LMFDB - Embedded newform 8021.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49455 q^{2} -1.79114 q^{3} +4.22277 q^{4} -0.0823474 q^{5} +4.46808 q^{6} +3.62956 q^{7} -5.54480 q^{8} +0.208181 q^{9} +O(q^{10})$	\(q-2.49455 q^{2} -1.79114 q^{3} +4.22277 q^{4} -0.0823474 q^{5} +4.46808 q^{6} +3.62956 q^{7} -5.54480 q^{8} +0.208181 q^{9} +0.205419 q^{10} +0.888360 q^{11} -7.56357 q^{12} -1.00000 q^{13} -9.05410 q^{14} +0.147496 q^{15} +5.38624 q^{16} -4.88754 q^{17} -0.519317 q^{18} -1.61473 q^{19} -0.347734 q^{20} -6.50104 q^{21} -2.21606 q^{22} +5.15462 q^{23} +9.93152 q^{24} -4.99322 q^{25} +2.49455 q^{26} +5.00054 q^{27} +15.3268 q^{28} +5.67927 q^{29} -0.367935 q^{30} -9.48756 q^{31} -2.34663 q^{32} -1.59118 q^{33} +12.1922 q^{34} -0.298884 q^{35} +0.879100 q^{36} -7.17582 q^{37} +4.02802 q^{38} +1.79114 q^{39} +0.456600 q^{40} +2.65270 q^{41} +16.2172 q^{42} +10.3357 q^{43} +3.75134 q^{44} -0.0171432 q^{45} -12.8585 q^{46} -5.62303 q^{47} -9.64751 q^{48} +6.17368 q^{49} +12.4558 q^{50} +8.75427 q^{51} -4.22277 q^{52} -4.51901 q^{53} -12.4741 q^{54} -0.0731541 q^{55} -20.1252 q^{56} +2.89220 q^{57} -14.1672 q^{58} +12.5520 q^{59} +0.622840 q^{60} -0.167765 q^{61} +23.6672 q^{62} +0.755605 q^{63} -4.91871 q^{64} +0.0823474 q^{65} +3.96926 q^{66} +8.75750 q^{67} -20.6390 q^{68} -9.23265 q^{69} +0.745581 q^{70} +16.6676 q^{71} -1.15432 q^{72} +1.41483 q^{73} +17.9004 q^{74} +8.94355 q^{75} -6.81862 q^{76} +3.22435 q^{77} -4.46808 q^{78} -1.75270 q^{79} -0.443543 q^{80} -9.58120 q^{81} -6.61730 q^{82} +4.78304 q^{83} -27.4524 q^{84} +0.402476 q^{85} -25.7829 q^{86} -10.1724 q^{87} -4.92578 q^{88} -9.43063 q^{89} +0.0427644 q^{90} -3.62956 q^{91} +21.7668 q^{92} +16.9935 q^{93} +14.0269 q^{94} +0.132969 q^{95} +4.20313 q^{96} -12.4694 q^{97} -15.4005 q^{98} +0.184940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.49455	−1.76391	−0.881956	−	0.471332i	$-0.843773\pi$
$2$	−2.49455	−1.76391	−0.881956	+	0.471332i	$0.843773\pi$
$3$	−1.79114	−1.03411	−0.517057	−	0.855951i	$-0.672973\pi$
$3$	−1.79114	−1.03411	−0.517057	+	0.855951i	$0.672973\pi$
$4$	4.22277	2.11138
$5$	−0.0823474	−0.0368269	−0.0184134	−	0.999830i	$-0.505862\pi$
$5$	−0.0823474	−0.0368269	−0.0184134	+	0.999830i	$0.505862\pi$
$6$	4.46808	1.82409
$7$	3.62956	1.37184	0.685922	−	0.727675i	$-0.259399\pi$
$7$	3.62956	1.37184	0.685922	+	0.727675i	$0.259399\pi$
$8$	−5.54480	−1.96038
$9$	0.208181	0.0693937
$10$	0.205419	0.0649593
$11$	0.888360	0.267850	0.133925	−	0.990991i	$-0.457242\pi$
$11$	0.888360	0.267850	0.133925	+	0.990991i	$0.457242\pi$
$12$	−7.56357	−2.18341
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.05410	−2.41981
$15$	0.147496	0.0380832
$16$	5.38624	1.34656
$17$	−4.88754	−1.18540	−0.592701	−	0.805422i	$-0.701939\pi$
$17$	−4.88754	−1.18540	−0.592701	+	0.805422i	$0.701939\pi$
$18$	−0.519317	−0.122404
$19$	−1.61473	−0.370444	−0.185222	−	0.982697i	$-0.559300\pi$
$19$	−1.61473	−0.370444	−0.185222	+	0.982697i	$0.559300\pi$
$20$	−0.347734	−0.0777557
$21$	−6.50104	−1.41864
$22$	−2.21606	−0.472465
$23$	5.15462	1.07481	0.537407	−	0.843323i	$-0.319404\pi$
$23$	5.15462	1.07481	0.537407	+	0.843323i	$0.319404\pi$
$24$	9.93152	2.02726
$25$	−4.99322	−0.998644
$26$	2.49455	0.489221
$27$	5.00054	0.962354
$28$	15.3268	2.89649
$29$	5.67927	1.05461	0.527307	−	0.849675i	$-0.323202\pi$
$29$	5.67927	1.05461	0.527307	+	0.849675i	$0.323202\pi$
$30$	−0.367935	−0.0671754
$31$	−9.48756	−1.70402	−0.852008	−	0.523529i	$-0.824615\pi$
$31$	−9.48756	−1.70402	−0.852008	+	0.523529i	$0.824615\pi$
$32$	−2.34663	−0.414829
$33$	−1.59118	−0.276988
$34$	12.1922	2.09095
$35$	−0.298884	−0.0505207
$36$	0.879100	0.146517
$37$	−7.17582	−1.17970	−0.589849	−	0.807514i	$-0.700813\pi$
$37$	−7.17582	−1.17970	−0.589849	+	0.807514i	$0.700813\pi$
$38$	4.02802	0.653431
$39$	1.79114	0.286812
$40$	0.456600	0.0721948
$41$	2.65270	0.414283	0.207141	−	0.978311i	$-0.433584\pi$
$41$	2.65270	0.414283	0.207141	+	0.978311i	$0.433584\pi$
$42$	16.2172	2.50236
$43$	10.3357	1.57618	0.788088	−	0.615562i	$-0.211071\pi$
$43$	10.3357	1.57618	0.788088	+	0.615562i	$0.211071\pi$
$44$	3.75134	0.565535
$45$	−0.0171432	−0.00255555
$46$	−12.8585	−1.89588
$47$	−5.62303	−0.820203	−0.410101	−	0.912040i	$-0.634507\pi$
$47$	−5.62303	−0.820203	−0.410101	+	0.912040i	$0.634507\pi$
$48$	−9.64751	−1.39250
$49$	6.17368	0.881954
$50$	12.4558	1.76152
$51$	8.75427	1.22584
$52$	−4.22277	−0.585593
$53$	−4.51901	−0.620733	−0.310367	−	0.950617i	$-0.600452\pi$
$53$	−4.51901	−0.620733	−0.310367	+	0.950617i	$0.600452\pi$
$54$	−12.4741	−1.69751
$55$	−0.0731541	−0.00986409
$56$	−20.1252	−2.68934
$57$	2.89220	0.383082
$58$	−14.1672	−1.86025
$59$	12.5520	1.63413	0.817067	−	0.576543i	$-0.195599\pi$
$59$	12.5520	1.63413	0.817067	+	0.576543i	$0.195599\pi$
$60$	0.622840	0.0804083
$61$	−0.167765	−0.0214801	−0.0107400	−	0.999942i	$-0.503419\pi$
$61$	−0.167765	−0.0214801	−0.0107400	+	0.999942i	$0.503419\pi$
$62$	23.6672	3.00573
$63$	0.755605	0.0951972
$64$	−4.91871	−0.614839
$65$	0.0823474	0.0102139
$66$	3.96926	0.488583
$67$	8.75750	1.06990	0.534950	−	0.844884i	$-0.320331\pi$
$67$	8.75750	1.06990	0.534950	+	0.844884i	$0.320331\pi$
$68$	−20.6390	−2.50284
$69$	−9.23265	−1.11148
$70$	0.745581	0.0891140
$71$	16.6676	1.97808	0.989040	−	0.147650i	$-0.0471708\pi$
$71$	16.6676	1.97808	0.989040	+	0.147650i	$0.0471708\pi$
$72$	−1.15432	−0.136038
$73$	1.41483	0.165593	0.0827967	−	0.996566i	$-0.473615\pi$
$73$	1.41483	0.165593	0.0827967	+	0.996566i	$0.473615\pi$
$74$	17.9004	2.08088
$75$	8.94355	1.03271
$76$	−6.81862	−0.782150
