LMFDB - Embedded newform 6034.2.a.m.1.17

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:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.34513 q^{3} +1.00000 q^{4} -2.31517 q^{5} +1.34513 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.19062 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.34513 q^{3} +1.00000 q^{4} -2.31517 q^{5} +1.34513 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.19062 q^{9} -2.31517 q^{10} +1.82099 q^{11} +1.34513 q^{12} +1.02705 q^{13} +1.00000 q^{14} -3.11421 q^{15} +1.00000 q^{16} -6.30346 q^{17} -1.19062 q^{18} +3.88262 q^{19} -2.31517 q^{20} +1.34513 q^{21} +1.82099 q^{22} -7.18335 q^{23} +1.34513 q^{24} +0.360007 q^{25} +1.02705 q^{26} -5.63694 q^{27} +1.00000 q^{28} -4.35921 q^{29} -3.11421 q^{30} +0.296499 q^{31} +1.00000 q^{32} +2.44948 q^{33} -6.30346 q^{34} -2.31517 q^{35} -1.19062 q^{36} -4.26392 q^{37} +3.88262 q^{38} +1.38152 q^{39} -2.31517 q^{40} -5.48050 q^{41} +1.34513 q^{42} +11.1174 q^{43} +1.82099 q^{44} +2.75648 q^{45} -7.18335 q^{46} -0.609939 q^{47} +1.34513 q^{48} +1.00000 q^{49} +0.360007 q^{50} -8.47900 q^{51} +1.02705 q^{52} -9.07701 q^{53} -5.63694 q^{54} -4.21590 q^{55} +1.00000 q^{56} +5.22265 q^{57} -4.35921 q^{58} -9.71171 q^{59} -3.11421 q^{60} +13.3714 q^{61} +0.296499 q^{62} -1.19062 q^{63} +1.00000 q^{64} -2.37780 q^{65} +2.44948 q^{66} -5.27796 q^{67} -6.30346 q^{68} -9.66256 q^{69} -2.31517 q^{70} -2.69207 q^{71} -1.19062 q^{72} +1.73088 q^{73} -4.26392 q^{74} +0.484257 q^{75} +3.88262 q^{76} +1.82099 q^{77} +1.38152 q^{78} -2.85527 q^{79} -2.31517 q^{80} -4.01059 q^{81} -5.48050 q^{82} -0.509380 q^{83} +1.34513 q^{84} +14.5936 q^{85} +11.1174 q^{86} -5.86372 q^{87} +1.82099 q^{88} -5.16029 q^{89} +2.75648 q^{90} +1.02705 q^{91} -7.18335 q^{92} +0.398831 q^{93} -0.609939 q^{94} -8.98893 q^{95} +1.34513 q^{96} -13.9570 q^{97} +1.00000 q^{98} -2.16810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	1.34513	0.776613	0.388307	−	0.921530i	$-0.373060\pi$
$3$	1.34513	0.776613	0.388307	+	0.921530i	$0.373060\pi$
$4$	1.00000	0.500000
$5$	−2.31517	−1.03537	−0.517687	−	0.855570i	$-0.673207\pi$
$5$	−2.31517	−1.03537	−0.517687	+	0.855570i	$0.673207\pi$
$6$	1.34513	0.549149
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.19062	−0.396872
$10$	−2.31517	−0.732121
$11$	1.82099	0.549050	0.274525	−	0.961580i	$-0.411479\pi$
$11$	1.82099	0.549050	0.274525	+	0.961580i	$0.411479\pi$
$12$	1.34513	0.388307
$13$	1.02705	0.284853	0.142426	−	0.989805i	$-0.454510\pi$
$13$	1.02705	0.284853	0.142426	+	0.989805i	$0.454510\pi$
$14$	1.00000	0.267261
$15$	−3.11421	−0.804086
$16$	1.00000	0.250000
$17$	−6.30346	−1.52881	−0.764407	−	0.644734i	$-0.776968\pi$
$17$	−6.30346	−1.52881	−0.764407	+	0.644734i	$0.776968\pi$
$18$	−1.19062	−0.280631
$19$	3.88262	0.890735	0.445367	−	0.895348i	$-0.353073\pi$
$19$	3.88262	0.890735	0.445367	+	0.895348i	$0.353073\pi$
$20$	−2.31517	−0.517687
$21$	1.34513	0.293532
$22$	1.82099	0.388237
$23$	−7.18335	−1.49783	−0.748916	−	0.662666i	$-0.769425\pi$
$23$	−7.18335	−1.49783	−0.748916	+	0.662666i	$0.769425\pi$
$24$	1.34513	0.274574
$25$	0.360007	0.0720014
$26$	1.02705	0.201421
$27$	−5.63694	−1.08483
$28$	1.00000	0.188982
$29$	−4.35921	−0.809485	−0.404742	−	0.914431i	$-0.632639\pi$
$29$	−4.35921	−0.809485	−0.404742	+	0.914431i	$0.632639\pi$
$30$	−3.11421	−0.568575
$31$	0.296499	0.0532528	0.0266264	−	0.999645i	$-0.491524\pi$
$31$	0.296499	0.0532528	0.0266264	+	0.999645i	$0.491524\pi$
$32$	1.00000	0.176777
$33$	2.44948	0.426399
$34$	−6.30346	−1.08103
$35$	−2.31517	−0.391335
$36$	−1.19062	−0.198436
$37$	−4.26392	−0.700985	−0.350492	−	0.936566i	$-0.613986\pi$
$37$	−4.26392	−0.700985	−0.350492	+	0.936566i	$0.613986\pi$
$38$	3.88262	0.629844
$39$	1.38152	0.221220
$40$	−2.31517	−0.366060
$41$	−5.48050	−0.855910	−0.427955	−	0.903800i	$-0.640766\pi$
$41$	−5.48050	−0.855910	−0.427955	+	0.903800i	$0.640766\pi$
$42$	1.34513	0.207559
$43$	11.1174	1.69538	0.847692	−	0.530489i	$-0.177992\pi$
$43$	11.1174	1.69538	0.847692	+	0.530489i	$0.177992\pi$
$44$	1.82099	0.274525
$45$	2.75648	0.410911
$46$	−7.18335	−1.05913
$47$	−0.609939	−0.0889687	−0.0444844	−	0.999010i	$-0.514164\pi$
$47$	−0.609939	−0.0889687	−0.0444844	+	0.999010i	$0.514164\pi$
$48$	1.34513	0.194153
$49$	1.00000	0.142857
$50$	0.360007	0.0509127
$51$	−8.47900	−1.18730
$52$	1.02705	0.142426
$53$	−9.07701	−1.24682	−0.623412	−	0.781894i	$-0.714254\pi$
$53$	−9.07701	−1.24682	−0.623412	+	0.781894i	$0.714254\pi$
$54$	−5.63694	−0.767090
$55$	−4.21590	−0.568472
$56$	1.00000	0.133631
$57$	5.22265	0.691756
$58$	−4.35921	−0.572392
$59$	−9.71171	−1.26436	−0.632178	−	0.774823i	$-0.717839\pi$
$59$	−9.71171	−1.26436	−0.632178	+	0.774823i	$0.717839\pi$
$60$	−3.11421	−0.402043
$61$	13.3714	1.71203	0.856013	−	0.516954i	$-0.172934\pi$
$61$	13.3714	1.71203	0.856013	+	0.516954i	$0.172934\pi$
$62$	0.296499	0.0376554
$63$	−1.19062	−0.150003
$64$	1.00000	0.125000
$65$	−2.37780	−0.294929
$66$	2.44948	0.301510
$67$	−5.27796	−0.644805	−0.322402	−	0.946603i	$-0.604490\pi$
$67$	−5.27796	−0.644805	−0.322402	+	0.946603i	$0.604490\pi$
$68$	−6.30346	−0.764407
$69$	−9.66256	−1.16324
$70$	−2.31517	−0.276716
$71$	−2.69207	−0.319490	−0.159745	−	0.987158i	$-0.551067\pi$
$71$	−2.69207	−0.319490	−0.159745	+	0.987158i	$0.551067\pi$
$72$	−1.19062	−0.140315
$73$	1.73088	0.202584	0.101292	−	0.994857i	$-0.467702\pi$
$73$	1.73088	0.202584	0.101292	+	0.994857i	$0.467702\pi$
$74$	−4.26392	−0.495671
$75$	0.484257	0.0559172
$76$	3.88262	0.445367
$77$	1.82099	0.207521
$78$	1.38152	0.156426
