LMFDB - Embedded newform 8018.2.a.d.1.1

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:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.23056 q^{3} +1.00000 q^{4} -3.65226 q^{5} -3.23056 q^{6} +2.39039 q^{7} +1.00000 q^{8} +7.43653 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.23056 q^{3} +1.00000 q^{4} -3.65226 q^{5} -3.23056 q^{6} +2.39039 q^{7} +1.00000 q^{8} +7.43653 q^{9} -3.65226 q^{10} +0.229147 q^{11} -3.23056 q^{12} -1.51971 q^{13} +2.39039 q^{14} +11.7989 q^{15} +1.00000 q^{16} +1.23485 q^{17} +7.43653 q^{18} +1.00000 q^{19} -3.65226 q^{20} -7.72231 q^{21} +0.229147 q^{22} -8.59225 q^{23} -3.23056 q^{24} +8.33901 q^{25} -1.51971 q^{26} -14.3325 q^{27} +2.39039 q^{28} -2.80955 q^{29} +11.7989 q^{30} +4.09925 q^{31} +1.00000 q^{32} -0.740273 q^{33} +1.23485 q^{34} -8.73034 q^{35} +7.43653 q^{36} -7.69336 q^{37} +1.00000 q^{38} +4.90953 q^{39} -3.65226 q^{40} +6.97582 q^{41} -7.72231 q^{42} -10.4732 q^{43} +0.229147 q^{44} -27.1601 q^{45} -8.59225 q^{46} +11.1963 q^{47} -3.23056 q^{48} -1.28603 q^{49} +8.33901 q^{50} -3.98926 q^{51} -1.51971 q^{52} +2.41819 q^{53} -14.3325 q^{54} -0.836904 q^{55} +2.39039 q^{56} -3.23056 q^{57} -2.80955 q^{58} +5.91884 q^{59} +11.7989 q^{60} +5.03288 q^{61} +4.09925 q^{62} +17.7762 q^{63} +1.00000 q^{64} +5.55039 q^{65} -0.740273 q^{66} -1.27570 q^{67} +1.23485 q^{68} +27.7578 q^{69} -8.73034 q^{70} +10.5869 q^{71} +7.43653 q^{72} -5.30920 q^{73} -7.69336 q^{74} -26.9397 q^{75} +1.00000 q^{76} +0.547751 q^{77} +4.90953 q^{78} +4.63819 q^{79} -3.65226 q^{80} +23.9924 q^{81} +6.97582 q^{82} +0.441306 q^{83} -7.72231 q^{84} -4.51000 q^{85} -10.4732 q^{86} +9.07644 q^{87} +0.229147 q^{88} +3.69080 q^{89} -27.1601 q^{90} -3.63271 q^{91} -8.59225 q^{92} -13.2429 q^{93} +11.1963 q^{94} -3.65226 q^{95} -3.23056 q^{96} +7.94507 q^{97} -1.28603 q^{98} +1.70406 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	−3.23056	−1.86517	−0.932583	−	0.360956i	$-0.882450\pi$
$3$	−3.23056	−1.86517	−0.932583	+	0.360956i	$0.882450\pi$
$4$	1.00000	0.500000
$5$	−3.65226	−1.63334	−0.816670	−	0.577104i	$-0.804183\pi$
$5$	−3.65226	−1.63334	−0.816670	+	0.577104i	$0.804183\pi$
$6$	−3.23056	−1.31887
$7$	2.39039	0.903483	0.451742	−	0.892149i	$-0.350803\pi$
$7$	2.39039	0.903483	0.451742	+	0.892149i	$0.350803\pi$
$8$	1.00000	0.353553
$9$	7.43653	2.47884
$10$	−3.65226	−1.15495
$11$	0.229147	0.0690904	0.0345452	−	0.999403i	$-0.489002\pi$
$11$	0.229147	0.0690904	0.0345452	+	0.999403i	$0.489002\pi$
$12$	−3.23056	−0.932583
$13$	−1.51971	−0.421493	−0.210746	−	0.977541i	$-0.567589\pi$
$13$	−1.51971	−0.421493	−0.210746	+	0.977541i	$0.567589\pi$
$14$	2.39039	0.638859
$15$	11.7989	3.04645
$16$	1.00000	0.250000
$17$	1.23485	0.299496	0.149748	−	0.988724i	$-0.452154\pi$
$17$	1.23485	0.299496	0.149748	+	0.988724i	$0.452154\pi$
$18$	7.43653	1.75281
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.65226	−0.816670
$21$	−7.72231	−1.68515
$22$	0.229147	0.0488543
$23$	−8.59225	−1.79161	−0.895804	−	0.444450i	$-0.853399\pi$
$23$	−8.59225	−1.79161	−0.895804	+	0.444450i	$0.853399\pi$
$24$	−3.23056	−0.659436
$25$	8.33901	1.66780
$26$	−1.51971	−0.298041
$27$	−14.3325	−2.75829
$28$	2.39039	0.451742
$29$	−2.80955	−0.521721	−0.260860	−	0.965377i	$-0.584006\pi$
$29$	−2.80955	−0.521721	−0.260860	+	0.965377i	$0.584006\pi$
$30$	11.7989	2.15417
$31$	4.09925	0.736246	0.368123	−	0.929777i	$-0.380000\pi$
$31$	4.09925	0.736246	0.368123	+	0.929777i	$0.380000\pi$
$32$	1.00000	0.176777
$33$	−0.740273	−0.128865
$34$	1.23485	0.211775
$35$	−8.73034	−1.47570
$36$	7.43653	1.23942
$37$	−7.69336	−1.26478	−0.632391	−	0.774650i	$-0.717926\pi$
$37$	−7.69336	−1.26478	−0.632391	+	0.774650i	$0.717926\pi$
$38$	1.00000	0.162221
$39$	4.90953	0.786154
$40$	−3.65226	−0.577473
$41$	6.97582	1.08944	0.544720	−	0.838618i	$-0.316636\pi$
$41$	6.97582	1.08944	0.544720	+	0.838618i	$0.316636\pi$
$42$	−7.72231	−1.19158
$43$	−10.4732	−1.59715	−0.798573	−	0.601898i	$-0.794411\pi$
$43$	−10.4732	−1.59715	−0.798573	+	0.601898i	$0.794411\pi$
$44$	0.229147	0.0345452
$45$	−27.1601	−4.04880
$46$	−8.59225	−1.26686
$47$	11.1963	1.63315	0.816574	−	0.577241i	$-0.195871\pi$
$47$	11.1963	1.63315	0.816574	+	0.577241i	$0.195871\pi$
$48$	−3.23056	−0.466291
$49$	−1.28603	−0.183718
$50$	8.33901	1.17931
$51$	−3.98926	−0.558609
$52$	−1.51971	−0.210746
$53$	2.41819	0.332164	0.166082	−	0.986112i	$-0.446888\pi$
$53$	2.41819	0.332164	0.166082	+	0.986112i	$0.446888\pi$
$54$	−14.3325	−1.95040
$55$	−0.836904	−0.112848
$56$	2.39039	0.319430
$57$	−3.23056	−0.427898
$58$	−2.80955	−0.368912
$59$	5.91884	0.770567	0.385284	−	0.922798i	$-0.374104\pi$
$59$	5.91884	0.770567	0.385284	+	0.922798i	$0.374104\pi$
$60$	11.7989	1.52323
$61$	5.03288	0.644394	0.322197	−	0.946673i	$-0.395579\pi$
$61$	5.03288	0.644394	0.322197	+	0.946673i	$0.395579\pi$
$62$	4.09925	0.520605
$63$	17.7762	2.23959
$64$	1.00000	0.125000
$65$	5.55039	0.688442
$66$	−0.740273	−0.0911214
$67$	−1.27570	−0.155851	−0.0779257	−	0.996959i	$-0.524830\pi$
$67$	−1.27570	−0.155851	−0.0779257	+	0.996959i	$0.524830\pi$
$68$	1.23485	0.149748
$69$	27.7578	3.34164
$70$	−8.73034	−1.04347
$71$	10.5869	1.25643	0.628214	−	0.778041i	$-0.283786\pi$
$71$	10.5869	1.25643	0.628214	+	0.778041i	$0.283786\pi$
$72$	7.43653	0.876403
$73$	−5.30920	−0.621395	−0.310697	−	0.950509i	$-0.600563\pi$
$73$	−5.30920	−0.621395	−0.310697	+	0.950509i	$0.600563\pi$
$74$	−7.69336	−0.894335
$75$	−26.9397	−3.11073
$76$	1.00000	0.114708
$77$	0.547751	0.0624220
$78$	4.90953	0.555895