$77$	3.22435	0.367449
$78$	−4.46808	−0.505911
$79$	−1.75270	−0.197194	−0.0985970	−	0.995127i	$-0.531435\pi$
$79$	−1.75270	−0.197194	−0.0985970	+	0.995127i	$0.531435\pi$
$80$	−0.443543	−0.0495896
$81$	−9.58120	−1.06458
$82$	−6.61730	−0.730758
$83$	4.78304	0.525006	0.262503	−	0.964931i	$-0.415452\pi$
$83$	4.78304	0.525006	0.262503	+	0.964931i	$0.415452\pi$
$84$	−27.4524	−2.99530
$85$	0.402476	0.0436547
$86$	−25.7829	−2.78024
$87$	−10.1724	−1.09059
$88$	−4.92578	−0.525090
$89$	−9.43063	−0.999645	−0.499822	−	0.866128i	$-0.666601\pi$
$89$	−9.43063	−0.999645	−0.499822	+	0.866128i	$0.666601\pi$
$90$	0.0427644	0.00450777
$91$	−3.62956	−0.380481
$92$	21.7668	2.26934
$93$	16.9935	1.76215
$94$	14.0269	1.44677
$95$	0.132969	0.0136423
$96$	4.20313	0.428981
$97$	−12.4694	−1.26608	−0.633038	−	0.774121i	$-0.718192\pi$
$97$	−12.4694	−1.26608	−0.633038	+	0.774121i	$0.718192\pi$
$98$	−15.4005	−1.55569
$99$	0.184940	0.0185871
$100$	−21.0852	−2.10852
$101$	−0.719119	−0.0715550	−0.0357775	−	0.999360i	$-0.511391\pi$
$101$	−0.719119	−0.0715550	−0.0357775	+	0.999360i	$0.511391\pi$
$102$	−21.8379	−2.16228
$103$	5.05146	0.497735	0.248867	−	0.968538i	$-0.419942\pi$
$103$	5.05146	0.497735	0.248867	+	0.968538i	$0.419942\pi$
$104$	5.54480	0.543713
$105$	0.535344	0.0522442
$106$	11.2729	1.09492
$107$	0.421782	0.0407752	0.0203876	−	0.999792i	$-0.493510\pi$
$107$	0.421782	0.0407752	0.0203876	+	0.999792i	$0.493510\pi$
$108$	21.1161	2.03190
$109$	5.83646	0.559031	0.279516	−	0.960141i	$-0.409826\pi$
$109$	5.83646	0.559031	0.279516	+	0.960141i	$0.409826\pi$
$110$	0.182486	0.0173994
$111$	12.8529	1.21994
$112$	19.5497	1.84727
$113$	−14.0110	−1.31804	−0.659021	−	0.752125i	$-0.729029\pi$
$113$	−14.0110	−1.31804	−0.659021	+	0.752125i	$0.729029\pi$
$114$	−7.21474	−0.675722
$115$	−0.424470	−0.0395820
$116$	23.9823	2.22670
$117$	−0.208181	−0.0192463
$118$	−31.3116	−2.88247
$119$	−17.7396	−1.62619
$120$	−0.817834	−0.0746577
$121$	−10.2108	−0.928256
$122$	0.418498	0.0378890
$123$	−4.75136	−0.428416
$124$	−40.0638	−3.59783
$125$	0.822915	0.0736038
$126$	−1.88489	−0.167920
$127$	−10.2894	−0.913037	−0.456519	−	0.889714i	$-0.650904\pi$
$127$	−10.2894	−0.913037	−0.456519	+	0.889714i	$0.650904\pi$
$128$	16.9632	1.49935
$129$	−18.5127	−1.62995
$130$	−0.205419	−0.0180165
$131$	12.8842	1.12570	0.562849	−	0.826560i	$-0.309705\pi$
$131$	12.8842	1.12570	0.562849	+	0.826560i	$0.309705\pi$
$132$	−6.71917	−0.584829
$133$	−5.86075	−0.508191
$134$	−21.8460	−1.88721
$135$	−0.411781	−0.0354405
$136$	27.1005	2.32384
$137$	2.41178	0.206053	0.103026	−	0.994679i	$-0.467147\pi$
$137$	2.41178	0.206053	0.103026	+	0.994679i	$0.467147\pi$
$138$	23.0313	1.96055
$139$	−21.2534	−1.80269	−0.901347	−	0.433098i	$-0.857420\pi$
$139$	−21.2534	−1.80269	−0.901347	+	0.433098i	$0.857420\pi$
$140$	−1.26212	−0.106669
$141$	10.0716	0.848184
$142$	−41.5781	−3.48916
$143$	−0.888360	−0.0742884
$144$	1.12131	0.0934427
$145$	−0.467673	−0.0388382
$146$	−3.52936	−0.292092
$147$	−11.0579	−0.912042
$148$	−30.3018	−2.49079
$149$	−19.2064	−1.57345	−0.786724	−	0.617305i	$-0.788225\pi$
$149$	−19.2064	−1.57345	−0.786724	+	0.617305i	$0.788225\pi$
$150$	−22.3101	−1.82161
$151$	−23.4432	−1.90778	−0.953890	−	0.300157i	$-0.902961\pi$
$151$	−23.4432	−1.90778	−0.953890	+	0.300157i	$0.902961\pi$
$152$	8.95335	0.726213
$153$	−1.01749	−0.0822594
$154$	−8.04330	−0.648147
$155$	0.781275	0.0627535
$156$	7.56357	0.605570
$157$	4.77134	0.380795	0.190397	−	0.981707i	$-0.439022\pi$
$157$	4.77134	0.380795	0.190397	+	0.981707i	$0.439022\pi$
$158$	4.37219	0.347833
$159$	8.09417	0.641910
$160$	0.193238	0.0152768
$161$	18.7090	1.47448
$162$	23.9008	1.87782
$163$	−3.84034	−0.300798	−0.150399	−	0.988625i	$-0.548056\pi$
$163$	−3.84034	−0.300798	−0.150399	+	0.988625i	$0.548056\pi$
$164$	11.2018	0.874710
$165$	0.131029	0.0102006
$166$	−11.9315	−0.926065
$167$	23.8510	1.84564	0.922821	−	0.385229i	$-0.125878\pi$
$167$	23.8510	1.84564	0.922821	+	0.385229i	$0.125878\pi$
$168$	36.0470	2.78109
$169$	1.00000	0.0769231
$170$	−1.00400	−0.0770030
$171$	−0.336156	−0.0257065
$172$	43.6452	3.32792
$173$	−5.50172	−0.418288	−0.209144	−	0.977885i	$-0.567068\pi$
$173$	−5.50172	−0.418288	−0.209144	+	0.977885i	$0.567068\pi$
$174$	25.3755	1.92371
$175$	−18.1232	−1.36998
$176$	4.78492	0.360677
$177$	−22.4824	−1.68988
$178$	23.5252	1.76328
$179$	19.2332	1.43755	0.718777	−	0.695240i	$-0.244702\pi$
$179$	19.2332	1.43755	0.718777	+	0.695240i	$0.244702\pi$
$180$	−0.0723916	−0.00539575
$181$	4.94895	0.367853	0.183926	−	0.982940i	$-0.441119\pi$
$181$	4.94895	0.367853	0.183926	+	0.982940i	$0.441119\pi$
$182$	9.05410	0.671135
$183$	0.300490	0.0222129
$184$	−28.5814	−2.10705
$185$	0.590910	0.0434445
$186$	−42.3912	−3.10827
$187$	−4.34189	−0.317511
$188$	−23.7447	−1.73176
$189$	18.1497	1.32020
$190$	−0.331697	−0.0240638
$191$	−14.5584	−1.05341	−0.526704	−	0.850048i	$-0.676573\pi$
$191$	−14.5584	−1.05341	−0.526704	+	0.850048i	$0.676573\pi$
$192$	8.81010	0.635814
$193$	13.7012	0.986233	0.493116	−	0.869963i	$-0.335858\pi$
$193$	13.7012	0.986233	0.493116	+	0.869963i	$0.335858\pi$
$194$	31.1055	2.23324
$195$	−0.147496	−0.0105624
$196$	26.0700	1.86214
$197$	−23.7512	−1.69220	−0.846101	−	0.533023i	$-0.821056\pi$
$197$	−23.7512	−1.69220	−0.846101	+	0.533023i	$0.821056\pi$
$198$	−0.461341	−0.0327860
$199$	17.3790	1.23197	0.615983	−	0.787759i	$-0.288759\pi$
$199$	17.3790	1.23197	0.615983	+	0.787759i	$0.288759\pi$
$200$	27.6864	1.95773
$201$	−15.6859	−1.10640
$202$	1.79388	0.126217
$203$	20.6132	1.44677
$204$	36.9673	2.58823
