LMFDB - Embedded newform 8015.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0912753 q^{2} +1.39308 q^{3} -1.99167 q^{4} +1.00000 q^{5} -0.127154 q^{6} +1.00000 q^{7} +0.364341 q^{8} -1.05934 q^{9} +O(q^{10})$	\(q-0.0912753 q^{2} +1.39308 q^{3} -1.99167 q^{4} +1.00000 q^{5} -0.127154 q^{6} +1.00000 q^{7} +0.364341 q^{8} -1.05934 q^{9} -0.0912753 q^{10} -3.28459 q^{11} -2.77455 q^{12} -4.46665 q^{13} -0.0912753 q^{14} +1.39308 q^{15} +3.95008 q^{16} +3.13663 q^{17} +0.0966912 q^{18} +5.44163 q^{19} -1.99167 q^{20} +1.39308 q^{21} +0.299802 q^{22} +6.43325 q^{23} +0.507555 q^{24} +1.00000 q^{25} +0.407695 q^{26} -5.65497 q^{27} -1.99167 q^{28} -8.98145 q^{29} -0.127154 q^{30} -0.433335 q^{31} -1.08923 q^{32} -4.57569 q^{33} -0.286297 q^{34} +1.00000 q^{35} +2.10985 q^{36} +6.99614 q^{37} -0.496687 q^{38} -6.22239 q^{39} +0.364341 q^{40} -2.90353 q^{41} -0.127154 q^{42} -6.71898 q^{43} +6.54182 q^{44} -1.05934 q^{45} -0.587197 q^{46} -3.74451 q^{47} +5.50277 q^{48} +1.00000 q^{49} -0.0912753 q^{50} +4.36956 q^{51} +8.89608 q^{52} +3.27811 q^{53} +0.516159 q^{54} -3.28459 q^{55} +0.364341 q^{56} +7.58061 q^{57} +0.819784 q^{58} +7.47012 q^{59} -2.77455 q^{60} +2.99535 q^{61} +0.0395527 q^{62} -1.05934 q^{63} -7.80075 q^{64} -4.46665 q^{65} +0.417647 q^{66} -1.29381 q^{67} -6.24712 q^{68} +8.96201 q^{69} -0.0912753 q^{70} -12.0108 q^{71} -0.385959 q^{72} -10.8202 q^{73} -0.638575 q^{74} +1.39308 q^{75} -10.8379 q^{76} -3.28459 q^{77} +0.567950 q^{78} +4.21285 q^{79} +3.95008 q^{80} -4.69980 q^{81} +0.265021 q^{82} +12.2113 q^{83} -2.77455 q^{84} +3.13663 q^{85} +0.613277 q^{86} -12.5118 q^{87} -1.19671 q^{88} +9.61205 q^{89} +0.0966912 q^{90} -4.46665 q^{91} -12.8129 q^{92} -0.603669 q^{93} +0.341781 q^{94} +5.44163 q^{95} -1.51738 q^{96} +3.55578 q^{97} -0.0912753 q^{98} +3.47948 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−0.0912753	−0.0645414	−0.0322707	−	0.999479i	$-0.510274\pi$
$2$	−0.0912753	−0.0645414	−0.0322707	+	0.999479i	$0.510274\pi$
$3$	1.39308	0.804294	0.402147	−	0.915575i	$-0.368264\pi$
$3$	1.39308	0.804294	0.402147	+	0.915575i	$0.368264\pi$
$4$	−1.99167	−0.995834
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.127154	−0.0519102
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.364341	0.128814
$9$	−1.05934	−0.353112
$10$	−0.0912753	−0.0288638
$11$	−3.28459	−0.990341	−0.495171	−	0.868796i	$-0.664894\pi$
$11$	−3.28459	−0.990341	−0.495171	+	0.868796i	$0.664894\pi$
$12$	−2.77455	−0.800943
$13$	−4.46665	−1.23883	−0.619413	−	0.785066i	$-0.712629\pi$
$13$	−4.46665	−1.23883	−0.619413	+	0.785066i	$0.712629\pi$
$14$	−0.0912753	−0.0243943
$15$	1.39308	0.359691
$16$	3.95008	0.987521
$17$	3.13663	0.760744	0.380372	−	0.924834i	$-0.375796\pi$
$17$	3.13663	0.760744	0.380372	+	0.924834i	$0.375796\pi$
$18$	0.0966912	0.0227903
$19$	5.44163	1.24840	0.624198	−	0.781266i	$-0.285426\pi$
$19$	5.44163	1.24840	0.624198	+	0.781266i	$0.285426\pi$
$20$	−1.99167	−0.445351
$21$	1.39308	0.303994
$22$	0.299802	0.0639180
$23$	6.43325	1.34143	0.670713	−	0.741717i	$-0.265988\pi$
$23$	6.43325	1.34143	0.670713	+	0.741717i	$0.265988\pi$
$24$	0.507555	0.103604
$25$	1.00000	0.200000
$26$	0.407695	0.0799555
$27$	−5.65497	−1.08830
$28$	−1.99167	−0.376390
$29$	−8.98145	−1.66781	−0.833906	−	0.551906i	$-0.813901\pi$
$29$	−8.98145	−1.66781	−0.833906	+	0.551906i	$0.813901\pi$
$30$	−0.127154	−0.0232150
$31$	−0.433335	−0.0778292	−0.0389146	−	0.999243i	$-0.512390\pi$
$31$	−0.433335	−0.0778292	−0.0389146	+	0.999243i	$0.512390\pi$
$32$	−1.08923	−0.192550
$33$	−4.57569	−0.796525
$34$	−0.286297	−0.0490995
$35$	1.00000	0.169031
$36$	2.10985	0.351641
$37$	6.99614	1.15016	0.575079	−	0.818098i	$-0.304971\pi$
$37$	6.99614	1.15016	0.575079	+	0.818098i	$0.304971\pi$
$38$	−0.496687	−0.0805732
$39$	−6.22239	−0.996379
$40$	0.364341	0.0576073
$41$	−2.90353	−0.453455	−0.226728	−	0.973958i	$-0.572803\pi$
$41$	−2.90353	−0.453455	−0.226728	+	0.973958i	$0.572803\pi$
$42$	−0.127154	−0.0196202
$43$	−6.71898	−1.02464	−0.512318	−	0.858796i	$-0.671213\pi$
$43$	−6.71898	−1.02464	−0.512318	+	0.858796i	$0.671213\pi$
$44$	6.54182	0.986216
$45$	−1.05934	−0.157916
$46$	−0.587197	−0.0865774
$47$	−3.74451	−0.546193	−0.273097	−	0.961987i	$-0.588048\pi$
$47$	−3.74451	−0.546193	−0.273097	+	0.961987i	$0.588048\pi$
$48$	5.50277	0.794256
$49$	1.00000	0.142857
$50$	−0.0912753	−0.0129083
$51$	4.36956	0.611861
$52$	8.89608	1.23366
$53$	3.27811	0.450283	0.225142	−	0.974326i	$-0.427716\pi$
$53$	3.27811	0.450283	0.225142	+	0.974326i	$0.427716\pi$
$54$	0.516159	0.0702403
$55$	−3.28459	−0.442894
$56$	0.364341	0.0486871
$57$	7.58061	1.00408
$58$	0.819784	0.107643
$59$	7.47012	0.972526	0.486263	−	0.873812i	$-0.338360\pi$
$59$	7.47012	0.972526	0.486263	+	0.873812i	$0.338360\pi$
$60$	−2.77455	−0.358193
$61$	2.99535	0.383515	0.191757	−	0.981442i	$-0.438581\pi$
$61$	2.99535	0.383515	0.191757	+	0.981442i	$0.438581\pi$
$62$	0.0395527	0.00502320
$63$	−1.05934	−0.133464
$64$	−7.80075	−0.975093
$65$	−4.46665	−0.554019
$66$	0.417647	0.0514088
$67$	−1.29381	−0.158064	−0.0790321	−	0.996872i	$-0.525183\pi$
$67$	−1.29381	−0.158064	−0.0790321	+	0.996872i	$0.525183\pi$
$68$	−6.24712	−0.757575
$69$	8.96201	1.07890
$70$	−0.0912753	−0.0109095
$71$	−12.0108	−1.42542	−0.712712	−	0.701457i	$-0.752533\pi$
$71$	−12.0108	−1.42542	−0.712712	+	0.701457i	$0.752533\pi$
$72$	−0.385959	−0.0454857
$73$	−10.8202	−1.26641	−0.633203	−	0.773986i	$-0.718260\pi$
$73$	−10.8202	−1.26641	−0.633203	+	0.773986i	$0.718260\pi$
$74$	−0.638575	−0.0742328
$75$	1.39308	0.160859
$76$	−10.8379	−1.24320
$77$	−3.28459	−0.374314
