LMFDB - Embedded newform 8015.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54658 q^{2} -2.85949 q^{3} +4.48508 q^{4} +1.00000 q^{5} +7.28192 q^{6} -1.00000 q^{7} -6.32845 q^{8} +5.17667 q^{9} +O(q^{10})$	\(q-2.54658 q^{2} -2.85949 q^{3} +4.48508 q^{4} +1.00000 q^{5} +7.28192 q^{6} -1.00000 q^{7} -6.32845 q^{8} +5.17667 q^{9} -2.54658 q^{10} +2.00521 q^{11} -12.8250 q^{12} +0.589448 q^{13} +2.54658 q^{14} -2.85949 q^{15} +7.14576 q^{16} +1.22825 q^{17} -13.1828 q^{18} +1.88719 q^{19} +4.48508 q^{20} +2.85949 q^{21} -5.10644 q^{22} -0.928474 q^{23} +18.0961 q^{24} +1.00000 q^{25} -1.50108 q^{26} -6.22416 q^{27} -4.48508 q^{28} +8.54257 q^{29} +7.28192 q^{30} -9.16859 q^{31} -5.54037 q^{32} -5.73389 q^{33} -3.12785 q^{34} -1.00000 q^{35} +23.2178 q^{36} +3.94020 q^{37} -4.80588 q^{38} -1.68552 q^{39} -6.32845 q^{40} +7.66848 q^{41} -7.28192 q^{42} -1.24957 q^{43} +8.99354 q^{44} +5.17667 q^{45} +2.36444 q^{46} -11.9013 q^{47} -20.4332 q^{48} +1.00000 q^{49} -2.54658 q^{50} -3.51218 q^{51} +2.64372 q^{52} +2.23556 q^{53} +15.8503 q^{54} +2.00521 q^{55} +6.32845 q^{56} -5.39640 q^{57} -21.7544 q^{58} +12.9759 q^{59} -12.8250 q^{60} +4.80804 q^{61} +23.3486 q^{62} -5.17667 q^{63} -0.182530 q^{64} +0.589448 q^{65} +14.6018 q^{66} -7.44106 q^{67} +5.50881 q^{68} +2.65496 q^{69} +2.54658 q^{70} -11.9324 q^{71} -32.7603 q^{72} +15.0997 q^{73} -10.0340 q^{74} -2.85949 q^{75} +8.46420 q^{76} -2.00521 q^{77} +4.29231 q^{78} +5.01824 q^{79} +7.14576 q^{80} +2.26789 q^{81} -19.5284 q^{82} +3.66021 q^{83} +12.8250 q^{84} +1.22825 q^{85} +3.18213 q^{86} -24.4274 q^{87} -12.6899 q^{88} -11.1582 q^{89} -13.1828 q^{90} -0.589448 q^{91} -4.16428 q^{92} +26.2175 q^{93} +30.3076 q^{94} +1.88719 q^{95} +15.8426 q^{96} +10.9403 q^{97} -2.54658 q^{98} +10.3803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.54658	−1.80071	−0.900353	−	0.435161i	$-0.856691\pi$
$2$	−2.54658	−1.80071	−0.900353	+	0.435161i	$0.856691\pi$
$3$	−2.85949	−1.65093	−0.825463	−	0.564456i	$-0.809086\pi$
$3$	−2.85949	−1.65093	−0.825463	+	0.564456i	$0.809086\pi$
$4$	4.48508	2.24254
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.28192	2.97283
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.32845	−2.23745
$9$	5.17667	1.72556
$10$	−2.54658	−0.805300
$11$	2.00521	0.604595	0.302297	−	0.953214i	$-0.402246\pi$
$11$	2.00521	0.604595	0.302297	+	0.953214i	$0.402246\pi$
$12$	−12.8250	−3.70227
$13$	0.589448	0.163483	0.0817417	−	0.996654i	$-0.473952\pi$
$13$	0.589448	0.163483	0.0817417	+	0.996654i	$0.473952\pi$
$14$	2.54658	0.680603
$15$	−2.85949	−0.738316
$16$	7.14576	1.78644
$17$	1.22825	0.297895	0.148948	−	0.988845i	$-0.452411\pi$
$17$	1.22825	0.297895	0.148948	+	0.988845i	$0.452411\pi$
$18$	−13.1828	−3.10722
$19$	1.88719	0.432951	0.216476	−	0.976288i	$-0.430544\pi$
$19$	1.88719	0.432951	0.216476	+	0.976288i	$0.430544\pi$
$20$	4.48508	1.00289
$21$	2.85949	0.623991
$22$	−5.10644	−1.08870
$23$	−0.928474	−0.193600	−0.0968001	−	0.995304i	$-0.530861\pi$
$23$	−0.928474	−0.193600	−0.0968001	+	0.995304i	$0.530861\pi$
$24$	18.0961	3.69386
$25$	1.00000	0.200000
$26$	−1.50108	−0.294386
$27$	−6.22416	−1.19784
$28$	−4.48508	−0.847600
$29$	8.54257	1.58632	0.793158	−	0.609016i	$-0.208435\pi$
$29$	8.54257	1.58632	0.793158	+	0.609016i	$0.208435\pi$
$30$	7.28192	1.32949
$31$	−9.16859	−1.64673	−0.823364	−	0.567514i	$-0.807905\pi$
$31$	−9.16859	−1.64673	−0.823364	+	0.567514i	$0.807905\pi$
$32$	−5.54037	−0.979408
$33$	−5.73389	−0.998141
$34$	−3.12785	−0.536422
$35$	−1.00000	−0.169031
$36$	23.2178	3.86963
$37$	3.94020	0.647765	0.323883	−	0.946097i	$-0.395012\pi$
$37$	3.94020	0.647765	0.323883	+	0.946097i	$0.395012\pi$
$38$	−4.80588	−0.779617
$39$	−1.68552	−0.269899
$40$	−6.32845	−1.00062
$41$	7.66848	1.19762	0.598808	−	0.800893i	$-0.295641\pi$
$41$	7.66848	1.19762	0.598808	+	0.800893i	$0.295641\pi$
$42$	−7.28192	−1.12362
$43$	−1.24957	−0.190557	−0.0952787	−	0.995451i	$-0.530374\pi$
$43$	−1.24957	−0.190557	−0.0952787	+	0.995451i	$0.530374\pi$
$44$	8.99354	1.35583
$45$	5.17667	0.771692
$46$	2.36444	0.348617
$47$	−11.9013	−1.73598	−0.867989	−	0.496583i	$-0.834588\pi$
$47$	−11.9013	−1.73598	−0.867989	+	0.496583i	$0.834588\pi$
$48$	−20.4332	−2.94928
$49$	1.00000	0.142857
$50$	−2.54658	−0.360141
$51$	−3.51218	−0.491803
$52$	2.64372	0.366618
$53$	2.23556	0.307078	0.153539	−	0.988143i	$-0.450933\pi$
$53$	2.23556	0.307078	0.153539	+	0.988143i	$0.450933\pi$
$54$	15.8503	2.15696
$55$	2.00521	0.270383
$56$	6.32845	0.845675
$57$	−5.39640	−0.714770
$58$	−21.7544	−2.85649
$59$	12.9759	1.68932	0.844660	−	0.535302i	$-0.179802\pi$
$59$	12.9759	1.68932	0.844660	+	0.535302i	$0.179802\pi$
$60$	−12.8250	−1.65570
$61$	4.80804	0.615607	0.307803	−	0.951450i	$-0.400406\pi$
$61$	4.80804	0.615607	0.307803	+	0.951450i	$0.400406\pi$
$62$	23.3486	2.96527
$63$	−5.17667	−0.652199
$64$	−0.182530	−0.0228163
$65$	0.589448	0.0731120
$66$	14.6018	1.79736
$67$	−7.44106	−0.909070	−0.454535	−	0.890729i	$-0.650195\pi$
$67$	−7.44106	−0.909070	−0.454535	+	0.890729i	$0.650195\pi$
$68$	5.50881	0.668042
$69$	2.65496	0.319620
$70$	2.54658	0.304375
$71$	−11.9324	−1.41611	−0.708056	−	0.706156i	$-0.750428\pi$
$71$	−11.9324	−1.41611	−0.708056	+	0.706156i	$0.750428\pi$
$72$	−32.7603	−3.86084
$73$	15.0997	1.76728	0.883642	−	0.468164i	$-0.155084\pi$
$73$	15.0997	1.76728	0.883642	+	0.468164i	$0.155084\pi$
$74$	−10.0340	−1.16643
$75$	−2.85949	−0.330185
$76$	8.46420	0.970910
$77$	−2.00521	−0.228515
$78$	4.29231	0.486009
