LMFDB - Embedded newform 8045.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$0$
Dimension:	$141$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33944 q^{2} +3.10966 q^{3} +3.47296 q^{4} -1.00000 q^{5} -7.27485 q^{6} -2.57808 q^{7} -3.44589 q^{8} +6.66998 q^{9} +O(q^{10})$	\(q-2.33944 q^{2} +3.10966 q^{3} +3.47296 q^{4} -1.00000 q^{5} -7.27485 q^{6} -2.57808 q^{7} -3.44589 q^{8} +6.66998 q^{9} +2.33944 q^{10} +5.47173 q^{11} +10.7997 q^{12} -4.87194 q^{13} +6.03126 q^{14} -3.10966 q^{15} +1.11553 q^{16} +5.50779 q^{17} -15.6040 q^{18} -0.954460 q^{19} -3.47296 q^{20} -8.01696 q^{21} -12.8008 q^{22} -3.87549 q^{23} -10.7156 q^{24} +1.00000 q^{25} +11.3976 q^{26} +11.4124 q^{27} -8.95358 q^{28} +7.06485 q^{29} +7.27485 q^{30} +3.21849 q^{31} +4.28208 q^{32} +17.0152 q^{33} -12.8851 q^{34} +2.57808 q^{35} +23.1646 q^{36} -6.97783 q^{37} +2.23290 q^{38} -15.1501 q^{39} +3.44589 q^{40} -1.26970 q^{41} +18.7552 q^{42} -8.29378 q^{43} +19.0031 q^{44} -6.66998 q^{45} +9.06646 q^{46} +4.84044 q^{47} +3.46891 q^{48} -0.353478 q^{49} -2.33944 q^{50} +17.1274 q^{51} -16.9200 q^{52} -2.18378 q^{53} -26.6985 q^{54} -5.47173 q^{55} +8.88381 q^{56} -2.96805 q^{57} -16.5278 q^{58} +5.51150 q^{59} -10.7997 q^{60} +1.96684 q^{61} -7.52944 q^{62} -17.1958 q^{63} -12.2487 q^{64} +4.87194 q^{65} -39.8060 q^{66} +2.24829 q^{67} +19.1283 q^{68} -12.0515 q^{69} -6.03126 q^{70} +5.55489 q^{71} -22.9840 q^{72} +16.0192 q^{73} +16.3242 q^{74} +3.10966 q^{75} -3.31480 q^{76} -14.1066 q^{77} +35.4426 q^{78} +5.26837 q^{79} -1.11553 q^{80} +15.4787 q^{81} +2.97038 q^{82} +6.44953 q^{83} -27.8426 q^{84} -5.50779 q^{85} +19.4028 q^{86} +21.9693 q^{87} -18.8550 q^{88} -2.58374 q^{89} +15.6040 q^{90} +12.5603 q^{91} -13.4594 q^{92} +10.0084 q^{93} -11.3239 q^{94} +0.954460 q^{95} +13.3158 q^{96} +0.742321 q^{97} +0.826939 q^{98} +36.4963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) $ 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * 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 $

$2$	−2.33944	−1.65423	−0.827115	−	0.562032i	$-0.810020\pi$
$2$	−2.33944	−1.65423	−0.827115	+	0.562032i	$0.810020\pi$
$3$	3.10966	1.79536	0.897681	−	0.440646i	$-0.145250\pi$
$3$	3.10966	1.79536	0.897681	+	0.440646i	$0.145250\pi$
$4$	3.47296	1.73648
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−7.27485	−2.96994
$7$	−2.57808	−0.974425	−0.487212	−	0.873284i	$-0.661986\pi$
$7$	−2.57808	−0.974425	−0.487212	+	0.873284i	$0.661986\pi$
$8$	−3.44589	−1.21831
$9$	6.66998	2.22333
$10$	2.33944	0.739795
$11$	5.47173	1.64979	0.824894	−	0.565287i	$-0.191235\pi$
$11$	5.47173	1.64979	0.824894	+	0.565287i	$0.191235\pi$
$12$	10.7997	3.11761
$13$	−4.87194	−1.35123	−0.675616	−	0.737253i	$-0.736122\pi$
$13$	−4.87194	−1.35123	−0.675616	+	0.737253i	$0.736122\pi$
$14$	6.03126	1.61192
$15$	−3.10966	−0.802910
$16$	1.11553	0.278882
$17$	5.50779	1.33584	0.667918	−	0.744235i	$-0.267186\pi$
$17$	5.50779	1.33584	0.667918	+	0.744235i	$0.267186\pi$
$18$	−15.6040	−3.67789
$19$	−0.954460	−0.218968	−0.109484	−	0.993989i	$-0.534920\pi$
$19$	−0.954460	−0.218968	−0.109484	+	0.993989i	$0.534920\pi$
$20$	−3.47296	−0.776577
$21$	−8.01696	−1.74945
$22$	−12.8008	−2.72913
$23$	−3.87549	−0.808096	−0.404048	−	0.914738i	$-0.632397\pi$
$23$	−3.87549	−0.808096	−0.404048	+	0.914738i	$0.632397\pi$
$24$	−10.7156	−2.18730
$25$	1.00000	0.200000
$26$	11.3976	2.23525
$27$	11.4124	2.19631
$28$	−8.95358	−1.69207
$29$	7.06485	1.31191	0.655955	−	0.754800i	$-0.272266\pi$
$29$	7.06485	1.31191	0.655955	+	0.754800i	$0.272266\pi$
$30$	7.27485	1.32820
$31$	3.21849	0.578057	0.289029	−	0.957320i	$-0.406668\pi$
$31$	3.21849	0.578057	0.289029	+	0.957320i	$0.406668\pi$
$32$	4.28208	0.756972
$33$	17.0152	2.96197
$34$	−12.8851	−2.20978
$35$	2.57808	0.435776
$36$	23.1646	3.86076
$37$	−6.97783	−1.14715	−0.573574	−	0.819154i	$-0.694444\pi$
$37$	−6.97783	−1.14715	−0.573574	+	0.819154i	$0.694444\pi$
$38$	2.23290	0.362224
$39$	−15.1501	−2.42595
$40$	3.44589	0.544844
$41$	−1.26970	−0.198294	−0.0991468	−	0.995073i	$-0.531611\pi$
$41$	−1.26970	−0.198294	−0.0991468	+	0.995073i	$0.531611\pi$
$42$	18.7552	2.89399
$43$	−8.29378	−1.26479	−0.632395	−	0.774646i	$-0.717928\pi$
$43$	−8.29378	−1.26479	−0.632395	+	0.774646i	$0.717928\pi$
$44$	19.0031	2.86482
$45$	−6.66998	−0.994301
$46$	9.06646	1.33678
$47$	4.84044	0.706051	0.353025	−	0.935614i	$-0.385153\pi$
$47$	4.84044	0.706051	0.353025	+	0.935614i	$0.385153\pi$
$48$	3.46891	0.500694
$49$	−0.353478	−0.0504968
$50$	−2.33944	−0.330846
$51$	17.1274	2.39831
$52$	−16.9200	−2.34639
$53$	−2.18378	−0.299966	−0.149983	−	0.988689i	$-0.547922\pi$
$53$	−2.18378	−0.299966	−0.149983	+	0.988689i	$0.547922\pi$
$54$	−26.6985	−3.63321
$55$	−5.47173	−0.737808
$56$	8.88381	1.18715
$57$	−2.96805	−0.393127
$58$	−16.5278	−2.17020
$59$	5.51150	0.717537	0.358768	−	0.933427i	$-0.383197\pi$
$59$	5.51150	0.717537	0.358768	+	0.933427i	$0.383197\pi$
$60$	−10.7997	−1.39424
$61$	1.96684	0.251828	0.125914	−	0.992041i	$-0.459814\pi$
$61$	1.96684	0.251828	0.125914	+	0.992041i	$0.459814\pi$
$62$	−7.52944	−0.956240
$63$	−17.1958	−2.16646
$64$	−12.2487	−1.53109
$65$	4.87194	0.604290
$66$	−39.8060	−4.89978
$67$	2.24829	0.274673	0.137336	−	0.990524i	$-0.456146\pi$
$67$	2.24829	0.274673	0.137336	+	0.990524i	$0.456146\pi$
$68$	19.1283	2.31965
$69$	−12.0515	−1.45082
$70$	−6.03126	−0.720874
$71$	5.55489	0.659244	0.329622	−	0.944113i	$-0.393079\pi$
$71$	5.55489	0.659244	0.329622	+	0.944113i	$0.393079\pi$
$72$	−22.9840	−2.70869
$73$	16.0192	1.87491	0.937453	−	0.348111i	$-0.113177\pi$
$73$	16.0192	1.87491	0.937453	+	0.348111i	$0.113177\pi$
$74$	16.3242	1.89765
$75$	3.10966	0.359072
