LMFDB - Embedded newform 8026.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.31833 q^{3} +1.00000 q^{4} +1.68969 q^{5} +2.31833 q^{6} -0.814652 q^{7} -1.00000 q^{8} +2.37465 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.31833 q^{3} +1.00000 q^{4} +1.68969 q^{5} +2.31833 q^{6} -0.814652 q^{7} -1.00000 q^{8} +2.37465 q^{9} -1.68969 q^{10} -5.83910 q^{11} -2.31833 q^{12} -4.73646 q^{13} +0.814652 q^{14} -3.91727 q^{15} +1.00000 q^{16} -1.01151 q^{17} -2.37465 q^{18} -2.53939 q^{19} +1.68969 q^{20} +1.88863 q^{21} +5.83910 q^{22} +2.68664 q^{23} +2.31833 q^{24} -2.14494 q^{25} +4.73646 q^{26} +1.44976 q^{27} -0.814652 q^{28} -2.75110 q^{29} +3.91727 q^{30} -4.44777 q^{31} -1.00000 q^{32} +13.5370 q^{33} +1.01151 q^{34} -1.37651 q^{35} +2.37465 q^{36} -8.47287 q^{37} +2.53939 q^{38} +10.9807 q^{39} -1.68969 q^{40} -8.32697 q^{41} -1.88863 q^{42} -3.72335 q^{43} -5.83910 q^{44} +4.01244 q^{45} -2.68664 q^{46} -0.952924 q^{47} -2.31833 q^{48} -6.33634 q^{49} +2.14494 q^{50} +2.34500 q^{51} -4.73646 q^{52} -10.2214 q^{53} -1.44976 q^{54} -9.86630 q^{55} +0.814652 q^{56} +5.88715 q^{57} +2.75110 q^{58} -5.71856 q^{59} -3.91727 q^{60} +10.5287 q^{61} +4.44777 q^{62} -1.93452 q^{63} +1.00000 q^{64} -8.00316 q^{65} -13.5370 q^{66} +8.23232 q^{67} -1.01151 q^{68} -6.22852 q^{69} +1.37651 q^{70} -3.16569 q^{71} -2.37465 q^{72} -2.69014 q^{73} +8.47287 q^{74} +4.97267 q^{75} -2.53939 q^{76} +4.75684 q^{77} -10.9807 q^{78} -5.66322 q^{79} +1.68969 q^{80} -10.4850 q^{81} +8.32697 q^{82} +9.07757 q^{83} +1.88863 q^{84} -1.70913 q^{85} +3.72335 q^{86} +6.37797 q^{87} +5.83910 q^{88} -10.1093 q^{89} -4.01244 q^{90} +3.85857 q^{91} +2.68664 q^{92} +10.3114 q^{93} +0.952924 q^{94} -4.29079 q^{95} +2.31833 q^{96} -18.1792 q^{97} +6.33634 q^{98} -13.8659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.31833	−1.33849	−0.669244	−	0.743043i	$-0.733382\pi$
$3$	−2.31833	−1.33849	−0.669244	+	0.743043i	$0.733382\pi$
$4$	1.00000	0.500000
$5$	1.68969	0.755654	0.377827	−	0.925876i	$-0.376671\pi$
$5$	1.68969	0.755654	0.377827	+	0.925876i	$0.376671\pi$
$6$	2.31833	0.946454
$7$	−0.814652	−0.307910	−0.153955	−	0.988078i	$-0.549201\pi$
$7$	−0.814652	−0.307910	−0.153955	+	0.988078i	$0.549201\pi$
$8$	−1.00000	−0.353553
$9$	2.37465	0.791551
$10$	−1.68969	−0.534328
$11$	−5.83910	−1.76056	−0.880278	−	0.474458i	$-0.842644\pi$
$11$	−5.83910	−1.76056	−0.880278	+	0.474458i	$0.842644\pi$
$12$	−2.31833	−0.669244
$13$	−4.73646	−1.31366	−0.656828	−	0.754040i	$-0.728102\pi$
$13$	−4.73646	−1.31366	−0.656828	+	0.754040i	$0.728102\pi$
$14$	0.814652	0.217725
$15$	−3.91727	−1.01143
$16$	1.00000	0.250000
$17$	−1.01151	−0.245326	−0.122663	−	0.992448i	$-0.539143\pi$
$17$	−1.01151	−0.245326	−0.122663	+	0.992448i	$0.539143\pi$
$18$	−2.37465	−0.559711
$19$	−2.53939	−0.582576	−0.291288	−	0.956635i	$-0.594084\pi$
$19$	−2.53939	−0.582576	−0.291288	+	0.956635i	$0.594084\pi$
$20$	1.68969	0.377827
$21$	1.88863	0.412134
$22$	5.83910	1.24490
$23$	2.68664	0.560204	0.280102	−	0.959970i	$-0.409632\pi$
$23$	2.68664	0.560204	0.280102	+	0.959970i	$0.409632\pi$
$24$	2.31833	0.473227
$25$	−2.14494	−0.428987
$26$	4.73646	0.928896
$27$	1.44976	0.279006
$28$	−0.814652	−0.153955
$29$	−2.75110	−0.510867	−0.255434	−	0.966827i	$-0.582218\pi$
$29$	−2.75110	−0.510867	−0.255434	+	0.966827i	$0.582218\pi$
$30$	3.91727	0.715192
$31$	−4.44777	−0.798843	−0.399421	−	0.916767i	$-0.630789\pi$
$31$	−4.44777	−0.798843	−0.399421	+	0.916767i	$0.630789\pi$
$32$	−1.00000	−0.176777
$33$	13.5370	2.35648
$34$	1.01151	0.173472
$35$	−1.37651	−0.232673
$36$	2.37465	0.395776
$37$	−8.47287	−1.39293	−0.696465	−	0.717591i	$-0.745245\pi$
$37$	−8.47287	−1.39293	−0.696465	+	0.717591i	$0.745245\pi$
$38$	2.53939	0.411944
$39$	10.9807	1.75831
$40$	−1.68969	−0.267164
$41$	−8.32697	−1.30045	−0.650227	−	0.759740i	$-0.725326\pi$
$41$	−8.32697	−1.30045	−0.650227	+	0.759740i	$0.725326\pi$
$42$	−1.88863	−0.291422
$43$	−3.72335	−0.567806	−0.283903	−	0.958853i	$-0.591629\pi$
$43$	−3.72335	−0.567806	−0.283903	+	0.958853i	$0.591629\pi$
$44$	−5.83910	−0.880278
$45$	4.01244	0.598139
$46$	−2.68664	−0.396124
$47$	−0.952924	−0.138998	−0.0694991	−	0.997582i	$-0.522140\pi$
$47$	−0.952924	−0.138998	−0.0694991	+	0.997582i	$0.522140\pi$
$48$	−2.31833	−0.334622
$49$	−6.33634	−0.905192
$50$	2.14494	0.303340
$51$	2.34500	0.328366
$52$	−4.73646	−0.656828
$53$	−10.2214	−1.40401	−0.702005	−	0.712172i	$-0.747712\pi$
$53$	−10.2214	−1.40401	−0.702005	+	0.712172i	$0.747712\pi$
$54$	−1.44976	−0.197287
$55$	−9.86630	−1.33037
$56$	0.814652	0.108863
$57$	5.88715	0.779772
$58$	2.75110	0.361238
$59$	−5.71856	−0.744493	−0.372246	−	0.928134i	$-0.621412\pi$
$59$	−5.71856	−0.744493	−0.372246	+	0.928134i	$0.621412\pi$
$60$	−3.91727	−0.505717
$61$	10.5287	1.34806	0.674031	−	0.738703i	$-0.264561\pi$
$61$	10.5287	1.34806	0.674031	+	0.738703i	$0.264561\pi$
$62$	4.44777	0.564867
$63$	−1.93452	−0.243726
$64$	1.00000	0.125000
$65$	−8.00316	−0.992670
$66$	−13.5370	−1.66629
$67$	8.23232	1.00574	0.502869	−	0.864362i	$-0.332278\pi$
$67$	8.23232	1.00574	0.502869	+	0.864362i	$0.332278\pi$
$68$	−1.01151	−0.122663
$69$	−6.22852	−0.749826
$70$	1.37651	0.164525
$71$	−3.16569	−0.375699	−0.187849	−	0.982198i	$-0.560152\pi$
$71$	−3.16569	−0.375699	−0.187849	+	0.982198i	$0.560152\pi$
$72$	−2.37465	−0.279856
$73$	−2.69014	−0.314857	−0.157429	−	0.987530i	$-0.550320\pi$
$73$	−2.69014	−0.314857	−0.157429	+	0.987530i	$0.550320\pi$
$74$	8.47287	0.984951
$75$	4.97267	0.574194
$76$	−2.53939	−0.291288
