LMFDB - Embedded newform 1805.2.a.s.1.2

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.28997$ 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)

$f(q)$	$=$	$q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +1.00000 q^{5} +7.57362 q^{6} -2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} +O(q^{10})$	\(q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +1.00000 q^{5} +7.57362 q^{6} -2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} -2.28997 q^{10} -0.577601 q^{11} -10.7287 q^{12} +0.670397 q^{13} +6.73045 q^{14} -3.30730 q^{15} +0.0353277 q^{16} -0.351901 q^{17} -18.1783 q^{18} +3.24395 q^{20} +9.72050 q^{21} +1.32269 q^{22} -4.12081 q^{23} +9.42123 q^{24} +1.00000 q^{25} -1.53519 q^{26} -16.3323 q^{27} -9.53431 q^{28} -3.00800 q^{29} +7.57362 q^{30} -0.297707 q^{31} +5.61633 q^{32} +1.91030 q^{33} +0.805843 q^{34} -2.93910 q^{35} +25.7513 q^{36} +8.30595 q^{37} -2.21721 q^{39} -2.84861 q^{40} -2.67214 q^{41} -22.2596 q^{42} -6.59830 q^{43} -1.87371 q^{44} +7.93825 q^{45} +9.43652 q^{46} +11.0325 q^{47} -0.116839 q^{48} +1.63832 q^{49} -2.28997 q^{50} +1.16384 q^{51} +2.17474 q^{52} +4.10660 q^{53} +37.4004 q^{54} -0.577601 q^{55} +8.37237 q^{56} +6.88822 q^{58} -0.610572 q^{59} -10.7287 q^{60} +1.02693 q^{61} +0.681739 q^{62} -23.3313 q^{63} -12.9319 q^{64} +0.670397 q^{65} -4.37452 q^{66} +3.33593 q^{67} -1.14155 q^{68} +13.6288 q^{69} +6.73045 q^{70} +13.2247 q^{71} -22.6130 q^{72} +7.13879 q^{73} -19.0204 q^{74} -3.30730 q^{75} +1.69763 q^{77} +5.07733 q^{78} -1.54232 q^{79} +0.0353277 q^{80} +30.2010 q^{81} +6.11911 q^{82} +13.3186 q^{83} +31.5328 q^{84} -0.351901 q^{85} +15.1099 q^{86} +9.94837 q^{87} +1.64536 q^{88} +6.57130 q^{89} -18.1783 q^{90} -1.97037 q^{91} -13.3677 q^{92} +0.984606 q^{93} -25.2640 q^{94} -18.5749 q^{96} -12.1979 q^{97} -3.75170 q^{98} -4.58513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−2.28997	−1.61925	−0.809626	−	0.586946i	$-0.800330\pi$
$2$	−2.28997	−1.61925	−0.809626	+	0.586946i	$0.800330\pi$
$3$	−3.30730	−1.90947	−0.954736	−	0.297455i	$-0.903862\pi$
$3$	−3.30730	−1.90947	−0.954736	+	0.297455i	$0.903862\pi$
$4$	3.24395	1.62198
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.57362	3.09192
$7$	−2.93910	−1.11088	−0.555438	−	0.831558i	$-0.687449\pi$
$7$	−2.93910	−1.11088	−0.555438	+	0.831558i	$0.687449\pi$
$8$	−2.84861	−1.00714
$9$	7.93825	2.64608
$10$	−2.28997	−0.724151
$11$	−0.577601	−0.174153	−0.0870766	−	0.996202i	$-0.527752\pi$
$11$	−0.577601	−0.174153	−0.0870766	+	0.996202i	$0.527752\pi$
$12$	−10.7287	−3.09712
$13$	0.670397	0.185935	0.0929673	−	0.995669i	$-0.470365\pi$
$13$	0.670397	0.185935	0.0929673	+	0.995669i	$0.470365\pi$
$14$	6.73045	1.79879
$15$	−3.30730	−0.853942
$16$	0.0353277	0.00883192
$17$	−0.351901	−0.0853486	−0.0426743	−	0.999089i	$-0.513588\pi$
$17$	−0.351901	−0.0853486	−0.0426743	+	0.999089i	$0.513588\pi$
$18$	−18.1783	−4.28467
$19$	0	0
$19$	0	0
$20$	3.24395	0.725370
$21$	9.72050	2.12119
$22$	1.32269	0.281998
$23$	−4.12081	−0.859248	−0.429624	−	0.903008i	$-0.641354\pi$
$23$	−4.12081	−0.859248	−0.429624	+	0.903008i	$0.641354\pi$
$24$	9.42123	1.92310
$25$	1.00000	0.200000
$26$	−1.53519	−0.301075
$27$	−16.3323	−3.14315
$28$	−9.53431	−1.80182
$29$	−3.00800	−0.558572	−0.279286	−	0.960208i	$-0.590098\pi$
$29$	−3.00800	−0.558572	−0.279286	+	0.960208i	$0.590098\pi$
$30$	7.57362	1.38275
$31$	−0.297707	−0.0534697	−0.0267348	−	0.999643i	$-0.508511\pi$
$31$	−0.297707	−0.0534697	−0.0267348	+	0.999643i	$0.508511\pi$
$32$	5.61633	0.992836
$33$	1.91030	0.332540
$34$	0.805843	0.138201
$35$	−2.93910	−0.496799
$36$	25.7513	4.29188
$37$	8.30595	1.36549	0.682745	−	0.730657i	$-0.260786\pi$
$37$	8.30595	1.36549	0.682745	+	0.730657i	$0.260786\pi$
$38$	0	0
$39$	−2.21721	−0.355037
$40$	−2.84861	−0.450405
$41$	−2.67214	−0.417318	−0.208659	−	0.977988i	$-0.566910\pi$
$41$	−2.67214	−0.417318	−0.208659	+	0.977988i	$0.566910\pi$
$42$	−22.2596	−3.43474
$43$	−6.59830	−1.00623	−0.503116	−	0.864219i	$-0.667813\pi$
$43$	−6.59830	−1.00623	−0.503116	+	0.864219i	$0.667813\pi$
$44$	−1.87371	−0.282472
$45$	7.93825	1.18336
$46$	9.43652	1.39134
$47$	11.0325	1.60925	0.804625	−	0.593784i	$-0.202367\pi$
$47$	11.0325	1.60925	0.804625	+	0.593784i	$0.202367\pi$
$48$	−0.116839	−0.0168643
$49$	1.63832	0.234046
$50$	−2.28997	−0.323850
$51$	1.16384	0.162971
$52$	2.17474	0.301582
$53$	4.10660	0.564085	0.282042	−	0.959402i	$-0.408988\pi$
$53$	4.10660	0.564085	0.282042	+	0.959402i	$0.408988\pi$
$54$	37.4004	5.08955
$55$	−0.577601	−0.0778836
$56$	8.37237	1.11880
$57$	0	0
$58$	6.88822	0.904468
$59$	−0.610572	−0.0794897	−0.0397448	−	0.999210i	$-0.512655\pi$
$59$	−0.610572	−0.0794897	−0.0397448	+	0.999210i	$0.512655\pi$
$60$	−10.7287	−1.38507
$61$	1.02693	0.131485	0.0657426	−	0.997837i	$-0.479058\pi$
$61$	1.02693	0.131485	0.0657426	+	0.997837i	$0.479058\pi$
$62$	0.681739	0.0865809
$63$	−23.3313	−2.93947
$64$	−12.9319	−1.61648
$65$	0.670397	0.0831525
$66$	−4.37452	−0.538467
$67$	3.33593	0.407548	0.203774	−	0.979018i	$-0.434679\pi$
$67$	3.33593	0.407548	0.203774	+	0.979018i	$0.434679\pi$
$68$	−1.14155	−0.138433
$69$	13.6288	1.64071
$70$	6.73045	0.804443
$71$	13.2247	1.56948	0.784742	−	0.619823i	$-0.212795\pi$
$71$	13.2247	1.56948	0.784742	+	0.619823i	$0.212795\pi$
$72$	−22.6130	−2.66497
$73$	7.13879	0.835532	0.417766	−	0.908555i	$-0.362813\pi$
$73$	7.13879	0.835532	0.417766	+	0.908555i	$0.362813\pi$
$74$	−19.0204	−2.21107
$75$	−3.30730	−0.381894
$76$	0	0
$77$	1.69763	0.193463
$78$	5.07733	0.574894
$79$	−1.54232	−0.173525	−0.0867623	−	0.996229i	$-0.527652\pi$
