LMFDB - Embedded newform 8018.2.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.75523 q^{3} +1.00000 q^{4} -0.0353436 q^{5} +1.75523 q^{6} -4.74271 q^{7} -1.00000 q^{8} +0.0808489 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.75523 q^{3} +1.00000 q^{4} -0.0353436 q^{5} +1.75523 q^{6} -4.74271 q^{7} -1.00000 q^{8} +0.0808489 q^{9} +0.0353436 q^{10} +1.60626 q^{11} -1.75523 q^{12} +1.95986 q^{13} +4.74271 q^{14} +0.0620364 q^{15} +1.00000 q^{16} +2.69733 q^{17} -0.0808489 q^{18} -1.00000 q^{19} -0.0353436 q^{20} +8.32457 q^{21} -1.60626 q^{22} +0.989478 q^{23} +1.75523 q^{24} -4.99875 q^{25} -1.95986 q^{26} +5.12380 q^{27} -4.74271 q^{28} -8.65124 q^{29} -0.0620364 q^{30} +4.25370 q^{31} -1.00000 q^{32} -2.81936 q^{33} -2.69733 q^{34} +0.167625 q^{35} +0.0808489 q^{36} -9.33639 q^{37} +1.00000 q^{38} -3.44002 q^{39} +0.0353436 q^{40} +0.956648 q^{41} -8.32457 q^{42} +1.61181 q^{43} +1.60626 q^{44} -0.00285750 q^{45} -0.989478 q^{46} +1.67388 q^{47} -1.75523 q^{48} +15.4933 q^{49} +4.99875 q^{50} -4.73445 q^{51} +1.95986 q^{52} +11.3038 q^{53} -5.12380 q^{54} -0.0567710 q^{55} +4.74271 q^{56} +1.75523 q^{57} +8.65124 q^{58} +5.80290 q^{59} +0.0620364 q^{60} -14.0420 q^{61} -4.25370 q^{62} -0.383443 q^{63} +1.00000 q^{64} -0.0692686 q^{65} +2.81936 q^{66} -14.4566 q^{67} +2.69733 q^{68} -1.73677 q^{69} -0.167625 q^{70} -6.21586 q^{71} -0.0808489 q^{72} +12.1039 q^{73} +9.33639 q^{74} +8.77398 q^{75} -1.00000 q^{76} -7.61801 q^{77} +3.44002 q^{78} +4.84035 q^{79} -0.0353436 q^{80} -9.23601 q^{81} -0.956648 q^{82} -11.8245 q^{83} +8.32457 q^{84} -0.0953335 q^{85} -1.61181 q^{86} +15.1850 q^{87} -1.60626 q^{88} -16.1354 q^{89} +0.00285750 q^{90} -9.29505 q^{91} +0.989478 q^{92} -7.46625 q^{93} -1.67388 q^{94} +0.0353436 q^{95} +1.75523 q^{96} +6.45988 q^{97} -15.4933 q^{98} +0.129864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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
$3$	−1.75523	−1.01339	−0.506693	−	0.862127i	$-0.669132\pi$
$3$	−1.75523	−1.01339	−0.506693	+	0.862127i	$0.669132\pi$
$4$	1.00000	0.500000
$5$	−0.0353436	−0.0158062	−0.00790308	−	0.999969i	$-0.502516\pi$
$5$	−0.0353436	−0.0158062	−0.00790308	+	0.999969i	$0.502516\pi$
$6$	1.75523	0.716572
$7$	−4.74271	−1.79258	−0.896288	−	0.443473i	$-0.853746\pi$
$7$	−4.74271	−1.79258	−0.896288	+	0.443473i	$0.853746\pi$
$8$	−1.00000	−0.353553
$9$	0.0808489	0.0269496
$10$	0.0353436	0.0111766
$11$	1.60626	0.484305	0.242152	−	0.970238i	$-0.422147\pi$
$11$	1.60626	0.484305	0.242152	+	0.970238i	$0.422147\pi$
$12$	−1.75523	−0.506693
$13$	1.95986	0.543567	0.271784	−	0.962358i	$-0.412386\pi$
$13$	1.95986	0.543567	0.271784	+	0.962358i	$0.412386\pi$
$14$	4.74271	1.26754
$15$	0.0620364	0.0160177
$16$	1.00000	0.250000
$17$	2.69733	0.654199	0.327100	−	0.944990i	$-0.393929\pi$
$17$	2.69733	0.654199	0.327100	+	0.944990i	$0.393929\pi$
$18$	−0.0808489	−0.0190563
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.0353436	−0.00790308
$21$	8.32457	1.81657
$22$	−1.60626	−0.342455
$23$	0.989478	0.206320	0.103160	−	0.994665i	$-0.467105\pi$
$23$	0.989478	0.206320	0.103160	+	0.994665i	$0.467105\pi$
$24$	1.75523	0.358286
$25$	−4.99875	−0.999750
$26$	−1.95986	−0.384360
$27$	5.12380	0.986075
$28$	−4.74271	−0.896288
$29$	−8.65124	−1.60650	−0.803248	−	0.595645i	$-0.796897\pi$
$29$	−8.65124	−1.60650	−0.803248	+	0.595645i	$0.796897\pi$
$30$	−0.0620364	−0.0113262
$31$	4.25370	0.763988	0.381994	−	0.924165i	$-0.375238\pi$
$31$	4.25370	0.763988	0.381994	+	0.924165i	$0.375238\pi$
$32$	−1.00000	−0.176777
$33$	−2.81936	−0.490787
$34$	−2.69733	−0.462589
$35$	0.167625	0.0283337
$36$	0.0808489	0.0134748
$37$	−9.33639	−1.53489	−0.767447	−	0.641113i	$-0.778473\pi$
$37$	−9.33639	−1.53489	−0.767447	+	0.641113i	$0.778473\pi$
$38$	1.00000	0.162221
$39$	−3.44002	−0.550843
$40$	0.0353436	0.00558832
$41$	0.956648	0.149403	0.0747016	−	0.997206i	$-0.476200\pi$
$41$	0.956648	0.149403	0.0747016	+	0.997206i	$0.476200\pi$
$42$	−8.32457	−1.28451
$43$	1.61181	0.245798	0.122899	−	0.992419i	$-0.460781\pi$
$43$	1.61181	0.245798	0.122899	+	0.992419i	$0.460781\pi$
$44$	1.60626	0.242152
$45$	−0.00285750	−0.000425970 0
$46$	−0.989478	−0.145891
$47$	1.67388	0.244161	0.122080	−	0.992520i	$-0.461043\pi$
$47$	1.67388	0.244161	0.122080	+	0.992520i	$0.461043\pi$
$48$	−1.75523	−0.253346
$49$	15.4933	2.21333
$50$	4.99875	0.706930
$51$	−4.73445	−0.662956
$52$	1.95986	0.271784
$53$	11.3038	1.55269	0.776346	−	0.630307i	$-0.217071\pi$
$53$	11.3038	1.55269	0.776346	+	0.630307i	$0.217071\pi$
$54$	−5.12380	−0.697260
$55$	−0.0567710	−0.00765500
$56$	4.74271	0.633771
$57$	1.75523	0.232487
$58$	8.65124	1.13596
$59$	5.80290	0.755473	0.377737	−	0.925913i	$-0.376702\pi$
$59$	5.80290	0.755473	0.377737	+	0.925913i	$0.376702\pi$
$60$	0.0620364	0.00800886
$61$	−14.0420	−1.79789	−0.898947	−	0.438058i	$-0.855667\pi$
$61$	−14.0420	−1.79789	−0.898947	+	0.438058i	$0.855667\pi$
$62$	−4.25370	−0.540221
$63$	−0.383443	−0.0483093
$64$	1.00000	0.125000
$65$	−0.0692686	−0.00859171
$66$	2.81936	0.347039
$67$	−14.4566	−1.76615	−0.883076	−	0.469230i	$-0.844532\pi$
$67$	−14.4566	−1.76615	−0.883076	+	0.469230i	$0.844532\pi$
$68$	2.69733	0.327100
$69$	−1.73677	−0.209082
$70$	−0.167625	−0.0200350
$71$	−6.21586	−0.737687	−0.368844	−	0.929492i	$-0.620246\pi$
$71$	−6.21586	−0.737687	−0.368844	+	0.929492i	$0.620246\pi$
$72$	−0.0808489	−0.00952814
$73$	12.1039	1.41665	0.708325	−	0.705886i	$-0.249451\pi$
$73$	12.1039	1.41665	0.708325	+	0.705886i	$0.249451\pi$
$74$	9.33639	1.08533
$75$	8.77398	1.01313
$76$	−1.00000	−0.114708
$77$	−7.61801	−0.868153
