LMFDB - Embedded newform 1334.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.179024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 8x^{3} + 6x - 2 $ x^5 - 8x^3 + 6x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.07149$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.243316 q^{3} +1.00000 q^{4} -0.634714 q^{5} +0.243316 q^{6} +0.795080 q^{7} +1.00000 q^{8} -2.94080 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.243316 q^{3} +1.00000 q^{4} -0.634714 q^{5} +0.243316 q^{6} +0.795080 q^{7} +1.00000 q^{8} -2.94080 q^{9} -0.634714 q^{10} -4.92340 q^{11} +0.243316 q^{12} -6.90496 q^{13} +0.795080 q^{14} -0.154436 q^{15} +1.00000 q^{16} -2.62600 q^{17} -2.94080 q^{18} +3.56405 q^{19} -0.634714 q^{20} +0.193456 q^{21} -4.92340 q^{22} -1.00000 q^{23} +0.243316 q^{24} -4.59714 q^{25} -6.90496 q^{26} -1.44549 q^{27} +0.795080 q^{28} +1.00000 q^{29} -0.154436 q^{30} -2.29380 q^{31} +1.00000 q^{32} -1.19794 q^{33} -2.62600 q^{34} -0.504649 q^{35} -2.94080 q^{36} +1.75332 q^{37} +3.56405 q^{38} -1.68009 q^{39} -0.634714 q^{40} +2.63235 q^{41} +0.193456 q^{42} +1.16734 q^{43} -4.92340 q^{44} +1.86657 q^{45} -1.00000 q^{46} +4.82476 q^{47} +0.243316 q^{48} -6.36785 q^{49} -4.59714 q^{50} -0.638947 q^{51} -6.90496 q^{52} +3.60798 q^{53} -1.44549 q^{54} +3.12496 q^{55} +0.795080 q^{56} +0.867190 q^{57} +1.00000 q^{58} +2.41597 q^{59} -0.154436 q^{60} -3.78810 q^{61} -2.29380 q^{62} -2.33817 q^{63} +1.00000 q^{64} +4.38268 q^{65} -1.19794 q^{66} +11.5753 q^{67} -2.62600 q^{68} -0.243316 q^{69} -0.504649 q^{70} +16.3873 q^{71} -2.94080 q^{72} +3.41066 q^{73} +1.75332 q^{74} -1.11856 q^{75} +3.56405 q^{76} -3.91450 q^{77} -1.68009 q^{78} -14.0870 q^{79} -0.634714 q^{80} +8.47068 q^{81} +2.63235 q^{82} -8.20574 q^{83} +0.193456 q^{84} +1.66676 q^{85} +1.16734 q^{86} +0.243316 q^{87} -4.92340 q^{88} +8.62980 q^{89} +1.86657 q^{90} -5.49000 q^{91} -1.00000 q^{92} -0.558118 q^{93} +4.82476 q^{94} -2.26215 q^{95} +0.243316 q^{96} -1.49261 q^{97} -6.36785 q^{98} +14.4787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * 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
$3$	0.243316	0.140479	0.0702393	−	0.997530i	$-0.477624\pi$
$3$	0.243316	0.140479	0.0702393	+	0.997530i	$0.477624\pi$
$4$	1.00000	0.500000
$5$	−0.634714	−0.283853	−0.141926	−	0.989877i	$-0.545330\pi$
$5$	−0.634714	−0.283853	−0.141926	+	0.989877i	$0.545330\pi$
$6$	0.243316	0.0993333
$7$	0.795080	0.300512	0.150256	−	0.988647i	$-0.451990\pi$
$7$	0.795080	0.300512	0.150256	+	0.988647i	$0.451990\pi$
$8$	1.00000	0.353553
$9$	−2.94080	−0.980266
$10$	−0.634714	−0.200714
$11$	−4.92340	−1.48446	−0.742231	−	0.670144i	$-0.766232\pi$
$11$	−4.92340	−1.48446	−0.742231	+	0.670144i	$0.766232\pi$
$12$	0.243316	0.0702393
$13$	−6.90496	−1.91509	−0.957546	−	0.288280i	$-0.906916\pi$
$13$	−6.90496	−1.91509	−0.957546	+	0.288280i	$0.906916\pi$
$14$	0.795080	0.212494
$15$	−0.154436	−0.0398752
$16$	1.00000	0.250000
$17$	−2.62600	−0.636897	−0.318449	−	0.947940i	$-0.603162\pi$
$17$	−2.62600	−0.636897	−0.318449	+	0.947940i	$0.603162\pi$
$18$	−2.94080	−0.693153
$19$	3.56405	0.817649	0.408824	−	0.912613i	$-0.365939\pi$
$19$	3.56405	0.817649	0.408824	+	0.912613i	$0.365939\pi$
$20$	−0.634714	−0.141926
$21$	0.193456	0.0422155
$22$	−4.92340	−1.04967
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.243316	0.0496667
$25$	−4.59714	−0.919428
$26$	−6.90496	−1.35417
$27$	−1.44549	−0.278185
$28$	0.795080	0.150256
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.154436	−0.0281961
$31$	−2.29380	−0.411979	−0.205989	−	0.978554i	$-0.566041\pi$
$31$	−2.29380	−0.411979	−0.205989	+	0.978554i	$0.566041\pi$
$32$	1.00000	0.176777
$33$	−1.19794	−0.208535
$34$	−2.62600	−0.450354
$35$	−0.504649	−0.0853012
$36$	−2.94080	−0.490133
$37$	1.75332	0.288243	0.144122	−	0.989560i	$-0.453964\pi$
$37$	1.75332	0.288243	0.144122	+	0.989560i	$0.453964\pi$
$38$	3.56405	0.578165
$39$	−1.68009	−0.269029
$40$	−0.634714	−0.100357
$41$	2.63235	0.411104	0.205552	−	0.978646i	$-0.434101\pi$
$41$	2.63235	0.411104	0.205552	+	0.978646i	$0.434101\pi$
$42$	0.193456	0.0298509
$43$	1.16734	0.178018	0.0890091	−	0.996031i	$-0.471630\pi$
$43$	1.16734	0.178018	0.0890091	+	0.996031i	$0.471630\pi$
$44$	−4.92340	−0.742231
$45$	1.86657	0.278251
$46$	−1.00000	−0.147442
$47$	4.82476	0.703763	0.351882	−	0.936045i	$-0.385542\pi$
$47$	4.82476	0.703763	0.351882	+	0.936045i	$0.385542\pi$
$48$	0.243316	0.0351196
$49$	−6.36785	−0.909692
$50$	−4.59714	−0.650133
$51$	−0.638947	−0.0894704
$52$	−6.90496	−0.957546
$53$	3.60798	0.495594	0.247797	−	0.968812i	$-0.420293\pi$
$53$	3.60798	0.495594	0.247797	+	0.968812i	$0.420293\pi$
$54$	−1.44549	−0.196706
$55$	3.12496	0.421369
$56$	0.795080	0.106247
$57$	0.867190	0.114862
$58$	1.00000	0.131306
$59$	2.41597	0.314532	0.157266	−	0.987556i	$-0.449732\pi$
$59$	2.41597	0.314532	0.157266	+	0.987556i	$0.449732\pi$
$60$	−0.154436	−0.0199376
$61$	−3.78810	−0.485017	−0.242508	−	0.970149i	$-0.577970\pi$
$61$	−3.78810	−0.485017	−0.242508	+	0.970149i	$0.577970\pi$
$62$	−2.29380	−0.291313
$63$	−2.33817	−0.294582
$64$	1.00000	0.125000
$65$	4.38268	0.543604
$66$	−1.19794	−0.147457
$67$	11.5753	1.41415	0.707076	−	0.707138i	$-0.250014\pi$
$67$	11.5753	1.41415	0.707076	+	0.707138i	$0.250014\pi$
$68$	−2.62600	−0.318449
$69$	−0.243316	−0.0292918
$70$	−0.504649	−0.0603171
$71$	16.3873	1.94482	0.972408	−	0.233288i	$-0.0749486\pi$
$71$	16.3873	1.94482	0.972408	+	0.233288i	$0.0749486\pi$
$72$	−2.94080	−0.346576
$73$	3.41066	0.399187	0.199594	−	0.979879i	$-0.436038\pi$
$73$	3.41066	0.399187	0.199594	+	0.979879i	$0.436038\pi$
