LMFDB - Embedded newform 6043.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, 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("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82300 q^{2} +0.597654 q^{3} +5.96933 q^{4} -3.72082 q^{5} -1.68718 q^{6} -3.33856 q^{7} -11.2054 q^{8} -2.64281 q^{9} +O(q^{10})$	\(q-2.82300 q^{2} +0.597654 q^{3} +5.96933 q^{4} -3.72082 q^{5} -1.68718 q^{6} -3.33856 q^{7} -11.2054 q^{8} -2.64281 q^{9} +10.5039 q^{10} -1.73054 q^{11} +3.56759 q^{12} -1.21237 q^{13} +9.42477 q^{14} -2.22376 q^{15} +19.6942 q^{16} -7.55550 q^{17} +7.46065 q^{18} -6.19875 q^{19} -22.2108 q^{20} -1.99531 q^{21} +4.88532 q^{22} +8.01885 q^{23} -6.69696 q^{24} +8.84449 q^{25} +3.42253 q^{26} -3.37245 q^{27} -19.9290 q^{28} +6.45469 q^{29} +6.27768 q^{30} +4.24692 q^{31} -33.1859 q^{32} -1.03426 q^{33} +21.3292 q^{34} +12.4222 q^{35} -15.7758 q^{36} +8.67346 q^{37} +17.4991 q^{38} -0.724579 q^{39} +41.6933 q^{40} -2.29649 q^{41} +5.63275 q^{42} +7.95868 q^{43} -10.3302 q^{44} +9.83342 q^{45} -22.6372 q^{46} -10.5821 q^{47} +11.7703 q^{48} +4.14601 q^{49} -24.9680 q^{50} -4.51558 q^{51} -7.23705 q^{52} +4.25553 q^{53} +9.52042 q^{54} +6.43903 q^{55} +37.4100 q^{56} -3.70471 q^{57} -18.2216 q^{58} -5.23318 q^{59} -13.2744 q^{60} -1.36840 q^{61} -11.9891 q^{62} +8.82319 q^{63} +54.2955 q^{64} +4.51102 q^{65} +2.91973 q^{66} +5.26621 q^{67} -45.1013 q^{68} +4.79250 q^{69} -35.0678 q^{70} +5.76859 q^{71} +29.6138 q^{72} +1.11339 q^{73} -24.4852 q^{74} +5.28595 q^{75} -37.0023 q^{76} +5.77752 q^{77} +2.04549 q^{78} +3.44428 q^{79} -73.2786 q^{80} +5.91287 q^{81} +6.48299 q^{82} +13.3730 q^{83} -11.9106 q^{84} +28.1127 q^{85} -22.4674 q^{86} +3.85767 q^{87} +19.3914 q^{88} -3.08598 q^{89} -27.7597 q^{90} +4.04758 q^{91} +47.8671 q^{92} +2.53819 q^{93} +29.8733 q^{94} +23.0644 q^{95} -19.8337 q^{96} +1.27250 q^{97} -11.7042 q^{98} +4.57349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) $ 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * 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 $

$2$	−2.82300	−1.99616	−0.998081	−	0.0619204i	$-0.980278\pi$
$2$	−2.82300	−1.99616	−0.998081	+	0.0619204i	$0.980278\pi$
$3$	0.597654	0.345056	0.172528	−	0.985005i	$-0.444807\pi$
$3$	0.597654	0.345056	0.172528	+	0.985005i	$0.444807\pi$
$4$	5.96933	2.98466
$5$	−3.72082	−1.66400	−0.832000	−	0.554775i	$-0.812804\pi$
$5$	−3.72082	−1.66400	−0.832000	+	0.554775i	$0.812804\pi$
$6$	−1.68718	−0.688787
$7$	−3.33856	−1.26186	−0.630929	−	0.775840i	$-0.717326\pi$
$7$	−3.33856	−1.26186	−0.630929	+	0.775840i	$0.717326\pi$
$8$	−11.2054	−3.96171
$9$	−2.64281	−0.880937
$10$	10.5039	3.32162
$11$	−1.73054	−0.521778	−0.260889	−	0.965369i	$-0.584016\pi$
$11$	−1.73054	−0.521778	−0.260889	+	0.965369i	$0.584016\pi$
$12$	3.56759	1.02988
$13$	−1.21237	−0.336252	−0.168126	−	0.985766i	$-0.553771\pi$
$13$	−1.21237	−0.336252	−0.168126	+	0.985766i	$0.553771\pi$
$14$	9.42477	2.51887
$15$	−2.22376	−0.574173
$16$	19.6942	4.92355
$17$	−7.55550	−1.83248	−0.916239	−	0.400631i	$-0.868791\pi$
$17$	−7.55550	−1.83248	−0.916239	+	0.400631i	$0.868791\pi$
$18$	7.46065	1.75849
$19$	−6.19875	−1.42209	−0.711045	−	0.703146i	$-0.751778\pi$
$19$	−6.19875	−1.42209	−0.711045	+	0.703146i	$0.751778\pi$
$20$	−22.2108	−4.96648
$21$	−1.99531	−0.435412
$22$	4.88532	1.04155
$23$	8.01885	1.67205	0.836023	−	0.548695i	$-0.184875\pi$
$23$	8.01885	1.67205	0.836023	+	0.548695i	$0.184875\pi$
$24$	−6.69696	−1.36701
$25$	8.84449	1.76890
$26$	3.42253	0.671213
$27$	−3.37245	−0.649028
$28$	−19.9290	−3.76622
$29$	6.45469	1.19861	0.599303	−	0.800522i	$-0.295445\pi$
$29$	6.45469	1.19861	0.599303	+	0.800522i	$0.295445\pi$
$30$	6.27768	1.14614
$31$	4.24692	0.762769	0.381385	−	0.924416i	$-0.375447\pi$
$31$	4.24692	0.762769	0.381385	+	0.924416i	$0.375447\pi$
$32$	−33.1859	−5.86650
$33$	−1.03426	−0.180042
$34$	21.3292	3.65792
$35$	12.4222	2.09973
$36$	−15.7758	−2.62930
$37$	8.67346	1.42591	0.712954	−	0.701210i	$-0.247357\pi$
$37$	8.67346	1.42591	0.712954	+	0.701210i	$0.247357\pi$
$38$	17.4991	2.83872
$39$	−0.724579	−0.116026
$40$	41.6933	6.59229
$41$	−2.29649	−0.358652	−0.179326	−	0.983790i	$-0.557392\pi$
$41$	−2.29649	−0.358652	−0.179326	+	0.983790i	$0.557392\pi$
$42$	5.63275	0.869152
$43$	7.95868	1.21369	0.606844	−	0.794821i	$-0.292435\pi$
$43$	7.95868	1.21369	0.606844	+	0.794821i	$0.292435\pi$
$44$	−10.3302	−1.55733
$45$	9.83342	1.46588
$46$	−22.6372	−3.33767
$47$	−10.5821	−1.54356	−0.771779	−	0.635891i	$-0.780633\pi$
$47$	−10.5821	−1.54356	−0.771779	+	0.635891i	$0.780633\pi$
$48$	11.7703	1.69890
$49$	4.14601	0.592287
$50$	−24.9680	−3.53101
$51$	−4.51558	−0.632307
$52$	−7.23705	−1.00360
$53$	4.25553	0.584542	0.292271	−	0.956336i	$-0.405589\pi$
$53$	4.25553	0.584542	0.292271	+	0.956336i	$0.405589\pi$
$54$	9.52042	1.29557
$55$	6.43903	0.868238
$56$	37.4100	4.99912
$57$	−3.70471	−0.490700
$58$	−18.2216	−2.39261
$59$	−5.23318	−0.681302	−0.340651	−	0.940190i	$-0.610648\pi$
$59$	−5.23318	−0.681302	−0.340651	+	0.940190i	$0.610648\pi$
$60$	−13.2744	−1.71371
$61$	−1.36840	−0.175205	−0.0876027	−	0.996155i	$-0.527921\pi$
$61$	−1.36840	−0.175205	−0.0876027	+	0.996155i	$0.527921\pi$
$62$	−11.9891	−1.52261
$63$	8.82319	1.11162
$64$	54.2955	6.78693
$65$	4.51102	0.559523
$66$	2.91973	0.359394
$67$	5.26621	0.643370	0.321685	−	0.946847i	$-0.395751\pi$
$67$	5.26621	0.643370	0.321685	+	0.946847i	$0.395751\pi$
$68$	−45.1013	−5.46933
$69$	4.79250	0.576949
$70$	−35.0678	−4.19141
$71$	5.76859	0.684606	0.342303	−	0.939590i	$-0.388793\pi$
