LMFDB - Embedded newform 8014.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.27677 q^{3} +1.00000 q^{4} -0.135024 q^{5} +3.27677 q^{6} -2.05105 q^{7} -1.00000 q^{8} +7.73722 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.27677 q^{3} +1.00000 q^{4} -0.135024 q^{5} +3.27677 q^{6} -2.05105 q^{7} -1.00000 q^{8} +7.73722 q^{9} +0.135024 q^{10} +1.66840 q^{11} -3.27677 q^{12} +0.748026 q^{13} +2.05105 q^{14} +0.442441 q^{15} +1.00000 q^{16} -6.44476 q^{17} -7.73722 q^{18} +6.18838 q^{19} -0.135024 q^{20} +6.72082 q^{21} -1.66840 q^{22} -7.87011 q^{23} +3.27677 q^{24} -4.98177 q^{25} -0.748026 q^{26} -15.5228 q^{27} -2.05105 q^{28} +4.48578 q^{29} -0.442441 q^{30} -1.84191 q^{31} -1.00000 q^{32} -5.46698 q^{33} +6.44476 q^{34} +0.276940 q^{35} +7.73722 q^{36} +9.98643 q^{37} -6.18838 q^{38} -2.45111 q^{39} +0.135024 q^{40} -4.02159 q^{41} -6.72082 q^{42} -2.24523 q^{43} +1.66840 q^{44} -1.04471 q^{45} +7.87011 q^{46} +3.30452 q^{47} -3.27677 q^{48} -2.79319 q^{49} +4.98177 q^{50} +21.1180 q^{51} +0.748026 q^{52} +10.9452 q^{53} +15.5228 q^{54} -0.225274 q^{55} +2.05105 q^{56} -20.2779 q^{57} -4.48578 q^{58} +14.3095 q^{59} +0.442441 q^{60} +0.298257 q^{61} +1.84191 q^{62} -15.8694 q^{63} +1.00000 q^{64} -0.101001 q^{65} +5.46698 q^{66} -12.6469 q^{67} -6.44476 q^{68} +25.7885 q^{69} -0.276940 q^{70} +14.0268 q^{71} -7.73722 q^{72} -10.2940 q^{73} -9.98643 q^{74} +16.3241 q^{75} +6.18838 q^{76} -3.42198 q^{77} +2.45111 q^{78} -6.98622 q^{79} -0.135024 q^{80} +27.6529 q^{81} +4.02159 q^{82} +4.87600 q^{83} +6.72082 q^{84} +0.870195 q^{85} +2.24523 q^{86} -14.6989 q^{87} -1.66840 q^{88} -11.7477 q^{89} +1.04471 q^{90} -1.53424 q^{91} -7.87011 q^{92} +6.03552 q^{93} -3.30452 q^{94} -0.835577 q^{95} +3.27677 q^{96} +10.2681 q^{97} +2.79319 q^{98} +12.9088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.27677	−1.89184	−0.945922	−	0.324394i	$-0.894840\pi$
$3$	−3.27677	−1.89184	−0.945922	+	0.324394i	$0.894840\pi$
$4$	1.00000	0.500000
$5$	−0.135024	−0.0603844	−0.0301922	−	0.999544i	$-0.509612\pi$
$5$	−0.135024	−0.0603844	−0.0301922	+	0.999544i	$0.509612\pi$
$6$	3.27677	1.33774
$7$	−2.05105	−0.775224	−0.387612	−	0.921823i	$-0.626700\pi$
$7$	−2.05105	−0.775224	−0.387612	+	0.921823i	$0.626700\pi$
$8$	−1.00000	−0.353553
$9$	7.73722	2.57907
$10$	0.135024	0.0426982
$11$	1.66840	0.503043	0.251521	−	0.967852i	$-0.419069\pi$
$11$	1.66840	0.503043	0.251521	+	0.967852i	$0.419069\pi$
$12$	−3.27677	−0.945922
$13$	0.748026	0.207465	0.103733	−	0.994605i	$-0.466921\pi$
$13$	0.748026	0.207465	0.103733	+	0.994605i	$0.466921\pi$
$14$	2.05105	0.548166
$15$	0.442441	0.114238
$16$	1.00000	0.250000
$17$	−6.44476	−1.56308	−0.781542	−	0.623852i	$-0.785567\pi$
$17$	−6.44476	−1.56308	−0.781542	+	0.623852i	$0.785567\pi$
$18$	−7.73722	−1.82368
$19$	6.18838	1.41971	0.709856	−	0.704347i	$-0.248760\pi$
$19$	6.18838	1.41971	0.709856	+	0.704347i	$0.248760\pi$
$20$	−0.135024	−0.0301922
$21$	6.72082	1.46660
$22$	−1.66840	−0.355705
$23$	−7.87011	−1.64103	−0.820515	−	0.571625i	$-0.806313\pi$
$23$	−7.87011	−1.64103	−0.820515	+	0.571625i	$0.806313\pi$
$24$	3.27677	0.668868
$25$	−4.98177	−0.996354
$26$	−0.748026	−0.146700
$27$	−15.5228	−2.98736
$28$	−2.05105	−0.387612
$29$	4.48578	0.832989	0.416494	−	0.909138i	$-0.363259\pi$
$29$	4.48578	0.832989	0.416494	+	0.909138i	$0.363259\pi$
$30$	−0.442441	−0.0807784
$31$	−1.84191	−0.330817	−0.165408	−	0.986225i	$-0.552894\pi$
$31$	−1.84191	−0.330817	−0.165408	+	0.986225i	$0.552894\pi$
$32$	−1.00000	−0.176777
$33$	−5.46698	−0.951679
$34$	6.44476	1.10527
$35$	0.276940	0.0468114
$36$	7.73722	1.28954
$37$	9.98643	1.64176	0.820880	−	0.571101i	$-0.193484\pi$
$37$	9.98643	1.64176	0.820880	+	0.571101i	$0.193484\pi$
$38$	−6.18838	−1.00389
$39$	−2.45111	−0.392491
$40$	0.135024	0.0213491
$41$	−4.02159	−0.628068	−0.314034	−	0.949412i	$-0.601681\pi$
$41$	−4.02159	−0.628068	−0.314034	+	0.949412i	$0.601681\pi$
$42$	−6.72082	−1.03704
$43$	−2.24523	−0.342394	−0.171197	−	0.985237i	$-0.554763\pi$
$43$	−2.24523	−0.342394	−0.171197	+	0.985237i	$0.554763\pi$
$44$	1.66840	0.251521
$45$	−1.04471	−0.155736
$46$	7.87011	1.16038
$47$	3.30452	0.482013	0.241007	−	0.970523i	$-0.422522\pi$
$47$	3.30452	0.482013	0.241007	+	0.970523i	$0.422522\pi$
$48$	−3.27677	−0.472961
$49$	−2.79319	−0.399028
$50$	4.98177	0.704528
$51$	21.1180	2.95711
$52$	0.748026	0.103733
$53$	10.9452	1.50344	0.751720	−	0.659483i	$-0.229225\pi$
$53$	10.9452	1.50344	0.751720	+	0.659483i	$0.229225\pi$
$54$	15.5228	2.11238
$55$	−0.225274	−0.0303759
$56$	2.05105	0.274083
$57$	−20.2779	−2.68587
$58$	−4.48578	−0.589012
$59$	14.3095	1.86294	0.931471	−	0.363817i	$-0.118526\pi$
$59$	14.3095	1.86294	0.931471	+	0.363817i	$0.118526\pi$
$60$	0.442441	0.0571189
$61$	0.298257	0.0381879	0.0190940	−	0.999818i	$-0.493922\pi$
$61$	0.298257	0.0381879	0.0190940	+	0.999818i	$0.493922\pi$
$62$	1.84191	0.233923
$63$	−15.8694	−1.99936
$64$	1.00000	0.125000
$65$	−0.101001	−0.0125277
$66$	5.46698	0.672938
$67$	−12.6469	−1.54507	−0.772534	−	0.634973i	$-0.781011\pi$
$67$	−12.6469	−1.54507	−0.772534	+	0.634973i	$0.781011\pi$
$68$	−6.44476	−0.781542
$69$	25.7885	3.10457
$70$	−0.276940	−0.0331007
$71$	14.0268	1.66468	0.832340	−	0.554265i	$-0.187001\pi$
$71$	14.0268	1.66468	0.832340	+	0.554265i	$0.187001\pi$
$72$	−7.73722	−0.911840
$73$	−10.2940	−1.20482	−0.602410	−	0.798187i	$-0.705793\pi$
$73$	−10.2940	−1.20482	−0.602410	+	0.798187i	$0.705793\pi$
$74$	−9.98643	−1.16090
$75$	16.3241	1.88495
$76$	6.18838	0.709856
$77$	−3.42198	−0.389971
