LMFDB - Embedded newform 6037.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +O(q^{10})$	\(q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +3.61596 q^{10} -3.02715 q^{11} +2.92808 q^{12} -6.88837 q^{13} -1.80856 q^{14} -0.876105 q^{15} +8.51988 q^{16} -2.89267 q^{17} +6.73911 q^{18} -3.24077 q^{19} -6.54480 q^{20} +0.438193 q^{21} +7.82208 q^{22} +1.81731 q^{23} -4.33060 q^{24} -3.04174 q^{25} +17.7994 q^{26} -3.51101 q^{27} +3.27345 q^{28} -0.222845 q^{29} +2.26384 q^{30} -4.74383 q^{31} -8.18088 q^{32} -1.89520 q^{33} +7.47459 q^{34} -0.979444 q^{35} -12.1976 q^{36} -10.9936 q^{37} +8.37406 q^{38} -4.31258 q^{39} +9.67970 q^{40} +8.51933 q^{41} -1.13228 q^{42} -0.0231683 q^{43} -14.1578 q^{44} +3.64963 q^{45} -4.69590 q^{46} +4.68142 q^{47} +5.33402 q^{48} -6.51012 q^{49} +7.85979 q^{50} -1.81101 q^{51} -32.2165 q^{52} -10.0007 q^{53} +9.07238 q^{54} +4.23612 q^{55} -4.84141 q^{56} -2.02894 q^{57} +0.575825 q^{58} -1.06556 q^{59} -4.09749 q^{60} -1.03567 q^{61} +12.2579 q^{62} -1.82540 q^{63} +4.09945 q^{64} +9.63943 q^{65} +4.89715 q^{66} +7.21240 q^{67} -13.5288 q^{68} +1.13776 q^{69} +2.53086 q^{70} -15.5141 q^{71} +18.0402 q^{72} -13.5076 q^{73} +28.4072 q^{74} -1.90434 q^{75} -15.1569 q^{76} -2.11874 q^{77} +11.1436 q^{78} -14.0586 q^{79} -11.9225 q^{80} +5.62599 q^{81} -22.0138 q^{82} +3.32541 q^{83} +2.04940 q^{84} +4.04794 q^{85} +0.0598664 q^{86} -0.139516 q^{87} +20.9392 q^{88} -14.1653 q^{89} -9.43057 q^{90} -4.82126 q^{91} +8.49947 q^{92} -2.96996 q^{93} -12.0967 q^{94} +4.53505 q^{95} -5.12178 q^{96} +13.3047 q^{97} +16.8220 q^{98} +7.89491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58398	−1.82715	−0.913574	−	0.406673i	$-0.866689\pi$
$2$	−2.58398	−1.82715	−0.913574	+	0.406673i	$0.866689\pi$
$3$	0.626068	0.361460	0.180730	−	0.983533i	$-0.442154\pi$
$3$	0.626068	0.361460	0.180730	+	0.983533i	$0.442154\pi$
$4$	4.67694	2.33847
$5$	−1.39938	−0.625821	−0.312910	−	0.949783i	$-0.601304\pi$
$5$	−1.39938	−0.625821	−0.312910	+	0.949783i	$0.601304\pi$
$6$	−1.61774	−0.660441
$7$	0.699914	0.264543	0.132271	−	0.991214i	$-0.457773\pi$
$7$	0.699914	0.264543	0.132271	+	0.991214i	$0.457773\pi$
$8$	−6.91715	−2.44558
$9$	−2.60804	−0.869346
$10$	3.61596	1.14347
$11$	−3.02715	−0.912719	−0.456359	−	0.889796i	$-0.650847\pi$
$11$	−3.02715	−0.912719	−0.456359	+	0.889796i	$0.650847\pi$
$12$	2.92808	0.845264
$13$	−6.88837	−1.91049	−0.955245	−	0.295816i	$-0.904408\pi$
$13$	−6.88837	−1.91049	−0.955245	+	0.295816i	$0.904408\pi$
$14$	−1.80856	−0.483358
$15$	−0.876105	−0.226209
$16$	8.51988	2.12997
$17$	−2.89267	−0.701575	−0.350788	−	0.936455i	$-0.614086\pi$
$17$	−2.89267	−0.701575	−0.350788	+	0.936455i	$0.614086\pi$
$18$	6.73911	1.58842
$19$	−3.24077	−0.743483	−0.371741	−	0.928336i	$-0.621239\pi$
$19$	−3.24077	−0.743483	−0.371741	+	0.928336i	$0.621239\pi$
$20$	−6.54480	−1.46346
$21$	0.438193	0.0956217
$22$	7.82208	1.66767
$23$	1.81731	0.378936	0.189468	−	0.981887i	$-0.439324\pi$
$23$	1.81731	0.378936	0.189468	+	0.981887i	$0.439324\pi$
$24$	−4.33060	−0.883981
$25$	−3.04174	−0.608348
$26$	17.7994	3.49075
$27$	−3.51101	−0.675695
$28$	3.27345	0.618625
$29$	−0.222845	−0.0413812	−0.0206906	−	0.999786i	$-0.506586\pi$
$29$	−0.222845	−0.0413812	−0.0206906	+	0.999786i	$0.506586\pi$
$30$	2.26384	0.413318
$31$	−4.74383	−0.852016	−0.426008	−	0.904719i	$-0.640081\pi$
$31$	−4.74383	−0.852016	−0.426008	+	0.904719i	$0.640081\pi$
$32$	−8.18088	−1.44619
$33$	−1.89520	−0.329912
$34$	7.47459	1.28188
$35$	−0.979444	−0.165556
$36$	−12.1976	−2.03294
$37$	−10.9936	−1.80734	−0.903668	−	0.428233i	$-0.859136\pi$
$37$	−10.9936	−1.80734	−0.903668	+	0.428233i	$0.859136\pi$
$38$	8.37406	1.35845
$39$	−4.31258	−0.690566
$40$	9.67970	1.53050
$41$	8.51933	1.33050	0.665248	−	0.746622i	$-0.268326\pi$
$41$	8.51933	1.33050	0.665248	+	0.746622i	$0.268326\pi$
$42$	−1.13228	−0.174715
$43$	−0.0231683	−0.00353314	−0.00176657	−	0.999998i	$-0.500562\pi$
$43$	−0.0231683	−0.00353314	−0.00176657	+	0.999998i	$0.500562\pi$
$44$	−14.1578	−2.13436
$45$	3.64963	0.544055
$46$	−4.69590	−0.692372
$47$	4.68142	0.682855	0.341428	−	0.939908i	$-0.389090\pi$
$47$	4.68142	0.682855	0.341428	+	0.939908i	$0.389090\pi$
$48$	5.33402	0.769900
$49$	−6.51012	−0.930017
$50$	7.85979	1.11154
$51$	−1.81101	−0.253592
$52$	−32.2165	−4.46762
$53$	−10.0007	−1.37370	−0.686851	−	0.726798i	$-0.741008\pi$
$53$	−10.0007	−1.37370	−0.686851	+	0.726798i	$0.741008\pi$
$54$	9.07238	1.23459
$55$	4.23612	0.571198
$56$	−4.84141	−0.646961
$57$	−2.02894	−0.268739
$58$	0.575825	0.0756096
$59$	−1.06556	−0.138724	−0.0693622	−	0.997592i	$-0.522096\pi$
$59$	−1.06556	−0.138724	−0.0693622	+	0.997592i	$0.522096\pi$
$60$	−4.09749	−0.528984
$61$	−1.03567	−0.132604	−0.0663022	−	0.997800i	$-0.521120\pi$
$61$	−1.03567	−0.132604	−0.0663022	+	0.997800i	$0.521120\pi$
$62$	12.2579	1.55676
$63$	−1.82540	−0.229979
$64$	4.09945	0.512431
$65$	9.63943	1.19562
$66$	4.89715	0.602797
$67$	7.21240	0.881135	0.440567	−	0.897720i	$-0.354777\pi$
$67$	7.21240	0.881135	0.440567	+	0.897720i	$0.354777\pi$
$68$	−13.5288	−1.64061
$69$	1.13776	0.136970
$70$	2.53086	0.302496
$71$	−15.5141	−1.84118	−0.920591	−	0.390528i	$-0.872293\pi$
$71$	−15.5141	−1.84118	−0.920591	+	0.390528i	$0.872293\pi$
$72$	18.0402	2.12606
$73$	−13.5076	−1.58094	−0.790470	−	0.612501i	$-0.790164\pi$
$73$	−13.5076	−1.58094	−0.790470	+	0.612501i	$0.790164\pi$
$74$	28.4072	3.30227
$75$	−1.90434	−0.219894
$76$	−15.1569	−1.73861
$77$	−2.11874	−0.241453
$78$	11.1436	1.26177
