LMFDB - Embedded newform 8027.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32136 q^{2} -1.73102 q^{3} +3.38869 q^{4} -3.82853 q^{5} +4.01832 q^{6} -3.14873 q^{7} -3.22365 q^{8} -0.00355516 q^{9} +O(q^{10})$	\(q-2.32136 q^{2} -1.73102 q^{3} +3.38869 q^{4} -3.82853 q^{5} +4.01832 q^{6} -3.14873 q^{7} -3.22365 q^{8} -0.00355516 q^{9} +8.88737 q^{10} -2.93348 q^{11} -5.86591 q^{12} +4.68197 q^{13} +7.30933 q^{14} +6.62727 q^{15} +0.705848 q^{16} +1.06447 q^{17} +0.00825278 q^{18} +5.52896 q^{19} -12.9737 q^{20} +5.45054 q^{21} +6.80966 q^{22} -1.00000 q^{23} +5.58021 q^{24} +9.65761 q^{25} -10.8685 q^{26} +5.19923 q^{27} -10.6701 q^{28} +1.48411 q^{29} -15.3843 q^{30} +8.67471 q^{31} +4.80877 q^{32} +5.07793 q^{33} -2.47102 q^{34} +12.0550 q^{35} -0.0120473 q^{36} +1.51544 q^{37} -12.8347 q^{38} -8.10460 q^{39} +12.3418 q^{40} +3.50089 q^{41} -12.6526 q^{42} +8.42279 q^{43} -9.94067 q^{44} +0.0136110 q^{45} +2.32136 q^{46} -3.12030 q^{47} -1.22184 q^{48} +2.91453 q^{49} -22.4188 q^{50} -1.84263 q^{51} +15.8657 q^{52} +8.29026 q^{53} -12.0693 q^{54} +11.2309 q^{55} +10.1504 q^{56} -9.57077 q^{57} -3.44514 q^{58} +6.69921 q^{59} +22.4578 q^{60} -0.230606 q^{61} -20.1371 q^{62} +0.0111942 q^{63} -12.5746 q^{64} -17.9250 q^{65} -11.7877 q^{66} +2.53613 q^{67} +3.60717 q^{68} +1.73102 q^{69} -27.9840 q^{70} +9.14701 q^{71} +0.0114606 q^{72} +4.95956 q^{73} -3.51787 q^{74} -16.7176 q^{75} +18.7360 q^{76} +9.23676 q^{77} +18.8137 q^{78} +13.7316 q^{79} -2.70236 q^{80} -8.98932 q^{81} -8.12680 q^{82} +1.64481 q^{83} +18.4702 q^{84} -4.07537 q^{85} -19.5523 q^{86} -2.56903 q^{87} +9.45652 q^{88} -4.77026 q^{89} -0.0315960 q^{90} -14.7423 q^{91} -3.38869 q^{92} -15.0161 q^{93} +7.24332 q^{94} -21.1678 q^{95} -8.32410 q^{96} +7.36014 q^{97} -6.76566 q^{98} +0.0104290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.32136	−1.64145	−0.820723	−	0.571326i	$-0.806429\pi$
$2$	−2.32136	−1.64145	−0.820723	+	0.571326i	$0.806429\pi$
$3$	−1.73102	−0.999407	−0.499704	−	0.866196i	$-0.666558\pi$
$3$	−1.73102	−0.999407	−0.499704	+	0.866196i	$0.666558\pi$
$4$	3.38869	1.69435
$5$	−3.82853	−1.71217	−0.856085	−	0.516836i	$-0.827110\pi$
$5$	−3.82853	−1.71217	−0.856085	+	0.516836i	$0.827110\pi$
$6$	4.01832	1.64047
$7$	−3.14873	−1.19011	−0.595055	−	0.803685i	$-0.702870\pi$
$7$	−3.14873	−1.19011	−0.595055	+	0.803685i	$0.702870\pi$
$8$	−3.22365	−1.13973
$9$	−0.00355516	−0.00118505
$10$	8.88737	2.81043
$11$	−2.93348	−0.884479	−0.442239	−	0.896897i	$-0.645816\pi$
$11$	−2.93348	−0.884479	−0.442239	+	0.896897i	$0.645816\pi$
$12$	−5.86591	−1.69334
$13$	4.68197	1.29854	0.649272	−	0.760556i	$-0.275074\pi$
$13$	4.68197	1.29854	0.649272	+	0.760556i	$0.275074\pi$
$14$	7.30933	1.95350
$15$	6.62727	1.71115
$16$	0.705848	0.176462
$17$	1.06447	0.258173	0.129086	−	0.991633i	$-0.458796\pi$
$17$	1.06447	0.258173	0.129086	+	0.991633i	$0.458796\pi$
$18$	0.00825278	0.00194520
$19$	5.52896	1.26843	0.634216	−	0.773156i	$-0.281323\pi$
$19$	5.52896	1.26843	0.634216	+	0.773156i	$0.281323\pi$
$20$	−12.9737	−2.90101
$21$	5.45054	1.18940
$22$	6.80966	1.45182
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	5.58021	1.13906
$25$	9.65761	1.93152
$26$	−10.8685	−2.13149
$27$	5.19923	1.00059
$28$	−10.6701	−2.01646
$29$	1.48411	0.275592	0.137796	−	0.990461i	$-0.455998\pi$
$29$	1.48411	0.275592	0.137796	+	0.990461i	$0.455998\pi$
$30$	−15.3843	−2.80877
$31$	8.67471	1.55802	0.779012	−	0.627009i	$-0.215721\pi$
$31$	8.67471	1.55802	0.779012	+	0.627009i	$0.215721\pi$
$32$	4.80877	0.850079
$33$	5.07793	0.883954
$34$	−2.47102	−0.423777
$35$	12.0550	2.03767
$36$	−0.0120473	−0.00200789
$37$	1.51544	0.249137	0.124568	−	0.992211i	$-0.460245\pi$
$37$	1.51544	0.249137	0.124568	+	0.992211i	$0.460245\pi$
$38$	−12.8347	−2.08206
$39$	−8.10460	−1.29777
$40$	12.3418	1.95141
$41$	3.50089	0.546746	0.273373	−	0.961908i	$-0.411861\pi$
$41$	3.50089	0.546746	0.273373	+	0.961908i	$0.411861\pi$
$42$	−12.6526	−1.95234
$43$	8.42279	1.28446	0.642232	−	0.766511i	$-0.278009\pi$
$43$	8.42279	1.28446	0.642232	+	0.766511i	$0.278009\pi$
$44$	−9.94067	−1.49861
$45$	0.0136110	0.00202901
$46$	2.32136	0.342265
$47$	−3.12030	−0.455142	−0.227571	−	0.973761i	$-0.573078\pi$
$47$	−3.12030	−0.455142	−0.227571	+	0.973761i	$0.573078\pi$
$48$	−1.22184	−0.176357
$49$	2.91453	0.416362
$50$	−22.4188	−3.17049
$51$	−1.84263	−0.258020
$52$	15.8657	2.20018
$53$	8.29026	1.13875	0.569377	−	0.822076i	$-0.307184\pi$
$53$	8.29026	1.13875	0.569377	+	0.822076i	$0.307184\pi$
$54$	−12.0693	−1.64242
$55$	11.2309	1.51438
$56$	10.1504	1.35641
$57$	−9.57077	−1.26768
$58$	−3.44514	−0.452369
$59$	6.69921	0.872162	0.436081	−	0.899907i	$-0.356366\pi$
$59$	6.69921	0.872162	0.436081	+	0.899907i	$0.356366\pi$
$60$	22.4578	2.89929
$61$	−0.230606	−0.0295261	−0.0147630	−	0.999891i	$-0.504699\pi$
$61$	−0.230606	−0.0295261	−0.0147630	+	0.999891i	$0.504699\pi$
$62$	−20.1371	−2.55741
$63$	0.0111942	0.00141034
$64$	−12.5746	−1.57182
$65$	−17.9250	−2.22333
$66$	−11.7877	−1.45096
$67$	2.53613	0.309837	0.154919	−	0.987927i	$-0.450488\pi$
$67$	2.53613	0.309837	0.154919	+	0.987927i	$0.450488\pi$
$68$	3.60717	0.437434
$69$	1.73102	0.208391
$70$	−27.9840	−3.34472
$71$	9.14701	1.08555	0.542775	−	0.839878i	$-0.317374\pi$
$71$	9.14701	1.08555	0.542775	+	0.839878i	$0.317374\pi$
$72$	0.0114606	0.00135064
$73$	4.95956	0.580473	0.290236	−	0.956955i	$-0.406266\pi$
$73$	4.95956	0.580473	0.290236	+	0.956955i	$0.406266\pi$
$74$	−3.51787	−0.408945
$75$	−16.7176	−1.93038
$76$	18.7360	2.14916
$77$	9.23676	1.05263
