LMFDB - Embedded newform 8007.2.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70394 q^{2} -1.00000 q^{3} +0.903397 q^{4} +3.92360 q^{5} +1.70394 q^{6} -2.84859 q^{7} +1.86854 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.70394 q^{2} -1.00000 q^{3} +0.903397 q^{4} +3.92360 q^{5} +1.70394 q^{6} -2.84859 q^{7} +1.86854 q^{8} +1.00000 q^{9} -6.68557 q^{10} -1.86713 q^{11} -0.903397 q^{12} +6.59965 q^{13} +4.85382 q^{14} -3.92360 q^{15} -4.99067 q^{16} +1.00000 q^{17} -1.70394 q^{18} +5.88070 q^{19} +3.54457 q^{20} +2.84859 q^{21} +3.18147 q^{22} +8.09177 q^{23} -1.86854 q^{24} +10.3947 q^{25} -11.2454 q^{26} -1.00000 q^{27} -2.57341 q^{28} +7.49767 q^{29} +6.68557 q^{30} -0.0109314 q^{31} +4.76669 q^{32} +1.86713 q^{33} -1.70394 q^{34} -11.1767 q^{35} +0.903397 q^{36} -3.18729 q^{37} -10.0203 q^{38} -6.59965 q^{39} +7.33141 q^{40} +8.13433 q^{41} -4.85382 q^{42} +8.10773 q^{43} -1.68676 q^{44} +3.92360 q^{45} -13.7879 q^{46} +5.27611 q^{47} +4.99067 q^{48} +1.11447 q^{49} -17.7118 q^{50} -1.00000 q^{51} +5.96210 q^{52} +1.77834 q^{53} +1.70394 q^{54} -7.32587 q^{55} -5.32271 q^{56} -5.88070 q^{57} -12.7755 q^{58} +6.72972 q^{59} -3.54457 q^{60} +9.82087 q^{61} +0.0186265 q^{62} -2.84859 q^{63} +1.85920 q^{64} +25.8944 q^{65} -3.18147 q^{66} -4.68216 q^{67} +0.903397 q^{68} -8.09177 q^{69} +19.0444 q^{70} -7.18037 q^{71} +1.86854 q^{72} +3.29779 q^{73} +5.43093 q^{74} -10.3947 q^{75} +5.31261 q^{76} +5.31869 q^{77} +11.2454 q^{78} -9.25247 q^{79} -19.5814 q^{80} +1.00000 q^{81} -13.8604 q^{82} +5.74483 q^{83} +2.57341 q^{84} +3.92360 q^{85} -13.8151 q^{86} -7.49767 q^{87} -3.48881 q^{88} -3.90125 q^{89} -6.68557 q^{90} -18.7997 q^{91} +7.31008 q^{92} +0.0109314 q^{93} -8.99015 q^{94} +23.0735 q^{95} -4.76669 q^{96} -10.7592 q^{97} -1.89899 q^{98} -1.86713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−1.70394	−1.20486	−0.602432	−	0.798170i	$-0.705802\pi$
$2$	−1.70394	−1.20486	−0.602432	+	0.798170i	$0.705802\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.903397	0.451698
$5$	3.92360	1.75469	0.877344	−	0.479862i	$-0.159313\pi$
$5$	3.92360	1.75469	0.877344	+	0.479862i	$0.159313\pi$
$6$	1.70394	0.695629
$7$	−2.84859	−1.07667	−0.538333	−	0.842732i	$-0.680946\pi$
$7$	−2.84859	−1.07667	−0.538333	+	0.842732i	$0.680946\pi$
$8$	1.86854	0.660629
$9$	1.00000	0.333333
$10$	−6.68557	−2.11416
$11$	−1.86713	−0.562961	−0.281480	−	0.959567i	$-0.590825\pi$
$11$	−1.86713	−0.562961	−0.281480	+	0.959567i	$0.590825\pi$
$12$	−0.903397	−0.260788
$13$	6.59965	1.83041	0.915207	−	0.402984i	$-0.132027\pi$
$13$	6.59965	1.83041	0.915207	+	0.402984i	$0.132027\pi$
$14$	4.85382	1.29724
$15$	−3.92360	−1.01307
$16$	−4.99067	−1.24767
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.70394	−0.401621
$19$	5.88070	1.34913	0.674563	−	0.738218i	$-0.264332\pi$
$19$	5.88070	1.34913	0.674563	+	0.738218i	$0.264332\pi$
$20$	3.54457	0.792590
$21$	2.84859	0.621614
$22$	3.18147	0.678291
$23$	8.09177	1.68725	0.843625	−	0.536933i	$-0.180417\pi$
$23$	8.09177	1.68725	0.843625	+	0.536933i	$0.180417\pi$
$24$	−1.86854	−0.381414
$25$	10.3947	2.07893
$26$	−11.2454	−2.20540
$27$	−1.00000	−0.192450
$28$	−2.57341	−0.486328
$29$	7.49767	1.39228	0.696141	−	0.717905i	$-0.254899\pi$
$29$	7.49767	1.39228	0.696141	+	0.717905i	$0.254899\pi$
$30$	6.68557	1.22061
$31$	−0.0109314	−0.00196334	−0.000981672	−	1.00000i	$-0.500312\pi$
$31$	−0.0109314	−0.00196334	−0.000981672		1.00000i	$0.500312\pi$
$32$	4.76669	0.842640
$33$	1.86713	0.325025
$34$	−1.70394	−0.292223
$35$	−11.1767	−1.88921
$36$	0.903397	0.150566
$37$	−3.18729	−0.523987	−0.261993	−	0.965070i	$-0.584380\pi$
$37$	−3.18729	−0.523987	−0.261993	+	0.965070i	$0.584380\pi$
$38$	−10.0203	−1.62551
$39$	−6.59965	−1.05679
$40$	7.33141	1.15920
$41$	8.13433	1.27037	0.635184	−	0.772361i	$-0.280924\pi$
$41$	8.13433	1.27037	0.635184	+	0.772361i	$0.280924\pi$
$42$	−4.85382	−0.748960
$43$	8.10773	1.23642	0.618209	−	0.786014i	$-0.287859\pi$
$43$	8.10773	1.23642	0.618209	+	0.786014i	$0.287859\pi$
$44$	−1.68676	−0.254288
$45$	3.92360	0.584896
$46$	−13.7879	−2.03291
$47$	5.27611	0.769600	0.384800	−	0.923000i	$-0.374270\pi$
$47$	5.27611	0.769600	0.384800	+	0.923000i	$0.374270\pi$
$48$	4.99067	0.720341
$49$	1.11447	0.159211
$50$	−17.7118	−2.50483
$51$	−1.00000	−0.140028
$52$	5.96210	0.826795
$53$	1.77834	0.244274	0.122137	−	0.992513i	$-0.461025\pi$
$53$	1.77834	0.244274	0.122137	+	0.992513i	$0.461025\pi$
$54$	1.70394	0.231876
$55$	−7.32587	−0.987820
$56$	−5.32271	−0.711277
$57$	−5.88070	−0.778918
$58$	−12.7755	−1.67751
$59$	6.72972	0.876134	0.438067	−	0.898942i	$-0.355663\pi$
$59$	6.72972	0.876134	0.438067	+	0.898942i	$0.355663\pi$
$60$	−3.54457	−0.457602
$61$	9.82087	1.25743	0.628717	−	0.777635i	$-0.283581\pi$
$61$	9.82087	1.25743	0.628717	+	0.777635i	$0.283581\pi$
$62$	0.0186265	0.00236556
$63$	−2.84859	−0.358889
$64$	1.85920	0.232400
$65$	25.8944	3.21181
$66$	−3.18147	−0.391612
$67$	−4.68216	−0.572017	−0.286008	−	0.958227i	$-0.592329\pi$
$67$	−4.68216	−0.572017	−0.286008	+	0.958227i	$0.592329\pi$
$68$	0.903397	0.109553
$69$	−8.09177	−0.974134
$70$	19.0444	2.27625
$71$	−7.18037	−0.852153	−0.426077	−	0.904687i	$-0.640105\pi$
$71$	−7.18037	−0.852153	−0.426077	+	0.904687i	$0.640105\pi$
$72$	1.86854	0.220210
$73$	3.29779	0.385977	0.192988	−	0.981201i	$-0.438182\pi$
$73$	3.29779	0.385977	0.192988	+	0.981201i	$0.438182\pi$
$74$	5.43093	0.631333
$75$	−10.3947	−1.20027
$76$	5.31261	0.609398
$77$	5.31869	0.606121
$78$	11.2454	1.27329
