LMFDB - Embedded newform 1849.2.a.p.1.11

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			1.11
Root			$0.173392$ 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)

$f(q)$	$=$	$q-0.173392 q^{2} -0.896458 q^{3} -1.96994 q^{4} +3.74986 q^{5} +0.155439 q^{6} +1.28742 q^{7} +0.688355 q^{8} -2.19636 q^{9} +O(q^{10})$	\(q-0.173392 q^{2} -0.896458 q^{3} -1.96994 q^{4} +3.74986 q^{5} +0.155439 q^{6} +1.28742 q^{7} +0.688355 q^{8} -2.19636 q^{9} -0.650196 q^{10} -4.72000 q^{11} +1.76596 q^{12} -4.53842 q^{13} -0.223228 q^{14} -3.36159 q^{15} +3.82051 q^{16} +2.76011 q^{17} +0.380832 q^{18} +2.71957 q^{19} -7.38698 q^{20} -1.15412 q^{21} +0.818411 q^{22} +4.99155 q^{23} -0.617082 q^{24} +9.06144 q^{25} +0.786927 q^{26} +4.65832 q^{27} -2.53613 q^{28} +1.47874 q^{29} +0.582873 q^{30} +3.76324 q^{31} -2.03916 q^{32} +4.23129 q^{33} -0.478581 q^{34} +4.82764 q^{35} +4.32669 q^{36} -5.53528 q^{37} -0.471553 q^{38} +4.06851 q^{39} +2.58124 q^{40} +1.04756 q^{41} +0.200115 q^{42} +9.29810 q^{44} -8.23605 q^{45} -0.865495 q^{46} +2.04767 q^{47} -3.42493 q^{48} -5.34255 q^{49} -1.57118 q^{50} -2.47432 q^{51} +8.94040 q^{52} +1.20753 q^{53} -0.807716 q^{54} -17.6993 q^{55} +0.886202 q^{56} -2.43799 q^{57} -0.256401 q^{58} -0.436150 q^{59} +6.62212 q^{60} +11.1148 q^{61} -0.652516 q^{62} -2.82764 q^{63} -7.28746 q^{64} -17.0184 q^{65} -0.733672 q^{66} +7.86202 q^{67} -5.43724 q^{68} -4.47472 q^{69} -0.837074 q^{70} +15.4494 q^{71} -1.51188 q^{72} +15.5029 q^{73} +0.959773 q^{74} -8.12320 q^{75} -5.35739 q^{76} -6.07662 q^{77} -0.705447 q^{78} -10.7742 q^{79} +14.3264 q^{80} +2.41310 q^{81} -0.181638 q^{82} +0.437792 q^{83} +2.27354 q^{84} +10.3500 q^{85} -1.32562 q^{87} -3.24904 q^{88} -5.41590 q^{89} +1.42807 q^{90} -5.84285 q^{91} -9.83303 q^{92} -3.37359 q^{93} -0.355049 q^{94} +10.1980 q^{95} +1.82802 q^{96} +6.46227 q^{97} +0.926356 q^{98} +10.3668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.173392	−0.122607	−0.0613034	−	0.998119i	$-0.519526\pi$
$2$	−0.173392	−0.122607	−0.0613034	+	0.998119i	$0.519526\pi$
$3$	−0.896458	−0.517570	−0.258785	−	0.965935i	$-0.583322\pi$
$3$	−0.896458	−0.517570	−0.258785	+	0.965935i	$0.583322\pi$
$4$	−1.96994	−0.984968
$5$	3.74986	1.67699	0.838494	−	0.544911i	$-0.183437\pi$
$5$	3.74986	1.67699	0.838494	+	0.544911i	$0.183437\pi$
$6$	0.155439	0.0634576
$7$	1.28742	0.486599	0.243299	−	0.969951i	$-0.421770\pi$
$7$	1.28742	0.486599	0.243299	+	0.969951i	$0.421770\pi$
$8$	0.688355	0.243370
$9$	−2.19636	−0.732121
$10$	−0.650196	−0.205610
$11$	−4.72000	−1.42313	−0.711567	−	0.702618i	$-0.752014\pi$
$11$	−4.72000	−1.42313	−0.711567	+	0.702618i	$0.752014\pi$
$12$	1.76596	0.509790
$13$	−4.53842	−1.25873	−0.629366	−	0.777109i	$-0.716685\pi$
$13$	−4.53842	−1.25873	−0.629366	+	0.777109i	$0.716685\pi$
$14$	−0.223228	−0.0596603
$15$	−3.36159	−0.867959
$16$	3.82051	0.955129
$17$	2.76011	0.669425	0.334713	−	0.942320i	$-0.391361\pi$
$17$	2.76011	0.669425	0.334713	+	0.942320i	$0.391361\pi$
$18$	0.380832	0.0897629
$19$	2.71957	0.623913	0.311957	−	0.950096i	$-0.399016\pi$
$19$	2.71957	0.623913	0.311957	+	0.950096i	$0.399016\pi$
$20$	−7.38698	−1.65178
$21$	−1.15412	−0.251849
$22$	0.818411	0.174486
$23$	4.99155	1.04081	0.520405	−	0.853920i	$-0.325781\pi$
$23$	4.99155	1.04081	0.520405	+	0.853920i	$0.325781\pi$
$24$	−0.617082	−0.125961
$25$	9.06144	1.81229
$26$	0.786927	0.154329
$27$	4.65832	0.896495
$28$	−2.53613	−0.479284
$29$	1.47874	0.274594	0.137297	−	0.990530i	$-0.456158\pi$
$29$	1.47874	0.274594	0.137297	+	0.990530i	$0.456158\pi$
$30$	0.582873	0.106418
$31$	3.76324	0.675898	0.337949	−	0.941164i	$-0.390267\pi$
$31$	3.76324	0.675898	0.337949	+	0.941164i	$0.390267\pi$
$32$	−2.03916	−0.360476
$33$	4.23129	0.736572
$34$	−0.478581	−0.0820760
$35$	4.82764	0.816020
$36$	4.32669	0.721115
$37$	−5.53528	−0.909994	−0.454997	−	0.890493i	$-0.650360\pi$
$37$	−5.53528	−0.909994	−0.454997	+	0.890493i	$0.650360\pi$
$38$	−0.471553	−0.0764960
$39$	4.06851	0.651483
$40$	2.58124	0.408129
$41$	1.04756	0.163601	0.0818004	−	0.996649i	$-0.473933\pi$
$41$	1.04756	0.163601	0.0818004	+	0.996649i	$0.473933\pi$
$42$	0.200115	0.0308784
$43$	0	0
$43$	0	0
$44$	9.29810	1.40174
$45$	−8.23605	−1.22776
$46$	−0.865495	−0.127610
$47$	2.04767	0.298683	0.149341	−	0.988786i	$-0.452285\pi$
$47$	2.04767	0.298683	0.149341	+	0.988786i	$0.452285\pi$
$48$	−3.42493	−0.494346
$49$	−5.34255	−0.763222
$50$	−1.57118	−0.222199
$51$	−2.47432	−0.346475
$52$	8.94040	1.23981
$53$	1.20753	0.165867	0.0829337	−	0.996555i	$-0.473571\pi$
$53$	1.20753	0.165867	0.0829337	+	0.996555i	$0.473571\pi$
$54$	−0.807716	−0.109916
$55$	−17.6993	−2.38658
$56$	0.886202	0.118424
$57$	−2.43799	−0.322919
$58$	−0.256401	−0.0336671
$59$	−0.436150	−0.0567818	−0.0283909	−	0.999597i	$-0.509038\pi$
$59$	−0.436150	−0.0567818	−0.0283909	+	0.999597i	$0.509038\pi$
$60$	6.62212	0.854912
$61$	11.1148	1.42311	0.711553	−	0.702632i	$-0.247992\pi$
$61$	11.1148	1.42311	0.711553	+	0.702632i	$0.247992\pi$
$62$	−0.652516	−0.0828696
$63$	−2.82764	−0.356249
$64$	−7.28746	−0.910932
$65$	−17.0184	−2.11088
$66$	−0.733672	−0.0903087
$67$	7.86202	0.960499	0.480249	−	0.877132i	$-0.340546\pi$
$67$	7.86202	0.960499	0.480249	+	0.877132i	$0.340546\pi$
$68$	−5.43724	−0.659362
$69$	−4.47472	−0.538692
$70$	−0.837074	−0.100050
$71$	15.4494	1.83351	0.916756	−	0.399448i	$-0.130798\pi$
$71$	15.4494	1.83351	0.916756	+	0.399448i	$0.130798\pi$
$72$	−1.51188	−0.178177
$73$	15.5029	1.81448	0.907240	−	0.420613i	$-0.138185\pi$
$73$	15.5029	1.81448	0.907240	+	0.420613i	$0.138185\pi$
