LMFDB - Embedded newform 6037.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +O(q^{10})$	\(q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +2.75288 q^{10} -2.91069 q^{11} -8.43835 q^{12} -3.14120 q^{13} -2.92951 q^{14} +2.45003 q^{15} +3.42500 q^{16} +6.74170 q^{17} -4.07021 q^{18} +5.77323 q^{19} -4.42199 q^{20} -2.60723 q^{21} +7.07160 q^{22} +4.19239 q^{23} +9.99471 q^{24} -3.71610 q^{25} +7.63161 q^{26} +2.86430 q^{27} +4.70571 q^{28} +3.14378 q^{29} -5.95240 q^{30} +7.21485 q^{31} +0.923640 q^{32} +6.29364 q^{33} -16.3791 q^{34} -1.36628 q^{35} +6.53804 q^{36} +2.54895 q^{37} -14.0262 q^{38} +6.79204 q^{39} +5.23758 q^{40} -3.09135 q^{41} +6.33432 q^{42} -12.7605 q^{43} -11.3592 q^{44} -1.89828 q^{45} -10.1855 q^{46} -0.275255 q^{47} -7.40569 q^{48} -5.54606 q^{49} +9.02835 q^{50} -14.5772 q^{51} -12.2588 q^{52} +11.1705 q^{53} -6.95889 q^{54} +3.29809 q^{55} -5.57363 q^{56} -12.4832 q^{57} -7.63788 q^{58} +11.9945 q^{59} +9.56143 q^{60} +7.71644 q^{61} -17.5286 q^{62} +2.02008 q^{63} -9.09399 q^{64} +3.55927 q^{65} -15.2905 q^{66} -1.90029 q^{67} +26.3101 q^{68} -9.06499 q^{69} +3.31940 q^{70} -9.99754 q^{71} -7.74391 q^{72} +3.08586 q^{73} -6.19273 q^{74} +8.03513 q^{75} +22.5305 q^{76} -3.50970 q^{77} -16.5014 q^{78} +1.25545 q^{79} -3.88084 q^{80} -11.2193 q^{81} +7.51050 q^{82} +12.8657 q^{83} -10.1749 q^{84} -7.63897 q^{85} +31.0019 q^{86} -6.79762 q^{87} +13.4543 q^{88} +7.72452 q^{89} +4.61192 q^{90} -3.78764 q^{91} +16.3612 q^{92} -15.6003 q^{93} +0.668739 q^{94} -6.54161 q^{95} -1.99714 q^{96} +9.59124 q^{97} +13.4743 q^{98} -4.87632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.42952	−1.71793	−0.858966	−	0.512032i	$-0.828893\pi$
$2$	−2.42952	−1.71793	−0.858966	+	0.512032i	$0.828893\pi$
$3$	−2.16225	−1.24837	−0.624187	−	0.781275i	$-0.714570\pi$
$3$	−2.16225	−1.24837	−0.624187	+	0.781275i	$0.714570\pi$
$4$	3.90258	1.95129
$5$	−1.13309	−0.506735	−0.253367	−	0.967370i	$-0.581538\pi$
$5$	−1.13309	−0.506735	−0.253367	+	0.967370i	$0.581538\pi$
$6$	5.25323	2.14462
$7$	1.20579	0.455747	0.227874	−	0.973691i	$-0.426823\pi$
$7$	1.20579	0.455747	0.227874	+	0.973691i	$0.426823\pi$
$8$	−4.62237	−1.63426
$9$	1.67531	0.558437
$10$	2.75288	0.870536
$11$	−2.91069	−0.877607	−0.438804	−	0.898583i	$-0.644598\pi$
$11$	−2.91069	−0.877607	−0.438804	+	0.898583i	$0.644598\pi$
$12$	−8.43835	−2.43594
$13$	−3.14120	−0.871211	−0.435606	−	0.900138i	$-0.643466\pi$
$13$	−3.14120	−0.871211	−0.435606	+	0.900138i	$0.643466\pi$
$14$	−2.92951	−0.782943
$15$	2.45003	0.632594
$16$	3.42500	0.856249
$17$	6.74170	1.63510	0.817551	−	0.575856i	$-0.195331\pi$
$17$	6.74170	1.63510	0.817551	+	0.575856i	$0.195331\pi$
$18$	−4.07021	−0.959357
$19$	5.77323	1.32447	0.662235	−	0.749296i	$-0.269608\pi$
$19$	5.77323	1.32447	0.662235	+	0.749296i	$0.269608\pi$
$20$	−4.42199	−0.988787
$21$	−2.60723	−0.568943
$22$	7.07160	1.50767
$23$	4.19239	0.874175	0.437087	−	0.899419i	$-0.356010\pi$
$23$	4.19239	0.874175	0.437087	+	0.899419i	$0.356010\pi$
$24$	9.99471	2.04016
$25$	−3.71610	−0.743220
$26$	7.63161	1.49668
$27$	2.86430	0.551236
$28$	4.70571	0.889296
$29$	3.14378	0.583784	0.291892	−	0.956451i	$-0.405715\pi$
$29$	3.14378	0.583784	0.291892	+	0.956451i	$0.405715\pi$
$30$	−5.95240	−1.08675
$31$	7.21485	1.29582	0.647912	−	0.761715i	$-0.275642\pi$
$31$	7.21485	1.29582	0.647912	+	0.761715i	$0.275642\pi$
$32$	0.923640	0.163278
$33$	6.29364	1.09558
$34$	−16.3791	−2.80900
$35$	−1.36628	−0.230943
$36$	6.53804	1.08967
$37$	2.54895	0.419044	0.209522	−	0.977804i	$-0.432809\pi$
$37$	2.54895	0.419044	0.209522	+	0.977804i	$0.432809\pi$
$38$	−14.0262	−2.27535
$39$	6.79204	1.08760
$40$	5.23758	0.828134
$41$	−3.09135	−0.482787	−0.241394	−	0.970427i	$-0.577605\pi$
$41$	−3.09135	−0.482787	−0.241394	+	0.970427i	$0.577605\pi$
$42$	6.33432	0.977406
$43$	−12.7605	−1.94596	−0.972978	−	0.230899i	$-0.925833\pi$
$43$	−12.7605	−1.94596	−0.972978	+	0.230899i	$0.925833\pi$
$44$	−11.3592	−1.71247
$45$	−1.89828	−0.282979
$46$	−10.1855	−1.50177
$47$	−0.275255	−0.0401501	−0.0200750	−	0.999798i	$-0.506391\pi$
$47$	−0.275255	−0.0401501	−0.0200750	+	0.999798i	$0.506391\pi$
$48$	−7.40569	−1.06892
$49$	−5.54606	−0.792294
$50$	9.02835	1.27680
$51$	−14.5772	−2.04122
$52$	−12.2588	−1.69999
$53$	11.1705	1.53438	0.767192	−	0.641417i	$-0.221653\pi$
$53$	11.1705	1.53438	0.767192	+	0.641417i	$0.221653\pi$
$54$	−6.95889	−0.946985
$55$	3.29809	0.444714
$56$	−5.57363	−0.744808
$57$	−12.4832	−1.65343
$58$	−7.63788	−1.00290
$59$	11.9945	1.56155	0.780774	−	0.624814i	$-0.214825\pi$
$59$	11.9945	1.56155	0.780774	+	0.624814i	$0.214825\pi$
$60$	9.56143	1.23438
$61$	7.71644	0.987989	0.493995	−	0.869465i	$-0.335536\pi$
$61$	7.71644	0.987989	0.493995	+	0.869465i	$0.335536\pi$
$62$	−17.5286	−2.22614
$63$	2.02008	0.254506
$64$	−9.09399	−1.13675
$65$	3.55927	0.441473
$66$	−15.2905	−1.88214
$67$	−1.90029	−0.232157	−0.116078	−	0.993240i	$-0.537032\pi$
$67$	−1.90029	−0.232157	−0.116078	+	0.993240i	$0.537032\pi$
$68$	26.3101	3.19056
$69$	−9.06499	−1.09130
$70$	3.31940	0.396744
$71$	−9.99754	−1.18649	−0.593245	−	0.805022i	$-0.702153\pi$
$71$	−9.99754	−1.18649	−0.593245	+	0.805022i	$0.702153\pi$
$72$	−7.74391	−0.912629
$73$	3.08586	0.361172	0.180586	−	0.983559i	$-0.442201\pi$
$73$	3.08586	0.361172	0.180586	+	0.983559i	$0.442201\pi$
$74$	−6.19273	−0.719890
$75$	8.03513	0.927817
$76$	22.5305	2.58443
$77$	−3.50970	−0.399967
$78$	−16.5014	−1.86842