$76$	−3.31480	−0.380234
$77$	−14.1066	−1.60759
$78$	35.4426	4.01308
$79$	5.26837	0.592737	0.296369	−	0.955074i	$-0.404224\pi$
$79$	5.26837	0.592737	0.296369	+	0.955074i	$0.404224\pi$
$80$	−1.11553	−0.124720
$81$	15.4787	1.71985
$82$	2.97038	0.328023
$83$	6.44953	0.707928	0.353964	−	0.935259i	$-0.384834\pi$
$83$	6.44953	0.707928	0.353964	+	0.935259i	$0.384834\pi$
$84$	−27.8426	−3.03788
$85$	−5.50779	−0.597404
$86$	19.4028	2.09225
$87$	21.9693	2.35535
$88$	−18.8550	−2.00995
$89$	−2.58374	−0.273876	−0.136938	−	0.990580i	$-0.543726\pi$
$89$	−2.58374	−0.273876	−0.136938	+	0.990580i	$0.543726\pi$
$90$	15.6040	1.64480
$91$	12.5603	1.31667
$92$	−13.4594	−1.40324
$93$	10.0084	1.03782
$94$	−11.3239	−1.16797
$95$	0.954460	0.0979256
$96$	13.3158	1.35904
$97$	0.742321	0.0753712	0.0376856	−	0.999290i	$-0.488001\pi$
$97$	0.742321	0.0753712	0.0376856	+	0.999290i	$0.488001\pi$
$98$	0.826939	0.0835334
$99$	36.4963	3.66802
$100$	3.47296	0.347296
$101$	6.62471	0.659183	0.329591	−	0.944124i	$-0.393089\pi$
$101$	6.62471	0.659183	0.329591	+	0.944124i	$0.393089\pi$
$102$	−40.0684	−3.96736
$103$	−7.82146	−0.770672	−0.385336	−	0.922776i	$-0.625914\pi$
$103$	−7.82146	−0.770672	−0.385336	+	0.922776i	$0.625914\pi$
$104$	16.7882	1.64622
$105$	8.01696	0.782376
$106$	5.10882	0.496213
$107$	2.01988	0.195270	0.0976348	−	0.995222i	$-0.468872\pi$
$107$	2.01988	0.195270	0.0976348	+	0.995222i	$0.468872\pi$
$108$	39.6347	3.81385
$109$	12.5941	1.20629	0.603146	−	0.797631i	$-0.293914\pi$
$109$	12.5941	1.20629	0.603146	+	0.797631i	$0.293914\pi$
$110$	12.8008	1.22050
$111$	−21.6987	−2.05955
$112$	−2.87592	−0.271749
$113$	6.02709	0.566981	0.283490	−	0.958975i	$-0.408508\pi$
$113$	6.02709	0.566981	0.283490	+	0.958975i	$0.408508\pi$
$114$	6.94355	0.650323
$115$	3.87549	0.361391
$116$	24.5359	2.27810
$117$	−32.4957	−3.00423
$118$	−12.8938	−1.18697
$119$	−14.1996	−1.30167
$120$	10.7156	0.978192
$121$	18.9398	1.72180
$122$	−4.60129	−0.416581
$123$	−3.94833	−0.356009
$124$	11.1777	1.00378
$125$	−1.00000	−0.0894427
$126$	40.2284	3.58383
$127$	−13.1101	−1.16333	−0.581665	−	0.813428i	$-0.697599\pi$
$127$	−13.1101	−1.16333	−0.581665	+	0.813428i	$0.697599\pi$
$128$	20.0909	1.77580
$129$	−25.7908	−2.27076
$130$	−11.3976	−0.999634
$131$	−11.4299	−0.998633	−0.499316	−	0.866420i	$-0.666415\pi$
$131$	−11.4299	−0.998633	−0.499316	+	0.866420i	$0.666415\pi$
$132$	59.0931	5.14340
$133$	2.46068	0.213368
$134$	−5.25974	−0.454372
$135$	−11.4124	−0.982221
$136$	−18.9793	−1.62746
$137$	−2.34791	−0.200595	−0.100298	−	0.994957i	$-0.531980\pi$
$137$	−2.34791	−0.200595	−0.100298	+	0.994957i	$0.531980\pi$
$138$	28.1936	2.40000
$139$	14.8138	1.25649	0.628245	−	0.778015i	$-0.283773\pi$
$139$	14.8138	1.25649	0.628245	+	0.778015i	$0.283773\pi$
$140$	8.95358	0.756716
$141$	15.0521	1.26762
$142$	−12.9953	−1.09054
$143$	−26.6579	−2.22925
$144$	7.44054	0.620045
$145$	−7.06485	−0.586704
$146$	−37.4759	−3.10153
$147$	−1.09920	−0.0906601
$148$	−24.2337	−1.99200
$149$	18.6227	1.52563	0.762815	−	0.646616i	$-0.223816\pi$
$149$	18.6227	1.52563	0.762815	+	0.646616i	$0.223816\pi$
$150$	−7.27485	−0.593989
$151$	9.68840	0.788431	0.394215	−	0.919018i	$-0.371016\pi$
$151$	9.68840	0.788431	0.394215	+	0.919018i	$0.371016\pi$
$152$	3.28897	0.266771
$153$	36.7369	2.97000
$154$	33.0014	2.65933
$155$	−3.21849	−0.258515
$156$	−52.6156	−4.21262
$157$	−17.6581	−1.40927	−0.704636	−	0.709569i	$-0.748890\pi$
$157$	−17.6581	−1.40927	−0.704636	+	0.709569i	$0.748890\pi$
$158$	−12.3250	−0.980524
$159$	−6.79082	−0.538547
$160$	−4.28208	−0.338528
$161$	9.99135	0.787428
$162$	−36.2113	−2.84503
$163$	21.0926	1.65210	0.826050	−	0.563597i	$-0.190583\pi$
$163$	21.0926	1.65210	0.826050	+	0.563597i	$0.190583\pi$
$164$	−4.40961	−0.344333
$165$	−17.0152	−1.32463
$166$	−15.0883	−1.17108
$167$	3.72629	0.288349	0.144175	−	0.989552i	$-0.453947\pi$
$167$	3.72629	0.288349	0.144175	+	0.989552i	$0.453947\pi$
$168$	27.6256	2.13136
$169$	10.7358	0.825829
$170$	12.8851	0.988244
$171$	−6.36623	−0.486838
$172$	−28.8040	−2.19628
$173$	−5.97872	−0.454554	−0.227277	−	0.973830i	$-0.572982\pi$
$173$	−5.97872	−0.454554	−0.227277	+	0.973830i	$0.572982\pi$
$174$	−51.3957	−3.89630
$175$	−2.57808	−0.194885
$176$	6.10386	0.460096
$177$	17.1389	1.28824
$178$	6.04450	0.453054
$179$	−13.7951	−1.03110	−0.515548	−	0.856860i	$-0.672412\pi$
$179$	−13.7951	−1.03110	−0.515548	+	0.856860i	$0.672412\pi$
$180$	−23.1646	−1.72658
$181$	4.47375	0.332531	0.166266	−	0.986081i	$-0.446829\pi$
$181$	4.47375	0.332531	0.166266	+	0.986081i	$0.446829\pi$
$182$	−29.3839	−2.17808
$183$	6.11619	0.452122
$184$	13.3545	0.984509
$185$	6.97783	0.513020
$186$	−23.4140	−1.71680
$187$	30.1372	2.20385
$188$	16.8106	1.22604
$189$	−29.4221	−2.14014
$190$	−2.23290	−0.161991
$191$	−5.12341	−0.370717	−0.185358	−	0.982671i	$-0.559345\pi$
$191$	−5.12341	−0.370717	−0.185358	+	0.982671i	$0.559345\pi$
$192$	−38.0893	−2.74886
$193$	1.76897	0.127333	0.0636665	−	0.997971i	$-0.479721\pi$
$193$	1.76897	0.127333	0.0636665	+	0.997971i	$0.479721\pi$
$194$	−1.73661	−0.124681
$195$	15.1501	1.08492
$196$	−1.22761	−0.0876867
$197$	−23.8035	−1.69593	−0.847963	−	0.530055i	$-0.822171\pi$
$197$	−23.8035	−1.69593	−0.847963	+	0.530055i	$0.822171\pi$
$198$	−85.3808	−6.06775
$199$	−23.3412	−1.65462	−0.827308	−	0.561749i	$-0.810129\pi$
$199$	−23.3412	−1.65462	−0.827308	+	0.561749i	$0.810129\pi$
$200$	−3.44589	−0.243661
$201$	6.99142	0.493137
$202$	−15.4981	−1.09044
$203$	−18.2138	−1.27836
$204$	59.4826	4.16462
$205$	1.26970	0.0886796
$206$	18.2978	1.27487
$207$	−25.8494	−1.79666
$208$	−5.43478	−0.376834
$209$	−5.22255	−0.361251
$210$	−18.7552	−1.29423
