LMFDB - Embedded newform 619.2.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +O(q^{10})$	\(q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +1.45055 q^{10} +0.341105 q^{11} +2.87415 q^{12} -4.58045 q^{13} +1.10105 q^{14} +5.82567 q^{15} +3.12494 q^{16} -4.50331 q^{17} +0.227200 q^{18} -4.60284 q^{19} +6.94035 q^{20} +4.42200 q^{21} -0.131920 q^{22} -6.46872 q^{23} -2.31297 q^{24} +9.06755 q^{25} +1.77147 q^{26} +5.57217 q^{27} +5.26811 q^{28} +9.68231 q^{29} -2.25305 q^{30} +7.65931 q^{31} -4.18682 q^{32} -0.529815 q^{33} +1.74163 q^{34} +10.6780 q^{35} +1.08707 q^{36} -0.361034 q^{37} +1.78012 q^{38} +7.11451 q^{39} -5.58525 q^{40} -7.84535 q^{41} -1.71018 q^{42} -9.06924 q^{43} -0.631190 q^{44} +2.20340 q^{45} +2.50174 q^{46} +2.68206 q^{47} -4.85376 q^{48} +1.10521 q^{49} -3.50683 q^{50} +6.99468 q^{51} +8.47580 q^{52} -1.93004 q^{53} -2.15501 q^{54} -1.27937 q^{55} -4.23951 q^{56} +7.14928 q^{57} -3.74458 q^{58} -0.518734 q^{59} -10.7800 q^{60} -7.90323 q^{61} -2.96219 q^{62} +1.67250 q^{63} -4.63066 q^{64} +17.1798 q^{65} +0.204903 q^{66} +6.35561 q^{67} +8.33305 q^{68} +10.0474 q^{69} -4.12967 q^{70} -6.34036 q^{71} -0.874818 q^{72} -13.6292 q^{73} +0.139628 q^{74} -14.0840 q^{75} +8.51722 q^{76} -0.971114 q^{77} -2.75150 q^{78} -12.1347 q^{79} -11.7206 q^{80} -6.89247 q^{81} +3.03415 q^{82} -5.17657 q^{83} -8.18259 q^{84} +16.8904 q^{85} +3.50748 q^{86} -15.0389 q^{87} +0.507950 q^{88} +0.605819 q^{89} -0.852154 q^{90} +13.0404 q^{91} +11.9699 q^{92} -11.8967 q^{93} -1.03727 q^{94} +17.2637 q^{95} +6.50310 q^{96} -0.592886 q^{97} -0.427434 q^{98} -0.200388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.386745	−0.273470	−0.136735	−	0.990608i	$-0.543661\pi$
$2$	−0.386745	−0.273470	−0.136735	+	0.990608i	$0.543661\pi$
$3$	−1.55323	−0.896759	−0.448380	−	0.893843i	$-0.647999\pi$
$3$	−1.55323	−0.896759	−0.448380	+	0.893843i	$0.647999\pi$
$4$	−1.85043	−0.925214
$5$	−3.75067	−1.67735	−0.838676	−	0.544630i	$-0.816670\pi$
$5$	−3.75067	−1.67735	−0.838676	+	0.544630i	$0.816670\pi$
$6$	0.600704	0.245236
$7$	−2.84697	−1.07605	−0.538026	−	0.842928i	$-0.680830\pi$
$7$	−2.84697	−1.07605	−0.538026	+	0.842928i	$0.680830\pi$
$8$	1.48913	0.526488
$9$	−0.587469	−0.195823
$10$	1.45055	0.458705
$11$	0.341105	0.102847	0.0514235	−	0.998677i	$-0.483624\pi$
$11$	0.341105	0.102847	0.0514235	+	0.998677i	$0.483624\pi$
$12$	2.87415	0.829695
$13$	−4.58045	−1.27039	−0.635195	−	0.772352i	$-0.719080\pi$
$13$	−4.58045	−1.27039	−0.635195	+	0.772352i	$0.719080\pi$
$14$	1.10105	0.294268
$15$	5.82567	1.50418
$16$	3.12494	0.781236
$17$	−4.50331	−1.09221	−0.546106	−	0.837716i	$-0.683891\pi$
$17$	−4.50331	−1.09221	−0.546106	+	0.837716i	$0.683891\pi$
$18$	0.227200	0.0535516
$19$	−4.60284	−1.05596	−0.527982	−	0.849256i	$-0.677051\pi$
$19$	−4.60284	−1.05596	−0.527982	+	0.849256i	$0.677051\pi$
$20$	6.94035	1.55191
$21$	4.42200	0.964959
$22$	−0.131920	−0.0281255
$23$	−6.46872	−1.34882	−0.674410	−	0.738357i	$-0.735602\pi$
$23$	−6.46872	−1.34882	−0.674410	+	0.738357i	$0.735602\pi$
$24$	−2.31297	−0.472133
$25$	9.06755	1.81351
$26$	1.77147	0.347413
$27$	5.57217	1.07237
$28$	5.26811	0.995578
$29$	9.68231	1.79796	0.898980	−	0.437989i	$-0.144309\pi$
$29$	9.68231	1.79796	0.898980	+	0.437989i	$0.144309\pi$
$30$	−2.25305	−0.411348
$31$	7.65931	1.37565	0.687826	−	0.725876i	$-0.258565\pi$
$31$	7.65931	1.37565	0.687826	+	0.725876i	$0.258565\pi$
$32$	−4.18682	−0.740132
$33$	−0.529815	−0.0922290
$34$	1.74163	0.298687
$35$	10.6780	1.80492
$36$	1.08707	0.181178
$37$	−0.361034	−0.0593537	−0.0296768	−	0.999560i	$-0.509448\pi$
$37$	−0.361034	−0.0593537	−0.0296768	+	0.999560i	$0.509448\pi$
$38$	1.78012	0.288774
$39$	7.11451	1.13923
$40$	−5.58525	−0.883105
$41$	−7.84535	−1.22524	−0.612619	−	0.790378i	$-0.709884\pi$
$41$	−7.84535	−1.22524	−0.612619	+	0.790378i	$0.709884\pi$
$42$	−1.71018	−0.263887
$43$	−9.06924	−1.38305	−0.691523	−	0.722354i	$-0.743060\pi$
$43$	−9.06924	−1.38305	−0.691523	+	0.722354i	$0.743060\pi$
$44$	−0.631190	−0.0951555
$45$	2.20340	0.328464
$46$	2.50174	0.368861
$47$	2.68206	0.391218	0.195609	−	0.980682i	$-0.437332\pi$
$47$	2.68206	0.391218	0.195609	+	0.980682i	$0.437332\pi$
$48$	−4.85376	−0.700581
$49$	1.10521	0.157887
$50$	−3.50683	−0.495940
$51$	6.99468	0.979452
$52$	8.47580	1.17538
$53$	−1.93004	−0.265112	−0.132556	−	0.991176i	$-0.542318\pi$
$53$	−1.93004	−0.265112	−0.132556	+	0.991176i	$0.542318\pi$
$54$	−2.15501	−0.293259
$55$	−1.27937	−0.172511
$56$	−4.23951	−0.566528
$57$	7.14928	0.946945
$58$	−3.74458	−0.491688
$59$	−0.518734	−0.0675335	−0.0337667	−	0.999430i	$-0.510750\pi$
$59$	−0.518734	−0.0675335	−0.0337667	+	0.999430i	$0.510750\pi$
$60$	−10.7800	−1.39169
$61$	−7.90323	−1.01190	−0.505952	−	0.862561i	$-0.668859\pi$
$61$	−7.90323	−1.01190	−0.505952	+	0.862561i	$0.668859\pi$
$62$	−2.96219	−0.376199
$63$	1.67250	0.210716
$64$	−4.63066	−0.578832
$65$	17.1798	2.13089
$66$	0.204903	0.0252218
$67$	6.35561	0.776461	0.388231	−	0.921562i	$-0.373086\pi$
$67$	6.35561	0.776461	0.388231	+	0.921562i	$0.373086\pi$
$68$	8.33305	1.01053
$69$	10.0474	1.20957
$70$	−4.12967	−0.493590
$71$	−6.34036	−0.752462	−0.376231	−	0.926526i	$-0.622780\pi$
$71$	−6.34036	−0.752462	−0.376231	+	0.926526i	$0.622780\pi$
$72$	−0.874818	−0.103098
$73$	−13.6292	−1.59518	−0.797588	−	0.603202i	$-0.793891\pi$
$73$	−13.6292	−1.59518	−0.797588	+	0.603202i	$0.793891\pi$
$74$	0.139628	0.0162314
$75$	−14.0840	−1.62628
$76$	8.51722	0.976992
$77$	−0.971114	−0.110669
$78$	−2.75150	−0.311546
$79$	−12.1347	−1.36526	−0.682631	−	0.730763i	$-0.739165\pi$