$79$	4.63819	0.521838	0.260919	−	0.965361i	$-0.415974\pi$
$79$	4.63819	0.521838	0.260919	+	0.965361i	$0.415974\pi$
$80$	−3.65226	−0.408335
$81$	23.9924	2.66582
$82$	6.97582	0.770350
$83$	0.441306	0.0484396	0.0242198	−	0.999707i	$-0.492290\pi$
$83$	0.441306	0.0484396	0.0242198	+	0.999707i	$0.492290\pi$
$84$	−7.72231	−0.842573
$85$	−4.51000	−0.489178
$86$	−10.4732	−1.12935
$87$	9.07644	0.973096
$88$	0.229147	0.0244271
$89$	3.69080	0.391224	0.195612	−	0.980681i	$-0.437331\pi$
$89$	3.69080	0.391224	0.195612	+	0.980681i	$0.437331\pi$
$90$	−27.1601	−2.86293
$91$	−3.63271	−0.380812
$92$	−8.59225	−0.895804
$93$	−13.2429	−1.37322
$94$	11.1963	1.15481
$95$	−3.65226	−0.374714
$96$	−3.23056	−0.329718
$97$	7.94507	0.806699	0.403350	−	0.915046i	$-0.367846\pi$
$97$	7.94507	0.806699	0.403350	+	0.915046i	$0.367846\pi$
$98$	−1.28603	−0.129908
$99$	1.70406	0.171264
$100$	8.33901	0.833901
$101$	15.3822	1.53059	0.765295	−	0.643679i	$-0.222593\pi$
$101$	15.3822	1.53059	0.765295	+	0.643679i	$0.222593\pi$
$102$	−3.98926	−0.394996
$103$	11.3311	1.11649	0.558243	−	0.829677i	$-0.311476\pi$
$103$	11.3311	1.11649	0.558243	+	0.829677i	$0.311476\pi$
$104$	−1.51971	−0.149020
$105$	28.2039	2.75242
$106$	2.41819	0.234875
$107$	−7.66030	−0.740549	−0.370275	−	0.928922i	$-0.620736\pi$
$107$	−7.66030	−0.740549	−0.370275	+	0.928922i	$0.620736\pi$
$108$	−14.3325	−1.37914
$109$	−3.71384	−0.355721	−0.177860	−	0.984056i	$-0.556918\pi$
$109$	−3.71384	−0.355721	−0.177860	+	0.984056i	$0.556918\pi$
$110$	−0.836904	−0.0797957
$111$	24.8539	2.35903
$112$	2.39039	0.225871
$113$	−11.5383	−1.08543	−0.542716	−	0.839916i	$-0.682604\pi$
$113$	−11.5383	−1.08543	−0.542716	+	0.839916i	$0.682604\pi$
$114$	−3.23056	−0.302570
$115$	31.3811	2.92631
$116$	−2.80955	−0.260860
$117$	−11.3014	−1.04481
$118$	5.91884	0.544873
$119$	2.95178	0.270589
$120$	11.7989	1.07708
$121$	−10.9475	−0.995227
$122$	5.03288	0.455656
$123$	−22.5358	−2.03199
$124$	4.09925	0.368123
$125$	−12.1949	−1.09075
$126$	17.7762	1.58363
$127$	3.97747	0.352943	0.176471	−	0.984306i	$-0.443532\pi$
$127$	3.97747	0.352943	0.176471	+	0.984306i	$0.443532\pi$
$128$	1.00000	0.0883883
$129$	33.8343	2.97894
$130$	5.55039	0.486802
$131$	12.8956	1.12669	0.563346	−	0.826221i	$-0.309514\pi$
$131$	12.8956	1.12669	0.563346	+	0.826221i	$0.309514\pi$
$132$	−0.740273	−0.0644325
$133$	2.39039	0.207273
$134$	−1.27570	−0.110204
$135$	52.3460	4.50522
$136$	1.23485	0.105888
$137$	8.89558	0.760001	0.380000	−	0.924986i	$-0.375924\pi$
$137$	8.89558	0.760001	0.380000	+	0.924986i	$0.375924\pi$
$138$	27.7578	2.36290
$139$	−18.2310	−1.54634	−0.773168	−	0.634202i	$-0.781329\pi$
$139$	−18.2310	−1.54634	−0.773168	+	0.634202i	$0.781329\pi$
$140$	−8.73034	−0.737848
$141$	−36.1703	−3.04609
$142$	10.5869	0.888429
$143$	−0.348238	−0.0291211
$144$	7.43653	0.619711
$145$	10.2612	0.852148
$146$	−5.30920	−0.439392
$147$	4.15458	0.342664
$148$	−7.69336	−0.632391
$149$	5.63027	0.461249	0.230625	−	0.973043i	$-0.425923\pi$
$149$	5.63027	0.461249	0.230625	+	0.973043i	$0.425923\pi$
$150$	−26.9397	−2.19962
$151$	−22.9354	−1.86646	−0.933228	−	0.359284i	$-0.883021\pi$
$151$	−22.9354	−1.86646	−0.933228	+	0.359284i	$0.883021\pi$
$152$	1.00000	0.0811107
$153$	9.18301	0.742402
$154$	0.547751	0.0441390
$155$	−14.9715	−1.20254
$156$	4.90953	0.393077
$157$	−14.9345	−1.19191	−0.595953	−	0.803020i	$-0.703225\pi$
$157$	−14.9345	−1.19191	−0.595953	+	0.803020i	$0.703225\pi$
$158$	4.63819	0.368995
$159$	−7.81211	−0.619541
$160$	−3.65226	−0.288737
$161$	−20.5388	−1.61869
$162$	23.9924	1.88502
$163$	9.70135	0.759868	0.379934	−	0.925014i	$-0.375947\pi$
$163$	9.70135	0.759868	0.379934	+	0.925014i	$0.375947\pi$
$164$	6.97582	0.544720
$165$	2.70367	0.210481
$166$	0.441306	0.0342520
$167$	−15.6073	−1.20773	−0.603863	−	0.797088i	$-0.706373\pi$
$167$	−15.6073	−1.20773	−0.603863	+	0.797088i	$0.706373\pi$
$168$	−7.72231	−0.595789
$169$	−10.6905	−0.822344
$170$	−4.51000	−0.345901
$171$	7.43653	0.568686
$172$	−10.4732	−0.798573
$173$	−6.52314	−0.495945	−0.247972	−	0.968767i	$-0.579764\pi$
$173$	−6.52314	−0.495945	−0.247972	+	0.968767i	$0.579764\pi$
$174$	9.07644	0.688083
$175$	19.9335	1.50683
$176$	0.229147	0.0172726
$177$	−19.1212	−1.43724
$178$	3.69080	0.276637
$179$	−6.02767	−0.450529	−0.225265	−	0.974298i	$-0.572325\pi$
$179$	−6.02767	−0.450529	−0.225265	+	0.974298i	$0.572325\pi$
$180$	−27.1601	−2.02440
$181$	2.88974	0.214793	0.107396	−	0.994216i	$-0.465749\pi$
$181$	2.88974	0.214793	0.107396	+	0.994216i	$0.465749\pi$
$182$	−3.63271	−0.269275
$183$	−16.2590	−1.20190
$184$	−8.59225	−0.633429
$185$	28.0982	2.06582
$186$	−13.2429	−0.971014
$187$	0.282963	0.0206923
$188$	11.1963	0.816574
$189$	−34.2603	−2.49207
$190$	−3.65226	−0.264963
$191$	6.86116	0.496456	0.248228	−	0.968702i	$-0.420152\pi$
$191$	6.86116	0.496456	0.248228	+	0.968702i	$0.420152\pi$
$192$	−3.23056	−0.233146
$193$	−1.24997	−0.0899747	−0.0449874	−	0.998988i	$-0.514325\pi$
$193$	−1.24997	−0.0899747	−0.0449874	+	0.998988i	$0.514325\pi$
$194$	7.94507	0.570423
$195$	−17.9309	−1.28406
$196$	−1.28603	−0.0918590
$197$	−0.390431	−0.0278171	−0.0139085	−	0.999903i	$-0.504427\pi$
$197$	−0.390431	−0.0278171	−0.0139085	+	0.999903i	$0.504427\pi$
$198$	1.70406	0.121102
$199$	−3.56651	−0.252823	−0.126411	−	0.991978i	$-0.540346\pi$
$199$	−3.56651	−0.252823	−0.126411	+	0.991978i	$0.540346\pi$
$200$	8.33901	0.589657
$201$	4.12122	0.290689
$202$	15.3822	1.08229
$203$	−6.71593	−0.471366
$204$	−3.98926	−0.279304
$205$	−25.4775	−1.77943
