LMFDB - Embedded newform 1849.2.a.o.1.14

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.78421$ 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)

$f(q)$	$=$	$q+1.78421 q^{2} -2.96672 q^{3} +1.18339 q^{4} +0.596316 q^{5} -5.29325 q^{6} +4.36308 q^{7} -1.45700 q^{8} +5.80145 q^{9} +O(q^{10})$	\(q+1.78421 q^{2} -2.96672 q^{3} +1.18339 q^{4} +0.596316 q^{5} -5.29325 q^{6} +4.36308 q^{7} -1.45700 q^{8} +5.80145 q^{9} +1.06395 q^{10} +2.03573 q^{11} -3.51080 q^{12} -1.74313 q^{13} +7.78463 q^{14} -1.76911 q^{15} -4.96637 q^{16} +1.46763 q^{17} +10.3510 q^{18} +2.17572 q^{19} +0.705676 q^{20} -12.9440 q^{21} +3.63216 q^{22} -2.72236 q^{23} +4.32250 q^{24} -4.64441 q^{25} -3.11011 q^{26} -8.31113 q^{27} +5.16324 q^{28} +7.57422 q^{29} -3.15645 q^{30} -0.569957 q^{31} -5.94703 q^{32} -6.03945 q^{33} +2.61856 q^{34} +2.60177 q^{35} +6.86539 q^{36} +3.96167 q^{37} +3.88193 q^{38} +5.17139 q^{39} -0.868830 q^{40} +2.12568 q^{41} -23.0949 q^{42} +2.40907 q^{44} +3.45950 q^{45} -4.85724 q^{46} +9.36309 q^{47} +14.7338 q^{48} +12.0365 q^{49} -8.28658 q^{50} -4.35406 q^{51} -2.06281 q^{52} -5.90594 q^{53} -14.8288 q^{54} +1.21394 q^{55} -6.35699 q^{56} -6.45476 q^{57} +13.5140 q^{58} +5.11026 q^{59} -2.09355 q^{60} +9.78609 q^{61} -1.01692 q^{62} +25.3122 q^{63} -0.678000 q^{64} -1.03946 q^{65} -10.7756 q^{66} -0.530129 q^{67} +1.73678 q^{68} +8.07648 q^{69} +4.64210 q^{70} +5.33822 q^{71} -8.45269 q^{72} +14.0584 q^{73} +7.06843 q^{74} +13.7787 q^{75} +2.57473 q^{76} +8.88205 q^{77} +9.22683 q^{78} +3.65266 q^{79} -2.96153 q^{80} +7.25248 q^{81} +3.79266 q^{82} -10.3460 q^{83} -15.3179 q^{84} +0.875173 q^{85} -22.4706 q^{87} -2.96605 q^{88} +6.03765 q^{89} +6.17246 q^{90} -7.60542 q^{91} -3.22162 q^{92} +1.69091 q^{93} +16.7057 q^{94} +1.29742 q^{95} +17.6432 q^{96} +10.2551 q^{97} +21.4755 q^{98} +11.8102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * 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 $

$2$	1.78421	1.26162	0.630812	−	0.775936i	$-0.282722\pi$
$2$	1.78421	1.26162	0.630812	+	0.775936i	$0.282722\pi$
$3$	−2.96672	−1.71284	−0.856419	−	0.516281i	$-0.827316\pi$
$3$	−2.96672	−1.71284	−0.856419	+	0.516281i	$0.827316\pi$
$4$	1.18339	0.591696
$5$	0.596316	0.266681	0.133340	−	0.991070i	$-0.457430\pi$
$5$	0.596316	0.266681	0.133340	+	0.991070i	$0.457430\pi$
$6$	−5.29325	−2.16096
$7$	4.36308	1.64909	0.824544	−	0.565797i	$-0.191432\pi$
$7$	4.36308	1.64909	0.824544	+	0.565797i	$0.191432\pi$
$8$	−1.45700	−0.515126
$9$	5.80145	1.93382
$10$	1.06395	0.336451
$11$	2.03573	0.613796	0.306898	−	0.951742i	$-0.400709\pi$
$11$	2.03573	0.613796	0.306898	+	0.951742i	$0.400709\pi$
$12$	−3.51080	−1.01348
$13$	−1.74313	−0.483458	−0.241729	−	0.970344i	$-0.577714\pi$
$13$	−1.74313	−0.483458	−0.241729	+	0.970344i	$0.577714\pi$
$14$	7.78463	2.08053
$15$	−1.76911	−0.456781
$16$	−4.96637	−1.24159
$17$	1.46763	0.355953	0.177976	−	0.984035i	$-0.443045\pi$
$17$	1.46763	0.355953	0.177976	+	0.984035i	$0.443045\pi$
$18$	10.3510	2.43975
$19$	2.17572	0.499144	0.249572	−	0.968356i	$-0.419710\pi$
$19$	2.17572	0.499144	0.249572	+	0.968356i	$0.419710\pi$
$20$	0.705676	0.157794
$21$	−12.9440	−2.82462
$22$	3.63216	0.774380
$23$	−2.72236	−0.567650	−0.283825	−	0.958876i	$-0.591604\pi$
$23$	−2.72236	−0.567650	−0.283825	+	0.958876i	$0.591604\pi$
$24$	4.32250	0.882328
$25$	−4.64441	−0.928881
$26$	−3.11011	−0.609942
$27$	−8.31113	−1.59948
$28$	5.16324	0.975760
$29$	7.57422	1.40650	0.703249	−	0.710944i	$-0.251732\pi$
$29$	7.57422	1.40650	0.703249	+	0.710944i	$0.251732\pi$
$30$	−3.15645	−0.576286
$31$	−0.569957	−0.102367	−0.0511837	−	0.998689i	$-0.516299\pi$
$31$	−0.569957	−0.102367	−0.0511837	+	0.998689i	$0.516299\pi$
$32$	−5.94703	−1.05130
$33$	−6.03945	−1.05133
$34$	2.61856	0.449079
$35$	2.60177	0.439780
$36$	6.86539	1.14423
$37$	3.96167	0.651294	0.325647	−	0.945491i	$-0.394418\pi$
$37$	3.96167	0.651294	0.325647	+	0.945491i	$0.394418\pi$
$38$	3.88193	0.629733
$39$	5.17139	0.828086
$40$	−0.868830	−0.137374
$41$	2.12568	0.331976	0.165988	−	0.986128i	$-0.446919\pi$
$41$	2.12568	0.331976	0.165988	+	0.986128i	$0.446919\pi$
$42$	−23.0949	−3.56361
$43$	0	0
$43$	0	0
$44$	2.40907	0.363181
$45$	3.45950	0.515712
$46$	−4.85724	−0.716161
$47$	9.36309	1.36575	0.682874	−	0.730536i	$-0.260730\pi$
$47$	9.36309	1.36575	0.682874	+	0.730536i	$0.260730\pi$
$48$	14.7338	2.12665
$49$	12.0365	1.71949
$50$	−8.28658	−1.17190
$51$	−4.35406	−0.609690
$52$	−2.06281	−0.286060
$53$	−5.90594	−0.811243	−0.405621	−	0.914041i	$-0.632945\pi$
$53$	−5.90594	−0.811243	−0.405621	+	0.914041i	$0.632945\pi$
$54$	−14.8288	−2.01794
$55$	1.21394	0.163687
$56$	−6.35699	−0.849488
$57$	−6.45476	−0.854954
$58$	13.5140	1.77447
$59$	5.11026	0.665299	0.332649	−	0.943051i	$-0.392057\pi$
$59$	5.11026	0.665299	0.332649	+	0.943051i	$0.392057\pi$
$60$	−2.09355	−0.270276
$61$	9.78609	1.25298	0.626490	−	0.779429i	$-0.284491\pi$
$61$	9.78609	1.25298	0.626490	+	0.779429i	$0.284491\pi$
$62$	−1.01692	−0.129149
$63$	25.3122	3.18904
$64$	−0.678000	−0.0847500
$65$	−1.03946	−0.128929
$66$	−10.7756	−1.32639
$67$	−0.530129	−0.0647656	−0.0323828	−	0.999476i	$-0.510310\pi$
$67$	−0.530129	−0.0647656	−0.0323828	+	0.999476i	$0.510310\pi$
$68$	1.73678	0.210616
$69$	8.07648	0.972293
$70$	4.64210	0.554837
$71$	5.33822	0.633530	0.316765	−	0.948504i	$-0.397403\pi$
$71$	5.33822	0.633530	0.316765	+	0.948504i	$0.397403\pi$
$72$	−8.45269	−0.996159
$73$	14.0584	1.64541	0.822703	−	0.568471i	$-0.192465\pi$
$73$	14.0584	1.64541	0.822703	+	0.568471i	$0.192465\pi$
$74$	7.06843	0.821688
$75$	13.7787	1.59102
$76$	2.57473	0.295342
$77$	8.88205	1.01220
$78$	9.22683	1.04473
$79$	3.65266	0.410957	0.205478	−	0.978662i	$-0.434125\pi$
$79$	3.65266	0.410957	0.205478	+	0.978662i	$0.434125\pi$
$80$	−2.96153	−0.331109
$81$	7.25248	0.805831
$82$	3.79266	0.418829