$78$	0.567950	0.0643077
$79$	4.21285	0.473983	0.236991	−	0.971512i	$-0.423839\pi$
$79$	4.21285	0.473983	0.236991	+	0.971512i	$0.423839\pi$
$80$	3.95008	0.441633
$81$	−4.69980	−0.522200
$82$	0.265021	0.0292666
$83$	12.2113	1.34036	0.670181	−	0.742197i	$-0.266216\pi$
$83$	12.2113	1.34036	0.670181	+	0.742197i	$0.266216\pi$
$84$	−2.77455	−0.302728
$85$	3.13663	0.340215
$86$	0.613277	0.0661314
$87$	−12.5118	−1.34141
$88$	−1.19671	−0.127570
$89$	9.61205	1.01887	0.509437	−	0.860508i	$-0.329854\pi$
$89$	9.61205	1.01887	0.509437	+	0.860508i	$0.329854\pi$
$90$	0.0966912	0.0101921
$91$	−4.46665	−0.468232
$92$	−12.8129	−1.33584
$93$	−0.603669	−0.0625975
$94$	0.341781	0.0352521
$95$	5.44163	0.558300
$96$	−1.51738	−0.154867
$97$	3.55578	0.361035	0.180517	−	0.983572i	$-0.442223\pi$
$97$	3.55578	0.361035	0.180517	+	0.983572i	$0.442223\pi$
$98$	−0.0912753	−0.00922020
$99$	3.47948	0.349701
$100$	−1.99167	−0.199167
$101$	−12.2115	−1.21509	−0.607547	−	0.794284i	$-0.707846\pi$
$101$	−12.2115	−1.21509	−0.607547	+	0.794284i	$0.707846\pi$
$102$	−0.398833	−0.0394904
$103$	−9.11033	−0.897667	−0.448834	−	0.893615i	$-0.648160\pi$
$103$	−9.11033	−0.897667	−0.448834	+	0.893615i	$0.648160\pi$
$104$	−1.62738	−0.159578
$105$	1.39308	0.135950
$106$	−0.299211	−0.0290619
$107$	11.5115	1.11285	0.556427	−	0.830896i	$-0.312172\pi$
$107$	11.5115	1.11285	0.556427	+	0.830896i	$0.312172\pi$
$108$	11.2628	1.08377
$109$	−0.737245	−0.0706153	−0.0353077	−	0.999376i	$-0.511241\pi$
$109$	−0.737245	−0.0706153	−0.0353077	+	0.999376i	$0.511241\pi$
$110$	0.299802	0.0285850
$111$	9.74617	0.925065
$112$	3.95008	0.373248
$113$	−18.8082	−1.76932	−0.884662	−	0.466232i	$-0.845611\pi$
$113$	−18.8082	−1.76932	−0.884662	+	0.466232i	$0.845611\pi$
$114$	−0.691923	−0.0648045
$115$	6.43325	0.599904
$116$	17.8881	1.66087
$117$	4.73168	0.437444
$118$	−0.681837	−0.0627682
$119$	3.13663	0.287534
$120$	0.507555	0.0463332
$121$	−0.211465	−0.0192241
$122$	−0.273401	−0.0247526
$123$	−4.04484	−0.364711
$124$	0.863059	0.0775050
$125$	1.00000	0.0894427
$126$	0.0966912	0.00861393
$127$	−13.7778	−1.22258	−0.611290	−	0.791406i	$-0.709349\pi$
$127$	−13.7778	−1.22258	−0.611290	+	0.791406i	$0.709349\pi$
$128$	2.89047	0.255484
$129$	−9.36006	−0.824107
$130$	0.407695	0.0357572
$131$	−22.6986	−1.98319	−0.991594	−	0.129388i	$-0.958699\pi$
$131$	−22.6986	−1.98319	−0.991594	+	0.129388i	$0.958699\pi$
$132$	9.11326	0.793207
$133$	5.44163	0.471849
$134$	0.118093	0.0102017
$135$	−5.65497	−0.486702
$136$	1.14280	0.0979944
$137$	−2.21283	−0.189055	−0.0945273	−	0.995522i	$-0.530134\pi$
$137$	−2.21283	−0.189055	−0.0945273	+	0.995522i	$0.530134\pi$
$138$	−0.818011	−0.0696337
$139$	−2.36781	−0.200835	−0.100417	−	0.994945i	$-0.532018\pi$
$139$	−2.36781	−0.200835	−0.100417	+	0.994945i	$0.532018\pi$
$140$	−1.99167	−0.168327
$141$	−5.21639	−0.439300
$142$	1.09629	0.0919988
$143$	14.6711	1.22686
$144$	−4.18446	−0.348705
$145$	−8.98145	−0.745869
$146$	0.987615	0.0817356
$147$	1.39308	0.114899
$148$	−13.9340	−1.14537
$149$	12.1250	0.993319	0.496659	−	0.867946i	$-0.334560\pi$
$149$	12.1250	0.993319	0.496659	+	0.867946i	$0.334560\pi$
$150$	−0.127154	−0.0103820
$151$	−11.2656	−0.916778	−0.458389	−	0.888752i	$-0.651573\pi$
$151$	−11.2656	−0.916778	−0.458389	+	0.888752i	$0.651573\pi$
$152$	1.98261	0.160811
$153$	−3.32274	−0.268628
$154$	0.299802	0.0241587
$155$	−0.433335	−0.0348063
$156$	12.3929	0.992229
$157$	−5.94740	−0.474654	−0.237327	−	0.971430i	$-0.576271\pi$
$157$	−5.94740	−0.474654	−0.237327	+	0.971430i	$0.576271\pi$
$158$	−0.384529	−0.0305915
$159$	4.56666	0.362160
$160$	−1.08923	−0.0861109
$161$	6.43325	0.507011
$162$	0.428976	0.0337035
$163$	−10.7955	−0.845571	−0.422786	−	0.906230i	$-0.638948\pi$
$163$	−10.7955	−0.845571	−0.422786	+	0.906230i	$0.638948\pi$
$164$	5.78287	0.451566
$165$	−4.57569	−0.356217
$166$	−1.11459	−0.0865088
$167$	−12.2343	−0.946720	−0.473360	−	0.880869i	$-0.656959\pi$
$167$	−12.2343	−0.946720	−0.473360	+	0.880869i	$0.656959\pi$
$168$	0.507555	0.0391587
$169$	6.95094	0.534688
$170$	−0.286297	−0.0219579
$171$	−5.76451	−0.440823
$172$	13.3820	1.02037
$173$	17.8022	1.35348	0.676739	−	0.736223i	$-0.263393\pi$
$173$	17.8022	1.35348	0.676739	+	0.736223i	$0.263393\pi$
$174$	1.14202	0.0865765
$175$	1.00000	0.0755929
$176$	−12.9744	−0.977982
$177$	10.4065	0.782197
$178$	−0.877342	−0.0657596
$179$	−3.24467	−0.242518	−0.121259	−	0.992621i	$-0.538693\pi$
$179$	−3.24467	−0.242518	−0.121259	+	0.992621i	$0.538693\pi$
$180$	2.10985	0.157259
$181$	−7.18720	−0.534220	−0.267110	−	0.963666i	$-0.586069\pi$
$181$	−7.18720	−0.534220	−0.267110	+	0.963666i	$0.586069\pi$
$182$	0.407695	0.0302203
$183$	4.17275	0.308459
$184$	2.34390	0.172794
$185$	6.99614	0.514367
$186$	0.0551000	0.00404013
$187$	−10.3025	−0.753396
$188$	7.45783	0.543918
$189$	−5.65497	−0.411338
$190$	−0.496687	−0.0360334
$191$	17.3783	1.25745	0.628723	−	0.777629i	$-0.283578\pi$
$191$	17.3783	1.25745	0.628723	+	0.777629i	$0.283578\pi$
$192$	−10.8670	−0.784261
$193$	−5.72987	−0.412445	−0.206223	−	0.978505i	$-0.566117\pi$
$193$	−5.72987	−0.412445	−0.206223	+	0.978505i	$0.566117\pi$
$194$	−0.324555	−0.0233017
$195$	−6.22239	−0.445594
$196$	−1.99167	−0.142262
$197$	−19.3061	−1.37550	−0.687752	−	0.725946i	$-0.741402\pi$
$197$	−19.3061	−1.37550	−0.687752	+	0.725946i	$0.741402\pi$
$198$	−0.317591	−0.0225702
$199$	−13.0622	−0.925954	−0.462977	−	0.886370i	$-0.653219\pi$
$199$	−13.0622	−0.925954	−0.462977	+	0.886370i	$0.653219\pi$
$200$	0.364341	0.0257628
$201$	−1.80238	−0.127130
$202$	1.11461	0.0784238
$203$	−8.98145	−0.630374
$204$	−8.70272	−0.609313