$74$	0.959773	0.111571
$75$	−8.12320	−0.937987
$76$	−5.35739	−0.614534
$77$	−6.07662	−0.692495
$78$	−0.705447	−0.0798762
$79$	−10.7742	−1.21219	−0.606096	−	0.795391i	$-0.707265\pi$
$79$	−10.7742	−1.21219	−0.606096	+	0.795391i	$0.707265\pi$
$80$	14.3264	1.60174
$81$	2.41310	0.268122
$82$	−0.181638	−0.0200586
$83$	0.437792	0.0480540	0.0240270	−	0.999711i	$-0.492351\pi$
$83$	0.437792	0.0480540	0.0240270	+	0.999711i	$0.492351\pi$
$84$	2.27354	0.248063
$85$	10.3500	1.12262
$86$	0	0
$87$	−1.32562	−0.142122
$88$	−3.24904	−0.346349
$89$	−5.41590	−0.574084	−0.287042	−	0.957918i	$-0.592672\pi$
$89$	−5.41590	−0.574084	−0.287042	+	0.957918i	$0.592672\pi$
$90$	1.42807	0.150531
$91$	−5.84285	−0.612497
$92$	−9.83303	−1.02516
$93$	−3.37359	−0.349825
$94$	−0.355049	−0.0366205
$95$	10.1980	1.04629
$96$	1.82802	0.186572
$97$	6.46227	0.656144	0.328072	−	0.944653i	$-0.393601\pi$
$97$	6.46227	0.656144	0.328072	+	0.944653i	$0.393601\pi$
$98$	0.926356	0.0935761
$99$	10.3668	1.04191
$100$	−17.8504	−1.78504
$101$	6.57781	0.654516	0.327258	−	0.944935i	$-0.393875\pi$
$101$	6.57781	0.654516	0.327258	+	0.944935i	$0.393875\pi$
$102$	0.429028	0.0424801
$103$	11.8784	1.17042	0.585209	−	0.810883i	$-0.301013\pi$
$103$	11.8784	1.17042	0.585209	+	0.810883i	$0.301013\pi$
$104$	−3.12405	−0.306338
$105$	−4.32778	−0.422348
$106$	−0.209377	−0.0203365
$107$	−10.9156	−1.05525	−0.527623	−	0.849479i	$-0.676917\pi$
$107$	−10.9156	−1.05525	−0.527623	+	0.849479i	$0.676917\pi$
$108$	−9.17659	−0.883018
$109$	−0.903480	−0.0865377	−0.0432689	−	0.999063i	$-0.513777\pi$
$109$	−0.903480	−0.0865377	−0.0432689	+	0.999063i	$0.513777\pi$
$110$	3.06893	0.292611
$111$	4.96215	0.470986
$112$	4.91860	0.464764
$113$	9.40706	0.884942	0.442471	−	0.896783i	$-0.354102\pi$
$113$	9.40706	0.884942	0.442471	+	0.896783i	$0.354102\pi$
$114$	0.422727	0.0395920
$115$	18.7176	1.74543
$116$	−2.91301	−0.270466
$117$	9.96802	0.921544
$118$	0.0756249	0.00696184
$119$	3.55342	0.325741
$120$	−2.31397	−0.211236
$121$	11.2784	1.02531
$122$	−1.92722	−0.174482
$123$	−0.939091	−0.0846750
$124$	−7.41334	−0.665737
$125$	15.2298	1.36220
$126$	0.490290	0.0436785
$127$	11.0737	0.982632	0.491316	−	0.870981i	$-0.336516\pi$
$127$	11.0737	0.982632	0.491316	+	0.870981i	$0.336516\pi$
$128$	5.34190	0.472162
$129$	0	0
$130$	2.95086	0.258808
$131$	−13.1041	−1.14491	−0.572456	−	0.819936i	$-0.694009\pi$
$131$	−13.1041	−1.14491	−0.572456	+	0.819936i	$0.694009\pi$
$132$	−8.33536	−0.725500
$133$	3.50123	0.303595
$134$	−1.36321	−0.117764
$135$	17.4680	1.50341
$136$	1.89994	0.162918
$137$	−8.92430	−0.762455	−0.381227	−	0.924481i	$-0.624498\pi$
$137$	−8.92430	−0.762455	−0.381227	+	0.924481i	$0.624498\pi$
$138$	0.775880	0.0660473
$139$	8.98053	0.761719	0.380859	−	0.924633i	$-0.375628\pi$
$139$	8.98053	0.761719	0.380859	+	0.924633i	$0.375628\pi$
$140$	−9.51014	−0.803753
$141$	−1.83565	−0.154589
$142$	−2.67881	−0.224801
$143$	21.4214	1.79135
$144$	−8.39124	−0.699270
$145$	5.54505	0.460491
$146$	−2.68808	−0.222467
$147$	4.78938	0.395021
$148$	10.9041	0.896314
$149$	−11.3492	−0.929765	−0.464883	−	0.885372i	$-0.653903\pi$
$149$	−11.3492	−0.929765	−0.464883	+	0.885372i	$0.653903\pi$
$150$	1.40850	0.115003
$151$	18.8508	1.53406	0.767028	−	0.641613i	$-0.221735\pi$
$151$	18.8508	1.53406	0.767028	+	0.641613i	$0.221735\pi$
$152$	1.87203	0.151842
$153$	−6.06220	−0.490100
$154$	1.05364	0.0849046
$155$	14.1116	1.13347
$156$	−8.01470	−0.641689
$157$	−9.78678	−0.781070	−0.390535	−	0.920588i	$-0.627710\pi$
$157$	−9.78678	−0.781070	−0.390535	+	0.920588i	$0.627710\pi$
$158$	1.86816	0.148623
$159$	−1.08250	−0.0858480
$160$	−7.64655	−0.604513
$161$	6.42621	0.506457
$162$	−0.418412	−0.0328735
$163$	18.5725	1.45471	0.727355	−	0.686261i	$-0.240749\pi$
$163$	18.5725	1.45471	0.727355	+	0.686261i	$0.240749\pi$
$164$	−2.06362	−0.161142
$165$	15.8667	1.23522
$166$	−0.0759098	−0.00589174
$167$	22.2200	1.71944	0.859718	−	0.510769i	$-0.170639\pi$
$167$	22.2200	1.71944	0.859718	+	0.510769i	$0.170639\pi$
$168$	−0.794443	−0.0612926
$169$	7.59729	0.584407
$170$	−1.79461	−0.137640
$171$	−5.97317	−0.456780
$172$	0	0
$173$	−1.55703	−0.118379	−0.0591893	−	0.998247i	$-0.518852\pi$
$173$	−1.55703	−0.118379	−0.0591893	+	0.998247i	$0.518852\pi$
$174$	0.229853	0.0174251
$175$	11.6659	0.881857
$176$	−18.0328	−1.35928
$177$	0.390990	0.0293886
$178$	0.939075	0.0703866
$179$	−0.918675	−0.0686650	−0.0343325	−	0.999410i	$-0.510931\pi$
$179$	−0.918675	−0.0686650	−0.0343325	+	0.999410i	$0.510931\pi$
$180$	16.2245	1.20930
$181$	−17.6681	−1.31326	−0.656629	−	0.754214i	$-0.728018\pi$
$181$	−17.6681	−1.31326	−0.656629	+	0.754214i	$0.728018\pi$
$182$	1.01310	0.0750963
$183$	−9.96397	−0.736558
$184$	3.43596	0.253302
$185$	−20.7565	−1.52605
$186$	0.584953	0.0428909
$187$	−13.0277	−0.952682
$188$	−4.03377	−0.294193
$189$	5.99721	0.436233
$190$	−1.76826	−0.128283
$191$	−0.513569	−0.0371606	−0.0185803	−	0.999827i	$-0.505915\pi$
$191$	−0.513569	−0.0371606	−0.0185803	+	0.999827i	$0.505915\pi$
$192$	6.53290	0.471471
$193$	11.9313	0.858835	0.429417	−	0.903106i	$-0.358719\pi$
$193$	11.9313	0.858835	0.429417	+	0.903106i	$0.358719\pi$
$194$	−1.12051	−0.0804477
$195$	15.2563	1.09253
$196$	10.5245	0.751749
$197$	19.0131	1.35463	0.677314	−	0.735694i	$-0.263144\pi$
$197$	19.0131	1.35463	0.677314	+	0.735694i	$0.263144\pi$
$198$	−1.79753	−0.127745
$199$	2.59383	0.183871	0.0919357	−	0.995765i	$-0.470695\pi$
$199$	2.59383	0.183871	0.0919357	+	0.995765i	$0.470695\pi$
$200$	6.23749	0.441057
$201$	−7.04798	−0.497126
$202$	−1.14054	−0.0802481
