LMFDB - Embedded newform 2671.2.a.b.1.106

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.106
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.33538 q^{2} -2.90179 q^{3} +3.45399 q^{4} +1.62391 q^{5} -6.77678 q^{6} +3.07108 q^{7} +3.39563 q^{8} +5.42039 q^{9} +O(q^{10})$	\(q+2.33538 q^{2} -2.90179 q^{3} +3.45399 q^{4} +1.62391 q^{5} -6.77678 q^{6} +3.07108 q^{7} +3.39563 q^{8} +5.42039 q^{9} +3.79244 q^{10} +4.58285 q^{11} -10.0228 q^{12} +3.94795 q^{13} +7.17214 q^{14} -4.71224 q^{15} +1.02209 q^{16} -2.33704 q^{17} +12.6587 q^{18} +4.12619 q^{19} +5.60897 q^{20} -8.91163 q^{21} +10.7027 q^{22} -4.52589 q^{23} -9.85340 q^{24} -2.36293 q^{25} +9.21995 q^{26} -7.02345 q^{27} +10.6075 q^{28} -2.90522 q^{29} -11.0049 q^{30} -1.57929 q^{31} -4.40429 q^{32} -13.2985 q^{33} -5.45788 q^{34} +4.98715 q^{35} +18.7220 q^{36} +8.02158 q^{37} +9.63622 q^{38} -11.4561 q^{39} +5.51419 q^{40} -0.390106 q^{41} -20.8120 q^{42} -1.93136 q^{43} +15.8292 q^{44} +8.80220 q^{45} -10.5697 q^{46} +3.68628 q^{47} -2.96589 q^{48} +2.43153 q^{49} -5.51833 q^{50} +6.78161 q^{51} +13.6362 q^{52} +1.97115 q^{53} -16.4024 q^{54} +7.44213 q^{55} +10.4282 q^{56} -11.9733 q^{57} -6.78480 q^{58} -6.45910 q^{59} -16.2760 q^{60} +3.50970 q^{61} -3.68824 q^{62} +16.6464 q^{63} -12.3299 q^{64} +6.41110 q^{65} -31.0570 q^{66} -8.45547 q^{67} -8.07214 q^{68} +13.1332 q^{69} +11.6469 q^{70} +8.09151 q^{71} +18.4056 q^{72} +6.20819 q^{73} +18.7334 q^{74} +6.85672 q^{75} +14.2518 q^{76} +14.0743 q^{77} -26.7544 q^{78} -13.0605 q^{79} +1.65978 q^{80} +4.11943 q^{81} -0.911045 q^{82} +12.8912 q^{83} -30.7807 q^{84} -3.79514 q^{85} -4.51046 q^{86} +8.43035 q^{87} +15.5617 q^{88} +1.54319 q^{89} +20.5565 q^{90} +12.1245 q^{91} -15.6324 q^{92} +4.58277 q^{93} +8.60886 q^{94} +6.70055 q^{95} +12.7803 q^{96} -10.8844 q^{97} +5.67856 q^{98} +24.8408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * 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 $

$2$	2.33538	1.65136	0.825681	−	0.564137i	$-0.190791\pi$
$2$	2.33538	1.65136	0.825681	+	0.564137i	$0.190791\pi$
$3$	−2.90179	−1.67535	−0.837675	−	0.546169i	$-0.816085\pi$
$3$	−2.90179	−1.67535	−0.837675	+	0.546169i	$0.816085\pi$
$4$	3.45399	1.72700
$5$	1.62391	0.726233	0.363117	−	0.931744i	$-0.381713\pi$
$5$	1.62391	0.726233	0.363117	+	0.931744i	$0.381713\pi$
$6$	−6.77678	−2.76661
$7$	3.07108	1.16076	0.580380	−	0.814346i	$-0.302904\pi$
$7$	3.07108	1.16076	0.580380	+	0.814346i	$0.302904\pi$
$8$	3.39563	1.20054
$9$	5.42039	1.80680
$10$	3.79244	1.19927
$11$	4.58285	1.38178	0.690891	−	0.722959i	$-0.257218\pi$
$11$	4.58285	1.38178	0.690891	+	0.722959i	$0.257218\pi$
$12$	−10.0228	−2.89332
$13$	3.94795	1.09496	0.547482	−	0.836818i	$-0.315587\pi$
$13$	3.94795	1.09496	0.547482	+	0.836818i	$0.315587\pi$
$14$	7.17214	1.91683
$15$	−4.71224	−1.21669
$16$	1.02209	0.255523
$17$	−2.33704	−0.566816	−0.283408	−	0.958999i	$-0.591465\pi$
$17$	−2.33704	−0.566816	−0.283408	+	0.958999i	$0.591465\pi$
$18$	12.6587	2.98367
$19$	4.12619	0.946613	0.473307	−	0.880898i	$-0.343060\pi$
$19$	4.12619	0.946613	0.473307	+	0.880898i	$0.343060\pi$
$20$	5.60897	1.25420
$21$	−8.91163	−1.94468
$22$	10.7027	2.28182
$23$	−4.52589	−0.943714	−0.471857	−	0.881675i	$-0.656416\pi$
$23$	−4.52589	−0.943714	−0.471857	+	0.881675i	$0.656416\pi$
$24$	−9.85340	−2.01132
$25$	−2.36293	−0.472585
$26$	9.21995	1.80818
$27$	−7.02345	−1.35166
$28$	10.6075	2.00463
$29$	−2.90522	−0.539487	−0.269743	−	0.962932i	$-0.586939\pi$
$29$	−2.90522	−0.539487	−0.269743	+	0.962932i	$0.586939\pi$
$30$	−11.0049	−2.00920
$31$	−1.57929	−0.283649	−0.141825	−	0.989892i	$-0.545297\pi$
$31$	−1.57929	−0.283649	−0.141825	+	0.989892i	$0.545297\pi$
$32$	−4.40429	−0.778576
$33$	−13.2985	−2.31497
$34$	−5.45788	−0.936019
$35$	4.98715	0.842982
$36$	18.7220	3.12033
$37$	8.02158	1.31874	0.659370	−	0.751818i	$-0.270823\pi$
$37$	8.02158	1.31874	0.659370	+	0.751818i	$0.270823\pi$
$38$	9.63622	1.56320
$39$	−11.4561	−1.83445
$40$	5.51419	0.871869
$41$	−0.390106	−0.0609243	−0.0304622	−	0.999536i	$-0.509698\pi$
$41$	−0.390106	−0.0609243	−0.0304622	+	0.999536i	$0.509698\pi$
$42$	−20.8120	−3.21137
$43$	−1.93136	−0.294530	−0.147265	−	0.989097i	$-0.547047\pi$
$43$	−1.93136	−0.294530	−0.147265	+	0.989097i	$0.547047\pi$
$44$	15.8292	2.38633
$45$	8.80220	1.31216
$46$	−10.5697	−1.55841
$47$	3.68628	0.537699	0.268850	−	0.963182i	$-0.413356\pi$
$47$	3.68628	0.537699	0.268850	+	0.963182i	$0.413356\pi$
$48$	−2.96589	−0.428090
$49$	2.43153	0.347362
$50$	−5.51833	−0.780409
$51$	6.78161	0.949615
$52$	13.6362	1.89100
$53$	1.97115	0.270758	0.135379	−	0.990794i	$-0.456775\pi$
$53$	1.97115	0.270758	0.135379	+	0.990794i	$0.456775\pi$
$54$	−16.4024	−2.23209
$55$	7.44213	1.00350
$56$	10.4282	1.39353
$57$	−11.9733	−1.58591
$58$	−6.78480	−0.890888
$59$	−6.45910	−0.840903	−0.420451	−	0.907315i	$-0.638128\pi$
$59$	−6.45910	−0.840903	−0.420451	+	0.907315i	$0.638128\pi$
$60$	−16.2760	−2.10123
$61$	3.50970	0.449371	0.224685	−	0.974431i	$-0.427865\pi$
$61$	3.50970	0.449371	0.224685	+	0.974431i	$0.427865\pi$
$62$	−3.68824	−0.468408
$63$	16.6464	2.09725
$64$	−12.3299	−1.54123
$65$	6.41110	0.795199
$66$	−31.0570	−3.82285
$67$	−8.45547	−1.03300	−0.516500	−	0.856287i	$-0.672765\pi$
$67$	−8.45547	−1.03300	−0.516500	+	0.856287i	$0.672765\pi$
$68$	−8.07214	−0.978890
$69$	13.1332	1.58105
$70$	11.6469	1.39207
$71$	8.09151	0.960285	0.480143	−	0.877190i	$-0.340585\pi$
$71$	8.09151	0.960285	0.480143	+	0.877190i	$0.340585\pi$
$72$	18.4056	2.16912
