LMFDB - Embedded newform 8034.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} + \cdots + 576 $ x^11 - 5x^10 - 31x^9 + 168x^8 + 300x^7 - 1928x^6 - 736x^5 + 8532x^4 - 2065x^3 - 10494x^2 + 4024x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.11723$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.11723 q^{5} +1.00000 q^{6} -0.395748 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.11723 q^{5} +1.00000 q^{6} -0.395748 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.11723 q^{10} -4.45504 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.395748 q^{14} -3.11723 q^{15} +1.00000 q^{16} -3.51577 q^{17} +1.00000 q^{18} -1.39575 q^{19} -3.11723 q^{20} -0.395748 q^{21} -4.45504 q^{22} +8.68105 q^{23} +1.00000 q^{24} +4.71715 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.395748 q^{28} +4.66037 q^{29} -3.11723 q^{30} +1.39575 q^{31} +1.00000 q^{32} -4.45504 q^{33} -3.51577 q^{34} +1.23364 q^{35} +1.00000 q^{36} -7.36973 q^{37} -1.39575 q^{38} +1.00000 q^{39} -3.11723 q^{40} -9.79488 q^{41} -0.395748 q^{42} +2.61985 q^{43} -4.45504 q^{44} -3.11723 q^{45} +8.68105 q^{46} +7.31044 q^{47} +1.00000 q^{48} -6.84338 q^{49} +4.71715 q^{50} -3.51577 q^{51} +1.00000 q^{52} +8.42466 q^{53} +1.00000 q^{54} +13.8874 q^{55} -0.395748 q^{56} -1.39575 q^{57} +4.66037 q^{58} +10.7201 q^{59} -3.11723 q^{60} -5.89487 q^{61} +1.39575 q^{62} -0.395748 q^{63} +1.00000 q^{64} -3.11723 q^{65} -4.45504 q^{66} +6.69566 q^{67} -3.51577 q^{68} +8.68105 q^{69} +1.23364 q^{70} +9.60739 q^{71} +1.00000 q^{72} -4.96846 q^{73} -7.36973 q^{74} +4.71715 q^{75} -1.39575 q^{76} +1.76307 q^{77} +1.00000 q^{78} +5.73789 q^{79} -3.11723 q^{80} +1.00000 q^{81} -9.79488 q^{82} +6.11228 q^{83} -0.395748 q^{84} +10.9595 q^{85} +2.61985 q^{86} +4.66037 q^{87} -4.45504 q^{88} -16.4938 q^{89} -3.11723 q^{90} -0.395748 q^{91} +8.68105 q^{92} +1.39575 q^{93} +7.31044 q^{94} +4.35087 q^{95} +1.00000 q^{96} -9.52005 q^{97} -6.84338 q^{98} -4.45504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.11723	−1.39407	−0.697035	−	0.717037i	$-0.745498\pi$
$5$	−3.11723	−1.39407	−0.697035	+	0.717037i	$0.745498\pi$
$6$	1.00000	0.408248
$7$	−0.395748	−0.149579	−0.0747893	−	0.997199i	$-0.523828\pi$
$7$	−0.395748	−0.149579	−0.0747893	+	0.997199i	$0.523828\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.11723	−0.985756
$11$	−4.45504	−1.34325	−0.671623	−	0.740893i	$-0.734402\pi$
$11$	−4.45504	−1.34325	−0.671623	+	0.740893i	$0.734402\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.395748	−0.105768
$15$	−3.11723	−0.804866
$16$	1.00000	0.250000
$17$	−3.51577	−0.852699	−0.426349	−	0.904559i	$-0.640201\pi$
$17$	−3.51577	−0.852699	−0.426349	+	0.904559i	$0.640201\pi$
$18$	1.00000	0.235702
$19$	−1.39575	−0.320207	−0.160103	−	0.987100i	$-0.551183\pi$
$19$	−1.39575	−0.320207	−0.160103	+	0.987100i	$0.551183\pi$
$20$	−3.11723	−0.697035
$21$	−0.395748	−0.0863593
$22$	−4.45504	−0.949818
$23$	8.68105	1.81012	0.905062	−	0.425279i	$-0.139824\pi$
$23$	8.68105	1.81012	0.905062	+	0.425279i	$0.139824\pi$
$24$	1.00000	0.204124
$25$	4.71715	0.943430
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−0.395748	−0.0747893
$29$	4.66037	0.865409	0.432705	−	0.901536i	$-0.357559\pi$
$29$	4.66037	0.865409	0.432705	+	0.901536i	$0.357559\pi$
$30$	−3.11723	−0.569126
$31$	1.39575	0.250684	0.125342	−	0.992114i	$-0.459997\pi$
$31$	1.39575	0.250684	0.125342	+	0.992114i	$0.459997\pi$
$32$	1.00000	0.176777
$33$	−4.45504	−0.775523