$78$	3.44002	0.389505
$79$	4.84035	0.544582	0.272291	−	0.962215i	$-0.412219\pi$
$79$	4.84035	0.544582	0.272291	+	0.962215i	$0.412219\pi$
$80$	−0.0353436	−0.00395154
$81$	−9.23601	−1.02622
$82$	−0.956648	−0.105644
$83$	−11.8245	−1.29791	−0.648955	−	0.760827i	$-0.724794\pi$
$83$	−11.8245	−1.29791	−0.648955	+	0.760827i	$0.724794\pi$
$84$	8.32457	0.908285
$85$	−0.0953335	−0.0103404
$86$	−1.61181	−0.173806
$87$	15.1850	1.62800
$88$	−1.60626	−0.171228
$89$	−16.1354	−1.71035	−0.855174	−	0.518342i	$-0.826549\pi$
$89$	−16.1354	−1.71035	−0.855174	+	0.518342i	$0.826549\pi$
$90$	0.00285750	0.000301207 0
$91$	−9.29505	−0.974386
$92$	0.989478	0.103160
$93$	−7.46625	−0.774214
$94$	−1.67388	−0.172648
$95$	0.0353436	0.00362618
$96$	1.75523	0.179143
$97$	6.45988	0.655901	0.327950	−	0.944695i	$-0.393642\pi$
$97$	6.45988	0.655901	0.327950	+	0.944695i	$0.393642\pi$
$98$	−15.4933	−1.56506
$99$	0.129864	0.0130518
$100$	−4.99875	−0.499875
$101$	−14.5869	−1.45145	−0.725727	−	0.687983i	$-0.758497\pi$
$101$	−14.5869	−1.45145	−0.725727	+	0.687983i	$0.758497\pi$
$102$	4.73445	0.468780
$103$	6.35026	0.625709	0.312855	−	0.949801i	$-0.398715\pi$
$103$	6.35026	0.625709	0.312855	+	0.949801i	$0.398715\pi$
$104$	−1.95986	−0.192180
$105$	−0.294221	−0.0287130
$106$	−11.3038	−1.09792
$107$	−12.2430	−1.18358	−0.591788	−	0.806094i	$-0.701578\pi$
$107$	−12.2430	−1.18358	−0.591788	+	0.806094i	$0.701578\pi$
$108$	5.12380	0.493037
$109$	−15.6716	−1.50107	−0.750534	−	0.660832i	$-0.770203\pi$
$109$	−15.6716	−1.50107	−0.750534	+	0.660832i	$0.770203\pi$
$110$	0.0567710	0.00541290
$111$	16.3876	1.55544
$112$	−4.74271	−0.448144
$113$	8.91991	0.839115	0.419557	−	0.907729i	$-0.362185\pi$
$113$	8.91991	0.839115	0.419557	+	0.907729i	$0.362185\pi$
$114$	−1.75523	−0.164393
$115$	−0.0349717	−0.00326113
$116$	−8.65124	−0.803248
$117$	0.158453	0.0146490
$118$	−5.80290	−0.534200
$119$	−12.7927	−1.17270
$120$	−0.0620364	−0.00566312
$121$	−8.41994	−0.765449
$122$	14.0420	1.27130
$123$	−1.67914	−0.151403
$124$	4.25370	0.381994
$125$	0.353392	0.0316084
$126$	0.383443	0.0341598
$127$	−9.40716	−0.834750	−0.417375	−	0.908734i	$-0.637050\pi$
$127$	−9.40716	−0.834750	−0.417375	+	0.908734i	$0.637050\pi$
$128$	−1.00000	−0.0883883
$129$	−2.82910	−0.249088
$130$	0.0692686	0.00607526
$131$	17.8612	1.56054	0.780271	−	0.625442i	$-0.215081\pi$
$131$	17.8612	1.56054	0.780271	+	0.625442i	$0.215081\pi$
$132$	−2.81936	−0.245394
$133$	4.74271	0.411245
$134$	14.4566	1.24886
$135$	−0.181094	−0.0155861
$136$	−2.69733	−0.231294
$137$	−9.64693	−0.824193	−0.412096	−	0.911140i	$-0.635203\pi$
$137$	−9.64693	−0.824193	−0.412096	+	0.911140i	$0.635203\pi$
$138$	1.73677	0.147843
$139$	3.81609	0.323677	0.161838	−	0.986817i	$-0.448258\pi$
$139$	3.81609	0.323677	0.161838	+	0.986817i	$0.448258\pi$
$140$	0.167625	0.0141669
$141$	−2.93805	−0.247429
$142$	6.21586	0.521623
$143$	3.14804	0.263252
$144$	0.0808489	0.00673741
$145$	0.305767	0.0253925
$146$	−12.1039	−1.00172
$147$	−27.1944	−2.24295
$148$	−9.33639	−0.767447
$149$	4.44640	0.364263	0.182132	−	0.983274i	$-0.441700\pi$
$149$	4.44640	0.364263	0.182132	+	0.983274i	$0.441700\pi$
$150$	−8.77398	−0.716393
$151$	−19.2374	−1.56551	−0.782757	−	0.622328i	$-0.786187\pi$
$151$	−19.2374	−1.56551	−0.782757	+	0.622328i	$0.786187\pi$
$152$	1.00000	0.0811107
$153$	0.218076	0.0176304
$154$	7.61801	0.613877
$155$	−0.150341	−0.0120757
$156$	−3.44002	−0.275422
$157$	−7.27756	−0.580813	−0.290406	−	0.956903i	$-0.593790\pi$
$157$	−7.27756	−0.580813	−0.290406	+	0.956903i	$0.593790\pi$
$158$	−4.84035	−0.385078
$159$	−19.8408	−1.57348
$160$	0.0353436	0.00279416
$161$	−4.69281	−0.369845
$162$	9.23601	0.725650
$163$	−18.0122	−1.41082	−0.705411	−	0.708798i	$-0.749238\pi$
$163$	−18.0122	−1.41082	−0.705411	+	0.708798i	$0.749238\pi$
$164$	0.956648	0.0747016
$165$	0.0996464	0.00775746
$166$	11.8245	0.917761
$167$	25.1217	1.94398	0.971988	−	0.235032i	$-0.0755195\pi$
$167$	25.1217	1.94398	0.971988	+	0.235032i	$0.0755195\pi$
$168$	−8.32457	−0.642254
$169$	−9.15895	−0.704534
$170$	0.0953335	0.00731175
$171$	−0.0808489	−0.00618267
$172$	1.61181	0.122899
$173$	20.3241	1.54522	0.772608	−	0.634884i	$-0.218952\pi$
$173$	20.3241	1.54522	0.772608	+	0.634884i	$0.218952\pi$
$174$	−15.1850	−1.15117
$175$	23.7076	1.79213
$176$	1.60626	0.121076
$177$	−10.1855	−0.765586
$178$	16.1354	1.20940
$179$	14.1983	1.06123	0.530615	−	0.847613i	$-0.321961\pi$
$179$	14.1983	1.06123	0.530615	+	0.847613i	$0.321961\pi$
$180$	−0.00285750	−0.000212985 0
$181$	6.10491	0.453774	0.226887	−	0.973921i	$-0.427145\pi$
$181$	6.10491	0.453774	0.226887	+	0.973921i	$0.427145\pi$
$182$	9.29505	0.688995
$183$	24.6470	1.82196
$184$	−0.989478	−0.0729453
$185$	0.329982	0.0242608
$186$	7.46625	0.547452
$187$	4.33261	0.316832
$188$	1.67388	0.122080
$189$	−24.3007	−1.76761
$190$	−0.0353436	−0.00256410
$191$	6.47015	0.468164	0.234082	−	0.972217i	$-0.424792\pi$
$191$	6.47015	0.468164	0.234082	+	0.972217i	$0.424792\pi$
$192$	−1.75523	−0.126673
$193$	−4.48753	−0.323019	−0.161510	−	0.986871i	$-0.551636\pi$
$193$	−4.48753	−0.323019	−0.161510	+	0.986871i	$0.551636\pi$
$194$	−6.45988	−0.463792
$195$	0.121583	0.00870672
$196$	15.4933	1.10666
$197$	22.9748	1.63689	0.818444	−	0.574587i	$-0.194837\pi$
$197$	22.9748	1.63689	0.818444	+	0.574587i	$0.194837\pi$
$198$	−0.129864	−0.00922904
$199$	−15.6258	−1.10768	−0.553840	−	0.832623i	$-0.686838\pi$
$199$	−15.6258	−1.10768	−0.553840	+	0.832623i	$0.686838\pi$
$200$	4.99875	0.353465
$201$	25.3747	1.78979
$202$	14.5869	1.02633
$203$	41.0303	2.87977
$204$	−4.73445	−0.331478
$205$	−0.0338114	−0.00236149
$206$	−6.35026	−0.442443
