LMFDB - Embedded newform 8033.2.a.d.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.57726 q^{2} +2.47639 q^{3} +4.64228 q^{4} +3.37343 q^{5} -6.38231 q^{6} -1.62921 q^{7} -6.80985 q^{8} +3.13252 q^{9} +O(q^{10})$	\(q-2.57726 q^{2} +2.47639 q^{3} +4.64228 q^{4} +3.37343 q^{5} -6.38231 q^{6} -1.62921 q^{7} -6.80985 q^{8} +3.13252 q^{9} -8.69420 q^{10} +5.67553 q^{11} +11.4961 q^{12} +1.67474 q^{13} +4.19891 q^{14} +8.35393 q^{15} +8.26620 q^{16} +7.57713 q^{17} -8.07333 q^{18} -0.143377 q^{19} +15.6604 q^{20} -4.03457 q^{21} -14.6273 q^{22} +5.07109 q^{23} -16.8639 q^{24} +6.38000 q^{25} -4.31624 q^{26} +0.328180 q^{27} -7.56326 q^{28} +1.00000 q^{29} -21.5303 q^{30} -7.53149 q^{31} -7.68446 q^{32} +14.0549 q^{33} -19.5282 q^{34} -5.49603 q^{35} +14.5420 q^{36} -8.62303 q^{37} +0.369521 q^{38} +4.14731 q^{39} -22.9725 q^{40} +3.78508 q^{41} +10.3981 q^{42} -0.919153 q^{43} +26.3474 q^{44} +10.5673 q^{45} -13.0695 q^{46} +4.89985 q^{47} +20.4704 q^{48} -4.34566 q^{49} -16.4429 q^{50} +18.7640 q^{51} +7.77461 q^{52} -6.12477 q^{53} -0.845806 q^{54} +19.1460 q^{55} +11.0947 q^{56} -0.355058 q^{57} -2.57726 q^{58} +4.29113 q^{59} +38.7813 q^{60} +1.08759 q^{61} +19.4106 q^{62} -5.10355 q^{63} +3.27248 q^{64} +5.64961 q^{65} -36.2230 q^{66} +5.53602 q^{67} +35.1752 q^{68} +12.5580 q^{69} +14.1647 q^{70} +14.4180 q^{71} -21.3320 q^{72} +10.2994 q^{73} +22.2238 q^{74} +15.7994 q^{75} -0.665597 q^{76} -9.24665 q^{77} -10.6887 q^{78} -5.36388 q^{79} +27.8854 q^{80} -8.58487 q^{81} -9.75515 q^{82} +5.32500 q^{83} -18.7296 q^{84} +25.5609 q^{85} +2.36890 q^{86} +2.47639 q^{87} -38.6495 q^{88} -14.3529 q^{89} -27.2348 q^{90} -2.72851 q^{91} +23.5414 q^{92} -18.6509 q^{93} -12.6282 q^{94} -0.483672 q^{95} -19.0298 q^{96} -8.33746 q^{97} +11.1999 q^{98} +17.7787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57726	−1.82240	−0.911200	−	0.411965i	$-0.864843\pi$
$2$	−2.57726	−1.82240	−0.911200	+	0.411965i	$0.864843\pi$
$3$	2.47639	1.42975	0.714873	−	0.699254i	$-0.246484\pi$
$3$	2.47639	1.42975	0.714873	+	0.699254i	$0.246484\pi$
$4$	4.64228	2.32114
$5$	3.37343	1.50864	0.754321	−	0.656506i	$-0.227966\pi$
$5$	3.37343	1.50864	0.754321	+	0.656506i	$0.227966\pi$
$6$	−6.38231	−2.60557
$7$	−1.62921	−0.615785	−0.307892	−	0.951421i	$-0.599624\pi$
$7$	−1.62921	−0.615785	−0.307892	+	0.951421i	$0.599624\pi$
$8$	−6.80985	−2.40764
$9$	3.13252	1.04417
$10$	−8.69420	−2.74935
$11$	5.67553	1.71124	0.855619	−	0.517606i	$-0.173177\pi$
$11$	5.67553	1.71124	0.855619	+	0.517606i	$0.173177\pi$
$12$	11.4961	3.31864
$13$	1.67474	0.464489	0.232245	−	0.972657i	$-0.425393\pi$
$13$	1.67474	0.464489	0.232245	+	0.972657i	$0.425393\pi$
$14$	4.19891	1.12221
$15$	8.35393	2.15698
$16$	8.26620	2.06655
$17$	7.57713	1.83772	0.918862	−	0.394579i	$-0.129110\pi$
$17$	7.57713	1.83772	0.918862	+	0.394579i	$0.129110\pi$
$18$	−8.07333	−1.90290
$19$	−0.143377	−0.0328930	−0.0164465	−	0.999865i	$-0.505235\pi$
$19$	−0.143377	−0.0328930	−0.0164465	+	0.999865i	$0.505235\pi$
$20$	15.6604	3.50177
$21$	−4.03457	−0.880416
$22$	−14.6273	−3.11856
$23$	5.07109	1.05739	0.528697	−	0.848810i	$-0.322681\pi$
$23$	5.07109	1.05739	0.528697	+	0.848810i	$0.322681\pi$
$24$	−16.8639	−3.44232
$25$	6.38000	1.27600
$26$	−4.31624	−0.846485
$27$	0.328180	0.0631583
$28$	−7.56326	−1.42932
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−21.5303	−3.93087
$31$	−7.53149	−1.35270	−0.676348	−	0.736583i	$-0.736438\pi$
$31$	−7.53149	−1.35270	−0.676348	+	0.736583i	$0.736438\pi$
$32$	−7.68446	−1.35843
$33$	14.0549	2.44664
$34$	−19.5282	−3.34907
$35$	−5.49603	−0.928999
$36$	14.5420	2.42367
$37$	−8.62303	−1.41762	−0.708809	−	0.705400i	$-0.750767\pi$
$37$	−8.62303	−1.41762	−0.708809	+	0.705400i	$0.750767\pi$
$38$	0.369521	0.0599441
$39$	4.14731	0.664102
$40$	−22.9725	−3.63227
$41$	3.78508	0.591130	0.295565	−	0.955323i	$-0.404492\pi$
$41$	3.78508	0.591130	0.295565	+	0.955323i	$0.404492\pi$
$42$	10.3981	1.60447
$43$	−0.919153	−0.140170	−0.0700848	−	0.997541i	$-0.522327\pi$
$43$	−0.919153	−0.140170	−0.0700848	+	0.997541i	$0.522327\pi$
$44$	26.3474	3.97202
$45$	10.5673	1.57529
$46$	−13.0695	−1.92700
$47$	4.89985	0.714717	0.357359	−	0.933967i	$-0.383677\pi$
$47$	4.89985	0.714717	0.357359	+	0.933967i	$0.383677\pi$
$48$	20.4704	2.95464
$49$	−4.34566	−0.620809
$50$	−16.4429	−2.32538
$51$	18.7640	2.62748
$52$	7.77461	1.07814
$53$	−6.12477	−0.841301	−0.420651	−	0.907223i	$-0.638198\pi$
$53$	−6.12477	−0.841301	−0.420651	+	0.907223i	$0.638198\pi$
$54$	−0.845806	−0.115100
$55$	19.1460	2.58165
$56$	11.0947	1.48259
$57$	−0.355058	−0.0470286
$58$	−2.57726	−0.338411
$59$	4.29113	0.558658	0.279329	−	0.960195i	$-0.409888\pi$
$59$	4.29113	0.558658	0.279329	+	0.960195i	$0.409888\pi$
$60$	38.7813	5.00664
$61$	1.08759	0.139252	0.0696260	−	0.997573i	$-0.477819\pi$
$61$	1.08759	0.139252	0.0696260	+	0.997573i	$0.477819\pi$
$62$	19.4106	2.46515
$63$	−5.10355	−0.642987
$64$	3.27248	0.409060
$65$	5.64961	0.700748
$66$	−36.2230	−4.45875
$67$	5.53602	0.676333	0.338166	−	0.941086i	$-0.390193\pi$
$67$	5.53602	0.676333	0.338166	+	0.941086i	$0.390193\pi$
$68$	35.1752	4.26561
$69$	12.5580	1.51181
$70$	14.1647	1.69301
$71$	14.4180	1.71110	0.855552	−	0.517717i	$-0.173218\pi$
$71$	14.4180	1.71110	0.855552	+	0.517717i	$0.173218\pi$
$72$	−21.3320	−2.51400
$73$	10.2994	1.20545	0.602725	−	0.797949i	$-0.294082\pi$
$73$	10.2994	1.20545	0.602725	+	0.797949i	$0.294082\pi$
$74$	22.2238	2.58347
$75$	15.7994	1.82436
