LMFDB - Embedded newform 8035.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31791 q^{2} +3.17051 q^{3} +3.37269 q^{4} -1.00000 q^{5} -7.34893 q^{6} +3.65453 q^{7} -3.18176 q^{8} +7.05211 q^{9} +O(q^{10})$	\(q-2.31791 q^{2} +3.17051 q^{3} +3.37269 q^{4} -1.00000 q^{5} -7.34893 q^{6} +3.65453 q^{7} -3.18176 q^{8} +7.05211 q^{9} +2.31791 q^{10} -5.54919 q^{11} +10.6931 q^{12} +1.46317 q^{13} -8.47086 q^{14} -3.17051 q^{15} +0.629651 q^{16} -6.00077 q^{17} -16.3461 q^{18} +1.05071 q^{19} -3.37269 q^{20} +11.5867 q^{21} +12.8625 q^{22} +8.91463 q^{23} -10.0878 q^{24} +1.00000 q^{25} -3.39150 q^{26} +12.8472 q^{27} +12.3256 q^{28} -10.1975 q^{29} +7.34893 q^{30} -4.33136 q^{31} +4.90405 q^{32} -17.5937 q^{33} +13.9092 q^{34} -3.65453 q^{35} +23.7846 q^{36} -5.79001 q^{37} -2.43546 q^{38} +4.63900 q^{39} +3.18176 q^{40} -8.73572 q^{41} -26.8569 q^{42} -11.4782 q^{43} -18.7157 q^{44} -7.05211 q^{45} -20.6633 q^{46} -3.09613 q^{47} +1.99631 q^{48} +6.35560 q^{49} -2.31791 q^{50} -19.0255 q^{51} +4.93483 q^{52} -7.27836 q^{53} -29.7787 q^{54} +5.54919 q^{55} -11.6279 q^{56} +3.33130 q^{57} +23.6368 q^{58} -2.85583 q^{59} -10.6931 q^{60} -9.39003 q^{61} +10.0397 q^{62} +25.7722 q^{63} -12.6264 q^{64} -1.46317 q^{65} +40.7807 q^{66} +9.52880 q^{67} -20.2387 q^{68} +28.2639 q^{69} +8.47086 q^{70} +0.485593 q^{71} -22.4381 q^{72} -5.03481 q^{73} +13.4207 q^{74} +3.17051 q^{75} +3.54373 q^{76} -20.2797 q^{77} -10.7528 q^{78} -7.89061 q^{79} -0.629651 q^{80} +19.5759 q^{81} +20.2486 q^{82} +8.96749 q^{83} +39.0784 q^{84} +6.00077 q^{85} +26.6053 q^{86} -32.3312 q^{87} +17.6562 q^{88} -10.8858 q^{89} +16.3461 q^{90} +5.34722 q^{91} +30.0663 q^{92} -13.7326 q^{93} +7.17655 q^{94} -1.05071 q^{95} +15.5483 q^{96} +10.1807 q^{97} -14.7317 q^{98} -39.1335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.31791	−1.63901	−0.819504	−	0.573074i	$-0.805751\pi$
$2$	−2.31791	−1.63901	−0.819504	+	0.573074i	$0.805751\pi$
$3$	3.17051	1.83049	0.915246	−	0.402895i	$-0.131996\pi$
$3$	3.17051	1.83049	0.915246	+	0.402895i	$0.131996\pi$
$4$	3.37269	1.68634
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−7.34893	−3.00019
$7$	3.65453	1.38128	0.690642	−	0.723197i	$-0.257328\pi$
$7$	3.65453	1.38128	0.690642	+	0.723197i	$0.257328\pi$
$8$	−3.18176	−1.12492
$9$	7.05211	2.35070
$10$	2.31791	0.732986
$11$	−5.54919	−1.67314	−0.836572	−	0.547857i	$-0.815444\pi$
$11$	−5.54919	−1.67314	−0.836572	+	0.547857i	$0.815444\pi$
$12$	10.6931	3.08684
$13$	1.46317	0.405811	0.202906	−	0.979198i	$-0.434962\pi$
$13$	1.46317	0.405811	0.202906	+	0.979198i	$0.434962\pi$
$14$	−8.47086	−2.26393
$15$	−3.17051	−0.818621
$16$	0.629651	0.157413
$17$	−6.00077	−1.45540	−0.727700	−	0.685896i	$-0.759411\pi$
$17$	−6.00077	−1.45540	−0.727700	+	0.685896i	$0.759411\pi$
$18$	−16.3461	−3.85282
$19$	1.05071	0.241051	0.120525	−	0.992710i	$-0.461542\pi$
$19$	1.05071	0.241051	0.120525	+	0.992710i	$0.461542\pi$
$20$	−3.37269	−0.754156
$21$	11.5867	2.52843
$22$	12.8625	2.74230
$23$	8.91463	1.85883	0.929414	−	0.369038i	$-0.120313\pi$
$23$	8.91463	1.85883	0.929414	+	0.369038i	$0.120313\pi$
$24$	−10.0878	−2.05916
$25$	1.00000	0.200000
$26$	−3.39150	−0.665128
$27$	12.8472	2.47245
$28$	12.3256	2.32932
$29$	−10.1975	−1.89363	−0.946813	−	0.321783i	$-0.895718\pi$
$29$	−10.1975	−1.89363	−0.946813	+	0.321783i	$0.895718\pi$
$30$	7.34893	1.34173
$31$	−4.33136	−0.777936	−0.388968	−	0.921251i	$-0.627168\pi$
$31$	−4.33136	−0.777936	−0.388968	+	0.921251i	$0.627168\pi$
$32$	4.90405	0.866922
$33$	−17.5937	−3.06268
$34$	13.9092	2.38541
$35$	−3.65453	−0.617729
$36$	23.7846	3.96409
$37$	−5.79001	−0.951872	−0.475936	−	0.879480i	$-0.657891\pi$
$37$	−5.79001	−0.951872	−0.475936	+	0.879480i	$0.657891\pi$
$38$	−2.43546	−0.395084
$39$	4.63900	0.742835
$40$	3.18176	0.503081
$41$	−8.73572	−1.36429	−0.682145	−	0.731217i	$-0.738953\pi$
$41$	−8.73572	−1.36429	−0.682145	+	0.731217i	$0.738953\pi$
$42$	−26.8569	−4.14411
$43$	−11.4782	−1.75040	−0.875202	−	0.483758i	$-0.839271\pi$
$43$	−11.4782	−1.75040	−0.875202	+	0.483758i	$0.839271\pi$
$44$	−18.7157	−2.82150
$45$	−7.05211	−1.05127
$46$	−20.6633	−3.04663
$47$	−3.09613	−0.451617	−0.225809	−	0.974172i	$-0.572502\pi$
$47$	−3.09613	−0.451617	−0.225809	+	0.974172i	$0.572502\pi$
$48$	1.99631	0.288143
$49$	6.35560	0.907943
$50$	−2.31791	−0.327801
$51$	−19.0255	−2.66410
$52$	4.93483	0.684338
$53$	−7.27836	−0.999759	−0.499879	−	0.866095i	$-0.666622\pi$
$53$	−7.27836	−0.999759	−0.499879	+	0.866095i	$0.666622\pi$
$54$	−29.7787	−4.05236
$55$	5.54919	0.748253
$56$	−11.6279	−1.55384
$57$	3.33130	0.441241
$58$	23.6368	3.10367
$59$	−2.85583	−0.371797	−0.185899	−	0.982569i	$-0.559520\pi$
$59$	−2.85583	−0.371797	−0.185899	+	0.982569i	$0.559520\pi$
$60$	−10.6931	−1.38048
$61$	−9.39003	−1.20227	−0.601135	−	0.799147i	$-0.705285\pi$
$61$	−9.39003	−1.20227	−0.601135	+	0.799147i	$0.705285\pi$
$62$	10.0397	1.27504
$63$	25.7722	3.24699
$64$	−12.6264	−1.57830
$65$	−1.46317	−0.181484
$66$	40.7807	5.01975
$67$	9.52880	1.16413	0.582064	−	0.813143i	$-0.302245\pi$
$67$	9.52880	1.16413	0.582064	+	0.813143i	$0.302245\pi$
$68$	−20.2387	−2.45431
$69$	28.2639	3.40257
$70$	8.47086	1.01246
$71$	0.485593	0.0576293	0.0288147	−	0.999585i	$-0.490827\pi$
$71$	0.485593	0.0576293	0.0288147	+	0.999585i	$0.490827\pi$
$72$	−22.4381	−2.64436
$73$	−5.03481	−0.589279	−0.294640	−	0.955608i	$-0.595200\pi$
$73$	−5.03481	−0.589279	−0.294640	+	0.955608i	$0.595200\pi$
$74$	13.4207	1.56012
$75$	3.17051	0.366098
