LMFDB - Embedded newform 1849.2.a.p.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 $ x^20 - 5x^19 - 19x^18 + 127x^17 + 95x^16 - 1293x^15 + 329x^14 + 6765x^13 - 5068x^12 - 19360x^11 + 20357x^10 + 29618x^9 - 37889x^8 - 21700x^7 + 32885x^6 + 6093x^5 - 11330x^4 - 1004x^3 + 1386x^2 + 87*x - 43
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-1.97560$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97560 q^{2} -0.955865 q^{3} +1.90300 q^{4} +3.57694 q^{5} -1.88841 q^{6} +2.56717 q^{7} -0.191632 q^{8} -2.08632 q^{9} +O(q^{10})$	\(q+1.97560 q^{2} -0.955865 q^{3} +1.90300 q^{4} +3.57694 q^{5} -1.88841 q^{6} +2.56717 q^{7} -0.191632 q^{8} -2.08632 q^{9} +7.06661 q^{10} -2.18849 q^{11} -1.81901 q^{12} +1.23161 q^{13} +5.07170 q^{14} -3.41907 q^{15} -4.18459 q^{16} +2.68326 q^{17} -4.12174 q^{18} +8.30695 q^{19} +6.80693 q^{20} -2.45387 q^{21} -4.32358 q^{22} +1.65235 q^{23} +0.183174 q^{24} +7.79452 q^{25} +2.43316 q^{26} +4.86184 q^{27} +4.88533 q^{28} +3.71729 q^{29} -6.75473 q^{30} -4.21521 q^{31} -7.88382 q^{32} +2.09190 q^{33} +5.30105 q^{34} +9.18262 q^{35} -3.97027 q^{36} +9.61519 q^{37} +16.4112 q^{38} -1.17725 q^{39} -0.685456 q^{40} -11.1712 q^{41} -4.84786 q^{42} -4.16469 q^{44} -7.46265 q^{45} +3.26438 q^{46} +1.54939 q^{47} +3.99990 q^{48} -0.409641 q^{49} +15.3989 q^{50} -2.56483 q^{51} +2.34375 q^{52} +3.99930 q^{53} +9.60505 q^{54} -7.82809 q^{55} -0.491952 q^{56} -7.94033 q^{57} +7.34389 q^{58} +4.71856 q^{59} -6.50650 q^{60} -10.3761 q^{61} -8.32757 q^{62} -5.35594 q^{63} -7.20610 q^{64} +4.40539 q^{65} +4.13276 q^{66} -2.17499 q^{67} +5.10624 q^{68} -1.57942 q^{69} +18.1412 q^{70} -2.35716 q^{71} +0.399806 q^{72} -5.37049 q^{73} +18.9958 q^{74} -7.45051 q^{75} +15.8081 q^{76} -5.61822 q^{77} -2.32578 q^{78} -1.60299 q^{79} -14.9680 q^{80} +1.61171 q^{81} -22.0698 q^{82} +7.02619 q^{83} -4.66971 q^{84} +9.59786 q^{85} -3.55323 q^{87} +0.419384 q^{88} -9.42959 q^{89} -14.7432 q^{90} +3.16174 q^{91} +3.14442 q^{92} +4.02917 q^{93} +3.06098 q^{94} +29.7135 q^{95} +7.53587 q^{96} -6.48531 q^{97} -0.809287 q^{98} +4.56589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9} + 21 q^{11} + 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} - 9 q^{18} + 7 q^{19} + 17 q^{20} + 8 q^{21} - 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} - 58 q^{26} + 22 q^{27} + 28 q^{28} + 12 q^{29} + 24 q^{30} + 26 q^{31} - 3 q^{32} + 17 q^{33} - 54 q^{34} + 26 q^{35} + 14 q^{36} + 19 q^{37} + 5 q^{38} + 7 q^{39} - 16 q^{40} + 27 q^{41} + 52 q^{42} + 32 q^{44} - 75 q^{45} - 59 q^{46} + 45 q^{47} + 66 q^{48} + 20 q^{49} - 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} + 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} - 30 q^{61} - 72 q^{62} + 21 q^{63} - 7 q^{64} + 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} + 35 q^{69} + 80 q^{70} + 31 q^{71} + 15 q^{72} + 26 q^{73} + 87 q^{74} - 73 q^{75} + 68 q^{76} + 21 q^{77} - 50 q^{78} + 39 q^{79} + 60 q^{80} + 16 q^{81} - 45 q^{82} + 13 q^{83} + 31 q^{84} + 22 q^{85} + 61 q^{87} - 50 q^{88} + 4 q^{89} - 13 q^{90} + 25 q^{91} + 5 q^{92} - 67 q^{93} - 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} + 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9 + 21 * q^11 + 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 - 9 * q^18 + 7 * q^19 + 17 * q^20 + 8 * q^21 - 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 - 58 * q^26 + 22 * q^27 + 28 * q^28 + 12 * q^29 + 24 * q^30 + 26 * q^31 - 3 * q^32 + 17 * q^33 - 54 * q^34 + 26 * q^35 + 14 * q^36 + 19 * q^37 + 5 * q^38 + 7 * q^39 - 16 * q^40 + 27 * q^41 + 52 * q^42 + 32 * q^44 - 75 * q^45 - 59 * q^46 + 45 * q^47 + 66 * q^48 + 20 * q^49 - 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 + 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 - 30 * q^61 - 72 * q^62 + 21 * q^63 - 7 * q^64 + 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 + 35 * q^69 + 80 * q^70 + 31 * q^71 + 15 * q^72 + 26 * q^73 + 87 * q^74 - 73 * q^75 + 68 * q^76 + 21 * q^77 - 50 * q^78 + 39 * q^79 + 60 * q^80 + 16 * q^81 - 45 * q^82 + 13 * q^83 + 31 * q^84 + 22 * q^85 + 61 * q^87 - 50 * q^88 + 4 * q^89 - 13 * q^90 + 25 * q^91 + 5 * q^92 - 67 * q^93 - 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 + 35 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.97560	1.39696	0.698481	−	0.715629i	$-0.253860\pi$
$2$	1.97560	1.39696	0.698481	+	0.715629i	$0.253860\pi$
$3$	−0.955865	−0.551869	−0.275934	−	0.961176i	$-0.588987\pi$
$3$	−0.955865	−0.551869	−0.275934	+	0.961176i	$0.588987\pi$
$4$	1.90300	0.951500
$5$	3.57694	1.59966	0.799829	−	0.600228i	$-0.204924\pi$
$5$	3.57694	1.59966	0.799829	+	0.600228i	$0.204924\pi$
$6$	−1.88841	−0.770939
$7$	2.56717	0.970299	0.485149	−	0.874431i	$-0.338765\pi$
$7$	2.56717	0.970299	0.485149	+	0.874431i	$0.338765\pi$
$8$	−0.191632	−0.0677521
$9$	−2.08632	−0.695441
$10$	7.06661	2.23466
$11$	−2.18849	−0.659854	−0.329927	−	0.944006i	$-0.607024\pi$
$11$	−2.18849	−0.659854	−0.329927	+	0.944006i	$0.607024\pi$
$12$	−1.81901	−0.525103
$13$	1.23161	0.341586	0.170793	−	0.985307i	$-0.445367\pi$
$13$	1.23161	0.341586	0.170793	+	0.985307i	$0.445367\pi$
$14$	5.07170	1.35547
$15$	−3.41907	−0.882801
$16$	−4.18459	−1.04615
$17$	2.68326	0.650786	0.325393	−	0.945579i	$-0.394503\pi$
$17$	2.68326	0.650786	0.325393	+	0.945579i	$0.394503\pi$
$18$	−4.12174	−0.971504
$19$	8.30695	1.90575	0.952873	−	0.303370i	$-0.0981119\pi$
$19$	8.30695	1.90575	0.952873	+	0.303370i	$0.0981119\pi$
$20$	6.80693	1.52207
$21$	−2.45387	−0.535478
$22$	−4.32358	−0.921790
$23$	1.65235	0.344538	0.172269	−	0.985050i	$-0.444890\pi$
$23$	1.65235	0.344538	0.172269	+	0.985050i	$0.444890\pi$
$24$	0.183174	0.0373903
$25$	7.79452	1.55890
$26$	2.43316	0.477183
$27$	4.86184	0.935661
$28$	4.88533	0.923240
$29$	3.71729	0.690284	0.345142	−	0.938551i	$-0.387831\pi$
$29$	3.71729	0.690284	0.345142	+	0.938551i	$0.387831\pi$
$30$	−6.75473	−1.23324
$31$	−4.21521	−0.757073	−0.378537	−	0.925586i	$-0.623573\pi$
$31$	−4.21521	−0.757073	−0.378537	+	0.925586i	$0.623573\pi$
$32$	−7.88382	−1.39368
