LMFDB - Embedded newform 8018.2.a.g.1.14

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:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00694 q^{3} +1.00000 q^{4} -1.74347 q^{5} +1.00694 q^{6} -4.04026 q^{7} -1.00000 q^{8} -1.98607 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00694 q^{3} +1.00000 q^{4} -1.74347 q^{5} +1.00694 q^{6} -4.04026 q^{7} -1.00000 q^{8} -1.98607 q^{9} +1.74347 q^{10} -4.02824 q^{11} -1.00694 q^{12} -3.01690 q^{13} +4.04026 q^{14} +1.75558 q^{15} +1.00000 q^{16} -0.409943 q^{17} +1.98607 q^{18} +1.00000 q^{19} -1.74347 q^{20} +4.06831 q^{21} +4.02824 q^{22} +4.34541 q^{23} +1.00694 q^{24} -1.96030 q^{25} +3.01690 q^{26} +5.02068 q^{27} -4.04026 q^{28} +1.15152 q^{29} -1.75558 q^{30} -7.13312 q^{31} -1.00000 q^{32} +4.05621 q^{33} +0.409943 q^{34} +7.04409 q^{35} -1.98607 q^{36} +10.6393 q^{37} -1.00000 q^{38} +3.03785 q^{39} +1.74347 q^{40} +7.02573 q^{41} -4.06831 q^{42} -1.02930 q^{43} -4.02824 q^{44} +3.46265 q^{45} -4.34541 q^{46} +0.0143463 q^{47} -1.00694 q^{48} +9.32371 q^{49} +1.96030 q^{50} +0.412789 q^{51} -3.01690 q^{52} -3.62887 q^{53} -5.02068 q^{54} +7.02314 q^{55} +4.04026 q^{56} -1.00694 q^{57} -1.15152 q^{58} +2.69333 q^{59} +1.75558 q^{60} +3.44330 q^{61} +7.13312 q^{62} +8.02422 q^{63} +1.00000 q^{64} +5.25989 q^{65} -4.05621 q^{66} -4.17380 q^{67} -0.409943 q^{68} -4.37558 q^{69} -7.04409 q^{70} -11.9178 q^{71} +1.98607 q^{72} +13.1562 q^{73} -10.6393 q^{74} +1.97391 q^{75} +1.00000 q^{76} +16.2752 q^{77} -3.03785 q^{78} +16.7663 q^{79} -1.74347 q^{80} +0.902653 q^{81} -7.02573 q^{82} -3.77607 q^{83} +4.06831 q^{84} +0.714725 q^{85} +1.02930 q^{86} -1.15952 q^{87} +4.02824 q^{88} +5.73192 q^{89} -3.46265 q^{90} +12.1891 q^{91} +4.34541 q^{92} +7.18265 q^{93} -0.0143463 q^{94} -1.74347 q^{95} +1.00694 q^{96} +0.191234 q^{97} -9.32371 q^{98} +8.00036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00694	−0.581359	−0.290679	−	0.956820i	$-0.593881\pi$
$3$	−1.00694	−0.581359	−0.290679	+	0.956820i	$0.593881\pi$
$4$	1.00000	0.500000
$5$	−1.74347	−0.779705	−0.389853	−	0.920877i	$-0.627474\pi$
$5$	−1.74347	−0.779705	−0.389853	+	0.920877i	$0.627474\pi$
$6$	1.00694	0.411083
$7$	−4.04026	−1.52707	−0.763537	−	0.645763i	$-0.776539\pi$
$7$	−4.04026	−1.52707	−0.763537	+	0.645763i	$0.776539\pi$
$8$	−1.00000	−0.353553
$9$	−1.98607	−0.662022
$10$	1.74347	0.551335
$11$	−4.02824	−1.21456	−0.607281	−	0.794487i	$-0.707740\pi$
$11$	−4.02824	−1.21456	−0.607281	+	0.794487i	$0.707740\pi$
$12$	−1.00694	−0.290679
$13$	−3.01690	−0.836738	−0.418369	−	0.908277i	$-0.637398\pi$
$13$	−3.01690	−0.836738	−0.418369	+	0.908277i	$0.637398\pi$
$14$	4.04026	1.07981
$15$	1.75558	0.453289
$16$	1.00000	0.250000
$17$	−0.409943	−0.0994258	−0.0497129	−	0.998764i	$-0.515831\pi$
$17$	−0.409943	−0.0994258	−0.0497129	+	0.998764i	$0.515831\pi$
$18$	1.98607	0.468120
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.74347	−0.389853
$21$	4.06831	0.887779
$22$	4.02824	0.858824
$23$	4.34541	0.906081	0.453040	−	0.891490i	$-0.350339\pi$
$23$	4.34541	0.906081	0.453040	+	0.891490i	$0.350339\pi$
$24$	1.00694	0.205541
$25$	−1.96030	−0.392060
$26$	3.01690	0.591663
$27$	5.02068	0.966231
$28$	−4.04026	−0.763537
$29$	1.15152	0.213832	0.106916	−	0.994268i	$-0.465902\pi$
$29$	1.15152	0.213832	0.106916	+	0.994268i	$0.465902\pi$
$30$	−1.75558	−0.320523
$31$	−7.13312	−1.28115	−0.640573	−	0.767897i	$-0.721303\pi$
$31$	−7.13312	−1.28115	−0.640573	+	0.767897i	$0.721303\pi$
$32$	−1.00000	−0.176777
$33$	4.05621	0.706096
$34$	0.409943	0.0703047
$35$	7.04409	1.19067
$36$	−1.98607	−0.331011
$37$	10.6393	1.74910	0.874548	−	0.484940i	$-0.161158\pi$
$37$	10.6393	1.74910	0.874548	+	0.484940i	$0.161158\pi$
$38$	−1.00000	−0.162221
$39$	3.03785	0.486445
$40$	1.74347	0.275667
$41$	7.02573	1.09724	0.548618	−	0.836073i	$-0.315154\pi$
$41$	7.02573	1.09724	0.548618	+	0.836073i	$0.315154\pi$
$42$	−4.06831	−0.627754
$43$	−1.02930	−0.156967	−0.0784834	−	0.996915i	$-0.525008\pi$
$43$	−1.02930	−0.156967	−0.0784834	+	0.996915i	$0.525008\pi$
$44$	−4.02824	−0.607281
$45$	3.46265	0.516182
$46$	−4.34541	−0.640696
$47$	0.0143463	0.00209262	0.00104631	−	0.999999i	$-0.499667\pi$
$47$	0.0143463	0.00209262	0.00104631	+	0.999999i	$0.499667\pi$
$48$	−1.00694	−0.145340
$49$	9.32371	1.33196
$50$	1.96030	0.277228
$51$	0.412789	0.0578021
$52$	−3.01690	−0.418369
$53$	−3.62887	−0.498464	−0.249232	−	0.968444i	$-0.580178\pi$
$53$	−3.62887	−0.498464	−0.249232	+	0.968444i	$0.580178\pi$
$54$	−5.02068	−0.683229
$55$	7.02314	0.947000
$56$	4.04026	0.539903
$57$	−1.00694	−0.133373
$58$	−1.15152	−0.151202
$59$	2.69333	0.350642	0.175321	−	0.984511i	$-0.443904\pi$
$59$	2.69333	0.350642	0.175321	+	0.984511i	$0.443904\pi$
$60$	1.75558	0.226644
$61$	3.44330	0.440870	0.220435	−	0.975402i	$-0.429252\pi$
$61$	3.44330	0.440870	0.220435	+	0.975402i	$0.429252\pi$
$62$	7.13312	0.905908
$63$	8.02422	1.01096
$64$	1.00000	0.125000
$65$	5.25989	0.652409
$66$	−4.05621	−0.499285
$67$	−4.17380	−0.509911	−0.254956	−	0.966953i	$-0.582061\pi$
$67$	−4.17380	−0.509911	−0.254956	+	0.966953i	$0.582061\pi$
$68$	−0.409943	−0.0497129
$69$	−4.37558	−0.526758
$70$	−7.04409	−0.841930
$71$	−11.9178	−1.41438	−0.707191	−	0.707023i	$-0.750038\pi$
$71$	−11.9178	−1.41438	−0.707191	+	0.707023i	$0.750038\pi$
$72$	1.98607	0.234060
$73$	13.1562	1.53982	0.769908	−	0.638155i	$-0.220302\pi$
$73$	13.1562	1.53982	0.769908	+	0.638155i	$0.220302\pi$
$74$	−10.6393	−1.23680
$75$	1.97391	0.227927
$76$	1.00000	0.114708
$77$	16.2752	1.85473
$78$	−3.03785	−0.343969