$71$	5.76859	0.684606	0.342303	+	0.939590i	$0.388793\pi$
$72$	29.6138	3.49002
$73$	1.11339	0.130312	0.0651561	−	0.997875i	$-0.479245\pi$
$73$	1.11339	0.130312	0.0651561	+	0.997875i	$0.479245\pi$
$74$	−24.4852	−2.84634
$75$	5.28595	0.610368
$76$	−37.0023	−4.24446
$77$	5.77752	0.658410
$78$	2.04549	0.231606
$79$	3.44428	0.387511	0.193756	−	0.981050i	$-0.437933\pi$
$79$	3.44428	0.387511	0.193756	+	0.981050i	$0.437933\pi$
$80$	−73.2786	−8.19279
$81$	5.91287	0.656986
$82$	6.48299	0.715927
$83$	13.3730	1.46788	0.733939	−	0.679215i	$-0.237680\pi$
$83$	13.3730	1.46788	0.733939	+	0.679215i	$0.237680\pi$
$84$	−11.9106	−1.29956
$85$	28.1127	3.04925
$86$	−22.4674	−2.42272
$87$	3.85767	0.413586
$88$	19.3914	2.06713
$89$	−3.08598	−0.327113	−0.163556	−	0.986534i	$-0.552297\pi$
$89$	−3.08598	−0.327113	−0.163556	+	0.986534i	$0.552297\pi$
$90$	−27.7597	−2.92613
$91$	4.04758	0.424302
$92$	47.8671	4.99049
$93$	2.53819	0.263198
$94$	29.8733	3.08119
$95$	23.0644	2.36636
$96$	−19.8337	−2.02427
$97$	1.27250	0.129202	0.0646012	−	0.997911i	$-0.479422\pi$
$97$	1.27250	0.129202	0.0646012	+	0.997911i	$0.479422\pi$
$98$	−11.7042	−1.18230
$99$	4.57349	0.459653
$100$	52.7957	5.27957
$101$	−1.77204	−0.176325	−0.0881623	−	0.996106i	$-0.528099\pi$
$101$	−1.77204	−0.176325	−0.0881623	+	0.996106i	$0.528099\pi$
$102$	12.7475	1.26219
$103$	0.372412	0.0366949	0.0183474	−	0.999832i	$-0.494160\pi$
$103$	0.372412	0.0366949	0.0183474	+	0.999832i	$0.494160\pi$
$104$	13.5851	1.33213
$105$	7.42417	0.724525
$106$	−12.0134	−1.16684
$107$	−6.35637	−0.614493	−0.307247	−	0.951630i	$-0.599408\pi$
$107$	−6.35637	−0.614493	−0.307247	+	0.951630i	$0.599408\pi$
$108$	−20.1312	−1.93713
$109$	15.2256	1.45835	0.729173	−	0.684329i	$-0.239905\pi$
$109$	15.2256	1.45835	0.729173	+	0.684329i	$0.239905\pi$
$110$	−18.1774	−1.73314
$111$	5.18373	0.492018
$112$	−65.7504	−6.21283
$113$	−16.6095	−1.56249	−0.781245	−	0.624224i	$-0.785415\pi$
$113$	−16.6095	−1.56249	−0.781245	+	0.624224i	$0.785415\pi$
$114$	10.4584	0.979517
$115$	−29.8367	−2.78228
$116$	38.5302	3.57743
$117$	3.20407	0.296216
$118$	14.7733	1.35999
$119$	25.2245	2.31233
$120$	24.9182	2.27471
$121$	−8.00523	−0.727748
$122$	3.86299	0.349738
$123$	−1.37251	−0.123755
$124$	25.3513	2.27661
$125$	−14.3047	−1.27945
$126$	−24.9079	−2.21897
$127$	−11.2761	−1.00059	−0.500295	−	0.865855i	$-0.666775\pi$
$127$	−11.2761	−1.00059	−0.500295	+	0.865855i	$0.666775\pi$
$128$	−86.9042	−7.68132
$129$	4.75654	0.418790
$130$	−12.7346	−1.11690
$131$	19.3041	1.68661	0.843303	−	0.537439i	$-0.180608\pi$
$131$	19.3041	1.68661	0.843303	+	0.537439i	$0.180608\pi$
$132$	−6.17386	−0.537366
$133$	20.6949	1.79448
$134$	−14.8665	−1.28427
$135$	12.5483	1.07998
$136$	84.6625	7.25975
$137$	3.76816	0.321935	0.160968	−	0.986960i	$-0.448538\pi$
$137$	3.76816	0.321935	0.160968	+	0.986960i	$0.448538\pi$
$138$	−13.5292	−1.15168
$139$	1.08513	0.0920393	0.0460196	−	0.998941i	$-0.485346\pi$
$139$	1.08513	0.0920393	0.0460196	+	0.998941i	$0.485346\pi$
$140$	74.1521	6.26700
$141$	−6.32444	−0.532614
$142$	−16.2847	−1.36658
$143$	2.09806	0.175449
$144$	−52.0480	−4.33734
$145$	−24.0167	−1.99448
$146$	−3.14309	−0.260124
$147$	2.47788	0.204372
$148$	51.7747	4.25586
$149$	8.21163	0.672723	0.336361	−	0.941733i	$-0.390804\pi$
$149$	8.21163	0.672723	0.336361	+	0.941733i	$0.390804\pi$
$150$	−14.9222	−1.21839
$151$	−8.21335	−0.668393	−0.334197	−	0.942503i	$-0.608465\pi$
$151$	−8.21335	−0.668393	−0.334197	+	0.942503i	$0.608465\pi$
$152$	69.4595	5.63391
$153$	19.9678	1.61430
$154$	−16.3099	−1.31429
$155$	−15.8020	−1.26925
$156$	−4.32525	−0.346297
$157$	−11.5434	−0.921261	−0.460630	−	0.887592i	$-0.652377\pi$
$157$	−11.5434	−0.921261	−0.460630	+	0.887592i	$0.652377\pi$
$158$	−9.72319	−0.773536
$159$	2.54333	0.201699
$160$	123.479	9.76186
$161$	−26.7714	−2.10988
$162$	−16.6920	−1.31145
$163$	−22.6897	−1.77719	−0.888595	−	0.458692i	$-0.848318\pi$
$163$	−22.6897	−1.77719	−0.888595	+	0.458692i	$0.848318\pi$
$164$	−13.7085	−1.07045
$165$	3.84831	0.299591
$166$	−37.7520	−2.93012
$167$	3.23533	0.250357	0.125179	−	0.992134i	$-0.460050\pi$
$167$	3.23533	0.250357	0.125179	+	0.992134i	$0.460050\pi$
$168$	22.3582	1.72497
$169$	−11.5302	−0.886935
$170$	−79.3620	−6.08679
$171$	16.3821	1.25277
$172$	47.5080	3.62245
$173$	−18.1779	−1.38204	−0.691022	−	0.722834i	$-0.742839\pi$
$173$	−18.1779	−1.38204	−0.691022	+	0.722834i	$0.742839\pi$
$174$	−10.8902	−0.825584
$175$	−29.5279	−2.23210
$176$	−34.0816	−2.56900
$177$	−3.12763	−0.235087
$178$	8.71171	0.652970
$179$	16.1170	1.20464	0.602320	−	0.798255i	$-0.294243\pi$
$179$	16.1170	1.20464	0.602320	+	0.798255i	$0.294243\pi$
$180$	58.6989	4.37516
$181$	17.3754	1.29150	0.645750	−	0.763549i	$-0.276545\pi$
$181$	17.3754	1.29150	0.645750	+	0.763549i	$0.276545\pi$
$182$	−11.4263	−0.846976
$183$	−0.817828	−0.0604556
$184$	−89.8544	−6.62416
$185$	−32.2724	−2.37271
$186$	−7.16531	−0.525386
$187$	13.0751	0.956147
$188$	−63.1680	−4.60700
$189$	11.2591	0.818982
$190$	−65.1108	−4.72364
$191$	−5.75282	−0.416259	−0.208130	−	0.978101i	$-0.566738\pi$
$191$	−5.75282	−0.416259	−0.208130	+	0.978101i	$0.566738\pi$
$192$	32.4499	2.34187
$193$	−8.77184	−0.631411	−0.315705	−	0.948857i	$-0.602241\pi$
$193$	−8.77184	−0.631411	−0.315705	+	0.948857i	$0.602241\pi$
$194$	−3.59226	−0.257909
$195$	2.69603	0.193067
$196$	24.7489	1.76778
$197$	−13.6434	−0.972054	−0.486027	−	0.873944i	$-0.661554\pi$
$197$	−13.6434	−0.972054	−0.486027	+	0.873944i	$0.661554\pi$
$198$	−12.9110	−0.917542