$74$	1.75332	0.203819
$75$	−1.11856	−0.129160
$76$	3.56405	0.408824
$77$	−3.91450	−0.446099
$78$	−1.68009	−0.190232
$79$	−14.0870	−1.58491	−0.792453	−	0.609933i	$-0.791196\pi$
$79$	−14.0870	−1.58491	−0.792453	+	0.609933i	$0.791196\pi$
$80$	−0.634714	−0.0709632
$81$	8.47068	0.941187
$82$	2.63235	0.290694
$83$	−8.20574	−0.900697	−0.450348	−	0.892853i	$-0.648700\pi$
$83$	−8.20574	−0.900697	−0.450348	+	0.892853i	$0.648700\pi$
$84$	0.193456	0.0211078
$85$	1.66676	0.180785
$86$	1.16734	0.125878
$87$	0.243316	0.0260862
$88$	−4.92340	−0.524837
$89$	8.62980	0.914757	0.457379	−	0.889272i	$-0.348788\pi$
$89$	8.62980	0.914757	0.457379	+	0.889272i	$0.348788\pi$
$90$	1.86657	0.196753
$91$	−5.49000	−0.575508
$92$	−1.00000	−0.104257
$93$	−0.558118	−0.0578741
$94$	4.82476	0.497636
$95$	−2.26215	−0.232092
$96$	0.243316	0.0248333
$97$	−1.49261	−0.151551	−0.0757756	−	0.997125i	$-0.524143\pi$
$97$	−1.49261	−0.151551	−0.0757756	+	0.997125i	$0.524143\pi$
$98$	−6.36785	−0.643250
$99$	14.4787	1.45517
$100$	−4.59714	−0.459714
$101$	−17.5292	−1.74422	−0.872112	−	0.489307i	$-0.837250\pi$
$101$	−17.5292	−1.74422	−0.872112	+	0.489307i	$0.837250\pi$
$102$	−0.638947	−0.0632651
$103$	−19.5267	−1.92402	−0.962012	−	0.273007i	$-0.911982\pi$
$103$	−19.5267	−1.92402	−0.962012	+	0.273007i	$0.911982\pi$
$104$	−6.90496	−0.677087
$105$	−0.122789	−0.0119830
$106$	3.60798	0.350438
$107$	4.24394	0.410277	0.205139	−	0.978733i	$-0.434236\pi$
$107$	4.24394	0.410277	0.205139	+	0.978733i	$0.434236\pi$
$108$	−1.44549	−0.139092
$109$	−8.83959	−0.846679	−0.423340	−	0.905971i	$-0.639142\pi$
$109$	−8.83959	−0.846679	−0.423340	+	0.905971i	$0.639142\pi$
$110$	3.12496	0.297953
$111$	0.426610	0.0404920
$112$	0.795080	0.0751280
$113$	−19.5558	−1.83965	−0.919826	−	0.392327i	$-0.871670\pi$
$113$	−19.5558	−1.83965	−0.919826	+	0.392327i	$0.871670\pi$
$114$	0.867190	0.0812198
$115$	0.634714	0.0591874
$116$	1.00000	0.0928477
$117$	20.3061	1.87730
$118$	2.41597	0.222408
$119$	−2.08788	−0.191395
$120$	−0.154436	−0.0140980
$121$	13.2399	1.20363
$122$	−3.78810	−0.342959
$123$	0.640493	0.0577513
$124$	−2.29380	−0.205989
$125$	6.09144	0.544835
$126$	−2.33817	−0.208301
$127$	−19.3186	−1.71425	−0.857123	−	0.515112i	$-0.827750\pi$
$127$	−19.3186	−1.71425	−0.857123	+	0.515112i	$0.827750\pi$
$128$	1.00000	0.0883883
$129$	0.284033	0.0250077
$130$	4.38268	0.384386
$131$	−7.64184	−0.667671	−0.333835	−	0.942631i	$-0.608343\pi$
$131$	−7.64184	−0.667671	−0.333835	+	0.942631i	$0.608343\pi$
$132$	−1.19794	−0.104268
$133$	2.83370	0.245713
$134$	11.5753	0.999956
$135$	0.917474	0.0789636
$136$	−2.62600	−0.225177
$137$	−6.99763	−0.597848	−0.298924	−	0.954277i	$-0.596628\pi$
$137$	−6.99763	−0.597848	−0.298924	+	0.954277i	$0.596628\pi$
$138$	−0.243316	−0.0207124
$139$	−0.959978	−0.0814243	−0.0407121	−	0.999171i	$-0.512963\pi$
$139$	−0.959978	−0.0814243	−0.0407121	+	0.999171i	$0.512963\pi$
$140$	−0.504649	−0.0426506
$141$	1.17394	0.0988636
$142$	16.3873	1.37519
$143$	33.9959	2.84288
$144$	−2.94080	−0.245066
$145$	−0.634714	−0.0527102
$146$	3.41066	0.282268
$147$	−1.54940	−0.127792
$148$	1.75332	0.144122
$149$	−12.1961	−0.999147	−0.499573	−	0.866272i	$-0.666510\pi$
$149$	−12.1961	−0.999147	−0.499573	+	0.866272i	$0.666510\pi$
$150$	−1.11856	−0.0913298
$151$	−17.1561	−1.39614	−0.698071	−	0.716029i	$-0.745958\pi$
$151$	−17.1561	−1.39614	−0.698071	+	0.716029i	$0.745958\pi$
$152$	3.56405	0.289082
$153$	7.72252	0.624329
$154$	−3.91450	−0.315440
$155$	1.45591	0.116941
$156$	−1.68009	−0.134515
$157$	23.2789	1.85786	0.928931	−	0.370254i	$-0.120729\pi$
$157$	23.2789	1.85786	0.928931	+	0.370254i	$0.120729\pi$
$158$	−14.0870	−1.12070
$159$	0.877879	0.0696203
$160$	−0.634714	−0.0501786
$161$	−0.795080	−0.0626611
$162$	8.47068	0.665520
$163$	−13.0373	−1.02116	−0.510580	−	0.859830i	$-0.670569\pi$
$163$	−13.0373	−1.02116	−0.510580	+	0.859830i	$0.670569\pi$
$164$	2.63235	0.205552
$165$	0.760351	0.0591933
$166$	−8.20574	−0.636889
$167$	14.7637	1.14245	0.571224	−	0.820794i	$-0.306469\pi$
$167$	14.7637	1.14245	0.571224	+	0.820794i	$0.306469\pi$
$168$	0.193456	0.0149254
$169$	34.6785	2.66758
$170$	1.66676	0.127834
$171$	−10.4811	−0.801513
$172$	1.16734	0.0890091
$173$	22.5405	1.71372	0.856861	−	0.515547i	$-0.172411\pi$
$173$	22.5405	1.71372	0.856861	+	0.515547i	$0.172411\pi$
$174$	0.243316	0.0184457
$175$	−3.65509	−0.276299
$176$	−4.92340	−0.371116
$177$	0.587843	0.0441850
$178$	8.62980	0.646831
$179$	13.6260	1.01846	0.509228	−	0.860632i	$-0.329931\pi$
$179$	13.6260	1.01846	0.509228	+	0.860632i	$0.329931\pi$
$180$	1.86657	0.139126
$181$	−1.04201	−0.0774516	−0.0387258	−	0.999250i	$-0.512330\pi$
$181$	−1.04201	−0.0774516	−0.0387258	+	0.999250i	$0.512330\pi$
$182$	−5.49000	−0.406946
$183$	−0.921706	−0.0681345
$184$	−1.00000	−0.0737210
$185$	−1.11285	−0.0818187
$186$	−0.558118	−0.0409232
$187$	12.9288	0.945450
$188$	4.82476	0.351882
$189$	−1.14928	−0.0835979
$190$	−2.26215	−0.164114
$191$	0.182175	0.0131817	0.00659086	−	0.999978i	$-0.497902\pi$
$191$	0.182175	0.0131817	0.00659086	+	0.999978i	$0.497902\pi$
$192$	0.243316	0.0175598
$193$	8.02008	0.577298	0.288649	−	0.957435i	$-0.406794\pi$
$193$	8.02008	0.577298	0.288649	+	0.957435i	$0.406794\pi$
$194$	−1.49261	−0.107163
$195$	1.06638	0.0763648
$196$	−6.36785	−0.454846
$197$	18.7087	1.33294	0.666470	−	0.745531i	$-0.267804\pi$
$197$	18.7087	1.33294	0.666470	+	0.745531i	$0.267804\pi$
$198$	14.4787	1.02896
$199$	−21.0810	−1.49439	−0.747196	−	0.664604i	$-0.768600\pi$
$199$	−21.0810	−1.49439	−0.747196	+	0.664604i	$0.768600\pi$
$200$	−4.59714	−0.325067
$201$	2.81646	0.198658
$202$	−17.5292	−1.23335
