LMFDB - Embedded newform 8031.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48341 q^{2} +1.00000 q^{3} +4.16735 q^{4} +1.79948 q^{5} -2.48341 q^{6} -1.15988 q^{7} -5.38242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48341 q^{2} +1.00000 q^{3} +4.16735 q^{4} +1.79948 q^{5} -2.48341 q^{6} -1.15988 q^{7} -5.38242 q^{8} +1.00000 q^{9} -4.46885 q^{10} -4.87835 q^{11} +4.16735 q^{12} +3.25769 q^{13} +2.88046 q^{14} +1.79948 q^{15} +5.03209 q^{16} +4.29427 q^{17} -2.48341 q^{18} -0.725285 q^{19} +7.49905 q^{20} -1.15988 q^{21} +12.1150 q^{22} +0.295652 q^{23} -5.38242 q^{24} -1.76188 q^{25} -8.09018 q^{26} +1.00000 q^{27} -4.83362 q^{28} +9.22403 q^{29} -4.46885 q^{30} +3.05282 q^{31} -1.73192 q^{32} -4.87835 q^{33} -10.6644 q^{34} -2.08718 q^{35} +4.16735 q^{36} -8.60741 q^{37} +1.80118 q^{38} +3.25769 q^{39} -9.68554 q^{40} -11.5067 q^{41} +2.88046 q^{42} -8.03785 q^{43} -20.3298 q^{44} +1.79948 q^{45} -0.734227 q^{46} +7.66011 q^{47} +5.03209 q^{48} -5.65468 q^{49} +4.37548 q^{50} +4.29427 q^{51} +13.5759 q^{52} -13.7919 q^{53} -2.48341 q^{54} -8.77848 q^{55} +6.24296 q^{56} -0.725285 q^{57} -22.9071 q^{58} +1.94334 q^{59} +7.49905 q^{60} -13.4845 q^{61} -7.58143 q^{62} -1.15988 q^{63} -5.76311 q^{64} +5.86213 q^{65} +12.1150 q^{66} +12.6651 q^{67} +17.8957 q^{68} +0.295652 q^{69} +5.18332 q^{70} +8.72900 q^{71} -5.38242 q^{72} -4.54706 q^{73} +21.3758 q^{74} -1.76188 q^{75} -3.02251 q^{76} +5.65829 q^{77} -8.09018 q^{78} -6.68609 q^{79} +9.05513 q^{80} +1.00000 q^{81} +28.5760 q^{82} -7.92719 q^{83} -4.83362 q^{84} +7.72743 q^{85} +19.9613 q^{86} +9.22403 q^{87} +26.2573 q^{88} +6.90384 q^{89} -4.46885 q^{90} -3.77852 q^{91} +1.23209 q^{92} +3.05282 q^{93} -19.0232 q^{94} -1.30513 q^{95} -1.73192 q^{96} -10.7006 q^{97} +14.0429 q^{98} -4.87835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.48341	−1.75604	−0.878020	−	0.478625i	$-0.841135\pi$
$2$	−2.48341	−1.75604	−0.878020	+	0.478625i	$0.841135\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.16735	2.08367
$5$	1.79948	0.804751	0.402375	−	0.915475i	$-0.368185\pi$
$5$	1.79948	0.804751	0.402375	+	0.915475i	$0.368185\pi$
$6$	−2.48341	−1.01385
$7$	−1.15988	−0.438393	−0.219197	−	0.975681i	$-0.570344\pi$
$7$	−1.15988	−0.438393	−0.219197	+	0.975681i	$0.570344\pi$
$8$	−5.38242	−1.90297
$9$	1.00000	0.333333
$10$	−4.46885	−1.41317
$11$	−4.87835	−1.47088	−0.735439	−	0.677591i	$-0.763024\pi$
$11$	−4.87835	−1.47088	−0.735439	+	0.677591i	$0.763024\pi$
$12$	4.16735	1.20301
$13$	3.25769	0.903520	0.451760	−	0.892140i	$-0.350796\pi$
$13$	3.25769	0.903520	0.451760	+	0.892140i	$0.350796\pi$
$14$	2.88046	0.769835
$15$	1.79948	0.464623
$16$	5.03209	1.25802
$17$	4.29427	1.04151	0.520756	−	0.853705i	$-0.325650\pi$
$17$	4.29427	1.04151	0.520756	+	0.853705i	$0.325650\pi$
$18$	−2.48341	−0.585346
$19$	−0.725285	−0.166392	−0.0831959	−	0.996533i	$-0.526513\pi$
$19$	−0.725285	−0.166392	−0.0831959	+	0.996533i	$0.526513\pi$
$20$	7.49905	1.67684
$21$	−1.15988	−0.253106
$22$	12.1150	2.58292
$23$	0.295652	0.0616478	0.0308239	−	0.999525i	$-0.490187\pi$
$23$	0.295652	0.0616478	0.0308239	+	0.999525i	$0.490187\pi$
$24$	−5.38242	−1.09868
$25$	−1.76188	−0.352377
$26$	−8.09018	−1.58662
$27$	1.00000	0.192450
$28$	−4.83362	−0.913468
$29$	9.22403	1.71286	0.856430	−	0.516264i	$-0.172678\pi$
$29$	9.22403	1.71286	0.856430	+	0.516264i	$0.172678\pi$
$30$	−4.46885	−0.815896
$31$	3.05282	0.548303	0.274152	−	0.961686i	$-0.411603\pi$
$31$	3.05282	0.548303	0.274152	+	0.961686i	$0.411603\pi$
$32$	−1.73192	−0.306163
$33$	−4.87835	−0.849212
$34$	−10.6644	−1.82894
$35$	−2.08718	−0.352797
$36$	4.16735	0.694558
$37$	−8.60741	−1.41505	−0.707525	−	0.706688i	$-0.750188\pi$
$37$	−8.60741	−1.41505	−0.707525	+	0.706688i	$0.750188\pi$
$38$	1.80118	0.292190
$39$	3.25769	0.521647
$40$	−9.68554	−1.53142
$41$	−11.5067	−1.79705	−0.898525	−	0.438923i	$-0.855360\pi$
$41$	−11.5067	−1.79705	−0.898525	+	0.438923i	$0.855360\pi$
$42$	2.88046	0.444465
$43$	−8.03785	−1.22576	−0.612880	−	0.790176i	$-0.709989\pi$
$43$	−8.03785	−1.22576	−0.612880	+	0.790176i	$0.709989\pi$
$44$	−20.3298	−3.06483
$45$	1.79948	0.268250
$46$	−0.734227	−0.108256
$47$	7.66011	1.11734	0.558671	−	0.829389i	$-0.311311\pi$
$47$	7.66011	1.11734	0.558671	+	0.829389i	$0.311311\pi$
$48$	5.03209	0.726319
$49$	−5.65468	−0.807812
$50$	4.37548	0.618787
$51$	4.29427	0.601318
$52$	13.5759	1.88264
$53$	−13.7919	−1.89447	−0.947233	−	0.320545i	$-0.896134\pi$
$53$	−13.7919	−1.89447	−0.947233	+	0.320545i	$0.896134\pi$
$54$	−2.48341	−0.337950
$55$	−8.77848	−1.18369
$56$	6.24296	0.834250
$57$	−0.725285	−0.0960663
$58$	−22.9071	−3.00785
$59$	1.94334	0.253001	0.126501	−	0.991967i	$-0.459625\pi$
$59$	1.94334	0.253001	0.126501	+	0.991967i	$0.459625\pi$
$60$	7.49905	0.968123
$61$	−13.4845	−1.72652	−0.863258	−	0.504763i	$-0.831580\pi$
$61$	−13.4845	−1.72652	−0.863258	+	0.504763i	$0.831580\pi$
$62$	−7.58143	−0.962842
$63$	−1.15988	−0.146131
$64$	−5.76311	−0.720388
$65$	5.86213	0.727108
$66$	12.1150	1.49125
$67$	12.6651	1.54729	0.773643	−	0.633622i	$-0.218432\pi$
$67$	12.6651	1.54729	0.773643	+	0.633622i	$0.218432\pi$
$68$	17.8957	2.17017
$69$	0.295652	0.0355924
$70$	5.18332	0.619525
$71$	8.72900	1.03594	0.517971	−	0.855398i	$-0.326688\pi$
$71$	8.72900	1.03594	0.517971	+	0.855398i	$0.326688\pi$
$72$	−5.38242	−0.634324
$73$	−4.54706	−0.532193	−0.266097	−	0.963946i	$-0.585734\pi$
$73$	−4.54706	−0.532193	−0.266097	+	0.963946i	$0.585734\pi$
$74$	21.3758	2.48488
$75$	−1.76188	−0.203445
$76$	−3.02251	−0.346706
$77$	5.65829	0.644822
$78$	−8.09018	−0.916033
$79$	−6.68609	−0.752244	−0.376122	−	0.926570i	$-0.622743\pi$
$79$	−6.68609	−0.752244	−0.376122	+	0.926570i	$0.622743\pi$
$80$	9.05513	1.01239
$81$	1.00000	0.111111
$82$	28.5760	3.15569
$83$	−7.92719	−0.870122	−0.435061	−	0.900401i	$-0.643273\pi$