$79$	16.7663	1.88636	0.943178	−	0.332288i	$-0.107821\pi$
$79$	16.7663	1.88636	0.943178	+	0.332288i	$0.107821\pi$
$80$	−1.74347	−0.194926
$81$	0.902653	0.100295
$82$	−7.02573	−0.775863
$83$	−3.77607	−0.414478	−0.207239	−	0.978290i	$-0.566448\pi$
$83$	−3.77607	−0.414478	−0.207239	+	0.978290i	$0.566448\pi$
$84$	4.06831	0.443889
$85$	0.714725	0.0775228
$86$	1.02930	0.110992
$87$	−1.15952	−0.124313
$88$	4.02824	0.429412
$89$	5.73192	0.607582	0.303791	−	0.952739i	$-0.401748\pi$
$89$	5.73192	0.607582	0.303791	+	0.952739i	$0.401748\pi$
$90$	−3.46265	−0.364996
$91$	12.1891	1.27776
$92$	4.34541	0.453040
$93$	7.18265	0.744806
$94$	−0.0143463	−0.00147971
$95$	−1.74347	−0.178877
$96$	1.00694	0.102771
$97$	0.191234	0.0194169	0.00970845	−	0.999953i	$-0.496910\pi$
$97$	0.191234	0.0194169	0.00970845	+	0.999953i	$0.496910\pi$
$98$	−9.32371	−0.941837
$99$	8.00036	0.804066
$100$	−1.96030	−0.196030
$101$	−3.82322	−0.380425	−0.190212	−	0.981743i	$-0.560918\pi$
$101$	−3.82322	−0.380425	−0.190212	+	0.981743i	$0.560918\pi$
$102$	−0.412789	−0.0408722
$103$	−4.03067	−0.397154	−0.198577	−	0.980085i	$-0.563632\pi$
$103$	−4.03067	−0.397154	−0.198577	+	0.980085i	$0.563632\pi$
$104$	3.01690	0.295832
$105$	−7.09300	−0.692206
$106$	3.62887	0.352467
$107$	5.33038	0.515307	0.257653	−	0.966237i	$-0.417051\pi$
$107$	5.33038	0.515307	0.257653	+	0.966237i	$0.417051\pi$
$108$	5.02068	0.483116
$109$	2.44508	0.234196	0.117098	−	0.993120i	$-0.462641\pi$
$109$	2.44508	0.234196	0.117098	+	0.993120i	$0.462641\pi$
$110$	−7.02314	−0.669630
$111$	−10.7132	−1.01685
$112$	−4.04026	−0.381769
$113$	1.93094	0.181648	0.0908238	−	0.995867i	$-0.471050\pi$
$113$	1.93094	0.181648	0.0908238	+	0.995867i	$0.471050\pi$
$114$	1.00694	0.0943089
$115$	−7.57611	−0.706476
$116$	1.15152	0.106916
$117$	5.99176	0.553939
$118$	−2.69333	−0.247941
$119$	1.65628	0.151831
$120$	−1.75558	−0.160262
$121$	5.22675	0.475159
$122$	−3.44330	−0.311742
$123$	−7.07451	−0.637887
$124$	−7.13312	−0.640573
$125$	12.1351	1.08540
$126$	−8.02422	−0.714855
$127$	−21.6697	−1.92287	−0.961437	−	0.275026i	$-0.911314\pi$
$127$	−21.6697	−1.92287	−0.961437	+	0.275026i	$0.911314\pi$
$128$	−1.00000	−0.0883883
$129$	1.03645	0.0912541
$130$	−5.25989	−0.461323
$131$	−6.43281	−0.562037	−0.281018	−	0.959702i	$-0.590672\pi$
$131$	−6.43281	−0.562037	−0.281018	+	0.959702i	$0.590672\pi$
$132$	4.05621	0.353048
$133$	−4.04026	−0.350335
$134$	4.17380	0.360562
$135$	−8.75343	−0.753376
$136$	0.409943	0.0351523
$137$	−4.03310	−0.344571	−0.172286	−	0.985047i	$-0.555115\pi$
$137$	−4.03310	−0.344571	−0.172286	+	0.985047i	$0.555115\pi$
$138$	4.37558	0.372474
$139$	12.9535	1.09870	0.549350	−	0.835593i	$-0.314875\pi$
$139$	12.9535	1.09870	0.549350	+	0.835593i	$0.314875\pi$
$140$	7.04409	0.595334
$141$	−0.0144459	−0.00121656
$142$	11.9178	1.00012
$143$	12.1528	1.01627
$144$	−1.98607	−0.165505
$145$	−2.00765	−0.166726
$146$	−13.1562	−1.08881
$147$	−9.38844	−0.774346
$148$	10.6393	0.874548
$149$	−1.48931	−0.122009	−0.0610045	−	0.998137i	$-0.519430\pi$
$149$	−1.48931	−0.122009	−0.0610045	+	0.998137i	$0.519430\pi$
$150$	−1.97391	−0.161169
$151$	0.0944794	0.00768862	0.00384431	−	0.999993i	$-0.498776\pi$
$151$	0.0944794	0.00768862	0.00384431	+	0.999993i	$0.498776\pi$
$152$	−1.00000	−0.0811107
$153$	0.814174	0.0658221
$154$	−16.2752	−1.31149
$155$	12.4364	0.998917
$156$	3.03785	0.243223
$157$	−14.7283	−1.17544	−0.587722	−	0.809063i	$-0.699975\pi$
$157$	−14.7283	−1.17544	−0.587722	+	0.809063i	$0.699975\pi$
$158$	−16.7663	−1.33386
$159$	3.65407	0.289786
$160$	1.74347	0.137834
$161$	−17.5566	−1.38365
$162$	−0.902653	−0.0709191
$163$	15.1273	1.18486	0.592430	−	0.805622i	$-0.298169\pi$
$163$	15.1273	1.18486	0.592430	+	0.805622i	$0.298169\pi$
$164$	7.02573	0.548618
$165$	−7.07190	−0.550547
$166$	3.77607	0.293080
$167$	5.93671	0.459396	0.229698	−	0.973262i	$-0.426226\pi$
$167$	5.93671	0.459396	0.229698	+	0.973262i	$0.426226\pi$
$168$	−4.06831	−0.313877
$169$	−3.89830	−0.299870
$170$	−0.714725	−0.0548169
$171$	−1.98607	−0.151878
$172$	−1.02930	−0.0784834
$173$	−24.6269	−1.87234	−0.936172	−	0.351541i	$-0.885658\pi$
$173$	−24.6269	−1.87234	−0.936172	+	0.351541i	$0.885658\pi$
$174$	1.15952	0.0879026
$175$	7.92011	0.598704
$176$	−4.02824	−0.303640
$177$	−2.71203	−0.203849
$178$	−5.73192	−0.429625
$179$	7.28031	0.544156	0.272078	−	0.962275i	$-0.412289\pi$
$179$	7.28031	0.544156	0.272078	+	0.962275i	$0.412289\pi$
$180$	3.46265	0.258091
$181$	−6.91862	−0.514257	−0.257128	−	0.966377i	$-0.582776\pi$
$181$	−6.91862	−0.514257	−0.257128	+	0.966377i	$0.582776\pi$
$182$	−12.1891	−0.903514
$183$	−3.46721	−0.256303
$184$	−4.34541	−0.320348
$185$	−18.5494	−1.36378
$186$	−7.18265	−0.526657
$187$	1.65135	0.120759
$188$	0.0143463	0.00104631
$189$	−20.2849	−1.47551
$190$	1.74347	0.126485
$191$	−1.76685	−0.127845	−0.0639225	−	0.997955i	$-0.520361\pi$
$191$	−1.76685	−0.127845	−0.0639225	+	0.997955i	$0.520361\pi$
$192$	−1.00694	−0.0726699
$193$	−5.81089	−0.418277	−0.209138	−	0.977886i	$-0.567066\pi$
$193$	−5.81089	−0.418277	−0.209138	+	0.977886i	$0.567066\pi$
$194$	−0.191234	−0.0137298
$195$	−5.29641	−0.379284
$196$	9.32371	0.665979
$197$	21.3406	1.52045	0.760227	−	0.649658i	$-0.225088\pi$
$197$	21.3406	1.52045	0.760227	+	0.649658i	$0.225088\pi$
$198$	−8.00036	−0.568561
$199$	22.2980	1.58066	0.790330	−	0.612681i	$-0.209909\pi$
$199$	22.2980	1.58066	0.790330	+	0.612681i	$0.209909\pi$
$200$	1.96030	0.138614
$201$	4.20278	0.296441
$202$	3.82322	0.269001
$203$	−4.65244	−0.326537
$204$	0.412789	0.0289010
$205$	−12.2492	−0.855520