$79$	1.25545	0.141249	0.0706245	−	0.997503i	$-0.477501\pi$
$79$	1.25545	0.141249	0.0706245	+	0.997503i	$0.477501\pi$
$80$	−3.88084	−0.433891
$81$	−11.2193	−1.24659
$82$	7.51050	0.829396
$83$	12.8657	1.41220	0.706099	−	0.708114i	$-0.250454\pi$
$83$	12.8657	1.41220	0.706099	+	0.708114i	$0.250454\pi$
$84$	−10.1749	−1.11017
$85$	−7.63897	−0.828563
$86$	31.0019	3.34302
$87$	−6.79762	−0.728781
$88$	13.4543	1.43423
$89$	7.72452	0.818797	0.409399	−	0.912356i	$-0.365739\pi$
$89$	7.72452	0.818797	0.409399	+	0.912356i	$0.365739\pi$
$90$	4.61192	0.486139
$91$	−3.78764	−0.397052
$92$	16.3612	1.70577
$93$	−15.6003	−1.61767
$94$	0.668739	0.0689751
$95$	−6.54161	−0.671155
$96$	−1.99714	−0.203832
$97$	9.59124	0.973843	0.486921	−	0.873446i	$-0.338120\pi$
$97$	9.59124	0.973843	0.486921	+	0.873446i	$0.338120\pi$
$98$	13.4743	1.36111
$99$	−4.87632	−0.490088
$100$	−14.5024	−1.45024
$101$	7.32798	0.729161	0.364580	−	0.931172i	$-0.381212\pi$
$101$	7.32798	0.729161	0.364580	+	0.931172i	$0.381212\pi$
$102$	35.4157	3.50668
$103$	−15.2574	−1.50336	−0.751678	−	0.659530i	$-0.770755\pi$
$103$	−15.2574	−1.50336	−0.751678	+	0.659530i	$0.770755\pi$
$104$	14.5198	1.42378
$105$	2.95423	0.288303
$106$	−27.1390	−2.63597
$107$	12.2896	1.18808	0.594039	−	0.804436i	$-0.297532\pi$
$107$	12.2896	1.18808	0.594039	+	0.804436i	$0.297532\pi$
$108$	11.1782	1.07562
$109$	8.18098	0.783595	0.391798	−	0.920051i	$-0.371853\pi$
$109$	8.18098	0.783595	0.391798	+	0.920051i	$0.371853\pi$
$110$	−8.01278	−0.763988
$111$	−5.51145	−0.523124
$112$	4.12984	0.390233
$113$	11.7704	1.10727	0.553633	−	0.832761i	$-0.313241\pi$
$113$	11.7704	1.10727	0.553633	+	0.832761i	$0.313241\pi$
$114$	30.3281	2.84049
$115$	−4.75037	−0.442974
$116$	12.2688	1.13913
$117$	−5.26248	−0.486517
$118$	−29.1409	−2.68263
$119$	8.12911	0.745194
$120$	−11.3249	−1.03382
$121$	−2.52786	−0.229806
$122$	−18.7473	−1.69730
$123$	6.68426	0.602699
$124$	28.1565	2.52853
$125$	9.87615	0.883350
$126$	−4.90783	−0.437225
$127$	−9.88332	−0.877003	−0.438501	−	0.898731i	$-0.644491\pi$
$127$	−9.88332	−0.877003	−0.438501	+	0.898731i	$0.644491\pi$
$128$	20.2468	1.78958
$129$	27.5913	2.42928
$130$	−8.64732	−0.758420
$131$	2.18432	0.190845	0.0954224	−	0.995437i	$-0.469580\pi$
$131$	2.18432	0.190845	0.0954224	+	0.995437i	$0.469580\pi$
$132$	24.5615	2.13780
$133$	6.96133	0.603624
$134$	4.61679	0.398830
$135$	−3.24552	−0.279330
$136$	−31.1627	−2.67218
$137$	−20.2271	−1.72812	−0.864059	−	0.503391i	$-0.832086\pi$
$137$	−20.2271	−1.72812	−0.864059	+	0.503391i	$0.832086\pi$
$138$	22.0236	1.87477
$139$	−14.8881	−1.26279	−0.631397	−	0.775460i	$-0.717518\pi$
$139$	−14.8881	−1.26279	−0.631397	+	0.775460i	$0.717518\pi$
$140$	−5.33201	−0.450637
$141$	0.595170	0.0501223
$142$	24.2892	2.03831
$143$	9.14306	0.764581
$144$	5.73793	0.478161
$145$	−3.56219	−0.295824
$146$	−7.49716	−0.620469
$147$	11.9919	0.989079
$148$	9.94748	0.817678
$149$	−16.9803	−1.39108	−0.695541	−	0.718486i	$-0.744835\pi$
$149$	−16.9803	−1.39108	−0.695541	+	0.718486i	$0.744835\pi$
$150$	−19.5215	−1.59393
$151$	−11.0082	−0.895838	−0.447919	−	0.894074i	$-0.647835\pi$
$151$	−11.0082	−0.895838	−0.447919	+	0.894074i	$0.647835\pi$
$152$	−26.6860	−2.16452
$153$	11.2944	0.913102
$154$	8.52690	0.687117
$155$	−8.17509	−0.656639
$156$	26.5065	2.12222
$157$	9.18206	0.732808	0.366404	−	0.930456i	$-0.380589\pi$
$157$	9.18206	0.732808	0.366404	+	0.930456i	$0.380589\pi$
$158$	−3.05014	−0.242656
$159$	−24.1534	−1.91549
$160$	−1.04657	−0.0827386
$161$	5.05517	0.398403
$162$	27.2575	2.14155
$163$	16.7118	1.30897	0.654484	−	0.756076i	$-0.272886\pi$
$163$	16.7118	1.30897	0.654484	+	0.756076i	$0.272886\pi$
$164$	−12.0642	−0.942059
$165$	−7.13128	−0.555169
$166$	−31.2576	−2.42606
$167$	8.47487	0.655805	0.327903	−	0.944711i	$-0.393658\pi$
$167$	8.47487	0.655805	0.327903	+	0.944711i	$0.393658\pi$
$168$	12.0516	0.929799
$169$	−3.13288	−0.240991
$170$	18.5591	1.42342
$171$	9.67196	0.739634
$172$	−49.7989	−3.79713
$173$	4.51158	0.343009	0.171504	−	0.985183i	$-0.445137\pi$
$173$	4.51158	0.343009	0.171504	+	0.985183i	$0.445137\pi$
$174$	16.5150	1.25200
$175$	−4.48085	−0.338721
$176$	−9.96911	−0.751450
$177$	−25.9350	−1.94939
$178$	−18.7669	−1.40664
$179$	−23.7476	−1.77498	−0.887490	−	0.460827i	$-0.847553\pi$
$179$	−23.7476	−1.77498	−0.887490	+	0.460827i	$0.847553\pi$
$180$	−7.40821	−0.552175
$181$	7.82315	0.581490	0.290745	−	0.956801i	$-0.406097\pi$
$181$	7.82315	0.581490	0.290745	+	0.956801i	$0.406097\pi$
$182$	9.20215	0.682109
$183$	−16.6849	−1.23338
$184$	−19.3788	−1.42862
$185$	−2.88819	−0.212344
$186$	37.9012	2.77905
$187$	−19.6230	−1.43498
$188$	−1.07421	−0.0783445
$189$	3.45376	0.251224
$190$	15.8930	1.15300
$191$	−12.2823	−0.888719	−0.444359	−	0.895849i	$-0.646569\pi$
$191$	−12.2823	−0.888719	−0.444359	+	0.895849i	$0.646569\pi$
$192$	19.6635	1.41909
$193$	−13.4364	−0.967170	−0.483585	−	0.875297i	$-0.660666\pi$
$193$	−13.4364	−0.967170	−0.483585	+	0.875297i	$0.660666\pi$
$194$	−23.3021	−1.67300
$195$	−7.69601	−0.551123
$196$	−21.6440	−1.54600
$197$	−13.0669	−0.930979	−0.465490	−	0.885053i	$-0.654122\pi$
$197$	−13.0669	−0.930979	−0.465490	+	0.885053i	$0.654122\pi$
$198$	11.8471	0.841939
$199$	−6.91379	−0.490105	−0.245053	−	0.969510i	$-0.578805\pi$
$199$	−6.91379	−0.490105	−0.245053	+	0.969510i	$0.578805\pi$
$200$	17.1772	1.21461
$201$	4.10889	0.289819
$202$	−17.8035	−1.25265
$203$	3.79075	0.266058
$204$	−56.8888	−3.98302
$205$	3.50278	0.244645