$79$	−12.1347	−1.36526	−0.682631	+	0.730763i	$0.739165\pi$
$80$	−11.7206	−1.31041
$81$	−6.89247	−0.765831
$82$	3.03415	0.335065
$83$	−5.17657	−0.568203	−0.284101	−	0.958794i	$-0.591695\pi$
$83$	−5.17657	−0.568203	−0.284101	+	0.958794i	$0.591695\pi$
$84$	−8.18259	−0.892794
$85$	16.8904	1.83203
$86$	3.50748	0.378221
$87$	−15.0389	−1.61234
$88$	0.507950	0.0541477
$89$	0.605819	0.0642167	0.0321084	−	0.999484i	$-0.489778\pi$
$89$	0.605819	0.0642167	0.0321084	+	0.999484i	$0.489778\pi$
$90$	−0.852154	−0.0898249
$91$	13.0404	1.36700
$92$	11.9699	1.24795
$93$	−11.8967	−1.23363
$94$	−1.03727	−0.106986
$95$	17.2637	1.77122
$96$	6.50310	0.663720
$97$	−0.592886	−0.0601985	−0.0300992	−	0.999547i	$-0.509582\pi$
$97$	−0.592886	−0.0601985	−0.0300992	+	0.999547i	$0.509582\pi$
$98$	−0.427434	−0.0431774
$99$	−0.200388	−0.0201398
$100$	−16.7789	−1.67789
$101$	18.3855	1.82943	0.914713	−	0.404104i	$-0.132417\pi$
$101$	18.3855	1.82943	0.914713	+	0.404104i	$0.132417\pi$
$102$	−2.70516	−0.267850
$103$	−16.4296	−1.61886	−0.809431	−	0.587216i	$-0.800224\pi$
$103$	−16.4296	−1.61886	−0.809431	+	0.587216i	$0.800224\pi$
$104$	−6.82090	−0.668844
$105$	−16.5855	−1.61858
$106$	0.746434	0.0725000
$107$	6.16752	0.596237	0.298118	−	0.954529i	$-0.403641\pi$
$107$	6.16752	0.596237	0.298118	+	0.954529i	$0.403641\pi$
$108$	−10.3109	−0.992168
$109$	−8.53548	−0.817551	−0.408775	−	0.912635i	$-0.634044\pi$
$109$	−8.53548	−0.817551	−0.408775	+	0.912635i	$0.634044\pi$
$110$	0.494791	0.0471764
$111$	0.560770	0.0532260
$112$	−8.89661	−0.840650
$113$	13.0938	1.23177	0.615883	−	0.787838i	$-0.288800\pi$
$113$	13.0938	1.23177	0.615883	+	0.787838i	$0.288800\pi$
$114$	−2.76494	−0.258961
$115$	24.2620	2.26245
$116$	−17.9164	−1.66350
$117$	2.69087	0.248771
$118$	0.200618	0.0184684
$119$	12.8208	1.17528
$120$	8.67519	0.791933
$121$	−10.8836	−0.989422
$122$	3.05653	0.276725
$123$	12.1857	1.09874
$124$	−14.1730	−1.27277
$125$	−15.2561	−1.36454
$126$	−0.646831	−0.0576243
$127$	15.5483	1.37969	0.689845	−	0.723957i	$-0.257678\pi$
$127$	15.5483	1.37969	0.689845	+	0.723957i	$0.257678\pi$
$128$	10.1645	0.898425
$129$	14.0866	1.24026
$130$	−6.64419	−0.582734
$131$	−2.54669	−0.222505	−0.111253	−	0.993792i	$-0.535486\pi$
$131$	−2.54669	−0.222505	−0.111253	+	0.993792i	$0.535486\pi$
$132$	0.980386	0.0853316
$133$	13.1041	1.13627
$134$	−2.45800	−0.212339
$135$	−20.8994	−1.79873
$136$	−6.70602	−0.575036
$137$	6.24822	0.533822	0.266911	−	0.963721i	$-0.413997\pi$
$137$	6.24822	0.533822	0.266911	+	0.963721i	$0.413997\pi$
$138$	−3.88578	−0.330780
$139$	−5.69101	−0.482705	−0.241353	−	0.970437i	$-0.577591\pi$
$139$	−5.69101	−0.482705	−0.241353	+	0.970437i	$0.577591\pi$
$140$	−19.7589	−1.66994
$141$	−4.16586	−0.350829
$142$	2.45210	0.205776
$143$	−1.56242	−0.130656
$144$	−1.83581	−0.152984
$145$	−36.3152	−3.01581
$146$	5.27102	0.436232
$147$	−1.71665	−0.141587
$148$	0.668068	0.0549149
$149$	22.5542	1.84771	0.923855	−	0.382743i	$-0.125020\pi$
$149$	22.5542	1.84771	0.923855	+	0.382743i	$0.125020\pi$
$150$	5.44692	0.444739
$151$	12.1464	0.988459	0.494229	−	0.869332i	$-0.335450\pi$
$151$	12.1464	0.988459	0.494229	+	0.869332i	$0.335450\pi$
$152$	−6.85423	−0.555952
$153$	2.64555	0.213880
$154$	0.375573	0.0302645
$155$	−28.7276	−2.30745
$156$	−13.1649	−1.05403
$157$	−12.6078	−1.00621	−0.503106	−	0.864225i	$-0.667809\pi$
$157$	−12.6078	−1.00621	−0.503106	+	0.864225i	$0.667809\pi$
$158$	4.69304	0.373358
$159$	2.99781	0.237741
$160$	15.7034	1.24146
$161$	18.4162	1.45140
$162$	2.66563	0.209431
$163$	−11.7366	−0.919281	−0.459640	−	0.888105i	$-0.652022\pi$
$163$	−11.7366	−0.919281	−0.459640	+	0.888105i	$0.652022\pi$
$164$	14.5173	1.13361
$165$	1.98716	0.154701
$166$	2.00201	0.155386
$167$	−17.2393	−1.33402	−0.667010	−	0.745049i	$-0.732426\pi$
$167$	−17.2393	−1.33402	−0.667010	+	0.745049i	$0.732426\pi$
$168$	6.58494	0.508039
$169$	7.98055	0.613889
$170$	−6.53228	−0.501003
$171$	2.70402	0.206782
$172$	16.7820	1.27961
$173$	18.6950	1.42135	0.710676	−	0.703520i	$-0.248389\pi$
$173$	18.6950	1.42135	0.710676	+	0.703520i	$0.248389\pi$
$174$	5.81621	0.440925
$175$	−25.8150	−1.95143
$176$	1.06593	0.0803478
$177$	0.805715	0.0605613
$178$	−0.234297	−0.0175613
$179$	−4.75236	−0.355208	−0.177604	−	0.984102i	$-0.556835\pi$
$179$	−4.75236	−0.355208	−0.177604	+	0.984102i	$0.556835\pi$
$180$	−4.07724	−0.303900
$181$	−0.480494	−0.0357149	−0.0178574	−	0.999841i	$-0.505684\pi$
$181$	−0.480494	−0.0357149	−0.0178574	+	0.999841i	$0.505684\pi$
$182$	−5.04330	−0.373834
$183$	12.2755	0.907435
$184$	−9.63277	−0.710137
$185$	1.35412	0.0995570
$186$	4.60098	0.337360
$187$	−1.53610	−0.112331
$188$	−4.96296	−0.361961
$189$	−15.8638	−1.15392
$190$	−6.67666	−0.484376
$191$	−18.7352	−1.35563	−0.677815	−	0.735232i	$-0.737073\pi$
$191$	−18.7352	−1.35563	−0.677815	+	0.735232i	$0.737073\pi$
$192$	7.19249	0.519073
$193$	23.6723	1.70397	0.851983	−	0.523569i	$-0.175400\pi$
$193$	23.6723	1.70397	0.851983	+	0.523569i	$0.175400\pi$
$194$	0.229296	0.0164625
$195$	−26.6842	−1.91090
$196$	−2.04511	−0.146080
$197$	13.6004	0.968986	0.484493	−	0.874795i	$-0.339004\pi$
$197$	13.6004	0.968986	0.484493	+	0.874795i	$0.339004\pi$
$198$	0.0774991	0.00550762
$199$	−1.24337	−0.0881403	−0.0440702	−	0.999028i	$-0.514033\pi$
$199$	−1.24337	−0.0881403	−0.0440702	+	0.999028i	$0.514033\pi$
$200$	13.5028	0.954791
$201$	−9.87174	−0.696299
$202$	−7.11049	−0.500293
$203$	−27.5652	−1.93470
$204$	−12.9432	−0.906203
$205$	29.4254	2.05516
$206$	6.35408	0.442709
$207$	3.80017	0.264130