$79$	−9.25247	−1.04098	−0.520492	−	0.853866i	$-0.674252\pi$
$79$	−9.25247	−1.04098	−0.520492	+	0.853866i	$0.674252\pi$
$80$	−19.5814	−2.18927
$81$	1.00000	0.111111
$82$	−13.8604	−1.53062
$83$	5.74483	0.630577	0.315288	−	0.948996i	$-0.397899\pi$
$83$	5.74483	0.630577	0.315288	+	0.948996i	$0.397899\pi$
$84$	2.57341	0.280782
$85$	3.92360	0.425574
$86$	−13.8151	−1.48972
$87$	−7.49767	−0.803834
$88$	−3.48881	−0.371908
$89$	−3.90125	−0.413531	−0.206766	−	0.978390i	$-0.566294\pi$
$89$	−3.90125	−0.413531	−0.206766	+	0.978390i	$0.566294\pi$
$90$	−6.68557	−0.704721
$91$	−18.7997	−1.97075
$92$	7.31008	0.762128
$93$	0.0109314	0.00113354
$94$	−8.99015	−0.927264
$95$	23.0735	2.36729
$96$	−4.76669	−0.486499
$97$	−10.7592	−1.09243	−0.546215	−	0.837645i	$-0.683932\pi$
$97$	−10.7592	−1.09243	−0.546215	+	0.837645i	$0.683932\pi$
$98$	−1.89899	−0.191827
$99$	−1.86713	−0.187654
$100$	9.39050	0.939050
$101$	4.23881	0.421777	0.210889	−	0.977510i	$-0.432364\pi$
$101$	4.23881	0.421777	0.210889	+	0.977510i	$0.432364\pi$
$102$	1.70394	0.168715
$103$	−18.0364	−1.77718	−0.888592	−	0.458698i	$-0.848316\pi$
$103$	−18.0364	−1.77718	−0.888592	+	0.458698i	$0.848316\pi$
$104$	12.3317	1.20923
$105$	11.1767	1.09074
$106$	−3.03018	−0.294317
$107$	−15.1586	−1.46544	−0.732720	−	0.680530i	$-0.761750\pi$
$107$	−15.1586	−1.46544	−0.732720	+	0.680530i	$0.761750\pi$
$108$	−0.903397	−0.0869294
$109$	−0.691952	−0.0662770	−0.0331385	−	0.999451i	$-0.510550\pi$
$109$	−0.691952	−0.0662770	−0.0331385	+	0.999451i	$0.510550\pi$
$110$	12.4828	1.19019
$111$	3.18729	0.302524
$112$	14.2164	1.34332
$113$	1.75574	0.165167	0.0825833	−	0.996584i	$-0.473683\pi$
$113$	1.75574	0.165167	0.0825833	+	0.996584i	$0.473683\pi$
$114$	10.0203	0.938490
$115$	31.7489	2.96060
$116$	6.77337	0.628891
$117$	6.59965	0.610138
$118$	−11.4670	−1.05562
$119$	−2.84859	−0.261130
$120$	−7.33141	−0.669264
$121$	−7.51383	−0.683075
$122$	−16.7341	−1.51504
$123$	−8.13433	−0.733448
$124$	−0.00987543	−0.000886840 0
$125$	21.1665	1.89319
$126$	4.85382	0.432412
$127$	6.68609	0.593294	0.296647	−	0.954987i	$-0.404131\pi$
$127$	6.68609	0.593294	0.296647	+	0.954987i	$0.404131\pi$
$128$	−12.7013	−1.12265
$129$	−8.10773	−0.713846
$130$	−44.1224	−3.86979
$131$	2.41675	0.211152	0.105576	−	0.994411i	$-0.466331\pi$
$131$	2.41675	0.211152	0.105576	+	0.994411i	$0.466331\pi$
$132$	1.68676	0.146813
$133$	−16.7517	−1.45256
$134$	7.97810	0.689203
$135$	−3.92360	−0.337690
$136$	1.86854	0.160226
$137$	7.72990	0.660410	0.330205	−	0.943909i	$-0.392882\pi$
$137$	7.72990	0.660410	0.330205	+	0.943909i	$0.392882\pi$
$138$	13.7879	1.17370
$139$	11.0080	0.933688	0.466844	−	0.884340i	$-0.345391\pi$
$139$	11.0080	0.933688	0.466844	+	0.884340i	$0.345391\pi$
$140$	−10.0970	−0.853355
$141$	−5.27611	−0.444329
$142$	12.2349	1.02673
$143$	−12.3224	−1.03045
$144$	−4.99067	−0.415889
$145$	29.4179	2.44302
$146$	−5.61922	−0.465050
$147$	−1.11447	−0.0919203
$148$	−2.87939	−0.236684
$149$	14.3407	1.17483	0.587417	−	0.809284i	$-0.300145\pi$
$149$	14.3407	1.17483	0.587417	+	0.809284i	$0.300145\pi$
$150$	17.7118	1.44616
$151$	4.08244	0.332224	0.166112	−	0.986107i	$-0.446879\pi$
$151$	4.08244	0.332224	0.166112	+	0.986107i	$0.446879\pi$
$152$	10.9883	0.891272
$153$	1.00000	0.0808452
$154$	−9.06270	−0.730293
$155$	−0.0428906	−0.00344506
$156$	−5.96210	−0.477350
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	15.7656	1.25425
$159$	−1.77834	−0.141032
$160$	18.7026	1.47857
$161$	−23.0501	−1.81661
$162$	−1.70394	−0.133874
$163$	−23.0729	−1.80721	−0.903605	−	0.428366i	$-0.859090\pi$
$163$	−23.0729	−1.80721	−0.903605	+	0.428366i	$0.859090\pi$
$164$	7.34853	0.573823
$165$	7.32587	0.570318
$166$	−9.78882	−0.759760
$167$	19.7822	1.53079	0.765394	−	0.643562i	$-0.222544\pi$
$167$	19.7822	1.53079	0.765394	+	0.643562i	$0.222544\pi$
$168$	5.32271	0.410656
$169$	30.5554	2.35042
$170$	−6.68557	−0.512760
$171$	5.88070	0.449708
$172$	7.32450	0.558488
$173$	5.37235	0.408452	0.204226	−	0.978924i	$-0.434532\pi$
$173$	5.37235	0.408452	0.204226	+	0.978924i	$0.434532\pi$
$174$	12.7755	0.968511
$175$	−29.6101	−2.23832
$176$	9.31822	0.702387
$177$	−6.72972	−0.505836
$178$	6.64747	0.498249
$179$	−24.1181	−1.80267	−0.901334	−	0.433124i	$-0.857411\pi$
$179$	−24.1181	−1.80267	−0.901334	+	0.433124i	$0.857411\pi$
$180$	3.54457	0.264197
$181$	7.99070	0.593944	0.296972	−	0.954886i	$-0.404023\pi$
$181$	7.99070	0.593944	0.296972	+	0.954886i	$0.404023\pi$
$182$	32.0335	2.37448
$183$	−9.82087	−0.725979
$184$	15.1198	1.11465
$185$	−12.5057	−0.919434
$186$	−0.0186265	−0.00136576
$187$	−1.86713	−0.136538
$188$	4.76642	0.347627
$189$	2.84859	0.207205
$190$	−39.3158	−2.85227
$191$	17.5796	1.27201	0.636007	−	0.771683i	$-0.280585\pi$
$191$	17.5796	1.27201	0.636007	+	0.771683i	$0.280585\pi$
$192$	−1.85920	−0.134176
$193$	3.15164	0.226860	0.113430	−	0.993546i	$-0.463816\pi$
$193$	3.15164	0.226860	0.113430	+	0.993546i	$0.463816\pi$
$194$	18.3330	1.31623
$195$	−25.8944	−1.85434
$196$	1.00681	0.0719152
$197$	22.4682	1.60079	0.800397	−	0.599470i	$-0.204622\pi$
$197$	22.4682	1.60079	0.800397	+	0.599470i	$0.204622\pi$
$198$	3.18147	0.226097
$199$	2.71973	0.192796	0.0963982	−	0.995343i	$-0.469268\pi$
$199$	2.71973	0.192796	0.0963982	+	0.995343i	$0.469268\pi$
$200$	19.4229	1.37340
$201$	4.68216	0.330254
$202$	−7.22265	−0.508184
$203$	−21.3578	−1.49902
$204$	−0.903397	−0.0632504
$205$	31.9159	2.22910
$206$	30.7329	2.14127
$207$	8.09177	0.562417
$208$	−32.9367	−2.28375
$209$	−10.9800	−0.759504
$210$	−19.0444	−1.31419
