LMFDB - Embedded newform 6005.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68633 q^{2} -0.538907 q^{3} +0.843700 q^{4} -1.00000 q^{5} +0.908773 q^{6} -3.51769 q^{7} +1.94990 q^{8} -2.70958 q^{9} +O(q^{10})$	\(q-1.68633 q^{2} -0.538907 q^{3} +0.843700 q^{4} -1.00000 q^{5} +0.908773 q^{6} -3.51769 q^{7} +1.94990 q^{8} -2.70958 q^{9} +1.68633 q^{10} -5.12324 q^{11} -0.454676 q^{12} +4.11716 q^{13} +5.93198 q^{14} +0.538907 q^{15} -4.97557 q^{16} -6.45625 q^{17} +4.56924 q^{18} -2.53710 q^{19} -0.843700 q^{20} +1.89571 q^{21} +8.63946 q^{22} -1.09855 q^{23} -1.05081 q^{24} +1.00000 q^{25} -6.94289 q^{26} +3.07693 q^{27} -2.96788 q^{28} +8.87785 q^{29} -0.908773 q^{30} +10.3960 q^{31} +4.49064 q^{32} +2.76095 q^{33} +10.8874 q^{34} +3.51769 q^{35} -2.28607 q^{36} -5.04848 q^{37} +4.27837 q^{38} -2.21877 q^{39} -1.94990 q^{40} -3.57562 q^{41} -3.19678 q^{42} -9.73224 q^{43} -4.32248 q^{44} +2.70958 q^{45} +1.85251 q^{46} +8.50950 q^{47} +2.68137 q^{48} +5.37414 q^{49} -1.68633 q^{50} +3.47932 q^{51} +3.47365 q^{52} +11.1865 q^{53} -5.18871 q^{54} +5.12324 q^{55} -6.85915 q^{56} +1.36726 q^{57} -14.9710 q^{58} +14.0946 q^{59} +0.454676 q^{60} +5.67995 q^{61} -17.5311 q^{62} +9.53146 q^{63} +2.37845 q^{64} -4.11716 q^{65} -4.65586 q^{66} -1.63768 q^{67} -5.44714 q^{68} +0.592014 q^{69} -5.93198 q^{70} -11.6063 q^{71} -5.28341 q^{72} +5.40454 q^{73} +8.51339 q^{74} -0.538907 q^{75} -2.14055 q^{76} +18.0220 q^{77} +3.74157 q^{78} -4.14076 q^{79} +4.97557 q^{80} +6.47056 q^{81} +6.02966 q^{82} +13.1144 q^{83} +1.59941 q^{84} +6.45625 q^{85} +16.4117 q^{86} -4.78433 q^{87} -9.98980 q^{88} -14.4809 q^{89} -4.56924 q^{90} -14.4829 q^{91} -0.926843 q^{92} -5.60248 q^{93} -14.3498 q^{94} +2.53710 q^{95} -2.42004 q^{96} -14.7255 q^{97} -9.06257 q^{98} +13.8818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−1.68633	−1.19241	−0.596207	−	0.802831i	$-0.703326\pi$
$2$	−1.68633	−1.19241	−0.596207	+	0.802831i	$0.703326\pi$
$3$	−0.538907	−0.311138	−0.155569	−	0.987825i	$-0.549721\pi$
$3$	−0.538907	−0.311138	−0.155569	+	0.987825i	$0.549721\pi$
$4$	0.843700	0.421850
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.908773	0.371005
$7$	−3.51769	−1.32956	−0.664781	−	0.747038i	$-0.731475\pi$
$7$	−3.51769	−1.32956	−0.664781	+	0.747038i	$0.731475\pi$
$8$	1.94990	0.689394
$9$	−2.70958	−0.903193
$10$	1.68633	0.533264
$11$	−5.12324	−1.54471	−0.772357	−	0.635189i	$-0.780922\pi$
$11$	−5.12324	−1.54471	−0.772357	+	0.635189i	$0.780922\pi$
$12$	−0.454676	−0.131254
$13$	4.11716	1.14190	0.570948	−	0.820986i	$-0.306576\pi$
$13$	4.11716	1.14190	0.570948	+	0.820986i	$0.306576\pi$
$14$	5.93198	1.58539
$15$	0.538907	0.139145
$16$	−4.97557	−1.24389
$17$	−6.45625	−1.56587	−0.782935	−	0.622103i	$-0.786278\pi$
$17$	−6.45625	−1.56587	−0.782935	+	0.622103i	$0.786278\pi$
$18$	4.56924	1.07698
$19$	−2.53710	−0.582050	−0.291025	−	0.956715i	$-0.593996\pi$
$19$	−2.53710	−0.582050	−0.291025	+	0.956715i	$0.593996\pi$
$20$	−0.843700	−0.188657
$21$	1.89571	0.413677
$22$	8.63946	1.84194
$23$	−1.09855	−0.229063	−0.114531	−	0.993420i	$-0.536537\pi$
$23$	−1.09855	−0.229063	−0.114531	+	0.993420i	$0.536537\pi$
$24$	−1.05081	−0.214497
$25$	1.00000	0.200000
$26$	−6.94289	−1.36161
$27$	3.07693	0.592155
$28$	−2.96788	−0.560876
$29$	8.87785	1.64858	0.824288	−	0.566171i	$-0.191576\pi$
$29$	8.87785	1.64858	0.824288	+	0.566171i	$0.191576\pi$
$30$	−0.908773	−0.165918
$31$	10.3960	1.86718	0.933590	−	0.358343i	$-0.116658\pi$
$31$	10.3960	1.86718	0.933590	+	0.358343i	$0.116658\pi$
$32$	4.49064	0.793840
$33$	2.76095	0.480619
$34$	10.8874	1.86717
$35$	3.51769	0.594598
$36$	−2.28607	−0.381012
$37$	−5.04848	−0.829965	−0.414982	−	0.909829i	$-0.636212\pi$
$37$	−5.04848	−0.829965	−0.414982	+	0.909829i	$0.636212\pi$
$38$	4.27837	0.694044
$39$	−2.21877	−0.355287
$40$	−1.94990	−0.308306
$41$	−3.57562	−0.558418	−0.279209	−	0.960230i	$-0.590072\pi$
$41$	−3.57562	−0.558418	−0.279209	+	0.960230i	$0.590072\pi$
$42$	−3.19678	−0.493274
$43$	−9.73224	−1.48415	−0.742076	−	0.670315i	$-0.766159\pi$
$43$	−9.73224	−1.48415	−0.742076	+	0.670315i	$0.766159\pi$
$44$	−4.32248	−0.651638
$45$	2.70958	0.403920
$46$	1.85251	0.273137
$47$	8.50950	1.24124	0.620619	−	0.784112i	$-0.286881\pi$
$47$	8.50950	1.24124	0.620619	+	0.784112i	$0.286881\pi$
$48$	2.68137	0.387022
$49$	5.37414	0.767735
$50$	−1.68633	−0.238483
$51$	3.47932	0.487202
$52$	3.47365	0.481709
$53$	11.1865	1.53659	0.768295	−	0.640096i	$-0.221105\pi$
$53$	11.1865	1.53659	0.768295	+	0.640096i	$0.221105\pi$
$54$	−5.18871	−0.706094
$55$	5.12324	0.690817
$56$	−6.85915	−0.916592
$57$	1.36726	0.181098
$58$	−14.9710	−1.96578
$59$	14.0946	1.83497	0.917483	−	0.397775i	$-0.130218\pi$
$59$	14.0946	1.83497	0.917483	+	0.397775i	$0.130218\pi$
$60$	0.454676	0.0586984
$61$	5.67995	0.727243	0.363622	−	0.931547i	$-0.381540\pi$
$61$	5.67995	0.727243	0.363622	+	0.931547i	$0.381540\pi$
$62$	−17.5311	−2.22645
$63$	9.53146	1.20085
$64$	2.37845	0.297306
$65$	−4.11716	−0.510671
$66$	−4.65586	−0.573097
$67$	−1.63768	−0.200074	−0.100037	−	0.994984i	$-0.531896\pi$
$67$	−1.63768	−0.200074	−0.100037	+	0.994984i	$0.531896\pi$
$68$	−5.44714	−0.660562
$69$	0.592014	0.0712701
$70$	−5.93198	−0.709007
$71$	−11.6063	−1.37741	−0.688705	−	0.725042i	$-0.741820\pi$
$71$	−11.6063	−1.37741	−0.688705	+	0.725042i	$0.741820\pi$
$72$	−5.28341	−0.622656
$73$	5.40454	0.632553	0.316277	−	0.948667i	$-0.397567\pi$
$73$	5.40454	0.632553	0.316277	+	0.948667i	$0.397567\pi$
$74$	8.51339	0.989661
$75$	−0.538907	−0.0622276
$76$	−2.14055	−0.245538