$79$	5.01824	0.564596	0.282298	−	0.959327i	$-0.408903\pi$
$79$	5.01824	0.564596	0.282298	+	0.959327i	$0.408903\pi$
$80$	7.14576	0.798921
$81$	2.26789	0.251988
$82$	−19.5284	−2.15655
$83$	3.66021	0.401760	0.200880	−	0.979616i	$-0.435620\pi$
$83$	3.66021	0.401760	0.200880	+	0.979616i	$0.435620\pi$
$84$	12.8250	1.39932
$85$	1.22825	0.133223
$86$	3.18213	0.343138
$87$	−24.4274	−2.61889
$88$	−12.6899	−1.35275
$89$	−11.1582	−1.18277	−0.591384	−	0.806390i	$-0.701418\pi$
$89$	−11.1582	−1.18277	−0.591384	+	0.806390i	$0.701418\pi$
$90$	−13.1828	−1.38959
$91$	−0.589448	−0.0617910
$92$	−4.16428	−0.434156
$93$	26.2175	2.71863
$94$	30.3076	3.12599
$95$	1.88719	0.193622
$96$	15.8426	1.61693
$97$	10.9403	1.11082	0.555410	−	0.831576i	$-0.312561\pi$
$97$	10.9403	1.11082	0.555410	+	0.831576i	$0.312561\pi$
$98$	−2.54658	−0.257244
$99$	10.3803	1.04326
$100$	4.48508	0.448508
$101$	3.80774	0.378884	0.189442	−	0.981892i	$-0.439332\pi$
$101$	3.80774	0.378884	0.189442	+	0.981892i	$0.439332\pi$
$102$	8.94405	0.885592
$103$	3.66678	0.361298	0.180649	−	0.983548i	$-0.442180\pi$
$103$	3.66678	0.361298	0.180649	+	0.983548i	$0.442180\pi$
$104$	−3.73029	−0.365785
$105$	2.85949	0.279057
$106$	−5.69305	−0.552957
$107$	10.0307	0.969703	0.484852	−	0.874596i	$-0.338874\pi$
$107$	10.0307	0.969703	0.484852	+	0.874596i	$0.338874\pi$
$108$	−27.9158	−2.68620
$109$	9.57007	0.916646	0.458323	−	0.888786i	$-0.348450\pi$
$109$	9.57007	0.916646	0.458323	+	0.888786i	$0.348450\pi$
$110$	−5.10644	−0.486880
$111$	−11.2670	−1.06941
$112$	−7.14576	−0.675211
$113$	−4.80897	−0.452390	−0.226195	−	0.974082i	$-0.572629\pi$
$113$	−4.80897	−0.452390	−0.226195	+	0.974082i	$0.572629\pi$
$114$	13.7424	1.28709
$115$	−0.928474	−0.0865807
$116$	38.3141	3.55738
$117$	3.05138	0.282100
$118$	−33.0442	−3.04197
$119$	−1.22825	−0.112594
$120$	18.0961	1.65194
$121$	−6.97912	−0.634465
$122$	−12.2441	−1.10853
$123$	−21.9279	−1.97717
$124$	−41.1219	−3.69285
$125$	1.00000	0.0894427
$126$	13.1828	1.17442
$127$	3.93756	0.349402	0.174701	−	0.984622i	$-0.444104\pi$
$127$	3.93756	0.349402	0.174701	+	0.984622i	$0.444104\pi$
$128$	11.5456	1.02049
$129$	3.57313	0.314596
$130$	−1.50108	−0.131653
$131$	13.9314	1.21719	0.608595	−	0.793481i	$-0.291734\pi$
$131$	13.9314	1.21719	0.608595	+	0.793481i	$0.291734\pi$
$132$	−25.7169	−2.23837
$133$	−1.88719	−0.163640
$134$	18.9493	1.63697
$135$	−6.22416	−0.535690
$136$	−7.77295	−0.666525
$137$	−14.0818	−1.20309	−0.601545	−	0.798839i	$-0.705448\pi$
$137$	−14.0818	−1.20309	−0.601545	+	0.798839i	$0.705448\pi$
$138$	−6.76107	−0.575541
$139$	17.3275	1.46970	0.734850	−	0.678230i	$-0.237253\pi$
$139$	17.3275	1.46970	0.734850	+	0.678230i	$0.237253\pi$
$140$	−4.48508	−0.379058
$141$	34.0315	2.86597
$142$	30.3868	2.55000
$143$	1.18197	0.0988413
$144$	36.9913	3.08260
$145$	8.54257	0.709422
$146$	−38.4525	−3.18236
$147$	−2.85949	−0.235847
$148$	17.6721	1.45264
$149$	−16.7150	−1.36934	−0.684671	−	0.728852i	$-0.740054\pi$
$149$	−16.7150	−1.36934	−0.684671	+	0.728852i	$0.740054\pi$
$150$	7.28192	0.594566
$151$	19.9468	1.62324	0.811622	−	0.584183i	$-0.198585\pi$
$151$	19.9468	1.62324	0.811622	+	0.584183i	$0.198585\pi$
$152$	−11.9430	−0.968705
$153$	6.35826	0.514035
$154$	5.10644	0.411489
$155$	−9.16859	−0.736439
$156$	−7.55969	−0.605259
$157$	13.8020	1.10152	0.550761	−	0.834663i	$-0.314338\pi$
$157$	13.8020	1.10152	0.550761	+	0.834663i	$0.314338\pi$
$158$	−12.7794	−1.01667
$159$	−6.39257	−0.506964
$160$	−5.54037	−0.438005
$161$	0.928474	0.0731740
$162$	−5.77537	−0.453756
$163$	18.3580	1.43791	0.718956	−	0.695055i	$-0.244620\pi$
$163$	18.3580	1.43791	0.718956	+	0.695055i	$0.244620\pi$
$164$	34.3937	2.68570
$165$	−5.73389	−0.446382
$166$	−9.32102	−0.723452
$167$	−3.93962	−0.304857	−0.152429	−	0.988314i	$-0.548709\pi$
$167$	−3.93962	−0.304857	−0.152429	+	0.988314i	$0.548709\pi$
$168$	−18.0961	−1.39615
$169$	−12.6526	−0.973273
$170$	−3.12785	−0.239895
$171$	9.76936	0.747082
$172$	−5.60441	−0.427332
$173$	12.8301	0.975458	0.487729	−	0.872995i	$-0.337825\pi$
$173$	12.8301	0.975458	0.487729	+	0.872995i	$0.337825\pi$
$174$	62.2063	4.71585
$175$	−1.00000	−0.0755929
$176$	14.3288	1.08007
$177$	−37.1045	−2.78894
$178$	28.4153	2.12982
$179$	−7.88670	−0.589480	−0.294740	−	0.955578i	$-0.595233\pi$
$179$	−7.88670	−0.589480	−0.294740	+	0.955578i	$0.595233\pi$
$180$	23.2178	1.73055
$181$	20.7548	1.54270	0.771348	−	0.636414i	$-0.219583\pi$
$181$	20.7548	1.54270	0.771348	+	0.636414i	$0.219583\pi$
$182$	1.50108	0.111267
$183$	−13.7485	−1.01632
$184$	5.87580	0.433170
$185$	3.94020	0.289689
$186$	−66.7649	−4.89544
$187$	2.46291	0.180106
$188$	−53.3781	−3.89300
$189$	6.22416	0.452741
$190$	−4.80588	−0.348656
$191$	−9.21282	−0.666616	−0.333308	−	0.942818i	$-0.608165\pi$
$191$	−9.21282	−0.666616	−0.333308	+	0.942818i	$0.608165\pi$
$192$	0.521944	0.0376680
$193$	−18.8450	−1.35649	−0.678246	−	0.734835i	$-0.737260\pi$
$193$	−18.8450	−1.35649	−0.678246	+	0.734835i	$0.737260\pi$
$194$	−27.8604	−2.00026
$195$	−1.68552	−0.120703
$196$	4.48508	0.320363
$197$	17.1954	1.22512	0.612560	−	0.790424i	$-0.290140\pi$
$197$	17.1954	1.22512	0.612560	+	0.790424i	$0.290140\pi$
$198$	−26.4344	−1.87861
$199$	7.76718	0.550601	0.275300	−	0.961358i	$-0.411223\pi$
$199$	7.76718	0.550601	0.275300	+	0.961358i	$0.411223\pi$
$200$	−6.32845	−0.447489
$201$	21.2776	1.50081
$202$	−9.69671	−0.682258
$203$	−8.54257	−0.599571
$204$	−15.7524	−1.10289
$205$	7.66848	0.535590
$206$	−9.33775	−0.650592
$207$	−4.80640	−0.334068
