LMFDB - Embedded newform 4017.2.a.j.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} -0.0946818 q^{10} +0.0498766 q^{11} +1.99862 q^{12} +1.00000 q^{13} -0.0722783 q^{14} -2.55043 q^{15} +3.99173 q^{16} -4.77817 q^{17} -0.0371239 q^{18} -6.56279 q^{19} -5.09734 q^{20} -1.94695 q^{21} -0.00185162 q^{22} +5.81689 q^{23} -0.148445 q^{24} +1.50467 q^{25} -0.0371239 q^{26} -1.00000 q^{27} -3.89121 q^{28} +7.77905 q^{29} +0.0946818 q^{30} +10.6323 q^{31} -0.445078 q^{32} -0.0498766 q^{33} +0.177384 q^{34} +4.96554 q^{35} -1.99862 q^{36} +6.38869 q^{37} +0.243637 q^{38} -1.00000 q^{39} +0.378597 q^{40} -4.46800 q^{41} +0.0722783 q^{42} -0.323564 q^{43} -0.0996845 q^{44} +2.55043 q^{45} -0.215946 q^{46} -2.86047 q^{47} -3.99173 q^{48} -3.20940 q^{49} -0.0558592 q^{50} +4.77817 q^{51} -1.99862 q^{52} +2.38415 q^{53} +0.0371239 q^{54} +0.127207 q^{55} +0.289014 q^{56} +6.56279 q^{57} -0.288789 q^{58} +5.13046 q^{59} +5.09734 q^{60} -10.4293 q^{61} -0.394712 q^{62} +1.94695 q^{63} -7.96694 q^{64} +2.55043 q^{65} +0.00185162 q^{66} -11.1123 q^{67} +9.54976 q^{68} -5.81689 q^{69} -0.184340 q^{70} +11.4913 q^{71} +0.148445 q^{72} +13.4821 q^{73} -0.237173 q^{74} -1.50467 q^{75} +13.1165 q^{76} +0.0971071 q^{77} +0.0371239 q^{78} +13.8364 q^{79} +10.1806 q^{80} +1.00000 q^{81} +0.165870 q^{82} -16.1941 q^{83} +3.89121 q^{84} -12.1864 q^{85} +0.0120120 q^{86} -7.77905 q^{87} +0.00740391 q^{88} -11.5802 q^{89} -0.0946818 q^{90} +1.94695 q^{91} -11.6258 q^{92} -10.6323 q^{93} +0.106192 q^{94} -16.7379 q^{95} +0.445078 q^{96} +10.5474 q^{97} +0.119146 q^{98} +0.0498766 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−0.0371239	−0.0262506	−0.0131253	−	0.999914i	$-0.504178\pi$
$2$	−0.0371239	−0.0262506	−0.0131253	+	0.999914i	$0.504178\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99862	−0.999311
$5$	2.55043	1.14058	0.570292	−	0.821442i	$-0.306830\pi$
$5$	2.55043	1.14058	0.570292	+	0.821442i	$0.306830\pi$
$6$	0.0371239	0.0151558
$7$	1.94695	0.735876	0.367938	−	0.929850i	$-0.380064\pi$
$7$	1.94695	0.735876	0.367938	+	0.929850i	$0.380064\pi$
$8$	0.148445	0.0524831
$9$	1.00000	0.333333
$10$	−0.0946818	−0.0299410
$11$	0.0498766	0.0150384	0.00751918	−	0.999972i	$-0.497607\pi$
$11$	0.0498766	0.0150384	0.00751918	+	0.999972i	$0.497607\pi$
$12$	1.99862	0.576952
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.0722783	−0.0193172
$15$	−2.55043	−0.658517
$16$	3.99173	0.997933
$17$	−4.77817	−1.15888	−0.579438	−	0.815016i	$-0.696728\pi$
$17$	−4.77817	−1.15888	−0.579438	+	0.815016i	$0.696728\pi$
$18$	−0.0371239	−0.00875019
$19$	−6.56279	−1.50561	−0.752804	−	0.658245i	$-0.771299\pi$
$19$	−6.56279	−1.50561	−0.752804	+	0.658245i	$0.771299\pi$
$20$	−5.09734	−1.13980
$21$	−1.94695	−0.424858
$22$	−0.00185162	−0.000394766 0
$23$	5.81689	1.21290	0.606452	−	0.795120i	$-0.292592\pi$
$23$	5.81689	1.21290	0.606452	+	0.795120i	$0.292592\pi$
$24$	−0.148445	−0.0303011
$25$	1.50467	0.300934
$26$	−0.0371239	−0.00728060
$27$	−1.00000	−0.192450
$28$	−3.89121	−0.735369
$29$	7.77905	1.44453	0.722267	−	0.691614i	$-0.243100\pi$
$29$	7.77905	1.44453	0.722267	+	0.691614i	$0.243100\pi$
$30$	0.0946818	0.0172865
$31$	10.6323	1.90961	0.954806	−	0.297228i	$-0.0960623\pi$
$31$	10.6323	1.90961	0.954806	+	0.297228i	$0.0960623\pi$
$32$	−0.445078	−0.0786794
$33$	−0.0498766	−0.00868240
$34$	0.177384	0.0304212
$35$	4.96554	0.839329
$36$	−1.99862	−0.333104
$37$	6.38869	1.05029	0.525147	−	0.851011i	$-0.324010\pi$
$37$	6.38869	1.05029	0.525147	+	0.851011i	$0.324010\pi$
$38$	0.243637	0.0395231
$39$	−1.00000	−0.160128
$40$	0.378597	0.0598614
$41$	−4.46800	−0.697785	−0.348893	−	0.937163i	$-0.613442\pi$
$41$	−4.46800	−0.697785	−0.348893	+	0.937163i	$0.613442\pi$
$42$	0.0722783	0.0111528
$43$	−0.323564	−0.0493431	−0.0246715	−	0.999696i	$-0.507854\pi$
$43$	−0.323564	−0.0493431	−0.0246715	+	0.999696i	$0.507854\pi$
$44$	−0.0996845	−0.0150280
$45$	2.55043	0.380195
$46$	−0.215946	−0.0318395
$47$	−2.86047	−0.417243	−0.208621	−	0.977996i	$-0.566898\pi$
$47$	−2.86047	−0.417243	−0.208621	+	0.977996i	$0.566898\pi$
$48$	−3.99173	−0.576157
$49$	−3.20940	−0.458486
$50$	−0.0558592	−0.00789968
$51$	4.77817	0.669078
$52$	−1.99862	−0.277159
$53$	2.38415	0.327488	0.163744	−	0.986503i	$-0.447643\pi$
$53$	2.38415	0.327488	0.163744	+	0.986503i	$0.447643\pi$
$54$	0.0371239	0.00505193
$55$	0.127207	0.0171525
$56$	0.289014	0.0386211
$57$	6.56279	0.869263
$58$	−0.288789	−0.0379199
$59$	5.13046	0.667929	0.333964	−	0.942586i	$-0.391614\pi$
$59$	5.13046	0.667929	0.333964	+	0.942586i	$0.391614\pi$
$60$	5.09734	0.658063
$61$	−10.4293	−1.33533	−0.667666	−	0.744461i	$-0.732707\pi$
$61$	−10.4293	−1.33533	−0.667666	+	0.744461i	$0.732707\pi$
$62$	−0.394712	−0.0501284
$63$	1.94695	0.245292
$64$	−7.96694	−0.995868
$65$	2.55043	0.316341
$66$	0.00185162	0.000227918 0
$67$	−11.1123	−1.35759	−0.678793	−	0.734330i	$-0.737497\pi$
$67$	−11.1123	−1.35759	−0.678793	+	0.734330i	$0.737497\pi$
$68$	9.54976	1.15808
$69$	−5.81689	−0.700271
$70$	−0.184340	−0.0220329
$71$	11.4913	1.36376	0.681881	−	0.731463i	$-0.261162\pi$
$71$	11.4913	1.36376	0.681881	+	0.731463i	$0.261162\pi$
$72$	0.148445	0.0174944
$73$	13.4821	1.57796	0.788981	−	0.614418i	$-0.210609\pi$
$73$	13.4821	1.57796	0.788981	+	0.614418i	$0.210609\pi$
$74$	−0.237173	−0.0275708
$75$	−1.50467	−0.173744
$76$	13.1165	1.50457
$77$	0.0971071	0.0110664
$78$	0.0371239	0.00420346
$79$	13.8364	1.55672	0.778360	−	0.627818i	$-0.216052\pi$
$79$	13.8364	1.55672	0.778360	+	0.627818i	$0.216052\pi$
$80$	10.1806	1.13823
$81$	1.00000	0.111111
$82$	0.165870	0.0183173
