LMFDB - Embedded newform 8018.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.656283 q^{3} +1.00000 q^{4} -1.22883 q^{5} +0.656283 q^{6} +2.46640 q^{7} -1.00000 q^{8} -2.56929 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.656283 q^{3} +1.00000 q^{4} -1.22883 q^{5} +0.656283 q^{6} +2.46640 q^{7} -1.00000 q^{8} -2.56929 q^{9} +1.22883 q^{10} +2.53318 q^{11} -0.656283 q^{12} +2.77706 q^{13} -2.46640 q^{14} +0.806463 q^{15} +1.00000 q^{16} -0.964185 q^{17} +2.56929 q^{18} -1.00000 q^{19} -1.22883 q^{20} -1.61866 q^{21} -2.53318 q^{22} +3.35525 q^{23} +0.656283 q^{24} -3.48997 q^{25} -2.77706 q^{26} +3.65503 q^{27} +2.46640 q^{28} +0.507372 q^{29} -0.806463 q^{30} +5.13456 q^{31} -1.00000 q^{32} -1.66248 q^{33} +0.964185 q^{34} -3.03080 q^{35} -2.56929 q^{36} -8.07137 q^{37} +1.00000 q^{38} -1.82253 q^{39} +1.22883 q^{40} -1.46881 q^{41} +1.61866 q^{42} -12.6564 q^{43} +2.53318 q^{44} +3.15724 q^{45} -3.35525 q^{46} -2.57855 q^{47} -0.656283 q^{48} -0.916878 q^{49} +3.48997 q^{50} +0.632778 q^{51} +2.77706 q^{52} -1.67655 q^{53} -3.65503 q^{54} -3.11286 q^{55} -2.46640 q^{56} +0.656283 q^{57} -0.507372 q^{58} -0.559232 q^{59} +0.806463 q^{60} -3.22268 q^{61} -5.13456 q^{62} -6.33690 q^{63} +1.00000 q^{64} -3.41254 q^{65} +1.66248 q^{66} +4.20151 q^{67} -0.964185 q^{68} -2.20199 q^{69} +3.03080 q^{70} +4.84164 q^{71} +2.56929 q^{72} -8.59432 q^{73} +8.07137 q^{74} +2.29041 q^{75} -1.00000 q^{76} +6.24783 q^{77} +1.82253 q^{78} +15.0772 q^{79} -1.22883 q^{80} +5.30914 q^{81} +1.46881 q^{82} +14.5687 q^{83} -1.61866 q^{84} +1.18482 q^{85} +12.6564 q^{86} -0.332979 q^{87} -2.53318 q^{88} -15.3041 q^{89} -3.15724 q^{90} +6.84932 q^{91} +3.35525 q^{92} -3.36972 q^{93} +2.57855 q^{94} +1.22883 q^{95} +0.656283 q^{96} +2.84413 q^{97} +0.916878 q^{98} -6.50848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.656283	−0.378905	−0.189453	−	0.981890i	$-0.560671\pi$
$3$	−0.656283	−0.378905	−0.189453	+	0.981890i	$0.560671\pi$
$4$	1.00000	0.500000
$5$	−1.22883	−0.549552	−0.274776	−	0.961508i	$-0.588604\pi$
$5$	−1.22883	−0.549552	−0.274776	+	0.961508i	$0.588604\pi$
$6$	0.656283	0.267926
$7$	2.46640	0.932211	0.466106	−	0.884729i	$-0.345657\pi$
$7$	2.46640	0.932211	0.466106	+	0.884729i	$0.345657\pi$
$8$	−1.00000	−0.353553
$9$	−2.56929	−0.856431
$10$	1.22883	0.388592
$11$	2.53318	0.763783	0.381891	−	0.924207i	$-0.375273\pi$
$11$	2.53318	0.763783	0.381891	+	0.924207i	$0.375273\pi$
$12$	−0.656283	−0.189453
$13$	2.77706	0.770217	0.385108	−	0.922871i	$-0.374164\pi$
$13$	2.77706	0.770217	0.385108	+	0.922871i	$0.374164\pi$
$14$	−2.46640	−0.659173
$15$	0.806463	0.208228
$16$	1.00000	0.250000
$17$	−0.964185	−0.233849	−0.116925	−	0.993141i	$-0.537304\pi$
$17$	−0.964185	−0.233849	−0.116925	+	0.993141i	$0.537304\pi$
$18$	2.56929	0.605588
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.22883	−0.274776
$21$	−1.61866	−0.353220
$22$	−2.53318	−0.540076
$23$	3.35525	0.699618	0.349809	−	0.936821i	$-0.386246\pi$
$23$	3.35525	0.699618	0.349809	+	0.936821i	$0.386246\pi$
$24$	0.656283	0.133963
$25$	−3.48997	−0.697993
$26$	−2.77706	−0.544625
$27$	3.65503	0.703411
$28$	2.46640	0.466106
$29$	0.507372	0.0942165	0.0471083	−	0.998890i	$-0.484999\pi$
$29$	0.507372	0.0942165	0.0471083	+	0.998890i	$0.484999\pi$
$30$	−0.806463	−0.147239
$31$	5.13456	0.922194	0.461097	−	0.887350i	$-0.347456\pi$
$31$	5.13456	0.922194	0.461097	+	0.887350i	$0.347456\pi$
$32$	−1.00000	−0.176777
$33$	−1.66248	−0.289401
$34$	0.964185	0.165356
$35$	−3.03080	−0.512298
$36$	−2.56929	−0.428215
$37$	−8.07137	−1.32693	−0.663463	−	0.748209i	$-0.730914\pi$
$37$	−8.07137	−1.32693	−0.663463	+	0.748209i	$0.730914\pi$
$38$	1.00000	0.162221
$39$	−1.82253	−0.291839
$40$	1.22883	0.194296
$41$	−1.46881	−0.229390	−0.114695	−	0.993401i	$-0.536589\pi$
$41$	−1.46881	−0.229390	−0.114695	+	0.993401i	$0.536589\pi$
$42$	1.61866	0.249764
$43$	−12.6564	−1.93008	−0.965041	−	0.262100i	$-0.915585\pi$
$43$	−12.6564	−1.93008	−0.965041	+	0.262100i	$0.915585\pi$
$44$	2.53318	0.381891
$45$	3.15724	0.470653
$46$	−3.35525	−0.494705
$47$	−2.57855	−0.376120	−0.188060	−	0.982158i	$-0.560220\pi$
$47$	−2.57855	−0.376120	−0.188060	+	0.982158i	$0.560220\pi$
$48$	−0.656283	−0.0947263
$49$	−0.916878	−0.130983
$50$	3.48997	0.493556
$51$	0.632778	0.0886067
$52$	2.77706	0.385108
$53$	−1.67655	−0.230292	−0.115146	−	0.993349i	$-0.536734\pi$
$53$	−1.67655	−0.230292	−0.115146	+	0.993349i	$0.536734\pi$
$54$	−3.65503	−0.497387
$55$	−3.11286	−0.419738
$56$	−2.46640	−0.329586
$57$	0.656283	0.0869268
$58$	−0.507372	−0.0666211
$59$	−0.559232	−0.0728058	−0.0364029	−	0.999337i	$-0.511590\pi$
$59$	−0.559232	−0.0728058	−0.0364029	+	0.999337i	$0.511590\pi$
$60$	0.806463	0.104114
$61$	−3.22268	−0.412622	−0.206311	−	0.978486i	$-0.566146\pi$
$61$	−3.22268	−0.412622	−0.206311	+	0.978486i	$0.566146\pi$
$62$	−5.13456	−0.652090
$63$	−6.33690	−0.798374
$64$	1.00000	0.125000
$65$	−3.41254	−0.423274
$66$	1.66248	0.204638
$67$	4.20151	0.513296	0.256648	−	0.966505i	$-0.417382\pi$
$67$	4.20151	0.513296	0.256648	+	0.966505i	$0.417382\pi$
$68$	−0.964185	−0.116925
$69$	−2.20199	−0.265089
$70$	3.03080	0.362249
$71$	4.84164	0.574597	0.287298	−	0.957841i	$-0.407243\pi$
$71$	4.84164	0.574597	0.287298	+	0.957841i	$0.407243\pi$
$72$	2.56929	0.302794
$73$	−8.59432	−1.00589	−0.502945	−	0.864319i	$-0.667750\pi$
$73$	−8.59432	−1.00589	−0.502945	+	0.864319i	$0.667750\pi$
$74$	8.07137	0.938278
$75$	2.29041	0.264473
$76$	−1.00000	−0.114708
$77$	6.24783	0.712007
$78$	1.82253	0.206361
