LMFDB - Embedded newform 322.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +0.853635 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +0.853635 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +0.853635 q^{10} +2.68585 q^{11} +1.14637 q^{12} +4.68585 q^{13} -1.00000 q^{14} +0.978577 q^{15} +1.00000 q^{16} -1.83221 q^{17} -1.68585 q^{18} -4.97858 q^{19} +0.853635 q^{20} -1.14637 q^{21} +2.68585 q^{22} -1.00000 q^{23} +1.14637 q^{24} -4.27131 q^{25} +4.68585 q^{26} -5.37169 q^{27} -1.00000 q^{28} -6.39312 q^{29} +0.978577 q^{30} +3.83221 q^{31} +1.00000 q^{32} +3.07896 q^{33} -1.83221 q^{34} -0.853635 q^{35} -1.68585 q^{36} +5.66442 q^{37} -4.97858 q^{38} +5.37169 q^{39} +0.853635 q^{40} +11.9572 q^{41} -1.14637 q^{42} -9.37169 q^{43} +2.68585 q^{44} -1.43910 q^{45} -1.00000 q^{46} -3.83221 q^{47} +1.14637 q^{48} +1.00000 q^{49} -4.27131 q^{50} -2.10038 q^{51} +4.68585 q^{52} -9.66442 q^{53} -5.37169 q^{54} +2.29273 q^{55} -1.00000 q^{56} -5.70727 q^{57} -6.39312 q^{58} +3.43910 q^{59} +0.978577 q^{60} -10.2253 q^{61} +3.83221 q^{62} +1.68585 q^{63} +1.00000 q^{64} +4.00000 q^{65} +3.07896 q^{66} -2.68585 q^{67} -1.83221 q^{68} -1.14637 q^{69} -0.853635 q^{70} -0.335577 q^{71} -1.68585 q^{72} +15.0361 q^{73} +5.66442 q^{74} -4.89648 q^{75} -4.97858 q^{76} -2.68585 q^{77} +5.37169 q^{78} -13.5640 q^{79} +0.853635 q^{80} -1.10038 q^{81} +11.9572 q^{82} +5.31415 q^{83} -1.14637 q^{84} -1.56404 q^{85} -9.37169 q^{86} -7.32885 q^{87} +2.68585 q^{88} +3.53948 q^{89} -1.43910 q^{90} -4.68585 q^{91} -1.00000 q^{92} +4.39312 q^{93} -3.83221 q^{94} -4.24989 q^{95} +1.14637 q^{96} +2.75325 q^{97} +1.00000 q^{98} -4.52792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * 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
$3$	1.14637	0.661854	0.330927	−	0.943656i	$-0.392639\pi$
$3$	1.14637	0.661854	0.330927	+	0.943656i	$0.392639\pi$
$4$	1.00000	0.500000
$5$	0.853635	0.381757	0.190878	−	0.981614i	$-0.438866\pi$
$5$	0.853635	0.381757	0.190878	+	0.981614i	$0.438866\pi$
$6$	1.14637	0.468002
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.68585	−0.561949
$10$	0.853635	0.269943
$11$	2.68585	0.809813	0.404907	−	0.914358i	$-0.367304\pi$
$11$	2.68585	0.809813	0.404907	+	0.914358i	$0.367304\pi$
$12$	1.14637	0.330927
$13$	4.68585	1.29962	0.649810	−	0.760097i	$-0.274848\pi$
$13$	4.68585	1.29962	0.649810	+	0.760097i	$0.274848\pi$
$14$	−1.00000	−0.267261
$15$	0.978577	0.252668
$16$	1.00000	0.250000
$17$	−1.83221	−0.444377	−0.222188	−	0.975004i	$-0.571320\pi$
$17$	−1.83221	−0.444377	−0.222188	+	0.975004i	$0.571320\pi$
$18$	−1.68585	−0.397358
$19$	−4.97858	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$19$	−4.97858	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$20$	0.853635	0.190878
$21$	−1.14637	−0.250157
$22$	2.68585	0.572624
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.14637	0.234001
$25$	−4.27131	−0.854262
$26$	4.68585	0.918970
$27$	−5.37169	−1.03378
$28$	−1.00000	−0.188982
$29$	−6.39312	−1.18717	−0.593586	−	0.804771i	$-0.702288\pi$
$29$	−6.39312	−1.18717	−0.593586	+	0.804771i	$0.702288\pi$
$30$	0.978577	0.178663
$31$	3.83221	0.688286	0.344143	−	0.938917i	$-0.388170\pi$
$31$	3.83221	0.688286	0.344143	+	0.938917i	$0.388170\pi$
$32$	1.00000	0.176777
$33$	3.07896	0.535978
$34$	−1.83221	−0.314222
$35$	−0.853635	−0.144291
$36$	−1.68585	−0.280974
$37$	5.66442	0.931225	0.465613	−	0.884989i	$-0.345834\pi$
$37$	5.66442	0.931225	0.465613	+	0.884989i	$0.345834\pi$
$38$	−4.97858	−0.807632
$39$	5.37169	0.860159
$40$	0.853635	0.134971
$41$	11.9572	1.86739	0.933697	−	0.358064i	$-0.116563\pi$
$41$	11.9572	1.86739	0.933697	+	0.358064i	$0.116563\pi$
$42$	−1.14637	−0.176888
$43$	−9.37169	−1.42917	−0.714585	−	0.699549i	$-0.753384\pi$
$43$	−9.37169	−1.42917	−0.714585	+	0.699549i	$0.753384\pi$
$44$	2.68585	0.404907
$45$	−1.43910	−0.214528
$46$	−1.00000	−0.147442
$47$	−3.83221	−0.558986	−0.279493	−	0.960148i	$-0.590166\pi$
$47$	−3.83221	−0.558986	−0.279493	+	0.960148i	$0.590166\pi$
$48$	1.14637	0.165464
$49$	1.00000	0.142857
$50$	−4.27131	−0.604054
$51$	−2.10038	−0.294113
$52$	4.68585	0.649810
$53$	−9.66442	−1.32751	−0.663755	−	0.747950i	$-0.731038\pi$
$53$	−9.66442	−1.32751	−0.663755	+	0.747950i	$0.731038\pi$
$54$	−5.37169	−0.730995
$55$	2.29273	0.309152
$56$	−1.00000	−0.133631
$57$	−5.70727	−0.755946
$58$	−6.39312	−0.839457
$59$	3.43910	0.447732	0.223866	−	0.974620i	$-0.428132\pi$
$59$	3.43910	0.447732	0.223866	+	0.974620i	$0.428132\pi$
$60$	0.978577	0.126334
$61$	−10.2253	−1.30922	−0.654609	−	0.755967i	$-0.727167\pi$
$61$	−10.2253	−1.30922	−0.654609	+	0.755967i	$0.727167\pi$
$62$	3.83221	0.486691
$63$	1.68585	0.212397
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	3.07896	0.378994
$67$	−2.68585	−0.328128	−0.164064	−	0.986450i	$-0.552460\pi$
$67$	−2.68585	−0.328128	−0.164064	+	0.986450i	$0.552460\pi$
$68$	−1.83221	−0.222188
$69$	−1.14637	−0.138006
$70$	−0.853635	−0.102029
$71$	−0.335577	−0.0398256	−0.0199128	−	0.999802i	$-0.506339\pi$
$71$	−0.335577	−0.0398256	−0.0199128	+	0.999802i	$0.506339\pi$
$72$	−1.68585	−0.198679
$73$	15.0361	1.75984	0.879922	−	0.475118i	$-0.157595\pi$
$73$	15.0361	1.75984	0.879922	+	0.475118i	$0.157595\pi$
$74$	5.66442	0.658476
$75$	−4.89648	−0.565397
$76$	−4.97858	−0.571082
$77$	−2.68585	−0.306081
$78$	5.37169	0.608224
$79$	−13.5640	−1.52607	−0.763037	−	0.646355i	$-0.776293\pi$
$79$	−13.5640	−1.52607	−0.763037	+	0.646355i	$0.776293\pi$
$80$	0.853635	0.0954392
$81$	−1.10038	−0.122265
