LMFDB - Embedded newform 6035.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12696 q^{2} +2.34856 q^{3} -0.729961 q^{4} +1.00000 q^{5} -2.64673 q^{6} -2.68480 q^{7} +3.07656 q^{8} +2.51573 q^{9} +O(q^{10})$	\(q-1.12696 q^{2} +2.34856 q^{3} -0.729961 q^{4} +1.00000 q^{5} -2.64673 q^{6} -2.68480 q^{7} +3.07656 q^{8} +2.51573 q^{9} -1.12696 q^{10} -4.99951 q^{11} -1.71436 q^{12} +2.96628 q^{13} +3.02566 q^{14} +2.34856 q^{15} -2.00724 q^{16} +1.00000 q^{17} -2.83513 q^{18} -0.146955 q^{19} -0.729961 q^{20} -6.30541 q^{21} +5.63425 q^{22} +2.74728 q^{23} +7.22548 q^{24} +1.00000 q^{25} -3.34288 q^{26} -1.13733 q^{27} +1.95980 q^{28} +3.29682 q^{29} -2.64673 q^{30} +2.91793 q^{31} -3.89104 q^{32} -11.7416 q^{33} -1.12696 q^{34} -2.68480 q^{35} -1.83639 q^{36} +0.817948 q^{37} +0.165613 q^{38} +6.96648 q^{39} +3.07656 q^{40} -11.4451 q^{41} +7.10595 q^{42} -11.1138 q^{43} +3.64944 q^{44} +2.51573 q^{45} -3.09608 q^{46} +7.61709 q^{47} -4.71411 q^{48} +0.208142 q^{49} -1.12696 q^{50} +2.34856 q^{51} -2.16527 q^{52} -1.43850 q^{53} +1.28172 q^{54} -4.99951 q^{55} -8.25993 q^{56} -0.345133 q^{57} -3.71538 q^{58} +4.83444 q^{59} -1.71436 q^{60} -0.863601 q^{61} -3.28839 q^{62} -6.75424 q^{63} +8.39952 q^{64} +2.96628 q^{65} +13.2324 q^{66} +3.69024 q^{67} -0.729961 q^{68} +6.45216 q^{69} +3.02566 q^{70} -1.00000 q^{71} +7.73980 q^{72} +0.104478 q^{73} -0.921794 q^{74} +2.34856 q^{75} +0.107272 q^{76} +13.4227 q^{77} -7.85095 q^{78} +1.98678 q^{79} -2.00724 q^{80} -10.2183 q^{81} +12.8981 q^{82} -3.90615 q^{83} +4.60270 q^{84} +1.00000 q^{85} +12.5248 q^{86} +7.74277 q^{87} -15.3813 q^{88} -10.2965 q^{89} -2.83513 q^{90} -7.96386 q^{91} -2.00541 q^{92} +6.85294 q^{93} -8.58416 q^{94} -0.146955 q^{95} -9.13834 q^{96} -13.5415 q^{97} -0.234567 q^{98} -12.5774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.12696	−0.796881	−0.398441	−	0.917194i	$-0.630448\pi$
$2$	−1.12696	−0.796881	−0.398441	+	0.917194i	$0.630448\pi$
$3$	2.34856	1.35594	0.677971	−	0.735089i	$-0.262860\pi$
$3$	2.34856	1.35594	0.677971	+	0.735089i	$0.262860\pi$
$4$	−0.729961	−0.364980
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.64673	−1.08052
$7$	−2.68480	−1.01476	−0.507379	−	0.861723i	$-0.669386\pi$
$7$	−2.68480	−1.01476	−0.507379	+	0.861723i	$0.669386\pi$
$8$	3.07656	1.08773
$9$	2.51573	0.838578
$10$	−1.12696	−0.356376
$11$	−4.99951	−1.50741	−0.753704	−	0.657214i	$-0.771735\pi$
$11$	−4.99951	−1.50741	−0.753704	+	0.657214i	$0.771735\pi$
$12$	−1.71436	−0.494892
$13$	2.96628	0.822697	0.411349	−	0.911478i	$-0.365058\pi$
$13$	2.96628	0.822697	0.411349	+	0.911478i	$0.365058\pi$
$14$	3.02566	0.808642
$15$	2.34856	0.606396
$16$	−2.00724	−0.501809
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.83513	−0.668247
$19$	−0.146955	−0.0337138	−0.0168569	−	0.999858i	$-0.505366\pi$
$19$	−0.146955	−0.0337138	−0.0168569	+	0.999858i	$0.505366\pi$
$20$	−0.729961	−0.163224
$21$	−6.30541	−1.37595
$22$	5.63425	1.20123
$23$	2.74728	0.572848	0.286424	−	0.958103i	$-0.407533\pi$
$23$	2.74728	0.572848	0.286424	+	0.958103i	$0.407533\pi$
$24$	7.22548	1.47489
$25$	1.00000	0.200000
$26$	−3.34288	−0.655592
$27$	−1.13733	−0.218879
$28$	1.95980	0.370367
$29$	3.29682	0.612203	0.306102	−	0.951999i	$-0.400975\pi$
$29$	3.29682	0.612203	0.306102	+	0.951999i	$0.400975\pi$
$30$	−2.64673	−0.483225
$31$	2.91793	0.524076	0.262038	−	0.965058i	$-0.415605\pi$
$31$	2.91793	0.524076	0.262038	+	0.965058i	$0.415605\pi$
$32$	−3.89104	−0.687845
$33$	−11.7416	−2.04396
$34$	−1.12696	−0.193272
$35$	−2.68480	−0.453814
$36$	−1.83639	−0.306065
$37$	0.817948	0.134470	0.0672349	−	0.997737i	$-0.478582\pi$
$37$	0.817948	0.134470	0.0672349	+	0.997737i	$0.478582\pi$
$38$	0.165613	0.0268659
$39$	6.96648	1.11553
$40$	3.07656	0.486446
$41$	−11.4451	−1.78742	−0.893709	−	0.448648i	$-0.851906\pi$
$41$	−11.4451	−1.78742	−0.893709	+	0.448648i	$0.851906\pi$
$42$	7.10595	1.09647
$43$	−11.1138	−1.69484	−0.847419	−	0.530925i	$-0.821845\pi$
$43$	−11.1138	−1.69484	−0.847419	+	0.530925i	$0.821845\pi$
$44$	3.64944	0.550175
$45$	2.51573	0.375024
$46$	−3.09608	−0.456492
$47$	7.61709	1.11107	0.555534	−	0.831494i	$-0.312514\pi$
$47$	7.61709	1.11107	0.555534	+	0.831494i	$0.312514\pi$
$48$	−4.71411	−0.680424
$49$	0.208142	0.0297345
$50$	−1.12696	−0.159376
$51$	2.34856	0.328864
$52$	−2.16527	−0.300268
$53$	−1.43850	−0.197593	−0.0987963	−	0.995108i	$-0.531499\pi$
$53$	−1.43850	−0.197593	−0.0987963	+	0.995108i	$0.531499\pi$
$54$	1.28172	0.174420
$55$	−4.99951	−0.674133
$56$	−8.25993	−1.10378
$57$	−0.345133	−0.0457140
$58$	−3.71538	−0.487853
$59$	4.83444	0.629390	0.314695	−	0.949193i	$-0.398098\pi$
$59$	4.83444	0.629390	0.314695	+	0.949193i	$0.398098\pi$
$60$	−1.71436	−0.221323
$61$	−0.863601	−0.110573	−0.0552864	−	0.998471i	$-0.517607\pi$
$61$	−0.863601	−0.110573	−0.0552864	+	0.998471i	$0.517607\pi$
$62$	−3.28839	−0.417626
$63$	−6.75424	−0.850954
$64$	8.39952	1.04994
$65$	2.96628	0.367921
$66$	13.2324	1.62879
$67$	3.69024	0.450835	0.225418	−	0.974262i	$-0.427625\pi$
$67$	3.69024	0.450835	0.225418	+	0.974262i	$0.427625\pi$
$68$	−0.729961	−0.0885208
$69$	6.45216	0.776749
$70$	3.02566	0.361636
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	7.73980	0.912144
$73$	0.104478	0.0122283	0.00611413	−	0.999981i	$-0.498054\pi$
$73$	0.104478	0.0122283	0.00611413	+	0.999981i	$0.498054\pi$
$74$	−0.921794	−0.107156
$75$	2.34856	0.271188
$76$	0.107272	0.0123049
$77$	13.4227	1.52966
$78$	−7.85095	−0.888945
$79$	1.98678	0.223530	0.111765	−	0.993735i	$-0.464350\pi$