$208$	−14.3137	−0.992474
$209$	−1.57005	−0.108603
$210$	6.41434	0.442632
$211$	5.32658	0.366697	0.183348	−	0.983048i	$-0.441306\pi$
$211$	5.32658	0.366697	0.183348	+	0.983048i	$0.441306\pi$
$212$	3.57141	0.245285
$213$	9.84805	0.674778
$214$	−2.38526	−0.163053
$215$	34.0158	2.31986
$216$	8.29770	0.564587
$217$	−21.8058	−1.48027
$218$	3.30105	0.223575
$219$	21.1693	1.43049
$220$	2.36739	0.159609
$221$	20.6272	1.38753
$222$	−0.216875	−0.0145557
$223$	−28.9946	−1.94162	−0.970811	−	0.239845i	$-0.922904\pi$
$223$	−28.9946	−1.94162	−0.970811	+	0.239845i	$0.922904\pi$
$224$	11.9197	0.796420
$225$	−5.32690	−0.355127
$226$	−5.06397	−0.336850
$227$	−20.9969	−1.39361	−0.696807	−	0.717258i	$-0.745397\pi$
$227$	−20.9969	−1.39361	−0.696807	+	0.717258i	$0.745397\pi$
$228$	−13.2292	−0.876127
$229$	11.7145	0.774119	0.387059	−	0.922055i	$-0.373491\pi$
$229$	11.7145	0.774119	0.387059	+	0.922055i	$0.373491\pi$
$230$	−9.38321	−0.618711
$231$	1.50837	0.0992432
$232$	14.4182	0.946604
$233$	−10.2552	−0.671841	−0.335920	−	0.941890i	$-0.609047\pi$
$233$	−10.2552	−0.671841	−0.335920	+	0.941890i	$0.609047\pi$
$234$	−1.04068	−0.0680314
$235$	−10.0595	−0.656211
$236$	0.959881	0.0624829
$237$	18.8480	1.22431
$238$	−4.95836	−0.321403
$239$	−15.7389	−1.01806	−0.509032	−	0.860748i	$-0.669996\pi$
$239$	−15.7389	−1.01806	−0.509032	+	0.860748i	$0.669996\pi$
$240$	18.2049	1.17512
$241$	20.2633	1.30527	0.652636	−	0.757672i	$-0.273663\pi$
$241$	20.2633	1.30527	0.652636	+	0.757672i	$0.273663\pi$
$242$	4.20919	0.270577
$243$	−6.01090	−0.385600
$244$	14.6244	0.936229
$245$	−4.14529	−0.264833
$246$	−4.71274	−0.300473
$247$	21.0831	1.34148
$248$	11.4057	0.724264
$249$	8.04042	0.509541
$250$	5.90020	0.373161
$251$	13.0249	0.822127	0.411064	−	0.911607i	$-0.365157\pi$
$251$	13.0249	0.822127	0.411064	+	0.911607i	$0.365157\pi$
$252$	−3.09485	−0.194957
$253$	−2.20651	−0.138722
$254$	−6.01323	−0.377304
$255$	−26.2348	−1.64289
$256$	5.33024	0.333140
$257$	−11.3779	−0.709735	−0.354868	−	0.934917i	$-0.615474\pi$
$257$	−11.3779	−0.709735	−0.354868	+	0.934917i	$0.615474\pi$
$258$	−5.44793	−0.339173
$259$	1.02785	0.0638676
$260$	−31.7900	−1.97153
$261$	−5.68806	−0.352082
$262$	0.984919	0.0608485
$263$	0.114792	0.00707838	0.00353919	−	0.999994i	$-0.498873\pi$
$263$	0.114792	0.00707838	0.00353919	+	0.999994i	$0.498873\pi$
$264$	−0.788965	−0.0485574
$265$	7.23896	0.444686
$266$	−5.06795	−0.310736
$267$	−0.940979	−0.0575870
$268$	−11.7606	−0.718393
$269$	3.61966	0.220694	0.110347	−	0.993893i	$-0.464804\pi$
$269$	3.61966	0.220694	0.110347	+	0.993893i	$0.464804\pi$
$270$	8.08273	0.491899
$271$	11.4084	0.693012	0.346506	−	0.938048i	$-0.387368\pi$
$271$	11.4084	0.693012	0.346506	+	0.938048i	$0.387368\pi$
$272$	−14.0726	−0.853276
$273$	−20.2548	−1.22587
$274$	−2.41647	−0.145984
$275$	3.09299	0.186514
$276$	−18.5920	−1.11911
$277$	−11.1126	−0.667690	−0.333845	−	0.942628i	$-0.608346\pi$
$277$	−11.1126	−0.667690	−0.333845	+	0.942628i	$0.608346\pi$
$278$	2.20097	0.132005
$279$	−4.49960	−0.269384
$280$	15.9010	0.950267
$281$	19.8098	1.18175	0.590876	−	0.806762i	$-0.298782\pi$
$281$	19.8098	1.18175	0.590876	+	0.806762i	$0.298782\pi$
$282$	1.61112	0.0959410
$283$	6.81139	0.404895	0.202448	−	0.979293i	$-0.435110\pi$
$283$	6.81139	0.404895	0.202448	+	0.979293i	$0.435110\pi$
$284$	11.7324	0.696189
$285$	−26.8146	−1.58836
$286$	0.604256	0.0357304
$287$	22.3354	1.31842
$288$	2.45962	0.144935
$289$	3.27978	0.192928
$290$	14.0447	0.824733
$291$	0.920890	0.0539835
$292$	25.2199	1.47588
$293$	18.8865	1.10336	0.551680	−	0.834056i	$-0.313987\pi$
$293$	18.8865	1.10336	0.551680	+	0.834056i	$0.313987\pi$
$294$	0.663905	0.0387197
$295$	1.94560	0.113277
$296$	−0.537628	−0.0312490
$297$	1.90070	0.110290
$298$	−8.72270	−0.505293
$299$	29.6296	1.71353
$300$	26.0615	1.50466
$301$	25.8198	1.48823
$302$	−4.69755	−0.270313
$303$	−28.5570	−1.64055
$304$	−14.3836	−0.824957
$305$	29.6424	1.69732
$306$	−1.02315	−0.0584897
$307$	−11.3470	−0.647609	−0.323805	−	0.946124i	$-0.604962\pi$
$307$	−11.3470	−0.647609	−0.323805	+	0.946124i	$0.604962\pi$
$308$	1.79698	0.102392
$309$	25.5191	1.45173
$310$	11.1102	0.631018
$311$	15.0458	0.853167	0.426583	−	0.904448i	$-0.359717\pi$
$311$	15.0458	0.853167	0.426583	+	0.904448i	$0.359717\pi$
$312$	10.5944	0.599792
$313$	−3.58250	−0.202495	−0.101247	−	0.994861i	$-0.532283\pi$
$313$	−3.58250	−0.202495	−0.101247	+	0.994861i	$0.532283\pi$
$314$	4.87600	0.275168
$315$	−6.27301	−0.353444
$316$	22.4544	1.26316
$317$	25.9494	1.45746	0.728731	−	0.684800i	$-0.240111\pi$
$317$	25.9494	1.45746	0.728731	+	0.684800i	$0.240111\pi$
$318$	−1.15938	−0.0650151
$319$	3.30269	0.184915
$320$	17.3681	0.970906
$321$	−9.57960	−0.534681
$322$	−7.12237	−0.396914
$323$	20.7280	1.15334
$324$	12.7540	0.708557
$325$	−41.5335	−2.30386
$326$	4.53906	0.251395
$327$	13.2576	0.733146
$328$	−11.6828	−0.645073
$329$	−7.63573	−0.420971
$330$	−0.768525	−0.0423059
$331$	−19.6181	−1.07831	−0.539153	−	0.842208i	$-0.681256\pi$
$331$	−19.6181	−1.07831	−0.539153	+	0.842208i	$0.681256\pi$
$332$	9.57888	0.525709
$333$	0.212096	0.0116228
$334$	6.66722	0.364814
$335$	−23.8378	−1.30240
$336$	13.8185	0.753861
$337$	−25.4533	−1.38653	−0.693265	−	0.720683i	$-0.743828\pi$
$337$	−25.4533	−1.38653	−0.693265	+	0.720683i	$0.743828\pi$
$338$	−3.08643	−0.167880
$339$	−20.3378	−1.10460
$340$	−31.2545	−1.69502
$341$	2.61263	0.141482
$342$	−1.04577	−0.0565485
$343$	16.7823	0.906157
$344$	−13.5053	−0.728157
$345$	−37.6846	−2.02887
$346$	−7.23017	−0.388696
$347$	14.9640	0.803310	0.401655	−	0.915791i	$-0.368435\pi$
