LMFDB - Embedded newform 1805.2.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.343361$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.274673 q^{2} -3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} -1.07797 q^{8} +6.57477 q^{9} +O(q^{10})$	\(q+0.274673 q^{2} -3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} -1.07797 q^{8} +6.57477 q^{9} -0.274673 q^{10} +2.45483 q^{11} +5.95517 q^{12} -3.81342 q^{13} +0.999184 q^{14} +3.09431 q^{15} +3.55302 q^{16} -3.62089 q^{17} +1.80591 q^{18} +1.92455 q^{20} -11.2562 q^{21} +0.674276 q^{22} -9.19377 q^{23} +3.33558 q^{24} +1.00000 q^{25} -1.04744 q^{26} -11.0614 q^{27} -7.00098 q^{28} +1.81600 q^{29} +0.849925 q^{30} -7.04948 q^{31} +3.13186 q^{32} -7.59601 q^{33} -0.994562 q^{34} -3.63772 q^{35} -12.6535 q^{36} +0.500137 q^{37} +11.7999 q^{39} +1.07797 q^{40} +1.42551 q^{41} -3.09179 q^{42} +6.78124 q^{43} -4.72445 q^{44} -6.57477 q^{45} -2.52528 q^{46} +0.193490 q^{47} -10.9942 q^{48} +6.23298 q^{49} +0.274673 q^{50} +11.2042 q^{51} +7.33913 q^{52} +4.54544 q^{53} -3.03828 q^{54} -2.45483 q^{55} -3.92135 q^{56} +0.498806 q^{58} +1.29597 q^{59} -5.95517 q^{60} +8.12536 q^{61} -1.93631 q^{62} +23.9171 q^{63} -6.24580 q^{64} +3.81342 q^{65} -2.08642 q^{66} +8.17102 q^{67} +6.96860 q^{68} +28.4484 q^{69} -0.999184 q^{70} -5.69618 q^{71} -7.08741 q^{72} +2.63792 q^{73} +0.137374 q^{74} -3.09431 q^{75} +8.92998 q^{77} +3.24112 q^{78} +5.11318 q^{79} -3.55302 q^{80} +14.5033 q^{81} +0.391549 q^{82} -0.287184 q^{83} +21.6632 q^{84} +3.62089 q^{85} +1.86263 q^{86} -5.61926 q^{87} -2.64623 q^{88} -4.91011 q^{89} -1.80591 q^{90} -13.8721 q^{91} +17.6939 q^{92} +21.8133 q^{93} +0.0531467 q^{94} -9.69096 q^{96} -8.24002 q^{97} +1.71203 q^{98} +16.1399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * 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 $

$2$	0.274673	0.194223	0.0971117	−	0.995273i	$-0.469040\pi$
$2$	0.274673	0.194223	0.0971117	+	0.995273i	$0.469040\pi$
$3$	−3.09431	−1.78650	−0.893251	−	0.449558i	$-0.851581\pi$
$3$	−3.09431	−1.78650	−0.893251	+	0.449558i	$0.851581\pi$
$4$	−1.92455	−0.962277
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.849925	−0.346980
$7$	3.63772	1.37493	0.687464	−	0.726219i	$-0.258724\pi$
$7$	3.63772	1.37493	0.687464	+	0.726219i	$0.258724\pi$
$8$	−1.07797	−0.381120
$9$	6.57477	2.19159
$10$	−0.274673	−0.0868593
$11$	2.45483	0.740159	0.370080	−	0.929000i	$-0.379330\pi$
$11$	2.45483	0.740159	0.370080	+	0.929000i	$0.379330\pi$
$12$	5.95517	1.71911
$13$	−3.81342	−1.05765	−0.528826	−	0.848730i	$-0.677367\pi$
$13$	−3.81342	−1.05765	−0.528826	+	0.848730i	$0.677367\pi$
$14$	0.999184	0.267043
$15$	3.09431	0.798948
$16$	3.55302	0.888255
$17$	−3.62089	−0.878195	−0.439097	−	0.898439i	$-0.644702\pi$
$17$	−3.62089	−0.878195	−0.439097	+	0.898439i	$0.644702\pi$
$18$	1.80591	0.425658
$19$	0	0
$19$	0	0
$20$	1.92455	0.430343
$21$	−11.2562	−2.45631
$22$	0.674276	0.143756
$23$	−9.19377	−1.91703	−0.958516	−	0.285038i	$-0.907994\pi$
$23$	−9.19377	−1.91703	−0.958516	+	0.285038i	$0.907994\pi$
$24$	3.33558	0.680872
$25$	1.00000	0.200000
$26$	−1.04744	−0.205421
$27$	−11.0614	−2.12878
$28$	−7.00098	−1.32306
$29$	1.81600	0.337222	0.168611	−	0.985683i	$-0.446072\pi$
$29$	1.81600	0.337222	0.168611	+	0.985683i	$0.446072\pi$
$30$	0.849925	0.155174
$31$	−7.04948	−1.26612	−0.633062	−	0.774101i	$-0.718202\pi$
$31$	−7.04948	−1.26612	−0.633062	+	0.774101i	$0.718202\pi$
$32$	3.13186	0.553640
$33$	−7.59601	−1.32230
$34$	−0.994562	−0.170566
$35$	−3.63772	−0.614886
$36$	−12.6535	−2.10892
$37$	0.500137	0.0822221	0.0411110	−	0.999155i	$-0.486910\pi$
$37$	0.500137	0.0822221	0.0411110	+	0.999155i	$0.486910\pi$
$38$	0	0
$39$	11.7999	1.88950
$40$	1.07797	0.170442
$41$	1.42551	0.222627	0.111313	−	0.993785i	$-0.464494\pi$
$41$	1.42551	0.222627	0.111313	+	0.993785i	$0.464494\pi$
$42$	−3.09179	−0.477073
$43$	6.78124	1.03413	0.517065	−	0.855946i	$-0.327025\pi$
$43$	6.78124	1.03413	0.517065	+	0.855946i	$0.327025\pi$
$44$	−4.72445	−0.712238
$45$	−6.57477	−0.980108
$46$	−2.52528	−0.372333
$47$	0.193490	0.0282235	0.0141117	−	0.999900i	$-0.495508\pi$
$47$	0.193490	0.0282235	0.0141117	+	0.999900i	$0.495508\pi$
$48$	−10.9942	−1.58687
$49$	6.23298	0.890426
$50$	0.274673	0.0388447
$51$	11.2042	1.56890
$52$	7.33913	1.01775
$53$	4.54544	0.624365	0.312182	−	0.950022i	$-0.398940\pi$
$53$	4.54544	0.624365	0.312182	+	0.950022i	$0.398940\pi$
$54$	−3.03828	−0.413458
$55$	−2.45483	−0.331009
$56$	−3.92135	−0.524013
$57$	0	0
$58$	0.498806	0.0654965
$59$	1.29597	0.168721	0.0843606	−	0.996435i	$-0.473115\pi$
$59$	1.29597	0.168721	0.0843606	+	0.996435i	$0.473115\pi$
$60$	−5.95517	−0.768809
$61$	8.12536	1.04035	0.520173	−	0.854061i	$-0.325868\pi$
$61$	8.12536	1.04035	0.520173	+	0.854061i	$0.325868\pi$
$62$	−1.93631	−0.245911
$63$	23.9171	3.01328
$64$	−6.24580	−0.780725
$65$	3.81342	0.472996
$66$	−2.08642	−0.256821
$67$	8.17102	0.998249	0.499125	−	0.866530i	$-0.333655\pi$
$67$	8.17102	0.998249	0.499125	+	0.866530i	$0.333655\pi$
$68$	6.96860	0.845067
$69$	28.4484	3.42478
$70$	−0.999184	−0.119425
$71$	−5.69618	−0.676012	−0.338006	−	0.941144i	$-0.609752\pi$
$71$	−5.69618	−0.676012	−0.338006	+	0.941144i	$0.609752\pi$
$72$	−7.08741	−0.835259
$73$	2.63792	0.308745	0.154373	−	0.988013i	$-0.450664\pi$
$73$	2.63792	0.308745	0.154373	+	0.988013i	$0.450664\pi$
$74$	0.137374	0.0159695
$75$	−3.09431	−0.357300
$76$	0	0
$77$	8.92998	1.01767
$78$	3.24112	0.366984
