LMFDB - Embedded newform 1849.2.a.n.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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.0953887$ 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)

$f(q)$	$=$	$q-0.0953887 q^{2} -2.36384 q^{3} -1.99090 q^{4} -3.81314 q^{5} +0.225484 q^{6} -2.61962 q^{7} +0.380687 q^{8} +2.58774 q^{9} +O(q^{10})$	\(q-0.0953887 q^{2} -2.36384 q^{3} -1.99090 q^{4} -3.81314 q^{5} +0.225484 q^{6} -2.61962 q^{7} +0.380687 q^{8} +2.58774 q^{9} +0.363731 q^{10} +2.05095 q^{11} +4.70617 q^{12} -2.14027 q^{13} +0.249882 q^{14} +9.01365 q^{15} +3.94549 q^{16} +5.20191 q^{17} -0.246841 q^{18} +0.822786 q^{19} +7.59158 q^{20} +6.19237 q^{21} -0.195638 q^{22} -2.73112 q^{23} -0.899883 q^{24} +9.54003 q^{25} +0.204157 q^{26} +0.974513 q^{27} +5.21541 q^{28} +3.93146 q^{29} -0.859801 q^{30} -7.48965 q^{31} -1.13773 q^{32} -4.84812 q^{33} -0.496203 q^{34} +9.98898 q^{35} -5.15194 q^{36} +0.862193 q^{37} -0.0784845 q^{38} +5.05925 q^{39} -1.45161 q^{40} -3.86498 q^{41} -0.590682 q^{42} -4.08324 q^{44} -9.86742 q^{45} +0.260518 q^{46} +0.00879364 q^{47} -9.32651 q^{48} -0.137587 q^{49} -0.910011 q^{50} -12.2965 q^{51} +4.26106 q^{52} +3.78694 q^{53} -0.0929576 q^{54} -7.82056 q^{55} -0.997256 q^{56} -1.94493 q^{57} -0.375017 q^{58} +3.93017 q^{59} -17.9453 q^{60} -6.27987 q^{61} +0.714429 q^{62} -6.77890 q^{63} -7.78245 q^{64} +8.16114 q^{65} +0.462456 q^{66} +12.7606 q^{67} -10.3565 q^{68} +6.45594 q^{69} -0.952836 q^{70} -0.230880 q^{71} +0.985120 q^{72} +10.9766 q^{73} -0.0822435 q^{74} -22.5511 q^{75} -1.63808 q^{76} -5.37271 q^{77} -0.482596 q^{78} +0.267285 q^{79} -15.0447 q^{80} -10.0668 q^{81} +0.368675 q^{82} -8.47083 q^{83} -12.3284 q^{84} -19.8356 q^{85} -9.29333 q^{87} +0.780771 q^{88} +14.1885 q^{89} +0.941241 q^{90} +5.60669 q^{91} +5.43740 q^{92} +17.7043 q^{93} -0.000838814 q^{94} -3.13740 q^{95} +2.68941 q^{96} -5.13775 q^{97} +0.0131242 q^{98} +5.30733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0953887	−0.0674500	−0.0337250	−	0.999431i	$-0.510737\pi$
$2$	−0.0953887	−0.0674500	−0.0337250	+	0.999431i	$0.510737\pi$
$3$	−2.36384	−1.36476	−0.682382	−	0.730996i	$-0.739056\pi$
$3$	−2.36384	−1.36476	−0.682382	+	0.730996i	$0.739056\pi$
$4$	−1.99090	−0.995450
$5$	−3.81314	−1.70529	−0.852644	−	0.522493i	$-0.825002\pi$
$5$	−3.81314	−1.70529	−0.852644	+	0.522493i	$0.825002\pi$
$6$	0.225484	0.0920534
$7$	−2.61962	−0.990124	−0.495062	−	0.868858i	$-0.664855\pi$
$7$	−2.61962	−0.990124	−0.495062	+	0.868858i	$0.664855\pi$
$8$	0.380687	0.134593
$9$	2.58774	0.862581
$10$	0.363731	0.115022
$11$	2.05095	0.618385	0.309193	−	0.950999i	$-0.399941\pi$
$11$	2.05095	0.618385	0.309193	+	0.950999i	$0.399941\pi$
$12$	4.70617	1.35855
$13$	−2.14027	−0.593604	−0.296802	−	0.954939i	$-0.595920\pi$
$13$	−2.14027	−0.593604	−0.296802	+	0.954939i	$0.595920\pi$
$14$	0.249882	0.0667839
$15$	9.01365	2.32731
$16$	3.94549	0.986372
$17$	5.20191	1.26165	0.630824	−	0.775926i	$-0.282717\pi$
$17$	5.20191	1.26165	0.630824	+	0.775926i	$0.282717\pi$
$18$	−0.246841	−0.0581811
$19$	0.822786	0.188760	0.0943800	−	0.995536i	$-0.469913\pi$
$19$	0.822786	0.188760	0.0943800	+	0.995536i	$0.469913\pi$
$20$	7.59158	1.69753
$21$	6.19237	1.35128
$22$	−0.195638	−0.0417101
$23$	−2.73112	−0.569479	−0.284739	−	0.958605i	$-0.591907\pi$
$23$	−2.73112	−0.569479	−0.284739	+	0.958605i	$0.591907\pi$
$24$	−0.899883	−0.183688
$25$	9.54003	1.90801
$26$	0.204157	0.0400386
$27$	0.974513	0.187545
$28$	5.21541	0.985619
$29$	3.93146	0.730053	0.365027	−	0.930997i	$-0.381060\pi$
$29$	3.93146	0.730053	0.365027	+	0.930997i	$0.381060\pi$
$30$	−0.859801	−0.156977
$31$	−7.48965	−1.34518	−0.672591	−	0.740015i	$-0.734819\pi$
$31$	−7.48965	−1.34518	−0.672591	+	0.740015i	$0.734819\pi$
$32$	−1.13773	−0.201124
$33$	−4.84812	−0.843950
$34$	−0.496203	−0.0850982
$35$	9.98898	1.68845
$36$	−5.15194	−0.858656
$37$	0.862193	0.141744	0.0708719	−	0.997485i	$-0.477422\pi$
$37$	0.862193	0.141744	0.0708719	+	0.997485i	$0.477422\pi$
$38$	−0.0784845	−0.0127319
$39$	5.05925	0.810129
$40$	−1.45161	−0.229520
$41$	−3.86498	−0.603608	−0.301804	−	0.953370i	$-0.597589\pi$
$41$	−3.86498	−0.603608	−0.301804	+	0.953370i	$0.597589\pi$
$42$	−0.590682	−0.0911442
$43$	0	0
$43$	0	0
$44$	−4.08324	−0.615572
$45$	−9.86742	−1.47095
$46$	0.260518	0.0384114
$47$	0.00879364	0.00128268	0.000641342	−	1.00000i	$-0.499796\pi$
$47$	0.00879364	0.00128268	0.000641342		1.00000i	$0.499796\pi$
$48$	−9.32651	−1.34617
$49$	−0.137587	−0.0196553
$50$	−0.910011	−0.128695
$51$	−12.2965	−1.72185
$52$	4.26106	0.590903
$53$	3.78694	0.520177	0.260088	−	0.965585i	$-0.416248\pi$
$53$	3.78694	0.520177	0.260088	+	0.965585i	$0.416248\pi$
$54$	−0.0929576	−0.0126499
$55$	−7.82056	−1.05452
$56$	−0.997256	−0.133264
$57$	−1.94493	−0.257613
$58$	−0.375017	−0.0492421
$59$	3.93017	0.511664	0.255832	−	0.966721i	$-0.417651\pi$
$59$	3.93017	0.511664	0.255832	+	0.966721i	$0.417651\pi$
$60$	−17.9453	−2.31673
$61$	−6.27987	−0.804055	−0.402028	−	0.915628i	$-0.631694\pi$
$61$	−6.27987	−0.804055	−0.402028	+	0.915628i	$0.631694\pi$
$62$	0.714429	0.0907325
$63$	−6.77890	−0.854061
$64$	−7.78245	−0.972806
$65$	8.16114	1.01226
$66$	0.462456	0.0569244
$67$	12.7606	1.55895	0.779477	−	0.626430i	$-0.215485\pi$
$67$	12.7606	1.55895	0.779477	+	0.626430i	$0.215485\pi$
$68$	−10.3565	−1.25591
$69$	6.45594	0.777204
$70$	−0.952836	−0.113886
$71$	−0.230880	−0.0274004	−0.0137002	−	0.999906i	$-0.504361\pi$
$71$	−0.230880	−0.0274004	−0.0137002	+	0.999906i	$0.504361\pi$
$72$	0.985120	0.116097
$73$	10.9766	1.28472	0.642358	−	0.766405i	$-0.277956\pi$
$73$	10.9766	1.28472	0.642358	+	0.766405i	$0.277956\pi$