$79$	−14.0586	−1.58172	−0.790858	−	0.612000i	$-0.790365\pi$
$79$	−14.0586	−1.58172	−0.790858	+	0.612000i	$0.790365\pi$
$80$	−11.9225	−1.33298
$81$	5.62599	0.625110
$82$	−22.0138	−2.43101
$83$	3.32541	0.365011	0.182505	−	0.983205i	$-0.441579\pi$
$83$	3.32541	0.365011	0.182505	+	0.983205i	$0.441579\pi$
$84$	2.04940	0.223608
$85$	4.04794	0.439060
$86$	0.0598664	0.00645556
$87$	−0.139516	−0.0149577
$88$	20.9392	2.23213
$89$	−14.1653	−1.50152	−0.750759	−	0.660576i	$-0.770312\pi$
$89$	−14.1653	−1.50152	−0.750759	+	0.660576i	$0.770312\pi$
$90$	−9.43057	−0.994069
$91$	−4.82126	−0.505406
$92$	8.49947	0.886131
$93$	−2.96996	−0.307970
$94$	−12.0967	−1.24768
$95$	4.53505	0.465287
$96$	−5.12178	−0.522740
$97$	13.3047	1.35089	0.675446	−	0.737410i	$-0.263951\pi$
$97$	13.3047	1.35089	0.675446	+	0.737410i	$0.263951\pi$
$98$	16.8220	1.69928
$99$	7.89491	0.793469
$100$	−14.2260	−1.42260
$101$	4.17271	0.415200	0.207600	−	0.978214i	$-0.433435\pi$
$101$	4.17271	0.415200	0.207600	+	0.978214i	$0.433435\pi$
$102$	4.67960	0.463349
$103$	1.42118	0.140033	0.0700167	−	0.997546i	$-0.477695\pi$
$103$	1.42118	0.140033	0.0700167	+	0.997546i	$0.477695\pi$
$104$	47.6479	4.67226
$105$	−0.613198	−0.0598420
$106$	25.8416	2.50996
$107$	14.3717	1.38937	0.694683	−	0.719316i	$-0.255545\pi$
$107$	14.3717	1.38937	0.694683	+	0.719316i	$0.255545\pi$
$108$	−16.4208	−1.58009
$109$	11.7517	1.12561	0.562804	−	0.826590i	$-0.309723\pi$
$109$	11.7517	1.12561	0.562804	+	0.826590i	$0.309723\pi$
$110$	−10.9460	−1.04366
$111$	−6.88274	−0.653280
$112$	5.96318	0.563468
$113$	−2.95361	−0.277853	−0.138926	−	0.990303i	$-0.544365\pi$
$113$	−2.95361	−0.277853	−0.138926	+	0.990303i	$0.544365\pi$
$114$	5.24273	0.491027
$115$	−2.54311	−0.237146
$116$	−1.04223	−0.0967687
$117$	17.9651	1.66088
$118$	2.75339	0.253470
$119$	−2.02462	−0.185597
$120$	6.06015	0.553213
$121$	−1.83639	−0.166945
$122$	2.67616	0.242288
$123$	5.33368	0.480922
$124$	−22.1866	−1.99241
$125$	11.2534	1.00654
$126$	4.71680	0.420206
$127$	−12.7663	−1.13283	−0.566415	−	0.824120i	$-0.691670\pi$
$127$	−12.7663	−1.13283	−0.566415	+	0.824120i	$0.691670\pi$
$128$	5.76888	0.509902
$129$	−0.0145049	−0.00127709
$130$	−24.9081	−2.18458
$131$	−14.9976	−1.31035	−0.655173	−	0.755479i	$-0.727404\pi$
$131$	−14.9976	−1.31035	−0.655173	+	0.755479i	$0.727404\pi$
$132$	−8.86372	−0.771488
$133$	−2.26826	−0.196683
$134$	−18.6367	−1.60996
$135$	4.91323	0.422864
$136$	20.0090	1.71576
$137$	10.1074	0.863532	0.431766	−	0.901986i	$-0.357891\pi$
$137$	10.1074	0.863532	0.431766	+	0.901986i	$0.357891\pi$
$138$	−2.93995	−0.250265
$139$	−15.0089	−1.27303	−0.636517	−	0.771263i	$-0.719626\pi$
$139$	−15.0089	−1.27303	−0.636517	+	0.771263i	$0.719626\pi$
$140$	−4.58080	−0.387148
$141$	2.93089	0.246825
$142$	40.0880	3.36411
$143$	20.8521	1.74374
$144$	−22.2202	−1.85168
$145$	0.311844	0.0258972
$146$	34.9032	2.88861
$147$	−4.07578	−0.336164
$148$	−51.4164	−4.22640
$149$	2.53230	0.207454	0.103727	−	0.994606i	$-0.466923\pi$
$149$	2.53230	0.207454	0.103727	+	0.994606i	$0.466923\pi$
$150$	4.92076	0.401779
$151$	−13.4690	−1.09609	−0.548047	−	0.836448i	$-0.684628\pi$
$151$	−13.4690	−1.09609	−0.548047	+	0.836448i	$0.684628\pi$
$152$	22.4169	1.81825
$153$	7.54419	0.609912
$154$	5.47478	0.441170
$155$	6.63840	0.533210
$156$	−20.1697	−1.61487
$157$	2.23540	0.178405	0.0892023	−	0.996014i	$-0.471568\pi$
$157$	2.23540	0.178405	0.0892023	+	0.996014i	$0.471568\pi$
$158$	36.3271	2.89003
$159$	−6.26112	−0.496539
$160$	11.4481	0.905055
$161$	1.27196	0.100245
$162$	−14.5374	−1.14217
$163$	−0.873560	−0.0684225	−0.0342112	−	0.999415i	$-0.510892\pi$
$163$	−0.873560	−0.0684225	−0.0342112	+	0.999415i	$0.510892\pi$
$164$	39.8444	3.11133
$165$	2.65210	0.206465
$166$	−8.59278	−0.666929
$167$	−5.41365	−0.418921	−0.209461	−	0.977817i	$-0.567171\pi$
$167$	−5.41365	−0.418921	−0.209461	+	0.977817i	$0.567171\pi$
$168$	−3.03105	−0.233851
$169$	34.4496	2.64997
$170$	−10.4598	−0.802228
$171$	8.45204	0.646344
$172$	−0.108357	−0.00826213
$173$	−7.65989	−0.582371	−0.291185	−	0.956667i	$-0.594050\pi$
$173$	−7.65989	−0.582371	−0.291185	+	0.956667i	$0.594050\pi$
$174$	0.360506	0.0273299
$175$	−2.12896	−0.160934
$176$	−25.7909	−1.94406
$177$	−0.667114	−0.0501434
$178$	36.6028	2.74349
$179$	4.87474	0.364355	0.182177	−	0.983266i	$-0.441685\pi$
$179$	4.87474	0.364355	0.182177	+	0.983266i	$0.441685\pi$
$180$	17.0691	1.27226
$181$	14.9660	1.11242	0.556209	−	0.831043i	$-0.312256\pi$
$181$	14.9660	1.11242	0.556209	+	0.831043i	$0.312256\pi$
$182$	12.4580	0.923451
$183$	−0.648402	−0.0479313
$184$	−12.5706	−0.926719
$185$	15.3842	1.13107
$186$	7.67430	0.562707
$187$	8.75653	0.640341
$188$	21.8947	1.59684
$189$	−2.45741	−0.178750
$190$	−11.7185	−0.850148
$191$	22.6861	1.64151	0.820753	−	0.571284i	$-0.193554\pi$
$191$	22.6861	1.64151	0.820753	+	0.571284i	$0.193554\pi$
$192$	2.56653	0.185223
$193$	−20.2776	−1.45962	−0.729808	−	0.683653i	$-0.760390\pi$
$193$	−20.2776	−1.45962	−0.729808	+	0.683653i	$0.760390\pi$
$194$	−34.3791	−2.46828
$195$	6.03493	0.432171
$196$	−30.4474	−2.17482
$197$	7.76892	0.553513	0.276756	−	0.960940i	$-0.410741\pi$
$197$	7.76892	0.553513	0.276756	+	0.960940i	$0.410741\pi$
$198$	−20.4003	−1.44978
$199$	5.73320	0.406416	0.203208	−	0.979136i	$-0.434863\pi$
$199$	5.73320	0.406416	0.203208	+	0.979136i	$0.434863\pi$
$200$	21.0402	1.48777
$201$	4.51545	0.318495
$202$	−10.7822	−0.758632
$203$	−0.155972	−0.0109471
$204$	−8.46997	−0.593016
$205$	−11.9218	−0.832652
$206$	−3.67231	−0.255862