$78$	18.8137	2.13023
$79$	13.7316	1.54492	0.772461	−	0.635062i	$-0.219025\pi$
$79$	13.7316	1.54492	0.772461	+	0.635062i	$0.219025\pi$
$80$	−2.70236	−0.302133
$81$	−8.98932	−0.998814
$82$	−8.12680	−0.897455
$83$	1.64481	0.180542	0.0902709	−	0.995917i	$-0.471227\pi$
$83$	1.64481	0.180542	0.0902709	+	0.995917i	$0.471227\pi$
$84$	18.4702	2.01526
$85$	−4.07537	−0.442035
$86$	−19.5523	−2.10838
$87$	−2.56903	−0.275429
$88$	9.45652	1.00807
$89$	−4.77026	−0.505647	−0.252824	−	0.967512i	$-0.581359\pi$
$89$	−4.77026	−0.505647	−0.252824	+	0.967512i	$0.581359\pi$
$90$	−0.0315960	−0.00333051
$91$	−14.7423	−1.54541
$92$	−3.38869	−0.353296
$93$	−15.0161	−1.55710
$94$	7.24332	0.747091
$95$	−21.1678	−2.17177
$96$	−8.32410	−0.849575
$97$	7.36014	0.747309	0.373654	−	0.927568i	$-0.378105\pi$
$97$	7.36014	0.747309	0.373654	+	0.927568i	$0.378105\pi$
$98$	−6.76566	−0.683435
$99$	0.0104290	0.00104815
$100$	32.7267	3.27267
$101$	−14.3175	−1.42465	−0.712324	−	0.701851i	$-0.752357\pi$
$101$	−14.3175	−1.42465	−0.712324	+	0.701851i	$0.752357\pi$
$102$	4.27740	0.423526
$103$	0.754530	0.0743460	0.0371730	−	0.999309i	$-0.488165\pi$
$103$	0.754530	0.0743460	0.0371730	+	0.999309i	$0.488165\pi$
$104$	−15.0930	−1.47999
$105$	−20.8675	−2.03646
$106$	−19.2446	−1.86921
$107$	−1.10122	−0.106459	−0.0532295	−	0.998582i	$-0.516951\pi$
$107$	−1.10122	−0.106459	−0.0532295	+	0.998582i	$0.516951\pi$
$108$	17.6186	1.69535
$109$	−0.480798	−0.0460521	−0.0230260	−	0.999735i	$-0.507330\pi$
$109$	−0.480798	−0.0460521	−0.0230260	+	0.999735i	$0.507330\pi$
$110$	−26.0710	−2.48577
$111$	−2.62326	−0.248989
$112$	−2.22253	−0.210009
$113$	12.1060	1.13884	0.569418	−	0.822048i	$-0.307169\pi$
$113$	12.1060	1.13884	0.569418	+	0.822048i	$0.307169\pi$
$114$	22.2172	2.08083
$115$	3.82853	0.357012
$116$	5.02918	0.466948
$117$	−0.0166451	−0.00153884
$118$	−15.5512	−1.43161
$119$	−3.35175	−0.307254
$120$	−21.3640	−1.95026
$121$	−2.39468	−0.217698
$122$	0.535319	0.0484655
$123$	−6.06012	−0.546422
$124$	29.3959	2.63983
$125$	−17.8318	−1.59492
$126$	−0.0259858	−0.00231500
$127$	1.90659	0.169182	0.0845911	−	0.996416i	$-0.473042\pi$
$127$	1.90659	0.169182	0.0845911	+	0.996416i	$0.473042\pi$
$128$	19.5725	1.72998
$129$	−14.5801	−1.28370
$130$	41.6104	3.64947
$131$	−7.22798	−0.631511	−0.315756	−	0.948841i	$-0.602258\pi$
$131$	−7.22798	−0.631511	−0.315756	+	0.948841i	$0.602258\pi$
$132$	17.2075	1.49772
$133$	−17.4092	−1.50957
$134$	−5.88725	−0.508581
$135$	−19.9054	−1.71318
$136$	−3.43149	−0.294248
$137$	5.45275	0.465860	0.232930	−	0.972493i	$-0.425169\pi$
$137$	5.45275	0.465860	0.232930	+	0.972493i	$0.425169\pi$
$138$	−4.01832	−0.342062
$139$	14.2543	1.20903	0.604515	−	0.796593i	$-0.293367\pi$
$139$	14.2543	1.20903	0.604515	+	0.796593i	$0.293367\pi$
$140$	40.8507	3.45252
$141$	5.40131	0.454872
$142$	−21.2335	−1.78187
$143$	−13.7345	−1.14853
$144$	−0.00250940	−0.000209117 0
$145$	−5.68195	−0.471860
$146$	−11.5129	−0.952815
$147$	−5.04513	−0.416115
$148$	5.13536	0.422124
$149$	16.0245	1.31278	0.656391	−	0.754421i	$-0.272082\pi$
$149$	16.0245	1.31278	0.656391	+	0.754421i	$0.272082\pi$
$150$	38.8074	3.16861
$151$	3.32036	0.270207	0.135104	−	0.990831i	$-0.456863\pi$
$151$	3.32036	0.270207	0.135104	+	0.990831i	$0.456863\pi$
$152$	−17.8234	−1.44567
$153$	−0.00378437	−0.000305948 0
$154$	−21.4418	−1.72783
$155$	−33.2113	−2.66760
$156$	−27.4640	−2.19888
$157$	4.70091	0.375173	0.187587	−	0.982248i	$-0.439933\pi$
$157$	4.70091	0.375173	0.187587	+	0.982248i	$0.439933\pi$
$158$	−31.8759	−2.53591
$159$	−14.3506	−1.13808
$160$	−18.4105	−1.45548
$161$	3.14873	0.248155
$162$	20.8674	1.63950
$163$	−20.6466	−1.61716	−0.808582	−	0.588384i	$-0.799764\pi$
$163$	−20.6466	−1.61716	−0.808582	+	0.588384i	$0.799764\pi$
$164$	11.8634	0.926378
$165$	−19.4410	−1.51348
$166$	−3.81820	−0.296350
$167$	14.8266	1.14732	0.573660	−	0.819093i	$-0.305523\pi$
$167$	14.8266	1.14732	0.573660	+	0.819093i	$0.305523\pi$
$168$	−17.5706	−1.35560
$169$	8.92083	0.686218
$170$	9.46037	0.725577
$171$	−0.0196563	−0.00150316
$172$	28.5422	2.17633
$173$	21.3577	1.62379	0.811896	−	0.583802i	$-0.198435\pi$
$173$	21.3577	1.62379	0.811896	+	0.583802i	$0.198435\pi$
$174$	5.96362	0.452101
$175$	−30.4093	−2.29872
$176$	−2.07059	−0.156077
$177$	−11.5965	−0.871645
$178$	11.0735	0.829992
$179$	−9.73235	−0.727430	−0.363715	−	0.931510i	$-0.618492\pi$
$179$	−9.73235	−0.727430	−0.363715	+	0.931510i	$0.618492\pi$
$180$	0.0461235	0.00343784
$181$	−1.16620	−0.0866833	−0.0433416	−	0.999060i	$-0.513800\pi$
$181$	−1.16620	−0.0866833	−0.0433416	+	0.999060i	$0.513800\pi$
$182$	34.2221	2.53671
$183$	0.399185	0.0295086
$184$	3.22365	0.237650
$185$	−5.80190	−0.426564
$186$	34.8578	2.55590
$187$	−3.12262	−0.228348
$188$	−10.5737	−0.771168
$189$	−16.3710	−1.19081
$190$	49.1379	3.56484
$191$	0.217135	0.0157114	0.00785568	−	0.999969i	$-0.497499\pi$
$191$	0.217135	0.0157114	0.00785568	+	0.999969i	$0.497499\pi$
$192$	21.7669	1.57089
$193$	20.7964	1.49696	0.748480	−	0.663157i	$-0.230784\pi$
$193$	20.7964	1.49696	0.748480	+	0.663157i	$0.230784\pi$
$194$	−17.0855	−1.22667
$195$	31.0287	2.22201
$196$	9.87645	0.705461
$197$	−4.62801	−0.329732	−0.164866	−	0.986316i	$-0.552719\pi$
$197$	−4.62801	−0.329732	−0.164866	+	0.986316i	$0.552719\pi$
$198$	−0.0242094	−0.00172049
$199$	15.8149	1.12109	0.560543	−	0.828126i	$-0.310593\pi$
$199$	15.8149	1.12109	0.560543	+	0.828126i	$0.310593\pi$
$200$	−31.1327	−2.20142
$201$	−4.39010	−0.309654
$202$	33.2361	2.33848
$203$	−4.67306	−0.327985
$204$	−6.24410	−0.437175