$83$	−10.3460	−1.13562	−0.567812	−	0.823159i	$-0.692210\pi$
$83$	−10.3460	−1.13562	−0.567812	+	0.823159i	$0.692210\pi$
$84$	−15.3179	−1.67132
$85$	0.875173	0.0949258
$86$	0	0
$87$	−22.4706	−2.40910
$88$	−2.96605	−0.316182
$89$	6.03765	0.639990	0.319995	−	0.947419i	$-0.396319\pi$
$89$	6.03765	0.639990	0.319995	+	0.947419i	$0.396319\pi$
$90$	6.17246	0.650634
$91$	−7.60542	−0.797265
$92$	−3.22162	−0.335877
$93$	1.69091	0.175339
$94$	16.7057	1.72306
$95$	1.29742	0.133112
$96$	17.6432	1.80070
$97$	10.2551	1.04125	0.520624	−	0.853786i	$-0.325699\pi$
$97$	10.2551	1.04125	0.520624	+	0.853786i	$0.325699\pi$
$98$	21.4755	2.16936
$99$	11.8102	1.18697
$100$	−5.49616	−0.549616
$101$	−11.1802	−1.11247	−0.556234	−	0.831026i	$-0.687754\pi$
$101$	−11.1802	−1.11247	−0.556234	+	0.831026i	$0.687754\pi$
$102$	−7.76854	−0.769200
$103$	−0.139535	−0.0137488	−0.00687442	−	0.999976i	$-0.502188\pi$
$103$	−0.139535	−0.0137488	−0.00687442	+	0.999976i	$0.502188\pi$
$104$	2.53974	0.249042
$105$	−7.71875	−0.753272
$106$	−10.5374	−1.02348
$107$	5.84873	0.565418	0.282709	−	0.959206i	$-0.408767\pi$
$107$	5.84873	0.565418	0.282709	+	0.959206i	$0.408767\pi$
$108$	−9.83533	−0.946405
$109$	0.788682	0.0755420	0.0377710	−	0.999286i	$-0.487974\pi$
$109$	0.788682	0.0755420	0.0377710	+	0.999286i	$0.487974\pi$
$110$	2.16592	0.206512
$111$	−11.7532	−1.11556
$112$	−21.6687	−2.04750
$113$	6.02142	0.566448	0.283224	−	0.959054i	$-0.408596\pi$
$113$	6.02142	0.566448	0.283224	+	0.959054i	$0.408596\pi$
$114$	−11.5166	−1.07863
$115$	−1.62338	−0.151381
$116$	8.96328	0.832220
$117$	−10.1127	−0.934919
$118$	9.11775	0.839357
$119$	6.40339	0.586998
$120$	2.57758	0.235300
$121$	−6.85580	−0.623255
$122$	17.4604	1.58079
$123$	−6.30632	−0.568622
$124$	−0.674483	−0.0605704
$125$	−5.75112	−0.514395
$126$	45.1622	4.02337
$127$	−3.78116	−0.335523	−0.167762	−	0.985828i	$-0.553654\pi$
$127$	−3.78116	−0.335523	−0.167762	+	0.985828i	$0.553654\pi$
$128$	10.6844	0.944374
$129$	0	0
$130$	−1.85461	−0.162660
$131$	17.3598	1.51673	0.758367	−	0.651827i	$-0.225997\pi$
$131$	17.3598	1.51673	0.758367	+	0.651827i	$0.225997\pi$
$132$	−7.14704	−0.622070
$133$	9.49284	0.823133
$134$	−0.945859	−0.0817098
$135$	−4.95606	−0.426550
$136$	−2.13833	−0.183361
$137$	−3.11074	−0.265768	−0.132884	−	0.991132i	$-0.542424\pi$
$137$	−3.11074	−0.265768	−0.132884	+	0.991132i	$0.542424\pi$
$138$	14.4101	1.22667
$139$	5.22160	0.442891	0.221445	−	0.975173i	$-0.428923\pi$
$139$	5.22160	0.442891	0.221445	+	0.975173i	$0.428923\pi$
$140$	3.07892	0.260216
$141$	−27.7777	−2.33931
$142$	9.52449	0.799277
$143$	−3.54855	−0.296744
$144$	−28.8121	−2.40101
$145$	4.51663	0.375086
$146$	25.0830	2.07589
$147$	−35.7088	−2.94522
$148$	4.68821	0.385368
$149$	−20.3627	−1.66818	−0.834090	−	0.551628i	$-0.814007\pi$
$149$	−20.3627	−1.66818	−0.834090	+	0.551628i	$0.814007\pi$
$150$	24.5840	2.00728
$151$	19.9663	1.62484	0.812418	−	0.583076i	$-0.198151\pi$
$151$	19.9663	1.62484	0.812418	+	0.583076i	$0.198151\pi$
$152$	−3.17001	−0.257122
$153$	8.51439	0.688348
$154$	15.8474	1.27702
$155$	−0.339875	−0.0272994
$156$	6.11979	0.489975
$157$	−17.2137	−1.37380	−0.686902	−	0.726750i	$-0.741030\pi$
$157$	−17.2137	−1.37380	−0.686902	+	0.726750i	$0.741030\pi$
$158$	6.51711	0.518473
$159$	17.5213	1.38953
$160$	−3.54631	−0.280361
$161$	−11.8778	−0.936106
$162$	12.9399	1.01666
$163$	−21.8239	−1.70938	−0.854689	−	0.519140i	$-0.826252\pi$
$163$	−21.8239	−1.70938	−0.854689	+	0.519140i	$0.826252\pi$
$164$	2.51552	0.196429
$165$	−3.60142	−0.280370
$166$	−18.4594	−1.43273
$167$	8.47992	0.656196	0.328098	−	0.944644i	$-0.393592\pi$
$167$	8.47992	0.656196	0.328098	+	0.944644i	$0.393592\pi$
$168$	18.8594	1.45504
$169$	−9.96149	−0.766268
$170$	1.56149	0.119761
$171$	12.6223	0.965254
$172$	0	0
$173$	−11.0837	−0.842677	−0.421338	−	0.906904i	$-0.638439\pi$
$173$	−11.0837	−0.842677	−0.421338	+	0.906904i	$0.638439\pi$
$174$	−40.0922	−3.03939
$175$	−20.2639	−1.53181
$176$	−10.1102	−0.762084
$177$	−15.1607	−1.13955
$178$	10.7724	0.807427
$179$	15.4163	1.15227	0.576135	−	0.817354i	$-0.304560\pi$
$179$	15.4163	1.15227	0.576135	+	0.817354i	$0.304560\pi$
$180$	4.09395	0.305145
$181$	−3.20803	−0.238451	−0.119225	−	0.992867i	$-0.538041\pi$
$181$	−3.20803	−0.238451	−0.119225	+	0.992867i	$0.538041\pi$
$182$	−13.5696	−1.00585
$183$	−29.0326	−2.14615
$184$	3.96646	0.292411
$185$	2.36241	0.173688
$186$	3.01693	0.221212
$187$	2.98770	0.218482
$188$	11.0802	0.808108
$189$	−36.2621	−2.63768
$190$	2.31486	0.167938
$191$	5.33299	0.385881	0.192941	−	0.981210i	$-0.438198\pi$
$191$	5.33299	0.385881	0.192941	+	0.981210i	$0.438198\pi$
$192$	2.01144	0.145163
$193$	−6.72178	−0.483844	−0.241922	−	0.970296i	$-0.577778\pi$
$193$	−6.72178	−0.483844	−0.241922	+	0.970296i	$0.577778\pi$
$194$	18.2972	1.31366
$195$	3.08379	0.220834
$196$	14.2439	1.01742
$197$	−4.86122	−0.346347	−0.173174	−	0.984891i	$-0.555402\pi$
$197$	−4.86122	−0.346347	−0.173174	+	0.984891i	$0.555402\pi$
$198$	21.0718	1.49751
$199$	22.6663	1.60677	0.803384	−	0.595461i	$-0.203031\pi$
$199$	22.6663	1.60677	0.803384	+	0.595461i	$0.203031\pi$
$200$	6.76688	0.478491
$201$	1.57275	0.110933
$202$	−19.9477	−1.40352
$203$	33.0469	2.31944
$204$	−5.15256	−0.360751
$205$	1.26758	0.0885316
$206$	−0.248960	−0.0173459
$207$	−15.7936	−1.09773
$208$	8.65704	0.600257
$209$	4.42918	0.306373
$210$	−13.7718	−0.950347
$211$	−18.9770	−1.30643	−0.653214	−	0.757174i	$-0.726580\pi$
$211$	−18.9770	−1.30643	−0.653214	+	0.757174i	$0.726580\pi$
$212$	−6.98904	−0.480009
$213$	−15.8370	−1.08513
$214$	10.4353	0.713346
$215$	0	0
$216$	12.1093	0.823932
$217$	−2.48677	−0.168813
$218$	1.40717	0.0953057
$219$	−41.7073	−2.81832
$220$	1.43657	0.0968533
$221$	−2.55828	−0.172088
$222$	−20.9701	−1.40742
$223$	−9.66301	−0.647083	−0.323541	−	0.946214i	$-0.604874\pi$
$223$	−9.66301	−0.647083	−0.323541	+	0.946214i	$0.604874\pi$
