LMFDB - Embedded newform 4034.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0555653 q^{3} +1.00000 q^{4} +0.675723 q^{5} -0.0555653 q^{6} -0.0958620 q^{7} -1.00000 q^{8} -2.99691 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0555653 q^{3} +1.00000 q^{4} +0.675723 q^{5} -0.0555653 q^{6} -0.0958620 q^{7} -1.00000 q^{8} -2.99691 q^{9} -0.675723 q^{10} +1.17421 q^{11} +0.0555653 q^{12} +5.23551 q^{13} +0.0958620 q^{14} +0.0375467 q^{15} +1.00000 q^{16} +0.451487 q^{17} +2.99691 q^{18} -0.859803 q^{19} +0.675723 q^{20} -0.00532660 q^{21} -1.17421 q^{22} -5.05092 q^{23} -0.0555653 q^{24} -4.54340 q^{25} -5.23551 q^{26} -0.333220 q^{27} -0.0958620 q^{28} -1.20567 q^{29} -0.0375467 q^{30} -8.98061 q^{31} -1.00000 q^{32} +0.0652453 q^{33} -0.451487 q^{34} -0.0647761 q^{35} -2.99691 q^{36} +4.78845 q^{37} +0.859803 q^{38} +0.290913 q^{39} -0.675723 q^{40} +3.83407 q^{41} +0.00532660 q^{42} -1.58945 q^{43} +1.17421 q^{44} -2.02508 q^{45} +5.05092 q^{46} +2.00629 q^{47} +0.0555653 q^{48} -6.99081 q^{49} +4.54340 q^{50} +0.0250870 q^{51} +5.23551 q^{52} -6.40238 q^{53} +0.333220 q^{54} +0.793440 q^{55} +0.0958620 q^{56} -0.0477752 q^{57} +1.20567 q^{58} +6.89903 q^{59} +0.0375467 q^{60} -6.76711 q^{61} +8.98061 q^{62} +0.287290 q^{63} +1.00000 q^{64} +3.53775 q^{65} -0.0652453 q^{66} -4.54784 q^{67} +0.451487 q^{68} -0.280656 q^{69} +0.0647761 q^{70} -3.45128 q^{71} +2.99691 q^{72} -0.329836 q^{73} -4.78845 q^{74} -0.252455 q^{75} -0.859803 q^{76} -0.112562 q^{77} -0.290913 q^{78} +11.9851 q^{79} +0.675723 q^{80} +8.97222 q^{81} -3.83407 q^{82} -11.7157 q^{83} -0.00532660 q^{84} +0.305080 q^{85} +1.58945 q^{86} -0.0669936 q^{87} -1.17421 q^{88} +16.2064 q^{89} +2.02508 q^{90} -0.501887 q^{91} -5.05092 q^{92} -0.499010 q^{93} -2.00629 q^{94} -0.580989 q^{95} -0.0555653 q^{96} -0.125378 q^{97} +6.99081 q^{98} -3.51900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	0.0555653	0.0320806	0.0160403	−	0.999871i	$-0.494894\pi$
$3$	0.0555653	0.0320806	0.0160403	+	0.999871i	$0.494894\pi$
$4$	1.00000	0.500000
$5$	0.675723	0.302192	0.151096	−	0.988519i	$-0.451720\pi$
$5$	0.675723	0.302192	0.151096	+	0.988519i	$0.451720\pi$
$6$	−0.0555653	−0.0226844
$7$	−0.0958620	−0.0362324	−0.0181162	−	0.999836i	$-0.505767\pi$
$7$	−0.0958620	−0.0362324	−0.0181162	+	0.999836i	$0.505767\pi$
$8$	−1.00000	−0.353553
$9$	−2.99691	−0.998971
$10$	−0.675723	−0.213682
$11$	1.17421	0.354038	0.177019	−	0.984207i	$-0.443355\pi$
$11$	1.17421	0.354038	0.177019	+	0.984207i	$0.443355\pi$
$12$	0.0555653	0.0160403
$13$	5.23551	1.45207	0.726035	−	0.687658i	$-0.241361\pi$
$13$	5.23551	1.45207	0.726035	+	0.687658i	$0.241361\pi$
$14$	0.0958620	0.0256202
$15$	0.0375467	0.00969452
$16$	1.00000	0.250000
$17$	0.451487	0.109502	0.0547509	−	0.998500i	$-0.482564\pi$
$17$	0.451487	0.109502	0.0547509	+	0.998500i	$0.482564\pi$
$18$	2.99691	0.706379
$19$	−0.859803	−0.197252	−0.0986262	−	0.995125i	$-0.531445\pi$
$19$	−0.859803	−0.197252	−0.0986262	+	0.995125i	$0.531445\pi$
$20$	0.675723	0.151096
$21$	−0.00532660	−0.00116236
$22$	−1.17421	−0.250342
$23$	−5.05092	−1.05319	−0.526595	−	0.850116i	$-0.676532\pi$
$23$	−5.05092	−1.05319	−0.526595	+	0.850116i	$0.676532\pi$
$24$	−0.0555653	−0.0113422
$25$	−4.54340	−0.908680
$26$	−5.23551	−1.02677
$27$	−0.333220	−0.0641282
$28$	−0.0958620	−0.0181162
$29$	−1.20567	−0.223888	−0.111944	−	0.993715i	$-0.535708\pi$
$29$	−1.20567	−0.223888	−0.111944	+	0.993715i	$0.535708\pi$
$30$	−0.0375467	−0.00685506
$31$	−8.98061	−1.61296	−0.806482	−	0.591258i	$-0.798631\pi$
$31$	−8.98061	−1.61296	−0.806482	+	0.591258i	$0.798631\pi$
$32$	−1.00000	−0.176777
$33$	0.0652453	0.0113577
$34$	−0.451487	−0.0774295
$35$	−0.0647761	−0.0109492
$36$	−2.99691	−0.499485
$37$	4.78845	0.787217	0.393608	−	0.919278i	$-0.371227\pi$
$37$	4.78845	0.787217	0.393608	+	0.919278i	$0.371227\pi$
$38$	0.859803	0.139479
$39$	0.290913	0.0465833
$40$	−0.675723	−0.106841
$41$	3.83407	0.598781	0.299391	−	0.954131i	$-0.403217\pi$
$41$	3.83407	0.598781	0.299391	+	0.954131i	$0.403217\pi$
$42$	0.00532660	0.000821912 0
$43$	−1.58945	−0.242389	−0.121195	−	0.992629i	$-0.538672\pi$
$43$	−1.58945	−0.242389	−0.121195	+	0.992629i	$0.538672\pi$
$44$	1.17421	0.177019
$45$	−2.02508	−0.301881
$46$	5.05092	0.744718
$47$	2.00629	0.292648	0.146324	−	0.989237i	$-0.453256\pi$
$47$	2.00629	0.292648	0.146324	+	0.989237i	$0.453256\pi$
$48$	0.0555653	0.00802016
$49$	−6.99081	−0.998687
$50$	4.54340	0.642534
$51$	0.0250870	0.00351289
$52$	5.23551	0.726035
$53$	−6.40238	−0.879435	−0.439717	−	0.898136i	$-0.644921\pi$
$53$	−6.40238	−0.879435	−0.439717	+	0.898136i	$0.644921\pi$
$54$	0.333220	0.0453455
$55$	0.793440	0.106987
$56$	0.0958620	0.0128101
$57$	−0.0477752	−0.00632798
$58$	1.20567	0.158313
$59$	6.89903	0.898177	0.449089	−	0.893487i	$-0.351749\pi$
$59$	6.89903	0.898177	0.449089	+	0.893487i	$0.351749\pi$
$60$	0.0375467	0.00484726
$61$	−6.76711	−0.866440	−0.433220	−	0.901288i	$-0.642623\pi$
$61$	−6.76711	−0.866440	−0.433220	+	0.901288i	$0.642623\pi$
$62$	8.98061	1.14054
$63$	0.287290	0.0361951
$64$	1.00000	0.125000
$65$	3.53775	0.438804
$66$	−0.0652453	−0.00803114
$67$	−4.54784	−0.555607	−0.277804	−	0.960638i	$-0.589606\pi$
$67$	−4.54784	−0.555607	−0.277804	+	0.960638i	$0.589606\pi$
$68$	0.451487	0.0547509
$69$	−0.280656	−0.0337870
$70$	0.0647761	0.00774223
$71$	−3.45128	−0.409591	−0.204796	−	0.978805i	$-0.565653\pi$
$71$	−3.45128	−0.409591	−0.204796	+	0.978805i	$0.565653\pi$
$72$	2.99691	0.353190
$73$	−0.329836	−0.0386044	−0.0193022	−	0.999814i	$-0.506144\pi$
$73$	−0.329836	−0.0386044	−0.0193022	+	0.999814i	$0.506144\pi$
$74$	−4.78845	−0.556646
$75$	−0.252455	−0.0291510
$76$	−0.859803	−0.0986262
$77$	−0.112562	−0.0128276
