LMFDB - Embedded newform 605.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.86620$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34889 q^{2} +2.86620 q^{3} +3.51730 q^{4} -1.00000 q^{5} +6.73240 q^{6} -3.38350 q^{7} +3.56399 q^{8} +5.21509 q^{9} +O(q^{10})$	\(q+2.34889 q^{2} +2.86620 q^{3} +3.51730 q^{4} -1.00000 q^{5} +6.73240 q^{6} -3.38350 q^{7} +3.56399 q^{8} +5.21509 q^{9} -2.34889 q^{10} +10.0813 q^{12} +1.48270 q^{13} -7.94749 q^{14} -2.86620 q^{15} +1.33682 q^{16} -3.73240 q^{17} +12.2497 q^{18} -3.21509 q^{19} -3.51730 q^{20} -9.69779 q^{21} -2.51730 q^{23} +10.2151 q^{24} +1.00000 q^{25} +3.48270 q^{26} +6.34889 q^{27} -11.9008 q^{28} +4.69779 q^{29} -6.73240 q^{30} +9.21509 q^{31} -3.98793 q^{32} -8.76700 q^{34} +3.38350 q^{35} +18.3431 q^{36} -2.69779 q^{37} -7.55191 q^{38} +4.24970 q^{39} -3.56399 q^{40} +4.55191 q^{41} -22.7791 q^{42} +5.38350 q^{43} -5.21509 q^{45} -5.91288 q^{46} -10.5294 q^{47} +3.83159 q^{48} +4.44809 q^{49} +2.34889 q^{50} -10.6978 q^{51} +5.21509 q^{52} -2.51730 q^{53} +14.9129 q^{54} -12.0588 q^{56} -9.21509 q^{57} +11.0346 q^{58} +11.9129 q^{59} -10.0813 q^{60} -13.6799 q^{61} +21.6453 q^{62} -17.6453 q^{63} -12.0409 q^{64} -1.48270 q^{65} +7.83159 q^{67} -13.1280 q^{68} -7.21509 q^{69} +7.94749 q^{70} +2.51730 q^{71} +18.5865 q^{72} -2.96539 q^{73} -6.33682 q^{74} +2.86620 q^{75} -11.3085 q^{76} +9.98210 q^{78} +6.76700 q^{79} -1.33682 q^{80} +2.55191 q^{81} +10.6920 q^{82} +7.55191 q^{83} -34.1101 q^{84} +3.73240 q^{85} +12.6453 q^{86} +13.4648 q^{87} +10.8016 q^{89} -12.2497 q^{90} -5.01671 q^{91} -8.85412 q^{92} +26.4123 q^{93} -24.7324 q^{94} +3.21509 q^{95} -11.4302 q^{96} +11.0167 q^{97} +10.4481 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9	$ 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 9 q^{12} + 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} - 9 q^{20} - 17 q^{21} - 6 q^{23} + 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} + 14 q^{31} - 27 q^{32} - 8 q^{34} + q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} - 35 q^{42} + 7 q^{43} - 2 q^{45} + 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} - 6 q^{53} + 19 q^{54} - 3 q^{56} - 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} + 29 q^{64} - 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} + q^{75} + 16 q^{76} - 2 q^{78} + 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} - 3 q^{86} + 10 q^{87} + 11 q^{89} - 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9 - q^10 + 9 * q^12 + 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 - 9 * q^20 - 17 * q^21 - 6 * q^23 + 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 + 14 * q^31 - 27 * q^32 - 8 * q^34 + q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 - 35 * q^42 + 7 * q^43 - 2 * q^45 + 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 - 6 * q^53 + 19 * q^54 - 3 * q^56 - 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 + 29 * q^64 - 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 + q^75 + 16 * q^76 - 2 * q^78 + 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 - 3 * q^86 + 10 * q^87 + 11 * q^89 - 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 - 2 * q^97 + 36 * q^98

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 $

$2$	2.34889	1.66092	0.830460	−	0.557079i	$-0.188078\pi$
$2$	2.34889	1.66092	0.830460	+	0.557079i	$0.188078\pi$
$3$	2.86620	1.65480	0.827400	−	0.561613i	$-0.189819\pi$
$3$	2.86620	1.65480	0.827400	+	0.561613i	$0.189819\pi$
$4$	3.51730	1.75865
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.73240	2.74849
$7$	−3.38350	−1.27884	−0.639422	−	0.768856i	$-0.720826\pi$
$7$	−3.38350	−1.27884	−0.639422	+	0.768856i	$0.720826\pi$
$8$	3.56399	1.26006
$9$	5.21509	1.73836
$10$	−2.34889	−0.742786
$11$	0	0
$11$	0	0
$12$	10.0813	2.91022
$13$	1.48270	0.411226	0.205613	−	0.978633i	$-0.434081\pi$
$13$	1.48270	0.411226	0.205613	+	0.978633i	$0.434081\pi$
$14$	−7.94749	−2.12406
$15$	−2.86620	−0.740049
$16$	1.33682	0.334205
$17$	−3.73240	−0.905239	−0.452620	−	0.891704i	$-0.649510\pi$
$17$	−3.73240	−0.905239	−0.452620	+	0.891704i	$0.649510\pi$
$18$	12.2497	2.88728
$19$	−3.21509	−0.737593	−0.368796	−	0.929510i	$-0.620230\pi$
$19$	−3.21509	−0.737593	−0.368796	+	0.929510i	$0.620230\pi$
$20$	−3.51730	−0.786493
$21$	−9.69779	−2.11623
$22$	0	0
$23$	−2.51730	−0.524894	−0.262447	−	0.964946i	$-0.584530\pi$
$23$	−2.51730	−0.524894	−0.262447	+	0.964946i	$0.584530\pi$
$24$	10.2151	2.08515
$25$	1.00000	0.200000
$26$	3.48270	0.683013
$27$	6.34889	1.22185
$28$	−11.9008	−2.24904
$29$	4.69779	0.872357	0.436179	−	0.899860i	$-0.356332\pi$
$29$	4.69779	0.872357	0.436179	+	0.899860i	$0.356332\pi$
$30$	−6.73240	−1.22916
$31$	9.21509	1.65508	0.827540	−	0.561407i	$-0.189740\pi$
$31$	9.21509	1.65508	0.827540	+	0.561407i	$0.189740\pi$
$32$	−3.98793	−0.704972
$33$	0	0
$34$	−8.76700	−1.50353
$35$	3.38350	0.571916
$36$	18.3431	3.05718
$37$	−2.69779	−0.443514	−0.221757	−	0.975102i	$-0.571179\pi$
$37$	−2.69779	−0.443514	−0.221757	+	0.975102i	$0.571179\pi$
$38$	−7.55191	−1.22508
$39$	4.24970	0.680497
$40$	−3.56399	−0.563516
$41$	4.55191	0.710889	0.355445	−	0.934697i	$-0.384329\pi$
$41$	4.55191	0.710889	0.355445	+	0.934697i	$0.384329\pi$
$42$	−22.7791	−3.51489
$43$	5.38350	0.820976	0.410488	−	0.911866i	$-0.365358\pi$
$43$	5.38350	0.820976	0.410488	+	0.911866i	$0.365358\pi$
$44$	0	0
$45$	−5.21509	−0.777420
$46$	−5.91288	−0.871807
$47$	−10.5294	−1.53587	−0.767934	−	0.640529i	$-0.778715\pi$
$47$	−10.5294	−1.53587	−0.767934	+	0.640529i	$0.778715\pi$
$48$	3.83159	0.553042
$49$	4.44809	0.635441
$50$	2.34889	0.332184
$51$	−10.6978	−1.49799
$52$	5.21509	0.723203
$53$	−2.51730	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$53$	−2.51730	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$54$	14.9129	2.02939
