	0.498375	0.249187	−	0.968455i	$-0.419837\pi$
$331$	9.06713	0.498375	0.249187	+	0.968455i	$0.419837\pi$
$332$	−6.57863	−0.361049
$333$	13.2766	0.727555
$334$	17.1930	0.940760
$335$	−11.4390	−0.624980
$336$	6.53890	0.356726
$337$	−7.85794	−0.428049	−0.214025	−	0.976828i	$-0.568657\pi$
$337$	−7.85794	−0.428049	−0.214025	+	0.976828i	$0.568657\pi$
$338$	−12.8963	−0.701468
$339$	7.95174	0.431879
$340$	−1.95844	−0.106211
$341$	−4.64394	−0.251483
$342$	−0.00746605	−0.000403718 0
$343$	15.0000	0.809924
$344$	5.25240	0.283190
$345$	11.9659	0.644223
$346$	−21.2766	−1.14384
$347$	−7.15297	−0.383992	−0.191996	−	0.981396i	$-0.561496\pi$
$347$	−7.15297	−0.383992	−0.191996	+	0.981396i	$0.561496\pi$
$348$	−22.8803	−1.22652
$349$	17.0152	0.910803	0.455402	−	0.890286i	$-0.349496\pi$
$349$	17.0152	0.910803	0.455402	+	0.890286i	$0.349496\pi$
$350$	−3.00000	−0.160357
$351$	−0.876653	−0.0467923
$352$	−1.00000	−0.0533002
$353$	−11.4174	−0.607688	−0.303844	−	0.952722i	$-0.598270\pi$
$353$	−11.4174	−0.607688	−0.303844	+	0.952722i	$0.598270\pi$
$354$	30.0496	1.59712
$355$	−1.02983	−0.0546578
$356$	13.7838	0.730542
$357$	−12.8060	−0.677767
$358$	6.32971	0.334536
$359$	−23.6901	−1.25031	−0.625157	−	0.780499i	$-0.714965\pi$
$359$	−23.6901	−1.25031	−0.625157	+	0.780499i	$0.714965\pi$
$360$	1.75080	0.0922753
$361$	−19.0000	−0.999999
$362$	21.7855	1.14502
$363$	−2.17963	−0.114401
$364$	0.965903	0.0506271
$365$	−1.00000	−0.0523424
$366$	−18.0330	−0.942602
$367$	−16.8849	−0.881384	−0.440692	−	0.897658i	$-0.645267\pi$
$367$	−16.8849	−0.881384	−0.440692	+	0.897658i	$0.645267\pi$
$368$	−5.48987	−0.286179
$369$	−3.02374	−0.157410
$370$	7.58318	0.394231
$371$	−13.8254	−0.717779
$372$	−10.1221	−0.524805
$373$	12.4486	0.644563	0.322282	−	0.946644i	$-0.395550\pi$
$373$	12.4486	0.644563	0.322282	+	0.946644i	$0.395550\pi$
$374$	1.95844	0.101268
$375$	−2.17963	−0.112556
$376$	1.19591	0.0616742
$377$	−3.37980	−0.174069
$378$	−8.16839	−0.420137
$379$	−4.79208	−0.246153	−0.123076	−	0.992397i	$-0.539276\pi$
$379$	−4.79208	−0.246153	−0.123076	+	0.992397i	$0.539276\pi$
$380$	−0.00426437	−0.000218757 0
$381$	1.14843	0.0588357
$382$	14.0227	0.717463
$383$	−16.5628	−0.846322	−0.423161	−	0.906055i	$-0.639080\pi$
$383$	−16.5628	−0.846322	−0.423161	+	0.906055i	$0.639080\pi$
$384$	−2.17963	−0.111229
$385$	3.00000	0.152894
$386$	−17.0690	−0.868789
$387$	9.19591	0.467454
$388$	−19.1575	−0.972577
$389$	−1.85206	−0.0939032	−0.0469516	−	0.998897i	$-0.514951\pi$
$389$	−1.85206	−0.0939032	−0.0469516	+	0.998897i	$0.514951\pi$
$390$	0.701772	0.0355356
$391$	10.7516	0.543730
$392$	2.00000	0.101015
$393$	0.390472	0.0196967
$394$	−5.21693	−0.262825
$395$	−13.6159	−0.685092
$396$	−1.75080	−0.0879810
$397$	36.0674	1.81017	0.905086	−	0.425228i	$-0.139806\pi$
$397$	36.0674	1.81017	0.905086	+	0.425228i	$0.139806\pi$
$398$	8.19911	0.410984
$399$	−0.0278843	−0.00139596
$400$	1.00000	0.0500000
$401$	9.86833	0.492801	0.246401	−	0.969168i	$-0.420752\pi$
$401$	9.86833	0.492801	0.246401	+	0.969168i	$0.420752\pi$
$402$	24.9329	1.24354
$403$	−1.49520	−0.0744811
$404$	−14.3177	−0.712332
$405$	−11.1871	−0.555891
$406$	−31.4920	−1.56292
$407$	−7.58318	−0.375884
$408$	4.26867	0.211331
$409$	7.49386	0.370547	0.185274	−	0.982687i	$-0.440683\pi$
$409$	7.49386	0.370547	0.185274	+	0.982687i	$0.440683\pi$
$410$	−1.72706	−0.0852935
$411$	24.0480	1.18620
$412$	0.305207	0.0150365
$413$	41.3596	2.03518
$414$	−9.61167	−0.472388
$415$	−6.57863	−0.322932
$416$	−0.321968	−0.0157858
$417$	26.5786	1.30156
$418$	0.00426437	0.000208577 0
$419$	−19.2841	−0.942090	−0.471045	−	0.882109i	$-0.656123\pi$
$419$	−19.2841	−0.942090	−0.471045	+	0.882109i	$0.656123\pi$
$420$	6.53890	0.319066
$421$	−13.5309	−0.659458	−0.329729	−	0.944076i	$-0.606957\pi$
$421$	−13.5309	−0.659458	−0.329729	+	0.944076i	$0.606957\pi$
$422$	10.0947	0.491401
