LMFDB - Embedded newform 4029.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52080 q^{2} -1.00000 q^{3} +0.312840 q^{4} +4.21021 q^{5} +1.52080 q^{6} -4.25725 q^{7} +2.56584 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52080 q^{2} -1.00000 q^{3} +0.312840 q^{4} +4.21021 q^{5} +1.52080 q^{6} -4.25725 q^{7} +2.56584 q^{8} +1.00000 q^{9} -6.40289 q^{10} -4.00541 q^{11} -0.312840 q^{12} +0.621157 q^{13} +6.47444 q^{14} -4.21021 q^{15} -4.52781 q^{16} -1.00000 q^{17} -1.52080 q^{18} -2.65387 q^{19} +1.31712 q^{20} +4.25725 q^{21} +6.09145 q^{22} +1.86255 q^{23} -2.56584 q^{24} +12.7258 q^{25} -0.944657 q^{26} -1.00000 q^{27} -1.33184 q^{28} +0.0363611 q^{29} +6.40289 q^{30} +9.91051 q^{31} +1.75423 q^{32} +4.00541 q^{33} +1.52080 q^{34} -17.9239 q^{35} +0.312840 q^{36} +6.05280 q^{37} +4.03602 q^{38} -0.621157 q^{39} +10.8027 q^{40} -0.793665 q^{41} -6.47444 q^{42} -5.86932 q^{43} -1.25306 q^{44} +4.21021 q^{45} -2.83257 q^{46} -1.80152 q^{47} +4.52781 q^{48} +11.1242 q^{49} -19.3535 q^{50} +1.00000 q^{51} +0.194323 q^{52} -1.76411 q^{53} +1.52080 q^{54} -16.8636 q^{55} -10.9234 q^{56} +2.65387 q^{57} -0.0552981 q^{58} -6.68131 q^{59} -1.31712 q^{60} +3.24585 q^{61} -15.0719 q^{62} -4.25725 q^{63} +6.38778 q^{64} +2.61520 q^{65} -6.09145 q^{66} -5.17163 q^{67} -0.312840 q^{68} -1.86255 q^{69} +27.2587 q^{70} -3.68906 q^{71} +2.56584 q^{72} -13.0782 q^{73} -9.20511 q^{74} -12.7258 q^{75} -0.830238 q^{76} +17.0521 q^{77} +0.944657 q^{78} -1.00000 q^{79} -19.0630 q^{80} +1.00000 q^{81} +1.20701 q^{82} +13.0395 q^{83} +1.33184 q^{84} -4.21021 q^{85} +8.92608 q^{86} -0.0363611 q^{87} -10.2772 q^{88} -3.36959 q^{89} -6.40289 q^{90} -2.64442 q^{91} +0.582681 q^{92} -9.91051 q^{93} +2.73976 q^{94} -11.1733 q^{95} -1.75423 q^{96} +11.4845 q^{97} -16.9177 q^{98} -4.00541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.52080	−1.07537	−0.537685	−	0.843146i	$-0.680701\pi$
$2$	−1.52080	−1.07537	−0.537685	+	0.843146i	$0.680701\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.312840	0.156420
$5$	4.21021	1.88286	0.941431	−	0.337207i	$-0.109482\pi$
$5$	4.21021	1.88286	0.941431	+	0.337207i	$0.109482\pi$
$6$	1.52080	0.620865
$7$	−4.25725	−1.60909	−0.804545	−	0.593891i	$-0.797591\pi$
$7$	−4.25725	−1.60909	−0.804545	+	0.593891i	$0.797591\pi$
$8$	2.56584	0.907160
$9$	1.00000	0.333333
$10$	−6.40289	−2.02477
$11$	−4.00541	−1.20768	−0.603839	−	0.797106i	$-0.706363\pi$
$11$	−4.00541	−1.20768	−0.603839	+	0.797106i	$0.706363\pi$
$12$	−0.312840	−0.0903092
$13$	0.621157	0.172278	0.0861389	−	0.996283i	$-0.472547\pi$
$13$	0.621157	0.172278	0.0861389	+	0.996283i	$0.472547\pi$
$14$	6.47444	1.73037
$15$	−4.21021	−1.08707
$16$	−4.52781	−1.13195
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.52080	−0.358457
$19$	−2.65387	−0.608840	−0.304420	−	0.952538i	$-0.598463\pi$
$19$	−2.65387	−0.608840	−0.304420	+	0.952538i	$0.598463\pi$
$20$	1.31712	0.294518
$21$	4.25725	0.929009
$22$	6.09145	1.29870
$23$	1.86255	0.388369	0.194184	−	0.980965i	$-0.437794\pi$
$23$	1.86255	0.388369	0.194184	+	0.980965i	$0.437794\pi$
$24$	−2.56584	−0.523749
$25$	12.7258	2.54517
$26$	−0.944657	−0.185262
$27$	−1.00000	−0.192450
$28$	−1.33184	−0.251694
$29$	0.0363611	0.00675209	0.00337604	−	0.999994i	$-0.498925\pi$
$29$	0.0363611	0.00675209	0.00337604	+	0.999994i	$0.498925\pi$
$30$	6.40289	1.16900
$31$	9.91051	1.77998	0.889990	−	0.455981i	$-0.150711\pi$
$31$	9.91051	1.77998	0.889990	+	0.455981i	$0.150711\pi$
$32$	1.75423	0.310108
$33$	4.00541	0.697253
$34$	1.52080	0.260815
$35$	−17.9239	−3.02969
$36$	0.312840	0.0521401
$37$	6.05280	0.995074	0.497537	−	0.867443i	$-0.334238\pi$
$37$	6.05280	0.995074	0.497537	+	0.867443i	$0.334238\pi$
$38$	4.03602	0.654728
$39$	−0.621157	−0.0994647
$40$	10.8027	1.70806
$41$	−0.793665	−0.123950	−0.0619748	−	0.998078i	$-0.519740\pi$
$41$	−0.793665	−0.123950	−0.0619748	+	0.998078i	$0.519740\pi$
$42$	−6.47444	−0.999028
$43$	−5.86932	−0.895064	−0.447532	−	0.894268i	$-0.647697\pi$
$43$	−5.86932	−0.895064	−0.447532	+	0.894268i	$0.647697\pi$
$44$	−1.25306	−0.188905
$45$	4.21021	0.627620
$46$	−2.83257	−0.417640
$47$	−1.80152	−0.262779	−0.131389	−	0.991331i	$-0.541944\pi$
$47$	−1.80152	−0.262779	−0.131389	+	0.991331i	$0.541944\pi$
$48$	4.52781	0.653533
$49$	11.1242	1.58917
$50$	−19.3535	−2.73700
$51$	1.00000	0.140028
$52$	0.194323	0.0269477
$53$	−1.76411	−0.242318	−0.121159	−	0.992633i	$-0.538661\pi$
$53$	−1.76411	−0.242318	−0.121159	+	0.992633i	$0.538661\pi$
$54$	1.52080	0.206955
$55$	−16.8636	−2.27389
$56$	−10.9234	−1.45970
$57$	2.65387	0.351514
$58$	−0.0552981	−0.00726099
$59$	−6.68131	−0.869832	−0.434916	−	0.900471i	$-0.643222\pi$
$59$	−6.68131	−0.869832	−0.434916	+	0.900471i	$0.643222\pi$
$60$	−1.31712	−0.170040
$61$	3.24585	0.415589	0.207795	−	0.978172i	$-0.433371\pi$
$61$	3.24585	0.415589	0.207795	+	0.978172i	$0.433371\pi$
$62$	−15.0719	−1.91414
$63$	−4.25725	−0.536364
$64$	6.38778	0.798472
$65$	2.61520	0.324375
$66$	−6.09145	−0.749805
$67$	−5.17163	−0.631815	−0.315907	−	0.948790i	$-0.602309\pi$
$67$	−5.17163	−0.631815	−0.315907	+	0.948790i	$0.602309\pi$
$68$	−0.312840	−0.0379375
$69$	−1.86255	−0.224225
$70$	27.2587	3.25804
$71$	−3.68906	−0.437811	−0.218905	−	0.975746i	$-0.570249\pi$
$71$	−3.68906	−0.437811	−0.218905	+	0.975746i	$0.570249\pi$
$72$	2.56584	0.302387
$73$	−13.0782	−1.53069	−0.765345	−	0.643620i	$-0.777432\pi$
$73$	−13.0782	−1.53069	−0.765345	+	0.643620i	$0.777432\pi$
$74$	−9.20511	−1.07007
$75$	−12.7258	−1.46945
$76$	−0.830238	−0.0952349
$77$	17.0521	1.94326