$203$	1.90375	0.133617
$204$	4.87426	0.341266
$205$	3.92819	0.274357
$206$	−2.05963	−0.143501
$207$	−10.9633	−0.761999
$208$	−17.3391	−1.20225
$209$	−12.8364	−0.887912
$210$	0.750402	0.0517827
$211$	−2.50530	−0.172472	−0.0862360	−	0.996275i	$-0.527484\pi$
$211$	−2.50530	−0.172472	−0.0862360	+	0.996275i	$0.527484\pi$
$212$	−2.37876	−0.163374
$213$	−13.8498	−0.948972
$214$	1.89267	0.129380
$215$	0	0
$216$	3.20658	0.218180
$217$	4.84487	0.328891
$218$	0.156656	0.0106101
$219$	−13.8977	−0.939121
$220$	34.8666	2.35070
$221$	−12.5265	−0.842627
$222$	−0.860397	−0.0577461
$223$	6.22422	0.416805	0.208402	−	0.978043i	$-0.433174\pi$
$223$	6.22422	0.416805	0.208402	+	0.978043i	$0.433174\pi$
$224$	−2.62525	−0.175407
$225$	−19.9022	−1.32681
$226$	−1.63111	−0.108500
$227$	20.0963	1.33384	0.666918	−	0.745131i	$-0.267613\pi$
$227$	20.0963	1.33384	0.666918	+	0.745131i	$0.267613\pi$
$228$	4.80267	0.318065
$229$	−1.98863	−0.131413	−0.0657063	−	0.997839i	$-0.520930\pi$
$229$	−1.98863	−0.131413	−0.0657063	+	0.997839i	$0.520930\pi$
$230$	−3.24548	−0.214001
$231$	5.44744	0.358415
$232$	1.01790	0.0668281
$233$	−20.7218	−1.35753	−0.678765	−	0.734356i	$-0.737484\pi$
$233$	−20.7218	−1.35753	−0.678765	+	0.734356i	$0.737484\pi$
$234$	−1.72838	−0.112988
$235$	7.67845	0.500887
$236$	0.859186	0.0559283
$237$	9.65863	0.627395
$238$	−0.616135	−0.0399381
$239$	−7.80550	−0.504896	−0.252448	−	0.967610i	$-0.581236\pi$
$239$	−7.80550	−0.504896	−0.252448	+	0.967610i	$0.581236\pi$
$240$	−12.8430	−0.829013
$241$	−0.497502	−0.0320469	−0.0160235	−	0.999872i	$-0.505101\pi$
$241$	−0.497502	−0.0320469	−0.0160235	+	0.999872i	$0.505101\pi$
$242$	−1.95559	−0.125710
$243$	−16.1382	−1.03527
$244$	−21.8955	−1.40171
$245$	−20.0338	−1.27991
$246$	0.162831	0.0103817
$247$	−12.3426	−0.785340
$248$	2.59045	0.164493
$249$	−0.392463	−0.0248713
$250$	−2.64073	−0.167014
$251$	8.56269	0.540472	0.270236	−	0.962794i	$-0.412898\pi$
$251$	8.56269	0.540472	0.270236	+	0.962794i	$0.412898\pi$
$252$	5.57026	0.350894
$253$	−23.5601	−1.48121
$254$	−1.92009	−0.120477
$255$	−9.27836	−0.581034
$256$	13.6487	0.853042
$257$	−23.6967	−1.47816	−0.739080	−	0.673617i	$-0.764740\pi$
$257$	−23.6967	−1.47816	−0.739080	+	0.673617i	$0.764740\pi$
$258$	0	0
$259$	−7.12622	−0.442802
$260$	33.5252	2.07915
$261$	−3.24784	−0.201036
$262$	2.27215	0.140374
$263$	−14.2516	−0.878790	−0.439395	−	0.898294i	$-0.644807\pi$
$263$	−14.2516	−0.878790	−0.439395	+	0.898294i	$0.644807\pi$
$264$	2.91263	0.179260
$265$	4.52808	0.278157
$266$	−0.607086	−0.0372228
$267$	4.85513	0.297129
$268$	−15.4877	−0.946060
$269$	−1.59532	−0.0972684	−0.0486342	−	0.998817i	$-0.515487\pi$
$269$	−1.59532	−0.0972684	−0.0486342	+	0.998817i	$0.515487\pi$
$270$	−3.02882	−0.184328
$271$	6.02629	0.366071	0.183035	−	0.983106i	$-0.441408\pi$
$271$	6.02629	0.366071	0.183035	+	0.983106i	$0.441408\pi$
$272$	10.5450	0.639387
$273$	5.23787	0.317011
$274$	1.54740	0.0934821
$275$	−42.7700	−2.57913
$276$	8.81490	0.530595
$277$	7.30551	0.438946	0.219473	−	0.975619i	$-0.429566\pi$
$277$	7.30551	0.438946	0.219473	+	0.975619i	$0.429566\pi$
$278$	−1.55715	−0.0933918
$279$	−8.26544	−0.494839
$280$	3.32313	0.198595
$281$	−18.6946	−1.11523	−0.557613	−	0.830101i	$-0.688283\pi$
$281$	−18.6946	−1.11523	−0.557613	+	0.830101i	$0.688283\pi$
$282$	0.318287	0.0189537
$283$	−18.6920	−1.11113	−0.555563	−	0.831475i	$-0.687497\pi$
$283$	−18.6920	−1.11113	−0.555563	+	0.831475i	$0.687497\pi$
$284$	−30.4344	−1.80595
$285$	−9.14210	−0.541531
$286$	−3.71430	−0.219631
$287$	1.34864	0.0796080
$288$	4.47873	0.263912
$289$	−9.38179	−0.551870
$290$	−0.961468	−0.0564593
$291$	−5.79316	−0.339601
$292$	−30.5398	−1.78720
$293$	13.4321	0.784714	0.392357	−	0.919813i	$-0.371660\pi$
$293$	13.4321	0.784714	0.392357	+	0.919813i	$0.371660\pi$
$294$	−0.830440	−0.0484322
$295$	−1.63550	−0.0952224
$296$	−3.81024	−0.221466
$297$	−21.9873	−1.27583
$298$	1.96787	0.113995
$299$	−22.6538	−1.31010
$300$	16.0022	0.923886
$301$	0	0
$302$	−3.26858	−0.188086
$303$	−5.89673	−0.338758
$304$	10.3902	0.595917
$305$	41.6790	2.38653
$306$	1.05114	0.0600896
$307$	0.447461	0.0255380	0.0127690	−	0.999918i	$-0.495935\pi$
$307$	0.447461	0.0255380	0.0127690	+	0.999918i	$0.495935\pi$
$308$	11.9706	0.682085
$309$	−10.6485	−0.605773
$310$	−2.44684	−0.138971
$311$	23.9641	1.35888	0.679440	−	0.733731i	$-0.262223\pi$
$311$	23.9641	1.35888	0.679440	+	0.733731i	$0.262223\pi$
$312$	2.80058	0.158552
$313$	−5.90628	−0.333843	−0.166921	−	0.985970i	$-0.553383\pi$
$313$	−5.90628	−0.333843	−0.166921	+	0.985970i	$0.553383\pi$
$314$	1.69695	0.0957645
$315$	−10.6032	−0.597425
$316$	21.2245	1.19397
$317$	−12.9476	−0.727207	−0.363604	−	0.931554i	$-0.618454\pi$
$317$	−12.9476	−0.727207	−0.363604	+	0.931554i	$0.618454\pi$
$318$	0.187697	0.0105255
$319$	−6.97964	−0.390785
$320$	−27.3269	−1.52762
$321$	9.78534	0.546164
$322$	−1.11425	−0.0620950
$323$	7.50632	0.417663
$324$	−4.75364	−0.264091
$325$	−41.1246	−2.28118
$326$	−3.22033	−0.178357
$327$	0.809932	0.0447894
$328$	0.721091	0.0398156
$329$	2.63620	0.145339
$330$	−2.75116	−0.151447
$331$	13.7626	0.756463	0.378232	−	0.925711i	$-0.376532\pi$
$331$	13.7626	0.756463	0.378232	+	0.925711i	$0.376532\pi$
$332$	−0.862423	−0.0473316
$333$	12.1575	0.666225
$334$	−3.85277	−0.210814
$335$	29.4815	1.61074
$336$	−4.40932	−0.240548
$337$	30.4226	1.65723	0.828613	−	0.559821i	$-0.189130\pi$
$337$	30.4226	1.65723	0.828613	+	0.559821i	$0.189130\pi$
$338$	−1.31731	−0.0716522
$339$	−8.43304	−0.458020
$340$	−20.3889	−1.10574
$341$	−17.7625	−0.961893
$342$	1.03570	0.0560043
