LMFDB - Embedded newform 1849.2.a.p.1.15

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			1.15
Root			$-1.22059$ 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)

$f(q)$	$=$	$q+1.22059 q^{2} -1.36553 q^{3} -0.510154 q^{4} -2.60720 q^{5} -1.66675 q^{6} -5.05996 q^{7} -3.06388 q^{8} -1.13534 q^{9} +O(q^{10})$	\(q+1.22059 q^{2} -1.36553 q^{3} -0.510154 q^{4} -2.60720 q^{5} -1.66675 q^{6} -5.05996 q^{7} -3.06388 q^{8} -1.13534 q^{9} -3.18232 q^{10} +1.31185 q^{11} +0.696630 q^{12} -2.43824 q^{13} -6.17615 q^{14} +3.56020 q^{15} -2.71943 q^{16} -0.535935 q^{17} -1.38578 q^{18} -5.23819 q^{19} +1.33007 q^{20} +6.90951 q^{21} +1.60123 q^{22} +4.15182 q^{23} +4.18380 q^{24} +1.79747 q^{25} -2.97609 q^{26} +5.64691 q^{27} +2.58136 q^{28} -5.78386 q^{29} +4.34555 q^{30} +1.84089 q^{31} +2.80843 q^{32} -1.79136 q^{33} -0.654158 q^{34} +13.1923 q^{35} +0.579197 q^{36} -3.58682 q^{37} -6.39370 q^{38} +3.32948 q^{39} +7.98812 q^{40} +0.598425 q^{41} +8.43370 q^{42} -0.669244 q^{44} +2.96004 q^{45} +5.06768 q^{46} -6.74718 q^{47} +3.71346 q^{48} +18.6032 q^{49} +2.19398 q^{50} +0.731833 q^{51} +1.24388 q^{52} -6.59809 q^{53} +6.89258 q^{54} -3.42024 q^{55} +15.5031 q^{56} +7.15290 q^{57} -7.05974 q^{58} -9.36611 q^{59} -1.81625 q^{60} +8.06101 q^{61} +2.24697 q^{62} +5.74475 q^{63} +8.86682 q^{64} +6.35696 q^{65} -2.18652 q^{66} -15.3694 q^{67} +0.273410 q^{68} -5.66943 q^{69} +16.1024 q^{70} -5.13844 q^{71} +3.47853 q^{72} +7.47727 q^{73} -4.37805 q^{74} -2.45449 q^{75} +2.67229 q^{76} -6.63789 q^{77} +4.06393 q^{78} -2.34859 q^{79} +7.09009 q^{80} -4.30500 q^{81} +0.730433 q^{82} -6.14848 q^{83} -3.52492 q^{84} +1.39729 q^{85} +7.89802 q^{87} -4.01933 q^{88} -6.17037 q^{89} +3.61301 q^{90} +12.3374 q^{91} -2.11807 q^{92} -2.51378 q^{93} -8.23555 q^{94} +13.6570 q^{95} -3.83499 q^{96} +12.2752 q^{97} +22.7069 q^{98} -1.48939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9} + 21 q^{11} + 12 q^{12} + 11 q^{13} + 8 q^{14} + 4 q^{15} + 29 q^{16} + 15 q^{17} - 9 q^{18} + 7 q^{19} + 17 q^{20} + 8 q^{21} - 47 q^{22} + 26 q^{23} - q^{24} + 11 q^{25} - 58 q^{26} + 22 q^{27} + 28 q^{28} + 12 q^{29} + 24 q^{30} + 26 q^{31} - 3 q^{32} + 17 q^{33} - 54 q^{34} + 26 q^{35} + 14 q^{36} + 19 q^{37} + 5 q^{38} + 7 q^{39} - 16 q^{40} + 27 q^{41} + 52 q^{42} + 32 q^{44} - 75 q^{45} - 59 q^{46} + 45 q^{47} + 66 q^{48} + 20 q^{49} - 75 q^{51} + 11 q^{52} + 3 q^{53} + 57 q^{54} + 2 q^{55} + 87 q^{56} - 24 q^{57} - 46 q^{58} + 66 q^{59} + 29 q^{60} - 30 q^{61} - 72 q^{62} + 21 q^{63} - 7 q^{64} + 6 q^{65} + 41 q^{66} - 6 q^{67} + 28 q^{68} + 35 q^{69} + 80 q^{70} + 31 q^{71} + 15 q^{72} + 26 q^{73} + 87 q^{74} - 73 q^{75} + 68 q^{76} + 21 q^{77} - 50 q^{78} + 39 q^{79} + 60 q^{80} + 16 q^{81} - 45 q^{82} + 13 q^{83} + 31 q^{84} + 22 q^{85} + 61 q^{87} - 50 q^{88} + 4 q^{89} - 13 q^{90} + 25 q^{91} + 5 q^{92} - 67 q^{93} - 42 q^{94} + 79 q^{95} + 36 q^{96} - 2 q^{97} + 35 q^{98} + 13 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 + q^3 + 23 * q^4 + 3 * q^5 + 5 * q^6 + 2 * q^7 - 9 * q^8 + 27 * q^9 + 21 * q^11 + 12 * q^12 + 11 * q^13 + 8 * q^14 + 4 * q^15 + 29 * q^16 + 15 * q^17 - 9 * q^18 + 7 * q^19 + 17 * q^20 + 8 * q^21 - 47 * q^22 + 26 * q^23 - q^24 + 11 * q^25 - 58 * q^26 + 22 * q^27 + 28 * q^28 + 12 * q^29 + 24 * q^30 + 26 * q^31 - 3 * q^32 + 17 * q^33 - 54 * q^34 + 26 * q^35 + 14 * q^36 + 19 * q^37 + 5 * q^38 + 7 * q^39 - 16 * q^40 + 27 * q^41 + 52 * q^42 + 32 * q^44 - 75 * q^45 - 59 * q^46 + 45 * q^47 + 66 * q^48 + 20 * q^49 - 75 * q^51 + 11 * q^52 + 3 * q^53 + 57 * q^54 + 2 * q^55 + 87 * q^56 - 24 * q^57 - 46 * q^58 + 66 * q^59 + 29 * q^60 - 30 * q^61 - 72 * q^62 + 21 * q^63 - 7 * q^64 + 6 * q^65 + 41 * q^66 - 6 * q^67 + 28 * q^68 + 35 * q^69 + 80 * q^70 + 31 * q^71 + 15 * q^72 + 26 * q^73 + 87 * q^74 - 73 * q^75 + 68 * q^76 + 21 * q^77 - 50 * q^78 + 39 * q^79 + 60 * q^80 + 16 * q^81 - 45 * q^82 + 13 * q^83 + 31 * q^84 + 22 * q^85 + 61 * q^87 - 50 * q^88 + 4 * q^89 - 13 * q^90 + 25 * q^91 + 5 * q^92 - 67 * q^93 - 42 * q^94 + 79 * q^95 + 36 * q^96 - 2 * q^97 + 35 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.22059	0.863089	0.431545	−	0.902092i	$-0.357969\pi$
$2$	1.22059	0.863089	0.431545	+	0.902092i	$0.357969\pi$
$3$	−1.36553	−0.788387	−0.394194	−	0.919027i	$-0.628976\pi$
$3$	−1.36553	−0.788387	−0.394194	+	0.919027i	$0.628976\pi$
$4$	−0.510154	−0.255077
$5$	−2.60720	−1.16597	−0.582987	−	0.812482i	$-0.698116\pi$
$5$	−2.60720	−1.16597	−0.582987	+	0.812482i	$0.698116\pi$
$6$	−1.66675	−0.680449
$7$	−5.05996	−1.91249	−0.956243	−	0.292575i	$-0.905488\pi$
$7$	−5.05996	−1.91249	−0.956243	+	0.292575i	$0.905488\pi$
$8$	−3.06388	−1.08324
$9$	−1.13534	−0.378445
$10$	−3.18232	−1.00634
$11$	1.31185	0.395536	0.197768	−	0.980249i	$-0.436631\pi$
$11$	1.31185	0.395536	0.197768	+	0.980249i	$0.436631\pi$
$12$	0.696630	0.201100
$13$	−2.43824	−0.676245	−0.338123	−	0.941102i	$-0.609792\pi$
$13$	−2.43824	−0.676245	−0.338123	+	0.941102i	$0.609792\pi$
$14$	−6.17615	−1.65064
$15$	3.56020	0.919239
$16$	−2.71943	−0.679858
$17$	−0.535935	−0.129983	−0.0649916	−	0.997886i	$-0.520702\pi$
$17$	−0.535935	−0.129983	−0.0649916	+	0.997886i	$0.520702\pi$
$18$	−1.38578	−0.326632
$19$	−5.23819	−1.20172	−0.600862	−	0.799353i	$-0.705176\pi$
$19$	−5.23819	−1.20172	−0.600862	+	0.799353i	$0.705176\pi$
$20$	1.33007	0.297413
$21$	6.90951	1.50778
$22$	1.60123	0.341383
$23$	4.15182	0.865715	0.432858	−	0.901462i	$-0.357505\pi$
$23$	4.15182	0.865715	0.432858	+	0.901462i	$0.357505\pi$
$24$	4.18380	0.854015
$25$	1.79747	0.359494
$26$	−2.97609	−0.583660
$27$	5.64691	1.08675
$28$	2.58136	0.487831
$29$	−5.78386	−1.07404	−0.537018	−	0.843571i	$-0.680449\pi$
$29$	−5.78386	−1.07404	−0.537018	+	0.843571i	$0.680449\pi$
$30$	4.34555	0.793385