$73$	6.20819	0.726613	0.363307	−	0.931670i	$-0.381648\pi$
$73$	6.20819	0.726613	0.363307	+	0.931670i	$0.381648\pi$
$74$	18.7334	2.17772
$75$	6.85672	0.791745
$76$	14.2518	1.63480
$77$	14.0743	1.60392
$78$	−26.7544	−3.02934
$79$	−13.0605	−1.46942	−0.734712	−	0.678379i	$-0.762683\pi$
$79$	−13.0605	−1.46942	−0.734712	+	0.678379i	$0.762683\pi$
$80$	1.65978	0.185569
$81$	4.11943	0.457715
$82$	−0.911045	−0.100608
$83$	12.8912	1.41499	0.707495	−	0.706718i	$-0.249825\pi$
$83$	12.8912	1.41499	0.707495	+	0.706718i	$0.249825\pi$
$84$	−30.7807	−3.35845
$85$	−3.79514	−0.411641
$86$	−4.51046	−0.486376
$87$	8.43035	0.903828
$88$	15.5617	1.65888
$89$	1.54319	0.163577	0.0817887	−	0.996650i	$-0.473937\pi$
$89$	1.54319	0.163577	0.0817887	+	0.996650i	$0.473937\pi$
$90$	20.5565	2.16684
$91$	12.1245	1.27099
$92$	−15.6324	−1.62979
$93$	4.58277	0.475211
$94$	8.60886	0.887937
$95$	6.70055	0.687462
$96$	12.7803	1.30439
$97$	−10.8844	−1.10514	−0.552570	−	0.833466i	$-0.686353\pi$
$97$	−10.8844	−1.10514	−0.552570	+	0.833466i	$0.686353\pi$
$98$	5.67856	0.573621
$99$	24.8408	2.49660
$100$	−8.16153	−0.816153
$101$	14.6917	1.46188	0.730940	−	0.682442i	$-0.239082\pi$
$101$	14.6917	1.46188	0.730940	+	0.682442i	$0.239082\pi$
$102$	15.8376	1.56816
$103$	4.47043	0.440485	0.220243	−	0.975445i	$-0.429315\pi$
$103$	4.47043	0.440485	0.220243	+	0.975445i	$0.429315\pi$
$104$	13.4058	1.31454
$105$	−14.4717	−1.41229
$106$	4.60338	0.447119
$107$	−4.35392	−0.420909	−0.210455	−	0.977604i	$-0.567494\pi$
$107$	−4.35392	−0.420909	−0.210455	+	0.977604i	$0.567494\pi$
$108$	−24.2590	−2.33432
$109$	13.0802	1.25285	0.626426	−	0.779481i	$-0.284517\pi$
$109$	13.0802	1.25285	0.626426	+	0.779481i	$0.284517\pi$
$110$	17.3802	1.65714
$111$	−23.2770	−2.20935
$112$	3.13892	0.296600
$113$	7.65059	0.719707	0.359854	−	0.933009i	$-0.382827\pi$
$113$	7.65059	0.719707	0.359854	+	0.933009i	$0.382827\pi$
$114$	−27.9623	−2.61891
$115$	−7.34963	−0.685357
$116$	−10.0346	−0.931692
$117$	21.3994	1.97837
$118$	−15.0844	−1.38864
$119$	−7.17725	−0.657937
$120$	−16.0010	−1.46069
$121$	10.0025	0.909323
$122$	8.19648	0.742074
$123$	1.13201	0.102070
$124$	−5.45487	−0.489861
$125$	−11.9567	−1.06944
$126$	38.8758	3.46333
$127$	2.58234	0.229145	0.114573	−	0.993415i	$-0.463450\pi$
$127$	2.58234	0.229145	0.114573	+	0.993415i	$0.463450\pi$
$128$	−19.9863	−1.76656
$129$	5.60441	0.493441
$130$	14.9723	1.31316
$131$	4.23858	0.370327	0.185163	−	0.982708i	$-0.440719\pi$
$131$	4.23858	0.370327	0.185163	+	0.982708i	$0.440719\pi$
$132$	−45.9329	−3.99794
$133$	12.6719	1.09879
$134$	−19.7467	−1.70586
$135$	−11.4054	−0.981624
$136$	−7.93573	−0.680483
$137$	−4.00240	−0.341948	−0.170974	−	0.985276i	$-0.554691\pi$
$137$	−4.00240	−0.341948	−0.170974	+	0.985276i	$0.554691\pi$
$138$	30.6710	2.61089
$139$	−14.9226	−1.26571	−0.632857	−	0.774269i	$-0.718118\pi$
$139$	−14.9226	−1.26571	−0.632857	+	0.774269i	$0.718118\pi$
$140$	17.2256	1.45583
$141$	−10.6968	−0.900834
$142$	18.8967	1.58578
$143$	18.0929	1.51300
$144$	5.54013	0.461677
$145$	−4.71781	−0.391793
$146$	14.4985	1.19990
$147$	−7.05580	−0.581953
$148$	27.7065	2.27746
$149$	17.5807	1.44026	0.720132	−	0.693837i	$-0.244081\pi$
$149$	17.5807	1.44026	0.720132	+	0.693837i	$0.244081\pi$
$150$	16.0130	1.30746
$151$	−3.28168	−0.267059	−0.133530	−	0.991045i	$-0.542631\pi$
$151$	−3.28168	−0.267059	−0.133530	+	0.991045i	$0.542631\pi$
$152$	14.0110	1.13644
$153$	−12.6677	−1.02412
$154$	32.8689	2.64865
$155$	−2.56462	−0.205995
$156$	−39.5694	−3.16808
$157$	−24.7818	−1.97781	−0.988903	−	0.148566i	$-0.952534\pi$
$157$	−24.7818	−1.97781	−0.988903	+	0.148566i	$0.952534\pi$
$158$	−30.5013	−2.42655
$159$	−5.71985	−0.453614
$160$	−7.15216	−0.565428
$161$	−13.8994	−1.09543
$162$	9.62044	0.755853
$163$	−16.0542	−1.25746	−0.628730	−	0.777624i	$-0.716425\pi$
$163$	−16.0542	−1.25746	−0.628730	+	0.777624i	$0.716425\pi$
$164$	−1.34742	−0.105216
$165$	−21.5955	−1.68121
$166$	30.1058	2.33666
$167$	7.19570	0.556820	0.278410	−	0.960462i	$-0.410193\pi$
$167$	7.19570	0.556820	0.278410	+	0.960462i	$0.410193\pi$
$168$	−30.2606	−2.33466
$169$	2.58628	0.198945
$170$	−8.86309	−0.679768
$171$	22.3656	1.71034
$172$	−6.67091	−0.508652
$173$	16.4831	1.25318	0.626592	−	0.779347i	$-0.284449\pi$
$173$	16.4831	1.25318	0.626592	+	0.779347i	$0.284449\pi$
$174$	19.6881	1.49255
$175$	−7.25674	−0.548558
$176$	4.68409	0.353077
$177$	18.7429	1.40881
$178$	3.60393	0.270126
$179$	−22.5283	−1.68384	−0.841922	−	0.539598i	$-0.818576\pi$
$179$	−22.5283	−1.68384	−0.841922	+	0.539598i	$0.818576\pi$
$180$	30.4028	2.26609
$181$	17.7672	1.32062	0.660312	−	0.750991i	$-0.270424\pi$
$181$	17.7672	1.32062	0.660312	+	0.750991i	$0.270424\pi$
$182$	28.3152	2.09886
$183$	−10.1844	−0.752853
$184$	−15.3683	−1.13296
$185$	13.0263	0.957713
$186$	10.7025	0.784746
$187$	−10.7103	−0.783217
$188$	12.7324	0.928606
$189$	−21.5696	−1.56896
$190$	15.6483	1.13525
$191$	1.91151	0.138312	0.0691562	−	0.997606i	$-0.477969\pi$
$191$	1.91151	0.138312	0.0691562	+	0.997606i	$0.477969\pi$
$192$	35.7787	2.58210
$193$	−22.2429	−1.60108	−0.800539	−	0.599281i	$-0.795453\pi$
$193$	−22.2429	−1.60108	−0.800539	+	0.599281i	$0.795453\pi$
$194$	−25.4191	−1.82499
$195$	−18.6037	−1.33224
$196$	8.39851	0.599893
$197$	13.2235	0.942133	0.471066	−	0.882098i	$-0.343869\pi$
$197$	13.2235	0.942133	0.471066	+	0.882098i	$0.343869\pi$
$198$	58.0128	4.12279
$199$	0.894495	0.0634090	0.0317045	−	0.999497i	$-0.489906\pi$
$199$	0.894495	0.0634090	0.0317045	+	0.999497i	$0.489906\pi$
