LMFDB - Embedded newform 8027.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21508 q^{2} +0.0631249 q^{3} +2.90657 q^{4} -0.959004 q^{5} -0.139827 q^{6} -0.280080 q^{7} -2.00812 q^{8} -2.99602 q^{9} +O(q^{10})$	\(q-2.21508 q^{2} +0.0631249 q^{3} +2.90657 q^{4} -0.959004 q^{5} -0.139827 q^{6} -0.280080 q^{7} -2.00812 q^{8} -2.99602 q^{9} +2.12427 q^{10} -1.70883 q^{11} +0.183477 q^{12} +3.69790 q^{13} +0.620399 q^{14} -0.0605371 q^{15} -1.36499 q^{16} +4.66809 q^{17} +6.63641 q^{18} +3.75392 q^{19} -2.78741 q^{20} -0.0176800 q^{21} +3.78518 q^{22} -1.00000 q^{23} -0.126763 q^{24} -4.08031 q^{25} -8.19114 q^{26} -0.378498 q^{27} -0.814072 q^{28} +3.11910 q^{29} +0.134094 q^{30} -1.28630 q^{31} +7.03981 q^{32} -0.107870 q^{33} -10.3402 q^{34} +0.268598 q^{35} -8.70813 q^{36} -0.259342 q^{37} -8.31523 q^{38} +0.233430 q^{39} +1.92580 q^{40} -10.1808 q^{41} +0.0391626 q^{42} -3.28679 q^{43} -4.96682 q^{44} +2.87319 q^{45} +2.21508 q^{46} +8.36939 q^{47} -0.0861652 q^{48} -6.92156 q^{49} +9.03821 q^{50} +0.294673 q^{51} +10.7482 q^{52} +8.76726 q^{53} +0.838403 q^{54} +1.63877 q^{55} +0.562435 q^{56} +0.236966 q^{57} -6.90906 q^{58} -10.1727 q^{59} -0.175955 q^{60} -2.87535 q^{61} +2.84925 q^{62} +0.839124 q^{63} -12.8637 q^{64} -3.54630 q^{65} +0.238939 q^{66} +1.34819 q^{67} +13.5681 q^{68} -0.0631249 q^{69} -0.594965 q^{70} -11.4642 q^{71} +6.01636 q^{72} -8.77726 q^{73} +0.574462 q^{74} -0.257569 q^{75} +10.9110 q^{76} +0.478608 q^{77} -0.517065 q^{78} -0.317086 q^{79} +1.30903 q^{80} +8.96415 q^{81} +22.5513 q^{82} +9.08249 q^{83} -0.0513882 q^{84} -4.47672 q^{85} +7.28049 q^{86} +0.196893 q^{87} +3.43153 q^{88} +0.460724 q^{89} -6.36434 q^{90} -1.03571 q^{91} -2.90657 q^{92} -0.0811975 q^{93} -18.5388 q^{94} -3.60002 q^{95} +0.444388 q^{96} -2.03458 q^{97} +15.3318 q^{98} +5.11967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.21508	−1.56630	−0.783148	−	0.621835i	$-0.786387\pi$
$2$	−2.21508	−1.56630	−0.783148	+	0.621835i	$0.786387\pi$
$3$	0.0631249	0.0364452	0.0182226	−	0.999834i	$-0.494199\pi$
$3$	0.0631249	0.0364452	0.0182226	+	0.999834i	$0.494199\pi$
$4$	2.90657	1.45328
$5$	−0.959004	−0.428880	−0.214440	−	0.976737i	$-0.568793\pi$
$5$	−0.959004	−0.428880	−0.214440	+	0.976737i	$0.568793\pi$
$6$	−0.139827	−0.0570840
$7$	−0.280080	−0.105860	−0.0529301	−	0.998598i	$-0.516856\pi$
$7$	−0.280080	−0.105860	−0.0529301	+	0.998598i	$0.516856\pi$
$8$	−2.00812	−0.709978
$9$	−2.99602	−0.998672
$10$	2.12427	0.671753
$11$	−1.70883	−0.515231	−0.257615	−	0.966248i	$-0.582937\pi$
$11$	−1.70883	−0.515231	−0.257615	+	0.966248i	$0.582937\pi$
$12$	0.183477	0.0529652
$13$	3.69790	1.02561	0.512806	−	0.858504i	$-0.328606\pi$
$13$	3.69790	1.02561	0.512806	+	0.858504i	$0.328606\pi$
$14$	0.620399	0.165809
$15$	−0.0605371	−0.0156306
$16$	−1.36499	−0.341249
$17$	4.66809	1.13218	0.566090	−	0.824344i	$-0.308456\pi$
$17$	4.66809	1.13218	0.566090	+	0.824344i	$0.308456\pi$
$18$	6.63641	1.56422
$19$	3.75392	0.861208	0.430604	−	0.902541i	$-0.358300\pi$
$19$	3.75392	0.861208	0.430604	+	0.902541i	$0.358300\pi$
$20$	−2.78741	−0.623284
$21$	−0.0176800	−0.00385810
$22$	3.78518	0.807004
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.126763	−0.0258753
$25$	−4.08031	−0.816062
$26$	−8.19114	−1.60641
$27$	−0.378498	−0.0728420
$28$	−0.814072	−0.153845
$29$	3.11910	0.579203	0.289602	−	0.957147i	$-0.406477\pi$
$29$	3.11910	0.579203	0.289602	+	0.957147i	$0.406477\pi$
$30$	0.134094	0.0244822
$31$	−1.28630	−0.231026	−0.115513	−	0.993306i	$-0.536851\pi$
$31$	−1.28630	−0.231026	−0.115513	+	0.993306i	$0.536851\pi$
$32$	7.03981	1.24447
$33$	−0.107870	−0.0187777
$34$	−10.3402	−1.77333
$35$	0.268598	0.0454013
$36$	−8.70813	−1.45135
$37$	−0.259342	−0.0426355	−0.0213178	−	0.999773i	$-0.506786\pi$
$37$	−0.259342	−0.0426355	−0.0213178	+	0.999773i	$0.506786\pi$
$38$	−8.31523	−1.34891
$39$	0.233430	0.0373787
$40$	1.92580	0.304495
$41$	−10.1808	−1.58997	−0.794987	−	0.606626i	$-0.792523\pi$
$41$	−10.1808	−1.58997	−0.794987	+	0.606626i	$0.792523\pi$
$42$	0.0391626	0.00604293
$43$	−3.28679	−0.501230	−0.250615	−	0.968087i	$-0.580633\pi$
$43$	−3.28679	−0.501230	−0.250615	+	0.968087i	$0.580633\pi$
$44$	−4.96682	−0.748777
$45$	2.87319	0.428310
$46$	2.21508	0.326595
$47$	8.36939	1.22080	0.610400	−	0.792093i	$-0.291009\pi$
$47$	8.36939	1.22080	0.610400	+	0.792093i	$0.291009\pi$
$48$	−0.0861652	−0.0124369
$49$	−6.92156	−0.988794
$50$	9.03821	1.27820
$51$	0.294673	0.0412625
$52$	10.7482	1.49051
$53$	8.76726	1.20428	0.602138	−	0.798392i	$-0.294316\pi$
$53$	8.76726	1.20428	0.602138	+	0.798392i	$0.294316\pi$
$54$	0.838403	0.114092
$55$	1.63877	0.220972
$56$	0.562435	0.0751585
$57$	0.236966	0.0313869
$58$	−6.90906	−0.907204
$59$	−10.1727	−1.32438	−0.662190	−	0.749336i	$-0.730373\pi$
$59$	−10.1727	−1.32438	−0.662190	+	0.749336i	$0.730373\pi$
$60$	−0.175955	−0.0227157
$61$	−2.87535	−0.368151	−0.184075	−	0.982912i	$-0.558929\pi$
$61$	−2.87535	−0.368151	−0.184075	+	0.982912i	$0.558929\pi$
$62$	2.84925	0.361855
$63$	0.839124	0.105720
$64$	−12.8637	−1.60797
$65$	−3.54630	−0.439864
$66$	0.238939	0.0294114
$67$	1.34819	0.164708	0.0823539	−	0.996603i	$-0.473756\pi$
$67$	1.34819	0.164708	0.0823539	+	0.996603i	$0.473756\pi$
$68$	13.5681	1.64538
$69$	−0.0631249	−0.00759935
$70$	−0.594965	−0.0711119
$71$	−11.4642	−1.36055	−0.680274	−	0.732958i	$-0.738139\pi$
$71$	−11.4642	−1.36055	−0.680274	+	0.732958i	$0.738139\pi$
$72$	6.01636	0.709035
$73$	−8.77726	−1.02730	−0.513650	−	0.858000i	$-0.671707\pi$
$73$	−8.77726	−1.02730	−0.513650	+	0.858000i	$0.671707\pi$
$74$	0.574462	0.0667799
$75$	−0.257569	−0.0297416
