LMFDB - Embedded newform 8033.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52129 q^{2} +1.55242 q^{3} +4.35693 q^{4} +3.41413 q^{5} -3.91411 q^{6} +1.49471 q^{7} -5.94251 q^{8} -0.589992 q^{9} +O(q^{10})$	\(q-2.52129 q^{2} +1.55242 q^{3} +4.35693 q^{4} +3.41413 q^{5} -3.91411 q^{6} +1.49471 q^{7} -5.94251 q^{8} -0.589992 q^{9} -8.60803 q^{10} -1.86512 q^{11} +6.76378 q^{12} +0.544238 q^{13} -3.76861 q^{14} +5.30016 q^{15} +6.26896 q^{16} -0.0145674 q^{17} +1.48754 q^{18} -3.92557 q^{19} +14.8751 q^{20} +2.32042 q^{21} +4.70251 q^{22} -5.93949 q^{23} -9.22527 q^{24} +6.65629 q^{25} -1.37218 q^{26} -5.57318 q^{27} +6.51235 q^{28} +1.00000 q^{29} -13.3633 q^{30} +8.17478 q^{31} -3.92089 q^{32} -2.89544 q^{33} +0.0367287 q^{34} +5.10314 q^{35} -2.57055 q^{36} +0.524314 q^{37} +9.89752 q^{38} +0.844886 q^{39} -20.2885 q^{40} +7.58963 q^{41} -5.85046 q^{42} +9.09038 q^{43} -8.12618 q^{44} -2.01431 q^{45} +14.9752 q^{46} -2.89470 q^{47} +9.73207 q^{48} -4.76584 q^{49} -16.7825 q^{50} -0.0226147 q^{51} +2.37121 q^{52} +10.5672 q^{53} +14.0516 q^{54} -6.36775 q^{55} -8.88234 q^{56} -6.09414 q^{57} -2.52129 q^{58} -4.70526 q^{59} +23.0924 q^{60} +1.64871 q^{61} -20.6110 q^{62} -0.881869 q^{63} -2.65221 q^{64} +1.85810 q^{65} +7.30027 q^{66} +9.43187 q^{67} -0.0634691 q^{68} -9.22058 q^{69} -12.8665 q^{70} +14.2890 q^{71} +3.50604 q^{72} +7.04779 q^{73} -1.32195 q^{74} +10.3334 q^{75} -17.1034 q^{76} -2.78781 q^{77} -2.13021 q^{78} +8.63641 q^{79} +21.4031 q^{80} -6.88193 q^{81} -19.1357 q^{82} -15.9731 q^{83} +10.1099 q^{84} -0.0497350 q^{85} -22.9195 q^{86} +1.55242 q^{87} +11.0835 q^{88} -1.62323 q^{89} +5.07867 q^{90} +0.813479 q^{91} -25.8779 q^{92} +12.6907 q^{93} +7.29839 q^{94} -13.4024 q^{95} -6.08687 q^{96} -1.64653 q^{97} +12.0161 q^{98} +1.10040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.52129	−1.78282	−0.891412	−	0.453193i	$-0.850285\pi$
$2$	−2.52129	−1.78282	−0.891412	+	0.453193i	$0.850285\pi$
$3$	1.55242	0.896290	0.448145	−	0.893961i	$-0.352085\pi$
$3$	1.55242	0.896290	0.448145	+	0.893961i	$0.352085\pi$
$4$	4.35693	2.17846
$5$	3.41413	1.52685	0.763423	−	0.645899i	$-0.223517\pi$
$5$	3.41413	1.52685	0.763423	+	0.645899i	$0.223517\pi$
$6$	−3.91411	−1.59793
$7$	1.49471	0.564948	0.282474	−	0.959275i	$-0.408845\pi$
$7$	1.49471	0.564948	0.282474	+	0.959275i	$0.408845\pi$
$8$	−5.94251	−2.10099
$9$	−0.589992	−0.196664
$10$	−8.60803	−2.72210
$11$	−1.86512	−0.562354	−0.281177	−	0.959656i	$-0.590725\pi$
$11$	−1.86512	−0.562354	−0.281177	+	0.959656i	$0.590725\pi$
$12$	6.76378	1.95254
$13$	0.544238	0.150944	0.0754722	−	0.997148i	$-0.475954\pi$
$13$	0.544238	0.150944	0.0754722	+	0.997148i	$0.475954\pi$
$14$	−3.76861	−1.00720
$15$	5.30016	1.36850
$16$	6.26896	1.56724
$17$	−0.0145674	−0.00353311	−0.00176656	−	0.999998i	$-0.500562\pi$
$17$	−0.0145674	−0.00353311	−0.00176656	+	0.999998i	$0.500562\pi$
$18$	1.48754	0.350618
$19$	−3.92557	−0.900588	−0.450294	−	0.892880i	$-0.648681\pi$
$19$	−3.92557	−0.900588	−0.450294	+	0.892880i	$0.648681\pi$
$20$	14.8751	3.32618
$21$	2.32042	0.506357
$22$	4.70251	1.00258
$23$	−5.93949	−1.23847	−0.619234	−	0.785206i	$-0.712557\pi$
$23$	−5.93949	−1.23847	−0.619234	+	0.785206i	$0.712557\pi$
$24$	−9.22527	−1.88310
$25$	6.65629	1.33126
$26$	−1.37218	−0.269108
$27$	−5.57318	−1.07256
$28$	6.51235	1.23072
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−13.3633	−2.43979
$31$	8.17478	1.46823	0.734117	−	0.679023i	$-0.237596\pi$
$31$	8.17478	1.46823	0.734117	+	0.679023i	$0.237596\pi$
$32$	−3.92089	−0.693122
$33$	−2.89544	−0.504032
$34$	0.0367287	0.00629892
$35$	5.10314	0.862588
$36$	−2.57055	−0.428426
$37$	0.524314	0.0861966	0.0430983	−	0.999071i	$-0.486277\pi$
$37$	0.524314	0.0861966	0.0430983	+	0.999071i	$0.486277\pi$
$38$	9.89752	1.60559
$39$	0.844886	0.135290
$40$	−20.2885	−3.20789
$41$	7.58963	1.18530	0.592650	−	0.805460i	$-0.298082\pi$
$41$	7.58963	1.18530	0.592650	+	0.805460i	$0.298082\pi$
$42$	−5.85046	−0.902746
$43$	9.09038	1.38627	0.693135	−	0.720808i	$-0.256229\pi$
$43$	9.09038	1.38627	0.693135	+	0.720808i	$0.256229\pi$
$44$	−8.12618	−1.22507
$45$	−2.01431	−0.300276
$46$	14.9752	2.20797
$47$	−2.89470	−0.422235	−0.211118	−	0.977461i	$-0.567710\pi$
$47$	−2.89470	−0.422235	−0.211118	+	0.977461i	$0.567710\pi$
$48$	9.73207	1.40470
$49$	−4.76584	−0.680834
$50$	−16.7825	−2.37340
$51$	−0.0226147	−0.00316669
$52$	2.37121	0.328827
$53$	10.5672	1.45152	0.725758	−	0.687950i	$-0.241489\pi$
$53$	10.5672	1.45152	0.725758	+	0.687950i	$0.241489\pi$
$54$	14.0516	1.91218
$55$	−6.36775	−0.858627
$56$	−8.88234	−1.18695
$57$	−6.09414	−0.807188
$58$	−2.52129	−0.331062
$59$	−4.70526	−0.612573	−0.306286	−	0.951939i	$-0.599086\pi$
$59$	−4.70526	−0.612573	−0.306286	+	0.951939i	$0.599086\pi$
$60$	23.0924	2.98122
$61$	1.64871	0.211096	0.105548	−	0.994414i	$-0.466340\pi$
$61$	1.64871	0.211096	0.105548	+	0.994414i	$0.466340\pi$
$62$	−20.6110	−2.61760
$63$	−0.881869	−0.111105
$64$	−2.65221	−0.331527
$65$	1.85810	0.230469
$66$	7.30027	0.898601
$67$	9.43187	1.15229	0.576143	−	0.817349i	$-0.304557\pi$
$67$	9.43187	1.15229	0.576143	+	0.817349i	$0.304557\pi$
$68$	−0.0634691	−0.00769676
$69$	−9.22058	−1.11003
$70$	−12.8665	−1.53784
$71$	14.2890	1.69579	0.847895	−	0.530165i	$-0.177870\pi$
$71$	14.2890	1.69579	0.847895	+	0.530165i	$0.177870\pi$
$72$	3.50604	0.413190
$73$	7.04779	0.824881	0.412441	−	0.910984i	$-0.364676\pi$
$73$	7.04779	0.824881	0.412441	+	0.910984i	$0.364676\pi$
$74$	−1.32195	−0.153674
$75$	10.3334	1.19319
$76$	−17.1034	−1.96190