$211$	4.58535	0.315668	0.157834	−	0.987466i	$-0.449549\pi$
$211$	4.58535	0.315668	0.157834	+	0.987466i	$0.449549\pi$
$212$	−7.58419	−0.520884
$213$	17.2738	1.18358
$214$	−4.72539	−0.323021
$215$	8.29378	0.565631
$216$	−39.3258	−2.67578
$217$	−8.29753	−0.563273
$218$	−29.4630	−1.99549
$219$	49.8143	3.36614
$220$	−19.0031	−1.28119
$221$	−26.8336	−1.80503
$222$	50.7627	3.40697
$223$	10.1395	0.678988	0.339494	−	0.940608i	$-0.389744\pi$
$223$	10.1395	0.678988	0.339494	+	0.940608i	$0.389744\pi$
$224$	−11.0396	−0.737613
$225$	6.66998	0.444665
$226$	−14.1000	−0.937917
$227$	−13.0787	−0.868067	−0.434033	−	0.900897i	$-0.642910\pi$
$227$	−13.0787	−0.868067	−0.434033	+	0.900897i	$0.642910\pi$
$228$	−10.3079	−0.682657
$229$	−15.1947	−1.00410	−0.502049	−	0.864839i	$-0.667420\pi$
$229$	−15.1947	−1.00410	−0.502049	+	0.864839i	$0.667420\pi$
$230$	−9.06646	−0.597825
$231$	−43.8667	−2.88621
$232$	−24.3447	−1.59831
$233$	6.57983	0.431059	0.215529	−	0.976497i	$-0.430852\pi$
$233$	6.57983	0.431059	0.215529	+	0.976497i	$0.430852\pi$
$234$	76.0216	4.96969
$235$	−4.84044	−0.315755
$236$	19.1412	1.24599
$237$	16.3828	1.06418
$238$	33.2190	2.15327
$239$	12.5348	0.810807	0.405403	−	0.914138i	$-0.367131\pi$
$239$	12.5348	0.810807	0.405403	+	0.914138i	$0.367131\pi$
$240$	−3.46891	−0.223917
$241$	13.0366	0.839759	0.419879	−	0.907580i	$-0.362072\pi$
$241$	13.0366	0.839759	0.419879	+	0.907580i	$0.362072\pi$
$242$	−44.3085	−2.84826
$243$	13.8962	0.891443
$244$	6.83074	0.437293
$245$	0.353478	0.0225829
$246$	9.23686	0.588921
$247$	4.65007	0.295877
$248$	−11.0906	−0.704251
$249$	20.0558	1.27099
$250$	2.33944	0.147959
$251$	−3.38693	−0.213781	−0.106890	−	0.994271i	$-0.534089\pi$
$251$	−3.38693	−0.213781	−0.106890	+	0.994271i	$0.534089\pi$
$252$	−59.7202	−3.76202
$253$	−21.2056	−1.33319
$254$	30.6702	1.92442
$255$	−17.1274	−1.07256
$256$	−22.5040	−1.40650
$257$	−13.2644	−0.827410	−0.413705	−	0.910411i	$-0.635766\pi$
$257$	−13.2644	−0.827410	−0.413705	+	0.910411i	$0.635766\pi$
$258$	60.3360	3.75635
$259$	17.9894	1.11781
$260$	16.9200	1.04934
$261$	47.1224	2.91680
$262$	26.7395	1.65197
$263$	28.0511	1.72971	0.864853	−	0.502025i	$-0.167412\pi$
$263$	28.0511	1.72971	0.864853	+	0.502025i	$0.167412\pi$
$264$	−58.6326	−3.60859
$265$	2.18378	0.134149
$266$	−5.75660	−0.352960
$267$	−8.03455	−0.491707
$268$	7.80823	0.476964
$269$	23.2626	1.41835	0.709173	−	0.705035i	$-0.249069\pi$
$269$	23.2626	1.41835	0.709173	+	0.705035i	$0.249069\pi$
$270$	26.6985	1.62482
$271$	2.13490	0.129686	0.0648430	−	0.997895i	$-0.479345\pi$
$271$	2.13490	0.129686	0.0648430	+	0.997895i	$0.479345\pi$
$272$	6.14409	0.372540
$273$	39.0582	2.36391
$274$	5.49278	0.331831
$275$	5.47173	0.329958
$276$	−41.8542	−2.51933
$277$	10.6502	0.639906	0.319953	−	0.947433i	$-0.396333\pi$
$277$	10.6502	0.639906	0.319953	+	0.947433i	$0.396333\pi$
$278$	−34.6559	−2.07853
$279$	21.4672	1.28521
$280$	−8.88381	−0.530909
$281$	−11.8081	−0.704412	−0.352206	−	0.935923i	$-0.614568\pi$
$281$	−11.8081	−0.704412	−0.352206	+	0.935923i	$0.614568\pi$
$282$	−35.2135	−2.09693
$283$	20.0804	1.19366	0.596829	−	0.802368i	$-0.296427\pi$
$283$	20.0804	1.19366	0.596829	+	0.802368i	$0.296427\pi$
$284$	19.2919	1.14476
$285$	2.96805	0.175812
$286$	62.3645	3.68769
$287$	3.27339	0.193222
$288$	28.5614	1.68300
$289$	13.3358	0.784458
$290$	16.5278	0.970543
$291$	2.30836	0.135319
$292$	55.6341	3.25574
$293$	−13.4811	−0.787573	−0.393786	−	0.919202i	$-0.628835\pi$
$293$	−13.4811	−0.787573	−0.393786	+	0.919202i	$0.628835\pi$
$294$	2.57150	0.149973
$295$	−5.51150	−0.320892
$296$	24.0449	1.39758
$297$	62.4454	3.62345
$298$	−43.5666	−2.52375
$299$	18.8812	1.09193
$300$	10.7997	0.623522
$301$	21.3821	1.23244
$302$	−22.6654	−1.30425
$303$	20.6006	1.18347
$304$	−1.06473	−0.0610662
$305$	−1.96684	−0.112621
$306$	−85.9435	−4.91306
$307$	14.0851	0.803881	0.401940	−	0.915666i	$-0.368336\pi$
$307$	14.0851	0.803881	0.401940	+	0.915666i	$0.368336\pi$
$308$	−48.9916	−2.79155
$309$	−24.3221	−1.38363
$310$	7.52944	0.427644
$311$	10.6678	0.604916	0.302458	−	0.953163i	$-0.402193\pi$
$311$	10.6678	0.604916	0.302458	+	0.953163i	$0.402193\pi$
$312$	52.2055	2.95555
$313$	29.5222	1.66869	0.834346	−	0.551242i	$-0.185846\pi$
$313$	29.5222	1.66869	0.834346	+	0.551242i	$0.185846\pi$
$314$	41.3100	2.33126
$315$	17.1958	0.968872
$316$	18.2968	1.02928
$317$	9.93301	0.557894	0.278947	−	0.960307i	$-0.410015\pi$
$317$	9.93301	0.557894	0.278947	+	0.960307i	$0.410015\pi$
$318$	15.8867	0.890881
$319$	38.6569	2.16437
$320$	12.2487	0.684724
$321$	6.28115	0.350580
$322$	−23.3741	−1.30259
$323$	−5.25697	−0.292506
$324$	53.7568	2.98649
$325$	−4.87194	−0.270247
$326$	−49.3448	−2.73295
$327$	39.1632	2.16573
$328$	4.37524	0.241582
$329$	−12.4791	−0.687993
$330$	39.8060	2.19125
$331$	−3.96146	−0.217742	−0.108871	−	0.994056i	$-0.534723\pi$
$331$	−3.96146	−0.217742	−0.108871	+	0.994056i	$0.534723\pi$
$332$	22.3990	1.22930
$333$	−46.5420	−2.55049
$334$	−8.71742	−0.476996
$335$	−2.24829	−0.122837
$336$	−8.94314	−0.487888
$337$	11.1293	0.606253	0.303127	−	0.952950i	$-0.401969\pi$
$337$	11.1293	0.606253	0.303127	+	0.952950i	$0.401969\pi$
$338$	−25.1157	−1.36611
$339$	18.7422	1.01794
$340$	−19.1283	−1.03738
$341$	17.6107	0.953672
$342$	14.8934	0.805342
$343$	18.9579	1.02363
$344$	28.5795	1.54090
$345$	12.0515	0.648829
$346$	13.9868	0.751937
$347$	10.9926	0.590115	0.295057	−	0.955480i	$-0.404661\pi$
$347$	10.9926	0.590115	0.295057	+	0.955480i	$0.404661\pi$
$348$	76.2984	4.09002
$349$	−12.8649	−0.688641	−0.344320	−	0.938852i	$-0.611891\pi$
$349$	−12.8649	−0.688641	−0.344320	+	0.938852i	$0.611891\pi$
$350$	6.03126	0.322385
$351$	−55.6004	−2.96773
$352$	23.4304	1.24884