$82$	11.9572	1.32045
$83$	5.31415	0.583304	0.291652	−	0.956524i	$-0.405795\pi$
$83$	5.31415	0.583304	0.291652	+	0.956524i	$0.405795\pi$
$84$	−1.14637	−0.125079
$85$	−1.56404	−0.169644
$86$	−9.37169	−1.01058
$87$	−7.32885	−0.785735
$88$	2.68585	0.286312
$89$	3.53948	0.375184	0.187592	−	0.982247i	$-0.439932\pi$
$89$	3.53948	0.375184	0.187592	+	0.982247i	$0.439932\pi$
$90$	−1.43910	−0.151694
$91$	−4.68585	−0.491210
$92$	−1.00000	−0.104257
$93$	4.39312	0.455545
$94$	−3.83221	−0.395262
$95$	−4.24989	−0.436029
$96$	1.14637	0.117000
$97$	2.75325	0.279550	0.139775	−	0.990183i	$-0.455362\pi$
$97$	2.75325	0.279550	0.139775	+	0.990183i	$0.455362\pi$
$98$	1.00000	0.101015
$99$	−4.52792	−0.455073
$100$	−4.27131	−0.427131
$101$	12.6858	1.26229	0.631144	−	0.775665i	$-0.282586\pi$
$101$	12.6858	1.26229	0.631144	+	0.775665i	$0.282586\pi$
$102$	−2.10038	−0.207969
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	4.68585	0.459485
$105$	−0.978577	−0.0954994
$106$	−9.66442	−0.938692
$107$	14.7434	1.42530	0.712648	−	0.701521i	$-0.247496\pi$
$107$	14.7434	1.42530	0.712648	+	0.701521i	$0.247496\pi$
$108$	−5.37169	−0.516891
$109$	7.95715	0.762157	0.381079	−	0.924543i	$-0.375553\pi$
$109$	7.95715	0.762157	0.381079	+	0.924543i	$0.375553\pi$
$110$	2.29273	0.218603
$111$	6.49350	0.616336
$112$	−1.00000	−0.0944911
$113$	7.70727	0.725039	0.362519	−	0.931976i	$-0.381917\pi$
$113$	7.70727	0.725039	0.362519	+	0.931976i	$0.381917\pi$
$114$	−5.70727	−0.534535
$115$	−0.853635	−0.0796018
$116$	−6.39312	−0.593586
$117$	−7.89962	−0.730320
$118$	3.43910	0.316594
$119$	1.83221	0.167959
$120$	0.978577	0.0893315
$121$	−3.78623	−0.344203
$122$	−10.2253	−0.925758
$123$	13.7073	1.23594
$124$	3.83221	0.344143
$125$	−7.91431	−0.707877
$126$	1.68585	0.150187
$127$	−10.2927	−0.913332	−0.456666	−	0.889638i	$-0.650957\pi$
$127$	−10.2927	−0.913332	−0.456666	+	0.889638i	$0.650957\pi$
$128$	1.00000	0.0883883
$129$	−10.7434	−0.945902
$130$	4.00000	0.350823
$131$	3.77467	0.329795	0.164897	−	0.986311i	$-0.447271\pi$
$131$	3.77467	0.329795	0.164897	+	0.986311i	$0.447271\pi$
$132$	3.07896	0.267989
$133$	4.97858	0.431697
$134$	−2.68585	−0.232022
$135$	−4.58546	−0.394654
$136$	−1.83221	−0.157111
$137$	19.6216	1.67638	0.838192	−	0.545375i	$-0.183613\pi$
$137$	19.6216	1.67638	0.838192	+	0.545375i	$0.183613\pi$
$138$	−1.14637	−0.0975851
$139$	12.2253	1.03694	0.518469	−	0.855096i	$-0.326502\pi$
$139$	12.2253	1.03694	0.518469	+	0.855096i	$0.326502\pi$
$140$	−0.853635	−0.0721453
$141$	−4.39312	−0.369967
$142$	−0.335577	−0.0281610
$143$	12.5855	1.05245
$144$	−1.68585	−0.140487
$145$	−5.45738	−0.453211
$146$	15.0361	1.24440
$147$	1.14637	0.0945506
$148$	5.66442	0.465613
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−4.89648	−0.399796
$151$	6.87819	0.559739	0.279870	−	0.960038i	$-0.409709\pi$
$151$	6.87819	0.559739	0.279870	+	0.960038i	$0.409709\pi$
$152$	−4.97858	−0.403816
$153$	3.08883	0.249717
$154$	−2.68585	−0.216432
$155$	3.27131	0.262758
$156$	5.37169	0.430080
$157$	8.85363	0.706597	0.353298	−	0.935511i	$-0.385060\pi$
$157$	8.85363	0.706597	0.353298	+	0.935511i	$0.385060\pi$
$158$	−13.5640	−1.07910
$159$	−11.0790	−0.878619
$160$	0.853635	0.0674857
$161$	1.00000	0.0788110
$162$	−1.10038	−0.0864543
$163$	−24.2499	−1.89940	−0.949699	−	0.313165i	$-0.898611\pi$
$163$	−24.2499	−1.89940	−0.949699	+	0.313165i	$0.898611\pi$
$164$	11.9572	0.933697
$165$	2.62831	0.204613
$166$	5.31415	0.412458
$167$	−4.16779	−0.322513	−0.161257	−	0.986913i	$-0.551555\pi$
$167$	−4.16779	−0.322513	−0.161257	+	0.986913i	$0.551555\pi$
$168$	−1.14637	−0.0884440
$169$	8.95715	0.689012
$170$	−1.56404	−0.119956
$171$	8.39312	0.641838
$172$	−9.37169	−0.714585
$173$	13.0214	0.990000	0.495000	−	0.868893i	$-0.335168\pi$
$173$	13.0214	0.990000	0.495000	+	0.868893i	$0.335168\pi$
$174$	−7.32885	−0.555598
$175$	4.27131	0.322881
$176$	2.68585	0.202453
$177$	3.94246	0.296334
$178$	3.53948	0.265295
$179$	12.7862	0.955688	0.477844	−	0.878445i	$-0.341418\pi$
$179$	12.7862	0.955688	0.477844	+	0.878445i	$0.341418\pi$
$180$	−1.43910	−0.107264
$181$	13.1035	0.973977	0.486988	−	0.873408i	$-0.338095\pi$
$181$	13.1035	0.973977	0.486988	+	0.873408i	$0.338095\pi$
$182$	−4.68585	−0.347338
$183$	−11.7220	−0.866512
$184$	−1.00000	−0.0737210
$185$	4.83535	0.355502
$186$	4.39312	0.322119
$187$	−4.92104	−0.359862
$188$	−3.83221	−0.279493
$189$	5.37169	0.390733
$190$	−4.24989	−0.308319
$191$	−19.9143	−1.44095	−0.720474	−	0.693482i	$-0.756076\pi$
$191$	−19.9143	−1.44095	−0.720474	+	0.693482i	$0.756076\pi$
$192$	1.14637	0.0827318
$193$	13.4145	0.965600	0.482800	−	0.875731i	$-0.339620\pi$
$193$	13.4145	0.965600	0.482800	+	0.875731i	$0.339620\pi$
$194$	2.75325	0.197672
$195$	4.58546	0.328372
$196$	1.00000	0.0714286
$197$	10.5855	0.754183	0.377091	−	0.926176i	$-0.376924\pi$
$197$	10.5855	0.754183	0.377091	+	0.926176i	$0.376924\pi$
$198$	−4.52792	−0.321786
$199$	−3.41454	−0.242050	−0.121025	−	0.992649i	$-0.538618\pi$
$199$	−3.41454	−0.242050	−0.121025	+	0.992649i	$0.538618\pi$
$200$	−4.27131	−0.302027
$201$	−3.07896	−0.217173
$202$	12.6858	0.892573
$203$	6.39312	0.448709
$204$	−2.10038	−0.147056
$205$	10.2070	0.712891
$206$	−8.00000	−0.557386
$207$	1.68585	0.117174
$208$	4.68585	0.324905
$209$	−13.3717	−0.924939
$210$	−0.978577	−0.0675282
$211$	2.04285	0.140635	0.0703176	−	0.997525i	$-0.477599\pi$
$211$	2.04285	0.140635	0.0703176	+	0.997525i	$0.477599\pi$
$212$	−9.66442	−0.663755
$213$	−0.384694	−0.0263588
$214$	14.7434	1.00784