$79$	1.98678	0.223530	0.111765	+	0.993735i	$0.464350\pi$
$80$	−2.00724	−0.224416
$81$	−10.2183	−1.13536
$82$	12.8981	1.42436
$83$	−3.90615	−0.428755	−0.214378	−	0.976751i	$-0.568772\pi$
$83$	−3.90615	−0.428755	−0.214378	+	0.976751i	$0.568772\pi$
$84$	4.60270	0.502196
$85$	1.00000	0.108465
$86$	12.5248	1.35058
$87$	7.74277	0.830112
$88$	−15.3813	−1.63965
$89$	−10.2965	−1.09143	−0.545713	−	0.837972i	$-0.683741\pi$
$89$	−10.2965	−1.09143	−0.545713	+	0.837972i	$0.683741\pi$
$90$	−2.83513	−0.298849
$91$	−7.96386	−0.834839
$92$	−2.00541	−0.209078
$93$	6.85294	0.710617
$94$	−8.58416	−0.885388
$95$	−0.146955	−0.0150773
$96$	−9.13834	−0.932678
$97$	−13.5415	−1.37493	−0.687464	−	0.726219i	$-0.741276\pi$
$97$	−13.5415	−1.37493	−0.687464	+	0.726219i	$0.741276\pi$
$98$	−0.234567	−0.0236949
$99$	−12.5774	−1.26408
$100$	−0.729961	−0.0729961
$101$	15.7254	1.56474	0.782370	−	0.622814i	$-0.214011\pi$
$101$	15.7254	1.56474	0.782370	+	0.622814i	$0.214011\pi$
$102$	−2.64673	−0.262066
$103$	−4.88342	−0.481178	−0.240589	−	0.970627i	$-0.577341\pi$
$103$	−4.88342	−0.481178	−0.240589	+	0.970627i	$0.577341\pi$
$104$	9.12592	0.894870
$105$	−6.30541	−0.615345
$106$	1.62113	0.157458
$107$	2.92658	0.282923	0.141462	−	0.989944i	$-0.454820\pi$
$107$	2.92658	0.282923	0.141462	+	0.989944i	$0.454820\pi$
$108$	0.830204	0.0798864
$109$	7.99251	0.765544	0.382772	−	0.923843i	$-0.374970\pi$
$109$	7.99251	0.765544	0.382772	+	0.923843i	$0.374970\pi$
$110$	5.63425	0.537204
$111$	1.92100	0.182333
$112$	5.38902	0.509215
$113$	−17.7241	−1.66734	−0.833672	−	0.552260i	$-0.813765\pi$
$113$	−17.7241	−1.66734	−0.833672	+	0.552260i	$0.813765\pi$
$114$	0.388951	0.0364286
$115$	2.74728	0.256186
$116$	−2.40655	−0.223442
$117$	7.46237	0.689896
$118$	−5.44822	−0.501549
$119$	−2.68480	−0.246115
$120$	7.22548	0.659593
$121$	13.9951	1.27228
$122$	0.973244	0.0881133
$123$	−26.8794	−2.42363
$124$	−2.12998	−0.191278
$125$	1.00000	0.0894427
$126$	7.61176	0.678109
$127$	−19.4885	−1.72932	−0.864661	−	0.502357i	$-0.832467\pi$
$127$	−19.4885	−1.72932	−0.864661	+	0.502357i	$0.832467\pi$
$128$	−1.68384	−0.148832
$129$	−26.1014	−2.29810
$130$	−3.34288	−0.293190
$131$	5.24467	0.458229	0.229114	−	0.973400i	$-0.426417\pi$
$131$	5.24467	0.458229	0.229114	+	0.973400i	$0.426417\pi$
$132$	8.57094	0.746005
$133$	0.394545	0.0342114
$134$	−4.15876	−0.359262
$135$	−1.13733	−0.0978855
$136$	3.07656	0.263813
$137$	−21.2939	−1.81926	−0.909632	−	0.415415i	$-0.863636\pi$
$137$	−21.2939	−1.81926	−0.909632	+	0.415415i	$0.863636\pi$
$138$	−7.27133	−0.618977
$139$	9.10798	0.772529	0.386264	−	0.922388i	$-0.373765\pi$
$139$	9.10798	0.772529	0.386264	+	0.922388i	$0.373765\pi$
$140$	1.95980	0.165633
$141$	17.8892	1.50654
$142$	1.12696	0.0945724
$143$	−14.8299	−1.24014
$144$	−5.04967	−0.420806
$145$	3.29682	0.273786
$146$	−0.117743	−0.00974447
$147$	0.488833	0.0403183
$148$	−0.597070	−0.0490788
$149$	−13.8985	−1.13861	−0.569304	−	0.822127i	$-0.692787\pi$
$149$	−13.8985	−1.13861	−0.569304	+	0.822127i	$0.692787\pi$
$150$	−2.64673	−0.216105
$151$	−2.94403	−0.239581	−0.119791	−	0.992799i	$-0.538222\pi$
$151$	−2.94403	−0.239581	−0.119791	+	0.992799i	$0.538222\pi$
$152$	−0.452116	−0.0366714
$153$	2.51573	0.203385
$154$	−15.1268	−1.21895
$155$	2.91793	0.234374
$156$	−5.08526	−0.407146
$157$	−6.89217	−0.550055	−0.275028	−	0.961436i	$-0.588687\pi$
$157$	−6.89217	−0.550055	−0.275028	+	0.961436i	$0.588687\pi$
$158$	−2.23902	−0.178127
$159$	−3.37839	−0.267924
$160$	−3.89104	−0.307614
$161$	−7.37590	−0.581303
$162$	11.5156	0.904751
$163$	19.5410	1.53057	0.765285	−	0.643691i	$-0.222598\pi$
$163$	19.5410	1.53057	0.765285	+	0.643691i	$0.222598\pi$
$164$	8.35444	0.652372
$165$	−11.7416	−0.914086
$166$	4.40207	0.341667
$167$	11.3954	0.881805	0.440903	−	0.897555i	$-0.354658\pi$
$167$	11.3954	0.881805	0.440903	+	0.897555i	$0.354658\pi$
$168$	−19.3990	−1.49666
$169$	−4.20120	−0.323169
$170$	−1.12696	−0.0864339
$171$	−0.369700	−0.0282717
$172$	8.11264	0.618583
$173$	6.64961	0.505560	0.252780	−	0.967524i	$-0.418655\pi$
$173$	6.64961	0.505560	0.252780	+	0.967524i	$0.418655\pi$
$174$	−8.72580	−0.661501
$175$	−2.68480	−0.202952
$176$	10.0352	0.756431
$177$	11.3540	0.853417
$178$	11.6037	0.869737
$179$	−13.0003	−0.971690	−0.485845	−	0.874045i	$-0.661488\pi$
$179$	−13.0003	−0.971690	−0.485845	+	0.874045i	$0.661488\pi$
$180$	−1.83639	−0.136876
$181$	−12.6371	−0.939306	−0.469653	−	0.882851i	$-0.655621\pi$
$181$	−12.6371	−0.939306	−0.469653	+	0.882851i	$0.655621\pi$
$182$	8.97495	0.665267
$183$	−2.02822	−0.149930
$184$	8.45218	0.623103
$185$	0.817948	0.0601367
$186$	−7.72299	−0.566277
$187$	−4.99951	−0.365600
$188$	−5.56018	−0.405518
$189$	3.05349	0.222109
$190$	0.165613	0.0120148
$191$	−20.5457	−1.48664	−0.743319	−	0.668937i	$-0.766750\pi$
$191$	−20.5457	−1.48664	−0.743319	+	0.668937i	$0.766750\pi$
$192$	19.7268	1.42366
$193$	−19.3515	−1.39295	−0.696476	−	0.717580i	$-0.745250\pi$
$193$	−19.3515	−1.39295	−0.696476	+	0.717580i	$0.745250\pi$
$194$	15.2607	1.09565
$195$	6.96648	0.498880
$196$	−0.151935	−0.0108525
$197$	25.0872	1.78739	0.893694	−	0.448676i	$-0.148104\pi$
$197$	25.0872	1.78739	0.893694	+	0.448676i	$0.148104\pi$
$198$	14.1743	1.00732
$199$	−1.16885	−0.0828576	−0.0414288	−	0.999141i	$-0.513191\pi$
$199$	−1.16885	−0.0828576	−0.0414288	+	0.999141i	$0.513191\pi$
$200$	3.07656	0.217545
$201$	8.66676	0.611306
$202$	−17.7219	−1.24691
$203$	−8.85129	−0.621239
$204$	−1.71436	−0.120029
$205$	−11.4451	−0.799357
$206$	5.50342	0.383441
$207$	6.91144	0.480378
$208$	−5.95402	−0.412837