$31$	1.84089	0.330633	0.165316	−	0.986241i	$-0.447135\pi$
$31$	1.84089	0.330633	0.165316	+	0.986241i	$0.447135\pi$
$32$	2.80843	0.496465
$33$	−1.79136	−0.311836
$34$	−0.654158	−0.112187
$35$	13.1923	2.22991
$36$	0.579197	0.0965328
$37$	−3.58682	−0.589670	−0.294835	−	0.955548i	$-0.595265\pi$
$37$	−3.58682	−0.589670	−0.294835	+	0.955548i	$0.595265\pi$
$38$	−6.39370	−1.03720
$39$	3.32948	0.533143
$40$	7.98812	1.26303
$41$	0.598425	0.0934583	0.0467291	−	0.998908i	$-0.485120\pi$
$41$	0.598425	0.0934583	0.0467291	+	0.998908i	$0.485120\pi$
$42$	8.43370	1.30135
$43$	0	0
$43$	0	0
$44$	−0.669244	−0.100892
$45$	2.96004	0.441257
$46$	5.06768	0.747189
$47$	−6.74718	−0.984177	−0.492089	−	0.870545i	$-0.663766\pi$
$47$	−6.74718	−0.984177	−0.492089	+	0.870545i	$0.663766\pi$
$48$	3.71346	0.535992
$49$	18.6032	2.65760
$50$	2.19398	0.310275
$51$	0.731833	0.102477
$52$	1.24388	0.172495
$53$	−6.59809	−0.906318	−0.453159	−	0.891430i	$-0.649703\pi$
$53$	−6.59809	−0.906318	−0.453159	+	0.891430i	$0.649703\pi$
$54$	6.89258	0.937961
$55$	−3.42024	−0.461185
$56$	15.5031	2.07169
$57$	7.15290	0.947424
$58$	−7.05974	−0.926989
$59$	−9.36611	−1.21936	−0.609682	−	0.792646i	$-0.708703\pi$
$59$	−9.36611	−1.21936	−0.609682	+	0.792646i	$0.708703\pi$
$60$	−1.81625	−0.234477
$61$	8.06101	1.03211	0.516053	−	0.856557i	$-0.327401\pi$
$61$	8.06101	1.03211	0.516053	+	0.856557i	$0.327401\pi$
$62$	2.24697	0.285366
$63$	5.74475	0.723771
$64$	8.86682	1.10835
$65$	6.35696	0.788484
$66$	−2.18652	−0.269142
$67$	−15.3694	−1.87767	−0.938837	−	0.344362i	$-0.888095\pi$
$67$	−15.3694	−1.87767	−0.938837	+	0.344362i	$0.888095\pi$
$68$	0.273410	0.0331558
$69$	−5.66943	−0.682519
$70$	16.1024	1.92461
$71$	−5.13844	−0.609820	−0.304910	−	0.952381i	$-0.598626\pi$
$71$	−5.13844	−0.609820	−0.304910	+	0.952381i	$0.598626\pi$
$72$	3.47853	0.409948
$73$	7.47727	0.875148	0.437574	−	0.899182i	$-0.355838\pi$
$73$	7.47727	0.875148	0.437574	+	0.899182i	$0.355838\pi$
$74$	−4.37805	−0.508938
$75$	−2.45449	−0.283420
$76$	2.67229	0.306533
$77$	−6.63789	−0.756458
$78$	4.06393	0.460150
$79$	−2.34859	−0.264237	−0.132119	−	0.991234i	$-0.542178\pi$
$79$	−2.34859	−0.264237	−0.132119	+	0.991234i	$0.542178\pi$
$80$	7.09009	0.792697
$81$	−4.30500	−0.478334
$82$	0.730433	0.0806628
$83$	−6.14848	−0.674883	−0.337442	−	0.941346i	$-0.609562\pi$
$83$	−6.14848	−0.674883	−0.337442	+	0.941346i	$0.609562\pi$
$84$	−3.52492	−0.384600
$85$	1.39729	0.151557
$86$	0	0
$87$	7.89802	0.846757
$88$	−4.01933	−0.428462
$89$	−6.17037	−0.654058	−0.327029	−	0.945014i	$-0.606047\pi$
$89$	−6.17037	−0.654058	−0.327029	+	0.945014i	$0.606047\pi$
$90$	3.61301	0.380844
$91$	12.3374	1.29331
$92$	−2.11807	−0.220824
$93$	−2.51378	−0.260667
$94$	−8.23555	−0.849433
$95$	13.6570	1.40118
$96$	−3.83499	−0.391407
$97$	12.2752	1.24636	0.623181	−	0.782078i	$-0.285840\pi$
$97$	12.2752	1.24636	0.623181	+	0.782078i	$0.285840\pi$
$98$	22.7069	2.29374
$99$	−1.48939	−0.149689
$100$	−0.916987	−0.0916987
$101$	3.74748	0.372888	0.186444	−	0.982466i	$-0.440304\pi$
$101$	3.74748	0.372888	0.186444	+	0.982466i	$0.440304\pi$
$102$	0.893270	0.0884469
$103$	7.15459	0.704963	0.352482	−	0.935819i	$-0.385338\pi$
$103$	7.15459	0.704963	0.352482	+	0.935819i	$0.385338\pi$
$104$	7.47045	0.732538
$105$	−18.0144	−1.75803
$106$	−8.05358	−0.782233
$107$	4.11840	0.398140	0.199070	−	0.979985i	$-0.436208\pi$
$107$	4.11840	0.398140	0.199070	+	0.979985i	$0.436208\pi$
$108$	−2.88080	−0.277205
$109$	0.781030	0.0748091	0.0374045	−	0.999300i	$-0.488091\pi$
$109$	0.781030	0.0748091	0.0374045	+	0.999300i	$0.488091\pi$
$110$	−4.17472	−0.398044
$111$	4.89790	0.464889
$112$	13.7602	1.30022
$113$	−16.3074	−1.53407	−0.767034	−	0.641606i	$-0.778268\pi$
$113$	−16.3074	−1.53407	−0.767034	+	0.641606i	$0.778268\pi$
$114$	8.73077	0.817712
$115$	−10.8246	−1.00940
$116$	2.95066	0.273962
$117$	2.76822	0.255922
$118$	−11.4322	−1.05242
$119$	2.71181	0.248591
$120$	−10.9080	−0.995759
$121$	−9.27906	−0.843551
$122$	9.83920	0.890799
$123$	−0.817165	−0.0736813
$124$	−0.939136	−0.0843369
$125$	8.34963	0.746813
$126$	7.01200	0.624679
$127$	1.50719	0.133742	0.0668708	−	0.997762i	$-0.478698\pi$
$127$	1.50719	0.133742	0.0668708	+	0.997762i	$0.478698\pi$
$128$	5.20591	0.460141
$129$	0	0
$130$	7.75926	0.680532
$131$	5.48835	0.479519	0.239760	−	0.970832i	$-0.422931\pi$
$131$	5.48835	0.479519	0.239760	+	0.970832i	$0.422931\pi$
$132$	0.913871	0.0795422
$133$	26.5051	2.29828
$134$	−18.7598	−1.62060
$135$	−14.7226	−1.26712
$136$	1.64204	0.140804
$137$	−20.2953	−1.73395	−0.866973	−	0.498355i	$-0.833938\pi$
$137$	−20.2953	−1.73395	−0.866973	+	0.498355i	$0.833938\pi$
$138$	−6.92006	−0.589075
$139$	−10.2295	−0.867658	−0.433829	−	0.900995i	$-0.642838\pi$
$139$	−10.2295	−0.867658	−0.433829	+	0.900995i	$0.642838\pi$
$140$	−6.73011	−0.568798
$141$	9.21345	0.775913
$142$	−6.27194	−0.526329
$143$	−3.19859	−0.267480
$144$	3.08747	0.257289
$145$	15.0797	1.25230
$146$	9.12670	0.755331
$147$	−25.4032	−2.09522
$148$	1.82983	0.150411
$149$	5.70541	0.467405	0.233703	−	0.972308i	$-0.424916\pi$
$149$	5.70541	0.467405	0.233703	+	0.972308i	$0.424916\pi$
$150$	−2.99593	−0.244617
$151$	0.734539	0.0597759	0.0298879	−	0.999553i	$-0.490485\pi$
$151$	0.734539	0.0597759	0.0298879	+	0.999553i	$0.490485\pi$
$152$	16.0492	1.30176
$153$	0.608466	0.0491916
$154$	−8.10215	−0.652890
$155$	−4.79955	−0.385509
$156$	−1.69855	−0.135993
$157$	−12.5977	−1.00540	−0.502701	−	0.864460i	$-0.667660\pi$
$157$	−12.5977	−1.00540	−0.502701	+	0.864460i	$0.667660\pi$
$158$	−2.86667	−0.228060
$159$	9.00988	0.714530
$160$	−7.32213	−0.578865
$161$	−21.0081	−1.65567
$162$	−5.25465	−0.412845
$163$	−4.22542	−0.330961	−0.165480	−	0.986213i	$-0.552917\pi$
$163$	−4.22542	−0.330961	−0.165480	+	0.986213i	$0.552917\pi$
$164$	−0.305289	−0.0238391
$165$	4.67043	0.363592
$166$	−7.50479	−0.582484