$79$	15.0772	1.69632	0.848161	−	0.529738i	$-0.177710\pi$
$79$	15.0772	1.69632	0.848161	+	0.529738i	$0.177710\pi$
$80$	−1.22883	−0.137388
$81$	5.30914	0.589905
$82$	1.46881	0.162203
$83$	14.5687	1.59912	0.799559	−	0.600587i	$-0.205067\pi$
$83$	14.5687	1.59912	0.799559	+	0.600587i	$0.205067\pi$
$84$	−1.61866	−0.176610
$85$	1.18482	0.128512
$86$	12.6564	1.36477
$87$	−0.332979	−0.0356991
$88$	−2.53318	−0.270038
$89$	−15.3041	−1.62223	−0.811117	−	0.584884i	$-0.801140\pi$
$89$	−15.3041	−1.62223	−0.811117	+	0.584884i	$0.801140\pi$
$90$	−3.15724	−0.332802
$91$	6.84932	0.718004
$92$	3.35525	0.349809
$93$	−3.36972	−0.349424
$94$	2.57855	0.265957
$95$	1.22883	0.126076
$96$	0.656283	0.0669816
$97$	2.84413	0.288777	0.144389	−	0.989521i	$-0.453878\pi$
$97$	2.84413	0.288777	0.144389	+	0.989521i	$0.453878\pi$
$98$	0.916878	0.0926187
$99$	−6.50848	−0.654127
$100$	−3.48997	−0.348997
$101$	−2.40413	−0.239220	−0.119610	−	0.992821i	$-0.538164\pi$
$101$	−2.40413	−0.239220	−0.119610	+	0.992821i	$0.538164\pi$
$102$	−0.632778	−0.0626544
$103$	1.08381	0.106791	0.0533954	−	0.998573i	$-0.482996\pi$
$103$	1.08381	0.106791	0.0533954	+	0.998573i	$0.482996\pi$
$104$	−2.77706	−0.272313
$105$	1.98906	0.194112
$106$	1.67655	0.162841
$107$	5.41633	0.523616	0.261808	−	0.965120i	$-0.415681\pi$
$107$	5.41633	0.523616	0.261808	+	0.965120i	$0.415681\pi$
$108$	3.65503	0.351706
$109$	−14.2925	−1.36897	−0.684486	−	0.729026i	$-0.739973\pi$
$109$	−14.2925	−1.36897	−0.684486	+	0.729026i	$0.739973\pi$
$110$	3.11286	0.296800
$111$	5.29711	0.502779
$112$	2.46640	0.233053
$113$	4.36519	0.410642	0.205321	−	0.978695i	$-0.434176\pi$
$113$	4.36519	0.410642	0.205321	+	0.978695i	$0.434176\pi$
$114$	−0.656283	−0.0614665
$115$	−4.12305	−0.384476
$116$	0.507372	0.0471083
$117$	−7.13507	−0.659637
$118$	0.559232	0.0514815
$119$	−2.37806	−0.217997
$120$	−0.806463	−0.0736197
$121$	−4.58300	−0.416636
$122$	3.22268	0.291768
$123$	0.963958	0.0869171
$124$	5.13456	0.461097
$125$	10.4328	0.933135
$126$	6.33690	0.564536
$127$	−4.68023	−0.415303	−0.207652	−	0.978203i	$-0.566582\pi$
$127$	−4.68023	−0.415303	−0.207652	+	0.978203i	$0.566582\pi$
$128$	−1.00000	−0.0883883
$129$	8.30618	0.731318
$130$	3.41254	0.299300
$131$	−11.5458	−1.00876	−0.504382	−	0.863481i	$-0.668280\pi$
$131$	−11.5458	−1.00876	−0.504382	+	0.863481i	$0.668280\pi$
$132$	−1.66248	−0.144701
$133$	−2.46640	−0.213864
$134$	−4.20151	−0.362955
$135$	−4.49143	−0.386561
$136$	0.964185	0.0826782
$137$	−16.0140	−1.36817	−0.684086	−	0.729402i	$-0.739799\pi$
$137$	−16.0140	−1.36817	−0.684086	+	0.729402i	$0.739799\pi$
$138$	2.20199	0.187446
$139$	−6.76188	−0.573535	−0.286768	−	0.958000i	$-0.592581\pi$
$139$	−6.76188	−0.573535	−0.286768	+	0.958000i	$0.592581\pi$
$140$	−3.03080	−0.256149
$141$	1.69226	0.142514
$142$	−4.84164	−0.406301
$143$	7.03478	0.588278
$144$	−2.56929	−0.214108
$145$	−0.623476	−0.0517768
$146$	8.59432	0.711271
$147$	0.601732	0.0496300
$148$	−8.07137	−0.663463
$149$	20.2752	1.66101	0.830505	−	0.557011i	$-0.188052\pi$
$149$	20.2752	1.66101	0.830505	+	0.557011i	$0.188052\pi$
$150$	−2.29041	−0.187011
$151$	−5.05919	−0.411711	−0.205855	−	0.978582i	$-0.565998\pi$
$151$	−5.05919	−0.411711	−0.205855	+	0.978582i	$0.565998\pi$
$152$	1.00000	0.0811107
$153$	2.47727	0.200276
$154$	−6.24783	−0.503465
$155$	−6.30952	−0.506793
$156$	−1.82253	−0.145920
$157$	4.42653	0.353276	0.176638	−	0.984276i	$-0.443478\pi$
$157$	4.42653	0.353276	0.176638	+	0.984276i	$0.443478\pi$
$158$	−15.0772	−1.19948
$159$	1.10029	0.0872588
$160$	1.22883	0.0971479
$161$	8.27538	0.652192
$162$	−5.30914	−0.417126
$163$	15.4583	1.21078	0.605392	−	0.795927i	$-0.293016\pi$
$163$	15.4583	1.21078	0.605392	+	0.795927i	$0.293016\pi$
$164$	−1.46881	−0.114695
$165$	2.04292	0.159041
$166$	−14.5687	−1.13075
$167$	−14.6812	−1.13607	−0.568034	−	0.823005i	$-0.692296\pi$
$167$	−14.6812	−1.13607	−0.568034	+	0.823005i	$0.692296\pi$
$168$	1.61866	0.124882
$169$	−5.28796	−0.406767
$170$	−1.18482	−0.0908718
$171$	2.56929	0.196479
$172$	−12.6564	−0.965041
$173$	2.84477	0.216284	0.108142	−	0.994135i	$-0.465510\pi$
$173$	2.84477	0.216284	0.108142	+	0.994135i	$0.465510\pi$
$174$	0.332979	0.0252431
$175$	−8.60765	−0.650677
$176$	2.53318	0.190946
$177$	0.367014	0.0275865
$178$	15.3041	1.14709
$179$	3.45578	0.258297	0.129149	−	0.991625i	$-0.458776\pi$
$179$	3.45578	0.258297	0.129149	+	0.991625i	$0.458776\pi$
$180$	3.15724	0.235326
$181$	−12.8494	−0.955089	−0.477545	−	0.878607i	$-0.658473\pi$
$181$	−12.8494	−0.955089	−0.477545	+	0.878607i	$0.658473\pi$
$182$	−6.84932	−0.507706
$183$	2.11499	0.156345
$184$	−3.35525	−0.247352
$185$	9.91838	0.729214
$186$	3.36972	0.247080
$187$	−2.44245	−0.178610
$188$	−2.57855	−0.188060
$189$	9.01477	0.655728
$190$	−1.22883	−0.0891490
$191$	25.9589	1.87832	0.939159	−	0.343484i	$-0.111607\pi$
$191$	25.9589	1.87832	0.939159	+	0.343484i	$0.111607\pi$
$192$	−0.656283	−0.0473632
$193$	−13.2961	−0.957075	−0.478537	−	0.878067i	$-0.658833\pi$
$193$	−13.2961	−0.957075	−0.478537	+	0.878067i	$0.658833\pi$
$194$	−2.84413	−0.204196
$195$	2.23959	0.160381
$196$	−0.916878	−0.0654913
$197$	2.67231	0.190394	0.0951972	−	0.995458i	$-0.469652\pi$
$197$	2.67231	0.190394	0.0951972	+	0.995458i	$0.469652\pi$
$198$	6.50848	0.462538
$199$	−7.84768	−0.556307	−0.278154	−	0.960537i	$-0.589722\pi$
$199$	−7.84768	−0.556307	−0.278154	+	0.960537i	$0.589722\pi$
$200$	3.48997	0.246778
$201$	−2.75738	−0.194491
$202$	2.40413	0.169154
$203$	1.25138	0.0878297
$204$	0.632778	0.0443033
$205$	1.80493	0.126062
$206$	−1.08381	−0.0755124
$207$	−8.62062	−0.599174