$78$	2.45111	0.277533
$79$	−6.98622	−0.786011	−0.393006	−	0.919536i	$-0.628565\pi$
$79$	−6.98622	−0.786011	−0.393006	+	0.919536i	$0.628565\pi$
$80$	−0.135024	−0.0150961
$81$	27.6529	3.07255
$82$	4.02159	0.444111
$83$	4.87600	0.535211	0.267606	−	0.963529i	$-0.413768\pi$
$83$	4.87600	0.535211	0.267606	+	0.963529i	$0.413768\pi$
$84$	6.72082	0.733301
$85$	0.870195	0.0943859
$86$	2.24523	0.242109
$87$	−14.6989	−1.57589
$88$	−1.66840	−0.177852
$89$	−11.7477	−1.24525	−0.622626	−	0.782520i	$-0.713934\pi$
$89$	−11.7477	−1.24525	−0.622626	+	0.782520i	$0.713934\pi$
$90$	1.04471	0.110122
$91$	−1.53424	−0.160832
$92$	−7.87011	−0.820515
$93$	6.03552	0.625854
$94$	−3.30452	−0.340835
$95$	−0.835577	−0.0857284
$96$	3.27677	0.334434
$97$	10.2681	1.04256	0.521282	−	0.853385i	$-0.325454\pi$
$97$	10.2681	1.04256	0.521282	+	0.853385i	$0.325454\pi$
$98$	2.79319	0.282155
$99$	12.9088	1.29738
$100$	−4.98177	−0.498177
$101$	−5.22215	−0.519624	−0.259812	−	0.965659i	$-0.583661\pi$
$101$	−5.22215	−0.519624	−0.259812	+	0.965659i	$0.583661\pi$
$102$	−21.1180	−2.09099
$103$	−7.96065	−0.784386	−0.392193	−	0.919883i	$-0.628283\pi$
$103$	−7.96065	−0.784386	−0.392193	+	0.919883i	$0.628283\pi$
$104$	−0.748026	−0.0733500
$105$	−0.907469	−0.0885599
$106$	−10.9452	−1.06309
$107$	−9.95708	−0.962587	−0.481294	−	0.876559i	$-0.659833\pi$
$107$	−9.95708	−0.962587	−0.481294	+	0.876559i	$0.659833\pi$
$108$	−15.5228	−1.49368
$109$	10.1994	0.976926	0.488463	−	0.872584i	$-0.337558\pi$
$109$	10.1994	0.976926	0.488463	+	0.872584i	$0.337558\pi$
$110$	0.225274	0.0214790
$111$	−32.7232	−3.10595
$112$	−2.05105	−0.193806
$113$	17.8383	1.67809	0.839043	−	0.544065i	$-0.183116\pi$
$113$	17.8383	1.67809	0.839043	+	0.544065i	$0.183116\pi$
$114$	20.2779	1.89920
$115$	1.06265	0.0990926
$116$	4.48578	0.416494
$117$	5.78764	0.535068
$118$	−14.3095	−1.31730
$119$	13.2185	1.21174
$120$	−0.442441	−0.0403892
$121$	−8.21643	−0.746948
$122$	−0.298257	−0.0270029
$123$	13.1778	1.18821
$124$	−1.84191	−0.165408
$125$	1.34777	0.120549
$126$	15.8694	1.41376
$127$	7.07828	0.628096	0.314048	−	0.949407i	$-0.398315\pi$
$127$	7.07828	0.628096	0.314048	+	0.949407i	$0.398315\pi$
$128$	−1.00000	−0.0883883
$129$	7.35709	0.647756
$130$	0.101001	0.00885839
$131$	−18.1012	−1.58151	−0.790755	−	0.612133i	$-0.790312\pi$
$131$	−18.1012	−1.58151	−0.790755	+	0.612133i	$0.790312\pi$
$132$	−5.46698	−0.475839
$133$	−12.6927	−1.10059
$134$	12.6469	1.09253
$135$	2.09594	0.180390
$136$	6.44476	0.552634
$137$	−4.23674	−0.361969	−0.180984	−	0.983486i	$-0.557928\pi$
$137$	−4.23674	−0.361969	−0.180984	+	0.983486i	$0.557928\pi$
$138$	−25.7885	−2.19527
$139$	−14.7615	−1.25206	−0.626029	−	0.779800i	$-0.715321\pi$
$139$	−14.7615	−1.25206	−0.626029	+	0.779800i	$0.715321\pi$
$140$	0.276940	0.0234057
$141$	−10.8281	−0.911894
$142$	−14.0268	−1.17711
$143$	1.24801	0.104364
$144$	7.73722	0.644769
$145$	−0.605687	−0.0502995
$146$	10.2940	0.851936
$147$	9.15266	0.754898
$148$	9.98643	0.820880
$149$	14.1732	1.16112	0.580558	−	0.814219i	$-0.302834\pi$
$149$	14.1732	1.16112	0.580558	+	0.814219i	$0.302834\pi$
$150$	−16.3241	−1.33286
$151$	−21.1386	−1.72024	−0.860119	−	0.510093i	$-0.829611\pi$
$151$	−21.1386	−1.72024	−0.860119	+	0.510093i	$0.829611\pi$
$152$	−6.18838	−0.501944
$153$	−49.8646	−4.03131
$154$	3.42198	0.275751
$155$	0.248701	0.0199762
$156$	−2.45111	−0.196246
$157$	−5.33755	−0.425983	−0.212991	−	0.977054i	$-0.568321\pi$
$157$	−5.33755	−0.425983	−0.212991	+	0.977054i	$0.568321\pi$
$158$	6.98622	0.555794
$159$	−35.8649	−2.84427
$160$	0.135024	0.0106746
$161$	16.1420	1.27217
$162$	−27.6529	−2.17262
$163$	−8.10885	−0.635134	−0.317567	−	0.948236i	$-0.602866\pi$
$163$	−8.10885	−0.635134	−0.317567	+	0.948236i	$0.602866\pi$
$164$	−4.02159	−0.314034
$165$	0.738171	0.0574665
$166$	−4.87600	−0.378451
$167$	−22.7397	−1.75965	−0.879825	−	0.475297i	$-0.842341\pi$
$167$	−22.7397	−1.75965	−0.879825	+	0.475297i	$0.842341\pi$
$168$	−6.72082	−0.518522
$169$	−12.4405	−0.956958
$170$	−0.870195	−0.0667409
$171$	47.8809	3.66154
$172$	−2.24523	−0.171197
$173$	0.953469	0.0724909	0.0362455	−	0.999343i	$-0.488460\pi$
$173$	0.953469	0.0724909	0.0362455	+	0.999343i	$0.488460\pi$
$174$	14.6989	1.11432
$175$	10.2179	0.772397
$176$	1.66840	0.125761
$177$	−46.8890	−3.52439
$178$	11.7477	0.880526
$179$	−7.71976	−0.577002	−0.288501	−	0.957480i	$-0.593157\pi$
$179$	−7.71976	−0.577002	−0.288501	+	0.957480i	$0.593157\pi$
$180$	−1.04471	−0.0778679
$181$	17.2728	1.28388	0.641938	−	0.766757i	$-0.278131\pi$
$181$	17.2728	1.28388	0.641938	+	0.766757i	$0.278131\pi$
$182$	1.53424	0.113725
$183$	−0.977320	−0.0722456
$184$	7.87011	0.580192
$185$	−1.34840	−0.0991366
$186$	−6.03552	−0.442546
$187$	−10.7525	−0.786299
$188$	3.30452	0.241007
$189$	31.8380	2.31587
$190$	0.835577	0.0606192
$191$	−22.7859	−1.64873	−0.824366	−	0.566057i	$-0.808468\pi$
$191$	−22.7859	−1.64873	−0.824366	+	0.566057i	$0.808468\pi$
$192$	−3.27677	−0.236481
$193$	26.4582	1.90450	0.952251	−	0.305315i	$-0.0987619\pi$
$193$	26.4582	1.90450	0.952251	+	0.305315i	$0.0987619\pi$
$194$	−10.2681	−0.737204
$195$	0.330958	0.0237004
$196$	−2.79319	−0.199514
$197$	17.6728	1.25913	0.629567	−	0.776946i	$-0.283232\pi$
$197$	17.6728	1.25913	0.629567	+	0.776946i	$0.283232\pi$
$198$	−12.9088	−0.917389
$199$	12.8593	0.911574	0.455787	−	0.890089i	$-0.349358\pi$
$199$	12.8593	0.911574	0.455787	+	0.890089i	$0.349358\pi$
$200$	4.98177	0.352264
$201$	41.4411	2.92303
$202$	5.22215	0.367429
$203$	−9.20056	−0.645753
$204$	21.1180	1.47856
$205$	0.543010	0.0379255