$167$	12.0902	0.935564	0.467782	−	0.883844i	$-0.345053\pi$
$167$	12.0902	0.935564	0.467782	+	0.883844i	$0.345053\pi$
$168$	−21.1699	−1.63329
$169$	−7.05500	−0.542693
$170$	1.70552	0.130807
$171$	5.94711	0.454787
$172$	0	0
$173$	−20.9053	−1.58940	−0.794701	−	0.607002i	$-0.792372\pi$
$173$	−20.9053	−1.58940	−0.794701	+	0.607002i	$0.792372\pi$
$174$	9.64026	0.730826
$175$	−9.09512	−0.687526
$176$	−3.56748	−0.268909
$177$	12.7897	0.961331
$178$	−7.53150	−0.564510
$179$	−9.95607	−0.744152	−0.372076	−	0.928202i	$-0.621354\pi$
$179$	−9.95607	−0.744152	−0.372076	+	0.928202i	$0.621354\pi$
$180$	−1.51008	−0.112555
$181$	−0.813271	−0.0604500	−0.0302250	−	0.999543i	$-0.509622\pi$
$181$	−0.813271	−0.0604500	−0.0302250	+	0.999543i	$0.509622\pi$
$182$	15.0589	1.11624
$183$	−11.0075	−0.813699
$184$	−12.7207	−0.937780
$185$	9.35155	0.687540
$186$	−3.06830	−0.224979
$187$	−0.703064	−0.0514131
$188$	3.44210	0.251041
$189$	−28.5732	−2.07839
$190$	16.6696	1.20934
$191$	20.9019	1.51241	0.756205	−	0.654335i	$-0.227051\pi$
$191$	20.9019	1.51241	0.756205	+	0.654335i	$0.227051\pi$
$192$	−12.1079	−0.873811
$193$	−14.8776	−1.07091	−0.535457	−	0.844562i	$-0.679861\pi$
$193$	−14.8776	−1.07091	−0.535457	+	0.844562i	$0.679861\pi$
$194$	14.9831	1.07572
$195$	−8.68060	−0.621631
$196$	−9.49050	−0.677893
$197$	11.0201	0.785147	0.392573	−	0.919721i	$-0.371585\pi$
$197$	11.0201	0.785147	0.392573	+	0.919721i	$0.371585\pi$
$198$	−1.81793	−0.129195
$199$	6.04369	0.428426	0.214213	−	0.976787i	$-0.431281\pi$
$199$	6.04369	0.428426	0.214213	+	0.976787i	$0.431281\pi$
$200$	−5.50722	−0.389419
$201$	20.9874	1.48033
$202$	4.57414	0.321836
$203$	29.2661	2.05408
$204$	−0.373348	−0.0261396
$205$	−1.56021	−0.108970
$206$	8.73284	0.608446
$207$	−4.71372	−0.327626
$208$	6.63062	0.459751
$209$	−6.87170	−0.475326
$210$	−21.9883	−1.51734
$211$	−7.32897	−0.504547	−0.252273	−	0.967656i	$-0.581178\pi$
$211$	−7.32897	−0.504547	−0.252273	+	0.967656i	$0.581178\pi$
$212$	3.36605	0.231181
$213$	7.01667	0.480775
$214$	5.02688	0.343631
$215$	0	0
$216$	−17.3014	−1.17721
$217$	−9.31481	−0.632330
$218$	0.953319	0.0645669
$219$	−10.2104	−0.689956
$220$	1.74485	0.117638
$221$	1.30674	0.0879006
$222$	5.97834	0.401240
$223$	27.9114	1.86909	0.934544	−	0.355846i	$-0.115807\pi$
$223$	27.9114	1.86909	0.934544	+	0.355846i	$0.115807\pi$
$224$	−14.2105	−0.949482
$225$	−2.04073	−0.136049
$226$	−19.9047	−1.32404
$227$	4.87549	0.323597	0.161799	−	0.986824i	$-0.448270\pi$
$227$	4.87549	0.323597	0.161799	+	0.986824i	$0.448270\pi$
$228$	−3.64908	−0.241666
$229$	13.7905	0.911299	0.455650	−	0.890159i	$-0.349407\pi$
$229$	13.7905	0.911299	0.455650	+	0.890159i	$0.349407\pi$
$230$	−13.2124	−0.871203
$231$	9.06421	0.596382
$232$	17.7210	1.16344
$233$	−7.80187	−0.511117	−0.255559	−	0.966794i	$-0.582259\pi$
$233$	−7.80187	−0.511117	−0.255559	+	0.966794i	$0.582259\pi$
$234$	3.37887	0.220883
$235$	17.5912	1.14752
$236$	4.77816	0.311032
$237$	3.20707	0.208321
$238$	3.31001	0.214556
$239$	21.2173	1.37243	0.686217	−	0.727397i	$-0.259270\pi$
$239$	21.2173	1.37243	0.686217	+	0.727397i	$0.259270\pi$
$240$	−9.68172	−0.624952
$241$	−15.3308	−0.987544	−0.493772	−	0.869592i	$-0.664382\pi$
$241$	−15.3308	−0.987544	−0.493772	+	0.869592i	$0.664382\pi$
$242$	−11.3259	−0.728060
$243$	−11.0621	−0.709637
$244$	−4.11236	−0.263267
$245$	−48.5022	−3.09869
$246$	−0.997426	−0.0635935
$247$	12.7720	0.812660
$248$	−5.64024	−0.358156
$249$	8.39591	0.532069
$250$	10.1915	0.644566
$251$	16.8655	1.06454	0.532272	−	0.846574i	$-0.321339\pi$
$251$	16.8655	1.06454	0.532272	+	0.846574i	$0.321339\pi$
$252$	−2.93071	−0.184618
$253$	5.44655	0.342422
$254$	1.83967	0.115431
$255$	−1.90803	−0.119486
$256$	−11.3793	−0.711209
$257$	−10.0674	−0.627987	−0.313993	−	0.949425i	$-0.601667\pi$
$257$	−10.0674	−0.627987	−0.313993	+	0.949425i	$0.601667\pi$
$258$	0	0
$259$	18.1492	1.12774
$260$	−3.24303	−0.201124
$261$	6.56663	0.406464
$262$	6.69903	0.413868
$263$	27.4622	1.69339	0.846696	−	0.532077i	$-0.178588\pi$
$263$	27.4622	1.69339	0.846696	+	0.532077i	$0.178588\pi$
$264$	5.48851	0.337794
$265$	17.2025	1.05674
$266$	32.3519	1.98362
$267$	8.42580	0.515651
$268$	7.84078	0.478952
$269$	13.5251	0.824639	0.412320	−	0.911039i	$-0.364719\pi$
$269$	13.5251	0.824639	0.412320	+	0.911039i	$0.364719\pi$
$270$	−17.9703	−1.09364
$271$	3.98557	0.242106	0.121053	−	0.992646i	$-0.461373\pi$
$271$	3.98557	0.242106	0.121053	+	0.992646i	$0.461373\pi$
$272$	1.45744	0.0883702
$273$	−16.8470	−1.01963
$274$	−24.7723	−1.49655
$275$	2.35800	0.142193
$276$	2.89228	0.174095
$277$	13.2146	0.793990	0.396995	−	0.917821i	$-0.370053\pi$
$277$	13.2146	0.793990	0.396995	+	0.917821i	$0.370053\pi$
$278$	−12.4861	−0.748866
$279$	−2.09002	−0.125126
$280$	−40.4196	−2.41553
$281$	−17.1050	−1.02040	−0.510199	−	0.860056i	$-0.670428\pi$
$281$	−17.1050	−1.02040	−0.510199	+	0.860056i	$0.670428\pi$
$282$	11.2459	0.669682
$283$	15.1260	0.899147	0.449574	−	0.893243i	$-0.351576\pi$
$283$	15.1260	0.899147	0.449574	+	0.893243i	$0.351576\pi$
$284$	2.62140	0.155551
$285$	−18.6490	−1.10467
$286$	−3.90418	−0.230859
$287$	−3.02801	−0.178738
$288$	−3.18851	−0.187885
$289$	−16.7128	−0.983104
$290$	18.4061	1.08084
$291$	−16.7622	−0.982615
$292$	−3.81456	−0.223230
$293$	−17.3089	−1.01120	−0.505598	−	0.862769i	$-0.668728\pi$
$293$	−17.3089	−1.01120	−0.505598	+	0.862769i	$0.668728\pi$
$294$	−31.0069	−1.80836
$295$	24.4193	1.42175
$296$	10.9896	0.638756
$297$	7.40788	0.429849
$298$	6.96398	0.403412
$299$	−10.1231	−0.585436
$300$	1.25217	0.0722941
$301$	0	0
$302$	0.896572	0.0515919
$303$	−5.11728	−0.293980
$304$	14.2449	0.817002
$305$	−21.0166	−1.20341
$306$	0.742689	0.0424567
$307$	1.06091	0.0605494	0.0302747	−	0.999542i	$-0.490362\pi$
$307$	1.06091	0.0605494	0.0302747	+	0.999542i	$0.490362\pi$
$308$	3.38635	0.192955