$33$	2.09190	0.364153
$34$	5.30105	0.909123
$35$	9.18262	1.55215
$36$	−3.97027	−0.661712
$37$	9.61519	1.58073	0.790364	−	0.612638i	$-0.209891\pi$
$37$	9.61519	1.58073	0.790364	+	0.612638i	$0.209891\pi$
$38$	16.4112	2.66225
$39$	−1.17725	−0.188511
$40$	−0.685456	−0.108380
$41$	−11.1712	−1.74464	−0.872321	−	0.488933i	$-0.837386\pi$
$41$	−11.1712	−1.74464	−0.872321	+	0.488933i	$0.837386\pi$
$42$	−4.84786	−0.748042
$43$	0	0
$43$	0	0
$44$	−4.16469	−0.627851
$45$	−7.46265	−1.11247
$46$	3.26438	0.481307
$47$	1.54939	0.226002	0.113001	−	0.993595i	$-0.463954\pi$
$47$	1.54939	0.226002	0.113001	+	0.993595i	$0.463954\pi$
$48$	3.99990	0.577336
$49$	−0.409641	−0.0585201
$50$	15.3989	2.17773
$51$	−2.56483	−0.359149
$52$	2.34375	0.325020
$53$	3.99930	0.549346	0.274673	−	0.961538i	$-0.411430\pi$
$53$	3.99930	0.549346	0.274673	+	0.961538i	$0.411430\pi$
$54$	9.60505	1.30708
$55$	−7.82809	−1.05554
$56$	−0.491952	−0.0657398
$57$	−7.94033	−1.05172
$58$	7.34389	0.964299
$59$	4.71856	0.614304	0.307152	−	0.951661i	$-0.400624\pi$
$59$	4.71856	0.614304	0.307152	+	0.951661i	$0.400624\pi$
$60$	−6.50650	−0.839986
$61$	−10.3761	−1.32853	−0.664264	−	0.747498i	$-0.731255\pi$
$61$	−10.3761	−1.32853	−0.664264	+	0.747498i	$0.731255\pi$
$62$	−8.32757	−1.05760
$63$	−5.35594	−0.674785
$64$	−7.20610	−0.900763
$65$	4.40539	0.546421
$66$	4.13276	0.508707
$67$	−2.17499	−0.265717	−0.132859	−	0.991135i	$-0.542416\pi$
$67$	−2.17499	−0.265717	−0.132859	+	0.991135i	$0.542416\pi$
$68$	5.10624	0.619223
$69$	−1.57942	−0.190140
$70$	18.1412	2.16829
$71$	−2.35716	−0.279743	−0.139872	−	0.990170i	$-0.544669\pi$
$71$	−2.35716	−0.279743	−0.139872	+	0.990170i	$0.544669\pi$
$72$	0.399806	0.0471176
$73$	−5.37049	−0.628569	−0.314284	−	0.949329i	$-0.601765\pi$
$73$	−5.37049	−0.628569	−0.314284	+	0.949329i	$0.601765\pi$
$74$	18.9958	2.20822
$75$	−7.45051	−0.860311
$76$	15.8081	1.81332
$77$	−5.61822	−0.640255
$78$	−2.32578	−0.263342
$79$	−1.60299	−0.180351	−0.0901753	−	0.995926i	$-0.528743\pi$
$79$	−1.60299	−0.180351	−0.0901753	+	0.995926i	$0.528743\pi$
$80$	−14.9680	−1.67348
$81$	1.61171	0.179078
$82$	−22.0698	−2.43720
$83$	7.02619	0.771225	0.385612	−	0.922661i	$-0.373990\pi$
$83$	7.02619	0.771225	0.385612	+	0.922661i	$0.373990\pi$
$84$	−4.66971	−0.509507
$85$	9.59786	1.04103
$86$	0	0
$87$	−3.55323	−0.380946
$88$	0.419384	0.0447065
$89$	−9.42959	−0.999534	−0.499767	−	0.866160i	$-0.666581\pi$
$89$	−9.42959	−0.999534	−0.499767	+	0.866160i	$0.666581\pi$
$90$	−14.7432	−1.55407
$91$	3.16174	0.331441
$92$	3.14442	0.327828
$93$	4.02917	0.417805
$94$	3.06098	0.315716
$95$	29.7135	3.04854
$96$	7.53587	0.769126
$97$	−6.48531	−0.658484	−0.329242	−	0.944246i	$-0.606793\pi$
$97$	−6.48531	−0.658484	−0.329242	+	0.944246i	$0.606793\pi$
$98$	−0.809287	−0.0817503
$99$	4.56589	0.458889
$100$	14.8330	1.48330
$101$	−1.31174	−0.130523	−0.0652615	−	0.997868i	$-0.520788\pi$
$101$	−1.31174	−0.130523	−0.0652615	+	0.997868i	$0.520788\pi$
$102$	−5.06709	−0.501717
$103$	3.56080	0.350856	0.175428	−	0.984492i	$-0.443869\pi$
$103$	3.56080	0.350856	0.175428	+	0.984492i	$0.443869\pi$
$104$	−0.236015	−0.0231432
$105$	−8.77734	−0.856581
$106$	7.90103	0.767416
$107$	17.1170	1.65477	0.827384	−	0.561637i	$-0.189828\pi$
$107$	17.1170	1.65477	0.827384	+	0.561637i	$0.189828\pi$
$108$	9.25208	0.890282
$109$	−5.58389	−0.534840	−0.267420	−	0.963580i	$-0.586171\pi$
$109$	−5.58389	−0.534840	−0.267420	+	0.963580i	$0.586171\pi$
$110$	−15.4652	−1.47455
$111$	−9.19083	−0.872355
$112$	−10.7426	−1.01508
$113$	−6.05365	−0.569479	−0.284740	−	0.958605i	$-0.591907\pi$
$113$	−6.05365	−0.569479	−0.284740	+	0.958605i	$0.591907\pi$
$114$	−15.6869	−1.46921
$115$	5.91036	0.551144
$116$	7.07401	0.656805
$117$	−2.56953	−0.237553
$118$	9.32199	0.858159
$119$	6.88838	0.631457
$120$	0.655204	0.0598116
$121$	−6.21052	−0.564593
$122$	−20.4991	−1.85590
$123$	10.6781	0.962814
$124$	−8.02154	−0.720356
$125$	9.99584	0.894055
$126$	−10.5812	−0.942649
$127$	4.06491	0.360703	0.180351	−	0.983602i	$-0.442276\pi$
$127$	4.06491	0.360703	0.180351	+	0.983602i	$0.442276\pi$
$128$	1.53125	0.135345
$129$	0	0
$130$	8.70329	0.763329
$131$	1.94840	0.170233	0.0851163	−	0.996371i	$-0.472874\pi$
$131$	1.94840	0.170233	0.0851163	+	0.996371i	$0.472874\pi$
$132$	3.98088	0.346491
$133$	21.3254	1.84914
$134$	−4.29691	−0.371196
$135$	17.3905	1.49674
$136$	−0.514198	−0.0440921
$137$	−1.36669	−0.116764	−0.0583819	−	0.998294i	$-0.518594\pi$
$137$	−1.36669	−0.116764	−0.0583819	+	0.998294i	$0.518594\pi$
$138$	−3.12031	−0.265618
$139$	−16.3408	−1.38601	−0.693005	−	0.720933i	$-0.743714\pi$
$139$	−16.3408	−1.38601	−0.693005	+	0.720933i	$0.743714\pi$
$140$	17.4745	1.47687
$141$	−1.48101	−0.124724
$142$	−4.65680	−0.390790
$143$	−2.69536	−0.225397
$144$	8.73040	0.727533
$145$	13.2965	1.10422
$146$	−10.6100	−0.878086
$147$	0.391561	0.0322954
$148$	18.2977	1.50406
$149$	11.1405	0.912664	0.456332	−	0.889810i	$-0.349163\pi$
$149$	11.1405	0.912664	0.456332	+	0.889810i	$0.349163\pi$
$150$	−14.7192	−1.20182
$151$	−16.8899	−1.37448	−0.687242	−	0.726428i	$-0.741179\pi$
$151$	−16.8899	−1.37448	−0.687242	+	0.726428i	$0.741179\pi$
$152$	−1.59188	−0.129118
$153$	−5.59814	−0.452583
$154$	−11.0994	−0.894412
$155$	−15.0776	−1.21106
$156$	−2.24031	−0.179368
$157$	9.49434	0.757731	0.378866	−	0.925452i	$-0.376314\pi$
$157$	9.49434	0.757731	0.378866	+	0.925452i	$0.376314\pi$
$158$	−3.16687	−0.251943
$159$	−3.82279	−0.303167
$160$	−28.2000	−2.22940
$161$	4.24186	0.334305
$162$	3.18409	0.250166
$163$	1.80302	0.141223	0.0706117	−	0.997504i	$-0.477505\pi$
$163$	1.80302	0.141223	0.0706117	+	0.997504i	$0.477505\pi$
$164$	−21.2587	−1.66003
$165$	7.48260	0.582520
$166$	13.8810	1.07737
$167$	−4.00256	−0.309727	−0.154864	−	0.987936i	$-0.549494\pi$
$167$	−4.00256	−0.309727	−0.154864	+	0.987936i	$0.549494\pi$
$168$	0.470239	0.0362797
$169$	−11.4831	−0.883319
$170$	18.9616	1.45428
$171$	−17.3310	−1.32533
$172$	0	0
$173$	11.2122	0.852448	0.426224	−	0.904618i	$-0.359844\pi$
$173$	11.2122	0.852448	0.426224	+	0.904618i	$0.359844\pi$
$174$	−7.01976	−0.532167
