LMFDB - Embedded newform 8018.2.a.f.1.2

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			1.2
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.17050 q^{3} +1.00000 q^{4} +4.15425 q^{5} +3.17050 q^{6} +1.45443 q^{7} -1.00000 q^{8} +7.05209 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.17050 q^{3} +1.00000 q^{4} +4.15425 q^{5} +3.17050 q^{6} +1.45443 q^{7} -1.00000 q^{8} +7.05209 q^{9} -4.15425 q^{10} -3.03789 q^{11} -3.17050 q^{12} +3.91980 q^{13} -1.45443 q^{14} -13.1711 q^{15} +1.00000 q^{16} -0.0576653 q^{17} -7.05209 q^{18} -1.00000 q^{19} +4.15425 q^{20} -4.61128 q^{21} +3.03789 q^{22} +0.939084 q^{23} +3.17050 q^{24} +12.2578 q^{25} -3.91980 q^{26} -12.8472 q^{27} +1.45443 q^{28} -9.74846 q^{29} +13.1711 q^{30} +3.98084 q^{31} -1.00000 q^{32} +9.63163 q^{33} +0.0576653 q^{34} +6.04207 q^{35} +7.05209 q^{36} -10.1478 q^{37} +1.00000 q^{38} -12.4277 q^{39} -4.15425 q^{40} +6.40788 q^{41} +4.61128 q^{42} -0.156989 q^{43} -3.03789 q^{44} +29.2962 q^{45} -0.939084 q^{46} -3.44285 q^{47} -3.17050 q^{48} -4.88463 q^{49} -12.2578 q^{50} +0.182828 q^{51} +3.91980 q^{52} +8.72651 q^{53} +12.8472 q^{54} -12.6201 q^{55} -1.45443 q^{56} +3.17050 q^{57} +9.74846 q^{58} -6.77204 q^{59} -13.1711 q^{60} +0.287029 q^{61} -3.98084 q^{62} +10.2568 q^{63} +1.00000 q^{64} +16.2838 q^{65} -9.63163 q^{66} -0.311296 q^{67} -0.0576653 q^{68} -2.97737 q^{69} -6.04207 q^{70} -4.31993 q^{71} -7.05209 q^{72} -12.8177 q^{73} +10.1478 q^{74} -38.8634 q^{75} -1.00000 q^{76} -4.41839 q^{77} +12.4277 q^{78} -12.9034 q^{79} +4.15425 q^{80} +19.5758 q^{81} -6.40788 q^{82} -3.11104 q^{83} -4.61128 q^{84} -0.239556 q^{85} +0.156989 q^{86} +30.9075 q^{87} +3.03789 q^{88} -9.56741 q^{89} -29.2962 q^{90} +5.70108 q^{91} +0.939084 q^{92} -12.6213 q^{93} +3.44285 q^{94} -4.15425 q^{95} +3.17050 q^{96} -18.1356 q^{97} +4.88463 q^{98} -21.4235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.17050	−1.83049	−0.915246	−	0.402896i	$-0.868004\pi$
$3$	−3.17050	−1.83049	−0.915246	+	0.402896i	$0.868004\pi$
$4$	1.00000	0.500000
$5$	4.15425	1.85784	0.928919	−	0.370284i	$-0.120740\pi$
$5$	4.15425	1.85784	0.928919	+	0.370284i	$0.120740\pi$
$6$	3.17050	1.29435
$7$	1.45443	0.549723	0.274862	−	0.961484i	$-0.411368\pi$
$7$	1.45443	0.549723	0.274862	+	0.961484i	$0.411368\pi$
$8$	−1.00000	−0.353553
$9$	7.05209	2.35070
$10$	−4.15425	−1.31369
$11$	−3.03789	−0.915957	−0.457979	−	0.888963i	$-0.651426\pi$
$11$	−3.03789	−0.915957	−0.457979	+	0.888963i	$0.651426\pi$
$12$	−3.17050	−0.915246
$13$	3.91980	1.08716	0.543579	−	0.839358i	$-0.317069\pi$
$13$	3.91980	1.08716	0.543579	+	0.839358i	$0.317069\pi$
$14$	−1.45443	−0.388713
$15$	−13.1711	−3.40075
$16$	1.00000	0.250000
$17$	−0.0576653	−0.0139859	−0.00699294	−	0.999976i	$-0.502226\pi$
$17$	−0.0576653	−0.0139859	−0.00699294	+	0.999976i	$0.502226\pi$
$18$	−7.05209	−1.66219
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.15425	0.928919
$21$	−4.61128	−1.00626
$22$	3.03789	0.647679
$23$	0.939084	0.195813	0.0979063	−	0.995196i	$-0.468785\pi$
$23$	0.939084	0.195813	0.0979063	+	0.995196i	$0.468785\pi$
$24$	3.17050	0.647176
$25$	12.2578	2.45156
$26$	−3.91980	−0.768736
$27$	−12.8472	−2.47244
$28$	1.45443	0.274862
$29$	−9.74846	−1.81024	−0.905122	−	0.425152i	$-0.860221\pi$
$29$	−9.74846	−1.81024	−0.905122	+	0.425152i	$0.860221\pi$
$30$	13.1711	2.40470
$31$	3.98084	0.714981	0.357490	−	0.933917i	$-0.383633\pi$
$31$	3.98084	0.714981	0.357490	+	0.933917i	$0.383633\pi$
$32$	−1.00000	−0.176777
$33$	9.63163	1.67665
$34$	0.0576653	0.00988951
$35$	6.04207	1.02130
$36$	7.05209	1.17535
$37$	−10.1478	−1.66829	−0.834145	−	0.551545i	$-0.814038\pi$
$37$	−10.1478	−1.66829	−0.834145	+	0.551545i	$0.814038\pi$
$38$	1.00000	0.162221
$39$	−12.4277	−1.99003
$40$	−4.15425	−0.656845
$41$	6.40788	1.00074	0.500372	−	0.865811i	$-0.333197\pi$
$41$	6.40788	1.00074	0.500372	+	0.865811i	$0.333197\pi$
$42$	4.61128	0.711536
$43$	−0.156989	−0.0239406	−0.0119703	−	0.999928i	$-0.503810\pi$
$43$	−0.156989	−0.0239406	−0.0119703	+	0.999928i	$0.503810\pi$
$44$	−3.03789	−0.457979
$45$	29.2962	4.36721
$46$	−0.939084	−0.138460
$47$	−3.44285	−0.502191	−0.251095	−	0.967962i	$-0.580791\pi$
$47$	−3.44285	−0.502191	−0.251095	+	0.967962i	$0.580791\pi$
$48$	−3.17050	−0.457623
$49$	−4.88463	−0.697805
$50$	−12.2578	−1.73351
$51$	0.182828	0.0256010
$52$	3.91980	0.543579
$53$	8.72651	1.19868	0.599339	−	0.800495i	$-0.295430\pi$
$53$	8.72651	1.19868	0.599339	+	0.800495i	$0.295430\pi$
$54$	12.8472	1.74828
$55$	−12.6201	−1.70170
$56$	−1.45443	−0.194356
$57$	3.17050	0.419943
$58$	9.74846	1.28004
$59$	−6.77204	−0.881644	−0.440822	−	0.897595i	$-0.645313\pi$
$59$	−6.77204	−0.881644	−0.440822	+	0.897595i	$0.645313\pi$
$60$	−13.1711	−1.70038
$61$	0.287029	0.0367503	0.0183751	−	0.999831i	$-0.494151\pi$
$61$	0.287029	0.0367503	0.0183751	+	0.999831i	$0.494151\pi$
$62$	−3.98084	−0.505568
$63$	10.2568	1.29223
$64$	1.00000	0.125000
$65$	16.2838	2.01976
$66$	−9.63163	−1.18557
$67$	−0.311296	−0.0380309	−0.0190155	−	0.999819i	$-0.506053\pi$
$67$	−0.311296	−0.0380309	−0.0190155	+	0.999819i	$0.506053\pi$
$68$	−0.0576653	−0.00699294
$69$	−2.97737	−0.358433
$70$	−6.04207	−0.722165
$71$	−4.31993	−0.512681	−0.256341	−	0.966587i	$-0.582517\pi$
$71$	−4.31993	−0.512681	−0.256341	+	0.966587i	$0.582517\pi$
$72$	−7.05209	−0.831097
$73$	−12.8177	−1.50020	−0.750099	−	0.661325i	$-0.769994\pi$
$73$	−12.8177	−1.50020	−0.750099	+	0.661325i	$0.769994\pi$
$74$	10.1478	1.17966
$75$	−38.8634	−4.48756
$76$	−1.00000	−0.114708