$79$	−1.54232	−0.173525	−0.0867623	+	0.996229i	$0.527652\pi$
$80$	0.0353277	0.00394976
$81$	30.2010	3.35567
$82$	6.11911	0.675743
$83$	13.3186	1.46191	0.730953	−	0.682428i	$-0.239076\pi$
$83$	13.3186	1.46191	0.730953	+	0.682428i	$0.239076\pi$
$84$	31.5328	3.44052
$85$	−0.351901	−0.0381690
$86$	15.1099	1.62934
$87$	9.94837	1.06658
$88$	1.64536	0.175396
$89$	6.57130	0.696556	0.348278	−	0.937391i	$-0.386766\pi$
$89$	6.57130	0.696556	0.348278	+	0.937391i	$0.386766\pi$
$90$	−18.1783	−1.91616
$91$	−1.97037	−0.206550
$92$	−13.3677	−1.39368
$93$	0.984606	0.102099
$94$	−25.2640	−2.60578
$95$	0	0
$96$	−18.5749	−1.89579
$97$	−12.1979	−1.23851	−0.619255	−	0.785190i	$-0.712565\pi$
$97$	−12.1979	−1.23851	−0.619255	+	0.785190i	$0.712565\pi$
$98$	−3.75170	−0.378979
$99$	−4.58513	−0.460823
$100$	3.24395	0.324395
$101$	−0.580821	−0.0577939	−0.0288969	−	0.999582i	$-0.509199\pi$
$101$	−0.580821	−0.0577939	−0.0288969	+	0.999582i	$0.509199\pi$
$102$	−2.66516	−0.263891
$103$	6.47111	0.637617	0.318809	−	0.947819i	$-0.396717\pi$
$103$	6.47111	0.637617	0.318809	+	0.947819i	$0.396717\pi$
$104$	−1.90970	−0.187262
$105$	9.72050	0.948623
$106$	−9.40398	−0.913396
$107$	−18.3788	−1.77675	−0.888374	−	0.459120i	$-0.848165\pi$
$107$	−18.3788	−1.77675	−0.888374	+	0.459120i	$0.848165\pi$
$108$	−52.9811	−5.09811
$109$	2.50969	0.240385	0.120192	−	0.992751i	$-0.461649\pi$
$109$	2.50969	0.240385	0.120192	+	0.992751i	$0.461649\pi$
$110$	1.32269	0.126113
$111$	−27.4703	−2.60737
$112$	−0.103832	−0.00981117
$113$	11.3386	1.06665	0.533325	−	0.845911i	$-0.320942\pi$
$113$	11.3386	1.06665	0.533325	+	0.845911i	$0.320942\pi$
$114$	0	0
$115$	−4.12081	−0.384267
$116$	−9.75781	−0.905990
$117$	5.32178	0.491998
$118$	1.39819	0.128714
$119$	1.03427	0.0948117
$120$	9.42123	0.860036
$121$	−10.6664	−0.969671
$122$	−2.35164	−0.212908
$123$	8.83757	0.796857
$124$	−0.965746	−0.0867266
$125$	1.00000	0.0894427
$126$	53.4280	4.75974
$127$	−19.1921	−1.70302	−0.851512	−	0.524336i	$-0.824314\pi$
$127$	−19.1921	−1.70302	−0.851512	+	0.524336i	$0.824314\pi$
$128$	18.3809	1.62466
$129$	21.8226	1.92137
$130$	−1.53519	−0.134645
$131$	−6.85020	−0.598505	−0.299252	−	0.954174i	$-0.596737\pi$
$131$	−6.85020	−0.598505	−0.299252	+	0.954174i	$0.596737\pi$
$132$	6.19692	0.539373
$133$	0	0
$134$	−7.63916	−0.659923
$135$	−16.3323	−1.40566
$136$	1.00243	0.0859577
$137$	13.2418	1.13132	0.565660	−	0.824638i	$-0.308621\pi$
$137$	13.2418	1.13132	0.565660	+	0.824638i	$0.308621\pi$
$138$	−31.2094	−2.65672
$139$	2.90988	0.246813	0.123406	−	0.992356i	$-0.460618\pi$
$139$	2.90988	0.246813	0.123406	+	0.992356i	$0.460618\pi$
$140$	−9.53431	−0.805796
$141$	−36.4877	−3.07282
$142$	−30.2842	−2.54139
$143$	−0.387222	−0.0323811
$144$	0.280440	0.0233700
$145$	−3.00800	−0.249801
$146$	−16.3476	−1.35294
$147$	−5.41842	−0.446904
$148$	26.9441	2.21479
$149$	−8.85659	−0.725560	−0.362780	−	0.931875i	$-0.618172\pi$
$149$	−8.85659	−0.725560	−0.362780	+	0.931875i	$0.618172\pi$
$150$	7.57362	0.618383
$151$	−8.37160	−0.681271	−0.340636	−	0.940195i	$-0.610642\pi$
$151$	−8.37160	−0.681271	−0.340636	+	0.940195i	$0.610642\pi$
$152$	0	0
$153$	−2.79348	−0.225839
$154$	−3.88751	−0.313265
$155$	−0.297707	−0.0239124
$156$	−7.19251	−0.575862
$157$	−15.8665	−1.26629	−0.633143	−	0.774035i	$-0.718236\pi$
$157$	−15.8665	−1.26629	−0.633143	+	0.774035i	$0.718236\pi$
$158$	3.53186	0.280980
$159$	−13.5818	−1.07710
$160$	5.61633	0.444010
$161$	12.1115	0.954518
$162$	−69.1593	−5.43367
$163$	9.72260	0.761533	0.380766	−	0.924671i	$-0.375660\pi$
$163$	9.72260	0.761533	0.380766	+	0.924671i	$0.375660\pi$
$164$	−8.66830	−0.676880
$165$	1.91030	0.148717
$166$	−30.4991	−2.36719
$167$	−0.282149	−0.0218333	−0.0109167	−	0.999940i	$-0.503475\pi$
$167$	−0.282149	−0.0218333	−0.0109167	+	0.999940i	$0.503475\pi$
$168$	−27.6899	−2.13633
$169$	−12.5506	−0.965428
$170$	0.805843	0.0618053
$171$	0	0
$172$	−21.4046	−1.63208
$173$	−15.1289	−1.15023	−0.575116	−	0.818072i	$-0.695043\pi$
$173$	−15.1289	−1.15023	−0.575116	+	0.818072i	$0.695043\pi$
$174$	−22.7814	−1.72706
$175$	−2.93910	−0.222175
$176$	−0.0204053	−0.00153811
$177$	2.01935	0.151783
$178$	−15.0481	−1.12790
$179$	14.4533	1.08029	0.540145	−	0.841572i	$-0.318370\pi$
$179$	14.4533	1.08029	0.540145	+	0.841572i	$0.318370\pi$
$180$	25.7513	1.91939
$181$	6.96487	0.517695	0.258847	−	0.965918i	$-0.416657\pi$
$181$	6.96487	0.517695	0.258847	+	0.965918i	$0.416657\pi$
$182$	4.51207	0.334457
$183$	−3.39637	−0.251067
$184$	11.7386	0.865380
$185$	8.30595	0.610666
$186$	−2.25472	−0.165324
$187$	0.203258	0.0148637
$188$	35.7888	2.61016
$189$	48.0022	3.49165
$190$	0	0
$191$	5.49050	0.397279	0.198639	−	0.980073i	$-0.436348\pi$
$191$	5.49050	0.397279	0.198639	+	0.980073i	$0.436348\pi$
$192$	42.7696	3.08663
$193$	6.47685	0.466214	0.233107	−	0.972451i	$-0.425111\pi$
$193$	6.47685	0.466214	0.233107	+	0.972451i	$0.425111\pi$
$194$	27.9328	2.00546
$195$	−2.21721	−0.158777
$196$	5.31463	0.379617
$197$	−9.29455	−0.662209	−0.331104	−	0.943594i	$-0.607421\pi$
$197$	−9.29455	−0.662209	−0.331104	+	0.943594i	$0.607421\pi$
$198$	10.4998	0.746189
$199$	−24.3069	−1.72307	−0.861534	−	0.507700i	$-0.830496\pi$
$199$	−24.3069	−1.72307	−0.861534	+	0.507700i	$0.830496\pi$
$200$	−2.84861	−0.201427
$201$	−11.0329	−0.778202
$202$	1.33006	0.0935828
$203$	8.84082	0.620504
$204$	3.77545	0.264335
$205$	−2.67214	−0.186630
$206$	−14.8186	−1.03246
$207$	−32.7120	−2.27364
$208$	0.0236836	0.00164216
$209$	0	0
$210$	−22.2596	−1.53606
$211$	−23.9674	−1.64999	−0.824994	−	0.565142i	$-0.808821\pi$
