LMFDB - Embedded newform 4026.2.a.bb.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 $ x^8 - 3x^7 - 22x^6 + 42x^5 + 182x^4 - 111x^3 - 538x^2 - 256*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.42288$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.10747 q^{5} +1.00000 q^{6} -1.42288 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.10747 q^{5} +1.00000 q^{6} -1.42288 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.10747 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.35771 q^{13} -1.42288 q^{14} +4.10747 q^{15} +1.00000 q^{16} +3.83039 q^{17} +1.00000 q^{18} -3.67648 q^{19} +4.10747 q^{20} -1.42288 q^{21} -1.00000 q^{22} +2.60600 q^{23} +1.00000 q^{24} +11.8713 q^{25} +1.35771 q^{26} +1.00000 q^{27} -1.42288 q^{28} +5.91127 q^{29} +4.10747 q^{30} -4.71346 q^{31} +1.00000 q^{32} -1.00000 q^{33} +3.83039 q^{34} -5.84445 q^{35} +1.00000 q^{36} -11.0578 q^{37} -3.67648 q^{38} +1.35771 q^{39} +4.10747 q^{40} +4.99190 q^{41} -1.42288 q^{42} +10.2658 q^{43} -1.00000 q^{44} +4.10747 q^{45} +2.60600 q^{46} -13.0197 q^{47} +1.00000 q^{48} -4.97540 q^{49} +11.8713 q^{50} +3.83039 q^{51} +1.35771 q^{52} +11.1134 q^{53} +1.00000 q^{54} -4.10747 q^{55} -1.42288 q^{56} -3.67648 q^{57} +5.91127 q^{58} -10.0544 q^{59} +4.10747 q^{60} +1.00000 q^{61} -4.71346 q^{62} -1.42288 q^{63} +1.00000 q^{64} +5.57674 q^{65} -1.00000 q^{66} -6.68998 q^{67} +3.83039 q^{68} +2.60600 q^{69} -5.84445 q^{70} +12.7780 q^{71} +1.00000 q^{72} +0.832592 q^{73} -11.0578 q^{74} +11.8713 q^{75} -3.67648 q^{76} +1.42288 q^{77} +1.35771 q^{78} -3.15180 q^{79} +4.10747 q^{80} +1.00000 q^{81} +4.99190 q^{82} +13.9256 q^{83} -1.42288 q^{84} +15.7332 q^{85} +10.2658 q^{86} +5.91127 q^{87} -1.00000 q^{88} +5.54212 q^{89} +4.10747 q^{90} -1.93186 q^{91} +2.60600 q^{92} -4.71346 q^{93} -13.0197 q^{94} -15.1010 q^{95} +1.00000 q^{96} -7.11901 q^{97} -4.97540 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	4.10747	1.83692	0.918458	−	0.395519i	$-0.129435\pi$
$5$	4.10747	1.83692	0.918458	+	0.395519i	$0.129435\pi$
$6$	1.00000	0.408248
$7$	−1.42288	−0.537800	−0.268900	−	0.963168i	$-0.586660\pi$
$7$	−1.42288	−0.537800	−0.268900	+	0.963168i	$0.586660\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.10747	1.29890
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	1.35771	0.376560	0.188280	−	0.982115i	$-0.439709\pi$
$13$	1.35771	0.376560	0.188280	+	0.982115i	$0.439709\pi$
$14$	−1.42288	−0.380282
$15$	4.10747	1.06054
$16$	1.00000	0.250000
$17$	3.83039	0.929006	0.464503	−	0.885572i	$-0.346233\pi$
$17$	3.83039	0.929006	0.464503	+	0.885572i	$0.346233\pi$
$18$	1.00000	0.235702
$19$	−3.67648	−0.843443	−0.421721	−	0.906726i	$-0.638574\pi$
$19$	−3.67648	−0.843443	−0.421721	+	0.906726i	$0.638574\pi$
$20$	4.10747	0.918458
$21$	−1.42288	−0.310499
$22$	−1.00000	−0.213201
$23$	2.60600	0.543388	0.271694	−	0.962384i	$-0.412416\pi$
$23$	2.60600	0.543388	0.271694	+	0.962384i	$0.412416\pi$
$24$	1.00000	0.204124
$25$	11.8713	2.37426
$26$	1.35771	0.266268
$27$	1.00000	0.192450
$28$	−1.42288	−0.268900
$29$	5.91127	1.09770	0.548848	−	0.835922i	$-0.315067\pi$
$29$	5.91127	1.09770	0.548848	+	0.835922i	$0.315067\pi$
$30$	4.10747	0.749918
$31$	−4.71346	−0.846563	−0.423282	−	0.905998i	$-0.639122\pi$
$31$	−4.71346	−0.846563	−0.423282	+	0.905998i	$0.639122\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	3.83039	0.656906
$35$	−5.84445	−0.987892
$36$	1.00000	0.166667
$37$	−11.0578	−1.81789	−0.908946	−	0.416913i	$-0.863112\pi$
$37$	−11.0578	−1.81789	−0.908946	+	0.416913i	$0.863112\pi$
$38$	−3.67648	−0.596404
$39$	1.35771	0.217407
$40$	4.10747	0.649448
$41$	4.99190	0.779603	0.389802	−	0.920899i	$-0.372544\pi$
$41$	4.99190	0.779603	0.389802	+	0.920899i	$0.372544\pi$
$42$	−1.42288	−0.219556
$43$	10.2658	1.56551	0.782757	−	0.622328i	$-0.213813\pi$
$43$	10.2658	1.56551	0.782757	+	0.622328i	$0.213813\pi$
$44$	−1.00000	−0.150756
$45$	4.10747	0.612305
$46$	2.60600	0.384233
$47$	−13.0197	−1.89912	−0.949558	−	0.313592i	$-0.898468\pi$
$47$	−13.0197	−1.89912	−0.949558	+	0.313592i	$0.898468\pi$
$48$	1.00000	0.144338
$49$	−4.97540	−0.710771
$50$	11.8713	1.67885
$51$	3.83039	0.536362
$52$	1.35771	0.188280
$53$	11.1134	1.52655	0.763273	−	0.646076i	$-0.223591\pi$
$53$	11.1134	1.52655	0.763273	+	0.646076i	$0.223591\pi$
$54$	1.00000	0.136083
$55$	−4.10747	−0.553851
$56$	−1.42288	−0.190141
$57$	−3.67648	−0.486962
$58$	5.91127	0.776188
$59$	−10.0544	−1.30897	−0.654486	−	0.756074i	$-0.727115\pi$
$59$	−10.0544	−1.30897	−0.654486	+	0.756074i	$0.727115\pi$
$60$	4.10747	0.530272
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.71346	−0.598610
$63$	−1.42288	−0.179267
$64$	1.00000	0.125000
$65$	5.57674	0.691710
$66$	−1.00000	−0.123091
$67$	−6.68998	−0.817311	−0.408656	−	0.912689i	$-0.634002\pi$
$67$	−6.68998	−0.817311	−0.408656	+	0.912689i	$0.634002\pi$
$68$	3.83039	0.464503
$69$	2.60600	0.313725
$70$	−5.84445	−0.698545
$71$	12.7780	1.51647	0.758235	−	0.651981i	$-0.226062\pi$
$71$	12.7780	1.51647	0.758235	+	0.651981i	$0.226062\pi$
$72$	1.00000	0.117851
$73$	0.832592	0.0974476	0.0487238	−	0.998812i	$-0.484485\pi$
$73$	0.832592	0.0974476	0.0487238	+	0.998812i	$0.484485\pi$
$74$	−11.0578	−1.28544
$75$	11.8713	1.37078
$76$	−3.67648	−0.421721
$77$	1.42288	0.162153
$78$	1.35771	0.153730
$79$	−3.15180	−0.354605	−0.177303	−	0.984156i	$-0.556737\pi$
$79$	−3.15180	−0.354605	−0.177303	+	0.984156i	$0.556737\pi$
$80$	4.10747	0.459229
$81$	1.00000	0.111111
$82$	4.99190	0.551263