$76$	3.54373	0.406494
$77$	−20.2797	−2.31109
$78$	−10.7528	−1.21751
$79$	−7.89061	−0.887763	−0.443882	−	0.896085i	$-0.646399\pi$
$79$	−7.89061	−0.887763	−0.443882	+	0.896085i	$0.646399\pi$
$80$	−0.629651	−0.0703971
$81$	19.5759	2.17510
$82$	20.2486	2.23608
$83$	8.96749	0.984309	0.492155	−	0.870508i	$-0.336209\pi$
$83$	8.96749	0.984309	0.492155	+	0.870508i	$0.336209\pi$
$84$	39.0784	4.26380
$85$	6.00077	0.650875
$86$	26.6053	2.86892
$87$	−32.3312	−3.46627
$88$	17.6562	1.88216
$89$	−10.8858	−1.15389	−0.576945	−	0.816783i	$-0.695755\pi$
$89$	−10.8858	−1.15389	−0.576945	+	0.816783i	$0.695755\pi$
$90$	16.3461	1.72303
$91$	5.34722	0.560541
$92$	30.0663	3.13462
$93$	−13.7326	−1.42401
$94$	7.17655	0.740204
$95$	−1.05071	−0.107801
$96$	15.5483	1.58690
$97$	10.1807	1.03370	0.516849	−	0.856077i	$-0.327105\pi$
$97$	10.1807	1.03370	0.516849	+	0.856077i	$0.327105\pi$
$98$	−14.7317	−1.48813
$99$	−39.1335	−3.93307
$100$	3.37269	0.337269
$101$	−9.82247	−0.977372	−0.488686	−	0.872460i	$-0.662524\pi$
$101$	−9.82247	−0.977372	−0.488686	+	0.872460i	$0.662524\pi$
$102$	44.0993	4.36648
$103$	8.07564	0.795716	0.397858	−	0.917447i	$-0.369754\pi$
$103$	8.07564	0.795716	0.397858	+	0.917447i	$0.369754\pi$
$104$	−4.65547	−0.456507
$105$	−11.5867	−1.13075
$106$	16.8705	1.63861
$107$	4.63446	0.448030	0.224015	−	0.974586i	$-0.428083\pi$
$107$	4.63446	0.448030	0.224015	+	0.974586i	$0.428083\pi$
$108$	43.3297	4.16940
$109$	−16.3174	−1.56292	−0.781459	−	0.623956i	$-0.785524\pi$
$109$	−16.3174	−1.56292	−0.781459	+	0.623956i	$0.785524\pi$
$110$	−12.8625	−1.22639
$111$	−18.3573	−1.74239
$112$	2.30108	0.217432
$113$	5.89865	0.554898	0.277449	−	0.960740i	$-0.410511\pi$
$113$	5.89865	0.554898	0.277449	+	0.960740i	$0.410511\pi$
$114$	−7.72164	−0.723197
$115$	−8.91463	−0.831293
$116$	−34.3930	−3.19331
$117$	10.3185	0.953942
$118$	6.61954	0.609378
$119$	−21.9300	−2.01032
$120$	10.0878	0.920886
$121$	19.7935	1.79941
$122$	21.7652	1.97053
$123$	−27.6966	−2.49732
$124$	−14.6083	−1.31187
$125$	−1.00000	−0.0894427
$126$	−59.7374	−5.32183
$127$	16.0448	1.42375	0.711873	−	0.702308i	$-0.247847\pi$
$127$	16.0448	1.42375	0.711873	+	0.702308i	$0.247847\pi$
$128$	19.4588	1.71993
$129$	−36.3916	−3.20410
$130$	3.39150	0.297454
$131$	−14.0574	−1.22820	−0.614102	−	0.789227i	$-0.710482\pi$
$131$	−14.0574	−1.22820	−0.614102	+	0.789227i	$0.710482\pi$
$132$	−59.3382	−5.16473
$133$	3.83987	0.332959
$134$	−22.0869	−1.90801
$135$	−12.8472	−1.10571
$136$	19.0930	1.63721
$137$	4.24354	0.362550	0.181275	−	0.983432i	$-0.441978\pi$
$137$	4.24354	0.362550	0.181275	+	0.983432i	$0.441978\pi$
$138$	−65.5130	−5.57684
$139$	−20.5492	−1.74296	−0.871479	−	0.490433i	$-0.836839\pi$
$139$	−20.5492	−1.74296	−0.871479	+	0.490433i	$0.836839\pi$
$140$	−12.3256	−1.04170
$141$	−9.81631	−0.826682
$142$	−1.12556	−0.0944549
$143$	−8.11943	−0.678981
$144$	4.44037	0.370031
$145$	10.1975	0.846856
$146$	11.6702	0.965833
$147$	20.1505	1.66198
$148$	−19.5279	−1.60518
$149$	13.5579	1.11071	0.555354	−	0.831614i	$-0.312583\pi$
$149$	13.5579	1.11071	0.555354	+	0.831614i	$0.312583\pi$
$150$	−7.34893	−0.600038
$151$	9.17256	0.746452	0.373226	−	0.927740i	$-0.378252\pi$
$151$	9.17256	0.746452	0.373226	+	0.927740i	$0.378252\pi$
$152$	−3.34313	−0.271163
$153$	−42.3181	−3.42121
$154$	47.0064	3.78789
$155$	4.33136	0.347903
$156$	15.6459	1.25268
$157$	17.5280	1.39889	0.699445	−	0.714686i	$-0.253430\pi$
$157$	17.5280	1.39889	0.699445	+	0.714686i	$0.253430\pi$
$158$	18.2897	1.45505
$159$	−23.0761	−1.83005
$160$	−4.90405	−0.387700
$161$	32.5788	2.56757
$162$	−45.3751	−3.56500
$163$	−20.3423	−1.59334	−0.796668	−	0.604418i	$-0.793406\pi$
$163$	−20.3423	−1.59334	−0.796668	+	0.604418i	$0.793406\pi$
$164$	−29.4628	−2.30066
$165$	17.5937	1.36967
$166$	−20.7858	−1.61329
$167$	0.442601	0.0342495	0.0171247	−	0.999853i	$-0.494549\pi$
$167$	0.442601	0.0342495	0.0171247	+	0.999853i	$0.494549\pi$
$168$	−36.8662	−2.84429
$169$	−10.8591	−0.835317
$170$	−13.9092	−1.06679
$171$	7.40976	0.566638
$172$	−38.7123	−2.95178
$173$	−14.1772	−1.07787	−0.538935	−	0.842347i	$-0.681173\pi$
$173$	−14.1772	−1.07787	−0.538935	+	0.842347i	$0.681173\pi$
$174$	74.9407	5.68124
$175$	3.65453	0.276257
$176$	−3.49406	−0.263374
$177$	−9.05442	−0.680572
$178$	25.2322	1.89123
$179$	−2.39139	−0.178741	−0.0893705	−	0.995998i	$-0.528486\pi$
$179$	−2.39139	−0.178741	−0.0893705	+	0.995998i	$0.528486\pi$
$180$	−23.7846	−1.77280
$181$	21.0849	1.56723	0.783613	−	0.621249i	$-0.213374\pi$
$181$	21.0849	1.56723	0.783613	+	0.621249i	$0.213374\pi$
$182$	−12.3943	−0.918730
$183$	−29.7711	−2.20075
$184$	−28.3642	−2.09104
$185$	5.79001	0.425690
$186$	31.8309	2.33396
$187$	33.2994	2.43509
$188$	−10.4423	−0.761582
$189$	46.9506	3.41515
$190$	2.43546	0.176687
$191$	−12.5242	−0.906218	−0.453109	−	0.891455i	$-0.649685\pi$
$191$	−12.5242	−0.906218	−0.453109	+	0.891455i	$0.649685\pi$
$192$	−40.0322	−2.88908
$193$	13.5966	0.978703	0.489351	−	0.872087i	$-0.337234\pi$
$193$	13.5966	0.978703	0.489351	+	0.872087i	$0.337234\pi$
$194$	−23.5980	−1.69424
$195$	−4.63900	−0.332206
$196$	21.4355	1.53110
$197$	6.70337	0.477595	0.238798	−	0.971069i	$-0.423247\pi$
$197$	6.70337	0.477595	0.238798	+	0.971069i	$0.423247\pi$
$198$	90.7078	6.44632
$199$	−3.07994	−0.218331	−0.109165	−	0.994024i	$-0.534818\pi$
$199$	−3.07994	−0.218331	−0.109165	+	0.994024i	$0.534818\pi$
$200$	−3.18176	−0.224985
$201$	30.2111	2.13093
$202$	22.7676	1.60192
$203$	−37.2671	−2.61563
$204$	−64.1670	−4.49259
