LMFDB - Embedded newform 8021.2.a.b.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.55171 q^{2} -0.135477 q^{3} +4.51121 q^{4} -1.86622 q^{5} +0.345697 q^{6} -2.01089 q^{7} -6.40787 q^{8} -2.98165 q^{9} +O(q^{10})$	\(q-2.55171 q^{2} -0.135477 q^{3} +4.51121 q^{4} -1.86622 q^{5} +0.345697 q^{6} -2.01089 q^{7} -6.40787 q^{8} -2.98165 q^{9} +4.76206 q^{10} -4.11149 q^{11} -0.611165 q^{12} -1.00000 q^{13} +5.13120 q^{14} +0.252830 q^{15} +7.32860 q^{16} +0.199720 q^{17} +7.60829 q^{18} -0.141209 q^{19} -8.41893 q^{20} +0.272429 q^{21} +10.4913 q^{22} -0.321604 q^{23} +0.868119 q^{24} -1.51721 q^{25} +2.55171 q^{26} +0.810375 q^{27} -9.07155 q^{28} +10.4830 q^{29} -0.645149 q^{30} -5.26621 q^{31} -5.88469 q^{32} +0.557012 q^{33} -0.509628 q^{34} +3.75277 q^{35} -13.4508 q^{36} +5.21707 q^{37} +0.360325 q^{38} +0.135477 q^{39} +11.9585 q^{40} -0.964257 q^{41} -0.695159 q^{42} -7.96180 q^{43} -18.5478 q^{44} +5.56442 q^{45} +0.820640 q^{46} -2.66262 q^{47} -0.992856 q^{48} -2.95632 q^{49} +3.87147 q^{50} -0.0270575 q^{51} -4.51121 q^{52} +6.99397 q^{53} -2.06784 q^{54} +7.67296 q^{55} +12.8855 q^{56} +0.0191306 q^{57} -26.7496 q^{58} +7.76891 q^{59} +1.14057 q^{60} +5.93498 q^{61} +13.4378 q^{62} +5.99576 q^{63} +0.358808 q^{64} +1.86622 q^{65} -1.42133 q^{66} +3.36318 q^{67} +0.900981 q^{68} +0.0435700 q^{69} -9.57597 q^{70} -2.03859 q^{71} +19.1060 q^{72} -10.9786 q^{73} -13.3124 q^{74} +0.205546 q^{75} -0.637025 q^{76} +8.26775 q^{77} -0.345697 q^{78} +7.72323 q^{79} -13.6768 q^{80} +8.83515 q^{81} +2.46050 q^{82} +7.27071 q^{83} +1.22899 q^{84} -0.372723 q^{85} +20.3162 q^{86} -1.42021 q^{87} +26.3459 q^{88} -4.95631 q^{89} -14.1988 q^{90} +2.01089 q^{91} -1.45083 q^{92} +0.713450 q^{93} +6.79422 q^{94} +0.263528 q^{95} +0.797239 q^{96} +6.95883 q^{97} +7.54367 q^{98} +12.2590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.55171	−1.80433	−0.902165	−	0.431392i	$-0.858023\pi$
$2$	−2.55171	−1.80433	−0.902165	+	0.431392i	$0.858023\pi$
$3$	−0.135477	−0.0782176	−0.0391088	−	0.999235i	$-0.512452\pi$
$3$	−0.135477	−0.0782176	−0.0391088	+	0.999235i	$0.512452\pi$
$4$	4.51121	2.25561
$5$	−1.86622	−0.834601	−0.417300	−	0.908769i	$-0.637024\pi$
$5$	−1.86622	−0.834601	−0.417300	+	0.908769i	$0.637024\pi$
$6$	0.345697	0.141130
$7$	−2.01089	−0.760045	−0.380022	−	0.924977i	$-0.624084\pi$
$7$	−2.01089	−0.760045	−0.380022	+	0.924977i	$0.624084\pi$
$8$	−6.40787	−2.26553
$9$	−2.98165	−0.993882
$10$	4.76206	1.50590
$11$	−4.11149	−1.23966	−0.619830	−	0.784736i	$-0.712799\pi$
$11$	−4.11149	−1.23966	−0.619830	+	0.784736i	$0.712799\pi$
$12$	−0.611165	−0.176428
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.13120	1.37137
$15$	0.252830	0.0652805
$16$	7.32860	1.83215
$17$	0.199720	0.0484393	0.0242197	−	0.999707i	$-0.492290\pi$
$17$	0.199720	0.0484393	0.0242197	+	0.999707i	$0.492290\pi$
$18$	7.60829	1.79329
$19$	−0.141209	−0.0323956	−0.0161978	−	0.999869i	$-0.505156\pi$
$19$	−0.141209	−0.0323956	−0.0161978	+	0.999869i	$0.505156\pi$
$20$	−8.41893	−1.88253
$21$	0.272429	0.0594489
$22$	10.4913	2.23676
$23$	−0.321604	−0.0670592	−0.0335296	−	0.999438i	$-0.510675\pi$
$23$	−0.321604	−0.0670592	−0.0335296	+	0.999438i	$0.510675\pi$
$24$	0.868119	0.177204
$25$	−1.51721	−0.303441
$26$	2.55171	0.500431
$27$	0.810375	0.155957
$28$	−9.07155	−1.71436
$29$	10.4830	1.94665	0.973323	−	0.229438i	$-0.0736887\pi$
$29$	10.4830	1.94665	0.973323	+	0.229438i	$0.0736887\pi$
$30$	−0.645149	−0.117788
$31$	−5.26621	−0.945840	−0.472920	−	0.881105i	$-0.656800\pi$
$31$	−5.26621	−0.945840	−0.472920	+	0.881105i	$0.656800\pi$
$32$	−5.88469	−1.04028
$33$	0.557012	0.0969633
$34$	−0.509628	−0.0874005
$35$	3.75277	0.634334
$36$	−13.4508	−2.24181
$37$	5.21707	0.857680	0.428840	−	0.903380i	$-0.358922\pi$
$37$	5.21707	0.857680	0.428840	+	0.903380i	$0.358922\pi$
$38$	0.360325	0.0584524
$39$	0.135477	0.0216937
$40$	11.9585	1.89081
$41$	−0.964257	−0.150592	−0.0752958	−	0.997161i	$-0.523990\pi$
$41$	−0.964257	−0.150592	−0.0752958	+	0.997161i	$0.523990\pi$
$42$	−0.695159	−0.107265
$43$	−7.96180	−1.21416	−0.607081	−	0.794640i	$-0.707660\pi$
$43$	−7.96180	−1.21416	−0.607081	+	0.794640i	$0.707660\pi$
$44$	−18.5478	−2.79619
$45$	5.56442	0.829495
$46$	0.820640	0.120997
$47$	−2.66262	−0.388383	−0.194191	−	0.980964i	$-0.562208\pi$
$47$	−2.66262	−0.388383	−0.194191	+	0.980964i	$0.562208\pi$
$48$	−0.992856	−0.143306
$49$	−2.95632	−0.422332
$50$	3.87147	0.547508
$51$	−0.0270575	−0.00378881
$52$	−4.51121	−0.625592
$53$	6.99397	0.960695	0.480348	−	0.877078i	$-0.340511\pi$
$53$	6.99397	0.960695	0.480348	+	0.877078i	$0.340511\pi$
$54$	−2.06784	−0.281397
$55$	7.67296	1.03462
$56$	12.8855	1.72190
$57$	0.0191306	0.00253391
$58$	−26.7496	−3.51239
$59$	7.76891	1.01143	0.505713	−	0.862702i	$-0.331229\pi$
$59$	7.76891	1.01143	0.505713	+	0.862702i	$0.331229\pi$
$60$	1.14057	0.147247
$61$	5.93498	0.759896	0.379948	−	0.925008i	$-0.375942\pi$
$61$	5.93498	0.759896	0.379948	+	0.925008i	$0.375942\pi$
$62$	13.4378	1.70661
$63$	5.99576	0.755395
$64$	0.358808	0.0448510
$65$	1.86622	0.231477
$66$	−1.42133	−0.174954
$67$	3.36318	0.410878	0.205439	−	0.978670i	$-0.434138\pi$
$67$	3.36318	0.410878	0.205439	+	0.978670i	$0.434138\pi$
$68$	0.900981	0.109260
$69$	0.0435700	0.00524521
$70$	−9.57597	−1.14455
$71$	−2.03859	−0.241937	−0.120968	−	0.992656i	$-0.538600\pi$
$71$	−2.03859	−0.241937	−0.120968	+	0.992656i	$0.538600\pi$
$72$	19.1060	2.25166
$73$	−10.9786	−1.28495	−0.642473	−	0.766308i	$-0.722091\pi$
$73$	−10.9786	−1.28495	−0.642473	+	0.766308i	$0.722091\pi$
$74$	−13.3124	−1.54754