$423$	2.09379	0.101804
$424$	4.60847	0.223807
$425$	−1.95844	−0.0949982
$426$	2.24466	0.108754
$427$	−24.8203	−1.20114
$428$	8.99467	0.434774
$429$	−0.701772	−0.0338819
$430$	5.25240	0.253293
$431$	−32.5544	−1.56809	−0.784045	−	0.620704i	$-0.786847\pi$
$431$	−32.5544	−1.56809	−0.784045	+	0.620704i	$0.786847\pi$
$432$	2.72280	0.131001
$433$	14.2308	0.683887	0.341944	−	0.939720i	$-0.388915\pi$
$433$	14.2308	0.683887	0.341944	+	0.939720i	$0.388915\pi$
$434$	−13.9318	−0.668748
$435$	−22.8803	−1.09703
$436$	6.67377	0.319616
$437$	0.0234108	0.00111989
$438$	2.17963	0.104147
$439$	−12.9768	−0.619351	−0.309676	−	0.950842i	$-0.600220\pi$
$439$	−12.9768	−0.619351	−0.309676	+	0.950842i	$0.600220\pi$
$440$	−1.00000	−0.0476731
$441$	3.50160	0.166743
$442$	0.630554	0.0299924
$443$	36.6104	1.73941	0.869707	−	0.493568i	$-0.164308\pi$
$443$	36.6104	1.73941	0.869707	+	0.493568i	$0.164308\pi$
$444$	−16.5285	−0.784410
$445$	13.7838	0.653416
$446$	−19.5629	−0.926331
$447$	−50.6538	−2.39584
$448$	−3.00000	−0.141737
$449$	−28.6479	−1.35198	−0.675989	−	0.736912i	$-0.736283\pi$
$449$	−28.6479	−1.35198	−0.675989	+	0.736912i	$0.736283\pi$
$450$	1.75080	0.0825335
$451$	1.72706	0.0813241
$452$	−3.64820	−0.171597
$453$	31.1533	1.46371
$454$	−17.0265	−0.799091
$455$	0.965903	0.0452822
$456$	0.00929475	0.000435267 0
$457$	28.2606	1.32198	0.660988	−	0.750396i	$-0.270137\pi$
$457$	28.2606	1.32198	0.660988	+	0.750396i	$0.270137\pi$
$458$	−9.88750	−0.462012
$459$	−5.33243	−0.248896
$460$	−5.48987	−0.255967
$461$	14.6295	0.681363	0.340682	−	0.940179i	$-0.389342\pi$
$461$	14.6295	0.681363	0.340682	+	0.940179i	$0.389342\pi$
$462$	−6.53890	−0.304217
$463$	−27.3179	−1.26957	−0.634785	−	0.772689i	$-0.718911\pi$
$463$	−27.3179	−1.26957	−0.634785	+	0.772689i	$0.718911\pi$
$464$	10.4973	0.487327
$465$	−10.1221	−0.469400
$466$	−24.4701	−1.13356
$467$	−5.37953	−0.248935	−0.124467	−	0.992224i	$-0.539722\pi$
$467$	−5.37953	−0.248935	−0.124467	+	0.992224i	$0.539722\pi$
$468$	−0.563701	−0.0260571
$469$	34.3170	1.58461
$470$	1.19591	0.0551630
$471$	40.8513	1.88233
$472$	−13.7865	−0.634577
$473$	−5.25240	−0.241506
$474$	29.6777	1.36314
$475$	−0.00426437	−0.000195663 0
$476$	5.87531	0.269294
$477$	8.06850	0.369431
$478$	1.90913	0.0873216
$479$	3.82519	0.174777	0.0873887	−	0.996174i	$-0.472148\pi$
$479$	3.82519	0.174777	0.0873887	+	0.996174i	$0.472148\pi$
$480$	−2.17963	−0.0994862
$481$	−2.44154	−0.111325
$482$	11.5445	0.525839
$483$	−35.8977	−1.63340
$484$	1.00000	0.0454545
$485$	−19.1575	−0.869899
$486$	16.2154	0.735545
$487$	29.7412	1.34770	0.673851	−	0.738867i	$-0.264639\pi$
$487$	29.7412	1.34770	0.673851	+	0.738867i	$0.264639\pi$
$488$	8.27343	0.374520
$489$	5.38118	0.243345
$490$	2.00000	0.0903508
$491$	−9.08478	−0.409990	−0.204995	−	0.978763i	$-0.565718\pi$
$491$	−9.08478	−0.409990	−0.204995	+	0.978763i	$0.565718\pi$
$492$	3.76436	0.169710
$493$	−20.5584	−0.925903
$494$	0.00137299	6.17737e−5 0
$495$	−1.75080	−0.0786926
$496$	4.64394	0.208519
$497$	3.08950	0.138583
$498$	14.3390	0.642546
$499$	−21.2125	−0.949601	−0.474801	−	0.880093i	$-0.657480\pi$
$499$	−21.2125	−0.949601	−0.474801	+	0.880093i	$0.657480\pi$
$500$	1.00000	0.0447214
$501$	−37.4745	−1.67424
$502$	1.51312	0.0675339
$503$	−30.6682	−1.36743	−0.683714	−	0.729750i	$-0.739637\pi$
$503$	−30.6682	−1.36743	−0.683714	+	0.729750i	$0.739637\pi$
$504$	−5.25240	−0.233961
$505$	−14.3177	−0.637129
$506$	5.48987	0.244055
$507$	28.1093	1.24838
$508$	−0.526890	−0.0233770
$509$	35.1716	1.55895	0.779477	−	0.626431i	$-0.215485\pi$
$509$	35.1716	1.55895	0.779477	+	0.626431i	$0.215485\pi$
$510$	4.26867	0.189020
$511$	3.00000	0.132712
$512$	1.00000	0.0441942
$513$	−0.0116110	−0.000512638 0
$514$	−18.5098	−0.816434
$515$	0.305207	0.0134490
$516$	−11.4483	−0.503984
$517$	−1.19591	−0.0525959
$518$	−22.7495	−0.999557
$519$	46.3752	2.03565
