LMFDB - Embedded newform 6034.2.a.q.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.368112 q^{3} +1.00000 q^{4} +1.13454 q^{5} -0.368112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.86449 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.368112 q^{3} +1.00000 q^{4} +1.13454 q^{5} -0.368112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.86449 q^{9} +1.13454 q^{10} +5.79606 q^{11} -0.368112 q^{12} +2.85664 q^{13} +1.00000 q^{14} -0.417638 q^{15} +1.00000 q^{16} -1.34462 q^{17} -2.86449 q^{18} -0.485712 q^{19} +1.13454 q^{20} -0.368112 q^{21} +5.79606 q^{22} +4.48547 q^{23} -0.368112 q^{24} -3.71282 q^{25} +2.85664 q^{26} +2.15879 q^{27} +1.00000 q^{28} +1.70716 q^{29} -0.417638 q^{30} +7.42995 q^{31} +1.00000 q^{32} -2.13360 q^{33} -1.34462 q^{34} +1.13454 q^{35} -2.86449 q^{36} -9.37015 q^{37} -0.485712 q^{38} -1.05156 q^{39} +1.13454 q^{40} +2.02639 q^{41} -0.368112 q^{42} -4.49189 q^{43} +5.79606 q^{44} -3.24989 q^{45} +4.48547 q^{46} +3.97767 q^{47} -0.368112 q^{48} +1.00000 q^{49} -3.71282 q^{50} +0.494971 q^{51} +2.85664 q^{52} +3.77032 q^{53} +2.15879 q^{54} +6.57587 q^{55} +1.00000 q^{56} +0.178796 q^{57} +1.70716 q^{58} -3.81011 q^{59} -0.417638 q^{60} +12.6467 q^{61} +7.42995 q^{62} -2.86449 q^{63} +1.00000 q^{64} +3.24098 q^{65} -2.13360 q^{66} +12.0924 q^{67} -1.34462 q^{68} -1.65115 q^{69} +1.13454 q^{70} +2.75732 q^{71} -2.86449 q^{72} -4.42449 q^{73} -9.37015 q^{74} +1.36673 q^{75} -0.485712 q^{76} +5.79606 q^{77} -1.05156 q^{78} -2.93789 q^{79} +1.13454 q^{80} +7.79881 q^{81} +2.02639 q^{82} -5.83159 q^{83} -0.368112 q^{84} -1.52553 q^{85} -4.49189 q^{86} -0.628425 q^{87} +5.79606 q^{88} -18.6991 q^{89} -3.24989 q^{90} +2.85664 q^{91} +4.48547 q^{92} -2.73505 q^{93} +3.97767 q^{94} -0.551060 q^{95} -0.368112 q^{96} -3.76583 q^{97} +1.00000 q^{98} -16.6028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * 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
$3$	−0.368112	−0.212529	−0.106265	−	0.994338i	$-0.533889\pi$
$3$	−0.368112	−0.212529	−0.106265	+	0.994338i	$0.533889\pi$
$4$	1.00000	0.500000
$5$	1.13454	0.507382	0.253691	−	0.967285i	$-0.418355\pi$
$5$	1.13454	0.507382	0.253691	+	0.967285i	$0.418355\pi$
$6$	−0.368112	−0.150281
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.86449	−0.954831
$10$	1.13454	0.358773
$11$	5.79606	1.74758	0.873789	−	0.486304i	$-0.161655\pi$
$11$	5.79606	1.74758	0.873789	+	0.486304i	$0.161655\pi$
$12$	−0.368112	−0.106265
$13$	2.85664	0.792289	0.396145	−	0.918188i	$-0.370348\pi$
$13$	2.85664	0.792289	0.396145	+	0.918188i	$0.370348\pi$
$14$	1.00000	0.267261
$15$	−0.417638	−0.107834
$16$	1.00000	0.250000
$17$	−1.34462	−0.326118	−0.163059	−	0.986616i	$-0.552136\pi$
$17$	−1.34462	−0.326118	−0.163059	+	0.986616i	$0.552136\pi$
$18$	−2.86449	−0.675168
$19$	−0.485712	−0.111430	−0.0557150	−	0.998447i	$-0.517744\pi$
$19$	−0.485712	−0.111430	−0.0557150	+	0.998447i	$0.517744\pi$
$20$	1.13454	0.253691
$21$	−0.368112	−0.0803286
$22$	5.79606	1.23572
$23$	4.48547	0.935284	0.467642	−	0.883918i	$-0.345104\pi$
$23$	4.48547	0.935284	0.467642	+	0.883918i	$0.345104\pi$
$24$	−0.368112	−0.0751405
$25$	−3.71282	−0.742563
$26$	2.85664	0.560233
$27$	2.15879	0.415459
$28$	1.00000	0.188982
$29$	1.70716	0.317011	0.158506	−	0.987358i	$-0.449332\pi$
$29$	1.70716	0.317011	0.158506	+	0.987358i	$0.449332\pi$
$30$	−0.417638	−0.0762499
$31$	7.42995	1.33446	0.667229	−	0.744852i	$-0.267480\pi$
$31$	7.42995	1.33446	0.667229	+	0.744852i	$0.267480\pi$
$32$	1.00000	0.176777
$33$	−2.13360	−0.371412
$34$	−1.34462	−0.230601
$35$	1.13454	0.191772
$36$	−2.86449	−0.477416
$37$	−9.37015	−1.54044	−0.770222	−	0.637776i	$-0.779854\pi$
$37$	−9.37015	−1.54044	−0.770222	+	0.637776i	$0.779854\pi$
$38$	−0.485712	−0.0787929
$39$	−1.05156	−0.168385
$40$	1.13454	0.179387
$41$	2.02639	0.316469	0.158234	−	0.987402i	$-0.449420\pi$
$41$	2.02639	0.316469	0.158234	+	0.987402i	$0.449420\pi$
$42$	−0.368112	−0.0568009
$43$	−4.49189	−0.685007	−0.342504	−	0.939517i	$-0.611275\pi$
$43$	−4.49189	−0.685007	−0.342504	+	0.939517i	$0.611275\pi$
$44$	5.79606	0.873789
$45$	−3.24989	−0.484464
$46$	4.48547	0.661346
$47$	3.97767	0.580202	0.290101	−	0.956996i	$-0.406311\pi$
$47$	3.97767	0.580202	0.290101	+	0.956996i	$0.406311\pi$
$48$	−0.368112	−0.0531324
$49$	1.00000	0.142857
$50$	−3.71282	−0.525071
$51$	0.494971	0.0693098
$52$	2.85664	0.396145
$53$	3.77032	0.517893	0.258946	−	0.965892i	$-0.416625\pi$
$53$	3.77032	0.517893	0.258946	+	0.965892i	$0.416625\pi$
$54$	2.15879	0.293774
$55$	6.57587	0.886691
$56$	1.00000	0.133631
$57$	0.178796	0.0236821
$58$	1.70716	0.224161
$59$	−3.81011	−0.496034	−0.248017	−	0.968756i	$-0.579779\pi$
$59$	−3.81011	−0.496034	−0.248017	+	0.968756i	$0.579779\pi$
$60$	−0.417638	−0.0539168
$61$	12.6467	1.61925	0.809624	−	0.586949i	$-0.199671\pi$
$61$	12.6467	1.61925	0.809624	+	0.586949i	$0.199671\pi$
$62$	7.42995	0.943605
$63$	−2.86449	−0.360892
$64$	1.00000	0.125000
$65$	3.24098	0.401993
$66$	−2.13360	−0.262628
$67$	12.0924	1.47732	0.738660	−	0.674078i	$-0.235459\pi$
$67$	12.0924	1.47732	0.738660	+	0.674078i	$0.235459\pi$
$68$	−1.34462	−0.163059
$69$	−1.65115	−0.198775
$70$	1.13454	0.135604
$71$	2.75732	0.327233	0.163617	−	0.986524i	$-0.447684\pi$
$71$	2.75732	0.327233	0.163617	+	0.986524i	$0.447684\pi$
$72$	−2.86449	−0.337584
$73$	−4.42449	−0.517847	−0.258923	−	0.965898i	$-0.583368\pi$
$73$	−4.42449	−0.517847	−0.258923	+	0.965898i	$0.583368\pi$
$74$	−9.37015	−1.08926
$75$	1.36673	0.157817
$76$	−0.485712	−0.0557150
$77$	5.79606	0.660523
$78$	−1.05156	−0.119066