$203$	0.795080	0.0558037
$204$	−0.638947	−0.0447352
$205$	−1.67079	−0.116693
$206$	−19.5267	−1.36049
$207$	2.94080	0.204400
$208$	−6.90496	−0.478773
$209$	−17.5472	−1.21377
$210$	−0.122789	−0.00847326
$211$	13.1197	0.903195	0.451597	−	0.892222i	$-0.350854\pi$
$211$	13.1197	0.903195	0.451597	+	0.892222i	$0.350854\pi$
$212$	3.60798	0.247797
$213$	3.98729	0.273205
$214$	4.24394	0.290110
$215$	−0.740929	−0.0505310
$216$	−1.44549	−0.0983532
$217$	−1.82375	−0.123805
$218$	−8.83959	−0.598693
$219$	0.829868	0.0560773
$220$	3.12496	0.210684
$221$	18.1324	1.21972
$222$	0.426610	0.0286322
$223$	10.8057	0.723602	0.361801	−	0.932255i	$-0.382162\pi$
$223$	10.8057	0.723602	0.361801	+	0.932255i	$0.382162\pi$
$224$	0.795080	0.0531235
$225$	13.5193	0.901283
$226$	−19.5558	−1.30083
$227$	−16.6355	−1.10414	−0.552070	−	0.833798i	$-0.686162\pi$
$227$	−16.6355	−1.10414	−0.552070	+	0.833798i	$0.686162\pi$
$228$	0.867190	0.0574310
$229$	11.8989	0.786303	0.393152	−	0.919474i	$-0.371385\pi$
$229$	11.8989	0.786303	0.393152	+	0.919474i	$0.371385\pi$
$230$	0.634714	0.0418518
$231$	−0.952461	−0.0626673
$232$	1.00000	0.0656532
$233$	−10.7319	−0.703069	−0.351535	−	0.936175i	$-0.614340\pi$
$233$	−10.7319	−0.703069	−0.351535	+	0.936175i	$0.614340\pi$
$234$	20.3061	1.32745
$235$	−3.06234	−0.199765
$236$	2.41597	0.157266
$237$	−3.42758	−0.222645
$238$	−2.08788	−0.135337
$239$	27.2961	1.76564	0.882818	−	0.469715i	$-0.155643\pi$
$239$	27.2961	1.76564	0.882818	+	0.469715i	$0.155643\pi$
$240$	−0.154436	−0.00996881
$241$	−19.5346	−1.25833	−0.629166	−	0.777271i	$-0.716603\pi$
$241$	−19.5346	−1.25833	−0.629166	+	0.777271i	$0.716603\pi$
$242$	13.2399	0.851093
$243$	6.39752	0.410401
$244$	−3.78810	−0.242508
$245$	4.04176	0.258219
$246$	0.640493	0.0408363
$247$	−24.6096	−1.56587
$248$	−2.29380	−0.145656
$249$	−1.99659	−0.126529
$250$	6.09144	0.385257
$251$	−13.5454	−0.854980	−0.427490	−	0.904020i	$-0.640602\pi$
$251$	−13.5454	−0.854980	−0.427490	+	0.904020i	$0.640602\pi$
$252$	−2.33817	−0.147291
$253$	4.92340	0.309532
$254$	−19.3186	−1.21215
$255$	0.405549	0.0253964
$256$	1.00000	0.0625000
$257$	−14.3806	−0.897034	−0.448517	−	0.893774i	$-0.648048\pi$
$257$	−14.3806	−0.897034	−0.448517	+	0.893774i	$0.648048\pi$
$258$	0.284033	0.0176831
$259$	1.39403	0.0866206
$260$	4.38268	0.271802
$261$	−2.94080	−0.182031
$262$	−7.64184	−0.472115
$263$	−21.0883	−1.30036	−0.650179	−	0.759781i	$-0.725306\pi$
$263$	−21.0883	−1.30036	−0.650179	+	0.759781i	$0.725306\pi$
$264$	−1.19794	−0.0737283
$265$	−2.29004	−0.140676
$266$	2.83370	0.173746
$267$	2.09977	0.128504
$268$	11.5753	0.707076
$269$	9.20305	0.561120	0.280560	−	0.959836i	$-0.409480\pi$
$269$	9.20305	0.561120	0.280560	+	0.959836i	$0.409480\pi$
$270$	0.917474	0.0558357
$271$	23.3618	1.41913	0.709563	−	0.704642i	$-0.248892\pi$
$271$	23.3618	1.41913	0.709563	+	0.704642i	$0.248892\pi$
$272$	−2.62600	−0.159224
$273$	−1.33580	−0.0808466
$274$	−6.99763	−0.422743
$275$	22.6336	1.36486
$276$	−0.243316	−0.0146459
$277$	−14.7902	−0.888658	−0.444329	−	0.895864i	$-0.646558\pi$
$277$	−14.7902	−0.888658	−0.444329	+	0.895864i	$0.646558\pi$
$278$	−0.959978	−0.0575756
$279$	6.74560	0.403848
$280$	−0.504649	−0.0301585
$281$	8.46792	0.505154	0.252577	−	0.967577i	$-0.418722\pi$
$281$	8.46792	0.505154	0.252577	+	0.967577i	$0.418722\pi$
$282$	1.17394	0.0699071
$283$	−4.08281	−0.242698	−0.121349	−	0.992610i	$-0.538722\pi$
$283$	−4.08281	−0.242698	−0.121349	+	0.992610i	$0.538722\pi$
$284$	16.3873	0.972408
$285$	−0.550418	−0.0326039
$286$	33.9959	2.01022
$287$	2.09293	0.123542
$288$	−2.94080	−0.173288
$289$	−10.1041	−0.594362
$290$	−0.634714	−0.0372717
$291$	−0.363175	−0.0212897
$292$	3.41066	0.199594
$293$	19.6527	1.14813	0.574063	−	0.818811i	$-0.305367\pi$
$293$	19.6527	1.14813	0.574063	+	0.818811i	$0.305367\pi$
$294$	−1.54940	−0.0903628
$295$	−1.53345	−0.0892808
$296$	1.75332	0.101909
$297$	7.11673	0.412955
$298$	−12.1961	−0.706504
$299$	6.90496	0.399324
$300$	−1.11856	−0.0645799
$301$	0.928131	0.0534966
$302$	−17.1561	−0.987221
$303$	−4.26514	−0.245026
$304$	3.56405	0.204412
$305$	2.40436	0.137673
$306$	7.72252	0.441467
$307$	1.93569	0.110476	0.0552378	−	0.998473i	$-0.482408\pi$
$307$	1.93569	0.110476	0.0552378	+	0.998473i	$0.482408\pi$
$308$	−3.91450	−0.223049
$309$	−4.75116	−0.270284
$310$	1.45591	0.0826900
$311$	−5.20930	−0.295393	−0.147696	−	0.989033i	$-0.547186\pi$
$311$	−5.20930	−0.295393	−0.147696	+	0.989033i	$0.547186\pi$
$312$	−1.68009	−0.0951162
$313$	−20.5012	−1.15880	−0.579398	−	0.815045i	$-0.696712\pi$
$313$	−20.5012	−1.15880	−0.579398	+	0.815045i	$0.696712\pi$
$314$	23.2789	1.31371
$315$	1.48407	0.0836179
$316$	−14.0870	−0.792453
$317$	−25.5364	−1.43427	−0.717135	−	0.696934i	$-0.754547\pi$
$317$	−25.5364	−1.43427	−0.717135	+	0.696934i	$0.754547\pi$
$318$	0.877879	0.0492290
$319$	−4.92340	−0.275658
$320$	−0.634714	−0.0354816
$321$	1.03262	0.0576351
$322$	−0.795080	−0.0443081
$323$	−9.35917	−0.520758
$324$	8.47068	0.470593
$325$	31.7431	1.76079
$326$	−13.0373	−0.722069
$327$	−2.15081	−0.118940
$328$	2.63235	0.145347
$329$	3.83607	0.211489
$330$	0.760351	0.0418560
$331$	−17.2910	−0.950399	−0.475200	−	0.879878i	$-0.657624\pi$
$331$	−17.2910	−0.950399	−0.475200	+	0.879878i	$0.657624\pi$
$332$	−8.20574	−0.450348
$333$	−5.15615	−0.282555
$334$	14.7637	0.807832
$335$	−7.34703	−0.401411
$336$	0.193456	0.0105539
$337$	−0.807435	−0.0439838	−0.0219919	−	0.999758i	$-0.507001\pi$
$337$	−0.807435	−0.0439838	−0.0219919	+	0.999758i	$0.507001\pi$
$338$	34.6785	1.88626
$339$	−4.75823	−0.258432
$340$	1.66676	0.0903926
$341$	11.2933	0.611567
$342$	−10.4811	−0.566755