$205$	−2.90353	−0.202791
$206$	0.831548	0.0579367
$207$	−6.81497	−0.473673
$208$	−17.6436	−1.22337
$209$	−17.8735	−1.23634
$210$	−0.127154	−0.00877443
$211$	−17.1104	−1.17793	−0.588964	−	0.808159i	$-0.700464\pi$
$211$	−17.1104	−1.17793	−0.588964	+	0.808159i	$0.700464\pi$
$212$	−6.52891	−0.448407
$213$	−16.7320	−1.14646
$214$	−1.05071	−0.0718251
$215$	−6.71898	−0.458231
$216$	−2.06034	−0.140188
$217$	−0.433335	−0.0294167
$218$	0.0672923	0.00455761
$219$	−15.0733	−1.01856
$220$	6.54182	0.441049
$221$	−14.0102	−0.942428
$222$	−0.889584	−0.0597050
$223$	23.5983	1.58026	0.790129	−	0.612940i	$-0.210013\pi$
$223$	23.5983	1.58026	0.790129	+	0.612940i	$0.210013\pi$
$224$	−1.08923	−0.0727770
$225$	−1.05934	−0.0706224
$226$	1.71672	0.114195
$227$	−24.8162	−1.64711	−0.823553	−	0.567239i	$-0.808012\pi$
$227$	−24.8162	−1.64711	−0.823553	+	0.567239i	$0.808012\pi$
$228$	−15.0981	−0.999894
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.587197	−0.0387186
$231$	−4.57569	−0.301058
$232$	−3.27231	−0.214837
$233$	−16.1950	−1.06097	−0.530485	−	0.847695i	$-0.677990\pi$
$233$	−16.1950	−1.06097	−0.530485	+	0.847695i	$0.677990\pi$
$234$	−0.431885	−0.0282332
$235$	−3.74451	−0.244265
$236$	−14.8780	−0.968475
$237$	5.86883	0.381221
$238$	−0.286297	−0.0185578
$239$	2.75362	0.178117	0.0890585	−	0.996026i	$-0.471614\pi$
$239$	2.75362	0.178117	0.0890585	+	0.996026i	$0.471614\pi$
$240$	5.50277	0.355202
$241$	1.96725	0.126721	0.0633607	−	0.997991i	$-0.479818\pi$
$241$	1.96725	0.126721	0.0633607	+	0.997991i	$0.479818\pi$
$242$	0.0193015	0.00124075
$243$	10.4177	0.668297
$244$	−5.96574	−0.381917
$245$	1.00000	0.0638877
$246$	0.369194	0.0235390
$247$	−24.3059	−1.54654
$248$	−0.157881	−0.0100255
$249$	17.0113	1.07804
$250$	−0.0912753	−0.00577276
$251$	−17.2723	−1.09022	−0.545108	−	0.838366i	$-0.683512\pi$
$251$	−17.2723	−1.09022	−0.545108	+	0.838366i	$0.683512\pi$
$252$	2.10985	0.132908
$253$	−21.1306	−1.32847
$254$	1.25757	0.0789070
$255$	4.36956	0.273633
$256$	15.3377	0.958604
$257$	−30.3905	−1.89571	−0.947853	−	0.318707i	$-0.896751\pi$
$257$	−30.3905	−1.89571	−0.947853	+	0.318707i	$0.896751\pi$
$258$	0.854342	0.0531890
$259$	6.99614	0.434719
$260$	8.89608	0.551712
$261$	9.51436	0.588924
$262$	2.07182	0.127998
$263$	−10.6496	−0.656682	−0.328341	−	0.944559i	$-0.606490\pi$
$263$	−10.6496	−0.656682	−0.328341	+	0.944559i	$0.606490\pi$
$264$	−1.66711	−0.102604
$265$	3.27811	0.201373
$266$	−0.496687	−0.0304538
$267$	13.3903	0.819475
$268$	2.57684	0.157406
$269$	−23.9865	−1.46248	−0.731242	−	0.682118i	$-0.761059\pi$
$269$	−23.9865	−1.46248	−0.731242	+	0.682118i	$0.761059\pi$
$270$	0.516159	0.0314124
$271$	3.42192	0.207867	0.103933	−	0.994584i	$-0.466857\pi$
$271$	3.42192	0.207867	0.103933	+	0.994584i	$0.466857\pi$
$272$	12.3899	0.751250
$273$	−6.22239	−0.376596
$274$	0.201976	0.0122018
$275$	−3.28459	−0.198068
$276$	−17.8494	−1.07441
$277$	7.97404	0.479113	0.239557	−	0.970882i	$-0.422998\pi$
$277$	7.97404	0.479113	0.239557	+	0.970882i	$0.422998\pi$
$278$	0.216122	0.0129622
$279$	0.459047	0.0274824
$280$	0.364341	0.0217735
$281$	16.7408	0.998674	0.499337	−	0.866408i	$-0.333577\pi$
$281$	16.7408	0.998674	0.499337	+	0.866408i	$0.333577\pi$
$282$	0.476128	0.0283530
$283$	17.8651	1.06197	0.530985	−	0.847381i	$-0.321822\pi$
$283$	17.8651	1.06197	0.530985	+	0.847381i	$0.321822\pi$
$284$	23.9216	1.41949
$285$	7.58061	0.449037
$286$	−1.33911	−0.0791832
$287$	−2.90353	−0.171390
$288$	1.15386	0.0679916
$289$	−7.16157	−0.421269
$290$	0.819784	0.0481394
$291$	4.95348	0.290378
$292$	21.5502	1.26113
$293$	31.0443	1.81363	0.906814	−	0.421531i	$-0.138507\pi$
$293$	31.0443	1.81363	0.906814	+	0.421531i	$0.138507\pi$
$294$	−0.127154	−0.00741575
$295$	7.47012	0.434927
$296$	2.54898	0.148156
$297$	18.5743	1.07779
$298$	−1.10671	−0.0641102
$299$	−28.7351	−1.66179
$300$	−2.77455	−0.160189
$301$	−6.71898	−0.387276
$302$	1.02827	0.0591701
$303$	−17.0116	−0.977292
$304$	21.4949	1.23282
$305$	2.99535	0.171513
$306$	0.303284	0.0173376
$307$	−11.9045	−0.679427	−0.339714	−	0.940529i	$-0.610330\pi$
$307$	−11.9045	−0.679427	−0.339714	+	0.940529i	$0.610330\pi$
$308$	6.54182	0.372755
$309$	−12.6914	−0.721988
$310$	0.0395527	0.00224645
$311$	14.7307	0.835303	0.417652	−	0.908607i	$-0.362853\pi$
$311$	14.7307	0.835303	0.417652	+	0.908607i	$0.362853\pi$
$312$	−2.26707	−0.128347
$313$	−0.0212285	−0.00119991	−0.000599953	−	1.00000i	$-0.500191\pi$
$313$	−0.0212285	−0.00119991	−0.000599953		1.00000i	$0.500191\pi$
$314$	0.542851	0.0306349
$315$	−1.05934	−0.0596868
$316$	−8.39061	−0.472009
$317$	−21.5915	−1.21270	−0.606349	−	0.795198i	$-0.707367\pi$
$317$	−21.5915	−1.21270	−0.606349	+	0.795198i	$0.707367\pi$
$318$	−0.416823	−0.0233743
$319$	29.5004	1.65170
$320$	−7.80075	−0.436075
$321$	16.0363	0.895061
$322$	−0.587197	−0.0327232
$323$	17.0684	0.949709
$324$	9.36045	0.520025
$325$	−4.46665	−0.247765
$326$	0.985366	0.0545744
$327$	−1.02704	−0.0567954
$328$	−1.05787	−0.0584113
$329$	−3.74451	−0.206442
$330$	0.417647	0.0229907
$331$	−2.81199	−0.154561	−0.0772804	−	0.997009i	$-0.524624\pi$
$331$	−2.81199	−0.154561	−0.0772804	+	0.997009i	$0.524624\pi$
$332$	−24.3208	−1.33478
$333$	−7.41126	−0.406135
$334$	1.11669	0.0611026
$335$	−1.29381	−0.0706885
$336$	5.50277	0.300201
$337$	25.8382	1.40750	0.703748	−	0.710450i	$-0.251508\pi$
$337$	25.8382	1.40750	0.703748	+	0.710450i	$0.251508\pi$
$338$	−0.634449	−0.0345095
$339$	−26.2012	−1.42306
$340$	−6.24712	−0.338798
$341$	1.42333	0.0770775
$342$	0.526158	0.0284514
$343$	1.00000	0.0539949
$344$	−2.44800	−0.131987
$345$	8.96201	0.482499
$346$	−1.62490	−0.0873553