$77$	4.75684	0.542092
$78$	−10.9807	−1.24332
$79$	−5.66322	−0.637162	−0.318581	−	0.947896i	$-0.603206\pi$
$79$	−5.66322	−0.637162	−0.318581	+	0.947896i	$0.603206\pi$
$80$	1.68969	0.188914
$81$	−10.4850	−1.16500
$82$	8.32697	0.919560
$83$	9.07757	0.996393	0.498196	−	0.867064i	$-0.333996\pi$
$83$	9.07757	0.996393	0.498196	+	0.867064i	$0.333996\pi$
$84$	1.88863	0.206067
$85$	−1.70913	−0.185382
$86$	3.72335	0.401500
$87$	6.37797	0.683790
$88$	5.83910	0.622451
$89$	−10.1093	−1.07158	−0.535790	−	0.844352i	$-0.679986\pi$
$89$	−10.1093	−1.07158	−0.535790	+	0.844352i	$0.679986\pi$
$90$	−4.01244	−0.422948
$91$	3.85857	0.404488
$92$	2.68664	0.280102
$93$	10.3114	1.06924
$94$	0.952924	0.0982866
$95$	−4.29079	−0.440226
$96$	2.31833	0.236614
$97$	−18.1792	−1.84581	−0.922907	−	0.385023i	$-0.874193\pi$
$97$	−18.1792	−1.84581	−0.922907	+	0.385023i	$0.874193\pi$
$98$	6.33634	0.640067
$99$	−13.8659	−1.39357
$100$	−2.14494	−0.214494
$101$	10.7997	1.07461	0.537307	−	0.843387i	$-0.319442\pi$
$101$	10.7997	1.07461	0.537307	+	0.843387i	$0.319442\pi$
$102$	−2.34500	−0.232190
$103$	14.8806	1.46623	0.733115	−	0.680105i	$-0.238066\pi$
$103$	14.8806	1.46623	0.733115	+	0.680105i	$0.238066\pi$
$104$	4.73646	0.464448
$105$	3.19121	0.311430
$106$	10.2214	0.992786
$107$	−12.9105	−1.24810	−0.624051	−	0.781383i	$-0.714514\pi$
$107$	−12.9105	−1.24810	−0.624051	+	0.781383i	$0.714514\pi$
$108$	1.44976	0.139503
$109$	1.66886	0.159848	0.0799238	−	0.996801i	$-0.474532\pi$
$109$	1.66886	0.159848	0.0799238	+	0.996801i	$0.474532\pi$
$110$	9.86630	0.940715
$111$	19.6429	1.86442
$112$	−0.814652	−0.0769774
$113$	−10.5034	−0.988073	−0.494036	−	0.869441i	$-0.664479\pi$
$113$	−10.5034	−0.988073	−0.494036	+	0.869441i	$0.664479\pi$
$114$	−5.88715	−0.551382
$115$	4.53960	0.423320
$116$	−2.75110	−0.255434
$117$	−11.2474	−1.03983
$118$	5.71856	0.526436
$119$	0.824025	0.0755383
$120$	3.91727	0.357596
$121$	23.0951	2.09956
$122$	−10.5287	−0.953224
$123$	19.3047	1.74064
$124$	−4.44777	−0.399421
$125$	−12.0728	−1.07982
$126$	1.93452	0.172341
$127$	10.3415	0.917657	0.458828	−	0.888525i	$-0.348269\pi$
$127$	10.3415	0.917657	0.458828	+	0.888525i	$0.348269\pi$
$128$	−1.00000	−0.0883883
$129$	8.63196	0.760002
$130$	8.00316	0.701924
$131$	7.81223	0.682558	0.341279	−	0.939962i	$-0.389140\pi$
$131$	7.81223	0.682558	0.341279	+	0.939962i	$0.389140\pi$
$132$	13.5370	1.17824
$133$	2.06872	0.179381
$134$	−8.23232	−0.711164
$135$	2.44965	0.210832
$136$	1.01151	0.0867359
$137$	−10.2482	−0.875559	−0.437780	−	0.899082i	$-0.644235\pi$
$137$	−10.2482	−0.875559	−0.437780	+	0.899082i	$0.644235\pi$
$138$	6.22852	0.530207
$139$	−10.6722	−0.905205	−0.452602	−	0.891713i	$-0.649504\pi$
$139$	−10.6722	−0.905205	−0.452602	+	0.891713i	$0.649504\pi$
$140$	−1.37651	−0.116337
$141$	2.20919	0.186047
$142$	3.16569	0.265659
$143$	27.6567	2.31277
$144$	2.37465	0.197888
$145$	−4.64852	−0.386039
$146$	2.69014	0.222638
$147$	14.6897	1.21159
$148$	−8.47287	−0.696465
$149$	−5.21187	−0.426973	−0.213487	−	0.976946i	$-0.568482\pi$
$149$	−5.21187	−0.426973	−0.213487	+	0.976946i	$0.568482\pi$
$150$	−4.97267	−0.406017
$151$	6.83386	0.556132	0.278066	−	0.960562i	$-0.410307\pi$
$151$	6.83386	0.556132	0.278066	+	0.960562i	$0.410307\pi$
$152$	2.53939	0.205972
$153$	−2.40198	−0.194188
$154$	−4.75684	−0.383317
$155$	−7.51537	−0.603649
$156$	10.9807	0.879157
$157$	−4.01248	−0.320231	−0.160115	−	0.987098i	$-0.551187\pi$
$157$	−4.01248	−0.320231	−0.160115	+	0.987098i	$0.551187\pi$
$158$	5.66322	0.450541
$159$	23.6965	1.87925
$160$	−1.68969	−0.133582
$161$	−2.18868	−0.172492
$162$	10.4850	0.823778
$163$	9.98607	0.782170	0.391085	−	0.920355i	$-0.372100\pi$
$163$	9.98607	0.782170	0.391085	+	0.920355i	$0.372100\pi$
$164$	−8.32697	−0.650227
$165$	22.8733	1.78069
$166$	−9.07757	−0.704556
$167$	−16.0394	−1.24117	−0.620584	−	0.784140i	$-0.713104\pi$
$167$	−16.0394	−1.24117	−0.620584	+	0.784140i	$0.713104\pi$
$168$	−1.88863	−0.145711
$169$	9.43402	0.725694
$170$	1.70913	0.131085
$171$	−6.03017	−0.461139
$172$	−3.72335	−0.283903
$173$	2.94315	0.223764	0.111882	−	0.993722i	$-0.464312\pi$
$173$	2.94315	0.223764	0.111882	+	0.993722i	$0.464312\pi$
$174$	−6.37797	−0.483512
$175$	1.74738	0.132089
$176$	−5.83910	−0.440139
$177$	13.2575	0.996495
$178$	10.1093	0.757721
$179$	16.8723	1.26109	0.630547	−	0.776151i	$-0.282831\pi$
$179$	16.8723	1.26109	0.630547	+	0.776151i	$0.282831\pi$
$180$	4.01244	0.299069
$181$	−14.1064	−1.04852	−0.524261	−	0.851558i	$-0.675658\pi$
$181$	−14.1064	−1.04852	−0.524261	+	0.851558i	$0.675658\pi$
$182$	−3.85857	−0.286016
$183$	−24.4090	−1.80437
$184$	−2.68664	−0.198062
$185$	−14.3165	−1.05257
$186$	−10.3114	−0.756068
$187$	5.90629	0.431910
$188$	−0.952924	−0.0694991
$189$	−1.18105	−0.0859087
$190$	4.29079	0.311287
$191$	19.6613	1.42264	0.711321	−	0.702867i	$-0.248097\pi$
$191$	19.6613	1.42264	0.711321	+	0.702867i	$0.248097\pi$
$192$	−2.31833	−0.167311
$193$	3.60799	0.259709	0.129854	−	0.991533i	$-0.458549\pi$
$193$	3.60799	0.259709	0.129854	+	0.991533i	$0.458549\pi$
$194$	18.1792	1.30519
$195$	18.5540	1.32868
$196$	−6.33634	−0.452596
$197$	5.96776	0.425185	0.212593	−	0.977141i	$-0.431809\pi$
$197$	5.96776	0.425185	0.212593	+	0.977141i	$0.431809\pi$
$198$	13.8659	0.985403
$199$	7.98637	0.566139	0.283069	−	0.959099i	$-0.408647\pi$
$199$	7.98637	0.566139	0.283069	+	0.959099i	$0.408647\pi$
$200$	2.14494	0.151670
$201$	−19.0852	−1.34617
$202$	−10.7997	−0.759867
$203$	2.24119	0.157301
$204$	2.34500	0.164183
$205$	−14.0700	−0.982694