$79$	−2.93789	−0.330538	−0.165269	−	0.986249i	$-0.552849\pi$
$79$	−2.93789	−0.330538	−0.165269	+	0.986249i	$0.552849\pi$
$80$	1.13454	0.126846
$81$	7.79881	0.866534
$82$	2.02639	0.223777
$83$	−5.83159	−0.640100	−0.320050	−	0.947401i	$-0.603700\pi$
$83$	−5.83159	−0.640100	−0.320050	+	0.947401i	$0.603700\pi$
$84$	−0.368112	−0.0401643
$85$	−1.52553	−0.165467
$86$	−4.49189	−0.484373
$87$	−0.628425	−0.0673742
$88$	5.79606	0.617862
$89$	−18.6991	−1.98210	−0.991052	−	0.133478i	$-0.957385\pi$
$89$	−18.6991	−1.98210	−0.991052	+	0.133478i	$0.957385\pi$
$90$	−3.24989	−0.342568
$91$	2.85664	0.299457
$92$	4.48547	0.467642
$93$	−2.73505	−0.283612
$94$	3.97767	0.410265
$95$	−0.551060	−0.0565376
$96$	−0.368112	−0.0375702
$97$	−3.76583	−0.382362	−0.191181	−	0.981555i	$-0.561232\pi$
$97$	−3.76583	−0.382362	−0.191181	+	0.981555i	$0.561232\pi$
$98$	1.00000	0.101015
$99$	−16.6028	−1.66864
$100$	−3.71282	−0.371282
$101$	3.59869	0.358083	0.179042	−	0.983842i	$-0.442700\pi$
$101$	3.59869	0.358083	0.179042	+	0.983842i	$0.442700\pi$
$102$	0.494971	0.0490094
$103$	−16.1413	−1.59045	−0.795224	−	0.606316i	$-0.792647\pi$
$103$	−16.1413	−1.59045	−0.795224	+	0.606316i	$0.792647\pi$
$104$	2.85664	0.280117
$105$	−0.417638	−0.0407573
$106$	3.77032	0.366206
$107$	−3.52764	−0.341030	−0.170515	−	0.985355i	$-0.554543\pi$
$107$	−3.52764	−0.341030	−0.170515	+	0.985355i	$0.554543\pi$
$108$	2.15879	0.207730
$109$	8.73999	0.837139	0.418569	−	0.908185i	$-0.362532\pi$
$109$	8.73999	0.837139	0.418569	+	0.908185i	$0.362532\pi$
$110$	6.57587	0.626985
$111$	3.44926	0.327390
$112$	1.00000	0.0944911
$113$	−11.4941	−1.08128	−0.540639	−	0.841255i	$-0.681817\pi$
$113$	−11.4941	−1.08128	−0.540639	+	0.841255i	$0.681817\pi$
$114$	0.178796	0.0167458
$115$	5.08895	0.474547
$116$	1.70716	0.158506
$117$	−8.18282	−0.756502
$118$	−3.81011	−0.350749
$119$	−1.34462	−0.123261
$120$	−0.417638	−0.0381250
$121$	22.5944	2.05403
$122$	12.6467	1.14498
$123$	−0.745937	−0.0672589
$124$	7.42995	0.667229
$125$	−9.88505	−0.884146
$126$	−2.86449	−0.255189
$127$	21.9218	1.94524	0.972620	−	0.232399i	$-0.0746576\pi$
$127$	21.9218	1.94524	0.972620	+	0.232399i	$0.0746576\pi$
$128$	1.00000	0.0883883
$129$	1.65352	0.145584
$130$	3.24098	0.284252
$131$	20.5229	1.79309	0.896546	−	0.442951i	$-0.146068\pi$
$131$	20.5229	1.79309	0.896546	+	0.442951i	$0.146068\pi$
$132$	−2.13360	−0.185706
$133$	−0.485712	−0.0421166
$134$	12.0924	1.04462
$135$	2.44924	0.210797
$136$	−1.34462	−0.115300
$137$	−16.2484	−1.38819	−0.694096	−	0.719882i	$-0.744196\pi$
$137$	−16.2484	−1.38819	−0.694096	+	0.719882i	$0.744196\pi$
$138$	−1.65115	−0.140555
$139$	3.04733	0.258471	0.129235	−	0.991614i	$-0.458748\pi$
$139$	3.04733	0.258471	0.129235	+	0.991614i	$0.458748\pi$
$140$	1.13454	0.0958862
$141$	−1.46423	−0.123310
$142$	2.75732	0.231389
$143$	16.5573	1.38459
$144$	−2.86449	−0.238708
$145$	1.93684	0.160846
$146$	−4.42449	−0.366173
$147$	−0.368112	−0.0303613
$148$	−9.37015	−0.770222
$149$	−0.663423	−0.0543497	−0.0271748	−	0.999631i	$-0.508651\pi$
$149$	−0.663423	−0.0543497	−0.0271748	+	0.999631i	$0.508651\pi$
$150$	1.36673	0.111593
$151$	14.7966	1.20413	0.602065	−	0.798447i	$-0.294345\pi$
$151$	14.7966	1.20413	0.602065	+	0.798447i	$0.294345\pi$
$152$	−0.485712	−0.0393964
$153$	3.85166	0.311388
$154$	5.79606	0.467060
$155$	8.42959	0.677081
$156$	−1.05156	−0.0841924
$157$	−4.79697	−0.382840	−0.191420	−	0.981508i	$-0.561309\pi$
$157$	−4.79697	−0.382840	−0.191420	+	0.981508i	$0.561309\pi$
$158$	−2.93789	−0.233726
$159$	−1.38790	−0.110067
$160$	1.13454	0.0896934
$161$	4.48547	0.353504
$162$	7.79881	0.612732
$163$	15.8145	1.23869	0.619343	−	0.785120i	$-0.287399\pi$
$163$	15.8145	1.23869	0.619343	+	0.785120i	$0.287399\pi$
$164$	2.02639	0.158234
$165$	−2.42066	−0.188448
$166$	−5.83159	−0.452619
$167$	8.90169	0.688833	0.344417	−	0.938817i	$-0.388077\pi$
$167$	8.90169	0.688833	0.344417	+	0.938817i	$0.388077\pi$
$168$	−0.368112	−0.0284004
$169$	−4.83961	−0.372278
$170$	−1.52553	−0.117003
$171$	1.39132	0.106397
$172$	−4.49189	−0.342504
$173$	−13.2604	−1.00817	−0.504085	−	0.863654i	$-0.668170\pi$
$173$	−13.2604	−1.00817	−0.504085	+	0.863654i	$0.668170\pi$
$174$	−0.628425	−0.0476408
$175$	−3.71282	−0.280663
$176$	5.79606	0.436895
$177$	1.40255	0.105422
$178$	−18.6991	−1.40156
$179$	13.9037	1.03921	0.519607	−	0.854405i	$-0.326078\pi$
$179$	13.9037	1.03921	0.519607	+	0.854405i	$0.326078\pi$
$180$	−3.24989	−0.242232
$181$	5.09657	0.378825	0.189412	−	0.981898i	$-0.439342\pi$
$181$	5.09657	0.378825	0.189412	+	0.981898i	$0.439342\pi$
$182$	2.85664	0.211748
$183$	−4.65541	−0.344138
$184$	4.48547	0.330673
$185$	−10.6308	−0.781594
$186$	−2.73505	−0.200544
$187$	−7.79351	−0.569918
$188$	3.97767	0.290101
$189$	2.15879	0.157029
$190$	−0.551060	−0.0399781
$191$	15.5332	1.12394	0.561971	−	0.827157i	$-0.310043\pi$
$191$	15.5332	1.12394	0.561971	+	0.827157i	$0.310043\pi$
$192$	−0.368112	−0.0265662
$193$	12.4585	0.896782	0.448391	−	0.893838i	$-0.351997\pi$
$193$	12.4585	0.896782	0.448391	+	0.893838i	$0.351997\pi$
$194$	−3.76583	−0.270371
$195$	−1.19304	−0.0854354
$196$	1.00000	0.0714286
$197$	1.42952	0.101849	0.0509246	−	0.998702i	$-0.483783\pi$
$197$	1.42952	0.101849	0.0509246	+	0.998702i	$0.483783\pi$
$198$	−16.6028	−1.17991
$199$	7.40057	0.524613	0.262306	−	0.964985i	$-0.415517\pi$
$199$	7.40057	0.524613	0.262306	+	0.964985i	$0.415517\pi$
$200$	−3.71282	−0.262536
$201$	−4.45135	−0.313974
$202$	3.59869	0.253203
$203$	1.70716	0.119819
$204$	0.494971	0.0346549
$205$	2.29902	0.160571
$206$	−16.1413	−1.12462