$309$	−9.76979	−0.555784
$310$	−5.85829	−0.332729
$311$	7.17079	0.406618	0.203309	−	0.979115i	$-0.434830\pi$
$311$	7.17079	0.406618	0.203309	+	0.979115i	$0.434830\pi$
$312$	−10.2011	−0.577524
$313$	−5.83483	−0.329804	−0.164902	−	0.986310i	$-0.552731\pi$
$313$	−5.83483	−0.329804	−0.164902	+	0.986310i	$0.552731\pi$
$314$	−15.3766	−0.867752
$315$	−14.9777	−0.843898
$316$	1.19814	0.0674009
$317$	10.4360	0.586143	0.293071	−	0.956091i	$-0.405323\pi$
$317$	10.4360	0.586143	0.293071	+	0.956091i	$0.405323\pi$
$318$	10.9974	0.616703
$319$	−7.58754	−0.424820
$320$	−23.1175	−1.29231
$321$	−5.62378	−0.313889
$322$	−25.6423	−1.42899
$323$	2.80733	0.156204
$324$	2.19622	0.122012
$325$	−4.38265	−0.243106
$326$	−5.15752	−0.285649
$327$	−1.06652	−0.0589785
$328$	−1.83350	−0.101238
$329$	34.1405	1.88222
$330$	5.70069	0.313813
$331$	10.0703	0.553511	0.276756	−	0.960940i	$-0.410741\pi$
$331$	10.0703	0.553511	0.276756	+	0.960940i	$0.410741\pi$
$332$	3.13667	0.172147
$333$	4.07225	0.223158
$334$	14.7571	0.807475
$335$	40.0711	2.18932
$336$	−18.7900	−1.02508
$337$	−33.1107	−1.80365	−0.901827	−	0.432098i	$-0.857773\pi$
$337$	−33.1107	−1.80365	−0.901827	+	0.432098i	$0.857773\pi$
$338$	−8.61128	−0.468392
$339$	22.2682	1.20944
$340$	−0.712832	−0.0386588
$341$	2.41496	0.130777
$342$	7.25900	0.392522
$343$	−58.7117	−3.17013
$344$	0	0
$345$	14.7813	0.795799
$346$	−25.5169	−1.37179
$347$	−19.2494	−1.03336	−0.516681	−	0.856178i	$-0.672833\pi$
$347$	−19.2494	−1.03336	−0.516681	+	0.856178i	$0.672833\pi$
$348$	−4.02921	−0.215988
$349$	−22.3633	−1.19708	−0.598539	−	0.801094i	$-0.704252\pi$
$349$	−22.3633	−1.19708	−0.598539	+	0.801094i	$0.704252\pi$
$350$	−11.1014	−0.593396
$351$	−13.7685	−0.734909
$352$	3.68423	0.196370
$353$	1.25729	0.0669189	0.0334594	−	0.999440i	$-0.489348\pi$
$353$	1.25729	0.0669189	0.0334594	+	0.999440i	$0.489348\pi$
$354$	15.6110	0.829714
$355$	13.3969	0.711034
$356$	3.14784	0.166835
$357$	−3.70305	−0.195986
$358$	−12.1523	−0.642269
$359$	18.7076	0.987347	0.493673	−	0.869647i	$-0.335654\pi$
$359$	18.7076	0.987347	0.493673	+	0.869647i	$0.335654\pi$
$360$	−9.06920	−0.477989
$361$	8.43868	0.444141
$362$	−0.992673	−0.0521737
$363$	12.6708	0.665045
$364$	−6.29397	−0.329894
$365$	−19.4947	−1.02040
$366$	−13.4357	−0.702295
$367$	−14.2094	−0.741724	−0.370862	−	0.928688i	$-0.620938\pi$
$367$	−14.2094	−0.741724	−0.370862	+	0.928688i	$0.620938\pi$
$368$	−11.2906	−0.588564
$369$	−0.679413	−0.0353688
$370$	11.4144	0.593408
$371$	33.3861	1.73332
$372$	1.28242	0.0664902
$373$	8.92047	0.461884	0.230942	−	0.972967i	$-0.425819\pi$
$373$	8.92047	0.461884	0.230942	+	0.972967i	$0.425819\pi$
$374$	−0.858154	−0.0443741
$375$	−11.4016	−0.588778
$376$	20.6725	1.06610
$377$	14.1024	0.726312
$378$	−34.8762	−1.79384
$379$	−2.05652	−0.105636	−0.0528182	−	0.998604i	$-0.516820\pi$
$379$	−2.05652	−0.105636	−0.0528182	+	0.998604i	$0.516820\pi$
$380$	−6.96718	−0.357409
$381$	−2.05811	−0.105440
$382$	25.5127	1.30534
$383$	−16.1380	−0.824615	−0.412308	−	0.911045i	$-0.635277\pi$
$383$	−16.1380	−0.824615	−0.412308	+	0.911045i	$0.635277\pi$
$384$	−7.10880	−0.362770
$385$	17.3063	0.882009
$386$	−18.1595	−0.924295
$387$	0	0
$388$	−6.26226	−0.317918
$389$	21.1672	1.07322	0.536609	−	0.843831i	$-0.319705\pi$
$389$	21.1672	1.07322	0.536609	+	0.843831i	$0.319705\pi$
$390$	−10.5955	−0.536523
$391$	−2.22511	−0.112529
$392$	−56.9979	−2.87883
$393$	−7.49448	−0.378047
$394$	13.4510	0.677651
$395$	6.12324	0.308094
$396$	0.759817	0.0381822
$397$	−27.2507	−1.36767	−0.683837	−	0.729635i	$-0.739690\pi$
$397$	−27.2507	−1.36767	−0.683837	+	0.729635i	$0.739690\pi$
$398$	7.37688	0.369770
$399$	−36.1934	−1.81193
$400$	−4.88810	−0.244405
$401$	29.3543	1.46589	0.732943	−	0.680290i	$-0.238146\pi$
$401$	29.3543	1.46589	0.732943	+	0.680290i	$0.238146\pi$
$402$	25.6170	1.27766
$403$	−4.48851	−0.223589
$404$	−1.91179	−0.0951152
$405$	11.2240	0.557724
$406$	35.7220	1.77285
$407$	−4.70536	−0.233236
$408$	−2.24225	−0.111008
$409$	−8.73409	−0.431873	−0.215936	−	0.976407i	$-0.569280\pi$
$409$	−8.73409	−0.431873	−0.215936	+	0.976407i	$0.569280\pi$
$410$	−1.90438	−0.0940507
$411$	27.7138	1.36702
$412$	−3.64995	−0.179820
$413$	47.3921	2.33201
$414$	−5.75353	−0.282770
$415$	16.0303	0.786896
$416$	−6.84762	−0.335732
$417$	13.9687	0.684051
$418$	−8.38755	−0.410248
$419$	21.0617	1.02893	0.514466	−	0.857511i	$-0.327990\pi$
$419$	21.0617	1.02893	0.514466	+	0.857511i	$0.327990\pi$
$420$	9.19015	0.448433
$421$	24.5931	1.19859	0.599296	−	0.800527i	$-0.295447\pi$
$421$	24.5931	1.19859	0.599296	+	0.800527i	$0.295447\pi$
$422$	−8.94568	−0.435469
$423$	7.66032	0.372457
$424$	20.2157	0.981763
$425$	−0.963326	−0.0467282
$426$	8.56450	0.414951
$427$	−40.7884	−1.97389
$428$	−2.10102	−0.101557
$429$	4.36776	0.210878
$430$	0	0
$431$	−2.81282	−0.135489	−0.0677445	−	0.997703i	$-0.521580\pi$
$431$	−2.81282	−0.135489	−0.0677445	+	0.997703i	$0.521580\pi$
$432$	−15.3564	−0.738835
$433$	26.0682	1.25276	0.626378	−	0.779520i	$-0.284537\pi$
$433$	26.0682	1.25276	0.626378	+	0.779520i	$0.284537\pi$
$434$	−11.3696	−0.545757
$435$	−20.5917	−0.987296
$436$	−0.398446	−0.0190821
$437$	−21.7481	−1.04035
$438$	−12.4628	−0.595493
$439$	−8.74820	−0.417529	−0.208764	−	0.977966i	$-0.566944\pi$
$439$	−8.74820	−0.417529	−0.208764	+	0.977966i	$0.566944\pi$
$440$	10.4792	0.499576
$441$	−21.1209	−1.00576
$442$	1.59499	0.0758660
$443$	−27.1002	−1.28757	−0.643784	−	0.765207i	$-0.722637\pi$
$443$	−27.1002	−1.28757	−0.643784	+	0.765207i	$0.722637\pi$
$444$	−2.49869	−0.118582
$445$	16.0874	0.762614
$446$	34.0685	1.61319
$447$	−7.79089	−0.368496
$448$	−44.8657	−2.11971
$449$	−24.2779	−1.14575	−0.572873	−	0.819644i	$-0.694171\pi$
$449$	−24.2779	−1.14575	−0.572873	+	0.819644i	$0.694171\pi$
$450$	−2.49090	−0.117422
$451$	0.785041	0.0369661