$75$	0.205546	0.0237345
$76$	−0.637025	−0.0730718
$77$	8.26775	0.942198
$78$	−0.345697	−0.0391425
$79$	7.72323	0.868931	0.434465	−	0.900689i	$-0.356937\pi$
$79$	7.72323	0.868931	0.434465	+	0.900689i	$0.356937\pi$
$80$	−13.6768	−1.52911
$81$	8.83515	0.981683
$82$	2.46050	0.271717
$83$	7.27071	0.798064	0.399032	−	0.916937i	$-0.369346\pi$
$83$	7.27071	0.798064	0.399032	+	0.916937i	$0.369346\pi$
$84$	1.22899	0.134093
$85$	−0.372723	−0.0404275
$86$	20.3162	2.19075
$87$	−1.42021	−0.152262
$88$	26.3459	2.80848
$89$	−4.95631	−0.525368	−0.262684	−	0.964882i	$-0.584608\pi$
$89$	−4.95631	−0.525368	−0.262684	+	0.964882i	$0.584608\pi$
$90$	−14.1988	−1.49668
$91$	2.01089	0.210799
$92$	−1.45083	−0.151259
$93$	0.713450	0.0739813
$94$	6.79422	0.700770
$95$	0.263528	0.0270374
$96$	0.797239	0.0813679
$97$	6.95883	0.706562	0.353281	−	0.935517i	$-0.385066\pi$
$97$	6.95883	0.706562	0.353281	+	0.935517i	$0.385066\pi$
$98$	7.54367	0.762026
$99$	12.2590	1.23208
$100$	−6.84444	−0.684444
$101$	3.31915	0.330268	0.165134	−	0.986271i	$-0.447194\pi$
$101$	3.31915	0.330268	0.165134	+	0.986271i	$0.447194\pi$
$102$	0.0690428	0.00683626
$103$	−2.55021	−0.251279	−0.125640	−	0.992076i	$-0.540098\pi$
$103$	−2.55021	−0.251279	−0.125640	+	0.992076i	$0.540098\pi$
$104$	6.40787	0.628344
$105$	−0.508414	−0.0496161
$106$	−17.8466	−1.73341
$107$	14.8152	1.43224	0.716121	−	0.697976i	$-0.245916\pi$
$107$	14.8152	1.43224	0.716121	+	0.697976i	$0.245916\pi$
$108$	3.65577	0.351777
$109$	−2.95125	−0.282679	−0.141339	−	0.989961i	$-0.545141\pi$
$109$	−2.95125	−0.282679	−0.141339	+	0.989961i	$0.545141\pi$
$110$	−19.5792	−1.86680
$111$	−0.706792	−0.0670857
$112$	−14.7370	−1.39252
$113$	15.8919	1.49499	0.747493	−	0.664270i	$-0.231257\pi$
$113$	15.8919	1.49499	0.747493	+	0.664270i	$0.231257\pi$
$114$	−0.0488157	−0.00457201
$115$	0.600186	0.0559676
$116$	47.2911	4.39087
$117$	2.98165	0.275653
$118$	−19.8240	−1.82495
$119$	−0.401616	−0.0368161
$120$	−1.62010	−0.147895
$121$	5.90435	0.536759
$122$	−15.1443	−1.37110
$123$	0.130635	0.0117789
$124$	−23.7570	−2.13344
$125$	12.1626	1.08785
$126$	−15.2994	−1.36298
$127$	−10.8518	−0.962944	−0.481472	−	0.876461i	$-0.659898\pi$
$127$	−10.8518	−0.962944	−0.481472	+	0.876461i	$0.659898\pi$
$128$	10.8538	0.959350
$129$	1.07864	0.0949689
$130$	−4.76206	−0.417660
$131$	4.07297	0.355857	0.177928	−	0.984043i	$-0.443060\pi$
$131$	4.07297	0.355857	0.177928	+	0.984043i	$0.443060\pi$
$132$	2.51280	0.218711
$133$	0.283956	0.0246221
$134$	−8.58185	−0.741358
$135$	−1.51234	−0.130162
$136$	−1.27978	−0.109741
$137$	11.6103	0.991939	0.495969	−	0.868340i	$-0.334813\pi$
$137$	11.6103	0.991939	0.495969	+	0.868340i	$0.334813\pi$
$138$	−0.111178	−0.00946408
$139$	−2.74778	−0.233063	−0.116532	−	0.993187i	$-0.537178\pi$
$139$	−2.74778	−0.233063	−0.116532	+	0.993187i	$0.537178\pi$
$140$	16.9295	1.43081
$141$	0.360723	0.0303784
$142$	5.20190	0.436533
$143$	4.11149	0.343820
$144$	−21.8513	−1.82094
$145$	−19.5637	−1.62467
$146$	28.0141	2.31847
$147$	0.400513	0.0330338
$148$	23.5353	1.93459
$149$	1.13690	0.0931382	0.0465691	−	0.998915i	$-0.485171\pi$
$149$	1.13690	0.0931382	0.0465691	+	0.998915i	$0.485171\pi$
$150$	−0.524494	−0.0428248
$151$	−19.0009	−1.54627	−0.773135	−	0.634242i	$-0.781312\pi$
$151$	−19.0009	−1.54627	−0.773135	+	0.634242i	$0.781312\pi$
$152$	0.904852	0.0733932
$153$	−0.595496	−0.0481430
$154$	−21.0969	−1.70004
$155$	9.82794	0.789399
$156$	0.611165	0.0489323
$157$	0.0609343	0.00486309	0.00243154	−	0.999997i	$-0.499226\pi$
$157$	0.0609343	0.00486309	0.00243154	+	0.999997i	$0.499226\pi$
$158$	−19.7074	−1.56784
$159$	−0.947521	−0.0751433
$160$	10.9821	0.868215
$161$	0.646711	0.0509680
$162$	−22.5447	−1.77128
$163$	7.00308	0.548524	0.274262	−	0.961655i	$-0.411566\pi$
$163$	7.00308	0.548524	0.274262	+	0.961655i	$0.411566\pi$
$164$	−4.34996	−0.339675
$165$	−1.03951	−0.0809257
$166$	−18.5527	−1.43997
$167$	−2.42821	−0.187901	−0.0939504	−	0.995577i	$-0.529950\pi$
$167$	−2.42821	−0.187901	−0.0939504	+	0.995577i	$0.529950\pi$
$168$	−1.74569	−0.134683
$169$	1.00000	0.0769231
$170$	0.951080	0.0729445
$171$	0.421036	0.0321974
$172$	−35.9173	−2.73867
$173$	12.1450	0.923371	0.461685	−	0.887044i	$-0.347245\pi$
$173$	12.1450	0.923371	0.461685	+	0.887044i	$0.347245\pi$
$174$	3.62395	0.274731
$175$	3.05094	0.230629
$176$	−30.1315	−2.27124
$177$	−1.05251	−0.0791114
$178$	12.6471	0.947937
$179$	−8.75843	−0.654636	−0.327318	−	0.944914i	$-0.606145\pi$
$179$	−8.75843	−0.654636	−0.327318	+	0.944914i	$0.606145\pi$
$180$	25.1023	1.87101
$181$	19.3877	1.44108	0.720538	−	0.693416i	$-0.243895\pi$
$181$	19.3877	1.44108	0.720538	+	0.693416i	$0.243895\pi$
$182$	−5.13120	−0.380350
$183$	−0.804052	−0.0594372
$184$	2.06080	0.151924
$185$	−9.73622	−0.715821
$186$	−1.82052	−0.133487
$187$	−0.821149	−0.0600483
$188$	−12.0116	−0.876038
$189$	−1.62957	−0.118534
$190$	−0.672447	−0.0487844
$191$	6.16942	0.446404	0.223202	−	0.974772i	$-0.428349\pi$
$191$	6.16942	0.446404	0.223202	+	0.974772i	$0.428349\pi$
$192$	−0.0486102	−0.00350814
$193$	15.2222	1.09572	0.547859	−	0.836571i	$-0.315443\pi$
$193$	15.2222	1.09572	0.547859	+	0.836571i	$0.315443\pi$
$194$	−17.7569	−1.27487
$195$	−0.252830	−0.0181056
$196$	−13.3366	−0.952614
$197$	−15.9233	−1.13449	−0.567244	−	0.823550i	$-0.691990\pi$
$197$	−15.9233	−1.13449	−0.567244	+	0.823550i	$0.691990\pi$
$198$	−31.2814	−2.22307
$199$	−17.2660	−1.22396	−0.611978	−	0.790875i	$-0.709626\pi$
$199$	−17.2660	−1.22396	−0.611978	+	0.790875i	$0.709626\pi$
$200$	9.72207	0.687454
$201$	−0.455633	−0.0321379
$202$	−8.46950	−0.595912
$203$	−21.0802	−1.47954
