LMFDB - Embedded newform 1334.2.a.h.1.3

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			1.3
Root			$0.458358$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.366335 q^{3} +1.00000 q^{4} +1.52258 q^{5} -0.366335 q^{6} -3.90505 q^{7} +1.00000 q^{8} -2.86580 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.366335 q^{3} +1.00000 q^{4} +1.52258 q^{5} -0.366335 q^{6} -3.90505 q^{7} +1.00000 q^{8} -2.86580 q^{9} +1.52258 q^{10} -4.33155 q^{11} -0.366335 q^{12} +4.63479 q^{13} -3.90505 q^{14} -0.557774 q^{15} +1.00000 q^{16} -4.69049 q^{17} -2.86580 q^{18} -2.13127 q^{19} +1.52258 q^{20} +1.43056 q^{21} -4.33155 q^{22} -1.00000 q^{23} -0.366335 q^{24} -2.68175 q^{25} +4.63479 q^{26} +2.14885 q^{27} -3.90505 q^{28} +1.00000 q^{29} -0.557774 q^{30} -5.98094 q^{31} +1.00000 q^{32} +1.58680 q^{33} -4.69049 q^{34} -5.94574 q^{35} -2.86580 q^{36} -11.4654 q^{37} -2.13127 q^{38} -1.69789 q^{39} +1.52258 q^{40} +6.03817 q^{41} +1.43056 q^{42} +6.10938 q^{43} -4.33155 q^{44} -4.36340 q^{45} -1.00000 q^{46} -0.963358 q^{47} -0.366335 q^{48} +8.24939 q^{49} -2.68175 q^{50} +1.71829 q^{51} +4.63479 q^{52} -0.987920 q^{53} +2.14885 q^{54} -6.59513 q^{55} -3.90505 q^{56} +0.780760 q^{57} +1.00000 q^{58} -2.34136 q^{59} -0.557774 q^{60} +8.39689 q^{61} -5.98094 q^{62} +11.1911 q^{63} +1.00000 q^{64} +7.05683 q^{65} +1.58680 q^{66} -15.1163 q^{67} -4.69049 q^{68} +0.366335 q^{69} -5.94574 q^{70} -3.56131 q^{71} -2.86580 q^{72} +7.74304 q^{73} -11.4654 q^{74} +0.982421 q^{75} -2.13127 q^{76} +16.9149 q^{77} -1.69789 q^{78} -0.321281 q^{79} +1.52258 q^{80} +7.81020 q^{81} +6.03817 q^{82} -7.83800 q^{83} +1.43056 q^{84} -7.14164 q^{85} +6.10938 q^{86} -0.366335 q^{87} -4.33155 q^{88} -6.86060 q^{89} -4.36340 q^{90} -18.0991 q^{91} -1.00000 q^{92} +2.19103 q^{93} -0.963358 q^{94} -3.24503 q^{95} -0.366335 q^{96} +11.6333 q^{97} +8.24939 q^{98} +12.4134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.366335	−0.211504	−0.105752	−	0.994393i	$-0.533725\pi$
$3$	−0.366335	−0.211504	−0.105752	+	0.994393i	$0.533725\pi$
$4$	1.00000	0.500000
$5$	1.52258	0.680918	0.340459	−	0.940259i	$-0.389418\pi$
$5$	1.52258	0.680918	0.340459	+	0.940259i	$0.389418\pi$
$6$	−0.366335	−0.149556
$7$	−3.90505	−1.47597	−0.737984	−	0.674818i	$-0.764222\pi$
$7$	−3.90505	−1.47597	−0.737984	+	0.674818i	$0.764222\pi$
$8$	1.00000	0.353553
$9$	−2.86580	−0.955266
$10$	1.52258	0.481482
$11$	−4.33155	−1.30601	−0.653006	−	0.757353i	$-0.726492\pi$
$11$	−4.33155	−1.30601	−0.653006	+	0.757353i	$0.726492\pi$
$12$	−0.366335	−0.105752
$13$	4.63479	1.28546	0.642729	−	0.766093i	$-0.277802\pi$
$13$	4.63479	1.28546	0.642729	+	0.766093i	$0.277802\pi$
$14$	−3.90505	−1.04367
$15$	−0.557774	−0.144017
$16$	1.00000	0.250000
$17$	−4.69049	−1.13761	−0.568806	−	0.822472i	$-0.692594\pi$
$17$	−4.69049	−1.13761	−0.568806	+	0.822472i	$0.692594\pi$
$18$	−2.86580	−0.675475
$19$	−2.13127	−0.488947	−0.244473	−	0.969656i	$-0.578615\pi$
$19$	−2.13127	−0.488947	−0.244473	+	0.969656i	$0.578615\pi$
$20$	1.52258	0.340459
$21$	1.43056	0.312173
$22$	−4.33155	−0.923490
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.366335	−0.0747779
$25$	−2.68175	−0.536351
$26$	4.63479	0.908956
$27$	2.14885	0.413546
$28$	−3.90505	−0.737984
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.557774	−0.101835
$31$	−5.98094	−1.07421	−0.537104	−	0.843516i	$-0.680482\pi$
$31$	−5.98094	−1.07421	−0.537104	+	0.843516i	$0.680482\pi$
$32$	1.00000	0.176777
$33$	1.58680	0.276226
$34$	−4.69049	−0.804413
$35$	−5.94574	−1.00501
$36$	−2.86580	−0.477633
$37$	−11.4654	−1.88490	−0.942449	−	0.334350i	$-0.891483\pi$
$37$	−11.4654	−1.88490	−0.942449	+	0.334350i	$0.891483\pi$
$38$	−2.13127	−0.345738
$39$	−1.69789	−0.271879
$40$	1.52258	0.240741
$41$	6.03817	0.943004	0.471502	−	0.881865i	$-0.343712\pi$
$41$	6.03817	0.943004	0.471502	+	0.881865i	$0.343712\pi$
$42$	1.43056	0.220740
$43$	6.10938	0.931672	0.465836	−	0.884871i	$-0.345754\pi$
$43$	6.10938	0.931672	0.465836	+	0.884871i	$0.345754\pi$
$44$	−4.33155	−0.653006
$45$	−4.36340	−0.650458
$46$	−1.00000	−0.147442
$47$	−0.963358	−0.140520	−0.0702601	−	0.997529i	$-0.522383\pi$
$47$	−0.963358	−0.140520	−0.0702601	+	0.997529i	$0.522383\pi$
$48$	−0.366335	−0.0528760
$49$	8.24939	1.17848
$50$	−2.68175	−0.379257
$51$	1.71829	0.240609
$52$	4.63479	0.642729
$53$	−0.987920	−0.135701	−0.0678506	−	0.997695i	$-0.521614\pi$
$53$	−0.987920	−0.135701	−0.0678506	+	0.997695i	$0.521614\pi$
$54$	2.14885	0.292421
$55$	−6.59513	−0.889287
$56$	−3.90505	−0.521834
$57$	0.780760	0.103414
$58$	1.00000	0.131306
$59$	−2.34136	−0.304819	−0.152410	−	0.988317i	$-0.548703\pi$
$59$	−2.34136	−0.304819	−0.152410	+	0.988317i	$0.548703\pi$
$60$	−0.557774	−0.0720084
$61$	8.39689	1.07511	0.537556	−	0.843228i	$-0.319348\pi$
$61$	8.39689	1.07511	0.537556	+	0.843228i	$0.319348\pi$
$62$	−5.98094	−0.759580
$63$	11.1911	1.40994
$64$	1.00000	0.125000
$65$	7.05683	0.875292
$66$	1.58680	0.195322
$67$	−15.1163	−1.84675	−0.923375	−	0.383898i	$-0.874581\pi$
$67$	−15.1163	−1.84675	−0.923375	+	0.383898i	$0.874581\pi$
$68$	−4.69049	−0.568806
$69$	0.366335	0.0441016
$70$	−5.94574	−0.710652
$71$	−3.56131	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$71$	−3.56131	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$72$	−2.86580	−0.337738
$73$	7.74304	0.906255	0.453127	−	0.891446i	$-0.350308\pi$
$73$	7.74304	0.906255	0.453127	+	0.891446i	$0.350308\pi$
$74$	−11.4654	−1.33282
$75$	0.982421	0.113440
$76$	−2.13127	−0.244473
$77$	16.9149	1.92763
$78$	−1.69789	−0.192248