$347$	14.9640	0.803310	0.401655	+	0.915791i	$0.368435\pi$
$348$	27.8284	1.49176
$349$	18.5127	0.990963	0.495481	−	0.868619i	$-0.334992\pi$
$349$	18.5127	0.990963	0.495481	+	0.868619i	$0.334992\pi$
$350$	9.98381	0.533657
$351$	−25.5231	−1.36232
$352$	−1.42814	−0.0761204
$353$	−23.0672	−1.22774	−0.613872	−	0.789406i	$-0.710389\pi$
$353$	−23.0672	−1.22774	−0.613872	+	0.789406i	$0.710389\pi$
$354$	−0.311606	−0.0165617
$355$	23.7806	1.26214
$356$	−1.12103	−0.0594142
$357$	−19.9136	−1.05394
$358$	1.83795	0.0971387
$359$	−24.0589	−1.26978	−0.634889	−	0.772603i	$-0.718954\pi$
$359$	−24.0589	−1.26978	−0.634889	+	0.772603i	$0.718954\pi$
$360$	3.28116	0.172932
$361$	2.18612	0.115059
$362$	0.185829	0.00976693
$363$	16.9048	0.887274
$364$	−24.1303	−1.26477
$365$	51.1187	2.67567
$366$	−4.74750	−0.248156
$367$	−10.8139	−0.564482	−0.282241	−	0.959343i	$-0.591078\pi$
$367$	−10.8139	−0.564482	−0.282241	+	0.959343i	$0.591078\pi$
$368$	−20.2144	−1.05375
$369$	4.60890	0.239930
$370$	−0.523699	−0.0272258
$371$	5.49477	0.285274
$372$	22.0140	1.14137
$373$	−2.09981	−0.108724	−0.0543620	−	0.998521i	$-0.517312\pi$
$373$	−2.09981	−0.108724	−0.0543620	+	0.998521i	$0.517312\pi$
$374$	0.594078	0.0307191
$375$	23.6962	1.22367
$376$	3.99394	0.205972
$377$	−44.3494	−2.28411
$378$	6.13523	0.315562
$379$	−21.1009	−1.08388	−0.541939	−	0.840418i	$-0.682310\pi$
$379$	−21.1009	−1.08388	−0.541939	+	0.840418i	$0.682310\pi$
$380$	−31.9453	−1.63876
$381$	−24.1502	−1.23725
$382$	7.24573	0.370724
$383$	7.65222	0.391010	0.195505	−	0.980703i	$-0.437365\pi$
$383$	7.65222	0.391010	0.195505	+	0.980703i	$0.437365\pi$
$384$	−15.7879	−0.805671
$385$	3.64233	0.185630
$386$	−9.15512	−0.465983
$387$	5.32790	0.270832
$388$	1.09709	0.0556965
$389$	−0.495935	−0.0251449	−0.0125725	−	0.999921i	$-0.504002\pi$
$389$	−0.495935	−0.0251449	−0.0125725	+	0.999921i	$0.504002\pi$
$390$	10.3200	0.522572
$391$	29.1306	1.47320
$392$	1.64581	0.0831257
$393$	3.95560	0.199534
$394$	−5.25987	−0.264988
$395$	45.5134	2.29003
$396$	0.370805	0.0186336
$397$	5.91573	0.296902	0.148451	−	0.988920i	$-0.452571\pi$
$397$	5.91573	0.296902	0.148451	+	0.988920i	$0.452571\pi$
$398$	0.480867	0.0241037
$399$	−20.3537	−1.01896
$400$	28.3356	1.41678
$401$	−12.2436	−0.611414	−0.305707	−	0.952126i	$-0.598893\pi$
$401$	−12.2436	−0.611414	−0.305707	+	0.952126i	$0.598893\pi$
$402$	3.81784	0.190417
$403$	−35.0831	−1.74761
$404$	−34.0211	−1.69261
$405$	25.8514	1.28457
$406$	10.6607	0.529081
$407$	−0.123151	−0.00610435
$408$	10.4160	0.515669
$409$	0.425047	0.0210172	0.0105086	−	0.999945i	$-0.496655\pi$
$409$	0.425047	0.0210172	0.0105086	+	0.999945i	$0.496655\pi$
$410$	−11.3801	−0.562023
$411$	−9.70494	−0.478709
$412$	30.4019	1.49779
$413$	1.47682	0.0726695
$414$	−1.46969	−0.0722315
$415$	19.4156	0.953076
$416$	19.1775	0.940256
$417$	8.83947	0.432871
$418$	0.607209	0.0296995
$419$	−6.01181	−0.293696	−0.146848	−	0.989159i	$-0.546913\pi$
$419$	−6.01181	−0.293696	−0.146848	+	0.989159i	$0.546913\pi$
$420$	30.6902	1.49753
$421$	13.1235	0.639598	0.319799	−	0.947485i	$-0.396385\pi$
$421$	13.1235	0.639598	0.319799	+	0.947485i	$0.396385\pi$
$422$	−2.06003	−0.100280
$423$	−1.57563	−0.0766095
$424$	−2.87409	−0.139578
$425$	−40.8340	−1.98074
$426$	−3.80868	−0.184531
$427$	22.5002	1.08886
$428$	−11.4126	−0.551647
$429$	2.42679	0.117167
$430$	−13.1554	−0.634410
$431$	−2.19415	−0.105688	−0.0528441	−	0.998603i	$-0.516829\pi$
$431$	−2.19415	−0.105688	−0.0528441	+	0.998603i	$0.516829\pi$
$432$	17.4127	0.837770
$433$	−25.9473	−1.24695	−0.623473	−	0.781845i	$-0.714279\pi$
$433$	−25.9473	−1.24695	−0.623473	+	0.781845i	$0.714279\pi$
$434$	8.43326	0.404810
$435$	56.4060	2.70446
$436$	15.7943	0.756410
$437$	29.7744	1.42430
$438$	−8.18711	−0.391195
$439$	23.0473	1.09999	0.549994	−	0.835169i	$-0.314630\pi$
$439$	23.0473	1.09999	0.549994	+	0.835169i	$0.314630\pi$
$440$	−1.90516	−0.0908248
$441$	−0.649277	−0.0309179
$442$	−7.97745	−0.379449
$443$	−8.60542	−0.408856	−0.204428	−	0.978882i	$-0.565533\pi$
$443$	−8.60542	−0.408856	−0.204428	+	0.978882i	$0.565533\pi$
$444$	−1.03767	−0.0492454
$445$	−2.27223	−0.107714
$446$	11.2135	0.530975
$447$	−35.0319	−1.65695
$448$	13.1833	0.622853
$449$	−11.5453	−0.544858	−0.272429	−	0.962176i	$-0.587827\pi$
$449$	−11.5453	−0.544858	−0.272429	+	0.962176i	$0.587827\pi$
$450$	2.06015	0.0971164
$451$	−2.67609	−0.126012
$452$	−24.2292	−1.13965
$453$	−18.8662	−0.886409
$454$	8.12045	0.381111
$455$	−48.9103	−2.29295
$456$	10.6462	0.498555
$457$	−20.4197	−0.955193	−0.477597	−	0.878579i	$-0.658492\pi$
$457$	−20.4197	−0.955193	−0.477597	+	0.878579i	$0.658492\pi$
$458$	−4.53054	−0.211698
$459$	−25.0932	−1.17125
$460$	−44.8952	−2.09325
$461$	11.4092	0.531377	0.265689	−	0.964059i	$-0.414401\pi$
$461$	11.4092	0.531377	0.265689	+	0.964059i	$0.414401\pi$
$462$	−0.583352	−0.0271400
$463$	14.9737	0.695887	0.347944	−	0.937515i	$-0.386880\pi$
$463$	14.9737	0.695887	0.347944	+	0.937515i	$0.386880\pi$
$464$	30.2567	1.40463
$465$	44.6206	2.06923
$466$	3.96614	0.183728
$467$	−5.56500	−0.257518	−0.128759	−	0.991676i	$-0.541099\pi$
$467$	−5.56500	−0.257518	−0.128759	+	0.991676i	$0.541099\pi$
$468$	−4.97927	−0.230167
$469$	−18.0942	−0.835513
$470$	3.89047	0.179454
$471$	19.5828	0.902330
$472$	−0.772464	−0.0355555
$473$	−3.09356	−0.142242
$474$	−7.28938	−0.334812
$475$	−41.7365	−1.91500
$476$	−23.7239	−1.08738
$477$	1.13384	0.0519150
$478$	6.08692	0.278409
$479$	1.52115	0.0695033	0.0347517	−	0.999396i	$-0.488936\pi$
$479$	1.52115	0.0695033	0.0347517	+	0.999396i	$0.488936\pi$
