LMFDB - Embedded newform 8018.2.a.f.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} -1.88296 q^{10} -2.76481 q^{11} -2.09965 q^{12} +1.57116 q^{13} +4.81740 q^{14} -3.95354 q^{15} +1.00000 q^{16} -7.15980 q^{17} -1.40851 q^{18} -1.00000 q^{19} +1.88296 q^{20} +10.1148 q^{21} +2.76481 q^{22} -0.301499 q^{23} +2.09965 q^{24} -1.45447 q^{25} -1.57116 q^{26} +3.34156 q^{27} -4.81740 q^{28} +5.33121 q^{29} +3.95354 q^{30} +1.70809 q^{31} -1.00000 q^{32} +5.80512 q^{33} +7.15980 q^{34} -9.07096 q^{35} +1.40851 q^{36} -0.603139 q^{37} +1.00000 q^{38} -3.29888 q^{39} -1.88296 q^{40} +10.5477 q^{41} -10.1148 q^{42} +1.20780 q^{43} -2.76481 q^{44} +2.65216 q^{45} +0.301499 q^{46} -0.389772 q^{47} -2.09965 q^{48} +16.2074 q^{49} +1.45447 q^{50} +15.0330 q^{51} +1.57116 q^{52} +1.22228 q^{53} -3.34156 q^{54} -5.20601 q^{55} +4.81740 q^{56} +2.09965 q^{57} -5.33121 q^{58} +5.27734 q^{59} -3.95354 q^{60} +12.5527 q^{61} -1.70809 q^{62} -6.78536 q^{63} +1.00000 q^{64} +2.95843 q^{65} -5.80512 q^{66} +1.65938 q^{67} -7.15980 q^{68} +0.633041 q^{69} +9.07096 q^{70} +1.20648 q^{71} -1.40851 q^{72} -4.43364 q^{73} +0.603139 q^{74} +3.05388 q^{75} -1.00000 q^{76} +13.3192 q^{77} +3.29888 q^{78} -5.43480 q^{79} +1.88296 q^{80} -11.2416 q^{81} -10.5477 q^{82} -0.714078 q^{83} +10.1148 q^{84} -13.4816 q^{85} -1.20780 q^{86} -11.1937 q^{87} +2.76481 q^{88} -4.35208 q^{89} -2.65216 q^{90} -7.56892 q^{91} -0.301499 q^{92} -3.58638 q^{93} +0.389772 q^{94} -1.88296 q^{95} +2.09965 q^{96} +6.13058 q^{97} -16.2074 q^{98} -3.89426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.09965	−1.21223	−0.606115	−	0.795377i	$-0.707273\pi$
$3$	−2.09965	−1.21223	−0.606115	+	0.795377i	$0.707273\pi$
$4$	1.00000	0.500000
$5$	1.88296	0.842084	0.421042	−	0.907041i	$-0.361665\pi$
$5$	1.88296	0.842084	0.421042	+	0.907041i	$0.361665\pi$
$6$	2.09965	0.857177
$7$	−4.81740	−1.82081	−0.910403	−	0.413722i	$-0.864229\pi$
$7$	−4.81740	−1.82081	−0.910403	+	0.413722i	$0.864229\pi$
$8$	−1.00000	−0.353553
$9$	1.40851	0.469504
$10$	−1.88296	−0.595443
$11$	−2.76481	−0.833621	−0.416811	−	0.908993i	$-0.636852\pi$
$11$	−2.76481	−0.833621	−0.416811	+	0.908993i	$0.636852\pi$
$12$	−2.09965	−0.606115
$13$	1.57116	0.435762	0.217881	−	0.975975i	$-0.430086\pi$
$13$	1.57116	0.435762	0.217881	+	0.975975i	$0.430086\pi$
$14$	4.81740	1.28750
$15$	−3.95354	−1.02080
$16$	1.00000	0.250000
$17$	−7.15980	−1.73651	−0.868253	−	0.496121i	$-0.834757\pi$
$17$	−7.15980	−1.73651	−0.868253	+	0.496121i	$0.834757\pi$
$18$	−1.40851	−0.331989
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.88296	0.421042
$21$	10.1148	2.20724
$22$	2.76481	0.589459
$23$	−0.301499	−0.0628669	−0.0314335	−	0.999506i	$-0.510007\pi$
$23$	−0.301499	−0.0628669	−0.0314335	+	0.999506i	$0.510007\pi$
$24$	2.09965	0.428588
$25$	−1.45447	−0.290895
$26$	−1.57116	−0.308130
$27$	3.34156	0.643084
$28$	−4.81740	−0.910403
$29$	5.33121	0.989981	0.494991	−	0.868898i	$-0.335172\pi$
$29$	5.33121	0.989981	0.494991	+	0.868898i	$0.335172\pi$
$30$	3.95354	0.721815
$31$	1.70809	0.306782	0.153391	−	0.988166i	$-0.450981\pi$
$31$	1.70809	0.306782	0.153391	+	0.988166i	$0.450981\pi$
$32$	−1.00000	−0.176777
$33$	5.80512	1.01054
$34$	7.15980	1.22790
$35$	−9.07096	−1.53327
$36$	1.40851	0.234752
$37$	−0.603139	−0.0991555	−0.0495777	−	0.998770i	$-0.515788\pi$
$37$	−0.603139	−0.0991555	−0.0495777	+	0.998770i	$0.515788\pi$
$38$	1.00000	0.162221
$39$	−3.29888	−0.528244
$40$	−1.88296	−0.297722
$41$	10.5477	1.64728	0.823639	−	0.567114i	$-0.191940\pi$
$41$	10.5477	1.64728	0.823639	+	0.567114i	$0.191940\pi$
$42$	−10.1148	−1.56075
$43$	1.20780	0.184188	0.0920940	−	0.995750i	$-0.470644\pi$
$43$	1.20780	0.184188	0.0920940	+	0.995750i	$0.470644\pi$
$44$	−2.76481	−0.416811
$45$	2.65216	0.395361
$46$	0.301499	0.0444536
$47$	−0.389772	−0.0568541	−0.0284271	−	0.999596i	$-0.509050\pi$
$47$	−0.389772	−0.0568541	−0.0284271	+	0.999596i	$0.509050\pi$
$48$	−2.09965	−0.303058
$49$	16.2074	2.31534
$50$	1.45447	0.205694
$51$	15.0330	2.10505
$52$	1.57116	0.217881
$53$	1.22228	0.167892	0.0839462	−	0.996470i	$-0.473248\pi$
$53$	1.22228	0.167892	0.0839462	+	0.996470i	$0.473248\pi$
$54$	−3.34156	−0.454729
$55$	−5.20601	−0.701979
$56$	4.81740	0.643752
$57$	2.09965	0.278105
$58$	−5.33121	−0.700022
$59$	5.27734	0.687051	0.343526	−	0.939143i	$-0.388379\pi$
$59$	5.27734	0.687051	0.343526	+	0.939143i	$0.388379\pi$
$60$	−3.95354	−0.510400
$61$	12.5527	1.60721	0.803605	−	0.595164i	$-0.202913\pi$
$61$	12.5527	1.60721	0.803605	+	0.595164i	$0.202913\pi$
$62$	−1.70809	−0.216927
$63$	−6.78536	−0.854875
$64$	1.00000	0.125000
$65$	2.95843	0.366948
$66$	−5.80512	−0.714560
$67$	1.65938	0.202725	0.101363	−	0.994850i	$-0.467680\pi$
$67$	1.65938	0.202725	0.101363	+	0.994850i	$0.467680\pi$
$68$	−7.15980	−0.868253
$69$	0.633041	0.0762092
$70$	9.07096	1.08419
$71$	1.20648	0.143183	0.0715915	−	0.997434i	$-0.477192\pi$
$71$	1.20648	0.143183	0.0715915	+	0.997434i	$0.477192\pi$
$72$	−1.40851	−0.165995
$73$	−4.43364	−0.518918	−0.259459	−	0.965754i	$-0.583544\pi$
$73$	−4.43364	−0.518918	−0.259459	+	0.965754i	$0.583544\pi$
$74$	0.603139	0.0701135
$75$	3.05388	0.352632
$76$	−1.00000	−0.114708
$77$	13.3192	1.51786
$78$	3.29888	0.373525
$79$	−5.43480	−0.611463	−0.305731	−	0.952118i	$-0.598901\pi$
$79$	−5.43480	−0.611463	−0.305731	+	0.952118i	$0.598901\pi$
$80$	1.88296	0.210521
$81$	−11.2416	−1.24907
$82$	−10.5477	−1.16480
$83$	−0.714078	−0.0783802	−0.0391901	−	0.999232i	$-0.512478\pi$