$83$	−16.1941	−1.77753	−0.888766	−	0.458361i	$-0.848437\pi$
$83$	−16.1941	−1.77753	−0.888766	+	0.458361i	$0.848437\pi$
$84$	3.89121	0.424566
$85$	−12.1864	−1.32180
$86$	0.0120120	0.00129528
$87$	−7.77905	−0.834002
$88$	0.00740391	0.000789260 0
$89$	−11.5802	−1.22750	−0.613750	−	0.789500i	$-0.710340\pi$
$89$	−11.5802	−1.22750	−0.613750	+	0.789500i	$0.710340\pi$
$90$	−0.0946818	−0.00998034
$91$	1.94695	0.204095
$92$	−11.6258	−1.21207
$93$	−10.6323	−1.10252
$94$	0.106192	0.0109529
$95$	−16.7379	−1.71727
$96$	0.445078	0.0454256
$97$	10.5474	1.07093	0.535463	−	0.844558i	$-0.320137\pi$
$97$	10.5474	1.07093	0.535463	+	0.844558i	$0.320137\pi$
$98$	0.119146	0.0120355
$99$	0.0498766	0.00501279
$100$	−3.00726	−0.300726
$101$	0.461424	0.0459134	0.0229567	−	0.999736i	$-0.492692\pi$
$101$	0.461424	0.0459134	0.0229567	+	0.999736i	$0.492692\pi$
$102$	−0.177384	−0.0175637
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	0.148445	0.0145562
$105$	−4.96554	−0.484587
$106$	−0.0885089	−0.00859675
$107$	4.61729	0.446370	0.223185	−	0.974776i	$-0.428355\pi$
$107$	4.61729	0.446370	0.223185	+	0.974776i	$0.428355\pi$
$108$	1.99862	0.192317
$109$	7.55061	0.723218	0.361609	−	0.932330i	$-0.382228\pi$
$109$	7.55061	0.723218	0.361609	+	0.932330i	$0.382228\pi$
$110$	−0.00472241	−0.000450264 0
$111$	−6.38869	−0.606388
$112$	7.77169	0.734356
$113$	10.1761	0.957287	0.478643	−	0.878009i	$-0.341129\pi$
$113$	10.1761	0.957287	0.478643	+	0.878009i	$0.341129\pi$
$114$	−0.243637	−0.0228187
$115$	14.8355	1.38342
$116$	−15.5474	−1.44354
$117$	1.00000	0.0924500
$118$	−0.190463	−0.0175335
$119$	−9.30284	−0.852790
$120$	−0.378597	−0.0345610
$121$	−10.9975	−0.999774
$122$	0.387176	0.0350533
$123$	4.46800	0.402866
$124$	−21.2499	−1.90830
$125$	−8.91458	−0.797344
$126$	−0.0722783	−0.00643906
$127$	2.86014	0.253796	0.126898	−	0.991916i	$-0.459498\pi$
$127$	2.86014	0.253796	0.126898	+	0.991916i	$0.459498\pi$
$128$	1.18592	0.104822
$129$	0.323564	0.0284882
$130$	−0.0946818	−0.00830414
$131$	−8.85763	−0.773894	−0.386947	−	0.922102i	$-0.626470\pi$
$131$	−8.85763	−0.773894	−0.386947	+	0.922102i	$0.626470\pi$
$132$	0.0996845	0.00867642
$133$	−12.7774	−1.10794
$134$	0.412533	0.0356374
$135$	−2.55043	−0.219506
$136$	−0.709293	−0.0608214
$137$	−6.59690	−0.563611	−0.281805	−	0.959472i	$-0.590933\pi$
$137$	−6.59690	−0.563611	−0.281805	+	0.959472i	$0.590933\pi$
$138$	0.215946	0.0183825
$139$	−15.4178	−1.30772	−0.653858	−	0.756617i	$-0.726851\pi$
$139$	−15.4178	−1.30772	−0.653858	+	0.756617i	$0.726851\pi$
$140$	−9.92424	−0.838751
$141$	2.86047	0.240895
$142$	−0.426601	−0.0357995
$143$	0.0498766	0.00417089
$144$	3.99173	0.332644
$145$	19.8399	1.64761
$146$	−0.500509	−0.0414224
$147$	3.20940	0.264707
$148$	−12.7686	−1.04957
$149$	0.198567	0.0162672	0.00813361	−	0.999967i	$-0.497411\pi$
$149$	0.198567	0.0162672	0.00813361	+	0.999967i	$0.497411\pi$
$150$	0.0558592	0.00456088
$151$	21.7587	1.77070	0.885348	−	0.464929i	$-0.153920\pi$
$151$	21.7587	1.77070	0.885348	+	0.464929i	$0.153920\pi$
$152$	−0.974210	−0.0790189
$153$	−4.77817	−0.386292
$154$	−0.00360500	−0.000290499 0
$155$	27.1168	2.17808
$156$	1.99862	0.160018
$157$	1.35049	0.107781	0.0538904	−	0.998547i	$-0.482838\pi$
$157$	1.35049	0.107781	0.0538904	+	0.998547i	$0.482838\pi$
$158$	−0.513663	−0.0408648
$159$	−2.38415	−0.189075
$160$	−1.13514	−0.0897405
$161$	11.3252	0.892548
$162$	−0.0371239	−0.00291673
$163$	15.3288	1.20064	0.600322	−	0.799759i	$-0.295039\pi$
$163$	15.3288	1.20064	0.600322	+	0.799759i	$0.295039\pi$
$164$	8.92985	0.697304
$165$	−0.127207	−0.00990302
$166$	0.601188	0.0466613
$167$	21.7145	1.68032	0.840159	−	0.542340i	$-0.182462\pi$
$167$	21.7145	1.68032	0.840159	+	0.542340i	$0.182462\pi$
$168$	−0.289014	−0.0222979
$169$	1.00000	0.0769231
$170$	0.452406	0.0346979
$171$	−6.56279	−0.501869
$172$	0.646682	0.0493091
$173$	7.00246	0.532387	0.266193	−	0.963920i	$-0.414234\pi$
$173$	7.00246	0.532387	0.266193	+	0.963920i	$0.414234\pi$
$174$	0.288789	0.0218930
$175$	2.92951	0.221450
$176$	0.199094	0.0150073
$177$	−5.13046	−0.385629
$178$	0.429903	0.0322226
$179$	11.9163	0.890663	0.445332	−	0.895366i	$-0.353086\pi$
$179$	11.9163	0.890663	0.445332	+	0.895366i	$0.353086\pi$
$180$	−5.09734	−0.379933
$181$	9.82491	0.730280	0.365140	−	0.930953i	$-0.381021\pi$
$181$	9.82491	0.730280	0.365140	+	0.930953i	$0.381021\pi$
$182$	−0.0722783	−0.00535762
$183$	10.4293	0.770955
$184$	0.863485	0.0636570
$185$	16.2939	1.19795
$186$	0.394712	0.0289417
$187$	−0.238319	−0.0174276
$188$	5.71700	0.416955
$189$	−1.94695	−0.141619
$190$	0.621377	0.0450794
$191$	1.27975	0.0925997	0.0462998	−	0.998928i	$-0.485257\pi$
$191$	1.27975	0.0925997	0.0462998	+	0.998928i	$0.485257\pi$
$192$	7.96694	0.574965
$193$	14.1365	1.01757	0.508784	−	0.860894i	$-0.330095\pi$
$193$	14.1365	1.01757	0.508784	+	0.860894i	$0.330095\pi$
$194$	−0.391561	−0.0281124
$195$	−2.55043	−0.182640
$196$	6.41438	0.458170
$197$	17.5154	1.24792	0.623960	−	0.781457i	$-0.285523\pi$
$197$	17.5154	1.24792	0.623960	+	0.781457i	$0.285523\pi$
$198$	−0.00185162	−0.000131589 0
$199$	0.938390	0.0665207	0.0332604	−	0.999447i	$-0.489411\pi$
$199$	0.938390	0.0665207	0.0332604	+	0.999447i	$0.489411\pi$
$200$	0.223360	0.0157939
$201$	11.1123	0.783803
$202$	−0.0171299	−0.00120525
$203$	15.1454	1.06300
$204$	−9.54976	−0.668617
$205$	−11.3953	−0.795883
$206$	0.0371239	0.00258655
$207$	5.81689	0.404302
$208$	3.99173	0.276777
$209$	−0.327330	−0.0226419
$210$	0.184340	0.0127207
$211$	20.4535	1.40808	0.704040	−	0.710161i	$-0.251378\pi$
$211$	20.4535	1.40808	0.704040	+	0.710161i	$0.251378\pi$