$175$	20.0099	1.51260
$176$	9.15792	0.690304
$177$	−4.51030	−0.339015
$178$	−18.6291	−1.39631
$179$	−23.2254	−1.73595	−0.867975	−	0.496607i	$-0.834579\pi$
$179$	−23.2254	−1.73595	−0.867975	+	0.496607i	$0.834579\pi$
$180$	−14.2014	−1.05851
$181$	−5.61074	−0.417043	−0.208522	−	0.978018i	$-0.566865\pi$
$181$	−5.61074	−0.417043	−0.208522	+	0.978018i	$0.566865\pi$
$182$	6.24635	0.463010
$183$	9.91819	0.733174
$184$	−0.316643	−0.0233432
$185$	34.3930	2.52862
$186$	7.96003	0.583658
$187$	−5.87228	−0.429423
$188$	2.94849	0.215041
$189$	12.4812	0.907871
$190$	58.7020	4.25869
$191$	−4.02540	−0.291268	−0.145634	−	0.989339i	$-0.546522\pi$
$191$	−4.02540	−0.291268	−0.145634	+	0.989339i	$0.546522\pi$
$192$	6.88806	0.497103
$193$	−11.8906	−0.855903	−0.427951	−	0.903802i	$-0.640765\pi$
$193$	−11.8906	−0.855903	−0.427951	+	0.903802i	$0.640765\pi$
$194$	−12.8124	−0.919876
$195$	−4.21096	−0.301553
$196$	−0.779546	−0.0556819
$197$	−16.5306	−1.17775	−0.588877	−	0.808222i	$-0.700430\pi$
$197$	−16.5306	−1.17775	−0.588877	+	0.808222i	$0.700430\pi$
$198$	9.02038	0.641050
$199$	−3.70628	−0.262731	−0.131366	−	0.991334i	$-0.541936\pi$
$199$	−3.70628	−0.262731	−0.131366	+	0.991334i	$0.541936\pi$
$200$	−1.49368	−0.105619
$201$	2.07899	0.146641
$202$	−2.59147	−0.182336
$203$	9.54292	0.669781
$204$	−4.88088	−0.341730
$205$	−39.9586	−2.79083
$206$	7.03471	0.490132
$207$	−3.44733	−0.239606
$208$	−5.15377	−0.357350
$209$	−18.1797	−1.25751
$210$	−17.3405	−1.19661
$211$	12.8791	0.886632	0.443316	−	0.896365i	$-0.353802\pi$
$211$	12.8791	0.886632	0.443316	+	0.896365i	$0.353802\pi$
$212$	7.61068	0.522703
$213$	2.25312	0.154382
$214$	33.8165	2.31165
$215$	0	0
$216$	−0.931683	−0.0633930
$217$	−10.8211	−0.734587
$218$	−11.0315	−0.747151
$219$	5.13347	0.346887
$220$	−14.8969	−1.00435
$221$	3.30472	0.222300
$222$	−18.1574	−1.21865
$223$	−22.1331	−1.48214	−0.741071	−	0.671426i	$-0.765682\pi$
$223$	−22.1331	−1.48214	−0.741071	+	0.671426i	$0.765682\pi$
$224$	−20.2391	−1.35228
$225$	−16.2619	−1.08413
$226$	−11.9596	−0.795541
$227$	16.0948	1.06825	0.534124	−	0.845406i	$-0.320641\pi$
$227$	16.0948	1.06825	0.534124	+	0.845406i	$0.320641\pi$
$228$	−15.1104	−1.00071
$229$	25.3506	1.67521	0.837607	−	0.546273i	$-0.183954\pi$
$229$	25.3506	1.67521	0.837607	+	0.546273i	$0.183954\pi$
$230$	11.6765	0.769926
$231$	5.37026	0.353337
$232$	−0.712352	−0.0467682
$233$	−24.5908	−1.61099	−0.805497	−	0.592599i	$-0.798102\pi$
$233$	−24.5908	−1.61099	−0.805497	+	0.592599i	$0.798102\pi$
$234$	−5.07637	−0.331852
$235$	5.54209	0.361526
$236$	8.97942	0.584510
$237$	1.53224	0.0995299
$238$	13.6087	0.882121
$239$	25.1557	1.62718	0.813592	−	0.581436i	$-0.197509\pi$
$239$	25.1557	1.62718	0.813592	+	0.581436i	$0.197509\pi$
$240$	14.3074	0.923540
$241$	−16.2930	−1.04952	−0.524761	−	0.851249i	$-0.675845\pi$
$241$	−16.2930	−1.04952	−0.524761	+	0.851249i	$0.675845\pi$
$242$	−12.2695	−0.788715
$243$	−16.1261	−1.03449
$244$	−19.7458	−1.26410
$245$	−1.46526	−0.0936121
$246$	21.0957	1.34501
$247$	10.2309	0.650977
$248$	0.807768	0.0512933
$249$	−6.71609	−0.425615
$250$	19.7478	1.24896
$251$	12.9337	0.816367	0.408183	−	0.912900i	$-0.366162\pi$
$251$	12.9337	0.816367	0.408183	+	0.912900i	$0.366162\pi$
$252$	−10.1924	−0.642058
$253$	−3.61614	−0.227345
$254$	8.03065	0.503888
$255$	−9.17426	−0.574515
$256$	17.4373	1.08983
$257$	4.44658	0.277370	0.138685	−	0.990337i	$-0.455712\pi$
$257$	4.44658	0.277370	0.138685	+	0.990337i	$0.455712\pi$
$258$	0	0
$259$	24.6838	1.53378
$260$	8.38346	0.519920
$261$	−7.75547	−0.480051
$262$	3.84927	0.237808
$263$	27.1428	1.67370	0.836848	−	0.547435i	$-0.184396\pi$
$263$	27.1428	1.67370	0.836848	+	0.547435i	$0.184396\pi$
$264$	−0.400874	−0.0246721
$265$	14.3053	0.878766
$266$	42.1304	2.58318
$267$	9.01341	0.551612
$268$	−4.13900	−0.252830
$269$	−18.6114	−1.13475	−0.567377	−	0.823458i	$-0.692042\pi$
$269$	−18.6114	−1.13475	−0.567377	+	0.823458i	$0.692042\pi$
$270$	34.3567	2.09088
$271$	−8.81077	−0.535216	−0.267608	−	0.963528i	$-0.586233\pi$
$271$	−8.81077	−0.535216	−0.267608	+	0.963528i	$0.586233\pi$
$272$	−11.2283	−0.680818
$273$	−3.02220	−0.182912
$274$	−2.70003	−0.163115
$275$	−17.0582	−1.02865
$276$	−3.00564	−0.180918
$277$	−7.46433	−0.448488	−0.224244	−	0.974533i	$-0.571991\pi$
$277$	−7.46433	−0.448488	−0.224244	+	0.974533i	$0.571991\pi$
$278$	−32.2830	−1.93620
$279$	8.79428	0.526500
$280$	−1.75968	−0.105161
$281$	7.73881	0.461659	0.230829	−	0.972994i	$-0.425856\pi$
$281$	7.73881	0.461659	0.230829	+	0.972994i	$0.425856\pi$
$282$	−2.92588	−0.174234
$283$	−9.42000	−0.559961	−0.279980	−	0.960006i	$-0.590328\pi$
$283$	−9.42000	−0.559961	−0.279980	+	0.960006i	$0.590328\pi$
$284$	−4.48567	−0.266176
$285$	−28.4021	−1.68239
$286$	−5.32495	−0.314871
$287$	−28.6783	−1.69282
$288$	16.4482	0.969218
$289$	−9.80012	−0.576478
$290$	26.2687	1.54255
$291$	6.19908	0.363397
$292$	−10.2201	−0.598083
$293$	−0.107188	−0.00626200	−0.00313100	−	0.999995i	$-0.500997\pi$
$293$	−0.107188	−0.00626200	−0.00313100	+	0.999995i	$0.500997\pi$
$294$	0.773569	0.0451154
$295$	16.8780	0.982676
$296$	−1.84258	−0.107098
$297$	−10.6401	−0.617399
$298$	22.0092	1.27496
$299$	2.03504	0.117690
$300$	−14.1783	−0.818586
$301$	0	0
$302$	−33.3678	−1.92010
$303$	1.25385	0.0720316
$304$	−34.7612	−1.99369
$305$	−37.1149	−2.12519
$306$	−11.0597	−0.632241
$307$	−26.5127	−1.51316	−0.756579	−	0.653902i	$-0.773131\pi$
$307$	−26.5127	−1.51316	−0.756579	+	0.653902i	$0.773131\pi$
$308$	−10.6915	−0.609203
$309$	−3.40364	−0.193626
$310$	−29.7872	−1.69180
$311$	−17.5860	−0.997208	−0.498604	−	0.866830i	$-0.666154\pi$
$311$	−17.5860	−0.997208	−0.498604	+	0.866830i	$0.666154\pi$
$312$	0.225599	0.0127720
$313$	1.38247	0.0781417	0.0390708	−	0.999236i	$-0.487560\pi$
$313$	1.38247	0.0781417	0.0390708	+	0.999236i	$0.487560\pi$
$314$	18.7570	1.05852
$315$	−19.1579	−1.07943
$316$	−3.05049	−0.171604
$317$	−13.0283	−0.731742	−0.365871	−	0.930666i	$-0.619229\pi$
$317$	−13.0283	−0.731742	−0.365871	+	0.930666i	$0.619229\pi$
$318$	−7.55232	−0.423513
$319$	−8.13524	−0.455486
$320$	−25.7758	−1.44091