$209$	0.734703	0.0508205
$210$	7.10595	0.490357
$211$	−4.46523	−0.307399	−0.153699	−	0.988118i	$-0.549119\pi$
$211$	−4.46523	−0.307399	−0.153699	+	0.988118i	$0.549119\pi$
$212$	1.05005	0.0721174
$213$	−2.34856	−0.160921
$214$	−3.29814	−0.225456
$215$	−11.1138	−0.757955
$216$	−3.49905	−0.238080
$217$	−7.83406	−0.531811
$218$	−9.00724	−0.610047
$219$	0.245373	0.0165808
$220$	3.64944	0.246046
$221$	2.96628	0.199533
$222$	−2.16489	−0.145298
$223$	−15.0665	−1.00893	−0.504465	−	0.863432i	$-0.668310\pi$
$223$	−15.0665	−1.00893	−0.504465	+	0.863432i	$0.668310\pi$
$224$	10.4467	0.697997
$225$	2.51573	0.167716
$226$	19.9744	1.32867
$227$	−18.3810	−1.21999	−0.609995	−	0.792405i	$-0.708829\pi$
$227$	−18.3810	−1.21999	−0.609995	+	0.792405i	$0.708829\pi$
$228$	0.251934	0.0166847
$229$	3.69028	0.243861	0.121930	−	0.992539i	$-0.461092\pi$
$229$	3.69028	0.243861	0.121930	+	0.992539i	$0.461092\pi$
$230$	−3.09608	−0.204149
$231$	31.5239	2.07412
$232$	10.1428	0.665910
$233$	−22.5926	−1.48009	−0.740046	−	0.672557i	$-0.765196\pi$
$233$	−22.5926	−1.48009	−0.740046	+	0.672557i	$0.765196\pi$
$234$	−8.40979	−0.549765
$235$	7.61709	0.496884
$236$	−3.52895	−0.229715
$237$	4.66606	0.303093
$238$	3.02566	0.196124
$239$	1.27459	0.0824461	0.0412230	−	0.999150i	$-0.486875\pi$
$239$	1.27459	0.0824461	0.0412230	+	0.999150i	$0.486875\pi$
$240$	−4.71411	−0.304295
$241$	2.62403	0.169029	0.0845144	−	0.996422i	$-0.473066\pi$
$241$	2.62403	0.169029	0.0845144	+	0.996422i	$0.473066\pi$
$242$	−15.7719	−1.01386
$243$	−20.5863	−1.32061
$244$	0.630395	0.0403569
$245$	0.208142	0.0132977
$246$	30.2920	1.93135
$247$	−0.435910	−0.0277363
$248$	8.97719	0.570052
$249$	−9.17382	−0.581367
$250$	−1.12696	−0.0712752
$251$	−19.3924	−1.22404	−0.612019	−	0.790843i	$-0.709642\pi$
$251$	−19.3924	−1.22404	−0.612019	+	0.790843i	$0.709642\pi$
$252$	4.93033	0.310582
$253$	−13.7351	−0.863516
$254$	21.9627	1.37806
$255$	2.34856	0.147073
$256$	−14.9014	−0.931338
$257$	−14.8163	−0.924214	−0.462107	−	0.886824i	$-0.652906\pi$
$257$	−14.8163	−0.924214	−0.462107	+	0.886824i	$0.652906\pi$
$258$	29.4153	1.83131
$259$	−2.19602	−0.136454
$260$	−2.16527	−0.134284
$261$	8.29392	0.513380
$262$	−5.91053	−0.365154
$263$	−3.21989	−0.198547	−0.0992734	−	0.995060i	$-0.531652\pi$
$263$	−3.21989	−0.198547	−0.0992734	+	0.995060i	$0.531652\pi$
$264$	−36.1238	−2.22327
$265$	−1.43850	−0.0883661
$266$	−0.444636	−0.0272624
$267$	−24.1819	−1.47991
$268$	−2.69373	−0.164546
$269$	−3.21799	−0.196204	−0.0981021	−	0.995176i	$-0.531277\pi$
$269$	−3.21799	−0.196204	−0.0981021	+	0.995176i	$0.531277\pi$
$270$	1.28172	0.0780031
$271$	−11.0559	−0.671598	−0.335799	−	0.941934i	$-0.609006\pi$
$271$	−11.0559	−0.671598	−0.335799	+	0.941934i	$0.609006\pi$
$272$	−2.00724	−0.121707
$273$	−18.7036	−1.13199
$274$	23.9974	1.44974
$275$	−4.99951	−0.301482
$276$	−4.70983	−0.283498
$277$	−7.80360	−0.468873	−0.234436	−	0.972131i	$-0.575324\pi$
$277$	−7.80360	−0.468873	−0.234436	+	0.972131i	$0.575324\pi$
$278$	−10.2643	−0.615614
$279$	7.34074	0.439479
$280$	−8.25993	−0.493626
$281$	−1.18549	−0.0707203	−0.0353602	−	0.999375i	$-0.511258\pi$
$281$	−1.18549	−0.0707203	−0.0353602	+	0.999375i	$0.511258\pi$
$282$	−20.1604	−1.20054
$283$	23.4952	1.39664	0.698322	−	0.715784i	$-0.253930\pi$
$283$	23.4952	1.39664	0.698322	+	0.715784i	$0.253930\pi$
$284$	0.729961	0.0433152
$285$	−0.345133	−0.0204439
$286$	16.7127	0.988245
$287$	30.7277	1.81380
$288$	−9.78882	−0.576812
$289$	1.00000	0.0588235
$290$	−3.71538	−0.218175
$291$	−31.8029	−1.86432
$292$	−0.0762650	−0.00446307
$293$	−4.96919	−0.290303	−0.145152	−	0.989409i	$-0.546367\pi$
$293$	−4.96919	−0.290303	−0.145152	+	0.989409i	$0.546367\pi$
$294$	−0.550895	−0.0321289
$295$	4.83444	0.281472
$296$	2.51646	0.146266
$297$	5.68607	0.329939
$298$	15.6630	0.907335
$299$	8.14921	0.471281
$300$	−1.71436	−0.0989784
$301$	29.8383	1.71985
$302$	3.31780	0.190918
$303$	36.9322	2.12170
$304$	0.294974	0.0169179
$305$	−0.863601	−0.0494496
$306$	−2.83513	−0.162074
$307$	26.3155	1.50191	0.750953	−	0.660355i	$-0.229594\pi$
$307$	26.3155	1.50191	0.750953	+	0.660355i	$0.229594\pi$
$308$	−9.79802	−0.558294
$309$	−11.4690	−0.652449
$310$	−3.28839	−0.186768
$311$	24.2779	1.37668	0.688338	−	0.725391i	$-0.258341\pi$
$311$	24.2779	1.37668	0.688338	+	0.725391i	$0.258341\pi$
$312$	21.4328	1.21339
$313$	−12.5498	−0.709354	−0.354677	−	0.934989i	$-0.615409\pi$
$313$	−12.5498	−0.709354	−0.354677	+	0.934989i	$0.615409\pi$
$314$	7.76721	0.438329
$315$	−6.75424	−0.380558
$316$	−1.45027	−0.0815840
$317$	17.3519	0.974578	0.487289	−	0.873241i	$-0.337986\pi$
$317$	17.3519	0.974578	0.487289	+	0.873241i	$0.337986\pi$
$318$	3.80731	0.213504
$319$	−16.4825	−0.922841
$320$	8.39952	0.469547
$321$	6.87325	0.383628
$322$	8.31235	0.463229
$323$	−0.146955	−0.00817680
$324$	7.45895	0.414386
$325$	2.96628	0.164539
$326$	−22.0219	−1.21968
$327$	18.7709	1.03803
$328$	−35.2114	−1.94422
$329$	−20.4504	−1.12746
$330$	13.2324	0.728418
$331$	32.9567	1.81146	0.905732	−	0.423851i	$-0.139322\pi$
$331$	32.9567	1.81146	0.905732	+	0.423851i	$0.139322\pi$
$332$	2.85133	0.156487
$333$	2.05774	0.112763
$334$	−12.8422	−0.702694
$335$	3.69024	0.201620
$336$	12.6564	0.690466
$337$	−10.0119	−0.545384	−0.272692	−	0.962101i	$-0.587914\pi$
$337$	−10.0119	−0.545384	−0.272692	+	0.962101i	$0.587914\pi$
$338$	4.73458	0.257527
$339$	−41.6261	−2.26082
$340$	−0.729961	−0.0395877
$341$	−14.5882	−0.789997
$342$	0.416637	0.0225292
$343$	18.2348	0.984585
$344$	−34.1922	−1.84352
$345$	6.45216	0.347373
$346$	−7.49385	−0.402872