$76$	−0.665597	−0.0763492
$77$	−9.24665	−1.05375
$78$	−10.6887	−1.21026
$79$	−5.36388	−0.603484	−0.301742	−	0.953390i	$-0.597568\pi$
$79$	−5.36388	−0.603484	−0.301742	+	0.953390i	$0.597568\pi$
$80$	27.8854	3.11768
$81$	−8.58487	−0.953874
$82$	−9.75515	−1.07728
$83$	5.32500	0.584495	0.292247	−	0.956343i	$-0.405597\pi$
$83$	5.32500	0.584495	0.292247	+	0.956343i	$0.405597\pi$
$84$	−18.7296	−2.04357
$85$	25.5609	2.77247
$86$	2.36890	0.255445
$87$	2.47639	0.265497
$88$	−38.6495	−4.12005
$89$	−14.3529	−1.52141	−0.760704	−	0.649099i	$-0.775146\pi$
$89$	−14.3529	−1.52141	−0.760704	+	0.649099i	$0.775146\pi$
$90$	−27.2348	−2.87080
$91$	−2.72851	−0.286025
$92$	23.5414	2.45436
$93$	−18.6509	−1.93401
$94$	−12.6282	−1.30250
$95$	−0.483672	−0.0496237
$96$	−19.0298	−1.94222
$97$	−8.33746	−0.846540	−0.423270	−	0.906003i	$-0.639118\pi$
$97$	−8.33746	−0.846540	−0.423270	+	0.906003i	$0.639118\pi$
$98$	11.1999	1.13136
$99$	17.7787	1.78683
$100$	29.6178	2.96178
$101$	4.12505	0.410457	0.205229	−	0.978714i	$-0.434206\pi$
$101$	4.12505	0.410457	0.205229	+	0.978714i	$0.434206\pi$
$102$	−48.3596	−4.78832
$103$	−15.6221	−1.53929	−0.769644	−	0.638473i	$-0.779566\pi$
$103$	−15.6221	−1.53929	−0.769644	+	0.638473i	$0.779566\pi$
$104$	−11.4047	−1.11832
$105$	−13.6103	−1.32823
$106$	15.7851	1.53319
$107$	−18.2526	−1.76454	−0.882272	−	0.470740i	$-0.843987\pi$
$107$	−18.2526	−1.76454	−0.882272	+	0.470740i	$0.843987\pi$
$108$	1.52350	0.146599
$109$	7.69487	0.737035	0.368518	−	0.929621i	$-0.379865\pi$
$109$	7.69487	0.737035	0.368518	+	0.929621i	$0.379865\pi$
$110$	−49.3442	−4.70479
$111$	−21.3540	−2.02683
$112$	−13.4674	−1.27255
$113$	17.0964	1.60830	0.804148	−	0.594429i	$-0.202622\pi$
$113$	17.0964	1.60830	0.804148	+	0.594429i	$0.202622\pi$
$114$	0.915078	0.0857049
$115$	17.1069	1.59523
$116$	4.64228	0.431025
$117$	5.24616	0.485008
$118$	−11.0594	−1.01810
$119$	−12.3448	−1.13164
$120$	−56.8890	−5.19323
$121$	21.2117	1.92833
$122$	−2.80301	−0.253773
$123$	9.37335	0.845166
$124$	−34.9633	−3.13979
$125$	4.65534	0.416386
$126$	13.1532	1.17178
$127$	19.9729	1.77231	0.886154	−	0.463391i	$-0.153368\pi$
$127$	19.9729	1.77231	0.886154	+	0.463391i	$0.153368\pi$
$128$	6.93488	0.612963
$129$	−2.27618	−0.200407
$130$	−14.5605	−1.27704
$131$	5.91053	0.516406	0.258203	−	0.966091i	$-0.416870\pi$
$131$	5.91053	0.516406	0.258203	+	0.966091i	$0.416870\pi$
$132$	65.2465	5.67898
$133$	0.233592	0.0202550
$134$	−14.2678	−1.23255
$135$	1.10709	0.0952833
$136$	−51.5991	−4.42458
$137$	−6.49476	−0.554884	−0.277442	−	0.960742i	$-0.589487\pi$
$137$	−6.49476	−0.554884	−0.277442	+	0.960742i	$0.589487\pi$
$138$	−32.3653	−2.75511
$139$	−3.21585	−0.272765	−0.136382	−	0.990656i	$-0.543548\pi$
$139$	−3.21585	−0.272765	−0.136382	+	0.990656i	$0.543548\pi$
$140$	−25.5141	−2.15634
$141$	12.1340	1.02186
$142$	−37.1590	−3.11831
$143$	9.50504	0.794851
$144$	25.8941	2.15784
$145$	3.37343	0.280148
$146$	−26.5442	−2.19681
$147$	−10.7616	−0.887600
$148$	−40.0305	−3.29049
$149$	4.90309	0.401676	0.200838	−	0.979624i	$-0.435633\pi$
$149$	4.90309	0.401676	0.200838	+	0.979624i	$0.435633\pi$
$150$	−40.7192	−3.32471
$151$	−11.6502	−0.948078	−0.474039	−	0.880504i	$-0.657204\pi$
$151$	−11.6502	−0.948078	−0.474039	+	0.880504i	$0.657204\pi$
$152$	0.976376	0.0791946
$153$	23.7355	1.91890
$154$	23.8310	1.92036
$155$	−25.4069	−2.04073
$156$	19.2530	1.54147
$157$	−6.13351	−0.489507	−0.244754	−	0.969585i	$-0.578707\pi$
$157$	−6.13351	−0.489507	−0.244754	+	0.969585i	$0.578707\pi$
$158$	13.8241	1.09979
$159$	−15.1673	−1.20285
$160$	−25.9230	−2.04939
$161$	−8.26188	−0.651127
$162$	22.1255	1.73834
$163$	−17.1565	−1.34380	−0.671899	−	0.740643i	$-0.734521\pi$
$163$	−17.1565	−1.34380	−0.671899	+	0.740643i	$0.734521\pi$
$164$	17.5714	1.37210
$165$	47.4130	3.69110
$166$	−13.7239	−1.06518
$167$	13.2492	1.02526	0.512628	−	0.858611i	$-0.328672\pi$
$167$	13.2492	1.02526	0.512628	+	0.858611i	$0.328672\pi$
$168$	27.4748	2.11973
$169$	−10.1952	−0.784250
$170$	−65.8771	−5.05254
$171$	−0.449132	−0.0343460
$172$	−4.26696	−0.325353
$173$	−7.89551	−0.600285	−0.300142	−	0.953894i	$-0.597034\pi$
$173$	−7.89551	−0.600285	−0.300142	+	0.953894i	$0.597034\pi$
$174$	−6.38231	−0.483842
$175$	−10.3944	−0.785742
$176$	46.9151	3.53636
$177$	10.6265	0.798739
$178$	36.9913	2.77261
$179$	−12.1750	−0.910000	−0.455000	−	0.890491i	$-0.650361\pi$
$179$	−12.1750	−0.910000	−0.455000	+	0.890491i	$0.650361\pi$
$180$	49.0565	3.65646
$181$	20.1417	1.49712	0.748562	−	0.663065i	$-0.230745\pi$
$181$	20.1417	1.49712	0.748562	+	0.663065i	$0.230745\pi$
$182$	7.03208	0.521252
$183$	2.69331	0.199095
$184$	−34.5333	−2.54583
$185$	−29.0892	−2.13868
$186$	48.0683	3.52454
$187$	43.0043	3.14478
$188$	22.7465	1.65896
$189$	−0.534675	−0.0388919
$190$	1.24655	0.0904343
$191$	7.24804	0.524449	0.262225	−	0.965007i	$-0.415544\pi$
$191$	7.24804	0.524449	0.262225	+	0.965007i	$0.415544\pi$
$192$	8.10395	0.584852
$193$	−27.3674	−1.96995	−0.984975	−	0.172699i	$-0.944751\pi$
$193$	−27.3674	−1.96995	−0.984975	+	0.172699i	$0.944751\pi$
$194$	21.4878	1.54273
$195$	13.9907	1.00189
$196$	−20.1738	−1.44098
$197$	15.5863	1.11048	0.555241	−	0.831690i	$-0.312626\pi$
$197$	15.5863	1.11048	0.555241	+	0.831690i	$0.312626\pi$
$198$	−45.8205	−3.25632
$199$	−17.3020	−1.22651	−0.613255	−	0.789885i	$-0.710140\pi$
$199$	−17.3020	−1.22651	−0.613255	+	0.789885i	$0.710140\pi$
$200$	−43.4468	−3.07216
$201$	13.7094	0.966984
$202$	−10.6313	−0.748017
$203$	−1.62921	−0.114348
$204$	87.1075	6.09875