$205$	8.73572	0.610129
$206$	−18.7186	−1.30418
$207$	62.8669	4.36955
$208$	0.921289	0.0638799
$209$	−5.83062	−0.403312
$210$	26.8569	1.85330
$211$	7.86046	0.541136	0.270568	−	0.962701i	$-0.412788\pi$
$211$	7.86046	0.541136	0.270568	+	0.962701i	$0.412788\pi$
$212$	−24.5476	−1.68594
$213$	1.53958	0.105490
$214$	−10.7423	−0.734325
$215$	11.4782	0.782804
$216$	−40.8769	−2.78132
$217$	−15.8291	−1.07455
$218$	37.8221	2.56164
$219$	−15.9629	−1.07867
$220$	18.7157	1.26181
$221$	−8.78017	−0.590618
$222$	42.5504	2.85580
$223$	24.4427	1.63681	0.818404	−	0.574644i	$-0.194859\pi$
$223$	24.4427	1.63681	0.818404	+	0.574644i	$0.194859\pi$
$224$	17.9220	1.19747
$225$	7.05211	0.470141
$226$	−13.6725	−0.909482
$227$	−19.9407	−1.32351	−0.661757	−	0.749718i	$-0.730189\pi$
$227$	−19.9407	−1.32351	−0.661757	+	0.749718i	$0.730189\pi$
$228$	11.2354	0.744085
$229$	14.4545	0.955179	0.477589	−	0.878583i	$-0.341511\pi$
$229$	14.4545	0.955179	0.477589	+	0.878583i	$0.341511\pi$
$230$	20.6633	1.36250
$231$	−64.2969	−4.23043
$232$	32.4460	2.13018
$233$	−20.7741	−1.36096	−0.680478	−	0.732769i	$-0.738228\pi$
$233$	−20.7741	−1.36096	−0.680478	+	0.732769i	$0.738228\pi$
$234$	−23.9172	−1.56352
$235$	3.09613	0.201969
$236$	−9.63182	−0.626978
$237$	−25.0172	−1.62504
$238$	50.8317	3.29493
$239$	−5.56166	−0.359754	−0.179877	−	0.983689i	$-0.557570\pi$
$239$	−5.56166	−0.359754	−0.179877	+	0.983689i	$0.557570\pi$
$240$	−1.99631	−0.128861
$241$	12.6607	0.815547	0.407773	−	0.913083i	$-0.366305\pi$
$241$	12.6607	0.815547	0.407773	+	0.913083i	$0.366305\pi$
$242$	−45.8796	−2.94925
$243$	23.5238	1.50905
$244$	−31.6697	−2.02744
$245$	−6.35560	−0.406045
$246$	64.1982	4.09313
$247$	1.53738	0.0978211
$248$	13.7814	0.875118
$249$	28.4315	1.80177
$250$	2.31791	0.146597
$251$	−13.8175	−0.872150	−0.436075	−	0.899910i	$-0.643632\pi$
$251$	−13.8175	−0.872150	−0.436075	+	0.899910i	$0.643632\pi$
$252$	86.9214	5.47554
$253$	−49.4690	−3.11009
$254$	−37.1904	−2.33353
$255$	19.0255	1.19142
$256$	−19.8508	−1.24067
$257$	−2.90418	−0.181158	−0.0905789	−	0.995889i	$-0.528872\pi$
$257$	−2.90418	−0.181158	−0.0905789	+	0.995889i	$0.528872\pi$
$258$	84.3523	5.25154
$259$	−21.1598	−1.31480
$260$	−4.93483	−0.306045
$261$	−71.9138	−4.45135
$262$	32.5838	2.01304
$263$	−1.37155	−0.0845731	−0.0422865	−	0.999106i	$-0.513464\pi$
$263$	−1.37155	−0.0845731	−0.0422865	+	0.999106i	$0.513464\pi$
$264$	55.9791	3.44528
$265$	7.27836	0.447106
$266$	−8.90046	−0.545722
$267$	−34.5134	−2.11219
$268$	32.1377	1.96312
$269$	3.66153	0.223247	0.111624	−	0.993751i	$-0.464395\pi$
$269$	3.66153	0.223247	0.111624	+	0.993751i	$0.464395\pi$
$270$	29.7787	1.81227
$271$	−11.0897	−0.673648	−0.336824	−	0.941568i	$-0.609353\pi$
$271$	−11.0897	−0.673648	−0.336824	+	0.941568i	$0.609353\pi$
$272$	−3.77839	−0.229099
$273$	16.9534	1.02607
$274$	−9.83614	−0.594223
$275$	−5.54919	−0.334629
$276$	95.3253	5.73791
$277$	26.0519	1.56530	0.782652	−	0.622459i	$-0.213866\pi$
$277$	26.0519	1.56530	0.782652	+	0.622459i	$0.213866\pi$
$278$	47.6311	2.85672
$279$	−30.5452	−1.82870
$280$	11.6279	0.694897
$281$	19.6432	1.17182	0.585908	−	0.810378i	$-0.300738\pi$
$281$	19.6432	1.17182	0.585908	+	0.810378i	$0.300738\pi$
$282$	22.7533	1.35494
$283$	−6.32178	−0.375791	−0.187895	−	0.982189i	$-0.560167\pi$
$283$	−6.32178	−0.375791	−0.187895	+	0.982189i	$0.560167\pi$
$284$	1.63775	0.0971829
$285$	−3.33130	−0.197329
$286$	18.8201	1.11285
$287$	−31.9250	−1.88447
$288$	34.5839	2.03788
$289$	19.0092	1.11819
$290$	−23.6368	−1.38800
$291$	32.2781	1.89218
$292$	−16.9808	−0.993728
$293$	21.5729	1.26030	0.630152	−	0.776472i	$-0.282993\pi$
$293$	21.5729	1.26030	0.630152	+	0.776472i	$0.282993\pi$
$294$	−46.7069	−2.72400
$295$	2.85583	0.166273
$296$	18.4224	1.07078
$297$	−71.2918	−4.13677
$298$	−31.4260	−1.82046
$299$	13.0437	0.754334
$300$	10.6931	0.617368
$301$	−41.9473	−2.41780
$302$	−21.2611	−1.22344
$303$	−31.1422	−1.78907
$304$	0.661584	0.0379444
$305$	9.39003	0.537672
$306$	98.0893	5.60739
$307$	−2.27296	−0.129725	−0.0648625	−	0.997894i	$-0.520661\pi$
$307$	−2.27296	−0.129725	−0.0648625	+	0.997894i	$0.520661\pi$
$308$	−68.3971	−3.89729
$309$	25.6039	1.45655
$310$	−10.0397	−0.570216
$311$	12.5621	0.712329	0.356165	−	0.934423i	$-0.384084\pi$
$311$	12.5621	0.712329	0.356165	+	0.934423i	$0.384084\pi$
$312$	−14.7602	−0.835632
$313$	−19.2743	−1.08945	−0.544724	−	0.838615i	$-0.683366\pi$
$313$	−19.2743	−1.08945	−0.544724	+	0.838615i	$0.683366\pi$
$314$	−40.6284	−2.29279
$315$	−25.7722	−1.45210
$316$	−26.6126	−1.49707
$317$	4.66448	0.261983	0.130992	−	0.991383i	$-0.458184\pi$
$317$	4.66448	0.261983	0.130992	+	0.991383i	$0.458184\pi$
$318$	53.4882	2.99947
$319$	56.5878	3.16831
$320$	12.6264	0.705839
$321$	14.6936	0.820116
$322$	−75.5146	−4.20826
$323$	−6.30510	−0.350825
$324$	66.0234	3.66797
$325$	1.46317	0.0811623
$326$	47.1516	2.61149
$327$	−51.7343	−2.86091
$328$	27.7950	1.53472
$329$	−11.3149	−0.623812
$330$	−40.7807	−2.24490
$331$	−10.6074	−0.583034	−0.291517	−	0.956566i	$-0.594160\pi$
$331$	−10.6074	−0.583034	−0.291517	+	0.956566i	$0.594160\pi$
$332$	30.2445	1.65988
$333$	−40.8318	−2.23757
$334$	−1.02591	−0.0561351
$335$	−9.52880	−0.520614
$336$	7.29559	0.398007
$337$	−25.5917	−1.39407	−0.697034	−	0.717038i	$-0.745497\pi$
$337$	−25.5917	−1.39407	−0.697034	+	0.717038i	$0.745497\pi$
$338$	25.1704	1.36909
$339$	18.7017	1.01574
$340$	20.2387	1.09760
$341$	24.0356	1.30160
$342$	−17.1751	−0.928724
$343$	−2.35497	−0.127156
$344$	36.5208	1.96907