$353$	33.2092	1.76755	0.883774	−	0.467914i	$-0.154994\pi$
$353$	33.2092	1.76755	0.883774	+	0.467914i	$0.154994\pi$
$354$	−40.0953	−2.13104
$355$	−5.55489	−0.294823
$356$	−8.97323	−0.475580
$357$	−44.1558	−2.33697
$358$	32.2728	1.70567
$359$	32.2397	1.70155	0.850773	−	0.525534i	$-0.176134\pi$
$359$	32.2397	1.70155	0.850773	+	0.525534i	$0.176134\pi$
$360$	22.9840	1.21136
$361$	−18.0890	−0.952053
$362$	−10.4660	−0.550083
$363$	58.8964	3.09126
$364$	43.6213	2.28638
$365$	−16.0192	−0.838484
$366$	−14.3084	−0.747914
$367$	−1.38893	−0.0725016	−0.0362508	−	0.999343i	$-0.511542\pi$
$367$	−1.38893	−0.0725016	−0.0362508	+	0.999343i	$0.511542\pi$
$368$	−4.32321	−0.225363
$369$	−8.46886	−0.440871
$370$	−16.3242	−0.848654
$371$	5.62998	0.292294
$372$	34.7587	1.80216
$373$	−14.2285	−0.736725	−0.368363	−	0.929682i	$-0.620081\pi$
$373$	−14.2285	−0.736725	−0.368363	+	0.929682i	$0.620081\pi$
$374$	−70.5039	−3.64567
$375$	−3.10966	−0.160582
$376$	−16.6796	−0.860187
$377$	−34.4195	−1.77269
$378$	68.8310	3.54029
$379$	−12.8501	−0.660065	−0.330032	−	0.943970i	$-0.607060\pi$
$379$	−12.8501	−0.660065	−0.330032	+	0.943970i	$0.607060\pi$
$380$	3.31480	0.170046
$381$	−40.7678	−2.08860
$382$	11.9859	0.613251
$383$	17.2821	0.883072	0.441536	−	0.897244i	$-0.354434\pi$
$383$	17.2821	0.883072	0.441536	+	0.897244i	$0.354434\pi$
$384$	62.4759	3.18821
$385$	14.1066	0.718938
$386$	−4.13839	−0.210638
$387$	−55.3193	−2.81204
$388$	2.57805	0.130881
$389$	−11.1717	−0.566429	−0.283214	−	0.959057i	$-0.591401\pi$
$389$	−11.1717	−0.566429	−0.283214	+	0.959057i	$0.591401\pi$
$390$	−35.4426	−1.79471
$391$	−21.3454	−1.07948
$392$	1.21805	0.0615206
$393$	−35.5430	−1.79291
$394$	55.6867	2.80545
$395$	−5.26837	−0.265080
$396$	126.750	6.36944
$397$	−16.3983	−0.823005	−0.411503	−	0.911409i	$-0.634996\pi$
$397$	−16.3983	−0.823005	−0.411503	+	0.911409i	$0.634996\pi$
$398$	54.6053	2.73712
$399$	7.65187	0.383073
$400$	1.11553	0.0557763
$401$	−8.80862	−0.439882	−0.219941	−	0.975513i	$-0.570586\pi$
$401$	−8.80862	−0.439882	−0.219941	+	0.975513i	$0.570586\pi$
$402$	−16.3560	−0.815763
$403$	−15.6803	−0.781090
$404$	23.0073	1.14466
$405$	−15.4787	−0.769141
$406$	42.6100	2.11470
$407$	−38.1808	−1.89255
$408$	−59.0190	−2.92188
$409$	−29.2947	−1.44853	−0.724265	−	0.689522i	$-0.757821\pi$
$409$	−29.2947	−1.44853	−0.724265	+	0.689522i	$0.757821\pi$
$410$	−2.97038	−0.146696
$411$	−7.30120	−0.360142
$412$	−27.1636	−1.33826
$413$	−14.2091	−0.699185
$414$	60.4731	2.97209
$415$	−6.44953	−0.316595
$416$	−20.8620	−1.02285
$417$	46.0659	2.25586
$418$	12.2178	0.597593
$419$	−19.8158	−0.968064	−0.484032	−	0.875050i	$-0.660828\pi$
$419$	−19.8158	−0.968064	−0.484032	+	0.875050i	$0.660828\pi$
$420$	27.8426	1.35858
$421$	34.6015	1.68637	0.843187	−	0.537621i	$-0.180677\pi$
$421$	34.6015	1.68637	0.843187	+	0.537621i	$0.180677\pi$
$422$	−10.7271	−0.522188
$423$	32.2856	1.56978
$424$	7.52509	0.365450
$425$	5.50779	0.267167
$426$	−40.4110	−1.95792
$427$	−5.07067	−0.245387
$428$	7.01497	0.339082
$429$	−82.8971	−4.00231
$430$	−19.4028	−0.935684
$431$	−16.8260	−0.810481	−0.405241	−	0.914210i	$-0.632812\pi$
$431$	−16.8260	−0.810481	−0.405241	+	0.914210i	$0.632812\pi$
$432$	12.7308	0.612511
$433$	23.6009	1.13419	0.567093	−	0.823654i	$-0.308068\pi$
$433$	23.6009	1.13419	0.567093	+	0.823654i	$0.308068\pi$
$434$	19.4115	0.931784
$435$	−21.9693	−1.05335
$436$	43.7387	2.09470
$437$	3.69900	0.176947
$438$	−116.537	−5.56837
$439$	−39.8709	−1.90294	−0.951468	−	0.307747i	$-0.900425\pi$
$439$	−39.8709	−1.90294	−0.951468	+	0.307747i	$0.900425\pi$
$440$	18.8550	0.898877
$441$	−2.35769	−0.112271
$442$	62.7756	2.98593
$443$	20.2469	0.961960	0.480980	−	0.876732i	$-0.340281\pi$
$443$	20.2469	0.961960	0.480980	+	0.876732i	$0.340281\pi$
$444$	−75.3586	−3.57636
$445$	2.58374	0.122481
$446$	−23.7206	−1.12320
$447$	57.9102	2.73906
$448$	31.5782	1.49193
$449$	−28.2818	−1.33470	−0.667352	−	0.744743i	$-0.732572\pi$
$449$	−28.2818	−1.33470	−0.667352	+	0.744743i	$0.732572\pi$
$450$	−15.6040	−0.735579
$451$	−6.94745	−0.327142
$452$	20.9318	0.984551
$453$	30.1276	1.41552
$454$	30.5969	1.43598
$455$	−12.5603	−0.588835
$456$	10.2276	0.478950
$457$	34.5601	1.61665	0.808326	−	0.588735i	$-0.200374\pi$
$457$	34.5601	1.61665	0.808326	+	0.588735i	$0.200374\pi$
$458$	35.5471	1.66101
$459$	62.8570	2.93391
$460$	13.4594	0.627549
$461$	38.7857	1.80643	0.903216	−	0.429186i	$-0.141199\pi$
$461$	38.7857	1.80643	0.903216	+	0.429186i	$0.141199\pi$
$462$	102.623	4.77446
$463$	−25.1291	−1.16785	−0.583925	−	0.811808i	$-0.698484\pi$
$463$	−25.1291	−1.16785	−0.583925	+	0.811808i	$0.698484\pi$
$464$	7.88103	0.365868
$465$	−10.0084	−0.464128
$466$	−15.3931	−0.713071
$467$	−18.5748	−0.859538	−0.429769	−	0.902939i	$-0.641405\pi$
$467$	−18.5748	−0.859538	−0.429769	+	0.902939i	$0.641405\pi$
$468$	−112.856	−5.21678
$469$	−5.79629	−0.267648
$470$	11.3239	0.522332
$471$	−54.9107	−2.53015
$472$	−18.9920	−0.874180
$473$	−45.3813	−2.08664
$474$	−38.3265	−1.76040
$475$	−0.954460	−0.0437936
$476$	−49.3145	−2.26033
$477$	−14.5658	−0.666922
$478$	−29.3243	−1.34126
$479$	26.0218	1.18897	0.594484	−	0.804108i	$-0.297356\pi$
$479$	26.0218	1.18897	0.594484	+	0.804108i	$0.297356\pi$
$480$	−13.3158	−0.607781
$481$	33.9956	1.55006
$482$	−30.4982	−1.38916
$483$	31.0697	1.41372
$484$	65.7772	2.98987
$485$	−0.742321	−0.0337070
$486$	−32.5093	−1.47465
$487$	−0.269145	−0.0121961	−0.00609805	−	0.999981i	$-0.501941\pi$
$487$	−0.269145	−0.0121961	−0.00609805	+	0.999981i	$0.501941\pi$
$488$	−6.77751	−0.306803
$489$	65.5908	2.96612
$490$	−0.826939	−0.0373573
$491$	14.2656	0.643796	0.321898	−	0.946774i	$-0.395679\pi$