$205$	12.7687	0.891804
$206$	40.2622	2.80520
$207$	15.8853	1.10410
$208$	13.8437	0.959890
$209$	−0.813742	−0.0562877
$210$	35.0774	2.42057
$211$	−5.98329	−0.411907	−0.205953	−	0.978562i	$-0.566030\pi$
$211$	−5.98329	−0.411907	−0.205953	+	0.978562i	$0.566030\pi$
$212$	−28.4329	−1.95278
$213$	35.7047	2.44644
$214$	47.0417	3.21570
$215$	−3.10069	−0.211466
$216$	−2.23486	−0.152063
$217$	12.2704	0.832969
$218$	−19.8317	−1.34317
$219$	25.5053	1.72349
$220$	88.8810	5.99236
$221$	12.6897	0.853603
$222$	55.0349	3.69370
$223$	−20.4008	−1.36614	−0.683070	−	0.730353i	$-0.739356\pi$
$223$	−20.4008	−1.36614	−0.683070	+	0.730353i	$0.739356\pi$
$224$	12.5196	0.836503
$225$	19.9855	1.33237
$226$	−44.0620	−2.93096
$227$	−17.4662	−1.15927	−0.579636	−	0.814876i	$-0.696805\pi$
$227$	−17.4662	−1.15927	−0.579636	+	0.814876i	$0.696805\pi$
$228$	−1.64828	−0.109160
$229$	6.93586	0.458335	0.229167	−	0.973387i	$-0.426400\pi$
$229$	6.93586	0.458335	0.229167	+	0.973387i	$0.426400\pi$
$230$	−44.0891	−2.90715
$231$	−22.8983	−1.50660
$232$	−6.80985	−0.447088
$233$	−1.03057	−0.0675149	−0.0337575	−	0.999430i	$-0.510747\pi$
$233$	−1.03057	−0.0675149	−0.0337575	+	0.999430i	$0.510747\pi$
$234$	−13.5207	−0.883878
$235$	16.5293	1.07825
$236$	19.9206	1.29672
$237$	−13.2831	−0.862829
$238$	31.8157	2.06230
$239$	5.63167	0.364282	0.182141	−	0.983272i	$-0.441697\pi$
$239$	5.63167	0.364282	0.182141	+	0.983272i	$0.441697\pi$
$240$	69.0552	4.45750
$241$	−23.5133	−1.51463	−0.757313	−	0.653052i	$-0.773488\pi$
$241$	−23.5133	−1.51463	−0.757313	+	0.653052i	$0.773488\pi$
$242$	−54.6680	−3.51420
$243$	−22.2440	−1.42696
$244$	5.04891	0.323223
$245$	−14.6598	−0.936579
$246$	−24.1576	−1.54023
$247$	−0.240119	−0.0152784
$248$	51.2883	3.25681
$249$	13.1868	0.835679
$250$	−11.9980	−0.758822
$251$	−19.9781	−1.26100	−0.630502	−	0.776188i	$-0.717151\pi$
$251$	−19.9781	−1.26100	−0.630502	+	0.776188i	$0.717151\pi$
$252$	−23.6921	−1.49246
$253$	28.7811	1.80945
$254$	−51.4754	−3.22985
$255$	63.2988	3.96393
$256$	−24.4180	−1.52612
$257$	15.4269	0.962302	0.481151	−	0.876638i	$-0.340219\pi$
$257$	15.4269	0.962302	0.481151	+	0.876638i	$0.340219\pi$
$258$	5.86632	0.365221
$259$	14.0488	0.872947
$260$	26.2271	1.62653
$261$	3.13252	0.193898
$262$	−15.2330	−0.941097
$263$	0.571590	0.0352457	0.0176229	−	0.999845i	$-0.494390\pi$
$263$	0.571590	0.0352457	0.0176229	+	0.999845i	$0.494390\pi$
$264$	−95.7114	−5.89063
$265$	−20.6614	−1.26922
$266$	−0.602028	−0.0369127
$267$	−35.5435	−2.17523
$268$	25.6998	1.56986
$269$	3.32515	0.202738	0.101369	−	0.994849i	$-0.467678\pi$
$269$	3.32515	0.202738	0.101369	+	0.994849i	$0.467678\pi$
$270$	−2.85326	−0.173644
$271$	16.2902	0.989561	0.494780	−	0.869018i	$-0.335248\pi$
$271$	16.2902	0.989561	0.494780	+	0.869018i	$0.335248\pi$
$272$	62.6340	3.79775
$273$	−6.75686	−0.408944
$274$	16.7387	1.01122
$275$	36.2099	2.18354
$276$	58.2978	3.50911
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	8.28809	0.497086
$279$	−23.5926	−1.41245
$280$	37.4271	2.23670
$281$	−7.65314	−0.456548	−0.228274	−	0.973597i	$-0.573308\pi$
$281$	−7.65314	−0.456548	−0.228274	+	0.973597i	$0.573308\pi$
$282$	−31.2724	−1.86224
$283$	23.5046	1.39720	0.698602	−	0.715511i	$-0.253806\pi$
$283$	23.5046	1.39720	0.698602	+	0.715511i	$0.253806\pi$
$284$	66.9325	3.97171
$285$	−1.19776	−0.0709493
$286$	−24.4970	−1.44854
$287$	−6.16670	−0.364009
$288$	−24.0718	−1.41844
$289$	40.4129	2.37723
$290$	−8.69420	−0.510541
$291$	−20.6468	−1.21034
$292$	47.8125	2.79802
$293$	−21.4752	−1.25459	−0.627297	−	0.778780i	$-0.715839\pi$
$293$	−21.4752	−1.25459	−0.627297	+	0.778780i	$0.715839\pi$
$294$	27.7354	1.61756
$295$	14.4758	0.842815
$296$	58.7215	3.41312
$297$	1.86260	0.108079
$298$	−12.6365	−0.732015
$299$	8.49275	0.491148
$300$	73.3452	4.23459
$301$	1.49750	0.0863142
$302$	30.0256	1.72778
$303$	10.2152	0.586850
$304$	−1.18518	−0.0679750
$305$	3.66892	0.210081
$306$	−61.1727	−3.49701
$307$	22.2226	1.26831	0.634155	−	0.773206i	$-0.281348\pi$
$307$	22.2226	1.26831	0.634155	+	0.773206i	$0.281348\pi$
$308$	−42.9255	−2.44591
$309$	−38.6864	−2.20079
$310$	65.4803	3.71903
$311$	30.1960	1.71226	0.856129	−	0.516762i	$-0.172863\pi$
$311$	30.1960	1.71226	0.856129	+	0.516762i	$0.172863\pi$
$312$	−28.2426	−1.59892
$313$	−2.80578	−0.158592	−0.0792961	−	0.996851i	$-0.525267\pi$
$313$	−2.80578	−0.158592	−0.0792961	+	0.996851i	$0.525267\pi$
$314$	15.8077	0.892078
$315$	−17.2164	−0.970037
$316$	−24.9006	−1.40077
$317$	−6.32939	−0.355494	−0.177747	−	0.984076i	$-0.556881\pi$
$317$	−6.32939	−0.355494	−0.177747	+	0.984076i	$0.556881\pi$
$318$	39.0902	2.19207
$319$	5.67553	0.317769
$320$	11.0395	0.617125
$321$	−45.2006	−2.52285
$322$	21.2930	1.18661
$323$	−1.08639	−0.0604482
$324$	−39.8533	−2.21407
$325$	10.6848	0.592689
$326$	44.2167	2.44894
$327$	19.0555	1.05377
$328$	−25.7758	−1.42323
$329$	−7.98291	−0.440112
$330$	−122.196	−6.72665
$331$	−24.7623	−1.36106	−0.680529	−	0.732721i	$-0.738250\pi$
$331$	−24.7623	−1.36106	−0.680529	+	0.732721i	$0.738250\pi$
$332$	24.7201	1.35669
$333$	−27.0119	−1.48024
$334$	−34.1468	−1.86843
$335$	18.6754	1.02034
$336$	−33.3506	−1.81942
$337$	−21.6394	−1.17877	−0.589387	−	0.807851i	$-0.700631\pi$
$337$	−21.6394	−1.17877	−0.589387	+	0.807851i	$0.700631\pi$
$338$	26.2758	1.42922
$339$	42.3375	2.29946
$340$	118.661	6.43528
$341$	−42.7452	−2.31478
$342$	1.15753	0.0625921
$343$	18.4845	0.998069
$344$	6.25929	0.337478
$345$	42.3635	2.28077
$346$	20.3488	1.09396