$74$	−0.0822435	−0.00956062
$75$	−22.5511	−2.60398
$76$	−1.63808	−0.187901
$77$	−5.37271	−0.612278
$78$	−0.482596	−0.0546432
$79$	0.267285	0.0300719	0.0150359	−	0.999887i	$-0.495214\pi$
$79$	0.267285	0.0300719	0.0150359	+	0.999887i	$0.495214\pi$
$80$	−15.0447	−1.68205
$81$	−10.0668	−1.11854
$82$	0.368675	0.0407134
$83$	−8.47083	−0.929794	−0.464897	−	0.885365i	$-0.653909\pi$
$83$	−8.47083	−0.929794	−0.464897	+	0.885365i	$0.653909\pi$
$84$	−12.3284	−1.34514
$85$	−19.8356	−2.15147
$86$	0	0
$87$	−9.29333	−0.996350
$88$	0.780771	0.0832304
$89$	14.1885	1.50398	0.751991	−	0.659173i	$-0.229094\pi$
$89$	14.1885	1.50398	0.751991	+	0.659173i	$0.229094\pi$
$90$	0.941241	0.0992155
$91$	5.60669	0.587741
$92$	5.43740	0.566888
$93$	17.7043	1.83586
$94$	−0.000838814 0	−8.65171e−5 0
$95$	−3.13740	−0.321890
$96$	2.68941	0.274487
$97$	−5.13775	−0.521660	−0.260830	−	0.965385i	$-0.583996\pi$
$97$	−5.13775	−0.521660	−0.260830	+	0.965385i	$0.583996\pi$
$98$	0.0131242	0.00132575
$99$	5.30733	0.533407
$100$	−18.9933	−1.89933
$101$	−12.3912	−1.23297	−0.616485	−	0.787366i	$-0.711444\pi$
$101$	−12.3912	−1.23297	−0.616485	+	0.787366i	$0.711444\pi$
$102$	1.17295	0.116139
$103$	5.75941	0.567491	0.283746	−	0.958900i	$-0.408423\pi$
$103$	5.75941	0.567491	0.283746	+	0.958900i	$0.408423\pi$
$104$	−0.814772	−0.0798950
$105$	−23.6124	−2.30433
$106$	−0.361232	−0.0350859
$107$	12.1553	1.17510	0.587550	−	0.809188i	$-0.300093\pi$
$107$	12.1553	1.17510	0.587550	+	0.809188i	$0.300093\pi$
$108$	−1.94016	−0.186692
$109$	17.7044	1.69577	0.847885	−	0.530180i	$-0.177876\pi$
$109$	17.7044	1.69577	0.847885	+	0.530180i	$0.177876\pi$
$110$	0.745994	0.0711277
$111$	−2.03809	−0.193447
$112$	−10.3357	−0.976630
$113$	11.3495	1.06767	0.533834	−	0.845590i	$-0.320751\pi$
$113$	11.3495	1.06767	0.533834	+	0.845590i	$0.320751\pi$
$114$	0.185525	0.0173760
$115$	10.4142	0.971125
$116$	−7.82714	−0.726732
$117$	−5.53846	−0.512031
$118$	−0.374894	−0.0345118
$119$	−13.6270	−1.24919
$120$	3.43138	0.313241
$121$	−6.79360	−0.617600
$122$	0.599029	0.0542335
$123$	9.13618	0.823782
$124$	14.9112	1.33906
$125$	−17.3118	−1.54841
$126$	0.646631	0.0576065
$127$	−1.47360	−0.130761	−0.0653805	−	0.997860i	$-0.520826\pi$
$127$	−1.47360	−0.130761	−0.0653805	+	0.997860i	$0.520826\pi$
$128$	3.01782	0.266740
$129$	0	0
$130$	−0.778481	−0.0682773
$131$	−13.2788	−1.16018	−0.580089	−	0.814553i	$-0.696982\pi$
$131$	−13.2788	−1.16018	−0.580089	+	0.814553i	$0.696982\pi$
$132$	9.65213	0.840110
$133$	−2.15539	−0.186896
$134$	−1.21722	−0.105152
$135$	−3.71595	−0.319818
$136$	1.98030	0.169809
$137$	−1.91989	−0.164027	−0.0820136	−	0.996631i	$-0.526135\pi$
$137$	−1.91989	−0.164027	−0.0820136	+	0.996631i	$0.526135\pi$
$138$	−0.615824	−0.0524224
$139$	−5.63278	−0.477767	−0.238883	−	0.971048i	$-0.576781\pi$
$139$	−5.63278	−0.477767	−0.238883	+	0.971048i	$0.576781\pi$
$140$	−19.8871	−1.68076
$141$	−0.0207868	−0.00175056
$142$	0.0220233	0.00184816
$143$	−4.38959	−0.367076
$144$	10.2099	0.850825
$145$	−14.9912	−1.24495
$146$	−1.04705	−0.0866541
$147$	0.325234	0.0268248
$148$	−1.71654	−0.141099
$149$	−2.32457	−0.190436	−0.0952181	−	0.995456i	$-0.530355\pi$
$149$	−2.32457	−0.190436	−0.0952181	+	0.995456i	$0.530355\pi$
$150$	2.15112	0.175638
$151$	−4.89044	−0.397978	−0.198989	−	0.980002i	$-0.563766\pi$
$151$	−4.89044	−0.397978	−0.198989	+	0.980002i	$0.563766\pi$
$152$	0.313224	0.0254058
$153$	13.4612	1.08827
$154$	0.512496	0.0412981
$155$	28.5591	2.29392
$156$	−10.0725	−0.806443
$157$	−18.2809	−1.45897	−0.729487	−	0.683995i	$-0.760241\pi$
$157$	−18.2809	−1.45897	−0.729487	+	0.683995i	$0.760241\pi$
$158$	−0.0254960	−0.00202835
$159$	−8.95173	−0.709919
$160$	4.33832	0.342974
$161$	7.15451	0.563854
$162$	0.960261	0.0754452
$163$	10.0731	0.788985	0.394493	−	0.918899i	$-0.370920\pi$
$163$	10.0731	0.788985	0.394493	+	0.918899i	$0.370920\pi$
$164$	7.69478	0.600862
$165$	18.4866	1.43918
$166$	0.808021	0.0627146
$167$	−1.63716	−0.126687	−0.0633435	−	0.997992i	$-0.520176\pi$
$167$	−1.63716	−0.126687	−0.0633435	+	0.997992i	$0.520176\pi$
$168$	2.35735	0.181874
$169$	−8.41925	−0.647635
$170$	1.89209	0.145117
$171$	2.12916	0.162821
$172$	0	0
$173$	19.9781	1.51891	0.759453	−	0.650562i	$-0.225467\pi$
$173$	19.9781	1.51891	0.759453	+	0.650562i	$0.225467\pi$
$174$	0.886480	0.0672038
$175$	−24.9913	−1.88916
$176$	8.09200	0.609958
$177$	−9.29028	−0.698301
$178$	−1.35343	−0.101444
$179$	−16.6621	−1.24539	−0.622693	−	0.782466i	$-0.713961\pi$
$179$	−16.6621	−1.24539	−0.622693	+	0.782466i	$0.713961\pi$
$180$	19.6451	1.46426
$181$	25.9443	1.92843	0.964213	−	0.265129i	$-0.0854146\pi$
$181$	25.9443	1.92843	0.964213	+	0.265129i	$0.0854146\pi$
$182$	−0.534815	−0.0396431
$183$	14.8446	1.09735
$184$	−1.03970	−0.0766480
$185$	−3.28766	−0.241714
$186$	−1.68880	−0.123828
$187$	10.6689	0.780184
$188$	−0.0175073	−0.00127685
$189$	−2.55285	−0.185693
$190$	0.299272	0.0217115
$191$	4.71387	0.341084	0.170542	−	0.985350i	$-0.445448\pi$
$191$	4.71387	0.341084	0.170542	+	0.985350i	$0.445448\pi$
$192$	18.3965	1.32765
$193$	15.9041	1.14480	0.572400	−	0.819974i	$-0.306012\pi$
$193$	15.9041	1.14480	0.572400	+	0.819974i	$0.306012\pi$
$194$	0.490084	0.0351860
$195$	−19.2916	−1.38150
$196$	0.273922	0.0195659
$197$	−23.7289	−1.69062	−0.845308	−	0.534280i	$-0.820583\pi$
$197$	−23.7289	−1.69062	−0.845308	+	0.534280i	$0.820583\pi$
$198$	−0.506260	−0.0359783
$199$	−5.90736	−0.418761	−0.209381	−	0.977834i	$-0.567145\pi$
$199$	−5.90736	−0.418761	−0.209381	+	0.977834i	$0.567145\pi$
$200$	3.63177	0.256805
$201$	−30.1640	−2.12761
$202$	1.18198	0.0831639
$203$	−10.2989	−0.722843