$207$	0.0799982	0.00556026
$208$	1.95986	0.135892
$209$	−1.60626	−0.111107
$210$	0.294221	0.0203032
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	11.3038	0.776346
$213$	10.9103	0.747561
$214$	12.2430	0.836914
$215$	−0.0569672	−0.00388513
$216$	−5.12380	−0.348630
$217$	−20.1741	−1.36951
$218$	15.6716	1.06141
$219$	−21.2451	−1.43561
$220$	−0.0567710	−0.00382750
$221$	5.28639	0.355601
$222$	−16.3876	−1.09986
$223$	10.1351	0.678698	0.339349	−	0.940661i	$-0.389793\pi$
$223$	10.1351	0.678698	0.339349	+	0.940661i	$0.389793\pi$
$224$	4.74271	0.316886
$225$	−0.404144	−0.0269429
$226$	−8.91991	−0.593344
$227$	−21.7369	−1.44273	−0.721364	−	0.692556i	$-0.756485\pi$
$227$	−21.7369	−1.44273	−0.721364	+	0.692556i	$0.756485\pi$
$228$	1.75523	0.116243
$229$	18.7100	1.23639	0.618195	−	0.786025i	$-0.287864\pi$
$229$	18.7100	1.23639	0.618195	+	0.786025i	$0.287864\pi$
$230$	0.0349717	0.00230597
$231$	13.3714	0.879773
$232$	8.65124	0.567982
$233$	−9.52044	−0.623705	−0.311853	−	0.950131i	$-0.600949\pi$
$233$	−9.52044	−0.623705	−0.311853	+	0.950131i	$0.600949\pi$
$234$	−0.158453	−0.0103584
$235$	−0.0591610	−0.00385924
$236$	5.80290	0.377737
$237$	−8.49596	−0.551872
$238$	12.7927	0.829225
$239$	22.4588	1.45274	0.726369	−	0.687305i	$-0.241206\pi$
$239$	22.4588	1.45274	0.726369	+	0.687305i	$0.241206\pi$
$240$	0.0620364	0.00400443
$241$	−8.10342	−0.521987	−0.260994	−	0.965341i	$-0.584050\pi$
$241$	−8.10342	−0.521987	−0.260994	+	0.965341i	$0.584050\pi$
$242$	8.41994	0.541254
$243$	0.839980	0.0538847
$244$	−14.0420	−0.898947
$245$	−0.547590	−0.0349842
$246$	1.67914	0.107058
$247$	−1.95986	−0.124703
$248$	−4.25370	−0.270110
$249$	20.7548	1.31528
$250$	−0.353392	−0.0223505
$251$	−4.42898	−0.279555	−0.139777	−	0.990183i	$-0.544639\pi$
$251$	−4.42898	−0.279555	−0.139777	+	0.990183i	$0.544639\pi$
$252$	−0.383443	−0.0241546
$253$	1.58936	0.0999219
$254$	9.40716	0.590258
$255$	0.167333	0.0104788
$256$	1.00000	0.0625000
$257$	10.7714	0.671899	0.335949	−	0.941880i	$-0.390943\pi$
$257$	10.7714	0.671899	0.335949	+	0.941880i	$0.390943\pi$
$258$	2.82910	0.176132
$259$	44.2798	2.75141
$260$	−0.0692686	−0.00429586
$261$	−0.699444	−0.0432945
$262$	−17.8612	−1.10347
$263$	−2.64832	−0.163302	−0.0816512	−	0.996661i	$-0.526019\pi$
$263$	−2.64832	−0.163302	−0.0816512	+	0.996661i	$0.526019\pi$
$264$	2.81936	0.173519
$265$	−0.399517	−0.0245421
$266$	−4.74271	−0.290794
$267$	28.3214	1.73324
$268$	−14.4566	−0.883076
$269$	−29.4392	−1.79494	−0.897471	−	0.441073i	$-0.854598\pi$
$269$	−29.4392	−1.79494	−0.897471	+	0.441073i	$0.854598\pi$
$270$	0.181094	0.0110210
$271$	1.07762	0.0654608	0.0327304	−	0.999464i	$-0.489580\pi$
$271$	1.07762	0.0654608	0.0327304	+	0.999464i	$0.489580\pi$
$272$	2.69733	0.163550
$273$	16.3150	0.987428
$274$	9.64693	0.582792
$275$	−8.02928	−0.484184
$276$	−1.73677	−0.104541
$277$	−13.6762	−0.821722	−0.410861	−	0.911698i	$-0.634772\pi$
$277$	−13.6762	−0.821722	−0.410861	+	0.911698i	$0.634772\pi$
$278$	−3.81609	−0.228874
$279$	0.343908	0.0205892
$280$	−0.167625	−0.0100175
$281$	−25.0851	−1.49645	−0.748225	−	0.663445i	$-0.769094\pi$
$281$	−25.0851	−1.49645	−0.748225	+	0.663445i	$0.769094\pi$
$282$	2.93805	0.174959
$283$	−1.73871	−0.103356	−0.0516779	−	0.998664i	$-0.516457\pi$
$283$	−1.73871	−0.103356	−0.0516779	+	0.998664i	$0.516457\pi$
$284$	−6.21586	−0.368844
$285$	−0.0620364	−0.00367472
$286$	−3.14804	−0.186147
$287$	−4.53710	−0.267817
$288$	−0.0808489	−0.00476407
$289$	−9.72440	−0.572024
$290$	−0.305767	−0.0179552
$291$	−11.3386	−0.664680
$292$	12.1039	0.708325
$293$	−12.7388	−0.744209	−0.372104	−	0.928191i	$-0.621364\pi$
$293$	−12.7388	−0.744209	−0.372104	+	0.928191i	$0.621364\pi$
$294$	27.1944	1.58601
$295$	−0.205096	−0.0119411
$296$	9.33639	0.542667
$297$	8.23013	0.477561
$298$	−4.44640	−0.257573
$299$	1.93924	0.112149
$300$	8.77398	0.506566
$301$	−7.64434	−0.440612
$302$	19.2374	1.10699
$303$	25.6035	1.47088
$304$	−1.00000	−0.0573539
$305$	0.496296	0.0284178
$306$	−0.218076	−0.0124666
$307$	31.3140	1.78719	0.893593	−	0.448878i	$-0.148176\pi$
$307$	31.3140	1.78719	0.893593	+	0.448878i	$0.148176\pi$
$308$	−7.61801	−0.434076
$309$	−11.1462	−0.634085
$310$	0.150341	0.00853882
$311$	3.35197	0.190073	0.0950365	−	0.995474i	$-0.469703\pi$
$311$	3.35197	0.190073	0.0950365	+	0.995474i	$0.469703\pi$
$312$	3.44002	0.194753
$313$	16.2497	0.918489	0.459244	−	0.888310i	$-0.348120\pi$
$313$	16.2497	0.918489	0.459244	+	0.888310i	$0.348120\pi$
$314$	7.27756	0.410697
$315$	0.0135523	0.000763584 0
$316$	4.84035	0.272291
$317$	6.37489	0.358049	0.179025	−	0.983845i	$-0.442706\pi$
$317$	6.37489	0.358049	0.179025	+	0.983845i	$0.442706\pi$
$318$	19.8408	1.11262
$319$	−13.8961	−0.778033
$320$	−0.0353436	−0.00197577
$321$	21.4893	1.19942
$322$	4.69281	0.261520
$323$	−2.69733	−0.150084
$324$	−9.23601	−0.513112
$325$	−9.79685	−0.543432
$326$	18.0122	0.997602
$327$	27.5073	1.52116
$328$	−0.956648	−0.0528220
$329$	−7.93873	−0.437676
$330$	−0.0996464	−0.00548535
$331$	−7.12440	−0.391592	−0.195796	−	0.980645i	$-0.562729\pi$
$331$	−7.12440	−0.391592	−0.195796	+	0.980645i	$0.562729\pi$
$332$	−11.8245	−0.648955
$333$	−0.754838	−0.0413648
$334$	−25.1217	−1.37460
$335$	0.510948	0.0279161
$336$	8.32457	0.454142
$337$	5.44672	0.296702	0.148351	−	0.988935i	$-0.452604\pi$
$337$	5.44672	0.296702	0.148351	+	0.988935i	$0.452604\pi$
$338$	9.15895	0.498181
$339$	−15.6565	−0.850347
$340$	−0.0953335	−0.00517019
$341$	6.83254	0.370003
$342$	0.0808489	0.00437181
$343$	−40.2812	−2.17498
$344$	−1.61181	−0.0869028
$345$	0.0613836	0.00330478
$346$	−20.3241	−1.09263