$208$	2.77706	0.192554
$209$	−2.53318	−0.175224
$210$	−1.98906	−0.137258
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−1.67655	−0.115146
$213$	−3.17749	−0.217718
$214$	−5.41633	−0.370253
$215$	15.5526	1.06068
$216$	−3.65503	−0.248693
$217$	12.6639	0.859679
$218$	14.2925	0.968009
$219$	5.64031	0.381137
$220$	−3.11286	−0.209869
$221$	−2.67759	−0.180115
$222$	−5.29711	−0.355518
$223$	3.87038	0.259180	0.129590	−	0.991568i	$-0.458634\pi$
$223$	3.87038	0.259180	0.129590	+	0.991568i	$0.458634\pi$
$224$	−2.46640	−0.164793
$225$	8.96674	0.597783
$226$	−4.36519	−0.290368
$227$	16.7652	1.11275	0.556374	−	0.830932i	$-0.312192\pi$
$227$	16.7652	1.11275	0.556374	+	0.830932i	$0.312192\pi$
$228$	0.656283	0.0434634
$229$	0.445190	0.0294190	0.0147095	−	0.999892i	$-0.495318\pi$
$229$	0.445190	0.0294190	0.0147095	+	0.999892i	$0.495318\pi$
$230$	4.12305	0.271866
$231$	−4.10035	−0.269783
$232$	−0.507372	−0.0333106
$233$	−18.5171	−1.21309	−0.606547	−	0.795048i	$-0.707446\pi$
$233$	−18.5171	−1.21309	−0.606547	+	0.795048i	$0.707446\pi$
$234$	7.13507	0.466434
$235$	3.16861	0.206697
$236$	−0.559232	−0.0364029
$237$	−9.89494	−0.642746
$238$	2.37806	0.154147
$239$	−1.71529	−0.110953	−0.0554765	−	0.998460i	$-0.517668\pi$
$239$	−1.71529	−0.110953	−0.0554765	+	0.998460i	$0.517668\pi$
$240$	0.806463	0.0520570
$241$	21.1313	1.36118	0.680592	−	0.732662i	$-0.261723\pi$
$241$	21.1313	1.36118	0.680592	+	0.732662i	$0.261723\pi$
$242$	4.58300	0.294606
$243$	−14.4494	−0.926929
$244$	−3.22268	−0.206311
$245$	1.12669	0.0719817
$246$	−0.963958	−0.0614597
$247$	−2.77706	−0.176700
$248$	−5.13456	−0.326045
$249$	−9.56117	−0.605914
$250$	−10.4328	−0.659826
$251$	−7.75851	−0.489713	−0.244856	−	0.969559i	$-0.578741\pi$
$251$	−7.75851	−0.489713	−0.244856	+	0.969559i	$0.578741\pi$
$252$	−6.33690	−0.399187
$253$	8.49945	0.534356
$254$	4.68023	0.293664
$255$	−0.777580	−0.0486939
$256$	1.00000	0.0625000
$257$	1.14498	0.0714222	0.0357111	−	0.999362i	$-0.488630\pi$
$257$	1.14498	0.0714222	0.0357111	+	0.999362i	$0.488630\pi$
$258$	−8.30618	−0.517120
$259$	−19.9072	−1.23697
$260$	−3.41254	−0.211637
$261$	−1.30359	−0.0806899
$262$	11.5458	0.713304
$263$	25.3912	1.56569	0.782843	−	0.622219i	$-0.213769\pi$
$263$	25.3912	1.56569	0.782843	+	0.622219i	$0.213769\pi$
$264$	1.66248	0.102319
$265$	2.06020	0.126557
$266$	2.46640	0.151225
$267$	10.0438	0.614673
$268$	4.20151	0.256648
$269$	3.37381	0.205705	0.102852	−	0.994697i	$-0.467203\pi$
$269$	3.37381	0.205705	0.102852	+	0.994697i	$0.467203\pi$
$270$	4.49143	0.273340
$271$	26.0833	1.58445	0.792223	−	0.610232i	$-0.208924\pi$
$271$	26.0833	1.58445	0.792223	+	0.610232i	$0.208924\pi$
$272$	−0.964185	−0.0584623
$273$	−4.49510	−0.272056
$274$	16.0140	0.967443
$275$	−8.84071	−0.533115
$276$	−2.20199	−0.132544
$277$	9.79155	0.588317	0.294159	−	0.955757i	$-0.404961\pi$
$277$	9.79155	0.588317	0.294159	+	0.955757i	$0.404961\pi$
$278$	6.76188	0.405551
$279$	−13.1922	−0.789795
$280$	3.03080	0.181125
$281$	−16.1406	−0.962865	−0.481433	−	0.876483i	$-0.659883\pi$
$281$	−16.1406	−0.962865	−0.481433	+	0.876483i	$0.659883\pi$
$282$	−1.69226	−0.100773
$283$	−19.1946	−1.14100	−0.570501	−	0.821297i	$-0.693251\pi$
$283$	−19.1946	−1.14100	−0.570501	+	0.821297i	$0.693251\pi$
$284$	4.84164	0.287298
$285$	−0.806463	−0.0477708
$286$	−7.03478	−0.415975
$287$	−3.62268	−0.213840
$288$	2.56929	0.151397
$289$	−16.0703	−0.945315
$290$	0.623476	0.0366118
$291$	−1.86655	−0.109419
$292$	−8.59432	−0.502945
$293$	−21.6518	−1.26491	−0.632455	−	0.774597i	$-0.717953\pi$
$293$	−21.6518	−1.26491	−0.632455	+	0.774597i	$0.717953\pi$
$294$	−0.601732	−0.0350937
$295$	0.687203	0.0400105
$296$	8.07137	0.469139
$297$	9.25886	0.537253
$298$	−20.2752	−1.17451
$299$	9.31771	0.538857
$300$	2.29041	0.132237
$301$	−31.2157	−1.79924
$302$	5.05919	0.291124
$303$	1.57779	0.0906415
$304$	−1.00000	−0.0573539
$305$	3.96014	0.226757
$306$	−2.47727	−0.141616
$307$	−0.731919	−0.0417728	−0.0208864	−	0.999782i	$-0.506649\pi$
$307$	−0.731919	−0.0417728	−0.0208864	+	0.999782i	$0.506649\pi$
$308$	6.24783	0.356003
$309$	−0.711284	−0.0404636
$310$	6.30952	0.358357
$311$	−21.8823	−1.24083	−0.620414	−	0.784274i	$-0.713036\pi$
$311$	−21.8823	−1.24083	−0.620414	+	0.784274i	$0.713036\pi$
$312$	1.82253	0.103181
$313$	−19.2489	−1.08801	−0.544007	−	0.839081i	$-0.683093\pi$
$313$	−19.2489	−1.08801	−0.544007	+	0.839081i	$0.683093\pi$
$314$	−4.42653	−0.249804
$315$	7.78700	0.438748
$316$	15.0772	0.848161
$317$	−20.9236	−1.17518	−0.587592	−	0.809157i	$-0.699924\pi$
$317$	−20.9236	−1.17518	−0.587592	+	0.809157i	$0.699924\pi$
$318$	−1.10029	−0.0617013
$319$	1.28526	0.0719610
$320$	−1.22883	−0.0686939
$321$	−3.55465	−0.198401
$322$	−8.27538	−0.461169
$323$	0.964185	0.0536487
$324$	5.30914	0.294952
$325$	−9.69183	−0.537606
$326$	−15.4583	−0.856154
$327$	9.37991	0.518710
$328$	1.46881	0.0811017
$329$	−6.35973	−0.350623
$330$	−2.04292	−0.112459
$331$	−26.3706	−1.44946	−0.724729	−	0.689034i	$-0.758035\pi$
$331$	−26.3706	−1.44946	−0.724729	+	0.689034i	$0.758035\pi$
$332$	14.5687	0.799559
$333$	20.7377	1.13642
$334$	14.6812	0.803322
$335$	−5.16296	−0.282083
$336$	−1.61866	−0.0883049
$337$	−22.0621	−1.20180	−0.600900	−	0.799324i	$-0.705191\pi$
$337$	−22.0621	−1.20180	−0.600900	+	0.799324i	$0.705191\pi$
$338$	5.28796	0.287627
$339$	−2.86480	−0.155595
$340$	1.18482	0.0642561
$341$	13.0068	0.704356
$342$	−2.56929	−0.138931
$343$	−19.5262	−1.05431
$344$	12.6564	0.682387
$345$	2.70589	0.145680
$346$	−2.84477	−0.152936
$347$	−5.03597	−0.270345	−0.135172	−	0.990822i	$-0.543159\pi$