$79$	−2.85527	−0.321243	−0.160621	−	0.987016i	$-0.551350\pi$
$79$	−2.85527	−0.321243	−0.160621	+	0.987016i	$0.551350\pi$
$80$	−2.31517	−0.258844
$81$	−4.01059	−0.445621
$82$	−5.48050	−0.605220
$83$	−0.509380	−0.0559117	−0.0279559	−	0.999609i	$-0.508900\pi$
$83$	−0.509380	−0.0559117	−0.0279559	+	0.999609i	$0.508900\pi$
$84$	1.34513	0.146766
$85$	14.5936	1.58290
$86$	11.1174	1.19882
$87$	−5.86372	−0.628657
$88$	1.82099	0.194118
$89$	−5.16029	−0.546989	−0.273495	−	0.961874i	$-0.588180\pi$
$89$	−5.16029	−0.546989	−0.273495	+	0.961874i	$0.588180\pi$
$90$	2.75648	0.290558
$91$	1.02705	0.107664
$92$	−7.18335	−0.748916
$93$	0.398831	0.0413568
$94$	−0.609939	−0.0629104
$95$	−8.98893	−0.922244
$96$	1.34513	0.137287
$97$	−13.9570	−1.41711	−0.708557	−	0.705653i	$-0.750654\pi$
$97$	−13.9570	−1.41711	−0.708557	+	0.705653i	$0.750654\pi$
$98$	1.00000	0.101015
$99$	−2.16810	−0.217902
$100$	0.360007	0.0360007
$101$	−2.82966	−0.281562	−0.140781	−	0.990041i	$-0.544961\pi$
$101$	−2.82966	−0.281562	−0.140781	+	0.990041i	$0.544961\pi$
$102$	−8.47900	−0.839546
$103$	7.19060	0.708511	0.354255	−	0.935149i	$-0.384734\pi$
$103$	7.19060	0.708511	0.354255	+	0.935149i	$0.384734\pi$
$104$	1.02705	0.100711
$105$	−3.11421	−0.303916
$106$	−9.07701	−0.881637
$107$	7.35379	0.710918	0.355459	−	0.934692i	$-0.384325\pi$
$107$	7.35379	0.710918	0.355459	+	0.934692i	$0.384325\pi$
$108$	−5.63694	−0.542415
$109$	15.1216	1.44839	0.724193	−	0.689597i	$-0.242212\pi$
$109$	15.1216	1.44839	0.724193	+	0.689597i	$0.242212\pi$
$110$	−4.21590	−0.401971
$111$	−5.73555	−0.544394
$112$	1.00000	0.0944911
$113$	−11.0889	−1.04316	−0.521579	−	0.853203i	$-0.674657\pi$
$113$	−11.0889	−1.04316	−0.521579	+	0.853203i	$0.674657\pi$
$114$	5.22265	0.489146
$115$	16.6307	1.55082
$116$	−4.35921	−0.404742
$117$	−1.22282	−0.113050
$118$	−9.71171	−0.894035
$119$	−6.30346	−0.577837
$120$	−3.11421	−0.284287
$121$	−7.68399	−0.698544
$122$	13.3714	1.21059
$123$	−7.37200	−0.664711
$124$	0.296499	0.0266264
$125$	10.7424	0.960827
$126$	−1.19062	−0.106068
$127$	−11.4104	−1.01251	−0.506254	−	0.862384i	$-0.668970\pi$
$127$	−11.4104	−1.01251	−0.506254	+	0.862384i	$0.668970\pi$
$128$	1.00000	0.0883883
$129$	14.9544	1.31666
$130$	−2.37780	−0.208547
$131$	−7.65248	−0.668600	−0.334300	−	0.942467i	$-0.608500\pi$
$131$	−7.65248	−0.668600	−0.334300	+	0.942467i	$0.608500\pi$
$132$	2.44948	0.213200
$133$	3.88262	0.336666
$134$	−5.27796	−0.455946
$135$	13.0505	1.12321
$136$	−6.30346	−0.540517
$137$	−1.38279	−0.118139	−0.0590697	−	0.998254i	$-0.518813\pi$
$137$	−1.38279	−0.118139	−0.0590697	+	0.998254i	$0.518813\pi$
$138$	−9.66256	−0.822532
$139$	6.48252	0.549840	0.274920	−	0.961467i	$-0.411349\pi$
$139$	6.48252	0.549840	0.274920	+	0.961467i	$0.411349\pi$
$140$	−2.31517	−0.195667
$141$	−0.820450	−0.0690943
$142$	−2.69207	−0.225914
$143$	1.87025	0.156398
$144$	−1.19062	−0.0992179
$145$	10.0923	0.838120
$146$	1.73088	0.143248
$147$	1.34513	0.110945
$148$	−4.26392	−0.350492
$149$	1.57774	0.129253	0.0646267	−	0.997910i	$-0.479414\pi$
$149$	1.57774	0.129253	0.0646267	+	0.997910i	$0.479414\pi$
$150$	0.484257	0.0395394
$151$	−11.1141	−0.904455	−0.452228	−	0.891903i	$-0.649371\pi$
$151$	−11.1141	−0.904455	−0.452228	+	0.891903i	$0.649371\pi$
$152$	3.88262	0.314922
$153$	7.50500	0.606743
$154$	1.82099	0.146740
$155$	−0.686445	−0.0551366
$156$	1.38152	0.110610
$157$	4.42246	0.352951	0.176475	−	0.984305i	$-0.443530\pi$
$157$	4.42246	0.352951	0.176475	+	0.984305i	$0.443530\pi$
$158$	−2.85527	−0.227153
$159$	−12.2098	−0.968299
$160$	−2.31517	−0.183030
$161$	−7.18335	−0.566127
$162$	−4.01059	−0.315102
$163$	4.51935	0.353983	0.176991	−	0.984212i	$-0.443364\pi$
$163$	4.51935	0.353983	0.176991	+	0.984212i	$0.443364\pi$
$164$	−5.48050	−0.427955
$165$	−5.67095	−0.441483
$166$	−0.509380	−0.0395356
$167$	−8.47745	−0.656004	−0.328002	−	0.944677i	$-0.606375\pi$
$167$	−8.47745	−0.656004	−0.328002	+	0.944677i	$0.606375\pi$
$168$	1.34513	0.103779
$169$	−11.9452	−0.918859
$170$	14.5936	1.11928
$171$	−4.62271	−0.353507
$172$	11.1174	0.847692
$173$	2.07783	0.157974	0.0789872	−	0.996876i	$-0.474831\pi$
$173$	2.07783	0.157974	0.0789872	+	0.996876i	$0.474831\pi$
$174$	−5.86372	−0.444527
$175$	0.360007	0.0272140
$176$	1.82099	0.137262
$177$	−13.0635	−0.981916
$178$	−5.16029	−0.386780
$179$	7.41172	0.553978	0.276989	−	0.960873i	$-0.410663\pi$
$179$	7.41172	0.553978	0.276989	+	0.960873i	$0.410663\pi$
$180$	2.75648	0.205456
$181$	19.8167	1.47297	0.736483	−	0.676456i	$-0.236485\pi$
$181$	19.8167	1.47297	0.736483	+	0.676456i	$0.236485\pi$
$182$	1.02705	0.0761301
$183$	17.9863	1.32958
$184$	−7.18335	−0.529563
$185$	9.87171	0.725782
$186$	0.398831	0.0292437
$187$	−11.4786	−0.839395
$188$	−0.609939	−0.0444844
$189$	−5.63694	−0.410027
$190$	−8.98893	−0.652125
$191$	−5.71144	−0.413265	−0.206633	−	0.978419i	$-0.566251\pi$
$191$	−5.71144	−0.413265	−0.206633	+	0.978419i	$0.566251\pi$
$192$	1.34513	0.0970767
$193$	−0.155001	−0.0111572	−0.00557859	−	0.999984i	$-0.501776\pi$
$193$	−0.155001	−0.0111572	−0.00557859	+	0.999984i	$0.501776\pi$
$194$	−13.9570	−1.00205
$195$	−3.19846	−0.229046
$196$	1.00000	0.0714286
$197$	−1.30758	−0.0931609	−0.0465805	−	0.998915i	$-0.514832\pi$
$197$	−1.30758	−0.0931609	−0.0465805	+	0.998915i	$0.514832\pi$
$198$	−2.16810	−0.154080
$199$	−20.2631	−1.43642	−0.718208	−	0.695829i	$-0.755037\pi$
$199$	−20.2631	−1.43642	−0.718208	+	0.695829i	$0.755037\pi$
$200$	0.360007	0.0254563
$201$	−7.09956	−0.500764
$202$	−2.82966	−0.199094
$203$	−4.35921	−0.305956
$204$	−8.47900	−0.593649
$205$	12.6883	0.886188