$347$	−14.4740	−0.777005	−0.388503	−	0.921448i	$-0.627008\pi$
$347$	−14.4740	−0.777005	−0.388503	+	0.921448i	$0.627008\pi$
$348$	15.1850	0.814000
$349$	10.1385	0.542702	0.271351	−	0.962480i	$-0.412530\pi$
$349$	10.1385	0.542702	0.271351	+	0.962480i	$0.412530\pi$
$350$	−23.7076	−1.26723
$351$	10.0419	0.535998
$352$	−1.60626	−0.0856138
$353$	−26.9975	−1.43693	−0.718465	−	0.695563i	$-0.755155\pi$
$353$	−26.9975	−1.43693	−0.718465	+	0.695563i	$0.755155\pi$
$354$	10.1855	0.541351
$355$	0.219691	0.0116600
$356$	−16.1354	−0.855174
$357$	22.4541	1.18840
$358$	−14.1983	−0.750403
$359$	7.05583	0.372392	0.186196	−	0.982513i	$-0.440384\pi$
$359$	7.05583	0.372392	0.186196	+	0.982513i	$0.440384\pi$
$360$	0.00285750	0.000150603 0
$361$	1.00000	0.0526316
$362$	−6.10491	−0.320867
$363$	14.7790	0.775695
$364$	−9.29505	−0.487193
$365$	−0.427795	−0.0223918
$366$	−24.6470	−1.28832
$367$	24.4308	1.27528	0.637638	−	0.770336i	$-0.279912\pi$
$367$	24.4308	1.27528	0.637638	+	0.770336i	$0.279912\pi$
$368$	0.989478	0.0515801
$369$	0.0773440	0.00402637
$370$	−0.329982	−0.0171550
$371$	−53.6105	−2.78332
$372$	−7.46625	−0.387107
$373$	8.69279	0.450096	0.225048	−	0.974348i	$-0.427746\pi$
$373$	8.69279	0.450096	0.225048	+	0.974348i	$0.427746\pi$
$374$	−4.33261	−0.224034
$375$	−0.620286	−0.0320315
$376$	−1.67388	−0.0863238
$377$	−16.9552	−0.873239
$378$	24.3007	1.24989
$379$	−14.0018	−0.719223	−0.359611	−	0.933102i	$-0.617091\pi$
$379$	−14.0018	−0.719223	−0.359611	+	0.933102i	$0.617091\pi$
$380$	0.0353436	0.00181309
$381$	16.5118	0.845924
$382$	−6.47015	−0.331042
$383$	20.5323	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$383$	20.5323	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$384$	1.75523	0.0895714
$385$	0.269248	0.0137222
$386$	4.48753	0.228409
$387$	0.130313	0.00662418
$388$	6.45988	0.327950
$389$	16.2401	0.823404	0.411702	−	0.911318i	$-0.364934\pi$
$389$	16.2401	0.823404	0.411702	+	0.911318i	$0.364934\pi$
$390$	−0.121583	−0.00615658
$391$	2.66895	0.134975
$392$	−15.4933	−0.782530
$393$	−31.3506	−1.58143
$394$	−22.9748	−1.15745
$395$	−0.171076	−0.00860775
$396$	0.129864	0.00652592
$397$	25.8970	1.29973	0.649867	−	0.760048i	$-0.274825\pi$
$397$	25.8970	1.29973	0.649867	+	0.760048i	$0.274825\pi$
$398$	15.6258	0.783249
$399$	−8.32457	−0.416750
$400$	−4.99875	−0.249938
$401$	−31.9004	−1.59303	−0.796515	−	0.604618i	$-0.793326\pi$
$401$	−31.9004	−1.59303	−0.796515	+	0.604618i	$0.793326\pi$
$402$	−25.3747	−1.26557
$403$	8.33667	0.415279
$404$	−14.5869	−0.725727
$405$	0.326434	0.0162207
$406$	−41.0303	−2.03630
$407$	−14.9966	−0.743356
$408$	4.73445	0.234390
$409$	9.40624	0.465109	0.232554	−	0.972583i	$-0.425292\pi$
$409$	9.40624	0.465109	0.232554	+	0.972583i	$0.425292\pi$
$410$	0.0338114	0.00166983
$411$	16.9326	0.835225
$412$	6.35026	0.312855
$413$	−27.5215	−1.35424
$414$	−0.0799982	−0.00393170
$415$	0.417922	0.0205150
$416$	−1.95986	−0.0960901
$417$	−6.69813	−0.328009
$418$	1.60626	0.0785646
$419$	−0.941641	−0.0460022	−0.0230011	−	0.999735i	$-0.507322\pi$
$419$	−0.941641	−0.0460022	−0.0230011	+	0.999735i	$0.507322\pi$
$420$	−0.294221	−0.0143565
$421$	−17.8188	−0.868437	−0.434218	−	0.900808i	$-0.642975\pi$
$421$	−17.8188	−0.868437	−0.434218	+	0.900808i	$0.642975\pi$
$422$	−1.00000	−0.0486792
$423$	0.135331	0.00658004
$424$	−11.3038	−0.548960
$425$	−13.4833	−0.654036
$426$	−10.9103	−0.528606
$427$	66.5971	3.22286
$428$	−12.2430	−0.591788
$429$	−5.52555	−0.266776
$430$	0.0569672	0.00274720
$431$	4.38323	0.211133	0.105566	−	0.994412i	$-0.466334\pi$
$431$	4.38323	0.211133	0.105566	+	0.994412i	$0.466334\pi$
$432$	5.12380	0.246519
$433$	29.7362	1.42903	0.714516	−	0.699619i	$-0.246647\pi$
$433$	29.7362	1.42903	0.714516	+	0.699619i	$0.246647\pi$
$434$	20.1741	0.968387
$435$	−0.536692	−0.0257324
$436$	−15.6716	−0.750534
$437$	−0.989478	−0.0473331
$438$	21.2451	1.01513
$439$	34.7177	1.65699	0.828493	−	0.560000i	$-0.189199\pi$
$439$	34.7177	1.65699	0.828493	+	0.560000i	$0.189199\pi$
$440$	0.0567710	0.00270645
$441$	1.25262	0.0596484
$442$	−5.28639	−0.251448
$443$	33.1367	1.57437	0.787185	−	0.616716i	$-0.211537\pi$
$443$	33.1367	1.57437	0.787185	+	0.616716i	$0.211537\pi$
$444$	16.3876	0.777719
$445$	0.570283	0.0270340
$446$	−10.1351	−0.479912
$447$	−7.80447	−0.369139
$448$	−4.74271	−0.224072
$449$	18.2492	0.861235	0.430618	−	0.902534i	$-0.358296\pi$
$449$	18.2492	0.861235	0.430618	+	0.902534i	$0.358296\pi$
$450$	0.404144	0.0190515
$451$	1.53662	0.0723567
$452$	8.91991	0.419557
$453$	33.7661	1.58647
$454$	21.7369	1.02016
$455$	0.328521	0.0154013
$456$	−1.75523	−0.0821964
$457$	−17.7575	−0.830659	−0.415329	−	0.909671i	$-0.636334\pi$
$457$	−17.7575	−0.830659	−0.415329	+	0.909671i	$0.636334\pi$
$458$	−18.7100	−0.874260
$459$	13.8206	0.645089
$460$	−0.0349717	−0.00163057
$461$	4.52158	0.210591	0.105296	−	0.994441i	$-0.466421\pi$
$461$	4.52158	0.210591	0.105296	+	0.994441i	$0.466421\pi$
$462$	−13.3714	−0.622094
$463$	24.9916	1.16146	0.580730	−	0.814096i	$-0.302767\pi$
$463$	24.9916	1.16146	0.580730	+	0.814096i	$0.302767\pi$
$464$	−8.65124	−0.401624
$465$	0.263884	0.0122373
$466$	9.52044	0.441026
$467$	−5.67070	−0.262409	−0.131204	−	0.991355i	$-0.541884\pi$
$467$	−5.67070	−0.262409	−0.131204	+	0.991355i	$0.541884\pi$
$468$	0.158453	0.00732448
$469$	68.5633	3.16596
$470$	0.0591610	0.00272890
$471$	12.7738	0.588587
$472$	−5.80290	−0.267100
$473$	2.58898	0.119041
$474$	8.49596	0.390232
$475$	4.99875	0.229358
$476$	−12.7927	−0.586351
$477$	0.913898	0.0418445
$478$	−22.4588	−1.02724
$479$	27.6887	1.26513	0.632564	−	0.774508i	$-0.282002\pi$
$479$	27.6887	1.26513	0.632564	+	0.774508i	$0.282002\pi$