$212$	−4.76501	−0.327262
$213$	−11.4913	−0.787368
$214$	−0.171412	−0.0117175
$215$	−0.825226	−0.0562799
$216$	−0.148445	−0.0101004
$217$	20.7005	1.40524
$218$	−0.280308	−0.0189849
$219$	−13.4821	−0.911036
$220$	−0.254238	−0.0171407
$221$	−4.77817	−0.321415
$222$	0.237173	0.0159180
$223$	−10.3658	−0.694143	−0.347071	−	0.937839i	$-0.612824\pi$
$223$	−10.3658	−0.694143	−0.347071	+	0.937839i	$0.612824\pi$
$224$	−0.866543	−0.0578983
$225$	1.50467	0.100311
$226$	−0.377777	−0.0251293
$227$	0.475721	0.0315747	0.0157873	−	0.999875i	$-0.494975\pi$
$227$	0.475721	0.0315747	0.0157873	+	0.999875i	$0.494975\pi$
$228$	−13.1165	−0.868664
$229$	−8.63360	−0.570525	−0.285262	−	0.958449i	$-0.592081\pi$
$229$	−8.63360	−0.570525	−0.285262	+	0.958449i	$0.592081\pi$
$230$	−0.550753	−0.0363156
$231$	−0.0971071	−0.00638918
$232$	1.15476	0.0758136
$233$	17.8265	1.16785	0.583927	−	0.811806i	$-0.301515\pi$
$233$	17.8265	1.16785	0.583927	+	0.811806i	$0.301515\pi$
$234$	−0.0371239	−0.00242687
$235$	−7.29542	−0.475901
$236$	−10.2538	−0.667468
$237$	−13.8364	−0.898773
$238$	0.345358	0.0223862
$239$	18.5128	1.19749	0.598745	−	0.800940i	$-0.295666\pi$
$239$	18.5128	1.19749	0.598745	+	0.800940i	$0.295666\pi$
$240$	−10.1806	−0.657156
$241$	5.41036	0.348512	0.174256	−	0.984700i	$-0.444248\pi$
$241$	5.41036	0.348512	0.174256	+	0.984700i	$0.444248\pi$
$242$	0.408271	0.0262446
$243$	−1.00000	−0.0641500
$244$	20.8442	1.33441
$245$	−8.18534	−0.522942
$246$	−0.165870	−0.0105755
$247$	−6.56279	−0.417580
$248$	1.57830	0.100222
$249$	16.1941	1.02626
$250$	0.330944	0.0209308
$251$	−1.25086	−0.0789535	−0.0394768	−	0.999220i	$-0.512569\pi$
$251$	−1.25086	−0.0789535	−0.0394768	+	0.999220i	$0.512569\pi$
$252$	−3.89121	−0.245123
$253$	0.290127	0.0182401
$254$	−0.106180	−0.00666230
$255$	12.1864	0.763140
$256$	15.8899	0.993116
$257$	−12.8742	−0.803071	−0.401535	−	0.915844i	$-0.631523\pi$
$257$	−12.8742	−0.803071	−0.401535	+	0.915844i	$0.631523\pi$
$258$	−0.0120120	−0.000747833 0
$259$	12.4384	0.772887
$260$	−5.09734	−0.316123
$261$	7.77905	0.481511
$262$	0.328830	0.0203152
$263$	15.6927	0.967651	0.483825	−	0.875165i	$-0.339247\pi$
$263$	15.6927	0.967651	0.483825	+	0.875165i	$0.339247\pi$
$264$	−0.00740391	−0.000455679 0
$265$	6.08059	0.373528
$266$	0.474347	0.0290841
$267$	11.5802	0.708697
$268$	22.2093	1.35665
$269$	23.9752	1.46180	0.730898	−	0.682486i	$-0.239101\pi$
$269$	23.9752	1.46180	0.730898	+	0.682486i	$0.239101\pi$
$270$	0.0946818	0.00576215
$271$	6.84031	0.415519	0.207760	−	0.978180i	$-0.433383\pi$
$271$	6.84031	0.415519	0.207760	+	0.978180i	$0.433383\pi$
$272$	−19.0732	−1.15648
$273$	−1.94695	−0.117835
$274$	0.244903	0.0147951
$275$	0.0750478	0.00452555
$276$	11.6258	0.699788
$277$	−2.42115	−0.145473	−0.0727365	−	0.997351i	$-0.523173\pi$
$277$	−2.42115	−0.145473	−0.0727365	+	0.997351i	$0.523173\pi$
$278$	0.572368	0.0343283
$279$	10.6323	0.636538
$280$	0.737107	0.0440506
$281$	8.36874	0.499237	0.249619	−	0.968344i	$-0.419695\pi$
$281$	8.36874	0.499237	0.249619	+	0.968344i	$0.419695\pi$
$282$	−0.106192	−0.00632364
$283$	9.64948	0.573602	0.286801	−	0.957990i	$-0.407408\pi$
$283$	9.64948	0.573602	0.286801	+	0.957990i	$0.407408\pi$
$284$	−22.9667	−1.36282
$285$	16.7379	0.991468
$286$	−0.00185162	−0.000109488 0
$287$	−8.69896	−0.513484
$288$	−0.445078	−0.0262265
$289$	5.83091	0.342995
$290$	−0.736535	−0.0432508
$291$	−10.5474	−0.618300
$292$	−26.9456	−1.57687
$293$	−13.6847	−0.799470	−0.399735	−	0.916631i	$-0.630898\pi$
$293$	−13.6847	−0.799470	−0.399735	+	0.916631i	$0.630898\pi$
$294$	−0.119146	−0.00694871
$295$	13.0848	0.761829
$296$	0.948367	0.0551227
$297$	−0.0498766	−0.00289413
$298$	−0.00737157	−0.000427024 0
$299$	5.81689	0.336399
$300$	3.00726	0.173624
$301$	−0.629962	−0.0363104
$302$	−0.807768	−0.0464818
$303$	−0.461424	−0.0265081
$304$	−26.1969	−1.50250
$305$	−26.5991	−1.52306
$306$	0.177384	0.0101404
$307$	4.10802	0.234457	0.117229	−	0.993105i	$-0.462599\pi$
$307$	4.10802	0.234457	0.117229	+	0.993105i	$0.462599\pi$
$308$	−0.194080	−0.0110588
$309$	1.00000	0.0568880
$310$	−1.00668	−0.0571757
$311$	−11.6679	−0.661628	−0.330814	−	0.943696i	$-0.607323\pi$
$311$	−11.6679	−0.661628	−0.330814	+	0.943696i	$0.607323\pi$
$312$	−0.148445	−0.00840402
$313$	−26.7163	−1.51010	−0.755048	−	0.655669i	$-0.772387\pi$
$313$	−26.7163	−1.51010	−0.755048	+	0.655669i	$0.772387\pi$
$314$	−0.0501354	−0.00282931
$315$	4.96554	0.279776
$316$	−27.6538	−1.55565
$317$	−8.32549	−0.467606	−0.233803	−	0.972284i	$-0.575117\pi$
$317$	−8.32549	−0.467606	−0.233803	+	0.972284i	$0.575117\pi$
$318$	0.0885089	0.00496333
$319$	0.387993	0.0217234
$320$	−20.3191	−1.13587
$321$	−4.61729	−0.257712
$322$	−0.420435	−0.0234299
$323$	31.3581	1.74481
$324$	−1.99862	−0.111035
$325$	1.50467	0.0834640
$326$	−0.569065	−0.0315176
$327$	−7.55061	−0.417550
$328$	−0.663251	−0.0366219
$329$	−5.56919	−0.307039
$330$	0.00472241	0.000259960 0
$331$	19.4071	1.06671	0.533355	−	0.845891i	$-0.320931\pi$
$331$	19.4071	1.06671	0.533355	+	0.845891i	$0.320931\pi$
$332$	32.3659	1.77631
$333$	6.38869	0.350098
$334$	−0.806127	−0.0441093
$335$	−28.3411	−1.54844
$336$	−7.77169	−0.423980
$337$	−28.1798	−1.53505	−0.767525	−	0.641019i	$-0.778512\pi$
$337$	−28.1798	−1.53505	−0.767525	+	0.641019i	$0.778512\pi$
$338$	−0.0371239	−0.00201928
$339$	−10.1761	−0.552690
$340$	24.3559	1.32089
$341$	0.530302	0.0287175
$342$	0.243637	0.0131744
$343$	−19.8772	−1.07327
$344$	−0.0480313	−0.00258968
$345$	−14.8355	−0.798718
$346$	−0.259959	−0.0139755
$347$	−3.08745	−0.165743	−0.0828715	−	0.996560i	$-0.526409\pi$