$199$	−7.47762	−0.530075	−0.265037	−	0.964238i	$-0.585384\pi$
$199$	−7.47762	−0.530075	−0.265037	+	0.964238i	$0.585384\pi$
$200$	−99.1061	−7.00786
$201$	3.14737	0.221998
$202$	5.00247	0.351973
$203$	−21.5494	−1.51247
$204$	−26.9550	−1.88722
$205$	8.54483	0.596797
$206$	−1.05132	−0.0732489
$207$	−21.1923	−1.47297
$208$	−23.8767	−1.65555
$209$	10.7272	0.742015
$210$	−20.9584	−1.44627
$211$	−2.47957	−0.170701	−0.0853503	−	0.996351i	$-0.527201\pi$
$211$	−2.47957	−0.170701	−0.0853503	+	0.996351i	$0.527201\pi$
$212$	25.4026	1.74466
$213$	3.44762	0.236227
$214$	17.9440	1.22663
$215$	−29.6128	−2.01958
$216$	37.7897	2.57126
$217$	−14.1786	−0.962507
$218$	−42.9818	−2.91110
$219$	0.665421	0.0449650
$220$	38.4367	2.59140
$221$	9.16008	0.616174
$222$	−14.6337	−0.982148
$223$	−3.29777	−0.220835	−0.110417	−	0.993885i	$-0.535219\pi$
$223$	−3.29777	−0.220835	−0.110417	+	0.993885i	$0.535219\pi$
$224$	110.793	7.40269
$225$	−23.3743	−1.55829
$226$	46.8886	3.11898
$227$	−4.54764	−0.301838	−0.150919	−	0.988546i	$-0.548223\pi$
$227$	−4.54764	−0.301838	−0.150919	+	0.988546i	$0.548223\pi$
$228$	−22.1146	−1.46458
$229$	17.3129	1.14407	0.572034	−	0.820230i	$-0.306154\pi$
$229$	17.3129	1.14407	0.572034	+	0.820230i	$0.306154\pi$
$230$	84.2289	5.55389
$231$	3.45296	0.227188
$232$	−72.3274	−4.74853
$233$	−19.5186	−1.27871	−0.639354	−	0.768912i	$-0.720798\pi$
$233$	−19.5186	−1.27871	−0.639354	+	0.768912i	$0.720798\pi$
$234$	−9.04509	−0.591296
$235$	39.3741	2.56848
$236$	−31.2386	−2.03346
$237$	2.05849	0.133713
$238$	−71.2089	−4.61578
$239$	−7.38447	−0.477661	−0.238831	−	0.971061i	$-0.576764\pi$
$239$	−7.38447	−0.477661	−0.238831	+	0.971061i	$0.576764\pi$
$240$	−43.7952	−2.82697
$241$	−6.31482	−0.406773	−0.203387	−	0.979099i	$-0.565195\pi$
$241$	−6.31482	−0.406773	−0.203387	+	0.979099i	$0.565195\pi$
$242$	22.5988	1.45270
$243$	13.6512	0.875725
$244$	−8.16841	−0.522929
$245$	−15.4266	−0.985567
$246$	3.87459	0.247035
$247$	7.51519	0.478180
$248$	−47.5885	−3.02187
$249$	7.99243	0.506500
$250$	40.3820	2.55398
$251$	−0.528208	−0.0333402	−0.0166701	−	0.999861i	$-0.505307\pi$
$251$	−0.528208	−0.0333402	−0.0166701	+	0.999861i	$0.505307\pi$
$252$	52.6685	3.31780
$253$	−13.8769	−0.872436
$254$	31.8323	1.99734
$255$	16.8016	1.05216
$256$	136.740	8.54622
$257$	13.1701	0.821525	0.410763	−	0.911742i	$-0.365262\pi$
$257$	13.1701	0.821525	0.410763	+	0.911742i	$0.365262\pi$
$258$	−13.4277	−0.835972
$259$	−28.9569	−1.79930
$260$	26.9277	1.66999
$261$	−17.0585	−1.05590
$262$	−54.4954	−3.36674
$263$	−15.1334	−0.933167	−0.466583	−	0.884477i	$-0.654515\pi$
$263$	−15.1334	−0.933167	−0.466583	+	0.884477i	$0.654515\pi$
$264$	11.5894	0.713276
$265$	−15.8340	−0.972678
$266$	−58.4217	−3.58207
$267$	−1.84435	−0.112872
$268$	31.4357	1.92024
$269$	15.7393	0.959640	0.479820	−	0.877367i	$-0.340702\pi$
$269$	15.7393	0.959640	0.479820	+	0.877367i	$0.340702\pi$
$270$	−35.4238	−2.15582
$271$	13.7742	0.836725	0.418363	−	0.908280i	$-0.362604\pi$
$271$	13.7742	0.836725	0.418363	+	0.908280i	$0.362604\pi$
$272$	−148.800	−9.02231
$273$	2.41905	0.146408
$274$	−10.6375	−0.642635
$275$	−15.3058	−0.922972
$276$	28.6080	1.72200
$277$	25.3440	1.52277	0.761386	−	0.648299i	$-0.224519\pi$
$277$	25.3440	1.52277	0.761386	+	0.648299i	$0.224519\pi$
$278$	−3.06331	−0.183725
$279$	−11.2238	−0.671951
$280$	−139.196	−8.31854
$281$	4.04188	0.241118	0.120559	−	0.992706i	$-0.461531\pi$
$281$	4.04188	0.241118	0.120559	+	0.992706i	$0.461531\pi$
$282$	17.8539	1.06318
$283$	−26.5549	−1.57853	−0.789263	−	0.614055i	$-0.789537\pi$
$283$	−26.5549	−1.57853	−0.789263	+	0.614055i	$0.789537\pi$
$284$	34.4346	2.04332
$285$	13.7845	0.816526
$286$	−5.92282	−0.350224
$287$	7.66698	0.452568
$288$	87.7041	5.16801
$289$	40.0856	2.35798
$290$	67.7992	3.98131
$291$	0.760513	0.0445820
$292$	6.64618	0.388938
$293$	−8.96609	−0.523805	−0.261902	−	0.965094i	$-0.584350\pi$
$293$	−8.96609	−0.523805	−0.261902	+	0.965094i	$0.584350\pi$
$294$	−6.99506	−0.407960
$295$	19.4717	1.13369
$296$	−97.1897	−5.64904
$297$	5.83616	0.338648
$298$	−23.1814	−1.34286
$299$	−9.72183	−0.562228
$300$	31.5535	1.82174
$301$	−26.5706	−1.53150
$302$	23.1863	1.33422
$303$	−1.05907	−0.0608418
$304$	−122.079	−7.00173
$305$	5.09156	0.291542
$306$	−56.3690	−3.22240
$307$	−23.9312	−1.36583	−0.682913	−	0.730499i	$-0.739287\pi$
$307$	−23.9312	−1.36583	−0.682913	+	0.730499i	$0.739287\pi$
$308$	34.4879	1.96513
$309$	0.222574	0.0126618
$310$	44.6091	2.53363
$311$	26.5395	1.50492	0.752460	−	0.658639i	$-0.228867\pi$
$311$	26.5395	1.50492	0.752460	+	0.658639i	$0.228867\pi$
$312$	8.11921	0.459660
$313$	−8.99460	−0.508405	−0.254202	−	0.967151i	$-0.581813\pi$
$313$	−8.99460	−0.508405	−0.254202	+	0.967151i	$0.581813\pi$
$314$	32.5869	1.83899
$315$	−32.8295	−1.84973
$316$	20.5600	1.15659
$317$	21.1187	1.18614	0.593071	−	0.805150i	$-0.297915\pi$
$317$	21.1187	1.18614	0.593071	+	0.805150i	$0.297915\pi$
$318$	−7.17983	−0.402625
$319$	−11.1701	−0.625406
$320$	−202.024	−11.2935
$321$	−3.79891	−0.212034
$322$	75.5757	4.21167
$323$	46.8347	2.60595
$324$	35.2959	1.96088
$325$	−10.7228	−0.594795
$326$	64.0529	3.54756
$327$	9.09963	0.503211
$328$	25.7331	1.42087
$329$	35.3290	1.94775
$330$	−10.8638	−0.598032
$331$	18.1325	0.996655	0.498327	−	0.866989i	$-0.333948\pi$
$331$	18.1325	0.996655	0.498327	+	0.866989i	$0.333948\pi$
$332$	79.8279	4.38112
$333$	−22.9223	−1.25613
$334$	−9.13334	−0.499754
$335$	−19.5946	−1.07057
$336$	−39.2960	−2.14377
$337$	−0.844951	−0.0460274	−0.0230137	−	0.999735i	$-0.507326\pi$
