LMFDB - Embedded newform 8041.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70525 q^{2} -2.86444 q^{3} +5.31840 q^{4} +1.46004 q^{5} +7.74904 q^{6} -3.90191 q^{7} -8.97712 q^{8} +5.20501 q^{9} +O(q^{10})$	\(q-2.70525 q^{2} -2.86444 q^{3} +5.31840 q^{4} +1.46004 q^{5} +7.74904 q^{6} -3.90191 q^{7} -8.97712 q^{8} +5.20501 q^{9} -3.94978 q^{10} +1.00000 q^{11} -15.2342 q^{12} -2.79985 q^{13} +10.5557 q^{14} -4.18220 q^{15} +13.6486 q^{16} +1.00000 q^{17} -14.0809 q^{18} +0.0854401 q^{19} +7.76508 q^{20} +11.1768 q^{21} -2.70525 q^{22} +2.41012 q^{23} +25.7144 q^{24} -2.86828 q^{25} +7.57432 q^{26} -6.31612 q^{27} -20.7519 q^{28} -3.04090 q^{29} +11.3139 q^{30} +10.3818 q^{31} -18.9686 q^{32} -2.86444 q^{33} -2.70525 q^{34} -5.69695 q^{35} +27.6823 q^{36} +8.69439 q^{37} -0.231137 q^{38} +8.02001 q^{39} -13.1070 q^{40} +3.21483 q^{41} -30.2360 q^{42} +1.00000 q^{43} +5.31840 q^{44} +7.59953 q^{45} -6.51998 q^{46} +5.14653 q^{47} -39.0955 q^{48} +8.22490 q^{49} +7.75943 q^{50} -2.86444 q^{51} -14.8907 q^{52} -8.25146 q^{53} +17.0867 q^{54} +1.46004 q^{55} +35.0279 q^{56} -0.244738 q^{57} +8.22640 q^{58} -1.57918 q^{59} -22.2426 q^{60} +4.41140 q^{61} -28.0854 q^{62} -20.3095 q^{63} +24.0179 q^{64} -4.08790 q^{65} +7.74904 q^{66} +11.0950 q^{67} +5.31840 q^{68} -6.90364 q^{69} +15.4117 q^{70} -6.21684 q^{71} -46.7260 q^{72} -13.0490 q^{73} -23.5205 q^{74} +8.21601 q^{75} +0.454405 q^{76} -3.90191 q^{77} -21.6962 q^{78} -13.3929 q^{79} +19.9275 q^{80} +2.47710 q^{81} -8.69693 q^{82} +4.11226 q^{83} +59.4426 q^{84} +1.46004 q^{85} -2.70525 q^{86} +8.71046 q^{87} -8.97712 q^{88} +2.09674 q^{89} -20.5587 q^{90} +10.9248 q^{91} +12.8180 q^{92} -29.7380 q^{93} -13.9227 q^{94} +0.124746 q^{95} +54.3345 q^{96} -8.47364 q^{97} -22.2504 q^{98} +5.20501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * 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 $

$2$	−2.70525	−1.91290	−0.956452	−	0.291890i	$-0.905716\pi$
$2$	−2.70525	−1.91290	−0.956452	+	0.291890i	$0.905716\pi$
$3$	−2.86444	−1.65378	−0.826892	−	0.562360i	$-0.809893\pi$
$3$	−2.86444	−1.65378	−0.826892	+	0.562360i	$0.809893\pi$
$4$	5.31840	2.65920
$5$	1.46004	0.652950	0.326475	−	0.945206i	$-0.394139\pi$
$5$	1.46004	0.652950	0.326475	+	0.945206i	$0.394139\pi$
$6$	7.74904	3.16353
$7$	−3.90191	−1.47478	−0.737392	−	0.675466i	$-0.763943\pi$
$7$	−3.90191	−1.47478	−0.737392	+	0.675466i	$0.763943\pi$
$8$	−8.97712	−3.17389
$9$	5.20501	1.73500
$10$	−3.94978	−1.24903
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−15.2342	−4.39774
$13$	−2.79985	−0.776540	−0.388270	−	0.921546i	$-0.626927\pi$
$13$	−2.79985	−0.776540	−0.388270	+	0.921546i	$0.626927\pi$
$14$	10.5557	2.82112
$15$	−4.18220	−1.07984
$16$	13.6486	3.41215
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−14.0809	−3.31889
$19$	0.0854401	0.0196013	0.00980066	−	0.999952i	$-0.496880\pi$
$19$	0.0854401	0.0196013	0.00980066	+	0.999952i	$0.496880\pi$
$20$	7.76508	1.73633
$21$	11.1768	2.43897
$22$	−2.70525	−0.576762
$23$	2.41012	0.502544	0.251272	−	0.967916i	$-0.419151\pi$
$23$	2.41012	0.502544	0.251272	+	0.967916i	$0.419151\pi$
$24$	25.7144	5.24893
$25$	−2.86828	−0.573656
$26$	7.57432	1.48545
$27$	−6.31612	−1.21554
$28$	−20.7519	−3.92174
$29$	−3.04090	−0.564680	−0.282340	−	0.959314i	$-0.591111\pi$
$29$	−3.04090	−0.564680	−0.282340	+	0.959314i	$0.591111\pi$
$30$	11.3139	2.06563
$31$	10.3818	1.86463	0.932313	−	0.361652i	$-0.117787\pi$
$31$	10.3818	1.86463	0.932313	+	0.361652i	$0.117787\pi$
$32$	−18.9686	−3.35322
$33$	−2.86444	−0.498635
$34$	−2.70525	−0.463947
$35$	−5.69695	−0.962960
$36$	27.6823	4.61372
$37$	8.69439	1.42935	0.714675	−	0.699457i	$-0.246575\pi$
$37$	8.69439	1.42935	0.714675	+	0.699457i	$0.246575\pi$
$38$	−0.231137	−0.0374954
$39$	8.02001	1.28423
$40$	−13.1070	−2.07239
$41$	3.21483	0.502072	0.251036	−	0.967978i	$-0.419229\pi$
$41$	3.21483	0.502072	0.251036	+	0.967978i	$0.419229\pi$
$42$	−30.2360	−4.66552
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.31840	0.801779
$45$	7.59953	1.13287
$46$	−6.51998	−0.961319
$47$	5.14653	0.750698	0.375349	−	0.926884i	$-0.377523\pi$
$47$	5.14653	0.750698	0.375349	+	0.926884i	$0.377523\pi$
$48$	−39.0955	−5.64295
$49$	8.22490	1.17499
$50$	7.75943	1.09735
$51$	−2.86444	−0.401102
$52$	−14.8907	−2.06497
$53$	−8.25146	−1.13342	−0.566712	−	0.823916i	$-0.691785\pi$
$53$	−8.25146	−1.13342	−0.566712	+	0.823916i	$0.691785\pi$
$54$	17.0867	2.32521
$55$	1.46004	0.196872
$56$	35.0279	4.68080
$57$	−0.244738	−0.0324163
$58$	8.22640	1.08018
$59$	−1.57918	−0.205592	−0.102796	−	0.994702i	$-0.532779\pi$
$59$	−1.57918	−0.205592	−0.102796	+	0.994702i	$0.532779\pi$
$60$	−22.2426	−2.87151
$61$	4.41140	0.564822	0.282411	−	0.959293i	$-0.408866\pi$
$61$	4.41140	0.564822	0.282411	+	0.959293i	$0.408866\pi$
$62$	−28.0854	−3.56685
$63$	−20.3095	−2.55875
$64$	24.0179	3.00223
$65$	−4.08790	−0.507042
$66$	7.74904	0.953840
$67$	11.0950	1.35547	0.677737	−	0.735305i	$-0.262961\pi$
$67$	11.0950	1.35547	0.677737	+	0.735305i	$0.262961\pi$
$68$	5.31840	0.644951
$69$	−6.90364	−0.831100
$70$	15.4117	1.84205
$71$	−6.21684	−0.737803	−0.368901	−	0.929469i	$-0.620266\pi$
$71$	−6.21684	−0.737803	−0.368901	+	0.929469i	$0.620266\pi$
$72$	−46.7260	−5.50671
$73$	−13.0490	−1.52727	−0.763636	−	0.645647i	$-0.776588\pi$
$73$	−13.0490	−1.52727	−0.763636	+	0.645647i	$0.776588\pi$
$74$	−23.5205	−2.73421
$75$	8.21601	0.948703
$76$	0.454405	0.0521238
$77$	−3.90191	−0.444664
$78$	−21.6962	−2.45661
