LMFDB - Embedded newform 3009.2.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3009,2,Mod(1,3009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3009 = 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3009.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:	$24.0269859682$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	3009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.749114 q^{2} +1.00000 q^{3} -1.43883 q^{4} -2.56478 q^{5} +0.749114 q^{6} +0.240543 q^{7} -2.57608 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.749114 q^{2} +1.00000 q^{3} -1.43883 q^{4} -2.56478 q^{5} +0.749114 q^{6} +0.240543 q^{7} -2.57608 q^{8} +1.00000 q^{9} -1.92132 q^{10} -3.97990 q^{11} -1.43883 q^{12} +0.832836 q^{13} +0.180194 q^{14} -2.56478 q^{15} +0.947880 q^{16} -1.00000 q^{17} +0.749114 q^{18} +4.07085 q^{19} +3.69028 q^{20} +0.240543 q^{21} -2.98140 q^{22} -1.24187 q^{23} -2.57608 q^{24} +1.57812 q^{25} +0.623890 q^{26} +1.00000 q^{27} -0.346100 q^{28} +4.85536 q^{29} -1.92132 q^{30} -7.67607 q^{31} +5.86222 q^{32} -3.97990 q^{33} -0.749114 q^{34} -0.616941 q^{35} -1.43883 q^{36} +8.34985 q^{37} +3.04953 q^{38} +0.832836 q^{39} +6.60708 q^{40} -4.16158 q^{41} +0.180194 q^{42} +10.5395 q^{43} +5.72639 q^{44} -2.56478 q^{45} -0.930299 q^{46} -10.7731 q^{47} +0.947880 q^{48} -6.94214 q^{49} +1.18219 q^{50} -1.00000 q^{51} -1.19831 q^{52} +4.05515 q^{53} +0.749114 q^{54} +10.2076 q^{55} -0.619657 q^{56} +4.07085 q^{57} +3.63722 q^{58} -1.00000 q^{59} +3.69028 q^{60} +11.1861 q^{61} -5.75026 q^{62} +0.240543 q^{63} +2.49571 q^{64} -2.13604 q^{65} -2.98140 q^{66} +11.1950 q^{67} +1.43883 q^{68} -1.24187 q^{69} -0.462159 q^{70} +15.6884 q^{71} -2.57608 q^{72} +3.43033 q^{73} +6.25499 q^{74} +1.57812 q^{75} -5.85725 q^{76} -0.957337 q^{77} +0.623890 q^{78} +11.0110 q^{79} -2.43111 q^{80} +1.00000 q^{81} -3.11750 q^{82} +11.9657 q^{83} -0.346100 q^{84} +2.56478 q^{85} +7.89530 q^{86} +4.85536 q^{87} +10.2525 q^{88} -3.41127 q^{89} -1.92132 q^{90} +0.200333 q^{91} +1.78683 q^{92} -7.67607 q^{93} -8.07025 q^{94} -10.4408 q^{95} +5.86222 q^{96} -2.28662 q^{97} -5.20046 q^{98} -3.97990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9} + 10 q^{10} + 11 q^{11} + 34 q^{12} + 21 q^{13} + 9 q^{14} - 3 q^{15} + 50 q^{16} - 24 q^{17} + 2 q^{18} + 13 q^{19} + q^{20} + 19 q^{21} + 5 q^{22} + 18 q^{23} + 3 q^{24} + 39 q^{25} - 7 q^{26} + 24 q^{27} + 40 q^{28} - 10 q^{29} + 10 q^{30} + 47 q^{31} + 18 q^{32} + 11 q^{33} - 2 q^{34} + 5 q^{35} + 34 q^{36} + 54 q^{37} + 5 q^{38} + 21 q^{39} + 29 q^{40} + 9 q^{42} + 16 q^{43} + 7 q^{44} - 3 q^{45} - 8 q^{46} + 10 q^{47} + 50 q^{48} + 55 q^{49} + 21 q^{50} - 24 q^{51} + 68 q^{52} + 6 q^{53} + 2 q^{54} + 15 q^{55} - 5 q^{56} + 13 q^{57} + q^{58} - 24 q^{59} + q^{60} + 42 q^{61} - 7 q^{62} + 19 q^{63} + 53 q^{64} - 9 q^{65} + 5 q^{66} + 28 q^{67} - 34 q^{68} + 18 q^{69} - 20 q^{70} + 54 q^{71} + 3 q^{72} + 33 q^{73} - 17 q^{74} + 39 q^{75} - 56 q^{76} - 23 q^{77} - 7 q^{78} + 35 q^{79} + 3 q^{80} + 24 q^{81} - 12 q^{82} - 17 q^{83} + 40 q^{84} + 3 q^{85} + 36 q^{86} - 10 q^{87} + 47 q^{88} + 15 q^{89} + 10 q^{90} + 74 q^{91} + 6 q^{92} + 47 q^{93} + 9 q^{94} + 12 q^{95} + 18 q^{96} + 52 q^{97} - 48 q^{98} + 11 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9 + 10 * q^10 + 11 * q^11 + 34 * q^12 + 21 * q^13 + 9 * q^14 - 3 * q^15 + 50 * q^16 - 24 * q^17 + 2 * q^18 + 13 * q^19 + q^20 + 19 * q^21 + 5 * q^22 + 18 * q^23 + 3 * q^24 + 39 * q^25 - 7 * q^26 + 24 * q^27 + 40 * q^28 - 10 * q^29 + 10 * q^30 + 47 * q^31 + 18 * q^32 + 11 * q^33 - 2 * q^34 + 5 * q^35 + 34 * q^36 + 54 * q^37 + 5 * q^38 + 21 * q^39 + 29 * q^40 + 9 * q^42 + 16 * q^43 + 7 * q^44 - 3 * q^45 - 8 * q^46 + 10 * q^47 + 50 * q^48 + 55 * q^49 + 21 * q^50 - 24 * q^51 + 68 * q^52 + 6 * q^53 + 2 * q^54 + 15 * q^55 - 5 * q^56 + 13 * q^57 + q^58 - 24 * q^59 + q^60 + 42 * q^61 - 7 * q^62 + 19 * q^63 + 53 * q^64 - 9 * q^65 + 5 * q^66 + 28 * q^67 - 34 * q^68 + 18 * q^69 - 20 * q^70 + 54 * q^71 + 3 * q^72 + 33 * q^73 - 17 * q^74 + 39 * q^75 - 56 * q^76 - 23 * q^77 - 7 * q^78 + 35 * q^79 + 3 * q^80 + 24 * q^81 - 12 * q^82 - 17 * q^83 + 40 * q^84 + 3 * q^85 + 36 * q^86 - 10 * q^87 + 47 * q^88 + 15 * q^89 + 10 * q^90 + 74 * q^91 + 6 * q^92 + 47 * q^93 + 9 * q^94 + 12 * q^95 + 18 * q^96 + 52 * q^97 - 48 * q^98 + 11 * 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 $

$2$	0.749114	0.529704	0.264852	−	0.964289i	$-0.414677\pi$
$2$	0.749114	0.529704	0.264852	+	0.964289i	$0.414677\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.43883	−0.719414
$5$	−2.56478	−1.14701	−0.573503	−	0.819203i	$-0.694416\pi$
$5$	−2.56478	−1.14701	−0.573503	+	0.819203i	$0.694416\pi$
$6$	0.749114	0.305825
$7$	0.240543	0.0909167	0.0454584	−	0.998966i	$-0.485525\pi$
$7$	0.240543	0.0909167	0.0454584	+	0.998966i	$0.485525\pi$
$8$	−2.57608	−0.910780
$9$	1.00000	0.333333
$10$	−1.92132	−0.607574
$11$	−3.97990	−1.19998	−0.599992	−	0.800006i	$-0.704830\pi$
$11$	−3.97990	−1.19998	−0.599992	+	0.800006i	$0.704830\pi$
$12$	−1.43883	−0.415354
$13$	0.832836	0.230987	0.115494	−	0.993308i	$-0.463155\pi$
$13$	0.832836	0.230987	0.115494	+	0.993308i	$0.463155\pi$
$14$	0.180194	0.0481590
$15$	−2.56478	−0.662224
$16$	0.947880	0.236970
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.749114	0.176568
$19$	4.07085	0.933917	0.466958	−	0.884279i	$-0.345350\pi$
$19$	4.07085	0.933917	0.466958	+	0.884279i	$0.345350\pi$
$20$	3.69028	0.825172
$21$	0.240543	0.0524908
$22$	−2.98140	−0.635637
$23$	−1.24187	−0.258947	−0.129473	−	0.991583i	$-0.541329\pi$
$23$	−1.24187	−0.258947	−0.129473	+	0.991583i	$0.541329\pi$
$24$	−2.57608	−0.525839
$25$	1.57812	0.315623
$26$	0.623890	0.122355
$27$	1.00000	0.192450
$28$	−0.346100	−0.0654068
$29$	4.85536	0.901617	0.450809	−	0.892621i	$-0.351136\pi$
$29$	4.85536	0.901617	0.450809	+	0.892621i	$0.351136\pi$
$30$	−1.92132	−0.350783
$31$	−7.67607	−1.37866	−0.689332	−	0.724446i	$-0.742096\pi$
$31$	−7.67607	−1.37866	−0.689332	+	0.724446i	$0.742096\pi$
$32$	5.86222	1.03630
$33$	−3.97990	−0.692811
$34$	−0.749114	−0.128472
$35$	−0.616941	−0.104282
$36$	−1.43883	−0.239805