$200$	−8.02362	−0.567356
$201$	24.5360	1.73064
$202$	34.3107	2.41409
$203$	−8.92218	−0.626214
$204$	23.4236	1.63998
$205$	−0.633496	−0.0442453
$206$	10.4402	0.727400
$207$	−24.5321	−1.70510
$208$	4.03516	0.279788
$209$	18.9097	1.30801
$210$	−33.7968	−2.33220
$211$	−0.923897	−0.0636037	−0.0318019	−	0.999494i	$-0.510125\pi$
$211$	−0.923897	−0.0636037	−0.0318019	+	0.999494i	$0.510125\pi$
$212$	6.80833	0.467598
$213$	−23.4799	−1.60881
$214$	−10.1681	−0.695074
$215$	−3.13635	−0.213897
$216$	−23.8490	−1.62272
$217$	−4.85013	−0.329248
$218$	30.5471	2.06891
$219$	−18.0149	−1.21733
$220$	25.7051	1.73304
$221$	−9.22652	−0.620643
$222$	−54.3605	−3.64844
$223$	18.6135	1.24645	0.623226	−	0.782042i	$-0.285822\pi$
$223$	18.6135	1.24645	0.623226	+	0.782042i	$0.285822\pi$
$224$	−13.5259	−0.903739
$225$	−12.8080	−0.853865
$226$	17.8670	1.18850
$227$	−21.4728	−1.42520	−0.712602	−	0.701569i	$-0.752483\pi$
$227$	−21.4728	−1.42520	−0.712602	+	0.701569i	$0.752483\pi$
$228$	−41.3559	−2.73886
$229$	−9.54628	−0.630836	−0.315418	−	0.948953i	$-0.602145\pi$
$229$	−9.54628	−0.630836	−0.315418	+	0.948953i	$0.602145\pi$
$230$	−17.1642	−1.13177
$231$	−40.8407	−2.68712
$232$	−9.86506	−0.647673
$233$	−27.6900	−1.81403	−0.907015	−	0.421097i	$-0.861645\pi$
$233$	−27.6900	−1.81403	−0.907015	+	0.421097i	$0.861645\pi$
$234$	49.9757	3.26701
$235$	5.98618	0.390495
$236$	−22.3097	−1.45224
$237$	37.8989	2.46180
$238$	−16.7616	−1.08649
$239$	−16.5584	−1.07107	−0.535536	−	0.844512i	$-0.679890\pi$
$239$	−16.5584	−1.07107	−0.535536	+	0.844512i	$0.679890\pi$
$240$	−4.81633	−0.310893
$241$	17.2290	1.10981	0.554907	−	0.831912i	$-0.312754\pi$
$241$	17.2290	1.10981	0.554907	+	0.831912i	$0.312754\pi$
$242$	23.3597	1.50162
$243$	9.11664	0.584832
$244$	12.1225	0.776062
$245$	3.94859	0.252266
$246$	2.64366	0.168554
$247$	16.2900	1.03651
$248$	−5.36269	−0.340531
$249$	−37.4075	−2.37060
$250$	−27.9234	−1.76603
$251$	20.6855	1.30566	0.652828	−	0.757506i	$-0.273582\pi$
$251$	20.6855	1.30566	0.652828	+	0.757506i	$0.273582\pi$
$252$	57.4967	3.62195
$253$	−20.7415	−1.30401
$254$	6.03074	0.378402
$255$	11.0127	0.689642
$256$	−22.0159	−1.37600
$257$	−4.11430	−0.256643	−0.128321	−	0.991733i	$-0.540959\pi$
$257$	−4.11430	−0.256643	−0.128321	+	0.991733i	$0.540959\pi$
$258$	13.0884	0.814849
$259$	24.6349	1.53074
$260$	22.1439	1.37331
$261$	−15.7474	−0.974742
$262$	9.89869	0.611543
$263$	−11.4378	−0.705285	−0.352643	−	0.935758i	$-0.614717\pi$
$263$	−11.4378	−0.705285	−0.352643	+	0.935758i	$0.614717\pi$
$264$	−45.1567	−2.77920
$265$	3.20096	0.196633
$266$	29.5936	1.81450
$267$	−4.47800	−0.274049
$268$	−29.2051	−1.78399
$269$	−10.7100	−0.653002	−0.326501	−	0.945197i	$-0.605870\pi$
$269$	−10.7100	−0.653002	−0.326501	+	0.945197i	$0.605870\pi$
$270$	−26.6360	−1.62102
$271$	−1.64620	−0.0999996	−0.0499998	−	0.998749i	$-0.515922\pi$
$271$	−1.64620	−0.0999996	−0.0499998	+	0.998749i	$0.515922\pi$
$272$	−2.38867	−0.144834
$273$	−35.1826	−2.12935
$274$	−9.34713	−0.564681
$275$	−10.8289	−0.653010
$276$	45.3620	2.73047
$277$	−17.1647	−1.03133	−0.515664	−	0.856791i	$-0.672455\pi$
$277$	−17.1647	−1.03133	−0.515664	+	0.856791i	$0.672455\pi$
$278$	−34.8498	−2.09015
$279$	−8.56037	−0.512496
$280$	16.9345	1.01203
$281$	28.4251	1.69570	0.847849	−	0.530237i	$-0.177897\pi$
$281$	28.4251	1.69570	0.847849	+	0.530237i	$0.177897\pi$
$282$	−24.9811	−1.48760
$283$	−9.83148	−0.584421	−0.292210	−	0.956354i	$-0.594391\pi$
$283$	−9.83148	−0.584421	−0.292210	+	0.956354i	$0.594391\pi$
$284$	27.9480	1.65841
$285$	−19.4436	−1.15174
$286$	42.2537	2.49851
$287$	−1.19805	−0.0707185
$288$	−23.8729	−1.40673
$289$	−11.5382	−0.678719
$290$	−11.0179	−0.646992
$291$	31.5842	1.85150
$292$	21.4430	1.25486
$293$	−5.73933	−0.335295	−0.167648	−	0.985847i	$-0.553617\pi$
$293$	−5.73933	−0.335295	−0.167648	+	0.985847i	$0.553617\pi$
$294$	−16.4780	−0.961015
$295$	−10.4890	−0.610692
$296$	27.2383	1.58320
$297$	−32.1875	−1.86771
$298$	41.0575	2.37840
$299$	−17.8680	−1.03333
$300$	23.6831	1.36734
$301$	−5.93137	−0.341878
$302$	−7.66396	−0.441011
$303$	−42.6322	−2.44916
$304$	4.21734	0.241881
$305$	5.69942	0.326348
$306$	−29.5838	−1.69120
$307$	−6.77472	−0.386654	−0.193327	−	0.981134i	$-0.561928\pi$
$307$	−6.77472	−0.386654	−0.193327	+	0.981134i	$0.561928\pi$
$308$	48.6126	2.76996
$309$	−12.9723	−0.737966
$310$	−5.98937	−0.340173
$311$	−13.6874	−0.776140	−0.388070	−	0.921630i	$-0.626858\pi$
$311$	−13.6874	−0.776140	−0.388070	+	0.921630i	$0.626858\pi$
$312$	−38.9007	−2.20232
$313$	−12.8228	−0.724790	−0.362395	−	0.932025i	$-0.618041\pi$
$313$	−12.8228	−0.724790	−0.362395	+	0.932025i	$0.618041\pi$
$314$	−57.8750	−3.26607
$315$	27.0323	1.52310
$316$	−45.1110	−2.53769
$317$	32.5959	1.83077	0.915384	−	0.402582i	$-0.131887\pi$
$317$	32.5959	1.83077	0.915384	+	0.402582i	$0.131887\pi$
$318$	−13.3580	−0.749081
$319$	−13.3142	−0.745453
$320$	−20.0226	−1.11929
$321$	12.6342	0.705170
$322$	−32.4603	−1.80894
$323$	−9.64309	−0.536556
$324$	14.2285	0.790472
$325$	−9.32871	−0.517463
$326$	−37.4926	−2.07652
$327$	−37.9559	−2.09896
$328$	−1.32466	−0.0731419
$329$	11.3209	0.624140
$330$	−50.4337	−2.77628
$331$	−29.2974	−1.61033	−0.805166	−	0.593050i	$-0.797924\pi$
$331$	−29.2974	−1.61033	−0.805166	+	0.593050i	$0.797924\pi$
$332$	44.5260	2.44368
$333$	43.4801	2.38269
$334$	16.8047	0.919512
$335$	−13.7309	−0.750199
$336$	−9.10850	−0.496909
$337$	14.5145	0.790657	0.395328	−	0.918540i	$-0.370631\pi$
$337$	14.5145	0.790657	0.395328	+	0.918540i	$0.370631\pi$
$338$	6.03995	0.328530