$79$	−13.3929	−1.50681	−0.753407	−	0.657554i	$-0.771591\pi$
$79$	−13.3929	−1.50681	−0.753407	+	0.657554i	$0.771591\pi$
$80$	19.9275	2.22796
$81$	2.47710	0.275233
$82$	−8.69693	−0.960416
$83$	4.11226	0.451379	0.225690	−	0.974199i	$-0.427536\pi$
$83$	4.11226	0.451379	0.225690	+	0.974199i	$0.427536\pi$
$84$	59.4426	6.48572
$85$	1.46004	0.158364
$86$	−2.70525	−0.291715
$87$	8.71046	0.933860
$88$	−8.97712	−0.956964
$89$	2.09674	0.222254	0.111127	−	0.993806i	$-0.464554\pi$
$89$	2.09674	0.222254	0.111127	+	0.993806i	$0.464554\pi$
$90$	−20.5587	−2.16707
$91$	10.9248	1.14523
$92$	12.8180	1.33637
$93$	−29.7380	−3.08369
$94$	−13.9227	−1.43601
$95$	0.124746	0.0127987
$96$	54.3345	5.54550
$97$	−8.47364	−0.860368	−0.430184	−	0.902741i	$-0.641551\pi$
$97$	−8.47364	−0.860368	−0.430184	+	0.902741i	$0.641551\pi$
$98$	−22.2504	−2.24763
$99$	5.20501	0.523123
$100$	−15.2547	−1.52547
$101$	−10.8536	−1.07997	−0.539986	−	0.841674i	$-0.681570\pi$
$101$	−10.8536	−1.07997	−0.539986	+	0.841674i	$0.681570\pi$
$102$	7.74904	0.767269
$103$	18.9072	1.86298	0.931492	−	0.363762i	$-0.118508\pi$
$103$	18.9072	1.86298	0.931492	+	0.363762i	$0.118508\pi$
$104$	25.1346	2.46465
$105$	16.3186	1.59253
$106$	22.3223	2.16813
$107$	12.1714	1.17665	0.588325	−	0.808625i	$-0.299788\pi$
$107$	12.1714	1.17665	0.588325	+	0.808625i	$0.299788\pi$
$108$	−33.5916	−3.23236
$109$	8.96218	0.858421	0.429211	−	0.903204i	$-0.358792\pi$
$109$	8.96218	0.858421	0.429211	+	0.903204i	$0.358792\pi$
$110$	−3.94978	−0.376597
$111$	−24.9046	−2.36384
$112$	−53.2555	−5.03217
$113$	15.6036	1.46786	0.733930	−	0.679226i	$-0.237684\pi$
$113$	15.6036	1.46786	0.733930	+	0.679226i	$0.237684\pi$
$114$	0.662079	0.0620094
$115$	3.51887	0.328136
$116$	−16.1727	−1.50160
$117$	−14.5733	−1.34730
$118$	4.27209	0.393277
$119$	−3.90191	−0.357687
$120$	37.5441	3.42729
$121$	1.00000	0.0909091
$122$	−11.9340	−1.08045
$123$	−9.20869	−0.830319
$124$	55.2146	4.95842
$125$	−11.4880	−1.02752
$126$	54.9423	4.89465
$127$	−4.09351	−0.363240	−0.181620	−	0.983369i	$-0.558134\pi$
$127$	−4.09351	−0.363240	−0.181620	+	0.983369i	$0.558134\pi$
$128$	−27.0371	−2.38977
$129$	−2.86444	−0.252200
$130$	11.0588	0.969922
$131$	5.03598	0.439996	0.219998	−	0.975500i	$-0.429395\pi$
$131$	5.03598	0.439996	0.219998	+	0.975500i	$0.429395\pi$
$132$	−15.2342	−1.32597
$133$	−0.333380	−0.0289077
$134$	−30.0149	−2.59289
$135$	−9.22179	−0.793685
$136$	−8.97712	−0.769781
$137$	−19.0186	−1.62487	−0.812436	−	0.583050i	$-0.801859\pi$
$137$	−19.0186	−1.62487	−0.812436	+	0.583050i	$0.801859\pi$
$138$	18.6761	1.58981
$139$	14.1586	1.20092	0.600460	−	0.799655i	$-0.294984\pi$
$139$	14.1586	1.20092	0.600460	+	0.799655i	$0.294984\pi$
$140$	−30.2986	−2.56070
$141$	−14.7419	−1.24149
$142$	16.8181	1.41135
$143$	−2.79985	−0.234136
$144$	71.0410	5.92008
$145$	−4.43983	−0.368708
$146$	35.3009	2.92152
$147$	−23.5597	−1.94317
$148$	46.2403	3.80093
$149$	5.96756	0.488882	0.244441	−	0.969664i	$-0.421396\pi$
$149$	5.96756	0.488882	0.244441	+	0.969664i	$0.421396\pi$
$150$	−22.2264	−1.81478
$151$	−1.83128	−0.149028	−0.0745138	−	0.997220i	$-0.523740\pi$
$151$	−1.83128	−0.149028	−0.0745138	+	0.997220i	$0.523740\pi$
$152$	−0.767006	−0.0622124
$153$	5.20501	0.420800
$154$	10.5557	0.850599
$155$	15.1579	1.21751
$156$	42.6536	3.41502
$157$	−13.6927	−1.09280	−0.546400	−	0.837524i	$-0.684002\pi$
$157$	−13.6927	−1.09280	−0.546400	+	0.837524i	$0.684002\pi$
$158$	36.2311	2.88239
$159$	23.6358	1.87444
$160$	−27.6950	−2.18948
$161$	−9.40406	−0.741144
$162$	−6.70118	−0.526494
$163$	−10.9932	−0.861057	−0.430528	−	0.902577i	$-0.641673\pi$
$163$	−10.9932	−0.861057	−0.430528	+	0.902577i	$0.641673\pi$
$164$	17.0978	1.33511
$165$	−4.18220	−0.325584
$166$	−11.1247	−0.863445
$167$	−0.717479	−0.0555202	−0.0277601	−	0.999615i	$-0.508837\pi$
$167$	−0.717479	−0.0555202	−0.0277601	+	0.999615i	$0.508837\pi$
$168$	−100.335	−7.74103
$169$	−5.16082	−0.396986
$170$	−3.94978	−0.302934
$171$	0.444717	0.0340083
$172$	5.31840	0.405524
$173$	14.3090	1.08790	0.543948	−	0.839119i	$-0.316929\pi$
$173$	14.3090	1.08790	0.543948	+	0.839119i	$0.316929\pi$
$174$	−23.5640	−1.78638
$175$	11.1918	0.846018
$176$	13.6486	1.02880
$177$	4.52347	0.340005
$178$	−5.67222	−0.425151
$179$	21.7483	1.62554	0.812772	−	0.582582i	$-0.197958\pi$
$179$	21.7483	1.62554	0.812772	+	0.582582i	$0.197958\pi$
$180$	40.4173	3.01253
$181$	−2.64099	−0.196303	−0.0981515	−	0.995171i	$-0.531293\pi$
$181$	−2.64099	−0.196303	−0.0981515	+	0.995171i	$0.531293\pi$
$182$	−29.5543	−2.19071
$183$	−12.6362	−0.934094
$184$	−21.6359	−1.59502
$185$	12.6942	0.933294
$186$	80.4489	5.89880
$187$	1.00000	0.0731272
$188$	27.3713	1.99626
$189$	24.6449	1.79265
$190$	−0.337470	−0.0244826
$191$	13.3372	0.965049	0.482525	−	0.875882i	$-0.339720\pi$
$191$	13.3372	0.965049	0.482525	+	0.875882i	$0.339720\pi$
$192$	−68.7977	−4.96504
$193$	−4.69011	−0.337602	−0.168801	−	0.985650i	$-0.553989\pi$
$193$	−4.69011	−0.337602	−0.168801	+	0.985650i	$0.553989\pi$
$194$	22.9234	1.64580
$195$	11.7095	0.838538
$196$	43.7433	3.12452
$197$	−5.93508	−0.422857	−0.211428	−	0.977393i	$-0.567812\pi$
$197$	−5.93508	−0.422857	−0.211428	+	0.977393i	$0.567812\pi$
$198$	−14.0809	−1.00068
$199$	−1.90194	−0.134825	−0.0674124	−	0.997725i	$-0.521474\pi$
$199$	−1.90194	−0.134825	−0.0674124	+	0.997725i	$0.521474\pi$
$200$	25.7489	1.82072
$201$	−31.7810	−2.24166
$202$	29.3617	2.06588
$203$	11.8653	0.832781
$204$	−15.2342	−1.06661
$205$	4.69378	0.327828
$206$	−51.1488	−3.56371