$78$	−0.290913	−0.0329394
$79$	11.9851	1.34843	0.674214	−	0.738536i	$-0.264483\pi$
$79$	11.9851	1.34843	0.674214	+	0.738536i	$0.264483\pi$
$80$	0.675723	0.0755481
$81$	8.97222	0.996914
$82$	−3.83407	−0.423402
$83$	−11.7157	−1.28597	−0.642983	−	0.765880i	$-0.722303\pi$
$83$	−11.7157	−1.28597	−0.642983	+	0.765880i	$0.722303\pi$
$84$	−0.00532660	−0.000581180 0
$85$	0.305080	0.0330906
$86$	1.58945	0.171395
$87$	−0.0669936	−0.00718247
$88$	−1.17421	−0.125171
$89$	16.2064	1.71788	0.858938	−	0.512080i	$-0.171125\pi$
$89$	16.2064	1.71788	0.858938	+	0.512080i	$0.171125\pi$
$90$	2.02508	0.213462
$91$	−0.501887	−0.0526120
$92$	−5.05092	−0.526595
$93$	−0.499010	−0.0517449
$94$	−2.00629	−0.206933
$95$	−0.580989	−0.0596082
$96$	−0.0555653	−0.00567111
$97$	−0.125378	−0.0127302	−0.00636508	−	0.999980i	$-0.502026\pi$
$97$	−0.125378	−0.0127302	−0.00636508	+	0.999980i	$0.502026\pi$
$98$	6.99081	0.706178
$99$	−3.51900	−0.353673
$100$	−4.54340	−0.454340
$101$	5.88922	0.586000	0.293000	−	0.956112i	$-0.405346\pi$
$101$	5.88922	0.586000	0.293000	+	0.956112i	$0.405346\pi$
$102$	−0.0250870	−0.00248399
$103$	−7.18283	−0.707745	−0.353873	−	0.935294i	$-0.615135\pi$
$103$	−7.18283	−0.707745	−0.353873	+	0.935294i	$0.615135\pi$
$104$	−5.23551	−0.513384
$105$	−0.00359930	−0.000351256 0
$106$	6.40238	0.621854
$107$	−1.79641	−0.173666	−0.0868328	−	0.996223i	$-0.527675\pi$
$107$	−1.79641	−0.173666	−0.0868328	+	0.996223i	$0.527675\pi$
$108$	−0.333220	−0.0320641
$109$	−1.08428	−0.103855	−0.0519276	−	0.998651i	$-0.516537\pi$
$109$	−1.08428	−0.103855	−0.0519276	+	0.998651i	$0.516537\pi$
$110$	−0.793440	−0.0756516
$111$	0.266072	0.0252544
$112$	−0.0958620	−0.00905811
$113$	−3.87307	−0.364348	−0.182174	−	0.983266i	$-0.558313\pi$
$113$	−3.87307	−0.364348	−0.182174	+	0.983266i	$0.558313\pi$
$114$	0.0477752	0.00447456
$115$	−3.41302	−0.318266
$116$	−1.20567	−0.111944
$117$	−15.6904	−1.45058
$118$	−6.89903	−0.635107
$119$	−0.0432805	−0.00396752
$120$	−0.0375467	−0.00342753
$121$	−9.62123	−0.874657
$122$	6.76711	0.612666
$123$	0.213041	0.0192093
$124$	−8.98061	−0.806482
$125$	−6.44869	−0.576789
$126$	−0.287290	−0.0255938
$127$	−15.9273	−1.41332	−0.706662	−	0.707552i	$-0.749800\pi$
$127$	−15.9273	−1.41332	−0.706662	+	0.707552i	$0.749800\pi$
$128$	−1.00000	−0.0883883
$129$	−0.0883183	−0.00777600
$130$	−3.53775	−0.310282
$131$	−5.46696	−0.477651	−0.238825	−	0.971063i	$-0.576762\pi$
$131$	−5.46696	−0.477651	−0.238825	+	0.971063i	$0.576762\pi$
$132$	0.0652453	0.00567887
$133$	0.0824225	0.00714693
$134$	4.54784	0.392874
$135$	−0.225164	−0.0193791
$136$	−0.451487	−0.0387147
$137$	−6.92623	−0.591748	−0.295874	−	0.955227i	$-0.595611\pi$
$137$	−6.92623	−0.591748	−0.295874	+	0.955227i	$0.595611\pi$
$138$	0.280656	0.0238910
$139$	−10.3086	−0.874364	−0.437182	−	0.899373i	$-0.644023\pi$
$139$	−10.3086	−0.874364	−0.437182	+	0.899373i	$0.644023\pi$
$140$	−0.0647761	−0.00547458
$141$	0.111480	0.00938833
$142$	3.45128	0.289625
$143$	6.14759	0.514087
$144$	−2.99691	−0.249743
$145$	−0.814702	−0.0676573
$146$	0.329836	0.0272974
$147$	−0.388446	−0.0320385
$148$	4.78845	0.393608
$149$	−0.269048	−0.0220412	−0.0110206	−	0.999939i	$-0.503508\pi$
$149$	−0.269048	−0.0220412	−0.0110206	+	0.999939i	$0.503508\pi$
$150$	0.252455	0.0206129
$151$	−14.5709	−1.18576	−0.592881	−	0.805290i	$-0.702010\pi$
$151$	−14.5709	−1.18576	−0.592881	+	0.805290i	$0.702010\pi$
$152$	0.859803	0.0697393
$153$	−1.35307	−0.109389
$154$	0.112562	0.00907051
$155$	−6.06840	−0.487426
$156$	0.290913	0.0232917
$157$	−5.52689	−0.441094	−0.220547	−	0.975376i	$-0.570784\pi$
$157$	−5.52689	−0.441094	−0.220547	+	0.975376i	$0.570784\pi$
$158$	−11.9851	−0.953482
$159$	−0.355750	−0.0282128
$160$	−0.675723	−0.0534206
$161$	0.484192	0.0381596
$162$	−8.97222	−0.704924
$163$	−6.28602	−0.492359	−0.246180	−	0.969224i	$-0.579175\pi$
$163$	−6.28602	−0.492359	−0.246180	+	0.969224i	$0.579175\pi$
$164$	3.83407	0.299391
$165$	0.0440877	0.00343223
$166$	11.7157	0.909315
$167$	9.30430	0.719988	0.359994	−	0.932955i	$-0.382779\pi$
$167$	9.30430	0.719988	0.359994	+	0.932955i	$0.382779\pi$
$168$	0.00532660	0.000410956 0
$169$	14.4106	1.10851
$170$	−0.305080	−0.0233986
$171$	2.57676	0.197049
$172$	−1.58945	−0.121195
$173$	−0.767522	−0.0583537	−0.0291768	−	0.999574i	$-0.509289\pi$
$173$	−0.767522	−0.0583537	−0.0291768	+	0.999574i	$0.509289\pi$
$174$	0.0669936	0.00507878
$175$	0.435539	0.0329237
$176$	1.17421	0.0885094
$177$	0.383346	0.0288141
$178$	−16.2064	−1.21472
$179$	−3.58161	−0.267702	−0.133851	−	0.991001i	$-0.542734\pi$
$179$	−3.58161	−0.267702	−0.133851	+	0.991001i	$0.542734\pi$
$180$	−2.02508	−0.150941
$181$	18.3386	1.36309	0.681547	−	0.731774i	$-0.261308\pi$
$181$	18.3386	1.36309	0.681547	+	0.731774i	$0.261308\pi$
$182$	0.501887	0.0372023
$183$	−0.376017	−0.0277959
$184$	5.05092	0.372359
$185$	3.23567	0.237891
$186$	0.499010	0.0365892
$187$	0.530141	0.0387677
$188$	2.00629	0.146324
$189$	0.0319431	0.00232352
$190$	0.580989	0.0421493
$191$	5.78018	0.418239	0.209120	−	0.977890i	$-0.432940\pi$
$191$	5.78018	0.418239	0.209120	+	0.977890i	$0.432940\pi$
$192$	0.0555653	0.00401008
$193$	−12.2867	−0.884415	−0.442207	−	0.896913i	$-0.645805\pi$
$193$	−12.2867	−0.884415	−0.442207	+	0.896913i	$0.645805\pi$
$194$	0.125378	0.00900159
$195$	0.196576	0.0140771
$196$	−6.99081	−0.499344
$197$	−4.91187	−0.349956	−0.174978	−	0.984572i	$-0.555985\pi$
$197$	−4.91187	−0.349956	−0.174978	+	0.984572i	$0.555985\pi$
$198$	3.51900	0.250085
$199$	−2.75104	−0.195016	−0.0975081	−	0.995235i	$-0.531087\pi$
$199$	−2.75104	−0.195016	−0.0975081	+	0.995235i	$0.531087\pi$
$200$	4.54340	0.321267
$201$	−0.252702	−0.0178242
$202$	−5.88922	−0.414364
$203$	0.115578	0.00811201