$77$	−4.41839	−0.503523
$78$	12.4277	1.40717
$79$	−12.9034	−1.45174	−0.725872	−	0.687830i	$-0.758564\pi$
$79$	−12.9034	−1.45174	−0.725872	+	0.687830i	$0.758564\pi$
$80$	4.15425	0.464459
$81$	19.5758	2.17508
$82$	−6.40788	−0.707632
$83$	−3.11104	−0.341481	−0.170741	−	0.985316i	$-0.554616\pi$
$83$	−3.11104	−0.341481	−0.170741	+	0.985316i	$0.554616\pi$
$84$	−4.61128	−0.503132
$85$	−0.239556	−0.0259835
$86$	0.156989	0.0169285
$87$	30.9075	3.31364
$88$	3.03789	0.323840
$89$	−9.56741	−1.01414	−0.507072	−	0.861904i	$-0.669272\pi$
$89$	−9.56741	−1.01414	−0.507072	+	0.861904i	$0.669272\pi$
$90$	−29.2962	−3.08809
$91$	5.70108	0.597635
$92$	0.939084	0.0979063
$93$	−12.6213	−1.30877
$94$	3.44285	0.355102
$95$	−4.15425	−0.426217
$96$	3.17050	0.323588
$97$	−18.1356	−1.84140	−0.920698	−	0.390276i	$-0.872380\pi$
$97$	−18.1356	−1.84140	−0.920698	+	0.390276i	$0.872380\pi$
$98$	4.88463	0.493422
$99$	−21.4235	−2.15314
$100$	12.2578	1.22578
$101$	−7.67850	−0.764039	−0.382019	−	0.924154i	$-0.624771\pi$
$101$	−7.67850	−0.764039	−0.382019	+	0.924154i	$0.624771\pi$
$102$	−0.182828	−0.0181027
$103$	−13.1794	−1.29861	−0.649304	−	0.760529i	$-0.724940\pi$
$103$	−13.1794	−1.29861	−0.649304	+	0.760529i	$0.724940\pi$
$104$	−3.91980	−0.384368
$105$	−19.1564	−1.86947
$106$	−8.72651	−0.847594
$107$	−14.2013	−1.37289	−0.686445	−	0.727182i	$-0.740830\pi$
$107$	−14.2013	−1.37289	−0.686445	+	0.727182i	$0.740830\pi$
$108$	−12.8472	−1.23622
$109$	−0.357816	−0.0342726	−0.0171363	−	0.999853i	$-0.505455\pi$
$109$	−0.357816	−0.0342726	−0.0171363	+	0.999853i	$0.505455\pi$
$110$	12.6201	1.20328
$111$	32.1737	3.05379
$112$	1.45443	0.137431
$113$	−6.97326	−0.655989	−0.327995	−	0.944680i	$-0.606373\pi$
$113$	−6.97326	−0.655989	−0.327995	+	0.944680i	$0.606373\pi$
$114$	−3.17050	−0.296945
$115$	3.90119	0.363788
$116$	−9.74846	−0.905122
$117$	27.6428	2.55558
$118$	6.77204	0.623416
$119$	−0.0838701	−0.00768836
$120$	13.1711	1.20235
$121$	−1.77125	−0.161023
$122$	−0.287029	−0.0259864
$123$	−20.3162	−1.83185
$124$	3.98084	0.357490
$125$	30.1507	2.69676
$126$	−10.2568	−0.913747
$127$	−8.53078	−0.756985	−0.378492	−	0.925604i	$-0.623557\pi$
$127$	−8.53078	−0.756985	−0.378492	+	0.925604i	$0.623557\pi$
$128$	−1.00000	−0.0883883
$129$	0.497733	0.0438230
$130$	−16.2838	−1.42819
$131$	10.4714	0.914889	0.457445	−	0.889238i	$-0.348765\pi$
$131$	10.4714	0.914889	0.457445	+	0.889238i	$0.348765\pi$
$132$	9.63163	0.838326
$133$	−1.45443	−0.126115
$134$	0.311296	0.0268919
$135$	−53.3704	−4.59339
$136$	0.0576653	0.00494476
$137$	2.96722	0.253507	0.126753	−	0.991934i	$-0.459544\pi$
$137$	2.96722	0.253507	0.126753	+	0.991934i	$0.459544\pi$
$138$	2.97737	0.253451
$139$	−13.6710	−1.15956	−0.579781	−	0.814772i	$-0.696862\pi$
$139$	−13.6710	−1.15956	−0.579781	+	0.814772i	$0.696862\pi$
$140$	6.04207	0.510648
$141$	10.9156	0.919256
$142$	4.31993	0.362520
$143$	−11.9079	−0.995789
$144$	7.05209	0.587675
$145$	−40.4975	−3.36314
$146$	12.8177	1.06080
$147$	15.4867	1.27733
$148$	−10.1478	−0.834145
$149$	23.5793	1.93169	0.965847	−	0.259114i	$-0.0834305\pi$
$149$	23.5793	1.93169	0.965847	+	0.259114i	$0.0834305\pi$
$150$	38.8634	3.17318
$151$	−10.2850	−0.836983	−0.418492	−	0.908221i	$-0.637441\pi$
$151$	−10.2850	−0.836983	−0.418492	+	0.908221i	$0.637441\pi$
$152$	1.00000	0.0811107
$153$	−0.406661	−0.0328766
$154$	4.41839	0.356044
$155$	16.5374	1.32832
$156$	−12.4277	−0.995016
$157$	12.3626	0.986643	0.493321	−	0.869847i	$-0.335783\pi$
$157$	12.3626	0.986643	0.493321	+	0.869847i	$0.335783\pi$
$158$	12.9034	1.02654
$159$	−27.6674	−2.19417
$160$	−4.15425	−0.328422
$161$	1.36583	0.107643
$162$	−19.5758	−1.53802
$163$	−6.34732	−0.497160	−0.248580	−	0.968611i	$-0.579964\pi$
$163$	−6.34732	−0.497160	−0.248580	+	0.968611i	$0.579964\pi$
$164$	6.40788	0.500372
$165$	40.0122	3.11495
$166$	3.11104	0.241464
$167$	−10.5337	−0.815122	−0.407561	−	0.913178i	$-0.633621\pi$
$167$	−10.5337	−0.815122	−0.407561	+	0.913178i	$0.633621\pi$
$168$	4.61128	0.355768
$169$	2.36484	0.181911
$170$	0.239556	0.0183731
$171$	−7.05209	−0.539287
$172$	−0.156989	−0.0119703
$173$	8.42256	0.640355	0.320178	−	0.947358i	$-0.396257\pi$
$173$	8.42256	0.640355	0.320178	+	0.947358i	$0.396257\pi$
$174$	−30.9075	−2.34309
$175$	17.8281	1.34768
$176$	−3.03789	−0.228989
$177$	21.4708	1.61384
$178$	9.56741	0.717107
$179$	7.95295	0.594431	0.297216	−	0.954810i	$-0.403942\pi$
$179$	7.95295	0.594431	0.297216	+	0.954810i	$0.403942\pi$
$180$	29.2962	2.18361
$181$	14.8269	1.10208	0.551038	−	0.834480i	$-0.314232\pi$
$181$	14.8269	1.10208	0.551038	+	0.834480i	$0.314232\pi$
$182$	−5.70108	−0.422592
$183$	−0.910026	−0.0672710
$184$	−0.939084	−0.0692302
$185$	−42.1566	−3.09941
$186$	12.6213	0.925437
$187$	0.175180	0.0128105
$188$	−3.44285	−0.251095
$189$	−18.6853	−1.35916
$190$	4.15425	0.301381
$191$	−9.97021	−0.721419	−0.360710	−	0.932678i	$-0.617465\pi$
$191$	−9.97021	−0.721419	−0.360710	+	0.932678i	$0.617465\pi$
$192$	−3.17050	−0.228811
$193$	1.78617	0.128572	0.0642858	−	0.997932i	$-0.479523\pi$
$193$	1.78617	0.128572	0.0642858	+	0.997932i	$0.479523\pi$
$194$	18.1356	1.30206
$195$	−51.6280	−3.69716
$196$	−4.88463	−0.348902
$197$	−13.7517	−0.979765	−0.489883	−	0.871788i	$-0.662960\pi$
$197$	−13.7517	−0.979765	−0.489883	+	0.871788i	$0.662960\pi$
$198$	21.4235	1.52250
$199$	−19.8784	−1.40914	−0.704571	−	0.709634i	$-0.748860\pi$
$199$	−19.8784	−1.40914	−0.704571	+	0.709634i	$0.748860\pi$
$200$	−12.2578	−0.866757
$201$	0.986967	0.0696153
$202$	7.67850	0.540257
$203$	−14.1785	−0.995133