$207$	12.5447	0.871916
$208$	−38.2140	−2.64967
$209$	0.0854401	0.00591002
$210$	−44.1458	−3.04635
$211$	−23.3274	−1.60593	−0.802963	−	0.596028i	$-0.796745\pi$
$211$	−23.3274	−1.60593	−0.802963	+	0.596028i	$0.796745\pi$
$212$	−43.8845	−3.01400
$213$	17.8077	1.22017
$214$	−32.9266	−2.25082
$215$	1.46004	0.0995740
$216$	56.7005	3.85798
$217$	−40.5088	−2.74992
$218$	−24.2450	−1.64208
$219$	37.3781	2.52578
$220$	7.76508	0.523522
$221$	−2.79985	−0.188339
$222$	67.3731	4.52179
$223$	0.170281	0.0114029	0.00570144	−	0.999984i	$-0.498185\pi$
$223$	0.170281	0.0114029	0.00570144	+	0.999984i	$0.498185\pi$
$224$	74.0139	4.94527
$225$	−14.9294	−0.995295
$226$	−42.2116	−2.80787
$227$	−13.9926	−0.928721	−0.464360	−	0.885646i	$-0.653716\pi$
$227$	−13.9926	−0.928721	−0.464360	+	0.885646i	$0.653716\pi$
$228$	−1.30162	−0.0862016
$229$	−10.3592	−0.684554	−0.342277	−	0.939599i	$-0.611198\pi$
$229$	−10.3592	−0.684554	−0.342277	+	0.939599i	$0.611198\pi$
$230$	−9.51944	−0.627693
$231$	11.1768	0.735378
$232$	27.2985	1.79223
$233$	21.2870	1.39455	0.697277	−	0.716801i	$-0.254395\pi$
$233$	21.2870	1.39455	0.697277	+	0.716801i	$0.254395\pi$
$234$	39.4244	2.57725
$235$	7.51414	0.490168
$236$	−8.39872	−0.546710
$237$	38.3630	2.49195
$238$	10.5557	0.684222
$239$	18.4546	1.19373	0.596866	−	0.802341i	$-0.296413\pi$
$239$	18.4546	1.19373	0.596866	+	0.802341i	$0.296413\pi$
$240$	−57.0811	−3.68457
$241$	11.8870	0.765706	0.382853	−	0.923809i	$-0.374942\pi$
$241$	11.8870	0.765706	0.382853	+	0.923809i	$0.374942\pi$
$242$	−2.70525	−0.173900
$243$	11.8529	0.760361
$244$	23.4616	1.50198
$245$	12.0087	0.767207
$246$	24.9118	1.58832
$247$	−0.239220	−0.0152212
$248$	−93.1986	−5.91812
$249$	−11.7793	−0.746484
$250$	31.0780	1.96554
$251$	3.39419	0.214239	0.107120	−	0.994246i	$-0.465837\pi$
$251$	3.39419	0.214239	0.107120	+	0.994246i	$0.465837\pi$
$252$	−108.014	−6.80424
$253$	2.41012	0.151523
$254$	11.0740	0.694844
$255$	−4.18220	−0.261899
$256$	25.1065	1.56916
$257$	−17.9527	−1.11986	−0.559930	−	0.828540i	$-0.689172\pi$
$257$	−17.9527	−1.11986	−0.559930	+	0.828540i	$0.689172\pi$
$258$	7.74904	0.482434
$259$	−33.9247	−2.10798
$260$	−21.7411	−1.34833
$261$	−15.8279	−0.979722
$262$	−13.6236	−0.841670
$263$	15.7554	0.971522	0.485761	−	0.874092i	$-0.338543\pi$
$263$	15.7554	0.971522	0.485761	+	0.874092i	$0.338543\pi$
$264$	25.7144	1.58261
$265$	−12.0475	−0.740070
$266$	0.901877	0.0552976
$267$	−6.00599	−0.367560
$268$	59.0078	3.60447
$269$	−5.23879	−0.319415	−0.159707	−	0.987164i	$-0.551055\pi$
$269$	−5.23879	−0.319415	−0.159707	+	0.987164i	$0.551055\pi$
$270$	24.9473	1.51824
$271$	21.1346	1.28384	0.641918	−	0.766773i	$-0.278139\pi$
$271$	21.1346	1.28384	0.641918	+	0.766773i	$0.278139\pi$
$272$	13.6486	0.827567
$273$	−31.2934	−1.89396
$274$	51.4503	3.10822
$275$	−2.86828	−0.172964
$276$	−36.7163	−2.21006
$277$	−20.3154	−1.22063	−0.610316	−	0.792158i	$-0.708958\pi$
$277$	−20.3154	−1.22063	−0.610316	+	0.792158i	$0.708958\pi$
$278$	−38.3027	−2.29725
$279$	54.0374	3.23513
$280$	51.1422	3.05633
$281$	11.7689	0.702076	0.351038	−	0.936361i	$-0.385829\pi$
$281$	11.7689	0.702076	0.351038	+	0.936361i	$0.385829\pi$
$282$	39.8806	2.37486
$283$	−19.3526	−1.15039	−0.575195	−	0.818016i	$-0.695074\pi$
$283$	−19.3526	−1.15039	−0.575195	+	0.818016i	$0.695074\pi$
$284$	−33.0636	−1.96196
$285$	−0.357328	−0.0211663
$286$	7.57432	0.447879
$287$	−12.5440	−0.740448
$288$	−98.7320	−5.81784
$289$	1.00000	0.0588235
$290$	12.0109	0.705303
$291$	24.2722	1.42286
$292$	−69.3999	−4.06132
$293$	−1.26343	−0.0738103	−0.0369051	−	0.999319i	$-0.511750\pi$
$293$	−1.26343	−0.0738103	−0.0369051	+	0.999319i	$0.511750\pi$
$294$	63.7350	3.71710
$295$	−2.30567	−0.134241
$296$	−78.0506	−4.53660
$297$	−6.31612	−0.366498
$298$	−16.1438	−0.935183
$299$	−6.74798	−0.390246
$300$	43.6960	2.52279
$301$	−3.90191	−0.224902
$302$	4.95408	0.285075
$303$	31.0894	1.78604
$304$	1.16614	0.0668825
$305$	6.44083	0.368801
$306$	−14.0809	−0.804950
$307$	−17.3585	−0.990701	−0.495351	−	0.868693i	$-0.664960\pi$
$307$	−17.3585	−0.990701	−0.495351	+	0.868693i	$0.664960\pi$
$308$	−20.7519	−1.18245
$309$	−54.1586	−3.08097
$310$	−41.0059	−2.32898
$311$	−4.55666	−0.258384	−0.129192	−	0.991620i	$-0.541238\pi$
$311$	−4.55666	−0.258384	−0.129192	+	0.991620i	$0.541238\pi$
$312$	−71.9966	−4.07600
$313$	−22.5999	−1.27742	−0.638711	−	0.769447i	$-0.720532\pi$
$313$	−22.5999	−1.27742	−0.638711	+	0.769447i	$0.720532\pi$
$314$	37.0423	2.09042
$315$	−29.6527	−1.67074
$316$	−71.2286	−4.00692
$317$	−20.3039	−1.14038	−0.570189	−	0.821513i	$-0.693130\pi$
$317$	−20.3039	−1.14038	−0.570189	+	0.821513i	$0.693130\pi$
$318$	−63.9408	−3.58562
$319$	−3.04090	−0.170258
$320$	35.0671	1.96031
$321$	−34.8641	−1.94592
$322$	25.4404	1.41774
$323$	0.0854401	0.00475402
$324$	13.1742	0.731900
$325$	8.03077	0.445467
$326$	29.7395	1.64712
$327$	−25.6716	−1.41964
$328$	−28.8599	−1.59352
$329$	−20.0813	−1.10712
$330$	11.3139	0.622810
$331$	−10.0546	−0.552650	−0.276325	−	0.961064i	$-0.589117\pi$
$331$	−10.0546	−0.552650	−0.276325	+	0.961064i	$0.589117\pi$
$332$	21.8707	1.20031
$333$	45.2544	2.47993
$334$	1.94096	0.106205
$335$	16.1992	0.885057
$336$	152.547	8.32213
$337$	−8.61303	−0.469182	−0.234591	−	0.972094i	$-0.575375\pi$
$337$	−8.61303	−0.469182	−0.234591	+	0.972094i	$0.575375\pi$
$338$	13.9613	0.759396
$339$	−44.6954	−2.42752
$340$	7.76508	0.421121
$341$	10.3818	0.562206
$342$	−1.20307	−0.0650547
$343$	−4.77943	−0.258065
$344$	−8.97712	−0.484014