$321$	−16.3616	−0.913215
$322$	8.38022	0.467011
$323$	22.2897	1.24023
$324$	3.06708	0.170393
$325$	9.59979	0.532500
$326$	3.56205	0.197284
$327$	5.33745	0.295162
$328$	2.14075	0.118203
$329$	3.97755	0.219290
$330$	14.7826	0.813757
$331$	16.8183	0.924415	0.462207	−	0.886772i	$-0.347058\pi$
$331$	16.8183	0.924415	0.462207	+	0.886772i	$0.347058\pi$
$332$	13.3708	0.733820
$333$	−20.0604	−1.09930
$334$	−7.90745	−0.432677
$335$	−7.77981	−0.425056
$336$	10.2684	0.560189
$337$	15.2529	0.830876	0.415438	−	0.909621i	$-0.363628\pi$
$337$	15.2529	0.830876	0.415438	+	0.909621i	$0.363628\pi$
$338$	−22.6861	−1.23396
$339$	5.78647	0.314278
$340$	18.2647	0.990545
$341$	9.22492	0.499558
$342$	−34.2391	−1.85144
$343$	−19.0218	−1.02708
$344$	0	0
$345$	−5.64950	−0.304159
$346$	22.1508	1.19084
$347$	25.3828	1.36262	0.681310	−	0.731995i	$-0.261411\pi$
$347$	25.3828	1.36262	0.681310	+	0.731995i	$0.261411\pi$
$348$	−6.76180	−0.362470
$349$	−34.2533	−1.83354	−0.916770	−	0.399417i	$-0.869213\pi$
$349$	−34.2533	−1.83354	−0.916770	+	0.399417i	$0.869213\pi$
$350$	39.5315	2.11305
$351$	5.98787	0.319609
$352$	17.2536	0.919622
$353$	−1.27972	−0.0681128	−0.0340564	−	0.999420i	$-0.510843\pi$
$353$	−1.27972	−0.0681128	−0.0340564	+	0.999420i	$0.510843\pi$
$354$	−8.91056	−0.473591
$355$	−8.43142	−0.447493
$356$	−17.9445	−0.951057
$357$	−6.58436	−0.348481
$358$	−45.8842	−2.42506
$359$	−5.01799	−0.264839	−0.132420	−	0.991194i	$-0.542275\pi$
$359$	−5.01799	−0.264839	−0.132420	+	0.991194i	$0.542275\pi$
$360$	1.43008	0.0753720
$361$	50.0055	2.63187
$362$	−11.0846	−0.582593
$363$	5.93642	0.311581
$364$	6.01680	0.315366
$365$	−19.2099	−1.00549
$366$	19.5944	1.02422
$367$	9.56331	0.499201	0.249600	−	0.968349i	$-0.419701\pi$
$367$	9.56331	0.499201	0.249600	+	0.968349i	$0.419701\pi$
$368$	−6.91440	−0.360438
$369$	23.3066	1.21330
$370$	67.9468	3.53239
$371$	10.2669	0.533030
$372$	7.66751	0.397542
$373$	29.0239	1.50280	0.751401	−	0.659846i	$-0.229378\pi$
$373$	29.0239	1.50280	0.751401	+	0.659846i	$0.229378\pi$
$374$	−11.6013	−0.599888
$375$	−9.55468	−0.493401
$376$	−0.296913	−0.0153121
$377$	4.57824	0.235791
$378$	24.6578	1.26826
$379$	−32.2574	−1.65695	−0.828477	−	0.560023i	$-0.810792\pi$
$379$	−32.2574	−1.65695	−0.828477	+	0.560023i	$0.810792\pi$
$380$	56.5448	2.90069
$381$	−3.88551	−0.199061
$382$	−7.95259	−0.406890
$383$	−3.86016	−0.197245	−0.0986224	−	0.995125i	$-0.531444\pi$
$383$	−3.86016	−0.197245	−0.0986224	+	0.995125i	$0.531444\pi$
$384$	−1.46367	−0.0746926
$385$	−20.0960	−1.02419
$386$	−23.4910	−1.19566
$387$	0	0
$388$	−12.3416	−0.626547
$389$	−15.2170	−0.771534	−0.385767	−	0.922596i	$-0.626063\pi$
$389$	−15.2170	−0.771534	−0.385767	+	0.922596i	$0.626063\pi$
$390$	−8.31917	−0.421258
$391$	4.43368	0.224221
$392$	0.0785002	0.00396486
$393$	−1.86241	−0.0939461
$394$	−32.6578	−1.64528
$395$	−5.73381	−0.288499
$396$	8.68889	0.436633
$397$	23.8160	1.19529	0.597645	−	0.801761i	$-0.296103\pi$
$397$	23.8160	1.19529	0.597645	+	0.801761i	$0.296103\pi$
$398$	−7.32214	−0.367025
$399$	−20.3842	−1.02048
$400$	−32.6169	−1.63084
$401$	−27.6524	−1.38089	−0.690446	−	0.723383i	$-0.742586\pi$
$401$	−27.6524	−1.38089	−0.690446	+	0.723383i	$0.742586\pi$
$402$	4.10727	0.204852
$403$	−5.19148	−0.258606
$404$	−2.49624	−0.124193
$405$	5.76498	0.286464
$406$	18.8530	0.935659
$407$	−21.0427	−1.04305
$408$	0.491504	0.0243331
$409$	10.3976	0.514126	0.257063	−	0.966395i	$-0.417245\pi$
$409$	10.3976	0.514126	0.257063	+	0.966395i	$0.417245\pi$
$410$	−78.9423	−3.89868
$411$	1.30637	0.0644384
$412$	6.77620	0.333839
$413$	12.1133	0.596058
$414$	−6.81055	−0.334720
$415$	25.1323	1.23370
$416$	−9.70977	−0.476060
$417$	15.6196	0.764896
$418$	−35.9158	−1.75670
$419$	−11.9546	−0.584021	−0.292010	−	0.956415i	$-0.594324\pi$
$419$	−11.9546	−0.584021	−0.292010	+	0.956415i	$0.594324\pi$
$420$	−16.7033	−0.815037
$421$	−2.25282	−0.109796	−0.0548978	−	0.998492i	$-0.517483\pi$
$421$	−2.25282	−0.109796	−0.0548978	+	0.998492i	$0.517483\pi$
$422$	25.4439	1.23859
$423$	−3.23253	−0.157171
$424$	−0.766394	−0.0372194
$425$	20.9147	1.01451
$426$	4.45128	0.215665
$427$	−26.6373	−1.28907
$428$	32.5737	1.57451
$429$	2.57640	0.124390
$430$	0	0
$431$	−4.45576	−0.214626	−0.107313	−	0.994225i	$-0.534225\pi$
$431$	−4.45576	−0.214626	−0.107313	+	0.994225i	$0.534225\pi$
$432$	−20.3448	−0.978839
$433$	32.6083	1.56705	0.783527	−	0.621357i	$-0.213418\pi$
$433$	32.6083	1.56705	0.783527	+	0.621357i	$0.213418\pi$
$434$	−21.3783	−1.02619
$435$	−12.7097	−0.609383
$436$	−10.6262	−0.508900
$437$	13.7260	0.656603
$438$	10.1417	0.484588
$439$	2.53238	0.120864	0.0604320	−	0.998172i	$-0.480752\pi$
$439$	2.53238	0.120864	0.0604320	+	0.998172i	$0.480752\pi$
$440$	1.50011	0.0715150
$441$	0.854642	0.0406973
$442$	6.52881	0.310544
$443$	−33.4862	−1.59098	−0.795489	−	0.605969i	$-0.792786\pi$
$443$	−33.4862	−1.59098	−0.795489	+	0.605969i	$0.792786\pi$
$444$	−17.4901	−0.830046
$445$	−33.7291	−1.59891
$446$	−43.7262	−2.07050
$447$	−10.6488	−0.503671
$448$	−18.4993	−0.874009
$449$	−15.4645	−0.729816	−0.364908	−	0.931044i	$-0.618900\pi$
$449$	−15.4645	−0.729816	−0.364908	+	0.931044i	$0.618900\pi$
$450$	−32.1270	−1.51448
$451$	24.4479	1.15121
$452$	−11.5201	−0.541860
$453$	16.1445	0.758535
$454$	31.7969	1.49230
$455$	11.3094	0.530192
$456$	1.52162	0.0712564
$457$	−16.5179	−0.772674	−0.386337	−	0.922358i	$-0.626260\pi$
$457$	−16.5179	−0.772674	−0.386337	+	0.922358i	$0.626260\pi$
$458$	50.0827	2.34021
$459$	13.0456	0.608915
$460$	11.2474	0.524413
$461$	−20.3775	−0.949075	−0.474537	−	0.880235i	$-0.657385\pi$
$461$	−20.3775	−0.949075	−0.474537	+	0.880235i	$0.657385\pi$
$462$	10.6095	0.493598
$463$	−2.14849	−0.0998490	−0.0499245	−	0.998753i	$-0.515898\pi$
$463$	−2.14849	−0.0998490	−0.0499245	+	0.998753i	$0.515898\pi$
$464$	−15.5553	−0.722139
$465$	14.4121	0.668345
$466$	−48.5816	−2.25050
$467$	19.4008	0.897761	0.448880	−	0.893592i	$-0.351823\pi$
$467$	19.4008	0.897761	0.448880	+	0.893592i	$0.351823\pi$
$468$	−4.88982	−0.226032
$469$	−5.58356	−0.257825
$470$	10.9490	0.505038
$471$	−9.07531	−0.418168