$224$	−25.9474	−1.73368
$225$	−26.9443	−1.79629
$226$	10.7435	0.714644
$227$	17.6565	1.17190	0.585952	−	0.810346i	$-0.300721\pi$
$227$	17.6565	1.17190	0.585952	+	0.810346i	$0.300721\pi$
$228$	−7.63852	−0.505873
$229$	−0.236812	−0.0156490	−0.00782449	−	0.999969i	$-0.502491\pi$
$229$	−0.236812	−0.0156490	−0.00782449	+	0.999969i	$0.502491\pi$
$230$	−2.89645	−0.190986
$231$	−26.3506	−1.73374
$232$	−11.0356	−0.724524
$233$	−6.96814	−0.456498	−0.228249	−	0.973603i	$-0.573300\pi$
$233$	−6.96814	−0.456498	−0.228249	+	0.973603i	$0.573300\pi$
$234$	−18.0431	−1.17952
$235$	5.58336	0.364219
$236$	6.04744	0.393655
$237$	−10.8364	−0.703903
$238$	11.4250	0.740571
$239$	−29.5224	−1.90964	−0.954822	−	0.297178i	$-0.903954\pi$
$239$	−29.5224	−1.90964	−0.954822	+	0.297178i	$0.903954\pi$
$240$	8.78603	0.567136
$241$	−17.3820	−1.11967	−0.559836	−	0.828603i	$-0.689136\pi$
$241$	−17.3820	−1.11967	−0.559836	+	0.828603i	$0.689136\pi$
$242$	−12.2322	−0.786314
$243$	3.41730	0.219220
$244$	11.5808	0.741384
$245$	7.17753	0.458556
$246$	−11.2518	−0.717387
$247$	−3.79257	−0.241315
$248$	0.830425	0.0527321
$249$	30.6938	1.94514
$250$	−10.2612	−0.648974
$251$	−19.5637	−1.23485	−0.617426	−	0.786629i	$-0.711824\pi$
$251$	−19.5637	−1.23485	−0.617426	+	0.786629i	$0.711824\pi$
$252$	29.9543	1.88694
$253$	−5.54198	−0.348421
$254$	−6.74636	−0.423304
$255$	−2.59640	−0.162593
$256$	20.4191	1.27620
$257$	−21.9755	−1.37080	−0.685398	−	0.728168i	$-0.740372\pi$
$257$	−21.9755	−1.37080	−0.685398	+	0.728168i	$0.740372\pi$
$258$	0	0
$259$	17.2851	1.07404
$260$	−1.23009	−0.0762868
$261$	43.9415	2.71991
$262$	30.9735	1.91355
$263$	21.1856	1.30636	0.653181	−	0.757202i	$-0.273434\pi$
$263$	21.1856	1.30636	0.653181	+	0.757202i	$0.273434\pi$
$264$	8.79945	0.541569
$265$	−3.52181	−0.216343
$266$	16.9372	1.03849
$267$	−17.9120	−1.09620
$268$	−0.627351	−0.0383215
$269$	−2.43036	−0.148182	−0.0740908	−	0.997251i	$-0.523605\pi$
$269$	−2.43036	−0.148182	−0.0740908	+	0.997251i	$0.523605\pi$
$270$	−8.84264	−0.538146
$271$	19.9289	1.21059	0.605296	−	0.796000i	$-0.293055\pi$
$271$	19.9289	1.21059	0.605296	+	0.796000i	$0.293055\pi$
$272$	−7.28880	−0.441948
$273$	22.5632	1.36559
$274$	−5.55020	−0.335300
$275$	−9.45476	−0.570143
$276$	9.55764	0.575303
$277$	−15.0216	−0.902558	−0.451279	−	0.892383i	$-0.649032\pi$
$277$	−15.0216	−0.902558	−0.451279	+	0.892383i	$0.649032\pi$
$278$	9.31642	0.558762
$279$	−3.30658	−0.197960
$280$	−3.79077	−0.226542
$281$	32.7779	1.95536	0.977682	−	0.210091i	$-0.0673761\pi$
$281$	32.7779	1.95536	0.977682	+	0.210091i	$0.0673761\pi$
$282$	−49.5612	−2.95133
$283$	12.5323	0.744967	0.372483	−	0.928039i	$-0.378506\pi$
$283$	12.5323	0.744967	0.372483	+	0.928039i	$0.378506\pi$
$284$	6.31721	0.374857
$285$	−3.84908	−0.228000
$286$	−6.33134	−0.374380
$287$	9.27453	0.547458
$288$	−34.5014	−2.03302
$289$	−14.8461	−0.873297
$290$	8.05861	0.473218
$291$	−30.4241	−1.78349
$292$	16.6366	0.973581
$293$	−7.34726	−0.429232	−0.214616	−	0.976699i	$-0.568850\pi$
$293$	−7.34726	−0.429232	−0.214616	+	0.976699i	$0.568850\pi$
$294$	−63.7119	−3.71576
$295$	3.04733	0.177422
$296$	−5.77213	−0.335498
$297$	−16.9192	−0.981753
$298$	−36.3313	−2.10462
$299$	4.74543	0.274435
$300$	16.3056	0.941403
$301$	0	0
$302$	35.6240	2.04993
$303$	33.1685	1.90548
$304$	−10.8054	−0.619734
$305$	5.83560	0.334146
$306$	15.1914	0.868436
$307$	11.3798	0.649480	0.324740	−	0.945803i	$-0.394723\pi$
$307$	11.3798	0.649480	0.324740	+	0.945803i	$0.394723\pi$
$308$	10.5110	0.598917
$309$	0.413963	0.0235495
$310$	−0.606407	−0.0344416
$311$	24.8424	1.40868	0.704342	−	0.709861i	$-0.251242\pi$
$311$	24.8424	1.40868	0.704342	+	0.709861i	$0.251242\pi$
$312$	−7.53470	−0.426568
$313$	−16.9309	−0.956989	−0.478495	−	0.878090i	$-0.658817\pi$
$313$	−16.9309	−0.956989	−0.478495	+	0.878090i	$0.658817\pi$
$314$	−30.7128	−1.73322
$315$	15.0941	0.850454
$316$	4.32254	0.243162
$317$	23.6541	1.32855	0.664273	−	0.747490i	$-0.268741\pi$
$317$	23.6541	1.32855	0.664273	+	0.747490i	$0.268741\pi$
$318$	31.2616	1.75306
$319$	15.4191	0.863303
$320$	−0.404302	−0.0226012
$321$	−17.3516	−0.968470
$322$	−21.1925	−1.18101
$323$	3.19316	0.177672
$324$	8.58253	0.476807
$325$	8.09582	0.449075
$326$	−38.9383	−2.15659
$327$	−2.33980	−0.129391
$328$	−3.09711	−0.171010
$329$	40.8519	2.25224
$330$	−6.42568	−0.353722
$331$	−24.1779	−1.32894	−0.664469	−	0.747316i	$-0.731342\pi$
$331$	−24.1779	−1.32894	−0.664469	+	0.747316i	$0.731342\pi$
$332$	−12.2434	−0.671944
$333$	22.9834	1.25948
$334$	15.1299	0.827873
$335$	−0.316124	−0.0172717
$336$	64.2849	3.50703
$337$	−15.5384	−0.846431	−0.423216	−	0.906029i	$-0.639099\pi$
$337$	−15.5384	−0.846431	−0.423216	+	0.906029i	$0.639099\pi$
$338$	−17.7734	−0.966743
$339$	−17.8639	−0.970234
$340$	1.03567	0.0561672
$341$	−1.16028	−0.0628326
$342$	22.5208	1.21779
$343$	21.9745	1.18651
$344$	0	0
$345$	4.81613	0.259292
$346$	−19.7756	−1.06314
$347$	13.7962	0.740618	0.370309	−	0.928909i	$-0.379252\pi$
$347$	13.7962	0.740618	0.370309	+	0.928909i	$0.379252\pi$
$348$	−26.5916	−1.42546
$349$	−13.4384	−0.719341	−0.359671	−	0.933079i	$-0.617111\pi$
$349$	−13.4384	−0.719341	−0.359671	+	0.933079i	$0.617111\pi$
$350$	−36.1550	−1.93257
$351$	14.4874	0.773280
$352$	−12.1066	−0.645281
$353$	7.62634	0.405909	0.202955	−	0.979188i	$-0.434946\pi$
$353$	7.62634	0.405909	0.202955	+	0.979188i	$0.434946\pi$
$354$	−27.0499	−1.43768
$355$	3.18327	0.168950
$356$	7.14491	0.378680
$357$	−18.9971	−1.00543
$358$	27.5059	1.45373
$359$	16.8262	0.888053	0.444026	−	0.896014i	$-0.353550\pi$
$359$	16.8262	0.888053	0.444026	+	0.896014i	$0.353550\pi$
$360$	−5.04048	−0.265656
$361$	−14.2662	−0.750855
$362$	−5.72379	−0.300836
$363$	20.3393	1.06754
$364$	−9.00020	−0.471739
$365$	8.38323	0.438798
$366$	−51.8002	−2.70764
$367$	0.0729401	0.00380744	0.00190372	−	0.999998i	$-0.499394\pi$
