LMFDB - Embedded newform 8002.2.a.d.1.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.43
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.562802 q^{3} +1.00000 q^{4} +3.54285 q^{5} +0.562802 q^{6} -3.91047 q^{7} +1.00000 q^{8} -2.68325 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.562802 q^{3} +1.00000 q^{4} +3.54285 q^{5} +0.562802 q^{6} -3.91047 q^{7} +1.00000 q^{8} -2.68325 q^{9} +3.54285 q^{10} +3.05436 q^{11} +0.562802 q^{12} -1.03133 q^{13} -3.91047 q^{14} +1.99392 q^{15} +1.00000 q^{16} -7.77376 q^{17} -2.68325 q^{18} -0.419428 q^{19} +3.54285 q^{20} -2.20082 q^{21} +3.05436 q^{22} -3.02899 q^{23} +0.562802 q^{24} +7.55178 q^{25} -1.03133 q^{26} -3.19855 q^{27} -3.91047 q^{28} +1.92252 q^{29} +1.99392 q^{30} +4.06878 q^{31} +1.00000 q^{32} +1.71900 q^{33} -7.77376 q^{34} -13.8542 q^{35} -2.68325 q^{36} -9.25629 q^{37} -0.419428 q^{38} -0.580438 q^{39} +3.54285 q^{40} -6.45288 q^{41} -2.20082 q^{42} -11.1616 q^{43} +3.05436 q^{44} -9.50636 q^{45} -3.02899 q^{46} -8.17335 q^{47} +0.562802 q^{48} +8.29174 q^{49} +7.55178 q^{50} -4.37509 q^{51} -1.03133 q^{52} +5.88657 q^{53} -3.19855 q^{54} +10.8211 q^{55} -3.91047 q^{56} -0.236055 q^{57} +1.92252 q^{58} +14.2237 q^{59} +1.99392 q^{60} +1.47291 q^{61} +4.06878 q^{62} +10.4928 q^{63} +1.00000 q^{64} -3.65386 q^{65} +1.71900 q^{66} +1.76992 q^{67} -7.77376 q^{68} -1.70472 q^{69} -13.8542 q^{70} -16.0914 q^{71} -2.68325 q^{72} +2.43347 q^{73} -9.25629 q^{74} +4.25016 q^{75} -0.419428 q^{76} -11.9440 q^{77} -0.580438 q^{78} -7.00005 q^{79} +3.54285 q^{80} +6.24961 q^{81} -6.45288 q^{82} -7.62795 q^{83} -2.20082 q^{84} -27.5412 q^{85} -11.1616 q^{86} +1.08200 q^{87} +3.05436 q^{88} -5.63602 q^{89} -9.50636 q^{90} +4.03300 q^{91} -3.02899 q^{92} +2.28992 q^{93} -8.17335 q^{94} -1.48597 q^{95} +0.562802 q^{96} +13.7798 q^{97} +8.29174 q^{98} -8.19563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	0.562802	0.324934	0.162467	−	0.986714i	$-0.448055\pi$
$3$	0.562802	0.324934	0.162467	+	0.986714i	$0.448055\pi$
$4$	1.00000	0.500000
$5$	3.54285	1.58441	0.792205	−	0.610255i	$-0.208933\pi$
$5$	3.54285	1.58441	0.792205	+	0.610255i	$0.208933\pi$
$6$	0.562802	0.229763
$7$	−3.91047	−1.47802	−0.739009	−	0.673696i	$-0.764706\pi$
$7$	−3.91047	−1.47802	−0.739009	+	0.673696i	$0.764706\pi$
$8$	1.00000	0.353553
$9$	−2.68325	−0.894418
$10$	3.54285	1.12035
$11$	3.05436	0.920925	0.460462	−	0.887679i	$-0.347684\pi$
$11$	3.05436	0.920925	0.460462	+	0.887679i	$0.347684\pi$
$12$	0.562802	0.162467
$13$	−1.03133	−0.286041	−0.143020	−	0.989720i	$-0.545681\pi$
$13$	−1.03133	−0.286041	−0.143020	+	0.989720i	$0.545681\pi$
$14$	−3.91047	−1.04512
$15$	1.99392	0.514829
$16$	1.00000	0.250000
$17$	−7.77376	−1.88541	−0.942706	−	0.333623i	$-0.891729\pi$
$17$	−7.77376	−1.88541	−0.942706	+	0.333623i	$0.891729\pi$
$18$	−2.68325	−0.632449
$19$	−0.419428	−0.0962234	−0.0481117	−	0.998842i	$-0.515320\pi$
$19$	−0.419428	−0.0962234	−0.0481117	+	0.998842i	$0.515320\pi$
$20$	3.54285	0.792205
$21$	−2.20082	−0.480258
$22$	3.05436	0.651192
$23$	−3.02899	−0.631588	−0.315794	−	0.948828i	$-0.602271\pi$
$23$	−3.02899	−0.631588	−0.315794	+	0.948828i	$0.602271\pi$
$24$	0.562802	0.114882
$25$	7.55178	1.51036
$26$	−1.03133	−0.202261
$27$	−3.19855	−0.615561
$28$	−3.91047	−0.739009
$29$	1.92252	0.357002	0.178501	−	0.983940i	$-0.442875\pi$
$29$	1.92252	0.357002	0.178501	+	0.983940i	$0.442875\pi$
$30$	1.99392	0.364039
$31$	4.06878	0.730775	0.365387	−	0.930856i	$-0.380937\pi$
$31$	4.06878	0.730775	0.365387	+	0.930856i	$0.380937\pi$
$32$	1.00000	0.176777
$33$	1.71900	0.299240
$34$	−7.77376	−1.33319
$35$	−13.8542	−2.34179
$36$	−2.68325	−0.447209
$37$	−9.25629	−1.52172	−0.760862	−	0.648914i	$-0.775224\pi$
$37$	−9.25629	−1.52172	−0.760862	+	0.648914i	$0.775224\pi$
$38$	−0.419428	−0.0680402
$39$	−0.580438	−0.0929444
$40$	3.54285	0.560174
$41$	−6.45288	−1.00777	−0.503885	−	0.863771i	$-0.668096\pi$
$41$	−6.45288	−1.00777	−0.503885	+	0.863771i	$0.668096\pi$
$42$	−2.20082	−0.339594
$43$	−11.1616	−1.70212	−0.851062	−	0.525065i	$-0.824041\pi$
$43$	−11.1616	−1.70212	−0.851062	+	0.525065i	$0.824041\pi$
$44$	3.05436	0.460462
$45$	−9.50636	−1.41712
$46$	−3.02899	−0.446600
$47$	−8.17335	−1.19221	−0.596103	−	0.802908i	$-0.703285\pi$
$47$	−8.17335	−1.19221	−0.596103	+	0.802908i	$0.703285\pi$
$48$	0.562802	0.0812335
$49$	8.29174	1.18453
$50$	7.55178	1.06798
$51$	−4.37509	−0.612635
$52$	−1.03133	−0.143020
$53$	5.88657	0.808582	0.404291	−	0.914630i	$-0.367518\pi$
$53$	5.88657	0.808582	0.404291	+	0.914630i	$0.367518\pi$
$54$	−3.19855	−0.435267
$55$	10.8211	1.45912
$56$	−3.91047	−0.522558
$57$	−0.236055	−0.0312663
$58$	1.92252	0.252439
$59$	14.2237	1.85177	0.925886	−	0.377803i	$-0.123320\pi$
$59$	14.2237	1.85177	0.925886	+	0.377803i	$0.123320\pi$
$60$	1.99392	0.257414
$61$	1.47291	0.188587	0.0942936	−	0.995544i	$-0.469941\pi$
$61$	1.47291	0.188587	0.0942936	+	0.995544i	$0.469941\pi$
$62$	4.06878	0.516736
$63$	10.4928	1.32196
$64$	1.00000	0.125000
$65$	−3.65386	−0.453206
$66$	1.71900	0.211595
$67$	1.76992	0.216230	0.108115	−	0.994138i	$-0.465519\pi$
$67$	1.76992	0.216230	0.108115	+	0.994138i	$0.465519\pi$
$68$	−7.77376	−0.942706
$69$	−1.70472	−0.205224
$70$	−13.8542	−1.65589
$71$	−16.0914	−1.90970	−0.954848	−	0.297096i	$-0.903982\pi$
$71$	−16.0914	−1.90970	−0.954848	+	0.297096i	$0.903982\pi$
$72$	−2.68325	−0.316224
$73$	2.43347	0.284816	0.142408	−	0.989808i	$-0.454515\pi$
$73$	2.43347	0.284816	0.142408	+	0.989808i	$0.454515\pi$
$74$	−9.25629	−1.07602
$75$	4.25016	0.490766