$206$	7.19060	0.500993
$207$	8.55260	0.594447
$208$	1.02705	0.0712132
$209$	7.07022	0.489058
$210$	−3.11421	−0.214901
$211$	−10.2278	−0.704113	−0.352057	−	0.935979i	$-0.614518\pi$
$211$	−10.2278	−0.704113	−0.352057	+	0.935979i	$0.614518\pi$
$212$	−9.07701	−0.623412
$213$	−3.62120	−0.248120
$214$	7.35379	0.502695
$215$	−25.7386	−1.75536
$216$	−5.63694	−0.383545
$217$	0.296499	0.0201277
$218$	15.1216	1.02416
$219$	2.32826	0.157329
$220$	−4.21590	−0.284236
$221$	−6.47398	−0.435487
$222$	−5.73555	−0.384945
$223$	−0.988408	−0.0661887	−0.0330943	−	0.999452i	$-0.510536\pi$
$223$	−0.988408	−0.0661887	−0.0330943	+	0.999452i	$0.510536\pi$
$224$	1.00000	0.0668153
$225$	−0.428630	−0.0285753
$226$	−11.0889	−0.737624
$227$	−8.40225	−0.557677	−0.278838	−	0.960338i	$-0.589949\pi$
$227$	−8.40225	−0.557677	−0.278838	+	0.960338i	$0.589949\pi$
$228$	5.22265	0.345878
$229$	−4.93262	−0.325957	−0.162978	−	0.986630i	$-0.552110\pi$
$229$	−4.93262	−0.325957	−0.162978	+	0.986630i	$0.552110\pi$
$230$	16.6307	1.09659
$231$	2.44948	0.161164
$232$	−4.35921	−0.286196
$233$	9.11465	0.597120	0.298560	−	0.954391i	$-0.403494\pi$
$233$	9.11465	0.597120	0.298560	+	0.954391i	$0.403494\pi$
$234$	−1.22282	−0.0799384
$235$	1.41211	0.0921160
$236$	−9.71171	−0.632178
$237$	−3.84072	−0.249481
$238$	−6.30346	−0.408593
$239$	−10.0198	−0.648128	−0.324064	−	0.946035i	$-0.605049\pi$
$239$	−10.0198	−0.648128	−0.324064	+	0.946035i	$0.605049\pi$
$240$	−3.11421	−0.201021
$241$	−13.9163	−0.896425	−0.448213	−	0.893927i	$-0.647939\pi$
$241$	−13.9163	−0.896425	−0.448213	+	0.893927i	$0.647939\pi$
$242$	−7.68399	−0.493946
$243$	11.5160	0.738754
$244$	13.3714	0.856013
$245$	−2.31517	−0.147911
$246$	−7.37200	−0.470022
$247$	3.98765	0.253728
$248$	0.296499	0.0188277
$249$	−0.685184	−0.0434218
$250$	10.7424	0.679407
$251$	−13.4977	−0.851966	−0.425983	−	0.904731i	$-0.640072\pi$
$251$	−13.4977	−0.851966	−0.425983	+	0.904731i	$0.640072\pi$
$252$	−1.19062	−0.0750017
$253$	−13.0808	−0.822384
$254$	−11.4104	−0.715952
$255$	19.6303	1.22930
$256$	1.00000	0.0625000
$257$	5.65029	0.352456	0.176228	−	0.984349i	$-0.443610\pi$
$257$	5.65029	0.352456	0.176228	+	0.984349i	$0.443610\pi$
$258$	14.9544	0.931017
$259$	−4.26392	−0.264947
$260$	−2.37780	−0.147465
$261$	5.19014	0.321262
$262$	−7.65248	−0.472772
$263$	−24.9351	−1.53756	−0.768781	−	0.639512i	$-0.779136\pi$
$263$	−24.9351	−1.53756	−0.768781	+	0.639512i	$0.779136\pi$
$264$	2.44948	0.150755
$265$	21.0148	1.29093
$266$	3.88262	0.238059
$267$	−6.94128	−0.424799
$268$	−5.27796	−0.322402
$269$	−1.32265	−0.0806431	−0.0403216	−	0.999187i	$-0.512838\pi$
$269$	−1.32265	−0.0806431	−0.0403216	+	0.999187i	$0.512838\pi$
$270$	13.0505	0.794226
$271$	32.6461	1.98311	0.991554	−	0.129695i	$-0.0413997\pi$
$271$	32.6461	1.98311	0.991554	+	0.129695i	$0.0413997\pi$
$272$	−6.30346	−0.382203
$273$	1.38152	0.0836135
$274$	−1.38279	−0.0835371
$275$	0.655570	0.0395323
$276$	−9.66256	−0.581618
$277$	−33.1231	−1.99017	−0.995087	−	0.0990054i	$-0.968434\pi$
$277$	−33.1231	−1.99017	−0.995087	+	0.0990054i	$0.968434\pi$
$278$	6.48252	0.388796
$279$	−0.353016	−0.0211345
$280$	−2.31517	−0.138358
$281$	14.1641	0.844961	0.422480	−	0.906372i	$-0.361160\pi$
$281$	14.1641	0.844961	0.422480	+	0.906372i	$0.361160\pi$
$282$	−0.820450	−0.0488571
$283$	5.71975	0.340004	0.170002	−	0.985444i	$-0.445623\pi$
$283$	5.71975	0.340004	0.170002	+	0.985444i	$0.445623\pi$
$284$	−2.69207	−0.159745
$285$	−12.0913	−0.716227
$286$	1.87025	0.110590
$287$	−5.48050	−0.323504
$288$	−1.19062	−0.0701577
$289$	22.7336	1.33727
$290$	10.0923	0.592641
$291$	−18.7740	−1.10055
$292$	1.73088	0.101292
$293$	17.3120	1.01138	0.505688	−	0.862717i	$-0.331239\pi$
$293$	17.3120	1.01138	0.505688	+	0.862717i	$0.331239\pi$
$294$	1.34513	0.0784498
$295$	22.4842	1.30908
$296$	−4.26392	−0.247836
$297$	−10.2648	−0.595625
$298$	1.57774	0.0913960
$299$	−7.37766	−0.426661
$300$	0.484257	0.0279586
$301$	11.1174	0.640795
$302$	−11.1141	−0.639547
$303$	−3.80627	−0.218665
$304$	3.88262	0.222684
$305$	−30.9569	−1.77259
$306$	7.50500	0.429032
$307$	28.9215	1.65064	0.825319	−	0.564667i	$-0.190995\pi$
$307$	28.9215	1.65064	0.825319	+	0.564667i	$0.190995\pi$
$308$	1.82099	0.103761
$309$	9.67232	0.550239
$310$	−0.686445	−0.0389875
$311$	5.72167	0.324446	0.162223	−	0.986754i	$-0.448134\pi$
$311$	5.72167	0.324446	0.162223	+	0.986754i	$0.448134\pi$
$312$	1.38152	0.0782132
$313$	7.28299	0.411659	0.205829	−	0.978588i	$-0.434011\pi$
$313$	7.28299	0.411659	0.205829	+	0.978588i	$0.434011\pi$
$314$	4.42246	0.249574
$315$	2.75648	0.155310
$316$	−2.85527	−0.160621
$317$	23.5361	1.32192	0.660960	−	0.750421i	$-0.270149\pi$
$317$	23.5361	1.32192	0.660960	+	0.750421i	$0.270149\pi$
$318$	−12.2098	−0.684691
$319$	−7.93808	−0.444447
$320$	−2.31517	−0.129422
$321$	9.89183	0.552108
$322$	−7.18335	−0.400312
$323$	−24.4740	−1.36177
$324$	−4.01059	−0.222811
$325$	0.369746	0.0205098
$326$	4.51935	0.250304
$327$	20.3406	1.12484
$328$	−5.48050	−0.302610
$329$	−0.609939	−0.0336270
$330$	−5.67095	−0.312176
$331$	−25.2029	−1.38528	−0.692639	−	0.721284i	$-0.743552\pi$
$331$	−25.2029	−1.38528	−0.692639	+	0.721284i	$0.743552\pi$
$332$	−0.509380	−0.0279559
$333$	5.07669	0.278201
$334$	−8.47745	−0.463865
$335$	12.2194	0.667615
$336$	1.34513	0.0733831
$337$	−5.43691	−0.296167	−0.148084	−	0.988975i	$-0.547310\pi$
$337$	−5.43691	−0.296167	−0.148084	+	0.988975i	$0.547310\pi$
$338$	−11.9452	−0.649731
$339$	−14.9161	−0.810130
$340$	14.5936	0.791448
$341$	0.539922	0.0292384
$342$	−4.62271	−0.249968
$343$	1.00000	0.0539949