$205$	−13.4032	−0.936122
$206$	−1.75153	−0.122035
$207$	0.00355516	0.000247100 0
$208$	3.30476	0.229144
$209$	−16.2191	−1.12190
$210$	48.4409	3.34274
$211$	−12.1848	−0.838836	−0.419418	−	0.907793i	$-0.637766\pi$
$211$	−12.1848	−0.838836	−0.419418	+	0.907793i	$0.637766\pi$
$212$	28.0931	1.92944
$213$	−15.8337	−1.08491
$214$	2.55632	0.174747
$215$	−32.2469	−2.19922
$216$	−16.7605	−1.14041
$217$	−27.3144	−1.85422
$218$	1.11610	0.0755920
$219$	−8.58512	−0.580129
$220$	38.0581	2.56588
$221$	4.98383	0.335249
$222$	6.08953	0.408702
$223$	3.49730	0.234197	0.117098	−	0.993120i	$-0.462641\pi$
$223$	3.49730	0.234197	0.117098	+	0.993120i	$0.462641\pi$
$224$	−15.1415	−1.01169
$225$	−0.0343343	−0.00228895
$226$	−28.1023	−1.86934
$227$	1.84996	0.122786	0.0613931	−	0.998114i	$-0.480446\pi$
$227$	1.84996	0.122786	0.0613931	+	0.998114i	$0.480446\pi$
$228$	−32.4324	−2.14789
$229$	−17.4452	−1.15281	−0.576406	−	0.817164i	$-0.695545\pi$
$229$	−17.4452	−1.15281	−0.576406	+	0.817164i	$0.695545\pi$
$230$	−8.88737	−0.586016
$231$	−15.9891	−1.05200
$232$	−4.78424	−0.314101
$233$	0.540857	0.0354327	0.0177164	−	0.999843i	$-0.494360\pi$
$233$	0.540857	0.0354327	0.0177164	+	0.999843i	$0.494360\pi$
$234$	0.0386393	0.00252593
$235$	11.9461	0.779280
$236$	22.7015	1.47774
$237$	−23.7697	−1.54401
$238$	7.78059	0.504341
$239$	5.83753	0.377599	0.188799	−	0.982016i	$-0.439540\pi$
$239$	5.83753	0.377599	0.188799	+	0.982016i	$0.439540\pi$
$240$	4.67785	0.301954
$241$	20.8211	1.34120	0.670601	−	0.741818i	$-0.266036\pi$
$241$	20.8211	1.34120	0.670601	+	0.741818i	$0.266036\pi$
$242$	5.55889	0.357339
$243$	−0.0369462	−0.00237010
$244$	−0.781453	−0.0500274
$245$	−11.1584	−0.712882
$246$	14.0677	0.896923
$247$	25.8864	1.64711
$248$	−27.9642	−1.77573
$249$	−2.84721	−0.180435
$250$	41.3939	2.61798
$251$	27.2860	1.72228	0.861139	−	0.508370i	$-0.169752\pi$
$251$	27.2860	1.72228	0.861139	+	0.508370i	$0.169752\pi$
$252$	0.0379338	0.00238961
$253$	2.93348	0.184427
$254$	−4.42586	−0.277703
$255$	7.05456	0.441773
$256$	−20.2856	−1.26785
$257$	5.54773	0.346058	0.173029	−	0.984917i	$-0.444645\pi$
$257$	5.54773	0.346058	0.173029	+	0.984917i	$0.444645\pi$
$258$	33.8455	2.10713
$259$	−4.77172	−0.296500
$260$	−60.7424	−3.76709
$261$	−0.00527623	−0.000326591 0
$262$	16.7787	1.03659
$263$	−12.6129	−0.777743	−0.388871	−	0.921292i	$-0.627135\pi$
$263$	−12.6129	−0.777743	−0.388871	+	0.921292i	$0.627135\pi$
$264$	−16.3695	−1.00747
$265$	−31.7395	−1.94974
$266$	40.4130	2.47788
$267$	8.25744	0.505347
$268$	8.59415	0.524971
$269$	−11.9709	−0.729877	−0.364939	−	0.931032i	$-0.618910\pi$
$269$	−11.9709	−0.729877	−0.364939	+	0.931032i	$0.618910\pi$
$270$	46.2075	2.81210
$271$	−0.679621	−0.0412841	−0.0206420	−	0.999787i	$-0.506571\pi$
$271$	−0.679621	−0.0412841	−0.0206420	+	0.999787i	$0.506571\pi$
$272$	0.751357	0.0455577
$273$	25.5192	1.54449
$274$	−12.6578	−0.764684
$275$	−28.3304	−1.70839
$276$	5.86591	0.353086
$277$	14.4050	0.865514	0.432757	−	0.901511i	$-0.357541\pi$
$277$	14.4050	0.865514	0.432757	+	0.901511i	$0.357541\pi$
$278$	−33.0892	−1.98456
$279$	−0.0308399	−0.00184634
$280$	−38.8611	−2.32240
$281$	−8.21141	−0.489851	−0.244926	−	0.969542i	$-0.578764\pi$
$281$	−8.21141	−0.489851	−0.244926	+	0.969542i	$0.578764\pi$
$282$	−12.5384	−0.746648
$283$	24.1392	1.43493	0.717463	−	0.696597i	$-0.245303\pi$
$283$	24.1392	1.43493	0.717463	+	0.696597i	$0.245303\pi$
$284$	30.9964	1.83930
$285$	36.6419	2.17048
$286$	31.8826	1.88526
$287$	−11.0234	−0.650688
$288$	−0.0170959	−0.00100739
$289$	−15.8669	−0.933347
$290$	13.1898	0.774533
$291$	−12.7406	−0.746866
$292$	16.8064	0.983522
$293$	16.5064	0.964315	0.482157	−	0.876085i	$-0.339853\pi$
$293$	16.5064	0.964315	0.482157	+	0.876085i	$0.339853\pi$
$294$	11.7115	0.683030
$295$	−25.6481	−1.49329
$296$	−4.88524	−0.283949
$297$	−15.2518	−0.885002
$298$	−37.1987	−2.15486
$299$	−4.68197	−0.270765
$300$	−56.6507	−3.27073
$301$	−26.5211	−1.52865
$302$	−7.70774	−0.443531
$303$	24.7840	1.42380
$304$	3.90261	0.223830
$305$	0.882882	0.0505537
$306$	0.00878487	0.000502197 0
$307$	−15.7760	−0.900385	−0.450193	−	0.892931i	$-0.648645\pi$
$307$	−15.7760	−0.900385	−0.450193	+	0.892931i	$0.648645\pi$
$308$	31.3005	1.78351
$309$	−1.30611	−0.0743020
$310$	77.0953	4.37872
$311$	−5.72757	−0.324781	−0.162390	−	0.986727i	$-0.551920\pi$
$311$	−5.72757	−0.324781	−0.162390	+	0.986727i	$0.551920\pi$
$312$	26.1264	1.47911
$313$	34.5349	1.95203	0.976013	−	0.217710i	$-0.0698587\pi$
$313$	34.5349	1.95203	0.976013	+	0.217710i	$0.0698587\pi$
$314$	−10.9125	−0.615826
$315$	−0.0428575	−0.00241474
$316$	46.5321	2.61763
$317$	33.1343	1.86101	0.930503	−	0.366284i	$-0.119370\pi$
$317$	33.1343	1.86101	0.930503	+	0.366284i	$0.119370\pi$
$318$	33.3129	1.86810
$319$	−4.35361	−0.243755
$320$	48.1420	2.69122
$321$	1.90624	0.106396
$322$	−7.30933	−0.407333
$323$	5.88544	0.327474
$324$	−30.4620	−1.69234
$325$	45.2166	2.50817
$326$	47.9280	2.65449
$327$	0.832273	0.0460248
$328$	−11.2856	−0.623144
$329$	9.82499	0.541669
$330$	45.1295	2.48429
$331$	−9.79233	−0.538235	−0.269117	−	0.963107i	$-0.586732\pi$
$331$	−9.79233	−0.538235	−0.269117	+	0.963107i	$0.586732\pi$
$332$	5.57377	0.305900
$333$	−0.00538762	−0.000295240 0
$334$	−34.4179	−1.88326
$335$	−9.70963	−0.530494
$336$	3.84725	0.209885
$337$	17.8538	0.972557	0.486279	−	0.873804i	$-0.338354\pi$
$337$	17.8538	0.972557	0.486279	+	0.873804i	$0.338354\pi$
$338$	−20.7084	−1.12639
$339$	−20.9558	−1.13816
$340$	−13.8102	−0.748961
$341$	−25.4471	−1.37804
$342$	0.0456293	0.00246735
$343$	12.8641	0.694594