$206$	37.0682	2.58266
$207$	7.02357	0.488172
$208$	−10.7586	−0.745974
$209$	−16.8041	−1.16237
$210$	−7.17737	−0.495285
$211$	15.5687	1.07179	0.535897	−	0.844284i	$-0.319974\pi$
$211$	15.5687	1.07179	0.535897	+	0.844284i	$0.319974\pi$
$212$	43.5938	2.99403
$213$	21.6171	1.48118
$214$	−29.8578	−2.04104
$215$	14.4588	0.986083
$216$	−13.2399	−0.900860
$217$	8.69962	0.590569
$218$	−19.8759	−1.34616
$219$	−6.67238	−0.450878
$220$	12.8711	0.867767
$221$	−21.1770	−1.42452
$222$	13.3902	0.898691
$223$	7.91555	0.530065	0.265032	−	0.964240i	$-0.414617\pi$
$223$	7.91555	0.530065	0.265032	+	0.964240i	$0.414617\pi$
$224$	1.11372	0.0744135
$225$	−6.22563	−0.415042
$226$	−28.5964	−1.90221
$227$	−24.1472	−1.60271	−0.801355	−	0.598190i	$-0.795887\pi$
$227$	−24.1472	−1.60271	−0.801355	+	0.598190i	$0.795887\pi$
$228$	−48.7166	−3.22633
$229$	−21.9075	−1.44769	−0.723845	−	0.689962i	$-0.757627\pi$
$229$	−21.9075	−1.44769	−0.723845	+	0.689962i	$0.757627\pi$
$230$	11.5411	0.761000
$231$	7.58883	0.499309
$232$	−14.5317	−0.954053
$233$	23.0093	1.50739	0.753694	−	0.657225i	$-0.228270\pi$
$233$	23.0093	1.50739	0.753694	+	0.657225i	$0.228270\pi$
$234$	12.7853	0.835803
$235$	0.311890	0.0203454
$236$	46.8094	3.04703
$237$	−2.71459	−0.176332
$238$	−19.7499	−1.28019
$239$	−6.51574	−0.421468	−0.210734	−	0.977543i	$-0.567585\pi$
$239$	−6.51574	−0.421468	−0.210734	+	0.977543i	$0.567585\pi$
$240$	8.39133	0.541658
$241$	−19.2571	−1.24046	−0.620228	−	0.784422i	$-0.712960\pi$
$241$	−19.2571	−1.24046	−0.620228	+	0.784422i	$0.712960\pi$
$242$	6.14150	0.394790
$243$	15.6659	1.00497
$244$	30.1141	1.92786
$245$	6.28420	0.401483
$246$	−16.2396	−1.03540
$247$	−18.1349	−1.15389
$248$	−33.3497	−2.11771
$249$	−27.8189	−1.76295
$250$	−23.9943	−1.51754
$251$	−9.02631	−0.569735	−0.284868	−	0.958567i	$-0.591950\pi$
$251$	−9.02631	−0.569735	−0.284868	+	0.958567i	$0.591950\pi$
$252$	7.88354	0.496616
$253$	−12.2028	−0.767182
$254$	24.0118	1.50663
$255$	16.5173	1.03436
$256$	−31.0021	−1.93763
$257$	14.7742	0.921592	0.460796	−	0.887506i	$-0.347564\pi$
$257$	14.7742	0.921592	0.460796	+	0.887506i	$0.347564\pi$
$258$	−67.0337	−4.17334
$259$	3.07351	0.190978
$260$	13.8903	0.861442
$261$	5.26680	0.326007
$262$	−5.30685	−0.327859
$263$	6.66917	0.411239	0.205619	−	0.978632i	$-0.434079\pi$
$263$	6.66917	0.411239	0.205619	+	0.978632i	$0.434079\pi$
$264$	−29.0915	−1.79046
$265$	−12.6572	−0.777526
$266$	−16.9127	−1.03699
$267$	−16.7023	−1.02217
$268$	−7.41603	−0.453006
$269$	−19.8172	−1.20827	−0.604137	−	0.796880i	$-0.706482\pi$
$269$	−19.8172	−1.20827	−0.604137	+	0.796880i	$0.706482\pi$
$270$	7.88507	0.479870
$271$	19.8253	1.20430	0.602151	−	0.798383i	$-0.294311\pi$
$271$	19.8253	1.20430	0.602151	+	0.798383i	$0.294311\pi$
$272$	23.0903	1.40005
$273$	8.18981	0.495670
$274$	49.1422	2.96879
$275$	10.8164	0.652255
$276$	−35.3769	−2.12944
$277$	17.8817	1.07441	0.537203	−	0.843453i	$-0.319481\pi$
$277$	17.8817	1.07441	0.537203	+	0.843453i	$0.319481\pi$
$278$	36.1710	2.16939
$279$	12.0871	0.723637
$280$	6.31544	0.377420
$281$	−3.24679	−0.193687	−0.0968437	−	0.995300i	$-0.530875\pi$
$281$	−3.24679	−0.193687	−0.0968437	+	0.995300i	$0.530875\pi$
$282$	−1.44598	−0.0861068
$283$	18.3239	1.08924	0.544620	−	0.838683i	$-0.316674\pi$
$283$	18.3239	1.08924	0.544620	+	0.838683i	$0.316674\pi$
$284$	−39.0162	−2.31519
$285$	14.1446	0.837852
$286$	−22.2133	−1.31350
$287$	−3.72753	−0.220029
$288$	1.54738	0.0911805
$289$	28.4505	1.67356
$290$	8.65442	0.508205
$291$	−20.7386	−1.21572
$292$	12.0428	0.704752
$293$	31.9594	1.86709	0.933545	−	0.358460i	$-0.116698\pi$
$293$	31.9594	1.86709	0.933545	+	0.358460i	$0.116698\pi$
$294$	−29.1347	−1.69917
$295$	−13.5908	−0.791290
$296$	−11.7822	−0.684825
$297$	−8.33711	−0.483768
$298$	41.2541	2.38979
$299$	−13.1691	−0.761591
$300$	31.3578	1.81044
$301$	−15.3865	−0.886864
$302$	26.7448	1.53899
$303$	−15.8449	−0.910265
$304$	19.7733	1.13408
$305$	−8.74345	−0.500648
$306$	−27.4401	−1.56865
$307$	−16.9910	−0.969725	−0.484862	−	0.874590i	$-0.661130\pi$
$307$	−16.9910	−0.969725	−0.484862	+	0.874590i	$0.661130\pi$
$308$	−13.6969	−0.780453
$309$	32.9903	1.87675
$310$	19.8616	1.12806
$311$	31.2893	1.77425	0.887126	−	0.461527i	$-0.152698\pi$
$311$	31.2893	1.77425	0.887126	+	0.461527i	$0.152698\pi$
$312$	−31.3954	−1.77741
$313$	4.73998	0.267920	0.133960	−	0.990987i	$-0.457231\pi$
$313$	4.73998	0.267920	0.133960	+	0.990987i	$0.457231\pi$
$314$	−22.3080	−1.25892
$315$	−2.28894	−0.128967
$316$	4.89949	0.275618
$317$	−1.57015	−0.0881884	−0.0440942	−	0.999027i	$-0.514040\pi$
$317$	−1.57015	−0.0881884	−0.0440942	+	0.999027i	$0.514040\pi$
$318$	58.6811	3.29067
$319$	−9.15057	−0.512333
$320$	10.3043	0.576030
$321$	−26.5731	−1.48317
$322$	−12.2816	−0.684429
$323$	38.9214	2.16565
$324$	−43.7841	−2.43245
$325$	11.6730	0.647502
$326$	−40.6017	−2.24872
$327$	−17.6893	−0.978220
$328$	14.2894	0.788998
$329$	−0.331901	−0.0182983
$330$	17.3256	0.953743
$331$	8.75076	0.480986	0.240493	−	0.970651i	$-0.422691\pi$
$331$	8.75076	0.480986	0.240493	+	0.970651i	$0.422691\pi$
$332$	50.2096	2.75561
$333$	4.27028	0.234010
$334$	−20.5899	−1.12663
$335$	2.15320	0.117642
$336$	−8.92973	−0.487157
$337$	−28.8013	−1.56890	−0.784452	−	0.620189i	$-0.787056\pi$
$337$	−28.8013	−1.56890	−0.784452	+	0.620189i	$0.787056\pi$
$338$	7.61141	0.414006
$339$	−25.4505	−1.38228
$340$	−29.8117	−1.61677
$341$	−21.0002	−1.13723
$342$	−23.4983	−1.27064
$343$	−15.1280	−0.816834