$344$	11.1174	0.599409
$345$	22.3705	1.20438
$346$	2.07783	0.111705
$347$	−20.6599	−1.10908	−0.554540	−	0.832157i	$-0.687106\pi$
$347$	−20.6599	−1.10908	−0.554540	+	0.832157i	$0.687106\pi$
$348$	−5.86372	−0.314328
$349$	−26.4503	−1.41585	−0.707927	−	0.706286i	$-0.750369\pi$
$349$	−26.4503	−1.41585	−0.707927	+	0.706286i	$0.750369\pi$
$350$	0.360007	0.0192432
$351$	−5.78942	−0.309017
$352$	1.82099	0.0970592
$353$	18.9614	1.00921	0.504606	−	0.863349i	$-0.331638\pi$
$353$	18.9614	1.00921	0.504606	+	0.863349i	$0.331638\pi$
$354$	−13.0635	−0.694320
$355$	6.23260	0.330792
$356$	−5.16029	−0.273495
$357$	−8.47900	−0.448756
$358$	7.41172	0.391722
$359$	−0.980074	−0.0517263	−0.0258632	−	0.999665i	$-0.508233\pi$
$359$	−0.980074	−0.0517263	−0.0258632	+	0.999665i	$0.508233\pi$
$360$	2.75648	0.145279
$361$	−3.92524	−0.206592
$362$	19.8167	1.04154
$363$	−10.3360	−0.542499
$364$	1.02705	0.0538321
$365$	−4.00727	−0.209750
$366$	17.9863	0.940157
$367$	−18.7161	−0.976974	−0.488487	−	0.872571i	$-0.662451\pi$
$367$	−18.7161	−0.976974	−0.488487	+	0.872571i	$0.662451\pi$
$368$	−7.18335	−0.374458
$369$	6.52517	0.339687
$370$	9.87171	0.513206
$371$	−9.07701	−0.471255
$372$	0.398831	0.0206784
$373$	−11.2753	−0.583814	−0.291907	−	0.956447i	$-0.594290\pi$
$373$	−11.2753	−0.583814	−0.291907	+	0.956447i	$0.594290\pi$
$374$	−11.4786	−0.593542
$375$	14.4499	0.746191
$376$	−0.609939	−0.0314552
$377$	−4.47713	−0.230584
$378$	−5.63694	−0.289933
$379$	−8.30266	−0.426479	−0.213239	−	0.977000i	$-0.568401\pi$
$379$	−8.30266	−0.426479	−0.213239	+	0.977000i	$0.568401\pi$
$380$	−8.98893	−0.461122
$381$	−15.3485	−0.786328
$382$	−5.71144	−0.292223
$383$	25.5669	1.30641	0.653205	−	0.757181i	$-0.273424\pi$
$383$	25.5669	1.30641	0.653205	+	0.757181i	$0.273424\pi$
$384$	1.34513	0.0686436
$385$	−4.21590	−0.214862
$386$	−0.155001	−0.00788932
$387$	−13.2365	−0.672850
$388$	−13.9570	−0.708557
$389$	29.9086	1.51643	0.758213	−	0.652007i	$-0.226073\pi$
$389$	29.9086	1.51643	0.758213	+	0.652007i	$0.226073\pi$
$390$	−3.19846	−0.161960
$391$	45.2799	2.28990
$392$	1.00000	0.0505076
$393$	−10.2936	−0.519244
$394$	−1.30758	−0.0658747
$395$	6.61043	0.332607
$396$	−2.16810	−0.108951
$397$	31.8776	1.59989	0.799945	−	0.600074i	$-0.204862\pi$
$397$	31.8776	1.59989	0.799945	+	0.600074i	$0.204862\pi$
$398$	−20.2631	−1.01570
$399$	5.22265	0.261459
$400$	0.360007	0.0180003
$401$	−11.4030	−0.569438	−0.284719	−	0.958611i	$-0.591900\pi$
$401$	−11.4030	−0.569438	−0.284719	+	0.958611i	$0.591900\pi$
$402$	−7.09956	−0.354094
$403$	0.304520	0.0151692
$404$	−2.82966	−0.140781
$405$	9.28519	0.461385
$406$	−4.35921	−0.216344
$407$	−7.76457	−0.384876
$408$	−8.47900	−0.419773
$409$	−34.8689	−1.72415	−0.862077	−	0.506777i	$-0.830837\pi$
$409$	−34.8689	−1.72415	−0.862077	+	0.506777i	$0.830837\pi$
$410$	12.6883	0.626630
$411$	−1.86003	−0.0917486
$412$	7.19060	0.354255
$413$	−9.71171	−0.477882
$414$	8.55260	0.420337
$415$	1.17930	0.0578896
$416$	1.02705	0.0503553
$417$	8.71986	0.427013
$418$	7.07022	0.345816
$419$	19.6912	0.961980	0.480990	−	0.876726i	$-0.340277\pi$
$419$	19.6912	0.961980	0.480990	+	0.876726i	$0.340277\pi$
$420$	−3.11421	−0.151958
$421$	23.1688	1.12918	0.564589	−	0.825372i	$-0.309035\pi$
$421$	23.1688	1.12918	0.564589	+	0.825372i	$0.309035\pi$
$422$	−10.2278	−0.497883
$423$	0.726203	0.0353092
$424$	−9.07701	−0.440819
$425$	−2.26929	−0.110077
$426$	−3.62120	−0.175448
$427$	13.3714	0.647085
$428$	7.35379	0.355459
$429$	2.51574	0.121461
$430$	−25.7386	−1.24123
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−5.63694	−0.271207
$433$	−1.13204	−0.0544025	−0.0272012	−	0.999630i	$-0.508659\pi$
$433$	−1.13204	−0.0544025	−0.0272012	+	0.999630i	$0.508659\pi$
$434$	0.296499	0.0142324
$435$	13.5755	0.650895
$436$	15.1216	0.724193
$437$	−27.8902	−1.33417
$438$	2.32826	0.111249
$439$	−25.1495	−1.20032	−0.600161	−	0.799879i	$-0.704897\pi$
$439$	−25.1495	−1.20032	−0.600161	+	0.799879i	$0.704897\pi$
$440$	−4.21590	−0.200985
$441$	−1.19062	−0.0566960
$442$	−6.47398	−0.307936
$443$	39.4788	1.87570	0.937848	−	0.347046i	$-0.112815\pi$
$443$	39.4788	1.87570	0.937848	+	0.347046i	$0.112815\pi$
$444$	−5.73555	−0.272197
$445$	11.9469	0.566339
$446$	−0.988408	−0.0468025
$447$	2.12227	0.100380
$448$	1.00000	0.0472456
$449$	−10.1433	−0.478692	−0.239346	−	0.970934i	$-0.576933\pi$
$449$	−10.1433	−0.478692	−0.239346	+	0.970934i	$0.576933\pi$
$450$	−0.428630	−0.0202058
$451$	−9.97994	−0.469937
$452$	−11.0889	−0.521579
$453$	−14.9500	−0.702412
$454$	−8.40225	−0.394337
$455$	−2.37780	−0.111473
$456$	5.22265	0.244573
$457$	12.6043	0.589604	0.294802	−	0.955558i	$-0.404746\pi$
$457$	12.6043	0.589604	0.294802	+	0.955558i	$0.404746\pi$
$458$	−4.93262	−0.230486
$459$	35.5322	1.65850
$460$	16.6307	0.775408
$461$	−18.0661	−0.841424	−0.420712	−	0.907194i	$-0.638220\pi$
$461$	−18.0661	−0.841424	−0.420712	+	0.907194i	$0.638220\pi$
$462$	2.44948	0.113960
$463$	−22.1284	−1.02839	−0.514196	−	0.857673i	$-0.671910\pi$
$463$	−22.1284	−1.02839	−0.514196	+	0.857673i	$0.671910\pi$
$464$	−4.35921	−0.202371
$465$	−0.923360	−0.0428198
$466$	9.11465	0.422228
$467$	27.8531	1.28889	0.644445	−	0.764651i	$-0.277089\pi$
$467$	27.8531	1.28889	0.644445	+	0.764651i	$0.277089\pi$
$468$	−1.22282	−0.0565250
$469$	−5.27796	−0.243713
$470$	1.41211	0.0651359
$471$	5.94880	0.274106
$472$	−9.71171	−0.447018
$473$	20.2446	0.930850
$474$	−3.84072	−0.176410
$475$	1.39777	0.0641341
$476$	−6.30346	−0.288919
$477$	10.8072	0.494829
$478$	−10.0198	−0.458296
$479$	7.54256	0.344628	0.172314	−	0.985042i	$-0.444876\pi$