$480$	−24.3910	−1.11329
$481$	1.65370	0.0754023
$482$	−7.83671	−0.356952
$483$	−28.6047	−1.30156
$484$	20.1394	0.915428
$485$	2.22372	0.100974
$486$	2.32468	0.105450
$487$	−5.20782	−0.235989	−0.117995	−	0.993014i	$-0.537647\pi$
$487$	−5.20782	−0.235989	−0.117995	+	0.993014i	$0.537647\pi$
$488$	−11.7689	−0.532755
$489$	18.2297	0.824373
$490$	1.60317	0.0724237
$491$	37.7702	1.70455	0.852273	−	0.523097i	$-0.175224\pi$
$491$	37.7702	1.70455	0.852273	+	0.523097i	$0.175224\pi$
$492$	−22.5487	−1.01657
$493$	−43.6024	−1.96376
$494$	−8.15377	−0.366855
$495$	0.751592	0.0337815
$496$	23.9349	1.07471
$497$	18.0508	0.809688
$498$	−3.10959	−0.139344
$499$	−26.8162	−1.20046	−0.600228	−	0.799829i	$-0.704924\pi$
$499$	−26.8162	−1.20046	−0.600228	+	0.799829i	$0.704924\pi$
$500$	28.2303	1.26250
$501$	26.7767	1.19629
$502$	−5.03733	−0.224827
$503$	15.9323	0.710386	0.355193	−	0.934793i	$-0.384415\pi$
$503$	15.9323	0.710386	0.355193	+	0.934793i	$0.384415\pi$
$504$	2.49058	0.110939
$505$	−68.9580	−3.06859
$506$	0.853356	0.0379363
$507$	−12.3957	−0.550510
$508$	−28.7711	−1.27651
$509$	−37.8221	−1.67644	−0.838218	−	0.545335i	$-0.816403\pi$
$509$	−37.8221	−1.67644	−0.838218	+	0.545335i	$0.816403\pi$
$510$	10.1462	0.449279
$511$	38.8018	1.71649
$512$	−22.3905	−0.989529
$513$	−25.6478	−1.13238
$514$	4.40035	0.194091
$515$	61.6222	2.71540
$516$	−26.0663	−1.14751
$517$	0.914864	0.0402357
$518$	−0.397516	−0.0174659
$519$	−29.0376	−1.27461
$520$	25.5830	1.12189
$521$	42.4318	1.85897	0.929486	−	0.368856i	$-0.120251\pi$
$521$	42.4318	1.85897	0.929486	+	0.368856i	$0.120251\pi$
$522$	2.19982	0.0962837
$523$	−33.0283	−1.44423	−0.722114	−	0.691774i	$-0.756829\pi$
$523$	−33.0283	−1.44423	−0.722114	+	0.691774i	$0.756829\pi$
$524$	4.71247	0.205865
$525$	40.0967	1.74996
$526$	−0.0443952	−0.00193572
$527$	−34.4922	−1.50250
$528$	−1.65564	−0.0720526
$529$	18.8443	0.819316
$530$	−2.79963	−0.121608
$531$	0.304740	0.0132246
$532$	−24.2482	−1.05129
$533$	35.9353	1.55653
$534$	0.363918	0.0157483
$535$	−23.1324	−1.00010
$536$	9.46434	0.408797
$537$	7.38152	0.318536
$538$	−1.39988	−0.0603532
$539$	0.376993	0.0162382
$540$	38.6729	1.66421
$541$	9.85861	0.423855	0.211927	−	0.977285i	$-0.432026\pi$
$541$	9.85861	0.423855	0.211927	+	0.977285i	$0.432026\pi$
$542$	−4.41214	−0.189518
$543$	0.746320	0.0320276
$544$	18.8545	0.808381
$545$	32.0138	1.37132
$546$	7.83342	0.335239
$547$	14.4283	0.616911	0.308455	−	0.951239i	$-0.400188\pi$
$547$	14.4283	0.616911	0.308455	+	0.951239i	$0.400188\pi$
$548$	−11.5619	−0.493899
$549$	4.64290	0.198154
$550$	−1.19620	−0.0510060
$551$	−44.5661	−1.89858
$552$	14.9619	0.636822
$553$	34.5471	1.46909
$554$	4.29772	0.182593
$555$	−2.10327	−0.0892787
$556$	10.5308	0.446606
$557$	−17.0881	−0.724048	−0.362024	−	0.932169i	$-0.617914\pi$
$557$	−17.0881	−0.724048	−0.362024	+	0.932169i	$0.617914\pi$
$558$	1.74020	0.0736684
$559$	41.5412	1.75701
$560$	33.3683	1.41007
$561$	2.38592	0.100734
$562$	−7.66132	−0.323173
$563$	−17.1848	−0.724252	−0.362126	−	0.932129i	$-0.617949\pi$
$563$	−17.1848	−0.724252	−0.362126	+	0.932129i	$0.617949\pi$
$564$	7.70863	0.324592
$565$	−49.1107	−2.06610
$566$	−2.63427	−0.110727
$567$	19.6226	0.824073
$568$	−9.44163	−0.396162
$569$	−10.2475	−0.429599	−0.214800	−	0.976658i	$-0.568910\pi$
$569$	−10.2475	−0.429599	−0.214800	+	0.976658i	$0.568910\pi$
$570$	10.3704	0.434368
$571$	−35.0635	−1.46736	−0.733681	−	0.679494i	$-0.762199\pi$
$571$	−35.0635	−1.46736	−0.733681	+	0.679494i	$0.762199\pi$
$572$	2.89114	0.120885
$573$	29.1001	1.21567
$574$	−8.63811	−0.360548
$575$	−58.6554	−2.44610
$576$	2.72037	0.113349
$577$	40.8544	1.70079	0.850396	−	0.526143i	$-0.176362\pi$
$577$	40.8544	1.70079	0.850396	+	0.526143i	$0.176362\pi$
$578$	−1.26844	−0.0527600
$579$	−36.7685	−1.52805
$580$	67.1987	2.79027
$581$	14.7375	0.611415
$582$	−0.356149	−0.0147629
$583$	−0.658347	−0.0272660
$584$	−20.2957	−0.839841
$585$	−10.0926	−0.417277
$586$	−7.30425	−0.301736
$587$	−29.2242	−1.20621	−0.603106	−	0.797661i	$-0.706070\pi$
$587$	−29.2242	−1.20621	−0.603106	+	0.797661i	$0.706070\pi$
$588$	3.17654	0.130998
$589$	−35.2545	−1.45264
$590$	−0.752451	−0.0309779
$591$	−21.1245	−0.868947
$592$	−1.12821	−0.0463692
$593$	−18.1141	−0.743855	−0.371928	−	0.928262i	$-0.621303\pi$
$593$	−18.1141	−0.743855	−0.371928	+	0.928262i	$0.621303\pi$
$594$	−0.735084	−0.0301609
$595$	−48.0865	−1.97135
$596$	−41.7349	−1.70953
$597$	1.93125	0.0790406
$598$	−11.4591	−0.468598
$599$	26.3879	1.07818	0.539089	−	0.842249i	$-0.318769\pi$
$599$	26.3879	1.07818	0.539089	+	0.842249i	$0.318769\pi$
$600$	−20.9730	−0.856218
$601$	−39.0984	−1.59486	−0.797428	−	0.603414i	$-0.793807\pi$
$601$	−39.0984	−1.59486	−0.797428	+	0.603414i	$0.793807\pi$
$602$	−9.98568	−0.406986
$603$	−3.73372	−0.152049
$604$	−22.4760	−0.914536
$605$	40.8210	1.65961
$606$	11.0443	0.448642
$607$	−10.6168	−0.430922	−0.215461	−	0.976512i	$-0.569125\pi$
$607$	−10.6168	−0.430922	−0.215461	+	0.976512i	$0.569125\pi$
$608$	19.2712	0.781552
$609$	42.8152	1.73496
$610$	−11.4640	−0.464166
$611$	−12.2850	−0.497000
$612$	−4.89540	−0.197885
$613$	17.5950	0.710655	0.355328	−	0.934742i	$-0.384369\pi$
$613$	17.5950	0.710655	0.355328	+	0.934742i	$0.384369\pi$
$614$	4.38840	0.177101
$615$	−45.7044	−1.84298
$616$	−1.44612	−0.0582657
$617$	−11.3845	−0.458322	−0.229161	−	0.973388i	$-0.573598\pi$
$617$	−11.3845	−0.458322	−0.229161	+	0.973388i	$0.573598\pi$
$618$	−9.86936	−0.397004
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	53.1583	2.13489
$621$	−36.0448	−1.44643