$55$	0	0
$56$	−12.0588	−1.61142
$57$	−9.21509	−1.22057
$58$	11.0346	1.44892
$59$	11.9129	1.55092	0.775462	−	0.631394i	$-0.217517\pi$
$59$	11.9129	1.55092	0.775462	+	0.631394i	$0.217517\pi$
$60$	−10.0813	−1.30149
$61$	−13.6799	−1.75153	−0.875765	−	0.482738i	$-0.839642\pi$
$61$	−13.6799	−1.75153	−0.875765	+	0.482738i	$0.839642\pi$
$62$	21.6453	2.74895
$63$	−17.6453	−2.22310
$64$	−12.0409	−1.50511
$65$	−1.48270	−0.183906
$66$	0	0
$67$	7.83159	0.956781	0.478391	−	0.878147i	$-0.341220\pi$
$67$	7.83159	0.956781	0.478391	+	0.878147i	$0.341220\pi$
$68$	−13.1280	−1.59200
$69$	−7.21509	−0.868595
$70$	7.94749	0.949907
$71$	2.51730	0.298749	0.149375	−	0.988781i	$-0.452274\pi$
$71$	2.51730	0.298749	0.149375	+	0.988781i	$0.452274\pi$
$72$	18.5865	2.19044
$73$	−2.96539	−0.347073	−0.173536	−	0.984827i	$-0.555519\pi$
$73$	−2.96539	−0.347073	−0.173536	+	0.984827i	$0.555519\pi$
$74$	−6.33682	−0.736640
$75$	2.86620	0.330960
$76$	−11.3085	−1.29717
$77$	0	0
$78$	9.98210	1.13025
$79$	6.76700	0.761348	0.380674	−	0.924709i	$-0.375692\pi$
$79$	6.76700	0.761348	0.380674	+	0.924709i	$0.375692\pi$
$80$	−1.33682	−0.149461
$81$	2.55191	0.283546
$82$	10.6920	1.18073
$83$	7.55191	0.828930	0.414465	−	0.910065i	$-0.363969\pi$
$83$	7.55191	0.828930	0.414465	+	0.910065i	$0.363969\pi$
$84$	−34.1101	−3.72171
$85$	3.73240	0.404835
$86$	12.6453	1.36358
$87$	13.4648	1.44358
$88$	0	0
$89$	10.8016	1.14497	0.572484	−	0.819916i	$-0.305980\pi$
$89$	10.8016	1.14497	0.572484	+	0.819916i	$0.305980\pi$
$90$	−12.2497	−1.29123
$91$	−5.01671	−0.525894
$92$	−8.85412	−0.923106
$93$	26.4123	2.73883
$94$	−24.7324	−2.55095
$95$	3.21509	0.329862
$96$	−11.4302	−1.16659
$97$	11.0167	1.11858	0.559288	−	0.828973i	$-0.311074\pi$
$97$	11.0167	1.11858	0.559288	+	0.828973i	$0.311074\pi$
$98$	10.4481	1.05542
$99$	0	0
$100$	3.51730	0.351730
$101$	−12.7324	−1.26692	−0.633460	−	0.773775i	$-0.718366\pi$
$101$	−12.7324	−1.26692	−0.633460	+	0.773775i	$0.718366\pi$
$102$	−25.1280	−2.48804
$103$	−18.3431	−1.80740	−0.903698	−	0.428170i	$-0.859158\pi$
$103$	−18.3431	−1.80740	−0.903698	+	0.428170i	$0.859158\pi$
$104$	5.28431	0.518169
$105$	9.69779	0.946407
$106$	−5.91288	−0.574310
$107$	7.13380	0.689651	0.344825	−	0.938667i	$-0.387938\pi$
$107$	7.13380	0.689651	0.344825	+	0.938667i	$0.387938\pi$
$108$	22.3310	2.14880
$109$	4.14588	0.397103	0.198551	−	0.980090i	$-0.436376\pi$
$109$	4.14588	0.397103	0.198551	+	0.980090i	$0.436376\pi$
$110$	0	0
$111$	−7.73240	−0.733927
$112$	−4.52313	−0.427396
$113$	1.46479	0.137796	0.0688981	−	0.997624i	$-0.478052\pi$
$113$	1.46479	0.137796	0.0688981	+	0.997624i	$0.478052\pi$
$114$	−21.6453	−2.02727
$115$	2.51730	0.234740
$116$	16.5236	1.53417
$117$	7.73240	0.714860
$118$	27.9821	2.57596
$119$	12.6286	1.15766
$120$	−10.2151	−0.932506
$121$	0	0
$122$	−32.1326	−2.90915
$123$	13.0467	1.17638
$124$	32.4123	2.91071
$125$	−1.00000	−0.0894427
$126$	−41.4469	−3.69238
$127$	11.2964	1.00239	0.501196	−	0.865334i	$-0.332894\pi$
$127$	11.2964	1.00239	0.501196	+	0.865334i	$0.332894\pi$
$128$	−20.3068	−1.79489
$129$	15.4302	1.35855
$130$	−3.48270	−0.305453
$131$	−14.6799	−1.28259	−0.641294	−	0.767295i	$-0.721602\pi$
$131$	−14.6799	−1.28259	−0.641294	+	0.767295i	$0.721602\pi$
$132$	0	0
$133$	10.8783	0.943266
$134$	18.3956	1.58914
$135$	−6.34889	−0.546426
$136$	−13.3022	−1.14066
$137$	−15.6453	−1.33667	−0.668333	−	0.743862i	$-0.732992\pi$
$137$	−15.6453	−1.33667	−0.668333	+	0.743862i	$0.732992\pi$
$138$	−16.9475	−1.44267
$139$	7.64528	0.648464	0.324232	−	0.945978i	$-0.394894\pi$
$139$	7.64528	0.648464	0.324232	+	0.945978i	$0.394894\pi$
$140$	11.9008	1.00580
$141$	−30.1793	−2.54155
$142$	5.91288	0.496198
$143$	0	0
$144$	6.97164	0.580970
$145$	−4.69779	−0.390130
$146$	−6.96539	−0.576460
$147$	12.7491	1.05153
$148$	−9.48894	−0.779986
$149$	6.48270	0.531083	0.265542	−	0.964099i	$-0.414449\pi$
$149$	6.48270	0.531083	0.265542	+	0.964099i	$0.414449\pi$
$150$	6.73240	0.549698
$151$	10.8783	0.885261	0.442631	−	0.896704i	$-0.354045\pi$
$151$	10.8783	0.885261	0.442631	+	0.896704i	$0.354045\pi$
$152$	−11.4585	−0.929411
$153$	−19.4648	−1.57364
$154$	0	0
$155$	−9.21509	−0.740174
$156$	14.9475	1.19676
$157$	10.4302	0.832419	0.416210	−	0.909269i	$-0.363358\pi$
$157$	10.4302	0.832419	0.416210	+	0.909269i	$0.363358\pi$
$158$	15.8950	1.26454
$159$	−7.21509	−0.572194
$160$	3.98793	0.315273
$161$	8.51730	0.671258
$162$	5.99417	0.470947
$163$	−10.2439	−0.802362	−0.401181	−	0.915999i	$-0.631400\pi$
$163$	−10.2439	−0.802362	−0.401181	+	0.915999i	$0.631400\pi$
$164$	16.0105	1.25021
$165$	0	0
$166$	17.7386	1.37679
$167$	−1.04668	−0.0809947	−0.0404974	−	0.999180i	$-0.512894\pi$
$167$	−1.04668	−0.0809947	−0.0404974	+	0.999180i	$0.512894\pi$
$168$	−34.5628	−2.66658
$169$	−10.8016	−0.830893
$170$	8.76700	0.672399
$171$	−16.7670	−1.28220
$172$	18.9354	1.44381
$173$	11.9129	0.905720	0.452860	−	0.891582i	$-0.350404\pi$
$173$	11.9129	0.905720	0.452860	+	0.891582i	$0.350404\pi$
$174$	31.6274	2.39767
$175$	−3.38350	−0.255769
$176$	0	0
$177$	34.1447	2.56647
$178$	25.3718	1.90170
$179$	−3.39558	−0.253797	−0.126899	−	0.991916i	$-0.540502\pi$
$179$	−3.39558	−0.253797	−0.126899	+	0.991916i	$0.540502\pi$
$180$	−18.3431	−1.36721
$181$	−5.69779	−0.423513	−0.211757	−	0.977322i	$-0.567918\pi$
$181$	−5.69779	−0.423513	−0.211757	+	0.977322i	$0.567918\pi$
$182$	−11.7837	−0.873467
$183$	−39.2093	−2.89843
$184$	−8.97164	−0.661398
$185$	2.69779	0.198345
$186$	62.0397	4.54897
$187$	0	0
$188$	−37.0350	−2.70106
$189$	−21.4815	−1.56255
$190$	7.55191	0.547873
$191$	−9.01671	−0.652426	−0.326213	−	0.945296i	$-0.605773\pi$
$191$	−9.01671	−0.652426	−0.326213	+	0.945296i	$0.605773\pi$
$192$	−34.5115	−2.49065
$193$	26.2318	1.88821	0.944103	−	0.329650i	$-0.106931\pi$