$343$	−10.6285	−0.573886
$344$	1.16734	0.0629389
$345$	0.154436	0.00831456
$346$	22.5405	1.21178
$347$	1.30531	0.0700726	0.0350363	−	0.999386i	$-0.488845\pi$
$347$	1.30531	0.0700726	0.0350363	+	0.999386i	$0.488845\pi$
$348$	0.243316	0.0130431
$349$	−25.3608	−1.35753	−0.678765	−	0.734356i	$-0.737484\pi$
$349$	−25.3608	−1.35753	−0.678765	+	0.734356i	$0.737484\pi$
$350$	−3.65509	−0.195373
$351$	9.98106	0.532750
$352$	−4.92340	−0.262418
$353$	16.9557	0.902460	0.451230	−	0.892408i	$-0.350985\pi$
$353$	16.9557	0.902460	0.451230	+	0.892408i	$0.350985\pi$
$354$	0.587843	0.0312435
$355$	−10.4013	−0.552041
$356$	8.62980	0.457379
$357$	−0.508014	−0.0268869
$358$	13.6260	0.720157
$359$	4.22806	0.223148	0.111574	−	0.993756i	$-0.464411\pi$
$359$	4.22806	0.223148	0.111574	+	0.993756i	$0.464411\pi$
$360$	1.86657	0.0983767
$361$	−6.29756	−0.331451
$362$	−1.04201	−0.0547666
$363$	3.22148	0.169084
$364$	−5.49000	−0.287754
$365$	−2.16479	−0.113311
$366$	−0.921706	−0.0481783
$367$	−22.4539	−1.17209	−0.586043	−	0.810280i	$-0.699315\pi$
$367$	−22.4539	−1.17209	−0.586043	+	0.810280i	$0.699315\pi$
$368$	−1.00000	−0.0521286
$369$	−7.74120	−0.402991
$370$	−1.11285	−0.0578546
$371$	2.86863	0.148932
$372$	−0.558118	−0.0289371
$373$	37.1234	1.92218	0.961088	−	0.276243i	$-0.0890895\pi$
$373$	37.1234	1.92218	0.961088	+	0.276243i	$0.0890895\pi$
$374$	12.9288	0.668534
$375$	1.48214	0.0765376
$376$	4.82476	0.248818
$377$	−6.90496	−0.355624
$378$	−1.14928	−0.0591127
$379$	37.6564	1.93428	0.967139	−	0.254249i	$-0.0818283\pi$
$379$	37.6564	1.93428	0.967139	+	0.254249i	$0.0818283\pi$
$380$	−2.26215	−0.116046
$381$	−4.70051	−0.240815
$382$	0.182175	0.00932088
$383$	−19.4565	−0.994179	−0.497090	−	0.867699i	$-0.665598\pi$
$383$	−19.4565	−0.994179	−0.497090	+	0.867699i	$0.665598\pi$
$384$	0.243316	0.0124167
$385$	2.48459	0.126626
$386$	8.02008	0.408211
$387$	−3.43292	−0.174505
$388$	−1.49261	−0.0757756
$389$	28.1334	1.42642	0.713210	−	0.700951i	$-0.247241\pi$
$389$	28.1334	1.42642	0.713210	+	0.700951i	$0.247241\pi$
$390$	1.06638	0.0539980
$391$	2.62600	0.132802
$392$	−6.36785	−0.321625
$393$	−1.85938	−0.0937934
$394$	18.7087	0.942532
$395$	8.94119	0.449880
$396$	14.4787	0.727584
$397$	32.7128	1.64181	0.820904	−	0.571067i	$-0.193470\pi$
$397$	32.7128	1.64181	0.820904	+	0.571067i	$0.193470\pi$
$398$	−21.0810	−1.05669
$399$	0.689485	0.0345174
$400$	−4.59714	−0.229857
$401$	15.5611	0.777083	0.388541	−	0.921431i	$-0.372979\pi$
$401$	15.5611	0.777083	0.388541	+	0.921431i	$0.372979\pi$
$402$	2.81646	0.140472
$403$	15.8386	0.788977
$404$	−17.5292	−0.872112
$405$	−5.37646	−0.267159
$406$	0.795080	0.0394592
$407$	−8.63228	−0.427886
$408$	−0.638947	−0.0316326
$409$	−22.2320	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$409$	−22.2320	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$410$	−1.67079	−0.0825144
$411$	−1.70264	−0.0839849
$412$	−19.5267	−0.962012
$413$	1.92089	0.0945206
$414$	2.94080	0.144532
$415$	5.20830	0.255665
$416$	−6.90496	−0.338544
$417$	−0.233578	−0.0114384
$418$	−17.5472	−0.858264
$419$	−16.5061	−0.806378	−0.403189	−	0.915117i	$-0.632098\pi$
$419$	−16.5061	−0.806378	−0.403189	+	0.915117i	$0.632098\pi$
$420$	−0.122789	−0.00599150
$421$	5.39560	0.262965	0.131483	−	0.991318i	$-0.458026\pi$
$421$	5.39560	0.262965	0.131483	+	0.991318i	$0.458026\pi$
$422$	13.1197	0.638655
$423$	−14.1886	−0.689875
$424$	3.60798	0.175219
$425$	12.0721	0.585581
$426$	3.98729	0.193185
$427$	−3.01185	−0.145753
$428$	4.24394	0.205139
$429$	8.27175	0.399364
$430$	−0.740929	−0.0357308
$431$	−30.6347	−1.47562	−0.737811	−	0.675007i	$-0.764141\pi$
$431$	−30.6347	−1.47562	−0.737811	+	0.675007i	$0.764141\pi$
$432$	−1.44549	−0.0695462
$433$	−22.8241	−1.09686	−0.548428	−	0.836198i	$-0.684773\pi$
$433$	−22.8241	−1.09686	−0.548428	+	0.836198i	$0.684773\pi$
$434$	−1.82375	−0.0875430
$435$	−0.154436	−0.00740465
$436$	−8.83959	−0.423340
$437$	−3.56405	−0.170492
$438$	0.829868	0.0396526
$439$	−25.5557	−1.21971	−0.609854	−	0.792514i	$-0.708772\pi$
$439$	−25.5557	−1.21971	−0.609854	+	0.792514i	$0.708772\pi$
$440$	3.12496	0.148976
$441$	18.7265	0.891740
$442$	18.1324	0.862470
$443$	16.3596	0.777269	0.388635	−	0.921392i	$-0.372947\pi$
$443$	16.3596	0.777269	0.388635	+	0.921392i	$0.372947\pi$
$444$	0.426610	0.0202460
$445$	−5.47746	−0.259656
$446$	10.8057	0.511664
$447$	−2.96752	−0.140359
$448$	0.795080	0.0375640
$449$	25.4225	1.19976	0.599881	−	0.800089i	$-0.295214\pi$
$449$	25.4225	1.19976	0.599881	+	0.800089i	$0.295214\pi$
$450$	13.5193	0.637304
$451$	−12.9601	−0.610268
$452$	−19.5558	−0.919826
$453$	−4.17435	−0.196128
$454$	−16.6355	−0.780744
$455$	3.48458	0.163360
$456$	0.867190	0.0406099
$457$	8.98560	0.420329	0.210164	−	0.977666i	$-0.432600\pi$
$457$	8.98560	0.420329	0.210164	+	0.977666i	$0.432600\pi$
$458$	11.8989	0.556000
$459$	3.79585	0.177175
$460$	0.634714	0.0295937
$461$	−26.4822	−1.23340	−0.616699	−	0.787199i	$-0.711530\pi$
$461$	−26.4822	−1.23340	−0.616699	+	0.787199i	$0.711530\pi$
$462$	−0.952461	−0.0443125
$463$	−1.99103	−0.0925308	−0.0462654	−	0.998929i	$-0.514732\pi$
$463$	−1.99103	−0.0925308	−0.0462654	+	0.998929i	$0.514732\pi$
$464$	1.00000	0.0464238
$465$	0.354246	0.0164277
$466$	−10.7319	−0.497145
$467$	−33.6408	−1.55671	−0.778355	−	0.627824i	$-0.783946\pi$
$467$	−33.6408	−1.55671	−0.778355	+	0.627824i	$0.783946\pi$
$468$	20.3061	0.938650
$469$	9.20332	0.424970
$470$	−3.06234	−0.141255
$471$	5.66414	0.260990
$472$	2.41597	0.111204
$473$	−5.74730	−0.264261
$474$	−3.42758	−0.157434
$475$	−16.3844	−0.751769
$476$	−2.08788	−0.0956977
$477$	−10.6103	−0.485814
$478$	27.2961	1.24849