$206$	4.03067	0.280830
$207$	−8.63027	−0.599845
$208$	−3.01690	−0.209184
$209$	−4.02824	−0.278639
$210$	7.09300	0.489463
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−3.62887	−0.249232
$213$	12.0005	0.822263
$214$	−5.33038	−0.364377
$215$	1.79456	0.122388
$216$	−5.02068	−0.341614
$217$	28.8197	1.95641
$218$	−2.44508	−0.165602
$219$	−13.2475	−0.895186
$220$	7.02314	0.473500
$221$	1.23676	0.0831934
$222$	10.7132	0.719023
$223$	−1.70994	−0.114506	−0.0572529	−	0.998360i	$-0.518234\pi$
$223$	−1.70994	−0.114506	−0.0572529	+	0.998360i	$0.518234\pi$
$224$	4.04026	0.269951
$225$	3.89328	0.259552
$226$	−1.93094	−0.128444
$227$	−13.3874	−0.888554	−0.444277	−	0.895889i	$-0.646539\pi$
$227$	−13.3874	−0.888554	−0.444277	+	0.895889i	$0.646539\pi$
$228$	−1.00694	−0.0666864
$229$	−17.1110	−1.13073	−0.565364	−	0.824842i	$-0.691264\pi$
$229$	−17.1110	−1.13073	−0.565364	+	0.824842i	$0.691264\pi$
$230$	7.57611	0.499554
$231$	−16.3882	−1.07826
$232$	−1.15152	−0.0756010
$233$	9.44988	0.619082	0.309541	−	0.950886i	$-0.399825\pi$
$233$	9.44988	0.619082	0.309541	+	0.950886i	$0.399825\pi$
$234$	−5.99176	−0.391694
$235$	−0.0250124	−0.00163163
$236$	2.69333	0.175321
$237$	−16.8827	−1.09665
$238$	−1.65628	−0.107361
$239$	3.75711	0.243027	0.121514	−	0.992590i	$-0.461225\pi$
$239$	3.75711	0.243027	0.121514	+	0.992590i	$0.461225\pi$
$240$	1.75558	0.113322
$241$	−8.80684	−0.567298	−0.283649	−	0.958928i	$-0.591545\pi$
$241$	−8.80684	−0.567298	−0.283649	+	0.958928i	$0.591545\pi$
$242$	−5.22675	−0.335988
$243$	−15.9710	−1.02454
$244$	3.44330	0.220435
$245$	−16.2556	−1.03853
$246$	7.07451	0.451055
$247$	−3.01690	−0.191961
$248$	7.13312	0.452954
$249$	3.80229	0.240960
$250$	−12.1351	−0.767491
$251$	−3.83750	−0.242221	−0.121110	−	0.992639i	$-0.538646\pi$
$251$	−3.83750	−0.242221	−0.121110	+	0.992639i	$0.538646\pi$
$252$	8.02422	0.505479
$253$	−17.5044	−1.10049
$254$	21.6697	1.35968
$255$	−0.719688	−0.0450686
$256$	1.00000	0.0625000
$257$	−14.1614	−0.883361	−0.441681	−	0.897172i	$-0.645618\pi$
$257$	−14.1614	−0.883361	−0.441681	+	0.897172i	$0.645618\pi$
$258$	−1.03645	−0.0645264
$259$	−42.9857	−2.67100
$260$	5.25989	0.326205
$261$	−2.28699	−0.141561
$262$	6.43281	0.397420
$263$	10.2962	0.634892	0.317446	−	0.948276i	$-0.397175\pi$
$263$	10.2962	0.634892	0.317446	+	0.948276i	$0.397175\pi$
$264$	−4.05621	−0.249643
$265$	6.32685	0.388655
$266$	4.04026	0.247724
$267$	−5.77172	−0.353223
$268$	−4.17380	−0.254956
$269$	8.91975	0.543847	0.271923	−	0.962319i	$-0.412340\pi$
$269$	8.91975	0.543847	0.271923	+	0.962319i	$0.412340\pi$
$270$	8.75343	0.532717
$271$	−2.52690	−0.153498	−0.0767492	−	0.997050i	$-0.524454\pi$
$271$	−2.52690	−0.153498	−0.0767492	+	0.997050i	$0.524454\pi$
$272$	−0.409943	−0.0248565
$273$	−12.2737	−0.742838
$274$	4.03310	0.243649
$275$	7.89656	0.476180
$276$	−4.37558	−0.263379
$277$	−27.6115	−1.65901	−0.829506	−	0.558498i	$-0.811378\pi$
$277$	−27.6115	−1.65901	−0.829506	+	0.558498i	$0.811378\pi$
$278$	−12.9535	−0.776898
$279$	14.1669	0.848147
$280$	−7.04409	−0.420965
$281$	17.0758	1.01865	0.509327	−	0.860573i	$-0.329894\pi$
$281$	17.0758	1.01865	0.509327	+	0.860573i	$0.329894\pi$
$282$	0.0144459	0.000860241 0
$283$	−11.8929	−0.706961	−0.353481	−	0.935442i	$-0.615002\pi$
$283$	−11.8929	−0.706961	−0.353481	+	0.935442i	$0.615002\pi$
$284$	−11.9178	−0.707191
$285$	1.75558	0.103992
$286$	−12.1528	−0.718611
$287$	−28.3858	−1.67556
$288$	1.98607	0.117030
$289$	−16.8319	−0.990115
$290$	2.00765	0.117893
$291$	−0.192562	−0.0112882
$292$	13.1562	0.769908
$293$	12.9292	0.755333	0.377667	−	0.925942i	$-0.376727\pi$
$293$	12.9292	0.755333	0.377667	+	0.925942i	$0.376727\pi$
$294$	9.38844	0.547545
$295$	−4.69575	−0.273397
$296$	−10.6393	−0.618399
$297$	−20.2245	−1.17355
$298$	1.48931	0.0862734
$299$	−13.1097	−0.758152
$300$	1.97391	0.113964
$301$	4.15864	0.239700
$302$	−0.0944794	−0.00543668
$303$	3.84976	0.221163
$304$	1.00000	0.0573539
$305$	−6.00331	−0.343748
$306$	−0.814174	−0.0465432
$307$	6.14502	0.350715	0.175357	−	0.984505i	$-0.443892\pi$
$307$	6.14502	0.350715	0.175357	+	0.984505i	$0.443892\pi$
$308$	16.2752	0.927363
$309$	4.05866	0.230889
$310$	−12.4364	−0.706341
$311$	22.4014	1.27027	0.635134	−	0.772402i	$-0.280945\pi$
$311$	22.4014	1.27027	0.635134	+	0.772402i	$0.280945\pi$
$312$	−3.03785	−0.171984
$313$	31.2709	1.76754	0.883769	−	0.467923i	$-0.154998\pi$
$313$	31.2709	1.76754	0.883769	+	0.467923i	$0.154998\pi$
$314$	14.7283	0.831164
$315$	−13.9900	−0.788249
$316$	16.7663	0.943178
$317$	13.8714	0.779094	0.389547	−	0.921007i	$-0.372632\pi$
$317$	13.8714	0.779094	0.389547	+	0.921007i	$0.372632\pi$
$318$	−3.65407	−0.204910
$319$	−4.63860	−0.259712
$320$	−1.74347	−0.0974632
$321$	−5.36738	−0.299578
$322$	17.5566	0.978390
$323$	−0.409943	−0.0228098
$324$	0.902653	0.0501474
$325$	5.91403	0.328051
$326$	−15.1273	−0.837822
$327$	−2.46206	−0.136152
$328$	−7.02573	−0.387931
$329$	−0.0579628	−0.00319559
$330$	7.07190	0.389295
$331$	−19.4694	−1.07014	−0.535068	−	0.844809i	$-0.679714\pi$
$331$	−19.4694	−1.07014	−0.535068	+	0.844809i	$0.679714\pi$
$332$	−3.77607	−0.207239
$333$	−21.1304	−1.15794
$334$	−5.93671	−0.324842
$335$	7.27692	0.397580
$336$	4.06831	0.221945
$337$	15.1856	0.827212	0.413606	−	0.910456i	$-0.364269\pi$
$337$	15.1856	0.827212	0.413606	+	0.910456i	$0.364269\pi$
$338$	3.89830	0.212040
$339$	−1.94435	−0.105602
$340$	0.714725	0.0387614
$341$	28.7340	1.55603
$342$	1.98607	0.107394
$343$	−9.38838	−0.506925
$344$	1.02930	0.0554962
$345$	7.62871	0.410716
$346$	24.6269	1.32395