$215$	−8.00000	−0.545595
$216$	−5.37169	−0.365497
$217$	−3.83221	−0.260147
$218$	7.95715	0.538926
$219$	17.2369	1.16476
$220$	2.29273	0.154576
$221$	−8.58546	−0.577521
$222$	6.49350	0.435815
$223$	6.91117	0.462806	0.231403	−	0.972858i	$-0.425668\pi$
$223$	6.91117	0.462806	0.231403	+	0.972858i	$0.425668\pi$
$224$	−1.00000	−0.0668153
$225$	7.20077	0.480051
$226$	7.70727	0.512680
$227$	1.56404	0.103809	0.0519045	−	0.998652i	$-0.483471\pi$
$227$	1.56404	0.103809	0.0519045	+	0.998652i	$0.483471\pi$
$228$	−5.70727	−0.377973
$229$	−6.81079	−0.450070	−0.225035	−	0.974351i	$-0.572250\pi$
$229$	−6.81079	−0.450070	−0.225035	+	0.974351i	$0.572250\pi$
$230$	−0.853635	−0.0562870
$231$	−3.07896	−0.202581
$232$	−6.39312	−0.419729
$233$	22.0575	1.44504	0.722519	−	0.691351i	$-0.242984\pi$
$233$	22.0575	1.44504	0.722519	+	0.691351i	$0.242984\pi$
$234$	−7.89962	−0.516414
$235$	−3.27131	−0.213397
$236$	3.43910	0.223866
$237$	−15.5493	−1.01004
$238$	1.83221	0.118765
$239$	−16.4507	−1.06410	−0.532052	−	0.846712i	$-0.678579\pi$
$239$	−16.4507	−1.06410	−0.532052	+	0.846712i	$0.678579\pi$
$240$	0.978577	0.0631669
$241$	−28.5756	−1.84072	−0.920358	−	0.391077i	$-0.872103\pi$
$241$	−28.5756	−1.84072	−0.920358	+	0.391077i	$0.872103\pi$
$242$	−3.78623	−0.243388
$243$	14.8536	0.952861
$244$	−10.2253	−0.654609
$245$	0.853635	0.0545367
$246$	13.7073	0.873944
$247$	−23.3288	−1.48438
$248$	3.83221	0.243346
$249$	6.09196	0.386062
$250$	−7.91431	−0.500545
$251$	−3.80765	−0.240337	−0.120168	−	0.992754i	$-0.538343\pi$
$251$	−3.80765	−0.240337	−0.120168	+	0.992754i	$0.538343\pi$
$252$	1.68585	0.106198
$253$	−2.68585	−0.168858
$254$	−10.2927	−0.645823
$255$	−1.79296	−0.112280
$256$	1.00000	0.0625000
$257$	10.7862	0.672827	0.336413	−	0.941714i	$-0.390786\pi$
$257$	10.7862	0.672827	0.336413	+	0.941714i	$0.390786\pi$
$258$	−10.7434	−0.668854
$259$	−5.66442	−0.351970
$260$	4.00000	0.248069
$261$	10.7778	0.667130
$262$	3.77467	0.233200
$263$	21.5640	1.32970	0.664848	−	0.746979i	$-0.268496\pi$
$263$	21.5640	1.32970	0.664848	+	0.746979i	$0.268496\pi$
$264$	3.07896	0.189497
$265$	−8.24989	−0.506786
$266$	4.97858	0.305256
$267$	4.05754	0.248317
$268$	−2.68585	−0.164064
$269$	19.1793	1.16939	0.584693	−	0.811255i	$-0.301215\pi$
$269$	19.1793	1.16939	0.584693	+	0.811255i	$0.301215\pi$
$270$	−4.58546	−0.279062
$271$	−12.1678	−0.739141	−0.369570	−	0.929203i	$-0.620495\pi$
$271$	−12.1678	−0.739141	−0.369570	+	0.929203i	$0.620495\pi$
$272$	−1.83221	−0.111094
$273$	−5.37169	−0.325110
$274$	19.6216	1.18538
$275$	−11.4721	−0.691792
$276$	−1.14637	−0.0690031
$277$	−7.56404	−0.454479	−0.227240	−	0.973839i	$-0.572970\pi$
$277$	−7.56404	−0.454479	−0.227240	+	0.973839i	$0.572970\pi$
$278$	12.2253	0.733226
$279$	−6.46052	−0.386781
$280$	−0.853635	−0.0510144
$281$	13.0790	0.780225	0.390113	−	0.920767i	$-0.372436\pi$
$281$	13.0790	0.780225	0.390113	+	0.920767i	$0.372436\pi$
$282$	−4.39312	−0.261606
$283$	−28.3074	−1.68270	−0.841351	−	0.540489i	$-0.818239\pi$
$283$	−28.3074	−1.68270	−0.841351	+	0.540489i	$0.818239\pi$
$284$	−0.335577	−0.0199128
$285$	−4.87192	−0.288588
$286$	12.5855	0.744194
$287$	−11.9572	−0.705809
$288$	−1.68585	−0.0993394
$289$	−13.6430	−0.802529
$290$	−5.45738	−0.320469
$291$	3.15623	0.185022
$292$	15.0361	0.879922
$293$	0.853635	0.0498699	0.0249349	−	0.999689i	$-0.492062\pi$
$293$	0.853635	0.0498699	0.0249349	+	0.999689i	$0.492062\pi$
$294$	1.14637	0.0668574
$295$	2.93573	0.170925
$296$	5.66442	0.329238
$297$	−14.4275	−0.837171
$298$	−2.00000	−0.115857
$299$	−4.68585	−0.270989
$300$	−4.89648	−0.282698
$301$	9.37169	0.540175
$302$	6.87819	0.395796
$303$	14.5426	0.835451
$304$	−4.97858	−0.285541
$305$	−8.72869	−0.499803
$306$	3.08883	0.176576
$307$	−9.14637	−0.522011	−0.261005	−	0.965337i	$-0.584054\pi$
$307$	−9.14637	−0.522011	−0.261005	+	0.965337i	$0.584054\pi$
$308$	−2.68585	−0.153040
$309$	−9.17092	−0.521716
$310$	3.27131	0.185798
$311$	−5.00314	−0.283702	−0.141851	−	0.989888i	$-0.545305\pi$
$311$	−5.00314	−0.283702	−0.141851	+	0.989888i	$0.545305\pi$
$312$	5.37169	0.304112
$313$	−25.8322	−1.46012	−0.730061	−	0.683381i	$-0.760509\pi$
$313$	−25.8322	−1.46012	−0.730061	+	0.683381i	$0.760509\pi$
$314$	8.85363	0.499640
$315$	1.43910	0.0810839
$316$	−13.5640	−0.763037
$317$	−17.1365	−0.962482	−0.481241	−	0.876588i	$-0.659814\pi$
$317$	−17.1365	−0.962482	−0.481241	+	0.876588i	$0.659814\pi$
$318$	−11.0790	−0.621277
$319$	−17.1709	−0.961387
$320$	0.853635	0.0477196
$321$	16.9013	0.943339
$322$	1.00000	0.0557278
$323$	9.12181	0.507551
$324$	−1.10038	−0.0611325
$325$	−20.0147	−1.11022
$326$	−24.2499	−1.34308
$327$	9.12181	0.504437
$328$	11.9572	0.660223
$329$	3.83221	0.211277
$330$	2.62831	0.144684
$331$	27.7795	1.52690	0.763450	−	0.645867i	$-0.223504\pi$
$331$	27.7795	1.52690	0.763450	+	0.645867i	$0.223504\pi$
$332$	5.31415	0.291652
$333$	−9.54935	−0.523301
$334$	−4.16779	−0.228051
$335$	−2.29273	−0.125265
$336$	−1.14637	−0.0625394
$337$	3.95715	0.215560	0.107780	−	0.994175i	$-0.465626\pi$
$337$	3.95715	0.215560	0.107780	+	0.994175i	$0.465626\pi$
$338$	8.95715	0.487205
$339$	8.83535	0.479870
$340$	−1.56404	−0.0848219
$341$	10.2927	0.557383
$342$	8.39312	0.453848
$343$	−1.00000	−0.0539949
$344$	−9.37169	−0.505288
$345$	−0.978577	−0.0526848
$346$	13.0214	0.700036
$347$	−20.8353	−1.11850	−0.559250	−	0.828999i	$-0.688911\pi$
$347$	−20.8353	−1.11850	−0.559250	+	0.828999i	$0.688911\pi$
$348$	−7.32885	−0.392867
$349$	−20.5510	−1.10007	−0.550036	−	0.835141i	$-0.685386\pi$