$345$	−10.0796	−0.542667
$346$	−38.7096	−2.08104
$347$	2.19565	0.117869	0.0589343	−	0.998262i	$-0.481230\pi$
$347$	2.19565	0.117869	0.0589343	+	0.998262i	$0.481230\pi$
$348$	46.3257	2.48332
$349$	−14.0518	−0.752174	−0.376087	−	0.926584i	$-0.622731\pi$
$349$	−14.0518	−0.752174	−0.376087	+	0.926584i	$0.622731\pi$
$350$	−30.2766	−1.61835
$351$	17.6842	0.943913
$352$	−18.9686	−1.01103
$353$	−10.2950	−0.547950	−0.273975	−	0.961737i	$-0.588339\pi$
$353$	−10.2950	−0.547950	−0.273975	+	0.961737i	$0.588339\pi$
$354$	−12.2371	−0.650396
$355$	−9.07683	−0.481748
$356$	11.1513	0.591018
$357$	11.1768	0.591538
$358$	−58.8347	−3.10951
$359$	−31.1739	−1.64529	−0.822647	−	0.568553i	$-0.807503\pi$
$359$	−31.1739	−1.64529	−0.822647	+	0.568553i	$0.807503\pi$
$360$	−68.2218	−3.59561
$361$	−18.9927	−0.999616
$362$	7.14454	0.375509
$363$	−2.86444	−0.150344
$364$	58.1023	3.04539
$365$	−19.0521	−0.997233
$366$	34.1841	1.78683
$367$	−24.1619	−1.26124	−0.630620	−	0.776092i	$-0.717199\pi$
$367$	−24.1619	−1.26124	−0.630620	+	0.776092i	$0.717199\pi$
$368$	32.8947	1.71475
$369$	16.7332	0.871097
$370$	−34.3410	−1.78530
$371$	32.1964	1.67156
$372$	−158.159	−8.20015
$373$	2.28471	0.118298	0.0591488	−	0.998249i	$-0.481161\pi$
$373$	2.28471	0.118298	0.0591488	+	0.998249i	$0.481161\pi$
$374$	−2.70525	−0.139885
$375$	32.9067	1.69930
$376$	−46.2010	−2.38263
$377$	8.51407	0.438497
$378$	−66.6707	−3.42917
$379$	−23.1819	−1.19077	−0.595387	−	0.803439i	$-0.703001\pi$
$379$	−23.1819	−1.19077	−0.595387	+	0.803439i	$0.703001\pi$
$380$	0.663450	0.0340343
$381$	11.7256	0.600721
$382$	−36.0806	−1.84605
$383$	−21.3515	−1.09101	−0.545504	−	0.838108i	$-0.683662\pi$
$383$	−21.3515	−1.09101	−0.545504	+	0.838108i	$0.683662\pi$
$384$	77.4461	3.95216
$385$	−5.69695	−0.290343
$386$	12.6879	0.645799
$387$	5.20501	0.264586
$388$	−45.0662	−2.28789
$389$	15.3077	0.776129	0.388065	−	0.921632i	$-0.373144\pi$
$389$	15.3077	0.776129	0.388065	+	0.921632i	$0.373144\pi$
$390$	−31.6773	−1.60404
$391$	2.41012	0.121885
$392$	−73.8358	−3.72927
$393$	−14.4253	−0.727659
$394$	16.0559	0.808885
$395$	−19.5541	−0.983875
$396$	27.6823	1.39109
$397$	15.0866	0.757175	0.378588	−	0.925565i	$-0.376410\pi$
$397$	15.0866	0.757175	0.378588	+	0.925565i	$0.376410\pi$
$398$	5.14522	0.257907
$399$	0.954946	0.0478071
$400$	−39.1480	−1.95740
$401$	15.0482	0.751471	0.375736	−	0.926727i	$-0.377390\pi$
$401$	15.0482	0.751471	0.375736	+	0.926727i	$0.377390\pi$
$402$	85.9758	4.28808
$403$	−29.0675	−1.44796
$404$	−57.7237	−2.87186
$405$	3.61666	0.179713
$406$	−32.0987	−1.59303
$407$	8.69439	0.430965
$408$	25.7144	1.27305
$409$	14.0337	0.693922	0.346961	−	0.937880i	$-0.387214\pi$
$409$	14.0337	0.693922	0.346961	+	0.937880i	$0.387214\pi$
$410$	−12.6979	−0.627104
$411$	54.4777	2.68719
$412$	100.556	4.95405
$413$	6.16182	0.303203
$414$	−33.9366	−1.66789
$415$	6.00407	0.294728
$416$	53.1095	2.60391
$417$	−40.5566	−1.98606
$418$	−0.231137	−0.0113053
$419$	−4.61075	−0.225250	−0.112625	−	0.993638i	$-0.535926\pi$
$419$	−4.61075	−0.225250	−0.112625	+	0.993638i	$0.535926\pi$
$420$	86.7886	4.23485
$421$	−11.8350	−0.576802	−0.288401	−	0.957510i	$-0.593124\pi$
$421$	−11.8350	−0.576802	−0.288401	+	0.957510i	$0.593124\pi$
$422$	63.1066	3.07198
$423$	26.7877	1.30246
$424$	74.0743	3.59737
$425$	−2.86828	−0.139132
$426$	−48.1745	−2.33406
$427$	−17.2129	−0.832990
$428$	64.7322	3.12895
$429$	8.02001	0.387210
$430$	−3.94978	−0.190475
$431$	30.1359	1.45160	0.725799	−	0.687907i	$-0.241470\pi$
$431$	30.1359	1.45160	0.725799	+	0.687907i	$0.241470\pi$
$432$	−86.2060	−4.14759
$433$	16.5008	0.792978	0.396489	−	0.918039i	$-0.370228\pi$
$433$	16.5008	0.792978	0.396489	+	0.918039i	$0.370228\pi$
$434$	109.587	5.26033
$435$	12.7176	0.609764
$436$	47.6645	2.28271
$437$	0.205921	0.00985053
$438$	−101.117	−4.83157
$439$	−36.3938	−1.73698	−0.868491	−	0.495705i	$-0.834910\pi$
$439$	−36.3938	−1.73698	−0.868491	+	0.495705i	$0.834910\pi$
$440$	−13.1070	−0.624850
$441$	42.8107	2.03860
$442$	7.57432	0.360274
$443$	20.5084	0.974382	0.487191	−	0.873295i	$-0.338022\pi$
$443$	20.5084	0.974382	0.487191	+	0.873295i	$0.338022\pi$
$444$	−132.452	−6.28591
$445$	3.06133	0.145121
$446$	−0.460654	−0.0218126
$447$	−17.0937	−0.808505
$448$	−93.7155	−4.42764
$449$	25.1863	1.18862	0.594308	−	0.804238i	$-0.297426\pi$
$449$	25.1863	1.18862	0.594308	+	0.804238i	$0.297426\pi$
$450$	40.3879	1.90390
$451$	3.21483	0.151380
$452$	82.9860	3.90333
$453$	5.24560	0.246460
$454$	37.8535	1.77655
$455$	15.9506	0.747777
$456$	2.19704	0.102886
$457$	−24.2591	−1.13479	−0.567397	−	0.823444i	$-0.692050\pi$
$457$	−24.2591	−1.13479	−0.567397	+	0.823444i	$0.692050\pi$
$458$	28.0242	1.30949
$459$	−6.31612	−0.294811
$460$	18.7148	0.872580
$461$	−5.33259	−0.248363	−0.124182	−	0.992259i	$-0.539631\pi$
$461$	−5.33259	−0.248363	−0.124182	+	0.992259i	$0.539631\pi$
$462$	−30.2360	−1.40671
$463$	39.9014	1.85438	0.927188	−	0.374595i	$-0.122218\pi$
$463$	39.9014	1.85438	0.927188	+	0.374595i	$0.122218\pi$
$464$	−41.5039	−1.92677
$465$	−43.4188	−2.01350
$466$	−57.5866	−2.66765
$467$	32.5132	1.50453	0.752267	−	0.658859i	$-0.228960\pi$
$467$	32.5132	1.50453	0.752267	+	0.658859i	$0.228960\pi$
$468$	−77.5065	−3.58274
$469$	−43.2918	−1.99903
$470$	−20.3277	−0.937645
$471$	39.2220	1.80726
$472$	14.1765	0.652526
$473$	1.00000	0.0459800
$474$	−103.782	−4.76685
$475$	−0.245066	−0.0112444
$476$	−20.7519	−0.951162
$477$	−42.9489	−1.96650
$478$	−49.9245	−2.28349