$337$	−0.844951	−0.0460274	−0.0230137	+	0.999735i	$0.507326\pi$
$338$	32.5496	1.77047
$339$	−9.92673	−0.539146
$340$	167.814	9.10097
$341$	−7.34947	−0.397996
$342$	−46.2467	−2.50073
$343$	9.52822	0.514476
$344$	−89.1803	−4.80828
$345$	−17.8320	−0.960043
$346$	51.3163	2.75878
$347$	−10.0944	−0.541897	−0.270949	−	0.962594i	$-0.587337\pi$
$347$	−10.0944	−0.541897	−0.270949	+	0.962594i	$0.587337\pi$
$348$	23.0277	1.23441
$349$	28.3075	1.51527	0.757633	−	0.652681i	$-0.226356\pi$
$349$	28.3075	1.51527	0.757633	+	0.652681i	$0.226356\pi$
$350$	83.3573	4.45563
$351$	4.08866	0.218237
$352$	57.4296	3.06101
$353$	26.3891	1.40455	0.702275	−	0.711906i	$-0.252168\pi$
$353$	26.3891	1.40455	0.702275	+	0.711906i	$0.252168\pi$
$354$	8.82931	0.469272
$355$	−21.4639	−1.13918
$356$	−18.4212	−0.976322
$357$	15.0755	0.797883
$358$	−45.4982	−2.40466
$359$	13.9218	0.734765	0.367383	−	0.930070i	$-0.380254\pi$
$359$	13.9218	0.734765	0.367383	+	0.930070i	$0.380254\pi$
$360$	−110.187	−5.80739
$361$	19.4245	1.02234
$362$	−49.0507	−2.57805
$363$	−4.78436	−0.251114
$364$	24.1613	1.26640
$365$	−4.14272	−0.216840
$366$	2.30873	0.120679
$367$	25.1195	1.31123	0.655614	−	0.755096i	$-0.272410\pi$
$367$	25.1195	1.31123	0.655614	+	0.755096i	$0.272410\pi$
$368$	157.925	8.23240
$369$	6.06919	0.315949
$370$	91.1049	4.73632
$371$	−14.2074	−0.737609
$372$	15.1513	0.785557
$373$	7.89929	0.409010	0.204505	−	0.978866i	$-0.434442\pi$
$373$	7.89929	0.409010	0.204505	+	0.978866i	$0.434442\pi$
$374$	−36.9110	−1.90862
$375$	−8.54923	−0.441481
$376$	118.577	6.11513
$377$	−7.82549	−0.403033
$378$	−31.7845	−1.63482
$379$	20.3577	1.04570	0.522852	−	0.852424i	$-0.324868\pi$
$379$	20.3577	1.04570	0.522852	+	0.852424i	$0.324868\pi$
$380$	137.679	7.06278
$381$	−6.73919	−0.345259
$382$	16.2402	0.830921
$383$	−10.6099	−0.542143	−0.271072	−	0.962559i	$-0.587378\pi$
$383$	−10.6099	−0.542143	−0.271072	+	0.962559i	$0.587378\pi$
$384$	−51.9386	−2.65048
$385$	−21.4971	−1.09559
$386$	24.7629	1.26040
$387$	−21.0333	−1.06918
$388$	7.59595	0.385626
$389$	20.3903	1.03383	0.516915	−	0.856037i	$-0.327080\pi$
$389$	20.3903	1.03383	0.516915	+	0.856037i	$0.327080\pi$
$390$	−7.61089	−0.385392
$391$	−60.5864	−3.06399
$392$	−46.4578	−2.34647
$393$	11.5372	0.581973
$394$	38.5154	1.94038
$395$	−12.8155	−0.644819
$396$	27.3007	1.37191
$397$	−17.7947	−0.893088	−0.446544	−	0.894762i	$-0.647345\pi$
$397$	−17.7947	−0.893088	−0.446544	+	0.894762i	$0.647345\pi$
$398$	21.1093	1.05812
$399$	12.3684	0.619194
$400$	174.185	8.70926
$401$	−34.5031	−1.72300	−0.861500	−	0.507757i	$-0.830475\pi$
$401$	−34.5031	−1.72300	−0.861500	+	0.507757i	$0.830475\pi$
$402$	−8.88502	−0.443145
$403$	−5.14885	−0.256482
$404$	−10.5779	−0.526270
$405$	−22.0007	−1.09322
$406$	60.8339	3.01914
$407$	−15.0098	−0.744007
$408$	50.5989	2.50502
$409$	2.00565	0.0991728	0.0495864	−	0.998770i	$-0.484210\pi$
$409$	2.00565	0.0991728	0.0495864	+	0.998770i	$0.484210\pi$
$410$	−24.1220	−1.19130
$411$	2.25205	0.111086
$412$	2.22305	0.109522
$413$	17.4713	0.859707
$414$	59.8258	2.94028
$415$	−49.7585	−2.44255
$416$	40.2337	1.97262
$417$	0.648531	0.0317587
$418$	−30.2828	−1.48118
$419$	−27.7507	−1.35571	−0.677856	−	0.735195i	$-0.737091\pi$
$419$	−27.7507	−1.35571	−0.677856	+	0.735195i	$0.737091\pi$
$420$	44.3173	2.16246
$421$	−23.6872	−1.15444	−0.577221	−	0.816588i	$-0.695863\pi$
$421$	−23.6872	−1.15444	−0.577221	+	0.816588i	$0.695863\pi$
$422$	6.99982	0.340746
$423$	27.9665	1.35978
$424$	−47.6849	−2.31579
$425$	−66.8246	−3.24147
$426$	−9.73264	−0.471548
$427$	4.56848	0.221084
$428$	−37.9432	−1.83406
$429$	1.25391	0.0605395
$430$	83.5969	4.03140
$431$	36.8142	1.77328	0.886639	−	0.462462i	$-0.153034\pi$
$431$	36.8142	1.77328	0.886639	+	0.462462i	$0.153034\pi$
$432$	−66.4177	−3.19552
$433$	32.0131	1.53845	0.769225	−	0.638978i	$-0.220643\pi$
$433$	32.0131	1.53845	0.769225	+	0.638978i	$0.220643\pi$
$434$	40.0262	1.92132
$435$	−14.3537	−0.688207
$436$	90.8865	4.35267
$437$	−49.7068	−2.37780
$438$	−1.87848	−0.0897574
$439$	25.7334	1.22819	0.614094	−	0.789233i	$-0.289522\pi$
$439$	25.7334	1.22819	0.614094	+	0.789233i	$0.289522\pi$
$440$	−72.1519	−3.43971
$441$	−10.9571	−0.521768
$442$	−25.8589	−1.22998
$443$	7.64228	0.363095	0.181548	−	0.983382i	$-0.441889\pi$
$443$	7.64228	0.363095	0.181548	+	0.983382i	$0.441889\pi$
$444$	30.9434	1.46851
$445$	11.4824	0.544316
$446$	9.30960	0.440822
$447$	4.90771	0.232127
$448$	−181.269	−8.56415
$449$	15.3349	0.723698	0.361849	−	0.932237i	$-0.382146\pi$
$449$	15.3349	0.723698	0.361849	+	0.932237i	$0.382146\pi$
$450$	65.9857	3.11059
$451$	3.97417	0.187136
$452$	−99.1475	−4.66351
$453$	−4.90874	−0.230633
$454$	12.8380	0.602517
$455$	−15.0603	−0.706039
$456$	41.5127	1.94401
$457$	12.9652	0.606486	0.303243	−	0.952913i	$-0.401931\pi$
$457$	12.9652	0.606486	0.303243	+	0.952913i	$0.401931\pi$
$458$	−48.8743	−2.28375
$459$	25.4805	1.18933
$460$	−178.105	−8.30418
$461$	−16.7791	−0.781480	−0.390740	−	0.920501i	$-0.627781\pi$
$461$	−16.7791	−0.781480	−0.390740	+	0.920501i	$0.627781\pi$
$462$	−9.74770	−0.453504
$463$	−14.2076	−0.660283	−0.330141	−	0.943931i	$-0.607096\pi$
$463$	−14.2076	−0.660283	−0.330141	+	0.943931i	$0.607096\pi$
$464$	127.120	5.90140
$465$	−9.44414	−0.437962
$466$	55.1011	2.55251
$467$	−26.9571	−1.24742	−0.623712	−	0.781654i	$-0.714376\pi$
$467$	−26.9571	−1.24742	−0.623712	+	0.781654i	$0.714376\pi$
$468$	19.1261	0.884106
$469$	−17.5816	−0.811842
$470$	−111.153	−5.12711
$471$	−6.89894	−0.317886
$472$	58.6399	2.69912
$473$	−13.7728	−0.633275
