LMFDB - Embedded newform 8018.2.a.g.1.4

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			1.4
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.69123 q^{3} +1.00000 q^{4} +2.65985 q^{5} +2.69123 q^{6} -4.28568 q^{7} -1.00000 q^{8} +4.24273 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.69123 q^{3} +1.00000 q^{4} +2.65985 q^{5} +2.69123 q^{6} -4.28568 q^{7} -1.00000 q^{8} +4.24273 q^{9} -2.65985 q^{10} -4.69404 q^{11} -2.69123 q^{12} +5.91866 q^{13} +4.28568 q^{14} -7.15826 q^{15} +1.00000 q^{16} +5.32428 q^{17} -4.24273 q^{18} +1.00000 q^{19} +2.65985 q^{20} +11.5338 q^{21} +4.69404 q^{22} -5.07503 q^{23} +2.69123 q^{24} +2.07479 q^{25} -5.91866 q^{26} -3.34446 q^{27} -4.28568 q^{28} +2.52432 q^{29} +7.15826 q^{30} -1.65916 q^{31} -1.00000 q^{32} +12.6328 q^{33} -5.32428 q^{34} -11.3993 q^{35} +4.24273 q^{36} -10.5174 q^{37} -1.00000 q^{38} -15.9285 q^{39} -2.65985 q^{40} -9.64910 q^{41} -11.5338 q^{42} +5.44346 q^{43} -4.69404 q^{44} +11.2850 q^{45} +5.07503 q^{46} +6.03502 q^{47} -2.69123 q^{48} +11.3671 q^{49} -2.07479 q^{50} -14.3289 q^{51} +5.91866 q^{52} -7.41039 q^{53} +3.34446 q^{54} -12.4854 q^{55} +4.28568 q^{56} -2.69123 q^{57} -2.52432 q^{58} +4.70675 q^{59} -7.15826 q^{60} +1.25167 q^{61} +1.65916 q^{62} -18.1830 q^{63} +1.00000 q^{64} +15.7427 q^{65} -12.6328 q^{66} +0.425266 q^{67} +5.32428 q^{68} +13.6581 q^{69} +11.3993 q^{70} +8.40828 q^{71} -4.24273 q^{72} -0.433348 q^{73} +10.5174 q^{74} -5.58373 q^{75} +1.00000 q^{76} +20.1172 q^{77} +15.9285 q^{78} -1.05218 q^{79} +2.65985 q^{80} -3.72746 q^{81} +9.64910 q^{82} +2.28065 q^{83} +11.5338 q^{84} +14.1618 q^{85} -5.44346 q^{86} -6.79354 q^{87} +4.69404 q^{88} +17.5173 q^{89} -11.2850 q^{90} -25.3655 q^{91} -5.07503 q^{92} +4.46518 q^{93} -6.03502 q^{94} +2.65985 q^{95} +2.69123 q^{96} -8.40302 q^{97} -11.3671 q^{98} -19.9155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.69123	−1.55378	−0.776892	−	0.629634i	$-0.783205\pi$
$3$	−2.69123	−1.55378	−0.776892	+	0.629634i	$0.783205\pi$
$4$	1.00000	0.500000
$5$	2.65985	1.18952	0.594760	−	0.803903i	$-0.297247\pi$
$5$	2.65985	1.18952	0.594760	+	0.803903i	$0.297247\pi$
$6$	2.69123	1.09869
$7$	−4.28568	−1.61984	−0.809918	−	0.586543i	$-0.800488\pi$
$7$	−4.28568	−1.61984	−0.809918	+	0.586543i	$0.800488\pi$
$8$	−1.00000	−0.353553
$9$	4.24273	1.41424
$10$	−2.65985	−0.841117
$11$	−4.69404	−1.41531	−0.707654	−	0.706559i	$-0.750246\pi$
$11$	−4.69404	−1.41531	−0.707654	+	0.706559i	$0.750246\pi$
$12$	−2.69123	−0.776892
$13$	5.91866	1.64154	0.820770	−	0.571258i	$-0.193545\pi$
$13$	5.91866	1.64154	0.820770	+	0.571258i	$0.193545\pi$
$14$	4.28568	1.14540
$15$	−7.15826	−1.84826
$16$	1.00000	0.250000
$17$	5.32428	1.29133	0.645663	−	0.763622i	$-0.276581\pi$
$17$	5.32428	1.29133	0.645663	+	0.763622i	$0.276581\pi$
$18$	−4.24273	−1.00002
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.65985	0.594760
$21$	11.5338	2.51687
$22$	4.69404	1.00077
$23$	−5.07503	−1.05822	−0.529108	−	0.848554i	$-0.677473\pi$
$23$	−5.07503	−1.05822	−0.529108	+	0.848554i	$0.677473\pi$
$24$	2.69123	0.549345
$25$	2.07479	0.414957
$26$	−5.91866	−1.16074
$27$	−3.34446	−0.643642
$28$	−4.28568	−0.809918
$29$	2.52432	0.468755	0.234378	−	0.972146i	$-0.424695\pi$
$29$	2.52432	0.468755	0.234378	+	0.972146i	$0.424695\pi$
$30$	7.15826	1.30691
$31$	−1.65916	−0.297994	−0.148997	−	0.988838i	$-0.547604\pi$
$31$	−1.65916	−0.297994	−0.148997	+	0.988838i	$0.547604\pi$
$32$	−1.00000	−0.176777
$33$	12.6328	2.19908
$34$	−5.32428	−0.913106
$35$	−11.3993	−1.92683
$36$	4.24273	0.707121
$37$	−10.5174	−1.72904	−0.864522	−	0.502595i	$-0.832379\pi$
$37$	−10.5174	−1.72904	−0.864522	+	0.502595i	$0.832379\pi$
$38$	−1.00000	−0.162221
$39$	−15.9285	−2.55060
$40$	−2.65985	−0.420559
$41$	−9.64910	−1.50694	−0.753468	−	0.657484i	$-0.771621\pi$
$41$	−9.64910	−1.50694	−0.753468	+	0.657484i	$0.771621\pi$
$42$	−11.5338	−1.77970
$43$	5.44346	0.830120	0.415060	−	0.909794i	$-0.363761\pi$
$43$	5.44346	0.830120	0.415060	+	0.909794i	$0.363761\pi$
$44$	−4.69404	−0.707654
$45$	11.2850	1.68227
$46$	5.07503	0.748272
$47$	6.03502	0.880298	0.440149	−	0.897925i	$-0.354926\pi$
$47$	6.03502	0.880298	0.440149	+	0.897925i	$0.354926\pi$
$48$	−2.69123	−0.388446
$49$	11.3671	1.62387
$50$	−2.07479	−0.293419
$51$	−14.3289	−2.00644
$52$	5.91866	0.820770
$53$	−7.41039	−1.01790	−0.508948	−	0.860797i	$-0.669965\pi$
$53$	−7.41039	−1.01790	−0.508948	+	0.860797i	$0.669965\pi$
$54$	3.34446	0.455124
$55$	−12.4854	−1.68354
$56$	4.28568	0.572698
$57$	−2.69123	−0.356462
$58$	−2.52432	−0.331460
$59$	4.70675	0.612766	0.306383	−	0.951908i	$-0.400881\pi$
$59$	4.70675	0.612766	0.306383	+	0.951908i	$0.400881\pi$
$60$	−7.15826	−0.924128
$61$	1.25167	0.160259	0.0801297	−	0.996784i	$-0.474467\pi$
$61$	1.25167	0.160259	0.0801297	+	0.996784i	$0.474467\pi$
$62$	1.65916	0.210713
$63$	−18.1830	−2.29084
$64$	1.00000	0.125000
$65$	15.7427	1.95264
$66$	−12.6328	−1.55499
$67$	0.425266	0.0519545	0.0259773	−	0.999663i	$-0.491730\pi$
$67$	0.425266	0.0519545	0.0259773	+	0.999663i	$0.491730\pi$
$68$	5.32428	0.645663
$69$	13.6581	1.64424
$70$	11.3993	1.36247
$71$	8.40828	0.997880	0.498940	−	0.866637i	$-0.333723\pi$
$71$	8.40828	0.997880	0.498940	+	0.866637i	$0.333723\pi$
$72$	−4.24273	−0.500010
$73$	−0.433348	−0.0507196	−0.0253598	−	0.999678i	$-0.508073\pi$
$73$	−0.433348	−0.0507196	−0.0253598	+	0.999678i	$0.508073\pi$
$74$	10.5174	1.22262
$75$	−5.58373	−0.644753
$76$	1.00000	0.114708
$77$	20.1172	2.29257
$78$	15.9285	1.80354