$349$	−20.5510	−1.10007	−0.550036	+	0.835141i	$0.685386\pi$
$350$	4.27131	0.228311
$351$	−25.1709	−1.34352
$352$	2.68585	0.143156
$353$	−32.4078	−1.72489	−0.862447	−	0.506148i	$-0.831069\pi$
$353$	−32.4078	−1.72489	−0.862447	+	0.506148i	$0.831069\pi$
$354$	3.94246	0.209539
$355$	−0.286460	−0.0152037
$356$	3.53948	0.187592
$357$	2.10038	0.111164
$358$	12.7862	0.675773
$359$	−14.3503	−0.757378	−0.378689	−	0.925524i	$-0.623625\pi$
$359$	−14.3503	−0.757378	−0.378689	+	0.925524i	$0.623625\pi$
$360$	−1.43910	−0.0758470
$361$	5.78623	0.304538
$362$	13.1035	0.688706
$363$	−4.34040	−0.227812
$364$	−4.68585	−0.245605
$365$	12.8353	0.671833
$366$	−11.7220	−0.612717
$367$	5.03612	0.262883	0.131442	−	0.991324i	$-0.458039\pi$
$367$	5.03612	0.262883	0.131442	+	0.991324i	$0.458039\pi$
$368$	−1.00000	−0.0521286
$369$	−20.1579	−1.04938
$370$	4.83535	0.251378
$371$	9.66442	0.501752
$372$	4.39312	0.227772
$373$	24.7434	1.28116	0.640582	−	0.767890i	$-0.278693\pi$
$373$	24.7434	1.28116	0.640582	+	0.767890i	$0.278693\pi$
$374$	−4.92104	−0.254461
$375$	−9.07269	−0.468512
$376$	−3.83221	−0.197631
$377$	−29.9572	−1.54287
$378$	5.37169	0.276290
$379$	−8.72869	−0.448363	−0.224181	−	0.974547i	$-0.571971\pi$
$379$	−8.72869	−0.448363	−0.224181	+	0.974547i	$0.571971\pi$
$380$	−4.24989	−0.218015
$381$	−11.7992	−0.604493
$382$	−19.9143	−1.01890
$383$	29.8223	1.52385	0.761925	−	0.647665i	$-0.224254\pi$
$383$	29.8223	1.52385	0.761925	+	0.647665i	$0.224254\pi$
$384$	1.14637	0.0585002
$385$	−2.29273	−0.116848
$386$	13.4145	0.682782
$387$	15.7992	0.803120
$388$	2.75325	0.139775
$389$	−26.7862	−1.35812	−0.679058	−	0.734085i	$-0.737611\pi$
$389$	−26.7862	−1.35812	−0.679058	+	0.734085i	$0.737611\pi$
$390$	4.58546	0.232194
$391$	1.83221	0.0926589
$392$	1.00000	0.0505076
$393$	4.32716	0.218276
$394$	10.5855	0.533288
$395$	−11.5787	−0.582589
$396$	−4.52792	−0.227537
$397$	−31.2285	−1.56731	−0.783656	−	0.621195i	$-0.786647\pi$
$397$	−31.2285	−1.56731	−0.783656	+	0.621195i	$0.786647\pi$
$398$	−3.41454	−0.171155
$399$	5.70727	0.285721
$400$	−4.27131	−0.213565
$401$	14.7005	0.734110	0.367055	−	0.930199i	$-0.380366\pi$
$401$	14.7005	0.734110	0.367055	+	0.930199i	$0.380366\pi$
$402$	−3.07896	−0.153565
$403$	17.9572	0.894510
$404$	12.6858	0.631144
$405$	−0.939326	−0.0466755
$406$	6.39312	0.317285
$407$	15.2138	0.754119
$408$	−2.10038	−0.103985
$409$	17.6644	0.873450	0.436725	−	0.899595i	$-0.356138\pi$
$409$	17.6644	0.873450	0.436725	+	0.899595i	$0.356138\pi$
$410$	10.2070	0.504090
$411$	22.4935	1.10952
$412$	−8.00000	−0.394132
$413$	−3.43910	−0.169227
$414$	1.68585	0.0828548
$415$	4.53635	0.222680
$416$	4.68585	0.229743
$417$	14.0147	0.686302
$418$	−13.3717	−0.654031
$419$	19.1365	0.934879	0.467440	−	0.884025i	$-0.345177\pi$
$419$	19.1365	0.934879	0.467440	+	0.884025i	$0.345177\pi$
$420$	−0.978577	−0.0477497
$421$	−14.2499	−0.694497	−0.347248	−	0.937773i	$-0.612884\pi$
$421$	−14.2499	−0.694497	−0.347248	+	0.937773i	$0.612884\pi$
$422$	2.04285	0.0994442
$423$	6.46052	0.314121
$424$	−9.66442	−0.469346
$425$	7.82594	0.379614
$426$	−0.384694	−0.0186385
$427$	10.2253	0.494838
$428$	14.7434	0.712648
$429$	14.4275	0.696568
$430$	−8.00000	−0.385794
$431$	−6.82908	−0.328945	−0.164473	−	0.986382i	$-0.552592\pi$
$431$	−6.82908	−0.328945	−0.164473	+	0.986382i	$0.552592\pi$
$432$	−5.37169	−0.258446
$433$	−17.1611	−0.824708	−0.412354	−	0.911024i	$-0.635293\pi$
$433$	−17.1611	−0.824708	−0.412354	+	0.911024i	$0.635293\pi$
$434$	−3.83221	−0.183952
$435$	−6.25616	−0.299960
$436$	7.95715	0.381079
$437$	4.97858	0.238158
$438$	17.2369	0.823610
$439$	−21.0031	−1.00242	−0.501212	−	0.865324i	$-0.667112\pi$
$439$	−21.0031	−1.00242	−0.501212	+	0.865324i	$0.667112\pi$
$440$	2.29273	0.109302
$441$	−1.68585	−0.0802784
$442$	−8.58546	−0.408369
$443$	18.5426	0.880986	0.440493	−	0.897756i	$-0.354804\pi$
$443$	18.5426	0.880986	0.440493	+	0.897756i	$0.354804\pi$
$444$	6.49350	0.308168
$445$	3.02142	0.143229
$446$	6.91117	0.327254
$447$	−2.29273	−0.108442
$448$	−1.00000	−0.0472456
$449$	−21.4721	−1.01333	−0.506665	−	0.862143i	$-0.669122\pi$
$449$	−21.4721	−1.01333	−0.506665	+	0.862143i	$0.669122\pi$
$450$	7.20077	0.339447
$451$	32.1151	1.51224
$452$	7.70727	0.362519
$453$	7.88492	0.370466
$454$	1.56404	0.0734040
$455$	−4.00000	−0.187523
$456$	−5.70727	−0.267267
$457$	6.92104	0.323753	0.161876	−	0.986811i	$-0.448245\pi$
$457$	6.92104	0.323753	0.161876	+	0.986811i	$0.448245\pi$
$458$	−6.81079	−0.318247
$459$	9.84208	0.459389
$460$	−0.853635	−0.0398009
$461$	−7.17935	−0.334375	−0.167188	−	0.985925i	$-0.553469\pi$
$461$	−7.17935	−0.334375	−0.167188	+	0.985925i	$0.553469\pi$
$462$	−3.07896	−0.143246
$463$	24.4998	1.13860	0.569300	−	0.822130i	$-0.307214\pi$
$463$	24.4998	1.13860	0.569300	+	0.822130i	$0.307214\pi$
$464$	−6.39312	−0.296793
$465$	3.75011	0.173907
$466$	22.0575	1.02180
$467$	12.9786	0.600577	0.300288	−	0.953848i	$-0.402917\pi$
$467$	12.9786	0.600577	0.300288	+	0.953848i	$0.402917\pi$
$468$	−7.89962	−0.365160
$469$	2.68585	0.124021
$470$	−3.27131	−0.150894
$471$	10.1495	0.467664
$472$	3.43910	0.158297
$473$	−25.1709	−1.15736
$474$	−15.5493	−0.714205
$475$	21.2650	0.975707
$476$	1.83221	0.0839793
$477$	16.2927	0.745993
$478$	−16.4507	−0.752435
$479$	4.20077	0.191938	0.0959690	−	0.995384i	$-0.469405\pi$
$479$	4.20077	0.191938	0.0959690	+	0.995384i	$0.469405\pi$
$480$	0.978577	0.0446657
$481$	26.5426	1.21024
$482$	−28.5756	−1.30158
$483$	1.14637	0.0521614
$484$	−3.78623	−0.172101
$485$	2.35027	0.106720