$83$	−0.714078	−0.0783802	−0.0391901	+	0.999232i	$0.512478\pi$
$84$	10.1148	1.10362
$85$	−13.4816	−1.46228
$86$	−1.20780	−0.130241
$87$	−11.1937	−1.20009
$88$	2.76481	0.294730
$89$	−4.35208	−0.461320	−0.230660	−	0.973034i	$-0.574088\pi$
$89$	−4.35208	−0.461320	−0.230660	+	0.973034i	$0.574088\pi$
$90$	−2.65216	−0.279563
$91$	−7.56892	−0.793438
$92$	−0.301499	−0.0314335
$93$	−3.58638	−0.371890
$94$	0.389772	0.0402019
$95$	−1.88296	−0.193187
$96$	2.09965	0.214294
$97$	6.13058	0.622466	0.311233	−	0.950334i	$-0.399258\pi$
$97$	6.13058	0.622466	0.311233	+	0.950334i	$0.399258\pi$
$98$	−16.2074	−1.63719
$99$	−3.89426	−0.391388
$100$	−1.45447	−0.145447
$101$	12.0025	1.19429	0.597146	−	0.802132i	$-0.296301\pi$
$101$	12.0025	1.19429	0.597146	+	0.802132i	$0.296301\pi$
$102$	−15.0330	−1.48849
$103$	−0.0219020	−0.00215807	−0.00107904	−	0.999999i	$-0.500343\pi$
$103$	−0.0219020	−0.00215807	−0.00107904	+	0.999999i	$0.500343\pi$
$104$	−1.57116	−0.154065
$105$	19.0458	1.85868
$106$	−1.22228	−0.118718
$107$	−12.4139	−1.20010	−0.600050	−	0.799962i	$-0.704853\pi$
$107$	−12.4139	−1.20010	−0.600050	+	0.799962i	$0.704853\pi$
$108$	3.34156	0.321542
$109$	11.4172	1.09357	0.546785	−	0.837273i	$-0.315851\pi$
$109$	11.4172	1.09357	0.546785	+	0.837273i	$0.315851\pi$
$110$	5.20601	0.496374
$111$	1.26638	0.120199
$112$	−4.81740	−0.455202
$113$	13.0848	1.23091	0.615456	−	0.788171i	$-0.288972\pi$
$113$	13.0848	1.23091	0.615456	+	0.788171i	$0.288972\pi$
$114$	−2.09965	−0.196650
$115$	−0.567710	−0.0529392
$116$	5.33121	0.494991
$117$	2.21300	0.204592
$118$	−5.27734	−0.485818
$119$	34.4916	3.16184
$120$	3.95354	0.360907
$121$	−3.35584	−0.305076
$122$	−12.5527	−1.13647
$123$	−22.1465	−1.99688
$124$	1.70809	0.153391
$125$	−12.1535	−1.08704
$126$	6.78536	0.604488
$127$	11.3371	1.00601	0.503003	−	0.864284i	$-0.332228\pi$
$127$	11.3371	1.00601	0.503003	+	0.864284i	$0.332228\pi$
$128$	−1.00000	−0.0883883
$129$	−2.53595	−0.223278
$130$	−2.95843	−0.259471
$131$	−12.1602	−1.06244	−0.531220	−	0.847234i	$-0.678266\pi$
$131$	−12.1602	−1.06244	−0.531220	+	0.847234i	$0.678266\pi$
$132$	5.80512	0.505271
$133$	4.81740	0.417722
$134$	−1.65938	−0.143348
$135$	6.29202	0.541531
$136$	7.15980	0.613948
$137$	0.297548	0.0254213	0.0127106	−	0.999919i	$-0.495954\pi$
$137$	0.297548	0.0254213	0.0127106	+	0.999919i	$0.495954\pi$
$138$	−0.633041	−0.0538881
$139$	−19.9823	−1.69488	−0.847440	−	0.530891i	$-0.821857\pi$
$139$	−19.9823	−1.69488	−0.847440	+	0.530891i	$0.821857\pi$
$140$	−9.07096	−0.766636
$141$	0.818383	0.0689203
$142$	−1.20648	−0.101246
$143$	−4.34396	−0.363260
$144$	1.40851	0.117376
$145$	10.0384	0.833647
$146$	4.43364	0.366931
$147$	−34.0297	−2.80672
$148$	−0.603139	−0.0495777
$149$	9.77017	0.800403	0.400202	−	0.916427i	$-0.368940\pi$
$149$	9.77017	0.800403	0.400202	+	0.916427i	$0.368940\pi$
$150$	−3.05388	−0.249348
$151$	0.836833	0.0681005	0.0340503	−	0.999420i	$-0.489159\pi$
$151$	0.836833	0.0681005	0.0340503	+	0.999420i	$0.489159\pi$
$152$	1.00000	0.0811107
$153$	−10.0847	−0.815296
$154$	−13.3192	−1.07329
$155$	3.21626	0.258336
$156$	−3.29888	−0.264122
$157$	3.32601	0.265444	0.132722	−	0.991153i	$-0.457628\pi$
$157$	3.32601	0.265444	0.132722	+	0.991153i	$0.457628\pi$
$158$	5.43480	0.432369
$159$	−2.56635	−0.203524
$160$	−1.88296	−0.148861
$161$	1.45244	0.114469
$162$	11.2416	0.883226
$163$	0.0658499	0.00515776	0.00257888	−	0.999997i	$-0.499179\pi$
$163$	0.0658499	0.00515776	0.00257888	+	0.999997i	$0.499179\pi$
$164$	10.5477	0.823639
$165$	10.9308	0.850960
$166$	0.714078	0.0554232
$167$	14.1717	1.09664	0.548318	−	0.836270i	$-0.315268\pi$
$167$	14.1717	1.09664	0.548318	+	0.836270i	$0.315268\pi$
$168$	−10.1148	−0.780376
$169$	−10.5315	−0.810112
$170$	13.4816	1.03399
$171$	−1.40851	−0.107712
$172$	1.20780	0.0920940
$173$	−12.7976	−0.972986	−0.486493	−	0.873685i	$-0.661724\pi$
$173$	−12.7976	−0.972986	−0.486493	+	0.873685i	$0.661724\pi$
$174$	11.1937	0.848589
$175$	7.00678	0.529663
$176$	−2.76481	−0.208405
$177$	−11.0805	−0.832864
$178$	4.35208	0.326202
$179$	−8.81510	−0.658871	−0.329436	−	0.944178i	$-0.606858\pi$
$179$	−8.81510	−0.658871	−0.329436	+	0.944178i	$0.606858\pi$
$180$	2.65216	0.197681
$181$	−0.282612	−0.0210064	−0.0105032	−	0.999945i	$-0.503343\pi$
$181$	−0.282612	−0.0210064	−0.0105032	+	0.999945i	$0.503343\pi$
$182$	7.56892	0.561045
$183$	−26.3562	−1.94831
$184$	0.301499	0.0222268
$185$	−1.13568	−0.0834972
$186$	3.58638	0.262966
$187$	19.7955	1.44759
$188$	−0.389772	−0.0284271
$189$	−16.0977	−1.17093
$190$	1.88296	0.136604
$191$	14.5928	1.05590	0.527949	−	0.849276i	$-0.322961\pi$
$191$	14.5928	1.05590	0.527949	+	0.849276i	$0.322961\pi$
$192$	−2.09965	−0.151529
$193$	−10.1633	−0.731571	−0.365786	−	0.930699i	$-0.619200\pi$
$193$	−10.1633	−0.731571	−0.365786	+	0.930699i	$0.619200\pi$
$194$	−6.13058	−0.440150
$195$	−6.21165	−0.444826
$196$	16.2074	1.15767
$197$	−24.2849	−1.73023	−0.865114	−	0.501575i	$-0.832754\pi$
$197$	−24.2849	−1.73023	−0.865114	+	0.501575i	$0.832754\pi$
$198$	3.89426	0.276753
$199$	−15.7566	−1.11696	−0.558480	−	0.829518i	$-0.688615\pi$
$199$	−15.7566	−1.11696	−0.558480	+	0.829518i	$0.688615\pi$
$200$	1.45447	0.102847
$201$	−3.48410	−0.245750
$202$	−12.0025	−0.844493
$203$	−25.6826	−1.80256
$204$	15.0330	1.05252
$205$	19.8609	1.38715
$206$	0.0219020	0.00152599
$207$	−0.424665	−0.0295163
$208$	1.57116	0.108940
$209$	2.76481	0.191246
$210$	−19.0458	−1.31428