$347$	16.0173	0.859856	0.429928	−	0.902863i	$-0.358539\pi$
$347$	16.0173	0.859856	0.429928	+	0.902863i	$0.358539\pi$
$348$	24.9195	1.33582
$349$	3.02232	0.161781	0.0808907	−	0.996723i	$-0.474224\pi$
$349$	3.02232	0.161781	0.0808907	+	0.996723i	$0.474224\pi$
$350$	−0.0912753	−0.00487887
$351$	25.2587	1.34821
$352$	3.57766	0.190690
$353$	25.3920	1.35148	0.675741	−	0.737139i	$-0.263824\pi$
$353$	25.3920	1.35148	0.675741	+	0.737139i	$0.263824\pi$
$354$	−0.949852	−0.0504841
$355$	−12.0108	−0.637469
$356$	−19.1440	−1.01463
$357$	4.36956	0.231262
$358$	0.296158	0.0156524
$359$	20.9385	1.10509	0.552545	−	0.833483i	$-0.313657\pi$
$359$	20.9385	1.10509	0.552545	+	0.833483i	$0.313657\pi$
$360$	−0.385959	−0.0203418
$361$	10.6114	0.558493
$362$	0.656013	0.0344793
$363$	−0.294587	−0.0154618
$364$	8.89608	0.466281
$365$	−10.8202	−0.566354
$366$	−0.380869	−0.0199083
$367$	−24.7169	−1.29021	−0.645105	−	0.764094i	$-0.723186\pi$
$367$	−24.7169	−1.29021	−0.645105	+	0.764094i	$0.723186\pi$
$368$	25.4119	1.32469
$369$	3.07581	0.160120
$370$	−0.638575	−0.0331979
$371$	3.27811	0.170191
$372$	1.20231	0.0623368
$373$	−36.3444	−1.88184	−0.940922	−	0.338623i	$-0.890039\pi$
$373$	−36.3444	−1.88184	−0.940922	+	0.338623i	$0.890039\pi$
$374$	0.940367	0.0486252
$375$	1.39308	0.0719382
$376$	−1.36428	−0.0703573
$377$	40.1170	2.06613
$378$	0.516159	0.0265484
$379$	29.0024	1.48975	0.744877	−	0.667201i	$-0.232508\pi$
$379$	29.0024	1.48975	0.744877	+	0.667201i	$0.232508\pi$
$380$	−10.8379	−0.555974
$381$	−19.1935	−0.983314
$382$	−1.58621	−0.0811574
$383$	−26.5586	−1.35708	−0.678540	−	0.734564i	$-0.737387\pi$
$383$	−26.5586	−1.35708	−0.678540	+	0.734564i	$0.737387\pi$
$384$	4.02665	0.205484
$385$	−3.28459	−0.167398
$386$	0.522996	0.0266198
$387$	7.11766	0.361811
$388$	−7.08194	−0.359531
$389$	36.4517	1.84818	0.924088	−	0.382180i	$-0.124827\pi$
$389$	36.4517	1.84818	0.924088	+	0.382180i	$0.124827\pi$
$390$	0.567950	0.0287593
$391$	20.1787	1.02048
$392$	0.364341	0.0184020
$393$	−31.6209	−1.59507
$394$	1.76217	0.0887769
$395$	4.21285	0.211972
$396$	−6.92998	−0.348245
$397$	−36.6704	−1.84044	−0.920218	−	0.391406i	$-0.871989\pi$
$397$	−36.6704	−1.84044	−0.920218	+	0.391406i	$0.871989\pi$
$398$	1.19225	0.0597623
$399$	7.58061	0.379505
$400$	3.95008	0.197504
$401$	37.0380	1.84959	0.924795	−	0.380466i	$-0.124236\pi$
$401$	37.0380	1.84959	0.924795	+	0.380466i	$0.124236\pi$
$402$	0.164513	0.00820515
$403$	1.93555	0.0964168
$404$	24.3213	1.21003
$405$	−4.69980	−0.233535
$406$	0.819784	0.0406852
$407$	−22.9795	−1.13905
$408$	1.59201	0.0788162
$409$	23.3971	1.15691	0.578457	−	0.815713i	$-0.303655\pi$
$409$	23.3971	1.15691	0.578457	+	0.815713i	$0.303655\pi$
$410$	0.265021	0.0130884
$411$	−3.08264	−0.152055
$412$	18.1448	0.893928
$413$	7.47012	0.367580
$414$	0.622038	0.0305715
$415$	12.2113	0.599428
$416$	4.86519	0.238536
$417$	−3.29854	−0.161530
$418$	1.63141	0.0797950
$419$	−25.5908	−1.25019	−0.625096	−	0.780548i	$-0.714940\pi$
$419$	−25.5908	−1.25019	−0.625096	+	0.780548i	$0.714940\pi$
$420$	−2.77455	−0.135384
$421$	12.4192	0.605273	0.302637	−	0.953106i	$-0.402133\pi$
$421$	12.4192	0.605273	0.302637	+	0.953106i	$0.402133\pi$
$422$	1.56176	0.0760251
$423$	3.96669	0.192867
$424$	1.19435	0.0580027
$425$	3.13663	0.152149
$426$	1.52722	0.0739940
$427$	2.99535	0.144955
$428$	−22.9270	−1.10822
$429$	20.4380	0.986755
$430$	0.613277	0.0295748
$431$	−19.2717	−0.928284	−0.464142	−	0.885761i	$-0.653637\pi$
$431$	−19.2717	−0.928284	−0.464142	+	0.885761i	$0.653637\pi$
$432$	−22.3376	−1.07472
$433$	−25.5135	−1.22610	−0.613051	−	0.790043i	$-0.710058\pi$
$433$	−25.5135	−1.22610	−0.613051	+	0.790043i	$0.710058\pi$
$434$	0.0395527	0.00189859
$435$	−12.5118	−0.599897
$436$	1.46835	0.0703211
$437$	35.0074	1.67463
$438$	1.37582	0.0657394
$439$	15.6435	0.746622	0.373311	−	0.927706i	$-0.378222\pi$
$439$	15.6435	0.746622	0.373311	+	0.927706i	$0.378222\pi$
$440$	−1.19671	−0.0570509
$441$	−1.05934	−0.0504445
$442$	1.27879	0.0608256
$443$	−3.67763	−0.174730	−0.0873648	−	0.996176i	$-0.527845\pi$
$443$	−3.67763	−0.174730	−0.0873648	+	0.996176i	$0.527845\pi$
$444$	−19.4111	−0.921212
$445$	9.61205	0.455655
$446$	−2.15394	−0.101992
$447$	16.8911	0.798920
$448$	−7.80075	−0.368551
$449$	11.8358	0.558565	0.279283	−	0.960209i	$-0.409903\pi$
$449$	11.8358	0.558565	0.279283	+	0.960209i	$0.409903\pi$
$450$	0.0966912	0.00455807
$451$	9.53691	0.449075
$452$	37.4597	1.76195
$453$	−15.6938	−0.737358
$454$	2.26510	0.106307
$455$	−4.46665	−0.209400
$456$	2.76193	0.129339
$457$	4.55566	0.213105	0.106552	−	0.994307i	$-0.466019\pi$
$457$	4.55566	0.213105	0.106552	+	0.994307i	$0.466019\pi$
$458$	0.0912753	0.00426501
$459$	−17.7375	−0.827917
$460$	−12.8129	−0.597405
$461$	−2.03862	−0.0949478	−0.0474739	−	0.998872i	$-0.515117\pi$
$461$	−2.03862	−0.0949478	−0.0474739	+	0.998872i	$0.515117\pi$
$462$	0.417647	0.0194307
$463$	2.98899	0.138910	0.0694550	−	0.997585i	$-0.477874\pi$
$463$	2.98899	0.138910	0.0694550	+	0.997585i	$0.477874\pi$
$464$	−35.4775	−1.64700
$465$	−0.603669	−0.0279945
$466$	1.47820	0.0684764
$467$	−4.23492	−0.195969	−0.0979844	−	0.995188i	$-0.531240\pi$
$467$	−4.23492	−0.195969	−0.0979844	+	0.995188i	$0.531240\pi$
$468$	−9.42394	−0.435622
$469$	−1.29381	−0.0597427
$470$	0.341781	0.0157652
$471$	−8.28519	−0.381762
$472$	2.72167	0.125275
$473$	22.0691	1.01474
$474$	−0.535679	−0.0246046
$475$	5.44163	0.249679
$476$	−6.24712	−0.286336
$477$	−3.47262	−0.159000
$478$	−0.251338	−0.0114959
$479$	24.8177	1.13395	0.566975	−	0.823735i	$-0.308113\pi$
$479$	24.8177	1.13395	0.566975	+	0.823735i	$0.308113\pi$