$204$	24.4811	1.71402
$205$	14.7377	1.02932
$206$	−0.549383	−0.0382773
$207$	−7.06744	−0.491221
$208$	−8.44440	−0.585514
$209$	1.68749	0.116726
$210$	2.25235	0.155427
$211$	5.17022	0.355933	0.177966	−	0.984037i	$-0.443048\pi$
$211$	5.17022	0.355933	0.177966	+	0.984037i	$0.443048\pi$
$212$	−7.53943	−0.517810
$213$	0.545763	0.0373950
$214$	−1.15948	−0.0792605
$215$	0	0
$216$	0.370984	0.0252423
$217$	19.6201	1.33190
$218$	−1.68880	−0.114380
$219$	−25.9470	−1.75333
$220$	15.5700	1.04973
$221$	−11.1335	−0.748919
$222$	0.194411	0.0130480
$223$	3.13481	0.209922	0.104961	−	0.994476i	$-0.466528\pi$
$223$	3.13481	0.209922	0.104961	+	0.994476i	$0.466528\pi$
$224$	2.98042	0.199138
$225$	24.6871	1.64581
$226$	−1.08261	−0.0720142
$227$	18.7981	1.24767	0.623835	−	0.781556i	$-0.285574\pi$
$227$	18.7981	1.24767	0.623835	+	0.781556i	$0.285574\pi$
$228$	3.87217	0.256441
$229$	8.19751	0.541706	0.270853	−	0.962621i	$-0.412694\pi$
$229$	8.19751	0.541706	0.270853	+	0.962621i	$0.412694\pi$
$230$	−0.993393	−0.0655024
$231$	12.7002	0.835614
$232$	1.49665	0.0982602
$233$	6.43836	0.421791	0.210895	−	0.977509i	$-0.432362\pi$
$233$	6.43836	0.421791	0.210895	+	0.977509i	$0.432362\pi$
$234$	0.528307	0.0345365
$235$	−0.0335314	−0.00218734
$236$	−7.82457	−0.509336
$237$	−0.631819	−0.0410410
$238$	1.29986	0.0842577
$239$	−29.0234	−1.87737	−0.938685	−	0.344775i	$-0.887955\pi$
$239$	−29.0234	−1.87737	−0.938685	+	0.344775i	$0.887955\pi$
$240$	35.5633	2.29560
$241$	−12.5007	−0.805239	−0.402619	−	0.915367i	$-0.631900\pi$
$241$	−12.5007	−0.805239	−0.402619	+	0.915367i	$0.631900\pi$
$242$	0.648033	0.0416571
$243$	20.8728	1.33899
$244$	12.5026	0.800397
$245$	0.524638	0.0335179
$246$	−0.871489	−0.0555641
$247$	−1.76098	−0.112049
$248$	−2.85121	−0.181052
$249$	20.0237	1.26895
$250$	1.65135	0.104440
$251$	−20.7292	−1.30841	−0.654207	−	0.756315i	$-0.726998\pi$
$251$	−20.7292	−1.30841	−0.654207	+	0.756315i	$0.726998\pi$
$252$	13.4961	0.850176
$253$	−5.60140	−0.352157
$254$	0.140565	0.00881983
$255$	46.8882	2.93625
$256$	15.2770	0.954815
$257$	−13.3077	−0.830114	−0.415057	−	0.909795i	$-0.636238\pi$
$257$	−13.3077	−0.830114	−0.415057	+	0.909795i	$0.636238\pi$
$258$	0	0
$259$	−2.25862	−0.140344
$260$	−16.2480	−1.00766
$261$	10.1736	0.629730
$262$	1.26665	0.0782541
$263$	−3.57598	−0.220504	−0.110252	−	0.993904i	$-0.535166\pi$
$263$	−3.57598	−0.220504	−0.110252	+	0.993904i	$0.535166\pi$
$264$	−1.84562	−0.113590
$265$	−14.4401	−0.887051
$266$	0.205600	0.0126061
$267$	−33.5394	−2.05258
$268$	−25.4051	−1.55186
$269$	22.3441	1.36234	0.681171	−	0.732124i	$-0.261471\pi$
$269$	22.3441	1.36234	0.681171	+	0.732124i	$0.261471\pi$
$270$	0.354460	0.0215718
$271$	−29.4801	−1.79079	−0.895394	−	0.445276i	$-0.853106\pi$
$271$	−29.4801	−1.79079	−0.895394	+	0.445276i	$0.853106\pi$
$272$	20.5241	1.24445
$273$	−13.2533	−0.802128
$274$	0.183136	0.0110636
$275$	19.5661	1.17988
$276$	−12.8531	−0.773668
$277$	17.5155	1.05241	0.526203	−	0.850359i	$-0.323615\pi$
$277$	17.5155	1.05241	0.526203	+	0.850359i	$0.323615\pi$
$278$	0.537304	0.0322254
$279$	−19.3813	−1.16033
$280$	3.80267	0.227253
$281$	−16.9322	−1.01009	−0.505045	−	0.863093i	$-0.668524\pi$
$281$	−16.9322	−1.01009	−0.505045	+	0.863093i	$0.668524\pi$
$282$	0.00198282	0.000118075 0
$283$	16.8035	0.998866	0.499433	−	0.866353i	$-0.333542\pi$
$283$	16.8035	0.998866	0.499433	+	0.866353i	$0.333542\pi$
$284$	0.459658	0.0272757
$285$	7.41630	0.439304
$286$	0.418717	0.0247593
$287$	10.1248	0.597646
$288$	−2.94415	−0.173486
$289$	10.0598	0.591755
$290$	1.42999	0.0839719
$291$	12.1448	0.711943
$292$	−21.8534	−1.27887
$293$	−16.0428	−0.937228	−0.468614	−	0.883403i	$-0.655246\pi$
$293$	−16.0428	−0.937228	−0.468614	+	0.883403i	$0.655246\pi$
$294$	−0.0310236	−0.00180933
$295$	−14.9863	−0.872534
$296$	0.328226	0.0190777
$297$	1.99868	0.115975
$298$	0.221738	0.0128449
$299$	5.84534	0.338045
$300$	44.8970	2.59213
$301$	0	0
$302$	0.466493	0.0268436
$303$	29.2908	1.68271
$304$	3.24629	0.186188
$305$	23.9460	1.37115
$306$	−1.28405	−0.0734040
$307$	9.96938	0.568983	0.284491	−	0.958679i	$-0.408175\pi$
$307$	9.96938	0.568983	0.284491	+	0.958679i	$0.408175\pi$
$308$	10.6965	0.609492
$309$	−13.6143	−0.774491
$310$	−2.72422	−0.154725
$311$	−5.39330	−0.305826	−0.152913	−	0.988240i	$-0.548865\pi$
$311$	−5.39330	−0.305826	−0.152913	+	0.988240i	$0.548865\pi$
$312$	1.92599	0.109038
$313$	−1.78936	−0.101141	−0.0505703	−	0.998721i	$-0.516104\pi$
$313$	−1.78936	−0.101141	−0.0505703	+	0.998721i	$0.516104\pi$
$314$	1.74379	0.0984078
$315$	25.8489	1.45642
$316$	−0.532138	−0.0299351
$317$	−9.09297	−0.510712	−0.255356	−	0.966847i	$-0.582193\pi$
$317$	−9.09297	−0.510712	−0.255356	+	0.966847i	$0.582193\pi$
$318$	0.853895	0.0478840
$319$	8.06322	0.451454
$320$	29.6756	1.65891
$321$	−28.7332	−1.60373
$322$	−0.682460	−0.0380320
$323$	4.28005	0.238149
$324$	20.0420	1.11345
$325$	−20.4182	−1.13260
$326$	−0.960859	−0.0532171
$327$	−41.8503	−2.31433
$328$	−1.47135	−0.0812415
$329$	−0.0230360	−0.00127002
$330$	−1.76341	−0.0970725
$331$	22.1000	1.21473	0.607363	−	0.794425i	$-0.292227\pi$
$331$	22.1000	1.21473	0.607363	+	0.794425i	$0.292227\pi$
$332$	16.8646	0.925564
$333$	2.23113	0.122265
$334$	0.156166	0.00854504
$335$	−48.6579	−2.65847
$336$	24.4319	1.33287
$337$	10.2969	0.560908	0.280454	−	0.959867i	$-0.409515\pi$
$337$	10.2969	0.560908	0.280454	+	0.959867i	$0.409515\pi$
$338$	0.803102	0.0436830
$339$	−26.8283	−1.45711
$340$	39.4907	2.14168
$341$	−15.3609	−0.831840
$342$	−0.203098	−0.0109823
$343$	18.6978	1.00958
$344$	0	0
$345$	−24.6174	−1.32536
$346$	−1.90569	−0.102450
$347$	−31.4332	−1.68742	−0.843711	−	0.536797i	$-0.819634\pi$
