LMFDB - Embedded newform 6034.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.84514$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.84514 q^{3} +1.00000 q^{4} -4.15918 q^{5} -2.84514 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.09480 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.84514 q^{3} +1.00000 q^{4} -4.15918 q^{5} -2.84514 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.09480 q^{9} -4.15918 q^{10} +1.36362 q^{11} -2.84514 q^{12} -2.86984 q^{13} -1.00000 q^{14} +11.8334 q^{15} +1.00000 q^{16} -0.0229402 q^{17} +5.09480 q^{18} -6.17386 q^{19} -4.15918 q^{20} +2.84514 q^{21} +1.36362 q^{22} -0.253845 q^{23} -2.84514 q^{24} +12.2988 q^{25} -2.86984 q^{26} -5.95999 q^{27} -1.00000 q^{28} -1.68464 q^{29} +11.8334 q^{30} +6.99943 q^{31} +1.00000 q^{32} -3.87969 q^{33} -0.0229402 q^{34} +4.15918 q^{35} +5.09480 q^{36} +3.00745 q^{37} -6.17386 q^{38} +8.16507 q^{39} -4.15918 q^{40} +2.66237 q^{41} +2.84514 q^{42} -1.51322 q^{43} +1.36362 q^{44} -21.1902 q^{45} -0.253845 q^{46} +7.63939 q^{47} -2.84514 q^{48} +1.00000 q^{49} +12.2988 q^{50} +0.0652680 q^{51} -2.86984 q^{52} -0.456590 q^{53} -5.95999 q^{54} -5.67154 q^{55} -1.00000 q^{56} +17.5655 q^{57} -1.68464 q^{58} -3.18325 q^{59} +11.8334 q^{60} -1.02112 q^{61} +6.99943 q^{62} -5.09480 q^{63} +1.00000 q^{64} +11.9362 q^{65} -3.87969 q^{66} +13.7903 q^{67} -0.0229402 q^{68} +0.722224 q^{69} +4.15918 q^{70} -3.59661 q^{71} +5.09480 q^{72} +8.74851 q^{73} +3.00745 q^{74} -34.9917 q^{75} -6.17386 q^{76} -1.36362 q^{77} +8.16507 q^{78} -0.0245325 q^{79} -4.15918 q^{80} +1.67259 q^{81} +2.66237 q^{82} -1.07182 q^{83} +2.84514 q^{84} +0.0954124 q^{85} -1.51322 q^{86} +4.79302 q^{87} +1.36362 q^{88} +11.2986 q^{89} -21.1902 q^{90} +2.86984 q^{91} -0.253845 q^{92} -19.9143 q^{93} +7.63939 q^{94} +25.6782 q^{95} -2.84514 q^{96} +4.40474 q^{97} +1.00000 q^{98} +6.94738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.84514	−1.64264	−0.821320	−	0.570468i	$-0.806762\pi$
$3$	−2.84514	−1.64264	−0.821320	+	0.570468i	$0.806762\pi$
$4$	1.00000	0.500000
$5$	−4.15918	−1.86004	−0.930021	−	0.367507i	$-0.880212\pi$
$5$	−4.15918	−1.86004	−0.930021	+	0.367507i	$0.880212\pi$
$6$	−2.84514	−1.16152
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	5.09480	1.69827
$10$	−4.15918	−1.31525
$11$	1.36362	0.411147	0.205574	−	0.978642i	$-0.434094\pi$
$11$	1.36362	0.411147	0.205574	+	0.978642i	$0.434094\pi$
$12$	−2.84514	−0.821320
$13$	−2.86984	−0.795949	−0.397975	−	0.917396i	$-0.630287\pi$
$13$	−2.86984	−0.795949	−0.397975	+	0.917396i	$0.630287\pi$
$14$	−1.00000	−0.267261
$15$	11.8334	3.05538
$16$	1.00000	0.250000
$17$	−0.0229402	−0.00556381	−0.00278191	−	0.999996i	$-0.500886\pi$
$17$	−0.0229402	−0.00556381	−0.00278191	+	0.999996i	$0.500886\pi$
$18$	5.09480	1.20086
$19$	−6.17386	−1.41638	−0.708190	−	0.706022i	$-0.750488\pi$
$19$	−6.17386	−1.41638	−0.708190	+	0.706022i	$0.750488\pi$
$20$	−4.15918	−0.930021
$21$	2.84514	0.620860
$22$	1.36362	0.290725
$23$	−0.253845	−0.0529304	−0.0264652	−	0.999650i	$-0.508425\pi$
$23$	−0.253845	−0.0529304	−0.0264652	+	0.999650i	$0.508425\pi$
$24$	−2.84514	−0.580761
$25$	12.2988	2.45976
$26$	−2.86984	−0.562821
$27$	−5.95999	−1.14700
$28$	−1.00000	−0.188982
$29$	−1.68464	−0.312829	−0.156415	−	0.987691i	$-0.549994\pi$
$29$	−1.68464	−0.312829	−0.156415	+	0.987691i	$0.549994\pi$
$30$	11.8334	2.16048
$31$	6.99943	1.25714	0.628568	−	0.777755i	$-0.283642\pi$
$31$	6.99943	1.25714	0.628568	+	0.777755i	$0.283642\pi$
$32$	1.00000	0.176777
$33$	−3.87969	−0.675367
$34$	−0.0229402	−0.00393421
$35$	4.15918	0.703030
$36$	5.09480	0.849133
$37$	3.00745	0.494422	0.247211	−	0.968962i	$-0.420486\pi$
$37$	3.00745	0.494422	0.247211	+	0.968962i	$0.420486\pi$
$38$	−6.17386	−1.00153
$39$	8.16507	1.30746
$40$	−4.15918	−0.657624
$41$	2.66237	0.415793	0.207896	−	0.978151i	$-0.433338\pi$
$41$	2.66237	0.415793	0.207896	+	0.978151i	$0.433338\pi$
$42$	2.84514	0.439014
$43$	−1.51322	−0.230764	−0.115382	−	0.993321i	$-0.536809\pi$
$43$	−1.51322	−0.230764	−0.115382	+	0.993321i	$0.536809\pi$
$44$	1.36362	0.205574
$45$	−21.1902	−3.15885
$46$	−0.253845	−0.0374274
$47$	7.63939	1.11432	0.557160	−	0.830405i	$-0.311891\pi$
$47$	7.63939	1.11432	0.557160	+	0.830405i	$0.311891\pi$
$48$	−2.84514	−0.410660
$49$	1.00000	0.142857
$50$	12.2988	1.73931
$51$	0.0652680	0.00913934
$52$	−2.86984	−0.397975
$53$	−0.456590	−0.0627175	−0.0313587	−	0.999508i	$-0.509983\pi$
$53$	−0.456590	−0.0627175	−0.0313587	+	0.999508i	$0.509983\pi$
$54$	−5.95999	−0.811052
$55$	−5.67154	−0.764751
$56$	−1.00000	−0.133631
$57$	17.5655	2.32660
$58$	−1.68464	−0.221204
$59$	−3.18325	−0.414423	−0.207212	−	0.978296i	$-0.566439\pi$
$59$	−3.18325	−0.414423	−0.207212	+	0.978296i	$0.566439\pi$
$60$	11.8334	1.52769
$61$	−1.02112	−0.130741	−0.0653703	−	0.997861i	$-0.520823\pi$
$61$	−1.02112	−0.130741	−0.0653703	+	0.997861i	$0.520823\pi$
$62$	6.99943	0.888929
$63$	−5.09480	−0.641884
$64$	1.00000	0.125000
$65$	11.9362	1.48050
$66$	−3.87969	−0.477556
$67$	13.7903	1.68475	0.842374	−	0.538893i	$-0.181157\pi$
$67$	13.7903	1.68475	0.842374	+	0.538893i	$0.181157\pi$
$68$	−0.0229402	−0.00278191
$69$	0.722224	0.0869456
$70$	4.15918	0.497117
$71$	−3.59661	−0.426839	−0.213420	−	0.976961i	$-0.568460\pi$
$71$	−3.59661	−0.426839	−0.213420	+	0.976961i	$0.568460\pi$
$72$	5.09480	0.600428
$73$	8.74851	1.02394	0.511968	−	0.859004i	$-0.328917\pi$
$73$	8.74851	1.02394	0.511968	+	0.859004i	$0.328917\pi$
$74$	3.00745	0.349609
$75$	−34.9917	−4.04049
$76$	−6.17386	−0.708190
$77$	−1.36362	−0.155399