$211$	7.38613	0.508482	0.254241	−	0.967141i	$-0.418174\pi$
$211$	7.38613	0.508482	0.254241	+	0.967141i	$0.418174\pi$
$212$	1.60655	0.110338
$213$	7.18037	0.491991
$214$	25.8293	1.76566
$215$	31.8115	2.16953
$216$	−1.86854	−0.127138
$217$	0.0311392	0.00211387
$218$	1.17904	0.0798548
$219$	−3.29779	−0.222844
$220$	−6.61817	−0.446197
$221$	6.59965	0.443941
$222$	−5.43093	−0.364500
$223$	−6.08366	−0.407392	−0.203696	−	0.979034i	$-0.565295\pi$
$223$	−6.08366	−0.407392	−0.203696	+	0.979034i	$0.565295\pi$
$224$	−13.5784	−0.907243
$225$	10.3947	0.692977
$226$	−2.99168	−0.199003
$227$	−4.28514	−0.284415	−0.142207	−	0.989837i	$-0.545420\pi$
$227$	−4.28514	−0.284415	−0.142207	+	0.989837i	$0.545420\pi$
$228$	−5.31261	−0.351836
$229$	−5.26508	−0.347926	−0.173963	−	0.984752i	$-0.555657\pi$
$229$	−5.26508	−0.347926	−0.173963	+	0.984752i	$0.555657\pi$
$230$	−54.0980	−3.56712
$231$	−5.31869	−0.349944
$232$	14.0097	0.919782
$233$	−27.2502	−1.78522	−0.892610	−	0.450830i	$-0.851128\pi$
$233$	−27.2502	−1.78522	−0.892610	+	0.450830i	$0.851128\pi$
$234$	−11.2454	−0.735134
$235$	20.7014	1.35041
$236$	6.07960	0.395748
$237$	9.25247	0.601013
$238$	4.85382	0.314626
$239$	−15.0549	−0.973818	−0.486909	−	0.873453i	$-0.661876\pi$
$239$	−15.0549	−0.973818	−0.486909	+	0.873453i	$0.661876\pi$
$240$	19.5814	1.26397
$241$	−4.87483	−0.314015	−0.157008	−	0.987597i	$-0.550185\pi$
$241$	−4.87483	−0.314015	−0.157008	+	0.987597i	$0.550185\pi$
$242$	12.8031	0.823013
$243$	−1.00000	−0.0641500
$244$	8.87214	0.567980
$245$	4.37276	0.279365
$246$	13.8604	0.883705
$247$	38.8106	2.46946
$248$	−0.0204258	−0.00129704
$249$	−5.74483	−0.364064
$250$	−36.0663	−2.28104
$251$	−22.6448	−1.42933	−0.714665	−	0.699467i	$-0.753421\pi$
$251$	−22.6448	−1.42933	−0.714665	+	0.699467i	$0.753421\pi$
$252$	−2.57341	−0.162109
$253$	−15.1084	−0.949855
$254$	−11.3927	−0.714839
$255$	−3.92360	−0.245706
$256$	17.9239	1.12024
$257$	−24.0439	−1.49982	−0.749910	−	0.661540i	$-0.769903\pi$
$257$	−24.0439	−1.49982	−0.749910	+	0.661540i	$0.769903\pi$
$258$	13.8151	0.860088
$259$	9.07928	0.564159
$260$	23.3929	1.45077
$261$	7.49767	0.464094
$262$	−4.11799	−0.254410
$263$	−31.2083	−1.92439	−0.962194	−	0.272364i	$-0.912195\pi$
$263$	−31.2083	−1.92439	−0.962194	+	0.272364i	$0.912195\pi$
$264$	3.48881	0.214721
$265$	6.97752	0.428625
$266$	28.5438	1.75014
$267$	3.90125	0.238752
$268$	−4.22985	−0.258379
$269$	−19.1859	−1.16978	−0.584892	−	0.811111i	$-0.698863\pi$
$269$	−19.1859	−1.16978	−0.584892	+	0.811111i	$0.698863\pi$
$270$	6.68557	0.406871
$271$	−23.1038	−1.40346	−0.701728	−	0.712445i	$-0.747588\pi$
$271$	−23.1038	−1.40346	−0.701728	+	0.712445i	$0.747588\pi$
$272$	−4.99067	−0.302604
$273$	18.7997	1.13781
$274$	−13.1713	−0.795704
$275$	−19.4082	−1.17036
$276$	−7.31008	−0.440015
$277$	−19.4800	−1.17044	−0.585220	−	0.810874i	$-0.698992\pi$
$277$	−19.4800	−1.17044	−0.585220	+	0.810874i	$0.698992\pi$
$278$	−18.7570	−1.12497
$279$	−0.0109314	−0.000654448 0
$280$	−20.8842	−1.24807
$281$	−27.0046	−1.61096	−0.805480	−	0.592623i	$-0.798092\pi$
$281$	−27.0046	−1.61096	−0.805480	+	0.592623i	$0.798092\pi$
$282$	8.99015	0.535356
$283$	−8.08803	−0.480784	−0.240392	−	0.970676i	$-0.577276\pi$
$283$	−8.08803	−0.480784	−0.240392	+	0.970676i	$0.577276\pi$
$284$	−6.48672	−0.384916
$285$	−23.0735	−1.36676
$286$	20.9966	1.24155
$287$	−23.1714	−1.36776
$288$	4.76669	0.280880
$289$	1.00000	0.0588235
$290$	−50.1261	−2.94351
$291$	10.7592	0.630714
$292$	2.97921	0.174345
$293$	−14.9382	−0.872696	−0.436348	−	0.899778i	$-0.643728\pi$
$293$	−14.9382	−0.872696	−0.436348	+	0.899778i	$0.643728\pi$
$294$	1.89899	0.110752
$295$	26.4047	1.53734
$296$	−5.95558	−0.346161
$297$	1.86713	0.108342
$298$	−24.4356	−1.41552
$299$	53.4029	3.08837
$300$	−9.39050	−0.542161
$301$	−23.0956	−1.33121
$302$	−6.95622	−0.400285
$303$	−4.23881	−0.243513
$304$	−29.3486	−1.68326
$305$	38.5332	2.20640
$306$	−1.70394	−0.0974075
$307$	9.47468	0.540749	0.270374	−	0.962755i	$-0.412853\pi$
$307$	9.47468	0.540749	0.270374	+	0.962755i	$0.412853\pi$
$308$	4.80489	0.273784
$309$	18.0364	1.02606
$310$	0.0730829	0.00415083
$311$	−18.9615	−1.07521	−0.537604	−	0.843198i	$-0.680670\pi$
$311$	−18.9615	−1.07521	−0.537604	+	0.843198i	$0.680670\pi$
$312$	−12.3317	−0.698146
$313$	−10.1151	−0.571739	−0.285870	−	0.958268i	$-0.592282\pi$
$313$	−10.1151	−0.571739	−0.285870	+	0.958268i	$0.592282\pi$
$314$	1.70394	0.0961587
$315$	−11.1767	−0.629738
$316$	−8.35865	−0.470211
$317$	−30.6649	−1.72231	−0.861156	−	0.508340i	$-0.830259\pi$
$317$	−30.6649	−1.72231	−0.861156	+	0.508340i	$0.830259\pi$
$318$	3.03018	0.169924
$319$	−13.9991	−0.783800
$320$	7.29475	0.407789
$321$	15.1586	0.846072
$322$	39.2760	2.18876
$323$	5.88070	0.327211
$324$	0.903397	0.0501887
$325$	68.6011	3.80531
$326$	39.3148	2.17744
$327$	0.691952	0.0382651
$328$	15.1993	0.839243
$329$	−15.0295	−0.828602
$330$	−12.4828	−0.687156
$331$	−25.0913	−1.37914	−0.689571	−	0.724218i	$-0.742201\pi$
$331$	−25.0913	−1.37914	−0.689571	+	0.724218i	$0.742201\pi$
$332$	5.18986	0.284831
$333$	−3.18729	−0.174662
$334$	−33.7075	−1.84439
$335$	−18.3709	−1.00371
$336$	−14.2164	−0.775567
$337$	9.12503	0.497072	0.248536	−	0.968623i	$-0.420051\pi$
$337$	9.12503	0.497072	0.248536	+	0.968623i	$0.420051\pi$
$338$	−52.0645	−2.83193
$339$	−1.75574	−0.0953590
$340$	3.54457	0.192231
$341$	0.0204104	0.00110529
$342$	−10.0203	−0.541838
$343$	16.7655	0.905250
$344$	15.1496	0.816813
$345$	−31.7489	−1.70930
$346$	−9.15414	−0.492130