$344$	−27.1521	−1.46394
$345$	−6.62727	−0.356800
$346$	−49.5787	−2.66537
$347$	−21.5912	−1.15908	−0.579539	−	0.814944i	$-0.696768\pi$
$347$	−21.5912	−1.15908	−0.579539	+	0.814944i	$0.696768\pi$
$348$	−8.70564	−0.466671
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	70.5907	3.77323
$351$	24.3426	1.29931
$352$	−14.1064	−0.751876
$353$	−7.62739	−0.405965	−0.202982	−	0.979182i	$-0.565063\pi$
$353$	−7.62739	−0.405965	−0.202982	+	0.979182i	$0.565063\pi$
$354$	26.9196	1.43076
$355$	−35.0196	−1.85865
$356$	−16.1650	−0.856741
$357$	5.80195	0.307072
$358$	22.5923	1.19404
$359$	−1.81454	−0.0957677	−0.0478838	−	0.998853i	$-0.515248\pi$
$359$	−1.81454	−0.0957677	−0.0478838	+	0.998853i	$0.515248\pi$
$360$	−0.0438771	−0.00231253
$361$	11.5694	0.608918
$362$	2.70717	0.142286
$363$	4.14524	0.217569
$364$	−49.9570	−2.61846
$365$	−18.9878	−0.993867
$366$	−0.926650	−0.0484368
$367$	−18.6455	−0.973286	−0.486643	−	0.873601i	$-0.661779\pi$
$367$	−18.6455	−0.973286	−0.486643	+	0.873601i	$0.661779\pi$
$368$	−0.705848	−0.0367949
$369$	−0.0124462	−0.000647923 0
$370$	13.4683	0.700182
$371$	−26.1038	−1.35524
$372$	−50.8850	−2.63827
$373$	−26.0925	−1.35102	−0.675509	−	0.737352i	$-0.736076\pi$
$373$	−26.0925	−1.35102	−0.675509	+	0.737352i	$0.736076\pi$
$374$	7.24870	0.374821
$375$	30.8673	1.59398
$376$	10.0587	0.518740
$377$	6.94855	0.357868
$378$	38.0029	1.95466
$379$	10.1757	0.522688	0.261344	−	0.965246i	$-0.415834\pi$
$379$	10.1757	0.522688	0.261344	+	0.965246i	$0.415834\pi$
$380$	−71.7311	−3.67973
$381$	−3.30035	−0.169082
$382$	−0.504048	−0.0257894
$383$	22.1826	1.13348	0.566739	−	0.823897i	$-0.308205\pi$
$383$	22.1826	1.13348	0.566739	+	0.823897i	$0.308205\pi$
$384$	−33.8805	−1.72895
$385$	−35.3632	−1.80227
$386$	−48.2759	−2.45718
$387$	−0.0299443	−0.00152216
$388$	24.9412	1.26620
$389$	6.80656	0.345106	0.172553	−	0.985000i	$-0.444798\pi$
$389$	6.80656	0.345106	0.172553	+	0.985000i	$0.444798\pi$
$390$	−72.0286	−3.64731
$391$	−1.06447	−0.0538327
$392$	−9.39542	−0.474541
$393$	12.5118	0.631137
$394$	10.7433	0.541237
$395$	−52.5717	−2.64517
$396$	0.0353406	0.00177593
$397$	15.3976	0.772782	0.386391	−	0.922335i	$-0.373722\pi$
$397$	15.3976	0.772782	0.386391	+	0.922335i	$0.373722\pi$
$398$	−36.7119	−1.84020
$399$	30.1358	1.50868
$400$	6.81681	0.340840
$401$	−1.47622	−0.0737191	−0.0368595	−	0.999320i	$-0.511735\pi$
$401$	−1.47622	−0.0737191	−0.0368595	+	0.999320i	$0.511735\pi$
$402$	10.1910	0.508280
$403$	40.6147	2.02316
$404$	−48.5177	−2.41385
$405$	34.4159	1.71014
$406$	10.8478	0.538369
$407$	−4.44552	−0.220356
$408$	5.93999	0.294073
$409$	6.06328	0.299810	0.149905	−	0.988700i	$-0.452103\pi$
$409$	6.06328	0.299810	0.149905	+	0.988700i	$0.452103\pi$
$410$	31.1137	1.53659
$411$	−9.43885	−0.465584
$412$	2.55687	0.125968
$413$	−21.0940	−1.03797
$414$	−0.00825278	−0.000405602 0
$415$	−6.29721	−0.309118
$416$	22.5145	1.10386
$417$	−24.6745	−1.20831
$418$	37.6504	1.84154
$419$	18.6315	0.910208	0.455104	−	0.890438i	$-0.349602\pi$
$419$	18.6315	0.910208	0.455104	+	0.890438i	$0.349602\pi$
$420$	−70.7136	−3.45047
$421$	26.9231	1.31215	0.656077	−	0.754694i	$-0.272215\pi$
$421$	26.9231	1.31215	0.656077	+	0.754694i	$0.272215\pi$
$422$	28.2852	1.37690
$423$	0.0110931	0.000539367 0
$424$	−26.7249	−1.29787
$425$	10.2803	0.498667
$426$	36.7556	1.78082
$427$	0.726118	0.0351393
$428$	−3.73170	−0.180378
$429$	23.7747	1.14785
$430$	74.8565	3.60990
$431$	−34.3305	−1.65364	−0.826821	−	0.562465i	$-0.809853\pi$
$431$	−34.3305	−1.65364	−0.826821	+	0.562465i	$0.809853\pi$
$432$	3.66986	0.176566
$433$	−29.5661	−1.42086	−0.710428	−	0.703770i	$-0.751499\pi$
$433$	−29.5661	−1.42086	−0.710428	+	0.703770i	$0.751499\pi$
$434$	63.4063	3.04360
$435$	9.83558	0.471580
$436$	−1.62928	−0.0780282
$437$	−5.52896	−0.264486
$438$	19.9291	0.952250
$439$	1.80581	0.0861867	0.0430934	−	0.999071i	$-0.486279\pi$
$439$	1.80581	0.0861867	0.0430934	+	0.999071i	$0.486279\pi$
$440$	−36.2045	−1.72598
$441$	−0.0103616	−0.000493410 0
$442$	−11.5692	−0.550293
$443$	−28.1944	−1.33956	−0.669778	−	0.742561i	$-0.733611\pi$
$443$	−28.1944	−1.33956	−0.669778	+	0.742561i	$0.733611\pi$
$444$	−8.88943	−0.421874
$445$	18.2631	0.865753
$446$	−8.11848	−0.384421
$447$	−27.7389	−1.31200
$448$	39.5940	1.87064
$449$	21.5921	1.01900	0.509498	−	0.860472i	$-0.329831\pi$
$449$	21.5921	1.01900	0.509498	+	0.860472i	$0.329831\pi$
$450$	0.0797022	0.00375720
$451$	−10.2698	−0.483585
$452$	41.0235	1.92958
$453$	−5.74763	−0.270047
$454$	−4.29442	−0.201547
$455$	56.4412	2.64600
$456$	30.8528	1.44481
$457$	9.51698	0.445185	0.222593	−	0.974912i	$-0.428548\pi$
$457$	9.51698	0.445185	0.222593	+	0.974912i	$0.428548\pi$
$458$	40.4965	1.89228
$459$	5.53444	0.258326
$460$	12.9737	0.604902
$461$	−12.1474	−0.565762	−0.282881	−	0.959155i	$-0.591290\pi$
$461$	−12.1474	−0.565762	−0.282881	+	0.959155i	$0.591290\pi$
$462$	37.1163	1.72681
$463$	−28.0285	−1.30259	−0.651297	−	0.758823i	$-0.725775\pi$
$463$	−28.0285	−1.30259	−0.651297	+	0.758823i	$0.725775\pi$
$464$	1.04755	0.0486315
$465$	57.4896	2.66602
$466$	−1.25552	−0.0581609
$467$	3.88114	0.179598	0.0897988	−	0.995960i	$-0.471378\pi$
$467$	3.88114	0.179598	0.0897988	+	0.995960i	$0.471378\pi$
$468$	−0.0564052	−0.00260733
$469$	−7.98559	−0.368740
$470$	−27.7312	−1.27915
$471$	−8.13738	−0.374951
$472$	−21.5959	−0.994031
$473$	−24.7081	−1.13608
$474$	55.1779	2.53440
$475$	53.3966	2.45000
$476$	−11.3580	−0.520595
$477$	−0.0294732	−0.00134948
$478$	−13.5510	−0.619808
$479$	−11.6758	−0.533483	−0.266741	−	0.963768i	$-0.585947\pi$
