LMFDB - Embedded newform 1334.2.a.k.1.7

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.290163$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.29016 q^{3} +1.00000 q^{4} +4.10547 q^{5} +1.29016 q^{6} -1.09974 q^{7} +1.00000 q^{8} -1.33548 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.29016 q^{3} +1.00000 q^{4} +4.10547 q^{5} +1.29016 q^{6} -1.09974 q^{7} +1.00000 q^{8} -1.33548 q^{9} +4.10547 q^{10} -0.113346 q^{11} +1.29016 q^{12} +0.757554 q^{13} -1.09974 q^{14} +5.29673 q^{15} +1.00000 q^{16} -5.71157 q^{17} -1.33548 q^{18} +5.76167 q^{19} +4.10547 q^{20} -1.41885 q^{21} -0.113346 q^{22} +1.00000 q^{23} +1.29016 q^{24} +11.8549 q^{25} +0.757554 q^{26} -5.59347 q^{27} -1.09974 q^{28} +1.00000 q^{29} +5.29673 q^{30} +6.93463 q^{31} +1.00000 q^{32} -0.146235 q^{33} -5.71157 q^{34} -4.51497 q^{35} -1.33548 q^{36} +2.47665 q^{37} +5.76167 q^{38} +0.977369 q^{39} +4.10547 q^{40} -2.08154 q^{41} -1.41885 q^{42} -9.56412 q^{43} -0.113346 q^{44} -5.48278 q^{45} +1.00000 q^{46} +6.64940 q^{47} +1.29016 q^{48} -5.79056 q^{49} +11.8549 q^{50} -7.36885 q^{51} +0.757554 q^{52} -8.15232 q^{53} -5.59347 q^{54} -0.465340 q^{55} -1.09974 q^{56} +7.43350 q^{57} +1.00000 q^{58} -9.27254 q^{59} +5.29673 q^{60} +4.85598 q^{61} +6.93463 q^{62} +1.46869 q^{63} +1.00000 q^{64} +3.11012 q^{65} -0.146235 q^{66} -4.94622 q^{67} -5.71157 q^{68} +1.29016 q^{69} -4.51497 q^{70} -11.2303 q^{71} -1.33548 q^{72} -4.10323 q^{73} +2.47665 q^{74} +15.2948 q^{75} +5.76167 q^{76} +0.124652 q^{77} +0.977369 q^{78} +12.0666 q^{79} +4.10547 q^{80} -3.21005 q^{81} -2.08154 q^{82} -5.56823 q^{83} -1.41885 q^{84} -23.4487 q^{85} -9.56412 q^{86} +1.29016 q^{87} -0.113346 q^{88} +6.56682 q^{89} -5.48278 q^{90} -0.833116 q^{91} +1.00000 q^{92} +8.94680 q^{93} +6.64940 q^{94} +23.6544 q^{95} +1.29016 q^{96} -4.87356 q^{97} -5.79056 q^{98} +0.151372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * 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
$3$	1.29016	0.744876	0.372438	−	0.928057i	$-0.378522\pi$
$3$	1.29016	0.744876	0.372438	+	0.928057i	$0.378522\pi$
$4$	1.00000	0.500000
$5$	4.10547	1.83602	0.918012	−	0.396553i	$-0.129794\pi$
$5$	4.10547	1.83602	0.918012	+	0.396553i	$0.129794\pi$
$6$	1.29016	0.526707
$7$	−1.09974	−0.415664	−0.207832	−	0.978165i	$-0.566641\pi$
$7$	−1.09974	−0.415664	−0.207832	+	0.978165i	$0.566641\pi$
$8$	1.00000	0.353553
$9$	−1.33548	−0.445160
$10$	4.10547	1.29826
$11$	−0.113346	−0.0341752	−0.0170876	−	0.999854i	$-0.505439\pi$
$11$	−0.113346	−0.0341752	−0.0170876	+	0.999854i	$0.505439\pi$
$12$	1.29016	0.372438
$13$	0.757554	0.210108	0.105054	−	0.994467i	$-0.466498\pi$
$13$	0.757554	0.210108	0.105054	+	0.994467i	$0.466498\pi$
$14$	−1.09974	−0.293919
$15$	5.29673	1.36761
$16$	1.00000	0.250000
$17$	−5.71157	−1.38526	−0.692630	−	0.721294i	$-0.743548\pi$
$17$	−5.71157	−1.38526	−0.692630	+	0.721294i	$0.743548\pi$
$18$	−1.33548	−0.314776
$19$	5.76167	1.32182	0.660909	−	0.750466i	$-0.270171\pi$
$19$	5.76167	1.32182	0.660909	+	0.750466i	$0.270171\pi$
$20$	4.10547	0.918012
$21$	−1.41885	−0.309618
$22$	−0.113346	−0.0241655
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.29016	0.263353
$25$	11.8549	2.37098
$26$	0.757554	0.148569
$27$	−5.59347	−1.07646
$28$	−1.09974	−0.207832
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	5.29673	0.967046
$31$	6.93463	1.24550	0.622748	−	0.782422i	$-0.286016\pi$
$31$	6.93463	1.24550	0.622748	+	0.782422i	$0.286016\pi$
$32$	1.00000	0.176777
$33$	−0.146235	−0.0254562
$34$	−5.71157	−0.979526
$35$	−4.51497	−0.763169
$36$	−1.33548	−0.222580
$37$	2.47665	0.407158	0.203579	−	0.979059i	$-0.434743\pi$
$37$	2.47665	0.407158	0.203579	+	0.979059i	$0.434743\pi$
$38$	5.76167	0.934667
$39$	0.977369	0.156504
$40$	4.10547	0.649132
$41$	−2.08154	−0.325082	−0.162541	−	0.986702i	$-0.551969\pi$
$41$	−2.08154	−0.325082	−0.162541	+	0.986702i	$0.551969\pi$
$42$	−1.41885	−0.218933
$43$	−9.56412	−1.45851	−0.729257	−	0.684240i	$-0.760134\pi$
$43$	−9.56412	−1.45851	−0.729257	+	0.684240i	$0.760134\pi$
$44$	−0.113346	−0.0170876
$45$	−5.48278	−0.817324
$46$	1.00000	0.147442
$47$	6.64940	0.969914	0.484957	−	0.874538i	$-0.338835\pi$
$47$	6.64940	0.969914	0.484957	+	0.874538i	$0.338835\pi$
$48$	1.29016	0.186219
$49$	−5.79056	−0.827223
$50$	11.8549	1.67654
$51$	−7.36885	−1.03185
$52$	0.757554	0.105054
$53$	−8.15232	−1.11981	−0.559903	−	0.828558i	$-0.689162\pi$
$53$	−8.15232	−1.11981	−0.559903	+	0.828558i	$0.689162\pi$
$54$	−5.59347	−0.761176
$55$	−0.465340	−0.0627464
$56$	−1.09974	−0.146959
$57$	7.43350	0.984591
$58$	1.00000	0.131306
$59$	−9.27254	−1.20718	−0.603591	−	0.797294i	$-0.706264\pi$
$59$	−9.27254	−1.20718	−0.603591	+	0.797294i	$0.706264\pi$
$60$	5.29673	0.683805
$61$	4.85598	0.621745	0.310872	−	0.950452i	$-0.399379\pi$
$61$	4.85598	0.621745	0.310872	+	0.950452i	$0.399379\pi$
$62$	6.93463	0.880699
$63$	1.46869	0.185037
$64$	1.00000	0.125000
$65$	3.11012	0.385763
$66$	−0.146235	−0.0180003
$67$	−4.94622	−0.604277	−0.302139	−	0.953264i	$-0.597701\pi$
$67$	−4.94622	−0.604277	−0.302139	+	0.953264i	$0.597701\pi$
$68$	−5.71157	−0.692630
$69$	1.29016	0.155317
$70$	−4.51497	−0.539642
$71$	−11.2303	−1.33279	−0.666394	−	0.745600i	$-0.732163\pi$
$71$	−11.2303	−1.33279	−0.666394	+	0.745600i	$0.732163\pi$
$72$	−1.33548	−0.157388
$73$	−4.10323	−0.480246	−0.240123	−	0.970742i	$-0.577188\pi$
$73$	−4.10323	−0.480246	−0.240123	+	0.970742i	$0.577188\pi$
$74$	2.47665	0.287904
$75$	15.2948	1.76609
$76$	5.76167	0.660909
$77$	0.124652	0.0142054
$78$	0.977369	0.110665