$347$	−3.08745	−0.165743	−0.0828715	+	0.996560i	$0.526409\pi$
$348$	15.5474	0.833427
$349$	−21.9241	−1.17357	−0.586784	−	0.809743i	$-0.699606\pi$
$349$	−21.9241	−1.17357	−0.586784	+	0.809743i	$0.699606\pi$
$350$	−0.108755	−0.00581319
$351$	−1.00000	−0.0533761
$352$	−0.0221990	−0.00118321
$353$	5.91437	0.314790	0.157395	−	0.987536i	$-0.449690\pi$
$353$	5.91437	0.314790	0.157395	+	0.987536i	$0.449690\pi$
$354$	0.190463	0.0101230
$355$	29.3076	1.55549
$356$	23.1445	1.22665
$357$	9.30284	0.492358
$358$	−0.442378	−0.0233804
$359$	−2.91048	−0.153609	−0.0768046	−	0.997046i	$-0.524472\pi$
$359$	−2.91048	−0.153609	−0.0768046	+	0.997046i	$0.524472\pi$
$360$	0.378597	0.0199538
$361$	24.0702	1.26685
$362$	−0.364739	−0.0191703
$363$	10.9975	0.577220
$364$	−3.89121	−0.203955
$365$	34.3851	1.79980
$366$	−0.387176	−0.0202380
$367$	16.5755	0.865232	0.432616	−	0.901578i	$-0.357591\pi$
$367$	16.5755	0.865232	0.432616	+	0.901578i	$0.357591\pi$
$368$	23.2195	1.21040
$369$	−4.46800	−0.232595
$370$	−0.604893	−0.0314469
$371$	4.64181	0.240991
$372$	21.2499	1.10176
$373$	−9.39657	−0.486536	−0.243268	−	0.969959i	$-0.578219\pi$
$373$	−9.39657	−0.486536	−0.243268	+	0.969959i	$0.578219\pi$
$374$	0.00884734	0.000457485 0
$375$	8.91458	0.460347
$376$	−0.424622	−0.0218982
$377$	7.77905	0.400642
$378$	0.0722783	0.00371759
$379$	1.86986	0.0960482	0.0480241	−	0.998846i	$-0.484708\pi$
$379$	1.86986	0.0960482	0.0480241	+	0.998846i	$0.484708\pi$
$380$	33.4527	1.71609
$381$	−2.86014	−0.146529
$382$	−0.0475094	−0.00243079
$383$	−22.6343	−1.15656	−0.578279	−	0.815839i	$-0.696275\pi$
$383$	−22.6343	−1.15656	−0.578279	+	0.815839i	$0.696275\pi$
$384$	−1.18592	−0.0605187
$385$	0.247664	0.0126221
$386$	−0.524802	−0.0267117
$387$	−0.323564	−0.0164477
$388$	−21.0803	−1.07019
$389$	18.4438	0.935139	0.467570	−	0.883956i	$-0.345130\pi$
$389$	18.4438	0.935139	0.467570	+	0.883956i	$0.345130\pi$
$390$	0.0946818	0.00479440
$391$	−27.7941	−1.40561
$392$	−0.476418	−0.0240627
$393$	8.85763	0.446808
$394$	−0.650240	−0.0327586
$395$	35.2888	1.77557
$396$	−0.0996845	−0.00500933
$397$	−30.4817	−1.52983	−0.764916	−	0.644130i	$-0.777220\pi$
$397$	−30.4817	−1.52983	−0.764916	+	0.644130i	$0.777220\pi$
$398$	−0.0348367	−0.00174621
$399$	12.7774	0.639670
$400$	6.00623	0.300312
$401$	37.7000	1.88265	0.941325	−	0.337502i	$-0.109582\pi$
$401$	37.7000	1.88265	0.941325	+	0.337502i	$0.109582\pi$
$402$	−0.412533	−0.0205753
$403$	10.6323	0.529631
$404$	−0.922212	−0.0458818
$405$	2.55043	0.126732
$406$	−0.562257	−0.0279043
$407$	0.318646	0.0157947
$408$	0.709293	0.0351153
$409$	−30.4914	−1.50770	−0.753851	−	0.657045i	$-0.771806\pi$
$409$	−30.4914	−1.50770	−0.753851	+	0.657045i	$0.771806\pi$
$410$	0.423039	0.0208924
$411$	6.59690	0.325401
$412$	1.99862	0.0984650
$413$	9.98872	0.491513
$414$	−0.215946	−0.0106132
$415$	−41.3018	−2.02743
$416$	−0.445078	−0.0218217
$417$	15.4178	0.755011
$418$	0.0121518	0.000594362 0
$419$	26.0498	1.27261	0.636307	−	0.771436i	$-0.280461\pi$
$419$	26.0498	1.27261	0.636307	+	0.771436i	$0.280461\pi$
$420$	9.92424	0.484253
$421$	2.11794	0.103222	0.0516111	−	0.998667i	$-0.483564\pi$
$421$	2.11794	0.103222	0.0516111	+	0.998667i	$0.483564\pi$
$422$	−0.759316	−0.0369629
$423$	−2.86047	−0.139081
$424$	0.353914	0.0171876
$425$	−7.18956	−0.348745
$426$	0.426601	0.0206689
$427$	−20.3053	−0.982640
$428$	−9.22821	−0.446062
$429$	−0.0498766	−0.00240807
$430$	0.0306356	0.00147738
$431$	10.1882	0.490747	0.245374	−	0.969429i	$-0.421089\pi$
$431$	10.1882	0.490747	0.245374	+	0.969429i	$0.421089\pi$
$432$	−3.99173	−0.192052
$433$	34.3380	1.65018	0.825090	−	0.565001i	$-0.191124\pi$
$433$	34.3380	1.65018	0.825090	+	0.565001i	$0.191124\pi$
$434$	−0.768483	−0.0368883
$435$	−19.8399	−0.951250
$436$	−15.0908	−0.722719
$437$	−38.1750	−1.82616
$438$	0.500509	0.0239152
$439$	29.9729	1.43053	0.715263	−	0.698855i	$-0.246307\pi$
$439$	29.9729	1.43053	0.715263	+	0.698855i	$0.246307\pi$
$440$	0.0188831	0.000900218 0
$441$	−3.20940	−0.152829
$442$	0.177384	0.00843732
$443$	27.0311	1.28429	0.642144	−	0.766584i	$-0.278045\pi$
$443$	27.0311	1.28429	0.642144	+	0.766584i	$0.278045\pi$
$444$	12.7686	0.605970
$445$	−29.5345	−1.40007
$446$	0.384818	0.0182217
$447$	−0.198567	−0.00939188
$448$	−15.5112	−0.732836
$449$	−13.6059	−0.642102	−0.321051	−	0.947062i	$-0.604036\pi$
$449$	−13.6059	−0.642102	−0.321051	+	0.947062i	$0.604036\pi$
$450$	−0.0558592	−0.00263323
$451$	−0.222849	−0.0104935
$452$	−20.3382	−0.956627
$453$	−21.7587	−1.02231
$454$	−0.0176606	−0.000828854 0
$455$	4.96554	0.232788
$456$	0.974210	0.0456216
$457$	−25.8243	−1.20801	−0.604005	−	0.796980i	$-0.706429\pi$
$457$	−25.8243	−1.20801	−0.604005	+	0.796980i	$0.706429\pi$
$458$	0.320513	0.0149766
$459$	4.77817	0.223026
$460$	−29.6506	−1.38247
$461$	−6.48186	−0.301890	−0.150945	−	0.988542i	$-0.548232\pi$
$461$	−6.48186	−0.301890	−0.150945	+	0.988542i	$0.548232\pi$
$462$	0.00360500	0.000167720 0
$463$	−1.85098	−0.0860225	−0.0430112	−	0.999075i	$-0.513695\pi$
$463$	−1.85098	−0.0860225	−0.0430112	+	0.999075i	$0.513695\pi$
$464$	31.0519	1.44155
$465$	−27.1168	−1.25751
$466$	−0.661791	−0.0306569
$467$	7.56847	0.350227	0.175114	−	0.984548i	$-0.443971\pi$
$467$	7.56847	0.350227	0.175114	+	0.984548i	$0.443971\pi$
$468$	−1.99862	−0.0923863
$469$	−21.6351	−0.999016
$470$	0.270835	0.0124927
$471$	−1.35049	−0.0622272
$472$	0.761588	0.0350549
$473$	−0.0161383	−0.000742039 0
$474$	0.513663	0.0235933
$475$	−9.87482	−0.453088
$476$	18.5929	0.852202
$477$	2.38415	0.109163
$478$	−0.687266	−0.0314348
$479$	1.82057	0.0831841	0.0415921	−	0.999135i	$-0.486757\pi$