$204$	0.182828	0.0128005
$205$	26.6200	1.85922
$206$	13.1794	0.918255
$207$	6.62251	0.460296
$208$	3.91980	0.271789
$209$	3.03789	0.210135
$210$	19.1564	1.32192
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	8.72651	0.599339
$213$	13.6964	0.938458
$214$	14.2013	0.970780
$215$	−0.652171	−0.0444777
$216$	12.8472	0.874140
$217$	5.78986	0.393041
$218$	0.357816	0.0242344
$219$	40.6386	2.74610
$220$	−12.6201	−0.850850
$221$	−0.226036	−0.0152049
$222$	−32.1737	−2.15936
$223$	4.38025	0.293323	0.146662	−	0.989187i	$-0.453147\pi$
$223$	4.38025	0.293323	0.146662	+	0.989187i	$0.453147\pi$
$224$	−1.45443	−0.0971782
$225$	86.4431	5.76288
$226$	6.97326	0.463854
$227$	19.0575	1.26489	0.632445	−	0.774605i	$-0.282051\pi$
$227$	19.0575	1.26489	0.632445	+	0.774605i	$0.282051\pi$
$228$	3.17050	0.209972
$229$	−11.0057	−0.727275	−0.363638	−	0.931540i	$-0.618465\pi$
$229$	−11.0057	−0.727275	−0.363638	+	0.931540i	$0.618465\pi$
$230$	−3.90119	−0.257237
$231$	14.0085	0.921694
$232$	9.74846	0.640018
$233$	20.5312	1.34504	0.672522	−	0.740077i	$-0.265211\pi$
$233$	20.5312	1.34504	0.672522	+	0.740077i	$0.265211\pi$
$234$	−27.6428	−1.80707
$235$	−14.3024	−0.932989
$236$	−6.77204	−0.440822
$237$	40.9102	2.65741
$238$	0.0838701	0.00543649
$239$	7.63091	0.493603	0.246801	−	0.969066i	$-0.420621\pi$
$239$	7.63091	0.493603	0.246801	+	0.969066i	$0.420621\pi$
$240$	−13.1711	−0.850189
$241$	7.91820	0.510056	0.255028	−	0.966934i	$-0.417915\pi$
$241$	7.91820	0.510056	0.255028	+	0.966934i	$0.417915\pi$
$242$	1.77125	0.113860
$243$	−23.5235	−1.50903
$244$	0.287029	0.0183751
$245$	−20.2920	−1.29641
$246$	20.3162	1.29531
$247$	−3.91980	−0.249411
$248$	−3.98084	−0.252784
$249$	9.86357	0.625078
$250$	−30.1507	−1.90690
$251$	16.9552	1.07020	0.535102	−	0.844787i	$-0.320273\pi$
$251$	16.9552	1.07020	0.535102	+	0.844787i	$0.320273\pi$
$252$	10.2568	0.646116
$253$	−2.85283	−0.179356
$254$	8.53078	0.535269
$255$	0.759513	0.0475625
$256$	1.00000	0.0625000
$257$	−6.24300	−0.389428	−0.194714	−	0.980860i	$-0.562378\pi$
$257$	−6.24300	−0.389428	−0.194714	+	0.980860i	$0.562378\pi$
$258$	−0.497733	−0.0309875
$259$	−14.7593	−0.917097
$260$	16.2838	1.00988
$261$	−68.7471	−4.25534
$262$	−10.4714	−0.646924
$263$	−12.6080	−0.777442	−0.388721	−	0.921356i	$-0.627083\pi$
$263$	−12.6080	−0.777442	−0.388721	+	0.921356i	$0.627083\pi$
$264$	−9.63163	−0.592786
$265$	36.2521	2.22695
$266$	1.45443	0.0891769
$267$	30.3335	1.85638
$268$	−0.311296	−0.0190155
$269$	29.0252	1.76970	0.884850	−	0.465876i	$-0.154261\pi$
$269$	29.0252	1.76970	0.884850	+	0.465876i	$0.154261\pi$
$270$	53.3704	3.24802
$271$	−7.49327	−0.455184	−0.227592	−	0.973757i	$-0.573085\pi$
$271$	−7.49327	−0.455184	−0.227592	+	0.973757i	$0.573085\pi$
$272$	−0.0576653	−0.00349647
$273$	−18.0753	−1.09397
$274$	−2.96722	−0.179256
$275$	−37.2378	−2.24552
$276$	−2.97737	−0.179217
$277$	−6.01689	−0.361520	−0.180760	−	0.983527i	$-0.557856\pi$
$277$	−6.01689	−0.361520	−0.180760	+	0.983527i	$0.557856\pi$
$278$	13.6710	0.819934
$279$	28.0733	1.68070
$280$	−6.04207	−0.361083
$281$	14.4898	0.864389	0.432194	−	0.901781i	$-0.357739\pi$
$281$	14.4898	0.864389	0.432194	+	0.901781i	$0.357739\pi$
$282$	−10.9156	−0.650012
$283$	−2.63201	−0.156457	−0.0782284	−	0.996935i	$-0.524926\pi$
$283$	−2.63201	−0.156457	−0.0782284	+	0.996935i	$0.524926\pi$
$284$	−4.31993	−0.256341
$285$	13.1711	0.780187
$286$	11.9079	0.704129
$287$	9.31982	0.550132
$288$	−7.05209	−0.415549
$289$	−16.9967	−0.999804
$290$	40.4975	2.37810
$291$	57.4991	3.37066
$292$	−12.8177	−0.750099
$293$	−24.2872	−1.41888	−0.709438	−	0.704768i	$-0.751051\pi$
$293$	−24.2872	−1.41888	−0.709438	+	0.704768i	$0.751051\pi$
$294$	−15.4867	−0.903205
$295$	−28.1327	−1.63795
$296$	10.1478	0.589830
$297$	39.0283	2.26465
$298$	−23.5793	−1.36591
$299$	3.68102	0.212879
$300$	−38.8634	−2.24378
$301$	−0.228329	−0.0131607
$302$	10.2850	0.591837
$303$	24.3447	1.39857
$304$	−1.00000	−0.0573539
$305$	1.19239	0.0682760
$306$	0.406661	0.0232473
$307$	8.75471	0.499658	0.249829	−	0.968290i	$-0.419626\pi$
$307$	8.75471	0.499658	0.249829	+	0.968290i	$0.419626\pi$
$308$	−4.41839	−0.251761
$309$	41.7855	2.37709
$310$	−16.5374	−0.939262
$311$	15.4390	0.875466	0.437733	−	0.899105i	$-0.355782\pi$
$311$	15.4390	0.875466	0.437733	+	0.899105i	$0.355782\pi$
$312$	12.4277	0.703583
$313$	−0.386613	−0.0218526	−0.0109263	−	0.999940i	$-0.503478\pi$
$313$	−0.386613	−0.0218526	−0.0109263	+	0.999940i	$0.503478\pi$
$314$	−12.3626	−0.697662
$315$	42.6092	2.40076
$316$	−12.9034	−0.725872
$317$	−13.7997	−0.775068	−0.387534	−	0.921855i	$-0.626673\pi$
$317$	−13.7997	−0.775068	−0.387534	+	0.921855i	$0.626673\pi$
$318$	27.6674	1.55151
$319$	29.6147	1.65811
$320$	4.15425	0.232230
$321$	45.0252	2.51306
$322$	−1.36583	−0.0761149
$323$	0.0576653	0.00320858
$324$	19.5758	1.08754
$325$	48.0481	2.66523
$326$	6.34732	0.351545
$327$	1.13446	0.0627356
$328$	−6.40788	−0.353816
$329$	−5.00738	−0.276066
$330$	−40.0122	−2.20260
$331$	19.8794	1.09267	0.546334	−	0.837567i	$-0.316023\pi$
$331$	19.8794	1.09267	0.546334	+	0.837567i	$0.316023\pi$
$332$	−3.11104	−0.170741
$333$	−71.5633	−3.92165
$334$	10.5337	0.576379
$335$	−1.29320	−0.0706552
$336$	−4.61128	−0.251566
$337$	−12.9732	−0.706693	−0.353346	−	0.935493i	$-0.614956\pi$
$337$	−12.9732	−0.706693	−0.353346	+	0.935493i	$0.614956\pi$
$338$	−2.36484	−0.128631
$339$	22.1087	1.20078
$340$	−0.239556	−0.0129917
$341$	−12.0933	−0.654892
$342$	7.05209	0.381334
$343$	−17.2854	−0.933322
$344$	0.156989	0.00846427
$345$	−12.3687	−0.665911