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	1.22228	0.0839462
$213$	−2.53318	−0.173571
$214$	12.4139	0.848599
$215$	2.27424	0.155102
$216$	−3.34156	−0.227365
$217$	−8.22855	−0.558590
$218$	−11.4172	−0.773271
$219$	9.30907	0.629049
$220$	−5.20601	−0.350989
$221$	−11.2492	−0.756703
$222$	−1.26638	−0.0849937
$223$	−15.0757	−1.00954	−0.504771	−	0.863253i	$-0.668423\pi$
$223$	−15.0757	−1.00954	−0.504771	+	0.863253i	$0.668423\pi$
$224$	4.81740	0.321876
$225$	−2.04864	−0.136576
$226$	−13.0848	−0.870386
$227$	−15.7486	−1.04527	−0.522635	−	0.852556i	$-0.675051\pi$
$227$	−15.7486	−1.04527	−0.522635	+	0.852556i	$0.675051\pi$
$228$	2.09965	0.139052
$229$	−19.8095	−1.30905	−0.654524	−	0.756041i	$-0.727131\pi$
$229$	−19.8095	−1.30905	−0.654524	+	0.756041i	$0.727131\pi$
$230$	0.567710	0.0374337
$231$	−27.9656	−1.84000
$232$	−5.33121	−0.350011
$233$	23.6366	1.54849	0.774244	−	0.632887i	$-0.218130\pi$
$233$	23.6366	1.54849	0.774244	+	0.632887i	$0.218130\pi$
$234$	−2.21300	−0.144668
$235$	−0.733924	−0.0478759
$236$	5.27734	0.343526
$237$	11.4111	0.741234
$238$	−34.4916	−2.23576
$239$	−9.80051	−0.633942	−0.316971	−	0.948435i	$-0.602666\pi$
$239$	−9.80051	−0.633942	−0.316971	+	0.948435i	$0.602666\pi$
$240$	−3.95354	−0.255200
$241$	−1.29987	−0.0837317	−0.0418658	−	0.999123i	$-0.513330\pi$
$241$	−1.29987	−0.0837317	−0.0418658	+	0.999123i	$0.513330\pi$
$242$	3.35584	0.215721
$243$	13.5787	0.871077
$244$	12.5527	0.803605
$245$	30.5178	1.94971
$246$	22.1465	1.41201
$247$	−1.57116	−0.0999706
$248$	−1.70809	−0.108464
$249$	1.49931	0.0950149
$250$	12.1535	0.768655
$251$	−6.79093	−0.428640	−0.214320	−	0.976764i	$-0.568753\pi$
$251$	−6.79093	−0.428640	−0.214320	+	0.976764i	$0.568753\pi$
$252$	−6.78536	−0.427438
$253$	0.833588	0.0524072
$254$	−11.3371	−0.711354
$255$	28.3066	1.77263
$256$	1.00000	0.0625000
$257$	3.29483	0.205526	0.102763	−	0.994706i	$-0.467232\pi$
$257$	3.29483	0.205526	0.102763	+	0.994706i	$0.467232\pi$
$258$	2.53595	0.157882
$259$	2.90556	0.180543
$260$	2.95843	0.183474
$261$	7.50907	0.464800
$262$	12.1602	0.751258
$263$	−3.69470	−0.227825	−0.113913	−	0.993491i	$-0.536338\pi$
$263$	−3.69470	−0.227825	−0.113913	+	0.993491i	$0.536338\pi$
$264$	−5.80512	−0.357280
$265$	2.30149	0.141380
$266$	−4.81740	−0.295374
$267$	9.13783	0.559226
$268$	1.65938	0.101363
$269$	7.28892	0.444413	0.222207	−	0.975000i	$-0.428674\pi$
$269$	7.28892	0.444413	0.222207	+	0.975000i	$0.428674\pi$
$270$	−6.29202	−0.382920
$271$	22.7217	1.38024	0.690122	−	0.723693i	$-0.257557\pi$
$271$	22.7217	1.38024	0.690122	+	0.723693i	$0.257557\pi$
$272$	−7.15980	−0.434127
$273$	15.8920	0.961830
$274$	−0.297548	−0.0179755
$275$	4.02134	0.242496
$276$	0.633041	0.0381046
$277$	18.6563	1.12095	0.560474	−	0.828172i	$-0.310619\pi$
$277$	18.6563	1.12095	0.560474	+	0.828172i	$0.310619\pi$
$278$	19.9823	1.19846
$279$	2.40586	0.144035
$280$	9.07096	0.542094
$281$	17.1150	1.02099	0.510497	−	0.859880i	$-0.329461\pi$
$281$	17.1150	1.02099	0.510497	+	0.859880i	$0.329461\pi$
$282$	−0.818383	−0.0487340
$283$	3.87042	0.230072	0.115036	−	0.993361i	$-0.463302\pi$
$283$	3.87042	0.230072	0.115036	+	0.993361i	$0.463302\pi$
$284$	1.20648	0.0715915
$285$	3.95354	0.234188
$286$	4.34396	0.256864
$287$	−50.8126	−2.99938
$288$	−1.40851	−0.0829973
$289$	34.2627	2.01545
$290$	−10.0384	−0.589477
$291$	−12.8720	−0.754573
$292$	−4.43364	−0.259459
$293$	−12.5471	−0.733012	−0.366506	−	0.930416i	$-0.619446\pi$
$293$	−12.5471	−0.733012	−0.366506	+	0.930416i	$0.619446\pi$
$294$	34.0297	1.98465
$295$	9.93700	0.578555
$296$	0.603139	0.0350567
$297$	−9.23878	−0.536088
$298$	−9.77017	−0.565970
$299$	−0.473704	−0.0273950
$300$	3.05388	0.176316
$301$	−5.81846	−0.335371
$302$	−0.836833	−0.0481543
$303$	−25.2010	−1.44776
$304$	−1.00000	−0.0573539
$305$	23.6362	1.35340
$306$	10.0847	0.576501
$307$	12.5847	0.718244	0.359122	−	0.933291i	$-0.383076\pi$
$307$	12.5847	0.718244	0.359122	+	0.933291i	$0.383076\pi$
$308$	13.3192	0.758931
$309$	0.0459865	0.00261608
$310$	−3.21626	−0.182671
$311$	20.4985	1.16237	0.581183	−	0.813773i	$-0.302590\pi$
$311$	20.4985	1.16237	0.581183	+	0.813773i	$0.302590\pi$
$312$	3.29888	0.186762
$313$	−25.9923	−1.46917	−0.734587	−	0.678515i	$-0.762624\pi$
$313$	−25.9923	−1.46917	−0.734587	+	0.678515i	$0.762624\pi$
$314$	−3.32601	−0.187697
$315$	−12.7765	−0.719877
$316$	−5.43480	−0.305731
$317$	−5.82998	−0.327444	−0.163722	−	0.986506i	$-0.552350\pi$
$317$	−5.82998	−0.327444	−0.163722	+	0.986506i	$0.552350\pi$
$318$	2.56635	0.143914
$319$	−14.7398	−0.825269
$320$	1.88296	0.105260
$321$	26.0649	1.45480
$322$	−1.45244	−0.0809415
$323$	7.15980	0.398382
$324$	−11.2416	−0.624535
$325$	−2.28521	−0.126761
$326$	−0.0658499	−0.00364709
$327$	−23.9721	−1.32566
$328$	−10.5477	−0.582401
$329$	1.87769	0.103520
$330$	−10.9308	−0.601720
$331$	35.7053	1.96254	0.981271	−	0.192632i	$-0.0617025\pi$
$331$	35.7053	1.96254	0.981271	+	0.192632i	$0.0617025\pi$
$332$	−0.714078	−0.0391901
$333$	−0.849528	−0.0465538
$334$	−14.1717	−0.775438
$335$	3.12453	0.170712
$336$	10.1148	0.551810
$337$	19.4861	1.06148	0.530739	−	0.847536i	$-0.321915\pi$
$337$	19.4861	1.06148	0.530739	+	0.847536i	$0.321915\pi$
$338$	10.5315	0.572835
$339$	−27.4734	−1.49215
$340$	−13.4816	−0.731142
$341$	−4.72254	−0.255740
$342$	1.40851	0.0761635
$343$	−44.3556	−2.39497
$344$	−1.20780	−0.0651203
$345$	1.19199	0.0641746
$346$	12.7976	0.688005
$347$	10.4246	0.559619	0.279810	−	0.960055i	$-0.409729\pi$
$347$	10.4246	0.559619	0.279810	+	0.960055i	$0.409729\pi$