$480$	−0.0620364	−0.00283156
$481$	−18.2980	−0.834318
$482$	8.10342	0.369101
$483$	8.23697	0.374795
$484$	−8.41994	−0.382725
$485$	−0.228316	−0.0103673
$486$	−0.839980	−0.0381023
$487$	28.2608	1.28062	0.640310	−	0.768117i	$-0.278806\pi$
$487$	28.2608	1.28062	0.640310	+	0.768117i	$0.278806\pi$
$488$	14.0420	0.635651
$489$	31.6156	1.42971
$490$	0.547590	0.0247376
$491$	−10.1257	−0.456967	−0.228483	−	0.973548i	$-0.573377\pi$
$491$	−10.1257	−0.456967	−0.228483	+	0.973548i	$0.573377\pi$
$492$	−1.67914	−0.0757015
$493$	−23.3353	−1.05097
$494$	1.95986	0.0881783
$495$	−0.00458987	−0.000206299 0
$496$	4.25370	0.190997
$497$	29.4800	1.32236
$498$	−20.7548	−0.930045
$499$	31.2429	1.39863	0.699313	−	0.714815i	$-0.253489\pi$
$499$	31.2429	1.39863	0.699313	+	0.714815i	$0.253489\pi$
$500$	0.353392	0.0158042
$501$	−44.0945	−1.97000
$502$	4.42898	0.197675
$503$	39.4212	1.75770	0.878851	−	0.477096i	$-0.158310\pi$
$503$	39.4212	1.75770	0.878851	+	0.477096i	$0.158310\pi$
$504$	0.383443	0.0170799
$505$	0.515556	0.0229419
$506$	−1.58936	−0.0706554
$507$	16.0761	0.713965
$508$	−9.40716	−0.417375
$509$	−2.75065	−0.121920	−0.0609601	−	0.998140i	$-0.519416\pi$
$509$	−2.75065	−0.121920	−0.0609601	+	0.998140i	$0.519416\pi$
$510$	−0.167333	−0.00740962
$511$	−57.4051	−2.53945
$512$	−1.00000	−0.0441942
$513$	−5.12380	−0.226221
$514$	−10.7714	−0.475104
$515$	−0.224441	−0.00989006
$516$	−2.82910	−0.124544
$517$	2.68868	0.118248
$518$	−44.2798	−1.94554
$519$	−35.6736	−1.56590
$520$	0.0692686	0.00303763
$521$	−35.9437	−1.57472	−0.787360	−	0.616493i	$-0.788553\pi$
$521$	−35.9437	−1.57472	−0.787360	+	0.616493i	$0.788553\pi$
$522$	0.699444	0.0306138
$523$	19.4787	0.851743	0.425871	−	0.904784i	$-0.359968\pi$
$523$	19.4787	0.851743	0.425871	+	0.904784i	$0.359968\pi$
$524$	17.8612	0.780271
$525$	−41.6124	−1.81612
$526$	2.64832	0.115472
$527$	11.4737	0.499800
$528$	−2.81936	−0.122697
$529$	−22.0209	−0.957432
$530$	0.399517	0.0173539
$531$	0.469159	0.0203597
$532$	4.74271	0.205623
$533$	1.87490	0.0812108
$534$	−28.3214	−1.22559
$535$	0.432712	0.0187078
$536$	14.4566	0.624429
$537$	−24.9213	−1.07544
$538$	29.4392	1.26922
$539$	24.8862	1.07192
$540$	−0.181094	−0.00779303
$541$	1.81453	0.0780129	0.0390065	−	0.999239i	$-0.487581\pi$
$541$	1.81453	0.0780129	0.0390065	+	0.999239i	$0.487581\pi$
$542$	−1.07762	−0.0462878
$543$	−10.7155	−0.459848
$544$	−2.69733	−0.115647
$545$	0.553892	0.0237261
$546$	−16.3150	−0.698217
$547$	33.9115	1.44995	0.724976	−	0.688774i	$-0.241851\pi$
$547$	33.9115	1.44995	0.724976	+	0.688774i	$0.241851\pi$
$548$	−9.64693	−0.412096
$549$	−1.13528	−0.0484526
$550$	8.02928	0.342370
$551$	8.65124	0.368555
$552$	1.73677	0.0739216
$553$	−22.9564	−0.976205
$554$	13.6762	0.581045
$555$	−0.579196	−0.0245855
$556$	3.81609	0.161838
$557$	−5.80424	−0.245933	−0.122967	−	0.992411i	$-0.539241\pi$
$557$	−5.80424	−0.245933	−0.122967	+	0.992411i	$0.539241\pi$
$558$	−0.343908	−0.0145588
$559$	3.15892	0.133608
$560$	0.167625	0.00708343
$561$	−7.60474	−0.321072
$562$	25.0851	1.05815
$563$	−7.49241	−0.315768	−0.157884	−	0.987458i	$-0.550467\pi$
$563$	−7.49241	−0.315768	−0.157884	+	0.987458i	$0.550467\pi$
$564$	−2.93805	−0.123714
$565$	−0.315262	−0.0132632
$566$	1.73871	0.0730836
$567$	43.8037	1.83958
$568$	6.21586	0.260812
$569$	9.91758	0.415767	0.207883	−	0.978154i	$-0.433343\pi$
$569$	9.91758	0.415767	0.207883	+	0.978154i	$0.433343\pi$
$570$	0.0620364	0.00259842
$571$	−7.39100	−0.309304	−0.154652	−	0.987969i	$-0.549426\pi$
$571$	−7.39100	−0.309304	−0.154652	+	0.987969i	$0.549426\pi$
$572$	3.14804	0.131626
$573$	−11.3566	−0.474430
$574$	4.53710	0.189375
$575$	−4.94615	−0.206269
$576$	0.0808489	0.00336871
$577$	34.0343	1.41686	0.708432	−	0.705779i	$-0.249403\pi$
$577$	34.0343	1.41686	0.708432	+	0.705779i	$0.249403\pi$
$578$	9.72440	0.404482
$579$	7.87667	0.327343
$580$	0.305767	0.0126963
$581$	56.0803	2.32660
$582$	11.3386	0.470000
$583$	18.1568	0.751976
$584$	−12.1039	−0.500862
$585$	−0.00560029	−0.000231544 0
$586$	12.7388	0.526235
$587$	−4.13642	−0.170728	−0.0853641	−	0.996350i	$-0.527205\pi$
$587$	−4.13642	−0.170728	−0.0853641	+	0.996350i	$0.527205\pi$
$588$	−27.1944	−1.12148
$589$	−4.25370	−0.175271
$590$	0.205096	0.00844366
$591$	−40.3262	−1.65880
$592$	−9.33639	−0.383723
$593$	−37.5323	−1.54127	−0.770634	−	0.637278i	$-0.780060\pi$
$593$	−37.5323	−1.54127	−0.770634	+	0.637278i	$0.780060\pi$
$594$	−8.23013	−0.337686
$595$	0.452139	0.0185359
$596$	4.44640	0.182132
$597$	27.4269	1.12251
$598$	−1.93924	−0.0793013
$599$	24.4053	0.997175	0.498587	−	0.866840i	$-0.333852\pi$
$599$	24.4053	0.997175	0.498587	+	0.866840i	$0.333852\pi$
$600$	−8.77398	−0.358196
$601$	−19.1187	−0.779867	−0.389934	−	0.920843i	$-0.627502\pi$
$601$	−19.1187	−0.779867	−0.389934	+	0.920843i	$0.627502\pi$
$602$	7.64434	0.311560
$603$	−1.16880	−0.0475972
$604$	−19.2374	−0.782757
$605$	0.297591	0.0120988
$606$	−25.6035	−1.04007
$607$	4.05886	0.164744	0.0823721	−	0.996602i	$-0.473750\pi$
$607$	4.05886	0.164744	0.0823721	+	0.996602i	$0.473750\pi$
$608$	1.00000	0.0405554
$609$	−72.0179	−2.91831
$610$	−0.496296	−0.0200944
$611$	3.28057	0.132718
$612$	0.218076	0.00881522
$613$	−22.1069	−0.892890	−0.446445	−	0.894811i	$-0.647310\pi$
$613$	−22.1069	−0.892890	−0.446445	+	0.894811i	$0.647310\pi$
$614$	−31.3140	−1.26373
$615$	0.0593470	0.00239310
$616$	7.61801	0.306938
$617$	−10.5835	−0.426074	−0.213037	−	0.977044i	$-0.568336\pi$
$617$	−10.5835	−0.426074	−0.213037	+	0.977044i	$0.568336\pi$
$618$	11.1462	0.448366
$619$	7.10198	0.285453	0.142726	−	0.989762i	$-0.454413\pi$
$619$	7.10198	0.285453	0.142726	+	0.989762i	$0.454413\pi$