$346$	−8.42256	−0.452799
$347$	27.7440	1.48937	0.744687	−	0.667414i	$-0.232599\pi$
$347$	27.7440	1.48937	0.744687	+	0.667414i	$0.232599\pi$
$348$	30.9075	1.65682
$349$	6.35553	0.340204	0.170102	−	0.985426i	$-0.445590\pi$
$349$	6.35553	0.340204	0.170102	+	0.985426i	$0.445590\pi$
$350$	−17.8281	−0.952953
$351$	−50.3584	−2.68793
$352$	3.03789	0.161920
$353$	7.68243	0.408894	0.204447	−	0.978878i	$-0.434460\pi$
$353$	7.68243	0.408894	0.204447	+	0.978878i	$0.434460\pi$
$354$	−21.4708	−1.14116
$355$	−17.9461	−0.952478
$356$	−9.56741	−0.507072
$357$	0.265911	0.0140735
$358$	−7.95295	−0.420326
$359$	9.93902	0.524561	0.262281	−	0.964992i	$-0.415525\pi$
$359$	9.93902	0.524561	0.262281	+	0.964992i	$0.415525\pi$
$360$	−29.2962	−1.54404
$361$	1.00000	0.0526316
$362$	−14.8269	−0.779285
$363$	5.61575	0.294750
$364$	5.70108	0.298818
$365$	−53.2479	−2.78712
$366$	0.910026	0.0475678
$367$	4.61257	0.240774	0.120387	−	0.992727i	$-0.461586\pi$
$367$	4.61257	0.240774	0.120387	+	0.992727i	$0.461586\pi$
$368$	0.939084	0.0489532
$369$	45.1890	2.35245
$370$	42.1566	2.19161
$371$	12.6921	0.658941
$372$	−12.6213	−0.654383
$373$	16.1022	0.833743	0.416871	−	0.908965i	$-0.363127\pi$
$373$	16.1022	0.833743	0.416871	+	0.908965i	$0.363127\pi$
$374$	−0.175180	−0.00905837
$375$	−95.5929	−4.93640
$376$	3.44285	0.177551
$377$	−38.2120	−1.96802
$378$	18.6853	0.961070
$379$	29.8705	1.53434	0.767171	−	0.641442i	$-0.221664\pi$
$379$	29.8705	1.53434	0.767171	+	0.641442i	$0.221664\pi$
$380$	−4.15425	−0.213109
$381$	27.0469	1.38565
$382$	9.97021	0.510120
$383$	−23.5745	−1.20460	−0.602301	−	0.798269i	$-0.705749\pi$
$383$	−23.5745	−1.20460	−0.602301	+	0.798269i	$0.705749\pi$
$384$	3.17050	0.161794
$385$	−18.3551	−0.935463
$386$	−1.78617	−0.0909138
$387$	−1.10710	−0.0562770
$388$	−18.1356	−0.920698
$389$	−19.8553	−1.00671	−0.503353	−	0.864081i	$-0.667900\pi$
$389$	−19.8553	−1.00671	−0.503353	+	0.864081i	$0.667900\pi$
$390$	51.6280	2.61428
$391$	−0.0541525	−0.00273861
$392$	4.88463	0.246711
$393$	−33.1996	−1.67470
$394$	13.7517	0.692799
$395$	−53.6039	−2.69710
$396$	−21.4235	−1.07657
$397$	−13.7957	−0.692388	−0.346194	−	0.938163i	$-0.612526\pi$
$397$	−13.7957	−0.692388	−0.346194	+	0.938163i	$0.612526\pi$
$398$	19.8784	0.996413
$399$	4.61128	0.230853
$400$	12.2578	0.612890
$401$	14.5213	0.725159	0.362579	−	0.931953i	$-0.381896\pi$
$401$	14.5213	0.725159	0.362579	+	0.931953i	$0.381896\pi$
$402$	−0.986967	−0.0492254
$403$	15.6041	0.777296
$404$	−7.67850	−0.382019
$405$	81.3226	4.04095
$406$	14.1785	0.703665
$407$	30.8279	1.52808
$408$	−0.182828	−0.00905133
$409$	11.8236	0.584637	0.292319	−	0.956321i	$-0.405573\pi$
$409$	11.8236	0.584637	0.292319	+	0.956321i	$0.405573\pi$
$410$	−26.6200	−1.31467
$411$	−9.40759	−0.464042
$412$	−13.1794	−0.649304
$413$	−9.84946	−0.484660
$414$	−6.62251	−0.325479
$415$	−12.9240	−0.634416
$416$	−3.91980	−0.192184
$417$	43.3441	2.12257
$418$	−3.03789	−0.148588
$419$	−33.1411	−1.61905	−0.809525	−	0.587085i	$-0.800276\pi$
$419$	−33.1411	−1.61905	−0.809525	+	0.587085i	$0.800276\pi$
$420$	−19.1564	−0.934737
$421$	19.8284	0.966377	0.483188	−	0.875516i	$-0.339479\pi$
$421$	19.8284	0.966377	0.483188	+	0.875516i	$0.339479\pi$
$422$	1.00000	0.0486792
$423$	−24.2793	−1.18050
$424$	−8.72651	−0.423797
$425$	−0.706849	−0.0342872
$426$	−13.6964	−0.663590
$427$	0.417463	0.0202025
$428$	−14.2013	−0.686445
$429$	37.7541	1.82278
$430$	0.652171	0.0314505
$431$	8.59521	0.414017	0.207008	−	0.978339i	$-0.433627\pi$
$431$	8.59521	0.414017	0.207008	+	0.978339i	$0.433627\pi$
$432$	−12.8472	−0.618110
$433$	32.5387	1.56371	0.781854	−	0.623461i	$-0.214274\pi$
$433$	32.5387	1.56371	0.781854	+	0.623461i	$0.214274\pi$
$434$	−5.78986	−0.277922
$435$	128.398	6.15620
$436$	−0.357816	−0.0171363
$437$	−0.939084	−0.0449225
$438$	−40.6386	−1.94179
$439$	−29.6704	−1.41609	−0.708045	−	0.706167i	$-0.750423\pi$
$439$	−29.6704	−1.41609	−0.708045	+	0.706167i	$0.750423\pi$
$440$	12.6201	0.601642
$441$	−34.4469	−1.64033
$442$	0.226036	0.0107515
$443$	24.8856	1.18235	0.591176	−	0.806543i	$-0.298664\pi$
$443$	24.8856	1.18235	0.591176	+	0.806543i	$0.298664\pi$
$444$	32.1737	1.52690
$445$	−39.7454	−1.88411
$446$	−4.38025	−0.207411
$447$	−74.7583	−3.53595
$448$	1.45443	0.0687154
$449$	9.84769	0.464741	0.232371	−	0.972627i	$-0.425352\pi$
$449$	9.84769	0.464741	0.232371	+	0.972627i	$0.425352\pi$
$450$	−86.4431	−4.07497
$451$	−19.4664	−0.916638
$452$	−6.97326	−0.327995
$453$	32.6087	1.53209
$454$	−19.0575	−0.894412
$455$	23.6837	1.11031
$456$	−3.17050	−0.148472
$457$	0.777880	0.0363877	0.0181939	−	0.999834i	$-0.494208\pi$
$457$	0.777880	0.0363877	0.0181939	+	0.999834i	$0.494208\pi$
$458$	11.0057	0.514261
$459$	0.740836	0.0345793
$460$	3.90119	0.181894
$461$	19.4510	0.905922	0.452961	−	0.891530i	$-0.350368\pi$
$461$	19.4510	0.905922	0.452961	+	0.891530i	$0.350368\pi$
$462$	−14.0085	−0.651736
$463$	−27.1820	−1.26325	−0.631626	−	0.775273i	$-0.717612\pi$
$463$	−27.1820	−1.26325	−0.631626	+	0.775273i	$0.717612\pi$
$464$	−9.74846	−0.452561
$465$	−52.4320	−2.43147
$466$	−20.5312	−0.951090
$467$	−24.0989	−1.11517	−0.557583	−	0.830121i	$-0.688271\pi$
$467$	−24.0989	−1.11517	−0.557583	+	0.830121i	$0.688271\pi$
$468$	27.6428	1.27779
$469$	−0.452759	−0.0209065
$470$	14.3024	0.659723
$471$	−39.1957	−1.80604
$472$	6.77204	0.311708
$473$	0.476914	0.0219285
$474$	−40.9102	−1.87907
$475$	−12.2578	−0.562426
$476$	−0.0838701	−0.00384418
$477$	61.5402	2.81773
$478$	−7.63091	−0.349030
$479$	−21.9273	−1.00188	−0.500942	−	0.865481i	$-0.667013\pi$