$77$	18.0220	2.05379
$78$	3.74157	0.423649
$79$	−4.14076	−0.465872	−0.232936	−	0.972492i	$-0.574833\pi$
$79$	−4.14076	−0.465872	−0.232936	+	0.972492i	$0.574833\pi$
$80$	4.97557	0.556286
$81$	6.47056	0.718951
$82$	6.02966	0.665865
$83$	13.1144	1.43949	0.719746	−	0.694238i	$-0.244258\pi$
$83$	13.1144	1.43949	0.719746	+	0.694238i	$0.244258\pi$
$84$	1.59941	0.174510
$85$	6.45625	0.700279
$86$	16.4117	1.76972
$87$	−4.78433	−0.512934
$88$	−9.98980	−1.06492
$89$	−14.4809	−1.53497	−0.767487	−	0.641065i	$-0.778493\pi$
$89$	−14.4809	−1.53497	−0.767487	+	0.641065i	$0.778493\pi$
$90$	−4.56924	−0.481640
$91$	−14.4829	−1.51822
$92$	−0.926843	−0.0966301
$93$	−5.60248	−0.580950
$94$	−14.3498	−1.48007
$95$	2.53710	0.260301
$96$	−2.42004	−0.246994
$97$	−14.7255	−1.49514	−0.747572	−	0.664181i	$-0.768781\pi$
$97$	−14.7255	−1.49514	−0.747572	+	0.664181i	$0.768781\pi$
$98$	−9.06257	−0.915457
$99$	13.8818	1.39518
$100$	0.843700	0.0843700
$101$	−4.75641	−0.473281	−0.236640	−	0.971597i	$-0.576046\pi$
$101$	−4.75641	−0.473281	−0.236640	+	0.971597i	$0.576046\pi$
$102$	−5.86726	−0.580946
$103$	0.822879	0.0810807	0.0405403	−	0.999178i	$-0.487092\pi$
$103$	0.822879	0.0810807	0.0405403	+	0.999178i	$0.487092\pi$
$104$	8.02806	0.787216
$105$	−1.89571	−0.185002
$106$	−18.8642	−1.83225
$107$	7.51011	0.726030	0.363015	−	0.931783i	$-0.381747\pi$
$107$	7.51011	0.726030	0.363015	+	0.931783i	$0.381747\pi$
$108$	2.59601	0.249801
$109$	−11.8135	−1.13153	−0.565765	−	0.824567i	$-0.691419\pi$
$109$	−11.8135	−1.13153	−0.565765	+	0.824567i	$0.691419\pi$
$110$	−8.63946	−0.823740
$111$	2.72066	0.258233
$112$	17.5025	1.65383
$113$	15.5124	1.45928	0.729642	−	0.683829i	$-0.239687\pi$
$113$	15.5124	1.45928	0.729642	+	0.683829i	$0.239687\pi$
$114$	−2.30564	−0.215943
$115$	1.09855	0.102440
$116$	7.49024	0.695452
$117$	−11.1558	−1.03135
$118$	−23.7682	−2.18804
$119$	22.7111	2.08192
$120$	1.05081	0.0959258
$121$	15.2476	1.38614
$122$	−9.57826	−0.867175
$123$	1.92692	0.173745
$124$	8.77112	0.787670
$125$	−1.00000	−0.0894427
$126$	−16.0732	−1.43191
$127$	−7.91127	−0.702012	−0.351006	−	0.936373i	$-0.614160\pi$
$127$	−7.91127	−0.702012	−0.351006	+	0.936373i	$0.614160\pi$
$128$	−12.9921	−1.14835
$129$	5.24477	0.461776
$130$	6.94289	0.608931
$131$	−12.2134	−1.06709	−0.533547	−	0.845770i	$-0.679141\pi$
$131$	−12.2134	−1.06709	−0.533547	+	0.845770i	$0.679141\pi$
$132$	2.32941	0.202749
$133$	8.92472	0.773871
$134$	2.76166	0.238571
$135$	−3.07693	−0.264820
$136$	−12.5890	−1.07950
$137$	6.70482	0.572832	0.286416	−	0.958105i	$-0.407536\pi$
$137$	6.70482	0.572832	0.286416	+	0.958105i	$0.407536\pi$
$138$	−0.998329	−0.0849834
$139$	17.2550	1.46355	0.731775	−	0.681546i	$-0.238692\pi$
$139$	17.2550	1.46355	0.731775	+	0.681546i	$0.238692\pi$
$140$	2.96788	0.250831
$141$	−4.58582	−0.386196
$142$	19.5720	1.64244
$143$	−21.0932	−1.76390
$144$	13.4817	1.12348
$145$	−8.87785	−0.737266
$146$	−9.11382	−0.754265
$147$	−2.89616	−0.238871
$148$	−4.25940	−0.350121
$149$	9.13891	0.748689	0.374345	−	0.927290i	$-0.377868\pi$
$149$	9.13891	0.748689	0.374345	+	0.927290i	$0.377868\pi$
$150$	0.908773	0.0742010
$151$	0.991498	0.0806870	0.0403435	−	0.999186i	$-0.487155\pi$
$151$	0.991498	0.0806870	0.0403435	+	0.999186i	$0.487155\pi$
$152$	−4.94708	−0.401262
$153$	17.4937	1.41428
$154$	−30.3909	−2.44897
$155$	−10.3960	−0.835028
$156$	−1.87197	−0.149878
$157$	16.3650	1.30607	0.653037	−	0.757326i	$-0.273495\pi$
$157$	16.3650	1.30607	0.653037	+	0.757326i	$0.273495\pi$
$158$	6.98267	0.555512
$159$	−6.02850	−0.478091
$160$	−4.49064	−0.355016
$161$	3.86434	0.304553
$162$	−10.9115	−0.857287
$163$	−1.74917	−0.137005	−0.0685026	−	0.997651i	$-0.521822\pi$
$163$	−1.74917	−0.137005	−0.0685026	+	0.997651i	$0.521822\pi$
$164$	−3.01675	−0.235569
$165$	−2.76095	−0.214939
$166$	−22.1152	−1.71647
$167$	−1.27817	−0.0989081	−0.0494541	−	0.998776i	$-0.515748\pi$
$167$	−1.27817	−0.0989081	−0.0494541	+	0.998776i	$0.515748\pi$
$168$	3.69644	0.285186
$169$	3.95104	0.303926
$170$	−10.8874	−0.835022
$171$	6.87446	0.525703
$172$	−8.21109	−0.626090
$173$	−2.87321	−0.218446	−0.109223	−	0.994017i	$-0.534836\pi$
$173$	−2.87321	−0.218446	−0.109223	+	0.994017i	$0.534836\pi$
$174$	8.06795	0.611630
$175$	−3.51769	−0.265912
$176$	25.4910	1.92146
$177$	−7.59569	−0.570927
$178$	24.4196	1.83032
$179$	3.14027	0.234715	0.117358	−	0.993090i	$-0.462558\pi$
$179$	3.14027	0.234715	0.117358	+	0.993090i	$0.462558\pi$
$180$	2.28607	0.170394
$181$	−3.42863	−0.254848	−0.127424	−	0.991848i	$-0.540671\pi$
$181$	−3.42863	−0.254848	−0.127424	+	0.991848i	$0.540671\pi$
$182$	24.4229	1.81035
$183$	−3.06096	−0.226273
$184$	−2.14206	−0.157914
$185$	5.04848	0.371171
$186$	9.44762	0.692733
$187$	33.0769	2.41882
$188$	7.17946	0.523616
$189$	−10.8237	−0.787307
$190$	−4.27837	−0.310386
$191$	−19.8150	−1.43377	−0.716883	−	0.697193i	$-0.754432\pi$
$191$	−19.8150	−1.43377	−0.716883	+	0.697193i	$0.754432\pi$
$192$	−1.28176	−0.0925033
$193$	13.6588	0.983181	0.491591	−	0.870826i	$-0.336416\pi$
$193$	13.6588	0.983181	0.491591	+	0.870826i	$0.336416\pi$
$194$	24.8319	1.78283
$195$	2.21877	0.158889
$196$	4.53416	0.323869
$197$	16.2487	1.15767	0.578837	−	0.815443i	$-0.303507\pi$
$197$	16.2487	1.15767	0.578837	+	0.815443i	$0.303507\pi$
$198$	−23.4093	−1.66363
$199$	−14.6558	−1.03892	−0.519462	−	0.854493i	$-0.673868\pi$
$199$	−14.6558	−1.03892	−0.519462	+	0.854493i	$0.673868\pi$
$200$	1.94990	0.137879
$201$	0.882557	0.0622507
$202$	8.02087	0.564347
$203$	−31.2295	−2.19188
$204$	2.93550	0.205526
$205$	3.57562	0.249732