$78$	0.944657	0.106961
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−19.0630	−2.13131
$81$	1.00000	0.111111
$82$	1.20701	0.133292
$83$	13.0395	1.43127	0.715633	−	0.698476i	$-0.246138\pi$
$83$	13.0395	1.43127	0.715633	+	0.698476i	$0.246138\pi$
$84$	1.33184	0.145316
$85$	−4.21021	−0.456661
$86$	8.92608	0.962524
$87$	−0.0363611	−0.00389832
$88$	−10.2772	−1.09556
$89$	−3.36959	−0.357176	−0.178588	−	0.983924i	$-0.557153\pi$
$89$	−3.36959	−0.357176	−0.178588	+	0.983924i	$0.557153\pi$
$90$	−6.40289	−0.674924
$91$	−2.64442	−0.277211
$92$	0.582681	0.0607487
$93$	−9.91051	−1.02767
$94$	2.73976	0.282585
$95$	−11.1733	−1.14636
$96$	−1.75423	−0.179041
$97$	11.4845	1.16608	0.583038	−	0.812445i	$-0.301864\pi$
$97$	11.4845	1.16608	0.583038	+	0.812445i	$0.301864\pi$
$98$	−16.9177	−1.70895
$99$	−4.00541	−0.402559
$100$	3.98115	0.398115
$101$	−6.31348	−0.628215	−0.314107	−	0.949387i	$-0.601705\pi$
$101$	−6.31348	−0.628215	−0.314107	+	0.949387i	$0.601705\pi$
$102$	−1.52080	−0.150582
$103$	−2.40948	−0.237413	−0.118707	−	0.992929i	$-0.537875\pi$
$103$	−2.40948	−0.237413	−0.118707	+	0.992929i	$0.537875\pi$
$104$	1.59379	0.156284
$105$	17.9239	1.74919
$106$	2.68286	0.260582
$107$	−10.0837	−0.974830	−0.487415	−	0.873170i	$-0.662060\pi$
$107$	−10.0837	−0.974830	−0.487415	+	0.873170i	$0.662060\pi$
$108$	−0.312840	−0.0301031
$109$	−14.7929	−1.41691	−0.708453	−	0.705758i	$-0.750606\pi$
$109$	−14.7929	−1.41691	−0.708453	+	0.705758i	$0.750606\pi$
$110$	25.6462	2.44527
$111$	−6.05280	−0.574506
$112$	19.2760	1.82141
$113$	12.6766	1.19252	0.596259	−	0.802792i	$-0.296653\pi$
$113$	12.6766	1.19252	0.596259	+	0.802792i	$0.296653\pi$
$114$	−4.03602	−0.378008
$115$	7.84172	0.731244
$116$	0.0113752	0.00105616
$117$	0.621157	0.0574260
$118$	10.1609	0.935391
$119$	4.25725	0.390262
$120$	−10.8027	−0.986147
$121$	5.04335	0.458486
$122$	−4.93630	−0.446912
$123$	0.793665	0.0715624
$124$	3.10041	0.278425
$125$	32.5273	2.90933
$126$	6.47444	0.576789
$127$	18.0598	1.60255	0.801276	−	0.598295i	$-0.204155\pi$
$127$	18.0598	1.60255	0.801276	+	0.598295i	$0.204155\pi$
$128$	−13.2230	−1.16876
$129$	5.86932	0.516765
$130$	−3.97720	−0.348823
$131$	−4.44555	−0.388409	−0.194205	−	0.980961i	$-0.562213\pi$
$131$	−4.44555	−0.388409	−0.194205	+	0.980961i	$0.562213\pi$
$132$	1.25306	0.109064
$133$	11.2982	0.979679
$134$	7.86502	0.679434
$135$	−4.21021	−0.362357
$136$	−2.56584	−0.220019
$137$	7.39901	0.632140	0.316070	−	0.948736i	$-0.397637\pi$
$137$	7.39901	0.632140	0.316070	+	0.948736i	$0.397637\pi$
$138$	2.83257	0.241124
$139$	−21.5215	−1.82543	−0.912716	−	0.408596i	$-0.866019\pi$
$139$	−21.5215	−1.82543	−0.912716	+	0.408596i	$0.866019\pi$
$140$	−5.60732	−0.473905
$141$	1.80152	0.151715
$142$	5.61033	0.470809
$143$	−2.48799	−0.208056
$144$	−4.52781	−0.377318
$145$	0.153088	0.0127132
$146$	19.8894	1.64606
$147$	−11.1242	−0.917509
$148$	1.89356	0.155650
$149$	3.34961	0.274411	0.137206	−	0.990543i	$-0.456188\pi$
$149$	3.34961	0.274411	0.137206	+	0.990543i	$0.456188\pi$
$150$	19.3535	1.58020
$151$	−11.8870	−0.967349	−0.483675	−	0.875248i	$-0.660698\pi$
$151$	−11.8870	−0.967349	−0.483675	+	0.875248i	$0.660698\pi$
$152$	−6.80940	−0.552316
$153$	−1.00000	−0.0808452
$154$	−25.9328	−2.08973
$155$	41.7253	3.35145
$156$	−0.194323	−0.0155583
$157$	−12.3185	−0.983125	−0.491563	−	0.870842i	$-0.663574\pi$
$157$	−12.3185	−0.983125	−0.491563	+	0.870842i	$0.663574\pi$
$158$	1.52080	0.120989
$159$	1.76411	0.139903
$160$	7.38569	0.583890
$161$	−7.92935	−0.624920
$162$	−1.52080	−0.119486
$163$	−5.21242	−0.408268	−0.204134	−	0.978943i	$-0.565438\pi$
$163$	−5.21242	−0.408268	−0.204134	+	0.978943i	$0.565438\pi$
$164$	−0.248291	−0.0193882
$165$	16.8636	1.31283
$166$	−19.8304	−1.53914
$167$	10.8841	0.842236	0.421118	−	0.907006i	$-0.361638\pi$
$167$	10.8841	0.842236	0.421118	+	0.907006i	$0.361638\pi$
$168$	10.9234	0.842760
$169$	−12.6142	−0.970320
$170$	6.40289	0.491079
$171$	−2.65387	−0.202947
$172$	−1.83616	−0.140006
$173$	−24.3579	−1.85189	−0.925947	−	0.377654i	$-0.876731\pi$
$173$	−24.3579	−1.85189	−0.925947	+	0.377654i	$0.876731\pi$
$174$	0.0552981	0.00419214
$175$	−54.1771	−4.09540
$176$	18.1358	1.36703
$177$	6.68131	0.502198
$178$	5.12448	0.384096
$179$	−11.2818	−0.843238	−0.421619	−	0.906773i	$-0.638538\pi$
$179$	−11.2818	−0.843238	−0.421619	+	0.906773i	$0.638538\pi$
$180$	1.31712	0.0981725
$181$	12.3569	0.918485	0.459242	−	0.888311i	$-0.348121\pi$
$181$	12.3569	0.918485	0.459242	+	0.888311i	$0.348121\pi$
$182$	4.02164	0.298104
$183$	−3.24585	−0.239940
$184$	4.77900	0.352313
$185$	25.4835	1.87359
$186$	15.0719	1.10513
$187$	4.00541	0.292905
$188$	−0.563589	−0.0411039
$189$	4.25725	0.309670
$190$	16.9925	1.23276
$191$	15.5272	1.12351	0.561753	−	0.827305i	$-0.310127\pi$
$191$	15.5272	1.12351	0.561753	+	0.827305i	$0.310127\pi$
$192$	−6.38778	−0.460998
$193$	−7.41344	−0.533631	−0.266816	−	0.963748i	$-0.585971\pi$
$193$	−7.41344	−0.533631	−0.266816	+	0.963748i	$0.585971\pi$
$194$	−17.4657	−1.25396
$195$	−2.61520	−0.187278
$196$	3.48010	0.248579
$197$	−15.6583	−1.11561	−0.557805	−	0.829972i	$-0.688356\pi$
$197$	−15.6583	−1.11561	−0.557805	+	0.829972i	$0.688356\pi$
$198$	6.09145	0.432900
$199$	−5.12316	−0.363171	−0.181586	−	0.983375i	$-0.558123\pi$
$199$	−5.12316	−0.363171	−0.181586	+	0.983375i	$0.558123\pi$
$200$	32.6524	2.30887
$201$	5.17163	0.364778
$202$	9.60155	0.675563
$203$	−0.154798	−0.0108647
$204$	0.312840	0.0219032
$205$	−3.34149	−0.233380
$206$	3.66435	0.255307
$207$	1.86255	0.129456
$208$	−2.81248	−0.195010