$480$	−1.51738	−0.0692585
$481$	−31.2493	−1.42485
$482$	−0.179561	−0.00817878
$483$	8.96201	0.407786
$484$	0.421168	0.0191440
$485$	3.55578	0.161460
$486$	−0.950880	−0.0431328
$487$	−19.5912	−0.887762	−0.443881	−	0.896086i	$-0.646399\pi$
$487$	−19.5912	−0.887762	−0.443881	+	0.896086i	$0.646399\pi$
$488$	1.09133	0.0494020
$489$	−15.0390	−0.680088
$490$	−0.0912753	−0.00412340
$491$	−36.6177	−1.65253	−0.826266	−	0.563280i	$-0.809539\pi$
$491$	−36.6177	−1.65253	−0.826266	+	0.563280i	$0.809539\pi$
$492$	8.05598	0.363192
$493$	−28.1714	−1.26878
$494$	2.21852	0.0998161
$495$	3.47948	0.156391
$496$	−1.71171	−0.0768579
$497$	−12.0108	−0.538759
$498$	−1.55271	−0.0695785
$499$	−36.6564	−1.64096	−0.820482	−	0.571672i	$-0.806295\pi$
$499$	−36.6564	−1.64096	−0.820482	+	0.571672i	$0.806295\pi$
$500$	−1.99167	−0.0890701
$501$	−17.0433	−0.761440
$502$	1.57653	0.0703641
$503$	−14.0056	−0.624478	−0.312239	−	0.950004i	$-0.601079\pi$
$503$	−14.0056	−0.624478	−0.312239	+	0.950004i	$0.601079\pi$
$504$	−0.385959	−0.0171920
$505$	−12.2115	−0.543406
$506$	1.92870	0.0857412
$507$	9.68319	0.430046
$508$	27.4408	1.21749
$509$	−10.1324	−0.449113	−0.224556	−	0.974461i	$-0.572093\pi$
$509$	−10.1324	−0.449113	−0.224556	+	0.974461i	$0.572093\pi$
$510$	−0.398833	−0.0176606
$511$	−10.8202	−0.478657
$512$	−7.18089	−0.317353
$513$	−30.7723	−1.35863
$514$	2.77390	0.122352
$515$	−9.11033	−0.401449
$516$	18.6421	0.820675
$517$	12.2992	0.540918
$518$	−0.638575	−0.0280574
$519$	24.7999	1.08859
$520$	−1.62738	−0.0713654
$521$	−35.6218	−1.56062	−0.780310	−	0.625392i	$-0.784939\pi$
$521$	−35.6218	−1.56062	−0.780310	+	0.625392i	$0.784939\pi$
$522$	−0.868426	−0.0380100
$523$	3.91862	0.171349	0.0856746	−	0.996323i	$-0.472695\pi$
$523$	3.91862	0.171349	0.0856746	+	0.996323i	$0.472695\pi$
$524$	45.2081	1.97493
$525$	1.39308	0.0607989
$526$	0.972045	0.0423832
$527$	−1.35921	−0.0592081
$528$	−18.0743	−0.786585
$529$	18.3867	0.799422
$530$	−0.299211	−0.0129969
$531$	−7.91336	−0.343411
$532$	−10.8379	−0.469884
$533$	12.9690	0.561752
$534$	−1.22221	−0.0528900
$535$	11.5115	0.497684
$536$	−0.471388	−0.0203609
$537$	−4.52007	−0.195055
$538$	2.18938	0.0943907
$539$	−3.28459	−0.141477
$540$	11.2628	0.484675
$541$	32.3998	1.39298	0.696489	−	0.717568i	$-0.254745\pi$
$541$	32.3998	1.39298	0.696489	+	0.717568i	$0.254745\pi$
$542$	−0.312337	−0.0134160
$543$	−10.0123	−0.429670
$544$	−3.41650	−0.146481
$545$	−0.737245	−0.0315801
$546$	0.567950	0.0243060
$547$	18.2757	0.781414	0.390707	−	0.920515i	$-0.372231\pi$
$547$	18.2757	0.781414	0.390707	+	0.920515i	$0.372231\pi$
$548$	4.40722	0.188267
$549$	−3.17308	−0.135424
$550$	0.299802	0.0127836
$551$	−48.8737	−2.08209
$552$	3.26523	0.138977
$553$	4.21285	0.179149
$554$	−0.727832	−0.0309226
$555$	9.74617	0.413702
$556$	4.71589	0.199998
$557$	−15.3175	−0.649022	−0.324511	−	0.945882i	$-0.605200\pi$
$557$	−15.3175	−0.649022	−0.324511	+	0.945882i	$0.605200\pi$
$558$	−0.0418996	−0.00177375
$559$	30.0113	1.26934
$560$	3.95008	0.166921
$561$	−14.3522	−0.605952
$562$	−1.52802	−0.0644558
$563$	−39.3470	−1.65828	−0.829140	−	0.559041i	$-0.811169\pi$
$563$	−39.3470	−1.65828	−0.829140	+	0.559041i	$0.811169\pi$
$564$	10.3893	0.437470
$565$	−18.8082	−0.791266
$566$	−1.63064	−0.0685411
$567$	−4.69980	−0.197373
$568$	−4.37603	−0.183614
$569$	28.0906	1.17762	0.588809	−	0.808272i	$-0.299597\pi$
$569$	28.0906	1.17762	0.588809	+	0.808272i	$0.299597\pi$
$570$	−0.691923	−0.0289815
$571$	2.07078	0.0866593	0.0433297	−	0.999061i	$-0.486203\pi$
$571$	2.07078	0.0866593	0.0433297	+	0.999061i	$0.486203\pi$
$572$	−29.2200	−1.22175
$573$	24.2093	1.01136
$574$	0.265021	0.0110617
$575$	6.43325	0.268285
$576$	8.26361	0.344317
$577$	−26.9641	−1.12253	−0.561266	−	0.827635i	$-0.689686\pi$
$577$	−26.9641	−1.12253	−0.561266	+	0.827635i	$0.689686\pi$
$578$	0.653675	0.0271893
$579$	−7.98215	−0.331727
$580$	17.8881	0.742762
$581$	12.2113	0.506609
$582$	−0.452130	−0.0187414
$583$	−10.7673	−0.445934
$584$	−3.94223	−0.163131
$585$	4.73168	0.195631
$586$	−2.83358	−0.117054
$587$	−26.3491	−1.08754	−0.543772	−	0.839233i	$-0.683005\pi$
$587$	−26.3491	−1.08754	−0.543772	+	0.839233i	$0.683005\pi$
$588$	−2.77455	−0.114420
$589$	−2.35805	−0.0971617
$590$	−0.681837	−0.0280708
$591$	−26.8949	−1.10631
$592$	27.6353	1.13581
$593$	−0.461528	−0.0189527	−0.00947635	−	0.999955i	$-0.503016\pi$
$593$	−0.461528	−0.0189527	−0.00947635	+	0.999955i	$0.503016\pi$
$594$	−1.69537	−0.0695619
$595$	3.13663	0.128589
$596$	−24.1490	−0.989181
$597$	−18.1966	−0.744739
$598$	2.62280	0.107254
$599$	−34.2624	−1.39992	−0.699961	−	0.714181i	$-0.746799\pi$
$599$	−34.2624	−1.39992	−0.699961	+	0.714181i	$0.746799\pi$
$600$	0.507555	0.0207208
$601$	4.82272	0.196723	0.0983614	−	0.995151i	$-0.468640\pi$
$601$	4.82272	0.196723	0.0983614	+	0.995151i	$0.468640\pi$
$602$	0.613277	0.0249953
$603$	1.37058	0.0558143
$604$	22.4373	0.912959
$605$	−0.211465	−0.00859726
$606$	1.55274	0.0630758
$607$	−13.2768	−0.538887	−0.269443	−	0.963016i	$-0.586840\pi$
$607$	−13.2768	−0.538887	−0.269443	+	0.963016i	$0.586840\pi$
$608$	−5.92717	−0.240378
$609$	−12.5118	−0.507006
$610$	−0.273401	−0.0110697
$611$	16.7254	0.676638
$612$	6.61780	0.267509
$613$	−25.1532	−1.01593	−0.507965	−	0.861378i	$-0.669602\pi$
$613$	−25.1532	−1.01593	−0.507965	+	0.861378i	$0.669602\pi$
$614$	1.08659	0.0438512
$615$	−4.04484	−0.163104
$616$	−1.19671	−0.0482168
$617$	17.9264	0.721690	0.360845	−	0.932626i	$-0.382488\pi$
$617$	17.9264	0.721690	0.360845	+	0.932626i	$0.382488\pi$
$618$	1.15841	0.0465981
$619$	40.7720	1.63877	0.819383	−	0.573247i	$-0.194316\pi$