$345$	−28.2639	−1.52168
$346$	32.8613	1.76664
$347$	29.8076	1.60016	0.800078	−	0.599896i	$-0.204791\pi$
$347$	29.8076	1.60016	0.800078	+	0.599896i	$0.204791\pi$
$348$	−109.043	−5.84532
$349$	11.4502	0.612914	0.306457	−	0.951884i	$-0.400856\pi$
$349$	11.4502	0.612914	0.306457	+	0.951884i	$0.400856\pi$
$350$	−8.47086	−0.452787
$351$	18.7977	1.00335
$352$	−27.2135	−1.45049
$353$	18.9561	1.00893	0.504467	−	0.863431i	$-0.331689\pi$
$353$	18.9561	1.00893	0.504467	+	0.863431i	$0.331689\pi$
$354$	20.9873	1.11546
$355$	−0.485593	−0.0257726
$356$	−36.7143	−1.94586
$357$	−69.5292	−3.67987
$358$	5.54302	0.292958
$359$	13.0808	0.690380	0.345190	−	0.938533i	$-0.387814\pi$
$359$	13.0808	0.690380	0.345190	+	0.938533i	$0.387814\pi$
$360$	22.4381	1.18259
$361$	−17.8960	−0.941895
$362$	−48.8728	−2.56870
$363$	62.7555	3.29381
$364$	18.0345	0.945264
$365$	5.03481	0.263534
$366$	69.0067	3.60704
$367$	−0.604837	−0.0315723	−0.0157861	−	0.999875i	$-0.505025\pi$
$367$	−0.604837	−0.0315723	−0.0157861	+	0.999875i	$0.505025\pi$
$368$	5.61311	0.292603
$369$	−61.6052	−3.20704
$370$	−13.4207	−0.697709
$371$	−26.5990	−1.38095
$372$	−46.3158	−2.40136
$373$	2.23855	0.115908	0.0579538	−	0.998319i	$-0.481542\pi$
$373$	2.23855	0.115908	0.0579538	+	0.998319i	$0.481542\pi$
$374$	−77.1849	−3.99114
$375$	−3.17051	−0.163724
$376$	9.85116	0.508035
$377$	−14.9207	−0.768455
$378$	−108.827	−5.59746
$379$	−12.6749	−0.651065	−0.325533	−	0.945531i	$-0.605544\pi$
$379$	−12.6749	−0.651065	−0.325533	+	0.945531i	$0.605544\pi$
$380$	−3.54373	−0.181790
$381$	50.8702	2.60616
$382$	29.0299	1.48530
$383$	31.0692	1.58756	0.793782	−	0.608202i	$-0.208109\pi$
$383$	31.0692	1.58756	0.793782	+	0.608202i	$0.208109\pi$
$384$	61.6942	3.14832
$385$	20.2797	1.03355
$386$	−31.5156	−1.60410
$387$	−80.9452	−4.11468
$388$	34.3365	1.74317
$389$	−20.3399	−1.03127	−0.515637	−	0.856807i	$-0.672445\pi$
$389$	−20.3399	−1.03127	−0.515637	+	0.856807i	$0.672445\pi$
$390$	10.7528	0.544488
$391$	−53.4946	−2.70534
$392$	−20.2220	−1.02137
$393$	−44.5692	−2.24822
$394$	−15.5378	−0.782782
$395$	7.89061	0.397020
$396$	−131.985	−6.63250
$397$	28.7111	1.44097	0.720486	−	0.693470i	$-0.243919\pi$
$397$	28.7111	1.44097	0.720486	+	0.693470i	$0.243919\pi$
$398$	7.13900	0.357846
$399$	12.1743	0.609479
$400$	0.629651	0.0314826
$401$	20.9794	1.04766	0.523832	−	0.851822i	$-0.324502\pi$
$401$	20.9794	1.04766	0.523832	+	0.851822i	$0.324502\pi$
$402$	−70.0265	−3.49261
$403$	−6.33754	−0.315695
$404$	−33.1281	−1.64819
$405$	−19.5759	−0.972734
$406$	86.3815	4.28704
$407$	32.1299	1.59262
$408$	60.5345	2.99691
$409$	21.4169	1.05900	0.529498	−	0.848311i	$-0.322380\pi$
$409$	21.4169	1.05900	0.529498	+	0.848311i	$0.322380\pi$
$410$	−20.2486	−1.00001
$411$	13.4542	0.663646
$412$	27.2366	1.34185
$413$	−10.4367	−0.513557
$414$	−145.720	−7.16173
$415$	−8.96749	−0.440197
$416$	7.17548	0.351807
$417$	−65.1513	−3.19047
$418$	13.5148	0.661032
$419$	−8.05826	−0.393672	−0.196836	−	0.980436i	$-0.563067\pi$
$419$	−8.05826	−0.393672	−0.196836	+	0.980436i	$0.563067\pi$
$420$	−39.0784	−1.90683
$421$	−24.4898	−1.19356	−0.596780	−	0.802405i	$-0.703554\pi$
$421$	−24.4898	−1.19356	−0.596780	+	0.802405i	$0.703554\pi$
$422$	−18.2198	−0.886926
$423$	−21.8343	−1.06162
$424$	23.1580	1.12465
$425$	−6.00077	−0.291080
$426$	−3.56859	−0.172899
$427$	−34.3162	−1.66068
$428$	15.6306	0.755534
$429$	−25.7427	−1.24287
$430$	−26.6053	−1.28302
$431$	19.6854	0.948214	0.474107	−	0.880467i	$-0.342771\pi$
$431$	19.6854	0.948214	0.474107	+	0.880467i	$0.342771\pi$
$432$	8.08928	0.389195
$433$	−10.0196	−0.481512	−0.240756	−	0.970586i	$-0.577395\pi$
$433$	−10.0196	−0.481512	−0.240756	+	0.970586i	$0.577395\pi$
$434$	36.6904	1.76119
$435$	32.3312	1.55016
$436$	−55.0333	−2.63562
$437$	9.36673	0.448072
$438$	37.0005	1.76795
$439$	1.85348	0.0884616	0.0442308	−	0.999021i	$-0.485916\pi$
$439$	1.85348	0.0884616	0.0442308	+	0.999021i	$0.485916\pi$
$440$	−17.6562	−0.841727
$441$	44.8204	2.13430
$442$	20.3516	0.968027
$443$	11.5745	0.549921	0.274960	−	0.961456i	$-0.411335\pi$
$443$	11.5745	0.549921	0.274960	+	0.961456i	$0.411335\pi$
$444$	−61.9133	−2.93828
$445$	10.8858	0.516035
$446$	−56.6560	−2.68274
$447$	42.9855	2.03314
$448$	−46.1437	−2.18009
$449$	16.4539	0.776509	0.388254	−	0.921552i	$-0.373078\pi$
$449$	16.4539	0.776509	0.388254	+	0.921552i	$0.373078\pi$
$450$	−16.3461	−0.770564
$451$	48.4762	2.28265
$452$	19.8943	0.935750
$453$	29.0817	1.36638
$454$	46.2208	2.16925
$455$	−5.34722	−0.250681
$456$	−10.5994	−0.496362
$457$	20.8648	0.976013	0.488007	−	0.872840i	$-0.337724\pi$
$457$	20.8648	0.976013	0.488007	+	0.872840i	$0.337724\pi$
$458$	−33.5041	−1.56554
$459$	−77.0933	−3.59841
$460$	−30.0663	−1.40185
$461$	−7.43067	−0.346081	−0.173040	−	0.984915i	$-0.555359\pi$
$461$	−7.43067	−0.346081	−0.173040	+	0.984915i	$0.555359\pi$
$462$	149.034	6.93370
$463$	18.7477	0.871277	0.435639	−	0.900122i	$-0.356523\pi$
$463$	18.7477	0.871277	0.435639	+	0.900122i	$0.356523\pi$
$464$	−6.42086	−0.298081
$465$	13.7326	0.636835
$466$	48.1524	2.23062
$467$	−26.0496	−1.20543	−0.602715	−	0.797957i	$-0.705914\pi$
$467$	−26.0496	−1.20543	−0.602715	+	0.797957i	$0.705914\pi$
$468$	34.8010	1.60867
$469$	34.8233	1.60799
$470$	−7.17655	−0.331029
$471$	55.5728	2.56066
$472$	9.08657	0.418243
$473$	63.6945	2.92868
$474$	57.9876	2.66346
$475$	1.05071	0.0482101
$476$	−73.9631	−3.39009
$477$	−51.3277	−2.35014
$478$	12.8914	0.589639
$479$	−14.4880	−0.661973	−0.330986	−	0.943635i	$-0.607381\pi$