$77$	−2.78781	−0.317701
$78$	−2.13021	−0.241198
$79$	8.63641	0.971673	0.485836	−	0.874050i	$-0.338515\pi$
$79$	8.63641	0.971673	0.485836	+	0.874050i	$0.338515\pi$
$80$	21.4031	2.39294
$81$	−6.88193	−0.764659
$82$	−19.1357	−2.11318
$83$	−15.9731	−1.75328	−0.876638	−	0.481151i	$-0.840219\pi$
$83$	−15.9731	−1.75328	−0.876638	+	0.481151i	$0.840219\pi$
$84$	10.1099	1.10308
$85$	−0.0497350	−0.00539452
$86$	−22.9195	−2.47148
$87$	1.55242	0.166437
$88$	11.0835	1.18150
$89$	−1.62323	−0.172062	−0.0860309	−	0.996292i	$-0.527418\pi$
$89$	−1.62323	−0.172062	−0.0860309	+	0.996292i	$0.527418\pi$
$90$	5.07867	0.535339
$91$	0.813479	0.0852758
$92$	−25.8779	−2.69796
$93$	12.6907	1.31596
$94$	7.29839	0.752772
$95$	−13.4024	−1.37506
$96$	−6.08687	−0.621238
$97$	−1.64653	−0.167179	−0.0835896	−	0.996500i	$-0.526638\pi$
$97$	−1.64653	−0.167179	−0.0835896	+	0.996500i	$0.526638\pi$
$98$	12.0161	1.21381
$99$	1.10040	0.110595
$100$	29.0010	2.90010
$101$	4.64309	0.462005	0.231003	−	0.972953i	$-0.425799\pi$
$101$	4.64309	0.462005	0.231003	+	0.972953i	$0.425799\pi$
$102$	0.0570184	0.00564566
$103$	7.83848	0.772349	0.386174	−	0.922426i	$-0.373796\pi$
$103$	7.83848	0.772349	0.386174	+	0.922426i	$0.373796\pi$
$104$	−3.23414	−0.317134
$105$	7.92222	0.773129
$106$	−26.6430	−2.58780
$107$	−2.55927	−0.247414	−0.123707	−	0.992319i	$-0.539478\pi$
$107$	−2.55927	−0.247414	−0.123707	+	0.992319i	$0.539478\pi$
$108$	−24.2819	−2.33653
$109$	−7.64532	−0.732289	−0.366144	−	0.930558i	$-0.619322\pi$
$109$	−7.64532	−0.732289	−0.366144	+	0.930558i	$0.619322\pi$
$110$	16.0550	1.53078
$111$	0.813955	0.0772572
$112$	9.37030	0.885410
$113$	14.3063	1.34582	0.672911	−	0.739723i	$-0.265044\pi$
$113$	14.3063	1.34582	0.672911	+	0.739723i	$0.265044\pi$
$114$	15.3651	1.43907
$115$	−20.2782	−1.89095
$116$	4.35693	0.404531
$117$	−0.321096	−0.0296854
$118$	11.8633	1.09211
$119$	−0.0217741	−0.00199603
$120$	−31.4963	−2.87520
$121$	−7.52134	−0.683758
$122$	−4.15689	−0.376347
$123$	11.7823	1.06237
$124$	35.6169	3.19849
$125$	5.65478	0.505779
$126$	2.22345	0.198081
$127$	9.03825	0.802015	0.401008	−	0.916075i	$-0.368660\pi$
$127$	9.03825	0.802015	0.401008	+	0.916075i	$0.368660\pi$
$128$	14.5288	1.28418
$129$	14.1121	1.24250
$130$	−4.68482	−0.410886
$131$	6.10633	0.533512	0.266756	−	0.963764i	$-0.414048\pi$
$131$	6.10633	0.533512	0.266756	+	0.963764i	$0.414048\pi$
$132$	−12.6152	−1.09802
$133$	−5.86760	−0.508785
$134$	−23.7805	−2.05432
$135$	−19.0275	−1.63763
$136$	0.0865669	0.00742305
$137$	−14.6682	−1.25319	−0.626594	−	0.779346i	$-0.715552\pi$
$137$	−14.6682	−1.25319	−0.626594	+	0.779346i	$0.715552\pi$
$138$	23.2478	1.97898
$139$	10.3917	0.881415	0.440708	−	0.897651i	$-0.354728\pi$
$139$	10.3917	0.881415	0.440708	+	0.897651i	$0.354728\pi$
$140$	22.2340	1.87912
$141$	−4.49379	−0.378445
$142$	−36.0267	−3.02330
$143$	−1.01507	−0.0848842
$144$	−3.69864	−0.308220
$145$	3.41413	0.283528
$146$	−17.7696	−1.47062
$147$	−7.39858	−0.610224
$148$	2.28440	0.187776
$149$	5.68649	0.465856	0.232928	−	0.972494i	$-0.425169\pi$
$149$	5.68649	0.465856	0.232928	+	0.972494i	$0.425169\pi$
$150$	−26.0534	−2.12725
$151$	−0.818627	−0.0666190	−0.0333095	−	0.999445i	$-0.510605\pi$
$151$	−0.818627	−0.0666190	−0.0333095	+	0.999445i	$0.510605\pi$
$152$	23.3278	1.89213
$153$	0.00859465	0.000694837 0
$154$	7.02890	0.566405
$155$	27.9098	2.24177
$156$	3.68111	0.294724
$157$	−10.7991	−0.861858	−0.430929	−	0.902386i	$-0.641814\pi$
$157$	−10.7991	−0.861858	−0.430929	+	0.902386i	$0.641814\pi$
$158$	−21.7749	−1.73232
$159$	16.4047	1.30098
$160$	−13.3864	−1.05829
$161$	−8.87782	−0.699670
$162$	17.3514	1.36325
$163$	24.1043	1.88799	0.943996	−	0.329958i	$-0.107034\pi$
$163$	24.1043	1.88799	0.943996	+	0.329958i	$0.107034\pi$
$164$	33.0675	2.58214
$165$	−9.88542	−0.769579
$166$	40.2729	3.12578
$167$	−9.79545	−0.757994	−0.378997	−	0.925398i	$-0.623731\pi$
$167$	−9.79545	−0.757994	−0.378997	+	0.925398i	$0.623731\pi$
$168$	−13.7891	−1.06385
$169$	−12.7038	−0.977216
$170$	0.125397	0.00961748
$171$	2.31606	0.177113
$172$	39.6061	3.01994
$173$	−2.80754	−0.213453	−0.106727	−	0.994288i	$-0.534037\pi$
$173$	−2.80754	−0.213453	−0.106727	+	0.994288i	$0.534037\pi$
$174$	−3.91411	−0.296728
$175$	9.94923	0.752091
$176$	−11.6923	−0.881344
$177$	−7.30454	−0.549043
$178$	4.09264	0.306756
$179$	8.57783	0.641137	0.320569	−	0.947225i	$-0.396126\pi$
$179$	8.57783	0.641137	0.320569	+	0.947225i	$0.396126\pi$
$180$	−8.77621	−0.654140
$181$	2.39161	0.177767	0.0888835	−	0.996042i	$-0.471670\pi$
$181$	2.39161	0.177767	0.0888835	+	0.996042i	$0.471670\pi$
$182$	−2.05102	−0.152032
$183$	2.55949	0.189203
$184$	35.2955	2.60202
$185$	1.79008	0.131609
$186$	−31.9970	−2.34613
$187$	0.0271699	0.00198686
$188$	−12.6120	−0.919825
$189$	−8.33029	−0.605940
$190$	33.7914	2.45149
$191$	5.15987	0.373355	0.186677	−	0.982421i	$-0.440228\pi$
$191$	5.15987	0.373355	0.186677	+	0.982421i	$0.440228\pi$
$192$	−4.11735	−0.297144
$193$	4.27444	0.307681	0.153840	−	0.988096i	$-0.450836\pi$
$193$	4.27444	0.307681	0.153840	+	0.988096i	$0.450836\pi$
$194$	4.15138	0.298051
$195$	2.88455	0.206567
$196$	−20.7644	−1.48317
$197$	18.0050	1.28280	0.641402	−	0.767205i	$-0.278353\pi$
$197$	18.0050	1.28280	0.641402	+	0.767205i	$0.278353\pi$
$198$	−2.77444	−0.197171
$199$	−2.62312	−0.185948	−0.0929741	−	0.995669i	$-0.529637\pi$
$199$	−2.62312	−0.185948	−0.0929741	+	0.995669i	$0.529637\pi$
$200$	−39.5551	−2.79696
$201$	14.6422	1.03278
$202$	−11.7066	−0.823674
$203$	1.49471	0.104908
$204$	−0.0985307	−0.00689853