$79$	−0.321281	−0.0361469	−0.0180735	−	0.999837i	$-0.505753\pi$
$79$	−0.321281	−0.0361469	−0.0180735	+	0.999837i	$0.505753\pi$
$80$	1.52258	0.170229
$81$	7.81020	0.867800
$82$	6.03817	0.666805
$83$	−7.83800	−0.860332	−0.430166	−	0.902750i	$-0.641545\pi$
$83$	−7.83800	−0.860332	−0.430166	+	0.902750i	$0.641545\pi$
$84$	1.43056	0.156087
$85$	−7.14164	−0.774620
$86$	6.10938	0.658791
$87$	−0.366335	−0.0392753
$88$	−4.33155	−0.461745
$89$	−6.86060	−0.727222	−0.363611	−	0.931551i	$-0.618456\pi$
$89$	−6.86060	−0.727222	−0.363611	+	0.931551i	$0.618456\pi$
$90$	−4.36340	−0.459943
$91$	−18.0991	−1.89730
$92$	−1.00000	−0.104257
$93$	2.19103	0.227199
$94$	−0.963358	−0.0993628
$95$	−3.24503	−0.332933
$96$	−0.366335	−0.0373889
$97$	11.6333	1.18118	0.590591	−	0.806971i	$-0.298895\pi$
$97$	11.6333	1.18118	0.590591	+	0.806971i	$0.298895\pi$
$98$	8.24939	0.833314
$99$	12.4134	1.24759
$100$	−2.68175	−0.268175
$101$	15.9101	1.58312	0.791558	−	0.611094i	$-0.209270\pi$
$101$	15.9101	1.58312	0.791558	+	0.611094i	$0.209270\pi$
$102$	1.71829	0.170136
$103$	6.09854	0.600907	0.300453	−	0.953796i	$-0.402862\pi$
$103$	6.09854	0.600907	0.300453	+	0.953796i	$0.402862\pi$
$104$	4.63479	0.454478
$105$	2.17814	0.212564
$106$	−0.987920	−0.0959553
$107$	9.77783	0.945258	0.472629	−	0.881261i	$-0.343305\pi$
$107$	9.77783	0.945258	0.472629	+	0.881261i	$0.343305\pi$
$108$	2.14885	0.206773
$109$	−20.3429	−1.94849	−0.974246	−	0.225487i	$-0.927603\pi$
$109$	−20.3429	−1.94849	−0.974246	+	0.225487i	$0.927603\pi$
$110$	−6.59513	−0.628821
$111$	4.20018	0.398663
$112$	−3.90505	−0.368992
$113$	13.3010	1.25125	0.625627	−	0.780122i	$-0.284843\pi$
$113$	13.3010	1.25125	0.625627	+	0.780122i	$0.284843\pi$
$114$	0.780760	0.0731248
$115$	−1.52258	−0.141981
$116$	1.00000	0.0928477
$117$	−13.2824	−1.22795
$118$	−2.34136	−0.215540
$119$	18.3166	1.67908
$120$	−0.557774	−0.0509176
$121$	7.76233	0.705666
$122$	8.39689	0.760219
$123$	−2.21200	−0.199449
$124$	−5.98094	−0.537104
$125$	−11.6961	−1.04613
$126$	11.1911	0.996980
$127$	−8.58461	−0.761761	−0.380880	−	0.924624i	$-0.624379\pi$
$127$	−8.58461	−0.761761	−0.380880	+	0.924624i	$0.624379\pi$
$128$	1.00000	0.0883883
$129$	−2.23808	−0.197052
$130$	7.05683	0.618925
$131$	−10.7184	−0.936475	−0.468237	−	0.883603i	$-0.655111\pi$
$131$	−10.7184	−0.936475	−0.468237	+	0.883603i	$0.655111\pi$
$132$	1.58680	0.138113
$133$	8.32271	0.721670
$134$	−15.1163	−1.30585
$135$	3.27179	0.281591
$136$	−4.69049	−0.402206
$137$	−12.5608	−1.07314	−0.536569	−	0.843857i	$-0.680280\pi$
$137$	−12.5608	−1.07314	−0.536569	+	0.843857i	$0.680280\pi$
$138$	0.366335	0.0311845
$139$	19.2653	1.63406	0.817029	−	0.576597i	$-0.195620\pi$
$139$	19.2653	1.63406	0.817029	+	0.576597i	$0.195620\pi$
$140$	−5.94574	−0.502507
$141$	0.352912	0.0297205
$142$	−3.56131	−0.298859
$143$	−20.0758	−1.67882
$144$	−2.86580	−0.238817
$145$	1.52258	0.126443
$146$	7.74304	0.640819
$147$	−3.02204	−0.249254
$148$	−11.4654	−0.942449
$149$	−13.7285	−1.12469	−0.562343	−	0.826904i	$-0.690100\pi$
$149$	−13.7285	−1.12469	−0.562343	+	0.826904i	$0.690100\pi$
$150$	0.982421	0.0802143
$151$	−7.42368	−0.604130	−0.302065	−	0.953287i	$-0.597676\pi$
$151$	−7.42368	−0.604130	−0.302065	+	0.953287i	$0.597676\pi$
$152$	−2.13127	−0.172869
$153$	13.4420	1.08672
$154$	16.9149	1.36304
$155$	−9.10645	−0.731447
$156$	−1.69789	−0.135940
$157$	−17.0356	−1.35959	−0.679796	−	0.733402i	$-0.737931\pi$
$157$	−17.0356	−1.35959	−0.679796	+	0.733402i	$0.737931\pi$
$158$	−0.321281	−0.0255597
$159$	0.361910	0.0287013
$160$	1.52258	0.120370
$161$	3.90505	0.307761
$162$	7.81020	0.613627
$163$	10.0930	0.790548	0.395274	−	0.918563i	$-0.370650\pi$
$163$	10.0930	0.790548	0.395274	+	0.918563i	$0.370650\pi$
$164$	6.03817	0.471502
$165$	2.41603	0.188088
$166$	−7.83800	−0.608347
$167$	−12.8126	−0.991465	−0.495733	−	0.868475i	$-0.665100\pi$
$167$	−12.8126	−0.991465	−0.495733	+	0.868475i	$0.665100\pi$
$168$	1.43056	0.110370
$169$	8.48124	0.652403
$170$	−7.14164	−0.547739
$171$	6.10779	0.467074
$172$	6.10938	0.465836
$173$	3.77559	0.287053	0.143526	−	0.989647i	$-0.454156\pi$
$173$	3.77559	0.287053	0.143526	+	0.989647i	$0.454156\pi$
$174$	−0.366335	−0.0277718
$175$	10.4724	0.791637
$176$	−4.33155	−0.326503
$177$	0.857724	0.0644705
$178$	−6.86060	−0.514224
$179$	−19.9802	−1.49339	−0.746697	−	0.665164i	$-0.768361\pi$
$179$	−19.9802	−1.49339	−0.746697	+	0.665164i	$0.768361\pi$
$180$	−4.36340	−0.325229
$181$	10.6113	0.788729	0.394364	−	0.918954i	$-0.370965\pi$
$181$	10.6113	0.788729	0.394364	+	0.918954i	$0.370965\pi$
$182$	−18.0991	−1.34159
$183$	−3.07608	−0.227390
$184$	−1.00000	−0.0737210
$185$	−17.4570	−1.28346
$186$	2.19103	0.160654
$187$	20.3171	1.48573
$188$	−0.963358	−0.0702601
$189$	−8.39136	−0.610381
$190$	−3.24503	−0.235419
$191$	22.4156	1.62194	0.810968	−	0.585091i	$-0.198941\pi$
$191$	22.4156	1.62194	0.810968	+	0.585091i	$0.198941\pi$
$192$	−0.366335	−0.0264380
$193$	8.83224	0.635758	0.317879	−	0.948131i	$-0.397029\pi$
$193$	8.83224	0.635758	0.317879	+	0.948131i	$0.397029\pi$
$194$	11.6333	0.835222
$195$	−2.58517	−0.185128
$196$	8.24939	0.589242
$197$	7.20749	0.513512	0.256756	−	0.966476i	$-0.417346\pi$
$197$	7.20749	0.513512	0.256756	+	0.966476i	$0.417346\pi$
$198$	12.4134	0.882178
$199$	16.4488	1.16603	0.583013	−	0.812463i	$-0.301874\pi$
$199$	16.4488	1.16603	0.583013	+	0.812463i	$0.301874\pi$
$200$	−2.68175	−0.189629
$201$	5.53764	0.390595
$202$	15.9101	1.11943
$203$	−3.90505	−0.274081
$204$	1.71829	0.120305
$205$	9.19360	0.642109
$206$	6.09854	0.424905
$207$	2.86580	0.199187
$208$	4.63479	0.321365