$348$	−11.1937	−0.600043
$349$	28.0471	1.50133	0.750663	−	0.660685i	$-0.229734\pi$
$349$	28.0471	1.50133	0.750663	+	0.660685i	$0.229734\pi$
$350$	−7.00678	−0.374528
$351$	5.25014	0.280232
$352$	2.76481	0.147365
$353$	4.32987	0.230456	0.115228	−	0.993339i	$-0.463240\pi$
$353$	4.32987	0.230456	0.115228	+	0.993339i	$0.463240\pi$
$354$	11.0805	0.588924
$355$	2.27175	0.120572
$356$	−4.35208	−0.230660
$357$	−72.4202	−3.83288
$358$	8.81510	0.465892
$359$	30.3696	1.60285	0.801424	−	0.598097i	$-0.204076\pi$
$359$	30.3696	1.60285	0.801424	+	0.598097i	$0.204076\pi$
$360$	−2.65216	−0.139781
$361$	1.00000	0.0526316
$362$	0.282612	0.0148538
$363$	7.04606	0.369823
$364$	−7.56892	−0.396719
$365$	−8.34835	−0.436973
$366$	26.3562	1.37766
$367$	2.72398	0.142190	0.0710952	−	0.997470i	$-0.477351\pi$
$367$	2.72398	0.142190	0.0710952	+	0.997470i	$0.477351\pi$
$368$	−0.301499	−0.0157167
$369$	14.8566	0.773403
$370$	1.13568	0.0590414
$371$	−5.88819	−0.305700
$372$	−3.58638	−0.185945
$373$	−12.8019	−0.662857	−0.331428	−	0.943480i	$-0.607530\pi$
$373$	−12.8019	−0.662857	−0.331428	+	0.943480i	$0.607530\pi$
$374$	−19.7955	−1.02360
$375$	25.5180	1.31775
$376$	0.389772	0.0201010
$377$	8.37619	0.431396
$378$	16.0977	0.827974
$379$	−11.3225	−0.581599	−0.290799	−	0.956784i	$-0.593921\pi$
$379$	−11.3225	−0.581599	−0.290799	+	0.956784i	$0.593921\pi$
$380$	−1.88296	−0.0965936
$381$	−23.8039	−1.21951
$382$	−14.5928	−0.746633
$383$	−30.3805	−1.55237	−0.776184	−	0.630506i	$-0.782847\pi$
$383$	−30.3805	−1.55237	−0.776184	+	0.630506i	$0.782847\pi$
$384$	2.09965	0.107147
$385$	25.0795	1.27817
$386$	10.1633	0.517299
$387$	1.70120	0.0864769
$388$	6.13058	0.311233
$389$	−26.6564	−1.35153	−0.675767	−	0.737115i	$-0.736188\pi$
$389$	−26.6564	−1.35153	−0.675767	+	0.737115i	$0.736188\pi$
$390$	6.21165	0.314539
$391$	2.15867	0.109169
$392$	−16.2074	−0.818595
$393$	25.5321	1.28792
$394$	24.2849	1.22346
$395$	−10.2335	−0.514903
$396$	−3.89426	−0.195694
$397$	33.4711	1.67987	0.839933	−	0.542690i	$-0.182594\pi$
$397$	33.4711	1.67987	0.839933	+	0.542690i	$0.182594\pi$
$398$	15.7566	0.789809
$399$	−10.1148	−0.506375
$400$	−1.45447	−0.0727237
$401$	−13.1479	−0.656575	−0.328288	−	0.944578i	$-0.606471\pi$
$401$	−13.1479	−0.656575	−0.328288	+	0.944578i	$0.606471\pi$
$402$	3.48410	0.173771
$403$	2.68368	0.133684
$404$	12.0025	0.597146
$405$	−21.1675	−1.05182
$406$	25.6826	1.27461
$407$	1.66756	0.0826581
$408$	−15.0330	−0.744246
$409$	−28.0181	−1.38541	−0.692703	−	0.721223i	$-0.743580\pi$
$409$	−28.0181	−1.38541	−0.692703	+	0.721223i	$0.743580\pi$
$410$	−19.8609	−0.980861
$411$	−0.624746	−0.0308164
$412$	−0.0219020	−0.00107904
$413$	−25.4231	−1.25099
$414$	0.424665	0.0208711
$415$	−1.34458	−0.0660027
$416$	−1.57116	−0.0770325
$417$	41.9558	2.05459
$418$	−2.76481	−0.135231
$419$	6.36647	0.311022	0.155511	−	0.987834i	$-0.450298\pi$
$419$	6.36647	0.311022	0.155511	+	0.987834i	$0.450298\pi$
$420$	19.0458	0.929340
$421$	34.1193	1.66287	0.831437	−	0.555619i	$-0.187519\pi$
$421$	34.1193	1.66287	0.831437	+	0.555619i	$0.187519\pi$
$422$	1.00000	0.0486792
$423$	−0.548998	−0.0266932
$424$	−1.22228	−0.0593590
$425$	10.4137	0.505141
$426$	2.53318	0.122733
$427$	−60.4714	−2.92642
$428$	−12.4139	−0.600050
$429$	9.12078	0.440355
$430$	−2.27424	−0.109673
$431$	3.08569	0.148632	0.0743161	−	0.997235i	$-0.476323\pi$
$431$	3.08569	0.148632	0.0743161	+	0.997235i	$0.476323\pi$
$432$	3.34156	0.160771
$433$	−25.2198	−1.21199	−0.605993	−	0.795470i	$-0.707224\pi$
$433$	−25.2198	−1.21199	−0.605993	+	0.795470i	$0.707224\pi$
$434$	8.22855	0.394983
$435$	−21.0772	−1.01057
$436$	11.4172	0.546785
$437$	0.301499	0.0144227
$438$	−9.30907	−0.444805
$439$	32.3903	1.54591	0.772953	−	0.634463i	$-0.218779\pi$
$439$	32.3903	1.54591	0.772953	+	0.634463i	$0.218779\pi$
$440$	5.20601	0.248187
$441$	22.8282	1.08706
$442$	11.2492	0.535070
$443$	−35.3050	−1.67739	−0.838695	−	0.544602i	$-0.816681\pi$
$443$	−35.3050	−1.67739	−0.838695	+	0.544602i	$0.816681\pi$
$444$	1.26638	0.0600997
$445$	−8.19478	−0.388470
$446$	15.0757	0.713854
$447$	−20.5139	−0.970273
$448$	−4.81740	−0.227601
$449$	−8.73012	−0.412000	−0.206000	−	0.978552i	$-0.566045\pi$
$449$	−8.73012	−0.412000	−0.206000	+	0.978552i	$0.566045\pi$
$450$	2.04864	0.0965739
$451$	−29.1624	−1.37321
$452$	13.0848	0.615456
$453$	−1.75705	−0.0825535
$454$	15.7486	0.739118
$455$	−14.2519	−0.668141
$456$	−2.09965	−0.0983249
$457$	24.2227	1.13309	0.566546	−	0.824030i	$-0.308279\pi$
$457$	24.2227	1.13309	0.566546	+	0.824030i	$0.308279\pi$
$458$	19.8095	0.925637
$459$	−23.9249	−1.11672
$460$	−0.567710	−0.0264696
$461$	−20.5729	−0.958178	−0.479089	−	0.877766i	$-0.659033\pi$
$461$	−20.5729	−0.958178	−0.479089	+	0.877766i	$0.659033\pi$
$462$	27.9656	1.30108
$463$	−15.5761	−0.723884	−0.361942	−	0.932201i	$-0.617886\pi$
$463$	−15.5761	−0.723884	−0.361942	+	0.932201i	$0.617886\pi$
$464$	5.33121	0.247495
$465$	−6.75300	−0.313163
$466$	−23.6366	−1.09495
$467$	23.7314	1.09816	0.549080	−	0.835770i	$-0.314978\pi$
$467$	23.7314	1.09816	0.549080	+	0.835770i	$0.314978\pi$
$468$	2.21300	0.102296
$469$	−7.99388	−0.369123
$470$	0.733924	0.0338534
$471$	−6.98343	−0.321780
$472$	−5.27734	−0.242909
$473$	−3.33934	−0.153543
$474$	−11.4111	−0.524131
$475$	1.45447	0.0667358
$476$	34.4916	1.58092
$477$	1.72159	0.0788261
$478$	9.80051	0.448265
$479$	9.61382	0.439267	0.219633	−	0.975582i	$-0.429514\pi$
$479$	9.61382	0.439267	0.219633	+	0.975582i	$0.429514\pi$