$79$	−1.05218	−0.118379	−0.0591897	−	0.998247i	$-0.518852\pi$
$79$	−1.05218	−0.118379	−0.0591897	+	0.998247i	$0.518852\pi$
$80$	2.65985	0.297380
$81$	−3.72746	−0.414162
$82$	9.64910	1.06556
$83$	2.28065	0.250334	0.125167	−	0.992136i	$-0.460053\pi$
$83$	2.28065	0.250334	0.125167	+	0.992136i	$0.460053\pi$
$84$	11.5338	1.25844
$85$	14.1618	1.53606
$86$	−5.44346	−0.586984
$87$	−6.79354	−0.728344
$88$	4.69404	0.500387
$89$	17.5173	1.85683	0.928416	−	0.371541i	$-0.121171\pi$
$89$	17.5173	1.85683	0.928416	+	0.371541i	$0.121171\pi$
$90$	−11.2850	−1.18954
$91$	−25.3655	−2.65903
$92$	−5.07503	−0.529108
$93$	4.46518	0.463017
$94$	−6.03502	−0.622465
$95$	2.65985	0.272895
$96$	2.69123	0.274673
$97$	−8.40302	−0.853197	−0.426599	−	0.904441i	$-0.640288\pi$
$97$	−8.40302	−0.853197	−0.426599	+	0.904441i	$0.640288\pi$
$98$	−11.3671	−1.14825
$99$	−19.9155	−2.00159
$100$	2.07479	0.207479
$101$	−8.49454	−0.845238	−0.422619	−	0.906307i	$-0.638889\pi$
$101$	−8.49454	−0.845238	−0.422619	+	0.906307i	$0.638889\pi$
$102$	14.3289	1.41877
$103$	−0.913885	−0.0900477	−0.0450239	−	0.998986i	$-0.514336\pi$
$103$	−0.913885	−0.0900477	−0.0450239	+	0.998986i	$0.514336\pi$
$104$	−5.91866	−0.580372
$105$	30.6780	2.99387
$106$	7.41039	0.719761
$107$	8.02074	0.775395	0.387697	−	0.921787i	$-0.373271\pi$
$107$	8.02074	0.775395	0.387697	+	0.921787i	$0.373271\pi$
$108$	−3.34446	−0.321821
$109$	6.97045	0.667648	0.333824	−	0.942635i	$-0.391661\pi$
$109$	6.97045	0.667648	0.333824	+	0.942635i	$0.391661\pi$
$110$	12.4854	1.19044
$111$	28.3047	2.68656
$112$	−4.28568	−0.404959
$113$	2.75521	0.259189	0.129594	−	0.991567i	$-0.458633\pi$
$113$	2.75521	0.259189	0.129594	+	0.991567i	$0.458633\pi$
$114$	2.69123	0.252057
$115$	−13.4988	−1.25877
$116$	2.52432	0.234378
$117$	25.1112	2.32154
$118$	−4.70675	−0.433291
$119$	−22.8182	−2.09174
$120$	7.15826	0.653457
$121$	11.0341	1.00310
$122$	−1.25167	−0.113321
$123$	25.9680	2.34145
$124$	−1.65916	−0.148997
$125$	−7.78062	−0.695920
$126$	18.1830	1.61987
$127$	−10.2657	−0.910933	−0.455467	−	0.890253i	$-0.650528\pi$
$127$	−10.2657	−0.910933	−0.455467	+	0.890253i	$0.650528\pi$
$128$	−1.00000	−0.0883883
$129$	−14.6496	−1.28983
$130$	−15.7427	−1.38073
$131$	−2.69993	−0.235894	−0.117947	−	0.993020i	$-0.537631\pi$
$131$	−2.69993	−0.235894	−0.117947	+	0.993020i	$0.537631\pi$
$132$	12.6328	1.09954
$133$	−4.28568	−0.371616
$134$	−0.425266	−0.0367374
$135$	−8.89576	−0.765625
$136$	−5.32428	−0.456553
$137$	−4.24723	−0.362866	−0.181433	−	0.983403i	$-0.558073\pi$
$137$	−4.24723	−0.362866	−0.181433	+	0.983403i	$0.558073\pi$
$138$	−13.6581	−1.16265
$139$	19.0726	1.61772	0.808860	−	0.588001i	$-0.200085\pi$
$139$	19.0726	1.61772	0.808860	+	0.588001i	$0.200085\pi$
$140$	−11.3993	−0.963413
$141$	−16.2416	−1.36779
$142$	−8.40828	−0.705607
$143$	−27.7824	−2.32328
$144$	4.24273	0.353560
$145$	6.71431	0.557593
$146$	0.433348	0.0358642
$147$	−30.5914	−2.52314
$148$	−10.5174	−0.864522
$149$	−17.4348	−1.42832	−0.714158	−	0.699984i	$-0.753190\pi$
$149$	−17.4348	−1.42832	−0.714158	+	0.699984i	$0.753190\pi$
$150$	5.58373	0.455909
$151$	9.90486	0.806046	0.403023	−	0.915190i	$-0.367959\pi$
$151$	9.90486	0.806046	0.403023	+	0.915190i	$0.367959\pi$
$152$	−1.00000	−0.0811107
$153$	22.5894	1.82625
$154$	−20.1172	−1.62109
$155$	−4.41311	−0.354469
$156$	−15.9285	−1.27530
$157$	−4.74040	−0.378325	−0.189162	−	0.981946i	$-0.560577\pi$
$157$	−4.74040	−0.378325	−0.189162	+	0.981946i	$0.560577\pi$
$158$	1.05218	0.0837068
$159$	19.9431	1.58159
$160$	−2.65985	−0.210279
$161$	21.7500	1.71414
$162$	3.72746	0.292857
$163$	−5.43262	−0.425516	−0.212758	−	0.977105i	$-0.568245\pi$
$163$	−5.43262	−0.425516	−0.212758	+	0.977105i	$0.568245\pi$
$164$	−9.64910	−0.753468
$165$	33.6012	2.61585
$166$	−2.28065	−0.177013
$167$	7.00611	0.542149	0.271075	−	0.962558i	$-0.412621\pi$
$167$	7.00611	0.542149	0.271075	+	0.962558i	$0.412621\pi$
$168$	−11.5338	−0.889849
$169$	22.0305	1.69465
$170$	−14.1618	−1.08616
$171$	4.24273	0.324449
$172$	5.44346	0.415060
$173$	−6.74912	−0.513126	−0.256563	−	0.966528i	$-0.582590\pi$
$173$	−6.74912	−0.513126	−0.256563	+	0.966528i	$0.582590\pi$
$174$	6.79354	0.515017
$175$	−8.89187	−0.672162
$176$	−4.69404	−0.353827
$177$	−12.6669	−0.952106
$178$	−17.5173	−1.31298
$179$	12.1394	0.907341	0.453671	−	0.891169i	$-0.350114\pi$
$179$	12.1394	0.907341	0.453671	+	0.891169i	$0.350114\pi$
$180$	11.2850	0.841134
$181$	−20.4562	−1.52050	−0.760250	−	0.649630i	$-0.774924\pi$
$181$	−20.4562	−1.52050	−0.760250	+	0.649630i	$0.774924\pi$
$182$	25.3655	1.88022
$183$	−3.36852	−0.249008
$184$	5.07503	0.374136
$185$	−27.9746	−2.05673
$186$	−4.46518	−0.327403
$187$	−24.9924	−1.82762
$188$	6.03502	0.440149
$189$	14.3333	1.04259
$190$	−2.65985	−0.192966
$191$	−2.62022	−0.189592	−0.0947962	−	0.995497i	$-0.530220\pi$
$191$	−2.62022	−0.189592	−0.0947962	+	0.995497i	$0.530220\pi$
$192$	−2.69123	−0.194223
$193$	−14.4574	−1.04067	−0.520334	−	0.853963i	$-0.674193\pi$
$193$	−14.4574	−1.04067	−0.520334	+	0.853963i	$0.674193\pi$
$194$	8.40302	0.603302
$195$	−42.3673	−3.03399
$196$	11.3671	0.811934
$197$	26.0394	1.85523	0.927616	−	0.373535i	$-0.121855\pi$
$197$	26.0394	1.85523	0.927616	+	0.373535i	$0.121855\pi$
$198$	19.9155	1.41534
$199$	14.4405	1.02366	0.511831	−	0.859086i	$-0.328967\pi$
$199$	14.4405	1.02366	0.511831	+	0.859086i	$0.328967\pi$
$200$	−2.07479	−0.146709
$201$	−1.14449	−0.0807260
$202$	8.49454	0.597674
$203$	−10.8184	−0.759306
$204$	−14.3289	−1.00322
$205$	−25.6651	−1.79253