$520$	−0.321968	−0.0141192
$521$	−10.0184	−0.438913	−0.219457	−	0.975622i	$-0.570428\pi$
$521$	−10.0184	−0.438913	−0.219457	+	0.975622i	$0.570428\pi$
$522$	18.3787	0.804416
$523$	−33.3870	−1.45991	−0.729955	−	0.683495i	$-0.760459\pi$
$523$	−33.3870	−1.45991	−0.729955	+	0.683495i	$0.760459\pi$
$524$	−0.179146	−0.00782601
$525$	6.53890	0.285381
$526$	6.86066	0.299139
$527$	−9.09486	−0.396178
$528$	2.17963	0.0948564
$529$	7.13868	0.310377
$530$	4.60847	0.200179
$531$	−24.1375	−1.04748
$532$	0.0127931	0.000554651 0
$533$	0.556058	0.0240855
$534$	−30.0437	−1.30012
$535$	8.99467	0.388874
$536$	−11.4390	−0.494090
$537$	−13.7965	−0.595361
$538$	28.2705	1.21883
$539$	−2.00000	−0.0861461
$540$	2.72280	0.117171
$541$	−9.99284	−0.429626	−0.214813	−	0.976655i	$-0.568914\pi$
$541$	−9.99284	−0.429626	−0.214813	+	0.976655i	$0.568914\pi$
$542$	9.79374	0.420677
$543$	−47.4844	−2.03775
$544$	−1.95844	−0.0839673
$545$	6.67377	0.285873
$546$	−2.10531	−0.0900992
$547$	−13.6314	−0.582837	−0.291419	−	0.956596i	$-0.594127\pi$
$547$	−13.6314	−0.582837	−0.291419	+	0.956596i	$0.594127\pi$
$548$	−11.0330	−0.471308
$549$	14.4851	0.618210
$550$	−1.00000	−0.0426401
$551$	−0.0447645	−0.00190703
$552$	11.9659	0.509303
$553$	40.8478	1.73702
$554$	9.76756	0.414984
$555$	−16.5285	−0.701598
$556$	−12.1941	−0.517144
$557$	−7.35451	−0.311621	−0.155810	−	0.987787i	$-0.549799\pi$
$557$	−7.35451	−0.311621	−0.155810	+	0.987787i	$0.549799\pi$
$558$	8.13060	0.344196
$559$	−1.69110	−0.0715261
$560$	−3.00000	−0.126773
$561$	−4.26867	−0.180224
$562$	−29.2814	−1.23516
$563$	−10.1096	−0.426069	−0.213035	−	0.977045i	$-0.568335\pi$
$563$	−10.1096	−0.426069	−0.213035	+	0.977045i	$0.568335\pi$
$564$	−2.60664	−0.109759
$565$	−3.64820	−0.153481
$566$	5.50480	0.231384
$567$	33.5613	1.40944
$568$	−1.02983	−0.0432108
$569$	−1.48406	−0.0622149	−0.0311074	−	0.999516i	$-0.509903\pi$
$569$	−1.48406	−0.0622149	−0.0311074	+	0.999516i	$0.509903\pi$
$570$	0.00929475	0.000389314 0
$571$	−42.9390	−1.79694	−0.898470	−	0.439035i	$-0.855321\pi$
$571$	−42.9390	−1.79694	−0.898470	+	0.439035i	$0.855321\pi$
$572$	0.321968	0.0134621
$573$	−30.5643	−1.27684
$574$	5.18118	0.216258
$575$	−5.48987	−0.228943
$576$	1.75080	0.0729500
$577$	−7.69878	−0.320504	−0.160252	−	0.987076i	$-0.551231\pi$
$577$	−7.69878	−0.320504	−0.160252	+	0.987076i	$0.551231\pi$
$578$	−13.1645	−0.547572
$579$	37.2041	1.54615
$580$	10.4973	0.435878
$581$	19.7359	0.818783
$582$	41.7564	1.73086
$583$	−4.60847	−0.190863
$584$	−1.00000	−0.0413803
$585$	−0.563701	−0.0233062
$586$	−18.2151	−0.752459
$587$	13.7116	0.565936	0.282968	−	0.959129i	$-0.408681\pi$
$587$	13.7116	0.565936	0.282968	+	0.959129i	$0.408681\pi$
$588$	−4.35927	−0.179773
$589$	−0.0198034	−0.000815987 0
$590$	−13.7865	−0.567583
$591$	11.3710	0.467740
$592$	7.58318	0.311667
$593$	−37.2188	−1.52839	−0.764196	−	0.644984i	$-0.776864\pi$
$593$	−37.2188	−1.52839	−0.764196	+	0.644984i	$0.776864\pi$
$594$	−2.72280	−0.111718
$595$	5.87531	0.240864
$596$	23.2396	0.951931
$597$	−17.8710	−0.731413
$598$	1.76756	0.0722810
$599$	4.06530	0.166104	0.0830519	−	0.996545i	$-0.473533\pi$
$599$	4.06530	0.166104	0.0830519	+	0.996545i	$0.473533\pi$
$600$	−2.17963	−0.0889831
$601$	−10.9184	−0.445372	−0.222686	−	0.974890i	$-0.571482\pi$
$601$	−10.9184	−0.445372	−0.222686	+	0.974890i	$0.571482\pi$
$602$	−15.7572	−0.642216
$603$	−20.0274	−0.815580
$604$	−14.2929	−0.581570
$605$	1.00000	0.0406558
$606$	31.2073	1.26771
$607$	42.9001	1.74126	0.870631	−	0.491937i	$-0.163711\pi$
$607$	42.9001	1.74126	0.870631	+	0.491937i	$0.163711\pi$
$608$	−0.00426437	−0.000172943 0
$609$	68.6410	2.78147
$610$	8.27343	0.334981
$611$	−0.385043	−0.0155772
$612$	−3.42883	−0.138602
$613$	1.84791	0.0746366	0.0373183	−	0.999303i	$-0.488118\pi$
$613$	1.84791	0.0746366	0.0373183	+	0.999303i	$0.488118\pi$
$614$	9.34251	0.377033