$491$	14.2656	0.643796	0.321898	+	0.946774i	$0.395679\pi$
$492$	−13.7124	−0.618202
$493$	38.9117	1.75250
$494$	−10.8785	−0.489449
$495$	−36.4963	−1.64039
$496$	3.59031	0.161210
$497$	−14.3210	−0.642384
$498$	−46.9193	−2.10251
$499$	22.1830	0.993047	0.496523	−	0.868023i	$-0.334610\pi$
$499$	22.1830	0.993047	0.496523	+	0.868023i	$0.334610\pi$
$500$	−3.47296	−0.155315
$501$	11.5875	0.517691
$502$	7.92350	0.353643
$503$	24.0172	1.07087	0.535436	−	0.844576i	$-0.320147\pi$
$503$	24.0172	1.07087	0.535436	+	0.844576i	$0.320147\pi$
$504$	59.2548	2.63942
$505$	−6.62471	−0.294796
$506$	49.6092	2.20540
$507$	33.3846	1.48266
$508$	−45.5307	−2.02010
$509$	37.4304	1.65907	0.829537	−	0.558451i	$-0.188604\pi$
$509$	37.4304	1.65907	0.829537	+	0.558451i	$0.188604\pi$
$510$	40.0684	1.77426
$511$	−41.2989	−1.82695
$512$	12.4647	0.550869
$513$	−10.8927	−0.480923
$514$	31.0312	1.36873
$515$	7.82146	0.344655
$516$	−89.5705	−3.94312
$517$	26.4856	1.16483
$518$	−42.0852	−1.84912
$519$	−18.5918	−0.816089
$520$	−16.7882	−0.736210
$521$	11.4141	0.500062	0.250031	−	0.968238i	$-0.419559\pi$
$521$	11.4141	0.500062	0.250031	+	0.968238i	$0.419559\pi$
$522$	−110.240	−4.82506
$523$	−27.5178	−1.20327	−0.601636	−	0.798771i	$-0.705484\pi$
$523$	−27.5178	−1.20327	−0.601636	+	0.798771i	$0.705484\pi$
$524$	−39.6955	−1.73411
$525$	−8.01696	−0.349889
$526$	−65.6238	−2.86133
$527$	17.7268	0.772190
$528$	18.9809	0.826039
$529$	−7.98056	−0.346981
$530$	−5.10882	−0.221913
$531$	36.7616	1.59532
$532$	8.54584	0.370509
$533$	6.18589	0.267941
$534$	18.7963	0.813396
$535$	−2.01988	−0.0873272
$536$	−7.74738	−0.334636
$537$	−42.8982	−1.85119
$538$	−54.4213	−2.34627
$539$	−1.93414	−0.0833091
$540$	−39.6347	−1.70561
$541$	−7.73091	−0.332378	−0.166189	−	0.986094i	$-0.553146\pi$
$541$	−7.73091	−0.332378	−0.166189	+	0.986094i	$0.553146\pi$
$542$	−4.99446	−0.214530
$543$	13.9118	0.597014
$544$	23.5848	1.01119
$545$	−12.5941	−0.539470
$546$	−91.3740	−3.91045
$547$	6.90607	0.295282	0.147641	−	0.989041i	$-0.452832\pi$
$547$	6.90607	0.295282	0.147641	+	0.989041i	$0.452832\pi$
$548$	−8.15419	−0.348330
$549$	13.1187	0.559895
$550$	−12.8008	−0.545826
$551$	−6.74312	−0.287266
$552$	41.5280	1.76755
$553$	−13.5823	−0.577578
$554$	−24.9153	−1.05855
$555$	21.6987	0.921058
$556$	51.4477	2.18187
$557$	1.03101	0.0436855	0.0218427	−	0.999761i	$-0.493047\pi$
$557$	1.03101	0.0436855	0.0218427	+	0.999761i	$0.493047\pi$
$558$	−50.2212	−2.12603
$559$	40.4068	1.70902
$560$	2.87592	0.121530
$561$	93.7163	3.95670
$562$	27.6243	1.16526
$563$	−30.0416	−1.26610	−0.633051	−	0.774110i	$-0.718198\pi$
$563$	−30.0416	−1.26610	−0.633051	+	0.774110i	$0.718198\pi$
$564$	52.2754	2.20119
$565$	−6.02709	−0.253562
$566$	−46.9769	−1.97459
$567$	−39.9053	−1.67587
$568$	−19.1416	−0.803162
$569$	24.5880	1.03078	0.515392	−	0.856954i	$-0.327646\pi$
$569$	24.5880	1.03078	0.515392	+	0.856954i	$0.327646\pi$
$570$	−6.94355	−0.290833
$571$	37.7132	1.57825	0.789124	−	0.614233i	$-0.210535\pi$
$571$	37.7132	1.57825	0.789124	+	0.614233i	$0.210535\pi$
$572$	−92.5819	−3.87104
$573$	−15.9320	−0.665571
$574$	−7.65789	−0.319634
$575$	−3.87549	−0.161619
$576$	−81.6986	−3.40411
$577$	−36.5741	−1.52260	−0.761300	−	0.648399i	$-0.775439\pi$
$577$	−36.5741	−1.52260	−0.761300	+	0.648399i	$0.775439\pi$
$578$	−31.1982	−1.29768
$579$	5.50088	0.228609
$580$	−24.5359	−1.01880
$581$	−16.6274	−0.689822
$582$	−5.40027	−0.223848
$583$	−11.9491	−0.494880
$584$	−55.2005	−2.28421
$585$	32.4957	1.34353
$586$	31.5381	1.30283
$587$	38.3720	1.58378	0.791892	−	0.610662i	$-0.209097\pi$
$587$	38.3720	1.58378	0.791892	+	0.610662i	$0.209097\pi$
$588$	−3.81746	−0.157429
$589$	−3.07192	−0.126576
$590$	12.8938	0.530830
$591$	−74.0206	−3.04480
$592$	−7.78396	−0.319919
$593$	4.01401	0.164836	0.0824179	−	0.996598i	$-0.473736\pi$
$593$	4.01401	0.164836	0.0824179	+	0.996598i	$0.473736\pi$
$594$	−146.087	−5.99403
$595$	14.1996	0.582125
$596$	64.6759	2.64923
$597$	−72.5833	−2.97063
$598$	−44.1712	−1.80630
$599$	−23.3723	−0.954968	−0.477484	−	0.878641i	$-0.658451\pi$
$599$	−23.3723	−0.954968	−0.477484	+	0.878641i	$0.658451\pi$
$600$	−10.7156	−0.437461
$601$	−33.4333	−1.36377	−0.681887	−	0.731458i	$-0.738840\pi$
$601$	−33.4333	−1.36377	−0.681887	+	0.731458i	$0.738840\pi$
$602$	−50.0220	−2.03874
$603$	14.9961	0.610687
$604$	33.6474	1.36909
$605$	−18.9398	−0.770013
$606$	−48.1937	−1.95774
$607$	29.1892	1.18475	0.592376	−	0.805662i	$-0.298190\pi$
$607$	29.1892	1.18475	0.592376	+	0.805662i	$0.298190\pi$
$608$	−4.08708	−0.165753
$609$	−56.6386	−2.29511
$610$	4.60129	0.186301
$611$	−23.5823	−0.954039
$612$	127.586	5.15734
$613$	38.2081	1.54321	0.771605	−	0.636103i	$-0.219454\pi$
$613$	38.2081	1.54321	0.771605	+	0.636103i	$0.219454\pi$
$614$	−32.9513	−1.32980
$615$	3.94833	0.159212
$616$	48.6098	1.95854
$617$	36.8936	1.48528	0.742641	−	0.669690i	$-0.233573\pi$
$617$	36.8936	1.48528	0.742641	+	0.669690i	$0.233573\pi$
$618$	56.8999	2.28885
$619$	14.2786	0.573906	0.286953	−	0.957945i	$-0.407358\pi$
$619$	14.2786	0.573906	0.286953	+	0.957945i	$0.407358\pi$
$620$	−11.1777	−0.448906
$621$	−44.2286	−1.77483
$622$	−24.9567	−1.00067
$623$	6.66110	0.266871
$624$	−16.9003	−0.676554
$625$	1.00000	0.0400000
$626$	−69.0652	−2.76040
$627$	−16.2403	−0.648577
$628$	−61.3259	−2.44717
$629$	−38.4325	−1.53240
$630$	−40.2284	−1.60274
$631$	−13.2662	−0.528121	−0.264061	−	0.964506i	$-0.585062\pi$
$631$	−13.2662	−0.528121	−0.264061	+	0.964506i	$0.585062\pi$
$632$	−18.1542	−0.722136
$633$	14.2589	0.566739
$634$	−23.2376	−0.922885
$635$	13.1101	0.520257
$636$	−23.5842	−0.935176
$637$	1.72212	0.0682330
$638$	−90.4354	−3.58037
$639$	37.0510	1.46571
$640$	−20.0909	−0.794163