$347$	21.0718	1.13119	0.565597	−	0.824682i	$-0.308646\pi$
$347$	21.0718	1.13119	0.565597	+	0.824682i	$0.308646\pi$
$348$	−5.65192	−0.302975
$349$	25.7502	1.37837	0.689187	−	0.724583i	$-0.257968\pi$
$349$	25.7502	1.37837	0.689187	+	0.724583i	$0.257968\pi$
$350$	3.02566	0.161728
$351$	−3.37363	−0.180071
$352$	19.4533	1.03686
$353$	−22.0584	−1.17405	−0.587026	−	0.809568i	$-0.699701\pi$
$353$	−22.0584	−1.17405	−0.587026	+	0.809568i	$0.699701\pi$
$354$	−12.7955	−0.680072
$355$	−1.00000	−0.0530745
$356$	7.51603	0.398349
$357$	−6.30541	−0.333718
$358$	14.6508	0.774321
$359$	−33.6360	−1.77524	−0.887620	−	0.460577i	$-0.847643\pi$
$359$	−33.6360	−1.77524	−0.887620	+	0.460577i	$0.847643\pi$
$360$	7.73980	0.407923
$361$	−18.9784	−0.998863
$362$	14.2415	0.748515
$363$	32.8683	1.72514
$364$	5.81330	0.304700
$365$	0.104478	0.00546864
$366$	2.28572	0.119477
$367$	−36.5345	−1.90708	−0.953542	−	0.301262i	$-0.902592\pi$
$367$	−36.5345	−1.90708	−0.953542	+	0.301262i	$0.902592\pi$
$368$	−5.51445	−0.287460
$369$	−28.7927	−1.49889
$370$	−0.921794	−0.0479218
$371$	3.86207	0.200509
$372$	−5.00238	−0.259361
$373$	−19.1209	−0.990041	−0.495020	−	0.868881i	$-0.664839\pi$
$373$	−19.1209	−0.990041	−0.495020	+	0.868881i	$0.664839\pi$
$374$	5.63425	0.291340
$375$	2.34856	0.121279
$376$	23.4344	1.20854
$377$	9.77927	0.503658
$378$	−3.44116	−0.176994
$379$	−13.3550	−0.686003	−0.343001	−	0.939335i	$-0.611444\pi$
$379$	−13.3550	−0.686003	−0.343001	+	0.939335i	$0.611444\pi$
$380$	0.107272	0.00550291
$381$	−45.7698	−2.34486
$382$	23.1542	1.18467
$383$	8.25907	0.422019	0.211009	−	0.977484i	$-0.432325\pi$
$383$	8.25907	0.422019	0.211009	+	0.977484i	$0.432325\pi$
$384$	−3.95460	−0.201808
$385$	13.4227	0.684083
$386$	21.8084	1.11002
$387$	−27.9594	−1.42125
$388$	9.88474	0.501822
$389$	17.1929	0.871714	0.435857	−	0.900016i	$-0.356445\pi$
$389$	17.1929	0.871714	0.435857	+	0.900016i	$0.356445\pi$
$390$	−7.85095	−0.397548
$391$	2.74728	0.138936
$392$	0.640359	0.0323430
$393$	12.3174	0.621331
$394$	−28.2723	−1.42434
$395$	1.98678	0.0999655
$396$	9.18103	0.461364
$397$	−27.7695	−1.39371	−0.696855	−	0.717212i	$-0.745418\pi$
$397$	−27.7695	−1.39371	−0.696855	+	0.717212i	$0.745418\pi$
$398$	1.31725	0.0660276
$399$	0.926613	0.0463887
$400$	−2.00724	−0.100362
$401$	−26.1535	−1.30604	−0.653021	−	0.757340i	$-0.726499\pi$
$401$	−26.1535	−1.30604	−0.653021	+	0.757340i	$0.726499\pi$
$402$	−9.76709	−0.487138
$403$	8.65540	0.431156
$404$	−11.4790	−0.571100
$405$	−10.2183	−0.507751
$406$	9.97505	0.495053
$407$	−4.08934	−0.202701
$408$	7.22548	0.357715
$409$	−1.71549	−0.0848256	−0.0424128	−	0.999100i	$-0.513504\pi$
$409$	−1.71549	−0.0848256	−0.0424128	+	0.999100i	$0.513504\pi$
$410$	12.8981	0.636993
$411$	−50.0101	−2.46682
$412$	3.56471	0.175620
$413$	−12.9795	−0.638679
$414$	−7.78892	−0.382804
$415$	−3.90615	−0.191745
$416$	−11.5419	−0.565888
$417$	21.3906	1.04750
$418$	−0.827981	−0.0404979
$419$	12.1179	0.591996	0.295998	−	0.955189i	$-0.404348\pi$
$419$	12.1179	0.591996	0.295998	+	0.955189i	$0.404348\pi$
$420$	4.60270	0.224589
$421$	20.7240	1.01003	0.505013	−	0.863112i	$-0.331488\pi$
$421$	20.7240	1.01003	0.505013	+	0.863112i	$0.331488\pi$
$422$	5.03213	0.244960
$423$	19.1626	0.931717
$424$	−4.42561	−0.214927
$425$	1.00000	0.0485071
$426$	2.64673	0.128235
$427$	2.31859	0.112205
$428$	−2.13629	−0.103262
$429$	−34.8290	−1.68156
$430$	12.5248	0.604000
$431$	−28.9123	−1.39266	−0.696329	−	0.717723i	$-0.745185\pi$
$431$	−28.9123	−1.39266	−0.696329	+	0.717723i	$0.745185\pi$
$432$	2.28288	0.109835
$433$	9.03485	0.434187	0.217094	−	0.976151i	$-0.430342\pi$
$433$	9.03485	0.434187	0.217094	+	0.976151i	$0.430342\pi$
$434$	8.82867	0.423790
$435$	7.74277	0.371237
$436$	−5.83422	−0.279408
$437$	−0.403728	−0.0193129
$438$	−0.276526	−0.0132129
$439$	6.55316	0.312765	0.156383	−	0.987697i	$-0.450017\pi$
$439$	6.55316	0.312765	0.156383	+	0.987697i	$0.450017\pi$
$440$	−15.3813	−0.733273
$441$	0.523629	0.0249347
$442$	−3.34288	−0.159004
$443$	−36.2994	−1.72464	−0.862318	−	0.506367i	$-0.830988\pi$
$443$	−36.2994	−1.72464	−0.862318	+	0.506367i	$0.830988\pi$
$444$	−1.40225	−0.0665480
$445$	−10.2965	−0.488100
$446$	16.9794	0.803997
$447$	−32.6414	−1.54388
$448$	−22.5510	−1.06544
$449$	−5.03531	−0.237631	−0.118816	−	0.992916i	$-0.537910\pi$
$449$	−5.03531	−0.237631	−0.118816	+	0.992916i	$0.537910\pi$
$450$	−2.83513	−0.133649
$451$	57.2196	2.69437
$452$	12.9379	0.608548
$453$	−6.91422	−0.324859
$454$	20.7147	0.972187
$455$	−7.96386	−0.373351
$456$	−1.06182	−0.0497243
$457$	−12.0907	−0.565579	−0.282790	−	0.959182i	$-0.591260\pi$
$457$	−12.0907	−0.565579	−0.282790	+	0.959182i	$0.591260\pi$
$458$	−4.15880	−0.194328
$459$	−1.13733	−0.0530859
$460$	−2.00541	−0.0935027
$461$	11.6127	0.540855	0.270428	−	0.962740i	$-0.412835\pi$
$461$	11.6127	0.540855	0.270428	+	0.962740i	$0.412835\pi$
$462$	−35.5262	−1.65283
$463$	36.1421	1.67966	0.839832	−	0.542846i	$-0.182653\pi$
$463$	36.1421	1.67966	0.839832	+	0.542846i	$0.182653\pi$
$464$	−6.61749	−0.307209
$465$	6.85294	0.317797
$466$	25.4610	1.17946
$467$	5.36109	0.248081	0.124041	−	0.992277i	$-0.460415\pi$
$467$	5.36109	0.248081	0.124041	+	0.992277i	$0.460415\pi$
$468$	−5.44724	−0.251799
$469$	−9.90756	−0.457489
$470$	−8.58416	−0.395958
$471$	−16.1867	−0.745843
$472$	14.8734	0.684605
$473$	55.5635	2.55481
$474$	−5.25846	−0.241529
$475$	−0.146955	−0.00674277
$476$	1.95980	0.0898272
$477$	−3.61887	−0.165697
$478$	−1.43641	−0.0656997
$479$	26.5602	1.21357	0.606783	−	0.794868i	$-0.292460\pi$