$76$	−0.419428	−0.0481117
$77$	−11.9440	−1.36114
$78$	−0.580438	−0.0657216
$79$	−7.00005	−0.787567	−0.393783	−	0.919203i	$-0.628834\pi$
$79$	−7.00005	−0.787567	−0.393783	+	0.919203i	$0.628834\pi$
$80$	3.54285	0.396103
$81$	6.24961	0.694401
$82$	−6.45288	−0.712601
$83$	−7.62795	−0.837277	−0.418638	−	0.908153i	$-0.637492\pi$
$83$	−7.62795	−0.837277	−0.418638	+	0.908153i	$0.637492\pi$
$84$	−2.20082	−0.240129
$85$	−27.5412	−2.98727
$86$	−11.1616	−1.20358
$87$	1.08200	0.116002
$88$	3.05436	0.325596
$89$	−5.63602	−0.597417	−0.298709	−	0.954344i	$-0.596556\pi$
$89$	−5.63602	−0.597417	−0.298709	+	0.954344i	$0.596556\pi$
$90$	−9.50636	−1.00206
$91$	4.03300	0.422773
$92$	−3.02899	−0.315794
$93$	2.28992	0.237454
$94$	−8.17335	−0.843016
$95$	−1.48597	−0.152457
$96$	0.562802	0.0574408
$97$	13.7798	1.39912	0.699562	−	0.714572i	$-0.253378\pi$
$97$	13.7798	1.39912	0.699562	+	0.714572i	$0.253378\pi$
$98$	8.29174	0.837593
$99$	−8.19563	−0.823691
$100$	7.55178	0.755178
$101$	−11.3031	−1.12470	−0.562349	−	0.826900i	$-0.690102\pi$
$101$	−11.3031	−1.12470	−0.562349	+	0.826900i	$0.690102\pi$
$102$	−4.37509	−0.433198
$103$	12.3814	1.21997	0.609987	−	0.792411i	$-0.291174\pi$
$103$	12.3814	1.21997	0.609987	+	0.792411i	$0.291174\pi$
$104$	−1.03133	−0.101131
$105$	−7.79717	−0.760926
$106$	5.88657	0.571754
$107$	−10.9308	−1.05672	−0.528358	−	0.849022i	$-0.677192\pi$
$107$	−10.9308	−1.05672	−0.528358	+	0.849022i	$0.677192\pi$
$108$	−3.19855	−0.307781
$109$	8.51824	0.815900	0.407950	−	0.913004i	$-0.366244\pi$
$109$	8.51824	0.815900	0.407950	+	0.913004i	$0.366244\pi$
$110$	10.8211	1.03176
$111$	−5.20946	−0.494460
$112$	−3.91047	−0.369504
$113$	−4.80471	−0.451989	−0.225994	−	0.974129i	$-0.572563\pi$
$113$	−4.80471	−0.451989	−0.225994	+	0.974129i	$0.572563\pi$
$114$	−0.236055	−0.0221086
$115$	−10.7312	−1.00069
$116$	1.92252	0.178501
$117$	2.76733	0.255840
$118$	14.2237	1.30940
$119$	30.3990	2.78667
$120$	1.99392	0.182020
$121$	−1.67088	−0.151898
$122$	1.47291	0.133351
$123$	−3.63169	−0.327459
$124$	4.06878	0.365387
$125$	9.04056	0.808612
$126$	10.4928	0.934770
$127$	4.19258	0.372031	0.186016	−	0.982547i	$-0.440443\pi$
$127$	4.19258	0.372031	0.186016	+	0.982547i	$0.440443\pi$
$128$	1.00000	0.0883883
$129$	−6.28176	−0.553078
$130$	−3.65386	−0.320465
$131$	−2.15756	−0.188507	−0.0942534	−	0.995548i	$-0.530046\pi$
$131$	−2.15756	−0.188507	−0.0942534	+	0.995548i	$0.530046\pi$
$132$	1.71900	0.149620
$133$	1.64016	0.142220
$134$	1.76992	0.152897
$135$	−11.3320	−0.975301
$136$	−7.77376	−0.666594
$137$	3.69568	0.315743	0.157872	−	0.987460i	$-0.449537\pi$
$137$	3.69568	0.315743	0.157872	+	0.987460i	$0.449537\pi$
$138$	−1.70472	−0.145116
$139$	5.10298	0.432829	0.216414	−	0.976302i	$-0.430564\pi$
$139$	5.10298	0.432829	0.216414	+	0.976302i	$0.430564\pi$
$140$	−13.8542	−1.17089
$141$	−4.59998	−0.387388
$142$	−16.0914	−1.35036
$143$	−3.15007	−0.263422
$144$	−2.68325	−0.223604
$145$	6.81118	0.565638
$146$	2.43347	0.201395
$147$	4.66661	0.384896
$148$	−9.25629	−0.760862
$149$	−17.6420	−1.44529	−0.722646	−	0.691218i	$-0.757074\pi$
$149$	−17.6420	−1.44529	−0.722646	+	0.691218i	$0.757074\pi$
$150$	4.25016	0.347024
$151$	14.6089	1.18886	0.594429	−	0.804148i	$-0.297378\pi$
$151$	14.6089	1.18886	0.594429	+	0.804148i	$0.297378\pi$
$152$	−0.419428	−0.0340201
$153$	20.8590	1.68635
$154$	−11.9440	−0.962473
$155$	14.4151	1.15785
$156$	−0.580438	−0.0464722
$157$	0.458123	0.0365622	0.0182811	−	0.999833i	$-0.494181\pi$
$157$	0.458123	0.0365622	0.0182811	+	0.999833i	$0.494181\pi$
$158$	−7.00005	−0.556894
$159$	3.31297	0.262736
$160$	3.54285	0.280087
$161$	11.8448	0.933498
$162$	6.24961	0.491016
$163$	4.66456	0.365356	0.182678	−	0.983173i	$-0.441523\pi$
$163$	4.66456	0.365356	0.182678	+	0.983173i	$0.441523\pi$
$164$	−6.45288	−0.503885
$165$	6.09016	0.474119
$166$	−7.62795	−0.592044
$167$	20.9217	1.61897	0.809485	−	0.587140i	$-0.199746\pi$
$167$	20.9217	1.61897	0.809485	+	0.587140i	$0.199746\pi$
$168$	−2.20082	−0.169797
$169$	−11.9363	−0.918181
$170$	−27.5412	−2.11232
$171$	1.12543	0.0860640
$172$	−11.1616	−0.851062
$173$	2.28063	0.173393	0.0866965	−	0.996235i	$-0.472369\pi$
$173$	2.28063	0.173393	0.0866965	+	0.996235i	$0.472369\pi$
$174$	1.08200	0.0820260
$175$	−29.5310	−2.23233
$176$	3.05436	0.230231
$177$	8.00515	0.601704
$178$	−5.63602	−0.422438
$179$	−8.25055	−0.616675	−0.308338	−	0.951277i	$-0.599773\pi$
$179$	−8.25055	−0.616675	−0.308338	+	0.951277i	$0.599773\pi$
$180$	−9.50636	−0.708562
$181$	−9.71209	−0.721894	−0.360947	−	0.932586i	$-0.617546\pi$
$181$	−9.71209	−0.721894	−0.360947	+	0.932586i	$0.617546\pi$
$182$	4.03300	0.298946
$183$	0.828959	0.0612784
$184$	−3.02899	−0.223300
$185$	−32.7936	−2.41104
$186$	2.28992	0.167905
$187$	−23.7439	−1.73632
$188$	−8.17335	−0.596103
$189$	12.5078	0.909810
$190$	−1.48597	−0.107804
$191$	−16.2387	−1.17499	−0.587497	−	0.809226i	$-0.699887\pi$
$191$	−16.2387	−1.17499	−0.587497	+	0.809226i	$0.699887\pi$
$192$	0.562802	0.0406168
$193$	−7.38460	−0.531555	−0.265778	−	0.964034i	$-0.585629\pi$
$193$	−7.38460	−0.531555	−0.265778	+	0.964034i	$0.585629\pi$
$194$	13.7798	0.989330
$195$	−2.05640	−0.147262
$196$	8.29174	0.592267
$197$	−7.23716	−0.515626	−0.257813	−	0.966195i	$-0.583002\pi$
$197$	−7.23716	−0.515626	−0.257813	+	0.966195i	$0.583002\pi$
$198$	−8.19563	−0.582438
$199$	18.8968	1.33956	0.669778	−	0.742562i	$-0.266389\pi$
$199$	18.8968	1.33956	0.669778	+	0.742562i	$0.266389\pi$
$200$	7.55178	0.533991
$201$	0.996113	0.0702604
$202$	−11.3031	−0.795282
$203$	−7.51793	−0.527655
$204$	−4.37509	−0.306318