$479$	1.82057	0.0831841	0.0415921	+	0.999135i	$0.486757\pi$
$480$	1.13514	0.0518117
$481$	6.38869	0.291299
$482$	−0.200854	−0.00914865
$483$	−11.3252	−0.515313
$484$	21.9799	0.999085
$485$	26.9004	1.22148
$486$	0.0371239	0.00168398
$487$	−30.2580	−1.37112	−0.685560	−	0.728016i	$-0.740443\pi$
$487$	−30.2580	−1.37112	−0.685560	+	0.728016i	$0.740443\pi$
$488$	−1.54817	−0.0700824
$489$	−15.3288	−0.693192
$490$	0.303872	0.0137275
$491$	10.5395	0.475641	0.237821	−	0.971309i	$-0.423567\pi$
$491$	10.5395	0.475641	0.237821	+	0.971309i	$0.423567\pi$
$492$	−8.92985	−0.402589
$493$	−37.1696	−1.67404
$494$	0.243637	0.0109617
$495$	0.127207	0.00571751
$496$	42.4412	1.90567
$497$	22.3729	1.00356
$498$	−0.601188	−0.0269399
$499$	−13.9722	−0.625482	−0.312741	−	0.949838i	$-0.601247\pi$
$499$	−13.9722	−0.625482	−0.312741	+	0.949838i	$0.601247\pi$
$500$	17.8169	0.796795
$501$	−21.7145	−0.970132
$502$	0.0464368	0.00207258
$503$	12.2658	0.546907	0.273453	−	0.961885i	$-0.411834\pi$
$503$	12.2658	0.546907	0.273453	+	0.961885i	$0.411834\pi$
$504$	0.289014	0.0128737
$505$	1.17683	0.0523681
$506$	−0.0107706	−0.000478813 0
$507$	−1.00000	−0.0444116
$508$	−5.71634	−0.253621
$509$	−1.38145	−0.0612318	−0.0306159	−	0.999531i	$-0.509747\pi$
$509$	−1.38145	−0.0612318	−0.0306159	+	0.999531i	$0.509747\pi$
$510$	−0.452406	−0.0200329
$511$	26.2489	1.16118
$512$	−2.96173	−0.130891
$513$	6.56279	0.289754
$514$	0.477941	0.0210811
$515$	−2.55043	−0.112385
$516$	−0.646682	−0.0284686
$517$	−0.142671	−0.00627465
$518$	−0.461764	−0.0202887
$519$	−7.00246	−0.307374
$520$	0.378597	0.0166026
$521$	−32.6388	−1.42993	−0.714966	−	0.699159i	$-0.753558\pi$
$521$	−32.6388	−1.42993	−0.714966	+	0.699159i	$0.753558\pi$
$522$	−0.288789	−0.0126400
$523$	8.60655	0.376338	0.188169	−	0.982137i	$-0.439745\pi$
$523$	8.60655	0.376338	0.188169	+	0.982137i	$0.439745\pi$
$524$	17.7030	0.773361
$525$	−2.92951	−0.127854
$526$	−0.582573	−0.0254014
$527$	−50.8028	−2.21301
$528$	−0.199094	−0.00866446
$529$	10.8362	0.471138
$530$	−0.225735	−0.00980532
$531$	5.13046	0.222643
$532$	25.5372	1.10718
$533$	−4.46800	−0.193531
$534$	−0.429903	−0.0186037
$535$	11.7760	0.509123
$536$	−1.64956	−0.0712503
$537$	−11.9163	−0.514225
$538$	−0.890055	−0.0383730
$539$	−0.160074	−0.00689488
$540$	5.09734	0.219354
$541$	−26.6511	−1.14582	−0.572910	−	0.819618i	$-0.694186\pi$
$541$	−26.6511	−1.14582	−0.572910	+	0.819618i	$0.694186\pi$
$542$	−0.253939	−0.0109076
$543$	−9.82491	−0.421627
$544$	2.12666	0.0911797
$545$	19.2573	0.824891
$546$	0.0722783	0.00309323
$547$	10.3460	0.442361	0.221181	−	0.975233i	$-0.429009\pi$
$547$	10.3460	0.442361	0.221181	+	0.975233i	$0.429009\pi$
$548$	13.1847	0.563222
$549$	−10.4293	−0.445111
$550$	−0.00278607	−0.000118798 0
$551$	−51.0523	−2.17490
$552$	−0.863485	−0.0367524
$553$	26.9388	1.14555
$554$	0.0898828	0.00381875
$555$	−16.2939	−0.691637
$556$	30.8143	1.30682
$557$	41.1497	1.74357	0.871784	−	0.489891i	$-0.162964\pi$
$557$	41.1497	1.74357	0.871784	+	0.489891i	$0.162964\pi$
$558$	−0.394712	−0.0167095
$559$	−0.323564	−0.0136853
$560$	19.8211	0.837595
$561$	0.238319	0.0100618
$562$	−0.310681	−0.0131053
$563$	14.2317	0.599796	0.299898	−	0.953971i	$-0.403047\pi$
$563$	14.2317	0.599796	0.299898	+	0.953971i	$0.403047\pi$
$564$	−5.71700	−0.240729
$565$	25.9534	1.09187
$566$	−0.358227	−0.0150574
$567$	1.94695	0.0817640
$568$	1.70581	0.0715744
$569$	−12.7864	−0.536032	−0.268016	−	0.963414i	$-0.586368\pi$
$569$	−12.7864	−0.536032	−0.268016	+	0.963414i	$0.586368\pi$
$570$	−0.621377	−0.0260266
$571$	8.82640	0.369374	0.184687	−	0.982797i	$-0.440873\pi$
$571$	8.82640	0.369374	0.184687	+	0.982797i	$0.440873\pi$
$572$	−0.0996845	−0.00416802
$573$	−1.27975	−0.0534624
$574$	0.322940	0.0134792
$575$	8.75249	0.365004
$576$	−7.96694	−0.331956
$577$	−12.4553	−0.518522	−0.259261	−	0.965807i	$-0.583479\pi$
$577$	−12.4553	−0.518522	−0.259261	+	0.965807i	$0.583479\pi$
$578$	−0.216466	−0.00900381
$579$	−14.1365	−0.587493
$580$	−39.6524	−1.64648
$581$	−31.5290	−1.30804
$582$	0.391561	0.0162307
$583$	0.118913	0.00492488
$584$	2.00135	0.0828163
$585$	2.55043	0.105447
$586$	0.508031	0.0209866
$587$	−6.78972	−0.280242	−0.140121	−	0.990134i	$-0.544749\pi$
$587$	−6.78972	−0.280242	−0.140121	+	0.990134i	$0.544749\pi$
$588$	−6.41438	−0.264525
$589$	−69.7774	−2.87513
$590$	−0.485761	−0.0199985
$591$	−17.5154	−0.720486
$592$	25.5020	1.04812
$593$	6.90788	0.283673	0.141836	−	0.989890i	$-0.454699\pi$
$593$	6.90788	0.283673	0.141836	+	0.989890i	$0.454699\pi$
$594$	0.00185162	7.59727e−5 0
$595$	−23.7262	−0.972679
$596$	−0.396860	−0.0162560
$597$	−0.938390	−0.0384057
$598$	−0.215946	−0.00883068
$599$	18.2094	0.744016	0.372008	−	0.928229i	$-0.378669\pi$
$599$	18.2094	0.744016	0.372008	+	0.928229i	$0.378669\pi$
$600$	−0.223360	−0.00911863
$601$	12.9665	0.528915	0.264458	−	0.964397i	$-0.414807\pi$
$601$	12.9665	0.528915	0.264458	+	0.964397i	$0.414807\pi$
$602$	0.0233867	0.000953169 0
$603$	−11.1123	−0.452529
$604$	−43.4874	−1.76948
$605$	−28.0483	−1.14033
$606$	0.0171299	0.000695854 0
$607$	9.83937	0.399368	0.199684	−	0.979860i	$-0.436008\pi$
$607$	9.83937	0.399368	0.199684	+	0.979860i	$0.436008\pi$
$608$	2.92095	0.118460
$609$	−15.1454	−0.613723
$610$	0.987463	0.0399812
$611$	−2.86047	−0.115722
$612$	9.54976	0.386026
$613$	−21.4508	−0.866389	−0.433194	−	0.901301i	$-0.642614\pi$
$613$	−21.4508	−0.866389	−0.433194	+	0.901301i	$0.642614\pi$
$614$	−0.152506	−0.00615464
$615$	11.3953	0.459503
$616$	0.0144150	0.000580798 0
$617$	47.7367	1.92181	0.960904	−	0.276882i	$-0.0893013\pi$
$617$	47.7367	1.92181	0.960904	+	0.276882i	$0.0893013\pi$