$78$	8.16507	0.924513
$79$	−0.0245325	−0.00276013	−0.00138006	−	0.999999i	$-0.500439\pi$
$79$	−0.0245325	−0.00276013	−0.00138006	+	0.999999i	$0.500439\pi$
$80$	−4.15918	−0.465010
$81$	1.67259	0.185843
$82$	2.66237	0.294010
$83$	−1.07182	−0.117648	−0.0588240	−	0.998268i	$-0.518735\pi$
$83$	−1.07182	−0.117648	−0.0588240	+	0.998268i	$0.518735\pi$
$84$	2.84514	0.310430
$85$	0.0954124	0.0103489
$86$	−1.51322	−0.163174
$87$	4.79302	0.513866
$88$	1.36362	0.145362
$89$	11.2986	1.19765	0.598826	−	0.800879i	$-0.295634\pi$
$89$	11.2986	1.19765	0.598826	+	0.800879i	$0.295634\pi$
$90$	−21.1902	−2.23364
$91$	2.86984	0.300841
$92$	−0.253845	−0.0264652
$93$	−19.9143	−2.06502
$94$	7.63939	0.787943
$95$	25.6782	2.63453
$96$	−2.84514	−0.290381
$97$	4.40474	0.447234	0.223617	−	0.974677i	$-0.428214\pi$
$97$	4.40474	0.447234	0.223617	+	0.974677i	$0.428214\pi$
$98$	1.00000	0.101015
$99$	6.94738	0.698238
$100$	12.2988	1.22988
$101$	4.39674	0.437492	0.218746	−	0.975782i	$-0.429803\pi$
$101$	4.39674	0.437492	0.218746	+	0.975782i	$0.429803\pi$
$102$	0.0652680	0.00646249
$103$	0.226352	0.0223031	0.0111516	−	0.999938i	$-0.496450\pi$
$103$	0.226352	0.0223031	0.0111516	+	0.999938i	$0.496450\pi$
$104$	−2.86984	−0.281411
$105$	−11.8334	−1.15482
$106$	−0.456590	−0.0443480
$107$	−2.60582	−0.251915	−0.125957	−	0.992036i	$-0.540200\pi$
$107$	−2.60582	−0.251915	−0.125957	+	0.992036i	$0.540200\pi$
$108$	−5.95999	−0.573501
$109$	−15.1920	−1.45513	−0.727563	−	0.686041i	$-0.759347\pi$
$109$	−15.1920	−1.45513	−0.727563	+	0.686041i	$0.759347\pi$
$110$	−5.67154	−0.540761
$111$	−8.55661	−0.812158
$112$	−1.00000	−0.0944911
$113$	−6.23253	−0.586307	−0.293153	−	0.956065i	$-0.594705\pi$
$113$	−6.23253	−0.586307	−0.293153	+	0.956065i	$0.594705\pi$
$114$	17.5655	1.64516
$115$	1.05579	0.0984527
$116$	−1.68464	−0.156415
$117$	−14.6212	−1.35173
$118$	−3.18325	−0.293042
$119$	0.0229402	0.00210292
$120$	11.8334	1.08024
$121$	−9.14054	−0.830958
$122$	−1.02112	−0.0924476
$123$	−7.57481	−0.682998
$124$	6.99943	0.628568
$125$	−30.3569	−2.71521
$126$	−5.09480	−0.453881
$127$	7.54397	0.669419	0.334710	−	0.942321i	$-0.391362\pi$
$127$	7.54397	0.669419	0.334710	+	0.942321i	$0.391362\pi$
$128$	1.00000	0.0883883
$129$	4.30531	0.379061
$130$	11.9362	1.04687
$131$	1.57975	0.138024	0.0690119	−	0.997616i	$-0.478015\pi$
$131$	1.57975	0.138024	0.0690119	+	0.997616i	$0.478015\pi$
$132$	−3.87969	−0.337683
$133$	6.17386	0.535341
$134$	13.7903	1.19130
$135$	24.7887	2.13347
$136$	−0.0229402	−0.00196710
$137$	−20.9754	−1.79205	−0.896024	−	0.444007i	$-0.853557\pi$
$137$	−20.9754	−1.79205	−0.896024	+	0.444007i	$0.853557\pi$
$138$	0.722224	0.0614798
$139$	−10.9023	−0.924723	−0.462362	−	0.886691i	$-0.652998\pi$
$139$	−10.9023	−0.924723	−0.462362	+	0.886691i	$0.652998\pi$
$140$	4.15918	0.351515
$141$	−21.7351	−1.83043
$142$	−3.59661	−0.301821
$143$	−3.91337	−0.327252
$144$	5.09480	0.424567
$145$	7.00670	0.581875
$146$	8.74851	0.724032
$147$	−2.84514	−0.234663
$148$	3.00745	0.247211
$149$	16.0771	1.31708	0.658542	−	0.752544i	$-0.271174\pi$
$149$	16.0771	1.31708	0.658542	+	0.752544i	$0.271174\pi$
$150$	−34.9917	−2.85706
$151$	−5.11497	−0.416250	−0.208125	−	0.978102i	$-0.566736\pi$
$151$	−5.11497	−0.416250	−0.208125	+	0.978102i	$0.566736\pi$
$152$	−6.17386	−0.500766
$153$	−0.116876	−0.00944884
$154$	−1.36362	−0.109884
$155$	−29.1119	−2.33832
$156$	8.16507	0.653729
$157$	−10.7724	−0.859727	−0.429864	−	0.902894i	$-0.641438\pi$
$157$	−10.7724	−0.859727	−0.429864	+	0.902894i	$0.641438\pi$
$158$	−0.0245325	−0.00195170
$159$	1.29906	0.103022
$160$	−4.15918	−0.328812
$161$	0.253845	0.0200058
$162$	1.67259	0.131411
$163$	7.09709	0.555887	0.277943	−	0.960597i	$-0.410347\pi$
$163$	7.09709	0.555887	0.277943	+	0.960597i	$0.410347\pi$
$164$	2.66237	0.207896
$165$	16.1363	1.25621
$166$	−1.07182	−0.0831897
$167$	8.54620	0.661325	0.330663	−	0.943749i	$-0.392728\pi$
$167$	8.54620	0.661325	0.330663	+	0.943749i	$0.392728\pi$
$168$	2.84514	0.219507
$169$	−4.76404	−0.366465
$170$	0.0954124	0.00731779
$171$	−31.4546	−2.40539
$172$	−1.51322	−0.115382
$173$	12.2491	0.931280	0.465640	−	0.884974i	$-0.345824\pi$
$173$	12.2491	0.931280	0.465640	+	0.884974i	$0.345824\pi$
$174$	4.79302	0.363358
$175$	−12.2988	−0.929700
$176$	1.36362	0.102787
$177$	9.05677	0.680749
$178$	11.2986	0.846867
$179$	−20.7406	−1.55023	−0.775113	−	0.631823i	$-0.782307\pi$
$179$	−20.7406	−1.55023	−0.775113	+	0.631823i	$0.782307\pi$
$180$	−21.1902	−1.57942
$181$	−0.418499	−0.0311068	−0.0155534	−	0.999879i	$-0.504951\pi$
$181$	−0.418499	−0.0311068	−0.0155534	+	0.999879i	$0.504951\pi$
$182$	2.86984	0.212726
$183$	2.90522	0.214760
$184$	−0.253845	−0.0187137
$185$	−12.5085	−0.919646
$186$	−19.9143	−1.46019
$187$	−0.0312817	−0.00228755
$188$	7.63939	0.557160
$189$	5.95999	0.433526
$190$	25.6782	1.86289
$191$	−7.14217	−0.516789	−0.258395	−	0.966039i	$-0.583193\pi$
$191$	−7.14217	−0.516789	−0.258395	+	0.966039i	$0.583193\pi$
$192$	−2.84514	−0.205330
$193$	16.6703	1.19996	0.599979	−	0.800016i	$-0.295176\pi$
$193$	16.6703	1.19996	0.599979	+	0.800016i	$0.295176\pi$
$194$	4.40474	0.316242
$195$	−33.9600	−2.43193
$196$	1.00000	0.0714286
$197$	17.1226	1.21994	0.609968	−	0.792426i	$-0.291182\pi$
$197$	17.1226	1.21994	0.609968	+	0.792426i	$0.291182\pi$
$198$	6.94738	0.493729
$199$	22.3985	1.58779	0.793894	−	0.608056i	$-0.208051\pi$
$199$	22.3985	1.58779	0.793894	+	0.608056i	$0.208051\pi$
$200$	12.2988	0.869655
$201$	−39.2352	−2.76744
$202$	4.39674	0.309354
$203$	1.68464	0.118238
$204$	0.0652680	0.00456967
$205$	−11.0733	−0.773392