$347$	−31.4332	−1.68742	−0.843711	+	0.536797i	$0.819634\pi$
$348$	18.5021	0.991817
$349$	4.06693	0.217698	0.108849	−	0.994058i	$-0.465284\pi$
$349$	4.06693	0.217698	0.108849	+	0.994058i	$0.465284\pi$
$350$	2.38388	0.127424
$351$	−2.08572	−0.111327
$352$	−2.33343	−0.124372
$353$	−19.4345	−1.03439	−0.517196	−	0.855867i	$-0.673024\pi$
$353$	−19.4345	−1.03439	−0.517196	+	0.855867i	$0.673024\pi$
$354$	0.886189	0.0471004
$355$	0.880376	0.0467255
$356$	−28.2480	−1.49714
$357$	32.2121	1.70485
$358$	1.58938	0.0840013
$359$	0.247832	0.0130801	0.00654003	−	0.999979i	$-0.497918\pi$
$359$	0.247832	0.0130801	0.00654003	+	0.999979i	$0.497918\pi$
$360$	−3.75640	−0.197980
$361$	−18.3230	−0.964370
$362$	−2.47480	−0.130072
$363$	16.0590	0.842878
$364$	−11.1624	−0.585067
$365$	−41.8554	−2.19081
$366$	−1.41601	−0.0740160
$367$	−1.58268	−0.0826151	−0.0413075	−	0.999146i	$-0.513152\pi$
$367$	−1.58268	−0.0826151	−0.0413075	+	0.999146i	$0.513152\pi$
$368$	−10.7756	−0.561718
$369$	−10.0016	−0.520660
$370$	0.313606	0.0163036
$371$	−9.92036	−0.515039
$372$	−35.2476	−1.82750
$373$	−10.9088	−0.564835	−0.282417	−	0.959292i	$-0.591136\pi$
$373$	−10.9088	−0.564835	−0.282417	+	0.959292i	$0.591136\pi$
$374$	−1.01769	−0.0526234
$375$	40.9222	2.11322
$376$	0.00334762	0.000172641 0
$377$	−8.41437	−0.433362
$378$	0.243514	0.0125250
$379$	2.41609	0.124106	0.0620531	−	0.998073i	$-0.480235\pi$
$379$	2.41609	0.124106	0.0620531	+	0.998073i	$0.480235\pi$
$380$	6.24624	0.320426
$381$	3.48336	0.178458
$382$	−0.449650	−0.0230061
$383$	−16.4077	−0.838392	−0.419196	−	0.907896i	$-0.637688\pi$
$383$	−16.4077	−0.838392	−0.419196	+	0.907896i	$0.637688\pi$
$384$	−7.13364	−0.364037
$385$	20.4869	1.04411
$386$	−1.51707	−0.0772169
$387$	0	0
$388$	10.2288	0.519287
$389$	25.0654	1.27087	0.635434	−	0.772155i	$-0.280821\pi$
$389$	25.0654	1.27087	0.635434	+	0.772155i	$0.280821\pi$
$390$	1.84020	0.0931824
$391$	−14.2071	−0.718481
$392$	−0.0523776	−0.00264547
$393$	31.3891	1.58337
$394$	2.26347	0.114032
$395$	−1.01919	−0.0512812
$396$	−10.5664	−0.530980
$397$	−5.27286	−0.264637	−0.132319	−	0.991207i	$-0.542242\pi$
$397$	−5.27286	−0.264637	−0.132319	+	0.991207i	$0.542242\pi$
$398$	0.563495	0.0282455
$399$	5.09499	0.255068
$400$	37.6401	1.88200
$401$	16.7238	0.835146	0.417573	−	0.908643i	$-0.362881\pi$
$401$	16.7238	0.835146	0.417573	+	0.908643i	$0.362881\pi$
$402$	2.87731	0.143507
$403$	16.0299	0.798505
$404$	24.6697	1.22736
$405$	38.3862	1.90742
$406$	0.982401	0.0487558
$407$	1.76832	0.0876522
$408$	−4.68111	−0.231749
$409$	−8.59625	−0.425057	−0.212529	−	0.977155i	$-0.568170\pi$
$409$	−8.59625	−0.425057	−0.212529	+	0.977155i	$0.568170\pi$
$410$	−1.40581	−0.0694280
$411$	4.53831	0.223858
$412$	−11.4664	−0.564909
$413$	−10.2955	−0.506611
$414$	0.674154	0.0331329
$415$	32.3004	1.58557
$416$	2.43505	0.119388
$417$	13.3150	0.652039
$418$	−0.160968	−0.00787319
$419$	−18.4031	−0.899048	−0.449524	−	0.893268i	$-0.648406\pi$
$419$	−18.4031	−0.899048	−0.449524	+	0.893268i	$0.648406\pi$
$420$	47.0099	2.29385
$421$	35.0592	1.70868	0.854341	−	0.519713i	$-0.173961\pi$
$421$	35.0592	1.70868	0.854341	+	0.519713i	$0.173961\pi$
$422$	−0.493181	−0.0240077
$423$	0.0227557	0.00110642
$424$	1.44164	0.0700123
$425$	49.6263	2.40723
$426$	−0.0520596	−0.00252230
$427$	16.4509	0.796114
$428$	−24.2000	−1.16975
$429$	10.3763	0.500971
$430$	0	0
$431$	6.64041	0.319857	0.159929	−	0.987129i	$-0.448874\pi$
$431$	6.64041	0.319857	0.159929	+	0.987129i	$0.448874\pi$
$432$	3.84493	0.184989
$433$	7.97179	0.383100	0.191550	−	0.981483i	$-0.438649\pi$
$433$	7.97179	0.383100	0.191550	+	0.981483i	$0.438649\pi$
$434$	−1.87153	−0.0898364
$435$	35.4368	1.69906
$436$	−35.2476	−1.68806
$437$	−2.24713	−0.107495
$438$	2.47505	0.118262
$439$	−26.4290	−1.26139	−0.630693	−	0.776032i	$-0.717229\pi$
$439$	−26.4290	−1.26139	−0.630693	+	0.776032i	$0.717229\pi$
$440$	−2.97719	−0.141932
$441$	−0.356039	−0.0169543
$442$	1.06201	0.0505146
$443$	−22.1427	−1.05203	−0.526015	−	0.850475i	$-0.676314\pi$
$443$	−22.1427	−1.05203	−0.526015	+	0.850475i	$0.676314\pi$
$444$	4.05763	0.192567
$445$	−54.1029	−2.56472
$446$	−0.299025	−0.0141593
$447$	5.49491	0.259901
$448$	20.3871	0.963199
$449$	5.27072	0.248740	0.124370	−	0.992236i	$-0.460309\pi$
$449$	5.27072	0.248740	0.124370	+	0.992236i	$0.460309\pi$
$450$	−2.35487	−0.111010
$451$	−7.92688	−0.373262
$452$	−22.5956	−1.06281
$453$	11.5602	0.543146
$454$	−1.79312	−0.0841554
$455$	−21.3791	−1.00227
$456$	−0.740411	−0.0346729
$457$	8.55918	0.400381	0.200191	−	0.979757i	$-0.435844\pi$
$457$	8.55918	0.400381	0.200191	+	0.979757i	$0.435844\pi$
$458$	−0.781950	−0.0365381
$459$	5.06933	0.236616
$460$	−20.7335	−0.966707
$461$	−26.3234	−1.22600	−0.613002	−	0.790081i	$-0.710038\pi$
$461$	−26.3234	−1.22600	−0.613002	+	0.790081i	$0.710038\pi$
$462$	−1.21146	−0.0563622
$463$	−0.467407	−0.0217222	−0.0108611	−	0.999941i	$-0.503457\pi$
$463$	−0.467407	−0.0217222	−0.0108611	+	0.999941i	$0.503457\pi$
$464$	15.5115	0.720104
$465$	−67.5091	−3.13066
$466$	−0.614147	−0.0284498
$467$	16.6788	0.771802	0.385901	−	0.922540i	$-0.373891\pi$
$467$	16.6788	0.771802	0.385901	+	0.922540i	$0.373891\pi$
$468$	11.0265	0.509701
$469$	−33.4279	−1.54356
$470$	0.00319851	0.000147536 0
$471$	43.2131	1.99115
$472$	1.49616	0.0688665
$473$	0	0
$474$	0.0602684	0.00276822
$475$	7.84940	0.360155
$476$	27.1301	1.24350
$477$	9.79963	0.448694
$478$	2.76851	0.126629
$479$	33.2289	1.51827	0.759133	−	0.650935i	$-0.225623\pi$
$479$	33.2289	1.51827	0.759133	+	0.650935i	$0.225623\pi$
$480$	−10.2551	−0.468079
$481$	−1.84532	−0.0841396
$482$	1.19242	0.0543134
$483$	−16.9121	−0.769528