$347$	15.1352	0.812498	0.406249	−	0.913763i	$-0.366837\pi$
$347$	15.1352	0.812498	0.406249	+	0.913763i	$0.366837\pi$
$348$	−6.77337	−0.363091
$349$	10.1377	0.542657	0.271328	−	0.962487i	$-0.412537\pi$
$349$	10.1377	0.542657	0.271328	+	0.962487i	$0.412537\pi$
$350$	50.4538	2.69687
$351$	−6.59965	−0.352263
$352$	−8.90003	−0.474373
$353$	6.83008	0.363528	0.181764	−	0.983342i	$-0.441819\pi$
$353$	6.83008	0.363528	0.181764	+	0.983342i	$0.441819\pi$
$354$	11.4670	0.609464
$355$	−28.1729	−1.49526
$356$	−3.52437	−0.186791
$357$	2.84859	0.150763
$358$	41.0956	2.17197
$359$	−16.9878	−0.896582	−0.448291	−	0.893888i	$-0.647967\pi$
$359$	−16.9878	−0.896582	−0.448291	+	0.893888i	$0.647967\pi$
$360$	7.33141	0.386399
$361$	15.5826	0.820139
$362$	−13.6156	−0.715622
$363$	7.51383	0.394374
$364$	−16.9836	−0.890183
$365$	12.9392	0.677269
$366$	16.7341	0.874707
$367$	−10.2984	−0.537571	−0.268786	−	0.963200i	$-0.586622\pi$
$367$	−10.2984	−0.537571	−0.268786	+	0.963200i	$0.586622\pi$
$368$	−40.3833	−2.10513
$369$	8.13433	0.423456
$370$	21.3088	1.10779
$371$	−5.06578	−0.263002
$372$	0.00987543	0.000512017 0
$373$	−2.30087	−0.119135	−0.0595674	−	0.998224i	$-0.518972\pi$
$373$	−2.30087	−0.119135	−0.0595674	+	0.998224i	$0.518972\pi$
$374$	3.18147	0.164510
$375$	−21.1665	−1.09303
$376$	9.85863	0.508420
$377$	49.4820	2.54845
$378$	−4.85382	−0.249653
$379$	30.1533	1.54887	0.774436	−	0.632652i	$-0.218034\pi$
$379$	30.1533	1.54887	0.774436	+	0.632652i	$0.218034\pi$
$380$	20.8446	1.06930
$381$	−6.68609	−0.342539
$382$	−29.9545	−1.53260
$383$	19.1114	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$383$	19.1114	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$384$	12.7013	0.648162
$385$	20.8684	1.06355
$386$	−5.37019	−0.273336
$387$	8.10773	0.412139
$388$	−9.71981	−0.493449
$389$	−1.84952	−0.0937743	−0.0468872	−	0.998900i	$-0.514930\pi$
$389$	−1.84952	−0.0937743	−0.0468872	+	0.998900i	$0.514930\pi$
$390$	44.1224	2.23423
$391$	8.09177	0.409218
$392$	2.08244	0.105179
$393$	−2.41675	−0.121909
$394$	−38.2844	−1.92874
$395$	−36.3030	−1.82660
$396$	−1.68676	−0.0847628
$397$	23.2381	1.16629	0.583145	−	0.812368i	$-0.301822\pi$
$397$	23.2381	1.16629	0.583145	+	0.812368i	$0.301822\pi$
$398$	−4.63424	−0.232294
$399$	16.7517	0.838635
$400$	−51.8763	−2.59381
$401$	−35.5020	−1.77289	−0.886444	−	0.462837i	$-0.846832\pi$
$401$	−35.5020	−1.77289	−0.886444	+	0.462837i	$0.846832\pi$
$402$	−7.97810	−0.397911
$403$	−0.0721437	−0.00359373
$404$	3.82932	0.190516
$405$	3.92360	0.194965
$406$	36.3923	1.80612
$407$	5.95108	0.294984
$408$	−1.86854	−0.0925066
$409$	30.7424	1.52011	0.760057	−	0.649856i	$-0.225171\pi$
$409$	30.7424	1.52011	0.760057	+	0.649856i	$0.225171\pi$
$410$	−54.3826	−2.68577
$411$	−7.72990	−0.381288
$412$	−16.2941	−0.802751
$413$	−19.1702	−0.943305
$414$	−13.7879	−0.677636
$415$	22.5404	1.10647
$416$	31.4585	1.54238
$417$	−11.0080	−0.539065
$418$	18.7093	0.915100
$419$	−18.9779	−0.927132	−0.463566	−	0.886062i	$-0.653430\pi$
$419$	−18.9779	−0.927132	−0.463566	+	0.886062i	$0.653430\pi$
$420$	10.0970	0.492685
$421$	−22.6584	−1.10430	−0.552151	−	0.833744i	$-0.686193\pi$
$421$	−22.6584	−1.10430	−0.552151	+	0.833744i	$0.686193\pi$
$422$	−12.5855	−0.612652
$423$	5.27611	0.256533
$424$	3.32291	0.161375
$425$	10.3947	0.504215
$426$	−12.2349	−0.592782
$427$	−27.9756	−1.35384
$428$	−13.6943	−0.661937
$429$	12.3224	0.594931
$430$	−54.2048	−2.61399
$431$	−19.7395	−0.950819	−0.475410	−	0.879765i	$-0.657700\pi$
$431$	−19.7395	−0.950819	−0.475410	+	0.879765i	$0.657700\pi$
$432$	4.99067	0.240114
$433$	21.3127	1.02422	0.512110	−	0.858920i	$-0.328864\pi$
$433$	21.3127	1.02422	0.512110	+	0.858920i	$0.328864\pi$
$434$	−0.0530592	−0.00254692
$435$	−29.4179	−1.41048
$436$	−0.625108	−0.0299372
$437$	47.5853	2.27631
$438$	5.61922	0.268497
$439$	−17.1388	−0.817990	−0.408995	−	0.912537i	$-0.634121\pi$
$439$	−17.1388	−0.817990	−0.408995	+	0.912537i	$0.634121\pi$
$440$	−13.6887	−0.652583
$441$	1.11447	0.0530702
$442$	−11.2454	−0.534888
$443$	34.7595	1.65147	0.825737	−	0.564055i	$-0.190759\pi$
$443$	34.7595	1.65147	0.825737	+	0.564055i	$0.190759\pi$
$444$	2.87939	0.136650
$445$	−15.3069	−0.725619
$446$	10.3662	0.490852
$447$	−14.3407	−0.678291
$448$	−5.29609	−0.250217
$449$	8.18046	0.386060	0.193030	−	0.981193i	$-0.438169\pi$
$449$	8.18046	0.386060	0.193030	+	0.981193i	$0.438169\pi$
$450$	−17.7118	−0.834944
$451$	−15.1878	−0.715168
$452$	1.58613	0.0746055
$453$	−4.08244	−0.191810
$454$	7.30161	0.342681
$455$	−73.7626	−3.45804
$456$	−10.9883	−0.514576
$457$	7.74931	0.362497	0.181249	−	0.983437i	$-0.441986\pi$
$457$	7.74931	0.362497	0.181249	+	0.983437i	$0.441986\pi$
$458$	8.97136	0.419204
$459$	−1.00000	−0.0466760
$460$	28.6818	1.33730
$461$	1.32226	0.0615838	0.0307919	−	0.999526i	$-0.490197\pi$
$461$	1.32226	0.0615838	0.0307919	+	0.999526i	$0.490197\pi$
$462$	9.06270	0.421635
$463$	22.0058	1.02270	0.511348	−	0.859374i	$-0.329146\pi$
$463$	22.0058	1.02270	0.511348	+	0.859374i	$0.329146\pi$
$464$	−37.4184	−1.73710
$465$	0.0428906	0.00198901
$466$	46.4326	2.15095
$467$	25.8450	1.19596	0.597981	−	0.801510i	$-0.295970\pi$
$467$	25.8450	1.19596	0.597981	+	0.801510i	$0.295970\pi$
$468$	5.96210	0.275598
$469$	13.3376	0.615871
$470$	−35.2738	−1.62706
$471$	1.00000	0.0460776
$472$	12.5748	0.578800
$473$	−15.1382	−0.696054
$474$	−15.7656	−0.724139
$475$	61.1279	2.80474
$476$	−2.57341	−0.117952
$477$	1.77834	0.0814248
$478$	25.6525	1.17332
$479$	0.381457	0.0174292	0.00871460	−	0.999962i	$-0.497226\pi$