$479$	7.54256	0.344628	0.172314	+	0.985042i	$0.444876\pi$
$480$	−3.11421	−0.142144
$481$	−4.37927	−0.199678
$482$	−13.9163	−0.633868
$483$	−9.66256	−0.439662
$484$	−7.68399	−0.349272
$485$	32.3127	1.46724
$486$	11.5160	0.522378
$487$	8.94353	0.405270	0.202635	−	0.979254i	$-0.435049\pi$
$487$	8.94353	0.405270	0.202635	+	0.979254i	$0.435049\pi$
$488$	13.3714	0.605293
$489$	6.07913	0.274908
$490$	−2.31517	−0.104589
$491$	−35.8923	−1.61980	−0.809898	−	0.586570i	$-0.800478\pi$
$491$	−35.8923	−1.61980	−0.809898	+	0.586570i	$0.800478\pi$
$492$	−7.37200	−0.332356
$493$	27.4781	1.23755
$494$	3.98765	0.179413
$495$	5.01952	0.225611
$496$	0.296499	0.0133132
$497$	−2.69207	−0.120756
$498$	−0.685184	−0.0307038
$499$	−27.1444	−1.21515	−0.607574	−	0.794263i	$-0.707857\pi$
$499$	−27.1444	−1.21515	−0.607574	+	0.794263i	$0.707857\pi$
$500$	10.7424	0.480413
$501$	−11.4033	−0.509462
$502$	−13.4977	−0.602431
$503$	32.7114	1.45853	0.729264	−	0.684232i	$-0.239863\pi$
$503$	32.7114	1.45853	0.729264	+	0.684232i	$0.239863\pi$
$504$	−1.19062	−0.0530342
$505$	6.55115	0.291522
$506$	−13.0808	−0.581513
$507$	−16.0678	−0.713598
$508$	−11.4104	−0.506254
$509$	40.7537	1.80638	0.903189	−	0.429243i	$-0.141220\pi$
$509$	40.7537	1.80638	0.903189	+	0.429243i	$0.141220\pi$
$510$	19.6303	0.869245
$511$	1.73088	0.0765695
$512$	1.00000	0.0441942
$513$	−21.8861	−0.966295
$514$	5.65029	0.249224
$515$	−16.6475	−0.733574
$516$	14.9544	0.658329
$517$	−1.11069	−0.0488483
$518$	−4.26392	−0.187346
$519$	2.79496	0.122685
$520$	−2.37780	−0.104273
$521$	6.12635	0.268400	0.134200	−	0.990954i	$-0.457154\pi$
$521$	6.12635	0.268400	0.134200	+	0.990954i	$0.457154\pi$
$522$	5.19014	0.227166
$523$	5.51300	0.241067	0.120533	−	0.992709i	$-0.461540\pi$
$523$	5.51300	0.241067	0.120533	+	0.992709i	$0.461540\pi$
$524$	−7.65248	−0.334300
$525$	0.484257	0.0211347
$526$	−24.9351	−1.08722
$527$	−1.86897	−0.0814136
$528$	2.44948	0.106600
$529$	28.6004	1.24350
$530$	21.0148	0.912825
$531$	11.5629	0.501787
$532$	3.88262	0.168333
$533$	−5.62875	−0.243808
$534$	−6.94128	−0.300378
$535$	−17.0253	−0.736066
$536$	−5.27796	−0.227973
$537$	9.96976	0.430227
$538$	−1.32265	−0.0570233
$539$	1.82099	0.0784357
$540$	13.0505	0.561603
$541$	37.8923	1.62912	0.814560	−	0.580080i	$-0.196979\pi$
$541$	37.8923	1.62912	0.814560	+	0.580080i	$0.196979\pi$
$542$	32.6461	1.40227
$543$	26.6562	1.14393
$544$	−6.30346	−0.270259
$545$	−35.0091	−1.49962
$546$	1.38152	0.0591237
$547$	27.3533	1.16954	0.584771	−	0.811199i	$-0.301185\pi$
$547$	27.3533	1.16954	0.584771	+	0.811199i	$0.301185\pi$
$548$	−1.38279	−0.0590697
$549$	−15.9201	−0.679455
$550$	0.655570	0.0279536
$551$	−16.9252	−0.721036
$552$	−9.66256	−0.411266
$553$	−2.85527	−0.121418
$554$	−33.1231	−1.40727
$555$	13.2788	0.563652
$556$	6.48252	0.274920
$557$	35.1948	1.49125	0.745626	−	0.666365i	$-0.232151\pi$
$557$	35.1948	1.49125	0.745626	+	0.666365i	$0.232151\pi$
$558$	−0.353016	−0.0149444
$559$	11.4181	0.482935
$560$	−2.31517	−0.0978337
$561$	−15.4402	−0.651885
$562$	14.1641	0.597478
$563$	−35.9112	−1.51347	−0.756737	−	0.653719i	$-0.773208\pi$
$563$	−35.9112	−1.51347	−0.756737	+	0.653719i	$0.773208\pi$
$564$	−0.820450	−0.0345472
$565$	25.6727	1.08006
$566$	5.71975	0.240419
$567$	−4.01059	−0.168429
$568$	−2.69207	−0.112957
$569$	31.6055	1.32497	0.662486	−	0.749074i	$-0.269501\pi$
$569$	31.6055	1.32497	0.662486	+	0.749074i	$0.269501\pi$
$570$	−12.0913	−0.506449
$571$	−0.521750	−0.0218345	−0.0109173	−	0.999940i	$-0.503475\pi$
$571$	−0.521750	−0.0218345	−0.0109173	+	0.999940i	$0.503475\pi$
$572$	1.87025	0.0781992
$573$	−7.68265	−0.320947
$574$	−5.48050	−0.228752
$575$	−2.58605	−0.107846
$576$	−1.19062	−0.0496090
$577$	34.6602	1.44292	0.721462	−	0.692454i	$-0.243471\pi$
$577$	34.6602	1.44292	0.721462	+	0.692454i	$0.243471\pi$
$578$	22.7336	0.945594
$579$	−0.208496	−0.00866482
$580$	10.0923	0.419060
$581$	−0.509380	−0.0211326
$582$	−18.7740	−0.778206
$583$	−16.5292	−0.684568
$584$	1.73088	0.0716242
$585$	2.83104	0.117049
$586$	17.3120	0.715150
$587$	−28.5654	−1.17902	−0.589510	−	0.807761i	$-0.700679\pi$
$587$	−28.5654	−1.17902	−0.589510	+	0.807761i	$0.700679\pi$
$588$	1.34513	0.0554724
$589$	1.15119	0.0474341
$590$	22.4842	0.925662
$591$	−1.75886	−0.0723500
$592$	−4.26392	−0.175246
$593$	14.1410	0.580701	0.290351	−	0.956920i	$-0.406228\pi$
$593$	14.1410	0.580701	0.290351	+	0.956920i	$0.406228\pi$
$594$	−10.2648	−0.421171
$595$	14.5936	0.598278
$596$	1.57774	0.0646267
$597$	−27.2566	−1.11554
$598$	−7.37766	−0.301695
$599$	−24.2444	−0.990600	−0.495300	−	0.868722i	$-0.664942\pi$
$599$	−24.2444	−0.990600	−0.495300	+	0.868722i	$0.664942\pi$
$600$	0.484257	0.0197697
$601$	−36.7763	−1.50013	−0.750067	−	0.661361i	$-0.769979\pi$
$601$	−36.7763	−1.50013	−0.750067	+	0.661361i	$0.769979\pi$
$602$	11.1174	0.453110
$603$	6.28402	0.255905
$604$	−11.1141	−0.452228
$605$	17.7897	0.723255
$606$	−3.80627	−0.154619
$607$	−4.36633	−0.177224	−0.0886119	−	0.996066i	$-0.528243\pi$
$607$	−4.36633	−0.177224	−0.0886119	+	0.996066i	$0.528243\pi$
$608$	3.88262	0.157461
$609$	−5.86372	−0.237610
$610$	−30.9569	−1.25341
$611$	−0.626439	−0.0253430
$612$	7.50500	0.303372
$613$	26.4880	1.06984	0.534920	−	0.844903i	$-0.320342\pi$
$613$	26.4880	1.06984	0.534920	+	0.844903i	$0.320342\pi$
$614$	28.9215	1.16718
$615$	17.0674	0.688225
$616$	1.82099	0.0733698
$617$	33.4978	1.34857	0.674285	−	0.738471i	$-0.264452\pi$
$617$	33.4978	1.34857	0.674285	+	0.738471i	$0.264452\pi$
$618$	9.67232	0.389078
$619$	27.8173	1.11807	0.559036	−	0.829143i	$-0.311171\pi$