$206$	−1.38764	−0.0966817
$207$	2.97660	0.206888
$208$	−20.4852	−1.42040
$209$	12.9981	0.899100
$210$	3.19678	0.220599
$211$	10.3974	0.715786	0.357893	−	0.933763i	$-0.383495\pi$
$211$	10.3974	0.715786	0.357893	+	0.933763i	$0.383495\pi$
$212$	9.43809	0.648210
$213$	6.25469	0.428564
$214$	−12.6645	−0.865728
$215$	9.73224	0.663733
$216$	5.99971	0.408228
$217$	−36.5700	−2.48253
$218$	19.9214	1.34925
$219$	−2.91254	−0.196811
$220$	4.32248	0.291421
$221$	−26.5814	−1.78806
$222$	−4.58792	−0.307921
$223$	−4.12566	−0.276275	−0.138137	−	0.990413i	$-0.544112\pi$
$223$	−4.12566	−0.276275	−0.138137	+	0.990413i	$0.544112\pi$
$224$	−15.7967	−1.05546
$225$	−2.70958	−0.180639
$226$	−26.1590	−1.74007
$227$	12.1223	0.804584	0.402292	−	0.915512i	$-0.368214\pi$
$227$	12.1223	0.804584	0.402292	+	0.915512i	$0.368214\pi$
$228$	1.15356	0.0763961
$229$	−26.8009	−1.77106	−0.885528	−	0.464586i	$-0.846203\pi$
$229$	−26.8009	−1.77106	−0.885528	+	0.464586i	$0.846203\pi$
$230$	−1.85251	−0.122151
$231$	−9.71215	−0.639013
$232$	17.3109	1.13652
$233$	−2.57028	−0.168385	−0.0841924	−	0.996450i	$-0.526831\pi$
$233$	−2.57028	−0.168385	−0.0841924	+	0.996450i	$0.526831\pi$
$234$	18.8123	1.22980
$235$	−8.50950	−0.555098
$236$	11.8916	0.774080
$237$	2.23148	0.144950
$238$	−38.2983	−2.48251
$239$	12.0917	0.782145	0.391073	−	0.920360i	$-0.372104\pi$
$239$	12.0917	0.782145	0.391073	+	0.920360i	$0.372104\pi$
$240$	−2.68137	−0.173082
$241$	5.52166	0.355681	0.177841	−	0.984059i	$-0.443089\pi$
$241$	5.52166	0.355681	0.177841	+	0.984059i	$0.443089\pi$
$242$	−25.7124	−1.65285
$243$	−12.7178	−0.815848
$244$	4.79218	0.306788
$245$	−5.37414	−0.343341
$246$	−3.24942	−0.207176
$247$	−10.4456	−0.664640
$248$	20.2712	1.28722
$249$	−7.06743	−0.447880
$250$	1.68633	0.106653
$251$	−18.6576	−1.17766	−0.588828	−	0.808258i	$-0.700411\pi$
$251$	−18.6576	−1.17766	−0.588828	+	0.808258i	$0.700411\pi$
$252$	8.04169	0.506579
$253$	5.62811	0.353836
$254$	13.3410	0.837089
$255$	−3.47932	−0.217883
$256$	17.1521	1.07200
$257$	4.20100	0.262051	0.131026	−	0.991379i	$-0.458173\pi$
$257$	4.20100	0.262051	0.131026	+	0.991379i	$0.458173\pi$
$258$	−8.84440	−0.550628
$259$	17.7590	1.10349
$260$	−3.47365	−0.215427
$261$	−24.0552	−1.48898
$262$	20.5959	1.27242
$263$	−9.73768	−0.600451	−0.300226	−	0.953868i	$-0.597062\pi$
$263$	−9.73768	−0.600451	−0.300226	+	0.953868i	$0.597062\pi$
$264$	5.38357	0.331336
$265$	−11.1865	−0.687184
$266$	−15.0500	−0.922774
$267$	7.80386	0.477588
$268$	−1.38171	−0.0844014
$269$	17.7740	1.08370	0.541849	−	0.840476i	$-0.317724\pi$
$269$	17.7740	1.08370	0.541849	+	0.840476i	$0.317724\pi$
$270$	5.18871	0.315775
$271$	−11.7034	−0.710929	−0.355464	−	0.934690i	$-0.615677\pi$
$271$	−11.7034	−0.710929	−0.355464	+	0.934690i	$0.615677\pi$
$272$	32.1235	1.94777
$273$	7.80493	0.472376
$274$	−11.3065	−0.683052
$275$	−5.12324	−0.308943
$276$	0.499482	0.0300653
$277$	−2.46935	−0.148369	−0.0741843	−	0.997245i	$-0.523635\pi$
$277$	−2.46935	−0.148369	−0.0741843	+	0.997245i	$0.523635\pi$
$278$	−29.0976	−1.74516
$279$	−28.1688	−1.68642
$280$	6.85915	0.409912
$281$	−2.03426	−0.121354	−0.0606768	−	0.998157i	$-0.519326\pi$
$281$	−2.03426	−0.121354	−0.0606768	+	0.998157i	$0.519326\pi$
$282$	7.73320	0.460505
$283$	−1.78146	−0.105897	−0.0529484	−	0.998597i	$-0.516862\pi$
$283$	−1.78146	−0.105897	−0.0529484	+	0.998597i	$0.516862\pi$
$284$	−9.79220	−0.581060
$285$	−1.36726	−0.0809894
$286$	35.5701	2.10330
$287$	12.5779	0.742451
$288$	−12.1677	−0.716991
$289$	24.6832	1.45195
$290$	14.9710	0.879125
$291$	7.93565	0.465196
$292$	4.55981	0.266843
$293$	12.4222	0.725711	0.362855	−	0.931845i	$-0.381802\pi$
$293$	12.4222	0.725711	0.362855	+	0.931845i	$0.381802\pi$
$294$	4.88388	0.284833
$295$	−14.0946	−0.820622
$296$	−9.84403	−0.572173
$297$	−15.7638	−0.914711
$298$	−15.4112	−0.892747
$299$	−4.52289	−0.261566
$300$	−0.454676	−0.0262507
$301$	34.2350	1.97327
$302$	−1.67199	−0.0962123
$303$	2.56326	0.147256
$304$	12.6235	0.724007
$305$	−5.67995	−0.325233
$306$	−29.5001	−1.68641
$307$	−14.7822	−0.843664	−0.421832	−	0.906674i	$-0.638613\pi$
$307$	−14.7822	−0.843664	−0.421832	+	0.906674i	$0.638613\pi$
$308$	15.2051	0.866393
$309$	−0.443455	−0.0252273
$310$	17.5311	0.995699
$311$	−22.5834	−1.28059	−0.640294	−	0.768130i	$-0.721187\pi$
$311$	−22.5834	−1.28059	−0.640294	+	0.768130i	$0.721187\pi$
$312$	−4.32637	−0.244933
$313$	28.3334	1.60150	0.800750	−	0.598999i	$-0.204435\pi$
$313$	28.3334	1.60150	0.800750	+	0.598999i	$0.204435\pi$
$314$	−27.5968	−1.55738
$315$	−9.53146	−0.537037
$316$	−3.49356	−0.196528
$317$	16.7383	0.940116	0.470058	−	0.882636i	$-0.344233\pi$
$317$	16.7383	0.940116	0.470058	+	0.882636i	$0.344233\pi$
$318$	10.1660	0.570082
$319$	−45.4833	−2.54658
$320$	−2.37845	−0.132960
$321$	−4.04725	−0.225895
$322$	−6.51655	−0.363153
$323$	16.3801	0.911414
$324$	5.45921	0.303290
$325$	4.11716	0.228379
$326$	2.94967	0.163367
$327$	6.36638	0.352062
$328$	−6.97210	−0.384970
$329$	−29.9338	−1.65030
$330$	4.65586	0.256297
$331$	−12.8319	−0.705303	−0.352651	−	0.935755i	$-0.614720\pi$
$331$	−12.8319	−0.705303	−0.352651	+	0.935755i	$0.614720\pi$
$332$	11.0646	0.607249
$333$	13.6793	0.749618
$334$	2.15542	0.117939
$335$	1.63768	0.0894760
$336$	−9.43222	−0.514570
$337$	−0.264702	−0.0144192	−0.00720962	−	0.999974i	$-0.502295\pi$
$337$	−0.264702	−0.0144192	−0.00720962	+	0.999974i	$0.502295\pi$
$338$	−6.66275	−0.362406
$339$	−8.35974	−0.454039
$340$	5.44714	0.295413
$341$	−53.2613	−2.88426
$342$	−11.5926	−0.626856
$343$	5.71926	0.308811