$211$	−23.9674	−1.64999	−0.824994	+	0.565142i	$0.808821\pi$
$212$	13.3216	0.914933
$213$	−43.7381	−2.99688
$214$	42.0869	2.87700
$215$	−6.59830	−0.450001
$216$	46.5243	3.16558
$217$	0.874990	0.0593982
$218$	−5.74711	−0.389243
$219$	−23.6101	−1.59542
$220$	−1.87371	−0.126325
$221$	−0.235914	−0.0158693
$222$	62.9061	4.22198
$223$	−20.5690	−1.37740	−0.688701	−	0.725045i	$-0.741819\pi$
$223$	−20.5690	−1.37740	−0.688701	+	0.725045i	$0.741819\pi$
$224$	−16.5070	−1.10292
$225$	7.93825	0.529216
$226$	−25.9651	−1.72717
$227$	−12.6949	−0.842593	−0.421297	−	0.906923i	$-0.638425\pi$
$227$	−12.6949	−0.842593	−0.421297	+	0.906923i	$0.638425\pi$
$228$	0	0
$229$	5.76019	0.380644	0.190322	−	0.981722i	$-0.439047\pi$
$229$	5.76019	0.380644	0.190322	+	0.981722i	$0.439047\pi$
$230$	9.43652	0.622226
$231$	−5.61456	−0.369411
$232$	8.56863	0.562558
$233$	−2.77852	−0.182027	−0.0910135	−	0.995850i	$-0.529011\pi$
$233$	−2.77852	−0.182027	−0.0910135	+	0.995850i	$0.529011\pi$
$234$	−12.1867	−0.796669
$235$	11.0325	0.719678
$236$	−1.98067	−0.128930
$237$	5.10092	0.331340
$238$	−2.36845	−0.153524
$239$	19.4587	1.25868	0.629340	−	0.777130i	$-0.283325\pi$
$239$	19.4587	1.25868	0.629340	+	0.777130i	$0.283325\pi$
$240$	−0.116839	−0.00754195
$241$	7.23964	0.466346	0.233173	−	0.972435i	$-0.425089\pi$
$241$	7.23964	0.466346	0.233173	+	0.972435i	$0.425089\pi$
$242$	24.4257	1.57014
$243$	−50.8870	−3.26441
$244$	3.33132	0.213266
$245$	1.63832	0.104668
$246$	−20.2378	−1.29031
$247$	0	0
$248$	0.848051	0.0538513
$249$	−44.0486	−2.79147
$250$	−2.28997	−0.144830
$251$	14.8558	0.937692	0.468846	−	0.883280i	$-0.344670\pi$
$251$	14.8558	0.937692	0.468846	+	0.883280i	$0.344670\pi$
$252$	−75.6857	−4.76775
$253$	2.38018	0.149641
$254$	43.9493	2.75762
$255$	1.16384	0.0728827
$256$	−16.2280	−1.01425
$257$	−19.7558	−1.23233	−0.616166	−	0.787616i	$-0.711315\pi$
$257$	−19.7558	−1.23233	−0.616166	+	0.787616i	$0.711315\pi$
$258$	−49.9730	−3.11118
$259$	−24.4120	−1.51689
$260$	2.17474	0.134871
$261$	−23.8782	−1.47803
$262$	15.6867	0.969130
$263$	11.8513	0.730780	0.365390	−	0.930854i	$-0.380936\pi$
$263$	11.8513	0.730780	0.365390	+	0.930854i	$0.380936\pi$
$264$	−5.44171	−0.334914
$265$	4.10660	0.252266
$266$	0	0
$267$	−21.7333	−1.33005
$268$	10.8216	0.661034
$269$	10.8758	0.663111	0.331555	−	0.943436i	$-0.392427\pi$
$269$	10.8758	0.663111	0.331555	+	0.943436i	$0.392427\pi$
$270$	37.4004	2.27611
$271$	−5.87245	−0.356726	−0.178363	−	0.983965i	$-0.557080\pi$
$271$	−5.87245	−0.356726	−0.178363	+	0.983965i	$0.557080\pi$
$272$	−0.0124319	−0.000753792 0
$273$	6.51659	0.394402
$274$	−30.3232	−1.83189
$275$	−0.577601	−0.0348306
$276$	44.2110	2.66119
$277$	−23.8127	−1.43077	−0.715385	−	0.698731i	$-0.753749\pi$
$277$	−23.8127	−1.43077	−0.715385	+	0.698731i	$0.753749\pi$
$278$	−6.66353	−0.399652
$279$	−2.36327	−0.141485
$280$	8.37237	0.500345
$281$	7.13920	0.425889	0.212945	−	0.977064i	$-0.431695\pi$
$281$	7.13920	0.425889	0.212945	+	0.977064i	$0.431695\pi$
$282$	83.5556	4.97566
$283$	26.7342	1.58918	0.794592	−	0.607144i	$-0.207685\pi$
$283$	26.7342	1.58918	0.794592	+	0.607144i	$0.207685\pi$
$284$	42.9003	2.54567
$285$	0	0
$286$	0.886725	0.0524332
$287$	7.85369	0.463589
$288$	44.5838	2.62713
$289$	−16.8762	−0.992716
$290$	6.88822	0.404490
$291$	40.3422	2.36490
$292$	23.1579	1.35521
$293$	−1.07337	−0.0627069	−0.0313535	−	0.999508i	$-0.509982\pi$
$293$	−1.07337	−0.0627069	−0.0313535	+	0.999508i	$0.509982\pi$
$294$	12.4080	0.723650
$295$	−0.610572	−0.0355489
$296$	−23.6605	−1.37524
$297$	9.43353	0.547389
$298$	20.2813	1.17486
$299$	−2.76258	−0.159764
$300$	−10.7287	−0.619424
$301$	19.3931	1.11780
$302$	19.1707	1.10315
$303$	1.92095	0.110356
$304$	0	0
$305$	1.02693	0.0588020
$306$	6.39698	0.365691
$307$	25.9701	1.48219	0.741097	−	0.671398i	$-0.234306\pi$
$307$	25.9701	1.48219	0.741097	+	0.671398i	$0.234306\pi$
$308$	5.50702	0.313792
$309$	−21.4019	−1.21751
$310$	0.681739	0.0387202
$311$	19.0509	1.08028	0.540139	−	0.841576i	$-0.318372\pi$
$311$	19.0509	1.08028	0.540139	+	0.841576i	$0.318372\pi$
$312$	6.31596	0.357571
$313$	−15.3992	−0.870416	−0.435208	−	0.900330i	$-0.643325\pi$
$313$	−15.3992	−0.870416	−0.435208	+	0.900330i	$0.643325\pi$
$314$	36.3338	2.05044
$315$	−23.3313	−1.31457
$316$	−5.00321	−0.281453
$317$	−25.5404	−1.43449	−0.717245	−	0.696821i	$-0.754597\pi$
$317$	−25.5404	−1.43449	−0.717245	+	0.696821i	$0.754597\pi$
$318$	31.1018	1.74410
$319$	1.73742	0.0972770
$320$	−12.9319	−0.722913
$321$	60.7843	3.39265
$322$	−27.7349	−1.54560
$323$	0	0
$324$	97.9707	5.44282
$325$	0.670397	0.0371869
$326$	−22.2644	−1.23311
$327$	−8.30030	−0.459008
$328$	7.61189	0.420297
$329$	−32.4255	−1.78768
$330$	−4.37452	−0.240810
$331$	−4.53178	−0.249089	−0.124545	−	0.992214i	$-0.539747\pi$
$331$	−4.53178	−0.249089	−0.124545	+	0.992214i	$0.539747\pi$
$332$	43.2049	2.37118
$333$	65.9347	3.61320
$334$	0.646112	0.0353537
$335$	3.33593	0.182261
$336$	0.343403	0.0187342
$337$	−20.3396	−1.10797	−0.553984	−	0.832527i	$-0.686893\pi$
$337$	−20.3396	−1.10797	−0.553984	+	0.832527i	$0.686893\pi$
$338$	28.7404	1.56327
$339$	−37.5003	−2.03674
$340$	−1.14155	−0.0619093
$341$	0.171955	0.00931191
$342$	0	0
$343$	15.7585	0.850880
$344$	18.7960	1.01341
$345$	13.6288	0.733748
$346$	34.6448	1.86252
$347$	27.2663	1.46373	0.731867	−	0.681448i	$-0.238649\pi$
$347$	27.2663	1.46373	0.731867	+	0.681448i	$0.238649\pi$
$348$	32.2720	1.72996
$349$	12.6223	0.675656	0.337828	−	0.941208i	$-0.390308\pi$
$349$	12.6223	0.675656	0.337828	+	0.941208i	$0.390308\pi$
$350$	6.73045	0.359758