$79$	5.11318	0.575278	0.287639	−	0.957739i	$-0.407130\pi$
$79$	5.11318	0.575278	0.287639	+	0.957739i	$0.407130\pi$
$80$	−3.55302	−0.397240
$81$	14.5033	1.61147
$82$	0.391549	0.0432394
$83$	−0.287184	−0.0315226	−0.0157613	−	0.999876i	$-0.505017\pi$
$83$	−0.287184	−0.0315226	−0.0157613	+	0.999876i	$0.505017\pi$
$84$	21.6632	2.36365
$85$	3.62089	0.392741
$86$	1.86263	0.200852
$87$	−5.61926	−0.602448
$88$	−2.64623	−0.282090
$89$	−4.91011	−0.520470	−0.260235	−	0.965545i	$-0.583800\pi$
$89$	−4.91011	−0.520470	−0.260235	+	0.965545i	$0.583800\pi$
$90$	−1.80591	−0.190360
$91$	−13.8721	−1.45419
$92$	17.6939	1.84472
$93$	21.8133	2.26193
$94$	0.0531467	0.00548166
$95$	0	0
$96$	−9.69096	−0.989079
$97$	−8.24002	−0.836647	−0.418323	−	0.908298i	$-0.637382\pi$
$97$	−8.24002	−0.836647	−0.418323	+	0.908298i	$0.637382\pi$
$98$	1.71203	0.172942
$99$	16.1399	1.62212
$100$	−1.92455	−0.192455
$101$	1.92411	0.191456	0.0957280	−	0.995408i	$-0.469482\pi$
$101$	1.92411	0.191456	0.0957280	+	0.995408i	$0.469482\pi$
$102$	3.07749	0.304716
$103$	−17.9037	−1.76411	−0.882054	−	0.471149i	$-0.843839\pi$
$103$	−17.9037	−1.76411	−0.882054	+	0.471149i	$0.843839\pi$
$104$	4.11075	0.403092
$105$	11.2562	1.09850
$106$	1.24851	0.121266
$107$	−5.07641	−0.490755	−0.245378	−	0.969428i	$-0.578912\pi$
$107$	−5.07641	−0.490755	−0.245378	+	0.969428i	$0.578912\pi$
$108$	21.2884	2.04847
$109$	13.3118	1.27504	0.637519	−	0.770435i	$-0.279961\pi$
$109$	13.3118	1.27504	0.637519	+	0.770435i	$0.279961\pi$
$110$	−0.674276	−0.0642897
$111$	−1.54758	−0.146890
$112$	12.9249	1.22129
$113$	6.27192	0.590012	0.295006	−	0.955495i	$-0.404678\pi$
$113$	6.27192	0.590012	0.295006	+	0.955495i	$0.404678\pi$
$114$	0	0
$115$	9.19377	0.857323
$116$	−3.49499	−0.324501
$117$	−25.0723	−2.31794
$118$	0.355969	0.0327696
$119$	−13.1718	−1.20745
$120$	−3.33558	−0.304495
$121$	−4.97381	−0.452164
$122$	2.23182	0.202059
$123$	−4.41097	−0.397723
$124$	13.5671	1.21836
$125$	−1.00000	−0.0894427
$126$	6.56940	0.585249
$127$	8.47737	0.752245	0.376122	−	0.926570i	$-0.377257\pi$
$127$	8.47737	0.752245	0.376122	+	0.926570i	$0.377257\pi$
$128$	−7.97928	−0.705275
$129$	−20.9833	−1.84747
$130$	1.04744	0.0918669
$131$	21.9423	1.91711	0.958554	−	0.284909i	$-0.0919635\pi$
$131$	21.9423	1.91711	0.958554	+	0.284909i	$0.0919635\pi$
$132$	14.6189	1.27242
$133$	0	0
$134$	2.24436	0.193883
$135$	11.0614	0.952018
$136$	3.90321	0.334698
$137$	10.2496	0.875685	0.437842	−	0.899052i	$-0.355743\pi$
$137$	10.2496	0.875685	0.437842	+	0.899052i	$0.355743\pi$
$138$	7.81401	0.665173
$139$	13.0518	1.10704	0.553518	−	0.832837i	$-0.313285\pi$
$139$	13.0518	1.10704	0.553518	+	0.832837i	$0.313285\pi$
$140$	7.00098	0.591691
$141$	−0.598720	−0.0504213
$142$	−1.56459	−0.131297
$143$	−9.36129	−0.782830
$144$	23.3603	1.94669
$145$	−1.81600	−0.150810
$146$	0.724567	0.0599656
$147$	−19.2868	−1.59075
$148$	−0.962542	−0.0791205
$149$	−14.3563	−1.17611	−0.588055	−	0.808821i	$-0.700106\pi$
$149$	−14.3563	−1.17611	−0.588055	+	0.808821i	$0.700106\pi$
$150$	−0.849925	−0.0693961
$151$	20.1550	1.64019	0.820094	−	0.572228i	$-0.193921\pi$
$151$	20.1550	1.64019	0.820094	+	0.572228i	$0.193921\pi$
$152$	0	0
$153$	−23.8065	−1.92464
$154$	2.45283	0.197654
$155$	7.04948	0.566228
$156$	−22.7096	−1.81822
$157$	−4.64044	−0.370348	−0.185174	−	0.982706i	$-0.559285\pi$
$157$	−4.64044	−0.370348	−0.185174	+	0.982706i	$0.559285\pi$
$158$	1.40445	0.111732
$159$	−14.0650	−1.11543
$160$	−3.13186	−0.247595
$161$	−33.4443	−2.63578
$162$	3.98366	0.312986
$163$	0.964446	0.0755412	0.0377706	−	0.999286i	$-0.487974\pi$
$163$	0.964446	0.0755412	0.0377706	+	0.999286i	$0.487974\pi$
$164$	−2.74347	−0.214229
$165$	7.59601	0.591349
$166$	−0.0788819	−0.00612242
$167$	20.1148	1.55653	0.778266	−	0.627935i	$-0.216100\pi$
$167$	20.1148	1.55653	0.778266	+	0.627935i	$0.216100\pi$
$168$	12.1339	0.936150
$169$	1.54214	0.118626
$170$	0.994562	0.0762794
$171$	0	0
$172$	−13.0509	−0.995119
$173$	−18.0664	−1.37356	−0.686782	−	0.726864i	$-0.740977\pi$
$173$	−18.0664	−1.37356	−0.686782	+	0.726864i	$0.740977\pi$
$174$	−1.54346	−0.117010
$175$	3.63772	0.274986
$176$	8.72206	0.657450
$177$	−4.01014	−0.301421
$178$	−1.34868	−0.101087
$179$	26.2990	1.96568	0.982838	−	0.184470i	$-0.0590569\pi$
$179$	26.2990	1.96568	0.982838	+	0.184470i	$0.0590569\pi$
$180$	12.6535	0.943136
$181$	14.0156	1.04177	0.520885	−	0.853627i	$-0.325602\pi$
$181$	14.0156	1.04177	0.520885	+	0.853627i	$0.325602\pi$
$182$	−3.81030	−0.282439
$183$	−25.1424	−1.85858
$184$	9.91061	0.730620
$185$	−0.500137	−0.0367708
$186$	5.99153	0.439321
$187$	−8.88867	−0.650004
$188$	−0.372383	−0.0271588
$189$	−40.2384	−2.92691
$190$	0	0
$191$	10.2065	0.738515	0.369258	−	0.929327i	$-0.379612\pi$
$191$	10.2065	0.738515	0.369258	+	0.929327i	$0.379612\pi$
$192$	19.3265	1.39477
$193$	21.2698	1.53103	0.765516	−	0.643416i	$-0.222484\pi$
$193$	21.2698	1.53103	0.765516	+	0.643416i	$0.222484\pi$
$194$	−2.26331	−0.162496
$195$	−11.7999	−0.845008
$196$	−11.9957	−0.856837
$197$	−20.3725	−1.45148	−0.725740	−	0.687969i	$-0.758502\pi$
$197$	−20.3725	−1.45148	−0.725740	+	0.687969i	$0.758502\pi$
$198$	4.43321	0.315055
$199$	21.0153	1.48974	0.744869	−	0.667210i	$-0.232512\pi$
$199$	21.0153	1.48974	0.744869	+	0.667210i	$0.232512\pi$
$200$	−1.07797	−0.0762240
$201$	−25.2837	−1.78337
$202$	0.528502	0.0371852
$203$	6.60608	0.463656
$204$	−21.5630	−1.50971
$205$	−1.42551	−0.0995618
$206$	−4.91768	−0.342631
$207$	−60.4469	−4.20135