$344$	58.9837	3.18019
$345$	10.2715	0.552998
$346$	−10.9610	−0.589266
$347$	−3.55521	−0.190854	−0.0954270	−	0.995436i	$-0.530422\pi$
$347$	−3.55521	−0.190854	−0.0954270	+	0.995436i	$0.530422\pi$
$348$	−26.5283	−1.42207
$349$	0.377854	0.0202261	0.0101130	−	0.999949i	$-0.496781\pi$
$349$	0.377854	0.0202261	0.0101130	+	0.999949i	$0.496781\pi$
$350$	10.8863	0.581899
$351$	−8.99734	−0.480243
$352$	−2.68843	−0.143294
$353$	−12.9341	−0.688412	−0.344206	−	0.938894i	$-0.611852\pi$
$353$	−12.9341	−0.688412	−0.344206	+	0.938894i	$0.611852\pi$
$354$	63.0097	3.34893
$355$	11.3281	0.601235
$356$	30.1456	1.59771
$357$	−17.5771	−0.930281
$358$	57.6954	3.04930
$359$	−4.71116	−0.248646	−0.124323	−	0.992242i	$-0.539676\pi$
$359$	−4.71116	−0.248646	−0.124323	+	0.992242i	$0.539676\pi$
$360$	8.77457	0.462461
$361$	14.3302	0.754223
$362$	−19.0065	−0.998961
$363$	5.46586	0.286883
$364$	−14.7816	−0.774765
$365$	−3.49656	−0.183018
$366$	40.5362	2.11886
$367$	25.8897	1.35143	0.675715	−	0.737163i	$-0.263835\pi$
$367$	25.8897	1.35143	0.675715	+	0.737163i	$0.263835\pi$
$368$	14.3589	0.748511
$369$	−5.17897	−0.269606
$370$	7.01693	0.364793
$371$	13.4693	0.699292
$372$	−60.8814	−3.15655
$373$	−1.31790	−0.0682383	−0.0341192	−	0.999418i	$-0.510863\pi$
$373$	−1.31790	−0.0682383	−0.0341192	+	0.999418i	$0.510863\pi$
$374$	47.6746	2.46520
$375$	−21.3547	−1.10275
$376$	1.27233	0.0656155
$377$	−9.87522	−0.508600
$378$	−8.39100	−0.431586
$379$	31.3631	1.61101	0.805506	−	0.592587i	$-0.201894\pi$
$379$	31.3631	1.61101	0.805506	+	0.592587i	$0.201894\pi$
$380$	−25.5292	−1.30962
$381$	21.3702	1.09483
$382$	29.8402	1.52676
$383$	−25.0157	−1.27824	−0.639122	−	0.769105i	$-0.720702\pi$
$383$	−25.0157	−1.27824	−0.639122	+	0.769105i	$0.720702\pi$
$384$	−43.7786	−2.23407
$385$	3.97681	0.202677
$386$	32.6439	1.66153
$387$	−21.3778	−1.08669
$388$	37.4306	1.90025
$389$	−4.73108	−0.239875	−0.119938	−	0.992781i	$-0.538269\pi$
$389$	−4.73108	−0.239875	−0.119938	+	0.992781i	$0.538269\pi$
$390$	18.6976	0.946792
$391$	28.2639	1.42937
$392$	25.6360	1.29481
$393$	−4.72304	−0.238246
$394$	31.7464	1.59936
$395$	−1.42254	−0.0715757
$396$	−19.0302	−0.956306
$397$	−32.4447	−1.62835	−0.814177	−	0.580617i	$-0.802811\pi$
$397$	−32.4447	−1.62835	−0.814177	+	0.580617i	$0.802811\pi$
$398$	16.7972	0.841968
$399$	−15.0521	−0.753549
$400$	−12.7276	−0.636381
$401$	−5.80611	−0.289943	−0.144972	−	0.989436i	$-0.546309\pi$
$401$	−5.80611	−0.289943	−0.144972	+	0.989436i	$0.546309\pi$
$402$	−9.98264	−0.497889
$403$	−22.6633	−1.12894
$404$	28.5980	1.42281
$405$	12.7125	0.631688
$406$	−9.20971	−0.457070
$407$	−7.41920	−0.367756
$408$	67.3814	3.33587
$409$	−11.3016	−0.558828	−0.279414	−	0.960171i	$-0.590140\pi$
$409$	−11.3016	−0.558828	−0.279414	+	0.960171i	$0.590140\pi$
$410$	−8.51010	−0.420284
$411$	43.7360	2.15734
$412$	−59.5433	−2.93349
$413$	14.4629	0.711671
$414$	−17.0639	−0.838646
$415$	−14.5781	−0.715609
$416$	−2.90133	−0.142250
$417$	32.1918	1.57644
$418$	40.8260	1.99686
$419$	12.7378	0.622283	0.311142	−	0.950364i	$-0.399289\pi$
$419$	12.7378	0.622283	0.311142	+	0.950364i	$0.399289\pi$
$420$	11.5291	0.562564
$421$	−25.2598	−1.23109	−0.615543	−	0.788103i	$-0.711063\pi$
$421$	−25.2598	−1.23109	−0.615543	+	0.788103i	$0.711063\pi$
$422$	−37.8245	−1.84127
$423$	−0.461138	−0.0224213
$424$	−51.6342	−2.50758
$425$	−25.0528	−1.21524
$426$	−52.5193	−2.54457
$427$	9.30444	0.450274
$428$	47.9611	2.31829
$429$	−19.7696	−0.954483
$430$	−35.1280	−1.69402
$431$	24.4161	1.17608	0.588041	−	0.808831i	$-0.299899\pi$
$431$	24.4161	1.17608	0.588041	+	0.808831i	$0.299899\pi$
$432$	9.81023	0.471995
$433$	28.2304	1.35667	0.678333	−	0.734754i	$-0.262703\pi$
$433$	28.2304	1.35667	0.678333	+	0.734754i	$0.262703\pi$
$434$	−21.1359	−1.01456
$435$	7.70233	0.369299
$436$	31.9270	1.52902
$437$	24.2037	1.15782
$438$	16.2107	0.774578
$439$	30.6244	1.46162	0.730810	−	0.682580i	$-0.239142\pi$
$439$	30.6244	1.46162	0.730810	+	0.682580i	$0.239142\pi$
$440$	−15.2450	−0.726776
$441$	−9.29138	−0.442447
$442$	51.4500	2.44723
$443$	9.40752	0.446965	0.223482	−	0.974708i	$-0.428257\pi$
$443$	9.40752	0.446965	0.223482	+	0.974708i	$0.428257\pi$
$444$	−21.5089	−1.02077
$445$	−8.75260	−0.414913
$446$	−19.2310	−0.910615
$447$	36.7157	1.73659
$448$	−10.9655	−0.518071
$449$	−26.1614	−1.23463	−0.617316	−	0.786715i	$-0.711780\pi$
$449$	−26.1614	−1.23463	−0.617316	+	0.786715i	$0.711780\pi$
$450$	15.1253	0.713014
$451$	8.99797	0.423698
$452$	45.9349	2.16060
$453$	23.8025	1.11834
$454$	58.6663	2.75335
$455$	4.29175	0.201200
$456$	57.7018	2.70213
$457$	−37.9355	−1.77455	−0.887274	−	0.461244i	$-0.847403\pi$
$457$	−37.9355	−1.77455	−0.887274	+	0.461244i	$0.847403\pi$
$458$	53.2249	2.48703
$459$	19.3103	0.901327
$460$	−18.5387	−0.864373
$461$	19.6902	0.917066	0.458533	−	0.888677i	$-0.348375\pi$
$461$	19.6902	0.917066	0.458533	+	0.888677i	$0.348375\pi$
$462$	−18.4373	−0.857779
$463$	7.02564	0.326509	0.163255	−	0.986584i	$-0.447801\pi$
$463$	7.02564	0.326509	0.163255	+	0.986584i	$0.447801\pi$
$464$	10.7674	0.499865
$465$	17.6766	0.819731
$466$	−55.9016	−2.58959
$467$	40.9087	1.89303	0.946514	−	0.322662i	$-0.104578\pi$
$467$	40.9087	1.89303	0.946514	+	0.322662i	$0.104578\pi$
$468$	−20.5373	−0.949336
$469$	−2.29135	−0.105805
$470$	−0.757743	−0.0349521
$471$	−19.8539	−0.914819
$472$	−55.4429	−2.55197
$473$	37.1419	1.70778
$474$	6.59516	0.302926
$475$	−21.4539	−0.984373
$476$	31.7245	1.45409