$206$	−14.8806	−1.03678
$207$	6.37985	0.443430
$208$	−4.73646	−0.328414
$209$	14.8278	1.02566
$210$	−3.19121	−0.220215
$211$	−20.0508	−1.38035	−0.690176	−	0.723641i	$-0.742467\pi$
$211$	−20.0508	−1.38035	−0.690176	+	0.723641i	$0.742467\pi$
$212$	−10.2214	−0.702005
$213$	7.33912	0.502868
$214$	12.9105	0.882542
$215$	−6.29133	−0.429065
$216$	−1.44976	−0.0986436
$217$	3.62339	0.245971
$218$	−1.66886	−0.113029
$219$	6.23664	0.421433
$220$	−9.86630	−0.665186
$221$	4.79095	0.322274
$222$	−19.6429	−1.31834
$223$	−20.2576	−1.35655	−0.678276	−	0.734807i	$-0.737273\pi$
$223$	−20.2576	−1.35655	−0.678276	+	0.734807i	$0.737273\pi$
$224$	0.814652	0.0544313
$225$	−5.09348	−0.339565
$226$	10.5034	0.698673
$227$	−22.6304	−1.50203	−0.751017	−	0.660283i	$-0.770436\pi$
$227$	−22.6304	−1.50203	−0.751017	+	0.660283i	$0.770436\pi$
$228$	5.88715	0.389886
$229$	3.41248	0.225503	0.112752	−	0.993623i	$-0.464034\pi$
$229$	3.41248	0.225503	0.112752	+	0.993623i	$0.464034\pi$
$230$	−4.53960	−0.299333
$231$	−11.0279	−0.725584
$232$	2.75110	0.180619
$233$	−6.91916	−0.453289	−0.226645	−	0.973978i	$-0.572776\pi$
$233$	−6.91916	−0.453289	−0.226645	+	0.973978i	$0.572776\pi$
$234$	11.2474	0.735268
$235$	−1.61015	−0.105035
$236$	−5.71856	−0.372246
$237$	13.1292	0.852833
$238$	−0.824025	−0.0534136
$239$	17.5957	1.13817	0.569086	−	0.822278i	$-0.307297\pi$
$239$	17.5957	1.13817	0.569086	+	0.822278i	$0.307297\pi$
$240$	−3.91727	−0.252859
$241$	−18.9874	−1.22308	−0.611542	−	0.791212i	$-0.709451\pi$
$241$	−18.9874	−1.22308	−0.611542	+	0.791212i	$0.709451\pi$
$242$	−23.0951	−1.48461
$243$	19.9584	1.28033
$244$	10.5287	0.674031
$245$	−10.7065	−0.684012
$246$	−19.3047	−1.23082
$247$	12.0277	0.765305
$248$	4.44777	0.282434
$249$	−21.0448	−1.33366
$250$	12.0728	0.763548
$251$	−7.75703	−0.489619	−0.244810	−	0.969571i	$-0.578725\pi$
$251$	−7.75703	−0.489619	−0.244810	+	0.969571i	$0.578725\pi$
$252$	−1.93452	−0.121863
$253$	−15.6876	−0.986270
$254$	−10.3415	−0.648881
$255$	3.96234	0.248131
$256$	1.00000	0.0625000
$257$	5.17545	0.322836	0.161418	−	0.986886i	$-0.448393\pi$
$257$	5.17545	0.322836	0.161418	+	0.986886i	$0.448393\pi$
$258$	−8.63196	−0.537403
$259$	6.90244	0.428897
$260$	−8.00316	−0.496335
$261$	−6.53292	−0.404378
$262$	−7.81223	−0.482641
$263$	−25.0072	−1.54201	−0.771005	−	0.636829i	$-0.780246\pi$
$263$	−25.0072	−1.54201	−0.771005	+	0.636829i	$0.780246\pi$
$264$	−13.5370	−0.833143
$265$	−17.2710	−1.06095
$266$	−2.06872	−0.126841
$267$	23.4366	1.43430
$268$	8.23232	0.502869
$269$	27.8095	1.69557	0.847787	−	0.530338i	$-0.177935\pi$
$269$	27.8095	1.69557	0.847787	+	0.530338i	$0.177935\pi$
$270$	−2.44965	−0.149081
$271$	−20.7328	−1.25943	−0.629714	−	0.776827i	$-0.716828\pi$
$271$	−20.7328	−1.25943	−0.629714	+	0.776827i	$0.716828\pi$
$272$	−1.01151	−0.0613315
$273$	−8.94543	−0.541402
$274$	10.2482	0.619114
$275$	12.5245	0.755256
$276$	−6.22852	−0.374913
$277$	−4.79540	−0.288128	−0.144064	−	0.989568i	$-0.546017\pi$
$277$	−4.79540	−0.288128	−0.144064	+	0.989568i	$0.546017\pi$
$278$	10.6722	0.640076
$279$	−10.5619	−0.632325
$280$	1.37651	0.0822624
$281$	7.45939	0.444990	0.222495	−	0.974934i	$-0.428580\pi$
$281$	7.45939	0.444990	0.222495	+	0.974934i	$0.428580\pi$
$282$	−2.20919	−0.131555
$283$	−29.5915	−1.75903	−0.879517	−	0.475868i	$-0.842134\pi$
$283$	−29.5915	−1.75903	−0.879517	+	0.475868i	$0.842134\pi$
$284$	−3.16569	−0.187849
$285$	9.94747	0.589238
$286$	−27.6567	−1.63537
$287$	6.78359	0.400423
$288$	−2.37465	−0.139928
$289$	−15.9769	−0.939815
$290$	4.64852	0.272971
$291$	42.1453	2.47060
$292$	−2.69014	−0.157429
$293$	−1.92817	−0.112645	−0.0563226	−	0.998413i	$-0.517938\pi$
$293$	−1.92817	−0.112645	−0.0563226	+	0.998413i	$0.517938\pi$
$294$	−14.6897	−0.856722
$295$	−9.66261	−0.562579
$296$	8.47287	0.492475
$297$	−8.46529	−0.491206
$298$	5.21187	0.301916
$299$	−12.7252	−0.735915
$300$	4.97267	0.287097
$301$	3.03324	0.174833
$302$	−6.83386	−0.393244
$303$	−25.0373	−1.43836
$304$	−2.53939	−0.145644
$305$	17.7903	1.01867
$306$	2.40198	0.137312
$307$	25.9462	1.48083	0.740414	−	0.672151i	$-0.234630\pi$
$307$	25.9462	1.48083	0.740414	+	0.672151i	$0.234630\pi$
$308$	4.75684	0.271046
$309$	−34.4981	−1.96253
$310$	7.51537	0.426844
$311$	−12.7681	−0.724014	−0.362007	−	0.932175i	$-0.617908\pi$
$311$	−12.7681	−0.724014	−0.362007	+	0.932175i	$0.617908\pi$
$312$	−10.9807	−0.621658
$313$	−20.1029	−1.13629	−0.568143	−	0.822930i	$-0.692338\pi$
$313$	−20.1029	−1.13629	−0.568143	+	0.822930i	$0.692338\pi$
$314$	4.01248	0.226437
$315$	−3.26874	−0.184173
$316$	−5.66322	−0.318581
$317$	−18.3957	−1.03321	−0.516604	−	0.856224i	$-0.672804\pi$
$317$	−18.3957	−1.03321	−0.516604	+	0.856224i	$0.672804\pi$
$318$	−23.6965	−1.32883
$319$	16.0640	0.899410
$320$	1.68969	0.0944568
$321$	29.9307	1.67057
$322$	2.18868	0.121970
$323$	2.56861	0.142921
$324$	−10.4850	−0.582499
$325$	10.1594	0.563542
$326$	−9.98607	−0.553078
$327$	−3.86896	−0.213954
$328$	8.32697	0.459780
$329$	0.776302	0.0427989
$330$	−22.8733	−1.25914
$331$	5.06035	0.278142	0.139071	−	0.990282i	$-0.455588\pi$
$331$	5.06035	0.278142	0.139071	+	0.990282i	$0.455588\pi$
$332$	9.07757	0.498196
$333$	−20.1201	−1.10258
$334$	16.0394	0.877638
$335$	13.9101	0.759990
$336$	1.88863	0.103033
$337$	−20.9144	−1.13928	−0.569641	−	0.821894i	$-0.692918\pi$
$337$	−20.9144	−1.13928	−0.569641	+	0.821894i	$0.692918\pi$
$338$	−9.43402	−0.513143
$339$	24.3503	1.32252
$340$	−1.70913	−0.0926908
$341$	25.9710	1.40641
$342$	6.03017	0.326075
$343$	10.8645	0.586627
$344$	3.72335	0.200750