$83$	13.9256	1.52854	0.764269	−	0.644898i	$-0.223100\pi$
$83$	13.9256	1.52854	0.764269	+	0.644898i	$0.223100\pi$
$84$	−1.42288	−0.155249
$85$	15.7332	1.70650
$86$	10.2658	1.10699
$87$	5.91127	0.633755
$88$	−1.00000	−0.106600
$89$	5.54212	0.587464	0.293732	−	0.955888i	$-0.405103\pi$
$89$	5.54212	0.587464	0.293732	+	0.955888i	$0.405103\pi$
$90$	4.10747	0.432965
$91$	−1.93186	−0.202514
$92$	2.60600	0.271694
$93$	−4.71346	−0.488763
$94$	−13.0197	−1.34288
$95$	−15.1010	−1.54933
$96$	1.00000	0.102062
$97$	−7.11901	−0.722826	−0.361413	−	0.932406i	$-0.617706\pi$
$97$	−7.11901	−0.722826	−0.361413	+	0.932406i	$0.617706\pi$
$98$	−4.97540	−0.502591
$99$	−1.00000	−0.100504
$100$	11.8713	1.18713
$101$	7.29628	0.726007	0.363004	−	0.931788i	$-0.381751\pi$
$101$	7.29628	0.726007	0.363004	+	0.931788i	$0.381751\pi$
$102$	3.83039	0.379265
$103$	12.2396	1.20600	0.603000	−	0.797742i	$-0.293972\pi$
$103$	12.2396	1.20600	0.603000	+	0.797742i	$0.293972\pi$
$104$	1.35771	0.133134
$105$	−5.84445	−0.570360
$106$	11.1134	1.07943
$107$	−14.3397	−1.38627	−0.693134	−	0.720809i	$-0.743771\pi$
$107$	−14.3397	−1.38627	−0.693134	+	0.720809i	$0.743771\pi$
$108$	1.00000	0.0962250
$109$	−10.7776	−1.03230	−0.516152	−	0.856497i	$-0.672636\pi$
$109$	−10.7776	−1.03230	−0.516152	+	0.856497i	$0.672636\pi$
$110$	−4.10747	−0.391632
$111$	−11.0578	−1.04956
$112$	−1.42288	−0.134450
$113$	−3.15790	−0.297070	−0.148535	−	0.988907i	$-0.547456\pi$
$113$	−3.15790	−0.297070	−0.148535	+	0.988907i	$0.547456\pi$
$114$	−3.67648	−0.344334
$115$	10.7040	0.998157
$116$	5.91127	0.548848
$117$	1.35771	0.125520
$118$	−10.0544	−0.925583
$119$	−5.45020	−0.499619
$120$	4.10747	0.374959
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	4.99190	0.450104
$124$	−4.71346	−0.423282
$125$	28.2236	2.52440
$126$	−1.42288	−0.126761
$127$	−10.3986	−0.922727	−0.461364	−	0.887211i	$-0.652640\pi$
$127$	−10.3986	−0.922727	−0.461364	+	0.887211i	$0.652640\pi$
$128$	1.00000	0.0883883
$129$	10.2658	0.903850
$130$	5.57674	0.489113
$131$	−2.37667	−0.207651	−0.103825	−	0.994596i	$-0.533108\pi$
$131$	−2.37667	−0.207651	−0.103825	+	0.994596i	$0.533108\pi$
$132$	−1.00000	−0.0870388
$133$	5.23121	0.453603
$134$	−6.68998	−0.577926
$135$	4.10747	0.353515
$136$	3.83039	0.328453
$137$	3.23285	0.276201	0.138100	−	0.990418i	$-0.455900\pi$
$137$	3.23285	0.276201	0.138100	+	0.990418i	$0.455900\pi$
$138$	2.60600	0.221837
$139$	−6.86229	−0.582052	−0.291026	−	0.956715i	$-0.593997\pi$
$139$	−6.86229	−0.582052	−0.291026	+	0.956715i	$0.593997\pi$
$140$	−5.84445	−0.493946
$141$	−13.0197	−1.09646
$142$	12.7780	1.07231
$143$	−1.35771	−0.113537
$144$	1.00000	0.0833333
$145$	24.2803	2.01637
$146$	0.832592	0.0689058
$147$	−4.97540	−0.410364
$148$	−11.0578	−0.908946
$149$	−2.54990	−0.208896	−0.104448	−	0.994530i	$-0.533308\pi$
$149$	−2.54990	−0.208896	−0.104448	+	0.994530i	$0.533308\pi$
$150$	11.8713	0.969287
$151$	−6.94441	−0.565128	−0.282564	−	0.959248i	$-0.591185\pi$
$151$	−6.94441	−0.565128	−0.282564	+	0.959248i	$0.591185\pi$
$152$	−3.67648	−0.298202
$153$	3.83039	0.309669
$154$	1.42288	0.114659
$155$	−19.3604	−1.55506
$156$	1.35771	0.108704
$157$	−13.2590	−1.05819	−0.529093	−	0.848564i	$-0.677468\pi$
$157$	−13.2590	−1.05819	−0.529093	+	0.848564i	$0.677468\pi$
$158$	−3.15180	−0.250744
$159$	11.1134	0.881352
$160$	4.10747	0.324724
$161$	−3.70803	−0.292234
$162$	1.00000	0.0785674
$163$	−21.6257	−1.69386	−0.846929	−	0.531706i	$-0.821551\pi$
$163$	−21.6257	−1.69386	−0.846929	+	0.531706i	$0.821551\pi$
$164$	4.99190	0.389802
$165$	−4.10747	−0.319766
$166$	13.9256	1.08084
$167$	7.91006	0.612098	0.306049	−	0.952016i	$-0.400993\pi$
$167$	7.91006	0.612098	0.306049	+	0.952016i	$0.400993\pi$
$168$	−1.42288	−0.109778
$169$	−11.1566	−0.858202
$170$	15.7332	1.20668
$171$	−3.67648	−0.281148
$172$	10.2658	0.782757
$173$	13.6471	1.03757	0.518786	−	0.854904i	$-0.326384\pi$
$173$	13.6471	1.03757	0.518786	+	0.854904i	$0.326384\pi$
$174$	5.91127	0.448132
$175$	−16.8915	−1.27688
$176$	−1.00000	−0.0753778
$177$	−10.0544	−0.755735
$178$	5.54212	0.415400
$179$	−11.8058	−0.882406	−0.441203	−	0.897407i	$-0.645448\pi$
$179$	−11.8058	−0.882406	−0.441203	+	0.897407i	$0.645448\pi$
$180$	4.10747	0.306153
$181$	1.97489	0.146793	0.0733963	−	0.997303i	$-0.476616\pi$
$181$	1.97489	0.146793	0.0733963	+	0.997303i	$0.476616\pi$
$182$	−1.93186	−0.143199
$183$	1.00000	0.0739221
$184$	2.60600	0.192117
$185$	−45.4196	−3.33931
$186$	−4.71346	−0.345608
$187$	−3.83039	−0.280106
$188$	−13.0197	−0.949558
$189$	−1.42288	−0.103500
$190$	−15.1010	−1.09554
$191$	−11.8090	−0.854469	−0.427234	−	0.904141i	$-0.640512\pi$
$191$	−11.8090	−0.854469	−0.427234	+	0.904141i	$0.640512\pi$
$192$	1.00000	0.0721688
$193$	−23.8698	−1.71819	−0.859094	−	0.511818i	$-0.828972\pi$
$193$	−23.8698	−1.71819	−0.859094	+	0.511818i	$0.828972\pi$
$194$	−7.11901	−0.511115
$195$	5.57674	0.399359
$196$	−4.97540	−0.355386
$197$	7.36122	0.524465	0.262233	−	0.965005i	$-0.415541\pi$
$197$	7.36122	0.524465	0.262233	+	0.965005i	$0.415541\pi$
$198$	−1.00000	−0.0710669
$199$	12.5538	0.889915	0.444958	−	0.895552i	$-0.353219\pi$
$199$	12.5538	0.889915	0.444958	+	0.895552i	$0.353219\pi$
$200$	11.8713	0.839427
$201$	−6.68998	−0.471875
$202$	7.29628	0.513365
$203$	−8.41105	−0.590340
$204$	3.83039	0.268181
$205$	20.5041	1.43207
$206$	12.2396	0.852770
$207$	2.60600	0.181129
$208$	1.35771	0.0941401
$209$	3.67648	0.254308
$210$	−5.84445	−0.403305
$211$	19.1327	1.31715	0.658575	−	0.752515i	$-0.271159\pi$