$367$	0.0729401	0.00380744	0.00190372	+	0.999998i	$0.499394\pi$
$368$	13.5202	0.704790
$369$	12.3321	0.641981
$370$	4.21502	0.219128
$371$	−25.7681	−1.33781
$372$	2.00101	0.103747
$373$	−25.7567	−1.33363	−0.666817	−	0.745222i	$-0.732344\pi$
$373$	−25.7567	−1.33363	−0.666817	+	0.745222i	$0.732344\pi$
$374$	5.33068	0.275643
$375$	17.0620	0.881076
$376$	−13.6420	−0.703532
$377$	−13.2029	−0.679983
$378$	−64.6991	−3.32776
$379$	−16.0471	−0.824284	−0.412142	−	0.911120i	$-0.635219\pi$
$379$	−16.0471	−0.824284	−0.412142	+	0.911120i	$0.635219\pi$
$380$	1.53535	0.0787620
$381$	11.2176	0.574697
$382$	9.51515	0.486837
$383$	24.1300	1.23299	0.616493	−	0.787360i	$-0.288553\pi$
$383$	24.1300	1.23299	0.616493	+	0.787360i	$0.288553\pi$
$384$	−31.6976	−1.61756
$385$	5.29651	0.269935
$386$	−11.9930	−0.610430
$387$	0	0
$388$	12.1358	0.616103
$389$	−16.4021	−0.831621	−0.415810	−	0.909451i	$-0.636502\pi$
$389$	−16.4021	−0.831621	−0.415810	+	0.909451i	$0.636502\pi$
$390$	5.50211	0.278610
$391$	−3.99541	−0.202057
$392$	−17.5371	−0.885756
$393$	−51.5018	−2.59792
$394$	−8.67342	−0.436960
$395$	2.17814	0.109594
$396$	13.9761	0.702325
$397$	−7.70285	−0.386595	−0.193298	−	0.981140i	$-0.561918\pi$
$397$	−7.70285	−0.386595	−0.193298	+	0.981140i	$0.561918\pi$
$398$	40.4413	2.02714
$399$	−28.1626	−1.40989
$400$	23.0658	1.15329
$401$	1.41296	0.0705600	0.0352800	−	0.999377i	$-0.488768\pi$
$401$	1.41296	0.0705600	0.0352800	+	0.999377i	$0.488768\pi$
$402$	2.80610	0.139956
$403$	0.993511	0.0494903
$404$	−13.2305	−0.658244
$405$	4.32477	0.214899
$406$	58.9626	2.92626
$407$	8.06488	0.399761
$408$	6.34384	0.314067
$409$	7.12388	0.352253	0.176127	−	0.984368i	$-0.443643\pi$
$409$	7.12388	0.352253	0.176127	+	0.984368i	$0.443643\pi$
$410$	2.26162	0.111694
$411$	9.22869	0.455218
$412$	−0.165125	−0.00813513
$413$	22.2965	1.09714
$414$	−28.1791	−1.38493
$415$	−6.16950	−0.302849
$416$	10.3665	0.508258
$417$	−15.4911	−0.758600
$418$	7.90257	0.386527
$419$	−13.7080	−0.669679	−0.334840	−	0.942275i	$-0.608682\pi$
$419$	−13.7080	−0.669679	−0.334840	+	0.942275i	$0.608682\pi$
$420$	−9.13431	−0.445709
$421$	1.86680	0.0909825	0.0454912	−	0.998965i	$-0.485515\pi$
$421$	1.86680	0.0909825	0.0454912	+	0.998965i	$0.485515\pi$
$422$	−33.8588	−1.64822
$423$	54.3195	2.64111
$424$	8.60492	0.417892
$425$	−6.81628	−0.330638
$426$	−28.2565	−1.36903
$427$	42.6975	2.06628
$428$	6.92135	0.334556
$429$	10.5276	0.508275
$430$	0	0
$431$	−23.8277	−1.14774	−0.573871	−	0.818946i	$-0.694559\pi$
$431$	−23.8277	−1.14774	−0.573871	+	0.818946i	$0.694559\pi$
$432$	41.2761	1.98590
$433$	−40.0874	−1.92648	−0.963240	−	0.268643i	$-0.913425\pi$
$433$	−40.0874	−1.92648	−0.963240	+	0.268643i	$0.913425\pi$
$434$	−4.43691	−0.212978
$435$	−13.3996	−0.642462
$436$	0.933320	0.0446979
$437$	−5.92308	−0.283339
$438$	−74.4144	−3.55566
$439$	8.29016	0.395668	0.197834	−	0.980236i	$-0.436609\pi$
$439$	8.29016	0.395668	0.197834	+	0.980236i	$0.436609\pi$
$440$	−1.76870	−0.0843196
$441$	69.8289	3.32519
$442$	−4.56449	−0.217111
$443$	−31.4964	−1.49644	−0.748219	−	0.663452i	$-0.769091\pi$
$443$	−31.4964	−1.49644	−0.748219	+	0.663452i	$0.769091\pi$
$444$	−13.9086	−0.660074
$445$	3.60035	0.170673
$446$	−17.2408	−0.816376
$447$	60.4106	2.85732
$448$	−2.95817	−0.139760
$449$	−15.4315	−0.728257	−0.364129	−	0.931349i	$-0.618633\pi$
$449$	−15.4315	−0.728257	−0.364129	+	0.931349i	$0.618633\pi$
$450$	−48.0742	−2.26624
$451$	4.32732	0.203766
$452$	7.12571	0.335165
$453$	−59.2345	−2.78308
$454$	31.5029	1.47850
$455$	−4.53524	−0.212615
$456$	9.40456	0.440409
$457$	9.28539	0.434352	0.217176	−	0.976132i	$-0.430315\pi$
$457$	9.28539	0.434352	0.217176	+	0.976132i	$0.430315\pi$
$458$	−0.422521	−0.0197431
$459$	−12.1977	−0.569339
$460$	−1.92110	−0.0895718
$461$	−20.9145	−0.974085	−0.487043	−	0.873378i	$-0.661924\pi$
$461$	−20.9145	−0.974085	−0.487043	+	0.873378i	$0.661924\pi$
$462$	−47.0149	−2.18733
$463$	−2.18915	−0.101738	−0.0508692	−	0.998705i	$-0.516199\pi$
$463$	−2.18915	−0.101738	−0.0508692	+	0.998705i	$0.516199\pi$
$464$	−37.6164	−1.74630
$465$	1.00831	0.0467595
$466$	−12.4326	−0.575929
$467$	0.230966	0.0106878	0.00534391	−	0.999986i	$-0.498299\pi$
$467$	0.230966	0.0106878	0.00534391	+	0.999986i	$0.498299\pi$
$468$	−11.9673	−0.553188
$469$	−2.31299	−0.106804
$470$	9.96188	0.459507
$471$	51.0683	2.35310
$472$	−7.44562	−0.342713
$473$	0	0
$474$	−19.3345	−0.888061
$475$	−10.1049	−0.463646
$476$	7.57773	0.347325
$477$	−34.2630	−1.56879
$478$	−52.6740	−2.40925
$479$	5.00954	0.228892	0.114446	−	0.993429i	$-0.463491\pi$
$479$	5.00954	0.228892	0.114446	+	0.993429i	$0.463491\pi$
$480$	10.5209	0.480212
$481$	−6.90571	−0.314873
$482$	−31.0131	−1.41261
$483$	35.2383	1.60340
$484$	−8.11311	−0.368778
$485$	6.11529	0.277681
$486$	6.09716	0.276573
$487$	−13.0400	−0.590899	−0.295450	−	0.955358i	$-0.595469\pi$
$487$	−13.0400	−0.590899	−0.295450	+	0.955358i	$0.595469\pi$
$488$	−14.2583	−0.645442
$489$	64.7454	2.92789
$490$	12.8062	0.578525
$491$	−25.3230	−1.14281	−0.571406	−	0.820668i	$-0.693602\pi$
$491$	−25.3230	−1.14281	−0.571406	+	0.820668i	$0.693602\pi$
$492$	−7.46285	−0.336451
$493$	11.1162	0.500647
$494$	−6.76672	−0.304449
$495$	7.04261	0.316542
$496$	2.83062	0.127098
$497$	23.2911	1.04475
$498$	54.7640	2.45404
$499$	−8.68477	−0.388784	−0.194392	−	0.980924i	$-0.562273\pi$
$499$	−8.68477	−0.388784	−0.194392	+	0.980924i	$0.562273\pi$
$500$	−6.80583	−0.304366
$501$	−25.1576	−1.12396
$502$	−34.9057	−1.55792
$503$	−28.7691	−1.28275	−0.641374	−	0.767228i	$-0.721635\pi$
$503$	−28.7691	−1.28275	−0.641374	+	0.767228i	$0.721635\pi$
$504$	−36.8797	−1.64275
$505$	−6.66692	−0.296674
$506$	−9.88804	−0.439577
$507$	29.5530	1.31249
$508$	−4.47459	−0.198528
$509$	26.5391	1.17632	0.588162	−	0.808743i	$-0.299852\pi$
$509$	26.5391	1.17632	0.588162	+	0.808743i	$0.299852\pi$