$345$	−10.5243	−0.566609
$346$	−2.94315	−0.158225
$347$	6.57917	0.353188	0.176594	−	0.984284i	$-0.443492\pi$
$347$	6.57917	0.353188	0.176594	+	0.984284i	$0.443492\pi$
$348$	6.37797	0.341895
$349$	27.1435	1.45296	0.726479	−	0.687188i	$-0.241155\pi$
$349$	27.1435	1.45296	0.726479	+	0.687188i	$0.241155\pi$
$350$	−1.74738	−0.0934012
$351$	−6.86672	−0.366518
$352$	5.83910	0.311225
$353$	5.93866	0.316083	0.158041	−	0.987432i	$-0.449482\pi$
$353$	5.93866	0.316083	0.158041	+	0.987432i	$0.449482\pi$
$354$	−13.2575	−0.704628
$355$	−5.34905	−0.283898
$356$	−10.1093	−0.535790
$357$	−1.91036	−0.101107
$358$	−16.8723	−0.891727
$359$	21.2416	1.12109	0.560545	−	0.828124i	$-0.310592\pi$
$359$	21.2416	1.12109	0.560545	+	0.828124i	$0.310592\pi$
$360$	−4.01244	−0.211474
$361$	−12.5515	−0.660605
$362$	14.1064	0.741417
$363$	−53.5422	−2.81023
$364$	3.85857	0.202244
$365$	−4.54552	−0.237923
$366$	24.4090	1.27588
$367$	−21.5755	−1.12623	−0.563116	−	0.826378i	$-0.690398\pi$
$367$	−21.5755	−1.12623	−0.563116	+	0.826378i	$0.690398\pi$
$368$	2.68664	0.140051
$369$	−19.7737	−1.02938
$370$	14.3165	0.744282
$371$	8.32685	0.432309
$372$	10.3114	0.534621
$373$	−34.4737	−1.78498	−0.892491	−	0.451065i	$-0.851044\pi$
$373$	−34.4737	−1.78498	−0.892491	+	0.451065i	$0.851044\pi$
$374$	−5.90629	−0.305407
$375$	27.9886	1.44533
$376$	0.952924	0.0491433
$377$	13.0305	0.671104
$378$	1.18105	0.0607466
$379$	32.4768	1.66822	0.834110	−	0.551598i	$-0.185982\pi$
$379$	32.4768	1.66822	0.834110	+	0.551598i	$0.185982\pi$
$380$	−4.29079	−0.220113
$381$	−23.9749	−1.22827
$382$	−19.6613	−1.00596
$383$	−31.9792	−1.63406	−0.817030	−	0.576595i	$-0.804381\pi$
$383$	−31.9792	−1.63406	−0.817030	+	0.576595i	$0.804381\pi$
$384$	2.31833	0.118307
$385$	8.03760	0.409634
$386$	−3.60799	−0.183642
$387$	−8.84168	−0.449448
$388$	−18.1792	−0.922907
$389$	13.8989	0.704705	0.352352	−	0.935867i	$-0.385382\pi$
$389$	13.8989	0.704705	0.352352	+	0.935867i	$0.385382\pi$
$390$	−18.5540	−0.939517
$391$	−2.71755	−0.137433
$392$	6.33634	0.320034
$393$	−18.1113	−0.913596
$394$	−5.96776	−0.300651
$395$	−9.56910	−0.481474
$396$	−13.8659	−0.696785
$397$	24.9044	1.24991	0.624957	−	0.780659i	$-0.285116\pi$
$397$	24.9044	1.24991	0.624957	+	0.780659i	$0.285116\pi$
$398$	−7.98637	−0.400321
$399$	−4.79598	−0.240099
$400$	−2.14494	−0.107247
$401$	10.9571	0.547173	0.273587	−	0.961847i	$-0.411790\pi$
$401$	10.9571	0.547173	0.273587	+	0.961847i	$0.411790\pi$
$402$	19.0852	0.951885
$403$	21.0667	1.04941
$404$	10.7997	0.537307
$405$	−17.7164	−0.880335
$406$	−2.24119	−0.111229
$407$	49.4739	2.45233
$408$	−2.34500	−0.116095
$409$	32.4094	1.60254	0.801271	−	0.598302i	$-0.204158\pi$
$409$	32.4094	1.60254	0.801271	+	0.598302i	$0.204158\pi$
$410$	14.0700	0.694869
$411$	23.7586	1.17193
$412$	14.8806	0.733115
$413$	4.65864	0.229236
$414$	−6.37985	−0.313552
$415$	15.3383	0.752928
$416$	4.73646	0.232224
$417$	24.7417	1.21161
$418$	−14.8278	−0.725250
$419$	3.24424	0.158491	0.0792457	−	0.996855i	$-0.474749\pi$
$419$	3.24424	0.158491	0.0792457	+	0.996855i	$0.474749\pi$
$420$	3.19121	0.155715
$421$	−1.63837	−0.0798492	−0.0399246	−	0.999203i	$-0.512712\pi$
$421$	−1.63837	−0.0798492	−0.0399246	+	0.999203i	$0.512712\pi$
$422$	20.0508	0.976056
$423$	−2.26286	−0.110024
$424$	10.2214	0.496393
$425$	2.16961	0.105242
$426$	−7.33912	−0.355582
$427$	−8.57724	−0.415082
$428$	−12.9105	−0.624051
$429$	−64.1173	−3.09561
$430$	6.29133	0.303395
$431$	28.6472	1.37989	0.689943	−	0.723863i	$-0.257635\pi$
$431$	28.6472	1.37989	0.689943	+	0.723863i	$0.257635\pi$
$432$	1.44976	0.0697516
$433$	−18.2427	−0.876690	−0.438345	−	0.898807i	$-0.644435\pi$
$433$	−18.2427	−0.876690	−0.438345	+	0.898807i	$0.644435\pi$
$434$	−3.62339	−0.173928
$435$	10.7768	0.516708
$436$	1.66886	0.0799238
$437$	−6.82244	−0.326361
$438$	−6.23664	−0.297998
$439$	−39.8164	−1.90033	−0.950167	−	0.311740i	$-0.899088\pi$
$439$	−39.8164	−1.90033	−0.950167	+	0.311740i	$0.899088\pi$
$440$	9.86630	0.470357
$441$	−15.0466	−0.716506
$442$	−4.79095	−0.227882
$443$	11.2069	0.532455	0.266228	−	0.963910i	$-0.414223\pi$
$443$	11.2069	0.532455	0.266228	+	0.963910i	$0.414223\pi$
$444$	19.6429	0.932211
$445$	−17.0815	−0.809743
$446$	20.2576	0.959228
$447$	12.0828	0.571499
$448$	−0.814652	−0.0384887
$449$	−17.5509	−0.828277	−0.414139	−	0.910214i	$-0.635917\pi$
$449$	−17.5509	−0.828277	−0.414139	+	0.910214i	$0.635917\pi$
$450$	5.09348	0.240109
$451$	48.6221	2.28952
$452$	−10.5034	−0.494036
$453$	−15.8431	−0.744376
$454$	22.6304	1.06210
$455$	6.51979	0.305653
$456$	−5.88715	−0.275691
$457$	5.62948	0.263336	0.131668	−	0.991294i	$-0.457967\pi$
$457$	5.62948	0.263336	0.131668	+	0.991294i	$0.457967\pi$
$458$	−3.41248	−0.159455
$459$	−1.46644	−0.0684475
$460$	4.53960	0.211660
$461$	7.38433	0.343923	0.171961	−	0.985104i	$-0.444990\pi$
$461$	7.38433	0.343923	0.171961	+	0.985104i	$0.444990\pi$
$462$	11.0279	0.513066
$463$	9.48950	0.441014	0.220507	−	0.975385i	$-0.429229\pi$
$463$	9.48950	0.441014	0.220507	+	0.975385i	$0.429229\pi$
$464$	−2.75110	−0.127717
$465$	17.4231	0.807977
$466$	6.91916	0.320524
$467$	−6.48042	−0.299878	−0.149939	−	0.988695i	$-0.547908\pi$
$467$	−6.48042	−0.299878	−0.149939	+	0.988695i	$0.547908\pi$
$468$	−11.2474	−0.519913
$469$	−6.70648	−0.309677
$470$	1.61015	0.0742706
$471$	9.30226	0.428625
$472$	5.71856	0.263218
$473$	21.7411	0.999655
$474$	−13.1292	−0.603044
$475$	5.44683	0.249918
$476$	0.824025	0.0377691
$477$	−24.2722	−1.11135
$478$	−17.5957	−0.804809
$479$	−17.1755	−0.784767	−0.392383	−	0.919802i	$-0.628349\pi$