$205$	−0.218443	−0.0152567
$206$	−12.6011	−0.877960
$207$	1.07309	0.0745852
$208$	−5.38624	−0.373469
$209$	−1.43446	−0.0992236
$210$	−1.33544	−0.0921541
$211$	−16.2223	−1.11679	−0.558393	−	0.829576i	$-0.688582\pi$
$211$	−16.2223	−1.11679	−0.558393	+	0.829576i	$0.688582\pi$
$212$	−19.0827	−1.31061
$213$	−29.8540	−2.04556
$214$	−1.05216	−0.0719239
$215$	−0.851116	−0.0580456
$216$	−27.7270	−1.88658
$217$	−34.4356	−2.33764
$218$	−14.5593	−0.986082
$219$	−2.53416	−0.171243
$220$	−0.308913	−0.0208269
$221$	4.88754	0.328772
$222$	−32.0622	−2.15187
$223$	17.9941	1.20498	0.602488	−	0.798128i	$-0.294176\pi$
$223$	17.9941	1.20498	0.602488	+	0.798128i	$0.294176\pi$
$224$	−8.51721	−0.569080
$225$	−1.03949	−0.0692996
$226$	34.9510	2.32491
$227$	2.80209	0.185981	0.0929905	−	0.995667i	$-0.470357\pi$
$227$	2.80209	0.185981	0.0929905	+	0.995667i	$0.470357\pi$
$228$	12.2131	0.808833
$229$	9.02986	0.596710	0.298355	−	0.954455i	$-0.403562\pi$
$229$	9.02986	0.596710	0.298355	+	0.954455i	$0.403562\pi$
$230$	1.05886	0.0698192
$231$	−5.77526	−0.379984
$232$	−31.4905	−2.06745
$233$	9.01807	0.590793	0.295397	−	0.955375i	$-0.404548\pi$
$233$	9.01807	0.590793	0.295397	+	0.955375i	$0.404548\pi$
$234$	0.519317	0.0339488
$235$	0.463042	0.0302055
$236$	53.0043	3.45029
$237$	3.13933	0.203921
$238$	44.2523	2.86845
$239$	9.87604	0.638828	0.319414	−	0.947615i	$-0.396514\pi$
$239$	9.87604	0.638828	0.319414	+	0.947615i	$0.396514\pi$
$240$	0.794447	0.0512813
$241$	8.27252	0.532880	0.266440	−	0.963852i	$-0.414153\pi$
$241$	8.27252	0.532880	0.266440	+	0.963852i	$0.414153\pi$
$242$	25.4714	1.63736
$243$	2.15966	0.138542
$244$	−0.708432	−0.0453527
$245$	−0.508386	−0.0324796
$246$	11.8525	0.755688
$247$	1.61473	0.102743
$248$	52.6066	3.34052
$249$	−8.56709	−0.542917
$250$	−2.05280	−0.129831
$251$	4.95313	0.312639	0.156319	−	0.987707i	$-0.450037\pi$
$251$	4.95313	0.312639	0.156319	+	0.987707i	$0.450037\pi$
$252$	3.19074	0.200998
$253$	4.57916	0.287889
$254$	25.6674	1.61052
$255$	−0.720891	−0.0451439
$256$	−32.4781	−2.02988
$257$	−9.17135	−0.572093	−0.286046	−	0.958216i	$-0.592341\pi$
$257$	−9.17135	−0.572093	−0.286046	+	0.958216i	$0.592341\pi$
$258$	46.1807	2.87508
$259$	−26.0450	−1.61836
$260$	0.347734	0.0215655
$261$	1.18232	0.0731836
$262$	−32.1403	−1.98563
$263$	18.2356	1.12446	0.562228	−	0.826982i	$-0.309944\pi$
$263$	18.2356	1.12446	0.562228	+	0.826982i	$0.309944\pi$
$264$	8.82276	0.543003
$265$	0.372128	0.0228597
$266$	14.6199	0.896404
$267$	16.8916	1.03375
$268$	36.9809	2.25897
$269$	−23.6910	−1.44447	−0.722234	−	0.691648i	$-0.756885\pi$
$269$	−23.6910	−1.44447	−0.722234	+	0.691648i	$0.756885\pi$
$270$	1.02721	0.0625139
$271$	−21.2656	−1.29180	−0.645898	−	0.763424i	$-0.723517\pi$
$271$	−21.2656	−1.29180	−0.645898	+	0.763424i	$0.723517\pi$
$272$	−26.3255	−1.59622
$273$	6.50104	0.393461
$274$	−6.01631	−0.363459
$275$	−4.43577	−0.267487
$276$	−38.9873	−2.34676
$277$	2.81332	0.169036	0.0845180	−	0.996422i	$-0.473065\pi$
$277$	2.81332	0.169036	0.0845180	+	0.996422i	$0.473065\pi$
$278$	53.0177	3.17979
$279$	−1.97513	−0.118248
$280$	1.65726	0.0990399
$281$	−4.84449	−0.288998	−0.144499	−	0.989505i	$-0.546157\pi$
$281$	−4.84449	−0.288998	−0.144499	+	0.989505i	$0.546157\pi$
$282$	−25.1242	−1.49612
$283$	−7.53937	−0.448169	−0.224084	−	0.974570i	$-0.571939\pi$
$283$	−7.53937	−0.448169	−0.224084	+	0.974570i	$0.571939\pi$
$284$	70.3834	4.17649
$285$	−0.238165	−0.0141077
$286$	2.21606	0.131038
$287$	9.62814	0.568331
$288$	−0.488523	−0.0287865
$289$	6.88806	0.405180
$290$	1.16663	0.0685071
$291$	22.3344	1.30927
$292$	5.97450	0.349631
$293$	−9.27261	−0.541712	−0.270856	−	0.962620i	$-0.587307\pi$
$293$	−9.27261	−0.541712	−0.270856	+	0.962620i	$0.587307\pi$
$294$	27.5845	1.60876
$295$	−1.03363	−0.0601800
$296$	39.7885	2.31266
$297$	4.44228	0.257767
$298$	47.9112	2.77542
$299$	−5.15462	−0.298100
$300$	37.7666	2.18045
$301$	37.5139	2.16227
$302$	58.4802	3.36516
$303$	1.28804	0.0739961
$304$	−8.69731	−0.498825
$305$	0.0138150	0.000791045 0
$306$	2.53819	0.145098
$307$	20.1955	1.15262	0.576310	−	0.817231i	$-0.304492\pi$
$307$	20.1955	1.15262	0.576310	+	0.817231i	$0.304492\pi$
$308$	13.6157	0.775826
$309$	−9.04786	−0.514715
$310$	−1.94893	−0.110692
$311$	14.2526	0.808190	0.404095	−	0.914717i	$-0.367587\pi$
$311$	14.2526	0.808190	0.404095	+	0.914717i	$0.367587\pi$
$312$	−9.93152	−0.562261
$313$	−4.06124	−0.229555	−0.114778	−	0.993391i	$-0.536616\pi$
$313$	−4.06124	−0.229555	−0.114778	+	0.993391i	$0.536616\pi$
$314$	−11.9023	−0.671688
$315$	−0.0622220	−0.00350582
$316$	−7.40124	−0.416352
$317$	1.93851	0.108877	0.0544387	−	0.998517i	$-0.482663\pi$
$317$	1.93851	0.108877	0.0544387	+	0.998517i	$0.482663\pi$
$318$	−20.1913	−1.13227
$319$	5.04524	0.282479
$320$	0.405043	0.0226426
$321$	−0.755470	−0.0421663
$322$	−46.6705	−2.60084
$323$	7.89205	0.439125
$324$	−40.4592	−2.24773
$325$	4.99322	0.276974
$326$	9.57990	0.530582
$327$	−10.4539	−0.578103
$328$	−14.7087	−0.812153
$329$	−20.4091	−1.12519
$330$	−0.326858	−0.0179930
$331$	−21.8402	−1.20045	−0.600223	−	0.799832i	$-0.704922\pi$
$331$	−21.8402	−1.20045	−0.600223	+	0.799832i	$0.704922\pi$
$332$	20.1977	1.10849
$333$	−1.49387	−0.0818635
$334$	−59.4973	−3.25555
$335$	−0.721157	−0.0394010
$336$	−35.0162	−1.91029
$337$	16.4979	0.898699	0.449350	−	0.893356i	$-0.351656\pi$
$337$	16.4979	0.898699	0.449350	+	0.893356i	$0.351656\pi$
$338$	−2.49455	−0.135686
$339$	25.0956	1.36301
$340$	1.69956	0.0921718
$341$	−8.42836	−0.456421
$342$	0.838556	0.0453439
$343$	−2.99919	−0.161941
$344$	−57.3093	−3.08991