$347$	−12.3151	−0.661109	−0.330554	−	0.943787i	$-0.607236\pi$
$347$	−12.3151	−0.661109	−0.330554	+	0.943787i	$0.607236\pi$
$348$	−1.15952	−0.0621565
$349$	18.4205	0.986025	0.493013	−	0.870022i	$-0.335896\pi$
$349$	18.4205	0.986025	0.493013	+	0.870022i	$0.335896\pi$
$350$	−7.92011	−0.423348
$351$	−15.1469	−0.808482
$352$	4.02824	0.214706
$353$	32.4757	1.72851	0.864254	−	0.503055i	$-0.167791\pi$
$353$	32.4757	1.72851	0.864254	+	0.503055i	$0.167791\pi$
$354$	2.71203	0.144143
$355$	20.7784	1.10280
$356$	5.73192	0.303791
$357$	−1.66778	−0.0882681
$358$	−7.28031	−0.384777
$359$	−14.4905	−0.764781	−0.382390	−	0.924001i	$-0.624899\pi$
$359$	−14.4905	−0.764781	−0.382390	+	0.924001i	$0.624899\pi$
$360$	−3.46265	−0.182498
$361$	1.00000	0.0526316
$362$	6.91862	0.363635
$363$	−5.26304	−0.276238
$364$	12.1891	0.638881
$365$	−22.9375	−1.20060
$366$	3.46721	0.181234
$367$	−20.8482	−1.08827	−0.544135	−	0.838998i	$-0.683142\pi$
$367$	−20.8482	−1.08827	−0.544135	+	0.838998i	$0.683142\pi$
$368$	4.34541	0.226520
$369$	−13.9536	−0.726394
$370$	18.5494	0.964337
$371$	14.6616	0.761192
$372$	7.18265	0.372403
$373$	−23.3019	−1.20653	−0.603263	−	0.797543i	$-0.706133\pi$
$373$	−23.3019	−1.20653	−0.603263	+	0.797543i	$0.706133\pi$
$374$	−1.65135	−0.0853893
$375$	−12.2194	−0.631005
$376$	−0.0143463	−0.000739854 0
$377$	−3.47402	−0.178921
$378$	20.2849	1.04334
$379$	17.3860	0.893057	0.446529	−	0.894769i	$-0.352660\pi$
$379$	17.3860	0.893057	0.446529	+	0.894769i	$0.352660\pi$
$380$	−1.74347	−0.0894383
$381$	21.8201	1.11788
$382$	1.76685	0.0904001
$383$	−12.6639	−0.647095	−0.323548	−	0.946212i	$-0.604876\pi$
$383$	−12.6639	−0.647095	−0.323548	+	0.946212i	$0.604876\pi$
$384$	1.00694	0.0513853
$385$	−28.3753	−1.44614
$386$	5.81089	0.295766
$387$	2.04426	0.103915
$388$	0.191234	0.00970845
$389$	11.9644	0.606619	0.303310	−	0.952892i	$-0.401908\pi$
$389$	11.9644	0.606619	0.303310	+	0.952892i	$0.401908\pi$
$390$	5.29641	0.268194
$391$	−1.78137	−0.0900878
$392$	−9.32371	−0.470918
$393$	6.47747	0.326745
$394$	−21.3406	−1.07512
$395$	−29.2316	−1.47080
$396$	8.00036	0.402033
$397$	14.0030	0.702793	0.351396	−	0.936227i	$-0.385707\pi$
$397$	14.0030	0.702793	0.351396	+	0.936227i	$0.385707\pi$
$398$	−22.2980	−1.11770
$399$	4.06831	0.203670
$400$	−1.96030	−0.0980149
$401$	9.93334	0.496047	0.248024	−	0.968754i	$-0.420219\pi$
$401$	9.93334	0.496047	0.248024	+	0.968754i	$0.420219\pi$
$402$	−4.20278	−0.209616
$403$	21.5199	1.07198
$404$	−3.82322	−0.190212
$405$	−1.57375	−0.0782004
$406$	4.65244	0.230897
$407$	−42.8578	−2.12438
$408$	−0.412789	−0.0204361
$409$	−22.4558	−1.11037	−0.555184	−	0.831728i	$-0.687352\pi$
$409$	−22.4558	−1.11037	−0.555184	+	0.831728i	$0.687352\pi$
$410$	12.2492	0.604944
$411$	4.06111	0.200320
$412$	−4.03067	−0.198577
$413$	−10.8818	−0.535456
$414$	8.63027	0.424155
$415$	6.58348	0.323171
$416$	3.01690	0.147916
$417$	−13.0434	−0.638739
$418$	4.02824	0.197028
$419$	18.7303	0.915035	0.457518	−	0.889200i	$-0.348739\pi$
$419$	18.7303	0.915035	0.457518	+	0.889200i	$0.348739\pi$
$420$	−7.09300	−0.346103
$421$	28.7341	1.40042	0.700208	−	0.713939i	$-0.253091\pi$
$421$	28.7341	1.40042	0.700208	+	0.713939i	$0.253091\pi$
$422$	−1.00000	−0.0486792
$423$	−0.0284927	−0.00138536
$424$	3.62887	0.176234
$425$	0.803611	0.0389808
$426$	−12.0005	−0.581428
$427$	−13.9118	−0.673241
$428$	5.33038	0.257653
$429$	−12.2372	−0.590817
$430$	−1.79456	−0.0865413
$431$	29.3568	1.41407	0.707034	−	0.707180i	$-0.250033\pi$
$431$	29.3568	1.41407	0.707034	+	0.707180i	$0.250033\pi$
$432$	5.02068	0.241558
$433$	4.48627	0.215596	0.107798	−	0.994173i	$-0.465620\pi$
$433$	4.48627	0.215596	0.107798	+	0.994173i	$0.465620\pi$
$434$	−28.8197	−1.38339
$435$	2.02159	0.0969276
$436$	2.44508	0.117098
$437$	4.34541	0.207869
$438$	13.2475	0.632992
$439$	22.5313	1.07536	0.537679	−	0.843150i	$-0.319301\pi$
$439$	22.5313	1.07536	0.537679	+	0.843150i	$0.319301\pi$
$440$	−7.02314	−0.334815
$441$	−18.5175	−0.881785
$442$	−1.23676	−0.0588266
$443$	19.5995	0.931201	0.465600	−	0.884995i	$-0.345838\pi$
$443$	19.5995	0.931201	0.465600	+	0.884995i	$0.345838\pi$
$444$	−10.7132	−0.508426
$445$	−9.99345	−0.473735
$446$	1.70994	0.0809679
$447$	1.49965	0.0709310
$448$	−4.04026	−0.190884
$449$	21.4115	1.01047	0.505235	−	0.862982i	$-0.331406\pi$
$449$	21.4115	1.01047	0.505235	+	0.862982i	$0.331406\pi$
$450$	−3.89328	−0.183531
$451$	−28.3014	−1.33266
$452$	1.93094	0.0908238
$453$	−0.0951354	−0.00446985
$454$	13.3874	0.628303
$455$	−21.2513	−0.996278
$456$	1.00694	0.0471544
$457$	−7.54692	−0.353030	−0.176515	−	0.984298i	$-0.556482\pi$
$457$	−7.54692	−0.353030	−0.176515	+	0.984298i	$0.556482\pi$
$458$	17.1110	0.799545
$459$	−2.05820	−0.0960683
$460$	−7.57611	−0.353238
$461$	3.61849	0.168530	0.0842649	−	0.996443i	$-0.473146\pi$
$461$	3.61849	0.168530	0.0842649	+	0.996443i	$0.473146\pi$
$462$	16.3882	0.762446
$463$	−27.2502	−1.26642	−0.633212	−	0.773979i	$-0.718264\pi$
$463$	−27.2502	−1.26642	−0.633212	+	0.773979i	$0.718264\pi$
$464$	1.15152	0.0534580
$465$	−12.5228	−0.580729
$466$	−9.44988	−0.437757
$467$	23.3696	1.08142	0.540708	−	0.841210i	$-0.318156\pi$
$467$	23.3696	1.08142	0.540708	+	0.841210i	$0.318156\pi$
$468$	5.99176	0.276969
$469$	16.8632	0.778672
$470$	0.0250124	0.00115374
$471$	14.8305	0.683354
$472$	−2.69333	−0.123971
$473$	4.14627	0.190646
$474$	16.8827	0.775449
$475$	−1.96030	−0.0899446
$476$	1.65628	0.0759153
$477$	7.20718	0.329994
$478$	−3.75711	−0.171846
$479$	−5.71892	−0.261304	−0.130652	−	0.991428i	$-0.541707\pi$
$479$	−5.71892	−0.261304	−0.130652	+	0.991428i	$0.541707\pi$