$207$	−12.8486	−0.893039
$208$	2.85664	0.198072
$209$	−2.81522	−0.194733
$210$	−0.417638	−0.0288198
$211$	−12.8753	−0.886374	−0.443187	−	0.896429i	$-0.646152\pi$
$211$	−12.8753	−0.886374	−0.443187	+	0.896429i	$0.646152\pi$
$212$	3.77032	0.258946
$213$	−1.01500	−0.0695467
$214$	−3.52764	−0.241145
$215$	−5.09624	−0.347561
$216$	2.15879	0.146887
$217$	7.42995	0.504378
$218$	8.73999	0.591947
$219$	1.62870	0.110058
$220$	6.57587	0.443345
$221$	−3.84110	−0.258380
$222$	3.44926	0.231499
$223$	15.0335	1.00672	0.503358	−	0.864078i	$-0.332098\pi$
$223$	15.0335	1.00672	0.503358	+	0.864078i	$0.332098\pi$
$224$	1.00000	0.0668153
$225$	10.6353	0.709023
$226$	−11.4941	−0.764579
$227$	−21.0298	−1.39580	−0.697898	−	0.716197i	$-0.745881\pi$
$227$	−21.0298	−1.39580	−0.697898	+	0.716197i	$0.745881\pi$
$228$	0.178796	0.0118411
$229$	−11.3592	−0.750634	−0.375317	−	0.926896i	$-0.622466\pi$
$229$	−11.3592	−0.750634	−0.375317	+	0.926896i	$0.622466\pi$
$230$	5.08895	0.335555
$231$	−2.13360	−0.140381
$232$	1.70716	0.112080
$233$	−19.2885	−1.26363	−0.631817	−	0.775117i	$-0.717691\pi$
$233$	−19.2885	−1.26363	−0.631817	+	0.775117i	$0.717691\pi$
$234$	−8.18282	−0.534928
$235$	4.51283	0.294384
$236$	−3.81011	−0.248017
$237$	1.08147	0.0702491
$238$	−1.34462	−0.0871588
$239$	−3.35793	−0.217206	−0.108603	−	0.994085i	$-0.534638\pi$
$239$	−3.35793	−0.217206	−0.108603	+	0.994085i	$0.534638\pi$
$240$	−0.417638	−0.0269584
$241$	17.3023	1.11454	0.557268	−	0.830332i	$-0.311849\pi$
$241$	17.3023	1.11454	0.557268	+	0.830332i	$0.311849\pi$
$242$	22.5944	1.45242
$243$	−9.34720	−0.599623
$244$	12.6467	0.809624
$245$	1.13454	0.0724832
$246$	−0.745937	−0.0475592
$247$	−1.38750	−0.0882847
$248$	7.42995	0.471802
$249$	2.14668	0.136040
$250$	−9.88505	−0.625185
$251$	−20.6124	−1.30104	−0.650520	−	0.759489i	$-0.725449\pi$
$251$	−20.6124	−1.30104	−0.650520	+	0.759489i	$0.725449\pi$
$252$	−2.86449	−0.180446
$253$	25.9980	1.63448
$254$	21.9218	1.37549
$255$	0.561565	0.0351665
$256$	1.00000	0.0625000
$257$	22.6409	1.41230	0.706152	−	0.708061i	$-0.250430\pi$
$257$	22.6409	1.41230	0.706152	+	0.708061i	$0.250430\pi$
$258$	1.65352	0.102944
$259$	−9.37015	−0.582233
$260$	3.24098	0.200997
$261$	−4.89014	−0.302692
$262$	20.5229	1.26791
$263$	27.5276	1.69743	0.848713	−	0.528854i	$-0.177378\pi$
$263$	27.5276	1.69743	0.848713	+	0.528854i	$0.177378\pi$
$264$	−2.13360	−0.131314
$265$	4.27758	0.262770
$266$	−0.485712	−0.0297809
$267$	6.88337	0.421255
$268$	12.0924	0.738660
$269$	−6.06301	−0.369668	−0.184834	−	0.982770i	$-0.559175\pi$
$269$	−6.06301	−0.369668	−0.184834	+	0.982770i	$0.559175\pi$
$270$	2.44924	0.149056
$271$	−13.0667	−0.793745	−0.396873	−	0.917874i	$-0.629905\pi$
$271$	−13.0667	−0.793745	−0.396873	+	0.917874i	$0.629905\pi$
$272$	−1.34462	−0.0815296
$273$	−1.05156	−0.0636434
$274$	−16.2484	−0.981601
$275$	−21.5197	−1.29769
$276$	−1.65115	−0.0993877
$277$	7.96433	0.478530	0.239265	−	0.970954i	$-0.423093\pi$
$277$	7.96433	0.478530	0.239265	+	0.970954i	$0.423093\pi$
$278$	3.04733	0.182767
$279$	−21.2831	−1.27418
$280$	1.13454	0.0678018
$281$	1.69923	0.101368	0.0506839	−	0.998715i	$-0.483860\pi$
$281$	1.69923	0.101368	0.0506839	+	0.998715i	$0.483860\pi$
$282$	−1.46423	−0.0871934
$283$	−26.6515	−1.58427	−0.792134	−	0.610347i	$-0.791030\pi$
$283$	−26.6515	−1.58427	−0.792134	+	0.610347i	$0.791030\pi$
$284$	2.75732	0.163617
$285$	0.202852	0.0120159
$286$	16.5573	0.979051
$287$	2.02639	0.119614
$288$	−2.86449	−0.168792
$289$	−15.1920	−0.893647
$290$	1.93684	0.113735
$291$	1.38625	0.0812631
$292$	−4.42449	−0.258923
$293$	23.1474	1.35228	0.676142	−	0.736771i	$-0.263651\pi$
$293$	23.1474	1.35228	0.676142	+	0.736771i	$0.263651\pi$
$294$	−0.368112	−0.0214687
$295$	−4.32273	−0.251679
$296$	−9.37015	−0.544629
$297$	12.5125	0.726048
$298$	−0.663423	−0.0384310
$299$	12.8134	0.741016
$300$	1.36673	0.0789083
$301$	−4.49189	−0.258908
$302$	14.7966	0.851448
$303$	−1.32472	−0.0761032
$304$	−0.485712	−0.0278575
$305$	14.3482	0.821578
$306$	3.85166	0.220185
$307$	−8.65532	−0.493985	−0.246993	−	0.969017i	$-0.579442\pi$
$307$	−8.65532	−0.493985	−0.246993	+	0.969017i	$0.579442\pi$
$308$	5.79606	0.330261
$309$	5.94179	0.338017
$310$	8.42959	0.478768
$311$	−16.8294	−0.954307	−0.477153	−	0.878820i	$-0.658331\pi$
$311$	−16.8294	−0.954307	−0.477153	+	0.878820i	$0.658331\pi$
$312$	−1.05156	−0.0595330
$313$	10.5999	0.599144	0.299572	−	0.954074i	$-0.403156\pi$
$313$	10.5999	0.599144	0.299572	+	0.954074i	$0.403156\pi$
$314$	−4.79697	−0.270709
$315$	−3.24989	−0.183110
$316$	−2.93789	−0.165269
$317$	19.5631	1.09877	0.549386	−	0.835569i	$-0.314862\pi$
$317$	19.5631	1.09877	0.549386	+	0.835569i	$0.314862\pi$
$318$	−1.38790	−0.0778295
$319$	9.89480	0.554002
$320$	1.13454	0.0634228
$321$	1.29857	0.0724790
$322$	4.48547	0.249965
$323$	0.653098	0.0363394
$324$	7.79881	0.433267
$325$	−10.6062	−0.588325
$326$	15.8145	0.875884
$327$	−3.21729	−0.177917
$328$	2.02639	0.111889
$329$	3.97767	0.219296
$330$	−2.42066	−0.133253
$331$	−0.271910	−0.0149455	−0.00747277	−	0.999972i	$-0.502379\pi$
$331$	−0.271910	−0.0149455	−0.00747277	+	0.999972i	$0.502379\pi$
$332$	−5.83159	−0.320050
$333$	26.8407	1.47086
$334$	8.90169	0.487079
$335$	13.7193	0.749567
$336$	−0.368112	−0.0200821
$337$	−3.76358	−0.205015	−0.102508	−	0.994732i	$-0.532687\pi$
$337$	−3.76358	−0.205015	−0.102508	+	0.994732i	$0.532687\pi$
$338$	−4.83961	−0.263240
$339$	4.23113	0.229803
$340$	−1.52553	−0.0827334
$341$	43.0645	2.33207
$342$	1.39132	0.0752339
$343$	1.00000	0.0539949
$344$	−4.49189	−0.242187
$345$	−1.87330	−0.100855