$345$	0.760284	0.0409323
$346$	13.7243	0.737823
$347$	−20.0605	−1.07690	−0.538452	−	0.842656i	$-0.680991\pi$
$347$	−20.0605	−1.07690	−0.538452	+	0.842656i	$0.680991\pi$
$348$	−42.9556	−2.30266
$349$	−4.89656	−0.262107	−0.131054	−	0.991375i	$-0.541836\pi$
$349$	−4.89656	−0.262107	−0.131054	+	0.991375i	$0.541836\pi$
$350$	45.2091	2.41653
$351$	−5.00054	−0.266909
$352$	−2.08465	−0.111112
$353$	−1.44624	−0.0769758	−0.0384879	−	0.999259i	$-0.512254\pi$
$353$	−1.44624	−0.0769758	−0.0384879	+	0.999259i	$0.512254\pi$
$354$	56.0835	2.98080
$355$	−1.37253	−0.0728465
$356$	−39.8234	−2.11063
$357$	31.7741	1.68166
$358$	−47.9781	−2.53572
$359$	−3.35160	−0.176890	−0.0884452	−	0.996081i	$-0.528190\pi$
$359$	−3.35160	−0.176890	−0.0884452	+	0.996081i	$0.528190\pi$
$360$	0.0950554	0.00500986
$361$	−16.3927	−0.862771
$362$	−12.3454	−0.648860
$363$	18.2890	0.959924
$364$	−15.3268	−0.803341
$365$	−0.116508	−0.00609828
$366$	−0.749588	−0.0391816
$367$	5.41478	0.282649	0.141325	−	0.989963i	$-0.454864\pi$
$367$	5.41478	0.282649	0.141325	+	0.989963i	$0.454864\pi$
$368$	27.7640	1.44730
$369$	0.552243	0.0287486
$370$	−1.47405	−0.0766323
$371$	−16.4020	−0.851549
$372$	71.7598	3.72057
$373$	21.0883	1.09191	0.545955	−	0.837814i	$-0.316167\pi$
$373$	21.0883	1.09191	0.545955	+	0.837814i	$0.316167\pi$
$374$	10.8311	0.560061
$375$	−1.47396	−0.0761148
$376$	31.1786	1.60791
$377$	−5.67927	−0.292497
$378$	−45.2754	−2.32871
$379$	5.12833	0.263425	0.131712	−	0.991288i	$-0.457952\pi$
$379$	5.12833	0.263425	0.131712	+	0.991288i	$0.457952\pi$
$380$	0.561496	0.0288041
$381$	18.4298	0.944186
$382$	36.3166	1.85812
$383$	27.8217	1.42162	0.710810	−	0.703384i	$-0.248329\pi$
$383$	27.8217	1.42162	0.710810	+	0.703384i	$0.248329\pi$
$384$	−30.3835	−1.55050
$385$	−0.265517	−0.0135320
$386$	−34.1782	−1.73963
$387$	2.15169	0.109377
$388$	−52.6554	−2.67317
$389$	24.9519	1.26511	0.632557	−	0.774514i	$-0.282006\pi$
$389$	24.9519	1.26511	0.632557	+	0.774514i	$0.282006\pi$
$390$	0.367935	0.0186311
$391$	−25.1934	−1.27409
$392$	−34.2318	−1.72897
$393$	−23.0774	−1.16410
$394$	59.2485	2.98489
$395$	0.144330	0.00726204
$396$	0.780957	0.0392446
$397$	1.31475	0.0659855	0.0329927	−	0.999456i	$-0.489496\pi$
$397$	1.31475	0.0659855	0.0329927	+	0.999456i	$0.489496\pi$
$398$	−43.3528	−2.17308
$399$	10.4974	0.525528
$400$	−26.8947	−1.34473
$401$	−18.0991	−0.903824	−0.451912	−	0.892063i	$-0.649258\pi$
$401$	−18.0991	−0.903824	−0.451912	+	0.892063i	$0.649258\pi$
$402$	39.1293	1.95159
$403$	9.48756	0.472609
$404$	−3.03667	−0.151080
$405$	0.788987	0.0392051
$406$	−51.4207	−2.55197
$407$	−6.37471	−0.315982
$408$	−48.5407	−2.40312
$409$	−4.26584	−0.210932	−0.105466	−	0.994423i	$-0.533633\pi$
$409$	−4.26584	−0.210932	−0.105466	+	0.994423i	$0.533633\pi$
$410$	0.544917	0.0269115
$411$	−4.31984	−0.213082
$412$	21.3311	1.05091
$413$	45.5583	2.24178
$414$	−2.67689	−0.131562
$415$	−0.393870	−0.0193343
$416$	2.34663	0.115053
$417$	38.0679	1.86419
$418$	3.57833	0.175022
$419$	18.3865	0.898238	0.449119	−	0.893472i	$-0.351738\pi$
$419$	18.3865	0.898238	0.449119	+	0.893472i	$0.351738\pi$
$420$	2.26063	0.110308
$421$	−29.9620	−1.46026	−0.730128	−	0.683310i	$-0.760540\pi$
$421$	−29.9620	−1.46026	−0.730128	+	0.683310i	$0.760540\pi$
$422$	40.4672	1.96991
$423$	−1.17061	−0.0569169
$424$	25.0570	1.21688
$425$	24.4046	1.18380
$426$	74.4722	3.60819
$427$	−0.608912	−0.0294673
$428$	1.78109	0.0860921
$429$	1.59118	0.0768227
$430$	2.12315	0.102387
$431$	−7.00138	−0.337244	−0.168622	−	0.985681i	$-0.553932\pi$
$431$	−7.00138	−0.337244	−0.168622	+	0.985681i	$0.553932\pi$
$432$	26.9341	1.29587
$433$	4.56036	0.219157	0.109578	−	0.993978i	$-0.465050\pi$
$433$	4.56036	0.219157	0.109578	+	0.993978i	$0.465050\pi$
$434$	85.9013	4.12339
$435$	0.837668	0.0401631
$436$	24.6460	1.18033
$437$	−8.32332	−0.398158
$438$	6.32158	0.302057
$439$	−26.3560	−1.25790	−0.628951	−	0.777445i	$-0.716515\pi$
$439$	−26.3560	−1.25790	−0.628951	+	0.777445i	$0.716515\pi$
$440$	0.405625	0.0193374
$441$	1.28524	0.0612020
$442$	−12.1922	−0.579924
$443$	−2.78028	−0.132095	−0.0660475	−	0.997816i	$-0.521039\pi$
$443$	−2.78028	−0.132095	−0.0660475	+	0.997816i	$0.521039\pi$
$444$	54.2748	2.57577
$445$	0.776587	0.0368138
$446$	−44.8872	−2.12547
$447$	34.4013	1.62713
$448$	−17.8527	−0.843462
$449$	11.1169	0.524639	0.262320	−	0.964981i	$-0.415513\pi$
$449$	11.1169	0.524639	0.262320	+	0.964981i	$0.415513\pi$
$450$	2.59307	0.122238
$451$	2.35656	0.110966
$452$	−59.1651	−2.78289
$453$	41.9900	1.97286
$454$	−6.98994	−0.328054
$455$	0.298884	0.0140119
$456$	−16.0367	−0.750987
$457$	−32.9786	−1.54267	−0.771336	−	0.636428i	$-0.780411\pi$
$457$	−32.9786	−1.54267	−0.771336	+	0.636428i	$0.780411\pi$
$458$	−22.5254	−1.05254
$459$	−24.4403	−1.14078
$460$	−1.79244	−0.0835728
$461$	−0.898796	−0.0418611	−0.0209305	−	0.999781i	$-0.506663\pi$
$461$	−0.898796	−0.0418611	−0.0209305	+	0.999781i	$0.506663\pi$
$462$	14.4067	0.670259
$463$	−4.57813	−0.212764	−0.106382	−	0.994325i	$-0.533927\pi$
$463$	−4.57813	−0.212764	−0.106382	+	0.994325i	$0.533927\pi$
$464$	30.5899	1.42010
$465$	−1.39937	−0.0648944
$466$	−22.4960	−1.04211
$467$	8.35448	0.386599	0.193300	−	0.981140i	$-0.438081\pi$
$467$	8.35448	0.386599	0.193300	+	0.981140i	$0.438081\pi$
$468$	−0.879100	−0.0406364
$469$	31.7859	1.46773
$470$	−1.15508	−0.0532798
$471$	−8.54614	−0.393785
$472$	−69.5985	−3.20353
$473$	9.18180	0.422180
$474$	−7.83120	−0.359699
$475$	8.06269	0.369942
$476$	−74.9103	−3.43351
$477$	−0.940772	−0.0430750
$478$	−24.6362	−1.12684
$479$	5.94627	0.271692	0.135846	−	0.990730i	$-0.456625\pi$