$193$	26.2318	1.88821	0.944103	+	0.329650i	$0.106931\pi$
$194$	25.8771	1.85787
$195$	−4.24970	−0.304327
$196$	15.6453	1.11752
$197$	−16.6978	−1.18967	−0.594834	−	0.803849i	$-0.702782\pi$
$197$	−16.6978	−1.18967	−0.594834	+	0.803849i	$0.702782\pi$
$198$	0	0
$199$	−16.7912	−1.19029	−0.595147	−	0.803617i	$-0.702906\pi$
$199$	−16.7912	−1.19029	−0.595147	+	0.803617i	$0.702906\pi$
$200$	3.56399	0.252012
$201$	22.4469	1.58328
$202$	−29.9071	−2.10425
$203$	−15.8950	−1.11561
$204$	−37.6274	−2.63444
$205$	−4.55191	−0.317919
$206$	−43.0859	−3.00194
$207$	−13.1280	−0.912457
$208$	1.98210	0.137434
$209$	0	0
$210$	22.7791	1.57191
$211$	7.64528	0.526323	0.263161	−	0.964752i	$-0.415235\pi$
$211$	7.64528	0.526323	0.263161	+	0.964752i	$0.415235\pi$
$212$	−8.85412	−0.608104
$213$	7.21509	0.494370
$214$	16.7565	1.14545
$215$	−5.38350	−0.367152
$216$	22.6274	1.53960
$217$	−31.1793	−2.11659
$218$	9.73822	0.659556
$219$	−8.49940	−0.574336
$220$	0	0
$221$	−5.53401	−0.372258
$222$	−18.1626	−1.21899
$223$	−3.78954	−0.253766	−0.126883	−	0.991918i	$-0.540497\pi$
$223$	−3.78954	−0.253766	−0.126883	+	0.991918i	$0.540497\pi$
$224$	13.4932	0.901549
$225$	5.21509	0.347673
$226$	3.44064	0.228868
$227$	−19.5461	−1.29732	−0.648660	−	0.761079i	$-0.724670\pi$
$227$	−19.5461	−1.29732	−0.648660	+	0.761079i	$0.724670\pi$
$228$	−32.4123	−2.14656
$229$	5.16258	0.341153	0.170576	−	0.985344i	$-0.445437\pi$
$229$	5.16258	0.341153	0.170576	+	0.985344i	$0.445437\pi$
$230$	5.91288	0.389884
$231$	0	0
$232$	16.7429	1.09922
$233$	6.24970	0.409431	0.204716	−	0.978821i	$-0.434373\pi$
$233$	6.24970	0.409431	0.204716	+	0.978821i	$0.434373\pi$
$234$	18.1626	1.18733
$235$	10.5294	0.686861
$236$	41.9012	2.72754
$237$	19.3956	1.25988
$238$	29.6632	1.92278
$239$	4.61067	0.298239	0.149120	−	0.988819i	$-0.452356\pi$
$239$	4.61067	0.298239	0.149120	+	0.988819i	$0.452356\pi$
$240$	−3.83159	−0.247328
$241$	7.87827	0.507484	0.253742	−	0.967272i	$-0.418339\pi$
$241$	7.87827	0.507484	0.253742	+	0.967272i	$0.418339\pi$
$242$	0	0
$243$	−11.7324	−0.752634
$244$	−48.1163	−3.08033
$245$	−4.44809	−0.284178
$246$	30.6453	1.95387
$247$	−4.76700	−0.303317
$248$	32.8425	2.08550
$249$	21.6453	1.37171
$250$	−2.34889	−0.148557
$251$	10.6557	0.672584	0.336292	−	0.941758i	$-0.390827\pi$
$251$	10.6557	0.672584	0.336292	+	0.941758i	$0.390827\pi$
$252$	−62.0638	−3.90965
$253$	0	0
$254$	26.5340	1.66489
$255$	10.6978	0.669921
$256$	−23.6169	−1.47606
$257$	2.80906	0.175224	0.0876121	−	0.996155i	$-0.472076\pi$
$257$	2.80906	0.175224	0.0876121	+	0.996155i	$0.472076\pi$
$258$	36.2439	2.25644
$259$	9.12797	0.567185
$260$	−5.21509	−0.323426
$261$	24.4994	1.51647
$262$	−34.4815	−2.13027
$263$	27.6453	1.70468	0.852340	−	0.522987i	$-0.175183\pi$
$263$	27.6453	1.70468	0.852340	+	0.522987i	$0.175183\pi$
$264$	0	0
$265$	2.51730	0.154637
$266$	25.5519	1.56669
$267$	30.9596	1.89469
$268$	27.5461	1.68264
$269$	−14.5761	−0.888718	−0.444359	−	0.895849i	$-0.646569\pi$
$269$	−14.5761	−0.888718	−0.444359	+	0.895849i	$0.646569\pi$
$270$	−14.9129	−0.907569
$271$	−2.16258	−0.131367	−0.0656837	−	0.997840i	$-0.520923\pi$
$271$	−2.16258	−0.131367	−0.0656837	+	0.997840i	$0.520923\pi$
$272$	−4.98954	−0.302535
$273$	−14.3789	−0.870249
$274$	−36.7491	−2.22009
$275$	0	0
$276$	−25.3777	−1.52756
$277$	−15.3022	−0.919421	−0.459710	−	0.888069i	$-0.652047\pi$
$277$	−15.3022	−0.919421	−0.459710	+	0.888069i	$0.652047\pi$
$278$	17.9579	1.07705
$279$	48.0576	2.87713
$280$	12.0588	0.720649
$281$	2.13843	0.127568	0.0637841	−	0.997964i	$-0.479683\pi$
$281$	2.13843	0.127568	0.0637841	+	0.997964i	$0.479683\pi$
$282$	−70.8880	−4.22132
$283$	4.33099	0.257451	0.128725	−	0.991680i	$-0.458911\pi$
$283$	4.33099	0.257451	0.128725	+	0.991680i	$0.458911\pi$
$284$	8.85412	0.525396
$285$	9.21509	0.545855
$286$	0	0
$287$	−15.4014	−0.909116
$288$	−20.7974	−1.22550
$289$	−3.06922	−0.180542
$290$	−11.0346	−0.647974
$291$	31.5761	1.85102
$292$	−10.4302	−0.610380
$293$	−13.5068	−0.789078	−0.394539	−	0.918879i	$-0.629096\pi$
$293$	−13.5068	−0.789078	−0.394539	+	0.918879i	$0.629096\pi$
$294$	29.9463	1.74650
$295$	−11.9129	−0.693595
$296$	−9.61488	−0.558854
$297$	0	0
$298$	15.2272	0.882086
$299$	−3.73240	−0.215850
$300$	10.0813	0.582044
$301$	−18.2151	−1.04990
$302$	25.5519	1.47035
$303$	−36.4936	−2.09650
$304$	−4.29800	−0.246507
$305$	13.6799	0.783308
$306$	−45.7207	−2.61368
$307$	−2.37887	−0.135769	−0.0678847	−	0.997693i	$-0.521625\pi$
$307$	−2.37887	−0.135769	−0.0678847	+	0.997693i	$0.521625\pi$
$308$	0	0
$309$	−52.5749	−2.99088
$310$	−21.6453	−1.22937
$311$	−22.1447	−1.25571	−0.627855	−	0.778331i	$-0.716067\pi$
$311$	−22.1447	−1.25571	−0.627855	+	0.778331i	$0.716067\pi$
$312$	15.1459	0.857466
$313$	−27.2843	−1.54220	−0.771100	−	0.636714i	$-0.780293\pi$
$313$	−27.2843	−1.54220	−0.771100	+	0.636714i	$0.780293\pi$
$314$	24.4994	1.38258
$315$	17.6453	0.994199
$316$	23.8016	1.33895
$317$	−15.3956	−0.864702	−0.432351	−	0.901705i	$-0.642316\pi$
$317$	−15.3956	−0.864702	−0.432351	+	0.901705i	$0.642316\pi$
$318$	−16.9475	−0.950368
$319$	0	0
$320$	12.0409	0.673104
$321$	20.4469	1.14123
$322$	20.0062	1.11490
$323$	12.0000	0.667698
$324$	8.97585	0.498658
$325$	1.48270	0.0822452
$326$	−24.0618	−1.33266
$327$	11.8829	0.657126
$328$	16.2230	0.895763
$329$	35.6262	1.96413
$330$	0	0
$331$	25.9129	1.42430	0.712150	−	0.702027i	$-0.247721\pi$
$331$	25.9129	1.42430	0.712150	+	0.702027i	$0.247721\pi$
$332$	26.5624	1.45780
$333$	−14.0692	−0.770988
$334$	−2.45855	−0.134526
$335$	−7.83159	−0.427885
$336$	−12.9642	−0.707255
$337$	13.9821	0.761653	0.380827	−	0.924646i	$-0.375639\pi$
$337$	13.9821	0.761653	0.380827	+	0.924646i	$0.375639\pi$
$338$	−25.3718	−1.38005
$339$	4.19839	0.228025
$340$	13.1280	0.711964
$341$	0	0
$342$	−39.3839	−2.12964
$343$	8.63440	0.466214