$206$	0.226352	0.0157707
$207$	−1.29329	−0.0898899
$208$	−2.86984	−0.198987
$209$	−8.41880	−0.582341
$210$	−11.8334	−0.816584
$211$	−10.5215	−0.724333	−0.362166	−	0.932113i	$-0.617963\pi$
$211$	−10.5215	−0.724333	−0.362166	+	0.932113i	$0.617963\pi$
$212$	−0.456590	−0.0313587
$213$	10.2328	0.701143
$214$	−2.60582	−0.178131
$215$	6.29374	0.429230
$216$	−5.95999	−0.405526
$217$	−6.99943	−0.475152
$218$	−15.1920	−1.02893
$219$	−24.8907	−1.68196
$220$	−5.67154	−0.382375
$221$	0.0658346	0.00442851
$222$	−8.55661	−0.574282
$223$	6.40714	0.429054	0.214527	−	0.976718i	$-0.431179\pi$
$223$	6.40714	0.429054	0.214527	+	0.976718i	$0.431179\pi$
$224$	−1.00000	−0.0668153
$225$	62.6598	4.17732
$226$	−6.23253	−0.414582
$227$	−2.63379	−0.174811	−0.0874053	−	0.996173i	$-0.527858\pi$
$227$	−2.63379	−0.174811	−0.0874053	+	0.996173i	$0.527858\pi$
$228$	17.5655	1.16330
$229$	−15.0651	−0.995528	−0.497764	−	0.867312i	$-0.665846\pi$
$229$	−15.0651	−0.995528	−0.497764	+	0.867312i	$0.665846\pi$
$230$	1.05579	0.0696166
$231$	3.87969	0.255265
$232$	−1.68464	−0.110602
$233$	−16.4402	−1.07703	−0.538517	−	0.842615i	$-0.681015\pi$
$233$	−16.4402	−1.07703	−0.538517	+	0.842615i	$0.681015\pi$
$234$	−14.6212	−0.955820
$235$	−31.7736	−2.07268
$236$	−3.18325	−0.207212
$237$	0.0697984	0.00453389
$238$	0.0229402	0.00148699
$239$	−23.6006	−1.52659	−0.763296	−	0.646048i	$-0.776420\pi$
$239$	−23.6006	−1.52659	−0.763296	+	0.646048i	$0.776420\pi$
$240$	11.8334	0.763845
$241$	8.47321	0.545808	0.272904	−	0.962041i	$-0.412016\pi$
$241$	8.47321	0.545808	0.272904	+	0.962041i	$0.412016\pi$
$242$	−9.14054	−0.587576
$243$	13.1212	0.841728
$244$	−1.02112	−0.0653703
$245$	−4.15918	−0.265720
$246$	−7.57481	−0.482952
$247$	17.7180	1.12737
$248$	6.99943	0.444464
$249$	3.04949	0.193253
$250$	−30.3569	−1.91994
$251$	−26.2460	−1.65663	−0.828316	−	0.560261i	$-0.810701\pi$
$251$	−26.2460	−1.65663	−0.828316	+	0.560261i	$0.810701\pi$
$252$	−5.09480	−0.320942
$253$	−0.346149	−0.0217622
$254$	7.54397	0.473351
$255$	−0.271461	−0.0169996
$256$	1.00000	0.0625000
$257$	−21.3433	−1.33136	−0.665679	−	0.746238i	$-0.731858\pi$
$257$	−21.3433	−1.33136	−0.665679	+	0.746238i	$0.731858\pi$
$258$	4.30531	0.268037
$259$	−3.00745	−0.186874
$260$	11.9362	0.740249
$261$	−8.58288	−0.531267
$262$	1.57975	0.0975976
$263$	−31.0724	−1.91600	−0.958002	−	0.286760i	$-0.907422\pi$
$263$	−31.0724	−1.91600	−0.958002	+	0.286760i	$0.907422\pi$
$264$	−3.87969	−0.238778
$265$	1.89904	0.116657
$266$	6.17386	0.378543
$267$	−32.1461	−1.96731
$268$	13.7903	0.842374
$269$	20.9171	1.27534	0.637668	−	0.770312i	$-0.279899\pi$
$269$	20.9171	1.27534	0.637668	+	0.770312i	$0.279899\pi$
$270$	24.7887	1.50859
$271$	7.49609	0.455355	0.227678	−	0.973737i	$-0.426887\pi$
$271$	7.49609	0.455355	0.227678	+	0.973737i	$0.426887\pi$
$272$	−0.0229402	−0.00139095
$273$	−8.16507	−0.494173
$274$	−20.9754	−1.26717
$275$	16.7709	1.01132
$276$	0.722224	0.0434728
$277$	−9.58032	−0.575626	−0.287813	−	0.957687i	$-0.592928\pi$
$277$	−9.58032	−0.575626	−0.287813	+	0.957687i	$0.592928\pi$
$278$	−10.9023	−0.653878
$279$	35.6607	2.13495
$280$	4.15918	0.248559
$281$	7.09488	0.423245	0.211623	−	0.977351i	$-0.432125\pi$
$281$	7.09488	0.423245	0.211623	+	0.977351i	$0.432125\pi$
$282$	−21.7351	−1.29431
$283$	9.60476	0.570944	0.285472	−	0.958387i	$-0.407850\pi$
$283$	9.60476	0.570944	0.285472	+	0.958387i	$0.407850\pi$
$284$	−3.59661	−0.213420
$285$	−73.0579	−4.32758
$286$	−3.91337	−0.231402
$287$	−2.66237	−0.157155
$288$	5.09480	0.300214
$289$	−16.9995	−0.999969
$290$	7.00670	0.411448
$291$	−12.5321	−0.734644
$292$	8.74851	0.511968
$293$	−28.5772	−1.66950	−0.834748	−	0.550633i	$-0.814387\pi$
$293$	−28.5772	−1.66950	−0.834748	+	0.550633i	$0.814387\pi$
$294$	−2.84514	−0.165932
$295$	13.2397	0.770845
$296$	3.00745	0.174805
$297$	−8.12717	−0.471586
$298$	16.0771	0.931319
$299$	0.728494	0.0421299
$300$	−34.9917	−2.02025
$301$	1.51322	0.0872204
$302$	−5.11497	−0.294333
$303$	−12.5093	−0.718642
$304$	−6.17386	−0.354095
$305$	4.24701	0.243183
$306$	−0.116876	−0.00668134
$307$	1.04549	0.0596692	0.0298346	−	0.999555i	$-0.490502\pi$
$307$	1.04549	0.0596692	0.0298346	+	0.999555i	$0.490502\pi$
$308$	−1.36362	−0.0776995
$309$	−0.644002	−0.0366360
$310$	−29.1119	−1.65344
$311$	−25.3653	−1.43834	−0.719168	−	0.694836i	$-0.755477\pi$
$311$	−25.3653	−1.43834	−0.719168	+	0.694836i	$0.755477\pi$
$312$	8.16507	0.462256
$313$	−26.9076	−1.52091	−0.760453	−	0.649393i	$-0.775023\pi$
$313$	−26.9076	−1.52091	−0.760453	+	0.649393i	$0.775023\pi$
$314$	−10.7724	−0.607919
$315$	21.1902	1.19393
$316$	−0.0245325	−0.00138006
$317$	12.6160	0.708583	0.354292	−	0.935135i	$-0.384722\pi$
$317$	12.6160	0.708583	0.354292	+	0.935135i	$0.384722\pi$
$318$	1.29906	0.0728477
$319$	−2.29720	−0.128619
$320$	−4.15918	−0.232505
$321$	7.41393	0.413805
$322$	0.253845	0.0141462
$323$	0.141629	0.00788047
$324$	1.67259	0.0929216
$325$	−35.2955	−1.95784
$326$	7.09709	0.393071
$327$	43.2232	2.39025
$328$	2.66237	0.147005
$329$	−7.63939	−0.421173
$330$	16.1363	0.888275
$331$	−12.5012	−0.687130	−0.343565	−	0.939129i	$-0.611635\pi$
$331$	−12.5012	−0.687130	−0.343565	+	0.939129i	$0.611635\pi$
$332$	−1.07182	−0.0588240
$333$	15.3224	0.839661
$334$	8.54620	0.467627
$335$	−57.3562	−3.13370
$336$	2.84514	0.155215
$337$	−28.7372	−1.56542	−0.782708	−	0.622389i	$-0.786162\pi$
$337$	−28.7372	−1.56542	−0.782708	+	0.622389i	$0.786162\pi$
$338$	−4.76404	−0.259130
$339$	17.7324	0.963091
$340$	0.0954124	0.00517446
$341$	9.54457	0.516868
$342$	−31.4546	−1.70087
$343$	−1.00000	−0.0539949