$351$	−10.9491	−0.584420
$352$	−3.24399	−0.172905
$353$	30.7991	1.63927	0.819636	−	0.572884i	$-0.194175\pi$
$353$	30.7991	1.63927	0.819636	+	0.572884i	$0.194175\pi$
$354$	−4.62424	−0.245775
$355$	13.2247	0.701895
$356$	21.3170	1.12980
$357$	−3.42066	−0.181040
$358$	−33.0976	−1.74926
$359$	−17.2365	−0.909708	−0.454854	−	0.890566i	$-0.650309\pi$
$359$	−17.2365	−0.909708	−0.454854	+	0.890566i	$0.650309\pi$
$360$	−22.6130	−1.19181
$361$	0	0
$362$	−15.9493	−0.838278
$363$	35.2769	1.85156
$364$	−6.39177	−0.335020
$365$	7.13879	0.373661
$366$	7.77759	0.406541
$367$	−30.0937	−1.57088	−0.785440	−	0.618938i	$-0.787563\pi$
$367$	−30.0937	−1.57088	−0.785440	+	0.618938i	$0.787563\pi$
$368$	−0.145579	−0.00758881
$369$	−21.2121	−1.10426
$370$	−19.0204	−0.988822
$371$	−12.0697	−0.626628
$372$	3.19401	0.165602
$373$	6.13352	0.317581	0.158791	−	0.987312i	$-0.449240\pi$
$373$	6.13352	0.317581	0.158791	+	0.987312i	$0.449240\pi$
$374$	−0.465455	−0.0240681
$375$	−3.30730	−0.170788
$376$	−31.4272	−1.62073
$377$	−2.01655	−0.103858
$378$	−109.924	−5.65386
$379$	−30.8958	−1.58701	−0.793505	−	0.608564i	$-0.791746\pi$
$379$	−30.8958	−1.58701	−0.793505	+	0.608564i	$0.791746\pi$
$380$	0	0
$381$	63.4741	3.25187
$382$	−12.5731	−0.643294
$383$	−4.65116	−0.237663	−0.118831	−	0.992914i	$-0.537915\pi$
$383$	−4.65116	−0.237663	−0.118831	+	0.992914i	$0.537915\pi$
$384$	−60.7912	−3.10224
$385$	1.69763	0.0865191
$386$	−14.8318	−0.754918
$387$	−52.3790	−2.66257
$388$	−39.5694	−2.00883
$389$	−16.1770	−0.820207	−0.410104	−	0.912039i	$-0.634507\pi$
$389$	−16.1770	−0.820207	−0.410104	+	0.912039i	$0.634507\pi$
$390$	5.07733	0.257101
$391$	1.45012	0.0733356
$392$	−4.66694	−0.235716
$393$	22.6557	1.14283
$394$	21.2842	1.07228
$395$	−1.54232	−0.0776025
$396$	−14.8740	−0.747445
$397$	−9.93505	−0.498626	−0.249313	−	0.968423i	$-0.580205\pi$
$397$	−9.93505	−0.498626	−0.249313	+	0.968423i	$0.580205\pi$
$398$	55.6619	2.79008
$399$	0	0
$400$	0.0353277	0.00176638
$401$	12.9340	0.645893	0.322946	−	0.946417i	$-0.395327\pi$
$401$	12.9340	0.645893	0.322946	+	0.946417i	$0.395327\pi$
$402$	25.2650	1.26010
$403$	−0.199582	−0.00994187
$404$	−1.88416	−0.0937403
$405$	30.2010	1.50070
$406$	−20.2452	−1.00475
$407$	−4.79752	−0.237804
$408$	−3.31534	−0.164134
$409$	6.24031	0.308564	0.154282	−	0.988027i	$-0.450694\pi$
$409$	6.24031	0.308564	0.154282	+	0.988027i	$0.450694\pi$
$410$	6.11911	0.302202
$411$	−43.7945	−2.16022
$412$	20.9920	1.03420
$413$	1.79453	0.0883032
$414$	74.9094	3.68160
$415$	13.3186	0.653784
$416$	3.76517	0.184603
$417$	−9.62385	−0.471282
$418$	0	0
$419$	−30.5403	−1.49199	−0.745995	−	0.665951i	$-0.768026\pi$
$419$	−30.5403	−1.49199	−0.745995	+	0.665951i	$0.768026\pi$
$420$	31.5328	1.53865
$421$	−36.5695	−1.78229	−0.891144	−	0.453721i	$-0.850096\pi$
$421$	−36.5695	−1.78229	−0.891144	+	0.453721i	$0.850096\pi$
$422$	54.8847	2.67174
$423$	87.5784	4.25821
$424$	−11.6981	−0.568111
$425$	−0.351901	−0.0170697
$426$	100.159	4.85271
$427$	−3.01826	−0.146064
$428$	−59.6201	−2.88184
$429$	1.28066	0.0618308
$430$	15.1099	0.728664
$431$	−23.9033	−1.15138	−0.575691	−	0.817667i	$-0.695267\pi$
$431$	−23.9033	−1.15138	−0.575691	+	0.817667i	$0.695267\pi$
$432$	−0.576981	−0.0277600
$433$	14.6544	0.704246	0.352123	−	0.935954i	$-0.385460\pi$
$433$	14.6544	0.704246	0.352123	+	0.935954i	$0.385460\pi$
$434$	−2.00370	−0.0961806
$435$	9.94837	0.476988
$436$	8.14132	0.389898
$437$	0	0
$438$	54.0664	2.58339
$439$	17.0244	0.812529	0.406264	−	0.913756i	$-0.366831\pi$
$439$	17.0244	0.812529	0.406264	+	0.913756i	$0.366831\pi$
$440$	1.64536	0.0784395
$441$	13.0054	0.619304
$442$	0.540234	0.0256963
$443$	−35.9913	−1.71000	−0.854999	−	0.518630i	$-0.826442\pi$
$443$	−35.9913	−1.71000	−0.854999	+	0.518630i	$0.826442\pi$
$444$	−89.1124	−4.22909
$445$	6.57130	0.311509
$446$	47.1024	2.23036
$447$	29.2914	1.38544
$448$	38.0081	1.79571
$449$	−3.55766	−0.167896	−0.0839481	−	0.996470i	$-0.526753\pi$
$449$	−3.55766	−0.167896	−0.0839481	+	0.996470i	$0.526753\pi$
$450$	−18.1783	−0.856935
$451$	1.54343	0.0726772
$452$	36.7820	1.73008
$453$	27.6874	1.30087
$454$	29.0710	1.36437
$455$	−1.97037	−0.0923721
$456$	0	0
$457$	−4.61695	−0.215972	−0.107986	−	0.994152i	$-0.534440\pi$
$457$	−4.61695	−0.215972	−0.107986	+	0.994152i	$0.534440\pi$
$458$	−13.1907	−0.616359
$459$	5.74735	0.268263
$460$	−13.3677	−0.623273
$461$	−29.1737	−1.35875	−0.679377	−	0.733790i	$-0.737750\pi$
$461$	−29.1737	−1.35875	−0.679377	+	0.733790i	$0.737750\pi$
$462$	12.8572	0.598170
$463$	−17.6378	−0.819696	−0.409848	−	0.912154i	$-0.634418\pi$
$463$	−17.6378	−0.819696	−0.409848	+	0.912154i	$0.634418\pi$
$464$	−0.106266	−0.00493326
$465$	0.984606	0.0456600
$466$	6.36272	0.294748
$467$	16.9435	0.784052	0.392026	−	0.919954i	$-0.371774\pi$
$467$	16.9435	0.784052	0.392026	+	0.919954i	$0.371774\pi$
$468$	17.2636	0.798010
$469$	−9.80462	−0.452735
$470$	−25.2640	−1.16534
$471$	52.4754	2.41794
$472$	1.73928	0.0800570
$473$	3.81118	0.175238
$474$	−11.6809	−0.536523
$475$	0	0
$476$	3.35514	0.153782
$477$	32.5992	1.49261
$478$	−44.5599	−2.03812
$479$	−14.4613	−0.660752	−0.330376	−	0.943849i	$-0.607176\pi$
$479$	−14.4613	−0.660752	−0.330376	+	0.943849i	$0.607176\pi$
$480$	−18.5749	−0.847824
$481$	5.56829	0.253892
$482$	−16.5785	−0.755132
$483$	−40.0563	−1.82262
$484$	−34.6012	−1.57278
$485$	−12.1979	−0.553878
$486$	116.530	5.28589
$487$	0.331932	0.0150413	0.00752064	−	0.999972i	$-0.497606\pi$
$487$	0.331932	0.0150413	0.00752064	+	0.999972i	$0.497606\pi$
$488$	−2.92533	−0.132424
$489$	−32.1556	−1.45413
$490$	−3.75170	−0.169485