$474$	−5.81111	−0.266913
$475$	−54.8248	−2.51553
$476$	150.573	6.90152
$477$	−11.2466	−0.514944
$478$	20.8463	0.953490
$479$	−26.5811	−1.21452	−0.607261	−	0.794502i	$-0.707732\pi$
$479$	−26.5811	−1.21452	−0.607261	+	0.794502i	$0.707732\pi$
$480$	73.7976	3.36839
$481$	−10.5155	−0.479464
$482$	17.8267	0.811985
$483$	−16.0001	−0.728028
$484$	−47.7858	−2.17208
$485$	−4.73473	−0.214993
$486$	−38.5373	−1.74809
$487$	0.891424	0.0403943	0.0201971	−	0.999796i	$-0.493571\pi$
$487$	0.891424	0.0403943	0.0201971	+	0.999796i	$0.493571\pi$
$488$	15.3335	0.694113
$489$	−13.5606	−0.613230
$490$	43.5492	1.96735
$491$	2.99797	0.135296	0.0676482	−	0.997709i	$-0.478450\pi$
$491$	2.99797	0.135296	0.0676482	+	0.997709i	$0.478450\pi$
$492$	−8.19294	−0.369366
$493$	−48.7684	−2.19642
$494$	−21.2154	−0.954525
$495$	−17.0171	−0.764863
$496$	83.6397	3.75554
$497$	−19.2588	−0.863876
$498$	−22.5626	−1.01106
$499$	3.85489	0.172569	0.0862843	−	0.996271i	$-0.472501\pi$
$499$	3.85489	0.172569	0.0862843	+	0.996271i	$0.472501\pi$
$500$	−85.3892	−3.81872
$501$	1.93361	0.0863873
$502$	1.49113	0.0665525
$503$	−22.6365	−1.00931	−0.504656	−	0.863321i	$-0.668381\pi$
$503$	−22.6365	−1.00931	−0.504656	+	0.863321i	$0.668381\pi$
$504$	−98.8674	−4.40391
$505$	6.59344	0.293404
$506$	39.1746	1.74152
$507$	−6.89104	−0.306042
$508$	−67.3105	−2.98642
$509$	−4.37885	−0.194089	−0.0970446	−	0.995280i	$-0.530939\pi$
$509$	−4.37885	−0.194089	−0.0970446	+	0.995280i	$0.530939\pi$
$510$	−47.4310	−2.10028
$511$	−3.71712	−0.164436
$512$	−212.207	−9.37833
$513$	20.9050	0.922976
$514$	−37.1791	−1.63990
$515$	−1.38568	−0.0610603
$516$	28.3933	1.24995
$517$	18.3128	0.805394
$518$	81.7454	3.59168
$519$	−10.8641	−0.476882
$520$	−50.5478	−2.21667
$521$	−1.64330	−0.0719944	−0.0359972	−	0.999352i	$-0.511461\pi$
$521$	−1.64330	−0.0719944	−0.0359972	+	0.999352i	$0.511461\pi$
$522$	48.1562	2.10774
$523$	34.8130	1.52227	0.761133	−	0.648596i	$-0.224644\pi$
$523$	34.8130	1.52227	0.761133	+	0.648596i	$0.224644\pi$
$524$	115.232	5.03395
$525$	−17.6475	−0.770199
$526$	42.7216	1.86275
$527$	−32.0876	−1.39776
$528$	−20.3690	−0.886448
$529$	41.3019	1.79573
$530$	44.6995	1.94162
$531$	13.8303	0.600184
$532$	123.535	5.35591
$533$	2.78420	0.120597
$534$	5.20659	0.225311
$535$	23.6509	1.02252
$536$	−59.0100	−2.54884
$537$	9.63238	0.415668
$538$	−44.4319	−1.91560
$539$	−7.17484	−0.309042
$540$	74.9047	3.22339
$541$	17.6864	0.760397	0.380198	−	0.924905i	$-0.375856\pi$
$541$	17.6864	0.760397	0.380198	+	0.924905i	$0.375856\pi$
$542$	−38.8847	−1.67024
$543$	10.3845	0.445640
$544$	250.736	10.7502
$545$	−56.6516	−2.42669
$546$	−6.82899	−0.292254
$547$	−29.2416	−1.25028	−0.625141	−	0.780512i	$-0.714959\pi$
$547$	−29.2416	−1.25028	−0.625141	+	0.780512i	$0.714959\pi$
$548$	22.4934	0.960869
$549$	3.61641	0.154345
$550$	43.2081	1.84240
$551$	−40.0110	−1.70453
$552$	−53.7019	−2.28570
$553$	−11.4989	−0.488985
$554$	−71.5460	−3.03970
$555$	−19.2877	−0.818718
$556$	6.47748	0.274706
$557$	−11.4800	−0.486424	−0.243212	−	0.969973i	$-0.578201\pi$
$557$	−11.4800	−0.486424	−0.243212	+	0.969973i	$0.578201\pi$
$558$	31.6848	1.34132
$559$	−9.64888	−0.408104
$560$	244.645	10.3381
$561$	7.81439	0.329924
$562$	−11.4102	−0.481311
$563$	30.5148	1.28604	0.643022	−	0.765848i	$-0.277680\pi$
$563$	30.5148	1.28604	0.643022	+	0.765848i	$0.277680\pi$
$564$	−37.7526	−1.58967
$565$	61.8009	2.59998
$566$	74.9645	3.15099
$567$	−19.7405	−0.829023
$568$	−64.6394	−2.71221
$569$	26.0219	1.09090	0.545448	−	0.838145i	$-0.316360\pi$
$569$	26.0219	1.09090	0.545448	+	0.838145i	$0.316360\pi$
$570$	−38.9138	−1.62992
$571$	14.5536	0.609051	0.304526	−	0.952504i	$-0.401502\pi$
$571$	14.5536	0.609051	0.304526	+	0.952504i	$0.401502\pi$
$572$	12.5240	0.523655
$573$	−3.43820	−0.143633
$574$	−21.6439	−0.903398
$575$	70.9226	2.95768
$576$	−143.493	−5.97886
$577$	35.6134	1.48261	0.741304	−	0.671170i	$-0.234208\pi$
$577$	35.6134	1.48261	0.741304	+	0.671170i	$0.234208\pi$
$578$	−113.162	−4.70691
$579$	−5.24252	−0.217872
$580$	−143.364	−5.95285
$581$	−44.6466	−1.85226
$582$	−2.14693	−0.0889930
$583$	−7.36437	−0.305001
$584$	−12.4760	−0.516259
$585$	−11.9218	−0.492904
$586$	25.3113	1.04560
$587$	39.6508	1.63656	0.818282	−	0.574817i	$-0.194927\pi$
$587$	39.6508	1.63656	0.818282	+	0.574817i	$0.194927\pi$
$588$	14.7913	0.609982
$589$	−26.3256	−1.08473
$590$	−54.9687	−2.26302
$591$	−8.15405	−0.335413
$592$	170.817	7.02054
$593$	17.3506	0.712504	0.356252	−	0.934390i	$-0.384054\pi$
$593$	17.3506	0.712504	0.356252	+	0.934390i	$0.384054\pi$
$594$	−16.4755	−0.675997
$595$	−93.8559	−3.84772
$596$	49.0179	2.00785
$597$	−4.46903	−0.182905
$598$	27.4447	1.12230
$599$	−12.0996	−0.494378	−0.247189	−	0.968967i	$-0.579507\pi$
$599$	−12.0996	−0.494378	−0.247189	+	0.968967i	$0.579507\pi$
$600$	−59.2312	−2.41810
$601$	−9.13920	−0.372796	−0.186398	−	0.982474i	$-0.559681\pi$
$601$	−9.13920	−0.372796	−0.186398	+	0.982474i	$0.559681\pi$
$602$	75.0087	3.05713
$603$	−13.9176	−0.566768
$604$	−49.0282	−1.99493
$605$	29.7860	1.21097
$606$	2.98975	0.121450
$607$	−11.7739	−0.477888	−0.238944	−	0.971033i	$-0.576801\pi$
$607$	−11.7739	−0.477888	−0.238944	+	0.971033i	$0.576801\pi$
$608$	205.711	8.34269
$609$	−12.8791	−0.521887
$610$	−14.3735	−0.581965
$611$	12.8294	0.519024
$612$	119.194	4.81813
$613$	25.4704	1.02874	0.514370	−	0.857568i	$-0.328026\pi$
$613$	25.4704	1.02874	0.514370	+	0.857568i	$0.328026\pi$
$614$	67.5578	2.72641
$615$	5.10685	0.205928
$616$	−64.7395	−2.60843
$617$	−18.4710	−0.743616	−0.371808	−	0.928310i	$-0.621262\pi$