$83$	−7.92719	−0.870122	−0.435061	+	0.900401i	$0.643273\pi$
$84$	−4.83362	−0.527391
$85$	7.72743	0.838158
$86$	19.9613	2.15248
$87$	9.22403	0.988920
$88$	26.2573	2.79904
$89$	6.90384	0.731806	0.365903	−	0.930653i	$-0.380760\pi$
$89$	6.90384	0.731806	0.365903	+	0.930653i	$0.380760\pi$
$90$	−4.46885	−0.471058
$91$	−3.77852	−0.396097
$92$	1.23209	0.128454
$93$	3.05282	0.316563
$94$	−19.0232	−1.96210
$95$	−1.30513	−0.133904
$96$	−1.73192	−0.176763
$97$	−10.7006	−1.08648	−0.543239	−	0.839578i	$-0.682802\pi$
$97$	−10.7006	−1.08648	−0.543239	+	0.839578i	$0.682802\pi$
$98$	14.0429	1.41855
$99$	−4.87835	−0.490292
$100$	−7.34238	−0.734238
$101$	4.78852	0.476475	0.238238	−	0.971207i	$-0.423430\pi$
$101$	4.78852	0.476475	0.238238	+	0.971207i	$0.423430\pi$
$102$	−10.6644	−1.05594
$103$	−9.20193	−0.906693	−0.453346	−	0.891334i	$-0.649770\pi$
$103$	−9.20193	−0.906693	−0.453346	+	0.891334i	$0.649770\pi$
$104$	−17.5342	−1.71937
$105$	−2.08718	−0.203687
$106$	34.2511	3.32676
$107$	−7.70993	−0.745347	−0.372674	−	0.927962i	$-0.621559\pi$
$107$	−7.70993	−0.745347	−0.372674	+	0.927962i	$0.621559\pi$
$108$	4.16735	0.401003
$109$	−0.283922	−0.0271948	−0.0135974	−	0.999908i	$-0.504328\pi$
$109$	−0.283922	−0.0271948	−0.0135974	+	0.999908i	$0.504328\pi$
$110$	21.8006	2.07861
$111$	−8.60741	−0.816979
$112$	−5.83661	−0.551508
$113$	0.527058	0.0495815	0.0247907	−	0.999693i	$-0.492108\pi$
$113$	0.527058	0.0495815	0.0247907	+	0.999693i	$0.492108\pi$
$114$	1.80118	0.168696
$115$	0.532019	0.0496111
$116$	38.4397	3.56904
$117$	3.25769	0.301173
$118$	−4.82612	−0.444280
$119$	−4.98083	−0.456592
$120$	−9.68554	−0.884165
$121$	12.7983	1.16348
$122$	33.4876	3.03183
$123$	−11.5067	−1.03753
$124$	12.7222	1.14249
$125$	−12.1679	−1.08833
$126$	2.88046	0.256612
$127$	−4.03922	−0.358423	−0.179212	−	0.983811i	$-0.557355\pi$
$127$	−4.03922	−0.358423	−0.179212	+	0.983811i	$0.557355\pi$
$128$	17.7760	1.57119
$129$	−8.03785	−0.707693
$130$	−14.5581	−1.27683
$131$	4.28439	0.374329	0.187164	−	0.982329i	$-0.440070\pi$
$131$	4.28439	0.374329	0.187164	+	0.982329i	$0.440070\pi$
$132$	−20.3298	−1.76948
$133$	0.841243	0.0729450
$134$	−31.4526	−2.71709
$135$	1.79948	0.154874
$136$	−23.1135	−1.98197
$137$	8.89707	0.760128	0.380064	−	0.924960i	$-0.375902\pi$
$137$	8.89707	0.760128	0.380064	+	0.924960i	$0.375902\pi$
$138$	−0.734227	−0.0625016
$139$	17.4563	1.48062	0.740310	−	0.672265i	$-0.234679\pi$
$139$	17.4563	1.48062	0.740310	+	0.672265i	$0.234679\pi$
$140$	−8.69798	−0.735114
$141$	7.66011	0.645098
$142$	−21.6777	−1.81915
$143$	−15.8921	−1.32897
$144$	5.03209	0.419341
$145$	16.5984	1.37842
$146$	11.2922	0.934552
$147$	−5.65468	−0.466390
$148$	−35.8701	−2.94850
$149$	−1.40750	−0.115307	−0.0576534	−	0.998337i	$-0.518362\pi$
$149$	−1.40750	−0.115307	−0.0576534	+	0.998337i	$0.518362\pi$
$150$	4.37548	0.357257
$151$	21.3313	1.73592	0.867959	−	0.496636i	$-0.165432\pi$
$151$	21.3313	1.73592	0.867959	+	0.496636i	$0.165432\pi$
$152$	3.90379	0.316639
$153$	4.29427	0.347171
$154$	−14.0519	−1.13233
$155$	5.49349	0.441247
$156$	13.5759	1.08694
$157$	5.68010	0.453321	0.226661	−	0.973974i	$-0.427219\pi$
$157$	5.68010	0.453321	0.226661	+	0.973974i	$0.427219\pi$
$158$	16.6043	1.32097
$159$	−13.7919	−1.09377
$160$	−3.11655	−0.246385
$161$	−0.342921	−0.0270260
$162$	−2.48341	−0.195115
$163$	5.37456	0.420968	0.210484	−	0.977597i	$-0.432496\pi$
$163$	5.37456	0.420968	0.210484	+	0.977597i	$0.432496\pi$
$164$	−47.9525	−3.74446
$165$	−8.77848	−0.683403
$166$	19.6865	1.52797
$167$	−10.7274	−0.830115	−0.415057	−	0.909795i	$-0.636238\pi$
$167$	−10.7274	−0.830115	−0.415057	+	0.909795i	$0.636238\pi$
$168$	6.24296	0.481655
$169$	−2.38748	−0.183652
$170$	−19.1904	−1.47184
$171$	−0.725285	−0.0554639
$172$	−33.4965	−2.55408
$173$	1.00151	0.0761436	0.0380718	−	0.999275i	$-0.487878\pi$
$173$	1.00151	0.0761436	0.0380718	+	0.999275i	$0.487878\pi$
$174$	−22.9071	−1.73658
$175$	2.04357	0.154479
$176$	−24.5483	−1.85040
$177$	1.94334	0.146070
$178$	−17.1451	−1.28508
$179$	−19.6477	−1.46854	−0.734269	−	0.678858i	$-0.762475\pi$
$179$	−19.6477	−1.46854	−0.734269	+	0.678858i	$0.762475\pi$
$180$	7.49905	0.558946
$181$	−9.42418	−0.700494	−0.350247	−	0.936657i	$-0.613902\pi$
$181$	−9.42418	−0.700494	−0.350247	+	0.936657i	$0.613902\pi$
$182$	9.38363	0.695561
$183$	−13.4845	−0.996804
$184$	−1.59133	−0.117314
$185$	−15.4888	−1.13876
$186$	−7.58143	−0.555897
$187$	−20.9489	−1.53194
$188$	31.9224	2.32818
$189$	−1.15988	−0.0843688
$190$	3.24119	0.235140
$191$	9.66187	0.699109	0.349554	−	0.936916i	$-0.386333\pi$
$191$	9.66187	0.699109	0.349554	+	0.936916i	$0.386333\pi$
$192$	−5.76311	−0.415916
$193$	−5.25091	−0.377969	−0.188984	−	0.981980i	$-0.560520\pi$
$193$	−5.25091	−0.377969	−0.188984	+	0.981980i	$0.560520\pi$
$194$	26.5740	1.90790
$195$	5.86213	0.419796
$196$	−23.5650	−1.68322
$197$	−10.0101	−0.713192	−0.356596	−	0.934259i	$-0.616063\pi$
$197$	−10.0101	−0.713192	−0.356596	+	0.934259i	$0.616063\pi$
$198$	12.1150	0.860973
$199$	−6.66156	−0.472225	−0.236113	−	0.971726i	$-0.575873\pi$
$199$	−6.66156	−0.472225	−0.236113	+	0.971726i	$0.575873\pi$
$200$	9.48319	0.670563
$201$	12.6651	0.893326
$202$	−11.8919	−0.836710
$203$	−10.6988	−0.750906
$204$	17.8957	1.25295
$205$	−20.7061	−1.44618
$206$	22.8522	1.59219
$207$	0.295652	0.0205493
$208$	16.3930	1.13665
$209$	3.53819	0.244742
$210$	5.18332	0.357683
$211$	3.81279	0.262483	0.131242	−	0.991350i	$-0.458104\pi$
$211$	3.81279	0.262483	0.131242	+	0.991350i	$0.458104\pi$
$212$	−57.4757	−3.94745
$213$	8.72900	0.598101
$214$	19.1470	1.30886
$215$	−14.4639	−0.986431
$216$	−5.38242	−0.366227
$217$	−3.54091	−0.240372
$218$	0.705096	0.0477551
$219$	−4.54706	−0.307262
$220$	−36.5830	−2.46642
$221$	13.9894	0.941027
$222$	21.3758	1.43465
$223$	−19.8600	−1.32993	−0.664963	−	0.746876i	$-0.731553\pi$