$347$	−4.74997	−0.254992	−0.127496	−	0.991839i	$-0.540694\pi$
$347$	−4.74997	−0.254992	−0.127496	+	0.991839i	$0.540694\pi$
$348$	11.4961	0.616256
$349$	5.83944	0.312578	0.156289	−	0.987711i	$-0.450047\pi$
$349$	5.83944	0.312578	0.156289	+	0.987711i	$0.450047\pi$
$350$	26.7891	1.43194
$351$	0.549616	0.0293363
$352$	−43.6134	−2.32460
$353$	−27.4540	−1.46123	−0.730613	−	0.682791i	$-0.760766\pi$
$353$	−27.4540	−1.46123	−0.730613	+	0.682791i	$0.760766\pi$
$354$	−27.3874	−1.45562
$355$	48.6381	2.58144
$356$	−66.6303	−3.53140
$357$	−30.5705	−1.61796
$358$	31.3781	1.65838
$359$	−18.0904	−0.954777	−0.477389	−	0.878692i	$-0.658417\pi$
$359$	−18.0904	−0.954777	−0.477389	+	0.878692i	$0.658417\pi$
$360$	−71.9619	−3.79273
$361$	−18.9794	−0.998918
$362$	−51.9105	−2.72836
$363$	52.5285	2.75703
$364$	−12.6665	−0.663905
$365$	34.7442	1.81859
$366$	−6.94136	−0.362831
$367$	33.7143	1.75987	0.879936	−	0.475093i	$-0.157586\pi$
$367$	33.7143	1.75987	0.879936	+	0.475093i	$0.157586\pi$
$368$	41.9186	2.18516
$369$	11.8569	0.617243
$370$	74.9704	3.89753
$371$	9.97855	0.518060
$372$	−86.5828	−4.48911
$373$	−12.4012	−0.642109	−0.321054	−	0.947061i	$-0.604037\pi$
$373$	−12.4012	−0.642109	−0.321054	+	0.947061i	$0.604037\pi$
$374$	−110.833	−5.73105
$375$	11.5285	0.595327
$376$	−33.3672	−1.72078
$377$	1.67474	0.0862535
$378$	1.37800	0.0708766
$379$	−24.7309	−1.27034	−0.635171	−	0.772371i	$-0.719070\pi$
$379$	−24.7309	−1.27034	−0.635171	+	0.772371i	$0.719070\pi$
$380$	−2.24534	−0.115184
$381$	49.4607	2.53395
$382$	−18.6801	−0.955756
$383$	18.1806	0.928987	0.464493	−	0.885577i	$-0.346236\pi$
$383$	18.1806	0.928987	0.464493	+	0.885577i	$0.346236\pi$
$384$	17.1735	0.876381
$385$	−31.1929	−1.58974
$386$	70.5330	3.59003
$387$	−2.87927	−0.146361
$388$	−38.7048	−1.96494
$389$	0.0926002	0.00469502	0.00234751	−	0.999997i	$-0.499253\pi$
$389$	0.0926002	0.00469502	0.00234751	+	0.999997i	$0.499253\pi$
$390$	−36.0576	−1.82585
$391$	38.4243	1.94320
$392$	29.5933	1.49469
$393$	14.6368	0.738329
$394$	−40.1701	−2.02374
$395$	−18.0947	−0.910441
$396$	82.5339	4.14748
$397$	−9.96346	−0.500052	−0.250026	−	0.968239i	$-0.580439\pi$
$397$	−9.96346	−0.500052	−0.250026	+	0.968239i	$0.580439\pi$
$398$	44.5919	2.23519
$399$	0.578466	0.0289595
$400$	52.7384	2.63692
$401$	4.38403	0.218928	0.109464	−	0.993991i	$-0.465087\pi$
$401$	4.38403	0.218928	0.109464	+	0.993991i	$0.465087\pi$
$402$	−35.3326	−1.76223
$403$	−12.6133	−0.628312
$404$	19.1496	0.952729
$405$	−28.9604	−1.43905
$406$	4.19891	0.208388
$407$	−48.9403	−2.42588
$408$	−127.780	−6.32603
$409$	0.264843	0.0130956	0.00654781	−	0.999979i	$-0.497916\pi$
$409$	0.264843	0.0130956	0.00654781	+	0.999979i	$0.497916\pi$
$410$	−32.9083	−1.62522
$411$	−16.0836	−0.793344
$412$	−72.5220	−3.57290
$413$	−6.99117	−0.344013
$414$	−40.9406	−2.01212
$415$	17.9635	0.881793
$416$	−12.8695	−0.630978
$417$	−7.96371	−0.389984
$418$	2.09723	0.102579
$419$	−25.2381	−1.23296	−0.616482	−	0.787369i	$-0.711443\pi$
$419$	−25.2381	−1.23296	−0.616482	+	0.787369i	$0.711443\pi$
$420$	−63.1830	−3.08301
$421$	33.4101	1.62831	0.814155	−	0.580648i	$-0.197201\pi$
$421$	33.4101	1.62831	0.814155	+	0.580648i	$0.197201\pi$
$422$	15.4205	0.750659
$423$	15.3489	0.746289
$424$	41.7087	2.02555
$425$	48.3421	2.34494
$426$	−92.0203	−4.45840
$427$	−1.77192	−0.0857493
$428$	−84.7336	−4.09575
$429$	23.5382	1.13644
$430$	7.99130	0.385375
$431$	−15.8776	−0.764798	−0.382399	−	0.923997i	$-0.624902\pi$
$431$	−15.8776	−0.764798	−0.382399	+	0.923997i	$0.624902\pi$
$432$	2.71280	0.130520
$433$	−10.9787	−0.527605	−0.263802	−	0.964577i	$-0.584977\pi$
$433$	−10.9787	−0.527605	−0.263802	+	0.964577i	$0.584977\pi$
$434$	−31.6240	−1.51800
$435$	8.35393	0.400540
$436$	35.7218	1.71076
$437$	−0.727078	−0.0347809
$438$	−65.7338	−3.14088
$439$	22.0696	1.05333	0.526663	−	0.850074i	$-0.323443\pi$
$439$	22.0696	1.05333	0.526663	+	0.850074i	$0.323443\pi$
$440$	−130.381	−6.21568
$441$	−13.6129	−0.648233
$442$	−32.7047	−1.55561
$443$	14.8853	0.707222	0.353611	−	0.935393i	$-0.384954\pi$
$443$	14.8853	0.707222	0.353611	+	0.935393i	$0.384954\pi$
$444$	−99.1313	−4.70456
$445$	−48.4186	−2.29526
$446$	52.5783	2.48965
$447$	12.1420	0.574295
$448$	−5.33157	−0.251893
$449$	−15.1162	−0.713378	−0.356689	−	0.934223i	$-0.616094\pi$
$449$	−15.1162	−0.713378	−0.356689	+	0.934223i	$0.616094\pi$
$450$	−51.5079	−2.42811
$451$	21.4824	1.01156
$452$	79.3664	3.73308
$453$	−28.8504	−1.35551
$454$	45.0149	2.11266
$455$	−9.20442	−0.431510
$456$	2.41789	0.113228
$457$	3.23462	0.151309	0.0756545	−	0.997134i	$-0.475895\pi$
$457$	3.23462	0.151309	0.0756545	+	0.997134i	$0.475895\pi$
$458$	−17.8755	−0.835269
$459$	2.48666	0.116068
$460$	79.4152	3.70275
$461$	−7.74773	−0.360848	−0.180424	−	0.983589i	$-0.557747\pi$
$461$	−7.74773	−0.360848	−0.180424	+	0.983589i	$0.557747\pi$
$462$	59.0150	2.74563
$463$	0.970994	0.0451259	0.0225630	−	0.999745i	$-0.492817\pi$
$463$	0.970994	0.0451259	0.0225630	+	0.999745i	$0.492817\pi$
$464$	8.26620	0.383749
$465$	−62.9175	−2.91773
$466$	2.65605	0.123039
$467$	−15.0092	−0.694541	−0.347270	−	0.937765i	$-0.612891\pi$
$467$	−15.0092	−0.694541	−0.347270	+	0.937765i	$0.612891\pi$
$468$	24.3541	1.12577
$469$	−9.01936	−0.416475
$470$	−42.6003	−1.96501
$471$	−15.1890	−0.699871
$472$	−29.2220	−1.34505
$473$	−5.21668	−0.239863
$474$	34.2340	1.57242
$475$	−0.914747	−0.0419715
$476$	−57.3078	−2.62670
$477$	−19.1860	−0.878465
$478$	−14.5143	−0.663868
$479$	1.16379	0.0531750	0.0265875	−	0.999646i	$-0.491536\pi$