$617$	−18.4710	−0.743616	−0.371808	+	0.928310i	$0.621262\pi$
$618$	−0.628325	−0.0252749
$619$	−6.14925	−0.247159	−0.123580	−	0.992335i	$-0.539437\pi$
$619$	−6.14925	−0.247159	−0.123580	+	0.992335i	$0.539437\pi$
$620$	−94.3274	−3.78828
$621$	−27.0431	−1.08520
$622$	−74.9211	−3.00406
$623$	10.3027	0.412770
$624$	−14.2700	−0.571258
$625$	9.00257	0.360103
$626$	25.3917	1.01486
$627$	6.41115	0.256036
$628$	−68.9061	−2.74965
$629$	−65.5324	−2.61295
$630$	92.6776	3.69237
$631$	−22.6156	−0.900314	−0.450157	−	0.892949i	$-0.648632\pi$
$631$	−22.6156	−0.900314	−0.450157	+	0.892949i	$0.648632\pi$
$632$	−38.5945	−1.53521
$633$	−1.48193	−0.0589012
$634$	−59.6180	−2.36773
$635$	41.9562	1.66498
$636$	15.1820	0.602005
$637$	−5.02651	−0.199158
$638$	31.5332	1.24841
$639$	−15.2453	−0.603094
$640$	323.355	12.7817
$641$	22.1009	0.872931	0.436466	−	0.899721i	$-0.356230\pi$
$641$	22.1009	0.872931	0.436466	+	0.899721i	$0.356230\pi$
$642$	10.7243	0.423255
$643$	−6.33196	−0.249708	−0.124854	−	0.992175i	$-0.539846\pi$
$643$	−6.33196	−0.249708	−0.124854	+	0.992175i	$0.539846\pi$
$644$	−159.807	−6.29730
$645$	−17.6982	−0.696866
$646$	−132.214	−5.20190
$647$	37.1000	1.45855	0.729275	−	0.684221i	$-0.239858\pi$
$647$	37.1000	1.45855	0.729275	+	0.684221i	$0.239858\pi$
$648$	−66.2561	−2.60279
$649$	9.05624	0.355488
$650$	30.2705	1.18731
$651$	−8.47391	−0.332119
$652$	−135.442	−5.30432
$653$	19.0530	0.745603	0.372802	−	0.927911i	$-0.378397\pi$
$653$	19.0530	0.745603	0.372802	+	0.927911i	$0.378397\pi$
$654$	−25.6883	−1.00449
$655$	−71.8270	−2.80651
$656$	−45.2276	−1.76584
$657$	−2.94247	−0.114797
$658$	−99.7338	−3.88803
$659$	−31.2605	−1.21773	−0.608867	−	0.793272i	$-0.708376\pi$
$659$	−31.2605	−1.21773	−0.608867	+	0.793272i	$0.708376\pi$
$660$	22.9718	0.894177
$661$	−15.6698	−0.609485	−0.304742	−	0.952435i	$-0.598570\pi$
$661$	−15.6698	−0.609485	−0.304742	+	0.952435i	$0.598570\pi$
$662$	−51.1882	−1.98948
$663$	5.47456	0.212614
$664$	−149.850	−5.81531
$665$	−77.0020	−2.98601
$666$	64.7097	2.50745
$667$	51.7592	2.00412
$668$	19.3127	0.747233
$669$	−1.97093	−0.0762004
$670$	55.3156	2.13703
$671$	2.36807	0.0914183
$672$	66.2161	2.55434
$673$	17.8506	0.688091	0.344046	−	0.938953i	$-0.388202\pi$
$673$	17.8506	0.688091	0.344046	+	0.938953i	$0.388202\pi$
$674$	2.38530	0.0918782
$675$	−29.8276	−1.14806
$676$	−68.8273	−2.64720
$677$	17.8879	0.687487	0.343744	−	0.939064i	$-0.388305\pi$
$677$	17.8879	0.687487	0.343744	+	0.939064i	$0.388305\pi$
$678$	28.0232	1.07622
$679$	−4.24831	−0.163035
$680$	−315.014	−12.0802
$681$	−2.71792	−0.104151
$682$	20.7476	0.794465
$683$	32.2057	1.23232	0.616158	−	0.787622i	$-0.288688\pi$
$683$	32.2057	1.23232	0.616158	+	0.787622i	$0.288688\pi$
$684$	97.7902	3.73910
$685$	−14.0206	−0.535701
$686$	−26.8982	−1.02698
$687$	10.3471	0.394768
$688$	156.740	5.97565
$689$	−5.15928	−0.196553
$690$	50.3398	1.91640
$691$	16.6742	0.634318	0.317159	−	0.948372i	$-0.397271\pi$
$691$	16.6742	0.634318	0.317159	+	0.948372i	$0.397271\pi$
$692$	−108.510	−4.12493
$693$	−15.2689	−0.580017
$694$	28.4966	1.08172
$695$	−4.03756	−0.153153
$696$	−43.2268	−1.63851
$697$	17.3511	0.657222
$698$	−79.9121	−3.02472
$699$	−11.6654	−0.441226
$700$	−176.262	−6.66207
$701$	19.4301	0.733866	0.366933	−	0.930247i	$-0.380408\pi$
$701$	19.4301	0.733866	0.366933	+	0.930247i	$0.380408\pi$
$702$	−11.5423	−0.435636
$703$	−53.7646	−2.02777
$704$	−93.9605	−3.54127
$705$	23.5321	0.886269
$706$	−74.4964	−2.80371
$707$	5.91607	0.222497
$708$	−18.6699	−0.701656
$709$	8.64155	0.324540	0.162270	−	0.986746i	$-0.448118\pi$
$709$	8.64155	0.324540	0.162270	+	0.986746i	$0.448118\pi$
$710$	60.5925	2.27400
$711$	−9.10257	−0.341373
$712$	34.5796	1.29593
$713$	34.0554	1.27538
$714$	−42.5583	−1.59270
$715$	−7.80650	−0.291947
$716$	96.2076	3.59545
$717$	−4.41336	−0.164820
$718$	−39.3013	−1.46671
$719$	30.7036	1.14505	0.572526	−	0.819887i	$-0.305964\pi$
$719$	30.7036	1.14505	0.572526	+	0.819887i	$0.305964\pi$
$720$	193.661	7.21733
$721$	−1.24332	−0.0463037
$722$	−54.8352	−2.04076
$723$	−3.77408	−0.140359
$724$	103.719	3.85470
$725$	57.0884	2.12021
$726$	13.5062	0.501264
$727$	−43.7061	−1.62097	−0.810484	−	0.585761i	$-0.800796\pi$
$727$	−43.7061	−1.62097	−0.810484	+	0.585761i	$0.800796\pi$
$728$	−45.3548	−1.68096
$729$	−9.57992	−0.354812
$730$	11.6949	0.432847
$731$	−60.1318	−2.22406
$732$	−4.88189	−0.180440
$733$	−4.07363	−0.150463	−0.0752314	−	0.997166i	$-0.523970\pi$
$733$	−4.07363	−0.150463	−0.0752314	+	0.997166i	$0.523970\pi$
$734$	−70.9124	−2.61742
$735$	−9.21974	−0.340075
$736$	−266.113	−9.80905
$737$	−9.11339	−0.335696
$738$	−17.1333	−0.630686
$739$	−27.6548	−1.01730	−0.508648	−	0.860974i	$-0.669855\pi$
$739$	−27.6548	−1.01730	−0.508648	+	0.860974i	$0.669855\pi$
$740$	−192.644	−7.08175
$741$	4.49148	0.164999
$742$	40.1074	1.47239
$743$	23.7394	0.870914	0.435457	−	0.900210i	$-0.356587\pi$
$743$	23.7394	0.870914	0.435457	+	0.900210i	$0.356587\pi$
$744$	−28.4414	−1.04271
$745$	−30.5540	−1.11941
$746$	−22.2997	−0.816450
$747$	−35.3423	−1.29311
$748$	78.0496	2.85378
$749$	21.2211	0.775403
$750$	24.1345	0.881267
$751$	23.5186	0.858207	0.429103	−	0.903255i	$-0.358830\pi$
$751$	23.5186	0.858207	0.429103	+	0.903255i	$0.358830\pi$
$752$	−208.406	−7.59979
$753$	−0.315686	−0.0115042
$754$	22.0913	0.804519
$755$	30.5604	1.11221
$756$	67.2095	2.44438
$757$	−16.6457	−0.604998	−0.302499	−	0.953150i	$-0.597821\pi$
$757$	−16.6457	−0.604998	−0.302499	+	0.953150i	$0.597821\pi$
$758$	−57.4697	−2.08739