$205$	−22.8616	−1.59672
$206$	12.3814	0.862653
$207$	8.12755	0.564903
$208$	−1.03133	−0.0715102
$209$	−1.28109	−0.0886145
$210$	−7.79717	−0.538056
$211$	−11.5641	−0.796102	−0.398051	−	0.917363i	$-0.630313\pi$
$211$	−11.5641	−0.796102	−0.398051	+	0.917363i	$0.630313\pi$
$212$	5.88657	0.404291
$213$	−9.05627	−0.620525
$214$	−10.9308	−0.747211
$215$	−39.5438	−2.69686
$216$	−3.19855	−0.217634
$217$	−15.9108	−1.08010
$218$	8.51824	0.576928
$219$	1.36956	0.0925464
$220$	10.8211	0.729561
$221$	8.01734	0.539305
$222$	−5.20946	−0.349636
$223$	13.5446	0.907011	0.453506	−	0.891253i	$-0.350173\pi$
$223$	13.5446	0.907011	0.453506	+	0.891253i	$0.350173\pi$
$224$	−3.91047	−0.261279
$225$	−20.2633	−1.35089
$226$	−4.80471	−0.319604
$227$	−18.1198	−1.20265	−0.601326	−	0.799004i	$-0.705361\pi$
$227$	−18.1198	−1.20265	−0.601326	+	0.799004i	$0.705361\pi$
$228$	−0.236055	−0.0156331
$229$	−0.432568	−0.0285849	−0.0142924	−	0.999898i	$-0.504550\pi$
$229$	−0.432568	−0.0285849	−0.0142924	+	0.999898i	$0.504550\pi$
$230$	−10.7312	−0.707598
$231$	−6.72210	−0.442282
$232$	1.92252	0.126219
$233$	−4.39872	−0.288170	−0.144085	−	0.989565i	$-0.546024\pi$
$233$	−4.39872	−0.288170	−0.144085	+	0.989565i	$0.546024\pi$
$234$	2.76733	0.180906
$235$	−28.9569	−1.88894
$236$	14.2237	0.925886
$237$	−3.93964	−0.255907
$238$	30.3990	1.97048
$239$	−17.9451	−1.16077	−0.580386	−	0.814342i	$-0.697098\pi$
$239$	−17.9451	−1.16077	−0.580386	+	0.814342i	$0.697098\pi$
$240$	1.99392	0.128707
$241$	−13.8190	−0.890163	−0.445081	−	0.895490i	$-0.646825\pi$
$241$	−13.8190	−0.890163	−0.445081	+	0.895490i	$0.646825\pi$
$242$	−1.67088	−0.107408
$243$	13.1129	0.841196
$244$	1.47291	0.0942936
$245$	29.3764	1.87679
$246$	−3.63169	−0.231548
$247$	0.432571	0.0275238
$248$	4.06878	0.258368
$249$	−4.29303	−0.272060
$250$	9.04056	0.571775
$251$	21.5732	1.36169	0.680844	−	0.732428i	$-0.261613\pi$
$251$	21.5732	1.36169	0.680844	+	0.732428i	$0.261613\pi$
$252$	10.4928	0.660982
$253$	−9.25163	−0.581645
$254$	4.19258	0.263066
$255$	−15.5003	−0.970665
$256$	1.00000	0.0625000
$257$	11.6543	0.726978	0.363489	−	0.931599i	$-0.381585\pi$
$257$	11.6543	0.726978	0.363489	+	0.931599i	$0.381585\pi$
$258$	−6.28176	−0.391085
$259$	36.1964	2.24913
$260$	−3.65386	−0.226603
$261$	−5.15860	−0.319309
$262$	−2.15756	−0.133294
$263$	24.7214	1.52439	0.762194	−	0.647349i	$-0.224122\pi$
$263$	24.7214	1.52439	0.762194	+	0.647349i	$0.224122\pi$
$264$	1.71900	0.105797
$265$	20.8552	1.28113
$266$	1.64016	0.100565
$267$	−3.17197	−0.194121
$268$	1.76992	0.108115
$269$	12.4793	0.760879	0.380439	−	0.924806i	$-0.375773\pi$
$269$	12.4793	0.760879	0.380439	+	0.924806i	$0.375773\pi$
$270$	−11.3320	−0.689642
$271$	7.81532	0.474747	0.237373	−	0.971418i	$-0.423714\pi$
$271$	7.81532	0.474747	0.237373	+	0.971418i	$0.423714\pi$
$272$	−7.77376	−0.471353
$273$	2.26978	0.137373
$274$	3.69568	0.223264
$275$	23.0659	1.39092
$276$	−1.70472	−0.102612
$277$	−10.6679	−0.640972	−0.320486	−	0.947253i	$-0.603846\pi$
$277$	−10.6679	−0.640972	−0.320486	+	0.947253i	$0.603846\pi$
$278$	5.10298	0.306056
$279$	−10.9176	−0.653618
$280$	−13.8542	−0.827946
$281$	19.4177	1.15836	0.579182	−	0.815198i	$-0.303372\pi$
$281$	19.4177	1.15836	0.579182	+	0.815198i	$0.303372\pi$
$282$	−4.59998	−0.273925
$283$	−14.3730	−0.854388	−0.427194	−	0.904160i	$-0.640498\pi$
$283$	−14.3730	−0.854388	−0.427194	+	0.904160i	$0.640498\pi$
$284$	−16.0914	−0.954848
$285$	−0.836308	−0.0495386
$286$	−3.15007	−0.186267
$287$	25.2338	1.48950
$288$	−2.68325	−0.158112
$289$	43.4313	2.55478
$290$	6.81118	0.399966
$291$	7.75529	0.454623
$292$	2.43347	0.142408
$293$	−17.8512	−1.04288	−0.521439	−	0.853288i	$-0.674605\pi$
$293$	−17.8512	−1.04288	−0.521439	+	0.853288i	$0.674605\pi$
$294$	4.66661	0.272162
$295$	50.3925	2.93397
$296$	−9.25629	−0.538011
$297$	−9.76953	−0.566885
$298$	−17.6420	−1.02198
$299$	3.12390	0.180660
$300$	4.25016	0.245383
$301$	43.6470	2.51577
$302$	14.6089	0.840649
$303$	−6.36140	−0.365453
$304$	−0.419428	−0.0240559
$305$	5.21831	0.298800
$306$	20.8590	1.19243
$307$	−0.405236	−0.0231280	−0.0115640	−	0.999933i	$-0.503681\pi$
$307$	−0.405236	−0.0231280	−0.0115640	+	0.999933i	$0.503681\pi$
$308$	−11.9440	−0.680571
$309$	6.96828	0.396412
$310$	14.4151	0.818721
$311$	12.3522	0.700426	0.350213	−	0.936670i	$-0.386109\pi$
$311$	12.3522	0.700426	0.350213	+	0.936670i	$0.386109\pi$
$312$	−0.580438	−0.0328608
$313$	−9.15580	−0.517516	−0.258758	−	0.965942i	$-0.583313\pi$
$313$	−9.15580	−0.517516	−0.258758	+	0.965942i	$0.583313\pi$
$314$	0.458123	0.0258534
$315$	37.1743	2.09453
$316$	−7.00005	−0.393783
$317$	−31.3439	−1.76045	−0.880224	−	0.474558i	$-0.842608\pi$
$317$	−31.3439	−1.76045	−0.880224	+	0.474558i	$0.842608\pi$
$318$	3.31297	0.185782
$319$	5.87206	0.328772
$320$	3.54285	0.198051
$321$	−6.15185	−0.343363
$322$	11.8448	0.660083
$323$	3.26053	0.181421
$324$	6.24961	0.347200
$325$	−7.78841	−0.432023
$326$	4.66456	0.258346
$327$	4.79409	0.265114
$328$	−6.45288	−0.356300
$329$	31.9616	1.76210
$330$	6.09016	0.335253
$331$	−22.6447	−1.24467	−0.622333	−	0.782753i	$-0.713815\pi$
$331$	−22.6447	−1.24467	−0.622333	+	0.782753i	$0.713815\pi$
$332$	−7.62795	−0.418638
$333$	24.8370	1.36106
$334$	20.9217	1.14479
$335$	6.27054	0.342596
$336$	−2.20082	−0.120065
$337$	9.64742	0.525529	0.262764	−	0.964860i	$-0.415366\pi$
$337$	9.64742	0.525529	0.262764	+	0.964860i	$0.415366\pi$
$338$	−11.9363	−0.649252
$339$	−2.70410	−0.146867
$340$	−27.5412	−1.49363
$341$	12.4275	0.672988
$342$	1.12543	0.0608564
$343$	−5.05132	−0.272746