$479$	11.1410	0.509044	0.254522	−	0.967067i	$-0.418082\pi$
$479$	11.1410	0.509044	0.254522	+	0.967067i	$0.418082\pi$
$480$	79.3307	3.62093
$481$	−24.3430	−1.10995
$482$	−32.1572	−1.46472
$483$	26.9374	1.22569
$484$	5.31840	0.241745
$485$	−12.3719	−0.561778
$486$	−32.0650	−1.45450
$487$	−20.6799	−0.937096	−0.468548	−	0.883438i	$-0.655223\pi$
$487$	−20.6799	−0.937096	−0.468548	+	0.883438i	$0.655223\pi$
$488$	−39.6017	−1.79268
$489$	31.4895	1.42400
$490$	−32.4865	−1.46759
$491$	−30.4785	−1.37548	−0.687738	−	0.725959i	$-0.741396\pi$
$491$	−30.4785	−1.37548	−0.687738	+	0.725959i	$0.741396\pi$
$492$	−48.9755	−2.20798
$493$	−3.04090	−0.136955
$494$	0.647151	0.0291167
$495$	7.59953	0.341573
$496$	141.697	6.36238
$497$	24.2575	1.08810
$498$	31.8661	1.42795
$499$	−9.37777	−0.419807	−0.209903	−	0.977722i	$-0.567315\pi$
$499$	−9.37777	−0.419807	−0.209903	+	0.977722i	$0.567315\pi$
$500$	−61.0978	−2.73238
$501$	2.05517	0.0918184
$502$	−9.18214	−0.409819
$503$	0.115930	0.00516908	0.00258454	−	0.999997i	$-0.499177\pi$
$503$	0.115930	0.00516908	0.00258454	+	0.999997i	$0.499177\pi$
$504$	182.321	8.12120
$505$	−15.8467	−0.705168
$506$	−6.51998	−0.289849
$507$	14.7828	0.656529
$508$	−21.7709	−0.965929
$509$	13.4272	0.595150	0.297575	−	0.954698i	$-0.403822\pi$
$509$	13.4272	0.595150	0.297575	+	0.954698i	$0.403822\pi$
$510$	11.3139	0.500988
$511$	50.9161	2.25240
$512$	−13.8453	−0.611884
$513$	−0.539650	−0.0238261
$514$	48.5666	2.14218
$515$	27.6053	1.21644
$516$	−15.2342	−0.670650
$517$	5.14653	0.226344
$518$	91.7750	4.03236
$519$	−40.9873	−1.79914
$520$	36.6976	1.60930
$521$	−37.5304	−1.64424	−0.822119	−	0.569316i	$-0.807208\pi$
$521$	−37.5304	−1.64424	−0.822119	+	0.569316i	$0.807208\pi$
$522$	42.8185	1.87411
$523$	30.8897	1.35071	0.675356	−	0.737492i	$-0.263990\pi$
$523$	30.8897	1.35071	0.675356	+	0.737492i	$0.263990\pi$
$524$	26.7834	1.17004
$525$	−32.0581	−1.39913
$526$	−42.6225	−1.85843
$527$	10.3818	0.452238
$528$	−39.0955	−1.70141
$529$	−17.1913	−0.747449
$530$	32.5915	1.41568
$531$	−8.21965	−0.356703
$532$	−1.77305	−0.0768713
$533$	−9.00106	−0.389879
$534$	16.2477	0.703108
$535$	17.7707	0.768294
$536$	−99.6013	−4.30212
$537$	−62.2967	−2.68830
$538$	14.1723	0.611010
$539$	8.22490	0.354271
$540$	−49.0452	−2.11057
$541$	−11.2165	−0.482233	−0.241117	−	0.970496i	$-0.577514\pi$
$541$	−11.2165	−0.482233	−0.241117	+	0.970496i	$0.577514\pi$
$542$	−57.1745	−2.45585
$543$	7.56494	0.324643
$544$	−18.9686	−0.813274
$545$	13.0852	0.560506
$546$	84.6565	3.62296
$547$	38.1870	1.63276	0.816379	−	0.577517i	$-0.195978\pi$
$547$	38.1870	1.63276	0.816379	+	0.577517i	$0.195978\pi$
$548$	−101.149	−4.32086
$549$	22.9614	0.979968
$550$	7.75943	0.330863
$551$	−0.259815	−0.0110685
$552$	61.9747	2.63782
$553$	52.2577	2.22222
$554$	54.9583	2.33495
$555$	−36.3617	−1.54347
$556$	75.3013	3.19349
$557$	−19.7566	−0.837114	−0.418557	−	0.908190i	$-0.637464\pi$
$557$	−19.7566	−0.837114	−0.418557	+	0.908190i	$0.637464\pi$
$558$	−146.185	−6.18850
$559$	−2.79985	−0.118421
$560$	−77.7553	−3.28576
$561$	−2.86444	−0.120937
$562$	−31.8380	−1.34300
$563$	34.7217	1.46335	0.731673	−	0.681655i	$-0.238740\pi$
$563$	34.7217	1.46335	0.731673	+	0.681655i	$0.238740\pi$
$564$	−78.4034	−3.30138
$565$	22.7818	0.958439
$566$	52.3536	2.20059
$567$	−9.66541	−0.405909
$568$	55.8093	2.34170
$569$	6.48624	0.271917	0.135959	−	0.990715i	$-0.456589\pi$
$569$	6.48624	0.271917	0.135959	+	0.990715i	$0.456589\pi$
$570$	0.966662	0.0404890
$571$	−21.4098	−0.895973	−0.447987	−	0.894040i	$-0.647859\pi$
$571$	−21.4098	−0.895973	−0.447987	+	0.894040i	$0.647859\pi$
$572$	−14.8907	−0.622613
$573$	−38.2037	−1.59598
$574$	33.9346	1.41640
$575$	−6.91289	−0.288288
$576$	125.013	5.20888
$577$	24.2099	1.00787	0.503936	−	0.863741i	$-0.331885\pi$
$577$	24.2099	1.00787	0.503936	+	0.863741i	$0.331885\pi$
$578$	−2.70525	−0.112524
$579$	13.4345	0.558320
$580$	−23.6128	−0.980469
$581$	−16.0457	−0.665687
$582$	−65.6626	−2.72180
$583$	−8.25146	−0.341740
$584$	117.143	4.84739
$585$	−21.2776	−0.879719
$586$	3.41789	0.141192
$587$	−14.3756	−0.593346	−0.296673	−	0.954979i	$-0.595877\pi$
$587$	−14.3756	−0.593346	−0.296673	+	0.954979i	$0.595877\pi$
$588$	−125.300	−5.16728
$589$	0.887023	0.0365491
$590$	6.23742	0.256791
$591$	17.0007	0.699314
$592$	118.666	4.87715
$593$	−12.6413	−0.519117	−0.259559	−	0.965727i	$-0.583577\pi$
$593$	−12.6413	−0.519117	−0.259559	+	0.965727i	$0.583577\pi$
$594$	17.0867	0.701076
$595$	−5.69695	−0.233552
$596$	31.7379	1.30003
$597$	5.44798	0.222971
$598$	18.2550	0.746502
$599$	10.6326	0.434438	0.217219	−	0.976123i	$-0.430301\pi$
$599$	10.6326	0.434438	0.217219	+	0.976123i	$0.430301\pi$
$600$	−73.7561	−3.01108
$601$	30.4403	1.24169	0.620843	−	0.783935i	$-0.286790\pi$
$601$	30.4403	1.24169	0.620843	+	0.783935i	$0.286790\pi$
$602$	10.5557	0.430216
$603$	57.7497	2.35175
$604$	−9.73949	−0.396294
$605$	1.46004	0.0593591
$606$	−84.1048	−3.41652
$607$	29.3697	1.19208	0.596039	−	0.802955i	$-0.296740\pi$
$607$	29.3697	1.19208	0.596039	+	0.802955i	$0.296740\pi$
$608$	−1.62068	−0.0657274
$609$	−33.9874	−1.37724
$610$	−17.4241	−0.705480
$611$	−14.4095	−0.582947
$612$	27.6823	1.11899
$613$	−16.3021	−0.658438	−0.329219	−	0.944254i	$-0.606785\pi$
$613$	−16.3021	−0.658438	−0.329219	+	0.944254i	$0.606785\pi$
$614$	46.9591	1.89512
$615$	−13.4451	−0.542157
$616$	35.0279	1.41131
$617$	19.4734	0.783968	0.391984	−	0.919972i	$-0.371789\pi$
$617$	19.4734	0.783968	0.391984	+	0.919972i	$0.371789\pi$
$618$	146.513	5.89361