$208$	−13.5491	−0.939464
$209$	0	0
$210$	3.09179	0.213354
$211$	11.0709	0.762151	0.381075	−	0.924544i	$-0.375554\pi$
$211$	11.0709	0.762151	0.381075	+	0.924544i	$0.375554\pi$
$212$	−8.74796	−0.600812
$213$	17.6258	1.20770
$214$	−1.39435	−0.0953161
$215$	−6.78124	−0.462477
$216$	11.9239	0.811319
$217$	−25.6440	−1.74083
$218$	3.65639	0.247642
$219$	−8.16255	−0.551574
$220$	4.72445	0.318523
$221$	13.8080	0.928824
$222$	−0.425079	−0.0285295
$223$	22.8433	1.52970	0.764849	−	0.644210i	$-0.222814\pi$
$223$	22.8433	1.52970	0.764849	+	0.644210i	$0.222814\pi$
$224$	11.3928	0.761215
$225$	6.57477	0.438318
$226$	1.72273	0.114594
$227$	22.4210	1.48814	0.744068	−	0.668104i	$-0.232894\pi$
$227$	22.4210	1.48814	0.744068	+	0.668104i	$0.232894\pi$
$228$	0	0
$229$	15.9279	1.05255	0.526273	−	0.850316i	$-0.323589\pi$
$229$	15.9279	1.05255	0.526273	+	0.850316i	$0.323589\pi$
$230$	2.52528	0.166512
$231$	−27.6321	−1.81806
$232$	−1.95759	−0.128522
$233$	9.19629	0.602469	0.301235	−	0.953550i	$-0.402601\pi$
$233$	9.19629	0.602469	0.301235	+	0.953550i	$0.402601\pi$
$234$	−6.88670	−0.450198
$235$	−0.193490	−0.0126219
$236$	−2.49417	−0.162357
$237$	−15.8218	−1.02773
$238$	−3.61794	−0.234516
$239$	−10.3057	−0.666620	−0.333310	−	0.942817i	$-0.608165\pi$
$239$	−10.3057	−0.666620	−0.333310	+	0.942817i	$0.608165\pi$
$240$	10.9942	0.709669
$241$	−16.4125	−1.05722	−0.528612	−	0.848864i	$-0.677287\pi$
$241$	−16.4125	−1.05722	−0.528612	+	0.848864i	$0.677287\pi$
$242$	−1.36617	−0.0878209
$243$	−11.6933	−0.750124
$244$	−15.6377	−1.00110
$245$	−6.23298	−0.398211
$246$	−1.21158	−0.0772472
$247$	0	0
$248$	7.59914	0.482546
$249$	0.888638	0.0563151
$250$	−0.274673	−0.0173719
$251$	−2.66094	−0.167957	−0.0839785	−	0.996468i	$-0.526763\pi$
$251$	−2.66094	−0.167957	−0.0839785	+	0.996468i	$0.526763\pi$
$252$	−46.0298	−2.89961
$253$	−22.5691	−1.41891
$254$	2.32851	0.146104
$255$	−11.2042	−0.701632
$256$	10.2999	0.643744
$257$	−8.21974	−0.512734	−0.256367	−	0.966580i	$-0.582525\pi$
$257$	−8.21974	−0.512734	−0.256367	+	0.966580i	$0.582525\pi$
$258$	−5.76354	−0.358823
$259$	1.81936	0.113049
$260$	−7.33913	−0.455153
$261$	11.9398	0.739053
$262$	6.02697	0.372347
$263$	0.310912	0.0191717	0.00958583	−	0.999954i	$-0.496949\pi$
$263$	0.310912	0.0191717	0.00958583	+	0.999954i	$0.496949\pi$
$264$	8.18828	0.503954
$265$	−4.54544	−0.279224
$266$	0	0
$267$	15.1934	0.929821
$268$	−15.7256	−0.960592
$269$	6.83610	0.416804	0.208402	−	0.978043i	$-0.433174\pi$
$269$	6.83610	0.416804	0.208402	+	0.978043i	$0.433174\pi$
$270$	3.03828	0.184904
$271$	−14.8797	−0.903879	−0.451939	−	0.892049i	$-0.649268\pi$
$271$	−14.8797	−0.903879	−0.451939	+	0.892049i	$0.649268\pi$
$272$	−12.8651	−0.780061
$273$	42.9247	2.59792
$274$	2.81530	0.170079
$275$	2.45483	0.148032
$276$	−54.7505	−3.29559
$277$	−1.75388	−0.105381	−0.0526903	−	0.998611i	$-0.516780\pi$
$277$	−1.75388	−0.105381	−0.0526903	+	0.998611i	$0.516780\pi$
$278$	3.58497	0.215012
$279$	−46.3487	−2.77483
$280$	3.92135	0.234346
$281$	1.61410	0.0962889	0.0481445	−	0.998840i	$-0.484669\pi$
$281$	1.61410	0.0962889	0.0481445	+	0.998840i	$0.484669\pi$
$282$	−0.164452	−0.00979300
$283$	−6.86254	−0.407936	−0.203968	−	0.978978i	$-0.565384\pi$
$283$	−6.86254	−0.407936	−0.203968	+	0.978978i	$0.565384\pi$
$284$	10.9626	0.650511
$285$	0	0
$286$	−2.57130	−0.152044
$287$	5.18559	0.306096
$288$	20.5913	1.21335
$289$	−3.88915	−0.228774
$290$	−0.498806	−0.0292909
$291$	25.4972	1.49467
$292$	−5.07682	−0.297099
$293$	−14.1064	−0.824106	−0.412053	−	0.911160i	$-0.635188\pi$
$293$	−14.1064	−0.824106	−0.412053	+	0.911160i	$0.635188\pi$
$294$	−5.29757	−0.308960
$295$	−1.29597	−0.0754545
$296$	−0.539134	−0.0313365
$297$	−27.1540	−1.57563
$298$	−3.94328	−0.228428
$299$	35.0597	2.02755
$300$	5.95517	0.343822
$301$	24.6682	1.42185
$302$	5.53604	0.318563
$303$	−5.95380	−0.342037
$304$	0	0
$305$	−8.12536	−0.465257
$306$	−6.53901	−0.373811
$307$	18.4079	1.05059	0.525297	−	0.850919i	$-0.323954\pi$
$307$	18.4079	1.05059	0.525297	+	0.850919i	$0.323954\pi$
$308$	−17.1862	−0.979276
$309$	55.3997	3.15158
$310$	1.93631	0.109975
$311$	16.5997	0.941283	0.470641	−	0.882325i	$-0.344023\pi$
$311$	16.5997	0.941283	0.470641	+	0.882325i	$0.344023\pi$
$312$	−12.7199	−0.720125
$313$	4.54809	0.257073	0.128537	−	0.991705i	$-0.458972\pi$
$313$	4.54809	0.257073	0.128537	+	0.991705i	$0.458972\pi$
$314$	−1.27461	−0.0719302
$315$	−23.9171	−1.34758
$316$	−9.84059	−0.553576
$317$	−13.0464	−0.732761	−0.366380	−	0.930465i	$-0.619403\pi$
$317$	−13.0464	−0.732761	−0.366380	+	0.930465i	$0.619403\pi$
$318$	−3.86329	−0.216642
$319$	4.45797	0.249598
$320$	6.24580	0.349151
$321$	15.7080	0.876735
$322$	−9.18626	−0.511930
$323$	0	0
$324$	−27.9123	−1.55068
$325$	−3.81342	−0.211530
$326$	0.264908	0.0146719
$327$	−41.1908	−2.27786
$328$	−1.53666	−0.0848476
$329$	0.703863	0.0388052
$330$	2.08642	0.114854
$331$	9.51322	0.522894	0.261447	−	0.965218i	$-0.415800\pi$
$331$	9.51322	0.522894	0.261447	+	0.965218i	$0.415800\pi$
$332$	0.552702	0.0303335
$333$	3.28829	0.180197
$334$	5.52501	0.302315
$335$	−8.17102	−0.446431
$336$	−39.9936	−2.18183
$337$	5.26448	0.286774	0.143387	−	0.989667i	$-0.454201\pi$
$337$	5.26448	0.286774	0.143387	+	0.989667i	$0.454201\pi$
$338$	0.423586	0.0230400
$339$	−19.4073	−1.05406
$340$	−6.96860	−0.377925
$341$	−17.3053	−0.937134
$342$	0	0
$343$	−2.79019	−0.150656
$344$	−7.30998	−0.394127
$345$	−28.4484	−1.53161
$346$	−4.96236	−0.266778