$480$	−1.75558	−0.0801309
$481$	−32.0978	−1.46353
$482$	8.80684	0.401140
$483$	17.6785	0.804399
$484$	5.22675	0.237579
$485$	−0.333412	−0.0151395
$486$	15.9710	0.724458
$487$	2.88202	0.130597	0.0652985	−	0.997866i	$-0.479200\pi$
$487$	2.88202	0.130597	0.0652985	+	0.997866i	$0.479200\pi$
$488$	−3.44330	−0.155871
$489$	−15.2323	−0.688829
$490$	16.2556	0.734355
$491$	−0.980568	−0.0442524	−0.0221262	−	0.999755i	$-0.507044\pi$
$491$	−0.980568	−0.0442524	−0.0221262	+	0.999755i	$0.507044\pi$
$492$	−7.07451	−0.318944
$493$	−0.472058	−0.0212604
$494$	3.01690	0.135737
$495$	−13.9484	−0.626935
$496$	−7.13312	−0.320287
$497$	48.1510	2.15987
$498$	−3.80229	−0.170385
$499$	19.4293	0.869776	0.434888	−	0.900485i	$-0.356788\pi$
$499$	19.4293	0.869776	0.434888	+	0.900485i	$0.356788\pi$
$500$	12.1351	0.542698
$501$	−5.97793	−0.267074
$502$	3.83750	0.171276
$503$	6.88891	0.307161	0.153581	−	0.988136i	$-0.450920\pi$
$503$	6.88891	0.307161	0.153581	+	0.988136i	$0.450920\pi$
$504$	−8.02422	−0.357427
$505$	6.66568	0.296619
$506$	17.5044	0.778164
$507$	3.92537	0.174332
$508$	−21.6697	−0.961437
$509$	5.58983	0.247765	0.123882	−	0.992297i	$-0.460465\pi$
$509$	5.58983	0.247765	0.123882	+	0.992297i	$0.460465\pi$
$510$	0.719688	0.0318683
$511$	−53.1544	−2.35141
$512$	−1.00000	−0.0441942
$513$	5.02068	0.221669
$514$	14.1614	0.624631
$515$	7.02737	0.309663
$516$	1.03645	0.0456270
$517$	−0.0577904	−0.00254162
$518$	42.9857	1.88868
$519$	24.7978	1.08850
$520$	−5.25989	−0.230661
$521$	−19.0742	−0.835656	−0.417828	−	0.908526i	$-0.637208\pi$
$521$	−19.0742	−0.835656	−0.417828	+	0.908526i	$0.637208\pi$
$522$	2.28699	0.100099
$523$	−39.1590	−1.71230	−0.856152	−	0.516724i	$-0.827151\pi$
$523$	−39.1590	−1.71230	−0.856152	+	0.516724i	$0.827151\pi$
$524$	−6.43281	−0.281018
$525$	−7.97510	−0.348062
$526$	−10.2962	−0.448937
$527$	2.92418	0.127379
$528$	4.05621	0.176524
$529$	−4.11742	−0.179018
$530$	−6.32685	−0.274821
$531$	−5.34913	−0.232133
$532$	−4.04026	−0.175168
$533$	−21.1959	−0.918098
$534$	5.77172	0.249767
$535$	−9.29337	−0.401788
$536$	4.17380	0.180281
$537$	−7.33086	−0.316350
$538$	−8.91975	−0.384558
$539$	−37.5582	−1.61774
$540$	−8.75343	−0.376688
$541$	19.8128	0.851817	0.425908	−	0.904766i	$-0.359955\pi$
$541$	19.8128	0.851817	0.425908	+	0.904766i	$0.359955\pi$
$542$	2.52690	0.108540
$543$	6.96666	0.298968
$544$	0.409943	0.0175762
$545$	−4.26294	−0.182604
$546$	12.2737	0.525266
$547$	−12.8077	−0.547617	−0.273809	−	0.961784i	$-0.588283\pi$
$547$	−12.8077	−0.547617	−0.273809	+	0.961784i	$0.588283\pi$
$548$	−4.03310	−0.172286
$549$	−6.83862	−0.291865
$550$	−7.89656	−0.336710
$551$	1.15152	0.0490564
$552$	4.37558	0.186237
$553$	−67.7402	−2.88061
$554$	27.6115	1.17310
$555$	18.6782	0.792845
$556$	12.9535	0.549350
$557$	−15.1629	−0.642474	−0.321237	−	0.946999i	$-0.604099\pi$
$557$	−15.1629	−0.642474	−0.321237	+	0.946999i	$0.604099\pi$
$558$	−14.1669	−0.599731
$559$	3.10530	0.131340
$560$	7.04409	0.297667
$561$	−1.66282	−0.0702042
$562$	−17.0758	−0.720298
$563$	4.52765	0.190818	0.0954089	−	0.995438i	$-0.469584\pi$
$563$	4.52765	0.190818	0.0954089	+	0.995438i	$0.469584\pi$
$564$	−0.0144459	−0.000608282 0
$565$	−3.36654	−0.141632
$566$	11.8929	0.499897
$567$	−3.64695	−0.153158
$568$	11.9178	0.500059
$569$	−11.9002	−0.498881	−0.249441	−	0.968390i	$-0.580247\pi$
$569$	−11.9002	−0.498881	−0.249441	+	0.968390i	$0.580247\pi$
$570$	−1.75558	−0.0735331
$571$	−20.0411	−0.838692	−0.419346	−	0.907826i	$-0.637741\pi$
$571$	−20.0411	−0.838692	−0.419346	+	0.907826i	$0.637741\pi$
$572$	12.1528	0.508135
$573$	1.77912	0.0743238
$574$	28.3858	1.18480
$575$	−8.51830	−0.355238
$576$	−1.98607	−0.0827527
$577$	11.6245	0.483935	0.241968	−	0.970284i	$-0.422207\pi$
$577$	11.6245	0.483935	0.241968	+	0.970284i	$0.422207\pi$
$578$	16.8319	0.700117
$579$	5.85123	0.243169
$580$	−2.00765	−0.0833630
$581$	15.2563	0.632939
$582$	0.192562	0.00798196
$583$	14.6180	0.605415
$584$	−13.1562	−0.544407
$585$	−10.4465	−0.431909
$586$	−12.9292	−0.534101
$587$	22.6070	0.933089	0.466544	−	0.884498i	$-0.345499\pi$
$587$	22.6070	0.933089	0.466544	+	0.884498i	$0.345499\pi$
$588$	−9.38844	−0.387173
$589$	−7.13312	−0.293915
$590$	4.69575	0.193321
$591$	−21.4888	−0.883929
$592$	10.6393	0.437274
$593$	27.7586	1.13991	0.569954	−	0.821677i	$-0.306961\pi$
$593$	27.7586	1.13991	0.569954	+	0.821677i	$0.306961\pi$
$594$	20.2245	0.829823
$595$	−2.88768	−0.118383
$596$	−1.48931	−0.0610045
$597$	−22.4528	−0.918931
$598$	13.1097	0.536094
$599$	−7.37733	−0.301430	−0.150715	−	0.988577i	$-0.548157\pi$
$599$	−7.37733	−0.301430	−0.150715	+	0.988577i	$0.548157\pi$
$600$	−1.97391	−0.0805845
$601$	−47.9007	−1.95391	−0.976956	−	0.213441i	$-0.931533\pi$
$601$	−47.9007	−1.95391	−0.976956	+	0.213441i	$0.931533\pi$
$602$	−4.15864	−0.169494
$603$	8.28944	0.337572
$604$	0.0944794	0.00384431
$605$	−9.11270	−0.370484
$606$	−3.84976	−0.156386
$607$	−35.3640	−1.43538	−0.717689	−	0.696363i	$-0.754800\pi$
$607$	−35.3640	−1.43538	−0.717689	+	0.696363i	$0.754800\pi$
$608$	−1.00000	−0.0405554
$609$	4.68474	0.189835
$610$	6.00331	0.243067
$611$	−0.0432814	−0.00175098
$612$	0.814174	0.0329110
$613$	30.3788	1.22699	0.613495	−	0.789699i	$-0.289763\pi$
$613$	30.3788	1.22699	0.613495	+	0.789699i	$0.289763\pi$
$614$	−6.14502	−0.247993
$615$	12.3342	0.497364
$616$	−16.2752	−0.655745
$617$	−1.47372	−0.0593299	−0.0296649	−	0.999560i	$-0.509444\pi$
$617$	−1.47372	−0.0593299	−0.0296649	+	0.999560i	$0.509444\pi$
$618$	−4.05866	−0.163263
$619$	−31.6298	−1.27131	−0.635655	−	0.771974i	$-0.719270\pi$