$347$	−5.03597	−0.270345	−0.135172	+	0.990822i	$0.543159\pi$
$348$	−0.332979	−0.0178496
$349$	−6.92267	−0.370562	−0.185281	−	0.982686i	$-0.559320\pi$
$349$	−6.92267	−0.370562	−0.185281	+	0.982686i	$0.559320\pi$
$350$	8.60765	0.460098
$351$	10.1502	0.541779
$352$	−2.53318	−0.135019
$353$	21.3368	1.13564	0.567822	−	0.823151i	$-0.307786\pi$
$353$	21.3368	1.13564	0.567822	+	0.823151i	$0.307786\pi$
$354$	−0.367014	−0.0195066
$355$	−5.94957	−0.315771
$356$	−15.3041	−0.811117
$357$	1.56068	0.0826001
$358$	−3.45578	−0.182644
$359$	32.2705	1.70317	0.851586	−	0.524215i	$-0.175641\pi$
$359$	32.2705	1.70317	0.851586	+	0.524215i	$0.175641\pi$
$360$	−3.15724	−0.166401
$361$	1.00000	0.0526316
$362$	12.8494	0.675350
$363$	3.00774	0.157866
$364$	6.84932	0.359002
$365$	10.5610	0.552788
$366$	−2.11499	−0.110552
$367$	31.8609	1.66312	0.831562	−	0.555432i	$-0.187447\pi$
$367$	31.8609	1.66312	0.831562	+	0.555432i	$0.187447\pi$
$368$	3.35525	0.174904
$369$	3.77381	0.196457
$370$	−9.91838	−0.515632
$371$	−4.13504	−0.214681
$372$	−3.36972	−0.174712
$373$	3.93302	0.203644	0.101822	−	0.994803i	$-0.467533\pi$
$373$	3.93302	0.203644	0.101822	+	0.994803i	$0.467533\pi$
$374$	2.44245	0.126296
$375$	−6.84685	−0.353570
$376$	2.57855	0.132979
$377$	1.40900	0.0725671
$378$	−9.01477	−0.463670
$379$	−16.4831	−0.846682	−0.423341	−	0.905970i	$-0.639143\pi$
$379$	−16.4831	−0.846682	−0.423341	+	0.905970i	$0.639143\pi$
$380$	1.22883	0.0630379
$381$	3.07156	0.157361
$382$	−25.9589	−1.32817
$383$	−5.90876	−0.301924	−0.150962	−	0.988540i	$-0.548237\pi$
$383$	−5.90876	−0.301924	−0.150962	+	0.988540i	$0.548237\pi$
$384$	0.656283	0.0334908
$385$	−7.67755	−0.391284
$386$	13.2961	0.676754
$387$	32.5180	1.65298
$388$	2.84413	0.144389
$389$	−26.5021	−1.34371	−0.671854	−	0.740683i	$-0.734502\pi$
$389$	−26.5021	−1.34371	−0.671854	+	0.740683i	$0.734502\pi$
$390$	−2.23959	−0.113406
$391$	−3.23508	−0.163605
$392$	0.916878	0.0463093
$393$	7.57733	0.382226
$394$	−2.67231	−0.134629
$395$	−18.5274	−0.932217
$396$	−6.50848	−0.327064
$397$	−29.4443	−1.47777	−0.738883	−	0.673834i	$-0.764646\pi$
$397$	−29.4443	−1.47777	−0.738883	+	0.673834i	$0.764646\pi$
$398$	7.84768	0.393369
$399$	1.61866	0.0810341
$400$	−3.48997	−0.174498
$401$	−16.0740	−0.802696	−0.401348	−	0.915926i	$-0.631458\pi$
$401$	−16.0740	−0.802696	−0.401348	+	0.915926i	$0.631458\pi$
$402$	2.75738	0.137526
$403$	14.2590	0.710289
$404$	−2.40413	−0.119610
$405$	−6.52406	−0.324183
$406$	−1.25138	−0.0621050
$407$	−20.4462	−1.01348
$408$	−0.632778	−0.0313272
$409$	−15.5578	−0.769282	−0.384641	−	0.923066i	$-0.625675\pi$
$409$	−15.5578	−0.769282	−0.384641	+	0.923066i	$0.625675\pi$
$410$	−1.80493	−0.0891391
$411$	10.5097	0.518407
$412$	1.08381	0.0533954
$413$	−1.37929	−0.0678703
$414$	8.62062	0.423680
$415$	−17.9025	−0.878798
$416$	−2.77706	−0.136156
$417$	4.43771	0.217315
$418$	2.53318	0.123902
$419$	30.8745	1.50832	0.754159	−	0.656692i	$-0.228045\pi$
$419$	30.8745	1.50832	0.754159	+	0.656692i	$0.228045\pi$
$420$	1.98906	0.0970562
$421$	17.9081	0.872786	0.436393	−	0.899756i	$-0.356256\pi$
$421$	17.9081	0.872786	0.436393	+	0.899756i	$0.356256\pi$
$422$	1.00000	0.0486792
$423$	6.62505	0.322121
$424$	1.67655	0.0814204
$425$	3.36497	0.163225
$426$	3.17749	0.153950
$427$	−7.94842	−0.384651
$428$	5.41633	0.261808
$429$	−4.61681	−0.222902
$430$	−15.5526	−0.750014
$431$	28.5173	1.37363	0.686816	−	0.726831i	$-0.259008\pi$
$431$	28.5173	1.37363	0.686816	+	0.726831i	$0.259008\pi$
$432$	3.65503	0.175853
$433$	−37.7724	−1.81523	−0.907614	−	0.419806i	$-0.862098\pi$
$433$	−37.7724	−1.81523	−0.907614	+	0.419806i	$0.862098\pi$
$434$	−12.6639	−0.607885
$435$	0.409177	0.0196185
$436$	−14.2925	−0.684486
$437$	−3.35525	−0.160503
$438$	−5.64031	−0.269504
$439$	−4.71110	−0.224849	−0.112424	−	0.993660i	$-0.535862\pi$
$439$	−4.71110	−0.224849	−0.112424	+	0.993660i	$0.535862\pi$
$440$	3.11286	0.148400
$441$	2.35573	0.112178
$442$	2.67759	0.127360
$443$	32.4557	1.54202	0.771008	−	0.636826i	$-0.219753\pi$
$443$	32.4557	1.54202	0.771008	+	0.636826i	$0.219753\pi$
$444$	5.29711	0.251389
$445$	18.8062	0.891501
$446$	−3.87038	−0.183268
$447$	−13.3063	−0.629365
$448$	2.46640	0.116526
$449$	−12.9548	−0.611376	−0.305688	−	0.952132i	$-0.598886\pi$
$449$	−12.9548	−0.611376	−0.305688	+	0.952132i	$0.598886\pi$
$450$	−8.96674	−0.422696
$451$	−3.72077	−0.175204
$452$	4.36519	0.205321
$453$	3.32026	0.155999
$454$	−16.7652	−0.786832
$455$	−8.41669	−0.394580
$456$	−0.656283	−0.0307333
$457$	−36.6463	−1.71424	−0.857121	−	0.515115i	$-0.827749\pi$
$457$	−36.6463	−1.71424	−0.857121	+	0.515115i	$0.827749\pi$
$458$	−0.445190	−0.0208024
$459$	−3.52413	−0.164492
$460$	−4.12305	−0.192238
$461$	28.7701	1.33996	0.669978	−	0.742381i	$-0.266303\pi$
$461$	28.7701	1.33996	0.669978	+	0.742381i	$0.266303\pi$
$462$	4.10035	0.190765
$463$	−34.5158	−1.60409	−0.802043	−	0.597266i	$-0.796254\pi$
$463$	−34.5158	−1.60409	−0.802043	+	0.597266i	$0.796254\pi$
$464$	0.507372	0.0235541
$465$	4.14083	0.192027
$466$	18.5171	0.857787
$467$	16.3066	0.754581	0.377291	−	0.926095i	$-0.376856\pi$
$467$	16.3066	0.754581	0.377291	+	0.926095i	$0.376856\pi$
$468$	−7.13507	−0.329819
$469$	10.3626	0.478501
$470$	−3.16861	−0.146157
$471$	−2.90506	−0.133858
$472$	0.559232	0.0257407
$473$	−32.0609	−1.47416
$474$	9.89494	0.454490
$475$	3.48997	0.160131
$476$	−2.37806	−0.108998
$477$	4.30755	0.197229
$478$	1.71529	0.0784556
$479$	−5.46908	−0.249888	−0.124944	−	0.992164i	$-0.539875\pi$
$479$	−5.46908	−0.249888	−0.124944	+	0.992164i	$0.539875\pi$