$206$	0.913885	0.0636734
$207$	−21.5319	−1.49657
$208$	5.91866	0.410385
$209$	−4.69404	−0.324694
$210$	−30.6780	−2.11699
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−7.41039	−0.508948
$213$	−22.6286	−1.55049
$214$	−8.02074	−0.548287
$215$	14.4788	0.987445
$216$	3.34446	0.227562
$217$	7.11062	0.482701
$218$	−6.97045	−0.472098
$219$	1.16624	0.0788072
$220$	−12.4854	−0.841768
$221$	31.5126	2.11976
$222$	−28.3047	−1.89968
$223$	14.3195	0.958904	0.479452	−	0.877568i	$-0.340835\pi$
$223$	14.3195	0.958904	0.479452	+	0.877568i	$0.340835\pi$
$224$	4.28568	0.286349
$225$	8.80274	0.586850
$226$	−2.75521	−0.183274
$227$	14.4984	0.962293	0.481146	−	0.876640i	$-0.340221\pi$
$227$	14.4984	0.962293	0.481146	+	0.876640i	$0.340221\pi$
$228$	−2.69123	−0.178231
$229$	18.0059	1.18986	0.594931	−	0.803777i	$-0.297179\pi$
$229$	18.0059	1.18986	0.594931	+	0.803777i	$0.297179\pi$
$230$	13.4988	0.890084
$231$	−54.1400	−3.56215
$232$	−2.52432	−0.165730
$233$	−10.7754	−0.705919	−0.352960	−	0.935639i	$-0.614825\pi$
$233$	−10.7754	−0.705919	−0.352960	+	0.935639i	$0.614825\pi$
$234$	−25.1112	−1.64157
$235$	16.0522	1.04713
$236$	4.70675	0.306383
$237$	2.83166	0.183936
$238$	22.8182	1.47908
$239$	9.56350	0.618612	0.309306	−	0.950963i	$-0.399903\pi$
$239$	9.56350	0.618612	0.309306	+	0.950963i	$0.399903\pi$
$240$	−7.15826	−0.462064
$241$	0.0232905	0.00150027	0.000750137	−	1.00000i	$-0.499761\pi$
$241$	0.0232905	0.00150027	0.000750137		1.00000i	$0.499761\pi$
$242$	−11.0341	−0.709296
$243$	20.0648	1.28716
$244$	1.25167	0.0801297
$245$	30.2347	1.93162
$246$	−25.9680	−1.65566
$247$	5.91866	0.376595
$248$	1.65916	0.105357
$249$	−6.13776	−0.388964
$250$	7.78062	0.492090
$251$	3.75737	0.237163	0.118581	−	0.992944i	$-0.462165\pi$
$251$	3.75737	0.237163	0.118581	+	0.992944i	$0.462165\pi$
$252$	−18.1830	−1.14542
$253$	23.8224	1.49770
$254$	10.2657	0.644127
$255$	−38.1126	−2.38670
$256$	1.00000	0.0625000
$257$	−5.35067	−0.333765	−0.166883	−	0.985977i	$-0.553370\pi$
$257$	−5.35067	−0.333765	−0.166883	+	0.985977i	$0.553370\pi$
$258$	14.6496	0.912045
$259$	45.0741	2.80077
$260$	15.7427	0.976322
$261$	10.7100	0.662933
$262$	2.69993	0.166802
$263$	−3.62669	−0.223631	−0.111816	−	0.993729i	$-0.535667\pi$
$263$	−3.62669	−0.223631	−0.111816	+	0.993729i	$0.535667\pi$
$264$	−12.6328	−0.777493
$265$	−19.7105	−1.21081
$266$	4.28568	0.262772
$267$	−47.1432	−2.88512
$268$	0.425266	0.0259773
$269$	25.4720	1.55305	0.776526	−	0.630085i	$-0.216980\pi$
$269$	25.4720	1.55305	0.776526	+	0.630085i	$0.216980\pi$
$270$	8.89576	0.541378
$271$	−20.6944	−1.25709	−0.628547	−	0.777772i	$-0.716350\pi$
$271$	−20.6944	−1.25709	−0.628547	+	0.777772i	$0.716350\pi$
$272$	5.32428	0.322832
$273$	68.2644	4.13155
$274$	4.24723	0.256585
$275$	−9.73913	−0.587292
$276$	13.6581	0.822119
$277$	−9.08278	−0.545731	−0.272866	−	0.962052i	$-0.587971\pi$
$277$	−9.08278	−0.545731	−0.272866	+	0.962052i	$0.587971\pi$
$278$	−19.0726	−1.14390
$279$	−7.03935	−0.421435
$280$	11.3993	0.681236
$281$	14.8708	0.887118	0.443559	−	0.896245i	$-0.353716\pi$
$281$	14.8708	0.887118	0.443559	+	0.896245i	$0.353716\pi$
$282$	16.2416	0.967175
$283$	−32.1089	−1.90868	−0.954338	−	0.298730i	$-0.903437\pi$
$283$	−32.1089	−1.90868	−0.954338	+	0.298730i	$0.903437\pi$
$284$	8.40828	0.498940
$285$	−7.15826	−0.424019
$286$	27.7824	1.64281
$287$	41.3530	2.44099
$288$	−4.24273	−0.250005
$289$	11.3479	0.667524
$290$	−6.71431	−0.394278
$291$	22.6145	1.32568
$292$	−0.433348	−0.0253598
$293$	−30.0455	−1.75528	−0.877638	−	0.479324i	$-0.840882\pi$
$293$	−30.0455	−1.75528	−0.877638	+	0.479324i	$0.840882\pi$
$294$	30.5914	1.78413
$295$	12.5192	0.728897
$296$	10.5174	0.611310
$297$	15.6991	0.910951
$298$	17.4348	1.00997
$299$	−30.0373	−1.73710
$300$	−5.58373	−0.322377
$301$	−23.3290	−1.34466
$302$	−9.90486	−0.569961
$303$	22.8608	1.31332
$304$	1.00000	0.0573539
$305$	3.32924	0.190632
$306$	−22.5894	−1.29135
$307$	15.1694	0.865764	0.432882	−	0.901451i	$-0.357497\pi$
$307$	15.1694	0.865764	0.432882	+	0.901451i	$0.357497\pi$
$308$	20.1172	1.14628
$309$	2.45947	0.139915
$310$	4.41311	0.250648
$311$	−31.2907	−1.77433	−0.887165	−	0.461452i	$-0.847329\pi$
$311$	−31.2907	−1.77433	−0.887165	+	0.461452i	$0.847329\pi$
$312$	15.9285	0.901772
$313$	12.4249	0.702299	0.351149	−	0.936319i	$-0.385791\pi$
$313$	12.4249	0.702299	0.351149	+	0.936319i	$0.385791\pi$
$314$	4.74040	0.267516
$315$	−48.3639	−2.72500
$316$	−1.05218	−0.0591897
$317$	−8.71203	−0.489316	−0.244658	−	0.969609i	$-0.578676\pi$
$317$	−8.71203	−0.489316	−0.244658	+	0.969609i	$0.578676\pi$
$318$	−19.9431	−1.11835
$319$	−11.8493	−0.663433
$320$	2.65985	0.148690
$321$	−21.5857	−1.20479
$322$	−21.7500	−1.21208
$323$	5.32428	0.296251
$324$	−3.72746	−0.207081
$325$	12.2799	0.681169
$326$	5.43262	0.300885
$327$	−18.7591	−1.03738
$328$	9.64910	0.532782
$329$	−25.8642	−1.42594
$330$	−33.6012	−1.84969
$331$	30.8184	1.69393	0.846965	−	0.531648i	$-0.178427\pi$
$331$	30.8184	1.69393	0.846965	+	0.531648i	$0.178427\pi$
$332$	2.28065	0.125167
$333$	−44.6223	−2.44529
$334$	−7.00611	−0.383357
$335$	1.13114	0.0618009
$336$	11.5338	0.629218
$337$	25.6204	1.39563	0.697816	−	0.716277i	$-0.254155\pi$
$337$	25.6204	1.39563	0.697816	+	0.716277i	$0.254155\pi$
$338$	−22.0305	−1.19830
$339$	−7.41491	−0.402723
$340$	14.1618	0.768029
$341$	7.78816	0.421752
$342$	−4.24273	−0.229420
$343$	−18.7159	−1.01056
$344$	−5.44346	−0.293492
$345$	36.3284	1.95585
$346$	6.74912	0.362835
$347$	−30.5941	−1.64238	−0.821188	−	0.570657i	$-0.806689\pi$