$76$	10.9110	1.25158
$77$	0.478608	0.0545424
$78$	−0.517065	−0.0585461
$79$	−0.317086	−0.0356750	−0.0178375	−	0.999841i	$-0.505678\pi$
$79$	−0.317086	−0.0356750	−0.0178375	+	0.999841i	$0.505678\pi$
$80$	1.30903	0.146355
$81$	8.96415	0.996017
$82$	22.5513	2.49037
$83$	9.08249	0.996933	0.498466	−	0.866909i	$-0.333897\pi$
$83$	9.08249	0.996933	0.498466	+	0.866909i	$0.333897\pi$
$84$	−0.0513882	−0.00560692
$85$	−4.47672	−0.485568
$86$	7.28049	0.785076
$87$	0.196893	0.0211092
$88$	3.43153	0.365802
$89$	0.460724	0.0488367	0.0244183	−	0.999702i	$-0.492227\pi$
$89$	0.460724	0.0488367	0.0244183	+	0.999702i	$0.492227\pi$
$90$	−6.36434	−0.670860
$91$	−1.03571	−0.108572
$92$	−2.90657	−0.303031
$93$	−0.0811975	−0.00841979
$94$	−18.5388	−1.91214
$95$	−3.60002	−0.369355
$96$	0.444388	0.0453551
$97$	−2.03458	−0.206580	−0.103290	−	0.994651i	$-0.532937\pi$
$97$	−2.03458	−0.206580	−0.103290	+	0.994651i	$0.532937\pi$
$98$	15.3318	1.54874
$99$	5.11967	0.514546
$100$	−11.8597	−1.18597
$101$	3.43349	0.341645	0.170822	−	0.985302i	$-0.445358\pi$
$101$	3.43349	0.341645	0.170822	+	0.985302i	$0.445358\pi$
$102$	−0.652724	−0.0646293
$103$	8.08151	0.796295	0.398147	−	0.917321i	$-0.369653\pi$
$103$	8.08151	0.796295	0.398147	+	0.917321i	$0.369653\pi$
$104$	−7.42583	−0.728163
$105$	0.0169552	0.00165466
$106$	−19.4202	−1.88625
$107$	10.0855	0.975001	0.487501	−	0.873123i	$-0.337909\pi$
$107$	10.0855	0.975001	0.487501	+	0.873123i	$0.337909\pi$
$108$	−1.10013	−0.105860
$109$	19.5623	1.87373	0.936863	−	0.349695i	$-0.113715\pi$
$109$	19.5623	1.87373	0.936863	+	0.349695i	$0.113715\pi$
$110$	−3.63001	−0.346107
$111$	−0.0163709	−0.00155386
$112$	0.382308	0.0361247
$113$	4.13938	0.389400	0.194700	−	0.980863i	$-0.437627\pi$
$113$	4.13938	0.389400	0.194700	+	0.980863i	$0.437627\pi$
$114$	−0.524898	−0.0491612
$115$	0.959004	0.0894276
$116$	9.06589	0.841747
$117$	−11.0790	−1.02425
$118$	22.5334	2.07437
$119$	−1.30744	−0.119853
$120$	0.121566	0.0110974
$121$	−8.07991	−0.734538
$122$	6.36912	0.576633
$123$	−0.642663	−0.0579469
$124$	−3.73872	−0.335747
$125$	8.70805	0.778872
$126$	−1.85872	−0.165588
$127$	−5.20304	−0.461695	−0.230848	−	0.972990i	$-0.574150\pi$
$127$	−5.20304	−0.461695	−0.230848	+	0.972990i	$0.574150\pi$
$128$	14.4146	1.27408
$129$	−0.207478	−0.0182674
$130$	7.85533	0.688958
$131$	12.2174	1.06744	0.533718	−	0.845662i	$-0.320794\pi$
$131$	12.2174	1.06744	0.533718	+	0.845662i	$0.320794\pi$
$132$	−0.313530	−0.0272893
$133$	−1.05140	−0.0911678
$134$	−2.98635	−0.257981
$135$	0.362981	0.0312404
$136$	−9.37410	−0.803822
$137$	11.8310	1.01079	0.505396	−	0.862888i	$-0.331346\pi$
$137$	11.8310	1.01079	0.505396	+	0.862888i	$0.331346\pi$
$138$	0.139827	0.0119028
$139$	2.33196	0.197794	0.0988972	−	0.995098i	$-0.468468\pi$
$139$	2.33196	0.197794	0.0988972	+	0.995098i	$0.468468\pi$
$140$	0.780698	0.0659810
$141$	0.528317	0.0444923
$142$	25.3940	2.13102
$143$	−6.31907	−0.528427
$144$	4.08954	0.340795
$145$	−2.99123	−0.248408
$146$	19.4423	1.60906
$147$	−0.436923	−0.0360368
$148$	−0.753795	−0.0619616
$149$	−4.13245	−0.338544	−0.169272	−	0.985569i	$-0.554142\pi$
$149$	−4.13245	−0.338544	−0.169272	+	0.985569i	$0.554142\pi$
$150$	0.570536	0.0465841
$151$	−6.87327	−0.559339	−0.279669	−	0.960096i	$-0.590225\pi$
$151$	−6.87327	−0.559339	−0.279669	+	0.960096i	$0.590225\pi$
$152$	−7.53833	−0.611439
$153$	−13.9857	−1.13068
$154$	−1.06015	−0.0854296
$155$	1.23357	0.0990824
$156$	0.678479	0.0543218
$157$	16.2592	1.29762	0.648812	−	0.760948i	$-0.275266\pi$
$157$	16.2592	1.29762	0.648812	+	0.760948i	$0.275266\pi$
$158$	0.702370	0.0558776
$159$	0.553433	0.0438901
$160$	−6.75121	−0.533730
$161$	0.280080	0.0220734
$162$	−19.8563	−1.56006
$163$	−9.95551	−0.779776	−0.389888	−	0.920862i	$-0.627486\pi$
$163$	−9.95551	−0.779776	−0.389888	+	0.920862i	$0.627486\pi$
$164$	−29.5912	−2.31069
$165$	0.103447	0.00805336
$166$	−20.1184	−1.56149
$167$	6.49662	0.502723	0.251362	−	0.967893i	$-0.419122\pi$
$167$	6.49662	0.502723	0.251362	+	0.967893i	$0.419122\pi$
$168$	0.0355036	0.00273917
$169$	0.674462	0.0518817
$170$	9.91628	0.760544
$171$	−11.2468	−0.860065
$172$	−9.55328	−0.728431
$173$	5.67121	0.431174	0.215587	−	0.976485i	$-0.430833\pi$
$173$	5.67121	0.431174	0.215587	+	0.976485i	$0.430833\pi$
$174$	−0.436134	−0.0330632
$175$	1.14281	0.0863886
$176$	2.33254	0.175822
$177$	−0.642154	−0.0482673
$178$	−1.02054	−0.0764927
$179$	−13.8459	−1.03489	−0.517445	−	0.855717i	$-0.673117\pi$
$179$	−13.8459	−1.03489	−0.517445	+	0.855717i	$0.673117\pi$
$180$	8.35113	0.622456
$181$	5.03827	0.374492	0.187246	−	0.982313i	$-0.440044\pi$
$181$	5.03827	0.374492	0.187246	+	0.982313i	$0.440044\pi$
$182$	2.29417	0.170055
$183$	−0.181506	−0.0134173
$184$	2.00812	0.148041
$185$	0.248710	0.0182855
$186$	0.179859	0.0131879
$187$	−7.97696	−0.583333
$188$	24.3262	1.77417
$189$	0.106010	0.00771107
$190$	7.97433	0.578519
$191$	6.91043	0.500021	0.250011	−	0.968243i	$-0.419566\pi$
$191$	6.91043	0.500021	0.250011	+	0.968243i	$0.419566\pi$
$192$	−0.812023	−0.0586027
$193$	−17.8110	−1.28207	−0.641033	−	0.767513i	$-0.721494\pi$
$193$	−17.8110	−1.28207	−0.641033	+	0.767513i	$0.721494\pi$
$194$	4.50675	0.323565
$195$	−0.223860	−0.0160309
$196$	−20.1180	−1.43700
$197$	−9.58306	−0.682764	−0.341382	−	0.939925i	$-0.610895\pi$
$197$	−9.58306	−0.682764	−0.341382	+	0.939925i	$0.610895\pi$
$198$	−11.3405	−0.805932
$199$	−13.6201	−0.965501	−0.482751	−	0.875758i	$-0.660362\pi$
$199$	−13.6201	−0.965501	−0.482751	+	0.875758i	$0.660362\pi$
$200$	8.19376	0.579386
$201$	0.0851045	0.00600281
$202$	−7.60545	−0.535117
$203$	−0.873599	−0.0613146
$204$	0.856488	0.0599661