$346$	−13.2604	−0.712884
$347$	−13.1793	−0.707501	−0.353750	−	0.935340i	$-0.615094\pi$
$347$	−13.1793	−0.707501	−0.353750	+	0.935340i	$0.615094\pi$
$348$	−0.628425	−0.0336871
$349$	5.26956	0.282073	0.141036	−	0.990004i	$-0.454957\pi$
$349$	5.26956	0.282073	0.141036	+	0.990004i	$0.454957\pi$
$350$	−3.71282	−0.198458
$351$	6.16688	0.329164
$352$	5.79606	0.308931
$353$	−9.72707	−0.517720	−0.258860	−	0.965915i	$-0.583347\pi$
$353$	−9.72707	−0.517720	−0.258860	+	0.965915i	$0.583347\pi$
$354$	1.40255	0.0745445
$355$	3.12829	0.166032
$356$	−18.6991	−0.991052
$357$	0.494971	0.0261966
$358$	13.9037	0.734835
$359$	28.6336	1.51123	0.755613	−	0.655019i	$-0.227339\pi$
$359$	28.6336	1.51123	0.755613	+	0.655019i	$0.227339\pi$
$360$	−3.24989	−0.171284
$361$	−18.7641	−0.987583
$362$	5.09657	0.267870
$363$	−8.31725	−0.436542
$364$	2.85664	0.149729
$365$	−5.01976	−0.262746
$366$	−4.65541	−0.243342
$367$	20.2733	1.05826	0.529128	−	0.848542i	$-0.322519\pi$
$367$	20.2733	1.05826	0.529128	+	0.848542i	$0.322519\pi$
$368$	4.48547	0.233821
$369$	−5.80457	−0.302174
$370$	−10.6308	−0.552670
$371$	3.77032	0.195745
$372$	−2.73505	−0.141806
$373$	−13.1982	−0.683377	−0.341689	−	0.939813i	$-0.610999\pi$
$373$	−13.1982	−0.683377	−0.341689	+	0.939813i	$0.610999\pi$
$374$	−7.79351	−0.402993
$375$	3.63880	0.187907
$376$	3.97767	0.205132
$377$	4.87673	0.251165
$378$	2.15879	0.111036
$379$	0.000193948 0	9.96242e−6 0	4.98121e−6	−	1.00000i	$-0.499998\pi$
$379$	0.000193948 0	9.96242e−6 0	4.98121e−6		1.00000i	$0.499998\pi$
$380$	−0.551060	−0.0282688
$381$	−8.06965	−0.413421
$382$	15.5332	0.794747
$383$	−13.1112	−0.669953	−0.334977	−	0.942226i	$-0.608728\pi$
$383$	−13.1112	−0.669953	−0.334977	+	0.942226i	$0.608728\pi$
$384$	−0.368112	−0.0187851
$385$	6.57587	0.335138
$386$	12.4585	0.634121
$387$	12.8670	0.654066
$388$	−3.76583	−0.191181
$389$	12.6542	0.641594	0.320797	−	0.947148i	$-0.396049\pi$
$389$	12.6542	0.641594	0.320797	+	0.947148i	$0.396049\pi$
$390$	−1.19304	−0.0604120
$391$	−6.03125	−0.305013
$392$	1.00000	0.0505076
$393$	−7.55471	−0.381085
$394$	1.42952	0.0720183
$395$	−3.33315	−0.167709
$396$	−16.6028	−0.834321
$397$	−6.08136	−0.305215	−0.152607	−	0.988287i	$-0.548767\pi$
$397$	−6.08136	−0.305215	−0.152607	+	0.988287i	$0.548767\pi$
$398$	7.40057	0.370957
$399$	0.178796	0.00895101
$400$	−3.71282	−0.185641
$401$	16.2816	0.813066	0.406533	−	0.913636i	$-0.366738\pi$
$401$	16.2816	0.813066	0.406533	+	0.913636i	$0.366738\pi$
$402$	−4.45135	−0.222013
$403$	21.2247	1.05728
$404$	3.59869	0.179042
$405$	8.84807	0.439664
$406$	1.70716	0.0847248
$407$	−54.3100	−2.69205
$408$	0.494971	0.0245047
$409$	−17.8675	−0.883491	−0.441746	−	0.897140i	$-0.645641\pi$
$409$	−17.8675	−0.883491	−0.441746	+	0.897140i	$0.645641\pi$
$410$	2.29902	0.113541
$411$	5.98122	0.295032
$412$	−16.1413	−0.795224
$413$	−3.81011	−0.187483
$414$	−12.8486	−0.631474
$415$	−6.61618	−0.324776
$416$	2.85664	0.140058
$417$	−1.12176	−0.0549327
$418$	−2.81522	−0.137697
$419$	29.4177	1.43715	0.718575	−	0.695450i	$-0.244795\pi$
$419$	29.4177	1.43715	0.718575	+	0.695450i	$0.244795\pi$
$420$	−0.417638	−0.0203786
$421$	3.86381	0.188311	0.0941554	−	0.995558i	$-0.469985\pi$
$421$	3.86381	0.188311	0.0941554	+	0.995558i	$0.469985\pi$
$422$	−12.8753	−0.626761
$423$	−11.3940	−0.553995
$424$	3.77032	0.183103
$425$	4.99233	0.242164
$426$	−1.01500	−0.0491769
$427$	12.6467	0.612018
$428$	−3.52764	−0.170515
$429$	−6.09492	−0.294266
$430$	−5.09624	−0.245762
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	2.15879	0.103865
$433$	−18.8715	−0.906907	−0.453454	−	0.891280i	$-0.649808\pi$
$433$	−18.8715	−0.906907	−0.453454	+	0.891280i	$0.649808\pi$
$434$	7.42995	0.356649
$435$	−0.712974	−0.0341845
$436$	8.73999	0.418569
$437$	−2.17864	−0.104219
$438$	1.62870	0.0778225
$439$	5.23695	0.249946	0.124973	−	0.992160i	$-0.460116\pi$
$439$	5.23695	0.249946	0.124973	+	0.992160i	$0.460116\pi$
$440$	6.57587	0.313492
$441$	−2.86449	−0.136404
$442$	−3.84110	−0.182702
$443$	−36.5891	−1.73840	−0.869200	−	0.494460i	$-0.835366\pi$
$443$	−36.5891	−1.73840	−0.869200	+	0.494460i	$0.835366\pi$
$444$	3.44926	0.163695
$445$	−21.2149	−1.00568
$446$	15.0335	0.711856
$447$	0.244214	0.0115509
$448$	1.00000	0.0472456
$449$	27.1928	1.28331	0.641654	−	0.766994i	$-0.278248\pi$
$449$	27.1928	1.28331	0.641654	+	0.766994i	$0.278248\pi$
$450$	10.6353	0.501355
$451$	11.7451	0.553054
$452$	−11.4941	−0.540639
$453$	−5.44680	−0.255913
$454$	−21.0298	−0.986976
$455$	3.24098	0.151939
$456$	0.178796	0.00837290
$457$	29.4826	1.37914	0.689568	−	0.724221i	$-0.257800\pi$
$457$	29.4826	1.37914	0.689568	+	0.724221i	$0.257800\pi$
$458$	−11.3592	−0.530779
$459$	−2.90275	−0.135489
$460$	5.08895	0.237273
$461$	−19.1793	−0.893268	−0.446634	−	0.894717i	$-0.647377\pi$
$461$	−19.1793	−0.893268	−0.446634	+	0.894717i	$0.647377\pi$
$462$	−2.13360	−0.0992640
$463$	−32.1264	−1.49304	−0.746520	−	0.665363i	$-0.768277\pi$
$463$	−32.1264	−1.49304	−0.746520	+	0.665363i	$0.768277\pi$
$464$	1.70716	0.0792528
$465$	−3.10303	−0.143900
$466$	−19.2885	−0.893524
$467$	−22.1444	−1.02472	−0.512360	−	0.858771i	$-0.671229\pi$
$467$	−22.1444	−1.02472	−0.512360	+	0.858771i	$0.671229\pi$
$468$	−8.18282	−0.378251
$469$	12.0924	0.558375
$470$	4.51283	0.208161
$471$	1.76582	0.0813647
$472$	−3.81011	−0.175374
$473$	−26.0353	−1.19710
$474$	1.08147	0.0496736
$475$	1.80336	0.0827438
$476$	−1.34462	−0.0616306
$477$	−10.8001	−0.494500
$478$	−3.35793	−0.153588
$479$	7.34482	0.335593	0.167797	−	0.985822i	$-0.446335\pi$
$479$	7.34482	0.335593	0.167797	+	0.985822i	$0.446335\pi$