$207$	−4.73963	−0.329427
$208$	−58.6881	−4.06929
$209$	9.81027	0.678590
$210$	1.58449	0.109340
$211$	−2.11447	−0.145566	−0.0727832	−	0.997348i	$-0.523188\pi$
$211$	−2.11447	−0.145566	−0.0727832	+	0.997348i	$0.523188\pi$
$212$	−46.7727	−3.21236
$213$	−9.71286	−0.665514
$214$	−37.1362	−2.53858
$215$	0.0324212	0.00221111
$216$	24.2862	1.65247
$217$	−3.32027	−0.225395
$218$	−30.3661	−2.05665
$219$	−8.45664	−0.571447
$220$	19.8121	1.33573
$221$	19.9258	1.34035
$222$	17.7848	1.19364
$223$	−4.49102	−0.300741	−0.150370	−	0.988630i	$-0.548047\pi$
$223$	−4.49102	−0.300741	−0.150370	+	0.988630i	$0.548047\pi$
$224$	−5.72591	−0.382579
$225$	7.93298	0.528866
$226$	7.63207	0.507678
$227$	−19.0441	−1.26400	−0.632000	−	0.774968i	$-0.717766\pi$
$227$	−19.0441	−1.26400	−0.632000	+	0.774968i	$0.717766\pi$
$228$	−9.48922	−0.628439
$229$	0.252318	0.0166737	0.00833683	−	0.999965i	$-0.497346\pi$
$229$	0.252318	0.0166737	0.00833683	+	0.999965i	$0.497346\pi$
$230$	6.57133	0.433301
$231$	−1.32648	−0.0872757
$232$	1.54145	0.101201
$233$	22.9092	1.50083	0.750416	−	0.660966i	$-0.229853\pi$
$233$	22.9092	1.50083	0.750416	+	0.660966i	$0.229853\pi$
$234$	−46.4215	−3.03467
$235$	−6.55108	−0.427345
$236$	−4.98357	−0.324403
$237$	−8.80163	−0.571727
$238$	5.23157	0.339112
$239$	−9.32745	−0.603342	−0.301671	−	0.953412i	$-0.597544\pi$
$239$	−9.32745	−0.603342	−0.301671	+	0.953412i	$0.597544\pi$
$240$	−7.46431	−0.481819
$241$	−9.27151	−0.597230	−0.298615	−	0.954374i	$-0.596525\pi$
$241$	−9.27151	−0.597230	−0.298615	+	0.954374i	$0.596525\pi$
$242$	4.74519	0.305033
$243$	14.0553	0.901647
$244$	−4.84378	−0.310091
$245$	9.11012	0.582024
$246$	−13.7821	−0.878715
$247$	22.3236	1.42042
$248$	32.8138	2.08368
$249$	2.08193	0.131937
$250$	−29.0786	−1.83909
$251$	−7.39907	−0.467025	−0.233512	−	0.972354i	$-0.575022\pi$
$251$	−7.39907	−0.467025	−0.233512	+	0.972354i	$0.575022\pi$
$252$	−8.53730	−0.537799
$253$	−5.50127	−0.345862
$254$	32.9879	2.06985
$255$	2.53428	0.158703
$256$	−23.1056	−1.44410
$257$	19.4871	1.21557	0.607787	−	0.794100i	$-0.292058\pi$
$257$	19.4871	1.21557	0.607787	+	0.794100i	$0.292058\pi$
$258$	0.0374804	0.00233343
$259$	−7.69457	−0.478117
$260$	45.0830	2.79593
$261$	0.581187	0.0359746
$262$	38.7534	2.39419
$263$	4.02946	0.248467	0.124234	−	0.992253i	$-0.460353\pi$
$263$	4.02946	0.248467	0.124234	+	0.992253i	$0.460353\pi$
$264$	13.1094	0.806826
$265$	13.9948	0.859691
$266$	5.86112	0.359369
$267$	−8.86843	−0.542739
$268$	33.7320	2.06051
$269$	−24.2207	−1.47676	−0.738381	−	0.674384i	$-0.764409\pi$
$269$	−24.2207	−1.47676	−0.738381	+	0.674384i	$0.764409\pi$
$270$	−12.6957	−0.772634
$271$	20.2125	1.22782	0.613910	−	0.789376i	$-0.289596\pi$
$271$	20.2125	1.22782	0.613910	+	0.789376i	$0.289596\pi$
$272$	−24.6452	−1.49433
$273$	−3.01844	−0.182684
$274$	−26.1172	−1.57780
$275$	9.20780	0.555251
$276$	5.32124	0.320301
$277$	7.74837	0.465555	0.232777	−	0.972530i	$-0.425219\pi$
$277$	7.74837	0.465555	0.232777	+	0.972530i	$0.425219\pi$
$278$	38.7825	2.32602
$279$	12.3721	0.740697
$280$	6.77496	0.404881
$281$	−6.73949	−0.402044	−0.201022	−	0.979587i	$-0.564426\pi$
$281$	−6.73949	−0.402044	−0.201022	+	0.979587i	$0.564426\pi$
$282$	−7.57334	−0.450986
$283$	10.9423	0.650453	0.325227	−	0.945636i	$-0.394559\pi$
$283$	10.9423	0.650453	0.325227	+	0.945636i	$0.394559\pi$
$284$	−72.5584	−4.30555
$285$	2.83925	0.168183
$286$	−53.8813	−3.18607
$287$	5.96280	0.351973
$288$	21.3361	1.25724
$289$	−8.63247	−0.507792
$290$	−0.805797	−0.0473180
$291$	8.32967	0.488294
$292$	−63.1740	−3.69698
$293$	−21.1312	−1.23450	−0.617250	−	0.786767i	$-0.711753\pi$
$293$	−21.1312	−1.23450	−0.617250	+	0.786767i	$0.711753\pi$
$294$	10.5317	0.614222
$295$	1.49112	0.0868166
$296$	76.0444	4.41999
$297$	10.6283	0.616719
$298$	−6.54341	−0.379050
$299$	−12.5183	−0.723954
$300$	−8.90647	−0.514215
$301$	−0.0162158	−0.000934665 0
$302$	34.8037	2.00273
$303$	2.61240	0.150078
$304$	−27.6109	−1.58360
$305$	1.44930	0.0829866
$306$	−19.4940	−1.11440
$307$	−7.10498	−0.405503	−0.202751	−	0.979230i	$-0.564988\pi$
$307$	−7.10498	−0.405503	−0.202751	+	0.979230i	$0.564988\pi$
$308$	−9.90922	−0.564630
$309$	0.889757	0.0506165
$310$	−17.1535	−0.974253
$311$	−1.61329	−0.0914812	−0.0457406	−	0.998953i	$-0.514565\pi$
$311$	−1.61329	−0.0914812	−0.0457406	+	0.998953i	$0.514565\pi$
$312$	29.8308	1.68884
$313$	−19.2902	−1.09035	−0.545173	−	0.838323i	$-0.683536\pi$
$313$	−19.2902	−1.09035	−0.545173	+	0.838323i	$0.683536\pi$
$314$	−5.77623	−0.325972
$315$	2.55443	0.143926
$316$	−65.7512	−3.69879
$317$	2.49836	0.140322	0.0701608	−	0.997536i	$-0.477649\pi$
$317$	2.49836	0.140322	0.0701608	+	0.997536i	$0.477649\pi$
$318$	16.1786	0.907250
$319$	0.674583	0.0377694
$320$	−5.73668	−0.320690
$321$	8.99766	0.502200
$322$	−3.28672	−0.183162
$323$	9.37446	0.521609
$324$	26.3124	1.46180
$325$	20.9526	1.16224
$326$	2.25726	0.125018
$327$	7.35736	0.406863
$328$	−58.9295	−3.25384
$329$	3.27659	0.180644
$330$	−6.85296	−0.377243
$331$	25.1031	1.37979	0.689896	−	0.723909i	$-0.257656\pi$
$331$	25.1031	1.37979	0.689896	+	0.723909i	$0.257656\pi$
$332$	15.5527	0.853567
$333$	28.6717	1.57120
$334$	13.9888	0.765431
$335$	−10.0929	−0.551432
$336$	3.73336	0.203671
$337$	−13.4755	−0.734058	−0.367029	−	0.930210i	$-0.619625\pi$
$337$	−13.4755	−0.734058	−0.367029	+	0.930210i	$0.619625\pi$
$338$	−89.0170	−4.84189
$339$	−1.84916	−0.100433
$340$	18.9320	1.02673
$341$	14.3603	0.777651
$342$	−21.8399	−1.18097
$343$	−9.45592	−0.510572