$205$	25.9120	1.80977
$206$	−19.7631	−1.37696
$207$	3.50425	0.243562
$208$	3.41181	0.236566
$209$	7.32165	0.506449
$210$	−19.9743	−1.37835
$211$	20.3589	1.40157	0.700783	−	0.713375i	$-0.252834\pi$
$211$	20.3589	1.40157	0.700783	+	0.713375i	$0.252834\pi$
$212$	46.0405	3.16208
$213$	22.1825	1.51992
$214$	6.45266	0.441095
$215$	31.0357	2.11662
$216$	33.1187	2.25344
$217$	12.2189	0.829476
$218$	19.2761	1.30554
$219$	10.9411	0.739333
$220$	−27.7438	−1.87049
$221$	−0.00792813	−0.000533304 0
$222$	−2.05222	−0.137736
$223$	9.96841	0.667534	0.333767	−	0.942656i	$-0.391680\pi$
$223$	9.96841	0.667534	0.333767	+	0.942656i	$0.391680\pi$
$224$	−5.86060	−0.391578
$225$	−3.92716	−0.261811
$226$	−36.0704	−2.39937
$227$	7.12150	0.472671	0.236335	−	0.971672i	$-0.424054\pi$
$227$	7.12150	0.472671	0.236335	+	0.971672i	$0.424054\pi$
$228$	−26.5517	−1.75843
$229$	19.9114	1.31578	0.657892	−	0.753113i	$-0.271449\pi$
$229$	19.9114	1.31578	0.657892	+	0.753113i	$0.271449\pi$
$230$	51.1273	3.37123
$231$	−4.32785	−0.284752
$232$	−5.94251	−0.390145
$233$	26.0271	1.70509	0.852547	−	0.522651i	$-0.175057\pi$
$233$	26.0271	1.70509	0.852547	+	0.522651i	$0.175057\pi$
$234$	0.809578	0.0529238
$235$	−9.88288	−0.644688
$236$	−20.5005	−1.33447
$237$	13.4073	0.870900
$238$	0.0548988	0.00355856
$239$	5.86706	0.379509	0.189754	−	0.981832i	$-0.439231\pi$
$239$	5.86706	0.379509	0.189754	+	0.981832i	$0.439231\pi$
$240$	33.2265	2.14476
$241$	21.3948	1.37816	0.689081	−	0.724685i	$-0.258015\pi$
$241$	21.3948	1.37816	0.689081	+	0.724685i	$0.258015\pi$
$242$	18.9635	1.21902
$243$	6.03588	0.387202
$244$	7.18332	0.459865
$245$	−16.2712	−1.03953
$246$	−29.7066	−1.89403
$247$	−2.13645	−0.135939
$248$	−48.5787	−3.08475
$249$	−24.7970	−1.57144
$250$	−14.2574	−0.901715
$251$	16.7039	1.05434	0.527171	−	0.849759i	$-0.323253\pi$
$251$	16.7039	1.05434	0.527171	+	0.849759i	$0.323253\pi$
$252$	−3.84224	−0.242038
$253$	11.0778	0.696457
$254$	−22.7881	−1.42985
$255$	−0.0772096	−0.00483505
$256$	−31.3269	−1.95793
$257$	−11.2533	−0.701964	−0.350982	−	0.936382i	$-0.614152\pi$
$257$	−11.2533	−0.701964	−0.350982	+	0.936382i	$0.614152\pi$
$258$	−35.5807	−2.21516
$259$	0.783698	0.0486966
$260$	8.09561	0.502068
$261$	−0.589992	−0.0365196
$262$	−15.3958	−0.951159
$263$	−3.80706	−0.234753	−0.117377	−	0.993087i	$-0.537448\pi$
$263$	−3.80706	−0.234753	−0.117377	+	0.993087i	$0.537448\pi$
$264$	17.2062	1.05897
$265$	36.0778	2.21624
$266$	14.7939	0.907075
$267$	−2.51993	−0.154217
$268$	41.0940	2.51021
$269$	−15.4831	−0.944021	−0.472011	−	0.881593i	$-0.656472\pi$
$269$	−15.4831	−0.944021	−0.472011	+	0.881593i	$0.656472\pi$
$270$	47.9741	2.91961
$271$	21.8392	1.32664	0.663320	−	0.748336i	$-0.269147\pi$
$271$	21.8392	1.32664	0.663320	+	0.748336i	$0.269147\pi$
$272$	−0.0913225	−0.00553724
$273$	1.26286	0.0764318
$274$	36.9828	2.23422
$275$	−12.4148	−0.748638
$276$	−40.1734	−2.41815
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−26.2006	−1.57141
$279$	−4.82306	−0.288749
$280$	−30.3255	−1.81229
$281$	14.1734	0.845514	0.422757	−	0.906243i	$-0.361062\pi$
$281$	14.1734	0.845514	0.422757	+	0.906243i	$0.361062\pi$
$282$	11.3302	0.674702
$283$	−19.6676	−1.16912	−0.584558	−	0.811352i	$-0.698732\pi$
$283$	−19.6676	−1.16912	−0.584558	+	0.811352i	$0.698732\pi$
$284$	62.2560	3.69422
$285$	−20.8062	−1.23245
$286$	2.55928	0.151334
$287$	11.3443	0.669633
$288$	2.31329	0.136312
$289$	−16.9998	−0.999988
$290$	−8.60803	−0.505481
$291$	−2.55610	−0.149841
$292$	30.7067	1.79697
$293$	−23.8174	−1.39143	−0.695713	−	0.718320i	$-0.744911\pi$
$293$	−23.8174	−1.39143	−0.695713	+	0.718320i	$0.744911\pi$
$294$	18.6540	1.08792
$295$	−16.0644	−0.935304
$296$	−3.11574	−0.181099
$297$	10.3946	0.603157
$298$	−14.3373	−0.830539
$299$	−3.23249	−0.186940
$300$	45.0217	2.59933
$301$	13.5875	0.783170
$302$	2.06400	0.118770
$303$	7.20803	0.414091
$304$	−24.6093	−1.41144
$305$	5.62892	0.322311
$306$	−0.0216697	−0.00123877
$307$	−0.191706	−0.0109412	−0.00547062	−	0.999985i	$-0.501741\pi$
$307$	−0.191706	−0.0109412	−0.00547062	+	0.999985i	$0.501741\pi$
$308$	−12.1463	−0.692099
$309$	12.1686	0.692248
$310$	−70.3688	−3.99668
$311$	−10.8247	−0.613811	−0.306906	−	0.951740i	$-0.599294\pi$
$311$	−10.8247	−0.613811	−0.306906	+	0.951740i	$0.599294\pi$
$312$	−5.02074	−0.284244
$313$	−14.5707	−0.823587	−0.411794	−	0.911277i	$-0.635098\pi$
$313$	−14.5707	−0.823587	−0.411794	+	0.911277i	$0.635098\pi$
$314$	27.2276	1.53654
$315$	−3.01082	−0.169640
$316$	37.6282	2.11675
$317$	12.9942	0.729828	0.364914	−	0.931041i	$-0.381098\pi$
$317$	12.9942	0.729828	0.364914	+	0.931041i	$0.381098\pi$
$318$	−41.3612	−2.31942
$319$	−1.86512	−0.104426
$320$	−9.05500	−0.506190
$321$	−3.97306	−0.221754
$322$	22.3836	1.24739
$323$	0.0571854	0.00318188
$324$	−29.9841	−1.66578
$325$	3.62260	0.200946
$326$	−60.7739	−3.36596
$327$	−11.8687	−0.656343
$328$	−45.1014	−2.49031
$329$	−4.32674	−0.238541
$330$	24.9241	1.37202
$331$	25.8615	1.42148	0.710738	−	0.703456i	$-0.248361\pi$
$331$	25.8615	1.42148	0.710738	+	0.703456i	$0.248361\pi$
$332$	−69.5937	−3.81945
$333$	−0.309341	−0.0169518
$334$	24.6972	1.35137
$335$	32.2016	1.75936
$336$	14.5466	0.793584
$337$	22.9898	1.25234	0.626168	−	0.779688i	$-0.284622\pi$
$337$	22.9898	1.25234	0.626168	+	0.779688i	$0.284622\pi$
$338$	32.0300	1.74220
$339$	22.2094	1.20625
$340$	−0.216692	−0.0117518
$341$	−15.2469	−0.825667
$342$	−5.83946	−0.315762
$343$	−17.5865	−0.949584
$344$	−54.0197	−2.91254
$345$	−31.4803	−1.69484
$346$	7.07864	0.380550