$204$	0.0250870	0.00175644
$205$	2.59077	0.180947
$206$	7.18283	0.500452
$207$	15.1372	1.05211
$208$	5.23551	0.363017
$209$	−1.00959	−0.0698348
$210$	0.00359930	0.000248376 0
$211$	18.3755	1.26502	0.632512	−	0.774551i	$-0.282024\pi$
$211$	18.3755	1.26502	0.632512	+	0.774551i	$0.282024\pi$
$212$	−6.40238	−0.439717
$213$	−0.191771	−0.0131399
$214$	1.79641	0.122800
$215$	−1.07403	−0.0732482
$216$	0.333220	0.0226728
$217$	0.860899	0.0584416
$218$	1.08428	0.0734367
$219$	−0.0183274	−0.00123845
$220$	0.793440	0.0534937
$221$	2.36377	0.159004
$222$	−0.266072	−0.0178576
$223$	12.7455	0.853500	0.426750	−	0.904370i	$-0.359658\pi$
$223$	12.7455	0.853500	0.426750	+	0.904370i	$0.359658\pi$
$224$	0.0958620	0.00640505
$225$	13.6162	0.907745
$226$	3.87307	0.257633
$227$	−23.3952	−1.55280	−0.776398	−	0.630244i	$-0.782955\pi$
$227$	−23.3952	−1.55280	−0.776398	+	0.630244i	$0.782955\pi$
$228$	−0.0477752	−0.00316399
$229$	−13.2759	−0.877295	−0.438648	−	0.898659i	$-0.644542\pi$
$229$	−13.2759	−0.877295	−0.438648	+	0.898659i	$0.644542\pi$
$230$	3.41302	0.225048
$231$	−0.00625454	−0.000411519 0
$232$	1.20567	0.0791564
$233$	7.04419	0.461481	0.230740	−	0.973015i	$-0.425885\pi$
$233$	7.04419	0.461481	0.230740	+	0.973015i	$0.425885\pi$
$234$	15.6904	1.02571
$235$	1.35570	0.0884359
$236$	6.89903	0.449089
$237$	0.665955	0.0432584
$238$	0.0432805	0.00280546
$239$	−13.8427	−0.895409	−0.447704	−	0.894182i	$-0.647758\pi$
$239$	−13.8427	−0.895409	−0.447704	+	0.894182i	$0.647758\pi$
$240$	0.0375467	0.00242363
$241$	−9.30921	−0.599659	−0.299829	−	0.953993i	$-0.596930\pi$
$241$	−9.30921	−0.599659	−0.299829	+	0.953993i	$0.596930\pi$
$242$	9.62123	0.618476
$243$	1.49820	0.0961099
$244$	−6.76711	−0.433220
$245$	−4.72385	−0.301796
$246$	−0.213041	−0.0135830
$247$	−4.50151	−0.286424
$248$	8.98061	0.570269
$249$	−0.650987	−0.0412546
$250$	6.44869	0.407851
$251$	15.1899	0.958776	0.479388	−	0.877603i	$-0.340859\pi$
$251$	15.1899	0.958776	0.479388	+	0.877603i	$0.340859\pi$
$252$	0.287290	0.0180976
$253$	−5.93084	−0.372869
$254$	15.9273	0.999371
$255$	0.0169519	0.00106157
$256$	1.00000	0.0625000
$257$	15.8010	0.985637	0.492819	−	0.870132i	$-0.335967\pi$
$257$	15.8010	0.985637	0.492819	+	0.870132i	$0.335967\pi$
$258$	0.0883183	0.00549846
$259$	−0.459031	−0.0285228
$260$	3.53775	0.219402
$261$	3.61330	0.223658
$262$	5.46696	0.337750
$263$	22.4380	1.38359	0.691794	−	0.722095i	$-0.256821\pi$
$263$	22.4380	1.38359	0.691794	+	0.722095i	$0.256821\pi$
$264$	−0.0652453	−0.00401557
$265$	−4.32624	−0.265759
$266$	−0.0824225	−0.00505365
$267$	0.900513	0.0551105
$268$	−4.54784	−0.277804
$269$	14.9779	0.913219	0.456609	−	0.889667i	$-0.349064\pi$
$269$	14.9779	0.913219	0.456609	+	0.889667i	$0.349064\pi$
$270$	0.225164	0.0137031
$271$	−19.4560	−1.18187	−0.590934	−	0.806720i	$-0.701241\pi$
$271$	−19.4560	−1.18187	−0.590934	+	0.806720i	$0.701241\pi$
$272$	0.451487	0.0273754
$273$	−0.0278875	−0.00168783
$274$	6.92623	0.418429
$275$	−5.33490	−0.321707
$276$	−0.280656	−0.0168935
$277$	−25.7618	−1.54788	−0.773939	−	0.633260i	$-0.781716\pi$
$277$	−25.7618	−1.54788	−0.773939	+	0.633260i	$0.781716\pi$
$278$	10.3086	0.618269
$279$	26.9141	1.61130
$280$	0.0647761	0.00387111
$281$	−25.3241	−1.51071	−0.755356	−	0.655315i	$-0.772536\pi$
$281$	−25.3241	−1.51071	−0.755356	+	0.655315i	$0.772536\pi$
$282$	−0.111480	−0.00663855
$283$	−15.8408	−0.941637	−0.470818	−	0.882230i	$-0.656041\pi$
$283$	−15.8408	−0.941637	−0.470818	+	0.882230i	$0.656041\pi$
$284$	−3.45128	−0.204796
$285$	−0.0322828	−0.00191227
$286$	−6.14759	−0.363515
$287$	−0.367542	−0.0216953
$288$	2.99691	0.176595
$289$	−16.7962	−0.988009
$290$	0.814702	0.0478409
$291$	−0.00696664	−0.000408392 0
$292$	−0.329836	−0.0193022
$293$	−15.8131	−0.923811	−0.461905	−	0.886929i	$-0.652834\pi$
$293$	−15.8131	−0.923811	−0.461905	+	0.886929i	$0.652834\pi$
$294$	0.388446	0.0226546
$295$	4.66183	0.271422
$296$	−4.78845	−0.278323
$297$	−0.391270	−0.0227038
$298$	0.269048	0.0155855
$299$	−26.4442	−1.52931
$300$	−0.252455	−0.0145755
$301$	0.152368	0.00878235
$302$	14.5709	0.838460
$303$	0.327236	0.0187992
$304$	−0.859803	−0.0493131
$305$	−4.57269	−0.261832
$306$	1.35307	0.0773498
$307$	−15.9381	−0.909636	−0.454818	−	0.890584i	$-0.650296\pi$
$307$	−15.9381	−0.909636	−0.454818	+	0.890584i	$0.650296\pi$
$308$	−0.112562	−0.00641382
$309$	−0.399116	−0.0227049
$310$	6.06840	0.344662
$311$	8.98534	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$311$	8.98534	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$312$	−0.290913	−0.0164697
$313$	26.6311	1.50528	0.752641	−	0.658432i	$-0.228780\pi$
$313$	26.6311	1.50528	0.752641	+	0.658432i	$0.228780\pi$
$314$	5.52689	0.311901
$315$	0.194128	0.0109379
$316$	11.9851	0.674214
$317$	−14.3503	−0.805991	−0.402995	−	0.915202i	$-0.632031\pi$
$317$	−14.3503	−0.805991	−0.402995	+	0.915202i	$0.632031\pi$
$318$	0.355750	0.0199495
$319$	−1.41571	−0.0792648
$320$	0.675723	0.0377741
$321$	−0.0998181	−0.00557130
$322$	−0.484192	−0.0269829
$323$	−0.388190	−0.0215995
$324$	8.97222	0.498457
$325$	−23.7870	−1.31947
$326$	6.28602	0.348151
$327$	−0.0602483	−0.00333174
$328$	−3.83407	−0.211701
$329$	−0.192327	−0.0106033
$330$	−0.0440877	−0.00242695
$331$	−15.3004	−0.840986	−0.420493	−	0.907296i	$-0.638143\pi$
$331$	−15.3004	−0.840986	−0.420493	+	0.907296i	$0.638143\pi$
$332$	−11.7157	−0.642983
$333$	−14.3506	−0.786407
$334$	−9.30430	−0.509109
$335$	−3.07308	−0.167900
$336$	−0.00532660	−0.000290590 0
$337$	15.8152	0.861507	0.430754	−	0.902470i	$-0.358248\pi$
$337$	15.8152	0.861507	0.430754	+	0.902470i	$0.358248\pi$
$338$	−14.4106	−0.783832
$339$	−0.215208	−0.0116885
$340$	0.305080	0.0165453
$341$	−10.5451	−0.571050
$342$	−2.57676	−0.139335