$347$	17.2556	0.926326	0.463163	−	0.886273i	$-0.346714\pi$
$347$	17.2556	0.926326	0.463163	+	0.886273i	$0.346714\pi$
$348$	10.8146	0.579722
$349$	18.2146	0.975005	0.487502	−	0.873122i	$-0.337908\pi$
$349$	18.2146	0.975005	0.487502	+	0.873122i	$0.337908\pi$
$350$	0.999184	0.0534086
$351$	42.1819	2.25150
$352$	7.68819	0.409782
$353$	31.7219	1.68839	0.844193	−	0.536039i	$-0.180080\pi$
$353$	31.7219	1.68839	0.844193	+	0.536039i	$0.180080\pi$
$354$	−1.10148	−0.0585430
$355$	5.69618	0.302322
$356$	9.44976	0.500837
$357$	40.7576	2.15712
$358$	7.22362	0.381780
$359$	−0.696745	−0.0367728	−0.0183864	−	0.999831i	$-0.505853\pi$
$359$	−0.696745	−0.0367728	−0.0183864	+	0.999831i	$0.505853\pi$
$360$	7.08741	0.373539
$361$	0	0
$362$	3.84971	0.202336
$363$	15.3905	0.807793
$364$	26.6977	1.39934
$365$	−2.63792	−0.138075
$366$	−6.90595	−0.360980
$367$	−36.6138	−1.91122	−0.955612	−	0.294629i	$-0.904804\pi$
$367$	−36.6138	−1.91122	−0.955612	+	0.294629i	$0.904804\pi$
$368$	−32.6656	−1.70281
$369$	9.37238	0.487907
$370$	−0.137374	−0.00714176
$371$	16.5350	0.858457
$372$	−41.9809	−2.17661
$373$	−5.11894	−0.265049	−0.132524	−	0.991180i	$-0.542308\pi$
$373$	−5.11894	−0.265049	−0.132524	+	0.991180i	$0.542308\pi$
$374$	−2.44148	−0.126246
$375$	3.09431	0.159790
$376$	−0.208577	−0.0107565
$377$	−6.92516	−0.356664
$378$	−11.0524	−0.568475
$379$	22.5010	1.15580	0.577898	−	0.816109i	$-0.303873\pi$
$379$	22.5010	1.15580	0.577898	+	0.816109i	$0.303873\pi$
$380$	0	0
$381$	−26.2316	−1.34389
$382$	2.80345	0.143437
$383$	−10.9940	−0.561769	−0.280884	−	0.959742i	$-0.590628\pi$
$383$	−10.9940	−0.561769	−0.280884	+	0.959742i	$0.590628\pi$
$384$	24.6904	1.25998
$385$	−8.92998	−0.455114
$386$	5.84224	0.297362
$387$	44.5851	2.26639
$388$	15.8584	0.805086
$389$	−27.6543	−1.40213	−0.701064	−	0.713098i	$-0.747291\pi$
$389$	−27.6543	−1.40213	−0.701064	+	0.713098i	$0.747291\pi$
$390$	−3.24112	−0.164120
$391$	33.2896	1.68353
$392$	−6.71897	−0.339359
$393$	−67.8964	−3.42492
$394$	−5.59578	−0.281911
$395$	−5.11318	−0.257272
$396$	−31.0622	−1.56093
$397$	−6.28147	−0.315258	−0.157629	−	0.987498i	$-0.550385\pi$
$397$	−6.28147	−0.315258	−0.157629	+	0.987498i	$0.550385\pi$
$398$	5.77236	0.289342
$399$	0	0
$400$	3.55302	0.177651
$401$	16.1708	0.807532	0.403766	−	0.914862i	$-0.367701\pi$
$401$	16.1708	0.807532	0.403766	+	0.914862i	$0.367701\pi$
$402$	−6.94476	−0.346373
$403$	26.8826	1.33912
$404$	−3.70305	−0.184234
$405$	−14.5033	−0.720673
$406$	1.81452	0.0900529
$407$	1.22775	0.0608574
$408$	−12.0778	−0.597938
$409$	−33.7233	−1.66751	−0.833754	−	0.552136i	$-0.813813\pi$
$409$	−33.7233	−1.66751	−0.833754	+	0.552136i	$0.813813\pi$
$410$	−0.391549	−0.0193372
$411$	−31.7156	−1.56441
$412$	34.4567	1.69756
$413$	4.71438	0.231980
$414$	−16.6031	−0.816000
$415$	0.287184	0.0140973
$416$	−11.9431	−0.585558
$417$	−40.3862	−1.97772
$418$	0	0
$419$	−35.5118	−1.73487	−0.867433	−	0.497553i	$-0.834232\pi$
$419$	−35.5118	−1.73487	−0.867433	+	0.497553i	$0.834232\pi$
$420$	−21.6632	−1.05706
$421$	27.5883	1.34457	0.672286	−	0.740292i	$-0.265313\pi$
$421$	27.5883	1.34457	0.672286	+	0.740292i	$0.265313\pi$
$422$	3.04088	0.148028
$423$	1.27215	0.0618543
$424$	−4.89986	−0.237958
$425$	−3.62089	−0.175639
$426$	4.84132	0.234563
$427$	29.5578	1.43040
$428$	9.76983	0.472242
$429$	28.9667	1.39853
$430$	−1.86263	−0.0898238
$431$	17.2312	0.830000	0.415000	−	0.909821i	$-0.363782\pi$
$431$	17.2312	0.830000	0.415000	+	0.909821i	$0.363782\pi$
$432$	−39.3015	−1.89090
$433$	7.75207	0.372541	0.186270	−	0.982499i	$-0.440360\pi$
$433$	7.75207	0.372541	0.186270	+	0.982499i	$0.440360\pi$
$434$	−7.04373	−0.338110
$435$	5.61926	0.269423
$436$	−25.6193	−1.22694
$437$	0	0
$438$	−2.24204	−0.107129
$439$	−14.3607	−0.685397	−0.342699	−	0.939445i	$-0.611341\pi$
$439$	−14.3607	−0.685397	−0.342699	+	0.939445i	$0.611341\pi$
$440$	2.64623	0.126154
$441$	40.9804	1.95145
$442$	3.79268	0.180399
$443$	−13.1725	−0.625844	−0.312922	−	0.949779i	$-0.601308\pi$
$443$	−13.1725	−0.625844	−0.312922	+	0.949779i	$0.601308\pi$
$444$	2.97840	0.141349
$445$	4.91011	0.232761
$446$	6.27443	0.297103
$447$	44.4228	2.10112
$448$	−22.7204	−1.07344
$449$	−18.3579	−0.866363	−0.433181	−	0.901307i	$-0.642609\pi$
$449$	−18.3579	−0.866363	−0.433181	+	0.901307i	$0.642609\pi$
$450$	1.80591	0.0851316
$451$	3.49938	0.164779
$452$	−12.0706	−0.567756
$453$	−62.3658	−2.93020
$454$	6.15846	0.289031
$455$	13.8721	0.650335
$456$	0	0
$457$	−6.56691	−0.307187	−0.153594	−	0.988134i	$-0.549085\pi$
$457$	−6.56691	−0.307187	−0.153594	+	0.988134i	$0.549085\pi$
$458$	4.37497	0.204429
$459$	40.0523	1.86948
$460$	−17.6939	−0.824982
$461$	−22.6799	−1.05631	−0.528155	−	0.849148i	$-0.677116\pi$
$461$	−22.6799	−1.05631	−0.528155	+	0.849148i	$0.677116\pi$
$462$	−7.58981	−0.353110
$463$	−8.95953	−0.416385	−0.208192	−	0.978088i	$-0.566758\pi$
$463$	−8.95953	−0.416385	−0.208192	+	0.978088i	$0.566758\pi$
$464$	6.45227	0.299539
$465$	−21.8133	−1.01157
$466$	2.52598	0.117014
$467$	−8.99842	−0.416397	−0.208199	−	0.978087i	$-0.566760\pi$
$467$	−8.99842	−0.416397	−0.208199	+	0.978087i	$0.566760\pi$
$468$	48.2531	2.23050
$469$	29.7239	1.37252
$470$	−0.0531467	−0.00245147
$471$	14.3590	0.661627
$472$	−1.39702	−0.0643031
$473$	16.6468	0.765420
$474$	−4.34582	−0.199610
$475$	0	0
$476$	25.3498	1.16191
$477$	29.8852	1.36835
$478$	−2.83070	−0.129473
$479$	10.8348	0.495054	0.247527	−	0.968881i	$-0.420382\pi$
$479$	10.8348	0.495054	0.247527	+	0.968881i	$0.420382\pi$
$480$	9.69096	0.442330