$206$	11.3311	0.789475
$207$	−63.8965	−4.44111
$208$	−1.51971	−0.105373
$209$	0.229147	0.0158504
$210$	28.2039	1.94625
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	2.41819	0.166082
$213$	−34.2015	−2.34345
$214$	−7.66030	−0.523647
$215$	38.2508	2.60868
$216$	−14.3325	−0.975202
$217$	9.79881	0.665186
$218$	−3.71384	−0.251533
$219$	17.1517	1.15900
$220$	−0.836904	−0.0564241
$221$	−1.87662	−0.126235
$222$	24.8539	1.66808
$223$	−9.58727	−0.642011	−0.321006	−	0.947077i	$-0.604021\pi$
$223$	−9.58727	−0.642011	−0.321006	+	0.947077i	$0.604021\pi$
$224$	2.39039	0.159715
$225$	62.0133	4.13422
$226$	−11.5383	−0.767516
$227$	−18.3617	−1.21871	−0.609354	−	0.792898i	$-0.708571\pi$
$227$	−18.3617	−1.21871	−0.609354	+	0.792898i	$0.708571\pi$
$228$	−3.23056	−0.213949
$229$	5.24337	0.346492	0.173246	−	0.984879i	$-0.444574\pi$
$229$	5.24337	0.346492	0.173246	+	0.984879i	$0.444574\pi$
$230$	31.3811	2.06921
$231$	−1.76954	−0.116427
$232$	−2.80955	−0.184456
$233$	2.53591	0.166133	0.0830666	−	0.996544i	$-0.473529\pi$
$233$	2.53591	0.166133	0.0830666	+	0.996544i	$0.473529\pi$
$234$	−11.3014	−0.738796
$235$	−40.8918	−2.66749
$236$	5.91884	0.385284
$237$	−14.9840	−0.973314
$238$	2.95178	0.191335
$239$	−20.2316	−1.30868	−0.654338	−	0.756202i	$-0.727052\pi$
$239$	−20.2316	−1.30868	−0.654338	+	0.756202i	$0.727052\pi$
$240$	11.7989	0.761613
$241$	1.33108	0.0857424	0.0428712	−	0.999081i	$-0.486349\pi$
$241$	1.33108	0.0857424	0.0428712	+	0.999081i	$0.486349\pi$
$242$	−10.9475	−0.703731
$243$	−34.5114	−2.21391
$244$	5.03288	0.322197
$245$	4.69690	0.300074
$246$	−22.5358	−1.43683
$247$	−1.51971	−0.0966971
$248$	4.09925	0.260302
$249$	−1.42567	−0.0903479
$250$	−12.1949	−0.771276
$251$	30.4215	1.92019	0.960093	−	0.279681i	$-0.0902286\pi$
$251$	30.4215	1.92019	0.960093	+	0.279681i	$0.0902286\pi$
$252$	17.7762	1.11980
$253$	−1.96889	−0.123783
$254$	3.97747	0.249568
$255$	14.5698	0.912399
$256$	1.00000	0.0625000
$257$	16.4111	1.02369	0.511847	−	0.859077i	$-0.328962\pi$
$257$	16.4111	1.02369	0.511847	+	0.859077i	$0.328962\pi$
$258$	33.8343	2.10643
$259$	−18.3902	−1.14271
$260$	5.55039	0.344221
$261$	−20.8933	−1.29326
$262$	12.8956	0.796691
$263$	−5.15303	−0.317749	−0.158875	−	0.987299i	$-0.550787\pi$
$263$	−5.15303	−0.317749	−0.158875	+	0.987299i	$0.550787\pi$
$264$	−0.740273	−0.0455607
$265$	−8.83186	−0.542537
$266$	2.39039	0.146564
$267$	−11.9234	−0.729698
$268$	−1.27570	−0.0779257
$269$	4.03782	0.246190	0.123095	−	0.992395i	$-0.460718\pi$
$269$	4.03782	0.246190	0.123095	+	0.992395i	$0.460718\pi$
$270$	52.3460	3.18567
$271$	−13.4426	−0.816579	−0.408289	−	0.912853i	$-0.633875\pi$
$271$	−13.4426	−0.816579	−0.408289	+	0.912853i	$0.633875\pi$
$272$	1.23485	0.0748739
$273$	11.7357	0.710277
$274$	8.89558	0.537402
$275$	1.91086	0.115229
$276$	27.7578	1.67082
$277$	11.7483	0.705889	0.352944	−	0.935644i	$-0.385180\pi$
$277$	11.7483	0.705889	0.352944	+	0.935644i	$0.385180\pi$
$278$	−18.2310	−1.09342
$279$	30.4842	1.82504
$280$	−8.73034	−0.521737
$281$	14.9416	0.891340	0.445670	−	0.895197i	$-0.352965\pi$
$281$	14.9416	0.891340	0.445670	+	0.895197i	$0.352965\pi$
$282$	−36.1703	−2.15391
$283$	1.92528	0.114446	0.0572229	−	0.998361i	$-0.481775\pi$
$283$	1.92528	0.114446	0.0572229	+	0.998361i	$0.481775\pi$
$284$	10.5869	0.628214
$285$	11.7989	0.698904
$286$	−0.348238	−0.0205917
$287$	16.6749	0.984291
$288$	7.43653	0.438202
$289$	−15.4751	−0.910302
$290$	10.2612	0.602560
$291$	−25.6670	−1.50463
$292$	−5.30920	−0.310697
$293$	−31.4958	−1.84000	−0.920002	−	0.391914i	$-0.871813\pi$
$293$	−31.4958	−1.84000	−0.920002	+	0.391914i	$0.871813\pi$
$294$	4.15458	0.242300
$295$	−21.6171	−1.25860
$296$	−7.69336	−0.447168
$297$	−3.28424	−0.190571
$298$	5.63027	0.326153
$299$	13.0578	0.755150
$300$	−26.9397	−1.55536
$301$	−25.0350	−1.44300
$302$	−22.9354	−1.31978
$303$	−49.6933	−2.85481
$304$	1.00000	0.0573539
$305$	−18.3814	−1.05252
$306$	9.18301	0.524958
$307$	12.8647	0.734228	0.367114	−	0.930176i	$-0.380346\pi$
$307$	12.8647	0.734228	0.367114	+	0.930176i	$0.380346\pi$
$308$	0.547751	0.0312110
$309$	−36.6058	−2.08243
$310$	−14.9715	−0.850325
$311$	−25.7290	−1.45896	−0.729478	−	0.684004i	$-0.760237\pi$
$311$	−25.7290	−1.45896	−0.729478	+	0.684004i	$0.760237\pi$
$312$	4.90953	0.277947
$313$	−24.5398	−1.38707	−0.693537	−	0.720421i	$-0.743948\pi$
$313$	−24.5398	−1.38707	−0.693537	+	0.720421i	$0.743948\pi$
$314$	−14.9345	−0.842804
$315$	−64.9234	−3.65802
$316$	4.63819	0.260919
$317$	19.5030	1.09540	0.547698	−	0.836676i	$-0.315504\pi$
$317$	19.5030	1.09540	0.547698	+	0.836676i	$0.315504\pi$
$318$	−7.81211	−0.438082
$319$	−0.643801	−0.0360459
$320$	−3.65226	−0.204168
$321$	24.7471	1.38125
$322$	−20.5388	−1.14458
$323$	1.23485	0.0687090
$324$	23.9924	1.33291
$325$	−12.6729	−0.702967
$326$	9.70135	0.537308
$327$	11.9978	0.663478
$328$	6.97582	0.385175
$329$	26.7635	1.47552
$330$	2.70367	0.148832
$331$	8.66544	0.476296	0.238148	−	0.971229i	$-0.423460\pi$
$331$	8.66544	0.476296	0.238148	+	0.971229i	$0.423460\pi$
$332$	0.441306	0.0242198
$333$	−57.2119	−3.13519
$334$	−15.6073	−0.853991
$335$	4.65919	0.254558
$336$	−7.72231	−0.421287
$337$	−14.4531	−0.787309	−0.393654	−	0.919259i	$-0.628789\pi$
$337$	−14.4531	−0.787309	−0.393654	+	0.919259i	$0.628789\pi$
$338$	−10.6905	−0.581485
$339$	37.2752	2.02451
$340$	−4.51000	−0.244589
$341$	0.939330	0.0508676
$342$	7.43653	0.402121
$343$	−19.8069	−1.06947
$344$	−10.4732	−0.564677
$345$	−101.379	−5.45804
$346$	−6.52314	−0.350686