$472$	−0.904226	−0.0416204
$473$	0	0
$474$	3.02710	0.139039
$475$	64.7487	2.97087
$476$	13.1086	0.600831
$477$	−8.34383	−0.382038
$478$	49.6976	2.27311
$479$	16.2455	0.742274	0.371137	−	0.928578i	$-0.378968\pi$
$479$	16.2455	0.742274	0.371137	+	0.928578i	$0.378968\pi$
$480$	26.9554	1.23034
$481$	11.8421	0.539955
$482$	−32.1884	−1.46614
$483$	−4.05464	−0.184493
$484$	−11.8186	−0.537211
$485$	−23.1976	−1.05335
$486$	−31.8587	−1.44514
$487$	24.3177	1.10194	0.550970	−	0.834525i	$-0.314258\pi$
$487$	24.3177	1.10194	0.550970	+	0.834525i	$0.314258\pi$
$488$	1.98840	0.0900106
$489$	−1.72344	−0.0779368
$490$	−2.89477	−0.130772
$491$	−15.9460	−0.719634	−0.359817	−	0.933023i	$-0.617161\pi$
$491$	−15.9460	−0.719634	−0.359817	+	0.933023i	$0.617161\pi$
$492$	20.3205	0.916118
$493$	9.97446	0.449227
$494$	20.2122	0.909389
$495$	16.3319	0.734065
$496$	17.6389	0.792010
$497$	−6.05122	−0.271434
$498$	−13.2683	−0.594567
$499$	23.1599	1.03678	0.518390	−	0.855145i	$-0.326532\pi$
$499$	23.1599	1.03678	0.518390	+	0.855145i	$0.326532\pi$
$500$	19.0221	0.850694
$501$	3.82590	0.170929
$502$	25.5518	1.14043
$503$	−3.24110	−0.144514	−0.0722568	−	0.997386i	$-0.523020\pi$
$503$	−3.24110	−0.144514	−0.0722568	+	0.997386i	$0.523020\pi$
$504$	1.02637	0.0457181
$505$	−4.69202	−0.208792
$506$	−7.14406	−0.317592
$507$	10.9763	0.487476
$508$	7.73554	0.343209
$509$	24.6896	1.09435	0.547173	−	0.837020i	$-0.315704\pi$
$509$	24.6896	1.09435	0.547173	+	0.837020i	$0.315704\pi$
$510$	−18.1247	−0.802575
$511$	−13.7870	−0.609899
$512$	31.3867	1.38711
$513$	40.3871	1.78313
$514$	8.78468	0.387476
$515$	12.7368	0.561249
$516$	0	0
$517$	−3.39082	−0.149128
$518$	48.7654	2.14263
$519$	−10.7174	−0.470439
$520$	−0.844213	−0.0370212
$521$	−8.48200	−0.371603	−0.185802	−	0.982587i	$-0.559488\pi$
$521$	−8.48200	−0.371603	−0.185802	+	0.982587i	$0.559488\pi$
$522$	−15.3217	−0.670613
$523$	17.5075	0.765550	0.382775	−	0.923842i	$-0.374969\pi$
$523$	17.5075	0.765550	0.382775	+	0.923842i	$0.374969\pi$
$524$	3.70781	0.161976
$525$	−19.1267	−0.834759
$526$	53.6233	2.33809
$527$	−11.3105	−0.492693
$528$	−8.75374	−0.380957
$529$	−20.2697	−0.881293
$530$	28.2615	1.22760
$531$	−9.84443	−0.427212
$532$	40.5822	1.75946
$533$	−13.7585	−0.595946
$534$	17.8069	0.770581
$535$	61.2267	2.64706
$536$	0.416797	0.0180029
$537$	22.2004	0.958017
$538$	−36.7686	−1.58521
$539$	0.896493	0.0386147
$540$	33.0942	1.42415
$541$	−12.7760	−0.549281	−0.274641	−	0.961547i	$-0.588559\pi$
$541$	−12.7760	−0.549281	−0.274641	+	0.961547i	$0.588559\pi$
$542$	−17.4066	−0.747676
$543$	5.36311	0.230153
$544$	−21.1543	−0.906984
$545$	−19.9733	−0.855561
$546$	−5.97066	−0.255521
$547$	35.3539	1.51163	0.755813	−	0.654788i	$-0.227242\pi$
$547$	35.3539	1.51163	0.755813	+	0.654788i	$0.227242\pi$
$548$	−2.60081	−0.111101
$549$	21.6480	0.923913
$550$	−33.7002	−1.43698
$551$	30.8794	1.31551
$552$	0.302668	0.0128824
$553$	−4.11515	−0.174994
$554$	−14.7465	−0.626520
$555$	−32.8751	−1.39547
$556$	−31.0966	−1.31879
$557$	−5.24349	−0.222174	−0.111087	−	0.993811i	$-0.535433\pi$
$557$	−5.24349	−0.222174	−0.111087	+	0.993811i	$0.535433\pi$
$558$	17.3740	0.735500
$559$	0	0
$560$	−38.4255	−1.62377
$561$	5.61311	0.236985
$562$	15.2888	0.644919
$563$	28.1753	1.18745	0.593725	−	0.804668i	$-0.297657\pi$
$563$	28.1753	1.18745	0.593725	+	0.804668i	$0.297657\pi$
$564$	−2.81836	−0.118674
$565$	−21.6536	−0.910972
$566$	−18.6102	−0.782243
$567$	4.13752	0.173760
$568$	0.451707	0.0189532
$569$	−2.05471	−0.0861378	−0.0430689	−	0.999072i	$-0.513714\pi$
$569$	−2.05471	−0.0861378	−0.0430689	+	0.999072i	$0.513714\pi$
$570$	−56.1112	−2.35024
$571$	27.0350	1.13138	0.565690	−	0.824618i	$-0.308610\pi$
$571$	27.0350	1.13138	0.565690	+	0.824618i	$0.308610\pi$
$572$	−5.12927	−0.214465
$573$	3.84774	0.160742
$574$	−56.6568	−2.36481
$575$	12.8793	0.537102
$576$	15.0342	0.626427
$577$	26.9788	1.12314	0.561570	−	0.827429i	$-0.310197\pi$
$577$	26.9788	1.12314	0.561570	+	0.827429i	$0.310197\pi$
$578$	−19.3611	−0.805317
$579$	11.3658	0.472346
$580$	25.3033	1.05066
$581$	18.0374	0.748318
$582$	12.2469	0.507651
$583$	−8.75242	−0.362488
$584$	1.02916	0.0425868
$585$	−9.19106	−0.380004
$586$	−0.211761	−0.00874778
$587$	34.1690	1.41030	0.705152	−	0.709056i	$-0.250879\pi$
$587$	34.1690	1.41030	0.705152	+	0.709056i	$0.250879\pi$
$588$	0.745141	0.0307291
$589$	−35.0155	−1.44279
$590$	33.3442	1.37276
$591$	15.8010	0.649966
$592$	−40.2356	−1.65367
$593$	9.26302	0.380386	0.190193	−	0.981747i	$-0.439089\pi$
$593$	9.26302	0.380386	0.190193	+	0.981747i	$0.439089\pi$
$594$	−21.0205	−0.862483
$595$	24.6393	1.01011
$596$	21.2004	0.868400
$597$	3.54271	0.144993
$598$	4.02044	0.164408
$599$	45.8631	1.87392	0.936958	−	0.349442i	$-0.113629\pi$
$599$	45.8631	1.87392	0.936958	+	0.349442i	$0.113629\pi$
$600$	1.42776	0.0582879
$601$	10.2588	0.418464	0.209232	−	0.977866i	$-0.432904\pi$
$601$	10.2588	0.418464	0.209232	+	0.977866i	$0.432904\pi$
$602$	0	0
$603$	4.53773	0.184790
$604$	−32.1416	−1.30782
$605$	−22.2147	−0.903156
$606$	2.47710	0.100625
$607$	20.7329	0.841523	0.420762	−	0.907171i	$-0.361763\pi$
$607$	20.7329	0.841523	0.420762	+	0.907171i	$0.361763\pi$
$608$	−65.4905	−2.65599
$609$	−9.12174	−0.369632
$610$	−73.3242	−2.96881
$611$	1.90824	0.0771992
$612$	−10.6533	−0.430633
$613$	21.5475	0.870297	0.435148	−	0.900359i	$-0.356696\pi$
$613$	21.5475	0.870297	0.435148	+	0.900359i	$0.356696\pi$
$614$	−52.3785	−2.11382
$615$	38.1950	1.54017
$616$	1.07663	0.0433786
$617$	−17.1816	−0.691704	−0.345852	−	0.938289i	$-0.612410\pi$
$617$	−17.1816	−0.691704	−0.345852	+	0.938289i	$0.612410\pi$
$618$	−6.72424	−0.270488
$619$	−17.8450	−0.717252	−0.358626	−	0.933481i	$-0.616755\pi$
$619$	−17.8450	−0.717252	−0.358626	+	0.933481i	$0.616755\pi$
$620$	−28.6926	−1.15232
$621$	8.03345	0.322371
$622$	−34.7428	−1.39306
$623$	−24.2074	−0.969847
$624$	4.92631	0.197210
$625$	−3.21805	−0.128722
$626$	2.73120	0.109161
$627$	17.3773	0.693983
$628$	18.0677	0.720981
$629$	25.8001	1.02872
$630$	−37.8484	−1.50792
$631$	−31.1239	−1.23902	−0.619511	−	0.784988i	$-0.712669\pi$