$480$	3.95354	0.180454
$481$	−0.947629	−0.0432082
$482$	1.29987	0.0592072
$483$	−3.04962	−0.138762
$484$	−3.35584	−0.152538
$485$	11.5436	0.524169
$486$	−13.5787	−0.615944
$487$	−19.2611	−0.872805	−0.436403	−	0.899752i	$-0.643748\pi$
$487$	−19.2611	−0.872805	−0.436403	+	0.899752i	$0.643748\pi$
$488$	−12.5527	−0.568234
$489$	−0.138261	−0.00625240
$490$	−30.5178	−1.37865
$491$	0.102718	0.00463559	0.00231780	−	0.999997i	$-0.499262\pi$
$491$	0.102718	0.00463559	0.00231780	+	0.999997i	$0.499262\pi$
$492$	−22.1465	−0.998441
$493$	−38.1704	−1.71911
$494$	1.57116	0.0706899
$495$	−7.33273	−0.329582
$496$	1.70809	0.0766954
$497$	−5.81211	−0.260709
$498$	−1.49931	−0.0671857
$499$	−2.23133	−0.0998879	−0.0499439	−	0.998752i	$-0.515904\pi$
$499$	−2.23133	−0.0998879	−0.0499439	+	0.998752i	$0.515904\pi$
$500$	−12.1535	−0.543521
$501$	−29.7554	−1.32938
$502$	6.79093	0.303094
$503$	5.29184	0.235951	0.117976	−	0.993016i	$-0.462359\pi$
$503$	5.29184	0.235951	0.117976	+	0.993016i	$0.462359\pi$
$504$	6.78536	0.302244
$505$	22.6002	1.00569
$506$	−0.833588	−0.0370575
$507$	22.1123	0.982042
$508$	11.3371	0.503003
$509$	−28.1957	−1.24975	−0.624877	−	0.780723i	$-0.714851\pi$
$509$	−28.1957	−1.24975	−0.624877	+	0.780723i	$0.714851\pi$
$510$	−28.3066	−1.25344
$511$	21.3586	0.944850
$512$	−1.00000	−0.0441942
$513$	−3.34156	−0.147534
$514$	−3.29483	−0.145329
$515$	−0.0412406	−0.00181728
$516$	−2.53595	−0.111639
$517$	1.07765	0.0473948
$518$	−2.90556	−0.127663
$519$	26.8705	1.17948
$520$	−2.95843	−0.129736
$521$	−24.0808	−1.05500	−0.527499	−	0.849556i	$-0.676870\pi$
$521$	−24.0808	−1.05500	−0.527499	+	0.849556i	$0.676870\pi$
$522$	−7.50907	−0.328663
$523$	31.5915	1.38140	0.690701	−	0.723141i	$-0.257302\pi$
$523$	31.5915	1.38140	0.690701	+	0.723141i	$0.257302\pi$
$524$	−12.1602	−0.531220
$525$	−14.7118	−0.642074
$526$	3.69470	0.161097
$527$	−12.2296	−0.532728
$528$	5.80512	0.252635
$529$	−22.9091	−0.996048
$530$	−2.30149	−0.0999704
$531$	7.43319	0.322573
$532$	4.81740	0.208861
$533$	16.5722	0.717821
$534$	−9.13783	−0.395432
$535$	−23.3749	−1.01059
$536$	−1.65938	−0.0716742
$537$	18.5086	0.798704
$538$	−7.28892	−0.314248
$539$	−44.8102	−1.93011
$540$	6.29202	0.270765
$541$	−25.7606	−1.10753	−0.553767	−	0.832672i	$-0.686810\pi$
$541$	−25.7606	−1.10753	−0.553767	+	0.832672i	$0.686810\pi$
$542$	−22.7217	−0.975980
$543$	0.593385	0.0254646
$544$	7.15980	0.306974
$545$	21.4981	0.920878
$546$	−15.8920	−0.680117
$547$	−22.5017	−0.962102	−0.481051	−	0.876693i	$-0.659745\pi$
$547$	−22.5017	−0.962102	−0.481051	+	0.876693i	$0.659745\pi$
$548$	0.297548	0.0127106
$549$	17.6806	0.754590
$550$	−4.02134	−0.171471
$551$	−5.33121	−0.227117
$552$	−0.633041	−0.0269440
$553$	26.1816	1.11336
$554$	−18.6563	−0.792631
$555$	2.38454	0.101218
$556$	−19.9823	−0.847440
$557$	4.47645	0.189673	0.0948367	−	0.995493i	$-0.469767\pi$
$557$	4.47645	0.189673	0.0948367	+	0.995493i	$0.469767\pi$
$558$	−2.40586	−0.101848
$559$	1.89765	0.0802621
$560$	−9.07096	−0.383318
$561$	−41.5635	−1.75481
$562$	−17.1150	−0.721952
$563$	11.6876	0.492573	0.246287	−	0.969197i	$-0.420790\pi$
$563$	11.6876	0.492573	0.246287	+	0.969197i	$0.420790\pi$
$564$	0.818383	0.0344602
$565$	24.6381	1.03653
$566$	−3.87042	−0.162686
$567$	54.1554	2.27431
$568$	−1.20648	−0.0506229
$569$	22.9851	0.963585	0.481793	−	0.876285i	$-0.339986\pi$
$569$	22.9851	0.963585	0.481793	+	0.876285i	$0.339986\pi$
$570$	−3.95354	−0.165596
$571$	−44.7367	−1.87217	−0.936087	−	0.351770i	$-0.885580\pi$
$571$	−44.7367	−1.87217	−0.936087	+	0.351770i	$0.885580\pi$
$572$	−4.34396	−0.181630
$573$	−30.6397	−1.27999
$574$	50.8126	2.12088
$575$	0.438523	0.0182877
$576$	1.40851	0.0586879
$577$	−16.6457	−0.692968	−0.346484	−	0.938056i	$-0.612624\pi$
$577$	−16.6457	−0.692968	−0.346484	+	0.938056i	$0.612624\pi$
$578$	−34.2627	−1.42514
$579$	21.3394	0.886833
$580$	10.0384	0.416824
$581$	3.44000	0.142715
$582$	12.8720	0.533563
$583$	−3.37936	−0.139959
$584$	4.43364	0.183465
$585$	4.16698	0.172283
$586$	12.5471	0.518318
$587$	−28.3542	−1.17030	−0.585152	−	0.810923i	$-0.698965\pi$
$587$	−28.3542	−1.17030	−0.585152	+	0.810923i	$0.698965\pi$
$588$	−34.0297	−1.40336
$589$	−1.70809	−0.0703805
$590$	−9.93700	−0.409100
$591$	50.9897	2.09744
$592$	−0.603139	−0.0247889
$593$	14.8584	0.610162	0.305081	−	0.952326i	$-0.401317\pi$
$593$	14.8584	0.610162	0.305081	+	0.952326i	$0.401317\pi$
$594$	9.23878	0.379072
$595$	64.9462	2.66254
$596$	9.77017	0.400202
$597$	33.0834	1.35401
$598$	0.473704	0.0193712
$599$	−23.1526	−0.945991	−0.472995	−	0.881065i	$-0.656827\pi$
$599$	−23.1526	−0.945991	−0.472995	+	0.881065i	$0.656827\pi$
$600$	−3.05388	−0.124674
$601$	−39.2724	−1.60196	−0.800978	−	0.598694i	$-0.795687\pi$
$601$	−39.2724	−1.60196	−0.800978	+	0.598694i	$0.795687\pi$
$602$	5.81846	0.237143
$603$	2.33725	0.0951802
$604$	0.836833	0.0340503
$605$	−6.31889	−0.256900
$606$	25.2010	1.02372
$607$	19.8278	0.804787	0.402394	−	0.915467i	$-0.368178\pi$
$607$	19.8278	0.804787	0.402394	+	0.915467i	$0.368178\pi$
$608$	1.00000	0.0405554
$609$	53.9243	2.18512
$610$	−23.6362	−0.957002
$611$	−0.612395	−0.0247749
$612$	−10.0847	−0.407648
$613$	0.610244	0.0246475	0.0123238	−	0.999924i	$-0.496077\pi$
$613$	0.610244	0.0246475	0.0123238	+	0.999924i	$0.496077\pi$
$614$	−12.5847	−0.507875
$615$	−41.7009	−1.68154
$616$	−13.3192	−0.536646
$617$	16.8365	0.677811	0.338906	−	0.940820i	$-0.389943\pi$
$617$	16.8365	0.677811	0.338906	+	0.940820i	$0.389943\pi$