$481$	−1.90723	−0.0869623
$482$	−4.50808	−0.205337
$483$	103.487	4.70883
$484$	9.57237	0.435108
$485$	8.24002	0.374160
$486$	−3.21183	−0.145692
$487$	−1.56541	−0.0709356	−0.0354678	−	0.999371i	$-0.511292\pi$
$487$	−1.56541	−0.0709356	−0.0354678	+	0.999371i	$0.511292\pi$
$488$	−8.75890	−0.396497
$489$	−2.98430	−0.134955
$490$	−1.71203	−0.0773418
$491$	32.7267	1.47693	0.738467	−	0.674290i	$-0.235550\pi$
$491$	32.7267	1.47693	0.738467	+	0.674290i	$0.235550\pi$
$492$	8.48915	0.382720
$493$	−6.57553	−0.296147
$494$	0	0
$495$	−16.1399	−0.725436
$496$	−25.0470	−1.12464
$497$	−20.7211	−0.929468
$498$	0.244085	0.0109377
$499$	32.8576	1.47091	0.735454	−	0.677575i	$-0.236969\pi$
$499$	32.8576	1.47091	0.735454	+	0.677575i	$0.236969\pi$
$500$	1.92455	0.0860687
$501$	−62.2416	−2.78075
$502$	−0.730889	−0.0326212
$503$	−32.7872	−1.46191	−0.730955	−	0.682426i	$-0.760925\pi$
$503$	−32.7872	−1.46191	−0.730955	+	0.682426i	$0.760925\pi$
$504$	−25.7820	−1.14842
$505$	−1.92411	−0.0856218
$506$	−6.19914	−0.275585
$507$	−4.77187	−0.211926
$508$	−16.3152	−0.723868
$509$	26.7934	1.18760	0.593798	−	0.804614i	$-0.297628\pi$
$509$	26.7934	1.18760	0.593798	+	0.804614i	$0.297628\pi$
$510$	−3.07749	−0.136273
$511$	9.59601	0.424502
$512$	18.7877	0.830305
$513$	0	0
$514$	−2.25774	−0.0995848
$515$	17.9037	0.788933
$516$	40.3834	1.77778
$517$	0.474986	0.0208899
$518$	0.499729	0.0219568
$519$	55.9031	2.45387
$520$	−4.11075	−0.180268
$521$	3.25012	0.142390	0.0711952	−	0.997462i	$-0.477319\pi$
$521$	3.25012	0.142390	0.0711952	+	0.997462i	$0.477319\pi$
$522$	3.27953	0.143541
$523$	−9.58082	−0.418940	−0.209470	−	0.977815i	$-0.567174\pi$
$523$	−9.58082	−0.418940	−0.209470	+	0.977815i	$0.567174\pi$
$524$	−42.2292	−1.84479
$525$	−11.2562	−0.491262
$526$	0.0853993	0.00372359
$527$	25.5254	1.11190
$528$	−26.9888	−1.17454
$529$	61.5253	2.67501
$530$	−1.24851	−0.0542319
$531$	8.52072	0.369768
$532$	0	0
$533$	−5.43606	−0.235462
$534$	4.17322	0.180593
$535$	5.07641	0.219472
$536$	−8.80812	−0.380453
$537$	−81.3772	−3.51168
$538$	1.87769	0.0809531
$539$	15.3009	0.659057
$540$	−21.2884	−0.916105
$541$	7.64121	0.328521	0.164261	−	0.986417i	$-0.447476\pi$
$541$	7.64121	0.328521	0.164261	+	0.986417i	$0.447476\pi$
$542$	−4.08706	−0.175554
$543$	−43.3686	−1.86112
$544$	−11.3401	−0.486204
$545$	−13.3118	−0.570214
$546$	11.7903	0.504577
$547$	−5.15767	−0.220526	−0.110263	−	0.993902i	$-0.535169\pi$
$547$	−5.15767	−0.220526	−0.110263	+	0.993902i	$0.535169\pi$
$548$	−19.7260	−0.842652
$549$	53.4223	2.28001
$550$	0.674276	0.0287512
$551$	0	0
$552$	−30.6665	−1.30525
$553$	18.6003	0.790965
$554$	−0.481745	−0.0204674
$555$	1.54758	0.0656912
$556$	−25.1188	−1.06527
$557$	24.0846	1.02050	0.510248	−	0.860027i	$-0.329554\pi$
$557$	24.0846	1.02050	0.510248	+	0.860027i	$0.329554\pi$
$558$	−12.7308	−0.538936
$559$	−25.8597	−1.09375
$560$	−12.9249	−0.546176
$561$	27.5043	1.16123
$562$	0.443349	0.0187016
$563$	36.0131	1.51777	0.758886	−	0.651224i	$-0.225744\pi$
$563$	36.0131	1.51777	0.758886	+	0.651224i	$0.225744\pi$
$564$	1.15227	0.0485193
$565$	−6.27192	−0.263862
$566$	−1.88496	−0.0792306
$567$	52.7587	2.21566
$568$	6.14031	0.257642
$569$	−34.5464	−1.44826	−0.724131	−	0.689663i	$-0.757759\pi$
$569$	−34.5464	−1.44826	−0.724131	+	0.689663i	$0.757759\pi$
$570$	0	0
$571$	−8.33925	−0.348987	−0.174493	−	0.984658i	$-0.555829\pi$
$571$	−8.33925	−0.348987	−0.174493	+	0.984658i	$0.555829\pi$
$572$	18.0163	0.753300
$573$	−31.5820	−1.31936
$574$	1.42434	0.0594510
$575$	−9.19377	−0.383407
$576$	−41.0647	−1.71103
$577$	11.1638	0.464754	0.232377	−	0.972626i	$-0.425350\pi$
$577$	11.1638	0.464754	0.232377	+	0.972626i	$0.425350\pi$
$578$	−1.06825	−0.0444332
$579$	−65.8154	−2.73519
$580$	3.49499	0.145121
$581$	−1.04470	−0.0433413
$582$	7.00340	0.290300
$583$	11.1583	0.462129
$584$	−2.84360	−0.117669
$585$	25.0723	1.03661
$586$	−3.87466	−0.160061
$587$	−3.12443	−0.128959	−0.0644796	−	0.997919i	$-0.520539\pi$
$587$	−3.12443	−0.128959	−0.0644796	+	0.997919i	$0.520539\pi$
$588$	37.1185	1.53074
$589$	0	0
$590$	−0.355969	−0.0146550
$591$	63.0389	2.59307
$592$	1.77700	0.0730342
$593$	−4.11412	−0.168947	−0.0844734	−	0.996426i	$-0.526921\pi$
$593$	−4.11412	−0.168947	−0.0844734	+	0.996426i	$0.526921\pi$
$594$	−7.45847	−0.306025
$595$	13.1718	0.539990
$596$	27.6294	1.13174
$597$	−65.0280	−2.66142
$598$	9.62995	0.393798
$599$	−20.7620	−0.848314	−0.424157	−	0.905589i	$-0.639430\pi$
$599$	−20.7620	−0.848314	−0.424157	+	0.905589i	$0.639430\pi$
$600$	3.33558	0.136174
$601$	12.2431	0.499405	0.249703	−	0.968323i	$-0.419667\pi$
$601$	12.2431	0.499405	0.249703	+	0.968323i	$0.419667\pi$
$602$	6.77570	0.276157
$603$	53.7226	2.18775
$604$	−38.7894	−1.57832
$605$	4.97381	0.202214
$606$	−1.63535	−0.0664315
$607$	39.2469	1.59298	0.796491	−	0.604650i	$-0.206687\pi$
$607$	39.2469	1.59298	0.796491	+	0.604650i	$0.206687\pi$
$608$	0	0
$609$	−20.4413	−0.828323
$610$	−2.23182	−0.0903637
$611$	−0.737860	−0.0298506
$612$	45.8169	1.85204
$613$	−19.8681	−0.802466	−0.401233	−	0.915976i	$-0.631418\pi$
$613$	−19.8681	−0.802466	−0.401233	+	0.915976i	$0.631418\pi$
$614$	5.05616	0.204050
$615$	4.41097	0.177867
$616$	−9.62625	−0.387853
$617$	23.8143	0.958726	0.479363	−	0.877617i	$-0.340868\pi$
$617$	23.8143	0.958726	0.479363	+	0.877617i	$0.340868\pi$
$618$	15.2168	0.612111
$619$	0.628838	0.0252751	0.0126376	−	0.999920i	$-0.495977\pi$
$619$	0.628838	0.0252751	0.0126376	+	0.999920i	$0.495977\pi$