$223$	−19.8600	−1.32993	−0.664963	+	0.746876i	$0.731553\pi$
$224$	2.00881	0.134220
$225$	−1.76188	−0.117459
$226$	−1.30890	−0.0870670
$227$	−3.31074	−0.219742	−0.109871	−	0.993946i	$-0.535044\pi$
$227$	−3.31074	−0.219742	−0.109871	+	0.993946i	$0.535044\pi$
$228$	−3.02251	−0.200171
$229$	25.1510	1.66202	0.831012	−	0.556254i	$-0.187762\pi$
$229$	25.1510	1.66202	0.831012	+	0.556254i	$0.187762\pi$
$230$	−1.32122	−0.0871190
$231$	5.65829	0.372288
$232$	−49.6476	−3.25953
$233$	−3.39301	−0.222284	−0.111142	−	0.993805i	$-0.535451\pi$
$233$	−3.39301	−0.222284	−0.111142	+	0.993805i	$0.535451\pi$
$234$	−8.09018	−0.528872
$235$	13.7842	0.899182
$236$	8.09857	0.527172
$237$	−6.68609	−0.434308
$238$	12.3695	0.801793
$239$	18.1167	1.17187	0.585937	−	0.810357i	$-0.300727\pi$
$239$	18.1167	1.17187	0.585937	+	0.810357i	$0.300727\pi$
$240$	9.05513	0.584506
$241$	−19.1771	−1.23531	−0.617653	−	0.786451i	$-0.711916\pi$
$241$	−19.1771	−1.23531	−0.617653	+	0.786451i	$0.711916\pi$
$242$	−31.7834	−2.04312
$243$	1.00000	0.0641500
$244$	−56.1947	−3.59750
$245$	−10.1755	−0.650087
$246$	28.5760	1.82194
$247$	−2.36275	−0.150338
$248$	−16.4316	−1.04341
$249$	−7.92719	−0.502365
$250$	30.2178	1.91114
$251$	−2.41784	−0.152612	−0.0763062	−	0.997084i	$-0.524313\pi$
$251$	−2.41784	−0.152612	−0.0763062	+	0.997084i	$0.524313\pi$
$252$	−4.83362	−0.304489
$253$	−1.44230	−0.0906763
$254$	10.0311	0.629405
$255$	7.72743	0.483911
$256$	−32.6190	−2.03869
$257$	25.9668	1.61976	0.809882	−	0.586593i	$-0.199531\pi$
$257$	25.9668	1.61976	0.809882	+	0.586593i	$0.199531\pi$
$258$	19.9613	1.24274
$259$	9.98356	0.620348
$260$	24.4295	1.51506
$261$	9.22403	0.570953
$262$	−10.6399	−0.657336
$263$	5.54174	0.341718	0.170859	−	0.985295i	$-0.445346\pi$
$263$	5.54174	0.341718	0.170859	+	0.985295i	$0.445346\pi$
$264$	26.2573	1.61603
$265$	−24.8183	−1.52457
$266$	−2.08915	−0.128094
$267$	6.90384	0.422508
$268$	52.7798	3.22404
$269$	−19.2964	−1.17652	−0.588262	−	0.808670i	$-0.700188\pi$
$269$	−19.2964	−1.17652	−0.588262	+	0.808670i	$0.700188\pi$
$270$	−4.46885	−0.271965
$271$	−23.2050	−1.40960	−0.704802	−	0.709404i	$-0.748964\pi$
$271$	−23.2050	−1.40960	−0.704802	+	0.709404i	$0.748964\pi$
$272$	21.6091	1.31025
$273$	−3.77852	−0.228687
$274$	−22.0951	−1.33481
$275$	8.59508	0.518303
$276$	1.23209	0.0741628
$277$	−14.3995	−0.865185	−0.432592	−	0.901590i	$-0.642401\pi$
$277$	−14.3995	−0.865185	−0.432592	+	0.901590i	$0.642401\pi$
$278$	−43.3511	−2.60003
$279$	3.05282	0.182768
$280$	11.2341	0.671363
$281$	16.6574	0.993697	0.496848	−	0.867837i	$-0.334491\pi$
$281$	16.6574	0.993697	0.496848	+	0.867837i	$0.334491\pi$
$282$	−19.0232	−1.13282
$283$	−12.1085	−0.719777	−0.359888	−	0.932995i	$-0.617185\pi$
$283$	−12.1085	−0.719777	−0.359888	+	0.932995i	$0.617185\pi$
$284$	36.3768	2.15856
$285$	−1.30513	−0.0773094
$286$	39.4667	2.33372
$287$	13.3464	0.787814
$288$	−1.73192	−0.102054
$289$	1.44072	0.0847484
$290$	−41.2208	−2.42057
$291$	−10.7006	−0.627279
$292$	−18.9492	−1.10892
$293$	−13.9965	−0.817685	−0.408842	−	0.912605i	$-0.634067\pi$
$293$	−13.9965	−0.817685	−0.408842	+	0.912605i	$0.634067\pi$
$294$	14.0429	0.818999
$295$	3.49700	0.203603
$296$	46.3287	2.69280
$297$	−4.87835	−0.283071
$298$	3.49540	0.202483
$299$	0.963142	0.0557000
$300$	−7.34238	−0.423912
$301$	9.32293	0.537365
$302$	−52.9745	−3.04834
$303$	4.78852	0.275093
$304$	−3.64970	−0.209325
$305$	−24.2651	−1.38941
$306$	−10.6644	−0.609646
$307$	6.26592	0.357615	0.178808	−	0.983884i	$-0.442776\pi$
$307$	6.26592	0.357615	0.178808	+	0.983884i	$0.442776\pi$
$308$	23.5801	1.34360
$309$	−9.20193	−0.523479
$310$	−13.6426	−0.774848
$311$	−29.2468	−1.65844	−0.829218	−	0.558925i	$-0.811214\pi$
$311$	−29.2468	−1.65844	−0.829218	+	0.558925i	$0.811214\pi$
$312$	−17.5342	−0.992681
$313$	−17.9737	−1.01593	−0.507967	−	0.861377i	$-0.669603\pi$
$313$	−17.9737	−1.01593	−0.507967	+	0.861377i	$0.669603\pi$
$314$	−14.1060	−0.796050
$315$	−2.08718	−0.117599
$316$	−27.8633	−1.56743
$317$	22.8093	1.28110	0.640548	−	0.767918i	$-0.278707\pi$
$317$	22.8093	1.28110	0.640548	+	0.767918i	$0.278707\pi$
$318$	34.2511	1.92070
$319$	−44.9980	−2.51941
$320$	−10.3706	−0.579733
$321$	−7.70993	−0.430327
$322$	0.851615	0.0474586
$323$	−3.11457	−0.173299
$324$	4.16735	0.231519
$325$	−5.73966	−0.318379
$326$	−13.3473	−0.739237
$327$	−0.283922	−0.0157009
$328$	61.9341	3.41974
$329$	−8.88481	−0.489835
$330$	21.8006	1.20008
$331$	−6.03222	−0.331561	−0.165780	−	0.986163i	$-0.553014\pi$
$331$	−6.03222	−0.331561	−0.165780	+	0.986163i	$0.553014\pi$
$332$	−33.0354	−1.81305
$333$	−8.60741	−0.471683
$334$	26.6407	1.45771
$335$	22.7905	1.24518
$336$	−5.83661	−0.318413
$337$	−26.0683	−1.42003	−0.710016	−	0.704185i	$-0.751312\pi$
$337$	−26.0683	−1.42003	−0.710016	+	0.704185i	$0.751312\pi$
$338$	5.92911	0.322501
$339$	0.527058	0.0286259
$340$	32.2029	1.74645
$341$	−14.8927	−0.806487
$342$	1.80118	0.0973968
$343$	14.6779	0.792532
$344$	43.2631	2.33259
$345$	0.532019	0.0286430
$346$	−2.48717	−0.133711
$347$	34.6988	1.86273	0.931364	−	0.364090i	$-0.118620\pi$
$347$	34.6988	1.86273	0.931364	+	0.364090i	$0.118620\pi$
$348$	38.4397	2.06059
$349$	−3.99262	−0.213720	−0.106860	−	0.994274i	$-0.534080\pi$
$349$	−3.99262	−0.213720	−0.106860	+	0.994274i	$0.534080\pi$
$350$	−5.07503	−0.271272
$351$	3.25769	0.173882
$352$	8.44890	0.450328
$353$	15.5082	0.825419	0.412710	−	0.910863i	$-0.364582\pi$
$353$	15.5082	0.825419	0.412710	+	0.910863i	$0.364582\pi$
$354$	−4.82612	−0.256505
$355$	15.7076	0.833674
$356$	28.7707	1.52484
$357$	−4.98083	−0.263613
$358$	48.7934	2.57881
$359$	−6.91623	−0.365025	−0.182512	−	0.983204i	$-0.558423\pi$
$359$	−6.91623	−0.365025	−0.182512	+	0.983204i	$0.558423\pi$
$360$	−9.68554	−0.510473
$361$	−18.4740	−0.972314
$362$	23.4042	1.23009
$363$	12.7983	0.671736
$364$	−15.7464	−0.825336
$365$	−8.18233	−0.428283
$366$	33.4876	1.75043