$615$	3.76436	0.151794
$616$	3.00000	0.120873
$617$	−5.95969	−0.239928	−0.119964	−	0.992778i	$-0.538278\pi$
$617$	−5.95969	−0.239928	−0.119964	+	0.992778i	$0.538278\pi$
$618$	−0.665239	−0.0267598
$619$	−8.61719	−0.346354	−0.173177	−	0.984891i	$-0.555403\pi$
$619$	−8.61719	−0.346354	−0.173177	+	0.984891i	$0.555403\pi$
$620$	4.64394	0.186505
$621$	−14.9478	−0.599835
$622$	−24.8968	−0.998272
$623$	−41.3515	−1.65671
$624$	0.701772	0.0280933
$625$	1.00000	0.0400000
$626$	−32.9496	−1.31693
$627$	−0.00929475	−0.000371197 0
$628$	−18.7423	−0.747898
$629$	−14.8512	−0.592155
$630$	−5.25240	−0.209261
$631$	−23.9480	−0.953353	−0.476677	−	0.879079i	$-0.658159\pi$
$631$	−23.9480	−0.953353	−0.476677	+	0.879079i	$0.658159\pi$
$632$	−13.6159	−0.541613
$633$	−22.0027	−0.874529
$634$	17.0997	0.679116
$635$	−0.526890	−0.0209090
$636$	−10.0448	−0.398301
$637$	−0.643936	−0.0255137
$638$	−10.4973	−0.415594
$639$	−1.80303	−0.0713268
$640$	1.00000	0.0395285
$641$	12.2399	0.483447	0.241724	−	0.970345i	$-0.422287\pi$
$641$	12.2399	0.483447	0.241724	+	0.970345i	$0.422287\pi$
$642$	−19.6051	−0.773751
$643$	26.5307	1.04627	0.523134	−	0.852250i	$-0.324763\pi$
$643$	26.5307	1.04627	0.523134	+	0.852250i	$0.324763\pi$
$644$	16.4696	0.648994
$645$	−11.4483	−0.450777
$646$	0.00835149	0.000328585 0
$647$	9.21063	0.362107	0.181054	−	0.983473i	$-0.442049\pi$
$647$	9.21063	0.362107	0.181054	+	0.983473i	$0.442049\pi$
$648$	−11.1871	−0.439471
$649$	13.7865	0.541169
$650$	−0.321968	−0.0126286
$651$	30.3662	1.19015
$652$	−2.46885	−0.0966874
$653$	49.0478	1.91939	0.959694	−	0.281048i	$-0.0906819\pi$
$653$	49.0478	1.91939	0.959694	+	0.281048i	$0.0906819\pi$
$654$	−14.5464	−0.568808
$655$	−0.179146	−0.00699980
$656$	−1.72706	−0.0674304
$657$	−1.75080	−0.0683052
$658$	−3.58772	−0.139864
$659$	34.4645	1.34254	0.671272	−	0.741211i	$-0.265748\pi$
$659$	34.4645	1.34254	0.671272	+	0.741211i	$0.265748\pi$
$660$	2.17963	0.0848421
$661$	22.2124	0.863962	0.431981	−	0.901883i	$-0.357815\pi$
$661$	22.2124	0.863962	0.431981	+	0.901883i	$0.357815\pi$
$662$	9.06713	0.352404
$663$	−1.37438	−0.0533763
$664$	−6.57863	−0.255300
$665$	0.0127931	0.000496095 0
$666$	13.2766	0.514459
$667$	−57.6290	−2.23140
$668$	17.1930	0.665218
$669$	42.6400	1.64856
$670$	−11.4390	−0.441928
$671$	−8.27343	−0.319392
$672$	6.53890	0.252244
$673$	5.78850	0.223130	0.111565	−	0.993757i	$-0.464414\pi$
$673$	5.78850	0.223130	0.111565	+	0.993757i	$0.464414\pi$
$674$	−7.85794	−0.302677
$675$	2.72280	0.104800
$676$	−12.8963	−0.496013
$677$	−45.8641	−1.76270	−0.881349	−	0.472465i	$-0.843364\pi$
$677$	−45.8641	−1.76270	−0.881349	+	0.472465i	$0.843364\pi$
$678$	7.95174	0.305385
$679$	57.4726	2.20560
$680$	−1.95844	−0.0751026
$681$	37.1114	1.42211
$682$	−4.64394	−0.177825
$683$	14.6945	0.562269	0.281135	−	0.959668i	$-0.409289\pi$
$683$	14.6945	0.562269	0.281135	+	0.959668i	$0.409289\pi$
$684$	−0.00746605	−0.000285472 0
$685$	−11.0330	−0.421551
$686$	15.0000	0.572703
$687$	21.5511	0.822226
$688$	5.25240	0.200246
$689$	−1.48378	−0.0565274
$690$	11.9659	0.455534
$691$	−46.9030	−1.78427	−0.892137	−	0.451764i	$-0.850795\pi$
$691$	−46.9030	−1.78427	−0.892137	+	0.451764i	$0.850795\pi$
$692$	−21.2766	−0.808816
$693$	5.25240	0.199522
$694$	−7.15297	−0.271523
$695$	−12.1941	−0.462548
$696$	−22.8803	−0.867277
$697$	3.38234	0.128115
$698$	17.0152	0.644035
$699$	53.3358	2.01735
$700$	−3.00000	−0.113389
$701$	6.62717	0.250305	0.125152	−	0.992138i	$-0.460058\pi$
$701$	6.62717	0.250305	0.125152	+	0.992138i	$0.460058\pi$
$702$	−0.876653	−0.0330871
$703$	−0.0323374	−0.00121963
$704$	−1.00000	−0.0376889
$705$	−2.60664	−0.0981716
$706$	−11.4174	−0.429700
$707$	42.9531	1.61542
$708$	30.0496	1.12933
$709$	−10.3116	−0.387259	−0.193630	−	0.981075i	$-0.562026\pi$
$709$	−10.3116	−0.387259	−0.193630	+	0.981075i	$0.562026\pi$
$710$	−1.02983	−0.0386489