$37$	8.34985	1.37271	0.686353	−	0.727268i	$-0.259210\pi$
$37$	8.34985	1.37271	0.686353	+	0.727268i	$0.259210\pi$
$38$	3.04953	0.494699
$39$	0.832836	0.133361
$40$	6.60708	1.04467
$41$	−4.16158	−0.649929	−0.324964	−	0.945726i	$-0.605352\pi$
$41$	−4.16158	−0.649929	−0.324964	+	0.945726i	$0.605352\pi$
$42$	0.180194	0.0278046
$43$	10.5395	1.60726	0.803631	−	0.595129i	$-0.202899\pi$
$43$	10.5395	1.60726	0.803631	+	0.595129i	$0.202899\pi$
$44$	5.72639	0.863285
$45$	−2.56478	−0.382335
$46$	−0.930299	−0.137165
$47$	−10.7731	−1.57141	−0.785706	−	0.618600i	$-0.787700\pi$
$47$	−10.7731	−1.57141	−0.785706	+	0.618600i	$0.787700\pi$
$48$	0.947880	0.136815
$49$	−6.94214	−0.991734
$50$	1.18219	0.167187
$51$	−1.00000	−0.140028
$52$	−1.19831	−0.166175
$53$	4.05515	0.557018	0.278509	−	0.960434i	$-0.410160\pi$
$53$	4.05515	0.557018	0.278509	+	0.960434i	$0.410160\pi$
$54$	0.749114	0.101942
$55$	10.2076	1.37639
$56$	−0.619657	−0.0828052
$57$	4.07085	0.539197
$58$	3.63722	0.477590
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.69028	0.476413
$61$	11.1861	1.43224	0.716118	−	0.697979i	$-0.245917\pi$
$61$	11.1861	1.43224	0.716118	+	0.697979i	$0.245917\pi$
$62$	−5.75026	−0.730283
$63$	0.240543	0.0303056
$64$	2.49571	0.311964
$65$	−2.13604	−0.264944
$66$	−2.98140	−0.366985
$67$	11.1950	1.36769	0.683844	−	0.729629i	$-0.260307\pi$
$67$	11.1950	1.36769	0.683844	+	0.729629i	$0.260307\pi$
$68$	1.43883	0.174483
$69$	−1.24187	−0.149503
$70$	−0.462159	−0.0552386
$71$	15.6884	1.86187	0.930934	−	0.365187i	$-0.118995\pi$
$71$	15.6884	1.86187	0.930934	+	0.365187i	$0.118995\pi$
$72$	−2.57608	−0.303593
$73$	3.43033	0.401490	0.200745	−	0.979644i	$-0.435664\pi$
$73$	3.43033	0.401490	0.200745	+	0.979644i	$0.435664\pi$
$74$	6.25499	0.727128
$75$	1.57812	0.182225
$76$	−5.85725	−0.671873
$77$	−0.957337	−0.109099
$78$	0.623890	0.0706416
$79$	11.0110	1.23884	0.619418	−	0.785061i	$-0.287369\pi$
$79$	11.0110	1.23884	0.619418	+	0.785061i	$0.287369\pi$
$80$	−2.43111	−0.271806
$81$	1.00000	0.111111
$82$	−3.11750	−0.344270
$83$	11.9657	1.31340	0.656701	−	0.754151i	$-0.271951\pi$
$83$	11.9657	1.31340	0.656701	+	0.754151i	$0.271951\pi$
$84$	−0.346100	−0.0377626
$85$	2.56478	0.278190
$86$	7.89530	0.851372
$87$	4.85536	0.520549
$88$	10.2525	1.09292
$89$	−3.41127	−0.361594	−0.180797	−	0.983520i	$-0.557868\pi$
$89$	−3.41127	−0.361594	−0.180797	+	0.983520i	$0.557868\pi$
$90$	−1.92132	−0.202525
$91$	0.200333	0.0210006
$92$	1.78683	0.186290
$93$	−7.67607	−0.795971
$94$	−8.07025	−0.832383
$95$	−10.4408	−1.07121
$96$	5.86222	0.598310
$97$	−2.28662	−0.232171	−0.116086	−	0.993239i	$-0.537035\pi$
$97$	−2.28662	−0.232171	−0.116086	+	0.993239i	$0.537035\pi$
$98$	−5.20046	−0.525325
$99$	−3.97990	−0.399995
$100$	−2.27064	−0.227064
$101$	−13.4101	−1.33436	−0.667180	−	0.744897i	$-0.732499\pi$
$101$	−13.4101	−1.33436	−0.667180	+	0.744897i	$0.732499\pi$
$102$	−0.749114	−0.0741734
$103$	4.17823	0.411693	0.205846	−	0.978584i	$-0.434005\pi$
$103$	4.17823	0.411693	0.205846	+	0.978584i	$0.434005\pi$
$104$	−2.14545	−0.210379
$105$	−0.616941	−0.0602073
$106$	3.03777	0.295055
$107$	2.10100	0.203111	0.101556	−	0.994830i	$-0.467618\pi$
$107$	2.10100	0.203111	0.101556	+	0.994830i	$0.467618\pi$
$108$	−1.43883	−0.138451
$109$	15.9278	1.52561	0.762804	−	0.646629i	$-0.223822\pi$
$109$	15.9278	1.52561	0.762804	+	0.646629i	$0.223822\pi$
$110$	7.64665	0.729079
$111$	8.34985	0.792533
$112$	0.228006	0.0215445
$113$	19.3301	1.81843	0.909214	−	0.416330i	$-0.136684\pi$
$113$	19.3301	1.81843	0.909214	+	0.416330i	$0.136684\pi$
$114$	3.04953	0.285615
$115$	3.18512	0.297014
$116$	−6.98602	−0.648636
$117$	0.832836	0.0769957
$118$	−0.749114	−0.0689616
$119$	−0.240543	−0.0220505
$120$	6.60708	0.603141
$121$	4.83959	0.439963
$122$	8.37969	0.758661
$123$	−4.16158	−0.375237
$124$	11.0445	0.991829
$125$	8.77639	0.784984
$126$	0.180194	0.0160530
$127$	−1.78086	−0.158026	−0.0790129	−	0.996874i	$-0.525177\pi$
$127$	−1.78086	−0.158026	−0.0790129	+	0.996874i	$0.525177\pi$
$128$	−9.85487	−0.871055
$129$	10.5395	0.927953
$130$	−1.60014	−0.140342
$131$	−12.3915	−1.08265	−0.541326	−	0.840813i	$-0.682078\pi$
$131$	−12.3915	−1.08265	−0.541326	+	0.840813i	$0.682078\pi$
$132$	5.72639	0.498418
$133$	0.979214	0.0849087
$134$	8.38634	0.724469
$135$	−2.56478	−0.220741
$136$	2.57608	0.220897
$137$	7.46105	0.637441	0.318720	−	0.947849i	$-0.396747\pi$
$137$	7.46105	0.637441	0.318720	+	0.947849i	$0.396747\pi$
$138$	−0.930299	−0.0791923
$139$	−6.87557	−0.583178	−0.291589	−	0.956544i	$-0.594184\pi$
$139$	−6.87557	−0.583178	−0.291589	+	0.956544i	$0.594184\pi$
$140$	0.887672	0.0750220
$141$	−10.7731	−0.907255
$142$	11.7524	0.986239
$143$	−3.31460	−0.277181
$144$	0.947880	0.0789900
$145$	−12.4529	−1.03416
$146$	2.56971	0.212671
$147$	−6.94214	−0.572578
$148$	−12.0140	−0.987544
$149$	−14.9375	−1.22373	−0.611865	−	0.790962i	$-0.709580\pi$
$149$	−14.9375	−1.22373	−0.611865	+	0.790962i	$0.709580\pi$
$150$	1.18219	0.0965254
$151$	−9.20026	−0.748706	−0.374353	−	0.927286i	$-0.622135\pi$
$151$	−9.20026	−0.748706	−0.374353	+	0.927286i	$0.622135\pi$
$152$	−10.4868	−0.850593
$153$	−1.00000	−0.0808452
$154$	−0.717155	−0.0577900
$155$	19.6875	1.58134
$156$	−1.19831	−0.0959414
$157$	−15.8188	−1.26247	−0.631237	−	0.775590i	$-0.717452\pi$
$157$	−15.8188	−1.26247	−0.631237	+	0.775590i	$0.717452\pi$
$158$	8.24851	0.656216
$159$	4.05515	0.321594
$160$	−15.0353	−1.18865
$161$	−0.298722	−0.0235426
$162$	0.749114	0.0588560
$163$	−8.03130	−0.629060	−0.314530	−	0.949248i	$-0.601847\pi$
$163$	−8.03130	−0.629060	−0.314530	+	0.949248i	$0.601847\pi$
$164$	5.98779	0.467568
$165$	10.2076	0.794659
$166$	8.96365	0.695714
$167$	24.4878	1.89492	0.947460	−	0.319874i	$-0.103641\pi$
$167$	24.4878	1.89492	0.947460	+	0.319874i	$0.103641\pi$
$168$	−0.619657	−0.0478076
$169$	−12.3064	−0.946645
$170$	1.92132	0.147358
$171$	4.07085	0.311306
$172$	−15.1645	−1.15629
$173$	−10.8351	−0.823775	−0.411888	−	0.911235i	$-0.635130\pi$
$173$	−10.8351	−0.823775	−0.411888	+	0.911235i	$0.635130\pi$
$174$	3.63722	0.275737
$175$	0.379605	0.0286954
$176$	−3.77247	−0.284360
$177$	−1.00000	−0.0751646
$178$	−2.55543	−0.191538
$179$	10.4438	0.780609	0.390304	−	0.920686i	$-0.372370\pi$