$619$	−31.6298	−1.27131	−0.635655	+	0.771974i	$0.719270\pi$
$620$	12.4364	0.499458
$621$	21.8169	0.875483
$622$	−22.4014	−0.898215
$623$	−23.1584	−0.927823
$624$	3.03785	0.121611
$625$	−11.3557	−0.454230
$626$	−31.2709	−1.24984
$627$	4.05621	0.161990
$628$	−14.7283	−0.587722
$629$	−4.36152	−0.173905
$630$	13.9900	0.557376
$631$	−12.1447	−0.483474	−0.241737	−	0.970342i	$-0.577717\pi$
$631$	−12.1447	−0.483474	−0.241737	+	0.970342i	$0.577717\pi$
$632$	−16.7663	−0.666928
$633$	−1.00694	−0.0400224
$634$	−13.8714	−0.550903
$635$	37.7805	1.49927
$636$	3.65407	0.144893
$637$	−28.1287	−1.11450
$638$	4.63860	0.183644
$639$	23.6695	0.936351
$640$	1.74347	0.0689169
$641$	27.3505	1.08028	0.540140	−	0.841575i	$-0.318371\pi$
$641$	27.3505	1.08028	0.540140	+	0.841575i	$0.318371\pi$
$642$	5.36738	0.211834
$643$	−45.4668	−1.79303	−0.896517	−	0.443009i	$-0.853911\pi$
$643$	−45.4668	−1.79303	−0.896517	+	0.443009i	$0.853911\pi$
$644$	−17.5566	−0.691826
$645$	−1.80702	−0.0711513
$646$	0.409943	0.0161290
$647$	−26.8546	−1.05576	−0.527881	−	0.849318i	$-0.677013\pi$
$647$	−26.8546	−1.05576	−0.527881	+	0.849318i	$0.677013\pi$
$648$	−0.902653	−0.0354596
$649$	−10.8494	−0.425876
$650$	−5.91403	−0.231967
$651$	−29.0198	−1.13737
$652$	15.1273	0.592430
$653$	25.5755	1.00085	0.500424	−	0.865781i	$-0.333178\pi$
$653$	25.5755	1.00085	0.500424	+	0.865781i	$0.333178\pi$
$654$	2.46206	0.0962742
$655$	11.2154	0.438223
$656$	7.02573	0.274309
$657$	−26.1291	−1.01939
$658$	0.0579628	0.00225962
$659$	14.3887	0.560504	0.280252	−	0.959926i	$-0.409582\pi$
$659$	14.3887	0.560504	0.280252	+	0.959926i	$0.409582\pi$
$660$	−7.07190	−0.275273
$661$	11.9253	0.463841	0.231921	−	0.972735i	$-0.425499\pi$
$661$	11.9253	0.463841	0.231921	+	0.972735i	$0.425499\pi$
$662$	19.4694	0.756701
$663$	−1.24535	−0.0483652
$664$	3.77607	0.146540
$665$	7.04409	0.273158
$666$	21.1304	0.818787
$667$	5.00383	0.193749
$668$	5.93671	0.229698
$669$	1.72181	0.0665690
$670$	−7.27692	−0.281132
$671$	−13.8705	−0.535463
$672$	−4.06831	−0.156939
$673$	−27.9856	−1.07877	−0.539383	−	0.842061i	$-0.681342\pi$
$673$	−27.9856	−1.07877	−0.539383	+	0.842061i	$0.681342\pi$
$674$	−15.1856	−0.584927
$675$	−9.84204	−0.378820
$676$	−3.89830	−0.149935
$677$	20.3821	0.783347	0.391673	−	0.920104i	$-0.371896\pi$
$677$	20.3821	0.783347	0.391673	+	0.920104i	$0.371896\pi$
$678$	1.94435	0.0746722
$679$	−0.772637	−0.0296511
$680$	−0.714725	−0.0274085
$681$	13.4804	0.516569
$682$	−28.7340	−1.10028
$683$	−28.0972	−1.07511	−0.537555	−	0.843229i	$-0.680652\pi$
$683$	−28.0972	−1.07511	−0.537555	+	0.843229i	$0.680652\pi$
$684$	−1.98607	−0.0759391
$685$	7.03161	0.268664
$686$	9.38838	0.358450
$687$	17.2298	0.657359
$688$	−1.02930	−0.0392417
$689$	10.9480	0.417084
$690$	−7.62871	−0.290420
$691$	16.4673	0.626446	0.313223	−	0.949680i	$-0.398591\pi$
$691$	16.4673	0.626446	0.313223	+	0.949680i	$0.398591\pi$
$692$	−24.6269	−0.936172
$693$	−32.3235	−1.22787
$694$	12.3151	0.467475
$695$	−22.5841	−0.856662
$696$	1.15952	0.0439513
$697$	−2.88015	−0.109094
$698$	−18.4205	−0.697225
$699$	−9.51549	−0.359909
$700$	7.92011	0.299352
$701$	−3.17228	−0.119815	−0.0599077	−	0.998204i	$-0.519081\pi$
$701$	−3.17228	−0.119815	−0.0599077	+	0.998204i	$0.519081\pi$
$702$	15.1469	0.571683
$703$	10.6393	0.401270
$704$	−4.02824	−0.151820
$705$	0.0251861	0.000948562 0
$706$	−32.4757	−1.22224
$707$	15.4468	0.580937
$708$	−2.71203	−0.101924
$709$	−16.8387	−0.632389	−0.316195	−	0.948694i	$-0.602405\pi$
$709$	−16.8387	−0.632389	−0.316195	+	0.948694i	$0.602405\pi$
$710$	−20.7784	−0.779798
$711$	−33.2990	−1.24881
$712$	−5.73192	−0.214813
$713$	−30.9963	−1.16082
$714$	1.66778	0.0624150
$715$	−21.1881	−0.792391
$716$	7.28031	0.272078
$717$	−3.78320	−0.141286
$718$	14.4905	0.540782
$719$	4.45742	0.166234	0.0831168	−	0.996540i	$-0.473513\pi$
$719$	4.45742	0.166234	0.0831168	+	0.996540i	$0.473513\pi$
$720$	3.46265	0.129045
$721$	16.2850	0.606484
$722$	−1.00000	−0.0372161
$723$	8.86798	0.329804
$724$	−6.91862	−0.257128
$725$	−2.25732	−0.0838349
$726$	5.26304	0.195330
$727$	−11.2404	−0.416882	−0.208441	−	0.978035i	$-0.566839\pi$
$727$	−11.2404	−0.416882	−0.208441	+	0.978035i	$0.566839\pi$
$728$	−12.1891	−0.451757
$729$	13.3739	0.495330
$730$	22.9375	0.848954
$731$	0.421955	0.0156066
$732$	−3.46721	−0.128152
$733$	0.294965	0.0108948	0.00544739	−	0.999985i	$-0.498266\pi$
$733$	0.294965	0.0108948	0.00544739	+	0.999985i	$0.498266\pi$
$734$	20.8482	0.769523
$735$	16.3685	0.603761
$736$	−4.34541	−0.160174
$737$	16.8131	0.619318
$738$	13.9536	0.513638
$739$	−22.7152	−0.835592	−0.417796	−	0.908541i	$-0.637197\pi$
$739$	−22.7152	−0.835592	−0.417796	+	0.908541i	$0.637197\pi$
$740$	−18.5494	−0.681889
$741$	3.03785	0.111598
$742$	−14.6616	−0.538244
$743$	−51.6878	−1.89624	−0.948120	−	0.317912i	$-0.897018\pi$
$743$	−51.6878	−1.89624	−0.948120	+	0.317912i	$0.897018\pi$
$744$	−7.18265	−0.263329
$745$	2.59657	0.0951311
$746$	23.3019	0.853142
$747$	7.49953	0.274393
$748$	1.65135	0.0603794
$749$	−21.5361	−0.786912
$750$	12.2194	0.446188
$751$	35.9924	1.31338	0.656692	−	0.754159i	$-0.271955\pi$
$751$	35.9924	1.31338	0.656692	+	0.754159i	$0.271955\pi$
$752$	0.0143463	0.000523156 0
$753$	3.86414	0.140817
$754$	3.47402	0.126516
$755$	−0.164722	−0.00599486
$756$	−20.2849	−0.737754
$757$	21.6234	0.785914	0.392957	−	0.919557i	$-0.371452\pi$
$757$	21.6234	0.785914	0.392957	+	0.919557i	$0.371452\pi$
$758$	−17.3860	−0.631487
$759$	17.6259	0.639780
$760$	1.74347	0.0632425
$761$	30.3790	1.10124	0.550618	−	0.834757i	$-0.314392\pi$