$618$	−0.0459865	−0.00184985
$619$	−41.7701	−1.67888	−0.839440	−	0.543452i	$-0.817117\pi$
$619$	−41.7701	−1.67888	−0.839440	+	0.543452i	$0.817117\pi$
$620$	3.21626	0.129168
$621$	−1.00748	−0.0404287
$622$	−20.4985	−0.821916
$623$	20.9657	0.839974
$624$	−3.29888	−0.132061
$625$	−15.6121	−0.624486
$626$	25.9923	1.03886
$627$	−5.80512	−0.231834
$628$	3.32601	0.132722
$629$	4.31835	0.172184
$630$	12.7765	0.509030
$631$	23.5367	0.936981	0.468490	−	0.883469i	$-0.344798\pi$
$631$	23.5367	0.936981	0.468490	+	0.883469i	$0.344798\pi$
$632$	5.43480	0.216185
$633$	2.09965	0.0834534
$634$	5.82998	0.231538
$635$	21.3473	0.847142
$636$	−2.56635	−0.101762
$637$	25.4644	1.00894
$638$	14.7398	0.583553
$639$	1.69934	0.0672250
$640$	−1.88296	−0.0744304
$641$	−1.66834	−0.0658955	−0.0329477	−	0.999457i	$-0.510489\pi$
$641$	−1.66834	−0.0658955	−0.0329477	+	0.999457i	$0.510489\pi$
$642$	−26.0649	−1.02870
$643$	−20.3749	−0.803508	−0.401754	−	0.915748i	$-0.631599\pi$
$643$	−20.3749	−0.803508	−0.401754	+	0.915748i	$0.631599\pi$
$644$	1.45244	0.0572343
$645$	−4.77509	−0.188019
$646$	−7.15980	−0.281699
$647$	−10.9925	−0.432161	−0.216080	−	0.976376i	$-0.569327\pi$
$647$	−10.9925	−0.432161	−0.216080	+	0.976376i	$0.569327\pi$
$648$	11.2416	0.441613
$649$	−14.5908	−0.572740
$650$	2.28521	0.0896334
$651$	17.2770	0.677140
$652$	0.0658499	0.00257888
$653$	5.40621	0.211561	0.105781	−	0.994389i	$-0.466266\pi$
$653$	5.40621	0.211561	0.105781	+	0.994389i	$0.466266\pi$
$654$	23.9721	0.937383
$655$	−22.8971	−0.894663
$656$	10.5477	0.411820
$657$	−6.24483	−0.243634
$658$	−1.87769	−0.0731999
$659$	−37.1232	−1.44611	−0.723057	−	0.690789i	$-0.757263\pi$
$659$	−37.1232	−1.44611	−0.723057	+	0.690789i	$0.757263\pi$
$660$	10.9308	0.425480
$661$	31.7345	1.23433	0.617165	−	0.786834i	$-0.288281\pi$
$661$	31.7345	1.23433	0.617165	+	0.786834i	$0.288281\pi$
$662$	−35.7053	−1.38773
$663$	23.6193	0.917299
$664$	0.714078	0.0277116
$665$	9.07096	0.351757
$666$	0.849528	0.0329185
$667$	−1.60736	−0.0622371
$668$	14.1717	0.548318
$669$	31.6536	1.22380
$670$	−3.12453	−0.120711
$671$	−34.7058	−1.33980
$672$	−10.1148	−0.390188
$673$	−0.335039	−0.0129148	−0.00645739	−	0.999979i	$-0.502055\pi$
$673$	−0.335039	−0.0129148	−0.00645739	+	0.999979i	$0.502055\pi$
$674$	−19.4861	−0.750578
$675$	−4.86022	−0.187070
$676$	−10.5315	−0.405056
$677$	−5.46449	−0.210017	−0.105009	−	0.994471i	$-0.533487\pi$
$677$	−5.46449	−0.210017	−0.105009	+	0.994471i	$0.533487\pi$
$678$	27.4734	1.05511
$679$	−29.5335	−1.13339
$680$	13.4816	0.516995
$681$	33.0664	1.26711
$682$	4.72254	0.180835
$683$	−50.9442	−1.94933	−0.974664	−	0.223675i	$-0.928195\pi$
$683$	−50.9442	−1.94933	−0.974664	+	0.223675i	$0.928195\pi$
$684$	−1.40851	−0.0538558
$685$	0.560270	0.0214068
$686$	44.3556	1.69350
$687$	41.5929	1.58687
$688$	1.20780	0.0460470
$689$	1.92039	0.0731611
$690$	−1.19199	−0.0453783
$691$	−47.8213	−1.81921	−0.909605	−	0.415475i	$-0.863615\pi$
$691$	−47.8213	−1.81921	−0.909605	+	0.415475i	$0.863615\pi$
$692$	−12.7976	−0.486493
$693$	18.7602	0.712642
$694$	−10.4246	−0.395711
$695$	−37.6259	−1.42723
$696$	11.1937	0.424294
$697$	−75.5196	−2.86051
$698$	−28.0471	−1.06160
$699$	−49.6286	−1.87713
$700$	7.00678	0.264832
$701$	30.3783	1.14737	0.573687	−	0.819074i	$-0.305513\pi$
$701$	30.3783	1.14737	0.573687	+	0.819074i	$0.305513\pi$
$702$	−5.25014	−0.198154
$703$	0.603139	0.0227478
$704$	−2.76481	−0.104203
$705$	1.54098	0.0580367
$706$	−4.32987	−0.162957
$707$	−57.8208	−2.17458
$708$	−11.0805	−0.416432
$709$	20.5173	0.770544	0.385272	−	0.922803i	$-0.374108\pi$
$709$	20.5173	0.770544	0.385272	+	0.922803i	$0.374108\pi$
$710$	−2.27175	−0.0852574
$711$	−7.65497	−0.287084
$712$	4.35208	0.163101
$713$	−0.514987	−0.0192864
$714$	72.4202	2.71026
$715$	−8.17949	−0.305896
$716$	−8.81510	−0.329436
$717$	20.5776	0.768484
$718$	−30.3696	−1.13338
$719$	20.1800	0.752588	0.376294	−	0.926500i	$-0.377198\pi$
$719$	20.1800	0.752588	0.376294	+	0.926500i	$0.377198\pi$
$720$	2.65216	0.0988403
$721$	0.105511	0.00392943
$722$	−1.00000	−0.0372161
$723$	2.72926	0.101502
$724$	−0.282612	−0.0105032
$725$	−7.75411	−0.287980
$726$	−7.04606	−0.261504
$727$	−11.1353	−0.412987	−0.206494	−	0.978448i	$-0.566205\pi$
$727$	−11.1353	−0.412987	−0.206494	+	0.978448i	$0.566205\pi$
$728$	7.56892	0.280523
$729$	5.21434	0.193124
$730$	8.34835	0.308986
$731$	−8.64761	−0.319843
$732$	−26.3562	−0.974154
$733$	−41.5712	−1.53547	−0.767734	−	0.640769i	$-0.778616\pi$
$733$	−41.5712	−1.53547	−0.767734	+	0.640769i	$0.778616\pi$
$734$	−2.72398	−0.100544
$735$	−64.0765	−2.36350
$736$	0.301499	0.0111134
$737$	−4.58786	−0.168996
$738$	−14.8566	−0.546878
$739$	0.761430	0.0280096	0.0140048	−	0.999902i	$-0.495542\pi$
$739$	0.761430	0.0280096	0.0140048	+	0.999902i	$0.495542\pi$
$740$	−1.13568	−0.0417486
$741$	3.29888	0.121187
$742$	5.88819	0.216162
$743$	1.01856	0.0373672	0.0186836	−	0.999825i	$-0.494052\pi$
$743$	1.01856	0.0373672	0.0186836	+	0.999825i	$0.494052\pi$
$744$	3.58638	0.131483
$745$	18.3968	0.674007
$746$	12.8019	0.468710
$747$	−1.00579	−0.0367998
$748$	19.7955	0.723794
$749$	59.8029	2.18515
$750$	−25.5180	−0.931787
$751$	1.28981	0.0470660	0.0235330	−	0.999723i	$-0.492509\pi$
$751$	1.28981	0.0470660	0.0235330	+	0.999723i	$0.492509\pi$
$752$	−0.389772	−0.0142135
$753$	14.2585	0.519610
$754$	−8.37619	−0.305043
$755$	1.57572	0.0573463
$756$	−16.0977	−0.585466
$757$	−6.34545	−0.230629	−0.115315	−	0.993329i	$-0.536788\pi$