$479$	0.381457	0.0174292	0.00871460	+	0.999962i	$0.497226\pi$
$480$	−18.7026	−0.853654
$481$	−21.0350	−0.959113
$482$	8.30639	0.378346
$483$	23.0501	1.04882
$484$	−6.78797	−0.308544
$485$	−42.2148	−1.91687
$486$	1.70394	0.0772921
$487$	−17.0150	−0.771022	−0.385511	−	0.922703i	$-0.625975\pi$
$487$	−17.0150	−0.771022	−0.385511	+	0.922703i	$0.625975\pi$
$488$	18.3507	0.830697
$489$	23.0729	1.04339
$490$	−7.45090	−0.336597
$491$	−44.0172	−1.98647	−0.993234	−	0.116133i	$-0.962950\pi$
$491$	−44.0172	−1.98647	−0.993234	+	0.116133i	$0.962950\pi$
$492$	−7.34853	−0.331297
$493$	7.49767	0.337678
$494$	−66.1307	−2.97536
$495$	−7.32587	−0.329273
$496$	0.0545552	0.00244960
$497$	20.4539	0.917485
$498$	9.78882	0.438647
$499$	13.0678	0.584995	0.292497	−	0.956266i	$-0.405514\pi$
$499$	13.0678	0.584995	0.292497	+	0.956266i	$0.405514\pi$
$500$	19.1217	0.855150
$501$	−19.7822	−0.883801
$502$	38.5853	1.72215
$503$	18.5410	0.826702	0.413351	−	0.910572i	$-0.364358\pi$
$503$	18.5410	0.826702	0.413351	+	0.910572i	$0.364358\pi$
$504$	−5.32271	−0.237092
$505$	16.6314	0.740087
$506$	25.7437	1.14445
$507$	−30.5554	−1.35701
$508$	6.04019	0.267990
$509$	−1.90452	−0.0844165	−0.0422082	−	0.999109i	$-0.513439\pi$
$509$	−1.90452	−0.0844165	−0.0422082	+	0.999109i	$0.513439\pi$
$510$	6.68557	0.296042
$511$	−9.39405	−0.415568
$512$	−5.13845	−0.227089
$513$	−5.88070	−0.259639
$514$	40.9693	1.80708
$515$	−70.7679	−3.11840
$516$	−7.32450	−0.322443
$517$	−9.85118	−0.433254
$518$	−15.4705	−0.679735
$519$	−5.37235	−0.235820
$520$	48.3848	2.12181
$521$	−15.0690	−0.660185	−0.330093	−	0.943949i	$-0.607080\pi$
$521$	−15.0690	−0.660185	−0.330093	+	0.943949i	$0.607080\pi$
$522$	−12.7755	−0.559170
$523$	20.5686	0.899403	0.449701	−	0.893179i	$-0.351530\pi$
$523$	20.5686	0.899403	0.449701	+	0.893179i	$0.351530\pi$
$524$	2.18328	0.0953772
$525$	29.6101	1.29229
$526$	53.1770	2.31863
$527$	−0.0109314	−0.000476181 0
$528$	−9.31822	−0.405523
$529$	42.4767	1.84681
$530$	−11.8892	−0.516435
$531$	6.72972	0.292045
$532$	−15.1334	−0.656118
$533$	53.6837	2.32530
$534$	−6.64747	−0.287664
$535$	−59.4765	−2.57139
$536$	−8.74881	−0.377891
$537$	24.1181	1.04077
$538$	32.6915	1.40943
$539$	−2.08087	−0.0896293
$540$	−3.54457	−0.152534
$541$	−42.1834	−1.81360	−0.906802	−	0.421556i	$-0.861484\pi$
$541$	−42.1834	−1.81360	−0.906802	+	0.421556i	$0.861484\pi$
$542$	39.3674	1.69097
$543$	−7.99070	−0.342914
$544$	4.76669	0.204370
$545$	−2.71495	−0.116296
$546$	−32.0335	−1.37091
$547$	22.9966	0.983262	0.491631	−	0.870804i	$-0.336401\pi$
$547$	22.9966	0.983262	0.491631	+	0.870804i	$0.336401\pi$
$548$	6.98317	0.298306
$549$	9.82087	0.419144
$550$	33.0703	1.41012
$551$	44.0915	1.87836
$552$	−15.1198	−0.643542
$553$	26.3565	1.12079
$554$	33.1927	1.41022
$555$	12.5057	0.530835
$556$	9.94461	0.421745
$557$	19.7995	0.838932	0.419466	−	0.907771i	$-0.362217\pi$
$557$	19.7995	0.838932	0.419466	+	0.907771i	$0.362217\pi$
$558$	0.0186265	0.000788521 0
$559$	53.5082	2.26316
$560$	55.7794	2.35711
$561$	1.86713	0.0788302
$562$	46.0141	1.94099
$563$	27.2447	1.14823	0.574114	−	0.818776i	$-0.305347\pi$
$563$	27.2447	1.14823	0.574114	+	0.818776i	$0.305347\pi$
$564$	−4.76642	−0.200703
$565$	6.88885	0.289816
$566$	13.7815	0.579279
$567$	−2.84859	−0.119630
$568$	−13.4168	−0.562957
$569$	9.46666	0.396863	0.198431	−	0.980115i	$-0.436415\pi$
$569$	9.46666	0.396863	0.198431	+	0.980115i	$0.436415\pi$
$570$	39.3158	1.64676
$571$	2.92871	0.122563	0.0612814	−	0.998121i	$-0.480481\pi$
$571$	2.92871	0.122563	0.0612814	+	0.998121i	$0.480481\pi$
$572$	−11.1320	−0.465453
$573$	−17.5796	−0.734398
$574$	39.4825	1.64797
$575$	84.1112	3.50768
$576$	1.85920	0.0774665
$577$	−8.37754	−0.348761	−0.174381	−	0.984678i	$-0.555792\pi$
$577$	−8.37754	−0.348761	−0.174381	+	0.984678i	$0.555792\pi$
$578$	−1.70394	−0.0708744
$579$	−3.15164	−0.130978
$580$	26.5760	1.10351
$581$	−16.3647	−0.678921
$582$	−18.3330	−0.759925
$583$	−3.32040	−0.137517
$584$	6.16205	0.254987
$585$	25.8944	1.07060
$586$	25.4536	1.05148
$587$	9.53243	0.393445	0.196723	−	0.980459i	$-0.436970\pi$
$587$	9.53243	0.393445	0.196723	+	0.980459i	$0.436970\pi$
$588$	−1.00681	−0.0415203
$589$	−0.0642845	−0.00264880
$590$	−44.9920	−1.85229
$591$	−22.4682	−0.924219
$592$	15.9067	0.653761
$593$	−32.0305	−1.31534	−0.657668	−	0.753308i	$-0.728457\pi$
$593$	−32.0305	−1.31534	−0.657668	+	0.753308i	$0.728457\pi$
$594$	−3.18147	−0.130537
$595$	−11.1767	−0.458202
$596$	12.9553	0.530671
$597$	−2.71973	−0.111311
$598$	−90.9950	−3.72106
$599$	−27.8490	−1.13788	−0.568939	−	0.822380i	$-0.692646\pi$
$599$	−27.8490	−1.13788	−0.568939	+	0.822380i	$0.692646\pi$
$600$	−19.4229	−0.792935
$601$	−2.18062	−0.0889495	−0.0444748	−	0.999011i	$-0.514161\pi$
$601$	−2.18062	−0.0889495	−0.0444748	+	0.999011i	$0.514161\pi$
$602$	39.3534	1.60393
$603$	−4.68216	−0.190672
$604$	3.68806	0.150065
$605$	−29.4813	−1.19858
$606$	7.22265	0.293400
$607$	−41.3614	−1.67881	−0.839403	−	0.543509i	$-0.817095\pi$
$607$	−41.3614	−1.67881	−0.839403	+	0.543509i	$0.817095\pi$
$608$	28.0315	1.13683
$609$	21.3578	0.865461
$610$	−65.6581	−2.65842
$611$	34.8205	1.40869
$612$	0.903397	0.0365176
$613$	−10.3646	−0.418623	−0.209312	−	0.977849i	$-0.567122\pi$
$613$	−10.3646	−0.418623	−0.209312	+	0.977849i	$0.567122\pi$
$614$	−16.1443	−0.651529
$615$	−31.9159	−1.28697
$616$	9.93819	0.400421
$617$	32.6854	1.31586	0.657932	−	0.753077i	$-0.271431\pi$
$617$	32.6854	1.31586	0.657932	+	0.753077i	$0.271431\pi$
$618$	−30.7329	−1.23626
$619$	−22.3478	−0.898235	−0.449118	−	0.893473i	$-0.648262\pi$