$479$	26.5602	1.21357	0.606783	+	0.794868i	$0.292460\pi$
$480$	−9.13834	−0.417106
$481$	2.42626	0.110628
$482$	−2.95718	−0.134696
$483$	−17.3228	−0.788213
$484$	−10.2159	−0.464357
$485$	−13.5415	−0.614886
$486$	23.1999	1.05237
$487$	21.1247	0.957253	0.478626	−	0.878019i	$-0.341135\pi$
$487$	21.1247	0.957253	0.478626	+	0.878019i	$0.341135\pi$
$488$	−2.65692	−0.120273
$489$	45.8932	2.07536
$490$	−0.234567	−0.0105967
$491$	14.8626	0.670740	0.335370	−	0.942087i	$-0.391139\pi$
$491$	14.8626	0.670740	0.335370	+	0.942087i	$0.391139\pi$
$492$	19.6209	0.884579
$493$	3.29682	0.148481
$494$	0.491253	0.0221025
$495$	−12.5774	−0.565314
$496$	−5.85698	−0.262986
$497$	2.68480	0.120430
$498$	10.3385	0.463281
$499$	34.3196	1.53636	0.768178	−	0.640236i	$-0.221164\pi$
$499$	34.3196	1.53636	0.768178	+	0.640236i	$0.221164\pi$
$500$	−0.729961	−0.0326448
$501$	26.7629	1.19568
$502$	21.8545	0.975412
$503$	−1.64210	−0.0732176	−0.0366088	−	0.999330i	$-0.511656\pi$
$503$	−1.64210	−0.0732176	−0.0366088	+	0.999330i	$0.511656\pi$
$504$	−20.7798	−0.925606
$505$	15.7254	0.699773
$506$	15.4789	0.688120
$507$	−9.86677	−0.438199
$508$	14.2258	0.631168
$509$	17.2088	0.762769	0.381384	−	0.924417i	$-0.375447\pi$
$509$	17.2088	0.762769	0.381384	+	0.924417i	$0.375447\pi$
$510$	−2.64673	−0.117199
$511$	−0.280503	−0.0124087
$512$	20.1610	0.890998
$513$	0.167136	0.00737924
$514$	16.6974	0.736489
$515$	−4.88342	−0.215189
$516$	19.0530	0.838762
$517$	−38.0817	−1.67483
$518$	2.47483	0.108738
$519$	15.6170	0.685511
$520$	9.12592	0.400198
$521$	−18.2944	−0.801492	−0.400746	−	0.916189i	$-0.631249\pi$
$521$	−18.2944	−0.801492	−0.400746	+	0.916189i	$0.631249\pi$
$522$	−9.34691	−0.409103
$523$	11.1540	0.487729	0.243864	−	0.969809i	$-0.421585\pi$
$523$	11.1540	0.487729	0.243864	+	0.969809i	$0.421585\pi$
$524$	−3.82840	−0.167244
$525$	−6.30541	−0.275191
$526$	3.62869	0.158218
$527$	2.91793	0.127107
$528$	23.5682	1.02568
$529$	−15.4524	−0.671845
$530$	1.62113	0.0704173
$531$	12.1622	0.527793
$532$	−0.288002	−0.0124865
$533$	−33.9492	−1.47050
$534$	27.2521	1.17931
$535$	2.92658	0.126527
$536$	11.3532	0.490386
$537$	−30.5320	−1.31756
$538$	3.62654	0.156351
$539$	−1.04061	−0.0448220
$540$	0.830204	0.0357263
$541$	−45.9818	−1.97691	−0.988457	−	0.151503i	$-0.951589\pi$
$541$	−45.9818	−1.97691	−0.988457	+	0.151503i	$0.951589\pi$
$542$	12.4596	0.535184
$543$	−29.6789	−1.27364
$544$	−3.89104	−0.166827
$545$	7.99251	0.342362
$546$	21.0782	0.902064
$547$	−24.3199	−1.03984	−0.519922	−	0.854214i	$-0.674039\pi$
$547$	−24.3199	−1.03984	−0.519922	+	0.854214i	$0.674039\pi$
$548$	15.5437	0.663996
$549$	−2.17259	−0.0927239
$550$	5.63425	0.240245
$551$	−0.484484	−0.0206397
$552$	19.8504	0.844891
$553$	−5.33409	−0.226829
$554$	8.79435	0.373636
$555$	1.92100	0.0815419
$556$	−6.64847	−0.281958
$557$	−5.45632	−0.231192	−0.115596	−	0.993296i	$-0.536878\pi$
$557$	−5.45632	−0.231192	−0.115596	+	0.993296i	$0.536878\pi$
$558$	−8.27273	−0.350212
$559$	−32.9666	−1.39434
$560$	5.38902	0.227728
$561$	−11.7416	−0.495733
$562$	1.33600	0.0563557
$563$	21.3345	0.899140	0.449570	−	0.893245i	$-0.351577\pi$
$563$	21.3345	0.899140	0.449570	+	0.893245i	$0.351577\pi$
$564$	−13.0584	−0.549858
$565$	−17.7241	−0.745659
$566$	−26.4781	−1.11296
$567$	27.4340	1.15212
$568$	−3.07656	−0.129089
$569$	40.2392	1.68692	0.843458	−	0.537195i	$-0.180516\pi$
$569$	40.2392	1.68692	0.843458	+	0.537195i	$0.180516\pi$
$570$	0.388951	0.0162914
$571$	21.4776	0.898808	0.449404	−	0.893329i	$-0.351636\pi$
$571$	21.4776	0.898808	0.449404	+	0.893329i	$0.351636\pi$
$572$	10.8253	0.452627
$573$	−48.2529	−2.01579
$574$	−34.6289	−1.44538
$575$	2.74728	0.114570
$576$	21.1310	0.880457
$577$	−15.5582	−0.647696	−0.323848	−	0.946109i	$-0.604977\pi$
$577$	−15.5582	−0.647696	−0.323848	+	0.946109i	$0.604977\pi$
$578$	−1.12696	−0.0468754
$579$	−45.4482	−1.88876
$580$	−2.40655	−0.0999264
$581$	10.4872	0.435083
$582$	35.8406	1.48564
$583$	7.19177	0.297853
$584$	0.321433	0.0133010
$585$	7.46237	0.308531
$586$	5.60008	0.231337
$587$	41.1890	1.70005	0.850026	−	0.526741i	$-0.176586\pi$
$587$	41.1890	1.70005	0.850026	+	0.526741i	$0.176586\pi$
$588$	−0.356829	−0.0147154
$589$	−0.428805	−0.0176686
$590$	−5.44822	−0.224300
$591$	58.9188	2.42359
$592$	−1.64181	−0.0674781
$593$	−29.5486	−1.21342	−0.606708	−	0.794925i	$-0.707510\pi$
$593$	−29.5486	−1.21342	−0.606708	+	0.794925i	$0.707510\pi$
$594$	−6.40798	−0.262923
$595$	−2.68480	−0.110066
$596$	10.1453	0.415569
$597$	−2.74511	−0.112350
$598$	−9.18383	−0.375555
$599$	11.7130	0.478581	0.239290	−	0.970948i	$-0.423085\pi$
$599$	11.7130	0.478581	0.239290	+	0.970948i	$0.423085\pi$
$600$	7.22548	0.294979
$601$	−42.5362	−1.73509	−0.867544	−	0.497360i	$-0.834303\pi$
$601$	−42.5362	−1.73509	−0.867544	+	0.497360i	$0.834303\pi$
$602$	−33.6266	−1.37052
$603$	9.28367	0.378060
$604$	2.14902	0.0874425
$605$	13.9951	0.568981
$606$	−41.6211	−1.69074
$607$	3.93930	0.159891	0.0799455	−	0.996799i	$-0.474525\pi$
$607$	3.93930	0.159891	0.0799455	+	0.996799i	$0.474525\pi$
$608$	0.571808	0.0231899
$609$	−20.7878	−0.842363
$610$	0.973244	0.0394055
$611$	22.5944	0.914072
$612$	−1.83639	−0.0742316
$613$	12.9917	0.524729	0.262364	−	0.964969i	$-0.415498\pi$
$613$	12.9917	0.524729	0.262364	+	0.964969i	$0.415498\pi$
$614$	−29.6565	−1.19684
$615$	−26.8794	−1.08388
$616$	41.2956	1.66385
$617$	24.4106	0.982736	0.491368	−	0.870952i	$-0.336497\pi$
$617$	24.4106	0.982736	0.491368	+	0.870952i	$0.336497\pi$
$618$	12.9251	0.519924
$619$	−17.0767	−0.686372	−0.343186	−	0.939267i	$-0.611506\pi$