$479$	2.83083	0.129344	0.0646719	−	0.997907i	$-0.479400\pi$
$479$	2.83083	0.129344	0.0646719	+	0.997907i	$0.479400\pi$
$480$	−0.154436	−0.00704901
$481$	−12.1066	−0.552013
$482$	−19.5346	−0.889775
$483$	−0.193456	−0.00880254
$484$	13.2399	0.601814
$485$	0.947379	0.0430183
$486$	6.39752	0.290198
$487$	16.3929	0.742834	0.371417	−	0.928466i	$-0.378872\pi$
$487$	16.3929	0.742834	0.371417	+	0.928466i	$0.378872\pi$
$488$	−3.78810	−0.171479
$489$	−3.17218	−0.143451
$490$	4.04176	0.182588
$491$	−8.08896	−0.365050	−0.182525	−	0.983201i	$-0.558427\pi$
$491$	−8.08896	−0.365050	−0.182525	+	0.983201i	$0.558427\pi$
$492$	0.640493	0.0288756
$493$	−2.62600	−0.118269
$494$	−24.6096	−1.10724
$495$	−9.18986	−0.413053
$496$	−2.29380	−0.102995
$497$	13.0292	0.584441
$498$	−1.99659	−0.0894692
$499$	18.4497	0.825920	0.412960	−	0.910749i	$-0.364495\pi$
$499$	18.4497	0.825920	0.412960	+	0.910749i	$0.364495\pi$
$500$	6.09144	0.272418
$501$	3.59224	0.160489
$502$	−13.5454	−0.604562
$503$	−9.67088	−0.431203	−0.215602	−	0.976481i	$-0.569171\pi$
$503$	−9.67088	−0.431203	−0.215602	+	0.976481i	$0.569171\pi$
$504$	−2.33817	−0.104150
$505$	11.1261	0.495103
$506$	4.92340	0.218872
$507$	8.43784	0.374737
$508$	−19.3186	−0.857123
$509$	−25.9501	−1.15022	−0.575109	−	0.818077i	$-0.695040\pi$
$509$	−25.9501	−1.15022	−0.575109	+	0.818077i	$0.695040\pi$
$510$	0.405549	0.0179580
$511$	2.71175	0.119961
$512$	1.00000	0.0441942
$513$	−5.15180	−0.227457
$514$	−14.3806	−0.634299
$515$	12.3939	0.546140
$516$	0.284033	0.0125039
$517$	−23.7542	−1.04471
$518$	1.39403	0.0612500
$519$	5.48446	0.240741
$520$	4.38268	0.192193
$521$	17.0947	0.748934	0.374467	−	0.927240i	$-0.377826\pi$
$521$	17.0947	0.748934	0.374467	+	0.927240i	$0.377826\pi$
$522$	−2.94080	−0.128715
$523$	−27.3809	−1.19728	−0.598642	−	0.801016i	$-0.704293\pi$
$523$	−27.3809	−1.19728	−0.598642	+	0.801016i	$0.704293\pi$
$524$	−7.64184	−0.333835
$525$	−0.889343	−0.0388141
$526$	−21.0883	−0.919492
$527$	6.02351	0.262388
$528$	−1.19794	−0.0521338
$529$	1.00000	0.0434783
$530$	−2.29004	−0.0994728
$531$	−7.10486	−0.308325
$532$	2.83370	0.122857
$533$	−18.1763	−0.787302
$534$	2.09977	0.0908659
$535$	−2.69369	−0.116458
$536$	11.5753	0.499978
$537$	3.31543	0.143071
$538$	9.20305	0.396772
$539$	31.3515	1.35040
$540$	0.917474	0.0394818
$541$	−7.57843	−0.325822	−0.162911	−	0.986641i	$-0.552088\pi$
$541$	−7.57843	−0.325822	−0.162911	+	0.986641i	$0.552088\pi$
$542$	23.3618	1.00347
$543$	−0.253536	−0.0108803
$544$	−2.62600	−0.112589
$545$	5.61061	0.240332
$546$	−1.33580	−0.0571672
$547$	−12.9311	−0.552893	−0.276446	−	0.961029i	$-0.589157\pi$
$547$	−12.9311	−0.552893	−0.276446	+	0.961029i	$0.589157\pi$
$548$	−6.99763	−0.298924
$549$	11.1400	0.475446
$550$	22.6336	0.965098
$551$	3.56405	0.151834
$552$	−0.243316	−0.0103562
$553$	−11.2003	−0.476284
$554$	−14.7902	−0.628376
$555$	−0.270775	−0.0114938
$556$	−0.959978	−0.0407121
$557$	1.14296	0.0484287	0.0242144	−	0.999707i	$-0.492292\pi$
$557$	1.14296	0.0484287	0.0242144	+	0.999707i	$0.492292\pi$
$558$	6.74560	0.285564
$559$	−8.06046	−0.340921
$560$	−0.504649	−0.0213253
$561$	3.14579	0.132815
$562$	8.46792	0.357198
$563$	−4.30334	−0.181364	−0.0906820	−	0.995880i	$-0.528905\pi$
$563$	−4.30334	−0.181364	−0.0906820	+	0.995880i	$0.528905\pi$
$564$	1.17394	0.0494318
$565$	12.4123	0.522190
$566$	−4.08281	−0.171613
$567$	6.73487	0.282838
$568$	16.3873	0.687596
$569$	7.01103	0.293918	0.146959	−	0.989143i	$-0.453052\pi$
$569$	7.01103	0.293918	0.146959	+	0.989143i	$0.453052\pi$
$570$	−0.550418	−0.0230545
$571$	−30.4920	−1.27605	−0.638025	−	0.770015i	$-0.720249\pi$
$571$	−30.4920	−1.27605	−0.638025	+	0.770015i	$0.720249\pi$
$572$	33.9959	1.42144
$573$	0.0443261	0.00185175
$574$	2.09293	0.0873572
$575$	4.59714	0.191714
$576$	−2.94080	−0.122533
$577$	−16.2957	−0.678397	−0.339199	−	0.940715i	$-0.610156\pi$
$577$	−16.2957	−0.678397	−0.339199	+	0.940715i	$0.610156\pi$
$578$	−10.1041	−0.420277
$579$	1.95141	0.0810980
$580$	−0.634714	−0.0263551
$581$	−6.52422	−0.270670
$582$	−0.363175	−0.0150541
$583$	−17.7635	−0.735690
$584$	3.41066	0.141134
$585$	−12.8886	−0.532877
$586$	19.6527	0.811847
$587$	−30.4338	−1.25614	−0.628069	−	0.778158i	$-0.716154\pi$
$587$	−30.4338	−1.25614	−0.628069	+	0.778158i	$0.716154\pi$
$588$	−1.54940	−0.0638961
$589$	−8.17521	−0.336854
$590$	−1.53345	−0.0631311
$591$	4.55213	0.187250
$592$	1.75332	0.0720608
$593$	17.0737	0.701134	0.350567	−	0.936538i	$-0.385989\pi$
$593$	17.0737	0.701134	0.350567	+	0.936538i	$0.385989\pi$
$594$	7.11673	0.292003
$595$	1.32521	0.0543281
$596$	−12.1961	−0.499573
$597$	−5.12934	−0.209930
$598$	6.90496	0.282365
$599$	23.8266	0.973530	0.486765	−	0.873533i	$-0.338177\pi$
$599$	23.8266	0.973530	0.486765	+	0.873533i	$0.338177\pi$
$600$	−1.11856	−0.0456649
$601$	34.3252	1.40015	0.700076	−	0.714068i	$-0.253149\pi$
$601$	34.3252	1.40015	0.700076	+	0.714068i	$0.253149\pi$
$602$	0.928131	0.0378278
$603$	−34.0407	−1.38624
$604$	−17.1561	−0.698071
$605$	−8.40356	−0.341653
$606$	−4.26514	−0.173260
$607$	36.9168	1.49841	0.749203	−	0.662341i	$-0.230437\pi$
$607$	36.9168	1.49841	0.749203	+	0.662341i	$0.230437\pi$
$608$	3.56405	0.144541
$609$	0.193456	0.00783922
$610$	2.40436	0.0973498
$611$	−33.3148	−1.34777
$612$	7.72252	0.312164
$613$	29.5287	1.19265	0.596327	−	0.802742i	$-0.296626\pi$
$613$	29.5287	1.19265	0.596327	+	0.802742i	$0.296626\pi$
$614$	1.93569	0.0781181
$615$	−0.406530	−0.0163929
$616$	−3.91450	−0.157720
$617$	−32.1905	−1.29594	−0.647970	−	0.761666i	$-0.724382\pi$
$617$	−32.1905	−1.29594	−0.647970	+	0.761666i	$0.724382\pi$
$618$	−4.75116	−0.191120