$619$	−22.3478	−0.898235	−0.449118	+	0.893473i	$0.648262\pi$
$620$	−0.0387473	−0.00155613
$621$	−8.09177	−0.324711
$622$	32.3092	1.29548
$623$	11.1131	0.445235
$624$	32.9367	1.31852
$625$	31.0756	1.24303
$626$	17.2355	0.688868
$627$	10.9800	0.438500
$628$	−0.903397	−0.0360495
$629$	−3.18729	−0.127086
$630$	19.0444	0.758749
$631$	24.9048	0.991443	0.495722	−	0.868482i	$-0.334904\pi$
$631$	24.9048	0.991443	0.495722	+	0.868482i	$0.334904\pi$
$632$	−17.2886	−0.687705
$633$	−7.38613	−0.293572
$634$	52.2510	2.07515
$635$	26.2336	1.04105
$636$	−1.60655	−0.0637039
$637$	7.35515	0.291422
$638$	23.8536	0.944372
$639$	−7.18037	−0.284051
$640$	−49.8350	−1.96990
$641$	−21.7337	−0.858431	−0.429216	−	0.903202i	$-0.641210\pi$
$641$	−21.7337	−0.858431	−0.429216	+	0.903202i	$0.641210\pi$
$642$	−25.8293	−1.01940
$643$	−11.8093	−0.465712	−0.232856	−	0.972511i	$-0.574807\pi$
$643$	−11.8093	−0.465712	−0.232856	+	0.972511i	$0.574807\pi$
$644$	−20.8234	−0.820558
$645$	−31.8115	−1.25258
$646$	−10.0203	−0.394245
$647$	−24.2154	−0.952006	−0.476003	−	0.879444i	$-0.657915\pi$
$647$	−24.2154	−0.952006	−0.476003	+	0.879444i	$0.657915\pi$
$648$	1.86854	0.0734032
$649$	−12.5652	−0.493229
$650$	−116.892	−4.58488
$651$	−0.0311392	−0.00122044
$652$	−20.8440	−0.816314
$653$	−37.1471	−1.45368	−0.726839	−	0.686808i	$-0.759011\pi$
$653$	−37.1471	−1.45368	−0.726839	+	0.686808i	$0.759011\pi$
$654$	−1.17904	−0.0461042
$655$	9.48237	0.370507
$656$	−40.5957	−1.58500
$657$	3.29779	0.128659
$658$	25.6093	0.998354
$659$	23.1020	0.899925	0.449962	−	0.893047i	$-0.351437\pi$
$659$	23.1020	0.899925	0.449962	+	0.893047i	$0.351437\pi$
$660$	6.61817	0.257612
$661$	25.4491	0.989857	0.494929	−	0.868934i	$-0.335194\pi$
$661$	25.4491	0.989857	0.494929	+	0.868934i	$0.335194\pi$
$662$	42.7540	1.66168
$663$	−6.59965	−0.256309
$664$	10.7345	0.416578
$665$	−65.7271	−2.54879
$666$	5.43093	0.210444
$667$	60.6694	2.34913
$668$	17.8711	0.691455
$669$	6.08366	0.235208
$670$	31.3029	1.20934
$671$	−18.3368	−0.707885
$672$	13.5784	0.523797
$673$	−7.73474	−0.298152	−0.149076	−	0.988826i	$-0.547630\pi$
$673$	−7.73474	−0.298152	−0.149076	+	0.988826i	$0.547630\pi$
$674$	−15.5485	−0.598904
$675$	−10.3947	−0.400091
$676$	27.6037	1.06168
$677$	−10.8148	−0.415645	−0.207822	−	0.978167i	$-0.566638\pi$
$677$	−10.8148	−0.415645	−0.207822	+	0.978167i	$0.566638\pi$
$678$	2.99168	0.114895
$679$	30.6485	1.17618
$680$	7.33141	0.281147
$681$	4.28514	0.164207
$682$	−0.0347780	−0.00133172
$683$	0.380002	0.0145404	0.00727018	−	0.999974i	$-0.497686\pi$
$683$	0.380002	0.0145404	0.00727018	+	0.999974i	$0.497686\pi$
$684$	5.31261	0.203133
$685$	30.3291	1.15881
$686$	−28.5673	−1.09070
$687$	5.26508	0.200875
$688$	−40.4630	−1.54264
$689$	11.7365	0.447123
$690$	54.0980	2.05948
$691$	38.2297	1.45433	0.727163	−	0.686465i	$-0.240839\pi$
$691$	38.2297	1.45433	0.727163	+	0.686465i	$0.240839\pi$
$692$	4.85336	0.184497
$693$	5.31869	0.202040
$694$	−25.7893	−0.978949
$695$	43.1911	1.63833
$696$	−14.0097	−0.531036
$697$	8.13433	0.308110
$698$	−17.2739	−0.653828
$699$	27.2502	1.03070
$700$	−26.7497	−1.01104
$701$	36.5737	1.38137	0.690684	−	0.723156i	$-0.257309\pi$
$701$	36.5737	1.38137	0.690684	+	0.723156i	$0.257309\pi$
$702$	11.2454	0.424430
$703$	−18.7435	−0.706924
$704$	−3.47136	−0.130832
$705$	−20.7014	−0.779658
$706$	−11.6380	−0.438002
$707$	−12.0746	−0.454113
$708$	−6.07960	−0.228486
$709$	−34.2094	−1.28476	−0.642380	−	0.766386i	$-0.722053\pi$
$709$	−34.2094	−1.28476	−0.642380	+	0.766386i	$0.722053\pi$
$710$	48.0048	1.80159
$711$	−9.25247	−0.346995
$712$	−7.28964	−0.273191
$713$	−0.0884547	−0.00331265
$714$	−4.85382	−0.181650
$715$	−48.3482	−1.80812
$716$	−21.7882	−0.814262
$717$	15.0549	0.562234
$718$	28.9461	1.08026
$719$	19.4549	0.725546	0.362773	−	0.931878i	$-0.381830\pi$
$719$	19.4549	0.725546	0.362773	+	0.931878i	$0.381830\pi$
$720$	−19.5814	−0.729756
$721$	51.3785	1.91343
$722$	−26.5518	−0.988156
$723$	4.87483	0.181297
$724$	7.21877	0.268283
$725$	77.9357	2.89446
$726$	−12.8031	−0.475167
$727$	29.2804	1.08595	0.542974	−	0.839749i	$-0.317298\pi$
$727$	29.2804	1.08595	0.542974	+	0.839749i	$0.317298\pi$
$728$	−35.1281	−1.30193
$729$	1.00000	0.0370370
$730$	−22.0476	−0.816017
$731$	8.10773	0.299875
$732$	−8.87214	−0.327924
$733$	44.0076	1.62546	0.812728	−	0.582643i	$-0.197981\pi$
$733$	44.0076	1.62546	0.812728	+	0.582643i	$0.197981\pi$
$734$	17.5478	0.647700
$735$	−4.37276	−0.161292
$736$	38.5710	1.42175
$737$	8.74220	0.322023
$738$	−13.8604	−0.510207
$739$	3.03536	0.111658	0.0558288	−	0.998440i	$-0.482220\pi$
$739$	3.03536	0.111658	0.0558288	+	0.998440i	$0.482220\pi$
$740$	−11.2976	−0.415307
$741$	−38.8106	−1.42574
$742$	8.63176	0.316882
$743$	−46.0920	−1.69095	−0.845476	−	0.534013i	$-0.820683\pi$
$743$	−46.0920	−1.69095	−0.845476	+	0.534013i	$0.820683\pi$
$744$	0.0204258	0.000748848 0
$745$	56.2671	2.06147
$746$	3.92054	0.143541
$747$	5.74483	0.210192
$748$	−1.68676	−0.0616740
$749$	43.1808	1.57779
$750$	36.0663	1.31696
$751$	−12.3363	−0.450158	−0.225079	−	0.974341i	$-0.572264\pi$
$751$	−12.3363	−0.450158	−0.225079	+	0.974341i	$0.572264\pi$
$752$	−26.3313	−0.960204
$753$	22.6448	0.825224
$754$	−84.3141	−3.07054
$755$	16.0179	0.582950
$756$	2.57341	0.0935940
$757$	0.328579	0.0119424	0.00597120	−	0.999982i	$-0.498099\pi$
$757$	0.328579	0.0119424	0.00597120	+	0.999982i	$0.498099\pi$
$758$	−51.3793	−1.86618
$759$	15.1084	0.548399
$760$	43.1139	1.56390
$761$	6.16435	0.223457	0.111729	−	0.993739i	$-0.464361\pi$