$79$	12.0666	1.35760	0.678798	−	0.734325i	$-0.262501\pi$
$79$	12.0666	1.35760	0.678798	+	0.734325i	$0.262501\pi$
$80$	4.10547	0.459006
$81$	−3.21005	−0.356673
$82$	−2.08154	−0.229868
$83$	−5.56823	−0.611193	−0.305596	−	0.952161i	$-0.598856\pi$
$83$	−5.56823	−0.611193	−0.305596	+	0.952161i	$0.598856\pi$
$84$	−1.41885	−0.154809
$85$	−23.4487	−2.54337
$86$	−9.56412	−1.03133
$87$	1.29016	0.138320
$88$	−0.113346	−0.0120827
$89$	6.56682	0.696081	0.348041	−	0.937479i	$-0.386847\pi$
$89$	6.56682	0.696081	0.348041	+	0.937479i	$0.386847\pi$
$90$	−5.48278	−0.577936
$91$	−0.833116	−0.0873343
$92$	1.00000	0.104257
$93$	8.94680	0.927740
$94$	6.64940	0.685833
$95$	23.6544	2.42689
$96$	1.29016	0.131677
$97$	−4.87356	−0.494835	−0.247417	−	0.968909i	$-0.579582\pi$
$97$	−4.87356	−0.494835	−0.247417	+	0.968909i	$0.579582\pi$
$98$	−5.79056	−0.584935
$99$	0.151372	0.0152134
$100$	11.8549	1.18549
$101$	−16.5875	−1.65052	−0.825258	−	0.564756i	$-0.808970\pi$
$101$	−16.5875	−1.65052	−0.825258	+	0.564756i	$0.808970\pi$
$102$	−7.36885	−0.729625
$103$	−17.8725	−1.76103	−0.880515	−	0.474018i	$-0.842803\pi$
$103$	−17.8725	−1.76103	−0.880515	+	0.474018i	$0.842803\pi$
$104$	0.757554	0.0742843
$105$	−5.82505	−0.568466
$106$	−8.15232	−0.791823
$107$	19.6999	1.90446	0.952232	−	0.305375i	$-0.0987819\pi$
$107$	19.6999	1.90446	0.952232	+	0.305375i	$0.0987819\pi$
$108$	−5.59347	−0.538232
$109$	8.46106	0.810423	0.405211	−	0.914223i	$-0.367198\pi$
$109$	8.46106	0.810423	0.405211	+	0.914223i	$0.367198\pi$
$110$	−0.465340	−0.0443684
$111$	3.19528	0.303282
$112$	−1.09974	−0.103916
$113$	−16.6761	−1.56875	−0.784377	−	0.620284i	$-0.787017\pi$
$113$	−16.6761	−1.56875	−0.784377	+	0.620284i	$0.787017\pi$
$114$	7.43350	0.696211
$115$	4.10547	0.382837
$116$	1.00000	0.0928477
$117$	−1.01170	−0.0935316
$118$	−9.27254	−0.853607
$119$	6.28126	0.575802
$120$	5.29673	0.483523
$121$	−10.9872	−0.998832
$122$	4.85598	0.439640
$123$	−2.68553	−0.242146
$124$	6.93463	0.622748
$125$	28.1427	2.51716
$126$	1.46869	0.130841
$127$	−7.60627	−0.674947	−0.337474	−	0.941335i	$-0.609572\pi$
$127$	−7.60627	−0.674947	−0.337474	+	0.941335i	$0.609572\pi$
$128$	1.00000	0.0883883
$129$	−12.3393	−1.08641
$130$	3.11012	0.272776
$131$	21.5873	1.88609	0.943047	−	0.332659i	$-0.107946\pi$
$131$	21.5873	1.88609	0.943047	+	0.332659i	$0.107946\pi$
$132$	−0.146235	−0.0127281
$133$	−6.33637	−0.549433
$134$	−4.94622	−0.427289
$135$	−22.9639	−1.97642
$136$	−5.71157	−0.489763
$137$	−13.9771	−1.19415	−0.597074	−	0.802186i	$-0.703670\pi$
$137$	−13.9771	−1.19415	−0.597074	+	0.802186i	$0.703670\pi$
$138$	1.29016	0.109826
$139$	5.15398	0.437155	0.218577	−	0.975820i	$-0.429858\pi$
$139$	5.15398	0.437155	0.218577	+	0.975820i	$0.429858\pi$
$140$	−4.51497	−0.381585
$141$	8.57881	0.722466
$142$	−11.2303	−0.942423
$143$	−0.0858659	−0.00718047
$144$	−1.33548	−0.111290
$145$	4.10547	0.340941
$146$	−4.10323	−0.339586
$147$	−7.47077	−0.616179
$148$	2.47665	0.203579
$149$	11.4161	0.935246	0.467623	−	0.883928i	$-0.345111\pi$
$149$	11.4161	0.935246	0.467623	+	0.883928i	$0.345111\pi$
$150$	15.2948	1.24881
$151$	19.9008	1.61950	0.809752	−	0.586772i	$-0.199601\pi$
$151$	19.9008	1.61950	0.809752	+	0.586772i	$0.199601\pi$
$152$	5.76167	0.467334
$153$	7.62769	0.616662
$154$	0.124652	0.0100447
$155$	28.4699	2.28676
$156$	0.977369	0.0782521
$157$	−6.11684	−0.488177	−0.244089	−	0.969753i	$-0.578489\pi$
$157$	−6.11684	−0.488177	−0.244089	+	0.969753i	$0.578489\pi$
$158$	12.0666	0.959966
$159$	−10.5178	−0.834117
$160$	4.10547	0.324566
$161$	−1.09974	−0.0866720
$162$	−3.21005	−0.252206
$163$	3.64827	0.285754	0.142877	−	0.989740i	$-0.454365\pi$
$163$	3.64827	0.285754	0.142877	+	0.989740i	$0.454365\pi$
$164$	−2.08154	−0.162541
$165$	−0.600364	−0.0467383
$166$	−5.56823	−0.432179
$167$	18.0692	1.39824	0.699118	−	0.715006i	$-0.253576\pi$
$167$	18.0692	1.39824	0.699118	+	0.715006i	$0.253576\pi$
$168$	−1.41885	−0.109467
$169$	−12.4261	−0.955855
$170$	−23.4487	−1.79843
$171$	−7.69460	−0.588421
$172$	−9.56412	−0.729257
$173$	−7.24199	−0.550599	−0.275299	−	0.961359i	$-0.588777\pi$
$173$	−7.24199	−0.550599	−0.275299	+	0.961359i	$0.588777\pi$
$174$	1.29016	0.0978070
$175$	−13.0374	−0.985533
$176$	−0.113346	−0.00854379
$177$	−11.9631	−0.899201
$178$	6.56682	0.492204
$179$	3.83996	0.287012	0.143506	−	0.989649i	$-0.454162\pi$
$179$	3.83996	0.287012	0.143506	+	0.989649i	$0.454162\pi$
$180$	−5.48278	−0.408662
$181$	18.2258	1.35472	0.677358	−	0.735654i	$-0.263125\pi$
$181$	18.2258	1.35472	0.677358	+	0.735654i	$0.263125\pi$
$182$	−0.833116	−0.0617547
$183$	6.26501	0.463123
$184$	1.00000	0.0737210
$185$	10.1678	0.747552
$186$	8.94680	0.656011
$187$	0.647384	0.0473414
$188$	6.64940	0.484957
$189$	6.15139	0.447448
$190$	23.6544	1.71607
$191$	−0.837724	−0.0606156	−0.0303078	−	0.999541i	$-0.509649\pi$
$191$	−0.837724	−0.0606156	−0.0303078	+	0.999541i	$0.509649\pi$
$192$	1.29016	0.0931095
$193$	−12.0939	−0.870537	−0.435268	−	0.900301i	$-0.643346\pi$
$193$	−12.0939	−0.870537	−0.435268	+	0.900301i	$0.643346\pi$
$194$	−4.87356	−0.349901
$195$	4.01256	0.287345
$196$	−5.79056	−0.413612
$197$	5.89003	0.419647	0.209824	−	0.977739i	$-0.432711\pi$
$197$	5.89003	0.419647	0.209824	+	0.977739i	$0.432711\pi$
$198$	0.151372	0.0107575
$199$	3.57062	0.253114	0.126557	−	0.991959i	$-0.459607\pi$
$199$	3.57062	0.253114	0.126557	+	0.991959i	$0.459607\pi$
$200$	11.8549	0.838269
$201$	−6.38143	−0.450112
$202$	−16.5875	−1.16709
$203$	−1.09974	−0.0771869
$204$	−7.36885	−0.515923
$205$	−8.54572	−0.596859
$206$	−17.8725	−1.24524