$641$	−18.0274	−0.712038	−0.356019	−	0.934479i	$-0.615866\pi$
$641$	−18.0274	−0.712038	−0.356019	+	0.934479i	$0.615866\pi$
$642$	−14.6943	−0.579940
$643$	−28.0824	−1.10746	−0.553732	−	0.832695i	$-0.686797\pi$
$643$	−28.0824	−1.10746	−0.553732	+	0.832695i	$0.686797\pi$
$644$	34.6995	1.36735
$645$	25.7908	1.01551
$646$	12.2983	0.483872
$647$	−41.0300	−1.61306	−0.806528	−	0.591196i	$-0.798656\pi$
$647$	−41.0300	−1.61306	−0.806528	+	0.591196i	$0.798656\pi$
$648$	−53.3378	−2.09531
$649$	30.1575	1.18378
$650$	11.3976	0.447050
$651$	−25.8025	−1.01128
$652$	73.2537	2.86884
$653$	20.7393	0.811590	0.405795	−	0.913964i	$-0.366995\pi$
$653$	20.7393	0.811590	0.405795	+	0.913964i	$0.366995\pi$
$654$	−91.6199	−3.58262
$655$	11.4299	0.446602
$656$	−1.41638	−0.0553004
$657$	106.848	4.16853
$658$	29.1940	1.13810
$659$	19.1116	0.744484	0.372242	−	0.928136i	$-0.378589\pi$
$659$	19.1116	0.744484	0.372242	+	0.928136i	$0.378589\pi$
$660$	−59.0931	−2.30020
$661$	7.42612	0.288843	0.144421	−	0.989516i	$-0.453868\pi$
$661$	7.42612	0.288843	0.144421	+	0.989516i	$0.453868\pi$
$662$	9.26758	0.360195
$663$	−83.4434	−3.24067
$664$	−22.2244	−0.862474
$665$	−2.46068	−0.0954211
$666$	108.882	4.21909
$667$	−27.3798	−1.06015
$668$	12.9413	0.500712
$669$	31.5303	1.21903
$670$	5.25974	0.203201
$671$	10.7620	0.415462
$672$	−34.3293	−1.32428
$673$	−39.0666	−1.50591	−0.752953	−	0.658074i	$-0.771371\pi$
$673$	−39.0666	−1.50591	−0.752953	+	0.658074i	$0.771371\pi$
$674$	−26.0364	−1.00288
$675$	11.4124	0.439263
$676$	37.2849	1.43404
$677$	2.52226	0.0969382	0.0484691	−	0.998825i	$-0.484566\pi$
$677$	2.52226	0.0969382	0.0484691	+	0.998825i	$0.484566\pi$
$678$	−43.8462	−1.68390
$679$	−1.91377	−0.0734436
$680$	18.9793	0.727822
$681$	−40.6704	−1.55849
$682$	−41.1991	−1.57759
$683$	−51.8437	−1.98374	−0.991872	−	0.127240i	$-0.959388\pi$
$683$	−51.8437	−1.98374	−0.991872	+	0.127240i	$0.959388\pi$
$684$	−22.1097	−0.845384
$685$	2.34791	0.0897090
$686$	−44.3508	−1.69332
$687$	−47.2505	−1.80272
$688$	−9.25193	−0.352727
$689$	10.6393	0.405324
$690$	−28.1936	−1.07331
$691$	12.1712	0.463015	0.231508	−	0.972833i	$-0.425634\pi$
$691$	12.1712	0.463015	0.231508	+	0.972833i	$0.425634\pi$
$692$	−20.7639	−0.789324
$693$	−94.0906	−3.57421
$694$	−25.7165	−0.976186
$695$	−14.8138	−0.561920
$696$	−75.7037	−2.86954
$697$	−6.99324	−0.264888
$698$	30.0965	1.13917
$699$	20.4610	0.773907
$700$	−8.95358	−0.338414
$701$	49.2016	1.85832	0.929159	−	0.369681i	$-0.120533\pi$
$701$	49.2016	1.85832	0.929159	+	0.369681i	$0.120533\pi$
$702$	130.074	4.90931
$703$	6.66006	0.251189
$704$	−67.0216	−2.52597
$705$	−15.0521	−0.566895
$706$	−77.6908	−2.92393
$707$	−17.0791	−0.642324
$708$	59.5227	2.23700
$709$	−46.1793	−1.73430	−0.867150	−	0.498048i	$-0.834050\pi$
$709$	−46.1793	−1.73430	−0.867150	+	0.498048i	$0.834050\pi$
$710$	12.9953	0.487705
$711$	35.1399	1.31785
$712$	8.90329	0.333665
$713$	−12.4732	−0.467126
$714$	103.300	3.86589
$715$	26.6579	0.996950
$716$	−47.9099	−1.79048
$717$	38.9788	1.45569
$718$	−75.4227	−2.81475
$719$	45.3526	1.69137	0.845683	−	0.533685i	$-0.179193\pi$
$719$	45.3526	1.69137	0.845683	+	0.533685i	$0.179193\pi$
$720$	−7.44054	−0.277292
$721$	20.1644	0.750961
$722$	42.3181	1.57492
$723$	40.5393	1.50767
$724$	15.5371	0.577433
$725$	7.06485	0.262382
$726$	−137.784	−5.11366
$727$	45.2277	1.67740	0.838701	−	0.544593i	$-0.183316\pi$
$727$	45.2277	1.67740	0.838701	+	0.544593i	$0.183316\pi$
$728$	−43.2813	−1.60411
$729$	−3.22346	−0.119388
$730$	37.4759	1.38705
$731$	−45.6804	−1.68955
$732$	21.2413	0.785100
$733$	20.9165	0.772568	0.386284	−	0.922380i	$-0.373758\pi$
$733$	20.9165	0.772568	0.386284	+	0.922380i	$0.373758\pi$
$734$	3.24931	0.119934
$735$	1.09920	0.0405444
$736$	−16.5952	−0.611706
$737$	12.3021	0.453152
$738$	19.8123	0.729303
$739$	−8.57154	−0.315309	−0.157655	−	0.987494i	$-0.550393\pi$
$739$	−8.57154	−0.315309	−0.157655	+	0.987494i	$0.550393\pi$
$740$	24.2337	0.890850
$741$	14.4601	0.531206
$742$	−13.1710	−0.483522
$743$	8.41871	0.308852	0.154426	−	0.988004i	$-0.450647\pi$
$743$	8.41871	0.308852	0.154426	+	0.988004i	$0.450647\pi$
$744$	−34.4879	−1.26439
$745$	−18.6227	−0.682283
$746$	33.2867	1.21871
$747$	43.0182	1.57395
$748$	104.665	3.82694
$749$	−5.20743	−0.190275
$750$	7.27485	0.265640
$751$	−6.06702	−0.221389	−0.110694	−	0.993854i	$-0.535307\pi$
$751$	−6.06702	−0.221389	−0.110694	+	0.993854i	$0.535307\pi$
$752$	5.39964	0.196905
$753$	−10.5322	−0.383814
$754$	80.5222	2.93245
$755$	−9.68840	−0.352597
$756$	−102.182	−3.71631
$757$	19.6528	0.714292	0.357146	−	0.934049i	$-0.383750\pi$
$757$	19.6528	0.714292	0.357146	+	0.934049i	$0.383750\pi$
$758$	30.0620	1.09190
$759$	−65.9423	−2.39355
$760$	−3.28897	−0.119303
$761$	−0.308394	−0.0111793	−0.00558964	−	0.999984i	$-0.501779\pi$
$761$	−0.308394	−0.0111793	−0.00558964	+	0.999984i	$0.501779\pi$
$762$	95.3737	3.45503
$763$	−32.4686	−1.17544
$764$	−17.7934	−0.643742
$765$	−36.7369	−1.32822
$766$	−40.4303	−1.46080
$767$	−26.8517	−0.969559
$768$	−69.9796	−2.52517
$769$	42.6855	1.53928	0.769640	−	0.638479i	$-0.220436\pi$
$769$	42.6855	1.53928	0.769640	+	0.638479i	$0.220436\pi$
$770$	−33.0014	−1.18929
$771$	−41.2477	−1.48550
$772$	6.14355	0.221111
$773$	12.4903	0.449245	0.224623	−	0.974446i	$-0.427885\pi$
$773$	12.4903	0.449245	0.224623	+	0.974446i	$0.427885\pi$
$774$	129.416	4.65176
$775$	3.21849	0.115611
$776$	−2.55796	−0.0918253
$777$	55.9410	2.00687
$778$	26.1355	0.937004
$779$	1.21188	0.0434200
$780$	52.6156	1.88394
$781$	30.3949	1.08761
$782$	49.9362	1.78572
$783$	80.6267	2.88136
$784$	−0.394314	−0.0140826
$785$	17.6581	0.630245
$786$	83.1506	2.96588
$787$	16.3075	0.581300	0.290650	−	0.956829i	$-0.406128\pi$
