LMFDB - Embedded newform 619.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +O(q^{10})$	\(q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +3.28140 q^{10} +2.81981 q^{11} +0.282919 q^{12} +1.19984 q^{13} +1.84959 q^{14} -5.43548 q^{15} -4.22098 q^{16} -3.27932 q^{17} -4.08850 q^{18} +4.87284 q^{19} -0.264693 q^{20} -3.06376 q^{21} -4.10317 q^{22} +9.08548 q^{23} +6.60299 q^{24} +0.0853300 q^{25} -1.74591 q^{26} -0.458606 q^{27} -0.149197 q^{28} +8.59083 q^{29} +7.90928 q^{30} +9.78712 q^{31} +0.663144 q^{32} +6.79670 q^{33} +4.77181 q^{34} +2.86640 q^{35} +0.329799 q^{36} -5.98121 q^{37} -7.09057 q^{38} +2.89202 q^{39} -6.17763 q^{40} -0.101904 q^{41} +4.45815 q^{42} +0.656035 q^{43} +0.330981 q^{44} -6.33614 q^{45} -13.2205 q^{46} +8.22008 q^{47} -10.1740 q^{48} -5.38432 q^{49} -0.124165 q^{50} -7.90427 q^{51} +0.140834 q^{52} +5.04461 q^{53} +0.667327 q^{54} -6.35886 q^{55} -3.48209 q^{56} +11.7452 q^{57} -12.5007 q^{58} -5.66022 q^{59} -0.638001 q^{60} +6.42480 q^{61} -14.2414 q^{62} -3.57143 q^{63} +7.47700 q^{64} -2.70572 q^{65} -9.89002 q^{66} +1.69588 q^{67} -0.384917 q^{68} +21.8991 q^{69} -4.17096 q^{70} +2.02566 q^{71} +7.69711 q^{72} -9.64772 q^{73} +8.70338 q^{74} +0.205674 q^{75} +0.571960 q^{76} -3.58424 q^{77} -4.20823 q^{78} -5.55932 q^{79} +9.51859 q^{80} -9.53460 q^{81} +0.148282 q^{82} +6.25367 q^{83} -0.359616 q^{84} +7.39509 q^{85} -0.954610 q^{86} +20.7068 q^{87} +7.72471 q^{88} +15.9399 q^{89} +9.21985 q^{90} -1.52511 q^{91} +1.06643 q^{92} +23.5903 q^{93} -11.9612 q^{94} -10.9886 q^{95} +1.59840 q^{96} -11.5366 q^{97} +7.83484 q^{98} +7.92292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	−1.45512	−1.02893	−0.514463	−	0.857513i	$-0.672009\pi$
$2$	−1.45512	−1.02893	−0.514463	+	0.857513i	$0.672009\pi$
$3$	2.41034	1.39161	0.695805	−	0.718231i	$-0.255048\pi$
$3$	2.41034	1.39161	0.695805	+	0.718231i	$0.255048\pi$
$4$	0.117377	0.0586886
$5$	−2.25507	−1.00850	−0.504248	−	0.863559i	$-0.668230\pi$
$5$	−2.25507	−1.00850	−0.504248	+	0.863559i	$0.668230\pi$
$6$	−3.50733	−1.43186
$7$	−1.27109	−0.480428	−0.240214	−	0.970720i	$-0.577218\pi$
$7$	−1.27109	−0.480428	−0.240214	+	0.970720i	$0.577218\pi$
$8$	2.73944	0.968540
$9$	2.80973	0.936578
$10$	3.28140	1.03767
$11$	2.81981	0.850205	0.425103	−	0.905145i	$-0.360238\pi$
$11$	2.81981	0.850205	0.425103	+	0.905145i	$0.360238\pi$
$12$	0.282919	0.0816716
$13$	1.19984	0.332775	0.166388	−	0.986060i	$-0.446790\pi$
$13$	1.19984	0.332775	0.166388	+	0.986060i	$0.446790\pi$
$14$	1.84959	0.494325
$15$	−5.43548	−1.40343
$16$	−4.22098	−1.05524
$17$	−3.27932	−0.795352	−0.397676	−	0.917526i	$-0.630183\pi$
$17$	−3.27932	−0.795352	−0.397676	+	0.917526i	$0.630183\pi$
$18$	−4.08850	−0.963669
$19$	4.87284	1.11791	0.558953	−	0.829199i	$-0.311203\pi$
$19$	4.87284	1.11791	0.558953	+	0.829199i	$0.311203\pi$
$20$	−0.264693	−0.0591872
$21$	−3.06376	−0.668568
$22$	−4.10317	−0.874798
$23$	9.08548	1.89445	0.947227	−	0.320564i	$-0.103872\pi$
$23$	9.08548	1.89445	0.947227	+	0.320564i	$0.103872\pi$
$24$	6.60299	1.34783
$25$	0.0853300	0.0170660
$26$	−1.74591	−0.342401
$27$	−0.458606	−0.0882588
$28$	−0.149197	−0.0281956
$29$	8.59083	1.59528	0.797638	−	0.603136i	$-0.206083\pi$
$29$	8.59083	1.59528	0.797638	+	0.603136i	$0.206083\pi$
$30$	7.90928	1.44403
$31$	9.78712	1.75782	0.878909	−	0.476989i	$-0.158272\pi$
$31$	9.78712	1.75782	0.878909	+	0.476989i	$0.158272\pi$
$32$	0.663144	0.117228
$33$	6.79670	1.18315
$34$	4.77181	0.818358
$35$	2.86640	0.484510
$36$	0.329799	0.0549664
$37$	−5.98121	−0.983304	−0.491652	−	0.870792i	$-0.663607\pi$
$37$	−5.98121	−0.983304	−0.491652	+	0.870792i	$0.663607\pi$
$38$	−7.09057	−1.15024
$39$	2.89202	0.463093
$40$	−6.17763	−0.976769
$41$	−0.101904	−0.0159147	−0.00795733	−	0.999968i	$-0.502533\pi$
$41$	−0.101904	−0.0159147	−0.00795733	+	0.999968i	$0.502533\pi$
$42$	4.45815	0.687907
$43$	0.656035	0.100044	0.0500222	−	0.998748i	$-0.484071\pi$
$43$	0.656035	0.100044	0.0500222	+	0.998748i	$0.484071\pi$
$44$	0.330981	0.0498973
$45$	−6.33614	−0.944536
$46$	−13.2205	−1.94925
$47$	8.22008	1.19902	0.599511	−	0.800367i	$-0.295362\pi$
$47$	8.22008	1.19902	0.599511	+	0.800367i	$0.295362\pi$
$48$	−10.1740	−1.46849
$49$	−5.38432	−0.769189
$50$	−0.124165	−0.0175596
$51$	−7.90427	−1.10682
$52$	0.140834	0.0195301
$53$	5.04461	0.692931	0.346465	−	0.938063i	$-0.387382\pi$
$53$	5.04461	0.692931	0.346465	+	0.938063i	$0.387382\pi$
$54$	0.667327	0.0908118
$55$	−6.35886	−0.857429
$56$	−3.48209	−0.465314
$57$	11.7452	1.55569
$58$	−12.5007	−1.64142
$59$	−5.66022	−0.736898	−0.368449	−	0.929648i	$-0.620111\pi$
$59$	−5.66022	−0.736898	−0.368449	+	0.929648i	$0.620111\pi$
$60$	−0.638001	−0.0823656
$61$	6.42480	0.822611	0.411305	−	0.911498i	$-0.365073\pi$
$61$	6.42480	0.822611	0.411305	+	0.911498i	$0.365073\pi$
$62$	−14.2414	−1.80867
$63$	−3.57143	−0.449958
$64$	7.47700	0.934625
$65$	−2.70572	−0.335603
$66$	−9.89002	−1.21738
$67$	1.69588	0.207184	0.103592	−	0.994620i	$-0.466966\pi$
$67$	1.69588	0.207184	0.103592	+	0.994620i	$0.466966\pi$
$68$	−0.384917	−0.0466781
$69$	21.8991	2.63634
$70$	−4.17096	−0.498525
$71$	2.02566	0.240402	0.120201	−	0.992750i	$-0.461646\pi$
$71$	2.02566	0.240402	0.120201	+	0.992750i	$0.461646\pi$
$72$	7.69711	0.907113
$73$	−9.64772	−1.12918	−0.564590	−	0.825372i	$-0.690966\pi$
$73$	−9.64772	−1.12918	−0.564590	+	0.825372i	$0.690966\pi$
$74$	8.70338	1.01175
$75$	0.205674	0.0237492
$76$	0.571960	0.0656083
$77$	−3.58424	−0.408462
$78$	−4.20823	−0.476489
$79$	−5.55932	−0.625472	−0.312736	−	0.949840i	$-0.601246\pi$