$207$	−1.33548	−0.0928223
$208$	0.757554	0.0525269
$209$	−0.653064	−0.0451734
$210$	−5.82505	−0.401966
$211$	4.21038	0.289854	0.144927	−	0.989442i	$-0.453705\pi$
$211$	4.21038	0.289854	0.144927	+	0.989442i	$0.453705\pi$
$212$	−8.15232	−0.559903
$213$	−14.4889	−0.992762
$214$	19.6999	1.34666
$215$	−39.2652	−2.67787
$216$	−5.59347	−0.380588
$217$	−7.62632	−0.517708
$218$	8.46106	0.573055
$219$	−5.29383	−0.357724
$220$	−0.465340	−0.0313732
$221$	−4.32682	−0.291054
$222$	3.19528	0.214453
$223$	2.71528	0.181829	0.0909143	−	0.995859i	$-0.471021\pi$
$223$	2.71528	0.181829	0.0909143	+	0.995859i	$0.471021\pi$
$224$	−1.09974	−0.0734797
$225$	−15.8320	−1.05547
$226$	−16.6761	−1.10928
$227$	−0.564403	−0.0374607	−0.0187304	−	0.999825i	$-0.505962\pi$
$227$	−0.564403	−0.0374607	−0.0187304	+	0.999825i	$0.505962\pi$
$228$	7.43350	0.492295
$229$	−14.0794	−0.930392	−0.465196	−	0.885208i	$-0.654016\pi$
$229$	−14.0794	−0.930392	−0.465196	+	0.885208i	$0.654016\pi$
$230$	4.10547	0.270707
$231$	0.160821	0.0105812
$232$	1.00000	0.0656532
$233$	26.3700	1.72756	0.863779	−	0.503870i	$-0.168091\pi$
$233$	26.3700	1.72756	0.863779	+	0.503870i	$0.168091\pi$
$234$	−1.01170	−0.0661368
$235$	27.2989	1.78079
$236$	−9.27254	−0.603591
$237$	15.5679	1.01124
$238$	6.28126	0.407154
$239$	3.55147	0.229726	0.114863	−	0.993381i	$-0.463357\pi$
$239$	3.55147	0.229726	0.114863	+	0.993381i	$0.463357\pi$
$240$	5.29673	0.341902
$241$	−24.7895	−1.59683	−0.798416	−	0.602107i	$-0.794328\pi$
$241$	−24.7895	−1.59683	−0.798416	+	0.602107i	$0.794328\pi$
$242$	−10.9872	−0.706281
$243$	12.6389	0.810788
$244$	4.85598	0.310872
$245$	−23.7730	−1.51880
$246$	−2.68553	−0.171223
$247$	4.36478	0.277724
$248$	6.93463	0.440349
$249$	−7.18392	−0.455263
$250$	28.1427	1.77990
$251$	−7.69243	−0.485542	−0.242771	−	0.970084i	$-0.578056\pi$
$251$	−7.69243	−0.485542	−0.242771	+	0.970084i	$0.578056\pi$
$252$	1.46869	0.0925185
$253$	−0.113346	−0.00712601
$254$	−7.60627	−0.477260
$255$	−30.2526	−1.89449
$256$	1.00000	0.0625000
$257$	−7.10413	−0.443144	−0.221572	−	0.975144i	$-0.571119\pi$
$257$	−7.10413	−0.443144	−0.221572	+	0.975144i	$0.571119\pi$
$258$	−12.3393	−0.768209
$259$	−2.72368	−0.169241
$260$	3.11012	0.192881
$261$	−1.33548	−0.0826641
$262$	21.5873	1.33367
$263$	−21.6905	−1.33750	−0.668748	−	0.743489i	$-0.733170\pi$
$263$	−21.6905	−1.33750	−0.668748	+	0.743489i	$0.733170\pi$
$264$	−0.146235	−0.00900014
$265$	−33.4691	−2.05599
$266$	−6.33637	−0.388508
$267$	8.47227	0.518494
$268$	−4.94622	−0.302139
$269$	−16.6519	−1.01529	−0.507643	−	0.861567i	$-0.669483\pi$
$269$	−16.6519	−1.01529	−0.507643	+	0.861567i	$0.669483\pi$
$270$	−22.9639	−1.39754
$271$	0.278758	0.0169334	0.00846668	−	0.999964i	$-0.497305\pi$
$271$	0.278758	0.0169334	0.00846668	+	0.999964i	$0.497305\pi$
$272$	−5.71157	−0.346315
$273$	−1.07486	−0.0650532
$274$	−13.9771	−0.844390
$275$	−1.34371	−0.0810287
$276$	1.29016	0.0776587
$277$	25.6007	1.53820	0.769100	−	0.639129i	$-0.220705\pi$
$277$	25.6007	1.53820	0.769100	+	0.639129i	$0.220705\pi$
$278$	5.15398	0.309115
$279$	−9.26106	−0.554445
$280$	−4.51497	−0.269821
$281$	0.542128	0.0323406	0.0161703	−	0.999869i	$-0.494853\pi$
$281$	0.542128	0.0323406	0.0161703	+	0.999869i	$0.494853\pi$
$282$	8.57881	0.510860
$283$	15.2437	0.906142	0.453071	−	0.891474i	$-0.350328\pi$
$283$	15.2437	0.906142	0.453071	+	0.891474i	$0.350328\pi$
$284$	−11.2303	−0.666394
$285$	30.5180	1.80773
$286$	−0.0858659	−0.00507736
$287$	2.28916	0.135125
$288$	−1.33548	−0.0786939
$289$	15.6220	0.918943
$290$	4.10547	0.241082
$291$	−6.28768	−0.368590
$292$	−4.10323	−0.240123
$293$	−28.1935	−1.64708	−0.823542	−	0.567255i	$-0.808005\pi$
$293$	−28.1935	−1.64708	−0.823542	+	0.567255i	$0.808005\pi$
$294$	−7.47077	−0.435704
$295$	−38.0682	−2.21642
$296$	2.47665	0.143952
$297$	0.633999	0.0367883
$298$	11.4161	0.661319
$299$	0.757554	0.0438105
$300$	15.2948	0.883044
$301$	10.5181	0.606252
$302$	19.9008	1.14516
$303$	−21.4005	−1.22943
$304$	5.76167	0.330455
$305$	19.9361	1.14154
$306$	7.62769	0.436046
$307$	−22.1564	−1.26453	−0.632266	−	0.774752i	$-0.717875\pi$
$307$	−22.1564	−1.26453	−0.632266	+	0.774752i	$0.717875\pi$
$308$	0.124652	0.00710269
$309$	−23.0584	−1.31175
$310$	28.4699	1.61698
$311$	28.4886	1.61544	0.807720	−	0.589566i	$-0.200701\pi$
$311$	28.4886	1.61544	0.807720	+	0.589566i	$0.200701\pi$
$312$	0.977369	0.0553326
$313$	−29.5312	−1.66920	−0.834602	−	0.550854i	$-0.814302\pi$
$313$	−29.5312	−1.66920	−0.834602	+	0.550854i	$0.814302\pi$
$314$	−6.11684	−0.345193
$315$	6.02965	0.339732
$316$	12.0666	0.678798
$317$	17.6073	0.988923	0.494461	−	0.869200i	$-0.335365\pi$
$317$	17.6073	0.988923	0.494461	+	0.869200i	$0.335365\pi$
$318$	−10.5178	−0.589810
$319$	−0.113346	−0.00634617
$320$	4.10547	0.229503
$321$	25.4161	1.41859
$322$	−1.09974	−0.0612863
$323$	−32.9082	−1.83106
$324$	−3.21005	−0.178336
$325$	8.98075	0.498162
$326$	3.64827	0.202059
$327$	10.9161	0.603664
$328$	−2.08154	−0.114934
$329$	−7.31263	−0.403159
$330$	−0.600364	−0.0330489
$331$	12.8409	0.705800	0.352900	−	0.935661i	$-0.385196\pi$
$331$	12.8409	0.705800	0.352900	+	0.935661i	$0.385196\pi$
$332$	−5.56823	−0.305596
$333$	−3.30751	−0.181250
$334$	18.0692	0.988702
$335$	−20.3066	−1.10947
$336$	−1.41885	−0.0774045
$337$	35.2057	1.91778	0.958888	−	0.283785i	$-0.0915904\pi$
$337$	35.2057	1.91778	0.958888	+	0.283785i	$0.0915904\pi$
$338$	−12.4261	−0.675891
$339$	−21.5149	−1.16853
$340$	−23.4487	−1.27168
$341$	−0.786014	−0.0425650
$342$	−7.69460	−0.416076
$343$	14.0663	0.759511
$344$	−9.56412	−0.515663