$620$	−13.5671	−0.544869
$621$	101.696	4.08093
$622$	4.55950	0.182819
$623$	−17.8616	−0.715609
$624$	41.9253	1.67835
$625$	1.00000	0.0400000
$626$	1.24924	0.0499296
$627$	0	0
$628$	8.93079	0.356377
$629$	−1.81094	−0.0722070
$630$	−6.56940	−0.261731
$631$	14.0216	0.558193	0.279096	−	0.960263i	$-0.409965\pi$
$631$	14.0216	0.558193	0.279096	+	0.960263i	$0.409965\pi$
$632$	−5.51186	−0.219250
$633$	−34.2568	−1.36158
$634$	−3.58351	−0.142319
$635$	−8.47737	−0.336414
$636$	27.0689	1.07335
$637$	−23.7690	−0.941760
$638$	1.22448	0.0484778
$639$	−37.4510	−1.48154
$640$	7.97928	0.315409
$641$	−45.6046	−1.80127	−0.900637	−	0.434573i	$-0.856899\pi$
$641$	−45.6046	−1.80127	−0.900637	+	0.434573i	$0.856899\pi$
$642$	4.31457	0.170282
$643$	20.4136	0.805034	0.402517	−	0.915412i	$-0.368135\pi$
$643$	20.4136	0.805034	0.402517	+	0.915412i	$0.368135\pi$
$644$	64.3654	2.53635
$645$	20.9833	0.826215
$646$	0	0
$647$	33.8616	1.33124	0.665619	−	0.746292i	$-0.268168\pi$
$647$	33.8616	1.33124	0.665619	+	0.746292i	$0.268168\pi$
$648$	−15.6341	−0.614165
$649$	3.18139	0.124881
$650$	−1.04744	−0.0410841
$651$	79.3506	3.11000
$652$	−1.85613	−0.0726916
$653$	−31.1781	−1.22009	−0.610046	−	0.792366i	$-0.708849\pi$
$653$	−31.1781	−1.22009	−0.610046	+	0.792366i	$0.708849\pi$
$654$	−11.3140	−0.442413
$655$	−21.9423	−0.857357
$656$	5.06486	0.197749
$657$	17.3437	0.676643
$658$	0.193333	0.00753689
$659$	−12.4310	−0.484243	−0.242121	−	0.970246i	$-0.577843\pi$
$659$	−12.4310	−0.484243	−0.242121	+	0.970246i	$0.577843\pi$
$660$	−14.6189	−0.569041
$661$	−37.5106	−1.45899	−0.729497	−	0.683984i	$-0.760246\pi$
$661$	−37.5106	−1.45899	−0.729497	+	0.683984i	$0.760246\pi$
$662$	2.61303	0.101558
$663$	−42.7261	−1.65935
$664$	0.309576	0.0120139
$665$	0	0
$666$	0.903205	0.0349985
$667$	−16.6959	−0.646466
$668$	−38.7121	−1.49782
$669$	−70.6842	−2.73281
$670$	−2.24436	−0.0867073
$671$	19.9464	0.770021
$672$	−35.2529	−1.35991
$673$	30.3081	1.16829	0.584145	−	0.811650i	$-0.301430\pi$
$673$	30.3081	1.16829	0.584145	+	0.811650i	$0.301430\pi$
$674$	1.44601	0.0556983
$675$	−11.0614	−0.425755
$676$	−2.96794	−0.114152
$677$	28.6126	1.09967	0.549835	−	0.835273i	$-0.314690\pi$
$677$	28.6126	1.09967	0.549835	+	0.835273i	$0.314690\pi$
$678$	−5.33066	−0.204723
$679$	−29.9748	−1.15033
$680$	−3.90321	−0.149681
$681$	−69.3776	−2.65856
$682$	−4.75330	−0.182013
$683$	−29.9256	−1.14507	−0.572535	−	0.819880i	$-0.694040\pi$
$683$	−29.9256	−1.14507	−0.572535	+	0.819880i	$0.694040\pi$
$684$	0	0
$685$	−10.2496	−0.391618
$686$	−0.766392	−0.0292610
$687$	−49.2859	−1.88038
$688$	24.0939	0.918570
$689$	−17.3337	−0.660360
$690$	−7.81401	−0.297474
$691$	21.7025	0.825601	0.412801	−	0.910821i	$-0.364551\pi$
$691$	21.7025	0.825601	0.412801	+	0.910821i	$0.364551\pi$
$692$	34.7698	1.32175
$693$	58.7125	2.23030
$694$	4.73964	0.179914
$695$	−13.0518	−0.495081
$696$	6.05740	0.229605
$697$	−5.16161	−0.195510
$698$	5.00306	0.189369
$699$	−28.4562	−1.07631
$700$	−7.00098	−0.264612
$701$	−28.4817	−1.07574	−0.537870	−	0.843028i	$-0.680771\pi$
$701$	−28.4817	−1.07574	−0.537870	+	0.843028i	$0.680771\pi$
$702$	11.5862	0.437295
$703$	0	0
$704$	−15.3324	−0.577861
$705$	0.598720	0.0225491
$706$	8.71316	0.327924
$707$	6.99937	0.263238
$708$	7.71774	0.290050
$709$	−11.1270	−0.417882	−0.208941	−	0.977928i	$-0.567002\pi$
$709$	−11.1270	−0.417882	−0.208941	+	0.977928i	$0.567002\pi$
$710$	1.56459	0.0587180
$711$	33.6180	1.26077
$712$	5.29295	0.198362
$713$	64.8113	2.42720
$714$	11.1950	0.418963
$715$	9.36129	0.350092
$716$	−50.6138	−1.89153
$717$	31.8890	1.19092
$718$	−0.191377	−0.00714214
$719$	−44.7414	−1.66857	−0.834287	−	0.551331i	$-0.814120\pi$
$719$	−44.7414	−1.66857	−0.834287	+	0.551331i	$0.814120\pi$
$720$	−23.3603	−0.870586
$721$	−65.1287	−2.42552
$722$	0	0
$723$	50.7855	1.88873
$724$	−26.9737	−1.00247
$725$	1.81600	0.0674445
$726$	4.22737	0.156892
$727$	1.09629	0.0406592	0.0203296	−	0.999793i	$-0.493528\pi$
$727$	1.09629	0.0406592	0.0203296	+	0.999793i	$0.493528\pi$
$728$	14.9537	0.554223
$729$	−7.32713	−0.271375
$730$	−0.724567	−0.0268174
$731$	−24.5541	−0.908167
$732$	48.3879	1.78847
$733$	−3.10835	−0.114809	−0.0574047	−	0.998351i	$-0.518283\pi$
$733$	−3.10835	−0.114809	−0.0574047	+	0.998351i	$0.518283\pi$
$734$	−10.0568	−0.371204
$735$	19.2868	0.711404
$736$	−28.7936	−1.06135
$737$	20.0585	0.738863
$738$	2.57434	0.0947629
$739$	−29.4118	−1.08193	−0.540965	−	0.841045i	$-0.681941\pi$
$739$	−29.4118	−1.08193	−0.540965	+	0.841045i	$0.681941\pi$
$740$	0.962542	0.0353837
$741$	0	0
$742$	4.54174	0.166732
$743$	21.8551	0.801784	0.400892	−	0.916125i	$-0.368700\pi$
$743$	21.8551	0.801784	0.400892	+	0.916125i	$0.368700\pi$
$744$	−23.5141	−0.862069
$745$	14.3563	0.525973
$746$	−1.40604	−0.0514787
$747$	−1.88817	−0.0690845
$748$	17.1067	0.625484
$749$	−18.4665	−0.674753
$750$	0.849925	0.0310349
$751$	26.6866	0.973807	0.486903	−	0.873456i	$-0.338126\pi$
$751$	26.6866	0.973807	0.486903	+	0.873456i	$0.338126\pi$
$752$	0.687475	0.0250696
$753$	8.23378	0.300056
$754$	−1.90216	−0.0692724
$755$	−20.1550	−0.733515
$756$	77.4410	2.81650
$757$	27.5577	1.00160	0.500800	−	0.865563i	$-0.333039\pi$
$757$	27.5577	1.00160	0.500800	+	0.865563i	$0.333039\pi$
$758$	6.18041	0.224483
$759$	69.8359	2.53488
$760$	0	0
$761$	35.1188	1.27306	0.636528	−	0.771253i	$-0.280370\pi$
$761$	35.1188	1.27306	0.636528	+	0.771253i	$0.280370\pi$
$762$	−7.20513	−0.261014
$763$	48.4245	1.75309
$764$	−19.6429	−0.710656