$711$	−23.8388	−0.894024
$712$	13.7838	0.516571
$713$	−25.4946	−0.954780
$714$	−12.8060	−0.479253
$715$	0.321968	0.0120409
$716$	6.32971	0.236552
$717$	−4.16120	−0.155403
$718$	−23.6901	−0.884106
$719$	−24.9729	−0.931331	−0.465665	−	0.884961i	$-0.654185\pi$
$719$	−24.9729	−0.931331	−0.465665	+	0.884961i	$0.654185\pi$
$720$	1.75080	0.0652485
$721$	−0.915621	−0.0340995
$722$	−19.0000	−0.707106
$723$	−25.1629	−0.935817
$724$	21.7855	0.809651
$725$	10.4973	0.389861
$726$	−2.17963	−0.0808938
$727$	26.3809	0.978413	0.489206	−	0.872168i	$-0.337286\pi$
$727$	26.3809	0.978413	0.489206	+	0.872168i	$0.337286\pi$
$728$	0.965903	0.0357988
$729$	−1.78228	−0.0660105
$730$	−1.00000	−0.0370117
$731$	−10.2865	−0.380460
$732$	−18.0330	−0.666520
$733$	−7.41606	−0.273918	−0.136959	−	0.990577i	$-0.543733\pi$
$733$	−7.41606	−0.273918	−0.136959	+	0.990577i	$0.543733\pi$
$734$	−16.8849	−0.623232
$735$	−4.35927	−0.160794
$736$	−5.48987	−0.202359
$737$	11.4390	0.421361
$738$	−3.02374	−0.111305
$739$	32.0554	1.17918	0.589588	−	0.807704i	$-0.299290\pi$
$739$	32.0554	1.17918	0.589588	+	0.807704i	$0.299290\pi$
$740$	7.58318	0.278763
$741$	−0.00299261	−0.000109936 0
$742$	−13.8254	−0.507546
$743$	0.303259	0.0111255	0.00556274	−	0.999985i	$-0.498229\pi$
$743$	0.303259	0.0111255	0.00556274	+	0.999985i	$0.498229\pi$
$744$	−10.1221	−0.371093
$745$	23.2396	0.851433
$746$	12.4486	0.455775
$747$	−11.5179	−0.421417
$748$	1.95844	0.0716076
$749$	−26.9840	−0.985975
$750$	−2.17963	−0.0795889
$751$	−4.00768	−0.146242	−0.0731211	−	0.997323i	$-0.523296\pi$
$751$	−4.00768	−0.146242	−0.0731211	+	0.997323i	$0.523296\pi$
$752$	1.19591	0.0436102
$753$	−3.29805	−0.120188
$754$	−3.37980	−0.123085
$755$	−14.2929	−0.520172
$756$	−8.16839	−0.297081
$757$	34.9096	1.26881	0.634405	−	0.773000i	$-0.281245\pi$
$757$	34.9096	1.26881	0.634405	+	0.773000i	$0.281245\pi$
$758$	−4.79208	−0.174056
$759$	−11.9659	−0.434335
$760$	−0.00426437	−0.000154685 0
$761$	−21.0832	−0.764266	−0.382133	−	0.924107i	$-0.624810\pi$
$761$	−21.0832	−0.764266	−0.382133	+	0.924107i	$0.624810\pi$
$762$	1.14843	0.0416031
$763$	−20.0213	−0.724820
$764$	14.0227	0.507323
$765$	−3.42883	−0.123970
$766$	−16.5628	−0.598440
$767$	4.43882	0.160277
$768$	−2.17963	−0.0786507
$769$	29.9272	1.07920	0.539602	−	0.841920i	$-0.318575\pi$
$769$	29.9272	1.07920	0.539602	+	0.841920i	$0.318575\pi$
$770$	3.00000	0.108112
$771$	40.3446	1.45298
$772$	−17.0690	−0.614326
$773$	−26.7450	−0.961951	−0.480976	−	0.876734i	$-0.659717\pi$
$773$	−26.7450	−0.961951	−0.480976	+	0.876734i	$0.659717\pi$
$774$	9.19591	0.330540
$775$	4.64394	0.166815
$776$	−19.1575	−0.687716
$777$	49.5856	1.77887
$778$	−1.85206	−0.0663996
$779$	0.00736482	0.000263872 0
$780$	0.701772	0.0251275
$781$	1.02983	0.0368503
$782$	10.7516	0.384475
$783$	28.5821	1.02144
$784$	2.00000	0.0714286
$785$	−18.7423	−0.668940
$786$	0.390472	0.0139277
$787$	−52.1508	−1.85897	−0.929487	−	0.368855i	$-0.879750\pi$
$787$	−52.1508	−1.85897	−0.929487	+	0.368855i	$0.879750\pi$
$788$	−5.21693	−0.185845
$789$	−14.9537	−0.532366
$790$	−13.6159	−0.484433
$791$	10.9446	0.389145
$792$	−1.75080	−0.0622120
$793$	−2.66378	−0.0945935
$794$	36.0674	1.27999
$795$	−10.0448	−0.356251
$796$	8.19911	0.290610
$797$	2.93701	0.104034	0.0520172	−	0.998646i	$-0.483435\pi$
$797$	2.93701	0.104034	0.0520172	+	0.998646i	$0.483435\pi$
$798$	−0.0278843	−0.000987092 0
$799$	−2.34211	−0.0828578
$800$	1.00000	0.0353553
$801$	24.1327	0.852689
$802$	9.86833	0.348463
$803$	1.00000	0.0352892
$804$	24.9329	0.879314
$805$	16.4696	0.580478
$806$	−1.49520	−0.0526661
$807$	−61.6194	−2.16911
$808$	−14.3177	−0.503695
$809$	35.3610	1.24323	0.621613	−	0.783324i	$-0.286478\pi$
$809$	35.3610	1.24323	0.621613	+	0.783324i	$0.286478\pi$
$810$	−11.1871	−0.393075
$811$	−20.6421	−0.724842	−0.362421	−	0.932014i	$-0.618050\pi$