$761$	30.3790	1.10124	0.550618	+	0.834757i	$0.314392\pi$
$762$	−21.8201	−0.790460
$763$	−9.87877	−0.357636
$764$	−1.76685	−0.0639225
$765$	−1.41949	−0.0513218
$766$	12.6639	0.457565
$767$	−8.12551	−0.293395
$768$	−1.00694	−0.0363349
$769$	8.37478	0.302002	0.151001	−	0.988534i	$-0.451750\pi$
$769$	8.37478	0.302002	0.151001	+	0.988534i	$0.451750\pi$
$770$	28.3753	1.02258
$771$	14.2597	0.513550
$772$	−5.81089	−0.209138
$773$	5.87442	0.211288	0.105644	−	0.994404i	$-0.466310\pi$
$773$	5.87442	0.211288	0.105644	+	0.994404i	$0.466310\pi$
$774$	−2.04426	−0.0734793
$775$	13.9830	0.502286
$776$	−0.191234	−0.00686491
$777$	43.2841	1.55281
$778$	−11.9644	−0.428945
$779$	7.02573	0.251723
$780$	−5.29641	−0.189642
$781$	48.0078	1.71785
$782$	1.78137	0.0637017
$783$	5.78142	0.206611
$784$	9.32371	0.332990
$785$	25.6783	0.916499
$786$	−6.47747	−0.231044
$787$	−35.8708	−1.27866	−0.639329	−	0.768934i	$-0.720788\pi$
$787$	−35.8708	−1.27866	−0.639329	+	0.768934i	$0.720788\pi$
$788$	21.3406	0.760227
$789$	−10.3677	−0.369100
$790$	29.2316	1.04001
$791$	−7.80150	−0.277389
$792$	−8.00036	−0.284280
$793$	−10.3881	−0.368892
$794$	−14.0030	−0.496949
$795$	−6.37077	−0.225948
$796$	22.2980	0.790330
$797$	25.0548	0.887485	0.443743	−	0.896154i	$-0.353650\pi$
$797$	25.0548	0.887485	0.443743	+	0.896154i	$0.353650\pi$
$798$	−4.06831	−0.144017
$799$	−0.00588117	−0.000208061 0
$800$	1.96030	0.0693070
$801$	−11.3840	−0.402233
$802$	−9.93334	−0.350758
$803$	−52.9964	−1.87020
$804$	4.20278	0.148221
$805$	30.6095	1.07884
$806$	−21.5199	−0.758007
$807$	−8.98168	−0.316170
$808$	3.82322	0.134500
$809$	27.6594	0.972454	0.486227	−	0.873833i	$-0.338373\pi$
$809$	27.6594	0.972454	0.486227	+	0.873833i	$0.338373\pi$
$810$	1.57375	0.0552960
$811$	25.7547	0.904369	0.452184	−	0.891924i	$-0.350645\pi$
$811$	25.7547	0.904369	0.452184	+	0.891924i	$0.350645\pi$
$812$	−4.65244	−0.163269
$813$	2.54445	0.0892377
$814$	42.8578	1.50217
$815$	−26.3740	−0.923841
$816$	0.412789	0.0144505
$817$	−1.02930	−0.0360107
$818$	22.4558	0.785148
$819$	−24.2083	−0.845906
$820$	−12.2492	−0.427760
$821$	8.70106	0.303669	0.151835	−	0.988406i	$-0.451482\pi$
$821$	8.70106	0.303669	0.151835	+	0.988406i	$0.451482\pi$
$822$	−4.06111	−0.141647
$823$	−21.8933	−0.763154	−0.381577	−	0.924337i	$-0.624619\pi$
$823$	−21.8933	−0.763154	−0.381577	+	0.924337i	$0.624619\pi$
$824$	4.03067	0.140415
$825$	−7.95138	−0.276832
$826$	10.8818	0.378625
$827$	−18.7609	−0.652380	−0.326190	−	0.945304i	$-0.605765\pi$
$827$	−18.7609	−0.652380	−0.326190	+	0.945304i	$0.605765\pi$
$828$	−8.63027	−0.299923
$829$	−12.7727	−0.443613	−0.221807	−	0.975091i	$-0.571195\pi$
$829$	−12.7727	−0.443613	−0.221807	+	0.975091i	$0.571195\pi$
$830$	−6.58348	−0.228516
$831$	27.8032	0.964481
$832$	−3.01690	−0.104592
$833$	−3.82219	−0.132431
$834$	13.0434	0.451656
$835$	−10.3505	−0.358194
$836$	−4.02824	−0.139320
$837$	−35.8132	−1.23788
$838$	−18.7303	−0.647028
$839$	13.0724	0.451309	0.225654	−	0.974207i	$-0.427548\pi$
$839$	13.0724	0.451309	0.225654	+	0.974207i	$0.427548\pi$
$840$	7.09300	0.244732
$841$	−27.6740	−0.954276
$842$	−28.7341	−0.990243
$843$	−17.1943	−0.592204
$844$	1.00000	0.0344214
$845$	6.79659	0.233810
$846$	0.0284927	0.000979599 0
$847$	−21.1174	−0.725603
$848$	−3.62887	−0.124616
$849$	11.9755	0.410998
$850$	−0.803611	−0.0275636
$851$	46.2323	1.58482
$852$	12.0005	0.411132
$853$	2.23896	0.0766605	0.0383303	−	0.999265i	$-0.487796\pi$
$853$	2.23896	0.0766605	0.0383303	+	0.999265i	$0.487796\pi$
$854$	13.9118	0.476053
$855$	3.46265	0.118420
$856$	−5.33038	−0.182188
$857$	40.1731	1.37229	0.686144	−	0.727466i	$-0.259302\pi$
$857$	40.1731	1.37229	0.686144	+	0.727466i	$0.259302\pi$
$858$	12.2372	0.417771
$859$	20.2232	0.690008	0.345004	−	0.938601i	$-0.387878\pi$
$859$	20.2232	0.690008	0.345004	+	0.938601i	$0.387878\pi$
$860$	1.79456	0.0611939
$861$	28.5829	0.974102
$862$	−29.3568	−0.999897
$863$	−22.2565	−0.757621	−0.378811	−	0.925474i	$-0.623667\pi$
$863$	−22.2565	−0.757621	−0.378811	+	0.925474i	$0.623667\pi$
$864$	−5.02068	−0.170807
$865$	42.9363	1.45988
$866$	−4.48627	−0.152450
$867$	16.9488	0.575612
$868$	28.8197	0.978204
$869$	−67.5387	−2.29109
$870$	−2.02159	−0.0685382
$871$	12.5919	0.426662
$872$	−2.44508	−0.0828010
$873$	−0.379804	−0.0128544
$874$	−4.34541	−0.146986
$875$	−49.0290	−1.65748
$876$	−13.2475	−0.447593
$877$	13.8031	0.466098	0.233049	−	0.972465i	$-0.425130\pi$
$877$	13.8031	0.466098	0.233049	+	0.972465i	$0.425130\pi$
$878$	−22.5313	−0.760393
$879$	−13.0190	−0.439120
$880$	7.02314	0.236750
$881$	11.2507	0.379044	0.189522	−	0.981876i	$-0.439306\pi$
$881$	11.2507	0.379044	0.189522	+	0.981876i	$0.439306\pi$
$882$	18.5175	0.623516
$883$	7.92365	0.266652	0.133326	−	0.991072i	$-0.457434\pi$
$883$	7.92365	0.266652	0.133326	+	0.991072i	$0.457434\pi$
$884$	1.23676	0.0415967
$885$	4.72836	0.158942
$886$	−19.5995	−0.658458
$887$	−4.19368	−0.140810	−0.0704050	−	0.997518i	$-0.522429\pi$
$887$	−4.19368	−0.140810	−0.0704050	+	0.997518i	$0.522429\pi$
$888$	10.7132	0.359511
$889$	87.5512	2.93637
$890$	9.99345	0.334981
$891$	−3.63611	−0.121814
$892$	−1.70994	−0.0572529
$893$	0.0143463	0.000480081 0
$894$	−1.49965	−0.0501558
$895$	−12.6930	−0.424282
$896$	4.04026	0.134976
$897$	13.2007	0.440758
$898$	−21.4115	−0.714510
$899$	−8.21394	−0.273950
$900$	3.89328	0.129776
$901$	1.48763	0.0495602
$902$	28.3014	0.942333
$903$	−4.18752	−0.139352
$904$	−1.93094	−0.0642221
$905$	12.0624	0.400969
$906$	0.0951354	0.00316066
$907$	−22.1548	−0.735638	−0.367819	−	0.929897i	$-0.619895\pi$
$907$	−22.1548	−0.735638	−0.367819	+	0.929897i	$0.619895\pi$