$765$	23.8065	0.860726
$766$	−3.01977	−0.109109
$767$	−4.94208	−0.178448
$768$	−31.8711	−1.15005
$769$	−9.04997	−0.326350	−0.163175	−	0.986597i	$-0.552174\pi$
$769$	−9.04997	−0.326350	−0.163175	+	0.986597i	$0.552174\pi$
$770$	−2.45283	−0.0883937
$771$	25.4345	0.915999
$772$	−40.9349	−1.47328
$773$	17.8731	0.642852	0.321426	−	0.946935i	$-0.395838\pi$
$773$	17.8731	0.642852	0.321426	+	0.946935i	$0.395838\pi$
$774$	12.2463	0.440185
$775$	−7.04948	−0.253225
$776$	8.88249	0.318863
$777$	−5.62966	−0.201963
$778$	−7.59590	−0.272326
$779$	0	0
$780$	22.7096	0.813132
$781$	−13.9831	−0.500356
$782$	9.14377	0.326981
$783$	−20.0876	−0.717871
$784$	22.1459	0.790925
$785$	4.64044	0.165625
$786$	−18.6493	−0.665199
$787$	−26.0736	−0.929425	−0.464713	−	0.885462i	$-0.653842\pi$
$787$	−26.0736	−0.929425	−0.464713	+	0.885462i	$0.653842\pi$
$788$	39.2080	1.39673
$789$	−0.962059	−0.0342502
$790$	−1.40445	−0.0499682
$791$	22.8155	0.811224
$792$	−17.3984	−0.618224
$793$	−30.9854	−1.10032
$794$	−1.72535	−0.0612305
$795$	14.0650	0.498835
$796$	−40.4452	−1.43354
$797$	4.82841	0.171031	0.0855156	−	0.996337i	$-0.472746\pi$
$797$	4.82841	0.171031	0.0855156	+	0.996337i	$0.472746\pi$
$798$	0	0
$799$	−0.700608	−0.0247857
$800$	3.13186	0.110728
$801$	−32.2828	−1.14066
$802$	4.44169	0.156842
$803$	6.47565	0.228521
$804$	48.6598	1.71610
$805$	33.4443	1.17876
$806$	7.38394	0.260088
$807$	−21.1530	−0.744622
$808$	−2.07413	−0.0729678
$809$	39.5224	1.38953	0.694766	−	0.719236i	$-0.255508\pi$
$809$	39.5224	1.38953	0.694766	+	0.719236i	$0.255508\pi$
$810$	−3.98366	−0.139972
$811$	−9.26116	−0.325203	−0.162602	−	0.986692i	$-0.551989\pi$
$811$	−9.26116	−0.325203	−0.162602	+	0.986692i	$0.551989\pi$
$812$	−12.7138	−0.446166
$813$	46.0425	1.61478
$814$	0.337231	0.0118199
$815$	−0.964446	−0.0337831
$816$	39.8086	1.39358
$817$	0	0
$818$	−9.26289	−0.323869
$819$	−91.2060	−3.18700
$820$	2.74347	0.0958061
$821$	−20.7559	−0.724387	−0.362194	−	0.932103i	$-0.617972\pi$
$821$	−20.7559	−0.724387	−0.362194	+	0.932103i	$0.617972\pi$
$822$	−8.71142	−0.303846
$823$	−19.6486	−0.684907	−0.342453	−	0.939535i	$-0.611258\pi$
$823$	−19.6486	−0.684907	−0.342453	+	0.939535i	$0.611258\pi$
$824$	19.2997	0.672337
$825$	−7.59601	−0.264459
$826$	1.29492	0.0450559
$827$	−53.4817	−1.85974	−0.929870	−	0.367888i	$-0.880081\pi$
$827$	−53.4817	−1.85974	−0.929870	+	0.367888i	$0.880081\pi$
$828$	116.333	4.04286
$829$	−0.0378061	−0.00131306	−0.000656531	−	1.00000i	$-0.500209\pi$
$829$	−0.0378061	−0.00131306	−0.000656531		1.00000i	$0.500209\pi$
$830$	0.0788819	0.00273803
$831$	5.42706	0.188263
$832$	23.8178	0.825735
$833$	−22.5689	−0.781968
$834$	−11.0930	−0.384120
$835$	−20.1148	−0.696102
$836$	0	0
$837$	77.9775	2.69530
$838$	−9.75416	−0.336952
$839$	−11.4861	−0.396544	−0.198272	−	0.980147i	$-0.563533\pi$
$839$	−11.4861	−0.396544	−0.198272	+	0.980147i	$0.563533\pi$
$840$	−12.1339	−0.418659
$841$	−25.7022	−0.886281
$842$	7.57777	0.261147
$843$	−4.99452	−0.172020
$844$	−21.3065	−0.733400
$845$	−1.54214	−0.0530514
$846$	0.349427	0.0120135
$847$	−18.0933	−0.621693
$848$	16.1501	0.554595
$849$	21.2348	0.728778
$850$	−0.994562	−0.0341132
$851$	−4.59815	−0.157622
$852$	−33.9217	−1.16214
$853$	5.83253	0.199702	0.0998510	−	0.995002i	$-0.468163\pi$
$853$	5.83253	0.199702	0.0998510	+	0.995002i	$0.468163\pi$
$854$	8.11873	0.277817
$855$	0	0
$856$	5.47222	0.187037
$857$	9.08506	0.310340	0.155170	−	0.987888i	$-0.450408\pi$
$857$	9.08506	0.310340	0.155170	+	0.987888i	$0.450408\pi$
$858$	7.95639	0.271627
$859$	45.9268	1.56700	0.783500	−	0.621391i	$-0.213432\pi$
$859$	45.9268	1.56700	0.783500	+	0.621391i	$0.213432\pi$
$860$	13.0509	0.445031
$861$	−16.0458	−0.546841
$862$	4.73296	0.161205
$863$	−20.4157	−0.694958	−0.347479	−	0.937688i	$-0.612962\pi$
$863$	−20.4157	−0.694958	−0.347479	+	0.937688i	$0.612962\pi$
$864$	−34.6429	−1.17858
$865$	18.0664	0.614276
$866$	2.12929	0.0723561
$867$	12.0343	0.408705
$868$	49.3533	1.67516
$869$	12.5520	0.425797
$870$	1.54346	0.0523283
$871$	−31.1595	−1.05580
$872$	−14.3497	−0.485943
$873$	−54.1762	−1.83359
$874$	0	0
$875$	−3.63772	−0.122977
$876$	15.7093	0.530767
$877$	−36.8908	−1.24571	−0.622857	−	0.782336i	$-0.714028\pi$
$877$	−36.8908	−1.24571	−0.622857	+	0.782336i	$0.714028\pi$
$878$	−3.94449	−0.133120
$879$	43.6497	1.47227
$880$	−8.72206	−0.294021
$881$	−11.1110	−0.374340	−0.187170	−	0.982328i	$-0.559932\pi$
$881$	−11.1110	−0.374340	−0.187170	+	0.982328i	$0.559932\pi$
$882$	11.2562	0.379017
$883$	26.5136	0.892253	0.446127	−	0.894970i	$-0.352803\pi$
$883$	26.5136	0.892253	0.446127	+	0.894970i	$0.352803\pi$
$884$	−26.5742	−0.893786
$885$	4.01014	0.134800
$886$	−3.61813	−0.121553
$887$	−8.31764	−0.279279	−0.139640	−	0.990202i	$-0.544594\pi$
$887$	−8.31764	−0.279279	−0.139640	+	0.990202i	$0.544594\pi$
$888$	1.66825	0.0559827
$889$	30.8383	1.03428
$890$	1.34868	0.0452077
$891$	35.6030	1.19275
$892$	−43.9631	−1.47199
$893$	0	0
$894$	12.2017	0.408088
$895$	−26.2990	−0.879077
$896$	−29.0263	−0.969702
$897$	−108.486	−3.62223
$898$	−5.04243	−0.168268
$899$	−12.8018	−0.426966
$900$	−12.6535	−0.421783
$901$	−16.4586	−0.548314
$902$	0.961187	0.0320040
$903$	−76.3312	−2.54014
$904$	−6.76094	−0.224866
$905$	−14.0156	−0.465894
$906$	−17.1302	−0.569114
$907$	17.0838	0.567260	0.283630	−	0.958934i	$-0.408461\pi$
$907$	17.0838	0.567260	0.283630	+	0.958934i	$0.408461\pi$
$908$	−43.1505	−1.43200
$909$	12.6506	0.419593
$910$	3.81030	0.126310