$619$	−17.5932	−0.707131	−0.353566	−	0.935410i	$-0.615031\pi$
$619$	−17.5932	−0.707131	−0.353566	+	0.935410i	$0.615031\pi$
$620$	1.45591	0.0584707
$621$	1.44549	0.0580055
$622$	−5.20930	−0.208874
$623$	6.86138	0.274896
$624$	−1.68009	−0.0672573
$625$	19.1194	0.764774
$626$	−20.5012	−0.819392
$627$	−4.26953	−0.170508
$628$	23.2789	0.928931
$629$	−4.60420	−0.183581
$630$	1.48407	0.0591268
$631$	−48.4227	−1.92768	−0.963839	−	0.266485i	$-0.914138\pi$
$631$	−48.4227	−1.92768	−0.963839	+	0.266485i	$0.914138\pi$
$632$	−14.0870	−0.560349
$633$	3.19222	0.126879
$634$	−25.5364	−1.01418
$635$	12.2618	0.486593
$636$	0.877879	0.0348102
$637$	43.9697	1.74214
$638$	−4.92340	−0.194919
$639$	−48.1917	−1.90644
$640$	−0.634714	−0.0250893
$641$	−1.54476	−0.0610144	−0.0305072	−	0.999535i	$-0.509712\pi$
$641$	−1.54476	−0.0610144	−0.0305072	+	0.999535i	$0.509712\pi$
$642$	1.03262	0.0407542
$643$	−39.2621	−1.54835	−0.774173	−	0.632974i	$-0.781834\pi$
$643$	−39.2621	−1.54835	−0.774173	+	0.632974i	$0.781834\pi$
$644$	−0.795080	−0.0313306
$645$	−0.180280	−0.00709852
$646$	−9.35917	−0.368232
$647$	−26.7543	−1.05182	−0.525911	−	0.850540i	$-0.676275\pi$
$647$	−26.7543	−1.05182	−0.525911	+	0.850540i	$0.676275\pi$
$648$	8.47068	0.332760
$649$	−11.8948	−0.466911
$650$	31.7431	1.24507
$651$	−0.443749	−0.0173919
$652$	−13.0373	−0.510580
$653$	8.19171	0.320567	0.160283	−	0.987071i	$-0.448759\pi$
$653$	8.19171	0.320567	0.160283	+	0.987071i	$0.448759\pi$
$654$	−2.15081	−0.0841035
$655$	4.85039	0.189520
$656$	2.63235	0.102776
$657$	−10.0301	−0.391310
$658$	3.83607	0.149546
$659$	14.2007	0.553183	0.276591	−	0.960988i	$-0.410795\pi$
$659$	14.2007	0.553183	0.276591	+	0.960988i	$0.410795\pi$
$660$	0.760351	0.0295966
$661$	−38.2475	−1.48766	−0.743828	−	0.668371i	$-0.766992\pi$
$661$	−38.2475	−1.48766	−0.743828	+	0.668371i	$0.766992\pi$
$662$	−17.2910	−0.672034
$663$	4.41190	0.171344
$664$	−8.20574	−0.318444
$665$	−1.79859	−0.0697464
$666$	−5.15615	−0.199797
$667$	−1.00000	−0.0387202
$668$	14.7637	0.571224
$669$	2.62919	0.101651
$670$	−7.34703	−0.283840
$671$	18.6504	0.719989
$672$	0.193456	0.00746272
$673$	28.5503	1.10053	0.550266	−	0.834989i	$-0.314526\pi$
$673$	28.5503	1.10053	0.550266	+	0.834989i	$0.314526\pi$
$674$	−0.807435	−0.0311013
$675$	6.64512	0.255771
$676$	34.6785	1.33379
$677$	28.9115	1.11116	0.555579	−	0.831464i	$-0.312497\pi$
$677$	28.9115	1.11116	0.555579	+	0.831464i	$0.312497\pi$
$678$	−4.75823	−0.182739
$679$	−1.18674	−0.0455430
$680$	1.66676	0.0639172
$681$	−4.04769	−0.155108
$682$	11.2933	0.432443
$683$	4.02493	0.154010	0.0770049	−	0.997031i	$-0.475464\pi$
$683$	4.02493	0.154010	0.0770049	+	0.997031i	$0.475464\pi$
$684$	−10.4811	−0.400756
$685$	4.44150	0.169701
$686$	−10.6285	−0.405798
$687$	2.89520	0.110459
$688$	1.16734	0.0445045
$689$	−24.9130	−0.949108
$690$	0.154436	0.00587928
$691$	−23.8066	−0.905647	−0.452823	−	0.891600i	$-0.649583\pi$
$691$	−23.8066	−0.905647	−0.452823	+	0.891600i	$0.649583\pi$
$692$	22.5405	0.856861
$693$	11.5118	0.437295
$694$	1.30531	0.0495488
$695$	0.609312	0.0231125
$696$	0.243316	0.00922287
$697$	−6.91254	−0.261831
$698$	−25.3608	−0.959919
$699$	−2.61124	−0.0987661
$700$	−3.65509	−0.138150
$701$	41.6890	1.57457	0.787286	−	0.616588i	$-0.211486\pi$
$701$	41.6890	1.57457	0.787286	+	0.616588i	$0.211486\pi$
$702$	9.98106	0.376711
$703$	6.24890	0.235682
$704$	−4.92340	−0.185558
$705$	−0.745117	−0.0280627
$706$	16.9557	0.638136
$707$	−13.9371	−0.524160
$708$	0.587843	0.0220925
$709$	2.08921	0.0784619	0.0392310	−	0.999230i	$-0.487509\pi$
$709$	2.08921	0.0784619	0.0392310	+	0.999230i	$0.487509\pi$
$710$	−10.4013	−0.390352
$711$	41.4269	1.55363
$712$	8.62980	0.323415
$713$	2.29380	0.0859035
$714$	−0.508014	−0.0190119
$715$	−21.5777	−0.806960
$716$	13.6260	0.509228
$717$	6.64157	0.248034
$718$	4.22806	0.157790
$719$	14.7709	0.550863	0.275432	−	0.961321i	$-0.411179\pi$
$719$	14.7709	0.550863	0.275432	+	0.961321i	$0.411179\pi$
$720$	1.86657	0.0695628
$721$	−15.5253	−0.578193
$722$	−6.29756	−0.234371
$723$	−4.75307	−0.176769
$724$	−1.04201	−0.0387258
$725$	−4.59714	−0.170733
$726$	3.22148	0.119560
$727$	2.64865	0.0982331	0.0491166	−	0.998793i	$-0.484359\pi$
$727$	2.64865	0.0982331	0.0491166	+	0.998793i	$0.484359\pi$
$728$	−5.49000	−0.203473
$729$	−23.8554	−0.883534
$730$	−2.16479	−0.0801226
$731$	−3.06544	−0.113379
$732$	−0.921706	−0.0340672
$733$	20.7801	0.767529	0.383764	−	0.923431i	$-0.374627\pi$
$733$	20.7801	0.767529	0.383764	+	0.923431i	$0.374627\pi$
$734$	−22.4539	−0.828790
$735$	0.983426	0.0362742
$736$	−1.00000	−0.0368605
$737$	−56.9900	−2.09925
$738$	−7.74120	−0.284958
$739$	26.4589	0.973306	0.486653	−	0.873595i	$-0.338218\pi$
$739$	26.4589	0.973306	0.486653	+	0.873595i	$0.338218\pi$
$740$	−1.11285	−0.0409094
$741$	−5.98791	−0.219971
$742$	2.86863	0.105311
$743$	−13.1319	−0.481762	−0.240881	−	0.970555i	$-0.577436\pi$
$743$	−13.1319	−0.481762	−0.240881	+	0.970555i	$0.577436\pi$
$744$	−0.558118	−0.0204616
$745$	7.74107	0.283611
$746$	37.1234	1.35918
$747$	24.1314	0.882922
$748$	12.9288	0.472725
$749$	3.37427	0.123293
$750$	1.48214	0.0541203
$751$	46.9709	1.71399	0.856996	−	0.515323i	$-0.172328\pi$
$751$	46.9709	1.71399	0.856996	+	0.515323i	$0.172328\pi$
$752$	4.82476	0.175941
$753$	−3.29582	−0.120106
$754$	−6.90496	−0.251464
$755$	10.8892	0.396299
$756$	−1.14928	−0.0417990
$757$	−54.1198	−1.96702	−0.983509	−	0.180858i	$-0.942113\pi$
$757$	−54.1198	−1.96702	−0.983509	+	0.180858i	$0.942113\pi$
$758$	37.6564	1.36774
$759$	1.19794	0.0434826
$760$	−2.26215	−0.0820569
$761$	−0.197746	−0.00716830	−0.00358415	−	0.999994i	$-0.501141\pi$