$206$	7.96065	0.554645
$207$	−60.8928	−4.23234
$208$	0.748026	0.0518663
$209$	10.3247	0.714176
$210$	0.907469	0.0626213
$211$	−15.9114	−1.09539	−0.547695	−	0.836678i	$-0.684494\pi$
$211$	−15.9114	−1.09539	−0.547695	+	0.836678i	$0.684494\pi$
$212$	10.9452	0.751720
$213$	−45.9627	−3.14932
$214$	9.95708	0.680652
$215$	0.303158	0.0206752
$216$	15.5228	1.05619
$217$	3.77785	0.256457
$218$	−10.1994	−0.690791
$219$	33.7310	2.27933
$220$	−0.225274	−0.0151880
$221$	−4.82085	−0.324285
$222$	32.7232	2.19624
$223$	−4.47076	−0.299384	−0.149692	−	0.988733i	$-0.547828\pi$
$223$	−4.47076	−0.299384	−0.149692	+	0.988733i	$0.547828\pi$
$224$	2.05105	0.137042
$225$	−38.5451	−2.56967
$226$	−17.8383	−1.18659
$227$	7.72624	0.512809	0.256404	−	0.966570i	$-0.417462\pi$
$227$	7.72624	0.512809	0.256404	+	0.966570i	$0.417462\pi$
$228$	−20.2779	−1.34294
$229$	−21.4518	−1.41757	−0.708786	−	0.705423i	$-0.750757\pi$
$229$	−21.4518	−1.41757	−0.708786	+	0.705423i	$0.750757\pi$
$230$	−1.06265	−0.0700691
$231$	11.2130	0.737764
$232$	−4.48578	−0.294506
$233$	−11.7767	−0.771515	−0.385757	−	0.922600i	$-0.626060\pi$
$233$	−11.7767	−0.771515	−0.385757	+	0.922600i	$0.626060\pi$
$234$	−5.78764	−0.378350
$235$	−0.446188	−0.0291061
$236$	14.3095	0.931471
$237$	22.8922	1.48701
$238$	−13.2185	−0.856830
$239$	16.1597	1.04529	0.522643	−	0.852552i	$-0.324946\pi$
$239$	16.1597	1.04529	0.522643	+	0.852552i	$0.324946\pi$
$240$	0.442441	0.0285595
$241$	−1.79358	−0.115535	−0.0577675	−	0.998330i	$-0.518398\pi$
$241$	−1.79358	−0.115535	−0.0577675	+	0.998330i	$0.518398\pi$
$242$	8.21643	0.528172
$243$	−44.0440	−2.82542
$244$	0.298257	0.0190940
$245$	0.377147	0.0240950
$246$	−13.1778	−0.840189
$247$	4.62907	0.294541
$248$	1.84191	0.116961
$249$	−15.9775	−1.01254
$250$	−1.34777	−0.0852407
$251$	15.9043	1.00387	0.501934	−	0.864906i	$-0.332622\pi$
$251$	15.9043	1.00387	0.501934	+	0.864906i	$0.332622\pi$
$252$	−15.8694	−0.999680
$253$	−13.1305	−0.825509
$254$	−7.07828	−0.444131
$255$	−2.85143	−0.178563
$256$	1.00000	0.0625000
$257$	−5.34665	−0.333515	−0.166758	−	0.985998i	$-0.553330\pi$
$257$	−5.34665	−0.333515	−0.166758	+	0.985998i	$0.553330\pi$
$258$	−7.35709	−0.458032
$259$	−20.4827	−1.27273
$260$	−0.101001	−0.00626383
$261$	34.7075	2.14834
$262$	18.1012	1.11830
$263$	−5.81381	−0.358495	−0.179247	−	0.983804i	$-0.557366\pi$
$263$	−5.81381	−0.358495	−0.179247	+	0.983804i	$0.557366\pi$
$264$	5.46698	0.336469
$265$	−1.47786	−0.0907843
$266$	12.6927	0.778238
$267$	38.4944	2.35582
$268$	−12.6469	−0.772534
$269$	26.7978	1.63389	0.816946	−	0.576714i	$-0.195665\pi$
$269$	26.7978	1.63389	0.816946	+	0.576714i	$0.195665\pi$
$270$	−2.09594	−0.127555
$271$	−8.98898	−0.546042	−0.273021	−	0.962008i	$-0.588023\pi$
$271$	−8.98898	−0.546042	−0.273021	+	0.962008i	$0.588023\pi$
$272$	−6.44476	−0.390771
$273$	5.02735	0.304269
$274$	4.23674	0.255951
$275$	−8.31160	−0.501209
$276$	25.7885	1.55229
$277$	5.53271	0.332428	0.166214	−	0.986090i	$-0.446846\pi$
$277$	5.53271	0.332428	0.166214	+	0.986090i	$0.446846\pi$
$278$	14.7615	0.885338
$279$	−14.2513	−0.853201
$280$	−0.276940	−0.0165503
$281$	−12.9431	−0.772122	−0.386061	−	0.922473i	$-0.626165\pi$
$281$	−12.9431	−0.772122	−0.386061	+	0.922473i	$0.626165\pi$
$282$	10.8281	0.644807
$283$	−15.3622	−0.913191	−0.456595	−	0.889674i	$-0.650931\pi$
$283$	−15.3622	−0.913191	−0.456595	+	0.889674i	$0.650931\pi$
$284$	14.0268	0.832340
$285$	2.73800	0.162185
$286$	−1.24801	−0.0737963
$287$	8.24849	0.486893
$288$	−7.73722	−0.455920
$289$	24.5350	1.44323
$290$	0.605687	0.0355671
$291$	−33.6461	−1.97237
$292$	−10.2940	−0.602410
$293$	23.8704	1.39452	0.697261	−	0.716818i	$-0.254402\pi$
$293$	23.8704	1.39452	0.697261	+	0.716818i	$0.254402\pi$
$294$	−9.15266	−0.533794
$295$	−1.93212	−0.112493
$296$	−9.98643	−0.580450
$297$	−25.8983	−1.50277
$298$	−14.1732	−0.821033
$299$	−5.88704	−0.340456
$300$	16.3241	0.942473
$301$	4.60507	0.265432
$302$	21.1386	1.21639
$303$	17.1118	0.983047
$304$	6.18838	0.354928
$305$	−0.0402718	−0.00230595
$306$	49.8646	2.85057
$307$	−2.10808	−0.120314	−0.0601571	−	0.998189i	$-0.519160\pi$
$307$	−2.10808	−0.120314	−0.0601571	+	0.998189i	$0.519160\pi$
$308$	−3.42198	−0.194985
$309$	26.0852	1.48394
$310$	−0.248701	−0.0141253
$311$	19.8295	1.12443	0.562214	−	0.826992i	$-0.309950\pi$
$311$	19.8295	1.12443	0.562214	+	0.826992i	$0.309950\pi$
$312$	2.45111	0.138767
$313$	−5.35907	−0.302913	−0.151456	−	0.988464i	$-0.548396\pi$
$313$	−5.35907	−0.302913	−0.151456	+	0.988464i	$0.548396\pi$
$314$	5.33755	0.301215
$315$	2.14275	0.120730
$316$	−6.98622	−0.393006
$317$	12.5143	0.702872	0.351436	−	0.936212i	$-0.385694\pi$
$317$	12.5143	0.702872	0.351436	+	0.936212i	$0.385694\pi$
$318$	35.8649	2.01120
$319$	7.48410	0.419029
$320$	−0.135024	−0.00754805
$321$	32.6271	1.82107
$322$	−16.1420	−0.899557
$323$	−39.8826	−2.21913
$324$	27.6529	1.53627
$325$	−3.72649	−0.206709
$326$	8.10885	0.449108
$327$	−33.4211	−1.84819
$328$	4.02159	0.222055
$329$	−6.77773	−0.373668
$330$	−0.738171	−0.0406350
$331$	−22.4592	−1.23447	−0.617236	−	0.786778i	$-0.711747\pi$
$331$	−22.4592	−1.23447	−0.617236	+	0.786778i	$0.711747\pi$
$332$	4.87600	0.267606
$333$	77.2672	4.23422
$334$	22.7397	1.24426
$335$	1.70763	0.0932980
$336$	6.72082	0.366651
$337$	33.6761	1.83446	0.917228	−	0.398363i	$-0.130422\pi$
$337$	33.6761	1.83446	0.917228	+	0.398363i	$0.130422\pi$
$338$	12.4405	0.676672
$339$	−58.4520	−3.17468
$340$	0.870195	0.0471930
$341$	−3.07305	−0.166415
$342$	−47.8809	−2.58910
$343$	20.0863	1.08456
$344$	2.24523	0.121054