$208$	4.21206	0.292054
$209$	3.78422	0.261760
$210$	−7.28192	−0.502500
$211$	−15.5881	−1.07313	−0.536566	−	0.843858i	$-0.680279\pi$
$211$	−15.5881	−1.07313	−0.536566	+	0.843858i	$0.680279\pi$
$212$	10.0267	0.688635
$213$	34.1205	2.33790
$214$	−25.5440	−1.74615
$215$	−1.24957	−0.0852199
$216$	39.3893	2.68010
$217$	9.16859	0.622405
$218$	−24.3710	−1.65061
$219$	−43.1773	−2.91765
$220$	8.99354	0.606344
$221$	0.723992	0.0487010
$222$	28.6922	1.92570
$223$	−7.22189	−0.483614	−0.241807	−	0.970324i	$-0.577740\pi$
$223$	−7.22189	−0.483614	−0.241807	+	0.970324i	$0.577740\pi$
$224$	5.54037	0.370181
$225$	5.17667	0.345111
$226$	12.2464	0.814621
$227$	3.00834	0.199671	0.0998353	−	0.995004i	$-0.468168\pi$
$227$	3.00834	0.199671	0.0998353	+	0.995004i	$0.468168\pi$
$228$	−24.2033	−1.60290
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	2.36444	0.155906
$231$	5.73389	0.377262
$232$	−54.0613	−3.54930
$233$	−19.4885	−1.27674	−0.638368	−	0.769731i	$-0.720390\pi$
$233$	−19.4885	−1.27674	−0.638368	+	0.769731i	$0.720390\pi$
$234$	−7.77058	−0.507979
$235$	−11.9013	−0.776353
$236$	58.1980	3.78837
$237$	−14.3496	−0.932107
$238$	3.12785	0.202748
$239$	6.03947	0.390661	0.195330	−	0.980737i	$-0.437422\pi$
$239$	6.03947	0.390661	0.195330	+	0.980737i	$0.437422\pi$
$240$	−20.4332	−1.31896
$241$	17.4541	1.12432	0.562159	−	0.827029i	$-0.309971\pi$
$241$	17.4541	1.12432	0.562159	+	0.827029i	$0.309971\pi$
$242$	17.7729	1.14248
$243$	12.1875	0.781826
$244$	21.5644	1.38052
$245$	1.00000	0.0638877
$246$	55.8412	3.56031
$247$	1.11240	0.0707804
$248$	58.0230	3.68446
$249$	−10.4663	−0.663276
$250$	−2.54658	−0.161060
$251$	−13.3765	−0.844315	−0.422157	−	0.906523i	$-0.638727\pi$
$251$	−13.3765	−0.844315	−0.422157	+	0.906523i	$0.638727\pi$
$252$	−23.2178	−1.46258
$253$	−1.86179	−0.117050
$254$	−10.0273	−0.629169
$255$	−3.51218	−0.219941
$256$	−29.0367	−1.81479
$257$	−4.78644	−0.298570	−0.149285	−	0.988794i	$-0.547697\pi$
$257$	−4.78644	−0.298570	−0.149285	+	0.988794i	$0.547697\pi$
$258$	−9.09926	−0.566495
$259$	−3.94020	−0.244832
$260$	2.64372	0.163957
$261$	44.2221	2.73728
$262$	−35.4774	−2.19180
$263$	−17.4142	−1.07381	−0.536904	−	0.843644i	$-0.680406\pi$
$263$	−17.4142	−1.07381	−0.536904	+	0.843644i	$0.680406\pi$
$264$	36.2866	2.23329
$265$	2.23556	0.137330
$266$	4.80588	0.294668
$267$	31.9068	1.95266
$268$	−33.3737	−2.03862
$269$	−30.7260	−1.87340	−0.936699	−	0.350136i	$-0.886135\pi$
$269$	−30.7260	−1.87340	−0.936699	+	0.350136i	$0.886135\pi$
$270$	15.8503	0.964620
$271$	16.3075	0.990611	0.495306	−	0.868719i	$-0.335056\pi$
$271$	16.3075	0.990611	0.495306	+	0.868719i	$0.335056\pi$
$272$	8.77681	0.532173
$273$	1.68552	0.102012
$274$	35.8605	2.16641
$275$	2.00521	0.120919
$276$	11.9077	0.716760
$277$	3.42696	0.205906	0.102953	−	0.994686i	$-0.467171\pi$
$277$	3.42696	0.205906	0.102953	+	0.994686i	$0.467171\pi$
$278$	−44.1259	−2.64650
$279$	−47.4628	−2.84152
$280$	6.32845	0.378197
$281$	−2.44613	−0.145924	−0.0729618	−	0.997335i	$-0.523245\pi$
$281$	−2.44613	−0.145924	−0.0729618	+	0.997335i	$0.523245\pi$
$282$	−86.6641	−5.16077
$283$	−24.5147	−1.45725	−0.728624	−	0.684914i	$-0.759840\pi$
$283$	−24.5147	−1.45725	−0.728624	+	0.684914i	$0.759840\pi$
$284$	−53.5176	−3.17569
$285$	−5.39640	−0.319655
$286$	−3.00998	−0.177984
$287$	−7.66848	−0.452656
$288$	−28.6807	−1.69002
$289$	−15.4914	−0.911258
$290$	−21.7544	−1.27746
$291$	−31.2837	−1.83388
$292$	67.7232	3.96320
$293$	8.91065	0.520566	0.260283	−	0.965532i	$-0.416184\pi$
$293$	8.91065	0.520566	0.260283	+	0.965532i	$0.416184\pi$
$294$	7.28192	0.424690
$295$	12.9759	0.755487
$296$	−24.9354	−1.44934
$297$	−12.4808	−0.724208
$298$	42.5660	2.46578
$299$	−0.547287	−0.0316504
$300$	−12.8250	−0.740453
$301$	1.24957	0.0720239
$302$	−50.7961	−2.92298
$303$	−10.8882	−0.625509
$304$	13.4854	0.773442
$305$	4.80804	0.275308
$306$	−16.1918	−0.925626
$307$	−16.2145	−0.925410	−0.462705	−	0.886512i	$-0.653121\pi$
$307$	−16.2145	−0.925410	−0.462705	+	0.886512i	$0.653121\pi$
$308$	−8.99354	−0.512455
$309$	−10.4851	−0.596477
$310$	23.3486	1.32611
$311$	−18.2843	−1.03681	−0.518404	−	0.855136i	$-0.673474\pi$
$311$	−18.2843	−1.03681	−0.518404	+	0.855136i	$0.673474\pi$
$312$	10.6667	0.603885
$313$	14.8779	0.840948	0.420474	−	0.907305i	$-0.361864\pi$
$313$	14.8779	0.840948	0.420474	+	0.907305i	$0.361864\pi$
$314$	−35.1480	−1.98352
$315$	−5.17667	−0.291672
$316$	22.5072	1.26613
$317$	−4.22819	−0.237479	−0.118739	−	0.992925i	$-0.537885\pi$
$317$	−4.22819	−0.237479	−0.118739	+	0.992925i	$0.537885\pi$
$318$	16.2792	0.912892
$319$	17.1297	0.959079
$320$	−0.182530	−0.0102038
$321$	−28.6826	−1.60091
$322$	−2.36444	−0.131765
$323$	2.31795	0.128974
$324$	10.1717	0.565093
$325$	0.589448	0.0326967
$326$	−46.7502	−2.58926
$327$	−27.3655	−1.51331
$328$	−48.5296	−2.67960
$329$	11.9013	0.656138
$330$	14.6018	0.803803
$331$	−20.5434	−1.12917	−0.564583	−	0.825377i	$-0.690963\pi$
$331$	−20.5434	−1.12917	−0.564583	+	0.825377i	$0.690963\pi$
$332$	16.4163	0.900963
$333$	20.3971	1.11776
$334$	10.0326	0.548958
$335$	−7.44106	−0.406549
$336$	20.4332	1.11472
$337$	32.5129	1.77109	0.885545	−	0.464554i	$-0.153785\pi$
$337$	32.5129	1.77109	0.885545	+	0.464554i	$0.153785\pi$
$338$	32.2208	1.75258
$339$	13.7512	0.746863
$340$	5.50881	0.298757
$341$	−18.3850	−0.995603
$342$	−24.8785	−1.34527
$343$	−1.00000	−0.0539949
$344$	7.90783	0.426362
$345$	2.65496	0.142938
$346$	−32.6730	−1.75651
$347$	−1.23249	−0.0661634	−0.0330817	−	0.999453i	$-0.510532\pi$