$205$	9.76343	0.681908
$206$	−17.9012	−1.24723
$207$	2.99602	0.208237
$208$	−5.04761	−0.349989
$209$	−6.41480	−0.443721
$210$	−0.0375571	−0.00259169
$211$	−17.7534	−1.22220	−0.611099	−	0.791554i	$-0.709272\pi$
$211$	−17.7534	−1.22220	−0.611099	+	0.791554i	$0.709272\pi$
$212$	25.4827	1.75016
$213$	−0.723675	−0.0495854
$214$	−22.3401	−1.52714
$215$	3.15204	0.214968
$216$	0.760070	0.0517162
$217$	0.360267	0.0244565
$218$	−43.3320	−2.93481
$219$	−0.554064	−0.0374402
$220$	4.76320	0.321135
$221$	17.2621	1.16118
$222$	0.0362629	0.00243381
$223$	−5.84127	−0.391160	−0.195580	−	0.980688i	$-0.562659\pi$
$223$	−5.84127	−0.391160	−0.195580	+	0.980688i	$0.562659\pi$
$224$	−1.97171	−0.131740
$225$	12.2247	0.814978
$226$	−9.16904	−0.609916
$227$	15.3837	1.02105	0.510527	−	0.859862i	$-0.329450\pi$
$227$	15.3837	1.02105	0.510527	+	0.859862i	$0.329450\pi$
$228$	0.688758	0.0456141
$229$	4.36025	0.288134	0.144067	−	0.989568i	$-0.453982\pi$
$229$	4.36025	0.288134	0.144067	+	0.989568i	$0.453982\pi$
$230$	−2.12427	−0.140070
$231$	0.0302121	0.00198781
$232$	−6.26354	−0.411221
$233$	−1.50423	−0.0985455	−0.0492728	−	0.998785i	$-0.515690\pi$
$233$	−1.50423	−0.0985455	−0.0492728	+	0.998785i	$0.515690\pi$
$234$	24.5408	1.60428
$235$	−8.02628	−0.523577
$236$	−29.5678	−1.92470
$237$	−0.0200160	−0.00130018
$238$	2.89608	0.187725
$239$	−13.3409	−0.862954	−0.431477	−	0.902124i	$-0.642007\pi$
$239$	−13.3409	−0.862954	−0.431477	+	0.902124i	$0.642007\pi$
$240$	0.0826327	0.00533392
$241$	−4.57547	−0.294732	−0.147366	−	0.989082i	$-0.547080\pi$
$241$	−4.57547	−0.294732	−0.147366	+	0.989082i	$0.547080\pi$
$242$	17.8976	1.15050
$243$	1.70136	0.109142
$244$	−8.35740	−0.535028
$245$	6.63780	0.424073
$246$	1.42355	0.0907621
$247$	13.8816	0.883266
$248$	2.58304	0.164023
$249$	0.573331	0.0363334
$250$	−19.2890	−1.21994
$251$	8.81450	0.556367	0.278183	−	0.960528i	$-0.410268\pi$
$251$	8.81450	0.556367	0.278183	+	0.960528i	$0.410268\pi$
$252$	2.43897	0.153641
$253$	1.70883	0.107433
$254$	11.5251	0.723152
$255$	−0.282593	−0.0176966
$256$	−6.20189	−0.387618
$257$	−26.1689	−1.63237	−0.816187	−	0.577788i	$-0.803916\pi$
$257$	−26.1689	−1.63237	−0.816187	+	0.577788i	$0.803916\pi$
$258$	0.459580	0.0286122
$259$	0.0726365	0.00451341
$260$	−10.3076	−0.639248
$261$	−9.34488	−0.578434
$262$	−27.0624	−1.67192
$263$	10.8971	0.671946	0.335973	−	0.941872i	$-0.390935\pi$
$263$	10.8971	0.671946	0.335973	+	0.941872i	$0.390935\pi$
$264$	0.216615	0.0133317
$265$	−8.40784	−0.516489
$266$	2.32893	0.142796
$267$	0.0290832	0.00177986
$268$	3.91861	0.239367
$269$	12.0544	0.734969	0.367485	−	0.930030i	$-0.380219\pi$
$269$	12.0544	0.734969	0.367485	+	0.930030i	$0.380219\pi$
$270$	−0.804031	−0.0489318
$271$	19.3590	1.17597	0.587987	−	0.808870i	$-0.299921\pi$
$271$	19.3590	1.17597	0.587987	+	0.808870i	$0.299921\pi$
$272$	−6.37192	−0.386354
$273$	−0.0653790	−0.00395692
$274$	−26.2066	−1.58320
$275$	6.97254	0.420460
$276$	−0.183477	−0.0110440
$277$	8.12953	0.488456	0.244228	−	0.969718i	$-0.421465\pi$
$277$	8.12953	0.488456	0.244228	+	0.969718i	$0.421465\pi$
$278$	−5.16548	−0.309805
$279$	3.85377	0.230719
$280$	−0.539377	−0.0322339
$281$	−17.1050	−1.02040	−0.510200	−	0.860056i	$-0.670429\pi$
$281$	−17.1050	−1.02040	−0.510200	+	0.860056i	$0.670429\pi$
$282$	−1.17026	−0.0696882
$283$	−20.5139	−1.21943	−0.609713	−	0.792622i	$-0.708715\pi$
$283$	−20.5139	−1.21943	−0.609713	+	0.792622i	$0.708715\pi$
$284$	−33.3214	−1.97726
$285$	−0.227251	−0.0134612
$286$	13.9972	0.827673
$287$	2.85144	0.168315
$288$	−21.0914	−1.24282
$289$	4.79110	0.281830
$290$	6.62581	0.389081
$291$	−0.128433	−0.00752885
$292$	−25.5117	−1.49296
$293$	8.24087	0.481437	0.240718	−	0.970595i	$-0.422617\pi$
$293$	8.24087	0.481437	0.240718	+	0.970595i	$0.422617\pi$
$294$	0.967818	0.0564443
$295$	9.75571	0.567999
$296$	0.520790	0.0302703
$297$	0.646787	0.0375304
$298$	9.15371	0.530260
$299$	−3.69790	−0.213855
$300$	−0.748643	−0.0432229
$301$	0.920564	0.0530604
$302$	15.2248	0.876091
$303$	0.216739	0.0124513
$304$	−5.12408	−0.293886
$305$	2.75747	0.157892
$306$	30.9794	1.77097
$307$	4.33238	0.247262	0.123631	−	0.992328i	$-0.460546\pi$
$307$	4.33238	0.247262	0.123631	+	0.992328i	$0.460546\pi$
$308$	1.39111	0.0792657
$309$	0.510145	0.0290211
$310$	−2.73244	−0.155192
$311$	−17.5107	−0.992941	−0.496470	−	0.868054i	$-0.665371\pi$
$311$	−17.5107	−0.992941	−0.496470	+	0.868054i	$0.665371\pi$
$312$	−0.468755	−0.0265380
$313$	−7.04460	−0.398184	−0.199092	−	0.979981i	$-0.563799\pi$
$313$	−7.04460	−0.398184	−0.199092	+	0.979981i	$0.563799\pi$
$314$	−36.0154	−2.03247
$315$	−0.804723	−0.0453410
$316$	−0.921632	−0.0518459
$317$	−11.6430	−0.653934	−0.326967	−	0.945036i	$-0.606027\pi$
$317$	−11.6430	−0.653934	−0.326967	+	0.945036i	$0.606027\pi$
$318$	−1.22590	−0.0687449
$319$	−5.33001	−0.298423
$320$	12.3364	0.689624
$321$	0.636646	0.0355341
$322$	−0.620399	−0.0345735
$323$	17.5237	0.975042
$324$	26.0549	1.44750
$325$	−15.0886	−0.836964
$326$	22.0522	1.22136
$327$	1.23487	0.0682883
$328$	20.4443	1.12885
$329$	−2.34410	−0.129234
$330$	−0.229144	−0.0126140
$331$	−2.86208	−0.157314	−0.0786570	−	0.996902i	$-0.525063\pi$
$331$	−2.86208	−0.157314	−0.0786570	+	0.996902i	$0.525063\pi$
$332$	26.3989	1.44883
$333$	0.776992	0.0425789
$334$	−14.3905	−0.787414
$335$	−1.29292	−0.0706398
$336$	0.0241331	0.00131657
$337$	−31.1186	−1.69514	−0.847568	−	0.530687i	$-0.821934\pi$
$337$	−31.1186	−1.69514	−0.847568	+	0.530687i	$0.821934\pi$
$338$	−1.49399	−0.0812621
$339$	0.261298	0.0141918
$340$	−13.0119	−0.705669
$341$	2.19806	0.119032
$342$	24.9125	1.34712
$343$	3.89915	0.210534