$344$	−1.51322	−0.0815872
$345$	−3.00386	−0.161722
$346$	12.2491	0.658515
$347$	35.4022	1.90049	0.950244	−	0.311507i	$-0.100834\pi$
$347$	35.4022	1.90049	0.950244	+	0.311507i	$0.100834\pi$
$348$	4.79302	0.256933
$349$	−22.3641	−1.19712	−0.598561	−	0.801077i	$-0.704261\pi$
$349$	−22.3641	−1.19712	−0.598561	+	0.801077i	$0.704261\pi$
$350$	−12.2988	−0.657397
$351$	17.1042	0.912955
$352$	1.36362	0.0726812
$353$	−2.52381	−0.134329	−0.0671644	−	0.997742i	$-0.521395\pi$
$353$	−2.52381	−0.134329	−0.0671644	+	0.997742i	$0.521395\pi$
$354$	9.05677	0.481362
$355$	14.9590	0.793939
$356$	11.2986	0.598826
$357$	−0.0652680	−0.00345435
$358$	−20.7406	−1.09618
$359$	10.3379	0.545616	0.272808	−	0.962068i	$-0.412048\pi$
$359$	10.3379	0.545616	0.272808	+	0.962068i	$0.412048\pi$
$360$	−21.1902	−1.11682
$361$	19.1165	1.00613
$362$	−0.418499	−0.0219958
$363$	26.0061	1.36496
$364$	2.86984	0.150420
$365$	−36.3866	−1.90456
$366$	2.90522	0.151858
$367$	−3.51219	−0.183335	−0.0916673	−	0.995790i	$-0.529220\pi$
$367$	−3.51219	−0.183335	−0.0916673	+	0.995790i	$0.529220\pi$
$368$	−0.253845	−0.0132326
$369$	13.5643	0.706127
$370$	−12.5085	−0.650288
$371$	0.456590	0.0237050
$372$	−19.9143	−1.03251
$373$	−1.30132	−0.0673800	−0.0336900	−	0.999432i	$-0.510726\pi$
$373$	−1.30132	−0.0673800	−0.0336900	+	0.999432i	$0.510726\pi$
$374$	−0.0312817	−0.00161754
$375$	86.3696	4.46011
$376$	7.63939	0.393971
$377$	4.83463	0.248996
$378$	5.95999	0.306549
$379$	11.0663	0.568439	0.284219	−	0.958759i	$-0.408266\pi$
$379$	11.0663	0.568439	0.284219	+	0.958759i	$0.408266\pi$
$380$	25.6782	1.31726
$381$	−21.4636	−1.09962
$382$	−7.14217	−0.365425
$383$	20.6987	1.05766	0.528828	−	0.848729i	$-0.322632\pi$
$383$	20.6987	1.05766	0.528828	+	0.848729i	$0.322632\pi$
$384$	−2.84514	−0.145190
$385$	5.67154	0.289049
$386$	16.6703	0.848498
$387$	−7.70954	−0.391898
$388$	4.40474	0.223617
$389$	10.5830	0.536580	0.268290	−	0.963338i	$-0.413541\pi$
$389$	10.5830	0.536580	0.268290	+	0.963338i	$0.413541\pi$
$390$	−33.9600	−1.71963
$391$	0.00582326	0.000294495 0
$392$	1.00000	0.0505076
$393$	−4.49462	−0.226723
$394$	17.1226	0.862626
$395$	0.102035	0.00513395
$396$	6.94738	0.349119
$397$	23.3680	1.17281	0.586403	−	0.810020i	$-0.300544\pi$
$397$	23.3680	1.17281	0.586403	+	0.810020i	$0.300544\pi$
$398$	22.3985	1.12274
$399$	−17.5655	−0.879373
$400$	12.2988	0.614939
$401$	24.7620	1.23656	0.618279	−	0.785959i	$-0.287830\pi$
$401$	24.7620	1.23656	0.618279	+	0.785959i	$0.287830\pi$
$402$	−39.2352	−1.95687
$403$	−20.0872	−1.00062
$404$	4.39674	0.218746
$405$	−6.95660	−0.345676
$406$	1.68464	0.0836071
$407$	4.10102	0.203280
$408$	0.0652680	0.00323125
$409$	−6.94235	−0.343277	−0.171639	−	0.985160i	$-0.554906\pi$
$409$	−6.94235	−0.343277	−0.171639	+	0.985160i	$0.554906\pi$
$410$	−11.0733	−0.546871
$411$	59.6778	2.94369
$412$	0.226352	0.0111516
$413$	3.18325	0.156637
$414$	−1.29329	−0.0635618
$415$	4.45791	0.218830
$416$	−2.86984	−0.140705
$417$	31.0186	1.51899
$418$	−8.41880	−0.411777
$419$	−27.3877	−1.33798	−0.668989	−	0.743273i	$-0.733272\pi$
$419$	−27.3877	−1.33798	−0.668989	+	0.743273i	$0.733272\pi$
$420$	−11.8334	−0.577412
$421$	2.62157	0.127768	0.0638838	−	0.997957i	$-0.479651\pi$
$421$	2.62157	0.127768	0.0638838	+	0.997957i	$0.479651\pi$
$422$	−10.5215	−0.512181
$423$	38.9212	1.89241
$424$	−0.456590	−0.0221740
$425$	−0.282136	−0.0136856
$426$	10.2328	0.495783
$427$	1.02112	0.0494153
$428$	−2.60582	−0.125957
$429$	11.1341	0.537558
$430$	6.29374	0.303511
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.95999	−0.286750
$433$	−10.3408	−0.496948	−0.248474	−	0.968639i	$-0.579929\pi$
$433$	−10.3408	−0.496948	−0.248474	+	0.968639i	$0.579929\pi$
$434$	−6.99943	−0.335983
$435$	−19.9350	−0.955811
$436$	−15.1920	−0.727563
$437$	1.56720	0.0749695
$438$	−24.8907	−1.18932
$439$	6.09725	0.291006	0.145503	−	0.989358i	$-0.453520\pi$
$439$	6.09725	0.291006	0.145503	+	0.989358i	$0.453520\pi$
$440$	−5.67154	−0.270380
$441$	5.09480	0.242610
$442$	0.0658346	0.00313143
$443$	1.78097	0.0846163	0.0423082	−	0.999105i	$-0.486529\pi$
$443$	1.78097	0.0846163	0.0423082	+	0.999105i	$0.486529\pi$
$444$	−8.55661	−0.406079
$445$	−46.9930	−2.22768
$446$	6.40714	0.303387
$447$	−45.7414	−2.16349
$448$	−1.00000	−0.0472456
$449$	−18.7588	−0.885281	−0.442641	−	0.896699i	$-0.645958\pi$
$449$	−18.7588	−0.885281	−0.442641	+	0.896699i	$0.645958\pi$
$450$	62.6598	2.95381
$451$	3.63047	0.170952
$452$	−6.23253	−0.293153
$453$	14.5528	0.683750
$454$	−2.63379	−0.123610
$455$	−11.9362	−0.559576
$456$	17.5655	0.822578
$457$	−22.5221	−1.05354	−0.526771	−	0.850008i	$-0.676597\pi$
$457$	−22.5221	−1.05354	−0.526771	+	0.850008i	$0.676597\pi$
$458$	−15.0651	−0.703945
$459$	0.136723	0.00638170
$460$	1.05579	0.0492264
$461$	−28.7581	−1.33940	−0.669700	−	0.742632i	$-0.733577\pi$
$461$	−28.7581	−1.33940	−0.669700	+	0.742632i	$0.733577\pi$
$462$	3.87969	0.180499
$463$	28.6786	1.33281	0.666404	−	0.745591i	$-0.267832\pi$
$463$	28.6786	1.33281	0.666404	+	0.745591i	$0.267832\pi$
$464$	−1.68464	−0.0782073
$465$	82.8273	3.84102
$466$	−16.4402	−0.761578
$467$	31.9248	1.47730	0.738652	−	0.674087i	$-0.235463\pi$
$467$	31.9248	1.47730	0.738652	+	0.674087i	$0.235463\pi$
$468$	−14.6212	−0.675867
$469$	−13.7903	−0.636775
$470$	−31.7736	−1.46561
$471$	30.6488	1.41222
$472$	−3.18325	−0.146521
$473$	−2.06346	−0.0948778
$474$	0.0697984	0.00320595
$475$	−75.9309	−3.48395
$476$	0.0229402	0.00105146
$477$	−2.32624	−0.106511
$478$	−23.6006	−1.07946
$479$	−12.2874	−0.561427	−0.280714	−	0.959792i	$-0.590571\pi$