$344$	19.1867	1.03448
$345$	7.21509	0.388448
$346$	27.9821	1.50433
$347$	−31.0467	−1.66667	−0.833337	−	0.552766i	$-0.813572\pi$
$347$	−31.0467	−1.66667	−0.833337	+	0.552766i	$0.813572\pi$
$348$	47.3598	2.53875
$349$	3.66318	0.196086	0.0980428	−	0.995182i	$-0.468742\pi$
$349$	3.66318	0.196086	0.0980428	+	0.995182i	$0.468742\pi$
$350$	−7.94749	−0.424811
$351$	9.41348	0.502454
$352$	0	0
$353$	24.5749	1.30799	0.653994	−	0.756500i	$-0.273092\pi$
$353$	24.5749	1.30799	0.653994	+	0.756500i	$0.273092\pi$
$354$	80.2022	4.26270
$355$	−2.51730	−0.133605
$356$	37.9926	2.01360
$357$	36.1960	1.91570
$358$	−7.97585	−0.421537
$359$	−6.58652	−0.347623	−0.173812	−	0.984779i	$-0.555608\pi$
$359$	−6.58652	−0.347623	−0.173812	+	0.984779i	$0.555608\pi$
$360$	−18.5865	−0.979596
$361$	−8.66318	−0.455957
$362$	−13.3835	−0.703421
$363$	0	0
$364$	−17.6453	−0.924864
$365$	2.96539	0.155216
$366$	−92.0984	−4.81406
$367$	8.16841	0.426388	0.213194	−	0.977010i	$-0.431613\pi$
$367$	8.16841	0.426388	0.213194	+	0.977010i	$0.431613\pi$
$368$	−3.36518	−0.175422
$369$	23.7386	1.23578
$370$	6.33682	0.329436
$371$	8.51730	0.442196
$372$	92.9000	4.81664
$373$	−27.0409	−1.40012	−0.700061	−	0.714083i	$-0.746844\pi$
$373$	−27.0409	−1.40012	−0.700061	+	0.714083i	$0.746844\pi$
$374$	0	0
$375$	−2.86620	−0.148010
$376$	−37.5266	−1.93528
$377$	6.96539	0.358736
$378$	−50.4578	−2.59527
$379$	32.6620	1.67773	0.838867	−	0.544337i	$-0.183219\pi$
$379$	32.6620	1.67773	0.838867	+	0.544337i	$0.183219\pi$
$380$	11.3085	0.580112
$381$	32.3777	1.65876
$382$	−21.1793	−1.08363
$383$	−2.64648	−0.135229	−0.0676143	−	0.997712i	$-0.521539\pi$
$383$	−2.64648	−0.135229	−0.0676143	+	0.997712i	$0.521539\pi$
$384$	−58.2034	−2.97018
$385$	0	0
$386$	61.6157	3.13616
$387$	28.0755	1.42716
$388$	38.7491	1.96719
$389$	−29.0513	−1.47296	−0.736480	−	0.676459i	$-0.763513\pi$
$389$	−29.0513	−1.47296	−0.736480	+	0.676459i	$0.763513\pi$
$390$	−9.98210	−0.505463
$391$	9.39558	0.475155
$392$	15.8529	0.800694
$393$	−42.0755	−2.12243
$394$	−39.2213	−1.97594
$395$	−6.76700	−0.340485
$396$	0	0
$397$	−9.35977	−0.469753	−0.234877	−	0.972025i	$-0.575469\pi$
$397$	−9.35977	−0.469753	−0.234877	+	0.972025i	$0.575469\pi$
$398$	−39.4406	−1.97698
$399$	31.1793	1.56092
$400$	1.33682	0.0668410
$401$	4.93078	0.246232	0.123116	−	0.992392i	$-0.460711\pi$
$401$	4.93078	0.246232	0.123116	+	0.992392i	$0.460711\pi$
$402$	52.7254	2.62970
$403$	13.6632	0.680611
$404$	−44.7837	−2.22807
$405$	−2.55191	−0.126806
$406$	−37.3356	−1.85294
$407$	0	0
$408$	−38.1268	−1.88756
$409$	−38.3085	−1.89423	−0.947116	−	0.320892i	$-0.896017\pi$
$409$	−38.3085	−1.89423	−0.947116	+	0.320892i	$0.896017\pi$
$410$	−10.6920	−0.528038
$411$	−44.8425	−2.21192
$412$	−64.5181	−3.17858
$413$	−40.3073	−1.98339
$414$	−30.8362	−1.51552
$415$	−7.55191	−0.370709
$416$	−5.91288	−0.289903
$417$	21.9129	1.07308
$418$	0	0
$419$	37.3777	1.82602	0.913009	−	0.407938i	$-0.133752\pi$
$419$	37.3777	1.82602	0.913009	+	0.407938i	$0.133752\pi$
$420$	34.1101	1.66440
$421$	29.4123	1.43347	0.716733	−	0.697347i	$-0.245636\pi$
$421$	29.4123	1.43347	0.716733	+	0.697347i	$0.245636\pi$
$422$	17.9579	0.874179
$423$	−54.9117	−2.66990
$424$	−8.97164	−0.435701
$425$	−3.73240	−0.181048
$426$	16.9475	0.821109
$427$	46.2859	2.23993
$428$	25.0917	1.21286
$429$	0	0
$430$	−12.6453	−0.609809
$431$	1.76820	0.0851713	0.0425857	−	0.999093i	$-0.486440\pi$
$431$	1.76820	0.0851713	0.0425857	+	0.999093i	$0.486440\pi$
$432$	8.48733	0.408347
$433$	10.0513	0.483035	0.241518	−	0.970396i	$-0.422355\pi$
$433$	10.0513	0.483035	0.241518	+	0.970396i	$0.422355\pi$
$434$	−73.2368	−3.51548
$435$	−13.4648	−0.645587
$436$	14.5823	0.698366
$437$	8.09337	0.387158
$438$	−19.9642	−0.953926
$439$	39.1972	1.87078	0.935390	−	0.353618i	$-0.115049\pi$
$439$	39.1972	1.87078	0.935390	+	0.353618i	$0.115049\pi$
$440$	0	0
$441$	23.1972	1.10463
$442$	−12.9988	−0.618290
$443$	−14.0121	−0.665734	−0.332867	−	0.942974i	$-0.608016\pi$
$443$	−14.0121	−0.665734	−0.332867	+	0.942974i	$0.608016\pi$
$444$	−27.1972	−1.29072
$445$	−10.8016	−0.512046
$446$	−8.90122	−0.421485
$447$	18.5807	0.878837
$448$	40.7403	1.92480
$449$	2.57606	0.121572	0.0607859	−	0.998151i	$-0.480639\pi$
$449$	2.57606	0.121572	0.0607859	+	0.998151i	$0.480639\pi$
$450$	12.2497	0.577456
$451$	0	0
$452$	5.15212	0.242335
$453$	31.1793	1.46493
$454$	−45.9117	−2.15474
$455$	5.01671	0.235187
$456$	−32.8425	−1.53799
$457$	15.1217	0.707365	0.353682	−	0.935366i	$-0.384929\pi$
$457$	15.1217	0.707365	0.353682	+	0.935366i	$0.384929\pi$
$458$	12.1264	0.566627
$459$	−23.6966	−1.10606
$460$	8.85412	0.412826
$461$	9.83622	0.458118	0.229059	−	0.973412i	$-0.426435\pi$
$461$	9.83622	0.458118	0.229059	+	0.973412i	$0.426435\pi$
$462$	0	0
$463$	21.2093	0.985678	0.492839	−	0.870120i	$-0.335959\pi$
$463$	21.2093	0.985678	0.492839	+	0.870120i	$0.335959\pi$
$464$	6.28010	0.291546
$465$	−26.4123	−1.22484
$466$	14.6799	0.680033
$467$	−9.56399	−0.442569	−0.221284	−	0.975209i	$-0.571025\pi$
$467$	−9.56399	−0.442569	−0.221284	+	0.975209i	$0.571025\pi$
$468$	27.1972	1.25719
$469$	−26.4982	−1.22357
$470$	24.7324	1.14082
$471$	29.8950	1.37749
$472$	42.4573	1.95426
$473$	0	0
$474$	45.5582	2.09256
$475$	−3.21509	−0.147519
$476$	44.4185	2.03592
$477$	−13.1280	−0.601089
$478$	10.8300	0.495352
$479$	−17.1972	−0.785760	−0.392880	−	0.919590i	$-0.628521\pi$
$479$	−17.1972	−0.785760	−0.392880	+	0.919590i	$0.628521\pi$
$480$	11.4302	0.521714
$481$	−4.00000	−0.182384
$482$	18.5052	0.842890
$483$	24.4123	1.11080
$484$	0	0
$485$	−11.0167	−0.500243
$486$	−27.5582	−1.25006
$487$	15.5519	0.704724	0.352362	−	0.935864i	$-0.385379\pi$
$487$	15.5519	0.704724	0.352362	+	0.935864i	$0.385379\pi$
$488$	−48.7549	−2.20703
$489$	−29.3610	−1.32775
$490$	−10.4481	−0.471996