$344$	−11.1616	−0.601792
$345$	−6.03957	−0.325160
$346$	2.28063	0.122607
$347$	3.49293	0.187510	0.0937550	−	0.995595i	$-0.470113\pi$
$347$	3.49293	0.187510	0.0937550	+	0.995595i	$0.470113\pi$
$348$	1.08200	0.0580011
$349$	−12.2111	−0.653643	−0.326822	−	0.945086i	$-0.605978\pi$
$349$	−12.2111	−0.653643	−0.326822	+	0.945086i	$0.605978\pi$
$350$	−29.5310	−1.57850
$351$	3.29877	0.176076
$352$	3.05436	0.162798
$353$	6.49707	0.345804	0.172902	−	0.984939i	$-0.444686\pi$
$353$	6.49707	0.345804	0.172902	+	0.984939i	$0.444686\pi$
$354$	8.00515	0.425469
$355$	−57.0093	−3.02574
$356$	−5.63602	−0.298709
$357$	17.1086	0.905485
$358$	−8.25055	−0.436055
$359$	−20.4258	−1.07803	−0.539016	−	0.842295i	$-0.681204\pi$
$359$	−20.4258	−1.07803	−0.539016	+	0.842295i	$0.681204\pi$
$360$	−9.50636	−0.501029
$361$	−18.8241	−0.990741
$362$	−9.71209	−0.510456
$363$	−0.940373	−0.0493568
$364$	4.03300	0.211387
$365$	8.62141	0.451265
$366$	0.828959	0.0433304
$367$	−22.8671	−1.19365	−0.596826	−	0.802371i	$-0.703572\pi$
$367$	−22.8671	−1.19365	−0.596826	+	0.802371i	$0.703572\pi$
$368$	−3.02899	−0.157897
$369$	17.3147	0.901367
$370$	−32.7936	−1.70486
$371$	−23.0192	−1.19510
$372$	2.28992	0.118727
$373$	3.38024	0.175022	0.0875112	−	0.996164i	$-0.472109\pi$
$373$	3.38024	0.175022	0.0875112	+	0.996164i	$0.472109\pi$
$374$	−23.7439	−1.22777
$375$	5.08805	0.262746
$376$	−8.17335	−0.421508
$377$	−1.98276	−0.102117
$378$	12.5078	0.643333
$379$	24.1916	1.24264	0.621318	−	0.783558i	$-0.286597\pi$
$379$	24.1916	1.24264	0.621318	+	0.783558i	$0.286597\pi$
$380$	−1.48597	−0.0762287
$381$	2.35959	0.120886
$382$	−16.2387	−0.830847
$383$	−25.5396	−1.30501	−0.652505	−	0.757784i	$-0.726282\pi$
$383$	−25.5396	−1.30501	−0.652505	+	0.757784i	$0.726282\pi$
$384$	0.562802	0.0287204
$385$	−42.3157	−2.15661
$386$	−7.38460	−0.375866
$387$	29.9493	1.52241
$388$	13.7798	0.699562
$389$	19.7660	1.00218	0.501089	−	0.865396i	$-0.332933\pi$
$389$	19.7660	1.00218	0.501089	+	0.865396i	$0.332933\pi$
$390$	−2.05640	−0.104130
$391$	23.5466	1.19080
$392$	8.29174	0.418796
$393$	−1.21428	−0.0612523
$394$	−7.23716	−0.364603
$395$	−24.8001	−1.24783
$396$	−8.19563	−0.411846
$397$	15.5918	0.782532	0.391266	−	0.920278i	$-0.372037\pi$
$397$	15.5918	0.782532	0.391266	+	0.920278i	$0.372037\pi$
$398$	18.8968	0.947209
$399$	0.923086	0.0462121
$400$	7.55178	0.377589
$401$	10.6454	0.531608	0.265804	−	0.964027i	$-0.414363\pi$
$401$	10.6454	0.531608	0.265804	+	0.964027i	$0.414363\pi$
$402$	0.996113	0.0496816
$403$	−4.19627	−0.209031
$404$	−11.3031	−0.562349
$405$	22.1414	1.10022
$406$	−7.51793	−0.373109
$407$	−28.2720	−1.40139
$408$	−4.37509	−0.216599
$409$	8.11595	0.401308	0.200654	−	0.979662i	$-0.435693\pi$
$409$	8.11595	0.401308	0.200654	+	0.979662i	$0.435693\pi$
$410$	−22.8616	−1.12905
$411$	2.07994	0.102596
$412$	12.3814	0.609987
$413$	−55.6214	−2.73695
$414$	8.12755	0.399447
$415$	−27.0247	−1.32659
$416$	−1.03133	−0.0505653
$417$	2.87197	0.140641
$418$	−1.28109	−0.0626599
$419$	39.5582	1.93254	0.966272	−	0.257522i	$-0.0829061\pi$
$419$	39.5582	1.93254	0.966272	+	0.257522i	$0.0829061\pi$
$420$	−7.79717	−0.380463
$421$	34.1344	1.66361	0.831805	−	0.555068i	$-0.187308\pi$
$421$	34.1344	1.66361	0.831805	+	0.555068i	$0.187308\pi$
$422$	−11.5641	−0.562929
$423$	21.9312	1.06633
$424$	5.88657	0.285877
$425$	−58.7057	−2.84764
$426$	−9.05627	−0.438778
$427$	−5.75978	−0.278735
$428$	−10.9308	−0.528358
$429$	−1.77287	−0.0855948
$430$	−39.5438	−1.90697
$431$	19.3481	0.931965	0.465983	−	0.884794i	$-0.345701\pi$
$431$	19.3481	0.931965	0.465983	+	0.884794i	$0.345701\pi$
$432$	−3.19855	−0.153890
$433$	−4.95190	−0.237973	−0.118986	−	0.992896i	$-0.537965\pi$
$433$	−4.95190	−0.237973	−0.118986	+	0.992896i	$0.537965\pi$
$434$	−15.9108	−0.763744
$435$	3.83335	0.183795
$436$	8.51824	0.407950
$437$	1.27044	0.0607736
$438$	1.36956	0.0654402
$439$	−39.6818	−1.89391	−0.946955	−	0.321366i	$-0.895858\pi$
$439$	−39.6818	−1.89391	−0.946955	+	0.321366i	$0.895858\pi$
$440$	10.8211	0.515878
$441$	−22.2488	−1.05947
$442$	8.01734	0.381346
$443$	−7.79321	−0.370266	−0.185133	−	0.982713i	$-0.559272\pi$
$443$	−7.79321	−0.370266	−0.185133	+	0.982713i	$0.559272\pi$
$444$	−5.20946	−0.247230
$445$	−19.9676	−0.946554
$446$	13.5446	0.641354
$447$	−9.92899	−0.469625
$448$	−3.91047	−0.184752
$449$	28.3246	1.33672	0.668361	−	0.743837i	$-0.266996\pi$
$449$	28.3246	1.33672	0.668361	+	0.743837i	$0.266996\pi$
$450$	−20.2633	−0.955222
$451$	−19.7094	−0.928080
$452$	−4.80471	−0.225994
$453$	8.22194	0.386300
$454$	−18.1198	−0.850404
$455$	14.2883	0.669846
$456$	−0.236055	−0.0110543
$457$	13.5261	0.632726	0.316363	−	0.948638i	$-0.397538\pi$
$457$	13.5261	0.632726	0.316363	+	0.948638i	$0.397538\pi$
$458$	−0.432568	−0.0202126
$459$	24.8647	1.16059
$460$	−10.7312	−0.500347
$461$	−11.5165	−0.536379	−0.268189	−	0.963366i	$-0.586425\pi$
$461$	−11.5165	−0.536379	−0.268189	+	0.963366i	$0.586425\pi$
$462$	−6.72210	−0.312740
$463$	13.1358	0.610471	0.305236	−	0.952277i	$-0.401265\pi$
$463$	13.1358	0.610471	0.305236	+	0.952277i	$0.401265\pi$
$464$	1.92252	0.0892506
$465$	8.11284	0.376224
$466$	−4.39872	−0.203767
$467$	−15.7418	−0.728444	−0.364222	−	0.931312i	$-0.618665\pi$
$467$	−15.7418	−0.728444	−0.364222	+	0.931312i	$0.618665\pi$
$468$	2.76733	0.127920
$469$	−6.92120	−0.319591
$470$	−28.9569	−1.33568
$471$	0.257833	0.0118803
$472$	14.2237	0.654700
$473$	−34.0915	−1.56753
$474$	−3.93964	−0.180954
$475$	−3.16743	−0.145332
$476$	30.3990	1.39334
$477$	−15.7952	−0.723210
$478$	−17.9451	−0.820789