$761$	−0.197746	−0.00716830	−0.00358415	+	0.999994i	$0.501141\pi$
$762$	−4.70051	−0.170282
$763$	−7.02818	−0.254437
$764$	0.182175	0.00659086
$765$	−4.90159	−0.177218
$766$	−19.4565	−0.702991
$767$	−16.6822	−0.602358
$768$	0.243316	0.00877991
$769$	−31.6650	−1.14187	−0.570935	−	0.820995i	$-0.693419\pi$
$769$	−31.6650	−1.14187	−0.570935	+	0.820995i	$0.693419\pi$
$770$	2.48459	0.0895384
$771$	−3.49902	−0.126014
$772$	8.02008	0.288649
$773$	41.1790	1.48110	0.740552	−	0.671999i	$-0.234564\pi$
$773$	41.1790	1.48110	0.740552	+	0.671999i	$0.234564\pi$
$774$	−3.43292	−0.123394
$775$	10.5449	0.378784
$776$	−1.49261	−0.0535814
$777$	0.339189	0.0121683
$778$	28.1334	1.00863
$779$	9.38182	0.336138
$780$	1.06638	0.0381824
$781$	−80.6813	−2.88700
$782$	2.62600	0.0939054
$783$	−1.44549	−0.0516576
$784$	−6.36785	−0.227423
$785$	−14.7755	−0.527359
$786$	−1.85938	−0.0663220
$787$	−13.5138	−0.481715	−0.240857	−	0.970561i	$-0.577429\pi$
$787$	−13.5138	−0.481715	−0.240857	+	0.970561i	$0.577429\pi$
$788$	18.7087	0.666470
$789$	−5.13111	−0.182672
$790$	8.94119	0.318113
$791$	−15.5484	−0.552838
$792$	14.4787	0.514479
$793$	26.1567	0.928852
$794$	32.7128	1.16093
$795$	−0.557202	−0.0197619
$796$	−21.0810	−0.747196
$797$	27.0672	0.958769	0.479385	−	0.877605i	$-0.340860\pi$
$797$	27.0672	0.958769	0.479385	+	0.877605i	$0.340860\pi$
$798$	0.689485	0.0244075
$799$	−12.6698	−0.448225
$800$	−4.59714	−0.162533
$801$	−25.3785	−0.896705
$802$	15.5611	0.549481
$803$	−16.7921	−0.592579
$804$	2.81646	0.0993290
$805$	0.504649	0.0177865
$806$	15.8386	0.557891
$807$	2.23925	0.0788253
$808$	−17.5292	−0.616676
$809$	−16.7554	−0.589089	−0.294545	−	0.955638i	$-0.595168\pi$
$809$	−16.7554	−0.589089	−0.294545	+	0.955638i	$0.595168\pi$
$810$	−5.37646	−0.188910
$811$	7.58791	0.266448	0.133224	−	0.991086i	$-0.457467\pi$
$811$	7.58791	0.266448	0.133224	+	0.991086i	$0.457467\pi$
$812$	0.795080	0.0279018
$813$	5.68429	0.199357
$814$	−8.63228	−0.302561
$815$	8.27496	0.289859
$816$	−0.638947	−0.0223676
$817$	4.16047	0.145556
$818$	−22.2320	−0.777323
$819$	16.1450	0.564151
$820$	−1.67079	−0.0583465
$821$	1.73397	0.0605160	0.0302580	−	0.999542i	$-0.490367\pi$
$821$	1.73397	0.0605160	0.0302580	+	0.999542i	$0.490367\pi$
$822$	−1.70264	−0.0593863
$823$	0.200477	0.00698820	0.00349410	−	0.999994i	$-0.498888\pi$
$823$	0.200477	0.00698820	0.00349410	+	0.999994i	$0.498888\pi$
$824$	−19.5267	−0.680245
$825$	5.50711	0.191733
$826$	1.92089	0.0668362
$827$	28.7857	1.00098	0.500489	−	0.865743i	$-0.333154\pi$
$827$	28.7857	1.00098	0.500489	+	0.865743i	$0.333154\pi$
$828$	2.94080	0.102200
$829$	−50.5248	−1.75480	−0.877399	−	0.479762i	$-0.840723\pi$
$829$	−50.5248	−1.75480	−0.877399	+	0.479762i	$0.840723\pi$
$830$	5.20830	0.180783
$831$	−3.59870	−0.124837
$832$	−6.90496	−0.239387
$833$	16.7219	0.579381
$834$	−0.233578	−0.00808814
$835$	−9.37072	−0.324287
$836$	−17.5472	−0.606884
$837$	3.31567	0.114606
$838$	−16.5061	−0.570195
$839$	3.61969	0.124966	0.0624828	−	0.998046i	$-0.480098\pi$
$839$	3.61969	0.124966	0.0624828	+	0.998046i	$0.480098\pi$
$840$	−0.122789	−0.00423663
$841$	1.00000	0.0344828
$842$	5.39560	0.185945
$843$	2.06038	0.0709633
$844$	13.1197	0.451597
$845$	−22.0109	−0.757200
$846$	−14.1886	−0.487815
$847$	10.5268	0.361705
$848$	3.60798	0.123898
$849$	−0.993413	−0.0340939
$850$	12.0721	0.414068
$851$	−1.75332	−0.0601029
$852$	3.98729	0.136602
$853$	40.5815	1.38948	0.694742	−	0.719259i	$-0.255519\pi$
$853$	40.5815	1.38948	0.694742	+	0.719259i	$0.255519\pi$
$854$	−3.01185	−0.103063
$855$	6.65253	0.227512
$856$	4.24394	0.145055
$857$	26.7392	0.913393	0.456697	−	0.889623i	$-0.349032\pi$
$857$	26.7392	0.913393	0.456697	+	0.889623i	$0.349032\pi$
$858$	8.27175	0.282393
$859$	−3.21508	−0.109697	−0.0548485	−	0.998495i	$-0.517468\pi$
$859$	−3.21508	−0.109697	−0.0548485	+	0.998495i	$0.517468\pi$
$860$	−0.740929	−0.0252655
$861$	0.509243	0.0173550
$862$	−30.6347	−1.04342
$863$	2.02117	0.0688014	0.0344007	−	0.999408i	$-0.489048\pi$
$863$	2.02117	0.0688014	0.0344007	+	0.999408i	$0.489048\pi$
$864$	−1.44549	−0.0491766
$865$	−14.3068	−0.486445
$866$	−22.8241	−0.775594
$867$	−2.45850	−0.0834951
$868$	−1.82375	−0.0619023
$869$	69.3558	2.35273
$870$	−0.154436	−0.00523588
$871$	−79.9272	−2.70823
$872$	−8.83959	−0.299346
$873$	4.38945	0.148560
$874$	−3.56405	−0.120556
$875$	4.84319	0.163730
$876$	0.829868	0.0280386
$877$	−12.6206	−0.426166	−0.213083	−	0.977034i	$-0.568351\pi$
$877$	−12.6206	−0.426166	−0.213083	+	0.977034i	$0.568351\pi$
$878$	−25.5557	−0.862464
$879$	4.78183	0.161287
$880$	3.12496	0.105342
$881$	−1.33788	−0.0450744	−0.0225372	−	0.999746i	$-0.507174\pi$
$881$	−1.33788	−0.0450744	−0.0225372	+	0.999746i	$0.507174\pi$
$882$	18.7265	0.630556
$883$	13.6849	0.460533	0.230267	−	0.973128i	$-0.426040\pi$
$883$	13.6849	0.460533	0.230267	+	0.973128i	$0.426040\pi$
$884$	18.1324	0.609859
$885$	−0.373112	−0.0125420
$886$	16.3596	0.549612
$887$	−29.8007	−1.00061	−0.500305	−	0.865849i	$-0.666779\pi$
$887$	−29.8007	−1.00061	−0.500305	+	0.865849i	$0.666779\pi$
$888$	0.426610	0.0143161
$889$	−15.3598	−0.515151
$890$	−5.47746	−0.183605
$891$	−41.7046	−1.39716
$892$	10.8057	0.361801
$893$	17.1957	0.575431
$894$	−2.96752	−0.0992486
$895$	−8.64862	−0.289092
$896$	0.795080	0.0265618
$897$	1.68009	0.0560965
$898$	25.4225	0.848360
$899$	−2.29380	−0.0765025
$900$	13.5193	0.450642
$901$	−9.47453	−0.315642
$902$	−12.9601	−0.431525
$903$	0.225829	0.00751512
$904$	−19.5558	−0.650415
$905$	0.661376	0.0219849
$906$	−4.17435	−0.138683
$907$	25.3639	0.842195	0.421097	−	0.907015i	$-0.361645\pi$
$907$	25.3639	0.842195	0.421097	+	0.907015i	$0.361645\pi$