$479$	1.16379	0.0531750	0.0265875	+	0.999646i	$0.491536\pi$
$480$	−64.1955	−2.93011
$481$	−14.4413	−0.658468
$482$	60.6000	2.76025
$483$	−20.4597	−0.930947
$484$	98.4705	4.47593
$485$	−28.1258	−1.27713
$486$	57.3287	2.60048
$487$	8.83182	0.400208	0.200104	−	0.979775i	$-0.435872\pi$
$487$	8.83182	0.400208	0.200104	+	0.979775i	$0.435872\pi$
$488$	−7.40634	−0.335269
$489$	−42.4862	−1.92129
$490$	37.7821	1.70682
$491$	23.1968	1.04686	0.523428	−	0.852070i	$-0.324653\pi$
$491$	23.1968	1.04686	0.523428	+	0.852070i	$0.324653\pi$
$492$	43.5137	1.96175
$493$	7.57713	0.341257
$494$	0.618851	0.0278434
$495$	59.9753	2.69569
$496$	−62.2568	−2.79541
$497$	−23.4900	−1.05367
$498$	−33.9858	−1.52294
$499$	−2.19573	−0.0982945	−0.0491473	−	0.998792i	$-0.515650\pi$
$499$	−2.19573	−0.0982945	−0.0491473	+	0.998792i	$0.515650\pi$
$500$	21.6114	0.966491
$501$	32.8103	1.46586
$502$	51.4887	2.29805
$503$	−13.3883	−0.596956	−0.298478	−	0.954416i	$-0.596479\pi$
$503$	−13.3883	−0.596956	−0.298478	+	0.954416i	$0.596479\pi$
$504$	34.7544	1.54808
$505$	13.9155	0.619233
$506$	−74.1765	−3.29755
$507$	−25.2474	−1.12128
$508$	92.7197	4.11377
$509$	−24.9213	−1.10462	−0.552309	−	0.833639i	$-0.686253\pi$
$509$	−24.9213	−1.10462	−0.552309	+	0.833639i	$0.686253\pi$
$510$	−163.138	−7.22385
$511$	−16.7799	−0.742298
$512$	49.0618	2.16824
$513$	−0.0470535	−0.00207746
$514$	−39.7591	−1.75370
$515$	−52.6999	−2.32223
$516$	−10.5667	−0.465172
$517$	27.8093	1.22305
$518$	−36.2073	−1.59086
$519$	−19.5524	−0.858255
$520$	−38.4730	−1.68715
$521$	12.6771	0.555394	0.277697	−	0.960669i	$-0.410429\pi$
$521$	12.6771	0.555394	0.277697	+	0.960669i	$0.410429\pi$
$522$	−8.07333	−0.353360
$523$	−1.34861	−0.0589708	−0.0294854	−	0.999565i	$-0.509387\pi$
$523$	−1.34861	−0.0589708	−0.0294854	+	0.999565i	$0.509387\pi$
$524$	27.4383	1.19865
$525$	−25.7406	−1.12341
$526$	−1.47314	−0.0642318
$527$	−57.0671	−2.48588
$528$	116.180	5.05609
$529$	2.71592	0.118084
$530$	53.2500	2.31303
$531$	13.4421	0.583337
$532$	1.08440	0.0470147
$533$	6.33903	0.274574
$534$	91.6049	3.96413
$535$	−61.5738	−2.66207
$536$	−37.6994	−1.62837
$537$	−30.1500	−1.30107
$538$	−8.56978	−0.369469
$539$	−24.6640	−1.06235
$540$	5.13943	0.221166
$541$	−33.6954	−1.44868	−0.724339	−	0.689444i	$-0.757855\pi$
$541$	−33.6954	−1.44868	−0.724339	+	0.689444i	$0.757855\pi$
$542$	−41.9842	−1.80338
$543$	49.8789	2.14051
$544$	−58.2262	−2.49643
$545$	25.9581	1.11192
$546$	17.4142	0.745259
$547$	16.7707	0.717063	0.358531	−	0.933518i	$-0.383278\pi$
$547$	16.7707	0.717063	0.358531	+	0.933518i	$0.383278\pi$
$548$	−30.1505	−1.28796
$549$	3.40691	0.145403
$550$	−93.3225	−3.97928
$551$	−0.143377	−0.00610807
$552$	−85.5181	−3.63989
$553$	8.73890	0.371616
$554$	2.57726	0.109497
$555$	−72.0362	−3.05777
$556$	−14.9289	−0.633125
$557$	37.2836	1.57976	0.789878	−	0.613264i	$-0.210144\pi$
$557$	37.2836	1.57976	0.789878	+	0.613264i	$0.210144\pi$
$558$	60.8042	2.57405
$559$	−1.53934	−0.0651072
$560$	−45.4313	−1.91982
$561$	106.495	4.49624
$562$	19.7242	0.832013
$563$	−37.6516	−1.58683	−0.793414	−	0.608683i	$-0.791698\pi$
$563$	−37.6516	−1.58683	−0.793414	+	0.608683i	$0.791698\pi$
$564$	56.3293	2.37189
$565$	57.6735	2.42634
$566$	−60.5775	−2.54626
$567$	13.9866	0.587381
$568$	−98.1845	−4.11973
$569$	28.5479	1.19679	0.598395	−	0.801201i	$-0.295805\pi$
$569$	28.5479	1.19679	0.598395	+	0.801201i	$0.295805\pi$
$570$	3.08695	0.129298
$571$	26.8118	1.12204	0.561019	−	0.827803i	$-0.310409\pi$
$571$	26.8118	1.12204	0.561019	+	0.827803i	$0.310409\pi$
$572$	44.1251	1.84496
$573$	17.9490	0.749830
$574$	15.8932	0.663370
$575$	32.3536	1.34924
$576$	10.2511	0.427130
$577$	33.3930	1.39017	0.695085	−	0.718928i	$-0.255367\pi$
$577$	33.3930	1.39017	0.695085	+	0.718928i	$0.255367\pi$
$578$	−104.155	−4.33226
$579$	−67.7725	−2.81653
$580$	15.6604	0.650262
$581$	−8.67556	−0.359923
$582$	53.2123	2.20572
$583$	−34.7613	−1.43967
$584$	−70.1371	−2.90229
$585$	17.6975	0.731703
$586$	55.3472	2.28637
$587$	3.02702	0.124939	0.0624693	−	0.998047i	$-0.480102\pi$
$587$	3.02702	0.124939	0.0624693	+	0.998047i	$0.480102\pi$
$588$	−49.9582	−2.06024
$589$	1.07984	0.0444942
$590$	−37.3080	−1.53595
$591$	38.5979	1.58771
$592$	−71.2797	−2.92958
$593$	7.56863	0.310806	0.155403	−	0.987851i	$-0.450332\pi$
$593$	7.56863	0.310806	0.155403	+	0.987851i	$0.450332\pi$
$594$	−4.80040	−0.196963
$595$	−41.6441	−1.70724
$596$	22.7615	0.932347
$597$	−42.8467	−1.75360
$598$	−21.8880	−0.895069
$599$	8.64686	0.353301	0.176650	−	0.984274i	$-0.443474\pi$
$599$	8.64686	0.353301	0.176650	+	0.984274i	$0.443474\pi$
$600$	−107.591	−4.39240
$601$	−46.5010	−1.89682	−0.948408	−	0.317052i	$-0.897307\pi$
$601$	−46.5010	−1.89682	−0.948408	+	0.317052i	$0.897307\pi$
$602$	−3.85944	−0.157299
$603$	17.3417	0.706209
$604$	−54.0834	−2.20062
$605$	71.5560	2.90917
$606$	−26.3273	−1.06948
$607$	41.6496	1.69051	0.845253	−	0.534366i	$-0.179450\pi$
$607$	41.6496	1.69051	0.845253	+	0.534366i	$0.179450\pi$
$608$	1.10178	0.0446829
$609$	−4.03457	−0.163489
$610$	−9.45576	−0.382852
$611$	8.20598	0.331978
$612$	110.187	4.45404
$613$	−14.2524	−0.575648	−0.287824	−	0.957683i	$-0.592932\pi$
$613$	−14.2524	−0.575648	−0.287824	+	0.957683i	$0.592932\pi$
$614$	−57.2734	−2.31137
$615$	31.6203	1.27505
$616$	62.9683	2.53706
$617$	39.6431	1.59597	0.797985	−	0.602678i	$-0.205900\pi$
$617$	39.6431	1.59597	0.797985	+	0.602678i	$0.205900\pi$
$618$	99.7049	4.01072
$619$	−49.4481	−1.98749	−0.993743	−	0.111693i	$-0.964373\pi$