$344$	−18.9769	−1.02317
$345$	−0.592014	−0.0318729
$346$	4.84517	0.260478
$347$	−3.08604	−0.165668	−0.0828338	−	0.996563i	$-0.526397\pi$
$347$	−3.08604	−0.165668	−0.0828338	+	0.996563i	$0.526397\pi$
$348$	−4.03654	−0.216381
$349$	−4.56860	−0.244551	−0.122276	−	0.992496i	$-0.539019\pi$
$349$	−4.56860	−0.244551	−0.122276	+	0.992496i	$0.539019\pi$
$350$	5.93198	0.317078
$351$	12.6682	0.676180
$352$	−23.0066	−1.22626
$353$	20.7973	1.10693	0.553465	−	0.832872i	$-0.313305\pi$
$353$	20.7973	1.10693	0.553465	+	0.832872i	$0.313305\pi$
$354$	12.8088	0.680781
$355$	11.6063	0.615997
$356$	−12.2175	−0.647528
$357$	−12.2392	−0.647765
$358$	−5.29553	−0.279877
$359$	−8.88142	−0.468744	−0.234372	−	0.972147i	$-0.575303\pi$
$359$	−8.88142	−0.468744	−0.234372	+	0.972147i	$0.575303\pi$
$360$	5.28341	0.278460
$361$	−12.5631	−0.661218
$362$	5.78179	0.303884
$363$	−8.21701	−0.431281
$364$	−12.2192	−0.640462
$365$	−5.40454	−0.282886
$366$	5.16179	0.269811
$367$	−10.7008	−0.558575	−0.279288	−	0.960208i	$-0.590098\pi$
$367$	−10.7008	−0.558575	−0.279288	+	0.960208i	$0.590098\pi$
$368$	5.46589	0.284929
$369$	9.68842	0.504359
$370$	−8.51339	−0.442590
$371$	−39.3508	−2.04299
$372$	−4.72682	−0.245074
$373$	−3.95542	−0.204804	−0.102402	−	0.994743i	$-0.532653\pi$
$373$	−3.95542	−0.204804	−0.102402	+	0.994743i	$0.532653\pi$
$374$	−55.7785	−2.88424
$375$	0.538907	0.0278290
$376$	16.5927	0.855701
$377$	36.5516	1.88250
$378$	18.2523	0.938796
$379$	22.0627	1.13328	0.566641	−	0.823965i	$-0.308243\pi$
$379$	22.0627	1.13328	0.566641	+	0.823965i	$0.308243\pi$
$380$	2.14055	0.109808
$381$	4.26344	0.218423
$382$	33.4147	1.70964
$383$	19.2972	0.986043	0.493021	−	0.870017i	$-0.335892\pi$
$383$	19.2972	0.986043	0.493021	+	0.870017i	$0.335892\pi$
$384$	7.00154	0.357296
$385$	−18.0220	−0.918484
$386$	−23.0332	−1.17236
$387$	26.3703	1.34048
$388$	−12.4239	−0.630727
$389$	−18.8935	−0.957936	−0.478968	−	0.877832i	$-0.658989\pi$
$389$	−18.8935	−0.957936	−0.478968	+	0.877832i	$0.658989\pi$
$390$	−3.74157	−0.189462
$391$	7.09249	0.358682
$392$	10.4790	0.529272
$393$	6.58191	0.332013
$394$	−27.4007	−1.38043
$395$	4.14076	0.208344
$396$	11.7121	0.588555
$397$	13.7527	0.690229	0.345115	−	0.938561i	$-0.387840\pi$
$397$	13.7527	0.690229	0.345115	+	0.938561i	$0.387840\pi$
$398$	24.7145	1.23883
$399$	−4.80959	−0.240781
$400$	−4.97557	−0.248779
$401$	−7.22568	−0.360833	−0.180417	−	0.983590i	$-0.557745\pi$
$401$	−7.22568	−0.360833	−0.180417	+	0.983590i	$0.557745\pi$
$402$	−1.48828	−0.0742286
$403$	42.8021	2.13213
$404$	−4.01299	−0.199654
$405$	−6.47056	−0.321525
$406$	52.6632	2.61363
$407$	25.8645	1.28206
$408$	6.78432	0.335874
$409$	7.13788	0.352945	0.176473	−	0.984306i	$-0.443531\pi$
$409$	7.13788	0.352945	0.176473	+	0.984306i	$0.443531\pi$
$410$	−6.02966	−0.297784
$411$	−3.61327	−0.178230
$412$	0.694263	0.0342039
$413$	−49.5806	−2.43970
$414$	−5.01952	−0.246696
$415$	−13.1144	−0.643760
$416$	18.4887	0.906483
$417$	−9.29884	−0.455366
$418$	−21.9191	−1.07210
$419$	−2.02084	−0.0987244	−0.0493622	−	0.998781i	$-0.515719\pi$
$419$	−2.02084	−0.0987244	−0.0493622	+	0.998781i	$0.515719\pi$
$420$	−1.59941	−0.0780431
$421$	14.8824	0.725323	0.362661	−	0.931921i	$-0.381868\pi$
$421$	14.8824	0.725323	0.362661	+	0.931921i	$0.381868\pi$
$422$	−17.5334	−0.853513
$423$	−23.0572	−1.12108
$424$	21.8126	1.05932
$425$	−6.45625	−0.313174
$426$	−10.5475	−0.511026
$427$	−19.9803	−0.966915
$428$	6.33628	0.306276
$429$	11.3673	0.548817
$430$	−16.4117	−0.791445
$431$	26.3199	1.26779	0.633893	−	0.773421i	$-0.281456\pi$
$431$	26.3199	1.26779	0.633893	+	0.773421i	$0.281456\pi$
$432$	−15.3095	−0.736578
$433$	−22.5726	−1.08477	−0.542384	−	0.840131i	$-0.682478\pi$
$433$	−22.5726	−1.08477	−0.542384	+	0.840131i	$0.682478\pi$
$434$	61.6689	2.96020
$435$	4.78433	0.229391
$436$	−9.96706	−0.477336
$437$	2.78712	0.133326
$438$	4.91150	0.234680
$439$	−24.5916	−1.17369	−0.586847	−	0.809698i	$-0.699631\pi$
$439$	−24.5916	−1.17369	−0.586847	+	0.809698i	$0.699631\pi$
$440$	9.98980	0.476245
$441$	−14.5617	−0.693413
$442$	44.8250	2.13211
$443$	5.48898	0.260789	0.130395	−	0.991462i	$-0.458376\pi$
$443$	5.48898	0.260789	0.130395	+	0.991462i	$0.458376\pi$
$444$	2.29542	0.108936
$445$	14.4809	0.686461
$446$	6.95721	0.329434
$447$	−4.92502	−0.232946
$448$	−8.36666	−0.395287
$449$	6.87113	0.324269	0.162134	−	0.986769i	$-0.448162\pi$
$449$	6.87113	0.324269	0.162134	+	0.986769i	$0.448162\pi$
$450$	4.56924	0.215396
$451$	18.3187	0.862596
$452$	13.0878	0.615599
$453$	−0.534325	−0.0251048
$454$	−20.4421	−0.959396
$455$	14.4829	0.678969
$456$	2.66602	0.124848
$457$	39.9268	1.86770	0.933848	−	0.357670i	$-0.116429\pi$
$457$	39.9268	1.86770	0.933848	+	0.357670i	$0.116429\pi$
$458$	45.1952	2.11183
$459$	−19.8654	−0.927239
$460$	0.926843	0.0432143
$461$	31.3659	1.46086	0.730429	−	0.682989i	$-0.239320\pi$
$461$	31.3659	1.46086	0.730429	+	0.682989i	$0.239320\pi$
$462$	16.3779	0.761968
$463$	−7.98957	−0.371307	−0.185653	−	0.982615i	$-0.559440\pi$
$463$	−7.98957	−0.371307	−0.185653	+	0.982615i	$0.559440\pi$
$464$	−44.1724	−2.05065
$465$	5.60248	0.259809
$466$	4.33434	0.200784
$467$	18.4872	0.855486	0.427743	−	0.903900i	$-0.359309\pi$
$467$	18.4872	0.855486	0.427743	+	0.903900i	$0.359309\pi$
$468$	−9.41214	−0.435076
$469$	5.76085	0.266011
$470$	14.3498	0.661907
$471$	−8.81923	−0.406369
$472$	27.4831	1.26501
$473$	49.8606	2.29259
$474$	−3.76301	−0.172841
$475$	−2.53710	−0.116410
$476$	19.1613	0.878259
$477$	−30.3108	−1.38784
$478$	−20.3905	−0.932640
$479$	−43.4322	−1.98447	−0.992233	−	0.124393i	$-0.960302\pi$