$510$	−4.63251	−0.205131
$511$	61.3377	2.71342
$512$	15.0632	0.665705
$513$	−18.0827	−0.798370
$514$	−39.2089	−1.72943
$515$	−0.0832072	−0.00366655
$516$	0	0
$517$	19.0607	0.838290
$518$	30.8401	1.35504
$519$	32.8822	1.44337
$520$	1.51449	0.0664146
$521$	35.6883	1.56353	0.781766	−	0.623572i	$-0.214319\pi$
$521$	35.6883	1.56353	0.781766	+	0.623572i	$0.214319\pi$
$522$	78.4007	3.43150
$523$	38.8890	1.70050	0.850249	−	0.526381i	$-0.176451\pi$
$523$	38.8890	1.70050	0.850249	+	0.526381i	$0.176451\pi$
$524$	20.5435	0.897447
$525$	60.1174	2.62374
$526$	37.7995	1.64814
$527$	−0.836487	−0.0364380
$528$	29.9941	1.30533
$529$	−15.5888	−0.677773
$530$	−6.28363	−0.272943
$531$	29.6469	1.28657
$532$	11.2338	0.487045
$533$	−3.70535	−0.160497
$534$	−31.9588	−1.38299
$535$	3.48769	0.150786
$536$	0.772396	0.0333624
$537$	−45.7360	−1.97365
$538$	−4.33626	−0.186950
$539$	24.5030	1.05542
$540$	−5.86497	−0.252388
$541$	19.1568	0.823615	0.411807	−	0.911271i	$-0.364898\pi$
$541$	19.1568	0.823615	0.411807	+	0.911271i	$0.364898\pi$
$542$	35.5572	1.52731
$543$	9.51734	0.408428
$544$	−8.72805	−0.374212
$545$	0.470304	0.0201456
$546$	40.2574	1.72286
$547$	−2.41686	−0.103337	−0.0516687	−	0.998664i	$-0.516454\pi$
$547$	−2.41686	−0.103337	−0.0516687	+	0.998664i	$0.516454\pi$
$548$	−3.68122	−0.157254
$549$	56.7735	2.42303
$550$	−16.8692	−0.719307
$551$	16.4794	0.702046
$552$	−11.7674	−0.500853
$553$	15.9369	0.677704
$554$	−26.8016	−1.13869
$555$	−7.00861	−0.297499
$556$	6.17921	0.262057
$557$	2.65074	0.112315	0.0561576	−	0.998422i	$-0.482115\pi$
$557$	2.65074	0.112315	0.0561576	+	0.998422i	$0.482115\pi$
$558$	−5.89962	−0.249751
$559$	0	0
$560$	−12.9214	−0.546027
$561$	−8.86369	−0.374225
$562$	58.4825	2.46693
$563$	4.82635	0.203407	0.101703	−	0.994815i	$-0.467571\pi$
$563$	4.82635	0.203407	0.101703	+	0.994815i	$0.467571\pi$
$564$	−32.8719	−1.38416
$565$	3.59067	0.151061
$566$	22.3602	0.939868
$567$	31.6431	1.32889
$568$	−7.77776	−0.326348
$569$	12.1025	0.507364	0.253682	−	0.967288i	$-0.418358\pi$
$569$	12.1025	0.507364	0.253682	+	0.967288i	$0.418358\pi$
$570$	−6.86755	−0.287650
$571$	28.1047	1.17614	0.588072	−	0.808809i	$-0.299887\pi$
$571$	28.1047	1.17614	0.588072	+	0.808809i	$0.299887\pi$
$572$	−4.19932	−0.175583
$573$	−15.8215	−0.660952
$574$	16.5477	0.690687
$575$	12.6437	0.527280
$576$	−3.93338	−0.163891
$577$	23.2153	0.966467	0.483233	−	0.875492i	$-0.339462\pi$
$577$	23.2153	0.966467	0.483233	+	0.875492i	$0.339462\pi$
$578$	−26.4884	−1.10177
$579$	19.9417	0.828747
$580$	5.34495	0.221937
$581$	−45.1405	−1.87274
$582$	−54.2828	−2.25010
$583$	−12.0229	−0.497937
$584$	−20.4830	−0.847591
$585$	−6.03036	−0.249325
$586$	−13.1090	−0.541529
$587$	−34.5213	−1.42485	−0.712424	−	0.701749i	$-0.752403\pi$
$587$	−34.5213	−1.42485	−0.712424	+	0.701749i	$0.752403\pi$
$588$	−42.2576	−1.74267
$589$	−1.24007	−0.0510961
$590$	5.43706	0.223840
$591$	14.4219	0.593237
$592$	−19.6751	−0.808641
$593$	−27.1159	−1.11352	−0.556758	−	0.830675i	$-0.687955\pi$
$593$	−27.1159	−1.11352	−0.556758	+	0.830675i	$0.687955\pi$
$594$	−30.1874	−1.23860
$595$	3.81845	0.156541
$596$	−24.0971	−0.987056
$597$	−67.2445	−2.75214
$598$	8.46682	0.346234
$599$	7.69678	0.314482	0.157241	−	0.987560i	$-0.449740\pi$
$599$	7.69678	0.314482	0.157241	+	0.987560i	$0.449740\pi$
$600$	−20.0755	−0.819578
$601$	31.0119	1.26500	0.632500	−	0.774560i	$-0.282029\pi$
$601$	31.0119	1.26500	0.632500	+	0.774560i	$0.282029\pi$
$602$	0	0
$603$	−3.07552	−0.125245
$604$	23.6280	0.961410
$605$	−4.08823	−0.166210
$606$	59.1794	2.40400
$607$	−4.76958	−0.193591	−0.0967957	−	0.995304i	$-0.530859\pi$
$607$	−4.76958	−0.193591	−0.0967957	+	0.995304i	$0.530859\pi$
$608$	−12.9391	−0.524749
$609$	−98.0411	−3.97283
$610$	10.4119	0.421566
$611$	−16.3211	−0.660282
$612$	10.0759	0.407293
$613$	−34.2509	−1.38338	−0.691691	−	0.722194i	$-0.743134\pi$
$613$	−34.2509	−1.38338	−0.691691	+	0.722194i	$0.743134\pi$
$614$	20.3039	0.819400
$615$	−3.76056	−0.151640
$616$	−12.9411	−0.521412
$617$	22.8354	0.919319	0.459659	−	0.888095i	$-0.347972\pi$
$617$	22.8354	0.919319	0.459659	+	0.888095i	$0.347972\pi$
$618$	0.738595	0.0297107
$619$	16.2615	0.653607	0.326803	−	0.945092i	$-0.394029\pi$
$619$	16.2615	0.653607	0.326803	+	0.945092i	$0.394029\pi$
$620$	−0.402205	−0.0161530
$621$	22.6258	0.907944
$622$	44.3240	1.77723
$623$	26.3427	1.05540
$624$	−25.6830	−1.02814
$625$	19.7926	0.791702
$626$	−30.2082	−1.20736
$627$	−13.1401	−0.524767
$628$	−20.3706	−0.812874
$629$	5.81427	0.231830
$630$	26.9309	1.07295
$631$	1.91996	0.0764323	0.0382162	−	0.999269i	$-0.487832\pi$
$631$	1.91996	0.0764323	0.0382162	+	0.999269i	$0.487832\pi$
$632$	−5.32192	−0.211695
$633$	56.2994	2.23770
$634$	42.2038	1.67613
$635$	−2.25476	−0.0894776
$636$	20.7346	0.822179
$637$	−20.9811	−0.831303
$638$	27.5108	1.08916
$639$	30.9694	1.22513
$640$	6.37126	0.251846
$641$	29.6154	1.16974	0.584869	−	0.811128i	$-0.301146\pi$
$641$	29.6154	1.16974	0.584869	+	0.811128i	$0.301146\pi$
$642$	−30.9588	−1.22185
$643$	−10.3385	−0.407710	−0.203855	−	0.979001i	$-0.565347\pi$
$643$	−10.3385	−0.407710	−0.203855	+	0.979001i	$0.565347\pi$
$644$	−14.0562	−0.553890
$645$	0	0
$646$	5.69725	0.224155
$647$	−15.2577	−0.599843	−0.299921	−	0.953964i	$-0.596960\pi$
$647$	−15.2577	−0.599843	−0.299921	+	0.953964i	$0.596960\pi$
$648$	−10.5668	−0.415104
$649$	10.4031	0.408358
$650$	14.4446	0.566564
$651$	7.37756	0.289149
$652$	−25.8262	−1.01143
$653$	1.96573	0.0769249	0.0384625	−	0.999260i	$-0.487754\pi$
$653$	1.96573	0.0769249	0.0384625	+	0.999260i	$0.487754\pi$
$654$	−4.17469	−0.163243
$655$	10.3519	0.404484
$656$	−10.5569	−0.412179
$657$	81.5589	3.18192
$658$	72.8883	2.84148
$659$	−29.7073	−1.15723	−0.578616	−	0.815600i	$-0.696407\pi$
$659$	−29.7073	−1.15723	−0.578616	+	0.815600i	$0.696407\pi$
$660$	−4.26190	−0.165894