$479$	−17.1755	−0.784767	−0.392383	+	0.919802i	$0.628349\pi$
$480$	3.91727	0.178798
$481$	40.1314	1.82983
$482$	18.9874	0.864852
$483$	5.07408	0.230879
$484$	23.0951	1.04978
$485$	−30.7172	−1.39480
$486$	−19.9584	−0.905330
$487$	−3.34097	−0.151394	−0.0756969	−	0.997131i	$-0.524118\pi$
$487$	−3.34097	−0.151394	−0.0756969	+	0.997131i	$0.524118\pi$
$488$	−10.5287	−0.476612
$489$	−23.1510	−1.04693
$490$	10.7065	0.483669
$491$	7.98483	0.360350	0.180175	−	0.983635i	$-0.442334\pi$
$491$	7.98483	0.360350	0.180175	+	0.983635i	$0.442334\pi$
$492$	19.3047	0.870322
$493$	2.78276	0.125329
$494$	−12.0277	−0.541153
$495$	−23.4290	−1.05306
$496$	−4.44777	−0.199711
$497$	2.57894	0.115681
$498$	21.0448	0.943040
$499$	−17.6200	−0.788779	−0.394389	−	0.918943i	$-0.629044\pi$
$499$	−17.6200	−0.788779	−0.394389	+	0.918943i	$0.629044\pi$
$500$	−12.0728	−0.539910
$501$	37.1847	1.66129
$502$	7.75703	0.346213
$503$	12.2062	0.544248	0.272124	−	0.962262i	$-0.412274\pi$
$503$	12.2062	0.544248	0.272124	+	0.962262i	$0.412274\pi$
$504$	1.93452	0.0861703
$505$	18.2482	0.812036
$506$	15.6876	0.697398
$507$	−21.8712	−0.971333
$508$	10.3415	0.458828
$509$	25.4382	1.12753	0.563765	−	0.825935i	$-0.309352\pi$
$509$	25.4382	1.12753	0.563765	+	0.825935i	$0.309352\pi$
$510$	−3.96234	−0.175455
$511$	2.19153	0.0969477
$512$	−1.00000	−0.0441942
$513$	−3.68150	−0.162542
$514$	−5.17545	−0.228279
$515$	25.1437	1.10796
$516$	8.63196	0.380001
$517$	5.56422	0.244714
$518$	−6.90244	−0.303276
$519$	−6.82320	−0.299505
$520$	8.00316	0.350962
$521$	−1.37333	−0.0601666	−0.0300833	−	0.999547i	$-0.509577\pi$
$521$	−1.37333	−0.0601666	−0.0300833	+	0.999547i	$0.509577\pi$
$522$	6.53292	0.285938
$523$	−4.17298	−0.182472	−0.0912359	−	0.995829i	$-0.529082\pi$
$523$	−4.17298	−0.182472	−0.0912359	+	0.995829i	$0.529082\pi$
$524$	7.81223	0.341279
$525$	−4.05100	−0.176800
$526$	25.0072	1.09037
$527$	4.49894	0.195977
$528$	13.5370	0.589121
$529$	−15.7820	−0.686172
$530$	17.2710	0.750202
$531$	−13.5796	−0.589304
$532$	2.06872	0.0896904
$533$	39.4403	1.70835
$534$	−23.4366	−1.01420
$535$	−21.8147	−0.943134
$536$	−8.23232	−0.355582
$537$	−39.1155	−1.68796
$538$	−27.8095	−1.19895
$539$	36.9986	1.59364
$540$	2.44965	0.105416
$541$	18.4521	0.793317	0.396659	−	0.917966i	$-0.370170\pi$
$541$	18.4521	0.793317	0.396659	+	0.917966i	$0.370170\pi$
$542$	20.7328	0.890549
$543$	32.7033	1.40343
$544$	1.01151	0.0433679
$545$	2.81986	0.120790
$546$	8.94543	0.382829
$547$	19.2458	0.822892	0.411446	−	0.911434i	$-0.365024\pi$
$547$	19.2458	0.822892	0.411446	+	0.911434i	$0.365024\pi$
$548$	−10.2482	−0.437780
$549$	25.0020	1.06706
$550$	−12.5245	−0.534046
$551$	6.98613	0.297619
$552$	6.22852	0.265104
$553$	4.61355	0.196188
$554$	4.79540	0.203737
$555$	33.1905	1.40886
$556$	−10.6722	−0.452602
$557$	34.7973	1.47441	0.737204	−	0.675671i	$-0.236146\pi$
$557$	34.7973	1.47441	0.737204	+	0.675671i	$0.236146\pi$
$558$	10.5619	0.447121
$559$	17.6355	0.745903
$560$	−1.37651	−0.0581683
$561$	−13.6927	−0.578107
$562$	−7.45939	−0.314655
$563$	−13.1064	−0.552368	−0.276184	−	0.961105i	$-0.589070\pi$
$563$	−13.1064	−0.552368	−0.276184	+	0.961105i	$0.589070\pi$
$564$	2.20919	0.0930237
$565$	−17.7475	−0.746641
$566$	29.5915	1.24382
$567$	8.54162	0.358714
$568$	3.16569	0.132830
$569$	−29.3012	−1.22837	−0.614184	−	0.789163i	$-0.710515\pi$
$569$	−29.3012	−1.22837	−0.614184	+	0.789163i	$0.710515\pi$
$570$	−9.94747	−0.416654
$571$	17.6196	0.737357	0.368679	−	0.929557i	$-0.379810\pi$
$571$	17.6196	0.737357	0.368679	+	0.929557i	$0.379810\pi$
$572$	27.6567	1.15638
$573$	−45.5814	−1.90419
$574$	−6.78359	−0.283142
$575$	−5.76267	−0.240320
$576$	2.37465	0.0989439
$577$	11.6384	0.484514	0.242257	−	0.970212i	$-0.422112\pi$
$577$	11.6384	0.484514	0.242257	+	0.970212i	$0.422112\pi$
$578$	15.9769	0.664550
$579$	−8.36450	−0.347617
$580$	−4.64852	−0.193019
$581$	−7.39506	−0.306799
$582$	−42.1453	−1.74698
$583$	59.6836	2.47184
$584$	2.69014	0.111319
$585$	−19.0047	−0.785749
$586$	1.92817	0.0796522
$587$	32.0595	1.32324	0.661618	−	0.749841i	$-0.269870\pi$
$587$	32.0595	1.32324	0.661618	+	0.749841i	$0.269870\pi$
$588$	14.6897	0.605794
$589$	11.2946	0.465387
$590$	9.66261	0.397803
$591$	−13.8352	−0.569105
$592$	−8.47287	−0.348233
$593$	−33.6691	−1.38262	−0.691312	−	0.722557i	$-0.742967\pi$
$593$	−33.6691	−1.38262	−0.691312	+	0.722557i	$0.742967\pi$
$594$	8.46529	0.347335
$595$	1.39235	0.0570808
$596$	−5.21187	−0.213487
$597$	−18.5150	−0.757770
$598$	12.7252	0.520371
$599$	−14.2267	−0.581289	−0.290644	−	0.956831i	$-0.593870\pi$
$599$	−14.2267	−0.581289	−0.290644	+	0.956831i	$0.593870\pi$
$600$	−4.97267	−0.203008
$601$	5.38031	0.219467	0.109734	−	0.993961i	$-0.465000\pi$
$601$	5.38031	0.219467	0.109734	+	0.993961i	$0.465000\pi$
$602$	−3.03324	−0.123626
$603$	19.5489	0.796094
$604$	6.83386	0.278066
$605$	39.0237	1.58654
$606$	25.0373	1.01707
$607$	−5.13074	−0.208250	−0.104125	−	0.994564i	$-0.533204\pi$
$607$	−5.13074	−0.208250	−0.104125	+	0.994564i	$0.533204\pi$
$608$	2.53939	0.102986
$609$	−5.19583	−0.210545
$610$	−17.7903	−0.720308
$611$	4.51348	0.182596
$612$	−2.40198	−0.0970941
$613$	2.40674	0.0972072	0.0486036	−	0.998818i	$-0.484523\pi$
$613$	2.40674	0.0972072	0.0486036	+	0.998818i	$0.484523\pi$
$614$	−25.9462	−1.04710
$615$	32.6190	1.31532
$616$	−4.75684	−0.191659
$617$	−34.1639	−1.37539	−0.687694	−	0.726000i	$-0.741377\pi$
$617$	−34.1639	−1.37539	−0.687694	+	0.726000i	$0.741377\pi$
$618$	34.4981	1.38772
$619$	34.9211	1.40360	0.701799	−	0.712375i	$-0.252381\pi$