$344$	6.60027	0.355863
$345$	0.0605371	0.00325921
$346$	−12.5622	−0.675347
$347$	14.9963	0.805045	0.402522	−	0.915410i	$-0.368134\pi$
$347$	14.9963	0.805045	0.402522	+	0.915410i	$0.368134\pi$
$348$	0.572284	0.0306776
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−2.53142	−0.135310
$351$	−1.39965	−0.0747077
$352$	−12.0298	−0.641191
$353$	5.18405	0.275919	0.137960	−	0.990438i	$-0.455946\pi$
$353$	5.18405	0.275919	0.137960	+	0.990438i	$0.455946\pi$
$354$	1.42242	0.0756008
$355$	10.9942	0.583511
$356$	1.33913	0.0709736
$357$	−0.0825320	−0.00436806
$358$	30.6697	1.62094
$359$	21.6138	1.14073	0.570365	−	0.821391i	$-0.306802\pi$
$359$	21.6138	1.14073	0.570365	+	0.821391i	$0.306802\pi$
$360$	−5.76971	−0.304091
$361$	−4.90808	−0.258320
$362$	−11.1602	−0.586565
$363$	−0.510044	−0.0267704
$364$	−3.01036	−0.157786
$365$	8.41743	0.440588
$366$	0.402050	0.0210155
$367$	32.2991	1.68600	0.843000	−	0.537914i	$-0.180787\pi$
$367$	32.2991	1.68600	0.843000	+	0.537914i	$0.180787\pi$
$368$	1.36499	0.0711552
$369$	30.5018	1.58786
$370$	−0.550912	−0.0286405
$371$	−2.45554	−0.127485
$372$	−0.236006	−0.0122364
$373$	32.3008	1.67247	0.836236	−	0.548370i	$-0.184751\pi$
$373$	32.3008	1.67247	0.836236	+	0.548370i	$0.184751\pi$
$374$	17.6696	0.913673
$375$	0.549695	0.0283861
$376$	−16.8067	−0.866742
$377$	11.5341	0.594038
$378$	−0.234820	−0.0120778
$379$	−7.23128	−0.371446	−0.185723	−	0.982602i	$-0.559463\pi$
$379$	−7.23128	−0.371446	−0.185723	+	0.982602i	$0.559463\pi$
$380$	−10.4637	−0.536778
$381$	−0.328442	−0.0168266
$382$	−15.3071	−0.783182
$383$	32.0238	1.63634	0.818169	−	0.574977i	$-0.194989\pi$
$383$	32.0238	1.63634	0.818169	+	0.574977i	$0.194989\pi$
$384$	0.909918	0.0464341
$385$	−0.458987	−0.0233921
$386$	39.4528	2.00810
$387$	9.84727	0.500565
$388$	−5.91364	−0.300219
$389$	−24.9118	−1.26308	−0.631538	−	0.775345i	$-0.717576\pi$
$389$	−24.9118	−1.26308	−0.631538	+	0.775345i	$0.717576\pi$
$390$	0.495867	0.0251092
$391$	−4.66809	−0.236076
$392$	13.8993	0.702022
$393$	0.771221	0.0389029
$394$	21.2272	1.06941
$395$	0.304087	0.0153003
$396$	14.8807	0.747782
$397$	−15.6772	−0.786818	−0.393409	−	0.919363i	$-0.628704\pi$
$397$	−15.6772	−0.786818	−0.393409	+	0.919363i	$0.628704\pi$
$398$	30.1695	1.51226
$399$	−0.0663694	−0.00332263
$400$	5.56960	0.278480
$401$	15.5551	0.776784	0.388392	−	0.921494i	$-0.373031\pi$
$401$	15.5551	0.776784	0.388392	+	0.921494i	$0.373031\pi$
$402$	−0.188513	−0.00940218
$403$	−4.75661	−0.236943
$404$	9.97967	0.496507
$405$	−8.59666	−0.427171
$406$	1.93509	0.0960369
$407$	0.443170	0.0219671
$408$	−0.591739	−0.0292955
$409$	−27.6229	−1.36586	−0.682931	−	0.730483i	$-0.739295\pi$
$409$	−27.6229	−1.36586	−0.682931	+	0.730483i	$0.739295\pi$
$410$	−21.6268	−1.06807
$411$	0.746832	0.0368385
$412$	23.4895	1.15724
$413$	2.84918	0.140199
$414$	−6.63641	−0.326162
$415$	−8.71014	−0.427564
$416$	26.0325	1.27635
$417$	0.147205	0.00720866
$418$	14.2093	0.694998
$419$	−10.8745	−0.531254	−0.265627	−	0.964076i	$-0.585579\pi$
$419$	−10.8745	−0.531254	−0.265627	+	0.964076i	$0.585579\pi$
$420$	0.0492815	0.00240469
$421$	12.9502	0.631154	0.315577	−	0.948900i	$-0.397802\pi$
$421$	12.9502	0.631154	0.315577	+	0.948900i	$0.397802\pi$
$422$	39.3253	1.91432
$423$	−25.0748	−1.21918
$424$	−17.6057	−0.855010
$425$	−19.0473	−0.923929
$426$	1.60300	0.0776654
$427$	0.805327	0.0389725
$428$	29.3142	1.41695
$429$	−0.398891	−0.0192586
$430$	−6.98202	−0.336703
$431$	−19.9001	−0.958553	−0.479277	−	0.877664i	$-0.659101\pi$
$431$	−19.9001	−0.958553	−0.479277	+	0.877664i	$0.659101\pi$
$432$	0.516648	0.0248572
$433$	−32.7359	−1.57319	−0.786594	−	0.617471i	$-0.788157\pi$
$433$	−32.7359	−1.57319	−0.786594	+	0.617471i	$0.788157\pi$
$434$	−0.798019	−0.0383061
$435$	−0.188821	−0.00905329
$436$	56.8591	2.72306
$437$	−3.75392	−0.179574
$438$	1.22730	0.0586424
$439$	−37.1492	−1.77304	−0.886518	−	0.462695i	$-0.846883\pi$
$439$	−37.1492	−1.77304	−0.886518	+	0.462695i	$0.846883\pi$
$440$	−3.29085	−0.156885
$441$	20.7371	0.987480
$442$	−38.2370	−1.81875
$443$	−18.8843	−0.897221	−0.448611	−	0.893727i	$-0.648081\pi$
$443$	−18.8843	−0.897221	−0.448611	+	0.893727i	$0.648081\pi$
$444$	−0.0475833	−0.00225820
$445$	−0.441836	−0.0209451
$446$	12.9389	0.612673
$447$	−0.260861	−0.0123383
$448$	3.60288	0.170220
$449$	20.2755	0.956861	0.478430	−	0.878125i	$-0.341206\pi$
$449$	20.2755	0.956861	0.478430	+	0.878125i	$0.341206\pi$
$450$	−27.0786	−1.27650
$451$	17.3972	0.819203
$452$	12.0314	0.565909
$453$	−0.433875	−0.0203852
$454$	−34.0761	−1.59927
$455$	0.993248	0.0465642
$456$	−0.475856	−0.0222840
$457$	−37.3768	−1.74841	−0.874206	−	0.485555i	$-0.838618\pi$
$457$	−37.3768	−1.74841	−0.874206	+	0.485555i	$0.838618\pi$
$458$	−9.65830	−0.451303
$459$	−1.76686	−0.0824702
$460$	2.78741	0.129964
$461$	−35.9128	−1.67263	−0.836314	−	0.548251i	$-0.815294\pi$
$461$	−35.9128	−1.67263	−0.836314	+	0.548251i	$0.815294\pi$
$462$	−0.0669222	−0.00311350
$463$	−16.8464	−0.782921	−0.391460	−	0.920195i	$-0.628030\pi$
$463$	−16.8464	−0.782921	−0.391460	+	0.920195i	$0.628030\pi$
$464$	−4.25756	−0.197652
$465$	0.0778688	0.00361108
$466$	3.33199	0.154351
$467$	3.13100	0.144886	0.0724428	−	0.997373i	$-0.476921\pi$
$467$	3.13100	0.144886	0.0724428	+	0.997373i	$0.476921\pi$
$468$	−32.2018	−1.48853
$469$	−0.377602	−0.0174360
$470$	17.7788	0.820076
$471$	1.02636	0.0472922
$472$	20.4281	0.940280
$473$	5.61655	0.258249
$474$	0.0443371	0.00203647
$475$	−15.3172	−0.702800
$476$	−3.80016	−0.174180
$477$	−26.2669	−1.20268
$478$	29.5512	1.35164
$479$	−19.4737	−0.889778	−0.444889	−	0.895586i	$-0.646757\pi$