$343$	1.34119	0.0724173
$344$	1.58945	0.0856975
$345$	−0.189646	−0.0102102
$346$	0.767522	0.0412623
$347$	−30.1118	−1.61649	−0.808244	−	0.588847i	$-0.799582\pi$
$347$	−30.1118	−1.61649	−0.808244	+	0.588847i	$0.799582\pi$
$348$	−0.0669936	−0.00359124
$349$	−32.4145	−1.73511	−0.867555	−	0.497342i	$-0.834309\pi$
$349$	−32.4145	−1.73511	−0.867555	+	0.497342i	$0.834309\pi$
$350$	−0.435539	−0.0232806
$351$	−1.74458	−0.0931187
$352$	−1.17421	−0.0625856
$353$	34.6287	1.84310	0.921549	−	0.388262i	$-0.126924\pi$
$353$	34.6287	1.84310	0.921549	+	0.388262i	$0.126924\pi$
$354$	−0.383346	−0.0203746
$355$	−2.33211	−0.123775
$356$	16.2064	0.858938
$357$	−0.00240489	−0.000127280 0
$358$	3.58161	0.189294
$359$	−33.2976	−1.75738	−0.878690	−	0.477392i	$-0.841582\pi$
$359$	−33.2976	−1.75738	−0.878690	+	0.477392i	$0.841582\pi$
$360$	2.02508	0.106731
$361$	−18.2607	−0.961091
$362$	−18.3386	−0.963853
$363$	−0.534606	−0.0280596
$364$	−0.501887	−0.0263060
$365$	−0.222878	−0.0116660
$366$	0.376017	0.0196547
$367$	8.34434	0.435571	0.217785	−	0.975997i	$-0.430117\pi$
$367$	8.34434	0.435571	0.217785	+	0.975997i	$0.430117\pi$
$368$	−5.05092	−0.263298
$369$	−11.4904	−0.598165
$370$	−3.23567	−0.168214
$371$	0.613745	0.0318641
$372$	−0.499010	−0.0258725
$373$	26.4901	1.37160	0.685802	−	0.727788i	$-0.259451\pi$
$373$	26.4901	1.37160	0.685802	+	0.727788i	$0.259451\pi$
$374$	−0.530141	−0.0274129
$375$	−0.358323	−0.0185037
$376$	−2.00629	−0.103467
$377$	−6.31232	−0.325101
$378$	−0.0319431	−0.00164298
$379$	38.3620	1.97052	0.985261	−	0.171058i	$-0.0547186\pi$
$379$	38.3620	1.97052	0.985261	+	0.171058i	$0.0547186\pi$
$380$	−0.580989	−0.0298041
$381$	−0.885007	−0.0453403
$382$	−5.78018	−0.295740
$383$	38.5728	1.97098	0.985488	−	0.169745i	$-0.0542944\pi$
$383$	38.5728	1.97098	0.985488	+	0.169745i	$0.0542944\pi$
$384$	−0.0555653	−0.00283555
$385$	−0.0760608	−0.00387642
$386$	12.2867	0.625376
$387$	4.76345	0.242140
$388$	−0.125378	−0.00636508
$389$	−14.1583	−0.717853	−0.358926	−	0.933366i	$-0.616857\pi$
$389$	−14.1583	−0.717853	−0.358926	+	0.933366i	$0.616857\pi$
$390$	−0.196576	−0.00995403
$391$	−2.28043	−0.115326
$392$	6.99081	0.353089
$393$	−0.303773	−0.0153233
$394$	4.91187	0.247456
$395$	8.09860	0.407485
$396$	−3.51900	−0.176837
$397$	−22.8407	−1.14634	−0.573171	−	0.819436i	$-0.694287\pi$
$397$	−22.8407	−1.14634	−0.573171	+	0.819436i	$0.694287\pi$
$398$	2.75104	0.137897
$399$	0.00457983	0.000229278 0
$400$	−4.54340	−0.227170
$401$	−18.2598	−0.911850	−0.455925	−	0.890018i	$-0.650691\pi$
$401$	−18.2598	−0.911850	−0.455925	+	0.890018i	$0.650691\pi$
$402$	0.252702	0.0126036
$403$	−47.0181	−2.34214
$404$	5.88922	0.293000
$405$	6.06273	0.301260
$406$	−0.115578	−0.00573606
$407$	5.62265	0.278704
$408$	−0.0250870	−0.00124199
$409$	−39.3802	−1.94723	−0.973613	−	0.228206i	$-0.926714\pi$
$409$	−39.3802	−1.94723	−0.973613	+	0.228206i	$0.926714\pi$
$410$	−2.59077	−0.127949
$411$	−0.384858	−0.0189836
$412$	−7.18283	−0.353873
$413$	−0.661355	−0.0325431
$414$	−15.1372	−0.743952
$415$	−7.91657	−0.388609
$416$	−5.23551	−0.256692
$417$	−0.572800	−0.0280501
$418$	1.00959	0.0493806
$419$	−38.5549	−1.88353	−0.941765	−	0.336273i	$-0.890834\pi$
$419$	−38.5549	−1.88353	−0.941765	+	0.336273i	$0.890834\pi$
$420$	−0.00359930	−0.000175628 0
$421$	24.8350	1.21038	0.605191	−	0.796080i	$-0.293097\pi$
$421$	24.8350	1.21038	0.605191	+	0.796080i	$0.293097\pi$
$422$	−18.3755	−0.894507
$423$	−6.01268	−0.292347
$424$	6.40238	0.310927
$425$	−2.05129	−0.0995021
$426$	0.191771	0.00929135
$427$	0.648709	0.0313932
$428$	−1.79641	−0.0868328
$429$	0.341593	0.0164922
$430$	1.07403	0.0517943
$431$	8.12719	0.391473	0.195736	−	0.980657i	$-0.437290\pi$
$431$	8.12719	0.391473	0.195736	+	0.980657i	$0.437290\pi$
$432$	−0.333220	−0.0160321
$433$	−9.71979	−0.467103	−0.233552	−	0.972344i	$-0.575035\pi$
$433$	−9.71979	−0.467103	−0.233552	+	0.972344i	$0.575035\pi$
$434$	−0.860899	−0.0413245
$435$	−0.0452691	−0.00217049
$436$	−1.08428	−0.0519276
$437$	4.34280	0.207744
$438$	0.0183274	0.000875719 0
$439$	37.9928	1.81330	0.906649	−	0.421885i	$-0.138631\pi$
$439$	37.9928	1.81330	0.906649	+	0.421885i	$0.138631\pi$
$440$	−0.793440	−0.0378258
$441$	20.9508	0.997659
$442$	−2.36377	−0.112433
$443$	2.89894	0.137733	0.0688663	−	0.997626i	$-0.478062\pi$
$443$	2.89894	0.137733	0.0688663	+	0.997626i	$0.478062\pi$
$444$	0.266072	0.0126272
$445$	10.9510	0.519129
$446$	−12.7455	−0.603515
$447$	−0.0149497	−0.000707097 0
$448$	−0.0958620	−0.00452905
$449$	−8.16991	−0.385562	−0.192781	−	0.981242i	$-0.561751\pi$
$449$	−8.16991	−0.385562	−0.192781	+	0.981242i	$0.561751\pi$
$450$	−13.6162	−0.641872
$451$	4.50201	0.211991
$452$	−3.87307	−0.182174
$453$	−0.809636	−0.0380400
$454$	23.3952	1.09799
$455$	−0.339136	−0.0158990
$456$	0.0477752	0.00223728
$457$	20.2760	0.948471	0.474236	−	0.880398i	$-0.342724\pi$
$457$	20.2760	0.948471	0.474236	+	0.880398i	$0.342724\pi$
$458$	13.2759	0.620342
$459$	−0.150445	−0.00702216
$460$	−3.41302	−0.159133
$461$	3.07167	0.143062	0.0715310	−	0.997438i	$-0.477212\pi$
$461$	3.07167	0.143062	0.0715310	+	0.997438i	$0.477212\pi$
$462$	0.00625454	0.000290988 0
$463$	0.253558	0.0117838	0.00589191	−	0.999983i	$-0.498125\pi$
$463$	0.253558	0.0117838	0.00589191	+	0.999983i	$0.498125\pi$
$464$	−1.20567	−0.0559720
$465$	−0.337192	−0.0156369
$466$	−7.04419	−0.326316
$467$	−27.8971	−1.29093	−0.645463	−	0.763792i	$-0.723335\pi$
$467$	−27.8971	−1.29093	−0.645463	+	0.763792i	$0.723335\pi$
$468$	−15.6904	−0.725288
$469$	0.435965	0.0201310
$470$	−1.35570	−0.0625337
$471$	−0.307103	−0.0141506
$472$	−6.89903	−0.317554
$473$	−1.86635	−0.0858149
$474$	−0.665955	−0.0305883
$475$	3.90643	0.179239
$476$	−0.0432805	−0.00198376