$619$	40.7720	1.63877	0.819383	+	0.573247i	$0.194316\pi$
$620$	0.863059	0.0346613
$621$	−36.3798	−1.45987
$622$	−1.34455	−0.0539116
$623$	9.61205	0.385099
$624$	−24.5789	−0.983945
$625$	1.00000	0.0400000
$626$	0.00193764	7.74436e−5 0
$627$	−24.8992	−0.994379
$628$	11.8453	0.472677
$629$	21.9443	0.874976
$630$	0.0966912	0.00385227
$631$	−12.7986	−0.509506	−0.254753	−	0.967006i	$-0.581994\pi$
$631$	−12.7986	−0.509506	−0.254753	+	0.967006i	$0.581994\pi$
$632$	1.53491	0.0610556
$633$	−23.8361	−0.947400
$634$	1.97077	0.0782693
$635$	−13.7778	−0.546755
$636$	−9.09528	−0.360651
$637$	−4.46665	−0.176975
$638$	−2.69266	−0.106603
$639$	12.7235	0.503334
$640$	2.89047	0.114256
$641$	−29.7696	−1.17583	−0.587914	−	0.808923i	$-0.700051\pi$
$641$	−29.7696	−1.17583	−0.587914	+	0.808923i	$0.700051\pi$
$642$	−1.46372	−0.0577685
$643$	−14.9518	−0.589642	−0.294821	−	0.955553i	$-0.595260\pi$
$643$	−14.9518	−0.589642	−0.294821	+	0.955553i	$0.595260\pi$
$644$	−12.8129	−0.504899
$645$	−9.36006	−0.368552
$646$	−1.55792	−0.0612956
$647$	−10.9196	−0.429293	−0.214646	−	0.976692i	$-0.568860\pi$
$647$	−10.9196	−0.429293	−0.214646	+	0.976692i	$0.568860\pi$
$648$	−1.71233	−0.0672667
$649$	−24.5363	−0.963133
$650$	0.407695	0.0159911
$651$	−0.603669	−0.0236596
$652$	21.5011	0.842049
$653$	25.1484	0.984135	0.492067	−	0.870557i	$-0.336241\pi$
$653$	25.1484	0.984135	0.492067	+	0.870557i	$0.336241\pi$
$654$	0.0937434	0.00366566
$655$	−22.6986	−0.886909
$656$	−11.4692	−0.447796
$657$	11.4622	0.447183
$658$	0.341781	0.0133240
$659$	22.6846	0.883668	0.441834	−	0.897097i	$-0.354328\pi$
$659$	22.6846	0.883668	0.441834	+	0.897097i	$0.354328\pi$
$660$	9.11326	0.354733
$661$	3.87538	0.150735	0.0753674	−	0.997156i	$-0.475987\pi$
$661$	3.87538	0.150735	0.0753674	+	0.997156i	$0.475987\pi$
$662$	0.256665	0.00997556
$663$	−19.5173	−0.757989
$664$	4.44907	0.172657
$665$	5.44163	0.211017
$666$	0.676465	0.0262125
$667$	−57.7799	−2.23725
$668$	24.3667	0.942776
$669$	32.8743	1.27099
$670$	0.118093	0.00456233
$671$	−9.83849	−0.379811
$672$	−1.51738	−0.0585341
$673$	−4.27162	−0.164659	−0.0823294	−	0.996605i	$-0.526236\pi$
$673$	−4.27162	−0.164659	−0.0823294	+	0.996605i	$0.526236\pi$
$674$	−2.35839	−0.0908417
$675$	−5.65497	−0.217660
$676$	−13.8440	−0.532460
$677$	4.56127	0.175304	0.0876518	−	0.996151i	$-0.472064\pi$
$677$	4.56127	0.175304	0.0876518	+	0.996151i	$0.472064\pi$
$678$	2.39153	0.0918460
$679$	3.55578	0.136458
$680$	1.14280	0.0438244
$681$	−34.5708	−1.32476
$682$	−0.129915	−0.00497469
$683$	−18.2544	−0.698487	−0.349244	−	0.937032i	$-0.613561\pi$
$683$	−18.2544	−0.698487	−0.349244	+	0.937032i	$0.613561\pi$
$684$	11.4810	0.438987
$685$	−2.21283	−0.0845478
$686$	−0.0912753	−0.00348491
$687$	−1.39308	−0.0531492
$688$	−26.5405	−1.01185
$689$	−14.6422	−0.557822
$690$	−0.818011	−0.0311411
$691$	28.6186	1.08870	0.544352	−	0.838857i	$-0.316776\pi$
$691$	28.6186	1.08870	0.544352	+	0.838857i	$0.316776\pi$
$692$	−35.4561	−1.34784
$693$	3.47948	0.132175
$694$	−1.46199	−0.0554963
$695$	−2.36781	−0.0898160
$696$	−4.55858	−0.172792
$697$	−9.10729	−0.344963
$698$	−0.275864	−0.0104416
$699$	−22.5609	−0.853331
$700$	−1.99167	−0.0752780
$701$	35.0867	1.32521	0.662603	−	0.748970i	$-0.269452\pi$
$701$	35.0867	1.32521	0.662603	+	0.748970i	$0.269452\pi$
$702$	−2.30550	−0.0870155
$703$	38.0704	1.43585
$704$	25.6223	0.965675
$705$	−5.21639	−0.196461
$706$	−2.31767	−0.0872265
$707$	−12.2115	−0.459262
$708$	−20.7262	−0.778938
$709$	6.56374	0.246506	0.123253	−	0.992375i	$-0.460667\pi$
$709$	6.56374	0.246506	0.123253	+	0.992375i	$0.460667\pi$
$710$	1.09629	0.0411431
$711$	−4.46282	−0.167369
$712$	3.50206	0.131245
$713$	−2.78775	−0.104402
$714$	−0.398833	−0.0149260
$715$	14.6711	0.548668
$716$	6.46230	0.241508
$717$	3.83601	0.143258
$718$	−1.91116	−0.0713240
$719$	−38.0218	−1.41798	−0.708988	−	0.705221i	$-0.750848\pi$
$719$	−38.0218	−1.41798	−0.708988	+	0.705221i	$0.750848\pi$
$720$	−4.18446	−0.155946
$721$	−9.11033	−0.339286
$722$	−0.968555	−0.0360459
$723$	2.74053	0.101921
$724$	14.3145	0.531995
$725$	−8.98145	−0.333563
$726$	0.0268885	0.000997925 0
$727$	0.957673	0.0355181	0.0177591	−	0.999842i	$-0.494347\pi$
$727$	0.957673	0.0355181	0.0177591	+	0.999842i	$0.494347\pi$
$728$	−1.62738	−0.0603148
$729$	28.6121	1.05971
$730$	0.987615	0.0365533
$731$	−21.0749	−0.779485
$732$	−8.31073	−0.307174
$733$	−15.7838	−0.582988	−0.291494	−	0.956573i	$-0.594152\pi$
$733$	−15.7838	−0.582988	−0.291494	+	0.956573i	$0.594152\pi$
$734$	2.25604	0.0832719
$735$	1.39308	0.0513844
$736$	−7.00727	−0.258291
$737$	4.24964	0.156538
$738$	−0.280746	−0.0103344
$739$	−43.5255	−1.60111	−0.800556	−	0.599259i	$-0.795462\pi$
$739$	−43.5255	−1.60111	−0.800556	+	0.599259i	$0.795462\pi$
$740$	−13.9340	−0.512224
$741$	−33.8599	−1.24388
$742$	−0.299211	−0.0109844
$743$	16.2523	0.596239	0.298120	−	0.954529i	$-0.403641\pi$
$743$	16.2523	0.596239	0.298120	+	0.954529i	$0.403641\pi$
$744$	−0.219941	−0.00806343
$745$	12.1250	0.444226
$746$	3.31735	0.121457
$747$	−12.9358	−0.473298
$748$	20.5192	0.750258
$749$	11.5115	0.420619
$750$	−0.127154	−0.00464299
$751$	−16.2769	−0.593951	−0.296976	−	0.954885i	$-0.595978\pi$
$751$	−16.2769	−0.593951	−0.296976	+	0.954885i	$0.595978\pi$
$752$	−14.7911	−0.539377
$753$	−24.0616	−0.876855
$754$	−3.66169	−0.133351
$755$	−11.2656	−0.409995
$756$	11.2628	0.409625
$757$	20.0155	0.727476	0.363738	−	0.931501i	$-0.381500\pi$
$757$	20.0155	0.727476	0.363738	+	0.931501i	$0.381500\pi$
$758$	−2.64721	−0.0961508
$759$	−29.4365	−1.06848
$760$	1.98261	0.0719168
$761$	0.439370	0.0159271	0.00796357	−	0.999968i	$-0.497465\pi$