$479$	−21.9273	−1.00188	−0.500942	+	0.865481i	$0.667013\pi$
$480$	13.1711	0.601174
$481$	−39.7774	−1.81369
$482$	−7.91820	−0.360664
$483$	−4.33038	−0.197039
$484$	−1.77125	−0.0805113
$485$	−75.3400	−3.42101
$486$	23.5235	1.06705
$487$	−21.2962	−0.965021	−0.482511	−	0.875890i	$-0.660275\pi$
$487$	−21.2962	−0.965021	−0.482511	+	0.875890i	$0.660275\pi$
$488$	−0.287029	−0.0129932
$489$	20.1242	0.910048
$490$	20.2920	0.916698
$491$	25.6131	1.15590	0.577952	−	0.816071i	$-0.303852\pi$
$491$	25.6131	1.15590	0.577952	+	0.816071i	$0.303852\pi$
$492$	−20.3162	−0.915926
$493$	0.562148	0.0253179
$494$	3.91980	0.176360
$495$	−88.9984	−4.00018
$496$	3.98084	0.178745
$497$	−6.28304	−0.281833
$498$	−9.86357	−0.441997
$499$	18.2866	0.818619	0.409309	−	0.912396i	$-0.365770\pi$
$499$	18.2866	0.818619	0.409309	+	0.912396i	$0.365770\pi$
$500$	30.1507	1.34838
$501$	33.3971	1.49207
$502$	−16.9552	−0.756749
$503$	−6.95013	−0.309891	−0.154945	−	0.987923i	$-0.549520\pi$
$503$	−6.95013	−0.309891	−0.154945	+	0.987923i	$0.549520\pi$
$504$	−10.2568	−0.456873
$505$	−31.8984	−1.41946
$506$	2.85283	0.126824
$507$	−7.49775	−0.332987
$508$	−8.53078	−0.378492
$509$	−20.8092	−0.922353	−0.461176	−	0.887308i	$-0.652572\pi$
$509$	−20.8092	−0.922353	−0.461176	+	0.887308i	$0.652572\pi$
$510$	−0.759513	−0.0336318
$511$	−18.6425	−0.824694
$512$	−1.00000	−0.0441942
$513$	12.8472	0.567217
$514$	6.24300	0.275367
$515$	−54.7507	−2.41260
$516$	0.497733	0.0219115
$517$	10.4590	0.459985
$518$	14.7593	0.648486
$519$	−26.7037	−1.17216
$520$	−16.2838	−0.714093
$521$	3.50225	0.153437	0.0767183	−	0.997053i	$-0.475556\pi$
$521$	3.50225	0.153437	0.0767183	+	0.997053i	$0.475556\pi$
$522$	68.7471	3.00898
$523$	−21.4134	−0.936342	−0.468171	−	0.883638i	$-0.655087\pi$
$523$	−21.4134	−0.936342	−0.468171	+	0.883638i	$0.655087\pi$
$524$	10.4714	0.457445
$525$	−56.5241	−2.46691
$526$	12.6080	0.549734
$527$	−0.229556	−0.00999963
$528$	9.63163	0.419163
$529$	−22.1181	−0.961657
$530$	−36.2521	−1.57469
$531$	−47.7570	−2.07248
$532$	−1.45443	−0.0630576
$533$	25.1176	1.08797
$534$	−30.3335	−1.31266
$535$	−58.9957	−2.55061
$536$	0.311296	0.0134460
$537$	−25.2148	−1.08810
$538$	−29.0252	−1.25137
$539$	14.8390	0.639159
$540$	−53.3704	−2.29670
$541$	−9.83922	−0.423021	−0.211511	−	0.977376i	$-0.567838\pi$
$541$	−9.83922	−0.423021	−0.211511	+	0.977376i	$0.567838\pi$
$542$	7.49327	0.321864
$543$	−47.0088	−2.01734
$544$	0.0576653	0.00247238
$545$	−1.48646	−0.0636728
$546$	18.0753	0.773551
$547$	37.8317	1.61757	0.808784	−	0.588106i	$-0.200126\pi$
$547$	37.8317	1.61757	0.808784	+	0.588106i	$0.200126\pi$
$548$	2.96722	0.126753
$549$	2.02415	0.0863888
$550$	37.2378	1.58782
$551$	9.74846	0.415298
$552$	2.97737	0.126725
$553$	−18.7671	−0.798057
$554$	6.01689	0.255633
$555$	133.658	5.67345
$556$	−13.6710	−0.579781
$557$	34.4159	1.45825	0.729123	−	0.684382i	$-0.239928\pi$
$557$	34.4159	1.45825	0.729123	+	0.684382i	$0.239928\pi$
$558$	−28.0733	−1.18844
$559$	−0.615365	−0.0260272
$560$	6.04207	0.255324
$561$	−0.555410	−0.0234494
$562$	−14.4898	−0.611215
$563$	−22.0278	−0.928360	−0.464180	−	0.885741i	$-0.653651\pi$
$563$	−22.0278	−0.928360	−0.464180	+	0.885741i	$0.653651\pi$
$564$	10.9156	0.459628
$565$	−28.9687	−1.21872
$566$	2.63201	0.110632
$567$	28.4716	1.19569
$568$	4.31993	0.181260
$569$	4.21399	0.176660	0.0883299	−	0.996091i	$-0.471847\pi$
$569$	4.21399	0.176660	0.0883299	+	0.996091i	$0.471847\pi$
$570$	−13.1711	−0.551675
$571$	17.3831	0.727460	0.363730	−	0.931505i	$-0.381503\pi$
$571$	17.3831	0.727460	0.363730	+	0.931505i	$0.381503\pi$
$572$	−11.9079	−0.497895
$573$	31.6106	1.32055
$574$	−9.31982	−0.389002
$575$	11.5111	0.480046
$576$	7.05209	0.293837
$577$	−4.62484	−0.192534	−0.0962672	−	0.995356i	$-0.530690\pi$
$577$	−4.62484	−0.192534	−0.0962672	+	0.995356i	$0.530690\pi$
$578$	16.9967	0.706968
$579$	−5.66307	−0.235349
$580$	−40.4975	−1.68157
$581$	−4.52479	−0.187720
$582$	−57.4991	−2.38342
$583$	−26.5102	−1.09794
$584$	12.8177	0.530400
$585$	114.835	4.74785
$586$	24.2872	1.00330
$587$	−42.3463	−1.74782	−0.873909	−	0.486090i	$-0.838423\pi$
$587$	−42.3463	−1.74782	−0.873909	+	0.486090i	$0.838423\pi$
$588$	15.4867	0.638663
$589$	−3.98084	−0.164028
$590$	28.1327	1.15821
$591$	43.5997	1.79345
$592$	−10.1478	−0.417073
$593$	2.60427	0.106944	0.0534722	−	0.998569i	$-0.482971\pi$
$593$	2.60427	0.106944	0.0534722	+	0.998569i	$0.482971\pi$
$594$	−39.0283	−1.60135
$595$	−0.348417	−0.0142837
$596$	23.5793	0.965847
$597$	63.0245	2.57942
$598$	−3.68102	−0.150528
$599$	−30.3389	−1.23961	−0.619806	−	0.784755i	$-0.712789\pi$
$599$	−30.3389	−1.23961	−0.619806	+	0.784755i	$0.712789\pi$
$600$	38.8634	1.58659
$601$	1.18657	0.0484014	0.0242007	−	0.999707i	$-0.492296\pi$
$601$	1.18657	0.0484014	0.0242007	+	0.999707i	$0.492296\pi$
$602$	0.228329	0.00930600
$603$	−2.19529	−0.0893992
$604$	−10.2850	−0.418492
$605$	−7.35821	−0.299154
$606$	−24.3447	−0.988936
$607$	14.9293	0.605961	0.302980	−	0.952997i	$-0.402018\pi$
$607$	14.9293	0.605961	0.302980	+	0.952997i	$0.402018\pi$
$608$	1.00000	0.0405554
$609$	44.9529	1.82158
$610$	−1.19239	−0.0482784
$611$	−13.4953	−0.545960
$612$	−0.406661	−0.0164383
$613$	−2.75792	−0.111391	−0.0556957	−	0.998448i	$-0.517738\pi$
$613$	−2.75792	−0.111391	−0.0556957	+	0.998448i	$0.517738\pi$
$614$	−8.75471	−0.353311
$615$	−84.3987	−3.40328
$616$	4.41839	0.178022
$617$	−44.1691	−1.77818	−0.889090	−	0.457733i	$-0.848662\pi$
$617$	−44.1691	−1.77818	−0.889090	+	0.457733i	$0.848662\pi$
$618$	−41.7855	−1.68086