$491$	−3.34188	−0.150817	−0.0754084	−	0.997153i	$-0.524026\pi$
$491$	−3.34188	−0.150817	−0.0754084	+	0.997153i	$0.524026\pi$
$492$	28.6687	1.29248
$493$	1.05852	0.0476733
$494$	0	0
$495$	−4.58513	−0.206086
$496$	−0.0105173	−0.000472240 0
$497$	−38.8688	−1.74350
$498$	100.870	4.52009
$499$	−14.0914	−0.630818	−0.315409	−	0.948956i	$-0.602142\pi$
$499$	−14.0914	−0.630818	−0.315409	+	0.948956i	$0.602142\pi$
$500$	3.24395	0.145074
$501$	0.933152	0.0416902
$502$	−34.0194	−1.51836
$503$	−3.70599	−0.165242	−0.0826210	−	0.996581i	$-0.526329\pi$
$503$	−3.70599	−0.165242	−0.0826210	+	0.996581i	$0.526329\pi$
$504$	66.4619	2.96045
$505$	−0.580821	−0.0258462
$506$	−5.45054	−0.242306
$507$	41.5085	1.84346
$508$	−62.2583	−2.76226
$509$	−35.3434	−1.56657	−0.783284	−	0.621664i	$-0.786457\pi$
$509$	−35.3434	−1.56657	−0.783284	+	0.621664i	$0.786457\pi$
$510$	−2.66516	−0.118015
$511$	−20.9816	−0.928172
$512$	0.399682	0.0176636
$513$	0	0
$514$	45.2401	1.99546
$515$	6.47111	0.285151
$516$	70.7915	3.11642
$517$	−6.37235	−0.280256
$518$	55.9028	2.45623
$519$	50.0360	2.19634
$520$	−1.90970	−0.0837460
$521$	−5.04908	−0.221204	−0.110602	−	0.993865i	$-0.535278\pi$
$521$	−5.04908	−0.221204	−0.110602	+	0.993865i	$0.535278\pi$
$522$	54.6804	2.39330
$523$	−23.3660	−1.02172	−0.510862	−	0.859663i	$-0.670674\pi$
$523$	−23.3660	−1.02172	−0.510862	+	0.859663i	$0.670674\pi$
$524$	−22.2217	−0.970761
$525$	9.72050	0.424237
$526$	−27.1390	−1.18332
$527$	0.104763	0.00456356
$528$	0.0674865	0.00293697
$529$	−6.01894	−0.261693
$530$	−9.40398	−0.408483
$531$	−4.84687	−0.210336
$532$	0	0
$533$	−1.79139	−0.0775939
$534$	49.7685	2.15369
$535$	−18.3788	−0.794586
$536$	−9.50276	−0.410457
$537$	−47.8014	−2.06278
$538$	−24.9053	−1.07374
$539$	−0.946294	−0.0407598
$540$	−52.9811	−2.27994
$541$	31.8509	1.36938	0.684689	−	0.728836i	$-0.259938\pi$
$541$	31.8509	1.36938	0.684689	+	0.728836i	$0.259938\pi$
$542$	13.4477	0.577629
$543$	−23.0349	−0.988523
$544$	−1.97639	−0.0847372
$545$	2.50969	0.107503
$546$	−14.9228	−0.638636
$547$	−29.7080	−1.27022	−0.635112	−	0.772420i	$-0.719046\pi$
$547$	−29.7080	−1.27022	−0.635112	+	0.772420i	$0.719046\pi$
$548$	42.9557	1.83498
$549$	8.15204	0.347921
$550$	1.32269	0.0563996
$551$	0	0
$552$	−38.8231	−1.65242
$553$	4.53303	0.192764
$554$	54.5304	2.31678
$555$	−27.4703	−1.16605
$556$	9.43951	0.400324
$557$	−21.6442	−0.917093	−0.458546	−	0.888670i	$-0.651630\pi$
$557$	−21.6442	−0.917093	−0.458546	+	0.888670i	$0.651630\pi$
$558$	5.41181	0.229100
$559$	−4.42348	−0.187093
$560$	−0.103832	−0.00438769
$561$	−0.672237	−0.0283819
$562$	−16.3485	−0.689622
$563$	5.92838	0.249852	0.124926	−	0.992166i	$-0.460131\pi$
$563$	5.92838	0.249852	0.124926	+	0.992166i	$0.460131\pi$
$564$	−118.364	−4.98404
$565$	11.3386	0.477020
$566$	−61.2205	−2.57329
$567$	−88.7638	−3.72773
$568$	−37.6721	−1.58069
$569$	5.27877	0.221297	0.110649	−	0.993860i	$-0.464707\pi$
$569$	5.27877	0.221297	0.110649	+	0.993860i	$0.464707\pi$
$570$	0	0
$571$	16.5322	0.691852	0.345926	−	0.938262i	$-0.387565\pi$
$571$	16.5322	0.691852	0.345926	+	0.938262i	$0.387565\pi$
$572$	−1.25613	−0.0525214
$573$	−18.1587	−0.758592
$574$	−17.9847	−0.750667
$575$	−4.12081	−0.171850
$576$	−102.656	−4.27735
$577$	36.2634	1.50966	0.754832	−	0.655918i	$-0.227718\pi$
$577$	36.2634	1.50966	0.754832	+	0.655918i	$0.227718\pi$
$578$	38.6459	1.60746
$579$	−21.4209	−0.890223
$580$	−9.75781	−0.405171
$581$	−39.1447	−1.62400
$582$	−92.3823	−3.82937
$583$	−2.37197	−0.0982371
$584$	−20.3356	−0.841495
$585$	5.32178	0.220028
$586$	2.45798	0.101538
$587$	−26.6519	−1.10004	−0.550021	−	0.835151i	$-0.685380\pi$
$587$	−26.6519	−1.10004	−0.550021	+	0.835151i	$0.685380\pi$
$588$	−17.5771	−0.724867
$589$	0	0
$590$	1.39819	0.0575626
$591$	30.7399	1.26447
$592$	0.293430	0.0120599
$593$	−27.6836	−1.13683	−0.568414	−	0.822742i	$-0.692443\pi$
$593$	−27.6836	−1.13683	−0.568414	+	0.822742i	$0.692443\pi$
$594$	−21.6025	−0.886360
$595$	1.03427	0.0424011
$596$	−28.7304	−1.17684
$597$	80.3901	3.29015
$598$	6.32621	0.258698
$599$	34.3545	1.40369	0.701843	−	0.712331i	$-0.252361\pi$
$599$	34.3545	1.40369	0.701843	+	0.712331i	$0.252361\pi$
$600$	9.42123	0.384620
$601$	−16.8903	−0.688970	−0.344485	−	0.938792i	$-0.611947\pi$
$601$	−16.8903	−0.688970	−0.344485	+	0.938792i	$0.611947\pi$
$602$	−44.4096	−1.81000
$603$	26.4814	1.07841
$604$	−27.1571	−1.10501
$605$	−10.6664	−0.433650
$606$	−4.39892	−0.178694
$607$	4.71187	0.191249	0.0956245	−	0.995417i	$-0.469515\pi$
$607$	4.71187	0.191249	0.0956245	+	0.995417i	$0.469515\pi$
$608$	0	0
$609$	−29.2393	−1.18483
$610$	−2.35164	−0.0952152
$611$	7.39613	0.299215
$612$	−9.06192	−0.366306
$613$	−41.0465	−1.65785	−0.828926	−	0.559358i	$-0.811048\pi$
$613$	−41.0465	−1.65785	−0.828926	+	0.559358i	$0.811048\pi$
$614$	−59.4708	−2.40005
$615$	8.83757	0.356365
$616$	−4.83588	−0.194843
$617$	−6.47810	−0.260798	−0.130399	−	0.991462i	$-0.541626\pi$
$617$	−6.47810	−0.260798	−0.130399	+	0.991462i	$0.541626\pi$
$618$	49.0097	1.97146
$619$	−36.6443	−1.47286	−0.736429	−	0.676514i	$-0.763490\pi$
$619$	−36.6443	−1.47286	−0.736429	+	0.676514i	$0.763490\pi$
$620$	−0.965746	−0.0387853
$621$	67.3021	2.70074
$622$	−43.6260	−1.74924
$623$	−19.3137	−0.773788
$624$	−0.0783287	−0.00313566
$625$	1.00000	0.0400000
$626$	35.2637	1.40942
$627$	0	0
$628$	−51.4703	−2.05389
$629$	−2.92288	−0.116543
$630$	53.4280	2.12862
$631$	−15.1190	−0.601878	−0.300939	−	0.953643i	$-0.597300\pi$
$631$	−15.1190	−0.601878	−0.300939	+	0.953643i	$0.597300\pi$
$632$	4.39347	0.174763
$633$	79.2676	3.15060