$761$	0.439370	0.0159271	0.00796357	+	0.999968i	$0.497465\pi$
$762$	1.75189	0.0634644
$763$	−0.737245	−0.0266901
$764$	−34.6117	−1.25221
$765$	−3.32274	−0.120134
$766$	2.42414	0.0875878
$767$	−33.3664	−1.20479
$768$	21.3665	0.770999
$769$	−25.4850	−0.919014	−0.459507	−	0.888174i	$-0.651974\pi$
$769$	−25.4850	−0.919014	−0.459507	+	0.888174i	$0.651974\pi$
$770$	0.299802	0.0108041
$771$	−42.3363	−1.52470
$772$	11.4120	0.410727
$773$	22.2581	0.800567	0.400283	−	0.916391i	$-0.368912\pi$
$773$	22.2581	0.800567	0.400283	+	0.916391i	$0.368912\pi$
$774$	−0.649666	−0.0233518
$775$	−0.433335	−0.0155658
$776$	1.29552	0.0465063
$777$	9.74617	0.349642
$778$	−3.32714	−0.119284
$779$	−15.7999	−0.566092
$780$	12.3929	0.443738
$781$	39.4507	1.41166
$782$	−1.84182	−0.0658632
$783$	50.7898	1.81508
$784$	3.95008	0.141074
$785$	−5.94740	−0.212272
$786$	2.88621	0.102948
$787$	38.0516	1.35639	0.678197	−	0.734880i	$-0.262762\pi$
$787$	38.0516	1.35639	0.678197	+	0.734880i	$0.262762\pi$
$788$	38.4514	1.36977
$789$	−14.8357	−0.528165
$790$	−0.384529	−0.0136809
$791$	−18.8082	−0.668742
$792$	1.26772	0.0450464
$793$	−13.3792	−0.475108
$794$	3.34710	0.118784
$795$	4.56666	0.161963
$796$	26.0155	0.922096
$797$	−1.93650	−0.0685944	−0.0342972	−	0.999412i	$-0.510919\pi$
$797$	−1.93650	−0.0685944	−0.0342972	+	0.999412i	$0.510919\pi$
$798$	−0.691923	−0.0244938
$799$	−11.7451	−0.415513
$800$	−1.08923	−0.0385100
$801$	−10.1824	−0.359777
$802$	−3.38066	−0.119375
$803$	35.5399	1.25417
$804$	3.58974	0.126600
$805$	6.43325	0.226742
$806$	−0.176668	−0.00622287
$807$	−33.4151	−1.17627
$808$	−4.44916	−0.156521
$809$	33.1191	1.16441	0.582203	−	0.813043i	$-0.302191\pi$
$809$	33.1191	1.16441	0.582203	+	0.813043i	$0.302191\pi$
$810$	0.428976	0.0150727
$811$	−36.1465	−1.26927	−0.634637	−	0.772810i	$-0.718850\pi$
$811$	−36.1465	−1.26927	−0.634637	+	0.772810i	$0.718850\pi$
$812$	17.8881	0.627748
$813$	4.76700	0.167186
$814$	2.09746	0.0735158
$815$	−10.7955	−0.378151
$816$	17.2601	0.604226
$817$	−36.5622	−1.27915
$818$	−2.13558	−0.0746688
$819$	4.73168	0.165338
$820$	5.78287	0.201947
$821$	−18.7664	−0.654951	−0.327475	−	0.944860i	$-0.606198\pi$
$821$	−18.7664	−0.654951	−0.327475	+	0.944860i	$0.606198\pi$
$822$	0.281369	0.00981386
$823$	21.1442	0.737039	0.368520	−	0.929620i	$-0.379865\pi$
$823$	21.1442	0.737039	0.368520	+	0.929620i	$0.379865\pi$
$824$	−3.31926	−0.115632
$825$	−4.57569	−0.159305
$826$	−0.681837	−0.0237241
$827$	35.3225	1.22828	0.614142	−	0.789196i	$-0.289502\pi$
$827$	35.3225	1.22828	0.614142	+	0.789196i	$0.289502\pi$
$828$	13.5732	0.471700
$829$	4.60932	0.160088	0.0800442	−	0.996791i	$-0.474494\pi$
$829$	4.60932	0.160088	0.0800442	+	0.996791i	$0.474494\pi$
$830$	−1.11459	−0.0386879
$831$	11.1084	0.385348
$832$	34.8432	1.20797
$833$	3.13663	0.108678
$834$	0.301075	0.0104254
$835$	−12.2343	−0.423386
$836$	35.5982	1.23119
$837$	2.45049	0.0847014
$838$	2.33581	0.0806891
$839$	52.8725	1.82536	0.912681	−	0.408673i	$-0.134008\pi$
$839$	52.8725	1.82536	0.912681	+	0.408673i	$0.134008\pi$
$840$	0.507555	0.0175123
$841$	51.6664	1.78160
$842$	−1.13356	−0.0390652
$843$	23.3213	0.803227
$844$	34.0783	1.17302
$845$	6.95094	0.239120
$846$	−0.362061	−0.0124479
$847$	−0.211465	−0.00726601
$848$	12.9488	0.444664
$849$	24.8875	0.854136
$850$	−0.286297	−0.00981989
$851$	45.0079	1.54285
$852$	33.3246	1.14168
$853$	12.4694	0.426945	0.213473	−	0.976949i	$-0.431523\pi$
$853$	12.4694	0.426945	0.213473	+	0.976949i	$0.431523\pi$
$854$	−0.273401	−0.00935559
$855$	−5.76451	−0.197142
$856$	4.19409	0.143351
$857$	29.8351	1.01915	0.509575	−	0.860427i	$-0.329803\pi$
$857$	29.8351	1.01915	0.509575	+	0.860427i	$0.329803\pi$
$858$	−1.86548	−0.0636866
$859$	40.3673	1.37731	0.688657	−	0.725088i	$-0.258201\pi$
$859$	40.3673	1.37731	0.688657	+	0.725088i	$0.258201\pi$
$860$	13.3820	0.456322
$861$	−4.04484	−0.137848
$862$	1.75903	0.0599128
$863$	7.89203	0.268648	0.134324	−	0.990937i	$-0.457114\pi$
$863$	7.89203	0.268648	0.134324	+	0.990937i	$0.457114\pi$
$864$	6.15954	0.209552
$865$	17.8022	0.605293
$866$	2.32876	0.0791344
$867$	−9.97662	−0.338824
$868$	0.863059	0.0292941
$869$	−13.8375	−0.469405
$870$	1.14202	0.0387182
$871$	5.77900	0.195814
$872$	−0.268609	−0.00909623
$873$	−3.76677	−0.127486
$874$	−3.19531	−0.108083
$875$	1.00000	0.0338062
$876$	30.0211	1.01432
$877$	10.0721	0.340110	0.170055	−	0.985435i	$-0.445606\pi$
$877$	10.0721	0.340110	0.170055	+	0.985435i	$0.445606\pi$
$878$	−1.42786	−0.0481880
$879$	43.2471	1.45869
$880$	−12.9744	−0.437367
$881$	−54.8146	−1.84675	−0.923376	−	0.383897i	$-0.874582\pi$
$881$	−54.8146	−1.84675	−0.923376	+	0.383897i	$0.874582\pi$
$882$	0.0966912	0.00325576
$883$	−36.8268	−1.23932	−0.619660	−	0.784870i	$-0.712729\pi$
$883$	−36.8268	−1.23932	−0.619660	+	0.784870i	$0.712729\pi$
$884$	27.9037	0.938503
$885$	10.4065	0.349809
$886$	0.335677	0.0112773
$887$	15.1972	0.510271	0.255136	−	0.966905i	$-0.417880\pi$
$887$	15.1972	0.510271	0.255136	+	0.966905i	$0.417880\pi$
$888$	3.55093	0.119161
$889$	−13.7778	−0.462092
$890$	−0.877342	−0.0294086
$891$	15.4369	0.517156
$892$	−47.0000	−1.57368
$893$	−20.3763	−0.681865
$894$	−1.54174	−0.0515634
$895$	−3.24467	−0.108457
$896$	2.89047	0.0965638
$897$	−40.0302	−1.33657
$898$	−1.08032	−0.0360506
$899$	3.89197	0.129805
$900$	2.10985	0.0703282
$901$	10.2822	0.342550
$902$	−0.870484	−0.0289839
$903$	−9.36006	−0.311483
$904$	−6.85259	−0.227914
$905$	−7.18720	−0.238910
$906$	1.43246	0.0475901
$907$	−30.6546	−1.01787	−0.508934	−	0.860805i	$-0.669960\pi$
$907$	−30.6546	−1.01787	−0.508934	+	0.860805i	$0.669960\pi$