$618$	−0.0371239	−0.00149334
$619$	−29.4694	−1.18447	−0.592237	−	0.805764i	$-0.701755\pi$
$619$	−29.4694	−1.18447	−0.592237	+	0.805764i	$0.701755\pi$
$620$	−54.1963	−2.17657
$621$	−5.81689	−0.233424
$622$	0.433160	0.0173681
$623$	−22.5460	−0.903288
$624$	−3.99173	−0.159797
$625$	−30.2593	−1.21037
$626$	0.991815	0.0396409
$627$	0.327330	0.0130723
$628$	−2.69912	−0.107706
$629$	−30.5263	−1.21716
$630$	−0.184340	−0.00734430
$631$	−35.9534	−1.43128	−0.715641	−	0.698469i	$-0.753865\pi$
$631$	−35.9534	−1.43128	−0.715641	+	0.698469i	$0.753865\pi$
$632$	2.05394	0.0817015
$633$	−20.4535	−0.812955
$634$	0.309075	0.0122749
$635$	7.29457	0.289476
$636$	4.76501	0.188945
$637$	−3.20940	−0.127161
$638$	−0.0144038	−0.000570253 0
$639$	11.4913	0.454587
$640$	3.02460	0.119558
$641$	9.12451	0.360396	0.180198	−	0.983630i	$-0.442326\pi$
$641$	9.12451	0.360396	0.180198	+	0.983630i	$0.442326\pi$
$642$	0.171412	0.00676508
$643$	−27.9447	−1.10203	−0.551016	−	0.834495i	$-0.685760\pi$
$643$	−27.9447	−1.10203	−0.551016	+	0.834495i	$0.685760\pi$
$644$	−22.6347	−0.891933
$645$	0.825226	0.0324932
$646$	−1.16414	−0.0458024
$647$	−17.7754	−0.698825	−0.349412	−	0.936969i	$-0.613619\pi$
$647$	−17.7754	−0.698825	−0.349412	+	0.936969i	$0.613619\pi$
$648$	0.148445	0.00583145
$649$	0.255890	0.0100446
$650$	−0.0558592	−0.00219098
$651$	−20.7005	−0.811315
$652$	−30.6365	−1.19982
$653$	30.6984	1.20132	0.600662	−	0.799503i	$-0.294904\pi$
$653$	30.6984	1.20132	0.600662	+	0.799503i	$0.294904\pi$
$654$	0.280308	0.0109609
$655$	−22.5907	−0.882692
$656$	−17.8351	−0.696343
$657$	13.4821	0.525987
$658$	0.206750	0.00805996
$659$	24.8822	0.969274	0.484637	−	0.874715i	$-0.338952\pi$
$659$	24.8822	0.969274	0.484637	+	0.874715i	$0.338952\pi$
$660$	0.254238	0.00989619
$661$	26.4240	1.02777	0.513886	−	0.857858i	$-0.328205\pi$
$661$	26.4240	1.02777	0.513886	+	0.857858i	$0.328205\pi$
$662$	−0.720468	−0.0280018
$663$	4.77817	0.185569
$664$	−2.40392	−0.0932904
$665$	−32.5878	−1.26370
$666$	−0.237173	−0.00919028
$667$	45.2499	1.75208
$668$	−43.3991	−1.67916
$669$	10.3658	0.400763
$670$	1.05213	0.0406475
$671$	−0.520177	−0.0200812
$672$	0.866543	0.0334276
$673$	−23.5149	−0.906433	−0.453217	−	0.891400i	$-0.649724\pi$
$673$	−23.5149	−0.906433	−0.453217	+	0.891400i	$0.649724\pi$
$674$	1.04614	0.0402960
$675$	−1.50467	−0.0579147
$676$	−1.99862	−0.0768701
$677$	−47.9322	−1.84219	−0.921093	−	0.389344i	$-0.872702\pi$
$677$	−47.9322	−1.84219	−0.921093	+	0.389344i	$0.872702\pi$
$678$	0.377777	0.0145084
$679$	20.5352	0.788070
$680$	−1.80900	−0.0693720
$681$	−0.475721	−0.0182297
$682$	−0.0196869	−0.000753850 0
$683$	24.0109	0.918750	0.459375	−	0.888242i	$-0.348073\pi$
$683$	24.0109	0.918750	0.459375	+	0.888242i	$0.348073\pi$
$684$	13.1165	0.501523
$685$	−16.8249	−0.642846
$686$	0.737918	0.0281738
$687$	8.63360	0.329393
$688$	−1.29158	−0.0492411
$689$	2.38415	0.0908288
$690$	0.550753	0.0209668
$691$	−17.2194	−0.655058	−0.327529	−	0.944841i	$-0.606216\pi$
$691$	−17.2194	−0.655058	−0.327529	+	0.944841i	$0.606216\pi$
$692$	−13.9953	−0.532020
$693$	0.0971071	0.00368879
$694$	0.114618	0.00435085
$695$	−39.3218	−1.49156
$696$	−1.15476	−0.0437710
$697$	21.3489	0.808647
$698$	0.813908	0.0308069
$699$	−17.8265	−0.674261
$700$	−5.85498	−0.221297
$701$	20.8067	0.785860	0.392930	−	0.919568i	$-0.371461\pi$
$701$	20.8067	0.785860	0.392930	+	0.919568i	$0.371461\pi$
$702$	0.0371239	0.00140115
$703$	−41.9276	−1.58133
$704$	−0.397364	−0.0149762
$705$	7.29542	0.274761
$706$	−0.219565	−0.00826343
$707$	0.898368	0.0337866
$708$	10.2538	0.385363
$709$	1.89439	0.0711452	0.0355726	−	0.999367i	$-0.488675\pi$
$709$	1.89439	0.0711452	0.0355726	+	0.999367i	$0.488675\pi$
$710$	−1.08801	−0.0408324
$711$	13.8364	0.518907
$712$	−1.71902	−0.0644230
$713$	61.8467	2.31618
$714$	−0.345358	−0.0129247
$715$	0.127207	0.00475726
$716$	−23.8161	−0.890049
$717$	−18.5128	−0.691371
$718$	0.108048	0.00403233
$719$	−2.51146	−0.0936616	−0.0468308	−	0.998903i	$-0.514912\pi$
$719$	−2.51146	−0.0936616	−0.0468308	+	0.998903i	$0.514912\pi$
$720$	10.1806	0.379409
$721$	−1.94695	−0.0725081
$722$	−0.893581	−0.0332556
$723$	−5.41036	−0.201214
$724$	−19.6363	−0.729777
$725$	11.7049	0.434709
$726$	−0.408271	−0.0151524
$727$	33.1643	1.23000	0.614998	−	0.788529i	$-0.289157\pi$
$727$	33.1643	1.23000	0.614998	+	0.788529i	$0.289157\pi$
$728$	0.289014	0.0107116
$729$	1.00000	0.0370370
$730$	−1.27651	−0.0472458
$731$	1.54604	0.0571825
$732$	−20.8442	−0.770423
$733$	27.2252	1.00559	0.502793	−	0.864407i	$-0.332306\pi$
$733$	27.2252	1.00559	0.502793	+	0.864407i	$0.332306\pi$
$734$	−0.615346	−0.0227128
$735$	8.18534	0.301921
$736$	−2.58897	−0.0954306
$737$	−0.554245	−0.0204159
$738$	0.165870	0.00610576
$739$	−26.2339	−0.965030	−0.482515	−	0.875888i	$-0.660277\pi$
$739$	−26.2339	−0.965030	−0.482515	+	0.875888i	$0.660277\pi$
$740$	−32.5653	−1.19712
$741$	6.56279	0.241090
$742$	−0.172322	−0.00632614
$743$	34.4633	1.26434	0.632168	−	0.774832i	$-0.282165\pi$
$743$	34.4633	1.26434	0.632168	+	0.774832i	$0.282165\pi$
$744$	−1.57830	−0.0578634
$745$	0.506429	0.0185541
$746$	0.348838	0.0127719
$747$	−16.1941	−0.592511
$748$	0.476309	0.0174156
$749$	8.98961	0.328473
$750$	−0.330944	−0.0120844
$751$	17.3190	0.631978	0.315989	−	0.948763i	$-0.397664\pi$
$751$	17.3190	0.631978	0.315989	+	0.948763i	$0.397664\pi$
$752$	−11.4182	−0.416380
$753$	1.25086	0.0455838
$754$	−0.288789	−0.0105171
$755$	55.4939	2.01963
$756$	3.89121	0.141522
$757$	−21.0093	−0.763596	−0.381798	−	0.924246i	$-0.624695\pi$
$757$	−21.0093	−0.763596	−0.381798	+	0.924246i	$0.624695\pi$