$479$	5.94627	0.271692	0.135846	+	0.990730i	$0.456625\pi$
$480$	−0.346117	−0.0157980
$481$	7.17582	0.327189
$482$	−20.6362	−0.939953
$483$	−33.5104	−1.52478
$484$	−43.1179	−1.95991
$485$	1.02682	0.0466256
$486$	−5.38738	−0.244376
$487$	24.2721	1.09987	0.549937	−	0.835206i	$-0.314652\pi$
$487$	24.2721	1.09987	0.549937	+	0.835206i	$0.314652\pi$
$488$	0.930224	0.0421092
$489$	6.87858	0.311060
$490$	1.26819	0.0572911
$491$	−17.9158	−0.808531	−0.404265	−	0.914642i	$-0.632473\pi$
$491$	−17.9158	−0.808531	−0.404265	+	0.914642i	$0.632473\pi$
$492$	−20.0639	−0.904551
$493$	−27.7577	−1.25014
$494$	−4.02802	−0.181229
$495$	−0.0152293	−0.000684506 0
$496$	−51.1023	−2.29456
$497$	60.4960	2.71361
$498$	21.3710	0.957658
$499$	−32.6493	−1.46158	−0.730792	−	0.682601i	$-0.760849\pi$
$499$	−32.6493	−1.46158	−0.730792	+	0.682601i	$0.760849\pi$
$500$	3.47498	0.155406
$501$	−42.7204	−1.90861
$502$	−12.3558	−0.551467
$503$	−0.256472	−0.0114355	−0.00571776	−	0.999984i	$-0.501820\pi$
$503$	−0.256472	−0.0114355	−0.00571776	+	0.999984i	$0.501820\pi$
$504$	−4.18968	−0.186623
$505$	0.0592176	0.00263515
$506$	−11.4229	−0.507811
$507$	−1.79114	−0.0795473
$508$	−43.4498	−1.92777
$509$	−1.17628	−0.0521377	−0.0260689	−	0.999660i	$-0.508299\pi$
$509$	−1.17628	−0.0521377	−0.0260689	+	0.999660i	$0.508299\pi$
$510$	1.79830	0.0796299
$511$	5.13521	0.227168
$512$	47.0918	2.08118
$513$	−8.07451	−0.356498
$514$	22.8784	1.00912
$515$	−0.415974	−0.0183300
$516$	−78.1746	−3.44145
$517$	−4.99527	−0.219692
$518$	64.9706	2.85464
$519$	9.85434	0.432558
$520$	−0.456600	−0.0200232
$521$	6.38137	0.279573	0.139786	−	0.990182i	$-0.455358\pi$
$521$	6.38137	0.279573	0.139786	+	0.990182i	$0.455358\pi$
$522$	−2.94935	−0.129089
$523$	7.72148	0.337637	0.168818	−	0.985647i	$-0.446005\pi$
$523$	7.72148	0.337637	0.168818	+	0.985647i	$0.446005\pi$
$524$	54.4070	2.37678
$525$	32.4611	1.41672
$526$	−45.4896	−1.98344
$527$	46.3708	2.01994
$528$	−8.57045	−0.372981
$529$	3.57014	0.155224
$530$	−0.928292	−0.0403224
$531$	2.61309	0.113399
$532$	−24.7486	−1.07299
$533$	−2.65270	−0.114901
$534$	−42.1368	−1.82344
$535$	−0.0347326	−0.00150162
$536$	−48.5586	−2.09741
$537$	−34.4493	−1.48660
$538$	59.0985	2.54792
$539$	5.48444	0.236232
$540$	−1.73886	−0.0748285
$541$	3.27533	0.140817	0.0704087	−	0.997518i	$-0.477570\pi$
$541$	3.27533	0.140817	0.0704087	+	0.997518i	$0.477570\pi$
$542$	53.0481	2.27861
$543$	−8.86426	−0.380402
$544$	11.4692	0.491739
$545$	−0.480617	−0.0205874
$546$	−16.2172	−0.694030
$547$	−19.6762	−0.841292	−0.420646	−	0.907225i	$-0.638197\pi$
$547$	−19.6762	−0.841292	−0.420646	+	0.907225i	$0.638197\pi$
$548$	10.1844	0.435056
$549$	−0.0349255	−0.00149058
$550$	11.0652	0.471824
$551$	−9.17048	−0.390676
$552$	51.1932	2.17893
$553$	−6.36152	−0.270519
$554$	−7.01796	−0.298165
$555$	−1.05840	−0.0449267
$556$	−89.7484	−3.80618
$557$	−11.2700	−0.477524	−0.238762	−	0.971078i	$-0.576742\pi$
$557$	−11.2700	−0.477524	−0.238762	+	0.971078i	$0.576742\pi$
$558$	4.92705	0.208579
$559$	−10.3357	−0.437153
$560$	−1.60986	−0.0680291
$561$	7.77694	0.328343
$562$	12.0848	0.509767
$563$	27.2759	1.14954	0.574770	−	0.818315i	$-0.305091\pi$
$563$	27.2759	1.14954	0.574770	+	0.818315i	$0.305091\pi$
$564$	42.5302	1.79084
$565$	1.15377	0.0485393
$566$	18.8073	0.790530
$567$	−34.7755	−1.46043
$568$	−92.4185	−3.87780
$569$	−40.9313	−1.71593	−0.857966	−	0.513707i	$-0.828272\pi$
$569$	−40.9313	−1.71593	−0.857966	+	0.513707i	$0.828272\pi$
$570$	0.594115	0.0248847
$571$	−9.47754	−0.396623	−0.198311	−	0.980139i	$-0.563546\pi$
$571$	−9.47754	−0.396623	−0.198311	+	0.980139i	$0.563546\pi$
$572$	−3.75134	−0.156851
$573$	26.0761	1.08935
$574$	−24.0179	−1.00249
$575$	−25.7382	−1.07336
$576$	−1.02398	−0.0426659
$577$	12.7919	0.532534	0.266267	−	0.963899i	$-0.414210\pi$
$577$	12.7919	0.532534	0.266267	+	0.963899i	$0.414210\pi$
$578$	−17.1826	−0.714702
$579$	−24.5407	−1.01988
$580$	−1.97488	−0.0820023
$581$	17.3603	0.720227
$582$	−55.7143	−2.30943
$583$	−4.01450	−0.166264
$584$	−7.84495	−0.324627
$585$	0.0171432	0.000708782 0
$586$	23.1310	0.955532
$587$	22.5420	0.930407	0.465204	−	0.885204i	$-0.345981\pi$
$587$	22.5420	0.930407	0.465204	+	0.885204i	$0.345981\pi$
$588$	−46.6950	−1.92567
$589$	15.3198	0.631242
$590$	2.57843	0.106152
$591$	42.5417	1.74993
$592$	−38.6507	−1.58853
$593$	−33.2849	−1.36685	−0.683423	−	0.730022i	$-0.739510\pi$
$593$	−33.2849	−1.36685	−0.683423	+	0.730022i	$0.739510\pi$
$594$	−11.0815	−0.454678
$595$	1.46081	0.0598874
$596$	−81.1041	−3.32215
$597$	−31.1283	−1.27400
$598$	12.8585	0.525821
$599$	−10.4464	−0.426830	−0.213415	−	0.976962i	$-0.568459\pi$
$599$	−10.4464	−0.426830	−0.213415	+	0.976962i	$0.568459\pi$
$600$	−49.5902	−2.02451
$601$	−13.8752	−0.565979	−0.282990	−	0.959123i	$-0.591326\pi$
$601$	−13.8752	−0.565979	−0.282990	+	0.959123i	$0.591326\pi$
$602$	−93.5803	−3.81405
$603$	1.82315	0.0742442
$604$	−98.9952	−4.02806
$605$	0.840834	0.0341848
$606$	−3.21308	−0.130523
$607$	−7.44446	−0.302161	−0.151081	−	0.988521i	$-0.548275\pi$
$607$	−7.44446	−0.302161	−0.151081	+	0.988521i	$0.548275\pi$
$608$	3.78916	0.153671
$609$	−36.9212	−1.49612
$610$	−0.0344622	−0.00139533
$611$	5.62303	0.227483
$612$	−4.29664	−0.173681
$613$	21.8497	0.882502	0.441251	−	0.897384i	$-0.354535\pi$
$613$	21.8497	0.882502	0.441251	+	0.897384i	$0.354535\pi$
$614$	−50.3787	−2.03312
$615$	0.391262	0.0157772
$616$	−17.8784	−0.720341
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	22.5703	0.907912
$619$	0.441764	0.0177560	0.00887800	−	0.999961i	$-0.497174\pi$