$631$	−31.1239	−1.23902	−0.619511	+	0.784988i	$0.712669\pi$
$632$	0.307184	0.0122191
$633$	−12.3107	−0.489305
$634$	−25.7387	−1.02222
$635$	14.5400	0.577001
$636$	−7.27478	−0.288464
$637$	−0.504516	−0.0199897
$638$	−16.0720	−0.636297
$639$	4.91779	0.194545
$640$	5.47720	0.216505
$641$	44.9844	1.77678	0.888389	−	0.459091i	$-0.151825\pi$
$641$	44.9844	1.77678	0.888389	+	0.459091i	$0.151825\pi$
$642$	−32.3240	−1.27573
$643$	32.2173	1.27053	0.635263	−	0.772296i	$-0.280892\pi$
$643$	32.2173	1.27053	0.635263	+	0.772296i	$0.280892\pi$
$644$	8.07226	0.318092
$645$	0	0
$646$	44.0356	1.73256
$647$	−33.5667	−1.31965	−0.659823	−	0.751421i	$-0.729369\pi$
$647$	−33.5667	−1.31965	−0.659823	+	0.751421i	$0.729369\pi$
$648$	−0.308854	−0.0121329
$649$	−10.3265	−0.405351
$650$	18.9654	0.743882
$651$	10.3436	0.405396
$652$	3.43115	0.134374
$653$	29.0643	1.13737	0.568687	−	0.822554i	$-0.307452\pi$
$653$	29.0643	1.13737	0.568687	+	0.822554i	$0.307452\pi$
$654$	10.5447	0.412329
$655$	6.96932	0.272314
$656$	46.7467	1.82515
$657$	11.2046	0.437132
$658$	7.85806	0.306339
$659$	−18.7549	−0.730588	−0.365294	−	0.930892i	$-0.619032\pi$
$659$	−18.7549	−0.730588	−0.365294	+	0.930892i	$0.619032\pi$
$660$	14.2394	0.554268
$661$	−12.6567	−0.492288	−0.246144	−	0.969233i	$-0.579164\pi$
$661$	−12.6567	−0.492288	−0.246144	+	0.969233i	$0.579164\pi$
$662$	33.2262	1.29137
$663$	−3.15887	−0.122680
$664$	−1.34644	−0.0522521
$665$	76.2796	2.95800
$666$	−39.6313	−1.53568
$667$	6.14226	0.237829
$668$	−7.61687	−0.294705
$669$	21.1563	0.817948
$670$	−15.3698	−0.593787
$671$	22.7080	0.876634
$672$	19.3458	0.746282
$673$	8.96879	0.345721	0.172861	−	0.984946i	$-0.444699\pi$
$673$	8.96879	0.345721	0.172861	+	0.984946i	$0.444699\pi$
$674$	30.1336	1.16070
$675$	37.8957	1.45861
$676$	−21.8524	−0.840478
$677$	23.5498	0.905092	0.452546	−	0.891741i	$-0.350516\pi$
$677$	23.5498	0.905092	0.452546	+	0.891741i	$0.350516\pi$
$678$	11.4318	0.439034
$679$	−16.6489	−0.638926
$680$	−1.83926	−0.0705323
$681$	−15.3844	−0.589533
$682$	18.2248	0.697863
$683$	38.0863	1.45733	0.728666	−	0.684869i	$-0.240141\pi$
$683$	38.0863	1.45733	0.728666	+	0.684869i	$0.240141\pi$
$684$	−32.9809	−1.26105
$685$	−4.88856	−0.186782
$686$	−37.5795	−1.43479
$687$	−24.2318	−0.924499
$688$	0	0
$689$	4.92557	0.187649
$690$	−11.1612	−0.424898
$691$	25.9017	0.985349	0.492674	−	0.870214i	$-0.336019\pi$
$691$	25.9017	0.985349	0.492674	+	0.870214i	$0.336019\pi$
$692$	21.3368	0.811104
$693$	11.7214	0.445260
$694$	50.1463	1.90353
$695$	−58.4502	−2.21714
$696$	0.680912	0.0258099
$697$	−29.9751	−1.13539
$698$	−67.6709	−2.56138
$699$	23.5055	0.889058
$700$	38.0788	1.43924
$701$	17.0138	0.642603	0.321302	−	0.946977i	$-0.395880\pi$
$701$	17.0138	0.642603	0.321302	+	0.946977i	$0.395880\pi$
$702$	11.8297	0.446481
$703$	79.8729	3.01247
$704$	15.7705	0.594372
$705$	−5.29749	−0.199515
$706$	−2.52822	−0.0951510
$707$	−3.36746	−0.126646
$708$	−8.58311	−0.322573
$709$	−10.9355	−0.410692	−0.205346	−	0.978689i	$-0.565832\pi$
$709$	−10.9355	−0.410692	−0.205346	+	0.978689i	$0.565832\pi$
$710$	−16.6571	−0.625131
$711$	3.34436	0.125423
$712$	1.80701	0.0677206
$713$	−6.96499	−0.260841
$714$	−13.0081	−0.486815
$715$	−9.64114	−0.360558
$716$	−44.1980	−1.65176
$717$	−24.0454	−0.897992
$718$	−9.91355	−0.369970
$719$	29.2791	1.09193	0.545963	−	0.837810i	$-0.316164\pi$
$719$	29.2791	1.09193	0.545963	+	0.837810i	$0.316164\pi$
$720$	31.2281	1.16380
$721$	9.14117	0.340435
$722$	98.7908	3.67661
$723$	15.5739	0.579199
$724$	−10.6773	−0.396817
$725$	28.9745	1.07609
$726$	11.7280	0.435267
$727$	22.9263	0.850291	0.425146	−	0.905125i	$-0.360223\pi$
$727$	22.9263	0.850291	0.425146	+	0.905125i	$0.360223\pi$
$728$	−0.605891	−0.0224558
$729$	10.5792	0.391824
$730$	−37.9512	−1.40464
$731$	0	0
$732$	18.8743	0.697615
$733$	−34.2723	−1.26588	−0.632938	−	0.774203i	$-0.718151\pi$
$733$	−34.2723	−1.26588	−0.632938	+	0.774203i	$0.718151\pi$
$734$	18.8933	0.697364
$735$	1.40059	0.0516616
$736$	−13.0268	−0.480175
$737$	4.75993	0.175334
$738$	46.0446	1.69493
$739$	−14.9479	−0.549868	−0.274934	−	0.961463i	$-0.588656\pi$
$739$	−14.9479	−0.549868	−0.274934	+	0.961463i	$0.588656\pi$
$740$	65.4499	2.40599
$741$	−9.77936	−0.359254
$742$	20.2833	0.744623
$743$	28.9550	1.06225	0.531127	−	0.847292i	$-0.321769\pi$
$743$	28.9550	1.06225	0.531127	+	0.847292i	$0.321769\pi$
$744$	−0.772117	−0.0283072
$745$	39.8489	1.45995
$746$	57.3397	2.09936
$747$	−14.6589	−0.536341
$748$	−11.1749	−0.408597
$749$	43.9424	1.60562
$750$	−18.8762	−0.689262
$751$	−24.1440	−0.881028	−0.440514	−	0.897746i	$-0.645204\pi$
$751$	−24.1440	−0.881028	−0.440514	+	0.897746i	$0.645204\pi$
$752$	−6.48357	−0.236431
$753$	−12.3629	−0.450527
$754$	9.04478	0.329392
$755$	−60.4144	−2.19870
$756$	23.7517	0.863839
$757$	−41.3282	−1.50210	−0.751049	−	0.660246i	$-0.770452\pi$
$757$	−41.3282	−1.50210	−0.751049	+	0.660246i	$0.770452\pi$
$758$	−63.7279	−2.31470
$759$	3.45654	0.125465
$760$	−5.69405	−0.206545
$761$	14.2095	0.515093	0.257546	−	0.966266i	$-0.417086\pi$
$761$	14.2095	0.515093	0.257546	+	0.966266i	$0.417086\pi$
$762$	−7.67622	−0.278080
$763$	−14.3348	−0.518955
$764$	−7.66034	−0.277141
$765$	−20.0242	−0.723978
$766$	−7.62613	−0.275543
$767$	5.81141	0.209838
$768$	−16.6677	−0.601446
$769$	−2.73758	−0.0987197	−0.0493598	−	0.998781i	$-0.515718\pi$
$769$	−2.73758	−0.0987197	−0.0493598	+	0.998781i	$0.515718\pi$
$770$	−39.7018	−1.43075
$771$	−4.25033	−0.153072
$772$	−22.6278	−0.814392
$773$	−35.9639	−1.29353	−0.646766	−	0.762688i	$-0.723879\pi$
$773$	−35.9639	−1.29353	−0.646766	+	0.762688i	$0.723879\pi$
$774$	0	0
$775$	−32.8555	−1.18020
$776$	1.24279	0.0446136
$777$	−23.5944	−0.846445
$778$	−30.0628	−1.07780
$779$	−92.7983	−3.32484
$780$	−8.01345	−0.286928
$781$	5.15861	0.184590
$782$	8.75918	0.313228
$783$	18.0729	0.645872
$784$	1.71418	0.0612206
$785$	33.9607	1.21211
$786$	−3.67938	−0.131239
$787$	43.6763	1.55689	0.778445	−	0.627712i	$-0.216009\pi$
$787$	43.6763	1.55689	0.778445	+	0.627712i	$0.216009\pi$
$788$	−31.4577	−1.12063