$479$	−43.4322	−1.98447	−0.992233	+	0.124393i	$0.960302\pi$
$480$	2.42004	0.110459
$481$	−20.7854	−0.947733
$482$	−9.31133	−0.424119
$483$	−2.08252	−0.0947580
$484$	12.8644	0.584744
$485$	14.7255	0.668649
$486$	21.4464	0.972829
$487$	−1.24509	−0.0564205	−0.0282102	−	0.999602i	$-0.508981\pi$
$487$	−1.24509	−0.0564205	−0.0282102	+	0.999602i	$0.508981\pi$
$488$	11.0753	0.501357
$489$	0.942637	0.0426275
$490$	9.06257	0.409405
$491$	−3.10747	−0.140238	−0.0701191	−	0.997539i	$-0.522338\pi$
$491$	−3.10747	−0.140238	−0.0701191	+	0.997539i	$0.522338\pi$
$492$	1.62575	0.0732943
$493$	−57.3176	−2.58146
$494$	17.6148	0.792526
$495$	−13.8818	−0.623941
$496$	−51.7261	−2.32257
$497$	40.8272	1.83135
$498$	11.9180	0.534058
$499$	9.19990	0.411844	0.205922	−	0.978568i	$-0.433981\pi$
$499$	9.19990	0.411844	0.205922	+	0.978568i	$0.433981\pi$
$500$	−0.843700	−0.0377314
$501$	0.688817	0.0307741
$502$	31.4628	1.40425
$503$	20.2866	0.904533	0.452266	−	0.891883i	$-0.350616\pi$
$503$	20.2866	0.904533	0.452266	+	0.891883i	$0.350616\pi$
$504$	18.5854	0.827860
$505$	4.75641	0.211658
$506$	−9.49084	−0.421919
$507$	−2.12924	−0.0945629
$508$	−6.67474	−0.296144
$509$	−43.9730	−1.94907	−0.974535	−	0.224234i	$-0.928012\pi$
$509$	−43.9730	−1.94907	−0.974535	+	0.224234i	$0.928012\pi$
$510$	5.86726	0.259807
$511$	−19.0115	−0.841019
$512$	−2.93976	−0.129920
$513$	−7.80647	−0.344664
$514$	−7.08426	−0.312473
$515$	−0.822879	−0.0362604
$516$	4.42501	0.194800
$517$	−43.5962	−1.91736
$518$	−29.9475	−1.31582
$519$	1.54839	0.0679668
$520$	−8.02806	−0.352054
$521$	33.3640	1.46170	0.730851	−	0.682537i	$-0.239124\pi$
$521$	33.3640	1.46170	0.730851	+	0.682537i	$0.239124\pi$
$522$	40.5650	1.77548
$523$	−28.0522	−1.22664	−0.613319	−	0.789835i	$-0.710166\pi$
$523$	−28.0522	−1.22664	−0.613319	+	0.789835i	$0.710166\pi$
$524$	−10.3045	−0.450154
$525$	1.89571	0.0827354
$526$	16.4209	0.715986
$527$	−67.1193	−2.92376
$528$	−13.7373	−0.597839
$529$	−21.7932	−0.947530
$530$	18.8642	0.819407
$531$	−38.1905	−1.65733
$532$	7.52978	0.326458
$533$	−14.7214	−0.637655
$534$	−13.1599	−0.569483
$535$	−7.51011	−0.324690
$536$	−3.19331	−0.137930
$537$	−1.69231	−0.0730287
$538$	−29.9727	−1.29222
$539$	−27.5330	−1.18593
$540$	−2.59601	−0.111714
$541$	32.4802	1.39643	0.698217	−	0.715887i	$-0.253977\pi$
$541$	32.4802	1.39643	0.698217	+	0.715887i	$0.253977\pi$
$542$	19.7357	0.847721
$543$	1.84771	0.0792929
$544$	−28.9927	−1.24305
$545$	11.8135	0.506035
$546$	−13.1617	−0.563268
$547$	−2.57829	−0.110240	−0.0551198	−	0.998480i	$-0.517554\pi$
$547$	−2.57829	−0.110240	−0.0551198	+	0.998480i	$0.517554\pi$
$548$	5.65686	0.241649
$549$	−15.3903	−0.656841
$550$	8.63946	0.368388
$551$	−22.5240	−0.959553
$552$	1.15437	0.0491331
$553$	14.5659	0.619405
$554$	4.16413	0.176917
$555$	−2.72066	−0.115486
$556$	14.5580	0.617399
$557$	−3.63365	−0.153963	−0.0769813	−	0.997033i	$-0.524528\pi$
$557$	−3.63365	−0.153963	−0.0769813	+	0.997033i	$0.524528\pi$
$558$	47.5019	2.01092
$559$	−40.0692	−1.69475
$560$	−17.5025	−0.739616
$561$	−17.8254	−0.752587
$562$	3.43042	0.144704
$563$	−19.9210	−0.839572	−0.419786	−	0.907623i	$-0.637895\pi$
$563$	−19.9210	−0.839572	−0.419786	+	0.907623i	$0.637895\pi$
$564$	−3.86906	−0.162917
$565$	−15.5124	−0.652612
$566$	3.00413	0.126273
$567$	−22.7614	−0.955890
$568$	−22.6311	−0.949578
$569$	−34.5504	−1.44843	−0.724213	−	0.689576i	$-0.757797\pi$
$569$	−34.5504	−1.44843	−0.724213	+	0.689576i	$0.757797\pi$
$570$	2.30564	0.0965728
$571$	8.13059	0.340255	0.170127	−	0.985422i	$-0.445582\pi$
$571$	8.13059	0.340255	0.170127	+	0.985422i	$0.445582\pi$
$572$	−17.7963	−0.744102
$573$	10.6785	0.446099
$574$	−21.2105	−0.885308
$575$	−1.09855	−0.0458125
$576$	−6.44460	−0.268525
$577$	−44.0996	−1.83589	−0.917944	−	0.396709i	$-0.870152\pi$
$577$	−44.0996	−1.83589	−0.917944	+	0.396709i	$0.870152\pi$
$578$	−41.6239	−1.73133
$579$	−7.36081	−0.305905
$580$	−7.49024	−0.311015
$581$	−46.1324	−1.91389
$582$	−13.3821	−0.554706
$583$	−57.3113	−2.37359
$584$	10.5383	0.436078
$585$	11.1558	0.461235
$586$	−20.9478	−0.865347
$587$	19.3817	0.799969	0.399985	−	0.916522i	$-0.369015\pi$
$587$	19.3817	0.799969	0.399985	+	0.916522i	$0.369015\pi$
$588$	−2.44349	−0.100768
$589$	−26.3757	−1.08679
$590$	23.7682	0.978520
$591$	−8.75655	−0.360196
$592$	25.1191	1.03239
$593$	−5.85045	−0.240249	−0.120125	−	0.992759i	$-0.538329\pi$
$593$	−5.85045	−0.240249	−0.120125	+	0.992759i	$0.538329\pi$
$594$	26.5830	1.09071
$595$	−22.7111	−0.931064
$596$	7.71050	0.315834
$597$	7.89813	0.323249
$598$	7.62708	0.311894
$599$	−18.9000	−0.772232	−0.386116	−	0.922450i	$-0.626184\pi$
$599$	−18.9000	−0.772232	−0.386116	+	0.922450i	$0.626184\pi$
$600$	−1.05081	−0.0428993
$601$	−39.3492	−1.60509	−0.802544	−	0.596593i	$-0.796521\pi$
$601$	−39.3492	−1.60509	−0.802544	+	0.596593i	$0.796521\pi$
$602$	−57.7314	−2.35296
$603$	4.43742	0.180706
$604$	0.836527	0.0340378
$605$	−15.2476	−0.619901
$606$	−4.32250	−0.175590
$607$	−22.2121	−0.901562	−0.450781	−	0.892635i	$-0.648854\pi$
$607$	−22.2121	−0.901562	−0.450781	+	0.892635i	$0.648854\pi$
$608$	−11.3932	−0.462055
$609$	16.8298	0.681978
$610$	9.57826	0.387812
$611$	35.0350	1.41736
$612$	14.7595	0.596616
$613$	40.2378	1.62519	0.812594	−	0.582830i	$-0.198054\pi$
$613$	40.2378	1.62519	0.812594	+	0.582830i	$0.198054\pi$
$614$	24.9276	1.00600
$615$	−1.92692	−0.0777011
$616$	35.1410	1.41587
$617$	−34.6859	−1.39640	−0.698200	−	0.715902i	$-0.746016\pi$
$617$	−34.6859	−1.39640	−0.698200	+	0.715902i	$0.746016\pi$
$618$	0.747810	0.0300813