$619$	−17.0767	−0.686372	−0.343186	+	0.939267i	$0.611506\pi$
$620$	−2.12998	−0.0855419
$621$	−3.12456	−0.125384
$622$	−27.3603	−1.09705
$623$	27.6440	1.10753
$624$	−13.9834	−0.559783
$625$	1.00000	0.0400000
$626$	14.1431	0.565271
$627$	1.72550	0.0689096
$628$	5.03102	0.200759
$629$	0.817948	0.0326137
$630$	7.61176	0.303260
$631$	30.6759	1.22119	0.610595	−	0.791943i	$-0.290930\pi$
$631$	30.6759	1.22119	0.610595	+	0.791943i	$0.290930\pi$
$632$	6.11243	0.243139
$633$	−10.4869	−0.416815
$634$	−19.5549	−0.776623
$635$	−19.4885	−0.773376
$636$	2.46609	0.0977870
$637$	0.617406	0.0244625
$638$	18.5751	0.735394
$639$	−2.51573	−0.0995209
$640$	−1.68384	−0.0665597
$641$	−29.4070	−1.16151	−0.580753	−	0.814080i	$-0.697242\pi$
$641$	−29.4070	−1.16151	−0.580753	+	0.814080i	$0.697242\pi$
$642$	−7.74588	−0.305706
$643$	−24.5392	−0.967731	−0.483866	−	0.875142i	$-0.660768\pi$
$643$	−24.5392	−0.967731	−0.483866	+	0.875142i	$0.660768\pi$
$644$	5.38412	0.212164
$645$	−26.1014	−1.02774
$646$	0.165613	0.00651594
$647$	−0.247164	−0.00971700	−0.00485850	−	0.999988i	$-0.501547\pi$
$647$	−0.247164	−0.00971700	−0.00485850	+	0.999988i	$0.501547\pi$
$648$	−31.4371	−1.23497
$649$	−24.1698	−0.948748
$650$	−3.34288	−0.131118
$651$	−18.3988	−0.721104
$652$	−14.2642	−0.558628
$653$	39.6048	1.54985	0.774927	−	0.632051i	$-0.217787\pi$
$653$	39.6048	1.54985	0.774927	+	0.632051i	$0.217787\pi$
$654$	−21.1540	−0.827189
$655$	5.24467	0.204926
$656$	22.9729	0.896942
$657$	0.262840	0.0102543
$658$	23.0467	0.898455
$659$	−18.8003	−0.732357	−0.366179	−	0.930545i	$-0.619334\pi$
$659$	−18.8003	−0.732357	−0.366179	+	0.930545i	$0.619334\pi$
$660$	8.57094	0.333623
$661$	0.480536	0.0186907	0.00934535	−	0.999956i	$-0.497025\pi$
$661$	0.480536	0.0186907	0.00934535	+	0.999956i	$0.497025\pi$
$662$	−37.1409	−1.44352
$663$	6.96648	0.270556
$664$	−12.0175	−0.466369
$665$	0.394545	0.0152998
$666$	−2.31899	−0.0898590
$667$	9.05729	0.350700
$668$	−8.31822	−0.321842
$669$	−35.3847	−1.36805
$670$	−4.15876	−0.160667
$671$	4.31758	0.166678
$672$	24.5346	0.946443
$673$	41.5197	1.60047	0.800234	−	0.599688i	$-0.204709\pi$
$673$	41.5197	1.60047	0.800234	+	0.599688i	$0.204709\pi$
$674$	11.2830	0.434607
$675$	−1.13733	−0.0437757
$676$	3.06671	0.117950
$677$	−19.0198	−0.730990	−0.365495	−	0.930813i	$-0.619100\pi$
$677$	−19.0198	−0.730990	−0.365495	+	0.930813i	$0.619100\pi$
$678$	46.9110	1.80161
$679$	36.3561	1.39522
$680$	3.07656	0.117981
$681$	−43.1689	−1.65424
$682$	16.4403	0.629534
$683$	12.9015	0.493661	0.246830	−	0.969059i	$-0.420611\pi$
$683$	12.9015	0.493661	0.246830	+	0.969059i	$0.420611\pi$
$684$	0.269867	0.0103186
$685$	−21.2939	−0.813599
$686$	−20.5499	−0.784597
$687$	8.66685	0.330661
$688$	22.3080	0.850485
$689$	−4.26698	−0.162559
$690$	−7.27133	−0.276815
$691$	−19.6431	−0.747258	−0.373629	−	0.927578i	$-0.621887\pi$
$691$	−19.6431	−0.747258	−0.373629	+	0.927578i	$0.621887\pi$
$692$	−4.85395	−0.184520
$693$	33.7679	1.28274
$694$	−23.7471	−0.901427
$695$	9.10798	0.345485
$696$	23.8211	0.902936
$697$	−11.4451	−0.433512
$698$	−29.0194	−1.09840
$699$	−53.0601	−2.00692
$700$	1.95980	0.0740734
$701$	−22.6569	−0.855739	−0.427869	−	0.903841i	$-0.640736\pi$
$701$	−22.6569	−0.855739	−0.427869	+	0.903841i	$0.640736\pi$
$702$	3.80194	0.143495
$703$	−0.120202	−0.00453349
$704$	−41.9935	−1.58269
$705$	17.8892	0.673746
$706$	24.8590	0.935580
$707$	−42.2196	−1.58783
$708$	−8.28796	−0.311480
$709$	−32.2049	−1.20948	−0.604740	−	0.796423i	$-0.706723\pi$
$709$	−32.2049	−1.20948	−0.604740	+	0.796423i	$0.706723\pi$
$710$	1.12696	0.0422941
$711$	4.99820	0.187447
$712$	−31.6777	−1.18717
$713$	8.01639	0.300216
$714$	7.10595	0.265933
$715$	−14.8299	−0.554608
$716$	9.48973	0.354648
$717$	2.99344	0.111792
$718$	37.9064	1.41466
$719$	11.3497	0.423272	0.211636	−	0.977349i	$-0.432121\pi$
$719$	11.3497	0.423272	0.211636	+	0.977349i	$0.432121\pi$
$720$	−5.04967	−0.188190
$721$	13.1110	0.488279
$722$	21.3879	0.795975
$723$	6.16270	0.229193
$724$	9.22456	0.342828
$725$	3.29682	0.122441
$726$	−37.0412	−1.37473
$727$	48.6214	1.80327	0.901635	−	0.432498i	$-0.142368\pi$
$727$	48.6214	1.80327	0.901635	+	0.432498i	$0.142368\pi$
$728$	−24.5013	−0.908077
$729$	−17.6932	−0.655305
$730$	−0.117743	−0.00435786
$731$	−11.1138	−0.411059
$732$	1.48052	0.0547216
$733$	−2.65393	−0.0980250	−0.0490125	−	0.998798i	$-0.515607\pi$
$733$	−2.65393	−0.0980250	−0.0490125	+	0.998798i	$0.515607\pi$
$734$	41.1729	1.51972
$735$	0.488833	0.0180309
$736$	−10.6898	−0.394031
$737$	−18.4494	−0.679592
$738$	32.4482	1.19444
$739$	20.1531	0.741344	0.370672	−	0.928764i	$-0.379127\pi$
$739$	20.1531	0.741344	0.370672	+	0.928764i	$0.379127\pi$
$740$	−0.597070	−0.0219487
$741$	−1.02376	−0.0376088
$742$	−4.35240	−0.159782
$743$	−34.3729	−1.26102	−0.630510	−	0.776181i	$-0.717154\pi$
$743$	−34.3729	−1.26102	−0.630510	+	0.776181i	$0.717154\pi$
$744$	21.0835	0.772957
$745$	−13.8985	−0.509201
$746$	21.5485	0.788945
$747$	−9.82683	−0.359545
$748$	3.64944	0.133437
$749$	−7.85728	−0.287099
$750$	−2.64673	−0.0966450
$751$	22.4103	0.817765	0.408882	−	0.912587i	$-0.365919\pi$
$751$	22.4103	0.817765	0.408882	+	0.912587i	$0.365919\pi$
$752$	−15.2893	−0.557543
$753$	−45.5442	−1.65972
$754$	−11.0208	−0.401356
$755$	−2.94403	−0.107144
$756$	−2.22893	−0.0810654
$757$	−37.8855	−1.37697	−0.688485	−	0.725250i	$-0.741724\pi$
$757$	−37.8855	−1.37697	−0.688485	+	0.725250i	$0.741724\pi$
$758$	15.0506	0.546663
$759$	−32.2576	−1.17088
$760$	−0.452116	−0.0164000
$761$	−17.3945	−0.630549	−0.315275	−	0.949000i	$-0.602097\pi$