$347$	−30.5941	−1.64238	−0.821188	+	0.570657i	$0.806689\pi$
$348$	−6.79354	−0.364172
$349$	−14.1956	−0.759873	−0.379937	−	0.925013i	$-0.624054\pi$
$349$	−14.1956	−0.759873	−0.379937	+	0.925013i	$0.624054\pi$
$350$	8.89187	0.475291
$351$	−19.7947	−1.05656
$352$	4.69404	0.250193
$353$	33.8736	1.80291	0.901455	−	0.432872i	$-0.142500\pi$
$353$	33.8736	1.80291	0.901455	+	0.432872i	$0.142500\pi$
$354$	12.6669	0.673240
$355$	22.3647	1.18700
$356$	17.5173	0.928416
$357$	61.4089	3.25011
$358$	−12.1394	−0.641587
$359$	0.857154	0.0452388	0.0226194	−	0.999744i	$-0.492799\pi$
$359$	0.857154	0.0452388	0.0226194	+	0.999744i	$0.492799\pi$
$360$	−11.2850	−0.594772
$361$	1.00000	0.0526316
$362$	20.4562	1.07516
$363$	−29.6952	−1.55859
$364$	−25.3655	−1.32951
$365$	−1.15264	−0.0603319
$366$	3.36852	0.176076
$367$	−22.6268	−1.18111	−0.590555	−	0.806998i	$-0.701091\pi$
$367$	−22.6268	−1.18111	−0.590555	+	0.806998i	$0.701091\pi$
$368$	−5.07503	−0.264554
$369$	−40.9385	−2.13117
$370$	27.9746	1.45433
$371$	31.7586	1.64882
$372$	4.46518	0.231509
$373$	−16.0341	−0.830214	−0.415107	−	0.909773i	$-0.636256\pi$
$373$	−16.0341	−0.830214	−0.415107	+	0.909773i	$0.636256\pi$
$374$	24.9924	1.29233
$375$	20.9395	1.08131
$376$	−6.03502	−0.311232
$377$	14.9406	0.769480
$378$	−14.3333	−0.737225
$379$	−29.9080	−1.53627	−0.768135	−	0.640287i	$-0.778815\pi$
$379$	−29.9080	−1.53627	−0.768135	+	0.640287i	$0.778815\pi$
$380$	2.65985	0.136447
$381$	27.6274	1.41539
$382$	2.62022	0.134062
$383$	−31.8944	−1.62973	−0.814864	−	0.579652i	$-0.803188\pi$
$383$	−31.8944	−1.62973	−0.814864	+	0.579652i	$0.803188\pi$
$384$	2.69123	0.137336
$385$	53.5086	2.72705
$386$	14.4574	0.735864
$387$	23.0951	1.17399
$388$	−8.40302	−0.426599
$389$	−24.2829	−1.23119	−0.615595	−	0.788062i	$-0.711084\pi$
$389$	−24.2829	−1.23119	−0.615595	+	0.788062i	$0.711084\pi$
$390$	42.3673	2.14535
$391$	−27.0208	−1.36650
$392$	−11.3671	−0.574124
$393$	7.26613	0.366528
$394$	−26.0394	−1.31185
$395$	−2.79863	−0.140815
$396$	−19.9155	−1.00079
$397$	−6.74975	−0.338760	−0.169380	−	0.985551i	$-0.554177\pi$
$397$	−6.74975	−0.338760	−0.169380	+	0.985551i	$0.554177\pi$
$398$	−14.4405	−0.723839
$399$	11.5338	0.577410
$400$	2.07479	0.103739
$401$	7.78480	0.388754	0.194377	−	0.980927i	$-0.437731\pi$
$401$	7.78480	0.388754	0.194377	+	0.980927i	$0.437731\pi$
$402$	1.14449	0.0570819
$403$	−9.81999	−0.489168
$404$	−8.49454	−0.422619
$405$	−9.91447	−0.492654
$406$	10.8184	0.536911
$407$	49.3690	2.44713
$408$	14.3289	0.709384
$409$	1.62851	0.0805245	0.0402622	−	0.999189i	$-0.487181\pi$
$409$	1.62851	0.0805245	0.0402622	+	0.999189i	$0.487181\pi$
$410$	25.6651	1.26751
$411$	11.4303	0.563814
$412$	−0.913885	−0.0450239
$413$	−20.1716	−0.992581
$414$	21.5319	1.05824
$415$	6.06618	0.297777
$416$	−5.91866	−0.290186
$417$	−51.3289	−2.51359
$418$	4.69404	0.229593
$419$	−2.96532	−0.144865	−0.0724327	−	0.997373i	$-0.523076\pi$
$419$	−2.96532	−0.144865	−0.0724327	+	0.997373i	$0.523076\pi$
$420$	30.6780	1.49694
$421$	25.6859	1.25186	0.625928	−	0.779881i	$-0.284720\pi$
$421$	25.6859	1.25186	0.625928	+	0.779881i	$0.284720\pi$
$422$	−1.00000	−0.0486792
$423$	25.6049	1.24495
$424$	7.41039	0.359880
$425$	11.0467	0.535845
$426$	22.6286	1.09636
$427$	−5.36424	−0.259594
$428$	8.02074	0.387697
$429$	74.7690	3.60988
$430$	−14.4788	−0.698229
$431$	−17.1749	−0.827287	−0.413644	−	0.910439i	$-0.635744\pi$
$431$	−17.1749	−0.827287	−0.413644	+	0.910439i	$0.635744\pi$
$432$	−3.34446	−0.160910
$433$	10.6151	0.510130	0.255065	−	0.966924i	$-0.417903\pi$
$433$	10.6151	0.510130	0.255065	+	0.966924i	$0.417903\pi$
$434$	−7.11062	−0.341321
$435$	−18.0698	−0.866379
$436$	6.97045	0.333824
$437$	−5.07503	−0.242771
$438$	−1.16624	−0.0557251
$439$	−8.10201	−0.386688	−0.193344	−	0.981131i	$-0.561933\pi$
$439$	−8.10201	−0.386688	−0.193344	+	0.981131i	$0.561933\pi$
$440$	12.4854	0.595220
$441$	48.2274	2.29654
$442$	−31.5126	−1.49890
$443$	−9.62776	−0.457429	−0.228714	−	0.973494i	$-0.573452\pi$
$443$	−9.62776	−0.457429	−0.228714	+	0.973494i	$0.573452\pi$
$444$	28.3047	1.34328
$445$	46.5934	2.20874
$446$	−14.3195	−0.678048
$447$	46.9211	2.21929
$448$	−4.28568	−0.202479
$449$	24.8103	1.17087	0.585435	−	0.810719i	$-0.300924\pi$
$449$	24.8103	1.17087	0.585435	+	0.810719i	$0.300924\pi$
$450$	−8.80274	−0.414965
$451$	45.2933	2.13278
$452$	2.75521	0.129594
$453$	−26.6563	−1.25242
$454$	−14.4984	−0.680444
$455$	−67.4683	−3.16296
$456$	2.69123	0.126028
$457$	−3.15879	−0.147762	−0.0738811	−	0.997267i	$-0.523539\pi$
$457$	−3.15879	−0.147762	−0.0738811	+	0.997267i	$0.523539\pi$
$458$	−18.0059	−0.841360
$459$	−17.8068	−0.831152
$460$	−13.4988	−0.629384
$461$	−14.5306	−0.676758	−0.338379	−	0.941010i	$-0.609879\pi$
$461$	−14.5306	−0.676758	−0.338379	+	0.941010i	$0.609879\pi$
$462$	54.1400	2.51882
$463$	−30.6492	−1.42439	−0.712194	−	0.701983i	$-0.752298\pi$
$463$	−30.6492	−1.42439	−0.712194	+	0.701983i	$0.752298\pi$
$464$	2.52432	0.117189
$465$	11.8767	0.550768
$466$	10.7754	0.499160
$467$	−5.07431	−0.234811	−0.117406	−	0.993084i	$-0.537458\pi$
$467$	−5.07431	−0.234811	−0.117406	+	0.993084i	$0.537458\pi$
$468$	25.1112	1.16077
$469$	−1.82255	−0.0841578
$470$	−16.0522	−0.740434
$471$	12.7575	0.587835
$472$	−4.70675	−0.216646
$473$	−25.5519	−1.17488
$474$	−2.83166	−0.130062
$475$	2.07479	0.0951977
$476$	−22.8182	−1.04587
$477$	−31.4403	−1.43955
$478$	−9.56350	−0.437425
$479$	−34.2965	−1.56705	−0.783524	−	0.621362i	$-0.786580\pi$
$479$	−34.2965	−1.56705	−0.783524	+	0.621362i	$0.786580\pi$