$477$	18.7140	0.856857
$478$	15.8301	0.724054
$479$	−12.7318	−0.581729	−0.290865	−	0.956764i	$-0.593943\pi$
$479$	−12.7318	−0.581729	−0.290865	+	0.956764i	$0.593943\pi$
$480$	2.26294	0.103289
$481$	−8.00674	−0.365076
$482$	46.7855	2.13102
$483$	−10.9305	−0.497356
$484$	−9.86519	−0.448418
$485$	−10.8678	−0.493480
$486$	−38.0607	−1.72647
$487$	−16.1689	−0.732682	−0.366341	−	0.930481i	$-0.619390\pi$
$487$	−16.1689	−0.732682	−0.366341	+	0.930481i	$0.619390\pi$
$488$	−35.6683	−1.61463
$489$	−36.1350	−1.63408
$490$	−15.2676	−0.689720
$491$	7.25375	0.327357	0.163679	−	0.986514i	$-0.447664\pi$
$491$	7.25375	0.327357	0.163679	+	0.986514i	$0.447664\pi$
$492$	26.0859	1.17604
$493$	21.1944	0.954548
$494$	44.0591	1.98231
$495$	5.52532	0.248345
$496$	24.7108	1.10955
$497$	−12.0550	−0.540739
$498$	67.5866	3.02863
$499$	−1.99545	−0.0893285	−0.0446642	−	0.999002i	$-0.514222\pi$
$499$	−1.99545	−0.0893285	−0.0446642	+	0.999002i	$0.514222\pi$
$500$	38.5425	1.72367
$501$	−18.3248	−0.818690
$502$	21.9296	0.978767
$503$	−6.02386	−0.268590	−0.134295	−	0.990941i	$-0.542877\pi$
$503$	−6.02386	−0.268590	−0.134295	+	0.990941i	$0.542877\pi$
$504$	−9.33757	−0.415928
$505$	−8.30328	−0.369491
$506$	29.6469	1.31797
$507$	6.77407	0.300847
$508$	−38.5705	−1.71129
$509$	5.84429	0.259044	0.129522	−	0.991577i	$-0.458656\pi$
$509$	5.84429	0.259044	0.129522	+	0.991577i	$0.458656\pi$
$510$	−40.1293	−1.77695
$511$	3.72091	0.164603
$512$	34.8267	1.53914
$513$	16.5363	0.730095
$514$	−35.8944	−1.58323
$515$	17.2880	0.761802
$516$	107.677	4.74023
$517$	0.801183	0.0352360
$518$	−7.46715	−0.328088
$519$	−9.75515	−0.428203
$520$	−16.4523	−0.721479
$521$	29.9497	1.31212	0.656060	−	0.754708i	$-0.272222\pi$
$521$	29.9497	1.31212	0.656060	+	0.754708i	$0.272222\pi$
$522$	−12.7958	−0.560058
$523$	−24.5879	−1.07516	−0.537578	−	0.843214i	$-0.680661\pi$
$523$	−24.5879	−1.07516	−0.537578	+	0.843214i	$0.680661\pi$
$524$	8.52449	0.372394
$525$	9.68871	0.422850
$526$	−16.2029	−0.706480
$527$	48.6403	2.11881
$528$	21.5557	0.938091
$529$	−5.42383	−0.235819
$530$	30.7510	1.33574
$531$	20.0945	0.872026
$532$	27.1672	1.17785
$533$	9.71053	0.420610
$534$	40.5787	1.75601
$535$	−13.9252	−0.602040
$536$	8.78383	0.379404
$537$	51.3482	2.21584
$538$	48.1463	2.07573
$539$	16.1429	0.695323
$540$	−12.6659	−0.545055
$541$	−25.6420	−1.10244	−0.551219	−	0.834361i	$-0.685837\pi$
$541$	−25.6420	−1.10244	−0.551219	+	0.834361i	$0.685837\pi$
$542$	−48.1660	−2.06891
$543$	−16.9156	−0.725917
$544$	6.22690	0.266976
$545$	−9.26981	−0.397075
$546$	−19.8973	−0.851527
$547$	0.383314	0.0163893	0.00819466	−	0.999966i	$-0.497392\pi$
$547$	0.383314	0.0163893	0.00819466	+	0.999966i	$0.497392\pi$
$548$	−78.9379	−3.37206
$549$	12.9274	0.551730
$550$	−26.2788	−1.12053
$551$	18.1498	0.773205
$552$	41.9018	1.78346
$553$	1.51381	0.0643739
$554$	−43.4440	−1.84576
$555$	6.24499	0.265085
$556$	−58.1021	−2.46408
$557$	10.2543	0.434489	0.217244	−	0.976117i	$-0.430293\pi$
$557$	10.2543	0.434489	0.217244	+	0.976117i	$0.430293\pi$
$558$	−29.3659	−1.24316
$559$	40.0832	1.69534
$560$	−4.67949	−0.197745
$561$	42.4298	1.79139
$562$	7.88816	0.332742
$563$	−7.14626	−0.301179	−0.150589	−	0.988596i	$-0.548117\pi$
$563$	−7.14626	−0.301179	−0.150589	+	0.988596i	$0.548117\pi$
$564$	2.32270	0.0978033
$565$	−13.3369	−0.561089
$566$	−44.5182	−1.87124
$567$	−13.5281	−0.568128
$568$	46.2123	1.93903
$569$	−38.5234	−1.61499	−0.807493	−	0.589878i	$-0.799176\pi$
$569$	−38.5234	−1.61499	−0.807493	+	0.589878i	$0.799176\pi$
$570$	−34.3646	−1.43937
$571$	32.1528	1.34555	0.672776	−	0.739847i	$-0.265102\pi$
$571$	32.1528	1.34555	0.672776	+	0.739847i	$0.265102\pi$
$572$	35.6816	1.49192
$573$	26.5575	1.10945
$574$	9.05612	0.377995
$575$	−15.5794	−0.649704
$576$	−15.2353	−0.634803
$577$	18.6254	0.775384	0.387692	−	0.921789i	$-0.373272\pi$
$577$	18.6254	0.775384	0.387692	+	0.921789i	$0.373272\pi$
$578$	−69.1212	−2.87506
$579$	29.0527	1.20739
$580$	−13.9017	−0.577239
$581$	15.5134	0.643605
$582$	50.3850	2.08852
$583$	−32.5139	−1.34659
$584$	−14.2640	−0.590248
$585$	5.96288	0.246535
$586$	−77.6462	−3.20754
$587$	11.7808	0.486245	0.243123	−	0.969996i	$-0.421828\pi$
$587$	11.7808	0.486245	0.243123	+	0.969996i	$0.421828\pi$
$588$	46.7996	1.92998
$589$	41.6530	1.71628
$590$	33.0193	1.35938
$591$	28.2539	1.16221
$592$	8.73013	0.358806
$593$	16.8458	0.691774	0.345887	−	0.938276i	$-0.387578\pi$
$593$	16.8458	0.691774	0.345887	+	0.938276i	$0.387578\pi$
$594$	20.2552	0.831081
$595$	−9.21103	−0.377615
$596$	−66.2672	−2.71441
$597$	14.9493	0.611835
$598$	31.9947	1.30836
$599$	−27.8880	−1.13947	−0.569736	−	0.821828i	$-0.692955\pi$
$599$	−27.8880	−1.13947	−0.569736	+	0.821828i	$0.692955\pi$
$600$	−37.1414	−1.51629
$601$	−21.4935	−0.876739	−0.438369	−	0.898795i	$-0.644444\pi$
$601$	−21.4935	−0.876739	−0.438369	+	0.898795i	$0.644444\pi$
$602$	37.3819	1.52357
$603$	−3.18357	−0.129645
$604$	−42.9606	−1.74804
$605$	2.86430	0.116450
$606$	38.4955	1.56377
$607$	33.1472	1.34540	0.672702	−	0.739913i	$-0.265133\pi$
$607$	33.1472	1.34540	0.672702	+	0.739913i	$0.265133\pi$
$608$	5.33239	0.216257
$609$	−8.19653	−0.332140
$610$	21.2424	0.860080
$611$	0.864630	0.0349792
$612$	44.0775	1.78173
$613$	37.0620	1.49692	0.748460	−	0.663180i	$-0.230794\pi$
$613$	37.0620	1.49692	0.748460	+	0.663180i	$0.230794\pi$
$614$	41.2799	1.66592
$615$	−7.57388	−0.305408
$616$	16.2231	0.653649
$617$	9.54452	0.384248	0.192124	−	0.981371i	$-0.438462\pi$