$479$	−14.4880	−0.661973	−0.330986	+	0.943635i	$0.607381\pi$
$480$	−15.5483	−0.709681
$481$	−8.47179	−0.386280
$482$	−29.3463	−1.33669
$483$	103.291	4.69991
$484$	66.7574	3.03443
$485$	−10.1807	−0.462284
$486$	−54.5260	−2.47335
$487$	−10.0845	−0.456971	−0.228486	−	0.973547i	$-0.573377\pi$
$487$	−10.0845	−0.456971	−0.228486	+	0.973547i	$0.573377\pi$
$488$	29.8769	1.35246
$489$	−64.4955	−2.91659
$490$	14.7317	0.665510
$491$	11.6854	0.527354	0.263677	−	0.964611i	$-0.415065\pi$
$491$	11.6854	0.527354	0.263677	+	0.964611i	$0.415065\pi$
$492$	−93.4121	−4.21134
$493$	61.1928	2.75598
$494$	−3.56350	−0.160329
$495$	39.1335	1.75892
$496$	−2.72725	−0.122457
$497$	1.77462	0.0796024
$498$	−65.9015	−2.95312
$499$	−3.55542	−0.159163	−0.0795813	−	0.996828i	$-0.525358\pi$
$499$	−3.55542	−0.159163	−0.0795813	+	0.996828i	$0.525358\pi$
$500$	−3.37269	−0.150831
$501$	1.40327	0.0626934
$502$	32.0276	1.42946
$503$	39.3935	1.75647	0.878235	−	0.478229i	$-0.158721\pi$
$503$	39.3935	1.75647	0.878235	+	0.478229i	$0.158721\pi$
$504$	−82.0009	−3.65261
$505$	9.82247	0.437094
$506$	114.664	5.09746
$507$	−34.4289	−1.52904
$508$	54.1141	2.40093
$509$	−14.7214	−0.652513	−0.326256	−	0.945281i	$-0.605787\pi$
$509$	−14.7214	−0.652513	−0.326256	+	0.945281i	$0.605787\pi$
$510$	−44.0993	−1.95275
$511$	−18.3999	−0.813962
$512$	7.09465	0.313542
$513$	13.4988	0.595986
$514$	6.73162	0.296919
$515$	−8.07564	−0.355855
$516$	−122.737	−5.40322
$517$	17.1810	0.755621
$518$	49.0464	2.15497
$519$	−44.9488	−1.97303
$520$	4.65547	0.204156
$521$	−8.13725	−0.356500	−0.178250	−	0.983985i	$-0.557044\pi$
$521$	−8.13725	−0.356500	−0.178250	+	0.983985i	$0.557044\pi$
$522$	166.689	7.29580
$523$	−6.25698	−0.273599	−0.136799	−	0.990599i	$-0.543682\pi$
$523$	−6.25698	−0.273599	−0.136799	+	0.990599i	$0.543682\pi$
$524$	−47.4114	−2.07117
$525$	11.5867	0.505686
$526$	3.17911	0.138616
$527$	25.9915	1.13221
$528$	−11.0779	−0.482105
$529$	56.4706	2.45524
$530$	−16.8705	−0.732810
$531$	−20.1396	−0.873985
$532$	12.9507	0.561484
$533$	−12.7819	−0.553644
$534$	79.9988	3.46189
$535$	−4.63446	−0.200365
$536$	−30.3184	−1.30955
$537$	−7.58193	−0.327184
$538$	−8.48708	−0.365904
$539$	−35.2685	−1.51912
$540$	−43.3297	−1.86461
$541$	−12.9523	−0.556863	−0.278431	−	0.960456i	$-0.589814\pi$
$541$	−12.9523	−0.556863	−0.278431	+	0.960456i	$0.589814\pi$
$542$	25.7048	1.10411
$543$	66.8497	2.86880
$544$	−29.4281	−1.26172
$545$	16.3174	0.698959
$546$	−39.2963	−1.68173
$547$	10.8671	0.464645	0.232322	−	0.972639i	$-0.425368\pi$
$547$	10.8671	0.464645	0.232322	+	0.972639i	$0.425368\pi$
$548$	14.3122	0.611385
$549$	−66.2195	−2.82618
$550$	12.8625	0.548459
$551$	−10.7147	−0.456460
$552$	−89.9290	−3.82763
$553$	−28.8365	−1.22625
$554$	−60.3858	−2.56555
$555$	18.3573	0.779222
$556$	−69.3060	−2.93923
$557$	1.01670	0.0430789	0.0215394	−	0.999768i	$-0.493143\pi$
$557$	1.01670	0.0430789	0.0215394	+	0.999768i	$0.493143\pi$
$558$	70.8010	2.99725
$559$	−16.7945	−0.710334
$560$	−2.30108	−0.0972384
$561$	105.576	4.45742
$562$	−45.5311	−1.92061
$563$	21.2164	0.894163	0.447081	−	0.894493i	$-0.352463\pi$
$563$	21.2164	0.894163	0.447081	+	0.894493i	$0.352463\pi$
$564$	−33.1073	−1.39407
$565$	−5.89865	−0.248158
$566$	14.6533	0.615924
$567$	71.5408	3.00443
$568$	−1.54504	−0.0648286
$569$	13.0288	0.546195	0.273098	−	0.961986i	$-0.411952\pi$
$569$	13.0288	0.546195	0.273098	+	0.961986i	$0.411952\pi$
$570$	7.72164	0.323424
$571$	−25.1353	−1.05188	−0.525940	−	0.850521i	$-0.676287\pi$
$571$	−25.1353	−1.05188	−0.525940	+	0.850521i	$0.676287\pi$
$572$	−27.3843	−1.14500
$573$	−39.7080	−1.65883
$574$	73.9990	3.08866
$575$	8.91463	0.371766
$576$	−89.0430	−3.71013
$577$	44.5823	1.85599	0.927993	−	0.372599i	$-0.121533\pi$
$577$	44.5823	1.85599	0.927993	+	0.372599i	$0.121533\pi$
$578$	−44.0616	−1.83272
$579$	43.1080	1.79151
$580$	34.3930	1.42809
$581$	32.7720	1.35961
$582$	−74.8176	−3.10129
$583$	40.3890	1.67274
$584$	16.0196	0.662894
$585$	−10.3185	−0.426616
$586$	−50.0040	−2.06565
$587$	−41.8568	−1.72761	−0.863807	−	0.503823i	$-0.831926\pi$
$587$	−41.8568	−1.72761	−0.863807	+	0.503823i	$0.831926\pi$
$588$	67.9613	2.80268
$589$	−4.55103	−0.187522
$590$	−6.61954	−0.272522
$591$	21.2531	0.874235
$592$	−3.64569	−0.149837
$593$	−27.3084	−1.12142	−0.560710	−	0.828012i	$-0.689472\pi$
$593$	−27.3084	−1.12142	−0.560710	+	0.828012i	$0.689472\pi$
$594$	165.248	6.78019
$595$	21.9300	0.899042
$596$	45.7267	1.87304
$597$	−9.76496	−0.399653
$598$	−30.2340	−1.23636
$599$	−12.0926	−0.494089	−0.247044	−	0.969004i	$-0.579459\pi$
$599$	−12.0926	−0.494089	−0.247044	+	0.969004i	$0.579459\pi$
$600$	−10.0878	−0.411833
$601$	−30.1721	−1.23075	−0.615373	−	0.788236i	$-0.710995\pi$
$601$	−30.1721	−1.23075	−0.615373	+	0.788236i	$0.710995\pi$
$602$	97.2299	3.96280
$603$	67.1981	2.73652
$604$	30.9362	1.25878
$605$	−19.7935	−0.804722
$606$	72.1847	2.93230
$607$	19.2862	0.782804	0.391402	−	0.920220i	$-0.371990\pi$
$607$	19.2862	0.782804	0.391402	+	0.920220i	$0.371990\pi$
$608$	5.15276	0.208972
$609$	−118.155	−4.78790
$610$	−21.7652	−0.881248
$611$	−4.53018	−0.183272
$612$	−142.726	−5.76934
$613$	−29.7626	−1.20210	−0.601050	−	0.799212i	$-0.705251\pi$
$613$	−29.7626	−1.20210	−0.601050	+	0.799212i	$0.705251\pi$
$614$	5.26852	0.212620
$615$	27.6966	1.11684
$616$	64.5252	2.59979
$617$	−1.37675	−0.0554261	−0.0277130	−	0.999616i	$-0.508822\pi$
$617$	−1.37675	−0.0554261	−0.0277130	+	0.999616i	$0.508822\pi$
$618$	−59.3473	−2.38730