$479$	−12.2874	−0.561427	−0.280714	+	0.959792i	$0.590571\pi$
$480$	11.8334	0.540120
$481$	−8.63089	−0.393535
$482$	8.47321	0.385944
$483$	−0.722224	−0.0328623
$484$	−9.14054	−0.415479
$485$	−18.3201	−0.831873
$486$	13.1212	0.595191
$487$	27.7468	1.25733	0.628664	−	0.777677i	$-0.283602\pi$
$487$	27.7468	1.25733	0.628664	+	0.777677i	$0.283602\pi$
$488$	−1.02112	−0.0462238
$489$	−20.1922	−0.913122
$490$	−4.15918	−0.187893
$491$	7.38581	0.333317	0.166658	−	0.986015i	$-0.446702\pi$
$491$	7.38581	0.333317	0.166658	+	0.986015i	$0.446702\pi$
$492$	−7.57481	−0.341499
$493$	0.0386459	0.00174052
$494$	17.7180	0.797169
$495$	−28.8954	−1.29875
$496$	6.99943	0.314284
$497$	3.59661	0.161330
$498$	3.04949	0.136651
$499$	−6.56048	−0.293687	−0.146844	−	0.989160i	$-0.546911\pi$
$499$	−6.56048	−0.293687	−0.146844	+	0.989160i	$0.546911\pi$
$500$	−30.3569	−1.35760
$501$	−24.3151	−1.08632
$502$	−26.2460	−1.17142
$503$	−10.0495	−0.448084	−0.224042	−	0.974580i	$-0.571925\pi$
$503$	−10.0495	−0.448084	−0.224042	+	0.974580i	$0.571925\pi$
$504$	−5.09480	−0.226940
$505$	−18.2868	−0.813753
$506$	−0.346149	−0.0153882
$507$	13.5544	0.601970
$508$	7.54397	0.334710
$509$	4.29149	0.190217	0.0951085	−	0.995467i	$-0.469680\pi$
$509$	4.29149	0.190217	0.0951085	+	0.995467i	$0.469680\pi$
$510$	−0.271461	−0.0120205
$511$	−8.74851	−0.387012
$512$	1.00000	0.0441942
$513$	36.7961	1.62459
$514$	−21.3433	−0.941412
$515$	−0.941438	−0.0414847
$516$	4.30531	0.189531
$517$	10.4172	0.458149
$518$	−3.00745	−0.132140
$519$	−34.8503	−1.52976
$520$	11.9362	0.523435
$521$	0.121183	0.00530912	0.00265456	−	0.999996i	$-0.499155\pi$
$521$	0.121183	0.00530912	0.00265456	+	0.999996i	$0.499155\pi$
$522$	−8.58288	−0.375663
$523$	4.15353	0.181621	0.0908106	−	0.995868i	$-0.471054\pi$
$523$	4.15353	0.181621	0.0908106	+	0.995868i	$0.471054\pi$
$524$	1.57975	0.0690119
$525$	34.9917	1.52716
$526$	−31.0724	−1.35482
$527$	−0.160568	−0.00699446
$528$	−3.87969	−0.168842
$529$	−22.9356	−0.997198
$530$	1.89904	0.0824891
$531$	−16.2180	−0.703801
$532$	6.17386	0.267671
$533$	−7.64057	−0.330950
$534$	−32.1461	−1.39110
$535$	10.8381	0.468572
$536$	13.7903	0.595648
$537$	59.0099	2.54646
$538$	20.9171	0.901798
$539$	1.36362	0.0587353
$540$	24.7887	1.06673
$541$	28.7237	1.23493	0.617465	−	0.786598i	$-0.288160\pi$
$541$	28.7237	1.23493	0.617465	+	0.786598i	$0.288160\pi$
$542$	7.49609	0.321985
$543$	1.19069	0.0510972
$544$	−0.0229402	−0.000983552 0
$545$	63.1861	2.70659
$546$	−8.16507	−0.349433
$547$	30.2809	1.29472	0.647359	−	0.762185i	$-0.275873\pi$
$547$	30.2809	1.29472	0.647359	+	0.762185i	$0.275873\pi$
$548$	−20.9754	−0.896024
$549$	−5.20239	−0.222032
$550$	16.7709	0.715112
$551$	10.4007	0.443085
$552$	0.722224	0.0307399
$553$	0.0245325	0.00104323
$554$	−9.58032	−0.407029
$555$	35.5885	1.51065
$556$	−10.9023	−0.462362
$557$	−9.72166	−0.411920	−0.205960	−	0.978560i	$-0.566032\pi$
$557$	−9.72166	−0.411920	−0.205960	+	0.978560i	$0.566032\pi$
$558$	35.6607	1.50964
$559$	4.34269	0.183676
$560$	4.15918	0.175757
$561$	0.0890008	0.00375761
$562$	7.09488	0.299279
$563$	16.0204	0.675179	0.337590	−	0.941293i	$-0.390388\pi$
$563$	16.0204	0.675179	0.337590	+	0.941293i	$0.390388\pi$
$564$	−21.7351	−0.915213
$565$	25.9222	1.09056
$566$	9.60476	0.403718
$567$	−1.67259	−0.0702421
$568$	−3.59661	−0.150910
$569$	14.8563	0.622811	0.311405	−	0.950277i	$-0.399200\pi$
$569$	14.8563	0.622811	0.311405	+	0.950277i	$0.399200\pi$
$570$	−73.0579	−3.06006
$571$	21.5104	0.900180	0.450090	−	0.892983i	$-0.351392\pi$
$571$	21.5104	0.900180	0.450090	+	0.892983i	$0.351392\pi$
$572$	−3.91337	−0.163626
$573$	20.3204	0.848899
$574$	−2.66237	−0.111125
$575$	−3.12199	−0.130196
$576$	5.09480	0.212283
$577$	5.34533	0.222529	0.111265	−	0.993791i	$-0.464510\pi$
$577$	5.34533	0.222529	0.111265	+	0.993791i	$0.464510\pi$
$578$	−16.9995	−0.707085
$579$	−47.4294	−1.97110
$580$	7.00670	0.290938
$581$	1.07182	0.0444668
$582$	−12.5321	−0.519472
$583$	−0.622616	−0.0257861
$584$	8.74851	0.362016
$585$	60.8124	2.51428
$586$	−28.5772	−1.18051
$587$	−6.06295	−0.250245	−0.125122	−	0.992141i	$-0.539932\pi$
$587$	−6.06295	−0.250245	−0.125122	+	0.992141i	$0.539932\pi$
$588$	−2.84514	−0.117331
$589$	−43.2135	−1.78058
$590$	13.2397	0.545070
$591$	−48.7162	−2.00392
$592$	3.00745	0.123606
$593$	24.3672	1.00064	0.500320	−	0.865841i	$-0.333216\pi$
$593$	24.3672	1.00064	0.500320	+	0.865841i	$0.333216\pi$
$594$	−8.12717	−0.333462
$595$	−0.0954124	−0.00391153
$596$	16.0771	0.658542
$597$	−63.7268	−2.60816
$598$	0.728494	0.0297903
$599$	4.45100	0.181863	0.0909315	−	0.995857i	$-0.471016\pi$
$599$	4.45100	0.181863	0.0909315	+	0.995857i	$0.471016\pi$
$600$	−34.9917	−1.42853
$601$	5.76531	0.235172	0.117586	−	0.993063i	$-0.462484\pi$
$601$	5.76531	0.235172	0.117586	+	0.993063i	$0.462484\pi$
$602$	1.51322	0.0616741
$603$	70.2586	2.86115
$604$	−5.11497	−0.208125
$605$	38.0171	1.54562
$606$	−12.5093	−0.508157
$607$	39.1137	1.58758	0.793788	−	0.608195i	$-0.208106\pi$
$607$	39.1137	1.58758	0.793788	+	0.608195i	$0.208106\pi$
$608$	−6.17386	−0.250383
$609$	−4.79302	−0.194223
$610$	4.24701	0.171956
$611$	−21.9238	−0.886941
$612$	−0.116876	−0.00472442
$613$	45.9933	1.85765	0.928825	−	0.370519i	$-0.120820\pi$
$613$	45.9933	1.85765	0.928825	+	0.370519i	$0.120820\pi$
$614$	1.04549	0.0421925
$615$	31.5050	1.27040
$616$	−1.36362	−0.0549419
$617$	16.0141	0.644703	0.322352	−	0.946620i	$-0.395527\pi$
$617$	16.0141	0.644703	0.322352	+	0.946620i	$0.395527\pi$
$618$	−0.644002	−0.0259055
$619$	21.5836	0.867518	0.433759	−	0.901029i	$-0.357187\pi$