$204$	−0.122062	−0.00854606
$205$	1.79952	0.125684
$206$	6.50738	0.453391
$207$	0.958911	0.0666489
$208$	−7.32860	−0.508147
$209$	0.580581	0.0401596
$210$	1.29732	0.0895238
$211$	25.8504	1.77961	0.889807	−	0.456336i	$-0.150839\pi$
$211$	25.8504	1.77961	0.889807	+	0.456336i	$0.150839\pi$
$212$	31.5512	2.16695
$213$	0.276182	0.0189237
$214$	−37.8041	−2.58424
$215$	14.8585	1.01334
$216$	−5.19278	−0.353324
$217$	10.5898	0.718881
$218$	7.53073	0.510045
$219$	1.48734	0.100505
$220$	34.6143	2.33370
$221$	−0.199720	−0.0134347
$222$	1.80353	0.121045
$223$	−16.3813	−1.09697	−0.548486	−	0.836160i	$-0.684796\pi$
$223$	−16.3813	−1.09697	−0.548486	+	0.836160i	$0.684796\pi$
$224$	11.8335	0.790656
$225$	4.52377	0.301585
$226$	−40.5515	−2.69745
$227$	−16.8272	−1.11686	−0.558430	−	0.829552i	$-0.688596\pi$
$227$	−16.8272	−1.11686	−0.558430	+	0.829552i	$0.688596\pi$
$228$	0.0863022	0.00571550
$229$	−13.6907	−0.904707	−0.452353	−	0.891839i	$-0.649415\pi$
$229$	−13.6907	−0.904707	−0.452353	+	0.891839i	$0.649415\pi$
$230$	−1.53150	−0.100984
$231$	−1.12009	−0.0736965
$232$	−67.1738	−4.41018
$233$	−3.41931	−0.224006	−0.112003	−	0.993708i	$-0.535727\pi$
$233$	−3.41931	−0.224006	−0.112003	+	0.993708i	$0.535727\pi$
$234$	−7.60829	−0.497369
$235$	4.96904	0.324145
$236$	35.0472	2.28138
$237$	−1.04632	−0.0679657
$238$	1.02481	0.0664283
$239$	−10.0567	−0.650516	−0.325258	−	0.945625i	$-0.605451\pi$
$239$	−10.0567	−0.650516	−0.325258	+	0.945625i	$0.605451\pi$
$240$	1.85289	0.119604
$241$	−11.7027	−0.753839	−0.376920	−	0.926246i	$-0.623017\pi$
$241$	−11.7027	−0.753839	−0.376920	+	0.926246i	$0.623017\pi$
$242$	−15.0662	−0.968490
$243$	−3.62808	−0.232742
$244$	26.7739	1.71402
$245$	5.51716	0.352478
$246$	−0.333341	−0.0212530
$247$	0.141209	0.00898493
$248$	33.7452	2.14282
$249$	−0.985014	−0.0624227
$250$	−31.0353	−1.96285
$251$	−4.12023	−0.260067	−0.130033	−	0.991510i	$-0.541508\pi$
$251$	−4.12023	−0.260067	−0.130033	+	0.991510i	$0.541508\pi$
$252$	27.0481	1.70387
$253$	1.32227	0.0831306
$254$	27.6907	1.73747
$255$	0.0504954	0.00316214
$256$	−28.4133	−1.77583
$257$	−5.78507	−0.360863	−0.180431	−	0.983588i	$-0.557749\pi$
$257$	−5.78507	−0.360863	−0.180431	+	0.983588i	$0.557749\pi$
$258$	−2.75237	−0.171355
$259$	−10.4909	−0.651876
$260$	8.41893	0.522120
$261$	−31.2566	−1.93474
$262$	−10.3930	−0.642083
$263$	−24.4829	−1.50968	−0.754841	−	0.655907i	$-0.772286\pi$
$263$	−24.4829	−1.50968	−0.754841	+	0.655907i	$0.772286\pi$
$264$	−3.56926	−0.219673
$265$	−13.0523	−0.801797
$266$	−0.724574	−0.0444265
$267$	0.671466	0.0410930
$268$	15.1720	0.926777
$269$	−5.22056	−0.318303	−0.159152	−	0.987254i	$-0.550876\pi$
$269$	−5.22056	−0.318303	−0.159152	+	0.987254i	$0.550876\pi$
$270$	3.85905	0.234854
$271$	−3.41680	−0.207556	−0.103778	−	0.994600i	$-0.533093\pi$
$271$	−3.41680	−0.207556	−0.103778	+	0.994600i	$0.533093\pi$
$272$	1.46367	0.0887481
$273$	−0.272429	−0.0164882
$274$	−29.6262	−1.78978
$275$	6.23798	0.376164
$276$	0.196553	0.0118311
$277$	31.2974	1.88048	0.940238	−	0.340517i	$-0.110602\pi$
$277$	31.2974	1.88048	0.940238	+	0.340517i	$0.110602\pi$
$278$	7.01152	0.420523
$279$	15.7020	0.940053
$280$	−24.0473	−1.43710
$281$	−0.277370	−0.0165465	−0.00827325	−	0.999966i	$-0.502633\pi$
$281$	−0.277370	−0.0165465	−0.00827325	+	0.999966i	$0.502633\pi$
$282$	−0.920460	−0.0548126
$283$	17.1736	1.02087	0.510433	−	0.859917i	$-0.329485\pi$
$283$	17.1736	1.02087	0.510433	+	0.859917i	$0.329485\pi$
$284$	−9.19653	−0.545713
$285$	−0.0357020	−0.00211480
$286$	−10.4913	−0.620365
$287$	1.93901	0.114456
$288$	17.5461	1.03391
$289$	−16.9601	−0.997654
$290$	49.9207	2.93145
$291$	−0.942760	−0.0552656
$292$	−49.5267	−2.89833
$293$	−11.2013	−0.654387	−0.327193	−	0.944957i	$-0.606103\pi$
$293$	−11.2013	−0.654387	−0.327193	+	0.944957i	$0.606103\pi$
$294$	−1.02199	−0.0596038
$295$	−14.4985	−0.844137
$296$	−33.4303	−1.94310
$297$	−3.33185	−0.193333
$298$	−2.90103	−0.168052
$299$	0.321604	0.0185989
$300$	0.927263	0.0535356
$301$	16.0103	0.922818
$302$	48.4847	2.78998
$303$	−0.449668	−0.0258328
$304$	−1.03487	−0.0593537
$305$	−11.0760	−0.634210
$306$	1.51953	0.0868658
$307$	2.47083	0.141018	0.0705088	−	0.997511i	$-0.477538\pi$
$307$	2.47083	0.141018	0.0705088	+	0.997511i	$0.477538\pi$
$308$	37.2976	2.12523
$309$	0.345494	0.0196545
$310$	−25.0780	−1.42434
$311$	22.8622	1.29640	0.648199	−	0.761471i	$-0.275523\pi$
$311$	22.8622	1.29640	0.648199	+	0.761471i	$0.275523\pi$
$312$	−0.868119	−0.0491476
$313$	32.2556	1.82319	0.911597	−	0.411085i	$-0.134850\pi$
$313$	32.2556	1.82319	0.911597	+	0.411085i	$0.134850\pi$
$314$	−0.155486	−0.00877461
$315$	−11.1894	−0.630453
$316$	34.8411	1.95996
$317$	−8.04572	−0.451893	−0.225946	−	0.974140i	$-0.572547\pi$
$317$	−8.04572	−0.451893	−0.225946	+	0.974140i	$0.572547\pi$
$318$	2.41780	0.135583
$319$	−43.1008	−2.41318
$320$	−0.669617	−0.0374327
$321$	−2.00712	−0.112027
$322$	−1.65022	−0.0919630
$323$	−0.0282024	−0.00156922
$324$	39.8572	2.21429
$325$	1.51721	0.0841595
$326$	−17.8698	−0.989718
$327$	0.399826	0.0221104
$328$	6.17883	0.341169
$329$	5.35423	0.295188
$330$	2.65252	0.146017
$331$	1.92025	0.105547	0.0527733	−	0.998607i	$-0.483194\pi$
$331$	1.92025	0.105547	0.0527733	+	0.998607i	$0.483194\pi$
$332$	32.7997	1.80012
$333$	−15.5554	−0.852433
$334$	6.19609	0.339035
$335$	−6.27644	−0.342919
$336$	1.99652	0.108919
$337$	−1.39791	−0.0761493	−0.0380746	−	0.999275i	$-0.512122\pi$
$337$	−1.39791	−0.0761493	−0.0380746	+	0.999275i	$0.512122\pi$
$338$	−2.55171	−0.138795
$339$	−2.15299	−0.116934
$340$	−1.68143	−0.0911885
$341$	21.6520	1.17252