$619$	−25.0258	−1.00587	−0.502935	−	0.864324i	$-0.667747\pi$
$619$	−25.0258	−1.00587	−0.502935	+	0.864324i	$0.667747\pi$
$620$	80.6156	3.23760
$621$	−15.2226	−0.610861
$622$	12.3269	0.494264
$623$	−8.18129	−0.327777
$624$	109.462	4.38198
$625$	−2.43157	−0.0972628
$626$	61.1385	2.44359
$627$	−0.244738	−0.00977390
$628$	−72.8235	−2.90597
$629$	8.69439	0.346668
$630$	80.2180	3.19596
$631$	−36.8409	−1.46661	−0.733306	−	0.679898i	$-0.762024\pi$
$631$	−36.8409	−1.46661	−0.733306	+	0.679898i	$0.762024\pi$
$632$	120.229	4.78246
$633$	66.8200	2.65586
$634$	54.9271	2.18143
$635$	−5.97670	−0.237178
$636$	125.705	4.98451
$637$	−23.0285	−0.912423
$638$	8.22640	0.325686
$639$	−32.3587	−1.28009
$640$	−39.4753	−1.56040
$641$	16.6208	0.656484	0.328242	−	0.944594i	$-0.393544\pi$
$641$	16.6208	0.656484	0.328242	+	0.944594i	$0.393544\pi$
$642$	94.3163	3.72237
$643$	28.0723	1.10706	0.553532	−	0.832828i	$-0.313280\pi$
$643$	28.0723	1.10706	0.553532	+	0.832828i	$0.313280\pi$
$644$	−50.0146	−1.97085
$645$	−4.18220	−0.164674
$646$	−0.231137	−0.00909398
$647$	−43.4375	−1.70771	−0.853853	−	0.520514i	$-0.825740\pi$
$647$	−43.4375	−1.70771	−0.853853	+	0.520514i	$0.825740\pi$
$648$	−22.2372	−0.873559
$649$	−1.57918	−0.0619883
$650$	−21.7253	−0.852135
$651$	116.035	4.54777
$652$	−58.4664	−2.28972
$653$	42.0792	1.64669	0.823344	−	0.567543i	$-0.192106\pi$
$653$	42.0792	1.64669	0.823344	+	0.567543i	$0.192106\pi$
$654$	69.4483	2.71564
$655$	7.35274	0.287295
$656$	43.8779	1.71314
$657$	−67.9203	−2.64982
$658$	54.3250	2.11781
$659$	−36.7559	−1.43181	−0.715904	−	0.698199i	$-0.753985\pi$
$659$	−36.7559	−1.43181	−0.715904	+	0.698199i	$0.753985\pi$
$660$	−22.2426	−0.865792
$661$	33.7598	1.31310	0.656552	−	0.754281i	$-0.272014\pi$
$661$	33.7598	1.31310	0.656552	+	0.754281i	$0.272014\pi$
$662$	27.2002	1.05717
$663$	8.02001	0.311471
$664$	−36.9162	−1.43263
$665$	−0.486748	−0.0188753
$666$	−122.425	−4.74386
$667$	−7.32892	−0.283777
$668$	−3.81584	−0.147639
$669$	−0.487760	−0.0188579
$670$	−43.8229	−1.69303
$671$	4.41140	0.170300
$672$	−212.008	−8.17840
$673$	27.9838	1.07870	0.539348	−	0.842083i	$-0.318671\pi$
$673$	27.9838	1.07870	0.539348	+	0.842083i	$0.318671\pi$
$674$	23.3004	0.897500
$675$	18.1164	0.697300
$676$	−27.4473	−1.05566
$677$	22.1185	0.850082	0.425041	−	0.905174i	$-0.360260\pi$
$677$	22.1185	0.850082	0.425041	+	0.905174i	$0.360260\pi$
$678$	120.912	4.64362
$679$	33.0634	1.26886
$680$	−13.1070	−0.502629
$681$	40.0809	1.53590
$682$	−28.0854	−1.07545
$683$	−35.8050	−1.37004	−0.685019	−	0.728525i	$-0.740206\pi$
$683$	−35.8050	−1.37004	−0.685019	+	0.728525i	$0.740206\pi$
$684$	2.36518	0.0904350
$685$	−27.7680	−1.06096
$686$	12.9296	0.493654
$687$	29.6732	1.13210
$688$	13.6486	0.520347
$689$	23.1029	0.880149
$690$	27.2679	1.03807
$691$	−23.0727	−0.877727	−0.438864	−	0.898554i	$-0.644619\pi$
$691$	−23.0727	−0.877727	−0.438864	+	0.898554i	$0.644619\pi$
$692$	76.1011	2.89293
$693$	−20.3095	−0.771493
$694$	−5.93979	−0.225471
$695$	20.6722	0.784141
$696$	−78.1948	−2.96397
$697$	3.21483	0.121770
$698$	38.0136	1.43884
$699$	−60.9752	−2.30629
$700$	59.5223	2.24973
$701$	14.8196	0.559728	0.279864	−	0.960040i	$-0.409711\pi$
$701$	14.8196	0.559728	0.279864	+	0.960040i	$0.409711\pi$
$702$	−47.8403	−1.80561
$703$	0.742850	0.0280171
$704$	24.0179	0.905207
$705$	−21.5238	−0.810633
$706$	27.8507	1.04818
$707$	42.3497	1.59272
$708$	24.0576	0.904141
$709$	31.8550	1.19634	0.598170	−	0.801369i	$-0.295895\pi$
$709$	31.8550	1.19634	0.598170	+	0.801369i	$0.295895\pi$
$710$	24.5551	0.921538
$711$	−69.7100	−2.61433
$712$	−18.8227	−0.705410
$713$	25.0214	0.937058
$714$	−30.2360	−1.13156
$715$	−4.08790	−0.152879
$716$	115.666	4.32265
$717$	−52.8622	−1.97417
$718$	84.3332	3.14729
$719$	24.8189	0.925588	0.462794	−	0.886466i	$-0.346847\pi$
$719$	24.8189	0.925588	0.462794	+	0.886466i	$0.346847\pi$
$720$	103.723	3.86552
$721$	−73.7743	−2.74750
$722$	51.3801	1.91217
$723$	−34.0495	−1.26631
$724$	−14.0458	−0.522009
$725$	8.72214	0.323932
$726$	7.74904	0.287594
$727$	26.8024	0.994046	0.497023	−	0.867737i	$-0.334427\pi$
$727$	26.8024	0.994046	0.497023	+	0.867737i	$0.334427\pi$
$728$	−98.0730	−3.63483
$729$	−41.3831	−1.53271
$730$	51.5408	1.90761
$731$	1.00000	0.0369863
$732$	−67.2043	−2.48394
$733$	17.0206	0.628672	0.314336	−	0.949312i	$-0.398218\pi$
$733$	17.0206	0.628672	0.314336	+	0.949312i	$0.398218\pi$
$734$	65.3641	2.41263
$735$	−34.3981	−1.26879
$736$	−45.7167	−1.68514
$737$	11.0950	0.408691
$738$	−45.2676	−1.66632
$739$	−22.8259	−0.839665	−0.419832	−	0.907602i	$-0.637911\pi$
$739$	−22.8259	−0.839665	−0.419832	+	0.907602i	$0.637911\pi$
$740$	67.5127	2.48181
$741$	0.685231	0.0251726
$742$	−87.0995	−3.19752
$743$	23.8125	0.873594	0.436797	−	0.899560i	$-0.356113\pi$
$743$	23.8125	0.873594	0.436797	+	0.899560i	$0.356113\pi$
$744$	266.962	9.78730
$745$	8.71288	0.319215
$746$	−6.18072	−0.226292
$747$	21.4044	0.783145
$748$	5.31840	0.194460
$749$	−47.4915	−1.73530
$750$	−89.0210	−3.25059
$751$	−17.3823	−0.634289	−0.317144	−	0.948377i	$-0.602724\pi$
$751$	−17.3823	−0.634289	−0.317144	+	0.948377i	$0.602724\pi$
$752$	70.2428	2.56149
$753$	−9.72244	−0.354305
$754$	−23.0327	−0.838802
$755$	−2.67375	−0.0973076
$756$	131.071	4.76702
$757$	36.2301	1.31680	0.658402	−	0.752666i	$-0.271233\pi$
$757$	36.2301	1.31680	0.658402	+	0.752666i	$0.271233\pi$
$758$	62.7129	2.27784
$759$	−6.90364	−0.250586
$760$	−1.11986	−0.0406216
$761$	27.2543	0.987969	0.493984	−	0.869471i	$-0.335540\pi$