$619$	21.5836	0.867518	0.433759	+	0.901029i	$0.357187\pi$
$620$	−29.1119	−1.16916
$621$	1.51292	0.0607112
$622$	−25.3653	−1.01706
$623$	−11.2986	−0.452670
$624$	8.16507	0.326865
$625$	64.7660	2.59064
$626$	−26.9076	−1.07544
$627$	23.9526	0.956576
$628$	−10.7724	−0.429864
$629$	−0.0689915	−0.00275087
$630$	21.1902	0.844237
$631$	−24.8425	−0.988966	−0.494483	−	0.869187i	$-0.664643\pi$
$631$	−24.8425	−0.988966	−0.494483	+	0.869187i	$0.664643\pi$
$632$	−0.0245325	−0.000975852 0
$633$	29.9352	1.18982
$634$	12.6160	0.501044
$635$	−31.3767	−1.24515
$636$	1.29906	0.0515111
$637$	−2.86984	−0.113707
$638$	−2.29720	−0.0909472
$639$	−18.3240	−0.724887
$640$	−4.15918	−0.164406
$641$	−28.2819	−1.11707	−0.558533	−	0.829482i	$-0.688636\pi$
$641$	−28.2819	−1.11707	−0.558533	+	0.829482i	$0.688636\pi$
$642$	7.41393	0.292604
$643$	−20.5048	−0.808629	−0.404314	−	0.914620i	$-0.632490\pi$
$643$	−20.5048	−0.808629	−0.404314	+	0.914620i	$0.632490\pi$
$644$	0.253845	0.0100029
$645$	−17.9066	−0.705070
$646$	0.141629	0.00557234
$647$	8.88899	0.349462	0.174731	−	0.984616i	$-0.444094\pi$
$647$	8.88899	0.349462	0.174731	+	0.984616i	$0.444094\pi$
$648$	1.67259	0.0657055
$649$	−4.34074	−0.170389
$650$	−35.2955	−1.38440
$651$	19.9143	0.780504
$652$	7.09709	0.277943
$653$	−15.0752	−0.589939	−0.294969	−	0.955507i	$-0.595309\pi$
$653$	−15.0752	−0.589939	−0.294969	+	0.955507i	$0.595309\pi$
$654$	43.2232	1.69016
$655$	−6.57048	−0.256730
$656$	2.66237	0.103948
$657$	44.5719	1.73892
$658$	−7.63939	−0.297814
$659$	24.2198	0.943471	0.471735	−	0.881740i	$-0.343628\pi$
$659$	24.2198	0.943471	0.471735	+	0.881740i	$0.343628\pi$
$660$	16.1363	0.628105
$661$	5.51234	0.214405	0.107203	−	0.994237i	$-0.465811\pi$
$661$	5.51234	0.214405	0.107203	+	0.994237i	$0.465811\pi$
$662$	−12.5012	−0.485875
$663$	−0.187308	−0.00727445
$664$	−1.07182	−0.0415949
$665$	−25.6782	−0.995757
$666$	15.3224	0.593730
$667$	0.427637	0.0165582
$668$	8.54620	0.330663
$669$	−18.2292	−0.704781
$670$	−57.3562	−2.21586
$671$	−1.39242	−0.0537536
$672$	2.84514	0.109754
$673$	−45.2565	−1.74451	−0.872255	−	0.489051i	$-0.837343\pi$
$673$	−45.2565	−1.74451	−0.872255	+	0.489051i	$0.837343\pi$
$674$	−28.7372	−1.10692
$675$	−73.3006	−2.82134
$676$	−4.76404	−0.183232
$677$	32.4704	1.24794	0.623970	−	0.781448i	$-0.285519\pi$
$677$	32.4704	1.24794	0.623970	+	0.781448i	$0.285519\pi$
$678$	17.7324	0.681008
$679$	−4.40474	−0.169038
$680$	0.0954124	0.00365890
$681$	7.49348	0.287151
$682$	9.54457	0.365481
$683$	−16.0591	−0.614484	−0.307242	−	0.951631i	$-0.599406\pi$
$683$	−16.0591	−0.614484	−0.307242	+	0.951631i	$0.599406\pi$
$684$	−31.4546	−1.20270
$685$	87.2404	3.33328
$686$	−1.00000	−0.0381802
$687$	42.8622	1.63530
$688$	−1.51322	−0.0576909
$689$	1.31034	0.0499199
$690$	−3.00386	−0.114355
$691$	17.7208	0.674131	0.337065	−	0.941481i	$-0.390566\pi$
$691$	17.7208	0.674131	0.337065	+	0.941481i	$0.390566\pi$
$692$	12.2491	0.465640
$693$	−6.94738	−0.263909
$694$	35.4022	1.34385
$695$	45.3447	1.72002
$696$	4.79302	0.181679
$697$	−0.0610753	−0.00231339
$698$	−22.3641	−0.846494
$699$	46.7746	1.76918
$700$	−12.2988	−0.464850
$701$	−1.25981	−0.0475824	−0.0237912	−	0.999717i	$-0.507574\pi$
$701$	−1.25981	−0.0475824	−0.0237912	+	0.999717i	$0.507574\pi$
$702$	17.1042	0.645556
$703$	−18.5676	−0.700290
$704$	1.36362	0.0513934
$705$	90.4002	3.40467
$706$	−2.52381	−0.0949847
$707$	−4.39674	−0.165356
$708$	9.05677	0.340374
$709$	5.73783	0.215489	0.107744	−	0.994179i	$-0.465637\pi$
$709$	5.73783	0.215489	0.107744	+	0.994179i	$0.465637\pi$
$710$	14.9590	0.561399
$711$	−0.124988	−0.00468743
$712$	11.2986	0.423434
$713$	−1.77677	−0.0665406
$714$	−0.0652680	−0.00244259
$715$	16.2764	0.608703
$716$	−20.7406	−0.775113
$717$	67.1468	2.50764
$718$	10.3379	0.385809
$719$	−16.5377	−0.616753	−0.308377	−	0.951264i	$-0.599786\pi$
$719$	−16.5377	−0.616753	−0.308377	+	0.951264i	$0.599786\pi$
$720$	−21.1902	−0.789712
$721$	−0.226352	−0.00842978
$722$	19.1165	0.711443
$723$	−24.1074	−0.896565
$724$	−0.418499	−0.0155534
$725$	−20.7190	−0.769483
$726$	26.0061	0.965176
$727$	33.0919	1.22731	0.613656	−	0.789574i	$-0.289698\pi$
$727$	33.0919	1.22731	0.613656	+	0.789574i	$0.289698\pi$
$728$	2.86984	0.106363
$729$	−42.3495	−1.56850
$730$	−36.3866	−1.34673
$731$	0.0347135	0.00128392
$732$	2.90522	0.107380
$733$	−35.5749	−1.31399	−0.656994	−	0.753895i	$-0.728173\pi$
$733$	−35.5749	−1.31399	−0.656994	+	0.753895i	$0.728173\pi$
$734$	−3.51219	−0.129637
$735$	11.8334	0.436483
$736$	−0.253845	−0.00935686
$737$	18.8047	0.692679
$738$	13.5643	0.499307
$739$	−34.0761	−1.25351	−0.626755	−	0.779217i	$-0.715617\pi$
$739$	−34.0761	−1.25351	−0.626755	+	0.779217i	$0.715617\pi$
$740$	−12.5085	−0.459823
$741$	−50.4100	−1.85186
$742$	0.456590	0.0167620
$743$	−3.47756	−0.127579	−0.0637896	−	0.997963i	$-0.520319\pi$
$743$	−3.47756	−0.127579	−0.0637896	+	0.997963i	$0.520319\pi$
$744$	−19.9143	−0.730095
$745$	−66.8674	−2.44983
$746$	−1.30132	−0.0476449
$747$	−5.46073	−0.199798
$748$	−0.0312817	−0.00114377
$749$	2.60582	0.0952148
$750$	86.3696	3.15377
$751$	6.54518	0.238837	0.119419	−	0.992844i	$-0.461897\pi$
$751$	6.54518	0.238837	0.119419	+	0.992844i	$0.461897\pi$
$752$	7.63939	0.278580
$753$	74.6734	2.72125
$754$	4.83463	0.176067
$755$	21.2741	0.774243
$756$	5.95999	0.216763
$757$	0.327635	0.0119081	0.00595406	−	0.999982i	$-0.498105\pi$
$757$	0.327635	0.0119081	0.00595406	+	0.999982i	$0.498105\pi$
$758$	11.0663	0.401947
$759$	0.984840	0.0357474
$760$	25.6782	0.931446
$761$	−9.37484	−0.339838	−0.169919	−	0.985458i	$-0.554351\pi$