$811$	−20.6421	−0.724842	−0.362421	+	0.932014i	$0.618050\pi$
$812$	−31.4920	−1.10515
$813$	−21.3468	−0.748663
$814$	−7.58318	−0.265790
$815$	−2.46885	−0.0864799
$816$	4.26867	0.149433
$817$	−0.0223982	−0.000783613 0
$818$	7.49386	0.262017
$819$	1.69110	0.0590919
$820$	−1.72706	−0.0603116
$821$	−6.08069	−0.212218	−0.106109	−	0.994355i	$-0.533839\pi$
$821$	−6.08069	−0.212218	−0.106109	+	0.994355i	$0.533839\pi$
$822$	24.0480	0.838769
$823$	32.8474	1.14499	0.572494	−	0.819909i	$-0.305976\pi$
$823$	32.8474	1.14499	0.572494	+	0.819909i	$0.305976\pi$
$824$	0.305207	0.0106324
$825$	2.17963	0.0758851
$826$	41.3596	1.43909
$827$	12.7231	0.442426	0.221213	−	0.975226i	$-0.428998\pi$
$827$	12.7231	0.442426	0.221213	+	0.975226i	$0.428998\pi$
$828$	−9.61167	−0.334029
$829$	20.3507	0.706810	0.353405	−	0.935470i	$-0.385024\pi$
$829$	20.3507	0.706810	0.353405	+	0.935470i	$0.385024\pi$
$830$	−6.57863	−0.228348
$831$	−21.2897	−0.738532
$832$	−0.321968	−0.0111622
$833$	−3.91687	−0.135712
$834$	26.5786	0.920342
$835$	17.1930	0.594989
$836$	0.00426437	0.000147486 0
$837$	12.6445	0.437058
$838$	−19.2841	−0.666158
$839$	57.3490	1.97991	0.989953	−	0.141394i	$-0.0451586\pi$
$839$	57.3490	1.97991	0.989953	+	0.141394i	$0.0451586\pi$
$840$	6.53890	0.225613
$841$	81.1941	2.79980
$842$	−13.5309	−0.466307
$843$	63.8228	2.19817
$844$	10.0947	0.347473
$845$	−12.8963	−0.443647
$846$	2.09379	0.0719861
$847$	−3.00000	−0.103081
$848$	4.60847	0.158255
$849$	−11.9984	−0.411786
$850$	−1.95844	−0.0671738
$851$	−41.6307	−1.42708
$852$	2.24466	0.0769007
$853$	−21.0641	−0.721220	−0.360610	−	0.932717i	$-0.617431\pi$
$853$	−21.0641	−0.721220	−0.360610	+	0.932717i	$0.617431\pi$
$854$	−24.8203	−0.849332
$855$	−0.00746605	−0.000255334 0
$856$	8.99467	0.307432
$857$	41.2786	1.41005	0.705025	−	0.709183i	$-0.250936\pi$
$857$	41.2786	1.41005	0.705025	+	0.709183i	$0.250936\pi$
$858$	−0.701772	−0.0239581
$859$	−9.47932	−0.323430	−0.161715	−	0.986837i	$-0.551703\pi$
$859$	−9.47932	−0.323430	−0.161715	+	0.986837i	$0.551703\pi$
$860$	5.25240	0.179105
$861$	−11.2931	−0.384867
$862$	−32.5544	−1.10881
$863$	16.1874	0.551025	0.275512	−	0.961298i	$-0.411152\pi$
$863$	16.1874	0.551025	0.275512	+	0.961298i	$0.411152\pi$
$864$	2.72280	0.0926314
$865$	−21.2766	−0.723427
$866$	14.2308	0.483581
$867$	28.6938	0.974494
$868$	−13.9318	−0.472876
$869$	13.6159	0.461889
$870$	−22.8803	−0.775716
$871$	3.68299	0.124793
$872$	6.67377	0.226002
$873$	−33.5410	−1.13519
$874$	0.0234108	0.000791883 0
$875$	−3.00000	−0.101419
$876$	2.17963	0.0736430
$877$	−34.9020	−1.17856	−0.589278	−	0.807930i	$-0.700588\pi$
$877$	−34.9020	−1.17856	−0.589278	+	0.807930i	$0.700588\pi$
$878$	−12.9768	−0.437947
$879$	39.7022	1.33912
$880$	−1.00000	−0.0337100
$881$	53.2757	1.79490	0.897451	−	0.441113i	$-0.145416\pi$
$881$	53.2757	1.79490	0.897451	+	0.441113i	$0.145416\pi$
$882$	3.50160	0.117905
$883$	−28.6432	−0.963920	−0.481960	−	0.876193i	$-0.660075\pi$
$883$	−28.6432	−0.963920	−0.481960	+	0.876193i	$0.660075\pi$
$884$	0.630554	0.0212078
$885$	30.0496	1.01011
$886$	36.6104	1.22995
$887$	−47.9253	−1.60917	−0.804587	−	0.593834i	$-0.797613\pi$
$887$	−47.9253	−1.60917	−0.804587	+	0.593834i	$0.797613\pi$
$888$	−16.5285	−0.554662
$889$	1.58067	0.0530140
$890$	13.7838	0.462035
$891$	11.1871	0.374782
$892$	−19.5629	−0.655015
$893$	−0.00509978	−0.000170658 0
$894$	−50.6538	−1.69412
$895$	6.32971	0.211579
$896$	−3.00000	−0.100223
$897$	−3.85263	−0.128636
$898$	−28.6479	−0.955993
$899$	48.7490	1.62587
$900$	1.75080	0.0583600
$901$	−9.02539	−0.300679
$902$	1.72706	0.0575048
$903$	34.3449	1.14293
$904$	−3.64820	−0.121337
$905$	21.7855	0.724174
$906$	31.1533	1.03500
$907$	−43.7211	−1.45174	−0.725868	−	0.687834i	$-0.758562\pi$
$907$	−43.7211	−1.45174	−0.725868	+	0.687834i	$0.758562\pi$
$908$	−17.0265	−0.565043
$909$	−25.0674	−0.831435