$342$	−1.07436	−0.0580948
$343$	20.0211	1.08104
$344$	51.0182	2.75072
$345$	−0.0813113	−0.00437766
$346$	−30.9906	−1.66606
$347$	−5.28747	−0.283846	−0.141923	−	0.989878i	$-0.545329\pi$
$347$	−5.28747	−0.283846	−0.141923	+	0.989878i	$0.545329\pi$
$348$	−6.40685	−0.343443
$349$	19.6703	1.05293	0.526465	−	0.850197i	$-0.323517\pi$
$349$	19.6703	1.05293	0.526465	+	0.850197i	$0.323517\pi$
$350$	−7.78509	−0.416131
$351$	−0.810375	−0.0432546
$352$	24.1948	1.28959
$353$	26.3404	1.40196	0.700979	−	0.713182i	$-0.252747\pi$
$353$	26.3404	1.40196	0.700979	+	0.713182i	$0.252747\pi$
$354$	2.68569	0.142743
$355$	3.80447	0.201920
$356$	−22.3590	−1.18502
$357$	0.0544097	0.00287966
$358$	22.3489	1.18118
$359$	−19.3133	−1.01931	−0.509657	−	0.860377i	$-0.670228\pi$
$359$	−19.3133	−1.01931	−0.509657	+	0.860377i	$0.670228\pi$
$360$	−35.6561	−1.87924
$361$	−18.9801	−0.998951
$362$	−49.4717	−2.60018
$363$	−0.799903	−0.0419840
$364$	9.07155	0.475478
$365$	20.4885	1.07242
$366$	2.05171	0.107244
$367$	5.48453	0.286290	0.143145	−	0.989702i	$-0.454278\pi$
$367$	5.48453	0.286290	0.143145	+	0.989702i	$0.454278\pi$
$368$	−2.35691	−0.122862
$369$	2.87507	0.149670
$370$	24.8440	1.29158
$371$	−14.0641	−0.730171
$372$	3.21852	0.166873
$373$	−31.3465	−1.62306	−0.811529	−	0.584312i	$-0.801364\pi$
$373$	−31.3465	−1.62306	−0.811529	+	0.584312i	$0.801364\pi$
$374$	2.09533	0.108347
$375$	−1.64775	−0.0850893
$376$	17.0617	0.879891
$377$	−10.4830	−0.539903
$378$	4.15820	0.213875
$379$	−9.84480	−0.505693	−0.252847	−	0.967506i	$-0.581367\pi$
$379$	−9.84480	−0.505693	−0.252847	+	0.967506i	$0.581367\pi$
$380$	1.18883	0.0609858
$381$	1.47017	0.0753192
$382$	−15.7426	−0.805459
$383$	15.7101	0.802751	0.401375	−	0.915914i	$-0.368532\pi$
$383$	15.7101	0.802751	0.401375	+	0.915914i	$0.368532\pi$
$384$	−1.47044	−0.0750381
$385$	−15.4295	−0.786359
$386$	−38.8426	−1.97704
$387$	23.7393	1.20673
$388$	31.3927	1.59372
$389$	−13.1766	−0.668081	−0.334041	−	0.942559i	$-0.608412\pi$
$389$	−13.1766	−0.668081	−0.334041	+	0.942559i	$0.608412\pi$
$390$	0.645149	0.0326684
$391$	−0.0642310	−0.00324830
$392$	18.9437	0.956803
$393$	−0.551793	−0.0278343
$394$	40.6316	2.04699
$395$	−14.4133	−0.725210
$396$	55.3030	2.77908
$397$	22.4406	1.12626	0.563132	−	0.826367i	$-0.309596\pi$
$397$	22.4406	1.12626	0.563132	+	0.826367i	$0.309596\pi$
$398$	44.0578	2.20842
$399$	−0.0384695	−0.00192589
$400$	−11.1190	−0.555950
$401$	−13.2258	−0.660467	−0.330234	−	0.943899i	$-0.607128\pi$
$401$	−13.2258	−0.660467	−0.330234	+	0.943899i	$0.607128\pi$
$402$	1.16264	0.0579873
$403$	5.26621	0.262329
$404$	14.9734	0.744954
$405$	−16.4884	−0.819314
$406$	53.7905	2.66958
$407$	−21.4499	−1.06323
$408$	0.173381	0.00858364
$409$	10.9233	0.540125	0.270062	−	0.962843i	$-0.412956\pi$
$409$	10.9233	0.540125	0.270062	+	0.962843i	$0.412956\pi$
$410$	−4.59185	−0.226775
$411$	−1.57293	−0.0775871
$412$	−11.5045	−0.566787
$413$	−15.6224	−0.768729
$414$	−2.44686	−0.120257
$415$	−13.5688	−0.666065
$416$	5.88469	0.288521
$417$	0.372260	0.0182297
$418$	−1.48147	−0.0724612
$419$	−4.78418	−0.233722	−0.116861	−	0.993148i	$-0.537283\pi$
$419$	−4.78418	−0.233722	−0.116861	+	0.993148i	$0.537283\pi$
$420$	−2.29356	−0.111914
$421$	30.9973	1.51071	0.755357	−	0.655314i	$-0.227464\pi$
$421$	30.9973	1.51071	0.755357	+	0.655314i	$0.227464\pi$
$422$	−65.9627	−3.21101
$423$	7.93898	0.386007
$424$	−44.8164	−2.17648
$425$	−0.303017	−0.0146985
$426$	−0.704737	−0.0341446
$427$	−11.9346	−0.577555
$428$	66.8346	3.23057
$429$	−0.557012	−0.0268928
$430$	−37.9145	−1.82840
$431$	−9.89187	−0.476474	−0.238237	−	0.971207i	$-0.576570\pi$
$431$	−9.89187	−0.476474	−0.238237	+	0.971207i	$0.576570\pi$
$432$	5.93891	0.285736
$433$	−6.64707	−0.319438	−0.159719	−	0.987163i	$-0.551059\pi$
$433$	−6.64707	−0.319438	−0.159719	+	0.987163i	$0.551059\pi$
$434$	−27.0220	−1.29710
$435$	2.65042	0.127078
$436$	−13.3137	−0.637611
$437$	0.0454135	0.00217242
$438$	−3.79527	−0.181345
$439$	−35.1290	−1.67661	−0.838307	−	0.545198i	$-0.816454\pi$
$439$	−35.1290	−1.67661	−0.838307	+	0.545198i	$0.816454\pi$
$440$	−49.1674	−2.34396
$441$	8.81471	0.419748
$442$	0.509628	0.0242405
$443$	7.55704	0.359046	0.179523	−	0.983754i	$-0.442545\pi$
$443$	7.55704	0.359046	0.179523	+	0.983754i	$0.442545\pi$
$444$	−3.18849	−0.151319
$445$	9.24959	0.438473
$446$	41.8003	1.97930
$447$	−0.154023	−0.00728505
$448$	−0.721524	−0.0340888
$449$	18.2573	0.861614	0.430807	−	0.902444i	$-0.358229\pi$
$449$	18.2573	0.861614	0.430807	+	0.902444i	$0.358229\pi$
$450$	−11.5433	−0.544159
$451$	3.96453	0.186682
$452$	71.6918	3.37210
$453$	2.57418	0.120946
$454$	42.9381	2.01518
$455$	−3.75277	−0.175933
$456$	−0.122586	−0.00574064
$457$	−33.1360	−1.55004	−0.775018	−	0.631939i	$-0.782259\pi$
$457$	−33.1360	−1.55004	−0.775018	+	0.631939i	$0.782259\pi$
$458$	34.9347	1.63239
$459$	0.161848	0.00755444
$460$	2.70757	0.126241
$461$	5.67554	0.264336	0.132168	−	0.991227i	$-0.457806\pi$
$461$	5.67554	0.264336	0.132168	+	0.991227i	$0.457806\pi$
$462$	2.85814	0.132973
$463$	−23.8363	−1.10777	−0.553884	−	0.832594i	$-0.686855\pi$
$463$	−23.8363	−1.10777	−0.553884	+	0.832594i	$0.686855\pi$
$464$	76.8258	3.56655
$465$	−1.33146	−0.0617449
$466$	8.72508	0.404181
$467$	2.14829	0.0994111	0.0497056	−	0.998764i	$-0.484172\pi$
$467$	2.14829	0.0994111	0.0497056	+	0.998764i	$0.484172\pi$
$468$	13.4508	0.621765
$469$	−6.76298	−0.312285
$470$	−12.6795	−0.584864
$471$	−0.00825519	−0.000380379 0
$472$	−49.7822	−2.29141
$473$	32.7348	1.50515
$474$	2.66990	0.122633
$475$	0.214244	0.00983018
$476$	−1.81177	−0.0830425