$491$	−9.05876	−0.408816	−0.204408	−	0.978886i	$-0.565527\pi$
$491$	−9.05876	−0.408816	−0.204408	+	0.978886i	$0.565527\pi$
$492$	45.8891	2.06884
$493$	−17.5340	−0.789692
$494$	−11.1972	−0.503785
$495$	0	0
$496$	12.3189	0.553136
$497$	−8.51730	−0.382053
$498$	50.8425	2.27831
$499$	24.5686	1.09984	0.549921	−	0.835217i	$-0.314658\pi$
$499$	24.5686	1.09984	0.549921	+	0.835217i	$0.314658\pi$
$500$	−3.51730	−0.157299
$501$	−3.00000	−0.134030
$502$	25.0292	1.11711
$503$	−11.3322	−0.505277	−0.252639	−	0.967561i	$-0.581298\pi$
$503$	−11.3322	−0.505277	−0.252639	+	0.967561i	$0.581298\pi$
$504$	−62.8875	−2.80123
$505$	12.7324	0.566584
$506$	0	0
$507$	−30.9596	−1.37496
$508$	39.7328	1.76286
$509$	−26.4889	−1.17410	−0.587051	−	0.809550i	$-0.699711\pi$
$509$	−26.4889	−1.17410	−0.587051	+	0.809550i	$0.699711\pi$
$510$	25.1280	1.11269
$511$	10.0334	0.443852
$512$	−14.8600	−0.656723
$513$	−20.4123	−0.901224
$514$	6.59818	0.291033
$515$	18.3431	0.808292
$516$	54.2727	2.38922
$517$	0	0
$518$	21.4406	0.942048
$519$	34.1447	1.49879
$520$	−5.28431	−0.231732
$521$	26.6966	1.16960	0.584799	−	0.811178i	$-0.301173\pi$
$521$	26.6966	1.16960	0.584799	+	0.811178i	$0.301173\pi$
$522$	57.5465	2.51874
$523$	−4.85412	−0.212256	−0.106128	−	0.994352i	$-0.533845\pi$
$523$	−4.85412	−0.212256	−0.106128	+	0.994352i	$0.533845\pi$
$524$	−51.6336	−2.25563
$525$	−9.69779	−0.423246
$526$	64.9358	2.83134
$527$	−34.3944	−1.49824
$528$	0	0
$529$	−16.6632	−0.724486
$530$	5.91288	0.256839
$531$	62.1268	2.69607
$532$	38.2622	1.65888
$533$	6.74910	0.292336
$534$	72.7207	3.14693
$535$	−7.13380	−0.308421
$536$	27.9117	1.20560
$537$	−9.73240	−0.419984
$538$	−34.2376	−1.47609
$539$	0	0
$540$	−22.3310	−0.960973
$541$	19.8246	0.852325	0.426162	−	0.904647i	$-0.359865\pi$
$541$	19.8246	0.852325	0.426162	+	0.904647i	$0.359865\pi$
$542$	−5.07968	−0.218191
$543$	−16.3310	−0.700830
$544$	14.8845	0.638168
$545$	−4.14588	−0.177590
$546$	−33.7744	−1.44541
$547$	14.6557	0.626634	0.313317	−	0.949649i	$-0.398560\pi$
$547$	14.6557	0.626634	0.313317	+	0.949649i	$0.398560\pi$
$548$	−55.0292	−2.35073
$549$	−71.3419	−3.04480
$550$	0	0
$551$	−15.1038	−0.643445
$552$	−25.7145	−1.09448
$553$	−22.8962	−0.973644
$554$	−35.9433	−1.52708
$555$	7.73240	0.328222
$556$	26.8908	1.14042
$557$	5.83742	0.247339	0.123670	−	0.992323i	$-0.460534\pi$
$557$	5.83742	0.247339	0.123670	+	0.992323i	$0.460534\pi$
$558$	112.882	4.77868
$559$	7.98210	0.337607
$560$	4.52313	0.191137
$561$	0	0
$562$	5.02295	0.211880
$563$	−39.3026	−1.65641	−0.828204	−	0.560426i	$-0.810637\pi$
$563$	−39.3026	−1.65641	−0.828204	+	0.560426i	$0.810637\pi$
$564$	−106.150	−4.46971
$565$	−1.46479	−0.0616243
$566$	10.1730	0.427605
$567$	−8.63440	−0.362611
$568$	8.97164	0.376442
$569$	−8.11007	−0.339992	−0.169996	−	0.985445i	$-0.554375\pi$
$569$	−8.11007	−0.339992	−0.169996	+	0.985445i	$0.554375\pi$
$570$	21.6453	0.906621
$571$	35.6274	1.49096	0.745480	−	0.666528i	$-0.232220\pi$
$571$	35.6274	1.49096	0.745480	+	0.666528i	$0.232220\pi$
$572$	0	0
$573$	−25.8437	−1.07963
$574$	−36.1763	−1.50997
$575$	−2.51730	−0.104979
$576$	−62.7942	−2.61642
$577$	−31.8529	−1.32605	−0.663027	−	0.748595i	$-0.730729\pi$
$577$	−31.8529	−1.32605	−0.663027	+	0.748595i	$0.730729\pi$
$578$	−7.20926	−0.299866
$579$	75.1855	3.12460
$580$	−16.5236	−0.686103
$581$	−25.5519	−1.06007
$582$	74.1688	3.07440
$583$	0	0
$584$	−10.5686	−0.437332
$585$	−7.73240	−0.319695
$586$	−31.7262	−1.31060
$587$	−44.3823	−1.83185	−0.915927	−	0.401345i	$-0.868543\pi$
$587$	−44.3823	−1.83185	−0.915927	+	0.401345i	$0.868543\pi$
$588$	44.8425	1.84927
$589$	−29.6274	−1.22077
$590$	−27.9821	−1.15200
$591$	−47.8592	−1.96866
$592$	−3.60646	−0.148224
$593$	−41.9463	−1.72253	−0.861264	−	0.508158i	$-0.830327\pi$
$593$	−41.9463	−1.72253	−0.861264	+	0.508158i	$0.830327\pi$
$594$	0	0
$595$	−12.6286	−0.517721
$596$	22.8016	0.933990
$597$	−48.1268	−1.96970
$598$	−8.76700	−0.358509
$599$	16.6107	0.678694	0.339347	−	0.940661i	$-0.389794\pi$
$599$	16.6107	0.678694	0.339347	+	0.940661i	$0.389794\pi$
$600$	10.2151	0.417029
$601$	−13.1972	−0.538325	−0.269162	−	0.963095i	$-0.586747\pi$
$601$	−13.1972	−0.538325	−0.269162	+	0.963095i	$0.586747\pi$
$602$	−42.7853	−1.74380
$603$	40.8425	1.66323
$604$	38.2622	1.55687
$605$	0	0
$606$	−85.7195	−3.48212
$607$	−9.04085	−0.366957	−0.183478	−	0.983024i	$-0.558736\pi$
$607$	−9.04085	−0.366957	−0.183478	+	0.983024i	$0.558736\pi$
$608$	12.8215	0.519982
$609$	−45.5582	−1.84611
$610$	32.1326	1.30101
$611$	−15.6119	−0.631589
$612$	−68.4636	−2.76748
$613$	−7.66318	−0.309513	−0.154756	−	0.987953i	$-0.549459\pi$
$613$	−7.66318	−0.309513	−0.154756	+	0.987953i	$0.549459\pi$
$614$	−5.58772	−0.225502
$615$	−13.0467	−0.526093
$616$	0	0
$617$	−2.67989	−0.107888	−0.0539441	−	0.998544i	$-0.517179\pi$
$617$	−2.67989	−0.107888	−0.0539441	+	0.998544i	$0.517179\pi$
$618$	−123.493	−4.96761
$619$	8.17424	0.328550	0.164275	−	0.986415i	$-0.447471\pi$
$619$	8.17424	0.328550	0.164275	+	0.986415i	$0.447471\pi$
$620$	−32.4123	−1.30171
$621$	−15.9821	−0.641339
$622$	−52.0155	−2.08563
$623$	−36.5473	−1.46424
$624$	5.68108	0.227425
$625$	1.00000	0.0400000
$626$	−64.0880	−2.56147
$627$	0	0
$628$	36.6861	1.46394
$629$	10.0692	0.401486
$630$	41.4469	1.65128
$631$	5.56982	0.221731	0.110865	−	0.993835i	$-0.464638\pi$
$631$	5.56982	0.221731	0.110865	+	0.993835i	$0.464638\pi$
$632$	24.1175	0.959343
$633$	21.9129	0.870959
$634$	−36.1626	−1.43620
$635$	−11.2964	−0.448283
$636$	−25.3777	−1.00629
$637$	6.59516	0.261310
$638$	0	0
$639$	13.1280	0.519335
$640$	20.3068	0.802698
$641$	−13.2906	−0.524945	−0.262473	−	0.964939i	$-0.584538\pi$
$641$	−13.2906	−0.524945	−0.262473	+	0.964939i	$0.584538\pi$
$642$	48.0276	1.89550
$643$	17.8137	0.702503	0.351252	−	0.936281i	$-0.385756\pi$
$643$	17.8137	0.702503	0.351252	+	0.936281i	$0.385756\pi$