$345$	5.29673	0.285166
$346$	−7.24199	−0.389332
$347$	−10.4496	−0.560965	−0.280482	−	0.959859i	$-0.590494\pi$
$347$	−10.4496	−0.560965	−0.280482	+	0.959859i	$0.590494\pi$
$348$	1.29016	0.0691600
$349$	5.07509	0.271663	0.135832	−	0.990732i	$-0.456629\pi$
$349$	5.07509	0.271663	0.135832	+	0.990732i	$0.456629\pi$
$350$	−13.0374	−0.696877
$351$	−4.23736	−0.226174
$352$	−0.113346	−0.00604137
$353$	9.92903	0.528469	0.264235	−	0.964458i	$-0.414881\pi$
$353$	9.92903	0.528469	0.264235	+	0.964458i	$0.414881\pi$
$354$	−11.9631	−0.635831
$355$	−46.1056	−2.44703
$356$	6.56682	0.348041
$357$	8.10385	0.428901
$358$	3.83996	0.202948
$359$	−12.7010	−0.670335	−0.335167	−	0.942159i	$-0.608793\pi$
$359$	−12.7010	−0.670335	−0.335167	+	0.942159i	$0.608793\pi$
$360$	−5.48278	−0.288968
$361$	14.1969	0.747205
$362$	18.2258	0.957929
$363$	−14.1752	−0.744006
$364$	−0.833116	−0.0436671
$365$	−16.8457	−0.881744
$366$	6.26501	0.327477
$367$	0.337308	0.0176074	0.00880368	−	0.999961i	$-0.497198\pi$
$367$	0.337308	0.0176074	0.00880368	+	0.999961i	$0.497198\pi$
$368$	1.00000	0.0521286
$369$	2.77986	0.144714
$370$	10.1678	0.528599
$371$	8.96546	0.465463
$372$	8.94680	0.463870
$373$	28.0535	1.45256	0.726279	−	0.687400i	$-0.241248\pi$
$373$	28.0535	1.45256	0.726279	+	0.687400i	$0.241248\pi$
$374$	0.647384	0.0334755
$375$	36.3087	1.87497
$376$	6.64940	0.342917
$377$	0.757554	0.0390160
$378$	6.15139	0.316393
$379$	−22.5014	−1.15582	−0.577909	−	0.816101i	$-0.696131\pi$
$379$	−22.5014	−1.15582	−0.577909	+	0.816101i	$0.696131\pi$
$380$	23.6544	1.21345
$381$	−9.81332	−0.502752
$382$	−0.837724	−0.0428617
$383$	27.7786	1.41942	0.709709	−	0.704495i	$-0.248826\pi$
$383$	27.7786	1.41942	0.709709	+	0.704495i	$0.248826\pi$
$384$	1.29016	0.0658383
$385$	0.511754	0.0260814
$386$	−12.0939	−0.615562
$387$	12.7727	0.649272
$388$	−4.87356	−0.247417
$389$	−3.31158	−0.167904	−0.0839518	−	0.996470i	$-0.526754\pi$
$389$	−3.31158	−0.167904	−0.0839518	+	0.996470i	$0.526754\pi$
$390$	4.01256	0.203184
$391$	−5.71157	−0.288846
$392$	−5.79056	−0.292468
$393$	27.8512	1.40491
$394$	5.89003	0.296735
$395$	49.5391	2.49258
$396$	0.151372	0.00760671
$397$	36.6919	1.84151	0.920756	−	0.390139i	$-0.127573\pi$
$397$	36.6919	1.84151	0.920756	+	0.390139i	$0.127573\pi$
$398$	3.57062	0.178979
$399$	−8.17494	−0.409259
$400$	11.8549	0.592746
$401$	−20.8312	−1.04026	−0.520131	−	0.854087i	$-0.674117\pi$
$401$	−20.8312	−1.04026	−0.520131	+	0.854087i	$0.674117\pi$
$402$	−6.38143	−0.318277
$403$	5.25336	0.261688
$404$	−16.5875	−0.825258
$405$	−13.1788	−0.654859
$406$	−1.09974	−0.0545794
$407$	−0.280718	−0.0139147
$408$	−7.36885	−0.364813
$409$	32.9326	1.62841	0.814206	−	0.580576i	$-0.197173\pi$
$409$	32.9326	1.62841	0.814206	+	0.580576i	$0.197173\pi$
$410$	−8.54572	−0.422043
$411$	−18.0328	−0.889492
$412$	−17.8725	−0.880515
$413$	10.1974	0.501782
$414$	−1.33548	−0.0656353
$415$	−22.8602	−1.12216
$416$	0.757554	0.0371422
$417$	6.64947	0.325626
$418$	−0.653064	−0.0319424
$419$	11.0189	0.538309	0.269155	−	0.963097i	$-0.413256\pi$
$419$	11.0189	0.538309	0.269155	+	0.963097i	$0.413256\pi$
$420$	−5.82505	−0.284233
$421$	−2.42018	−0.117952	−0.0589762	−	0.998259i	$-0.518784\pi$
$421$	−2.42018	−0.117952	−0.0589762	+	0.998259i	$0.518784\pi$
$422$	4.21038	0.204958
$423$	−8.88014	−0.431767
$424$	−8.15232	−0.395912
$425$	−67.7102	−3.28443
$426$	−14.4889	−0.701988
$427$	−5.34034	−0.258437
$428$	19.6999	0.952232
$429$	−0.110781	−0.00534856
$430$	−39.2652	−1.89354
$431$	−5.65656	−0.272467	−0.136233	−	0.990677i	$-0.543500\pi$
$431$	−5.65656	−0.272467	−0.136233	+	0.990677i	$0.543500\pi$
$432$	−5.59347	−0.269116
$433$	−11.9795	−0.575699	−0.287850	−	0.957676i	$-0.592940\pi$
$433$	−11.9795	−0.575699	−0.287850	+	0.957676i	$0.592940\pi$
$434$	−7.62632	−0.366075
$435$	5.29673	0.253959
$436$	8.46106	0.405211
$437$	5.76167	0.275618
$438$	−5.29383	−0.252949
$439$	3.41122	0.162809	0.0814044	−	0.996681i	$-0.474059\pi$
$439$	3.41122	0.162809	0.0814044	+	0.996681i	$0.474059\pi$
$440$	−0.465340	−0.0221842
$441$	7.73318	0.368247
$442$	−4.32682	−0.205806
$443$	2.08963	0.0992814	0.0496407	−	0.998767i	$-0.484192\pi$
$443$	2.08963	0.0992814	0.0496407	+	0.998767i	$0.484192\pi$
$444$	3.19528	0.151641
$445$	26.9599	1.27802
$446$	2.71528	0.128572
$447$	14.7287	0.696642
$448$	−1.09974	−0.0519580
$449$	−11.7914	−0.556470	−0.278235	−	0.960513i	$-0.589749\pi$
$449$	−11.7914	−0.556470	−0.278235	+	0.960513i	$0.589749\pi$
$450$	−15.8320	−0.746328
$451$	0.235935	0.0111097
$452$	−16.6761	−0.784377
$453$	25.6753	1.20633
$454$	−0.564403	−0.0264887
$455$	−3.42034	−0.160348
$456$	7.43350	0.348105
$457$	−11.9922	−0.560972	−0.280486	−	0.959858i	$-0.590496\pi$
$457$	−11.9922	−0.560972	−0.280486	+	0.959858i	$0.590496\pi$
$458$	−14.0794	−0.657886
$459$	31.9475	1.49118
$460$	4.10547	0.191419
$461$	22.0663	1.02773	0.513866	−	0.857871i	$-0.328213\pi$
$461$	22.0663	1.02773	0.513866	+	0.857871i	$0.328213\pi$
$462$	0.160821	0.00748207
$463$	16.4612	0.765017	0.382509	−	0.923952i	$-0.375060\pi$
$463$	16.4612	0.765017	0.382509	+	0.923952i	$0.375060\pi$
$464$	1.00000	0.0464238
$465$	36.7309	1.70335
$466$	26.3700	1.22157
$467$	−1.59036	−0.0735932	−0.0367966	−	0.999323i	$-0.511715\pi$
$467$	−1.59036	−0.0735932	−0.0367966	+	0.999323i	$0.511715\pi$
$468$	−1.01170	−0.0467658
$469$	5.43958	0.251176
$470$	27.2989	1.25921
$471$	−7.89172	−0.363631
$472$	−9.27254	−0.426803
$473$	1.08406	0.0498450
$474$	15.5679	0.715055
$475$	68.3042	3.13401
$476$	6.28126	0.287901
$477$	10.8873	0.498493
$478$	3.55147	0.162440