$479$	−11.6758	−0.533483	−0.266741	+	0.963768i	$0.585947\pi$
$480$	31.8690	1.45462
$481$	7.09524	0.323515
$482$	−48.3331	−2.20151
$483$	−5.45054	−0.248008
$484$	−8.11482	−0.368855
$485$	−28.1785	−1.27952
$486$	0.0857654	0.00389040
$487$	0.851932	0.0386047	0.0193024	−	0.999814i	$-0.493855\pi$
$487$	0.851932	0.0386047	0.0193024	+	0.999814i	$0.493855\pi$
$488$	0.743393	0.0336518
$489$	35.7397	1.61621
$490$	25.9025	1.17016
$491$	−9.99280	−0.450969	−0.225484	−	0.974247i	$-0.572396\pi$
$491$	−9.99280	−0.450969	−0.225484	+	0.974247i	$0.572396\pi$
$492$	−20.5359	−0.925828
$493$	1.57979	0.0711503
$494$	−60.0916	−2.70365
$495$	−0.0399277	−0.00179461
$496$	6.12302	0.274932
$497$	−28.8015	−1.29192
$498$	6.60939	0.296174
$499$	−42.2214	−1.89009	−0.945044	−	0.326943i	$-0.893982\pi$
$499$	−42.2214	−1.89009	−0.945044	+	0.326943i	$0.893982\pi$
$500$	−60.4265	−2.70235
$501$	−25.6653	−1.14664
$502$	−63.3405	−2.82703
$503$	−28.6486	−1.27738	−0.638688	−	0.769466i	$-0.720523\pi$
$503$	−28.6486	−1.27738	−0.638688	+	0.769466i	$0.720523\pi$
$504$	−0.0360863	−0.00160741
$505$	54.8150	2.43924
$506$	−6.80966	−0.302726
$507$	−15.4422	−0.685811
$508$	6.46083	0.286653
$509$	−13.3049	−0.589729	−0.294864	−	0.955539i	$-0.595275\pi$
$509$	−13.3049	−0.589729	−0.294864	+	0.955539i	$0.595275\pi$
$510$	−16.3761	−0.725147
$511$	−15.6163	−0.690826
$512$	7.94507	0.351126
$513$	28.7463	1.26918
$514$	−12.8783	−0.568036
$515$	−2.88874	−0.127293
$516$	−49.4073	−2.17504
$517$	9.15334	0.402563
$518$	11.0769	0.486689
$519$	−36.9706	−1.62283
$520$	57.7840	2.53400
$521$	22.6088	0.990509	0.495255	−	0.868748i	$-0.335075\pi$
$521$	22.6088	0.990509	0.495255	+	0.868748i	$0.335075\pi$
$522$	0.0122480	0.000536081 0
$523$	13.7625	0.601793	0.300897	−	0.953657i	$-0.402714\pi$
$523$	13.7625	0.601793	0.300897	+	0.953657i	$0.402714\pi$
$524$	−24.4934	−1.07000
$525$	52.6392	2.29736
$526$	29.2790	1.27662
$527$	9.23400	0.402239
$528$	3.58425	0.155984
$529$	1.00000	0.0434783
$530$	73.6786	3.20039
$531$	−0.0238167	−0.00103356
$532$	−58.9946	−2.55774
$533$	16.3910	0.709975
$534$	−19.1685	−0.829500
$535$	4.21605	0.182276
$536$	−8.17558	−0.353131
$537$	16.8469	0.726999
$538$	27.7887	1.19805
$539$	−8.54973	−0.368263
$540$	−67.4532	−2.90272
$541$	−40.7436	−1.75170	−0.875852	−	0.482580i	$-0.839700\pi$
$541$	−40.7436	−1.75170	−0.875852	+	0.482580i	$0.839700\pi$
$542$	1.57764	0.0677656
$543$	2.01873	0.0866319
$544$	5.11881	0.219467
$545$	1.84075	0.0788490
$546$	−59.2392	−2.53521
$547$	−16.7271	−0.715199	−0.357599	−	0.933875i	$-0.616405\pi$
$547$	−16.7271	−0.715199	−0.357599	+	0.933875i	$0.616405\pi$
$548$	18.4777	0.789328
$549$	0.000819841 0	3.49899e−5 0
$550$	65.7650	2.80423
$551$	8.20558	0.349569
$552$	−5.58021	−0.237510
$553$	−43.2371	−1.83863
$554$	−33.4392	−1.42070
$555$	10.0432	0.426311
$556$	48.3033	2.04852
$557$	28.1021	1.19073	0.595363	−	0.803457i	$-0.297008\pi$
$557$	28.1021	1.19073	0.595363	+	0.803457i	$0.297008\pi$
$558$	0.0715905	0.00303067
$559$	39.4352	1.66793
$560$	8.50901	0.359571
$561$	5.40532	0.228213
$562$	19.0616	0.804065
$563$	40.9083	1.72408	0.862039	−	0.506841i	$-0.169187\pi$
$563$	40.9083	1.72408	0.862039	+	0.506841i	$0.169187\pi$
$564$	18.3034	0.770711
$565$	−46.3481	−1.94988
$566$	−56.0357	−2.35535
$567$	28.3050	1.18870
$568$	−29.4867	−1.23724
$569$	5.73869	0.240578	0.120289	−	0.992739i	$-0.461618\pi$
$569$	5.73869	0.240578	0.120289	+	0.992739i	$0.461618\pi$
$570$	−85.0590	−3.56273
$571$	−13.4569	−0.563154	−0.281577	−	0.959539i	$-0.590858\pi$
$571$	−13.4569	−0.563154	−0.281577	+	0.959539i	$0.590858\pi$
$572$	−46.5419	−1.94602
$573$	−0.375867	−0.0157020
$574$	25.5891	1.06807
$575$	−9.65761	−0.402750
$576$	0.0447045	0.00186269
$577$	17.4813	0.727756	0.363878	−	0.931447i	$-0.381452\pi$
$577$	17.4813	0.727756	0.363878	+	0.931447i	$0.381452\pi$
$578$	36.8327	1.53204
$579$	−35.9991	−1.49607
$580$	−19.2544	−0.799494
$581$	−5.17908	−0.214864
$582$	29.5754	1.22594
$583$	−24.3193	−1.00720
$584$	−15.9879	−0.661583
$585$	0.0637263	0.00263476
$586$	−38.3172	−1.58287
$587$	28.0006	1.15571	0.577854	−	0.816140i	$-0.303890\pi$
$587$	28.0006	1.15571	0.577854	+	0.816140i	$0.303890\pi$
$588$	−17.0964	−0.705043
$589$	47.9621	1.97625
$590$	59.5383	2.45115
$591$	8.01119	0.329536
$592$	1.06967	0.0439632
$593$	−30.3826	−1.24766	−0.623832	−	0.781558i	$-0.714425\pi$
$593$	−30.3826	−1.24766	−0.623832	+	0.781558i	$0.714425\pi$
$594$	35.4050	1.45268
$595$	12.8322	0.526071
$596$	54.3022	2.22431
$597$	−27.3759	−1.12042
$598$	10.8685	0.444447
$599$	5.80057	0.237005	0.118502	−	0.992954i	$-0.462191\pi$
$599$	5.80057	0.237005	0.118502	+	0.992954i	$0.462191\pi$
$600$	53.8915	2.20011
$601$	1.32291	0.0539627	0.0269814	−	0.999636i	$-0.491411\pi$
$601$	1.32291	0.0539627	0.0269814	+	0.999636i	$0.491411\pi$
$602$	61.5650	2.50920
$603$	−0.00901633	−0.000367173 0
$604$	11.2517	0.457825
$605$	9.16808	0.372735
$606$	−57.5325	−2.33710
$607$	13.8645	0.562743	0.281371	−	0.959599i	$-0.409211\pi$
$607$	13.8645	0.562743	0.281371	+	0.959599i	$0.409211\pi$
$608$	26.5875	1.07827
$609$	8.08918	0.327790
$610$	−2.04948	−0.0829811
$611$	−14.6091	−0.591022
$612$	−0.0128241	−0.000518382 0
$613$	26.7688	1.08118	0.540591	−	0.841286i	$-0.318201\pi$
$613$	26.7688	1.08118	0.540591	+	0.841286i	$0.318201\pi$
$614$	36.6218	1.47793
$615$	23.2013	0.935567
$616$	−29.7761	−1.19971
$617$	22.1689	0.892487	0.446244	−	0.894912i	$-0.352762\pi$
$617$	22.1689	0.892487	0.446244	+	0.894912i	$0.352762\pi$
$618$	3.03194	0.121963
$619$	−18.1779	−0.730632	−0.365316	−	0.930884i	$-0.619039\pi$