$347$	−29.5654	−1.58716	−0.793578	−	0.608469i	$-0.791784\pi$
$347$	−29.5654	−1.58716	−0.793578	+	0.608469i	$0.791784\pi$
$348$	6.76378	0.362577
$349$	−10.0249	−0.536621	−0.268310	−	0.963333i	$-0.586465\pi$
$349$	−10.0249	−0.536621	−0.268310	+	0.963333i	$0.586465\pi$
$350$	−25.0850	−1.34085
$351$	−3.03313	−0.161897
$352$	7.31291	0.389780
$353$	−22.3851	−1.19144	−0.595721	−	0.803192i	$-0.703133\pi$
$353$	−22.3851	−1.19144	−0.595721	+	0.803192i	$0.703133\pi$
$354$	18.4169	0.978847
$355$	48.7844	2.58921
$356$	−7.07229	−0.374830
$357$	−0.0338025	−0.00178902
$358$	−21.6272	−1.14304
$359$	26.8645	1.41786	0.708928	−	0.705281i	$-0.249179\pi$
$359$	26.8645	1.41786	0.708928	+	0.705281i	$0.249179\pi$
$360$	11.9701	0.630878
$361$	−3.58988	−0.188941
$362$	−6.02995	−0.316927
$363$	−11.6763	−0.612846
$364$	3.54427	0.185770
$365$	24.0621	1.25947
$366$	−6.45324	−0.337316
$367$	0.968552	0.0505580	0.0252790	−	0.999680i	$-0.491953\pi$
$367$	0.968552	0.0505580	0.0252790	+	0.999680i	$0.491953\pi$
$368$	−37.2344	−1.94098
$369$	−4.47782	−0.233106
$370$	−4.51331	−0.234636
$371$	15.7949	0.820031
$372$	55.2924	2.86678
$373$	−1.34622	−0.0697046	−0.0348523	−	0.999392i	$-0.511096\pi$
$373$	−1.34622	−0.0697046	−0.0348523	+	0.999392i	$0.511096\pi$
$374$	−0.0685033	−0.00354222
$375$	8.77860	0.453325
$376$	17.2018	0.887114
$377$	0.544238	0.0280297
$378$	21.0031	1.08028
$379$	−30.2893	−1.55586	−0.777928	−	0.628353i	$-0.783729\pi$
$379$	−30.2893	−1.55586	−0.777928	+	0.628353i	$0.783729\pi$
$380$	−58.3934	−2.99552
$381$	14.0312	0.718838
$382$	−13.0095	−0.665626
$383$	13.8106	0.705687	0.352843	−	0.935682i	$-0.385215\pi$
$383$	13.8106	0.705687	0.352843	+	0.935682i	$0.385215\pi$
$384$	22.5548	1.15099
$385$	−9.51795	−0.485080
$386$	−10.7771	−0.548541
$387$	−5.36325	−0.272630
$388$	−7.17379	−0.364194
$389$	−30.4192	−1.54231	−0.771157	−	0.636646i	$-0.780321\pi$
$389$	−30.4192	−1.54231	−0.771157	+	0.636646i	$0.780321\pi$
$390$	−7.27280	−0.368273
$391$	0.0865228	0.00437565
$392$	28.3210	1.43043
$393$	9.47958	0.478182
$394$	−45.3960	−2.28702
$395$	29.4858	1.48359
$396$	4.79438	0.240927
$397$	4.88520	0.245181	0.122591	−	0.992457i	$-0.460880\pi$
$397$	4.88520	0.245181	0.122591	+	0.992457i	$0.460880\pi$
$398$	6.61367	0.331513
$399$	−9.10898	−0.456019
$400$	41.7280	2.08640
$401$	−7.52133	−0.375597	−0.187799	−	0.982208i	$-0.560135\pi$
$401$	−7.52133	−0.375597	−0.187799	+	0.982208i	$0.560135\pi$
$402$	−36.9173	−1.84127
$403$	4.44903	0.221622
$404$	20.2296	1.00646
$405$	−23.4958	−1.16752
$406$	−3.76861	−0.187033
$407$	−0.977906	−0.0484730
$408$	0.134388	0.00665321
$409$	−4.80575	−0.237629	−0.118815	−	0.992916i	$-0.537909\pi$
$409$	−4.80575	−0.237629	−0.118815	+	0.992916i	$0.537909\pi$
$410$	−65.3317	−3.22651
$411$	−22.7712	−1.12322
$412$	34.1517	1.68253
$413$	−7.03301	−0.346072
$414$	−8.83525	−0.434229
$415$	−54.5343	−2.67698
$416$	−2.13390	−0.104623
$417$	16.1323	0.790004
$418$	−18.4600	−0.902910
$419$	−9.67916	−0.472858	−0.236429	−	0.971649i	$-0.575977\pi$
$419$	−9.67916	−0.472858	−0.236429	+	0.971649i	$0.575977\pi$
$420$	34.5165	1.68423
$421$	−5.99875	−0.292361	−0.146181	−	0.989258i	$-0.546698\pi$
$421$	−5.99875	−0.292361	−0.146181	+	0.989258i	$0.546698\pi$
$422$	−51.3308	−2.49875
$423$	1.70785	0.0830386
$424$	−62.7957	−3.04963
$425$	−0.0969648	−0.00470348
$426$	−55.9286	−2.70975
$427$	2.46435	0.119258
$428$	−11.1505	−0.538982
$429$	−1.57581	−0.0760809
$430$	−78.2502	−3.77356
$431$	3.83281	0.184620	0.0923099	−	0.995730i	$-0.470575\pi$
$431$	3.83281	0.184620	0.0923099	+	0.995730i	$0.470575\pi$
$432$	−34.9380	−1.68096
$433$	−4.49832	−0.216175	−0.108088	−	0.994141i	$-0.534473\pi$
$433$	−4.49832	−0.216175	−0.108088	+	0.994141i	$0.534473\pi$
$434$	−30.8076	−1.47881
$435$	5.30016	0.254123
$436$	−33.3101	−1.59526
$437$	23.3159	1.11535
$438$	−27.5858	−1.31810
$439$	39.5778	1.88895	0.944473	−	0.328590i	$-0.106573\pi$
$439$	39.5778	1.88895	0.944473	+	0.328590i	$0.106573\pi$
$440$	37.8404	1.80397
$441$	2.81181	0.133896
$442$	0.0199892	0.000950787 0
$443$	−11.1352	−0.529048	−0.264524	−	0.964379i	$-0.585215\pi$
$443$	−11.1352	−0.529048	−0.264524	+	0.964379i	$0.585215\pi$
$444$	3.54634	0.168302
$445$	−5.54191	−0.262712
$446$	−25.1333	−1.19010
$447$	8.82783	0.417542
$448$	−3.96430	−0.187295
$449$	−28.2095	−1.33129	−0.665645	−	0.746269i	$-0.731843\pi$
$449$	−28.2095	−1.33129	−0.665645	+	0.746269i	$0.731843\pi$
$450$	9.90153	0.466762
$451$	−14.1555	−0.666558
$452$	62.3315	2.93183
$453$	−1.27085	−0.0597099
$454$	−17.9554	−0.842689
$455$	2.77732	0.130203
$456$	36.2145	1.69590
$457$	26.2905	1.22982	0.614908	−	0.788599i	$-0.289193\pi$
$457$	26.2905	1.22982	0.614908	+	0.788599i	$0.289193\pi$
$458$	−50.2025	−2.34581
$459$	0.0811867	0.00378947
$460$	−88.3506	−4.11937
$461$	−25.3513	−1.18073	−0.590364	−	0.807137i	$-0.701016\pi$
$461$	−25.3513	−1.18073	−0.590364	+	0.807137i	$0.701016\pi$
$462$	10.9118	0.507663
$463$	28.1422	1.30788	0.653940	−	0.756546i	$-0.273115\pi$
$463$	28.1422	1.30788	0.653940	+	0.756546i	$0.273115\pi$
$464$	6.26896	0.291029
$465$	43.3277	2.00927
$466$	−65.6220	−3.03988
$467$	27.3713	1.26659	0.633296	−	0.773909i	$-0.281701\pi$
$467$	27.3713	1.26659	0.633296	+	0.773909i	$0.281701\pi$
$468$	−1.39899	−0.0646685
$469$	14.0979	0.650982
$470$	24.9177	1.14937
$471$	−16.7647	−0.772475
$472$	27.9611	1.28701
$473$	−16.9546	−0.779574
$474$	−33.8039	−1.55266
$475$	−26.1297	−1.19891
$476$	−0.0948680	−0.00434827
$477$	−6.23457	−0.285461
$478$	−14.7926	−0.676597
$479$	−7.73881	−0.353595	−0.176798	−	0.984247i	$-0.556574\pi$