$347$	−1.23249	−0.0661634	−0.0330817	+	0.999453i	$0.510532\pi$
$348$	−109.559	−5.87296
$349$	−15.6160	−0.835908	−0.417954	−	0.908468i	$-0.637253\pi$
$349$	−15.6160	−0.835908	−0.417954	+	0.908468i	$0.637253\pi$
$350$	2.54658	0.136121
$351$	−3.66882	−0.195827
$352$	−11.1096	−0.592145
$353$	7.42126	0.394994	0.197497	−	0.980303i	$-0.436719\pi$
$353$	7.42126	0.394994	0.197497	+	0.980303i	$0.436719\pi$
$354$	94.4896	5.02207
$355$	−11.9324	−0.633305
$356$	−50.0454	−2.65240
$357$	3.51218	0.185884
$358$	20.0841	1.06148
$359$	−0.170291	−0.00898761	−0.00449380	−	0.999990i	$-0.501430\pi$
$359$	−0.170291	−0.00898761	−0.00449380	+	0.999990i	$0.501430\pi$
$360$	−32.7603	−1.72662
$361$	−15.4385	−0.812553
$362$	−52.8539	−2.77794
$363$	19.9567	1.04745
$364$	−2.64372	−0.138569
$365$	15.0997	0.790353
$366$	35.0118	1.83009
$367$	−19.4158	−1.01350	−0.506748	−	0.862094i	$-0.669153\pi$
$367$	−19.4158	−1.01350	−0.506748	+	0.862094i	$0.669153\pi$
$368$	−6.63466	−0.345855
$369$	39.6972	2.06655
$370$	−10.0340	−0.521645
$371$	−2.23556	−0.116065
$372$	117.587	6.09662
$373$	−36.0845	−1.86838	−0.934191	−	0.356773i	$-0.883877\pi$
$373$	−36.0845	−1.86838	−0.934191	+	0.356773i	$0.883877\pi$
$374$	−6.27201	−0.324318
$375$	−2.85949	−0.147663
$376$	75.3166	3.88416
$377$	5.03540	0.259337
$378$	−15.8503	−0.815253
$379$	22.8381	1.17311	0.586557	−	0.809908i	$-0.300483\pi$
$379$	22.8381	1.17311	0.586557	+	0.809908i	$0.300483\pi$
$380$	8.46420	0.434204
$381$	−11.2594	−0.576836
$382$	23.4612	1.20038
$383$	−14.9065	−0.761684	−0.380842	−	0.924640i	$-0.624366\pi$
$383$	−14.9065	−0.761684	−0.380842	+	0.924640i	$0.624366\pi$
$384$	−33.0144	−1.68476
$385$	−2.00521	−0.102195
$386$	47.9903	2.44264
$387$	−6.46860	−0.328818
$388$	49.0682	2.49106
$389$	−19.1544	−0.971166	−0.485583	−	0.874191i	$-0.661393\pi$
$389$	−19.1544	−0.971166	−0.485583	+	0.874191i	$0.661393\pi$
$390$	4.29231	0.217350
$391$	−1.14040	−0.0576726
$392$	−6.32845	−0.319635
$393$	−39.8366	−2.00949
$394$	−43.7895	−2.20608
$395$	5.01824	0.252495
$396$	46.5566	2.33956
$397$	−12.3128	−0.617962	−0.308981	−	0.951068i	$-0.599988\pi$
$397$	−12.3128	−0.617962	−0.308981	+	0.951068i	$0.599988\pi$
$398$	−19.7798	−0.991470
$399$	5.39640	0.270158
$400$	7.14576	0.357288
$401$	−28.9809	−1.44724	−0.723618	−	0.690201i	$-0.757522\pi$
$401$	−28.9809	−1.44724	−0.723618	+	0.690201i	$0.757522\pi$
$402$	−54.1852	−2.70251
$403$	−5.40441	−0.269213
$404$	17.0780	0.849662
$405$	2.26789	0.112692
$406$	21.7544	1.07965
$407$	7.90095	0.391636
$408$	22.2266	1.10038
$409$	18.2036	0.900108	0.450054	−	0.893001i	$-0.351405\pi$
$409$	18.2036	0.900108	0.450054	+	0.893001i	$0.351405\pi$
$410$	−19.5284	−0.964439
$411$	40.2667	1.98621
$412$	16.4458	0.810226
$413$	−12.9759	−0.638503
$414$	12.2399	0.601558
$415$	3.66021	0.179673
$416$	−3.26576	−0.160117
$417$	−49.5478	−2.42636
$418$	−9.63683	−0.471353
$419$	18.1481	0.886590	0.443295	−	0.896376i	$-0.353809\pi$
$419$	18.1481	0.886590	0.443295	+	0.896376i	$0.353809\pi$
$420$	12.8250	0.625797
$421$	−0.254348	−0.0123962	−0.00619809	−	0.999981i	$-0.501973\pi$
$421$	−0.254348	−0.0123962	−0.00619809	+	0.999981i	$0.501973\pi$
$422$	39.6965	1.93239
$423$	−61.6089	−2.99553
$424$	−14.1477	−0.687071
$425$	1.22825	0.0595791
$426$	−86.8906	−4.20986
$427$	−4.80804	−0.232677
$428$	44.9884	2.17460
$429$	−3.37983	−0.163180
$430$	3.18213	0.153456
$431$	−7.93664	−0.382295	−0.191147	−	0.981561i	$-0.561221\pi$
$431$	−7.93664	−0.382295	−0.191147	+	0.981561i	$0.561221\pi$
$432$	−44.4764	−2.13987
$433$	30.0280	1.44305	0.721527	−	0.692386i	$-0.243441\pi$
$433$	30.0280	1.44305	0.721527	+	0.692386i	$0.243441\pi$
$434$	−23.3486	−1.12077
$435$	−24.4274	−1.17120
$436$	42.9225	2.05561
$437$	−1.75221	−0.0838195
$438$	109.955	5.25383
$439$	−25.2614	−1.20566	−0.602831	−	0.797869i	$-0.705961\pi$
$439$	−25.2614	−1.20566	−0.602831	+	0.797869i	$0.705961\pi$
$440$	−12.6899	−0.604967
$441$	5.17667	0.246508
$442$	−1.84370	−0.0876961
$443$	28.5139	1.35474	0.677368	−	0.735644i	$-0.263121\pi$
$443$	28.5139	1.35474	0.677368	+	0.735644i	$0.263121\pi$
$444$	−50.5332	−2.39820
$445$	−11.1582	−0.528950
$446$	18.3911	0.870846
$447$	47.7962	2.26068
$448$	0.182530	0.00862375
$449$	29.2481	1.38030	0.690152	−	0.723665i	$-0.257544\pi$
$449$	29.2481	1.38030	0.690152	+	0.723665i	$0.257544\pi$
$450$	−13.1828	−0.621444
$451$	15.3769	0.724072
$452$	−21.5686	−1.01450
$453$	−57.0375	−2.67986
$454$	−7.66098	−0.359548
$455$	−0.589448	−0.0276338
$456$	34.1508	1.59926
$457$	−13.9277	−0.651509	−0.325754	−	0.945454i	$-0.605618\pi$
$457$	−13.9277	−0.651509	−0.325754	+	0.945454i	$0.605618\pi$
$458$	2.54658	0.118994
$459$	−7.64485	−0.356831
$460$	−4.16428	−0.194161
$461$	30.9237	1.44026	0.720129	−	0.693840i	$-0.244083\pi$
$461$	30.9237	1.44026	0.720129	+	0.693840i	$0.244083\pi$
$462$	−14.6018	−0.679338
$463$	24.8376	1.15430	0.577151	−	0.816637i	$-0.304164\pi$
$463$	24.8376	1.15430	0.577151	+	0.816637i	$0.304164\pi$
$464$	61.0432	2.83386
$465$	26.2175	1.21581
$466$	49.6292	2.29903
$467$	−27.0084	−1.24980	−0.624901	−	0.780704i	$-0.714861\pi$
$467$	−27.0084	−1.24980	−0.624901	+	0.780704i	$0.714861\pi$
$468$	13.6857	0.632620
$469$	7.44106	0.343596
$470$	30.3076	1.39798
$471$	−39.4667	−1.81853
$472$	−82.1175	−3.77976
$473$	−2.50565	−0.115210
$474$	36.5424	1.67845
$475$	1.88719	0.0865902
$476$	−5.50881	−0.252496
$477$	11.5728	0.529881
$478$	−15.3800	−0.703465
$479$	26.3816	1.20541	0.602704	−	0.797965i	$-0.294090\pi$