$619$	−15.9528	−0.641199	−0.320600	−	0.947215i	$-0.603884\pi$
$619$	−15.9528	−0.641199	−0.320600	+	0.947215i	$0.603884\pi$
$620$	−8.77112	−0.352257
$621$	−3.38015	−0.135641
$622$	38.0830	1.52699
$623$	50.9393	2.04084
$624$	11.0396	0.441939
$625$	1.00000	0.0400000
$626$	−47.7794	−1.90965
$627$	−7.00479	−0.279744
$628$	13.8072	0.550967
$629$	32.5942	1.29962
$630$	16.0732	0.640370
$631$	−16.2802	−0.648103	−0.324052	−	0.946039i	$-0.605045\pi$
$631$	−16.2802	−0.648103	−0.324052	+	0.946039i	$0.605045\pi$
$632$	−8.07406	−0.321169
$633$	−5.60322	−0.222708
$634$	−28.2262	−1.12101
$635$	7.91127	0.313949
$636$	−5.08625	−0.201683
$637$	22.1262	0.876673
$638$	76.6998	3.03657
$639$	31.4481	1.24407
$640$	12.9921	0.513559
$641$	49.1773	1.94239	0.971193	−	0.238295i	$-0.0765884\pi$
$641$	49.1773	1.94239	0.971193	+	0.238295i	$0.0765884\pi$
$642$	6.82499	0.269361
$643$	−28.5854	−1.12730	−0.563648	−	0.826015i	$-0.690603\pi$
$643$	−28.5854	−1.12730	−0.563648	+	0.826015i	$0.690603\pi$
$644$	3.26035	0.128476
$645$	−5.24477	−0.206513
$646$	−27.6223	−1.08678
$647$	−5.70921	−0.224452	−0.112226	−	0.993683i	$-0.535798\pi$
$647$	−5.70921	−0.224452	−0.112226	+	0.993683i	$0.535798\pi$
$648$	12.6169	0.495641
$649$	−72.2102	−2.83450
$650$	−6.94289	−0.272322
$651$	19.7078	0.772410
$652$	−1.47577	−0.0577957
$653$	−32.7836	−1.28292	−0.641461	−	0.767156i	$-0.721671\pi$
$653$	−32.7836	−1.28292	−0.641461	+	0.767156i	$0.721671\pi$
$654$	−10.7358	−0.419803
$655$	12.2134	0.477219
$656$	17.7907	0.694612
$657$	−14.6440	−0.571318
$658$	50.4781	1.96784
$659$	19.1215	0.744866	0.372433	−	0.928059i	$-0.378524\pi$
$659$	19.1215	0.744866	0.372433	+	0.928059i	$0.378524\pi$
$660$	−2.32941	−0.0906722
$661$	40.1437	1.56141	0.780704	−	0.624901i	$-0.214861\pi$
$661$	40.1437	1.56141	0.780704	+	0.624901i	$0.214861\pi$
$662$	21.6387	0.841013
$663$	14.3249	0.556334
$664$	25.5718	0.992376
$665$	−8.92472	−0.346086
$666$	−23.0677	−0.893855
$667$	−9.75273	−0.377627
$668$	−1.07840	−0.0417244
$669$	2.22334	0.0859595
$670$	−2.76166	−0.106692
$671$	−29.0997	−1.12338
$672$	8.51293	0.328394
$673$	−29.0559	−1.12002	−0.560011	−	0.828485i	$-0.689203\pi$
$673$	−29.0559	−1.12002	−0.560011	+	0.828485i	$0.689203\pi$
$674$	0.446374	0.0171937
$675$	3.07693	0.118431
$676$	3.33349	0.128211
$677$	−20.5471	−0.789690	−0.394845	−	0.918748i	$-0.629202\pi$
$677$	−20.5471	−0.789690	−0.394845	+	0.918748i	$0.629202\pi$
$678$	14.0973	0.541402
$679$	51.7996	1.98789
$680$	12.5890	0.482768
$681$	−6.53277	−0.250336
$682$	89.8159	3.43923
$683$	8.15771	0.312146	0.156073	−	0.987746i	$-0.450116\pi$
$683$	8.15771	0.312146	0.156073	+	0.987746i	$0.450116\pi$
$684$	5.79998	0.221768
$685$	−6.70482	−0.256178
$686$	−9.64454	−0.368230
$687$	14.4432	0.551043
$688$	48.4235	1.84613
$689$	46.0568	1.75463
$690$	0.998329	0.0380057
$691$	−26.1976	−0.996604	−0.498302	−	0.867004i	$-0.666043\pi$
$691$	−26.1976	−0.996604	−0.498302	+	0.867004i	$0.666043\pi$
$692$	−2.42413	−0.0921515
$693$	−48.8319	−1.85497
$694$	5.20408	0.197544
$695$	−17.2550	−0.654520
$696$	−9.32897	−0.353614
$697$	23.0851	0.874410
$698$	7.70415	0.291606
$699$	1.38514	0.0523909
$700$	−2.96788	−0.112175
$701$	30.9712	1.16977	0.584884	−	0.811117i	$-0.301140\pi$
$701$	30.9712	1.16977	0.584884	+	0.811117i	$0.301140\pi$
$702$	−21.3628	−0.806286
$703$	12.8085	0.483081
$704$	−12.1854	−0.459254
$705$	4.58582	0.172712
$706$	−35.0711	−1.31992
$707$	16.7316	0.629256
$708$	−6.40849	−0.240846
$709$	−37.4042	−1.40474	−0.702371	−	0.711811i	$-0.747875\pi$
$709$	−37.4042	−1.40474	−0.702371	+	0.711811i	$0.747875\pi$
$710$	−19.5720	−0.734523
$711$	11.2197	0.420772
$712$	−28.2363	−1.05820
$713$	−11.4205	−0.427701
$714$	20.6392	0.772403
$715$	21.0932	0.788841
$716$	2.64945	0.0990145
$717$	−6.51628	−0.243355
$718$	14.9770	0.558936
$719$	−0.611739	−0.0228140	−0.0114070	−	0.999935i	$-0.503631\pi$
$719$	−0.611739	−0.0228140	−0.0114070	+	0.999935i	$0.503631\pi$
$720$	−13.4817	−0.502433
$721$	−2.89463	−0.107802
$722$	21.1856	0.788445
$723$	−2.97566	−0.110666
$724$	−2.89273	−0.107508
$725$	8.87785	0.329715
$726$	13.8566	0.514266
$727$	−47.3298	−1.75537	−0.877683	−	0.479242i	$-0.840912\pi$
$727$	−47.3298	−1.75537	−0.877683	+	0.479242i	$0.840912\pi$
$728$	−28.2402	−1.04665
$729$	−12.5580	−0.465110
$730$	9.11382	0.337318
$731$	62.8338	2.32399
$732$	−2.58254	−0.0954533
$733$	−11.4110	−0.421475	−0.210737	−	0.977543i	$-0.567586\pi$
$733$	−11.4110	−0.421475	−0.210737	+	0.977543i	$0.567586\pi$
$734$	18.0450	0.666053
$735$	2.89616	0.106827
$736$	−4.93317	−0.181839
$737$	8.39022	0.309058
$738$	−16.3379	−0.601405
$739$	−36.0875	−1.32750	−0.663749	−	0.747955i	$-0.731036\pi$
$739$	−36.0875	−1.32750	−0.663749	+	0.747955i	$0.731036\pi$
$740$	4.25940	0.156579
$741$	5.62922	0.206795
$742$	66.3583	2.43609
$743$	15.0692	0.552835	0.276417	−	0.961038i	$-0.410853\pi$
$743$	15.0692	0.552835	0.276417	+	0.961038i	$0.410853\pi$
$744$	−10.9243	−0.400504
$745$	−9.13891	−0.334824
$746$	6.67013	0.244211
$747$	−35.5345	−1.30014
$748$	27.9070	1.02038
$749$	−26.4182	−0.965302
$750$	−0.908773	−0.0331837
$751$	−39.7714	−1.45128	−0.725639	−	0.688076i	$-0.758456\pi$
$751$	−39.7714	−1.45128	−0.725639	+	0.688076i	$0.758456\pi$
$752$	−42.3396	−1.54397
$753$	10.0547	0.366414
$754$	−61.6379	−2.24472
$755$	−0.991498	−0.0360843
$756$	−9.13194	−0.332126
$757$	1.21620	0.0442035	0.0221017	−	0.999756i	$-0.492964\pi$
$757$	1.21620	0.0442035	0.0221017	+	0.999756i	$0.492964\pi$
$758$	−37.2049	−1.35134
$759$	−3.03303	−0.110092
$760$	4.94708	0.179450