$211$	19.1327	1.31715	0.658575	+	0.752515i	$0.271159\pi$
$212$	11.1134	0.763273
$213$	12.7780	0.875535
$214$	−14.3397	−0.980240
$215$	42.1663	2.87572
$216$	1.00000	0.0680414
$217$	6.70671	0.455281
$218$	−10.7776	−0.729949
$219$	0.832592	0.0562614
$220$	−4.10747	−0.276925
$221$	5.20055	0.349827
$222$	−11.0578	−0.742152
$223$	5.86877	0.393002	0.196501	−	0.980504i	$-0.437042\pi$
$223$	5.86877	0.393002	0.196501	+	0.980504i	$0.437042\pi$
$224$	−1.42288	−0.0950705
$225$	11.8713	0.791419
$226$	−3.15790	−0.210060
$227$	16.8179	1.11624	0.558120	−	0.829760i	$-0.311523\pi$
$227$	16.8179	1.11624	0.558120	+	0.829760i	$0.311523\pi$
$228$	−3.67648	−0.243481
$229$	−21.5733	−1.42560	−0.712802	−	0.701365i	$-0.752574\pi$
$229$	−21.5733	−1.42560	−0.712802	+	0.701365i	$0.752574\pi$
$230$	10.7040	0.705804
$231$	1.42288	0.0936189
$232$	5.91127	0.388094
$233$	−11.7417	−0.769227	−0.384614	−	0.923078i	$-0.625665\pi$
$233$	−11.7417	−0.769227	−0.384614	+	0.923078i	$0.625665\pi$
$234$	1.35771	0.0887561
$235$	−53.4779	−3.48852
$236$	−10.0544	−0.654486
$237$	−3.15180	−0.204731
$238$	−5.45020	−0.353284
$239$	23.1597	1.49808	0.749038	−	0.662528i	$-0.230516\pi$
$239$	23.1597	1.49808	0.749038	+	0.662528i	$0.230516\pi$
$240$	4.10747	0.265136
$241$	9.55766	0.615663	0.307831	−	0.951441i	$-0.400397\pi$
$241$	9.55766	0.615663	0.307831	+	0.951441i	$0.400397\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−20.4363	−1.30563
$246$	4.99190	0.318272
$247$	−4.99159	−0.317607
$248$	−4.71346	−0.299305
$249$	13.9256	0.882502
$250$	28.2236	1.78502
$251$	−0.638796	−0.0403205	−0.0201602	−	0.999797i	$-0.506418\pi$
$251$	−0.638796	−0.0403205	−0.0201602	+	0.999797i	$0.506418\pi$
$252$	−1.42288	−0.0896333
$253$	−2.60600	−0.163838
$254$	−10.3986	−0.652467
$255$	15.7332	0.985251
$256$	1.00000	0.0625000
$257$	23.7374	1.48070	0.740350	−	0.672221i	$-0.234660\pi$
$257$	23.7374	1.48070	0.740350	+	0.672221i	$0.234660\pi$
$258$	10.2658	0.639118
$259$	15.7340	0.977662
$260$	5.57674	0.345855
$261$	5.91127	0.365898
$262$	−2.37667	−0.146831
$263$	16.5229	1.01884	0.509422	−	0.860517i	$-0.329859\pi$
$263$	16.5229	1.01884	0.509422	+	0.860517i	$0.329859\pi$
$264$	−1.00000	−0.0615457
$265$	45.6480	2.80414
$266$	5.23121	0.320746
$267$	5.54212	0.339172
$268$	−6.68998	−0.408656
$269$	−7.99577	−0.487511	−0.243755	−	0.969837i	$-0.578379\pi$
$269$	−7.99577	−0.487511	−0.243755	+	0.969837i	$0.578379\pi$
$270$	4.10747	0.249973
$271$	−4.76725	−0.289590	−0.144795	−	0.989462i	$-0.546252\pi$
$271$	−4.76725	−0.289590	−0.144795	+	0.989462i	$0.546252\pi$
$272$	3.83039	0.232251
$273$	−1.93186	−0.116922
$274$	3.23285	0.195304
$275$	−11.8713	−0.715866
$276$	2.60600	0.156863
$277$	−16.9682	−1.01952	−0.509761	−	0.860316i	$-0.670266\pi$
$277$	−16.9682	−1.01952	−0.509761	+	0.860316i	$0.670266\pi$
$278$	−6.86229	−0.411573
$279$	−4.71346	−0.282188
$280$	−5.84445	−0.349273
$281$	−13.4780	−0.804031	−0.402015	−	0.915633i	$-0.631690\pi$
$281$	−13.4780	−0.804031	−0.402015	+	0.915633i	$0.631690\pi$
$282$	−13.0197	−0.775311
$283$	−31.7376	−1.88661	−0.943303	−	0.331934i	$-0.892299\pi$
$283$	−31.7376	−1.88661	−0.943303	+	0.331934i	$0.892299\pi$
$284$	12.7780	0.758235
$285$	−15.1010	−0.894508
$286$	−1.35771	−0.0802829
$287$	−7.10289	−0.419271
$288$	1.00000	0.0589256
$289$	−2.32812	−0.136948
$290$	24.2803	1.42579
$291$	−7.11901	−0.417324
$292$	0.832592	0.0487238
$293$	−29.0309	−1.69601	−0.848003	−	0.529992i	$-0.822195\pi$
$293$	−29.0309	−1.69601	−0.848003	+	0.529992i	$0.822195\pi$
$294$	−4.97540	−0.290171
$295$	−41.2981	−2.40447
$296$	−11.0578	−0.642722
$297$	−1.00000	−0.0580259
$298$	−2.54990	−0.147712
$299$	3.53818	0.204618
$300$	11.8713	0.685389
$301$	−14.6070	−0.841933
$302$	−6.94441	−0.399606
$303$	7.29628	0.419160
$304$	−3.67648	−0.210861
$305$	4.10747	0.235193
$306$	3.83039	0.218969
$307$	−1.57252	−0.0897484	−0.0448742	−	0.998993i	$-0.514289\pi$
$307$	−1.57252	−0.0897484	−0.0448742	+	0.998993i	$0.514289\pi$
$308$	1.42288	0.0810764
$309$	12.2396	0.696284
$310$	−19.3604	−1.09960
$311$	−26.9163	−1.52628	−0.763142	−	0.646231i	$-0.776344\pi$
$311$	−26.9163	−1.52628	−0.763142	+	0.646231i	$0.776344\pi$
$312$	1.35771	0.0768651
$313$	9.09300	0.513967	0.256983	−	0.966416i	$-0.417271\pi$
$313$	9.09300	0.513967	0.256983	+	0.966416i	$0.417271\pi$
$314$	−13.2590	−0.748250
$315$	−5.84445	−0.329297
$316$	−3.15180	−0.177303
$317$	19.7222	1.10771	0.553856	−	0.832613i	$-0.313156\pi$
$317$	19.7222	1.10771	0.553856	+	0.832613i	$0.313156\pi$
$318$	11.1134	0.623210
$319$	−5.91127	−0.330968
$320$	4.10747	0.229614
$321$	−14.3397	−0.800362
$322$	−3.70803	−0.206640
$323$	−14.0824	−0.783563
$324$	1.00000	0.0555556
$325$	16.1177	0.894052
$326$	−21.6257	−1.19774
$327$	−10.7776	−0.596001
$328$	4.99190	0.275631
$329$	18.5255	1.02134
$330$	−4.10747	−0.226109
$331$	17.4514	0.959214	0.479607	−	0.877483i	$-0.340779\pi$
$331$	17.4514	0.959214	0.479607	+	0.877483i	$0.340779\pi$
$332$	13.9256	0.764269
$333$	−11.0578	−0.605964
$334$	7.91006	0.432819
$335$	−27.4789	−1.50133
$336$	−1.42288	−0.0776247
$337$	31.2281	1.70110	0.850551	−	0.525893i	$-0.176269\pi$
$337$	31.2281	1.70110	0.850551	+	0.525893i	$0.176269\pi$
$338$	−11.1566	−0.606841
$339$	−3.15790	−0.171513
$340$	15.7332	0.853252
$341$	4.71346	0.255248
$342$	−3.67648	−0.198801
$343$	17.0396	0.920052
$344$	10.2658	0.553493
$345$	10.7040	0.576286
$346$	13.6471	0.733675
$347$	−7.77055	−0.417145	−0.208573	−	0.978007i	$-0.566882\pi$
$347$	−7.77055	−0.417145	−0.208573	+	0.978007i	$0.566882\pi$