$619$	44.7128	1.79716	0.898580	−	0.438810i	$-0.144600\pi$
$619$	44.7128	1.79716	0.898580	+	0.438810i	$0.144600\pi$
$620$	16.5374	0.664159
$621$	−12.0646	−0.484135
$622$	−15.4390	−0.619048
$623$	−13.9151	−0.557498
$624$	−12.4277	−0.497508
$625$	63.9646	2.55858
$626$	0.386613	0.0154521
$627$	−9.63163	−0.384650
$628$	12.3626	0.493321
$629$	0.585176	0.0233325
$630$	−42.6092	−1.69759
$631$	−37.2117	−1.48137	−0.740687	−	0.671851i	$-0.765500\pi$
$631$	−37.2117	−1.48137	−0.740687	+	0.671851i	$0.765500\pi$
$632$	12.9034	0.513269
$633$	3.17050	0.126016
$634$	13.7997	0.548056
$635$	−35.4390	−1.40635
$636$	−27.6674	−1.09709
$637$	−19.1468	−0.758623
$638$	−29.6147	−1.17246
$639$	−30.4645	−1.20516
$640$	−4.15425	−0.164211
$641$	−28.2909	−1.11742	−0.558711	−	0.829362i	$-0.688704\pi$
$641$	−28.2909	−1.11742	−0.558711	+	0.829362i	$0.688704\pi$
$642$	−45.0252	−1.77700
$643$	19.9394	0.786334	0.393167	−	0.919467i	$-0.371380\pi$
$643$	19.9394	0.786334	0.393167	+	0.919467i	$0.371380\pi$
$644$	1.36583	0.0538214
$645$	2.06771	0.0814160
$646$	−0.0576653	−0.00226881
$647$	10.1935	0.400747	0.200374	−	0.979720i	$-0.435784\pi$
$647$	10.1935	0.400747	0.200374	+	0.979720i	$0.435784\pi$
$648$	−19.5758	−0.769008
$649$	20.5727	0.807548
$650$	−48.0481	−1.88460
$651$	−18.3568	−0.719459
$652$	−6.34732	−0.248580
$653$	30.1532	1.17998	0.589992	−	0.807409i	$-0.299131\pi$
$653$	30.1532	1.17998	0.589992	+	0.807409i	$0.299131\pi$
$654$	−1.13446	−0.0443608
$655$	43.5008	1.69972
$656$	6.40788	0.250186
$657$	−90.3916	−3.52651
$658$	5.00738	0.195208
$659$	48.1829	1.87694	0.938470	−	0.345361i	$-0.112244\pi$
$659$	48.1829	1.87694	0.938470	+	0.345361i	$0.112244\pi$
$660$	40.0122	1.55747
$661$	−27.8493	−1.08321	−0.541606	−	0.840633i	$-0.682183\pi$
$661$	−27.8493	−1.08321	−0.541606	+	0.840633i	$0.682183\pi$
$662$	−19.8794	−0.772634
$663$	0.716649	0.0278323
$664$	3.11104	0.120732
$665$	−6.04207	−0.234301
$666$	71.5633	2.77302
$667$	−9.15463	−0.354469
$668$	−10.5337	−0.407561
$669$	−13.8876	−0.536926
$670$	1.29320	0.0499608
$671$	−0.871961	−0.0336617
$672$	4.61128	0.177884
$673$	−9.17870	−0.353813	−0.176906	−	0.984228i	$-0.556609\pi$
$673$	−9.17870	−0.353813	−0.176906	+	0.984228i	$0.556609\pi$
$674$	12.9732	0.499707
$675$	−157.478	−6.06134
$676$	2.36484	0.0909555
$677$	−24.6506	−0.947398	−0.473699	−	0.880687i	$-0.657082\pi$
$677$	−24.6506	−0.947398	−0.473699	+	0.880687i	$0.657082\pi$
$678$	−22.1087	−0.849081
$679$	−26.3770	−1.01226
$680$	0.239556	0.00918655
$681$	−60.4218	−2.31537
$682$	12.0933	0.463078
$683$	25.3240	0.968996	0.484498	−	0.874792i	$-0.339002\pi$
$683$	25.3240	0.968996	0.484498	+	0.874792i	$0.339002\pi$
$684$	−7.05209	−0.269644
$685$	12.3266	0.470975
$686$	17.2854	0.659959
$687$	34.8935	1.33127
$688$	−0.156989	−0.00598514
$689$	34.2062	1.30315
$690$	12.3687	0.470870
$691$	−17.2389	−0.655799	−0.327900	−	0.944713i	$-0.606341\pi$
$691$	−17.2389	−0.655799	−0.327900	+	0.944713i	$0.606341\pi$
$692$	8.42256	0.320178
$693$	−31.1589	−1.18363
$694$	−27.7440	−1.05315
$695$	−56.7929	−2.15428
$696$	−30.9075	−1.17155
$697$	−0.369512	−0.0139963
$698$	−6.35553	−0.240560
$699$	−65.0943	−2.46209
$700$	17.8281	0.673839
$701$	−4.73529	−0.178850	−0.0894248	−	0.995994i	$-0.528503\pi$
$701$	−4.73529	−0.178850	−0.0894248	+	0.995994i	$0.528503\pi$
$702$	50.3584	1.90066
$703$	10.1478	0.382732
$704$	−3.03789	−0.114495
$705$	45.3460	1.70783
$706$	−7.68243	−0.289132
$707$	−11.1678	−0.420010
$708$	21.4708	0.806921
$709$	20.3422	0.763969	0.381984	−	0.924169i	$-0.375241\pi$
$709$	20.3422	0.763969	0.381984	+	0.924169i	$0.375241\pi$
$710$	17.9461	0.673504
$711$	−90.9959	−3.41261
$712$	9.56741	0.358554
$713$	3.73835	0.140002
$714$	−0.265911	−0.00995145
$715$	−49.4684	−1.85001
$716$	7.95295	0.297216
$717$	−24.1938	−0.903535
$718$	−9.93902	−0.370921
$719$	34.9210	1.30233	0.651167	−	0.758935i	$-0.274280\pi$
$719$	34.9210	1.30233	0.651167	+	0.758935i	$0.274280\pi$
$720$	29.2962	1.09180
$721$	−19.1686	−0.713875
$722$	−1.00000	−0.0372161
$723$	−25.1047	−0.933653
$724$	14.8269	0.551038
$725$	−119.495	−4.43792
$726$	−5.61575	−0.208420
$727$	37.0004	1.37227	0.686134	−	0.727475i	$-0.259306\pi$
$727$	37.0004	1.37227	0.686134	+	0.727475i	$0.259306\pi$
$728$	−5.70108	−0.211296
$729$	15.8539	0.587183
$730$	53.2479	1.97079
$731$	0.00905280	0.000334830 0
$732$	−0.910026	−0.0336355
$733$	5.92531	0.218856	0.109428	−	0.993995i	$-0.465098\pi$
$733$	5.92531	0.218856	0.109428	+	0.993995i	$0.465098\pi$
$734$	−4.61257	−0.170253
$735$	64.3358	2.37306
$736$	−0.939084	−0.0346151
$737$	0.945683	0.0348347
$738$	−45.1890	−1.66343
$739$	−5.80209	−0.213433	−0.106717	−	0.994289i	$-0.534034\pi$
$739$	−5.80209	−0.213433	−0.106717	+	0.994289i	$0.534034\pi$
$740$	−42.1566	−1.54971
$741$	12.4277	0.456545
$742$	−12.6921	−0.465942
$743$	−30.1097	−1.10462	−0.552309	−	0.833640i	$-0.686253\pi$
$743$	−30.1097	−1.10462	−0.552309	+	0.833640i	$0.686253\pi$
$744$	12.6213	0.462719
$745$	97.9544	3.58877
$746$	−16.1022	−0.589545
$747$	−21.9394	−0.802719
$748$	0.175180	0.00640523
$749$	−20.6548	−0.754709
$750$	95.5929	3.49056
$751$	35.8092	1.30670	0.653348	−	0.757058i	$-0.273364\pi$
$751$	35.8092	1.30670	0.653348	+	0.757058i	$0.273364\pi$
$752$	−3.44285	−0.125548
$753$	−53.7566	−1.95900
$754$	38.2120	1.39160
$755$	−42.7266	−1.55498
$756$	−18.6853	−0.679579
$757$	−51.7008	−1.87910	−0.939549	−	0.342413i	$-0.888756\pi$
$757$	−51.7008	−1.87910	−0.939549	+	0.342413i	$0.888756\pi$
$758$	−29.8705	−1.08494
$759$	9.04491	0.328310
$760$	4.15425	0.150691