$339$	−22.2004	−1.20576
$340$	−13.1084	−0.710903
$341$	−7.23766	−0.391941
$342$	52.2321	2.82439
$343$	−14.0301	−0.757555
$344$	−6.55819	−0.353594
$345$	21.3271	1.14821
$346$	38.4942	2.06946
$347$	−10.1052	−0.542474	−0.271237	−	0.962513i	$-0.587433\pi$
$347$	−10.1052	−0.542474	−0.271237	+	0.962513i	$0.587433\pi$
$348$	29.1184	1.56091
$349$	29.7353	1.59170	0.795848	−	0.605497i	$-0.207025\pi$
$349$	29.7353	1.59170	0.795848	+	0.605497i	$0.207025\pi$
$350$	−16.9472	−0.905867
$351$	−27.7282	−1.48002
$352$	−20.1842	−1.07582
$353$	4.14731	0.220739	0.110369	−	0.993891i	$-0.464797\pi$
$353$	4.14731	0.220739	0.110369	+	0.993891i	$0.464797\pi$
$354$	43.7719	2.32645
$355$	13.1399	0.697391
$356$	5.33016	0.282498
$357$	20.8269	1.10227
$358$	−52.6121	−2.78064
$359$	−21.1212	−1.11473	−0.557367	−	0.830266i	$-0.688188\pi$
$359$	−21.1212	−1.11473	−0.557367	+	0.830266i	$0.688188\pi$
$360$	29.8890	1.57529
$361$	−1.97454	−0.103923
$362$	41.4931	2.18083
$363$	−29.0253	−1.52343
$364$	41.8778	2.19499
$365$	10.0815	0.527691
$366$	−23.7845	−1.24323
$367$	−5.45112	−0.284546	−0.142273	−	0.989827i	$-0.545441\pi$
$367$	−5.45112	−0.284546	−0.142273	+	0.989827i	$0.545441\pi$
$368$	−4.62588	−0.241140
$369$	−2.11453	−0.110078
$370$	30.4214	1.58153
$371$	6.05355	0.314285
$372$	15.8289	0.820689
$373$	−22.2916	−1.15422	−0.577108	−	0.816668i	$-0.695819\pi$
$373$	−22.2916	−1.15422	−0.577108	+	0.816668i	$0.695819\pi$
$374$	−25.0127	−1.29337
$375$	34.6959	1.79169
$376$	12.5172	0.645528
$377$	−11.4697	−0.590718
$378$	−50.3732	−2.59092
$379$	15.7066	0.806796	0.403398	−	0.915025i	$-0.367829\pi$
$379$	15.7066	0.806796	0.403398	+	0.915025i	$0.367829\pi$
$380$	23.1437	1.18725
$381$	−7.49340	−0.383899
$382$	4.46411	0.228404
$383$	26.9258	1.37585	0.687923	−	0.725784i	$-0.258523\pi$
$383$	26.9258	1.37585	0.687923	+	0.725784i	$0.258523\pi$
$384$	57.9961	2.95960
$385$	22.8554	1.16482
$386$	−51.9456	−2.64396
$387$	−10.4687	−0.532155
$388$	−37.5946	−1.90858
$389$	22.5576	1.14371	0.571857	−	0.820353i	$-0.306223\pi$
$389$	22.5576	1.14371	0.571857	+	0.820353i	$0.306223\pi$
$390$	−43.4466	−2.20000
$391$	10.5772	0.534913
$392$	8.25659	0.417021
$393$	−12.2995	−0.620426
$394$	30.8818	1.55580
$395$	−21.2091	−1.06715
$396$	85.8001	4.31162
$397$	8.58910	0.431075	0.215537	−	0.976496i	$-0.430850\pi$
$397$	8.58910	0.431075	0.215537	+	0.976496i	$0.430850\pi$
$398$	2.08898	0.104711
$399$	−36.7711	−1.84086
$400$	−2.41512	−0.120756
$401$	22.0414	1.10070	0.550349	−	0.834935i	$-0.314495\pi$
$401$	22.0414	1.10070	0.550349	+	0.834935i	$0.314495\pi$
$402$	57.3008	2.85791
$403$	−6.23496	−0.310585
$404$	50.7451	2.52466
$405$	6.68958	0.332408
$406$	−20.8367	−1.03411
$407$	36.7617	1.82221
$408$	23.0278	1.14005
$409$	14.2178	0.703025	0.351512	−	0.936183i	$-0.385668\pi$
$409$	14.2178	0.703025	0.351512	+	0.936183i	$0.385668\pi$
$410$	−1.47945	−0.0730650
$411$	11.6141	0.572883
$412$	15.4409	0.760717
$413$	−19.8364	−0.976086
$414$	−57.2918	−2.81574
$415$	20.9341	1.02761
$416$	−17.3879	−0.852512
$417$	43.3021	2.12051
$418$	44.1614	2.16000
$419$	−28.7725	−1.40563	−0.702815	−	0.711372i	$-0.748074\pi$
$419$	−28.7725	−1.40563	−0.702815	+	0.711372i	$0.748074\pi$
$420$	−49.9850	−2.43902
$421$	17.1308	0.834903	0.417452	−	0.908699i	$-0.362923\pi$
$421$	17.1308	0.834903	0.417452	+	0.908699i	$0.362923\pi$
$422$	−2.15765	−0.105033
$423$	19.9811	0.971513
$424$	6.69328	0.325055
$425$	5.52226	0.267869
$426$	−54.8344	−2.65673
$427$	10.7786	0.521611
$428$	−15.0384	−0.726910
$429$	−52.5017	−2.53481
$430$	−7.32457	−0.353222
$431$	−11.9967	−0.577863	−0.288932	−	0.957350i	$-0.593300\pi$
$431$	−11.9967	−0.577863	−0.288932	+	0.957350i	$0.593300\pi$
$432$	−7.17861	−0.345381
$433$	−6.23183	−0.299483	−0.149741	−	0.988725i	$-0.547844\pi$
$433$	−6.23183	−0.299483	−0.149741	+	0.988725i	$0.547844\pi$
$434$	−11.3269	−0.543708
$435$	13.6901	0.656390
$436$	45.1788	2.16367
$437$	−18.6747	−0.893333
$438$	−42.0715	−2.01026
$439$	14.2149	0.678440	0.339220	−	0.940707i	$-0.389837\pi$
$439$	14.2149	0.678440	0.339220	+	0.940707i	$0.389837\pi$
$440$	25.2707	1.20473
$441$	13.1799	0.627612
$442$	−21.5474	−1.02491
$443$	−17.0391	−0.809553	−0.404776	−	0.914416i	$-0.632651\pi$
$443$	−17.0391	−0.809553	−0.404776	+	0.914416i	$0.632651\pi$
$444$	−80.3985	−3.81554
$445$	2.50599	0.118795
$446$	43.4696	2.05834
$447$	−51.0154	−2.41295
$448$	−37.8660	−1.78900
$449$	19.5649	0.923325	0.461662	−	0.887056i	$-0.347253\pi$
$449$	19.5649	0.923325	0.461662	+	0.887056i	$0.347253\pi$
$450$	−29.9115	−1.41004
$451$	−1.78780	−0.0841842
$452$	26.4251	1.24293
$453$	9.52274	0.447417
$454$	−50.1472	−2.35353
$455$	19.6890	0.923034
$456$	−40.6570	−1.90394
$457$	−15.1172	−0.707154	−0.353577	−	0.935405i	$-0.615035\pi$
$457$	−15.1172	−0.707154	−0.353577	+	0.935405i	$0.615035\pi$
$458$	−22.2942	−1.04174
$459$	16.4141	0.766145
$460$	−25.3856	−1.18361
$461$	8.92971	0.415898	0.207949	−	0.978140i	$-0.433321\pi$
$461$	8.92971	0.415898	0.207949	+	0.978140i	$0.433321\pi$
$462$	−95.3785	−4.43741
$463$	6.50543	0.302333	0.151166	−	0.988508i	$-0.451697\pi$
$463$	6.50543	0.302333	0.151166	+	0.988508i	$0.451697\pi$
$464$	−2.96940	−0.137851
$465$	7.44200	0.345114
$466$	−64.6666	−2.99562
$467$	15.3512	0.710367	0.355184	−	0.934797i	$-0.384418\pi$
$467$	15.3512	0.710367	0.355184	+	0.934797i	$0.384418\pi$
$468$	73.9134	3.41665
$469$	−25.9674	−1.19906
$470$	13.9800	0.644849
$471$	71.9117	3.31351
$472$	−21.9327	−1.00953
$473$	−8.85115	−0.406976
$474$	88.5084	4.06532
$475$	−9.74989	−0.447356