$757$	−6.34545	−0.230629	−0.115315	+	0.993329i	$0.536788\pi$
$758$	11.3225	0.411252
$759$	−1.75024	−0.0635296
$760$	1.88296	0.0683020
$761$	9.26100	0.335711	0.167855	−	0.985812i	$-0.446316\pi$
$761$	9.26100	0.335711	0.167855	+	0.985812i	$0.446316\pi$
$762$	23.8039	0.862325
$763$	−55.0013	−1.99118
$764$	14.5928	0.527949
$765$	−18.9890	−0.686548
$766$	30.3805	1.09769
$767$	8.29155	0.299391
$768$	−2.09965	−0.0757644
$769$	−36.5070	−1.31647	−0.658237	−	0.752811i	$-0.728698\pi$
$769$	−36.5070	−1.31647	−0.658237	+	0.752811i	$0.728698\pi$
$770$	−25.0795	−0.903801
$771$	−6.91797	−0.249145
$772$	−10.1633	−0.365786
$773$	−42.6475	−1.53392	−0.766961	−	0.641693i	$-0.778232\pi$
$773$	−42.6475	−1.53392	−0.766961	+	0.641693i	$0.778232\pi$
$774$	−1.70120	−0.0611484
$775$	−2.48437	−0.0892412
$776$	−6.13058	−0.220075
$777$	−6.10065	−0.218860
$778$	26.6564	0.955680
$779$	−10.5477	−0.377912
$780$	−6.21165	−0.222413
$781$	−3.33569	−0.119360
$782$	−2.15867	−0.0771940
$783$	17.8146	0.636641
$784$	16.2074	0.578834
$785$	6.26272	0.223526
$786$	−25.5321	−0.910698
$787$	24.8932	0.887347	0.443674	−	0.896188i	$-0.353675\pi$
$787$	24.8932	0.887347	0.443674	+	0.896188i	$0.353675\pi$
$788$	−24.2849	−0.865114
$789$	7.75756	0.276177
$790$	10.2335	0.364091
$791$	−63.0346	−2.24125
$792$	3.89426	0.138377
$793$	19.7223	0.700360
$794$	−33.4711	−1.18784
$795$	−4.83232	−0.171385
$796$	−15.7566	−0.558480
$797$	34.7978	1.23260	0.616301	−	0.787510i	$-0.288630\pi$
$797$	34.7978	1.23260	0.616301	+	0.787510i	$0.288630\pi$
$798$	10.1148	0.358061
$799$	2.79069	0.0987275
$800$	1.45447	0.0514234
$801$	−6.12995	−0.216591
$802$	13.1479	0.464269
$803$	12.2582	0.432581
$804$	−3.48410	−0.122875
$805$	2.73489	0.0963921
$806$	−2.68368	−0.0945287
$807$	−15.3041	−0.538731
$808$	−12.0025	−0.422246
$809$	−22.5330	−0.792219	−0.396110	−	0.918203i	$-0.629640\pi$
$809$	−22.5330	−0.792219	−0.396110	+	0.918203i	$0.629640\pi$
$810$	21.1675	0.743750
$811$	−34.8520	−1.22382	−0.611910	−	0.790928i	$-0.709598\pi$
$811$	−34.8520	−1.22382	−0.611910	+	0.790928i	$0.709598\pi$
$812$	−25.6826	−0.901282
$813$	−47.7075	−1.67318
$814$	−1.66756	−0.0584481
$815$	0.123993	0.00434327
$816$	15.0330	0.526262
$817$	−1.20780	−0.0422556
$818$	28.0181	0.979630
$819$	−10.6609	−0.372522
$820$	19.8609	0.693573
$821$	44.5870	1.55610	0.778049	−	0.628203i	$-0.216209\pi$
$821$	44.5870	1.55610	0.778049	+	0.628203i	$0.216209\pi$
$822$	0.624746	0.0217905
$823$	0.516472	0.0180031	0.00900153	−	0.999959i	$-0.497135\pi$
$823$	0.516472	0.0180031	0.00900153	+	0.999959i	$0.497135\pi$
$824$	0.0219020	0.000762993 0
$825$	−8.44339	−0.293961
$826$	25.4231	0.884582
$827$	19.0151	0.661218	0.330609	−	0.943768i	$-0.392746\pi$
$827$	19.0151	0.661218	0.330609	+	0.943768i	$0.392746\pi$
$828$	−0.424665	−0.0147581
$829$	−3.86305	−0.134169	−0.0670846	−	0.997747i	$-0.521370\pi$
$829$	−3.86305	−0.134169	−0.0670846	+	0.997747i	$0.521370\pi$
$830$	1.34458	0.0466710
$831$	−39.1716	−1.35885
$832$	1.57116	0.0544702
$833$	−116.041	−4.02060
$834$	−41.9558	−1.45281
$835$	26.6846	0.923459
$836$	2.76481	0.0956229
$837$	5.70768	0.197286
$838$	−6.36647	−0.219926
$839$	17.1653	0.592610	0.296305	−	0.955093i	$-0.404245\pi$
$839$	17.1653	0.592610	0.296305	+	0.955093i	$0.404245\pi$
$840$	−19.0458	−0.657142
$841$	−0.578191	−0.0199376
$842$	−34.1193	−1.17583
$843$	−35.9354	−1.23768
$844$	−1.00000	−0.0344214
$845$	−19.8303	−0.682182
$846$	0.548998	0.0188749
$847$	16.1664	0.555484
$848$	1.22228	0.0419731
$849$	−8.12650	−0.278901
$850$	−10.4137	−0.357188
$851$	0.181846	0.00623360
$852$	−2.53318	−0.0867855
$853$	2.00624	0.0686923	0.0343462	−	0.999410i	$-0.489065\pi$
$853$	2.00624	0.0686923	0.0343462	+	0.999410i	$0.489065\pi$
$854$	60.4714	2.06929
$855$	−2.65216	−0.0907021
$856$	12.4139	0.424300
$857$	19.6955	0.672786	0.336393	−	0.941722i	$-0.390793\pi$
$857$	19.6955	0.672786	0.336393	+	0.941722i	$0.390793\pi$
$858$	−9.12078	−0.311378
$859$	−39.1665	−1.33634	−0.668172	−	0.744007i	$-0.732923\pi$
$859$	−39.1665	−1.33634	−0.668172	+	0.744007i	$0.732923\pi$
$860$	2.27424	0.0775508
$861$	106.689	3.63593
$862$	−3.08569	−0.105099
$863$	−7.20329	−0.245203	−0.122601	−	0.992456i	$-0.539124\pi$
$863$	−7.20329	−0.245203	−0.122601	+	0.992456i	$0.539124\pi$
$864$	−3.34156	−0.113682
$865$	−24.0974	−0.819336
$866$	25.2198	0.857004
$867$	−71.9396	−2.44320
$868$	−8.22855	−0.279295
$869$	15.0262	0.509728
$870$	21.0772	0.714583
$871$	2.60715	0.0883399
$872$	−11.4172	−0.386635
$873$	8.63499	0.292250
$874$	−0.301499	−0.0101984
$875$	58.5483	1.97929
$876$	9.30907	0.314524
$877$	−36.1355	−1.22021	−0.610104	−	0.792321i	$-0.708872\pi$
$877$	−36.1355	−1.22021	−0.610104	+	0.792321i	$0.708872\pi$
$878$	−32.3903	−1.09312
$879$	26.3446	0.888580
$880$	−5.20601	−0.175495
$881$	8.11551	0.273418	0.136709	−	0.990611i	$-0.456347\pi$
$881$	8.11551	0.273418	0.136709	+	0.990611i	$0.456347\pi$
$882$	−22.8282	−0.768667
$883$	−49.1371	−1.65360	−0.826798	−	0.562500i	$-0.809840\pi$
$883$	−49.1371	−1.65360	−0.826798	+	0.562500i	$0.809840\pi$
$884$	−11.2492	−0.378352
$885$	−20.8642	−0.701342
$886$	35.3050	1.18609
$887$	−1.70519	−0.0572545	−0.0286273	−	0.999590i	$-0.509114\pi$
$887$	−1.70519	−0.0572545	−0.0286273	+	0.999590i	$0.509114\pi$
$888$	−1.26638	−0.0424969
$889$	−54.6155	−1.83174
$890$	8.19478	0.274690
$891$	31.0809	1.04125
$892$	−15.0757	−0.504771
$893$	0.389772	0.0130432
$894$	20.5139	0.686087
$895$	−16.5984	−0.554825
$896$	4.81740	0.160938
$897$	0.994611	0.0332091
$898$	8.73012	0.291328