$484$	13.5254	0.614790
$485$	19.5910	0.889580
$486$	−1.99103	−0.0903150
$487$	−18.4814	−0.837473	−0.418737	−	0.908108i	$-0.637527\pi$
$487$	−18.4814	−0.837473	−0.418737	+	0.908108i	$0.637527\pi$
$488$	−2.39067	−0.108220
$489$	−23.8112	−1.07678
$490$	−0.0500446	−0.00226078
$491$	−32.8288	−1.48154	−0.740772	−	0.671756i	$-0.765540\pi$
$491$	−32.8288	−1.48154	−0.740772	+	0.671756i	$0.765540\pi$
$492$	−18.1892	−0.820034
$493$	20.4511	0.921070
$494$	0.167978	0.00755768
$495$	−20.2376	−0.909612
$496$	−29.5503	−1.32685
$497$	0.604817	0.0271298
$498$	−1.91003	−0.0855907
$499$	10.8861	0.487330	0.243665	−	0.969860i	$-0.421650\pi$
$499$	10.8861	0.487330	0.243665	+	0.969860i	$0.421650\pi$
$500$	34.4660	1.54137
$501$	3.86998	0.172898
$502$	1.97733	0.0882526
$503$	−28.2290	−1.25867	−0.629335	−	0.777134i	$-0.716673\pi$
$503$	−28.2290	−1.25867	−0.629335	+	0.777134i	$0.716673\pi$
$504$	−2.58064	−0.114951
$505$	47.2494	2.10257
$506$	0.534311	0.0237530
$507$	19.9018	0.883869
$508$	2.93379	0.130166
$509$	11.1938	0.496158	0.248079	−	0.968740i	$-0.420201\pi$
$509$	11.1938	0.496158	0.248079	+	0.968740i	$0.420201\pi$
$510$	−4.47261	−0.198050
$511$	−28.7546	−1.27203
$512$	−7.49289	−0.331142
$513$	0.801815	0.0354010
$514$	1.26941	0.0559912
$515$	−21.9614	−0.967736
$516$	0	0
$517$	0.0180353	0.000793193 0
$518$	0.215447	0.00946619
$519$	−47.2250	−2.07295
$520$	3.10684	0.136244
$521$	41.6149	1.82318	0.911590	−	0.411100i	$-0.134855\pi$
$521$	41.6149	1.82318	0.911590	+	0.411100i	$0.134855\pi$
$522$	−0.970446	−0.0424753
$523$	6.85433	0.299719	0.149859	−	0.988707i	$-0.452118\pi$
$523$	6.85433	0.299719	0.149859	+	0.988707i	$0.452118\pi$
$524$	26.4369	1.15490
$525$	59.0753	2.57826
$526$	0.341108	0.0148730
$527$	−38.9605	−1.69715
$528$	−19.1282	−0.832448
$529$	−15.5410	−0.675694
$530$	1.37743	0.0598316
$531$	10.1703	0.441351
$532$	4.29116	0.186045
$533$	8.27208	0.358304
$534$	3.19929	0.138447
$535$	−46.3499	−2.00388
$536$	4.85779	0.209825
$537$	39.3866	1.69966
$538$	−2.13137	−0.0918900
$539$	−0.282184	−0.0121545
$540$	7.39810	0.318363
$541$	−15.4711	−0.665156	−0.332578	−	0.943076i	$-0.607918\pi$
$541$	−15.4711	−0.665156	−0.332578	+	0.943076i	$0.607918\pi$
$542$	2.81207	0.120789
$543$	−61.3282	−2.63185
$544$	−5.91836	−0.253748
$545$	−67.5092	−2.89178
$546$	1.26422	0.0541035
$547$	15.3738	0.657334	0.328667	−	0.944446i	$-0.393401\pi$
$547$	15.3738	0.657334	0.328667	+	0.944446i	$0.393401\pi$
$548$	3.82231	0.163281
$549$	−16.2507	−0.693562
$550$	−1.86639	−0.0795831
$551$	3.23474	0.137805
$552$	2.45769	0.104606
$553$	−0.700185	−0.0297749
$554$	−1.67078	−0.0709848
$555$	7.77151	0.329882
$556$	11.2143	0.475593
$557$	31.0940	1.31750	0.658748	−	0.752364i	$-0.271086\pi$
$557$	31.0940	1.31750	0.658748	+	0.752364i	$0.271086\pi$
$558$	1.84876	0.0782641
$559$	0	0
$560$	39.4114	1.66544
$561$	−25.2195	−1.06477
$562$	1.61514	0.0681306
$563$	0.209412	0.00882567	0.00441284	−	0.999990i	$-0.498595\pi$
$563$	0.209412	0.00882567	0.00441284	+	0.999990i	$0.498595\pi$
$564$	0.0413844	0.00174260
$565$	−43.2771	−1.82068
$566$	−1.60287	−0.0673735
$567$	26.3712	1.10749
$568$	−0.0878929	−0.00368790
$569$	12.3601	0.518162	0.259081	−	0.965856i	$-0.416580\pi$
$569$	12.3601	0.518162	0.259081	+	0.965856i	$0.416580\pi$
$570$	−0.707432	−0.0296311
$571$	−28.6777	−1.20012	−0.600061	−	0.799954i	$-0.704857\pi$
$571$	−28.6777	−1.20012	−0.600061	+	0.799954i	$0.704857\pi$
$572$	8.73923	0.365406
$573$	−11.1428	−0.465499
$574$	−0.965789	−0.0403113
$575$	−26.0550	−1.08657
$576$	−20.1390	−0.839124
$577$	21.4284	0.892075	0.446038	−	0.895014i	$-0.352835\pi$
$577$	21.4284	0.892075	0.446038	+	0.895014i	$0.352835\pi$
$578$	−0.959595	−0.0399139
$579$	−37.5947	−1.56238
$580$	29.8460	1.23929
$581$	22.1904	0.920611
$582$	−1.15848	−0.0480205
$583$	7.76684	0.321670
$584$	4.17866	0.172914
$585$	21.1189	0.873160
$586$	1.53030	0.0632160
$587$	−37.1696	−1.53415	−0.767076	−	0.641556i	$-0.778289\pi$
$587$	−37.1696	−1.53415	−0.767076	+	0.641556i	$0.778289\pi$
$588$	−0.647508	−0.0267028
$589$	−6.16238	−0.253916
$590$	1.42952	0.0588525
$591$	56.0914	2.30729
$592$	3.40177	0.139812
$593$	−22.3430	−0.917518	−0.458759	−	0.888561i	$-0.651706\pi$
$593$	−22.3430	−0.917518	−0.458759	+	0.888561i	$0.651706\pi$
$594$	−0.190651	−0.00782252
$595$	51.9617	2.13022
$596$	4.62799	0.189570
$597$	13.9640	0.571510
$598$	−0.557579	−0.0228011
$599$	−21.0030	−0.858160	−0.429080	−	0.903266i	$-0.641162\pi$
$599$	−21.0030	−0.858160	−0.429080	+	0.903266i	$0.641162\pi$
$600$	−8.58491	−0.350478
$601$	25.2099	1.02833	0.514167	−	0.857690i	$-0.328101\pi$
$601$	25.2099	1.02833	0.514167	+	0.857690i	$0.328101\pi$
$602$	0	0
$603$	33.0211	1.34472
$604$	9.73638	0.396168
$605$	25.9049	1.05319
$606$	−2.79401	−0.113499
$607$	−33.5889	−1.36333	−0.681665	−	0.731664i	$-0.738744\pi$
$607$	−33.5889	−1.36333	−0.681665	+	0.731664i	$0.738744\pi$
$608$	−0.936107	−0.0379642
$609$	24.3450	0.986510
$610$	−2.28418	−0.0924838
$611$	−0.0188207	−0.000761406 0
$612$	−26.7999	−1.08332
$613$	1.79822	0.0726293	0.0363147	−	0.999340i	$-0.488438\pi$
$613$	1.79822	0.0726293	0.0363147	+	0.999340i	$0.488438\pi$
$614$	−0.950967	−0.0383779
$615$	−34.8375	−1.40479
$616$	−2.04532	−0.0824084
$617$	34.1308	1.37405	0.687027	−	0.726632i	$-0.258915\pi$
$617$	34.1308	1.37405	0.687027	+	0.726632i	$0.258915\pi$
$618$	1.29865	0.0522395
$619$	4.70466	0.189096	0.0945482	−	0.995520i	$-0.469859\pi$
$619$	4.70466	0.189096	0.0945482	+	0.995520i	$0.469859\pi$
$620$	−56.8583	−2.28349
$621$	−2.66152	−0.106803
$622$	0.514460	0.0206280
$623$	−37.1686	−1.48913
$624$	19.9612	0.799088
$625$	18.3120	0.732480
$626$	0.170685	0.00682194