$761$	−17.3945	−0.630549	−0.315275	+	0.949000i	$0.602097\pi$
$762$	51.5808	1.86857
$763$	−21.4583	−0.776842
$764$	14.9976	0.542594
$765$	2.51573	0.0909566
$766$	−9.30764	−0.336299
$767$	14.3403	0.517798
$768$	−34.9969	−1.26284
$769$	13.7044	0.494192	0.247096	−	0.968991i	$-0.420524\pi$
$769$	13.7044	0.494192	0.247096	+	0.968991i	$0.420524\pi$
$770$	−15.1268	−0.545132
$771$	−34.7969	−1.25318
$772$	14.1258	0.508400
$773$	51.0529	1.83624	0.918122	−	0.396297i	$-0.129705\pi$
$773$	51.0529	1.83624	0.918122	+	0.396297i	$0.129705\pi$
$774$	31.5091	1.13257
$775$	2.91793	0.104815
$776$	−41.6611	−1.49555
$777$	−5.15750	−0.185024
$778$	−19.3757	−0.694652
$779$	1.68191	0.0602607
$780$	−5.08526	−0.182081
$781$	4.99951	0.178896
$782$	−3.09608	−0.110716
$783$	−3.74956	−0.133998
$784$	−0.417789	−0.0149210
$785$	−6.89217	−0.245992
$786$	−13.8812	−0.495127
$787$	−17.3692	−0.619143	−0.309572	−	0.950876i	$-0.600186\pi$
$787$	−17.3692	−0.619143	−0.309572	+	0.950876i	$0.600186\pi$
$788$	−18.3127	−0.652362
$789$	−7.56210	−0.269218
$790$	−2.23902	−0.0796606
$791$	47.5856	1.69195
$792$	−38.6952	−1.37497
$793$	−2.56168	−0.0909679
$794$	31.2951	1.11062
$795$	−3.37839	−0.119819
$796$	0.853215	0.0302414
$797$	3.68049	0.130370	0.0651849	−	0.997873i	$-0.479236\pi$
$797$	3.68049	0.130370	0.0651849	+	0.997873i	$0.479236\pi$
$798$	−1.04426	−0.0369662
$799$	7.61709	0.269473
$800$	−3.89104	−0.137569
$801$	−25.9032	−0.915246
$802$	29.4739	1.04076
$803$	−0.522340	−0.0184330
$804$	−6.32639	−0.223115
$805$	−7.37590	−0.259966
$806$	−9.75429	−0.343580
$807$	−7.55764	−0.266042
$808$	48.3802	1.70201
$809$	5.24641	0.184454	0.0922270	−	0.995738i	$-0.470601\pi$
$809$	5.24641	0.184454	0.0922270	+	0.995738i	$0.470601\pi$
$810$	11.5156	0.404617
$811$	22.3698	0.785511	0.392756	−	0.919643i	$-0.371522\pi$
$811$	22.3698	0.785511	0.392756	+	0.919643i	$0.371522\pi$
$812$	6.46109	0.226740
$813$	−25.9654	−0.910648
$814$	4.60852	0.161528
$815$	19.5410	0.684492
$816$	−4.71411	−0.165027
$817$	1.63323	0.0571395
$818$	1.93329	0.0675960
$819$	−20.0349	−0.700078
$820$	8.35444	0.291750
$821$	49.8347	1.73924	0.869622	−	0.493718i	$-0.164362\pi$
$821$	49.8347	1.73924	0.869622	+	0.493718i	$0.164362\pi$
$822$	56.3594	1.96576
$823$	−30.0235	−1.04655	−0.523277	−	0.852163i	$-0.675291\pi$
$823$	−30.0235	−1.04655	−0.523277	+	0.852163i	$0.675291\pi$
$824$	−15.0241	−0.523390
$825$	−11.7416	−0.408792
$826$	14.6274	0.508951
$827$	39.9957	1.39079	0.695393	−	0.718630i	$-0.255231\pi$
$827$	39.9957	1.39079	0.695393	+	0.718630i	$0.255231\pi$
$828$	−5.04508	−0.175329
$829$	−13.2116	−0.458858	−0.229429	−	0.973325i	$-0.573686\pi$
$829$	−13.2116	−0.458858	−0.229429	+	0.973325i	$0.573686\pi$
$830$	4.40207	0.152798
$831$	−18.3272	−0.635764
$832$	24.9153	0.863783
$833$	0.208142	0.00721168
$834$	−24.1064	−0.834736
$835$	11.3954	0.394355
$836$	−0.536305	−0.0185485
$837$	−3.31864	−0.114709
$838$	−13.6563	−0.471750
$839$	25.5501	0.882088	0.441044	−	0.897485i	$-0.354608\pi$
$839$	25.5501	0.882088	0.441044	+	0.897485i	$0.354608\pi$
$840$	−19.3990	−0.669327
$841$	−18.1310	−0.625207
$842$	−23.3551	−0.804870
$843$	−2.78419	−0.0958926
$844$	3.25944	0.112195
$845$	−4.20120	−0.144526
$846$	−21.5955	−0.742467
$847$	−37.5740	−1.29106
$848$	2.88740	0.0991537
$849$	55.1799	1.89377
$850$	−1.12696	−0.0386544
$851$	2.24714	0.0770308
$852$	1.71436	0.0587329
$853$	−5.88191	−0.201393	−0.100696	−	0.994917i	$-0.532107\pi$
$853$	−5.88191	−0.201393	−0.100696	+	0.994917i	$0.532107\pi$
$854$	−2.61296	−0.0894138
$855$	−0.369700	−0.0126435
$856$	9.00380	0.307743
$857$	32.9948	1.12708	0.563541	−	0.826088i	$-0.309439\pi$
$857$	32.9948	1.12708	0.563541	+	0.826088i	$0.309439\pi$
$858$	39.2509	1.34000
$859$	−21.2109	−0.723706	−0.361853	−	0.932235i	$-0.617856\pi$
$859$	−21.2109	−0.723706	−0.361853	+	0.932235i	$0.617856\pi$
$860$	8.11264	0.276639
$861$	72.1658	2.45940
$862$	32.5831	1.10978
$863$	−21.6471	−0.736875	−0.368438	−	0.929652i	$-0.620107\pi$
$863$	−21.6471	−0.736875	−0.368438	+	0.929652i	$0.620107\pi$
$864$	4.42538	0.150555
$865$	6.64961	0.226094
$866$	−10.1819	−0.345995
$867$	2.34856	0.0797613
$868$	5.71856	0.194100
$869$	−9.93290	−0.336950
$870$	−8.72580	−0.295832
$871$	10.9463	0.370901
$872$	24.5894	0.832703
$873$	−34.0667	−1.15298
$874$	0.454985	0.0153901
$875$	−2.68480	−0.0907627
$876$	−0.179113	−0.00605167
$877$	−16.5538	−0.558981	−0.279490	−	0.960148i	$-0.590166\pi$
$877$	−16.5538	−0.558981	−0.279490	+	0.960148i	$0.590166\pi$
$878$	−7.38514	−0.249237
$879$	−11.6705	−0.393635
$880$	10.0352	0.338286
$881$	−29.8503	−1.00568	−0.502841	−	0.864379i	$-0.667712\pi$
$881$	−29.8503	−1.00568	−0.502841	+	0.864379i	$0.667712\pi$
$882$	−0.590109	−0.0198700
$883$	−8.16052	−0.274623	−0.137312	−	0.990528i	$-0.543846\pi$
$883$	−8.16052	−0.274623	−0.137312	+	0.990528i	$0.543846\pi$
$884$	−2.16527	−0.0728258
$885$	11.3540	0.381660
$886$	40.9080	1.37433
$887$	−29.1148	−0.977579	−0.488790	−	0.872402i	$-0.662561\pi$
$887$	−29.1148	−0.977579	−0.488790	+	0.872402i	$0.662561\pi$
$888$	5.91006	0.198329
$889$	52.3226	1.75484
$890$	11.6037	0.388958
$891$	51.0864	1.71146
$892$	10.9980	0.368240
$893$	−1.11937	−0.0374583
$894$	36.7856	1.23029
$895$	−13.0003	−0.434553
$896$	4.52078	0.151029
$897$	19.1389	0.639029
$898$	5.67460	0.189364
$899$	9.61989	0.320841
$900$	−1.83639	−0.0612129
$901$	−1.43850	−0.0479232
$902$	−64.4842	−2.14709
$903$	70.0770	2.33202
$904$	−54.5292	−1.81361
$905$	−12.6371	−0.420070
$906$	7.79205	0.258874
$907$	−27.1575	−0.901749	−0.450874	−	0.892587i	$-0.648888\pi$