$347$	−0.431535	−0.0231660	−0.0115830	−	0.999933i	$-0.503687\pi$
$347$	−0.431535	−0.0231660	−0.0115830	+	0.999933i	$0.503687\pi$
$348$	9.07644	0.486548
$349$	−5.76879	−0.308796	−0.154398	−	0.988009i	$-0.549344\pi$
$349$	−5.76879	−0.308796	−0.154398	+	0.988009i	$0.549344\pi$
$350$	19.9335	1.06549
$351$	21.7813	1.16260
$352$	0.229147	0.0122136
$353$	−16.3363	−0.869494	−0.434747	−	0.900553i	$-0.643162\pi$
$353$	−16.3363	−0.869494	−0.434747	+	0.900553i	$0.643162\pi$
$354$	−19.1212	−1.01628
$355$	−38.6659	−2.05218
$356$	3.69080	0.195612
$357$	−9.53591	−0.504694
$358$	−6.02767	−0.318572
$359$	10.6597	0.562600	0.281300	−	0.959620i	$-0.409234\pi$
$359$	10.6597	0.562600	0.281300	+	0.959620i	$0.409234\pi$
$360$	−27.1601	−1.43147
$361$	1.00000	0.0526316
$362$	2.88974	0.151881
$363$	35.3665	1.85626
$364$	−3.63271	−0.190406
$365$	19.3906	1.01495
$366$	−16.2590	−0.849873
$367$	−23.8708	−1.24605	−0.623023	−	0.782204i	$-0.714096\pi$
$367$	−23.8708	−1.24605	−0.623023	+	0.782204i	$0.714096\pi$
$368$	−8.59225	−0.447902
$369$	51.8759	2.70055
$370$	28.0982	1.46075
$371$	5.78042	0.300105
$372$	−13.2429	−0.686611
$373$	−27.5695	−1.42749	−0.713747	−	0.700404i	$-0.753003\pi$
$373$	−27.5695	−1.42749	−0.713747	+	0.700404i	$0.753003\pi$
$374$	0.282963	0.0146316
$375$	39.3965	2.03443
$376$	11.1963	0.577405
$377$	4.26972	0.219902
$378$	−34.2603	−1.76216
$379$	4.83139	0.248172	0.124086	−	0.992271i	$-0.460400\pi$
$379$	4.83139	0.248172	0.124086	+	0.992271i	$0.460400\pi$
$380$	−3.65226	−0.187357
$381$	−12.8494	−0.658297
$382$	6.86116	0.351047
$383$	28.5696	1.45984	0.729919	−	0.683534i	$-0.239558\pi$
$383$	28.5696	1.45984	0.729919	+	0.683534i	$0.239558\pi$
$384$	−3.23056	−0.164859
$385$	−2.00053	−0.101956
$386$	−1.24997	−0.0636217
$387$	−77.8842	−3.95908
$388$	7.94507	0.403350
$389$	17.6906	0.896947	0.448474	−	0.893796i	$-0.351968\pi$
$389$	17.6906	0.896947	0.448474	+	0.893796i	$0.351968\pi$
$390$	−17.9309	−0.907966
$391$	−10.6102	−0.536578
$392$	−1.28603	−0.0649541
$393$	−41.6600	−2.10147
$394$	−0.390431	−0.0196696
$395$	−16.9399	−0.852339
$396$	1.70406	0.0856321
$397$	−26.1741	−1.31364	−0.656821	−	0.754047i	$-0.728099\pi$
$397$	−26.1741	−1.31364	−0.656821	+	0.754047i	$0.728099\pi$
$398$	−3.56651	−0.178773
$399$	−7.72231	−0.386599
$400$	8.33901	0.416951
$401$	−39.1083	−1.95298	−0.976489	−	0.215569i	$-0.930839\pi$
$401$	−39.1083	−1.95298	−0.976489	+	0.215569i	$0.930839\pi$
$402$	4.12122	0.205548
$403$	−6.22968	−0.310323
$404$	15.3822	0.765295
$405$	−87.6264	−4.35419
$406$	−6.71593	−0.333306
$407$	−1.76291	−0.0873842
$408$	−3.98926	−0.197498
$409$	−30.0877	−1.48774	−0.743870	−	0.668324i	$-0.767012\pi$
$409$	−30.0877	−1.48774	−0.743870	+	0.668324i	$0.767012\pi$
$410$	−25.4775	−1.25824
$411$	−28.7377	−1.41753
$412$	11.3311	0.558243
$413$	14.1483	0.696195
$414$	−63.8965	−3.14034
$415$	−1.61176	−0.0791184
$416$	−1.51971	−0.0745101
$417$	58.8964	2.88417
$418$	0.229147	0.0112079
$419$	−1.17310	−0.0573098	−0.0286549	−	0.999589i	$-0.509122\pi$
$419$	−1.17310	−0.0573098	−0.0286549	+	0.999589i	$0.509122\pi$
$420$	28.2039	1.37621
$421$	16.7829	0.817950	0.408975	−	0.912546i	$-0.365886\pi$
$421$	16.7829	0.817950	0.408975	+	0.912546i	$0.365886\pi$
$422$	−1.00000	−0.0486792
$423$	83.2616	4.04832
$424$	2.41819	0.117438
$425$	10.2974	0.499499
$426$	−34.2015	−1.65707
$427$	12.0306	0.582200
$428$	−7.66030	−0.370275
$429$	1.12500	0.0543157
$430$	38.2508	1.84462
$431$	−7.56515	−0.364401	−0.182200	−	0.983261i	$-0.558322\pi$
$431$	−7.56515	−0.364401	−0.182200	+	0.983261i	$0.558322\pi$
$432$	−14.3325	−0.689572
$433$	7.92605	0.380902	0.190451	−	0.981697i	$-0.439005\pi$
$433$	7.92605	0.380902	0.190451	+	0.981697i	$0.439005\pi$
$434$	9.79881	0.470358
$435$	−33.1495	−1.58940
$436$	−3.71384	−0.177860
$437$	−8.59225	−0.411023
$438$	17.1517	0.819539
$439$	8.97895	0.428542	0.214271	−	0.976774i	$-0.431262\pi$
$439$	8.97895	0.428542	0.214271	+	0.976774i	$0.431262\pi$
$440$	−0.836904	−0.0398979
$441$	−9.56357	−0.455408
$442$	−1.87662	−0.0892618
$443$	31.4899	1.49613	0.748065	−	0.663625i	$-0.230983\pi$
$443$	31.4899	1.49613	0.748065	+	0.663625i	$0.230983\pi$
$444$	24.8539	1.17951
$445$	−13.4798	−0.639002
$446$	−9.58727	−0.453970
$447$	−18.1889	−0.860306
$448$	2.39039	0.112935
$449$	15.3450	0.724176	0.362088	−	0.932144i	$-0.382064\pi$
$449$	15.3450	0.724176	0.362088	+	0.932144i	$0.382064\pi$
$450$	62.0133	2.92333
$451$	1.59849	0.0752698
$452$	−11.5383	−0.542716
$453$	74.0942	3.48125
$454$	−18.3617	−0.861756
$455$	13.2676	0.621995
$456$	−3.23056	−0.151285
$457$	−19.5714	−0.915510	−0.457755	−	0.889078i	$-0.651346\pi$
$457$	−19.5714	−0.915510	−0.457755	+	0.889078i	$0.651346\pi$
$458$	5.24337	0.245007
$459$	−17.6985	−0.826095
$460$	31.3811	1.46315
$461$	−6.56806	−0.305905	−0.152953	−	0.988234i	$-0.548878\pi$
$461$	−6.56806	−0.305905	−0.152953	+	0.988234i	$0.548878\pi$
$462$	−1.76954	−0.0823266
$463$	−30.7081	−1.42713	−0.713563	−	0.700591i	$-0.752920\pi$
$463$	−30.7081	−1.42713	−0.713563	+	0.700591i	$0.752920\pi$
$464$	−2.80955	−0.130430
$465$	48.3664	2.24294
$466$	2.53591	0.117474
$467$	13.3222	0.616480	0.308240	−	0.951309i	$-0.400260\pi$
$467$	13.3222	0.616480	0.308240	+	0.951309i	$0.400260\pi$
$468$	−11.3014	−0.522407
$469$	−3.04942	−0.140809
$470$	−40.8918	−1.88620
$471$	48.2469	2.22310
$472$	5.91884	0.272437
$473$	−2.39990	−0.110347
$474$	−14.9840	−0.688237
$475$	8.33901	0.382620
$476$	2.95178	0.135295
$477$	17.9829	0.823383
$478$	−20.2316	−0.925373
$479$	32.9788	1.50684	0.753420	−	0.657540i	$-0.228403\pi$