$367$	−6.24561	−0.326018	−0.163009	−	0.986625i	$-0.552120\pi$
$367$	−6.24561	−0.326018	−0.163009	+	0.986625i	$0.552120\pi$
$368$	1.48775	0.0775542
$369$	−11.5067	−0.599017
$370$	38.4652	1.99971
$371$	15.9970	0.830521
$372$	12.7222	0.659614
$373$	−10.0009	−0.517828	−0.258914	−	0.965900i	$-0.583365\pi$
$373$	−10.0009	−0.517828	−0.258914	+	0.965900i	$0.583365\pi$
$374$	52.0249	2.69014
$375$	−12.1679	−0.628345
$376$	−41.2300	−2.12627
$377$	30.0490	1.54760
$378$	2.88046	0.148155
$379$	−8.97705	−0.461120	−0.230560	−	0.973058i	$-0.574056\pi$
$379$	−8.97705	−0.461120	−0.230560	+	0.973058i	$0.574056\pi$
$380$	−5.43894	−0.279012
$381$	−4.03922	−0.206936
$382$	−23.9944	−1.22766
$383$	10.0886	0.515501	0.257751	−	0.966212i	$-0.417019\pi$
$383$	10.0886	0.515501	0.257751	+	0.966212i	$0.417019\pi$
$384$	17.7760	0.907129
$385$	10.1820	0.518921
$386$	13.0402	0.663728
$387$	−8.03785	−0.408587
$388$	−44.5930	−2.26387
$389$	−3.25341	−0.164955	−0.0824773	−	0.996593i	$-0.526283\pi$
$389$	−3.25341	−0.164955	−0.0824773	+	0.996593i	$0.526283\pi$
$390$	−14.5581	−0.737178
$391$	1.26961	0.0642069
$392$	30.4359	1.53724
$393$	4.28439	0.216119
$394$	24.8593	1.25239
$395$	−12.0315	−0.605369
$396$	−20.3298	−1.02161
$397$	4.32837	0.217234	0.108617	−	0.994084i	$-0.465358\pi$
$397$	4.32837	0.217234	0.108617	+	0.994084i	$0.465358\pi$
$398$	16.5434	0.829246
$399$	0.841243	0.0421148
$400$	−8.86595	−0.443297
$401$	−17.1590	−0.856880	−0.428440	−	0.903570i	$-0.640937\pi$
$401$	−17.1590	−0.856880	−0.428440	+	0.903570i	$0.640937\pi$
$402$	−31.4526	−1.56872
$403$	9.94514	0.495403
$404$	19.9554	0.992819
$405$	1.79948	0.0894167
$406$	26.5694	1.31862
$407$	41.9900	2.08137
$408$	−23.1135	−1.14429
$409$	−16.8938	−0.835342	−0.417671	−	0.908598i	$-0.637154\pi$
$409$	−16.8938	−0.835342	−0.417671	+	0.908598i	$0.637154\pi$
$410$	51.4218	2.53954
$411$	8.89707	0.438860
$412$	−38.3476	−1.88925
$413$	−2.25404	−0.110914
$414$	−0.734227	−0.0360853
$415$	−14.2648	−0.700231
$416$	−5.64204	−0.276624
$417$	17.4563	0.854837
$418$	−8.78680	−0.429776
$419$	−27.3541	−1.33633	−0.668167	−	0.744011i	$-0.732921\pi$
$419$	−27.3541	−1.33633	−0.668167	+	0.744011i	$0.732921\pi$
$420$	−8.69798	−0.424418
$421$	−12.2025	−0.594714	−0.297357	−	0.954766i	$-0.596105\pi$
$421$	−12.2025	−0.594714	−0.297357	+	0.954766i	$0.596105\pi$
$422$	−9.46873	−0.460931
$423$	7.66011	0.372448
$424$	74.2340	3.60512
$425$	−7.56599	−0.367005
$426$	−21.6777	−1.05029
$427$	15.6404	0.756893
$428$	−32.1300	−1.55306
$429$	−15.8921	−0.767279
$430$	35.9199	1.73221
$431$	18.5405	0.893066	0.446533	−	0.894767i	$-0.352659\pi$
$431$	18.5405	0.893066	0.446533	+	0.894767i	$0.352659\pi$
$432$	5.03209	0.242106
$433$	26.6003	1.27833	0.639164	−	0.769071i	$-0.279281\pi$
$433$	26.6003	1.27833	0.639164	+	0.769071i	$0.279281\pi$
$434$	8.79354	0.422103
$435$	16.5984	0.795834
$436$	−1.18320	−0.0566651
$437$	−0.214432	−0.0102577
$438$	11.2922	0.539564
$439$	29.1616	1.39181	0.695904	−	0.718135i	$-0.255004\pi$
$439$	29.1616	1.39181	0.695904	+	0.718135i	$0.255004\pi$
$440$	47.2495	2.25253
$441$	−5.65468	−0.269271
$442$	−34.7414	−1.65248
$443$	35.3944	1.68164	0.840819	−	0.541316i	$-0.182074\pi$
$443$	35.3944	1.68164	0.840819	+	0.541316i	$0.182074\pi$
$444$	−35.8701	−1.70232
$445$	12.4233	0.588921
$446$	49.3207	2.33540
$447$	−1.40750	−0.0665724
$448$	6.68451	0.315813
$449$	30.7435	1.45087	0.725437	−	0.688288i	$-0.241638\pi$
$449$	30.7435	1.45087	0.725437	+	0.688288i	$0.241638\pi$
$450$	4.37548	0.206262
$451$	56.1339	2.64324
$452$	2.19643	0.103312
$453$	21.3313	1.00223
$454$	8.22194	0.385875
$455$	−6.79936	−0.318759
$456$	3.90379	0.182812
$457$	−20.1795	−0.943956	−0.471978	−	0.881610i	$-0.656460\pi$
$457$	−20.1795	−0.943956	−0.471978	+	0.881610i	$0.656460\pi$
$458$	−62.4604	−2.91858
$459$	4.29427	0.200439
$460$	2.21711	0.103373
$461$	−28.9659	−1.34908	−0.674538	−	0.738240i	$-0.735657\pi$
$461$	−28.9659	−1.34908	−0.674538	+	0.738240i	$0.735657\pi$
$462$	−14.0519	−0.653753
$463$	17.1786	0.798355	0.399177	−	0.916874i	$-0.369296\pi$
$463$	17.1786	0.798355	0.399177	+	0.916874i	$0.369296\pi$
$464$	46.4161	2.15481
$465$	5.49349	0.254754
$466$	8.42626	0.390339
$467$	26.1437	1.20979	0.604893	−	0.796307i	$-0.293216\pi$
$467$	26.1437	1.20979	0.604893	+	0.796307i	$0.293216\pi$
$468$	13.5759	0.627547
$469$	−14.6900	−0.678319
$470$	−34.2319	−1.57900
$471$	5.68010	0.261725
$472$	−10.4599	−0.481455
$473$	39.2114	1.80294
$474$	16.6043	0.762662
$475$	1.27787	0.0586326
$476$	−20.7568	−0.951388
$477$	−13.7919	−0.631489
$478$	−44.9914	−2.05786
$479$	−41.8467	−1.91202	−0.956011	−	0.293330i	$-0.905236\pi$
$479$	−41.8467	−1.91202	−0.956011	+	0.293330i	$0.905236\pi$
$480$	−3.11655	−0.142250
$481$	−28.0402	−1.27853
$482$	47.6247	2.16925
$483$	−0.342921	−0.0156034
$484$	53.3349	2.42431
$485$	−19.2554	−0.874344
$486$	−2.48341	−0.112650
$487$	42.7315	1.93635	0.968174	−	0.250278i	$-0.0805219\pi$
$487$	42.7315	1.93635	0.968174	+	0.250278i	$0.0805219\pi$
$488$	72.5794	3.28551
$489$	5.37456	0.243046
$490$	25.2699	1.14158
$491$	8.06888	0.364143	0.182072	−	0.983285i	$-0.441720\pi$
$491$	8.06888	0.364143	0.182072	+	0.983285i	$0.441720\pi$
$492$	−47.9525	−2.16187
$493$	39.6104	1.78396
$494$	5.86769	0.264000
$495$	−8.77848	−0.394563
$496$	15.3621	0.689778
$497$	−10.1246	−0.454150
$498$	19.6865	0.882173
$499$	−6.41411	−0.287135	−0.143568	−	0.989641i	$-0.545857\pi$
$499$	−6.41411	−0.287135	−0.143568	+	0.989641i	$0.545857\pi$
$500$	−50.7077	−2.26772
$501$	−10.7274	−0.479267
$502$	6.00449	0.267994
$503$	−13.3137	−0.593628	−0.296814	−	0.954935i	$-0.595924\pi$
$503$	−13.3137	−0.593628	−0.296814	+	0.954935i	$0.595924\pi$
$504$	6.24296	0.278083
$505$	8.61683	0.383444
$506$	3.58182	0.159231
$507$	−2.38748	−0.106032
$508$	−16.8328	−0.746837
$509$	−19.3475	−0.857565	−0.428782	−	0.903408i	$-0.641057\pi$