$179$	10.4438	0.780609	0.390304	+	0.920686i	$0.372370\pi$
$180$	3.69028	0.275057
$181$	−13.5463	−1.00689	−0.503445	−	0.864027i	$-0.667934\pi$
$181$	−13.5463	−1.00689	−0.503445	+	0.864027i	$0.667934\pi$
$182$	0.150072	0.0111241
$183$	11.1861	0.826902
$184$	3.19914	0.235844
$185$	−21.4156	−1.57450
$186$	−5.75026	−0.421629
$187$	3.97990	0.291039
$188$	15.5006	1.13050
$189$	0.240543	0.0174969
$190$	−7.82139	−0.567423
$191$	2.53783	0.183631	0.0918155	−	0.995776i	$-0.470733\pi$
$191$	2.53783	0.183631	0.0918155	+	0.995776i	$0.470733\pi$
$192$	2.49571	0.180113
$193$	12.5001	0.899778	0.449889	−	0.893085i	$-0.351464\pi$
$193$	12.5001	0.899778	0.449889	+	0.893085i	$0.351464\pi$
$194$	−1.71294	−0.122982
$195$	−2.13604	−0.152965
$196$	9.98854	0.713467
$197$	24.3383	1.73403	0.867016	−	0.498281i	$-0.166035\pi$
$197$	24.3383	1.73403	0.867016	+	0.498281i	$0.166035\pi$
$198$	−2.98140	−0.211879
$199$	−0.842179	−0.0597005	−0.0298503	−	0.999554i	$-0.509503\pi$
$199$	−0.842179	−0.0597005	−0.0298503	+	0.999554i	$0.509503\pi$
$200$	−4.06535	−0.287463
$201$	11.1950	0.789635
$202$	−10.0457	−0.706815
$203$	1.16792	0.0819721
$204$	1.43883	0.100738
$205$	10.6735	0.745473
$206$	3.12997	0.218075
$207$	−1.24187	−0.0863156
$208$	0.789429	0.0547370
$209$	−16.2016	−1.12069
$210$	−0.462159	−0.0318920
$211$	22.5488	1.55233	0.776163	−	0.630532i	$-0.217163\pi$
$211$	22.5488	1.55233	0.776163	+	0.630532i	$0.217163\pi$
$212$	−5.83466	−0.400726
$213$	15.6884	1.07495
$214$	1.57389	0.107589
$215$	−27.0316	−1.84354
$216$	−2.57608	−0.175280
$217$	−1.84643	−0.125344
$218$	11.9318	0.808121
$219$	3.43033	0.231800
$220$	−14.6869	−0.990194
$221$	−0.832836	−0.0560226
$222$	6.25499	0.419808
$223$	−3.64319	−0.243966	−0.121983	−	0.992532i	$-0.538925\pi$
$223$	−3.64319	−0.243966	−0.121983	+	0.992532i	$0.538925\pi$
$224$	1.41012	0.0942174
$225$	1.57812	0.105208
$226$	14.4805	0.963228
$227$	−18.9445	−1.25739	−0.628695	−	0.777652i	$-0.716411\pi$
$227$	−18.9445	−1.25739	−0.628695	+	0.777652i	$0.716411\pi$
$228$	−5.85725	−0.387906
$229$	−8.49490	−0.561359	−0.280679	−	0.959802i	$-0.590560\pi$
$229$	−8.49490	−0.561359	−0.280679	+	0.959802i	$0.590560\pi$
$230$	2.38602	0.157329
$231$	−0.957337	−0.0629882
$232$	−12.5078	−0.821175
$233$	−20.0502	−1.31353	−0.656766	−	0.754094i	$-0.728076\pi$
$233$	−20.0502	−1.31353	−0.656766	+	0.754094i	$0.728076\pi$
$234$	0.623890	0.0407849
$235$	27.6306	1.80242
$236$	1.43883	0.0936597
$237$	11.0110	0.715242
$238$	−0.180194	−0.0116803
$239$	−24.2952	−1.57152	−0.785762	−	0.618529i	$-0.787729\pi$
$239$	−24.2952	−1.57152	−0.785762	+	0.618529i	$0.787729\pi$
$240$	−2.43111	−0.156927
$241$	17.7513	1.14346	0.571729	−	0.820442i	$-0.306273\pi$
$241$	17.7513	1.14346	0.571729	+	0.820442i	$0.306273\pi$
$242$	3.62541	0.233050
$243$	1.00000	0.0641500
$244$	−16.0949	−1.03037
$245$	17.8051	1.13753
$246$	−3.11750	−0.198764
$247$	3.39035	0.215723
$248$	19.7741	1.25566
$249$	11.9657	0.758293
$250$	6.57452	0.415809
$251$	14.8267	0.935854	0.467927	−	0.883767i	$-0.345001\pi$
$251$	14.8267	0.935854	0.467927	+	0.883767i	$0.345001\pi$
$252$	−0.346100	−0.0218023
$253$	4.94250	0.310732
$254$	−1.33407	−0.0837069
$255$	2.56478	0.160613
$256$	−12.3739	−0.773366
$257$	−10.6358	−0.663441	−0.331721	−	0.943378i	$-0.607629\pi$
$257$	−10.6358	−0.663441	−0.331721	+	0.943378i	$0.607629\pi$
$258$	7.89530	0.491540
$259$	2.00850	0.124802
$260$	3.07340	0.190604
$261$	4.85536	0.300539
$262$	−9.28267	−0.573485
$263$	3.19983	0.197310	0.0986551	−	0.995122i	$-0.468546\pi$
$263$	3.19983	0.197310	0.0986551	+	0.995122i	$0.468546\pi$
$264$	10.2525	0.630999
$265$	−10.4006	−0.638903
$266$	0.733544	0.0449764
$267$	−3.41127	−0.208766
$268$	−16.1077	−0.983933
$269$	28.4748	1.73614	0.868070	−	0.496442i	$-0.165360\pi$
$269$	28.4748	1.73614	0.868070	+	0.496442i	$0.165360\pi$
$270$	−1.92132	−0.116928
$271$	30.8137	1.87180	0.935901	−	0.352264i	$-0.114588\pi$
$271$	30.8137	1.87180	0.935901	+	0.352264i	$0.114588\pi$
$272$	−0.947880	−0.0574737
$273$	0.200333	0.0121247
$274$	5.58918	0.337655
$275$	−6.28074	−0.378743
$276$	1.78683	0.107555
$277$	−11.7830	−0.707973	−0.353987	−	0.935250i	$-0.615174\pi$
$277$	−11.7830	−0.707973	−0.353987	+	0.935250i	$0.615174\pi$
$278$	−5.15059	−0.308912
$279$	−7.67607	−0.459554
$280$	1.58929	0.0949780
$281$	−8.92785	−0.532591	−0.266295	−	0.963891i	$-0.585800\pi$
$281$	−8.92785	−0.532591	−0.266295	+	0.963891i	$0.585800\pi$
$282$	−8.07025	−0.480577
$283$	15.4564	0.918790	0.459395	−	0.888232i	$-0.348066\pi$
$283$	15.4564	0.918790	0.459395	+	0.888232i	$0.348066\pi$
$284$	−22.5729	−1.33945
$285$	−10.4408	−0.618462
$286$	−2.48302	−0.146824
$287$	−1.00104	−0.0590894
$288$	5.86222	0.345435
$289$	1.00000	0.0588235
$290$	−9.32868	−0.547799
$291$	−2.28662	−0.134044
$292$	−4.93565	−0.288837
$293$	22.0692	1.28930	0.644648	−	0.764480i	$-0.277004\pi$
$293$	22.0692	1.28930	0.644648	+	0.764480i	$0.277004\pi$
$294$	−5.20046	−0.303297
$295$	2.56478	0.149327
$296$	−21.5098	−1.25023
$297$	−3.97990	−0.230937
$298$	−11.1899	−0.648214
$299$	−1.03427	−0.0598134
$300$	−2.27064	−0.131095
$301$	2.53521	0.146127
$302$	−6.89205	−0.396593
$303$	−13.4101	−0.770393
$304$	3.85868	0.221310
$305$	−28.6900	−1.64278
$306$	−0.749114	−0.0428240
$307$	−7.36295	−0.420226	−0.210113	−	0.977677i	$-0.567383\pi$
$307$	−7.36295	−0.420226	−0.210113	+	0.977677i	$0.567383\pi$
$308$	1.37744	0.0784871
$309$	4.17823	0.237691
$310$	14.7482	0.837639
$311$	−19.5398	−1.10800	−0.554001	−	0.832516i	$-0.686900\pi$
$311$	−19.5398	−1.10800	−0.554001	+	0.832516i	$0.686900\pi$
$312$	−2.14545	−0.121462
$313$	−7.03297	−0.397527	−0.198763	−	0.980047i	$-0.563693\pi$
$313$	−7.03297	−0.397527	−0.198763	+	0.980047i	$0.563693\pi$
$314$	−11.8501	−0.668737
$315$	−0.616941	−0.0347607
$316$	−15.8430	−0.891236
$317$	−9.04985	−0.508290	−0.254145	−	0.967166i	$-0.581794\pi$
$317$	−9.04985	−0.508290	−0.254145	+	0.967166i	$0.581794\pi$
$318$	3.03777	0.170350
$319$	−19.3238	−1.08193
$320$	−6.40097	−0.357825
$321$	2.10100	0.117266
$322$	−0.223777	−0.0124706
$323$	−4.07085	−0.226508
$324$	−1.43883	−0.0799349
$325$	1.31431	0.0729049
$326$	−6.01636	−0.333215
$327$	15.9278	0.880810
$328$	10.7205	0.591942
$329$	−2.59138	−0.142868