$644$	29.9579	1.18051
$645$	−15.4302	−0.607563
$646$	28.1867	1.10899
$647$	−25.8829	−1.01756	−0.508781	−	0.860896i	$-0.669904\pi$
$647$	−25.8829	−1.01756	−0.508781	+	0.860896i	$0.669904\pi$
$648$	9.09498	0.357285
$649$	0	0
$650$	3.48270	0.136603
$651$	−89.3660	−3.50253
$652$	−36.0308	−1.41108
$653$	13.3356	0.521863	0.260932	−	0.965357i	$-0.415970\pi$
$653$	13.3356	0.521863	0.260932	+	0.965357i	$0.415970\pi$
$654$	27.9117	1.09143
$655$	14.6799	0.573591
$656$	6.08509	0.237583
$657$	−15.4648	−0.603339
$658$	83.6821	3.26227
$659$	−24.4877	−0.953907	−0.476954	−	0.878929i	$-0.658259\pi$
$659$	−24.4877	−0.953907	−0.476954	+	0.878929i	$0.658259\pi$
$660$	0	0
$661$	−23.2738	−0.905248	−0.452624	−	0.891702i	$-0.649512\pi$
$661$	−23.2738	−0.905248	−0.452624	+	0.891702i	$0.649512\pi$
$662$	60.8666	2.36565
$663$	−15.8616	−0.616012
$664$	26.9149	1.04450
$665$	−10.8783	−0.421841
$666$	−33.0471	−1.28055
$667$	−11.8258	−0.457895
$668$	−3.68150	−0.142442
$669$	−10.8616	−0.419932
$670$	−18.3956	−0.710683
$671$	0	0
$672$	38.6741	1.49188
$673$	11.3443	0.437289	0.218645	−	0.975805i	$-0.429836\pi$
$673$	11.3443	0.437289	0.218645	+	0.975805i	$0.429836\pi$
$674$	32.8425	1.26504
$675$	6.34889	0.244369
$676$	−37.9926	−1.46125
$677$	−21.3956	−0.822299	−0.411149	−	0.911568i	$-0.634873\pi$
$677$	−21.3956	−0.822299	−0.411149	+	0.911568i	$0.634873\pi$
$678$	9.86157	0.378731
$679$	−37.2750	−1.43049
$680$	13.3022	0.510117
$681$	−56.0230	−2.14680
$682$	0	0
$683$	−5.11590	−0.195754	−0.0978772	−	0.995198i	$-0.531205\pi$
$683$	−5.11590	−0.195754	−0.0978772	+	0.995198i	$0.531205\pi$
$684$	−58.9747	−2.25495
$685$	15.6453	0.597775
$686$	20.2813	0.774343
$687$	14.7970	0.564540
$688$	7.19677	0.274374
$689$	−3.73240	−0.142193
$690$	16.9475	0.645180
$691$	−22.9117	−0.871602	−0.435801	−	0.900043i	$-0.643535\pi$
$691$	−22.9117	−0.871602	−0.435801	+	0.900043i	$0.643535\pi$
$692$	41.9012	1.59285
$693$	0	0
$694$	−72.9254	−2.76821
$695$	−7.64528	−0.290002
$696$	47.9883	1.81899
$697$	−16.9895	−0.643525
$698$	8.60442	0.325682
$699$	17.9129	0.677527
$700$	−11.9008	−0.449808
$701$	−37.9191	−1.43219	−0.716093	−	0.698005i	$-0.754071\pi$
$701$	−37.9191	−1.43219	−0.716093	+	0.698005i	$0.754071\pi$
$702$	22.1113	0.834536
$703$	8.67364	0.327133
$704$	0	0
$705$	30.1793	1.13662
$706$	57.7238	2.17246
$707$	43.0801	1.62019
$708$	120.097	4.51353
$709$	−5.27686	−0.198177	−0.0990884	−	0.995079i	$-0.531593\pi$
$709$	−5.27686	−0.198177	−0.0990884	+	0.995079i	$0.531593\pi$
$710$	−5.91288	−0.221906
$711$	35.2906	1.32350
$712$	38.4968	1.44273
$713$	−23.1972	−0.868742
$714$	85.0206	3.18181
$715$	0	0
$716$	−11.9433	−0.446341
$717$	13.2151	0.493527
$718$	−15.4710	−0.577374
$719$	30.9117	1.15281	0.576406	−	0.817164i	$-0.304455\pi$
$719$	30.9117	1.15281	0.576406	+	0.817164i	$0.304455\pi$
$720$	−6.97164	−0.259818
$721$	62.0638	2.31138
$722$	−20.3489	−0.757307
$723$	22.5807	0.839785
$724$	−20.0409	−0.744812
$725$	4.69779	0.174471
$726$	0	0
$727$	8.24387	0.305748	0.152874	−	0.988246i	$-0.451147\pi$
$727$	8.24387	0.305748	0.152874	+	0.988246i	$0.451147\pi$
$728$	−17.8795	−0.662657
$729$	−41.2831	−1.52900
$730$	6.96539	0.257801
$731$	−20.0934	−0.743180
$732$	−137.911	−5.09733
$733$	43.3839	1.60242	0.801211	−	0.598382i	$-0.204190\pi$
$733$	43.3839	1.60242	0.801211	+	0.598382i	$0.204190\pi$
$734$	19.1867	0.708195
$735$	−12.7491	−0.470258
$736$	10.0388	0.370036
$737$	0	0
$738$	55.7596	2.05254
$739$	0.301014	0.0110730	0.00553649	−	0.999985i	$-0.498238\pi$
$739$	0.301014	0.0110730	0.00553649	+	0.999985i	$0.498238\pi$
$740$	9.48894	0.348820
$741$	−13.6632	−0.501929
$742$	20.0062	0.734452
$743$	31.5040	1.15577	0.577885	−	0.816118i	$-0.303878\pi$
$743$	31.5040	1.15577	0.577885	+	0.816118i	$0.303878\pi$
$744$	94.1330	3.45108
$745$	−6.48270	−0.237508
$746$	−63.5161	−2.32549
$747$	39.3839	1.44098
$748$	0	0
$749$	−24.1372	−0.881955
$750$	−6.73240	−0.245832
$751$	33.2906	1.21479	0.607395	−	0.794400i	$-0.292215\pi$
$751$	33.2906	1.21479	0.607395	+	0.794400i	$0.292215\pi$
$752$	−14.0759	−0.513295
$753$	30.5415	1.11299
$754$	16.3610	0.595831
$755$	−10.8783	−0.395901
$756$	−75.5570	−2.74798
$757$	15.5068	0.563606	0.281803	−	0.959472i	$-0.409068\pi$
$757$	15.5068	0.563606	0.281803	+	0.959472i	$0.409068\pi$
$758$	76.7195	2.78658
$759$	0	0
$760$	11.4585	0.415645
$761$	−52.3944	−1.89929	−0.949647	−	0.313321i	$-0.898559\pi$
$761$	−52.3944	−1.89929	−0.949647	+	0.313321i	$0.898559\pi$
$762$	76.0517	2.75506
$763$	−14.0276	−0.507833
$764$	−31.7145	−1.14739
$765$	19.4648	0.703751
$766$	−6.21629	−0.224604
$767$	17.6632	0.637780
$768$	−67.6908	−2.44258
$769$	44.2652	1.59624	0.798122	−	0.602496i	$-0.205827\pi$
$769$	44.2652	1.59624	0.798122	+	0.602496i	$0.205827\pi$
$770$	0	0
$771$	8.05131	0.289961
$772$	92.2652	3.32070
$773$	−35.3177	−1.27029	−0.635145	−	0.772393i	$-0.719060\pi$
$773$	−35.3177	−1.27029	−0.635145	+	0.772393i	$0.719060\pi$
$774$	65.9463	2.37039
$775$	9.21509	0.331016
$776$	39.2634	1.40947
$777$	26.1626	0.938577
$778$	−68.2385	−2.44647
$779$	−14.6348	−0.524347
$780$	−14.9475	−0.535206
$781$	0	0
$782$	22.0692	0.789194
$783$	29.8258	1.06589
$784$	5.94629	0.212368
$785$	−10.4302	−0.372269
$786$	−98.8308	−3.52518
$787$	−36.6920	−1.30793	−0.653964	−	0.756526i	$-0.726895\pi$
$787$	−36.6920	−1.30793	−0.653964	+	0.756526i	$0.726895\pi$
$788$	−58.7312	−2.09221
$789$	79.2368	2.82091
$790$	−15.8950	−0.565518
$791$	−4.95613	−0.176220
$792$	0	0
$793$	−20.2831	−0.720274
$794$	−21.9851	−0.780222
$795$	7.21509	0.255893
$796$	−59.0596	−2.09331
$797$	−2.85412	−0.101098	−0.0505491	−	0.998722i	$-0.516097\pi$
$797$	−2.85412	−0.101098	−0.0505491	+	0.998722i	$0.516097\pi$
$798$	73.2368	2.59256
$799$	39.2998	1.39033
$800$	−3.98793	−0.140994
$801$	56.3314	1.99037
$802$	11.5819	0.408971