$479$	38.5513	1.76146	0.880728	−	0.473623i	$-0.157054\pi$
$479$	38.5513	1.76146	0.880728	+	0.473623i	$0.157054\pi$
$480$	1.99392	0.0910098
$481$	9.54633	0.435275
$482$	−13.8190	−0.629440
$483$	6.66626	0.303325
$484$	−1.67088	−0.0759489
$485$	48.8197	2.21679
$486$	13.1129	0.594815
$487$	−1.53491	−0.0695535	−0.0347767	−	0.999395i	$-0.511072\pi$
$487$	−1.53491	−0.0695535	−0.0347767	+	0.999395i	$0.511072\pi$
$488$	1.47291	0.0666757
$489$	2.62522	0.118717
$490$	29.3764	1.32709
$491$	19.8170	0.894330	0.447165	−	0.894451i	$-0.352434\pi$
$491$	19.8170	0.894330	0.447165	+	0.894451i	$0.352434\pi$
$492$	−3.63169	−0.163729
$493$	−14.9452	−0.673097
$494$	0.432571	0.0194623
$495$	−29.0359	−1.30506
$496$	4.06878	0.182694
$497$	62.9248	2.82256
$498$	−4.29303	−0.192375
$499$	40.2678	1.80264	0.901318	−	0.433158i	$-0.142601\pi$
$499$	40.2678	1.80264	0.901318	+	0.433158i	$0.142601\pi$
$500$	9.04056	0.404306
$501$	11.7748	0.526059
$502$	21.5732	0.962859
$503$	17.0472	0.760097	0.380048	−	0.924967i	$-0.375907\pi$
$503$	17.0472	0.760097	0.380048	+	0.924967i	$0.375907\pi$
$504$	10.4928	0.467385
$505$	−40.0451	−1.78198
$506$	−9.25163	−0.411285
$507$	−6.71781	−0.298348
$508$	4.19258	0.186016
$509$	−30.2329	−1.34005	−0.670024	−	0.742339i	$-0.733716\pi$
$509$	−30.2329	−1.34005	−0.670024	+	0.742339i	$0.733716\pi$
$510$	−15.5003	−0.686364
$511$	−9.51600	−0.420963
$512$	1.00000	0.0441942
$513$	1.34156	0.0592314
$514$	11.6543	0.514051
$515$	43.8654	1.93294
$516$	−6.28176	−0.276539
$517$	−24.9644	−1.09793
$518$	36.1964	1.59038
$519$	1.28354	0.0563413
$520$	−3.65386	−0.160232
$521$	−43.7163	−1.91524	−0.957622	−	0.288027i	$-0.907001\pi$
$521$	−43.7163	−1.91524	−0.957622	+	0.288027i	$0.907001\pi$
$522$	−5.15860	−0.225786
$523$	15.7535	0.688851	0.344426	−	0.938814i	$-0.388074\pi$
$523$	15.7535	0.688851	0.344426	+	0.938814i	$0.388074\pi$
$524$	−2.15756	−0.0942534
$525$	−16.6201	−0.725361
$526$	24.7214	1.07791
$527$	−31.6297	−1.37781
$528$	1.71900	0.0748100
$529$	−13.8252	−0.601097
$530$	20.8552	0.905893
$531$	−38.1659	−1.65626
$532$	1.64016	0.0711099
$533$	6.65507	0.288263
$534$	−3.17197	−0.137264
$535$	−38.7260	−1.67427
$536$	1.76992	0.0764487
$537$	−4.64343	−0.200379
$538$	12.4793	0.538022
$539$	25.3260	1.09087
$540$	−11.3320	−0.487651
$541$	−4.05014	−0.174129	−0.0870645	−	0.996203i	$-0.527749\pi$
$541$	−4.05014	−0.174129	−0.0870645	+	0.996203i	$0.527749\pi$
$542$	7.81532	0.335697
$543$	−5.46599	−0.234568
$544$	−7.77376	−0.333297
$545$	30.1789	1.29272
$546$	2.26978	0.0971377
$547$	23.6662	1.01189	0.505946	−	0.862565i	$-0.331143\pi$
$547$	23.6662	1.01189	0.505946	+	0.862565i	$0.331143\pi$
$548$	3.69568	0.157872
$549$	−3.95220	−0.168676
$550$	23.0659	0.983531
$551$	−0.806357	−0.0343520
$552$	−1.70472	−0.0725578
$553$	27.3735	1.16404
$554$	−10.6679	−0.453236
$555$	−18.4563	−0.783428
$556$	5.10298	0.216414
$557$	4.60299	0.195035	0.0975174	−	0.995234i	$-0.468910\pi$
$557$	4.60299	0.195035	0.0975174	+	0.995234i	$0.468910\pi$
$558$	−10.9176	−0.462178
$559$	11.5113	0.486877
$560$	−13.8542	−0.585446
$561$	−13.3631	−0.564191
$562$	19.4177	0.819087
$563$	−3.75299	−0.158170	−0.0790849	−	0.996868i	$-0.525200\pi$
$563$	−3.75299	−0.158170	−0.0790849	+	0.996868i	$0.525200\pi$
$564$	−4.59998	−0.193694
$565$	−17.0223	−0.716135
$566$	−14.3730	−0.604144
$567$	−24.4389	−1.02634
$568$	−16.0914	−0.675179
$569$	34.8449	1.46077	0.730387	−	0.683034i	$-0.239340\pi$
$569$	34.8449	1.46077	0.730387	+	0.683034i	$0.239340\pi$
$570$	−0.836308	−0.0350291
$571$	3.38722	0.141751	0.0708755	−	0.997485i	$-0.477421\pi$
$571$	3.38722	0.141751	0.0708755	+	0.997485i	$0.477421\pi$
$572$	−3.15007	−0.131711
$573$	−9.13921	−0.381796
$574$	25.2338	1.05324
$575$	−22.8742	−0.953922
$576$	−2.68325	−0.111802
$577$	1.65543	0.0689166	0.0344583	−	0.999406i	$-0.489029\pi$
$577$	1.65543	0.0689166	0.0344583	+	0.999406i	$0.489029\pi$
$578$	43.4313	1.80650
$579$	−4.15607	−0.172720
$580$	6.81118	0.282819
$581$	29.8288	1.23751
$582$	7.75529	0.321467
$583$	17.9797	0.744643
$584$	2.43347	0.100698
$585$	9.80424	0.405355
$586$	−17.8512	−0.737427
$587$	7.18497	0.296555	0.148278	−	0.988946i	$-0.452627\pi$
$587$	7.18497	0.296555	0.148278	+	0.988946i	$0.452627\pi$
$588$	4.66661	0.192448
$589$	−1.70656	−0.0703176
$590$	50.3925	2.07463
$591$	−4.07309	−0.167545
$592$	−9.25629	−0.380431
$593$	−33.2158	−1.36401	−0.682004	−	0.731349i	$-0.738891\pi$
$593$	−33.2158	−1.36401	−0.682004	+	0.731349i	$0.738891\pi$
$594$	−9.76953	−0.400848
$595$	107.699	4.41523
$596$	−17.6420	−0.722646
$597$	10.6351	0.435267
$598$	3.12390	0.127746
$599$	14.4822	0.591727	0.295863	−	0.955230i	$-0.404393\pi$
$599$	14.4822	0.591727	0.295863	+	0.955230i	$0.404393\pi$
$600$	4.25016	0.173512
$601$	22.5407	0.919452	0.459726	−	0.888061i	$-0.347948\pi$
$601$	22.5407	0.919452	0.459726	+	0.888061i	$0.347948\pi$
$602$	43.6470	1.77892
$603$	−4.74913	−0.193400
$604$	14.6089	0.594429
$605$	−5.91966	−0.240668
$606$	−6.36140	−0.258414
$607$	−20.0939	−0.815588	−0.407794	−	0.913074i	$-0.633702\pi$
$607$	−20.0939	−0.815588	−0.407794	+	0.913074i	$0.633702\pi$
$608$	−0.419428	−0.0170101
$609$	−4.23111	−0.171453
$610$	5.21831	0.211283
$611$	8.42945	0.341019
$612$	20.8590	0.843173
$613$	−43.7468	−1.76692	−0.883458	−	0.468510i	$-0.844791\pi$
$613$	−43.7468	−1.76692	−0.883458	+	0.468510i	$0.844791\pi$
$614$	−0.405236	−0.0163540
$615$	−12.8665	−0.518829
$616$	−11.9440	−0.481237
$617$	−5.03693	−0.202779	−0.101389	−	0.994847i	$-0.532329\pi$
$617$	−5.03693	−0.202779	−0.101389	+	0.994847i	$0.532329\pi$
$618$	6.96828	0.280305