$330$	7.64665	0.420934
$331$	−31.5042	−1.73163	−0.865815	−	0.500364i	$-0.833199\pi$
$331$	−31.5042	−1.73163	−0.865815	+	0.500364i	$0.833199\pi$
$332$	−17.2165	−0.944879
$333$	8.34985	0.457569
$334$	18.3441	1.00375
$335$	−28.7128	−1.56875
$336$	0.228006	0.0124387
$337$	16.9865	0.925315	0.462658	−	0.886537i	$-0.346896\pi$
$337$	16.9865	0.925315	0.462658	+	0.886537i	$0.346896\pi$
$338$	−9.21889	−0.501441
$339$	19.3301	1.04987
$340$	−3.69028	−0.200134
$341$	30.5500	1.65437
$342$	3.04953	0.164900
$343$	−3.35369	−0.181082
$344$	−27.1506	−1.46386
$345$	3.18512	0.171481
$346$	−8.11671	−0.436357
$347$	24.1107	1.29433	0.647165	−	0.762350i	$-0.275954\pi$
$347$	24.1107	1.29433	0.647165	+	0.762350i	$0.275954\pi$
$348$	−6.98602	−0.374490
$349$	15.3817	0.823362	0.411681	−	0.911328i	$-0.364942\pi$
$349$	15.3817	0.823362	0.411681	+	0.911328i	$0.364942\pi$
$350$	0.284368	0.0152001
$351$	0.832836	0.0444535
$352$	−23.3310	−1.24355
$353$	10.4503	0.556215	0.278107	−	0.960550i	$-0.410293\pi$
$353$	10.4503	0.556215	0.278107	+	0.960550i	$0.410293\pi$
$354$	−0.749114	−0.0398150
$355$	−40.2373	−2.13557
$356$	4.90823	0.260136
$357$	−0.240543	−0.0127309
$358$	7.82363	0.413492
$359$	10.4628	0.552208	0.276104	−	0.961128i	$-0.410957\pi$
$359$	10.4628	0.552208	0.276104	+	0.961128i	$0.410957\pi$
$360$	6.60708	0.348224
$361$	−2.42819	−0.127800
$362$	−10.1477	−0.533354
$363$	4.83959	0.254013
$364$	−0.288245	−0.0151081
$365$	−8.79805	−0.460511
$366$	8.37969	0.438013
$367$	−21.7789	−1.13685	−0.568426	−	0.822734i	$-0.692447\pi$
$367$	−21.7789	−1.13685	−0.568426	+	0.822734i	$0.692447\pi$
$368$	−1.17714	−0.0613626
$369$	−4.16158	−0.216643
$370$	−16.0427	−0.834021
$371$	0.975439	0.0506423
$372$	11.0445	0.572633
$373$	−21.9623	−1.13716	−0.568582	−	0.822627i	$-0.692508\pi$
$373$	−21.9623	−1.13716	−0.568582	+	0.822627i	$0.692508\pi$
$374$	2.98140	0.154164
$375$	8.77639	0.453211
$376$	27.7522	1.43121
$377$	4.04372	0.208262
$378$	0.180194	0.00926819
$379$	17.8756	0.918206	0.459103	−	0.888383i	$-0.348171\pi$
$379$	17.8756	0.918206	0.459103	+	0.888383i	$0.348171\pi$
$380$	15.0226	0.770642
$381$	−1.78086	−0.0912362
$382$	1.90113	0.0972700
$383$	−23.6449	−1.20820	−0.604100	−	0.796909i	$-0.706467\pi$
$383$	−23.6449	−1.20820	−0.604100	+	0.796909i	$0.706467\pi$
$384$	−9.85487	−0.502904
$385$	2.45536	0.125137
$386$	9.36402	0.476616
$387$	10.5395	0.535754
$388$	3.29005	0.167027
$389$	−18.0473	−0.915033	−0.457517	−	0.889201i	$-0.651261\pi$
$389$	−18.0473	−0.915033	−0.457517	+	0.889201i	$0.651261\pi$
$390$	−1.60014	−0.0810263
$391$	1.24187	0.0628038
$392$	17.8835	0.903252
$393$	−12.3915	−0.625070
$394$	18.2322	0.918523
$395$	−28.2409	−1.42095
$396$	5.72639	0.287762
$397$	19.1608	0.961654	0.480827	−	0.876815i	$-0.340337\pi$
$397$	19.1608	0.961654	0.480827	+	0.876815i	$0.340337\pi$
$398$	−0.630889	−0.0316236
$399$	0.979214	0.0490220
$400$	1.49586	0.0747932
$401$	0.885545	0.0442220	0.0221110	−	0.999756i	$-0.492961\pi$
$401$	0.885545	0.0442220	0.0221110	+	0.999756i	$0.492961\pi$
$402$	8.38634	0.418273
$403$	−6.39291	−0.318454
$404$	19.2949	0.959956
$405$	−2.56478	−0.127445
$406$	0.874908	0.0434209
$407$	−33.2316	−1.64723
$408$	2.57608	0.127535
$409$	15.5449	0.768648	0.384324	−	0.923198i	$-0.374435\pi$
$409$	15.5449	0.768648	0.384324	+	0.923198i	$0.374435\pi$
$410$	7.99570	0.394880
$411$	7.46105	0.368027
$412$	−6.01175	−0.296178
$413$	−0.240543	−0.0118364
$414$	−0.930299	−0.0457217
$415$	−30.6893	−1.50648
$416$	4.88227	0.239373
$417$	−6.87557	−0.336698
$418$	−12.1368	−0.593632
$419$	−38.8866	−1.89974	−0.949868	−	0.312653i	$-0.898782\pi$
$419$	−38.8866	−1.89974	−0.949868	+	0.312653i	$0.898782\pi$
$420$	0.887672	0.0433139
$421$	20.5136	0.999771	0.499886	−	0.866091i	$-0.333375\pi$
$421$	20.5136	0.999771	0.499886	+	0.866091i	$0.333375\pi$
$422$	16.8917	0.822273
$423$	−10.7731	−0.523804
$424$	−10.4464	−0.507321
$425$	−1.57812	−0.0765499
$426$	11.7524	0.569405
$427$	2.69074	0.130214
$428$	−3.02297	−0.146121
$429$	−3.31460	−0.160031
$430$	−20.2497	−0.976530
$431$	−8.81727	−0.424713	−0.212357	−	0.977192i	$-0.568114\pi$
$431$	−8.81727	−0.424713	−0.212357	+	0.977192i	$0.568114\pi$
$432$	0.947880	0.0456049
$433$	−14.1815	−0.681520	−0.340760	−	0.940150i	$-0.610684\pi$
$433$	−14.1815	−0.681520	−0.340760	+	0.940150i	$0.610684\pi$
$434$	−1.38318	−0.0663950
$435$	−12.4529	−0.597073
$436$	−22.9174	−1.09754
$437$	−5.05545	−0.241835
$438$	2.56971	0.122785
$439$	−10.5321	−0.502671	−0.251335	−	0.967900i	$-0.580870\pi$
$439$	−10.5321	−0.502671	−0.251335	+	0.967900i	$0.580870\pi$
$440$	−26.2955	−1.25359
$441$	−6.94214	−0.330578
$442$	−0.623890	−0.0296754
$443$	5.87296	0.279033	0.139516	−	0.990220i	$-0.455445\pi$
$443$	5.87296	0.279033	0.139516	+	0.990220i	$0.455445\pi$
$444$	−12.0140	−0.570159
$445$	8.74917	0.414750
$446$	−2.72917	−0.129230
$447$	−14.9375	−0.706521
$448$	0.600327	0.0283628
$449$	11.3960	0.537810	0.268905	−	0.963167i	$-0.413338\pi$
$449$	11.3960	0.537810	0.268905	+	0.963167i	$0.413338\pi$
$450$	1.18219	0.0557290
$451$	16.5626	0.779905
$452$	−27.8128	−1.30820
$453$	−9.20026	−0.432266
$454$	−14.1916	−0.666045
$455$	−0.513811	−0.0240878
$456$	−10.4868	−0.491090
$457$	11.0434	0.516589	0.258294	−	0.966066i	$-0.416840\pi$
$457$	11.0434	0.516589	0.258294	+	0.966066i	$0.416840\pi$
$458$	−6.36365	−0.297354
$459$	−1.00000	−0.0466760
$460$	−4.58283	−0.213676
$461$	−17.8168	−0.829812	−0.414906	−	0.909864i	$-0.636186\pi$
$461$	−17.8168	−0.829812	−0.414906	+	0.909864i	$0.636186\pi$
$462$	−0.717155	−0.0333651
$463$	29.2281	1.35835	0.679173	−	0.733978i	$-0.262339\pi$
$463$	29.2281	1.35835	0.679173	+	0.733978i	$0.262339\pi$
$464$	4.60230	0.213656
$465$	19.6875	0.912984
$466$	−15.0199	−0.695783
$467$	22.2277	1.02858	0.514289	−	0.857617i	$-0.328056\pi$
$467$	22.2277	1.02858	0.514289	+	0.857617i	$0.328056\pi$
$468$	−1.19831	−0.0553918
$469$	2.69288	0.124346
$470$	20.6985	0.954749
$471$	−15.8188	−0.728890
$472$	2.57608	0.118573
$473$	−41.9462	−1.92869
$474$	8.24851	0.378867
$475$	6.42427	0.294766
$476$	0.346100	0.0158635
$477$	4.05515	0.185673
$478$	−18.1999	−0.832442
$479$	39.7426	1.81589	0.907943	−	0.419094i	$-0.137652\pi$