$479$	32.9788	1.50684	0.753420	+	0.657540i	$0.228403\pi$
$480$	11.7989	0.538542
$481$	11.6917	0.533096
$482$	1.33108	0.0606290
$483$	66.3520	3.01912
$484$	−10.9475	−0.497613
$485$	−29.0175	−1.31762
$486$	−34.5114	−1.56547
$487$	30.1843	1.36778	0.683891	−	0.729584i	$-0.260286\pi$
$487$	30.1843	1.36778	0.683891	+	0.729584i	$0.260286\pi$
$488$	5.03288	0.227828
$489$	−31.3408	−1.41728
$490$	4.69690	0.212184
$491$	−5.62352	−0.253786	−0.126893	−	0.991916i	$-0.540500\pi$
$491$	−5.62352	−0.253786	−0.126893	+	0.991916i	$0.540500\pi$
$492$	−22.5358	−1.01599
$493$	−3.46938	−0.156253
$494$	−1.51971	−0.0683752
$495$	−6.22366	−0.279733
$496$	4.09925	0.184062
$497$	25.3067	1.13516
$498$	−1.42567	−0.0638856
$499$	−7.32951	−0.328114	−0.164057	−	0.986451i	$-0.552458\pi$
$499$	−7.32951	−0.328114	−0.164057	+	0.986451i	$0.552458\pi$
$500$	−12.1949	−0.545374
$501$	50.4202	2.25261
$502$	30.4215	1.35778
$503$	−43.4235	−1.93616	−0.968078	−	0.250649i	$-0.919356\pi$
$503$	−43.4235	−1.93616	−0.968078	+	0.250649i	$0.919356\pi$
$504$	17.7762	0.791816
$505$	−56.1800	−2.49998
$506$	−1.96889	−0.0875277
$507$	34.5362	1.53381
$508$	3.97747	0.176471
$509$	−3.39862	−0.150641	−0.0753206	−	0.997159i	$-0.523998\pi$
$509$	−3.39862	−0.150641	−0.0753206	+	0.997159i	$0.523998\pi$
$510$	14.5698	0.645163
$511$	−12.6911	−0.561420
$512$	1.00000	0.0441942
$513$	−14.3325	−0.632795
$514$	16.4111	0.723860
$515$	−41.3841	−1.82360
$516$	33.8343	1.48947
$517$	2.56560	0.112835
$518$	−18.3902	−0.808017
$519$	21.0734	0.925020
$520$	5.55039	0.243401
$521$	−13.3063	−0.582960	−0.291480	−	0.956577i	$-0.594148\pi$
$521$	−13.3063	−0.582960	−0.291480	+	0.956577i	$0.594148\pi$
$522$	−20.8933	−0.914476
$523$	7.85981	0.343686	0.171843	−	0.985124i	$-0.445028\pi$
$523$	7.85981	0.343686	0.171843	+	0.985124i	$0.445028\pi$
$524$	12.8956	0.563346
$525$	−64.3964	−2.81049
$526$	−5.15303	−0.224683
$527$	5.06196	0.220503
$528$	−0.740273	−0.0322163
$529$	50.8267	2.20986
$530$	−8.83186	−0.383632
$531$	44.0156	1.91012
$532$	2.39039	0.103637
$533$	−10.6013	−0.459191
$534$	−11.9234	−0.515974
$535$	27.9774	1.20957
$536$	−1.27570	−0.0551018
$537$	19.4728	0.840311
$538$	4.03782	0.174083
$539$	−0.294689	−0.0126931
$540$	52.3460	2.25261
$541$	−27.9735	−1.20268	−0.601338	−	0.798995i	$-0.705366\pi$
$541$	−27.9735	−1.20268	−0.601338	+	0.798995i	$0.705366\pi$
$542$	−13.4426	−0.577409
$543$	−9.33549	−0.400624
$544$	1.23485	0.0529438
$545$	13.5639	0.581013
$546$	11.7357	0.502242
$547$	37.5390	1.60505	0.802525	−	0.596618i	$-0.203489\pi$
$547$	37.5390	1.60505	0.802525	+	0.596618i	$0.203489\pi$
$548$	8.89558	0.380000
$549$	37.4272	1.59735
$550$	1.91086	0.0814793
$551$	−2.80955	−0.119691
$552$	27.7578	1.18145
$553$	11.0871	0.471472
$554$	11.7483	0.499139
$555$	−90.7729	−3.85309
$556$	−18.2310	−0.773168
$557$	17.5000	0.741498	0.370749	−	0.928733i	$-0.379101\pi$
$557$	17.5000	0.741498	0.370749	+	0.928733i	$0.379101\pi$
$558$	30.4842	1.29050
$559$	15.9163	0.673186
$560$	−8.73034	−0.368924
$561$	−0.914128	−0.0385945
$562$	14.9416	0.630273
$563$	−41.3629	−1.74324	−0.871619	−	0.490183i	$-0.836930\pi$
$563$	−41.3629	−1.74324	−0.871619	+	0.490183i	$0.836930\pi$
$564$	−36.1703	−1.52304
$565$	42.1409	1.77288
$566$	1.92528	0.0809253
$567$	57.3512	2.40852
$568$	10.5869	0.444214
$569$	1.60985	0.0674882	0.0337441	−	0.999431i	$-0.489257\pi$
$569$	1.60985	0.0674882	0.0337441	+	0.999431i	$0.489257\pi$
$570$	11.7989	0.494200
$571$	−24.5836	−1.02879	−0.514396	−	0.857553i	$-0.671984\pi$
$571$	−24.5836	−1.02879	−0.514396	+	0.857553i	$0.671984\pi$
$572$	−0.348238	−0.0145606
$573$	−22.1654	−0.925972
$574$	16.6749	0.695999
$575$	−71.6508	−2.98805
$576$	7.43653	0.309855
$577$	−9.27040	−0.385932	−0.192966	−	0.981205i	$-0.561811\pi$
$577$	−9.27040	−0.385932	−0.192966	+	0.981205i	$0.561811\pi$
$578$	−15.4751	−0.643681
$579$	4.03810	0.167818
$580$	10.2612	0.426074
$581$	1.05489	0.0437644
$582$	−25.6670	−1.06393
$583$	0.554121	0.0229493
$584$	−5.30920	−0.219696
$585$	41.2757	1.70654
$586$	−31.4958	−1.30108
$587$	−18.0076	−0.743252	−0.371626	−	0.928383i	$-0.621200\pi$
$587$	−18.0076	−0.743252	−0.371626	+	0.928383i	$0.621200\pi$
$588$	4.15458	0.171332
$589$	4.09925	0.168907
$590$	−21.6171	−0.889964
$591$	1.26131	0.0518834
$592$	−7.69336	−0.316195
$593$	−23.9198	−0.982270	−0.491135	−	0.871084i	$-0.663418\pi$
$593$	−23.9198	−0.982270	−0.491135	+	0.871084i	$0.663418\pi$
$594$	−3.28424	−0.134754
$595$	−10.7807	−0.441964
$596$	5.63027	0.230625
$597$	11.5218	0.471557
$598$	13.0578	0.533972
$599$	−11.3110	−0.462156	−0.231078	−	0.972935i	$-0.574225\pi$
$599$	−11.3110	−0.462156	−0.231078	+	0.972935i	$0.574225\pi$
$600$	−26.9397	−1.09981
$601$	13.2639	0.541047	0.270524	−	0.962713i	$-0.412803\pi$
$601$	13.2639	0.541047	0.270524	+	0.962713i	$0.412803\pi$
$602$	−25.0350	−1.02035
$603$	−9.48677	−0.386331
$604$	−22.9354	−0.933228
$605$	39.9831	1.62554
$606$	−49.6933	−2.01865
$607$	0.994203	0.0403535	0.0201767	−	0.999796i	$-0.493577\pi$
$607$	0.994203	0.0403535	0.0201767	+	0.999796i	$0.493577\pi$
$608$	1.00000	0.0405554
$609$	21.6962	0.879176
$610$	−18.3814	−0.744241
$611$	−17.0152	−0.688360
$612$	9.18301	0.371201
$613$	−10.7488	−0.434139	−0.217069	−	0.976156i	$-0.569650\pi$
$613$	−10.7488	−0.434139	−0.217069	+	0.976156i	$0.569650\pi$
$614$	12.8647	0.519178
$615$	82.3067	3.31892
$616$	0.547751	0.0220695
$617$	−37.3375	−1.50315	−0.751575	−	0.659647i	$-0.770706\pi$
$617$	−37.3375	−1.50315	−0.751575	+	0.659647i	$0.770706\pi$
$618$	−36.6058	−1.47250
$619$	−29.9203	−1.20260	−0.601300	−	0.799023i	$-0.705350\pi$