$619$	−1.90587	−0.0766034	−0.0383017	−	0.999266i	$-0.512195\pi$
$619$	−1.90587	−0.0766034	−0.0383017	+	0.999266i	$0.512195\pi$
$620$	14.4151	0.578923
$621$	9.68837	0.388781
$622$	12.3522	0.495276
$623$	22.0395	0.882993
$624$	−0.580438	−0.0232361
$625$	−5.72956	−0.229182
$626$	−9.15580	−0.365939
$627$	−0.720998	−0.0287939
$628$	0.458123	0.0182811
$629$	71.9561	2.86908
$630$	37.1743	1.48106
$631$	9.18526	0.365660	0.182830	−	0.983145i	$-0.441474\pi$
$631$	9.18526	0.365660	0.182830	+	0.983145i	$0.441474\pi$
$632$	−7.00005	−0.278447
$633$	−6.50828	−0.258681
$634$	−31.3439	−1.24482
$635$	14.8537	0.589450
$636$	3.31297	0.131368
$637$	−8.55156	−0.338825
$638$	5.87206	0.232477
$639$	43.1772	1.70807
$640$	3.54285	0.140043
$641$	−20.3615	−0.804229	−0.402115	−	0.915589i	$-0.631725\pi$
$641$	−20.3615	−0.804229	−0.402115	+	0.915589i	$0.631725\pi$
$642$	−6.15185	−0.242794
$643$	−40.3082	−1.58960	−0.794800	−	0.606871i	$-0.792424\pi$
$643$	−40.3082	−1.58960	−0.794800	+	0.606871i	$0.792424\pi$
$644$	11.8448	0.466749
$645$	−22.2553	−0.876303
$646$	3.26053	0.128284
$647$	40.8444	1.60576	0.802879	−	0.596142i	$-0.203301\pi$
$647$	40.8444	1.60576	0.802879	+	0.596142i	$0.203301\pi$
$648$	6.24961	0.245508
$649$	43.4444	1.70534
$650$	−7.78841	−0.305486
$651$	−8.95465	−0.350961
$652$	4.66456	0.182678
$653$	−21.8453	−0.854872	−0.427436	−	0.904046i	$-0.640583\pi$
$653$	−21.8453	−0.854872	−0.427436	+	0.904046i	$0.640583\pi$
$654$	4.79409	0.187464
$655$	−7.64390	−0.298672
$656$	−6.45288	−0.251942
$657$	−6.52961	−0.254744
$658$	31.9616	1.24599
$659$	−24.2388	−0.944210	−0.472105	−	0.881542i	$-0.656506\pi$
$659$	−24.2388	−0.944210	−0.472105	+	0.881542i	$0.656506\pi$
$660$	6.09016	0.237059
$661$	−41.6369	−1.61949	−0.809743	−	0.586784i	$-0.800394\pi$
$661$	−41.6369	−1.61949	−0.809743	+	0.586784i	$0.800394\pi$
$662$	−22.6447	−0.880112
$663$	4.51218	0.175239
$664$	−7.62795	−0.296022
$665$	5.81084	0.225335
$666$	24.8370	0.962413
$667$	−5.82328	−0.225478
$668$	20.9217	0.809485
$669$	7.62292	0.294719
$670$	6.27054	0.242252
$671$	4.49881	0.173675
$672$	−2.20082	−0.0848985
$673$	−33.7183	−1.29974	−0.649872	−	0.760043i	$-0.725178\pi$
$673$	−33.7183	−1.29974	−0.649872	+	0.760043i	$0.725178\pi$
$674$	9.64742	0.371605
$675$	−24.1547	−0.929716
$676$	−11.9363	−0.459090
$677$	−22.6845	−0.871837	−0.435918	−	0.899986i	$-0.643576\pi$
$677$	−22.6845	−0.871837	−0.435918	+	0.899986i	$0.643576\pi$
$678$	−2.70410	−0.103850
$679$	−53.8853	−2.06793
$680$	−27.5412	−1.05616
$681$	−10.1979	−0.390783
$682$	12.4275	0.475875
$683$	−43.3545	−1.65892	−0.829458	−	0.558569i	$-0.811350\pi$
$683$	−43.3545	−1.65892	−0.829458	+	0.558569i	$0.811350\pi$
$684$	1.12543	0.0430320
$685$	13.0932	0.500266
$686$	−5.05132	−0.192860
$687$	−0.243450	−0.00928820
$688$	−11.1616	−0.425531
$689$	−6.07102	−0.231287
$690$	−6.03957	−0.229923
$691$	−47.4489	−1.80504	−0.902520	−	0.430647i	$-0.858285\pi$
$691$	−47.4489	−1.80504	−0.902520	+	0.430647i	$0.858285\pi$
$692$	2.28063	0.0866965
$693$	32.0487	1.21743
$694$	3.49293	0.132590
$695$	18.0791	0.685778
$696$	1.08200	0.0410130
$697$	50.1631	1.90006
$698$	−12.2111	−0.462195
$699$	−2.47561	−0.0936362
$700$	−29.5310	−1.11617
$701$	40.3660	1.52460	0.762302	−	0.647221i	$-0.224069\pi$
$701$	40.3660	1.52460	0.762302	+	0.647221i	$0.224069\pi$
$702$	3.29877	0.124504
$703$	3.88235	0.146426
$704$	3.05436	0.115116
$705$	−16.2970	−0.613782
$706$	6.49707	0.244520
$707$	44.2003	1.66232
$708$	8.00515	0.300852
$709$	−2.10693	−0.0791274	−0.0395637	−	0.999217i	$-0.512597\pi$
$709$	−2.10693	−0.0791274	−0.0395637	+	0.999217i	$0.512597\pi$
$710$	−57.0093	−2.13952
$711$	18.7829	0.704414
$712$	−5.63602	−0.211219
$713$	−12.3243	−0.461548
$714$	17.1086	0.640275
$715$	−11.1602	−0.417368
$716$	−8.25055	−0.308338
$717$	−10.0995	−0.377174
$718$	−20.4258	−0.762284
$719$	−8.25798	−0.307971	−0.153985	−	0.988073i	$-0.549211\pi$
$719$	−8.25798	−0.307971	−0.153985	+	0.988073i	$0.549211\pi$
$720$	−9.50636	−0.354281
$721$	−48.4170	−1.80314
$722$	−18.8241	−0.700560
$723$	−7.77739	−0.289244
$724$	−9.71209	−0.360947
$725$	14.5184	0.539200
$726$	−0.940373	−0.0349005
$727$	25.4480	0.943814	0.471907	−	0.881648i	$-0.343566\pi$
$727$	25.4480	0.943814	0.471907	+	0.881648i	$0.343566\pi$
$728$	4.03300	0.149473
$729$	−11.3688	−0.421068
$730$	8.62141	0.319093
$731$	86.7674	3.20921
$732$	0.828959	0.0306392
$733$	−7.29180	−0.269329	−0.134664	−	0.990891i	$-0.542996\pi$
$733$	−7.29180	−0.269329	−0.134664	+	0.990891i	$0.542996\pi$
$734$	−22.8671	−0.844039
$735$	16.5331	0.609833
$736$	−3.02899	−0.111650
$737$	5.40596	0.199131
$738$	17.3147	0.637363
$739$	52.8952	1.94578	0.972890	−	0.231269i	$-0.0742878\pi$
$739$	52.8952	1.94578	0.972890	+	0.231269i	$0.0742878\pi$
$740$	−32.7936	−1.20552
$741$	0.243452	0.00894343
$742$	−23.0192	−0.845062
$743$	−5.11976	−0.187826	−0.0939129	−	0.995580i	$-0.529938\pi$
$743$	−5.11976	−0.187826	−0.0939129	+	0.995580i	$0.529938\pi$
$744$	2.28992	0.0839525
$745$	−62.5031	−2.28994
$746$	3.38024	0.123759
$747$	20.4677	0.748875
$748$	−23.7439	−0.868162
$749$	42.7443	1.56184
$750$	5.08805	0.185789
$751$	−15.9830	−0.583227	−0.291614	−	0.956536i	$-0.594192\pi$
$751$	−15.9830	−0.583227	−0.291614	+	0.956536i	$0.594192\pi$
$752$	−8.17335	−0.298051
$753$	12.1415	0.442459
$754$	−1.98276	−0.0722077
$755$	51.7572	1.88364
$756$	12.5078	0.454905
$757$	−32.5717	−1.18384	−0.591920	−	0.805997i	$-0.701630\pi$
$757$	−32.5717	−1.18384	−0.591920	+	0.805997i	$0.701630\pi$
$758$	24.1916	0.878677
$759$	−5.20684	−0.188996
$760$	−1.48597	−0.0539018
$761$	−12.7129	−0.460841	−0.230420	−	0.973091i	$-0.574010\pi$