$486$	14.8536	0.673775
$487$	32.4998	1.47271	0.736353	−	0.676598i	$-0.236546\pi$
$487$	32.4998	1.47271	0.736353	+	0.676598i	$0.236546\pi$
$488$	−10.2253	−0.462879
$489$	−27.7992	−1.25712
$490$	0.853635	0.0385633
$491$	−28.4998	−1.28618	−0.643088	−	0.765792i	$-0.722347\pi$
$491$	−28.4998	−1.28618	−0.643088	+	0.765792i	$0.722347\pi$
$492$	13.7073	0.617971
$493$	11.7135	0.527551
$494$	−23.3288	−1.04961
$495$	−3.86519	−0.173727
$496$	3.83221	0.172071
$497$	0.335577	0.0150527
$498$	6.09196	0.272987
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	−7.91431	−0.353939
$501$	−4.77781	−0.213457
$502$	−3.80765	−0.169944
$503$	14.5426	0.648423	0.324212	−	0.945985i	$-0.394901\pi$
$503$	14.5426	0.648423	0.324212	+	0.945985i	$0.394901\pi$
$504$	1.68585	0.0750936
$505$	10.8291	0.481888
$506$	−2.68585	−0.119400
$507$	10.2682	0.456026
$508$	−10.2927	−0.456666
$509$	−9.52119	−0.422019	−0.211010	−	0.977484i	$-0.567675\pi$
$509$	−9.52119	−0.422019	−0.211010	+	0.977484i	$0.567675\pi$
$510$	−1.79296	−0.0793936
$511$	−15.0361	−0.665159
$512$	1.00000	0.0441942
$513$	26.7434	1.18075
$514$	10.7862	0.475760
$515$	−6.82908	−0.300925
$516$	−10.7434	−0.472951
$517$	−10.2927	−0.452674
$518$	−5.66442	−0.248880
$519$	14.9273	0.655236
$520$	4.00000	0.175412
$521$	−19.0031	−0.832542	−0.416271	−	0.909240i	$-0.636663\pi$
$521$	−19.0031	−0.832542	−0.416271	+	0.909240i	$0.636663\pi$
$522$	10.7778	0.471732
$523$	−1.56404	−0.0683907	−0.0341953	−	0.999415i	$-0.510887\pi$
$523$	−1.56404	−0.0683907	−0.0341953	+	0.999415i	$0.510887\pi$
$524$	3.77467	0.164897
$525$	4.89648	0.213700
$526$	21.5640	0.940237
$527$	−7.02142	−0.305858
$528$	3.07896	0.133995
$529$	1.00000	0.0434783
$530$	−8.24989	−0.358352
$531$	−5.79779	−0.251603
$532$	4.97858	0.215849
$533$	56.0294	2.42690
$534$	4.05754	0.175587
$535$	12.5855	0.544117
$536$	−2.68585	−0.116011
$537$	14.6577	0.632526
$538$	19.1793	0.826880
$539$	2.68585	0.115688
$540$	−4.58546	−0.197327
$541$	−17.1365	−0.736756	−0.368378	−	0.929676i	$-0.620087\pi$
$541$	−17.1365	−0.736756	−0.368378	+	0.929676i	$0.620087\pi$
$542$	−12.1678	−0.522651
$543$	15.0214	0.644631
$544$	−1.83221	−0.0785554
$545$	6.79250	0.290959
$546$	−5.37169	−0.229887
$547$	31.5787	1.35021	0.675105	−	0.737722i	$-0.264099\pi$
$547$	31.5787	1.35021	0.675105	+	0.737722i	$0.264099\pi$
$548$	19.6216	0.838192
$549$	17.2383	0.735714
$550$	−11.4721	−0.489171
$551$	31.8286	1.35594
$552$	−1.14637	−0.0487926
$553$	13.5640	0.576802
$554$	−7.56404	−0.321365
$555$	5.54308	0.235290
$556$	12.2253	0.518469
$557$	−45.2432	−1.91701	−0.958507	−	0.285069i	$-0.907983\pi$
$557$	−45.2432	−1.91701	−0.958507	+	0.285069i	$0.907983\pi$
$558$	−6.46052	−0.273496
$559$	−43.9143	−1.85738
$560$	−0.853635	−0.0360726
$561$	−5.64131	−0.238176
$562$	13.0790	0.551703
$563$	25.6791	1.08225	0.541123	−	0.840944i	$-0.317999\pi$
$563$	25.6791	1.08225	0.541123	+	0.840944i	$0.317999\pi$
$564$	−4.39312	−0.184984
$565$	6.57919	0.276789
$566$	−28.3074	−1.18985
$567$	1.10038	0.0462118
$568$	−0.335577	−0.0140805
$569$	31.4868	1.31999	0.659997	−	0.751268i	$-0.270558\pi$
$569$	31.4868	1.31999	0.659997	+	0.751268i	$0.270558\pi$
$570$	−4.87192	−0.204062
$571$	11.2138	0.469282	0.234641	−	0.972082i	$-0.424609\pi$
$571$	11.2138	0.469282	0.234641	+	0.972082i	$0.424609\pi$
$572$	12.5855	0.526225
$573$	−22.8291	−0.953698
$574$	−11.9572	−0.499082
$575$	4.27131	0.178126
$576$	−1.68585	−0.0702436
$577$	0.878193	0.0365597	0.0182798	−	0.999833i	$-0.494181\pi$
$577$	0.878193	0.0365597	0.0182798	+	0.999833i	$0.494181\pi$
$578$	−13.6430	−0.567474
$579$	15.3780	0.639086
$580$	−5.45738	−0.226606
$581$	−5.31415	−0.220468
$582$	3.15623	0.130830
$583$	−25.9572	−1.07504
$584$	15.0361	0.622199
$585$	−6.74338	−0.278805
$586$	0.853635	0.0352633
$587$	−12.2744	−0.506621	−0.253310	−	0.967385i	$-0.581519\pi$
$587$	−12.2744	−0.506621	−0.253310	+	0.967385i	$0.581519\pi$
$588$	1.14637	0.0472753
$589$	−19.0790	−0.786135
$590$	2.93573	0.120862
$591$	12.1348	0.499159
$592$	5.66442	0.232806
$593$	15.3717	0.631240	0.315620	−	0.948886i	$-0.397788\pi$
$593$	15.3717	0.631240	0.315620	+	0.948886i	$0.397788\pi$
$594$	−14.4275	−0.591969
$595$	1.56404	0.0641194
$596$	−2.00000	−0.0819232
$597$	−3.91431	−0.160202
$598$	−4.68585	−0.191618
$599$	−23.7135	−0.968909	−0.484454	−	0.874816i	$-0.660982\pi$
$599$	−23.7135	−0.968909	−0.484454	+	0.874816i	$0.660982\pi$
$600$	−4.89648	−0.199898
$601$	−22.4507	−0.915781	−0.457891	−	0.889009i	$-0.651395\pi$
$601$	−22.4507	−0.915781	−0.457891	+	0.889009i	$0.651395\pi$
$602$	9.37169	0.381962
$603$	4.52792	0.184391
$604$	6.87819	0.279870
$605$	−3.23206	−0.131402
$606$	14.5426	0.590753
$607$	−36.4471	−1.47934	−0.739670	−	0.672969i	$-0.765019\pi$
$607$	−36.4471	−1.47934	−0.739670	+	0.672969i	$0.765019\pi$
$608$	−4.97858	−0.201908
$609$	7.32885	0.296980
$610$	−8.72869	−0.353414
$611$	−17.9572	−0.726469
$612$	3.08883	0.124858
$613$	26.7005	1.07842	0.539212	−	0.842170i	$-0.318722\pi$
$613$	26.7005	1.07842	0.539212	+	0.842170i	$0.318722\pi$
$614$	−9.14637	−0.369117
$615$	11.7010	0.471830
$616$	−2.68585	−0.108216
$617$	−7.57246	−0.304856	−0.152428	−	0.988315i	$-0.548709\pi$
$617$	−7.57246	−0.304856	−0.152428	+	0.988315i	$0.548709\pi$
$618$	−9.17092	−0.368909
$619$	−40.5573	−1.63014	−0.815068	−	0.579365i	$-0.803300\pi$
$619$	−40.5573	−1.63014	−0.815068	+	0.579365i	$0.803300\pi$
$620$	3.27131	0.131379
$621$	5.37169	0.215559
$622$	−5.00314	−0.200607
$623$	−3.53948	−0.141806
$624$	5.37169	0.215040
$625$	14.6006	0.584025