$452$	8.31928	0.391306
$453$	−1.00303	−0.0471266
$454$	5.95098	0.279293
$455$	−32.1660	−1.50796
$456$	−21.9156	−1.02629
$457$	−24.1326	−1.12888	−0.564438	−	0.825476i	$-0.690907\pi$
$457$	−24.1326	−1.12888	−0.564438	+	0.825476i	$0.690907\pi$
$458$	16.8325	0.786532
$459$	−3.02638	−0.141259
$460$	5.52223	0.257475
$461$	1.65546	0.0771026	0.0385513	−	0.999257i	$-0.487726\pi$
$461$	1.65546	0.0771026	0.0385513	+	0.999257i	$0.487726\pi$
$462$	11.0637	0.514730
$463$	3.67298	0.170698	0.0853490	−	0.996351i	$-0.472799\pi$
$463$	3.67298	0.170698	0.0853490	+	0.996351i	$0.472799\pi$
$464$	15.7288	0.730192
$465$	6.55391	0.303930
$466$	−9.52290	−0.441140
$467$	−17.6557	−0.817010	−0.408505	−	0.912756i	$-0.633950\pi$
$467$	−17.6557	−0.817010	−0.408505	+	0.912756i	$0.633950\pi$
$468$	−1.41222	−0.0652798
$469$	77.7687	3.59102
$470$	21.4717	0.990416
$471$	17.2024	0.792646
$472$	28.6966	1.32087
$473$	0	0
$474$	3.91452	0.179800
$475$	−9.41549	−0.432012
$476$	−1.38344	−0.0634099
$477$	7.49106	0.342992
$478$	25.8977	1.18453
$479$	−6.53201	−0.298455	−0.149228	−	0.988803i	$-0.547679\pi$
$479$	−6.53201	−0.298455	−0.149228	+	0.988803i	$0.547679\pi$
$480$	9.99856	0.456370
$481$	8.74552	0.398762
$482$	−18.7127	−0.852338
$483$	28.6871	1.30531
$484$	4.73375	0.215171
$485$	−32.0039	−1.45322
$486$	−13.5024	−0.612480
$487$	−15.1807	−0.687903	−0.343952	−	0.938987i	$-0.611766\pi$
$487$	−15.1807	−0.687903	−0.343952	+	0.938987i	$0.611766\pi$
$488$	−24.6979	−1.11802
$489$	5.76993	0.260925
$490$	−59.2014	−2.67445
$491$	27.5701	1.24422	0.622110	−	0.782930i	$-0.286276\pi$
$491$	27.5701	1.24422	0.622110	+	0.782930i	$0.286276\pi$
$492$	0.416880	0.0187944
$493$	3.09977	0.139607
$494$	15.5894	0.701398
$495$	3.88312	0.174533
$496$	−5.00617	−0.224783
$497$	26.0003	1.16627
$498$	10.2480	0.459223
$499$	−8.80000	−0.393942	−0.196971	−	0.980409i	$-0.563110\pi$
$499$	−8.80000	−0.393942	−0.196971	+	0.980409i	$0.563110\pi$
$500$	−4.25960	−0.190495
$501$	−16.5094	−0.737587
$502$	20.5859	0.918796
$503$	−41.4859	−1.84976	−0.924882	−	0.380254i	$-0.875837\pi$
$503$	−41.4859	−1.84976	−0.924882	+	0.380254i	$0.875837\pi$
$504$	−17.6012	−0.784020
$505$	−9.77041	−0.434777
$506$	6.64802	0.295541
$507$	9.63380	0.427852
$508$	−0.768901	−0.0341145
$509$	16.2095	0.718474	0.359237	−	0.933246i	$-0.383037\pi$
$509$	16.2095	0.718474	0.359237	+	0.933246i	$0.383037\pi$
$510$	−2.32893	−0.103127
$511$	−37.8347	−1.67371
$512$	−24.3014	−1.07398
$513$	−29.5796	−1.30597
$514$	−12.2882	−0.542008
$515$	−18.6534	−0.821968
$516$	0	0
$517$	−8.85126	−0.389278
$518$	22.1528	0.973336
$519$	28.5468	1.25306
$520$	−19.4769	−0.854120
$521$	9.62165	0.421532	0.210766	−	0.977537i	$-0.432404\pi$
$521$	9.62165	0.421532	0.210766	+	0.977537i	$0.432404\pi$
$522$	8.01517	0.350815
$523$	26.6186	1.16395	0.581975	−	0.813206i	$-0.302280\pi$
$523$	26.6186	1.16395	0.581975	+	0.813206i	$0.302280\pi$
$524$	−2.79990	−0.122314
$525$	12.4196	0.542037
$526$	33.5201	1.46155
$527$	−0.986595	−0.0429767
$528$	4.87149	0.212004
$529$	−5.76235	−0.250537
$530$	20.9973	0.912063
$531$	10.6337	0.461463
$532$	−13.5217	−0.586239
$533$	−1.45910	−0.0632007
$534$	10.2845	0.445053
$535$	−10.7375	−0.464221
$536$	47.0900	2.03398
$537$	13.5953	0.586680
$538$	16.5086	0.711737
$539$	24.4045	1.05118
$540$	7.51080	0.323214
$541$	−32.4296	−1.39426	−0.697128	−	0.716946i	$-0.745539\pi$
$541$	−32.4296	−1.39426	−0.697128	+	0.716946i	$0.745539\pi$
$542$	4.86475	0.208959
$543$	1.11054	0.0476580
$544$	−1.50514	−0.0645322
$545$	−2.03630	−0.0872254
$546$	−20.5633	−0.880030
$547$	−19.5246	−0.834812	−0.417406	−	0.908720i	$-0.637061\pi$
$547$	−19.5246	−0.834812	−0.417406	+	0.908720i	$0.637061\pi$
$548$	10.3538	0.442290
$549$	−9.15195	−0.390596
$550$	2.87816	0.122725
$551$	30.2970	1.29070
$552$	17.3704	0.739334
$553$	11.8838	0.505350
$554$	16.1297	0.685284
$555$	−12.7698	−0.542048
$556$	5.21864	0.221320
$557$	−30.8959	−1.30910	−0.654552	−	0.756017i	$-0.727143\pi$
$557$	−30.8959	−1.30910	−0.654552	+	0.756017i	$0.727143\pi$
$558$	−2.55107	−0.107995
$559$	0	0
$560$	−35.8756	−1.51602
$561$	0.960053	0.0405335
$562$	−20.8782	−0.880695
$563$	8.41495	0.354648	0.177324	−	0.984153i	$-0.443256\pi$
$563$	8.41495	0.354648	0.177324	+	0.984153i	$0.443256\pi$
$564$	−4.70029	−0.197918
$565$	42.5165	1.78868
$566$	18.4627	0.776044
$567$	21.7831	0.914806
$568$	15.7435	0.660584
$569$	28.2288	1.18341	0.591707	−	0.806153i	$-0.298454\pi$
$569$	28.2288	1.18341	0.591707	+	0.806153i	$0.298454\pi$
$570$	−22.7628	−0.953430
$571$	11.4180	0.477827	0.238913	−	0.971041i	$-0.423209\pi$
$571$	11.4180	0.477827	0.238913	+	0.971041i	$0.423209\pi$
$572$	1.63178	0.0682280
$573$	−28.5421	−1.19236
$574$	−3.69596	−0.154266
$575$	7.46277	0.311219
$576$	−10.0668	−0.419451
$577$	27.3856	1.14008	0.570038	−	0.821618i	$-0.306929\pi$
$577$	27.3856	1.14008	0.570038	+	0.821618i	$0.306929\pi$
$578$	−20.3995	−0.848507
$579$	20.3158	0.844295
$580$	−7.69296	−0.319433
$581$	31.1111	1.29070
$582$	−20.4598	−0.848085
$583$	−8.65568	−0.358482
$584$	−22.9094	−0.947999
$585$	−7.21729	−0.298398
$586$	−21.1271	−0.872752
$587$	−20.7335	−0.855762	−0.427881	−	0.903835i	$-0.640740\pi$
$587$	−20.7335	−0.855762	−0.427881	+	0.903835i	$0.640740\pi$
$588$	12.9595	0.534442
$589$	−9.64292	−0.397330
$590$	29.8060	1.22709
$591$	−15.0482	−0.619000
$592$	9.75413	0.400892
$593$	14.3994	0.591314	0.295657	−	0.955294i	$-0.404461\pi$
$593$	14.3994	0.591314	0.295657	+	0.955294i	$0.404461\pi$
$594$	9.04200	0.370998
$595$	−7.07022	−0.289851
$596$	−2.91064	−0.119224
$597$	−8.25282	−0.337766
$598$	−12.3562	−0.505283
$599$	7.66984	0.313381	0.156691	−	0.987648i	$-0.449917\pi$
$599$	7.66984	0.313381	0.156691	+	0.987648i	$0.449917\pi$
$600$	7.52026	0.307013
$601$	47.6112	1.94210	0.971051	−	0.238870i	$-0.0767771\pi$
$601$	47.6112	1.94210	0.971051	+	0.238870i	$0.0767771\pi$