$477$	19.1874	0.878530
$478$	13.8427	0.633150
$479$	−22.0735	−1.00856	−0.504281	−	0.863540i	$-0.668242\pi$
$479$	−22.0735	−1.00856	−0.504281	+	0.863540i	$0.668242\pi$
$480$	−0.0375467	−0.00171377
$481$	25.0700	1.14309
$482$	9.30921	0.424023
$483$	0.0269042	0.00122419
$484$	−9.62123	−0.437329
$485$	−0.0847205	−0.00384696
$486$	−1.49820	−0.0679599
$487$	−41.3898	−1.87555	−0.937775	−	0.347244i	$-0.887118\pi$
$487$	−41.3898	−1.87555	−0.937775	+	0.347244i	$0.887118\pi$
$488$	6.76711	0.306333
$489$	−0.349285	−0.0157952
$490$	4.72385	0.213402
$491$	−26.8891	−1.21349	−0.606744	−	0.794897i	$-0.707525\pi$
$491$	−26.8891	−1.21349	−0.606744	+	0.794897i	$0.707525\pi$
$492$	0.213041	0.00960464
$493$	−0.544347	−0.0245162
$494$	4.50151	0.202533
$495$	−2.37787	−0.106877
$496$	−8.98061	−0.403241
$497$	0.330846	0.0148405
$498$	0.650987	0.0291714
$499$	−41.0909	−1.83948	−0.919740	−	0.392527i	$-0.871601\pi$
$499$	−41.0909	−1.83948	−0.919740	+	0.392527i	$0.871601\pi$
$500$	−6.44869	−0.288394
$501$	0.516996	0.0230977
$502$	−15.1899	−0.677957
$503$	31.9037	1.42251	0.711257	−	0.702932i	$-0.248126\pi$
$503$	31.9037	1.42251	0.711257	+	0.702932i	$0.248126\pi$
$504$	−0.287290	−0.0127969
$505$	3.97948	0.177085
$506$	5.93084	0.263658
$507$	0.800728	0.0355616
$508$	−15.9273	−0.706662
$509$	−15.2583	−0.676312	−0.338156	−	0.941090i	$-0.609803\pi$
$509$	−15.2583	−0.676312	−0.338156	+	0.941090i	$0.609803\pi$
$510$	−0.0169519	−0.000750642 0
$511$	0.0316188	0.00139873
$512$	−1.00000	−0.0441942
$513$	0.286504	0.0126494
$514$	−15.8010	−0.696951
$515$	−4.85360	−0.213875
$516$	−0.0883183	−0.00388800
$517$	2.35581	0.103608
$518$	0.459031	0.0201687
$519$	−0.0426476	−0.00187202
$520$	−3.53775	−0.155141
$521$	24.3559	1.06705	0.533525	−	0.845784i	$-0.320867\pi$
$521$	24.3559	1.06705	0.533525	+	0.845784i	$0.320867\pi$
$522$	−3.61330	−0.158150
$523$	−2.83380	−0.123913	−0.0619567	−	0.998079i	$-0.519734\pi$
$523$	−2.83380	−0.123913	−0.0619567	+	0.998079i	$0.519734\pi$
$524$	−5.46696	−0.238825
$525$	0.0242009	0.00105621
$526$	−22.4380	−0.978344
$527$	−4.05463	−0.176623
$528$	0.0652453	0.00283944
$529$	2.51182	0.109210
$530$	4.32624	0.187920
$531$	−20.6758	−0.897253
$532$	0.0824225	0.00357347
$533$	20.0733	0.869472
$534$	−0.900513	−0.0389690
$535$	−1.21388	−0.0524804
$536$	4.54784	0.196437
$537$	−0.199013	−0.00858806
$538$	−14.9779	−0.645743
$539$	−8.20868	−0.353573
$540$	−0.225164	−0.00968953
$541$	18.7307	0.805296	0.402648	−	0.915355i	$-0.368090\pi$
$541$	18.7307	0.805296	0.402648	+	0.915355i	$0.368090\pi$
$542$	19.4560	0.835708
$543$	1.01899	0.0437289
$544$	−0.451487	−0.0193574
$545$	−0.732673	−0.0313842
$546$	0.0278875	0.00119347
$547$	13.2628	0.567075	0.283537	−	0.958961i	$-0.408492\pi$
$547$	13.2628	0.567075	0.283537	+	0.958961i	$0.408492\pi$
$548$	−6.92623	−0.295874
$549$	20.2804	0.865548
$550$	5.33490	0.227481
$551$	1.03664	0.0441625
$552$	0.280656	0.0119455
$553$	−1.14891	−0.0488568
$554$	25.7618	1.09451
$555$	0.179791	0.00763169
$556$	−10.3086	−0.437182
$557$	0.765544	0.0324372	0.0162186	−	0.999868i	$-0.494837\pi$
$557$	0.765544	0.0324372	0.0162186	+	0.999868i	$0.494837\pi$
$558$	−26.9141	−1.13936
$559$	−8.32159	−0.351966
$560$	−0.0647761	−0.00273729
$561$	0.0294574	0.00124369
$562$	25.3241	1.06823
$563$	28.6219	1.20627	0.603135	−	0.797639i	$-0.293918\pi$
$563$	28.6219	1.20627	0.603135	+	0.797639i	$0.293918\pi$
$564$	0.111480	0.00469416
$565$	−2.61712	−0.110103
$566$	15.8408	0.665838
$567$	−0.860095	−0.0361206
$568$	3.45128	0.144812
$569$	−11.8919	−0.498534	−0.249267	−	0.968435i	$-0.580190\pi$
$569$	−11.8919	−0.498534	−0.249267	+	0.968435i	$0.580190\pi$
$570$	0.0322828	0.00135218
$571$	−28.1851	−1.17951	−0.589754	−	0.807583i	$-0.700775\pi$
$571$	−28.1851	−1.17951	−0.589754	+	0.807583i	$0.700775\pi$
$572$	6.14759	0.257044
$573$	0.321177	0.0134174
$574$	0.367542	0.0153409
$575$	22.9484	0.957013
$576$	−2.99691	−0.124871
$577$	4.27226	0.177856	0.0889282	−	0.996038i	$-0.471656\pi$
$577$	4.27226	0.177856	0.0889282	+	0.996038i	$0.471656\pi$
$578$	16.7962	0.698628
$579$	−0.682713	−0.0283726
$580$	−0.814702	−0.0338286
$581$	1.12309	0.0465937
$582$	0.00696664	0.000288777 0
$583$	−7.51774	−0.311353
$584$	0.329836	0.0136487
$585$	−10.6023	−0.438353
$586$	15.8131	0.653233
$587$	20.9103	0.863060	0.431530	−	0.902099i	$-0.357974\pi$
$587$	20.9103	0.863060	0.431530	+	0.902099i	$0.357974\pi$
$588$	−0.388446	−0.0160193
$589$	7.72156	0.318161
$590$	−4.66183	−0.191925
$591$	−0.272929	−0.0112268
$592$	4.78845	0.196804
$593$	23.8111	0.977806	0.488903	−	0.872338i	$-0.337397\pi$
$593$	23.8111	0.977806	0.488903	+	0.872338i	$0.337397\pi$
$594$	0.391270	0.0160540
$595$	−0.0292456	−0.00119895
$596$	−0.269048	−0.0110206
$597$	−0.152862	−0.00625624
$598$	26.4442	1.08138
$599$	−21.6482	−0.884523	−0.442261	−	0.896886i	$-0.645824\pi$
$599$	−21.6482	−0.884523	−0.442261	+	0.896886i	$0.645824\pi$
$600$	0.252455	0.0103064
$601$	20.3941	0.831894	0.415947	−	0.909389i	$-0.363450\pi$
$601$	20.3941	0.831894	0.415947	+	0.909389i	$0.363450\pi$
$602$	−0.152368	−0.00621006
$603$	13.6295	0.555036
$604$	−14.5709	−0.592881
$605$	−6.50129	−0.264315
$606$	−0.327236	−0.0132931
$607$	−5.03915	−0.204533	−0.102266	−	0.994757i	$-0.532609\pi$
$607$	−5.03915	−0.204533	−0.102266	+	0.994757i	$0.532609\pi$
$608$	0.859803	0.0348696
$609$	0.00642215	0.000260238 0
$610$	4.57269	0.185143
$611$	10.5040	0.424945
$612$	−1.35307	−0.0546946
$613$	−6.45980	−0.260909	−0.130454	−	0.991454i	$-0.541644\pi$
$613$	−6.45980	−0.260909	−0.130454	+	0.991454i	$0.541644\pi$
$614$	15.9381	0.643210
$615$	0.143957	0.00580490
$616$	0.112562	0.00453526
$617$	29.9893	1.20732	0.603662	−	0.797240i	$-0.293708\pi$
$617$	29.9893	1.20732	0.603662	+	0.797240i	$0.293708\pi$