$789$	−25.9449	−0.923661
$790$	−11.3277	−0.403022
$791$	−15.5407	−0.552565
$792$	−0.874970	−0.0310907
$793$	−12.7793	−0.453807
$794$	47.0509	1.66977
$795$	−13.6739	−0.484964
$796$	−7.05306	−0.249989
$797$	−14.4749	−0.512728	−0.256364	−	0.966580i	$-0.582525\pi$
$797$	−14.4749	−0.512728	−0.256364	+	0.966580i	$0.582525\pi$
$798$	−40.2710	−1.42558
$799$	4.15742	0.147079
$800$	−61.4506	−2.17261
$801$	19.6732	0.695117
$802$	−54.6300	−1.92905
$803$	11.7533	0.414763
$804$	3.95633	0.139529
$805$	15.1729	0.534774
$806$	−10.2563	−0.361262
$807$	17.7899	0.626236
$808$	0.251371	0.00884321
$809$	−35.6211	−1.25237	−0.626186	−	0.779674i	$-0.715385\pi$
$809$	−35.6211	−1.25237	−0.626186	+	0.779674i	$0.715385\pi$
$810$	11.3893	0.400179
$811$	−42.5507	−1.49416	−0.747079	−	0.664735i	$-0.768545\pi$
$811$	−42.5507	−1.49416	−0.747079	+	0.664735i	$0.768545\pi$
$812$	18.1602	0.637297
$813$	8.42191	0.295369
$814$	−41.5720	−1.45710
$815$	6.44930	0.225909
$816$	10.7328	0.375722
$817$	0	0
$818$	20.5414	0.718214
$819$	−6.59642	−0.230497
$820$	−76.0413	−2.65548
$821$	10.9102	0.380767	0.190384	−	0.981710i	$-0.439027\pi$
$821$	10.9102	0.380767	0.190384	+	0.981710i	$0.439027\pi$
$822$	2.58086	0.0900179
$823$	24.8587	0.866520	0.433260	−	0.901269i	$-0.357363\pi$
$823$	24.8587	0.866520	0.433260	+	0.901269i	$0.357363\pi$
$824$	−0.682362	−0.0237712
$825$	16.3053	0.567679
$826$	23.9311	0.832670
$827$	33.7121	1.17229	0.586143	−	0.810208i	$-0.300646\pi$
$827$	33.7121	1.17229	0.586143	+	0.810208i	$0.300646\pi$
$828$	−6.56027	−0.227985
$829$	−30.5682	−1.06168	−0.530839	−	0.847473i	$-0.678123\pi$
$829$	−30.5682	−1.06168	−0.530839	+	0.847473i	$0.678123\pi$
$830$	49.6514	1.72342
$831$	7.13489	0.247507
$832$	−8.87508	−0.307688
$833$	−1.09917	−0.0380841
$834$	30.8581	1.06853
$835$	−14.3169	−0.495457
$836$	−34.5959	−1.19652
$837$	−20.4936	−0.708364
$838$	−23.6175	−0.815854
$839$	−40.6542	−1.40354	−0.701769	−	0.712404i	$-0.747606\pi$
$839$	−40.6542	−1.40354	−0.701769	+	0.712404i	$0.747606\pi$
$840$	1.68202	0.0580352
$841$	−15.1817	−0.523508
$842$	−4.45067	−0.153380
$843$	−7.39726	−0.254775
$844$	24.5089	0.843631
$845$	−41.0746	−1.41301
$846$	−6.38619	−0.219562
$847$	−15.9435	−0.547824
$848$	−16.7354	−0.574697
$849$	9.00425	0.309025
$850$	41.3191	1.41724
$851$	15.8876	0.544622
$852$	4.28770	0.146894
$853$	−52.7654	−1.80665	−0.903327	−	0.428953i	$-0.858882\pi$
$853$	−52.7654	−1.80665	−0.903327	+	0.428953i	$0.858882\pi$
$854$	−52.6247	−1.80078
$855$	−61.9919	−2.12008
$856$	−3.28017	−0.112114
$857$	41.7400	1.42581	0.712905	−	0.701260i	$-0.247379\pi$
$857$	41.7400	1.42581	0.712905	+	0.701260i	$0.247379\pi$
$858$	5.08993	0.173767
$859$	39.9384	1.36268	0.681340	−	0.731967i	$-0.261397\pi$
$859$	39.9384	1.36268	0.681340	+	0.731967i	$0.261397\pi$
$860$	0	0
$861$	27.4125	0.934217
$862$	−8.80281	−0.299825
$863$	−27.1051	−0.922669	−0.461334	−	0.887226i	$-0.652629\pi$
$863$	−27.1051	−0.922669	−0.461334	+	0.887226i	$0.652629\pi$
$864$	−38.3298	−1.30401
$865$	40.1054	1.36362
$866$	64.4210	2.18911
$867$	9.36759	0.318140
$868$	−20.5927	−0.698960
$869$	3.50812	0.119005
$870$	−25.1093	−0.851285
$871$	−2.67873	−0.0907653
$872$	1.07005	0.0362365
$873$	13.5304	0.457936
$874$	27.1171	0.917248
$875$	25.6610	0.867501
$876$	9.76899	0.330064
$877$	−43.6034	−1.47238	−0.736191	−	0.676774i	$-0.763377\pi$
$877$	−43.6034	−1.47238	−0.736191	+	0.676774i	$0.763377\pi$
$878$	5.00298	0.168842
$879$	0.102457	0.00345581
$880$	32.7574	1.10425
$881$	19.0610	0.642182	0.321091	−	0.947048i	$-0.395950\pi$
$881$	19.0610	0.642182	0.321091	+	0.947048i	$0.395950\pi$
$882$	1.68843	0.0568525
$883$	40.8649	1.37521	0.687607	−	0.726083i	$-0.258661\pi$
$883$	40.8649	1.37521	0.687607	+	0.726083i	$0.258661\pi$
$884$	6.28889	0.211518
$885$	−16.1331	−0.542308
$886$	−66.1554	−2.22253
$887$	−18.7052	−0.628059	−0.314029	−	0.949413i	$-0.601679\pi$
$887$	−18.7052	−0.628059	−0.314029	+	0.949413i	$0.601679\pi$
$888$	1.76126	0.0591039
$889$	10.4353	0.349990
$890$	−66.6353	−2.23362
$891$	−3.52720	−0.118166
$892$	−42.1193	−1.41026
$893$	12.8707	0.430702
$894$	−21.0378	−0.703609
$895$	−83.0761	−2.77693
$896$	3.93098	0.131325
$897$	−1.94523	−0.0649493
$898$	−30.5517	−1.01952
$899$	−15.6691	−0.522595
$900$	−30.9464	−1.03155
$901$	10.7312	0.357507
$902$	48.2994	1.60819
$903$	0	0
$904$	1.16007	0.0385834
$905$	−20.0693	−0.667127
$906$	31.8951	1.05964
$907$	6.19913	0.205839	0.102919	−	0.994690i	$-0.467182\pi$
$907$	6.19913	0.205839	0.102919	+	0.994690i	$0.467182\pi$
$908$	30.6284	1.01644
$909$	2.73671	0.0907710
$910$	22.3428	0.740657
$911$	40.0897	1.32823	0.664116	−	0.747630i	$-0.268808\pi$
$911$	40.0897	1.32823	0.664116	+	0.747630i	$0.268808\pi$
$912$	33.2270	1.10026
$913$	−15.3767	−0.508895
$914$	−32.6327	−1.07940
$915$	35.4768	1.17283
$916$	48.2422	1.59397
$917$	5.00188	0.165177
$918$	25.7728	0.850631
$919$	32.0671	1.05780	0.528898	−	0.848685i	$-0.322605\pi$
$919$	32.0671	1.05780	0.528898	+	0.848685i	$0.322605\pi$
$920$	−1.13261	−0.0373411
$921$	25.3425	0.835065
$922$	−40.2578	−1.32582
$923$	−2.90309	−0.0955564
$924$	10.2196	0.336200
$925$	74.9458	2.46420
$926$	−4.24457	−0.139485
$927$	−7.42897	−0.243999
$928$	−29.3064	−0.962031
$929$	15.6108	0.512175	0.256087	−	0.966654i	$-0.417567\pi$
$929$	15.6108	0.512175	0.256087	+	0.966654i	$0.417567\pi$
$930$	28.4726	0.933652
$931$	−3.40287	−0.111524
$932$	−46.7963	−1.53286
$933$	16.8098	0.550328
$934$	38.3282	1.25414
$935$	−21.0048	−0.686931
$936$	0.492404	0.0160947
$937$	−38.7024	−1.26435	−0.632177	−	0.774824i	$-0.717838\pi$
$937$	−38.7024	−1.26435	−0.632177	+	0.774824i	$0.717838\pi$
$938$	−11.0309	−0.360171
$939$	−1.32145	−0.0431240
$940$	10.5466	0.343992
$941$	−2.86050	−0.0932495	−0.0466247	−	0.998912i	$-0.514846\pi$
$941$	−2.86050	−0.0932495	−0.0466247	+	0.998912i	$0.514846\pi$
$942$	−17.9292	−0.584165
$943$	−18.4586	−0.601096
$944$	−19.7452	−0.642652
$945$	44.6444	1.45228
$946$	0	0
$947$	−1.79165	−0.0582209	−0.0291105	−	0.999576i	$-0.509267\pi$
$947$	−1.79165	−0.0582209	−0.0291105	+	0.999576i	$0.509267\pi$
$948$	2.91586	0.0947027
$949$	−6.61434	−0.214710