$620$	−0.150341	−0.00603786
$621$	5.06988	0.203447
$622$	−3.35197	−0.134402
$623$	76.5254	3.06593
$624$	−3.44002	−0.137711
$625$	24.9813	0.999251
$626$	−16.2497	−0.649470
$627$	2.81936	0.112594
$628$	−7.27756	−0.290406
$629$	−25.1834	−1.00413
$630$	−0.0135523	−0.000539936 0
$631$	26.6112	1.05937	0.529687	−	0.848193i	$-0.322309\pi$
$631$	26.6112	1.05937	0.529687	+	0.848193i	$0.322309\pi$
$632$	−4.84035	−0.192539
$633$	−1.75523	−0.0697643
$634$	−6.37489	−0.253179
$635$	0.332483	0.0131942
$636$	−19.8408	−0.786738
$637$	30.3647	1.20309
$638$	13.8961	0.550153
$639$	−0.502546	−0.0198804
$640$	0.0353436	0.00139708
$641$	−11.6986	−0.462068	−0.231034	−	0.972946i	$-0.574211\pi$
$641$	−11.6986	−0.462068	−0.231034	+	0.972946i	$0.574211\pi$
$642$	−21.4893	−0.848117
$643$	−34.2590	−1.35104	−0.675521	−	0.737340i	$-0.736081\pi$
$643$	−34.2590	−1.35104	−0.675521	+	0.737340i	$0.736081\pi$
$644$	−4.69281	−0.184922
$645$	0.0999907	0.00393713
$646$	2.69733	0.106125
$647$	−3.67648	−0.144537	−0.0722687	−	0.997385i	$-0.523024\pi$
$647$	−3.67648	−0.144537	−0.0722687	+	0.997385i	$0.523024\pi$
$648$	9.23601	0.362825
$649$	9.32095	0.365879
$650$	9.79685	0.384264
$651$	35.4103	1.38784
$652$	−18.0122	−0.705411
$653$	−5.52115	−0.216059	−0.108030	−	0.994148i	$-0.534454\pi$
$653$	−5.52115	−0.216059	−0.108030	+	0.994148i	$0.534454\pi$
$654$	−27.5073	−1.07562
$655$	−0.631280	−0.0246662
$656$	0.956648	0.0373508
$657$	0.978585	0.0381782
$658$	7.93873	0.309484
$659$	25.9286	1.01003	0.505017	−	0.863109i	$-0.331486\pi$
$659$	25.9286	1.01003	0.505017	+	0.863109i	$0.331486\pi$
$660$	0.0996464	0.00387873
$661$	46.1491	1.79499	0.897495	−	0.441024i	$-0.145385\pi$
$661$	46.1491	1.79499	0.897495	+	0.441024i	$0.145385\pi$
$662$	7.12440	0.276897
$663$	−9.27886	−0.360361
$664$	11.8245	0.458880
$665$	−0.167625	−0.00650021
$666$	0.754838	0.0292494
$667$	−8.56021	−0.331453
$668$	25.1217	0.971988
$669$	−17.7895	−0.687782
$670$	−0.510948	−0.0197396
$671$	−22.5551	−0.870728
$672$	−8.32457	−0.321127
$673$	19.4766	0.750768	0.375384	−	0.926869i	$-0.377511\pi$
$673$	19.4766	0.750768	0.375384	+	0.926869i	$0.377511\pi$
$674$	−5.44672	−0.209800
$675$	−25.6126	−0.985829
$676$	−9.15895	−0.352267
$677$	−40.6676	−1.56298	−0.781491	−	0.623916i	$-0.785541\pi$
$677$	−40.6676	−1.56298	−0.781491	+	0.623916i	$0.785541\pi$
$678$	15.6565	0.601286
$679$	−30.6373	−1.17575
$680$	0.0953335	0.00365587
$681$	38.1533	1.46204
$682$	−6.83254	−0.261632
$683$	27.5798	1.05531	0.527656	−	0.849458i	$-0.323071\pi$
$683$	27.5798	1.05531	0.527656	+	0.849458i	$0.323071\pi$
$684$	−0.0808489	−0.00309134
$685$	0.340958	0.0130273
$686$	40.2812	1.53794
$687$	−32.8404	−1.25294
$688$	1.61181	0.0614496
$689$	22.1538	0.843993
$690$	−0.0613836	−0.00233683
$691$	−28.0220	−1.06601	−0.533003	−	0.846113i	$-0.678936\pi$
$691$	−28.0220	−1.06601	−0.533003	+	0.846113i	$0.678936\pi$
$692$	20.3241	0.772608
$693$	−0.615908	−0.0233964
$694$	14.4740	0.549426
$695$	−0.134875	−0.00511608
$696$	−15.1850	−0.575585
$697$	2.58040	0.0977395
$698$	−10.1385	−0.383748
$699$	16.7106	0.632053
$700$	23.7076	0.896064
$701$	8.64123	0.326375	0.163187	−	0.986595i	$-0.447822\pi$
$701$	8.64123	0.326375	0.163187	+	0.986595i	$0.447822\pi$
$702$	−10.0419	−0.379008
$703$	9.33639	0.352129
$704$	1.60626	0.0605381
$705$	0.103842	0.00391090
$706$	26.9975	1.01606
$707$	69.1816	2.60184
$708$	−10.1855	−0.382793
$709$	−36.7796	−1.38129	−0.690643	−	0.723196i	$-0.742672\pi$
$709$	−36.7796	−1.38129	−0.690643	+	0.723196i	$0.742672\pi$
$710$	−0.219691	−0.00824486
$711$	0.391337	0.0146763
$712$	16.1354	0.604699
$713$	4.20895	0.157626
$714$	−22.4541	−0.840324
$715$	−0.111263	−0.00416101
$716$	14.1983	0.530615
$717$	−39.4205	−1.47218
$718$	−7.05583	−0.263321
$719$	26.0773	0.972521	0.486260	−	0.873814i	$-0.338361\pi$
$719$	26.0773	0.972521	0.486260	+	0.873814i	$0.338361\pi$
$720$	−0.00285750	−0.000106493 0
$721$	−30.1174	−1.12163
$722$	−1.00000	−0.0372161
$723$	14.2234	0.528974
$724$	6.10491	0.226887
$725$	43.2454	1.60609
$726$	−14.7790	−0.548499
$727$	15.7655	0.584711	0.292355	−	0.956310i	$-0.405561\pi$
$727$	15.7655	0.584711	0.292355	+	0.956310i	$0.405561\pi$
$728$	9.29505	0.344497
$729$	26.2337	0.971617
$730$	0.427795	0.0158334
$731$	4.34758	0.160801
$732$	24.6470	0.910980
$733$	4.94203	0.182538	0.0912690	−	0.995826i	$-0.470908\pi$
$733$	4.94203	0.182538	0.0912690	+	0.995826i	$0.470908\pi$
$734$	−24.4308	−0.901756
$735$	0.961148	0.0354525
$736$	−0.989478	−0.0364726
$737$	−23.2210	−0.855356
$738$	−0.0773440	−0.00284707
$739$	26.7061	0.982399	0.491200	−	0.871047i	$-0.336559\pi$
$739$	26.7061	0.982399	0.491200	+	0.871047i	$0.336559\pi$
$740$	0.329982	0.0121304
$741$	3.44002	0.126372
$742$	53.6105	1.96810
$743$	−42.9624	−1.57614	−0.788068	−	0.615588i	$-0.788919\pi$
$743$	−42.9624	−1.57614	−0.788068	+	0.615588i	$0.788919\pi$
$744$	7.46625	0.273726
$745$	−0.157152	−0.00575760
$746$	−8.69279	−0.318266
$747$	−0.956000	−0.0349782
$748$	4.33261	0.158416
$749$	58.0650	2.12165
$750$	0.620286	0.0226497
$751$	−11.3166	−0.412947	−0.206474	−	0.978452i	$-0.566199\pi$
$751$	−11.3166	−0.412947	−0.206474	+	0.978452i	$0.566199\pi$
$752$	1.67388	0.0610401
$753$	7.77389	0.283296
$754$	16.9552	0.617473
$755$	0.679918	0.0247448
$756$	−24.3007	−0.883807
$757$	−2.81881	−0.102451	−0.0512257	−	0.998687i	$-0.516313\pi$
$757$	−2.81881	−0.102451	−0.0512257	+	0.998687i	$0.516313\pi$
$758$	14.0018	0.508567
$759$	−2.78969	−0.101259
$760$	−0.0353436	−0.00128205
$761$	−5.58451	−0.202438	−0.101219	−	0.994864i	$-0.532274\pi$
$761$	−5.58451	−0.202438	−0.101219	+	0.994864i	$0.532274\pi$