$480$	7.15826	0.326729
$481$	−62.2487	−2.83830
$482$	−0.0232905	−0.00106085
$483$	−58.5342	−2.66340
$484$	11.0341	0.501548
$485$	−22.3507	−1.01490
$486$	−20.0648	−0.910159
$487$	16.7487	0.758955	0.379477	−	0.925201i	$-0.376104\pi$
$487$	16.7487	0.758955	0.379477	+	0.925201i	$0.376104\pi$
$488$	−1.25167	−0.0566603
$489$	14.6204	0.661160
$490$	−30.2347	−1.36586
$491$	−28.7643	−1.29812	−0.649058	−	0.760739i	$-0.724837\pi$
$491$	−28.7643	−1.29812	−0.649058	+	0.760739i	$0.724837\pi$
$492$	25.9680	1.17073
$493$	13.4402	0.605316
$494$	−5.91866	−0.266293
$495$	−52.9723	−2.38093
$496$	−1.65916	−0.0744984
$497$	−36.0352	−1.61640
$498$	6.13776	0.275039
$499$	19.4468	0.870559	0.435280	−	0.900295i	$-0.356649\pi$
$499$	19.4468	0.870559	0.435280	+	0.900295i	$0.356649\pi$
$500$	−7.78062	−0.347960
$501$	−18.8551	−0.842382
$502$	−3.75737	−0.167699
$503$	−43.3775	−1.93411	−0.967054	−	0.254572i	$-0.918065\pi$
$503$	−43.3775	−1.93411	−0.967054	+	0.254572i	$0.918065\pi$
$504$	18.1830	0.809934
$505$	−22.5942	−1.00543
$506$	−23.8224	−1.05903
$507$	−59.2892	−2.63313
$508$	−10.2657	−0.455467
$509$	−22.9851	−1.01880	−0.509399	−	0.860531i	$-0.670132\pi$
$509$	−22.9851	−1.01880	−0.509399	+	0.860531i	$0.670132\pi$
$510$	38.1126	1.68765
$511$	1.85719	0.0821574
$512$	−1.00000	−0.0441942
$513$	−3.34446	−0.147662
$514$	5.35067	0.236008
$515$	−2.43079	−0.107114
$516$	−14.6496	−0.644913
$517$	−28.3286	−1.24589
$518$	−45.0741	−1.98044
$519$	18.1634	0.797286
$520$	−15.7427	−0.690364
$521$	−30.5215	−1.33717	−0.668585	−	0.743636i	$-0.733100\pi$
$521$	−30.5215	−1.33717	−0.668585	+	0.743636i	$0.733100\pi$
$522$	−10.7100	−0.468764
$523$	−18.5131	−0.809520	−0.404760	−	0.914423i	$-0.632645\pi$
$523$	−18.5131	−0.809520	−0.404760	+	0.914423i	$0.632645\pi$
$524$	−2.69993	−0.117947
$525$	23.9301	1.04439
$526$	3.62669	0.158131
$527$	−8.83381	−0.384807
$528$	12.6328	0.549770
$529$	2.75589	0.119821
$530$	19.7105	0.856170
$531$	19.9694	0.866599
$532$	−4.28568	−0.185808
$533$	−57.1097	−2.47370
$534$	47.1432	2.04008
$535$	21.3339	0.922347
$536$	−0.425266	−0.0183687
$537$	−32.6699	−1.40981
$538$	−25.4720	−1.09817
$539$	−53.3576	−2.29827
$540$	−8.89576	−0.382812
$541$	−13.2229	−0.568497	−0.284249	−	0.958751i	$-0.591744\pi$
$541$	−13.2229	−0.568497	−0.284249	+	0.958751i	$0.591744\pi$
$542$	20.6944	0.888899
$543$	55.0525	2.36253
$544$	−5.32428	−0.228276
$545$	18.5403	0.794180
$546$	−68.2644	−2.92145
$547$	−22.0999	−0.944923	−0.472461	−	0.881351i	$-0.656634\pi$
$547$	−22.0999	−0.944923	−0.472461	+	0.881351i	$0.656634\pi$
$548$	−4.24723	−0.181433
$549$	5.31048	0.226646
$550$	9.73913	0.415278
$551$	2.52432	0.107540
$552$	−13.6581	−0.581326
$553$	4.50930	0.191755
$554$	9.08278	0.385890
$555$	75.2861	3.19572
$556$	19.0726	0.808860
$557$	−13.3732	−0.566640	−0.283320	−	0.959025i	$-0.591436\pi$
$557$	−13.3732	−0.566640	−0.283320	+	0.959025i	$0.591436\pi$
$558$	7.03935	0.297999
$559$	32.2180	1.36268
$560$	−11.3993	−0.481707
$561$	67.2603	2.83973
$562$	−14.8708	−0.627287
$563$	2.35025	0.0990510	0.0495255	−	0.998773i	$-0.484229\pi$
$563$	2.35025	0.0990510	0.0495255	+	0.998773i	$0.484229\pi$
$564$	−16.2416	−0.683896
$565$	7.32844	0.308310
$566$	32.1089	1.34964
$567$	15.9747	0.670874
$568$	−8.40828	−0.352804
$569$	33.4778	1.40346	0.701731	−	0.712442i	$-0.252411\pi$
$569$	33.4778	1.40346	0.701731	+	0.712442i	$0.252411\pi$
$570$	7.15826	0.299827
$571$	−35.3873	−1.48091	−0.740456	−	0.672105i	$-0.765390\pi$
$571$	−35.3873	−1.48091	−0.740456	+	0.672105i	$0.765390\pi$
$572$	−27.7824	−1.16164
$573$	7.05162	0.294585
$574$	−41.3530	−1.72604
$575$	−10.5296	−0.439114
$576$	4.24273	0.176780
$577$	−42.5375	−1.77086	−0.885429	−	0.464774i	$-0.846136\pi$
$577$	−42.5375	−1.77086	−0.885429	+	0.464774i	$0.846136\pi$
$578$	−11.3479	−0.472011
$579$	38.9083	1.61697
$580$	6.71431	0.278797
$581$	−9.77414	−0.405500
$582$	−22.6145	−0.937400
$583$	34.7847	1.44064
$584$	0.433348	0.0179321
$585$	66.7921	2.76151
$586$	30.0455	1.24117
$587$	−32.5625	−1.34400	−0.672000	−	0.740551i	$-0.734565\pi$
$587$	−32.5625	−1.34400	−0.672000	+	0.740551i	$0.734565\pi$
$588$	−30.5914	−1.26157
$589$	−1.65916	−0.0683644
$590$	−12.5192	−0.515408
$591$	−70.0781	−2.88263
$592$	−10.5174	−0.432261
$593$	16.1475	0.663099	0.331550	−	0.943438i	$-0.392429\pi$
$593$	16.1475	0.663099	0.331550	+	0.943438i	$0.392429\pi$
$594$	−15.6991	−0.644140
$595$	−60.6928	−2.48816
$596$	−17.4348	−0.714158
$597$	−38.8628	−1.59055
$598$	30.0373	1.22832
$599$	32.2112	1.31611	0.658056	−	0.752969i	$-0.271379\pi$
$599$	32.2112	1.31611	0.658056	+	0.752969i	$0.271379\pi$
$600$	5.58373	0.227955
$601$	40.6615	1.65862	0.829309	−	0.558790i	$-0.188734\pi$
$601$	40.6615	1.65862	0.829309	+	0.558790i	$0.188734\pi$
$602$	23.3290	0.950817
$603$	1.80429	0.0734762
$604$	9.90486	0.403023
$605$	29.3489	1.19320
$606$	−22.8608	−0.928655
$607$	−13.4208	−0.544733	−0.272367	−	0.962194i	$-0.587806\pi$
$607$	−13.4208	−0.544733	−0.272367	+	0.962194i	$0.587806\pi$
$608$	−1.00000	−0.0405554
$609$	29.1149	1.17980
$610$	−3.32924	−0.134797
$611$	35.7192	1.44504
$612$	22.5894	0.913124
$613$	−19.9576	−0.806079	−0.403040	−	0.915182i	$-0.632046\pi$
$613$	−19.9576	−0.806079	−0.403040	+	0.915182i	$0.632046\pi$
$614$	−15.1694	−0.612188
$615$	69.0708	2.78520
$616$	−20.1172	−0.810544
$617$	27.1970	1.09491	0.547456	−	0.836835i	$-0.315596\pi$
$617$	27.1970	1.09491	0.547456	+	0.836835i	$0.315596\pi$
$618$	−2.45947	−0.0989346
$619$	4.07968	0.163976	0.0819881	−	0.996633i	$-0.473873\pi$