$761$	−9.37484	−0.339838	−0.169919	+	0.985458i	$0.554351\pi$
$762$	−21.4636	−0.777545
$763$	15.1920	0.549986
$764$	−7.14217	−0.258395
$765$	0.486107	0.0175752
$766$	20.6987	0.747876
$767$	9.13539	0.329860
$768$	−2.84514	−0.102665
$769$	7.17215	0.258634	0.129317	−	0.991603i	$-0.458721\pi$
$769$	7.17215	0.258634	0.129317	+	0.991603i	$0.458721\pi$
$770$	5.67154	0.204388
$771$	60.7246	2.18694
$772$	16.6703	0.599979
$773$	−37.9392	−1.36458	−0.682290	−	0.731082i	$-0.739016\pi$
$773$	−37.9392	−1.36458	−0.682290	+	0.731082i	$0.739016\pi$
$774$	−7.70954	−0.277114
$775$	86.0845	3.09224
$776$	4.40474	0.158121
$777$	8.55661	0.306967
$778$	10.5830	0.379419
$779$	−16.4371	−0.588921
$780$	−33.9600	−1.21596
$781$	−4.90441	−0.175494
$782$	0.00582326	0.000208239 0
$783$	10.0404	0.358815
$784$	1.00000	0.0357143
$785$	44.8042	1.59913
$786$	−4.49462	−0.160318
$787$	11.4065	0.406598	0.203299	−	0.979117i	$-0.434834\pi$
$787$	11.4065	0.406598	0.203299	+	0.979117i	$0.434834\pi$
$788$	17.1226	0.609968
$789$	88.4051	3.14731
$790$	0.102035	0.00363025
$791$	6.23253	0.221603
$792$	6.94738	0.246864
$793$	2.93044	0.104063
$794$	23.3680	0.829299
$795$	−5.40303	−0.191626
$796$	22.3985	0.793894
$797$	−49.0081	−1.73596	−0.867978	−	0.496602i	$-0.834581\pi$
$797$	−49.0081	−1.73596	−0.867978	+	0.496602i	$0.834581\pi$
$798$	−17.5655	−0.621811
$799$	−0.175249	−0.00619986
$800$	12.2988	0.434827
$801$	57.5642	2.03393
$802$	24.7620	0.874378
$803$	11.9297	0.420988
$804$	−39.2352	−1.38372
$805$	−1.05579	−0.0372116
$806$	−20.0872	−0.707542
$807$	−59.5119	−2.09492
$808$	4.39674	0.154677
$809$	−31.7645	−1.11678	−0.558390	−	0.829578i	$-0.688581\pi$
$809$	−31.7645	−1.11678	−0.558390	+	0.829578i	$0.688581\pi$
$810$	−6.95660	−0.244430
$811$	−12.2340	−0.429594	−0.214797	−	0.976659i	$-0.568909\pi$
$811$	−12.2340	−0.429594	−0.214797	+	0.976659i	$0.568909\pi$
$812$	1.68464	0.0591191
$813$	−21.3274	−0.747984
$814$	4.10102	0.143741
$815$	−29.5181	−1.03397
$816$	0.0652680	0.00228484
$817$	9.34239	0.326849
$818$	−6.94235	−0.242734
$819$	14.6212	0.510907
$820$	−11.0733	−0.386696
$821$	−7.08176	−0.247155	−0.123578	−	0.992335i	$-0.539437\pi$
$821$	−7.08176	−0.247155	−0.123578	+	0.992335i	$0.539437\pi$
$822$	59.6778	2.08150
$823$	31.0486	1.08228	0.541142	−	0.840931i	$-0.317992\pi$
$823$	31.0486	1.08228	0.541142	+	0.840931i	$0.317992\pi$
$824$	0.226352	0.00788534
$825$	−47.7154	−1.66124
$826$	3.18325	0.110759
$827$	−11.8990	−0.413770	−0.206885	−	0.978365i	$-0.566333\pi$
$827$	−11.8990	−0.413770	−0.206885	+	0.978365i	$0.566333\pi$
$828$	−1.29329	−0.0449450
$829$	−2.06843	−0.0718396	−0.0359198	−	0.999355i	$-0.511436\pi$
$829$	−2.06843	−0.0718396	−0.0359198	+	0.999355i	$0.511436\pi$
$830$	4.45791	0.154736
$831$	27.2573	0.945546
$832$	−2.86984	−0.0994936
$833$	−0.0229402	−0.000794830 0
$834$	31.0186	1.07409
$835$	−35.5452	−1.23009
$836$	−8.41880	−0.291170
$837$	−41.7166	−1.44194
$838$	−27.3877	−0.946093
$839$	−57.5768	−1.98777	−0.993887	−	0.110407i	$-0.964785\pi$
$839$	−57.5768	−1.98777	−0.993887	+	0.110407i	$0.964785\pi$
$840$	−11.8334	−0.408292
$841$	−26.1620	−0.902138
$842$	2.62157	0.0903453
$843$	−20.1859	−0.695239
$844$	−10.5215	−0.362166
$845$	19.8145	0.681640
$846$	38.9212	1.33814
$847$	9.14054	0.314073
$848$	−0.456590	−0.0156794
$849$	−27.3269	−0.937855
$850$	−0.282136	−0.00967719
$851$	−0.763427	−0.0261700
$852$	10.2328	0.350572
$853$	16.7382	0.573105	0.286552	−	0.958065i	$-0.407491\pi$
$853$	16.7382	0.573105	0.286552	+	0.958065i	$0.407491\pi$
$854$	1.02112	0.0349419
$855$	130.825	4.47413
$856$	−2.60582	−0.0890653
$857$	−31.2169	−1.06635	−0.533174	−	0.846006i	$-0.679001\pi$
$857$	−31.2169	−1.06635	−0.533174	+	0.846006i	$0.679001\pi$
$858$	11.1341	0.380111
$859$	46.1785	1.57559	0.787795	−	0.615937i	$-0.211222\pi$
$859$	46.1785	1.57559	0.787795	+	0.615937i	$0.211222\pi$
$860$	6.29374	0.214615
$861$	7.57481	0.258149
$862$	1.00000	0.0340601
$863$	14.9134	0.507657	0.253828	−	0.967249i	$-0.418310\pi$
$863$	14.9134	0.507657	0.253828	+	0.967249i	$0.418310\pi$
$864$	−5.95999	−0.202763
$865$	−50.9461	−1.73222
$866$	−10.3408	−0.351395
$867$	48.3658	1.64259
$868$	−6.99943	−0.237576
$869$	−0.0334531	−0.00113482
$870$	−19.9350	−0.675861
$871$	−39.5758	−1.34097
$872$	−15.1920	−0.514464
$873$	22.4413	0.759522
$874$	1.56720	0.0530115
$875$	30.3569	1.02625
$876$	−24.8907	−0.840979
$877$	−15.9959	−0.540144	−0.270072	−	0.962840i	$-0.587047\pi$
$877$	−15.9959	−0.540144	−0.270072	+	0.962840i	$0.587047\pi$
$878$	6.09725	0.205772
$879$	81.3059	2.74238
$880$	−5.67154	−0.191188
$881$	−14.2444	−0.479907	−0.239953	−	0.970784i	$-0.577132\pi$
$881$	−14.2444	−0.479907	−0.239953	+	0.970784i	$0.577132\pi$
$882$	5.09480	0.171551
$883$	−3.35755	−0.112991	−0.0564953	−	0.998403i	$-0.517993\pi$
$883$	−3.35755	−0.112991	−0.0564953	+	0.998403i	$0.517993\pi$
$884$	0.0658346	0.00221426
$885$	−37.6687	−1.26622
$886$	1.78097	0.0598328
$887$	−22.0438	−0.740158	−0.370079	−	0.929000i	$-0.620669\pi$
$887$	−22.0438	−0.740158	−0.370079	+	0.929000i	$0.620669\pi$
$888$	−8.55661	−0.287141
$889$	−7.54397	−0.253017
$890$	−46.9930	−1.57521
$891$	2.28078	0.0764089
$892$	6.40714	0.214527
$893$	−47.1645	−1.57830
$894$	−45.7414	−1.52982
$895$	86.2639	2.88349
$896$	−1.00000	−0.0334077
$897$	−2.07266	−0.0692043
$898$	−18.7588	−0.625988
$899$	−11.7915	−0.393268
$900$	62.6598	2.08866
$901$	0.0104743	0.000348948 0
$902$	3.63047	0.120881
$903$	−4.30531	−0.143272
$904$	−6.23253	−0.207291
$905$	1.74061	0.0578599
$906$	14.5528	0.483484
$907$	−6.62536	−0.219991	−0.109996	−	0.993932i	$-0.535084\pi$