$477$	−20.8535	−0.954817
$478$	25.6618	1.17375
$479$	14.0837	0.643499	0.321750	−	0.946825i	$-0.395729\pi$
$479$	14.0837	0.643499	0.321750	+	0.946825i	$0.395729\pi$
$480$	−1.48783	−0.0679097
$481$	−5.21707	−0.237878
$482$	29.8619	1.36017
$483$	−0.0876144	−0.00398659
$484$	26.6358	1.21072
$485$	−12.9867	−0.589697
$486$	9.25781	0.419943
$487$	−20.2950	−0.919656	−0.459828	−	0.888008i	$-0.652089\pi$
$487$	−20.2950	−0.919656	−0.459828	+	0.888008i	$0.652089\pi$
$488$	−38.0306	−1.72156
$489$	−0.948756	−0.0429042
$490$	−14.0782	−0.635987
$491$	9.94889	0.448987	0.224494	−	0.974476i	$-0.427927\pi$
$491$	9.94889	0.448987	0.224494	+	0.974476i	$0.427927\pi$
$492$	0.589320	0.0265686
$493$	2.09367	0.0942942
$494$	−0.360325	−0.0162118
$495$	−22.8781	−1.02829
$496$	−38.5940	−1.73292
$497$	4.09939	0.183883
$498$	2.51347	0.112631
$499$	14.1817	0.634862	0.317431	−	0.948281i	$-0.397180\pi$
$499$	14.1817	0.634862	0.317431	+	0.948281i	$0.397180\pi$
$500$	54.8679	2.45377
$501$	0.328967	0.0146972
$502$	10.5136	0.469246
$503$	22.0191	0.981785	0.490893	−	0.871220i	$-0.336671\pi$
$503$	22.0191	0.981785	0.490893	+	0.871220i	$0.336671\pi$
$504$	−38.4201	−1.71137
$505$	−6.19428	−0.275642
$506$	−3.37405	−0.149995
$507$	−0.135477	−0.00601674
$508$	−48.9549	−2.17202
$509$	25.9449	1.14999	0.574993	−	0.818158i	$-0.305005\pi$
$509$	25.9449	1.14999	0.574993	+	0.818158i	$0.305005\pi$
$510$	−0.128849	−0.00570555
$511$	22.0767	0.976616
$512$	50.7949	2.24484
$513$	−0.114432	−0.00505232
$514$	14.7618	0.651116
$515$	4.75926	0.209718
$516$	4.86597	0.214212
$517$	10.9473	0.481463
$518$	26.7698	1.17620
$519$	−1.64537	−0.0722239
$520$	−11.9585	−0.524416
$521$	4.79655	0.210140	0.105070	−	0.994465i	$-0.466493\pi$
$521$	4.79655	0.210140	0.105070	+	0.994465i	$0.466493\pi$
$522$	79.7578	3.49090
$523$	9.90878	0.433281	0.216640	−	0.976251i	$-0.430490\pi$
$523$	9.90878	0.433281	0.216640	+	0.976251i	$0.430490\pi$
$524$	18.3740	0.802672
$525$	−0.413331	−0.0180393
$526$	62.4733	2.72397
$527$	−1.05177	−0.0458158
$528$	4.08212	0.177651
$529$	−22.8966	−0.995503
$530$	33.3057	1.44671
$531$	−23.1641	−1.00524
$532$	1.28099	0.0555378
$533$	0.964257	0.0417666
$534$	−1.71338	−0.0741454
$535$	−27.6485	−1.19535
$536$	−21.5508	−0.930854
$537$	1.18656	0.0512041
$538$	13.3214	0.574324
$539$	12.1549	0.523548
$540$	−6.82249	−0.293593
$541$	−11.2386	−0.483184	−0.241592	−	0.970378i	$-0.577670\pi$
$541$	−11.2386	−0.483184	−0.241592	+	0.970378i	$0.577670\pi$
$542$	8.71869	0.374500
$543$	−2.62658	−0.112718
$544$	−1.17529	−0.0503903
$545$	5.50770	0.235924
$546$	0.695159	0.0297501
$547$	17.1554	0.733512	0.366756	−	0.930317i	$-0.380468\pi$
$547$	17.1554	0.733512	0.366756	+	0.930317i	$0.380468\pi$
$548$	52.3767	2.23742
$549$	−17.6960	−0.755247
$550$	−15.9175	−0.678724
$551$	−1.48030	−0.0630629
$552$	−0.279191	−0.0118832
$553$	−15.5306	−0.660426
$554$	−79.8617	−3.39300
$555$	1.31903	0.0559898
$556$	−12.3958	−0.525699
$557$	−25.9129	−1.09796	−0.548982	−	0.835834i	$-0.684985\pi$
$557$	−25.9129	−1.09796	−0.548982	+	0.835834i	$0.684985\pi$
$558$	−40.0669	−1.69617
$559$	7.96180	0.336748
$560$	27.5026	1.16219
$561$	0.111247	0.00469684
$562$	0.707767	0.0298553
$563$	−39.0320	−1.64500	−0.822501	−	0.568763i	$-0.807422\pi$
$563$	−39.0320	−1.64500	−0.822501	+	0.568763i	$0.807422\pi$
$564$	1.62730	0.0685216
$565$	−29.6579	−1.24772
$566$	−43.8221	−1.84198
$567$	−17.7665	−0.746123
$568$	13.0631	0.548114
$569$	10.4657	0.438745	0.219373	−	0.975641i	$-0.429599\pi$
$569$	10.4657	0.438745	0.219373	+	0.975641i	$0.429599\pi$
$570$	0.0911010	0.00381580
$571$	33.0855	1.38458	0.692292	−	0.721618i	$-0.256601\pi$
$571$	33.0855	1.38458	0.692292	+	0.721618i	$0.256601\pi$
$572$	18.5478	0.775522
$573$	−0.835814	−0.0349166
$574$	−4.94780	−0.206517
$575$	0.487940	0.0203485
$576$	−1.06984	−0.0445766
$577$	34.0397	1.41709	0.708546	−	0.705665i	$-0.249352\pi$
$577$	34.0397	1.41709	0.708546	+	0.705665i	$0.249352\pi$
$578$	43.2772	1.80010
$579$	−2.06226	−0.0857044
$580$	−88.2558	−3.66462
$581$	−14.6206	−0.606565
$582$	2.40565	0.0997173
$583$	−28.7556	−1.19094
$584$	70.3494	2.91108
$585$	−5.56442	−0.230060
$586$	28.5824	1.18073
$587$	17.7675	0.733342	0.366671	−	0.930351i	$-0.380497\pi$
$587$	17.7675	0.733342	0.366671	+	0.930351i	$0.380497\pi$
$588$	1.80680	0.0745112
$589$	0.743639	0.0306411
$590$	36.9960	1.52310
$591$	2.15724	0.0887370
$592$	38.2338	1.57140
$593$	42.1511	1.73094	0.865468	−	0.500964i	$-0.167021\pi$
$593$	42.1511	1.73094	0.865468	+	0.500964i	$0.167021\pi$
$594$	8.50190	0.348837
$595$	0.749505	0.0307267
$596$	5.12878	0.210083
$597$	2.33915	0.0957349
$598$	−0.820640	−0.0335585
$599$	26.9689	1.10192	0.550960	−	0.834532i	$-0.314262\pi$
$599$	26.9689	1.10192	0.550960	+	0.834532i	$0.314262\pi$
$600$	−1.31712	−0.0537710
$601$	−18.3392	−0.748070	−0.374035	−	0.927415i	$-0.622026\pi$
$601$	−18.3392	−0.748070	−0.374035	+	0.927415i	$0.622026\pi$
$602$	−40.8536	−1.66507
$603$	−10.0278	−0.408364
$604$	−85.7170	−3.48777
$605$	−11.0188	−0.447980
$606$	1.14742	0.0466108
$607$	17.0040	0.690171	0.345086	−	0.938571i	$-0.387850\pi$
$607$	17.0040	0.690171	0.345086	+	0.938571i	$0.387850\pi$
$608$	0.830973	0.0337004
$609$	2.85588	0.115726
$610$	28.2627	1.14432
$611$	2.66262	0.107718
$612$	−2.68641	−0.108592
$613$	8.28007	0.334429	0.167214	−	0.985921i	$-0.446523\pi$
$613$	8.28007	0.334429	0.167214	+	0.985921i	$0.446523\pi$
$614$	−6.30483	−0.254442
$615$	−0.243793	−0.00983069
$616$	−52.9787	−2.13457
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−0.881600	−0.0354631
$619$	−17.0773	−0.686397	−0.343198	−	0.939263i	$-0.611510\pi$