$479$	−19.4737	−0.889778	−0.444889	+	0.895586i	$0.646757\pi$
$480$	−0.426169	−0.0194519
$481$	−0.959020	−0.0437275
$482$	10.1350	0.461638
$483$	0.0176800	0.000804469 0
$484$	−23.4848	−1.06749
$485$	1.95117	0.0885979
$486$	−3.76864	−0.170949
$487$	15.1320	0.685694	0.342847	−	0.939391i	$-0.388609\pi$
$487$	15.1320	0.685694	0.342847	+	0.939391i	$0.388609\pi$
$488$	5.77405	0.261379
$489$	−0.628441	−0.0284191
$490$	−14.7032	−0.664225
$491$	12.4250	0.560730	0.280365	−	0.959893i	$-0.409544\pi$
$491$	12.4250	0.560730	0.280365	+	0.959893i	$0.409544\pi$
$492$	−1.86794	−0.0842134
$493$	14.5603	0.655762
$494$	−30.7489	−1.38346
$495$	−4.90978	−0.220678
$496$	1.75579	0.0788373
$497$	3.21089	0.144028
$498$	−1.26997	−0.0569089
$499$	22.4907	1.00682	0.503410	−	0.864047i	$-0.332078\pi$
$499$	22.4907	1.00682	0.503410	+	0.864047i	$0.332078\pi$
$500$	25.3106	1.13192
$501$	0.410099	0.0183219
$502$	−19.5248	−0.871435
$503$	−30.9883	−1.38170	−0.690851	−	0.722997i	$-0.742764\pi$
$503$	−30.9883	−1.38170	−0.690851	+	0.722997i	$0.742764\pi$
$504$	−1.68506	−0.0750586
$505$	−3.29273	−0.146525
$506$	−3.78518	−0.168272
$507$	0.0425754	0.00189084
$508$	−15.1230	−0.670975
$509$	20.5527	0.910983	0.455491	−	0.890240i	$-0.349464\pi$
$509$	20.5527	0.910983	0.455491	+	0.890240i	$0.349464\pi$
$510$	0.625965	0.0277182
$511$	2.45834	0.108750
$512$	−15.0914	−0.666954
$513$	−1.42085	−0.0627321
$514$	57.9663	2.55678
$515$	−7.75020	−0.341515
$516$	−0.603050	−0.0265478
$517$	−14.3018	−0.628994
$518$	−0.160895	−0.00706934
$519$	0.357995	0.0157142
$520$	7.12140	0.312294
$521$	24.8519	1.08878	0.544390	−	0.838832i	$-0.316761\pi$
$521$	24.8519	1.08878	0.544390	+	0.838832i	$0.316761\pi$
$522$	20.6996	0.905999
$523$	−9.79101	−0.428131	−0.214065	−	0.976819i	$-0.568671\pi$
$523$	−9.79101	−0.428131	−0.214065	+	0.976819i	$0.568671\pi$
$524$	35.5106	1.55129
$525$	0.0721400	0.00314845
$526$	−24.1380	−1.05247
$527$	−6.00457	−0.261563
$528$	0.147241	0.00640785
$529$	1.00000	0.0434783
$530$	18.6240	0.808976
$531$	30.4777	1.32262
$532$	−3.05596	−0.132493
$533$	−37.6476	−1.63070
$534$	−0.0644215	−0.00278779
$535$	−9.67202	−0.418158
$536$	−2.70733	−0.116939
$537$	−0.874020	−0.0377168
$538$	−26.7014	−1.15118
$539$	11.8277	0.509457
$540$	1.05503	0.0454012
$541$	14.6478	0.629757	0.314879	−	0.949132i	$-0.398036\pi$
$541$	14.6478	0.629757	0.314879	+	0.949132i	$0.398036\pi$
$542$	−42.8816	−1.84192
$543$	0.318040	0.0136484
$544$	32.8625	1.40897
$545$	−18.7603	−0.803603
$546$	0.144820	0.00619770
$547$	41.3185	1.76665	0.883325	−	0.468760i	$-0.155299\pi$
$547$	41.3185	1.76665	0.883325	+	0.468760i	$0.155299\pi$
$548$	34.3877	1.46897
$549$	8.61459	0.367662
$550$	−15.4447	−0.658565
$551$	11.7089	0.498815
$552$	0.126763	0.00539537
$553$	0.0888094	0.00377656
$554$	−18.0075	−0.765067
$555$	0.0156998	0.000666419 0
$556$	6.77801	0.287452
$557$	−40.8710	−1.73176	−0.865879	−	0.500253i	$-0.833240\pi$
$557$	−40.8710	−1.73176	−0.865879	+	0.500253i	$0.833240\pi$
$558$	−8.53640	−0.361375
$559$	−12.1542	−0.514068
$560$	−0.366634	−0.0154931
$561$	−0.503545	−0.0212597
$562$	37.8890	1.59825
$563$	27.2086	1.14671	0.573353	−	0.819309i	$-0.305642\pi$
$563$	27.2086	1.14671	0.573353	+	0.819309i	$0.305642\pi$
$564$	1.53559	0.0646600
$565$	−3.96968	−0.167006
$566$	45.4399	1.90998
$567$	−2.51068	−0.105439
$568$	23.0214	0.965959
$569$	−13.1548	−0.551480	−0.275740	−	0.961232i	$-0.588923\pi$
$569$	−13.1548	−0.551480	−0.275740	+	0.961232i	$0.588923\pi$
$570$	0.503379	0.0210842
$571$	−24.7011	−1.03371	−0.516855	−	0.856073i	$-0.672897\pi$
$571$	−24.7011	−1.03371	−0.516855	+	0.856073i	$0.672897\pi$
$572$	−18.3668	−0.767955
$573$	0.436221	0.0182234
$574$	−6.31616	−0.263631
$575$	4.08031	0.170161
$576$	38.5400	1.60583
$577$	−5.23252	−0.217833	−0.108916	−	0.994051i	$-0.534738\pi$
$577$	−5.23252	−0.217833	−0.108916	+	0.994051i	$0.534738\pi$
$578$	−10.6127	−0.441429
$579$	−1.12432	−0.0467252
$580$	−8.69423	−0.361008
$581$	−2.54382	−0.105536
$582$	0.284488	0.0117924
$583$	−14.9817	−0.620480
$584$	17.6258	0.729361
$585$	10.6248	0.439280
$586$	−18.2542	−0.754073
$587$	37.8813	1.56353	0.781765	−	0.623573i	$-0.214320\pi$
$587$	37.8813	1.56353	0.781765	+	0.623573i	$0.214320\pi$
$588$	−1.26995	−0.0523717
$589$	−4.82866	−0.198962
$590$	−21.6096	−0.889655
$591$	−0.604930	−0.0248835
$592$	0.354000	0.0145493
$593$	−3.26950	−0.134262	−0.0671311	−	0.997744i	$-0.521385\pi$
$593$	−3.26950	−0.134262	−0.0671311	+	0.997744i	$0.521385\pi$
$594$	−1.43268	−0.0587838
$595$	1.25384	0.0514024
$596$	−12.0113	−0.492001
$597$	−0.859766	−0.0351879
$598$	8.19114	0.334960
$599$	−29.3384	−1.19873	−0.599367	−	0.800475i	$-0.704581\pi$
$599$	−29.3384	−1.19873	−0.599367	+	0.800475i	$0.704581\pi$
$600$	0.517231	0.0211158
$601$	29.5018	1.20340	0.601702	−	0.798721i	$-0.294489\pi$
$601$	29.5018	1.20340	0.601702	+	0.798721i	$0.294489\pi$
$602$	−2.03912	−0.0831083
$603$	−4.03920	−0.164489
$604$	−19.9776	−0.812879
$605$	7.74867	0.315028
$606$	−0.480093	−0.0195025
$607$	−26.7288	−1.08489	−0.542443	−	0.840092i	$-0.682501\pi$
$607$	−26.7288	−1.08489	−0.542443	+	0.840092i	$0.682501\pi$
$608$	26.4269	1.07175
$609$	−0.0551459	−0.00223462
$610$	−6.10801	−0.247306
$611$	30.9492	1.25207
$612$	−40.6503	−1.64319
$613$	−3.94770	−0.159446	−0.0797231	−	0.996817i	$-0.525404\pi$
$613$	−3.94770	−0.159446	−0.0797231	+	0.996817i	$0.525404\pi$
$614$	−9.59657	−0.387286
$615$	0.616316	0.0248523
$616$	−0.961103	−0.0387239
$617$	−15.6335	−0.629380	−0.314690	−	0.949194i	$-0.601901\pi$
$617$	−15.6335	−0.629380	−0.314690	+	0.949194i	$0.601901\pi$
$618$	−1.13001	−0.0454557
$619$	−1.09845	−0.0441503	−0.0220751	−	0.999756i	$-0.507027\pi$