$619$	25.0596	1.00723	0.503615	−	0.863928i	$-0.332003\pi$
$619$	25.0596	1.00723	0.503615	+	0.863928i	$0.332003\pi$
$620$	14.6083	0.586685
$621$	114.528	4.59586
$622$	−29.1177	−1.16751
$623$	−39.7824	−1.59385
$624$	2.92095	0.116932
$625$	1.00000	0.0400000
$626$	44.6761	1.78561
$627$	−18.4860	−0.738260
$628$	59.1166	2.35901
$629$	34.7445	1.38535
$630$	59.7374	2.38000
$631$	3.25783	0.129692	0.0648462	−	0.997895i	$-0.479344\pi$
$631$	3.25783	0.129692	0.0648462	+	0.997895i	$0.479344\pi$
$632$	25.1061	0.998665
$633$	24.9216	0.990546
$634$	−10.8118	−0.429392
$635$	−16.0448	−0.636719
$636$	−77.8284	−3.08610
$637$	9.29935	0.368454
$638$	−131.165	−5.19288
$639$	3.42446	0.135469
$640$	−19.4588	−0.769176
$641$	−12.5956	−0.497498	−0.248749	−	0.968568i	$-0.580019\pi$
$641$	−12.5956	−0.497498	−0.248749	+	0.968568i	$0.580019\pi$
$642$	−34.0584	−1.34418
$643$	−28.6624	−1.13034	−0.565168	−	0.824976i	$-0.691189\pi$
$643$	−28.6624	−1.13034	−0.565168	+	0.824976i	$0.691189\pi$
$644$	109.878	4.32980
$645$	36.3916	1.43292
$646$	14.6146	0.575005
$647$	−35.1579	−1.38220	−0.691099	−	0.722760i	$-0.742873\pi$
$647$	−35.1579	−1.38220	−0.691099	+	0.722760i	$0.742873\pi$
$648$	−62.2859	−2.44682
$649$	15.8475	0.622071
$650$	−3.39150	−0.133026
$651$	−50.1863	−1.96695
$652$	−68.6084	−2.68691
$653$	−3.76810	−0.147457	−0.0737286	−	0.997278i	$-0.523490\pi$
$653$	−3.76810	−0.147457	−0.0737286	+	0.997278i	$0.523490\pi$
$654$	119.915	4.68905
$655$	14.0574	0.549270
$656$	−5.50045	−0.214757
$657$	−35.5060	−1.38522
$658$	26.2269	1.02243
$659$	10.7036	0.416954	0.208477	−	0.978027i	$-0.433149\pi$
$659$	10.7036	0.416954	0.208477	+	0.978027i	$0.433149\pi$
$660$	59.3382	2.30974
$661$	−34.3165	−1.33476	−0.667379	−	0.744718i	$-0.732584\pi$
$661$	−34.3165	−1.33476	−0.667379	+	0.744718i	$0.732584\pi$
$662$	24.5869	0.955597
$663$	−27.8376	−1.08112
$664$	−28.5324	−1.10727
$665$	−3.83987	−0.148904
$666$	94.6442	3.66739
$667$	−90.9068	−3.51993
$668$	1.49275	0.0577564
$669$	77.4959	2.99616
$670$	22.0869	0.853290
$671$	52.1071	2.01157
$672$	56.8219	2.19195
$673$	18.4697	0.711956	0.355978	−	0.934494i	$-0.384148\pi$
$673$	18.4697	0.711956	0.355978	+	0.934494i	$0.384148\pi$
$674$	59.3191	2.28489
$675$	12.8472	0.494490
$676$	−36.6244	−1.40863
$677$	−20.9421	−0.804871	−0.402436	−	0.915448i	$-0.631836\pi$
$677$	−20.9421	−0.804871	−0.402436	+	0.915448i	$0.631836\pi$
$678$	−43.3488	−1.66480
$679$	37.2058	1.42783
$680$	−19.0930	−0.732184
$681$	−63.2223	−2.42268
$682$	−55.7122	−2.13333
$683$	15.1627	0.580184	0.290092	−	0.956999i	$-0.406314\pi$
$683$	15.1627	0.580184	0.290092	+	0.956999i	$0.406314\pi$
$684$	24.9908	0.955547
$685$	−4.24354	−0.162137
$686$	5.45860	0.208410
$687$	45.8280	1.74845
$688$	−7.22724	−0.275536
$689$	−10.6495	−0.405714
$690$	65.5130	2.49404
$691$	15.3437	0.583701	0.291850	−	0.956464i	$-0.405729\pi$
$691$	15.3437	0.583701	0.291850	+	0.956464i	$0.405729\pi$
$692$	−47.8152	−1.81766
$693$	−143.015	−5.43268
$694$	−69.0912	−2.62267
$695$	20.5492	0.779475
$696$	102.870	3.89929
$697$	52.4210	1.98559
$698$	−26.5405	−1.00457
$699$	−65.8644	−2.49122
$700$	12.3256	0.465864
$701$	−37.5568	−1.41850	−0.709250	−	0.704958i	$-0.750966\pi$
$701$	−37.5568	−1.41850	−0.709250	+	0.704958i	$0.750966\pi$
$702$	−43.5714	−1.64450
$703$	−6.08365	−0.229449
$704$	70.0665	2.64073
$705$	9.81631	0.369704
$706$	−43.9386	−1.65365
$707$	−35.8965	−1.35003
$708$	−30.5377	−1.14768
$709$	9.12936	0.342860	0.171430	−	0.985196i	$-0.445161\pi$
$709$	9.12936	0.342860	0.171430	+	0.985196i	$0.445161\pi$
$710$	1.12556	0.0422415
$711$	−55.6454	−2.08687
$712$	34.6360	1.29804
$713$	−38.6125	−1.44605
$714$	161.162	6.03134
$715$	8.11943	0.303650
$716$	−8.06542	−0.301419
$717$	−17.6333	−0.658527
$718$	−30.3202	−1.13154
$719$	29.9287	1.11615	0.558075	−	0.829790i	$-0.311540\pi$
$719$	29.9287	1.11615	0.558075	+	0.829790i	$0.311540\pi$
$720$	−4.44037	−0.165483
$721$	29.5127	1.09911
$722$	41.4812	1.54377
$723$	40.1408	1.49285
$724$	71.1127	2.64288
$725$	−10.1975	−0.378725
$726$	−145.461	−5.39858
$727$	−49.5196	−1.83658	−0.918289	−	0.395910i	$-0.870429\pi$
$727$	−49.5196	−1.83658	−0.918289	+	0.395910i	$0.870429\pi$
$728$	−17.0136	−0.630565
$729$	15.8547	0.587211
$730$	−11.6702	−0.431934
$731$	68.8778	2.54754
$732$	−100.409	−3.71122
$733$	−47.4025	−1.75085	−0.875426	−	0.483352i	$-0.839419\pi$
$733$	−47.4025	−1.75085	−0.875426	+	0.483352i	$0.839419\pi$
$734$	1.40196	0.0517472
$735$	−20.1505	−0.743261
$736$	43.7178	1.61146
$737$	−52.8772	−1.94775
$738$	142.795	5.25636
$739$	−35.5255	−1.30683	−0.653414	−	0.757001i	$-0.726664\pi$
$739$	−35.5255	−1.30683	−0.653414	+	0.757001i	$0.726664\pi$
$740$	19.5279	0.717860
$741$	4.87427	0.179061
$742$	61.6539	2.26339
$743$	33.3410	1.22316	0.611581	−	0.791182i	$-0.290534\pi$
$743$	33.3410	1.22316	0.611581	+	0.791182i	$0.290534\pi$
$744$	43.6939	1.60190
$745$	−13.5579	−0.496724
$746$	−5.18874	−0.189973
$747$	63.2397	2.31382
$748$	112.309	4.10641
$749$	16.9368	0.618857
$750$	7.34893	0.268345
$751$	−4.65270	−0.169779	−0.0848896	−	0.996390i	$-0.527054\pi$
$751$	−4.65270	−0.169779	−0.0848896	+	0.996390i	$0.527054\pi$
$752$	−1.94948	−0.0710904
$753$	−43.8083	−1.59646
$754$	34.5848	1.25950
$755$	−9.17256	−0.333824
$756$	158.350	5.75913
$757$	44.2882	1.60968	0.804841	−	0.593491i	$-0.202251\pi$
$757$	44.2882	1.60968	0.804841	+	0.593491i	$0.202251\pi$
$758$	29.3792	1.06710
$759$	−156.842	−5.69299
$760$	3.34313	0.121268
$761$	42.2732	1.53240	0.766201	−	0.642602i	$-0.222145\pi$