$661$	−11.8003	−0.458978	−0.229489	−	0.973311i	$-0.573705\pi$
$661$	−11.8003	−0.458978	−0.229489	+	0.973311i	$0.573705\pi$
$662$	−43.1384	−1.67662
$663$	7.58970	0.294759
$664$	15.0741	0.584989
$665$	5.66073	0.219514
$666$	41.0072	1.58899
$667$	−20.6197	−0.798399
$668$	10.0351	0.388269
$669$	28.6675	1.10835
$670$	−0.564031	−0.0217904
$671$	19.9218	0.769074
$672$	76.9787	2.96952
$673$	−20.3486	−0.784383	−0.392191	−	0.919884i	$-0.628283\pi$
$673$	−20.3486	−0.784383	−0.392191	+	0.919884i	$0.628283\pi$
$674$	−27.7237	−1.06788
$675$	38.6003	1.48573
$676$	−11.7884	−0.453398
$677$	23.8419	0.916320	0.458160	−	0.888870i	$-0.348509\pi$
$677$	23.8419	0.916320	0.458160	+	0.888870i	$0.348509\pi$
$678$	−31.8729	−1.22407
$679$	44.7438	1.71711
$680$	−1.27512	−0.0488987
$681$	−52.3820	−2.00728
$682$	−2.07018	−0.0792712
$683$	35.4165	1.35518	0.677588	−	0.735442i	$-0.263025\pi$
$683$	35.4165	1.35518	0.677588	+	0.735442i	$0.263025\pi$
$684$	14.9372	0.571137
$685$	−1.85498	−0.0708752
$686$	39.2070	1.49693
$687$	0.702556	0.0268042
$688$	0	0
$689$	10.2948	0.392202
$690$	8.59298	0.327129
$691$	−15.5979	−0.593373	−0.296687	−	0.954975i	$-0.595882\pi$
$691$	−15.5979	−0.593373	−0.296687	+	0.954975i	$0.595882\pi$
$692$	−13.1163	−0.498609
$693$	51.5288	1.95742
$694$	24.6152	0.934382
$695$	3.11373	0.118110
$696$	32.7396	1.24099
$697$	3.11972	0.118168
$698$	−23.9769	−0.907539
$699$	20.6725	0.781908
$700$	−23.9802	−0.906365
$701$	10.9798	0.414702	0.207351	−	0.978267i	$-0.433516\pi$
$701$	10.9798	0.414702	0.207351	+	0.978267i	$0.433516\pi$
$702$	25.8485	0.975589
$703$	8.61948	0.325090
$704$	−1.38022	−0.0520192
$705$	−16.5643	−0.623848
$706$	13.6070	0.512105
$707$	−48.7800	−1.83456
$708$	−17.9411	−0.674267
$709$	33.2542	1.24889	0.624445	−	0.781069i	$-0.285325\pi$
$709$	33.2542	1.24889	0.624445	+	0.781069i	$0.285325\pi$
$710$	5.67961	0.213152
$711$	21.1908	0.794715
$712$	−8.79683	−0.329675
$713$	1.55163	0.0581089
$714$	−33.8947	−1.26848
$715$	−2.11606	−0.0791360
$716$	18.2436	0.681795
$717$	87.5847	3.27091
$718$	30.0214	1.12039
$719$	−23.0531	−0.859734	−0.429867	−	0.902892i	$-0.641440\pi$
$719$	−23.0531	−0.859734	−0.429867	+	0.902892i	$0.641440\pi$
$720$	−17.1811	−0.640303
$721$	−0.608804	−0.0226730
$722$	−25.4539	−0.947297
$723$	51.5676	1.91782
$724$	−3.79636	−0.141091
$725$	−35.1778	−1.30647
$726$	36.2895	1.34683
$727$	−27.9375	−1.03614	−0.518072	−	0.855337i	$-0.673350\pi$
$727$	−27.9375	−1.03614	−0.518072	+	0.855337i	$0.673350\pi$
$728$	11.0811	0.410692
$729$	−31.8956	−1.18132
$730$	14.9574	0.553599
$731$	0	0
$732$	−34.3570	−1.26987
$733$	−6.77186	−0.250124	−0.125062	−	0.992149i	$-0.539913\pi$
$733$	−6.77186	−0.250124	−0.125062	+	0.992149i	$0.539913\pi$
$734$	0.130140	0.00480356
$735$	−21.2938	−0.785432
$736$	16.1899	0.596769
$737$	−1.07920	−0.0397528
$738$	22.0029	0.809939
$739$	−15.0999	−0.555458	−0.277729	−	0.960660i	$-0.589582\pi$
$739$	−15.0999	−0.555458	−0.277729	+	0.960660i	$0.589582\pi$
$740$	2.79565	0.102770
$741$	11.2515	0.413334
$742$	−45.9755	−1.68782
$743$	−25.5817	−0.938501	−0.469250	−	0.883065i	$-0.655476\pi$
$743$	−25.5817	−0.938501	−0.469250	+	0.883065i	$0.655476\pi$
$744$	−2.46364	−0.0903215
$745$	−12.1426	−0.444871
$746$	−45.9553	−1.68254
$747$	−60.0219	−2.19609
$748$	3.53562	0.129275
$749$	25.5185	0.932425
$750$	30.4421	1.11159
$751$	−26.5575	−0.969097	−0.484548	−	0.874764i	$-0.661016\pi$
$751$	−26.5575	−0.969097	−0.484548	+	0.874764i	$0.661016\pi$
$752$	−46.5006	−1.69570
$753$	58.0402	2.11510
$754$	−23.5567	−0.857883
$755$	11.9062	0.433312
$756$	−42.9123	−1.56071
$757$	43.3142	1.57428	0.787140	−	0.616774i	$-0.211561\pi$
$757$	43.3142	1.57428	0.787140	+	0.616774i	$0.211561\pi$
$758$	−28.6313	−1.03994
$759$	16.4415	0.596790
$760$	−1.89033	−0.0685695
$761$	34.7007	1.25790	0.628949	−	0.777446i	$-0.283485\pi$
$761$	34.7007	1.25790	0.628949	+	0.777446i	$0.283485\pi$
$762$	20.0146	0.725052
$763$	3.44108	0.124576
$764$	6.31102	0.228325
$765$	5.07727	0.183569
$766$	43.0530	1.55557
$767$	−8.90785	−0.321644
$768$	−60.5779	−2.18592
$769$	−15.6400	−0.563992	−0.281996	−	0.959416i	$-0.590996\pi$
$769$	−15.6400	−0.563992	−0.281996	+	0.959416i	$0.590996\pi$
$770$	9.45007	0.340557
$771$	65.1954	2.34795
$772$	−7.95450	−0.286289
$773$	−36.9024	−1.32729	−0.663643	−	0.748049i	$-0.730991\pi$
$773$	−36.9024	−1.32729	−0.663643	+	0.748049i	$0.730991\pi$
$774$	0	0
$775$	2.64711	0.0950871
$776$	−14.9417	−0.536374
$777$	−51.2800	−1.83966
$778$	−29.2648	−1.04919
$779$	4.62489	0.165704
$780$	3.64933	0.130667
$781$	10.8672	0.388858
$782$	−7.12864	−0.254920
$783$	−62.9504	−2.24966
$784$	−59.7775	−2.13491
$785$	−10.2648	−0.366367
$786$	−91.8899	−3.27760
$787$	−38.7287	−1.38053	−0.690265	−	0.723557i	$-0.742506\pi$
$787$	−38.7287	−1.38053	−0.690265	+	0.723557i	$0.742506\pi$
$788$	−5.75273	−0.204932
$789$	−62.8519	−2.23759
$790$	3.88626	0.138267
$791$	26.2719	0.934123
$792$	−17.2074	−0.611438
$793$	−17.0584	−0.605763
$794$	−13.7435	−0.487738
$795$	10.4482	0.370560
$796$	26.8231	0.950719
$797$	38.7160	1.37139	0.685695	−	0.727889i	$-0.259498\pi$
$797$	38.7160	1.37139	0.685695	+	0.727889i	$0.259498\pi$
$798$	−50.2479	−1.77876
$799$	13.7416	0.486142
$800$	27.6204	0.976530
$801$	35.0271	1.23762
$802$	2.52102	0.0890203
$803$	28.6190	1.00994
$804$	1.86118	0.0656386
$805$	−7.08295	−0.249641
$806$	1.77263	0.0624382
$807$	7.21021	0.253811
$808$	16.2895	0.573061
$809$	−25.9190	−0.911262	−0.455631	−	0.890169i	$-0.650586\pi$
$809$	−25.9190	−0.911262	−0.455631	+	0.890169i	$0.650586\pi$
$810$	7.71628	0.271122
$811$	−11.6619	−0.409504	−0.204752	−	0.978814i	$-0.565639\pi$
$811$	−11.6619	−0.409504	−0.204752	+	0.978814i	$0.565639\pi$
$812$	39.1075	1.37240
$813$	−59.1234	−2.07355
$814$	14.3894	0.504349
$815$	−13.0139	−0.455858
$816$	21.6238	0.756986
$817$	0	0
$818$	12.7105	0.444411
$819$	−44.1225	−1.54176