$209$	9.23170	0.638570
$210$	2.17814	0.150306
$211$	−23.1815	−1.59588	−0.797939	−	0.602739i	$-0.794076\pi$
$211$	−23.1815	−1.59588	−0.797939	+	0.602739i	$0.794076\pi$
$212$	−0.987920	−0.0678506
$213$	1.30463	0.0893921
$214$	9.77783	0.668399
$215$	9.30201	0.634392
$216$	2.14885	0.146211
$217$	23.3558	1.58550
$218$	−20.3429	−1.37779
$219$	−2.83655	−0.191676
$220$	−6.59513	−0.444643
$221$	−21.7394	−1.46235
$222$	4.20018	0.281897
$223$	−28.4238	−1.90340	−0.951700	−	0.307030i	$-0.900665\pi$
$223$	−28.4238	−1.90340	−0.951700	+	0.307030i	$0.900665\pi$
$224$	−3.90505	−0.260917
$225$	7.68537	0.512358
$226$	13.3010	0.884770
$227$	−9.41037	−0.624588	−0.312294	−	0.949985i	$-0.601097\pi$
$227$	−9.41037	−0.624588	−0.312294	+	0.949985i	$0.601097\pi$
$228$	0.780760	0.0517071
$229$	4.87627	0.322233	0.161117	−	0.986935i	$-0.448490\pi$
$229$	4.87627	0.322233	0.161117	+	0.986935i	$0.448490\pi$
$230$	−1.52258	−0.100396
$231$	−6.19653	−0.407702
$232$	1.00000	0.0656532
$233$	14.0151	0.918162	0.459081	−	0.888394i	$-0.348179\pi$
$233$	14.0151	0.918162	0.459081	+	0.888394i	$0.348179\pi$
$234$	−13.2824	−0.868295
$235$	−1.46679	−0.0956827
$236$	−2.34136	−0.152410
$237$	0.117697	0.00764521
$238$	18.3166	1.18729
$239$	−8.67974	−0.561446	−0.280723	−	0.959789i	$-0.590574\pi$
$239$	−8.67974	−0.561446	−0.280723	+	0.959789i	$0.590574\pi$
$240$	−0.557774	−0.0360042
$241$	−3.71583	−0.239358	−0.119679	−	0.992813i	$-0.538186\pi$
$241$	−3.71583	−0.239358	−0.119679	+	0.992813i	$0.538186\pi$
$242$	7.76233	0.498981
$243$	−9.30770	−0.597089
$244$	8.39689	0.537556
$245$	12.5603	0.802451
$246$	−2.21200	−0.141032
$247$	−9.87798	−0.628521
$248$	−5.98094	−0.379790
$249$	2.87134	0.181963
$250$	−11.6961	−0.739725
$251$	27.5571	1.73939	0.869695	−	0.493589i	$-0.164315\pi$
$251$	27.5571	1.73939	0.869695	+	0.493589i	$0.164315\pi$
$252$	11.1911	0.704972
$253$	4.33155	0.272322
$254$	−8.58461	−0.538646
$255$	2.61624	0.163835
$256$	1.00000	0.0625000
$257$	−2.44598	−0.152576	−0.0762880	−	0.997086i	$-0.524307\pi$
$257$	−2.44598	−0.152576	−0.0762880	+	0.997086i	$0.524307\pi$
$258$	−2.23808	−0.139337
$259$	44.7729	2.78205
$260$	7.05683	0.437646
$261$	−2.86580	−0.177388
$262$	−10.7184	−0.662188
$263$	21.7390	1.34048	0.670242	−	0.742142i	$-0.266190\pi$
$263$	21.7390	1.34048	0.670242	+	0.742142i	$0.266190\pi$
$264$	1.58680	0.0976608
$265$	−1.50419	−0.0924014
$266$	8.32271	0.510298
$267$	2.51328	0.153810
$268$	−15.1163	−0.923375
$269$	8.54001	0.520693	0.260347	−	0.965515i	$-0.416163\pi$
$269$	8.54001	0.520693	0.260347	+	0.965515i	$0.416163\pi$
$270$	3.27179	0.199115
$271$	22.2221	1.34989	0.674947	−	0.737866i	$-0.264166\pi$
$271$	22.2221	1.34989	0.674947	+	0.737866i	$0.264166\pi$
$272$	−4.69049	−0.284403
$273$	6.63032	0.401285
$274$	−12.5608	−0.758823
$275$	11.6162	0.700480
$276$	0.366335	0.0220508
$277$	−4.14650	−0.249139	−0.124570	−	0.992211i	$-0.539755\pi$
$277$	−4.14650	−0.249139	−0.124570	+	0.992211i	$0.539755\pi$
$278$	19.2653	1.15545
$279$	17.1402	1.02615
$280$	−5.94574	−0.355326
$281$	22.7259	1.35571	0.677857	−	0.735193i	$-0.262909\pi$
$281$	22.7259	1.35571	0.677857	+	0.735193i	$0.262909\pi$
$282$	0.352912	0.0210156
$283$	27.4038	1.62899	0.814493	−	0.580174i	$-0.197015\pi$
$283$	27.4038	1.62899	0.814493	+	0.580174i	$0.197015\pi$
$284$	−3.56131	−0.211325
$285$	1.18877	0.0704165
$286$	−20.0758	−1.18711
$287$	−23.5793	−1.39185
$288$	−2.86580	−0.168869
$289$	5.00071	0.294159
$290$	1.52258	0.0894089
$291$	−4.26169	−0.249825
$292$	7.74304	0.453127
$293$	−24.5824	−1.43612	−0.718058	−	0.695983i	$-0.754969\pi$
$293$	−24.5824	−1.43612	−0.718058	+	0.695983i	$0.754969\pi$
$294$	−3.02204	−0.176249
$295$	−3.56491	−0.207557
$296$	−11.4654	−0.666412
$297$	−9.30785	−0.540096
$298$	−13.7285	−0.795273
$299$	−4.63479	−0.268037
$300$	0.982421	0.0567201
$301$	−23.8574	−1.37512
$302$	−7.42368	−0.427185
$303$	−5.82844	−0.334835
$304$	−2.13127	−0.122237
$305$	12.7849	0.732063
$306$	13.4420	0.768428
$307$	12.8064	0.730902	0.365451	−	0.930831i	$-0.380915\pi$
$307$	12.8064	0.730902	0.365451	+	0.930831i	$0.380915\pi$
$308$	16.9149	0.963816
$309$	−2.23411	−0.127094
$310$	−9.10645	−0.517211
$311$	−7.45851	−0.422933	−0.211467	−	0.977385i	$-0.567824\pi$
$311$	−7.45851	−0.422933	−0.211467	+	0.977385i	$0.567824\pi$
$312$	−1.69789	−0.0961239
$313$	−13.6848	−0.773513	−0.386756	−	0.922182i	$-0.626405\pi$
$313$	−13.6848	−0.773513	−0.386756	+	0.922182i	$0.626405\pi$
$314$	−17.0356	−0.961376
$315$	17.0393	0.960056
$316$	−0.321281	−0.0180735
$317$	20.5899	1.15644	0.578221	−	0.815880i	$-0.303747\pi$
$317$	20.5899	1.15644	0.578221	+	0.815880i	$0.303747\pi$
$318$	0.361910	0.0202949
$319$	−4.33155	−0.242520
$320$	1.52258	0.0851147
$321$	−3.58196	−0.199926
$322$	3.90505	0.217620
$323$	9.99671	0.556232
$324$	7.81020	0.433900
$325$	−12.4294	−0.689456
$326$	10.0930	0.559002
$327$	7.45231	0.412114
$328$	6.03817	0.333402
$329$	3.76196	0.207403
$330$	2.41603	0.132998
$331$	−5.90381	−0.324503	−0.162251	−	0.986749i	$-0.551876\pi$
$331$	−5.90381	−0.324503	−0.162251	+	0.986749i	$0.551876\pi$
$332$	−7.83800	−0.430166
$333$	32.8575	1.80058
$334$	−12.8126	−0.701072
$335$	−23.0158	−1.25749
$336$	1.43056	0.0780433
$337$	33.7788	1.84005	0.920024	−	0.391863i	$-0.128169\pi$
$337$	33.7788	1.84005	0.920024	+	0.391863i	$0.128169\pi$
$338$	8.48124	0.461319
$339$	−4.87263	−0.264645
$340$	−7.14164	−0.387310
$341$	25.9067	1.40293
$342$	6.10779	0.330272
$343$	−4.87891	−0.263437
$344$	6.10938	0.329396
$345$	0.557774	0.0300296
$346$	3.77559	0.202977
$347$	−0.504962	−0.0271078	−0.0135539	−	0.999908i	$-0.504314\pi$