$209$	10.6299	0.735283
$210$	−27.2587	−1.88103
$211$	15.2568	1.05032	0.525161	−	0.851003i	$-0.324005\pi$
$211$	15.2568	1.05032	0.525161	+	0.851003i	$0.324005\pi$
$212$	−0.551883	−0.0379035
$213$	3.68906	0.252770
$214$	15.3353	1.04830
$215$	−24.7111	−1.68528
$216$	−2.56584	−0.174583
$217$	−42.1915	−2.86415
$218$	22.4971	1.52370
$219$	13.0782	0.883745
$220$	−5.27562	−0.355682
$221$	−0.621157	−0.0417835
$222$	9.20511	0.617807
$223$	26.5978	1.78112	0.890562	−	0.454862i	$-0.150312\pi$
$223$	26.5978	1.78112	0.890562	+	0.454862i	$0.150312\pi$
$224$	−7.46822	−0.498991
$225$	12.7258	0.848389
$226$	−19.2787	−1.28240
$227$	−7.89082	−0.523732	−0.261866	−	0.965104i	$-0.584338\pi$
$227$	−7.89082	−0.523732	−0.261866	+	0.965104i	$0.584338\pi$
$228$	0.830238	0.0549839
$229$	−10.5356	−0.696209	−0.348105	−	0.937456i	$-0.613175\pi$
$229$	−10.5356	−0.696209	−0.348105	+	0.937456i	$0.613175\pi$
$230$	−11.9257	−0.786358
$231$	−17.0521	−1.12194
$232$	0.0932967	0.00612523
$233$	0.178665	0.0117047	0.00585236	−	0.999983i	$-0.498137\pi$
$233$	0.178665	0.0117047	0.00585236	+	0.999983i	$0.498137\pi$
$234$	−0.944657	−0.0617541
$235$	−7.58478	−0.494776
$236$	−2.09018	−0.136059
$237$	1.00000	0.0649570
$238$	−6.47444	−0.419676
$239$	−15.8572	−1.02572	−0.512859	−	0.858473i	$-0.671413\pi$
$239$	−15.8572	−1.02572	−0.512859	+	0.858473i	$0.671413\pi$
$240$	19.0630	1.23051
$241$	7.53564	0.485413	0.242706	−	0.970100i	$-0.421965\pi$
$241$	7.53564	0.485413	0.242706	+	0.970100i	$0.421965\pi$
$242$	−7.66994	−0.493042
$243$	−1.00000	−0.0641500
$244$	1.01543	0.0650065
$245$	46.8352	2.99219
$246$	−1.20701	−0.0769560
$247$	−1.64847	−0.104890
$248$	25.4287	1.61473
$249$	−13.0395	−0.826342
$250$	−49.4677	−3.12861
$251$	−3.15925	−0.199410	−0.0997051	−	0.995017i	$-0.531790\pi$
$251$	−3.15925	−0.199410	−0.0997051	+	0.995017i	$0.531790\pi$
$252$	−1.33184	−0.0838981
$253$	−7.46029	−0.469024
$254$	−27.4654	−1.72334
$255$	4.21021	0.263653
$256$	7.33404	0.458378
$257$	−1.30399	−0.0813405	−0.0406702	−	0.999173i	$-0.512949\pi$
$257$	−1.30399	−0.0813405	−0.0406702	+	0.999173i	$0.512949\pi$
$258$	−8.92608	−0.555714
$259$	−25.7683	−1.60116
$260$	0.818139	0.0507389
$261$	0.0363611	0.00225070
$262$	6.76080	0.417684
$263$	19.6214	1.20991	0.604953	−	0.796262i	$-0.293192\pi$
$263$	19.6214	1.20991	0.604953	+	0.796262i	$0.293192\pi$
$264$	10.2772	0.632520
$265$	−7.42725	−0.456252
$266$	−17.1823	−1.05352
$267$	3.36959	0.206216
$268$	−1.61789	−0.0988286
$269$	−17.3382	−1.05713	−0.528564	−	0.848894i	$-0.677269\pi$
$269$	−17.3382	−1.05713	−0.528564	+	0.848894i	$0.677269\pi$
$270$	6.40289	0.389668
$271$	8.70529	0.528808	0.264404	−	0.964412i	$-0.414825\pi$
$271$	8.70529	0.528808	0.264404	+	0.964412i	$0.414825\pi$
$272$	4.52781	0.274539
$273$	2.64442	0.160048
$274$	−11.2524	−0.679784
$275$	−50.9722	−3.07374
$276$	−0.582681	−0.0350733
$277$	−28.5627	−1.71617	−0.858083	−	0.513511i	$-0.828344\pi$
$277$	−28.5627	−1.71617	−0.858083	+	0.513511i	$0.828344\pi$
$278$	32.7300	1.96301
$279$	9.91051	0.593326
$280$	−45.9898	−2.74842
$281$	5.59457	0.333744	0.166872	−	0.985979i	$-0.446633\pi$
$281$	5.59457	0.333744	0.166872	+	0.985979i	$0.446633\pi$
$282$	−2.73976	−0.163150
$283$	−26.5463	−1.57802	−0.789008	−	0.614383i	$-0.789405\pi$
$283$	−26.5463	−1.57802	−0.789008	+	0.614383i	$0.789405\pi$
$284$	−1.15409	−0.0684825
$285$	11.1733	0.661852
$286$	3.78374	0.223737
$287$	3.37883	0.199446
$288$	1.75423	0.103369
$289$	1.00000	0.0588235
$290$	−0.232816	−0.0136714
$291$	−11.4845	−0.673234
$292$	−4.09140	−0.239431
$293$	−2.19965	−0.128505	−0.0642525	−	0.997934i	$-0.520466\pi$
$293$	−2.19965	−0.128505	−0.0642525	+	0.997934i	$0.520466\pi$
$294$	16.9177	0.986662
$295$	−28.1297	−1.63777
$296$	15.5305	0.902692
$297$	4.00541	0.232418
$298$	−5.09410	−0.295093
$299$	1.15694	0.0669073
$300$	−3.98115	−0.229852
$301$	24.9872	1.44024
$302$	18.0778	1.04026
$303$	6.31348	0.362700
$304$	12.0162	0.689178
$305$	13.6657	0.782497
$306$	1.52080	0.0869385
$307$	9.53692	0.544301	0.272150	−	0.962255i	$-0.412265\pi$
$307$	9.53692	0.544301	0.272150	+	0.962255i	$0.412265\pi$
$308$	5.33457	0.303966
$309$	2.40948	0.137071
$310$	−63.4559	−3.60405
$311$	−10.1816	−0.577348	−0.288674	−	0.957427i	$-0.593214\pi$
$311$	−10.1816	−0.577348	−0.288674	+	0.957427i	$0.593214\pi$
$312$	−1.59379	−0.0902304
$313$	−14.1128	−0.797700	−0.398850	−	0.917016i	$-0.630591\pi$
$313$	−14.1128	−0.797700	−0.398850	+	0.917016i	$0.630591\pi$
$314$	18.7340	1.05722
$315$	−17.9239	−1.00990
$316$	−0.312840	−0.0175986
$317$	−25.3057	−1.42131	−0.710655	−	0.703541i	$-0.751601\pi$
$317$	−25.3057	−1.42131	−0.710655	+	0.703541i	$0.751601\pi$
$318$	−2.68286	−0.150447
$319$	−0.145641	−0.00815435
$320$	26.8939	1.50341
$321$	10.0837	0.562818
$322$	12.0590	0.672020
$323$	2.65387	0.147665
$324$	0.312840	0.0173800
$325$	7.90474	0.438476
$326$	7.92706	0.439039
$327$	14.7929	0.818051
$328$	−2.03642	−0.112442
$329$	7.66953	0.422835
$330$	−25.6462	−1.41178
$331$	0.118837	0.00653190	0.00326595	−	0.999995i	$-0.498960\pi$
$331$	0.118837	0.00653190	0.00326595	+	0.999995i	$0.498960\pi$
$332$	4.07927	0.223879
$333$	6.05280	0.331691
$334$	−16.5525	−0.905715
$335$	−21.7736	−1.18962
$336$	−19.2760	−1.05159
$337$	29.1070	1.58556	0.792778	−	0.609510i	$-0.208634\pi$
$337$	29.1070	1.58556	0.792778	+	0.609510i	$0.208634\pi$
$338$	19.1837	1.04345
$339$	−12.6766	−0.688501
$340$	−1.31712	−0.0714310
$341$	−39.6957	−2.14964
$342$	4.03602	0.218243
$343$	−17.5578	−0.948032
$344$	−15.0597	−0.811966
$345$	−7.84172	−0.422184
$346$	37.0435	1.99147