$479$	39.7426	1.81589	0.907943	+	0.419094i	$0.137652\pi$
$480$	−15.0353	−0.686266
$481$	6.95406	0.317078
$482$	13.2977	0.605694
$483$	−0.298722	−0.0135923
$484$	−6.96334	−0.316515
$485$	5.86469	0.266302
$486$	0.749114	0.0339805
$487$	34.7160	1.57313	0.786565	−	0.617507i	$-0.211857\pi$
$487$	34.7160	1.57313	0.786565	+	0.617507i	$0.211857\pi$
$488$	−28.8163	−1.30445
$489$	−8.03130	−0.363188
$490$	13.3380	0.602552
$491$	11.9915	0.541168	0.270584	−	0.962696i	$-0.412783\pi$
$491$	11.9915	0.541168	0.270584	+	0.962696i	$0.412783\pi$
$492$	5.98779	0.269950
$493$	−4.85536	−0.218674
$494$	2.53976	0.114269
$495$	10.2076	0.458797
$496$	−7.27599	−0.326702
$497$	3.77373	0.169275
$498$	8.96365	0.401671
$499$	−38.7949	−1.73670	−0.868349	−	0.495954i	$-0.834818\pi$
$499$	−38.7949	−1.73670	−0.868349	+	0.495954i	$0.834818\pi$
$500$	−12.6277	−0.564729
$501$	24.4878	1.09403
$502$	11.1069	0.495725
$503$	6.36351	0.283735	0.141867	−	0.989886i	$-0.454689\pi$
$503$	6.36351	0.283735	0.141867	+	0.989886i	$0.454689\pi$
$504$	−0.619657	−0.0276017
$505$	34.3941	1.53052
$506$	3.70250	0.164596
$507$	−12.3064	−0.546546
$508$	2.56235	0.113686
$509$	27.8067	1.23251	0.616256	−	0.787546i	$-0.288649\pi$
$509$	27.8067	1.23251	0.616256	+	0.787546i	$0.288649\pi$
$510$	1.92132	0.0850773
$511$	0.825142	0.0365021
$512$	10.4403	0.461401
$513$	4.07085	0.179732
$514$	−7.96741	−0.351427
$515$	−10.7162	−0.472214
$516$	−15.1645	−0.667582
$517$	42.8757	1.88567
$518$	1.50460	0.0661081
$519$	−10.8351	−0.475607
$520$	5.50261	0.241306
$521$	−15.1188	−0.662367	−0.331183	−	0.943566i	$-0.607448\pi$
$521$	−15.1188	−0.662367	−0.331183	+	0.943566i	$0.607448\pi$
$522$	3.63722	0.159197
$523$	−26.3202	−1.15090	−0.575451	−	0.817836i	$-0.695174\pi$
$523$	−26.3202	−1.15090	−0.575451	+	0.817836i	$0.695174\pi$
$524$	17.8293	0.778875
$525$	0.379605	0.0165673
$526$	2.39704	0.104516
$527$	7.67607	0.334375
$528$	−3.77247	−0.164176
$529$	−21.4578	−0.932947
$530$	−7.79123	−0.338429
$531$	−1.00000	−0.0433963
$532$	−1.40892	−0.0610845
$533$	−3.46591	−0.150125
$534$	−2.55543	−0.110584
$535$	−5.38860	−0.232970
$536$	−28.8392	−1.24566
$537$	10.4438	0.450685
$538$	21.3309	0.919640
$539$	27.6290	1.19007
$540$	3.69028	0.158804
$541$	15.7567	0.677435	0.338718	−	0.940888i	$-0.390007\pi$
$541$	15.7567	0.677435	0.338718	+	0.940888i	$0.390007\pi$
$542$	23.0830	0.991500
$543$	−13.5463	−0.581328
$544$	−5.86222	−0.251341
$545$	−40.8514	−1.74988
$546$	0.150072	0.00642250
$547$	37.5432	1.60523	0.802616	−	0.596496i	$-0.203441\pi$
$547$	37.5432	1.60523	0.802616	+	0.596496i	$0.203441\pi$
$548$	−10.7352	−0.458584
$549$	11.1861	0.477412
$550$	−4.70500	−0.200622
$551$	19.7654	0.842035
$552$	3.19914	0.136164
$553$	2.64862	0.112631
$554$	−8.82684	−0.375016
$555$	−21.4156	−0.909040
$556$	9.89276	0.419546
$557$	−19.1234	−0.810285	−0.405143	−	0.914254i	$-0.632778\pi$
$557$	−19.1234	−0.810285	−0.405143	+	0.914254i	$0.632778\pi$
$558$	−5.75026	−0.243428
$559$	8.77769	0.371257
$560$	−0.584786	−0.0247117
$561$	3.97990	0.168031
$562$	−6.68798	−0.282115
$563$	12.1200	0.510796	0.255398	−	0.966836i	$-0.417794\pi$
$563$	12.1200	0.510796	0.255398	+	0.966836i	$0.417794\pi$
$564$	15.5006	0.652692
$565$	−49.5777	−2.08575
$566$	11.5786	0.486687
$567$	0.240543	0.0101019
$568$	−40.4145	−1.69575
$569$	30.5375	1.28020	0.640099	−	0.768292i	$-0.278893\pi$
$569$	30.5375	1.28020	0.640099	+	0.768292i	$0.278893\pi$
$570$	−7.82139	−0.327602
$571$	35.0850	1.46826	0.734131	−	0.679007i	$-0.237590\pi$
$571$	35.0850	1.46826	0.734131	+	0.679007i	$0.237590\pi$
$572$	4.76914	0.199408
$573$	2.53783	0.106019
$574$	−0.749892	−0.0312999
$575$	−1.95981	−0.0817297
$576$	2.49571	0.103988
$577$	3.60845	0.150222	0.0751109	−	0.997175i	$-0.476069\pi$
$577$	3.60845	0.150222	0.0751109	+	0.997175i	$0.476069\pi$
$578$	0.749114	0.0311591
$579$	12.5001	0.519487
$580$	17.9176	0.743989
$581$	2.87826	0.119410
$582$	−1.71294	−0.0710036
$583$	−16.1391	−0.668413
$584$	−8.83679	−0.365669
$585$	−2.13604	−0.0883146
$586$	16.5323	0.682945
$587$	31.9201	1.31748	0.658741	−	0.752370i	$-0.271089\pi$
$587$	31.9201	1.31748	0.658741	+	0.752370i	$0.271089\pi$
$588$	9.98854	0.411920
$589$	−31.2481	−1.28756
$590$	1.92132	0.0790994
$591$	24.3383	1.00114
$592$	7.91466	0.325290
$593$	−26.0003	−1.06771	−0.533853	−	0.845577i	$-0.679256\pi$
$593$	−26.0003	−1.06771	−0.533853	+	0.845577i	$0.679256\pi$
$594$	−2.98140	−0.122328
$595$	0.616941	0.0252921
$596$	21.4925	0.880368
$597$	−0.842179	−0.0344681
$598$	−0.774787	−0.0316834
$599$	18.6909	0.763689	0.381844	−	0.924227i	$-0.375289\pi$
$599$	18.6909	0.763689	0.381844	+	0.924227i	$0.375289\pi$
$600$	−4.06535	−0.165967
$601$	32.1533	1.31156	0.655780	−	0.754952i	$-0.272340\pi$
$601$	32.1533	1.31156	0.655780	+	0.754952i	$0.272340\pi$
$602$	1.89916	0.0774040
$603$	11.1950	0.455896
$604$	13.2376	0.538630
$605$	−12.4125	−0.504640
$606$	−10.0457	−0.408080
$607$	20.4580	0.830364	0.415182	−	0.909738i	$-0.363718\pi$
$607$	20.4580	0.830364	0.415182	+	0.909738i	$0.363718\pi$
$608$	23.8642	0.967822
$609$	1.16792	0.0473266
$610$	−21.4921	−0.870189
$611$	−8.97219	−0.362976
$612$	1.43883	0.0581612
$613$	27.0554	1.09276	0.546379	−	0.837538i	$-0.316006\pi$
$613$	27.0554	1.09276	0.546379	+	0.837538i	$0.316006\pi$
$614$	−5.51569	−0.222595
$615$	10.6735	0.430399
$616$	2.46617	0.0993649
$617$	−1.82939	−0.0736485	−0.0368242	−	0.999322i	$-0.511724\pi$
$617$	−1.82939	−0.0736485	−0.0368242	+	0.999322i	$0.511724\pi$
$618$	3.12997	0.125906
$619$	3.52748	0.141782	0.0708908	−	0.997484i	$-0.477416\pi$
$619$	3.52748	0.141782	0.0708908	+	0.997484i	$0.477416\pi$
$620$	−28.3269	−1.13763
$621$	−1.24187	−0.0498343
$622$	−14.6376	−0.586913
$623$	−0.820557	−0.0328749
$624$	0.789429	0.0316024
$625$	−30.4001	−1.21601
$626$	−5.26850	−0.210572
$627$	−16.2016	−0.647028
$628$	22.7605	0.908241
$629$	−8.34985	−0.332930
$630$	−0.462159	−0.0184129
$631$	29.2321	1.16371	0.581857	−	0.813291i	$-0.302326\pi$
$631$	29.2321	1.16371	0.581857	+	0.813291i	$0.302326\pi$
$632$	−28.3652	−1.12831
$633$	22.5488	0.896236
$634$	−6.77937	−0.269243
$635$	4.56752	0.181257
$636$	−5.83466	−0.231359
$637$	−5.78166	−0.229078
$638$	−14.4758	−0.573101
$639$	15.6884	0.620623
$640$	25.2756	0.999106