$619$	−1.09845	−0.0441503	−0.0220751	+	0.999756i	$0.507027\pi$
$620$	3.58544	0.143995
$621$	0.378498	0.0151886
$622$	38.7876	1.55524
$623$	−0.129040	−0.00516986
$624$	−0.318630	−0.0127554
$625$	12.0505	0.482020
$626$	15.6043	0.623674
$627$	−0.404934	−0.0161715
$628$	47.2585	1.88582
$629$	−1.21063	−0.0482711
$630$	1.78252	0.0710175
$631$	−14.6979	−0.585113	−0.292556	−	0.956248i	$-0.594506\pi$
$631$	−14.6979	−0.585113	−0.292556	+	0.956248i	$0.594506\pi$
$632$	0.636747	0.0253284
$633$	−1.12068	−0.0445432
$634$	25.7901	1.02426
$635$	4.98974	0.198012
$636$	1.60859	0.0637848
$637$	−25.5952	−1.01412
$638$	11.8064	0.467419
$639$	34.3468	1.35874
$640$	−13.8236	−0.546426
$641$	19.2218	0.759217	0.379609	−	0.925147i	$-0.376059\pi$
$641$	19.2218	0.759217	0.379609	+	0.925147i	$0.376059\pi$
$642$	−1.41022	−0.0556569
$643$	−29.7330	−1.17255	−0.586277	−	0.810111i	$-0.699407\pi$
$643$	−29.7330	−1.17255	−0.586277	+	0.810111i	$0.699407\pi$
$644$	0.814072	0.0320789
$645$	0.198972	0.00783453
$646$	−38.8163	−1.52721
$647$	−23.1876	−0.911597	−0.455798	−	0.890083i	$-0.650646\pi$
$647$	−23.1876	−0.911597	−0.455798	+	0.890083i	$0.650646\pi$
$648$	−18.0011	−0.707150
$649$	17.3835	0.682360
$650$	33.4224	1.31093
$651$	0.0227418	0.000891322 0
$652$	−28.9364	−1.13324
$653$	44.2232	1.73059	0.865294	−	0.501265i	$-0.167132\pi$
$653$	44.2232	1.73059	0.865294	+	0.501265i	$0.167132\pi$
$654$	−2.73533	−0.106960
$655$	−11.7165	−0.457802
$656$	13.8967	0.542577
$657$	26.2968	1.02594
$658$	5.19236	0.202419
$659$	−44.4881	−1.73301	−0.866506	−	0.499167i	$-0.833639\pi$
$659$	−44.4881	−1.73301	−0.866506	+	0.499167i	$0.833639\pi$
$660$	0.300677	0.0117038
$661$	8.65583	0.336673	0.168336	−	0.985730i	$-0.446160\pi$
$661$	8.65583	0.336673	0.168336	+	0.985730i	$0.446160\pi$
$662$	6.33972	0.246400
$663$	1.08967	0.0423193
$664$	−18.2387	−0.707800
$665$	1.00829	0.0391000
$666$	−1.72110	−0.0666912
$667$	−3.11910	−0.120772
$668$	18.8829	0.730600
$669$	−0.368730	−0.0142559
$670$	2.86392	0.110643
$671$	4.91347	0.189682
$672$	−0.124464	−0.00480131
$673$	−31.8451	−1.22754	−0.613770	−	0.789485i	$-0.710348\pi$
$673$	−31.8451	−1.22754	−0.613770	+	0.789485i	$0.710348\pi$
$674$	68.9300	2.65508
$675$	1.54439	0.0594436
$676$	1.96037	0.0753989
$677$	−22.8756	−0.879183	−0.439591	−	0.898198i	$-0.644877\pi$
$677$	−22.8756	−0.879183	−0.439591	+	0.898198i	$0.644877\pi$
$678$	−0.578795	−0.0222285
$679$	0.569844	0.0218686
$680$	8.98980	0.344743
$681$	0.971096	0.0372125
$682$	−4.86888	−0.186439
$683$	−16.5319	−0.632577	−0.316288	−	0.948663i	$-0.602437\pi$
$683$	−16.5319	−0.632577	−0.316288	+	0.948663i	$0.602437\pi$
$684$	−32.6896	−1.24992
$685$	−11.3460	−0.433508
$686$	−8.63692	−0.329759
$687$	0.275241	0.0105011
$688$	4.48645	0.171044
$689$	32.4205	1.23512
$690$	−0.134094	−0.00510488
$691$	−42.1670	−1.60411	−0.802054	−	0.597252i	$-0.796259\pi$
$691$	−42.1670	−1.60411	−0.802054	+	0.597252i	$0.796259\pi$
$692$	16.4838	0.626619
$693$	−1.43392	−0.0544700
$694$	−33.2180	−1.26094
$695$	−2.23636	−0.0848300
$696$	−0.395385	−0.0149870
$697$	−47.5250	−1.80014
$698$	2.21508	0.0838419
$699$	−0.0949545	−0.00359151
$700$	3.32167	0.125547
$701$	36.2381	1.36870	0.684348	−	0.729156i	$-0.260087\pi$
$701$	36.2381	1.36870	0.684348	+	0.729156i	$0.260087\pi$
$702$	3.10033	0.117014
$703$	−0.973549	−0.0367181
$704$	21.9819	0.828474
$705$	−0.506658	−0.0190818
$706$	−11.4831	−0.432171
$707$	−0.961652	−0.0361666
$708$	−1.86647	−0.0701461
$709$	22.0034	0.826357	0.413178	−	0.910650i	$-0.364419\pi$
$709$	22.0034	0.826357	0.413178	+	0.910650i	$0.364419\pi$
$710$	−24.3530	−0.913951
$711$	0.949994	0.0356276
$712$	−0.925190	−0.0346730
$713$	1.28630	0.0481723
$714$	0.182815	0.00684168
$715$	6.06001	0.226632
$716$	−40.2440	−1.50399
$717$	−0.842146	−0.0314505
$718$	−47.8762	−1.78672
$719$	−10.5304	−0.392717	−0.196358	−	0.980532i	$-0.562912\pi$
$719$	−10.5304	−0.392717	−0.196358	+	0.980532i	$0.562912\pi$
$720$	−3.92189	−0.146160
$721$	−2.26347	−0.0842960
$722$	10.8718	0.404606
$723$	−0.288826	−0.0107416
$724$	14.6441	0.544243
$725$	−12.7269	−0.472666
$726$	1.12979	0.0419303
$727$	0.800153	0.0296760	0.0148380	−	0.999890i	$-0.495277\pi$
$727$	0.800153	0.0296760	0.0148380	+	0.999890i	$0.495277\pi$
$728$	2.07983	0.0770835
$729$	−26.7851	−0.992039
$730$	−18.6453	−0.690092
$731$	−15.3430	−0.567483
$732$	−0.527560	−0.0194992
$733$	−22.8020	−0.842211	−0.421105	−	0.907012i	$-0.638358\pi$
$733$	−22.8020	−0.842211	−0.421105	+	0.907012i	$0.638358\pi$
$734$	−71.5450	−2.64077
$735$	0.419011	0.0154554
$736$	−7.03981	−0.259491
$737$	−2.30383	−0.0848625
$738$	−67.5640	−2.48706
$739$	10.7703	0.396193	0.198097	−	0.980182i	$-0.436524\pi$
$739$	10.7703	0.396193	0.198097	+	0.980182i	$0.436524\pi$
$740$	0.722892	0.0265740
$741$	0.876276	0.0321908
$742$	5.43920	0.199679
$743$	33.7625	1.23863	0.619313	−	0.785144i	$-0.287411\pi$
$743$	33.7625	1.23863	0.619313	+	0.785144i	$0.287411\pi$
$744$	0.163055	0.00597787
$745$	3.96304	0.145195
$746$	−71.5488	−2.61959
$747$	−27.2113	−0.995608
$748$	−23.1856	−0.847749
$749$	−2.82474	−0.103214
$750$	−1.21762	−0.0444611
$751$	3.93290	0.143513	0.0717567	−	0.997422i	$-0.477139\pi$
$751$	3.93290	0.143513	0.0717567	+	0.997422i	$0.477139\pi$
$752$	−11.4242	−0.416596
$753$	0.556415	0.0202769
$754$	−25.5490	−0.930440
$755$	6.59149	0.239889
$756$	0.308125	0.0112064
$757$	41.4781	1.50755	0.753773	−	0.657135i	$-0.228232\pi$
$757$	41.4781	1.50755	0.753773	+	0.657135i	$0.228232\pi$
$758$	16.0178	0.581794
$759$	0.107870	0.00391542
$760$	7.22929	0.262234
$761$	−18.5750	−0.673342	−0.336671	−	0.941622i	$-0.609301\pi$