$761$	−12.7129	−0.460841	−0.230420	+	0.973091i	$0.574010\pi$
$762$	2.35959	0.0854791
$763$	−33.3103	−1.20591
$764$	−16.2387	−0.587497
$765$	73.9001	2.67186
$766$	−25.5396	−0.922782
$767$	−14.6694	−0.529682
$768$	0.562802	0.0203084
$769$	−32.1290	−1.15860	−0.579300	−	0.815114i	$-0.696674\pi$
$769$	−32.1290	−1.15860	−0.579300	+	0.815114i	$0.696674\pi$
$770$	−42.3157	−1.52495
$771$	6.55909	0.236220
$772$	−7.38460	−0.265778
$773$	38.3274	1.37854	0.689270	−	0.724504i	$-0.257931\pi$
$773$	38.3274	1.37854	0.689270	+	0.724504i	$0.257931\pi$
$774$	29.9493	1.07651
$775$	30.7265	1.10373
$776$	13.7798	0.494665
$777$	20.3714	0.730821
$778$	19.7660	0.708647
$779$	2.70652	0.0969711
$780$	−2.05640	−0.0736310
$781$	−49.1489	−1.75869
$782$	23.5466	0.842026
$783$	−6.14926	−0.219757
$784$	8.29174	0.296134
$785$	1.62306	0.0579295
$786$	−1.21428	−0.0433119
$787$	14.1808	0.505493	0.252746	−	0.967533i	$-0.418666\pi$
$787$	14.1808	0.505493	0.252746	+	0.967533i	$0.418666\pi$
$788$	−7.23716	−0.257813
$789$	13.9133	0.495326
$790$	−24.8001	−0.882348
$791$	18.7886	0.668047
$792$	−8.19563	−0.291219
$793$	−1.51907	−0.0539436
$794$	15.5918	0.553333
$795$	11.7374	0.416282
$796$	18.8968	0.669778
$797$	29.7226	1.05283	0.526414	−	0.850229i	$-0.323536\pi$
$797$	29.7226	1.05283	0.526414	+	0.850229i	$0.323536\pi$
$798$	0.923086	0.0326769
$799$	63.5376	2.24780
$800$	7.55178	0.266996
$801$	15.1229	0.534341
$802$	10.6454	0.375904
$803$	7.43269	0.262294
$804$	0.996113	0.0351302
$805$	41.9642	1.47904
$806$	−4.19627	−0.147807
$807$	7.02340	0.247235
$808$	−11.3031	−0.397641
$809$	−0.498748	−0.0175350	−0.00876751	−	0.999962i	$-0.502791\pi$
$809$	−0.498748	−0.0175350	−0.00876751	+	0.999962i	$0.502791\pi$
$810$	22.1414	0.777970
$811$	48.8785	1.71635	0.858177	−	0.513353i	$-0.171597\pi$
$811$	48.8785	1.71635	0.858177	+	0.513353i	$0.171597\pi$
$812$	−7.51793	−0.263828
$813$	4.39848	0.154261
$814$	−28.2720	−0.990935
$815$	16.5258	0.578874
$816$	−4.37509	−0.153159
$817$	4.68148	0.163784
$818$	8.11595	0.283768
$819$	−10.8216	−0.378136
$820$	−22.8616	−0.798360
$821$	−21.2866	−0.742908	−0.371454	−	0.928451i	$-0.621141\pi$
$821$	−21.2866	−0.742908	−0.371454	+	0.928451i	$0.621141\pi$
$822$	2.07994	0.0725461
$823$	−25.6493	−0.894079	−0.447040	−	0.894514i	$-0.647522\pi$
$823$	−25.6493	−0.894079	−0.447040	+	0.894514i	$0.647522\pi$
$824$	12.3814	0.431326
$825$	12.9815	0.451959
$826$	−55.6214	−1.93532
$827$	−24.5651	−0.854212	−0.427106	−	0.904202i	$-0.640467\pi$
$827$	−24.5651	−0.854212	−0.427106	+	0.904202i	$0.640467\pi$
$828$	8.12755	0.282452
$829$	30.8973	1.07311	0.536553	−	0.843866i	$-0.319726\pi$
$829$	30.8973	1.07311	0.536553	+	0.843866i	$0.319726\pi$
$830$	−27.0247	−0.938040
$831$	−6.00392	−0.208274
$832$	−1.03133	−0.0357551
$833$	−64.4580	−2.23334
$834$	2.87197	0.0994481
$835$	74.1224	2.56511
$836$	−1.28109	−0.0443073
$837$	−13.0142	−0.449836
$838$	39.5582	1.36652
$839$	−15.9211	−0.549659	−0.274829	−	0.961493i	$-0.588621\pi$
$839$	−15.9211	−0.549659	−0.274829	+	0.961493i	$0.588621\pi$
$840$	−7.79717	−0.269028
$841$	−25.3039	−0.872549
$842$	34.1344	1.17635
$843$	10.9283	0.376392
$844$	−11.5641	−0.398051
$845$	−42.2887	−1.45477
$846$	21.9312	0.754009
$847$	6.53390	0.224508
$848$	5.88657	0.202146
$849$	−8.08918	−0.277620
$850$	−58.7057	−2.01359
$851$	28.0372	0.961103
$852$	−9.05627	−0.310263
$853$	−40.1005	−1.37302	−0.686508	−	0.727122i	$-0.740857\pi$
$853$	−40.1005	−1.37302	−0.686508	+	0.727122i	$0.740857\pi$
$854$	−5.75978	−0.197096
$855$	3.98724	0.136361
$856$	−10.9308	−0.373605
$857$	0.809352	0.0276469	0.0138235	−	0.999904i	$-0.495600\pi$
$857$	0.809352	0.0276469	0.0138235	+	0.999904i	$0.495600\pi$
$858$	−1.77287	−0.0605247
$859$	11.2690	0.384493	0.192247	−	0.981347i	$-0.438423\pi$
$859$	11.2690	0.384493	0.192247	+	0.981347i	$0.438423\pi$
$860$	−39.5438	−1.34843
$861$	14.2016	0.483990
$862$	19.3481	0.658999
$863$	1.08403	0.0369009	0.0184504	−	0.999830i	$-0.494127\pi$
$863$	1.08403	0.0369009	0.0184504	+	0.999830i	$0.494127\pi$
$864$	−3.19855	−0.108817
$865$	8.07992	0.274726
$866$	−4.95190	−0.168272
$867$	24.4432	0.830136
$868$	−15.9108	−0.540049
$869$	−21.3807	−0.725290
$870$	3.83335	0.129963
$871$	−1.82538	−0.0618505
$872$	8.51824	0.288464
$873$	−36.9746	−1.25140
$874$	1.27044	0.0429734
$875$	−35.3528	−1.19514
$876$	1.36956	0.0462732
$877$	−54.9553	−1.85571	−0.927854	−	0.372943i	$-0.878349\pi$
$877$	−54.9553	−1.85571	−0.927854	+	0.372943i	$0.878349\pi$
$878$	−39.6818	−1.33920
$879$	−10.0467	−0.338867
$880$	10.8211	0.364781
$881$	−6.16347	−0.207652	−0.103826	−	0.994595i	$-0.533109\pi$
$881$	−6.16347	−0.207652	−0.103826	+	0.994595i	$0.533109\pi$
$882$	−22.2488	−0.749158
$883$	31.6199	1.06410	0.532048	−	0.846714i	$-0.321423\pi$
$883$	31.6199	1.06410	0.532048	+	0.846714i	$0.321423\pi$
$884$	8.01734	0.269652
$885$	28.3610	0.953346
$886$	−7.79321	−0.261818
$887$	1.20785	0.0405558	0.0202779	−	0.999794i	$-0.493545\pi$
$887$	1.20785	0.0405558	0.0202779	+	0.999794i	$0.493545\pi$
$888$	−5.20946	−0.174818
$889$	−16.3949	−0.549868
$890$	−19.9676	−0.669315
$891$	19.0886	0.639491
$892$	13.5446	0.453506
$893$	3.42813	0.114718
$894$	−9.92899	−0.332075
$895$	−29.2305	−0.977067
$896$	−3.91047	−0.130639
$897$	1.75814	0.0587026
$898$	28.3246	0.945205
$899$	7.82229	0.260888
$900$	−20.2633	−0.675444
$901$	−45.7607	−1.52451
$902$	−19.7094	−0.656252
$903$	24.5646	0.817459
$904$	−4.80471	−0.159802
$905$	−34.4085	−1.14378
$906$	8.22194	0.273156
$907$	8.93794	0.296780	0.148390	−	0.988929i	$-0.452591\pi$