$761$	6.50864	0.235938	0.117969	−	0.993017i	$-0.462362\pi$
$761$	6.50864	0.235938	0.117969	+	0.993017i	$0.462362\pi$
$762$	−27.0469	−0.979805
$763$	−0.520419	−0.0188404
$764$	−9.97021	−0.360710
$765$	−1.68937	−0.0610793
$766$	23.5745	0.851782
$767$	−26.5450	−0.958486
$768$	−3.17050	−0.114406
$769$	43.9051	1.58326	0.791630	−	0.611001i	$-0.209233\pi$
$769$	43.9051	1.58326	0.791630	+	0.611001i	$0.209233\pi$
$770$	18.3551	0.661472
$771$	19.7935	0.712844
$772$	1.78617	0.0642858
$773$	2.09840	0.0754742	0.0377371	−	0.999288i	$-0.487985\pi$
$773$	2.09840	0.0754742	0.0377371	+	0.999288i	$0.487985\pi$
$774$	1.10710	0.0397939
$775$	48.7964	1.75282
$776$	18.1356	0.651032
$777$	46.7944	1.67874
$778$	19.8553	0.711848
$779$	−6.40788	−0.229586
$780$	−51.6280	−1.84858
$781$	13.1235	0.469594
$782$	0.0541525	0.00193649
$783$	125.240	4.47572
$784$	−4.88463	−0.174451
$785$	51.3573	1.83302
$786$	33.1996	1.18419
$787$	−33.1316	−1.18101	−0.590507	−	0.807033i	$-0.701072\pi$
$787$	−33.1316	−1.18101	−0.590507	+	0.807033i	$0.701072\pi$
$788$	−13.7517	−0.489883
$789$	39.9737	1.42310
$790$	53.6039	1.90714
$791$	−10.1421	−0.360612
$792$	21.4235	0.761249
$793$	1.12510	0.0399533
$794$	13.7957	0.489592
$795$	−114.937	−4.07641
$796$	−19.8784	−0.704571
$797$	−33.8646	−1.19955	−0.599773	−	0.800170i	$-0.704742\pi$
$797$	−33.8646	−1.19955	−0.599773	+	0.800170i	$0.704742\pi$
$798$	−4.61128	−0.163237
$799$	0.198533	0.00702358
$800$	−12.2578	−0.433379
$801$	−67.4703	−2.38394
$802$	−14.5213	−0.512765
$803$	38.9387	1.37412
$804$	0.986967	0.0348076
$805$	5.67401	0.199983
$806$	−15.6041	−0.549632
$807$	−92.0246	−3.23942
$808$	7.67850	0.270129
$809$	−20.2397	−0.711589	−0.355794	−	0.934564i	$-0.615790\pi$
$809$	−20.2397	−0.711589	−0.355794	+	0.934564i	$0.615790\pi$
$810$	−81.3226	−2.85738
$811$	10.4968	0.368593	0.184297	−	0.982871i	$-0.440999\pi$
$811$	10.4968	0.368593	0.184297	+	0.982871i	$0.440999\pi$
$812$	−14.1785	−0.497566
$813$	23.7575	0.833210
$814$	−30.8279	−1.08052
$815$	−26.3684	−0.923643
$816$	0.182828	0.00640026
$817$	0.156989	0.00549234
$818$	−11.8236	−0.413401
$819$	40.2045	1.40486
$820$	26.6200	0.929609
$821$	52.5147	1.83277	0.916387	−	0.400293i	$-0.131092\pi$
$821$	52.5147	1.83277	0.916387	+	0.400293i	$0.131092\pi$
$822$	9.40759	0.328127
$823$	−33.5956	−1.17107	−0.585534	−	0.810648i	$-0.699115\pi$
$823$	−33.5956	−1.17107	−0.585534	+	0.810648i	$0.699115\pi$
$824$	13.1794	0.459127
$825$	118.063	4.11041
$826$	9.84946	0.342706
$827$	3.54004	0.123099	0.0615497	−	0.998104i	$-0.480396\pi$
$827$	3.54004	0.123099	0.0615497	+	0.998104i	$0.480396\pi$
$828$	6.62251	0.230148
$829$	33.7704	1.17289	0.586447	−	0.809988i	$-0.300526\pi$
$829$	33.7704	1.17289	0.586447	+	0.809988i	$0.300526\pi$
$830$	12.9240	0.448600
$831$	19.0766	0.661759
$832$	3.91980	0.135895
$833$	0.281674	0.00975941
$834$	−43.3441	−1.50088
$835$	−43.7596	−1.51436
$836$	3.03789	0.105067
$837$	−51.1426	−1.76775
$838$	33.1411	1.14484
$839$	45.3293	1.56494	0.782471	−	0.622687i	$-0.213959\pi$
$839$	45.3293	1.56494	0.782471	+	0.622687i	$0.213959\pi$
$840$	19.1564	0.660959
$841$	66.0325	2.27698
$842$	−19.8284	−0.683332
$843$	−45.9399	−1.58226
$844$	−1.00000	−0.0344214
$845$	9.82415	0.337961
$846$	24.2793	0.834739
$847$	−2.57616	−0.0885178
$848$	8.72651	0.299670
$849$	8.34480	0.286393
$850$	0.706849	0.0242447
$851$	−9.52965	−0.326672
$852$	13.6964	0.469229
$853$	−6.92761	−0.237197	−0.118598	−	0.992942i	$-0.537840\pi$
$853$	−6.92761	−0.237197	−0.118598	+	0.992942i	$0.537840\pi$
$854$	−0.417463	−0.0142853
$855$	−29.2962	−1.00191
$856$	14.2013	0.485390
$857$	−41.2487	−1.40903	−0.704515	−	0.709689i	$-0.748836\pi$
$857$	−41.2487	−1.40903	−0.704515	+	0.709689i	$0.748836\pi$
$858$	−37.7541	−1.28890
$859$	45.2548	1.54407	0.772037	−	0.635578i	$-0.219238\pi$
$859$	45.2548	1.54407	0.772037	+	0.635578i	$0.219238\pi$
$860$	−0.652171	−0.0222388
$861$	−29.5485	−1.00701
$862$	−8.59521	−0.292754
$863$	49.3379	1.67948	0.839741	−	0.542987i	$-0.182707\pi$
$863$	49.3379	1.67948	0.839741	+	0.542987i	$0.182707\pi$
$864$	12.8472	0.437070
$865$	34.9894	1.18968
$866$	−32.5387	−1.10571
$867$	53.8880	1.83013
$868$	5.78986	0.196521
$869$	39.1990	1.32974
$870$	−128.398	−4.35309
$871$	−1.22022	−0.0413456
$872$	0.357816	0.0121172
$873$	−127.894	−4.32857
$874$	0.939084	0.0317650
$875$	43.8521	1.48247
$876$	40.6386	1.37305
$877$	−32.3710	−1.09309	−0.546545	−	0.837430i	$-0.684057\pi$
$877$	−32.3710	−1.09309	−0.546545	+	0.837430i	$0.684057\pi$
$878$	29.6704	1.00133
$879$	77.0028	2.59724
$880$	−12.6201	−0.425425
$881$	−39.5537	−1.33260	−0.666299	−	0.745685i	$-0.732123\pi$
$881$	−39.5537	−1.33260	−0.666299	+	0.745685i	$0.732123\pi$
$882$	34.4469	1.15989
$883$	39.4514	1.32765	0.663823	−	0.747890i	$-0.268933\pi$
$883$	39.4514	1.32765	0.663823	+	0.747890i	$0.268933\pi$
$884$	−0.226036	−0.00760243
$885$	89.1949	2.99826
$886$	−24.8856	−0.836049
$887$	8.24868	0.276964	0.138482	−	0.990365i	$-0.455778\pi$
$887$	8.24868	0.276964	0.138482	+	0.990365i	$0.455778\pi$
$888$	−32.1737	−1.07968
$889$	−12.4074	−0.416132
$890$	39.7454	1.33227
$891$	−59.4689	−1.99228
$892$	4.38025	0.146662
$893$	3.44285	0.115210
$894$	74.7583	2.50029
$895$	33.0385	1.10436
$896$	−1.45443	−0.0485891
$897$	−11.6707	−0.389673
$898$	−9.84769	−0.328622
$899$	−38.8071	−1.29429
$900$	86.4431	2.88144
$901$	−0.503217	−0.0167646
$902$	19.4664	0.648161
$903$	0.723919	0.0240905
$904$	6.97326	0.231927
$905$	61.5947	2.04748
$906$	−32.6087	−1.08335
$907$	0.955559	0.0317288	0.0158644	−	0.999874i	$-0.494950\pi$