$480$	−0.417638	−0.0190625
$481$	−26.7671	−1.22048
$482$	17.3023	0.788096
$483$	−1.65115	−0.0751300
$484$	22.5944	1.02702
$485$	−4.27249	−0.194004
$486$	−9.34720	−0.423998
$487$	−23.7224	−1.07497	−0.537483	−	0.843275i	$-0.680625\pi$
$487$	−23.7224	−1.07497	−0.537483	+	0.843275i	$0.680625\pi$
$488$	12.6467	0.572491
$489$	−5.82150	−0.263257
$490$	1.13454	0.0512534
$491$	−30.9071	−1.39482	−0.697409	−	0.716674i	$-0.745664\pi$
$491$	−30.9071	−1.39482	−0.697409	+	0.716674i	$0.745664\pi$
$492$	−0.745937	−0.0336294
$493$	−2.29548	−0.103383
$494$	−1.38750	−0.0624267
$495$	−18.8365	−0.846640
$496$	7.42995	0.333615
$497$	2.75732	0.123682
$498$	2.14668	0.0961949
$499$	−21.4916	−0.962094	−0.481047	−	0.876695i	$-0.659743\pi$
$499$	−21.4916	−0.962094	−0.481047	+	0.876695i	$0.659743\pi$
$500$	−9.88505	−0.442073
$501$	−3.27682	−0.146397
$502$	−20.6124	−0.919975
$503$	43.8579	1.95553	0.977763	−	0.209714i	$-0.0672534\pi$
$503$	43.8579	1.95553	0.977763	+	0.209714i	$0.0672534\pi$
$504$	−2.86449	−0.127595
$505$	4.08286	0.181685
$506$	25.9980	1.15575
$507$	1.78152	0.0791200
$508$	21.9218	0.972620
$509$	−4.49591	−0.199278	−0.0996389	−	0.995024i	$-0.531769\pi$
$509$	−4.49591	−0.199278	−0.0996389	+	0.995024i	$0.531769\pi$
$510$	0.561565	0.0248665
$511$	−4.42449	−0.195728
$512$	1.00000	0.0441942
$513$	−1.04855	−0.0462946
$514$	22.6409	0.998649
$515$	−18.3129	−0.806965
$516$	1.65352	0.0727921
$517$	23.0548	1.01395
$518$	−9.37015	−0.411701
$519$	4.88131	0.214266
$520$	3.24098	0.142126
$521$	−8.55757	−0.374914	−0.187457	−	0.982273i	$-0.560024\pi$
$521$	−8.55757	−0.374914	−0.187457	+	0.982273i	$0.560024\pi$
$522$	−4.89014	−0.214036
$523$	16.7115	0.730745	0.365372	−	0.930861i	$-0.380942\pi$
$523$	16.7115	0.730745	0.365372	+	0.930861i	$0.380942\pi$
$524$	20.5229	0.896546
$525$	1.36673	0.0596490
$526$	27.5276	1.20026
$527$	−9.99047	−0.435192
$528$	−2.13360	−0.0928530
$529$	−2.88060	−0.125243
$530$	4.27758	0.185806
$531$	10.9140	0.473629
$532$	−0.485712	−0.0210583
$533$	5.78866	0.250735
$534$	6.88337	0.297872
$535$	−4.00226	−0.173033
$536$	12.0924	0.522312
$537$	−5.11813	−0.220863
$538$	−6.06301	−0.261395
$539$	5.79606	0.249654
$540$	2.44924	0.105398
$541$	36.8481	1.58422	0.792111	−	0.610377i	$-0.208982\pi$
$541$	36.8481	1.58422	0.792111	+	0.610377i	$0.208982\pi$
$542$	−13.0667	−0.561263
$543$	−1.87611	−0.0805114
$544$	−1.34462	−0.0576501
$545$	9.91588	0.424750
$546$	−1.05156	−0.0450027
$547$	−7.93343	−0.339209	−0.169605	−	0.985512i	$-0.554249\pi$
$547$	−7.93343	−0.339209	−0.169605	+	0.985512i	$0.554249\pi$
$548$	−16.2484	−0.694096
$549$	−36.2265	−1.54611
$550$	−21.5197	−0.917604
$551$	−0.829187	−0.0353245
$552$	−1.65115	−0.0702777
$553$	−2.93789	−0.124932
$554$	7.96433	0.338372
$555$	3.91333	0.166112
$556$	3.04733	0.129235
$557$	−6.14723	−0.260466	−0.130233	−	0.991483i	$-0.541573\pi$
$557$	−6.14723	−0.260466	−0.130233	+	0.991483i	$0.541573\pi$
$558$	−21.2831	−0.900983
$559$	−12.8317	−0.542724
$560$	1.13454	0.0479431
$561$	2.86888	0.121124
$562$	1.69923	0.0716778
$563$	−4.83489	−0.203766	−0.101883	−	0.994796i	$-0.532487\pi$
$563$	−4.83489	−0.203766	−0.101883	+	0.994796i	$0.532487\pi$
$564$	−1.46423	−0.0616550
$565$	−13.0406	−0.548621
$566$	−26.6515	−1.12025
$567$	7.79881	0.327519
$568$	2.75732	0.115694
$569$	−26.3919	−1.10641	−0.553204	−	0.833046i	$-0.686595\pi$
$569$	−26.3919	−1.10641	−0.553204	+	0.833046i	$0.686595\pi$
$570$	0.202852	0.00849652
$571$	17.1525	0.717811	0.358905	−	0.933374i	$-0.383150\pi$
$571$	17.1525	0.717811	0.358905	+	0.933374i	$0.383150\pi$
$572$	16.5573	0.692294
$573$	−5.71795	−0.238871
$574$	2.02639	0.0845798
$575$	−16.6537	−0.694508
$576$	−2.86449	−0.119354
$577$	30.5560	1.27206	0.636031	−	0.771664i	$-0.280575\pi$
$577$	30.5560	1.27206	0.636031	+	0.771664i	$0.280575\pi$
$578$	−15.1920	−0.631904
$579$	−4.58612	−0.190593
$580$	1.93684	0.0804230
$581$	−5.83159	−0.241935
$582$	1.38625	0.0574617
$583$	21.8530	0.905059
$584$	−4.42449	−0.183087
$585$	−9.28375	−0.383836
$586$	23.1474	0.956209
$587$	−30.0962	−1.24220	−0.621102	−	0.783730i	$-0.713315\pi$
$587$	−30.0962	−1.24220	−0.621102	+	0.783730i	$0.713315\pi$
$588$	−0.368112	−0.0151807
$589$	−3.60882	−0.148699
$590$	−4.32273	−0.177964
$591$	−0.526224	−0.0216460
$592$	−9.37015	−0.385111
$593$	2.34189	0.0961701	0.0480850	−	0.998843i	$-0.484688\pi$
$593$	2.34189	0.0961701	0.0480850	+	0.998843i	$0.484688\pi$
$594$	12.5125	0.513393
$595$	−1.52553	−0.0625405
$596$	−0.663423	−0.0271748
$597$	−2.72424	−0.111496
$598$	12.8134	0.523977
$599$	11.9817	0.489558	0.244779	−	0.969579i	$-0.421285\pi$
$599$	11.9817	0.489558	0.244779	+	0.969579i	$0.421285\pi$
$600$	1.36673	0.0557966
$601$	−33.0239	−1.34707	−0.673537	−	0.739153i	$-0.735226\pi$
$601$	−33.0239	−1.34707	−0.673537	+	0.739153i	$0.735226\pi$
$602$	−4.49189	−0.183076
$603$	−34.6386	−1.41059
$604$	14.7966	0.602065
$605$	25.6342	1.04218
$606$	−1.32472	−0.0538131
$607$	−41.6799	−1.69173	−0.845867	−	0.533394i	$-0.820916\pi$
$607$	−41.6799	−1.69173	−0.845867	+	0.533394i	$0.820916\pi$
$608$	−0.485712	−0.0196982
$609$	−0.628425	−0.0254651
$610$	14.3482	0.580943
$611$	11.3628	0.459688
$612$	3.85166	0.155694
$613$	−5.83716	−0.235761	−0.117880	−	0.993028i	$-0.537610\pi$
$613$	−5.83716	−0.235761	−0.117880	+	0.993028i	$0.537610\pi$
$614$	−8.65532	−0.349300
$615$	−0.846296	−0.0341260
$616$	5.79606	0.233530
$617$	42.9218	1.72796	0.863982	−	0.503522i	$-0.167963\pi$
$617$	42.9218	1.72796	0.863982	+	0.503522i	$0.167963\pi$
$618$	5.94179	0.239014
$619$	24.3270	0.977784	0.488892	−	0.872344i	$-0.337401\pi$