$476$	−24.7902	−1.13626
$477$	10.6844	0.489204
$478$	−38.6701	−1.76873
$479$	−4.92977	−0.225247	−0.112623	−	0.993638i	$-0.535925\pi$
$479$	−4.92977	−0.225247	−0.112623	+	0.993638i	$0.535925\pi$
$480$	20.7541	0.947289
$481$	31.6688	1.44397
$482$	40.2361	1.83271
$483$	40.3331	1.83522
$484$	34.5488	1.57040
$485$	−17.6752	−0.802590
$486$	21.2908	0.965770
$487$	−0.800635	−0.0362802	−0.0181401	−	0.999835i	$-0.505774\pi$
$487$	−0.800635	−0.0362802	−0.0181401	+	0.999835i	$0.505774\pi$
$488$	11.9176	0.539486
$489$	46.5858	2.10668
$490$	9.22145	0.416582
$491$	25.9610	1.17160	0.585802	−	0.810454i	$-0.300779\pi$
$491$	25.9610	1.17160	0.585802	+	0.810454i	$0.300779\pi$
$492$	3.90994	0.176274
$493$	6.78963	0.305790
$494$	38.0433	1.71165
$495$	40.3392	1.81311
$496$	−1.61418	−0.0724788
$497$	24.8497	1.11466
$498$	−87.3606	−3.91472
$499$	−16.7935	−0.751781	−0.375891	−	0.926664i	$-0.622663\pi$
$499$	−16.7935	−0.751781	−0.375891	+	0.926664i	$0.622663\pi$
$500$	−41.2984	−1.84692
$501$	−20.8804	−0.932869
$502$	48.3084	2.15611
$503$	10.3140	0.459877	0.229939	−	0.973205i	$-0.426147\pi$
$503$	10.3140	0.459877	0.229939	+	0.973205i	$0.426147\pi$
$504$	56.5251	2.51783
$505$	23.8580	1.06167
$506$	−48.4393	−2.15339
$507$	−7.50485	−0.333302
$508$	8.91938	0.395734
$509$	−9.25414	−0.410183	−0.205091	−	0.978743i	$-0.565749\pi$
$509$	−9.25414	−0.410183	−0.205091	+	0.978743i	$0.565749\pi$
$510$	25.7188	1.13885
$511$	19.0658	0.843423
$512$	−11.4429	−0.505708
$513$	−28.9801	−1.27950
$514$	−9.60845	−0.423810
$515$	7.25957	0.319895
$516$	19.3576	0.852171
$517$	16.8937	0.742984
$518$	57.5319	2.52781
$519$	−47.8304	−2.09952
$520$	21.7697	0.954665
$521$	14.1046	0.617934	0.308967	−	0.951073i	$-0.400017\pi$
$521$	14.1046	0.617934	0.308967	+	0.951073i	$0.400017\pi$
$522$	−36.7762	−1.60965
$523$	15.9626	0.697994	0.348997	−	0.937124i	$-0.386522\pi$
$523$	15.9626	0.697994	0.348997	+	0.937124i	$0.386522\pi$
$524$	14.6400	0.639553
$525$	21.0575	0.919026
$526$	−26.7116	−1.16468
$527$	3.69087	0.160777
$528$	−13.5923	−0.591527
$529$	−2.51628	−0.109403
$530$	7.47545	0.324713
$531$	−35.0108	−1.51934
$532$	43.7686	1.89761
$533$	−1.54012	−0.0667099
$534$	−10.4578	−0.452555
$535$	−7.07036	−0.305678
$536$	−28.7116	−1.24015
$537$	65.3724	2.82103
$538$	−25.0120	−1.07834
$539$	11.1434	0.479979
$540$	−39.3943	−1.69526
$541$	−32.8240	−1.41121	−0.705607	−	0.708604i	$-0.749326\pi$
$541$	−32.8240	−1.41121	−0.705607	+	0.708604i	$0.749326\pi$
$542$	−3.84450	−0.165136
$543$	−51.5566	−2.21251
$544$	10.2930	0.441309
$545$	21.2409	0.909862
$546$	−82.1648	−3.51633
$547$	−31.7289	−1.35663	−0.678316	−	0.734771i	$-0.737290\pi$
$547$	−31.7289	−1.35663	−0.678316	+	0.734771i	$0.737290\pi$
$548$	−13.8243	−0.590544
$549$	19.0239	0.811921
$550$	−25.2897	−1.07836
$551$	−11.9875	−0.510685
$552$	44.5955	1.89811
$553$	−40.1099	−1.70565
$554$	−40.0862	−1.70310
$555$	−37.7996	−1.60450
$556$	−51.5424	−2.18589
$557$	−21.9386	−0.929568	−0.464784	−	0.885424i	$-0.653868\pi$
$557$	−21.9386	−0.929568	−0.464784	+	0.885424i	$0.653868\pi$
$558$	−19.9917	−0.846317
$559$	−7.62491	−0.322499
$560$	5.09732	0.215401
$561$	31.0791	1.31216
$562$	66.3833	2.80021
$563$	−7.70297	−0.324641	−0.162321	−	0.986738i	$-0.551898\pi$
$563$	−7.70297	−0.324641	−0.162321	+	0.986738i	$0.551898\pi$
$564$	−36.9468	−1.55574
$565$	12.4239	0.522675
$566$	−22.9602	−0.965091
$567$	12.6511	0.531297
$568$	27.4758	1.15286
$569$	−38.7961	−1.62642	−0.813209	−	0.581971i	$-0.802282\pi$
$569$	−38.7961	−1.62642	−0.813209	+	0.581971i	$0.802282\pi$
$570$	−45.4082	−1.90194
$571$	−31.7276	−1.32776	−0.663879	−	0.747840i	$-0.731091\pi$
$571$	−31.7276	−1.32776	−0.663879	+	0.747840i	$0.731091\pi$
$572$	62.4927	2.61295
$573$	−5.54681	−0.231721
$574$	−2.79789	−0.116782
$575$	10.6944	0.445985
$576$	−66.8326	−2.78469
$577$	−39.0030	−1.62372	−0.811859	−	0.583853i	$-0.801544\pi$
$577$	−39.0030	−1.62372	−0.811859	+	0.583853i	$0.801544\pi$
$578$	−26.9461	−1.12081
$579$	64.5442	2.68237
$580$	−16.2953	−0.676626
$581$	39.5898	1.64246
$582$	73.7610	3.05749
$583$	9.03348	0.374128
$584$	21.0807	0.872326
$585$	34.7506	1.43676
$586$	−13.4035	−0.553694
$587$	−3.85845	−0.159255	−0.0796277	−	0.996825i	$-0.525373\pi$
$587$	−3.85845	−0.159255	−0.0796277	+	0.996825i	$0.525373\pi$
$588$	−24.3707	−1.00503
$589$	−6.51646	−0.268506
$590$	−24.4957	−1.00847
$591$	−38.3717	−1.57840
$592$	8.19879	0.336968
$593$	8.27131	0.339662	0.169831	−	0.985473i	$-0.445678\pi$
$593$	8.27131	0.339662	0.169831	+	0.985473i	$0.445678\pi$
$594$	−75.1699	−3.08426
$595$	−11.6552	−0.477816
$596$	60.7236	2.48733
$597$	−2.59564	−0.106232
$598$	−41.7285	−1.70641
$599$	−8.48515	−0.346694	−0.173347	−	0.984861i	$-0.555458\pi$
$599$	−8.48515	−0.346694	−0.173347	+	0.984861i	$0.555458\pi$
$600$	23.2829	0.950519
$601$	26.3815	1.07612	0.538062	−	0.842905i	$-0.319157\pi$
$601$	26.3815	1.07612	0.538062	+	0.842905i	$0.319157\pi$
$602$	−13.8520	−0.564565
$603$	−45.8319	−1.86642
$604$	−11.3349	−0.461211
$605$	16.2432	0.660380
$606$	−99.5624	−4.04445
$607$	−31.7371	−1.28817	−0.644084	−	0.764955i	$-0.722761\pi$
$607$	−31.7371	−1.28817	−0.644084	+	0.764955i	$0.722761\pi$
$608$	−18.1729	−0.737010
$609$	25.8903	1.04913
$610$	13.3103	0.538919
$611$	14.5532	0.588761
$612$	−43.7541	−1.76865
$613$	32.5523	1.31478	0.657388	−	0.753552i	$-0.271661\pi$
$613$	32.5523	1.31478	0.657388	+	0.753552i	$0.271661\pi$
$614$	−15.8215	−0.638505
$615$	1.83827	0.0741263
$616$	47.7911	1.92556
$617$	12.5546	0.505428	0.252714	−	0.967541i	$-0.418677\pi$