$347$	11.9087	0.639293	0.319647	−	0.947537i	$-0.396436\pi$
$347$	11.9087	0.639293	0.319647	+	0.947537i	$0.396436\pi$
$348$	−0.0113752	−0.000609776 0
$349$	−1.46015	−0.0781599	−0.0390800	−	0.999236i	$-0.512443\pi$
$349$	−1.46015	−0.0781599	−0.0390800	+	0.999236i	$0.512443\pi$
$350$	82.3927	4.40407
$351$	−0.621157	−0.0331549
$352$	−7.02644	−0.374510
$353$	−6.06500	−0.322807	−0.161404	−	0.986888i	$-0.551602\pi$
$353$	−6.06500	−0.322807	−0.161404	+	0.986888i	$0.551602\pi$
$354$	−10.1609	−0.540048
$355$	−15.5317	−0.824337
$356$	−1.05414	−0.0558695
$357$	−4.25725	−0.225318
$358$	17.1573	0.906793
$359$	0.143649	0.00758150	0.00379075	−	0.999993i	$-0.498793\pi$
$359$	0.143649	0.00758150	0.00379075	+	0.999993i	$0.498793\pi$
$360$	10.8027	0.569352
$361$	−11.9570	−0.629314
$362$	−18.7925	−0.987711
$363$	−5.04335	−0.264707
$364$	−0.827282	−0.0433614
$365$	−55.0620	−2.88208
$366$	4.93630	0.258025
$367$	10.2282	0.533908	0.266954	−	0.963709i	$-0.413983\pi$
$367$	10.2282	0.533908	0.266954	+	0.963709i	$0.413983\pi$
$368$	−8.43328	−0.439615
$369$	−0.793665	−0.0413166
$370$	−38.7554	−2.01480
$371$	7.51024	0.389912
$372$	−3.10041	−0.160749
$373$	−23.5072	−1.21716	−0.608579	−	0.793493i	$-0.708260\pi$
$373$	−23.5072	−1.21716	−0.608579	+	0.793493i	$0.708260\pi$
$374$	−6.09145	−0.314981
$375$	−32.5273	−1.67971
$376$	−4.62241	−0.238383
$377$	0.0225860	0.00116324
$378$	−6.47444	−0.333009
$379$	−9.84100	−0.505498	−0.252749	−	0.967532i	$-0.581335\pi$
$379$	−9.84100	−0.505498	−0.252749	+	0.967532i	$0.581335\pi$
$380$	−3.49547	−0.179314
$381$	−18.0598	−0.925233
$382$	−23.6138	−1.20819
$383$	−15.9337	−0.814176	−0.407088	−	0.913389i	$-0.633456\pi$
$383$	−15.9337	−0.814176	−0.407088	+	0.913389i	$0.633456\pi$
$384$	13.2230	0.674784
$385$	71.7927	3.65890
$386$	11.2744	0.573851
$387$	−5.86932	−0.298355
$388$	3.59282	0.182398
$389$	−33.4585	−1.69641	−0.848206	−	0.529666i	$-0.822317\pi$
$389$	−33.4585	−1.69641	−0.848206	+	0.529666i	$0.822317\pi$
$390$	3.97720	0.201393
$391$	−1.86255	−0.0941932
$392$	28.5429	1.44163
$393$	4.44555	0.224248
$394$	23.8132	1.19969
$395$	−4.21021	−0.211838
$396$	−1.25306	−0.0629684
$397$	−18.5855	−0.932781	−0.466390	−	0.884579i	$-0.654446\pi$
$397$	−18.5855	−0.932781	−0.466390	+	0.884579i	$0.654446\pi$
$398$	7.79132	0.390544
$399$	−11.2982	−0.565618
$400$	−57.6202	−2.88101
$401$	36.3728	1.81637	0.908184	−	0.418571i	$-0.137469\pi$
$401$	36.3728	1.81637	0.908184	+	0.418571i	$0.137469\pi$
$402$	−7.86502	−0.392272
$403$	6.15598	0.306651
$404$	−1.97511	−0.0982654
$405$	4.21021	0.209207
$406$	0.235418	0.0116836
$407$	−24.2440	−1.20173
$408$	2.56584	0.127028
$409$	−5.99747	−0.296556	−0.148278	−	0.988946i	$-0.547373\pi$
$409$	−5.99747	−0.296556	−0.148278	+	0.988946i	$0.547373\pi$
$410$	5.08175	0.250970
$411$	−7.39901	−0.364966
$412$	−0.753783	−0.0371362
$413$	28.4440	1.39964
$414$	−2.83257	−0.139213
$415$	54.8988	2.69488
$416$	1.08965	0.0534247
$417$	21.5215	1.05391
$418$	−16.1659	−0.790701
$419$	0.803187	0.0392382	0.0196191	−	0.999808i	$-0.493755\pi$
$419$	0.803187	0.0392382	0.0196191	+	0.999808i	$0.493755\pi$
$420$	5.60732	0.273609
$421$	−23.0407	−1.12294	−0.561468	−	0.827499i	$-0.689763\pi$
$421$	−23.0407	−1.12294	−0.561468	+	0.827499i	$0.689763\pi$
$422$	−23.2026	−1.12948
$423$	−1.80152	−0.0875930
$424$	−4.52641	−0.219822
$425$	−12.7258	−0.617294
$426$	−5.61033	−0.271821
$427$	−13.8184	−0.668721
$428$	−3.15459	−0.152483
$429$	2.48799	0.120121
$430$	37.5806	1.81230
$431$	−40.0067	−1.92706	−0.963528	−	0.267609i	$-0.913766\pi$
$431$	−40.0067	−1.92706	−0.963528	+	0.267609i	$0.913766\pi$
$432$	4.52781	0.217844
$433$	−37.6419	−1.80895	−0.904477	−	0.426523i	$-0.859738\pi$
$433$	−37.6419	−1.80895	−0.904477	+	0.426523i	$0.859738\pi$
$434$	64.1650	3.08002
$435$	−0.153088	−0.00734000
$436$	−4.62782	−0.221633
$437$	−4.94297	−0.236454
$438$	−19.8894	−0.950352
$439$	8.09146	0.386184	0.193092	−	0.981181i	$-0.438148\pi$
$439$	8.09146	0.386184	0.193092	+	0.981181i	$0.438148\pi$
$440$	−43.2693	−2.06278
$441$	11.1242	0.529724
$442$	0.944657	0.0449327
$443$	11.5898	0.550647	0.275324	−	0.961352i	$-0.411215\pi$
$443$	11.5898	0.550647	0.275324	+	0.961352i	$0.411215\pi$
$444$	−1.89356	−0.0898644
$445$	−14.1867	−0.672513
$446$	−40.4501	−1.91537
$447$	−3.34961	−0.158431
$448$	−27.1944	−1.28481
$449$	−40.0261	−1.88895	−0.944474	−	0.328586i	$-0.893428\pi$
$449$	−40.0261	−1.88895	−0.944474	+	0.328586i	$0.893428\pi$
$450$	−19.3535	−0.912332
$451$	3.17896	0.149691
$452$	3.96577	0.186534
$453$	11.8870	0.558499
$454$	12.0004	0.563206
$455$	−11.1336	−0.521949
$456$	6.80940	0.318880
$457$	−26.4202	−1.23588	−0.617942	−	0.786224i	$-0.712033\pi$
$457$	−26.4202	−1.23588	−0.617942	+	0.786224i	$0.712033\pi$
$458$	16.0225	0.748682
$459$	1.00000	0.0466760
$460$	2.45321	0.114381
$461$	−14.1392	−0.658530	−0.329265	−	0.944238i	$-0.606801\pi$
$461$	−14.1392	−0.658530	−0.329265	+	0.944238i	$0.606801\pi$
$462$	25.9328	1.20650
$463$	−40.1978	−1.86815	−0.934076	−	0.357074i	$-0.883774\pi$
$463$	−40.1978	−1.86815	−0.934076	+	0.357074i	$0.883774\pi$
$464$	−0.164636	−0.00764305
$465$	−41.7253	−1.93496
$466$	−0.271714	−0.0125869
$467$	9.92312	0.459187	0.229594	−	0.973287i	$-0.426260\pi$
$467$	9.92312	0.459187	0.229594	+	0.973287i	$0.426260\pi$
$468$	0.194323	0.00898258
$469$	22.0169	1.01665
$470$	11.5349	0.532067
$471$	12.3185	0.567607
$472$	−17.1431	−0.789077
$473$	23.5091	1.08095
$474$	−1.52080	−0.0698528
$475$	−33.7727	−1.54960
$476$	1.33184	0.0610448
$477$	−1.76411	−0.0807728
$478$	24.1157	1.10303