$343$	−15.8900	−0.857981
$344$	0	0
$345$	−16.7795	−0.903381
$346$	0.269976	0.0145140
$347$	17.9851	0.965489	0.482744	−	0.875761i	$-0.339640\pi$
$347$	17.9851	0.965489	0.482744	+	0.875761i	$0.339640\pi$
$348$	2.61140	0.139985
$349$	−29.8015	−1.59524	−0.797619	−	0.603161i	$-0.793907\pi$
$349$	−29.8015	−1.59524	−0.797619	+	0.603161i	$0.793907\pi$
$350$	−2.02277	−0.108122
$351$	−21.1414	−1.12845
$352$	9.62483	0.513005
$353$	12.9853	0.691140	0.345570	−	0.938393i	$-0.387686\pi$
$353$	12.9853	0.691140	0.345570	+	0.938393i	$0.387686\pi$
$354$	−0.0677946	−0.00360324
$355$	57.9332	3.07478
$356$	10.6690	0.565455
$357$	−3.18549	−0.168594
$358$	0.159291	0.00841880
$359$	33.4100	1.76331	0.881655	−	0.471894i	$-0.156429\pi$
$359$	33.4100	1.76331	0.881655	+	0.471894i	$0.156429\pi$
$360$	−5.66933	−0.298800
$361$	−11.6039	−0.610732
$362$	3.06350	0.161014
$363$	−10.1106	−0.530671
$364$	11.5100	0.603290
$365$	58.1338	3.04286
$366$	1.72767	0.0903070
$367$	−23.8201	−1.24340	−0.621700	−	0.783256i	$-0.713558\pi$
$367$	−23.8201	−1.24340	−0.621700	+	0.783256i	$0.713558\pi$
$368$	19.0703	0.994107
$369$	−2.30081	−0.119776
$370$	3.59901	0.187104
$371$	1.55460	0.0807108
$372$	6.64575	0.344566
$373$	−22.0022	−1.13923	−0.569615	−	0.821911i	$-0.692908\pi$
$373$	−22.0022	−1.13923	−0.569615	+	0.821911i	$0.692908\pi$
$374$	2.25891	0.116805
$375$	−13.6529	−0.705033
$376$	1.40952	0.0726905
$377$	−6.71113	−0.345641
$378$	−1.03987	−0.0534851
$379$	−26.6146	−1.36710	−0.683550	−	0.729903i	$-0.739565\pi$
$379$	−26.6146	−1.36710	−0.683550	+	0.729903i	$0.739565\pi$
$380$	−20.0894	−1.03057
$381$	−9.92711	−0.508582
$382$	0.0890489	0.00455614
$383$	−4.01558	−0.205186	−0.102593	−	0.994723i	$-0.532714\pi$
$383$	−4.01558	−0.205186	−0.102593	+	0.994723i	$0.532714\pi$
$384$	−4.78879	−0.244377
$385$	−22.7865	−1.16131
$386$	−2.06880	−0.105299
$387$	0	0
$388$	−12.7303	−0.646281
$389$	5.01939	0.254493	0.127246	−	0.991871i	$-0.459386\pi$
$389$	5.01939	0.254493	0.127246	+	0.991871i	$0.459386\pi$
$390$	−2.64533	−0.133951
$391$	13.7772	0.696744
$392$	−3.67758	−0.185746
$393$	11.7473	0.592573
$394$	−3.29672	−0.166086
$395$	−40.4017	−2.03283
$396$	−20.4220	−1.02624
$397$	0.953961	0.0478779	0.0239390	−	0.999713i	$-0.492379\pi$
$397$	0.953961	0.0478779	0.0239390	+	0.999713i	$0.492379\pi$
$398$	−0.449749	−0.0225439
$399$	−3.13871	−0.157132
$400$	34.6194	1.73097
$401$	−5.05098	−0.252234	−0.126117	−	0.992015i	$-0.540251\pi$
$401$	−5.05098	−0.252234	−0.126117	+	0.992015i	$0.540251\pi$
$402$	1.22206	0.0609510
$403$	−17.0792	−0.850774
$404$	−12.9579	−0.644677
$405$	9.04877	0.449637
$406$	−0.330096	−0.0163824
$407$	26.1265	1.29504
$408$	−1.70321	−0.0843217
$409$	−3.11544	−0.154048	−0.0770242	−	0.997029i	$-0.524542\pi$
$409$	−3.11544	−0.154048	−0.0770242	+	0.997029i	$0.524542\pi$
$410$	−0.681117	−0.0336380
$411$	8.00027	0.394624
$412$	−23.3998	−1.15282
$413$	−0.561507	−0.0276300
$414$	1.90094	0.0934262
$415$	1.64166	0.0805859
$416$	9.25456	0.453742
$417$	−8.05067	−0.394243
$418$	2.22573	0.108864
$419$	14.9155	0.728672	0.364336	−	0.931268i	$-0.381296\pi$
$419$	14.9155	0.728672	0.364336	+	0.931268i	$0.381296\pi$
$420$	8.52544	0.415999
$421$	−8.61076	−0.419663	−0.209831	−	0.977738i	$-0.567291\pi$
$421$	−8.61076	−0.419663	−0.209831	+	0.977738i	$0.567291\pi$
$422$	0.434399	0.0211462
$423$	−4.49741	−0.218672
$424$	0.831211	0.0403672
$425$	25.0106	1.21319
$426$	2.40144	0.116350
$427$	14.3094	0.692482
$428$	21.5029	1.03938
$429$	−19.2034	−0.927147
$430$	0	0
$431$	−1.33423	−0.0642676	−0.0321338	−	0.999484i	$-0.510230\pi$
$431$	−1.33423	−0.0642676	−0.0321338	+	0.999484i	$0.510230\pi$
$432$	17.7972	0.856268
$433$	−13.5246	−0.649951	−0.324976	−	0.945722i	$-0.605356\pi$
$433$	−13.5246	−0.649951	−0.324976	+	0.945722i	$0.605356\pi$
$434$	−0.840061	−0.0403242
$435$	−4.97091	−0.238337
$436$	1.77980	0.0852368
$437$	13.5749	0.649375
$438$	2.40976	0.115143
$439$	−24.1197	−1.15117	−0.575586	−	0.817741i	$-0.695226\pi$
$439$	−24.1197	−1.15117	−0.575586	+	0.817741i	$0.695226\pi$
$440$	−12.1834	−0.580823
$441$	11.7342	0.558771
$442$	2.17200	0.103312
$443$	0.319346	0.0151726	0.00758629	−	0.999971i	$-0.497585\pi$
$443$	0.319346	0.0151726	0.00758629	+	0.999971i	$0.497585\pi$
$444$	−9.77510	−0.463906
$445$	−20.3089	−0.962733
$446$	−1.07923	−0.0511030
$447$	10.1741	0.481219
$448$	−9.38201	−0.443258
$449$	36.3704	1.71643	0.858213	−	0.513294i	$-0.171575\pi$
$449$	36.3704	1.71643	0.858213	+	0.513294i	$0.171575\pi$
$450$	3.45088	0.162676
$451$	−4.94447	−0.232826
$452$	−18.5313	−0.871639
$453$	−16.8990	−0.793983
$454$	−3.48453	−0.163537
$455$	−21.9099	−1.02715
$456$	−1.67820	−0.0785889
$457$	−21.6311	−1.01186	−0.505929	−	0.862575i	$-0.668850\pi$
$457$	−21.6311	−1.01186	−0.505929	+	0.862575i	$0.668850\pi$
$458$	0.344813	0.0161121
$459$	12.8575	0.600136
$460$	−36.8725	−1.71919
$461$	−32.6478	−1.52056	−0.760281	−	0.649595i	$-0.774939\pi$
$461$	−32.6478	−1.52056	−0.760281	+	0.649595i	$0.774939\pi$
$462$	−0.944543	−0.0439441
$463$	−9.74471	−0.452875	−0.226438	−	0.974026i	$-0.572708\pi$
$463$	−9.74471	−0.452875	−0.226438	+	0.974026i	$0.572708\pi$
$464$	5.64953	0.262273
$465$	−12.6505	−0.586652
$466$	3.59300	0.166442
$467$	12.6828	0.586888	0.293444	−	0.955976i	$-0.405199\pi$
$467$	12.6828	0.586888	0.293444	+	0.955976i	$0.405199\pi$
$468$	−19.6364	−0.907691
$469$	10.1217	0.467377
$470$	−1.33138	−0.0614121
$471$	8.77344	0.404259
$472$	−0.300226	−0.0138190
$473$	0	0
$474$	−1.67473	−0.0769229
$475$	24.6433	1.13071
$476$	−7.00000	−0.320845
$477$	−2.65218	−0.121435
$478$	1.35341	0.0619036