$602$	0	0
$603$	17.4495	0.710597
$604$	−0.374728	−0.0152475
$605$	24.1923	0.983558
$606$	−6.24612	−0.253731
$607$	−8.62055	−0.349897	−0.174949	−	0.984578i	$-0.555976\pi$
$607$	−8.62055	−0.349897	−0.174949	+	0.984578i	$0.555976\pi$
$608$	−14.7111	−0.596614
$609$	−39.9637	−1.61941
$610$	−25.6527	−1.03865
$611$	16.4512	0.665545
$612$	−0.310412	−0.0125477
$613$	−22.8189	−0.921647	−0.460824	−	0.887492i	$-0.652446\pi$
$613$	−22.8189	−0.921647	−0.460824	+	0.887492i	$0.652446\pi$
$614$	1.29494	0.0522596
$615$	2.13051	0.0859104
$616$	20.3377	0.819428
$617$	8.69437	0.350022	0.175011	−	0.984566i	$-0.444004\pi$
$617$	8.69437	0.350022	0.175011	+	0.984566i	$0.444004\pi$
$618$	−11.9249	−0.479691
$619$	9.10940	0.366138	0.183069	−	0.983100i	$-0.441397\pi$
$619$	9.10940	0.366138	0.183069	+	0.983100i	$0.441397\pi$
$620$	2.44851	0.0983346
$621$	23.4450	0.940815
$622$	8.75262	0.350948
$623$	31.2218	1.25088
$624$	−9.05429	−0.362462
$625$	−30.7564	−1.23026
$626$	−7.12195	−0.284650
$627$	9.38350	0.374741
$628$	6.42675	0.256455
$629$	1.92230	0.0766473
$630$	−18.2817	−0.728359
$631$	42.0801	1.67518	0.837592	−	0.546296i	$-0.183963\pi$
$631$	42.0801	1.67518	0.837592	+	0.546296i	$0.183963\pi$
$632$	7.19579	0.286233
$633$	10.0079	0.397778
$634$	12.7381	0.505893
$635$	−3.92954	−0.155939
$636$	−4.59643	−0.182260
$637$	−45.3590	−1.79719
$638$	−9.26129	−0.366658
$639$	5.83385	0.230784
$640$	−13.5728	−0.536513
$641$	−18.0793	−0.714091	−0.357046	−	0.934087i	$-0.616216\pi$
$641$	−18.0793	−0.714091	−0.357046	+	0.934087i	$0.616216\pi$
$642$	−6.86435	−0.270914
$643$	40.9501	1.61492	0.807458	−	0.589925i	$-0.200843\pi$
$643$	40.9501	1.61492	0.807458	+	0.589925i	$0.200843\pi$
$644$	10.7174	0.422323
$645$	0	0
$646$	3.42661	0.134818
$647$	40.8528	1.60609	0.803045	−	0.595919i	$-0.203212\pi$
$647$	40.8528	1.60609	0.803045	+	0.595919i	$0.203212\pi$
$648$	13.1900	0.518152
$649$	−12.2869	−0.482303
$650$	−5.34943	−0.209822
$651$	12.7196	0.498521
$652$	2.15562	0.0844206
$653$	15.6990	0.614348	0.307174	−	0.951653i	$-0.400617\pi$
$653$	15.6990	0.614348	0.307174	+	0.951653i	$0.400617\pi$
$654$	−1.30178	−0.0509037
$655$	−14.3092	−0.559106
$656$	−1.62738	−0.0635384
$657$	−8.48921	−0.331196
$658$	41.6716	1.62453
$659$	44.9051	1.74925	0.874627	−	0.484796i	$-0.161106\pi$
$659$	44.9051	1.74925	0.874627	+	0.484796i	$0.161106\pi$
$660$	−2.38264	−0.0927441
$661$	−36.2032	−1.40814	−0.704070	−	0.710131i	$-0.748636\pi$
$661$	−36.2032	−1.40814	−0.704070	+	0.710131i	$0.748636\pi$
$662$	12.2917	0.477730
$663$	−1.78438	−0.0692997
$664$	18.8382	0.731063
$665$	−69.1039	−2.67973
$666$	4.97056	0.192605
$667$	−24.0136	−0.929809
$668$	−6.16785	−0.238641
$669$	−38.1138	−1.47357
$670$	48.9105	1.88958
$671$	10.5748	0.408236
$672$	19.4049	0.748560
$673$	18.7227	0.721706	0.360853	−	0.932623i	$-0.382486\pi$
$673$	18.7227	0.721706	0.360853	+	0.932623i	$0.382486\pi$
$674$	−40.4146	−1.55671
$675$	10.1501	0.390679
$676$	3.59914	0.138429
$677$	−46.3423	−1.78108	−0.890540	−	0.454906i	$-0.849673\pi$
$677$	−46.3423	−1.78108	−0.890540	+	0.454906i	$0.849673\pi$
$678$	27.1803	1.04385
$679$	−62.1122	−2.38365
$680$	−4.28111	−0.164173
$681$	−6.65761	−0.255120
$682$	2.94768	0.112872
$683$	2.17280	0.0831397	0.0415699	−	0.999136i	$-0.486764\pi$
$683$	2.17280	0.0831397	0.0415699	+	0.999136i	$0.486764\pi$
$684$	−3.03395	−0.116006
$685$	52.9139	2.02174
$686$	−71.6630	−2.73611
$687$	−18.8312	−0.718457
$688$	0	0
$689$	16.0877	0.612893
$690$	18.0420	0.686845
$691$	−18.9355	−0.720341	−0.360171	−	0.932886i	$-0.617281\pi$
$691$	−18.9355	−0.720341	−0.360171	+	0.932886i	$0.617281\pi$
$692$	10.6649	0.405420
$693$	7.53623	0.286278
$694$	−23.4957	−0.891883
$695$	26.6704	1.01167
$696$	−24.1985	−0.917243
$697$	−0.320717	−0.0121480
$698$	−27.2964	−1.03319
$699$	10.6537	0.402958
$700$	4.63992	0.175372
$701$	−2.17323	−0.0820817	−0.0410408	−	0.999157i	$-0.513067\pi$
$701$	−2.17323	−0.0820817	−0.0410408	+	0.999157i	$0.513067\pi$
$702$	−16.8057	−0.634292
$703$	18.7885	0.708621
$704$	11.6319	0.438394
$705$	−24.0213	−0.904694
$706$	1.53464	0.0577569
$707$	−18.9621	−0.713143
$708$	−6.52471	−0.245214
$709$	−44.0685	−1.65503	−0.827514	−	0.561445i	$-0.810246\pi$
$709$	−44.0685	−1.65503	−0.827514	+	0.561445i	$0.810246\pi$
$710$	16.3522	0.613686
$711$	2.66644	0.0999994
$712$	18.9052	0.708504
$713$	7.64303	0.286234
$714$	−4.51991	−0.169153
$715$	8.33935	0.311874
$716$	5.07913	0.189816
$717$	−28.9728	−1.08201
$718$	22.8343	0.852168
$719$	−36.0076	−1.34286	−0.671429	−	0.741069i	$-0.734319\pi$
$719$	−36.0076	−1.34286	−0.671429	+	0.741069i	$0.734319\pi$
$720$	−8.04964	−0.299992
$721$	−36.2020	−1.34823
$722$	10.3002	0.383334
$723$	20.9346	0.778567
$724$	0.414894	0.0154194
$725$	−10.3963	−0.386109
$726$	15.4659	0.573993
$727$	−2.26424	−0.0839762	−0.0419881	−	0.999118i	$-0.513369\pi$
$727$	−2.26424	−0.0839762	−0.0419881	+	0.999118i	$0.513369\pi$
$728$	−37.8002	−1.40097
$729$	28.0207	1.03780
$730$	−23.7951	−0.880696
$731$	0	0
$732$	5.61554	0.207556
$733$	−21.8155	−0.805776	−0.402888	−	0.915249i	$-0.631994\pi$
$733$	−21.8155	−0.805776	−0.402888	+	0.915249i	$0.631994\pi$
$734$	−17.3439	−0.640174
$735$	66.2310	2.44297
$736$	11.6601	0.429797
$737$	−20.1623	−0.742689
$738$	−0.829287	−0.0305265
$739$	−18.0397	−0.663603	−0.331801	−	0.943349i	$-0.607656\pi$
$739$	−18.0397	−0.663603	−0.331801	+	0.943349i	$0.607656\pi$
$740$	−4.77074	−0.175376
$741$	−17.4405	−0.640691
$742$	40.7508	1.49601
$743$	51.2998	1.88201	0.941003	−	0.338399i	$-0.109885\pi$
$743$	51.2998	1.88201	0.941003	+	0.338399i	$0.109885\pi$
$744$	7.70191	0.282366
$745$	−14.8751	−0.544982
$746$	10.8883	0.398647
$747$	6.98059	0.255406
$748$	0.358671	0.0131143
$749$	−20.8389	−0.761438
$750$	−13.9168	−0.508168
$751$	11.8433	0.432169	0.216084	−	0.976375i	$-0.430671\pi$