$347$	−0.504962	−0.0271078	−0.0135539	+	0.999908i	$0.504314\pi$
$348$	−0.366335	−0.0196376
$349$	−27.4329	−1.46845	−0.734224	−	0.678907i	$-0.762454\pi$
$349$	−27.4329	−1.46845	−0.734224	+	0.678907i	$0.762454\pi$
$350$	10.4724	0.559772
$351$	9.95946	0.531596
$352$	−4.33155	−0.230872
$353$	−10.4591	−0.556683	−0.278341	−	0.960482i	$-0.589785\pi$
$353$	−10.4591	−0.556683	−0.278341	+	0.960482i	$0.589785\pi$
$354$	0.857724	0.0455875
$355$	−5.42238	−0.287790
$356$	−6.86060	−0.363611
$357$	−6.71001	−0.355132
$358$	−19.9802	−1.05599
$359$	−17.9605	−0.947918	−0.473959	−	0.880547i	$-0.657175\pi$
$359$	−17.9605	−0.947918	−0.473959	+	0.880547i	$0.657175\pi$
$360$	−4.36340	−0.229972
$361$	−14.4577	−0.760931
$362$	10.6113	0.557715
$363$	−2.84362	−0.149251
$364$	−18.0991	−0.948648
$365$	11.7894	0.617085
$366$	−3.07608	−0.160789
$367$	−8.09933	−0.422782	−0.211391	−	0.977402i	$-0.567799\pi$
$367$	−8.09933	−0.422782	−0.211391	+	0.977402i	$0.567799\pi$
$368$	−1.00000	−0.0521286
$369$	−17.3042	−0.900820
$370$	−17.4570	−0.907544
$371$	3.85787	0.200291
$372$	2.19103	0.113600
$373$	1.18823	0.0615240	0.0307620	−	0.999527i	$-0.490207\pi$
$373$	1.18823	0.0615240	0.0307620	+	0.999527i	$0.490207\pi$
$374$	20.3171	1.05057
$375$	4.28469	0.221260
$376$	−0.963358	−0.0496814
$377$	4.63479	0.238704
$378$	−8.39136	−0.431605
$379$	−35.5255	−1.82482	−0.912412	−	0.409273i	$-0.865782\pi$
$379$	−35.5255	−1.82482	−0.912412	+	0.409273i	$0.865782\pi$
$380$	−3.24503	−0.166466
$381$	3.14484	0.161115
$382$	22.4156	1.14688
$383$	5.41931	0.276914	0.138457	−	0.990368i	$-0.455786\pi$
$383$	5.41931	0.276914	0.138457	+	0.990368i	$0.455786\pi$
$384$	−0.366335	−0.0186945
$385$	25.7543	1.31256
$386$	8.83224	0.449549
$387$	−17.5082	−0.889994
$388$	11.6333	0.590591
$389$	−8.69691	−0.440951	−0.220475	−	0.975393i	$-0.570761\pi$
$389$	−8.69691	−0.440951	−0.220475	+	0.975393i	$0.570761\pi$
$390$	−2.58517	−0.130905
$391$	4.69049	0.237208
$392$	8.24939	0.416657
$393$	3.92654	0.198068
$394$	7.20749	0.363108
$395$	−0.489175	−0.0246131
$396$	12.4134	0.623794
$397$	−0.165247	−0.00829350	−0.00414675	−	0.999991i	$-0.501320\pi$
$397$	−0.165247	−0.00829350	−0.00414675	+	0.999991i	$0.501320\pi$
$398$	16.4488	0.824505
$399$	−3.04890	−0.152636
$400$	−2.68175	−0.134088
$401$	−26.3854	−1.31763	−0.658813	−	0.752307i	$-0.728941\pi$
$401$	−26.3854	−1.31763	−0.658813	+	0.752307i	$0.728941\pi$
$402$	5.53764	0.276192
$403$	−27.7204	−1.38085
$404$	15.9101	0.791558
$405$	11.8916	0.590900
$406$	−3.90505	−0.193804
$407$	49.6629	2.46170
$408$	1.71829	0.0850682
$409$	−35.2291	−1.74197	−0.870984	−	0.491311i	$-0.836518\pi$
$409$	−35.2291	−1.74197	−0.870984	+	0.491311i	$0.836518\pi$
$410$	9.19360	0.454039
$411$	4.60145	0.226973
$412$	6.09854	0.300453
$413$	9.14313	0.449904
$414$	2.86580	0.140846
$415$	−11.9340	−0.585815
$416$	4.63479	0.227239
$417$	−7.05755	−0.345609
$418$	9.23170	0.451537
$419$	21.6083	1.05563	0.527817	−	0.849358i	$-0.323011\pi$
$419$	21.6083	1.05563	0.527817	+	0.849358i	$0.323011\pi$
$420$	2.17814	0.106282
$421$	−23.0623	−1.12399	−0.561994	−	0.827141i	$-0.689966\pi$
$421$	−23.0623	−1.12399	−0.561994	+	0.827141i	$0.689966\pi$
$422$	−23.1815	−1.12846
$423$	2.76079	0.134234
$424$	−0.987920	−0.0479776
$425$	12.5787	0.610159
$426$	1.30463	0.0632098
$427$	−32.7903	−1.58683
$428$	9.77783	0.472629
$429$	7.35448	0.355078
$430$	9.30201	0.448583
$431$	7.19332	0.346490	0.173245	−	0.984879i	$-0.444575\pi$
$431$	7.19332	0.346490	0.173245	+	0.984879i	$0.444575\pi$
$432$	2.14885	0.103387
$433$	−16.5704	−0.796321	−0.398160	−	0.917316i	$-0.630351\pi$
$433$	−16.5704	−0.796321	−0.398160	+	0.917316i	$0.630351\pi$
$434$	23.3558	1.12112
$435$	−0.557774	−0.0267432
$436$	−20.3429	−0.974246
$437$	2.13127	0.101952
$438$	−2.83655	−0.135536
$439$	−14.7268	−0.702873	−0.351437	−	0.936212i	$-0.614307\pi$
$439$	−14.7268	−0.702873	−0.351437	+	0.936212i	$0.614307\pi$
$440$	−6.59513	−0.314410
$441$	−23.6411	−1.12577
$442$	−21.7394	−1.03404
$443$	−18.0296	−0.856610	−0.428305	−	0.903634i	$-0.640889\pi$
$443$	−18.0296	−0.856610	−0.428305	+	0.903634i	$0.640889\pi$
$444$	4.20018	0.199332
$445$	−10.4458	−0.495179
$446$	−28.4238	−1.34591
$447$	5.02925	0.237875
$448$	−3.90505	−0.184496
$449$	23.8626	1.12614	0.563072	−	0.826408i	$-0.309619\pi$
$449$	23.8626	1.12614	0.563072	+	0.826408i	$0.309619\pi$
$450$	7.68537	0.362292
$451$	−26.1547	−1.23157
$452$	13.3010	0.625627
$453$	2.71955	0.127776
$454$	−9.41037	−0.441651
$455$	−27.5572	−1.29190
$456$	0.780760	0.0365624
$457$	−39.6890	−1.85657	−0.928287	−	0.371864i	$-0.878719\pi$
$457$	−39.6890	−1.85657	−0.928287	+	0.371864i	$0.878719\pi$
$458$	4.87627	0.227853
$459$	−10.0792	−0.470455
$460$	−1.52258	−0.0709906
$461$	3.10355	0.144547	0.0722733	−	0.997385i	$-0.476975\pi$
$461$	3.10355	0.144547	0.0722733	+	0.997385i	$0.476975\pi$
$462$	−6.19653	−0.288289
$463$	−10.0347	−0.466353	−0.233176	−	0.972434i	$-0.574912\pi$
$463$	−10.0347	−0.466353	−0.233176	+	0.972434i	$0.574912\pi$
$464$	1.00000	0.0464238
$465$	3.33601	0.154704
$466$	14.0151	0.649239
$467$	−26.2864	−1.21639	−0.608194	−	0.793789i	$-0.708106\pi$
$467$	−26.2864	−1.21639	−0.608194	+	0.793789i	$0.708106\pi$
$468$	−13.2824	−0.613977
$469$	59.0299	2.72575
$470$	−1.46679	−0.0676579
$471$	6.24075	0.287559
$472$	−2.34136	−0.107770
$473$	−26.4631	−1.21677
$474$	0.117697	0.00540598
$475$	5.71554	0.262247
$476$	18.3166	0.839539
$477$	2.83118	0.129631
$478$	−8.67974	−0.397002
$479$	27.5163	1.25725	0.628626	−	0.777708i	$-0.283618\pi$
$479$	27.5163	1.25725	0.628626	+	0.777708i	$0.283618\pi$