$344$	0.160259	0.00864057
$345$	−1.59216	−0.0857189
$346$	19.7930	1.06408
$347$	2.67885	0.143808	0.0719041	−	0.997412i	$-0.477092\pi$
$347$	2.67885	0.143808	0.0719041	+	0.997412i	$0.477092\pi$
$348$	−0.652507	−0.0349780
$349$	−9.76413	−0.522662	−0.261331	−	0.965249i	$-0.584161\pi$
$349$	−9.76413	−0.522662	−0.261331	+	0.965249i	$0.584161\pi$
$350$	5.50118	0.294050
$351$	24.1851	1.29091
$352$	24.7647	1.31996
$353$	16.4302	0.874491	0.437245	−	0.899342i	$-0.355954\pi$
$353$	16.4302	0.874491	0.437245	+	0.899342i	$0.355954\pi$
$354$	1.72381	0.0916194
$355$	21.7101	1.15225
$356$	−66.2502	−3.51125
$357$	−1.26755	−0.0670858
$358$	−12.5962	−0.665730
$359$	4.51482	0.238283	0.119142	−	0.992877i	$-0.461986\pi$
$359$	4.51482	0.238283	0.119142	+	0.992877i	$0.461986\pi$
$360$	−25.2451	−1.33053
$361$	−8.49744	−0.447234
$362$	−38.6719	−2.03255
$363$	−1.14971	−0.0603439
$364$	−22.5488	−1.18188
$365$	18.9022	0.989385
$366$	1.67546	0.0875775
$367$	−28.4491	−1.48503	−0.742516	−	0.669829i	$-0.766368\pi$
$367$	−28.4491	−1.48503	−0.742516	+	0.669829i	$0.766368\pi$
$368$	15.4833	0.807123
$369$	−22.2188	−1.15666
$370$	−39.7524	−2.06663
$371$	−6.99963	−0.363403
$372$	−13.8903	−0.720179
$373$	10.4080	0.538907	0.269454	−	0.963013i	$-0.413157\pi$
$373$	10.4080	0.538907	0.269454	+	0.963013i	$0.413157\pi$
$374$	−22.6267	−1.17000
$375$	7.04541	0.363823
$376$	−32.3821	−1.66998
$377$	1.53504	0.0790583
$378$	6.34988	0.326603
$379$	−11.8996	−0.611242	−0.305621	−	0.952153i	$-0.598864\pi$
$379$	−11.8996	−0.611242	−0.305621	+	0.952153i	$0.598864\pi$
$380$	21.2102	1.08806
$381$	−7.99259	−0.409473
$382$	−58.6203	−2.99927
$383$	6.77230	0.346048	0.173024	−	0.984918i	$-0.444646\pi$
$383$	6.77230	0.346048	0.173024	+	0.984918i	$0.444646\pi$
$384$	3.61171	0.184309
$385$	2.96492	0.151106
$386$	52.3969	2.66693
$387$	0.0604239	0.00307152
$388$	62.2255	3.15902
$389$	−18.7466	−0.950489	−0.475244	−	0.879854i	$-0.657640\pi$
$389$	−18.7466	−0.950489	−0.475244	+	0.879854i	$0.657640\pi$
$390$	−15.5941	−0.789640
$391$	−5.25689	−0.265852
$392$	45.0315	2.27443
$393$	−9.38951	−0.473638
$394$	−20.0747	−1.01135
$395$	19.6733	0.989870
$396$	36.9240	1.85550
$397$	−15.1719	−0.761457	−0.380729	−	0.924687i	$-0.624327\pi$
$397$	−15.1719	−0.761457	−0.380729	+	0.924687i	$0.624327\pi$
$398$	−14.8145	−0.742582
$399$	−1.42008	−0.0710930
$400$	−25.9153	−1.29576
$401$	−0.777098	−0.0388064	−0.0194032	−	0.999812i	$-0.506177\pi$
$401$	−0.777098	−0.0388064	−0.0194032	+	0.999812i	$0.506177\pi$
$402$	−11.6678	−0.581938
$403$	32.6772	1.62777
$404$	19.5155	0.970933
$405$	−7.87288	−0.391207
$406$	0.403028	0.0200020
$407$	33.2792	1.64959
$408$	12.5270	0.620179
$409$	26.4764	1.30917	0.654587	−	0.755987i	$-0.272843\pi$
$409$	26.4764	1.30917	0.654587	+	0.755987i	$0.272843\pi$
$410$	30.8056	1.52138
$411$	6.32791	0.312133
$412$	6.64679	0.327464
$413$	−0.745802	−0.0366985
$414$	12.2471	0.601911
$415$	−4.65350	−0.228431
$416$	56.3529	2.76293
$417$	−9.39656	−0.460151
$418$	−25.3495	−1.23989
$419$	−24.3403	−1.18910	−0.594551	−	0.804058i	$-0.702670\pi$
$419$	−24.3403	−1.18910	−0.594551	+	0.804058i	$0.702670\pi$
$420$	−2.86789	−0.139939
$421$	−8.67616	−0.422850	−0.211425	−	0.977394i	$-0.567810\pi$
$421$	−8.67616	−0.422850	−0.211425	+	0.977394i	$0.567810\pi$
$422$	5.46375	0.265971
$423$	−12.2093	−0.593638
$424$	69.1764	3.35950
$425$	8.79875	0.426802
$426$	25.0978	1.21599
$427$	−0.724883	−0.0350795
$428$	67.2156	3.24899
$429$	13.0548	0.630293
$430$	−0.0837757	−0.00404002
$431$	−24.8809	−1.19847	−0.599236	−	0.800573i	$-0.704529\pi$
$431$	−24.8809	−1.19847	−0.599236	+	0.800573i	$0.704529\pi$
$432$	−29.9134	−1.43921
$433$	−22.8532	−1.09826	−0.549128	−	0.835738i	$-0.685040\pi$
$433$	−22.8532	−1.09826	−0.549128	+	0.835738i	$0.685040\pi$
$434$	8.57950	0.411829
$435$	0.195235	0.00936081
$436$	54.9620	2.63220
$437$	−5.88949	−0.281732
$438$	21.8518	1.04412
$439$	−25.2549	−1.20535	−0.602675	−	0.797987i	$-0.705899\pi$
$439$	−25.2549	−1.20535	−0.602675	+	0.797987i	$0.705899\pi$
$440$	−29.3019	−1.39691
$441$	16.9787	0.808507
$442$	−51.4877	−2.44902
$443$	−22.2833	−1.05871	−0.529355	−	0.848400i	$-0.677566\pi$
$443$	−22.2833	−1.05871	−0.529355	+	0.848400i	$0.677566\pi$
$444$	−32.1901	−1.52768
$445$	19.8226	0.939681
$446$	11.6047	0.549498
$447$	1.58539	0.0749865
$448$	2.86926	0.135560
$449$	−8.75715	−0.413276	−0.206638	−	0.978418i	$-0.566252\pi$
$449$	−8.75715	−0.413276	−0.206638	+	0.978418i	$0.566252\pi$
$450$	−20.4987	−0.966316
$451$	−25.7893	−1.21437
$452$	−13.8139	−0.649750
$453$	−8.43252	−0.396194
$454$	49.2095	2.30952
$455$	6.74677	0.316293
$456$	14.0345	0.657224
$457$	10.7524	0.502975	0.251487	−	0.967861i	$-0.419080\pi$
$457$	10.7524	0.502975	0.251487	+	0.967861i	$0.419080\pi$
$458$	−0.651985	−0.0304652
$459$	10.1562	0.474051
$460$	−11.8940	−0.554559
$461$	−19.4465	−0.905715	−0.452858	−	0.891583i	$-0.649595\pi$
$461$	−19.4465	−0.905715	−0.452858	+	0.891583i	$0.649595\pi$
$462$	3.42758	0.159466
$463$	−28.0390	−1.30308	−0.651542	−	0.758613i	$-0.725877\pi$
$463$	−28.0390	−1.30308	−0.651542	+	0.758613i	$0.725877\pi$
$464$	−1.89861	−0.0881407
$465$	4.15609	0.192734
$466$	−59.1968	−2.74224
$467$	−6.04116	−0.279552	−0.139776	−	0.990183i	$-0.544638\pi$
$467$	−6.04116	−0.279552	−0.139776	+	0.990183i	$0.544638\pi$
$468$	84.0218	3.88391
$469$	5.04806	0.233098
$470$	16.9278	0.780823
$471$	1.39951	0.0644862
$472$	7.37066	0.339262
$473$	0.0701339	0.00322476
$474$	22.7432	1.04463
$475$	9.85757	0.452297
$476$	−9.46902	−0.434012