$79$	−5.55932	−0.625472	−0.312736	+	0.949840i	$0.601246\pi$
$80$	9.51859	1.06421
$81$	−9.53460	−1.05940
$82$	0.148282	0.0163750
$83$	6.25367	0.686429	0.343215	−	0.939257i	$-0.388484\pi$
$83$	6.25367	0.686429	0.343215	+	0.939257i	$0.388484\pi$
$84$	−0.359616	−0.0392373
$85$	7.39509	0.802110
$86$	−0.954610	−0.102938
$87$	20.7068	2.22000
$88$	7.72471	0.823457
$89$	15.9399	1.68963	0.844813	−	0.535062i	$-0.179712\pi$
$89$	15.9399	1.68963	0.844813	+	0.535062i	$0.179712\pi$
$90$	9.21985	0.971858
$91$	−1.52511	−0.159874
$92$	1.06643	0.111183
$93$	23.5903	2.44620
$94$	−11.9612	−1.23370
$95$	−10.9886	−1.12740
$96$	1.59840	0.163136
$97$	−11.5366	−1.17136	−0.585681	−	0.810542i	$-0.699173\pi$
$97$	−11.5366	−1.17136	−0.585681	+	0.810542i	$0.699173\pi$
$98$	7.83484	0.791438
$99$	7.92292	0.796283
$100$	0.0100158	0.00100158
$101$	−12.4750	−1.24131	−0.620653	−	0.784086i	$-0.713132\pi$
$101$	−12.4750	−1.24131	−0.620653	+	0.784086i	$0.713132\pi$
$102$	11.5017	1.13884
$103$	13.3216	1.31262	0.656308	−	0.754493i	$-0.272117\pi$
$103$	13.3216	1.31262	0.656308	+	0.754493i	$0.272117\pi$
$104$	3.28689	0.322306
$105$	6.90900	0.674249
$106$	−7.34052	−0.712974
$107$	8.02008	0.775331	0.387665	−	0.921800i	$-0.373282\pi$
$107$	8.02008	0.775331	0.387665	+	0.921800i	$0.373282\pi$
$108$	−0.0538299	−0.00517978
$109$	−14.9962	−1.43637	−0.718187	−	0.695850i	$-0.755028\pi$
$109$	−14.9962	−1.43637	−0.718187	+	0.695850i	$0.755028\pi$
$110$	9.25292	0.882231
$111$	−14.4167	−1.36838
$112$	5.36525	0.506969
$113$	−1.99561	−0.187732	−0.0938658	−	0.995585i	$-0.529922\pi$
$113$	−1.99561	−0.187732	−0.0938658	+	0.995585i	$0.529922\pi$
$114$	−17.0907	−1.60069
$115$	−20.4884	−1.91055
$116$	1.00837	0.0936245
$117$	3.37123	0.311670
$118$	8.23631	0.758213
$119$	4.16832	0.382109
$120$	−14.8902	−1.35928
$121$	−3.04867	−0.277151
$122$	−9.34886	−0.846406
$123$	−0.245622	−0.0221470
$124$	1.14878	0.103164
$125$	11.0829	0.991286
$126$	5.19687	0.462974
$127$	−8.25231	−0.732274	−0.366137	−	0.930561i	$-0.619320\pi$
$127$	−8.25231	−0.732274	−0.366137	+	0.930561i	$0.619320\pi$
$128$	−12.2062	−1.07889
$129$	1.58127	0.139223
$130$	3.93714	0.345310
$131$	15.4250	1.34769	0.673843	−	0.738875i	$-0.264642\pi$
$131$	15.4250	1.34769	0.673843	+	0.738875i	$0.264642\pi$
$132$	0.797777	0.0694376
$133$	−6.19383	−0.537073
$134$	−2.46771	−0.213177
$135$	1.03419	0.0890087
$136$	−8.98351	−0.770330
$137$	−16.2510	−1.38841	−0.694207	−	0.719775i	$-0.744245\pi$
$137$	−16.2510	−1.38841	−0.694207	+	0.719775i	$0.744245\pi$
$138$	−31.8658	−2.71260
$139$	−4.38715	−0.372113	−0.186057	−	0.982539i	$-0.559571\pi$
$139$	−4.38715	−0.372113	−0.186057	+	0.982539i	$0.559571\pi$
$140$	0.336450	0.0284352
$141$	19.8132	1.66857
$142$	−2.94759	−0.247356
$143$	3.38332	0.282927
$144$	−11.8598	−0.988318
$145$	−19.3729	−1.60883
$146$	14.0386	1.16184
$147$	−12.9780	−1.07041
$148$	−0.702057	−0.0577087
$149$	1.03300	0.0846265	0.0423132	−	0.999104i	$-0.486527\pi$
$149$	1.03300	0.0846265	0.0423132	+	0.999104i	$0.486527\pi$
$150$	−0.299281	−0.0244362
$151$	18.7956	1.52957	0.764783	−	0.644288i	$-0.222846\pi$
$151$	18.7956	1.52957	0.764783	+	0.644288i	$0.222846\pi$
$152$	13.3489	1.08274
$153$	−9.21401	−0.744909
$154$	5.21551	0.420277
$155$	−22.0706	−1.77275
$156$	0.339457	0.0271783
$157$	−7.30975	−0.583381	−0.291691	−	0.956513i	$-0.594218\pi$
$157$	−7.30975	−0.583381	−0.291691	+	0.956513i	$0.594218\pi$
$158$	8.08948	0.643565
$159$	12.1592	0.964289
$160$	−1.49543	−0.118224
$161$	−11.5485	−0.910149
$162$	13.8740	1.09004
$163$	−8.59779	−0.673431	−0.336715	−	0.941606i	$-0.609316\pi$
$163$	−8.59779	−0.673431	−0.336715	+	0.941606i	$0.609316\pi$
$164$	−0.0119611	−0.000934009 0
$165$	−15.3270	−1.19321
$166$	−9.09985	−0.706285
$167$	2.32471	0.179892	0.0899459	−	0.995947i	$-0.471331\pi$
$167$	2.32471	0.179892	0.0899459	+	0.995947i	$0.471331\pi$
$168$	−8.39301	−0.647535
$169$	−11.5604	−0.889261
$170$	−10.7607	−0.825312
$171$	13.6914	1.04701
$172$	0.0770035	0.00587146
$173$	−26.1646	−1.98926	−0.994630	−	0.103499i	$-0.966996\pi$
$173$	−26.1646	−1.98926	−0.994630	+	0.103499i	$0.966996\pi$
$174$	−30.1309	−2.28422
$175$	−0.108462	−0.00819898
$176$	−11.9024	−0.897174
$177$	−13.6430	−1.02547
$178$	−23.1945	−1.73850
$179$	−17.0938	−1.27765	−0.638824	−	0.769353i	$-0.720579\pi$
$179$	−17.0938	−1.27765	−0.638824	+	0.769353i	$0.720579\pi$
$180$	−0.743718	−0.0554335
$181$	−20.3727	−1.51429	−0.757144	−	0.653248i	$-0.773406\pi$
$181$	−20.3727	−1.51429	−0.757144	+	0.653248i	$0.773406\pi$
$182$	2.21921	0.164499
$183$	15.4859	1.14475
$184$	24.8892	1.83485
$185$	13.4880	0.991659
$186$	−34.3267	−2.51696
$187$	−9.24706	−0.676212
$188$	0.964849	0.0703689
$189$	0.582931	0.0424020
$190$	15.9897	1.16002
$191$	13.3300	0.964529	0.482264	−	0.876026i	$-0.339815\pi$
$191$	13.3300	0.964529	0.482264	+	0.876026i	$0.339815\pi$
$192$	18.0221	1.30063
$193$	21.9679	1.58129	0.790644	−	0.612277i	$-0.209746\pi$
$193$	21.9679	1.58129	0.790644	+	0.612277i	$0.209746\pi$
$194$	16.7871	1.20524
$195$	−6.52169	−0.467028
$196$	−0.631996	−0.0451426
$197$	12.7697	0.909804	0.454902	−	0.890541i	$-0.349674\pi$
$197$	12.7697	0.909804	0.454902	+	0.890541i	$0.349674\pi$
$198$	−11.5288	−0.819316
$199$	−6.43943	−0.456479	−0.228240	−	0.973605i	$-0.573297\pi$
$199$	−6.43943	−0.456479	−0.228240	+	0.973605i	$0.573297\pi$
$200$	0.233757	0.0165291
$201$	4.08764	0.288320
$202$	18.1526	1.27721
$203$	−10.9197	−0.766415
$204$	−0.927781	−0.0649576
$205$	0.229799	0.0160499
$206$	−19.3845	−1.35058
$207$	25.5278	1.77430
$208$	−5.06449	−0.351159