$619$	−29.9203	−1.20260	−0.601300	+	0.799023i	$0.705350\pi$
$620$	−14.9715	−0.601271
$621$	123.148	4.94177
$622$	−25.7290	−1.03164
$623$	8.82246	0.353464
$624$	4.90953	0.196539
$625$	2.84404	0.113762
$626$	−24.5398	−0.980809
$627$	−0.740273	−0.0295637
$628$	−14.9345	−0.595953
$629$	−9.50016	−0.378796
$630$	−64.9234	−2.58661
$631$	8.60650	0.342619	0.171310	−	0.985217i	$-0.445200\pi$
$631$	8.60650	0.342619	0.171310	+	0.985217i	$0.445200\pi$
$632$	4.63819	0.184497
$633$	3.23056	0.128403
$634$	19.5030	0.774562
$635$	−14.5267	−0.576476
$636$	−7.81211	−0.309770
$637$	1.95439	0.0774358
$638$	−0.643801	−0.0254883
$639$	78.7294	3.11449
$640$	−3.65226	−0.144368
$641$	−18.2571	−0.721111	−0.360556	−	0.932738i	$-0.617413\pi$
$641$	−18.2571	−0.721111	−0.360556	+	0.932738i	$0.617413\pi$
$642$	24.7471	0.976689
$643$	−39.5014	−1.55778	−0.778892	−	0.627158i	$-0.784218\pi$
$643$	−39.5014	−1.55778	−0.778892	+	0.627158i	$0.784218\pi$
$644$	−20.5388	−0.809344
$645$	−123.572	−4.86563
$646$	1.23485	0.0485846
$647$	−12.9526	−0.509219	−0.254609	−	0.967044i	$-0.581947\pi$
$647$	−12.9526	−0.509219	−0.254609	+	0.967044i	$0.581947\pi$
$648$	23.9924	0.942510
$649$	1.35628	0.0532388
$650$	−12.6729	−0.497073
$651$	−31.6557	−1.24068
$652$	9.70135	0.379934
$653$	−30.0711	−1.17677	−0.588387	−	0.808579i	$-0.700237\pi$
$653$	−30.0711	−1.17677	−0.588387	+	0.808579i	$0.700237\pi$
$654$	11.9978	0.469150
$655$	−47.0980	−1.84027
$656$	6.97582	0.272360
$657$	−39.4820	−1.54034
$658$	26.7635	1.04335
$659$	0.699015	0.0272298	0.0136149	−	0.999907i	$-0.495666\pi$
$659$	0.699015	0.0272298	0.0136149	+	0.999907i	$0.495666\pi$
$660$	2.70367	0.105240
$661$	−18.0802	−0.703239	−0.351619	−	0.936143i	$-0.614369\pi$
$661$	−18.0802	−0.703239	−0.351619	+	0.936143i	$0.614369\pi$
$662$	8.66544	0.336792
$663$	6.06254	0.235450
$664$	0.441306	0.0171260
$665$	−8.73034	−0.338548
$666$	−57.2119	−2.21692
$667$	24.1404	0.934719
$668$	−15.6073	−0.603863
$669$	30.9723	1.19746
$670$	4.65919	0.180000
$671$	1.15327	0.0445215
$672$	−7.72231	−0.297895
$673$	−21.9960	−0.847885	−0.423943	−	0.905689i	$-0.639354\pi$
$673$	−21.9960	−0.847885	−0.423943	+	0.905689i	$0.639354\pi$
$674$	−14.4531	−0.556711
$675$	−119.519	−4.60028
$676$	−10.6905	−0.411172
$677$	39.9127	1.53397	0.766985	−	0.641665i	$-0.221756\pi$
$677$	39.9127	1.53397	0.766985	+	0.641665i	$0.221756\pi$
$678$	37.2752	1.43154
$679$	18.9918	0.728839
$680$	−4.51000	−0.172951
$681$	59.3185	2.27309
$682$	0.939330	0.0359688
$683$	4.85952	0.185945	0.0929723	−	0.995669i	$-0.470363\pi$
$683$	4.85952	0.185945	0.0929723	+	0.995669i	$0.470363\pi$
$684$	7.43653	0.284343
$685$	−32.4890	−1.24134
$686$	−19.8069	−0.756229
$687$	−16.9390	−0.646265
$688$	−10.4732	−0.399287
$689$	−3.67496	−0.140005
$690$	−101.379	−3.85942
$691$	−17.1704	−0.653194	−0.326597	−	0.945164i	$-0.605902\pi$
$691$	−17.1704	−0.653194	−0.326597	+	0.945164i	$0.605902\pi$
$692$	−6.52314	−0.247972
$693$	4.07337	0.154734
$694$	−0.431535	−0.0163808
$695$	66.5845	2.52569
$696$	9.07644	0.344041
$697$	8.61410	0.326282
$698$	−5.76879	−0.218352
$699$	−8.19242	−0.309866
$700$	19.9335	0.753416
$701$	−40.5003	−1.52968	−0.764838	−	0.644223i	$-0.777181\pi$
$701$	−40.5003	−1.52968	−0.764838	+	0.644223i	$0.777181\pi$
$702$	21.7813	0.822081
$703$	−7.69336	−0.290161
$704$	0.229147	0.00863630
$705$	132.103	4.97530
$706$	−16.3363	−0.614825
$707$	36.7696	1.38286
$708$	−19.1212	−0.718618
$709$	−6.78729	−0.254902	−0.127451	−	0.991845i	$-0.540680\pi$
$709$	−6.78729	−0.254902	−0.127451	+	0.991845i	$0.540680\pi$
$710$	−38.6659	−1.45111
$711$	34.4921	1.29355
$712$	3.69080	0.138319
$713$	−35.2217	−1.31906
$714$	−9.53591	−0.356872
$715$	1.27186	0.0475647
$716$	−6.02767	−0.225265
$717$	65.3595	2.44090
$718$	10.6597	0.397818
$719$	−25.9395	−0.967379	−0.483690	−	0.875240i	$-0.660704\pi$
$719$	−25.9395	−0.967379	−0.483690	+	0.875240i	$0.660704\pi$
$720$	−27.1601	−1.01220
$721$	27.0858	1.00873
$722$	1.00000	0.0372161
$723$	−4.30013	−0.159924
$724$	2.88974	0.107396
$725$	−23.4289	−0.870127
$726$	35.3665	1.31258
$727$	48.0383	1.78164	0.890821	−	0.454354i	$-0.150130\pi$
$727$	48.0383	1.78164	0.890821	+	0.454354i	$0.150130\pi$
$728$	−3.63271	−0.134637
$729$	39.5141	1.46349
$730$	19.3906	0.717677
$731$	−12.9328	−0.478338
$732$	−16.2590	−0.600951
$733$	38.1311	1.40840	0.704202	−	0.710000i	$-0.251305\pi$
$733$	38.1311	1.40840	0.704202	+	0.710000i	$0.251305\pi$
$734$	−23.8708	−0.881087
$735$	−15.1736	−0.559688
$736$	−8.59225	−0.316714
$737$	−0.292322	−0.0107678
$738$	51.8759	1.90958
$739$	30.5081	1.12226	0.561130	−	0.827728i	$-0.310367\pi$
$739$	30.5081	1.12226	0.561130	+	0.827728i	$0.310367\pi$
$740$	28.0982	1.03291
$741$	4.90953	0.180356
$742$	5.78042	0.212206
$743$	49.0897	1.80093	0.900464	−	0.434931i	$-0.143227\pi$
$743$	49.0897	1.80093	0.900464	+	0.434931i	$0.143227\pi$
$744$	−13.2429	−0.485507
$745$	−20.5632	−0.753377
$746$	−27.5695	−1.00939
$747$	3.28178	0.120074
$748$	0.282963	0.0103461
$749$	−18.3111	−0.669074
$750$	39.3965	1.43856
$751$	−20.4439	−0.746009	−0.373004	−	0.927830i	$-0.621672\pi$
$751$	−20.4439	−0.746009	−0.373004	+	0.927830i	$0.621672\pi$
$752$	11.1963	0.408287
$753$	−98.2784	−3.58147
$754$	4.26972	0.155494
$755$	83.7661	3.04856
$756$	−34.2603	−1.24603
$757$	−10.5719	−0.384242	−0.192121	−	0.981371i	$-0.561537\pi$
$757$	−10.5719	−0.384242	−0.192121	+	0.981371i	$0.561537\pi$
$758$	4.83139	0.175484
$759$	6.36061	0.230876
$760$	−3.65226	−0.132481
$761$	−32.1882	−1.16682	−0.583410	−	0.812178i	$-0.698282\pi$