$348$	5.91127	0.316877
$349$	−10.9441	−0.585824	−0.292912	−	0.956139i	$-0.594624\pi$
$349$	−10.9441	−0.585824	−0.292912	+	0.956139i	$0.594624\pi$
$350$	−16.8915	−0.902887
$351$	1.35771	0.0724691
$352$	−1.00000	−0.0533002
$353$	17.6048	0.937007	0.468504	−	0.883462i	$-0.344793\pi$
$353$	17.6048	0.937007	0.468504	+	0.883462i	$0.344793\pi$
$354$	−10.0544	−0.534385
$355$	52.4853	2.78563
$356$	5.54212	0.293732
$357$	−5.45020	−0.288455
$358$	−11.8058	−0.623955
$359$	−9.83321	−0.518977	−0.259488	−	0.965746i	$-0.583554\pi$
$359$	−9.83321	−0.518977	−0.259488	+	0.965746i	$0.583554\pi$
$360$	4.10747	0.216483
$361$	−5.48349	−0.288605
$362$	1.97489	0.103798
$363$	1.00000	0.0524864
$364$	−1.93186	−0.101257
$365$	3.41985	0.179003
$366$	1.00000	0.0522708
$367$	−20.7128	−1.08120	−0.540600	−	0.841280i	$-0.681803\pi$
$367$	−20.7128	−1.08120	−0.540600	+	0.841280i	$0.681803\pi$
$368$	2.60600	0.135847
$369$	4.99190	0.259868
$370$	−45.4196	−2.36125
$371$	−15.8131	−0.820976
$372$	−4.71346	−0.244382
$373$	22.9216	1.18684	0.593418	−	0.804894i	$-0.297778\pi$
$373$	22.9216	1.18684	0.593418	+	0.804894i	$0.297778\pi$
$374$	−3.83039	−0.198065
$375$	28.2236	1.45746
$376$	−13.0197	−0.671439
$377$	8.02578	0.413349
$378$	−1.42288	−0.0731853
$379$	3.58342	0.184068	0.0920339	−	0.995756i	$-0.470663\pi$
$379$	3.58342	0.184068	0.0920339	+	0.995756i	$0.470663\pi$
$380$	−15.1010	−0.774666
$381$	−10.3986	−0.532737
$382$	−11.8090	−0.604201
$383$	−36.2661	−1.85311	−0.926556	−	0.376158i	$-0.877245\pi$
$383$	−36.2661	−1.85311	−0.926556	+	0.376158i	$0.877245\pi$
$384$	1.00000	0.0510310
$385$	5.84445	0.297861
$386$	−23.8698	−1.21494
$387$	10.2658	0.521838
$388$	−7.11901	−0.361413
$389$	−26.9353	−1.36567	−0.682836	−	0.730572i	$-0.739254\pi$
$389$	−26.9353	−1.36567	−0.682836	+	0.730572i	$0.739254\pi$
$390$	5.57674	0.282389
$391$	9.98198	0.504810
$392$	−4.97540	−0.251296
$393$	−2.37667	−0.119887
$394$	7.36122	0.370853
$395$	−12.9459	−0.651380
$396$	−1.00000	−0.0502519
$397$	6.90455	0.346530	0.173265	−	0.984875i	$-0.444568\pi$
$397$	6.90455	0.346530	0.173265	+	0.984875i	$0.444568\pi$
$398$	12.5538	0.629265
$399$	5.23121	0.261888
$400$	11.8713	0.593564
$401$	15.3687	0.767476	0.383738	−	0.923442i	$-0.374637\pi$
$401$	15.3687	0.767476	0.383738	+	0.923442i	$0.374637\pi$
$402$	−6.68998	−0.333666
$403$	−6.39951	−0.318782
$404$	7.29628	0.363004
$405$	4.10747	0.204102
$406$	−8.41105	−0.417433
$407$	11.0578	0.548115
$408$	3.83039	0.189632
$409$	−11.1119	−0.549448	−0.274724	−	0.961523i	$-0.588587\pi$
$409$	−11.1119	−0.549448	−0.274724	+	0.961523i	$0.588587\pi$
$410$	20.5041	1.01262
$411$	3.23285	0.159465
$412$	12.2396	0.603000
$413$	14.3062	0.703964
$414$	2.60600	0.128078
$415$	57.1991	2.80779
$416$	1.35771	0.0665671
$417$	−6.86229	−0.336048
$418$	3.67648	0.179823
$419$	18.5086	0.904204	0.452102	−	0.891966i	$-0.350674\pi$
$419$	18.5086	0.904204	0.452102	+	0.891966i	$0.350674\pi$
$420$	−5.84445	−0.285180
$421$	−25.2737	−1.23177	−0.615883	−	0.787837i	$-0.711201\pi$
$421$	−25.2737	−1.23177	−0.615883	+	0.787837i	$0.711201\pi$
$422$	19.1327	0.931366
$423$	−13.0197	−0.633039
$424$	11.1134	0.539716
$425$	45.4717	2.20570
$426$	12.7780	0.619097
$427$	−1.42288	−0.0688582
$428$	−14.3397	−0.693134
$429$	−1.35771	−0.0655508
$430$	42.1663	2.03344
$431$	10.5667	0.508979	0.254490	−	0.967076i	$-0.418093\pi$
$431$	10.5667	0.508979	0.254490	+	0.967076i	$0.418093\pi$
$432$	1.00000	0.0481125
$433$	3.13640	0.150726	0.0753629	−	0.997156i	$-0.475988\pi$
$433$	3.13640	0.150726	0.0753629	+	0.997156i	$0.475988\pi$
$434$	6.70671	0.321933
$435$	24.2803	1.16415
$436$	−10.7776	−0.516152
$437$	−9.58089	−0.458316
$438$	0.832592	0.0397828
$439$	−18.6958	−0.892303	−0.446151	−	0.894957i	$-0.647206\pi$
$439$	−18.6958	−0.892303	−0.446151	+	0.894957i	$0.647206\pi$
$440$	−4.10747	−0.195816
$441$	−4.97540	−0.236924
$442$	5.20055	0.247365
$443$	−3.94422	−0.187396	−0.0936978	−	0.995601i	$-0.529869\pi$
$443$	−3.94422	−0.187396	−0.0936978	+	0.995601i	$0.529869\pi$
$444$	−11.0578	−0.524780
$445$	22.7641	1.07912
$446$	5.86877	0.277895
$447$	−2.54990	−0.120606
$448$	−1.42288	−0.0672250
$449$	−35.3741	−1.66941	−0.834704	−	0.550699i	$-0.814361\pi$
$449$	−35.3741	−1.66941	−0.834704	+	0.550699i	$0.814361\pi$
$450$	11.8713	0.559618
$451$	−4.99190	−0.235059
$452$	−3.15790	−0.148535
$453$	−6.94441	−0.326277
$454$	16.8179	0.789301
$455$	−7.93506	−0.372001
$456$	−3.67648	−0.172167
$457$	34.1323	1.59664	0.798321	−	0.602232i	$-0.205722\pi$
$457$	34.1323	1.59664	0.798321	+	0.602232i	$0.205722\pi$
$458$	−21.5733	−1.00805
$459$	3.83039	0.178787
$460$	10.7040	0.499079
$461$	29.0729	1.35406	0.677030	−	0.735956i	$-0.263267\pi$
$461$	29.0729	1.35406	0.677030	+	0.735956i	$0.263267\pi$
$462$	1.42288	0.0661986
$463$	15.8931	0.738617	0.369309	−	0.929307i	$-0.379595\pi$
$463$	15.8931	0.738617	0.369309	+	0.929307i	$0.379595\pi$
$464$	5.91127	0.274424
$465$	−19.3604	−0.897817
$466$	−11.7417	−0.543926
$467$	−6.87174	−0.317986	−0.158993	−	0.987280i	$-0.550825\pi$
$467$	−6.87174	−0.317986	−0.158993	+	0.987280i	$0.550825\pi$
$468$	1.35771	0.0627601
$469$	9.51907	0.439550
$470$	−53.4779	−2.46675
$471$	−13.2590	−0.610943
$472$	−10.0544	−0.462791
$473$	−10.2658	−0.472020
$474$	−3.15180	−0.144767
$475$	−43.6446	−2.00255
$476$	−5.45020	−0.249809
$477$	11.1134	0.508849
$478$	23.1597	1.05930
$479$	−12.0445	−0.550329	−0.275165	−	0.961397i	$-0.588732\pi$
$479$	−12.0445	−0.550329	−0.275165	+	0.961397i	$0.588732\pi$
$480$	4.10747	0.187479
$481$	−15.0133	−0.684546