$479$	−32.8227	−1.49971	−0.749853	−	0.661604i	$-0.769876\pi$
$479$	−32.8227	−1.49971	−0.749853	+	0.661604i	$0.769876\pi$
$480$	5.29673	0.241762
$481$	1.87619	0.0855471
$482$	−24.7895	−1.12913
$483$	−1.41885	−0.0645598
$484$	−10.9872	−0.499416
$485$	−20.0083	−0.908528
$486$	12.6389	0.573314
$487$	18.4188	0.834636	0.417318	−	0.908761i	$-0.362970\pi$
$487$	18.4188	0.834636	0.417318	+	0.908761i	$0.362970\pi$
$488$	4.85598	0.219820
$489$	4.70686	0.212851
$490$	−23.7730	−1.07396
$491$	23.8454	1.07613	0.538063	−	0.842905i	$-0.319156\pi$
$491$	23.8454	1.07613	0.538063	+	0.842905i	$0.319156\pi$
$492$	−2.68553	−0.121073
$493$	−5.71157	−0.257236
$494$	4.36478	0.196381
$495$	0.621452	0.0279322
$496$	6.93463	0.311374
$497$	12.3504	0.553992
$498$	−7.18392	−0.321919
$499$	17.3787	0.777979	0.388990	−	0.921242i	$-0.372824\pi$
$499$	17.3787	0.777979	0.388990	+	0.921242i	$0.372824\pi$
$500$	28.1427	1.25858
$501$	23.3122	1.04151
$502$	−7.69243	−0.343330
$503$	−10.2183	−0.455612	−0.227806	−	0.973707i	$-0.573155\pi$
$503$	−10.2183	−0.455612	−0.227806	+	0.973707i	$0.573155\pi$
$504$	1.46869	0.0654205
$505$	−68.0995	−3.03039
$506$	−0.113346	−0.00503885
$507$	−16.0317	−0.711993
$508$	−7.60627	−0.337474
$509$	−28.7361	−1.27370	−0.636852	−	0.770986i	$-0.719764\pi$
$509$	−28.7361	−1.27370	−0.636852	+	0.770986i	$0.719764\pi$
$510$	−30.2526	−1.33961
$511$	4.51250	0.199621
$512$	1.00000	0.0441942
$513$	−32.2278	−1.42289
$514$	−7.10413	−0.313350
$515$	−73.3751	−3.23329
$516$	−12.3393	−0.543206
$517$	−0.753684	−0.0331470
$518$	−2.72368	−0.119671
$519$	−9.34335	−0.410128
$520$	3.11012	0.136388
$521$	−38.2368	−1.67518	−0.837592	−	0.546297i	$-0.816037\pi$
$521$	−38.2368	−1.67518	−0.837592	+	0.546297i	$0.816037\pi$
$522$	−1.33548	−0.0584524
$523$	26.0405	1.13867	0.569336	−	0.822105i	$-0.307201\pi$
$523$	26.0405	1.13867	0.569336	+	0.822105i	$0.307201\pi$
$524$	21.5873	0.943047
$525$	−16.8203	−0.734100
$526$	−21.6905	−0.945753
$527$	−39.6076	−1.72533
$528$	−0.146235	−0.00636406
$529$	1.00000	0.0434783
$530$	−33.4691	−1.45381
$531$	12.3833	0.537389
$532$	−6.33637	−0.274716
$533$	−1.57688	−0.0683023
$534$	8.47227	0.366631
$535$	80.8776	3.49664
$536$	−4.94622	−0.213644
$537$	4.95417	0.213788
$538$	−16.6519	−0.717916
$539$	0.656338	0.0282705
$540$	−22.9639	−0.988208
$541$	7.37191	0.316943	0.158472	−	0.987364i	$-0.449343\pi$
$541$	7.37191	0.316943	0.158472	+	0.987364i	$0.449343\pi$
$542$	0.278758	0.0119737
$543$	23.5143	1.00909
$544$	−5.71157	−0.244882
$545$	34.7367	1.48796
$546$	−1.07486	−0.0459995
$547$	25.1760	1.07645	0.538224	−	0.842802i	$-0.319095\pi$
$547$	25.1760	1.07645	0.538224	+	0.842802i	$0.319095\pi$
$548$	−13.9771	−0.597074
$549$	−6.48507	−0.276776
$550$	−1.34371	−0.0572960
$551$	5.76167	0.245456
$552$	1.29016	0.0549130
$553$	−13.2702	−0.564304
$554$	25.6007	1.08767
$555$	13.1181	0.556833
$556$	5.15398	0.218577
$557$	−25.8801	−1.09658	−0.548288	−	0.836290i	$-0.684720\pi$
$557$	−25.8801	−1.09658	−0.548288	+	0.836290i	$0.684720\pi$
$558$	−9.26106	−0.392052
$559$	−7.24534	−0.306445
$560$	−4.51497	−0.190792
$561$	0.835231	0.0352635
$562$	0.542128	0.0228683
$563$	−10.1378	−0.427258	−0.213629	−	0.976915i	$-0.568528\pi$
$563$	−10.1378	−0.427258	−0.213629	+	0.976915i	$0.568528\pi$
$564$	8.57881	0.361233
$565$	−68.4632	−2.88027
$566$	15.2437	0.640739
$567$	3.53024	0.148256
$568$	−11.2303	−0.471212
$569$	18.1714	0.761784	0.380892	−	0.924620i	$-0.375617\pi$
$569$	18.1714	0.761784	0.380892	+	0.924620i	$0.375617\pi$
$570$	30.5180	1.27826
$571$	13.1978	0.552313	0.276156	−	0.961113i	$-0.410939\pi$
$571$	13.1978	0.552313	0.276156	+	0.961113i	$0.410939\pi$
$572$	−0.0858659	−0.00359023
$573$	−1.08080	−0.0451511
$574$	2.28916	0.0955478
$575$	11.8549	0.494384
$576$	−1.33548	−0.0556450
$577$	−1.40365	−0.0584349	−0.0292175	−	0.999573i	$-0.509302\pi$
$577$	−1.40365	−0.0584349	−0.0292175	+	0.999573i	$0.509302\pi$
$578$	15.6220	0.649791
$579$	−15.6031	−0.648442
$580$	4.10547	0.170471
$581$	6.12363	0.254051
$582$	−6.28768	−0.260633
$583$	0.924034	0.0382696
$584$	−4.10323	−0.169793
$585$	−4.15350	−0.171726
$586$	−28.1935	−1.16466
$587$	−8.87204	−0.366188	−0.183094	−	0.983095i	$-0.558611\pi$
$587$	−8.87204	−0.366188	−0.183094	+	0.983095i	$0.558611\pi$
$588$	−7.47077	−0.308089
$589$	39.9551	1.64632
$590$	−38.0682	−1.56724
$591$	7.59909	0.312585
$592$	2.47665	0.101789
$593$	−24.9132	−1.02306	−0.511531	−	0.859265i	$-0.670921\pi$
$593$	−24.9132	−1.02306	−0.511531	+	0.859265i	$0.670921\pi$
$594$	0.633999	0.0260133
$595$	25.7876	1.05719
$596$	11.4161	0.467623
$597$	4.60668	0.188539
$598$	0.757554	0.0309787
$599$	21.2360	0.867678	0.433839	−	0.900990i	$-0.357159\pi$
$599$	21.2360	0.867678	0.433839	+	0.900990i	$0.357159\pi$
$600$	15.2948	0.624407
$601$	−5.76430	−0.235131	−0.117565	−	0.993065i	$-0.537509\pi$
$601$	−5.76430	−0.235131	−0.117565	+	0.993065i	$0.537509\pi$
$602$	10.5181	0.428685
$603$	6.60558	0.269000
$604$	19.9008	0.809752
$605$	−45.1075	−1.83388
$606$	−21.4005	−0.869338
$607$	1.48706	0.0603579	0.0301790	−	0.999545i	$-0.490392\pi$
$607$	1.48706	0.0603579	0.0301790	+	0.999545i	$0.490392\pi$
$608$	5.76167	0.233667
$609$	−1.41885	−0.0574946
$610$	19.9361	0.807190
$611$	5.03728	0.203787
$612$	7.62769	0.308331
$613$	28.4796	1.15028	0.575139	−	0.818056i	$-0.304948\pi$
$613$	28.4796	1.15028	0.575139	+	0.818056i	$0.304948\pi$
$614$	−22.1564	−0.894158
$615$	−11.0254	−0.444586
$616$	0.124652	0.00502236
$617$	10.8867	0.438281	0.219141	−	0.975693i	$-0.429675\pi$
$617$	10.8867	0.438281	0.219141	+	0.975693i	$0.429675\pi$
$618$	−23.0584	−0.927547