$619$	4.07968	0.163976	0.0819881	+	0.996633i	$0.473873\pi$
$620$	−4.41311	−0.177235
$621$	16.9732	0.681112
$622$	31.2907	1.25464
$623$	−75.0737	−3.00776
$624$	−15.9285	−0.637649
$625$	−31.0692	−1.24277
$626$	−12.4249	−0.496600
$627$	12.6328	0.504504
$628$	−4.74040	−0.189162
$629$	−55.9974	−2.23276
$630$	48.3639	1.92687
$631$	34.8484	1.38729	0.693646	−	0.720316i	$-0.256003\pi$
$631$	34.8484	1.38729	0.693646	+	0.720316i	$0.256003\pi$
$632$	1.05218	0.0418534
$633$	−2.69123	−0.106967
$634$	8.71203	0.345999
$635$	−27.3052	−1.08357
$636$	19.9431	0.790794
$637$	67.2778	2.66565
$638$	11.8493	0.469118
$639$	35.6740	1.41124
$640$	−2.65985	−0.105140
$641$	38.9472	1.53832	0.769161	−	0.639055i	$-0.220675\pi$
$641$	38.9472	1.53832	0.769161	+	0.639055i	$0.220675\pi$
$642$	21.5857	0.851919
$643$	−3.83486	−0.151232	−0.0756161	−	0.997137i	$-0.524092\pi$
$643$	−3.83486	−0.151232	−0.0756161	+	0.997137i	$0.524092\pi$
$644$	21.7500	0.857068
$645$	−38.9657	−1.53427
$646$	−5.32428	−0.209481
$647$	37.3290	1.46755	0.733777	−	0.679390i	$-0.237756\pi$
$647$	37.3290	1.46755	0.733777	+	0.679390i	$0.237756\pi$
$648$	3.72746	0.146428
$649$	−22.0937	−0.867253
$650$	−12.2799	−0.481659
$651$	−19.1363	−0.750012
$652$	−5.43262	−0.212758
$653$	−20.9627	−0.820334	−0.410167	−	0.912010i	$-0.634530\pi$
$653$	−20.9627	−0.820334	−0.410167	+	0.912010i	$0.634530\pi$
$654$	18.7591	0.733538
$655$	−7.18139	−0.280600
$656$	−9.64910	−0.376734
$657$	−1.83858	−0.0717298
$658$	25.8642	1.00829
$659$	37.4138	1.45744	0.728718	−	0.684814i	$-0.240116\pi$
$659$	37.4138	1.45744	0.728718	+	0.684814i	$0.240116\pi$
$660$	33.6012	1.30793
$661$	27.0923	1.05377	0.526885	−	0.849936i	$-0.323360\pi$
$661$	27.0923	1.05377	0.526885	+	0.849936i	$0.323360\pi$
$662$	−30.8184	−1.19779
$663$	−84.8076	−3.29365
$664$	−2.28065	−0.0885064
$665$	−11.3993	−0.442044
$666$	44.6223	1.72908
$667$	−12.8110	−0.496044
$668$	7.00611	0.271075
$669$	−38.5371	−1.48993
$670$	−1.13114	−0.0436998
$671$	−5.87538	−0.226816
$672$	−11.5338	−0.444925
$673$	−37.4632	−1.44410	−0.722051	−	0.691840i	$-0.756800\pi$
$673$	−37.4632	−1.44410	−0.722051	+	0.691840i	$0.756800\pi$
$674$	−25.6204	−0.986861
$675$	−6.93904	−0.267084
$676$	22.0305	0.847327
$677$	−1.66841	−0.0641222	−0.0320611	−	0.999486i	$-0.510207\pi$
$677$	−1.66841	−0.0641222	−0.0320611	+	0.999486i	$0.510207\pi$
$678$	7.41491	0.284768
$679$	36.0127	1.38204
$680$	−14.1618	−0.543079
$681$	−39.0186	−1.49519
$682$	−7.78816	−0.298224
$683$	4.71978	0.180597	0.0902987	−	0.995915i	$-0.471218\pi$
$683$	4.71978	0.180597	0.0902987	+	0.995915i	$0.471218\pi$
$684$	4.24273	0.162225
$685$	−11.2970	−0.431636
$686$	18.7159	0.714577
$687$	−48.4580	−1.84879
$688$	5.44346	0.207530
$689$	−43.8596	−1.67092
$690$	−36.3284	−1.38300
$691$	14.8708	0.565713	0.282857	−	0.959162i	$-0.408718\pi$
$691$	14.8708	0.565713	0.282857	+	0.959162i	$0.408718\pi$
$692$	−6.74912	−0.256563
$693$	85.3517	3.24224
$694$	30.5941	1.16134
$695$	50.7303	1.92431
$696$	6.79354	0.257508
$697$	−51.3745	−1.94595
$698$	14.1956	0.537311
$699$	28.9991	1.09685
$700$	−8.89187	−0.336081
$701$	13.2568	0.500701	0.250350	−	0.968155i	$-0.419454\pi$
$701$	13.2568	0.500701	0.250350	+	0.968155i	$0.419454\pi$
$702$	19.7947	0.747104
$703$	−10.5174	−0.396670
$704$	−4.69404	−0.176913
$705$	−43.2002	−1.62702
$706$	−33.8736	−1.27485
$707$	36.4049	1.36915
$708$	−12.6669	−0.476053
$709$	12.9607	0.486751	0.243375	−	0.969932i	$-0.421745\pi$
$709$	12.9607	0.486751	0.243375	+	0.969932i	$0.421745\pi$
$710$	−22.3647	−0.839334
$711$	−4.46411	−0.167417
$712$	−17.5173	−0.656490
$713$	8.42027	0.315342
$714$	−61.4089	−2.29817
$715$	−73.8970	−2.76359
$716$	12.1394	0.453671
$717$	−25.7376	−0.961188
$718$	−0.857154	−0.0319887
$719$	21.8992	0.816702	0.408351	−	0.912825i	$-0.366104\pi$
$719$	21.8992	0.816702	0.408351	+	0.912825i	$0.366104\pi$
$720$	11.2850	0.420567
$721$	3.91662	0.145863
$722$	−1.00000	−0.0372161
$723$	−0.0626801	−0.00233110
$724$	−20.4562	−0.760250
$725$	5.23743	0.194513
$726$	29.6952	1.10209
$727$	−4.82564	−0.178973	−0.0894865	−	0.995988i	$-0.528523\pi$
$727$	−4.82564	−0.178973	−0.0894865	+	0.995988i	$0.528523\pi$
$728$	25.3655	0.940108
$729$	−42.8167	−1.58580
$730$	1.15264	0.0426611
$731$	28.9825	1.07196
$732$	−3.36852	−0.124504
$733$	−26.8084	−0.990192	−0.495096	−	0.868838i	$-0.664867\pi$
$733$	−26.8084	−0.990192	−0.495096	+	0.868838i	$0.664867\pi$
$734$	22.6268	0.835170
$735$	−81.3685	−3.00132
$736$	5.07503	0.187068
$737$	−1.99622	−0.0735316
$738$	40.9385	1.50697
$739$	−44.9612	−1.65392	−0.826962	−	0.562257i	$-0.809933\pi$
$739$	−44.9612	−1.65392	−0.826962	+	0.562257i	$0.809933\pi$
$740$	−27.9746	−1.02837
$741$	−15.9285	−0.585147
$742$	−31.7586	−1.16589
$743$	−31.4216	−1.15275	−0.576373	−	0.817187i	$-0.695533\pi$
$743$	−31.4216	−1.15275	−0.576373	+	0.817187i	$0.695533\pi$
$744$	−4.46518	−0.163701
$745$	−46.3740	−1.69901
$746$	16.0341	0.587050
$747$	9.67617	0.354033
$748$	−24.9924	−0.913812
$749$	−34.3744	−1.25601
$750$	−20.9395	−0.764601
$751$	−18.5758	−0.677840	−0.338920	−	0.940815i	$-0.610062\pi$
$751$	−18.5758	−0.677840	−0.338920	+	0.940815i	$0.610062\pi$
$752$	6.03502	0.220074
$753$	−10.1119	−0.368500
$754$	−14.9406	−0.544105
$755$	26.3454	0.958808
$756$	14.3333	0.521297
$757$	−32.5918	−1.18457	−0.592284	−	0.805729i	$-0.701774\pi$
$757$	−32.5918	−1.18457	−0.592284	+	0.805729i	$0.701774\pi$
$758$	29.9080	1.08631
$759$	−64.1116	−2.32710
$760$	−2.65985	−0.0964828
$761$	−42.2393	−1.53117	−0.765586	−	0.643334i	$-0.777551\pi$