$627$	−3.98896	−0.159304
$628$	36.3954	1.45234
$629$	4.48505	0.178831
$630$	−2.46569	−0.0982356
$631$	−0.990959	−0.0394495	−0.0197247	−	0.999805i	$-0.506279\pi$
$631$	−0.990959	−0.0394495	−0.0197247	+	0.999805i	$0.506279\pi$
$632$	0.101752	0.00404747
$633$	−12.2216	−0.485764
$634$	0.867367	0.0344475
$635$	5.61905	0.222985
$636$	17.8220	0.706689
$637$	0.294473	0.0116674
$638$	−0.769141	−0.0304506
$639$	−0.597457	−0.0236350
$640$	−11.5074	−0.454868
$641$	6.35508	0.251010	0.125505	−	0.992093i	$-0.459945\pi$
$641$	6.35508	0.251010	0.125505	+	0.992093i	$0.459945\pi$
$642$	2.74083	0.108172
$643$	−40.7748	−1.60800	−0.804001	−	0.594628i	$-0.797299\pi$
$643$	−40.7748	−1.60800	−0.804001	+	0.594628i	$0.797299\pi$
$644$	−14.2439	−0.561289
$645$	0	0
$646$	−0.408269	−0.0160631
$647$	−25.4857	−1.00195	−0.500973	−	0.865463i	$-0.667025\pi$
$647$	−25.4857	−1.00195	−0.500973	+	0.865463i	$0.667025\pi$
$648$	−3.83231	−0.150547
$649$	8.06058	0.316405
$650$	1.94767	0.0763938
$651$	−46.3787	−1.81772
$652$	−20.0545	−0.785396
$653$	34.0393	1.33206	0.666030	−	0.745925i	$-0.267992\pi$
$653$	34.0393	1.33206	0.666030	+	0.745925i	$0.267992\pi$
$654$	3.99205	0.156101
$655$	50.6341	1.97844
$656$	−15.2492	−0.595382
$657$	28.4046	1.10817
$658$	0.00219737	8.56626e−5 0
$659$	−38.1148	−1.48474	−0.742370	−	0.669990i	$-0.766298\pi$
$659$	−38.1148	−1.48474	−0.742370	+	0.669990i	$0.766298\pi$
$660$	−36.8049	−1.43263
$661$	20.3243	0.790524	0.395262	−	0.918569i	$-0.370654\pi$
$661$	20.3243	0.790524	0.395262	+	0.918569i	$0.370654\pi$
$662$	−2.10809	−0.0819333
$663$	26.3178	1.02210
$664$	−3.22473	−0.125144
$665$	8.21879	0.318711
$666$	−0.212825	−0.00824680
$667$	−10.7373	−0.415750
$668$	3.25942	0.126111
$669$	−7.41018	−0.286494
$670$	4.64142	0.179314
$671$	−12.8797	−0.497216
$672$	−7.04524	−0.271776
$673$	−32.6954	−1.26031	−0.630157	−	0.776468i	$-0.717009\pi$
$673$	−32.6954	−1.26031	−0.630157	+	0.776468i	$0.717009\pi$
$674$	−0.982208	−0.0378333
$675$	9.29688	0.357837
$676$	16.7619	0.644688
$677$	−13.4438	−0.516686	−0.258343	−	0.966053i	$-0.583176\pi$
$677$	−13.4438	−0.516686	−0.258343	+	0.966053i	$0.583176\pi$
$678$	2.55912	0.0982824
$679$	13.4590	0.516508
$680$	−7.55115	−0.289574
$681$	−44.4356	−1.70278
$682$	1.46526	0.0561076
$683$	18.9039	0.723337	0.361669	−	0.932307i	$-0.382207\pi$
$683$	18.9039	0.723337	0.361669	+	0.932307i	$0.382207\pi$
$684$	−4.23894	−0.162080
$685$	7.32081	0.279714
$686$	−1.78356	−0.0680965
$687$	−19.3776	−0.739301
$688$	0	0
$689$	−8.10508	−0.308779
$690$	2.34822	0.0893953
$691$	32.7768	1.24689	0.623445	−	0.781867i	$-0.285733\pi$
$691$	32.7768	1.24689	0.623445	+	0.781867i	$0.285733\pi$
$692$	−39.7744	−1.51200
$693$	−13.9032	−0.528139
$694$	2.99837	0.113817
$695$	21.4786	0.814729
$696$	−3.53785	−0.134102
$697$	−20.1052	−0.761540
$698$	−0.387939	−0.0146837
$699$	−15.2192	−0.575645
$700$	49.7551	1.88057
$701$	−2.89575	−0.109371	−0.0546855	−	0.998504i	$-0.517416\pi$
$701$	−2.89575	−0.109371	−0.0546855	+	0.998504i	$0.517416\pi$
$702$	0.198954	0.00750904
$703$	0.709400	0.0267555
$704$	−15.9614	−0.601569
$705$	0.0792628	0.00298521
$706$	1.85383	0.0697698
$707$	32.4602	1.22079
$708$	18.4960	0.695124
$709$	27.6398	1.03803	0.519017	−	0.854764i	$-0.326298\pi$
$709$	27.6398	1.03803	0.519017	+	0.854764i	$0.326298\pi$
$710$	−0.0839780	−0.00315164
$711$	0.691664	0.0259394
$712$	5.40139	0.202426
$713$	20.4552	0.766052
$714$	−3.07267	−0.114992
$715$	16.7381	0.625969
$716$	33.1726	1.23972
$717$	68.6068	2.56217
$718$	−0.0236404	−0.000882251 0
$719$	−14.0869	−0.525354	−0.262677	−	0.964884i	$-0.584605\pi$
$719$	−14.0869	−0.525354	−0.262677	+	0.964884i	$0.584605\pi$
$720$	−38.9318	−1.45090
$721$	−15.0875	−0.561886
$722$	1.74781	0.0650468
$723$	29.5496	1.09896
$724$	−51.6526	−1.91965
$725$	37.5062	1.39295
$726$	−1.53185	−0.0568522
$727$	−42.6084	−1.58026	−0.790130	−	0.612940i	$-0.789987\pi$
$727$	−42.6084	−1.58026	−0.790130	+	0.612940i	$0.789987\pi$
$728$	2.13439	0.0791059
$729$	−19.1395	−0.708872
$730$	3.99253	0.147770
$731$	0	0
$732$	−29.5542	−1.09235
$733$	36.7890	1.35883	0.679416	−	0.733753i	$-0.262233\pi$
$733$	36.7890	1.35883	0.679416	+	0.733753i	$0.262233\pi$
$734$	0.150970	0.00557239
$735$	−1.24016	−0.0457440
$736$	3.10728	0.114536
$737$	26.1714	0.964034
$738$	0.954036	0.0351186
$739$	−22.4603	−0.826215	−0.413107	−	0.910682i	$-0.635557\pi$
$739$	−22.4603	−0.826215	−0.413107	+	0.910682i	$0.635557\pi$
$740$	6.54541	0.240614
$741$	4.16268	0.152920
$742$	0.946291	0.0347394
$743$	−35.0322	−1.28521	−0.642603	−	0.766199i	$-0.722146\pi$
$743$	−35.0322	−1.28521	−0.642603	+	0.766199i	$0.722146\pi$
$744$	6.73982	0.247094
$745$	8.86391	0.324749
$746$	1.04057	0.0380981
$747$	−21.9203	−0.802022
$748$	−21.2406	−0.776635
$749$	−31.8423	−1.16349
$750$	−3.90352	−0.142536
$751$	21.7819	0.794833	0.397416	−	0.917638i	$-0.369907\pi$
$751$	21.7819	0.794833	0.397416	+	0.917638i	$0.369907\pi$
$752$	0.0346952	0.00126520
$753$	49.0005	1.78568
$754$	0.802636	0.0292303
$755$	18.6479	0.678667
$756$	5.08248	0.184848
$757$	−23.7948	−0.864838	−0.432419	−	0.901673i	$-0.642340\pi$
$757$	−23.7948	−0.864838	−0.432419	+	0.901673i	$0.642340\pi$
$758$	−0.230468	−0.00837096
$759$	13.2408	0.480611
$760$	−1.19437	−0.0433242
$761$	−18.2452	−0.661387	−0.330693	−	0.943738i	$-0.607283\pi$
$761$	−18.2452	−0.661387	−0.330693	+	0.943738i	$0.607283\pi$
$762$	−0.332273	−0.0120370
$763$	−46.3787	−1.67902
$764$	−9.38485	−0.339532
$765$	−51.3294	−1.85582
$766$	1.56511	0.0565496
$767$	−8.41161	−0.303726
$768$	−36.1125	−1.30310
$769$	−38.6617	−1.39418	−0.697088	−	0.716986i	$-0.745521\pi$
$769$	−38.6617	−1.39418	−0.697088	+	0.716986i	$0.745521\pi$