$479$	−24.4279	−1.11614	−0.558069	−	0.829794i	$-0.688458\pi$
$479$	−24.4279	−1.11614	−0.558069	+	0.829794i	$0.688458\pi$
$480$	−7.38569	−0.337109
$481$	3.75974	0.171429
$482$	−11.4602	−0.521998
$483$	7.92935	0.360798
$484$	1.57776	0.0717165
$485$	48.3522	2.19556
$486$	1.52080	0.0689850
$487$	18.7339	0.848914	0.424457	−	0.905448i	$-0.360465\pi$
$487$	18.7339	0.848914	0.424457	+	0.905448i	$0.360465\pi$
$488$	8.32833	0.377006
$489$	5.21242	0.235714
$490$	−71.2271	−3.21771
$491$	1.50389	0.0678697	0.0339348	−	0.999424i	$-0.489196\pi$
$491$	1.50389	0.0678697	0.0339348	+	0.999424i	$0.489196\pi$
$492$	0.248291	0.0111938
$493$	−0.0363611	−0.00163762
$494$	2.50700	0.112795
$495$	−16.8636	−0.757963
$496$	−44.8729	−2.01485
$497$	15.7053	0.704477
$498$	19.8304	0.888623
$499$	−7.23463	−0.323867	−0.161933	−	0.986802i	$-0.551773\pi$
$499$	−7.23463	−0.323867	−0.161933	+	0.986802i	$0.551773\pi$
$500$	10.1759	0.455079
$501$	−10.8841	−0.486265
$502$	4.80460	0.214440
$503$	−11.3647	−0.506725	−0.253363	−	0.967371i	$-0.581537\pi$
$503$	−11.3647	−0.506725	−0.253363	+	0.967371i	$0.581537\pi$
$504$	−10.9234	−0.486568
$505$	−26.5810	−1.18284
$506$	11.3456	0.504374
$507$	12.6142	0.560215
$508$	5.64985	0.250671
$509$	−43.9105	−1.94630	−0.973150	−	0.230172i	$-0.926071\pi$
$509$	−43.9105	−1.94630	−0.973150	+	0.230172i	$0.926071\pi$
$510$	−6.40289	−0.283525
$511$	55.6773	2.46302
$512$	15.2924	0.675835
$513$	2.65387	0.117171
$514$	1.98311	0.0874711
$515$	−10.1444	−0.447016
$516$	1.83616	0.0808325
$517$	7.21584	0.317352
$518$	39.1885	1.72184
$519$	24.3579	1.06919
$520$	6.71017	0.294260
$521$	41.5417	1.81998	0.909988	−	0.414636i	$-0.136091\pi$
$521$	41.5417	1.81998	0.909988	+	0.414636i	$0.136091\pi$
$522$	−0.0552981	−0.00242033
$523$	−17.1002	−0.747738	−0.373869	−	0.927481i	$-0.621969\pi$
$523$	−17.1002	−0.747738	−0.373869	+	0.927481i	$0.621969\pi$
$524$	−1.39075	−0.0607551
$525$	54.1771	2.36448
$526$	−29.8402	−1.30110
$527$	−9.91051	−0.431708
$528$	−18.1358	−0.789258
$529$	−19.5309	−0.849170
$530$	11.2954	0.490640
$531$	−6.68131	−0.289944
$532$	3.53454	0.153242
$533$	−0.492990	−0.0213538
$534$	−5.12448	−0.221758
$535$	−42.4545	−1.83547
$536$	−13.2695	−0.573157
$537$	11.2818	0.486844
$538$	26.3680	1.13680
$539$	−44.5571	−1.91921
$540$	−1.31712	−0.0566799
$541$	20.2704	0.871493	0.435746	−	0.900070i	$-0.356484\pi$
$541$	20.2704	0.871493	0.435746	+	0.900070i	$0.356484\pi$
$542$	−13.2390	−0.568665
$543$	−12.3569	−0.530287
$544$	−1.75423	−0.0752122
$545$	−62.2813	−2.66784
$546$	−4.02164	−0.172110
$547$	42.0636	1.79851	0.899254	−	0.437426i	$-0.144110\pi$
$547$	42.0636	1.79851	0.899254	+	0.437426i	$0.144110\pi$
$548$	2.31471	0.0988794
$549$	3.24585	0.138530
$550$	77.5187	3.30541
$551$	−0.0964978	−0.00411094
$552$	−4.77900	−0.203408
$553$	4.25725	0.181037
$554$	43.4382	1.84551
$555$	−25.4835	−1.08172
$556$	−6.73280	−0.285534
$557$	24.9650	1.05780	0.528901	−	0.848684i	$-0.322604\pi$
$557$	24.9650	1.05780	0.528901	+	0.848684i	$0.322604\pi$
$558$	−15.0719	−0.638045
$559$	−3.64577	−0.154200
$560$	81.1561	3.42947
$561$	−4.00541	−0.169109
$562$	−8.50823	−0.358898
$563$	−28.0629	−1.18271	−0.591355	−	0.806411i	$-0.701407\pi$
$563$	−28.0629	−1.18271	−0.591355	+	0.806411i	$0.701407\pi$
$564$	0.563589	0.0237314
$565$	53.3713	2.24535
$566$	40.3717	1.69695
$567$	−4.25725	−0.178788
$568$	−9.46552	−0.397165
$569$	43.8422	1.83796	0.918980	−	0.394303i	$-0.129014\pi$
$569$	43.8422	1.83796	0.918980	+	0.394303i	$0.129014\pi$
$570$	−16.9925	−0.711736
$571$	−16.6643	−0.697380	−0.348690	−	0.937238i	$-0.613373\pi$
$571$	−16.6643	−0.697380	−0.348690	+	0.937238i	$0.613373\pi$
$572$	−0.778344	−0.0325442
$573$	−15.5272	−0.648657
$574$	−5.13854	−0.214478
$575$	23.7025	0.988463
$576$	6.38778	0.266157
$577$	−29.7183	−1.23719	−0.618595	−	0.785710i	$-0.712298\pi$
$577$	−29.7183	−1.23719	−0.618595	+	0.785710i	$0.712298\pi$
$578$	−1.52080	−0.0632570
$579$	7.41344	0.308092
$580$	0.0478920	0.00198861
$581$	−55.5123	−2.30304
$582$	17.4657	0.723976
$583$	7.06597	0.292643
$584$	−33.5566	−1.38858
$585$	2.61520	0.108125
$586$	3.34524	0.138190
$587$	35.8368	1.47914	0.739571	−	0.673078i	$-0.235028\pi$
$587$	35.8368	1.47914	0.739571	+	0.673078i	$0.235028\pi$
$588$	−3.48010	−0.143517
$589$	−26.3012	−1.08372
$590$	42.7797	1.76121
$591$	15.6583	0.644098
$592$	−27.4059	−1.12638
$593$	16.8762	0.693021	0.346511	−	0.938046i	$-0.387366\pi$
$593$	16.8762	0.693021	0.346511	+	0.938046i	$0.387366\pi$
$594$	−6.09145	−0.249935
$595$	17.9239	0.734809
$596$	1.04789	0.0429234
$597$	5.12316	0.209677
$598$	−1.75947	−0.0719501
$599$	37.3023	1.52413	0.762066	−	0.647499i	$-0.224185\pi$
$599$	37.3023	1.52413	0.762066	+	0.647499i	$0.224185\pi$
$600$	−32.6524	−1.33303
$601$	2.78962	0.113791	0.0568955	−	0.998380i	$-0.481880\pi$
$601$	2.78962	0.113791	0.0568955	+	0.998380i	$0.481880\pi$
$602$	−38.0006	−1.54879
$603$	−5.17163	−0.210605
$604$	−3.71873	−0.151313
$605$	21.2335	0.863266
$606$	−9.60155	−0.390036
$607$	−31.1529	−1.26446	−0.632229	−	0.774781i	$-0.717860\pi$
$607$	−31.1529	−1.26446	−0.632229	+	0.774781i	$0.717860\pi$
$608$	−4.65551	−0.188806
$609$	0.154798	0.00627275
$610$	−20.7829	−0.841473
$611$	−1.11903	−0.0452710
$612$	−0.312840	−0.0126458
$613$	−24.2512	−0.979498	−0.489749	−	0.871863i	$-0.662912\pi$
$613$	−24.2512	−0.979498	−0.489749	+	0.871863i	$0.662912\pi$
$614$	−14.5038	−0.585324
$615$	3.34149	0.134742
$616$	43.7528	1.76285
$617$	26.5723	1.06976	0.534880	−	0.844928i	$-0.320357\pi$
$617$	26.5723	1.06976	0.534880	+	0.844928i	$0.320357\pi$
$618$	−3.66435	−0.147402