$209$	13.7405	0.950449
$210$	−10.0534	−0.693752
$211$	3.70816	0.255281	0.127640	−	0.991821i	$-0.459260\pi$
$211$	3.70816	0.255281	0.127640	+	0.991821i	$0.459260\pi$
$212$	0.592122	0.0406671
$213$	4.88254	0.334546
$214$	−11.6702	−0.797758
$215$	−1.47940	−0.100894
$216$	−1.25633	−0.0854822
$217$	−12.4403	−0.844505
$218$	21.8213	1.47792
$219$	−23.2543	−1.57138
$220$	−0.746385	−0.0503213
$221$	−3.93465	−0.264673
$222$	20.9781	1.40796
$223$	1.57390	0.105396	0.0526982	−	0.998610i	$-0.483218\pi$
$223$	1.57390	0.105396	0.0526982	+	0.998610i	$0.483218\pi$
$224$	−0.842918	−0.0563198
$225$	0.239754	0.0159836
$226$	2.90386	0.193162
$227$	1.07023	0.0710337	0.0355169	−	0.999369i	$-0.488692\pi$
$227$	1.07023	0.0710337	0.0355169	+	0.999369i	$0.488692\pi$
$228$	1.37862	0.0913012
$229$	4.48075	0.296097	0.148048	−	0.988980i	$-0.452701\pi$
$229$	4.48075	0.296097	0.148048	+	0.988980i	$0.452701\pi$
$230$	29.8131	1.96582
$231$	−8.63924	−0.568420
$232$	23.5341	1.54509
$233$	−4.42879	−0.290140	−0.145070	−	0.989421i	$-0.546341\pi$
$233$	−4.42879	−0.290140	−0.145070	+	0.989421i	$0.546341\pi$
$234$	−4.90554	−0.320685
$235$	−18.5368	−1.20921
$236$	−0.664381	−0.0432475
$237$	−13.3998	−0.870413
$238$	−6.06541	−0.393162
$239$	11.5886	0.749603	0.374802	−	0.927105i	$-0.377711\pi$
$239$	11.5886	0.749603	0.374802	+	0.927105i	$0.377711\pi$
$240$	22.9430	1.48097
$241$	−12.9016	−0.831066	−0.415533	−	0.909578i	$-0.636405\pi$
$241$	−12.9016	−0.831066	−0.415533	+	0.909578i	$0.636405\pi$
$242$	4.43618	0.285168
$243$	−21.6058	−1.38601
$244$	0.754124	0.0482779
$245$	12.1420	0.775725
$246$	0.357410	0.0227876
$247$	5.84662	0.372011
$248$	26.8113	1.70252
$249$	15.0735	0.955242
$250$	−16.1270	−1.01996
$251$	−20.1137	−1.26956	−0.634782	−	0.772691i	$-0.718910\pi$
$251$	−20.1137	−1.26956	−0.634782	+	0.772691i	$0.718910\pi$
$252$	−0.419205	−0.0264074
$253$	25.6193	1.61067
$254$	12.0081	0.753455
$255$	17.8247	1.11622
$256$	2.80754	0.175471
$257$	3.79278	0.236587	0.118293	−	0.992979i	$-0.462258\pi$
$257$	3.79278	0.236587	0.118293	+	0.992979i	$0.462258\pi$
$258$	−2.30093	−0.143250
$259$	7.60267	0.472407
$260$	−0.317589	−0.0196960
$261$	24.1379	1.49410
$262$	−22.4452	−1.38667
$263$	−21.9708	−1.35478	−0.677388	−	0.735626i	$-0.736888\pi$
$263$	−21.9708	−1.35478	−0.677388	+	0.735626i	$0.736888\pi$
$264$	18.6192	1.14593
$265$	−11.3759	−0.698818
$266$	9.01277	0.552609
$267$	38.4206	2.35130
$268$	0.199057	0.0121594
$269$	6.37593	0.388748	0.194374	−	0.980928i	$-0.437733\pi$
$269$	6.37593	0.388748	0.194374	+	0.980928i	$0.437733\pi$
$270$	−1.50487	−0.0915834
$271$	−9.29331	−0.564529	−0.282264	−	0.959337i	$-0.591086\pi$
$271$	−9.29331	−0.564529	−0.282264	+	0.959337i	$0.591086\pi$
$272$	13.8419	0.839290
$273$	−3.67602	−0.222483
$274$	23.6471	1.42858
$275$	0.240614	0.0145096
$276$	2.57045	0.154723
$277$	−1.86135	−0.111838	−0.0559189	−	0.998435i	$-0.517809\pi$
$277$	−1.86135	−0.111838	−0.0559189	+	0.998435i	$0.517809\pi$
$278$	6.38383	0.382877
$279$	27.4992	1.64633
$280$	7.85234	0.469267
$281$	18.5118	1.10432	0.552162	−	0.833737i	$-0.313803\pi$
$281$	18.5118	1.10432	0.552162	+	0.833737i	$0.313803\pi$
$282$	−28.8306	−1.71683
$283$	6.10833	0.363102	0.181551	−	0.983381i	$-0.441888\pi$
$283$	6.10833	0.363102	0.181551	+	0.983381i	$0.441888\pi$
$284$	0.237767	0.0141089
$285$	−26.4862	−1.56891
$286$	−4.92313	−0.291111
$287$	0.129529	0.00764585
$288$	1.86326	0.109794
$289$	−6.24607	−0.367416
$290$	28.1899	1.65537
$291$	−27.8070	−1.63008
$292$	−1.13242	−0.0662699
$293$	−16.9613	−0.990889	−0.495445	−	0.868639i	$-0.664995\pi$
$293$	−16.9613	−0.990889	−0.495445	+	0.868639i	$0.664995\pi$
$294$	18.8846	1.10137
$295$	12.7642	0.743159
$296$	−16.3852	−0.952369
$297$	−1.29318	−0.0750381
$298$	−1.50314	−0.0870744
$299$	10.9011	0.630427
$300$	0.0241414	0.00139381
$301$	−0.833881	−0.0480641
$302$	−27.3499	−1.57381
$303$	−30.0689	−1.72741
$304$	−20.5681	−1.17966
$305$	−14.4884	−0.829601
$306$	13.4075	0.766456
$307$	10.4450	0.596129	0.298065	−	0.954546i	$-0.403659\pi$
$307$	10.4450	0.596129	0.298065	+	0.954546i	$0.403659\pi$
$308$	−0.420708	−0.0239721
$309$	32.1096	1.82665
$310$	32.1154	1.82403
$311$	25.6027	1.45179	0.725897	−	0.687804i	$-0.241425\pi$
$311$	25.6027	1.45179	0.725897	+	0.687804i	$0.241425\pi$
$312$	7.92252	0.448524
$313$	−12.0009	−0.678330	−0.339165	−	0.940727i	$-0.610144\pi$
$313$	−12.0009	−0.678330	−0.339165	+	0.940727i	$0.610144\pi$
$314$	10.6366	0.600256
$315$	8.05382	0.453781
$316$	−0.652537	−0.0367081
$317$	9.21967	0.517828	0.258914	−	0.965900i	$-0.416635\pi$
$317$	9.21967	0.517828	0.258914	+	0.965900i	$0.416635\pi$
$318$	−17.6931	−0.992182
$319$	24.2245	1.35631
$320$	−16.8611	−0.942566
$321$	19.3311	1.07896
$322$	16.8045	0.936476
$323$	−15.9796	−0.889129
$324$	−1.11914	−0.0621747
$325$	0.102382	0.00567914
$326$	12.5108	0.692911
$327$	−36.1459	−1.99887
$328$	−0.279159	−0.0154140
$329$	−10.4485	−0.576043
$330$	22.3027	1.22772
$331$	16.3162	0.896822	0.448411	−	0.893827i	$-0.351990\pi$
$331$	16.3162	0.896822	0.448411	+	0.893827i	$0.351990\pi$
$332$	0.734038	0.0402856
$333$	−16.8056	−0.920941
$334$	−3.38274	−0.185095
$335$	−3.82432	−0.208945
$336$	12.9321	0.705503
$337$	33.7094	1.83627	0.918134	−	0.396269i	$-0.129695\pi$
$337$	33.7094	1.83627	0.918134	+	0.396269i	$0.129695\pi$
$338$	16.8218	0.914983
$339$	−4.81011	−0.261249
$340$	0.868014	0.0470747
$341$	27.5978	1.49451
$342$	−19.9226	−1.07729
$343$	15.7416	0.849968
$344$	1.79717	0.0968969
$345$	−49.3839	−2.65874
$346$	38.0727	2.04680