$480$	−0.557774	−0.0254588
$481$	−53.1396	−2.42296
$482$	−3.71583	−0.169251
$483$	−1.43056	−0.0650926
$484$	7.76233	0.352833
$485$	17.7126	0.804289
$486$	−9.30770	−0.422206
$487$	−12.3603	−0.560099	−0.280049	−	0.959986i	$-0.590351\pi$
$487$	−12.3603	−0.560099	−0.280049	+	0.959986i	$0.590351\pi$
$488$	8.39689	0.380109
$489$	−3.69744	−0.167204
$490$	12.5603	0.567418
$491$	−33.1062	−1.49406	−0.747032	−	0.664788i	$-0.768522\pi$
$491$	−33.1062	−1.49406	−0.747032	+	0.664788i	$0.768522\pi$
$492$	−2.21200	−0.0997245
$493$	−4.69049	−0.211249
$494$	−9.87798	−0.444431
$495$	18.9003	0.849506
$496$	−5.98094	−0.268552
$497$	13.9071	0.623818
$498$	2.87134	0.128668
$499$	13.2554	0.593395	0.296697	−	0.954972i	$-0.404115\pi$
$499$	13.2554	0.593395	0.296697	+	0.954972i	$0.404115\pi$
$500$	−11.6961	−0.523064
$501$	4.69369	0.209699
$502$	27.5571	1.22994
$503$	−41.1867	−1.83642	−0.918212	−	0.396089i	$-0.870367\pi$
$503$	−41.1867	−1.83642	−0.918212	+	0.396089i	$0.870367\pi$
$504$	11.1911	0.498490
$505$	24.2244	1.07797
$506$	4.33155	0.192561
$507$	−3.10698	−0.137986
$508$	−8.58461	−0.380880
$509$	15.2634	0.676539	0.338270	−	0.941049i	$-0.390158\pi$
$509$	15.2634	0.676539	0.338270	+	0.941049i	$0.390158\pi$
$510$	2.61624	0.115849
$511$	−30.2369	−1.33760
$512$	1.00000	0.0441942
$513$	−4.57978	−0.202202
$514$	−2.44598	−0.107887
$515$	9.28551	0.409168
$516$	−2.23808	−0.0985260
$517$	4.17283	0.183521
$518$	44.7729	1.96721
$519$	−1.38313	−0.0607127
$520$	7.05683	0.309462
$521$	−7.32137	−0.320755	−0.160378	−	0.987056i	$-0.551271\pi$
$521$	−7.32137	−0.320755	−0.160378	+	0.987056i	$0.551271\pi$
$522$	−2.86580	−0.125433
$523$	−41.7617	−1.82611	−0.913057	−	0.407832i	$-0.866285\pi$
$523$	−41.7617	−1.82611	−0.913057	+	0.407832i	$0.866285\pi$
$524$	−10.7184	−0.468237
$525$	−3.83640	−0.167434
$526$	21.7390	0.947866
$527$	28.0535	1.22203
$528$	1.58680	0.0690566
$529$	1.00000	0.0434783
$530$	−1.50419	−0.0653377
$531$	6.70987	0.291184
$532$	8.32271	0.360835
$533$	27.9856	1.21219
$534$	2.51328	0.108760
$535$	14.8875	0.643643
$536$	−15.1163	−0.652925
$537$	7.31947	0.315858
$538$	8.54001	0.368186
$539$	−35.7326	−1.53911
$540$	3.27179	0.140796
$541$	−21.1403	−0.908895	−0.454447	−	0.890774i	$-0.650163\pi$
$541$	−21.1403	−0.908895	−0.454447	+	0.890774i	$0.650163\pi$
$542$	22.2221	0.954519
$543$	−3.88728	−0.166819
$544$	−4.69049	−0.201103
$545$	−30.9736	−1.32676
$546$	6.63032	0.283752
$547$	15.3811	0.657647	0.328823	−	0.944391i	$-0.393348\pi$
$547$	15.3811	0.657647	0.328823	+	0.944391i	$0.393348\pi$
$548$	−12.5608	−0.536569
$549$	−24.0638	−1.02702
$550$	11.6162	0.495314
$551$	−2.13127	−0.0907952
$552$	0.366335	0.0155923
$553$	1.25462	0.0533517
$554$	−4.14650	−0.176168
$555$	6.39510	0.271457
$556$	19.2653	0.817029
$557$	33.7540	1.43020	0.715102	−	0.699020i	$-0.246380\pi$
$557$	33.7540	1.43020	0.715102	+	0.699020i	$0.246380\pi$
$558$	17.1402	0.725601
$559$	28.3157	1.19762
$560$	−5.94574	−0.251253
$561$	−7.44287	−0.314238
$562$	22.7259	0.958635
$563$	1.29918	0.0547540	0.0273770	−	0.999625i	$-0.491285\pi$
$563$	1.29918	0.0547540	0.0273770	+	0.999625i	$0.491285\pi$
$564$	0.352912	0.0148603
$565$	20.2518	0.852001
$566$	27.4038	1.15187
$567$	−30.4992	−1.28085
$568$	−3.56131	−0.149429
$569$	−10.1634	−0.426072	−0.213036	−	0.977044i	$-0.568335\pi$
$569$	−10.1634	−0.426072	−0.213036	+	0.977044i	$0.568335\pi$
$570$	1.18877	0.0497920
$571$	−29.8633	−1.24974	−0.624870	−	0.780729i	$-0.714848\pi$
$571$	−29.8633	−1.24974	−0.624870	+	0.780729i	$0.714848\pi$
$572$	−20.0758	−0.839412
$573$	−8.21162	−0.343045
$574$	−23.5793	−0.984183
$575$	2.68175	0.111837
$576$	−2.86580	−0.119408
$577$	−12.2785	−0.511162	−0.255581	−	0.966788i	$-0.582267\pi$
$577$	−12.2785	−0.511162	−0.255581	+	0.966788i	$0.582267\pi$
$578$	5.00071	0.208002
$579$	−3.23556	−0.134465
$580$	1.52258	0.0632216
$581$	30.6077	1.26982
$582$	−4.26169	−0.176653
$583$	4.27923	0.177227
$584$	7.74304	0.320409
$585$	−20.2234	−0.836136
$586$	−24.5824	−1.01549
$587$	5.18993	0.214211	0.107106	−	0.994248i	$-0.465842\pi$
$587$	5.18993	0.214211	0.107106	+	0.994248i	$0.465842\pi$
$588$	−3.02204	−0.124627
$589$	12.7470	0.525231
$590$	−3.56491	−0.146765
$591$	−2.64036	−0.108610
$592$	−11.4654	−0.471225
$593$	−4.79825	−0.197041	−0.0985203	−	0.995135i	$-0.531411\pi$
$593$	−4.79825	−0.197041	−0.0985203	+	0.995135i	$0.531411\pi$
$594$	−9.30785	−0.381906
$595$	27.8884	1.14331
$596$	−13.7285	−0.562343
$597$	−6.02579	−0.246619
$598$	−4.63479	−0.189530
$599$	−12.2691	−0.501300	−0.250650	−	0.968078i	$-0.580644\pi$
$599$	−12.2691	−0.501300	−0.250650	+	0.968078i	$0.580644\pi$
$600$	0.982421	0.0401072
$601$	−28.2030	−1.15042	−0.575212	−	0.818004i	$-0.695080\pi$
$601$	−28.2030	−1.15042	−0.575212	+	0.818004i	$0.695080\pi$
$602$	−23.8574	−0.972355
$603$	43.3203	1.76414
$604$	−7.42368	−0.302065
$605$	11.8188	0.480501
$606$	−5.82844	−0.236764
$607$	−0.972292	−0.0394641	−0.0197321	−	0.999805i	$-0.506281\pi$
$607$	−0.972292	−0.0394641	−0.0197321	+	0.999805i	$0.506281\pi$
$608$	−2.13127	−0.0864344
$609$	1.43056	0.0579691
$610$	12.7849	0.517647
$611$	−4.46496	−0.180633
$612$	13.4420	0.543361
$613$	29.6190	1.19630	0.598149	−	0.801385i	$-0.295903\pi$
$613$	29.6190	1.19630	0.598149	+	0.801385i	$0.295903\pi$
$614$	12.8064	0.516826
$615$	−3.36794	−0.135808
$616$	16.9149	0.681521
$617$	38.4943	1.54972	0.774862	−	0.632131i	$-0.217819\pi$
$617$	38.4943	1.54972	0.774862	+	0.632131i	$0.217819\pi$
$618$	−2.23411	−0.0898691
$619$	32.5753	1.30931	0.654656	−	0.755927i	$-0.272814\pi$
$619$	32.5753	1.30931	0.654656	+	0.755927i	$0.272814\pi$