$617$	12.5546	0.505428	0.252714	+	0.967541i	$0.418677\pi$
$618$	−30.2952	−1.21865
$619$	−8.31032	−0.334020	−0.167010	−	0.985955i	$-0.553411\pi$
$619$	−8.31032	−0.334020	−0.167010	+	0.985955i	$0.553411\pi$
$620$	−8.85819	−0.355754
$621$	31.7874	1.27559
$622$	−31.9652	−1.28169
$623$	4.73925	0.189874
$624$	−11.7092	−0.468743
$625$	−7.60195	−0.304078
$626$	−29.9462	−1.19689
$627$	−54.8721	−2.19138
$628$	−85.5963	−3.41566
$629$	−18.7468	−0.747483
$630$	63.1306	2.51518
$631$	6.61598	0.263378	0.131689	−	0.991291i	$-0.457960\pi$
$631$	6.61598	0.263378	0.131689	+	0.991291i	$0.457960\pi$
$632$	−44.3487	−1.76410
$633$	2.68096	0.106558
$634$	76.1238	3.02326
$635$	4.19348	0.166413
$636$	−19.7563	−0.783390
$637$	9.59957	0.380349
$638$	−31.0937	−1.23101
$639$	43.8591	1.73504
$640$	−32.4559	−1.28293
$641$	44.7667	1.76818	0.884090	−	0.467317i	$-0.154779\pi$
$641$	44.7667	1.76818	0.884090	+	0.467317i	$0.154779\pi$
$642$	29.5056	1.16449
$643$	−35.8339	−1.41315	−0.706575	−	0.707638i	$-0.749761\pi$
$643$	−35.8339	−1.41315	−0.706575	+	0.707638i	$0.749761\pi$
$644$	−48.0084	−1.89180
$645$	9.10104	0.358353
$646$	−22.5203	−0.886048
$647$	−13.6057	−0.534896	−0.267448	−	0.963572i	$-0.586180\pi$
$647$	−13.6057	−0.534896	−0.267448	+	0.963572i	$0.586180\pi$
$648$	13.9881	0.549503
$649$	−29.6011	−1.16194
$650$	−21.7861	−0.854520
$651$	14.0741	0.551606
$652$	−55.4510	−2.17163
$653$	−42.4626	−1.66169	−0.830846	−	0.556503i	$-0.812143\pi$
$653$	−42.4626	−1.66169	−0.830846	+	0.556503i	$0.812143\pi$
$654$	−88.6413	−3.46615
$655$	6.88306	0.268944
$656$	−0.398724	−0.0155675
$657$	33.6508	1.31284
$658$	26.4385	1.03068
$659$	−41.7067	−1.62466	−0.812331	−	0.583196i	$-0.801802\pi$
$659$	−41.7067	−1.62466	−0.812331	+	0.583196i	$0.801802\pi$
$660$	−74.5907	−2.90344
$661$	18.7915	0.730905	0.365453	−	0.930830i	$-0.380914\pi$
$661$	18.7915	0.730905	0.365453	+	0.930830i	$0.380914\pi$
$662$	−68.4206	−2.65924
$663$	26.7734	1.03979
$664$	43.7736	1.69875
$665$	20.5779	0.797978
$666$	101.542	3.93469
$667$	13.1487	0.509121
$668$	24.8539	0.961627
$669$	−54.0125	−2.08824
$670$	−32.0668	−1.23885
$671$	16.0844	0.620933
$672$	39.2494	1.51408
$673$	−29.8210	−1.14952	−0.574758	−	0.818323i	$-0.694904\pi$
$673$	−29.8210	−1.14952	−0.574758	+	0.818323i	$0.694904\pi$
$674$	33.8969	1.30566
$675$	16.5959	0.638777
$676$	8.93300	0.343577
$677$	−24.9498	−0.958898	−0.479449	−	0.877570i	$-0.659163\pi$
$677$	−24.9498	−0.958898	−0.479449	+	0.877570i	$0.659163\pi$
$678$	−51.8464	−1.99115
$679$	−33.4268	−1.28280
$680$	−12.8869	−0.494190
$681$	62.3097	2.38771
$682$	−16.9027	−0.647237
$683$	−22.1904	−0.849092	−0.424546	−	0.905406i	$-0.639566\pi$
$683$	−22.1904	−0.849092	−0.424546	+	0.905406i	$0.639566\pi$
$684$	77.2505	2.95375
$685$	−6.49953	−0.248334
$686$	−32.7657	−1.25100
$687$	27.7013	1.05687
$688$	−1.97403	−0.0752591
$689$	7.78198	0.296470
$690$	49.8068	1.89611
$691$	11.7818	0.448201	0.224100	−	0.974566i	$-0.428056\pi$
$691$	11.7818	0.448201	0.224100	+	0.974566i	$0.428056\pi$
$692$	56.9324	2.16425
$693$	76.2882	2.89795
$694$	−23.5994	−0.895821
$695$	−24.2328	−0.919204
$696$	28.6263	1.08508
$697$	0.911695	0.0345329
$698$	69.4433	2.62847
$699$	80.3505	3.03914
$700$	−25.0647	−0.947358
$701$	−17.7590	−0.670747	−0.335374	−	0.942085i	$-0.608863\pi$
$701$	−17.7590	−0.670747	−0.335374	+	0.942085i	$0.608863\pi$
$702$	−64.7559	−2.44405
$703$	33.0986	1.24834
$704$	−56.5060	−2.12965
$705$	−17.3706	−0.654216
$706$	9.68553	0.364520
$707$	45.1194	1.69689
$708$	64.7380	2.43300
$709$	30.3099	1.13831	0.569156	−	0.822229i	$-0.307270\pi$
$709$	30.3099	1.13831	0.569156	+	0.822229i	$0.307270\pi$
$710$	30.6865	1.15165
$711$	−70.7931	−2.65495
$712$	5.24009	0.196381
$713$	7.14771	0.267684
$714$	48.6386	1.82025
$715$	29.3811	1.09879
$716$	−77.8127	−2.90800
$717$	48.0489	1.79442
$718$	−49.3260	−1.84083
$719$	17.2380	0.642868	0.321434	−	0.946932i	$-0.395835\pi$
$719$	17.2380	0.642868	0.321434	+	0.946932i	$0.395835\pi$
$720$	8.99665	0.335285
$721$	13.7291	0.511297
$722$	−4.61129	−0.171614
$723$	−49.9948	−1.85933
$724$	61.3678	2.28071
$725$	6.86483	0.254953
$726$	−67.7851	−2.51574
$727$	−33.7827	−1.25293	−0.626465	−	0.779450i	$-0.715499\pi$
$727$	−33.7827	−1.25293	−0.626465	+	0.779450i	$0.715499\pi$
$728$	41.1702	1.52587
$729$	−38.8129	−1.43751
$730$	23.5442	0.871409
$731$	4.51368	0.166944
$732$	−35.1769	−1.30018
$733$	−22.4647	−0.829752	−0.414876	−	0.909878i	$-0.636175\pi$
$733$	−22.4647	−0.829752	−0.414876	+	0.909878i	$0.636175\pi$
$734$	−12.7304	−0.469888
$735$	−11.4580	−0.422634
$736$	19.9333	0.734753
$737$	−38.7502	−1.42738
$738$	−4.93822	−0.181778
$739$	11.2270	0.412993	0.206497	−	0.978447i	$-0.433794\pi$
$739$	11.2270	0.412993	0.206497	+	0.978447i	$0.433794\pi$
$740$	44.9928	1.65397
$741$	−47.2701	−1.73651
$742$	14.1373	0.518998
$743$	1.85973	0.0682268	0.0341134	−	0.999418i	$-0.489139\pi$
$743$	1.85973	0.0682268	0.0341134	+	0.999418i	$0.489139\pi$
$744$	15.5614	0.570509
$745$	28.5494	1.04597
$746$	−52.0593	−1.90603
$747$	69.8751	2.55660
$748$	−36.9934	−1.35261
$749$	−13.3712	−0.488575
$750$	81.0280	2.95872
$751$	−1.76976	−0.0645796	−0.0322898	−	0.999479i	$-0.510280\pi$
$751$	−1.76976	−0.0645796	−0.0322898	+	0.999479i	$0.510280\pi$
$752$	3.76771	0.137394
$753$	−60.0249	−2.18743
$754$	−26.7860	−0.975489
$755$	−5.32914	−0.193947
$756$	−74.5013	−2.70958
$757$	7.20191	0.261758	0.130879	−	0.991398i	$-0.458220\pi$
$757$	7.20191	0.261758	0.130879	+	0.991398i	$0.458220\pi$
$758$	36.6810	1.33231
$759$	60.1875	2.18467