$758$	−0.0694165	−0.00252132
$759$	−0.290127	−0.0105309
$760$	−2.48465	−0.0901277
$761$	12.5542	0.455088	0.227544	−	0.973768i	$-0.426930\pi$
$761$	12.5542	0.455088	0.227544	+	0.973768i	$0.426930\pi$
$762$	0.106180	0.00384648
$763$	14.7006	0.532199
$764$	−2.55774	−0.0925358
$765$	−12.1864	−0.440599
$766$	0.840274	0.0303603
$767$	5.13046	0.185250
$768$	−15.8899	−0.573376
$769$	−32.4897	−1.17161	−0.585805	−	0.810452i	$-0.699221\pi$
$769$	−32.4897	−1.17161	−0.585805	+	0.810452i	$0.699221\pi$
$770$	−0.00919427	−0.000331339 0
$771$	12.8742	0.463653
$772$	−28.2535	−1.01687
$773$	34.6872	1.24761	0.623805	−	0.781580i	$-0.285586\pi$
$773$	34.6872	1.24761	0.623805	+	0.781580i	$0.285586\pi$
$774$	0.0120120	0.000431761 0
$775$	15.9980	0.574667
$776$	1.56570	0.0562055
$777$	−12.4384	−0.446227
$778$	−0.684707	−0.0245479
$779$	29.3226	1.05059
$780$	5.09734	0.182514
$781$	0.573145	0.0205087
$782$	1.03183	0.0368980
$783$	−7.77905	−0.278001
$784$	−12.8111	−0.457538
$785$	3.44432	0.122933
$786$	−0.328830	−0.0117290
$787$	−17.9722	−0.640640	−0.320320	−	0.947309i	$-0.603790\pi$
$787$	−17.9722	−0.640640	−0.320320	+	0.947309i	$0.603790\pi$
$788$	−35.0066	−1.24706
$789$	−15.6927	−0.558673
$790$	−1.31006	−0.0466098
$791$	19.8123	0.704445
$792$	0.00740391	0.000263087 0
$793$	−10.4293	−0.370355
$794$	1.13160	0.0401590
$795$	−6.08059	−0.215656
$796$	−1.87549	−0.0664749
$797$	−24.2753	−0.859875	−0.429938	−	0.902859i	$-0.641464\pi$
$797$	−24.2753	−0.859875	−0.429938	+	0.902859i	$0.641464\pi$
$798$	−0.474347	−0.0167917
$799$	13.6678	0.483533
$800$	−0.669695	−0.0236773
$801$	−11.5802	−0.409167
$802$	−1.39957	−0.0494206
$803$	0.672442	0.0237300
$804$	−22.2093	−0.783263
$805$	28.8840	1.01803
$806$	−0.394712	−0.0139031
$807$	−23.9752	−0.843969
$808$	0.0684959	0.00240968
$809$	−4.36519	−0.153472	−0.0767360	−	0.997051i	$-0.524450\pi$
$809$	−4.36519	−0.153472	−0.0767360	+	0.997051i	$0.524450\pi$
$810$	−0.0946818	−0.00332678
$811$	−18.2835	−0.642021	−0.321011	−	0.947076i	$-0.604023\pi$
$811$	−18.2835	−0.642021	−0.321011	+	0.947076i	$0.604023\pi$
$812$	−30.2699	−1.06227
$813$	−6.84031	−0.239900
$814$	−0.0118294	−0.000414620 0
$815$	39.0949	1.36944
$816$	19.0732	0.667695
$817$	2.12348	0.0742913
$818$	1.13196	0.0395781
$819$	1.94695	0.0680318
$820$	22.7749	0.795335
$821$	−37.1048	−1.29497	−0.647483	−	0.762080i	$-0.724179\pi$
$821$	−37.1048	−1.29497	−0.647483	+	0.762080i	$0.724179\pi$
$822$	−0.244903	−0.00854196
$823$	44.6479	1.55633	0.778165	−	0.628060i	$-0.216151\pi$
$823$	44.6479	1.55633	0.778165	+	0.628060i	$0.216151\pi$
$824$	−0.148445	−0.00517131
$825$	−0.0750478	−0.00261283
$826$	−0.370821	−0.0129025
$827$	−16.5969	−0.577132	−0.288566	−	0.957460i	$-0.593178\pi$
$827$	−16.5969	−0.577132	−0.288566	+	0.957460i	$0.593178\pi$
$828$	−11.6258	−0.404023
$829$	−9.90980	−0.344182	−0.172091	−	0.985081i	$-0.555052\pi$
$829$	−9.90980	−0.344182	−0.172091	+	0.985081i	$0.555052\pi$
$830$	1.53329	0.0532211
$831$	2.42115	0.0839889
$832$	−7.96694	−0.276204
$833$	15.3351	0.531329
$834$	−0.572368	−0.0198195
$835$	55.3812	1.91654
$836$	0.654208	0.0226263
$837$	−10.6323	−0.367505
$838$	−0.967070	−0.0334069
$839$	33.2864	1.14917	0.574587	−	0.818443i	$-0.305163\pi$
$839$	33.2864	1.14917	0.574587	+	0.818443i	$0.305163\pi$
$840$	−0.737107	−0.0254326
$841$	31.5137	1.08668
$842$	−0.0786263	−0.00270964
$843$	−8.36874	−0.288235
$844$	−40.8789	−1.40711
$845$	2.55043	0.0877373
$846$	0.106192	0.00365096
$847$	−21.4116	−0.735710
$848$	9.51688	0.326811
$849$	−9.64948	−0.331169
$850$	0.266905	0.00915476
$851$	37.1623	1.27391
$852$	22.9667	0.786825
$853$	27.5576	0.943554	0.471777	−	0.881718i	$-0.343613\pi$
$853$	27.5576	0.943554	0.471777	+	0.881718i	$0.343613\pi$
$854$	0.753811	0.0257949
$855$	−16.7379	−0.572424
$856$	0.685411	0.0234269
$857$	−29.9475	−1.02299	−0.511494	−	0.859287i	$-0.670908\pi$
$857$	−29.9475	−1.02299	−0.511494	+	0.859287i	$0.670908\pi$
$858$	0.00185162	6.32131e−5 0
$859$	−12.2554	−0.418148	−0.209074	−	0.977900i	$-0.567045\pi$
$859$	−12.2554	−0.418148	−0.209074	+	0.977900i	$0.567045\pi$
$860$	1.64931	0.0562412
$861$	8.69896	0.296460
$862$	−0.378225	−0.0128824
$863$	−22.4984	−0.765856	−0.382928	−	0.923778i	$-0.625084\pi$
$863$	−22.4984	−0.765856	−0.382928	+	0.923778i	$0.625084\pi$
$864$	0.445078	0.0151419
$865$	17.8592	0.607232
$866$	−1.27476	−0.0433182
$867$	−5.83091	−0.198028
$868$	−41.3724	−1.40427
$869$	0.690114	0.0234105
$870$	0.736535	0.0249709
$871$	−11.1123	−0.376527
$872$	1.12085	0.0379567
$873$	10.5474	0.356976
$874$	1.41721	0.0479377
$875$	−17.3562	−0.586747
$876$	26.9456	0.910409
$877$	−49.6211	−1.67559	−0.837794	−	0.545987i	$-0.816155\pi$
$877$	−49.6211	−1.67559	−0.837794	+	0.545987i	$0.816155\pi$
$878$	−1.11271	−0.0375522
$879$	13.6847	0.461574
$880$	0.507775	0.0171171
$881$	−55.6520	−1.87496	−0.937482	−	0.348033i	$-0.886850\pi$
$881$	−55.6520	−1.87496	−0.937482	+	0.348033i	$0.886850\pi$
$882$	0.119146	0.00401184
$883$	−48.1208	−1.61939	−0.809697	−	0.586849i	$-0.800368\pi$
$883$	−48.1208	−1.61939	−0.809697	+	0.586849i	$0.800368\pi$
$884$	9.54976	0.321193
$885$	−13.0848	−0.439842
$886$	−1.00350	−0.0337133
$887$	−7.92397	−0.266061	−0.133030	−	0.991112i	$-0.542471\pi$
$887$	−7.92397	−0.266061	−0.133030	+	0.991112i	$0.542471\pi$
$888$	−0.948367	−0.0318251
$889$	5.56854	0.186763
$890$	1.09644	0.0367526
$891$	0.0498766	0.00167093
$892$	20.7172	0.693664
$893$	18.7727	0.628204
$894$	0.00737157	0.000246542 0
$895$	30.3915	1.01588
$896$	2.30892	0.0771357
$897$	−5.81689	−0.194220
$898$	0.505104	0.0168555
$899$	82.7090	2.75850
$900$	−3.00726	−0.100242
$901$	−11.3919	−0.379518