$345$	−3.48206	−0.187468
$346$	−0.953469	−0.0512588
$347$	−6.83418	−0.366878	−0.183439	−	0.983031i	$-0.558723\pi$
$347$	−6.83418	−0.366878	−0.183439	+	0.983031i	$0.558723\pi$
$348$	−14.6989	−0.787943
$349$	−8.72885	−0.467244	−0.233622	−	0.972327i	$-0.575058\pi$
$349$	−8.72885	−0.467244	−0.233622	+	0.972327i	$0.575058\pi$
$350$	−10.2179	−0.546167
$351$	−11.6114	−0.619773
$352$	−1.66840	−0.0889262
$353$	1.85245	0.0985962	0.0492981	−	0.998784i	$-0.484302\pi$
$353$	1.85245	0.0985962	0.0492981	+	0.998784i	$0.484302\pi$
$354$	46.8890	2.49212
$355$	−1.89396	−0.100521
$356$	−11.7477	−0.622626
$357$	−43.3141	−2.29242
$358$	7.71976	0.408002
$359$	−4.28225	−0.226009	−0.113004	−	0.993595i	$-0.536047\pi$
$359$	−4.28225	−0.226009	−0.113004	+	0.993595i	$0.536047\pi$
$360$	1.04471	0.0550609
$361$	19.2960	1.01558
$362$	−17.2728	−0.907837
$363$	26.9233	1.41311
$364$	−1.53424	−0.0804159
$365$	1.38993	0.0727523
$366$	0.977320	0.0510854
$367$	−5.31177	−0.277272	−0.138636	−	0.990343i	$-0.544272\pi$
$367$	−5.31177	−0.277272	−0.138636	+	0.990343i	$0.544272\pi$
$368$	−7.87011	−0.410258
$369$	−31.1160	−1.61983
$370$	1.34840	0.0701002
$371$	−22.4492	−1.16550
$372$	6.03552	0.312927
$373$	10.3027	0.533452	0.266726	−	0.963772i	$-0.414058\pi$
$373$	10.3027	0.533452	0.266726	+	0.963772i	$0.414058\pi$
$374$	10.7525	0.555997
$375$	−4.41635	−0.228059
$376$	−3.30452	−0.170417
$377$	3.35548	0.172816
$378$	−31.8380	−1.63757
$379$	−17.4197	−0.894787	−0.447394	−	0.894337i	$-0.647648\pi$
$379$	−17.4197	−0.894787	−0.447394	+	0.894337i	$0.647648\pi$
$380$	−0.835577	−0.0428642
$381$	−23.1939	−1.18826
$382$	22.7859	1.16583
$383$	−19.8524	−1.01441	−0.507205	−	0.861826i	$-0.669321\pi$
$383$	−19.8524	−1.01441	−0.507205	+	0.861826i	$0.669321\pi$
$384$	3.27677	0.167217
$385$	0.462048	0.0235482
$386$	−26.4582	−1.34669
$387$	−17.3718	−0.883059
$388$	10.2681	0.521282
$389$	−10.3794	−0.526254	−0.263127	−	0.964761i	$-0.584754\pi$
$389$	−10.3794	−0.526254	−0.263127	+	0.964761i	$0.584754\pi$
$390$	−0.330958	−0.0167587
$391$	50.7210	2.56507
$392$	2.79319	0.141078
$393$	59.3135	2.99197
$394$	−17.6728	−0.890342
$395$	0.943305	0.0474628
$396$	12.9088	0.648692
$397$	−22.2858	−1.11849	−0.559245	−	0.829002i	$-0.688909\pi$
$397$	−22.2858	−1.11849	−0.559245	+	0.829002i	$0.688909\pi$
$398$	−12.8593	−0.644580
$399$	41.5910	2.08215
$400$	−4.98177	−0.249088
$401$	−38.5988	−1.92753	−0.963766	−	0.266750i	$-0.914050\pi$
$401$	−38.5988	−1.92753	−0.963766	+	0.266750i	$0.914050\pi$
$402$	−41.4411	−2.06689
$403$	−1.37780	−0.0686329
$404$	−5.22215	−0.259812
$405$	−3.73380	−0.185534
$406$	9.20056	0.456616
$407$	16.6614	0.825875
$408$	−21.1180	−1.04550
$409$	−33.6934	−1.66603	−0.833017	−	0.553248i	$-0.813388\pi$
$409$	−33.6934	−1.66603	−0.833017	+	0.553248i	$0.813388\pi$
$410$	−0.543010	−0.0268174
$411$	13.8828	0.684789
$412$	−7.96065	−0.392193
$413$	−29.3495	−1.44420
$414$	60.8928	2.99272
$415$	−0.658376	−0.0323184
$416$	−0.748026	−0.0366750
$417$	48.3702	2.36870
$418$	−10.3247	−0.504999
$419$	13.9375	0.680892	0.340446	−	0.940264i	$-0.389422\pi$
$419$	13.9375	0.680892	0.340446	+	0.940264i	$0.389422\pi$
$420$	−0.907469	−0.0442800
$421$	29.9605	1.46019	0.730093	−	0.683348i	$-0.239477\pi$
$421$	29.9605	1.46019	0.730093	+	0.683348i	$0.239477\pi$
$422$	15.9114	0.774557
$423$	25.5678	1.24315
$424$	−10.9452	−0.531546
$425$	32.1063	1.55739
$426$	45.9627	2.22690
$427$	−0.611740	−0.0296042
$428$	−9.95708	−0.481294
$429$	−4.08944	−0.197440
$430$	−0.303158	−0.0146196
$431$	14.8712	0.716321	0.358161	−	0.933660i	$-0.383404\pi$
$431$	14.8712	0.716321	0.358161	+	0.933660i	$0.383404\pi$
$432$	−15.5228	−0.746841
$433$	29.4885	1.41712	0.708562	−	0.705648i	$-0.249344\pi$
$433$	29.4885	1.41712	0.708562	+	0.705648i	$0.249344\pi$
$434$	−3.77785	−0.181343
$435$	1.98470	0.0951589
$436$	10.1994	0.488463
$437$	−48.7032	−2.32979
$438$	−33.7310	−1.61173
$439$	14.7325	0.703145	0.351572	−	0.936161i	$-0.385647\pi$
$439$	14.7325	0.703145	0.351572	+	0.936161i	$0.385647\pi$
$440$	0.225274	0.0107395
$441$	−21.6116	−1.02912
$442$	4.82085	0.229304
$443$	35.2862	1.67650	0.838248	−	0.545289i	$-0.183580\pi$
$443$	35.2862	1.67650	0.838248	+	0.545289i	$0.183580\pi$
$444$	−32.7232	−1.55298
$445$	1.58621	0.0751938
$446$	4.47076	0.211697
$447$	−46.4424	−2.19665
$448$	−2.05105	−0.0969030
$449$	11.1763	0.527443	0.263721	−	0.964599i	$-0.415050\pi$
$449$	11.1763	0.527443	0.263721	+	0.964599i	$0.415050\pi$
$450$	38.5451	1.81703
$451$	−6.70965	−0.315945
$452$	17.8383	0.839043
$453$	69.2665	3.25442
$454$	−7.72624	−0.362611
$455$	0.207158	0.00971174
$456$	20.2779	0.949600
$457$	−42.1268	−1.97061	−0.985303	−	0.170814i	$-0.945360\pi$
$457$	−42.1268	−1.97061	−0.985303	+	0.170814i	$0.945360\pi$
$458$	21.4518	1.00238
$459$	100.041	4.66950
$460$	1.06265	0.0495463
$461$	−0.649091	−0.0302312	−0.0151156	−	0.999886i	$-0.504812\pi$
$461$	−0.649091	−0.0302312	−0.0151156	+	0.999886i	$0.504812\pi$
$462$	−11.2130	−0.521678
$463$	35.3858	1.64452	0.822259	−	0.569113i	$-0.192713\pi$
$463$	35.3858	1.64452	0.822259	+	0.569113i	$0.192713\pi$
$464$	4.48578	0.208247
$465$	−0.814938	−0.0377918
$466$	11.7767	0.545543
$467$	1.66767	0.0771703	0.0385852	−	0.999255i	$-0.487715\pi$
$467$	1.66767	0.0771703	0.0385852	+	0.999255i	$0.487715\pi$
$468$	5.78764	0.267534
$469$	25.9395	1.19777
$470$	0.446188	0.0205811
$471$	17.4899	0.805893
$472$	−14.3095	−0.658649
$473$	−3.74594	−0.172239
$474$	−22.8922	−1.05148
$475$	−30.8291	−1.41454
$476$	13.2185	0.605870
$477$	84.6855	3.87748
$478$	−16.1597	−0.739128