$759$	−8.29361	−0.301039
$760$	−258.446	−9.37483
$761$	−14.4908	−0.525290	−0.262645	−	0.964892i	$-0.584595\pi$
$761$	−14.4908	−0.525290	−0.262645	+	0.964892i	$0.584595\pi$
$762$	19.0247	0.689193
$763$	−50.8316	−1.84023
$764$	−34.3405	−1.24239
$765$	−74.2964	−2.68619
$766$	29.9519	1.08221
$767$	6.34457	0.229089
$768$	81.7230	2.94892
$769$	16.7576	0.604294	0.302147	−	0.953261i	$-0.402297\pi$
$769$	16.7576	0.604294	0.302147	+	0.953261i	$0.402297\pi$
$770$	60.6863	2.18698
$771$	7.87114	0.283472
$772$	−52.3620	−1.88455
$773$	7.02025	0.252501	0.126250	−	0.991998i	$-0.459706\pi$
$773$	7.02025	0.252501	0.126250	+	0.991998i	$0.459706\pi$
$774$	59.3769	2.13426
$775$	37.5619	1.34926
$776$	−14.2588	−0.511863
$777$	−17.3062	−0.620857
$778$	−57.5619	−2.06369
$779$	14.2354	0.510035
$780$	16.0935	0.576239
$781$	−9.98278	−0.357212
$782$	171.035	6.11622
$783$	−21.7681	−0.777929
$784$	81.6524	2.91616
$785$	42.9508	1.53298
$786$	−32.5694	−1.16171
$787$	8.73854	0.311495	0.155748	−	0.987797i	$-0.450221\pi$
$787$	8.73854	0.311495	0.155748	+	0.987797i	$0.450221\pi$
$788$	−81.4421	−2.90125
$789$	−9.04455	−0.321995
$790$	36.1782	1.28716
$791$	55.4519	1.97164
$792$	−51.2478	−1.82101
$793$	1.65901	0.0589131
$794$	50.2343	1.78275
$795$	−9.46328	−0.335628
$796$	−44.6364	−1.58209
$797$	−13.4158	−0.475211	−0.237606	−	0.971362i	$-0.576363\pi$
$797$	−13.4158	−0.475211	−0.237606	+	0.971362i	$0.576363\pi$
$798$	−34.9160	−1.23601
$799$	79.9531	2.82854
$800$	−293.513	−10.3772
$801$	8.15565	0.288166
$802$	97.4021	3.43939
$803$	−1.92676	−0.0679940
$804$	18.7877	0.662590
$805$	99.6116	3.51085
$806$	14.5352	0.511981
$807$	9.40664	0.331129
$808$	19.8564	0.698547
$809$	25.8973	0.910501	0.455251	−	0.890363i	$-0.349550\pi$
$809$	25.8973	0.910501	0.455251	+	0.890363i	$0.349550\pi$
$810$	62.1080	2.18225
$811$	−46.1281	−1.61978	−0.809889	−	0.586583i	$-0.800473\pi$
$811$	−46.1281	−1.61978	−0.809889	+	0.586583i	$0.800473\pi$
$812$	−128.635	−4.51422
$813$	8.23223	0.288717
$814$	42.3726	1.48516
$815$	84.4241	2.95725
$816$	−88.9307	−3.11320
$817$	−49.3338	−1.72597
$818$	−5.66194	−0.197965
$819$	−10.6970	−0.373783
$820$	51.0069	1.78124
$821$	−26.7987	−0.935279	−0.467640	−	0.883919i	$-0.654896\pi$
$821$	−26.7987	−0.935279	−0.467640	+	0.883919i	$0.654896\pi$
$822$	−6.35755	−0.221745
$823$	−29.5607	−1.03042	−0.515210	−	0.857064i	$-0.672286\pi$
$823$	−29.5607	−1.03042	−0.515210	+	0.857064i	$0.672286\pi$
$824$	−4.17303	−0.145374
$825$	−9.14755	−0.318477
$826$	−49.3215	−1.71612
$827$	37.6739	1.31005	0.655025	−	0.755607i	$-0.272658\pi$
$827$	37.6739	1.31005	0.655025	+	0.755607i	$0.272658\pi$
$828$	−126.504	−4.39631
$829$	−42.5447	−1.47764	−0.738820	−	0.673903i	$-0.764616\pi$
$829$	−42.5447	−1.47764	−0.738820	+	0.673903i	$0.764616\pi$
$830$	140.468	4.87573
$831$	15.1469	0.525441
$832$	−65.8263	−2.28212
$833$	−31.3252	−1.08535
$834$	−1.83080	−0.0633955
$835$	−12.0381	−0.416595
$836$	64.0341	2.21466
$837$	−14.3225	−0.495059
$838$	78.3403	2.70622
$839$	−31.2272	−1.07808	−0.539042	−	0.842279i	$-0.681213\pi$
$839$	−31.2272	−1.07808	−0.539042	+	0.842279i	$0.681213\pi$
$840$	−83.1909	−2.87036
$841$	12.6630	0.436656
$842$	66.8689	2.30446
$843$	2.41565	0.0831993
$844$	−14.8014	−0.509484
$845$	42.9016	1.47586
$846$	−78.9494	−2.71434
$847$	26.7260	0.918315
$848$	83.8093	2.87802
$849$	−15.8707	−0.544680
$850$	188.646	6.47050
$851$	69.5512	2.38418
$852$	20.5800	0.705059
$853$	−45.0494	−1.54246	−0.771230	−	0.636556i	$-0.780358\pi$
$853$	−45.0494	−1.54246	−0.771230	+	0.636556i	$0.780358\pi$
$854$	−12.8968	−0.441320
$855$	−60.9548	−2.08461
$856$	71.2257	2.43444
$857$	53.3004	1.82071	0.910354	−	0.413831i	$-0.135810\pi$
$857$	53.3004	1.82071	0.910354	+	0.413831i	$0.135810\pi$
$858$	−3.53980	−0.120847
$859$	10.3211	0.352151	0.176076	−	0.984377i	$-0.443660\pi$
$859$	10.3211	0.352151	0.176076	+	0.984377i	$0.443660\pi$
$860$	−176.769	−6.02776
$861$	4.58220	0.156161
$862$	−103.927	−3.53975
$863$	20.3151	0.691535	0.345767	−	0.938320i	$-0.387619\pi$
$863$	20.3151	0.691535	0.345767	+	0.938320i	$0.387619\pi$
$864$	111.918	3.80752
$865$	67.6368	2.29972
$866$	−90.3729	−3.07100
$867$	23.9573	0.813634
$868$	−84.6368	−2.87276
$869$	−5.96046	−0.202195
$870$	40.5205	1.37377
$871$	−6.38460	−0.216334
$872$	−170.609	−5.77755
$873$	−3.36297	−0.113819
$874$	140.322	4.74647
$875$	47.7570	1.61448
$876$	3.97212	0.134205
$877$	−32.9289	−1.11193	−0.555964	−	0.831206i	$-0.687651\pi$
$877$	−32.9289	−1.11193	−0.555964	+	0.831206i	$0.687651\pi$
$878$	−72.6453	−2.45166
$879$	−5.35862	−0.180742
$880$	126.812	4.27482
$881$	−47.1149	−1.58734	−0.793671	−	0.608347i	$-0.791833\pi$
$881$	−47.1149	−1.58734	−0.793671	+	0.608347i	$0.791833\pi$
$882$	30.9319	1.04153
$883$	−11.5259	−0.387876	−0.193938	−	0.981014i	$-0.562126\pi$
$883$	−11.5259	−0.387876	−0.193938	+	0.981014i	$0.562126\pi$
$884$	54.6795	1.83907
$885$	11.6374	0.391185
$886$	−21.5741	−0.724797
$887$	−10.4567	−0.351103	−0.175552	−	0.984470i	$-0.556171\pi$
$887$	−10.4567	−0.351103	−0.175552	+	0.984470i	$0.556171\pi$
$888$	−58.0858	−1.94923
$889$	37.6459	1.26260
$890$	−32.4147	−1.08654
$891$	−10.2325	−0.342800
$892$	−19.6855	−0.659118
$893$	65.5958	2.19508
$894$	−13.8545	−0.463363
$895$	−59.9684	−2.00452
$896$	290.135	9.69274
$897$	−5.81029	−0.194000
$898$	−43.2904	−1.44462
$899$	27.4126	0.914260
$900$	−139.529	−4.65096
$901$	−32.1527	−1.07116
$902$	−11.2191	−0.373555
$903$	−15.8800	−0.528454
$904$	186.116	6.19013
$905$	−64.6506	−2.14906
$906$	13.8574	0.460381