$908$	49.4256	1.64025
$909$	12.9361	0.429064
$910$	0.407695	0.0135149
$911$	−5.55492	−0.184043	−0.0920214	−	0.995757i	$-0.529333\pi$
$911$	−5.55492	−0.184043	−0.0920214	+	0.995757i	$0.529333\pi$
$912$	29.9441	0.991547
$913$	−40.1091	−1.32742
$914$	−0.415819	−0.0137541
$915$	4.17275	0.137947
$916$	1.99167	0.0658066
$917$	−22.6986	−0.749575
$918$	1.61900	0.0534349
$919$	46.6722	1.53958	0.769788	−	0.638300i	$-0.220362\pi$
$919$	46.6722	1.53958	0.769788	+	0.638300i	$0.220362\pi$
$920$	2.34390	0.0772759
$921$	−16.5839	−0.546459
$922$	0.186075	0.00612806
$923$	53.6481	1.76585
$924$	9.11326	0.299804
$925$	6.99614	0.230032
$926$	−0.272821	−0.00896544
$927$	9.65090	0.316977
$928$	9.78283	0.321137
$929$	14.1732	0.465008	0.232504	−	0.972595i	$-0.425308\pi$
$929$	14.1732	0.465008	0.232504	+	0.972595i	$0.425308\pi$
$930$	0.0551000	0.00180680
$931$	5.44163	0.178342
$932$	32.2551	1.05655
$933$	20.5211	0.671829
$934$	0.386544	0.0126481
$935$	−10.3025	−0.336929
$936$	1.72394	0.0563488
$937$	13.2822	0.433912	0.216956	−	0.976181i	$-0.430387\pi$
$937$	13.2822	0.433912	0.216956	+	0.976181i	$0.430387\pi$
$938$	0.118093	0.00385587
$939$	−0.0295729	−0.000965076 0
$940$	7.45783	0.243247
$941$	−18.4555	−0.601633	−0.300816	−	0.953682i	$-0.597259\pi$
$941$	−18.4555	−0.601633	−0.300816	+	0.953682i	$0.597259\pi$
$942$	0.756233	0.0246394
$943$	−18.6791	−0.608276
$944$	29.5076	0.960390
$945$	−5.65497	−0.183956
$946$	−2.01436	−0.0654926
$947$	50.3752	1.63697	0.818486	−	0.574526i	$-0.194814\pi$
$947$	50.3752	1.63697	0.818486	+	0.574526i	$0.194814\pi$
$948$	−11.6888	−0.379633
$949$	48.3299	1.56886
$950$	−0.496687	−0.0161146
$951$	−30.0786	−0.975366
$952$	1.14280	0.0370384
$953$	−30.4291	−0.985694	−0.492847	−	0.870116i	$-0.664044\pi$
$953$	−30.4291	−0.985694	−0.492847	+	0.870116i	$0.664044\pi$
$954$	0.316964	0.0102621
$955$	17.3783	0.562347
$956$	−5.48430	−0.177375
$957$	41.0963	1.32845
$958$	−2.26525	−0.0731868
$959$	−2.21283	−0.0714559
$960$	−10.8670	−0.350732
$961$	−30.8122	−0.993943
$962$	2.85229	0.0919615
$963$	−12.1945	−0.392962
$964$	−3.91810	−0.126194
$965$	−5.72987	−0.184451
$966$	−0.818011	−0.0263191
$967$	23.1148	0.743321	0.371661	−	0.928369i	$-0.378789\pi$
$967$	23.1148	0.743321	0.371661	+	0.928369i	$0.378789\pi$
$968$	−0.0770452	−0.00247633
$969$	23.7776	0.763845
$970$	−0.324555	−0.0104208
$971$	14.6673	0.470695	0.235347	−	0.971911i	$-0.424377\pi$
$971$	14.6673	0.470695	0.235347	+	0.971911i	$0.424377\pi$
$972$	−20.7486	−0.665513
$973$	−2.36781	−0.0759084
$974$	1.78819	0.0572974
$975$	−6.22239	−0.199276
$976$	11.8319	0.378729
$977$	7.00864	0.224226	0.112113	−	0.993695i	$-0.464238\pi$
$977$	7.00864	0.224226	0.112113	+	0.993695i	$0.464238\pi$
$978$	1.37269	0.0438938
$979$	−31.5716	−1.00903
$980$	−1.99167	−0.0636215
$981$	0.780990	0.0249351
$982$	3.34229	0.106657
$983$	−55.8845	−1.78244	−0.891220	−	0.453571i	$-0.850150\pi$
$983$	−55.8845	−1.78244	−0.891220	+	0.453571i	$0.850150\pi$
$984$	−1.47370	−0.0469799
$985$	−19.3061	−0.615144
$986$	2.57136	0.0818887
$987$	−5.21639	−0.166040
$988$	48.4092	1.54010
$989$	−43.2249	−1.37447
$990$	−0.317591	−0.0100937
$991$	−55.3542	−1.75838	−0.879192	−	0.476468i	$-0.841917\pi$
$991$	−55.3542	−1.75838	−0.879192	+	0.476468i	$0.841917\pi$
$992$	0.472000	0.0149860
$993$	−3.91731	−0.124312
$994$	1.09629	0.0347723
$995$	−13.0622	−0.414099
$996$	−33.8808	−1.07355
$997$	1.93241	0.0611999	0.0306000	−	0.999532i	$-0.490258\pi$
$997$	1.93241	0.0611999	0.0306000	+	0.999532i	$0.490258\pi$
$998$	3.34582	0.105910
$999$	−39.5630	−1.25172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.19	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.19	✓	38	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0912753 q^{2} +1.39308 q^{3} -1.99167 q^{4} +1.00000 q^{5} -0.127154 q^{6} +1.00000 q^{7} +0.364341 q^{8} -1.05934 q^{9} +O(q^{10})\)	\(q-0.0912753 q^{2} +1.39308 q^{3} -1.99167 q^{4} +1.00000 q^{5} -0.127154 q^{6} +1.00000 q^{7} +0.364341 q^{8} -1.05934 q^{9} -0.0912753 q^{10} -3.28459 q^{11} -2.77455 q^{12} -4.46665 q^{13} -0.0912753 q^{14} +1.39308 q^{15} +3.95008 q^{16} +3.13663 q^{17} +0.0966912 q^{18} +5.44163 q^{19} -1.99167 q^{20} +1.39308 q^{21} +0.299802 q^{22} +6.43325 q^{23} +0.507555 q^{24} +1.00000 q^{25} +0.407695 q^{26} -5.65497 q^{27} -1.99167 q^{28} -8.98145 q^{29} -0.127154 q^{30} -0.433335 q^{31} -1.08923 q^{32} -4.57569 q^{33} -0.286297 q^{34} +1.00000 q^{35} +2.10985 q^{36} +6.99614 q^{37} -0.496687 q^{38} -6.22239 q^{39} +0.364341 q^{40} -2.90353 q^{41} -0.127154 q^{42} -6.71898 q^{43} +6.54182 q^{44} -1.05934 q^{45} -0.587197 q^{46} -3.74451 q^{47} +5.50277 q^{48} +1.00000 q^{49} -0.0912753 q^{50} +4.36956 q^{51} +8.89608 q^{52} +3.27811 q^{53} +0.516159 q^{54} -3.28459 q^{55} +0.364341 q^{56} +7.58061 q^{57} +0.819784 q^{58} +7.47012 q^{59} -2.77455 q^{60} +2.99535 q^{61} +0.0395527 q^{62} -1.05934 q^{63} -7.80075 q^{64} -4.46665 q^{65} +0.417647 q^{66} -1.29381 q^{67} -6.24712 q^{68} +8.96201 q^{69} -0.0912753 q^{70} -12.0108 q^{71} -0.385959 q^{72} -10.8202 q^{73} -0.638575 q^{74} +1.39308 q^{75} -10.8379 q^{76} -3.28459 q^{77} +0.567950 q^{78} +4.21285 q^{79} +3.95008 q^{80} -4.69980 q^{81} +0.265021 q^{82} +12.2113 q^{83} -2.77455 q^{84} +3.13663 q^{85} +0.613277 q^{86} -12.5118 q^{87} -1.19671 q^{88} +9.61205 q^{89} +0.0966912 q^{90} -4.46665 q^{91} -12.8129 q^{92} -0.603669 q^{93} +0.341781 q^{94} +5.44163 q^{95} -1.51738 q^{96} +3.55578 q^{97} -0.0912753 q^{98} +3.47948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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