$479$	−13.9513	−0.637449	−0.318725	−	0.947847i	$-0.603254\pi$
$479$	−13.9513	−0.637449	−0.318725	+	0.947847i	$0.603254\pi$
$480$	−0.442441	−0.0201946
$481$	7.47011	0.340608
$482$	1.79358	0.0816955
$483$	−52.8936	−2.40674
$484$	−8.21643	−0.373474
$485$	−1.38643	−0.0629546
$486$	44.0440	1.99788
$487$	−20.2570	−0.917933	−0.458967	−	0.888453i	$-0.651780\pi$
$487$	−20.2570	−0.917933	−0.458967	+	0.888453i	$0.651780\pi$
$488$	−0.298257	−0.0135015
$489$	26.5709	1.20158
$490$	−0.377147	−0.0170378
$491$	−9.88411	−0.446064	−0.223032	−	0.974811i	$-0.571595\pi$
$491$	−9.88411	−0.446064	−0.223032	+	0.974811i	$0.571595\pi$
$492$	13.1778	0.594103
$493$	−28.9098	−1.30203
$494$	−4.62907	−0.208272
$495$	−1.74299	−0.0783418
$496$	−1.84191	−0.0827042
$497$	−28.7698	−1.29050
$498$	15.9775	0.715971
$499$	17.7503	0.794613	0.397306	−	0.917686i	$-0.369945\pi$
$499$	17.7503	0.794613	0.397306	+	0.917686i	$0.369945\pi$
$500$	1.34777	0.0602743
$501$	74.5128	3.32898
$502$	−15.9043	−0.709841
$503$	−5.00753	−0.223275	−0.111637	−	0.993749i	$-0.535609\pi$
$503$	−5.00753	−0.223275	−0.111637	+	0.993749i	$0.535609\pi$
$504$	15.8694	0.706881
$505$	0.705114	0.0313772
$506$	13.1305	0.583723
$507$	40.7645	1.81042
$508$	7.07828	0.314048
$509$	−0.797424	−0.0353452	−0.0176726	−	0.999844i	$-0.505626\pi$
$509$	−0.797424	−0.0353452	−0.0176726	+	0.999844i	$0.505626\pi$
$510$	2.85143	0.126263
$511$	21.1135	0.934005
$512$	−1.00000	−0.0441942
$513$	−96.0609	−4.24119
$514$	5.34665	0.235831
$515$	1.07488	0.0473647
$516$	7.35709	0.323878
$517$	5.51327	0.242473
$518$	20.4827	0.899957
$519$	−3.12430	−0.137142
$520$	0.101001	0.00442919
$521$	−18.1978	−0.797259	−0.398630	−	0.917112i	$-0.630514\pi$
$521$	−18.1978	−0.797259	−0.398630	+	0.917112i	$0.630514\pi$
$522$	−34.7075	−1.51911
$523$	−20.8163	−0.910232	−0.455116	−	0.890432i	$-0.650402\pi$
$523$	−20.8163	−0.910232	−0.455116	+	0.890432i	$0.650402\pi$
$524$	−18.1012	−0.790755
$525$	−33.4816	−1.46126
$526$	5.81381	0.253494
$527$	11.8707	0.517095
$528$	−5.46698	−0.237920
$529$	38.9386	1.69298
$530$	1.47786	0.0641942
$531$	110.716	4.80466
$532$	−12.6927	−0.550297
$533$	−3.00826	−0.130302
$534$	−38.4944	−1.66582
$535$	1.34444	0.0581253
$536$	12.6469	0.546264
$537$	25.2959	1.09160
$538$	−26.7978	−1.15534
$539$	−4.66018	−0.200728
$540$	2.09594	0.0901950
$541$	16.5323	0.710777	0.355389	−	0.934719i	$-0.384349\pi$
$541$	16.5323	0.710777	0.355389	+	0.934719i	$0.384349\pi$
$542$	8.98898	0.386110
$543$	−56.5989	−2.42889
$544$	6.44476	0.276317
$545$	−1.37716	−0.0589911
$546$	−5.02735	−0.215151
$547$	14.9940	0.641096	0.320548	−	0.947232i	$-0.396133\pi$
$547$	14.9940	0.641096	0.320548	+	0.947232i	$0.396133\pi$
$548$	−4.23674	−0.180984
$549$	2.30768	0.0984895
$550$	8.31160	0.354408
$551$	27.7597	1.18260
$552$	−25.7885	−1.09763
$553$	14.3291	0.609335
$554$	−5.53271	−0.235062
$555$	4.41841	0.187551
$556$	−14.7615	−0.626029
$557$	34.3787	1.45667	0.728335	−	0.685221i	$-0.240294\pi$
$557$	34.3787	1.45667	0.728335	+	0.685221i	$0.240294\pi$
$558$	14.2513	0.603305
$559$	−1.67949	−0.0710347
$560$	0.276940	0.0117029
$561$	35.2334	1.48755
$562$	12.9431	0.545973
$563$	−10.9060	−0.459632	−0.229816	−	0.973234i	$-0.573812\pi$
$563$	−10.9060	−0.459632	−0.229816	+	0.973234i	$0.573812\pi$
$564$	−10.8281	−0.455947
$565$	−2.40859	−0.101330
$566$	15.3622	0.645724
$567$	−56.7176	−2.38191
$568$	−14.0268	−0.588553
$569$	27.1061	1.13635	0.568174	−	0.822908i	$-0.307650\pi$
$569$	27.1061	1.13635	0.568174	+	0.822908i	$0.307650\pi$
$570$	−2.73800	−0.114682
$571$	−10.1929	−0.426561	−0.213280	−	0.976991i	$-0.568415\pi$
$571$	−10.1929	−0.426561	−0.213280	+	0.976991i	$0.568415\pi$
$572$	1.24801	0.0521819
$573$	74.6643	3.11915
$574$	−8.24849	−0.344285
$575$	39.2071	1.63505
$576$	7.73722	0.322384
$577$	−22.0952	−0.919834	−0.459917	−	0.887962i	$-0.652121\pi$
$577$	−22.0952	−0.919834	−0.459917	+	0.887962i	$0.652121\pi$
$578$	−24.5350	−1.02052
$579$	−86.6974	−3.60302
$580$	−0.605687	−0.0251498
$581$	−10.0009	−0.414908
$582$	33.6461	1.39467
$583$	18.2610	0.756294
$584$	10.2940	0.425968
$585$	−0.781468	−0.0323097
$586$	−23.8704	−0.986076
$587$	24.6577	1.01773	0.508866	−	0.860846i	$-0.330065\pi$
$587$	24.6577	1.01773	0.508866	+	0.860846i	$0.330065\pi$
$588$	9.15266	0.377449
$589$	−11.3984	−0.469665
$590$	1.93212	0.0795443
$591$	−57.9097	−2.38209
$592$	9.98643	0.410440
$593$	−18.4525	−0.757752	−0.378876	−	0.925447i	$-0.623689\pi$
$593$	−18.4525	−0.757752	−0.378876	+	0.925447i	$0.623689\pi$
$594$	25.8983	1.06262
$595$	−1.78481	−0.0731702
$596$	14.1732	0.580558
$597$	−42.1371	−1.72456
$598$	5.88704	0.240739
$599$	32.2098	1.31606	0.658029	−	0.752993i	$-0.271390\pi$
$599$	32.2098	1.31606	0.658029	+	0.752993i	$0.271390\pi$
$600$	−16.3241	−0.666429
$601$	26.1987	1.06867	0.534333	−	0.845274i	$-0.320563\pi$
$601$	26.1987	1.06867	0.534333	+	0.845274i	$0.320563\pi$
$602$	−4.60507	−0.187689
$603$	−97.8521	−3.98484
$604$	−21.1386	−0.860119
$605$	1.10941	0.0451040
$606$	−17.1118	−0.695119
$607$	−7.41965	−0.301154	−0.150577	−	0.988598i	$-0.548113\pi$
$607$	−7.41965	−0.301154	−0.150577	+	0.988598i	$0.548113\pi$
$608$	−6.18838	−0.250972
$609$	30.1481	1.22166
$610$	0.0402718	0.00163056
$611$	2.47186	0.100001
$612$	−49.8646	−2.01566
$613$	1.68073	0.0678839	0.0339420	−	0.999424i	$-0.489194\pi$
$613$	1.68073	0.0678839	0.0339420	+	0.999424i	$0.489194\pi$
$614$	2.10808	0.0850750
$615$	−1.77932	−0.0717491
$616$	3.42198	0.137876
$617$	30.7372	1.23743	0.618716	−	0.785615i	$-0.287653\pi$
$617$	30.7372	1.23743	0.618716	+	0.785615i	$0.287653\pi$