$820$	1.50005	0.0523839
$821$	−6.92887	−0.241819	−0.120910	−	0.992664i	$-0.538581\pi$
$821$	−6.92887	−0.241819	−0.120910	+	0.992664i	$0.538581\pi$
$822$	16.4659	0.574314
$823$	2.20617	0.0769022	0.0384511	−	0.999260i	$-0.487758\pi$
$823$	2.20617	0.0769022	0.0384511	+	0.999260i	$0.487758\pi$
$824$	0.203303	0.00708238
$825$	28.0497	0.976564
$826$	39.7815	1.38417
$827$	−11.5425	−0.401373	−0.200686	−	0.979656i	$-0.564317\pi$
$827$	−11.5425	−0.401373	−0.200686	+	0.979656i	$0.564317\pi$
$828$	−18.6900	−0.649524
$829$	−48.7103	−1.69178	−0.845890	−	0.533358i	$-0.820930\pi$
$829$	−48.7103	−1.69178	−0.845890	+	0.533358i	$0.820930\pi$
$830$	−11.0077	−0.382081
$831$	44.5648	1.54594
$832$	1.18184	0.0409731
$833$	17.6651	0.612059
$834$	−27.6392	−0.957069
$835$	5.05672	0.174995
$836$	5.24146	0.181280
$837$	4.73699	0.163734
$838$	−24.4579	−0.844884
$839$	5.82683	0.201164	0.100582	−	0.994929i	$-0.467929\pi$
$839$	5.82683	0.201164	0.100582	+	0.994929i	$0.467929\pi$
$840$	11.2462	0.388030
$841$	28.3689	0.978237
$842$	3.33076	0.114786
$843$	−97.2429	−3.34922
$844$	−22.4572	−0.773008
$845$	−5.94020	−0.204349
$846$	96.9173	3.33208
$847$	−29.9124	−1.02780
$848$	29.3310	1.00723
$849$	−37.1798	−1.27601
$850$	−12.1616	−0.417141
$851$	−10.7851	−0.369707
$852$	−18.7414	−0.642070
$853$	13.2215	0.452694	0.226347	−	0.974047i	$-0.427322\pi$
$853$	13.2215	0.452694	0.226347	+	0.974047i	$0.427322\pi$
$854$	76.1811	2.60686
$855$	7.52690	0.257415
$856$	−8.52158	−0.291262
$857$	0.657370	0.0224553	0.0112277	−	0.999937i	$-0.496426\pi$
$857$	0.657370	0.0224553	0.0112277	+	0.999937i	$0.496426\pi$
$858$	18.7833	0.641253
$859$	−38.6154	−1.31754	−0.658771	−	0.752344i	$-0.728923\pi$
$859$	−38.6154	−1.31754	−0.658771	+	0.752344i	$0.728923\pi$
$860$	0	0
$861$	−27.5150	−0.937708
$862$	−42.5136	−1.44802
$863$	16.5212	0.562390	0.281195	−	0.959651i	$-0.409269\pi$
$863$	16.5212	0.562390	0.281195	+	0.959651i	$0.409269\pi$
$864$	49.4266	1.68153
$865$	−6.60938	−0.224726
$866$	−71.5243	−2.43049
$867$	44.0442	1.49582
$868$	−2.94282	−0.0998860
$869$	7.43584	0.252244
$870$	−23.9077	−0.810545
$871$	0.924085	0.0313114
$872$	−1.14911	−0.0389136
$873$	59.4945	2.01358
$874$	−10.5680	−0.357468
$875$	−25.0926	−0.848284
$876$	−49.3561	−1.66759
$877$	−47.0958	−1.59031	−0.795156	−	0.606405i	$-0.792611\pi$
$877$	−47.0958	−1.59031	−0.795156	+	0.606405i	$0.792611\pi$
$878$	14.7914	0.499184
$879$	21.7973	0.735205
$880$	−6.02887	−0.203233
$881$	25.7188	0.866488	0.433244	−	0.901277i	$-0.357369\pi$
$881$	25.7188	0.866488	0.433244	+	0.901277i	$0.357369\pi$
$882$	124.589	4.19514
$883$	−8.18378	−0.275406	−0.137703	−	0.990474i	$-0.543972\pi$
$883$	−8.18378	−0.275406	−0.137703	+	0.990474i	$0.543972\pi$
$884$	−3.02745	−0.101824
$885$	−9.04058	−0.303896
$886$	−56.1960	−1.88794
$887$	−28.6814	−0.963027	−0.481514	−	0.876439i	$-0.659913\pi$
$887$	−28.6814	−0.963027	−0.481514	+	0.876439i	$0.659913\pi$
$888$	17.1243	0.574655
$889$	−16.4975	−0.553308
$890$	6.42376	0.215325
$891$	14.7641	0.494615
$892$	−11.4351	−0.382877
$893$	20.3715	0.681705
$894$	107.785	3.60487
$895$	9.19301	0.307288
$896$	46.6168	1.55736
$897$	−14.0784	−0.470063
$898$	−27.5330	−0.918787
$899$	−4.31698	−0.143979
$900$	−31.8857	−1.06286
$901$	−8.66774	−0.288764
$902$	7.72083	0.257076
$903$	0	0
$904$	−8.77319	−0.291792
$905$	−1.91300	−0.0635903
$906$	−105.687	−3.51120
$907$	9.35838	0.310740	0.155370	−	0.987856i	$-0.450343\pi$
$907$	9.35838	0.310740	0.155370	+	0.987856i	$0.450343\pi$
$908$	20.8946	0.693411
$909$	−64.8612	−2.15131
$910$	−8.09180	−0.268241
$911$	17.3043	0.573318	0.286659	−	0.958033i	$-0.407455\pi$
$911$	17.3043	0.573318	0.286659	+	0.958033i	$0.407455\pi$
$912$	32.0567	1.06150
$913$	−21.0617	−0.697041
$914$	16.5671	0.547990
$915$	−17.3126	−0.572338
$916$	−0.280241	−0.00925944
$917$	75.7423	2.50123
$918$	−21.7632	−0.718292
$919$	−36.0906	−1.19052	−0.595259	−	0.803534i	$-0.702951\pi$
$919$	−36.0906	−1.19052	−0.595259	+	0.803534i	$0.702951\pi$
$920$	2.36526	0.0779805
$921$	−33.7607	−1.11245
$922$	−37.3158	−1.22893
$923$	−9.30522	−0.306285
$924$	−31.1831	−1.02585
$925$	−18.3996	−0.604975
$926$	−3.90589	−0.128356
$927$	−0.809508	−0.0265877
$928$	−45.0442	−1.47865
$929$	−14.4903	−0.475411	−0.237705	−	0.971337i	$-0.576395\pi$
$929$	−14.4903	−0.475411	−0.237705	+	0.971337i	$0.576395\pi$
$930$	1.79904	0.0589929
$931$	26.1880	0.858276
$932$	−8.24605	−0.270108
$933$	−73.7006	−2.41285
$934$	0.412091	0.0134840
$935$	1.78161	0.0582650
$936$	14.7342	0.481601
$937$	−11.3372	−0.370370	−0.185185	−	0.982704i	$-0.559288\pi$
$937$	−11.3372	−0.370370	−0.185185	+	0.982704i	$0.559288\pi$
$938$	−4.12686	−0.134747
$939$	50.2292	1.63917
$940$	6.60731	0.215507
$941$	−34.8232	−1.13520	−0.567602	−	0.823303i	$-0.692129\pi$
$941$	−34.8232	−1.13520	−0.567602	+	0.823303i	$0.692129\pi$
$942$	91.1164	2.96873
$943$	−5.78687	−0.188446
$944$	−25.3794	−0.826029
$945$	−21.6237	−0.703419
$946$	0	0
$947$	34.7749	1.13003	0.565016	−	0.825080i	$-0.308870\pi$
$947$	34.7749	1.13003	0.565016	+	0.825080i	$0.308870\pi$
$948$	−12.8238	−0.416497
$949$	−24.5056	−0.795485
$950$	−18.0293	−0.584947
$951$	−70.1752	−2.27559
$952$	−9.32972	−0.302378
$953$	−7.89785	−0.255836	−0.127918	−	0.991785i	$-0.540829\pi$
$953$	−7.89785	−0.255836	−0.127918	+	0.991785i	$0.540829\pi$
$954$	−61.1323	−1.97923
$955$	3.18015	0.102907
$956$	−34.9366	−1.12993
$957$	−45.7441	−1.47870
$958$	8.93806	0.288776
$959$	−13.5724	−0.438275
$960$	1.19945	0.0387122
$961$	−30.6751	−0.989521
$962$	−12.3212	−0.397252
$963$	33.9311	1.09342
$964$	−20.5697	−0.662506
$965$	−4.00831	−0.129032
$966$	62.8724	2.02289
$967$	−3.36262	−0.108134	−0.0540672	−	0.998537i	$-0.517219\pi$
$967$	−3.36262	−0.108134	−0.0540672	+	0.998537i	$0.517219\pi$
$968$	9.98888	0.321055
$969$	−9.47321	−0.304323
$970$	10.9109	0.350329
$971$	−48.5656	−1.55854	−0.779272	−	0.626686i	$-0.784411\pi$