$479$	14.5454	0.664594	0.332297	−	0.943175i	$-0.392176\pi$
$479$	14.5454	0.664594	0.332297	+	0.943175i	$0.392176\pi$
$480$	6.85482	0.312878
$481$	25.1214	1.14544
$482$	0.0862629	0.00392917
$483$	−5.76083	−0.262127
$484$	−22.2178	−1.00990
$485$	24.2326	1.10035
$486$	2.79824	0.126931
$487$	37.8405	1.71472	0.857359	−	0.514719i	$-0.172104\pi$
$487$	37.8405	1.71472	0.857359	+	0.514719i	$0.172104\pi$
$488$	7.65095	0.346342
$489$	−16.6495	−0.752915
$490$	3.47371	0.156926
$491$	−28.2201	−1.27355	−0.636777	−	0.771048i	$-0.719733\pi$
$491$	−28.2201	−1.27355	−0.636777	+	0.771048i	$0.719733\pi$
$492$	1.84995	0.0834021
$493$	4.08147	0.183820
$494$	2.14011	0.0962879
$495$	38.8742	1.74726
$496$	14.3775	0.645569
$497$	19.8899	0.892184
$498$	0.0680499	0.00304939
$499$	8.26465	0.369977	0.184988	−	0.982741i	$-0.440775\pi$
$499$	8.26465	0.369977	0.184988	+	0.982741i	$0.440775\pi$
$500$	−30.0018	−1.34172
$501$	−19.9193	−0.889929
$502$	−1.48470	−0.0662656
$503$	−29.8923	−1.33283	−0.666415	−	0.745581i	$-0.732172\pi$
$503$	−29.8923	−1.33283	−0.666415	+	0.745581i	$0.732172\pi$
$504$	−1.94642	−0.0867005
$505$	24.6658	1.09762
$506$	4.08514	0.181607
$507$	−6.81065	−0.302472
$508$	−21.8145	−0.967861
$509$	−22.2426	−0.985884	−0.492942	−	0.870062i	$-0.664079\pi$
$509$	−22.2426	−0.985884	−0.492942	+	0.870062i	$0.664079\pi$
$510$	1.60880	0.0712386
$511$	19.9588	0.882923
$512$	−13.0504	−0.576751
$513$	12.6687	0.559335
$514$	4.10882	0.181232
$515$	44.5425	1.96278
$516$	0	0
$517$	−9.66499	−0.425066
$518$	1.23563	0.0542905
$519$	1.39581	0.0612692
$520$	−11.7147	−0.513725
$521$	17.8713	0.782954	0.391477	−	0.920188i	$-0.371964\pi$
$521$	17.8713	0.782954	0.391477	+	0.920188i	$0.371964\pi$
$522$	0.563150	0.0246484
$523$	9.87947	0.431999	0.216000	−	0.976393i	$-0.430699\pi$
$523$	9.87947	0.431999	0.216000	+	0.976393i	$0.430699\pi$
$524$	25.8143	1.12770
$525$	−10.4580	−0.456423
$526$	2.47111	0.107746
$527$	10.3870	0.452463
$528$	16.1657	0.703521
$529$	1.91556	0.0832852
$530$	−0.785133	−0.0341040
$531$	0.957943	0.0415712
$532$	−6.89720	−0.299031
$533$	−4.75426	−0.205930
$534$	−0.841841	−0.0364300
$535$	−40.9318	−1.76964
$536$	5.41187	0.233757
$537$	0.823554	0.0355390
$538$	0.276616	0.0119258
$539$	25.2169	1.08617
$540$	−34.4109	−1.48081
$541$	15.4611	0.664726	0.332363	−	0.943152i	$-0.392154\pi$
$541$	15.4611	0.664726	0.332363	+	0.943152i	$0.392154\pi$
$542$	−1.04491	−0.0448828
$543$	15.8387	0.679703
$544$	−5.62830	−0.241311
$545$	−3.38792	−0.145123
$546$	−0.908206	−0.0388676
$547$	38.6245	1.65146	0.825732	−	0.564063i	$-0.190762\pi$
$547$	38.6245	1.65146	0.825732	+	0.564063i	$0.190762\pi$
$548$	17.5803	0.750993
$549$	−24.4122	−1.04189
$550$	7.41598	0.316219
$551$	4.02153	0.171323
$552$	−3.08019	−0.131102
$553$	−13.8709	−0.589851
$554$	−1.26672	−0.0538177
$555$	18.6073	0.789838
$556$	−17.6911	−0.750268
$557$	−3.85403	−0.163300	−0.0816502	−	0.996661i	$-0.526019\pi$
$557$	−3.85403	−0.163300	−0.0816502	+	0.996661i	$0.526019\pi$
$558$	1.43316	0.0606706
$559$	0	0
$560$	18.4441	0.779404
$561$	11.6788	0.493080
$562$	3.24149	0.136734
$563$	−47.2566	−1.99163	−0.995815	−	0.0913962i	$-0.970867\pi$
$563$	−47.2566	−1.99163	−0.995815	+	0.0913962i	$0.970867\pi$
$564$	3.61610	0.152265
$565$	35.2751	1.48404
$566$	3.24105	0.136231
$567$	3.10666	0.130468
$568$	10.6347	0.446222
$569$	36.0982	1.51331	0.756657	−	0.653811i	$-0.226831\pi$
$569$	36.0982	1.51331	0.756657	+	0.653811i	$0.226831\pi$
$570$	1.58517	0.0663954
$571$	31.8292	1.33201	0.666006	−	0.745946i	$-0.268002\pi$
$571$	31.8292	1.33201	0.666006	+	0.745946i	$0.268002\pi$
$572$	−42.1987	−1.76442
$573$	0.460394	0.0192332
$574$	−0.233844	−0.00976047
$575$	45.2306	1.88625
$576$	16.0059	0.666912
$577$	17.1365	0.713403	0.356702	−	0.934218i	$-0.383901\pi$
$577$	17.1365	0.713403	0.356702	+	0.934218i	$0.383901\pi$
$578$	1.62673	0.0676630
$579$	−10.6959	−0.444508
$580$	−10.9234	−0.453569
$581$	0.563622	0.0233830
$582$	1.00449	0.0416374
$583$	−5.69956	−0.236052
$584$	10.6715	0.441591
$585$	37.3787	1.54542
$586$	−2.32903	−0.0962112
$587$	−23.8807	−0.985662	−0.492831	−	0.870125i	$-0.664038\pi$
$587$	−23.8807	−0.985662	−0.492831	+	0.870125i	$0.664038\pi$
$588$	−9.43476	−0.389083
$589$	10.2344	0.421701
$590$	0.283583	0.0116749
$591$	−17.0445	−0.701115
$592$	−21.1476	−0.869161
$593$	10.8615	0.446028	0.223014	−	0.974815i	$-0.428410\pi$
$593$	10.8615	0.446028	0.223014	+	0.974815i	$0.428410\pi$
$594$	3.81242	0.156426
$595$	13.3248	0.546264
$596$	22.3572	0.915788
$597$	−2.32526	−0.0951664
$598$	3.92798	0.160627
$599$	21.5460	0.880345	0.440172	−	0.897913i	$-0.354917\pi$
$599$	21.5460	0.880345	0.440172	+	0.897913i	$0.354917\pi$
$600$	−5.59165	−0.228278
$601$	−35.3358	−1.44138	−0.720690	−	0.693258i	$-0.756175\pi$
$601$	−35.3358	−1.44138	−0.720690	+	0.693258i	$0.756175\pi$
$602$	0	0
$603$	−17.2679	−0.703201
$604$	−37.1349	−1.51100
$605$	42.2925	1.71944
$606$	1.02245	0.0415340
$607$	−0.431261	−0.0175044	−0.00875218	−	0.999962i	$-0.502786\pi$
$607$	−0.431261	−0.0175044	−0.00875218	+	0.999962i	$0.502786\pi$
$608$	−5.54564	−0.224905
$609$	−1.70663	−0.0691563
$610$	−7.22681	−0.292605
$611$	−9.29317	−0.375961
$612$	11.9421	0.482733
$613$	−39.4834	−1.59472	−0.797359	−	0.603506i	$-0.793770\pi$
$613$	−39.4834	−1.59472	−0.797359	+	0.603506i	$0.793770\pi$
$614$	−0.0775863	−0.00313113
$615$	−3.52146	−0.141999
$616$	−4.18288	−0.168533
$617$	−21.5383	−0.867099	−0.433549	−	0.901130i	$-0.642739\pi$
$617$	−21.5383	−0.867099	−0.433549	+	0.901130i	$0.642739\pi$
$618$	1.84637	0.0742719
$619$	−30.8064	−1.23821	−0.619106	−	0.785308i	$-0.712505\pi$