$479$	26.3816	1.20541	0.602704	+	0.797965i	$0.294090\pi$
$480$	15.8426	0.723113
$481$	2.32255	0.105899
$482$	−44.4483	−2.02456
$483$	−2.65496	−0.120805
$484$	−31.3019	−1.42281
$485$	10.9403	0.496774
$486$	−31.0364	−1.40784
$487$	7.54551	0.341920	0.170960	−	0.985278i	$-0.445313\pi$
$487$	7.54551	0.341920	0.170960	+	0.985278i	$0.445313\pi$
$488$	−30.4275	−1.37739
$489$	−52.4946	−2.37389
$490$	−2.54658	−0.115043
$491$	22.6246	1.02103	0.510517	−	0.859868i	$-0.329454\pi$
$491$	22.6246	1.02103	0.510517	+	0.859868i	$0.329454\pi$
$492$	−98.3484	−4.43389
$493$	10.4925	0.472556
$494$	−2.83282	−0.127455
$495$	10.3803	0.466561
$496$	−65.5166	−2.94178
$497$	11.9324	0.535240
$498$	26.6533	1.19436
$499$	0.682048	0.0305326	0.0152663	−	0.999883i	$-0.495140\pi$
$499$	0.682048	0.0305326	0.0152663	+	0.999883i	$0.495140\pi$
$500$	4.48508	0.200579
$501$	11.2653	0.503296
$502$	34.0643	1.52036
$503$	−3.00082	−0.133800	−0.0668999	−	0.997760i	$-0.521311\pi$
$503$	−3.00082	−0.133800	−0.0668999	+	0.997760i	$0.521311\pi$
$504$	32.7603	1.45926
$505$	3.80774	0.169442
$506$	4.74120	0.210772
$507$	36.1798	1.60680
$508$	17.6602	0.783547
$509$	−22.6023	−1.00183	−0.500915	−	0.865496i	$-0.667003\pi$
$509$	−22.6023	−1.00183	−0.500915	+	0.865496i	$0.667003\pi$
$510$	8.94405	0.396049
$511$	−15.0997	−0.667970
$512$	50.8531	2.24741
$513$	−11.7462	−0.518606
$514$	12.1890	0.537636
$515$	3.66678	0.161578
$516$	16.0257	0.705494
$517$	−23.8646	−1.04956
$518$	10.0340	0.440871
$519$	−36.6876	−1.61041
$520$	−3.73029	−0.163584
$521$	−41.7339	−1.82840	−0.914198	−	0.405269i	$-0.867178\pi$
$521$	−41.7339	−1.82840	−0.914198	+	0.405269i	$0.867178\pi$
$522$	−112.615	−4.92903
$523$	11.8917	0.519988	0.259994	−	0.965610i	$-0.416279\pi$
$523$	11.8917	0.519988	0.259994	+	0.965610i	$0.416279\pi$
$524$	62.4833	2.72959
$525$	2.85949	0.124798
$526$	44.3468	1.93361
$527$	−11.2614	−0.490553
$528$	−40.9730	−1.78312
$529$	−22.1379	−0.962519
$530$	−5.69305	−0.247290
$531$	67.1720	2.91502
$532$	−8.46420	−0.366969
$533$	4.52017	0.195790
$534$	−81.2532	−3.51617
$535$	10.0307	0.433664
$536$	47.0904	2.03400
$537$	22.5519	0.973187
$538$	78.2463	3.37344
$539$	2.00521	0.0863707
$540$	−27.9158	−1.20131
$541$	−5.51478	−0.237099	−0.118549	−	0.992948i	$-0.537824\pi$
$541$	−5.51478	−0.237099	−0.118549	+	0.992948i	$0.537824\pi$
$542$	−41.5284	−1.78380
$543$	−59.3482	−2.54688
$544$	−6.80498	−0.291761
$545$	9.57007	0.409937
$546$	−4.29231	−0.183694
$547$	−8.78713	−0.375710	−0.187855	−	0.982197i	$-0.560154\pi$
$547$	−8.78713	−0.375710	−0.187855	+	0.982197i	$0.560154\pi$
$548$	−63.1580	−2.69797
$549$	24.8896	1.06226
$550$	−5.10644	−0.217739
$551$	16.1215	0.686797
$552$	−16.8018	−0.715132
$553$	−5.01824	−0.213397
$554$	−8.72704	−0.370776
$555$	−11.2670	−0.478256
$556$	77.7152	3.29586
$557$	−3.91337	−0.165815	−0.0829073	−	0.996557i	$-0.526421\pi$
$557$	−3.91337	−0.165815	−0.0829073	+	0.996557i	$0.526421\pi$
$558$	120.868	5.11674
$559$	−0.736556	−0.0311530
$560$	−7.14576	−0.301964
$561$	−7.04267	−0.297342
$562$	6.22926	0.262766
$563$	−10.4105	−0.438749	−0.219374	−	0.975641i	$-0.570402\pi$
$563$	−10.4105	−0.438749	−0.219374	+	0.975641i	$0.570402\pi$
$564$	152.634	6.42705
$565$	−4.80897	−0.202315
$566$	62.4287	2.62407
$567$	−2.26789	−0.0952425
$568$	75.5135	3.16847
$569$	−8.05237	−0.337573	−0.168786	−	0.985653i	$-0.553985\pi$
$569$	−8.05237	−0.337573	−0.168786	+	0.985653i	$0.553985\pi$
$570$	13.7424	0.575604
$571$	2.42022	0.101283	0.0506415	−	0.998717i	$-0.483873\pi$
$571$	2.42022	0.101283	0.0506415	+	0.998717i	$0.483873\pi$
$572$	5.30123	0.221655
$573$	26.3439	1.10053
$574$	19.5284	0.815100
$575$	−0.928474	−0.0387201
$576$	−0.944900	−0.0393708
$577$	29.1675	1.21426	0.607130	−	0.794603i	$-0.292321\pi$
$577$	29.1675	1.21426	0.607130	+	0.794603i	$0.292321\pi$
$578$	39.4501	1.64091
$579$	53.8870	2.23947
$580$	38.3141	1.59091
$581$	−3.66021	−0.151851
$582$	79.6665	3.30228
$583$	4.48278	0.185658
$584$	−95.5576	−3.95420
$585$	3.05138	0.126159
$586$	−22.6917	−0.937386
$587$	4.70685	0.194273	0.0971363	−	0.995271i	$-0.469032\pi$
$587$	4.70685	0.194273	0.0971363	+	0.995271i	$0.469032\pi$
$588$	−12.8250	−0.528895
$589$	−17.3029	−0.712953
$590$	−33.0442	−1.36041
$591$	−49.1700	−2.02258
$592$	28.1558	1.15719
$593$	−33.6134	−1.38034	−0.690169	−	0.723648i	$-0.742464\pi$
$593$	−33.6134	−1.38034	−0.690169	+	0.723648i	$0.742464\pi$
$594$	31.7833	1.30408
$595$	−1.22825	−0.0503535
$596$	−74.9679	−3.07080
$597$	−22.2102	−0.909001
$598$	1.39371	0.0569931
$599$	23.7702	0.971222	0.485611	−	0.874175i	$-0.338597\pi$
$599$	23.7702	0.971222	0.485611	+	0.874175i	$0.338597\pi$
$600$	18.0961	0.738771
$601$	16.3134	0.665438	0.332719	−	0.943026i	$-0.392034\pi$
$601$	16.3134	0.665438	0.332719	+	0.943026i	$0.392034\pi$
$602$	−3.18213	−0.129694
$603$	−38.5199	−1.56865
$604$	89.4628	3.64019
$605$	−6.97912	−0.283741
$606$	27.7276	1.12636
$607$	−4.58267	−0.186005	−0.0930025	−	0.995666i	$-0.529646\pi$
$607$	−4.58267	−0.186005	−0.0930025	+	0.995666i	$0.529646\pi$
$608$	−10.4557	−0.424036
$609$	24.4274	0.989847
$610$	−12.2441	−0.495748
$611$	−7.01518	−0.283804
$612$	28.5173	1.15274
$613$	31.0110	1.25252	0.626262	−	0.779613i	$-0.284584\pi$
$613$	31.0110	1.25252	0.626262	+	0.779613i	$0.284584\pi$
$614$	41.2915	1.66639
$615$	−21.9279	−0.884219
$616$	12.6899	0.511291
$617$	40.9398	1.64817	0.824087	−	0.566463i	$-0.191689\pi$
$617$	40.9398	1.64817	0.824087	+	0.566463i	$0.191689\pi$
$618$	26.7012	1.07408
$619$	31.2255	1.25506	0.627530	−	0.778593i	$-0.284066\pi$