$347$	−11.6182	−0.623695	−0.311848	−	0.950132i	$-0.600948\pi$
$347$	−11.6182	−0.623695	−0.311848	+	0.950132i	$0.600948\pi$
$348$	2.43051	0.130289
$349$	28.4712	1.52403	0.762014	−	0.647560i	$-0.224211\pi$
$349$	28.4712	1.52403	0.762014	+	0.647560i	$0.224211\pi$
$350$	0.157826	0.00843614
$351$	−0.550253	−0.0293703
$352$	1.86994	0.0996682
$353$	−24.7286	−1.31617	−0.658086	−	0.752943i	$-0.728634\pi$
$353$	−24.7286	−1.31617	−0.658086	+	0.752943i	$0.728634\pi$
$354$	19.8523	1.05514
$355$	−4.56801	−0.242445
$356$	1.87098	0.0991617
$357$	10.0471	0.531747
$358$	24.8735	1.31461
$359$	20.3672	1.07494	0.537469	−	0.843284i	$-0.319381\pi$
$359$	20.3672	1.07494	0.537469	+	0.843284i	$0.319381\pi$
$360$	−17.3575	−0.914821
$361$	4.74457	0.249714
$362$	29.6447	1.55809
$363$	−7.34832	−0.385687
$364$	−0.179013	−0.00938281
$365$	21.7563	1.13877
$366$	−22.5339	−1.17787
$367$	2.29419	0.119756	0.0598780	−	0.998206i	$-0.480929\pi$
$367$	2.29419	0.119756	0.0598780	+	0.998206i	$0.480929\pi$
$368$	−38.3496	−1.99911
$369$	−0.286322	−0.0149053
$370$	−19.6267	−1.02034
$371$	−6.41217	−0.332903
$372$	2.76896	0.143564
$373$	4.97209	0.257445	0.128723	−	0.991681i	$-0.458912\pi$
$373$	4.97209	0.257445	0.128723	+	0.991681i	$0.458912\pi$
$374$	13.4556	0.695772
$375$	26.7136	1.37948
$376$	22.5184	1.16130
$377$	10.3076	0.530868
$378$	−0.848235	−0.0436285
$379$	20.6330	1.05985	0.529924	−	0.848045i	$-0.322220\pi$
$379$	20.6330	1.05985	0.529924	+	0.848045i	$0.322220\pi$
$380$	−1.28981	−0.0661658
$381$	−19.8909	−1.01904
$382$	−19.3968	−0.992428
$383$	−19.9239	−1.01806	−0.509032	−	0.860747i	$-0.669997\pi$
$383$	−19.9239	−1.01806	−0.509032	+	0.860747i	$0.669997\pi$
$384$	−29.4211	−1.50139
$385$	8.08271	0.411933
$386$	−31.9660	−1.62703
$387$	1.84328	0.0936993
$388$	−1.35413	−0.0687455
$389$	−24.4179	−1.23804	−0.619018	−	0.785377i	$-0.712469\pi$
$389$	−24.4179	−1.23804	−0.619018	+	0.785377i	$0.712469\pi$
$390$	9.48985	0.480537
$391$	−29.7942	−1.50676
$392$	−14.7501	−0.744990
$393$	37.1794	1.87545
$394$	−18.5815	−0.936121
$395$	12.5366	0.630787
$396$	0.929970	0.0467327
$397$	−13.0744	−0.656185	−0.328092	−	0.944646i	$-0.606406\pi$
$397$	−13.0744	−0.656185	−0.328092	+	0.944646i	$0.606406\pi$
$398$	9.37015	0.469683
$399$	−14.9292	−0.747397
$400$	−0.360176	−0.0180088
$401$	33.3744	1.66664	0.833318	−	0.552794i	$-0.186438\pi$
$401$	33.3744	1.66664	0.833318	+	0.552794i	$0.186438\pi$
$402$	−5.94801	−0.296660
$403$	11.7430	0.584958
$404$	−1.46428	−0.0728504
$405$	21.5012	1.06840
$406$	15.8895	0.788585
$407$	−16.8659	−0.836010
$408$	−21.6533	−1.07200
$409$	9.32317	0.461001	0.230501	−	0.973072i	$-0.425964\pi$
$409$	9.32317	0.461001	0.230501	+	0.973072i	$0.425964\pi$
$410$	−0.334386	−0.0165141
$411$	−39.1704	−1.93213
$412$	1.56365	0.0770356
$413$	7.19467	0.354026
$414$	−37.1460	−1.82563
$415$	−14.1024	−0.692262
$416$	0.795665	0.0390107
$417$	−10.5745	−0.517836
$418$	−19.9941	−0.977942
$419$	−9.39551	−0.459001	−0.229500	−	0.973309i	$-0.573709\pi$
$419$	−9.39551	−0.459001	−0.229500	+	0.973309i	$0.573709\pi$
$420$	0.810958	0.0395707
$421$	−28.8517	−1.40614	−0.703072	−	0.711118i	$-0.748189\pi$
$421$	−28.8517	−1.40614	−0.703072	+	0.711118i	$0.748189\pi$
$422$	−5.39583	−0.262665
$423$	23.0962	1.12298
$424$	13.8194	0.671131
$425$	−0.279824	−0.0135735
$426$	−7.10468	−0.344223
$427$	−8.16651	−0.395205
$428$	0.941375	0.0455031
$429$	8.15494	0.393724
$430$	2.15271	0.103813
$431$	−22.2344	−1.07099	−0.535497	−	0.844537i	$-0.679876\pi$
$431$	−22.2344	−1.07099	−0.535497	+	0.844537i	$0.679876\pi$
$432$	1.93577	0.0931346
$433$	−28.4182	−1.36569	−0.682846	−	0.730562i	$-0.739258\pi$
$433$	−28.4182	−1.36569	−0.682846	+	0.730562i	$0.739258\pi$
$434$	18.1022	0.868933
$435$	−46.6952	−2.23887
$436$	−1.76021	−0.0842988
$437$	44.2721	2.11782
$438$	33.8378	1.61683
$439$	−23.5027	−1.12172	−0.560862	−	0.827910i	$-0.689530\pi$
$439$	−23.5027	−1.12172	−0.560862	+	0.827910i	$0.689530\pi$
$440$	−17.4198	−0.830454
$441$	−15.1285	−0.720405
$442$	5.72539	0.272329
$443$	−6.64797	−0.315855	−0.157927	−	0.987451i	$-0.550481\pi$
$443$	−6.64797	−0.315855	−0.157927	+	0.987451i	$0.550481\pi$
$444$	−1.69220	−0.0803080
$445$	−35.9455	−1.70398
$446$	−2.29022	−0.108445
$447$	2.48987	0.117767
$448$	−9.50396	−0.449020
$449$	8.06570	0.380644	0.190322	−	0.981722i	$-0.439047\pi$
$449$	8.06570	0.380644	0.190322	+	0.981722i	$0.439047\pi$
$450$	−0.348872	−0.0164460
$451$	−0.287349	−0.0135307
$452$	−0.234239	−0.0110177
$453$	45.3038	2.12856
$454$	−1.55732	−0.0730884
$455$	3.43922	0.161233
$456$	32.1753	1.50675
$457$	22.7762	1.06543	0.532713	−	0.846296i	$-0.321173\pi$
$457$	22.7762	1.06543	0.532713	+	0.846296i	$0.321173\pi$
$458$	−6.52004	−0.304661
$459$	1.50392	0.0701968
$460$	−2.40487	−0.112128
$461$	38.7077	1.80280	0.901398	−	0.432992i	$-0.142542\pi$
$461$	38.7077	1.80280	0.901398	+	0.432992i	$0.142542\pi$
$462$	12.5711	0.584862
$463$	16.7000	0.776113	0.388056	−	0.921636i	$-0.373147\pi$
$463$	16.7000	0.776113	0.388056	+	0.921636i	$0.373147\pi$
$464$	−36.2617	−1.68341
$465$	−53.1977	−2.46698
$466$	6.44443	0.298532
$467$	−9.30878	−0.430759	−0.215380	−	0.976530i	$-0.569099\pi$
$467$	−9.30878	−0.430759	−0.215380	+	0.976530i	$0.569099\pi$
$468$	0.395705	0.0182915
$469$	−2.15562	−0.0995372
$470$	26.9733	1.24419
$471$	−17.6190	−0.811839
$472$	−15.5059	−0.713715
$473$	1.84989	0.0850582
$474$	19.4984	0.895591
$475$	0.415799	0.0190782
$476$	0.489265	0.0224254
$477$	14.1740	0.648984
$478$	−16.8628	−0.771286
$479$	−6.66857	−0.304695	−0.152347	−	0.988327i	$-0.548683\pi$
$479$	−6.66857	−0.304695	−0.152347	+	0.988327i	$0.548683\pi$