$619$	−21.2722	−0.855003	−0.427501	−	0.904015i	$-0.640606\pi$
$619$	−21.2722	−0.855003	−0.427501	+	0.904015i	$0.640606\pi$
$620$	28.4699	1.14338
$621$	−5.59347	−0.224458
$622$	28.4886	1.14229
$623$	−7.22182	−0.289336
$624$	0.977369	0.0391261
$625$	56.2645	2.25058
$626$	−29.5312	−1.18031
$627$	−0.842558	−0.0336485
$628$	−6.11684	−0.244089
$629$	−14.1455	−0.564019
$630$	6.02965	0.240227
$631$	28.2617	1.12508	0.562540	−	0.826770i	$-0.309824\pi$
$631$	28.2617	1.12508	0.562540	+	0.826770i	$0.309824\pi$
$632$	12.0666	0.479983
$633$	5.43208	0.215906
$634$	17.6073	0.699274
$635$	−31.2273	−1.23922
$636$	−10.5178	−0.417059
$637$	−4.38667	−0.173806
$638$	−0.113346	−0.00448742
$639$	14.9978	0.593304
$640$	4.10547	0.162283
$641$	26.8883	1.06202	0.531012	−	0.847364i	$-0.321812\pi$
$641$	26.8883	1.06202	0.531012	+	0.847364i	$0.321812\pi$
$642$	25.4161	1.00309
$643$	29.9350	1.18052	0.590261	−	0.807213i	$-0.299025\pi$
$643$	29.9350	1.18052	0.590261	+	0.807213i	$0.299025\pi$
$644$	−1.09974	−0.0433360
$645$	−50.6586	−1.99468
$646$	−32.9082	−1.29476
$647$	−33.4378	−1.31458	−0.657289	−	0.753639i	$-0.728297\pi$
$647$	−33.4378	−1.31458	−0.657289	+	0.753639i	$0.728297\pi$
$648$	−3.21005	−0.126103
$649$	1.05101	0.0412556
$650$	8.98075	0.352254
$651$	−9.83919	−0.385628
$652$	3.64827	0.142877
$653$	47.0305	1.84044	0.920222	−	0.391397i	$-0.128008\pi$
$653$	47.0305	1.84044	0.920222	+	0.391397i	$0.128008\pi$
$654$	10.9161	0.426855
$655$	88.6263	3.46291
$656$	−2.08154	−0.0812706
$657$	5.47978	0.213787
$658$	−7.31263	−0.285076
$659$	21.7765	0.848292	0.424146	−	0.905594i	$-0.360574\pi$
$659$	21.7765	0.848292	0.424146	+	0.905594i	$0.360574\pi$
$660$	−0.600364	−0.0233691
$661$	−22.3469	−0.869192	−0.434596	−	0.900626i	$-0.643109\pi$
$661$	−22.3469	−0.869192	−0.434596	+	0.900626i	$0.643109\pi$
$662$	12.8409	0.499076
$663$	−5.58231	−0.216799
$664$	−5.56823	−0.216089
$665$	−26.0138	−1.00877
$666$	−3.30751	−0.128163
$667$	1.00000	0.0387202
$668$	18.0692	0.699118
$669$	3.50315	0.135440
$670$	−20.3066	−0.784512
$671$	−0.550407	−0.0212482
$672$	−1.41885	−0.0547333
$673$	−21.4114	−0.825348	−0.412674	−	0.910879i	$-0.635405\pi$
$673$	−21.4114	−0.825348	−0.412674	+	0.910879i	$0.635405\pi$
$674$	35.2057	1.35607
$675$	−66.3102	−2.55228
$676$	−12.4261	−0.477927
$677$	39.2249	1.50753	0.753767	−	0.657142i	$-0.228235\pi$
$677$	39.2249	1.50753	0.753767	+	0.657142i	$0.228235\pi$
$678$	−21.5149	−0.826273
$679$	5.35966	0.205685
$680$	−23.4487	−0.899217
$681$	−0.728171	−0.0279036
$682$	−0.786014	−0.0300980
$683$	13.9964	0.535559	0.267780	−	0.963480i	$-0.413710\pi$
$683$	13.9964	0.535559	0.267780	+	0.963480i	$0.413710\pi$
$684$	−7.69460	−0.294210
$685$	−57.3828	−2.19248
$686$	14.0663	0.537055
$687$	−18.1647	−0.693027
$688$	−9.56412	−0.364629
$689$	−6.17582	−0.235280
$690$	5.29673	0.201643
$691$	8.73211	0.332185	0.166093	−	0.986110i	$-0.446885\pi$
$691$	8.73211	0.332185	0.166093	+	0.986110i	$0.446885\pi$
$692$	−7.24199	−0.275299
$693$	−0.166470	−0.00632367
$694$	−10.4496	−0.396662
$695$	21.1595	0.802626
$696$	1.29016	0.0489035
$697$	11.8889	0.450323
$698$	5.07509	0.192095
$699$	34.0216	1.28682
$700$	−13.0374	−0.492766
$701$	−5.89180	−0.222530	−0.111265	−	0.993791i	$-0.535490\pi$
$701$	−5.89180	−0.222530	−0.111265	+	0.993791i	$0.535490\pi$
$702$	−4.23736	−0.159929
$703$	14.2696	0.538189
$704$	−0.113346	−0.00427189
$705$	35.2201	1.32646
$706$	9.92903	0.373684
$707$	18.2420	0.686060
$708$	−11.9631	−0.449600
$709$	29.0922	1.09258	0.546290	−	0.837596i	$-0.316040\pi$
$709$	29.0922	1.09258	0.546290	+	0.837596i	$0.316040\pi$
$710$	−46.1056	−1.73031
$711$	−16.1147	−0.604348
$712$	6.56682	0.246102
$713$	6.93463	0.259704
$714$	8.10385	0.303279
$715$	−0.352520	−0.0131835
$716$	3.83996	0.143506
$717$	4.58197	0.171117
$718$	−12.7010	−0.473998
$719$	20.6125	0.768718	0.384359	−	0.923184i	$-0.374422\pi$
$719$	20.6125	0.768718	0.384359	+	0.923184i	$0.374422\pi$
$720$	−5.48278	−0.204331
$721$	19.6552	0.731997
$722$	14.1969	0.528354
$723$	−31.9825	−1.18944
$724$	18.2258	0.677358
$725$	11.8549	0.440281
$726$	−14.1752	−0.526092
$727$	11.0982	0.411608	0.205804	−	0.978593i	$-0.434019\pi$
$727$	11.0982	0.411608	0.205804	+	0.978593i	$0.434019\pi$
$728$	−0.833116	−0.0308773
$729$	25.9364	0.960609
$730$	−16.8457	−0.623487
$731$	54.6261	2.02042
$732$	6.26501	0.231561
$733$	−1.00154	−0.0369926	−0.0184963	−	0.999829i	$-0.505888\pi$
$733$	−1.00154	−0.0369926	−0.0184963	+	0.999829i	$0.505888\pi$
$734$	0.337308	0.0124503
$735$	−30.6711	−1.13132
$736$	1.00000	0.0368605
$737$	0.560635	0.0206513
$738$	2.77986	0.102328
$739$	9.48006	0.348730	0.174365	−	0.984681i	$-0.444213\pi$
$739$	9.48006	0.348730	0.174365	+	0.984681i	$0.444213\pi$
$740$	10.1678	0.373776
$741$	5.63128	0.206870
$742$	8.96546	0.329132
$743$	9.81160	0.359953	0.179976	−	0.983671i	$-0.442398\pi$
$743$	9.81160	0.359953	0.179976	+	0.983671i	$0.442398\pi$
$744$	8.94680	0.328006
$745$	46.8686	1.71713
$746$	28.0535	1.02711
$747$	7.43626	0.272079
$748$	0.647384	0.0236707
$749$	−21.6649	−0.791617
$750$	36.3087	1.32580
$751$	−34.6391	−1.26400	−0.631998	−	0.774970i	$-0.717765\pi$
$751$	−34.6391	−1.26400	−0.631998	+	0.774970i	$0.717765\pi$
$752$	6.64940	0.242479
$753$	−9.92449	−0.361668
$754$	0.757554	0.0275885
$755$	81.7022	2.97345
$756$	6.15139	0.223724
$757$	−13.7005	−0.497954	−0.248977	−	0.968509i	$-0.580094\pi$
$757$	−13.7005	−0.497954	−0.248977	+	0.968509i	$0.580094\pi$
$758$	−22.5014	−0.817286
$759$	−0.146235	−0.00530799
$760$	23.6544	0.858036
$761$	47.9357	1.73767	0.868833	−	0.495105i	$-0.164870\pi$