$618$	−26.0852	−1.04930
$619$	20.3179	0.816647	0.408323	−	0.912837i	$-0.366114\pi$
$619$	20.3179	0.816647	0.408323	+	0.912837i	$0.366114\pi$
$620$	0.248701	0.00998809
$621$	122.166	4.90235
$622$	−19.8295	−0.795091
$623$	24.0951	0.965349
$624$	−2.45111	−0.0981229
$625$	24.7269	0.989074
$626$	5.35907	0.214192
$627$	−33.8317	−1.35111
$628$	−5.33755	−0.212991
$629$	−64.3602	−2.56621
$630$	−2.14275	−0.0853691
$631$	16.8014	0.668854	0.334427	−	0.942422i	$-0.391457\pi$
$631$	16.8014	0.668854	0.334427	+	0.942422i	$0.391457\pi$
$632$	6.98622	0.277897
$633$	52.1382	2.07231
$634$	−12.5143	−0.497005
$635$	−0.955735	−0.0379272
$636$	−35.8649	−1.42214
$637$	−2.08938	−0.0827843
$638$	−7.48410	−0.296298
$639$	108.529	4.29333
$640$	0.135024	0.00533728
$641$	−40.0961	−1.58370	−0.791851	−	0.610714i	$-0.790883\pi$
$641$	−40.0961	−1.58370	−0.791851	+	0.610714i	$0.790883\pi$
$642$	−32.6271	−1.28769
$643$	35.1369	1.38566	0.692832	−	0.721099i	$-0.256363\pi$
$643$	35.1369	1.38566	0.692832	+	0.721099i	$0.256363\pi$
$644$	16.1420	0.636083
$645$	−0.993381	−0.0391143
$646$	39.8826	1.56916
$647$	43.9907	1.72945	0.864727	−	0.502243i	$-0.167492\pi$
$647$	43.9907	1.72945	0.864727	+	0.502243i	$0.167492\pi$
$648$	−27.6529	−1.08631
$649$	23.8741	0.937139
$650$	3.72649	0.146165
$651$	−12.3791	−0.485177
$652$	−8.10885	−0.317567
$653$	14.0422	0.549513	0.274757	−	0.961514i	$-0.411403\pi$
$653$	14.0422	0.549513	0.274757	+	0.961514i	$0.411403\pi$
$654$	33.4211	1.30687
$655$	2.44409	0.0954985
$656$	−4.02159	−0.157017
$657$	−79.6468	−3.10732
$658$	6.77773	0.264223
$659$	13.0666	0.509004	0.254502	−	0.967072i	$-0.418089\pi$
$659$	13.0666	0.509004	0.254502	+	0.967072i	$0.418089\pi$
$660$	0.738171	0.0287333
$661$	−4.24539	−0.165127	−0.0825633	−	0.996586i	$-0.526311\pi$
$661$	−4.24539	−0.165127	−0.0825633	+	0.996586i	$0.526311\pi$
$662$	22.4592	0.872903
$663$	15.7968	0.613497
$664$	−4.87600	−0.189226
$665$	1.71381	0.0664587
$666$	−77.2672	−2.99404
$667$	−35.3036	−1.36696
$668$	−22.7397	−0.879825
$669$	14.6497	0.566388
$670$	−1.70763	−0.0659716
$671$	0.497614	0.0192102
$672$	−6.72082	−0.259261
$673$	45.6175	1.75843	0.879214	−	0.476428i	$-0.158069\pi$
$673$	45.6175	1.75843	0.879214	+	0.476428i	$0.158069\pi$
$674$	−33.6761	−1.29716
$675$	77.3309	2.97647
$676$	−12.4405	−0.478479
$677$	22.3951	0.860712	0.430356	−	0.902659i	$-0.358388\pi$
$677$	22.3951	0.860712	0.430356	+	0.902659i	$0.358388\pi$
$678$	58.4520	2.24484
$679$	−21.0603	−0.808220
$680$	−0.870195	−0.0333705
$681$	−25.3171	−0.970154
$682$	3.07305	0.117673
$683$	21.7819	0.833462	0.416731	−	0.909030i	$-0.363176\pi$
$683$	21.7819	0.833462	0.416731	+	0.909030i	$0.363176\pi$
$684$	47.8809	1.83077
$685$	0.572060	0.0218573
$686$	−20.0863	−0.766900
$687$	70.2925	2.68183
$688$	−2.24523	−0.0855984
$689$	8.18729	0.311911
$690$	3.48206	0.132560
$691$	30.7194	1.16862	0.584310	−	0.811530i	$-0.301365\pi$
$691$	30.7194	1.16862	0.584310	+	0.811530i	$0.301365\pi$
$692$	0.953469	0.0362455
$693$	−26.4766	−1.00576
$694$	6.83418	0.259422
$695$	1.99316	0.0756047
$696$	14.6989	0.557160
$697$	25.9182	0.981723
$698$	8.72885	0.330392
$699$	38.5894	1.45959
$700$	10.2179	0.386199
$701$	−44.1466	−1.66739	−0.833697	−	0.552222i	$-0.813780\pi$
$701$	−44.1466	−1.66739	−0.833697	+	0.552222i	$0.813780\pi$
$702$	11.6114	0.438246
$703$	61.7998	2.33082
$704$	1.66840	0.0628803
$705$	1.46206	0.0550642
$706$	−1.85245	−0.0697181
$707$	10.7109	0.402825
$708$	−46.8890	−1.76220
$709$	22.2262	0.834724	0.417362	−	0.908740i	$-0.362955\pi$
$709$	22.2262	0.834724	0.417362	+	0.908740i	$0.362955\pi$
$710$	1.89396	0.0710789
$711$	−54.0539	−2.02718
$712$	11.7477	0.440263
$713$	14.4960	0.542881
$714$	43.3141	1.62099
$715$	−0.168511	−0.00630194
$716$	−7.71976	−0.288501
$717$	−52.9517	−1.97752
$718$	4.28225	0.159812
$719$	−19.6218	−0.731771	−0.365885	−	0.930660i	$-0.619234\pi$
$719$	−19.6218	−0.731771	−0.365885	+	0.930660i	$0.619234\pi$
$720$	−1.04471	−0.0389340
$721$	16.3277	0.608075
$722$	−19.2960	−0.718125
$723$	5.87716	0.218574
$724$	17.2728	0.641938
$725$	−22.3471	−0.829952
$726$	−26.9233	−0.999219
$727$	−49.3290	−1.82951	−0.914756	−	0.404007i	$-0.867617\pi$
$727$	−49.3290	−1.82951	−0.914756	+	0.404007i	$0.867617\pi$
$728$	1.53424	0.0568627
$729$	61.3632	2.27271
$730$	−1.38993	−0.0514436
$731$	14.4699	0.535190
$732$	−0.977320	−0.0361228
$733$	−39.4105	−1.45566	−0.727830	−	0.685757i	$-0.759471\pi$
$733$	−39.4105	−1.45566	−0.727830	+	0.685757i	$0.759471\pi$
$734$	5.31177	0.196061
$735$	−1.23582	−0.0455841
$736$	7.87011	0.290096
$737$	−21.1002	−0.777235
$738$	31.1160	1.14539
$739$	−12.0021	−0.441505	−0.220753	−	0.975330i	$-0.570851\pi$
$739$	−12.0021	−0.441505	−0.220753	+	0.975330i	$0.570851\pi$
$740$	−1.34840	−0.0495683
$741$	−15.1684	−0.557225
$742$	22.4492	0.824135
$743$	28.6835	1.05230	0.526148	−	0.850393i	$-0.323636\pi$
$743$	28.6835	1.05230	0.526148	+	0.850393i	$0.323636\pi$
$744$	−6.03552	−0.221273
$745$	−1.91372	−0.0701133
$746$	−10.3027	−0.377207
$747$	37.7267	1.38035
$748$	−10.7525	−0.393149
$749$	20.4225	0.746221
$750$	4.41635	0.161262
$751$	−12.3038	−0.448971	−0.224486	−	0.974477i	$-0.572070\pi$
$751$	−12.3038	−0.448971	−0.224486	+	0.974477i	$0.572070\pi$
$752$	3.30452	0.120503
$753$	−52.1146	−1.89916
$754$	−3.35548	−0.122199
$755$	2.85422	0.103876
$756$	31.8380	1.15794
$757$	2.13323	0.0775335	0.0387667	−	0.999248i	$-0.487657\pi$
$757$	2.13323	0.0775335	0.0387667	+	0.999248i	$0.487657\pi$
$758$	17.4197	0.632710
$759$	43.0257	1.56173
$760$	0.835577	0.0303096
$761$	−6.93248	−0.251302	−0.125651	−	0.992074i	$-0.540102\pi$