$908$	−16.6355	−0.552070
$909$	51.5499	1.70980
$910$	3.48458	0.115513
$911$	−32.6389	−1.08138	−0.540688	−	0.841223i	$-0.681836\pi$
$911$	−32.6389	−1.08138	−0.540688	+	0.841223i	$0.681836\pi$
$912$	0.867190	0.0287155
$913$	40.4002	1.33705
$914$	8.98560	0.297217
$915$	0.585020	0.0193402
$916$	11.8989	0.393152
$917$	−6.07588	−0.200643
$918$	3.79585	0.125282
$919$	−25.3518	−0.836280	−0.418140	−	0.908383i	$-0.637318\pi$
$919$	−25.3518	−0.836280	−0.418140	+	0.908383i	$0.637318\pi$
$920$	0.634714	0.0209259
$921$	0.470984	0.0155195
$922$	−26.4822	−0.872144
$923$	−113.154	−3.72450
$924$	−0.952461	−0.0313337
$925$	−8.06023	−0.265019
$926$	−1.99103	−0.0654292
$927$	57.4241	1.88605
$928$	1.00000	0.0328266
$929$	−26.6176	−0.873295	−0.436647	−	0.899633i	$-0.643834\pi$
$929$	−26.6176	−0.873295	−0.436647	+	0.899633i	$0.643834\pi$
$930$	0.354246	0.0116162
$931$	−22.6953	−0.743809
$932$	−10.7319	−0.351535
$933$	−1.26751	−0.0414963
$934$	−33.6408	−1.10076
$935$	−8.20612	−0.268369
$936$	20.3061	0.663726
$937$	11.8880	0.388365	0.194183	−	0.980965i	$-0.437795\pi$
$937$	11.8880	0.388365	0.194183	+	0.980965i	$0.437795\pi$
$938$	9.20332	0.300499
$939$	−4.98826	−0.162786
$940$	−3.06234	−0.0998826
$941$	−25.4117	−0.828397	−0.414198	−	0.910187i	$-0.635938\pi$
$941$	−25.4117	−0.828397	−0.414198	+	0.910187i	$0.635938\pi$
$942$	5.66414	0.184548
$943$	−2.63235	−0.0857211
$944$	2.41597	0.0786330
$945$	0.729465	0.0237295
$946$	−5.74730	−0.186861
$947$	19.0952	0.620512	0.310256	−	0.950653i	$-0.399585\pi$
$947$	19.0952	0.620512	0.310256	+	0.950653i	$0.399585\pi$
$948$	−3.42758	−0.111323
$949$	−23.5505	−0.764481
$950$	−16.3844	−0.531581
$951$	−6.21343	−0.201484
$952$	−2.08788	−0.0676685
$953$	−24.8120	−0.803739	−0.401870	−	0.915697i	$-0.631639\pi$
$953$	−24.8120	−0.803739	−0.401870	+	0.915697i	$0.631639\pi$
$954$	−10.6103	−0.343522
$955$	−0.115629	−0.00374167
$956$	27.2961	0.882818
$957$	−1.19794	−0.0387240
$958$	2.83083	0.0914598
$959$	−5.56368	−0.179661
$960$	−0.154436	−0.00498441
$961$	−25.7385	−0.830274
$962$	−12.1066	−0.390332
$963$	−12.4806	−0.402181
$964$	−19.5346	−0.629166
$965$	−5.09046	−0.163868
$966$	−0.193456	−0.00622434
$967$	−17.8124	−0.572808	−0.286404	−	0.958109i	$-0.592460\pi$
$967$	−17.8124	−0.572808	−0.286404	+	0.958109i	$0.592460\pi$
$968$	13.2399	0.425547
$969$	−2.27724	−0.0731554
$970$	0.947379	0.0304185
$971$	39.8122	1.27764	0.638818	−	0.769358i	$-0.279424\pi$
$971$	39.8122	1.27764	0.638818	+	0.769358i	$0.279424\pi$
$972$	6.39752	0.205201
$973$	−0.763259	−0.0244690
$974$	16.3929	0.525263
$975$	7.72359	0.247353
$976$	−3.78810	−0.121254
$977$	2.67025	0.0854288	0.0427144	−	0.999087i	$-0.486399\pi$
$977$	2.67025	0.0854288	0.0427144	+	0.999087i	$0.486399\pi$
$978$	−3.17218	−0.101435
$979$	−42.4880	−1.35792
$980$	4.04176	0.129109
$981$	25.9954	0.829971
$982$	−8.08896	−0.258129
$983$	30.7527	0.980860	0.490430	−	0.871481i	$-0.336840\pi$
$983$	30.7527	0.980860	0.490430	+	0.871481i	$0.336840\pi$
$984$	0.640493	0.0204182
$985$	−11.8747	−0.378359
$986$	−2.62600	−0.0836287
$987$	0.933377	0.0297097
$988$	−24.6096	−0.782936
$989$	−1.16734	−0.0371193
$990$	−9.18986	−0.292073
$991$	7.47434	0.237430	0.118715	−	0.992928i	$-0.462122\pi$
$991$	7.47434	0.237430	0.118715	+	0.992928i	$0.462122\pi$
$992$	−2.29380	−0.0728282
$993$	−4.20718	−0.133511
$994$	13.0292	0.413262
$995$	13.3804	0.424188
$996$	−1.99659	−0.0632643
$997$	−33.5272	−1.06182	−0.530909	−	0.847429i	$-0.678149\pi$
$997$	−33.5272	−1.06182	−0.530909	+	0.847429i	$0.678149\pi$
$998$	18.4497	0.584014
$999$	−2.53440	−0.0801849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.h.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.h.1.4	✓	5	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.243316 q^{3} +1.00000 q^{4} -0.634714 q^{5} +0.243316 q^{6} +0.795080 q^{7} +1.00000 q^{8} -2.94080 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.243316 q^{3} +1.00000 q^{4} -0.634714 q^{5} +0.243316 q^{6} +0.795080 q^{7} +1.00000 q^{8} -2.94080 q^{9} -0.634714 q^{10} -4.92340 q^{11} +0.243316 q^{12} -6.90496 q^{13} +0.795080 q^{14} -0.154436 q^{15} +1.00000 q^{16} -2.62600 q^{17} -2.94080 q^{18} +3.56405 q^{19} -0.634714 q^{20} +0.193456 q^{21} -4.92340 q^{22} -1.00000 q^{23} +0.243316 q^{24} -4.59714 q^{25} -6.90496 q^{26} -1.44549 q^{27} +0.795080 q^{28} +1.00000 q^{29} -0.154436 q^{30} -2.29380 q^{31} +1.00000 q^{32} -1.19794 q^{33} -2.62600 q^{34} -0.504649 q^{35} -2.94080 q^{36} +1.75332 q^{37} +3.56405 q^{38} -1.68009 q^{39} -0.634714 q^{40} +2.63235 q^{41} +0.193456 q^{42} +1.16734 q^{43} -4.92340 q^{44} +1.86657 q^{45} -1.00000 q^{46} +4.82476 q^{47} +0.243316 q^{48} -6.36785 q^{49} -4.59714 q^{50} -0.638947 q^{51} -6.90496 q^{52} +3.60798 q^{53} -1.44549 q^{54} +3.12496 q^{55} +0.795080 q^{56} +0.867190 q^{57} +1.00000 q^{58} +2.41597 q^{59} -0.154436 q^{60} -3.78810 q^{61} -2.29380 q^{62} -2.33817 q^{63} +1.00000 q^{64} +4.38268 q^{65} -1.19794 q^{66} +11.5753 q^{67} -2.62600 q^{68} -0.243316 q^{69} -0.504649 q^{70} +16.3873 q^{71} -2.94080 q^{72} +3.41066 q^{73} +1.75332 q^{74} -1.11856 q^{75} +3.56405 q^{76} -3.91450 q^{77} -1.68009 q^{78} -14.0870 q^{79} -0.634714 q^{80} +8.47068 q^{81} +2.63235 q^{82} -8.20574 q^{83} +0.193456 q^{84} +1.66676 q^{85} +1.16734 q^{86} +0.243316 q^{87} -4.92340 q^{88} +8.62980 q^{89} +1.86657 q^{90} -5.49000 q^{91} -1.00000 q^{92} -0.558118 q^{93} +4.82476 q^{94} -2.26215 q^{95} +0.243316 q^{96} -1.49261 q^{97} -6.36785 q^{98} +14.4787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * q^99

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