$617$	9.54452	0.384248	0.192124	+	0.981371i	$0.438462\pi$
$618$	−80.1506	−3.22413
$619$	5.13604	0.206435	0.103217	−	0.994659i	$-0.467086\pi$
$619$	5.13604	0.206435	0.103217	+	0.994659i	$0.467086\pi$
$620$	−31.9040	−1.28129
$621$	12.0083	0.481876
$622$	−76.0180	−3.04805
$623$	9.31418	0.373165
$624$	23.2627	0.931254
$625$	7.38991	0.295596
$626$	−11.5159	−0.460268
$627$	36.3346	1.45107
$628$	35.8338	1.42992
$629$	17.1842	0.685180
$630$	5.56103	0.221557
$631$	21.0297	0.837179	0.418589	−	0.908176i	$-0.362525\pi$
$631$	21.0297	0.837179	0.418589	+	0.908176i	$0.362525\pi$
$632$	−5.80315	−0.230837
$633$	−33.6634	−1.33800
$634$	3.81471	0.151502
$635$	11.1987	0.444408
$636$	−94.2605	−3.73767
$637$	17.4213	0.690256
$638$	22.2315	0.880154
$639$	−16.7490	−0.662580
$640$	−22.9415	−0.906842
$641$	−18.5599	−0.733074	−0.366537	−	0.930404i	$-0.619457\pi$
$641$	−18.5599	−0.733074	−0.366537	+	0.930404i	$0.619457\pi$
$642$	64.5600	2.54798
$643$	−11.9071	−0.469571	−0.234786	−	0.972047i	$-0.575439\pi$
$643$	−11.9071	−0.469571	−0.234786	+	0.972047i	$0.575439\pi$
$644$	19.7282	0.777400
$645$	−31.2635	−1.23100
$646$	−94.5605	−3.72043
$647$	29.3573	1.15416	0.577078	−	0.816689i	$-0.304193\pi$
$647$	29.3573	1.15416	0.577078	+	0.816689i	$0.304193\pi$
$648$	51.8596	2.03724
$649$	−34.9122	−1.37043
$650$	−28.3598	−1.11236
$651$	−18.8107	−0.737251
$652$	65.2192	2.55418
$653$	−2.30916	−0.0903645	−0.0451822	−	0.998979i	$-0.514387\pi$
$653$	−2.30916	−0.0903645	−0.0451822	+	0.998979i	$0.514387\pi$
$654$	42.9765	1.68052
$655$	−2.47504	−0.0967077
$656$	−10.5879	−0.413386
$657$	5.16977	0.201692
$658$	0.806362	0.0314352
$659$	−24.8218	−0.966922	−0.483461	−	0.875366i	$-0.660620\pi$
$659$	−24.8218	−0.966922	−0.483461	+	0.875366i	$0.660620\pi$
$660$	−27.8304	−1.08330
$661$	−5.06761	−0.197107	−0.0985536	−	0.995132i	$-0.531422\pi$
$661$	−5.06761	−0.197107	−0.0985536	+	0.995132i	$0.531422\pi$
$662$	−21.2602	−0.826301
$663$	45.7899	1.77833
$664$	−59.4702	−2.30789
$665$	−7.88784	−0.305877
$666$	−10.3747	−0.402013
$667$	13.1799	0.510330
$668$	33.0739	1.27967
$669$	−17.1154	−0.661719
$670$	−5.23125	−0.202101
$671$	−22.4602	−0.867067
$672$	−2.40814	−0.0928959
$673$	−29.6257	−1.14199	−0.570994	−	0.820954i	$-0.693442\pi$
$673$	−29.6257	−1.14199	−0.570994	+	0.820954i	$0.693442\pi$
$674$	69.9733	2.69527
$675$	−10.6440	−0.409689
$676$	−12.2263	−0.470244
$677$	28.3482	1.08951	0.544755	−	0.838595i	$-0.316623\pi$
$677$	28.3482	1.08951	0.544755	+	0.838595i	$0.316623\pi$
$678$	61.8326	2.37466
$679$	11.5651	0.443826
$680$	35.3102	1.35408
$681$	52.2123	2.00078
$682$	51.0205	1.95368
$683$	−5.83526	−0.223280	−0.111640	−	0.993749i	$-0.535610\pi$
$683$	−5.83526	−0.223280	−0.111640	+	0.993749i	$0.535610\pi$
$684$	37.7457	1.44324
$685$	22.9192	0.875697
$686$	36.7538	1.40326
$687$	47.3695	1.80726
$688$	−43.7046	−1.66622
$689$	−35.0887	−1.33677
$690$	−24.9548	−0.950013
$691$	−38.2946	−1.45680	−0.728398	−	0.685154i	$-0.759735\pi$
$691$	−38.2946	−1.45680	−0.728398	+	0.685154i	$0.759735\pi$
$692$	17.6068	0.669311
$693$	−5.87984	−0.223357
$694$	8.63748	0.327874
$695$	16.8696	0.639901
$696$	31.4211	1.19101
$697$	−20.8409	−0.789407
$698$	−0.918006	−0.0347471
$699$	−49.7517	−1.88178
$700$	−17.4869	−0.660943
$701$	39.3678	1.48690	0.743451	−	0.668790i	$-0.233188\pi$
$701$	39.3678	1.48690	0.743451	+	0.668790i	$0.233188\pi$
$702$	21.8593	0.825024
$703$	14.7157	0.555012
$704$	26.4698	0.997619
$705$	−0.674382	−0.0253987
$706$	31.4237	1.18265
$707$	8.83603	0.332313
$708$	−101.214	−3.80384
$709$	16.9692	0.637291	0.318646	−	0.947874i	$-0.396772\pi$
$709$	16.9692	0.637291	0.318646	+	0.947874i	$0.396772\pi$
$710$	−27.5220	−1.03288
$711$	2.10327	0.0788787
$712$	−35.7056	−1.33812
$713$	30.2475	1.13278
$714$	42.7041	1.59816
$715$	−10.3599	−0.387440
$716$	−92.6771	−3.46350
$717$	14.0886	0.526150
$718$	11.4459	0.427156
$719$	13.4575	0.501880	0.250940	−	0.968003i	$-0.419260\pi$
$719$	13.4575	0.501880	0.250940	+	0.968003i	$0.419260\pi$
$720$	−6.50161	−0.242301
$721$	−18.3973	−0.685151
$722$	−34.8156	−1.29570
$723$	41.6385	1.54855
$724$	30.5305	1.13466
$725$	−11.6826	−0.433880
$726$	−13.2794	−0.492846
$727$	−20.7508	−0.769604	−0.384802	−	0.922999i	$-0.625730\pi$
$727$	−20.7508	−0.769604	−0.384802	+	0.922999i	$0.625730\pi$
$728$	17.5079	0.648885
$729$	−0.215769	−0.00799144
$730$	8.49498	0.314413
$731$	−86.0274	−3.18184
$732$	−65.1140	−2.40668
$733$	16.8567	0.622616	0.311308	−	0.950309i	$-0.399233\pi$
$733$	16.8567	0.622616	0.311308	+	0.950309i	$0.399233\pi$
$734$	−62.8995	−2.32166
$735$	−13.5880	−0.501201
$736$	3.87226	0.142733
$737$	5.53115	0.203743
$738$	12.5824	0.463166
$739$	33.3778	1.22782	0.613912	−	0.789375i	$-0.289595\pi$
$739$	33.3778	1.22782	0.613912	+	0.789375i	$0.289595\pi$
$740$	−11.2714	−0.414345
$741$	39.2121	1.44049
$742$	−32.7240	−1.20134
$743$	46.2811	1.69789	0.848944	−	0.528483i	$-0.177239\pi$
$743$	46.2811	1.69789	0.848944	+	0.528483i	$0.177239\pi$
$744$	72.1103	2.64369
$745$	19.2403	0.704910
$746$	3.20187	0.117229
$747$	21.5541	0.788623
$748$	−76.5805	−2.80006
$749$	14.8187	0.541464
$750$	51.8817	1.89445
$751$	−42.1144	−1.53677	−0.768387	−	0.639985i	$-0.778941\pi$
$751$	−42.1144	−1.53677	−0.768387	+	0.639985i	$0.778941\pi$
$752$	−0.942747	−0.0343785
$753$	19.5171	0.711243
$754$	23.9921	0.873740
$755$	12.4734	0.453952
$756$	13.4786	0.490212
$757$	24.2739	0.882250	0.441125	−	0.897446i	$-0.354579\pi$
$757$	24.2739	0.882250	0.441125	+	0.897446i	$0.354579\pi$