$641$	−41.7536	−1.64917	−0.824584	−	0.565740i	$-0.808591\pi$
$641$	−41.7536	−1.64917	−0.824584	+	0.565740i	$0.808591\pi$
$642$	1.57389	0.0621164
$643$	−31.7437	−1.25185	−0.625924	−	0.779884i	$-0.715278\pi$
$643$	−31.7437	−1.25185	−0.625924	+	0.779884i	$0.715278\pi$
$644$	0.429810	0.0169369
$645$	−27.0316	−1.06437
$646$	−3.04953	−0.119982
$647$	19.7220	0.775351	0.387675	−	0.921796i	$-0.373278\pi$
$647$	19.7220	0.775351	0.387675	+	0.921796i	$0.373278\pi$
$648$	−2.57608	−0.101198
$649$	3.97990	0.156225
$650$	0.984570	0.0386180
$651$	−1.84643	−0.0723671
$652$	11.5557	0.452554
$653$	−33.6117	−1.31533	−0.657663	−	0.753312i	$-0.728455\pi$
$653$	−33.6117	−1.31533	−0.657663	+	0.753312i	$0.728455\pi$
$654$	11.9318	0.466569
$655$	31.7816	1.24181
$656$	−3.94467	−0.154014
$657$	3.43033	0.133830
$658$	−1.94124	−0.0756776
$659$	−48.8350	−1.90234	−0.951171	−	0.308666i	$-0.900118\pi$
$659$	−48.8350	−1.90234	−0.951171	+	0.308666i	$0.900118\pi$
$660$	−14.6869	−0.571689
$661$	19.8135	0.770657	0.385328	−	0.922779i	$-0.374088\pi$
$661$	19.8135	0.770657	0.385328	+	0.922779i	$0.374088\pi$
$662$	−23.6003	−0.917251
$663$	−0.832836	−0.0323447
$664$	−30.8244	−1.19622
$665$	−2.51147	−0.0973908
$666$	6.25499	0.242376
$667$	−6.02970	−0.233471
$668$	−35.2337	−1.36323
$669$	−3.64319	−0.140854
$670$	−21.5091	−0.830971
$671$	−44.5196	−1.71866
$672$	1.41012	0.0543964
$673$	−21.2354	−0.818565	−0.409282	−	0.912408i	$-0.634221\pi$
$673$	−21.2354	−0.818565	−0.409282	+	0.912408i	$0.634221\pi$
$674$	12.7249	0.490143
$675$	1.57812	0.0607417
$676$	17.7068	0.681029
$677$	40.3462	1.55063	0.775315	−	0.631575i	$-0.217591\pi$
$677$	40.3462	1.55063	0.775315	+	0.631575i	$0.217591\pi$
$678$	14.4805	0.556120
$679$	−0.550031	−0.0211082
$680$	−6.60708	−0.253370
$681$	−18.9445	−0.725955
$682$	22.8854	0.876329
$683$	−35.2406	−1.34844	−0.674222	−	0.738529i	$-0.735521\pi$
$683$	−35.2406	−1.34844	−0.674222	+	0.738529i	$0.735521\pi$
$684$	−5.85725	−0.223958
$685$	−19.1360	−0.731149
$686$	−2.51229	−0.0959198
$687$	−8.49490	−0.324101
$688$	9.99020	0.380873
$689$	3.37728	0.128664
$690$	2.38602	0.0908341
$691$	−6.90299	−0.262602	−0.131301	−	0.991343i	$-0.541915\pi$
$691$	−6.90299	−0.262602	−0.131301	+	0.991343i	$0.541915\pi$
$692$	15.5898	0.592635
$693$	−0.957337	−0.0363662
$694$	18.0617	0.685612
$695$	17.6343	0.668909
$696$	−12.5078	−0.474106
$697$	4.16158	0.157631
$698$	11.5226	0.436138
$699$	−20.0502	−0.758368
$700$	−0.546186	−0.0206439
$701$	−5.42152	−0.204768	−0.102384	−	0.994745i	$-0.532647\pi$
$701$	−5.42152	−0.204768	−0.102384	+	0.994745i	$0.532647\pi$
$702$	0.623890	0.0235472
$703$	33.9910	1.28199
$704$	−9.93269	−0.374352
$705$	27.6306	1.04063
$706$	7.82849	0.294629
$707$	−3.22572	−0.121316
$708$	1.43883	0.0540745
$709$	−14.0134	−0.526283	−0.263142	−	0.964757i	$-0.584759\pi$
$709$	−14.0134	−0.526283	−0.263142	+	0.964757i	$0.584759\pi$
$710$	−30.1424	−1.13122
$711$	11.0110	0.412945
$712$	8.78768	0.329332
$713$	9.53265	0.357000
$714$	−0.180194	−0.00674360
$715$	8.50124	0.317928
$716$	−15.0269	−0.561581
$717$	−24.2952	−0.907320
$718$	7.83787	0.292507
$719$	−7.05059	−0.262943	−0.131471	−	0.991320i	$-0.541970\pi$
$719$	−7.05059	−0.262943	−0.131471	+	0.991320i	$0.541970\pi$
$720$	−2.43111	−0.0906020
$721$	1.00504	0.0374298
$722$	−1.81899	−0.0676960
$723$	17.7513	0.660176
$724$	19.4908	0.724371
$725$	7.66232	0.284571
$726$	3.62541	0.134552
$727$	36.9766	1.37139	0.685694	−	0.727890i	$-0.259499\pi$
$727$	36.9766	1.37139	0.685694	+	0.727890i	$0.259499\pi$
$728$	−0.516073	−0.0191269
$729$	1.00000	0.0370370
$730$	−6.59075	−0.243935
$731$	−10.5395	−0.389818
$732$	−16.0949	−0.594885
$733$	44.6675	1.64983	0.824916	−	0.565255i	$-0.191222\pi$
$733$	44.6675	1.64983	0.824916	+	0.565255i	$0.191222\pi$
$734$	−16.3149	−0.602195
$735$	17.8051	0.656750
$736$	−7.28009	−0.268348
$737$	−44.5550	−1.64120
$738$	−3.11750	−0.114757
$739$	−38.1389	−1.40296	−0.701481	−	0.712688i	$-0.747478\pi$
$739$	−38.1389	−1.40296	−0.701481	+	0.712688i	$0.747478\pi$
$740$	30.8133	1.13272
$741$	3.39035	0.124548
$742$	0.730715	0.0268254
$743$	53.4420	1.96060	0.980298	−	0.197522i	$-0.0632895\pi$
$743$	53.4420	1.96060	0.980298	+	0.197522i	$0.0632895\pi$
$744$	19.7741	0.724955
$745$	38.3115	1.40363
$746$	−16.4523	−0.602360
$747$	11.9657	0.437801
$748$	−5.72639	−0.209377
$749$	0.505380	0.0184662
$750$	6.57452	0.240068
$751$	27.8437	1.01603	0.508016	−	0.861348i	$-0.330379\pi$
$751$	27.8437	1.01603	0.508016	+	0.861348i	$0.330379\pi$
$752$	−10.2116	−0.372377
$753$	14.8267	0.540315
$754$	3.02921	0.110317
$755$	23.5967	0.858771
$756$	−0.346100	−0.0125875
$757$	21.7455	0.790355	0.395177	−	0.918605i	$-0.370683\pi$
$757$	21.7455	0.790355	0.395177	+	0.918605i	$0.370683\pi$
$758$	13.3908	0.486377
$759$	4.94250	0.179401
$760$	26.8964	0.975635
$761$	4.60859	0.167061	0.0835306	−	0.996505i	$-0.473380\pi$
$761$	4.60859	0.167061	0.0835306	+	0.996505i	$0.473380\pi$
$762$	−1.33407	−0.0483282
$763$	3.83133	0.138703
$764$	−3.65150	−0.132107
$765$	2.56478	0.0927300
$766$	−17.7128	−0.639988
$767$	−0.832836	−0.0300720
$768$	−12.3739	−0.446503
$769$	48.3125	1.74219	0.871096	−	0.491113i	$-0.163410\pi$
$769$	48.3125	1.74219	0.871096	+	0.491113i	$0.163410\pi$
$770$	1.83935	0.0662855
$771$	−10.6358	−0.383038
$772$	−17.9855	−0.647313
$773$	27.2376	0.979670	0.489835	−	0.871815i	$-0.337057\pi$
$773$	27.2376	0.979670	0.489835	+	0.871815i	$0.337057\pi$
$774$	7.89530	0.283791
$775$	−12.1137	−0.435138
$776$	5.89050	0.211457
$777$	2.00850	0.0720545
$778$	−13.5195	−0.484697
$779$	−16.9411	−0.606979
$780$	3.07340	0.110045
$781$	−62.4382	−2.23421
$782$	0.930299	0.0332674
$783$	4.85536	0.173516
$784$	−6.58031	−0.235011
$785$	40.5717	1.44807
$786$	−9.28267	−0.331102
$787$	−30.0509	−1.07120	−0.535599	−	0.844472i	$-0.679914\pi$
$787$	−30.0509	−1.07120	−0.535599	+	0.844472i	$0.679914\pi$
$788$	−35.0186	−1.24749
$789$	3.19983	0.113917
$790$	−21.1556	−0.752684
$791$	4.64973	0.165326
$792$	10.2525	0.364307
$793$	9.31621	0.330828
$794$	14.3536	0.509392
$795$	−10.4006	−0.368871
$796$	1.21175	0.0429494
$797$	−33.0010	−1.16895	−0.584477	−	0.811410i	$-0.698700\pi$
$797$	−33.0010	−1.16895	−0.584477	+	0.811410i	$0.698700\pi$