$618$	0.399116	0.0160548
$619$	−1.89457	−0.0761491	−0.0380745	−	0.999275i	$-0.512122\pi$
$619$	−1.89457	−0.0761491	−0.0380745	+	0.999275i	$0.512122\pi$
$620$	−6.06840	−0.243713
$621$	1.68307	0.0675392
$622$	−8.98534	−0.360279
$623$	−1.55358	−0.0622428
$624$	0.290913	0.0116458
$625$	18.3595	0.734379
$626$	−26.6311	−1.06439
$627$	−0.0560981	−0.00224034
$628$	−5.52689	−0.220547
$629$	2.16193	0.0862017
$630$	−0.194128	−0.00773426
$631$	−48.3456	−1.92461	−0.962303	−	0.271979i	$-0.912322\pi$
$631$	−48.3456	−1.92461	−0.962303	+	0.271979i	$0.912322\pi$
$632$	−11.9851	−0.476741
$633$	1.02104	0.0405828
$634$	14.3503	0.569921
$635$	−10.7625	−0.427096
$636$	−0.355750	−0.0141064
$637$	−36.6005	−1.45016
$638$	1.41571	0.0560487
$639$	10.3432	0.409170
$640$	−0.675723	−0.0267103
$641$	13.1968	0.521240	0.260620	−	0.965441i	$-0.416073\pi$
$641$	13.1968	0.521240	0.260620	+	0.965441i	$0.416073\pi$
$642$	0.0998181	0.00393951
$643$	27.5902	1.08805	0.544025	−	0.839069i	$-0.316900\pi$
$643$	27.5902	1.08805	0.544025	+	0.839069i	$0.316900\pi$
$644$	0.484192	0.0190798
$645$	−0.0596787	−0.00234985
$646$	0.388190	0.0152731
$647$	−17.5147	−0.688573	−0.344286	−	0.938865i	$-0.611879\pi$
$647$	−17.5147	−0.688573	−0.344286	+	0.938865i	$0.611879\pi$
$648$	−8.97222	−0.352462
$649$	8.10091	0.317988
$650$	23.7870	0.933004
$651$	0.0478361	0.00187484
$652$	−6.28602	−0.246180
$653$	22.5302	0.881676	0.440838	−	0.897587i	$-0.354681\pi$
$653$	22.5302	0.881676	0.440838	+	0.897587i	$0.354681\pi$
$654$	0.0602483	0.00235590
$655$	−3.69415	−0.144342
$656$	3.83407	0.149695
$657$	0.988490	0.0385647
$658$	0.192327	0.00749770
$659$	17.1695	0.668830	0.334415	−	0.942426i	$-0.391461\pi$
$659$	17.1695	0.668830	0.334415	+	0.942426i	$0.391461\pi$
$660$	0.0440877	0.00171611
$661$	28.2953	1.10056	0.550280	−	0.834980i	$-0.314521\pi$
$661$	28.2953	1.10056	0.550280	+	0.834980i	$0.314521\pi$
$662$	15.3004	0.594667
$663$	0.131343	0.00510096
$664$	11.7157	0.454658
$665$	0.0556947	0.00215975
$666$	14.3506	0.556074
$667$	6.08977	0.235797
$668$	9.30430	0.359994
$669$	0.708206	0.0273808
$670$	3.07308	0.118723
$671$	−7.94601	−0.306752
$672$	0.00532660	0.000205478 0
$673$	−14.1080	−0.543824	−0.271912	−	0.962322i	$-0.587656\pi$
$673$	−14.1080	−0.543824	−0.271912	+	0.962322i	$0.587656\pi$
$674$	−15.8152	−0.609178
$675$	1.51395	0.0582720
$676$	14.4106	0.554253
$677$	20.5576	0.790092	0.395046	−	0.918661i	$-0.370729\pi$
$677$	20.5576	0.790092	0.395046	+	0.918661i	$0.370729\pi$
$678$	0.215208	0.00826502
$679$	0.0120189	0.000461245 0
$680$	−0.305080	−0.0116993
$681$	−1.29996	−0.0498146
$682$	10.5451	0.403793
$683$	−19.6991	−0.753763	−0.376882	−	0.926261i	$-0.623004\pi$
$683$	−19.6991	−0.753763	−0.376882	+	0.926261i	$0.623004\pi$
$684$	2.57676	0.0985247
$685$	−4.68021	−0.178822
$686$	−1.34119	−0.0512068
$687$	−0.737678	−0.0281442
$688$	−1.58945	−0.0605973
$689$	−33.5198	−1.27700
$690$	0.189646	0.00721968
$691$	−15.0785	−0.573615	−0.286807	−	0.957988i	$-0.592594\pi$
$691$	−15.0785	−0.573615	−0.286807	+	0.957988i	$0.592594\pi$
$692$	−0.767522	−0.0291768
$693$	0.337339	0.0128144
$694$	30.1118	1.14303
$695$	−6.96576	−0.264226
$696$	0.0669936	0.00253939
$697$	1.73104	0.0655676
$698$	32.4145	1.22691
$699$	0.391413	0.0148046
$700$	0.435539	0.0164618
$701$	32.0100	1.20900	0.604500	−	0.796605i	$-0.293373\pi$
$701$	32.0100	1.20900	0.604500	+	0.796605i	$0.293373\pi$
$702$	1.74458	0.0658448
$703$	−4.11713	−0.155280
$704$	1.17421	0.0442547
$705$	0.0753297	0.00283708
$706$	−34.6287	−1.30327
$707$	−0.564553	−0.0212322
$708$	0.383346	0.0144070
$709$	−6.17807	−0.232022	−0.116011	−	0.993248i	$-0.537011\pi$
$709$	−6.17807	−0.232022	−0.116011	+	0.993248i	$0.537011\pi$
$710$	2.33211	0.0875224
$711$	−35.9183	−1.34704
$712$	−16.2064	−0.607361
$713$	45.3604	1.69876
$714$	0.00240489	9.00009e−5 0
$715$	4.15407	0.155353
$716$	−3.58161	−0.133851
$717$	−0.769172	−0.0287253
$718$	33.2976	1.24266
$719$	−12.7356	−0.474958	−0.237479	−	0.971393i	$-0.576321\pi$
$719$	−12.7356	−0.474958	−0.237479	+	0.971393i	$0.576321\pi$
$720$	−2.02508	−0.0754703
$721$	0.688561	0.0256433
$722$	18.2607	0.679594
$723$	−0.517269	−0.0192374
$724$	18.3386	0.681547
$725$	5.47786	0.203443
$726$	0.534606	0.0198411
$727$	23.5701	0.874165	0.437083	−	0.899421i	$-0.356012\pi$
$727$	23.5701	0.874165	0.437083	+	0.899421i	$0.356012\pi$
$728$	0.501887	0.0186012
$729$	−26.8334	−0.993830
$730$	0.222878	0.00824908
$731$	−0.717618	−0.0265420
$732$	−0.376017	−0.0138980
$733$	45.9364	1.69670	0.848349	−	0.529437i	$-0.177597\pi$
$733$	45.9364	1.69670	0.848349	+	0.529437i	$0.177597\pi$
$734$	−8.34434	−0.307995
$735$	−0.262482	−0.00968180
$736$	5.05092	0.186179
$737$	−5.34012	−0.196706
$738$	11.4904	0.422967
$739$	47.5075	1.74759	0.873796	−	0.486293i	$-0.161651\pi$
$739$	47.5075	1.74759	0.873796	+	0.486293i	$0.161651\pi$
$740$	3.23567	0.118945
$741$	−0.250128	−0.00918867
$742$	−0.613745	−0.0225313
$743$	9.83968	0.360983	0.180491	−	0.983577i	$-0.442231\pi$
$743$	9.83968	0.360983	0.180491	+	0.983577i	$0.442231\pi$
$744$	0.499010	0.0182946
$745$	−0.181802	−0.00666069
$746$	−26.4901	−0.969871
$747$	35.1110	1.28464
$748$	0.530141	0.0193839
$749$	0.172208	0.00629233
$750$	0.358323	0.0130841
$751$	35.2436	1.28606	0.643029	−	0.765842i	$-0.277677\pi$
$751$	35.2436	1.28606	0.643029	+	0.765842i	$0.277677\pi$
$752$	2.00629	0.0731620
$753$	0.844030	0.0307582
$754$	6.31232	0.229881
$755$	−9.84588	−0.358328
$756$	0.0319431	0.00116176
$757$	−19.9107	−0.723667	−0.361833	−	0.932243i	$-0.617849\pi$
$757$	−19.9107	−0.723667	−0.361833	+	0.932243i	$0.617849\pi$
$758$	−38.3620	−1.39337
$759$	−0.329549	−0.0119619
$760$	0.580989	0.0210747
$761$	24.8494	0.900790	0.450395	−	0.892829i	$-0.351283\pi$