$626$	−25.8322	−1.03246
$627$	−15.3288	−0.612175
$628$	8.85363	0.353298
$629$	−10.3784	−0.413815
$630$	1.43910	0.0573350
$631$	−39.1365	−1.55800	−0.779000	−	0.627024i	$-0.784273\pi$
$631$	−39.1365	−1.55800	−0.779000	+	0.627024i	$0.784273\pi$
$632$	−13.5640	−0.539549
$633$	2.34185	0.0930801
$634$	−17.1365	−0.680577
$635$	−8.78623	−0.348671
$636$	−11.0790	−0.439309
$637$	4.68585	0.185660
$638$	−17.1709	−0.679803
$639$	0.565731	0.0223800
$640$	0.853635	0.0337429
$641$	−49.9143	−1.97150	−0.985748	−	0.168227i	$-0.946196\pi$
$641$	−49.9143	−1.97150	−0.985748	+	0.168227i	$0.946196\pi$
$642$	16.9013	0.667041
$643$	40.3931	1.59295	0.796474	−	0.604672i	$-0.206696\pi$
$643$	40.3931	1.59295	0.796474	+	0.604672i	$0.206696\pi$
$644$	1.00000	0.0394055
$645$	−9.17092	−0.361105
$646$	9.12181	0.358893
$647$	21.0031	0.825718	0.412859	−	0.910795i	$-0.364530\pi$
$647$	21.0031	0.825718	0.412859	+	0.910795i	$0.364530\pi$
$648$	−1.10038	−0.0432272
$649$	9.23688	0.362579
$650$	−20.0147	−0.785041
$651$	−4.39312	−0.172180
$652$	−24.2499	−0.949699
$653$	−46.7005	−1.82753	−0.913767	−	0.406239i	$-0.866840\pi$
$653$	−46.7005	−1.82753	−0.913767	+	0.406239i	$0.866840\pi$
$654$	9.12181	0.356691
$655$	3.22219	0.125901
$656$	11.9572	0.466848
$657$	−25.3486	−0.988942
$658$	3.83221	0.149395
$659$	−30.4569	−1.18643	−0.593217	−	0.805043i	$-0.702142\pi$
$659$	−30.4569	−1.18643	−0.593217	+	0.805043i	$0.702142\pi$
$660$	2.62831	0.102307
$661$	−6.81079	−0.264909	−0.132454	−	0.991189i	$-0.542286\pi$
$661$	−6.81079	−0.264909	−0.132454	+	0.991189i	$0.542286\pi$
$662$	27.7795	1.07968
$663$	−9.84208	−0.382235
$664$	5.31415	0.206229
$665$	4.24989	0.164803
$666$	−9.54935	−0.370030
$667$	6.39312	0.247542
$668$	−4.16779	−0.161257
$669$	7.92273	0.306310
$670$	−2.29273	−0.0885759
$671$	−27.4637	−1.06022
$672$	−1.14637	−0.0442220
$673$	7.89962	0.304508	0.152254	−	0.988341i	$-0.451347\pi$
$673$	7.89962	0.304508	0.152254	+	0.988341i	$0.451347\pi$
$674$	3.95715	0.152424
$675$	22.9442	0.883121
$676$	8.95715	0.344506
$677$	11.8175	0.454184	0.227092	−	0.973873i	$-0.427078\pi$
$677$	11.8175	0.454184	0.227092	+	0.973873i	$0.427078\pi$
$678$	8.83535	0.339319
$679$	−2.75325	−0.105660
$680$	−1.56404	−0.0599782
$681$	1.79296	0.0687064
$682$	10.2927	0.394129
$683$	−17.3717	−0.664709	−0.332355	−	0.943154i	$-0.607843\pi$
$683$	−17.3717	−0.664709	−0.332355	+	0.943154i	$0.607843\pi$
$684$	8.39312	0.320919
$685$	16.7497	0.639971
$686$	−1.00000	−0.0381802
$687$	−7.80765	−0.297881
$688$	−9.37169	−0.357292
$689$	−45.2860	−1.72526
$690$	−0.978577	−0.0372538
$691$	48.9259	1.86123	0.930614	−	0.366003i	$-0.119274\pi$
$691$	48.9259	1.86123	0.930614	+	0.366003i	$0.119274\pi$
$692$	13.0214	0.495000
$693$	4.52792	0.172002
$694$	−20.8353	−0.790899
$695$	10.4360	0.395859
$696$	−7.32885	−0.277799
$697$	−21.9080	−0.829826
$698$	−20.5510	−0.777868
$699$	25.2860	0.956404
$700$	4.27131	0.161440
$701$	−13.0790	−0.493986	−0.246993	−	0.969017i	$-0.579442\pi$
$701$	−13.0790	−0.493986	−0.246993	+	0.969017i	$0.579442\pi$
$702$	−25.1709	−0.950015
$703$	−28.2008	−1.06361
$704$	2.68585	0.101227
$705$	−3.75011	−0.141237
$706$	−32.4078	−1.21968
$707$	−12.6858	−0.477100
$708$	3.94246	0.148167
$709$	35.0361	1.31581	0.657904	−	0.753101i	$-0.271443\pi$
$709$	35.0361	1.31581	0.657904	+	0.753101i	$0.271443\pi$
$710$	−0.286460	−0.0107506
$711$	22.8669	0.857575
$712$	3.53948	0.132648
$713$	−3.83221	−0.143517
$714$	2.10038	0.0786049
$715$	10.7434	0.401780
$716$	12.7862	0.477844
$717$	−18.8585	−0.704282
$718$	−14.3503	−0.535547
$719$	−42.8255	−1.59712	−0.798560	−	0.601915i	$-0.794405\pi$
$719$	−42.8255	−1.59712	−0.798560	+	0.601915i	$0.794405\pi$
$720$	−1.43910	−0.0536320
$721$	8.00000	0.297936
$722$	5.78623	0.215341
$723$	−32.7581	−1.21829
$724$	13.1035	0.486988
$725$	27.3070	1.01416
$726$	−4.34040	−0.161087
$727$	3.79923	0.140906	0.0704528	−	0.997515i	$-0.477556\pi$
$727$	3.79923	0.140906	0.0704528	+	0.997515i	$0.477556\pi$
$728$	−4.68585	−0.173669
$729$	20.3288	0.752920
$730$	12.8353	0.475058
$731$	17.1709	0.635090
$732$	−11.7220	−0.433256
$733$	31.0116	1.14544	0.572719	−	0.819752i	$-0.305889\pi$
$733$	31.0116	1.14544	0.572719	+	0.819752i	$0.305889\pi$
$734$	5.03612	0.185886
$735$	0.978577	0.0360954
$736$	−1.00000	−0.0368605
$737$	−7.21377	−0.265723
$738$	−20.1579	−0.742023
$739$	11.2797	0.414932	0.207466	−	0.978242i	$-0.433478\pi$
$739$	11.2797	0.414932	0.207466	+	0.978242i	$0.433478\pi$
$740$	4.83535	0.177751
$741$	−26.7434	−0.982443
$742$	9.66442	0.354792
$743$	41.0937	1.50758	0.753790	−	0.657115i	$-0.228224\pi$
$743$	41.0937	1.50758	0.753790	+	0.657115i	$0.228224\pi$
$744$	4.39312	0.161059
$745$	−1.70727	−0.0625495
$746$	24.7434	0.905920
$747$	−8.95885	−0.327787
$748$	−4.92104	−0.179931
$749$	−14.7434	−0.538712
$750$	−9.07269	−0.331288
$751$	4.39312	0.160307	0.0801535	−	0.996783i	$-0.474459\pi$
$751$	4.39312	0.160307	0.0801535	+	0.996783i	$0.474459\pi$
$752$	−3.83221	−0.139746
$753$	−4.36496	−0.159068
$754$	−29.9572	−1.09098
$755$	5.87146	0.213684
$756$	5.37169	0.195367
$757$	3.25662	0.118364	0.0591818	−	0.998247i	$-0.481151\pi$
$757$	3.25662	0.118364	0.0591818	+	0.998247i	$0.481151\pi$
$758$	−8.72869	−0.317040
$759$	−3.07896	−0.111759
$760$	−4.24989	−0.154160
$761$	−28.3221	−1.02668	−0.513338	−	0.858187i	$-0.671591\pi$
$761$	−28.3221	−1.02668	−0.513338	+	0.858187i	$0.671591\pi$
$762$	−11.7992	−0.427441
$763$	−7.95715	−0.288068
$764$	−19.9143	−0.720474
$765$	2.63673	0.0953311
$766$	29.8223	1.07753
$767$	16.1151	0.581882