$477$	26.0822	1.19422
$478$	24.1019	1.10240
$479$	11.3273	0.517557	0.258779	−	0.965937i	$-0.416680\pi$
$479$	11.3273	0.517557	0.258779	+	0.965937i	$0.416680\pi$
$480$	7.16731	0.327141
$481$	75.7280	3.45290
$482$	23.9574	1.09123
$483$	0.796335	0.0362345
$484$	−8.58869	−0.390395
$485$	−18.6184	−0.845416
$486$	−36.3185	−1.64744
$487$	−30.1218	−1.36495	−0.682475	−	0.730909i	$-0.739096\pi$
$487$	−30.1218	−1.36495	−0.682475	+	0.730909i	$0.739096\pi$
$488$	7.16391	0.324295
$489$	−0.546908	−0.0247320
$490$	−23.5403	−1.06344
$491$	−13.8237	−0.623857	−0.311928	−	0.950106i	$-0.600975\pi$
$491$	−13.8237	−0.623857	−0.311928	+	0.950106i	$0.600975\pi$
$492$	24.9453	1.12462
$493$	0.644616	0.0290320
$494$	−57.6836	−2.59531
$495$	−11.0480	−0.496569
$496$	−40.4168	−1.81477
$497$	−10.8585	−0.487071
$498$	−5.37966	−0.241068
$499$	16.9795	0.760106	0.380053	−	0.924965i	$-0.375906\pi$
$499$	16.9795	0.760106	0.380053	+	0.924965i	$0.375906\pi$
$500$	52.6316	2.35376
$501$	−3.38931	−0.151423
$502$	19.1190	0.853324
$503$	−19.9737	−0.890584	−0.445292	−	0.895385i	$-0.646900\pi$
$503$	−19.9737	−0.890584	−0.445292	+	0.895385i	$0.646900\pi$
$504$	12.6266	0.562433
$505$	−5.83920	−0.259841
$506$	14.2152	0.631941
$507$	21.5678	0.957859
$508$	−59.7074	−2.64909
$509$	16.2070	0.718364	0.359182	−	0.933268i	$-0.383056\pi$
$509$	16.2070	0.718364	0.359182	+	0.933268i	$0.383056\pi$
$510$	−6.54853	−0.289974
$511$	−9.45412	−0.418226
$512$	48.1665	2.12868
$513$	11.3784	0.502367
$514$	−50.3543	−2.22103
$515$	−1.98877	−0.0876358
$516$	−0.0678387	−0.00298643
$517$	−14.1713	−0.623255
$518$	19.8826	0.873591
$519$	−4.79561	−0.210504
$520$	−66.6774	−2.92400
$521$	−1.24066	−0.0543543	−0.0271772	−	0.999631i	$-0.508652\pi$
$521$	−1.24066	−0.0543543	−0.0271772	+	0.999631i	$0.508652\pi$
$522$	−1.50178	−0.0657309
$523$	35.9724	1.57296	0.786481	−	0.617615i	$-0.211901\pi$
$523$	35.9724	1.57296	0.786481	+	0.617615i	$0.211901\pi$
$524$	−70.1428	−3.06420
$525$	−1.33287	−0.0581713
$526$	−10.4120	−0.453986
$527$	13.7223	0.597754
$528$	−16.1469	−0.702702
$529$	−19.6974	−0.856407
$530$	−36.1621	−1.57078
$531$	2.77903	0.120600
$532$	−10.6085	−0.459937
$533$	−58.6843	−2.54190
$534$	22.9158	0.991665
$535$	−20.1114	−0.869493
$536$	−49.8892	−2.15489
$537$	3.05191	0.131700
$538$	62.5857	2.69826
$539$	19.7071	0.848844
$540$	22.9789	0.988854
$541$	9.11925	0.392067	0.196034	−	0.980597i	$-0.437194\pi$
$541$	9.11925	0.392067	0.196034	+	0.980597i	$0.437194\pi$
$542$	−52.2286	−2.24341
$543$	9.36976	0.402095
$544$	23.6646	1.01461
$545$	−16.4451	−0.704429
$546$	7.79958	0.333791
$547$	7.95075	0.339950	0.169975	−	0.985448i	$-0.445631\pi$
$547$	7.95075	0.339950	0.169975	+	0.985448i	$0.445631\pi$
$548$	47.2716	2.01934
$549$	2.70108	0.115279
$550$	−23.7927	−1.01453
$551$	0.722187	0.0307662
$552$	−7.87007	−0.334972
$553$	−9.83981	−0.418431
$554$	−20.0216	−0.850637
$555$	9.63155	0.408836
$556$	−70.1955	−2.97695
$557$	24.5538	1.04038	0.520189	−	0.854051i	$-0.325861\pi$
$557$	24.5538	1.04038	0.520189	+	0.854051i	$0.325861\pi$
$558$	−31.9692	−1.35336
$559$	0.159592	0.00675002
$560$	−8.34475	−0.352630
$561$	5.48218	0.231458
$562$	17.4147	0.734594
$563$	27.0620	1.14053	0.570264	−	0.821462i	$-0.306841\pi$
$563$	27.0620	1.14053	0.570264	+	0.821462i	$0.306841\pi$
$564$	13.7076	0.577193
$565$	4.13322	0.173886
$566$	−28.2747	−1.18847
$567$	3.93771	0.165368
$568$	107.313	4.50276
$569$	17.0815	0.716094	0.358047	−	0.933704i	$-0.383443\pi$
$569$	17.0815	0.716094	0.358047	+	0.933704i	$0.383443\pi$
$570$	−7.33656	−0.307295
$571$	−22.3587	−0.935684	−0.467842	−	0.883812i	$-0.654968\pi$
$571$	−22.3587	−0.935684	−0.467842	+	0.883812i	$0.654968\pi$
$572$	97.5240	4.07768
$573$	14.2030	0.593339
$574$	−15.4077	−0.643107
$575$	−5.52780	−0.230525
$576$	−10.6915	−0.445480
$577$	17.2800	0.719376	0.359688	−	0.933073i	$-0.382883\pi$
$577$	17.2800	0.719376	0.359688	+	0.933073i	$0.382883\pi$
$578$	22.3061	0.927811
$579$	−12.6952	−0.527593
$580$	1.45847	0.0605598
$581$	2.32750	0.0965609
$582$	−21.5237	−0.892185
$583$	30.2736	1.25380
$584$	93.4338	3.86632
$585$	−25.1400	−1.03941
$586$	54.6026	2.25561
$587$	−17.3807	−0.717380	−0.358690	−	0.933457i	$-0.616776\pi$
$587$	−17.3807	−0.717380	−0.358690	+	0.933457i	$0.616776\pi$
$588$	−19.0622	−0.786110
$589$	15.3736	0.633459
$590$	−3.85303	−0.158627
$591$	4.86387	0.200073
$592$	−93.6642	−3.84957
$593$	27.9992	1.14979	0.574896	−	0.818227i	$-0.305043\pi$
$593$	27.9992	1.14979	0.574896	+	0.818227i	$0.305043\pi$
$594$	−27.4634	−1.12684
$595$	2.83321	0.116150
$596$	11.8434	0.485126
$597$	3.58937	0.146903
$598$	32.3471	1.32277
$599$	−25.4871	−1.04138	−0.520688	−	0.853747i	$-0.674324\pi$
$599$	−25.4871	−1.04138	−0.520688	+	0.853747i	$0.674324\pi$
$600$	13.1726	0.537768
$601$	9.03306	0.368466	0.184233	−	0.982883i	$-0.441020\pi$
$601$	9.03306	0.368466	0.184233	+	0.982883i	$0.441020\pi$
$602$	0.0419013	0.00170777
$603$	−18.8102	−0.766011
$604$	−62.9938	−2.56318
$605$	2.56980	0.104477
$606$	−6.75038	−0.274215
$607$	11.8368	0.480442	0.240221	−	0.970718i	$-0.422780\pi$
$607$	11.8368	0.480442	0.240221	+	0.970718i	$0.422780\pi$
$608$	26.5123	1.07522
$609$	−0.0976490	−0.00395694
$610$	−3.74496	−0.151629
$611$	−32.2474	−1.30459
$612$	35.2837	1.42626
$613$	11.9870	0.484152	0.242076	−	0.970257i	$-0.422172\pi$
$613$	11.9870	0.484152	0.242076	+	0.970257i	$0.422172\pi$
$614$	18.3591	0.740913
$615$	−7.46383	−0.300971
$616$	14.6557	0.590493
$617$	−22.5867	−0.909308	−0.454654	−	0.890668i	$-0.650237\pi$