$803$	0	0
$804$	78.9525	2.78444
$805$	−8.51730	−0.300196
$806$	32.0934	1.13044
$807$	−41.7779	−1.47065
$808$	−45.3781	−1.59640
$809$	−26.0934	−0.917394	−0.458697	−	0.888593i	$-0.651684\pi$
$809$	−26.0934	−0.917394	−0.458697	+	0.888593i	$0.651684\pi$
$810$	−5.99417	−0.210614
$811$	19.6453	0.689839	0.344919	−	0.938632i	$-0.387906\pi$
$811$	19.6453	0.689839	0.344919	+	0.938632i	$0.387906\pi$
$812$	−55.9075	−1.96197
$813$	−6.19839	−0.217387
$814$	0	0
$815$	10.2439	0.358827
$816$	−14.3010	−0.500636
$817$	−17.3085	−0.605546
$818$	−89.9825	−3.14616
$819$	−26.1626	−0.914195
$820$	−16.0105	−0.559109
$821$	51.9117	1.81173	0.905865	−	0.423566i	$-0.139222\pi$
$821$	51.9117	1.81173	0.905865	+	0.423566i	$0.139222\pi$
$822$	−105.330	−3.67381
$823$	15.9250	0.555109	0.277555	−	0.960710i	$-0.410476\pi$
$823$	15.9250	0.555109	0.277555	+	0.960710i	$0.410476\pi$
$824$	−65.3744	−2.27743
$825$	0	0
$826$	−94.6775	−3.29425
$827$	−9.77164	−0.339793	−0.169897	−	0.985462i	$-0.554343\pi$
$827$	−9.77164	−0.339793	−0.169897	+	0.985462i	$0.554343\pi$
$828$	−46.1751	−1.60469
$829$	1.01790	0.0353532	0.0176766	−	0.999844i	$-0.494373\pi$
$829$	1.01790	0.0353532	0.0176766	+	0.999844i	$0.494373\pi$
$830$	−17.7386	−0.615717
$831$	−43.8592	−1.52146
$832$	−17.8529	−0.618939
$833$	−16.6020	−0.575226
$834$	51.4710	1.78230
$835$	1.04668	0.0362219
$836$	0	0
$837$	58.5056	2.02225
$838$	87.7962	3.03287
$839$	13.7900	0.476082	0.238041	−	0.971255i	$-0.423495\pi$
$839$	13.7900	0.476082	0.238041	+	0.971255i	$0.423495\pi$
$840$	34.5628	1.19253
$841$	−6.93078	−0.238993
$842$	69.0863	2.38087
$843$	6.12917	0.211100
$844$	26.8908	0.925618
$845$	10.8016	0.371587
$846$	−128.982	−4.43448
$847$	0	0
$848$	−3.36518	−0.115561
$849$	12.4135	0.426030
$850$	−8.76700	−0.300706
$851$	6.79115	0.232798
$852$	25.3777	0.869425
$853$	27.3264	0.935637	0.467818	−	0.883825i	$-0.345040\pi$
$853$	27.3264	0.935637	0.467818	+	0.883825i	$0.345040\pi$
$854$	108.721	3.72035
$855$	16.7670	0.573419
$856$	25.4248	0.869001
$857$	22.2318	0.759424	0.379712	−	0.925105i	$-0.376023\pi$
$857$	22.2318	0.759424	0.379712	+	0.925105i	$0.376023\pi$
$858$	0	0
$859$	28.5173	0.972998	0.486499	−	0.873681i	$-0.338274\pi$
$859$	28.5173	0.972998	0.486499	+	0.873681i	$0.338274\pi$
$860$	−18.9354	−0.645692
$861$	−44.1435	−1.50441
$862$	4.15332	0.141463
$863$	52.2594	1.77893	0.889465	−	0.457003i	$-0.151077\pi$
$863$	52.2594	1.77893	0.889465	+	0.457003i	$0.151077\pi$
$864$	−25.3189	−0.861367
$865$	−11.9129	−0.405050
$866$	23.6095	0.802283
$867$	−8.79698	−0.298761
$868$	−109.667	−3.72234
$869$	0	0
$870$	−31.6274	−1.07227
$871$	11.6119	0.393453
$872$	14.7758	0.500373
$873$	57.4531	1.94449
$874$	19.0105	0.643038
$875$	3.38350	0.114383
$876$	−29.8950	−1.01006
$877$	−21.0074	−0.709371	−0.354685	−	0.934986i	$-0.615412\pi$
$877$	−21.0074	−0.709371	−0.354685	+	0.934986i	$0.615412\pi$
$878$	92.0701	3.10721
$879$	−38.7133	−1.30577
$880$	0	0
$881$	46.0743	1.55228	0.776141	−	0.630560i	$-0.217175\pi$
$881$	46.0743	1.55228	0.776141	+	0.630560i	$0.217175\pi$
$882$	54.4877	1.83470
$883$	0.622326	0.0209429	0.0104715	−	0.999945i	$-0.496667\pi$
$883$	0.622326	0.0209429	0.0104715	+	0.999945i	$0.496667\pi$
$884$	−19.4648	−0.654672
$885$	−34.1447	−1.14776
$886$	−32.9129	−1.10573
$887$	11.4077	0.383031	0.191516	−	0.981490i	$-0.438660\pi$
$887$	11.4077	0.383031	0.191516	+	0.981490i	$0.438660\pi$
$888$	−27.5582	−0.924791
$889$	−38.2213	−1.28190
$890$	−25.3718	−0.850466
$891$	0	0
$892$	−13.3290	−0.446287
$893$	33.8529	1.13284
$894$	43.6441	1.45968
$895$	3.39558	0.113502
$896$	68.7082	2.29538
$897$	−10.6978	−0.357189
$898$	6.05090	0.201921
$899$	43.2906	1.44382
$900$	18.3431	0.611436
$901$	9.39558	0.313012
$902$	0	0
$903$	−52.2081	−1.73738
$904$	5.22050	0.173631
$905$	5.69779	0.189401
$906$	73.2368	2.43313
$907$	38.9175	1.29223	0.646117	−	0.763238i	$-0.276392\pi$
$907$	38.9175	1.29223	0.646117	+	0.763238i	$0.276392\pi$
$908$	−68.7495	−2.28153
$909$	−66.4006	−2.20237
$910$	11.7837	0.390626
$911$	38.0934	1.26209	0.631045	−	0.775746i	$-0.282626\pi$
$911$	38.0934	1.26209	0.631045	+	0.775746i	$0.282626\pi$
$912$	−12.3189	−0.407920
$913$	0	0
$914$	35.5193	1.17488
$915$	39.2093	1.29622
$916$	18.1584	0.599969
$917$	49.6694	1.64023
$918$	−55.6608	−1.83708
$919$	−19.2727	−0.635746	−0.317873	−	0.948133i	$-0.602969\pi$
$919$	−19.2727	−0.635746	−0.317873	+	0.948133i	$0.602969\pi$
$920$	8.97164	0.295786
$921$	−6.81832	−0.224671
$922$	23.1042	0.760898
$923$	3.73240	0.122853
$924$	0	0
$925$	−2.69779	−0.0887027
$926$	49.8183	1.63713
$927$	−95.6608	−3.14191
$928$	−18.7344	−0.614988
$929$	31.1730	1.02275	0.511377	−	0.859356i	$-0.329136\pi$
$929$	31.1730	1.02275	0.511377	+	0.859356i	$0.329136\pi$
$930$	−62.0397	−2.03436
$931$	−14.3010	−0.468697
$932$	21.9821	0.720048
$933$	−63.4710	−2.07795
$934$	−22.4648	−0.735070
$935$	0	0
$936$	27.5582	0.900767
$937$	−25.8708	−0.845163	−0.422582	−	0.906325i	$-0.638876\pi$
$937$	−25.8708	−0.845163	−0.422582	+	0.906325i	$0.638876\pi$
$938$	−62.2415	−2.03226
$939$	−78.2022	−2.55203
$940$	37.0350	1.20795
$941$	−29.4636	−0.960486	−0.480243	−	0.877136i	$-0.659451\pi$
$941$	−29.4636	−0.960486	−0.480243	+	0.877136i	$0.659451\pi$
$942$	70.2201	2.28790
$943$	−11.4585	−0.373142
$944$	15.9254	0.518327
$945$	21.4815	0.698793
$946$	0	0
$947$	−14.3881	−0.467551	−0.233776	−	0.972291i	$-0.575108\pi$
$947$	−14.3881	−0.467551	−0.233776	+	0.972291i	$0.575108\pi$
$948$	68.2201	2.21569
$949$	−4.39677	−0.142725
$950$	−7.55191	−0.245016
$951$	−44.1268	−1.43091
$952$	45.0081	1.45872
$953$	31.9191	1.03396	0.516981	−	0.855997i	$-0.327056\pi$
$953$	31.9191	1.03396	0.516981	+	0.855997i	$0.327056\pi$
$954$	−30.8362	−0.998360
$955$	9.01671	0.291774
$956$	16.2171	0.524499
$957$	0	0
$958$	−40.3944	−1.30508
$959$	52.9358	1.70939