$634$	58.4866	2.32280
$635$	−19.1921	−0.761615
$636$	−44.0586	−1.74704
$637$	1.09832	0.0435172
$638$	−3.97864	−0.157516
$639$	104.981	4.15298
$640$	18.3809	0.726569
$641$	10.5736	0.417632	0.208816	−	0.977955i	$-0.433039\pi$
$641$	10.5736	0.417632	0.208816	+	0.977955i	$0.433039\pi$
$642$	−139.194	−5.49356
$643$	−3.49394	−0.137788	−0.0688938	−	0.997624i	$-0.521947\pi$
$643$	−3.49394	−0.137788	−0.0688938	+	0.997624i	$0.521947\pi$
$644$	39.2891	1.54821
$645$	21.8226	0.859263
$646$	0	0
$647$	21.5689	0.847961	0.423981	−	0.905671i	$-0.360632\pi$
$647$	21.5689	0.847961	0.423981	+	0.905671i	$0.360632\pi$
$648$	−86.0310	−3.37962
$649$	0.352667	0.0138434
$650$	−1.53519	−0.0602150
$651$	−2.89386	−0.113419
$652$	31.5397	1.23519
$653$	−27.9780	−1.09486	−0.547432	−	0.836850i	$-0.684395\pi$
$653$	−27.9780	−1.09486	−0.547432	+	0.836850i	$0.684395\pi$
$654$	19.0074	0.743249
$655$	−6.85020	−0.267659
$656$	−0.0944005	−0.00368572
$657$	56.6694	2.21089
$658$	74.2534	2.89470
$659$	−5.66571	−0.220705	−0.110352	−	0.993893i	$-0.535198\pi$
$659$	−5.66571	−0.220705	−0.110352	+	0.993893i	$0.535198\pi$
$660$	6.19692	0.241215
$661$	0.130235	0.00506555	0.00253277	−	0.999997i	$-0.499194\pi$
$661$	0.130235	0.00506555	0.00253277	+	0.999997i	$0.499194\pi$
$662$	10.3776	0.403338
$663$	0.780237	0.0303019
$664$	−37.9395	−1.47234
$665$	0	0
$666$	−150.988	−5.85068
$667$	12.3954	0.479951
$668$	−0.915278	−0.0354132
$669$	68.0279	2.63011
$670$	−7.63916	−0.295127
$671$	−0.593157	−0.0228986
$672$	54.5935	2.10599
$673$	41.4320	1.59709	0.798543	−	0.601937i	$-0.205604\pi$
$673$	41.4320	1.59709	0.798543	+	0.601937i	$0.205604\pi$
$674$	46.5770	1.79408
$675$	−16.3323	−0.628629
$676$	−40.7135	−1.56590
$677$	−19.2643	−0.740386	−0.370193	−	0.928955i	$-0.620708\pi$
$677$	−19.2643	−0.740386	−0.370193	+	0.928955i	$0.620708\pi$
$678$	85.8745	3.29799
$679$	35.8509	1.37583
$680$	1.00243	0.0384415
$681$	41.9860	1.60891
$682$	−0.393773	−0.0150783
$683$	−14.0647	−0.538170	−0.269085	−	0.963116i	$-0.586721\pi$
$683$	−14.0647	−0.538170	−0.269085	+	0.963116i	$0.586721\pi$
$684$	0	0
$685$	13.2418	0.505942
$686$	−36.0865	−1.37779
$687$	−19.0507	−0.726829
$688$	−0.233103	−0.00888696
$689$	2.75305	0.104883
$690$	−31.2094	−1.18812
$691$	−11.3257	−0.430849	−0.215425	−	0.976520i	$-0.569114\pi$
$691$	−11.3257	−0.430849	−0.215425	+	0.976520i	$0.569114\pi$
$692$	−49.0776	−1.86565
$693$	13.4762	0.511918
$694$	−62.4390	−2.37015
$695$	2.90988	0.110378
$696$	−28.3391	−1.07419
$697$	0.940329	0.0356175
$698$	−28.9046	−1.09406
$699$	9.18941	0.347575
$700$	−9.53431	−0.360363
$701$	−15.4332	−0.582905	−0.291453	−	0.956585i	$-0.594139\pi$
$701$	−15.4332	−0.582905	−0.291453	+	0.956585i	$0.594139\pi$
$702$	25.0731	0.946323
$703$	0	0
$704$	7.46945	0.281516
$705$	−36.4877	−1.37420
$706$	−70.5290	−2.65440
$707$	1.70709	0.0642018
$708$	6.55066	0.246189
$709$	19.0828	0.716671	0.358335	−	0.933593i	$-0.383344\pi$
$709$	19.0828	0.716671	0.358335	+	0.933593i	$0.383344\pi$
$710$	−30.2842	−1.13654
$711$	−12.2433	−0.459160
$712$	−18.7191	−0.701528
$713$	1.22679	0.0459437
$714$	7.83319	0.293150
$715$	−0.387222	−0.0144813
$716$	46.8858	1.75220
$717$	−64.3559	−2.40341
$718$	39.4710	1.47305
$719$	−11.4199	−0.425891	−0.212946	−	0.977064i	$-0.568306\pi$
$719$	−11.4199	−0.425891	−0.212946	+	0.977064i	$0.568306\pi$
$720$	0.280440	0.0104514
$721$	−19.0192	−0.708314
$722$	0	0
$723$	−23.9437	−0.890475
$724$	22.5937	0.839689
$725$	−3.00800	−0.111714
$726$	−80.7830	−2.99814
$727$	−10.9252	−0.405192	−0.202596	−	0.979262i	$-0.564938\pi$
$727$	−10.9252	−0.405192	−0.202596	+	0.979262i	$0.564938\pi$
$728$	5.61281	0.208025
$729$	77.6958	2.87762
$730$	−16.3476	−0.605052
$731$	2.32195	0.0858805
$732$	−11.0177	−0.407225
$733$	23.5729	0.870685	0.435343	−	0.900265i	$-0.356627\pi$
$733$	23.5729	0.870685	0.435343	+	0.900265i	$0.356627\pi$
$734$	68.9137	2.54365
$735$	−5.41842	−0.199861
$736$	−23.1438	−0.853092
$737$	−1.92683	−0.0709758
$738$	48.5750	1.78807
$739$	−2.24661	−0.0826429	−0.0413214	−	0.999146i	$-0.513157\pi$
$739$	−2.24661	−0.0826429	−0.0413214	+	0.999146i	$0.513157\pi$
$740$	26.9441	0.990486
$741$	0	0
$742$	27.6393	1.01467
$743$	26.9188	0.987554	0.493777	−	0.869588i	$-0.335616\pi$
$743$	26.9188	0.987554	0.493777	+	0.869588i	$0.335616\pi$
$744$	−2.80476	−0.102828
$745$	−8.85659	−0.324480
$746$	−14.0456	−0.514244
$747$	105.726	3.86832
$748$	0.659361	0.0241086
$749$	54.0173	1.97375
$750$	7.57362	0.276549
$751$	34.1357	1.24563	0.622816	−	0.782369i	$-0.285989\pi$
$751$	34.1357	1.24563	0.622816	+	0.782369i	$0.285989\pi$
$752$	0.389751	0.0142128
$753$	−49.1327	−1.79050
$754$	4.61785	0.168172
$755$	−8.37160	−0.304674
$756$	155.717	5.66337
$757$	18.8443	0.684909	0.342455	−	0.939534i	$-0.388742\pi$
$757$	18.8443	0.684909	0.342455	+	0.939534i	$0.388742\pi$
$758$	70.7504	2.56977
$759$	−7.87198	−0.285735
$760$	0	0
$761$	−10.8012	−0.391544	−0.195772	−	0.980649i	$-0.562721\pi$
$761$	−10.8012	−0.391544	−0.195772	+	0.980649i	$0.562721\pi$
$762$	−145.354	−5.26560
$763$	−7.37623	−0.267038
$764$	17.8109	0.644377
$765$	−2.79348	−0.100998
$766$	10.6510	0.384836
$767$	−0.409325	−0.0147799
$768$	53.6707	1.93668
$769$	48.9272	1.76436	0.882179	−	0.470914i	$-0.156076\pi$
$769$	48.9272	1.76436	0.882179	+	0.470914i	$0.156076\pi$
$770$	−3.88751	−0.140096
$771$	65.3384	2.35310
$772$	21.0106	0.756188
$773$	26.7556	0.962332	0.481166	−	0.876630i	$-0.340213\pi$
$773$	26.7556	0.962332	0.481166	+	0.876630i	$0.340213\pi$
$774$	119.946	4.31138
$775$	−0.297707	−0.0106939
$776$	34.7471	1.24735
$777$	80.7380	2.89646
$778$	37.0448	1.32812