$761$	24.8494	0.900790	0.450395	+	0.892829i	$0.351283\pi$
$762$	0.885007	0.0320604
$763$	0.103941	0.00376293
$764$	5.78018	0.209120
$765$	−0.914299	−0.0330566
$766$	−38.5728	−1.39369
$767$	36.1199	1.30422
$768$	0.0555653	0.00200504
$769$	−34.4673	−1.24292	−0.621461	−	0.783445i	$-0.713460\pi$
$769$	−34.4673	−1.24292	−0.621461	+	0.783445i	$0.713460\pi$
$770$	0.0760608	0.00274104
$771$	0.877985	0.0316199
$772$	−12.2867	−0.442207
$773$	53.9954	1.94208	0.971040	−	0.238919i	$-0.0767929\pi$
$773$	53.9954	1.94208	0.971040	+	0.238919i	$0.0767929\pi$
$774$	−4.76345	−0.171219
$775$	40.8025	1.46567
$776$	0.125378	0.00450079
$777$	−0.0255062	−0.000915029 0
$778$	14.1583	0.507599
$779$	−3.29655	−0.118111
$780$	0.196576	0.00703856
$781$	−4.05252	−0.145011
$782$	2.28043	0.0815480
$783$	0.401755	0.0143576
$784$	−6.99081	−0.249672
$785$	−3.73465	−0.133295
$786$	0.303773	0.0108352
$787$	−10.0626	−0.358693	−0.179346	−	0.983786i	$-0.557398\pi$
$787$	−10.0626	−0.358693	−0.179346	+	0.983786i	$0.557398\pi$
$788$	−4.91187	−0.174978
$789$	1.24677	0.0443864
$790$	−8.09860	−0.288135
$791$	0.371280	0.0132012
$792$	3.51900	0.125042
$793$	−35.4293	−1.25813
$794$	22.8407	0.810587
$795$	−0.240388	−0.00852570
$796$	−2.75104	−0.0975081
$797$	−4.92738	−0.174537	−0.0872684	−	0.996185i	$-0.527814\pi$
$797$	−4.92738	−0.174537	−0.0872684	+	0.996185i	$0.527814\pi$
$798$	−0.00457983	−0.000162124 0
$799$	0.905816	0.0320455
$800$	4.54340	0.160633
$801$	−48.5692	−1.71611
$802$	18.2598	0.644775
$803$	−0.387297	−0.0136674
$804$	−0.252702	−0.00891212
$805$	0.327179	0.0115316
$806$	47.0181	1.65614
$807$	0.832251	0.0292966
$808$	−5.88922	−0.207182
$809$	34.5286	1.21396	0.606980	−	0.794717i	$-0.292381\pi$
$809$	34.5286	1.21396	0.606980	+	0.794717i	$0.292381\pi$
$810$	−6.06273	−0.213023
$811$	11.0556	0.388215	0.194107	−	0.980980i	$-0.437819\pi$
$811$	11.0556	0.388215	0.194107	+	0.980980i	$0.437819\pi$
$812$	0.115578	0.00405601
$813$	−1.08108	−0.0379151
$814$	−5.62265	−0.197074
$815$	−4.24761	−0.148787
$816$	0.0250870	0.000878222 0
$817$	1.36662	0.0478118
$818$	39.3802	1.37690
$819$	1.50411	0.0525579
$820$	2.59077	0.0904736
$821$	34.0466	1.18823	0.594117	−	0.804378i	$-0.297501\pi$
$821$	34.0466	1.18823	0.594117	+	0.804378i	$0.297501\pi$
$822$	0.384858	0.0134235
$823$	3.37021	0.117478	0.0587390	−	0.998273i	$-0.481292\pi$
$823$	3.37021	0.117478	0.0587390	+	0.998273i	$0.481292\pi$
$824$	7.18283	0.250226
$825$	−0.296435	−0.0103206
$826$	0.661355	0.0230115
$827$	3.08754	0.107364	0.0536821	−	0.998558i	$-0.482904\pi$
$827$	3.08754	0.107364	0.0536821	+	0.998558i	$0.482904\pi$
$828$	15.1372	0.526053
$829$	−44.6214	−1.54977	−0.774883	−	0.632105i	$-0.782191\pi$
$829$	−44.6214	−1.54977	−0.774883	+	0.632105i	$0.782191\pi$
$830$	7.91657	0.274788
$831$	−1.43146	−0.0496569
$832$	5.23551	0.181509
$833$	−3.15626	−0.109358
$834$	0.572800	0.0198345
$835$	6.28713	0.217575
$836$	−1.00959	−0.0349174
$837$	2.99252	0.103437
$838$	38.5549	1.33186
$839$	39.4395	1.36160	0.680802	−	0.732467i	$-0.261631\pi$
$839$	39.4395	1.36160	0.680802	+	0.732467i	$0.261631\pi$
$840$	0.00359930	0.000124188 0
$841$	−27.5463	−0.949874
$842$	−24.8350	−0.855869
$843$	−1.40714	−0.0484646
$844$	18.3755	0.632512
$845$	9.73756	0.334982
$846$	6.01268	0.206720
$847$	0.922311	0.0316910
$848$	−6.40238	−0.219859
$849$	−0.880197	−0.0302083
$850$	2.05129	0.0703586
$851$	−24.1861	−0.829089
$852$	−0.191771	−0.00656997
$853$	8.60827	0.294742	0.147371	−	0.989081i	$-0.452919\pi$
$853$	8.60827	0.294742	0.147371	+	0.989081i	$0.452919\pi$
$854$	−0.648709	−0.0221984
$855$	1.74117	0.0595468
$856$	1.79641	0.0614001
$857$	23.8219	0.813741	0.406871	−	0.913486i	$-0.366620\pi$
$857$	23.8219	0.813741	0.406871	+	0.913486i	$0.366620\pi$
$858$	−0.341593	−0.0116618
$859$	5.61575	0.191607	0.0958035	−	0.995400i	$-0.469458\pi$
$859$	5.61575	0.191607	0.0958035	+	0.995400i	$0.469458\pi$
$860$	−1.07403	−0.0366241
$861$	−0.0204226	−0.000695999 0
$862$	−8.12719	−0.276813
$863$	17.0806	0.581429	0.290715	−	0.956810i	$-0.406107\pi$
$863$	17.0806	0.581429	0.290715	+	0.956810i	$0.406107\pi$
$864$	0.333220	0.0113364
$865$	−0.518632	−0.0176340
$866$	9.71979	0.330292
$867$	−0.933283	−0.0316960
$868$	0.860899	0.0292208
$869$	14.0730	0.477394
$870$	0.0452691	0.00153477
$871$	−23.8103	−0.806781
$872$	1.08428	0.0367183
$873$	0.375746	0.0127171
$874$	−4.34280	−0.146897
$875$	0.618185	0.0208985
$876$	−0.0183274	−0.000619227 0
$877$	28.0271	0.946408	0.473204	−	0.880953i	$-0.343097\pi$
$877$	28.0271	0.946408	0.473204	+	0.880953i	$0.343097\pi$
$878$	−37.9928	−1.28220
$879$	−0.878659	−0.0296364
$880$	0.793440	0.0267469
$881$	−21.5117	−0.724747	−0.362373	−	0.932033i	$-0.618034\pi$
$881$	−21.5117	−0.724747	−0.362373	+	0.932033i	$0.618034\pi$
$882$	−20.9508	−0.705452
$883$	11.7195	0.394391	0.197196	−	0.980364i	$-0.436817\pi$
$883$	11.7195	0.394391	0.197196	+	0.980364i	$0.436817\pi$
$884$	2.36377	0.0795021
$885$	0.259036	0.00870740
$886$	−2.89894	−0.0973917
$887$	46.0446	1.54603	0.773013	−	0.634390i	$-0.218749\pi$
$887$	46.0446	1.54603	0.773013	+	0.634390i	$0.218749\pi$
$888$	−0.266072	−0.00892878
$889$	1.52683	0.0512081
$890$	−10.9510	−0.367080
$891$	10.5353	0.352945
$892$	12.7455	0.426750
$893$	−1.72502	−0.0577255
$894$	0.0149497	0.000499993 0
$895$	−2.42018	−0.0808976
$896$	0.0958620	0.00320252
$897$	−1.46938	−0.0490611
$898$	8.16991	0.272634
$899$	10.8277	0.361124
$900$	13.6162	0.453872
$901$	−2.89060	−0.0962997
$902$	−4.50201	−0.149900
$903$	0.00846637	0.000281743 0
$904$	3.87307	0.128816
$905$	12.3918	0.411917
$906$	0.809636	0.0268983
$907$	−1.28994	−0.0428316	−0.0214158	−	0.999771i	$-0.506817\pi$
$907$	−1.28994	−0.0428316	−0.0214158	+	0.999771i	$0.506817\pi$