$619$	24.3270	0.977784	0.488892	+	0.872344i	$0.337401\pi$
$620$	8.42959	0.338540
$621$	9.68317	0.388572
$622$	−16.8294	−0.674797
$623$	−18.6991	−0.749165
$624$	−1.05156	−0.0420962
$625$	7.34908	0.293963
$626$	10.5999	0.423659
$627$	1.03631	0.0413864
$628$	−4.79697	−0.191420
$629$	12.5993	0.502367
$630$	−3.24989	−0.129479
$631$	−11.2415	−0.447518	−0.223759	−	0.974644i	$-0.571833\pi$
$631$	−11.2415	−0.447518	−0.223759	+	0.974644i	$0.571833\pi$
$632$	−2.93789	−0.116863
$633$	4.73956	0.188381
$634$	19.5631	0.776949
$635$	24.8711	0.986981
$636$	−1.38790	−0.0550337
$637$	2.85664	0.113184
$638$	9.89480	0.391739
$639$	−7.89831	−0.312452
$640$	1.13454	0.0448467
$641$	11.7569	0.464370	0.232185	−	0.972672i	$-0.425413\pi$
$641$	11.7569	0.464370	0.232185	+	0.972672i	$0.425413\pi$
$642$	1.29857	0.0512504
$643$	−27.1293	−1.06988	−0.534938	−	0.844891i	$-0.679665\pi$
$643$	−27.1293	−1.06988	−0.534938	+	0.844891i	$0.679665\pi$
$644$	4.48547	0.176752
$645$	1.87598	0.0738668
$646$	0.653098	0.0256958
$647$	1.96799	0.0773697	0.0386849	−	0.999251i	$-0.487683\pi$
$647$	1.96799	0.0773697	0.0386849	+	0.999251i	$0.487683\pi$
$648$	7.79881	0.306366
$649$	−22.0836	−0.866858
$650$	−10.6062	−0.416008
$651$	−2.73505	−0.107195
$652$	15.8145	0.619343
$653$	−28.5592	−1.11761	−0.558805	−	0.829299i	$-0.688740\pi$
$653$	−28.5592	−1.11761	−0.558805	+	0.829299i	$0.688740\pi$
$654$	−3.21729	−0.125806
$655$	23.2841	0.909783
$656$	2.02639	0.0791171
$657$	12.6739	0.494456
$658$	3.97767	0.155066
$659$	−29.5117	−1.14961	−0.574807	−	0.818289i	$-0.694923\pi$
$659$	−29.5117	−1.14961	−0.574807	+	0.818289i	$0.694923\pi$
$660$	−2.42066	−0.0942239
$661$	−40.6576	−1.58140	−0.790699	−	0.612206i	$-0.790283\pi$
$661$	−40.6576	−1.58140	−0.790699	+	0.612206i	$0.790283\pi$
$662$	−0.271910	−0.0105681
$663$	1.41395	0.0549134
$664$	−5.83159	−0.226310
$665$	−0.551060	−0.0213692
$666$	26.8407	1.04006
$667$	7.65740	0.296496
$668$	8.90169	0.344417
$669$	−5.53400	−0.213957
$670$	13.7193	0.530024
$671$	73.3013	2.82976
$672$	−0.368112	−0.0142002
$673$	30.9101	1.19150	0.595749	−	0.803170i	$-0.296855\pi$
$673$	30.9101	1.19150	0.595749	+	0.803170i	$0.296855\pi$
$674$	−3.76358	−0.144968
$675$	−8.01519	−0.308505
$676$	−4.83961	−0.186139
$677$	38.1903	1.46777	0.733886	−	0.679272i	$-0.237704\pi$
$677$	38.1903	1.46777	0.733886	+	0.679272i	$0.237704\pi$
$678$	4.23113	0.162495
$679$	−3.76583	−0.144519
$680$	−1.52553	−0.0585013
$681$	7.74131	0.296648
$682$	43.0645	1.64902
$683$	−34.4698	−1.31895	−0.659476	−	0.751726i	$-0.729222\pi$
$683$	−34.4698	−1.31895	−0.659476	+	0.751726i	$0.729222\pi$
$684$	1.39132	0.0531984
$685$	−18.4345	−0.704344
$686$	1.00000	0.0381802
$687$	4.18144	0.159532
$688$	−4.49189	−0.171252
$689$	10.7704	0.410321
$690$	−1.87330	−0.0713153
$691$	4.88671	0.185899	0.0929495	−	0.995671i	$-0.470370\pi$
$691$	4.88671	0.185899	0.0929495	+	0.995671i	$0.470370\pi$
$692$	−13.2604	−0.504085
$693$	−16.6028	−0.630688
$694$	−13.1793	−0.500279
$695$	3.45732	0.131144
$696$	−0.628425	−0.0238204
$697$	−2.72472	−0.103206
$698$	5.26956	0.199456
$699$	7.10034	0.268559
$700$	−3.71282	−0.140331
$701$	2.68351	0.101355	0.0506775	−	0.998715i	$-0.483862\pi$
$701$	2.68351	0.101355	0.0506775	+	0.998715i	$0.483862\pi$
$702$	6.16688	0.232754
$703$	4.55119	0.171652
$704$	5.79606	0.218447
$705$	−1.66122	−0.0625653
$706$	−9.72707	−0.366083
$707$	3.59869	0.135343
$708$	1.40255	0.0527109
$709$	30.6096	1.14957	0.574784	−	0.818305i	$-0.305086\pi$
$709$	30.6096	1.14957	0.574784	+	0.818305i	$0.305086\pi$
$710$	3.12829	0.117403
$711$	8.41556	0.315608
$712$	−18.6991	−0.700779
$713$	33.3268	1.24810
$714$	0.494971	0.0185238
$715$	18.7849	0.702515
$716$	13.9037	0.519607
$717$	1.23609	0.0461627
$718$	28.6336	1.06860
$719$	−50.2134	−1.87264	−0.936321	−	0.351144i	$-0.885793\pi$
$719$	−50.2134	−1.87264	−0.936321	+	0.351144i	$0.885793\pi$
$720$	−3.24989	−0.121116
$721$	−16.1413	−0.601132
$722$	−18.7641	−0.698327
$723$	−6.36917	−0.236872
$724$	5.09657	0.189412
$725$	−6.33836	−0.235401
$726$	−8.31725	−0.308682
$727$	−23.9977	−0.890024	−0.445012	−	0.895525i	$-0.646801\pi$
$727$	−23.9977	−0.890024	−0.445012	+	0.895525i	$0.646801\pi$
$728$	2.85664	0.105874
$729$	−19.9556	−0.739096
$730$	−5.01976	−0.185790
$731$	6.03989	0.223393
$732$	−4.65541	−0.172069
$733$	−38.8370	−1.43448	−0.717238	−	0.696828i	$-0.754594\pi$
$733$	−38.8370	−1.43448	−0.717238	+	0.696828i	$0.754594\pi$
$734$	20.2733	0.748301
$735$	−0.417638	−0.0154048
$736$	4.48547	0.165336
$737$	70.0883	2.58173
$738$	−5.80457	−0.213669
$739$	−9.53029	−0.350577	−0.175289	−	0.984517i	$-0.556086\pi$
$739$	−9.53029	−0.350577	−0.175289	+	0.984517i	$0.556086\pi$
$740$	−10.6308	−0.390797
$741$	0.510756	0.0187631
$742$	3.77032	0.138413
$743$	8.14379	0.298767	0.149383	−	0.988779i	$-0.452271\pi$
$743$	8.14379	0.298767	0.149383	+	0.988779i	$0.452271\pi$
$744$	−2.73505	−0.100272
$745$	−0.752680	−0.0275761
$746$	−13.1982	−0.483221
$747$	16.7046	0.611188
$748$	−7.79351	−0.284959
$749$	−3.52764	−0.128897
$750$	3.63880	0.132870
$751$	−16.6622	−0.608011	−0.304005	−	0.952670i	$-0.598324\pi$
$751$	−16.6622	−0.608011	−0.304005	+	0.952670i	$0.598324\pi$
$752$	3.97767	0.145051
$753$	7.58765	0.276509
$754$	4.87673	0.177600
$755$	16.7874	0.610954
$756$	2.15879	0.0785144
$757$	29.1867	1.06081	0.530404	−	0.847745i	$-0.322040\pi$
$757$	29.1867	1.06081	0.530404	+	0.847745i	$0.322040\pi$
$758$	0.000193948 0	7.04449e−6 0
$759$	−9.57019	−0.347376
$760$	−0.551060	−0.0199891
$761$	10.3401	0.374828	0.187414	−	0.982281i	$-0.439989\pi$