$761$	−19.4252	−0.704164	−0.352082	−	0.935969i	$-0.614526\pi$
$761$	−19.4252	−0.704164	−0.352082	+	0.935969i	$0.614526\pi$
$762$	−7.18955	−0.260450
$763$	41.5563	1.50444
$764$	−16.7180	−0.604834
$765$	−17.4937	−0.632487
$766$	−32.5415	−1.17577
$767$	58.0299	2.09534
$768$	−9.24337	−0.333541
$769$	8.53079	0.307628	0.153814	−	0.988100i	$-0.450844\pi$
$769$	8.53079	0.307628	0.153814	+	0.988100i	$0.450844\pi$
$770$	30.3909	1.09521
$771$	−2.26395	−0.0815340
$772$	11.5239	0.414755
$773$	−4.89163	−0.175940	−0.0879698	−	0.996123i	$-0.528038\pi$
$773$	−4.89163	−0.175940	−0.0879698	+	0.996123i	$0.528038\pi$
$774$	−44.4689	−1.59840
$775$	10.3960	0.373436
$776$	−28.7132	−1.03074
$777$	−9.57043	−0.343337
$778$	31.8606	1.14226
$779$	9.07169	0.325027
$780$	1.87197	0.0670274
$781$	59.4616	2.12770
$782$	−11.9603	−0.427698
$783$	27.3165	0.976213
$784$	−26.7394	−0.954980
$785$	−16.3650	−0.584094
$786$	−11.0993	−0.395897
$787$	−2.73092	−0.0973469	−0.0486735	−	0.998815i	$-0.515499\pi$
$787$	−2.73092	−0.0973469	−0.0486735	+	0.998815i	$0.515499\pi$
$788$	13.7091	0.488365
$789$	5.24770	0.186823
$790$	−6.98267	−0.248432
$791$	−54.5678	−1.94021
$792$	27.0682	0.961825
$793$	23.3853	0.830436
$794$	−23.1916	−0.823039
$795$	6.02850	0.213809
$796$	−12.3651	−0.438270
$797$	−23.3247	−0.826202	−0.413101	−	0.910685i	$-0.635554\pi$
$797$	−23.3247	−0.826202	−0.413101	+	0.910685i	$0.635554\pi$
$798$	8.11054	0.287110
$799$	−54.9394	−1.94362
$800$	4.49064	0.158768
$801$	39.2372	1.38638
$802$	12.1849	0.430262
$803$	−27.6887	−0.977114
$804$	0.744613	0.0262605
$805$	−3.86434	−0.136200
$806$	−72.1784	−2.54237
$807$	−9.57851	−0.337180
$808$	−9.27453	−0.326277
$809$	21.2561	0.747325	0.373662	−	0.927565i	$-0.378102\pi$
$809$	21.2561	0.747325	0.373662	+	0.927565i	$0.378102\pi$
$810$	10.9115	0.383390
$811$	−47.6327	−1.67261	−0.836304	−	0.548266i	$-0.815288\pi$
$811$	−47.6327	−1.67261	−0.836304	+	0.548266i	$0.815288\pi$
$812$	−26.3484	−0.924646
$813$	6.30702	0.221197
$814$	−43.6161	−1.52874
$815$	1.74917	0.0612706
$816$	−17.3116	−0.606026
$817$	24.6916	0.863851
$818$	−12.0368	−0.420857
$819$	39.2426	1.37125
$820$	3.01675	0.105349
$821$	0.683616	0.0238583	0.0119292	−	0.999929i	$-0.496203\pi$
$821$	0.683616	0.0238583	0.0119292	+	0.999929i	$0.496203\pi$
$822$	6.09316	0.212523
$823$	−9.00251	−0.313808	−0.156904	−	0.987614i	$-0.550151\pi$
$823$	−9.00251	−0.313808	−0.156904	+	0.987614i	$0.550151\pi$
$824$	1.60453	0.0558965
$825$	2.76095	0.0961238
$826$	83.6091	2.90913
$827$	−12.4888	−0.434278	−0.217139	−	0.976141i	$-0.569673\pi$
$827$	−12.4888	−0.434278	−0.217139	+	0.976141i	$0.569673\pi$
$828$	2.51136	0.0872756
$829$	43.5811	1.51363	0.756816	−	0.653628i	$-0.226754\pi$
$829$	43.5811	1.51363	0.756816	+	0.653628i	$0.226754\pi$
$830$	22.1152	0.767628
$831$	1.33075	0.0461631
$832$	9.79248	0.339493
$833$	−34.6968	−1.20217
$834$	15.6809	0.542984
$835$	1.27817	0.0442331
$836$	10.9665	0.379286
$837$	31.9878	1.10566
$838$	3.40779	0.117720
$839$	−40.2887	−1.39092	−0.695461	−	0.718564i	$-0.744800\pi$
$839$	−40.2887	−1.39092	−0.695461	+	0.718564i	$0.744800\pi$
$840$	−3.69644	−0.127539
$841$	49.8163	1.71780
$842$	−25.0966	−0.864884
$843$	1.09627	0.0377577
$844$	8.77228	0.301954
$845$	−3.95104	−0.135920
$846$	38.8819	1.33679
$847$	−53.6362	−1.84296
$848$	−55.6594	−1.91135
$849$	0.960041	0.0329485
$850$	10.8874	0.373433
$851$	5.54598	0.190114
$852$	5.27708	0.180790
$853$	−17.0140	−0.582550	−0.291275	−	0.956639i	$-0.594079\pi$
$853$	−17.0140	−0.582550	−0.291275	+	0.956639i	$0.594079\pi$
$854$	33.6933	1.15296
$855$	−6.87446	−0.235102
$856$	14.6440	0.500521
$857$	43.6792	1.49205	0.746027	−	0.665915i	$-0.231959\pi$
$857$	43.6792	1.49205	0.746027	+	0.665915i	$0.231959\pi$
$858$	−19.1689	−0.654417
$859$	56.4303	1.92538	0.962688	−	0.270612i	$-0.0872261\pi$
$859$	56.4303	1.92538	0.962688	+	0.270612i	$0.0872261\pi$
$860$	8.21109	0.279996
$861$	−6.77832	−0.231005
$862$	−44.3840	−1.51173
$863$	−40.6125	−1.38247	−0.691233	−	0.722631i	$-0.742932\pi$
$863$	−40.6125	−1.38247	−0.691233	+	0.722631i	$0.742932\pi$
$864$	13.8174	0.470077
$865$	2.87321	0.0976921
$866$	38.0647	1.29349
$867$	−13.3019	−0.451757
$868$	−30.8541	−1.04726
$869$	21.2141	0.719638
$870$	−8.06795	−0.273529
$871$	−6.74260	−0.228464
$872$	−23.0352	−0.780069
$873$	39.8998	1.35040
$874$	−4.69999	−0.158980
$875$	3.51769	0.118920
$876$	−2.45731	−0.0830248
$877$	47.1123	1.59087	0.795435	−	0.606039i	$-0.207242\pi$
$877$	47.1123	1.59087	0.795435	+	0.606039i	$0.207242\pi$
$878$	41.4695	1.39953
$879$	−6.69439	−0.225796
$880$	−25.4910	−0.859302
$881$	3.89315	0.131164	0.0655818	−	0.997847i	$-0.479110\pi$
$881$	3.89315	0.131164	0.0655818	+	0.997847i	$0.479110\pi$
$882$	24.5557	0.826835
$883$	−29.1763	−0.981859	−0.490930	−	0.871199i	$-0.663343\pi$
$883$	−29.1763	−0.981859	−0.490930	+	0.871199i	$0.663343\pi$
$884$	−22.4268	−0.754294
$885$	7.59569	0.255326
$886$	−9.25621	−0.310969
$887$	18.8722	0.633666	0.316833	−	0.948481i	$-0.397381\pi$
$887$	18.8722	0.633666	0.316833	+	0.948481i	$0.397381\pi$
$888$	5.30501	0.178025
$889$	27.8294	0.933368
$890$	−24.4196	−0.818545
$891$	−33.1502	−1.11057
$892$	−3.48082	−0.116546
$893$	−21.5894	−0.722462
$894$	8.30520	0.277767
$895$	−3.14027	−0.104968
$896$	45.7023	1.52681
$897$	2.43742	0.0813830
$898$	−11.5870	−0.386662
$899$	92.2943	3.07819
$900$	−2.28607	−0.0762024
$901$	−72.2231	−2.40610
$902$	−30.8914	−1.02857
$903$	−18.4495	−0.613960
$904$	30.2476	1.00602
$905$	3.42863	0.113971
$906$	0.901047	0.0299353
$907$	−32.2079	−1.06945	−0.534723	−	0.845027i	$-0.679584\pi$