$619$	34.9211	1.40360	0.701799	+	0.712375i	$0.252381\pi$
$620$	−7.51537	−0.301824
$621$	3.89498	0.156300
$622$	12.7681	0.511955
$623$	8.23553	0.329950
$624$	10.9807	0.439579
$625$	−9.67458	−0.386983
$626$	20.1029	0.803475
$627$	−34.3757	−1.37283
$628$	−4.01248	−0.160115
$629$	8.57035	0.341722
$630$	3.26874	0.130230
$631$	17.9399	0.714177	0.357088	−	0.934071i	$-0.383769\pi$
$631$	17.9399	0.714177	0.357088	+	0.934071i	$0.383769\pi$
$632$	5.66322	0.225271
$633$	46.4843	1.84759
$634$	18.3957	0.730588
$635$	17.4739	0.693431
$636$	23.6965	0.939626
$637$	30.0118	1.18911
$638$	−16.0640	−0.635979
$639$	−7.51742	−0.297385
$640$	−1.68969	−0.0667910
$641$	23.8592	0.942381	0.471191	−	0.882031i	$-0.343824\pi$
$641$	23.8592	0.942381	0.471191	+	0.882031i	$0.343824\pi$
$642$	−29.9307	−1.18127
$643$	−13.6166	−0.536986	−0.268493	−	0.963282i	$-0.586526\pi$
$643$	−13.6166	−0.536986	−0.268493	+	0.963282i	$0.586526\pi$
$644$	−2.18868	−0.0862461
$645$	14.5854	0.574299
$646$	−2.56861	−0.101061
$647$	35.0614	1.37841	0.689203	−	0.724568i	$-0.257961\pi$
$647$	35.0614	1.37841	0.689203	+	0.724568i	$0.257961\pi$
$648$	10.4850	0.411889
$649$	33.3912	1.31072
$650$	−10.1594	−0.398484
$651$	−8.40020	−0.329230
$652$	9.98607	0.391085
$653$	−4.26953	−0.167080	−0.0835399	−	0.996504i	$-0.526623\pi$
$653$	−4.26953	−0.167080	−0.0835399	+	0.996504i	$0.526623\pi$
$654$	3.86896	0.151288
$655$	13.2003	0.515778
$656$	−8.32697	−0.325114
$657$	−6.38816	−0.249226
$658$	−0.776302	−0.0302634
$659$	14.8169	0.577183	0.288591	−	0.957452i	$-0.406813\pi$
$659$	14.8169	0.577183	0.288591	+	0.957452i	$0.406813\pi$
$660$	22.8733	0.890343
$661$	−28.2238	−1.09778	−0.548888	−	0.835896i	$-0.684949\pi$
$661$	−28.2238	−1.09778	−0.548888	+	0.835896i	$0.684949\pi$
$662$	−5.06035	−0.196676
$663$	−11.1070	−0.431360
$664$	−9.07757	−0.352278
$665$	3.49551	0.135550
$666$	20.1201	0.779639
$667$	−7.39123	−0.286190
$668$	−16.0394	−0.620584
$669$	46.9639	1.81573
$670$	−13.9101	−0.537394
$671$	−61.4782	−2.37334
$672$	−1.88863	−0.0728556
$673$	−9.10712	−0.351054	−0.175527	−	0.984475i	$-0.556163\pi$
$673$	−9.10712	−0.351054	−0.175527	+	0.984475i	$0.556163\pi$
$674$	20.9144	0.805594
$675$	−3.10964	−0.119690
$676$	9.43402	0.362847
$677$	45.2018	1.73725	0.868623	−	0.495473i	$-0.165005\pi$
$677$	45.2018	1.73725	0.868623	+	0.495473i	$0.165005\pi$
$678$	−24.3503	−0.935166
$679$	14.8097	0.568344
$680$	1.70913	0.0655423
$681$	52.4648	2.01046
$682$	−25.9710	−0.994480
$683$	39.6810	1.51835	0.759176	−	0.650885i	$-0.225602\pi$
$683$	39.6810	1.51835	0.759176	+	0.650885i	$0.225602\pi$
$684$	−6.03017	−0.230569
$685$	−17.3162	−0.661620
$686$	−10.8645	−0.414808
$687$	−7.91126	−0.301833
$688$	−3.72335	−0.141952
$689$	48.4130	1.84439
$690$	10.5243	0.400653
$691$	−18.7323	−0.712611	−0.356306	−	0.934369i	$-0.615964\pi$
$691$	−18.7323	−0.712611	−0.356306	+	0.934369i	$0.615964\pi$
$692$	2.94315	0.111882
$693$	11.2959	0.429094
$694$	−6.57917	−0.249742
$695$	−18.0328	−0.684021
$696$	−6.37797	−0.241756
$697$	8.42278	0.319036
$698$	−27.1435	−1.02740
$699$	16.0409	0.606723
$700$	1.74738	0.0660446
$701$	−7.87974	−0.297614	−0.148807	−	0.988866i	$-0.547543\pi$
$701$	−7.87974	−0.297614	−0.148807	+	0.988866i	$0.547543\pi$
$702$	6.86672	0.259168
$703$	21.5159	0.811488
$704$	−5.83910	−0.220070
$705$	3.73286	0.140588
$706$	−5.93866	−0.223504
$707$	−8.79803	−0.330884
$708$	13.2575	0.498247
$709$	31.3165	1.17612	0.588058	−	0.808819i	$-0.299893\pi$
$709$	31.3165	1.17612	0.588058	+	0.808819i	$0.299893\pi$
$710$	5.34905	0.200746
$711$	−13.4482	−0.504346
$712$	10.1093	0.378860
$713$	−11.9496	−0.447515
$714$	1.91036	0.0714935
$715$	46.7313	1.74765
$716$	16.8723	0.630547
$717$	−40.7926	−1.52343
$718$	−21.2416	−0.792731
$719$	9.99954	0.372920	0.186460	−	0.982463i	$-0.440299\pi$
$719$	9.99954	0.372920	0.186460	+	0.982463i	$0.440299\pi$
$720$	4.01244	0.149535
$721$	−12.1225	−0.451466
$722$	12.5515	0.467118
$723$	44.0190	1.63708
$724$	−14.1064	−0.524261
$725$	5.90094	0.219155
$726$	53.5422	1.98714
$727$	−20.5279	−0.761339	−0.380670	−	0.924711i	$-0.624306\pi$
$727$	−20.5279	−0.761339	−0.380670	+	0.924711i	$0.624306\pi$
$728$	−3.85857	−0.143008
$729$	−14.8151	−0.548709
$730$	4.54552	0.168237
$731$	3.76619	0.139298
$732$	−24.4090	−0.902183
$733$	−22.4019	−0.827432	−0.413716	−	0.910406i	$-0.635769\pi$
$733$	−22.4019	−0.827432	−0.413716	+	0.910406i	$0.635769\pi$
$734$	21.5755	0.796367
$735$	24.8211	0.915542
$736$	−2.68664	−0.0990310
$737$	−48.0694	−1.77066
$738$	19.7737	0.727879
$739$	10.6323	0.391116	0.195558	−	0.980692i	$-0.437348\pi$
$739$	10.6323	0.391116	0.195558	+	0.980692i	$0.437348\pi$
$740$	−14.3165	−0.526287
$741$	−27.8842	−1.02435
$742$	−8.32685	−0.305688
$743$	−19.7891	−0.725990	−0.362995	−	0.931791i	$-0.618246\pi$
$743$	−19.7891	−0.725990	−0.362995	+	0.931791i	$0.618246\pi$
$744$	−10.3114	−0.378034
$745$	−8.80647	−0.322644
$746$	34.4737	1.26217
$747$	21.5561	0.788696
$748$	5.90629	0.215955
$749$	10.5175	0.384303
$750$	−27.9886	−1.02200
$751$	−36.9204	−1.34724	−0.673621	−	0.739077i	$-0.735262\pi$
$751$	−36.9204	−1.34724	−0.673621	+	0.739077i	$0.735262\pi$
$752$	−0.952924	−0.0347496
$753$	17.9833	0.655350
$754$	−13.0305	−0.474542
$755$	11.5471	0.420243
$756$	−1.18105	−0.0429544
$757$	−30.9255	−1.12400	−0.562002	−	0.827136i	$-0.689969\pi$
$757$	−30.9255	−1.12400	−0.562002	+	0.827136i	$0.689969\pi$
$758$	−32.4768	−1.17961
$759$	36.3690	1.32011
$760$	4.29079	0.155643
$761$	41.3446	1.49874	0.749370	−	0.662151i	$-0.230356\pi$