$619$	−17.0773	−0.686397	−0.343198	+	0.939263i	$0.611510\pi$
$620$	44.3359	1.78057
$621$	−0.260620	−0.0104583
$622$	−58.3377	−2.33913
$623$	9.96660	0.399303
$624$	0.992856	0.0397460
$625$	−15.1121	−0.604482
$626$	−82.3069	−3.28964
$627$	−0.0786553	−0.00314119
$628$	0.274887	0.0109692
$629$	1.04195	0.0415455
$630$	28.5522	1.13755
$631$	−23.7153	−0.944090	−0.472045	−	0.881574i	$-0.656484\pi$
$631$	−23.7153	−0.944090	−0.472045	+	0.881574i	$0.656484\pi$
$632$	−49.4895	−1.96858
$633$	−3.50213	−0.139197
$634$	20.5303	0.815363
$635$	20.2519	0.803674
$636$	−4.27447	−0.169494
$637$	2.95632	0.117134
$638$	109.981	4.35417
$639$	6.07837	0.240456
$640$	−20.2556	−0.800674
$641$	−39.0580	−1.54270	−0.771350	−	0.636411i	$-0.780418\pi$
$641$	−39.0580	−1.54270	−0.771350	+	0.636411i	$0.780418\pi$
$642$	5.12159	0.202133
$643$	4.75253	0.187421	0.0937107	−	0.995599i	$-0.470127\pi$
$643$	4.75253	0.187421	0.0937107	+	0.995599i	$0.470127\pi$
$644$	2.91745	0.114964
$645$	−2.01298	−0.0792612
$646$	0.0719643	0.00283140
$647$	21.4055	0.841537	0.420768	−	0.907168i	$-0.361760\pi$
$647$	21.4055	0.841537	0.420768	+	0.907168i	$0.361760\pi$
$648$	−56.6145	−2.22403
$649$	−31.9418	−1.25383
$650$	−3.87147	−0.151851
$651$	−1.43467	−0.0562291
$652$	31.5924	1.23725
$653$	13.1459	0.514440	0.257220	−	0.966353i	$-0.417193\pi$
$653$	13.1459	0.514440	0.257220	+	0.966353i	$0.417193\pi$
$654$	−1.02024	−0.0398945
$655$	−7.60107	−0.296998
$656$	−7.06665	−0.275906
$657$	32.7342	1.27708
$658$	−13.6624	−0.532617
$659$	1.00682	0.0392202	0.0196101	−	0.999808i	$-0.493758\pi$
$659$	1.00682	0.0392202	0.0196101	+	0.999808i	$0.493758\pi$
$660$	−4.68944	−0.182536
$661$	−35.7044	−1.38874	−0.694371	−	0.719618i	$-0.744317\pi$
$661$	−35.7044	−1.38874	−0.694371	+	0.719618i	$0.744317\pi$
$662$	−4.89992	−0.190441
$663$	0.0270575	0.00105083
$664$	−46.5898	−1.80804
$665$	−0.529926	−0.0205497
$666$	39.6929	1.53807
$667$	−3.37138	−0.130540
$668$	−10.9542	−0.423830
$669$	2.21929	0.0858026
$670$	16.0156	0.618738
$671$	−24.4016	−0.942013
$672$	−1.60316	−0.0618433
$673$	−32.6925	−1.26020	−0.630102	−	0.776512i	$-0.716987\pi$
$673$	−32.6925	−1.26020	−0.630102	+	0.776512i	$0.716987\pi$
$674$	3.56707	0.137398
$675$	−1.22951	−0.0473237
$676$	4.51121	0.173508
$677$	19.6112	0.753719	0.376859	−	0.926270i	$-0.377004\pi$
$677$	19.6112	0.753719	0.376859	+	0.926270i	$0.377004\pi$
$678$	5.49379	0.210988
$679$	−13.9934	−0.537019
$680$	2.38836	0.0915895
$681$	2.27970	0.0873581
$682$	−55.2495	−2.11561
$683$	−26.8551	−1.02758	−0.513791	−	0.857916i	$-0.671759\pi$
$683$	−26.8551	−1.02758	−0.513791	+	0.857916i	$0.671759\pi$
$684$	1.89938	0.0726247
$685$	−21.6675	−0.827873
$686$	−51.0879	−1.95055
$687$	1.85477	0.0707640
$688$	−58.3488	−2.22453
$689$	−6.99397	−0.266449
$690$	0.207483	0.00789873
$691$	−3.19957	−0.121717	−0.0608587	−	0.998146i	$-0.519384\pi$
$691$	−3.19957	−0.121717	−0.0608587	+	0.998146i	$0.519384\pi$
$692$	54.7889	2.08276
$693$	−24.6515	−0.936434
$694$	13.4921	0.512152
$695$	5.12797	0.194515
$696$	9.10050	0.344954
$697$	−0.192582	−0.00729455
$698$	−50.1930	−1.89983
$699$	0.463237	0.0175213
$700$	13.7634	0.520208
$701$	8.05904	0.304386	0.152193	−	0.988351i	$-0.451367\pi$
$701$	8.05904	0.304386	0.152193	+	0.988351i	$0.451367\pi$
$702$	2.06784	0.0780456
$703$	−0.736698	−0.0277851
$704$	−1.47524	−0.0556001
$705$	−0.673190	−0.0253538
$706$	−67.2130	−2.52959
$707$	−6.67445	−0.251018
$708$	−4.74809	−0.178444
$709$	39.0271	1.46569	0.732847	−	0.680393i	$-0.238191\pi$
$709$	39.0271	1.46569	0.732847	+	0.680393i	$0.238191\pi$
$710$	−9.70790	−0.364331
$711$	−23.0279	−0.863615
$712$	31.7594	1.19023
$713$	1.69364	0.0634272
$714$	−0.138838	−0.00519586
$715$	−7.67296	−0.286953
$716$	−39.5111	−1.47660
$717$	1.36246	0.0508818
$718$	49.2818	1.83918
$719$	−32.6226	−1.21662	−0.608309	−	0.793700i	$-0.708152\pi$
$719$	−32.6226	−1.21662	−0.608309	+	0.793700i	$0.708152\pi$
$720$	40.7794	1.51976
$721$	5.12818	0.190984
$722$	48.4316	1.80244
$723$	1.58545	0.0589635
$724$	87.4619	3.25050
$725$	−15.9049	−0.590693
$726$	2.04112	0.0757530
$727$	47.3923	1.75768	0.878842	−	0.477113i	$-0.158317\pi$
$727$	47.3923	1.75768	0.878842	+	0.477113i	$0.158317\pi$
$728$	−12.8855	−0.477569
$729$	−26.0139	−0.963479
$730$	−52.2806	−1.93499
$731$	−1.59013	−0.0588132
$732$	−3.62725	−0.134067
$733$	−19.1244	−0.706375	−0.353187	−	0.935553i	$-0.614902\pi$
$733$	−19.1244	−0.706375	−0.353187	+	0.935553i	$0.614902\pi$
$734$	−13.9949	−0.516562
$735$	−0.747448	−0.0275700
$736$	1.89254	0.0697600
$737$	−13.8277	−0.509349
$738$	−7.33634	−0.270054
$739$	3.51583	0.129332	0.0646659	−	0.997907i	$-0.479402\pi$
$739$	3.51583	0.129332	0.0646659	+	0.997907i	$0.479402\pi$
$740$	−43.9221	−1.61461
$741$	−0.0191306	−0.000702780 0
$742$	35.8874	1.31747
$743$	−18.8557	−0.691750	−0.345875	−	0.938281i	$-0.612418\pi$
$743$	−18.8557	−0.691750	−0.345875	+	0.938281i	$0.612418\pi$
$744$	−4.57170	−0.167607
$745$	−2.12170	−0.0777332
$746$	79.9870	2.92853
$747$	−21.6787	−0.793182
$748$	−3.70437	−0.135445
$749$	−29.7918	−1.08857
$750$	4.20457	0.153529
$751$	−16.3440	−0.596402	−0.298201	−	0.954503i	$-0.596387\pi$
$751$	−16.3440	−0.596402	−0.298201	+	0.954503i	$0.596387\pi$
$752$	−19.5133	−0.711575
$753$	0.558196	0.0203418
$754$	26.7496	0.974162
$755$	35.4599	1.29052
$756$	−7.35135	−0.267366
$757$	−18.8194	−0.684003	−0.342001	−	0.939699i	$-0.611105\pi$
$757$	−18.8194	−0.684003	−0.342001	+	0.939699i	$0.611105\pi$
$758$	25.1210	0.912437
$759$	−0.179137	−0.00650228
$760$	−1.68866	−0.0612540
$761$	−20.0254	−0.725921	−0.362960	−	0.931805i	$-0.618234\pi$