$960$	34.5115	1.11385
$961$	53.9179	1.73929
$962$	−9.39558	−0.302926
$963$	37.2034	1.19886
$964$	27.7103	0.892488
$965$	−26.2318	−0.844431
$966$	57.3419	1.84494
$967$	−46.8425	−1.50635	−0.753176	−	0.657819i	$-0.771479\pi$
$967$	−46.8425	−1.50635	−0.753176	+	0.657819i	$0.771479\pi$
$968$	0	0
$969$	34.3944	1.10491
$970$	−25.8771	−0.830863
$971$	−6.66198	−0.213793	−0.106897	−	0.994270i	$-0.534091\pi$
$971$	−6.66198	−0.213793	−0.106897	+	0.994270i	$0.534091\pi$
$972$	−41.2664	−1.32362
$973$	−25.8678	−0.829284
$974$	36.5298	1.17049
$975$	4.24970	0.136099
$976$	−18.2875	−0.585370
$977$	−24.1960	−0.774098	−0.387049	−	0.922059i	$-0.626506\pi$
$977$	−24.1960	−0.774098	−0.387049	+	0.922059i	$0.626506\pi$
$978$	−68.9658	−2.20528
$979$	0	0
$980$	−15.6453	−0.499770
$981$	21.6211	0.690310
$982$	−21.2781	−0.679010
$983$	−27.7716	−0.885778	−0.442889	−	0.896577i	$-0.646046\pi$
$983$	−27.7716	−0.885778	−0.442889	+	0.896577i	$0.646046\pi$
$984$	46.4982	1.48231
$985$	16.6978	0.532036
$986$	−41.1855	−1.31161
$987$	102.112	3.25025
$988$	−16.7670	−0.533429
$989$	−13.5519	−0.430926
$990$	0	0
$991$	45.4227	1.44290	0.721450	−	0.692466i	$-0.243476\pi$
$991$	45.4227	1.44290	0.721450	+	0.692466i	$0.243476\pi$
$992$	−36.7491	−1.16679
$993$	74.2715	2.35693
$994$	−20.0062	−0.634560
$995$	16.7912	0.532315
$996$	76.1330	2.41237
$997$	−50.7491	−1.60724	−0.803620	−	0.595143i	$-0.797096\pi$
$997$	−50.7491	−1.60724	−0.803620	+	0.595143i	$0.797096\pi$
$998$	57.7091	1.82675
$999$	−17.1280	−0.541905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.h.1.3	yes	3
3.2	odd	2		5445.2.a.bb.1.1		3
4.3	odd	2		9680.2.a.cb.1.1		3
5.4	even	2		3025.2.a.p.1.1		3
11.2	odd	10		605.2.g.p.81.3		12
11.3	even	5		605.2.g.o.251.3		12
11.4	even	5		605.2.g.o.511.3		12
11.5	even	5		605.2.g.o.366.1		12
11.6	odd	10		605.2.g.p.366.3		12
11.7	odd	10		605.2.g.p.511.1		12
11.8	odd	10		605.2.g.p.251.1		12
11.9	even	5		605.2.g.o.81.1		12
11.10	odd	2		605.2.a.g.1.1	✓	3
33.32	even	2		5445.2.a.bd.1.3		3
44.43	even	2		9680.2.a.bz.1.1		3
55.54	odd	2		3025.2.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.1	✓	3	11.10	odd	2
605.2.a.h.1.3	yes	3	1.1	even	1	trivial
605.2.g.o.81.1		12	11.9	even	5
605.2.g.o.251.3		12	11.3	even	5
605.2.g.o.366.1		12	11.5	even	5
605.2.g.o.511.3		12	11.4	even	5
605.2.g.p.81.3		12	11.2	odd	10
605.2.g.p.251.1		12	11.8	odd	10
605.2.g.p.366.3		12	11.6	odd	10
605.2.g.p.511.1		12	11.7	odd	10
3025.2.a.p.1.1		3	5.4	even	2
3025.2.a.u.1.3		3	55.54	odd	2
5445.2.a.bb.1.1		3	3.2	odd	2
5445.2.a.bd.1.3		3	33.32	even	2
9680.2.a.bz.1.1		3	44.43	even	2
9680.2.a.cb.1.1		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34889 q^{2} +2.86620 q^{3} +3.51730 q^{4} -1.00000 q^{5} +6.73240 q^{6} -3.38350 q^{7} +3.56399 q^{8} +5.21509 q^{9} +O(q^{10})\)	\(q+2.34889 q^{2} +2.86620 q^{3} +3.51730 q^{4} -1.00000 q^{5} +6.73240 q^{6} -3.38350 q^{7} +3.56399 q^{8} +5.21509 q^{9} -2.34889 q^{10} +10.0813 q^{12} +1.48270 q^{13} -7.94749 q^{14} -2.86620 q^{15} +1.33682 q^{16} -3.73240 q^{17} +12.2497 q^{18} -3.21509 q^{19} -3.51730 q^{20} -9.69779 q^{21} -2.51730 q^{23} +10.2151 q^{24} +1.00000 q^{25} +3.48270 q^{26} +6.34889 q^{27} -11.9008 q^{28} +4.69779 q^{29} -6.73240 q^{30} +9.21509 q^{31} -3.98793 q^{32} -8.76700 q^{34} +3.38350 q^{35} +18.3431 q^{36} -2.69779 q^{37} -7.55191 q^{38} +4.24970 q^{39} -3.56399 q^{40} +4.55191 q^{41} -22.7791 q^{42} +5.38350 q^{43} -5.21509 q^{45} -5.91288 q^{46} -10.5294 q^{47} +3.83159 q^{48} +4.44809 q^{49} +2.34889 q^{50} -10.6978 q^{51} +5.21509 q^{52} -2.51730 q^{53} +14.9129 q^{54} -12.0588 q^{56} -9.21509 q^{57} +11.0346 q^{58} +11.9129 q^{59} -10.0813 q^{60} -13.6799 q^{61} +21.6453 q^{62} -17.6453 q^{63} -12.0409 q^{64} -1.48270 q^{65} +7.83159 q^{67} -13.1280 q^{68} -7.21509 q^{69} +7.94749 q^{70} +2.51730 q^{71} +18.5865 q^{72} -2.96539 q^{73} -6.33682 q^{74} +2.86620 q^{75} -11.3085 q^{76} +9.98210 q^{78} +6.76700 q^{79} -1.33682 q^{80} +2.55191 q^{81} +10.6920 q^{82} +7.55191 q^{83} -34.1101 q^{84} +3.73240 q^{85} +12.6453 q^{86} +13.4648 q^{87} +10.8016 q^{89} -12.2497 q^{90} -5.01671 q^{91} -8.85412 q^{92} +26.4123 q^{93} -24.7324 q^{94} +3.21509 q^{95} -11.4302 q^{96} +11.0167 q^{97} +10.4481 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9	\( 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 9 q^{12} + 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} - 9 q^{20} - 17 q^{21} - 6 q^{23} + 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} + 14 q^{31} - 27 q^{32} - 8 q^{34} + q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} - 35 q^{42} + 7 q^{43} - 2 q^{45} + 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} - 6 q^{53} + 19 q^{54} - 3 q^{56} - 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} + 29 q^{64} - 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} + q^{75} + 16 q^{76} - 2 q^{78} + 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} - 3 q^{86} + 10 q^{87} + 11 q^{89} - 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9 - q^10 + 9 * q^12 + 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 - 9 * q^20 - 17 * q^21 - 6 * q^23 + 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 + 14 * q^31 - 27 * q^32 - 8 * q^34 + q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 - 35 * q^42 + 7 * q^43 - 2 * q^45 + 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 - 6 * q^53 + 19 * q^54 - 3 * q^56 - 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 + 29 * q^64 - 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 + q^75 + 16 * q^76 - 2 * q^78 + 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 - 3 * q^86 + 10 * q^87 + 11 * q^89 - 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 - 2 * q^97 + 36 * q^98

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