$619$	−30.8064	−1.23821	−0.619106	+	0.785308i	$0.712505\pi$
$620$	−27.7990	−1.11643
$621$	23.2522	0.933080
$622$	−4.15519	−0.166608
$623$	−6.97254	−0.279349
$624$	15.5438	0.622250
$625$	11.8025	0.472099
$626$	1.02410	0.0409314
$627$	11.5073	0.459557
$628$	19.2793	0.769329
$629$	−15.2780	−0.609173
$630$	1.83852	0.0732483
$631$	32.5214	1.29466	0.647328	−	0.762211i	$-0.275886\pi$
$631$	32.5214	1.29466	0.647328	+	0.762211i	$0.275886\pi$
$632$	−7.41648	−0.295012
$633$	2.24590	0.0892664
$634$	2.24500	0.0891605
$635$	41.5248	1.64786
$636$	2.13246	0.0845575
$637$	24.2468	0.960692
$638$	1.21021	0.0479128
$639$	−33.9326	−1.34235
$640$	20.0314	0.791810
$641$	−5.46273	−0.215765	−0.107882	−	0.994164i	$-0.534407\pi$
$641$	−5.46273	−0.215765	−0.107882	+	0.994164i	$0.534407\pi$
$642$	−1.69670	−0.0669634
$643$	−28.5630	−1.12641	−0.563207	−	0.826316i	$-0.690432\pi$
$643$	−28.5630	−1.12641	−0.563207	+	0.826316i	$0.690432\pi$
$644$	−12.6592	−0.498843
$645$	0	0
$646$	−1.30154	−0.0512083
$647$	−6.49241	−0.255243	−0.127622	−	0.991823i	$-0.540734\pi$
$647$	−6.49241	−0.255243	−0.127622	+	0.991823i	$0.540734\pi$
$648$	1.66107	0.0652529
$649$	2.05863	0.0808082
$650$	7.13069	0.279689
$651$	−4.34322	−0.170224
$652$	−36.5866	−1.43284
$653$	−24.2888	−0.950493	−0.475246	−	0.879853i	$-0.657641\pi$
$653$	−24.2888	−0.950493	−0.475246	+	0.879853i	$0.657641\pi$
$654$	−0.140436	−0.00549148
$655$	−49.1386	−1.92000
$656$	4.00221	0.156260
$657$	−34.0500	−1.32842
$658$	−0.457097	−0.0178195
$659$	36.4889	1.42140	0.710702	−	0.703493i	$-0.248377\pi$
$659$	36.4889	1.42140	0.710702	+	0.703493i	$0.248377\pi$
$660$	−31.2564	−1.21665
$661$	−25.3533	−0.986131	−0.493065	−	0.869992i	$-0.664124\pi$
$661$	−25.3533	−0.986131	−0.493065	+	0.869992i	$0.664124\pi$
$662$	−2.38633	−0.0927475
$663$	11.2295	0.436119
$664$	0.301357	0.0116949
$665$	13.1291	0.509126
$666$	−2.10801	−0.0816837
$667$	7.38118	0.285800
$668$	−43.7720	−1.69359
$669$	−5.57975	−0.215726
$670$	−5.11185	−0.197488
$671$	−52.4620	−2.02527
$672$	2.35343	0.0907854
$673$	31.1668	1.20139	0.600696	−	0.799477i	$-0.294890\pi$
$673$	31.1668	1.20139	0.600696	+	0.799477i	$0.294890\pi$
$674$	−5.27504	−0.203187
$675$	42.2111	1.62471
$676$	−14.9662	−0.575622
$677$	−25.5584	−0.982291	−0.491145	−	0.871078i	$-0.663422\pi$
$677$	−25.5584	−0.982291	−0.491145	+	0.871078i	$0.663422\pi$
$678$	1.46222	0.0561563
$679$	8.31965	0.319279
$680$	7.12449	0.273212
$681$	−18.0155	−0.690354
$682$	3.07988	0.117935
$683$	−23.1944	−0.887510	−0.443755	−	0.896148i	$-0.646354\pi$
$683$	−23.1944	−0.887510	−0.443755	+	0.896148i	$0.646354\pi$
$684$	11.7668	0.449913
$685$	−33.4649	−1.27863
$686$	2.75521	0.105194
$687$	1.78273	0.0680153
$688$	0	0
$689$	−5.48029	−0.208783
$690$	2.90944	0.110761
$691$	−35.7877	−1.36143	−0.680714	−	0.732549i	$-0.738331\pi$
$691$	−35.7877	−1.36143	−0.680714	+	0.732549i	$0.738331\pi$
$692$	3.06724	0.116599
$693$	13.3465	0.506990
$694$	−3.11847	−0.118375
$695$	33.6757	1.27739
$696$	−0.912501	−0.0345883
$697$	2.89137	0.109519
$698$	5.16735	0.195587
$699$	18.5762	0.702617
$700$	−22.9810	−0.868600
$701$	14.7767	0.558107	0.279053	−	0.960276i	$-0.409979\pi$
$701$	14.7767	0.558107	0.279053	+	0.960276i	$0.409979\pi$
$702$	3.66576	0.138355
$703$	−15.0536	−0.567757
$704$	34.3968	1.29638
$705$	−6.88341	−0.259244
$706$	−2.25155	−0.0847384
$707$	8.46839	0.318487
$708$	−0.770225	−0.0289468
$709$	−25.9700	−0.975324	−0.487662	−	0.873032i	$-0.662150\pi$
$709$	−25.9700	−0.975324	−0.487662	+	0.873032i	$0.662150\pi$
$710$	−10.0452	−0.376988
$711$	23.6641	0.887472
$712$	−3.72807	−0.139715
$713$	18.7844	0.703481
$714$	0.552339	0.0206708
$715$	80.3271	3.00406
$716$	1.80973	0.0676328
$717$	6.99730	0.261319
$718$	−5.79303	−0.216194
$719$	−4.03692	−0.150552	−0.0752759	−	0.997163i	$-0.523984\pi$
$719$	−4.03692	−0.150552	−0.0752759	+	0.997163i	$0.523984\pi$
$720$	−31.4659	−1.17267
$721$	15.2925	0.569523
$722$	2.01203	0.0748799
$723$	0.445990	0.0165865
$724$	34.8050	1.29352
$725$	13.3995	0.497644
$726$	1.75311	0.0650639
$727$	−14.6132	−0.541973	−0.270987	−	0.962583i	$-0.587350\pi$
$727$	−14.6132	−0.541973	−0.270987	+	0.962583i	$0.587350\pi$
$728$	−4.02196	−0.149064
$729$	7.22794	0.267702
$730$	−10.0799	−0.373075
$731$	0	0
$732$	19.6284	0.725486
$733$	−26.2291	−0.968794	−0.484397	−	0.874848i	$-0.660961\pi$
$733$	−26.2291	−0.968794	−0.484397	+	0.874848i	$0.660961\pi$
$734$	4.13022	0.152449
$735$	17.9595	0.662445
$736$	−10.1786	−0.375187
$737$	−37.1088	−1.36692
$738$	0.398943	0.0146853
$739$	5.99448	0.220510	0.110255	−	0.993903i	$-0.464833\pi$
$739$	5.99448	0.220510	0.110255	+	0.993903i	$0.464833\pi$
$740$	40.8890	1.50311
$741$	11.0646	0.406469
$742$	−0.269555	−0.00989569
$743$	−28.1441	−1.03251	−0.516253	−	0.856436i	$-0.672674\pi$
$743$	−28.1441	−1.03251	−0.516253	+	0.856436i	$0.672674\pi$
$744$	−2.32223	−0.0851370
$745$	−42.5580	−1.55920
$746$	3.81501	0.139677
$747$	−0.961551	−0.0351813
$748$	25.6638	0.938361
$749$	−14.0529	−0.513481
$750$	2.36730	0.0864417
$751$	−27.5881	−1.00670	−0.503352	−	0.864081i	$-0.667900\pi$
$751$	−27.5881	−1.00670	−0.503352	+	0.864081i	$0.667900\pi$
$752$	7.82313	0.285280
$753$	−7.67610	−0.279733
$754$	1.16366	0.0423779
$755$	70.6879	2.57259
$756$	−11.8141	−0.429675
$757$	−22.9603	−0.834507	−0.417254	−	0.908790i	$-0.637007\pi$
$757$	−22.9603	−0.834507	−0.417254	+	0.908790i	$0.637007\pi$
$758$	4.61476	0.167616
$759$	21.1207	0.766632
$760$	7.01986	0.254637
$761$	31.0617	1.12598	0.562992	−	0.826462i	$-0.309650\pi$
$761$	31.0617	1.12598	0.562992	+	0.826462i	$0.309650\pi$