$762$	−16.5118	−0.598158
$763$	74.3259	2.69078
$764$	6.47015	0.234082
$765$	−0.00770762	−0.000278669 0
$766$	−20.5323	−0.741861
$767$	11.3729	0.410651
$768$	−1.75523	−0.0633366
$769$	−20.3515	−0.733895	−0.366948	−	0.930242i	$-0.619597\pi$
$769$	−20.3515	−0.733895	−0.366948	+	0.930242i	$0.619597\pi$
$770$	−0.269248	−0.00970303
$771$	−18.9063	−0.680892
$772$	−4.48753	−0.161510
$773$	21.5060	0.773516	0.386758	−	0.922181i	$-0.373595\pi$
$773$	21.5060	0.773516	0.386758	+	0.922181i	$0.373595\pi$
$774$	−0.130313	−0.00468400
$775$	−21.2632	−0.763797
$776$	−6.45988	−0.231896
$777$	−77.7215	−2.78824
$778$	−16.2401	−0.582235
$779$	−0.956648	−0.0342755
$780$	0.121583	0.00435336
$781$	−9.98427	−0.357265
$782$	−2.66895	−0.0954414
$783$	−44.3272	−1.58413
$784$	15.4933	0.553332
$785$	0.257216	0.00918042
$786$	31.3506	1.11824
$787$	26.6384	0.949555	0.474777	−	0.880106i	$-0.342529\pi$
$787$	26.6384	0.949555	0.474777	+	0.880106i	$0.342529\pi$
$788$	22.9748	0.818444
$789$	4.64842	0.165488
$790$	0.171076	0.00608660
$791$	−42.3046	−1.50418
$792$	−0.129864	−0.00461452
$793$	−27.5204	−0.977277
$794$	−25.8970	−0.919051
$795$	0.701245	0.0248706
$796$	−15.6258	−0.553840
$797$	4.61923	0.163622	0.0818108	−	0.996648i	$-0.473930\pi$
$797$	4.61923	0.163622	0.0818108	+	0.996648i	$0.473930\pi$
$798$	8.32457	0.294687
$799$	4.51501	0.159730
$800$	4.99875	0.176733
$801$	−1.30453	−0.0460933
$802$	31.9004	1.12644
$803$	19.4419	0.686090
$804$	25.3747	0.894896
$805$	0.165861	0.00584583
$806$	−8.33667	−0.293647
$807$	51.6728	1.81897
$808$	14.5869	0.513167
$809$	4.09119	0.143839	0.0719193	−	0.997410i	$-0.477088\pi$
$809$	4.09119	0.143839	0.0719193	+	0.997410i	$0.477088\pi$
$810$	−0.326434	−0.0114697
$811$	43.3456	1.52207	0.761035	−	0.648710i	$-0.224691\pi$
$811$	43.3456	1.52207	0.761035	+	0.648710i	$0.224691\pi$
$812$	41.0303	1.43988
$813$	−1.89148	−0.0663371
$814$	14.9966	0.525632
$815$	0.636616	0.0222997
$816$	−4.73445	−0.165739
$817$	−1.61181	−0.0563900
$818$	−9.40624	−0.328881
$819$	−0.751495	−0.0262594
$820$	−0.0338114	−0.00118075
$821$	−0.730224	−0.0254850	−0.0127425	−	0.999919i	$-0.504056\pi$
$821$	−0.730224	−0.0254850	−0.0127425	+	0.999919i	$0.504056\pi$
$822$	−16.9326	−0.590593
$823$	−24.0370	−0.837878	−0.418939	−	0.908014i	$-0.637598\pi$
$823$	−24.0370	−0.837878	−0.418939	+	0.908014i	$0.637598\pi$
$824$	−6.35026	−0.221222
$825$	14.0933	0.490665
$826$	27.5215	0.957595
$827$	0.949273	0.0330094	0.0165047	−	0.999864i	$-0.494746\pi$
$827$	0.949273	0.0330094	0.0165047	+	0.999864i	$0.494746\pi$
$828$	0.0799982	0.00278013
$829$	44.9463	1.56105	0.780525	−	0.625124i	$-0.214952\pi$
$829$	44.9463	1.56105	0.780525	+	0.625124i	$0.214952\pi$
$830$	−0.417922	−0.0145063
$831$	24.0049	0.832721
$832$	1.95986	0.0679459
$833$	41.7906	1.44796
$834$	6.69813	0.231937
$835$	−0.887892	−0.0307268
$836$	−1.60626	−0.0555535
$837$	21.7951	0.753349
$838$	0.941641	0.0325285
$839$	18.4965	0.638570	0.319285	−	0.947659i	$-0.396557\pi$
$839$	18.4965	0.638570	0.319285	+	0.947659i	$0.396557\pi$
$840$	0.294221	0.0101516
$841$	45.8440	1.58083
$842$	17.8188	0.614078
$843$	44.0302	1.51648
$844$	1.00000	0.0344214
$845$	0.323711	0.0111360
$846$	−0.135331	−0.00465279
$847$	39.9333	1.37213
$848$	11.3038	0.388173
$849$	3.05185	0.104739
$850$	13.4833	0.462473
$851$	−9.23815	−0.316680
$852$	10.9103	0.373781
$853$	−6.02278	−0.206216	−0.103108	−	0.994670i	$-0.532879\pi$
$853$	−6.02278	−0.206216	−0.103108	+	0.994670i	$0.532879\pi$
$854$	−66.5971	−2.27891
$855$	0.00285750	9.77243e−5 0
$856$	12.2430	0.418457
$857$	36.7900	1.25672	0.628362	−	0.777921i	$-0.283726\pi$
$857$	36.7900	1.25672	0.628362	+	0.777921i	$0.283726\pi$
$858$	5.52555	0.188639
$859$	−43.2459	−1.47553	−0.737766	−	0.675056i	$-0.764119\pi$
$859$	−43.2459	−1.47553	−0.737766	+	0.675056i	$0.764119\pi$
$860$	−0.0569672	−0.00194256
$861$	7.96368	0.271401
$862$	−4.38323	−0.149293
$863$	−17.5232	−0.596497	−0.298248	−	0.954488i	$-0.596402\pi$
$863$	−17.5232	−0.596497	−0.298248	+	0.954488i	$0.596402\pi$
$864$	−5.12380	−0.174315
$865$	−0.718329	−0.0244239
$866$	−29.7362	−1.01048
$867$	17.0686	0.579680
$868$	−20.1741	−0.684753
$869$	7.77485	0.263744
$870$	0.536692	0.0181956
$871$	−28.3329	−0.960023
$872$	15.6716	0.530707
$873$	0.522274	0.0176763
$874$	0.989478	0.0334696
$875$	−1.67604	−0.0566604
$876$	−21.2451	−0.717806
$877$	3.77727	0.127549	0.0637747	−	0.997964i	$-0.479686\pi$
$877$	3.77727	0.127549	0.0637747	+	0.997964i	$0.479686\pi$
$878$	−34.7177	−1.17167
$879$	22.3596	0.754170
$880$	−0.0567710	−0.00191375
$881$	2.33825	0.0787775	0.0393888	−	0.999224i	$-0.487459\pi$
$881$	2.33825	0.0787775	0.0393888	+	0.999224i	$0.487459\pi$
$882$	−1.25262	−0.0421778
$883$	51.9862	1.74948	0.874738	−	0.484596i	$-0.161033\pi$
$883$	51.9862	1.74948	0.874738	+	0.484596i	$0.161033\pi$
$884$	5.28639	0.177801
$885$	0.359991	0.0121010
$886$	−33.1367	−1.11325
$887$	−51.6806	−1.73526	−0.867632	−	0.497208i	$-0.834359\pi$
$887$	−51.6806	−1.73526	−0.867632	+	0.497208i	$0.834359\pi$
$888$	−16.3876	−0.549931
$889$	44.6154	1.49635
$890$	−0.570283	−0.0191159
$891$	−14.8354	−0.497005
$892$	10.1351	0.339349
$893$	−1.67388	−0.0560143
$894$	7.80447	0.261021
$895$	−0.501820	−0.0167740
$896$	4.74271	0.158443
$897$	−3.40382	−0.113650
$898$	−18.2492	−0.608985
$899$	−36.7998	−1.22734
$900$	−0.404144	−0.0134715
$901$	30.4900	1.01577
$902$	−1.53662	−0.0511639
$903$	13.4176	0.446510
$904$	−8.91991	−0.296672
$905$	−0.215770	−0.00717243
$906$	−33.7661	−1.12180
$907$	11.8248	0.392635	0.196317	−	0.980540i	$-0.437102\pi$
$907$	11.8248	0.392635	0.196317	+	0.980540i	$0.437102\pi$
$908$	−21.7369	−0.721364