$761$	10.3401	0.374828	0.187414	+	0.982281i	$0.439989\pi$
$762$	−8.06965	−0.292333
$763$	8.73999	0.316409
$764$	15.5332	0.561971
$765$	4.36986	0.157993
$766$	−13.1112	−0.473729
$767$	−10.8841	−0.393002
$768$	−0.368112	−0.0132831
$769$	−35.4301	−1.27764	−0.638822	−	0.769355i	$-0.720578\pi$
$769$	−35.4301	−1.27764	−0.638822	+	0.769355i	$0.720578\pi$
$770$	6.57587	0.236978
$771$	−8.33440	−0.300156
$772$	12.4585	0.448391
$773$	−42.9331	−1.54419	−0.772097	−	0.635504i	$-0.780792\pi$
$773$	−42.9331	−1.54419	−0.772097	+	0.635504i	$0.780792\pi$
$774$	12.8670	0.462495
$775$	−27.5860	−0.990920
$776$	−3.76583	−0.135185
$777$	3.44926	0.123742
$778$	12.6542	0.453675
$779$	−0.984240	−0.0352641
$780$	−1.19304	−0.0427177
$781$	15.9816	0.571866
$782$	−6.03125	−0.215677
$783$	3.68539	0.131705
$784$	1.00000	0.0357143
$785$	−5.44236	−0.194246
$786$	−7.55471	−0.269468
$787$	28.4754	1.01504	0.507520	−	0.861640i	$-0.330562\pi$
$787$	28.4754	1.01504	0.507520	+	0.861640i	$0.330562\pi$
$788$	1.42952	0.0509246
$789$	−10.1332	−0.360753
$790$	−3.33315	−0.118588
$791$	−11.4941	−0.408684
$792$	−16.6028	−0.589954
$793$	36.1272	1.28291
$794$	−6.08136	−0.215820
$795$	−1.57463	−0.0558463
$796$	7.40057	0.262306
$797$	−19.2742	−0.682726	−0.341363	−	0.939932i	$-0.610889\pi$
$797$	−19.2742	−0.682726	−0.341363	+	0.939932i	$0.610889\pi$
$798$	0.178796	0.00632932
$799$	−5.34845	−0.189215
$800$	−3.71282	−0.131268
$801$	53.5635	1.89257
$802$	16.2816	0.574924
$803$	−25.6446	−0.904978
$804$	−4.45135	−0.156987
$805$	5.08895	0.179362
$806$	21.2247	0.747608
$807$	2.23187	0.0785654
$808$	3.59869	0.126602
$809$	−5.30625	−0.186558	−0.0932790	−	0.995640i	$-0.529735\pi$
$809$	−5.30625	−0.186558	−0.0932790	+	0.995640i	$0.529735\pi$
$810$	8.84807	0.310889
$811$	−29.8608	−1.04856	−0.524278	−	0.851547i	$-0.675665\pi$
$811$	−29.8608	−1.04856	−0.524278	+	0.851547i	$0.675665\pi$
$812$	1.70716	0.0599095
$813$	4.81000	0.168694
$814$	−54.3100	−1.90356
$815$	17.9422	0.628488
$816$	0.494971	0.0173274
$817$	2.18177	0.0763303
$818$	−17.8675	−0.624723
$819$	−8.18282	−0.285931
$820$	2.29902	0.0802853
$821$	23.4726	0.819198	0.409599	−	0.912266i	$-0.365669\pi$
$821$	23.4726	0.819198	0.409599	+	0.912266i	$0.365669\pi$
$822$	5.98122	0.208619
$823$	35.4762	1.23662	0.618312	−	0.785933i	$-0.287817\pi$
$823$	35.4762	1.23662	0.618312	+	0.785933i	$0.287817\pi$
$824$	−16.1413	−0.562308
$825$	7.92166	0.275797
$826$	−3.81011	−0.132571
$827$	−54.8060	−1.90579	−0.952895	−	0.303299i	$-0.901912\pi$
$827$	−54.8060	−1.90579	−0.952895	+	0.303299i	$0.901912\pi$
$828$	−12.8486	−0.446519
$829$	−18.3867	−0.638596	−0.319298	−	0.947654i	$-0.603447\pi$
$829$	−18.3867	−0.638596	−0.319298	+	0.947654i	$0.603447\pi$
$830$	−6.61618	−0.229651
$831$	−2.93176	−0.101702
$832$	2.85664	0.0990361
$833$	−1.34462	−0.0465883
$834$	−1.12176	−0.0388433
$835$	10.0993	0.349502
$836$	−2.81522	−0.0973663
$837$	16.0397	0.554413
$838$	29.4177	1.01622
$839$	−18.2569	−0.630297	−0.315148	−	0.949042i	$-0.602054\pi$
$839$	−18.2569	−0.630297	−0.315148	+	0.949042i	$0.602054\pi$
$840$	−0.417638	−0.0144099
$841$	−26.0856	−0.899504
$842$	3.86381	0.133156
$843$	−0.625508	−0.0215436
$844$	−12.8753	−0.443187
$845$	−5.49074	−0.188887
$846$	−11.3940	−0.391734
$847$	22.5944	0.776351
$848$	3.77032	0.129473
$849$	9.81074	0.336704
$850$	4.99233	0.171235
$851$	−42.0295	−1.44075
$852$	−1.01500	−0.0347733
$853$	−30.1363	−1.03185	−0.515924	−	0.856634i	$-0.672551\pi$
$853$	−30.1363	−1.03185	−0.515924	+	0.856634i	$0.672551\pi$
$854$	12.6467	0.432762
$855$	1.57851	0.0539838
$856$	−3.52764	−0.120572
$857$	9.92884	0.339163	0.169581	−	0.985516i	$-0.445758\pi$
$857$	9.92884	0.339163	0.169581	+	0.985516i	$0.445758\pi$
$858$	−6.09492	−0.208077
$859$	−20.7668	−0.708555	−0.354277	−	0.935140i	$-0.615273\pi$
$859$	−20.7668	−0.708555	−0.354277	+	0.935140i	$0.615273\pi$
$860$	−5.09624	−0.173780
$861$	−0.745937	−0.0254215
$862$	1.00000	0.0340601
$863$	22.3635	0.761263	0.380632	−	0.924727i	$-0.375707\pi$
$863$	22.3635	0.761263	0.380632	+	0.924727i	$0.375707\pi$
$864$	2.15879	0.0734435
$865$	−15.0445	−0.511528
$866$	−18.8715	−0.641280
$867$	5.59235	0.189926
$868$	7.42995	0.252189
$869$	−17.0282	−0.577641
$870$	−0.712974	−0.0241721
$871$	34.5436	1.17047
$872$	8.73999	0.295973
$873$	10.7872	0.365091
$874$	−2.17864	−0.0736937
$875$	−9.88505	−0.334176
$876$	1.62870	0.0550288
$877$	52.6170	1.77675	0.888374	−	0.459120i	$-0.151835\pi$
$877$	52.6170	1.77675	0.888374	+	0.459120i	$0.151835\pi$
$878$	5.23695	0.176738
$879$	−8.52082	−0.287400
$880$	6.57587	0.221673
$881$	−35.5250	−1.19687	−0.598434	−	0.801172i	$-0.704210\pi$
$881$	−35.5250	−1.19687	−0.598434	+	0.801172i	$0.704210\pi$
$882$	−2.86449	−0.0964525
$883$	−47.4973	−1.59841	−0.799205	−	0.601058i	$-0.794746\pi$
$883$	−47.4973	−1.59841	−0.799205	+	0.601058i	$0.794746\pi$
$884$	−3.84110	−0.129190
$885$	1.59125	0.0534892
$886$	−36.5891	−1.22923
$887$	−15.0992	−0.506982	−0.253491	−	0.967338i	$-0.581579\pi$
$887$	−15.0992	−0.506982	−0.253491	+	0.967338i	$0.581579\pi$
$888$	3.44926	0.115750
$889$	21.9218	0.735232
$890$	−21.2149	−0.711126
$891$	45.2024	1.51434
$892$	15.0335	0.503358
$893$	−1.93200	−0.0646519
$894$	0.244214	0.00816773
$895$	15.7744	0.527279
$896$	1.00000	0.0334077
$897$	−4.71675	−0.157488
$898$	27.1928	0.907436
$899$	12.6841	0.423039
$900$	10.6353	0.354511
$901$	−5.06965	−0.168894
$902$	11.7451	0.391068
$903$	1.65352	0.0550256
$904$	−11.4941	−0.382289
$905$	5.78227	0.192209
$906$	−5.44680	−0.180958
$907$	−17.3688	−0.576720	−0.288360	−	0.957522i	$-0.593110\pi$