$482$	9.55766	0.435339
$483$	−3.70803	−0.168721
$484$	1.00000	0.0454545
$485$	−29.2411	−1.32777
$486$	1.00000	0.0453609
$487$	17.1802	0.778511	0.389255	−	0.921130i	$-0.372732\pi$
$487$	17.1802	0.778511	0.389255	+	0.921130i	$0.372732\pi$
$488$	1.00000	0.0452679
$489$	−21.6257	−0.977949
$490$	−20.4363	−0.923218
$491$	10.5248	0.474978	0.237489	−	0.971390i	$-0.423676\pi$
$491$	10.5248	0.474978	0.237489	+	0.971390i	$0.423676\pi$
$492$	4.99190	0.225052
$493$	22.6425	1.01976
$494$	−4.99159	−0.224582
$495$	−4.10747	−0.184617
$496$	−4.71346	−0.211641
$497$	−18.1816	−0.815557
$498$	13.9256	0.624023
$499$	28.7356	1.28638	0.643192	−	0.765705i	$-0.277610\pi$
$499$	28.7356	1.28638	0.643192	+	0.765705i	$0.277610\pi$
$500$	28.2236	1.26220
$501$	7.91006	0.353395
$502$	−0.638796	−0.0285109
$503$	1.24265	0.0554071	0.0277035	−	0.999616i	$-0.491181\pi$
$503$	1.24265	0.0554071	0.0277035	+	0.999616i	$0.491181\pi$
$504$	−1.42288	−0.0633803
$505$	29.9692	1.33361
$506$	−2.60600	−0.115851
$507$	−11.1566	−0.495483
$508$	−10.3986	−0.461364
$509$	−25.9689	−1.15105	−0.575526	−	0.817783i	$-0.695203\pi$
$509$	−25.9689	−1.15105	−0.575526	+	0.817783i	$0.695203\pi$
$510$	15.7332	0.696678
$511$	−1.18468	−0.0524073
$512$	1.00000	0.0441942
$513$	−3.67648	−0.162321
$514$	23.7374	1.04701
$515$	50.2736	2.21532
$516$	10.2658	0.451925
$517$	13.0197	0.572605
$518$	15.7340	0.691311
$519$	13.6471	0.599043
$520$	5.57674	0.244556
$521$	16.2047	0.709939	0.354970	−	0.934878i	$-0.384491\pi$
$521$	16.2047	0.709939	0.354970	+	0.934878i	$0.384491\pi$
$522$	5.91127	0.258729
$523$	28.2588	1.23567	0.617835	−	0.786308i	$-0.288010\pi$
$523$	28.2588	1.23567	0.617835	+	0.786308i	$0.288010\pi$
$524$	−2.37667	−0.103825
$525$	−16.8915	−0.737204
$526$	16.5229	0.720431
$527$	−18.0544	−0.786462
$528$	−1.00000	−0.0435194
$529$	−16.2088	−0.704730
$530$	45.6480	1.98282
$531$	−10.0544	−0.436324
$532$	5.23121	0.226802
$533$	6.77754	0.293568
$534$	5.54212	0.239831
$535$	−58.8997	−2.54646
$536$	−6.68998	−0.288963
$537$	−11.8058	−0.509457
$538$	−7.99577	−0.344722
$539$	4.97540	0.214306
$540$	4.10747	0.176757
$541$	31.7978	1.36709	0.683547	−	0.729907i	$-0.260436\pi$
$541$	31.7978	1.36709	0.683547	+	0.729907i	$0.260436\pi$
$542$	−4.76725	−0.204771
$543$	1.97489	0.0847507
$544$	3.83039	0.164227
$545$	−44.2685	−1.89626
$546$	−1.93186	−0.0826760
$547$	−23.9072	−1.02220	−0.511100	−	0.859521i	$-0.670762\pi$
$547$	−23.9072	−1.02220	−0.511100	+	0.859521i	$0.670762\pi$
$548$	3.23285	0.138100
$549$	1.00000	0.0426790
$550$	−11.8713	−0.506193
$551$	−21.7327	−0.925843
$552$	2.60600	0.110919
$553$	4.48465	0.190707
$554$	−16.9682	−0.720910
$555$	−45.4196	−1.92795
$556$	−6.86229	−0.291026
$557$	−21.7193	−0.920278	−0.460139	−	0.887847i	$-0.652200\pi$
$557$	−21.7193	−0.920278	−0.460139	+	0.887847i	$0.652200\pi$
$558$	−4.71346	−0.199537
$559$	13.9379	0.589510
$560$	−5.84445	−0.246973
$561$	−3.83039	−0.161719
$562$	−13.4780	−0.568536
$563$	−14.4630	−0.609543	−0.304772	−	0.952425i	$-0.598580\pi$
$563$	−14.4630	−0.609543	−0.304772	+	0.952425i	$0.598580\pi$
$564$	−13.0197	−0.548228
$565$	−12.9710	−0.545692
$566$	−31.7376	−1.33403
$567$	−1.42288	−0.0597555
$568$	12.7780	0.536153
$569$	12.1466	0.509210	0.254605	−	0.967045i	$-0.418055\pi$
$569$	12.1466	0.509210	0.254605	+	0.967045i	$0.418055\pi$
$570$	−15.1010	−0.632512
$571$	11.4183	0.477839	0.238920	−	0.971039i	$-0.423207\pi$
$571$	11.4183	0.477839	0.238920	+	0.971039i	$0.423207\pi$
$572$	−1.35771	−0.0567686
$573$	−11.8090	−0.493328
$574$	−7.10289	−0.296469
$575$	30.9365	1.29014
$576$	1.00000	0.0416667
$577$	16.6000	0.691067	0.345534	−	0.938406i	$-0.387698\pi$
$577$	16.6000	0.691067	0.345534	+	0.938406i	$0.387698\pi$
$578$	−2.32812	−0.0968372
$579$	−23.8698	−0.991996
$580$	24.2803	1.00819
$581$	−19.8146	−0.822047
$582$	−7.11901	−0.295092
$583$	−11.1134	−0.460271
$584$	0.832592	0.0344529
$585$	5.57674	0.230570
$586$	−29.0309	−1.19926
$587$	3.05147	0.125948	0.0629738	−	0.998015i	$-0.479942\pi$
$587$	3.05147	0.125948	0.0629738	+	0.998015i	$0.479942\pi$
$588$	−4.97540	−0.205182
$589$	17.3290	0.714027
$590$	−41.2981	−1.70022
$591$	7.36122	0.302800
$592$	−11.0578	−0.454473
$593$	−14.7290	−0.604848	−0.302424	−	0.953173i	$-0.597796\pi$
$593$	−14.7290	−0.604848	−0.302424	+	0.953173i	$0.597796\pi$
$594$	−1.00000	−0.0410305
$595$	−22.3865	−0.917758
$596$	−2.54990	−0.104448
$597$	12.5538	0.513793
$598$	3.53818	0.144687
$599$	45.3750	1.85397	0.926987	−	0.375094i	$-0.122389\pi$
$599$	45.3750	1.85397	0.926987	+	0.375094i	$0.122389\pi$
$600$	11.8713	0.484643
$601$	−17.3276	−0.706807	−0.353404	−	0.935471i	$-0.614976\pi$
$601$	−17.3276	−0.706807	−0.353404	+	0.935471i	$0.614976\pi$
$602$	−14.6070	−0.595336
$603$	−6.68998	−0.272437
$604$	−6.94441	−0.282564
$605$	4.10747	0.166992
$606$	7.29628	0.296391
$607$	34.5021	1.40040	0.700199	−	0.713948i	$-0.253095\pi$
$607$	34.5021	1.40040	0.700199	+	0.713948i	$0.253095\pi$
$608$	−3.67648	−0.149101
$609$	−8.41105	−0.340833
$610$	4.10747	0.166306
$611$	−17.6769	−0.715132
$612$	3.83039	0.154834
$613$	25.2513	1.01989	0.509946	−	0.860207i	$-0.329665\pi$
$613$	25.2513	1.01989	0.509946	+	0.860207i	$0.329665\pi$
$614$	−1.57252	−0.0634617
$615$	20.5041	0.826803
$616$	1.42288	0.0573296
$617$	−28.3837	−1.14268	−0.571342	−	0.820712i	$-0.693577\pi$
$617$	−28.3837	−1.14268	−0.571342	+	0.820712i	$0.693577\pi$
$618$	12.2396	0.492347
$619$	17.3561	0.697599	0.348800	−	0.937197i	$-0.386589\pi$
$619$	17.3561	0.697599	0.348800	+	0.937197i	$0.386589\pi$