$779$	0	0
$780$	−7.19251	−0.257533
$781$	−7.63860	−0.273330
$782$	−3.32072	−0.118749
$783$	49.1275	1.75567
$784$	0.0578781	0.00206707
$785$	−15.8665	−0.566301
$786$	−51.8808	−1.85053
$787$	−21.8346	−0.778320	−0.389160	−	0.921170i	$-0.627235\pi$
$787$	−21.8346	−0.778320	−0.389160	+	0.921170i	$0.627235\pi$
$788$	−30.1511	−1.07409
$789$	−39.1957	−1.39540
$790$	3.53186	0.125658
$791$	−33.3254	−1.18492
$792$	13.0613	0.464112
$793$	0.688452	0.0244477
$794$	22.7509	0.807401
$795$	−13.5818	−0.481696
$796$	−78.8503	−2.79478
$797$	13.0244	0.461347	0.230673	−	0.973031i	$-0.425907\pi$
$797$	13.0244	0.461347	0.230673	+	0.973031i	$0.425907\pi$
$798$	0	0
$799$	−3.88234	−0.137347
$800$	5.61633	0.198567
$801$	52.1646	1.84315
$802$	−29.6184	−1.04586
$803$	−4.12337	−0.145510
$804$	−35.7903	−1.26222
$805$	12.1115	0.426873
$806$	0.457036	0.0160984
$807$	−35.9696	−1.26619
$808$	1.65454	0.0582063
$809$	−9.02269	−0.317221	−0.158610	−	0.987341i	$-0.550701\pi$
$809$	−9.02269	−0.317221	−0.158610	+	0.987341i	$0.550701\pi$
$810$	−69.1593	−2.43001
$811$	22.3544	0.784969	0.392484	−	0.919759i	$-0.371616\pi$
$811$	22.3544	0.784969	0.392484	+	0.919759i	$0.371616\pi$
$812$	28.6792	1.00644
$813$	19.4220	0.681158
$814$	10.9862	0.385065
$815$	9.72260	0.340568
$816$	0.0411159	0.00143934
$817$	0	0
$818$	−14.2901	−0.499642
$819$	−15.6412	−0.546549
$820$	−8.66830	−0.302710
$821$	−34.8750	−1.21715	−0.608573	−	0.793498i	$-0.708258\pi$
$821$	−34.8750	−1.21715	−0.608573	+	0.793498i	$0.708258\pi$
$822$	100.288	3.49795
$823$	−5.04786	−0.175957	−0.0879786	−	0.996122i	$-0.528041\pi$
$823$	−5.04786	−0.175957	−0.0879786	+	0.996122i	$0.528041\pi$
$824$	−18.4337	−0.642168
$825$	1.91030	0.0665081
$826$	−4.10942	−0.142985
$827$	−50.2402	−1.74702	−0.873512	−	0.486804i	$-0.838163\pi$
$827$	−50.2402	−1.74702	−0.873512	+	0.486804i	$0.838163\pi$
$828$	−106.116	−3.68779
$829$	−16.2711	−0.565117	−0.282559	−	0.959250i	$-0.591183\pi$
$829$	−16.2711	−0.565117	−0.282559	+	0.959250i	$0.591183\pi$
$830$	−30.4991	−1.05864
$831$	78.7559	2.73201
$832$	−8.66949	−0.300560
$833$	−0.576527	−0.0199755
$834$	22.0383	0.763124
$835$	−0.282149	−0.00976417
$836$	0	0
$837$	4.86222	0.168063
$838$	69.9363	2.41591
$839$	21.6242	0.746551	0.373275	−	0.927721i	$-0.378235\pi$
$839$	21.6242	0.746551	0.373275	+	0.927721i	$0.378235\pi$
$840$	−27.6899	−0.955394
$841$	−19.9519	−0.687998
$842$	83.7429	2.88597
$843$	−23.6115	−0.813223
$844$	−77.7493	−2.67624
$845$	−12.5506	−0.431753
$846$	−200.552	−6.89511
$847$	31.3496	1.07718
$848$	0.145077	0.00498195
$849$	−88.4181	−3.03450
$850$	0.805843	0.0276402
$851$	−34.2272	−1.17329
$852$	−141.884	−4.86088
$853$	−39.5026	−1.35254	−0.676271	−	0.736653i	$-0.736405\pi$
$853$	−39.5026	−1.35254	−0.676271	+	0.736653i	$0.736405\pi$
$854$	6.91172	0.236514
$855$	0	0
$856$	52.3542	1.78943
$857$	12.4592	0.425599	0.212799	−	0.977096i	$-0.431742\pi$
$857$	12.4592	0.425599	0.212799	+	0.977096i	$0.431742\pi$
$858$	−2.93267	−0.100120
$859$	33.0423	1.12739	0.563694	−	0.825984i	$-0.309380\pi$
$859$	33.0423	1.12739	0.563694	+	0.825984i	$0.309380\pi$
$860$	−21.4046	−0.729891
$861$	−25.9745	−0.885209
$862$	54.7378	1.86438
$863$	8.86619	0.301809	0.150904	−	0.988548i	$-0.451781\pi$
$863$	8.86619	0.301809	0.150904	+	0.988548i	$0.451781\pi$
$864$	−91.7274	−3.12063
$865$	−15.1289	−0.514400
$866$	−33.5581	−1.14035
$867$	55.8146	1.89556
$868$	2.83843	0.0963425
$869$	0.890845	0.0302198
$870$	−22.7814	−0.772363
$871$	2.23639	0.0757773
$872$	−7.14914	−0.242100
$873$	−96.8300	−3.27720
$874$	0	0
$875$	−2.93910	−0.0993598
$876$	−76.5901	−2.58774
$877$	−11.1008	−0.374847	−0.187424	−	0.982279i	$-0.560014\pi$
$877$	−11.1008	−0.374847	−0.187424	+	0.982279i	$0.560014\pi$
$878$	−38.9852	−1.31569
$879$	3.54996	0.119737
$880$	−0.0204053	−0.000687862 0
$881$	41.9175	1.41224	0.706119	−	0.708094i	$-0.250445\pi$
$881$	41.9175	1.41224	0.706119	+	0.708094i	$0.250445\pi$
$882$	−29.7819	−1.00281
$883$	26.5966	0.895047	0.447524	−	0.894272i	$-0.352306\pi$
$883$	26.5966	0.895047	0.447524	+	0.894272i	$0.352306\pi$
$884$	−0.765293	−0.0257396
$885$	2.01935	0.0678795
$886$	82.4189	2.76892
$887$	−20.8117	−0.698788	−0.349394	−	0.936976i	$-0.613613\pi$
$887$	−20.8117	−0.698788	−0.349394	+	0.936976i	$0.613613\pi$
$888$	78.2523	2.62597
$889$	56.4075	1.89185
$890$	−15.0481	−0.504412
$891$	−17.4441	−0.584400
$892$	−66.7249	−2.23412
$893$	0	0
$894$	−67.0764	−2.24337
$895$	14.4533	0.483120
$896$	−54.0234	−1.80479
$897$	9.13668	0.305065
$898$	8.14692	0.271866
$899$	0.895502	0.0298666
$900$	25.7513	0.858377
$901$	−1.44512	−0.0481438
$902$	−3.53440	−0.117683
$903$	−64.1388	−2.13441
$904$	−32.2994	−1.07426
$905$	6.96487	0.231520
$906$	−63.4033	−2.10643
$907$	0.805231	0.0267372	0.0133686	−	0.999911i	$-0.495745\pi$
$907$	0.805231	0.0267372	0.0133686	+	0.999911i	$0.495745\pi$
$908$	−41.1818	−1.36667
$909$	−4.61070	−0.152927
$910$	4.51207	0.149574
$911$	−33.6958	−1.11639	−0.558196	−	0.829709i	$-0.688506\pi$
$911$	−33.6958	−1.11639	−0.558196	+	0.829709i	$0.688506\pi$
$912$	0	0
$913$	−7.69283	−0.254595
$914$	10.5727	0.349713
$915$	−3.39637	−0.112281
$916$	18.6858	0.617396
$917$	20.1334	0.664865
$918$	−13.1612	−0.434386
$919$	−14.2935	−0.471500	−0.235750	−	0.971814i	$-0.575755\pi$
$919$	−14.2935	−0.471500	−0.235750	+	0.971814i	$0.575755\pi$
$920$	11.7386	0.387010
$921$	−85.8911	−2.83021
$922$	66.8068	2.20016
$923$	8.86580	0.291821
$924$	−18.2134	−0.599176
$925$	8.30595	0.273098
$926$	40.3899	1.32729
$927$	51.3692	1.68719
$928$	−16.8939	−0.554570
$929$	14.8180	0.486163	0.243082	−	0.970006i	$-0.421842\pi$