$971$	−48.5656	−1.55854	−0.779272	+	0.626686i	$0.784411\pi$
$972$	4.04400	0.129712
$973$	22.7823	0.730366
$974$	−23.2661	−0.745493
$975$	−24.0181	−0.769193
$976$	−48.6013	−1.55569
$977$	1.03175	0.0330085	0.0165042	−	0.999864i	$-0.494746\pi$
$977$	1.03175	0.0330085	0.0165042	+	0.999864i	$0.494746\pi$
$978$	115.519	3.69390
$979$	12.2910	0.392823
$980$	8.49384	0.271326
$981$	4.57550	0.146084
$982$	−45.1815	−1.44180
$983$	55.6019	1.77343	0.886713	−	0.462320i	$-0.152983\pi$
$983$	55.6019	1.77343	0.886713	+	0.462320i	$0.152983\pi$
$984$	9.18828	0.292912
$985$	−2.89882	−0.0923642
$986$	19.8335	0.631629
$987$	−121.196	−3.85772
$988$	−4.48810	−0.142785
$989$	0	0
$990$	12.5655	0.399357
$991$	41.7282	1.32554	0.662770	−	0.748823i	$-0.269381\pi$
$991$	41.7282	1.32554	0.662770	+	0.748823i	$0.269381\pi$
$992$	3.38955	0.107618
$993$	71.7292	2.27626
$994$	41.5561	1.31808
$995$	13.5163	0.428494
$996$	36.3228	1.15093
$997$	−16.7365	−0.530050	−0.265025	−	0.964242i	$-0.585380\pi$
$997$	−16.7365	−0.530050	−0.265025	+	0.964242i	$0.585380\pi$
$998$	−15.4954	−0.490499
$999$	−32.9259	−1.04173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.o.1.14		18
43.3	odd	42		43.2.g.a.9.2	✓	36
43.29	odd	42		43.2.g.a.24.2	yes	36
43.42	odd	2		1849.2.a.n.1.5		18
129.29	even	42		387.2.y.c.325.2		36
129.89	even	42		387.2.y.c.181.2		36
172.3	even	42		688.2.bg.c.353.3		36
172.115	even	42		688.2.bg.c.497.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.2	✓	36	43.3	odd	42
43.2.g.a.24.2	yes	36	43.29	odd	42
387.2.y.c.181.2		36	129.89	even	42
387.2.y.c.325.2		36	129.29	even	42
688.2.bg.c.353.3		36	172.3	even	42
688.2.bg.c.497.3		36	172.115	even	42
1849.2.a.n.1.5		18	43.42	odd	2
1849.2.a.o.1.14		18	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.78421 q^{2} -2.96672 q^{3} +1.18339 q^{4} +0.596316 q^{5} -5.29325 q^{6} +4.36308 q^{7} -1.45700 q^{8} +5.80145 q^{9} +O(q^{10})\)	\(q+1.78421 q^{2} -2.96672 q^{3} +1.18339 q^{4} +0.596316 q^{5} -5.29325 q^{6} +4.36308 q^{7} -1.45700 q^{8} +5.80145 q^{9} +1.06395 q^{10} +2.03573 q^{11} -3.51080 q^{12} -1.74313 q^{13} +7.78463 q^{14} -1.76911 q^{15} -4.96637 q^{16} +1.46763 q^{17} +10.3510 q^{18} +2.17572 q^{19} +0.705676 q^{20} -12.9440 q^{21} +3.63216 q^{22} -2.72236 q^{23} +4.32250 q^{24} -4.64441 q^{25} -3.11011 q^{26} -8.31113 q^{27} +5.16324 q^{28} +7.57422 q^{29} -3.15645 q^{30} -0.569957 q^{31} -5.94703 q^{32} -6.03945 q^{33} +2.61856 q^{34} +2.60177 q^{35} +6.86539 q^{36} +3.96167 q^{37} +3.88193 q^{38} +5.17139 q^{39} -0.868830 q^{40} +2.12568 q^{41} -23.0949 q^{42} +2.40907 q^{44} +3.45950 q^{45} -4.85724 q^{46} +9.36309 q^{47} +14.7338 q^{48} +12.0365 q^{49} -8.28658 q^{50} -4.35406 q^{51} -2.06281 q^{52} -5.90594 q^{53} -14.8288 q^{54} +1.21394 q^{55} -6.35699 q^{56} -6.45476 q^{57} +13.5140 q^{58} +5.11026 q^{59} -2.09355 q^{60} +9.78609 q^{61} -1.01692 q^{62} +25.3122 q^{63} -0.678000 q^{64} -1.03946 q^{65} -10.7756 q^{66} -0.530129 q^{67} +1.73678 q^{68} +8.07648 q^{69} +4.64210 q^{70} +5.33822 q^{71} -8.45269 q^{72} +14.0584 q^{73} +7.06843 q^{74} +13.7787 q^{75} +2.57473 q^{76} +8.88205 q^{77} +9.22683 q^{78} +3.65266 q^{79} -2.96153 q^{80} +7.25248 q^{81} +3.79266 q^{82} -10.3460 q^{83} -15.3179 q^{84} +0.875173 q^{85} -22.4706 q^{87} -2.96605 q^{88} +6.03765 q^{89} +6.17246 q^{90} -7.60542 q^{91} -3.22162 q^{92} +1.69091 q^{93} +16.7057 q^{94} +1.29742 q^{95} +17.6432 q^{96} +10.2551 q^{97} +21.4755 q^{98} +11.8102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9	\( 18 q + 5 q^{2} + 5 q^{3} + 19 q^{4} + 11 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} + 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} + 25 q^{18} + 31 q^{19} + 25 q^{20} + 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} + 27 q^{26} + 23 q^{27} + 20 q^{28} + 37 q^{29} - 17 q^{30} - 12 q^{31} + 39 q^{32} + 38 q^{33} + 14 q^{34} + 16 q^{35} + 47 q^{36} - 19 q^{37} + 56 q^{38} + 46 q^{39} + 6 q^{40} - 7 q^{41} - q^{42} + 7 q^{44} + 23 q^{45} - 47 q^{46} - q^{47} + 15 q^{48} - 6 q^{49} - 3 q^{50} + 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} + 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} + 28 q^{61} + 33 q^{62} + 26 q^{63} + 10 q^{64} + 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} + 7 q^{69} - 34 q^{70} + 86 q^{71} - 2 q^{72} - 27 q^{73} - 79 q^{74} + 31 q^{75} + 59 q^{76} + 43 q^{77} + 91 q^{78} + 17 q^{79} + 8 q^{80} - 10 q^{81} + 13 q^{82} - 12 q^{83} - 32 q^{84} + 28 q^{85} - 43 q^{87} - 23 q^{88} + 51 q^{89} + 10 q^{90} - 20 q^{91} + 18 q^{92} - 30 q^{93} - 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} - 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + 5 * q^3 + 19 * q^4 + 11 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 + 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 + 25 * q^18 + 31 * q^19 + 25 * q^20 + 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 + 27 * q^26 + 23 * q^27 + 20 * q^28 + 37 * q^29 - 17 * q^30 - 12 * q^31 + 39 * q^32 + 38 * q^33 + 14 * q^34 + 16 * q^35 + 47 * q^36 - 19 * q^37 + 56 * q^38 + 46 * q^39 + 6 * q^40 - 7 * q^41 - q^42 + 7 * q^44 + 23 * q^45 - 47 * q^46 - q^47 + 15 * q^48 - 6 * q^49 - 3 * q^50 + 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 + 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 + 28 * q^61 + 33 * q^62 + 26 * q^63 + 10 * q^64 + 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 + 7 * q^69 - 34 * q^70 + 86 * q^71 - 2 * q^72 - 27 * q^73 - 79 * q^74 + 31 * q^75 + 59 * q^76 + 43 * q^77 + 91 * q^78 + 17 * q^79 + 8 * q^80 - 10 * q^81 + 13 * q^82 - 12 * q^83 - 32 * q^84 + 28 * q^85 - 43 * q^87 - 23 * q^88 + 51 * q^89 + 10 * q^90 - 20 * q^91 + 18 * q^92 - 30 * q^93 - 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 - 5 * q^98 + 38 * q^99

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