$761$	−42.2393	−1.53117	−0.765586	+	0.643334i	$0.777551\pi$
$762$	−27.6274	−1.00083
$763$	−29.8731	−1.08148
$764$	−2.62022	−0.0947962
$765$	60.0844	2.17236
$766$	31.8944	1.15239
$767$	27.8576	1.00588
$768$	−2.69123	−0.0971114
$769$	−8.48100	−0.305833	−0.152916	−	0.988239i	$-0.548867\pi$
$769$	−8.48100	−0.305833	−0.152916	+	0.988239i	$0.548867\pi$
$770$	−53.5086	−1.92832
$771$	14.3999	0.518599
$772$	−14.4574	−0.520334
$773$	1.40239	0.0504404	0.0252202	−	0.999682i	$-0.491971\pi$
$773$	1.40239	0.0504404	0.0252202	+	0.999682i	$0.491971\pi$
$774$	−23.0951	−0.830137
$775$	−3.44240	−0.123655
$776$	8.40302	0.301651
$777$	−121.305	−4.35179
$778$	24.2829	0.870583
$779$	−9.64910	−0.345715
$780$	−42.3673	−1.51699
$781$	−39.4689	−1.41231
$782$	27.0208	0.966263
$783$	−8.44250	−0.301710
$784$	11.3671	0.405967
$785$	−12.6087	−0.450025
$786$	−7.26613	−0.259174
$787$	39.1747	1.39643	0.698214	−	0.715889i	$-0.253978\pi$
$787$	39.1747	1.39643	0.698214	+	0.715889i	$0.253978\pi$
$788$	26.0394	0.927616
$789$	9.76027	0.347475
$790$	2.79863	0.0995709
$791$	−11.8080	−0.419843
$792$	19.9155	0.707668
$793$	7.40818	0.263072
$794$	6.74975	0.239540
$795$	53.0455	1.88133
$796$	14.4405	0.511831
$797$	−27.9406	−0.989708	−0.494854	−	0.868976i	$-0.664778\pi$
$797$	−27.9406	−0.989708	−0.494854	+	0.868976i	$0.664778\pi$
$798$	−11.5338	−0.408291
$799$	32.1321	1.13675
$800$	−2.07479	−0.0733547
$801$	74.3212	2.62601
$802$	−7.78480	−0.274891
$803$	2.03416	0.0717838
$804$	−1.14449	−0.0403630
$805$	57.8515	2.03900
$806$	9.81999	0.345894
$807$	−68.5509	−2.41311
$808$	8.49454	0.298837
$809$	32.0246	1.12592	0.562962	−	0.826483i	$-0.309662\pi$
$809$	32.0246	1.12592	0.562962	+	0.826483i	$0.309662\pi$
$810$	9.91447	0.348359
$811$	−6.03475	−0.211909	−0.105954	−	0.994371i	$-0.533790\pi$
$811$	−6.03475	−0.211909	−0.105954	+	0.994371i	$0.533790\pi$
$812$	−10.8184	−0.379653
$813$	55.6933	1.95325
$814$	−49.3690	−1.73038
$815$	−14.4500	−0.506160
$816$	−14.3289	−0.501610
$817$	5.44346	0.190443
$818$	−1.62851	−0.0569394
$819$	−107.619	−3.76051
$820$	−25.6651	−0.896265
$821$	38.2478	1.33486	0.667429	−	0.744673i	$-0.267395\pi$
$821$	38.2478	1.33486	0.667429	+	0.744673i	$0.267395\pi$
$822$	−11.4303	−0.398677
$823$	−42.6990	−1.48839	−0.744197	−	0.667961i	$-0.767167\pi$
$823$	−42.6990	−1.48839	−0.744197	+	0.667961i	$0.767167\pi$
$824$	0.913885	0.0318367
$825$	26.2103	0.912524
$826$	20.1716	0.701860
$827$	−39.1396	−1.36102	−0.680509	−	0.732739i	$-0.738241\pi$
$827$	−39.1396	−1.36102	−0.680509	+	0.732739i	$0.738241\pi$
$828$	−21.5319	−0.748287
$829$	−5.63414	−0.195682	−0.0978409	−	0.995202i	$-0.531194\pi$
$829$	−5.63414	−0.195682	−0.0978409	+	0.995202i	$0.531194\pi$
$830$	−6.06618	−0.210560
$831$	24.4439	0.847948
$832$	5.91866	0.205193
$833$	60.5214	2.09694
$834$	51.3289	1.77737
$835$	18.6352	0.644897
$836$	−4.69404	−0.162347
$837$	5.54899	0.191801
$838$	2.96532	0.102435
$839$	−12.5689	−0.433927	−0.216963	−	0.976180i	$-0.569615\pi$
$839$	−12.5689	−0.433927	−0.216963	+	0.976180i	$0.569615\pi$
$840$	−30.6780	−1.05849
$841$	−22.6278	−0.780269
$842$	−25.6859	−0.885196
$843$	−40.0208	−1.37839
$844$	1.00000	0.0344214
$845$	58.5978	2.01583
$846$	−25.6049	−0.880315
$847$	−47.2884	−1.62485
$848$	−7.41039	−0.254474
$849$	86.4124	2.96567
$850$	−11.0467	−0.378900
$851$	53.3759	1.82970
$852$	−22.6286	−0.775244
$853$	7.00306	0.239780	0.119890	−	0.992787i	$-0.461746\pi$
$853$	7.00306	0.239780	0.119890	+	0.992787i	$0.461746\pi$
$854$	5.36424	0.183561
$855$	11.2850	0.385939
$856$	−8.02074	−0.274143
$857$	−34.9235	−1.19297	−0.596483	−	0.802626i	$-0.703436\pi$
$857$	−34.9235	−1.19297	−0.596483	+	0.802626i	$0.703436\pi$
$858$	−74.7690	−2.55257
$859$	−32.0900	−1.09490	−0.547448	−	0.836840i	$-0.684401\pi$
$859$	−32.0900	−1.09490	−0.547448	+	0.836840i	$0.684401\pi$
$860$	14.4788	0.493722
$861$	−111.290	−3.79277
$862$	17.1749	0.584980
$863$	32.1501	1.09440	0.547201	−	0.837001i	$-0.315693\pi$
$863$	32.1501	1.09440	0.547201	+	0.837001i	$0.315693\pi$
$864$	3.34446	0.113781
$865$	−17.9516	−0.610373
$866$	−10.6151	−0.360716
$867$	−30.5398	−1.03719
$868$	7.11062	0.241350
$869$	4.93897	0.167543
$870$	18.0698	0.612623
$871$	2.51700	0.0852854
$872$	−6.97045	−0.236049
$873$	−35.6517	−1.20663
$874$	5.07503	0.171665
$875$	33.3453	1.12728
$876$	1.16624	0.0394036
$877$	−47.4858	−1.60348	−0.801740	−	0.597673i	$-0.796092\pi$
$877$	−47.4858	−1.60348	−0.801740	+	0.597673i	$0.796092\pi$
$878$	8.10201	0.273430
$879$	80.8594	2.72732
$880$	−12.4854	−0.420884
$881$	−8.52756	−0.287301	−0.143650	−	0.989629i	$-0.545884\pi$
$881$	−8.52756	−0.287301	−0.143650	+	0.989629i	$0.545884\pi$
$882$	−48.2274	−1.62390
$883$	40.2611	1.35489	0.677447	−	0.735572i	$-0.263086\pi$
$883$	40.2611	1.35489	0.677447	+	0.735572i	$0.263086\pi$
$884$	31.5126	1.05988
$885$	−33.6921	−1.13255
$886$	9.62776	0.323451
$887$	20.4789	0.687615	0.343807	−	0.939040i	$-0.388283\pi$
$887$	20.4789	0.687615	0.343807	+	0.939040i	$0.388283\pi$
$888$	−28.3047	−0.949842
$889$	43.9955	1.47556
$890$	−46.5934	−1.56181
$891$	17.4968	0.586166
$892$	14.3195	0.479452
$893$	6.03502	0.201954
$894$	−46.9211	−1.56928
$895$	32.2889	1.07930
$896$	4.28568	0.143175
$897$	80.8374	2.69908
$898$	−24.8103	−0.827930
$899$	−4.18825	−0.139686
$900$	8.80274	0.293425
$901$	−39.4550	−1.31444
$902$	−45.2933	−1.50810
$903$	62.7836	2.08931
$904$	−2.75521	−0.0916370
$905$	−54.4105	−1.80867
$906$	26.6563	0.885595
$907$	−0.227607	−0.00755758	−0.00377879	−	0.999993i	$-0.501203\pi$