$617$	−22.5867	−0.909308	−0.454654	+	0.890668i	$0.650237\pi$
$618$	−2.29911	−0.0924839
$619$	21.9122	0.880727	0.440364	−	0.897820i	$-0.354850\pi$
$619$	21.9122	0.880727	0.440364	+	0.897820i	$0.354850\pi$
$620$	31.0474	1.24689
$621$	−6.38061	−0.256045
$622$	4.16870	0.167150
$623$	−9.91448	−0.397215
$624$	−36.7427	−1.47089
$625$	−0.539091	−0.0215636
$626$	49.8455	1.99222
$627$	6.14189	0.245284
$628$	10.4549	0.417194
$629$	31.8008	1.26798
$630$	−6.60058	−0.262974
$631$	25.6828	1.02242	0.511208	−	0.859457i	$-0.329198\pi$
$631$	25.6828	1.02242	0.511208	+	0.859457i	$0.329198\pi$
$632$	97.2454	3.86822
$633$	−1.32380	−0.0526165
$634$	−6.45570	−0.256388
$635$	17.8649	0.708948
$636$	−29.2829	−1.16114
$637$	44.8441	1.77679
$638$	−1.74311	−0.0690103
$639$	40.4613	1.60063
$640$	−8.07284	−0.319107
$641$	−10.7846	−0.425967	−0.212983	−	0.977056i	$-0.568318\pi$
$641$	−10.7846	−0.425967	−0.212983	+	0.977056i	$0.568318\pi$
$642$	−23.2497	−0.917594
$643$	30.2443	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$643$	30.2443	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$644$	5.94889	0.234419
$645$	0.0202979	0.000799228 0
$646$	−24.2234	−0.953057
$647$	−8.28070	−0.325548	−0.162774	−	0.986663i	$-0.552044\pi$
$647$	−8.28070	−0.325548	−0.162774	+	0.986663i	$0.552044\pi$
$648$	−38.9158	−1.52876
$649$	3.22561	0.126616
$650$	−54.1412	−2.12359
$651$	−2.07871	−0.0814712
$652$	−4.08559	−0.160004
$653$	29.3822	1.14981	0.574906	−	0.818219i	$-0.305038\pi$
$653$	29.3822	1.14981	0.574906	+	0.818219i	$0.305038\pi$
$654$	−19.0112	−0.743398
$655$	20.9873	0.820041
$656$	72.5837	2.83392
$657$	35.2282	1.37438
$658$	−8.46664	−0.330064
$659$	20.9313	0.815368	0.407684	−	0.913123i	$-0.366337\pi$
$659$	20.9313	0.815368	0.407684	+	0.913123i	$0.366337\pi$
$660$	12.4037	0.482813
$661$	16.7971	0.653331	0.326665	−	0.945140i	$-0.394075\pi$
$661$	16.7971	0.653331	0.326665	+	0.945140i	$0.394075\pi$
$662$	−64.8659	−2.52108
$663$	12.4749	0.484484
$664$	−23.0023	−0.892664
$665$	3.17415	0.123088
$666$	−74.0871	−2.87082
$667$	−0.404979	−0.0156808
$668$	−25.3193	−0.979634
$669$	−2.81168	−0.108706
$670$	26.0797	1.00755
$671$	3.13514	0.121031
$672$	−3.58481	−0.138287
$673$	−32.0943	−1.23715	−0.618573	−	0.785727i	$-0.712289\pi$
$673$	−32.0943	−1.23715	−0.618573	+	0.785727i	$0.712289\pi$
$674$	34.8204	1.34123
$675$	10.6796	0.411058
$676$	161.119	6.19688
$677$	13.0335	0.500918	0.250459	−	0.968127i	$-0.419418\pi$
$677$	13.0335	0.500918	0.250459	+	0.968127i	$0.419418\pi$
$678$	4.77819	0.183505
$679$	9.31217	0.357368
$680$	−28.0002	−1.07376
$681$	−11.9229	−0.456886
$682$	−37.1066	−1.42088
$683$	−11.0359	−0.422277	−0.211139	−	0.977456i	$-0.567717\pi$
$683$	−11.0359	−0.422277	−0.211139	+	0.977456i	$0.567717\pi$
$684$	39.5297	1.51146
$685$	−14.1440	−0.540416
$686$	24.4339	0.932890
$687$	0.157968	0.00602687
$688$	−0.197391	−0.00752548
$689$	68.8885	2.62444
$690$	4.11410	0.156621
$691$	20.1701	0.767308	0.383654	−	0.923477i	$-0.374666\pi$
$691$	20.1701	0.767308	0.383654	+	0.923477i	$0.374666\pi$
$692$	−35.8248	−1.36186
$693$	5.52576	0.209906
$694$	−6.92209	−0.262759
$695$	21.0031	0.796691
$696$	0.965052	0.0365802
$697$	−24.6436	−0.933444
$698$	25.2303	0.954981
$699$	14.3427	0.542491
$700$	−9.95701	−0.376339
$701$	19.2959	0.728796	0.364398	−	0.931243i	$-0.381275\pi$
$701$	19.2959	0.728796	0.364398	+	0.931243i	$0.381275\pi$
$702$	−62.4939	−2.35868
$703$	35.6277	1.34372
$704$	−12.4096	−0.467705
$705$	−4.10142	−0.154468
$706$	−42.4552	−1.59782
$707$	2.92054	0.109838
$708$	−3.12005	−0.117259
$709$	29.9703	1.12556	0.562779	−	0.826607i	$-0.309732\pi$
$709$	29.9703	1.12556	0.562779	+	0.826607i	$0.309732\pi$
$710$	−56.0983	−2.10533
$711$	36.6654	1.37506
$712$	97.9834	3.67208
$713$	−8.62102	−0.322860
$714$	3.27532	0.122576
$715$	−29.1799	−1.09127
$716$	22.7988	0.852033
$717$	−5.83961	−0.218084
$718$	−11.6662	−0.435379
$719$	−52.1807	−1.94601	−0.973005	−	0.230782i	$-0.925871\pi$
$719$	−52.1807	−1.94601	−0.973005	+	0.230782i	$0.925871\pi$
$720$	31.0944	1.15882
$721$	0.994706	0.0370448
$722$	21.9572	0.817162
$723$	−5.80459	−0.215875
$724$	69.9953	2.60135
$725$	0.677836	0.0251742
$726$	2.97081	0.110257
$727$	33.8166	1.25419	0.627095	−	0.778943i	$-0.284244\pi$
$727$	33.8166	1.25419	0.627095	+	0.778943i	$0.284244\pi$
$728$	33.3494	1.23601
$729$	−8.07840	−0.299200
$730$	−48.8428	−1.80775
$731$	0.0670183	0.00247876
$732$	−3.03254	−0.112086
$733$	33.3532	1.23193	0.615965	−	0.787774i	$-0.288766\pi$
$733$	33.3532	1.23193	0.615965	+	0.787774i	$0.288766\pi$
$734$	73.5118	2.71337
$735$	5.70355	0.210379
$736$	−14.8672	−0.548013
$737$	−21.8330	−0.804228
$738$	57.4128	2.11339
$739$	−31.0837	−1.14343	−0.571716	−	0.820452i	$-0.693722\pi$
$739$	−31.0837	−1.14343	−0.571716	+	0.820452i	$0.693722\pi$
$740$	71.9509	2.64497
$741$	13.9761	0.513424
$742$	18.0869	0.663991
$743$	−19.6728	−0.721723	−0.360862	−	0.932619i	$-0.617517\pi$
$743$	−19.6728	−0.721723	−0.360862	+	0.932619i	$0.617517\pi$
$744$	20.5436	0.753166
$745$	−3.54365	−0.129829
$746$	−26.8941	−0.984663
$747$	−8.67279	−0.317321
$748$	40.9538	1.49742
$749$	10.0590	0.367546
$750$	−18.2052	−0.664759
$751$	−47.4211	−1.73042	−0.865210	−	0.501410i	$-0.832815\pi$
$751$	−47.4211	−1.73042	−0.865210	+	0.501410i	$0.832815\pi$
$752$	39.8852	1.45446
$753$	−4.63232	−0.168811
$754$	−3.96650	−0.144451
$755$	18.8483	0.685958
$756$	−11.4931	−0.418001
$757$	32.4881	1.18080	0.590400	−	0.807111i	$-0.298970\pi$
$757$	32.4881	1.18080	0.590400	+	0.807111i	$0.298970\pi$
$758$	30.7483	1.11683