$479$	−7.73881	−0.353595	−0.176798	+	0.984247i	$0.556574\pi$
$480$	−20.7814	−0.948535
$481$	0.285351	0.0130109
$482$	−53.9426	−2.45702
$483$	−13.7821	−0.627108
$484$	−32.7699	−1.48954
$485$	−5.62145	−0.255257
$486$	−15.2182	−0.690313
$487$	−16.5111	−0.748188	−0.374094	−	0.927391i	$-0.622046\pi$
$487$	−16.5111	−0.748188	−0.374094	+	0.927391i	$0.622046\pi$
$488$	−9.79749	−0.443511
$489$	37.4199	1.69219
$490$	41.0245	1.85330
$491$	−9.26388	−0.418073	−0.209037	−	0.977908i	$-0.567033\pi$
$491$	−9.26388	−0.418073	−0.209037	+	0.977908i	$0.567033\pi$
$492$	51.3346	2.31434
$493$	−0.0145674	−0.000656083 0
$494$	5.38661	0.242355
$495$	3.75693	0.168861
$496$	51.2474	2.30108
$497$	21.3579	0.958033
$498$	62.5205	2.80161
$499$	32.3569	1.44850	0.724248	−	0.689540i	$-0.242187\pi$
$499$	32.3569	1.44850	0.724248	+	0.689540i	$0.242187\pi$
$500$	24.6375	1.10182
$501$	−15.2066	−0.679383
$502$	−42.1155	−1.87971
$503$	−30.5105	−1.36040	−0.680198	−	0.733029i	$-0.738106\pi$
$503$	−30.5105	−1.36040	−0.680198	+	0.733029i	$0.738106\pi$
$504$	5.24051	0.233431
$505$	15.8521	0.705411
$506$	−27.9305	−1.24166
$507$	−19.7216	−0.875869
$508$	39.3790	1.74716
$509$	−5.52387	−0.244841	−0.122421	−	0.992478i	$-0.539066\pi$
$509$	−5.52387	−0.244841	−0.122421	+	0.992478i	$0.539066\pi$
$510$	0.194668	0.00862005
$511$	10.5344	0.466015
$512$	49.9269	2.20648
$513$	21.8779	0.965933
$514$	28.3730	1.25148
$515$	26.7616	1.17926
$516$	61.4853	2.70674
$517$	5.39895	0.237446
$518$	−1.97593	−0.0868176
$519$	−4.35848	−0.191316
$520$	−11.0418	−0.484214
$521$	−37.9686	−1.66343	−0.831716	−	0.555201i	$-0.812641\pi$
$521$	−37.9686	−1.66343	−0.831716	+	0.555201i	$0.812641\pi$
$522$	1.48754	0.0651081
$523$	−42.8957	−1.87570	−0.937849	−	0.347044i	$-0.887185\pi$
$523$	−42.8957	−1.87570	−0.937849	+	0.347044i	$0.887185\pi$
$524$	26.6048	1.16224
$525$	15.4454	0.674092
$526$	9.59872	0.418524
$527$	−0.119085	−0.00518744
$528$	−18.1514	−0.789940
$529$	12.2775	0.533804
$530$	−90.9628	−3.95117
$531$	2.77607	0.120471
$532$	−25.5647	−1.10837
$533$	4.13056	0.178915
$534$	6.35349	0.274942
$535$	−8.73767	−0.377762
$536$	−56.0490	−2.42095
$537$	13.3164	0.574645
$538$	39.0375	1.68302
$539$	8.88884	0.382869
$540$	−82.9017	−3.56752
$541$	7.65927	0.329298	0.164649	−	0.986352i	$-0.447351\pi$
$541$	7.65927	0.329298	0.164649	+	0.986352i	$0.447351\pi$
$542$	−55.0632	−2.36517
$543$	3.71278	0.159331
$544$	0.0571171	0.00244888
$545$	−26.1021	−1.11809
$546$	−3.18405	−0.136265
$547$	−7.55983	−0.323235	−0.161617	−	0.986853i	$-0.551671\pi$
$547$	−7.55983	−0.323235	−0.161617	+	0.986853i	$0.551671\pi$
$548$	−63.9083	−2.73003
$549$	−0.972728	−0.0415150
$550$	31.3012	1.33469
$551$	−3.92557	−0.167235
$552$	54.7934	2.33216
$553$	12.9090	0.548944
$554$	2.52129	0.107120
$555$	2.77895	0.117960
$556$	45.2760	1.92013
$557$	−20.2820	−0.859378	−0.429689	−	0.902977i	$-0.641377\pi$
$557$	−20.2820	−0.859378	−0.429689	+	0.902977i	$0.641377\pi$
$558$	12.1604	0.514789
$559$	4.94733	0.209250
$560$	31.9914	1.35188
$561$	0.0421791	0.00178080
$562$	−35.7353	−1.50740
$563$	31.4988	1.32752	0.663758	−	0.747947i	$-0.268960\pi$
$563$	31.4988	1.32752	0.663758	+	0.747947i	$0.268960\pi$
$564$	−19.5791	−0.824430
$565$	48.8435	2.05486
$566$	49.5877	2.08433
$567$	−10.2865	−0.431993
$568$	−84.9124	−3.56284
$569$	−26.2542	−1.10063	−0.550317	−	0.834956i	$-0.685493\pi$
$569$	−26.2542	−1.10063	−0.550317	+	0.834956i	$0.685493\pi$
$570$	52.4585	2.19725
$571$	−9.29087	−0.388811	−0.194405	−	0.980921i	$-0.562278\pi$
$571$	−9.29087	−0.388811	−0.194405	+	0.980921i	$0.562278\pi$
$572$	−4.42257	−0.184917
$573$	8.01028	0.334634
$574$	−28.6023	−1.19384
$575$	−39.5349	−1.64872
$576$	1.56479	0.0651994
$577$	14.1310	0.588280	0.294140	−	0.955762i	$-0.404967\pi$
$577$	14.1310	0.588280	0.294140	+	0.955762i	$0.404967\pi$
$578$	42.8615	1.78280
$579$	6.63572	0.275771
$580$	14.8751	0.617656
$581$	−23.8752	−0.990510
$582$	6.44468	0.267140
$583$	−19.7091	−0.816266
$584$	−41.8816	−1.73307
$585$	−1.09626	−0.0453250
$586$	60.0506	2.48067
$587$	7.94427	0.327895	0.163948	−	0.986469i	$-0.447577\pi$
$587$	7.94427	0.327895	0.163948	+	0.986469i	$0.447577\pi$
$588$	−32.2351	−1.32935
$589$	−32.0907	−1.32227
$590$	40.5030	1.66748
$591$	27.9513	1.14976
$592$	3.28690	0.135091
$593$	−20.9454	−0.860126	−0.430063	−	0.902799i	$-0.641509\pi$
$593$	−20.9454	−0.860126	−0.430063	+	0.902799i	$0.641509\pi$
$594$	−26.2079	−1.07532
$595$	−0.0743395	−0.00304762
$596$	24.7756	1.01485
$597$	−4.07219	−0.166664
$598$	8.15007	0.333281
$599$	−23.8245	−0.973441	−0.486720	−	0.873558i	$-0.661807\pi$
$599$	−23.8245	−0.973441	−0.486720	+	0.873558i	$0.661807\pi$
$600$	−61.4061	−2.50689
$601$	−32.8274	−1.33906	−0.669529	−	0.742786i	$-0.733504\pi$
$601$	−32.8274	−1.33906	−0.669529	+	0.742786i	$0.733504\pi$
$602$	−34.2581	−1.39626
$603$	−5.56473	−0.226613
$604$	−3.56670	−0.145127
$605$	−25.6788	−1.04399
$606$	−18.1736	−0.738251
$607$	37.3629	1.51651	0.758256	−	0.651957i	$-0.226052\pi$
$607$	37.3629	1.51651	0.758256	+	0.651957i	$0.226052\pi$
$608$	15.3917	0.624217
$609$	2.32042	0.0940282
$610$	−14.1922	−0.574624
$611$	−1.57541	−0.0637341
$612$	0.0374463	0.00151368
$613$	−21.1311	−0.853477	−0.426738	−	0.904375i	$-0.640338\pi$
$613$	−21.1311	−0.853477	−0.426738	+	0.904375i	$0.640338\pi$
$614$	0.483347	0.0195063
$615$	40.2263	1.62208
$616$	16.5666	0.667487
$617$	−15.5675	−0.626724	−0.313362	−	0.949634i	$-0.601455\pi$
$617$	−15.5675	−0.626724	−0.313362	+	0.949634i	$0.601455\pi$
$618$	−30.6807	−1.23416
$619$	25.3024	1.01699	0.508495	−	0.861065i	$-0.330202\pi$