$619$	27.8173	1.11807	0.559036	+	0.829143i	$0.311171\pi$
$620$	−0.686445	−0.0275683
$621$	40.4921	1.62489
$622$	5.72167	0.229418
$623$	−5.16029	−0.206743
$624$	1.38152	0.0553051
$625$	−26.6704	−1.06682
$626$	7.28299	0.291087
$627$	9.51040	0.379809
$628$	4.42246	0.176475
$629$	26.8775	1.07168
$630$	2.75648	0.109821
$631$	−28.6059	−1.13878	−0.569390	−	0.822067i	$-0.692821\pi$
$631$	−28.6059	−1.13878	−0.569390	+	0.822067i	$0.692821\pi$
$632$	−2.85527	−0.113576
$633$	−13.7578	−0.546824
$634$	23.5361	0.934739
$635$	26.4170	1.04833
$636$	−12.2098	−0.484150
$637$	1.02705	0.0406933
$638$	−7.93808	−0.314272
$639$	3.20522	0.126797
$640$	−2.31517	−0.0915151
$641$	−47.7228	−1.88494	−0.942468	−	0.334296i	$-0.891501\pi$
$641$	−47.7228	−1.88494	−0.942468	+	0.334296i	$0.891501\pi$
$642$	9.89183	0.390399
$643$	18.9928	0.749002	0.374501	−	0.927227i	$-0.377814\pi$
$643$	18.9928	0.749002	0.374501	+	0.927227i	$0.377814\pi$
$644$	−7.18335	−0.283063
$645$	−34.6218	−1.36323
$646$	−24.4740	−0.962915
$647$	8.92520	0.350886	0.175443	−	0.984490i	$-0.443864\pi$
$647$	8.92520	0.350886	0.175443	+	0.984490i	$0.443864\pi$
$648$	−4.01059	−0.157551
$649$	−17.6849	−0.694195
$650$	0.369746	0.0145026
$651$	0.398831	0.0156314
$652$	4.51935	0.176991
$653$	33.0459	1.29319	0.646593	−	0.762835i	$-0.276193\pi$
$653$	33.0459	1.29319	0.646593	+	0.762835i	$0.276193\pi$
$654$	20.3406	0.795379
$655$	17.7168	0.692252
$656$	−5.48050	−0.213978
$657$	−2.06081	−0.0803998
$658$	−0.609939	−0.0237779
$659$	−29.9660	−1.16731	−0.583654	−	0.812002i	$-0.698378\pi$
$659$	−29.9660	−1.16731	−0.583654	+	0.812002i	$0.698378\pi$
$660$	−5.67095	−0.220742
$661$	11.5059	0.447530	0.223765	−	0.974643i	$-0.428165\pi$
$661$	11.5059	0.447530	0.223765	+	0.974643i	$0.428165\pi$
$662$	−25.2029	−0.979540
$663$	−8.70837	−0.338205
$664$	−0.509380	−0.0197678
$665$	−8.98893	−0.348576
$666$	5.07669	0.196718
$667$	31.3137	1.21247
$668$	−8.47745	−0.328002
$669$	−1.32954	−0.0514030
$670$	12.2194	0.472075
$671$	24.3491	0.939987
$672$	1.34513	0.0518897
$673$	−9.05346	−0.348985	−0.174493	−	0.984658i	$-0.555828\pi$
$673$	−9.05346	−0.348985	−0.174493	+	0.984658i	$0.555828\pi$
$674$	−5.43691	−0.209422
$675$	−2.02934	−0.0781092
$676$	−11.9452	−0.459429
$677$	41.6816	1.60196	0.800978	−	0.598694i	$-0.204314\pi$
$677$	41.6816	1.60196	0.800978	+	0.598694i	$0.204314\pi$
$678$	−14.9161	−0.572848
$679$	−13.9570	−0.535619
$680$	14.5936	0.559638
$681$	−11.3022	−0.433099
$682$	0.539922	0.0206747
$683$	26.0177	0.995540	0.497770	−	0.867309i	$-0.334152\pi$
$683$	26.0177	0.995540	0.497770	+	0.867309i	$0.334152\pi$
$684$	−4.62271	−0.176754
$685$	3.20138	0.122318
$686$	1.00000	0.0381802
$687$	−6.63504	−0.253143
$688$	11.1174	0.423846
$689$	−9.32255	−0.355161
$690$	22.3705	0.851629
$691$	15.4502	0.587755	0.293877	−	0.955843i	$-0.405054\pi$
$691$	15.4502	0.587755	0.293877	+	0.955843i	$0.405054\pi$
$692$	2.07783	0.0789872
$693$	−2.16810	−0.0823593
$694$	−20.6599	−0.784238
$695$	−15.0081	−0.569291
$696$	−5.86372	−0.222264
$697$	34.5461	1.30853
$698$	−26.4503	−1.00116
$699$	12.2604	0.463732
$700$	0.360007	0.0136070
$701$	11.9344	0.450757	0.225378	−	0.974271i	$-0.427638\pi$
$701$	11.9344	0.450757	0.225378	+	0.974271i	$0.427638\pi$
$702$	−5.78942	−0.218508
$703$	−16.5552	−0.624392
$704$	1.82099	0.0686312
$705$	1.89948	0.0715385
$706$	18.9614	0.713621
$707$	−2.82966	−0.106420
$708$	−13.0635	−0.490958
$709$	−37.0282	−1.39062	−0.695312	−	0.718708i	$-0.744734\pi$
$709$	−37.0282	−1.39062	−0.695312	+	0.718708i	$0.744734\pi$
$710$	6.23260	0.233905
$711$	3.39953	0.127492
$712$	−5.16029	−0.193390
$713$	−2.12985	−0.0797637
$714$	−8.47900	−0.317319
$715$	−4.32995	−0.161931
$716$	7.41172	0.276989
$717$	−13.4780	−0.503345
$718$	−0.980074	−0.0365760
$719$	18.2126	0.679214	0.339607	−	0.940567i	$-0.389706\pi$
$719$	18.2126	0.679214	0.339607	+	0.940567i	$0.389706\pi$
$720$	2.75648	0.102728
$721$	7.19060	0.267792
$722$	−3.92524	−0.146082
$723$	−18.7192	−0.696176
$724$	19.8167	0.736483
$725$	−1.56935	−0.0582840
$726$	−10.3360	−0.383605
$727$	−18.4884	−0.685698	−0.342849	−	0.939391i	$-0.611392\pi$
$727$	−18.4884	−0.685698	−0.342849	+	0.939391i	$0.611392\pi$
$728$	1.02705	0.0380651
$729$	27.5224	1.01935
$730$	−4.00727	−0.148316
$731$	−70.0779	−2.59193
$732$	17.9863	0.664791
$733$	−5.28196	−0.195094	−0.0975469	−	0.995231i	$-0.531100\pi$
$733$	−5.28196	−0.195094	−0.0975469	+	0.995231i	$0.531100\pi$
$734$	−18.7161	−0.690825
$735$	−3.11421	−0.114869
$736$	−7.18335	−0.264782
$737$	−9.61111	−0.354030
$738$	6.52517	0.240195
$739$	−47.4158	−1.74422	−0.872110	−	0.489310i	$-0.837249\pi$
$739$	−47.4158	−1.74422	−0.872110	+	0.489310i	$0.837249\pi$
$740$	9.87171	0.362891
$741$	5.36393	0.197049
$742$	−9.07701	−0.333227
$743$	32.9494	1.20880	0.604399	−	0.796682i	$-0.293413\pi$
$743$	32.9494	1.20880	0.604399	+	0.796682i	$0.293413\pi$
$744$	0.398831	0.0146218
$745$	−3.65273	−0.133826
$746$	−11.2753	−0.412819
$747$	0.606476	0.0221898
$748$	−11.4786	−0.419697
$749$	7.35379	0.268702
$750$	14.4499	0.527636
$751$	−14.3356	−0.523114	−0.261557	−	0.965188i	$-0.584236\pi$
$751$	−14.3356	−0.523114	−0.261557	+	0.965188i	$0.584236\pi$
$752$	−0.609939	−0.0222422
$753$	−18.1562	−0.661648
$754$	−4.47713	−0.163047
$755$	25.7311	0.936450
$756$	−5.63694	−0.205013
$757$	−37.1488	−1.35020	−0.675098	−	0.737728i	$-0.735899\pi$
$757$	−37.1488	−1.35020	−0.675098	+	0.737728i	$0.735899\pi$
$758$	−8.30266	−0.301566
$759$	−17.5954	−0.638674
$760$	−8.98893	−0.326063
$761$	−10.6962	−0.387737	−0.193868	−	0.981028i	$-0.562103\pi$
$761$	−10.6962	−0.387737	−0.193868	+	0.981028i	$0.562103\pi$