$620$	−19.3604	−0.777532
$621$	2.60600	0.104575
$622$	−26.9163	−1.07925
$623$	−7.88580	−0.315938
$624$	1.35771	0.0543518
$625$	56.5711	2.26284
$626$	9.09300	0.363430
$627$	3.67648	0.146825
$628$	−13.2590	−0.529093
$629$	−42.3557	−1.68883
$630$	−5.84445	−0.232848
$631$	−23.1140	−0.920156	−0.460078	−	0.887879i	$-0.652178\pi$
$631$	−23.1140	−0.920156	−0.460078	+	0.887879i	$0.652178\pi$
$632$	−3.15180	−0.125372
$633$	19.1327	0.760457
$634$	19.7222	0.783271
$635$	−42.7119	−1.69497
$636$	11.1134	0.440676
$637$	−6.75514	−0.267648
$638$	−5.91127	−0.234029
$639$	12.7780	0.505490
$640$	4.10747	0.162362
$641$	−32.9678	−1.30215	−0.651075	−	0.759013i	$-0.725682\pi$
$641$	−32.9678	−1.30215	−0.651075	+	0.759013i	$0.725682\pi$
$642$	−14.3397	−0.565942
$643$	38.4964	1.51815	0.759075	−	0.651004i	$-0.225652\pi$
$643$	38.4964	1.51815	0.759075	+	0.651004i	$0.225652\pi$
$644$	−3.70803	−0.146117
$645$	42.1663	1.66030
$646$	−14.0824	−0.554063
$647$	−27.4947	−1.08093	−0.540464	−	0.841367i	$-0.681751\pi$
$647$	−27.4947	−1.08093	−0.540464	+	0.841367i	$0.681751\pi$
$648$	1.00000	0.0392837
$649$	10.0544	0.394670
$650$	16.1177	0.632190
$651$	6.70671	0.262857
$652$	−21.6257	−0.846929
$653$	16.4779	0.644830	0.322415	−	0.946598i	$-0.395505\pi$
$653$	16.4779	0.644830	0.322415	+	0.946598i	$0.395505\pi$
$654$	−10.7776	−0.421436
$655$	−9.76210	−0.381437
$656$	4.99190	0.194901
$657$	0.832592	0.0324825
$658$	18.5255	0.722199
$659$	−42.8787	−1.67032	−0.835159	−	0.550008i	$-0.814625\pi$
$659$	−42.8787	−1.67032	−0.835159	+	0.550008i	$0.814625\pi$
$660$	−4.10747	−0.159883
$661$	−23.3718	−0.909057	−0.454528	−	0.890732i	$-0.650192\pi$
$661$	−23.3718	−0.909057	−0.454528	+	0.890732i	$0.650192\pi$
$662$	17.4514	0.678267
$663$	5.20055	0.201973
$664$	13.9256	0.540420
$665$	21.4870	0.833231
$666$	−11.0578	−0.428481
$667$	15.4047	0.596474
$668$	7.91006	0.306049
$669$	5.86877	0.226900
$670$	−27.4789	−1.06160
$671$	−1.00000	−0.0386046
$672$	−1.42288	−0.0548890
$673$	34.9598	1.34760	0.673801	−	0.738913i	$-0.264661\pi$
$673$	34.9598	1.34760	0.673801	+	0.738913i	$0.264661\pi$
$674$	31.2281	1.20286
$675$	11.8713	0.456926
$676$	−11.1566	−0.429101
$677$	−21.3537	−0.820689	−0.410344	−	0.911931i	$-0.634592\pi$
$677$	−21.3537	−0.820689	−0.410344	+	0.911931i	$0.634592\pi$
$678$	−3.15790	−0.121278
$679$	10.1295	0.388736
$680$	15.7332	0.603341
$681$	16.8179	0.644462
$682$	4.71346	0.180488
$683$	−39.9344	−1.52805	−0.764023	−	0.645189i	$-0.776779\pi$
$683$	−39.9344	−1.52805	−0.764023	+	0.645189i	$0.776779\pi$
$684$	−3.67648	−0.140574
$685$	13.2788	0.507358
$686$	17.0396	0.650575
$687$	−21.5733	−0.823073
$688$	10.2658	0.391378
$689$	15.0888	0.574837
$690$	10.7040	0.407496
$691$	−43.3431	−1.64885	−0.824425	−	0.565971i	$-0.808502\pi$
$691$	−43.3431	−1.64885	−0.824425	+	0.565971i	$0.808502\pi$
$692$	13.6471	0.518786
$693$	1.42288	0.0540509
$694$	−7.77055	−0.294966
$695$	−28.1866	−1.06918
$696$	5.91127	0.224066
$697$	19.1209	0.724256
$698$	−10.9441	−0.414240
$699$	−11.7417	−0.444114
$700$	−16.8915	−0.638438
$701$	−8.10204	−0.306010	−0.153005	−	0.988225i	$-0.548895\pi$
$701$	−8.10204	−0.306010	−0.153005	+	0.988225i	$0.548895\pi$
$702$	1.35771	0.0512434
$703$	40.6538	1.53329
$704$	−1.00000	−0.0376889
$705$	−53.4779	−2.01410
$706$	17.6048	0.662564
$707$	−10.3818	−0.390446
$708$	−10.0544	−0.377868
$709$	−46.0294	−1.72867	−0.864335	−	0.502917i	$-0.832260\pi$
$709$	−46.0294	−1.72867	−0.864335	+	0.502917i	$0.832260\pi$
$710$	52.4853	1.96974
$711$	−3.15180	−0.118202
$712$	5.54212	0.207700
$713$	−12.2833	−0.460012
$714$	−5.45020	−0.203969
$715$	−5.57674	−0.208558
$716$	−11.8058	−0.441203
$717$	23.1597	0.864914
$718$	−9.83321	−0.366972
$719$	39.9491	1.48985	0.744926	−	0.667147i	$-0.232485\pi$
$719$	39.9491	1.48985	0.744926	+	0.667147i	$0.232485\pi$
$720$	4.10747	0.153076
$721$	−17.4155	−0.648586
$722$	−5.48349	−0.204074
$723$	9.55766	0.355453
$724$	1.97489	0.0733963
$725$	70.1744	2.60621
$726$	1.00000	0.0371135
$727$	−24.4008	−0.904976	−0.452488	−	0.891771i	$-0.649463\pi$
$727$	−24.4008	−0.904976	−0.452488	+	0.891771i	$0.649463\pi$
$728$	−1.93186	−0.0715995
$729$	1.00000	0.0370370
$730$	3.41985	0.126574
$731$	39.3218	1.45437
$732$	1.00000	0.0369611
$733$	−38.9607	−1.43904	−0.719522	−	0.694469i	$-0.755639\pi$
$733$	−38.9607	−1.43904	−0.719522	+	0.694469i	$0.755639\pi$
$734$	−20.7128	−0.764524
$735$	−20.4363	−0.753804
$736$	2.60600	0.0960583
$737$	6.68998	0.246429
$738$	4.99190	0.183754
$739$	19.0974	0.702510	0.351255	−	0.936280i	$-0.385755\pi$
$739$	19.0974	0.702510	0.351255	+	0.936280i	$0.385755\pi$
$740$	−45.4196	−1.66966
$741$	−4.99159	−0.183371
$742$	−15.8131	−0.580518
$743$	−9.78625	−0.359023	−0.179511	−	0.983756i	$-0.557452\pi$
$743$	−9.78625	−0.359023	−0.179511	+	0.983756i	$0.557452\pi$
$744$	−4.71346	−0.172804
$745$	−10.4736	−0.383724
$746$	22.9216	0.839220
$747$	13.9256	0.509513
$748$	−3.83039	−0.140053
$749$	20.4037	0.745535
$750$	28.2236	1.03058
$751$	−9.80629	−0.357837	−0.178918	−	0.983864i	$-0.557260\pi$
$751$	−9.80629	−0.357837	−0.178918	+	0.983864i	$0.557260\pi$
$752$	−13.0197	−0.474779
$753$	−0.638796	−0.0232790
$754$	8.02578	0.292282
$755$	−28.5240	−1.03809
$756$	−1.42288	−0.0517498
$757$	24.9314	0.906148	0.453074	−	0.891473i	$-0.350327\pi$
$757$	24.9314	0.906148	0.453074	+	0.891473i	$0.350327\pi$
$758$	3.58342	0.130156
$759$	−2.60600	−0.0945917
$760$	−15.1010	−0.547772
$761$	18.3660	0.665767	0.332883	−	0.942968i	$-0.391978\pi$
$761$	18.3660	0.665767	0.332883	+	0.942968i	$0.391978\pi$