$619$	0.441764	0.0177560	0.00887800	+	0.999961i	$0.497174\pi$
$620$	3.29914	0.132497
$621$	25.7759	1.03435
$622$	−35.5537	−1.42557
$623$	−34.2290	−1.37136
$624$	9.64751	0.386209
$625$	24.8983	0.995933
$626$	10.1310	0.404915
$627$	2.56932	0.102609
$628$	20.1483	0.804004
$629$	35.0721	1.39842
$630$	0.155216	0.00618395
$631$	3.28013	0.130580	0.0652899	−	0.997866i	$-0.479203\pi$
$631$	3.28013	0.130580	0.0652899	+	0.997866i	$0.479203\pi$
$632$	9.71837	0.386576
$633$	29.0563	1.15489
$634$	−4.83570	−0.192050
$635$	0.847306	0.0336243
$636$	34.1798	1.35532
$637$	−6.17368	−0.244610
$638$	−12.5856	−0.498268
$639$	3.46988	0.137266
$640$	−1.39688	−0.0552164
$641$	−15.7766	−0.623140	−0.311570	−	0.950223i	$-0.600855\pi$
$641$	−15.7766	−0.623140	−0.311570	+	0.950223i	$0.600855\pi$
$642$	1.88456	0.0743775
$643$	−9.06094	−0.357329	−0.178664	−	0.983910i	$-0.557178\pi$
$643$	−9.06094	−0.357329	−0.178664	+	0.983910i	$0.557178\pi$
$644$	79.0038	3.11318
$645$	1.52447	0.0600259
$646$	−19.6871	−0.774579
$647$	24.7784	0.974141	0.487070	−	0.873363i	$-0.338066\pi$
$647$	24.7784	0.974141	0.487070	+	0.873363i	$0.338066\pi$
$648$	53.1259	2.08698
$649$	11.1507	0.437704
$650$	−12.4558	−0.488558
$651$	61.6790	2.41739
$652$	−16.2169	−0.635101
$653$	12.0730	0.472452	0.236226	−	0.971698i	$-0.424089\pi$
$653$	12.0730	0.472452	0.236226	+	0.971698i	$0.424089\pi$
$654$	26.0778	1.01972
$655$	−1.06098	−0.0414559
$656$	14.2881	0.557857
$657$	0.294541	0.0114911
$658$	50.9115	1.98474
$659$	−37.5889	−1.46426	−0.732128	−	0.681167i	$-0.761473\pi$
$659$	−37.5889	−1.46426	−0.732128	+	0.681167i	$0.761473\pi$
$660$	0.553306	0.0215374
$661$	−28.4652	−1.10717	−0.553584	−	0.832794i	$-0.686740\pi$
$661$	−28.4652	−1.10717	−0.553584	+	0.832794i	$0.686740\pi$
$662$	54.4815	2.11748
$663$	−8.75427	−0.339988
$664$	−26.5210	−1.02921
$665$	0.482617	0.0187151
$666$	3.72653	0.144400
$667$	29.2745	1.13351
$668$	100.717	3.89686
$669$	−32.2300	−1.24608
$670$	1.79896	0.0695000
$671$	−0.149036	−0.00575345
$672$	15.2555	0.588494
$673$	36.4963	1.40683	0.703415	−	0.710779i	$-0.251658\pi$
$673$	36.4963	1.40683	0.703415	+	0.710779i	$0.251658\pi$
$674$	−41.1549	−1.58523
$675$	−24.9688	−0.961049
$676$	4.22277	0.162414
$677$	−2.98759	−0.114822	−0.0574111	−	0.998351i	$-0.518285\pi$
$677$	−2.98759	−0.114822	−0.0574111	+	0.998351i	$0.518285\pi$
$678$	−62.6022	−2.40422
$679$	−45.2584	−1.73686
$680$	−2.23165	−0.0855799
$681$	−5.01893	−0.192326
$682$	21.0249	0.805087
$683$	11.2996	0.432368	0.216184	−	0.976353i	$-0.430639\pi$
$683$	11.2996	0.432368	0.216184	+	0.976353i	$0.430639\pi$
$684$	−1.41951	−0.0542762
$685$	−0.198604	−0.00758827
$686$	7.48161	0.285649
$687$	−16.1737	−0.617067
$688$	55.6705	2.12242
$689$	4.51901	0.172160
$690$	−1.89657	−0.0722010
$691$	18.8038	0.715331	0.357666	−	0.933850i	$-0.383573\pi$
$691$	18.8038	0.715331	0.357666	+	0.933850i	$0.383573\pi$
$692$	−23.2325	−0.883166
$693$	0.671249	0.0254986
$694$	50.0419	1.89956
$695$	1.75016	0.0663875
$696$	56.4038	2.13798
$697$	−12.9652	−0.491092
$698$	12.2147	0.462334
$699$	−16.1526	−0.610948
$700$	−76.5300	−2.89256
$701$	−28.5325	−1.07766	−0.538829	−	0.842415i	$-0.681133\pi$
$701$	−28.5325	−1.07766	−0.538829	+	0.842415i	$0.681133\pi$
$702$	12.4741	0.470804
$703$	11.5870	0.437012
$704$	−4.36958	−0.164685
$705$	−0.829372	−0.0312360
$706$	3.60773	0.135779
$707$	−2.61008	−0.0981623
$708$	−94.9381	−3.56799
$709$	−31.9252	−1.19898	−0.599488	−	0.800384i	$-0.704629\pi$
$709$	−31.9252	−1.19898	−0.599488	+	0.800384i	$0.704629\pi$
$710$	3.42385	0.128495
$711$	−0.364879	−0.0136840
$712$	52.2910	1.95969
$713$	−48.9048	−1.83150
$714$	−79.2620	−2.96631
$715$	0.0731541	0.00273581
$716$	81.2172	3.03523
$717$	−17.6894	−0.660621
$718$	8.36072	0.312019
$719$	5.34063	0.199172	0.0995859	−	0.995029i	$-0.468248\pi$
$719$	5.34063	0.199172	0.0995859	+	0.995029i	$0.468248\pi$
$720$	−0.0923371	−0.00344120
$721$	18.3345	0.682814
$722$	40.8923	1.52185
$723$	−14.8172	−0.551059
$724$	20.8983	0.776678
$725$	−28.3579	−1.05318
$726$	−45.6228	−1.69322
$727$	15.3320	0.568631	0.284316	−	0.958731i	$-0.408234\pi$
$727$	15.3320	0.568631	0.284316	+	0.958731i	$0.408234\pi$
$728$	20.1252	0.745889
$729$	24.8754	0.921310
$730$	0.290634	0.0107568
$731$	−50.5161	−1.86840
$732$	1.26890	0.0468999
$733$	−2.30435	−0.0851131	−0.0425566	−	0.999094i	$-0.513550\pi$
$733$	−2.30435	−0.0851131	−0.0425566	+	0.999094i	$0.513550\pi$
$734$	−13.5074	−0.498568
$735$	0.910590	0.0335876
$736$	−12.0960	−0.445863
$737$	7.77981	0.286573
$738$	−1.37760	−0.0507100
$739$	−44.8179	−1.64865	−0.824326	−	0.566116i	$-0.808445\pi$
$739$	−44.8179	−1.64865	−0.824326	+	0.566116i	$0.808445\pi$
$740$	2.49528	0.0917281
$741$	−2.89220	−0.106248
$742$	40.9156	1.50206
$743$	−49.9351	−1.83194	−0.915970	−	0.401247i	$-0.868577\pi$
$743$	−49.9351	−1.83194	−0.915970	+	0.401247i	$0.868577\pi$
$744$	−94.2258	−3.45449
$745$	1.58160	0.0579452
$746$	−52.6057	−1.92603
$747$	0.995737	0.0364321
$748$	−18.3348	−0.670387
$749$	1.53088	0.0559372
$750$	3.67685	0.134260
$751$	33.4515	1.22066	0.610331	−	0.792147i	$-0.291037\pi$
$751$	33.4515	1.22066	0.610331	+	0.792147i	$0.291037\pi$
$752$	−30.2870	−1.10445
$753$	−8.87175	−0.323304
$754$	14.1672	0.515940
$755$	1.93049	0.0702575
$756$	76.6421	2.78745
$757$	−16.8018	−0.610672	−0.305336	−	0.952245i	$-0.598769\pi$
$757$	−16.8018	−0.610672	−0.305336	+	0.952245i	$0.598769\pi$
$758$	−12.7929	−0.464658
$759$	−8.20191	−0.297711
$760$	−0.737285	−0.0267441
$761$	−11.4194	−0.413954	−0.206977	−	0.978346i	$-0.566363\pi$
$761$	−11.4194	−0.413954	−0.206977	+	0.978346i	$0.566363\pi$