$907$	−0.227607	−0.00755758	−0.00377879	+	0.999993i	$0.501203\pi$
$908$	14.4984	0.481146
$909$	−36.0400	−1.19537
$910$	67.4683	2.23655
$911$	40.6386	1.34642	0.673208	−	0.739453i	$-0.264916\pi$
$911$	40.6386	1.34642	0.673208	+	0.739453i	$0.264916\pi$
$912$	−2.69123	−0.0891156
$913$	−10.7055	−0.354299
$914$	3.15879	0.104484
$915$	−8.95976	−0.296200
$916$	18.0059	0.594931
$917$	11.5710	0.382109
$918$	17.8068	0.587713
$919$	−3.22306	−0.106319	−0.0531595	−	0.998586i	$-0.516929\pi$
$919$	−3.22306	−0.106319	−0.0531595	+	0.998586i	$0.516929\pi$
$920$	13.4988	0.445042
$921$	−40.8244	−1.34521
$922$	14.5306	0.478540
$923$	49.7658	1.63806
$924$	−54.1400	−1.78108
$925$	−21.8213	−0.717479
$926$	30.6492	1.00719
$927$	−3.87736	−0.127349
$928$	−2.52432	−0.0828650
$929$	−22.6973	−0.744675	−0.372337	−	0.928097i	$-0.621444\pi$
$929$	−22.6973	−0.744675	−0.372337	+	0.928097i	$0.621444\pi$
$930$	−11.8767	−0.389452
$931$	11.3671	0.372541
$932$	−10.7754	−0.352960
$933$	84.2104	2.75692
$934$	5.07431	0.166037
$935$	−66.4759	−2.17399
$936$	−25.1112	−0.820787
$937$	−15.9661	−0.521589	−0.260795	−	0.965394i	$-0.583985\pi$
$937$	−15.9661	−0.521589	−0.260795	+	0.965394i	$0.583985\pi$
$938$	1.82255	0.0595085
$939$	−33.4384	−1.09122
$940$	16.0522	0.523566
$941$	−39.7668	−1.29636	−0.648180	−	0.761487i	$-0.724469\pi$
$941$	−39.7668	−1.29636	−0.648180	+	0.761487i	$0.724469\pi$
$942$	−12.7575	−0.415662
$943$	48.9694	1.59466
$944$	4.70675	0.153192
$945$	38.1244	1.24019
$946$	25.5519	0.830763
$947$	−5.60981	−0.182294	−0.0911471	−	0.995837i	$-0.529053\pi$
$947$	−5.60981	−0.182294	−0.0911471	+	0.995837i	$0.529053\pi$
$948$	2.83166	0.0919679
$949$	−2.56484	−0.0832582
$950$	−2.07479	−0.0673149
$951$	23.4461	0.760291
$952$	22.8182	0.739541
$953$	25.1316	0.814091	0.407046	−	0.913408i	$-0.366559\pi$
$953$	25.1316	0.814091	0.407046	+	0.913408i	$0.366559\pi$
$954$	31.4403	1.01792
$955$	−6.96938	−0.225524
$956$	9.56350	0.309306
$957$	31.8892	1.03083
$958$	34.2965	1.10807
$959$	18.2023	0.587783
$960$	−7.15826	−0.231032
$961$	−28.2472	−0.911200
$962$	62.2487	2.00698
$963$	34.0298	1.09660
$964$	0.0232905	0.000750137 0
$965$	−38.4545	−1.23790
$966$	58.5342	1.88331
$967$	−1.65515	−0.0532261	−0.0266130	−	0.999646i	$-0.508472\pi$
$967$	−1.65515	−0.0532261	−0.0266130	+	0.999646i	$0.508472\pi$
$968$	−11.0341	−0.354648
$969$	−14.3289	−0.460309
$970$	22.3507	0.717639
$971$	−51.9353	−1.66668	−0.833341	−	0.552759i	$-0.813575\pi$
$971$	−51.9353	−1.66668	−0.833341	+	0.552759i	$0.813575\pi$
$972$	20.0648	0.643580
$973$	−81.7393	−2.62044
$974$	−16.7487	−0.536662
$975$	−33.0482	−1.05839
$976$	1.25167	0.0400649
$977$	−28.4167	−0.909131	−0.454565	−	0.890713i	$-0.650205\pi$
$977$	−28.4167	−0.909131	−0.454565	+	0.890713i	$0.650205\pi$
$978$	−14.6204	−0.467510
$979$	−82.2271	−2.62799
$980$	30.2347	0.965812
$981$	29.5737	0.944215
$982$	28.7643	0.917907
$983$	0.535807	0.0170896	0.00854480	−	0.999963i	$-0.497280\pi$
$983$	0.535807	0.0170896	0.00854480	+	0.999963i	$0.497280\pi$
$984$	−25.9680	−0.827828
$985$	69.2609	2.20683
$986$	−13.4402	−0.428023
$987$	69.6065	2.21560
$988$	5.91866	0.188298
$989$	−27.6257	−0.878447
$990$	52.9723	1.68357
$991$	−48.3860	−1.53703	−0.768517	−	0.639830i	$-0.779005\pi$
$991$	−48.3860	−1.53703	−0.768517	+	0.639830i	$0.779005\pi$
$992$	1.65916	0.0526783
$993$	−82.9393	−2.63200
$994$	36.0352	1.14297
$995$	38.4096	1.21767
$996$	−6.13776	−0.194482
$997$	−27.2049	−0.861587	−0.430794	−	0.902450i	$-0.641766\pi$
$997$	−27.2049	−0.861587	−0.430794	+	0.902450i	$0.641766\pi$
$998$	−19.4468	−0.615578
$999$	35.1749	1.11289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.4	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.69123 q^{3} +1.00000 q^{4} +2.65985 q^{5} +2.69123 q^{6} -4.28568 q^{7} -1.00000 q^{8} +4.24273 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.69123 q^{3} +1.00000 q^{4} +2.65985 q^{5} +2.69123 q^{6} -4.28568 q^{7} -1.00000 q^{8} +4.24273 q^{9} -2.65985 q^{10} -4.69404 q^{11} -2.69123 q^{12} +5.91866 q^{13} +4.28568 q^{14} -7.15826 q^{15} +1.00000 q^{16} +5.32428 q^{17} -4.24273 q^{18} +1.00000 q^{19} +2.65985 q^{20} +11.5338 q^{21} +4.69404 q^{22} -5.07503 q^{23} +2.69123 q^{24} +2.07479 q^{25} -5.91866 q^{26} -3.34446 q^{27} -4.28568 q^{28} +2.52432 q^{29} +7.15826 q^{30} -1.65916 q^{31} -1.00000 q^{32} +12.6328 q^{33} -5.32428 q^{34} -11.3993 q^{35} +4.24273 q^{36} -10.5174 q^{37} -1.00000 q^{38} -15.9285 q^{39} -2.65985 q^{40} -9.64910 q^{41} -11.5338 q^{42} +5.44346 q^{43} -4.69404 q^{44} +11.2850 q^{45} +5.07503 q^{46} +6.03502 q^{47} -2.69123 q^{48} +11.3671 q^{49} -2.07479 q^{50} -14.3289 q^{51} +5.91866 q^{52} -7.41039 q^{53} +3.34446 q^{54} -12.4854 q^{55} +4.28568 q^{56} -2.69123 q^{57} -2.52432 q^{58} +4.70675 q^{59} -7.15826 q^{60} +1.25167 q^{61} +1.65916 q^{62} -18.1830 q^{63} +1.00000 q^{64} +15.7427 q^{65} -12.6328 q^{66} +0.425266 q^{67} +5.32428 q^{68} +13.6581 q^{69} +11.3993 q^{70} +8.40828 q^{71} -4.24273 q^{72} -0.433348 q^{73} +10.5174 q^{74} -5.58373 q^{75} +1.00000 q^{76} +20.1172 q^{77} +15.9285 q^{78} -1.05218 q^{79} +2.65985 q^{80} -3.72746 q^{81} +9.64910 q^{82} +2.28065 q^{83} +11.5338 q^{84} +14.1618 q^{85} -5.44346 q^{86} -6.79354 q^{87} +4.69404 q^{88} +17.5173 q^{89} -11.2850 q^{90} -25.3655 q^{91} -5.07503 q^{92} +4.46518 q^{93} -6.03502 q^{94} +2.65985 q^{95} +2.69123 q^{96} -8.40302 q^{97} -11.3671 q^{98} -19.9155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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