$909$	−1.17934	−0.0391162
$910$	−0.328521	−0.0108904
$911$	5.92477	0.196296	0.0981481	−	0.995172i	$-0.468708\pi$
$911$	5.92477	0.196296	0.0981481	+	0.995172i	$0.468708\pi$
$912$	1.75523	0.0581216
$913$	−18.9932	−0.628584
$914$	17.7575	0.587364
$915$	−0.871115	−0.0287982
$916$	18.7100	0.618195
$917$	−84.7105	−2.79739
$918$	−13.8206	−0.456147
$919$	−25.1157	−0.828491	−0.414246	−	0.910165i	$-0.635955\pi$
$919$	−25.1157	−0.828491	−0.414246	+	0.910165i	$0.635955\pi$
$920$	0.0349717	0.00115298
$921$	−54.9635	−1.81111
$922$	−4.52158	−0.148910
$923$	−12.1822	−0.400983
$924$	13.3714	0.439887
$925$	46.6703	1.53451
$926$	−24.9916	−0.821276
$927$	0.513412	0.0168626
$928$	8.65124	0.283991
$929$	1.18147	0.0387628	0.0193814	−	0.999812i	$-0.493830\pi$
$929$	1.18147	0.0387628	0.0193814	+	0.999812i	$0.493830\pi$
$930$	−0.263884	−0.00865311
$931$	−15.4933	−0.507772
$932$	−9.52044	−0.311853
$933$	−5.88350	−0.192617
$934$	5.67070	0.185551
$935$	−0.153130	−0.00500789
$936$	−0.158453	−0.00517919
$937$	−34.7184	−1.13420	−0.567100	−	0.823649i	$-0.691935\pi$
$937$	−34.7184	−1.13420	−0.567100	+	0.823649i	$0.691935\pi$
$938$	−68.5633	−2.23867
$939$	−28.5221	−0.930783
$940$	−0.0591610	−0.00192962
$941$	−0.973551	−0.0317369	−0.0158684	−	0.999874i	$-0.505051\pi$
$941$	−0.973551	−0.0317369	−0.0158684	+	0.999874i	$0.505051\pi$
$942$	−12.7738	−0.416194
$943$	0.946582	0.0308249
$944$	5.80290	0.188868
$945$	0.858874	0.0279392
$946$	−2.58898	−0.0841749
$947$	−4.86878	−0.158214	−0.0791071	−	0.996866i	$-0.525207\pi$
$947$	−4.86878	−0.158214	−0.0791071	+	0.996866i	$0.525207\pi$
$948$	−8.49596	−0.275936
$949$	23.7219	0.770045
$950$	−4.99875	−0.162181
$951$	−11.1894	−0.362842
$952$	12.7927	0.414613
$953$	51.3994	1.66499	0.832495	−	0.554033i	$-0.186912\pi$
$953$	51.3994	1.66499	0.832495	+	0.554033i	$0.186912\pi$
$954$	−0.913898	−0.0295885
$955$	−0.228679	−0.00739987
$956$	22.4588	0.726369
$957$	24.3910	0.788447
$958$	−27.6887	−0.894581
$959$	45.7526	1.47743
$960$	0.0620364	0.00200222
$961$	−12.9060	−0.416323
$962$	18.2980	0.589952
$963$	−0.989834	−0.0318970
$964$	−8.10342	−0.260994
$965$	0.158606	0.00510570
$966$	−8.23697	−0.265020
$967$	22.7194	0.730608	0.365304	−	0.930888i	$-0.380965\pi$
$967$	22.7194	0.730608	0.365304	+	0.930888i	$0.380965\pi$
$968$	8.41994	0.270627
$969$	4.73445	0.152092
$970$	0.228316	0.00733077
$971$	55.1126	1.76865	0.884324	−	0.466875i	$-0.154620\pi$
$971$	55.1126	1.76865	0.884324	+	0.466875i	$0.154620\pi$
$972$	0.839980	0.0269424
$973$	−18.0986	−0.580215
$974$	−28.2608	−0.905535
$975$	17.1958	0.550706
$976$	−14.0420	−0.449473
$977$	36.3686	1.16353	0.581767	−	0.813356i	$-0.302362\pi$
$977$	36.3686	1.16353	0.581767	+	0.813356i	$0.302362\pi$
$978$	−31.6156	−1.01096
$979$	−25.9176	−0.828329
$980$	−0.547590	−0.0174921
$981$	−1.26703	−0.0404532
$982$	10.1257	0.323124
$983$	−35.1947	−1.12254	−0.561269	−	0.827633i	$-0.689687\pi$
$983$	−35.1947	−1.12254	−0.561269	+	0.827633i	$0.689687\pi$
$984$	1.67914	0.0535291
$985$	−0.812014	−0.0258729
$986$	23.3353	0.743147
$987$	13.9343	0.443535
$988$	−1.95986	−0.0623515
$989$	1.59485	0.0507132
$990$	0.00458987	0.000145876 0
$991$	8.03217	0.255150	0.127575	−	0.991829i	$-0.459281\pi$
$991$	8.03217	0.255150	0.127575	+	0.991829i	$0.459281\pi$
$992$	−4.25370	−0.135055
$993$	12.5050	0.396834
$994$	−29.4800	−0.935050
$995$	0.552271	0.0175082
$996$	20.7548	0.657641
$997$	60.0852	1.90292	0.951459	−	0.307775i	$-0.0995844\pi$
$997$	60.0852	1.90292	0.951459	+	0.307775i	$0.0995844\pi$
$998$	−31.2429	−0.988978
$999$	−47.8378	−1.51352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.10	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.10	✓	41	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.75523 q^{3} +1.00000 q^{4} -0.0353436 q^{5} +1.75523 q^{6} -4.74271 q^{7} -1.00000 q^{8} +0.0808489 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.75523 q^{3} +1.00000 q^{4} -0.0353436 q^{5} +1.75523 q^{6} -4.74271 q^{7} -1.00000 q^{8} +0.0808489 q^{9} +0.0353436 q^{10} +1.60626 q^{11} -1.75523 q^{12} +1.95986 q^{13} +4.74271 q^{14} +0.0620364 q^{15} +1.00000 q^{16} +2.69733 q^{17} -0.0808489 q^{18} -1.00000 q^{19} -0.0353436 q^{20} +8.32457 q^{21} -1.60626 q^{22} +0.989478 q^{23} +1.75523 q^{24} -4.99875 q^{25} -1.95986 q^{26} +5.12380 q^{27} -4.74271 q^{28} -8.65124 q^{29} -0.0620364 q^{30} +4.25370 q^{31} -1.00000 q^{32} -2.81936 q^{33} -2.69733 q^{34} +0.167625 q^{35} +0.0808489 q^{36} -9.33639 q^{37} +1.00000 q^{38} -3.44002 q^{39} +0.0353436 q^{40} +0.956648 q^{41} -8.32457 q^{42} +1.61181 q^{43} +1.60626 q^{44} -0.00285750 q^{45} -0.989478 q^{46} +1.67388 q^{47} -1.75523 q^{48} +15.4933 q^{49} +4.99875 q^{50} -4.73445 q^{51} +1.95986 q^{52} +11.3038 q^{53} -5.12380 q^{54} -0.0567710 q^{55} +4.74271 q^{56} +1.75523 q^{57} +8.65124 q^{58} +5.80290 q^{59} +0.0620364 q^{60} -14.0420 q^{61} -4.25370 q^{62} -0.383443 q^{63} +1.00000 q^{64} -0.0692686 q^{65} +2.81936 q^{66} -14.4566 q^{67} +2.69733 q^{68} -1.73677 q^{69} -0.167625 q^{70} -6.21586 q^{71} -0.0808489 q^{72} +12.1039 q^{73} +9.33639 q^{74} +8.77398 q^{75} -1.00000 q^{76} -7.61801 q^{77} +3.44002 q^{78} +4.84035 q^{79} -0.0353436 q^{80} -9.23601 q^{81} -0.956648 q^{82} -11.8245 q^{83} +8.32457 q^{84} -0.0953335 q^{85} -1.61181 q^{86} +15.1850 q^{87} -1.60626 q^{88} -16.1354 q^{89} +0.00285750 q^{90} -9.29505 q^{91} +0.989478 q^{92} -7.46625 q^{93} -1.67388 q^{94} +0.0353436 q^{95} +1.75523 q^{96} +6.45988 q^{97} -15.4933 q^{98} +0.129864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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