$480$	−3.60450	−0.164522
$481$	−7.17648	−0.327219
$482$	18.7734	0.855106
$483$	−27.8358	−1.26657
$484$	−0.357844	−0.0162656
$485$	26.0157	1.18131
$486$	31.4390	1.42610
$487$	10.6950	0.484636	0.242318	−	0.970197i	$-0.422092\pi$
$487$	10.6950	0.484636	0.242318	+	0.970197i	$0.422092\pi$
$488$	17.6004	0.796731
$489$	−20.7236	−0.937153
$490$	−17.6681	−0.798163
$491$	16.1788	0.730137	0.365068	−	0.930981i	$-0.381046\pi$
$491$	16.1788	0.730137	0.365068	+	0.930981i	$0.381046\pi$
$492$	−0.0288304	−0.00129978
$493$	−28.1721	−1.26881
$494$	−8.50754	−0.382772
$495$	−17.8667	−0.803049
$496$	−41.3112	−1.85493
$497$	−2.57481	−0.115496
$498$	−21.9337	−0.982873
$499$	−23.1743	−1.03742	−0.518712	−	0.854949i	$-0.673588\pi$
$499$	−23.1743	−1.03742	−0.518712	+	0.854949i	$0.673588\pi$
$500$	1.30088	0.0581772
$501$	5.60335	0.250339
$502$	29.2679	1.30629
$503$	−31.5186	−1.40534	−0.702672	−	0.711514i	$-0.748010\pi$
$503$	−31.5186	−1.40534	−0.702672	+	0.711514i	$0.748010\pi$
$504$	−9.78374	−0.435802
$505$	28.1319	1.25185
$506$	−37.2792	−1.65726
$507$	−27.8645	−1.23750
$508$	−0.968632	−0.0429761
$509$	33.5085	1.48524	0.742618	−	0.669715i	$-0.233584\pi$
$509$	33.5085	1.48524	0.742618	+	0.669715i	$0.233584\pi$
$510$	−25.9370	−1.14851
$511$	12.2631	0.542489
$512$	20.3271	0.898341
$513$	−2.23471	−0.0986650
$514$	−5.51895	−0.243430
$515$	−30.0411	−1.32377
$516$	0.185604	0.00817078
$517$	23.1791	1.01941
$518$	−11.0628	−0.486072
$519$	−63.0656	−2.76827
$520$	−7.41216	−0.325045
$521$	−22.7960	−0.998712	−0.499356	−	0.866397i	$-0.666430\pi$
$521$	−22.7960	−0.998712	−0.499356	+	0.866397i	$0.666430\pi$
$522$	−35.1236	−1.53732
$523$	29.8928	1.30712	0.653560	−	0.756874i	$-0.273275\pi$
$523$	29.8928	1.30712	0.653560	+	0.756874i	$0.273275\pi$
$524$	1.81054	0.0790938
$525$	−0.261431	−0.0114098
$526$	31.9701	1.39396
$527$	−32.0951	−1.39808
$528$	−28.6887	−1.24852
$529$	59.5460	2.58896
$530$	16.5534	0.719032
$531$	−15.9037	−0.690162
$532$	−0.727014	−0.0315201
$533$	−0.122268	−0.00529600
$534$	−55.9066	−2.41931
$535$	−18.0858	−0.781919
$536$	4.64576	0.200666
$537$	−41.2018	−1.77799
$538$	−9.27776	−0.399992
$539$	−15.1828	−0.653968
$540$	0.121390	0.00522380
$541$	36.5305	1.57057	0.785283	−	0.619136i	$-0.212517\pi$
$541$	36.5305	1.57057	0.785283	+	0.619136i	$0.212517\pi$
$542$	13.5229	0.580858
$543$	−49.1050	−2.10730
$544$	−2.17466	−0.0932378
$545$	33.8174	1.44858
$546$	5.34906	0.228918
$547$	−21.9611	−0.938987	−0.469493	−	0.882936i	$-0.655563\pi$
$547$	−21.9611	−0.938987	−0.469493	+	0.882936i	$0.655563\pi$
$548$	−1.90749	−0.0814841
$549$	18.0520	0.770439
$550$	−0.350123	−0.0149293
$551$	41.8617	1.78337
$552$	59.9913	2.55340
$553$	7.06641	0.300494
$554$	2.70849	0.115073
$555$	32.5107	1.38000
$556$	−0.514951	−0.0218388
$557$	0.927328	0.0392922	0.0196461	−	0.999807i	$-0.493746\pi$
$557$	0.927328	0.0392922	0.0196461	+	0.999807i	$0.493746\pi$
$558$	−40.0147	−1.69396
$559$	0.787135	0.0332923
$560$	−12.0990	−0.511276
$561$	−22.2886	−0.941023
$562$	−26.9370	−1.13627
$563$	−13.4615	−0.567334	−0.283667	−	0.958923i	$-0.591551\pi$
$563$	−13.4615	−0.567334	−0.283667	+	0.958923i	$0.591551\pi$
$564$	2.32561	0.0979260
$565$	4.50024	0.189327
$566$	−8.88836	−0.373606
$567$	12.1194	0.508965
$568$	5.54919	0.232839
$569$	−17.9315	−0.751727	−0.375863	−	0.926675i	$-0.622654\pi$
$569$	−17.9315	−0.751727	−0.375863	+	0.926675i	$0.622654\pi$
$570$	38.5406	1.61429
$571$	10.3154	0.431688	0.215844	−	0.976428i	$-0.430750\pi$
$571$	10.3154	0.431688	0.215844	+	0.976428i	$0.430750\pi$
$572$	0.397124	0.0166046
$573$	32.1299	1.34225
$574$	−0.188480	−0.00786701
$575$	0.775264	0.0323307
$576$	21.0084	0.875349
$577$	−40.7762	−1.69754	−0.848768	−	0.528766i	$-0.822655\pi$
$577$	−40.7762	−1.69754	−0.848768	+	0.528766i	$0.822655\pi$
$578$	9.08878	0.378043
$579$	52.9502	2.20053
$580$	−2.27393	−0.0944200
$581$	−7.94900	−0.329780
$582$	40.4626	1.67723
$583$	14.2249	0.589133
$584$	−26.4294	−1.09366
$585$	−7.60234	−0.314318
$586$	24.6807	1.01955
$587$	−23.5853	−0.973470	−0.486735	−	0.873550i	$-0.661812\pi$
$587$	−23.5853	−0.973470	−0.486735	+	0.873550i	$0.661812\pi$
$588$	−1.52333	−0.0628209
$589$	47.6911	1.96508
$590$	−18.5734	−0.764656
$591$	30.7793	1.26609
$592$	25.2465	1.03763
$593$	8.37847	0.344062	0.172031	−	0.985092i	$-0.444967\pi$
$593$	8.37847	0.344062	0.172031	+	0.985092i	$0.444967\pi$
$594$	1.88174	0.0772086
$595$	−9.39984	−0.385356
$596$	0.121250	0.00496661
$597$	−15.5212	−0.635241
$598$	−15.8624	−0.648663
$599$	37.5552	1.53446	0.767232	−	0.641369i	$-0.221633\pi$
$599$	37.5552	1.53446	0.767232	+	0.641369i	$0.221633\pi$
$600$	0.563433	0.0230020
$601$	41.2307	1.68184	0.840918	−	0.541162i	$-0.182016\pi$
$601$	41.2307	1.68184	0.840918	+	0.541162i	$0.182016\pi$
$602$	1.21340	0.0494544
$603$	4.76497	0.194044
$604$	2.20618	0.0897680
$605$	6.87495	0.279506
$606$	43.7539	1.77738
$607$	−30.0555	−1.21992	−0.609958	−	0.792434i	$-0.708814\pi$
$607$	−30.0555	−1.21992	−0.609958	+	0.792434i	$0.708814\pi$
$608$	3.23139	0.131050
$609$	−26.3203	−1.06655
$610$	21.0823	0.853598
$611$	9.86276	0.399005
$612$	−1.08151	−0.0437176
$613$	−23.1151	−0.933608	−0.466804	−	0.884361i	$-0.654595\pi$
$613$	−23.1151	−0.933608	−0.466804	+	0.884361i	$0.654595\pi$
$614$	−15.1988	−0.613373
$615$	0.553894	0.0223352
$616$	−9.81883	−0.395612
$617$	20.3152	0.817858	0.408929	−	0.912566i	$-0.365902\pi$
$617$	20.3152	0.817858	0.408929	+	0.912566i	$0.365902\pi$
$618$	−46.7233	−1.87949
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−2.59059	−0.104040