$480$	−0.806463	−0.0368098
$481$	−22.4146	−1.02202
$482$	−21.1313	−0.962503
$483$	−5.43099	−0.247119
$484$	−4.58300	−0.208318
$485$	−3.49496	−0.158698
$486$	14.4494	0.655438
$487$	20.2075	0.915689	0.457845	−	0.889032i	$-0.348622\pi$
$487$	20.2075	0.915689	0.457845	+	0.889032i	$0.348622\pi$
$488$	3.22268	0.145884
$489$	−10.1450	−0.458773
$490$	−1.12669	−0.0508987
$491$	−28.7727	−1.29850	−0.649248	−	0.760577i	$-0.724916\pi$
$491$	−28.7727	−1.29850	−0.649248	+	0.760577i	$0.724916\pi$
$492$	0.963958	0.0434586
$493$	−0.489200	−0.0220325
$494$	2.77706	0.124946
$495$	7.99785	0.359477
$496$	5.13456	0.230548
$497$	11.9414	0.535646
$498$	9.56117	0.428446
$499$	−30.5754	−1.36874	−0.684372	−	0.729133i	$-0.739924\pi$
$499$	−30.5754	−1.36874	−0.684372	+	0.729133i	$0.739924\pi$
$500$	10.4328	0.466567
$501$	9.63505	0.430462
$502$	7.75851	0.346279
$503$	−17.2476	−0.769034	−0.384517	−	0.923118i	$-0.625632\pi$
$503$	−17.2476	−0.769034	−0.384517	+	0.923118i	$0.625632\pi$
$504$	6.33690	0.282268
$505$	2.95427	0.131463
$506$	−8.49945	−0.377847
$507$	3.47040	0.154126
$508$	−4.68023	−0.207652
$509$	−9.55011	−0.423301	−0.211651	−	0.977345i	$-0.567884\pi$
$509$	−9.55011	−0.423301	−0.211651	+	0.977345i	$0.567884\pi$
$510$	0.777580	0.0344318
$511$	−21.1970	−0.937701
$512$	−1.00000	−0.0441942
$513$	−3.65503	−0.161374
$514$	−1.14498	−0.0505031
$515$	−1.33182	−0.0586870
$516$	8.30618	0.365659
$517$	−6.53194	−0.287274
$518$	19.9072	0.874673
$519$	−1.86697	−0.0819510
$520$	3.41254	0.149650
$521$	−34.9260	−1.53014	−0.765068	−	0.643950i	$-0.777295\pi$
$521$	−34.9260	−1.53014	−0.765068	+	0.643950i	$0.777295\pi$
$522$	1.30359	0.0570564
$523$	−29.9788	−1.31088	−0.655441	−	0.755246i	$-0.727517\pi$
$523$	−29.9788	−1.31088	−0.655441	+	0.755246i	$0.727517\pi$
$524$	−11.5458	−0.504382
$525$	5.64905	0.246545
$526$	−25.3912	−1.10711
$527$	−4.95066	−0.215654
$528$	−1.66248	−0.0723503
$529$	−11.7423	−0.510535
$530$	−2.06020	−0.0894895
$531$	1.43683	0.0623531
$532$	−2.46640	−0.106932
$533$	−4.07898	−0.176680
$534$	−10.0438	−0.434639
$535$	−6.65577	−0.287754
$536$	−4.20151	−0.181478
$537$	−2.26797	−0.0978703
$538$	−3.37381	−0.145455
$539$	−2.32262	−0.100042
$540$	−4.49143	−0.193280
$541$	36.7983	1.58208	0.791041	−	0.611763i	$-0.209539\pi$
$541$	36.7983	1.58208	0.791041	+	0.611763i	$0.209539\pi$
$542$	−26.0833	−1.12037
$543$	8.43285	0.361888
$544$	0.964185	0.0413391
$545$	17.5631	0.752320
$546$	4.49510	0.192372
$547$	1.26217	0.0539664	0.0269832	−	0.999636i	$-0.491410\pi$
$547$	1.26217	0.0539664	0.0269832	+	0.999636i	$0.491410\pi$
$548$	−16.0140	−0.684086
$549$	8.28001	0.353382
$550$	8.84071	0.376969
$551$	−0.507372	−0.0216148
$552$	2.20199	0.0937231
$553$	37.1865	1.58133
$554$	−9.79155	−0.416003
$555$	−6.50927	−0.276303
$556$	−6.76188	−0.286768
$557$	7.59417	0.321775	0.160888	−	0.986973i	$-0.448564\pi$
$557$	7.59417	0.321775	0.160888	+	0.986973i	$0.448564\pi$
$558$	13.1922	0.558470
$559$	−35.1475	−1.48658
$560$	−3.03080	−0.128074
$561$	1.60294	0.0676763
$562$	16.1406	0.680849
$563$	28.7440	1.21141	0.605707	−	0.795688i	$-0.292891\pi$
$563$	28.7440	1.21141	0.605707	+	0.795688i	$0.292891\pi$
$564$	1.69226	0.0712570
$565$	−5.36409	−0.225669
$566$	19.1946	0.806810
$567$	13.0945	0.549916
$568$	−4.84164	−0.203151
$569$	−26.2671	−1.10117	−0.550586	−	0.834778i	$-0.685596\pi$
$569$	−26.2671	−1.10117	−0.550586	+	0.834778i	$0.685596\pi$
$570$	0.806463	0.0337790
$571$	24.2872	1.01639	0.508194	−	0.861243i	$-0.330313\pi$
$571$	24.2872	1.01639	0.508194	+	0.861243i	$0.330313\pi$
$572$	7.03478	0.294139
$573$	−17.0364	−0.711704
$574$	3.62268	0.151208
$575$	−11.7097	−0.488329
$576$	−2.56929	−0.107054
$577$	24.1157	1.00395	0.501975	−	0.864882i	$-0.332607\pi$
$577$	24.1157	1.00395	0.501975	+	0.864882i	$0.332607\pi$
$578$	16.0703	0.668438
$579$	8.72601	0.362641
$580$	−0.623476	−0.0258884
$581$	35.9321	1.49072
$582$	1.86655	0.0773711
$583$	−4.24700	−0.175893
$584$	8.59432	0.355636
$585$	8.76782	0.362505
$586$	21.6518	0.894426
$587$	−18.2212	−0.752068	−0.376034	−	0.926606i	$-0.622712\pi$
$587$	−18.2212	−0.752068	−0.376034	+	0.926606i	$0.622712\pi$
$588$	0.601732	0.0248150
$589$	−5.13456	−0.211566
$590$	−0.687203	−0.0282917
$591$	−1.75379	−0.0721414
$592$	−8.07137	−0.331731
$593$	24.6583	1.01260	0.506298	−	0.862359i	$-0.331014\pi$
$593$	24.6583	1.01260	0.506298	+	0.862359i	$0.331014\pi$
$594$	−9.25886	−0.379896
$595$	2.92225	0.119800
$596$	20.2752	0.830505
$597$	5.15030	0.210788
$598$	−9.31771	−0.381030
$599$	−1.97385	−0.0806495	−0.0403247	−	0.999187i	$-0.512839\pi$
$599$	−1.97385	−0.0806495	−0.0403247	+	0.999187i	$0.512839\pi$
$600$	−2.29041	−0.0935054
$601$	−4.08788	−0.166748	−0.0833741	−	0.996518i	$-0.526570\pi$
$601$	−4.08788	−0.166748	−0.0833741	+	0.996518i	$0.526570\pi$
$602$	31.2157	1.27226
$603$	−10.7949	−0.439603
$604$	−5.05919	−0.205855
$605$	5.63174	0.228963
$606$	−1.57779	−0.0640932
$607$	−28.6796	−1.16407	−0.582035	−	0.813164i	$-0.697743\pi$
$607$	−28.6796	−1.16407	−0.582035	+	0.813164i	$0.697743\pi$
$608$	1.00000	0.0405554
$609$	−0.821260	−0.0332791
$610$	−3.96014	−0.160342
$611$	−7.16078	−0.289694
$612$	2.47727	0.100138
$613$	0.249598	0.0100812	0.00504059	−	0.999987i	$-0.498396\pi$
$613$	0.249598	0.0100812	0.00504059	+	0.999987i	$0.498396\pi$
$614$	0.731919	0.0295378
$615$	−1.18454	−0.0477654
$616$	−6.24783	−0.251732
$617$	−8.63308	−0.347555	−0.173777	−	0.984785i	$-0.555597\pi$
$617$	−8.63308	−0.347555	−0.173777	+	0.984785i	$0.555597\pi$
$618$	0.711284	0.0286121
$619$	−1.09586	−0.0440463	−0.0220231	−	0.999757i	$-0.507011\pi$