$762$	−15.3485	−0.556018
$763$	15.1216	0.547439
$764$	−5.71144	−0.206633
$765$	−17.3753	−0.628207
$766$	25.5669	0.923771
$767$	−9.97442	−0.360155
$768$	1.34513	0.0485383
$769$	−12.6391	−0.455778	−0.227889	−	0.973687i	$-0.573182\pi$
$769$	−12.6391	−0.455778	−0.227889	+	0.973687i	$0.573182\pi$
$770$	−4.21590	−0.151931
$771$	7.60040	0.273722
$772$	−0.155001	−0.00557859
$773$	15.1688	0.545583	0.272791	−	0.962073i	$-0.412053\pi$
$773$	15.1688	0.545583	0.272791	+	0.962073i	$0.412053\pi$
$774$	−13.2365	−0.475777
$775$	0.106742	0.00383427
$776$	−13.9570	−0.501026
$777$	−5.73555	−0.205762
$778$	29.9086	1.07228
$779$	−21.2787	−0.762389
$780$	−3.19846	−0.114523
$781$	−4.90224	−0.175416
$782$	45.2799	1.61921
$783$	24.5726	0.878153
$784$	1.00000	0.0357143
$785$	−10.2387	−0.365436
$786$	−10.2936	−0.367161
$787$	5.30568	0.189127	0.0945635	−	0.995519i	$-0.469854\pi$
$787$	5.30568	0.189127	0.0945635	+	0.995519i	$0.469854\pi$
$788$	−1.30758	−0.0465805
$789$	−33.5410	−1.19409
$790$	6.61043	0.235188
$791$	−11.0889	−0.394277
$792$	−2.16810	−0.0770401
$793$	13.7331	0.487675
$794$	31.8776	1.13129
$795$	28.2677	1.00255
$796$	−20.2631	−0.718208
$797$	−1.89545	−0.0671403	−0.0335701	−	0.999436i	$-0.510688\pi$
$797$	−1.89545	−0.0671403	−0.0335701	+	0.999436i	$0.510688\pi$
$798$	5.22265	0.184880
$799$	3.84473	0.136017
$800$	0.360007	0.0127282
$801$	6.14392	0.217085
$802$	−11.4030	−0.402653
$803$	3.15191	0.111229
$804$	−7.09956	−0.250382
$805$	16.6307	0.586154
$806$	0.304520	0.0107262
$807$	−1.77914	−0.0626285
$808$	−2.82966	−0.0995472
$809$	46.1206	1.62152	0.810758	−	0.585382i	$-0.199055\pi$
$809$	46.1206	1.62152	0.810758	+	0.585382i	$0.199055\pi$
$810$	9.28519	0.326248
$811$	20.5964	0.723238	0.361619	−	0.932326i	$-0.382224\pi$
$811$	20.5964	0.723238	0.361619	+	0.932326i	$0.382224\pi$
$812$	−4.35921	−0.152978
$813$	43.9133	1.54011
$814$	−7.76457	−0.272148
$815$	−10.4631	−0.366505
$816$	−8.47900	−0.296824
$817$	43.1646	1.51014
$818$	−34.8689	−1.21916
$819$	−1.22282	−0.0427289
$820$	12.6883	0.443094
$821$	−28.8291	−1.00614	−0.503072	−	0.864245i	$-0.667797\pi$
$821$	−28.8291	−1.00614	−0.503072	+	0.864245i	$0.667797\pi$
$822$	−1.86003	−0.0648760
$823$	−15.4151	−0.537338	−0.268669	−	0.963233i	$-0.586584\pi$
$823$	−15.4151	−0.537338	−0.268669	+	0.963233i	$0.586584\pi$
$824$	7.19060	0.250496
$825$	0.881829	0.0307013
$826$	−9.71171	−0.337914
$827$	23.0588	0.801832	0.400916	−	0.916115i	$-0.368692\pi$
$827$	23.0588	0.801832	0.400916	+	0.916115i	$0.368692\pi$
$828$	8.55260	0.297223
$829$	28.6997	0.996783	0.498391	−	0.866952i	$-0.333924\pi$
$829$	28.6997	0.996783	0.498391	+	0.866952i	$0.333924\pi$
$830$	1.17930	0.0409341
$831$	−44.5550	−1.54560
$832$	1.02705	0.0356066
$833$	−6.30346	−0.218402
$834$	8.71986	0.301944
$835$	19.6267	0.679211
$836$	7.07022	0.244529
$837$	−1.67135	−0.0577702
$838$	19.6912	0.680222
$839$	42.0912	1.45315	0.726575	−	0.687087i	$-0.241111\pi$
$839$	42.0912	1.45315	0.726575	+	0.687087i	$0.241111\pi$
$840$	−3.11421	−0.107451
$841$	−9.99730	−0.344734
$842$	23.1688	0.798450
$843$	19.0526	0.656208
$844$	−10.2278	−0.352057
$845$	27.6551	0.951364
$846$	0.726203	0.0249674
$847$	−7.68399	−0.264025
$848$	−9.07701	−0.311706
$849$	7.69383	0.264052
$850$	−2.26929	−0.0778360
$851$	30.6292	1.04996
$852$	−3.62120	−0.124060
$853$	−9.34734	−0.320047	−0.160023	−	0.987113i	$-0.551157\pi$
$853$	−9.34734	−0.320047	−0.160023	+	0.987113i	$0.551157\pi$
$854$	13.3714	0.457558
$855$	10.7024	0.366013
$856$	7.35379	0.251347
$857$	−9.37499	−0.320244	−0.160122	−	0.987097i	$-0.551189\pi$
$857$	−9.37499	−0.320244	−0.160122	+	0.987097i	$0.551189\pi$
$858$	2.51574	0.0858859
$859$	−30.5504	−1.04236	−0.521182	−	0.853445i	$-0.674509\pi$
$859$	−30.5504	−1.04236	−0.521182	+	0.853445i	$0.674509\pi$
$860$	−25.7386	−0.877679
$861$	−7.37200	−0.251237
$862$	−1.00000	−0.0340601
$863$	36.2743	1.23479	0.617396	−	0.786652i	$-0.288187\pi$
$863$	36.2743	1.23479	0.617396	+	0.786652i	$0.288187\pi$
$864$	−5.63694	−0.191773
$865$	−4.81052	−0.163563
$866$	−1.13204	−0.0384684
$867$	30.5798	1.03854
$868$	0.296499	0.0100638
$869$	−5.19942	−0.176378
$870$	13.5755	0.460252
$871$	−5.42073	−0.183674
$872$	15.1216	0.512082
$873$	16.6174	0.562413
$874$	−27.8902	−0.943401
$875$	10.7424	0.363158
$876$	2.32826	0.0786647
$877$	47.2987	1.59716	0.798582	−	0.601887i	$-0.205584\pi$
$877$	47.2987	1.59716	0.798582	+	0.601887i	$0.205584\pi$
$878$	−25.1495	−0.848756
$879$	23.2869	0.785447
$880$	−4.21590	−0.142118
$881$	23.0318	0.775961	0.387981	−	0.921668i	$-0.373173\pi$
$881$	23.0318	0.775961	0.387981	+	0.921668i	$0.373173\pi$
$882$	−1.19062	−0.0400901
$883$	−13.6038	−0.457804	−0.228902	−	0.973450i	$-0.573513\pi$
$883$	−13.6038	−0.457804	−0.228902	+	0.973450i	$0.573513\pi$
$884$	−6.47398	−0.217743
$885$	30.2443	1.01665
$886$	39.4788	1.32632
$887$	−26.5315	−0.890839	−0.445420	−	0.895322i	$-0.646946\pi$
$887$	−26.5315	−0.890839	−0.445420	+	0.895322i	$0.646946\pi$
$888$	−5.73555	−0.192472
$889$	−11.4104	−0.382692
$890$	11.9469	0.400462
$891$	−7.30325	−0.244668
$892$	−0.988408	−0.0330943
$893$	−2.36816	−0.0792475
$894$	2.12227	0.0709794
$895$	−17.1594	−0.573575
$896$	1.00000	0.0334077
$897$	−9.92394	−0.331351
$898$	−10.1433	−0.338487
$899$	−1.29250	−0.0431073
$900$	−0.428630	−0.0142877
$901$	57.2166	1.90616
$902$	−9.97994	−0.332296
$903$	14.9544	0.497650
$904$	−11.0889	−0.368812
$905$	−45.8791	−1.52507
$906$	−14.9500	−0.496680
$907$	−18.4609	−0.612985	−0.306493	−	0.951873i	$-0.599155\pi$
$907$	−18.4609	−0.612985	−0.306493	+	0.951873i	$0.599155\pi$