$910$	0.965903	0.0320194
$911$	−53.9448	−1.78727	−0.893635	−	0.448794i	$-0.851854\pi$
$911$	−53.9448	−1.78727	−0.893635	+	0.448794i	$0.851854\pi$
$912$	0.00929475	0.000307780 0
$913$	6.57863	0.217721
$914$	28.2606	0.934779
$915$	−18.0330	−0.596154
$916$	−9.88750	−0.326692
$917$	0.537437	0.0177477
$918$	−5.33243	−0.175996
$919$	38.7004	1.27661	0.638304	−	0.769784i	$-0.279636\pi$
$919$	38.7004	1.27661	0.638304	+	0.769784i	$0.279636\pi$
$920$	−5.48987	−0.180996
$921$	−20.3632	−0.670991
$922$	14.6295	0.481797
$923$	0.331573	0.0109139
$924$	−6.53890	−0.215114
$925$	7.58318	0.249333
$926$	−27.3179	−0.897722
$927$	0.534356	0.0175506
$928$	10.4973	0.344592
$929$	−20.4321	−0.670354	−0.335177	−	0.942155i	$-0.608796\pi$
$929$	−20.4321	−0.670354	−0.335177	+	0.942155i	$0.608796\pi$
$930$	−10.1221	−0.331916
$931$	−0.00852873	−0.000279518 0
$932$	−24.4701	−0.801545
$933$	54.2659	1.77659
$934$	−5.37953	−0.176023
$935$	1.95844	0.0640477
$936$	−0.563701	−0.0184252
$937$	5.21141	0.170249	0.0851247	−	0.996370i	$-0.472871\pi$
$937$	5.21141	0.170249	0.0851247	+	0.996370i	$0.472871\pi$
$938$	34.3170	1.12049
$939$	71.8181	2.34369
$940$	1.19591	0.0390062
$941$	−22.6362	−0.737919	−0.368959	−	0.929446i	$-0.620286\pi$
$941$	−22.6362	−0.737919	−0.368959	+	0.929446i	$0.620286\pi$
$942$	40.8513	1.33101
$943$	9.48134	0.308755
$944$	−13.7865	−0.448714
$945$	−8.16839	−0.265718
$946$	−5.25240	−0.170770
$947$	40.8829	1.32852	0.664258	−	0.747503i	$-0.268747\pi$
$947$	40.8829	1.32852	0.664258	+	0.747503i	$0.268747\pi$
$948$	29.6777	0.963888
$949$	0.321968	0.0104515
$950$	−0.00426437	−0.000138354 0
$951$	−37.2711	−1.20860
$952$	5.87531	0.190420
$953$	49.9933	1.61944	0.809721	−	0.586815i	$-0.199618\pi$
$953$	49.9933	1.61944	0.809721	+	0.586815i	$0.199618\pi$
$954$	8.06850	0.261227
$955$	14.0227	0.453763
$956$	1.90913	0.0617457
$957$	22.8803	0.739616
$958$	3.82519	0.123586
$959$	33.0991	1.06883
$960$	−2.17963	−0.0703474
$961$	−9.43386	−0.304318
$962$	−2.44154	−0.0787184
$963$	15.7479	0.507468
$964$	11.5445	0.371824
$965$	−17.0690	−0.549470
$966$	−35.8977	−1.15499
$967$	20.0220	0.643864	0.321932	−	0.946763i	$-0.395668\pi$
$967$	20.0220	0.643864	0.321932	+	0.946763i	$0.395668\pi$
$968$	1.00000	0.0321412
$969$	−0.0182032	−0.000584771 0
$970$	−19.1575	−0.615112
$971$	24.3384	0.781057	0.390529	−	0.920591i	$-0.372292\pi$
$971$	24.3384	0.781057	0.390529	+	0.920591i	$0.372292\pi$
$972$	16.2154	0.520109
$973$	36.5822	1.17277
$974$	29.7412	0.952970
$975$	0.701772	0.0224747
$976$	8.27343	0.264826
$977$	−59.7179	−1.91055	−0.955273	−	0.295725i	$-0.904439\pi$
$977$	−59.7179	−1.91055	−0.955273	+	0.295725i	$0.904439\pi$
$978$	5.38118	0.172071
$979$	−13.7838	−0.440533
$980$	2.00000	0.0638877
$981$	11.6844	0.373055
$982$	−9.08478	−0.289907
$983$	45.5438	1.45262	0.726310	−	0.687367i	$-0.241234\pi$
$983$	45.5438	1.45262	0.726310	+	0.687367i	$0.241234\pi$
$984$	3.76436	0.120003
$985$	−5.21693	−0.166225
$986$	−20.5584	−0.654712
$987$	7.81991	0.248911
$988$	0.00137299	4.36806e−5 0
$989$	−28.8350	−0.916900
$990$	−1.75080	−0.0556441
$991$	5.64914	0.179451	0.0897255	−	0.995967i	$-0.471401\pi$
$991$	5.64914	0.179451	0.0897255	+	0.995967i	$0.471401\pi$
$992$	4.64394	0.147445
$993$	−19.7630	−0.627160
$994$	3.08950	0.0979929
$995$	8.19911	0.259929
$996$	14.3390	0.454349
$997$	−56.1980	−1.77981	−0.889905	−	0.456146i	$-0.849229\pi$
$997$	−56.1980	−1.77981	−0.889905	+	0.456146i	$0.849229\pi$
$998$	−21.2125	−0.671470