$902$	0.00827303	0.000275462 0
$903$	0.629962	0.0209638
$904$	1.51059	0.0502414
$905$	25.0577	0.832946
$906$	0.807768	0.0268363
$907$	21.5885	0.716833	0.358417	−	0.933562i	$-0.383317\pi$
$907$	21.5885	0.716833	0.358417	+	0.933562i	$0.383317\pi$
$908$	−0.950786	−0.0315529
$909$	0.461424	0.0153045
$910$	−0.184340	−0.00611082
$911$	−2.11267	−0.0699958	−0.0349979	−	0.999387i	$-0.511142\pi$
$911$	−2.11267	−0.0699958	−0.0349979	+	0.999387i	$0.511142\pi$
$912$	26.1969	0.867466
$913$	−0.807706	−0.0267312
$914$	0.958700	0.0317110
$915$	26.5991	0.879339
$916$	17.2553	0.570131
$917$	−17.2453	−0.569491
$918$	−0.177384	−0.00585456
$919$	−40.0866	−1.32234	−0.661168	−	0.750238i	$-0.729939\pi$
$919$	−40.0866	−1.32234	−0.661168	+	0.750238i	$0.729939\pi$
$920$	2.20225	0.0726062
$921$	−4.10802	−0.135364
$922$	0.240632	0.00792479
$923$	11.4913	0.378239
$924$	0.194080	0.00638477
$925$	9.61286	0.316069
$926$	0.0687157	0.00225814
$927$	−1.00000	−0.0328443
$928$	−3.46229	−0.113655
$929$	−46.9629	−1.54080	−0.770401	−	0.637559i	$-0.779944\pi$
$929$	−46.9629	−1.54080	−0.770401	+	0.637559i	$0.779944\pi$
$930$	1.00668	0.0330104
$931$	21.0626	0.690300
$932$	−35.6285	−1.16705
$933$	11.6679	0.381991
$934$	−0.280971	−0.00919367
$935$	−0.607815	−0.0198777
$936$	0.148445	0.00485206
$937$	1.48904	0.0486449	0.0243225	−	0.999704i	$-0.492257\pi$
$937$	1.48904	0.0486449	0.0243225	+	0.999704i	$0.492257\pi$
$938$	0.803180	0.0262247
$939$	26.7163	0.871855
$940$	14.5808	0.475573
$941$	36.9928	1.20593	0.602966	−	0.797767i	$-0.293985\pi$
$941$	36.9928	1.20593	0.602966	+	0.797767i	$0.293985\pi$
$942$	0.0501354	0.00163350
$943$	−25.9899	−0.846347
$944$	20.4794	0.666548
$945$	−4.96554	−0.161529
$946$	0.000599116 0	1.94790e−5 0
$947$	−3.01243	−0.0978909	−0.0489454	−	0.998801i	$-0.515586\pi$
$947$	−3.01243	−0.0978909	−0.0489454	+	0.998801i	$0.515586\pi$
$948$	27.6538	0.898154
$949$	13.4821	0.437648
$950$	0.366592	0.0118938
$951$	8.32549	0.269973
$952$	−1.38096	−0.0447570
$953$	−52.8784	−1.71290	−0.856449	−	0.516231i	$-0.827335\pi$
$953$	−52.8784	−1.71290	−0.856449	+	0.516231i	$0.827335\pi$
$954$	−0.0885089	−0.00286558
$955$	3.26391	0.105618
$956$	−37.0000	−1.19667
$957$	−0.387993	−0.0125420
$958$	−0.0675869	−0.00218363
$959$	−12.8438	−0.414748
$960$	20.3191	0.655796
$961$	82.0453	2.64662
$962$	−0.237173	−0.00764678
$963$	4.61729	0.148790
$964$	−10.8133	−0.348272
$965$	36.0541	1.16062
$966$	0.420435	0.0135273
$967$	23.8672	0.767518	0.383759	−	0.923433i	$-0.374629\pi$
$967$	23.8672	0.767518	0.383759	+	0.923433i	$0.374629\pi$
$968$	−1.63252	−0.0524712
$969$	−31.3581	−1.00737
$970$	−0.998647	−0.0320646
$971$	10.7346	0.344491	0.172245	−	0.985054i	$-0.444898\pi$
$971$	10.7346	0.344491	0.172245	+	0.985054i	$0.444898\pi$
$972$	1.99862	0.0641058
$973$	−30.0175	−0.962318
$974$	1.12330	0.0359927
$975$	−1.50467	−0.0481880
$976$	−41.6309	−1.33257
$977$	5.66977	0.181392	0.0906960	−	0.995879i	$-0.471091\pi$
$977$	5.66977	0.181392	0.0906960	+	0.995879i	$0.471091\pi$
$978$	0.569065	0.0181967
$979$	−0.577582	−0.0184596
$980$	16.3594	0.522582
$981$	7.55061	0.241073
$982$	−0.391268	−0.0124859
$983$	53.1999	1.69681	0.848406	−	0.529346i	$-0.177563\pi$
$983$	53.1999	1.69681	0.848406	+	0.529346i	$0.177563\pi$
$984$	0.663251	0.0211437
$985$	44.6717	1.42336
$986$	1.37988	0.0439444
$987$	5.56919	0.177269
$988$	13.1165	0.417293
$989$	−1.88214	−0.0598484
$990$	−0.00472241	−0.000150088 0
$991$	−37.2820	−1.18430	−0.592150	−	0.805828i	$-0.701721\pi$
$991$	−37.2820	−1.18430	−0.592150	+	0.805828i	$0.701721\pi$
$992$	−4.73219	−0.150247
$993$	−19.4071	−0.615866
$994$	−0.830568	−0.0263440
$995$	2.39329	0.0758725
$996$	−32.3659	−1.02555
$997$	−36.5586	−1.15782	−0.578911	−	0.815391i	$-0.696522\pi$
$997$	−36.5586	−1.15782	−0.578911	+	0.815391i	$0.696522\pi$
$998$	0.518704	0.0164193
$999$	−6.38869	−0.202129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.12	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} -0.0946818 q^{10} +0.0498766 q^{11} +1.99862 q^{12} +1.00000 q^{13} -0.0722783 q^{14} -2.55043 q^{15} +3.99173 q^{16} -4.77817 q^{17} -0.0371239 q^{18} -6.56279 q^{19} -5.09734 q^{20} -1.94695 q^{21} -0.00185162 q^{22} +5.81689 q^{23} -0.148445 q^{24} +1.50467 q^{25} -0.0371239 q^{26} -1.00000 q^{27} -3.89121 q^{28} +7.77905 q^{29} +0.0946818 q^{30} +10.6323 q^{31} -0.445078 q^{32} -0.0498766 q^{33} +0.177384 q^{34} +4.96554 q^{35} -1.99862 q^{36} +6.38869 q^{37} +0.243637 q^{38} -1.00000 q^{39} +0.378597 q^{40} -4.46800 q^{41} +0.0722783 q^{42} -0.323564 q^{43} -0.0996845 q^{44} +2.55043 q^{45} -0.215946 q^{46} -2.86047 q^{47} -3.99173 q^{48} -3.20940 q^{49} -0.0558592 q^{50} +4.77817 q^{51} -1.99862 q^{52} +2.38415 q^{53} +0.0371239 q^{54} +0.127207 q^{55} +0.289014 q^{56} +6.56279 q^{57} -0.288789 q^{58} +5.13046 q^{59} +5.09734 q^{60} -10.4293 q^{61} -0.394712 q^{62} +1.94695 q^{63} -7.96694 q^{64} +2.55043 q^{65} +0.00185162 q^{66} -11.1123 q^{67} +9.54976 q^{68} -5.81689 q^{69} -0.184340 q^{70} +11.4913 q^{71} +0.148445 q^{72} +13.4821 q^{73} -0.237173 q^{74} -1.50467 q^{75} +13.1165 q^{76} +0.0971071 q^{77} +0.0371239 q^{78} +13.8364 q^{79} +10.1806 q^{80} +1.00000 q^{81} +0.165870 q^{82} -16.1941 q^{83} +3.89121 q^{84} -12.1864 q^{85} +0.0120120 q^{86} -7.77905 q^{87} +0.00740391 q^{88} -11.5802 q^{89} -0.0946818 q^{90} +1.94695 q^{91} -11.6258 q^{92} -10.6323 q^{93} +0.106192 q^{94} -16.7379 q^{95} +0.445078 q^{96} +10.5474 q^{97} +0.119146 q^{98} +0.0498766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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