$761$	−20.0254	−0.725921	−0.362960	+	0.931805i	$0.618234\pi$
$762$	−3.75145	−0.135901
$763$	5.93464	0.214848
$764$	27.8316	1.00691
$765$	1.11133	0.0401802
$766$	−40.0877	−1.44843
$767$	−7.76891	−0.280519
$768$	3.84935	0.138902
$769$	−44.9620	−1.62137	−0.810685	−	0.585482i	$-0.800905\pi$
$769$	−44.9620	−1.62137	−0.810685	+	0.585482i	$0.800905\pi$
$770$	39.3715	1.41885
$771$	0.783744	0.0282258
$772$	68.6705	2.47151
$773$	−32.8590	−1.18186	−0.590928	−	0.806724i	$-0.701238\pi$
$773$	−32.8590	−1.18186	−0.590928	+	0.806724i	$0.701238\pi$
$774$	−60.5756	−2.17735
$775$	7.98993	0.287007
$776$	−44.5913	−1.60073
$777$	1.42128	0.0509882
$778$	33.6229	1.20544
$779$	0.136162	0.00487851
$780$	−1.14057	−0.0408390
$781$	8.38166	0.299919
$782$	0.163899	0.00586100
$783$	8.49517	0.303593
$784$	−21.6657	−0.773775
$785$	−0.113717	−0.00405874
$786$	1.40801	0.0502222
$787$	15.2805	0.544689	0.272345	−	0.962200i	$-0.412201\pi$
$787$	15.2805	0.544689	0.272345	+	0.962200i	$0.412201\pi$
$788$	−71.8333	−2.55896
$789$	3.31687	0.118084
$790$	36.7785	1.30852
$791$	−31.9569	−1.13626
$792$	−78.5542	−2.79130
$793$	−5.93498	−0.210757
$794$	−57.2619	−2.03215
$795$	1.76829	0.0627147
$796$	−77.8907	−2.76076
$797$	−39.8760	−1.41248	−0.706241	−	0.707972i	$-0.749610\pi$
$797$	−39.8760	−1.41248	−0.706241	+	0.707972i	$0.749610\pi$
$798$	0.0981630	0.00347493
$799$	−0.531779	−0.0188130
$800$	8.92829	0.315663
$801$	14.7780	0.522154
$802$	33.7485	1.19170
$803$	45.1383	1.59290
$804$	−2.05546	−0.0724903
$805$	−1.20691	−0.0425379
$806$	−13.4378	−0.473328
$807$	0.707266	0.0248969
$808$	−21.2687	−0.748230
$809$	−27.4377	−0.964659	−0.482329	−	0.875990i	$-0.660209\pi$
$809$	−27.4377	−0.964659	−0.482329	+	0.875990i	$0.660209\pi$
$810$	42.0735	1.47831
$811$	47.4160	1.66500	0.832500	−	0.554025i	$-0.186909\pi$
$811$	47.4160	1.66500	0.832500	+	0.554025i	$0.186909\pi$
$812$	−95.0971	−3.33726
$813$	0.462898	0.0162345
$814$	54.7339	1.91842
$815$	−13.0693	−0.457798
$816$	−0.198294	−0.00694166
$817$	1.12428	0.0393336
$818$	−27.8732	−0.974563
$819$	−5.99576	−0.209509
$820$	8.11801	0.283493
$821$	−49.5821	−1.73043	−0.865213	−	0.501404i	$-0.832817\pi$
$821$	−49.5821	−1.73043	−0.865213	+	0.501404i	$0.832817\pi$
$822$	4.01367	0.139993
$823$	−41.4379	−1.44443	−0.722217	−	0.691667i	$-0.756877\pi$
$823$	−41.4379	−1.44443	−0.722217	+	0.691667i	$0.756877\pi$
$824$	16.3414	0.569280
$825$	−0.845102	−0.0294227
$826$	39.8639	1.38704
$827$	−10.5308	−0.366192	−0.183096	−	0.983095i	$-0.558612\pi$
$827$	−10.5308	−0.366192	−0.183096	+	0.983095i	$0.558612\pi$
$828$	4.32585	0.150334
$829$	−55.2409	−1.91859	−0.959297	−	0.282398i	$-0.908870\pi$
$829$	−55.2409	−1.91859	−0.959297	+	0.282398i	$0.908870\pi$
$830$	34.6236	1.20180
$831$	−4.24007	−0.147086
$832$	−0.358808	−0.0124394
$833$	−0.590438	−0.0204575
$834$	−0.949899	−0.0328923
$835$	4.53159	0.156822
$836$	2.61912	0.0905842
$837$	−4.26761	−0.147510
$838$	12.2078	0.421712
$839$	−53.7709	−1.85638	−0.928189	−	0.372110i	$-0.878634\pi$
$839$	−53.7709	−1.85638	−0.928189	+	0.372110i	$0.878634\pi$
$840$	3.25785	0.112407
$841$	80.8936	2.78943
$842$	−79.0959	−2.72583
$843$	0.0375772	0.00129423
$844$	116.617	4.01411
$845$	−1.86622	−0.0642001
$846$	−20.2580	−0.696483
$847$	−11.8730	−0.407961
$848$	51.2560	1.76014
$849$	−2.32663	−0.0798498
$850$	0.773211	0.0265209
$851$	−1.67783	−0.0575153
$852$	1.24592	0.0426844
$853$	−13.6174	−0.466250	−0.233125	−	0.972447i	$-0.574895\pi$
$853$	−13.6174	−0.466250	−0.233125	+	0.972447i	$0.574895\pi$
$854$	30.4536	1.04210
$855$	−0.785748	−0.0268720
$856$	−94.9341	−3.24478
$857$	38.6197	1.31922	0.659612	−	0.751606i	$-0.270720\pi$
$857$	38.6197	1.31922	0.659612	+	0.751606i	$0.270720\pi$
$858$	1.42133	0.0485235
$859$	15.5824	0.531665	0.265832	−	0.964019i	$-0.414353\pi$
$859$	15.5824	0.531665	0.265832	+	0.964019i	$0.414353\pi$
$860$	67.0298	2.28570
$861$	−0.262692	−0.00895251
$862$	25.2411	0.859717
$863$	49.9055	1.69880	0.849401	−	0.527748i	$-0.176964\pi$
$863$	49.9055	1.69880	0.849401	+	0.527748i	$0.176964\pi$
$864$	−4.76880	−0.162238
$865$	−22.6654	−0.770646
$866$	16.9614	0.576371
$867$	2.29770	0.0780341
$868$	47.7727	1.62151
$869$	−31.7540	−1.07718
$870$	−6.76310	−0.229291
$871$	−3.36318	−0.113957
$872$	18.9112	0.640415
$873$	−20.7488	−0.702239
$874$	−0.115882	−0.00391977
$875$	−24.4576	−0.826817
$876$	6.70972	0.226700
$877$	27.7571	0.937292	0.468646	−	0.883386i	$-0.344742\pi$
$877$	27.7571	0.937292	0.468646	+	0.883386i	$0.344742\pi$
$878$	89.6388	3.02516
$879$	1.51752	0.0511846
$880$	56.2321	1.89558
$881$	−31.2193	−1.05181	−0.525903	−	0.850545i	$-0.676273\pi$
$881$	−31.2193	−1.05181	−0.525903	+	0.850545i	$0.676273\pi$
$882$	−22.4926	−0.757364
$883$	−13.8252	−0.465255	−0.232628	−	0.972566i	$-0.574732\pi$
$883$	−13.8252	−0.465255	−0.232628	+	0.972566i	$0.574732\pi$
$884$	−0.900981	−0.0303033
$885$	1.96422	0.0660264
$886$	−19.2833	−0.647837
$887$	−0.912318	−0.0306326	−0.0153163	−	0.999883i	$-0.504876\pi$
$887$	−0.912318	−0.0306326	−0.0153163	+	0.999883i	$0.504876\pi$
$888$	4.52903	0.151984
$889$	21.8218	0.731881
$890$	−23.6023	−0.791149
$891$	−36.3256	−1.21695
$892$	−73.8995	−2.47434
$893$	0.375986	0.0125819
$894$	0.393022	0.0131446
$895$	16.3452	0.546360
$896$	−21.8258	−0.729149
$897$	−0.0435700	−0.00145476
$898$	−46.5872	−1.55464
$899$	−55.2058	−1.84122
$900$	20.4077	0.680256
$901$	1.39684	0.0465354
$902$	−10.1163	−0.336837
$903$	−2.16903	−0.0721806
$904$	−101.833	−3.38693
$905$	−36.1818	−1.20272
$906$	−6.56856	−0.218226
$907$	−10.0615	−0.334088	−0.167044	−	0.985949i	$-0.553422\pi$
$907$	−10.0615	−0.334088	−0.167044	+	0.985949i	$0.553422\pi$