$620$	−9.10645	−0.365724
$621$	−2.14885	−0.0862303
$622$	−7.45851	−0.299059
$623$	26.7910	1.07336
$624$	−1.69789	−0.0679698
$625$	−4.39943	−0.175977
$626$	−13.6848	−0.546956
$627$	−3.38190	−0.135060
$628$	−17.0356	−0.679796
$629$	53.7783	2.14428
$630$	17.0393	0.678862
$631$	0.0193923	0.000771996 0	0.000385998	−	1.00000i	$-0.499877\pi$
$631$	0.0193923	0.000771996 0	0.000385998		1.00000i	$0.499877\pi$
$632$	−0.321281	−0.0127799
$633$	8.49219	0.337534
$634$	20.5899	0.817728
$635$	−13.0707	−0.518696
$636$	0.361910	0.0143507
$637$	38.2341	1.51489
$638$	−4.33155	−0.171488
$639$	10.2060	0.403743
$640$	1.52258	0.0601852
$641$	−9.29022	−0.366942	−0.183471	−	0.983025i	$-0.558733\pi$
$641$	−9.29022	−0.366942	−0.183471	+	0.983025i	$0.558733\pi$
$642$	−3.58196	−0.141369
$643$	−0.467225	−0.0184255	−0.00921277	−	0.999958i	$-0.502933\pi$
$643$	−0.467225	−0.0184255	−0.00921277	+	0.999958i	$0.502933\pi$
$644$	3.90505	0.153880
$645$	−3.40766	−0.134176
$646$	9.99671	0.393315
$647$	2.74365	0.107864	0.0539320	−	0.998545i	$-0.482825\pi$
$647$	2.74365	0.107864	0.0539320	+	0.998545i	$0.482825\pi$
$648$	7.81020	0.306813
$649$	10.1417	0.398098
$650$	−12.4294	−0.487519
$651$	−8.55607	−0.335339
$652$	10.0930	0.395274
$653$	21.1355	0.827095	0.413547	−	0.910483i	$-0.364290\pi$
$653$	21.1355	0.827095	0.413547	+	0.910483i	$0.364290\pi$
$654$	7.45231	0.291408
$655$	−16.3197	−0.637662
$656$	6.03817	0.235751
$657$	−22.1900	−0.865714
$658$	3.76196	0.146656
$659$	−12.4629	−0.485486	−0.242743	−	0.970091i	$-0.578047\pi$
$659$	−12.4629	−0.485486	−0.242743	+	0.970091i	$0.578047\pi$
$660$	2.41603	0.0940438
$661$	−33.3309	−1.29642	−0.648211	−	0.761461i	$-0.724482\pi$
$661$	−33.3309	−1.29642	−0.648211	+	0.761461i	$0.724482\pi$
$662$	−5.90381	−0.229458
$663$	7.96392	0.309293
$664$	−7.83800	−0.304173
$665$	12.6720	0.491398
$666$	32.8575	1.27320
$667$	−1.00000	−0.0387202
$668$	−12.8126	−0.495733
$669$	10.4126	0.402576
$670$	−23.0158	−0.889177
$671$	−36.3716	−1.40411
$672$	1.43056	0.0551849
$673$	−19.6761	−0.758459	−0.379230	−	0.925303i	$-0.623811\pi$
$673$	−19.6761	−0.758459	−0.379230	+	0.925303i	$0.623811\pi$
$674$	33.7788	1.30111
$675$	−5.76268	−0.221806
$676$	8.48124	0.326202
$677$	16.4621	0.632689	0.316344	−	0.948644i	$-0.397544\pi$
$677$	16.4621	0.632689	0.316344	+	0.948644i	$0.397544\pi$
$678$	−4.87263	−0.187132
$679$	−45.4286	−1.74339
$680$	−7.14164	−0.273870
$681$	3.44735	0.132103
$682$	25.9067	0.992020
$683$	49.7339	1.90302	0.951508	−	0.307624i	$-0.0995338\pi$
$683$	49.7339	1.90302	0.951508	+	0.307624i	$0.0995338\pi$
$684$	6.10779	0.233537
$685$	−19.1247	−0.730719
$686$	−4.87891	−0.186278
$687$	−1.78635	−0.0681536
$688$	6.10938	0.232918
$689$	−4.57880	−0.174438
$690$	0.557774	0.0212341
$691$	−35.5323	−1.35171	−0.675857	−	0.737033i	$-0.736226\pi$
$691$	−35.5323	−1.35171	−0.675857	+	0.737033i	$0.736226\pi$
$692$	3.77559	0.143526
$693$	−48.4747	−1.84140
$694$	−0.504962	−0.0191681
$695$	29.3329	1.11266
$696$	−0.366335	−0.0138859
$697$	−28.3220	−1.07277
$698$	−27.4329	−1.03835
$699$	−5.13424	−0.194195
$700$	10.4724	0.395818
$701$	−36.1075	−1.36376	−0.681880	−	0.731464i	$-0.738838\pi$
$701$	−36.1075	−1.36376	−0.681880	+	0.731464i	$0.738838\pi$
$702$	9.95946	0.375895
$703$	24.4358	0.921615
$704$	−4.33155	−0.163251
$705$	0.537336	0.0202373
$706$	−10.4591	−0.393634
$707$	−62.1297	−2.33663
$708$	0.857724	0.0322352
$709$	−37.0165	−1.39018	−0.695092	−	0.718921i	$-0.744636\pi$
$709$	−37.0165	−1.39018	−0.695092	+	0.718921i	$0.744636\pi$
$710$	−5.42238	−0.203498
$711$	0.920726	0.0345299
$712$	−6.86060	−0.257112
$713$	5.98094	0.223988
$714$	−6.71001	−0.251116
$715$	−30.5670	−1.14314
$716$	−19.9802	−0.746697
$717$	3.17969	0.118748
$718$	−17.9605	−0.670279
$719$	17.5680	0.655176	0.327588	−	0.944821i	$-0.393764\pi$
$719$	17.5680	0.655176	0.327588	+	0.944821i	$0.393764\pi$
$720$	−4.36340	−0.162614
$721$	−23.8151	−0.886920
$722$	−14.4577	−0.538059
$723$	1.36124	0.0506250
$724$	10.6113	0.394364
$725$	−2.68175	−0.0995978
$726$	−2.84362	−0.105536
$727$	18.1682	0.673820	0.336910	−	0.941537i	$-0.390618\pi$
$727$	18.1682	0.673820	0.336910	+	0.941537i	$0.390618\pi$
$728$	−18.0991	−0.670796
$729$	−20.0208	−0.741513
$730$	11.7894	0.436345
$731$	−28.6560	−1.05988
$732$	−3.07608	−0.113695
$733$	9.99995	0.369357	0.184678	−	0.982799i	$-0.440876\pi$
$733$	9.99995	0.369357	0.184678	+	0.982799i	$0.440876\pi$
$734$	−8.09933	−0.298952
$735$	−4.60130	−0.169721
$736$	−1.00000	−0.0368605
$737$	65.4770	2.41188
$738$	−17.3042	−0.636976
$739$	3.40951	0.125421	0.0627104	−	0.998032i	$-0.480026\pi$
$739$	3.40951	0.125421	0.0627104	+	0.998032i	$0.480026\pi$
$740$	−17.4570	−0.641731
$741$	3.61865	0.132935
$742$	3.85787	0.141627
$743$	−6.78966	−0.249088	−0.124544	−	0.992214i	$-0.539747\pi$
$743$	−6.78966	−0.249088	−0.124544	+	0.992214i	$0.539747\pi$
$744$	2.19103	0.0803270
$745$	−20.9028	−0.765819
$746$	1.18823	0.0435041
$747$	22.4621	0.821846
$748$	20.3171	0.742867
$749$	−38.1829	−1.39517
$750$	4.28469	0.156455
$751$	−12.2857	−0.448311	−0.224155	−	0.974553i	$-0.571962\pi$
$751$	−12.2857	−0.448311	−0.224155	+	0.974553i	$0.571962\pi$
$752$	−0.963358	−0.0351300
$753$	−10.0952	−0.367888
$754$	4.63479	0.168789
$755$	−11.3031	−0.411363
$756$	−8.39136	−0.305191
$757$	20.1030	0.730657	0.365328	−	0.930879i	$-0.380957\pi$
$757$	20.1030	0.730657	0.365328	+	0.930879i	$0.380957\pi$
$758$	−35.5255	−1.29035
$759$	−1.58680	−0.0575972
$760$	−3.24503	−0.117710
$761$	−8.62441	−0.312635	−0.156317	−	0.987707i	$-0.549962\pi$
$761$	−8.62441	−0.312635	−0.156317	+	0.987707i	$0.549962\pi$