$761$	41.3446	1.49874	0.749370	+	0.662151i	$0.230356\pi$
$762$	23.9749	0.868520
$763$	−1.35954	−0.0492186
$764$	19.6613	0.711321
$765$	−4.05860	−0.146739
$766$	31.9792	1.15545
$767$	27.0857	0.978008
$768$	−2.31833	−0.0836555
$769$	21.1501	0.762694	0.381347	−	0.924432i	$-0.375460\pi$
$769$	21.1501	0.762694	0.381347	+	0.924432i	$0.375460\pi$
$770$	−8.03760	−0.289655
$771$	−11.9984	−0.432112
$772$	3.60799	0.129854
$773$	11.1983	0.402775	0.201387	−	0.979512i	$-0.435455\pi$
$773$	11.1983	0.402775	0.201387	+	0.979512i	$0.435455\pi$
$774$	8.84168	0.317808
$775$	9.54017	0.342693
$776$	18.1792	0.652594
$777$	−16.0021	−0.574073
$778$	−13.8989	−0.498301
$779$	21.1454	0.757614
$780$	18.5540	0.664339
$781$	18.4848	0.661439
$782$	2.71755	0.0971795
$783$	−3.98844	−0.142535
$784$	−6.33634	−0.226298
$785$	−6.77987	−0.241984
$786$	18.1113	0.646010
$787$	0.381565	0.0136013	0.00680066	−	0.999977i	$-0.497835\pi$
$787$	0.381565	0.0136013	0.00680066	+	0.999977i	$0.497835\pi$
$788$	5.96776	0.212593
$789$	57.9750	2.06396
$790$	9.56910	0.340453
$791$	8.55659	0.304237
$792$	13.8659	0.492702
$793$	−49.8688	−1.77089
$794$	−24.9044	−0.883823
$795$	40.0398	1.42006
$796$	7.98637	0.283069
$797$	−5.35771	−0.189780	−0.0948899	−	0.995488i	$-0.530250\pi$
$797$	−5.35771	−0.189780	−0.0948899	+	0.995488i	$0.530250\pi$
$798$	4.79598	0.169776
$799$	0.963888	0.0340999
$800$	2.14494	0.0758349
$801$	−24.0060	−0.848210
$802$	−10.9571	−0.386910
$803$	15.7080	0.554324
$804$	−19.0852	−0.673085
$805$	−3.69820	−0.130344
$806$	−21.0667	−0.742041
$807$	−64.4715	−2.26950
$808$	−10.7997	−0.379933
$809$	−29.9189	−1.05189	−0.525946	−	0.850518i	$-0.676288\pi$
$809$	−29.9189	−1.05189	−0.525946	+	0.850518i	$0.676288\pi$
$810$	17.7164	0.622491
$811$	−42.8165	−1.50349	−0.751745	−	0.659454i	$-0.770788\pi$
$811$	−42.8165	−1.50349	−0.751745	+	0.659454i	$0.770788\pi$
$812$	2.24119	0.0786505
$813$	48.0654	1.68573
$814$	−49.4739	−1.73406
$815$	16.8734	0.591050
$816$	2.34500	0.0820915
$817$	9.45505	0.330790
$818$	−32.4094	−1.13317
$819$	9.16276	0.320173
$820$	−14.0700	−0.491347
$821$	−56.2395	−1.96277	−0.981386	−	0.192047i	$-0.938488\pi$
$821$	−56.2395	−1.96277	−0.981386	+	0.192047i	$0.938488\pi$
$822$	−23.7586	−0.828677
$823$	−17.1440	−0.597603	−0.298802	−	0.954315i	$-0.596587\pi$
$823$	−17.1440	−0.597603	−0.298802	+	0.954315i	$0.596587\pi$
$824$	−14.8806	−0.518390
$825$	−29.0359	−1.01090
$826$	−4.65864	−0.162095
$827$	−29.3609	−1.02098	−0.510490	−	0.859884i	$-0.670536\pi$
$827$	−29.3609	−1.02098	−0.510490	+	0.859884i	$0.670536\pi$
$828$	6.37985	0.221715
$829$	2.85472	0.0991487	0.0495743	−	0.998770i	$-0.484214\pi$
$829$	2.85472	0.0991487	0.0495743	+	0.998770i	$0.484214\pi$
$830$	−15.3383	−0.532401
$831$	11.1173	0.385655
$832$	−4.73646	−0.164207
$833$	6.40924	0.222067
$834$	−24.7417	−0.856735
$835$	−27.1017	−0.937893
$836$	14.8278	0.512829
$837$	−6.44819	−0.222882
$838$	−3.24424	−0.112070
$839$	−37.6460	−1.29969	−0.649843	−	0.760069i	$-0.725165\pi$
$839$	−37.6460	−1.29969	−0.649843	+	0.760069i	$0.725165\pi$
$840$	−3.19121	−0.110107
$841$	−21.4314	−0.739015
$842$	1.63837	0.0564619
$843$	−17.2933	−0.595614
$844$	−20.0508	−0.690176
$845$	15.9406	0.548374
$846$	2.26286	0.0777989
$847$	−18.8145	−0.646474
$848$	−10.2214	−0.351003
$849$	68.6029	2.35445
$850$	−2.16961	−0.0744171
$851$	−22.7636	−0.780325
$852$	7.33912	0.251434
$853$	1.03256	0.0353543	0.0176772	−	0.999844i	$-0.494373\pi$
$853$	1.03256	0.0353543	0.0176772	+	0.999844i	$0.494373\pi$
$854$	8.57724	0.293507
$855$	−10.1891	−0.348462
$856$	12.9105	0.441271
$857$	26.6100	0.908982	0.454491	−	0.890751i	$-0.349821\pi$
$857$	26.6100	0.908982	0.454491	+	0.890751i	$0.349821\pi$
$858$	64.1173	2.18893
$859$	7.84080	0.267525	0.133762	−	0.991013i	$-0.457294\pi$
$859$	7.84080	0.267525	0.133762	+	0.991013i	$0.457294\pi$
$860$	−6.29133	−0.214533
$861$	−15.7266	−0.535961
$862$	−28.6472	−0.975727
$863$	30.7488	1.04670	0.523350	−	0.852118i	$-0.324682\pi$
$863$	30.7488	1.04670	0.523350	+	0.852118i	$0.324682\pi$
$864$	−1.44976	−0.0493218
$865$	4.97303	0.169088
$866$	18.2427	0.619913
$867$	37.0396	1.25793
$868$	3.62339	0.122986
$869$	33.0681	1.12176
$870$	−10.7768	−0.365368
$871$	−38.9920	−1.32120
$872$	−1.66886	−0.0565147
$873$	−43.1692	−1.46106
$874$	6.82244	0.230772
$875$	9.83510	0.332487
$876$	6.23664	0.210717
$877$	33.0449	1.11585	0.557924	−	0.829892i	$-0.311598\pi$
$877$	33.0449	1.11585	0.557924	+	0.829892i	$0.311598\pi$
$878$	39.8164	1.34374
$879$	4.47015	0.150774
$880$	−9.86630	−0.332593
$881$	14.1286	0.476004	0.238002	−	0.971265i	$-0.423508\pi$
$881$	14.1286	0.476004	0.238002	+	0.971265i	$0.423508\pi$
$882$	15.0466	0.506646
$883$	−25.2623	−0.850145	−0.425072	−	0.905159i	$-0.639751\pi$
$883$	−25.2623	−0.850145	−0.425072	+	0.905159i	$0.639751\pi$
$884$	4.79095	0.161137
$885$	22.4011	0.753005
$886$	−11.2069	−0.376503
$887$	9.53593	0.320185	0.160093	−	0.987102i	$-0.448821\pi$
$887$	9.53593	0.320185	0.160093	+	0.987102i	$0.448821\pi$
$888$	−19.6429	−0.659172
$889$	−8.42470	−0.282555
$890$	17.0815	0.572575
$891$	61.2229	2.05104
$892$	−20.2576	−0.678276
$893$	2.41985	0.0809771
$894$	−12.0828	−0.404110
$895$	28.5090	0.952950
$896$	0.814652	0.0272156
$897$	29.5011	0.985014
$898$	17.5509	0.585680
$899$	12.2363	0.408102
$900$	−5.09348	−0.169783
$901$	10.3390	0.344441
$902$	−48.6221	−1.61894
$903$	−7.03205	−0.234012
$904$	10.5034	0.349337
$905$	−23.8355	−0.792320
$906$	15.8431	0.526353
$907$	−44.7260	−1.48510	−0.742551	−	0.669790i	$-0.766384\pi$
$907$	−44.7260	−1.48510	−0.742551	+	0.669790i	$0.766384\pi$