$509$	−19.3475	−0.857565	−0.428782	+	0.903408i	$0.641057\pi$
$510$	−19.1904	−0.849766
$511$	5.27404	0.233310
$512$	45.4545	2.00882
$513$	−0.725285	−0.0320221
$514$	−64.4863	−2.84437
$515$	−16.5587	−0.729662
$516$	−33.4965	−1.47460
$517$	−37.3687	−1.64347
$518$	−24.7933	−1.08936
$519$	1.00151	0.0439616
$520$	−31.5525	−1.38367
$521$	−25.5896	−1.12110	−0.560551	−	0.828120i	$-0.689411\pi$
$521$	−25.5896	−1.12110	−0.560551	+	0.828120i	$0.689411\pi$
$522$	−22.9071	−1.00262
$523$	2.18589	0.0955821	0.0477911	−	0.998857i	$-0.484782\pi$
$523$	2.18589	0.0955821	0.0477911	+	0.998857i	$0.484782\pi$
$524$	17.8545	0.779979
$525$	2.04357	0.0891887
$526$	−13.7624	−0.600071
$527$	13.1096	0.571065
$528$	−24.5483	−1.06833
$529$	−22.9126	−0.996200
$530$	61.6340	2.67721
$531$	1.94334	0.0843338
$532$	3.50575	0.151994
$533$	−37.4853	−1.62367
$534$	−17.1451	−0.741941
$535$	−13.8738	−0.599819
$536$	−68.1688	−2.94444
$537$	−19.6477	−0.847861
$538$	47.9210	2.06602
$539$	27.5855	1.18819
$540$	7.49905	0.322708
$541$	9.59986	0.412730	0.206365	−	0.978475i	$-0.433837\pi$
$541$	9.59986	0.412730	0.206365	+	0.978475i	$0.433837\pi$
$542$	57.6277	2.47532
$543$	−9.42418	−0.404430
$544$	−7.43731	−0.318872
$545$	−0.510911	−0.0218850
$546$	9.38363	0.401582
$547$	6.87406	0.293914	0.146957	−	0.989143i	$-0.453052\pi$
$547$	6.87406	0.293914	0.146957	+	0.989143i	$0.453052\pi$
$548$	37.0772	1.58386
$549$	−13.4845	−0.575505
$550$	−21.3451	−0.910160
$551$	−6.69005	−0.285006
$552$	−1.59133	−0.0677313
$553$	7.75506	0.329779
$554$	35.7600	1.51930
$555$	−15.4888	−0.657465
$556$	72.7463	3.08513
$557$	−13.4416	−0.569538	−0.284769	−	0.958596i	$-0.591917\pi$
$557$	−13.4416	−0.569538	−0.284769	+	0.958596i	$0.591917\pi$
$558$	−7.58143	−0.320947
$559$	−26.1848	−1.10750
$560$	−10.5029	−0.443826
$561$	−20.9489	−0.884464
$562$	−41.3672	−1.74497
$563$	19.8632	0.837134	0.418567	−	0.908186i	$-0.362532\pi$
$563$	19.8632	0.837134	0.418567	+	0.908186i	$0.362532\pi$
$564$	31.9224	1.34417
$565$	0.948429	0.0399007
$566$	30.0705	1.26396
$567$	−1.15988	−0.0487103
$568$	−46.9831	−1.97137
$569$	4.81370	0.201801	0.100900	−	0.994897i	$-0.467828\pi$
$569$	4.81370	0.201801	0.100900	+	0.994897i	$0.467828\pi$
$570$	3.24119	0.135758
$571$	6.11084	0.255731	0.127865	−	0.991792i	$-0.459187\pi$
$571$	6.11084	0.255731	0.127865	+	0.991792i	$0.459187\pi$
$572$	−66.2280	−2.76913
$573$	9.66187	0.403631
$574$	−33.1447	−1.38343
$575$	−0.520905	−0.0217232
$576$	−5.76311	−0.240129
$577$	32.2579	1.34291	0.671457	−	0.741044i	$-0.265669\pi$
$577$	32.2579	1.34291	0.671457	+	0.741044i	$0.265669\pi$
$578$	−3.57791	−0.148821
$579$	−5.25091	−0.218220
$580$	69.1714	2.87219
$581$	9.19458	0.381456
$582$	26.5740	1.10153
$583$	67.2818	2.78653
$584$	24.4742	1.01275
$585$	5.86213	0.242369
$586$	34.7591	1.43589
$587$	25.8406	1.06656	0.533279	−	0.845940i	$-0.320960\pi$
$587$	25.8406	1.06656	0.533279	+	0.845940i	$0.320960\pi$
$588$	−23.5650	−0.971805
$589$	−2.21417	−0.0912332
$590$	−8.68449	−0.357535
$591$	−10.0101	−0.411761
$592$	−43.3133	−1.78016
$593$	−25.7516	−1.05749	−0.528745	−	0.848781i	$-0.677337\pi$
$593$	−25.7516	−1.05749	−0.528745	+	0.848781i	$0.677337\pi$
$594$	12.1150	0.497083
$595$	−8.96289	−0.367443
$596$	−5.86554	−0.240262
$597$	−6.66156	−0.272639
$598$	−2.39188	−0.0978113
$599$	−2.54673	−0.104057	−0.0520284	−	0.998646i	$-0.516569\pi$
$599$	−2.54673	−0.104057	−0.0520284	+	0.998646i	$0.516569\pi$
$600$	9.48319	0.387150
$601$	−40.3025	−1.64397	−0.821987	−	0.569507i	$-0.807134\pi$
$601$	−40.3025	−1.64397	−0.821987	+	0.569507i	$0.807134\pi$
$602$	−23.1527	−0.943634
$603$	12.6651	0.515762
$604$	88.8950	3.61709
$605$	23.0302	0.936312
$606$	−11.8919	−0.483075
$607$	−18.5219	−0.751780	−0.375890	−	0.926664i	$-0.622663\pi$
$607$	−18.5219	−0.751780	−0.375890	+	0.926664i	$0.622663\pi$
$608$	1.25613	0.0509429
$609$	−10.6988	−0.433536
$610$	60.2603	2.43987
$611$	24.9542	1.00954
$612$	17.8957	0.723391
$613$	−5.03094	−0.203198	−0.101599	−	0.994825i	$-0.532396\pi$
$613$	−5.03094	−0.203198	−0.101599	+	0.994825i	$0.532396\pi$
$614$	−15.5609	−0.627986
$615$	−20.7061	−0.834950
$616$	−30.4553	−1.22708
$617$	31.7066	1.27646	0.638230	−	0.769845i	$-0.279667\pi$
$617$	31.7066	1.27646	0.638230	+	0.769845i	$0.279667\pi$
$618$	22.8522	0.919250
$619$	−12.6093	−0.506810	−0.253405	−	0.967360i	$-0.581550\pi$
$619$	−12.6093	−0.506810	−0.253405	+	0.967360i	$0.581550\pi$
$620$	22.8933	0.919415
$621$	0.295652	0.0118641
$622$	72.6320	2.91228
$623$	−8.00762	−0.320819
$624$	16.3930	0.656244
$625$	−13.0864	−0.523454
$626$	44.6362	1.78402
$627$	3.53819	0.141302
$628$	23.6709	0.944573
$629$	−36.9625	−1.47379
$630$	5.18332	0.206508
$631$	−9.15620	−0.364502	−0.182251	−	0.983252i	$-0.558338\pi$
$631$	−9.15620	−0.364502	−0.182251	+	0.983252i	$0.558338\pi$
$632$	35.9874	1.43150
$633$	3.81279	0.151545
$634$	−56.6449	−2.24966
$635$	−7.26849	−0.288441
$636$	−57.4757	−2.27906
$637$	−18.4212	−0.729874
$638$	111.749	4.42418
$639$	8.72900	0.345314
$640$	31.9875	1.26442
$641$	−19.2473	−0.760224	−0.380112	−	0.924940i	$-0.624115\pi$
$641$	−19.2473	−0.760224	−0.380112	+	0.924940i	$0.624115\pi$
$642$	19.1470	0.755670
$643$	−29.5458	−1.16517	−0.582587	−	0.812768i	$-0.697959\pi$
$643$	−29.5458	−1.16517	−0.582587	+	0.812768i	$0.697959\pi$
$644$	−1.42907	−0.0563133
$645$	−14.4639	−0.569516
$646$	7.73476	0.304320
$647$	−47.0979	−1.85161	−0.925806	−	0.378000i	$-0.876612\pi$
$647$	−47.0979	−1.85161	−0.925806	+	0.378000i	$0.876612\pi$
$648$	−5.38242	−0.211441
$649$	−9.48029	−0.372134
$650$	14.2540	0.559086
$651$	−3.54091	−0.138779
$652$	22.3977	0.877161
$653$	−23.0598	−0.902399	−0.451199	−	0.892423i	$-0.649004\pi$
$653$	−23.0598	−0.902399	−0.451199	+	0.892423i	$0.649004\pi$
$654$	0.705096	0.0275714
$655$	7.70966	0.301241
$656$	−57.9029	−2.26073
$657$	−4.54706	−0.177398
$658$	22.0647	0.860170