$907$	0.955559	0.0317288	0.0158644	+	0.999874i	$0.494950\pi$
$908$	19.0575	0.632445
$909$	−54.1495	−1.79602
$910$	−23.6837	−0.785107
$911$	48.9747	1.62260	0.811302	−	0.584628i	$-0.198759\pi$
$911$	48.9747	1.62260	0.811302	+	0.584628i	$0.198759\pi$
$912$	3.17050	0.104986
$913$	9.45099	0.312782
$914$	−0.777880	−0.0257300
$915$	−3.78047	−0.124979
$916$	−11.0057	−0.363638
$917$	15.2299	0.502936
$918$	−0.740836	−0.0244512
$919$	30.8314	1.01704	0.508518	−	0.861051i	$-0.330194\pi$
$919$	30.8314	1.01704	0.508518	+	0.861051i	$0.330194\pi$
$920$	−3.90119	−0.128618
$921$	−27.7568	−0.914619
$922$	−19.4510	−0.640584
$923$	−16.9333	−0.557365
$924$	14.0085	0.460847
$925$	−124.390	−4.08991
$926$	27.1820	0.893255
$927$	−92.9426	−3.05264
$928$	9.74846	0.320009
$929$	9.70941	0.318555	0.159278	−	0.987234i	$-0.449083\pi$
$929$	9.70941	0.318555	0.159278	+	0.987234i	$0.449083\pi$
$930$	52.4320	1.71931
$931$	4.88463	0.160087
$932$	20.5312	0.672522
$933$	−48.9494	−1.60253
$934$	24.0989	0.788541
$935$	0.727744	0.0237998
$936$	−27.6428	−0.903533
$937$	−8.70932	−0.284521	−0.142260	−	0.989829i	$-0.545437\pi$
$937$	−8.70932	−0.284521	−0.142260	+	0.989829i	$0.545437\pi$
$938$	0.452759	0.0147831
$939$	1.22576	0.0400010
$940$	−14.3024	−0.466494
$941$	−33.6765	−1.09782	−0.548911	−	0.835881i	$-0.684957\pi$
$941$	−33.6765	−1.09782	−0.548911	+	0.835881i	$0.684957\pi$
$942$	39.1957	1.27706
$943$	6.01754	0.195958
$944$	−6.77204	−0.220411
$945$	−77.6235	−2.52509
$946$	−0.476914	−0.0155058
$947$	−33.7792	−1.09768	−0.548838	−	0.835929i	$-0.684930\pi$
$947$	−33.7792	−1.09768	−0.548838	+	0.835929i	$0.684930\pi$
$948$	40.9102	1.32870
$949$	−50.2428	−1.63095
$950$	12.2578	0.397695
$951$	43.7520	1.41875
$952$	0.0838701	0.00271825
$953$	3.70589	0.120045	0.0600227	−	0.998197i	$-0.480883\pi$
$953$	3.70589	0.120045	0.0600227	+	0.998197i	$0.480883\pi$
$954$	−61.5402	−1.99244
$955$	−41.4188	−1.34028
$956$	7.63091	0.246801
$957$	−93.8936	−3.03515
$958$	21.9273	0.708439
$959$	4.31562	0.139359
$960$	−13.1711	−0.425094
$961$	−15.1529	−0.488803
$962$	39.7774	1.28248
$963$	−100.149	−3.22725
$964$	7.91820	0.255028
$965$	7.42021	0.238865
$966$	4.33038	0.139328
$967$	21.3235	0.685716	0.342858	−	0.939387i	$-0.388605\pi$
$967$	21.3235	0.685716	0.342858	+	0.939387i	$0.388605\pi$
$968$	1.77125	0.0569301
$969$	−0.182828	−0.00587328
$970$	75.3400	2.41902
$971$	25.9844	0.833877	0.416939	−	0.908935i	$-0.363103\pi$
$971$	25.9844	0.833877	0.416939	+	0.908935i	$0.363103\pi$
$972$	−23.5235	−0.754515
$973$	−19.8836	−0.637438
$974$	21.2962	0.682373
$975$	−152.337	−4.87868
$976$	0.287029	0.00918757
$977$	−3.60541	−0.115347	−0.0576737	−	0.998335i	$-0.518368\pi$
$977$	−3.60541	−0.115347	−0.0576737	+	0.998335i	$0.518368\pi$
$978$	−20.1242	−0.643501
$979$	29.0647	0.928912
$980$	−20.2920	−0.648204
$981$	−2.52335	−0.0805645
$982$	−25.6131	−0.817348
$983$	−23.2306	−0.740941	−0.370470	−	0.928844i	$-0.620803\pi$
$983$	−23.2306	−0.740941	−0.370470	+	0.928844i	$0.620803\pi$
$984$	20.3162	0.647657
$985$	−57.1279	−1.82024
$986$	−0.562148	−0.0179024
$987$	15.8759	0.505336
$988$	−3.91980	−0.124705
$989$	−0.147426	−0.00468786
$990$	88.9984	2.82856
$991$	−0.555456	−0.0176446	−0.00882232	−	0.999961i	$-0.502808\pi$
$991$	−0.555456	−0.0176446	−0.00882232	+	0.999961i	$0.502808\pi$
$992$	−3.98084	−0.126392
$993$	−63.0276	−2.00012
$994$	6.28304	0.199286
$995$	−82.5798	−2.61795
$996$	9.86357	0.312539
$997$	−42.7170	−1.35286	−0.676431	−	0.736506i	$-0.736474\pi$
$997$	−42.7170	−1.35286	−0.676431	+	0.736506i	$0.736474\pi$
$998$	−18.2866	−0.578851
$999$	130.371	4.12475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.2	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.17050 q^{3} +1.00000 q^{4} +4.15425 q^{5} +3.17050 q^{6} +1.45443 q^{7} -1.00000 q^{8} +7.05209 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.17050 q^{3} +1.00000 q^{4} +4.15425 q^{5} +3.17050 q^{6} +1.45443 q^{7} -1.00000 q^{8} +7.05209 q^{9} -4.15425 q^{10} -3.03789 q^{11} -3.17050 q^{12} +3.91980 q^{13} -1.45443 q^{14} -13.1711 q^{15} +1.00000 q^{16} -0.0576653 q^{17} -7.05209 q^{18} -1.00000 q^{19} +4.15425 q^{20} -4.61128 q^{21} +3.03789 q^{22} +0.939084 q^{23} +3.17050 q^{24} +12.2578 q^{25} -3.91980 q^{26} -12.8472 q^{27} +1.45443 q^{28} -9.74846 q^{29} +13.1711 q^{30} +3.98084 q^{31} -1.00000 q^{32} +9.63163 q^{33} +0.0576653 q^{34} +6.04207 q^{35} +7.05209 q^{36} -10.1478 q^{37} +1.00000 q^{38} -12.4277 q^{39} -4.15425 q^{40} +6.40788 q^{41} +4.61128 q^{42} -0.156989 q^{43} -3.03789 q^{44} +29.2962 q^{45} -0.939084 q^{46} -3.44285 q^{47} -3.17050 q^{48} -4.88463 q^{49} -12.2578 q^{50} +0.182828 q^{51} +3.91980 q^{52} +8.72651 q^{53} +12.8472 q^{54} -12.6201 q^{55} -1.45443 q^{56} +3.17050 q^{57} +9.74846 q^{58} -6.77204 q^{59} -13.1711 q^{60} +0.287029 q^{61} -3.98084 q^{62} +10.2568 q^{63} +1.00000 q^{64} +16.2838 q^{65} -9.63163 q^{66} -0.311296 q^{67} -0.0576653 q^{68} -2.97737 q^{69} -6.04207 q^{70} -4.31993 q^{71} -7.05209 q^{72} -12.8177 q^{73} +10.1478 q^{74} -38.8634 q^{75} -1.00000 q^{76} -4.41839 q^{77} +12.4277 q^{78} -12.9034 q^{79} +4.15425 q^{80} +19.5758 q^{81} -6.40788 q^{82} -3.11104 q^{83} -4.61128 q^{84} -0.239556 q^{85} +0.156989 q^{86} +30.9075 q^{87} +3.03789 q^{88} -9.56741 q^{89} -29.2962 q^{90} +5.70108 q^{91} +0.939084 q^{92} -12.6213 q^{93} +3.44285 q^{94} -4.15425 q^{95} +3.17050 q^{96} -18.1356 q^{97} +4.88463 q^{98} -21.4235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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