$759$	−3.44417	−0.125015
$760$	−31.3697	−1.13790
$761$	−25.4961	−0.924231	−0.462116	−	0.886820i	$-0.652910\pi$
$761$	−25.4961	−0.924231	−0.462116	+	0.886820i	$0.652910\pi$
$762$	20.6527	0.748167
$763$	8.22518	0.297771
$764$	106.101	3.83861
$765$	−10.5572	−0.381696
$766$	−17.4995	−0.632282
$767$	7.33999	0.265032
$768$	−14.4656	−0.521984
$769$	30.8680	1.11313	0.556564	−	0.830805i	$-0.312119\pi$
$769$	30.8680	1.11313	0.556564	+	0.830805i	$0.312119\pi$
$770$	−7.66128	−0.276093
$771$	12.2003	0.439381
$772$	−94.8372	−3.41327
$773$	24.3108	0.874400	0.437200	−	0.899364i	$-0.355970\pi$
$773$	24.3108	0.874400	0.437200	+	0.899364i	$0.355970\pi$
$774$	−0.156134	−0.00561212
$775$	14.4295	0.518323
$776$	−92.0309	−3.30372
$777$	−4.81732	−0.172820
$778$	48.4407	1.73668
$779$	−27.6092	−0.989201
$780$	28.2250	1.01062
$781$	46.9634	1.68048
$782$	13.5837	0.485751
$783$	0.782410	0.0279611
$784$	−55.4655	−1.98091
$785$	−3.12817	−0.111649
$786$	24.2623	0.865406
$787$	−13.4463	−0.479310	−0.239655	−	0.970858i	$-0.577034\pi$
$787$	−13.4463	−0.479310	−0.239655	+	0.970858i	$0.577034\pi$
$788$	36.3348	1.29437
$789$	2.52271	0.0898110
$790$	−50.8353	−1.80864
$791$	−2.06727	−0.0735038
$792$	−54.6103	−1.94049
$793$	7.13410	0.253339
$794$	39.2039	1.39129
$795$	8.76167	0.310744
$796$	26.8138	0.950391
$797$	−22.8816	−0.810507	−0.405253	−	0.914204i	$-0.632817\pi$
$797$	−22.8816	−0.810507	−0.405253	+	0.914204i	$0.632817\pi$
$798$	3.66946	0.129897
$799$	−13.5418	−0.479075
$800$	24.8841	0.879787
$801$	36.9436	1.30534
$802$	2.00800	0.0709050
$803$	40.8893	1.44295
$804$	21.1185	0.744792
$805$	−1.77996	−0.0627352
$806$	−84.4372	−2.97417
$807$	−15.1638	−0.533791
$808$	−28.8633	−1.01541
$809$	12.0450	0.423478	0.211739	−	0.977326i	$-0.432087\pi$
$809$	12.0450	0.423478	0.211739	+	0.977326i	$0.432087\pi$
$810$	20.3433	0.714792
$811$	33.3915	1.17253	0.586266	−	0.810118i	$-0.300597\pi$
$811$	33.3915	1.17253	0.586266	+	0.810118i	$0.300597\pi$
$812$	−0.729472	−0.0255994
$813$	12.6544	0.443808
$814$	−85.9927	−3.01404
$815$	1.22244	0.0428202
$816$	−15.4296	−0.540143
$817$	0.0750831	0.00262683
$818$	−68.4144	−2.39205
$819$	12.5740	0.439373
$820$	−55.7574	−1.94713
$821$	−1.19373	−0.0416616	−0.0208308	−	0.999783i	$-0.506631\pi$
$821$	−1.19373	−0.0416616	−0.0208308	+	0.999783i	$0.506631\pi$
$822$	−16.3512	−0.570312
$823$	−43.6389	−1.52116	−0.760578	−	0.649247i	$-0.775084\pi$
$823$	−43.6389	−1.52116	−0.760578	+	0.649247i	$0.775084\pi$
$824$	−9.83054	−0.342463
$825$	5.76470	0.200701
$826$	1.92714	0.0670536
$827$	4.59153	0.159663	0.0798315	−	0.996808i	$-0.474562\pi$
$827$	4.59153	0.159663	0.0798315	+	0.996808i	$0.474562\pi$
$828$	−22.1669	−0.770354
$829$	−6.31638	−0.219377	−0.109688	−	0.993966i	$-0.534985\pi$
$829$	−6.31638	−0.219377	−0.109688	+	0.993966i	$0.534985\pi$
$830$	12.0245	0.417378
$831$	4.85100	0.168279
$832$	−28.2385	−0.978994
$833$	18.8316	0.652477
$834$	24.2805	0.840765
$835$	7.57575	0.262170
$836$	45.8820	1.58686
$837$	16.6556	0.575703
$838$	62.8948	2.17266
$839$	17.1067	0.590588	0.295294	−	0.955406i	$-0.404582\pi$
$839$	17.1067	0.590588	0.295294	+	0.955406i	$0.404582\pi$
$840$	4.24158	0.146349
$841$	−28.9503	−0.998288
$842$	22.4190	0.772610
$843$	−4.21938	−0.145323
$844$	−9.88926	−0.340403
$845$	−48.2080	−1.65841
$846$	31.5486	1.08466
$847$	−1.28532	−0.0441640
$848$	−85.2048	−2.92594
$849$	6.85063	0.235113
$850$	−22.7358	−0.779831
$851$	−19.9788	−0.684865
$852$	−45.4265	−1.55629
$853$	−30.2106	−1.03439	−0.517196	−	0.855867i	$-0.673024\pi$
$853$	−30.2106	−1.03439	−0.517196	+	0.855867i	$0.673024\pi$
$854$	1.87308	0.0640955
$855$	−11.8276	−0.404495
$856$	−99.4112	−3.39781
$857$	34.7559	1.18724	0.593620	−	0.804746i	$-0.297698\pi$
$857$	34.7559	1.18724	0.593620	+	0.804746i	$0.297698\pi$
$858$	−33.7334	−1.15164
$859$	48.3871	1.65095	0.825473	−	0.564441i	$-0.190908\pi$
$859$	48.3871	1.65095	0.825473	+	0.564441i	$0.190908\pi$
$860$	0.151632	0.00517061
$861$	3.73312	0.127224
$862$	64.2917	2.18978
$863$	38.3726	1.30622	0.653109	−	0.757264i	$-0.273464\pi$
$863$	38.3726	1.30622	0.653109	+	0.757264i	$0.273464\pi$
$864$	28.7232	0.977182
$865$	10.7191	0.364460
$866$	59.0522	2.00668
$867$	−5.40451	−0.183547
$868$	−15.5287	−0.527079
$869$	42.5574	1.44366
$870$	−0.504483	−0.0171036
$871$	−49.6817	−1.68340
$872$	−81.2882	−2.75277
$873$	−34.6993	−1.17439
$874$	15.2183	0.514767
$875$	7.87643	0.266272
$876$	−39.5512	−1.33631
$877$	39.1132	1.32076	0.660380	−	0.750932i	$-0.270395\pi$
$877$	39.1132	1.32076	0.660380	+	0.750932i	$0.270395\pi$
$878$	65.2581	2.20235
$879$	−13.2296	−0.446223
$880$	36.0912	1.21664
$881$	−41.1181	−1.38530	−0.692652	−	0.721272i	$-0.743558\pi$
$881$	−41.1181	−1.38530	−0.692652	+	0.721272i	$0.743558\pi$
$882$	−43.8724	−1.47726
$883$	−14.4750	−0.487123	−0.243561	−	0.969886i	$-0.578316\pi$
$883$	−14.4750	−0.487123	−0.243561	+	0.969886i	$0.578316\pi$
$884$	93.1916	3.13437
$885$	0.933545	0.0313808
$886$	57.5795	1.93442
$887$	−6.82479	−0.229154	−0.114577	−	0.993414i	$-0.536551\pi$
$887$	−6.82479	−0.229154	−0.114577	+	0.993414i	$0.536551\pi$
$888$	47.6089	1.59765
$889$	−8.93534	−0.299682
$890$	−51.2211	−1.71694
$891$	−17.0307	−0.570549
$892$	−21.0042	−0.703273
$893$	−15.1714	−0.507691
$894$	−4.09662	−0.137011
$895$	−6.82160	−0.228021
$896$	4.03772	0.134891
$897$	−7.83732	−0.261680
$898$	22.6283	0.755116
$899$	1.05714	0.0352575
$900$	37.1021	1.23674
$901$	28.9287	0.963756
$902$	66.6389	2.21883
$903$	−0.0101522	−0.000337844 0
$904$	20.4306	0.679511