$761$	47.9357	1.73767	0.868833	+	0.495105i	$0.164870\pi$
$762$	−9.81332	−0.355499
$763$	−9.30500	−0.336864
$764$	−0.837724	−0.0303078
$765$	31.3153	1.13221
$766$	27.7786	1.00368
$767$	−7.02445	−0.253638
$768$	1.29016	0.0465547
$769$	−2.76391	−0.0996690	−0.0498345	−	0.998757i	$-0.515869\pi$
$769$	−2.76391	−0.0996690	−0.0498345	+	0.998757i	$0.515869\pi$
$770$	0.511754	0.0184424
$771$	−9.16549	−0.330087
$772$	−12.0939	−0.435268
$773$	−41.5148	−1.49318	−0.746592	−	0.665282i	$-0.768311\pi$
$773$	−41.5148	−1.49318	−0.746592	+	0.665282i	$0.768311\pi$
$774$	12.7727	0.459105
$775$	82.2095	2.95305
$776$	−4.87356	−0.174950
$777$	−3.51398	−0.126063
$778$	−3.31158	−0.118726
$779$	−11.9932	−0.429700
$780$	4.01256	0.143673
$781$	1.27291	0.0455482
$782$	−5.71157	−0.204245
$783$	−5.59347	−0.199894
$784$	−5.79056	−0.206806
$785$	−25.1125	−0.896305
$786$	27.8512	0.993419
$787$	24.2548	0.864590	0.432295	−	0.901732i	$-0.357704\pi$
$787$	24.2548	0.864590	0.432295	+	0.901732i	$0.357704\pi$
$788$	5.89003	0.209824
$789$	−27.9843	−0.996269
$790$	49.5391	1.76252
$791$	18.3394	0.652075
$792$	0.151372	0.00537875
$793$	3.67867	0.130633
$794$	36.6919	1.30215
$795$	−43.1806	−1.53146
$796$	3.57062	0.126557
$797$	−22.4818	−0.796347	−0.398173	−	0.917310i	$-0.630356\pi$
$797$	−22.4818	−0.796347	−0.398173	+	0.917310i	$0.630356\pi$
$798$	−8.17494	−0.289390
$799$	−37.9785	−1.34358
$800$	11.8549	0.419135
$801$	−8.76986	−0.309868
$802$	−20.8312	−0.735576
$803$	0.465085	0.0164125
$804$	−6.38143	−0.225056
$805$	−4.51497	−0.159132
$806$	5.25336	0.185042
$807$	−21.4837	−0.756262
$808$	−16.5875	−0.583545
$809$	−15.0667	−0.529716	−0.264858	−	0.964287i	$-0.585325\pi$
$809$	−15.0667	−0.529716	−0.264858	+	0.964287i	$0.585325\pi$
$810$	−13.1788	−0.463056
$811$	−6.47006	−0.227195	−0.113597	−	0.993527i	$-0.536237\pi$
$811$	−6.47006	−0.227195	−0.113597	+	0.993527i	$0.536237\pi$
$812$	−1.09974	−0.0385934
$813$	0.359643	0.0126132
$814$	−0.280718	−0.00983917
$815$	14.9779	0.524652
$816$	−7.36885	−0.257961
$817$	−55.1053	−1.92789
$818$	32.9326	1.15146
$819$	1.11261	0.0388777
$820$	−8.54572	−0.298429
$821$	9.44751	0.329720	0.164860	−	0.986317i	$-0.447283\pi$
$821$	9.44751	0.329720	0.164860	+	0.986317i	$0.447283\pi$
$822$	−18.0328	−0.628966
$823$	1.41064	0.0491719	0.0245860	−	0.999698i	$-0.492173\pi$
$823$	1.41064	0.0491719	0.0245860	+	0.999698i	$0.492173\pi$
$824$	−17.8725	−0.622618
$825$	−1.73360	−0.0603563
$826$	10.1974	0.354814
$827$	−35.7319	−1.24252	−0.621261	−	0.783604i	$-0.713379\pi$
$827$	−35.7319	−1.24252	−0.621261	+	0.783604i	$0.713379\pi$
$828$	−1.33548	−0.0464111
$829$	−1.59276	−0.0553188	−0.0276594	−	0.999617i	$-0.508805\pi$
$829$	−1.59276	−0.0553188	−0.0276594	+	0.999617i	$0.508805\pi$
$830$	−22.8602	−0.793490
$831$	33.0291	1.14577
$832$	0.757554	0.0262635
$833$	33.0732	1.14592
$834$	6.64947	0.230252
$835$	74.1826	2.56719
$836$	−0.653064	−0.0225867
$837$	−38.7887	−1.34073
$838$	11.0189	0.380642
$839$	−19.5721	−0.675703	−0.337851	−	0.941199i	$-0.609700\pi$
$839$	−19.5721	−0.675703	−0.337851	+	0.941199i	$0.609700\pi$
$840$	−5.82505	−0.200983
$841$	1.00000	0.0344828
$842$	−2.42018	−0.0834049
$843$	0.699433	0.0240898
$844$	4.21038	0.144927
$845$	−51.0151	−1.75497
$846$	−8.88014	−0.305305
$847$	12.0831	0.415179
$848$	−8.15232	−0.279952
$849$	19.6668	0.674964
$850$	−67.7102	−2.32244
$851$	2.47665	0.0848983
$852$	−14.4889	−0.496381
$853$	−30.4962	−1.04417	−0.522085	−	0.852893i	$-0.674846\pi$
$853$	−30.4962	−1.04417	−0.522085	+	0.852893i	$0.674846\pi$
$854$	−5.34034	−0.182743
$855$	−31.5900	−1.08035
$856$	19.6999	0.673330
$857$	34.7968	1.18864	0.594319	−	0.804230i	$-0.297422\pi$
$857$	34.7968	1.18864	0.594319	+	0.804230i	$0.297422\pi$
$858$	−0.110781	−0.00378200
$859$	−7.53537	−0.257103	−0.128552	−	0.991703i	$-0.541033\pi$
$859$	−7.53537	−0.257103	−0.128552	+	0.991703i	$0.541033\pi$
$860$	−39.2652	−1.33893
$861$	2.95339	0.100651
$862$	−5.65656	−0.192663
$863$	−26.8831	−0.915111	−0.457555	−	0.889181i	$-0.651275\pi$
$863$	−26.8831	−0.915111	−0.457555	+	0.889181i	$0.651275\pi$
$864$	−5.59347	−0.190294
$865$	−29.7318	−1.01091
$866$	−11.9795	−0.407081
$867$	20.1550	0.684498
$868$	−7.62632	−0.258854
$869$	−1.36770	−0.0463961
$870$	5.29673	0.179576
$871$	−3.74703	−0.126963
$872$	8.46106	0.286528
$873$	6.50854	0.220281
$874$	5.76167	0.194892
$875$	−30.9498	−1.04629
$876$	−5.29383	−0.178862
$877$	−52.0878	−1.75888	−0.879441	−	0.476009i	$-0.842083\pi$
$877$	−52.0878	−1.75888	−0.879441	+	0.476009i	$0.842083\pi$
$878$	3.41122	0.115123
$879$	−36.3743	−1.22687
$880$	−0.465340	−0.0156866
$881$	−9.72940	−0.327792	−0.163896	−	0.986478i	$-0.552406\pi$
$881$	−9.72940	−0.327792	−0.163896	+	0.986478i	$0.552406\pi$
$882$	7.73318	0.260390
$883$	52.8410	1.77824	0.889121	−	0.457672i	$-0.151317\pi$
$883$	52.8410	1.77824	0.889121	+	0.457672i	$0.151317\pi$
$884$	−4.32682	−0.145527
$885$	−49.1141	−1.65095
$886$	2.08963	0.0702026
$887$	17.7340	0.595448	0.297724	−	0.954652i	$-0.403772\pi$
$887$	17.7340	0.595448	0.297724	+	0.954652i	$0.403772\pi$
$888$	3.19528	0.107226
$889$	8.36495	0.280551
$890$	26.9599	0.903698
$891$	0.363847	0.0121893
$892$	2.71528	0.0909143
$893$	38.3117	1.28205
$894$	14.7287	0.492600
$895$	15.7649	0.526961
$896$	−1.09974	−0.0367399
$897$	0.977369	0.0326334
$898$	−11.7914	−0.393484
$899$	6.93463	0.231283
$900$	−15.8320	−0.527734
$901$	46.5625	1.55122
$902$	0.235935	0.00785577
$903$	13.5700	0.451583
$904$	−16.6761	−0.554638
$905$	74.8257	2.48729
$906$	25.6753	0.853004
$907$	10.3091	0.342309	0.171154	−	0.985244i	$-0.445250\pi$