$761$	42.2732	1.53240	0.766201	+	0.642602i	$0.222145\pi$
$762$	−117.912	−4.27151
$763$	−59.6323	−2.15883
$764$	−42.2402	−1.52820
$765$	42.3181	1.53001
$766$	−72.0156	−2.60203
$767$	−4.17857	−0.150880
$768$	−62.9370	−2.27104
$769$	9.35474	0.337341	0.168670	−	0.985673i	$-0.446053\pi$
$769$	9.35474	0.337341	0.168670	+	0.985673i	$0.446053\pi$
$770$	−47.0064	−1.69399
$771$	−9.20773	−0.331608
$772$	45.8570	1.65043
$773$	0.975841	0.0350986	0.0175493	−	0.999846i	$-0.494414\pi$
$773$	0.975841	0.0350986	0.0175493	+	0.999846i	$0.494414\pi$
$774$	187.623	6.74399
$775$	−4.33136	−0.155587
$776$	−32.3927	−1.16283
$777$	−67.0872	−2.40674
$778$	47.1460	1.69027
$779$	−9.17875	−0.328863
$780$	−15.6459	−0.560213
$781$	−2.69465	−0.0964222
$782$	123.995	4.43407
$783$	−131.010	−4.68190
$784$	4.00181	0.142922
$785$	−17.5280	−0.625603
$786$	103.307	3.68485
$787$	−9.35571	−0.333495	−0.166748	−	0.986000i	$-0.553327\pi$
$787$	−9.35571	−0.333495	−0.166748	+	0.986000i	$0.553327\pi$
$788$	22.6084	0.805390
$789$	−4.34849	−0.154810
$790$	−18.2897	−0.650718
$791$	21.5568	0.766472
$792$	124.514	4.42440
$793$	−13.7392	−0.487895
$794$	−66.5497	−2.36176
$795$	23.0761	0.818424
$796$	−10.3877	−0.368181
$797$	53.6799	1.90144	0.950720	−	0.310052i	$-0.100346\pi$
$797$	53.6799	1.90144	0.950720	+	0.310052i	$0.100346\pi$
$798$	−28.2190	−0.998940
$799$	18.5792	0.657284
$800$	4.90405	0.173384
$801$	−76.7676	−2.71245
$802$	−48.6284	−1.71713
$803$	27.9391	0.985950
$804$	101.893	3.59348
$805$	−32.5788	−1.14825
$806$	14.6898	0.517427
$807$	11.6089	0.408653
$808$	31.2528	1.09947
$809$	33.9414	1.19332	0.596659	−	0.802495i	$-0.296495\pi$
$809$	33.9414	1.19332	0.596659	+	0.802495i	$0.296495\pi$
$810$	45.3751	1.59432
$811$	43.1620	1.51562	0.757812	−	0.652473i	$-0.226268\pi$
$811$	43.1620	1.51562	0.757812	+	0.652473i	$0.226268\pi$
$812$	−125.690	−4.41086
$813$	−35.1598	−1.23311
$814$	−74.4740	−2.61031
$815$	20.3423	0.712561
$816$	−11.9794	−0.419363
$817$	−12.0603	−0.421936
$818$	−49.6423	−1.73570
$819$	37.7091	1.31766
$820$	29.4628	1.02889
$821$	−52.1823	−1.82118	−0.910588	−	0.413315i	$-0.864371\pi$
$821$	−52.1823	−1.82118	−0.910588	+	0.413315i	$0.864371\pi$
$822$	−31.1855	−1.08772
$823$	−14.3666	−0.500790	−0.250395	−	0.968144i	$-0.580560\pi$
$823$	−14.3666	−0.500790	−0.250395	+	0.968144i	$0.580560\pi$
$824$	−25.6948	−0.895120
$825$	−17.5937	−0.612536
$826$	24.1913	0.841724
$827$	−28.4319	−0.988675	−0.494337	−	0.869270i	$-0.664589\pi$
$827$	−28.4319	−0.988675	−0.494337	+	0.869270i	$0.664589\pi$
$828$	212.031	7.36857
$829$	8.22910	0.285808	0.142904	−	0.989737i	$-0.454356\pi$
$829$	8.22910	0.285808	0.142904	+	0.989737i	$0.454356\pi$
$830$	20.7858	0.721485
$831$	82.5976	2.86528
$832$	−18.4747	−0.640494
$833$	−38.1385	−1.32142
$834$	151.015	5.22921
$835$	−0.442601	−0.0153168
$836$	−19.6649	−0.680124
$837$	−55.6460	−1.92341
$838$	18.6783	0.645231
$839$	−42.6131	−1.47117	−0.735584	−	0.677433i	$-0.763092\pi$
$839$	−42.6131	−1.47117	−0.735584	+	0.677433i	$0.763092\pi$
$840$	36.8662	1.27200
$841$	74.9888	2.58582
$842$	56.7651	1.95625
$843$	62.2789	2.14500
$844$	26.5109	0.912542
$845$	10.8591	0.373565
$846$	50.6098	1.74000
$847$	72.3361	2.48550
$848$	−4.58283	−0.157375
$849$	−20.0432	−0.687882
$850$	13.9092	0.477082
$851$	−51.6158	−1.76937
$852$	5.19251	0.177893
$853$	26.5157	0.907882	0.453941	−	0.891032i	$-0.350018\pi$
$853$	26.5157	0.907882	0.453941	+	0.891032i	$0.350018\pi$
$854$	79.5417	2.72186
$855$	−7.40976	−0.253408
$856$	−14.7458	−0.504000
$857$	−2.74132	−0.0936418	−0.0468209	−	0.998903i	$-0.514909\pi$
$857$	−2.74132	−0.0936418	−0.0468209	+	0.998903i	$0.514909\pi$
$858$	59.6692	2.03707
$859$	26.1909	0.893622	0.446811	−	0.894628i	$-0.352560\pi$
$859$	26.1909	0.893622	0.446811	+	0.894628i	$0.352560\pi$
$860$	38.7123	1.32008
$861$	−101.218	−3.44951
$862$	−45.6290	−1.55413
$863$	7.84886	0.267178	0.133589	−	0.991037i	$-0.457350\pi$
$863$	7.84886	0.267178	0.133589	+	0.991037i	$0.457350\pi$
$864$	63.0035	2.14342
$865$	14.1772	0.482038
$866$	23.2245	0.789201
$867$	60.2688	2.04684
$868$	−53.3866	−1.81206
$869$	43.7865	1.48536
$870$	−74.9407	−2.54073
$871$	13.9423	0.472417
$872$	51.9180	1.75816
$873$	71.7957	2.42992
$874$	−21.7112	−0.734392
$875$	−3.65453	−0.123546
$876$	−53.8378	−1.81901
$877$	−26.4394	−0.892794	−0.446397	−	0.894835i	$-0.647293\pi$
$877$	−26.4394	−0.892794	−0.446397	+	0.894835i	$0.647293\pi$
$878$	−4.29618	−0.144989
$879$	68.3971	2.30698
$880$	3.49406	0.117785
$881$	28.0842	0.946181	0.473090	−	0.881014i	$-0.343138\pi$
$881$	28.0842	0.946181	0.473090	+	0.881014i	$0.343138\pi$
$882$	−103.889	−3.49814
$883$	−18.3673	−0.618108	−0.309054	−	0.951045i	$-0.600012\pi$
$883$	−18.3673	−0.618108	−0.309054	+	0.951045i	$0.600012\pi$
$884$	−29.6128	−0.995985
$885$	9.05442	0.304361
$886$	−26.8286	−0.901324
$887$	17.8599	0.599678	0.299839	−	0.953990i	$-0.403067\pi$
$887$	17.8599	0.599678	0.299839	+	0.953990i	$0.403067\pi$
$888$	58.4084	1.96006
$889$	58.6363	1.96660
$890$	−25.2322	−0.845785
$891$	−108.630	−3.63926
$892$	82.4378	2.76022
$893$	−3.25315	−0.108863
$894$	−99.6363	−3.33234
$895$	2.39139	0.0799354
$896$	71.1128	2.37571
$897$	41.3550	1.38080
$898$	−38.1386	−1.27270
$899$	44.1690	1.47312
$900$	23.7846	0.792819
$901$	43.6757	1.45505
$902$	−112.363	−3.74129
$903$	−132.994	−4.42577
$904$	−18.7681	−0.624218
$905$	−21.0849	−0.700885
$906$	−67.4086	−2.23950
$907$	−21.7837	−0.723315	−0.361658	−	0.932311i	$-0.617789\pi$
$907$	−21.7837	−0.723315	−0.361658	+	0.932311i	$0.617789\pi$