$762$	1.72128	0.0623555
$763$	−1.16316	−0.0421091
$764$	1.01170	0.0366020
$765$	−22.7324	−0.821892
$766$	0.696270	0.0251572
$767$	1.97943	0.0714731
$768$	−12.2355	−0.441509
$769$	−13.0535	−0.470722	−0.235361	−	0.971908i	$-0.575627\pi$
$769$	−13.0535	−0.470722	−0.235361	+	0.971908i	$0.575627\pi$
$770$	3.95099	0.142384
$771$	21.2431	0.765052
$772$	−23.5039	−0.845925
$773$	48.6075	1.74829	0.874145	−	0.485666i	$-0.161423\pi$
$773$	48.6075	1.74829	0.874145	+	0.485666i	$0.161423\pi$
$774$	0	0
$775$	34.1004	1.22492
$776$	4.44834	0.159686
$777$	6.38836	0.229181
$778$	−0.870322	−0.0312026
$779$	2.84891	0.102073
$780$	−30.0540	−1.07611
$781$	−72.9214	−2.60933
$782$	−2.38886	−0.0854255
$783$	6.88843	0.246172
$784$	−20.4113	−0.728975
$785$	−36.6990	−1.30985
$786$	−2.03689	−0.0726534
$787$	24.5540	0.875257	0.437628	−	0.899156i	$-0.355819\pi$
$787$	24.5540	0.875257	0.437628	+	0.899156i	$0.355819\pi$
$788$	−37.4546	−1.33426
$789$	12.7759	0.454836
$790$	7.00534	0.249239
$791$	12.1108	0.430611
$792$	7.13607	0.253569
$793$	−50.4438	−1.79131
$794$	−0.165409	−0.00587015
$795$	−4.05923	−0.143966
$796$	−5.10967	−0.181107
$797$	31.5442	1.11735	0.558676	−	0.829386i	$-0.311310\pi$
$797$	31.5442	1.11735	0.558676	+	0.829386i	$0.311310\pi$
$798$	0.544227	0.0192654
$799$	5.65178	0.199946
$800$	−18.4777	−0.653285
$801$	11.8953	0.420299
$802$	0.875799	0.0309256
$803$	−73.1739	−2.58225
$804$	13.8841	0.489653
$805$	24.0974	0.849322
$806$	2.96139	0.104311
$807$	1.43014	0.0503433
$808$	4.52787	0.159290
$809$	35.1426	1.23555	0.617774	−	0.786356i	$-0.288035\pi$
$809$	35.1426	1.23555	0.617774	+	0.786356i	$0.288035\pi$
$810$	−1.56898	−0.0551285
$811$	43.7911	1.53771	0.768857	−	0.639421i	$-0.220826\pi$
$811$	43.7911	1.53771	0.768857	+	0.639421i	$0.220826\pi$
$812$	−3.75027	−0.131609
$813$	−5.40231	−0.189467
$814$	−4.53013	−0.158781
$815$	69.6442	2.43953
$816$	−9.45319	−0.330928
$817$	0	0
$818$	0.540192	0.0188874
$819$	12.8330	0.448422
$820$	−7.73828	−0.270232
$821$	42.0166	1.46639	0.733195	−	0.680018i	$-0.238028\pi$
$821$	42.0166	1.46639	0.733195	+	0.680018i	$0.238028\pi$
$822$	−1.38718	−0.0483836
$823$	−15.1340	−0.527539	−0.263770	−	0.964586i	$-0.584966\pi$
$823$	−15.1340	−0.527539	−0.263770	+	0.964586i	$0.584966\pi$
$824$	8.17659	0.284845
$825$	38.3415	1.33488
$826$	0.0973609	0.00338762
$827$	20.2018	0.702486	0.351243	−	0.936284i	$-0.385759\pi$
$827$	20.2018	0.702486	0.351243	+	0.936284i	$0.385759\pi$
$828$	21.5969	0.750544
$829$	−25.3002	−0.878713	−0.439356	−	0.898313i	$-0.644793\pi$
$829$	−25.3002	−0.878713	−0.439356	+	0.898313i	$0.644793\pi$
$830$	−0.284651	−0.00988037
$831$	−6.54909	−0.227185
$832$	33.0736	1.14662
$833$	−14.7460	−0.510920
$834$	1.39592	0.0483369
$835$	83.3219	2.88347
$836$	25.2869	0.874565
$837$	17.5304	0.605939
$838$	−2.58624	−0.0893401
$839$	−42.6109	−1.47109	−0.735546	−	0.677474i	$-0.763074\pi$
$839$	−42.6109	−1.47109	−0.735546	+	0.677474i	$0.763074\pi$
$840$	−2.97905	−0.102787
$841$	−26.8133	−0.924598
$842$	1.49304	0.0514535
$843$	16.7589	0.577208
$844$	4.93528	0.169879
$845$	28.4888	0.980043
$846$	0.779816	0.0268106
$847$	14.5201	0.498915
$848$	4.61340	0.158425
$849$	16.7566	0.575086
$850$	−4.33663	−0.148745
$851$	−27.6296	−0.947131
$852$	27.2832	0.934706
$853$	−18.7681	−0.642607	−0.321304	−	0.946976i	$-0.604121\pi$
$853$	−18.7681	−0.642607	−0.321304	+	0.946976i	$0.604121\pi$
$854$	−2.48114	−0.0849029
$855$	−22.3985	−0.766014
$856$	−7.51378	−0.256816
$857$	−21.8895	−0.747731	−0.373865	−	0.927483i	$-0.621968\pi$
$857$	−21.8895	−0.747731	−0.373865	+	0.927483i	$0.621968\pi$
$858$	3.32971	0.113675
$859$	7.09658	0.242132	0.121066	−	0.992644i	$-0.461369\pi$
$859$	7.09658	0.242132	0.121066	+	0.992644i	$0.461369\pi$
$860$	0	0
$861$	−1.20900	−0.0412027
$862$	0.231345	0.00787964
$863$	15.5005	0.527643	0.263822	−	0.964571i	$-0.415017\pi$
$863$	15.5005	0.527643	0.263822	+	0.964571i	$0.415017\pi$
$864$	−9.49906	−0.323164
$865$	−5.83863	−0.198519
$866$	2.34506	0.0796884
$867$	8.41039	0.285632
$868$	−9.54407	−0.323947
$869$	50.8543	1.72511
$870$	0.861916	0.0292217
$871$	−35.6812	−1.20901
$872$	−0.621916	−0.0210607
$873$	−14.1935	−0.480377
$874$	−2.35378	−0.0796177
$875$	19.6072	0.662843
$876$	27.3776	0.925004
$877$	30.1286	1.01737	0.508685	−	0.860953i	$-0.330132\pi$
$877$	30.1286	1.01737	0.508685	+	0.860953i	$0.330132\pi$
$878$	4.18217	0.141142
$879$	−12.0414	−0.406145
$880$	−67.6206	−2.27949
$881$	−17.3905	−0.585899	−0.292950	−	0.956128i	$-0.594637\pi$
$881$	−17.3905	−0.585899	−0.292950	+	0.956128i	$0.594637\pi$
$882$	−2.03461	−0.0685090
$883$	−23.7234	−0.798357	−0.399179	−	0.916873i	$-0.630705\pi$
$883$	−23.7234	−0.798357	−0.399179	+	0.916873i	$0.630705\pi$
$884$	24.6765	0.829960
$885$	1.46616	0.0492843
$886$	−0.0553720	−0.00186026
$887$	−51.3944	−1.72565	−0.862827	−	0.505500i	$-0.831308\pi$
$887$	−51.3944	−1.72565	−0.862827	+	0.505500i	$0.831308\pi$
$888$	3.41572	0.114624
$889$	14.2565	0.478148
$890$	3.52140	0.118038
$891$	−11.3898	−0.381573
$892$	−12.2613	−0.410539
$893$	5.56878	0.186352
$894$	−1.76411	−0.0590007
$895$	−3.44490	−0.115150
$896$	6.87727	0.229753
$897$	20.3082	0.678070
$898$	−6.30634	−0.210445
$899$	5.56484	0.185598
$900$	39.2060	1.30687
$901$	3.33292	0.111036
$902$	0.857332	0.0285460
$903$	0	0
$904$	6.47540	0.215369
$905$	−66.2528	−2.20232
$906$	2.93015	0.0973476
$907$	−7.61195	−0.252751	−0.126375	−	0.991982i	$-0.540334\pi$
$907$	−7.61195	−0.252751	−0.126375	+	0.991982i	$0.540334\pi$
$908$	−39.5883	−1.31379
$909$	−14.4472	−0.479185
$910$	3.79900	0.125936