$907$	−26.2290	−0.870921	−0.435460	−	0.900208i	$-0.643414\pi$
$907$	−26.2290	−0.870921	−0.435460	+	0.900208i	$0.643414\pi$
$908$	−27.1464	−0.900884
$909$	4.68317	0.155331
$910$	42.5153	1.40937
$911$	−41.5288	−1.37591	−0.687955	−	0.725754i	$-0.741491\pi$
$911$	−41.5288	−1.37591	−0.687955	+	0.725754i	$0.741491\pi$
$912$	−72.9613	−2.41599
$913$	−23.1425	−0.765906
$914$	−36.6007	−1.21064
$915$	3.04299	0.100598
$916$	103.346	3.41466
$917$	−64.4479	−2.12826
$918$	−71.9316	−2.37410
$919$	−26.5966	−0.877342	−0.438671	−	0.898648i	$-0.644551\pi$
$919$	−26.5966	−0.877342	−0.438671	+	0.898648i	$0.644551\pi$
$920$	334.332	11.0226
$921$	−14.3026	−0.471286
$922$	47.3674	1.55996
$923$	−6.99368	−0.230200
$924$	20.6118	0.678080
$925$	76.7124	2.52229
$926$	40.1080	1.31803
$927$	−0.984214	−0.0323258
$928$	−214.205	−7.03162
$929$	−0.722654	−0.0237095	−0.0118548	−	0.999930i	$-0.503774\pi$
$929$	−0.722654	−0.0237095	−0.0118548	+	0.999930i	$0.503774\pi$
$930$	26.6608	0.874242
$931$	−25.7001	−0.842286
$932$	−116.513	−3.81651
$933$	15.8615	0.519281
$934$	76.0998	2.49006
$935$	−48.6501	−1.59103
$936$	−35.9029	−1.17352
$937$	−36.8844	−1.20496	−0.602480	−	0.798134i	$-0.705821\pi$
$937$	−36.8844	−1.20496	−0.602480	+	0.798134i	$0.705821\pi$
$938$	49.6328	1.62057
$939$	−5.37566	−0.175428
$940$	235.037	7.66605
$941$	−42.2118	−1.37606	−0.688032	−	0.725680i	$-0.741525\pi$
$941$	−42.2118	−1.37606	−0.688032	+	0.725680i	$0.741525\pi$
$942$	19.4757	0.634553
$943$	−18.4152	−0.599682
$944$	−103.063	−3.35443
$945$	−41.8932	−1.36279
$946$	38.8807	1.26412
$947$	−20.3646	−0.661759	−0.330880	−	0.943673i	$-0.607345\pi$
$947$	−20.3646	−0.661759	−0.330880	+	0.943673i	$0.607345\pi$
$948$	12.2878	0.399088
$949$	−1.34984	−0.0438177
$950$	154.770	5.02141
$951$	12.6217	0.409285
$952$	−282.651	−9.16078
$953$	−15.2645	−0.494464	−0.247232	−	0.968956i	$-0.579521\pi$
$953$	−15.2645	−0.494464	−0.247232	+	0.968956i	$0.579521\pi$
$954$	31.7490	1.02791
$955$	21.4052	0.692656
$956$	−44.0803	−1.42566
$957$	−6.67586	−0.215800
$958$	75.0385	2.42438
$959$	−12.5802	−0.406237
$960$	−120.740	−3.89687
$961$	−12.9637	−0.418183
$962$	29.6852	0.957088
$963$	16.7987	0.541329
$964$	−37.6952	−1.21408
$965$	32.6384	1.05067
$966$	45.1682	1.45326
$967$	15.5696	0.500686	0.250343	−	0.968157i	$-0.419457\pi$
$967$	15.5696	0.500686	0.250343	+	0.968157i	$0.419457\pi$
$968$	89.7019	2.88313
$969$	27.9909	0.899198
$970$	13.3661	0.429161
$971$	11.8525	0.380366	0.190183	−	0.981749i	$-0.439092\pi$
$971$	11.8525	0.380366	0.190183	+	0.981749i	$0.439092\pi$
$972$	81.4885	2.61374
$973$	−3.62277	−0.116141
$974$	−2.51649	−0.0806335
$975$	−6.40853	−0.205237
$976$	−26.9495	−0.862633
$977$	45.3181	1.44985	0.724927	−	0.688825i	$-0.241873\pi$
$977$	45.3181	1.44985	0.724927	+	0.688825i	$0.241873\pi$
$978$	38.2815	1.22411
$979$	5.34041	0.170680
$980$	−92.0862	−2.94158
$981$	−40.2383	−1.28471
$982$	−8.46327	−0.270074
$983$	22.1248	0.705671	0.352835	−	0.935685i	$-0.385218\pi$
$983$	22.1248	0.705671	0.352835	+	0.935685i	$0.385218\pi$
$984$	15.3795	0.490281
$985$	50.7647	1.61750
$986$	137.673	4.38441
$987$	21.1145	0.672083
$988$	44.8606	1.42721
$989$	63.8194	2.02934
$990$	48.0393	1.52679
$991$	−30.2114	−0.959695	−0.479848	−	0.877352i	$-0.659308\pi$
$991$	−30.2114	−0.959695	−0.479848	+	0.877352i	$0.659308\pi$
$992$	−140.938	−4.47479
$993$	10.8370	0.343901
$994$	54.3676	1.72444
$995$	27.8229	0.882045
$996$	47.7094	1.51173
$997$	−24.1425	−0.764601	−0.382301	−	0.924038i	$-0.624868\pi$
$997$	−24.1425	−0.764601	−0.382301	+	0.924038i	$0.624868\pi$
$998$	−10.8823	−0.344475
$999$	−29.2508	−0.925455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.1	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.1	✓	243	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82300 q^{2} +0.597654 q^{3} +5.96933 q^{4} -3.72082 q^{5} -1.68718 q^{6} -3.33856 q^{7} -11.2054 q^{8} -2.64281 q^{9} +O(q^{10})\)	\(q-2.82300 q^{2} +0.597654 q^{3} +5.96933 q^{4} -3.72082 q^{5} -1.68718 q^{6} -3.33856 q^{7} -11.2054 q^{8} -2.64281 q^{9} +10.5039 q^{10} -1.73054 q^{11} +3.56759 q^{12} -1.21237 q^{13} +9.42477 q^{14} -2.22376 q^{15} +19.6942 q^{16} -7.55550 q^{17} +7.46065 q^{18} -6.19875 q^{19} -22.2108 q^{20} -1.99531 q^{21} +4.88532 q^{22} +8.01885 q^{23} -6.69696 q^{24} +8.84449 q^{25} +3.42253 q^{26} -3.37245 q^{27} -19.9290 q^{28} +6.45469 q^{29} +6.27768 q^{30} +4.24692 q^{31} -33.1859 q^{32} -1.03426 q^{33} +21.3292 q^{34} +12.4222 q^{35} -15.7758 q^{36} +8.67346 q^{37} +17.4991 q^{38} -0.724579 q^{39} +41.6933 q^{40} -2.29649 q^{41} +5.63275 q^{42} +7.95868 q^{43} -10.3302 q^{44} +9.83342 q^{45} -22.6372 q^{46} -10.5821 q^{47} +11.7703 q^{48} +4.14601 q^{49} -24.9680 q^{50} -4.51558 q^{51} -7.23705 q^{52} +4.25553 q^{53} +9.52042 q^{54} +6.43903 q^{55} +37.4100 q^{56} -3.70471 q^{57} -18.2216 q^{58} -5.23318 q^{59} -13.2744 q^{60} -1.36840 q^{61} -11.9891 q^{62} +8.82319 q^{63} +54.2955 q^{64} +4.51102 q^{65} +2.91973 q^{66} +5.26621 q^{67} -45.1013 q^{68} +4.79250 q^{69} -35.0678 q^{70} +5.76859 q^{71} +29.6138 q^{72} +1.11339 q^{73} -24.4852 q^{74} +5.28595 q^{75} -37.0023 q^{76} +5.77752 q^{77} +2.04549 q^{78} +3.44428 q^{79} -73.2786 q^{80} +5.91287 q^{81} +6.48299 q^{82} +13.3730 q^{83} -11.9106 q^{84} +28.1127 q^{85} -22.4674 q^{86} +3.85767 q^{87} +19.3914 q^{88} -3.08598 q^{89} -27.7597 q^{90} +4.04758 q^{91} +47.8671 q^{92} +2.53819 q^{93} +29.8733 q^{94} +23.0644 q^{95} -19.8337 q^{96} +1.27250 q^{97} -11.7042 q^{98} +4.57349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more