$621$	−4.16666	−0.167202
$622$	−37.2550	−1.49379
$623$	−20.2611	−0.811743
$624$	−12.2071	−0.488676
$625$	−25.4194	−1.01677
$626$	17.4627	0.697951
$627$	33.1192	1.32265
$628$	−0.857997	−0.0342378
$629$	19.6143	0.782073
$630$	−11.7193	−0.466908
$631$	12.3255	0.490672	0.245336	−	0.969438i	$-0.421102\pi$
$631$	12.3255	0.490672	0.245336	+	0.969438i	$0.421102\pi$
$632$	−15.2294	−0.605795
$633$	8.93793	0.355251
$634$	−13.4157	−0.532807
$635$	18.6095	0.738496
$636$	1.42722	0.0565928
$637$	−6.46032	−0.255967
$638$	−35.2496	−1.39554
$639$	5.69158	0.225155
$640$	27.5259	1.08806
$641$	−8.05058	−0.317979	−0.158989	−	0.987280i	$-0.550824\pi$
$641$	−8.05058	−0.317979	−0.158989	+	0.987280i	$0.550824\pi$
$642$	−28.1291	−1.11017
$643$	−3.32324	−0.131056	−0.0655279	−	0.997851i	$-0.520873\pi$
$643$	−3.32324	−0.131056	−0.0655279	+	0.997851i	$0.520873\pi$
$644$	−1.35553	−0.0534153
$645$	−3.56586	−0.140406
$646$	23.2522	0.914847
$647$	12.5973	0.495250	0.247625	−	0.968856i	$-0.420350\pi$
$647$	12.5973	0.495250	0.247625	+	0.968856i	$0.420350\pi$
$648$	−26.1195	−1.02607
$649$	−15.9608	−0.626514
$650$	−0.148978	−0.00584341
$651$	−29.9854	−1.17522
$652$	−1.00918	−0.0395227
$653$	29.3506	1.14858	0.574289	−	0.818653i	$-0.305279\pi$
$653$	29.3506	1.14858	0.574289	+	0.818653i	$0.305279\pi$
$654$	52.5967	2.05669
$655$	−34.7844	−1.35914
$656$	0.430132	0.0167939
$657$	−27.1075	−1.05756
$658$	15.2038	0.592706
$659$	6.74528	0.262759	0.131379	−	0.991332i	$-0.458059\pi$
$659$	6.74528	0.262759	0.131379	+	0.991332i	$0.458059\pi$
$660$	−1.79904	−0.0700276
$661$	−14.0612	−0.546918	−0.273459	−	0.961884i	$-0.588168\pi$
$661$	−14.0612	−0.546918	−0.273459	+	0.961884i	$0.588168\pi$
$662$	−23.7421	−0.922764
$663$	−9.48384	−0.368322
$664$	17.1316	0.664834
$665$	13.9675	0.541637
$666$	24.4542	0.947580
$667$	78.0518	3.02218
$668$	0.272868	0.0105576
$669$	3.79364	0.146671
$670$	5.56485	0.214989
$671$	18.1167	0.699388
$672$	−2.03172	−0.0783752
$673$	−34.2462	−1.32009	−0.660047	−	0.751224i	$-0.729464\pi$
$673$	−34.2462	−1.32009	−0.660047	+	0.751224i	$0.729464\pi$
$674$	−49.0513	−1.88938
$675$	−0.0391328	−0.00150622
$676$	−1.35693	−0.0521894
$677$	−15.8548	−0.609349	−0.304674	−	0.952457i	$-0.598548\pi$
$677$	−15.8548	−0.609349	−0.304674	+	0.952457i	$0.598548\pi$
$678$	6.99929	0.268806
$679$	14.6641	0.562755
$680$	20.2584	0.776875
$681$	2.57962	0.0988512
$682$	−40.1582	−1.53774
$683$	−18.6499	−0.713617	−0.356808	−	0.934178i	$-0.616135\pi$
$683$	−18.6499	−0.713617	−0.356808	+	0.934178i	$0.616135\pi$
$684$	1.60706	0.0614473
$685$	36.6471	1.40021
$686$	−22.9060	−0.874554
$687$	10.8001	0.412051
$688$	−2.76911	−0.105571
$689$	6.05272	0.230590
$690$	71.8596	2.73565
$691$	11.6482	0.443118	0.221559	−	0.975147i	$-0.428885\pi$
$691$	11.6482	0.443118	0.221559	+	0.975147i	$0.428885\pi$
$692$	−3.07113	−0.116747
$693$	−10.0708	−0.382557
$694$	16.9058	0.641736
$695$	9.89332	0.375275
$696$	56.7251	2.15016
$697$	0.334174	0.0126578
$698$	−41.4290	−1.56811
$699$	−10.6749	−0.403761
$700$	−0.0127310	−0.000481186 0
$701$	−13.3080	−0.502635	−0.251318	−	0.967905i	$-0.580864\pi$
$701$	−13.3080	−0.502635	−0.251318	+	0.967905i	$0.580864\pi$
$702$	0.800685	0.0302199
$703$	−29.1455	−1.09924
$704$	21.0837	0.794623
$705$	−44.6800	−1.68275
$706$	35.9831	1.35424
$707$	15.8568	0.596358
$708$	−1.60138	−0.0601836
$709$	−24.9024	−0.935229	−0.467615	−	0.883932i	$-0.654886\pi$
$709$	−24.9024	−0.935229	−0.467615	+	0.883932i	$0.654886\pi$
$710$	6.64701	0.249458
$711$	−15.6202	−0.585803
$712$	43.6665	1.63647
$713$	88.9207	3.33011
$714$	−14.6197	−0.547128
$715$	−7.62961	−0.285331
$716$	−2.00642	−0.0749834
$717$	27.9324	1.04316
$718$	−29.6367	−1.10603
$719$	−46.5236	−1.73504	−0.867519	−	0.497404i	$-0.834287\pi$
$719$	−46.5236	−1.73504	−0.867519	+	0.497404i	$0.834287\pi$
$720$	26.7447	0.996716
$721$	−16.9330	−0.630618
$722$	−6.90392	−0.256937
$723$	−31.0973	−1.15652
$724$	−2.39128	−0.0888714
$725$	0.733055	0.0272250
$726$	10.6927	0.396843
$727$	−15.9297	−0.590801	−0.295401	−	0.955373i	$-0.595453\pi$
$727$	−15.9297	−0.590801	−0.295401	+	0.955373i	$0.595453\pi$
$728$	−4.17794	−0.154845
$729$	−23.4735	−0.869389
$730$	−31.6580	−1.17171
$731$	−2.15135	−0.0795704
$732$	1.81770	0.0671840
$733$	3.17341	0.117212	0.0586062	−	0.998281i	$-0.481334\pi$
$733$	3.17341	0.117212	0.0586062	+	0.998281i	$0.481334\pi$
$734$	−3.33833	−0.123220
$735$	29.2664	1.07951
$736$	6.02498	0.222084
$737$	4.78206	0.176149
$738$	0.416633	0.0153365
$739$	12.2055	0.448986	0.224493	−	0.974476i	$-0.427927\pi$
$739$	12.2055	0.448986	0.224493	+	0.974476i	$0.427927\pi$
$740$	1.58319	0.0581991
$741$	14.0923	0.517695
$742$	9.33048	0.342533
$743$	−4.89107	−0.179436	−0.0897181	−	0.995967i	$-0.528597\pi$
$743$	−4.89107	−0.179436	−0.0897181	+	0.995967i	$0.528597\pi$
$744$	64.6242	2.36924
$745$	−2.32948	−0.0853455
$746$	−7.23500	−0.264892
$747$	17.5711	0.642895
$748$	−1.08539	−0.0396859
$749$	−10.1943	−0.372491
$750$	−38.8715	−1.41939
$751$	−6.73617	−0.245806	−0.122903	−	0.992419i	$-0.539220\pi$
$751$	−6.73617	−0.245806	−0.122903	+	0.992419i	$0.539220\pi$
$752$	−34.6967	−1.26526
$753$	−48.4808	−1.76674
$754$	−14.9988	−0.546224
$755$	−42.3854	−1.54256
$756$	0.0684228	0.00248851
$757$	−38.5115	−1.39972	−0.699862	−	0.714278i	$-0.746755\pi$
$757$	−38.5115	−1.39972	−0.699862	+	0.714278i	$0.746755\pi$
$758$	−30.0236	−1.09050
$759$	61.7513	2.24143
$760$	−30.1026	−1.09194
$761$	14.8273	0.537490	0.268745	−	0.963211i	$-0.413391\pi$
$761$	14.8273	0.537490	0.268745	+	0.963211i	$0.413391\pi$
$762$	28.9436	1.04852