$770$	−1.95422	−0.0704252
$771$	31.4574	1.13291
$772$	−31.6635	−1.13959
$773$	−25.0975	−0.902696	−0.451348	−	0.892348i	$-0.649057\pi$
$773$	−25.0975	−0.902696	−0.451348	+	0.892348i	$0.649057\pi$
$774$	0	0
$775$	−71.4515	−2.56661
$776$	−1.95588	−0.0702119
$777$	5.33902	0.191536
$778$	−2.39096	−0.0857200
$779$	−3.18005	−0.113937
$780$	38.4077	1.37522
$781$	−0.473523	−0.0169440
$782$	1.35519	0.0484616
$783$	3.83125	0.136918
$784$	−0.542848	−0.0193874
$785$	69.7076	2.48797
$786$	−2.99416	−0.106798
$787$	46.8203	1.66896	0.834482	−	0.551035i	$-0.185767\pi$
$787$	46.8203	1.66896	0.834482	+	0.551035i	$0.185767\pi$
$788$	47.2419	1.68292
$789$	8.45304	0.300936
$790$	0.0972196	0.00345892
$791$	−29.7313	−1.05712
$792$	2.02043	0.0717929
$793$	13.4406	0.477290
$794$	0.502971	0.0178498
$795$	34.1342	1.21062
$796$	11.7610	0.416856
$797$	35.7658	1.26689	0.633444	−	0.773788i	$-0.281641\pi$
$797$	35.7658	1.26689	0.633444	+	0.773788i	$0.281641\pi$
$798$	−0.486005	−0.0172044
$799$	0.0457437	0.00161830
$800$	−10.8540	−0.383746
$801$	36.7163	1.29731
$802$	−1.59526	−0.0563306
$803$	22.5125	0.794449
$804$	60.0536	2.11793
$805$	−27.2811	−0.961534
$806$	−1.52907	−0.0538592
$807$	−52.8178	−1.85927
$808$	−4.71717	−0.165949
$809$	18.8179	0.661601	0.330801	−	0.943701i	$-0.392681\pi$
$809$	18.8179	0.661601	0.330801	+	0.943701i	$0.392681\pi$
$810$	−3.66161	−0.128656
$811$	−19.4728	−0.683784	−0.341892	−	0.939739i	$-0.611068\pi$
$811$	−19.4728	−0.683784	−0.341892	+	0.939739i	$0.611068\pi$
$812$	20.5041	0.719554
$813$	69.6862	2.44400
$814$	−0.168677	−0.00591214
$815$	−38.4101	−1.34545
$816$	−48.5156	−1.69839
$817$	0	0
$818$	0.819986	0.0286701
$819$	14.5087	0.506974
$820$	−29.3413	−1.02464
$821$	25.6855	0.896430	0.448215	−	0.893926i	$-0.352060\pi$
$821$	25.6855	0.896430	0.448215	+	0.893926i	$0.352060\pi$
$822$	−0.432904	−0.0150993
$823$	31.8884	1.11156	0.555780	−	0.831329i	$-0.312420\pi$
$823$	31.8884	1.11156	0.555780	+	0.831329i	$0.312420\pi$
$824$	2.19253	0.0763804
$825$	−46.2512	−1.61026
$826$	0.982079	0.0341709
$827$	−0.959542	−0.0333665	−0.0166833	−	0.999861i	$-0.505311\pi$
$827$	−0.959542	−0.0333665	−0.0166833	+	0.999861i	$0.505311\pi$
$828$	14.0706	0.488986
$829$	33.0761	1.14878	0.574389	−	0.818582i	$-0.305240\pi$
$829$	33.0761	1.14878	0.574389	+	0.818582i	$0.305240\pi$
$830$	−3.08110	−0.106946
$831$	−41.4039	−1.43628
$832$	16.6565	0.577461
$833$	−0.715714	−0.0247980
$834$	−1.27010	−0.0439800
$835$	6.24271	0.216038
$836$	−3.35963	−0.116195
$837$	−7.29877	−0.252282
$838$	1.75545	0.0606408
$839$	−24.7789	−0.855464	−0.427732	−	0.903906i	$-0.640687\pi$
$839$	−24.7789	−0.855464	−0.427732	+	0.903906i	$0.640687\pi$
$840$	−8.98892	−0.310147
$841$	−13.5437	−0.467023
$842$	−3.34426	−0.115251
$843$	40.0250	1.37853
$844$	−10.2934	−0.354313
$845$	32.1038	1.10440
$846$	−0.00217063	−7.46279e−5 0
$847$	17.7967	0.611500
$848$	14.9413	0.513088
$849$	−39.7209	−1.36322
$850$	−4.73379	−0.162368
$851$	−2.35476	−0.0807200
$852$	−1.08656	−0.0372249
$853$	32.6019	1.11627	0.558133	−	0.829751i	$-0.311518\pi$
$853$	32.6019	1.11627	0.558133	+	0.829751i	$0.311518\pi$
$854$	−1.56923	−0.0536979
$855$	−8.11877	−0.277656
$856$	4.62737	0.158160
$857$	−45.4937	−1.55404	−0.777018	−	0.629478i	$-0.783269\pi$
$857$	−45.4937	−1.55404	−0.777018	+	0.629478i	$0.783269\pi$
$858$	−0.989780	−0.0337905
$859$	39.0901	1.33374	0.666868	−	0.745176i	$-0.267635\pi$
$859$	39.0901	1.33374	0.666868	+	0.745176i	$0.267635\pi$
$860$	0	0
$861$	−23.9333	−0.815646
$862$	−0.633420	−0.0215744
$863$	4.55797	0.155155	0.0775775	−	0.996986i	$-0.475281\pi$
$863$	4.55797	0.155155	0.0775775	+	0.996986i	$0.475281\pi$
$864$	−1.10873	−0.0377198
$865$	−76.1792	−2.59017
$866$	−0.760419	−0.0258401
$867$	−23.7799	−0.807606
$868$	−39.0616	−1.32584
$869$	0.548188	0.0185960
$870$	−3.38027	−0.114602
$871$	−27.3111	−0.925401
$872$	6.73982	0.228239
$873$	−13.2952	−0.449974
$874$	0.214351	0.00725052
$875$	45.3502	1.53312
$876$	51.6578	1.74536
$877$	2.73844	0.0924706	0.0462353	−	0.998931i	$-0.485278\pi$
$877$	2.73844	0.0924706	0.0462353	+	0.998931i	$0.485278\pi$
$878$	2.52103	0.0850805
$879$	37.9225	1.27909
$880$	−30.8559	−1.04015
$881$	−44.0350	−1.48358	−0.741788	−	0.670634i	$-0.766022\pi$
$881$	−44.0350	−1.48358	−0.741788	+	0.670634i	$0.766022\pi$
$882$	0.0339622	0.00114357
$883$	−21.8059	−0.733827	−0.366914	−	0.930255i	$-0.619586\pi$
$883$	−21.8059	−0.733827	−0.366914	+	0.930255i	$0.619586\pi$
$884$	22.1656	0.745511
$885$	35.4251	1.19080
$886$	2.11216	0.0709595
$887$	−30.5980	−1.02738	−0.513690	−	0.857976i	$-0.671722\pi$
$887$	−30.5980	−1.02738	−0.513690	+	0.857976i	$0.671722\pi$
$888$	−0.775873	−0.0260366
$889$	3.86028	0.129470
$890$	5.16081	0.172991
$891$	−20.6466	−0.691686
$892$	−6.24109	−0.208967
$893$	0.00723528	0.000242119 0
$894$	−0.524153	−0.0175303
$895$	63.5350	2.12374
$896$	−7.90554	−0.264105
$897$	−13.8174	−0.461351
$898$	−0.502767	−0.0167776
$899$	−29.4452	−0.982054
$900$	−49.1496	−1.63832
$901$	19.6993	0.656280
$902$	0.756135	0.0251765
$903$	0	0
$904$	4.32059	0.143701
$905$	−98.9293	−3.28852
$906$	−1.10271	−0.0366352
$907$	11.4030	0.378632	0.189316	−	0.981916i	$-0.439373\pi$
$907$	11.4030	0.378632	0.189316	+	0.981916i	$0.439373\pi$
$908$	−37.4251	−1.24199
$909$	−32.0652	−1.06354
$910$	2.03932	0.0676030
$911$	−50.8219	−1.68380	−0.841902	−	0.539630i	$-0.818564\pi$
$911$	−50.8219	−1.68380	−0.841902	+	0.539630i	$0.818564\pi$
$912$	−7.67371	−0.254102
$913$	−17.3732	−0.574971
$914$	−0.816449	−0.0270057
$915$	−56.6046	−1.87129
$916$	−16.3204	−0.539242
$917$	34.7855	1.14872
$918$	−0.483557	−0.0159597
$919$	16.4183	0.541590	0.270795	−	0.962637i	$-0.412713\pi$