$907$	−6.62536	−0.219991	−0.109996	+	0.993932i	$0.535084\pi$
$908$	−2.63379	−0.0874053
$909$	22.4005	0.742978
$910$	−11.9362	−0.395680
$911$	58.7316	1.94586	0.972932	−	0.231092i	$-0.0742298\pi$
$911$	58.7316	1.94586	0.972932	+	0.231092i	$0.0742298\pi$
$912$	17.5655	0.581651
$913$	−1.46156	−0.0483707
$914$	−22.5221	−0.744966
$915$	−12.0833	−0.399462
$916$	−15.0651	−0.497764
$917$	−1.57975	−0.0521681
$918$	0.136723	0.00451254
$919$	38.1421	1.25819	0.629097	−	0.777327i	$-0.283425\pi$
$919$	38.1421	1.25819	0.629097	+	0.777327i	$0.283425\pi$
$920$	1.05579	0.0348083
$921$	−2.97456	−0.0980150
$922$	−28.7581	−0.947099
$923$	10.3217	0.339742
$924$	3.87969	0.127632
$925$	36.9880	1.21616
$926$	28.6786	0.942438
$927$	1.15322	0.0378766
$928$	−1.68464	−0.0553009
$929$	−35.5920	−1.16774	−0.583868	−	0.811848i	$-0.698462\pi$
$929$	−35.5920	−1.16774	−0.583868	+	0.811848i	$0.698462\pi$
$930$	82.8273	2.71601
$931$	−6.17386	−0.202340
$932$	−16.4402	−0.538517
$933$	72.1679	2.36267
$934$	31.9248	1.04461
$935$	0.130106	0.00425493
$936$	−14.6212	−0.477910
$937$	38.4444	1.25592	0.627962	−	0.778244i	$-0.283889\pi$
$937$	38.4444	1.25592	0.627962	+	0.778244i	$0.283889\pi$
$938$	−13.7903	−0.450268
$939$	76.5557	2.49830
$940$	−31.7736	−1.03634
$941$	−15.3531	−0.500496	−0.250248	−	0.968182i	$-0.580512\pi$
$941$	−15.3531	−0.500496	−0.250248	+	0.968182i	$0.580512\pi$
$942$	30.6488	0.998592
$943$	−0.675830	−0.0220081
$944$	−3.18325	−0.103606
$945$	−24.7887	−0.806376
$946$	−2.06346	−0.0670887
$947$	30.4274	0.988757	0.494378	−	0.869247i	$-0.335396\pi$
$947$	30.4274	0.988757	0.494378	+	0.869247i	$0.335396\pi$
$948$	0.0697984	0.00226695
$949$	−25.1068	−0.815001
$950$	−75.9309	−2.46352
$951$	−35.8942	−1.16395
$952$	0.0229402	0.000743496 0
$953$	−25.4641	−0.824864	−0.412432	−	0.910988i	$-0.635320\pi$
$953$	−25.4641	−0.824864	−0.412432	+	0.910988i	$0.635320\pi$
$954$	−2.32624	−0.0753147
$955$	29.7056	0.961250
$956$	−23.6006	−0.763296
$957$	6.53586	0.211274
$958$	−12.2874	−0.396989
$959$	20.9754	0.677330
$960$	11.8334	0.381922
$961$	17.9920	0.580389
$962$	−8.63089	−0.278271
$963$	−13.2762	−0.427818
$964$	8.47321	0.272904
$965$	−69.3349	−2.23197
$966$	−0.722224	−0.0232372
$967$	8.55239	0.275026	0.137513	−	0.990500i	$-0.456089\pi$
$967$	8.55239	0.275026	0.137513	+	0.990500i	$0.456089\pi$
$968$	−9.14054	−0.293788
$969$	−0.402955	−0.0129448
$970$	−18.3201	−0.588223
$971$	−28.2049	−0.905140	−0.452570	−	0.891729i	$-0.649493\pi$
$971$	−28.2049	−0.905140	−0.452570	+	0.891729i	$0.649493\pi$
$972$	13.1212	0.420864
$973$	10.9023	0.349513
$974$	27.7468	0.889065
$975$	100.420	3.21603
$976$	−1.02112	−0.0326852
$977$	−47.5702	−1.52191	−0.760953	−	0.648807i	$-0.775268\pi$
$977$	−47.5702	−1.52191	−0.760953	+	0.648807i	$0.775268\pi$
$978$	−20.1922	−0.645675
$979$	15.4070	0.492411
$980$	−4.15918	−0.132860
$981$	−77.4000	−2.47119
$982$	7.38581	0.235691
$983$	−35.2790	−1.12522	−0.562612	−	0.826721i	$-0.690204\pi$
$983$	−35.2790	−1.12522	−0.562612	+	0.826721i	$0.690204\pi$
$984$	−7.57481	−0.241476
$985$	−71.2161	−2.26913
$986$	0.0386459	0.00123074
$987$	21.7351	0.691836
$988$	17.7180	0.563683
$989$	0.384123	0.0122144
$990$	−28.8954	−0.918356
$991$	12.9667	0.411902	0.205951	−	0.978562i	$-0.433971\pi$
$991$	12.9667	0.411902	0.205951	+	0.978562i	$0.433971\pi$
$992$	6.99943	0.222232
$993$	35.5677	1.12871
$994$	3.59661	0.114078
$995$	−93.1594	−2.95335
$996$	3.04949	0.0966267
$997$	−60.1704	−1.90561	−0.952807	−	0.303576i	$-0.901819\pi$
$997$	−60.1704	−1.90561	−0.952807	+	0.303576i	$0.901819\pi$
$998$	−6.56048	−0.207668
$999$	−17.9244	−0.567103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.3	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.84514 q^{3} +1.00000 q^{4} -4.15918 q^{5} -2.84514 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.09480 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.84514 q^{3} +1.00000 q^{4} -4.15918 q^{5} -2.84514 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.09480 q^{9} -4.15918 q^{10} +1.36362 q^{11} -2.84514 q^{12} -2.86984 q^{13} -1.00000 q^{14} +11.8334 q^{15} +1.00000 q^{16} -0.0229402 q^{17} +5.09480 q^{18} -6.17386 q^{19} -4.15918 q^{20} +2.84514 q^{21} +1.36362 q^{22} -0.253845 q^{23} -2.84514 q^{24} +12.2988 q^{25} -2.86984 q^{26} -5.95999 q^{27} -1.00000 q^{28} -1.68464 q^{29} +11.8334 q^{30} +6.99943 q^{31} +1.00000 q^{32} -3.87969 q^{33} -0.0229402 q^{34} +4.15918 q^{35} +5.09480 q^{36} +3.00745 q^{37} -6.17386 q^{38} +8.16507 q^{39} -4.15918 q^{40} +2.66237 q^{41} +2.84514 q^{42} -1.51322 q^{43} +1.36362 q^{44} -21.1902 q^{45} -0.253845 q^{46} +7.63939 q^{47} -2.84514 q^{48} +1.00000 q^{49} +12.2988 q^{50} +0.0652680 q^{51} -2.86984 q^{52} -0.456590 q^{53} -5.95999 q^{54} -5.67154 q^{55} -1.00000 q^{56} +17.5655 q^{57} -1.68464 q^{58} -3.18325 q^{59} +11.8334 q^{60} -1.02112 q^{61} +6.99943 q^{62} -5.09480 q^{63} +1.00000 q^{64} +11.9362 q^{65} -3.87969 q^{66} +13.7903 q^{67} -0.0229402 q^{68} +0.722224 q^{69} +4.15918 q^{70} -3.59661 q^{71} +5.09480 q^{72} +8.74851 q^{73} +3.00745 q^{74} -34.9917 q^{75} -6.17386 q^{76} -1.36362 q^{77} +8.16507 q^{78} -0.0245325 q^{79} -4.15918 q^{80} +1.67259 q^{81} +2.66237 q^{82} -1.07182 q^{83} +2.84514 q^{84} +0.0954124 q^{85} -1.51322 q^{86} +4.79302 q^{87} +1.36362 q^{88} +11.2986 q^{89} -21.1902 q^{90} +2.86984 q^{91} -0.253845 q^{92} -19.9143 q^{93} +7.63939 q^{94} +25.6782 q^{95} -2.84514 q^{96} +4.40474 q^{97} +1.00000 q^{98} +6.94738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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