$761$	27.2543	0.987969	0.493984	+	0.869471i	$0.335540\pi$
$762$	−31.7208	−1.14912
$763$	−34.9696	−1.26599
$764$	70.9328	2.56626
$765$	7.59953	0.274762
$766$	57.7611	2.08699
$767$	4.42148	0.159650
$768$	−71.9161	−2.59505
$769$	26.8922	0.969759	0.484880	−	0.874581i	$-0.338863\pi$
$769$	26.8922	0.969759	0.484880	+	0.874581i	$0.338863\pi$
$770$	15.4117	0.555399
$771$	51.4244	1.85201
$772$	−24.9439	−0.897750
$773$	14.2146	0.511264	0.255632	−	0.966774i	$-0.417717\pi$
$773$	14.2146	0.511264	0.255632	+	0.966774i	$0.417717\pi$
$774$	−14.0809	−0.506127
$775$	−29.7779	−1.06965
$776$	76.0689	2.73071
$777$	97.1753	3.48614
$778$	−41.4111	−1.48466
$779$	0.274676	0.00984127
$780$	62.2761	2.22984
$781$	−6.21684	−0.222456
$782$	−6.51998	−0.233154
$783$	19.2067	0.686390
$784$	112.258	4.00922
$785$	−19.9920	−0.713544
$786$	39.0240	1.39194
$787$	33.6463	1.19936	0.599681	−	0.800239i	$-0.295294\pi$
$787$	33.6463	1.19936	0.599681	+	0.800239i	$0.295294\pi$
$788$	−31.5651	−1.12446
$789$	−45.1305	−1.60669
$790$	52.8989	1.88206
$791$	−60.8837	−2.16477
$792$	−46.7260	−1.66034
$793$	−12.3513	−0.438607
$794$	−40.8131	−1.44840
$795$	34.5092	1.22392
$796$	−10.1153	−0.358526
$797$	22.7785	0.806856	0.403428	−	0.915011i	$-0.367819\pi$
$797$	22.7785	0.806856	0.403428	+	0.915011i	$0.367819\pi$
$798$	−2.58337	−0.0914503
$799$	5.14653	0.182071
$800$	54.4074	1.92359
$801$	10.9136	0.385612
$802$	−40.7092	−1.43749
$803$	−13.0490	−0.460490
$804$	−169.024	−5.96102
$805$	−13.7303	−0.483930
$806$	78.6351	2.76980
$807$	15.0062	0.528243
$808$	97.4339	3.42771
$809$	−0.776410	−0.0272971	−0.0136486	−	0.999907i	$-0.504345\pi$
$809$	−0.776410	−0.0272971	−0.0136486	+	0.999907i	$0.504345\pi$
$810$	−9.78399	−0.343774
$811$	14.7897	0.519337	0.259669	−	0.965698i	$-0.416387\pi$
$811$	14.7897	0.519337	0.259669	+	0.965698i	$0.416387\pi$
$812$	63.1044	2.21453
$813$	−60.5388	−2.12319
$814$	−23.5205	−0.824394
$815$	−16.0506	−0.562227
$816$	−39.0955	−1.36862
$817$	0.0854401	0.00298917
$818$	−37.9647	−1.32741
$819$	56.8636	1.98697
$820$	24.9634	0.871761
$821$	−18.2421	−0.636653	−0.318327	−	0.947981i	$-0.603121\pi$
$821$	−18.2421	−0.636653	−0.318327	+	0.947981i	$0.603121\pi$
$822$	−147.376	−5.14033
$823$	−23.2228	−0.809496	−0.404748	−	0.914428i	$-0.632641\pi$
$823$	−23.2228	−0.809496	−0.404748	+	0.914428i	$0.632641\pi$
$824$	−169.732	−5.91291
$825$	8.21601	0.286045
$826$	−16.6693	−0.579999
$827$	−38.2993	−1.33180	−0.665899	−	0.746042i	$-0.731952\pi$
$827$	−38.2993	−1.33180	−0.665899	+	0.746042i	$0.731952\pi$
$828$	66.7177	2.31860
$829$	8.96084	0.311223	0.155611	−	0.987818i	$-0.450265\pi$
$829$	8.96084	0.311223	0.155611	+	0.987818i	$0.450265\pi$
$830$	−16.2425	−0.563787
$831$	58.1922	2.01866
$832$	−67.2465	−2.33135
$833$	8.22490	0.284976
$834$	109.716	3.79915
$835$	−1.04755	−0.0362519
$836$	0.454405	0.0157159
$837$	−65.5727	−2.26652
$838$	12.4732	0.430881
$839$	−38.2289	−1.31981	−0.659904	−	0.751349i	$-0.729403\pi$
$839$	−38.2289	−1.31981	−0.659904	+	0.751349i	$0.729403\pi$
$840$	−146.494	−5.05451
$841$	−19.7529	−0.681136
$842$	32.0166	1.10337
$843$	−33.7114	−1.16108
$844$	−124.065	−4.27048
$845$	−7.53500	−0.259212
$846$	−72.4676	−2.49149
$847$	−3.90191	−0.134071
$848$	−112.621	−3.86741
$849$	55.4342	1.90250
$850$	7.75943	0.266146
$851$	20.9545	0.718311
$852$	94.7087	3.24467
$853$	−50.1829	−1.71823	−0.859114	−	0.511784i	$-0.828985\pi$
$853$	−50.1829	−1.71823	−0.859114	+	0.511784i	$0.828985\pi$
$854$	46.5653	1.59343
$855$	0.649305	0.0222058
$856$	−109.264	−3.73456
$857$	45.4847	1.55373	0.776864	−	0.629669i	$-0.216809\pi$
$857$	45.4847	1.55373	0.776864	+	0.629669i	$0.216809\pi$
$858$	−21.6962	−0.740695
$859$	27.3259	0.932348	0.466174	−	0.884693i	$-0.345632\pi$
$859$	27.3259	0.932348	0.466174	+	0.884693i	$0.345632\pi$
$860$	7.76508	0.264787
$861$	35.9315	1.22454
$862$	−81.5254	−2.77677
$863$	−7.09436	−0.241495	−0.120747	−	0.992683i	$-0.538529\pi$
$863$	−7.09436	−0.241495	−0.120747	+	0.992683i	$0.538529\pi$
$864$	119.808	4.07596
$865$	20.8918	0.710341
$866$	−44.6389	−1.51689
$867$	−2.86444	−0.0972814
$868$	−215.442	−7.31259
$869$	−13.3929	−0.454322
$870$	−34.4044	−1.16642
$871$	−31.0645	−1.05258
$872$	−80.4545	−2.72453
$873$	−44.1054	−1.49274
$874$	−0.557068	−0.0188431
$875$	44.8252	1.51537
$876$	198.792	6.71655
$877$	49.8966	1.68489	0.842444	−	0.538784i	$-0.181116\pi$
$877$	49.8966	1.68489	0.842444	+	0.538784i	$0.181116\pi$
$878$	98.4545	3.32268
$879$	3.61901	0.122066
$880$	19.9275	0.671756
$881$	42.7205	1.43929	0.719645	−	0.694342i	$-0.244304\pi$
$881$	42.7205	1.43929	0.719645	+	0.694342i	$0.244304\pi$
$882$	−115.814	−3.89965
$883$	−16.1800	−0.544500	−0.272250	−	0.962227i	$-0.587768\pi$
$883$	−16.1800	−0.544500	−0.272250	+	0.962227i	$0.587768\pi$
$884$	−14.8907	−0.500830
$885$	6.60445	0.222006
$886$	−55.4804	−1.86390
$887$	−15.6534	−0.525589	−0.262794	−	0.964852i	$-0.584644\pi$
$887$	−15.6534	−0.525589	−0.262794	+	0.964852i	$0.584644\pi$
$888$	223.571	7.50255
$889$	15.9725	0.535701
$890$	−8.28167	−0.277602
$891$	2.47710	0.0829859
$892$	0.905624	0.0303225
$893$	0.439720	0.0147147
$894$	46.2428	1.54659
$895$	31.7534	1.06140
$896$	105.496	3.52439
$897$	19.3292	0.645382
$898$	−68.1354	−2.27371
$899$	−31.5700	−1.05292
$900$	−79.4007	−2.64669
$901$	−8.25146	−0.274896
$902$	−8.69693	−0.289576
$903$	11.1768	0.371940
$904$	−140.075	−4.65882
$905$	−3.85595	−0.128176
$906$	−14.1907	−0.471453
$907$	28.9493	0.961244	0.480622	−	0.876928i	$-0.340411\pi$