$619$	−1.09586	−0.0440463	−0.0220231	+	0.999757i	$0.507011\pi$
$620$	−6.30952	−0.253397
$621$	12.2635	0.492119
$622$	21.8823	0.877398
$623$	−37.7461	−1.51226
$624$	−1.82253	−0.0729598
$625$	4.62969	0.185188
$626$	19.2489	0.769342
$627$	1.66248	0.0663932
$628$	4.42653	0.176638
$629$	7.78230	0.310300
$630$	−7.78700	−0.310242
$631$	18.1954	0.724348	0.362174	−	0.932111i	$-0.382035\pi$
$631$	18.1954	0.724348	0.362174	+	0.932111i	$0.382035\pi$
$632$	−15.0772	−0.599741
$633$	0.656283	0.0260849
$634$	20.9236	0.830981
$635$	5.75123	0.228231
$636$	1.10029	0.0436294
$637$	−2.54622	−0.100885
$638$	−1.28526	−0.0508841
$639$	−12.4396	−0.492103
$640$	1.22883	0.0485740
$641$	33.4455	1.32102	0.660509	−	0.750818i	$-0.270341\pi$
$641$	33.4455	1.32102	0.660509	+	0.750818i	$0.270341\pi$
$642$	3.55465	0.140291
$643$	−17.2875	−0.681753	−0.340876	−	0.940108i	$-0.610724\pi$
$643$	−17.2875	−0.681753	−0.340876	+	0.940108i	$0.610724\pi$
$644$	8.27538	0.326096
$645$	−10.2069	−0.401897
$646$	−0.964185	−0.0379354
$647$	25.7407	1.01197	0.505986	−	0.862541i	$-0.331129\pi$
$647$	25.7407	1.01197	0.505986	+	0.862541i	$0.331129\pi$
$648$	−5.30914	−0.208563
$649$	−1.41664	−0.0556078
$650$	9.69183	0.380145
$651$	−8.31108	−0.325737
$652$	15.4583	0.605392
$653$	0.984346	0.0385204	0.0192602	−	0.999815i	$-0.493869\pi$
$653$	0.984346	0.0385204	0.0192602	+	0.999815i	$0.493869\pi$
$654$	−9.37991	−0.366784
$655$	14.1879	0.554368
$656$	−1.46881	−0.0573475
$657$	22.0813	0.861475
$658$	6.35973	0.247928
$659$	−46.4564	−1.80968	−0.904842	−	0.425746i	$-0.860012\pi$
$659$	−46.4564	−1.80968	−0.904842	+	0.425746i	$0.860012\pi$
$660$	2.04292	0.0795205
$661$	−30.8462	−1.19978	−0.599888	−	0.800084i	$-0.704788\pi$
$661$	−30.8462	−1.19978	−0.599888	+	0.800084i	$0.704788\pi$
$662$	26.3706	1.02492
$663$	1.75726	0.0682463
$664$	−14.5687	−0.565374
$665$	3.03080	0.117529
$666$	−20.7377	−0.803570
$667$	1.70236	0.0659156
$668$	−14.6812	−0.568034
$669$	−2.54006	−0.0982045
$670$	5.16296	0.199463
$671$	−8.16364	−0.315154
$672$	1.61866	0.0624410
$673$	10.6344	0.409925	0.204963	−	0.978770i	$-0.434293\pi$
$673$	10.6344	0.409925	0.204963	+	0.978770i	$0.434293\pi$
$674$	22.0621	0.849802
$675$	−12.7559	−0.490976
$676$	−5.28796	−0.203383
$677$	5.33569	0.205067	0.102534	−	0.994730i	$-0.467305\pi$
$677$	5.33569	0.205067	0.102534	+	0.994730i	$0.467305\pi$
$678$	2.86480	0.110022
$679$	7.01475	0.269201
$680$	−1.18482	−0.0454359
$681$	−11.0027	−0.421626
$682$	−13.0068	−0.498055
$683$	−38.0068	−1.45429	−0.727145	−	0.686483i	$-0.759153\pi$
$683$	−38.0068	−1.45429	−0.727145	+	0.686483i	$0.759153\pi$
$684$	2.56929	0.0982394
$685$	19.6786	0.751881
$686$	19.5262	0.745513
$687$	−0.292171	−0.0111470
$688$	−12.6564	−0.482520
$689$	−4.65587	−0.177375
$690$	−2.70589	−0.103011
$691$	25.4522	0.968247	0.484124	−	0.875000i	$-0.339139\pi$
$691$	25.4522	0.968247	0.484124	+	0.875000i	$0.339139\pi$
$692$	2.84477	0.108142
$693$	−16.0525	−0.609784
$694$	5.03597	0.191163
$695$	8.30923	0.315187
$696$	0.332979	0.0126216
$697$	1.41621	0.0536427
$698$	6.92267	0.262027
$699$	12.1524	0.459647
$700$	−8.60765	−0.325338
$701$	23.8630	0.901293	0.450647	−	0.892702i	$-0.351193\pi$
$701$	23.8630	0.901293	0.450647	+	0.892702i	$0.351193\pi$
$702$	−10.1502	−0.383096
$703$	8.07137	0.304418
$704$	2.53318	0.0954728
$705$	−2.07951	−0.0783188
$706$	−21.3368	−0.803022
$707$	−5.92953	−0.223003
$708$	0.367014	0.0137932
$709$	−4.16387	−0.156378	−0.0781888	−	0.996939i	$-0.524914\pi$
$709$	−4.16387	−0.156378	−0.0781888	+	0.996939i	$0.524914\pi$
$710$	5.94957	0.223284
$711$	−38.7379	−1.45278
$712$	15.3041	0.573546
$713$	17.2277	0.645183
$714$	−1.56068	−0.0584071
$715$	−8.64458	−0.323289
$716$	3.45578	0.129149
$717$	1.12572	0.0420407
$718$	−32.2705	−1.20432
$719$	−0.560009	−0.0208848	−0.0104424	−	0.999945i	$-0.503324\pi$
$719$	−0.560009	−0.0208848	−0.0104424	+	0.999945i	$0.503324\pi$
$720$	3.15724	0.117663
$721$	2.67310	0.0995515
$722$	−1.00000	−0.0372161
$723$	−13.8681	−0.515760
$724$	−12.8494	−0.477545
$725$	−1.77071	−0.0657625
$726$	−3.00774	−0.111628
$727$	−19.6820	−0.729966	−0.364983	−	0.931014i	$-0.618925\pi$
$727$	−19.6820	−0.729966	−0.364983	+	0.931014i	$0.618925\pi$
$728$	−6.84932	−0.253853
$729$	−6.44453	−0.238686
$730$	−10.5610	−0.390880
$731$	12.2031	0.451348
$732$	2.11499	0.0781724
$733$	−18.4815	−0.682629	−0.341314	−	0.939949i	$-0.610872\pi$
$733$	−18.4815	−0.682629	−0.341314	+	0.939949i	$0.610872\pi$
$734$	−31.8609	−1.17601
$735$	−0.739429	−0.0272742
$736$	−3.35525	−0.123676
$737$	10.6432	0.392047
$738$	−3.77381	−0.138916
$739$	−46.4157	−1.70743	−0.853715	−	0.520741i	$-0.825656\pi$
$739$	−46.4157	−1.70743	−0.853715	+	0.520741i	$0.825656\pi$
$740$	9.91838	0.364607
$741$	1.82253	0.0669525
$742$	4.13504	0.151802
$743$	−48.5036	−1.77942	−0.889712	−	0.456522i	$-0.849095\pi$
$743$	−48.5036	−1.77942	−0.889712	+	0.456522i	$0.849095\pi$
$744$	3.36972	0.123540
$745$	−24.9149	−0.912811
$746$	−3.93302	−0.143998
$747$	−37.4311	−1.36953
$748$	−2.44245	−0.0893050
$749$	13.3588	0.488121
$750$	6.84685	0.250011
$751$	52.9738	1.93304	0.966521	−	0.256588i	$-0.0825983\pi$
$751$	52.9738	1.93304	0.966521	+	0.256588i	$0.0825983\pi$
$752$	−2.57855	−0.0940301
$753$	5.09178	0.185555
$754$	−1.40900	−0.0513127
$755$	6.21691	0.226256
$756$	9.01477	0.327864
$757$	−2.75771	−0.100231	−0.0501153	−	0.998743i	$-0.515959\pi$
$757$	−2.75771	−0.100231	−0.0501153	+	0.998743i	$0.515959\pi$
$758$	16.4831	0.598695
$759$	−5.57805	−0.202470
$760$	−1.22883	−0.0445745