$950$	127.918	4.15020
$951$	12.4533	0.403826
$952$	−1.32003	−0.0427825
$953$	15.8148	0.512291	0.256145	−	0.966638i	$-0.417547\pi$
$953$	15.8148	0.512291	0.256145	+	0.966638i	$0.417547\pi$
$954$	−16.4841	−0.533692
$955$	−14.3986	−0.465929
$956$	47.8712	1.54827
$957$	7.77620	0.251369
$958$	32.0945	1.03693
$959$	−3.50852	−0.113296
$960$	24.6382	0.795194
$961$	−13.2320	−0.426840
$962$	23.3953	0.754296
$963$	−35.7117	−1.15079
$964$	−31.0055	−0.998621
$965$	−42.5319	−1.36915
$966$	−8.01036	−0.257729
$967$	−37.0086	−1.19012	−0.595058	−	0.803683i	$-0.702871\pi$
$967$	−37.0086	−1.19012	−0.595058	+	0.803683i	$0.702871\pi$
$968$	1.19013	0.0382524
$969$	−21.3059	−0.684446
$970$	−45.8292	−1.47149
$971$	−8.72980	−0.280153	−0.140076	−	0.990141i	$-0.544735\pi$
$971$	−8.72980	−0.280153	−0.140076	+	0.990141i	$0.544735\pi$
$972$	−30.6880	−0.984317
$973$	−41.9497	−1.34484
$974$	48.0420	1.53937
$975$	−9.17610	−0.293870
$976$	43.4199	1.38984
$977$	−17.1361	−0.548232	−0.274116	−	0.961697i	$-0.588385\pi$
$977$	−17.1361	−0.548232	−0.274116	+	0.961697i	$0.588385\pi$
$978$	−3.40484	−0.108875
$979$	20.6365	0.659547
$980$	−2.78839	−0.0890720
$981$	11.6498	0.371949
$982$	−31.5030	−1.00530
$983$	19.7893	0.631182	0.315591	−	0.948895i	$-0.397797\pi$
$983$	19.7893	0.631182	0.315591	+	0.948895i	$0.397797\pi$
$984$	−2.04627	−0.0652327
$985$	−59.1289	−1.88400
$986$	19.7055	0.627553
$987$	−3.80200	−0.121019
$988$	19.4694	0.619405
$989$	0	0
$990$	32.2654	1.02546
$991$	13.3939	0.425471	0.212735	−	0.977110i	$-0.431763\pi$
$991$	13.3939	0.425471	0.212735	+	0.977110i	$0.431763\pi$
$992$	33.2319	1.05511
$993$	−16.0760	−0.510156
$994$	−11.9548	−0.379183
$995$	−13.2572	−0.420280
$996$	−12.7807	−0.404973
$997$	−29.3884	−0.930740	−0.465370	−	0.885116i	$-0.654079\pi$
$997$	−29.3884	−0.930740	−0.465370	+	0.885116i	$0.654079\pi$
$998$	45.7547	1.44834
$999$	46.7475	1.47903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.p.1.18	✓	20
43.42	odd	2		1849.2.a.r.1.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.18	✓	20	1.1	even	1	trivial
1849.2.a.r.1.3	yes	20	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97560 q^{2} -0.955865 q^{3} +1.90300 q^{4} +3.57694 q^{5} -1.88841 q^{6} +2.56717 q^{7} -0.191632 q^{8} -2.08632 q^{9} +O(q^{10})\)	\(q+1.97560 q^{2} -0.955865 q^{3} +1.90300 q^{4} +3.57694 q^{5} -1.88841 q^{6} +2.56717 q^{7} -0.191632 q^{8} -2.08632 q^{9} +7.06661 q^{10} -2.18849 q^{11} -1.81901 q^{12} +1.23161 q^{13} +5.07170 q^{14} -3.41907 q^{15} -4.18459 q^{16} +2.68326 q^{17} -4.12174 q^{18} +8.30695 q^{19} +6.80693 q^{20} -2.45387 q^{21} -4.32358 q^{22} +1.65235 q^{23} +0.183174 q^{24} +7.79452 q^{25} +2.43316 q^{26} +4.86184 q^{27} +4.88533 q^{28} +3.71729 q^{29} -6.75473 q^{30} -4.21521 q^{31} -7.88382 q^{32} +2.09190 q^{33} +5.30105 q^{34} +9.18262 q^{35} -3.97027 q^{36} +9.61519 q^{37} +16.4112 q^{38} -1.17725 q^{39} -0.685456 q^{40} -11.1712 q^{41} -4.84786 q^{42} -4.16469 q^{44} -7.46265 q^{45} +3.26438 q^{46} +1.54939 q^{47} +3.99990 q^{48} -0.409641 q^{49} +15.3989 q^{50} -2.56483 q^{51} +2.34375 q^{52} +3.99930 q^{53} +9.60505 q^{54} -7.82809 q^{55} -0.491952 q^{56} -7.94033 q^{57} +7.34389 q^{58} +4.71856 q^{59} -6.50650 q^{60} -10.3761 q^{61} -8.32757 q^{62} -5.35594 q^{63} -7.20610 q^{64} +4.40539 q^{65} +4.13276 q^{66} -2.17499 q^{67} +5.10624 q^{68} -1.57942 q^{69} +18.1412 q^{70} -2.35716 q^{71} +0.399806 q^{72} -5.37049 q^{73} +18.9958 q^{74} -7.45051 q^{75} +15.8081 q^{76} -5.61822 q^{77} -2.32578 q^{78} -1.60299 q^{79} -14.9680 q^{80} +1.61171 q^{81} -22.0698 q^{82} +7.02619 q^{83} -4.66971 q^{84} +9.59786 q^{85} -3.55323 q^{87} +0.419384 q^{88} -9.42959 q^{89} -14.7432 q^{90} +3.16174 q^{91} +3.14442 q^{92} +4.02917 q^{93} +3.06098 q^{94} +29.7135 q^{95} +7.53587 q^{96} -6.48531 q^{97} -0.809287 q^{98} +4.56589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9} + 21 q^{11} + 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} - 9 q^{18} + 7 q^{19} + 17 q^{20} + 8 q^{21} - 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} - 58 q^{26} + 22 q^{27} + 28 q^{28} + 12 q^{29} + 24 q^{30} + 26 q^{31} - 3 q^{32} + 17 q^{33} - 54 q^{34} + 26 q^{35} + 14 q^{36} + 19 q^{37} + 5 q^{38} + 7 q^{39} - 16 q^{40} + 27 q^{41} + 52 q^{42} + 32 q^{44} - 75 q^{45} - 59 q^{46} + 45 q^{47} + 66 q^{48} + 20 q^{49} - 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} + 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} - 30 q^{61} - 72 q^{62} + 21 q^{63} - 7 q^{64} + 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} + 35 q^{69} + 80 q^{70} + 31 q^{71} + 15 q^{72} + 26 q^{73} + 87 q^{74} - 73 q^{75} + 68 q^{76} + 21 q^{77} - 50 q^{78} + 39 q^{79} + 60 q^{80} + 16 q^{81} - 45 q^{82} + 13 q^{83} + 31 q^{84} + 22 q^{85} + 61 q^{87} - 50 q^{88} + 4 q^{89} - 13 q^{90} + 25 q^{91} + 5 q^{92} - 67 q^{93} - 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} + 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9 + 21 * q^11 + 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 - 9 * q^18 + 7 * q^19 + 17 * q^20 + 8 * q^21 - 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 - 58 * q^26 + 22 * q^27 + 28 * q^28 + 12 * q^29 + 24 * q^30 + 26 * q^31 - 3 * q^32 + 17 * q^33 - 54 * q^34 + 26 * q^35 + 14 * q^36 + 19 * q^37 + 5 * q^38 + 7 * q^39 - 16 * q^40 + 27 * q^41 + 52 * q^42 + 32 * q^44 - 75 * q^45 - 59 * q^46 + 45 * q^47 + 66 * q^48 + 20 * q^49 - 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 + 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 - 30 * q^61 - 72 * q^62 + 21 * q^63 - 7 * q^64 + 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 + 35 * q^69 + 80 * q^70 + 31 * q^71 + 15 * q^72 + 26 * q^73 + 87 * q^74 - 73 * q^75 + 68 * q^76 + 21 * q^77 - 50 * q^78 + 39 * q^79 + 60 * q^80 + 16 * q^81 - 45 * q^82 + 13 * q^83 + 31 * q^84 + 22 * q^85 + 61 * q^87 - 50 * q^88 + 4 * q^89 - 13 * q^90 + 25 * q^91 + 5 * q^92 - 67 * q^93 - 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 + 35 * q^98 + 13 * q^99

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