$619$	−49.4481	−1.98749	−0.993743	+	0.111693i	$0.964373\pi$
$620$	−117.946	−4.73683
$621$	1.66423	0.0667832
$622$	−77.8230	−3.12042
$623$	23.3840	0.936860
$624$	34.2825	1.37240
$625$	−16.1956	−0.647823
$626$	7.23124	0.289018
$627$	−2.01514	−0.0804771
$628$	−28.4735	−1.13622
$629$	−65.3378	−2.60519
$630$	44.3713	1.76779
$631$	23.4562	0.933776	0.466888	−	0.884317i	$-0.345375\pi$
$631$	23.4562	0.933776	0.466888	+	0.884317i	$0.345375\pi$
$632$	36.5272	1.45297
$633$	−14.8170	−0.588922
$634$	16.3125	0.647852
$635$	67.3771	2.67378
$636$	−70.4110	−2.79198
$637$	−7.27786	−0.288359
$638$	−14.6273	−0.579102
$639$	45.1648	1.78669
$640$	23.3943	0.924742
$641$	17.5948	0.694954	0.347477	−	0.937689i	$-0.387039\pi$
$641$	17.5948	0.694954	0.347477	+	0.937689i	$0.387039\pi$
$642$	116.494	4.59764
$643$	−16.6251	−0.655628	−0.327814	−	0.944742i	$-0.606312\pi$
$643$	−16.6251	−0.655628	−0.327814	+	0.944742i	$0.606312\pi$
$644$	−38.3540	−1.51136
$645$	−7.67854	−0.302342
$646$	2.79990	0.110161
$647$	26.0792	1.02528	0.512639	−	0.858604i	$-0.328668\pi$
$647$	26.0792	1.02528	0.512639	+	0.858604i	$0.328668\pi$
$648$	58.4616	2.29659
$649$	24.3545	0.955997
$650$	−27.5376	−1.08012
$651$	30.3863	1.19093
$652$	−79.6451	−3.11914
$653$	24.8300	0.971672	0.485836	−	0.874050i	$-0.338515\pi$
$653$	24.8300	0.971672	0.485836	+	0.874050i	$0.338515\pi$
$654$	−49.1111	−1.92040
$655$	19.9387	0.779071
$656$	31.2882	1.22160
$657$	32.2630	1.25870
$658$	20.5740	0.802060
$659$	−6.47610	−0.252273	−0.126137	−	0.992013i	$-0.540258\pi$
$659$	−6.47610	−0.252273	−0.126137	+	0.992013i	$0.540258\pi$
$660$	220.104	8.56755
$661$	−21.5392	−0.837776	−0.418888	−	0.908038i	$-0.637580\pi$
$661$	−21.5392	−0.837776	−0.418888	+	0.908038i	$0.637580\pi$
$662$	63.8189	2.48039
$663$	31.4247	1.22044
$664$	−36.2624	−1.40725
$665$	0.788005	0.0305575
$666$	69.6166	2.69759
$667$	5.07109	0.196353
$668$	61.5067	2.37976
$669$	−50.5205	−1.95323
$670$	−48.1313	−1.85947
$671$	6.17267	0.238293
$672$	31.0035	1.19599
$673$	−13.5702	−0.523092	−0.261546	−	0.965191i	$-0.584232\pi$
$673$	−13.5702	−0.523092	−0.261546	+	0.965191i	$0.584232\pi$
$674$	55.7705	2.14820
$675$	2.09379	0.0805900
$676$	−47.3292	−1.82035
$677$	28.9866	1.11405	0.557023	−	0.830497i	$-0.311943\pi$
$677$	28.9866	1.11405	0.557023	+	0.830497i	$0.311943\pi$
$678$	−109.115	−4.19053
$679$	13.5835	0.521287
$680$	−174.066	−6.67511
$681$	−43.2531	−1.65746
$682$	110.166	4.21846
$683$	4.71763	0.180515	0.0902576	−	0.995918i	$-0.471231\pi$
$683$	4.71763	0.180515	0.0902576	+	0.995918i	$0.471231\pi$
$684$	−2.08500	−0.0797219
$685$	−21.9096	−0.837122
$686$	−47.6394	−1.81888
$687$	17.1759	0.655302
$688$	−7.59790	−0.289667
$689$	−10.2574	−0.390775
$690$	−109.182	−4.15648
$691$	−37.8367	−1.43937	−0.719687	−	0.694298i	$-0.755715\pi$
$691$	−37.8367	−1.43937	−0.719687	+	0.694298i	$0.755715\pi$
$692$	−36.6532	−1.39334
$693$	−28.9654	−1.10030
$694$	12.2419	0.464697
$695$	−10.8484	−0.411504
$696$	−16.8639	−0.639223
$697$	28.6801	1.08633
$698$	−15.0498	−0.569642
$699$	−2.55210	−0.0965292
$700$	−48.2536	−1.82382
$701$	−6.06572	−0.229099	−0.114550	−	0.993418i	$-0.536542\pi$
$701$	−6.06572	−0.229099	−0.114550	+	0.993418i	$0.536542\pi$
$702$	−1.41651	−0.0534625
$703$	1.23635	0.0466297
$704$	18.5731	0.699999
$705$	40.9330	1.54163
$706$	70.7560	2.66294
$707$	−6.72058	−0.252753
$708$	49.3313	1.85399
$709$	−11.5440	−0.433542	−0.216771	−	0.976222i	$-0.569553\pi$
$709$	−11.5440	−0.433542	−0.216771	+	0.976222i	$0.569553\pi$
$710$	−125.353	−4.70442
$711$	−16.8025	−0.630142
$712$	97.7413	3.66301
$713$	−38.1928	−1.43033
$714$	78.7881	2.94857
$715$	32.0646	1.19915
$716$	−56.5196	−2.11224
$717$	13.9462	0.520831
$718$	46.6238	1.73999
$719$	−15.6883	−0.585075	−0.292537	−	0.956254i	$-0.594500\pi$
$719$	−15.6883	−0.585075	−0.292537	+	0.956254i	$0.594500\pi$
$720$	87.3517	3.25540
$721$	25.4517	0.947870
$722$	48.9150	1.82043
$723$	−58.2282	−2.16553
$724$	93.5036	3.47503
$725$	6.38000	0.236947
$726$	−135.380	−5.02441
$727$	−9.92460	−0.368083	−0.184041	−	0.982918i	$-0.558918\pi$
$727$	−9.92460	−0.368083	−0.184041	+	0.982918i	$0.558918\pi$
$728$	18.5807	0.688647
$729$	−29.3304	−1.08631
$730$	−89.5448	−3.31420
$731$	−6.96454	−0.257593
$732$	12.5031	0.462127
$733$	8.63081	0.318786	0.159393	−	0.987215i	$-0.449046\pi$
$733$	8.63081	0.318786	0.159393	+	0.987215i	$0.449046\pi$
$734$	−86.8905	−3.20719
$735$	−36.3034	−1.33907
$736$	−38.9686	−1.43640
$737$	31.4199	1.15737
$738$	−30.5582	−1.12486
$739$	−20.2487	−0.744859	−0.372430	−	0.928060i	$-0.621475\pi$
$739$	−20.2487	−0.744859	−0.372430	+	0.928060i	$0.621475\pi$
$740$	−135.040	−4.96417
$741$	−0.594630	−0.0218443
$742$	−25.7173	−0.944113
$743$	19.1780	0.703572	0.351786	−	0.936080i	$-0.385574\pi$
$743$	19.1780	0.703572	0.351786	+	0.936080i	$0.385574\pi$
$744$	127.010	4.65641
$745$	16.5402	0.605986
$746$	31.9611	1.17018
$747$	16.6807	0.610314
$748$	199.638	7.29948
$749$	29.7374	1.08658
$750$	−29.7118	−1.08492
$751$	49.0858	1.79117	0.895584	−	0.444892i	$-0.146758\pi$
$751$	49.0858	1.79117	0.895584	+	0.444892i	$0.146758\pi$
$752$	40.5032	1.47700
$753$	−49.4735	−1.80291
$754$	−4.31624	−0.157188
$755$	−39.3010	−1.43031
$756$	−2.48211	−0.0902735
$757$	15.3383	0.557478	0.278739	−	0.960367i	$-0.410084\pi$
$757$	15.3383	0.557478	0.278739	+	0.960367i	$0.410084\pi$
$758$	63.7381	2.31507
$759$	71.2734	2.58706
$760$	3.29373	0.119476
$761$	19.8641	0.720072	0.360036	−	0.932938i	$-0.382764\pi$