$798$	0.733544	0.0259672
$799$	10.7731	0.381123
$800$	9.25127	0.327082
$801$	−3.41127	−0.120531
$802$	0.663375	0.0234246
$803$	−13.6524	−0.481781
$804$	−16.1077	−0.568074
$805$	0.766158	0.0270035
$806$	−4.78902	−0.168686
$807$	28.4748	1.00236
$808$	34.5455	1.21531
$809$	33.4123	1.17472	0.587358	−	0.809328i	$-0.300168\pi$
$809$	33.4123	1.17472	0.587358	+	0.809328i	$0.300168\pi$
$810$	−1.92132	−0.0675082
$811$	3.13591	0.110117	0.0550583	−	0.998483i	$-0.482466\pi$
$811$	3.13591	0.110117	0.0550583	+	0.998483i	$0.482466\pi$
$812$	−1.68044	−0.0589719
$813$	30.8137	1.08069
$814$	−24.8942	−0.872543
$815$	20.5985	0.721535
$816$	−0.947880	−0.0331824
$817$	42.9048	1.50105
$818$	11.6449	0.407156
$819$	0.200333	0.00700020
$820$	−15.3574	−0.536303
$821$	34.7782	1.21377	0.606884	−	0.794791i	$-0.292419\pi$
$821$	34.7782	1.21377	0.606884	+	0.794791i	$0.292419\pi$
$822$	5.58918	0.194945
$823$	−45.3266	−1.57999	−0.789994	−	0.613115i	$-0.789916\pi$
$823$	−45.3266	−1.57999	−0.789994	+	0.613115i	$0.789916\pi$
$824$	−10.7634	−0.374962
$825$	−6.28074	−0.218667
$826$	−0.180194	−0.00626976
$827$	−1.55625	−0.0541160	−0.0270580	−	0.999634i	$-0.508614\pi$
$827$	−1.55625	−0.0541160	−0.0270580	+	0.999634i	$0.508614\pi$
$828$	1.78683	0.0620966
$829$	−27.1101	−0.941572	−0.470786	−	0.882247i	$-0.656030\pi$
$829$	−27.1101	−0.941572	−0.470786	+	0.882247i	$0.656030\pi$
$830$	−22.9898	−0.797988
$831$	−11.7830	−0.408749
$832$	2.07852	0.0720598
$833$	6.94214	0.240531
$834$	−5.15059	−0.178350
$835$	−62.8058	−2.17349
$836$	23.3113	0.806237
$837$	−7.67607	−0.265324
$838$	−29.1305	−1.00630
$839$	−30.0048	−1.03588	−0.517941	−	0.855416i	$-0.673301\pi$
$839$	−30.0048	−1.03588	−0.517941	+	0.855416i	$0.673301\pi$
$840$	1.58929	0.0548356
$841$	−5.42551	−0.187087
$842$	15.3670	0.529583
$843$	−8.92785	−0.307491
$844$	−32.4439	−1.11677
$845$	31.5632	1.08581
$846$	−8.07025	−0.277461
$847$	1.16413	0.0400000
$848$	3.84380	0.131997
$849$	15.4564	0.530464
$850$	−1.18219	−0.0405488
$851$	−10.3694	−0.355458
$852$	−22.5729	−0.773334
$853$	5.73269	0.196284	0.0981418	−	0.995172i	$-0.468710\pi$
$853$	5.73269	0.196284	0.0981418	+	0.995172i	$0.468710\pi$
$854$	2.01568	0.0689750
$855$	−10.4408	−0.357069
$856$	−5.41233	−0.184989
$857$	−5.00136	−0.170843	−0.0854216	−	0.996345i	$-0.527224\pi$
$857$	−5.00136	−0.170843	−0.0854216	+	0.996345i	$0.527224\pi$
$858$	−2.48302	−0.0847688
$859$	−3.05885	−0.104366	−0.0521832	−	0.998638i	$-0.516618\pi$
$859$	−3.05885	−0.104366	−0.0521832	+	0.998638i	$0.516618\pi$
$860$	38.8938	1.32627
$861$	−1.00104	−0.0341153
$862$	−6.60515	−0.224972
$863$	−44.5205	−1.51549	−0.757747	−	0.652548i	$-0.773700\pi$
$863$	−44.5205	−1.51549	−0.757747	+	0.652548i	$0.773700\pi$
$864$	5.86222	0.199437
$865$	27.7896	0.944875
$866$	−10.6236	−0.361004
$867$	1.00000	0.0339618
$868$	2.65669	0.0901739
$869$	−43.8227	−1.48658
$870$	−9.32868	−0.316272
$871$	9.32360	0.315918
$872$	−41.0313	−1.38949
$873$	−2.28662	−0.0773903
$874$	−3.78711	−0.128101
$875$	2.11110	0.0713682
$876$	−4.93565	−0.166760
$877$	48.2472	1.62919	0.814596	−	0.580028i	$-0.196958\pi$
$877$	48.2472	1.62919	0.814596	+	0.580028i	$0.196958\pi$
$878$	−7.88977	−0.266267
$879$	22.0692	0.744375
$880$	9.67556	0.326163
$881$	−9.74348	−0.328266	−0.164133	−	0.986438i	$-0.552483\pi$
$881$	−9.74348	−0.328266	−0.164133	+	0.986438i	$0.552483\pi$
$882$	−5.20046	−0.175108
$883$	−54.9550	−1.84938	−0.924691	−	0.380719i	$-0.875677\pi$
$883$	−54.9550	−1.84938	−0.924691	+	0.380719i	$0.875677\pi$
$884$	1.19831	0.0403034
$885$	2.56478	0.0862143
$886$	4.39952	0.147805
$887$	−55.2236	−1.85423	−0.927113	−	0.374782i	$-0.877718\pi$
$887$	−55.2236	−1.85423	−0.927113	+	0.374782i	$0.877718\pi$
$888$	−21.5098	−0.721823
$889$	−0.428373	−0.0143672
$890$	6.55413	0.219695
$891$	−3.97990	−0.133332
$892$	5.24193	0.175513
$893$	−43.8555	−1.46757
$894$	−11.1899	−0.374247
$895$	−26.7862	−0.895363
$896$	−2.37052	−0.0791935
$897$	−1.03427	−0.0345333
$898$	8.53690	0.284880
$899$	−37.2701	−1.24303
$900$	−2.27064	−0.0756879
$901$	−4.05515	−0.135097
$902$	12.4073	0.413119
$903$	2.53521	0.0843664
$904$	−49.7959	−1.65619
$905$	34.7434	1.15491
$906$	−6.89205	−0.228973
$907$	31.2256	1.03683	0.518415	−	0.855129i	$-0.326522\pi$
$907$	31.2256	1.03683	0.518415	+	0.855129i	$0.326522\pi$
$908$	27.2579	0.904584
$909$	−13.4101	−0.444786
$910$	−0.384903	−0.0127594
$911$	58.0919	1.92467	0.962334	−	0.271868i	$-0.0876416\pi$
$911$	58.0919	1.92467	0.962334	+	0.271868i	$0.0876416\pi$
$912$	3.85868	0.127774
$913$	−47.6221	−1.57606
$914$	8.27278	0.273639
$915$	−28.6900	−0.948462
$916$	12.2227	0.403849
$917$	−2.98070	−0.0984312
$918$	−0.749114	−0.0247245
$919$	10.7777	0.355523	0.177761	−	0.984074i	$-0.443114\pi$
$919$	10.7777	0.355523	0.177761	+	0.984074i	$0.443114\pi$
$920$	−8.20510	−0.270514
$921$	−7.36295	−0.242617
$922$	−13.3468	−0.439555
$923$	13.0659	0.430068
$924$	1.37744	0.0453145
$925$	13.1770	0.433258
$926$	21.8952	0.719521
$927$	4.17823	0.137231
$928$	28.4632	0.934350
$929$	9.30348	0.305237	0.152619	−	0.988285i	$-0.451229\pi$
$929$	9.30348	0.305237	0.152619	+	0.988285i	$0.451229\pi$
$930$	14.7482	0.483611
$931$	−28.2604	−0.926197
$932$	28.8488	0.944973
$933$	−19.5398	−0.639706
$934$	16.6511	0.544841
$935$	−10.2076	−0.333824
$936$	−2.14545	−0.0701262
$937$	7.28379	0.237951	0.118976	−	0.992897i	$-0.462039\pi$
$937$	7.28379	0.237951	0.118976	+	0.992897i	$0.462039\pi$
$938$	2.01728	0.0658664
$939$	−7.03297	−0.229512
$940$	−39.7556	−1.29669
$941$	30.3359	0.988922	0.494461	−	0.869200i	$-0.335365\pi$
$941$	30.3359	0.988922	0.494461	+	0.869200i	$0.335365\pi$
$942$	−11.8501	−0.386096
$943$	5.16812	0.168297
$944$	−0.947880	−0.0308509
$945$	−0.616941	−0.0200691
$946$	−31.4225	−1.02163
$947$	−54.5282	−1.77193	−0.885964	−	0.463754i	$-0.846502\pi$
$947$	−54.5282	−1.77193	−0.885964	+	0.463754i	$0.846502\pi$
$948$	−15.8430	−0.514555
$949$	2.85690	0.0927390
$950$	4.81252	0.156139
$951$	−9.04985	−0.293461
$952$	0.619657	0.0200832
$953$	−0.420159	−0.0136103	−0.00680514	−	0.999977i	$-0.502166\pi$
$953$	−0.420159	−0.0136103	−0.00680514	+	0.999977i	$0.502166\pi$
$954$	3.03777	0.0983515
$955$	−6.50899	−0.210626
$956$	34.9566	1.13058
$957$	−19.3238	−0.624651