$911$	41.2327	1.36610	0.683050	−	0.730372i	$-0.260653\pi$
$911$	41.2327	1.36610	0.683050	+	0.730372i	$0.260653\pi$
$912$	0	0
$913$	−0.704989	−0.0233317
$914$	−1.80376	−0.0596629
$915$	25.1424	0.831182
$916$	−30.6541	−1.01284
$917$	79.8199	2.63589
$918$	11.0013	0.363097
$919$	25.1985	0.831222	0.415611	−	0.909542i	$-0.363568\pi$
$919$	25.1985	0.831222	0.415611	+	0.909542i	$0.363568\pi$
$920$	−9.91061	−0.326743
$921$	−56.9597	−1.87689
$922$	−6.22957	−0.205160
$923$	21.7219	0.714985
$924$	53.1795	1.74948
$925$	0.500137	0.0164444
$926$	−2.46094	−0.0808716
$927$	−117.713	−3.86620
$928$	5.68745	0.186700
$929$	−34.7803	−1.14111	−0.570553	−	0.821261i	$-0.693271\pi$
$929$	−34.7803	−1.14111	−0.570553	+	0.821261i	$0.693271\pi$
$930$	−5.99153	−0.196470
$931$	0	0
$932$	−17.6988	−0.579742
$933$	−51.3647	−1.68160
$934$	−2.47163	−0.0808741
$935$	8.88867	0.290691
$936$	27.0272	0.883413
$937$	16.0407	0.524026	0.262013	−	0.965064i	$-0.415614\pi$
$937$	16.0407	0.524026	0.262013	+	0.965064i	$0.415614\pi$
$938$	8.16435	0.266576
$939$	−14.0732	−0.459261
$940$	0.372383	0.0121458
$941$	−58.2227	−1.89801	−0.949003	−	0.315268i	$-0.897906\pi$
$941$	−58.2227	−1.89801	−0.949003	+	0.315268i	$0.897906\pi$
$942$	3.94403	0.128503
$943$	−13.1058	−0.426783
$944$	4.60462	0.149868
$945$	40.2384	1.30896
$946$	4.57243	0.148662
$947$	−5.48637	−0.178283	−0.0891415	−	0.996019i	$-0.528412\pi$
$947$	−5.48637	−0.178283	−0.0891415	+	0.996019i	$0.528412\pi$
$948$	30.4499	0.988965
$949$	−10.0595	−0.326545
$950$	0	0
$951$	40.3697	1.30908
$952$	14.1988	0.460185
$953$	43.2618	1.40139	0.700694	−	0.713462i	$-0.252874\pi$
$953$	43.2618	1.40139	0.700694	+	0.713462i	$0.252874\pi$
$954$	8.20868	0.265766
$955$	−10.2065	−0.330274
$956$	19.8339	0.641473
$957$	−13.7943	−0.445908
$958$	2.97603	0.0961511
$959$	37.2852	1.20400
$960$	−19.3265	−0.623759
$961$	18.6952	0.603072
$962$	−0.523866	−0.0168901
$963$	−33.3762	−1.07553
$964$	31.5868	1.01734
$965$	−21.2698	−0.684699
$966$	28.4252	0.914565
$967$	−0.579244	−0.0186272	−0.00931362	−	0.999957i	$-0.502965\pi$
$967$	−0.579244	−0.0186272	−0.00931362	+	0.999957i	$0.502965\pi$
$968$	5.36162	0.172329
$969$	0	0
$970$	2.26331	0.0726706
$971$	−51.2908	−1.64600	−0.822999	−	0.568042i	$-0.807701\pi$
$971$	−51.2908	−1.64600	−0.822999	+	0.568042i	$0.807701\pi$
$972$	22.5043	0.721827
$973$	47.4786	1.52209
$974$	−0.429977	−0.0137774
$975$	11.7999	0.377899
$976$	28.8696	0.924092
$977$	−21.5880	−0.690662	−0.345331	−	0.938481i	$-0.612233\pi$
$977$	−21.5880	−0.690662	−0.345331	+	0.938481i	$0.612233\pi$
$978$	−0.819707	−0.0262113
$979$	−12.0535	−0.385231
$980$	11.9957	0.383189
$981$	87.5219	2.79436
$982$	8.98915	0.286855
$983$	22.9384	0.731621	0.365811	−	0.930689i	$-0.380792\pi$
$983$	22.9384	0.731621	0.365811	+	0.930689i	$0.380792\pi$
$984$	4.75489	0.151580
$985$	20.3725	0.649122
$986$	−1.80612	−0.0575187
$987$	−2.17797	−0.0693256
$988$	0	0
$989$	−62.3451	−1.98246
$990$	−4.43321	−0.140897
$991$	−1.82776	−0.0580606	−0.0290303	−	0.999579i	$-0.509242\pi$
$991$	−1.82776	−0.0580606	−0.0290303	+	0.999579i	$0.509242\pi$
$992$	−22.0780	−0.700977
$993$	−29.4369	−0.934151
$994$	−5.69153	−0.180524
$995$	−21.0153	−0.666231
$996$	−1.71023	−0.0541908
$997$	33.0058	1.04531	0.522653	−	0.852546i	$-0.324942\pi$
$997$	33.0058	1.04531	0.522653	+	0.852546i	$0.324942\pi$
$998$	9.02511	0.285685
$999$	−5.53224	−0.175032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.q.1.4	✓	6
5.4	even	2		9025.2.a.ca.1.3		6
19.18	odd	2		1805.2.a.r.1.3	yes	6
95.94	odd	2		9025.2.a.bq.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.4	✓	6	1.1	even	1	trivial
1805.2.a.r.1.3	yes	6	19.18	odd	2
9025.2.a.bq.1.4		6	95.94	odd	2
9025.2.a.ca.1.3		6	5.4	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+0.274673 q^{2} -3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} -1.07797 q^{8} +6.57477 q^{9} +O(q^{10})\)	\(q+0.274673 q^{2} -3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} -1.07797 q^{8} +6.57477 q^{9} -0.274673 q^{10} +2.45483 q^{11} +5.95517 q^{12} -3.81342 q^{13} +0.999184 q^{14} +3.09431 q^{15} +3.55302 q^{16} -3.62089 q^{17} +1.80591 q^{18} +1.92455 q^{20} -11.2562 q^{21} +0.674276 q^{22} -9.19377 q^{23} +3.33558 q^{24} +1.00000 q^{25} -1.04744 q^{26} -11.0614 q^{27} -7.00098 q^{28} +1.81600 q^{29} +0.849925 q^{30} -7.04948 q^{31} +3.13186 q^{32} -7.59601 q^{33} -0.994562 q^{34} -3.63772 q^{35} -12.6535 q^{36} +0.500137 q^{37} +11.7999 q^{39} +1.07797 q^{40} +1.42551 q^{41} -3.09179 q^{42} +6.78124 q^{43} -4.72445 q^{44} -6.57477 q^{45} -2.52528 q^{46} +0.193490 q^{47} -10.9942 q^{48} +6.23298 q^{49} +0.274673 q^{50} +11.2042 q^{51} +7.33913 q^{52} +4.54544 q^{53} -3.03828 q^{54} -2.45483 q^{55} -3.92135 q^{56} +0.498806 q^{58} +1.29597 q^{59} -5.95517 q^{60} +8.12536 q^{61} -1.93631 q^{62} +23.9171 q^{63} -6.24580 q^{64} +3.81342 q^{65} -2.08642 q^{66} +8.17102 q^{67} +6.96860 q^{68} +28.4484 q^{69} -0.999184 q^{70} -5.69618 q^{71} -7.08741 q^{72} +2.63792 q^{73} +0.137374 q^{74} -3.09431 q^{75} +8.92998 q^{77} +3.24112 q^{78} +5.11318 q^{79} -3.55302 q^{80} +14.5033 q^{81} +0.391549 q^{82} -0.287184 q^{83} +21.6632 q^{84} +3.62089 q^{85} +1.86263 q^{86} -5.61926 q^{87} -2.64623 q^{88} -4.91011 q^{89} -1.80591 q^{90} -13.8721 q^{91} +17.6939 q^{92} +21.8133 q^{93} +0.0531467 q^{94} -9.69096 q^{96} -8.24002 q^{97} +1.71203 q^{98} +16.1399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * q^99

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