$659$	−35.7555	−1.39284	−0.696418	−	0.717637i	$-0.745224\pi$
$659$	−35.7555	−1.39284	−0.696418	+	0.717637i	$0.745224\pi$
$660$	−36.5830	−1.42399
$661$	3.28470	0.127760	0.0638799	−	0.997958i	$-0.479653\pi$
$661$	3.28470	0.127760	0.0638799	+	0.997958i	$0.479653\pi$
$662$	14.9805	0.582234
$663$	13.9894	0.543302
$664$	42.6675	1.65582
$665$	1.51380	0.0587025
$666$	21.3758	0.828294
$667$	2.72711	0.105594
$668$	−44.7050	−1.72969
$669$	−19.8600	−0.767833
$670$	−56.5983	−2.18658
$671$	65.7822	2.53949
$672$	2.00881	0.0774917
$673$	−35.3233	−1.36161	−0.680807	−	0.732463i	$-0.738371\pi$
$673$	−35.3233	−1.36161	−0.680807	+	0.732463i	$0.738371\pi$
$674$	64.7385	2.49363
$675$	−1.76188	−0.0678149
$676$	−9.94947	−0.382672
$677$	−10.1855	−0.391459	−0.195729	−	0.980658i	$-0.562707\pi$
$677$	−10.1855	−0.391459	−0.195729	+	0.980658i	$0.562707\pi$
$678$	−1.30890	−0.0502682
$679$	12.4114	0.476305
$680$	−41.5923	−1.59499
$681$	−3.31074	−0.126868
$682$	36.9848	1.41622
$683$	7.09434	0.271457	0.135729	−	0.990746i	$-0.456662\pi$
$683$	7.09434	0.271457	0.135729	+	0.990746i	$0.456662\pi$
$684$	−3.02251	−0.115569
$685$	16.0101	0.611713
$686$	−36.4513	−1.39172
$687$	25.1510	0.959570
$688$	−40.4472	−1.54203
$689$	−44.9298	−1.71169
$690$	−1.32122	−0.0502982
$691$	12.3358	0.469276	0.234638	−	0.972083i	$-0.424610\pi$
$691$	12.3358	0.469276	0.234638	+	0.972083i	$0.424610\pi$
$692$	4.17365	0.158658
$693$	5.65829	0.214941
$694$	−86.1714	−3.27102
$695$	31.4121	1.19153
$696$	−49.6476	−1.88189
$697$	−49.4130	−1.87165
$698$	9.91534	0.375301
$699$	−3.39301	−0.128336
$700$	8.51627	0.321885
$701$	8.95720	0.338309	0.169154	−	0.985590i	$-0.445896\pi$
$701$	8.95720	0.338309	0.169154	+	0.985590i	$0.445896\pi$
$702$	−8.09018	−0.305344
$703$	6.24283	0.235453
$704$	28.1144	1.05960
$705$	13.7842	0.519143
$706$	−38.5133	−1.44947
$707$	−5.55410	−0.208884
$708$	8.09857	0.304363
$709$	14.9782	0.562519	0.281260	−	0.959632i	$-0.409248\pi$
$709$	14.9782	0.562519	0.281260	+	0.959632i	$0.409248\pi$
$710$	−39.0086	−1.46397
$711$	−6.68609	−0.250748
$712$	−37.1594	−1.39261
$713$	0.902574	0.0338017
$714$	12.3695	0.462916
$715$	−28.5975	−1.06949
$716$	−81.8788	−3.05996
$717$	18.1167	0.676582
$718$	17.1759	0.640997
$719$	−4.16806	−0.155442	−0.0777212	−	0.996975i	$-0.524764\pi$
$719$	−4.16806	−0.155442	−0.0777212	+	0.996975i	$0.524764\pi$
$720$	9.05513	0.337465
$721$	10.6731	0.397488
$722$	45.8785	1.70742
$723$	−19.1771	−0.713204
$724$	−39.2738	−1.45960
$725$	−16.2517	−0.603571
$726$	−31.7834	−1.17959
$727$	−15.1987	−0.563687	−0.281844	−	0.959460i	$-0.590946\pi$
$727$	−15.1987	−0.563687	−0.281844	+	0.959460i	$0.590946\pi$
$728$	20.3376	0.753761
$729$	1.00000	0.0370370
$730$	20.3201	0.752081
$731$	−34.5167	−1.27664
$732$	−56.1947	−2.07701
$733$	−45.4502	−1.67874	−0.839371	−	0.543559i	$-0.817077\pi$
$733$	−45.4502	−1.67874	−0.839371	+	0.543559i	$0.817077\pi$
$734$	15.5104	0.572501
$735$	−10.1755	−0.375328
$736$	−0.512045	−0.0188742
$737$	−61.7847	−2.27587
$738$	28.5760	1.05190
$739$	−29.3160	−1.07841	−0.539203	−	0.842176i	$-0.681274\pi$
$739$	−29.3160	−1.07841	−0.539203	+	0.842176i	$0.681274\pi$
$740$	−64.5474	−2.37281
$741$	−2.36275	−0.0867978
$742$	−39.7271	−1.45843
$743$	−32.6409	−1.19748	−0.598738	−	0.800945i	$-0.704331\pi$
$743$	−32.6409	−1.19748	−0.598738	+	0.800945i	$0.704331\pi$
$744$	−16.4316	−0.602411
$745$	−2.53276	−0.0927932
$746$	24.8364	0.909326
$747$	−7.92719	−0.290041
$748$	−87.3015	−3.19206
$749$	8.94259	0.326755
$750$	30.2178	1.10340
$751$	−22.9161	−0.836221	−0.418111	−	0.908396i	$-0.637308\pi$
$751$	−22.9161	−0.836221	−0.418111	+	0.908396i	$0.637308\pi$
$752$	38.5464	1.40564
$753$	−2.41784	−0.0881109
$754$	−74.6241	−2.71765
$755$	38.3852	1.39698
$756$	−4.83362	−0.175797
$757$	−21.5966	−0.784940	−0.392470	−	0.919765i	$-0.628379\pi$
$757$	−21.5966	−0.784940	−0.392470	+	0.919765i	$0.628379\pi$
$758$	22.2937	0.809745
$759$	−1.44230	−0.0523520
$760$	7.02478	0.254815
$761$	−6.95218	−0.252016	−0.126008	−	0.992029i	$-0.540217\pi$
$761$	−6.95218	−0.252016	−0.126008	+	0.992029i	$0.540217\pi$
$762$	10.0311	0.363387
$763$	0.329315	0.0119220
$764$	40.2644	1.45671
$765$	7.72743	0.279386
$766$	−25.0541	−0.905240
$767$	6.33079	0.228592
$768$	−32.6190	−1.17704
$769$	−23.5832	−0.850431	−0.425216	−	0.905092i	$-0.639802\pi$
$769$	−23.5832	−0.850431	−0.425216	+	0.905092i	$0.639802\pi$
$770$	−25.2861	−0.911246
$771$	25.9668	0.935171
$772$	−21.8824	−0.787564
$773$	−1.50258	−0.0540441	−0.0270221	−	0.999635i	$-0.508602\pi$
$773$	−1.50258	−0.0540441	−0.0270221	+	0.999635i	$0.508602\pi$
$774$	19.9613	0.717494
$775$	−5.37872	−0.193209
$776$	57.5950	2.06754
$777$	9.98356	0.358158
$778$	8.07958	0.289667
$779$	8.34566	0.299014
$780$	24.4295	0.874718
$781$	−42.5831	−1.52374
$782$	−3.15297	−0.112750
$783$	9.22403	0.329640
$784$	−28.4549	−1.01624
$785$	10.2212	0.364810
$786$	−10.6399	−0.379513
$787$	27.0922	0.965733	0.482866	−	0.875694i	$-0.339596\pi$
$787$	27.0922	0.965733	0.482866	+	0.875694i	$0.339596\pi$
$788$	−41.7157	−1.48606
$789$	5.54174	0.197291
$790$	29.8791	1.06305
$791$	−0.611324	−0.0217362
$792$	26.2573	0.933013
$793$	−43.9283	−1.55994
$794$	−10.7491	−0.381472
$795$	−24.8183	−0.880213
$796$	−27.7610	−0.983964
$797$	−5.20814	−0.184482	−0.0922409	−	0.995737i	$-0.529403\pi$
$797$	−5.20814	−0.184482	−0.0922409	+	0.995737i	$0.529403\pi$
$798$	−2.08915	−0.0739553
$799$	32.8946	1.16373
$800$	3.05144	0.107885
$801$	6.90384	0.243935
$802$	42.6129	1.50471
$803$	22.1822	0.782791
$804$	52.7798	1.86140
$805$	−0.617078	−0.0217491
$806$	−24.6979	−0.869947
$807$	−19.2964	−0.679266
$808$	−25.7738	−0.906720
$809$	0.642461	0.0225877	0.0112939	−	0.999936i	$-0.496405\pi$
$809$	0.642461	0.0225877	0.0112939	+	0.999936i	$0.496405\pi$
$810$	−4.46885	−0.157019
$811$	29.9594	1.05202	0.526009	−	0.850479i	$-0.323688\pi$