$761$	19.8641	0.720072	0.360036	+	0.932938i	$0.382764\pi$
$762$	−127.473	−4.61787
$763$	−12.5366	−0.453855
$764$	33.6474	1.21732
$765$	80.0701	2.89494
$766$	−46.8562	−1.69298
$767$	7.18653	0.259491
$768$	−60.4685	−2.18197
$769$	−23.2573	−0.838679	−0.419339	−	0.907830i	$-0.637738\pi$
$769$	−23.2573	−0.838679	−0.419339	+	0.907830i	$0.637738\pi$
$770$	80.3923	2.89714
$771$	38.2030	1.37585
$772$	−127.047	−4.57253
$773$	41.3809	1.48837	0.744184	−	0.667975i	$-0.232839\pi$
$773$	41.3809	1.48837	0.744184	+	0.667975i	$0.232839\pi$
$774$	7.42063	0.266729
$775$	−48.0509	−1.72604
$776$	56.7768	2.03817
$777$	34.7903	1.24809
$778$	−0.238655	−0.00855620
$779$	−0.542694	−0.0194440
$780$	64.9485	2.32553
$781$	81.8299	2.92811
$782$	−99.0294	−3.54129
$783$	0.328180	0.0117282
$784$	−35.9221	−1.28293
$785$	−20.6909	−0.738492
$786$	−37.7229	−1.34553
$787$	23.1613	0.825612	0.412806	−	0.910819i	$-0.364549\pi$
$787$	23.1613	0.825612	0.412806	+	0.910819i	$0.364549\pi$
$788$	72.3562	2.57758
$789$	1.41548	0.0503925
$790$	46.6347	1.65919
$791$	−27.8537	−0.990364
$792$	−121.070	−4.30205
$793$	1.82144	0.0646811
$794$	25.6785	0.911294
$795$	−51.1659	−1.81467
$796$	−80.3209	−2.84690
$797$	47.0338	1.66602	0.833011	−	0.553257i	$-0.186615\pi$
$797$	47.0338	1.66602	0.833011	+	0.553257i	$0.186615\pi$
$798$	−1.49086	−0.0527758
$799$	37.1268	1.31345
$800$	−49.0269	−1.73336
$801$	−44.9609	−1.58862
$802$	−11.2988	−0.398975
$803$	58.4544	2.06281
$804$	63.6427	2.24450
$805$	−27.8708	−0.982318
$806$	32.5077	1.14504
$807$	8.23438	0.289864
$808$	−28.0909	−0.988235
$809$	−39.9419	−1.40428	−0.702142	−	0.712037i	$-0.747773\pi$
$809$	−39.9419	−1.40428	−0.702142	+	0.712037i	$0.747773\pi$
$810$	74.6386	2.62253
$811$	20.4709	0.718831	0.359415	−	0.933178i	$-0.382976\pi$
$811$	20.4709	0.718831	0.359415	+	0.933178i	$0.382976\pi$
$812$	−7.56326	−0.265418
$813$	40.3410	1.41482
$814$	126.132	4.42092
$815$	−57.8761	−2.02731
$816$	155.107	5.42981
$817$	0.131786	0.00461059
$818$	−0.682569	−0.0238655
$819$	−8.54711	−0.298660
$820$	59.2758	2.07000
$821$	18.3225	0.639459	0.319730	−	0.947509i	$-0.396408\pi$
$821$	18.3225	0.639459	0.319730	+	0.947509i	$0.396408\pi$
$822$	41.4516	1.44579
$823$	38.2971	1.33495	0.667477	−	0.744631i	$-0.267374\pi$
$823$	38.2971	1.33495	0.667477	+	0.744631i	$0.267374\pi$
$824$	106.384	3.70606
$825$	89.6700	3.12191
$826$	18.0181	0.626929
$827$	−22.3223	−0.776223	−0.388111	−	0.921613i	$-0.626872\pi$
$827$	−22.3223	−0.776223	−0.388111	+	0.921613i	$0.626872\pi$
$828$	73.7440	2.56278
$829$	−47.2274	−1.64028	−0.820138	−	0.572166i	$-0.806103\pi$
$829$	−47.2274	−1.64028	−0.820138	+	0.572166i	$0.806103\pi$
$830$	−46.2966	−1.60698
$831$	−2.47639	−0.0859051
$832$	5.48056	0.190004
$833$	−32.9277	−1.14088
$834$	20.5246	0.710707
$835$	44.6953	1.54675
$836$	−3.77762	−0.130652
$837$	−2.47168	−0.0854339
$838$	65.0453	2.24695
$839$	0.00260916	9.00782e−5 0	4.50391e−5	−	1.00000i	$-0.499986\pi$
$839$	0.00260916	9.00782e−5 0	4.50391e−5		1.00000i	$0.499986\pi$
$840$	92.6843	3.19791
$841$	1.00000	0.0344828
$842$	−86.1066	−2.96743
$843$	−18.9522	−0.652748
$844$	−27.7761	−0.956093
$845$	−34.3929	−1.18315
$846$	−39.5582	−1.36004
$847$	−34.5583	−1.18744
$848$	−50.6285	−1.73859
$849$	58.2066	1.99765
$850$	−124.590	−4.27341
$851$	−43.7282	−1.49898
$852$	165.751	5.67854
$853$	−54.6881	−1.87248	−0.936242	−	0.351356i	$-0.885721\pi$
$853$	−54.6881	−1.87248	−0.936242	+	0.351356i	$0.885721\pi$
$854$	4.56670	0.156269
$855$	−1.51511	−0.0518158
$856$	124.297	4.24839
$857$	55.1798	1.88490	0.942452	−	0.334340i	$-0.108513\pi$
$857$	55.1798	1.88490	0.942452	+	0.334340i	$0.108513\pi$
$858$	−60.6642	−2.07104
$859$	18.1561	0.619477	0.309739	−	0.950822i	$-0.399758\pi$
$859$	18.1561	0.619477	0.309739	+	0.950822i	$0.399758\pi$
$860$	−14.3943	−0.490841
$861$	−15.2712	−0.520441
$862$	40.9208	1.39377
$863$	−12.0837	−0.411335	−0.205668	−	0.978622i	$-0.565937\pi$
$863$	−12.0837	−0.411335	−0.205668	+	0.978622i	$0.565937\pi$
$864$	−2.52189	−0.0857964
$865$	−26.6349	−0.905615
$866$	28.2951	0.961506
$867$	100.078	3.39883
$868$	56.9626	1.93344
$869$	−30.4429	−1.03270
$870$	−21.5303	−0.729944
$871$	9.27139	0.314149
$872$	−52.4009	−1.77452
$873$	−26.1173	−0.883936
$874$	1.87387	0.0633846
$875$	−7.58454	−0.256404
$876$	118.403	4.00046
$877$	46.0251	1.55416	0.777079	−	0.629404i	$-0.216701\pi$
$877$	46.0251	1.55416	0.777079	+	0.629404i	$0.216701\pi$
$878$	−56.8792	−1.91958
$879$	−53.1811	−1.79375
$880$	158.265	5.33510
$881$	−10.1857	−0.343165	−0.171582	−	0.985170i	$-0.554888\pi$
$881$	−10.1857	−0.343165	−0.171582	+	0.985170i	$0.554888\pi$
$882$	35.0840	1.18134
$883$	−16.2962	−0.548411	−0.274205	−	0.961671i	$-0.588415\pi$
$883$	−16.2962	−0.548411	−0.274205	+	0.961671i	$0.588415\pi$
$884$	58.9092	1.98133
$885$	35.8478	1.20501
$886$	−38.3633	−1.28884
$887$	44.7261	1.50175	0.750877	−	0.660442i	$-0.229631\pi$
$887$	44.7261	1.50175	0.750877	+	0.660442i	$0.229631\pi$
$888$	145.418	4.87989
$889$	−32.5401	−1.09136
$890$	124.787	4.18288
$891$	−48.7237	−1.63231
$892$	−94.7063	−3.17100
$893$	−0.702527	−0.0235092
$894$	−31.2930	−1.04660
$895$	−41.0714	−1.37286
$896$	−11.2984	−0.377453
$897$	21.0314	0.702218
$898$	38.9585	1.30006
$899$	−7.53149	−0.251189
$900$	92.7783	3.09261
$901$	−46.4082	−1.54608
$902$	−55.3657	−1.84347
$903$	3.70839	0.123407
$904$	−116.424	−3.87220
$905$	67.9467	2.25862
$906$	74.3551	2.47028
$907$	5.55865	0.184572	0.0922860	−	0.995733i	$-0.470583\pi$
$907$	5.55865	0.184572	0.0922860	+	0.995733i	$0.470583\pi$