$761$	−6.93248	−0.251302	−0.125651	+	0.992074i	$0.540102\pi$
$762$	23.1939	0.840226
$763$	−20.9195	−0.757337
$764$	−22.7859	−0.824366
$765$	6.73289	0.243428
$766$	19.8524	0.717296
$767$	10.7039	0.386495
$768$	−3.27677	−0.118240
$769$	−11.3529	−0.409394	−0.204697	−	0.978825i	$-0.565621\pi$
$769$	−11.3529	−0.409394	−0.204697	+	0.978825i	$0.565621\pi$
$770$	−0.462048	−0.0166511
$771$	17.5198	0.630959
$772$	26.4582	0.952251
$773$	23.3838	0.841055	0.420528	−	0.907280i	$-0.361845\pi$
$773$	23.3838	0.841055	0.420528	+	0.907280i	$0.361845\pi$
$774$	17.3718	0.624417
$775$	9.17597	0.329611
$776$	−10.2681	−0.368602
$777$	67.1170	2.40781
$778$	10.3794	0.372118
$779$	−24.8872	−0.891675
$780$	0.330958	0.0118502
$781$	23.4024	0.837405
$782$	−50.7210	−1.81378
$783$	−69.6319	−2.48844
$784$	−2.79319	−0.0997569
$785$	0.720695	0.0257227
$786$	−59.3135	−2.11564
$787$	46.2823	1.64979	0.824893	−	0.565289i	$-0.191235\pi$
$787$	46.2823	1.64979	0.824893	+	0.565289i	$0.191235\pi$
$788$	17.6728	0.629567
$789$	19.0505	0.678216
$790$	−0.943305	−0.0335613
$791$	−36.5872	−1.30089
$792$	−12.9088	−0.458695
$793$	0.223104	0.00792266
$794$	22.2858	0.790892
$795$	4.84261	0.171750
$796$	12.8593	0.455787
$797$	45.1649	1.59982	0.799911	−	0.600118i	$-0.204880\pi$
$797$	45.1649	1.59982	0.799911	+	0.600118i	$0.204880\pi$
$798$	−41.5910	−1.47230
$799$	−21.2968	−0.753428
$800$	4.98177	0.176132
$801$	−90.8944	−3.21160
$802$	38.5988	1.36297
$803$	−17.1745	−0.606076
$804$	41.4411	1.46151
$805$	−2.17955	−0.0768190
$806$	1.37780	0.0485308
$807$	−87.8103	−3.09107
$808$	5.22215	0.183715
$809$	1.59324	0.0560155	0.0280077	−	0.999608i	$-0.491084\pi$
$809$	1.59324	0.0560155	0.0280077	+	0.999608i	$0.491084\pi$
$810$	3.73380	0.131192
$811$	38.3250	1.34577	0.672887	−	0.739745i	$-0.265054\pi$
$811$	38.3250	1.34577	0.672887	+	0.739745i	$0.265054\pi$
$812$	−9.20056	−0.322876
$813$	29.4548	1.03303
$814$	−16.6614	−0.583982
$815$	1.09489	0.0383522
$816$	21.1180	0.739278
$817$	−13.8943	−0.486100
$818$	33.6934	1.17806
$819$	−11.8707	−0.414797
$820$	0.543010	0.0189627
$821$	−53.6567	−1.87263	−0.936317	−	0.351157i	$-0.885788\pi$
$821$	−53.6567	−1.87263	−0.936317	+	0.351157i	$0.885788\pi$
$822$	−13.8828	−0.484219
$823$	40.5956	1.41507	0.707537	−	0.706676i	$-0.249806\pi$
$823$	40.5956	1.41507	0.707537	+	0.706676i	$0.249806\pi$
$824$	7.96065	0.277322
$825$	27.2352	0.948208
$826$	29.3495	1.02120
$827$	37.1480	1.29176	0.645881	−	0.763438i	$-0.276490\pi$
$827$	37.1480	1.29176	0.645881	+	0.763438i	$0.276490\pi$
$828$	−60.8928	−2.11617
$829$	41.0081	1.42427	0.712136	−	0.702042i	$-0.247728\pi$
$829$	41.0081	1.42427	0.712136	+	0.702042i	$0.247728\pi$
$830$	0.658376	0.0228526
$831$	−18.1294	−0.628902
$832$	0.748026	0.0259331
$833$	18.0015	0.623714
$834$	−48.3702	−1.67492
$835$	3.07040	0.106255
$836$	10.3247	0.357088
$837$	28.5916	0.988270
$838$	−13.9375	−0.481463
$839$	−40.3776	−1.39399	−0.696994	−	0.717077i	$-0.745480\pi$
$839$	−40.3776	−1.39399	−0.696994	+	0.717077i	$0.745480\pi$
$840$	0.907469	0.0313107
$841$	−8.87776	−0.306130
$842$	−29.9605	−1.03251
$843$	42.4117	1.46073
$844$	−15.9114	−0.547695
$845$	1.67976	0.0577853
$846$	−25.5678	−0.879039
$847$	16.8523	0.579052
$848$	10.9452	0.375860
$849$	50.3386	1.72761
$850$	−32.1063	−1.10124
$851$	−78.5943	−2.69418
$852$	−45.9627	−1.57466
$853$	23.5634	0.806797	0.403399	−	0.915024i	$-0.367829\pi$
$853$	23.5634	0.806797	0.403399	+	0.915024i	$0.367829\pi$
$854$	0.611740	0.0209333
$855$	−6.46505	−0.221100
$856$	9.95708	0.340326
$857$	5.70582	0.194907	0.0974535	−	0.995240i	$-0.468930\pi$
$857$	5.70582	0.194907	0.0974535	+	0.995240i	$0.468930\pi$
$858$	4.08944	0.139611
$859$	−12.4594	−0.425111	−0.212555	−	0.977149i	$-0.568179\pi$
$859$	−12.4594	−0.425111	−0.212555	+	0.977149i	$0.568179\pi$
$860$	0.303158	0.0103376
$861$	−27.0284	−0.921126
$862$	−14.8712	−0.506516
$863$	13.3720	0.455188	0.227594	−	0.973756i	$-0.426914\pi$
$863$	13.3720	0.455188	0.227594	+	0.973756i	$0.426914\pi$
$864$	15.5228	0.528096
$865$	−0.128741	−0.00437732
$866$	−29.4885	−1.00206
$867$	−80.3955	−2.73037
$868$	3.77785	0.128229
$869$	−11.6558	−0.395397
$870$	−1.98470	−0.0672875
$871$	−9.46023	−0.320548
$872$	−10.1994	−0.345396
$873$	79.4462	2.68885
$874$	48.7032	1.64741
$875$	−2.76435	−0.0934522
$876$	33.7310	1.13967
$877$	−2.30725	−0.0779103	−0.0389552	−	0.999241i	$-0.512403\pi$
$877$	−2.30725	−0.0779103	−0.0389552	+	0.999241i	$0.512403\pi$
$878$	−14.7325	−0.497199
$879$	−78.2177	−2.63822
$880$	−0.225274	−0.00759398
$881$	−6.21265	−0.209309	−0.104655	−	0.994509i	$-0.533374\pi$
$881$	−6.21265	−0.209309	−0.104655	+	0.994509i	$0.533374\pi$
$882$	21.6116	0.727699
$883$	48.4512	1.63051	0.815257	−	0.579100i	$-0.196596\pi$
$883$	48.4512	1.63051	0.815257	+	0.579100i	$0.196596\pi$
$884$	−4.82085	−0.162143
$885$	6.33112	0.212818
$886$	−35.2862	−1.18546
$887$	−37.9576	−1.27449	−0.637247	−	0.770660i	$-0.719927\pi$
$887$	−37.9576	−1.27449	−0.637247	+	0.770660i	$0.719927\pi$
$888$	32.7232	1.09812
$889$	−14.5179	−0.486915
$890$	−1.58621	−0.0531700
$891$	46.1363	1.54562
$892$	−4.47076	−0.149692
$893$	20.4496	0.684320
$894$	46.4424	1.55327
$895$	1.04235	0.0348419
$896$	2.05105	0.0685208
$897$	19.2905	0.644091
$898$	−11.1763	−0.372958
$899$	−8.26241	−0.275567
$900$	−38.5451	−1.28484
$901$	−70.5393	−2.35000
$902$	6.70965	0.223407
$903$	−15.0898	−0.502156
$904$	−17.8383	−0.593293
$905$	−2.33223	−0.0775260
$906$	−69.2665	−2.30122
$907$	−39.3133	−1.30538	−0.652688	−	0.757627i	$-0.726359\pi$