$787$	16.3075	0.581300	0.290650	+	0.956829i	$0.406128\pi$
$788$	−82.6685	−2.94494
$789$	87.2294	3.10545
$790$	12.3250	0.438504
$791$	−15.5384	−0.552480
$792$	−125.762	−4.46877
$793$	−9.58230	−0.340278
$794$	38.3627	1.36144
$795$	6.79082	0.240846
$796$	−81.0631	−2.87321
$797$	37.4795	1.32759	0.663796	−	0.747913i	$-0.268944\pi$
$797$	37.4795	1.32759	0.663796	+	0.747913i	$0.268944\pi$
$798$	−17.9011	−0.633691
$799$	26.6601	0.943168
$800$	4.28208	0.151394
$801$	−17.2335	−0.608915
$802$	20.6072	0.727666
$803$	87.6528	3.09320
$804$	24.2809	0.856322
$805$	−9.99135	−0.352149
$806$	36.6830	1.29210
$807$	72.3387	2.54644
$808$	−22.8280	−0.803087
$809$	−19.9677	−0.702028	−0.351014	−	0.936370i	$-0.614163\pi$
$809$	−19.9677	−0.702028	−0.351014	+	0.936370i	$0.614163\pi$
$810$	36.2113	1.27234
$811$	−20.9026	−0.733988	−0.366994	−	0.930223i	$-0.619613\pi$
$811$	−20.9026	−0.733988	−0.366994	+	0.930223i	$0.619613\pi$
$812$	−63.2557	−2.21984
$813$	6.63881	0.232833
$814$	89.3216	3.13072
$815$	−21.0926	−0.738841
$816$	19.1060	0.668845
$817$	7.91608	0.276949
$818$	68.5331	2.39620
$819$	83.7767	2.92740
$820$	4.40961	0.153990
$821$	−49.5772	−1.73026	−0.865129	−	0.501550i	$-0.832763\pi$
$821$	−49.5772	−1.73026	−0.865129	+	0.501550i	$0.832763\pi$
$822$	17.0807	0.595757
$823$	−39.1447	−1.36450	−0.682249	−	0.731120i	$-0.738998\pi$
$823$	−39.1447	−1.36450	−0.682249	+	0.731120i	$0.738998\pi$
$824$	26.9519	0.938915
$825$	17.0152	0.592394
$826$	33.2413	1.15661
$827$	−7.23126	−0.251456	−0.125728	−	0.992065i	$-0.540127\pi$
$827$	−7.23126	−0.251456	−0.125728	+	0.992065i	$0.540127\pi$
$828$	−89.7740	−3.11986
$829$	36.6589	1.27322	0.636608	−	0.771188i	$-0.280337\pi$
$829$	36.6589	1.27322	0.636608	+	0.771188i	$0.280337\pi$
$830$	15.0883	0.523721
$831$	33.1183	1.14886
$832$	59.6750	2.06886
$833$	−1.94688	−0.0674555
$834$	−107.768	−3.73171
$835$	−3.72629	−0.128954
$836$	−18.1377	−0.627305
$837$	36.7306	1.26959
$838$	46.3577	1.60140
$839$	11.8511	0.409144	0.204572	−	0.978852i	$-0.434420\pi$
$839$	11.8511	0.409144	0.204572	+	0.978852i	$0.434420\pi$
$840$	−27.6256	−0.953174
$841$	20.9121	0.721107
$842$	−80.9480	−2.78965
$843$	−36.7191	−1.26467
$844$	15.9247	0.548152
$845$	−10.7358	−0.369322
$846$	−75.5301	−2.59678
$847$	−48.8285	−1.67777
$848$	−2.43607	−0.0836550
$849$	62.4433	2.14305
$850$	−12.8851	−0.441956
$851$	27.0425	0.927006
$852$	59.9912	2.05527
$853$	−35.1594	−1.20383	−0.601917	−	0.798558i	$-0.705596\pi$
$853$	−35.1594	−1.20383	−0.601917	+	0.798558i	$0.705596\pi$
$854$	11.8625	0.405927
$855$	6.36623	0.217720
$856$	−6.96030	−0.237898
$857$	−52.6517	−1.79855	−0.899274	−	0.437386i	$-0.855904\pi$
$857$	−52.6517	−1.79855	−0.899274	+	0.437386i	$0.855904\pi$
$858$	193.932	6.62074
$859$	34.2345	1.16806	0.584032	−	0.811730i	$-0.301474\pi$
$859$	34.2345	1.16806	0.584032	+	0.811730i	$0.301474\pi$
$860$	28.8040	0.982207
$861$	10.1791	0.346904
$862$	39.3634	1.34072
$863$	32.5121	1.10673	0.553363	−	0.832940i	$-0.313344\pi$
$863$	32.5121	1.10673	0.553363	+	0.832940i	$0.313344\pi$
$864$	48.8687	1.66255
$865$	5.97872	0.203283
$866$	−55.2127	−1.87620
$867$	41.4698	1.40839
$868$	−28.8170	−0.978112
$869$	28.8271	0.977891
$870$	51.3957	1.74248
$871$	−10.9535	−0.371147
$872$	−43.3978	−1.46963
$873$	4.95126	0.167575
$874$	−8.65358	−0.292712
$875$	2.57808	0.0871552
$876$	173.003	5.84523
$877$	−26.2276	−0.885644	−0.442822	−	0.896610i	$-0.646023\pi$
$877$	−26.2276	−0.885644	−0.442822	+	0.896610i	$0.646023\pi$
$878$	93.2755	3.14790
$879$	−41.9215	−1.41398
$880$	−6.10386	−0.205761
$881$	−51.4491	−1.73336	−0.866682	−	0.498861i	$-0.833752\pi$
$881$	−51.4491	−1.73336	−0.866682	+	0.498861i	$0.833752\pi$
$882$	5.51566	0.185722
$883$	34.7657	1.16996	0.584979	−	0.811048i	$-0.301103\pi$
$883$	34.7657	1.16996	0.584979	+	0.811048i	$0.301103\pi$
$884$	−93.1921	−3.13439
$885$	−17.1389	−0.576118
$886$	−47.3664	−1.59130
$887$	−56.2689	−1.88933	−0.944663	−	0.328042i	$-0.893611\pi$
$887$	−56.2689	−1.88933	−0.944663	+	0.328042i	$0.893611\pi$
$888$	74.7713	2.50916
$889$	33.7989	1.13358
$890$	−6.04450	−0.202612
$891$	84.6951	2.83739
$892$	35.2139	1.17905
$893$	−4.62001	−0.154603
$894$	−135.477	−4.53104
$895$	13.7951	0.461121
$896$	−51.7961	−1.73038
$897$	58.7140	1.96040
$898$	66.1636	2.20791
$899$	22.7381	0.758359
$900$	23.1646	0.772152
$901$	−12.0278	−0.400705
$902$	16.2531	0.541169
$903$	66.4909	2.21268
$904$	−20.7687	−0.690757
$905$	−4.47375	−0.148712
$906$	−70.4816	−2.34159
$907$	−22.9201	−0.761049	−0.380525	−	0.924771i	$-0.624257\pi$
$907$	−22.9201	−0.761049	−0.380525	+	0.924771i	$0.624257\pi$
$908$	−45.4219	−1.50738
$909$	44.1866	1.46558
$910$	29.3839	0.974068
$911$	5.76459	0.190989	0.0954946	−	0.995430i	$-0.469557\pi$
$911$	5.76459	0.190989	0.0954946	+	0.995430i	$0.469557\pi$
$912$	−3.31093	−0.109636
$913$	35.2901	1.16793
$914$	−80.8511	−2.67432
$915$	−6.11619	−0.202195
$916$	−52.7707	−1.74359
$917$	29.4672	0.973092
$918$	−147.050	−4.85337
$919$	−38.7762	−1.27911	−0.639555	−	0.768745i	$-0.720881\pi$
$919$	−38.7762	−1.27911	−0.639555	+	0.768745i	$0.720881\pi$
$920$	−13.3545	−0.440286
$921$	43.7999	1.44326
$922$	−90.7368	−2.98826
$923$	−27.0631	−0.890792
$924$	−152.347	−5.01185
$925$	−6.97783	−0.229430
$926$	58.7880	1.93189
$927$	−52.1690	−1.71345
$928$	30.2523	0.993079
$929$	−6.94472	−0.227849	−0.113924	−	0.993489i	$-0.536342\pi$
$929$	−6.94472	−0.227849	−0.113924	+	0.993489i	$0.536342\pi$
$930$	23.4140	0.767775
$931$	0.337381	0.0110572
$932$	22.8515	0.748525
$933$	33.1733	1.08604
$934$	43.4545	1.42187
$935$	−30.1372	−0.985590
$936$	111.977	3.66007
$937$	−42.2852	−1.38140	−0.690699	−	0.723142i	$-0.742697\pi$
$937$	−42.2852	−1.38140	−0.690699	+	0.723142i	$0.742697\pi$