$761$	−18.5750	−0.673342	−0.336671	+	0.941622i	$0.609301\pi$
$762$	0.727524	0.0263554
$763$	−5.47900	−0.198353
$764$	20.0857	0.726673
$765$	13.4123	0.484924
$766$	−70.9352	−2.56299
$767$	−37.6178	−1.35830
$768$	−0.391494	−0.0141268
$769$	−39.0642	−1.40869	−0.704345	−	0.709857i	$-0.748759\pi$
$769$	−39.0642	−1.40869	−0.704345	+	0.709857i	$0.748759\pi$
$770$	1.01669	0.0366390
$771$	−1.65191	−0.0594922
$772$	−51.7690	−1.86321
$773$	−49.3192	−1.77389	−0.886945	−	0.461876i	$-0.847177\pi$
$773$	−49.3192	−1.77389	−0.886945	+	0.461876i	$0.847177\pi$
$774$	−21.8125	−0.784033
$775$	5.24850	0.188532
$776$	4.08568	0.146667
$777$	0.00458517	0.000164492 0
$778$	55.1815	1.97835
$779$	−38.2179	−1.36930
$780$	−0.650664	−0.0232975
$781$	19.5903	0.700995
$782$	10.3402	0.369764
$783$	−1.18057	−0.0421903
$784$	9.44788	0.337424
$785$	−15.5926	−0.556525
$786$	−1.70831	−0.0609335
$787$	−53.2724	−1.89896	−0.949478	−	0.313832i	$-0.898387\pi$
$787$	−53.2724	−1.89896	−0.949478	+	0.313832i	$0.898387\pi$
$788$	−27.8538	−0.992251
$789$	0.687881	0.0244892
$790$	−0.673575	−0.0239647
$791$	−1.15936	−0.0412220
$792$	−10.2809	−0.365316
$793$	−10.6327	−0.377580
$794$	34.7263	1.23239
$795$	−0.530744	−0.0188236
$796$	−39.5877	−1.40315
$797$	−20.0613	−0.710609	−0.355304	−	0.934751i	$-0.615623\pi$
$797$	−20.0613	−0.710609	−0.355304	+	0.934751i	$0.615623\pi$
$798$	0.147013	0.00520422
$799$	39.0691	1.38217
$800$	−28.7246	−1.01557
$801$	−1.38034	−0.0487718
$802$	−34.4557	−1.21667
$803$	14.9988	0.529297
$804$	0.247362	0.00872379
$805$	−0.268598	−0.00946683
$806$	10.5363	0.371124
$807$	0.760933	0.0267861
$808$	−6.89486	−0.242560
$809$	−22.2830	−0.783428	−0.391714	−	0.920087i	$-0.628118\pi$
$809$	−22.2830	−0.783428	−0.391714	+	0.920087i	$0.628118\pi$
$810$	19.0423	0.669077
$811$	−30.3944	−1.06729	−0.533646	−	0.845708i	$-0.679179\pi$
$811$	−30.3944	−1.06729	−0.533646	+	0.845708i	$0.679179\pi$
$812$	−2.53918	−0.0891076
$813$	1.22203	0.0428586
$814$	−0.981656	−0.0344070
$815$	9.54737	0.334430
$816$	−0.402227	−0.0140808
$817$	−12.3383	−0.431664
$818$	61.1868	2.13935
$819$	3.10300	0.108427
$820$	28.3781	0.991006
$821$	−29.1323	−1.01673	−0.508363	−	0.861143i	$-0.669749\pi$
$821$	−29.1323	−1.01673	−0.508363	+	0.861143i	$0.669749\pi$
$822$	−1.65429	−0.0577000
$823$	−9.07146	−0.316211	−0.158106	−	0.987422i	$-0.550539\pi$
$823$	−9.07146	−0.316211	−0.158106	+	0.987422i	$0.550539\pi$
$824$	−16.2286	−0.565352
$825$	0.440141	0.0153238
$826$	−6.31116	−0.219593
$827$	4.76975	0.165861	0.0829303	−	0.996555i	$-0.473572\pi$
$827$	4.76975	0.165861	0.0829303	+	0.996555i	$0.473572\pi$
$828$	8.70813	0.302628
$829$	14.8530	0.515865	0.257933	−	0.966163i	$-0.416959\pi$
$829$	14.8530	0.515865	0.257933	+	0.966163i	$0.416959\pi$
$830$	19.2936	0.669692
$831$	0.513176	0.0178019
$832$	−47.5688	−1.64915
$833$	−32.3105	−1.11949
$834$	−0.326070	−0.0112909
$835$	−6.23028	−0.215608
$836$	−18.6451	−0.644853
$837$	0.486862	0.0168284
$838$	24.0879	0.832101
$839$	−11.4206	−0.394285	−0.197142	−	0.980375i	$-0.563166\pi$
$839$	−11.4206	−0.394285	−0.197142	+	0.980375i	$0.563166\pi$
$840$	−0.0340481	−0.00117477
$841$	−19.2712	−0.664524
$842$	−28.6857	−0.988575
$843$	−1.07975	−0.0371887
$844$	−51.6016	−1.77620
$845$	−0.646812	−0.0222510
$846$	55.5427	1.90960
$847$	2.26302	0.0777584
$848$	−11.9673	−0.410957
$849$	−1.29494	−0.0444422
$850$	42.1912	1.44715
$851$	0.259342	0.00889012
$852$	−2.10341	−0.0720617
$853$	24.8082	0.849415	0.424707	−	0.905331i	$-0.360377\pi$
$853$	24.8082	0.849415	0.424707	+	0.905331i	$0.360377\pi$
$854$	−1.78386	−0.0610425
$855$	10.7857	0.368864
$856$	−20.2529	−0.692229
$857$	−27.3764	−0.935160	−0.467580	−	0.883951i	$-0.654874\pi$
$857$	−27.3764	−0.935160	−0.467580	+	0.883951i	$0.654874\pi$
$858$	0.883574	0.0301647
$859$	−43.4240	−1.48161	−0.740805	−	0.671721i	$-0.765556\pi$
$859$	−43.4240	−1.48161	−0.740805	+	0.671721i	$0.765556\pi$
$860$	9.16163	0.312409
$861$	0.179997	0.00613428
$862$	44.0802	1.50138
$863$	45.0089	1.53212	0.766061	−	0.642768i	$-0.222214\pi$
$863$	45.0089	1.53212	0.766061	+	0.642768i	$0.222214\pi$
$864$	−2.66455	−0.0906500
$865$	−5.43872	−0.184922
$866$	72.5126	2.46408
$867$	0.302438	0.0102713
$868$	1.04714	0.0355422
$869$	0.541845	0.0183808
$870$	0.418254	0.0141801
$871$	4.98548	0.168926
$872$	−39.2834	−1.33030
$873$	6.09562	0.206306
$874$	8.31523	0.281267
$875$	−2.43895	−0.0824516
$876$	−1.61043	−0.0544112
$877$	−45.0884	−1.52253	−0.761264	−	0.648442i	$-0.775421\pi$
$877$	−45.0884	−1.52253	−0.761264	+	0.648442i	$0.775421\pi$
$878$	82.2884	2.77710
$879$	0.520205	0.0175461
$880$	−2.23691	−0.0754063
$881$	−37.4318	−1.26111	−0.630555	−	0.776144i	$-0.717173\pi$
$881$	−37.4318	−1.26111	−0.630555	+	0.776144i	$0.717173\pi$
$882$	−45.9343	−1.54669
$883$	35.1035	1.18133	0.590663	−	0.806918i	$-0.298866\pi$
$883$	35.1035	1.18133	0.590663	+	0.806918i	$0.298866\pi$
$884$	50.1736	1.68752
$885$	0.615828	0.0207008
$886$	41.8302	1.40531
$887$	11.1670	0.374950	0.187475	−	0.982269i	$-0.439970\pi$
$887$	11.1670	0.374950	0.187475	+	0.982269i	$0.439970\pi$
$888$	0.0328748	0.00110321
$889$	1.45727	0.0488752
$890$	0.978702	0.0328062
$891$	−15.3182	−0.513178
$892$	−16.9781	−0.568467
$893$	31.4180	1.05136
$894$	0.577827	0.0193254
$895$	13.2783	0.443843
$896$	−4.03723	−0.134874
$897$	−0.233430	−0.00779399
$898$	−44.9118	−1.49873
$899$	−4.01210	−0.133811
$900$	35.5319	1.18440
$901$	40.9264	1.36346
$902$	−38.5362	−1.28312
$903$	0.0581105	0.00193380
$904$	−8.31237	−0.276465
$905$	−4.83172	−0.160612
$906$	0.961066	0.0319293
$907$	−30.1114	−0.999834	−0.499917	−	0.866073i	$-0.666636\pi$
$907$	−30.1114	−0.999834	−0.499917	+	0.866073i	$0.666636\pi$