$958$	29.7718	0.961882
$959$	1.79471	0.0579540
$960$	−6.40097	−0.206590
$961$	27.9221	0.900712
$962$	5.20939	0.167957
$963$	2.10100	0.0677037
$964$	−25.5410	−0.822620
$965$	−32.0601	−1.03205
$966$	−0.223777	−0.00719991
$967$	43.8183	1.40910	0.704550	−	0.709654i	$-0.251149\pi$
$967$	43.8183	1.40910	0.704550	+	0.709654i	$0.251149\pi$
$968$	−12.4672	−0.400710
$969$	−4.07085	−0.130774
$970$	4.39332	0.141061
$971$	3.85842	0.123823	0.0619113	−	0.998082i	$-0.480280\pi$
$971$	3.85842	0.123823	0.0619113	+	0.998082i	$0.480280\pi$
$972$	−1.43883	−0.0461504
$973$	−1.65387	−0.0530207
$974$	26.0062	0.833293
$975$	1.31431	0.0420917
$976$	10.6031	0.339397
$977$	25.5319	0.816837	0.408419	−	0.912795i	$-0.366080\pi$
$977$	25.5319	0.816837	0.408419	+	0.912795i	$0.366080\pi$
$978$	−6.01636	−0.192382
$979$	13.5765	0.433907
$980$	−25.6184	−0.818351
$981$	15.9278	0.508536
$982$	8.98298	0.286659
$983$	40.6378	1.29614	0.648072	−	0.761579i	$-0.275575\pi$
$983$	40.6378	1.29614	0.648072	+	0.761579i	$0.275575\pi$
$984$	10.7205	0.341758
$985$	−62.4224	−1.98894
$986$	−3.63722	−0.115833
$987$	−2.59138	−0.0824847
$988$	−4.87813	−0.155194
$989$	−13.0887	−0.416195
$990$	7.64665	0.243026
$991$	−42.1574	−1.33917	−0.669587	−	0.742733i	$-0.733529\pi$
$991$	−42.1574	−1.33917	−0.669587	+	0.742733i	$0.733529\pi$
$992$	−44.9988	−1.42871
$993$	−31.5042	−0.999757
$994$	2.82696	0.0896656
$995$	2.16001	0.0684768
$996$	−17.2165	−0.545526
$997$	20.7630	0.657571	0.328785	−	0.944405i	$-0.393361\pi$
$997$	20.7630	0.657571	0.328785	+	0.944405i	$0.393361\pi$
$998$	−29.0618	−0.919935
$999$	8.34985	0.264178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3009.2.a.j.1.14	✓	24
3.2	odd	2		9027.2.a.t.1.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3009.2.a.j.1.14	✓	24	1.1	even	1	trivial
9027.2.a.t.1.11		24	3.2	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:	\( N \)	\(=\)	\( 3009 = 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3009.a (trivial)

\(f(q)\)	\(=\)	\(q+0.749114 q^{2} +1.00000 q^{3} -1.43883 q^{4} -2.56478 q^{5} +0.749114 q^{6} +0.240543 q^{7} -2.57608 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.749114 q^{2} +1.00000 q^{3} -1.43883 q^{4} -2.56478 q^{5} +0.749114 q^{6} +0.240543 q^{7} -2.57608 q^{8} +1.00000 q^{9} -1.92132 q^{10} -3.97990 q^{11} -1.43883 q^{12} +0.832836 q^{13} +0.180194 q^{14} -2.56478 q^{15} +0.947880 q^{16} -1.00000 q^{17} +0.749114 q^{18} +4.07085 q^{19} +3.69028 q^{20} +0.240543 q^{21} -2.98140 q^{22} -1.24187 q^{23} -2.57608 q^{24} +1.57812 q^{25} +0.623890 q^{26} +1.00000 q^{27} -0.346100 q^{28} +4.85536 q^{29} -1.92132 q^{30} -7.67607 q^{31} +5.86222 q^{32} -3.97990 q^{33} -0.749114 q^{34} -0.616941 q^{35} -1.43883 q^{36} +8.34985 q^{37} +3.04953 q^{38} +0.832836 q^{39} +6.60708 q^{40} -4.16158 q^{41} +0.180194 q^{42} +10.5395 q^{43} +5.72639 q^{44} -2.56478 q^{45} -0.930299 q^{46} -10.7731 q^{47} +0.947880 q^{48} -6.94214 q^{49} +1.18219 q^{50} -1.00000 q^{51} -1.19831 q^{52} +4.05515 q^{53} +0.749114 q^{54} +10.2076 q^{55} -0.619657 q^{56} +4.07085 q^{57} +3.63722 q^{58} -1.00000 q^{59} +3.69028 q^{60} +11.1861 q^{61} -5.75026 q^{62} +0.240543 q^{63} +2.49571 q^{64} -2.13604 q^{65} -2.98140 q^{66} +11.1950 q^{67} +1.43883 q^{68} -1.24187 q^{69} -0.462159 q^{70} +15.6884 q^{71} -2.57608 q^{72} +3.43033 q^{73} +6.25499 q^{74} +1.57812 q^{75} -5.85725 q^{76} -0.957337 q^{77} +0.623890 q^{78} +11.0110 q^{79} -2.43111 q^{80} +1.00000 q^{81} -3.11750 q^{82} +11.9657 q^{83} -0.346100 q^{84} +2.56478 q^{85} +7.89530 q^{86} +4.85536 q^{87} +10.2525 q^{88} -3.41127 q^{89} -1.92132 q^{90} +0.200333 q^{91} +1.78683 q^{92} -7.67607 q^{93} -8.07025 q^{94} -10.4408 q^{95} +5.86222 q^{96} -2.28662 q^{97} -5.20046 q^{98} -3.97990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9	\( 24 q + 2 q^{2} + 24 q^{3} + 34 q^{4} - 3 q^{5} + 2 q^{6} + 19 q^{7} + 3 q^{8} + 24 q^{9} + 10 q^{10} + 11 q^{11} + 34 q^{12} + 21 q^{13} + 9 q^{14} - 3 q^{15} + 50 q^{16} - 24 q^{17} + 2 q^{18} + 13 q^{19} + q^{20} + 19 q^{21} + 5 q^{22} + 18 q^{23} + 3 q^{24} + 39 q^{25} - 7 q^{26} + 24 q^{27} + 40 q^{28} - 10 q^{29} + 10 q^{30} + 47 q^{31} + 18 q^{32} + 11 q^{33} - 2 q^{34} + 5 q^{35} + 34 q^{36} + 54 q^{37} + 5 q^{38} + 21 q^{39} + 29 q^{40} + 9 q^{42} + 16 q^{43} + 7 q^{44} - 3 q^{45} - 8 q^{46} + 10 q^{47} + 50 q^{48} + 55 q^{49} + 21 q^{50} - 24 q^{51} + 68 q^{52} + 6 q^{53} + 2 q^{54} + 15 q^{55} - 5 q^{56} + 13 q^{57} + q^{58} - 24 q^{59} + q^{60} + 42 q^{61} - 7 q^{62} + 19 q^{63} + 53 q^{64} - 9 q^{65} + 5 q^{66} + 28 q^{67} - 34 q^{68} + 18 q^{69} - 20 q^{70} + 54 q^{71} + 3 q^{72} + 33 q^{73} - 17 q^{74} + 39 q^{75} - 56 q^{76} - 23 q^{77} - 7 q^{78} + 35 q^{79} + 3 q^{80} + 24 q^{81} - 12 q^{82} - 17 q^{83} + 40 q^{84} + 3 q^{85} + 36 q^{86} - 10 q^{87} + 47 q^{88} + 15 q^{89} + 10 q^{90} + 74 q^{91} + 6 q^{92} + 47 q^{93} + 9 q^{94} + 12 q^{95} + 18 q^{96} + 52 q^{97} - 48 q^{98} + 11 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 24 * q^3 + 34 * q^4 - 3 * q^5 + 2 * q^6 + 19 * q^7 + 3 * q^8 + 24 * q^9 + 10 * q^10 + 11 * q^11 + 34 * q^12 + 21 * q^13 + 9 * q^14 - 3 * q^15 + 50 * q^16 - 24 * q^17 + 2 * q^18 + 13 * q^19 + q^20 + 19 * q^21 + 5 * q^22 + 18 * q^23 + 3 * q^24 + 39 * q^25 - 7 * q^26 + 24 * q^27 + 40 * q^28 - 10 * q^29 + 10 * q^30 + 47 * q^31 + 18 * q^32 + 11 * q^33 - 2 * q^34 + 5 * q^35 + 34 * q^36 + 54 * q^37 + 5 * q^38 + 21 * q^39 + 29 * q^40 + 9 * q^42 + 16 * q^43 + 7 * q^44 - 3 * q^45 - 8 * q^46 + 10 * q^47 + 50 * q^48 + 55 * q^49 + 21 * q^50 - 24 * q^51 + 68 * q^52 + 6 * q^53 + 2 * q^54 + 15 * q^55 - 5 * q^56 + 13 * q^57 + q^58 - 24 * q^59 + q^60 + 42 * q^61 - 7 * q^62 + 19 * q^63 + 53 * q^64 - 9 * q^65 + 5 * q^66 + 28 * q^67 - 34 * q^68 + 18 * q^69 - 20 * q^70 + 54 * q^71 + 3 * q^72 + 33 * q^73 - 17 * q^74 + 39 * q^75 - 56 * q^76 - 23 * q^77 - 7 * q^78 + 35 * q^79 + 3 * q^80 + 24 * q^81 - 12 * q^82 - 17 * q^83 + 40 * q^84 + 3 * q^85 + 36 * q^86 - 10 * q^87 + 47 * q^88 + 15 * q^89 + 10 * q^90 + 74 * q^91 + 6 * q^92 + 47 * q^93 + 9 * q^94 + 12 * q^95 + 18 * q^96 + 52 * q^97 - 48 * q^98 + 11 * q^99

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