$619$	31.2255	1.25506	0.627530	+	0.778593i	$0.284066\pi$
$620$	−41.1219	−1.65149
$621$	5.77897	0.231902
$622$	46.5625	1.86698
$623$	11.1582	0.447044
$624$	−12.0443	−0.482159
$625$	1.00000	0.0400000
$626$	−37.8878	−1.51430
$627$	−10.8209	−0.432146
$628$	61.9032	2.47020
$629$	4.83957	0.192966
$630$	13.1828	0.525216
$631$	36.9513	1.47101	0.735504	−	0.677520i	$-0.236945\pi$
$631$	36.9513	1.47101	0.735504	+	0.677520i	$0.236945\pi$
$632$	−31.7577	−1.26325
$633$	44.5741	1.77166
$634$	10.7674	0.427629
$635$	3.93756	0.156257
$636$	−28.6712	−1.13689
$637$	0.589448	0.0233548
$638$	−43.6222	−1.72702
$639$	−61.7700	−2.44358
$640$	11.5456	0.456379
$641$	1.42824	0.0564120	0.0282060	−	0.999602i	$-0.491021\pi$
$641$	1.42824	0.0564120	0.0282060	+	0.999602i	$0.491021\pi$
$642$	73.0426	2.88276
$643$	−43.4699	−1.71429	−0.857144	−	0.515077i	$-0.827763\pi$
$643$	−43.4699	−1.71429	−0.857144	+	0.515077i	$0.827763\pi$
$644$	4.16428	0.164096
$645$	3.57313	0.140692
$646$	−5.90285	−0.232244
$647$	−40.8007	−1.60404	−0.802020	−	0.597297i	$-0.796242\pi$
$647$	−40.8007	−1.60404	−0.802020	+	0.597297i	$0.796242\pi$
$648$	−14.3522	−0.563809
$649$	26.0195	1.02135
$650$	−1.50108	−0.0588771
$651$	−26.2175	−1.02754
$652$	82.3372	3.22457
$653$	31.1950	1.22075	0.610377	−	0.792111i	$-0.291018\pi$
$653$	31.1950	1.22075	0.610377	+	0.792111i	$0.291018\pi$
$654$	69.6884	2.72503
$655$	13.9314	0.544344
$656$	54.7972	2.13947
$657$	78.1660	3.04955
$658$	−30.3076	−1.18151
$659$	−39.5098	−1.53908	−0.769541	−	0.638597i	$-0.779515\pi$
$659$	−39.5098	−1.53908	−0.769541	+	0.638597i	$0.779515\pi$
$660$	−25.7169	−1.00103
$661$	10.8977	0.423870	0.211935	−	0.977284i	$-0.432023\pi$
$661$	10.8977	0.423870	0.211935	+	0.977284i	$0.432023\pi$
$662$	52.3154	2.03329
$663$	−2.07025	−0.0804017
$664$	−23.1635	−0.898917
$665$	−1.88719	−0.0731821
$666$	−51.9429	−2.01275
$667$	−7.93156	−0.307111
$668$	−17.6695	−0.683654
$669$	20.6509	0.798411
$670$	18.9493	0.732074
$671$	9.64115	0.372193
$672$	−15.8426	−0.611142
$673$	46.6770	1.79927	0.899633	−	0.436648i	$-0.143834\pi$
$673$	46.6770	1.79927	0.899633	+	0.436648i	$0.143834\pi$
$674$	−82.7967	−3.18921
$675$	−6.22416	−0.239568
$676$	−56.7477	−2.18260
$677$	−4.37530	−0.168156	−0.0840782	−	0.996459i	$-0.526795\pi$
$677$	−4.37530	−0.168156	−0.0840782	+	0.996459i	$0.526795\pi$
$678$	−35.0186	−1.34488
$679$	−10.9403	−0.419851
$680$	−7.77295	−0.298079
$681$	−8.60231	−0.329641
$682$	46.8189	1.79279
$683$	27.9977	1.07130	0.535650	−	0.844440i	$-0.320066\pi$
$683$	27.9977	1.07130	0.535650	+	0.844440i	$0.320066\pi$
$684$	43.8163	1.67536
$685$	−14.0818	−0.538038
$686$	2.54658	0.0972289
$687$	2.85949	0.109096
$688$	−8.92912	−0.340420
$689$	1.31775	0.0502022
$690$	−6.76107	−0.257390
$691$	−4.48070	−0.170454	−0.0852269	−	0.996362i	$-0.527162\pi$
$691$	−4.48070	−0.170454	−0.0852269	+	0.996362i	$0.527162\pi$
$692$	57.5442	2.18750
$693$	−10.3803	−0.394316
$694$	3.13863	0.119141
$695$	17.3275	0.657270
$696$	154.588	5.85963
$697$	9.41884	0.356764
$698$	39.7675	1.50522
$699$	55.7272	2.10780
$700$	−4.48508	−0.169520
$701$	−5.38570	−0.203415	−0.101708	−	0.994814i	$-0.532431\pi$
$701$	−5.38570	−0.203415	−0.101708	+	0.994814i	$0.532431\pi$
$702$	9.34294	0.352627
$703$	7.43591	0.280451
$704$	−0.366013	−0.0137946
$705$	34.0315	1.28170
$706$	−18.8989	−0.711268
$707$	−3.80774	−0.143205
$708$	−166.416	−6.25431
$709$	−3.79816	−0.142643	−0.0713214	−	0.997453i	$-0.522722\pi$
$709$	−3.79816	−0.142643	−0.0713214	+	0.997453i	$0.522722\pi$
$710$	30.3868	1.14040
$711$	25.9778	0.974243
$712$	70.6142	2.64638
$713$	8.51280	0.318807
$714$	−8.94405	−0.334722
$715$	1.18197	0.0442032
$716$	−35.3725	−1.32193
$717$	−17.2698	−0.644952
$718$	0.433659	0.0161840
$719$	−10.5775	−0.394475	−0.197238	−	0.980356i	$-0.563197\pi$
$719$	−10.5775	−0.394475	−0.197238	+	0.980356i	$0.563197\pi$
$720$	36.9913	1.37858
$721$	−3.66678	−0.136558
$722$	39.3154	1.46317
$723$	−49.9098	−1.85617
$724$	93.0871	3.45955
$725$	8.54257	0.317263
$726$	−50.8213	−1.88616
$727$	25.0466	0.928928	0.464464	−	0.885592i	$-0.346247\pi$
$727$	25.0466	0.928928	0.464464	+	0.885592i	$0.346247\pi$
$728$	3.73029	0.138254
$729$	−41.6536	−1.54272
$730$	−38.4525	−1.42319
$731$	−1.53479	−0.0567662
$732$	−61.6632	−2.27914
$733$	−21.7489	−0.803312	−0.401656	−	0.915791i	$-0.631565\pi$
$733$	−21.7489	−0.803312	−0.401656	+	0.915791i	$0.631565\pi$
$734$	49.4439	1.82501
$735$	−2.85949	−0.105474
$736$	5.14409	0.189614
$737$	−14.9209	−0.549619
$738$	−101.092	−3.72125
$739$	−19.2466	−0.707999	−0.354000	−	0.935246i	$-0.615179\pi$
$739$	−19.2466	−0.707999	−0.354000	+	0.935246i	$0.615179\pi$
$740$	17.6721	0.649640
$741$	−3.18090	−0.116853
$742$	5.69305	0.208998
$743$	8.08358	0.296558	0.148279	−	0.988946i	$-0.452627\pi$
$743$	8.08358	0.296558	0.148279	+	0.988946i	$0.452627\pi$
$744$	−165.916	−6.08278
$745$	−16.7150	−0.612388
$746$	91.8920	3.36441
$747$	18.9477	0.693260
$748$	11.0464	0.403895
$749$	−10.0307	−0.366513
$750$	7.28192	0.265898
$751$	42.2541	1.54187	0.770937	−	0.636911i	$-0.219788\pi$
$751$	42.2541	1.54187	0.770937	+	0.636911i	$0.219788\pi$
$752$	−85.0437	−3.10122
$753$	38.2498	1.39390
$754$	−12.8231	−0.466989
$755$	19.9468	0.725937
$756$	27.9158	1.01529
$757$	−12.9020	−0.468931	−0.234466	−	0.972124i	$-0.575334\pi$
$757$	−12.9020	−0.468931	−0.234466	+	0.972124i	$0.575334\pi$
$758$	−58.1591	−2.11243
$759$	5.32376	0.193240
$760$	−11.9430	−0.433218
$761$	−7.27635	−0.263767	−0.131884	−	0.991265i	$-0.542103\pi$