$908$	−23.3952	−0.776398
$909$	−17.6495	−0.585397
$910$	0.339136	0.0112423
$911$	−1.86888	−0.0619186	−0.0309593	−	0.999521i	$-0.509856\pi$
$911$	−1.86888	−0.0619186	−0.0309593	+	0.999521i	$0.509856\pi$
$912$	−0.0477752	−0.00158200
$913$	−13.7567	−0.455280
$914$	−20.2760	−0.670671
$915$	−0.254083	−0.00839972
$916$	−13.2759	−0.438648
$917$	0.524074	0.0173064
$918$	0.150445	0.00496542
$919$	−21.6035	−0.712635	−0.356318	−	0.934365i	$-0.615968\pi$
$919$	−21.6035	−0.712635	−0.356318	+	0.934365i	$0.615968\pi$
$920$	3.41302	0.112524
$921$	−0.885606	−0.0291817
$922$	−3.07167	−0.101160
$923$	−18.0692	−0.594755
$924$	−0.00625454	−0.000205759 0
$925$	−21.7559	−0.715328
$926$	−0.253558	−0.00833242
$927$	21.5263	0.707017
$928$	1.20567	0.0395782
$929$	53.8649	1.76725	0.883624	−	0.468197i	$-0.155096\pi$
$929$	53.8649	1.76725	0.883624	+	0.468197i	$0.155096\pi$
$930$	0.337192	0.0110570
$931$	6.01072	0.196993
$932$	7.04419	0.230740
$933$	0.499273	0.0163455
$934$	27.8971	0.912822
$935$	0.358228	0.0117153
$936$	15.6904	0.512856
$937$	14.4026	0.470511	0.235256	−	0.971934i	$-0.424407\pi$
$937$	14.4026	0.470511	0.235256	+	0.971934i	$0.424407\pi$
$938$	−0.435965	−0.0142348
$939$	1.47977	0.0482904
$940$	1.35570	0.0442180
$941$	26.9410	0.878251	0.439126	−	0.898426i	$-0.355288\pi$
$941$	26.9410	0.878251	0.439126	+	0.898426i	$0.355288\pi$
$942$	0.307103	0.0100060
$943$	−19.3656	−0.630631
$944$	6.89903	0.224544
$945$	0.0215847	0.000702151 0
$946$	1.86635	0.0606803
$947$	−37.1445	−1.20703	−0.603516	−	0.797351i	$-0.706234\pi$
$947$	−37.1445	−1.20703	−0.603516	+	0.797351i	$0.706234\pi$
$948$	0.665955	0.0216292
$949$	−1.72686	−0.0560563
$950$	−3.90643	−0.126741
$951$	−0.797376	−0.0258567
$952$	0.0432805	0.00140273
$953$	17.7407	0.574677	0.287339	−	0.957829i	$-0.407230\pi$
$953$	17.7407	0.574677	0.287339	+	0.957829i	$0.407230\pi$
$954$	−19.1874	−0.621214
$955$	3.90580	0.126389
$956$	−13.8427	−0.447704
$957$	−0.0786646	−0.00254287
$958$	22.0735	0.713161
$959$	0.663962	0.0214405
$960$	0.0375467	0.00121182
$961$	49.6513	1.60166
$962$	−25.0700	−0.808289
$963$	5.38369	0.173487
$964$	−9.30921	−0.299829
$965$	−8.30239	−0.267263
$966$	−0.0269042	−0.000865630 0
$967$	−9.05089	−0.291057	−0.145529	−	0.989354i	$-0.546488\pi$
$967$	−9.05089	−0.291057	−0.145529	+	0.989354i	$0.546488\pi$
$968$	9.62123	0.309238
$969$	−0.0215699	−0.000692925 0
$970$	0.0847205	0.00272021
$971$	−20.1532	−0.646745	−0.323373	−	0.946272i	$-0.604817\pi$
$971$	−20.1532	−0.646745	−0.323373	+	0.946272i	$0.604817\pi$
$972$	1.49820	0.0480549
$973$	0.988203	0.0316803
$974$	41.3898	1.32621
$975$	−1.32173	−0.0423293
$976$	−6.76711	−0.216610
$977$	−47.1402	−1.50815	−0.754074	−	0.656790i	$-0.771914\pi$
$977$	−47.1402	−1.50815	−0.754074	+	0.656790i	$0.771914\pi$
$978$	0.349285	0.0111689
$979$	19.0297	0.608192
$980$	−4.72385	−0.150898
$981$	3.24949	0.103748
$982$	26.8891	0.858066
$983$	−56.1296	−1.79026	−0.895128	−	0.445809i	$-0.852916\pi$
$983$	−56.1296	−1.79026	−0.895128	+	0.445809i	$0.852916\pi$
$984$	−0.213041	−0.00679151
$985$	−3.31906	−0.105754
$986$	0.544347	0.0173355
$987$	−0.0106867	−0.000340162 0
$988$	−4.50151	−0.143212
$989$	8.02820	0.255282
$990$	2.37787	0.0755737
$991$	−44.1415	−1.40220	−0.701101	−	0.713062i	$-0.747308\pi$
$991$	−44.1415	−1.40220	−0.701101	+	0.713062i	$0.747308\pi$
$992$	8.98061	0.285135
$993$	−0.850171	−0.0269793
$994$	−0.330846	−0.0104938
$995$	−1.85894	−0.0589324
$996$	−0.650987	−0.0206273
$997$	−40.0153	−1.26730	−0.633648	−	0.773621i	$-0.718443\pi$
$997$	−40.0153	−1.26730	−0.633648	+	0.773621i	$0.718443\pi$
$998$	41.0909	1.30071
$999$	−1.59561	−0.0504828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.19	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.19	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0555653 q^{3} +1.00000 q^{4} +0.675723 q^{5} -0.0555653 q^{6} -0.0958620 q^{7} -1.00000 q^{8} -2.99691 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0555653 q^{3} +1.00000 q^{4} +0.675723 q^{5} -0.0555653 q^{6} -0.0958620 q^{7} -1.00000 q^{8} -2.99691 q^{9} -0.675723 q^{10} +1.17421 q^{11} +0.0555653 q^{12} +5.23551 q^{13} +0.0958620 q^{14} +0.0375467 q^{15} +1.00000 q^{16} +0.451487 q^{17} +2.99691 q^{18} -0.859803 q^{19} +0.675723 q^{20} -0.00532660 q^{21} -1.17421 q^{22} -5.05092 q^{23} -0.0555653 q^{24} -4.54340 q^{25} -5.23551 q^{26} -0.333220 q^{27} -0.0958620 q^{28} -1.20567 q^{29} -0.0375467 q^{30} -8.98061 q^{31} -1.00000 q^{32} +0.0652453 q^{33} -0.451487 q^{34} -0.0647761 q^{35} -2.99691 q^{36} +4.78845 q^{37} +0.859803 q^{38} +0.290913 q^{39} -0.675723 q^{40} +3.83407 q^{41} +0.00532660 q^{42} -1.58945 q^{43} +1.17421 q^{44} -2.02508 q^{45} +5.05092 q^{46} +2.00629 q^{47} +0.0555653 q^{48} -6.99081 q^{49} +4.54340 q^{50} +0.0250870 q^{51} +5.23551 q^{52} -6.40238 q^{53} +0.333220 q^{54} +0.793440 q^{55} +0.0958620 q^{56} -0.0477752 q^{57} +1.20567 q^{58} +6.89903 q^{59} +0.0375467 q^{60} -6.76711 q^{61} +8.98061 q^{62} +0.287290 q^{63} +1.00000 q^{64} +3.53775 q^{65} -0.0652453 q^{66} -4.54784 q^{67} +0.451487 q^{68} -0.280656 q^{69} +0.0647761 q^{70} -3.45128 q^{71} +2.99691 q^{72} -0.329836 q^{73} -4.78845 q^{74} -0.252455 q^{75} -0.859803 q^{76} -0.112562 q^{77} -0.290913 q^{78} +11.9851 q^{79} +0.675723 q^{80} +8.97222 q^{81} -3.83407 q^{82} -11.7157 q^{83} -0.00532660 q^{84} +0.305080 q^{85} +1.58945 q^{86} -0.0669936 q^{87} -1.17421 q^{88} +16.2064 q^{89} +2.02508 q^{90} -0.501887 q^{91} -5.05092 q^{92} -0.499010 q^{93} -2.00629 q^{94} -0.580989 q^{95} -0.0555653 q^{96} -0.125378 q^{97} +6.99081 q^{98} -3.51900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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