$761$	−42.9698	−1.55765	−0.778827	−	0.627239i	$-0.784185\pi$
$761$	−42.9698	−1.55765	−0.778827	+	0.627239i	$0.784185\pi$
$762$	−3.07156	−0.111271
$763$	−35.2509	−1.27617
$764$	25.9589	0.939159
$765$	−3.04416	−0.110062
$766$	5.90876	0.213492
$767$	−1.55302	−0.0560762
$768$	−0.656283	−0.0236816
$769$	−6.64548	−0.239642	−0.119821	−	0.992796i	$-0.538232\pi$
$769$	−6.64548	−0.239642	−0.119821	+	0.992796i	$0.538232\pi$
$770$	7.67755	0.276680
$771$	−0.751434	−0.0270622
$772$	−13.2961	−0.478537
$773$	−13.2313	−0.475897	−0.237949	−	0.971278i	$-0.576475\pi$
$773$	−13.2313	−0.475897	−0.237949	+	0.971278i	$0.576475\pi$
$774$	−32.5180	−1.16883
$775$	−17.9194	−0.643685
$776$	−2.84413	−0.102098
$777$	13.0648	0.468696
$778$	26.5021	0.950145
$779$	1.46881	0.0526257
$780$	2.23959	0.0801903
$781$	12.2647	0.438867
$782$	3.23508	0.115686
$783$	1.85446	0.0662730
$784$	−0.916878	−0.0327457
$785$	−5.43948	−0.194143
$786$	−7.57733	−0.270274
$787$	−52.1463	−1.85882	−0.929408	−	0.369054i	$-0.879682\pi$
$787$	−52.1463	−1.85882	−0.929408	+	0.369054i	$0.879682\pi$
$788$	2.67231	0.0951972
$789$	−16.6638	−0.593247
$790$	18.5274	0.659177
$791$	10.7663	0.382805
$792$	6.50848	0.231269
$793$	−8.94957	−0.317808
$794$	29.4443	1.04494
$795$	−1.35208	−0.0479532
$796$	−7.84768	−0.278154
$797$	−19.7145	−0.698324	−0.349162	−	0.937062i	$-0.613534\pi$
$797$	−19.7145	−0.698324	−0.349162	+	0.937062i	$0.613534\pi$
$798$	−1.61866	−0.0572998
$799$	2.48620	0.0879554
$800$	3.48997	0.123389
$801$	39.3208	1.38933
$802$	16.0740	0.567592
$803$	−21.7710	−0.768281
$804$	−2.75738	−0.0972454
$805$	−10.1691	−0.358413
$806$	−14.2590	−0.502250
$807$	−2.21418	−0.0779427
$808$	2.40413	0.0845769
$809$	−14.5695	−0.512237	−0.256119	−	0.966645i	$-0.582444\pi$
$809$	−14.5695	−0.512237	−0.256119	+	0.966645i	$0.582444\pi$
$810$	6.52406	0.229232
$811$	1.76128	0.0618471	0.0309235	−	0.999522i	$-0.490155\pi$
$811$	1.76128	0.0618471	0.0309235	+	0.999522i	$0.490155\pi$
$812$	1.25138	0.0439148
$813$	−17.1180	−0.600355
$814$	20.4462	0.716641
$815$	−18.9956	−0.665389
$816$	0.632778	0.0221517
$817$	12.6564	0.442791
$818$	15.5578	0.543965
$819$	−17.5979	−0.614921
$820$	1.80493	0.0630309
$821$	−36.4323	−1.27149	−0.635747	−	0.771897i	$-0.719308\pi$
$821$	−36.4323	−1.27149	−0.635747	+	0.771897i	$0.719308\pi$
$822$	−10.5097	−0.366569
$823$	36.2487	1.26355	0.631775	−	0.775151i	$-0.282326\pi$
$823$	36.2487	1.26355	0.631775	+	0.775151i	$0.282326\pi$
$824$	−1.08381	−0.0377562
$825$	5.80201	0.202000
$826$	1.37929	0.0479916
$827$	−10.9360	−0.380282	−0.190141	−	0.981757i	$-0.560894\pi$
$827$	−10.9360	−0.380282	−0.190141	+	0.981757i	$0.560894\pi$
$828$	−8.62062	−0.299587
$829$	−39.1854	−1.36097	−0.680483	−	0.732764i	$-0.738230\pi$
$829$	−39.1854	−1.36097	−0.680483	+	0.732764i	$0.738230\pi$
$830$	17.9025	0.621404
$831$	−6.42603	−0.222916
$832$	2.77706	0.0962771
$833$	0.884040	0.0306302
$834$	−4.43771	−0.153665
$835$	18.0408	0.624328
$836$	−2.53318	−0.0876119
$837$	18.7670	0.648682
$838$	−30.8745	−1.06654
$839$	−45.2169	−1.56106	−0.780530	−	0.625119i	$-0.785051\pi$
$839$	−45.2169	−1.56106	−0.780530	+	0.625119i	$0.785051\pi$
$840$	−1.98906	−0.0686291
$841$	−28.7426	−0.991123
$842$	−17.9081	−0.617153
$843$	10.5928	0.364835
$844$	−1.00000	−0.0344214
$845$	6.49803	0.223539
$846$	−6.62505	−0.227774
$847$	−11.3035	−0.388393
$848$	−1.67655	−0.0575729
$849$	12.5971	0.432332
$850$	−3.36497	−0.115418
$851$	−27.0815	−0.928341
$852$	−3.17749	−0.108859
$853$	14.0127	0.479786	0.239893	−	0.970799i	$-0.422888\pi$
$853$	14.0127	0.479786	0.239893	+	0.970799i	$0.422888\pi$
$854$	7.94842	0.271989
$855$	−3.15724	−0.107975
$856$	−5.41633	−0.185126
$857$	56.7653	1.93907	0.969533	−	0.244960i	$-0.0787748\pi$
$857$	56.7653	1.93907	0.969533	+	0.244960i	$0.0787748\pi$
$858$	4.61681	0.157615
$859$	−40.7536	−1.39049	−0.695247	−	0.718771i	$-0.744705\pi$
$859$	−40.7536	−1.39049	−0.695247	+	0.718771i	$0.744705\pi$
$860$	15.5526	0.530340
$861$	2.37750	0.0810251
$862$	−28.5173	−0.971304
$863$	10.2198	0.347885	0.173943	−	0.984756i	$-0.444349\pi$
$863$	10.2198	0.347885	0.173943	+	0.984756i	$0.444349\pi$
$864$	−3.65503	−0.124347
$865$	−3.49575	−0.118859
$866$	37.7724	1.28356
$867$	10.5467	0.358185
$868$	12.6639	0.429840
$869$	38.1934	1.29562
$870$	−0.409177	−0.0138724
$871$	11.6678	0.395349
$872$	14.2925	0.484004
$873$	−7.30739	−0.247318
$874$	3.35525	0.113493
$875$	25.7314	0.869878
$876$	5.64031	0.190568
$877$	−22.5041	−0.759911	−0.379955	−	0.925005i	$-0.624061\pi$
$877$	−22.5041	−0.759911	−0.379955	+	0.925005i	$0.624061\pi$
$878$	4.71110	0.158992
$879$	14.2097	0.479281
$880$	−3.11286	−0.104934
$881$	−44.2344	−1.49029	−0.745147	−	0.666900i	$-0.767621\pi$
$881$	−44.2344	−1.49029	−0.745147	+	0.666900i	$0.767621\pi$
$882$	−2.35573	−0.0793215
$883$	−20.1243	−0.677236	−0.338618	−	0.940924i	$-0.609959\pi$
$883$	−20.1243	−0.677236	−0.338618	+	0.940924i	$0.609959\pi$
$884$	−2.67759	−0.0900573
$885$	−0.451000	−0.0151602
$886$	−32.4557	−1.09037
$887$	11.4870	0.385697	0.192848	−	0.981229i	$-0.438227\pi$
$887$	11.4870	0.385697	0.192848	+	0.981229i	$0.438227\pi$
$888$	−5.29711	−0.177759
$889$	−11.5433	−0.387150
$890$	−18.8062	−0.630386
$891$	13.4490	0.450559
$892$	3.87038	0.129590
$893$	2.57855	0.0862879
$894$	13.3063	0.445029
$895$	−4.24659	−0.141948
$896$	−2.46640	−0.0823966
$897$	−6.11506	−0.204176
$898$	12.9548	0.432308
$899$	2.60513	0.0868859
$900$	8.96674	0.298891
$901$	1.61650	0.0538536
$902$	3.72077	0.123888
$903$	20.4863	0.681743
$904$	−4.36519	−0.145184
$905$	15.7898	0.524871
$906$	−3.32026	−0.110308