$907$	10.3091	0.342309	0.171154	+	0.985244i	$0.445250\pi$
$908$	−0.564403	−0.0187304
$909$	22.1522	0.734743
$910$	−3.42034	−0.113383
$911$	−30.1081	−0.997527	−0.498764	−	0.866738i	$-0.666212\pi$
$911$	−30.1081	−0.997527	−0.498764	+	0.866738i	$0.666212\pi$
$912$	7.43350	0.246148
$913$	0.631138	0.0208876
$914$	−11.9922	−0.396667
$915$	25.7208	0.850304
$916$	−14.0794	−0.465196
$917$	−23.7405	−0.783982
$918$	31.9475	1.05443
$919$	−16.4895	−0.543938	−0.271969	−	0.962306i	$-0.587675\pi$
$919$	−16.4895	−0.543938	−0.271969	+	0.962306i	$0.587675\pi$
$920$	4.10547	0.135353
$921$	−28.5853	−0.941919
$922$	22.0663	0.726716
$923$	−8.50754	−0.280029
$924$	0.160821	0.00529062
$925$	29.3604	0.965365
$926$	16.4612	0.540949
$927$	23.8684	0.783940
$928$	1.00000	0.0328266
$929$	−15.9896	−0.524600	−0.262300	−	0.964986i	$-0.584481\pi$
$929$	−15.9896	−0.524600	−0.262300	+	0.964986i	$0.584481\pi$
$930$	36.7309	1.20445
$931$	−33.3633	−1.09344
$932$	26.3700	0.863779
$933$	36.7549	1.20330
$934$	−1.59036	−0.0520382
$935$	2.65782	0.0869200
$936$	−1.01170	−0.0330684
$937$	56.2275	1.83687	0.918437	−	0.395567i	$-0.129452\pi$
$937$	56.2275	1.83687	0.918437	+	0.395567i	$0.129452\pi$
$938$	5.43958	0.177609
$939$	−38.1001	−1.24335
$940$	27.2989	0.890393
$941$	29.5786	0.964235	0.482118	−	0.876107i	$-0.339868\pi$
$941$	29.5786	0.964235	0.482118	+	0.876107i	$0.339868\pi$
$942$	−7.89172	−0.257126
$943$	−2.08154	−0.0677843
$944$	−9.27254	−0.301796
$945$	25.2544	0.821525
$946$	1.08406	0.0352457
$947$	29.2553	0.950671	0.475336	−	0.879805i	$-0.342327\pi$
$947$	29.2553	0.950671	0.475336	+	0.879805i	$0.342327\pi$
$948$	15.5679	0.505621
$949$	−3.10842	−0.100904
$950$	68.3042	2.21608
$951$	22.7162	0.736625
$952$	6.28126	0.203577
$953$	31.8784	1.03264	0.516322	−	0.856395i	$-0.327301\pi$
$953$	31.8784	1.03264	0.516322	+	0.856395i	$0.327301\pi$
$954$	10.8873	0.352488
$955$	−3.43926	−0.111292
$956$	3.55147	0.114863
$957$	−0.146235	−0.00472711
$958$	−32.8227	−1.06045
$959$	15.3713	0.496365
$960$	5.29673	0.170951
$961$	17.0891	0.551261
$962$	1.87619	0.0604909
$963$	−26.3089	−0.847791
$964$	−24.7895	−0.798416
$965$	−49.6511	−1.59833
$966$	−1.41885	−0.0456507
$967$	−54.6869	−1.75861	−0.879305	−	0.476258i	$-0.841993\pi$
$967$	−54.6869	−1.75861	−0.879305	+	0.476258i	$0.841993\pi$
$968$	−10.9872	−0.353140
$969$	−42.4569	−1.36391
$970$	−20.0083	−0.642427
$971$	31.3636	1.00651	0.503253	−	0.864139i	$-0.332136\pi$
$971$	31.3636	1.00651	0.503253	+	0.864139i	$0.332136\pi$
$972$	12.6389	0.405394
$973$	−5.66805	−0.181709
$974$	18.4188	0.590177
$975$	11.5866	0.371069
$976$	4.85598	0.155436
$977$	−33.1944	−1.06198	−0.530991	−	0.847377i	$-0.678180\pi$
$977$	−33.1944	−1.06198	−0.530991	+	0.847377i	$0.678180\pi$
$978$	4.70686	0.150509
$979$	−0.744324	−0.0237887
$980$	−23.7730	−0.759401
$981$	−11.2996	−0.360768
$982$	23.8454	0.760936
$983$	−14.0464	−0.448011	−0.224006	−	0.974588i	$-0.571913\pi$
$983$	−14.0464	−0.448011	−0.224006	+	0.974588i	$0.571913\pi$
$984$	−2.68553	−0.0856115
$985$	24.1814	0.770482
$986$	−5.71157	−0.181893
$987$	−9.43449	−0.300303
$988$	4.36478	0.138862
$989$	−9.56412	−0.304121
$990$	0.621452	0.0197510
$991$	−20.4682	−0.650193	−0.325096	−	0.945681i	$-0.605397\pi$
$991$	−20.4682	−0.650193	−0.325096	+	0.945681i	$0.605397\pi$
$992$	6.93463	0.220175
$993$	16.5669	0.525733
$994$	12.3504	0.391732
$995$	14.6591	0.464724
$996$	−7.18392	−0.227631
$997$	20.0124	0.633800	0.316900	−	0.948459i	$-0.397358\pi$
$997$	20.0124	0.633800	0.316900	+	0.948459i	$0.397358\pi$
$998$	17.3787	0.550114
$999$	−13.8531	−0.438291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.7	✓	10	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.29016 q^{3} +1.00000 q^{4} +4.10547 q^{5} +1.29016 q^{6} -1.09974 q^{7} +1.00000 q^{8} -1.33548 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.29016 q^{3} +1.00000 q^{4} +4.10547 q^{5} +1.29016 q^{6} -1.09974 q^{7} +1.00000 q^{8} -1.33548 q^{9} +4.10547 q^{10} -0.113346 q^{11} +1.29016 q^{12} +0.757554 q^{13} -1.09974 q^{14} +5.29673 q^{15} +1.00000 q^{16} -5.71157 q^{17} -1.33548 q^{18} +5.76167 q^{19} +4.10547 q^{20} -1.41885 q^{21} -0.113346 q^{22} +1.00000 q^{23} +1.29016 q^{24} +11.8549 q^{25} +0.757554 q^{26} -5.59347 q^{27} -1.09974 q^{28} +1.00000 q^{29} +5.29673 q^{30} +6.93463 q^{31} +1.00000 q^{32} -0.146235 q^{33} -5.71157 q^{34} -4.51497 q^{35} -1.33548 q^{36} +2.47665 q^{37} +5.76167 q^{38} +0.977369 q^{39} +4.10547 q^{40} -2.08154 q^{41} -1.41885 q^{42} -9.56412 q^{43} -0.113346 q^{44} -5.48278 q^{45} +1.00000 q^{46} +6.64940 q^{47} +1.29016 q^{48} -5.79056 q^{49} +11.8549 q^{50} -7.36885 q^{51} +0.757554 q^{52} -8.15232 q^{53} -5.59347 q^{54} -0.465340 q^{55} -1.09974 q^{56} +7.43350 q^{57} +1.00000 q^{58} -9.27254 q^{59} +5.29673 q^{60} +4.85598 q^{61} +6.93463 q^{62} +1.46869 q^{63} +1.00000 q^{64} +3.11012 q^{65} -0.146235 q^{66} -4.94622 q^{67} -5.71157 q^{68} +1.29016 q^{69} -4.51497 q^{70} -11.2303 q^{71} -1.33548 q^{72} -4.10323 q^{73} +2.47665 q^{74} +15.2948 q^{75} +5.76167 q^{76} +0.124652 q^{77} +0.977369 q^{78} +12.0666 q^{79} +4.10547 q^{80} -3.21005 q^{81} -2.08154 q^{82} -5.56823 q^{83} -1.41885 q^{84} -23.4487 q^{85} -9.56412 q^{86} +1.29016 q^{87} -0.113346 q^{88} +6.56682 q^{89} -5.48278 q^{90} -0.833116 q^{91} +1.00000 q^{92} +8.94680 q^{93} +6.64940 q^{94} +23.6544 q^{95} +1.29016 q^{96} -4.87356 q^{97} -5.79056 q^{98} +0.151372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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