$763$	19.0616	0.690075
$764$	1.56464	0.0566068
$765$	20.7782	0.751238
$766$	28.9917	1.04751
$767$	−6.79135	−0.245221
$768$	6.76712	0.244187
$769$	0.228352	0.00823460	0.00411730	−	0.999992i	$-0.498689\pi$
$769$	0.228352	0.00823460	0.00411730	+	0.999992i	$0.498689\pi$
$770$	−11.7613	−0.423848
$771$	9.14188	0.329237
$772$	2.57853	0.0928035
$773$	−25.7779	−0.927167	−0.463584	−	0.886053i	$-0.653437\pi$
$773$	−25.7779	−0.927167	−0.463584	+	0.886053i	$0.653437\pi$
$774$	−2.68220	−0.0964096
$775$	0.835134	0.0299989
$776$	−31.6038	−1.13451
$777$	18.3250	0.657406
$778$	35.5310	1.27385
$779$	−0.496560	−0.0177911
$780$	−0.765498	−0.0274092
$781$	5.71199	0.204391
$782$	43.3542	1.55034
$783$	−3.93981	−0.140797
$784$	22.7271	0.811682
$785$	16.4840	0.588338
$786$	−54.1005	−1.92970
$787$	7.22305	0.257474	0.128737	−	0.991679i	$-0.458908\pi$
$787$	7.22305	0.257474	0.128737	+	0.991679i	$0.458908\pi$
$788$	1.49887	0.0533951
$789$	−52.9570	−1.88532
$790$	−18.2423	−0.649033
$791$	2.53661	0.0901915
$792$	21.7044	0.771232
$793$	7.70872	0.273745
$794$	19.0248	0.675165
$795$	−27.4199	−0.972483
$796$	−0.755842	−0.0267901
$797$	−43.2130	−1.53068	−0.765341	−	0.643625i	$-0.777430\pi$
$797$	−43.2130	−1.53068	−0.765341	+	0.643625i	$0.777430\pi$
$798$	21.7238	0.769016
$799$	−26.9563	−0.953644
$800$	0.0565861	0.00200062
$801$	44.7869	1.58247
$802$	−48.5637	−1.71484
$803$	−27.2047	−0.960034
$804$	0.479796	0.0169211
$805$	26.0426	0.917882
$806$	−17.0874	−0.601879
$807$	15.3682	0.540985
$808$	−34.1745	−1.20225
$809$	21.2090	0.745668	0.372834	−	0.927898i	$-0.378386\pi$
$809$	21.2090	0.745668	0.372834	+	0.927898i	$0.378386\pi$
$810$	−31.2868	−1.09931
$811$	21.3226	0.748738	0.374369	−	0.927280i	$-0.377859\pi$
$811$	21.3226	0.748738	0.374369	+	0.927280i	$0.377859\pi$
$812$	−1.28173	−0.0449798
$813$	−22.4000	−0.785604
$814$	24.5419	0.860193
$815$	19.3886	0.679153
$816$	33.3637	1.16796
$817$	3.19675	0.111840
$818$	−13.5663	−0.474336
$819$	−4.28514	−0.149735
$820$	0.0269732	0.000941945 0
$821$	2.54292	0.0887486	0.0443743	−	0.999015i	$-0.485871\pi$
$821$	2.54292	0.0887486	0.0443743	+	0.999015i	$0.485871\pi$
$822$	56.9976	1.98802
$823$	−56.7854	−1.97942	−0.989708	−	0.143100i	$-0.954293\pi$
$823$	−56.7854	−1.97942	−0.989708	+	0.143100i	$0.954293\pi$
$824$	36.4938	1.27132
$825$	0.579962	0.0201917
$826$	−10.4691	−0.364267
$827$	−41.8297	−1.45456	−0.727281	−	0.686340i	$-0.759216\pi$
$827$	−41.8297	−1.45456	−0.727281	+	0.686340i	$0.759216\pi$
$828$	2.99638	0.104131
$829$	−34.0210	−1.18160	−0.590800	−	0.806818i	$-0.701188\pi$
$829$	−34.0210	−1.18160	−0.590800	+	0.806818i	$0.701188\pi$
$830$	20.5208	0.712286
$831$	−4.48649	−0.155634
$832$	8.97119	0.311020
$833$	17.6569	0.611776
$834$	15.3872	0.532815
$835$	−5.24239	−0.181420
$836$	1.61282	0.0557805
$837$	−4.48843	−0.155143
$838$	13.6716	0.472278
$839$	−29.1800	−1.00741	−0.503703	−	0.863877i	$-0.668029\pi$
$839$	−29.1800	−1.00741	−0.503703	+	0.863877i	$0.668029\pi$
$840$	18.9268	0.653037
$841$	44.8023	1.54491
$842$	41.9827	1.44682
$843$	44.6198	1.53679
$844$	0.435254	0.0149821
$845$	26.0695	0.896817
$846$	−33.6078	−1.15546
$847$	3.87514	0.133151
$848$	−21.2932	−0.731211
$849$	14.7231	0.505297
$850$	0.407178	0.0139661
$851$	−54.3421	−1.86282
$852$	0.573098	0.0196340
$853$	−28.9232	−0.990313	−0.495156	−	0.868804i	$-0.664889\pi$
$853$	−28.9232	−0.990313	−0.495156	+	0.868804i	$0.664889\pi$
$854$	11.8833	0.406637
$855$	−30.8750	−1.05590
$856$	21.9706	0.750939
$857$	11.0508	0.377489	0.188744	−	0.982026i	$-0.439558\pi$
$857$	11.0508	0.377489	0.188744	+	0.982026i	$0.439558\pi$
$858$	−11.8664	−0.405113
$859$	2.24428	0.0765739	0.0382870	−	0.999267i	$-0.487810\pi$
$859$	2.24428	0.0765739	0.0382870	+	0.999267i	$0.487810\pi$
$860$	−0.173648	−0.00592135
$861$	0.312208	0.0106400
$862$	32.3538	1.10197
$863$	−48.1246	−1.63818	−0.819090	−	0.573665i	$-0.805521\pi$
$863$	−48.1246	−1.63818	−0.819090	+	0.573665i	$0.805521\pi$
$864$	−0.304122	−0.0103464
$865$	59.0030	2.00616
$866$	41.3519	1.40520
$867$	−15.0551	−0.511299
$868$	−1.46021	−0.0495628
$869$	−15.6762	−0.531780
$870$	67.9472	2.30363
$871$	2.03478	0.0689458
$872$	−41.0812	−1.39119
$873$	−32.4147	−1.09707
$874$	−64.4213	−2.17908
$875$	−14.0874	−0.476241
$876$	−2.72952	−0.0922219
$877$	−34.8726	−1.17756	−0.588782	−	0.808292i	$-0.700392\pi$
$877$	−34.8726	−1.17756	−0.588782	+	0.808292i	$0.700392\pi$
$878$	34.1993	1.15417
$879$	−40.8825	−1.37893
$880$	26.8406	0.904797
$881$	−40.8075	−1.37484	−0.687420	−	0.726261i	$-0.741257\pi$
$881$	−40.8075	−1.37484	−0.687420	+	0.726261i	$0.741257\pi$
$882$	22.0138	0.741244
$883$	18.5720	0.624998	0.312499	−	0.949918i	$-0.398834\pi$
$883$	18.5720	0.624998	0.312499	+	0.949918i	$0.398834\pi$
$884$	−0.461838	−0.0155333
$885$	30.7660	1.03419
$886$	9.67361	0.324991
$887$	−8.15171	−0.273708	−0.136854	−	0.990591i	$-0.543699\pi$
$887$	−8.15171	−0.273708	−0.136854	+	0.990591i	$0.543699\pi$
$888$	−39.4938	−1.32533
$889$	10.4894	0.351805
$890$	52.3051	1.75327
$891$	−26.8858	−0.900707
$892$	0.184740	0.00618557
$893$	40.0551	1.34039
$894$	−3.62307	−0.121174
$895$	38.5476	1.28850
$896$	15.5152	0.518328
$897$	26.2754	0.877309
$898$	−11.7366	−0.391654
$899$	84.0794	2.80421
$900$	0.0281417	0.000938056 0
$901$	−16.5429	−0.551124
$902$	0.418127	0.0139221
$903$	−2.00994	−0.0668865
$904$	−5.46687	−0.181825
$905$	45.9417	1.52715
$906$	−65.9225	−2.19013
$907$	−32.6381	−1.08373	−0.541866	−	0.840465i	$-0.682282\pi$
$907$	−32.6381	−1.08373	−0.541866	+	0.840465i	$0.682282\pi$
$908$	0.125621	0.00416887