$908$	−75.9110	−2.51920
$909$	−9.89653	−0.328247
$910$	9.57597	0.317440
$911$	8.86364	0.293665	0.146833	−	0.989161i	$-0.453092\pi$
$911$	8.86364	0.293665	0.146833	+	0.989161i	$0.453092\pi$
$912$	0.140200	0.00464250
$913$	−29.8935	−0.989329
$914$	84.5533	2.79678
$915$	1.50054	0.0496064
$916$	−61.7616	−2.04066
$917$	−8.19028	−0.270467
$918$	−0.412990	−0.0136307
$919$	5.38226	0.177544	0.0887722	−	0.996052i	$-0.471706\pi$
$919$	5.38226	0.177544	0.0887722	+	0.996052i	$0.471706\pi$
$920$	−3.84592	−0.126796
$921$	−0.334740	−0.0110301
$922$	−14.4823	−0.476950
$923$	2.03859	0.0671011
$924$	−5.05296	−0.166230
$925$	−7.91537	−0.260256
$926$	60.8233	1.99878
$927$	7.60381	0.249742
$928$	−61.6893	−2.02505
$929$	−12.0045	−0.393854	−0.196927	−	0.980418i	$-0.563096\pi$
$929$	−12.0045	−0.393854	−0.196927	+	0.980418i	$0.563096\pi$
$930$	3.39749	0.111408
$931$	0.417460	0.0136817
$932$	−15.4252	−0.505270
$933$	−3.09730	−0.101401
$934$	−5.48181	−0.179370
$935$	1.53245	0.0501164
$936$	−19.1060	−0.624499
$937$	−52.1051	−1.70220	−0.851100	−	0.525003i	$-0.824064\pi$
$937$	−52.1051	−1.70220	−0.851100	+	0.525003i	$0.824064\pi$
$938$	17.2571	0.563466
$939$	−4.36989	−0.142606
$940$	22.4164	0.731142
$941$	19.6922	0.641946	0.320973	−	0.947088i	$-0.395990\pi$
$941$	19.6922	0.641946	0.320973	+	0.947088i	$0.395990\pi$
$942$	0.0210648	0.000686329 0
$943$	0.310109	0.0100985
$944$	56.9352	1.85308
$945$	3.04115	0.0989287
$946$	−83.5298	−2.71579
$947$	5.88879	0.191360	0.0956800	−	0.995412i	$-0.469497\pi$
$947$	5.88879	0.191360	0.0956800	+	0.995412i	$0.469497\pi$
$948$	−4.72016	−0.153304
$949$	10.9786	0.356380
$950$	−0.546687	−0.0177369
$951$	1.09001	0.0353460
$952$	2.57350	0.0834077
$953$	35.1869	1.13982	0.569908	−	0.821708i	$-0.306979\pi$
$953$	35.1869	1.13982	0.569908	+	0.821708i	$0.306979\pi$
$954$	53.2121	1.72281
$955$	−11.5135	−0.372569
$956$	−45.3680	−1.46731
$957$	5.83916	0.188753
$958$	−35.9374	−1.16108
$959$	−23.3471	−0.753918
$960$	0.0907176	0.00292790
$961$	−3.26700	−0.105387
$962$	13.3124	0.429210
$963$	−44.1738	−1.42348
$964$	−52.7935	−1.70036
$965$	−28.4080	−0.914487
$966$	0.223566	0.00719313
$967$	41.3097	1.32843	0.664216	−	0.747541i	$-0.268766\pi$
$967$	41.3097	1.32843	0.664216	+	0.747541i	$0.268766\pi$
$968$	−37.8343	−1.21604
$969$	0.00382077	0.000122741 0
$970$	33.1383	1.06401
$971$	−23.8721	−0.766094	−0.383047	−	0.923729i	$-0.625125\pi$
$971$	−23.8721	−0.766094	−0.383047	+	0.923729i	$0.625125\pi$
$972$	−16.3670	−0.524973
$973$	5.52548	0.177139
$974$	51.7870	1.65936
$975$	−0.205546	−0.00658276
$976$	43.4951	1.39224
$977$	0.0853342	0.00273008	0.00136504	−	0.999999i	$-0.499565\pi$
$977$	0.0853342	0.00273008	0.00136504	+	0.999999i	$0.499565\pi$
$978$	2.42095	0.0774134
$979$	20.3778	0.651278
$980$	24.8891	0.795052
$981$	8.79959	0.280949
$982$	−25.3867	−0.810121
$983$	−33.5044	−1.06862	−0.534312	−	0.845287i	$-0.679429\pi$
$983$	−33.5044	−1.06862	−0.534312	+	0.845287i	$0.679429\pi$
$984$	−0.837089	−0.0266854
$985$	29.7164	0.946845
$986$	−5.34244	−0.170138
$987$	−0.725375	−0.0230889
$988$	0.637025	0.0202665
$989$	2.56055	0.0814207
$990$	58.3781	1.85538
$991$	−52.1746	−1.65738	−0.828690	−	0.559708i	$-0.810913\pi$
$991$	−52.1746	−1.65738	−0.828690	+	0.559708i	$0.810913\pi$
$992$	30.9900	0.983934
$993$	−0.260150	−0.00825561
$994$	−10.4604	−0.331785
$995$	32.2223	1.02151
$996$	−4.44360	−0.140801
$997$	−32.2408	−1.02108	−0.510538	−	0.859855i	$-0.670554\pi$
$997$	−32.2408	−1.02108	−0.510538	+	0.859855i	$0.670554\pi$
$998$	−36.1876	−1.14550
$999$	4.22778	0.133761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.7	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.55171 q^{2} -0.135477 q^{3} +4.51121 q^{4} -1.86622 q^{5} +0.345697 q^{6} -2.01089 q^{7} -6.40787 q^{8} -2.98165 q^{9} +O(q^{10})\)	\(q-2.55171 q^{2} -0.135477 q^{3} +4.51121 q^{4} -1.86622 q^{5} +0.345697 q^{6} -2.01089 q^{7} -6.40787 q^{8} -2.98165 q^{9} +4.76206 q^{10} -4.11149 q^{11} -0.611165 q^{12} -1.00000 q^{13} +5.13120 q^{14} +0.252830 q^{15} +7.32860 q^{16} +0.199720 q^{17} +7.60829 q^{18} -0.141209 q^{19} -8.41893 q^{20} +0.272429 q^{21} +10.4913 q^{22} -0.321604 q^{23} +0.868119 q^{24} -1.51721 q^{25} +2.55171 q^{26} +0.810375 q^{27} -9.07155 q^{28} +10.4830 q^{29} -0.645149 q^{30} -5.26621 q^{31} -5.88469 q^{32} +0.557012 q^{33} -0.509628 q^{34} +3.75277 q^{35} -13.4508 q^{36} +5.21707 q^{37} +0.360325 q^{38} +0.135477 q^{39} +11.9585 q^{40} -0.964257 q^{41} -0.695159 q^{42} -7.96180 q^{43} -18.5478 q^{44} +5.56442 q^{45} +0.820640 q^{46} -2.66262 q^{47} -0.992856 q^{48} -2.95632 q^{49} +3.87147 q^{50} -0.0270575 q^{51} -4.51121 q^{52} +6.99397 q^{53} -2.06784 q^{54} +7.67296 q^{55} +12.8855 q^{56} +0.0191306 q^{57} -26.7496 q^{58} +7.76891 q^{59} +1.14057 q^{60} +5.93498 q^{61} +13.4378 q^{62} +5.99576 q^{63} +0.358808 q^{64} +1.86622 q^{65} -1.42133 q^{66} +3.36318 q^{67} +0.900981 q^{68} +0.0435700 q^{69} -9.57597 q^{70} -2.03859 q^{71} +19.1060 q^{72} -10.9786 q^{73} -13.3124 q^{74} +0.205546 q^{75} -0.637025 q^{76} +8.26775 q^{77} -0.345697 q^{78} +7.72323 q^{79} -13.6768 q^{80} +8.83515 q^{81} +2.46050 q^{82} +7.27071 q^{83} +1.22899 q^{84} -0.372723 q^{85} +20.3162 q^{86} -1.42021 q^{87} +26.3459 q^{88} -4.95631 q^{89} -14.1988 q^{90} +2.01089 q^{91} -1.45083 q^{92} +0.713450 q^{93} +6.79422 q^{94} +0.263528 q^{95} +0.797239 q^{96} +6.95883 q^{97} +7.54367 q^{98} +12.2590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 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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