$619$	−9.76226	−0.392378	−0.196189	−	0.980566i	$-0.562857\pi$
$619$	−9.76226	−0.392378	−0.196189	+	0.980566i	$0.562857\pi$
$620$	13.0533	0.524235
$621$	−1.86255	−0.0747416
$622$	15.4843	0.620863
$623$	14.3452	0.574729
$624$	2.81248	0.112589
$625$	73.3177	2.93271
$626$	21.4627	0.857823
$627$	−10.6299	−0.424516
$628$	−3.85373	−0.153781
$629$	−6.05280	−0.241341
$630$	27.2587	1.08601
$631$	−32.7577	−1.30406	−0.652032	−	0.758192i	$-0.726083\pi$
$631$	−32.7577	−1.30406	−0.652032	+	0.758192i	$0.726083\pi$
$632$	−2.56584	−0.102064
$633$	−15.2568	−0.606403
$634$	38.4850	1.52843
$635$	76.0356	3.01738
$636$	0.551883	0.0218836
$637$	6.90988	0.273779
$638$	0.221492	0.00876894
$639$	−3.68906	−0.145937
$640$	−55.6716	−2.20061
$641$	32.3871	1.27921	0.639607	−	0.768702i	$-0.279097\pi$
$641$	32.3871	1.27921	0.639607	+	0.768702i	$0.279097\pi$
$642$	−15.3353	−0.605238
$643$	3.40517	0.134287	0.0671434	−	0.997743i	$-0.478612\pi$
$643$	3.40517	0.134287	0.0671434	+	0.997743i	$0.478612\pi$
$644$	−2.48062	−0.0977501
$645$	24.7111	0.972997
$646$	−4.03602	−0.158795
$647$	8.96242	0.352349	0.176175	−	0.984359i	$-0.443628\pi$
$647$	8.96242	0.352349	0.176175	+	0.984359i	$0.443628\pi$
$648$	2.56584	0.100796
$649$	26.7614	1.05048
$650$	−12.0215	−0.471524
$651$	42.1915	1.65362
$652$	−1.63066	−0.0638614
$653$	12.3222	0.482206	0.241103	−	0.970500i	$-0.422491\pi$
$653$	12.3222	0.482206	0.241103	+	0.970500i	$0.422491\pi$
$654$	−22.4971	−0.879707
$655$	−18.7167	−0.731321
$656$	3.59357	0.140305
$657$	−13.0782	−0.510230
$658$	−11.6638	−0.454704
$659$	−28.7729	−1.12083	−0.560417	−	0.828210i	$-0.689359\pi$
$659$	−28.7729	−1.12083	−0.560417	+	0.828210i	$0.689359\pi$
$660$	5.27562	0.205353
$661$	14.0456	0.546311	0.273155	−	0.961970i	$-0.411933\pi$
$661$	14.0456	0.546311	0.273155	+	0.961970i	$0.411933\pi$
$662$	−0.180728	−0.00702420
$663$	0.621157	0.0241237
$664$	33.4571	1.29839
$665$	47.5678	1.84460
$666$	−9.20511	−0.356691
$667$	0.0677244	0.00262230
$668$	3.40498	0.131743
$669$	−26.5978	−1.02833
$670$	33.1134	1.27928
$671$	−13.0010	−0.501898
$672$	7.46822	0.288093
$673$	30.5623	1.17809	0.589044	−	0.808101i	$-0.299504\pi$
$673$	30.5623	1.17809	0.589044	+	0.808101i	$0.299504\pi$
$674$	−44.2659	−1.70506
$675$	−12.7258	−0.489818
$676$	−3.94622	−0.151778
$677$	−7.80439	−0.299947	−0.149974	−	0.988690i	$-0.547919\pi$
$677$	−7.80439	−0.299947	−0.149974	+	0.988690i	$0.547919\pi$
$678$	19.2787	0.740393
$679$	−48.8925	−1.87632
$680$	−10.8027	−0.414265
$681$	7.89082	0.302377
$682$	60.3693	2.31166
$683$	46.7577	1.78914	0.894568	−	0.446933i	$-0.147484\pi$
$683$	46.7577	1.78914	0.894568	+	0.446933i	$0.147484\pi$
$684$	−0.830238	−0.0317450
$685$	31.1513	1.19023
$686$	26.7019	1.01948
$687$	10.5356	0.401956
$688$	26.5752	1.01317
$689$	−1.09579	−0.0417461
$690$	11.9257	0.454004
$691$	−28.0752	−1.06803	−0.534016	−	0.845475i	$-0.679318\pi$
$691$	−28.0752	−1.06803	−0.534016	+	0.845475i	$0.679318\pi$
$692$	−7.62012	−0.289674
$693$	17.0521	0.647754
$694$	−18.1108	−0.687476
$695$	−90.6100	−3.43703
$696$	−0.0932967	−0.00353640
$697$	0.793665	0.0300622
$698$	2.22060	0.0840508
$699$	−0.178665	−0.00675772
$700$	−16.9488	−0.640604
$701$	34.2579	1.29390	0.646952	−	0.762531i	$-0.276044\pi$
$701$	34.2579	1.29390	0.646952	+	0.762531i	$0.276044\pi$
$702$	0.944657	0.0356538
$703$	−16.0634	−0.605841
$704$	−25.5857	−0.964298
$705$	7.58478	0.285659
$706$	9.22366	0.347137
$707$	26.8781	1.01085
$708$	2.09018	0.0785539
$709$	20.3888	0.765716	0.382858	−	0.923807i	$-0.374940\pi$
$709$	20.3888	0.765716	0.382858	+	0.923807i	$0.374940\pi$
$710$	23.6207	0.886467
$711$	−1.00000	−0.0375029
$712$	−8.64582	−0.324016
$713$	18.4588	0.691288
$714$	6.47444	0.242300
$715$	−10.4750	−0.391741
$716$	−3.52939	−0.131899
$717$	15.8572	0.592198
$718$	−0.218462	−0.00815292
$719$	32.0051	1.19359	0.596795	−	0.802394i	$-0.296441\pi$
$719$	32.0051	1.19359	0.596795	+	0.802394i	$0.296441\pi$
$720$	−19.0630	−0.710437
$721$	10.2578	0.382020
$722$	18.1842	0.676745
$723$	−7.53564	−0.280253
$724$	3.86575	0.143670
$725$	0.462725	0.0171852
$726$	7.66994	0.284658
$727$	23.0972	0.856627	0.428313	−	0.903630i	$-0.359108\pi$
$727$	23.0972	0.856627	0.428313	+	0.903630i	$0.359108\pi$
$728$	−6.78515	−0.251475
$729$	1.00000	0.0370370
$730$	83.7385	3.09930
$731$	5.86932	0.217085
$732$	−1.01543	−0.0375315
$733$	37.0494	1.36845	0.684225	−	0.729271i	$-0.260141\pi$
$733$	37.0494	1.36845	0.684225	+	0.729271i	$0.260141\pi$
$734$	−15.5551	−0.574148
$735$	−46.8352	−1.72754
$736$	3.26735	0.120436
$737$	20.7145	0.763029
$738$	1.20701	0.0444306
$739$	−17.0985	−0.628977	−0.314489	−	0.949261i	$-0.601833\pi$
$739$	−17.0985	−0.628977	−0.314489	+	0.949261i	$0.601833\pi$
$740$	7.97228	0.293067
$741$	1.64847	0.0605581
$742$	−11.4216	−0.419300
$743$	3.10898	0.114057	0.0570287	−	0.998373i	$-0.481837\pi$
$743$	3.10898	0.114057	0.0570287	+	0.998373i	$0.481837\pi$
$744$	−25.4287	−0.932263
$745$	14.1026	0.516678
$746$	35.7499	1.30890
$747$	13.0395	0.477089
$748$	1.25306	0.0458162
$749$	42.9289	1.56859
$750$	49.4677	1.80630
$751$	−28.3099	−1.03304	−0.516521	−	0.856275i	$-0.672773\pi$
$751$	−28.3099	−1.03304	−0.516521	+	0.856275i	$0.672773\pi$
$752$	8.15695	0.297453
$753$	3.15925	0.115130
$754$	−0.0343488	−0.00125091
$755$	−50.0467	−1.82138
$756$	1.33184	0.0484386
$757$	−11.5221	−0.418776	−0.209388	−	0.977833i	$-0.567147\pi$
$757$	−11.5221	−0.418776	−0.209388	+	0.977833i	$0.567147\pi$
$758$	14.9662	0.543597
$759$	7.46029	0.270791
$760$	−28.6690	−1.03993
$761$	34.8976	1.26504	0.632519	−	0.774545i	$-0.282021\pi$