$762$	3.14484	0.113926
$763$	79.4398	2.87591
$764$	22.4156	0.810968
$765$	20.4665	0.739968
$766$	5.41931	0.195807
$767$	−10.8517	−0.391833
$768$	−0.366335	−0.0132190
$769$	−53.2040	−1.91859	−0.959294	−	0.282411i	$-0.908866\pi$
$769$	−53.2040	−1.91859	−0.959294	+	0.282411i	$0.908866\pi$
$770$	25.7543	0.928120
$771$	0.896048	0.0322704
$772$	8.83224	0.317879
$773$	11.6623	0.419464	0.209732	−	0.977759i	$-0.432741\pi$
$773$	11.6623	0.419464	0.209732	+	0.977759i	$0.432741\pi$
$774$	−17.5082	−0.629321
$775$	16.0394	0.576152
$776$	11.6333	0.417611
$777$	−16.4019	−0.588414
$778$	−8.69691	−0.311799
$779$	−12.8690	−0.461079
$780$	−2.58517	−0.0925638
$781$	15.4260	0.551986
$782$	4.69049	0.167732
$783$	2.14885	0.0767936
$784$	8.24939	0.294621
$785$	−25.9381	−0.925770
$786$	3.92654	0.140055
$787$	13.9431	0.497017	0.248509	−	0.968630i	$-0.420060\pi$
$787$	13.9431	0.497017	0.248509	+	0.968630i	$0.420060\pi$
$788$	7.20749	0.256756
$789$	−7.96377	−0.283518
$790$	−0.489175	−0.0174041
$791$	−51.9411	−1.84681
$792$	12.4134	0.441089
$793$	38.9178	1.38201
$794$	−0.165247	−0.00586439
$795$	0.551037	0.0195433
$796$	16.4488	0.583013
$797$	−14.6159	−0.517721	−0.258861	−	0.965915i	$-0.583347\pi$
$797$	−14.6159	−0.517721	−0.258861	+	0.965915i	$0.583347\pi$
$798$	−3.04890	−0.107930
$799$	4.51862	0.159857
$800$	−2.68175	−0.0948143
$801$	19.6611	0.694691
$802$	−26.3854	−0.931702
$803$	−33.5394	−1.18358
$804$	5.53764	0.195297
$805$	5.94574	0.209560
$806$	−27.7204	−0.976408
$807$	−3.12851	−0.110129
$808$	15.9101	0.559716
$809$	44.2356	1.55524	0.777621	−	0.628733i	$-0.216426\pi$
$809$	44.2356	1.55524	0.777621	+	0.628733i	$0.216426\pi$
$810$	11.8916	0.417830
$811$	−33.4909	−1.17602	−0.588012	−	0.808852i	$-0.700089\pi$
$811$	−33.4909	−1.17602	−0.588012	+	0.808852i	$0.700089\pi$
$812$	−3.90505	−0.137040
$813$	−8.14073	−0.285508
$814$	49.6629	1.74068
$815$	15.3674	0.538298
$816$	1.71829	0.0601523
$817$	−13.0207	−0.455538
$818$	−35.2291	−1.23176
$819$	51.8682	1.81242
$820$	9.19360	0.321054
$821$	−5.43347	−0.189629	−0.0948146	−	0.995495i	$-0.530226\pi$
$821$	−5.43347	−0.189629	−0.0948146	+	0.995495i	$0.530226\pi$
$822$	4.60145	0.160494
$823$	−0.0379859	−0.00132410	−0.000662052	−	1.00000i	$-0.500211\pi$
$823$	−0.0379859	−0.00132410	−0.000662052		1.00000i	$0.500211\pi$
$824$	6.09854	0.212453
$825$	−4.25541	−0.148154
$826$	9.14313	0.318130
$827$	−29.8568	−1.03822	−0.519112	−	0.854706i	$-0.673737\pi$
$827$	−29.8568	−1.03822	−0.519112	+	0.854706i	$0.673737\pi$
$828$	2.86580	0.0995934
$829$	−1.78646	−0.0620463	−0.0310232	−	0.999519i	$-0.509877\pi$
$829$	−1.78646	−0.0620463	−0.0310232	+	0.999519i	$0.509877\pi$
$830$	−11.9340	−0.414234
$831$	1.51901	0.0526939
$832$	4.63479	0.160682
$833$	−38.6937	−1.34066
$834$	−7.05755	−0.244383
$835$	−19.5081	−0.675107
$836$	9.23170	0.319285
$837$	−12.8521	−0.444235
$838$	21.6083	0.746445
$839$	8.44987	0.291722	0.145861	−	0.989305i	$-0.453405\pi$
$839$	8.44987	0.291722	0.145861	+	0.989305i	$0.453405\pi$
$840$	2.17814	0.0751528
$841$	1.00000	0.0344828
$842$	−23.0623	−0.794780
$843$	−8.32531	−0.286739
$844$	−23.1815	−0.797939
$845$	12.9134	0.444233
$846$	2.76079	0.0949179
$847$	−30.3123	−1.04154
$848$	−0.987920	−0.0339253
$849$	−10.0390	−0.344537
$850$	12.5787	0.431447
$851$	11.4654	0.393028
$852$	1.30463	0.0446961
$853$	21.6555	0.741471	0.370735	−	0.928739i	$-0.379106\pi$
$853$	21.6555	0.741471	0.370735	+	0.928739i	$0.379106\pi$
$854$	−32.7903	−1.12206
$855$	9.29959	0.318039
$856$	9.77783	0.334199
$857$	28.4029	0.970225	0.485112	−	0.874452i	$-0.338779\pi$
$857$	28.4029	0.970225	0.485112	+	0.874452i	$0.338779\pi$
$858$	7.35448	0.251078
$859$	−43.7223	−1.49179	−0.745893	−	0.666065i	$-0.767977\pi$
$859$	−43.7223	−1.49179	−0.745893	+	0.666065i	$0.767977\pi$
$860$	9.30201	0.317196
$861$	8.63795	0.294381
$862$	7.19332	0.245005
$863$	43.2572	1.47249	0.736246	−	0.676714i	$-0.236597\pi$
$863$	43.2572	1.47249	0.736246	+	0.676714i	$0.236597\pi$
$864$	2.14885	0.0731053
$865$	5.74863	0.195459
$866$	−16.5704	−0.563084
$867$	−1.83194	−0.0622158
$868$	23.3558	0.792749
$869$	1.39164	0.0472083
$870$	−0.557774	−0.0189103
$871$	−70.0608	−2.37392
$872$	−20.3429	−0.688896
$873$	−33.3387	−1.12834
$874$	2.13127	0.0720913
$875$	45.6737	1.54405
$876$	−2.83655	−0.0958382
$877$	−14.9853	−0.506018	−0.253009	−	0.967464i	$-0.581420\pi$
$877$	−14.9853	−0.506018	−0.253009	+	0.967464i	$0.581420\pi$
$878$	−14.7268	−0.497006
$879$	9.00539	0.303744
$880$	−6.59513	−0.222322
$881$	−3.87346	−0.130500	−0.0652501	−	0.997869i	$-0.520785\pi$
$881$	−3.87346	−0.130500	−0.0652501	+	0.997869i	$0.520785\pi$
$882$	−23.6411	−0.796037
$883$	12.2568	0.412473	0.206236	−	0.978502i	$-0.433878\pi$
$883$	12.2568	0.412473	0.206236	+	0.978502i	$0.433878\pi$
$884$	−21.7394	−0.731176
$885$	1.30595	0.0438991
$886$	−18.0296	−0.605715
$887$	−18.5868	−0.624083	−0.312042	−	0.950068i	$-0.601013\pi$
$887$	−18.5868	−0.624083	−0.312042	+	0.950068i	$0.601013\pi$
$888$	4.20018	0.140949
$889$	33.5233	1.12433
$890$	−10.4458	−0.350144
$891$	−33.8303	−1.13336
$892$	−28.4238	−0.951700
$893$	2.05318	0.0687069
$894$	5.02925	0.168203
$895$	−30.4215	−1.01688
$896$	−3.90505	−0.130458
$897$	1.69789	0.0566908
$898$	23.8626	0.796304
$899$	−5.98094	−0.199475
$900$	7.68537	0.256179
$901$	4.63383	0.154375
$902$	−26.1547	−0.870855
$903$	8.73981	0.290843
$904$	13.3010	0.442385
$905$	16.1565	0.537060
$906$	2.71955	0.0903512
$907$	36.1258	1.19954	0.599770	−	0.800173i	$-0.295259\pi$
$907$	36.1258	1.19954	0.599770	+	0.800173i	$0.295259\pi$
$908$	−9.41037	−0.312294