$907$	−32.2079	−1.06945	−0.534723	+	0.845027i	$0.679584\pi$
$908$	10.2276	0.339414
$909$	12.8879	0.427464
$910$	−24.4229	−0.809612
$911$	−23.1152	−0.765840	−0.382920	−	0.923781i	$-0.625082\pi$
$911$	−23.1152	−0.765840	−0.382920	+	0.923781i	$0.625082\pi$
$912$	−6.80289	−0.225266
$913$	−67.1881	−2.22360
$914$	−67.3296	−2.22707
$915$	3.06096	0.101192
$916$	−22.6120	−0.747120
$917$	42.9631	1.41877
$918$	33.4996	1.10565
$919$	3.38354	0.111613	0.0558064	−	0.998442i	$-0.482227\pi$
$919$	3.38354	0.111613	0.0558064	+	0.998442i	$0.482227\pi$
$920$	2.14206	0.0706215
$921$	7.96622	0.262496
$922$	−52.8933	−1.74195
$923$	−47.7849	−1.57286
$924$	−8.19414	−0.269568
$925$	−5.04848	−0.165993
$926$	13.4730	0.442751
$927$	−2.22966	−0.0732315
$928$	39.8672	1.30871
$929$	37.6663	1.23579	0.617896	−	0.786260i	$-0.287985\pi$
$929$	37.6663	1.23579	0.617896	+	0.786260i	$0.287985\pi$
$930$	−9.44762	−0.309800
$931$	−13.6347	−0.446860
$932$	−2.16855	−0.0710331
$933$	12.1703	0.398439
$934$	−31.1755	−1.02009
$935$	−33.0769	−1.08173
$936$	−21.7527	−0.711008
$937$	28.0481	0.916290	0.458145	−	0.888877i	$-0.348514\pi$
$937$	28.0481	0.916290	0.458145	+	0.888877i	$0.348514\pi$
$938$	−9.71468	−0.317196
$939$	−15.2691	−0.498287
$940$	−7.17946	−0.234168
$941$	9.40043	0.306445	0.153223	−	0.988192i	$-0.451035\pi$
$941$	9.40043	0.306445	0.153223	+	0.988192i	$0.451035\pi$
$942$	14.8721	0.484560
$943$	3.92798	0.127913
$944$	−70.1289	−2.28250
$945$	10.8237	0.352095
$946$	−84.0813	−2.73372
$947$	46.5884	1.51392	0.756960	−	0.653461i	$-0.226684\pi$
$947$	46.5884	1.51392	0.756960	+	0.653461i	$0.226684\pi$
$948$	1.88270	0.0611473
$949$	22.2514	0.722310
$950$	4.27837	0.138809
$951$	−9.02037	−0.292506
$952$	44.2844	1.43526
$953$	33.3456	1.08017	0.540085	−	0.841610i	$-0.318392\pi$
$953$	33.3456	1.08017	0.540085	+	0.841610i	$0.318392\pi$
$954$	51.1140	1.65488
$955$	19.8150	0.641200
$956$	10.2017	0.329948
$957$	24.5113	0.792337
$958$	73.2408	2.36630
$959$	−23.5855	−0.761615
$960$	1.28176	0.0413687
$961$	77.0772	2.48636
$962$	35.0510	1.13009
$963$	−20.3492	−0.655745
$964$	4.65863	0.150044
$965$	−13.6588	−0.439692
$966$	3.51181	0.112991
$967$	26.8974	0.864963	0.432481	−	0.901643i	$-0.357638\pi$
$967$	26.8974	0.864963	0.432481	+	0.901643i	$0.357638\pi$
$968$	29.7312	0.955598
$969$	−8.82736	−0.283576
$970$	−24.8319	−0.797306
$971$	−36.3117	−1.16530	−0.582649	−	0.812724i	$-0.697984\pi$
$971$	−36.3117	−1.16530	−0.582649	+	0.812724i	$0.697984\pi$
$972$	−10.7300	−0.344166
$973$	−60.6978	−1.94588
$974$	2.09963	0.0672765
$975$	−2.21877	−0.0710574
$976$	−28.2610	−0.904613
$977$	−29.7728	−0.952515	−0.476258	−	0.879306i	$-0.658007\pi$
$977$	−29.7728	−0.952515	−0.476258	+	0.879306i	$0.658007\pi$
$978$	−1.58960	−0.0508296
$979$	74.1891	2.37109
$980$	−4.53416	−0.144839
$981$	32.0096	1.02199
$982$	5.24022	0.167222
$983$	25.0322	0.798405	0.399202	−	0.916863i	$-0.369287\pi$
$983$	25.0322	0.798405	0.399202	+	0.916863i	$0.369287\pi$
$984$	3.75731	0.119779
$985$	−16.2487	−0.517728
$986$	96.6563	3.07816
$987$	16.1315	0.513471
$988$	−8.81299	−0.280378
$989$	10.6913	0.339964
$990$	23.4093	0.743996
$991$	1.86257	0.0591664	0.0295832	−	0.999562i	$-0.490582\pi$
$991$	1.86257	0.0591664	0.0295832	+	0.999562i	$0.490582\pi$
$992$	46.6848	1.48224
$993$	6.91517	0.219446
$994$	−68.8481	−2.18373
$995$	14.6558	0.464621
$996$	−5.96279	−0.188938
$997$	50.7860	1.60841	0.804205	−	0.594353i	$-0.202592\pi$
$997$	50.7860	1.60841	0.804205	+	0.594353i	$0.202592\pi$
$998$	−15.5140	−0.491088
$999$	−15.5338	−0.491468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.17	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.17	✓	83	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.68633 q^{2} -0.538907 q^{3} +0.843700 q^{4} -1.00000 q^{5} +0.908773 q^{6} -3.51769 q^{7} +1.94990 q^{8} -2.70958 q^{9} +O(q^{10})\)	\(q-1.68633 q^{2} -0.538907 q^{3} +0.843700 q^{4} -1.00000 q^{5} +0.908773 q^{6} -3.51769 q^{7} +1.94990 q^{8} -2.70958 q^{9} +1.68633 q^{10} -5.12324 q^{11} -0.454676 q^{12} +4.11716 q^{13} +5.93198 q^{14} +0.538907 q^{15} -4.97557 q^{16} -6.45625 q^{17} +4.56924 q^{18} -2.53710 q^{19} -0.843700 q^{20} +1.89571 q^{21} +8.63946 q^{22} -1.09855 q^{23} -1.05081 q^{24} +1.00000 q^{25} -6.94289 q^{26} +3.07693 q^{27} -2.96788 q^{28} +8.87785 q^{29} -0.908773 q^{30} +10.3960 q^{31} +4.49064 q^{32} +2.76095 q^{33} +10.8874 q^{34} +3.51769 q^{35} -2.28607 q^{36} -5.04848 q^{37} +4.27837 q^{38} -2.21877 q^{39} -1.94990 q^{40} -3.57562 q^{41} -3.19678 q^{42} -9.73224 q^{43} -4.32248 q^{44} +2.70958 q^{45} +1.85251 q^{46} +8.50950 q^{47} +2.68137 q^{48} +5.37414 q^{49} -1.68633 q^{50} +3.47932 q^{51} +3.47365 q^{52} +11.1865 q^{53} -5.18871 q^{54} +5.12324 q^{55} -6.85915 q^{56} +1.36726 q^{57} -14.9710 q^{58} +14.0946 q^{59} +0.454676 q^{60} +5.67995 q^{61} -17.5311 q^{62} +9.53146 q^{63} +2.37845 q^{64} -4.11716 q^{65} -4.65586 q^{66} -1.63768 q^{67} -5.44714 q^{68} +0.592014 q^{69} -5.93198 q^{70} -11.6063 q^{71} -5.28341 q^{72} +5.40454 q^{73} +8.51339 q^{74} -0.538907 q^{75} -2.14055 q^{76} +18.0220 q^{77} +3.74157 q^{78} -4.14076 q^{79} +4.97557 q^{80} +6.47056 q^{81} +6.02966 q^{82} +13.1144 q^{83} +1.59941 q^{84} +6.45625 q^{85} +16.4117 q^{86} -4.78433 q^{87} -9.98980 q^{88} -14.4809 q^{89} -4.56924 q^{90} -14.4829 q^{91} -0.926843 q^{92} -5.60248 q^{93} -14.3498 q^{94} +2.53710 q^{95} -2.42004 q^{96} -14.7255 q^{97} -9.06257 q^{98} +13.8818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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