$907$	8.93794	0.296780	0.148390	+	0.988929i	$0.452591\pi$
$908$	−18.1198	−0.601326
$909$	30.3290	1.00595
$910$	14.2883	0.473653
$911$	4.46544	0.147947	0.0739733	−	0.997260i	$-0.476432\pi$
$911$	4.46544	0.147947	0.0739733	+	0.997260i	$0.476432\pi$
$912$	−0.236055	−0.00781657
$913$	−23.2985	−0.771069
$914$	13.5261	0.447405
$915$	2.93688	0.0970902
$916$	−0.432568	−0.0142924
$917$	8.43706	0.278616
$918$	24.8647	0.820659
$919$	−10.5009	−0.346394	−0.173197	−	0.984887i	$-0.555410\pi$
$919$	−10.5009	−0.346394	−0.173197	+	0.984887i	$0.555410\pi$
$920$	−10.7312	−0.353799
$921$	−0.228068	−0.00751509
$922$	−11.5165	−0.379277
$923$	16.5956	0.546251
$924$	−6.72210	−0.221141
$925$	−69.9014	−2.29834
$926$	13.1358	0.431669
$927$	−33.2224	−1.09117
$928$	1.92252	0.0631097
$929$	8.25330	0.270782	0.135391	−	0.990792i	$-0.456771\pi$
$929$	8.25330	0.270782	0.135391	+	0.990792i	$0.456771\pi$
$930$	8.11284	0.266030
$931$	−3.47779	−0.113980
$932$	−4.39872	−0.144085
$933$	6.95182	0.227592
$934$	−15.7418	−0.515088
$935$	−84.1209	−2.75105
$936$	2.76733	0.0904531
$937$	−39.2629	−1.28266	−0.641332	−	0.767264i	$-0.721618\pi$
$937$	−39.2629	−1.28266	−0.641332	+	0.767264i	$0.721618\pi$
$938$	−6.92120	−0.225985
$939$	−5.15291	−0.168159
$940$	−28.9569	−0.944471
$941$	−35.9892	−1.17321	−0.586607	−	0.809872i	$-0.699537\pi$
$941$	−35.9892	−1.17321	−0.586607	+	0.809872i	$0.699537\pi$
$942$	0.257833	0.00840065
$943$	19.5457	0.636495
$944$	14.2237	0.462943
$945$	44.3133	1.44151
$946$	−34.0915	−1.10841
$947$	46.3713	1.50686	0.753432	−	0.657526i	$-0.228397\pi$
$947$	46.3713	1.50686	0.753432	+	0.657526i	$0.228397\pi$
$948$	−3.93964	−0.127954
$949$	−2.50972	−0.0814690
$950$	−3.16743	−0.102765
$951$	−17.6404	−0.572030
$952$	30.3990	0.985238
$953$	15.9731	0.517420	0.258710	−	0.965955i	$-0.416703\pi$
$953$	15.9731	0.517420	0.258710	+	0.965955i	$0.416703\pi$
$954$	−15.7952	−0.511387
$955$	−57.5314	−1.86167
$956$	−17.9451	−0.580386
$957$	3.30481	0.106829
$958$	38.5513	1.24554
$959$	−14.4518	−0.466674
$960$	1.99392	0.0643536
$961$	−14.4450	−0.465969
$962$	9.54633	0.307786
$963$	29.3300	0.945145
$964$	−13.8190	−0.445081
$965$	−26.1625	−0.842201
$966$	6.66626	0.214483
$967$	17.8989	0.575591	0.287796	−	0.957692i	$-0.407078\pi$
$967$	17.8989	0.575591	0.287796	+	0.957692i	$0.407078\pi$
$968$	−1.67088	−0.0537040
$969$	1.83504	0.0589499
$970$	48.8197	1.56750
$971$	41.7601	1.34014	0.670072	−	0.742296i	$-0.266263\pi$
$971$	41.7601	1.34014	0.670072	+	0.742296i	$0.266263\pi$
$972$	13.1129	0.420598
$973$	−19.9550	−0.639728
$974$	−1.53491	−0.0491817
$975$	−4.38333	−0.140379
$976$	1.47291	0.0471468
$977$	2.89516	0.0926244	0.0463122	−	0.998927i	$-0.485253\pi$
$977$	2.89516	0.0926244	0.0463122	+	0.998927i	$0.485253\pi$
$978$	2.62522	0.0839454
$979$	−17.2145	−0.550176
$980$	29.3764	0.938394
$981$	−22.8566	−0.729755
$982$	19.8170	0.632387
$983$	5.04761	0.160994	0.0804969	−	0.996755i	$-0.474349\pi$
$983$	5.04761	0.160994	0.0804969	+	0.996755i	$0.474349\pi$
$984$	−3.63169	−0.115774
$985$	−25.6401	−0.816963
$986$	−14.9452	−0.475951
$987$	17.9881	0.572566
$988$	0.432571	0.0137619
$989$	33.8083	1.07504
$990$	−29.0359	−0.922820
$991$	21.7139	0.689766	0.344883	−	0.938646i	$-0.387919\pi$
$991$	21.7139	0.689766	0.344883	+	0.938646i	$0.387919\pi$
$992$	4.06878	0.129184
$993$	−12.7445	−0.404434
$994$	62.9248	1.99585
$995$	66.9483	2.12241
$996$	−4.29303	−0.136030
$997$	−15.0742	−0.477405	−0.238702	−	0.971093i	$-0.576722\pi$
$997$	−15.0742	−0.477405	−0.238702	+	0.971093i	$0.576722\pi$
$998$	40.2678	1.27466
$999$	29.6067	0.936714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.43	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.43	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.562802 q^{3} +1.00000 q^{4} +3.54285 q^{5} +0.562802 q^{6} -3.91047 q^{7} +1.00000 q^{8} -2.68325 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.562802 q^{3} +1.00000 q^{4} +3.54285 q^{5} +0.562802 q^{6} -3.91047 q^{7} +1.00000 q^{8} -2.68325 q^{9} +3.54285 q^{10} +3.05436 q^{11} +0.562802 q^{12} -1.03133 q^{13} -3.91047 q^{14} +1.99392 q^{15} +1.00000 q^{16} -7.77376 q^{17} -2.68325 q^{18} -0.419428 q^{19} +3.54285 q^{20} -2.20082 q^{21} +3.05436 q^{22} -3.02899 q^{23} +0.562802 q^{24} +7.55178 q^{25} -1.03133 q^{26} -3.19855 q^{27} -3.91047 q^{28} +1.92252 q^{29} +1.99392 q^{30} +4.06878 q^{31} +1.00000 q^{32} +1.71900 q^{33} -7.77376 q^{34} -13.8542 q^{35} -2.68325 q^{36} -9.25629 q^{37} -0.419428 q^{38} -0.580438 q^{39} +3.54285 q^{40} -6.45288 q^{41} -2.20082 q^{42} -11.1616 q^{43} +3.05436 q^{44} -9.50636 q^{45} -3.02899 q^{46} -8.17335 q^{47} +0.562802 q^{48} +8.29174 q^{49} +7.55178 q^{50} -4.37509 q^{51} -1.03133 q^{52} +5.88657 q^{53} -3.19855 q^{54} +10.8211 q^{55} -3.91047 q^{56} -0.236055 q^{57} +1.92252 q^{58} +14.2237 q^{59} +1.99392 q^{60} +1.47291 q^{61} +4.06878 q^{62} +10.4928 q^{63} +1.00000 q^{64} -3.65386 q^{65} +1.71900 q^{66} +1.76992 q^{67} -7.77376 q^{68} -1.70472 q^{69} -13.8542 q^{70} -16.0914 q^{71} -2.68325 q^{72} +2.43347 q^{73} -9.25629 q^{74} +4.25016 q^{75} -0.419428 q^{76} -11.9440 q^{77} -0.580438 q^{78} -7.00005 q^{79} +3.54285 q^{80} +6.24961 q^{81} -6.45288 q^{82} -7.62795 q^{83} -2.20082 q^{84} -27.5412 q^{85} -11.1616 q^{86} +1.08200 q^{87} +3.05436 q^{88} -5.63602 q^{89} -9.50636 q^{90} +4.03300 q^{91} -3.02899 q^{92} +2.28992 q^{93} -8.17335 q^{94} -1.48597 q^{95} +0.562802 q^{96} +13.7798 q^{97} +8.29174 q^{98} -8.19563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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