$762$	−45.9739	−1.66546
$763$	21.1838	0.766904
$764$	−61.4768	−2.22415
$765$	0.0837879	0.00302936
$766$	−69.4024	−2.50761
$767$	−12.5520	−0.453227
$768$	58.1728	2.09913
$769$	−35.2356	−1.27063	−0.635314	−	0.772254i	$-0.719129\pi$
$769$	−35.2356	−1.27063	−0.635314	+	0.772254i	$0.719129\pi$
$770$	0.662344	0.0238692
$771$	16.4272	0.591610
$772$	57.8569	2.08232
$773$	−3.42873	−0.123323	−0.0616615	−	0.998097i	$-0.519640\pi$
$773$	−3.42873	−0.123323	−0.0616615	+	0.998097i	$0.519640\pi$
$774$	−5.36750	−0.192931
$775$	47.3734	1.70170
$776$	69.1403	2.48199
$777$	46.6503	1.67357
$778$	−62.2438	−2.23155
$779$	−4.28340	−0.153469
$780$	−0.622840	−0.0223012
$781$	14.8068	0.529830
$782$	62.8462	2.24738
$783$	28.3994	1.01491
$784$	33.2529	1.18760
$785$	−0.392908	−0.0140235
$786$	57.5677	2.05337
$787$	28.7211	1.02380	0.511898	−	0.859046i	$-0.328943\pi$
$787$	28.7211	1.02380	0.511898	+	0.859046i	$0.328943\pi$
$788$	−100.296	−3.57289
$789$	−32.6625	−1.16282
$790$	−0.360038	−0.0128096
$791$	−50.8536	−1.80815
$792$	−1.02545	−0.0364379
$793$	0.167765	0.00595751
$794$	−3.27971	−0.116393
$795$	−0.666534	−0.0236395
$796$	73.3876	2.60116
$797$	43.0757	1.52582	0.762909	−	0.646506i	$-0.223770\pi$
$797$	43.0757	1.52582	0.762909	+	0.646506i	$0.223770\pi$
$798$	−26.1863	−0.926985
$799$	27.4828	0.972271
$800$	11.7172	0.414266
$801$	−1.96328	−0.0693690
$802$	45.1490	1.59427
$803$	1.25688	0.0443543
$804$	−66.2380	−2.33603
$805$	−1.54064	−0.0543003
$806$	−23.6672	−0.833640
$807$	42.4340	1.49375
$808$	3.98737	0.140275
$809$	−26.5609	−0.933832	−0.466916	−	0.884302i	$-0.654635\pi$
$809$	−26.5609	−0.933832	−0.466916	+	0.884302i	$0.654635\pi$
$810$	−1.96817	−0.0691543
$811$	43.2000	1.51696	0.758479	−	0.651698i	$-0.225943\pi$
$811$	43.2000	1.51696	0.758479	+	0.651698i	$0.225943\pi$
$812$	87.0450	3.05468
$813$	38.0897	1.33586
$814$	15.9020	0.557365
$815$	0.316242	0.0110775
$816$	47.1526	1.65067
$817$	−16.6893	−0.583885
$818$	10.6413	0.372066
$819$	−0.755605	−0.0264030
$820$	−0.922435	−0.0322128
$821$	−5.33872	−0.186323	−0.0931613	−	0.995651i	$-0.529697\pi$
$821$	−5.33872	−0.186323	−0.0931613	+	0.995651i	$0.529697\pi$
$822$	10.7760	0.375858
$823$	−34.9392	−1.21790	−0.608952	−	0.793207i	$-0.708410\pi$
$823$	−34.9392	−1.21790	−0.608952	+	0.793207i	$0.708410\pi$
$824$	−28.0093	−0.975751
$825$	7.94509	0.276613
$826$	−113.647	−3.95429
$827$	−47.2866	−1.64432	−0.822159	−	0.569258i	$-0.807230\pi$
$827$	−47.2866	−1.64432	−0.822159	+	0.569258i	$0.807230\pi$
$828$	4.53143	0.157478
$829$	−45.4826	−1.57968	−0.789838	−	0.613315i	$-0.789836\pi$
$829$	−45.4826	−1.57968	−0.789838	+	0.613315i	$0.789836\pi$
$830$	0.982529	0.0341041
$831$	−5.03905	−0.174803
$832$	4.91871	0.170526
$833$	−30.1741	−1.04547
$834$	−94.9622	−3.28827
$835$	−1.96406	−0.0679692
$836$	−6.05739	−0.209499
$837$	−47.4429	−1.63987
$838$	−45.8659	−1.58441
$839$	−0.351953	−0.0121508	−0.00607538	−	0.999982i	$-0.501934\pi$
$839$	−0.351953	−0.0121508	−0.00607538	+	0.999982i	$0.501934\pi$
$840$	−2.96838	−0.102419
$841$	3.25415	0.112212
$842$	74.7416	2.57576
$843$	8.67715	0.298857
$844$	−68.5029	−2.35797
$845$	−0.0823474	−0.00283284
$846$	2.92014	0.100396
$847$	−37.0607	−1.27342
$848$	−24.3405	−0.835855
$849$	13.5041	0.463458
$850$	−60.8784	−2.08811
$851$	−36.9886	−1.26795
$852$	−126.066	−4.31897
$853$	−38.7928	−1.32824	−0.664121	−	0.747625i	$-0.731194\pi$
$853$	−38.7928	−1.32824	−0.664121	+	0.747625i	$0.731194\pi$
$854$	1.51896	0.0519778
$855$	0.0276815	0.000946689 0
$856$	−2.33870	−0.0799351
$857$	−37.5057	−1.28117	−0.640586	−	0.767887i	$-0.721308\pi$
$857$	−37.5057	−1.28117	−0.640586	+	0.767887i	$0.721308\pi$
$858$	−3.96926	−0.135508
$859$	14.2856	0.487419	0.243710	−	0.969848i	$-0.421636\pi$
$859$	14.2856	0.487419	0.243710	+	0.969848i	$0.421636\pi$
$860$	−3.59407	−0.122557
$861$	−17.2453	−0.587720
$862$	17.4653	0.594869
$863$	−15.3255	−0.521685	−0.260842	−	0.965381i	$-0.584000\pi$
$863$	−15.3255	−0.521685	−0.260842	+	0.965381i	$0.584000\pi$
$864$	−11.7344	−0.399212
$865$	0.453052	0.0154042
$866$	−11.3760	−0.386573
$867$	−12.3375	−0.419003
$868$	−145.414	−4.93566
$869$	−1.55703	−0.0528185
$870$	−2.08960	−0.0708442
$871$	−8.75750	−0.296737
$872$	−32.3620	−1.09592
$873$	−2.59589	−0.0878576
$874$	20.7629	0.702316
$875$	2.98682	0.100973
$876$	−10.7012	−0.361559
$877$	−36.2663	−1.22463	−0.612314	−	0.790615i	$-0.709761\pi$
$877$	−36.2663	−1.22463	−0.612314	+	0.790615i	$0.709761\pi$
$878$	65.7462	2.21883
$879$	16.6085	0.560192
$880$	−0.394025	−0.0132826
$881$	7.89746	0.266072	0.133036	−	0.991111i	$-0.457527\pi$
$881$	7.89746	0.266072	0.133036	+	0.991111i	$0.457527\pi$
$882$	−3.20610	−0.107955
$883$	−1.52101	−0.0511862	−0.0255931	−	0.999672i	$-0.508147\pi$
$883$	−1.52101	−0.0511862	−0.0255931	+	0.999672i	$0.508147\pi$
$884$	20.6390	0.694163
$885$	1.85137	0.0622331
$886$	6.93554	0.233004
$887$	47.1331	1.58257	0.791287	−	0.611445i	$-0.209411\pi$
$887$	47.1331	1.58257	0.791287	+	0.611445i	$0.209411\pi$
$888$	−71.2668	−2.39156
$889$	−37.3460	−1.25254
$890$	−1.93723	−0.0649362
$891$	−8.51155	−0.285148
$892$	75.9851	2.54417
$893$	9.07966	0.303839
$894$	−85.8157	−2.87011
$895$	−1.58380	−0.0529406
$896$	61.5689	2.05687
$897$	9.23265	0.308269
$898$	−27.7317	−0.925417
$899$	−53.8824	−1.79708
$900$	−4.38954	−0.146318
$901$	22.0868	0.735819
$902$	−5.87854	−0.195734
$903$	−67.1927	−2.23603
$904$	77.6881	2.58387
$905$	−0.407533	−0.0135469
$906$	−104.746	−3.47996
$907$	−29.3687	−0.975171	−0.487585	−	0.873075i	$-0.662122\pi$
$907$	−29.3687	−0.975171	−0.487585	+	0.873075i	$0.662122\pi$