$811$	29.9594	1.05202	0.526009	+	0.850479i	$0.323688\pi$
$812$	−44.5854	−1.56464
$813$	−23.2050	−0.813835
$814$	−104.278	−3.65496
$815$	9.67140	0.338774
$816$	21.6091	0.756471
$817$	5.82973	0.203956
$818$	41.9542	1.46689
$819$	−3.77852	−0.132032
$820$	−86.2895	−3.01336
$821$	48.8549	1.70505	0.852524	−	0.522689i	$-0.175071\pi$
$821$	48.8549	1.70505	0.852524	+	0.522689i	$0.175071\pi$
$822$	−22.0951	−0.770656
$823$	46.5677	1.62325	0.811625	−	0.584179i	$-0.198584\pi$
$823$	46.5677	1.62325	0.811625	+	0.584179i	$0.198584\pi$
$824$	49.5287	1.72541
$825$	8.59508	0.299242
$826$	5.59771	0.194769
$827$	−13.3876	−0.465532	−0.232766	−	0.972533i	$-0.574778\pi$
$827$	−13.3876	−0.465532	−0.232766	+	0.972533i	$0.574778\pi$
$828$	1.23209	0.0428179
$829$	8.64596	0.300287	0.150143	−	0.988664i	$-0.452027\pi$
$829$	8.64596	0.300287	0.150143	+	0.988664i	$0.452027\pi$
$830$	35.4254	1.22963
$831$	−14.3995	−0.499515
$832$	−18.7744	−0.650885
$833$	−24.2827	−0.841346
$834$	−43.3511	−1.50113
$835$	−19.3038	−0.668035
$836$	14.7449	0.509962
$837$	3.05282	0.105521
$838$	67.9315	2.34666
$839$	−26.6436	−0.919841	−0.459920	−	0.887960i	$-0.652122\pi$
$839$	−26.6436	−0.919841	−0.459920	+	0.887960i	$0.652122\pi$
$840$	11.2341	0.387612
$841$	56.0827	1.93389
$842$	30.3039	1.04434
$843$	16.6574	0.573711
$844$	15.8892	0.546929
$845$	−4.29622	−0.147794
$846$	−19.0232	−0.654032
$847$	−14.8445	−0.510062
$848$	−69.4022	−2.38328
$849$	−12.1085	−0.415563
$850$	18.7895	0.644474
$851$	−2.54480	−0.0872347
$852$	36.3768	1.24625
$853$	22.0742	0.755808	0.377904	−	0.925845i	$-0.376645\pi$
$853$	22.0742	0.755808	0.377904	+	0.925845i	$0.376645\pi$
$854$	−38.8416	−1.32913
$855$	−1.30513	−0.0446346
$856$	41.4981	1.41838
$857$	20.6640	0.705870	0.352935	−	0.935648i	$-0.385184\pi$
$857$	20.6640	0.705870	0.352935	+	0.935648i	$0.385184\pi$
$858$	39.4667	1.34737
$859$	14.6463	0.499724	0.249862	−	0.968281i	$-0.419615\pi$
$859$	14.6463	0.499724	0.249862	+	0.968281i	$0.419615\pi$
$860$	−60.2762	−2.05540
$861$	13.3464	0.454845
$862$	−46.0438	−1.56826
$863$	−41.2273	−1.40339	−0.701696	−	0.712476i	$-0.747574\pi$
$863$	−41.2273	−1.40339	−0.701696	+	0.712476i	$0.747574\pi$
$864$	−1.73192	−0.0589210
$865$	1.80220	0.0612766
$866$	−66.0595	−2.24479
$867$	1.44072	0.0489295
$868$	−14.7562	−0.500857
$869$	32.6171	1.10646
$870$	−41.2208	−1.39752
$871$	41.2589	1.39800
$872$	1.52819	0.0517509
$873$	−10.7006	−0.362160
$874$	0.532524	0.0180129
$875$	14.1132	0.477114
$876$	−18.9492	−0.640234
$877$	−5.42656	−0.183242	−0.0916210	−	0.995794i	$-0.529205\pi$
$877$	−5.42656	−0.183242	−0.0916210	+	0.995794i	$0.529205\pi$
$878$	−72.4203	−2.44407
$879$	−13.9965	−0.472090
$880$	−44.1741	−1.48911
$881$	53.1705	1.79136	0.895680	−	0.444700i	$-0.146690\pi$
$881$	53.1705	1.79136	0.895680	+	0.444700i	$0.146690\pi$
$882$	14.0429	0.472850
$883$	23.1016	0.777432	0.388716	−	0.921358i	$-0.372919\pi$
$883$	23.1016	0.777432	0.388716	+	0.921358i	$0.372919\pi$
$884$	58.2986	1.96079
$885$	3.49700	0.117550
$886$	−87.8990	−2.95302
$887$	−50.7014	−1.70239	−0.851194	−	0.524851i	$-0.824121\pi$
$887$	−50.7014	−1.70239	−0.851194	+	0.524851i	$0.824121\pi$
$888$	46.3287	1.55469
$889$	4.68501	0.157130
$890$	−30.8522	−1.03417
$891$	−4.87835	−0.163431
$892$	−82.7636	−2.77113
$893$	−5.55577	−0.185917
$894$	3.49540	0.116904
$895$	−35.3556	−1.18181
$896$	−20.6180	−0.688800
$897$	0.963142	0.0321584
$898$	−76.3488	−2.54779
$899$	28.1593	0.939166
$900$	−7.34238	−0.244746
$901$	−59.2262	−1.97311
$902$	−139.404	−4.64163
$903$	9.32293	0.310248
$904$	−2.83685	−0.0943522
$905$	−16.9586	−0.563723
$906$	−52.9745	−1.75996
$907$	2.44582	0.0812123	0.0406061	−	0.999175i	$-0.487071\pi$
$907$	2.44582	0.0812123	0.0406061	+	0.999175i	$0.487071\pi$
$908$	−13.7970	−0.457870
$909$	4.78852	0.158825
$910$	16.8856	0.559753
$911$	18.8114	0.623250	0.311625	−	0.950205i	$-0.399127\pi$
$911$	18.8114	0.623250	0.311625	+	0.950205i	$0.399127\pi$
$912$	−3.64970	−0.120854
$913$	38.6716	1.27984
$914$	50.1140	1.65762
$915$	−24.2651	−0.802179
$916$	104.813	3.46312
$917$	−4.96937	−0.164103
$918$	−10.6644	−0.351979
$919$	−15.1862	−0.500948	−0.250474	−	0.968123i	$-0.580586\pi$
$919$	−15.1862	−0.500948	−0.250474	+	0.968123i	$0.580586\pi$
$920$	−2.86355	−0.0944085
$921$	6.26592	0.206469
$922$	71.9343	2.36903
$923$	28.4363	0.935993
$924$	23.5801	0.775728
$925$	15.1653	0.498630
$926$	−42.6615	−1.40194
$927$	−9.20193	−0.302231
$928$	−15.9753	−0.524414
$929$	15.5512	0.510217	0.255108	−	0.966912i	$-0.417889\pi$
$929$	15.5512	0.510217	0.255108	+	0.966912i	$0.417889\pi$
$930$	−13.6426	−0.447359
$931$	4.10125	0.134413
$932$	−14.1399	−0.463167
$933$	−29.2468	−0.957499
$934$	−64.9256	−2.12443
$935$	−37.6971	−1.23283
$936$	−17.5342	−0.573125
$937$	−26.6218	−0.869696	−0.434848	−	0.900504i	$-0.643198\pi$
$937$	−26.6218	−0.869696	−0.434848	+	0.900504i	$0.643198\pi$
$938$	36.4813	1.19116
$939$	−17.9737	−0.586550
$940$	57.4435	1.87360
$941$	−20.3633	−0.663823	−0.331912	−	0.943310i	$-0.607694\pi$
$941$	−20.3633	−0.663823	−0.331912	+	0.943310i	$0.607694\pi$
$942$	−14.1060	−0.459599
$943$	−3.40199	−0.110784
$944$	9.77906	0.318281
$945$	−2.08718	−0.0678958
$946$	−97.3782	−3.16604
$947$	36.4327	1.18390	0.591952	−	0.805973i	$-0.298357\pi$
$947$	36.4327	1.18390	0.591952	+	0.805973i	$0.298357\pi$
$948$	−27.8633	−0.904957
$949$	−14.8129	−0.480847
$950$	−3.17347	−0.102961
$951$	22.8093	0.739641
$952$	26.8089	0.868882
$953$	−23.6528	−0.766190	−0.383095	−	0.923709i	$-0.625142\pi$
$953$	−23.6528	−0.766190	−0.383095	+	0.923709i	$0.625142\pi$
$954$	34.2511	1.10892
$955$	17.3863	0.562608
$956$	75.4987	2.44180
$957$	−44.9980	−1.45458
$958$	103.923	3.35759
$959$	−10.3195	−0.333235
$960$	−10.3706	−0.334709
$961$	−21.6803	−0.699364
$962$	69.6356	2.24514
$963$	−7.70993	−0.248449
$964$	−79.9177	−2.57397
$965$	−9.44890	−0.304171
$966$	0.851615	0.0274003