$761$	6.16435	0.223457	0.111729	+	0.993739i	$0.464361\pi$
$762$	11.3927	0.412713
$763$	1.97109	0.0713582
$764$	15.8813	0.574567
$765$	3.92360	0.141858
$766$	−32.5646	−1.17661
$767$	44.4138	1.60369
$768$	−17.9239	−0.646772
$769$	−19.5054	−0.703382	−0.351691	−	0.936116i	$-0.614393\pi$
$769$	−19.5054	−0.703382	−0.351691	+	0.936116i	$0.614393\pi$
$770$	−35.5584	−1.28144
$771$	24.0439	0.865921
$772$	2.84718	0.102472
$773$	38.4023	1.38124	0.690618	−	0.723220i	$-0.257339\pi$
$773$	38.4023	1.38124	0.690618	+	0.723220i	$0.257339\pi$
$774$	−13.8151	−0.496572
$775$	−0.113629	−0.00408166
$776$	−20.1040	−0.721691
$777$	−9.07928	−0.325717
$778$	3.15146	0.112985
$779$	47.8356	1.71389
$780$	−23.3929	−0.837601
$781$	13.4067	0.479729
$782$	−13.7879	−0.493053
$783$	−7.49767	−0.267945
$784$	−5.56197	−0.198642
$785$	−3.92360	−0.140039
$786$	4.11799	0.146884
$787$	−14.0214	−0.499808	−0.249904	−	0.968271i	$-0.580399\pi$
$787$	−14.0214	−0.499808	−0.249904	+	0.968271i	$0.580399\pi$
$788$	20.2977	0.723076
$789$	31.2083	1.11105
$790$	61.8580	2.20081
$791$	−5.00140	−0.177829
$792$	−3.48881	−0.123969
$793$	64.8143	2.30162
$794$	−39.5963	−1.40522
$795$	−6.97752	−0.247467
$796$	2.45699	0.0870858
$797$	10.7655	0.381332	0.190666	−	0.981655i	$-0.438935\pi$
$797$	10.7655	0.381332	0.190666	+	0.981655i	$0.438935\pi$
$798$	−28.5438	−1.01044
$799$	5.27611	0.186655
$800$	49.5482	1.75179
$801$	−3.90125	−0.137844
$802$	60.4932	2.13609
$803$	−6.15739	−0.217290
$804$	4.22985	0.149175
$805$	−90.4396	−3.18758
$806$	0.122928	0.00432996
$807$	19.1859	0.675376
$808$	7.92039	0.278638
$809$	1.56251	0.0549349	0.0274675	−	0.999623i	$-0.491256\pi$
$809$	1.56251	0.0549349	0.0274675	+	0.999623i	$0.491256\pi$
$810$	−6.68557	−0.234907
$811$	−20.2601	−0.711430	−0.355715	−	0.934595i	$-0.615763\pi$
$811$	−20.2601	−0.711430	−0.355715	+	0.934595i	$0.615763\pi$
$812$	−19.2946	−0.677106
$813$	23.1038	0.810286
$814$	−10.1403	−0.355416
$815$	−90.5290	−3.17109
$816$	4.99067	0.174708
$817$	47.6791	1.66808
$818$	−52.3831	−1.83153
$819$	−18.7997	−0.656915
$820$	28.8327	1.00688
$821$	−26.5636	−0.927075	−0.463538	−	0.886077i	$-0.653420\pi$
$821$	−26.5636	−0.927075	−0.463538	+	0.886077i	$0.653420\pi$
$822$	13.1713	0.459400
$823$	48.7647	1.69983	0.849916	−	0.526919i	$-0.176653\pi$
$823$	48.7647	1.69983	0.849916	+	0.526919i	$0.176653\pi$
$824$	−33.7019	−1.17406
$825$	19.4082	0.675706
$826$	32.6648	1.13655
$827$	−18.2547	−0.634780	−0.317390	−	0.948295i	$-0.602806\pi$
$827$	−18.2547	−0.634780	−0.317390	+	0.948295i	$0.602806\pi$
$828$	7.31008	0.254043
$829$	−21.2287	−0.737303	−0.368652	−	0.929568i	$-0.620180\pi$
$829$	−21.2287	−0.737303	−0.368652	+	0.929568i	$0.620180\pi$
$830$	−38.4074	−1.33314
$831$	19.4800	0.675754
$832$	12.2700	0.425387
$833$	1.11447	0.0386143
$834$	18.7570	0.649500
$835$	77.6173	2.68606
$836$	−9.91932	−0.343067
$837$	0.0109314	0.000377846 0
$838$	32.3372	1.11707
$839$	11.1966	0.386548	0.193274	−	0.981145i	$-0.438089\pi$
$839$	11.1966	0.386548	0.193274	+	0.981145i	$0.438089\pi$
$840$	20.8842	0.720574
$841$	27.2150	0.938448
$842$	38.6084	1.33053
$843$	27.0046	0.930088
$844$	6.67261	0.229681
$845$	119.887	4.12425
$846$	−8.99015	−0.309088
$847$	21.4038	0.735444
$848$	−8.87512	−0.304773
$849$	8.08803	0.277580
$850$	−17.7118	−0.607511
$851$	−25.7908	−0.884097
$852$	6.48672	0.222231
$853$	2.77793	0.0951146	0.0475573	−	0.998869i	$-0.484856\pi$
$853$	2.77793	0.0951146	0.0475573	+	0.998869i	$0.484856\pi$
$854$	47.6687	1.63119
$855$	23.0735	0.789098
$856$	−28.3245	−0.968113
$857$	−20.5496	−0.701960	−0.350980	−	0.936383i	$-0.614151\pi$
$857$	−20.5496	−0.701960	−0.350980	+	0.936383i	$0.614151\pi$
$858$	−20.9966	−0.716811
$859$	−2.19682	−0.0749545	−0.0374772	−	0.999297i	$-0.511932\pi$
$859$	−2.19682	−0.0749545	−0.0374772	+	0.999297i	$0.511932\pi$
$860$	28.7384	0.979972
$861$	23.1714	0.789679
$862$	33.6349	1.14561
$863$	10.1013	0.343854	0.171927	−	0.985110i	$-0.445001\pi$
$863$	10.1013	0.343854	0.171927	+	0.985110i	$0.445001\pi$
$864$	−4.76669	−0.162166
$865$	21.0790	0.716707
$866$	−36.3154	−1.23405
$867$	−1.00000	−0.0339618
$868$	0.0281311	0.000954830 0
$869$	17.2756	0.586033
$870$	50.1261	1.69944
$871$	−30.9006	−1.04703
$872$	−1.29294	−0.0437845
$873$	−10.7592	−0.364143
$874$	−81.0822	−2.74265
$875$	−60.2947	−2.03833
$876$	−2.97921	−0.100658
$877$	5.15256	0.173990	0.0869948	−	0.996209i	$-0.472274\pi$
$877$	5.15256	0.173990	0.0869948	+	0.996209i	$0.472274\pi$
$878$	29.2034	0.985567
$879$	14.9382	0.503851
$880$	36.5610	1.23247
$881$	−16.3677	−0.551441	−0.275720	−	0.961238i	$-0.588916\pi$
$881$	−16.3677	−0.551441	−0.275720	+	0.961238i	$0.588916\pi$
$882$	−1.89899	−0.0639424
$883$	35.0608	1.17989	0.589944	−	0.807444i	$-0.299150\pi$
$883$	35.0608	1.17989	0.589944	+	0.807444i	$0.299150\pi$
$884$	5.96210	0.200527
$885$	−26.4047	−0.887585
$886$	−59.2280	−1.98980
$887$	46.3982	1.55790	0.778950	−	0.627086i	$-0.215752\pi$
$887$	46.3982	1.55790	0.778950	+	0.627086i	$0.215752\pi$
$888$	5.95558	0.199856
$889$	−19.0459	−0.638780
$890$	26.0820	0.874272
$891$	−1.86713	−0.0625512
$892$	−5.49596	−0.184018
$893$	31.0272	1.03829
$894$	24.4356	0.817249
$895$	−94.6297	−3.16312
$896$	36.1809	1.20872
$897$	−53.4029	−1.78307
$898$	−13.9390	−0.465150
$899$	−0.0819603	−0.00273353
$900$	9.39050	0.313017
$901$	1.77834	0.0592452
$902$	25.8791	0.861680
$903$	23.0956	0.768574
$904$	3.28068	0.109114
$905$	31.3523	1.04219
$906$	6.95622	0.231105
$907$	−55.9541	−1.85792	−0.928962	−	0.370175i	$-0.879298\pi$