$905$	−20.9431	−0.696174
$906$	21.7894	0.723906
$907$	7.58795	0.251954	0.125977	−	0.992033i	$-0.459793\pi$
$907$	7.58795	0.251954	0.125977	+	0.992033i	$0.459793\pi$
$908$	−89.0680	−2.95583
$909$	−10.8826	−0.360953
$910$	−17.4335	−0.577915
$911$	−53.7662	−1.78135	−0.890676	−	0.454638i	$-0.849769\pi$
$911$	−53.7662	−1.78135	−0.890676	+	0.454638i	$0.849769\pi$
$912$	−17.2863	−0.572407
$913$	−10.0665	−0.333152
$914$	−27.7839	−0.919010
$915$	0.907359	0.0299964
$916$	1.18008	0.0389908
$917$	−10.4970	−0.346642
$918$	−26.2434	−0.866161
$919$	23.2464	0.766828	0.383414	−	0.923577i	$-0.374748\pi$
$919$	23.2464	0.766828	0.383414	+	0.923577i	$0.374748\pi$
$920$	17.5911	0.579960
$921$	−4.44820	−0.146573
$922$	50.2494	1.65488
$923$	106.867	3.51756
$924$	−6.20384	−0.204091
$925$	33.4397	1.09949
$926$	72.4522	2.38093
$927$	−3.70650	−0.121738
$928$	1.82306	0.0598450
$929$	−56.9903	−1.86979	−0.934896	−	0.354921i	$-0.884508\pi$
$929$	−56.9903	−1.86979	−0.934896	+	0.354921i	$0.884508\pi$
$930$	−10.7392	−0.352154
$931$	21.0978	0.691452
$932$	107.145	3.50965
$933$	−1.01003	−0.0330668
$934$	15.6102	0.510782
$935$	−12.2537	−0.400739
$936$	−124.268	−4.06181
$937$	−23.6415	−0.772333	−0.386167	−	0.922429i	$-0.626201\pi$
$937$	−23.6415	−0.772333	−0.386167	+	0.922429i	$0.626201\pi$
$938$	−13.0441	−0.425904
$939$	−12.0770	−0.394117
$940$	−30.6390	−0.999333
$941$	22.0207	0.717855	0.358927	−	0.933365i	$-0.383143\pi$
$941$	22.0207	0.717855	0.358927	+	0.933365i	$0.383143\pi$
$942$	−3.61631	−0.117826
$943$	15.4823	0.504173
$944$	−9.07847	−0.295479
$945$	3.43884	0.111865
$946$	−0.181224	−0.00589211
$947$	−9.91359	−0.322149	−0.161074	−	0.986942i	$-0.551496\pi$
$947$	−9.91359	−0.322149	−0.161074	+	0.986942i	$0.551496\pi$
$948$	−41.1647	−1.33697
$949$	93.0450	3.02037
$950$	−25.4717	−0.826413
$951$	1.56414	0.0507207
$952$	14.0046	0.453892
$953$	0.188075	0.00609233	0.00304617	−	0.999995i	$-0.499030\pi$
$953$	0.188075	0.00609233	0.00304617	+	0.999995i	$0.499030\pi$
$954$	−67.3959	−2.18202
$955$	−31.7464	−1.02729
$956$	−43.6239	−1.41090
$957$	0.422335	0.0136521
$958$	−29.2695	−0.945654
$959$	7.07430	0.228441
$960$	−3.59155	−0.115917
$961$	−8.49611	−0.274068
$962$	−195.679	−6.30895
$963$	−37.4820	−1.20784
$964$	−43.3623	−1.39660
$965$	28.3760	0.913457
$966$	−2.05771	−0.0662058
$967$	0.0656192	0.00211017	0.00105509	−	0.999999i	$-0.499664\pi$
$967$	0.0656192	0.00211017	0.00105509	+	0.999999i	$0.499664\pi$
$968$	12.7026	0.408277
$969$	5.86905	0.188541
$970$	48.1094	1.54470
$971$	−15.4909	−0.497127	−0.248563	−	0.968616i	$-0.579958\pi$
$971$	−15.4909	−0.497127	−0.248563	+	0.968616i	$0.579958\pi$
$972$	65.7357	2.10847
$973$	−10.5049	−0.336772
$974$	77.8341	2.49397
$975$	13.1178	0.420105
$976$	−8.82382	−0.282444
$977$	11.2387	0.359558	0.179779	−	0.983707i	$-0.442462\pi$
$977$	11.2387	0.359558	0.179779	+	0.983707i	$0.442462\pi$
$978$	1.41320	0.0451891
$979$	42.8804	1.37046
$980$	42.6075	1.36105
$981$	−30.6489	−0.978544
$982$	35.7202	1.13988
$983$	−56.5750	−1.80446	−0.902231	−	0.431254i	$-0.858071\pi$
$983$	−56.5750	−1.80446	−0.902231	+	0.431254i	$0.858071\pi$
$984$	−36.8939	−1.17613
$985$	−10.8717	−0.346400
$986$	−1.66567	−0.0530458
$987$	2.05137	0.0652958
$988$	104.406	3.32160
$989$	−0.0421041	−0.00133883
$990$	28.5477	0.907305
$991$	−36.6590	−1.16451	−0.582255	−	0.813006i	$-0.697830\pi$
$991$	−36.6590	−1.16451	−0.582255	+	0.813006i	$0.697830\pi$
$992$	38.8087	1.23218
$993$	15.7162	0.498740
$994$	28.0582	0.889951
$995$	−8.02291	−0.254343
$996$	9.73706	0.308531
$997$	7.83835	0.248243	0.124122	−	0.992267i	$-0.460389\pi$
$997$	7.83835	0.248243	0.124122	+	0.992267i	$0.460389\pi$
$998$	−43.8746	−1.38883
$999$	38.5987	1.22121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.11	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +O(q^{10})\)	\(q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +3.61596 q^{10} -3.02715 q^{11} +2.92808 q^{12} -6.88837 q^{13} -1.80856 q^{14} -0.876105 q^{15} +8.51988 q^{16} -2.89267 q^{17} +6.73911 q^{18} -3.24077 q^{19} -6.54480 q^{20} +0.438193 q^{21} +7.82208 q^{22} +1.81731 q^{23} -4.33060 q^{24} -3.04174 q^{25} +17.7994 q^{26} -3.51101 q^{27} +3.27345 q^{28} -0.222845 q^{29} +2.26384 q^{30} -4.74383 q^{31} -8.18088 q^{32} -1.89520 q^{33} +7.47459 q^{34} -0.979444 q^{35} -12.1976 q^{36} -10.9936 q^{37} +8.37406 q^{38} -4.31258 q^{39} +9.67970 q^{40} +8.51933 q^{41} -1.13228 q^{42} -0.0231683 q^{43} -14.1578 q^{44} +3.64963 q^{45} -4.69590 q^{46} +4.68142 q^{47} +5.33402 q^{48} -6.51012 q^{49} +7.85979 q^{50} -1.81101 q^{51} -32.2165 q^{52} -10.0007 q^{53} +9.07238 q^{54} +4.23612 q^{55} -4.84141 q^{56} -2.02894 q^{57} +0.575825 q^{58} -1.06556 q^{59} -4.09749 q^{60} -1.03567 q^{61} +12.2579 q^{62} -1.82540 q^{63} +4.09945 q^{64} +9.63943 q^{65} +4.89715 q^{66} +7.21240 q^{67} -13.5288 q^{68} +1.13776 q^{69} +2.53086 q^{70} -15.5141 q^{71} +18.0402 q^{72} -13.5076 q^{73} +28.4072 q^{74} -1.90434 q^{75} -15.1569 q^{76} -2.11874 q^{77} +11.1436 q^{78} -14.0586 q^{79} -11.9225 q^{80} +5.62599 q^{81} -22.0138 q^{82} +3.32541 q^{83} +2.04940 q^{84} +4.04794 q^{85} +0.0598664 q^{86} -0.139516 q^{87} +20.9392 q^{88} -14.1653 q^{89} -9.43057 q^{90} -4.82126 q^{91} +8.49947 q^{92} -2.96996 q^{93} -12.0967 q^{94} +4.53505 q^{95} -5.12178 q^{96} +13.3047 q^{97} +16.8220 q^{98} +7.89491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 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

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