$758$	−76.1973	−2.76761
$759$	26.3854	0.957730
$760$	30.2378	1.09684
$761$	−37.9078	−1.37416	−0.687078	−	0.726583i	$-0.741107\pi$
$761$	−37.9078	−1.37416	−0.687078	+	0.726583i	$0.741107\pi$
$762$	−51.9193	−1.88084
$763$	9.86458	0.357122
$764$	−47.9329	−1.73415
$765$	−12.7977	−0.462700
$766$	60.7763	2.19594
$767$	−37.6770	−1.36044
$768$	67.0341	2.41889
$769$	50.0151	1.80359	0.901795	−	0.432164i	$-0.142250\pi$
$769$	50.0151	1.80359	0.901795	+	0.432164i	$0.142250\pi$
$770$	−9.66176	−0.348186
$771$	−31.9456	−1.15049
$772$	−52.4365	−1.88723
$773$	−12.1258	−0.436136	−0.218068	−	0.975934i	$-0.569976\pi$
$773$	−12.1258	−0.436136	−0.218068	+	0.975934i	$0.569976\pi$
$774$	51.9378	1.86687
$775$	−26.8111	−0.963083
$776$	−44.3343	−1.59151
$777$	−6.64568	−0.238412
$778$	11.4943	0.412090
$779$	−17.8471	−0.639438
$780$	−30.0343	−1.07540
$781$	29.0998	1.04127
$782$	−68.6677	−2.45555
$783$	9.00473	0.321803
$784$	−18.9952	−0.678401
$785$	−10.4041	−0.371339
$786$	11.4747	0.409290
$787$	41.5952	1.48271	0.741354	−	0.671114i	$-0.234184\pi$
$787$	41.5952	1.48271	0.741354	+	0.671114i	$0.234184\pi$
$788$	−50.9947	−1.81661
$789$	−14.4204	−0.513380
$790$	3.45609	0.122962
$791$	14.1927	0.504633
$792$	22.5402	0.800930
$793$	−24.2389	−0.860747
$794$	78.8252	2.79740
$795$	27.3680	0.970643
$796$	−26.9816	−0.956339
$797$	30.0828	1.06559	0.532795	−	0.846245i	$-0.321142\pi$
$797$	30.0828	1.06559	0.532795	+	0.846245i	$0.321142\pi$
$798$	36.5695	1.29455
$799$	−1.85569	−0.0656495
$800$	−3.43234	−0.121351
$801$	12.9410	0.457247
$802$	14.1061	0.498103
$803$	−8.98198	−0.316967
$804$	16.0353	0.565521
$805$	−5.72797	−0.201885
$806$	55.0609	1.93944
$807$	42.8496	1.50838
$808$	−33.8726	−1.19164
$809$	5.10173	0.179367	0.0896836	−	0.995970i	$-0.471414\pi$
$809$	5.10173	0.179367	0.0896836	+	0.995970i	$0.471414\pi$
$810$	−30.8852	−1.08520
$811$	48.5151	1.70360	0.851798	−	0.523870i	$-0.175512\pi$
$811$	48.5151	1.70360	0.851798	+	0.523870i	$0.175512\pi$
$812$	14.7937	0.519157
$813$	−42.8672	−1.50342
$814$	18.0251	0.631780
$815$	−18.9360	−0.663299
$816$	−49.9269	−1.74779
$817$	−73.6692	−2.57736
$818$	27.4575	0.960029
$819$	−6.34547	−0.221729
$820$	13.6699	0.477374
$821$	29.7966	1.03991	0.519954	−	0.854194i	$-0.325949\pi$
$821$	29.7966	1.03991	0.519954	+	0.854194i	$0.325949\pi$
$822$	−106.258	−3.70616
$823$	54.2447	1.89085	0.945425	−	0.325840i	$-0.105647\pi$
$823$	54.2447	1.89085	0.945425	+	0.325840i	$0.105647\pi$
$824$	70.5254	2.45687
$825$	−23.3878	−0.814259
$826$	−35.1379	−1.22260
$827$	−23.0355	−0.801024	−0.400512	−	0.916292i	$-0.631168\pi$
$827$	−23.0355	−0.801024	−0.400512	+	0.916292i	$0.631168\pi$
$828$	27.4101	0.952565
$829$	−23.6140	−0.820149	−0.410074	−	0.912052i	$-0.634497\pi$
$829$	−23.6140	−0.820149	−0.410074	+	0.912052i	$0.634497\pi$
$830$	35.4177	1.22937
$831$	−38.6646	−1.34126
$832$	28.5660	0.990349
$833$	−37.3899	−1.29548
$834$	−78.2107	−2.70822
$835$	−9.60282	−0.332319
$836$	−65.5795	−2.26811
$837$	20.6655	0.714305
$838$	−30.9468	−1.06904
$839$	31.4672	1.08637	0.543184	−	0.839614i	$-0.317219\pi$
$839$	31.4672	1.08637	0.543184	+	0.839614i	$0.317219\pi$
$840$	−13.6555	−0.471161
$841$	−19.1167	−0.659196
$842$	61.3692	2.11492
$843$	7.02037	0.241794
$844$	60.7581	2.09138
$845$	3.54985	0.122118
$846$	1.12035	0.0385183
$847$	−3.04808	−0.104733
$848$	38.2589	1.31382
$849$	−39.6207	−1.35978
$850$	60.8665	2.08770
$851$	10.6862	0.366318
$852$	84.3627	2.89022
$853$	38.0626	1.30324	0.651619	−	0.758546i	$-0.274090\pi$
$853$	38.0626	1.30324	0.651619	+	0.758546i	$0.274090\pi$
$854$	−22.6054	−0.773540
$855$	−10.9592	−0.374798
$856$	−56.8070	−1.94162
$857$	−56.3698	−1.92555	−0.962777	−	0.270296i	$-0.912879\pi$
$857$	−56.3698	−1.92555	−0.962777	+	0.270296i	$0.912879\pi$
$858$	48.0306	1.63974
$859$	50.7563	1.73178	0.865892	−	0.500232i	$-0.166752\pi$
$859$	50.7563	1.73178	0.865892	+	0.500232i	$0.166752\pi$
$860$	56.4267	1.92414
$861$	8.05984	0.274679
$862$	−59.3195	−2.02043
$863$	−5.43595	−0.185042	−0.0925210	−	0.995711i	$-0.529493\pi$
$863$	−5.43595	−0.185042	−0.0925210	+	0.995711i	$0.529493\pi$
$864$	2.64558	0.0900046
$865$	−5.11204	−0.173814
$866$	−68.5864	−2.33066
$867$	−61.5171	−2.08923
$868$	33.9510	1.15237
$869$	−3.65423	−0.123961
$870$	−18.7130	−0.634430
$871$	5.96917	0.202258
$872$	−37.8155	−1.28060
$873$	16.0683	0.543830
$874$	−58.8034	−1.98905
$875$	11.9086	0.402584
$876$	−26.0395	−0.879794
$877$	−35.5748	−1.20128	−0.600639	−	0.799521i	$-0.705087\pi$
$877$	−35.5748	−1.20128	−0.600639	+	0.799521i	$0.705087\pi$
$878$	−74.4026	−2.51097
$879$	−69.1042	−2.33083
$880$	11.2959	0.380786
$881$	−14.3705	−0.484155	−0.242077	−	0.970257i	$-0.577829\pi$
$881$	−14.3705	−0.484155	−0.242077	+	0.970257i	$0.577829\pi$
$882$	22.5736	0.760093
$883$	55.2397	1.85896	0.929482	−	0.368869i	$-0.120255\pi$
$883$	55.2397	1.85896	0.929482	+	0.368869i	$0.120255\pi$
$884$	−82.6451	−2.77965
$885$	29.3868	0.987826
$886$	−22.8558	−0.767855
$887$	−2.67705	−0.0898865	−0.0449432	−	0.998990i	$-0.514311\pi$
$887$	−2.67705	−0.0898865	−0.0449432	+	0.998990i	$0.514311\pi$
$888$	25.4760	0.854918
$889$	−11.9173	−0.399692
$890$	21.2646	0.712792
$891$	32.6558	1.09401
$892$	30.8911	1.03431
$893$	−1.58911	−0.0531776
$894$	−89.2016	−2.98335
$895$	26.9083	0.899444
$896$	24.4135	0.815597
$897$	28.4749	0.950750
$898$	63.5597	2.12101
$899$	22.6819	0.756482
$900$	−24.2960	−0.809868
$901$	75.3081	2.50888
$902$	−21.8608	−0.727884