$999$	20.6474	0.653256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.u.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.u.1.1	✓	4	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.17963 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.17963 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.75080 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.17963 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.17963 q^{6} -3.00000 q^{7} +1.00000 q^{8} +1.75080 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.17963 q^{12} -0.321968 q^{13} -3.00000 q^{14} -2.17963 q^{15} +1.00000 q^{16} -1.95844 q^{17} +1.75080 q^{18} -0.00426437 q^{19} +1.00000 q^{20} +6.53890 q^{21} -1.00000 q^{22} -5.48987 q^{23} -2.17963 q^{24} +1.00000 q^{25} -0.321968 q^{26} +2.72280 q^{27} -3.00000 q^{28} +10.4973 q^{29} -2.17963 q^{30} +4.64394 q^{31} +1.00000 q^{32} +2.17963 q^{33} -1.95844 q^{34} -3.00000 q^{35} +1.75080 q^{36} +7.58318 q^{37} -0.00426437 q^{38} +0.701772 q^{39} +1.00000 q^{40} -1.72706 q^{41} +6.53890 q^{42} +5.25240 q^{43} -1.00000 q^{44} +1.75080 q^{45} -5.48987 q^{46} +1.19591 q^{47} -2.17963 q^{48} +2.00000 q^{49} +1.00000 q^{50} +4.26867 q^{51} -0.321968 q^{52} +4.60847 q^{53} +2.72280 q^{54} -1.00000 q^{55} -3.00000 q^{56} +0.00929475 q^{57} +10.4973 q^{58} -13.7865 q^{59} -2.17963 q^{60} +8.27343 q^{61} +4.64394 q^{62} -5.25240 q^{63} +1.00000 q^{64} -0.321968 q^{65} +2.17963 q^{66} -11.4390 q^{67} -1.95844 q^{68} +11.9659 q^{69} -3.00000 q^{70} -1.02983 q^{71} +1.75080 q^{72} -1.00000 q^{73} +7.58318 q^{74} -2.17963 q^{75} -0.00426437 q^{76} +3.00000 q^{77} +0.701772 q^{78} -13.6159 q^{79} +1.00000 q^{80} -11.1871 q^{81} -1.72706 q^{82} -6.57863 q^{83} +6.53890 q^{84} -1.95844 q^{85} +5.25240 q^{86} -22.8803 q^{87} -1.00000 q^{88} +13.7838 q^{89} +1.75080 q^{90} +0.965903 q^{91} -5.48987 q^{92} -10.1221 q^{93} +1.19591 q^{94} -0.00426437 q^{95} -2.17963 q^{96} -19.1575 q^{97} +2.00000 q^{98} -1.75080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + 4 q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + 4 * q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + 4 q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} - 4 q^{11} - q^{12} + 7 q^{13} - 12 q^{14} - q^{15} + 4 q^{16} + 4 q^{17} - q^{18} - 19 q^{19} + 4 q^{20} + 3 q^{21} - 4 q^{22} - q^{24} + 4 q^{25} + 7 q^{26} - q^{27} - 12 q^{28} + 7 q^{29} - q^{30} + 2 q^{31} + 4 q^{32} + q^{33} + 4 q^{34} - 12 q^{35} - q^{36} + 9 q^{37} - 19 q^{38} - 4 q^{39} + 4 q^{40} - 14 q^{41} + 3 q^{42} - 3 q^{43} - 4 q^{44} - q^{45} - 5 q^{47} - q^{48} + 8 q^{49} + 4 q^{50} - 9 q^{51} + 7 q^{52} + 11 q^{53} - q^{54} - 4 q^{55} - 12 q^{56} - 11 q^{57} + 7 q^{58} - 11 q^{59} - q^{60} + 4 q^{61} + 2 q^{62} + 3 q^{63} + 4 q^{64} + 7 q^{65} + q^{66} - 23 q^{67} + 4 q^{68} + 23 q^{69} - 12 q^{70} - 10 q^{71} - q^{72} - 4 q^{73} + 9 q^{74} - q^{75} - 19 q^{76} + 12 q^{77} - 4 q^{78} - 34 q^{79} + 4 q^{80} - 24 q^{81} - 14 q^{82} - 13 q^{83} + 3 q^{84} + 4 q^{85} - 3 q^{86} - 26 q^{87} - 4 q^{88} + 21 q^{89} - q^{90} - 21 q^{91} + 4 q^{93} - 5 q^{94} - 19 q^{95} - q^{96} - 23 q^{97} + 8 q^{98} + q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + 4 * q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 - 4 * q^11 - q^12 + 7 * q^13 - 12 * q^14 - q^15 + 4 * q^16 + 4 * q^17 - q^18 - 19 * q^19 + 4 * q^20 + 3 * q^21 - 4 * q^22 - q^24 + 4 * q^25 + 7 * q^26 - q^27 - 12 * q^28 + 7 * q^29 - q^30 + 2 * q^31 + 4 * q^32 + q^33 + 4 * q^34 - 12 * q^35 - q^36 + 9 * q^37 - 19 * q^38 - 4 * q^39 + 4 * q^40 - 14 * q^41 + 3 * q^42 - 3 * q^43 - 4 * q^44 - q^45 - 5 * q^47 - q^48 + 8 * q^49 + 4 * q^50 - 9 * q^51 + 7 * q^52 + 11 * q^53 - q^54 - 4 * q^55 - 12 * q^56 - 11 * q^57 + 7 * q^58 - 11 * q^59 - q^60 + 4 * q^61 + 2 * q^62 + 3 * q^63 + 4 * q^64 + 7 * q^65 + q^66 - 23 * q^67 + 4 * q^68 + 23 * q^69 - 12 * q^70 - 10 * q^71 - q^72 - 4 * q^73 + 9 * q^74 - q^75 - 19 * q^76 + 12 * q^77 - 4 * q^78 - 34 * q^79 + 4 * q^80 - 24 * q^81 - 14 * q^82 - 13 * q^83 + 3 * q^84 + 4 * q^85 - 3 * q^86 - 26 * q^87 - 4 * q^88 + 21 * q^89 - q^90 - 21 * q^91 + 4 * q^93 - 5 * q^94 - 19 * q^95 - q^96 - 23 * q^97 + 8 * q^98 + q^99

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