$761$	34.8976	1.26504	0.632519	+	0.774545i	$0.282021\pi$
$762$	27.4654	0.994968
$763$	62.9772	2.27993
$764$	4.85753	0.175739
$765$	−4.21021	−0.152220
$766$	24.2321	0.875540
$767$	−4.15014	−0.149853
$768$	−7.33404	−0.264644
$769$	−7.72684	−0.278637	−0.139319	−	0.990248i	$-0.544491\pi$
$769$	−7.72684	−0.278637	−0.139319	+	0.990248i	$0.544491\pi$
$770$	−109.183	−3.93467
$771$	1.30399	0.0469619
$772$	−2.31922	−0.0834707
$773$	25.0969	0.902672	0.451336	−	0.892354i	$-0.350948\pi$
$773$	25.0969	0.902672	0.451336	+	0.892354i	$0.350948\pi$
$774$	8.92608	0.320841
$775$	126.119	4.53034
$776$	29.4674	1.05782
$777$	25.7683	0.924433
$778$	50.8838	1.82427
$779$	2.10629	0.0754655
$780$	−0.818139	−0.0292941
$781$	14.7762	0.528735
$782$	2.83257	0.101293
$783$	−0.0363611	−0.00129944
$784$	−50.3683	−1.79887
$785$	−51.8635	−1.85109
$786$	−6.76080	−0.241150
$787$	40.2145	1.43349	0.716746	−	0.697334i	$-0.245631\pi$
$787$	40.2145	1.43349	0.716746	+	0.697334i	$0.245631\pi$
$788$	−4.89856	−0.174504
$789$	−19.6214	−0.698539
$790$	6.40289	0.227805
$791$	−53.9677	−1.91887
$792$	−10.2772	−0.365186
$793$	2.01618	0.0715968
$794$	28.2649	1.00308
$795$	7.42725	0.263417
$796$	−1.60273	−0.0568073
$797$	25.4948	0.903072	0.451536	−	0.892253i	$-0.350876\pi$
$797$	25.4948	0.903072	0.451536	+	0.892253i	$0.350876\pi$
$798$	17.1823	0.608248
$799$	1.80152	0.0637333
$800$	22.3241	0.789276
$801$	−3.36959	−0.119059
$802$	−55.3158	−1.95327
$803$	52.3837	1.84858
$804$	1.61789	0.0570587
$805$	−33.3842	−1.17664
$806$	−9.36203	−0.329763
$807$	17.3382	0.610333
$808$	−16.1994	−0.569891
$809$	−41.8124	−1.47005	−0.735023	−	0.678042i	$-0.762829\pi$
$809$	−41.8124	−1.47005	−0.735023	+	0.678042i	$0.762829\pi$
$810$	−6.40289	−0.224975
$811$	−3.39758	−0.119305	−0.0596527	−	0.998219i	$-0.518999\pi$
$811$	−3.39758	−0.119305	−0.0596527	+	0.998219i	$0.518999\pi$
$812$	−0.0484272	−0.00169946
$813$	−8.70529	−0.305308
$814$	36.8703	1.29230
$815$	−21.9454	−0.768712
$816$	−4.52781	−0.158505
$817$	15.5764	0.544951
$818$	9.12097	0.318907
$819$	−2.64442	−0.0924036
$820$	−1.04535	−0.0365054
$821$	−40.4387	−1.41132	−0.705660	−	0.708550i	$-0.749350\pi$
$821$	−40.4387	−1.41132	−0.705660	+	0.708550i	$0.749350\pi$
$822$	11.2524	0.392474
$823$	−25.7826	−0.898726	−0.449363	−	0.893349i	$-0.648349\pi$
$823$	−25.7826	−0.898726	−0.449363	+	0.893349i	$0.648349\pi$
$824$	−6.18234	−0.215372
$825$	50.9722	1.77463
$826$	−43.2577	−1.50513
$827$	−15.3578	−0.534044	−0.267022	−	0.963690i	$-0.586040\pi$
$827$	−15.3578	−0.534044	−0.267022	+	0.963690i	$0.586040\pi$
$828$	0.582681	0.0202496
$829$	−44.4567	−1.54404	−0.772022	−	0.635596i	$-0.780755\pi$
$829$	−44.4567	−1.54404	−0.772022	+	0.635596i	$0.780755\pi$
$830$	−83.4902	−2.89799
$831$	28.5627	0.990829
$832$	3.96781	0.137559
$833$	−11.1242	−0.385431
$834$	−32.7300	−1.13335
$835$	45.8242	1.58581
$836$	3.32545	0.115013
$837$	−9.91051	−0.342557
$838$	−1.22149	−0.0421956
$839$	15.3727	0.530724	0.265362	−	0.964149i	$-0.414509\pi$
$839$	15.3727	0.530724	0.265362	+	0.964149i	$0.414509\pi$
$840$	45.9898	1.58680
$841$	−28.9987	−0.999954
$842$	35.0404	1.20757
$843$	−5.59457	−0.192687
$844$	4.77294	0.164291
$845$	−53.1082	−1.82698
$846$	2.73976	0.0941948
$847$	−21.4708	−0.737746
$848$	7.98754	0.274293
$849$	26.5463	0.911068
$850$	19.3535	0.663819
$851$	11.2736	0.386456
$852$	1.15409	0.0395384
$853$	45.9022	1.57166	0.785830	−	0.618442i	$-0.212236\pi$
$853$	45.9022	1.57166	0.785830	+	0.618442i	$0.212236\pi$
$854$	21.0151	0.719122
$855$	−11.1733	−0.382120
$856$	−25.8732	−0.884327
$857$	37.8012	1.29127	0.645633	−	0.763648i	$-0.276594\pi$
$857$	37.8012	1.29127	0.645633	+	0.763648i	$0.276594\pi$
$858$	−3.78374	−0.129175
$859$	−21.8026	−0.743897	−0.371948	−	0.928253i	$-0.621310\pi$
$859$	−21.8026	−0.743897	−0.371948	+	0.928253i	$0.621310\pi$
$860$	−7.73062	−0.263612
$861$	−3.37883	−0.115150
$862$	60.8423	2.07230
$863$	17.9378	0.610611	0.305306	−	0.952254i	$-0.401241\pi$
$863$	17.9378	0.610611	0.305306	+	0.952254i	$0.401241\pi$
$864$	−1.75423	−0.0596803
$865$	−102.552	−3.48686
$866$	57.2459	1.94529
$867$	−1.00000	−0.0339618
$868$	−13.1992	−0.448011
$869$	4.00541	0.135874
$870$	0.232816	0.00789321
$871$	−3.21239	−0.108848
$872$	−37.9562	−1.28536
$873$	11.4845	0.388692
$874$	7.51728	0.254276
$875$	−138.477	−4.68138
$876$	4.09140	0.138236
$877$	21.9721	0.741946	0.370973	−	0.928644i	$-0.379024\pi$
$877$	21.9721	0.741946	0.370973	+	0.928644i	$0.379024\pi$
$878$	−12.3055	−0.415291
$879$	2.19965	0.0741924
$880$	76.3553	2.57394
$881$	−44.1173	−1.48635	−0.743176	−	0.669097i	$-0.766681\pi$
$881$	−44.1173	−1.48635	−0.743176	+	0.669097i	$0.766681\pi$
$882$	−16.9177	−0.569649
$883$	−19.8124	−0.666741	−0.333370	−	0.942796i	$-0.608186\pi$
$883$	−19.8124	−0.666741	−0.333370	+	0.942796i	$0.608186\pi$
$884$	−0.194323	−0.00653579
$885$	28.1297	0.945569
$886$	−17.6258	−0.592149
$887$	−5.88596	−0.197631	−0.0988155	−	0.995106i	$-0.531505\pi$
$887$	−5.88596	−0.197631	−0.0988155	+	0.995106i	$0.531505\pi$
$888$	−15.5305	−0.521169
$889$	−76.8853	−2.57865
$890$	21.5751	0.723200
$891$	−4.00541	−0.134186
$892$	8.32088	0.278604
$893$	4.78101	0.159990
$894$	5.09410	0.170372
$895$	−47.4985	−1.58770
$896$	56.2937	1.88064
$897$	−1.15694	−0.0386290
$898$	60.8718	2.03132
$899$	0.360357	0.0120186
$900$	3.98115	0.132705
$901$	1.76411	0.0587709
$902$	−4.83457	−0.160974
$903$	−24.9872	−0.831522
$904$	32.5262	1.08181
$905$	52.0253	1.72938
$906$	−18.0778	−0.600593
$907$	15.0820	0.500790	0.250395	−	0.968144i	$-0.419439\pi$