$762$	−10.3986	−0.376702
$763$	15.3352	0.555173
$764$	−11.8090	−0.427234
$765$	15.7332	0.568835
$766$	−36.2661	−1.31035
$767$	−13.6509	−0.492907
$768$	1.00000	0.0360844
$769$	31.4932	1.13567	0.567837	−	0.823141i	$-0.307780\pi$
$769$	31.4932	1.13567	0.567837	+	0.823141i	$0.307780\pi$
$770$	5.84445	0.210619
$771$	23.7374	0.854883
$772$	−23.8698	−0.859094
$773$	27.8403	1.00135	0.500673	−	0.865637i	$-0.333086\pi$
$773$	27.8403	1.00135	0.500673	+	0.865637i	$0.333086\pi$
$774$	10.2658	0.368995
$775$	−55.9549	−2.00996
$776$	−7.11901	−0.255558
$777$	15.7340	0.564453
$778$	−26.9353	−0.965676
$779$	−18.3526	−0.657551
$780$	5.57674	0.199679
$781$	−12.7780	−0.457233
$782$	9.98198	0.356955
$783$	5.91127	0.211252
$784$	−4.97540	−0.177693
$785$	−54.4610	−1.94380
$786$	−2.37667	−0.0847731
$787$	−27.4533	−0.978605	−0.489302	−	0.872114i	$-0.662749\pi$
$787$	−27.4533	−0.978605	−0.489302	+	0.872114i	$0.662749\pi$
$788$	7.36122	0.262233
$789$	16.5229	0.588230
$790$	−12.9459	−0.460595
$791$	4.49332	0.159764
$792$	−1.00000	−0.0355335
$793$	1.35771	0.0482136
$794$	6.90455	0.245033
$795$	45.6480	1.61897
$796$	12.5538	0.444958
$797$	−9.07171	−0.321336	−0.160668	−	0.987008i	$-0.551365\pi$
$797$	−9.07171	−0.321336	−0.160668	+	0.987008i	$0.551365\pi$
$798$	5.23121	0.185183
$799$	−49.8704	−1.76429
$800$	11.8713	0.419713
$801$	5.54212	0.195821
$802$	15.3687	0.542688
$803$	−0.832592	−0.0293815
$804$	−6.68998	−0.235937
$805$	−15.2306	−0.536809
$806$	−6.39951	−0.225413
$807$	−7.99577	−0.281464
$808$	7.29628	0.256682
$809$	−24.4519	−0.859682	−0.429841	−	0.902905i	$-0.641430\pi$
$809$	−24.4519	−0.859682	−0.429841	+	0.902905i	$0.641430\pi$
$810$	4.10747	0.144322
$811$	43.4625	1.52618	0.763088	−	0.646295i	$-0.223682\pi$
$811$	43.4625	1.52618	0.763088	+	0.646295i	$0.223682\pi$
$812$	−8.41105	−0.295170
$813$	−4.76725	−0.167195
$814$	11.0578	0.387576
$815$	−88.8270	−3.11147
$816$	3.83039	0.134090
$817$	−37.7419	−1.32042
$818$	−11.1119	−0.388519
$819$	−1.93186	−0.0675047
$820$	20.5041	0.716033
$821$	−9.99288	−0.348754	−0.174377	−	0.984679i	$-0.555791\pi$
$821$	−9.99288	−0.348754	−0.174377	+	0.984679i	$0.555791\pi$
$822$	3.23285	0.112759
$823$	47.9700	1.67213	0.836064	−	0.548631i	$-0.184851\pi$
$823$	47.9700	1.67213	0.836064	+	0.548631i	$0.184851\pi$
$824$	12.2396	0.426385
$825$	−11.8713	−0.413305
$826$	14.3062	0.497778
$827$	19.1979	0.667578	0.333789	−	0.942648i	$-0.391673\pi$
$827$	19.1979	0.667578	0.333789	+	0.942648i	$0.391673\pi$
$828$	2.60600	0.0905646
$829$	−21.9741	−0.763193	−0.381597	−	0.924329i	$-0.624626\pi$
$829$	−21.9741	−0.763193	−0.381597	+	0.924329i	$0.624626\pi$
$830$	57.1991	1.98541
$831$	−16.9682	−0.588621
$832$	1.35771	0.0470701
$833$	−19.0577	−0.660311
$834$	−6.86229	−0.237622
$835$	32.4903	1.12437
$836$	3.67648	0.127154
$837$	−4.71346	−0.162921
$838$	18.5086	0.639369
$839$	−36.2986	−1.25317	−0.626583	−	0.779355i	$-0.715547\pi$
$839$	−36.2986	−1.25317	−0.626583	+	0.779355i	$0.715547\pi$
$840$	−5.84445	−0.201653
$841$	5.94310	0.204935
$842$	−25.2737	−0.870991
$843$	−13.4780	−0.464207
$844$	19.1327	0.658575
$845$	−45.8255	−1.57644
$846$	−13.0197	−0.447626
$847$	−1.42288	−0.0488909
$848$	11.1134	0.381637
$849$	−31.7376	−1.08923
$850$	45.4717	1.55966
$851$	−28.8166	−0.987820
$852$	12.7780	0.437767
$853$	−53.6070	−1.83547	−0.917734	−	0.397195i	$-0.869984\pi$
$853$	−53.6070	−1.83547	−0.917734	+	0.397195i	$0.869984\pi$
$854$	−1.42288	−0.0486901
$855$	−15.1010	−0.516444
$856$	−14.3397	−0.490120
$857$	−35.4071	−1.20948	−0.604742	−	0.796422i	$-0.706724\pi$
$857$	−35.4071	−1.20948	−0.604742	+	0.796422i	$0.706724\pi$
$858$	−1.35771	−0.0463514
$859$	−12.1934	−0.416034	−0.208017	−	0.978125i	$-0.566701\pi$
$859$	−12.1934	−0.416034	−0.208017	+	0.978125i	$0.566701\pi$
$860$	42.1663	1.43786
$861$	−7.10289	−0.242066
$862$	10.5667	0.359903
$863$	−19.6425	−0.668637	−0.334319	−	0.942460i	$-0.608506\pi$
$863$	−19.6425	−0.668637	−0.334319	+	0.942460i	$0.608506\pi$
$864$	1.00000	0.0340207
$865$	56.0552	1.90593
$866$	3.13640	0.106579
$867$	−2.32812	−0.0790672
$868$	6.70671	0.227641
$869$	3.15180	0.106917
$870$	24.2803	0.823181
$871$	−9.08304	−0.307767
$872$	−10.7776	−0.364975
$873$	−7.11901	−0.240942
$874$	−9.58089	−0.324079
$875$	−40.1589	−1.35762
$876$	0.832592	0.0281307
$877$	28.4046	0.959155	0.479577	−	0.877500i	$-0.340790\pi$
$877$	28.4046	0.959155	0.479577	+	0.877500i	$0.340790\pi$
$878$	−18.6958	−0.630953
$879$	−29.0309	−0.979189
$880$	−4.10747	−0.138463
$881$	7.07692	0.238427	0.119214	−	0.992869i	$-0.461963\pi$
$881$	7.07692	0.238427	0.119214	+	0.992869i	$0.461963\pi$
$882$	−4.97540	−0.167530
$883$	50.2257	1.69023	0.845115	−	0.534584i	$-0.179532\pi$
$883$	50.2257	1.69023	0.845115	+	0.534584i	$0.179532\pi$
$884$	5.20055	0.174913
$885$	−41.2981	−1.38822
$886$	−3.94422	−0.132509
$887$	31.3499	1.05263	0.526314	−	0.850290i	$-0.323574\pi$
$887$	31.3499	1.05263	0.526314	+	0.850290i	$0.323574\pi$
$888$	−11.0578	−0.371076
$889$	14.7960	0.496242
$890$	22.7641	0.763054
$891$	−1.00000	−0.0335013
$892$	5.86877	0.196501
$893$	47.8666	1.60180
$894$	−2.54990	−0.0852813
$895$	−48.4919	−1.62091
$896$	−1.42288	−0.0475352
$897$	3.53818	0.118136
$898$	−35.3741	−1.18045
$899$	−27.8626	−0.929268
$900$	11.8713	0.395710
$901$	42.5687	1.41817
$902$	−4.99190	−0.166212
$903$	−14.6070	−0.486090
$904$	−3.15790	−0.105030
$905$	8.11181	0.269646
$906$	−6.94441	−0.230713
$907$	3.99294	0.132583	0.0662917	−	0.997800i	$-0.478883\pi$