$622$	−5.81887	−0.233315
$623$	−1.72475	−0.0691005
$624$	22.2324	0.890010
$625$	11.8828	0.475310
$626$	1.38551	0.0553762
$627$	2.43865	0.0973905
$628$	23.3298	0.930962
$629$	1.62585	0.0648268
$630$	2.42605	0.0966563
$631$	−27.4304	−1.09198	−0.545992	−	0.837790i	$-0.683847\pi$
$631$	−27.4304	−1.09198	−0.545992	+	0.837790i	$0.683847\pi$
$632$	−18.0702	−0.718794
$633$	−8.27342	−0.328839
$634$	−10.0358	−0.398572
$635$	−58.3167	−2.31423
$636$	−5.54723	−0.219962
$637$	−5.06237	−0.200578
$638$	−1.27730	−0.0505686
$639$	3.72476	0.147349
$640$	−38.1238	−1.50698
$641$	−12.0302	−0.475166	−0.237583	−	0.971367i	$-0.576355\pi$
$641$	−12.0302	−0.475166	−0.237583	+	0.971367i	$0.576355\pi$
$642$	3.70486	0.146219
$643$	27.9994	1.10419	0.552094	−	0.833782i	$-0.313829\pi$
$643$	27.9994	1.10419	0.552094	+	0.833782i	$0.313829\pi$
$644$	−34.0779	−1.34286
$645$	−52.8344	−2.08035
$646$	−8.01644	−0.315403
$647$	−2.24425	−0.0882307	−0.0441153	−	0.999026i	$-0.514047\pi$
$647$	−2.24425	−0.0882307	−0.0441153	+	0.999026i	$0.514047\pi$
$648$	−10.2638	−0.403200
$649$	−0.176943	−0.00694561
$650$	16.0629	0.630037
$651$	33.8694	1.32745
$652$	21.7177	0.850532
$653$	27.0093	1.05696	0.528478	−	0.848947i	$-0.322763\pi$
$653$	27.0093	1.05696	0.528478	+	0.848947i	$0.322763\pi$
$654$	−5.12730	−0.200493
$655$	9.55181	0.373220
$656$	−24.5163	−0.957200
$657$	8.00672	0.312372
$658$	2.95308	0.115123
$659$	−15.2364	−0.593526	−0.296763	−	0.954951i	$-0.595907\pi$
$659$	−15.2364	−0.593526	−0.296763	+	0.954951i	$0.595907\pi$
$660$	−3.67711	−0.143131
$661$	−35.0111	−1.36178	−0.680888	−	0.732388i	$-0.738406\pi$
$661$	−35.0111	−1.36178	−0.680888	+	0.732388i	$0.738406\pi$
$662$	7.58718	0.294884
$663$	−32.0388	−1.24428
$664$	−7.70860	−0.299152
$665$	−49.1493	−1.90593
$666$	−0.0820271	−0.00317849
$667$	−62.6321	−2.42513
$668$	31.9001	1.23425
$669$	45.0354	1.74117
$670$	9.21915	0.356167
$671$	−2.69583	−0.104071
$672$	−18.5141	−0.714197
$673$	9.46682	0.364919	0.182460	−	0.983213i	$-0.441594\pi$
$673$	9.46682	0.364919	0.182460	+	0.983213i	$0.441594\pi$
$674$	9.84393	0.379174
$675$	50.5260	1.94475
$676$	−14.7674	−0.567978
$677$	27.3050	1.04941	0.524707	−	0.851283i	$-0.324175\pi$
$677$	27.3050	1.04941	0.524707	+	0.851283i	$0.324175\pi$
$678$	7.86553	0.302074
$679$	1.68793	0.0647767
$680$	25.1521	0.964539
$681$	32.6131	1.24974
$682$	−1.01042	−0.0386909
$683$	−19.2637	−0.737105	−0.368552	−	0.929607i	$-0.620146\pi$
$683$	−19.2637	−0.737105	−0.368552	+	0.929607i	$0.620146\pi$
$684$	−5.00360	−0.191317
$685$	−23.4350	−0.895407
$686$	−6.49045	−0.247806
$687$	−18.1954	−0.694198
$688$	−28.3409	−1.08049
$689$	8.84047	0.336795
$690$	14.5743	0.554834
$691$	36.9687	1.40635	0.703177	−	0.711014i	$-0.251764\pi$
$691$	36.9687	1.40635	0.703177	+	0.711014i	$0.251764\pi$
$692$	−34.5937	−1.31505
$693$	0.570499	0.0216715
$694$	−5.78725	−0.219681
$695$	21.3451	0.809667
$696$	−22.3949	−0.848876
$697$	35.3300	1.33822
$698$	−7.15969	−0.270998
$699$	15.9287	0.602479
$700$	47.7688	1.80549
$701$	14.1153	0.533128	0.266564	−	0.963817i	$-0.414112\pi$
$701$	14.1153	0.533128	0.266564	+	0.963817i	$0.414112\pi$
$702$	9.87091	0.372554
$703$	1.66178	0.0626753
$704$	−1.57954	−0.0595312
$705$	15.6248	0.588463
$706$	8.92112	0.335751
$707$	−52.3429	−1.96856
$708$	−1.49092	−0.0560321
$709$	37.2243	1.39799	0.698994	−	0.715127i	$-0.253631\pi$
$709$	37.2243	1.39799	0.698994	+	0.715127i	$0.253631\pi$
$710$	−9.19703	−0.345158
$711$	7.12877	0.267350
$712$	0.902145	0.0338093
$713$	−49.5459	−1.85551
$714$	7.70148	0.288221
$715$	5.86011	0.219156
$716$	8.79391	0.328644
$717$	24.4461	0.912958
$718$	9.30463	0.347246
$719$	2.46349	0.0918729	0.0459364	−	0.998944i	$-0.485373\pi$
$719$	2.46349	0.0918729	0.0459364	+	0.998944i	$0.485373\pi$
$720$	6.88551	0.256608
$721$	46.7746	1.74198
$722$	−0.845468	−0.0314651
$723$	−31.4736	−1.17051
$724$	0.889121	0.0330439
$725$	87.7949	3.26062
$726$	−6.53785	−0.242642
$727$	−27.8800	−1.03401	−0.517005	−	0.855982i	$-0.672953\pi$
$727$	−27.8800	−1.03401	−0.517005	+	0.855982i	$0.672953\pi$
$728$	19.4189	0.719711
$729$	30.0138	1.11162
$730$	−19.7699	−0.731715
$731$	40.8416	1.51058
$732$	−22.7150	−0.839572
$733$	1.06781	0.0394404	0.0197202	−	0.999806i	$-0.493722\pi$
$733$	1.06781	0.0394404	0.0197202	+	0.999806i	$0.493722\pi$
$734$	4.18223	0.154369
$735$	6.43859	0.237491
$736$	27.0833	0.998305
$737$	2.16793	0.0798567
$738$	−1.78247	−0.0656135
$739$	−19.5195	−0.718037	−0.359019	−	0.933330i	$-0.616889\pi$
$739$	−19.5195	−0.718037	−0.359019	+	0.933330i	$0.616889\pi$
$740$	−2.50571	−0.0921116
$741$	−32.7469	−1.20299
$742$	−2.12507	−0.0780138
$743$	12.4563	0.456978	0.228489	−	0.973547i	$-0.426622\pi$
$743$	12.4563	0.456978	0.228489	+	0.973547i	$0.426622\pi$
$744$	−17.7157	−0.649490
$745$	−84.5934	−3.09926
$746$	0.812089	0.0297327
$747$	3.04107	0.111267
$748$	2.84244	0.103930
$749$	−17.5587	−0.641582
$750$	−9.16438	−0.334636
$751$	−25.7804	−0.940741	−0.470371	−	0.882469i	$-0.655880\pi$
$751$	−25.7804	−0.940741	−0.470371	+	0.882469i	$0.655880\pi$
$752$	8.38128	0.305634
$753$	−20.2308	−0.737250
$754$	17.1519	0.624635
$755$	−45.5571	−1.65799
$756$	29.3548	1.06762
$757$	18.2009	0.661521	0.330761	−	0.943715i	$-0.392695\pi$
$757$	18.2009	0.661521	0.330761	+	0.943715i	$0.392695\pi$
$758$	8.16065	0.296408
$759$	3.42722	0.124400
$760$	25.7080	0.932527
$761$	−32.0271	−1.16098	−0.580491	−	0.814266i	$-0.697139\pi$
$761$	−32.0271	−1.16098	−0.580491	+	0.814266i	$0.697139\pi$
$762$	9.33994	0.338350
$763$	24.3002	0.879727
$764$	34.6681	1.25425
$765$	−9.92260	−0.358752