$760$	22.7526	0.825323
$761$	10.8899	0.394760	0.197380	−	0.980327i	$-0.436757\pi$
$761$	10.8899	0.394760	0.197380	+	0.980327i	$0.436757\pi$
$762$	−17.4999	−0.633956
$763$	40.1702	1.45426
$764$	6.60236	0.238865
$765$	−20.5711	−0.743751
$766$	62.8820	2.27202
$767$	−25.5002	−0.920758
$768$	63.8856	2.30527
$769$	52.6635	1.89909	0.949547	−	0.313626i	$-0.101544\pi$
$769$	52.6635	1.89909	0.949547	+	0.313626i	$0.101544\pi$
$770$	53.3760	1.92354
$771$	11.9388	0.429967
$772$	−76.8268	−2.76506
$773$	15.2260	0.547640	0.273820	−	0.961781i	$-0.411713\pi$
$773$	15.2260	0.547640	0.273820	+	0.961781i	$0.411713\pi$
$774$	−24.4484	−0.878781
$775$	3.73175	0.134048
$776$	−36.9593	−1.32676
$777$	−71.4854	−2.56452
$778$	52.6805	1.88869
$779$	−1.60965	−0.0576718
$780$	−64.2570	−2.30077
$781$	37.0822	1.32691
$782$	24.7018	0.883335
$783$	20.4047	0.729205
$784$	2.48525	0.0887589
$785$	−40.2434	−1.43635
$786$	−28.7239	−1.02455
$787$	−25.9599	−0.925372	−0.462686	−	0.886522i	$-0.653114\pi$
$787$	−25.9599	−0.925372	−0.462686	+	0.886522i	$0.653114\pi$
$788$	45.6738	1.62706
$789$	33.1901	1.18160
$790$	−49.5313	−1.76224
$791$	23.4956	0.835407
$792$	84.3503	2.99726
$793$	13.8561	0.492045
$794$	20.0588	0.711861
$795$	−9.28851	−0.329430
$796$	3.08958	0.109507
$797$	−34.0089	−1.20466	−0.602329	−	0.798248i	$-0.705761\pi$
$797$	−34.0089	−1.20466	−0.602329	+	0.798248i	$0.705761\pi$
$798$	−85.8745	−3.03992
$799$	−8.61500	−0.304777
$800$	10.4070	0.367943
$801$	8.36467	0.295551
$802$	51.4751	1.81765
$803$	28.4512	1.00402
$804$	84.7472	2.98880
$805$	−22.5713	−0.795534
$806$	−14.5610	−0.512889
$807$	31.0783	1.09401
$808$	49.8876	1.75504
$809$	28.1310	0.989035	0.494517	−	0.869168i	$-0.335345\pi$
$809$	28.1310	0.989035	0.494517	+	0.869168i	$0.335345\pi$
$810$	15.6227	0.548925
$811$	49.7846	1.74817	0.874086	−	0.485771i	$-0.161461\pi$
$811$	49.7846	1.74817	0.874086	+	0.485771i	$0.161461\pi$
$812$	−30.8172	−1.08147
$813$	4.77693	0.167534
$814$	85.8526	3.00913
$815$	−26.0705	−0.913209
$816$	6.93142	0.242648
$817$	−7.96917	−0.278806
$818$	33.2039	1.16095
$819$	65.7193	2.29642
$820$	−2.18809	−0.0764115
$821$	35.7301	1.24699	0.623494	−	0.781828i	$-0.285713\pi$
$821$	35.7301	1.24699	0.623494	+	0.781828i	$0.285713\pi$
$822$	27.1234	0.946037
$823$	−32.7664	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$823$	−32.7664	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$824$	15.1799	0.528818
$825$	31.4233	1.09402
$826$	−46.3255	−1.61187
$827$	13.4879	0.469019	0.234510	−	0.972114i	$-0.424652\pi$
$827$	13.4879	0.469019	0.234510	+	0.972114i	$0.424652\pi$
$828$	−84.7337	−2.94470
$829$	−9.86206	−0.342523	−0.171262	−	0.985226i	$-0.554784\pi$
$829$	−9.86206	−0.342523	−0.171262	+	0.985226i	$0.554784\pi$
$830$	48.8890	1.69696
$831$	49.8085	1.72784
$832$	−48.6776	−1.68759
$833$	−5.68260	−0.196891
$834$	101.127	3.50174
$835$	11.6852	0.404381
$836$	65.3141	2.25894
$837$	11.0921	0.383399
$838$	−67.1948	−2.32121
$839$	−15.6581	−0.540579	−0.270289	−	0.962779i	$-0.587119\pi$
$839$	−15.6581	−0.540579	−0.270289	+	0.962779i	$0.587119\pi$
$840$	−49.1404	−1.69550
$841$	−20.5597	−0.708954
$842$	40.0069	1.37873
$843$	−82.4836	−2.84089
$844$	−3.19114	−0.109843
$845$	4.19988	0.144480
$846$	46.6634	1.60432
$847$	30.7186	1.05550
$848$	2.01469	0.0691848
$849$	28.5289	0.979109
$850$	12.8966	0.442349
$851$	−36.3048	−1.24451
$852$	−81.0993	−2.77842
$853$	0.399767	0.0136878	0.00684388	−	0.999977i	$-0.497822\pi$
$853$	0.399767	0.0136878	0.00684388	+	0.999977i	$0.497822\pi$
$854$	25.1720	0.861369
$855$	36.3196	1.24210
$856$	−14.7843	−0.505317
$857$	−33.5653	−1.14657	−0.573284	−	0.819356i	$-0.694331\pi$
$857$	−33.5653	−1.14657	−0.573284	+	0.819356i	$0.694331\pi$
$858$	−122.611	−4.18588
$859$	13.2138	0.450848	0.225424	−	0.974261i	$-0.427623\pi$
$859$	13.2138	0.450848	0.225424	+	0.974261i	$0.427623\pi$
$860$	−10.8329	−0.369400
$861$	3.47648	0.118478
$862$	−28.0170	−0.954261
$863$	20.4271	0.695345	0.347673	−	0.937616i	$-0.386972\pi$
$863$	20.4271	0.695345	0.347673	+	0.937616i	$0.386972\pi$
$864$	30.9333	1.05237
$865$	26.7670	0.910104
$866$	−14.5537	−0.494555
$867$	33.4815	1.13709
$868$	−16.7523	−0.568611
$869$	−59.8545	−2.03043
$870$	31.9716	1.08394
$871$	−33.3817	−1.13110
$872$	44.4153	1.50409
$873$	−58.9975	−1.99676
$874$	−43.6125	−1.47522
$875$	−36.7200	−1.24136
$876$	−62.2232	−2.10233
$877$	23.0401	0.778008	0.389004	−	0.921236i	$-0.372819\pi$
$877$	23.0401	0.778008	0.389004	+	0.921236i	$0.372819\pi$
$878$	33.1972	1.12035
$879$	16.6543	0.561737
$880$	7.60653	0.256416
$881$	−13.2788	−0.447374	−0.223687	−	0.974661i	$-0.571809\pi$
$881$	−13.2788	−0.447374	−0.223687	+	0.974661i	$0.571809\pi$
$882$	30.7800	1.03642
$883$	−3.03101	−0.102002	−0.0510008	−	0.998699i	$-0.516241\pi$
$883$	−3.03101	−0.102002	−0.0510008	+	0.998699i	$0.516241\pi$
$884$	−31.8684	−1.07185
$885$	30.4368	1.02312
$886$	−39.7928	−1.33686
$887$	19.5324	0.655834	0.327917	−	0.944706i	$-0.393653\pi$
$887$	19.5324	0.655834	0.327917	+	0.944706i	$0.393653\pi$
$888$	−79.0399	−2.65241
$889$	7.93057	0.265983
$890$	5.85244	0.196174
$891$	18.8788	0.632462
$892$	64.2910	2.15262
$893$	15.2103	0.508994
$894$	−119.140	−3.98465
$895$	−36.5839	−1.22286
$896$	−61.3796	−2.05055
$897$	51.8492	1.73119
$898$	45.6915	1.52474
$899$	4.58820	0.153025
$900$	−44.2387	−1.47462
$901$	−4.60666	−0.153470
$902$	−4.17519	−0.139019
$903$	17.2116	0.572766
$904$	25.9786	0.864035
$905$	28.8522	0.959081
$906$	22.2392	0.738848
$907$	48.6214	1.61445	0.807224	−	0.590246i	$-0.200969\pi$