$761$	−32.1882	−1.16682	−0.583410	+	0.812178i	$0.698282\pi$
$762$	−12.8494	−0.465486
$763$	−8.87752	−0.321388
$764$	6.86116	0.248228
$765$	−33.5388	−1.21260
$766$	28.5696	1.03226
$767$	−8.99495	−0.324789
$768$	−3.23056	−0.116573
$769$	−51.8063	−1.86818	−0.934092	−	0.357032i	$-0.883789\pi$
$769$	−51.8063	−1.86818	−0.934092	+	0.357032i	$0.883789\pi$
$770$	−2.00053	−0.0720941
$771$	−53.0169	−1.90936
$772$	−1.24997	−0.0449874
$773$	16.1272	0.580056	0.290028	−	0.957018i	$-0.406335\pi$
$773$	16.1272	0.580056	0.290028	+	0.957018i	$0.406335\pi$
$774$	−77.8842	−2.79949
$775$	34.1837	1.22791
$776$	7.94507	0.285211
$777$	59.4105	2.13134
$778$	17.6906	0.634238
$779$	6.97582	0.249935
$780$	−17.9309	−0.642029
$781$	2.42594	0.0868071
$782$	−10.6102	−0.379418
$783$	40.2679	1.43906
$784$	−1.28603	−0.0459295
$785$	54.5448	1.94679
$786$	−41.6600	−1.48596
$787$	6.45141	0.229968	0.114984	−	0.993367i	$-0.463318\pi$
$787$	6.45141	0.229968	0.114984	+	0.993367i	$0.463318\pi$
$788$	−0.390431	−0.0139085
$789$	16.6472	0.592655
$790$	−16.9399	−0.602695
$791$	−27.5811	−0.980669
$792$	1.70406	0.0605511
$793$	−7.64854	−0.271608
$794$	−26.1741	−0.928885
$795$	28.5319	1.01192
$796$	−3.56651	−0.126411
$797$	12.7652	0.452166	0.226083	−	0.974108i	$-0.427408\pi$
$797$	12.7652	0.452166	0.226083	+	0.974108i	$0.427408\pi$
$798$	−7.72231	−0.273367
$799$	13.8258	0.489120
$800$	8.33901	0.294829
$801$	27.4467	0.969783
$802$	−39.1083	−1.38096
$803$	−1.21659	−0.0429324
$804$	4.12122	0.145344
$805$	75.0132	2.64387
$806$	−6.22968	−0.219431
$807$	−13.0444	−0.459186
$808$	15.3822	0.541146
$809$	−24.6877	−0.867973	−0.433986	−	0.900919i	$-0.642893\pi$
$809$	−24.6877	−0.867973	−0.433986	+	0.900919i	$0.642893\pi$
$810$	−87.6264	−3.07888
$811$	−17.4948	−0.614326	−0.307163	−	0.951657i	$-0.599380\pi$
$811$	−17.4948	−0.614326	−0.307163	+	0.951657i	$0.599380\pi$
$812$	−6.71593	−0.235683
$813$	43.4271	1.52306
$814$	−1.76291	−0.0617900
$815$	−35.4319	−1.24112
$816$	−3.98926	−0.139652
$817$	−10.4732	−0.366411
$818$	−30.0877	−1.05199
$819$	−27.0148	−0.943973
$820$	−25.4775	−0.889713
$821$	−51.4035	−1.79400	−0.896998	−	0.442035i	$-0.854257\pi$
$821$	−51.4035	−1.79400	−0.896998	+	0.442035i	$0.854257\pi$
$822$	−28.7377	−1.00234
$823$	23.3674	0.814537	0.407268	−	0.913308i	$-0.366481\pi$
$823$	23.3674	0.814537	0.407268	+	0.913308i	$0.366481\pi$
$824$	11.3311	0.394738
$825$	−6.17315	−0.214921
$826$	14.1483	0.492284
$827$	0.778285	0.0270636	0.0135318	−	0.999908i	$-0.495693\pi$
$827$	0.778285	0.0270636	0.0135318	+	0.999908i	$0.495693\pi$
$828$	−63.8965	−2.22056
$829$	−40.8249	−1.41791	−0.708954	−	0.705255i	$-0.750832\pi$
$829$	−40.8249	−1.41791	−0.708954	+	0.705255i	$0.750832\pi$
$830$	−1.61176	−0.0559451
$831$	−37.9537	−1.31660
$832$	−1.51971	−0.0526866
$833$	−1.58805	−0.0550227
$834$	58.8964	2.03942
$835$	57.0018	1.97263
$836$	0.229147	0.00792521
$837$	−58.7524	−2.03078
$838$	−1.17310	−0.0405242
$839$	19.6042	0.676813	0.338407	−	0.941000i	$-0.390112\pi$
$839$	19.6042	0.676813	0.338407	+	0.941000i	$0.390112\pi$
$840$	28.2039	0.973127
$841$	−21.1064	−0.727807
$842$	16.7829	0.578378
$843$	−48.2697	−1.66250
$844$	−1.00000	−0.0344214
$845$	39.0444	1.34317
$846$	83.2616	2.86259
$847$	−26.1688	−0.899171
$848$	2.41819	0.0830410
$849$	−6.21972	−0.213460
$850$	10.2974	0.353199
$851$	66.1033	2.26599
$852$	−34.2015	−1.17172
$853$	36.3411	1.24429	0.622147	−	0.782900i	$-0.286261\pi$
$853$	36.3411	1.24429	0.622147	+	0.782900i	$0.286261\pi$
$854$	12.0306	0.411677
$855$	−27.1601	−0.928857
$856$	−7.66030	−0.261824
$857$	−30.1884	−1.03122	−0.515609	−	0.856824i	$-0.672434\pi$
$857$	−30.1884	−1.03122	−0.515609	+	0.856824i	$0.672434\pi$
$858$	1.12500	0.0384070
$859$	47.8902	1.63399	0.816996	−	0.576643i	$-0.195638\pi$
$859$	47.8902	1.63399	0.816996	+	0.576643i	$0.195638\pi$
$860$	38.2508	1.30434
$861$	−53.8694	−1.83587
$862$	−7.56515	−0.257670
$863$	−35.5990	−1.21180	−0.605901	−	0.795540i	$-0.707187\pi$
$863$	−35.5990	−1.21180	−0.605901	+	0.795540i	$0.707187\pi$
$864$	−14.3325	−0.487601
$865$	23.8242	0.810047
$866$	7.92605	0.269338
$867$	49.9934	1.69786
$868$	9.79881	0.332593
$869$	1.06283	0.0360540
$870$	−33.1495	−1.12387
$871$	1.93870	0.0656903
$872$	−3.71384	−0.125766
$873$	59.0837	1.99968
$874$	−8.59225	−0.290637
$875$	−29.1507	−0.985473
$876$	17.1517	0.579502
$877$	−26.1504	−0.883035	−0.441518	−	0.897253i	$-0.645560\pi$
$877$	−26.1504	−0.883035	−0.441518	+	0.897253i	$0.645560\pi$
$878$	8.97895	0.303025
$879$	101.749	3.43191
$880$	−0.836904	−0.0282120
$881$	19.1848	0.646353	0.323176	−	0.946339i	$-0.395249\pi$
$881$	19.1848	0.646353	0.323176	+	0.946339i	$0.395249\pi$
$882$	−9.56357	−0.322022
$883$	−17.2507	−0.580532	−0.290266	−	0.956946i	$-0.593744\pi$
$883$	−17.2507	−0.580532	−0.290266	+	0.956946i	$0.593744\pi$
$884$	−1.87662	−0.0631176
$885$	69.8355	2.34750
$886$	31.4899	1.05792
$887$	18.2485	0.612726	0.306363	−	0.951915i	$-0.400888\pi$
$887$	18.2485	0.612726	0.306363	+	0.951915i	$0.400888\pi$
$888$	24.8539	0.834042
$889$	9.50770	0.318878
$890$	−13.4798	−0.451843
$891$	5.49778	0.184183
$892$	−9.58727	−0.321006
$893$	11.1963	0.374670
$894$	−18.1889	−0.608328
$895$	22.0146	0.735867
$896$	2.39039	0.0798574
$897$	−42.1839	−1.40848
$898$	15.3450	0.512070
$899$	−11.5171	−0.384115
$900$	62.0133	2.06711
$901$	2.98611	0.0994816
$902$	1.59849	0.0532238
$903$	80.8772	2.69143
$904$	−11.5383	−0.383758
$905$	−10.5541	−0.350830
$906$	74.0942	2.46162
$907$	−36.7014	−1.21865	−0.609325	−	0.792920i	$-0.708560\pi$