$919$	16.4183	0.541590	0.270795	+	0.962637i	$0.412713\pi$
$920$	3.96453	0.130707
$921$	−23.5660	−0.776527
$922$	2.51096	0.0826940
$923$	0.494144	0.0162650
$924$	−25.2849	−0.831813
$925$	8.22535	0.270448
$926$	0.0445853	0.00146516
$927$	14.9039	0.489507
$928$	−4.47293	−0.146831
$929$	−22.0449	−0.723270	−0.361635	−	0.932320i	$-0.617781\pi$
$929$	−22.0449	−0.723270	−0.361635	+	0.932320i	$0.617781\pi$
$930$	6.43961	0.211163
$931$	−0.113205	−0.00371013
$932$	−12.8181	−0.419872
$933$	12.7489	0.417380
$934$	−1.59097	−0.0520581
$935$	−40.6818	−1.33044
$936$	−2.10842	−0.0689159
$937$	−21.8233	−0.712936	−0.356468	−	0.934307i	$-0.616019\pi$
$937$	−21.8233	−0.712936	−0.356468	+	0.934307i	$0.616019\pi$
$938$	3.18865	0.104113
$939$	4.22976	0.138033
$940$	0.0667576	0.00217739
$941$	−33.9678	−1.10732	−0.553659	−	0.832743i	$-0.686769\pi$
$941$	−33.9678	−1.10732	−0.553659	+	0.832743i	$0.686769\pi$
$942$	−4.12204	−0.134303
$943$	10.5557	0.343742
$944$	15.5064	0.504691
$945$	9.73439	0.316660
$946$	0	0
$947$	39.0671	1.26951	0.634756	−	0.772713i	$-0.281101\pi$
$947$	39.0671	1.26951	0.634756	+	0.772713i	$0.281101\pi$
$948$	1.25789	0.0408543
$949$	−23.4929	−0.762612
$950$	−0.748744	−0.0242925
$951$	21.4943	0.697001
$952$	−5.18763	−0.168132
$953$	8.07371	0.261533	0.130767	−	0.991413i	$-0.458256\pi$
$953$	8.07371	0.261533	0.130767	+	0.991413i	$0.458256\pi$
$954$	−0.934775	−0.0302645
$955$	−17.9747	−0.581646
$956$	57.7828	1.86883
$957$	−19.0602	−0.616128
$958$	−3.16966	−0.102407
$959$	5.02938	0.162407
$960$	−70.1483	−2.26403
$961$	25.0949	0.809513
$962$	0.176023	0.00567522
$963$	31.4548	1.01362
$964$	24.8876	0.801575
$965$	−60.6445	−1.95221
$966$	1.61323	0.0519047
$967$	13.2296	0.425437	0.212718	−	0.977114i	$-0.431768\pi$
$967$	13.2296	0.425437	0.212718	+	0.977114i	$0.431768\pi$
$968$	−2.58624	−0.0831248
$969$	−10.1174	−0.325017
$970$	−1.86876	−0.0600022
$971$	35.9638	1.15413	0.577066	−	0.816698i	$-0.304198\pi$
$971$	35.9638	1.15413	0.577066	+	0.816698i	$0.304198\pi$
$972$	−41.5557	−1.33290
$973$	14.7558	0.473048
$974$	1.76292	0.0564876
$975$	48.2654	1.54573
$976$	−24.7772	−0.793098
$977$	15.5499	0.497484	0.248742	−	0.968570i	$-0.419983\pi$
$977$	15.5499	0.497484	0.248742	+	0.968570i	$0.419983\pi$
$978$	2.27132	0.0726288
$979$	29.1000	0.930040
$980$	−1.04450	−0.0333654
$981$	45.8143	1.46274
$982$	3.13150	0.0999302
$983$	−25.2604	−0.805680	−0.402840	−	0.915270i	$-0.631977\pi$
$983$	−25.2604	−0.805680	−0.402840	+	0.915270i	$0.631977\pi$
$984$	3.47803	0.110875
$985$	90.4817	2.88299
$986$	−1.95080	−0.0621262
$987$	0.0544534	0.00173327
$988$	3.50594	0.111539
$989$	0	0
$990$	1.93044	0.0613534
$991$	−59.0709	−1.87645	−0.938225	−	0.346026i	$-0.887531\pi$
$991$	−59.0709	−1.87645	−0.938225	+	0.346026i	$0.887531\pi$
$992$	8.52120	0.270548
$993$	−52.2409	−1.65781
$994$	−0.0576927	−0.00182990
$995$	22.5256	0.714109
$996$	−39.8652	−1.26318
$997$	−37.6115	−1.19117	−0.595584	−	0.803293i	$-0.703079\pi$
$997$	−37.6115	−1.19117	−0.595584	+	0.803293i	$0.703079\pi$
$998$	−1.03841	−0.0328704
$999$	0.840219	0.0265833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.11		18
43.25	even	21		43.2.g.a.23.3	yes	36
43.31	even	21		43.2.g.a.15.3	✓	36
43.42	odd	2		1849.2.a.o.1.8		18
129.68	odd	42		387.2.y.c.109.1		36
129.74	odd	42		387.2.y.c.316.1		36
172.31	odd	42		688.2.bg.c.273.3		36
172.111	odd	42		688.2.bg.c.625.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.15.3	✓	36	43.31	even	21
43.2.g.a.23.3	yes	36	43.25	even	21
387.2.y.c.109.1		36	129.68	odd	42
387.2.y.c.316.1		36	129.74	odd	42
688.2.bg.c.273.3		36	172.31	odd	42
688.2.bg.c.625.3		36	172.111	odd	42
1849.2.a.n.1.11		18	1.1	even	1	trivial
1849.2.a.o.1.8		18	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)

\(f(q)\)	\(=\)	\(q-0.0953887 q^{2} -2.36384 q^{3} -1.99090 q^{4} -3.81314 q^{5} +0.225484 q^{6} -2.61962 q^{7} +0.380687 q^{8} +2.58774 q^{9} +O(q^{10})\)	\(q-0.0953887 q^{2} -2.36384 q^{3} -1.99090 q^{4} -3.81314 q^{5} +0.225484 q^{6} -2.61962 q^{7} +0.380687 q^{8} +2.58774 q^{9} +0.363731 q^{10} +2.05095 q^{11} +4.70617 q^{12} -2.14027 q^{13} +0.249882 q^{14} +9.01365 q^{15} +3.94549 q^{16} +5.20191 q^{17} -0.246841 q^{18} +0.822786 q^{19} +7.59158 q^{20} +6.19237 q^{21} -0.195638 q^{22} -2.73112 q^{23} -0.899883 q^{24} +9.54003 q^{25} +0.204157 q^{26} +0.974513 q^{27} +5.21541 q^{28} +3.93146 q^{29} -0.859801 q^{30} -7.48965 q^{31} -1.13773 q^{32} -4.84812 q^{33} -0.496203 q^{34} +9.98898 q^{35} -5.15194 q^{36} +0.862193 q^{37} -0.0784845 q^{38} +5.05925 q^{39} -1.45161 q^{40} -3.86498 q^{41} -0.590682 q^{42} -4.08324 q^{44} -9.86742 q^{45} +0.260518 q^{46} +0.00879364 q^{47} -9.32651 q^{48} -0.137587 q^{49} -0.910011 q^{50} -12.2965 q^{51} +4.26106 q^{52} +3.78694 q^{53} -0.0929576 q^{54} -7.82056 q^{55} -0.997256 q^{56} -1.94493 q^{57} -0.375017 q^{58} +3.93017 q^{59} -17.9453 q^{60} -6.27987 q^{61} +0.714429 q^{62} -6.77890 q^{63} -7.78245 q^{64} +8.16114 q^{65} +0.462456 q^{66} +12.7606 q^{67} -10.3565 q^{68} +6.45594 q^{69} -0.952836 q^{70} -0.230880 q^{71} +0.985120 q^{72} +10.9766 q^{73} -0.0822435 q^{74} -22.5511 q^{75} -1.63808 q^{76} -5.37271 q^{77} -0.482596 q^{78} +0.267285 q^{79} -15.0447 q^{80} -10.0668 q^{81} +0.368675 q^{82} -8.47083 q^{83} -12.3284 q^{84} -19.8356 q^{85} -9.29333 q^{87} +0.780771 q^{88} +14.1885 q^{89} +0.941241 q^{90} +5.60669 q^{91} +5.43740 q^{92} +17.7043 q^{93} -0.000838814 q^{94} -3.13740 q^{95} +2.68941 q^{96} -5.13775 q^{97} +0.0131242 q^{98} +5.30733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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