$909$	−45.5952	−1.51230
$910$	−27.5572	−0.913513
$911$	42.4598	1.40676	0.703378	−	0.710816i	$-0.251674\pi$
$911$	42.4598	1.40676	0.703378	+	0.710816i	$0.251674\pi$
$912$	0.780760	0.0258535
$913$	33.9507	1.12360
$914$	−39.6890	−1.31280
$915$	−4.68357	−0.154834
$916$	4.87627	0.161117
$917$	41.8560	1.38221
$918$	−10.0792	−0.332662
$919$	−9.89348	−0.326356	−0.163178	−	0.986597i	$-0.552174\pi$
$919$	−9.89348	−0.326356	−0.163178	+	0.986597i	$0.552174\pi$
$920$	−1.52258	−0.0501979
$921$	−4.69145	−0.154589
$922$	3.10355	0.102210
$923$	−16.5059	−0.543299
$924$	−6.19653	−0.203851
$925$	30.7473	1.01097
$926$	−10.0347	−0.329761
$927$	−17.4772	−0.574026
$928$	1.00000	0.0328266
$929$	−25.6949	−0.843021	−0.421510	−	0.906824i	$-0.638500\pi$
$929$	−25.6949	−0.843021	−0.421510	+	0.906824i	$0.638500\pi$
$930$	3.33601	0.109392
$931$	−17.5817	−0.576216
$932$	14.0151	0.459081
$933$	2.73232	0.0894520
$934$	−26.2864	−0.860116
$935$	30.9344	1.01166
$936$	−13.2824	−0.434148
$937$	3.43888	0.112343	0.0561717	−	0.998421i	$-0.482111\pi$
$937$	3.43888	0.112343	0.0561717	+	0.998421i	$0.482111\pi$
$938$	59.0299	1.92739
$939$	5.01324	0.163601
$940$	−1.46679	−0.0478414
$941$	−52.4180	−1.70878	−0.854389	−	0.519633i	$-0.826069\pi$
$941$	−52.4180	−1.70878	−0.854389	+	0.519633i	$0.826069\pi$
$942$	6.24075	0.203335
$943$	−6.03817	−0.196630
$944$	−2.34136	−0.0762048
$945$	−12.7765	−0.415620
$946$	−26.4631	−0.860389
$947$	19.4236	0.631181	0.315591	−	0.948895i	$-0.397797\pi$
$947$	19.4236	0.631181	0.315591	+	0.948895i	$0.397797\pi$
$948$	0.117697	0.00382260
$949$	35.8873	1.16495
$950$	5.71554	0.185437
$951$	−7.54280	−0.244592
$952$	18.3166	0.593644
$953$	4.11575	0.133322	0.0666610	−	0.997776i	$-0.478765\pi$
$953$	4.11575	0.133322	0.0666610	+	0.997776i	$0.478765\pi$
$954$	2.83118	0.0916628
$955$	34.1295	1.10440
$956$	−8.67974	−0.280723
$957$	1.58680	0.0512940
$958$	27.5163	0.889012
$959$	49.0503	1.58392
$960$	−0.557774	−0.0180021
$961$	4.77160	0.153923
$962$	−53.1396	−1.71329
$963$	−28.0213	−0.902973
$964$	−3.71583	−0.119679
$965$	13.4478	0.432899
$966$	−1.43056	−0.0460274
$967$	20.4707	0.658294	0.329147	−	0.944279i	$-0.393239\pi$
$967$	20.4707	0.658294	0.329147	+	0.944279i	$0.393239\pi$
$968$	7.76233	0.249491
$969$	−3.66215	−0.117645
$970$	17.7126	0.568718
$971$	20.1301	0.646005	0.323002	−	0.946398i	$-0.395308\pi$
$971$	20.1301	0.646005	0.323002	+	0.946398i	$0.395308\pi$
$972$	−9.30770	−0.298545
$973$	−75.2317	−2.41182
$974$	−12.3603	−0.396049
$975$	4.55331	0.145823
$976$	8.39689	0.268778
$977$	11.6926	0.374079	0.187039	−	0.982352i	$-0.440111\pi$
$977$	11.6926	0.374079	0.187039	+	0.982352i	$0.440111\pi$
$978$	−3.69744	−0.118231
$979$	29.7170	0.949760
$980$	12.5603	0.401225
$981$	58.2985	1.86133
$982$	−33.1062	−1.05646
$983$	33.3137	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$983$	33.3137	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$984$	−2.21200	−0.0705159
$985$	10.9740	0.349660
$986$	−4.69049	−0.149376
$987$	−1.37814	−0.0438666
$988$	−9.87798	−0.314260
$989$	−6.10938	−0.194267
$990$	18.9003	0.600691
$991$	−38.1712	−1.21255	−0.606275	−	0.795255i	$-0.707337\pi$
$991$	−38.1712	−1.21255	−0.606275	+	0.795255i	$0.707337\pi$
$992$	−5.98094	−0.189895
$993$	2.16277	0.0686335
$994$	13.9071	0.441106
$995$	25.0446	0.793968
$996$	2.87134	0.0909817
$997$	38.6951	1.22549	0.612743	−	0.790283i	$-0.290066\pi$
$997$	38.6951	1.22549	0.612743	+	0.790283i	$0.290066\pi$
$998$	13.2554	0.419593
$999$	−24.6374	−0.779493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.h.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.h.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.366335 q^{3} +1.00000 q^{4} +1.52258 q^{5} -0.366335 q^{6} -3.90505 q^{7} +1.00000 q^{8} -2.86580 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.366335 q^{3} +1.00000 q^{4} +1.52258 q^{5} -0.366335 q^{6} -3.90505 q^{7} +1.00000 q^{8} -2.86580 q^{9} +1.52258 q^{10} -4.33155 q^{11} -0.366335 q^{12} +4.63479 q^{13} -3.90505 q^{14} -0.557774 q^{15} +1.00000 q^{16} -4.69049 q^{17} -2.86580 q^{18} -2.13127 q^{19} +1.52258 q^{20} +1.43056 q^{21} -4.33155 q^{22} -1.00000 q^{23} -0.366335 q^{24} -2.68175 q^{25} +4.63479 q^{26} +2.14885 q^{27} -3.90505 q^{28} +1.00000 q^{29} -0.557774 q^{30} -5.98094 q^{31} +1.00000 q^{32} +1.58680 q^{33} -4.69049 q^{34} -5.94574 q^{35} -2.86580 q^{36} -11.4654 q^{37} -2.13127 q^{38} -1.69789 q^{39} +1.52258 q^{40} +6.03817 q^{41} +1.43056 q^{42} +6.10938 q^{43} -4.33155 q^{44} -4.36340 q^{45} -1.00000 q^{46} -0.963358 q^{47} -0.366335 q^{48} +8.24939 q^{49} -2.68175 q^{50} +1.71829 q^{51} +4.63479 q^{52} -0.987920 q^{53} +2.14885 q^{54} -6.59513 q^{55} -3.90505 q^{56} +0.780760 q^{57} +1.00000 q^{58} -2.34136 q^{59} -0.557774 q^{60} +8.39689 q^{61} -5.98094 q^{62} +11.1911 q^{63} +1.00000 q^{64} +7.05683 q^{65} +1.58680 q^{66} -15.1163 q^{67} -4.69049 q^{68} +0.366335 q^{69} -5.94574 q^{70} -3.56131 q^{71} -2.86580 q^{72} +7.74304 q^{73} -11.4654 q^{74} +0.982421 q^{75} -2.13127 q^{76} +16.9149 q^{77} -1.69789 q^{78} -0.321281 q^{79} +1.52258 q^{80} +7.81020 q^{81} +6.03817 q^{82} -7.83800 q^{83} +1.43056 q^{84} -7.14164 q^{85} +6.10938 q^{86} -0.366335 q^{87} -4.33155 q^{88} -6.86060 q^{89} -4.36340 q^{90} -18.0991 q^{91} -1.00000 q^{92} +2.19103 q^{93} -0.963358 q^{94} -3.24503 q^{95} -0.366335 q^{96} +11.6333 q^{97} +8.24939 q^{98} +12.4134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 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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