$908$	11.8326	0.392677
$909$	−0.149707	−0.00496547
$910$	−0.745581	−0.0247158
$911$	0.298382	0.00988585	0.00494293	−	0.999988i	$-0.498427\pi$
$911$	0.298382	0.00988585	0.00494293	+	0.999988i	$0.498427\pi$
$912$	15.5781	0.515842
$913$	4.24906	0.140623
$914$	82.2666	2.72114
$915$	−0.0247446	−0.000818031 0
$916$	38.1310	1.25988
$917$	46.7640	1.54428
$918$	60.9676	2.01223
$919$	−11.2975	−0.372671	−0.186335	−	0.982486i	$-0.559661\pi$
$919$	−11.2975	−0.372671	−0.186335	+	0.982486i	$0.559661\pi$
$920$	2.35360	0.0775959
$921$	−36.1730	−1.19194
$922$	2.24209	0.0738393
$923$	−16.6676	−0.548621
$924$	−24.3876	−0.802293
$925$	35.8304	1.17810
$926$	11.4204	0.375296
$927$	1.05162	0.0345396
$928$	−13.3271	−0.437484
$929$	−56.9328	−1.86790	−0.933952	−	0.357399i	$-0.883664\pi$
$929$	−56.9328	−1.86790	−0.933952	+	0.357399i	$0.883664\pi$
$930$	3.49080	0.114468
$931$	−9.96881	−0.326715
$932$	38.0812	1.24739
$933$	−25.5284	−0.835761
$934$	−20.8406	−0.681927
$935$	0.357544	0.0116929
$936$	1.15432	0.0377302
$937$	−3.79570	−0.124000	−0.0620000	−	0.998076i	$-0.519748\pi$
$937$	−3.79570	−0.124000	−0.0620000	+	0.998076i	$0.519748\pi$
$938$	−79.2913	−2.58895
$939$	7.27425	0.237386
$940$	1.95532	0.0637754
$941$	−25.5500	−0.832906	−0.416453	−	0.909157i	$-0.636727\pi$
$941$	−25.5500	−0.832906	−0.416453	+	0.909157i	$0.636727\pi$
$942$	21.3188	0.694603
$943$	13.6737	0.445277
$944$	67.6082	2.20046
$945$	−1.49458	−0.0486188
$946$	−22.9044	−0.744688
$947$	−46.9860	−1.52684	−0.763420	−	0.645902i	$-0.776481\pi$
$947$	−46.9860	−1.52684	−0.763420	+	0.645902i	$0.776481\pi$
$948$	13.2567	0.430556
$949$	−1.41483	−0.0459273
$950$	−20.1128	−0.652544
$951$	−3.47214	−0.112592
$952$	98.3626	3.18795
$953$	−56.1016	−1.81731	−0.908654	−	0.417550i	$-0.862889\pi$
$953$	−56.1016	−1.81731	−0.908654	+	0.417550i	$0.862889\pi$
$954$	2.34680	0.0759804
$955$	1.19885	0.0387937
$956$	41.7042	1.34881
$957$	−9.03672	−0.292116
$958$	−14.8333	−0.479241
$959$	8.75370	0.282672
$960$	−0.725488	−0.0234150
$961$	59.0137	1.90367
$962$	−17.9004	−0.577133
$963$	0.0878070	0.00282954
$964$	34.9329	1.12511
$965$	−1.12826	−0.0363198
$966$	83.5934	2.68957
$967$	7.91170	0.254423	0.127212	−	0.991876i	$-0.459397\pi$
$967$	7.91170	0.254423	0.127212	+	0.991876i	$0.459397\pi$
$968$	56.6170	1.81974
$969$	−14.1358	−0.454106
$970$	−2.56146	−0.0822434
$971$	−47.7697	−1.53300	−0.766501	−	0.642243i	$-0.778004\pi$
$971$	−47.7697	−1.53300	−0.766501	+	0.642243i	$0.778004\pi$
$972$	9.11975	0.292516
$973$	−77.1406	−2.47301
$974$	−60.5479	−1.94008
$975$	−8.94355	−0.286423
$976$	−0.903622	−0.0289242
$977$	32.9776	1.05505	0.527523	−	0.849541i	$-0.323121\pi$
$977$	32.9776	1.05505	0.527523	+	0.849541i	$0.323121\pi$
$978$	−17.1589	−0.548683
$979$	−8.37779	−0.267755
$980$	−2.14680	−0.0685769
$981$	1.21504	0.0387932
$982$	44.6919	1.42618
$983$	15.3754	0.490399	0.245199	−	0.969473i	$-0.421147\pi$
$983$	15.3754	0.490399	0.245199	+	0.969473i	$0.421147\pi$
$984$	26.3454	0.839860
$985$	1.95585	0.0623185
$986$	69.2429	2.20514
$987$	36.5555	1.16358
$988$	6.81862	0.216929
$989$	53.2766	1.69410
$990$	0.0379902	0.00120741
$991$	51.4633	1.63479	0.817393	−	0.576080i	$-0.195418\pi$
$991$	51.4633	1.63479	0.817393	+	0.576080i	$0.195418\pi$
$992$	22.2637	0.706874
$993$	39.1189	1.24140
$994$	−150.910	−4.78658
$995$	−1.43112	−0.0453695
$996$	−36.1768	−1.14631
$997$	13.7326	0.434915	0.217458	−	0.976070i	$-0.430224\pi$
$997$	13.7326	0.434915	0.217458	+	0.976070i	$0.430224\pi$
$998$	81.4452	2.57810
$999$	−35.8829	−1.13529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.9	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.9	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49455 q^{2} -1.79114 q^{3} +4.22277 q^{4} -0.0823474 q^{5} +4.46808 q^{6} +3.62956 q^{7} -5.54480 q^{8} +0.208181 q^{9} +O(q^{10})\)	\(q-2.49455 q^{2} -1.79114 q^{3} +4.22277 q^{4} -0.0823474 q^{5} +4.46808 q^{6} +3.62956 q^{7} -5.54480 q^{8} +0.208181 q^{9} +0.205419 q^{10} +0.888360 q^{11} -7.56357 q^{12} -1.00000 q^{13} -9.05410 q^{14} +0.147496 q^{15} +5.38624 q^{16} -4.88754 q^{17} -0.519317 q^{18} -1.61473 q^{19} -0.347734 q^{20} -6.50104 q^{21} -2.21606 q^{22} +5.15462 q^{23} +9.93152 q^{24} -4.99322 q^{25} +2.49455 q^{26} +5.00054 q^{27} +15.3268 q^{28} +5.67927 q^{29} -0.367935 q^{30} -9.48756 q^{31} -2.34663 q^{32} -1.59118 q^{33} +12.1922 q^{34} -0.298884 q^{35} +0.879100 q^{36} -7.17582 q^{37} +4.02802 q^{38} +1.79114 q^{39} +0.456600 q^{40} +2.65270 q^{41} +16.2172 q^{42} +10.3357 q^{43} +3.75134 q^{44} -0.0171432 q^{45} -12.8585 q^{46} -5.62303 q^{47} -9.64751 q^{48} +6.17368 q^{49} +12.4558 q^{50} +8.75427 q^{51} -4.22277 q^{52} -4.51901 q^{53} -12.4741 q^{54} -0.0731541 q^{55} -20.1252 q^{56} +2.89220 q^{57} -14.1672 q^{58} +12.5520 q^{59} +0.622840 q^{60} -0.167765 q^{61} +23.6672 q^{62} +0.755605 q^{63} -4.91871 q^{64} +0.0823474 q^{65} +3.96926 q^{66} +8.75750 q^{67} -20.6390 q^{68} -9.23265 q^{69} +0.745581 q^{70} +16.6676 q^{71} -1.15432 q^{72} +1.41483 q^{73} +17.9004 q^{74} +8.94355 q^{75} -6.81862 q^{76} +3.22435 q^{77} -4.46808 q^{78} -1.75270 q^{79} -0.443543 q^{80} -9.58120 q^{81} -6.61730 q^{82} +4.78304 q^{83} -27.4524 q^{84} +0.402476 q^{85} -25.7829 q^{86} -10.1724 q^{87} -4.92578 q^{88} -9.43063 q^{89} +0.0427644 q^{90} -3.62956 q^{91} +21.7668 q^{92} +16.9935 q^{93} +14.0269 q^{94} +0.132969 q^{95} +4.20313 q^{96} -12.4694 q^{97} -15.4005 q^{98} +0.184940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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