$619$	−18.1779	−0.730632	−0.365316	+	0.930884i	$0.619039\pi$
$620$	−112.543	−4.51984
$621$	−5.19923	−0.208638
$622$	13.2957	0.533110
$623$	15.0203	0.601776
$624$	−5.72062	−0.229008
$625$	19.9814	0.799257
$626$	−80.1677	−3.20415
$627$	28.0757	1.12124
$628$	15.9299	0.635673
$629$	1.61315	0.0643203
$630$	0.0994874	0.00396367
$631$	−17.1616	−0.683193	−0.341597	−	0.939847i	$-0.610968\pi$
$631$	−17.1616	−0.683193	−0.341597	+	0.939847i	$0.610968\pi$
$632$	−44.2657	−1.76080
$633$	21.0922	0.838339
$634$	−76.9164	−3.05474
$635$	−7.29942	−0.289668
$636$	−48.6299	−1.92830
$637$	13.6457	0.540664
$638$	10.1063	0.400111
$639$	−0.0325190	−0.00128643
$640$	−74.9338	−2.96202
$641$	1.31806	0.0520601	0.0260301	−	0.999661i	$-0.491713\pi$
$641$	1.31806	0.0520601	0.0260301	+	0.999661i	$0.491713\pi$
$642$	−4.42506	−0.174643
$643$	18.7981	0.741325	0.370663	−	0.928768i	$-0.379131\pi$
$643$	18.7981	0.741325	0.370663	+	0.928768i	$0.379131\pi$
$644$	10.6701	0.420461
$645$	55.8201	2.19792
$646$	−13.6622	−0.537532
$647$	−42.9988	−1.69046	−0.845228	−	0.534406i	$-0.820535\pi$
$647$	−42.9988	−1.69046	−0.845228	+	0.534406i	$0.820535\pi$
$648$	28.9784	1.13838
$649$	−19.6520	−0.771409
$650$	−104.964	−4.11702
$651$	47.2818	1.85312
$652$	−69.9648	−2.74003
$653$	38.5051	1.50682	0.753411	−	0.657550i	$-0.228407\pi$
$653$	38.5051	1.50682	0.753411	+	0.657550i	$0.228407\pi$
$654$	−1.93200	−0.0755472
$655$	27.6725	1.08125
$656$	2.47109	0.0964800
$657$	−0.0176320	−0.000687890 0
$658$	−22.8073	−0.889121
$659$	−6.91849	−0.269506	−0.134753	−	0.990879i	$-0.543024\pi$
$659$	−6.91849	−0.269506	−0.134753	+	0.990879i	$0.543024\pi$
$660$	−65.8795	−2.56436
$661$	33.7433	1.31246	0.656231	−	0.754560i	$-0.272150\pi$
$661$	33.7433	1.31246	0.656231	+	0.754560i	$0.272150\pi$
$662$	22.7315	0.883484
$663$	−8.62714	−0.335050
$664$	−5.30230	−0.205769
$665$	66.6517	2.58464
$666$	0.0125066	0.000484620 0
$667$	−1.48411	−0.0574649
$668$	50.2429	1.94396
$669$	−6.05391	−0.234058
$670$	22.5395	0.870777
$671$	0.676479	0.0261152
$672$	26.2104	1.01109
$673$	7.02794	0.270907	0.135453	−	0.990784i	$-0.456751\pi$
$673$	7.02794	0.270907	0.135453	+	0.990784i	$0.456751\pi$
$674$	−41.4450	−1.59640
$675$	50.2121	1.93267
$676$	30.2300	1.16269
$677$	51.6231	1.98404	0.992019	−	0.126090i	$-0.0402427\pi$
$677$	51.6231	1.98404	0.992019	+	0.126090i	$0.0402427\pi$
$678$	48.6458	1.86823
$679$	−23.1751	−0.889380
$680$	13.1375	0.503802
$681$	−3.20233	−0.122713
$682$	59.0718	2.26198
$683$	14.6895	0.562078	0.281039	−	0.959696i	$-0.409321\pi$
$683$	14.6895	0.562078	0.281039	+	0.959696i	$0.409321\pi$
$684$	−0.0666092	−0.00254687
$685$	−20.8760	−0.797631
$686$	−29.8620	−1.14014
$687$	30.1981	1.15213
$688$	5.94521	0.226659
$689$	38.8147	1.47872
$690$	15.3843	0.585669
$691$	34.6114	1.31668	0.658340	−	0.752721i	$-0.271259\pi$
$691$	34.6114	1.31668	0.658340	+	0.752721i	$0.271259\pi$
$692$	72.3745	2.75127
$693$	−0.0328381	−0.00124742
$694$	50.1210	1.90257
$695$	−54.5728	−2.07007
$696$	8.28163	0.313915
$697$	3.72660	0.141155
$698$	−2.32136	−0.0878646
$699$	−0.936237	−0.0354117
$700$	−103.048	−3.89483
$701$	−19.5935	−0.740035	−0.370018	−	0.929025i	$-0.620648\pi$
$701$	−19.5935	−0.740035	−0.370018	+	0.929025i	$0.620648\pi$
$702$	−56.5079	−2.13275
$703$	8.37881	0.316013
$704$	36.8873	1.39024
$705$	−20.6791	−0.778818
$706$	17.7059	0.666370
$707$	45.0821	1.69549
$708$	−39.2969	−1.47687
$709$	40.5502	1.52289	0.761447	−	0.648228i	$-0.224489\pi$
$709$	40.5502	1.52289	0.761447	+	0.648228i	$0.224489\pi$
$710$	81.2928	3.05087
$711$	−0.0488179	−0.00183081
$712$	15.3776	0.576302
$713$	−8.67471	−0.324870
$714$	−13.4684	−0.504042
$715$	52.5828	1.96649
$716$	−32.9799	−1.23252
$717$	−10.1049	−0.377375
$718$	4.21219	0.157198
$719$	12.8042	0.477515	0.238758	−	0.971079i	$-0.423260\pi$
$719$	12.8042	0.477515	0.238758	+	0.971079i	$0.423260\pi$
$720$	0.00960730	0.000358043 0
$721$	−2.37581	−0.0884799
$722$	−26.8568	−0.999506
$723$	−36.0418	−1.34041
$724$	−3.95191	−0.146871
$725$	14.3329	0.532312
$726$	−9.62258	−0.357127
$727$	−37.3503	−1.38524	−0.692622	−	0.721300i	$-0.743545\pi$
$727$	−37.3503	−1.38524	−0.692622	+	0.721300i	$0.743545\pi$
$728$	47.5239	1.76135
$729$	27.0319	1.00118
$730$	44.0775	1.63138
$731$	8.96584	0.331614
$732$	1.35271	0.0499978
$733$	10.5695	0.390392	0.195196	−	0.980764i	$-0.437466\pi$
$733$	10.5695	0.390392	0.195196	+	0.980764i	$0.437466\pi$
$734$	43.2828	1.59760
$735$	19.3154	0.712459
$736$	−4.80877	−0.177254
$737$	−7.43969	−0.274044
$738$	0.0288920	0.00106353
$739$	−30.2864	−1.11410	−0.557051	−	0.830478i	$-0.688067\pi$
$739$	−30.2864	−1.11410	−0.557051	+	0.830478i	$0.688067\pi$
$740$	−19.6609	−0.722747
$741$	−44.8100	−1.64614
$742$	60.5963	2.22456
$743$	46.0150	1.68813	0.844064	−	0.536242i	$-0.180157\pi$
$743$	46.0150	1.68813	0.844064	+	0.536242i	$0.180157\pi$
$744$	48.4067	1.77468
$745$	−61.3504	−2.24770
$746$	60.5699	2.21762
$747$	−0.00584757	−0.000213951 0
$748$	−10.5816	−0.386901
$749$	3.46745	0.126698
$750$	−71.6539	−2.61643
$751$	−41.8952	−1.52878	−0.764389	−	0.644755i	$-0.776959\pi$
$751$	−41.8952	−1.52878	−0.764389	+	0.644755i	$0.776959\pi$
$752$	−2.20245	−0.0803153
$753$	−47.2327	−1.72126
$754$	−16.1300	−0.587422
$755$	−12.7121	−0.462641
$756$	−55.4762	−2.01765
$757$	42.9972	1.56276	0.781381	−	0.624055i	$-0.214516\pi$
$757$	42.9972	1.56276	0.781381	+	0.624055i	$0.214516\pi$
$758$	−23.6213	−0.857965
$759$	−5.07793	−0.184317
$760$	68.2375	2.47523
$761$	−23.1777	−0.840190	−0.420095	−	0.907480i	$-0.638003\pi$