$908$	−13.3874	−0.444277
$909$	7.59316	0.251849
$910$	21.2513	0.704475
$911$	−30.5635	−1.01261	−0.506307	−	0.862353i	$-0.668990\pi$
$911$	−30.5635	−1.01261	−0.506307	+	0.862353i	$0.668990\pi$
$912$	−1.00694	−0.0333432
$913$	15.2109	0.503409
$914$	7.54692	0.249630
$915$	6.04499	0.199841
$916$	−17.1110	−0.565364
$917$	25.9902	0.858273
$918$	2.05820	0.0679306
$919$	−23.5250	−0.776019	−0.388009	−	0.921655i	$-0.626837\pi$
$919$	−23.5250	−0.776019	−0.388009	+	0.921655i	$0.626837\pi$
$920$	7.57611	0.249777
$921$	−6.18769	−0.203891
$922$	−3.61849	−0.119169
$923$	35.9548	1.18347
$924$	−16.3882	−0.539131
$925$	−20.8563	−0.685750
$926$	27.2502	0.895496
$927$	8.00518	0.262925
$928$	−1.15152	−0.0378005
$929$	22.2468	0.729892	0.364946	−	0.931029i	$-0.381087\pi$
$929$	22.2468	0.729892	0.364946	+	0.931029i	$0.381087\pi$
$930$	12.5228	0.410638
$931$	9.32371	0.305572
$932$	9.44988	0.309541
$933$	−22.5570	−0.738481
$934$	−23.3696	−0.764677
$935$	−2.87909	−0.0941562
$936$	−5.99176	−0.195847
$937$	−25.2570	−0.825109	−0.412555	−	0.910933i	$-0.635363\pi$
$937$	−25.2570	−0.825109	−0.412555	+	0.910933i	$0.635363\pi$
$938$	−16.8632	−0.550605
$939$	−31.4881	−1.02757
$940$	−0.0250124	−0.000815815 0
$941$	33.7522	1.10029	0.550144	−	0.835070i	$-0.314573\pi$
$941$	33.7522	1.10029	0.550144	+	0.835070i	$0.314573\pi$
$942$	−14.8305	−0.483204
$943$	30.5297	0.994184
$944$	2.69333	0.0876604
$945$	35.3662	1.15046
$946$	−4.14627	−0.134807
$947$	−8.03087	−0.260968	−0.130484	−	0.991450i	$-0.541653\pi$
$947$	−8.03087	−0.260968	−0.130484	+	0.991450i	$0.541653\pi$
$948$	−16.8827	−0.548325
$949$	−39.6909	−1.28842
$950$	1.96030	0.0636005
$951$	−13.9677	−0.452933
$952$	−1.65628	−0.0536803
$953$	−41.9775	−1.35978	−0.679892	−	0.733312i	$-0.737973\pi$
$953$	−41.9775	−1.35978	−0.679892	+	0.733312i	$0.737973\pi$
$954$	−7.20718	−0.233341
$955$	3.08046	0.0996814
$956$	3.75711	0.121514
$957$	4.67081	0.150986
$958$	5.71892	0.184770
$959$	16.2948	0.526186
$960$	1.75558	0.0566611
$961$	19.8814	0.641337
$962$	32.0978	1.03488
$963$	−10.5865	−0.341144
$964$	−8.80684	−0.283649
$965$	10.1311	0.326133
$966$	−17.6785	−0.568796
$967$	3.58460	0.115273	0.0576365	−	0.998338i	$-0.481644\pi$
$967$	3.58460	0.115273	0.0576365	+	0.998338i	$0.481644\pi$
$968$	−5.22675	−0.167994
$969$	0.412789	0.0132607
$970$	0.333412	0.0107052
$971$	3.83124	0.122950	0.0614751	−	0.998109i	$-0.480420\pi$
$971$	3.83124	0.122950	0.0614751	+	0.998109i	$0.480420\pi$
$972$	−15.9710	−0.512269
$973$	−52.3354	−1.67780
$974$	−2.88202	−0.0923460
$975$	−5.95509	−0.190715
$976$	3.44330	0.110217
$977$	2.30436	0.0737231	0.0368616	−	0.999320i	$-0.488264\pi$
$977$	2.30436	0.0737231	0.0368616	+	0.999320i	$0.488264\pi$
$978$	15.2323	0.487075
$979$	−23.0896	−0.737946
$980$	−16.2556	−0.519267
$981$	−4.85610	−0.155043
$982$	0.980568	0.0312912
$983$	−50.6920	−1.61682	−0.808412	−	0.588617i	$-0.799673\pi$
$983$	−50.6920	−1.61682	−0.808412	+	0.588617i	$0.799673\pi$
$984$	7.07451	0.225527
$985$	−37.2068	−1.18551
$986$	0.472058	0.0150334
$987$	0.0583652	0.00185779
$988$	−3.01690	−0.0959804
$989$	−4.47273	−0.142225
$990$	13.9484	0.443310
$991$	13.9268	0.442400	0.221200	−	0.975228i	$-0.429003\pi$
$991$	13.9268	0.442400	0.221200	+	0.975228i	$0.429003\pi$
$992$	7.13312	0.226477
$993$	19.6046	0.622134
$994$	−48.1510	−1.52726
$995$	−38.8759	−1.23245
$996$	3.80229	0.120480
$997$	−11.4699	−0.363257	−0.181628	−	0.983367i	$-0.558137\pi$
$997$	−11.4699	−0.363257	−0.181628	+	0.983367i	$0.558137\pi$
$998$	−19.4293	−0.615025
$999$	53.4167	1.69003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.14	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.14	✓	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00694 q^{3} +1.00000 q^{4} -1.74347 q^{5} +1.00694 q^{6} -4.04026 q^{7} -1.00000 q^{8} -1.98607 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00694 q^{3} +1.00000 q^{4} -1.74347 q^{5} +1.00694 q^{6} -4.04026 q^{7} -1.00000 q^{8} -1.98607 q^{9} +1.74347 q^{10} -4.02824 q^{11} -1.00694 q^{12} -3.01690 q^{13} +4.04026 q^{14} +1.75558 q^{15} +1.00000 q^{16} -0.409943 q^{17} +1.98607 q^{18} +1.00000 q^{19} -1.74347 q^{20} +4.06831 q^{21} +4.02824 q^{22} +4.34541 q^{23} +1.00694 q^{24} -1.96030 q^{25} +3.01690 q^{26} +5.02068 q^{27} -4.04026 q^{28} +1.15152 q^{29} -1.75558 q^{30} -7.13312 q^{31} -1.00000 q^{32} +4.05621 q^{33} +0.409943 q^{34} +7.04409 q^{35} -1.98607 q^{36} +10.6393 q^{37} -1.00000 q^{38} +3.03785 q^{39} +1.74347 q^{40} +7.02573 q^{41} -4.06831 q^{42} -1.02930 q^{43} -4.02824 q^{44} +3.46265 q^{45} -4.34541 q^{46} +0.0143463 q^{47} -1.00694 q^{48} +9.32371 q^{49} +1.96030 q^{50} +0.412789 q^{51} -3.01690 q^{52} -3.62887 q^{53} -5.02068 q^{54} +7.02314 q^{55} +4.04026 q^{56} -1.00694 q^{57} -1.15152 q^{58} +2.69333 q^{59} +1.75558 q^{60} +3.44330 q^{61} +7.13312 q^{62} +8.02422 q^{63} +1.00000 q^{64} +5.25989 q^{65} -4.05621 q^{66} -4.17380 q^{67} -0.409943 q^{68} -4.37558 q^{69} -7.04409 q^{70} -11.9178 q^{71} +1.98607 q^{72} +13.1562 q^{73} -10.6393 q^{74} +1.97391 q^{75} +1.00000 q^{76} +16.2752 q^{77} -3.03785 q^{78} +16.7663 q^{79} -1.74347 q^{80} +0.902653 q^{81} -7.02573 q^{82} -3.77607 q^{83} +4.06831 q^{84} +0.714725 q^{85} +1.02930 q^{86} -1.15952 q^{87} +4.02824 q^{88} +5.73192 q^{89} -3.46265 q^{90} +12.1891 q^{91} +4.34541 q^{92} +7.18265 q^{93} -0.0143463 q^{94} -1.74347 q^{95} +1.00694 q^{96} +0.191234 q^{97} -9.32371 q^{98} +8.00036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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