$907$	−39.3133	−1.30538	−0.652688	+	0.757627i	$0.726359\pi$
$908$	7.72624	0.256404
$909$	−40.4050	−1.34015
$910$	−0.207158	−0.00686723
$911$	24.8913	0.824687	0.412343	−	0.911028i	$-0.364710\pi$
$911$	24.8913	0.824687	0.412343	+	0.911028i	$0.364710\pi$
$912$	−20.2779	−0.671468
$913$	8.13515	0.269234
$914$	42.1268	1.39343
$915$	0.131961	0.00436251
$916$	−21.4518	−0.708786
$917$	37.1265	1.22602
$918$	−100.041	−3.30184
$919$	17.5835	0.580028	0.290014	−	0.957022i	$-0.406340\pi$
$919$	17.5835	0.580028	0.290014	+	0.957022i	$0.406340\pi$
$920$	−1.06265	−0.0350345
$921$	6.90768	0.227616
$922$	0.649091	0.0213767
$923$	10.4924	0.345363
$924$	11.2130	0.368882
$925$	−49.7501	−1.63577
$926$	−35.3858	−1.16285
$927$	−61.5933	−2.02299
$928$	−4.48578	−0.147253
$929$	38.8033	1.27310	0.636548	−	0.771237i	$-0.280362\pi$
$929$	38.8033	1.27310	0.636548	+	0.771237i	$0.280362\pi$
$930$	0.814938	0.0267229
$931$	−17.2853	−0.566504
$932$	−11.7767	−0.385757
$933$	−64.9767	−2.12724
$934$	−1.66767	−0.0545677
$935$	1.45184	0.0474802
$936$	−5.78764	−0.189175
$937$	−16.9707	−0.554409	−0.277205	−	0.960811i	$-0.589408\pi$
$937$	−16.9707	−0.554409	−0.277205	+	0.960811i	$0.589408\pi$
$938$	−25.9395	−0.846954
$939$	17.5604	0.573063
$940$	−0.446188	−0.0145530
$941$	55.1111	1.79657	0.898286	−	0.439411i	$-0.144813\pi$
$941$	55.1111	1.79657	0.898286	+	0.439411i	$0.144813\pi$
$942$	−17.4899	−0.569852
$943$	31.6504	1.03068
$944$	14.3095	0.465735
$945$	−4.29888	−0.139843
$946$	3.74594	0.121791
$947$	16.8749	0.548360	0.274180	−	0.961678i	$-0.411594\pi$
$947$	16.8749	0.548360	0.274180	+	0.961678i	$0.411594\pi$
$948$	22.8922	0.743505
$949$	−7.70016	−0.249958
$950$	30.8291	1.00023
$951$	−41.0064	−1.32972
$952$	−13.2185	−0.428415
$953$	48.2723	1.56369	0.781847	−	0.623471i	$-0.214278\pi$
$953$	48.2723	1.56369	0.781847	+	0.623471i	$0.214278\pi$
$954$	−84.6855	−2.74179
$955$	3.07664	0.0995577
$956$	16.1597	0.522643
$957$	−24.5237	−0.792738
$958$	13.9513	0.450745
$959$	8.68976	0.280607
$960$	0.442441	0.0142797
$961$	−27.6074	−0.890560
$962$	−7.47011	−0.240846
$963$	−77.0402	−2.48258
$964$	−1.79358	−0.0577675
$965$	−3.57248	−0.115002
$966$	52.8936	1.70182
$967$	−3.81018	−0.122527	−0.0612636	−	0.998122i	$-0.519513\pi$
$967$	−3.81018	−0.122527	−0.0612636	+	0.998122i	$0.519513\pi$
$968$	8.21643	0.264086
$969$	130.686	4.19825
$970$	1.38643	0.0445156
$971$	1.09684	0.0351992	0.0175996	−	0.999845i	$-0.494398\pi$
$971$	1.09684	0.0351992	0.0175996	+	0.999845i	$0.494398\pi$
$972$	−44.0440	−1.41271
$973$	30.2767	0.970625
$974$	20.2570	0.649077
$975$	12.2109	0.391060
$976$	0.298257	0.00954698
$977$	11.4902	0.367605	0.183802	−	0.982963i	$-0.441159\pi$
$977$	11.4902	0.367605	0.183802	+	0.982963i	$0.441159\pi$
$978$	−26.5709	−0.849642
$979$	−19.5999	−0.626415
$980$	0.377147	0.0120475
$981$	78.9151	2.51957
$982$	9.88411	0.315415
$983$	27.3509	0.872359	0.436180	−	0.899860i	$-0.356331\pi$
$983$	27.3509	0.872359	0.436180	+	0.899860i	$0.356331\pi$
$984$	−13.1778	−0.420094
$985$	−2.38624	−0.0760321
$986$	28.9098	0.920676
$987$	22.2091	0.706922
$988$	4.62907	0.147270
$989$	17.6702	0.561879
$990$	1.74299	0.0553960
$991$	26.3354	0.836572	0.418286	−	0.908315i	$-0.362631\pi$
$991$	26.3354	0.836572	0.418286	+	0.908315i	$0.362631\pi$
$992$	1.84191	0.0584807
$993$	73.5938	2.33543
$994$	28.7698	0.912521
$995$	−1.73631	−0.0550449
$996$	−15.9775	−0.506268
$997$	31.2377	0.989307	0.494654	−	0.869090i	$-0.335295\pi$
$997$	31.2377	0.989307	0.494654	+	0.869090i	$0.335295\pi$
$998$	−17.7503	−0.561876
$999$	−155.017	−4.90453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.4	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.4	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.27677 q^{3} +1.00000 q^{4} -0.135024 q^{5} +3.27677 q^{6} -2.05105 q^{7} -1.00000 q^{8} +7.73722 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.27677 q^{3} +1.00000 q^{4} -0.135024 q^{5} +3.27677 q^{6} -2.05105 q^{7} -1.00000 q^{8} +7.73722 q^{9} +0.135024 q^{10} +1.66840 q^{11} -3.27677 q^{12} +0.748026 q^{13} +2.05105 q^{14} +0.442441 q^{15} +1.00000 q^{16} -6.44476 q^{17} -7.73722 q^{18} +6.18838 q^{19} -0.135024 q^{20} +6.72082 q^{21} -1.66840 q^{22} -7.87011 q^{23} +3.27677 q^{24} -4.98177 q^{25} -0.748026 q^{26} -15.5228 q^{27} -2.05105 q^{28} +4.48578 q^{29} -0.442441 q^{30} -1.84191 q^{31} -1.00000 q^{32} -5.46698 q^{33} +6.44476 q^{34} +0.276940 q^{35} +7.73722 q^{36} +9.98643 q^{37} -6.18838 q^{38} -2.45111 q^{39} +0.135024 q^{40} -4.02159 q^{41} -6.72082 q^{42} -2.24523 q^{43} +1.66840 q^{44} -1.04471 q^{45} +7.87011 q^{46} +3.30452 q^{47} -3.27677 q^{48} -2.79319 q^{49} +4.98177 q^{50} +21.1180 q^{51} +0.748026 q^{52} +10.9452 q^{53} +15.5228 q^{54} -0.225274 q^{55} +2.05105 q^{56} -20.2779 q^{57} -4.48578 q^{58} +14.3095 q^{59} +0.442441 q^{60} +0.298257 q^{61} +1.84191 q^{62} -15.8694 q^{63} +1.00000 q^{64} -0.101001 q^{65} +5.46698 q^{66} -12.6469 q^{67} -6.44476 q^{68} +25.7885 q^{69} -0.276940 q^{70} +14.0268 q^{71} -7.73722 q^{72} -10.2940 q^{73} -9.98643 q^{74} +16.3241 q^{75} +6.18838 q^{76} -3.42198 q^{77} +2.45111 q^{78} -6.98622 q^{79} -0.135024 q^{80} +27.6529 q^{81} +4.02159 q^{82} +4.87600 q^{83} +6.72082 q^{84} +0.870195 q^{85} +2.24523 q^{86} -14.6989 q^{87} -1.66840 q^{88} -11.7477 q^{89} +1.04471 q^{90} -1.53424 q^{91} -7.87011 q^{92} +6.03552 q^{93} -3.30452 q^{94} -0.835577 q^{95} +3.27677 q^{96} +10.2681 q^{97} +2.79319 q^{98} +12.9088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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