$619$	25.3024	1.01699	0.508495	+	0.861065i	$0.330202\pi$
$620$	121.601	4.88361
$621$	33.1018	1.32833
$622$	27.2922	1.09432
$623$	−2.42626	−0.0972060
$624$	5.29656	0.212032
$625$	−13.9753	−0.559011
$626$	36.7372	1.46831
$627$	11.3663	0.453925
$628$	−47.0507	−1.87753
$629$	−0.00763789	−0.000304542 0
$630$	7.59115	0.302439
$631$	−2.49869	−0.0994714	−0.0497357	−	0.998762i	$-0.515838\pi$
$631$	−2.49869	−0.0994714	−0.0497357	+	0.998762i	$0.515838\pi$
$632$	−51.3220	−2.04148
$633$	31.6056	1.25621
$634$	−32.7622	−1.30115
$635$	30.8578	1.22455
$636$	71.4742	2.83414
$637$	−2.59375	−0.102768
$638$	4.70251	0.186174
$639$	−8.43039	−0.333501
$640$	49.6032	1.96074
$641$	23.1054	0.912610	0.456305	−	0.889824i	$-0.349173\pi$
$641$	23.1054	0.912610	0.456305	+	0.889824i	$0.349173\pi$
$642$	10.0172	0.395349
$643$	−23.0036	−0.907174	−0.453587	−	0.891212i	$-0.649856\pi$
$643$	−23.0036	−0.907174	−0.453587	+	0.891212i	$0.649856\pi$
$644$	−38.6800	−1.52421
$645$	48.1805	1.89711
$646$	−0.144181	−0.00567273
$647$	−12.5267	−0.492475	−0.246238	−	0.969209i	$-0.579194\pi$
$647$	−12.5267	−0.492475	−0.246238	+	0.969209i	$0.579194\pi$
$648$	40.8959	1.60654
$649$	8.77586	0.344483
$650$	−9.13365	−0.358251
$651$	18.9689	0.743451
$652$	105.021	4.11292
$653$	−36.7467	−1.43801	−0.719005	−	0.695005i	$-0.755402\pi$
$653$	−36.7467	−1.43801	−0.719005	+	0.695005i	$0.755402\pi$
$654$	29.9246	1.17014
$655$	20.8478	0.814591
$656$	47.5791	1.85765
$657$	−4.15814	−0.162225
$658$	10.9090	0.425277
$659$	45.8400	1.78567	0.892836	−	0.450381i	$-0.148712\pi$
$659$	45.8400	1.78567	0.892836	+	0.450381i	$0.148712\pi$
$660$	−43.0701	−1.67650
$661$	29.3464	1.14144	0.570721	−	0.821144i	$-0.306664\pi$
$661$	29.3464	1.14144	0.570721	+	0.821144i	$0.306664\pi$
$662$	−65.2045	−2.53424
$663$	−0.0123078	−0.000477995 0
$664$	94.9203	3.68362
$665$	−20.0328	−0.776837
$666$	0.779940	0.0302221
$667$	−5.93949	−0.229978
$668$	−42.6781	−1.65126
$669$	15.4752	0.598304
$670$	−81.1898	−3.13664
$671$	−3.07504	−0.118711
$672$	−9.09811	−0.350967
$673$	40.4445	1.55902	0.779510	−	0.626390i	$-0.215468\pi$
$673$	40.4445	1.55902	0.779510	+	0.626390i	$0.215468\pi$
$674$	−57.9641	−2.23269
$675$	−37.0967	−1.42785
$676$	−55.3496	−2.12883
$677$	−5.91716	−0.227415	−0.113707	−	0.993514i	$-0.536273\pi$
$677$	−5.91716	−0.227415	−0.113707	+	0.993514i	$0.536273\pi$
$678$	−55.9964	−2.15053
$679$	−2.46108	−0.0944476
$680$	0.295551	0.0113339
$681$	11.0556	0.423650
$682$	38.4420	1.47202
$683$	26.2765	1.00544	0.502722	−	0.864448i	$-0.332332\pi$
$683$	26.2765	1.00544	0.502722	+	0.864448i	$0.332332\pi$
$684$	10.0909	0.385835
$685$	−50.0791	−1.91343
$686$	44.3408	1.69294
$687$	30.9109	1.17932
$688$	56.9873	2.17262
$689$	5.75107	0.219098
$690$	79.3710	3.02160
$691$	10.8380	0.412295	0.206148	−	0.978521i	$-0.433907\pi$
$691$	10.8380	0.412295	0.206148	+	0.978521i	$0.433907\pi$
$692$	−12.2322	−0.465000
$693$	1.64479	0.0624803
$694$	74.5432	2.82962
$695$	35.4787	1.34578
$696$	−9.22527	−0.349683
$697$	−0.110561	−0.00418780
$698$	25.2757	0.956701
$699$	40.4050	1.52826
$700$	43.3481	1.63840
$701$	−10.2371	−0.386650	−0.193325	−	0.981135i	$-0.561927\pi$
$701$	−10.2371	−0.386650	−0.193325	+	0.981135i	$0.561927\pi$
$702$	7.64743	0.288633
$703$	−2.05823	−0.0776277
$704$	4.94669	0.186435
$705$	−15.3424	−0.577828
$706$	56.4396	2.12413
$707$	6.94009	0.261009
$708$	−31.8253	−1.19607
$709$	−27.0004	−1.01402	−0.507011	−	0.861939i	$-0.669250\pi$
$709$	−27.0004	−1.01402	−0.507011	+	0.861939i	$0.669250\pi$
$710$	−123.000	−4.61610
$711$	−5.09542	−0.191093
$712$	9.64605	0.361501
$713$	−48.5540	−1.81836
$714$	0.0852260	0.00318950
$715$	−3.46557	−0.129605
$716$	37.3730	1.39669
$717$	9.10814	0.340150
$718$	−67.7334	−2.52779
$719$	−0.0338324	−0.00126173	−0.000630867	−	1.00000i	$-0.500201\pi$
$719$	−0.0338324	−0.00126173	−0.000630867		1.00000i	$0.500201\pi$
$720$	−12.6276	−0.470605
$721$	11.7163	0.436337
$722$	9.05116	0.336849
$723$	33.2137	1.23523
$724$	10.4201	0.387259
$725$	6.65629	0.247208
$726$	29.4393	1.09260
$727$	24.7622	0.918378	0.459189	−	0.888339i	$-0.348140\pi$
$727$	24.7622	0.918378	0.459189	+	0.888339i	$0.348140\pi$
$728$	−4.83411	−0.179164
$729$	30.0160	1.11170
$730$	−60.6676	−2.24541
$731$	−0.132423	−0.00489785
$732$	11.1515	0.412172
$733$	39.0895	1.44380	0.721901	−	0.691996i	$-0.243268\pi$
$733$	39.0895	1.44380	0.721901	+	0.691996i	$0.243268\pi$
$734$	−2.44200	−0.0901360
$735$	−25.2597	−0.931719
$736$	23.2881	0.858409
$737$	−17.5915	−0.647992
$738$	11.2899	0.415587
$739$	−17.1148	−0.629579	−0.314790	−	0.949161i	$-0.601934\pi$
$739$	−17.1148	−0.629579	−0.314790	+	0.949161i	$0.601934\pi$
$740$	7.79923	0.286705
$741$	−3.31666	−0.121841
$742$	−39.8236	−1.46197
$743$	11.3819	0.417561	0.208780	−	0.977963i	$-0.433051\pi$
$743$	11.3819	0.417561	0.208780	+	0.977963i	$0.433051\pi$
$744$	−75.4146	−2.76483
$745$	19.4144	0.711290
$746$	3.39422	0.124271
$747$	9.42401	0.344807
$748$	0.118377	0.00432830
$749$	−3.82537	−0.139776
$750$	−22.1334	−0.808198
$751$	−43.6027	−1.59108	−0.795542	−	0.605899i	$-0.792814\pi$
$751$	−43.6027	−1.59108	−0.795542	+	0.605899i	$0.792814\pi$
$752$	−18.1468	−0.661745
$753$	25.9315	0.944996
$754$	−1.37218	−0.0499720
$755$	−2.79490	−0.101717
$756$	−36.2945	−1.32002
$757$	−15.5994	−0.566970	−0.283485	−	0.958977i	$-0.591491\pi$
$757$	−15.5994	−0.566970	−0.283485	+	0.958977i	$0.591491\pi$
$758$	76.3683	2.77382
$759$	17.1974	0.624228
$760$	79.6440	2.88899
$761$	51.3491	1.86140	0.930701	−	0.365781i	$-0.119198\pi$