$768$	1.14637	0.0413659
$769$	35.6546	1.28574	0.642868	−	0.765977i	$-0.277744\pi$
$769$	35.6546	1.28574	0.642868	+	0.765977i	$0.277744\pi$
$770$	−2.29273	−0.0826243
$771$	12.3650	0.445313
$772$	13.4145	0.482800
$773$	2.81079	0.101097	0.0505485	−	0.998722i	$-0.483903\pi$
$773$	2.81079	0.101097	0.0505485	+	0.998722i	$0.483903\pi$
$774$	15.7992	0.567892
$775$	−16.3686	−0.587976
$776$	2.75325	0.0988359
$777$	−6.49350	−0.232953
$778$	−26.7862	−0.960333
$779$	−59.5296	−2.13287
$780$	4.58546	0.164186
$781$	−0.901307	−0.0322513
$782$	1.83221	0.0655198
$783$	34.3418	1.22728
$784$	1.00000	0.0357143
$785$	7.55777	0.269748
$786$	4.32716	0.154345
$787$	36.6430	1.30618	0.653091	−	0.757279i	$-0.273472\pi$
$787$	36.6430	1.30618	0.653091	+	0.757279i	$0.273472\pi$
$788$	10.5855	0.377091
$789$	24.7203	0.880065
$790$	−11.5787	−0.411953
$791$	−7.70727	−0.274039
$792$	−4.52792	−0.160893
$793$	−47.9143	−1.70149
$794$	−31.2285	−1.10826
$795$	−9.45738	−0.335419
$796$	−3.41454	−0.121025
$797$	−10.8965	−0.385973	−0.192987	−	0.981201i	$-0.561817\pi$
$797$	−10.8965	−0.385973	−0.192987	+	0.981201i	$0.561817\pi$
$798$	5.70727	0.202035
$799$	7.02142	0.248400
$800$	−4.27131	−0.151014
$801$	−5.96702	−0.210834
$802$	14.7005	0.519094
$803$	40.3847	1.42514
$804$	−3.07896	−0.108587
$805$	0.853635	0.0300867
$806$	17.9572	0.632514
$807$	21.9865	0.773963
$808$	12.6858	0.446287
$809$	−10.5855	−0.372165	−0.186083	−	0.982534i	$-0.559579\pi$
$809$	−10.5855	−0.372165	−0.186083	+	0.982534i	$0.559579\pi$
$810$	−0.939326	−0.0330045
$811$	27.1035	0.951733	0.475867	−	0.879517i	$-0.342134\pi$
$811$	27.1035	0.951733	0.475867	+	0.879517i	$0.342134\pi$
$812$	6.39312	0.224354
$813$	−13.9487	−0.489203
$814$	15.2138	0.533242
$815$	−20.7005	−0.725108
$816$	−2.10038	−0.0735282
$817$	46.6577	1.63235
$818$	17.6644	0.617622
$819$	7.89962	0.276035
$820$	10.2070	0.356445
$821$	12.7350	0.444453	0.222227	−	0.974995i	$-0.428668\pi$
$821$	12.7350	0.444453	0.222227	+	0.974995i	$0.428668\pi$
$822$	22.4935	0.784551
$823$	−55.1083	−1.92096	−0.960478	−	0.278356i	$-0.910211\pi$
$823$	−55.1083	−1.92096	−0.960478	+	0.278356i	$0.910211\pi$
$824$	−8.00000	−0.278693
$825$	−13.1512	−0.457866
$826$	−3.43910	−0.119661
$827$	36.9013	1.28318	0.641592	−	0.767046i	$-0.278274\pi$
$827$	36.9013	1.28318	0.641592	+	0.767046i	$0.278274\pi$
$828$	1.68585	0.0585872
$829$	26.1067	0.906722	0.453361	−	0.891327i	$-0.350225\pi$
$829$	26.1067	0.906722	0.453361	+	0.891327i	$0.350225\pi$
$830$	4.53635	0.157459
$831$	−8.67115	−0.300799
$832$	4.68585	0.162452
$833$	−1.83221	−0.0634824
$834$	14.0147	0.485289
$835$	−3.55777	−0.123122
$836$	−13.3717	−0.462470
$837$	−20.5855	−0.711538
$838$	19.1365	0.661059
$839$	25.1218	0.867301	0.433651	−	0.901081i	$-0.357225\pi$
$839$	25.1218	0.867301	0.433651	+	0.901081i	$0.357225\pi$
$840$	−0.978577	−0.0337641
$841$	11.8719	0.409377
$842$	−14.2499	−0.491083
$843$	14.9933	0.516396
$844$	2.04285	0.0703176
$845$	7.64614	0.263035
$846$	6.46052	0.222117
$847$	3.78623	0.130096
$848$	−9.66442	−0.331878
$849$	−32.4507	−1.11370
$850$	7.82594	0.268428
$851$	−5.66442	−0.194174
$852$	−0.384694	−0.0131794
$853$	52.1298	1.78489	0.892445	−	0.451157i	$-0.148989\pi$
$853$	52.1298	1.78489	0.892445	+	0.451157i	$0.148989\pi$
$854$	10.2253	0.349903
$855$	7.16465	0.245026
$856$	14.7434	0.503919
$857$	7.75639	0.264953	0.132477	−	0.991186i	$-0.457707\pi$
$857$	7.75639	0.264953	0.132477	+	0.991186i	$0.457707\pi$
$858$	14.4275	0.492548
$859$	−44.2744	−1.51062	−0.755312	−	0.655365i	$-0.772515\pi$
$859$	−44.2744	−1.51062	−0.755312	+	0.655365i	$0.772515\pi$
$860$	−8.00000	−0.272798
$861$	−13.7073	−0.467142
$862$	−6.82908	−0.232599
$863$	−7.66442	−0.260900	−0.130450	−	0.991455i	$-0.541642\pi$
$863$	−7.66442	−0.260900	−0.130450	+	0.991455i	$0.541642\pi$
$864$	−5.37169	−0.182749
$865$	11.1155	0.377940
$866$	−17.1611	−0.583156
$867$	−15.6399	−0.531158
$868$	−3.83221	−0.130074
$869$	−36.4309	−1.23583
$870$	−6.25616	−0.212104
$871$	−12.5855	−0.426442
$872$	7.95715	0.269463
$873$	−4.64156	−0.157093
$874$	4.97858	0.168403
$875$	7.91431	0.267552
$876$	17.2369	0.582380
$877$	24.9357	0.842020	0.421010	−	0.907056i	$-0.361676\pi$
$877$	24.9357	0.842020	0.421010	+	0.907056i	$0.361676\pi$
$878$	−21.0031	−0.708821
$879$	0.978577	0.0330066
$880$	2.29273	0.0772879
$881$	−22.1972	−0.747842	−0.373921	−	0.927461i	$-0.621987\pi$
$881$	−22.1972	−0.747842	−0.373921	+	0.927461i	$0.621987\pi$
$882$	−1.68585	−0.0567654
$883$	−24.7005	−0.831239	−0.415620	−	0.909539i	$-0.636435\pi$
$883$	−24.7005	−0.831239	−0.415620	+	0.909539i	$0.636435\pi$
$884$	−8.58546	−0.288760
$885$	3.36542	0.113127
$886$	18.5426	0.622951
$887$	24.3686	0.818216	0.409108	−	0.912486i	$-0.365840\pi$
$887$	24.3686	0.818216	0.409108	+	0.912486i	$0.365840\pi$
$888$	6.49350	0.217908
$889$	10.2927	0.345207
$890$	3.02142	0.101278
$891$	−2.95546	−0.0990117
$892$	6.91117	0.231403
$893$	19.0790	0.638453
$894$	−2.29273	−0.0766804
$895$	10.9148	0.364840
$896$	−1.00000	−0.0334077
$897$	−5.37169	−0.179356
$898$	−21.4721	−0.716532
$899$	−24.4998	−0.817113
$900$	7.20077	0.240026
$901$	17.7073	0.589915
$902$	32.1151	1.06932
$903$	10.7434	0.357517
$904$	7.70727	0.256340
$905$	11.1856	0.371822
$906$	7.88492	0.261959
$907$	37.6707	1.25083	0.625417	−	0.780290i	$-0.284929\pi$
$907$	37.6707	1.25083	0.625417	+	0.780290i	$0.284929\pi$
$908$	1.56404	0.0519045
$909$	−21.3864	−0.709342
$910$	−4.00000	−0.132599
$911$	−6.73496	−0.223139	−0.111570	−	0.993757i	$-0.535588\pi$