$907$	−17.3688	−0.576720	−0.288360	+	0.957522i	$0.593110\pi$
$908$	−21.0298	−0.697898
$909$	−10.3084	−0.341909
$910$	3.24098	0.107437
$911$	−34.9035	−1.15641	−0.578203	−	0.815893i	$-0.696246\pi$
$911$	−34.9035	−1.15641	−0.578203	+	0.815893i	$0.696246\pi$
$912$	0.178796	0.00592053
$913$	−33.8003	−1.11863
$914$	29.4826	0.975197
$915$	−5.28176	−0.174610
$916$	−11.3592	−0.375317
$917$	20.5229	0.677725
$918$	−2.90275	−0.0958051
$919$	38.6712	1.27564	0.637822	−	0.770184i	$-0.279836\pi$
$919$	38.6712	1.27564	0.637822	+	0.770184i	$0.279836\pi$
$920$	5.08895	0.167778
$921$	3.18613	0.104986
$922$	−19.1793	−0.631636
$923$	7.87665	0.259263
$924$	−2.13360	−0.0701903
$925$	34.7896	1.14388
$926$	−32.1264	−1.05574
$927$	46.2366	1.51861
$928$	1.70716	0.0560402
$929$	−6.94741	−0.227937	−0.113969	−	0.993484i	$-0.536356\pi$
$929$	−6.94741	−0.227937	−0.113969	+	0.993484i	$0.536356\pi$
$930$	−3.10303	−0.101752
$931$	−0.485712	−0.0159186
$932$	−19.2885	−0.631817
$933$	6.19509	0.202818
$934$	−22.1444	−0.724586
$935$	−8.84206	−0.289166
$936$	−8.18282	−0.267464
$937$	−33.9373	−1.10868	−0.554341	−	0.832290i	$-0.687030\pi$
$937$	−33.9373	−1.10868	−0.554341	+	0.832290i	$0.687030\pi$
$938$	12.0924	0.394831
$939$	−3.90196	−0.127336
$940$	4.51283	0.147192
$941$	−25.7126	−0.838206	−0.419103	−	0.907939i	$-0.637655\pi$
$941$	−25.7126	−0.838206	−0.419103	+	0.907939i	$0.637655\pi$
$942$	1.76582	0.0575335
$943$	9.08929	0.295988
$944$	−3.81011	−0.124008
$945$	2.44924	0.0796736
$946$	−26.0353	−0.846480
$947$	43.7250	1.42087	0.710435	−	0.703763i	$-0.248498\pi$
$947$	43.7250	1.42087	0.710435	+	0.703763i	$0.248498\pi$
$948$	1.08147	0.0351245
$949$	−12.6392	−0.410284
$950$	1.80336	0.0585087
$951$	−7.20140	−0.233521
$952$	−1.34462	−0.0435794
$953$	−46.1728	−1.49568	−0.747841	−	0.663878i	$-0.768910\pi$
$953$	−46.1728	−1.49568	−0.747841	+	0.663878i	$0.768910\pi$
$954$	−10.8001	−0.349665
$955$	17.6230	0.570268
$956$	−3.35793	−0.108603
$957$	−3.64239	−0.117742
$958$	7.34482	0.237300
$959$	−16.2484	−0.524688
$960$	−0.417638	−0.0134792
$961$	24.2042	0.780780
$962$	−26.7671	−0.863007
$963$	10.1049	0.325626
$964$	17.3023	0.557268
$965$	14.1347	0.455011
$966$	−1.65115	−0.0531250
$967$	−19.1892	−0.617084	−0.308542	−	0.951211i	$-0.599841\pi$
$967$	−19.1892	−0.617084	−0.308542	+	0.951211i	$0.599841\pi$
$968$	22.5944	0.726210
$969$	−0.240413	−0.00772318
$970$	−4.27249	−0.137181
$971$	16.7193	0.536549	0.268274	−	0.963343i	$-0.413547\pi$
$971$	16.7193	0.536549	0.268274	+	0.963343i	$0.413547\pi$
$972$	−9.34720	−0.299812
$973$	3.04733	0.0976928
$974$	−23.7224	−0.760116
$975$	3.90426	0.125036
$976$	12.6467	0.404812
$977$	−42.0530	−1.34539	−0.672697	−	0.739918i	$-0.734864\pi$
$977$	−42.0530	−1.34539	−0.672697	+	0.739918i	$0.734864\pi$
$978$	−5.82150	−0.186151
$979$	−108.381	−3.46388
$980$	1.13454	0.0362416
$981$	−25.0356	−0.799326
$982$	−30.9071	−0.986285
$983$	47.9863	1.53052	0.765262	−	0.643719i	$-0.222609\pi$
$983$	47.9863	1.53052	0.765262	+	0.643719i	$0.222609\pi$
$984$	−0.745937	−0.0237796
$985$	1.62185	0.0516765
$986$	−2.29548	−0.0731030
$987$	−1.46423	−0.0466068
$988$	−1.38750	−0.0441424
$989$	−20.1482	−0.640676
$990$	−18.8365	−0.598665
$991$	18.7532	0.595714	0.297857	−	0.954610i	$-0.403728\pi$
$991$	18.7532	0.595714	0.297857	+	0.954610i	$0.403728\pi$
$992$	7.42995	0.235901
$993$	0.100093	0.00317637
$994$	2.75732	0.0874567
$995$	8.39625	0.266179
$996$	2.14668	0.0680201
$997$	−30.1783	−0.955756	−0.477878	−	0.878426i	$-0.658594\pi$
$997$	−30.1783	−0.955756	−0.477878	+	0.878426i	$0.658594\pi$
$998$	−21.4916	−0.680303
$999$	−20.2282	−0.639991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.14	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.368112 q^{3} +1.00000 q^{4} +1.13454 q^{5} -0.368112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.86449 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.368112 q^{3} +1.00000 q^{4} +1.13454 q^{5} -0.368112 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.86449 q^{9} +1.13454 q^{10} +5.79606 q^{11} -0.368112 q^{12} +2.85664 q^{13} +1.00000 q^{14} -0.417638 q^{15} +1.00000 q^{16} -1.34462 q^{17} -2.86449 q^{18} -0.485712 q^{19} +1.13454 q^{20} -0.368112 q^{21} +5.79606 q^{22} +4.48547 q^{23} -0.368112 q^{24} -3.71282 q^{25} +2.85664 q^{26} +2.15879 q^{27} +1.00000 q^{28} +1.70716 q^{29} -0.417638 q^{30} +7.42995 q^{31} +1.00000 q^{32} -2.13360 q^{33} -1.34462 q^{34} +1.13454 q^{35} -2.86449 q^{36} -9.37015 q^{37} -0.485712 q^{38} -1.05156 q^{39} +1.13454 q^{40} +2.02639 q^{41} -0.368112 q^{42} -4.49189 q^{43} +5.79606 q^{44} -3.24989 q^{45} +4.48547 q^{46} +3.97767 q^{47} -0.368112 q^{48} +1.00000 q^{49} -3.71282 q^{50} +0.494971 q^{51} +2.85664 q^{52} +3.77032 q^{53} +2.15879 q^{54} +6.57587 q^{55} +1.00000 q^{56} +0.178796 q^{57} +1.70716 q^{58} -3.81011 q^{59} -0.417638 q^{60} +12.6467 q^{61} +7.42995 q^{62} -2.86449 q^{63} +1.00000 q^{64} +3.24098 q^{65} -2.13360 q^{66} +12.0924 q^{67} -1.34462 q^{68} -1.65115 q^{69} +1.13454 q^{70} +2.75732 q^{71} -2.86449 q^{72} -4.42449 q^{73} -9.37015 q^{74} +1.36673 q^{75} -0.485712 q^{76} +5.79606 q^{77} -1.05156 q^{78} -2.93789 q^{79} +1.13454 q^{80} +7.79881 q^{81} +2.02639 q^{82} -5.83159 q^{83} -0.368112 q^{84} -1.52553 q^{85} -4.49189 q^{86} -0.628425 q^{87} +5.79606 q^{88} -18.6991 q^{89} -3.24989 q^{90} +2.85664 q^{91} +4.48547 q^{92} -2.73505 q^{93} +3.97767 q^{94} -0.551060 q^{95} -0.368112 q^{96} -3.76583 q^{97} +1.00000 q^{98} -16.6028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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