$907$	15.0820	0.500790	0.250395	+	0.968144i	$0.419439\pi$
$908$	−2.46857	−0.0819223
$909$	−6.31348	−0.209405
$910$	16.9319	0.561289
$911$	−47.5781	−1.57633	−0.788166	−	0.615463i	$-0.788969\pi$
$911$	−47.5781	−1.57633	−0.788166	+	0.615463i	$0.788969\pi$
$912$	−12.0162	−0.397897
$913$	−52.2284	−1.72851
$914$	40.1799	1.32903
$915$	−13.6657	−0.451775
$916$	−3.29595	−0.108901
$917$	18.9258	0.624986
$918$	−1.52080	−0.0501940
$919$	10.5748	0.348830	0.174415	−	0.984672i	$-0.444197\pi$
$919$	10.5748	0.348830	0.174415	+	0.984672i	$0.444197\pi$
$920$	20.1206	0.663356
$921$	−9.53692	−0.314252
$922$	21.5030	0.708163
$923$	−2.29148	−0.0754251
$924$	−5.33457	−0.175495
$925$	77.0269	2.53263
$926$	61.1330	2.00895
$927$	−2.40948	−0.0791378
$928$	0.0637859	0.00209388
$929$	−35.9716	−1.18019	−0.590094	−	0.807334i	$-0.700909\pi$
$929$	−35.9716	−1.18019	−0.590094	+	0.807334i	$0.700909\pi$
$930$	63.4559	2.08080
$931$	−29.5222	−0.967552
$932$	0.0558935	0.00183085
$933$	10.1816	0.333332
$934$	−15.0911	−0.493796
$935$	16.8636	0.551499
$936$	1.59379	0.0520945
$937$	−18.0085	−0.588312	−0.294156	−	0.955757i	$-0.595039\pi$
$937$	−18.0085	−0.588312	−0.294156	+	0.955757i	$0.595039\pi$
$938$	−33.4834	−1.09327
$939$	14.1128	0.460552
$940$	−2.37282	−0.0773930
$941$	42.1584	1.37432	0.687162	−	0.726504i	$-0.258856\pi$
$941$	42.1584	1.37432	0.687162	+	0.726504i	$0.258856\pi$
$942$	−18.7340	−0.610388
$943$	−1.47824	−0.0481382
$944$	30.2517	0.984609
$945$	17.9239	0.583065
$946$	−35.7527	−1.16242
$947$	33.1908	1.07856	0.539279	−	0.842127i	$-0.318697\pi$
$947$	33.1908	1.07856	0.539279	+	0.842127i	$0.318697\pi$
$948$	0.312840	0.0101606
$949$	−8.12363	−0.263704
$950$	51.3617	1.66639
$951$	25.3057	0.820594
$952$	10.9234	0.354030
$953$	−43.0961	−1.39602	−0.698011	−	0.716087i	$-0.745931\pi$
$953$	−43.0961	−1.39602	−0.698011	+	0.716087i	$0.745931\pi$
$954$	2.68286	0.0868607
$955$	65.3726	2.11541
$956$	−4.96077	−0.160443
$957$	0.145641	0.00470792
$958$	37.1500	1.20026
$959$	−31.4994	−1.01717
$960$	−26.8939	−0.867996
$961$	67.2181	2.16833
$962$	−5.71782	−0.184350
$963$	−10.0837	−0.324943
$964$	2.35745	0.0759284
$965$	−31.2121	−1.00475
$966$	−12.0590	−0.387991
$967$	−38.2969	−1.23155	−0.615773	−	0.787923i	$-0.711156\pi$
$967$	−38.2969	−1.23155	−0.615773	+	0.787923i	$0.711156\pi$
$968$	12.9404	0.415920
$969$	−2.65387	−0.0852547
$970$	−73.5341	−2.36104
$971$	−52.0266	−1.66961	−0.834806	−	0.550544i	$-0.814420\pi$
$971$	−52.0266	−1.66961	−0.834806	+	0.550544i	$0.814420\pi$
$972$	−0.312840	−0.0100344
$973$	91.6225	2.93728
$974$	−28.4906	−0.912897
$975$	−7.90474	−0.253154
$976$	−14.6966	−0.470427
$977$	−21.2050	−0.678409	−0.339205	−	0.940713i	$-0.610158\pi$
$977$	−21.2050	−0.678409	−0.339205	+	0.940713i	$0.610158\pi$
$978$	−7.92706	−0.253479
$979$	13.4966	0.431354
$980$	14.6519	0.468039
$981$	−14.7929	−0.472302
$982$	−2.28712	−0.0729850
$983$	−27.3023	−0.870807	−0.435404	−	0.900235i	$-0.643394\pi$
$983$	−27.3023	−0.870807	−0.435404	+	0.900235i	$0.643394\pi$
$984$	2.03642	0.0649186
$985$	−65.9248	−2.10054
$986$	0.0552981	0.00176105
$987$	−7.66953	−0.244124
$988$	−0.515708	−0.0164069
$989$	−10.9319	−0.347615
$990$	25.6462	0.815091
$991$	−34.4373	−1.09394	−0.546969	−	0.837153i	$-0.684219\pi$
$991$	−34.4373	−1.09394	−0.546969	+	0.837153i	$0.684219\pi$
$992$	17.3853	0.551985
$993$	−0.118837	−0.00377119
$994$	−23.8846	−0.757574
$995$	−21.5696	−0.683801
$996$	−4.07927	−0.129257
$997$	−34.7150	−1.09944	−0.549718	−	0.835350i	$-0.685265\pi$
$997$	−34.7150	−1.09944	−0.549718	+	0.835350i	$0.685265\pi$
$998$	11.0024	0.348276
$999$	−6.05280	−0.191502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.5	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52080 q^{2} -1.00000 q^{3} +0.312840 q^{4} +4.21021 q^{5} +1.52080 q^{6} -4.25725 q^{7} +2.56584 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52080 q^{2} -1.00000 q^{3} +0.312840 q^{4} +4.21021 q^{5} +1.52080 q^{6} -4.25725 q^{7} +2.56584 q^{8} +1.00000 q^{9} -6.40289 q^{10} -4.00541 q^{11} -0.312840 q^{12} +0.621157 q^{13} +6.47444 q^{14} -4.21021 q^{15} -4.52781 q^{16} -1.00000 q^{17} -1.52080 q^{18} -2.65387 q^{19} +1.31712 q^{20} +4.25725 q^{21} +6.09145 q^{22} +1.86255 q^{23} -2.56584 q^{24} +12.7258 q^{25} -0.944657 q^{26} -1.00000 q^{27} -1.33184 q^{28} +0.0363611 q^{29} +6.40289 q^{30} +9.91051 q^{31} +1.75423 q^{32} +4.00541 q^{33} +1.52080 q^{34} -17.9239 q^{35} +0.312840 q^{36} +6.05280 q^{37} +4.03602 q^{38} -0.621157 q^{39} +10.8027 q^{40} -0.793665 q^{41} -6.47444 q^{42} -5.86932 q^{43} -1.25306 q^{44} +4.21021 q^{45} -2.83257 q^{46} -1.80152 q^{47} +4.52781 q^{48} +11.1242 q^{49} -19.3535 q^{50} +1.00000 q^{51} +0.194323 q^{52} -1.76411 q^{53} +1.52080 q^{54} -16.8636 q^{55} -10.9234 q^{56} +2.65387 q^{57} -0.0552981 q^{58} -6.68131 q^{59} -1.31712 q^{60} +3.24585 q^{61} -15.0719 q^{62} -4.25725 q^{63} +6.38778 q^{64} +2.61520 q^{65} -6.09145 q^{66} -5.17163 q^{67} -0.312840 q^{68} -1.86255 q^{69} +27.2587 q^{70} -3.68906 q^{71} +2.56584 q^{72} -13.0782 q^{73} -9.20511 q^{74} -12.7258 q^{75} -0.830238 q^{76} +17.0521 q^{77} +0.944657 q^{78} -1.00000 q^{79} -19.0630 q^{80} +1.00000 q^{81} +1.20701 q^{82} +13.0395 q^{83} +1.33184 q^{84} -4.21021 q^{85} +8.92608 q^{86} -0.0363611 q^{87} -10.2772 q^{88} -3.36959 q^{89} -6.40289 q^{90} -2.64442 q^{91} +0.582681 q^{92} -9.91051 q^{93} +2.73976 q^{94} -11.1733 q^{95} -1.75423 q^{96} +11.4845 q^{97} -16.9177 q^{98} -4.00541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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