$751$	11.8433	0.432169	0.216084	+	0.976375i	$0.430671\pi$
$752$	18.3485	0.669101
$753$	−23.0303	−0.839272
$754$	17.2133	0.626872
$755$	−1.91509	−0.0696971
$756$	14.5767	0.530150
$757$	−4.49650	−0.163428	−0.0817140	−	0.996656i	$-0.526039\pi$
$757$	−4.49650	−0.163428	−0.0817140	+	0.996656i	$0.526039\pi$
$758$	−2.51017	−0.0911736
$759$	−7.43742	−0.269961
$760$	−41.8433	−1.51782
$761$	46.1729	1.67377	0.836883	−	0.547381i	$-0.184375\pi$
$761$	46.1729	1.67377	0.836883	+	0.547381i	$0.184375\pi$
$762$	−2.51211	−0.0910043
$763$	−3.95198	−0.143071
$764$	−10.6632	−0.385781
$765$	−1.58639	−0.0573561
$766$	−19.6980	−0.711716
$767$	22.8368	0.824589
$768$	15.5388	0.560708
$769$	32.5736	1.17463	0.587317	−	0.809357i	$-0.300184\pi$
$769$	32.5736	1.17463	0.587317	+	0.809357i	$0.300184\pi$
$770$	21.1239	0.761253
$771$	13.7473	0.495097
$772$	7.58988	0.273166
$773$	−5.76438	−0.207330	−0.103665	−	0.994612i	$-0.533057\pi$
$773$	−5.76438	−0.207330	−0.103665	+	0.994612i	$0.533057\pi$
$774$	0	0
$775$	3.30893	0.118860
$776$	−37.6098	−1.35011
$777$	−24.7832	−0.889092
$778$	25.8365	0.926283
$779$	−3.13467	−0.112311
$780$	4.42845	0.158564
$781$	−6.74084	−0.241206
$782$	−2.71595	−0.0971221
$783$	−32.6610	−1.16721
$784$	−50.5901	−1.80679
$785$	32.8445	1.17227
$786$	−9.14771	−0.326288
$787$	−5.12931	−0.182840	−0.0914201	−	0.995812i	$-0.529141\pi$
$787$	−5.12931	−0.182840	−0.0914201	+	0.995812i	$0.529141\pi$
$788$	−5.62193	−0.200273
$789$	−37.5004	−1.33505
$790$	7.47398	0.265912
$791$	82.5146	2.93388
$792$	4.56329	0.162150
$793$	−19.6546	−0.697957
$794$	−33.2620	−1.18043
$795$	−23.4905	−0.833123
$796$	−3.08322	−0.109282
$797$	50.3290	1.78274	0.891372	−	0.453272i	$-0.149743\pi$
$797$	50.3290	1.78274	0.891372	+	0.453272i	$0.149743\pi$
$798$	−44.1773	−1.56386
$799$	3.61605	0.127927
$800$	5.04807	0.178476
$801$	7.00544	0.247525
$802$	35.8297	1.26519
$803$	9.80903	0.346153
$804$	−10.7068	−0.377600
$805$	54.7721	1.93046
$806$	−5.47865	−0.192977
$807$	−18.4689	−0.650135
$808$	−11.4818	−0.403928
$809$	−9.87981	−0.347356	−0.173678	−	0.984803i	$-0.555565\pi$
$809$	−9.87981	−0.347356	−0.173678	+	0.984803i	$0.555565\pi$
$810$	13.6999	0.481366
$811$	3.99253	0.140197	0.0700984	−	0.997540i	$-0.477669\pi$
$811$	3.99253	0.140197	0.0700984	+	0.997540i	$0.477669\pi$
$812$	−14.9302	−0.523949
$813$	−5.44240	−0.190873
$814$	−5.74333	−0.201303
$815$	11.0165	0.385891
$816$	−1.99017	−0.0696700
$817$	0	0
$818$	−10.6608	−0.372745
$819$	−14.0071	−0.489447
$820$	0.795948	0.0277957
$821$	−51.7192	−1.80501	−0.902505	−	0.430678i	$-0.858274\pi$
$821$	−51.7192	−1.80501	−0.902505	+	0.430678i	$0.858274\pi$
$822$	33.8273	1.17986
$823$	−5.32772	−0.185713	−0.0928564	−	0.995680i	$-0.529600\pi$
$823$	−5.32772	−0.185713	−0.0928564	+	0.995680i	$0.529600\pi$
$824$	−21.9208	−0.763647
$825$	−3.21992	−0.112103
$826$	57.8465	2.01274
$827$	−17.4651	−0.607321	−0.303660	−	0.952780i	$-0.598209\pi$
$827$	−17.4651	−0.607321	−0.303660	+	0.952780i	$0.598209\pi$
$828$	2.40472	0.0835699
$829$	46.0126	1.59808	0.799042	−	0.601276i	$-0.205341\pi$
$829$	46.0126	1.59808	0.799042	+	0.601276i	$0.205341\pi$
$830$	19.5664	0.679161
$831$	−18.0449	−0.625972
$832$	−21.6194	−0.749518
$833$	−9.97010	−0.345443
$834$	17.0501	0.590397
$835$	−31.5214	−1.09084
$836$	3.50563	0.121245
$837$	10.3953	0.359315
$838$	25.7078	0.888060
$839$	13.6877	0.472552	0.236276	−	0.971686i	$-0.424073\pi$
$839$	13.6877	0.472552	0.236276	+	0.971686i	$0.424073\pi$
$840$	55.1940	1.90437
$841$	4.45306	0.153554
$842$	30.0181	1.03449
$843$	23.3573	0.804470
$844$	3.73891	0.128698
$845$	18.3938	0.632765
$846$	9.35012	0.321464
$847$	46.9517	1.61328
$848$	17.9431	0.616168
$849$	−20.6550	−0.708876
$850$	−1.17583	−0.0403306
$851$	−14.8919	−0.510486
$852$	−3.57959	−0.122635
$853$	13.2320	0.453055	0.226528	−	0.974005i	$-0.427263\pi$
$853$	13.2320	0.453055	0.226528	+	0.974005i	$0.427263\pi$
$854$	−49.7860	−1.70364
$855$	−15.5053	−0.530269
$856$	−12.6183	−0.431283
$857$	12.4008	0.423603	0.211801	−	0.977313i	$-0.432067\pi$
$857$	12.4008	0.423603	0.211801	+	0.977313i	$0.432067\pi$
$858$	5.33126	0.182006
$859$	24.8023	0.846243	0.423121	−	0.906073i	$-0.360934\pi$
$859$	24.8023	0.846243	0.423121	+	0.906073i	$0.360934\pi$
$860$	0	0
$861$	4.13482	0.140914
$862$	−3.43331	−0.116939
$863$	−36.0194	−1.22611	−0.613056	−	0.790039i	$-0.710060\pi$
$863$	−36.0194	−1.22611	−0.613056	+	0.790039i	$0.710060\pi$
$864$	15.8590	0.539533
$865$	54.5042	1.85320
$866$	31.8186	1.08124
$867$	22.8217	0.775067
$868$	4.75199	0.161293
$869$	−3.08099	−0.104515
$870$	−25.1340	−0.852124
$871$	37.4743	1.26977
$872$	−2.39298	−0.0810364
$873$	−13.9365	−0.471680
$874$	−26.5455	−0.897916
$875$	−42.2488	−1.42827
$876$	5.20889	0.175992
$877$	16.1845	0.546512	0.273256	−	0.961941i	$-0.411899\pi$
$877$	16.1845	0.546512	0.273256	+	0.961941i	$0.411899\pi$
$878$	−10.6780	−0.360364
$879$	23.6358	0.797214
$880$	9.30111	0.313540
$881$	−8.31463	−0.280127	−0.140063	−	0.990143i	$-0.544731\pi$
$881$	−8.31463	−0.280127	−0.140063	+	0.990143i	$0.544731\pi$
$882$	−25.7800	−0.868057
$883$	−39.0036	−1.31257	−0.656287	−	0.754511i	$-0.727874\pi$
$883$	−39.0036	−1.31257	−0.656287	+	0.754511i	$0.727874\pi$
$884$	−0.666637	−0.0224214
$885$	−33.3452	−1.12089
$886$	−33.0783	−1.11129
$887$	0.545211	0.0183064	0.00915320	−	0.999958i	$-0.497086\pi$
$887$	0.545211	0.0183064	0.00915320	+	0.999958i	$0.497086\pi$
$888$	−15.0066	−0.503587
$889$	−7.62633	−0.255779
$890$	19.6361	0.658204
$891$	−5.64750	−0.189198
$892$	−14.2392	−0.476762
$893$	35.3430	1.18271
$894$	−9.50950	−0.318045
$895$	25.9574	0.867661
$896$	−26.3417	−0.880013
$897$	13.8234	0.461550
$898$	−29.6335	−0.988881
$899$	−10.6474	−0.355112
$900$	1.04109	0.0347029
$901$	3.53615	0.117806
$902$	0.958215	0.0319051
$903$	0	0
$904$	49.9638	1.66177
$905$	2.12036	0.0704831