$907$	28.9493	0.961244	0.480622	+	0.876928i	$0.340411\pi$
$908$	−74.4182	−2.46965
$909$	−56.4930	−1.87375
$910$	−43.1505	−1.43042
$911$	19.4549	0.644569	0.322284	−	0.946643i	$-0.395549\pi$
$911$	19.4549	0.644569	0.322284	+	0.946643i	$0.395549\pi$
$912$	−3.34033	−0.110609
$913$	4.11226	0.136096
$914$	65.6271	2.17075
$915$	−18.4494	−0.609917
$916$	−55.0943	−1.82037
$917$	−19.6500	−0.648899
$918$	17.0867	0.563945
$919$	34.5423	1.13944	0.569722	−	0.821837i	$-0.307051\pi$
$919$	34.5423	1.13944	0.569722	+	0.821837i	$0.307051\pi$
$920$	−31.5893	−1.04147
$921$	49.7223	1.63841
$922$	14.4260	0.475095
$923$	17.4062	0.572933
$924$	59.4426	1.95552
$925$	−24.9379	−0.819955
$926$	−107.944	−3.54724
$927$	98.4123	3.23228
$928$	57.6817	1.89349
$929$	−20.7106	−0.679493	−0.339746	−	0.940517i	$-0.610341\pi$
$929$	−20.7106	−0.679493	−0.339746	+	0.940517i	$0.610341\pi$
$930$	117.459	3.85162
$931$	0.702736	0.0230313
$932$	113.213	3.70840
$933$	13.0523	0.427312
$934$	−87.9566	−2.87803
$935$	1.46004	0.0477484
$936$	130.826	4.27618
$937$	−41.4977	−1.35567	−0.677835	−	0.735214i	$-0.737082\pi$
$937$	−41.4977	−1.35567	−0.677835	+	0.735214i	$0.737082\pi$
$938$	117.115	3.82395
$939$	64.7360	2.11258
$940$	39.9632	1.30346
$941$	−3.43324	−0.111920	−0.0559602	−	0.998433i	$-0.517822\pi$
$941$	−3.43324	−0.111920	−0.0559602	+	0.998433i	$0.517822\pi$
$942$	−106.106	−3.45710
$943$	7.74812	0.252314
$944$	−21.5536	−0.701509
$945$	35.9826	1.17051
$946$	−2.70525	−0.0879554
$947$	32.4824	1.05554	0.527768	−	0.849388i	$-0.323029\pi$
$947$	32.4824	1.05554	0.527768	+	0.849388i	$0.323029\pi$
$948$	204.030	6.62658
$949$	36.5354	1.18599
$950$	0.662967	0.0215095
$951$	58.1592	1.88594
$952$	35.0279	1.13526
$953$	21.3202	0.690630	0.345315	−	0.938487i	$-0.387772\pi$
$953$	21.3202	0.690630	0.345315	+	0.938487i	$0.387772\pi$
$954$	116.188	3.76172
$955$	19.4729	0.630129
$956$	98.1491	3.17437
$957$	8.71046	0.281569
$958$	−30.1391	−0.973752
$959$	74.2090	2.39633
$960$	−100.447	−3.24193
$961$	76.7818	2.47683
$962$	65.8541	2.12322
$963$	63.3520	2.04149
$964$	63.2196	2.03617
$965$	−6.84775	−0.220437
$966$	−72.8724	−2.34463
$967$	15.3744	0.494409	0.247204	−	0.968963i	$-0.420488\pi$
$967$	15.3744	0.494409	0.247204	+	0.968963i	$0.420488\pi$
$968$	−8.97712	−0.288535
$969$	−0.244738	−0.00786212
$970$	33.4691	1.07463
$971$	6.79781	0.218152	0.109076	−	0.994033i	$-0.465211\pi$
$971$	6.79781	0.218152	0.109076	+	0.994033i	$0.465211\pi$
$972$	63.0382	2.02195
$973$	−55.2457	−1.77110
$974$	55.9444	1.79257
$975$	−23.0036	−0.736706
$976$	60.2094	1.92726
$977$	10.5447	0.337355	0.168678	−	0.985671i	$-0.446050\pi$
$977$	10.5447	0.337355	0.168678	+	0.985671i	$0.446050\pi$
$978$	−85.1870	−2.72398
$979$	2.09674	0.0670121
$980$	63.8670	2.04016
$981$	46.6482	1.48936
$982$	82.4521	2.63115
$983$	3.58198	0.114248	0.0571238	−	0.998367i	$-0.481807\pi$
$983$	3.58198	0.114248	0.0571238	+	0.998367i	$0.481807\pi$
$984$	82.6674	2.63534
$985$	−8.66546	−0.276105
$986$	8.22640	0.261982
$987$	57.5216	1.83093
$988$	−1.27227	−0.0404762
$989$	2.41012	0.0766373
$990$	−20.5587	−0.653397
$991$	−31.3561	−0.996059	−0.498029	−	0.867160i	$-0.665943\pi$
$991$	−31.3561	−0.996059	−0.498029	+	0.867160i	$0.665943\pi$
$992$	−196.929	−6.25249
$993$	28.8007	0.913963
$994$	−65.6228	−2.08143
$995$	−2.77691	−0.0880338
$996$	−62.6471	−1.98505
$997$	−49.7996	−1.57717	−0.788584	−	0.614927i	$-0.789186\pi$
$997$	−49.7996	−1.57717	−0.788584	+	0.614927i	$0.789186\pi$
$998$	25.3692	0.803050
$999$	−54.9148	−1.73743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.2	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.2	✓	82	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70525 q^{2} -2.86444 q^{3} +5.31840 q^{4} +1.46004 q^{5} +7.74904 q^{6} -3.90191 q^{7} -8.97712 q^{8} +5.20501 q^{9} +O(q^{10})\)	\(q-2.70525 q^{2} -2.86444 q^{3} +5.31840 q^{4} +1.46004 q^{5} +7.74904 q^{6} -3.90191 q^{7} -8.97712 q^{8} +5.20501 q^{9} -3.94978 q^{10} +1.00000 q^{11} -15.2342 q^{12} -2.79985 q^{13} +10.5557 q^{14} -4.18220 q^{15} +13.6486 q^{16} +1.00000 q^{17} -14.0809 q^{18} +0.0854401 q^{19} +7.76508 q^{20} +11.1768 q^{21} -2.70525 q^{22} +2.41012 q^{23} +25.7144 q^{24} -2.86828 q^{25} +7.57432 q^{26} -6.31612 q^{27} -20.7519 q^{28} -3.04090 q^{29} +11.3139 q^{30} +10.3818 q^{31} -18.9686 q^{32} -2.86444 q^{33} -2.70525 q^{34} -5.69695 q^{35} +27.6823 q^{36} +8.69439 q^{37} -0.231137 q^{38} +8.02001 q^{39} -13.1070 q^{40} +3.21483 q^{41} -30.2360 q^{42} +1.00000 q^{43} +5.31840 q^{44} +7.59953 q^{45} -6.51998 q^{46} +5.14653 q^{47} -39.0955 q^{48} +8.22490 q^{49} +7.75943 q^{50} -2.86444 q^{51} -14.8907 q^{52} -8.25146 q^{53} +17.0867 q^{54} +1.46004 q^{55} +35.0279 q^{56} -0.244738 q^{57} +8.22640 q^{58} -1.57918 q^{59} -22.2426 q^{60} +4.41140 q^{61} -28.0854 q^{62} -20.3095 q^{63} +24.0179 q^{64} -4.08790 q^{65} +7.74904 q^{66} +11.0950 q^{67} +5.31840 q^{68} -6.90364 q^{69} +15.4117 q^{70} -6.21684 q^{71} -46.7260 q^{72} -13.0490 q^{73} -23.5205 q^{74} +8.21601 q^{75} +0.454405 q^{76} -3.90191 q^{77} -21.6962 q^{78} -13.3929 q^{79} +19.9275 q^{80} +2.47710 q^{81} -8.69693 q^{82} +4.11226 q^{83} +59.4426 q^{84} +1.46004 q^{85} -2.70525 q^{86} +8.71046 q^{87} -8.97712 q^{88} +2.09674 q^{89} -20.5587 q^{90} +10.9248 q^{91} +12.8180 q^{92} -29.7380 q^{93} -13.9227 q^{94} +0.124746 q^{95} +54.3345 q^{96} -8.47364 q^{97} -22.2504 q^{98} +5.20501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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