$761$	−7.27635	−0.263767	−0.131884	+	0.991265i	$0.542103\pi$
$762$	28.6730	1.03871
$763$	−9.57007	−0.346460
$764$	−41.3202	−1.49491
$765$	6.35826	0.229884
$766$	37.9605	1.37157
$767$	7.64863	0.276176
$768$	83.0300	2.99609
$769$	−4.91840	−0.177362	−0.0886811	−	0.996060i	$-0.528265\pi$
$769$	−4.91840	−0.177362	−0.0886811	+	0.996060i	$0.528265\pi$
$770$	5.10644	0.184023
$771$	13.6868	0.492916
$772$	−84.5212	−3.04199
$773$	4.57821	0.164667	0.0823334	−	0.996605i	$-0.473763\pi$
$773$	4.57821	0.164667	0.0823334	+	0.996605i	$0.473763\pi$
$774$	16.4728	0.592103
$775$	−9.16859	−0.329346
$776$	−69.2353	−2.48540
$777$	11.2670	0.404200
$778$	48.7782	1.74878
$779$	14.4719	0.518509
$780$	−7.55969	−0.270680
$781$	−23.9270	−0.856174
$782$	2.90413	0.103851
$783$	−53.1703	−1.90015
$784$	7.14576	0.255206
$785$	13.8020	0.492615
$786$	101.447	3.61850
$787$	33.9024	1.20849	0.604244	−	0.796799i	$-0.293475\pi$
$787$	33.9024	1.20849	0.604244	+	0.796799i	$0.293475\pi$
$788$	77.1226	2.74738
$789$	49.7958	1.77278
$790$	−12.7794	−0.454669
$791$	4.80897	0.170987
$792$	−65.6914	−2.33424
$793$	2.83409	0.100642
$794$	31.3555	1.11277
$795$	−6.39257	−0.226721
$796$	34.8364	1.23474
$797$	46.3775	1.64277	0.821387	−	0.570371i	$-0.193201\pi$
$797$	46.3775	1.64277	0.821387	+	0.570371i	$0.193201\pi$
$798$	−13.7424	−0.486475
$799$	−14.6178	−0.517140
$800$	−5.54037	−0.195882
$801$	−57.7623	−2.04093
$802$	73.8021	2.60604
$803$	30.2781	1.06849
$804$	95.4318	3.36562
$805$	0.928474	0.0327244
$806$	13.7628	0.484773
$807$	87.8606	3.09284
$808$	−24.0971	−0.847732
$809$	−46.8251	−1.64628	−0.823141	−	0.567837i	$-0.807781\pi$
$809$	−46.8251	−1.64628	−0.823141	+	0.567837i	$0.807781\pi$
$810$	−5.77537	−0.202926
$811$	1.08081	0.0379525	0.0189762	−	0.999820i	$-0.493959\pi$
$811$	1.08081	0.0379525	0.0189762	+	0.999820i	$0.493959\pi$
$812$	−38.3141	−1.34456
$813$	−46.6312	−1.63543
$814$	−20.1204	−0.705220
$815$	18.3580	0.643054
$816$	−25.0972	−0.878577
$817$	−2.35817	−0.0825021
$818$	−46.3568	−1.62083
$819$	−3.05138	−0.106624
$820$	34.3937	1.20108
$821$	23.5058	0.820357	0.410179	−	0.912005i	$-0.365466\pi$
$821$	23.5058	0.820357	0.410179	+	0.912005i	$0.365466\pi$
$822$	−102.543	−3.57658
$823$	2.78208	0.0969771	0.0484886	−	0.998824i	$-0.484560\pi$
$823$	2.78208	0.0969771	0.0484886	+	0.998824i	$0.484560\pi$
$824$	−23.2050	−0.808386
$825$	−5.73389	−0.199628
$826$	33.0442	1.14976
$827$	18.4447	0.641385	0.320693	−	0.947183i	$-0.396084\pi$
$827$	18.4447	0.641385	0.320693	+	0.947183i	$0.396084\pi$
$828$	−21.5571	−0.749161
$829$	18.2854	0.635078	0.317539	−	0.948245i	$-0.397144\pi$
$829$	18.2854	0.635078	0.317539	+	0.948245i	$0.397144\pi$
$830$	−9.32102	−0.323537
$831$	−9.79936	−0.339936
$832$	−0.107592	−0.00373009
$833$	1.22825	0.0425565
$834$	126.177	4.36917
$835$	−3.93962	−0.136336
$836$	16.9725	0.587007
$837$	57.0668	1.97252
$838$	−46.2155	−1.59649
$839$	−6.13575	−0.211830	−0.105915	−	0.994375i	$-0.533777\pi$
$839$	−6.13575	−0.211830	−0.105915	+	0.994375i	$0.533777\pi$
$840$	−18.0961	−0.624376
$841$	43.9756	1.51640
$842$	0.647719	0.0223219
$843$	6.99467	0.240909
$844$	−69.9140	−2.40654
$845$	−12.6526	−0.435261
$846$	156.892	5.39406
$847$	6.97912	0.239805
$848$	15.9748	0.548577
$849$	70.0995	2.40581
$850$	−3.12785	−0.107284
$851$	−3.65838	−0.125408
$852$	153.033	5.24282
$853$	−31.6076	−1.08222	−0.541111	−	0.840951i	$-0.681996\pi$
$853$	−31.6076	−1.08222	−0.541111	+	0.840951i	$0.681996\pi$
$854$	12.2441	0.418983
$855$	9.76936	0.334105
$856$	−63.4787	−2.16966
$857$	31.5580	1.07800	0.539000	−	0.842306i	$-0.318802\pi$
$857$	31.5580	1.07800	0.539000	+	0.842306i	$0.318802\pi$
$858$	8.60701	0.293838
$859$	−11.1488	−0.380392	−0.190196	−	0.981746i	$-0.560912\pi$
$859$	−11.1488	−0.380392	−0.190196	+	0.981746i	$0.560912\pi$
$860$	−5.60441	−0.191109
$861$	21.9279	0.747302
$862$	20.2113	0.688400
$863$	39.3162	1.33834	0.669169	−	0.743110i	$-0.266650\pi$
$863$	39.3162	1.33834	0.669169	+	0.743110i	$0.266650\pi$
$864$	34.4841	1.17317
$865$	12.8301	0.436238
$866$	−76.4688	−2.59852
$867$	44.2974	1.50442
$868$	41.1219	1.39577
$869$	10.0627	0.341352
$870$	62.2063	2.10899
$871$	−4.38612	−0.148618
$872$	−60.5637	−2.05095
$873$	56.6344	1.91678
$874$	4.46214	0.150934
$875$	−1.00000	−0.0338062
$876$	−193.654	−6.54295
$877$	−2.98053	−0.100645	−0.0503227	−	0.998733i	$-0.516025\pi$
$877$	−2.98053	−0.100645	−0.0503227	+	0.998733i	$0.516025\pi$
$878$	64.3302	2.17104
$879$	−25.4799	−0.859416
$880$	14.3288	0.483023
$881$	−35.9732	−1.21197	−0.605985	−	0.795476i	$-0.707221\pi$
$881$	−35.9732	−1.21197	−0.605985	+	0.795476i	$0.707221\pi$
$882$	−13.1828	−0.443888
$883$	−42.5996	−1.43359	−0.716795	−	0.697284i	$-0.754392\pi$
$883$	−42.5996	−1.43359	−0.716795	+	0.697284i	$0.754392\pi$
$884$	3.24716	0.109214
$885$	−37.1045	−1.24725
$886$	−72.6129	−2.43948
$887$	47.3184	1.58879	0.794397	−	0.607398i	$-0.207787\pi$
$887$	47.3184	1.58879	0.794397	+	0.607398i	$0.207787\pi$
$888$	71.3024	2.39275
$889$	−3.93756	−0.132061
$890$	28.4153	0.952483
$891$	4.54761	0.152351
$892$	−32.3908	−1.08452
$893$	−22.4600	−0.751594
$894$	−121.717	−4.07082
$895$	−7.88670	−0.263623
$896$	−11.5456	−0.385710
$897$	1.56496	0.0522525
$898$	−74.4827	−2.48552
$899$	−78.3234	−2.61223
$900$	23.2178	0.773925
$901$	2.74584	0.0914772
$902$	−39.1587	−1.30384
$903$	−3.57313	−0.118906
$904$	30.4334	1.01220
$905$	20.7548	0.689914
$906$	145.251	4.82563
$907$	27.9556	0.928251	0.464126	−	0.885769i	$-0.346369\pi$
$907$	27.9556	0.928251	0.464126	+	0.885769i	$0.346369\pi$