$911$	−6.73496	−0.223139	−0.111570	+	0.993757i	$0.535588\pi$
$912$	−5.70727	−0.188987
$913$	14.2730	0.472367
$914$	6.92104	0.228928
$915$	−10.0063	−0.330797
$916$	−6.81079	−0.225035
$917$	−3.77467	−0.124651
$918$	9.84208	0.324837
$919$	4.89289	0.161401	0.0807007	−	0.996738i	$-0.474284\pi$
$919$	4.89289	0.161401	0.0807007	+	0.996738i	$0.474284\pi$
$920$	−0.853635	−0.0281435
$921$	−10.4851	−0.345495
$922$	−7.17935	−0.236439
$923$	−1.57246	−0.0517582
$924$	−3.07896	−0.101290
$925$	−24.1945	−0.795510
$926$	24.4998	0.805112
$927$	13.4868	0.442964
$928$	−6.39312	−0.209864
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	3.75011	0.122971
$931$	−4.97858	−0.163166
$932$	22.0575	0.722519
$933$	−5.73542	−0.187769
$934$	12.9786	0.424672
$935$	−4.20077	−0.137380
$936$	−7.89962	−0.258207
$937$	21.0460	0.687542	0.343771	−	0.939053i	$-0.388296\pi$
$937$	21.0460	0.687542	0.343771	+	0.939053i	$0.388296\pi$
$938$	2.68585	0.0876960
$939$	−29.6132	−0.966389
$940$	−3.27131	−0.106698
$941$	13.8898	0.452793	0.226396	−	0.974035i	$-0.427306\pi$
$941$	13.8898	0.452793	0.226396	+	0.974035i	$0.427306\pi$
$942$	10.1495	0.330689
$943$	−11.9572	−0.389379
$944$	3.43910	0.111933
$945$	4.58546	0.149165
$946$	−25.1709	−0.818377
$947$	13.6216	0.442642	0.221321	−	0.975201i	$-0.428963\pi$
$947$	13.6216	0.442642	0.221321	+	0.975201i	$0.428963\pi$
$948$	−15.5493	−0.505019
$949$	70.4569	2.28713
$950$	21.2650	0.689929
$951$	−19.6447	−0.637023
$952$	1.83221	0.0593823
$953$	39.3717	1.27537	0.637687	−	0.770295i	$-0.279891\pi$
$953$	39.3717	1.27537	0.637687	+	0.770295i	$0.279891\pi$
$954$	16.2927	0.527497
$955$	−16.9995	−0.550092
$956$	−16.4507	−0.532052
$957$	−19.6842	−0.636298
$958$	4.20077	0.135721
$959$	−19.6216	−0.633614
$960$	0.978577	0.0315834
$961$	−16.3142	−0.526263
$962$	26.5426	0.855768
$963$	−24.8551	−0.800944
$964$	−28.5756	−0.920358
$965$	11.4511	0.368624
$966$	1.14637	0.0368837
$967$	15.2138	0.489242	0.244621	−	0.969619i	$-0.421336\pi$
$967$	15.2138	0.489242	0.244621	+	0.969619i	$0.421336\pi$
$968$	−3.78623	−0.121694
$969$	10.4569	0.335925
$970$	2.35027	0.0754626
$971$	26.3994	0.847197	0.423598	−	0.905850i	$-0.360767\pi$
$971$	26.3994	0.847197	0.423598	+	0.905850i	$0.360767\pi$
$972$	14.8536	0.476431
$973$	−12.2253	−0.391926
$974$	32.4998	1.04136
$975$	−22.9442	−0.734801
$976$	−10.2253	−0.327305
$977$	−32.4078	−1.03682	−0.518409	−	0.855133i	$-0.673475\pi$
$977$	−32.4078	−1.03682	−0.518409	+	0.855133i	$0.673475\pi$
$978$	−27.7992	−0.888921
$979$	9.50650	0.303829
$980$	0.853635	0.0272684
$981$	−13.4145	−0.428293
$982$	−28.4998	−0.909464
$983$	−27.4637	−0.875955	−0.437977	−	0.898986i	$-0.644305\pi$
$983$	−27.4637	−0.875955	−0.437977	+	0.898986i	$0.644305\pi$
$984$	13.7073	0.436972
$985$	9.03612	0.287915
$986$	11.7135	0.373035
$987$	4.39312	0.139834
$988$	−23.3288	−0.742189
$989$	9.37169	0.298002
$990$	−3.86519	−0.122844
$991$	−51.9803	−1.65121	−0.825604	−	0.564250i	$-0.809165\pi$
$991$	−51.9803	−1.65121	−0.825604	+	0.564250i	$0.809165\pi$
$992$	3.83221	0.121673
$993$	31.8455	1.01059
$994$	0.335577	0.0106438
$995$	−2.91477	−0.0924043
$996$	6.09196	0.193031
$997$	−14.8929	−0.471662	−0.235831	−	0.971794i	$-0.575781\pi$
$997$	−14.8929	−0.471662	−0.235831	+	0.971794i	$0.575781\pi$
$998$	4.00000	0.126618
$999$	−30.4275	−0.962685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.a.g.1.2	✓	3
3.2	odd	2		2898.2.a.be.1.2		3
4.3	odd	2		2576.2.a.w.1.2		3
5.4	even	2		8050.2.a.bh.1.2		3
7.6	odd	2		2254.2.a.p.1.2		3
23.22	odd	2		7406.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.a.g.1.2	✓	3	1.1	even	1	trivial
2254.2.a.p.1.2		3	7.6	odd	2
2576.2.a.w.1.2		3	4.3	odd	2
2898.2.a.be.1.2		3	3.2	odd	2
7406.2.a.x.1.2		3	23.22	odd	2
8050.2.a.bh.1.2		3	5.4	even	2

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +0.853635 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +0.853635 q^{5} +1.14637 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +0.853635 q^{10} +2.68585 q^{11} +1.14637 q^{12} +4.68585 q^{13} -1.00000 q^{14} +0.978577 q^{15} +1.00000 q^{16} -1.83221 q^{17} -1.68585 q^{18} -4.97858 q^{19} +0.853635 q^{20} -1.14637 q^{21} +2.68585 q^{22} -1.00000 q^{23} +1.14637 q^{24} -4.27131 q^{25} +4.68585 q^{26} -5.37169 q^{27} -1.00000 q^{28} -6.39312 q^{29} +0.978577 q^{30} +3.83221 q^{31} +1.00000 q^{32} +3.07896 q^{33} -1.83221 q^{34} -0.853635 q^{35} -1.68585 q^{36} +5.66442 q^{37} -4.97858 q^{38} +5.37169 q^{39} +0.853635 q^{40} +11.9572 q^{41} -1.14637 q^{42} -9.37169 q^{43} +2.68585 q^{44} -1.43910 q^{45} -1.00000 q^{46} -3.83221 q^{47} +1.14637 q^{48} +1.00000 q^{49} -4.27131 q^{50} -2.10038 q^{51} +4.68585 q^{52} -9.66442 q^{53} -5.37169 q^{54} +2.29273 q^{55} -1.00000 q^{56} -5.70727 q^{57} -6.39312 q^{58} +3.43910 q^{59} +0.978577 q^{60} -10.2253 q^{61} +3.83221 q^{62} +1.68585 q^{63} +1.00000 q^{64} +4.00000 q^{65} +3.07896 q^{66} -2.68585 q^{67} -1.83221 q^{68} -1.14637 q^{69} -0.853635 q^{70} -0.335577 q^{71} -1.68585 q^{72} +15.0361 q^{73} +5.66442 q^{74} -4.89648 q^{75} -4.97858 q^{76} -2.68585 q^{77} +5.37169 q^{78} -13.5640 q^{79} +0.853635 q^{80} -1.10038 q^{81} +11.9572 q^{82} +5.31415 q^{83} -1.14637 q^{84} -1.56404 q^{85} -9.37169 q^{86} -7.32885 q^{87} +2.68585 q^{88} +3.53948 q^{89} -1.43910 q^{90} -4.68585 q^{91} -1.00000 q^{92} +4.39312 q^{93} -3.83221 q^{94} -4.24989 q^{95} +1.14637 q^{96} +2.75325 q^{97} +1.00000 q^{98} -4.52792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * q^99

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