$967$	10.8171	0.347854	0.173927	−	0.984759i	$-0.444354\pi$
$967$	10.8171	0.347854	0.173927	+	0.984759i	$0.444354\pi$
$968$	−68.8858	−2.21407
$969$	−3.11457	−0.100054
$970$	47.8192	1.53538
$971$	14.7661	0.473866	0.236933	−	0.971526i	$-0.423858\pi$
$971$	14.7661	0.473866	0.236933	+	0.971526i	$0.423858\pi$
$972$	4.16735	0.133668
$973$	−20.2471	−0.649094
$974$	−106.120	−3.40030
$975$	−5.73966	−0.183816
$976$	−67.8553	−2.17199
$977$	9.83224	0.314561	0.157281	−	0.987554i	$-0.449727\pi$
$977$	9.83224	0.314561	0.157281	+	0.987554i	$0.449727\pi$
$978$	−13.3473	−0.426799
$979$	−33.6793	−1.07640
$980$	−42.4047	−1.35457
$981$	−0.283922	−0.00906493
$982$	−20.0384	−0.639450
$983$	1.19573	0.0381380	0.0190690	−	0.999818i	$-0.493930\pi$
$983$	1.19573	0.0381380	0.0190690	+	0.999818i	$0.493930\pi$
$984$	61.9341	1.97439
$985$	−18.0130	−0.573942
$986$	−98.3691	−3.13271
$987$	−8.88481	−0.282806
$988$	−9.84640	−0.313256
$989$	−2.37641	−0.0755654
$990$	21.8006	0.692868
$991$	5.01386	0.159270	0.0796352	−	0.996824i	$-0.474624\pi$
$991$	5.01386	0.159270	0.0796352	+	0.996824i	$0.474624\pi$
$992$	−5.28724	−0.167870
$993$	−6.03222	−0.191427
$994$	25.1435	0.797504
$995$	−11.9873	−0.380024
$996$	−33.0354	−1.04677
$997$	−4.50593	−0.142704	−0.0713521	−	0.997451i	$-0.522731\pi$
$997$	−4.50593	−0.142704	−0.0713521	+	0.997451i	$0.522731\pi$
$998$	15.9289	0.504220
$999$	−8.60741	−0.272326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.a.1.7	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.a.1.7	✓	92	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48341 q^{2} +1.00000 q^{3} +4.16735 q^{4} +1.79948 q^{5} -2.48341 q^{6} -1.15988 q^{7} -5.38242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48341 q^{2} +1.00000 q^{3} +4.16735 q^{4} +1.79948 q^{5} -2.48341 q^{6} -1.15988 q^{7} -5.38242 q^{8} +1.00000 q^{9} -4.46885 q^{10} -4.87835 q^{11} +4.16735 q^{12} +3.25769 q^{13} +2.88046 q^{14} +1.79948 q^{15} +5.03209 q^{16} +4.29427 q^{17} -2.48341 q^{18} -0.725285 q^{19} +7.49905 q^{20} -1.15988 q^{21} +12.1150 q^{22} +0.295652 q^{23} -5.38242 q^{24} -1.76188 q^{25} -8.09018 q^{26} +1.00000 q^{27} -4.83362 q^{28} +9.22403 q^{29} -4.46885 q^{30} +3.05282 q^{31} -1.73192 q^{32} -4.87835 q^{33} -10.6644 q^{34} -2.08718 q^{35} +4.16735 q^{36} -8.60741 q^{37} +1.80118 q^{38} +3.25769 q^{39} -9.68554 q^{40} -11.5067 q^{41} +2.88046 q^{42} -8.03785 q^{43} -20.3298 q^{44} +1.79948 q^{45} -0.734227 q^{46} +7.66011 q^{47} +5.03209 q^{48} -5.65468 q^{49} +4.37548 q^{50} +4.29427 q^{51} +13.5759 q^{52} -13.7919 q^{53} -2.48341 q^{54} -8.77848 q^{55} +6.24296 q^{56} -0.725285 q^{57} -22.9071 q^{58} +1.94334 q^{59} +7.49905 q^{60} -13.4845 q^{61} -7.58143 q^{62} -1.15988 q^{63} -5.76311 q^{64} +5.86213 q^{65} +12.1150 q^{66} +12.6651 q^{67} +17.8957 q^{68} +0.295652 q^{69} +5.18332 q^{70} +8.72900 q^{71} -5.38242 q^{72} -4.54706 q^{73} +21.3758 q^{74} -1.76188 q^{75} -3.02251 q^{76} +5.65829 q^{77} -8.09018 q^{78} -6.68609 q^{79} +9.05513 q^{80} +1.00000 q^{81} +28.5760 q^{82} -7.92719 q^{83} -4.83362 q^{84} +7.72743 q^{85} +19.9613 q^{86} +9.22403 q^{87} +26.2573 q^{88} +6.90384 q^{89} -4.46885 q^{90} -3.77852 q^{91} +1.23209 q^{92} +3.05282 q^{93} -19.0232 q^{94} -1.30513 q^{95} -1.73192 q^{96} -10.7006 q^{97} +14.0429 q^{98} -4.87835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9	\( 92 q - 6 q^{2} + 92 q^{3} + 70 q^{4} - 18 q^{5} - 6 q^{6} - 42 q^{7} - 15 q^{8} + 92 q^{9} - 44 q^{10} - 24 q^{11} + 70 q^{12} - 48 q^{13} - 29 q^{14} - 18 q^{15} + 26 q^{16} - 69 q^{17} - 6 q^{18} - 74 q^{19} - 42 q^{20} - 42 q^{21} - 62 q^{22} - 19 q^{23} - 15 q^{24} + 16 q^{25} - 27 q^{26} + 92 q^{27} - 101 q^{28} - 54 q^{29} - 44 q^{30} - 67 q^{31} - 36 q^{32} - 24 q^{33} - 63 q^{34} - 31 q^{35} + 70 q^{36} - 70 q^{37} - 18 q^{38} - 48 q^{39} - 125 q^{40} - 98 q^{41} - 29 q^{42} - 159 q^{43} - 52 q^{44} - 18 q^{45} - 68 q^{46} - 15 q^{47} + 26 q^{48} - 28 q^{49} - 7 q^{50} - 69 q^{51} - 98 q^{52} - 23 q^{53} - 6 q^{54} - 93 q^{55} - 48 q^{56} - 74 q^{57} - 37 q^{58} - 36 q^{59} - 42 q^{60} - 172 q^{61} - 26 q^{62} - 42 q^{63} - 23 q^{64} - 66 q^{65} - 62 q^{66} - 143 q^{67} - 74 q^{68} - 19 q^{69} - 30 q^{70} - 9 q^{71} - 15 q^{72} - 134 q^{73} - 19 q^{74} + 16 q^{75} - 157 q^{76} - 25 q^{77} - 27 q^{78} - 138 q^{79} - 29 q^{80} + 92 q^{81} - 61 q^{82} - 24 q^{83} - 101 q^{84} - 84 q^{85} + 14 q^{86} - 54 q^{87} - 140 q^{88} - 148 q^{89} - 44 q^{90} - 115 q^{91} - 12 q^{92} - 67 q^{93} - 79 q^{94} - 10 q^{95} - 36 q^{96} - 165 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 92 * q - 6 * q^2 + 92 * q^3 + 70 * q^4 - 18 * q^5 - 6 * q^6 - 42 * q^7 - 15 * q^8 + 92 * q^9 - 44 * q^10 - 24 * q^11 + 70 * q^12 - 48 * q^13 - 29 * q^14 - 18 * q^15 + 26 * q^16 - 69 * q^17 - 6 * q^18 - 74 * q^19 - 42 * q^20 - 42 * q^21 - 62 * q^22 - 19 * q^23 - 15 * q^24 + 16 * q^25 - 27 * q^26 + 92 * q^27 - 101 * q^28 - 54 * q^29 - 44 * q^30 - 67 * q^31 - 36 * q^32 - 24 * q^33 - 63 * q^34 - 31 * q^35 + 70 * q^36 - 70 * q^37 - 18 * q^38 - 48 * q^39 - 125 * q^40 - 98 * q^41 - 29 * q^42 - 159 * q^43 - 52 * q^44 - 18 * q^45 - 68 * q^46 - 15 * q^47 + 26 * q^48 - 28 * q^49 - 7 * q^50 - 69 * q^51 - 98 * q^52 - 23 * q^53 - 6 * q^54 - 93 * q^55 - 48 * q^56 - 74 * q^57 - 37 * q^58 - 36 * q^59 - 42 * q^60 - 172 * q^61 - 26 * q^62 - 42 * q^63 - 23 * q^64 - 66 * q^65 - 62 * q^66 - 143 * q^67 - 74 * q^68 - 19 * q^69 - 30 * q^70 - 9 * q^71 - 15 * q^72 - 134 * q^73 - 19 * q^74 + 16 * q^75 - 157 * q^76 - 25 * q^77 - 27 * q^78 - 138 * q^79 - 29 * q^80 + 92 * q^81 - 61 * q^82 - 24 * q^83 - 101 * q^84 - 84 * q^85 + 14 * q^86 - 54 * q^87 - 140 * q^88 - 148 * q^89 - 44 * q^90 - 115 * q^91 - 12 * q^92 - 67 * q^93 - 79 * q^94 - 10 * q^95 - 36 * q^96 - 165 * q^97 + 36 * q^98 - 24 * q^99

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