$908$	−67.2539	−2.23190
$909$	−69.2691	−2.29751
$910$	12.3943	0.410869
$911$	3.60186	0.119335	0.0596675	−	0.998218i	$-0.480996\pi$
$911$	3.60186	0.119335	0.0596675	+	0.998218i	$0.480996\pi$
$912$	2.09756	0.0694570
$913$	−49.7623	−1.64689
$914$	−48.3626	−1.59969
$915$	29.7711	0.984204
$916$	48.7505	1.61076
$917$	−51.3734	−1.69650
$918$	178.695	5.89781
$919$	−53.3028	−1.75830	−0.879149	−	0.476547i	$-0.841888\pi$
$919$	−53.3028	−1.75830	−0.879149	+	0.476547i	$0.841888\pi$
$920$	28.3642	0.935141
$921$	−7.20645	−0.237460
$922$	17.2236	0.567229
$923$	0.710507	0.0233866
$924$	−216.853	−7.13395
$925$	−5.79001	−0.190374
$926$	−43.4553	−1.42803
$927$	56.9503	1.87049
$928$	−50.0091	−1.64163
$929$	−17.0868	−0.560601	−0.280300	−	0.959912i	$-0.590434\pi$
$929$	−17.0868	−0.560601	−0.280300	+	0.959912i	$0.590434\pi$
$930$	−31.8309	−1.04378
$931$	6.67793	0.218860
$932$	−70.0645	−2.29504
$933$	39.8281	1.30391
$934$	60.3804	1.97571
$935$	−33.2994	−1.08901
$936$	−32.8309	−1.07311
$937$	−12.4455	−0.406578	−0.203289	−	0.979119i	$-0.565163\pi$
$937$	−12.4455	−0.406578	−0.203289	+	0.979119i	$0.565163\pi$
$938$	−80.7172	−2.63551
$939$	−61.1093	−1.99423
$940$	10.4423	0.340590
$941$	−10.4487	−0.340618	−0.170309	−	0.985391i	$-0.554477\pi$
$941$	−10.4487	−0.340618	−0.170309	+	0.985391i	$0.554477\pi$
$942$	−128.812	−4.19694
$943$	−77.8756	−2.53598
$944$	−1.79818	−0.0585257
$945$	−46.9506	−1.52730
$946$	−147.638	−4.80012
$947$	30.9590	1.00603	0.503016	−	0.864277i	$-0.332224\pi$
$947$	30.9590	1.00603	0.503016	+	0.864277i	$0.332224\pi$
$948$	−84.3753	−2.74038
$949$	−7.36680	−0.239136
$950$	−2.43546	−0.0790167
$951$	14.7888	0.479558
$952$	69.7761	2.26146
$953$	−25.5768	−0.828514	−0.414257	−	0.910160i	$-0.635958\pi$
$953$	−25.5768	−0.828514	−0.414257	+	0.910160i	$0.635958\pi$
$954$	118.973	3.85189
$955$	12.5242	0.405273
$956$	−18.7577	−0.606669
$957$	179.412	5.79957
$958$	33.5818	1.08498
$959$	15.5082	0.500785
$960$	40.0322	1.29203
$961$	−12.2393	−0.394816
$962$	19.6368	0.633116
$963$	32.6827	1.05319
$964$	42.7006	1.37529
$965$	−13.5966	−0.437689
$966$	−239.419	−7.70319
$967$	−11.8743	−0.381853	−0.190926	−	0.981604i	$-0.561149\pi$
$967$	−11.8743	−0.381853	−0.190926	+	0.981604i	$0.561149\pi$
$968$	−62.9783	−2.02420
$969$	−19.9903	−0.642182
$970$	23.5980	0.757686
$971$	36.2967	1.16482	0.582408	−	0.812897i	$-0.302111\pi$
$971$	36.2967	1.16482	0.582408	+	0.812897i	$0.302111\pi$
$972$	79.3385	2.54478
$973$	−75.0976	−2.40752
$974$	23.3749	0.748979
$975$	4.63900	0.148567
$976$	−5.91244	−0.189253
$977$	−39.7662	−1.27223	−0.636117	−	0.771593i	$-0.719460\pi$
$977$	−39.7662	−1.27223	−0.636117	+	0.771593i	$0.719460\pi$
$978$	149.495	4.78031
$979$	60.4072	1.93062
$980$	−21.4355	−0.684731
$981$	−115.072	−3.67396
$982$	−27.0856	−0.864337
$983$	−24.4234	−0.778986	−0.389493	−	0.921029i	$-0.627350\pi$
$983$	−24.4234	−0.778986	−0.389493	+	0.921029i	$0.627350\pi$
$984$	88.1241	2.80930
$985$	−6.70337	−0.213587
$986$	−141.839	−4.51708
$987$	−35.8740	−1.14188
$988$	5.18510	0.164960
$989$	−102.324	−3.25370
$990$	−90.7078	−2.88288
$991$	−41.2636	−1.31078	−0.655390	−	0.755290i	$-0.727496\pi$
$991$	−41.2636	−1.31078	−0.655390	+	0.755290i	$0.727496\pi$
$992$	−21.2412	−0.674410
$993$	−33.6307	−1.06724
$994$	−4.11339	−0.130469
$995$	3.07994	0.0976406
$996$	95.8905	3.03841
$997$	−32.6407	−1.03374	−0.516870	−	0.856064i	$-0.672903\pi$
$997$	−32.6407	−1.03374	−0.516870	+	0.856064i	$0.672903\pi$
$998$	8.24114	0.260869
$999$	−74.3856	−2.35346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.20	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.20	✓	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31791 q^{2} +3.17051 q^{3} +3.37269 q^{4} -1.00000 q^{5} -7.34893 q^{6} +3.65453 q^{7} -3.18176 q^{8} +7.05211 q^{9} +O(q^{10})\)	\(q-2.31791 q^{2} +3.17051 q^{3} +3.37269 q^{4} -1.00000 q^{5} -7.34893 q^{6} +3.65453 q^{7} -3.18176 q^{8} +7.05211 q^{9} +2.31791 q^{10} -5.54919 q^{11} +10.6931 q^{12} +1.46317 q^{13} -8.47086 q^{14} -3.17051 q^{15} +0.629651 q^{16} -6.00077 q^{17} -16.3461 q^{18} +1.05071 q^{19} -3.37269 q^{20} +11.5867 q^{21} +12.8625 q^{22} +8.91463 q^{23} -10.0878 q^{24} +1.00000 q^{25} -3.39150 q^{26} +12.8472 q^{27} +12.3256 q^{28} -10.1975 q^{29} +7.34893 q^{30} -4.33136 q^{31} +4.90405 q^{32} -17.5937 q^{33} +13.9092 q^{34} -3.65453 q^{35} +23.7846 q^{36} -5.79001 q^{37} -2.43546 q^{38} +4.63900 q^{39} +3.18176 q^{40} -8.73572 q^{41} -26.8569 q^{42} -11.4782 q^{43} -18.7157 q^{44} -7.05211 q^{45} -20.6633 q^{46} -3.09613 q^{47} +1.99631 q^{48} +6.35560 q^{49} -2.31791 q^{50} -19.0255 q^{51} +4.93483 q^{52} -7.27836 q^{53} -29.7787 q^{54} +5.54919 q^{55} -11.6279 q^{56} +3.33130 q^{57} +23.6368 q^{58} -2.85583 q^{59} -10.6931 q^{60} -9.39003 q^{61} +10.0397 q^{62} +25.7722 q^{63} -12.6264 q^{64} -1.46317 q^{65} +40.7807 q^{66} +9.52880 q^{67} -20.2387 q^{68} +28.2639 q^{69} +8.47086 q^{70} +0.485593 q^{71} -22.4381 q^{72} -5.03481 q^{73} +13.4207 q^{74} +3.17051 q^{75} +3.54373 q^{76} -20.2797 q^{77} -10.7528 q^{78} -7.89061 q^{79} -0.629651 q^{80} +19.5759 q^{81} +20.2486 q^{82} +8.96749 q^{83} +39.0784 q^{84} +6.00077 q^{85} +26.6053 q^{86} -32.3312 q^{87} +17.6562 q^{88} -10.8858 q^{89} +16.3461 q^{90} +5.34722 q^{91} +30.0663 q^{92} -13.7326 q^{93} +7.17655 q^{94} -1.05071 q^{95} +15.5483 q^{96} +10.1807 q^{97} -14.7317 q^{98} -39.1335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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