$909$	−35.0513	−1.16258
$910$	−5.00448	−0.165897
$911$	−11.9018	−0.394324	−0.197162	−	0.980371i	$-0.563173\pi$
$911$	−11.9018	−0.394324	−0.197162	+	0.980371i	$0.563173\pi$
$912$	−49.5762	−1.64163
$913$	17.6342	0.583606
$914$	−33.1421	−1.09624
$915$	−34.9218	−1.15448
$916$	0.525938	0.0173775
$917$	−19.6066	−0.647466
$918$	−2.18838	−0.0722273
$919$	−15.2268	−0.502286	−0.251143	−	0.967950i	$-0.580806\pi$
$919$	−15.2268	−0.502286	−0.251143	+	0.967950i	$0.580806\pi$
$920$	−56.1268	−1.85044
$921$	25.1761	0.829579
$922$	−56.3243	−1.85494
$923$	2.43047	0.0799999
$924$	−1.01405	−0.0333598
$925$	−0.510376	−0.0167811
$926$	−24.3004	−0.798562
$927$	37.4301	1.22937
$928$	5.69695	0.187012
$929$	−47.7928	−1.56803	−0.784015	−	0.620742i	$-0.786832\pi$
$929$	−47.7928	−1.56803	−0.784015	+	0.620742i	$0.786832\pi$
$930$	77.4090	2.53834
$931$	−26.2369	−0.859881
$932$	−0.519839	−0.0170279
$933$	61.7111	2.02033
$934$	13.5454	0.443219
$935$	20.8527	0.681958
$936$	9.23528	0.301865
$937$	−9.48310	−0.309799	−0.154900	−	0.987930i	$-0.549505\pi$
$937$	−9.48310	−0.309799	−0.154900	+	0.987930i	$0.549505\pi$
$938$	3.13669	0.102416
$939$	−28.9262	−0.943970
$940$	−2.17580	−0.0709668
$941$	−4.95823	−0.161634	−0.0808168	−	0.996729i	$-0.525753\pi$
$941$	−4.95823	−0.161634	−0.0808168	+	0.996729i	$0.525753\pi$
$942$	25.6377	0.835323
$943$	−0.925843	−0.0301496
$944$	23.8917	0.777607
$945$	−1.31455	−0.0427623
$946$	−2.69182	−0.0875186
$947$	15.6500	0.508558	0.254279	−	0.967131i	$-0.418162\pi$
$947$	15.6500	0.508558	0.254279	+	0.967131i	$0.418162\pi$
$948$	−1.57284	−0.0510833
$949$	−11.5757	−0.375763
$950$	−0.605038	−0.0196300
$951$	22.2225	0.720615
$952$	11.4189	0.370088
$953$	−11.1551	−0.361351	−0.180675	−	0.983543i	$-0.557828\pi$
$953$	−11.1551	−0.361351	−0.180675	+	0.983543i	$0.557828\pi$
$954$	−20.6249	−0.667756
$955$	−30.0602	−0.972724
$956$	1.36024	0.0439932
$957$	58.3893	1.88746
$958$	9.70358	0.313508
$959$	20.6565	0.667033
$960$	−40.6411	−1.31168
$961$	64.7877	2.08993
$962$	10.4426	0.336684
$963$	22.5343	0.726158
$964$	−1.51436	−0.0487741
$965$	−49.5392	−1.59472
$966$	40.5044	1.30321
$967$	0.462563	0.0148750	0.00743752	−	0.999972i	$-0.497633\pi$
$967$	0.462563	0.0148750	0.00743752	+	0.999972i	$0.497633\pi$
$968$	−8.35165	−0.268432
$969$	−38.5162	−1.23732
$970$	−37.8561	−1.21548
$971$	−2.43944	−0.0782854	−0.0391427	−	0.999234i	$-0.512463\pi$
$971$	−2.43944	−0.0782854	−0.0391427	+	0.999234i	$0.512463\pi$
$972$	−2.53603	−0.0813431
$973$	5.57648	0.178774
$974$	−15.5625	−0.498655
$975$	0.246776	0.00790314
$976$	−27.1189	−0.868056
$977$	−47.8043	−1.52939	−0.764697	−	0.644390i	$-0.777111\pi$
$977$	−47.8043	−1.52939	−0.764697	+	0.644390i	$0.777111\pi$
$978$	30.1553	0.964261
$979$	44.9475	1.43653
$980$	1.42519	0.0455262
$981$	−42.1353	−1.34528
$982$	−23.5420	−0.751257
$983$	−20.6062	−0.657236	−0.328618	−	0.944463i	$-0.606583\pi$
$983$	−20.6062	−0.657236	−0.328618	+	0.944463i	$0.606583\pi$
$984$	−0.672868	−0.0214502
$985$	−28.7966	−0.917535
$986$	40.9938	1.30551
$987$	−25.1844	−0.801628
$988$	0.686259	0.0218328
$989$	5.96039	0.189529
$990$	25.9982	0.826278
$991$	−35.4600	−1.12642	−0.563212	−	0.826312i	$-0.690435\pi$
$991$	−35.4600	−1.12642	−0.563212	+	0.826312i	$0.690435\pi$
$992$	6.49027	0.206066
$993$	39.3277	1.24803
$994$	3.74666	0.118837
$995$	14.5214	0.460358
$996$	1.76928	0.0560618
$997$	59.7846	1.89340	0.946698	−	0.322123i	$-0.104396\pi$
$997$	59.7846	1.89340	0.946698	+	0.322123i	$0.104396\pi$
$998$	33.7214	1.06743
$999$	2.74302	0.0867852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.7	✓	30
3.2	odd	2		5571.2.a.g.1.24		30
4.3	odd	2		9904.2.a.n.1.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.7	✓	30	1.1	even	1	trivial
5571.2.a.g.1.24		30	3.2	odd	2
9904.2.a.n.1.5		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +O(q^{10})\)	\(q-1.45512 q^{2} +2.41034 q^{3} +0.117377 q^{4} -2.25507 q^{5} -3.50733 q^{6} -1.27109 q^{7} +2.73944 q^{8} +2.80973 q^{9} +3.28140 q^{10} +2.81981 q^{11} +0.282919 q^{12} +1.19984 q^{13} +1.84959 q^{14} -5.43548 q^{15} -4.22098 q^{16} -3.27932 q^{17} -4.08850 q^{18} +4.87284 q^{19} -0.264693 q^{20} -3.06376 q^{21} -4.10317 q^{22} +9.08548 q^{23} +6.60299 q^{24} +0.0853300 q^{25} -1.74591 q^{26} -0.458606 q^{27} -0.149197 q^{28} +8.59083 q^{29} +7.90928 q^{30} +9.78712 q^{31} +0.663144 q^{32} +6.79670 q^{33} +4.77181 q^{34} +2.86640 q^{35} +0.329799 q^{36} -5.98121 q^{37} -7.09057 q^{38} +2.89202 q^{39} -6.17763 q^{40} -0.101904 q^{41} +4.45815 q^{42} +0.656035 q^{43} +0.330981 q^{44} -6.33614 q^{45} -13.2205 q^{46} +8.22008 q^{47} -10.1740 q^{48} -5.38432 q^{49} -0.124165 q^{50} -7.90427 q^{51} +0.140834 q^{52} +5.04461 q^{53} +0.667327 q^{54} -6.35886 q^{55} -3.48209 q^{56} +11.7452 q^{57} -12.5007 q^{58} -5.66022 q^{59} -0.638001 q^{60} +6.42480 q^{61} -14.2414 q^{62} -3.57143 q^{63} +7.47700 q^{64} -2.70572 q^{65} -9.89002 q^{66} +1.69588 q^{67} -0.384917 q^{68} +21.8991 q^{69} -4.17096 q^{70} +2.02566 q^{71} +7.69711 q^{72} -9.64772 q^{73} +8.70338 q^{74} +0.205674 q^{75} +0.571960 q^{76} -3.58424 q^{77} -4.20823 q^{78} -5.55932 q^{79} +9.51859 q^{80} -9.53460 q^{81} +0.148282 q^{82} +6.25367 q^{83} -0.359616 q^{84} +7.39509 q^{85} -0.954610 q^{86} +20.7068 q^{87} +7.72471 q^{88} +15.9399 q^{89} +9.21985 q^{90} -1.52511 q^{91} +1.06643 q^{92} +23.5903 q^{93} -11.9612 q^{94} -10.9886 q^{95} +1.59840 q^{96} -11.5366 q^{97} +7.83484 q^{98} +7.92292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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