$907$	−36.7014	−1.21865	−0.609325	+	0.792920i	$0.708560\pi$
$908$	−18.3617	−0.609354
$909$	114.391	3.79409
$910$	13.2676	0.439817
$911$	56.9332	1.88628	0.943141	−	0.332392i	$-0.107856\pi$
$911$	56.9332	1.88628	0.943141	+	0.332392i	$0.107856\pi$
$912$	−3.23056	−0.106975
$913$	0.101124	0.00334671
$914$	−19.5714	−0.647363
$915$	59.3822	1.96312
$916$	5.24337	0.173246
$917$	30.8255	1.01795
$918$	−17.6985	−0.584137
$919$	−10.3542	−0.341555	−0.170777	−	0.985310i	$-0.554628\pi$
$919$	−10.3542	−0.341555	−0.170777	+	0.985310i	$0.554628\pi$
$920$	31.3811	1.03461
$921$	−41.5603	−1.36946
$922$	−6.56806	−0.216308
$923$	−16.0890	−0.529576
$924$	−1.76954	−0.0582137
$925$	−64.1550	−2.10940
$926$	−30.7081	−1.00913
$927$	84.2640	2.76759
$928$	−2.80955	−0.0922281
$929$	47.3203	1.55253	0.776265	−	0.630407i	$-0.217112\pi$
$929$	47.3203	1.55253	0.776265	+	0.630407i	$0.217112\pi$
$930$	48.3664	1.58600
$931$	−1.28603	−0.0421478
$932$	2.53591	0.0830666
$933$	83.1191	2.72120
$934$	13.3222	0.435917
$935$	−1.03345	−0.0337975
$936$	−11.3014	−0.369398
$937$	49.3905	1.61352	0.806759	−	0.590880i	$-0.201219\pi$
$937$	49.3905	1.61352	0.806759	+	0.590880i	$0.201219\pi$
$938$	−3.04942	−0.0995671
$939$	79.2774	2.58712
$940$	−40.8918	−1.33374
$941$	−45.4484	−1.48157	−0.740787	−	0.671740i	$-0.765547\pi$
$941$	−45.4484	−1.48157	−0.740787	+	0.671740i	$0.765547\pi$
$942$	48.2469	1.57197
$943$	−59.9379	−1.95185
$944$	5.91884	0.192642
$945$	125.127	4.07039
$946$	−2.39990	−0.0780275
$947$	−20.7896	−0.675572	−0.337786	−	0.941223i	$-0.609678\pi$
$947$	−20.7896	−0.675572	−0.337786	+	0.941223i	$0.609678\pi$
$948$	−14.9840	−0.486657
$949$	8.06846	0.261913
$950$	8.33901	0.270553
$951$	−63.0055	−2.04309
$952$	2.95178	0.0956677
$953$	−20.4516	−0.662492	−0.331246	−	0.943545i	$-0.607469\pi$
$953$	−20.4516	−0.662492	−0.331246	+	0.943545i	$0.607469\pi$
$954$	17.9829	0.582219
$955$	−25.0587	−0.810882
$956$	−20.2316	−0.654338
$957$	2.07984	0.0672316
$958$	32.9788	1.06550
$959$	21.2639	0.686648
$960$	11.7989	0.380806
$961$	−14.1962	−0.457941
$962$	11.6917	0.376956
$963$	−56.9661	−1.83571
$964$	1.33108	0.0428712
$965$	4.56521	0.146959
$966$	66.3520	2.13484
$967$	−14.1009	−0.453453	−0.226727	−	0.973958i	$-0.572802\pi$
$967$	−14.1009	−0.453453	−0.226727	+	0.973958i	$0.572802\pi$
$968$	−10.9475	−0.351866
$969$	−3.98926	−0.128154
$970$	−29.0175	−0.931695
$971$	−47.7636	−1.53281	−0.766404	−	0.642359i	$-0.777956\pi$
$971$	−47.7636	−1.53281	−0.766404	+	0.642359i	$0.777956\pi$
$972$	−34.5114	−1.10695
$973$	−43.5793	−1.39709
$974$	30.1843	0.967168
$975$	40.9406	1.31115
$976$	5.03288	0.161099
$977$	−29.6642	−0.949041	−0.474520	−	0.880245i	$-0.657378\pi$
$977$	−29.6642	−0.949041	−0.474520	+	0.880245i	$0.657378\pi$
$978$	−31.3408	−1.00217
$979$	0.845736	0.0270298
$980$	4.69690	0.150037
$981$	−27.6180	−0.881776
$982$	−5.62352	−0.179454
$983$	37.5964	1.19914	0.599569	−	0.800323i	$-0.295339\pi$
$983$	37.5964	1.19914	0.599569	+	0.800323i	$0.295339\pi$
$984$	−22.5358	−0.718415
$985$	1.42596	0.0454348
$986$	−3.46938	−0.110488
$987$	−86.4612	−2.75209
$988$	−1.51971	−0.0483486
$989$	89.9882	2.86146
$990$	−6.22366	−0.197801
$991$	55.2980	1.75660	0.878300	−	0.478110i	$-0.158678\pi$
$991$	55.2980	1.75660	0.878300	+	0.478110i	$0.158678\pi$
$992$	4.09925	0.130151
$993$	−27.9942	−0.888370
$994$	25.3067	0.802681
$995$	13.0258	0.412946
$996$	−1.42567	−0.0451739
$997$	−41.9755	−1.32938	−0.664689	−	0.747120i	$-0.731436\pi$
$997$	−41.9755	−1.32938	−0.664689	+	0.747120i	$0.731436\pi$
$998$	−7.32951	−0.232012
$999$	110.265	3.48863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.1	✓	30	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.23056 q^{3} +1.00000 q^{4} -3.65226 q^{5} -3.23056 q^{6} +2.39039 q^{7} +1.00000 q^{8} +7.43653 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.23056 q^{3} +1.00000 q^{4} -3.65226 q^{5} -3.23056 q^{6} +2.39039 q^{7} +1.00000 q^{8} +7.43653 q^{9} -3.65226 q^{10} +0.229147 q^{11} -3.23056 q^{12} -1.51971 q^{13} +2.39039 q^{14} +11.7989 q^{15} +1.00000 q^{16} +1.23485 q^{17} +7.43653 q^{18} +1.00000 q^{19} -3.65226 q^{20} -7.72231 q^{21} +0.229147 q^{22} -8.59225 q^{23} -3.23056 q^{24} +8.33901 q^{25} -1.51971 q^{26} -14.3325 q^{27} +2.39039 q^{28} -2.80955 q^{29} +11.7989 q^{30} +4.09925 q^{31} +1.00000 q^{32} -0.740273 q^{33} +1.23485 q^{34} -8.73034 q^{35} +7.43653 q^{36} -7.69336 q^{37} +1.00000 q^{38} +4.90953 q^{39} -3.65226 q^{40} +6.97582 q^{41} -7.72231 q^{42} -10.4732 q^{43} +0.229147 q^{44} -27.1601 q^{45} -8.59225 q^{46} +11.1963 q^{47} -3.23056 q^{48} -1.28603 q^{49} +8.33901 q^{50} -3.98926 q^{51} -1.51971 q^{52} +2.41819 q^{53} -14.3325 q^{54} -0.836904 q^{55} +2.39039 q^{56} -3.23056 q^{57} -2.80955 q^{58} +5.91884 q^{59} +11.7989 q^{60} +5.03288 q^{61} +4.09925 q^{62} +17.7762 q^{63} +1.00000 q^{64} +5.55039 q^{65} -0.740273 q^{66} -1.27570 q^{67} +1.23485 q^{68} +27.7578 q^{69} -8.73034 q^{70} +10.5869 q^{71} +7.43653 q^{72} -5.30920 q^{73} -7.69336 q^{74} -26.9397 q^{75} +1.00000 q^{76} +0.547751 q^{77} +4.90953 q^{78} +4.63819 q^{79} -3.65226 q^{80} +23.9924 q^{81} +6.97582 q^{82} +0.441306 q^{83} -7.72231 q^{84} -4.51000 q^{85} -10.4732 q^{86} +9.07644 q^{87} +0.229147 q^{88} +3.69080 q^{89} -27.1601 q^{90} -3.63271 q^{91} -8.59225 q^{92} -13.2429 q^{93} +11.1963 q^{94} -3.65226 q^{95} -3.23056 q^{96} +7.94507 q^{97} -1.28603 q^{98} +1.70406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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