$938$	13.5601	0.442751
$939$	91.8039	2.99591
$940$	−16.8106	−0.548303
$941$	51.4674	1.67779	0.838894	−	0.544295i	$-0.183203\pi$
$941$	51.4674	1.67779	0.838894	+	0.544295i	$0.183203\pi$
$942$	128.460	4.18546
$943$	4.92071	0.160240
$944$	6.14823	0.200108
$945$	29.4221	0.957100
$946$	106.167	3.45178
$947$	−40.5163	−1.31660	−0.658301	−	0.752755i	$-0.728725\pi$
$947$	−40.5163	−1.31660	−0.658301	+	0.752755i	$0.728725\pi$
$948$	56.8969	1.84792
$949$	−78.0446	−2.53343
$950$	2.23290	0.0724448
$951$	30.8883	1.00162
$952$	48.9302	1.58584
$953$	11.6616	0.377757	0.188878	−	0.982001i	$-0.439515\pi$
$953$	11.6616	0.377757	0.188878	+	0.982001i	$0.439515\pi$
$954$	34.0757	1.10324
$955$	5.12341	0.165789
$956$	43.5327	1.40795
$957$	120.210	3.88583
$958$	−60.8764	−1.96683
$959$	6.05311	0.195465
$960$	38.0893	1.22933
$961$	−20.6413	−0.665850
$962$	−79.5304	−2.56416
$963$	13.4726	0.434148
$964$	45.2755	1.45822
$965$	−1.76897	−0.0569451
$966$	−72.6855	−2.33862
$967$	−4.40252	−0.141576	−0.0707878	−	0.997491i	$-0.522551\pi$
$967$	−4.40252	−0.141576	−0.0707878	+	0.997491i	$0.522551\pi$
$968$	−65.2646	−2.09768
$969$	−16.3474	−0.525154
$970$	1.73661	0.0557592
$971$	16.2089	0.520170	0.260085	−	0.965586i	$-0.416249\pi$
$971$	16.2089	0.520170	0.260085	+	0.965586i	$0.416249\pi$
$972$	48.2610	1.54797
$973$	−38.1912	−1.22436
$974$	0.629646	0.0201752
$975$	−15.1501	−0.485190
$976$	2.19406	0.0702301
$977$	−52.4245	−1.67721	−0.838604	−	0.544742i	$-0.816628\pi$
$977$	−52.4245	−1.67721	−0.838604	+	0.544742i	$0.816628\pi$
$978$	−153.445	−4.90664
$979$	−14.1375	−0.451837
$980$	1.22761	0.0392147
$981$	84.0021	2.68198
$982$	−33.3734	−1.06499
$983$	24.8449	0.792431	0.396215	−	0.918158i	$-0.370323\pi$
$983$	24.8449	0.792431	0.396215	+	0.918158i	$0.370323\pi$
$984$	13.6055	0.433728
$985$	23.8035	0.758441
$986$	−91.0315	−2.89903
$987$	−38.8056	−1.23520
$988$	16.1495	0.513784
$989$	32.1425	1.02207
$990$	85.3808	2.71358
$991$	−28.7415	−0.913004	−0.456502	−	0.889722i	$-0.650898\pi$
$991$	−28.7415	−0.913004	−0.456502	+	0.889722i	$0.650898\pi$
$992$	13.7818	0.437573
$993$	−12.3188	−0.390925
$994$	33.5030	1.06265
$995$	23.3412	0.739967
$996$	69.6531	2.20704
$997$	−35.8604	−1.13571	−0.567855	−	0.823129i	$-0.692227\pi$
$997$	−35.8604	−1.13571	−0.567855	+	0.823129i	$0.692227\pi$
$998$	−51.8957	−1.64273
$999$	−79.6336	−2.51950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.d.1.18	✓	141

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.d.1.18	✓	141	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33944 q^{2} +3.10966 q^{3} +3.47296 q^{4} -1.00000 q^{5} -7.27485 q^{6} -2.57808 q^{7} -3.44589 q^{8} +6.66998 q^{9} +O(q^{10})\)	\(q-2.33944 q^{2} +3.10966 q^{3} +3.47296 q^{4} -1.00000 q^{5} -7.27485 q^{6} -2.57808 q^{7} -3.44589 q^{8} +6.66998 q^{9} +2.33944 q^{10} +5.47173 q^{11} +10.7997 q^{12} -4.87194 q^{13} +6.03126 q^{14} -3.10966 q^{15} +1.11553 q^{16} +5.50779 q^{17} -15.6040 q^{18} -0.954460 q^{19} -3.47296 q^{20} -8.01696 q^{21} -12.8008 q^{22} -3.87549 q^{23} -10.7156 q^{24} +1.00000 q^{25} +11.3976 q^{26} +11.4124 q^{27} -8.95358 q^{28} +7.06485 q^{29} +7.27485 q^{30} +3.21849 q^{31} +4.28208 q^{32} +17.0152 q^{33} -12.8851 q^{34} +2.57808 q^{35} +23.1646 q^{36} -6.97783 q^{37} +2.23290 q^{38} -15.1501 q^{39} +3.44589 q^{40} -1.26970 q^{41} +18.7552 q^{42} -8.29378 q^{43} +19.0031 q^{44} -6.66998 q^{45} +9.06646 q^{46} +4.84044 q^{47} +3.46891 q^{48} -0.353478 q^{49} -2.33944 q^{50} +17.1274 q^{51} -16.9200 q^{52} -2.18378 q^{53} -26.6985 q^{54} -5.47173 q^{55} +8.88381 q^{56} -2.96805 q^{57} -16.5278 q^{58} +5.51150 q^{59} -10.7997 q^{60} +1.96684 q^{61} -7.52944 q^{62} -17.1958 q^{63} -12.2487 q^{64} +4.87194 q^{65} -39.8060 q^{66} +2.24829 q^{67} +19.1283 q^{68} -12.0515 q^{69} -6.03126 q^{70} +5.55489 q^{71} -22.9840 q^{72} +16.0192 q^{73} +16.3242 q^{74} +3.10966 q^{75} -3.31480 q^{76} -14.1066 q^{77} +35.4426 q^{78} +5.26837 q^{79} -1.11553 q^{80} +15.4787 q^{81} +2.97038 q^{82} +6.44953 q^{83} -27.8426 q^{84} -5.50779 q^{85} +19.4028 q^{86} +21.9693 q^{87} -18.8550 q^{88} -2.58374 q^{89} +15.6040 q^{90} +12.5603 q^{91} -13.4594 q^{92} +10.0084 q^{93} -11.3239 q^{94} +0.954460 q^{95} +13.3158 q^{96} +0.742321 q^{97} +0.826939 q^{98} +36.4963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9	\( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 141 * q - 8 * q^2 + 11 * q^3 + 158 * q^4 - 141 * q^5 + 23 * q^6 + 29 * q^7 - 21 * q^8 + 160 * q^9 + 8 * q^10 + 32 * q^11 + 17 * q^12 + 35 * q^13 + 18 * q^14 - 11 * q^15 + 188 * q^16 - 13 * q^17 - 16 * q^18 + 152 * q^19 - 158 * q^20 + 40 * q^21 + 14 * q^22 - 77 * q^23 + 69 * q^24 + 141 * q^25 + 27 * q^26 + 38 * q^27 + 67 * q^28 + 22 * q^29 - 23 * q^30 + 86 * q^31 - 65 * q^32 + 51 * q^33 + 79 * q^34 - 29 * q^35 + 191 * q^36 + 45 * q^37 - 9 * q^38 + 55 * q^39 + 21 * q^40 + 36 * q^41 + 6 * q^42 + 132 * q^43 + 74 * q^44 - 160 * q^45 + 72 * q^46 - 16 * q^47 + 22 * q^48 + 212 * q^49 - 8 * q^50 + 82 * q^51 + 106 * q^52 - 28 * q^53 + 86 * q^54 - 32 * q^55 + 27 * q^56 + 10 * q^57 + 23 * q^58 + 71 * q^59 - 17 * q^60 + 116 * q^61 - 36 * q^62 + 45 * q^63 + 237 * q^64 - 35 * q^65 + 69 * q^66 + 99 * q^67 - 7 * q^68 + 45 * q^69 - 18 * q^70 + 34 * q^71 - 53 * q^72 + 125 * q^73 + 50 * q^74 + 11 * q^75 + 271 * q^76 - 31 * q^77 + 2 * q^78 + 101 * q^79 - 188 * q^80 + 221 * q^81 + 67 * q^82 + 67 * q^83 + 141 * q^84 + 13 * q^85 + 48 * q^86 - 21 * q^87 + 71 * q^88 + 79 * q^89 + 16 * q^90 + 228 * q^91 - 198 * q^92 - 12 * q^93 + 114 * q^94 - 152 * q^95 + 129 * q^96 + 98 * q^97 - 31 * q^98 + 195 * q^99

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