$907$	−27.1575	−0.901749	−0.450874	+	0.892587i	$0.648888\pi$
$908$	13.4174	0.445272
$909$	39.5610	1.31216
$910$	8.97495	0.297517
$911$	5.30145	0.175645	0.0878224	−	0.996136i	$-0.472009\pi$
$911$	5.30145	0.175645	0.0878224	+	0.996136i	$0.472009\pi$
$912$	0.692763	0.0229397
$913$	19.5288	0.646309
$914$	13.6257	0.450700
$915$	−2.02822	−0.0670508
$916$	−2.69376	−0.0890043
$917$	−14.0809	−0.464991
$918$	1.28172	0.0423031
$919$	−48.1008	−1.58670	−0.793349	−	0.608767i	$-0.791665\pi$
$919$	−48.1008	−1.58670	−0.793349	+	0.608767i	$0.791665\pi$
$920$	8.45218	0.278660
$921$	61.8036	2.03650
$922$	−13.0870	−0.430997
$923$	−2.96628	−0.0976362
$924$	−23.0112	−0.757014
$925$	0.817948	0.0268940
$926$	−40.7307	−1.33849
$927$	−12.2854	−0.403505
$928$	−12.8280	−0.421101
$929$	−37.1286	−1.21815	−0.609075	−	0.793112i	$-0.708459\pi$
$929$	−37.1286	−1.21815	−0.609075	+	0.793112i	$0.708459\pi$
$930$	−7.72299	−0.253247
$931$	−0.0305875	−0.00100246
$932$	16.4917	0.540204
$933$	57.0182	1.86669
$934$	−6.04173	−0.197691
$935$	−4.99951	−0.163501
$936$	22.9584	0.750419
$937$	−1.33314	−0.0435519	−0.0217760	−	0.999763i	$-0.506932\pi$
$937$	−1.33314	−0.0435519	−0.0217760	+	0.999763i	$0.506932\pi$
$938$	11.1654	0.364564
$939$	−29.4739	−0.961843
$940$	−5.56018	−0.181353
$941$	−38.3388	−1.24981	−0.624905	−	0.780701i	$-0.714862\pi$
$941$	−38.3388	−1.24981	−0.624905	+	0.780701i	$0.714862\pi$
$942$	18.2417	0.594348
$943$	−31.4428	−1.02392
$944$	−9.70386	−0.315834
$945$	3.05349	0.0993301
$946$	−62.6179	−2.03588
$947$	−13.8809	−0.451070	−0.225535	−	0.974235i	$-0.572413\pi$
$947$	−13.8809	−0.451070	−0.225535	+	0.974235i	$0.572413\pi$
$948$	−3.40604	−0.110623
$949$	0.309911	0.0100602
$950$	0.165613	0.00537318
$951$	40.7519	1.32147
$952$	−8.25993	−0.267706
$953$	32.7695	1.06151	0.530754	−	0.847526i	$-0.321909\pi$
$953$	32.7695	1.06151	0.530754	+	0.847526i	$0.321909\pi$
$954$	4.07833	0.132041
$955$	−20.5457	−0.664845
$956$	−0.930398	−0.0300912
$957$	−38.7100	−1.25132
$958$	−29.9323	−0.967068
$959$	57.1699	1.84611
$960$	19.7268	0.636679
$961$	−22.4857	−0.725344
$962$	−2.73430	−0.0881573
$963$	7.36250	0.237253
$964$	−1.91544	−0.0616922
$965$	−19.3515	−0.622947
$966$	19.5221	0.628112
$967$	−6.33345	−0.203670	−0.101835	−	0.994801i	$-0.532471\pi$
$967$	−6.33345	−0.203670	−0.101835	+	0.994801i	$0.532471\pi$
$968$	43.0566	1.38389
$969$	−0.345133	−0.0110873
$970$	15.2607	0.489991
$971$	11.0347	0.354121	0.177061	−	0.984200i	$-0.443341\pi$
$971$	11.0347	0.354121	0.177061	+	0.984200i	$0.443341\pi$
$972$	15.0272	0.481997
$973$	−24.4531	−0.783930
$974$	−23.8067	−0.762817
$975$	6.96648	0.223106
$976$	1.73345	0.0554864
$977$	32.2096	1.03048	0.515238	−	0.857047i	$-0.327704\pi$
$977$	32.2096	1.03048	0.515238	+	0.857047i	$0.327704\pi$
$978$	−51.7199	−1.65382
$979$	51.4774	1.64522
$980$	−0.151935	−0.00485339
$981$	20.1070	0.641968
$982$	−16.7496	−0.534500
$983$	−10.0485	−0.320496	−0.160248	−	0.987077i	$-0.551229\pi$
$983$	−10.0485	−0.320496	−0.160248	+	0.987077i	$0.551229\pi$
$984$	−82.6960	−2.63625
$985$	25.0872	0.799344
$986$	−3.71538	−0.118322
$987$	−48.0289	−1.52878
$988$	0.318197	0.0101232
$989$	−30.5328	−0.970885
$990$	14.1743	0.450488
$991$	−0.504810	−0.0160358	−0.00801791	−	0.999968i	$-0.502552\pi$
$991$	−0.504810	−0.0160358	−0.00801791	+	0.999968i	$0.502552\pi$
$992$	−11.3538	−0.360483
$993$	77.4008	2.45624
$994$	−3.02566	−0.0959681
$995$	−1.16885	−0.0370550
$996$	6.69653	0.212188
$997$	21.7813	0.689822	0.344911	−	0.938635i	$-0.387909\pi$
$997$	21.7813	0.689822	0.344911	+	0.938635i	$0.387909\pi$
$998$	−38.6768	−1.22429
$999$	−0.930274	−0.0294326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.11	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12696 q^{2} +2.34856 q^{3} -0.729961 q^{4} +1.00000 q^{5} -2.64673 q^{6} -2.68480 q^{7} +3.07656 q^{8} +2.51573 q^{9} +O(q^{10})\)	\(q-1.12696 q^{2} +2.34856 q^{3} -0.729961 q^{4} +1.00000 q^{5} -2.64673 q^{6} -2.68480 q^{7} +3.07656 q^{8} +2.51573 q^{9} -1.12696 q^{10} -4.99951 q^{11} -1.71436 q^{12} +2.96628 q^{13} +3.02566 q^{14} +2.34856 q^{15} -2.00724 q^{16} +1.00000 q^{17} -2.83513 q^{18} -0.146955 q^{19} -0.729961 q^{20} -6.30541 q^{21} +5.63425 q^{22} +2.74728 q^{23} +7.22548 q^{24} +1.00000 q^{25} -3.34288 q^{26} -1.13733 q^{27} +1.95980 q^{28} +3.29682 q^{29} -2.64673 q^{30} +2.91793 q^{31} -3.89104 q^{32} -11.7416 q^{33} -1.12696 q^{34} -2.68480 q^{35} -1.83639 q^{36} +0.817948 q^{37} +0.165613 q^{38} +6.96648 q^{39} +3.07656 q^{40} -11.4451 q^{41} +7.10595 q^{42} -11.1138 q^{43} +3.64944 q^{44} +2.51573 q^{45} -3.09608 q^{46} +7.61709 q^{47} -4.71411 q^{48} +0.208142 q^{49} -1.12696 q^{50} +2.34856 q^{51} -2.16527 q^{52} -1.43850 q^{53} +1.28172 q^{54} -4.99951 q^{55} -8.25993 q^{56} -0.345133 q^{57} -3.71538 q^{58} +4.83444 q^{59} -1.71436 q^{60} -0.863601 q^{61} -3.28839 q^{62} -6.75424 q^{63} +8.39952 q^{64} +2.96628 q^{65} +13.2324 q^{66} +3.69024 q^{67} -0.729961 q^{68} +6.45216 q^{69} +3.02566 q^{70} -1.00000 q^{71} +7.73980 q^{72} +0.104478 q^{73} -0.921794 q^{74} +2.34856 q^{75} +0.107272 q^{76} +13.4227 q^{77} -7.85095 q^{78} +1.98678 q^{79} -2.00724 q^{80} -10.2183 q^{81} +12.8981 q^{82} -3.90615 q^{83} +4.60270 q^{84} +1.00000 q^{85} +12.5248 q^{86} +7.74277 q^{87} -15.3813 q^{88} -10.2965 q^{89} -2.83513 q^{90} -7.96386 q^{91} -2.00541 q^{92} +6.85294 q^{93} -8.58416 q^{94} -0.146955 q^{95} -9.13834 q^{96} -13.5415 q^{97} -0.234567 q^{98} -12.5774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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