$907$	3.99294	0.132583	0.0662917	+	0.997800i	$0.478883\pi$
$908$	16.8179	0.558120
$909$	7.29628	0.242002
$910$	−7.93506	−0.263045
$911$	18.7650	0.621711	0.310855	−	0.950457i	$-0.399385\pi$
$911$	18.7650	0.621711	0.310855	+	0.950457i	$0.399385\pi$
$912$	−3.67648	−0.121740
$913$	−13.9256	−0.460872
$914$	34.1323	1.12900
$915$	4.10747	0.135789
$916$	−21.5733	−0.712802
$917$	3.38173	0.111675
$918$	3.83039	0.126422
$919$	−15.6989	−0.517858	−0.258929	−	0.965896i	$-0.583370\pi$
$919$	−15.6989	−0.517858	−0.258929	+	0.965896i	$0.583370\pi$
$920$	10.7040	0.352902
$921$	−1.57252	−0.0518163
$922$	29.0729	0.957464
$923$	17.3488	0.571043
$924$	1.42288	0.0468095
$925$	−131.270	−4.31615
$926$	15.8931	0.522281
$927$	12.2396	0.402000
$928$	5.91127	0.194047
$929$	−32.4492	−1.06463	−0.532313	−	0.846548i	$-0.678677\pi$
$929$	−32.4492	−1.06463	−0.532313	+	0.846548i	$0.678677\pi$
$930$	−19.3604	−0.634852
$931$	18.2920	0.599495
$932$	−11.7417	−0.384614
$933$	−26.9163	−0.881200
$934$	−6.87174	−0.224850
$935$	−15.7332	−0.514531
$936$	1.35771	0.0443781
$937$	−44.6431	−1.45843	−0.729214	−	0.684286i	$-0.760114\pi$
$937$	−44.6431	−1.45843	−0.729214	+	0.684286i	$0.760114\pi$
$938$	9.51907	0.310809
$939$	9.09300	0.296739
$940$	−53.4779	−1.74426
$941$	38.6171	1.25888	0.629440	−	0.777049i	$-0.283284\pi$
$941$	38.6171	1.25888	0.629440	+	0.777049i	$0.283284\pi$
$942$	−13.2590	−0.432002
$943$	13.0089	0.423627
$944$	−10.0544	−0.327243
$945$	−5.84445	−0.190120
$946$	−10.2658	−0.333769
$947$	−28.4307	−0.923873	−0.461937	−	0.886913i	$-0.652845\pi$
$947$	−28.4307	−0.923873	−0.461937	+	0.886913i	$0.652845\pi$
$948$	−3.15180	−0.102366
$949$	1.13042	0.0366949
$950$	−43.6446	−1.41602
$951$	19.7222	0.639538
$952$	−5.45020	−0.176642
$953$	27.3787	0.886882	0.443441	−	0.896304i	$-0.353758\pi$
$953$	27.3787	0.886882	0.443441	+	0.896304i	$0.353758\pi$
$954$	11.1134	0.359811
$955$	−48.5051	−1.56959
$956$	23.1597	0.749038
$957$	−5.91127	−0.191084
$958$	−12.0445	−0.389142
$959$	−4.59997	−0.148541
$960$	4.10747	0.132568
$961$	−8.78326	−0.283331
$962$	−15.0133	−0.484047
$963$	−14.3397	−0.462089
$964$	9.55766	0.307831
$965$	−98.0446	−3.15617
$966$	−3.70803	−0.119304
$967$	−18.9518	−0.609450	−0.304725	−	0.952440i	$-0.598565\pi$
$967$	−18.9518	−0.609450	−0.304725	+	0.952440i	$0.598565\pi$
$968$	1.00000	0.0321412
$969$	−14.0824	−0.452390
$970$	−29.2411	−0.938875
$971$	−7.16615	−0.229973	−0.114986	−	0.993367i	$-0.536682\pi$
$971$	−7.16615	−0.229973	−0.114986	+	0.993367i	$0.536682\pi$
$972$	1.00000	0.0320750
$973$	9.76425	0.313027
$974$	17.1802	0.550490
$975$	16.1177	0.516181
$976$	1.00000	0.0320092
$977$	−6.00204	−0.192022	−0.0960111	−	0.995380i	$-0.530608\pi$
$977$	−6.00204	−0.192022	−0.0960111	+	0.995380i	$0.530608\pi$
$978$	−21.6257	−0.691514
$979$	−5.54212	−0.177127
$980$	−20.4363	−0.652814
$981$	−10.7776	−0.344101
$982$	10.5248	0.335860
$983$	−44.5011	−1.41937	−0.709683	−	0.704522i	$-0.751162\pi$
$983$	−44.5011	−1.41937	−0.709683	+	0.704522i	$0.751162\pi$
$984$	4.99190	0.159136
$985$	30.2360	0.963398
$986$	22.6425	0.721083
$987$	18.5255	0.589673
$988$	−4.99159	−0.158804
$989$	26.7525	0.850681
$990$	−4.10747	−0.130544
$991$	−18.1181	−0.575540	−0.287770	−	0.957700i	$-0.592914\pi$
$991$	−18.1181	−0.575540	−0.287770	+	0.957700i	$0.592914\pi$
$992$	−4.71346	−0.149653
$993$	17.4514	0.553802
$994$	−18.1816	−0.576686
$995$	51.5643	1.63470
$996$	13.9256	0.441251
$997$	−26.1634	−0.828603	−0.414301	−	0.910140i	$-0.635974\pi$
$997$	−26.1634	−0.828603	−0.414301	+	0.910140i	$0.635974\pi$
$998$	28.7356	0.909611
$999$	−11.0578	−0.349854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bb.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bb.1.8	✓	8	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.10747 q^{5} +1.00000 q^{6} -1.42288 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.10747 q^{5} +1.00000 q^{6} -1.42288 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.10747 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.35771 q^{13} -1.42288 q^{14} +4.10747 q^{15} +1.00000 q^{16} +3.83039 q^{17} +1.00000 q^{18} -3.67648 q^{19} +4.10747 q^{20} -1.42288 q^{21} -1.00000 q^{22} +2.60600 q^{23} +1.00000 q^{24} +11.8713 q^{25} +1.35771 q^{26} +1.00000 q^{27} -1.42288 q^{28} +5.91127 q^{29} +4.10747 q^{30} -4.71346 q^{31} +1.00000 q^{32} -1.00000 q^{33} +3.83039 q^{34} -5.84445 q^{35} +1.00000 q^{36} -11.0578 q^{37} -3.67648 q^{38} +1.35771 q^{39} +4.10747 q^{40} +4.99190 q^{41} -1.42288 q^{42} +10.2658 q^{43} -1.00000 q^{44} +4.10747 q^{45} +2.60600 q^{46} -13.0197 q^{47} +1.00000 q^{48} -4.97540 q^{49} +11.8713 q^{50} +3.83039 q^{51} +1.35771 q^{52} +11.1134 q^{53} +1.00000 q^{54} -4.10747 q^{55} -1.42288 q^{56} -3.67648 q^{57} +5.91127 q^{58} -10.0544 q^{59} +4.10747 q^{60} +1.00000 q^{61} -4.71346 q^{62} -1.42288 q^{63} +1.00000 q^{64} +5.57674 q^{65} -1.00000 q^{66} -6.68998 q^{67} +3.83039 q^{68} +2.60600 q^{69} -5.84445 q^{70} +12.7780 q^{71} +1.00000 q^{72} +0.832592 q^{73} -11.0578 q^{74} +11.8713 q^{75} -3.67648 q^{76} +1.42288 q^{77} +1.35771 q^{78} -3.15180 q^{79} +4.10747 q^{80} +1.00000 q^{81} +4.99190 q^{82} +13.9256 q^{83} -1.42288 q^{84} +15.7332 q^{85} +10.2658 q^{86} +5.91127 q^{87} -1.00000 q^{88} +5.54212 q^{89} +4.10747 q^{90} -1.93186 q^{91} +2.60600 q^{92} -4.71346 q^{93} -13.0197 q^{94} -15.1010 q^{95} +1.00000 q^{96} -7.11901 q^{97} -4.97540 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * q^99

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