$908$	−22.6304	−0.751017
$909$	25.6456	0.850612
$910$	−6.51979	−0.216129
$911$	17.7793	0.589053	0.294526	−	0.955643i	$-0.404838\pi$
$911$	17.7793	0.589053	0.294526	+	0.955643i	$0.404838\pi$
$912$	5.88715	0.194943
$913$	−53.0049	−1.75421
$914$	−5.62948	−0.186207
$915$	−41.2438	−1.36348
$916$	3.41248	0.112752
$917$	−6.36426	−0.210166
$918$	1.46644	0.0483997
$919$	20.6157	0.680048	0.340024	−	0.940417i	$-0.389565\pi$
$919$	20.6157	0.680048	0.340024	+	0.940417i	$0.389565\pi$
$920$	−4.53960	−0.149666
$921$	−60.1518	−1.98207
$922$	−7.38433	−0.243190
$923$	14.9942	0.493539
$924$	−11.0279	−0.362792
$925$	18.1737	0.597549
$926$	−9.48950	−0.311844
$927$	35.3363	1.16060
$928$	2.75110	0.0903094
$929$	−21.7672	−0.714160	−0.357080	−	0.934074i	$-0.616228\pi$
$929$	−21.7672	−0.714160	−0.357080	+	0.934074i	$0.616228\pi$
$930$	−17.4231	−0.571326
$931$	16.0904	0.527343
$932$	−6.91916	−0.226645
$933$	29.6007	0.969084
$934$	6.48042	0.212046
$935$	9.97982	0.326375
$936$	11.2474	0.367634
$937$	10.8618	0.354838	0.177419	−	0.984135i	$-0.443225\pi$
$937$	10.8618	0.354838	0.177419	+	0.984135i	$0.443225\pi$
$938$	6.70648	0.218974
$939$	46.6052	1.52090
$940$	−1.61015	−0.0525173
$941$	38.8475	1.26639	0.633197	−	0.773991i	$-0.281742\pi$
$941$	38.8475	1.26639	0.633197	+	0.773991i	$0.281742\pi$
$942$	−9.30226	−0.303084
$943$	−22.3716	−0.728520
$944$	−5.71856	−0.186123
$945$	−1.99561	−0.0649173
$946$	−21.7411	−0.706863
$947$	−25.5164	−0.829172	−0.414586	−	0.910010i	$-0.636074\pi$
$947$	−25.5164	−0.829172	−0.414586	+	0.910010i	$0.636074\pi$
$948$	13.1292	0.426417
$949$	12.7417	0.413615
$950$	−5.44683	−0.176718
$951$	42.6474	1.38294
$952$	−0.824025	−0.0267068
$953$	−50.2681	−1.62834	−0.814172	−	0.580624i	$-0.802809\pi$
$953$	−50.2681	−1.62834	−0.814172	+	0.580624i	$0.802809\pi$
$954$	24.2722	0.785841
$955$	33.2216	1.07503
$956$	17.5957	0.569086
$957$	−37.2416	−1.20385
$958$	17.1755	0.554914
$959$	8.34869	0.269593
$960$	−3.91727	−0.126429
$961$	−11.2174	−0.361850
$962$	−40.1314	−1.29389
$963$	−30.6579	−0.987937
$964$	−18.9874	−0.611542
$965$	6.09639	0.196250
$966$	−5.07408	−0.163256
$967$	−50.2037	−1.61444	−0.807220	−	0.590250i	$-0.799029\pi$
$967$	−50.2037	−1.61444	−0.807220	+	0.590250i	$0.799029\pi$
$968$	−23.0951	−0.742306
$969$	−5.95488	−0.191298
$970$	30.7172	0.986270
$971$	35.4747	1.13844	0.569218	−	0.822187i	$-0.307246\pi$
$971$	35.4747	1.13844	0.569218	+	0.822187i	$0.307246\pi$
$972$	19.9584	0.640165
$973$	8.69414	0.278721
$974$	3.34097	0.107052
$975$	−23.5528	−0.754294
$976$	10.5287	0.337016
$977$	−42.8878	−1.37210	−0.686051	−	0.727554i	$-0.740657\pi$
$977$	−42.8878	−1.37210	−0.686051	+	0.727554i	$0.740657\pi$
$978$	23.1510	0.740288
$979$	59.0290	1.88658
$980$	−10.7065	−0.342006
$981$	3.96296	0.126528
$982$	−7.98483	−0.254806
$983$	7.83095	0.249769	0.124884	−	0.992171i	$-0.460144\pi$
$983$	7.83095	0.249769	0.124884	+	0.992171i	$0.460144\pi$
$984$	−19.3047	−0.615410
$985$	10.0837	0.321293
$986$	−2.78276	−0.0886210
$987$	−1.79972	−0.0572858
$988$	12.0277	0.382653
$989$	−10.0033	−0.318087
$990$	23.4290	0.744624
$991$	−32.6401	−1.03685	−0.518423	−	0.855124i	$-0.673481\pi$
$991$	−32.6401	−1.03685	−0.518423	+	0.855124i	$0.673481\pi$
$992$	4.44777	0.141217
$993$	−11.7316	−0.372290
$994$	−2.57894	−0.0817990
$995$	13.4945	0.427805
$996$	−21.0448	−0.666830
$997$	−21.9360	−0.694721	−0.347361	−	0.937732i	$-0.612922\pi$
$997$	−21.9360	−0.694721	−0.347361	+	0.937732i	$0.612922\pi$
$998$	17.6200	0.557751
$999$	−12.2836	−0.388636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.14	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.14	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.31833 q^{3} +1.00000 q^{4} +1.68969 q^{5} +2.31833 q^{6} -0.814652 q^{7} -1.00000 q^{8} +2.37465 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.31833 q^{3} +1.00000 q^{4} +1.68969 q^{5} +2.31833 q^{6} -0.814652 q^{7} -1.00000 q^{8} +2.37465 q^{9} -1.68969 q^{10} -5.83910 q^{11} -2.31833 q^{12} -4.73646 q^{13} +0.814652 q^{14} -3.91727 q^{15} +1.00000 q^{16} -1.01151 q^{17} -2.37465 q^{18} -2.53939 q^{19} +1.68969 q^{20} +1.88863 q^{21} +5.83910 q^{22} +2.68664 q^{23} +2.31833 q^{24} -2.14494 q^{25} +4.73646 q^{26} +1.44976 q^{27} -0.814652 q^{28} -2.75110 q^{29} +3.91727 q^{30} -4.44777 q^{31} -1.00000 q^{32} +13.5370 q^{33} +1.01151 q^{34} -1.37651 q^{35} +2.37465 q^{36} -8.47287 q^{37} +2.53939 q^{38} +10.9807 q^{39} -1.68969 q^{40} -8.32697 q^{41} -1.88863 q^{42} -3.72335 q^{43} -5.83910 q^{44} +4.01244 q^{45} -2.68664 q^{46} -0.952924 q^{47} -2.31833 q^{48} -6.33634 q^{49} +2.14494 q^{50} +2.34500 q^{51} -4.73646 q^{52} -10.2214 q^{53} -1.44976 q^{54} -9.86630 q^{55} +0.814652 q^{56} +5.88715 q^{57} +2.75110 q^{58} -5.71856 q^{59} -3.91727 q^{60} +10.5287 q^{61} +4.44777 q^{62} -1.93452 q^{63} +1.00000 q^{64} -8.00316 q^{65} -13.5370 q^{66} +8.23232 q^{67} -1.01151 q^{68} -6.22852 q^{69} +1.37651 q^{70} -3.16569 q^{71} -2.37465 q^{72} -2.69014 q^{73} +8.47287 q^{74} +4.97267 q^{75} -2.53939 q^{76} +4.75684 q^{77} -10.9807 q^{78} -5.66322 q^{79} +1.68969 q^{80} -10.4850 q^{81} +8.32697 q^{82} +9.07757 q^{83} +1.88863 q^{84} -1.70913 q^{85} +3.72335 q^{86} +6.37797 q^{87} +5.83910 q^{88} -10.1093 q^{89} -4.01244 q^{90} +3.85857 q^{91} +2.68664 q^{92} +10.3114 q^{93} +0.952924 q^{94} -4.29079 q^{95} +2.31833 q^{96} -18.1792 q^{97} +6.33634 q^{98} -13.8659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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