$908$	13.4926	0.447769
$909$	19.7114	0.653786
$910$	1.50108	0.0497602
$911$	−24.8813	−0.824353	−0.412176	−	0.911104i	$-0.635231\pi$
$911$	−24.8813	−0.824353	−0.412176	+	0.911104i	$0.635231\pi$
$912$	−38.5614	−1.27690
$913$	7.33950	0.242902
$914$	35.4679	1.17318
$915$	−13.7485	−0.454513
$916$	−4.48508	−0.148191
$917$	−13.9314	−0.460054
$918$	19.4682	0.642547
$919$	−21.5946	−0.712339	−0.356170	−	0.934421i	$-0.615917\pi$
$919$	−21.5946	−0.712339	−0.356170	+	0.934421i	$0.615917\pi$
$920$	5.87580	0.193720
$921$	46.3651	1.52778
$922$	−78.7496	−2.59348
$923$	−7.03352	−0.231511
$924$	25.7169	0.846025
$925$	3.94020	0.129553
$926$	−63.2510	−2.07856
$927$	18.9817	0.623441
$928$	−47.3290	−1.55365
$929$	−22.5835	−0.740941	−0.370471	−	0.928844i	$-0.620804\pi$
$929$	−22.5835	−0.740941	−0.370471	+	0.928844i	$0.620804\pi$
$930$	−66.7649	−2.18931
$931$	1.88719	0.0618502
$932$	−87.4076	−2.86313
$933$	52.2837	1.71169
$934$	68.7792	2.25052
$935$	2.46291	0.0805459
$936$	−19.3105	−0.631183
$937$	18.9378	0.618671	0.309335	−	0.950953i	$-0.399893\pi$
$937$	18.9378	0.618671	0.309335	+	0.950953i	$0.399893\pi$
$938$	−18.9493	−0.618715
$939$	−42.5431	−1.38834
$940$	−53.3781	−1.74100
$941$	21.0131	0.685008	0.342504	−	0.939516i	$-0.388725\pi$
$941$	21.0131	0.685008	0.342504	+	0.939516i	$0.388725\pi$
$942$	100.505	3.27464
$943$	−7.11999	−0.231859
$944$	92.7229	3.01787
$945$	6.22416	0.202472
$946$	6.38085	0.207459
$947$	25.9149	0.842122	0.421061	−	0.907032i	$-0.361658\pi$
$947$	25.9149	0.842122	0.421061	+	0.907032i	$0.361658\pi$
$948$	−64.3591	−2.09029
$949$	8.90047	0.288922
$950$	−4.80588	−0.155923
$951$	12.0905	0.392060
$952$	7.77295	0.251923
$953$	38.6205	1.25104	0.625520	−	0.780208i	$-0.284887\pi$
$953$	38.6205	1.25104	0.625520	+	0.780208i	$0.284887\pi$
$954$	−29.4710	−0.954159
$955$	−9.21282	−0.298120
$956$	27.0875	0.876072
$957$	−48.9821	−1.58337
$958$	−67.1830	−2.17058
$959$	14.0818	0.454725
$960$	0.521944	0.0168457
$961$	53.0631	1.71171
$962$	−5.91455	−0.190693
$963$	51.9255	1.67328
$964$	78.2830	2.52133
$965$	−18.8450	−0.606642
$966$	6.76107	0.217534
$967$	7.33535	0.235889	0.117944	−	0.993020i	$-0.462370\pi$
$967$	7.33535	0.235889	0.117944	+	0.993020i	$0.462370\pi$
$968$	44.1670	1.41958
$969$	−6.62815	−0.212927
$970$	−27.8604	−0.894544
$971$	−4.69187	−0.150569	−0.0752846	−	0.997162i	$-0.523987\pi$
$971$	−4.69187	−0.150569	−0.0752846	+	0.997162i	$0.523987\pi$
$972$	54.6617	1.75328
$973$	−17.3275	−0.555494
$974$	−19.2152	−0.615696
$975$	−1.68552	−0.0539798
$976$	34.3571	1.09975
$977$	−2.56317	−0.0820030	−0.0410015	−	0.999159i	$-0.513055\pi$
$977$	−2.56317	−0.0820030	−0.0410015	+	0.999159i	$0.513055\pi$
$978$	133.682	4.27467
$979$	−22.3746	−0.715095
$980$	4.48508	0.143271
$981$	49.5411	1.58172
$982$	−57.6154	−1.83858
$983$	17.3687	0.553977	0.276988	−	0.960873i	$-0.410664\pi$
$983$	17.3687	0.553977	0.276988	+	0.960873i	$0.410664\pi$
$984$	138.770	4.42382
$985$	17.1954	0.547891
$986$	−26.7199	−0.850934
$987$	−34.0315	−1.08324
$988$	4.98920	0.158728
$989$	1.16019	0.0368920
$990$	−26.4344	−0.840139
$991$	18.9935	0.603347	0.301674	−	0.953411i	$-0.402455\pi$
$991$	18.9935	0.603347	0.301674	+	0.953411i	$0.402455\pi$
$992$	50.7974	1.61282
$993$	58.7435	1.86417
$994$	−30.3868	−0.963810
$995$	7.76718	0.246236
$996$	−46.9423	−1.48742
$997$	37.7474	1.19547	0.597737	−	0.801692i	$-0.296067\pi$
$997$	37.7474	1.19547	0.597737	+	0.801692i	$0.296067\pi$
$998$	−1.73689	−0.0549803
$999$	−24.5244	−0.775919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.5	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.5	✓	67	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54658 q^{2} -2.85949 q^{3} +4.48508 q^{4} +1.00000 q^{5} +7.28192 q^{6} -1.00000 q^{7} -6.32845 q^{8} +5.17667 q^{9} +O(q^{10})\)	\(q-2.54658 q^{2} -2.85949 q^{3} +4.48508 q^{4} +1.00000 q^{5} +7.28192 q^{6} -1.00000 q^{7} -6.32845 q^{8} +5.17667 q^{9} -2.54658 q^{10} +2.00521 q^{11} -12.8250 q^{12} +0.589448 q^{13} +2.54658 q^{14} -2.85949 q^{15} +7.14576 q^{16} +1.22825 q^{17} -13.1828 q^{18} +1.88719 q^{19} +4.48508 q^{20} +2.85949 q^{21} -5.10644 q^{22} -0.928474 q^{23} +18.0961 q^{24} +1.00000 q^{25} -1.50108 q^{26} -6.22416 q^{27} -4.48508 q^{28} +8.54257 q^{29} +7.28192 q^{30} -9.16859 q^{31} -5.54037 q^{32} -5.73389 q^{33} -3.12785 q^{34} -1.00000 q^{35} +23.2178 q^{36} +3.94020 q^{37} -4.80588 q^{38} -1.68552 q^{39} -6.32845 q^{40} +7.66848 q^{41} -7.28192 q^{42} -1.24957 q^{43} +8.99354 q^{44} +5.17667 q^{45} +2.36444 q^{46} -11.9013 q^{47} -20.4332 q^{48} +1.00000 q^{49} -2.54658 q^{50} -3.51218 q^{51} +2.64372 q^{52} +2.23556 q^{53} +15.8503 q^{54} +2.00521 q^{55} +6.32845 q^{56} -5.39640 q^{57} -21.7544 q^{58} +12.9759 q^{59} -12.8250 q^{60} +4.80804 q^{61} +23.3486 q^{62} -5.17667 q^{63} -0.182530 q^{64} +0.589448 q^{65} +14.6018 q^{66} -7.44106 q^{67} +5.50881 q^{68} +2.65496 q^{69} +2.54658 q^{70} -11.9324 q^{71} -32.7603 q^{72} +15.0997 q^{73} -10.0340 q^{74} -2.85949 q^{75} +8.46420 q^{76} -2.00521 q^{77} +4.29231 q^{78} +5.01824 q^{79} +7.14576 q^{80} +2.26789 q^{81} -19.5284 q^{82} +3.66021 q^{83} +12.8250 q^{84} +1.22825 q^{85} +3.18213 q^{86} -24.4274 q^{87} -12.6899 q^{88} -11.1582 q^{89} -13.1828 q^{90} -0.589448 q^{91} -4.16428 q^{92} +26.2175 q^{93} +30.3076 q^{94} +1.88719 q^{95} +15.8426 q^{96} +10.9403 q^{97} -2.54658 q^{98} +10.3803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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