$908$	−8.40225	−0.278838
$909$	3.36904	0.111744
$910$	−2.37780	−0.0788232
$911$	−25.1156	−0.832117	−0.416059	−	0.909338i	$-0.636589\pi$
$911$	−25.1156	−0.832117	−0.416059	+	0.909338i	$0.636589\pi$
$912$	5.22265	0.172939
$913$	−0.927577	−0.0306983
$914$	12.6043	0.416913
$915$	−41.6412	−1.37662
$916$	−4.93262	−0.162978
$917$	−7.65248	−0.252707
$918$	35.5322	1.17274
$919$	−8.97466	−0.296047	−0.148023	−	0.988984i	$-0.547291\pi$
$919$	−8.97466	−0.296047	−0.148023	+	0.988984i	$0.547291\pi$
$920$	16.6307	0.548297
$921$	38.9033	1.28191
$922$	−18.0661	−0.594977
$923$	−2.76490	−0.0910077
$924$	2.44948	0.0805819
$925$	−1.53504	−0.0504719
$926$	−22.1284	−0.727183
$927$	−8.56124	−0.281188
$928$	−4.35921	−0.143098
$929$	−21.8055	−0.715415	−0.357708	−	0.933834i	$-0.616442\pi$
$929$	−21.8055	−0.715415	−0.357708	+	0.933834i	$0.616442\pi$
$930$	−0.923360	−0.0302782
$931$	3.88262	0.127248
$932$	9.11465	0.298560
$933$	7.69641	0.251969
$934$	27.8531	0.911383
$935$	26.5748	0.869088
$936$	−1.22282	−0.0399692
$937$	−23.1819	−0.757319	−0.378659	−	0.925536i	$-0.623615\pi$
$937$	−23.1819	−0.757319	−0.378659	+	0.925536i	$0.623615\pi$
$938$	−5.27796	−0.172331
$939$	9.79660	0.319700
$940$	1.41211	0.0460580
$941$	−59.3173	−1.93369	−0.966844	−	0.255369i	$-0.917803\pi$
$941$	−59.3173	−1.93369	−0.966844	+	0.255369i	$0.917803\pi$
$942$	5.94880	0.193822
$943$	39.3683	1.28201
$944$	−9.71171	−0.316089
$945$	13.0505	0.424532
$946$	20.2446	0.658210
$947$	40.8224	1.32655	0.663274	−	0.748376i	$-0.269166\pi$
$947$	40.8224	1.32655	0.663274	+	0.748376i	$0.269166\pi$
$948$	−3.84072	−0.124741
$949$	1.77770	0.0577066
$950$	1.39777	0.0453497
$951$	31.6592	1.02662
$952$	−6.30346	−0.204296
$953$	−42.5019	−1.37677	−0.688385	−	0.725346i	$-0.741680\pi$
$953$	−42.5019	−1.37677	−0.688385	+	0.725346i	$0.741680\pi$
$954$	10.8072	0.349897
$955$	13.2230	0.427885
$956$	−10.0198	−0.324064
$957$	−10.6778	−0.345164
$958$	7.54256	0.243689
$959$	−1.38279	−0.0446525
$960$	−3.11421	−0.100511
$961$	−30.9121	−0.997164
$962$	−4.37927	−0.141193
$963$	−8.75553	−0.282143
$964$	−13.9163	−0.448213
$965$	0.358853	0.0115519
$966$	−9.66256	−0.310888
$967$	−24.4206	−0.785313	−0.392656	−	0.919685i	$-0.628444\pi$
$967$	−24.4206	−0.785313	−0.392656	+	0.919685i	$0.628444\pi$
$968$	−7.68399	−0.246973
$969$	−32.9207	−1.05757
$970$	32.3127	1.03750
$971$	47.1755	1.51394	0.756968	−	0.653452i	$-0.226680\pi$
$971$	47.1755	1.51394	0.756968	+	0.653452i	$0.226680\pi$
$972$	11.5160	0.369377
$973$	6.48252	0.207820
$974$	8.94353	0.286569
$975$	0.497357	0.0159282
$976$	13.3714	0.428007
$977$	−8.43250	−0.269780	−0.134890	−	0.990861i	$-0.543068\pi$
$977$	−8.43250	−0.269780	−0.134890	+	0.990861i	$0.543068\pi$
$978$	6.07913	0.194389
$979$	−9.39684	−0.300324
$980$	−2.31517	−0.0739554
$981$	−18.0040	−0.574824
$982$	−35.8923	−1.14537
$983$	−6.61558	−0.211004	−0.105502	−	0.994419i	$-0.533645\pi$
$983$	−6.61558	−0.211004	−0.105502	+	0.994419i	$0.533645\pi$
$984$	−7.37200	−0.235011
$985$	3.02726	0.0964565
$986$	27.4781	0.875081
$987$	−0.820450	−0.0261152
$988$	3.98765	0.126864
$989$	−79.8599	−2.53940
$990$	5.01952	0.159531
$991$	11.7155	0.372156	0.186078	−	0.982535i	$-0.440422\pi$
$991$	11.7155	0.372156	0.186078	+	0.982535i	$0.440422\pi$
$992$	0.296499	0.00941385
$993$	−33.9013	−1.07583
$994$	−2.69207	−0.0853874
$995$	46.9126	1.48723
$996$	−0.685184	−0.0217109
$997$	−11.1932	−0.354493	−0.177246	−	0.984167i	$-0.556719\pi$
$997$	−11.1932	−0.354493	−0.177246	+	0.984167i	$0.556719\pi$
$998$	−27.1444	−0.859240
$999$	24.0355	0.760449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.17	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.17	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.34513 q^{3} +1.00000 q^{4} -2.31517 q^{5} +1.34513 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.19062 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.34513 q^{3} +1.00000 q^{4} -2.31517 q^{5} +1.34513 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.19062 q^{9} -2.31517 q^{10} +1.82099 q^{11} +1.34513 q^{12} +1.02705 q^{13} +1.00000 q^{14} -3.11421 q^{15} +1.00000 q^{16} -6.30346 q^{17} -1.19062 q^{18} +3.88262 q^{19} -2.31517 q^{20} +1.34513 q^{21} +1.82099 q^{22} -7.18335 q^{23} +1.34513 q^{24} +0.360007 q^{25} +1.02705 q^{26} -5.63694 q^{27} +1.00000 q^{28} -4.35921 q^{29} -3.11421 q^{30} +0.296499 q^{31} +1.00000 q^{32} +2.44948 q^{33} -6.30346 q^{34} -2.31517 q^{35} -1.19062 q^{36} -4.26392 q^{37} +3.88262 q^{38} +1.38152 q^{39} -2.31517 q^{40} -5.48050 q^{41} +1.34513 q^{42} +11.1174 q^{43} +1.82099 q^{44} +2.75648 q^{45} -7.18335 q^{46} -0.609939 q^{47} +1.34513 q^{48} +1.00000 q^{49} +0.360007 q^{50} -8.47900 q^{51} +1.02705 q^{52} -9.07701 q^{53} -5.63694 q^{54} -4.21590 q^{55} +1.00000 q^{56} +5.22265 q^{57} -4.35921 q^{58} -9.71171 q^{59} -3.11421 q^{60} +13.3714 q^{61} +0.296499 q^{62} -1.19062 q^{63} +1.00000 q^{64} -2.37780 q^{65} +2.44948 q^{66} -5.27796 q^{67} -6.30346 q^{68} -9.66256 q^{69} -2.31517 q^{70} -2.69207 q^{71} -1.19062 q^{72} +1.73088 q^{73} -4.26392 q^{74} +0.484257 q^{75} +3.88262 q^{76} +1.82099 q^{77} +1.38152 q^{78} -2.85527 q^{79} -2.31517 q^{80} -4.01059 q^{81} -5.48050 q^{82} -0.509380 q^{83} +1.34513 q^{84} +14.5936 q^{85} +11.1174 q^{86} -5.86372 q^{87} +1.82099 q^{88} -5.16029 q^{89} +2.75648 q^{90} +1.02705 q^{91} -7.18335 q^{92} +0.398831 q^{93} -0.609939 q^{94} -8.98893 q^{95} +1.34513 q^{96} -13.9570 q^{97} +1.00000 q^{98} -2.16810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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