$761$	−23.1777	−0.840190	−0.420095	+	0.907480i	$0.638003\pi$
$762$	7.66128	0.277539
$763$	1.51391	0.0548070
$764$	0.735805	0.0266205
$765$	0.0144886	0.000523835 0
$766$	−51.4937	−1.86054
$767$	31.3655	1.13254
$768$	35.1148	1.26710
$769$	18.9303	0.682645	0.341322	−	0.939946i	$-0.389125\pi$
$769$	18.9303	0.682645	0.341322	+	0.939946i	$0.389125\pi$
$770$	82.0905	2.95834
$771$	−9.60326	−0.345853
$772$	70.4727	2.53637
$773$	−9.18936	−0.330518	−0.165259	−	0.986250i	$-0.552846\pi$
$773$	−9.18936	−0.330518	−0.165259	+	0.986250i	$0.552846\pi$
$774$	0.0695114	0.00249854
$775$	83.7770	3.00936
$776$	−23.7265	−0.851731
$777$	8.25996	0.296324
$778$	−15.8004	−0.566473
$779$	19.3563	0.693510
$780$	105.147	3.76485
$781$	−26.8326	−0.960146
$782$	2.47102	0.0883636
$783$	7.71621	0.275755
$784$	2.05722	0.0734720
$785$	−17.9975	−0.642360
$786$	−29.0443	−1.03598
$787$	19.4759	0.694241	0.347121	−	0.937820i	$-0.387159\pi$
$787$	19.4759	0.694241	0.347121	+	0.937820i	$0.387159\pi$
$788$	−15.6829	−0.558680
$789$	21.8332	0.777282
$790$	122.038	4.34190
$791$	−38.1186	−1.35534
$792$	−0.0336194	−0.00119461
$793$	−1.07969	−0.0383409
$794$	−35.7432	−1.26848
$795$	54.9418	1.94859
$796$	53.5917	1.89951
$797$	−21.2620	−0.753140	−0.376570	−	0.926388i	$-0.622897\pi$
$797$	−21.2620	−0.753140	−0.376570	+	0.926388i	$0.622897\pi$
$798$	−69.9559	−2.47641
$799$	−3.32147	−0.117505
$800$	46.4412	1.64195
$801$	0.0169590	0.000599218 0
$802$	3.42684	0.121006
$803$	−14.5488	−0.513416
$804$	−14.8767	−0.524660
$805$	−12.0550	−0.424883
$806$	−94.2812	−3.32091
$807$	20.7219	0.729445
$808$	46.1547	1.62372
$809$	52.7316	1.85394	0.926971	−	0.375132i	$-0.122403\pi$
$809$	52.7316	1.85394	0.926971	+	0.375132i	$0.122403\pi$
$810$	−79.8914	−2.80710
$811$	10.1051	0.354839	0.177419	−	0.984135i	$-0.443225\pi$
$811$	10.1051	0.354839	0.177419	+	0.984135i	$0.443225\pi$
$812$	−15.8356	−0.555719
$813$	1.17644	0.0412596
$814$	10.3196	0.361703
$815$	79.0459	2.76886
$816$	−1.30062	−0.0455307
$817$	46.5693	1.62925
$818$	−14.0750	−0.492122
$819$	0.0524111	0.00183139
$820$	−45.4194	−1.58611
$821$	−22.4103	−0.782124	−0.391062	−	0.920364i	$-0.627892\pi$
$821$	−22.4103	−0.782124	−0.391062	+	0.920364i	$0.627892\pi$
$822$	21.9109	0.764231
$823$	24.6317	0.858608	0.429304	−	0.903160i	$-0.358759\pi$
$823$	24.6317	0.858608	0.429304	+	0.903160i	$0.358759\pi$
$824$	−2.43234	−0.0847345
$825$	49.0407	1.70738
$826$	48.9667	1.70377
$827$	6.66569	0.231789	0.115894	−	0.993262i	$-0.463027\pi$
$827$	6.66569	0.231789	0.115894	+	0.993262i	$0.463027\pi$
$828$	0.0120473	0.000418674 0
$829$	−14.6716	−0.509567	−0.254783	−	0.966998i	$-0.582004\pi$
$829$	−14.6716	−0.509567	−0.254783	+	0.966998i	$0.582004\pi$
$830$	14.6181	0.507400
$831$	−24.9355	−0.865001
$832$	−58.8737	−2.04108
$833$	3.10244	0.107493
$834$	57.2782	1.98338
$835$	−56.7642	−1.96441
$836$	−54.9616	−1.90089
$837$	45.1018	1.55895
$838$	−43.2503	−1.49406
$839$	33.3948	1.15292	0.576458	−	0.817127i	$-0.304435\pi$
$839$	33.3948	1.15292	0.576458	+	0.817127i	$0.304435\pi$
$840$	67.2695	2.32102
$841$	−26.7974	−0.924049
$842$	−62.4982	−2.15383
$843$	14.2141	0.489561
$844$	−41.2905	−1.42128
$845$	−34.1536	−1.17492
$846$	−0.0257511	−0.000885342 0
$847$	7.54020	0.259084
$848$	5.85166	0.200947
$849$	−41.7855	−1.43408
$850$	−23.8642	−0.818534
$851$	−1.51544	−0.0519486
$852$	−53.6555	−1.83821
$853$	50.3786	1.72493	0.862465	−	0.506116i	$-0.168919\pi$
$853$	50.3786	1.72493	0.862465	+	0.506116i	$0.168919\pi$
$854$	−1.68558	−0.0576793
$855$	0.0752548	0.00257366
$856$	3.54995	0.121335
$857$	−30.6211	−1.04600	−0.522999	−	0.852333i	$-0.675187\pi$
$857$	−30.6211	−1.04600	−0.522999	+	0.852333i	$0.675187\pi$
$858$	−55.1896	−1.88414
$859$	36.5172	1.24595	0.622975	−	0.782241i	$-0.285924\pi$
$859$	36.5172	1.24595	0.622975	+	0.782241i	$0.285924\pi$
$860$	−109.275	−3.72624
$861$	19.0817	0.650303
$862$	79.6933	2.71437
$863$	−29.5514	−1.00594	−0.502970	−	0.864304i	$-0.667759\pi$
$863$	−29.5514	−1.00594	−0.502970	+	0.864304i	$0.667759\pi$
$864$	25.0019	0.850581
$865$	−81.7684	−2.78021
$866$	68.6334	2.33226
$867$	27.4660	0.932794
$868$	−92.5599	−3.14169
$869$	−40.2813	−1.36645
$870$	−22.8319	−0.774074
$871$	11.8741	0.402337
$872$	1.54992	0.0524870
$873$	−0.0261664	−0.000885600 0
$874$	12.8347	0.434140
$875$	56.1476	1.89814
$876$	−29.0923	−0.982939
$877$	−24.1313	−0.814855	−0.407427	−	0.913238i	$-0.633574\pi$
$877$	−24.1313	−0.814855	−0.407427	+	0.913238i	$0.633574\pi$
$878$	−4.19193	−0.141471
$879$	−28.5730	−0.963743
$880$	7.92732	0.267230
$881$	16.5590	0.557888	0.278944	−	0.960307i	$-0.410016\pi$
$881$	16.5590	0.557888	0.278944	+	0.960307i	$0.410016\pi$
$882$	0.0240530	0.000809906 0
$883$	−14.5167	−0.488525	−0.244263	−	0.969709i	$-0.578546\pi$
$883$	−14.5167	−0.488525	−0.244263	+	0.969709i	$0.578546\pi$
$884$	16.8887	0.568028
$885$	44.3975	1.49240
$886$	65.4492	2.19881
$887$	10.0381	0.337045	0.168522	−	0.985698i	$-0.446100\pi$
$887$	10.0381	0.337045	0.168522	+	0.985698i	$0.446100\pi$
$888$	8.45647	0.283781
$889$	−6.00333	−0.201345
$890$	−42.3951	−1.42109
$891$	26.3700	0.883429
$892$	11.8513	0.396810
$893$	−17.2520	−0.577316
$894$	64.3918	2.15358
$895$	37.2606	1.24548
$896$	−61.6286	−2.05887
$897$	8.10460	0.270605
$898$	−50.1230	−1.67263
$899$	12.8742	0.429379
$900$	−0.116348	−0.00387828
$901$	8.82477	0.293996
$902$	23.8398	0.793780
$903$	45.9087	1.52775
$904$	−39.0255	−1.29797
$905$	4.46484	0.148416
$906$	13.3423	0.443268
$907$	−15.1259	−0.502246	−0.251123	−	0.967955i	$-0.580800\pi$
$907$	−15.1259	−0.502246	−0.251123	+	0.967955i	$0.580800\pi$