$907$	−55.9541	−1.85792	−0.928962	+	0.370175i	$0.879298\pi$
$908$	−3.87118	−0.128470
$909$	4.23881	0.140592
$910$	125.687	4.16648
$911$	−28.4904	−0.943930	−0.471965	−	0.881617i	$-0.656455\pi$
$911$	−28.4904	−0.943930	−0.471965	+	0.881617i	$0.656455\pi$
$912$	29.3486	0.971830
$913$	−10.7263	−0.354990
$914$	−13.2043	−0.436760
$915$	−38.5332	−1.27387
$916$	−4.75646	−0.157158
$917$	−6.88434	−0.227341
$918$	1.70394	0.0562383
$919$	28.0612	0.925654	0.462827	−	0.886449i	$-0.346835\pi$
$919$	28.0612	0.925654	0.462827	+	0.886449i	$0.346835\pi$
$920$	59.3241	1.95586
$921$	−9.47468	−0.312201
$922$	−2.25305	−0.0742001
$923$	−47.3880	−1.55979
$924$	−4.80489	−0.158069
$925$	−33.1308	−1.08933
$926$	−37.4964	−1.23221
$927$	−18.0364	−0.592395
$928$	35.7391	1.17319
$929$	19.6650	0.645186	0.322593	−	0.946538i	$-0.395445\pi$
$929$	19.6650	0.645186	0.322593	+	0.946538i	$0.395445\pi$
$930$	−0.0730829	−0.00239648
$931$	6.55389	0.214795
$932$	−24.6177	−0.806381
$933$	18.9615	0.620771
$934$	−44.0382	−1.44097
$935$	−7.32587	−0.239582
$936$	12.3317	0.403075
$937$	−13.2346	−0.432354	−0.216177	−	0.976354i	$-0.569359\pi$
$937$	−13.2346	−0.432354	−0.216177	+	0.976354i	$0.569359\pi$
$938$	−22.7264	−0.742042
$939$	10.1151	0.330094
$940$	18.7015	0.609977
$941$	24.2665	0.791064	0.395532	−	0.918452i	$-0.370560\pi$
$941$	24.2665	0.791064	0.395532	+	0.918452i	$0.370560\pi$
$942$	−1.70394	−0.0555172
$943$	65.8211	2.14343
$944$	−33.5858	−1.09312
$945$	11.1767	0.363579
$946$	25.7945	0.838651
$947$	−2.65087	−0.0861418	−0.0430709	−	0.999072i	$-0.513714\pi$
$947$	−2.65087	−0.0861418	−0.0430709	+	0.999072i	$0.513714\pi$
$948$	8.35865	0.271476
$949$	21.7642	0.706497
$950$	−104.158	−3.37933
$951$	30.6649	0.994378
$952$	−5.32271	−0.172510
$953$	17.2406	0.558478	0.279239	−	0.960222i	$-0.409918\pi$
$953$	17.2406	0.558478	0.279239	+	0.960222i	$0.409918\pi$
$954$	−3.03018	−0.0981058
$955$	68.9753	2.23199
$956$	−13.6005	−0.439872
$957$	13.9991	0.452527
$958$	−0.649978	−0.0209998
$959$	−22.0193	−0.711041
$960$	−7.29475	−0.235437
$961$	−30.9999	−0.999996
$962$	35.8423	1.15560
$963$	−15.1586	−0.488480
$964$	−4.40390	−0.141840
$965$	12.3658	0.398069
$966$	−39.2760	−1.26368
$967$	−32.7996	−1.05476	−0.527381	−	0.849629i	$-0.676826\pi$
$967$	−32.7996	−1.05476	−0.527381	+	0.849629i	$0.676826\pi$
$968$	−14.0399	−0.451260
$969$	−5.88070	−0.188915
$970$	71.9312	2.30957
$971$	25.9416	0.832504	0.416252	−	0.909249i	$-0.363343\pi$
$971$	25.9416	0.832504	0.416252	+	0.909249i	$0.363343\pi$
$972$	−0.903397	−0.0289765
$973$	−31.3574	−1.00527
$974$	28.9924	0.928977
$975$	−68.6011	−2.19699
$976$	−49.0127	−1.56886
$977$	20.2416	0.647587	0.323794	−	0.946128i	$-0.395042\pi$
$977$	20.2416	0.647587	0.323794	+	0.946128i	$0.395042\pi$
$978$	−39.3148	−1.25715
$979$	7.28413	0.232802
$980$	3.95033	0.126189
$981$	−0.691952	−0.0220923
$982$	75.0024	2.39342
$983$	−25.4260	−0.810963	−0.405481	−	0.914103i	$-0.632896\pi$
$983$	−25.4260	−0.810963	−0.405481	+	0.914103i	$0.632896\pi$
$984$	−15.1993	−0.484537
$985$	88.1563	2.80889
$986$	−12.7755	−0.406856
$987$	15.0295	0.478394
$988$	35.0614	1.11545
$989$	65.6059	2.08615
$990$	12.4828	0.396730
$991$	61.1192	1.94151	0.970757	−	0.240063i	$-0.0771680\pi$
$991$	61.1192	1.94151	0.970757	+	0.240063i	$0.0771680\pi$
$992$	−0.0521068	−0.00165439
$993$	25.0913	0.796248
$994$	−34.8522	−1.10544
$995$	10.6711	0.338298
$996$	−5.18986	−0.164447
$997$	51.7981	1.64046	0.820231	−	0.572032i	$-0.193845\pi$
$997$	51.7981	1.64046	0.820231	+	0.572032i	$0.193845\pi$
$998$	−22.2667	−0.704839
$999$	3.18729	0.100841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.14	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70394 q^{2} -1.00000 q^{3} +0.903397 q^{4} +3.92360 q^{5} +1.70394 q^{6} -2.84859 q^{7} +1.86854 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.70394 q^{2} -1.00000 q^{3} +0.903397 q^{4} +3.92360 q^{5} +1.70394 q^{6} -2.84859 q^{7} +1.86854 q^{8} +1.00000 q^{9} -6.68557 q^{10} -1.86713 q^{11} -0.903397 q^{12} +6.59965 q^{13} +4.85382 q^{14} -3.92360 q^{15} -4.99067 q^{16} +1.00000 q^{17} -1.70394 q^{18} +5.88070 q^{19} +3.54457 q^{20} +2.84859 q^{21} +3.18147 q^{22} +8.09177 q^{23} -1.86854 q^{24} +10.3947 q^{25} -11.2454 q^{26} -1.00000 q^{27} -2.57341 q^{28} +7.49767 q^{29} +6.68557 q^{30} -0.0109314 q^{31} +4.76669 q^{32} +1.86713 q^{33} -1.70394 q^{34} -11.1767 q^{35} +0.903397 q^{36} -3.18729 q^{37} -10.0203 q^{38} -6.59965 q^{39} +7.33141 q^{40} +8.13433 q^{41} -4.85382 q^{42} +8.10773 q^{43} -1.68676 q^{44} +3.92360 q^{45} -13.7879 q^{46} +5.27611 q^{47} +4.99067 q^{48} +1.11447 q^{49} -17.7118 q^{50} -1.00000 q^{51} +5.96210 q^{52} +1.77834 q^{53} +1.70394 q^{54} -7.32587 q^{55} -5.32271 q^{56} -5.88070 q^{57} -12.7755 q^{58} +6.72972 q^{59} -3.54457 q^{60} +9.82087 q^{61} +0.0186265 q^{62} -2.84859 q^{63} +1.85920 q^{64} +25.8944 q^{65} -3.18147 q^{66} -4.68216 q^{67} +0.903397 q^{68} -8.09177 q^{69} +19.0444 q^{70} -7.18037 q^{71} +1.86854 q^{72} +3.29779 q^{73} +5.43093 q^{74} -10.3947 q^{75} +5.31261 q^{76} +5.31869 q^{77} +11.2454 q^{78} -9.25247 q^{79} -19.5814 q^{80} +1.00000 q^{81} -13.8604 q^{82} +5.74483 q^{83} +2.57341 q^{84} +3.92360 q^{85} -13.8151 q^{86} -7.49767 q^{87} -3.48881 q^{88} -3.90125 q^{89} -6.68557 q^{90} -18.7997 q^{91} +7.31008 q^{92} +0.0109314 q^{93} -8.99015 q^{94} +23.0735 q^{95} -4.76669 q^{96} -10.7592 q^{97} -1.89899 q^{98} -1.86713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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