$908$	−81.0829	−2.69083
$909$	12.9218	0.428589
$910$	23.7222	0.786383
$911$	−8.68033	−0.287592	−0.143796	−	0.989607i	$-0.545931\pi$
$911$	−8.68033	−0.287592	−0.143796	+	0.989607i	$0.545931\pi$
$912$	−2.93498	−0.0971869
$913$	30.2222	1.00021
$914$	−8.33646	−0.275746
$915$	9.08568	0.300363
$916$	32.1982	1.06386
$917$	−9.62952	−0.317995
$918$	−6.40878	−0.211521
$919$	26.7228	0.881503	0.440751	−	0.897629i	$-0.354712\pi$
$919$	26.7228	0.881503	0.440751	+	0.897629i	$0.354712\pi$
$920$	−116.496	−3.84075
$921$	55.0318	1.81336
$922$	19.9679	0.657609
$923$	24.1464	0.794789
$924$	−106.301	−3.49703
$925$	−55.0150	−1.80888
$926$	−2.50251	−0.0822375
$927$	−48.9365	−1.60729
$928$	−7.68446	−0.252255
$929$	−37.1136	−1.21766	−0.608828	−	0.793302i	$-0.708360\pi$
$929$	−37.1136	−1.21766	−0.608828	+	0.793302i	$0.708360\pi$
$930$	162.155	5.31727
$931$	0.623069	0.0204203
$932$	−4.78420	−0.156712
$933$	74.7772	2.44809
$934$	38.6825	1.26573
$935$	145.072	4.74435
$936$	−35.7255	−1.16773
$937$	−35.4084	−1.15674	−0.578371	−	0.815774i	$-0.696311\pi$
$937$	−35.4084	−1.15674	−0.578371	+	0.815774i	$0.696311\pi$
$938$	23.2452	0.758984
$939$	−6.94822	−0.226747
$940$	76.7336	2.50277
$941$	−31.4943	−1.02668	−0.513342	−	0.858184i	$-0.671593\pi$
$941$	−31.4943	−1.02668	−0.513342	+	0.858184i	$0.671593\pi$
$942$	39.1460	1.27545
$943$	19.1945	0.625058
$944$	35.4714	1.15449
$945$	−1.80369	−0.0586740
$946$	13.4448	0.437127
$947$	21.6531	0.703632	0.351816	−	0.936069i	$-0.385564\pi$
$947$	21.6531	0.703632	0.351816	+	0.936069i	$0.385564\pi$
$948$	−61.6638	−2.00275
$949$	17.2488	0.559919
$950$	2.35754	0.0764888
$951$	−15.6741	−0.508266
$952$	84.0659	2.72459
$953$	−30.2423	−0.979643	−0.489822	−	0.871823i	$-0.662938\pi$
$953$	−30.2423	−0.979643	−0.489822	+	0.871823i	$0.662938\pi$
$954$	49.4473	1.60091
$955$	24.4507	0.791207
$956$	26.1438	0.845550
$957$	14.0549	0.454329
$958$	−2.99940	−0.0969062
$959$	10.5813	0.341689
$960$	27.3381	0.882333
$961$	25.7233	0.829785
$962$	37.2191	1.19999
$963$	−57.1767	−1.84249
$964$	−109.155	−3.51566
$965$	−92.3219	−2.97195
$966$	52.7299	1.69656
$967$	16.7533	0.538750	0.269375	−	0.963035i	$-0.413183\pi$
$967$	16.7533	0.538750	0.269375	+	0.963035i	$0.413183\pi$
$968$	−144.448	−4.64274
$969$	−2.69032	−0.0864256
$970$	72.4875	2.32743
$971$	38.4905	1.23522	0.617610	−	0.786485i	$-0.288101\pi$
$971$	38.4905	1.23522	0.617610	+	0.786485i	$0.288101\pi$
$972$	−103.263	−3.31216
$973$	5.23930	0.167964
$974$	−22.7619	−0.729339
$975$	26.4599	0.847394
$976$	8.99026	0.287771
$977$	25.7441	0.823628	0.411814	−	0.911268i	$-0.364895\pi$
$977$	25.7441	0.823628	0.411814	+	0.911268i	$0.364895\pi$
$978$	109.498	3.50136
$979$	−81.4606	−2.60349
$980$	−68.0548	−2.17393
$981$	24.1044	0.769593
$982$	−59.7842	−1.90779
$983$	51.8030	1.65226	0.826130	−	0.563480i	$-0.190538\pi$
$983$	51.8030	1.65226	0.826130	+	0.563480i	$0.190538\pi$
$984$	−63.8311	−2.03486
$985$	52.5794	1.67532
$986$	−19.5282	−0.621906
$987$	−19.7688	−0.629248
$988$	−1.11470	−0.0354634
$989$	−4.66110	−0.148214
$990$	−154.572	−4.91262
$991$	25.7519	0.818036	0.409018	−	0.912526i	$-0.365871\pi$
$991$	25.7519	0.818036	0.409018	+	0.912526i	$0.365871\pi$
$992$	57.8754	1.83755
$993$	−61.3211	−1.94597
$994$	60.5399	1.92021
$995$	−58.3672	−1.85036
$996$	61.2168	1.93973
$997$	20.4746	0.648438	0.324219	−	0.945982i	$-0.394898\pi$
$997$	20.4746	0.648438	0.324219	+	0.945982i	$0.394898\pi$
$998$	5.65898	0.179132
$999$	−2.82991	−0.0895343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.8	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.57726 q^{2} +2.47639 q^{3} +4.64228 q^{4} +3.37343 q^{5} -6.38231 q^{6} -1.62921 q^{7} -6.80985 q^{8} +3.13252 q^{9} +O(q^{10})\)	\(q-2.57726 q^{2} +2.47639 q^{3} +4.64228 q^{4} +3.37343 q^{5} -6.38231 q^{6} -1.62921 q^{7} -6.80985 q^{8} +3.13252 q^{9} -8.69420 q^{10} +5.67553 q^{11} +11.4961 q^{12} +1.67474 q^{13} +4.19891 q^{14} +8.35393 q^{15} +8.26620 q^{16} +7.57713 q^{17} -8.07333 q^{18} -0.143377 q^{19} +15.6604 q^{20} -4.03457 q^{21} -14.6273 q^{22} +5.07109 q^{23} -16.8639 q^{24} +6.38000 q^{25} -4.31624 q^{26} +0.328180 q^{27} -7.56326 q^{28} +1.00000 q^{29} -21.5303 q^{30} -7.53149 q^{31} -7.68446 q^{32} +14.0549 q^{33} -19.5282 q^{34} -5.49603 q^{35} +14.5420 q^{36} -8.62303 q^{37} +0.369521 q^{38} +4.14731 q^{39} -22.9725 q^{40} +3.78508 q^{41} +10.3981 q^{42} -0.919153 q^{43} +26.3474 q^{44} +10.5673 q^{45} -13.0695 q^{46} +4.89985 q^{47} +20.4704 q^{48} -4.34566 q^{49} -16.4429 q^{50} +18.7640 q^{51} +7.77461 q^{52} -6.12477 q^{53} -0.845806 q^{54} +19.1460 q^{55} +11.0947 q^{56} -0.355058 q^{57} -2.57726 q^{58} +4.29113 q^{59} +38.7813 q^{60} +1.08759 q^{61} +19.4106 q^{62} -5.10355 q^{63} +3.27248 q^{64} +5.64961 q^{65} -36.2230 q^{66} +5.53602 q^{67} +35.1752 q^{68} +12.5580 q^{69} +14.1647 q^{70} +14.4180 q^{71} -21.3320 q^{72} +10.2994 q^{73} +22.2238 q^{74} +15.7994 q^{75} -0.665597 q^{76} -9.24665 q^{77} -10.6887 q^{78} -5.36388 q^{79} +27.8854 q^{80} -8.58487 q^{81} -9.75515 q^{82} +5.32500 q^{83} -18.7296 q^{84} +25.5609 q^{85} +2.36890 q^{86} +2.47639 q^{87} -38.6495 q^{88} -14.3529 q^{89} -27.2348 q^{90} -2.72851 q^{91} +23.5414 q^{92} -18.6509 q^{93} -12.6282 q^{94} -0.483672 q^{95} -19.0298 q^{96} -8.33746 q^{97} +11.1999 q^{98} +17.7787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 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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