$766$	−2.95946	−0.106929
$767$	2.37604	0.0857938
$768$	−8.27911	−0.298747
$769$	40.8355	1.47256	0.736282	−	0.676675i	$-0.236580\pi$
$769$	40.8355	1.47256	0.736282	+	0.676675i	$0.236580\pi$
$770$	−1.40865	−0.0507643
$771$	17.6726	0.636462
$772$	−43.8038	−1.57653
$773$	−21.9644	−0.790003	−0.395002	−	0.918680i	$-0.629256\pi$
$773$	−21.9644	−0.790003	−0.395002	+	0.918680i	$0.629256\pi$
$774$	−2.06053	−0.0740644
$775$	69.4512	2.49476
$776$	−0.882886	−0.0316938
$777$	−1.59649	−0.0572739
$778$	0.191800	0.00687637
$779$	36.1109	1.29381
$780$	49.3772	1.76799
$781$	−2.16273	−0.0773885
$782$	−11.2661	−0.402875
$783$	53.9515	1.92807
$784$	3.45372	0.123347
$785$	47.2877	1.68777
$786$	−1.52981	−0.0545664
$787$	55.4908	1.97803	0.989017	−	0.147803i	$-0.0472201\pi$
$787$	55.4908	1.97803	0.989017	+	0.147803i	$0.0472201\pi$
$788$	−25.1665	−0.896520
$789$	−0.178299	−0.00634760
$790$	−17.6021	−0.626253
$791$	−37.2777	−1.32544
$792$	−0.298405	−0.0106034
$793$	36.2004	1.28551
$794$	−2.28788	−0.0811937
$795$	−11.2438	−0.398776
$796$	2.30077	0.0815487
$797$	−12.9732	−0.459534	−0.229767	−	0.973246i	$-0.573796\pi$
$797$	−12.9732	−0.459534	−0.229767	+	0.973246i	$0.573796\pi$
$798$	7.87170	0.278655
$799$	−12.0781	−0.427294
$800$	−37.9642	−1.34224
$801$	−0.355900	−0.0125751
$802$	4.73513	0.167203
$803$	−4.64899	−0.164059
$804$	18.2670	0.644226
$805$	−69.0732	−2.43451
$806$	13.5682	0.477919
$807$	−5.62217	−0.197910
$808$	27.3784	0.963170
$809$	−20.3113	−0.714109	−0.357054	−	0.934084i	$-0.616219\pi$
$809$	−20.3113	−0.714109	−0.357054	+	0.934084i	$0.616219\pi$
$810$	−9.99790	−0.351290
$811$	25.2796	0.887688	0.443844	−	0.896104i	$-0.353614\pi$
$811$	25.2796	0.887688	0.443844	+	0.896104i	$0.353614\pi$
$812$	51.0075	1.79001
$813$	−17.7199	−0.621465
$814$	0.0476278	0.00166935
$815$	44.0201	1.54196
$816$	21.8580	0.765183
$817$	41.7443	1.46045
$818$	−0.164385	−0.00574758
$819$	−7.66082	−0.267691
$820$	−54.4495	−1.90146
$821$	39.8004	1.38904	0.694522	−	0.719471i	$-0.255616\pi$
$821$	39.8004	1.38904	0.694522	+	0.719471i	$0.255616\pi$
$822$	3.75333	0.130913
$823$	12.2526	0.427100	0.213550	−	0.976932i	$-0.431497\pi$
$823$	12.2526	0.427100	0.213550	+	0.976932i	$0.431497\pi$
$824$	−24.4659	−0.852311
$825$	−4.80413	−0.167258
$826$	−0.571151	−0.0198729
$827$	34.7706	1.20909	0.604547	−	0.796570i	$-0.293354\pi$
$827$	34.7706	1.20909	0.604547	+	0.796570i	$0.293354\pi$
$828$	−7.03194	−0.244377
$829$	0.614738	0.0213507	0.0106754	−	0.999943i	$-0.496602\pi$
$829$	0.614738	0.0213507	0.0106754	+	0.999943i	$0.496602\pi$
$830$	−7.50889	−0.260637
$831$	17.2604	0.598757
$832$	21.2105	0.735342
$833$	−4.97710	−0.172446
$834$	−3.41862	−0.118377
$835$	64.6591	2.23762
$836$	2.90527	0.100481
$837$	42.6790	1.47520
$838$	2.32503	0.0803170
$839$	25.7977	0.890637	0.445318	−	0.895372i	$-0.353091\pi$
$839$	25.7977	0.890637	0.445318	+	0.895372i	$0.353091\pi$
$840$	−24.6980	−0.852161
$841$	64.7472	2.23266
$842$	−5.07542	−0.174911
$843$	−30.7692	−1.05975
$844$	−9.85646	−0.339273
$845$	−29.9324	−1.02971
$846$	0.609364	0.0209504
$847$	30.9854	1.06467
$848$	−6.03128	−0.207115
$849$	−10.5797	−0.363094
$850$	15.7923	0.541672
$851$	2.33543	0.0800575
$852$	−18.2231	−0.624314
$853$	1.99666	0.0683643	0.0341822	−	0.999416i	$-0.489117\pi$
$853$	1.99666	0.0683643	0.0341822	+	0.999416i	$0.489117\pi$
$854$	−8.70183	−0.297771
$855$	−10.1419	−0.346846
$856$	9.18426	0.313911
$857$	−54.5879	−1.86469	−0.932343	−	0.361575i	$-0.882239\pi$
$857$	−54.5879	−1.86469	−0.932343	+	0.361575i	$0.882239\pi$
$858$	−0.938549	−0.0320415
$859$	−37.4710	−1.27849	−0.639247	−	0.769001i	$-0.720754\pi$
$859$	−37.4710	−1.27849	−0.639247	+	0.769001i	$0.720754\pi$
$860$	−62.9438	−2.14636
$861$	−34.6921	−1.18230
$862$	0.848574	0.0289025
$863$	11.8377	0.402960	0.201480	−	0.979493i	$-0.435425\pi$
$863$	11.8377	0.402960	0.201480	+	0.979493i	$0.435425\pi$
$864$	−23.3297	−0.793692
$865$	−70.1187	−2.38411
$866$	10.0350	0.341002
$867$	−5.09426	−0.173010
$868$	40.3500	1.36957
$869$	−4.13921	−0.140413
$870$	−21.8147	−0.739587
$871$	−29.1116	−0.986408
$872$	−12.7105	−0.430431
$873$	0.348302	0.0117882
$874$	−11.5151	−0.389504
$875$	43.4335	1.46832
$876$	−39.1723	−1.32351
$877$	30.5821	1.03268	0.516342	−	0.856383i	$-0.327293\pi$
$877$	30.5821	1.03268	0.516342	+	0.856383i	$0.327293\pi$
$878$	−8.91341	−0.300813
$879$	−29.3351	−0.989449
$880$	−3.99797	−0.134772
$881$	−14.1448	−0.476552	−0.238276	−	0.971198i	$-0.576582\pi$
$881$	−14.1448	−0.476552	−0.238276	+	0.971198i	$0.576582\pi$
$882$	0.251104	0.00845512
$883$	35.5810	1.19739	0.598697	−	0.800975i	$-0.295685\pi$
$883$	35.5810	1.19739	0.598697	+	0.800975i	$0.295685\pi$
$884$	−38.1691	−1.28377
$885$	−3.02197	−0.101583
$886$	3.32810	0.111810
$887$	30.2855	1.01689	0.508443	−	0.861095i	$-0.330221\pi$
$887$	30.2855	1.01689	0.508443	+	0.861095i	$0.330221\pi$
$888$	0.835061	0.0280228
$889$	−44.2655	−1.48462
$890$	0.878773	0.0294565
$891$	−2.35106	−0.0787634
$892$	53.6525	1.79642
$893$	−12.3451	−0.413112
$894$	13.5484	0.453126
$895$	17.8246	0.595809
$896$	−28.9380	−0.966752
$897$	−46.0217	−1.53662
$898$	4.46509	0.149002
$899$	74.1598	2.47337
$900$	9.85705	0.328568
$901$	8.69158	0.289558
$902$	1.03496	0.0344605
$903$	−40.1042	−1.33458
$904$	19.4985	0.648509
$905$	1.80218	0.0599064
$906$	7.29638	0.242406
$907$	−29.3799	−0.975545	−0.487772	−	0.872971i	$-0.662190\pi$
$907$	−29.3799	−0.975545	−0.487772	+	0.872971i	$0.662190\pi$
$908$	38.8533	1.28939
$909$	−10.8009	−0.358243
$910$	18.9158	0.627052
$911$	−26.0571	−0.863310	−0.431655	−	0.902039i	$-0.642070\pi$