$906$	−1.22429	−0.0406744
$907$	13.6916	0.454623	0.227311	−	0.973822i	$-0.427006\pi$
$907$	13.6916	0.454623	0.227311	+	0.973822i	$0.427006\pi$
$908$	−2.48725	−0.0825424
$909$	−4.25465	−0.141118
$910$	−39.2615	−1.30151
$911$	9.78890	0.324321	0.162160	−	0.986764i	$-0.448154\pi$
$911$	9.78890	0.324321	0.162160	+	0.986764i	$0.448154\pi$
$912$	−19.4518	−0.644114
$913$	−8.06586	−0.266941
$914$	−29.4561	−0.974320
$915$	28.6988	0.948752
$916$	−7.03526	−0.232452
$917$	−27.7708	−0.917073
$918$	−3.69397	−0.121919
$919$	56.0864	1.85012	0.925060	−	0.379821i	$-0.124014\pi$
$919$	56.0864	1.85012	0.925060	+	0.379821i	$0.124014\pi$
$920$	33.1653	1.09343
$921$	−1.44870	−0.0477364
$922$	2.02065	0.0665464
$923$	12.5287	0.412388
$924$	−4.62415	−0.152123
$925$	−6.44720	−0.211983
$926$	4.48322	0.147328
$927$	−8.12287	−0.266790
$928$	−16.2436	−0.533222
$929$	−50.0759	−1.64294	−0.821469	−	0.570254i	$-0.806845\pi$
$929$	−50.0759	−1.64294	−0.821469	+	0.570254i	$0.806845\pi$
$930$	7.99966	0.262319
$931$	−97.4471	−3.19370
$932$	3.98016	0.130374
$933$	−9.79191	−0.320573
$934$	−21.5504	−0.705152
$935$	1.83303	0.0599463
$936$	−8.48147	−0.277226
$937$	−30.1282	−0.984245	−0.492122	−	0.870526i	$-0.663779\pi$
$937$	−30.1282	−0.984245	−0.492122	+	0.870526i	$0.663779\pi$
$938$	94.9238	3.09937
$939$	7.96762	0.260013
$940$	−8.97424	−0.292707
$941$	−25.7476	−0.839347	−0.419674	−	0.907675i	$-0.637856\pi$
$941$	−25.7476	−0.839347	−0.419674	+	0.907675i	$0.637856\pi$
$942$	20.9972	0.684124
$943$	2.48455	0.0809082
$944$	25.4705	0.828995
$945$	74.4958	2.42335
$946$	0	0
$947$	−30.1385	−0.979369	−0.489684	−	0.871900i	$-0.662888\pi$
$947$	−30.1385	−0.979369	−0.489684	+	0.871900i	$0.662888\pi$
$948$	−1.63610	−0.0531380
$949$	−18.2314	−0.591815
$950$	−11.4925	−0.372865
$951$	−14.2506	−0.462107
$952$	−8.30864	−0.269285
$953$	−42.6454	−1.38142	−0.690710	−	0.723132i	$-0.742702\pi$
$953$	−42.6454	−1.38142	−0.690710	+	0.723132i	$0.742702\pi$
$954$	9.14352	0.296033
$955$	−54.4954	−1.76343
$956$	−10.8241	−0.350076
$957$	10.3610	0.334923
$958$	−7.97292	−0.257593
$959$	102.694	3.31615
$960$	31.5676	1.01884
$961$	−27.6111	−0.890682
$962$	10.6747	0.344167
$963$	−4.67576	−0.150674
$964$	7.82108	0.251900
$965$	38.7889	1.24866
$966$	35.0152	1.12660
$967$	35.4051	1.13855	0.569275	−	0.822147i	$-0.307224\pi$
$967$	35.4051	1.13855	0.569275	+	0.822147i	$0.307224\pi$
$968$	28.4299	0.913771
$969$	−3.83349	−0.123149
$970$	−39.0638	−1.25426
$971$	46.8345	1.50299	0.751495	−	0.659739i	$-0.229333\pi$
$971$	46.8345	1.50299	0.751495	+	0.659739i	$0.229333\pi$
$972$	5.64340	0.181012
$973$	51.7610	1.65938
$974$	−18.5294	−0.593722
$975$	5.98463	0.191662
$976$	−21.9214	−0.701686
$977$	53.2920	1.70496	0.852481	−	0.522757i	$-0.175097\pi$
$977$	53.2920	1.70496	0.852481	+	0.522757i	$0.175097\pi$
$978$	7.04273	0.225202
$979$	−8.09457	−0.258704
$980$	24.7436	0.790405
$981$	−0.886731	−0.0283111
$982$	33.6518	1.07387
$983$	19.7320	0.629354	0.314677	−	0.949199i	$-0.398104\pi$
$983$	19.7320	0.629354	0.314677	+	0.949199i	$0.398104\pi$
$984$	2.50369	0.0798148
$985$	−28.7314	−0.915460
$986$	3.78356	0.120493
$987$	−46.6197	−1.48392
$988$	−6.51567	−0.207291
$989$	0	0
$990$	4.73971	0.150638
$991$	19.9723	0.634440	0.317220	−	0.948352i	$-0.397251\pi$
$991$	19.9723	0.634440	0.317220	+	0.948352i	$0.397251\pi$
$992$	5.17000	0.164148
$993$	−13.7512	−0.436381
$994$	31.7357	1.00660
$995$	−15.7571	−0.499533
$996$	−4.28321	−0.135719
$997$	−3.70312	−0.117279	−0.0586394	−	0.998279i	$-0.518676\pi$
$997$	−3.70312	−0.117279	−0.0586394	+	0.998279i	$0.518676\pi$
$998$	−10.7412	−0.340007
$999$	−20.2545	−0.640823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.p.1.15	✓	20
43.42	odd	2		1849.2.a.r.1.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.p.1.15	✓	20	1.1	even	1	trivial
1849.2.a.r.1.6	yes	20	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.22059 q^{2} -1.36553 q^{3} -0.510154 q^{4} -2.60720 q^{5} -1.66675 q^{6} -5.05996 q^{7} -3.06388 q^{8} -1.13534 q^{9} +O(q^{10})\)	\(q+1.22059 q^{2} -1.36553 q^{3} -0.510154 q^{4} -2.60720 q^{5} -1.66675 q^{6} -5.05996 q^{7} -3.06388 q^{8} -1.13534 q^{9} -3.18232 q^{10} +1.31185 q^{11} +0.696630 q^{12} -2.43824 q^{13} -6.17615 q^{14} +3.56020 q^{15} -2.71943 q^{16} -0.535935 q^{17} -1.38578 q^{18} -5.23819 q^{19} +1.33007 q^{20} +6.90951 q^{21} +1.60123 q^{22} +4.15182 q^{23} +4.18380 q^{24} +1.79747 q^{25} -2.97609 q^{26} +5.64691 q^{27} +2.58136 q^{28} -5.78386 q^{29} +4.34555 q^{30} +1.84089 q^{31} +2.80843 q^{32} -1.79136 q^{33} -0.654158 q^{34} +13.1923 q^{35} +0.579197 q^{36} -3.58682 q^{37} -6.39370 q^{38} +3.32948 q^{39} +7.98812 q^{40} +0.598425 q^{41} +8.43370 q^{42} -0.669244 q^{44} +2.96004 q^{45} +5.06768 q^{46} -6.74718 q^{47} +3.71346 q^{48} +18.6032 q^{49} +2.19398 q^{50} +0.731833 q^{51} +1.24388 q^{52} -6.59809 q^{53} +6.89258 q^{54} -3.42024 q^{55} +15.5031 q^{56} +7.15290 q^{57} -7.05974 q^{58} -9.36611 q^{59} -1.81625 q^{60} +8.06101 q^{61} +2.24697 q^{62} +5.74475 q^{63} +8.86682 q^{64} +6.35696 q^{65} -2.18652 q^{66} -15.3694 q^{67} +0.273410 q^{68} -5.66943 q^{69} +16.1024 q^{70} -5.13844 q^{71} +3.47853 q^{72} +7.47727 q^{73} -4.37805 q^{74} -2.45449 q^{75} +2.67229 q^{76} -6.63789 q^{77} +4.06393 q^{78} -2.34859 q^{79} +7.09009 q^{80} -4.30500 q^{81} +0.730433 q^{82} -6.14848 q^{83} -3.52492 q^{84} +1.39729 q^{85} +7.89802 q^{87} -4.01933 q^{88} -6.17037 q^{89} +3.61301 q^{90} +12.3374 q^{91} -2.11807 q^{92} -2.51378 q^{93} -8.23555 q^{94} +13.6570 q^{95} -3.83499 q^{96} +12.2752 q^{97} +22.7069 q^{98} -1.48939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} + q^{3} + 23 q^{4} + 3 q^{5} + 5 q^{6} + 2 q^{7} - 9 q^{8} + 27 q^{9}+O(q^{10}) \) 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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