$907$	40.8797	1.35739	0.678695	−	0.734421i	$-0.262546\pi$
$907$	40.8797	1.35739	0.678695	+	0.734421i	$0.262546\pi$
$908$	16.7652	0.556374
$909$	6.17690	0.204875
$910$	8.41669	0.279010
$911$	−26.9274	−0.892143	−0.446071	−	0.894997i	$-0.647177\pi$
$911$	−26.9274	−0.892143	−0.446071	+	0.894997i	$0.647177\pi$
$912$	0.656283	0.0217317
$913$	36.9050	1.22138
$914$	36.6463	1.21215
$915$	−2.59898	−0.0859195
$916$	0.445190	0.0147095
$917$	−28.4766	−0.940381
$918$	3.52413	0.116314
$919$	21.1727	0.698424	0.349212	−	0.937044i	$-0.386449\pi$
$919$	21.1727	0.698424	0.349212	+	0.937044i	$0.386449\pi$
$920$	4.12305	0.135933
$921$	0.480346	0.0158279
$922$	−28.7701	−0.947492
$923$	13.4455	0.442564
$924$	−4.10035	−0.134892
$925$	28.1688	0.926185
$926$	34.5158	1.13426
$927$	−2.78462	−0.0914589
$928$	−0.507372	−0.0166553
$929$	36.8654	1.20952	0.604758	−	0.796410i	$-0.293270\pi$
$929$	36.8654	1.20952	0.604758	+	0.796410i	$0.293270\pi$
$930$	−4.14083	−0.135783
$931$	0.916878	0.0300495
$932$	−18.5171	−0.606547
$933$	14.3610	0.470156
$934$	−16.3066	−0.533569
$935$	3.00137	0.0981554
$936$	7.13507	0.233217
$937$	−25.4699	−0.832067	−0.416033	−	0.909349i	$-0.636580\pi$
$937$	−25.4699	−0.832067	−0.416033	+	0.909349i	$0.636580\pi$
$938$	−10.3626	−0.338351
$939$	12.6327	0.412254
$940$	3.16861	0.103349
$941$	−20.5582	−0.670179	−0.335089	−	0.942186i	$-0.608767\pi$
$941$	−20.5582	−0.670179	−0.335089	+	0.942186i	$0.608767\pi$
$942$	2.90506	0.0946519
$943$	−4.92824	−0.160485
$944$	−0.559232	−0.0182014
$945$	−11.0777	−0.360356
$946$	32.0609	1.04239
$947$	−48.2835	−1.56900	−0.784502	−	0.620127i	$-0.787081\pi$
$947$	−48.2835	−1.56900	−0.784502	+	0.620127i	$0.787081\pi$
$948$	−9.89494	−0.321373
$949$	−23.8669	−0.774752
$950$	−3.48997	−0.113229
$951$	13.7318	0.445284
$952$	2.37806	0.0770735
$953$	−35.6738	−1.15559	−0.577794	−	0.816183i	$-0.696086\pi$
$953$	−35.6738	−1.15559	−0.577794	+	0.816183i	$0.696086\pi$
$954$	−4.30755	−0.139462
$955$	−31.8991	−1.03223
$956$	−1.71529	−0.0554765
$957$	−0.843497	−0.0272664
$958$	5.46908	0.176698
$959$	−39.4970	−1.27542
$960$	0.806463	0.0260285
$961$	−4.63631	−0.149558
$962$	22.4146	0.722677
$963$	−13.9161	−0.448441
$964$	21.1313	0.680592
$965$	16.3387	0.525962
$966$	5.43099	0.174739
$967$	30.2767	0.973632	0.486816	−	0.873505i	$-0.338158\pi$
$967$	30.2767	0.973632	0.486816	+	0.873505i	$0.338158\pi$
$968$	4.58300	0.147303
$969$	−0.632778	−0.0203278
$970$	3.49496	0.112216
$971$	−9.19295	−0.295016	−0.147508	−	0.989061i	$-0.547125\pi$
$971$	−9.19295	−0.295016	−0.147508	+	0.989061i	$0.547125\pi$
$972$	−14.4494	−0.463465
$973$	−16.6775	−0.534656
$974$	−20.2075	−0.647490
$975$	6.36058	0.203702
$976$	−3.22268	−0.103156
$977$	−23.0252	−0.736642	−0.368321	−	0.929699i	$-0.620067\pi$
$977$	−23.0252	−0.736642	−0.368321	+	0.929699i	$0.620067\pi$
$978$	10.1450	0.324401
$979$	−38.7681	−1.23903
$980$	1.12669	0.0359908
$981$	36.7216	1.17243
$982$	28.7727	0.918175
$983$	−33.3707	−1.06436	−0.532179	−	0.846632i	$-0.678627\pi$
$983$	−33.3707	−1.06436	−0.532179	+	0.846632i	$0.678627\pi$
$984$	−0.963958	−0.0307298
$985$	−3.28383	−0.104632
$986$	0.489200	0.0155793
$987$	4.17379	0.132853
$988$	−2.77706	−0.0883499
$989$	−42.4654	−1.35032
$990$	−7.99785	−0.254188
$991$	−9.97660	−0.316917	−0.158459	−	0.987366i	$-0.550652\pi$
$991$	−9.97660	−0.316917	−0.158459	+	0.987366i	$0.550652\pi$
$992$	−5.13456	−0.163022
$993$	17.3066	0.549208
$994$	−11.9414	−0.378759
$995$	9.64350	0.305720
$996$	−9.56117	−0.302957
$997$	−16.3622	−0.518197	−0.259099	−	0.965851i	$-0.583425\pi$
$997$	−16.3622	−0.518197	−0.259099	+	0.965851i	$0.583425\pi$
$998$	30.5754	0.967848
$999$	−29.5011	−0.933374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.656283 q^{3} +1.00000 q^{4} -1.22883 q^{5} +0.656283 q^{6} +2.46640 q^{7} -1.00000 q^{8} -2.56929 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.656283 q^{3} +1.00000 q^{4} -1.22883 q^{5} +0.656283 q^{6} +2.46640 q^{7} -1.00000 q^{8} -2.56929 q^{9} +1.22883 q^{10} +2.53318 q^{11} -0.656283 q^{12} +2.77706 q^{13} -2.46640 q^{14} +0.806463 q^{15} +1.00000 q^{16} -0.964185 q^{17} +2.56929 q^{18} -1.00000 q^{19} -1.22883 q^{20} -1.61866 q^{21} -2.53318 q^{22} +3.35525 q^{23} +0.656283 q^{24} -3.48997 q^{25} -2.77706 q^{26} +3.65503 q^{27} +2.46640 q^{28} +0.507372 q^{29} -0.806463 q^{30} +5.13456 q^{31} -1.00000 q^{32} -1.66248 q^{33} +0.964185 q^{34} -3.03080 q^{35} -2.56929 q^{36} -8.07137 q^{37} +1.00000 q^{38} -1.82253 q^{39} +1.22883 q^{40} -1.46881 q^{41} +1.61866 q^{42} -12.6564 q^{43} +2.53318 q^{44} +3.15724 q^{45} -3.35525 q^{46} -2.57855 q^{47} -0.656283 q^{48} -0.916878 q^{49} +3.48997 q^{50} +0.632778 q^{51} +2.77706 q^{52} -1.67655 q^{53} -3.65503 q^{54} -3.11286 q^{55} -2.46640 q^{56} +0.656283 q^{57} -0.507372 q^{58} -0.559232 q^{59} +0.806463 q^{60} -3.22268 q^{61} -5.13456 q^{62} -6.33690 q^{63} +1.00000 q^{64} -3.41254 q^{65} +1.66248 q^{66} +4.20151 q^{67} -0.964185 q^{68} -2.20199 q^{69} +3.03080 q^{70} +4.84164 q^{71} +2.56929 q^{72} -8.59432 q^{73} +8.07137 q^{74} +2.29041 q^{75} -1.00000 q^{76} +6.24783 q^{77} +1.82253 q^{78} +15.0772 q^{79} -1.22883 q^{80} +5.30914 q^{81} +1.46881 q^{82} +14.5687 q^{83} -1.61866 q^{84} +1.18482 q^{85} +12.6564 q^{86} -0.332979 q^{87} -2.53318 q^{88} -15.3041 q^{89} -3.15724 q^{90} +6.84932 q^{91} +3.35525 q^{92} -3.36972 q^{93} +2.57855 q^{94} +1.22883 q^{95} +0.656283 q^{96} +2.84413 q^{97} +0.916878 q^{98} -6.50848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 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