$911$	−35.9994	−1.19271	−0.596357	−	0.802719i	$-0.703386\pi$
$911$	−35.9994	−1.19271	−0.596357	+	0.802719i	$0.703386\pi$
$912$	−9.31436	−0.308429
$913$	−2.06638	−0.0683873
$914$	3.75065	0.124061
$915$	−37.3635	−1.23520
$916$	3.91748	0.129437
$917$	−16.8705	−0.557112
$918$	−2.22939	−0.0735807
$919$	−9.73512	−0.321132	−0.160566	−	0.987025i	$-0.551332\pi$
$919$	−9.73512	−0.321132	−0.160566	+	0.987025i	$0.551332\pi$
$920$	12.8844	0.424785
$921$	−0.401131	−0.0132177
$922$	5.66088	0.186431
$923$	−70.1161	−2.30790
$924$	−10.7311	−0.353027
$925$	−50.1576	−1.64917
$926$	1.68966	0.0555255
$927$	−26.0894	−0.856887
$928$	−3.01538	−0.0989846
$929$	12.0728	0.396095	0.198047	−	0.980192i	$-0.436540\pi$
$929$	12.0728	0.396095	0.198047	+	0.980192i	$0.436540\pi$
$930$	2.19349	0.0719274
$931$	−14.5295	−0.476184
$932$	40.8206	1.33712
$933$	−21.4828	−0.703316
$934$	−2.19909	−0.0719565
$935$	−48.8521	−1.59764
$936$	6.86154	0.224277
$937$	−36.6495	−1.19729	−0.598643	−	0.801016i	$-0.704293\pi$
$937$	−36.6495	−1.19729	−0.598643	+	0.801016i	$0.704293\pi$
$938$	−1.75503	−0.0573036
$939$	5.29474	0.172787
$940$	−15.1261	−0.493358
$941$	29.2866	0.954715	0.477357	−	0.878709i	$-0.341595\pi$
$941$	29.2866	0.954715	0.477357	+	0.878709i	$0.341595\pi$
$942$	−1.52125	−0.0495649
$943$	5.22893	0.170277
$944$	−1.66632	−0.0542340
$945$	22.4887	0.731557
$946$	0	0
$947$	48.4088	1.57307	0.786537	−	0.617543i	$-0.211872\pi$
$947$	48.4088	1.57307	0.786537	+	0.617543i	$0.211872\pi$
$948$	−19.0269	−0.617964
$949$	−70.3588	−2.28394
$950$	−4.27295	−0.138633
$951$	11.6069	0.376381
$952$	2.44601	0.0792758
$953$	56.7901	1.83961	0.919806	−	0.392374i	$-0.128346\pi$
$953$	56.7901	1.83961	0.919806	+	0.392374i	$0.128346\pi$
$954$	0.459867	0.0148887
$955$	−1.92581	−0.0623178
$956$	15.3763	0.497306
$957$	6.25695	0.202259
$958$	−2.52205	−0.0814837
$959$	−11.4893	−0.371009
$960$	24.4975	0.790652
$961$	−16.8380	−0.543162
$962$	−4.35586	−0.140439
$963$	23.9745	0.772568
$964$	0.980047	0.0315652
$965$	44.7407	1.44026
$966$	0.998883	0.0321385
$967$	10.2369	0.329197	0.164598	−	0.986361i	$-0.447367\pi$
$967$	10.2369	0.329197	0.164598	+	0.986361i	$0.447367\pi$
$968$	7.76357	0.249531
$969$	−6.72911	−0.216170
$970$	−4.20174	−0.134910
$971$	40.2133	1.29051	0.645253	−	0.763969i	$-0.276752\pi$
$971$	40.2133	1.29051	0.645253	+	0.763969i	$0.276752\pi$
$972$	31.7912	1.01970
$973$	11.5617	0.370651
$974$	−6.56125	−0.210236
$975$	36.8665	1.18067
$976$	42.4643	1.35925
$977$	30.9631	0.990596	0.495298	−	0.868723i	$-0.335059\pi$
$977$	30.9631	0.990596	0.495298	+	0.868723i	$0.335059\pi$
$978$	2.88689	0.0923125
$979$	25.5631	0.816999
$980$	39.4653	1.26067
$981$	1.98437	0.0633561
$982$	4.89314	0.156146
$983$	−53.4586	−1.70506	−0.852532	−	0.522674i	$-0.824934\pi$
$983$	−53.4586	−1.70506	−0.852532	+	0.522674i	$0.824934\pi$
$984$	−0.646428	−0.0206074
$985$	71.2965	2.27169
$986$	−0.707695	−0.0225376
$987$	−2.36325	−0.0752229
$988$	24.3141	0.773534
$989$	0	0
$990$	−6.74047	−0.214226
$991$	9.04068	0.287187	0.143593	−	0.989637i	$-0.454134\pi$
$991$	9.04068	0.287187	0.143593	+	0.989637i	$0.454134\pi$
$992$	−7.67384	−0.243645
$993$	−12.3376	−0.391523
$994$	−3.44875	−0.109388
$995$	9.72648	0.308350
$996$	0.773126	0.0244974
$997$	14.0612	0.445321	0.222661	−	0.974896i	$-0.428526\pi$
$997$	14.0612	0.445321	0.222661	+	0.974896i	$0.428526\pi$
$998$	−1.43303	−0.0453616
$999$	−25.7851	−0.815805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.p.1.11	✓	20
43.42	odd	2		1849.2.a.r.1.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.11	✓	20	1.1	even	1	trivial
1849.2.a.r.1.10	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)

\(f(q)\)	\(=\)	\(q-0.173392 q^{2} -0.896458 q^{3} -1.96994 q^{4} +3.74986 q^{5} +0.155439 q^{6} +1.28742 q^{7} +0.688355 q^{8} -2.19636 q^{9} +O(q^{10})\)	\(q-0.173392 q^{2} -0.896458 q^{3} -1.96994 q^{4} +3.74986 q^{5} +0.155439 q^{6} +1.28742 q^{7} +0.688355 q^{8} -2.19636 q^{9} -0.650196 q^{10} -4.72000 q^{11} +1.76596 q^{12} -4.53842 q^{13} -0.223228 q^{14} -3.36159 q^{15} +3.82051 q^{16} +2.76011 q^{17} +0.380832 q^{18} +2.71957 q^{19} -7.38698 q^{20} -1.15412 q^{21} +0.818411 q^{22} +4.99155 q^{23} -0.617082 q^{24} +9.06144 q^{25} +0.786927 q^{26} +4.65832 q^{27} -2.53613 q^{28} +1.47874 q^{29} +0.582873 q^{30} +3.76324 q^{31} -2.03916 q^{32} +4.23129 q^{33} -0.478581 q^{34} +4.82764 q^{35} +4.32669 q^{36} -5.53528 q^{37} -0.471553 q^{38} +4.06851 q^{39} +2.58124 q^{40} +1.04756 q^{41} +0.200115 q^{42} +9.29810 q^{44} -8.23605 q^{45} -0.865495 q^{46} +2.04767 q^{47} -3.42493 q^{48} -5.34255 q^{49} -1.57118 q^{50} -2.47432 q^{51} +8.94040 q^{52} +1.20753 q^{53} -0.807716 q^{54} -17.6993 q^{55} +0.886202 q^{56} -2.43799 q^{57} -0.256401 q^{58} -0.436150 q^{59} +6.62212 q^{60} +11.1148 q^{61} -0.652516 q^{62} -2.82764 q^{63} -7.28746 q^{64} -17.0184 q^{65} -0.733672 q^{66} +7.86202 q^{67} -5.43724 q^{68} -4.47472 q^{69} -0.837074 q^{70} +15.4494 q^{71} -1.51188 q^{72} +15.5029 q^{73} +0.959773 q^{74} -8.12320 q^{75} -5.35739 q^{76} -6.07662 q^{77} -0.705447 q^{78} -10.7742 q^{79} +14.3264 q^{80} +2.41310 q^{81} -0.181638 q^{82} +0.437792 q^{83} +2.27354 q^{84} +10.3500 q^{85} -1.32562 q^{87} -3.24904 q^{88} -5.41590 q^{89} +1.42807 q^{90} -5.84285 q^{91} -9.83303 q^{92} -3.37359 q^{93} -0.355049 q^{94} +10.1980 q^{95} +1.82802 q^{96} +6.46227 q^{97} +0.926356 q^{98} +10.3668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9}+O(q^{10}) \) 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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