$911$	−26.0571	−0.863310	−0.431655	+	0.902039i	$0.642070\pi$
$912$	22.3411	0.739787
$913$	−1.76575	−0.0584379
$914$	7.89721	0.261216
$915$	−46.0416	−1.52209
$916$	−21.6769	−0.716226
$917$	7.25034	0.239427
$918$	9.70466	0.320302
$919$	21.7610	0.717829	0.358914	−	0.933370i	$-0.383147\pi$
$919$	21.7610	0.717829	0.358914	+	0.933370i	$0.383147\pi$
$920$	36.1294	1.19115
$921$	17.6246	0.580749
$922$	−4.41243	−0.145316
$923$	29.0417	0.955920
$924$	−2.79112	−0.0918212
$925$	−3.27370	−0.107639
$926$	−5.79100	−0.190304
$927$	9.65190	0.317010
$928$	−40.5381	−1.33073
$929$	20.7461	0.680657	0.340329	−	0.940307i	$-0.389462\pi$
$929$	20.7461	0.680657	0.340329	+	0.940307i	$0.389462\pi$
$930$	−17.2568	−0.565872
$931$	−5.08711	−0.166723
$932$	18.9765	0.621597
$933$	−23.3696	−0.765085
$934$	2.15223	0.0704233
$935$	5.76141	0.188418
$936$	4.00706	0.130975
$937$	−20.0324	−0.654429	−0.327215	−	0.944950i	$-0.606110\pi$
$937$	−20.0324	−0.654429	−0.327215	+	0.944950i	$0.606110\pi$
$938$	6.99783	0.228487
$939$	5.56445	0.181589
$940$	18.6144	0.607136
$941$	14.9045	0.485874	0.242937	−	0.970042i	$-0.421889\pi$
$941$	14.9045	0.485874	0.242937	+	0.970042i	$0.421889\pi$
$942$	−7.57356	−0.246760
$943$	50.7493	1.65263
$944$	−1.62102	−0.0527596
$945$	59.4999	1.93553
$946$	1.19642	0.0388989
$947$	12.9596	0.421131	0.210565	−	0.977580i	$-0.432469\pi$
$947$	12.9596	0.421131	0.210565	+	0.977580i	$0.432469\pi$
$948$	−34.8770	−1.13275
$949$	62.4279	2.02650
$950$	16.1414	0.523695
$951$	−40.3054	−1.30699
$952$	19.0918	0.618769
$953$	−31.5188	−1.02099	−0.510497	−	0.859880i	$-0.670539\pi$
$953$	−31.5188	−1.02099	−0.510497	+	0.859880i	$0.670539\pi$
$954$	−0.438506	−0.0141972
$955$	70.2696	2.27387
$956$	29.1237	0.941927
$957$	−5.12984	−0.165824
$958$	−0.588298	−0.0190071
$959$	−17.7885	−0.574420
$960$	−26.9767	−0.870669
$961$	27.6650	0.892418
$962$	−0.639560	−0.0206202
$963$	−3.62323	−0.116757
$964$	−37.4957	−1.20766
$965$	−88.7869	−2.85815
$966$	11.0627	0.355936
$967$	2.60046	0.0836253	0.0418126	−	0.999125i	$-0.486687\pi$
$967$	2.60046	0.0836253	0.0418126	+	0.999125i	$0.486687\pi$
$968$	−16.2072	−0.520919
$969$	−32.1954	−1.03427
$970$	−0.860013	−0.0276133
$971$	−27.1651	−0.871769	−0.435885	−	0.900003i	$-0.643564\pi$
$971$	−27.1651	−0.871769	−0.435885	+	0.900003i	$0.643564\pi$
$972$	11.1227	0.356762
$973$	16.2021	0.519416
$974$	2.01410	0.0645359
$975$	64.5112	2.06601
$976$	−24.6971	−0.790536
$977$	−44.4185	−1.42107	−0.710537	−	0.703660i	$-0.751548\pi$
$977$	−44.4185	−1.42107	−0.710537	+	0.703660i	$0.751548\pi$
$978$	−7.05022	−0.225441
$979$	0.206648	0.00660450
$980$	7.67056	0.245027
$981$	5.01433	0.160095
$982$	−14.6074	−0.466142
$983$	−50.1035	−1.59805	−0.799027	−	0.601295i	$-0.794652\pi$
$983$	−50.1035	−1.59805	−0.799027	+	0.601295i	$0.794652\pi$
$984$	18.1461	0.578475
$985$	−51.0105	−1.62533
$986$	16.8630	0.537027
$987$	11.8601	0.377510
$988$	−39.0127	−1.24116
$989$	58.6664	1.86548
$990$	−0.290674	−0.00923823
$991$	2.48996	0.0790961	0.0395480	−	0.999218i	$-0.487408\pi$
$991$	2.48996	0.0790961	0.0395480	+	0.999218i	$0.487408\pi$
$992$	−32.0681	−1.01816
$993$	30.4714	0.966981
$994$	−6.98104	−0.221425
$995$	4.66348	0.147842
$996$	−14.8782	−0.471435
$997$	−36.6815	−1.16171	−0.580857	−	0.814006i	$-0.697282\pi$
$997$	−36.6815	−1.16171	−0.580857	+	0.814006i	$0.697282\pi$
$998$	10.3710	0.328288
$999$	−2.01175	−0.0636488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.12	✓	30
3.2	odd	2		5571.2.a.g.1.19		30
4.3	odd	2		9904.2.a.n.1.21		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.12	✓	30	1.1	even	1	trivial
5571.2.a.g.1.19		30	3.2	odd	2
9904.2.a.n.1.21		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)

\(f(q)\)	\(=\)	\(q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +O(q^{10})\)	\(q-0.386745 q^{2} -1.55323 q^{3} -1.85043 q^{4} -3.75067 q^{5} +0.600704 q^{6} -2.84697 q^{7} +1.48913 q^{8} -0.587469 q^{9} +1.45055 q^{10} +0.341105 q^{11} +2.87415 q^{12} -4.58045 q^{13} +1.10105 q^{14} +5.82567 q^{15} +3.12494 q^{16} -4.50331 q^{17} +0.227200 q^{18} -4.60284 q^{19} +6.94035 q^{20} +4.42200 q^{21} -0.131920 q^{22} -6.46872 q^{23} -2.31297 q^{24} +9.06755 q^{25} +1.77147 q^{26} +5.57217 q^{27} +5.26811 q^{28} +9.68231 q^{29} -2.25305 q^{30} +7.65931 q^{31} -4.18682 q^{32} -0.529815 q^{33} +1.74163 q^{34} +10.6780 q^{35} +1.08707 q^{36} -0.361034 q^{37} +1.78012 q^{38} +7.11451 q^{39} -5.58525 q^{40} -7.84535 q^{41} -1.71018 q^{42} -9.06924 q^{43} -0.631190 q^{44} +2.20340 q^{45} +2.50174 q^{46} +2.68206 q^{47} -4.85376 q^{48} +1.10521 q^{49} -3.50683 q^{50} +6.99468 q^{51} +8.47580 q^{52} -1.93004 q^{53} -2.15501 q^{54} -1.27937 q^{55} -4.23951 q^{56} +7.14928 q^{57} -3.74458 q^{58} -0.518734 q^{59} -10.7800 q^{60} -7.90323 q^{61} -2.96219 q^{62} +1.67250 q^{63} -4.63066 q^{64} +17.1798 q^{65} +0.204903 q^{66} +6.35561 q^{67} +8.33305 q^{68} +10.0474 q^{69} -4.12967 q^{70} -6.34036 q^{71} -0.874818 q^{72} -13.6292 q^{73} +0.139628 q^{74} -14.0840 q^{75} +8.51722 q^{76} -0.971114 q^{77} -2.75150 q^{78} -12.1347 q^{79} -11.7206 q^{80} -6.89247 q^{81} +3.03415 q^{82} -5.17657 q^{83} -8.18259 q^{84} +16.8904 q^{85} +3.50748 q^{86} -15.0389 q^{87} +0.507950 q^{88} +0.605819 q^{89} -0.852154 q^{90} +13.0404 q^{91} +11.9699 q^{92} -11.8967 q^{93} -1.03727 q^{94} +17.2637 q^{95} +6.50310 q^{96} -0.592886 q^{97} -0.427434 q^{98} -0.200388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 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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