$908$	6.26895	0.208042
$909$	0.0509011	0.00168828
$910$	−131.020	−4.34327
$911$	−31.2093	−1.03401	−0.517006	−	0.855982i	$-0.672953\pi$
$911$	−31.2093	−1.03401	−0.517006	+	0.855982i	$0.672953\pi$
$912$	−6.75551	−0.223697
$913$	−4.82503	−0.159685
$914$	−22.0923	−0.730748
$915$	−1.52829	−0.0505237
$916$	−59.1164	−1.95326
$917$	22.7590	0.751568
$918$	−12.8474	−0.424027
$919$	24.5064	0.808390	0.404195	−	0.914673i	$-0.367552\pi$
$919$	24.5064	0.808390	0.404195	+	0.914673i	$0.367552\pi$
$920$	−12.3418	−0.406898
$921$	27.3087	0.899852
$922$	28.1985	0.928668
$923$	42.8260	1.40964
$924$	−54.1820	−1.78246
$925$	14.6355	0.481213
$926$	65.0641	2.13814
$927$	−0.00268247	−8.81039e−5 0
$928$	7.13673	0.234275
$929$	−22.8774	−0.750583	−0.375291	−	0.926907i	$-0.622457\pi$
$929$	−22.8774	−0.750583	−0.375291	+	0.926907i	$0.622457\pi$
$930$	−133.454	−4.37613
$931$	16.1143	0.528126
$932$	1.83280	0.0600353
$933$	9.91456	0.324588
$934$	−9.00950	−0.294800
$935$	11.9550	0.390971
$936$	0.0536580	0.00175387
$937$	60.2689	1.96890	0.984449	−	0.175670i	$-0.0562092\pi$
$937$	60.2689	1.96890	0.984449	+	0.175670i	$0.0562092\pi$
$938$	18.5374	0.605268
$939$	−59.7807	−1.95087
$940$	40.4818	1.32037
$941$	14.9007	0.485749	0.242874	−	0.970058i	$-0.421910\pi$
$941$	14.9007	0.485749	0.242874	+	0.970058i	$0.421910\pi$
$942$	18.8898	0.615461
$943$	−3.50089	−0.114005
$944$	4.72862	0.153904
$945$	62.6768	2.03887
$946$	57.3563	1.86481
$947$	30.4867	0.990683	0.495342	−	0.868698i	$-0.335043\pi$
$947$	30.4867	0.990683	0.495342	+	0.868698i	$0.335043\pi$
$948$	−80.5481	−2.61608
$949$	23.2205	0.753770
$950$	−123.952	−4.02155
$951$	−57.3562	−1.85990
$952$	10.8048	0.350187
$953$	−27.0609	−0.876588	−0.438294	−	0.898832i	$-0.644417\pi$
$953$	−27.0609	−0.876588	−0.438294	+	0.898832i	$0.644417\pi$
$954$	0.0684177	0.00221510
$955$	−0.831308	−0.0269005
$956$	19.7816	0.639783
$957$	7.53620	0.243611
$958$	27.1038	0.875683
$959$	−17.1693	−0.554425
$960$	−83.3350	−2.68963
$961$	44.2506	1.42744
$962$	−16.4706	−0.531033
$963$	0.00391501	0.000126159 0
$964$	70.5562	2.27246
$965$	−79.6197	−2.56305
$966$	12.6526	0.407092
$967$	21.1156	0.679033	0.339517	−	0.940600i	$-0.389736\pi$
$967$	21.1156	0.679033	0.339517	+	0.940600i	$0.389736\pi$
$968$	7.71959	0.248117
$969$	−10.1878	−0.327280
$970$	65.4123	2.10026
$971$	−20.5926	−0.660849	−0.330425	−	0.943832i	$-0.607192\pi$
$971$	−20.5926	−0.660849	−0.330425	+	0.943832i	$0.607192\pi$
$972$	−0.125199	−0.00401577
$973$	−44.8829	−1.43888
$974$	−1.97764	−0.0633676
$975$	−78.2711	−2.50668
$976$	−0.162773	−0.00521023
$977$	−27.0052	−0.863972	−0.431986	−	0.901880i	$-0.642187\pi$
$977$	−27.0052	−0.863972	−0.431986	+	0.901880i	$0.642187\pi$
$978$	−82.9646	−2.65291
$979$	13.9935	0.447234
$980$	−37.8122	−1.20787
$981$	0.00170931	5.45741e−5 0
$982$	23.1968	0.740241
$983$	−18.5156	−0.590555	−0.295278	−	0.955411i	$-0.595412\pi$
$983$	−18.5156	−0.590555	−0.295278	+	0.955411i	$0.595412\pi$
$984$	19.5357	0.622775
$985$	17.7184	0.564557
$986$	−3.66726	−0.116789
$987$	−17.0073	−0.541348
$988$	87.7212	2.79078
$989$	−8.42279	−0.267829
$990$	0.0926863	0.00294576
$991$	−7.68625	−0.244162	−0.122081	−	0.992520i	$-0.538957\pi$
$991$	−7.68625	−0.244162	−0.122081	+	0.992520i	$0.538957\pi$
$992$	41.7147	1.32444
$993$	16.9508	0.537916
$994$	66.8585	2.12062
$995$	−60.5476	−1.91949
$996$	−9.64832	−0.305719
$997$	55.6352	1.76199	0.880993	−	0.473129i	$-0.156876\pi$
$997$	55.6352	1.76199	0.880993	+	0.473129i	$0.156876\pi$
$998$	98.0108	3.10248
$999$	7.87911	0.249284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.19	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.19	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32136 q^{2} -1.73102 q^{3} +3.38869 q^{4} -3.82853 q^{5} +4.01832 q^{6} -3.14873 q^{7} -3.22365 q^{8} -0.00355516 q^{9} +O(q^{10})\)	\(q-2.32136 q^{2} -1.73102 q^{3} +3.38869 q^{4} -3.82853 q^{5} +4.01832 q^{6} -3.14873 q^{7} -3.22365 q^{8} -0.00355516 q^{9} +8.88737 q^{10} -2.93348 q^{11} -5.86591 q^{12} +4.68197 q^{13} +7.30933 q^{14} +6.62727 q^{15} +0.705848 q^{16} +1.06447 q^{17} +0.00825278 q^{18} +5.52896 q^{19} -12.9737 q^{20} +5.45054 q^{21} +6.80966 q^{22} -1.00000 q^{23} +5.58021 q^{24} +9.65761 q^{25} -10.8685 q^{26} +5.19923 q^{27} -10.6701 q^{28} +1.48411 q^{29} -15.3843 q^{30} +8.67471 q^{31} +4.80877 q^{32} +5.07793 q^{33} -2.47102 q^{34} +12.0550 q^{35} -0.0120473 q^{36} +1.51544 q^{37} -12.8347 q^{38} -8.10460 q^{39} +12.3418 q^{40} +3.50089 q^{41} -12.6526 q^{42} +8.42279 q^{43} -9.94067 q^{44} +0.0136110 q^{45} +2.32136 q^{46} -3.12030 q^{47} -1.22184 q^{48} +2.91453 q^{49} -22.4188 q^{50} -1.84263 q^{51} +15.8657 q^{52} +8.29026 q^{53} -12.0693 q^{54} +11.2309 q^{55} +10.1504 q^{56} -9.57077 q^{57} -3.44514 q^{58} +6.69921 q^{59} +22.4578 q^{60} -0.230606 q^{61} -20.1371 q^{62} +0.0111942 q^{63} -12.5746 q^{64} -17.9250 q^{65} -11.7877 q^{66} +2.53613 q^{67} +3.60717 q^{68} +1.73102 q^{69} -27.9840 q^{70} +9.14701 q^{71} +0.0114606 q^{72} +4.95956 q^{73} -3.51787 q^{74} -16.7176 q^{75} +18.7360 q^{76} +9.23676 q^{77} +18.8137 q^{78} +13.7316 q^{79} -2.70236 q^{80} -8.98932 q^{81} -8.12680 q^{82} +1.64481 q^{83} +18.4702 q^{84} -4.07537 q^{85} -19.5523 q^{86} -2.56903 q^{87} +9.45652 q^{88} -4.77026 q^{89} -0.0315960 q^{90} -14.7423 q^{91} -3.38869 q^{92} -15.0161 q^{93} +7.24332 q^{94} -21.1678 q^{95} -8.32410 q^{96} +7.36014 q^{97} -6.76566 q^{98} +0.0104290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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