$903$	33.2695	1.10714
$904$	−54.4071	−1.80955
$905$	−8.86435	−0.294661
$906$	−57.8288	−1.92123
$907$	26.0065	0.863531	0.431765	−	0.901986i	$-0.357891\pi$
$907$	26.0065	0.863531	0.431765	+	0.901986i	$0.357891\pi$
$908$	−94.2367	−3.12735
$909$	12.2766	0.407190
$910$	−10.4269	−0.345648
$911$	2.07456	0.0687333	0.0343666	−	0.999409i	$-0.489059\pi$
$911$	2.07456	0.0687333	0.0343666	+	0.999409i	$0.489059\pi$
$912$	−42.7548	−1.41575
$913$	−37.4482	−1.23935
$914$	92.1651	3.04855
$915$	18.9055	0.624996
$916$	−85.4960	−2.82487
$917$	2.63384	0.0869771
$918$	−46.9148	−1.54842
$919$	−52.2370	−1.72314	−0.861570	−	0.507638i	$-0.830519\pi$
$919$	−52.2370	−1.72314	−0.861570	+	0.507638i	$0.830519\pi$
$920$	21.9580	0.723934
$921$	36.7386	1.21058
$922$	−47.8379	−1.57546
$923$	31.4042	1.03368
$924$	29.6161	0.974297
$925$	−9.47214	−0.311442
$926$	−17.0690	−0.560921
$927$	−25.5609	−0.839530
$928$	2.90372	0.0953192
$929$	10.1992	0.334625	0.167312	−	0.985904i	$-0.446491\pi$
$929$	10.1992	0.334625	0.167312	+	0.985904i	$0.446491\pi$
$930$	−42.9456	−1.40824
$931$	−32.0187	−1.04937
$932$	89.7957	2.94135
$933$	−67.6551	−2.21493
$934$	−99.3886	−3.25210
$935$	22.2347	0.727153
$936$	24.3252	0.795093
$937$	−30.2886	−0.989484	−0.494742	−	0.869040i	$-0.664737\pi$
$937$	−30.2886	−0.989484	−0.494742	+	0.869040i	$0.664737\pi$
$938$	5.56690	0.181766
$939$	−10.2490	−0.334464
$940$	1.21718	0.0396999
$941$	−39.0125	−1.27177	−0.635885	−	0.771784i	$-0.719365\pi$
$941$	−39.0125	−1.27177	−0.635885	+	0.771784i	$0.719365\pi$
$942$	48.2355	1.57160
$943$	−12.9602	−0.422041
$944$	41.0810	1.33707
$945$	−3.91343	−0.127304
$946$	−90.2370	−2.93386
$947$	57.0512	1.85392	0.926958	−	0.375166i	$-0.122414\pi$
$947$	57.0512	1.85392	0.926958	+	0.375166i	$0.122414\pi$
$948$	−10.5939	−0.344074
$949$	−9.69328	−0.314657
$950$	52.1228	1.69109
$951$	3.39505	0.110092
$952$	−37.5758	−1.21784
$953$	−10.9520	−0.354770	−0.177385	−	0.984142i	$-0.556764\pi$
$953$	−10.9520	−0.354770	−0.177385	+	0.984142i	$0.556764\pi$
$954$	−45.4662	−1.47202
$955$	13.9170	0.450345
$956$	−25.4282	−0.822408
$957$	19.7858	0.639584
$958$	30.9321	0.999371
$959$	−24.3897	−0.787585
$960$	−22.2805	−0.719101
$961$	21.0540	0.679162
$962$	19.4526	0.627176
$963$	20.5889	0.663467
$964$	−75.1523	−2.42049
$965$	15.2246	0.490098
$966$	26.5559	0.854424
$967$	40.9674	1.31742	0.658711	−	0.752396i	$-0.271102\pi$
$967$	40.9674	1.31742	0.658711	+	0.752396i	$0.271102\pi$
$968$	11.6847	0.375561
$969$	−84.1577	−2.70354
$970$	26.4035	0.847765
$971$	−0.341254	−0.0109514	−0.00547568	−	0.999985i	$-0.501743\pi$
$971$	−0.341254	−0.0109514	−0.00547568	+	0.999985i	$0.501743\pi$
$972$	61.1375	1.96099
$973$	−17.9520	−0.575515
$974$	39.2827	1.25870
$975$	−25.2399	−0.808324
$976$	26.4288	0.845965
$977$	−7.30258	−0.233630	−0.116815	−	0.993154i	$-0.537268\pi$
$977$	−7.30258	−0.233630	−0.116815	+	0.993154i	$0.537268\pi$
$978$	87.7909	2.80724
$979$	−22.4837	−0.718582
$980$	24.5246	0.783410
$981$	13.7057	0.437589
$982$	−17.6231	−0.562377
$983$	38.1253	1.21601	0.608004	−	0.793934i	$-0.291970\pi$
$983$	38.1253	1.21601	0.608004	+	0.793934i	$0.291970\pi$
$984$	−30.8971	−0.984965
$985$	14.8060	0.471759
$986$	−51.4923	−1.63985
$987$	0.717652	0.0228431
$988$	−70.7728	−2.25158
$989$	−53.4970	−1.70110
$990$	−13.4239	−0.426639
$991$	36.2273	1.15080	0.575400	−	0.817872i	$-0.304846\pi$
$991$	36.2273	1.15080	0.575400	+	0.817872i	$0.304846\pi$
$992$	6.66392	0.211580
$993$	−18.9213	−0.600450
$994$	29.2878	0.928954
$995$	7.83396	0.248353
$996$	−108.566	−3.44003
$997$	48.9334	1.54974	0.774868	−	0.632124i	$-0.217817\pi$
$997$	48.9334	1.54974	0.774868	+	0.632124i	$0.217817\pi$
$998$	4.84799	0.153460
$999$	7.30096	0.230992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.18	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.18	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +O(q^{10})\)	\(q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +2.75288 q^{10} -2.91069 q^{11} -8.43835 q^{12} -3.14120 q^{13} -2.92951 q^{14} +2.45003 q^{15} +3.42500 q^{16} +6.74170 q^{17} -4.07021 q^{18} +5.77323 q^{19} -4.42199 q^{20} -2.60723 q^{21} +7.07160 q^{22} +4.19239 q^{23} +9.99471 q^{24} -3.71610 q^{25} +7.63161 q^{26} +2.86430 q^{27} +4.70571 q^{28} +3.14378 q^{29} -5.95240 q^{30} +7.21485 q^{31} +0.923640 q^{32} +6.29364 q^{33} -16.3791 q^{34} -1.36628 q^{35} +6.53804 q^{36} +2.54895 q^{37} -14.0262 q^{38} +6.79204 q^{39} +5.23758 q^{40} -3.09135 q^{41} +6.33432 q^{42} -12.7605 q^{43} -11.3592 q^{44} -1.89828 q^{45} -10.1855 q^{46} -0.275255 q^{47} -7.40569 q^{48} -5.54606 q^{49} +9.02835 q^{50} -14.5772 q^{51} -12.2588 q^{52} +11.1705 q^{53} -6.95889 q^{54} +3.29809 q^{55} -5.57363 q^{56} -12.4832 q^{57} -7.63788 q^{58} +11.9945 q^{59} +9.56143 q^{60} +7.71644 q^{61} -17.5286 q^{62} +2.02008 q^{63} -9.09399 q^{64} +3.55927 q^{65} -15.2905 q^{66} -1.90029 q^{67} +26.3101 q^{68} -9.06499 q^{69} +3.31940 q^{70} -9.99754 q^{71} -7.74391 q^{72} +3.08586 q^{73} -6.19273 q^{74} +8.03513 q^{75} +22.5305 q^{76} -3.50970 q^{77} -16.5014 q^{78} +1.25545 q^{79} -3.88084 q^{80} -11.2193 q^{81} +7.51050 q^{82} +12.8657 q^{83} -10.1749 q^{84} -7.63897 q^{85} +31.0019 q^{86} -6.79762 q^{87} +13.4543 q^{88} +7.72452 q^{89} +4.61192 q^{90} -3.78764 q^{91} +16.3612 q^{92} -15.6003 q^{93} +0.668739 q^{94} -6.54161 q^{95} -1.99714 q^{96} +9.59124 q^{97} +13.4743 q^{98} -4.87632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more