$899$	9.10618	0.303708
$900$	−2.04864	−0.0682881
$901$	−8.75125	−0.291546
$902$	29.1624	0.971003
$903$	12.2167	0.406547
$904$	−13.0848	−0.435193
$905$	−0.532146	−0.0176891
$906$	1.75705	0.0583742
$907$	37.3227	1.23928	0.619639	−	0.784887i	$-0.287279\pi$
$907$	37.3227	1.23928	0.619639	+	0.784887i	$0.287279\pi$
$908$	−15.7486	−0.522635
$909$	16.9056	0.560725
$910$	14.2519	0.472447
$911$	−21.9240	−0.726373	−0.363186	−	0.931716i	$-0.618311\pi$
$911$	−21.9240	−0.726373	−0.363186	+	0.931716i	$0.618311\pi$
$912$	2.09965	0.0695262
$913$	1.97429	0.0653394
$914$	−24.2227	−0.801217
$915$	−49.6276	−1.64064
$916$	−19.8095	−0.654524
$917$	58.5804	1.93450
$918$	23.9249	0.789640
$919$	−7.93458	−0.261738	−0.130869	−	0.991400i	$-0.541777\pi$
$919$	−7.93458	−0.261738	−0.130869	+	0.991400i	$0.541777\pi$
$920$	0.567710	0.0187168
$921$	−26.4233	−0.870678
$922$	20.5729	0.677534
$923$	1.89558	0.0623937
$924$	−27.9656	−0.920000
$925$	0.877250	0.0288438
$926$	15.5761	0.511864
$927$	−0.0308492	−0.00101322
$928$	−5.33121	−0.175006
$929$	29.3169	0.961857	0.480928	−	0.876760i	$-0.340300\pi$
$929$	29.3169	0.961857	0.480928	+	0.876760i	$0.340300\pi$
$930$	6.75300	0.221440
$931$	−16.2074	−0.531175
$932$	23.6366	0.774244
$933$	−43.0397	−1.40906
$934$	−23.7314	−0.776516
$935$	37.2740	1.21899
$936$	−2.21300	−0.0723341
$937$	25.7349	0.840723	0.420362	−	0.907357i	$-0.361903\pi$
$937$	25.7349	0.840723	0.420362	+	0.907357i	$0.361903\pi$
$938$	7.99388	0.261010
$939$	54.5747	1.78098
$940$	−0.733924	−0.0239380
$941$	8.03342	0.261882	0.130941	−	0.991390i	$-0.458200\pi$
$941$	8.03342	0.261882	0.130941	+	0.991390i	$0.458200\pi$
$942$	6.98343	0.227532
$943$	−3.18013	−0.103559
$944$	5.27734	0.171763
$945$	−30.3112	−0.986023
$946$	3.33934	0.108571
$947$	−20.7320	−0.673699	−0.336849	−	0.941559i	$-0.609361\pi$
$947$	−20.7320	−0.673699	−0.336849	+	0.941559i	$0.609361\pi$
$948$	11.4111	0.370617
$949$	−6.96597	−0.226125
$950$	−1.45447	−0.0471894
$951$	12.2409	0.396938
$952$	−34.4916	−1.11788
$953$	−14.5358	−0.470862	−0.235431	−	0.971891i	$-0.575650\pi$
$953$	−14.5358	−0.470862	−0.235431	+	0.971891i	$0.575650\pi$
$954$	−1.72159	−0.0557385
$955$	27.4776	0.889155
$956$	−9.80051	−0.316971
$957$	30.9483	1.00042
$958$	−9.61382	−0.310609
$959$	−1.43341	−0.0462872
$960$	−3.95354	−0.127600
$961$	−28.0824	−0.905885
$962$	0.947629	0.0305528
$963$	−17.4852	−0.563452
$964$	−1.29987	−0.0418658
$965$	−19.1371	−0.616044
$966$	3.04962	0.0981198
$967$	21.0905	0.678225	0.339112	−	0.940746i	$-0.389873\pi$
$967$	21.0905	0.678225	0.339112	+	0.940746i	$0.389873\pi$
$968$	3.35584	0.107861
$969$	−15.0330	−0.482931
$970$	−11.5436	−0.370643
$971$	50.2581	1.61286	0.806430	−	0.591329i	$-0.201397\pi$
$971$	50.2581	1.61286	0.806430	+	0.591329i	$0.201397\pi$
$972$	13.5787	0.435538
$973$	96.2630	3.08605
$974$	19.2611	0.617166
$975$	4.79814	0.153663
$976$	12.5527	0.401802
$977$	36.1532	1.15664	0.578322	−	0.815808i	$-0.303708\pi$
$977$	36.1532	1.15664	0.578322	+	0.815808i	$0.303708\pi$
$978$	0.138261	0.00442111
$979$	12.0327	0.384566
$980$	30.5178	0.974854
$981$	16.0813	0.513435
$982$	−0.102718	−0.00327786
$983$	−13.1095	−0.418128	−0.209064	−	0.977902i	$-0.567042\pi$
$983$	−13.1095	−0.418128	−0.209064	+	0.977902i	$0.567042\pi$
$984$	22.1465	0.706004
$985$	−45.7274	−1.45700
$986$	38.1704	1.21559
$987$	−3.94248	−0.125491
$988$	−1.57116	−0.0499853
$989$	−0.364151	−0.0115793
$990$	7.33273	0.233049
$991$	−50.6783	−1.60985	−0.804924	−	0.593378i	$-0.797794\pi$
$991$	−50.6783	−1.60985	−0.804924	+	0.593378i	$0.797794\pi$
$992$	−1.70809	−0.0542319
$993$	−74.9685	−2.37905
$994$	5.81211	0.184349
$995$	−29.6691	−0.940573
$996$	1.49931	0.0475074
$997$	45.4307	1.43880	0.719402	−	0.694594i	$-0.244416\pi$
$997$	45.4307	1.43880	0.719402	+	0.694594i	$0.244416\pi$
$998$	2.23133	0.0706314
$999$	−2.01543	−0.0637653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.9	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} -1.88296 q^{10} -2.76481 q^{11} -2.09965 q^{12} +1.57116 q^{13} +4.81740 q^{14} -3.95354 q^{15} +1.00000 q^{16} -7.15980 q^{17} -1.40851 q^{18} -1.00000 q^{19} +1.88296 q^{20} +10.1148 q^{21} +2.76481 q^{22} -0.301499 q^{23} +2.09965 q^{24} -1.45447 q^{25} -1.57116 q^{26} +3.34156 q^{27} -4.81740 q^{28} +5.33121 q^{29} +3.95354 q^{30} +1.70809 q^{31} -1.00000 q^{32} +5.80512 q^{33} +7.15980 q^{34} -9.07096 q^{35} +1.40851 q^{36} -0.603139 q^{37} +1.00000 q^{38} -3.29888 q^{39} -1.88296 q^{40} +10.5477 q^{41} -10.1148 q^{42} +1.20780 q^{43} -2.76481 q^{44} +2.65216 q^{45} +0.301499 q^{46} -0.389772 q^{47} -2.09965 q^{48} +16.2074 q^{49} +1.45447 q^{50} +15.0330 q^{51} +1.57116 q^{52} +1.22228 q^{53} -3.34156 q^{54} -5.20601 q^{55} +4.81740 q^{56} +2.09965 q^{57} -5.33121 q^{58} +5.27734 q^{59} -3.95354 q^{60} +12.5527 q^{61} -1.70809 q^{62} -6.78536 q^{63} +1.00000 q^{64} +2.95843 q^{65} -5.80512 q^{66} +1.65938 q^{67} -7.15980 q^{68} +0.633041 q^{69} +9.07096 q^{70} +1.20648 q^{71} -1.40851 q^{72} -4.43364 q^{73} +0.603139 q^{74} +3.05388 q^{75} -1.00000 q^{76} +13.3192 q^{77} +3.29888 q^{78} -5.43480 q^{79} +1.88296 q^{80} -11.2416 q^{81} -10.5477 q^{82} -0.714078 q^{83} +10.1148 q^{84} -13.4816 q^{85} -1.20780 q^{86} -11.1937 q^{87} +2.76481 q^{88} -4.35208 q^{89} -2.65216 q^{90} -7.56892 q^{91} -0.301499 q^{92} -3.58638 q^{93} +0.389772 q^{94} -1.88296 q^{95} +2.09965 q^{96} +6.13058 q^{97} -16.2074 q^{98} -3.89426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more