$761$	51.3491	1.86140	0.930701	+	0.365781i	$0.119198\pi$
$762$	−35.3767	−1.28156
$763$	−11.4275	−0.413705
$764$	22.4812	0.813340
$765$	0.0293433	0.00106091
$766$	−34.8205	−1.25812
$767$	−2.56078	−0.0924644
$768$	−48.6326	−1.75488
$769$	19.7920	0.713716	0.356858	−	0.934159i	$-0.383848\pi$
$769$	19.7920	0.713716	0.356858	+	0.934159i	$0.383848\pi$
$770$	23.9976	0.864812
$771$	−17.4699	−0.629163
$772$	18.6234	0.670271
$773$	1.52355	0.0547983	0.0273991	−	0.999625i	$-0.491277\pi$
$773$	1.52355	0.0547983	0.0273991	+	0.999625i	$0.491277\pi$
$774$	13.5223	0.486051
$775$	54.4137	1.95460
$776$	9.78449	0.351243
$777$	1.21663	0.0436463
$778$	76.6957	2.74967
$779$	−29.7936	−1.06747
$780$	12.5678	0.449999
$781$	−26.6506	−0.953634
$782$	−0.218150	−0.00780101
$783$	−5.57318	−0.199169
$784$	−29.8769	−1.06703
$785$	−36.8694	−1.31592
$786$	−23.9008	−0.852514
$787$	41.4540	1.47768	0.738838	−	0.673883i	$-0.235375\pi$
$787$	41.4540	1.47768	0.738838	+	0.673883i	$0.235375\pi$
$788$	78.4466	2.79454
$789$	−5.91015	−0.210407
$790$	−74.3425	−2.64499
$791$	21.3838	0.760320
$792$	−6.53917	−0.232359
$793$	0.897292	0.0318638
$794$	−12.3170	−0.437115
$795$	56.0079	1.98640
$796$	−11.4288	−0.405082
$797$	29.7138	1.05252	0.526259	−	0.850325i	$-0.323594\pi$
$797$	29.7138	1.05252	0.526259	+	0.850325i	$0.323594\pi$
$798$	22.9664	0.813003
$799$	0.0421682	0.00149181
$800$	−26.0986	−0.922724
$801$	0.957692	0.0338384
$802$	18.9635	0.669624
$803$	−13.1449	−0.463875
$804$	63.7951	2.24988
$805$	−30.3100	−1.06829
$806$	−11.2173	−0.395113
$807$	−24.0363	−0.846117
$808$	−27.5916	−0.970670
$809$	28.3218	0.995742	0.497871	−	0.867251i	$-0.334115\pi$
$809$	28.3218	0.995742	0.497871	+	0.867251i	$0.334115\pi$
$810$	59.2399	2.08148
$811$	−32.0453	−1.12526	−0.562632	−	0.826708i	$-0.690211\pi$
$811$	−32.0453	−1.12526	−0.562632	+	0.826708i	$0.690211\pi$
$812$	6.51235	0.228539
$813$	33.9037	1.18905
$814$	2.46559	0.0864189
$815$	82.2951	2.88267
$816$	−0.141771	−0.00496297
$817$	−35.6849	−1.24846
$818$	12.1167	0.423651
$819$	−0.479947	−0.0167707
$820$	112.897	3.94252
$821$	−21.1703	−0.738850	−0.369425	−	0.929261i	$-0.620445\pi$
$821$	−21.1703	−0.738850	−0.369425	+	0.929261i	$0.620445\pi$
$822$	57.4129	2.00250
$823$	12.8626	0.448362	0.224181	−	0.974548i	$-0.428029\pi$
$823$	12.8626	0.448362	0.224181	+	0.974548i	$0.428029\pi$
$824$	−46.5803	−1.62270
$825$	−19.2729	−0.670996
$826$	17.7323	0.616985
$827$	−33.8694	−1.17775	−0.588877	−	0.808223i	$-0.700430\pi$
$827$	−33.8694	−1.17775	−0.588877	+	0.808223i	$0.700430\pi$
$828$	15.2678	0.530592
$829$	25.0007	0.868310	0.434155	−	0.900838i	$-0.357047\pi$
$829$	25.0007	0.868310	0.434155	+	0.900838i	$0.357047\pi$
$830$	137.497	4.77259
$831$	−1.55242	−0.0538528
$832$	−1.44344	−0.0500421
$833$	0.0694258	0.00240546
$834$	−40.6744	−1.40844
$835$	−33.4429	−1.15734
$836$	31.8999	1.10328
$837$	−45.5595	−1.57477
$838$	24.4040	0.843023
$839$	−4.91197	−0.169580	−0.0847900	−	0.996399i	$-0.527022\pi$
$839$	−4.91197	−0.169580	−0.0847900	+	0.996399i	$0.527022\pi$
$840$	−47.0779	−1.62434
$841$	1.00000	0.0344828
$842$	15.1246	0.521229
$843$	22.0031	0.757825
$844$	88.7023	3.05326
$845$	−43.3724	−1.49206
$846$	−4.30600	−0.148043
$847$	−11.2422	−0.386288
$848$	66.2454	2.27488
$849$	−30.5323	−1.04787
$850$	0.244477	0.00838549
$851$	−3.11415	−0.106752
$852$	96.6475	3.31109
$853$	−21.5724	−0.738626	−0.369313	−	0.929305i	$-0.620407\pi$
$853$	−21.5724	−0.738626	−0.369313	+	0.929305i	$0.620407\pi$
$854$	−6.21335	−0.212617
$855$	7.90732	0.270425
$856$	15.2085	0.519815
$857$	−9.55164	−0.326278	−0.163139	−	0.986603i	$-0.552162\pi$
$857$	−9.55164	−0.326278	−0.163139	+	0.986603i	$0.552162\pi$
$858$	3.97308	0.135639
$859$	16.5376	0.564254	0.282127	−	0.959377i	$-0.408960\pi$
$859$	16.5376	0.564254	0.282127	+	0.959377i	$0.408960\pi$
$860$	135.220	4.61098
$861$	17.6111	0.600186
$862$	−9.66364	−0.329145
$863$	6.32209	0.215206	0.107603	−	0.994194i	$-0.465682\pi$
$863$	6.32209	0.215206	0.107603	+	0.994194i	$0.465682\pi$
$864$	21.8518	0.743413
$865$	−9.58531	−0.325910
$866$	11.3416	0.385403
$867$	−26.3908	−0.896279
$868$	53.2371	1.80698
$869$	−16.1079	−0.546424
$870$	−13.3633	−0.453058
$871$	5.13318	0.173931
$872$	45.4324	1.53853
$873$	0.971437	0.0328782
$874$	−58.7862	−1.98847
$875$	8.45227	0.285739
$876$	47.6697	1.61061
$877$	−50.7388	−1.71333	−0.856665	−	0.515874i	$-0.827467\pi$
$877$	−50.7388	−1.71333	−0.856665	+	0.515874i	$0.827467\pi$
$878$	−99.7873	−3.36766
$879$	−36.9746	−1.24712
$880$	−39.9192	−1.34568
$881$	−20.4694	−0.689633	−0.344816	−	0.938670i	$-0.612059\pi$
$881$	−20.4694	−0.689633	−0.344816	+	0.938670i	$0.612059\pi$
$882$	−7.08940	−0.238712
$883$	−31.5026	−1.06015	−0.530074	−	0.847951i	$-0.677836\pi$
$883$	−31.5026	−1.06015	−0.530074	+	0.847951i	$0.677836\pi$
$884$	−0.0345423	−0.00116178
$885$	−24.9386	−0.838304
$886$	28.0751	0.943201
$887$	−12.7073	−0.426669	−0.213335	−	0.976979i	$-0.568432\pi$
$887$	−12.7073	−0.426669	−0.213335	+	0.976979i	$0.568432\pi$
$888$	−4.83694	−0.162317
$889$	13.5096	0.453097
$890$	13.9728	0.468369
$891$	12.8356	0.430009
$892$	43.4316	1.45420
$893$	11.3634	0.380260
$894$	−22.2576	−0.744404
$895$	29.2858	0.978918
$896$	21.7164	0.725493
$897$	−5.01819	−0.167552
$898$	71.1245	2.37346
$899$	8.17478	0.272644
$900$	−17.1104	−0.570345
$901$	−0.153937	−0.00512837
$902$	35.6903	1.18836
$903$	21.0935	0.701948
$904$	−85.0153	−2.82757
$905$	8.16527	0.271423
$906$	3.20420	0.106452
$907$	−36.3709	−1.20768	−0.603838	−	0.797107i	$-0.706362\pi$
$907$	−36.3709	−1.20768	−0.603838	+	0.797107i	$0.706362\pi$