$907$	48.6214	1.61445	0.807224	+	0.590246i	$0.200969\pi$
$908$	−74.1671	−2.46132
$909$	79.6347	2.64132
$910$	45.9813	1.52426
$911$	−30.0671	−0.996167	−0.498084	−	0.867129i	$-0.665963\pi$
$911$	−30.0671	−0.996167	−0.498084	+	0.867129i	$0.665963\pi$
$912$	−12.2378	−0.405236
$913$	59.0784	1.95521
$914$	−35.3044	−1.16777
$915$	−16.5385	−0.546747
$916$	−32.9728	−1.08945
$917$	13.0170	0.429860
$918$	38.3332	1.26518
$919$	−11.1195	−0.366798	−0.183399	−	0.983039i	$-0.558710\pi$
$919$	−11.1195	−0.366798	−0.183399	+	0.983039i	$0.558710\pi$
$920$	−24.9566	−0.822796
$921$	19.6588	0.647780
$922$	20.8543	0.686799
$923$	31.9448	1.05148
$924$	−141.064	−4.64065
$925$	−18.9544	−0.623217
$926$	15.1926	0.499261
$927$	24.2315	0.795866
$928$	12.7954	0.420031
$929$	18.1494	0.595463	0.297731	−	0.954650i	$-0.403770\pi$
$929$	18.1494	0.595463	0.297731	+	0.954650i	$0.403770\pi$
$930$	17.3799	0.569909
$931$	10.0330	0.328818
$932$	−95.6410	−3.13283
$933$	39.7179	1.30031
$934$	35.8508	1.17307
$935$	−17.3926	−0.568798
$936$	72.6644	2.37511
$937$	47.0239	1.53620	0.768101	−	0.640328i	$-0.221202\pi$
$937$	47.0239	1.53620	0.768101	+	0.640328i	$0.221202\pi$
$938$	−60.6438	−1.98009
$939$	37.2092	1.21428
$940$	20.6762	0.674384
$941$	−36.9771	−1.20542	−0.602709	−	0.797961i	$-0.705912\pi$
$941$	−36.9771	−1.20542	−0.602709	+	0.797961i	$0.705912\pi$
$942$	167.941	5.47181
$943$	1.76558	0.0574952
$944$	−6.60178	−0.214870
$945$	−35.0270	−1.13943
$946$	−20.6708	−0.672065
$947$	−10.4899	−0.340875	−0.170437	−	0.985368i	$-0.554518\pi$
$947$	−10.4899	−0.340875	−0.170437	+	0.985368i	$0.554518\pi$
$948$	130.903	4.25152
$949$	24.5096	0.795615
$950$	−22.7697	−0.738746
$951$	−94.5865	−3.06718
$952$	−24.3713	−0.789877
$953$	2.81906	0.0913184	0.0456592	−	0.998957i	$-0.485461\pi$
$953$	2.81906	0.0913184	0.0456592	+	0.998957i	$0.485461\pi$
$954$	24.9521	0.807853
$955$	3.10412	0.100447
$956$	−57.1926	−1.84974
$957$	38.6351	1.24889
$958$	−11.5129	−0.371964
$959$	−12.2917	−0.396920
$960$	58.1013	1.87521
$961$	−28.5058	−0.919543
$962$	73.9586	2.38452
$963$	−23.5999	−0.760497
$964$	59.5087	1.91665
$965$	−36.1204	−1.16276
$966$	94.1931	3.03061
$967$	54.7088	1.75932	0.879658	−	0.475606i	$-0.157771\pi$
$967$	54.7088	1.75932	0.879658	+	0.475606i	$0.157771\pi$
$968$	33.9649	1.09167
$969$	27.9822	0.898919
$970$	−41.2783	−1.32537
$971$	43.9998	1.41202	0.706010	−	0.708202i	$-0.250493\pi$
$971$	43.9998	1.41202	0.706010	+	0.708202i	$0.250493\pi$
$972$	31.4888	1.01000
$973$	−45.8284	−1.46919
$974$	−1.86979	−0.0599118
$975$	27.0699	0.866932
$976$	3.58723	0.114824
$977$	−11.1504	−0.356731	−0.178366	−	0.983964i	$-0.557081\pi$
$977$	−11.1504	−0.356731	−0.178366	+	0.983964i	$0.557081\pi$
$978$	108.796	3.47890
$979$	7.07220	0.226028
$980$	13.6384	0.435663
$981$	70.8995	2.26365
$982$	60.6288	1.93474
$983$	−11.8977	−0.379476	−0.189738	−	0.981835i	$-0.560764\pi$
$983$	−11.8977	−0.379476	−0.189738	+	0.981835i	$0.560764\pi$
$984$	3.84387	0.122538
$985$	21.4737	0.684208
$986$	15.8564	0.504970
$987$	−32.8508	−1.04565
$988$	56.2655	1.79004
$989$	8.74114	0.277952
$990$	94.2074	2.99411
$991$	61.3500	1.94885	0.974424	−	0.224716i	$-0.0721455\pi$
$991$	61.3500	1.94885	0.974424	+	0.224716i	$0.0721455\pi$
$992$	6.95566	0.220842
$993$	85.0149	2.69787
$994$	58.0334	1.84071
$995$	1.45258	0.0460498
$996$	−129.205	−4.09402
$997$	−54.0735	−1.71253	−0.856263	−	0.516541i	$-0.827219\pi$
$997$	−54.0735	−1.71253	−0.856263	+	0.516541i	$0.827219\pi$
$998$	−39.2192	−1.24146
$999$	−56.3392	−1.78249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.106	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.106	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q+2.33538 q^{2} -2.90179 q^{3} +3.45399 q^{4} +1.62391 q^{5} -6.77678 q^{6} +3.07108 q^{7} +3.39563 q^{8} +5.42039 q^{9} +O(q^{10})\)	\(q+2.33538 q^{2} -2.90179 q^{3} +3.45399 q^{4} +1.62391 q^{5} -6.77678 q^{6} +3.07108 q^{7} +3.39563 q^{8} +5.42039 q^{9} +3.79244 q^{10} +4.58285 q^{11} -10.0228 q^{12} +3.94795 q^{13} +7.17214 q^{14} -4.71224 q^{15} +1.02209 q^{16} -2.33704 q^{17} +12.6587 q^{18} +4.12619 q^{19} +5.60897 q^{20} -8.91163 q^{21} +10.7027 q^{22} -4.52589 q^{23} -9.85340 q^{24} -2.36293 q^{25} +9.21995 q^{26} -7.02345 q^{27} +10.6075 q^{28} -2.90522 q^{29} -11.0049 q^{30} -1.57929 q^{31} -4.40429 q^{32} -13.2985 q^{33} -5.45788 q^{34} +4.98715 q^{35} +18.7220 q^{36} +8.02158 q^{37} +9.63622 q^{38} -11.4561 q^{39} +5.51419 q^{40} -0.390106 q^{41} -20.8120 q^{42} -1.93136 q^{43} +15.8292 q^{44} +8.80220 q^{45} -10.5697 q^{46} +3.68628 q^{47} -2.96589 q^{48} +2.43153 q^{49} -5.51833 q^{50} +6.78161 q^{51} +13.6362 q^{52} +1.97115 q^{53} -16.4024 q^{54} +7.44213 q^{55} +10.4282 q^{56} -11.9733 q^{57} -6.78480 q^{58} -6.45910 q^{59} -16.2760 q^{60} +3.50970 q^{61} -3.68824 q^{62} +16.6464 q^{63} -12.3299 q^{64} +6.41110 q^{65} -31.0570 q^{66} -8.45547 q^{67} -8.07214 q^{68} +13.1332 q^{69} +11.6469 q^{70} +8.09151 q^{71} +18.4056 q^{72} +6.20819 q^{73} +18.7334 q^{74} +6.85672 q^{75} +14.2518 q^{76} +14.0743 q^{77} -26.7544 q^{78} -13.0605 q^{79} +1.65978 q^{80} +4.11943 q^{81} -0.911045 q^{82} +12.8912 q^{83} -30.7807 q^{84} -3.79514 q^{85} -4.51046 q^{86} +8.43035 q^{87} +15.5617 q^{88} +1.54319 q^{89} +20.5565 q^{90} +12.1245 q^{91} -15.6324 q^{92} +4.58277 q^{93} +8.60886 q^{94} +6.70055 q^{95} +12.7803 q^{96} -10.8844 q^{97} +5.67856 q^{98} +24.8408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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