$908$	44.7138	1.48388
$909$	−10.2868	−0.341191
$910$	−2.20012	−0.0729333
$911$	−2.06016	−0.0682562	−0.0341281	−	0.999417i	$-0.510865\pi$
$911$	−2.06016	−0.0682562	−0.0341281	+	0.999417i	$0.510865\pi$
$912$	−0.323457	−0.0107107
$913$	−15.5204	−0.513650
$914$	82.7925	2.73853
$915$	0.174065	0.00575442
$916$	12.6734	0.418740
$917$	−3.42184	−0.112999
$918$	3.91374	0.129173
$919$	45.5190	1.50153	0.750766	−	0.660568i	$-0.229685\pi$
$919$	45.5190	1.50153	0.750766	+	0.660568i	$0.229685\pi$
$920$	−1.92580	−0.0634916
$921$	0.273481	0.00901152
$922$	79.5497	2.61983
$923$	−42.3934	−1.39539
$924$	0.0878136	0.00288885
$925$	1.05820	0.0347933
$926$	37.3162	1.22629
$927$	−24.2123	−0.795237
$928$	21.9579	0.720803
$929$	−29.7102	−0.974760	−0.487380	−	0.873190i	$-0.662047\pi$
$929$	−29.7102	−0.974760	−0.487380	+	0.873190i	$0.662047\pi$
$930$	−0.172485	−0.00565602
$931$	−25.9830	−0.851557
$932$	−4.37215	−0.143215
$933$	−1.10536	−0.0361879
$934$	−6.93542	−0.226934
$935$	7.64994	0.250180
$936$	22.2479	0.727195
$937$	13.3106	0.434839	0.217420	−	0.976078i	$-0.430236\pi$
$937$	13.3106	0.434839	0.217420	+	0.976078i	$0.430236\pi$
$938$	0.836417	0.0273100
$939$	−0.444690	−0.0145119
$940$	−23.3289	−0.760906
$941$	−41.6129	−1.35654	−0.678271	−	0.734812i	$-0.737270\pi$
$941$	−41.6129	−1.35654	−0.678271	+	0.734812i	$0.737270\pi$
$942$	−2.27347	−0.0740736
$943$	10.1808	0.331533
$944$	13.8857	0.451942
$945$	−0.101664	−0.00330712
$946$	−12.4411	−0.404495
$947$	−21.6999	−0.705152	−0.352576	−	0.935783i	$-0.614694\pi$
$947$	−21.6999	−0.705152	−0.352576	+	0.935783i	$0.614694\pi$
$948$	−0.0581780	−0.00188953
$949$	−32.4574	−1.05361
$950$	33.9287	1.10079
$951$	−0.734962	−0.0238328
$952$	2.62550	0.0850929
$953$	−55.1446	−1.78631	−0.893155	−	0.449749i	$-0.851513\pi$
$953$	−55.1446	−1.78631	−0.893155	+	0.449749i	$0.851513\pi$
$954$	58.1831	1.88375
$955$	−6.62713	−0.214449
$956$	−38.7764	−1.25412
$957$	−0.336456	−0.0108761
$958$	43.1358	1.39366
$959$	−3.31363	−0.107003
$960$	0.778733	0.0251335
$961$	−29.3454	−0.946627
$962$	2.12430	0.0684903
$963$	−30.2163	−0.973706
$964$	−13.2989	−0.428329
$965$	17.0809	0.549852
$966$	−0.0391626	−0.00126004
$967$	17.4139	0.559994	0.279997	−	0.960001i	$-0.409666\pi$
$967$	17.4139	0.559994	0.279997	+	0.960001i	$0.409666\pi$
$968$	16.2254	0.521505
$969$	1.10618	0.0355356
$970$	−4.32199	−0.138771
$971$	3.38632	0.108672	0.0543361	−	0.998523i	$-0.482696\pi$
$971$	3.38632	0.108672	0.0543361	+	0.998523i	$0.482696\pi$
$972$	4.94511	0.158614
$973$	−0.653136	−0.0209386
$974$	−33.5185	−1.07400
$975$	−0.952466	−0.0305033
$976$	3.92483	0.125631
$977$	16.3934	0.524471	0.262236	−	0.965004i	$-0.415540\pi$
$977$	16.3934	0.524471	0.262236	+	0.965004i	$0.415540\pi$
$978$	1.39205	0.0445127
$979$	−0.787298	−0.0251621
$980$	19.2932	0.616299
$981$	−58.6089	−1.87124
$982$	−27.5222	−0.878270
$983$	−10.3640	−0.330560	−0.165280	−	0.986247i	$-0.552853\pi$
$983$	−10.3640	−0.330560	−0.165280	+	0.986247i	$0.552853\pi$
$984$	1.29054	0.0411411
$985$	9.19019	0.292824
$986$	−32.2521	−1.02712
$987$	−0.147971	−0.00470997
$988$	40.3479	1.28364
$989$	3.28679	0.104514
$990$	10.8756	0.345648
$991$	7.24314	0.230086	0.115043	−	0.993361i	$-0.463299\pi$
$991$	7.24314	0.230086	0.115043	+	0.993361i	$0.463299\pi$
$992$	−9.05530	−0.287506
$993$	−0.180668	−0.00573334
$994$	−7.11236	−0.225590
$995$	13.0617	0.414084
$996$	1.66643	0.0528028
$997$	−40.5512	−1.28427	−0.642135	−	0.766592i	$-0.721951\pi$
$997$	−40.5512	−1.28427	−0.642135	+	0.766592i	$0.721951\pi$
$998$	−49.8186	−1.57698
$999$	0.0981604	0.00310566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.19	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.19	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21508 q^{2} +0.0631249 q^{3} +2.90657 q^{4} -0.959004 q^{5} -0.139827 q^{6} -0.280080 q^{7} -2.00812 q^{8} -2.99602 q^{9} +O(q^{10})\)	\(q-2.21508 q^{2} +0.0631249 q^{3} +2.90657 q^{4} -0.959004 q^{5} -0.139827 q^{6} -0.280080 q^{7} -2.00812 q^{8} -2.99602 q^{9} +2.12427 q^{10} -1.70883 q^{11} +0.183477 q^{12} +3.69790 q^{13} +0.620399 q^{14} -0.0605371 q^{15} -1.36499 q^{16} +4.66809 q^{17} +6.63641 q^{18} +3.75392 q^{19} -2.78741 q^{20} -0.0176800 q^{21} +3.78518 q^{22} -1.00000 q^{23} -0.126763 q^{24} -4.08031 q^{25} -8.19114 q^{26} -0.378498 q^{27} -0.814072 q^{28} +3.11910 q^{29} +0.134094 q^{30} -1.28630 q^{31} +7.03981 q^{32} -0.107870 q^{33} -10.3402 q^{34} +0.268598 q^{35} -8.70813 q^{36} -0.259342 q^{37} -8.31523 q^{38} +0.233430 q^{39} +1.92580 q^{40} -10.1808 q^{41} +0.0391626 q^{42} -3.28679 q^{43} -4.96682 q^{44} +2.87319 q^{45} +2.21508 q^{46} +8.36939 q^{47} -0.0861652 q^{48} -6.92156 q^{49} +9.03821 q^{50} +0.294673 q^{51} +10.7482 q^{52} +8.76726 q^{53} +0.838403 q^{54} +1.63877 q^{55} +0.562435 q^{56} +0.236966 q^{57} -6.90906 q^{58} -10.1727 q^{59} -0.175955 q^{60} -2.87535 q^{61} +2.84925 q^{62} +0.839124 q^{63} -12.8637 q^{64} -3.54630 q^{65} +0.238939 q^{66} +1.34819 q^{67} +13.5681 q^{68} -0.0631249 q^{69} -0.594965 q^{70} -11.4642 q^{71} +6.01636 q^{72} -8.77726 q^{73} +0.574462 q^{74} -0.257569 q^{75} +10.9110 q^{76} +0.478608 q^{77} -0.517065 q^{78} -0.317086 q^{79} +1.30903 q^{80} +8.96415 q^{81} +22.5513 q^{82} +9.08249 q^{83} -0.0513882 q^{84} -4.47672 q^{85} +7.28049 q^{86} +0.196893 q^{87} +3.43153 q^{88} +0.460724 q^{89} -6.36434 q^{90} -1.03571 q^{91} -2.90657 q^{92} -0.0811975 q^{93} -18.5388 q^{94} -3.60002 q^{95} +0.444388 q^{96} -2.03458 q^{97} +15.3318 q^{98} +5.11967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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