$908$	31.0279	1.02970
$909$	−2.73939	−0.0908599
$910$	−7.00245	−0.232129
$911$	−47.6368	−1.57828	−0.789139	−	0.614215i	$-0.789473\pi$
$911$	−47.6368	−1.57828	−0.789139	+	0.614215i	$0.789473\pi$
$912$	−38.2039	−1.26506
$913$	29.7917	0.985961
$914$	−66.2861	−2.19255
$915$	8.73845	0.288884
$916$	86.7526	2.86639
$917$	9.12720	0.301407
$918$	−0.204696	−0.00675596
$919$	13.7239	0.452709	0.226355	−	0.974045i	$-0.427319\pi$
$919$	13.7239	0.452709	0.226355	+	0.974045i	$0.427319\pi$
$920$	120.503	3.97288
$921$	−0.297608	−0.00980652
$922$	63.9181	2.10503
$923$	7.77660	0.255970
$924$	−18.8562	−0.620322
$925$	3.48998	0.114750
$926$	−70.9548	−2.33172
$927$	−4.62464	−0.151893
$928$	−3.92089	−0.128709
$929$	−18.1238	−0.594622	−0.297311	−	0.954781i	$-0.596090\pi$
$929$	−18.1238	−0.594622	−0.297311	+	0.954781i	$0.596090\pi$
$930$	−109.242	−3.58218
$931$	18.7086	0.613151
$932$	113.398	3.71448
$933$	−16.8045	−0.550153
$934$	−69.0111	−2.25811
$935$	0.0927616	0.00303363
$936$	1.90812	0.0623688
$937$	13.8544	0.452602	0.226301	−	0.974057i	$-0.427337\pi$
$937$	13.8544	0.452602	0.226301	+	0.974057i	$0.427337\pi$
$938$	−35.5450	−1.16059
$939$	−22.6199	−0.738173
$940$	−43.0590	−1.40443
$941$	31.4751	1.02606	0.513030	−	0.858371i	$-0.328523\pi$
$941$	31.4751	1.02606	0.513030	+	0.858371i	$0.328523\pi$
$942$	42.2687	1.37719
$943$	−45.0785	−1.46796
$944$	−29.4971	−0.960049
$945$	−28.4407	−0.925176
$946$	42.7476	1.38984
$947$	37.7602	1.22704	0.613521	−	0.789679i	$-0.289753\pi$
$947$	37.7602	1.22704	0.613521	+	0.789679i	$0.289753\pi$
$948$	58.4148	1.89723
$949$	3.83567	0.124511
$950$	65.8808	2.13745
$951$	20.1725	0.654137
$952$	0.129393	0.00419364
$953$	−7.86395	−0.254738	−0.127369	−	0.991855i	$-0.540653\pi$
$953$	−7.86395	−0.254738	−0.127369	+	0.991855i	$0.540653\pi$
$954$	15.7192	0.508927
$955$	17.6165	0.570055
$956$	25.5624	0.826746
$957$	−2.89544	−0.0935964
$958$	19.5118	0.630398
$959$	−21.9247	−0.707986
$960$	−14.0572	−0.453693
$961$	35.8270	1.15571
$962$	−0.719455	−0.0231962
$963$	1.50995	0.0486574
$964$	93.2157	3.00227
$965$	14.5935	0.469781
$966$	34.7488	1.11802
$967$	−21.2576	−0.683599	−0.341799	−	0.939773i	$-0.611036\pi$
$967$	−21.2576	−0.683599	−0.341799	+	0.939773i	$0.611036\pi$
$968$	44.6956	1.43657
$969$	0.0887757	0.00285189
$970$	14.1733	0.455078
$971$	−59.3572	−1.90486	−0.952431	−	0.304753i	$-0.901426\pi$
$971$	−59.3572	−1.90486	−0.952431	+	0.304753i	$0.901426\pi$
$972$	26.2979	0.843505
$973$	15.5326	0.497954
$974$	41.6293	1.33389
$975$	5.62380	0.180106
$976$	10.3357	0.330838
$977$	−5.70418	−0.182493	−0.0912464	−	0.995828i	$-0.529085\pi$
$977$	−5.70418	−0.182493	−0.0912464	+	0.995828i	$0.529085\pi$
$978$	−94.3467	−3.01687
$979$	3.02751	0.0967596
$980$	−70.8924	−2.26457
$981$	4.51068	0.144015
$982$	23.3570	0.745351
$983$	−27.4452	−0.875367	−0.437684	−	0.899129i	$-0.644201\pi$
$983$	−27.4452	−0.875367	−0.437684	+	0.899129i	$0.644201\pi$
$984$	−70.0164	−2.23204
$985$	61.4715	1.95864
$986$	0.0367287	0.00116968
$987$	−6.71692	−0.213802
$988$	−9.30834	−0.296138
$989$	−53.9922	−1.71685
$990$	−9.47232	−0.301050
$991$	−44.4653	−1.41249	−0.706243	−	0.707969i	$-0.749611\pi$
$991$	−44.4653	−1.41249	−0.706243	+	0.707969i	$0.749611\pi$
$992$	−32.0524	−1.01766
$993$	40.1479	1.27406
$994$	−53.8496	−1.70800
$995$	−8.95569	−0.283914
$996$	−108.039	−3.42333
$997$	54.6117	1.72957	0.864785	−	0.502142i	$-0.167455\pi$
$997$	54.6117	1.72957	0.864785	+	0.502142i	$0.167455\pi$
$998$	−81.5814	−2.58241
$999$	−2.92209	−0.0924509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.11	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.11	✓	168	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52129 q^{2} +1.55242 q^{3} +4.35693 q^{4} +3.41413 q^{5} -3.91411 q^{6} +1.49471 q^{7} -5.94251 q^{8} -0.589992 q^{9} +O(q^{10})\)	\(q-2.52129 q^{2} +1.55242 q^{3} +4.35693 q^{4} +3.41413 q^{5} -3.91411 q^{6} +1.49471 q^{7} -5.94251 q^{8} -0.589992 q^{9} -8.60803 q^{10} -1.86512 q^{11} +6.76378 q^{12} +0.544238 q^{13} -3.76861 q^{14} +5.30016 q^{15} +6.26896 q^{16} -0.0145674 q^{17} +1.48754 q^{18} -3.92557 q^{19} +14.8751 q^{20} +2.32042 q^{21} +4.70251 q^{22} -5.93949 q^{23} -9.22527 q^{24} +6.65629 q^{25} -1.37218 q^{26} -5.57318 q^{27} +6.51235 q^{28} +1.00000 q^{29} -13.3633 q^{30} +8.17478 q^{31} -3.92089 q^{32} -2.89544 q^{33} +0.0367287 q^{34} +5.10314 q^{35} -2.57055 q^{36} +0.524314 q^{37} +9.89752 q^{38} +0.844886 q^{39} -20.2885 q^{40} +7.58963 q^{41} -5.85046 q^{42} +9.09038 q^{43} -8.12618 q^{44} -2.01431 q^{45} +14.9752 q^{46} -2.89470 q^{47} +9.73207 q^{48} -4.76584 q^{49} -16.7825 q^{50} -0.0226147 q^{51} +2.37121 q^{52} +10.5672 q^{53} +14.0516 q^{54} -6.36775 q^{55} -8.88234 q^{56} -6.09414 q^{57} -2.52129 q^{58} -4.70526 q^{59} +23.0924 q^{60} +1.64871 q^{61} -20.6110 q^{62} -0.881869 q^{63} -2.65221 q^{64} +1.85810 q^{65} +7.30027 q^{66} +9.43187 q^{67} -0.0634691 q^{68} -9.22058 q^{69} -12.8665 q^{70} +14.2890 q^{71} +3.50604 q^{72} +7.04779 q^{73} -1.32195 q^{74} +10.3334 q^{75} -17.1034 q^{76} -2.78781 q^{77} -2.13021 q^{78} +8.63641 q^{79} +21.4031 q^{80} -6.88193 q^{81} -19.1357 q^{82} -15.9731 q^{83} +10.1099 q^{84} -0.0497350 q^{85} -22.9195 q^{86} +1.55242 q^{87} +11.0835 q^{88} -1.62323 q^{89} +5.07867 q^{90} +0.813479 q^{91} -25.8779 q^{92} +12.6907 q^{93} +7.29839 q^{94} -13.4024 q^{95} -6.08687 q^{96} -1.64653 q^{97} +12.0161 q^{98} +1.10040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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