$929$	14.8180	0.486163	0.243082	+	0.970006i	$0.421842\pi$
$930$	−2.25472	−0.0739350
$931$	0	0
$932$	−9.01339	−0.295244
$933$	−63.0071	−2.06276
$934$	−38.8001	−1.26958
$935$	0.203258	0.00664726
$936$	−15.1597	−0.495510
$937$	−48.5601	−1.58639	−0.793195	−	0.608968i	$-0.791584\pi$
$937$	−48.5601	−1.58639	−0.793195	+	0.608968i	$0.791584\pi$
$938$	22.4523	0.733093
$939$	50.9299	1.66203
$940$	35.7888	1.16730
$941$	−19.0289	−0.620323	−0.310162	−	0.950684i	$-0.600383\pi$
$941$	−19.0289	−0.620323	−0.310162	+	0.950684i	$0.600383\pi$
$942$	−120.167	−3.91525
$943$	11.0114	0.358580
$944$	−0.0215701	−0.000702047 0
$945$	48.0022	1.56151
$946$	−8.72749	−0.283755
$947$	−40.5470	−1.31760	−0.658801	−	0.752317i	$-0.728936\pi$
$947$	−40.5470	−1.31760	−0.658801	+	0.752317i	$0.728936\pi$
$948$	16.5471	0.537426
$949$	4.78582	0.155354
$950$	0	0
$951$	84.4697	2.73912
$952$	−2.94625	−0.0954884
$953$	37.8295	1.22542	0.612710	−	0.790308i	$-0.290080\pi$
$953$	37.8295	1.22542	0.612710	+	0.790308i	$0.290080\pi$
$954$	−74.6511	−2.41692
$955$	5.49050	0.177668
$956$	63.1232	2.04155
$957$	−5.74618	−0.185748
$958$	33.1159	1.06992
$959$	−38.9189	−1.25676
$960$	42.7696	1.38038
$961$	−30.9114	−0.997141
$962$	−12.7512	−0.411115
$963$	−145.896	−4.70142
$964$	23.4851	0.756403
$965$	6.47685	0.208497
$966$	91.7276	2.95129
$967$	28.0754	0.902843	0.451421	−	0.892311i	$-0.350917\pi$
$967$	28.0754	0.902843	0.451421	+	0.892311i	$0.350917\pi$
$968$	30.3844	0.976591
$969$	0	0
$970$	27.9328	0.896869
$971$	35.1868	1.12920	0.564599	−	0.825365i	$-0.309031\pi$
$971$	35.1868	1.12920	0.564599	+	0.825365i	$0.309031\pi$
$972$	−165.075	−5.29479
$973$	−8.55243	−0.274178
$974$	−0.760114	−0.0243556
$975$	−2.21721	−0.0710074
$976$	0.0362791	0.00116127
$977$	−53.3032	−1.70532	−0.852659	−	0.522467i	$-0.825012\pi$
$977$	−53.3032	−1.70532	−0.852659	+	0.522467i	$0.825012\pi$
$978$	73.6352	2.35460
$979$	−3.79559	−0.121307
$980$	5.31463	0.169770
$981$	19.9225	0.636077
$982$	7.65279	0.244210
$983$	50.8137	1.62070	0.810352	−	0.585943i	$-0.199276\pi$
$983$	50.8137	1.62070	0.810352	+	0.585943i	$0.199276\pi$
$984$	−25.1748	−0.802544
$985$	−9.29455	−0.296149
$986$	−2.42397	−0.0771951
$987$	107.241	3.41352
$988$	0	0
$989$	27.1903	0.864603
$990$	10.4998	0.333706
$991$	56.2102	1.78557	0.892787	−	0.450478i	$-0.148747\pi$
$991$	56.2102	1.78557	0.892787	+	0.450478i	$0.148747\pi$
$992$	−1.67202	−0.0530866
$993$	14.9880	0.475629
$994$	89.0082	2.82317
$995$	−24.3069	−0.770579
$996$	−142.892	−4.52769
$997$	37.4723	1.18676	0.593379	−	0.804923i	$-0.297793\pi$
$997$	37.4723	1.18676	0.593379	+	0.804923i	$0.297793\pi$
$998$	32.2689	1.02145
$999$	−135.655	−4.29194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.2		9
5.4	even	2		9025.2.a.cf.1.8		9
19.14	odd	18		95.2.k.a.6.3	✓	18
19.15	odd	18		95.2.k.a.16.3	yes	18
19.18	odd	2		1805.2.a.v.1.8		9
57.14	even	18		855.2.bs.c.766.1		18
57.53	even	18		855.2.bs.c.586.1		18
95.14	odd	18		475.2.l.c.101.1		18
95.33	even	36		475.2.u.b.424.1		36
95.34	odd	18		475.2.l.c.301.1		18
95.52	even	36		475.2.u.b.424.6		36
95.53	even	36		475.2.u.b.149.6		36
95.72	even	36		475.2.u.b.149.1		36
95.94	odd	2		9025.2.a.cc.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.3	✓	18	19.14	odd	18
95.2.k.a.16.3	yes	18	19.15	odd	18
475.2.l.c.101.1		18	95.14	odd	18
475.2.l.c.301.1		18	95.34	odd	18
475.2.u.b.149.1		36	95.72	even	36
475.2.u.b.149.6		36	95.53	even	36
475.2.u.b.424.1		36	95.33	even	36
475.2.u.b.424.6		36	95.52	even	36
855.2.bs.c.586.1		18	57.53	even	18
855.2.bs.c.766.1		18	57.14	even	18
1805.2.a.s.1.2		9	1.1	even	1	trivial
1805.2.a.v.1.8		9	19.18	odd	2
9025.2.a.cc.1.2		9	95.94	odd	2
9025.2.a.cf.1.8		9	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)

\(f(q)\)	\(=\)	\(q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +1.00000 q^{5} +7.57362 q^{6} -2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} +O(q^{10})\)	\(q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +1.00000 q^{5} +7.57362 q^{6} -2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} -2.28997 q^{10} -0.577601 q^{11} -10.7287 q^{12} +0.670397 q^{13} +6.73045 q^{14} -3.30730 q^{15} +0.0353277 q^{16} -0.351901 q^{17} -18.1783 q^{18} +3.24395 q^{20} +9.72050 q^{21} +1.32269 q^{22} -4.12081 q^{23} +9.42123 q^{24} +1.00000 q^{25} -1.53519 q^{26} -16.3323 q^{27} -9.53431 q^{28} -3.00800 q^{29} +7.57362 q^{30} -0.297707 q^{31} +5.61633 q^{32} +1.91030 q^{33} +0.805843 q^{34} -2.93910 q^{35} +25.7513 q^{36} +8.30595 q^{37} -2.21721 q^{39} -2.84861 q^{40} -2.67214 q^{41} -22.2596 q^{42} -6.59830 q^{43} -1.87371 q^{44} +7.93825 q^{45} +9.43652 q^{46} +11.0325 q^{47} -0.116839 q^{48} +1.63832 q^{49} -2.28997 q^{50} +1.16384 q^{51} +2.17474 q^{52} +4.10660 q^{53} +37.4004 q^{54} -0.577601 q^{55} +8.37237 q^{56} +6.88822 q^{58} -0.610572 q^{59} -10.7287 q^{60} +1.02693 q^{61} +0.681739 q^{62} -23.3313 q^{63} -12.9319 q^{64} +0.670397 q^{65} -4.37452 q^{66} +3.33593 q^{67} -1.14155 q^{68} +13.6288 q^{69} +6.73045 q^{70} +13.2247 q^{71} -22.6130 q^{72} +7.13879 q^{73} -19.0204 q^{74} -3.30730 q^{75} +1.69763 q^{77} +5.07733 q^{78} -1.54232 q^{79} +0.0353277 q^{80} +30.2010 q^{81} +6.11911 q^{82} +13.3186 q^{83} +31.5328 q^{84} -0.351901 q^{85} +15.1099 q^{86} +9.94837 q^{87} +1.64536 q^{88} +6.57130 q^{89} -18.1783 q^{90} -1.97037 q^{91} -13.3677 q^{92} +0.984606 q^{93} -25.2640 q^{94} -18.5749 q^{96} -12.1979 q^{97} -3.75170 q^{98} -4.58513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

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