$34$	−3.51577	−0.602949
$35$	1.23364	0.208523
$36$	1.00000	0.166667
$37$	−7.36973	−1.21158	−0.605788	−	0.795626i	$-0.707142\pi$
$37$	−7.36973	−1.21158	−0.605788	+	0.795626i	$0.707142\pi$
$38$	−1.39575	−0.226420
$39$	1.00000	0.160128
$40$	−3.11723	−0.492878
$41$	−9.79488	−1.52970	−0.764851	−	0.644207i	$-0.777188\pi$
$41$	−9.79488	−1.52970	−0.764851	+	0.644207i	$0.777188\pi$
$42$	−0.395748	−0.0610652
$43$	2.61985	0.399523	0.199761	−	0.979845i	$-0.435983\pi$
$43$	2.61985	0.399523	0.199761	+	0.979845i	$0.435983\pi$
$44$	−4.45504	−0.671623
$45$	−3.11723	−0.464690
$46$	8.68105	1.27995
$47$	7.31044	1.06634	0.533169	−	0.846009i	$-0.321001\pi$
$47$	7.31044	1.06634	0.533169	+	0.846009i	$0.321001\pi$
$48$	1.00000	0.144338
$49$	−6.84338	−0.977626
$50$	4.71715	0.667105
$51$	−3.51577	−0.492306
$52$	1.00000	0.138675
$53$	8.42466	1.15722	0.578608	−	0.815606i	$-0.303596\pi$
$53$	8.42466	1.15722	0.578608	+	0.815606i	$0.303596\pi$
$54$	1.00000	0.136083
$55$	13.8874	1.87258
$56$	−0.395748	−0.0528840
$57$	−1.39575	−0.184871
$58$	4.66037	0.611937
$59$	10.7201	1.39564	0.697819	−	0.716274i	$-0.254154\pi$
$59$	10.7201	1.39564	0.697819	+	0.716274i	$0.254154\pi$
$60$	−3.11723	−0.402433
$61$	−5.89487	−0.754761	−0.377381	−	0.926058i	$-0.623175\pi$
$61$	−5.89487	−0.754761	−0.377381	+	0.926058i	$0.623175\pi$
$62$	1.39575	0.177260
$63$	−0.395748	−0.0498596
$64$	1.00000	0.125000
$65$	−3.11723	−0.386645
$66$	−4.45504	−0.548378
$67$	6.69566	0.818005	0.409002	−	0.912533i	$-0.365877\pi$
$67$	6.69566	0.818005	0.409002	+	0.912533i	$0.365877\pi$
$68$	−3.51577	−0.426349
$69$	8.68105	1.04508
$70$	1.23364	0.147448
$71$	9.60739	1.14019	0.570093	−	0.821580i	$-0.306907\pi$
$71$	9.60739	1.14019	0.570093	+	0.821580i	$0.306907\pi$
$72$	1.00000	0.117851
$73$	−4.96846	−0.581514	−0.290757	−	0.956797i	$-0.593907\pi$
$73$	−4.96846	−0.581514	−0.290757	+	0.956797i	$0.593907\pi$
$74$	−7.36973	−0.856714
$75$	4.71715	0.544689
$76$	−1.39575	−0.160103
$77$	1.76307	0.200921
$78$	1.00000	0.113228
$79$	5.73789	0.645564	0.322782	−	0.946473i	$-0.395382\pi$
$79$	5.73789	0.645564	0.322782	+	0.946473i	$0.395382\pi$
$80$	−3.11723	−0.348517
$81$	1.00000	0.111111
$82$	−9.79488	−1.08166
$83$	6.11228	0.670910	0.335455	−	0.942056i	$-0.391110\pi$
$83$	6.11228	0.670910	0.335455	+	0.942056i	$0.391110\pi$
$84$	−0.395748	−0.0431796
$85$	10.9595	1.18872
$86$	2.61985	0.282505
$87$	4.66037	0.499644
$88$	−4.45504	−0.474909
$89$	−16.4938	−1.74834	−0.874170	−	0.485620i	$-0.838594\pi$
$89$	−16.4938	−1.74834	−0.874170	+	0.485620i	$0.838594\pi$
$90$	−3.11723	−0.328585
$91$	−0.395748	−0.0414857
$92$	8.68105	0.905062
$93$	1.39575	0.144732
$94$	7.31044	0.754014
$95$	4.35087	0.446390
$96$	1.00000	0.102062
$97$	−9.52005	−0.966615	−0.483307	−	0.875451i	$-0.660565\pi$
$97$	−9.52005	−0.966615	−0.483307	+	0.875451i	$0.660565\pi$
$98$	−6.84338	−0.691286
$99$	−4.45504	−0.447749
$100$	4.71715	0.471715
$101$	10.9949	1.09404	0.547019	−	0.837120i	$-0.315762\pi$
$101$	10.9949	1.09404	0.547019	+	0.837120i	$0.315762\pi$
$102$	−3.51577	−0.348113
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	1.23364	0.120391
$106$	8.42466	0.818276
$107$	0.878878	0.0849643	0.0424822	−	0.999097i	$-0.486473\pi$
$107$	0.878878	0.0849643	0.0424822	+	0.999097i	$0.486473\pi$
$108$	1.00000	0.0962250
$109$	7.53530	0.721750	0.360875	−	0.932614i	$-0.382478\pi$
$109$	7.53530	0.721750	0.360875	+	0.932614i	$0.382478\pi$
$110$	13.8874	1.32411
$111$	−7.36973	−0.699504
$112$	−0.395748	−0.0373947
$113$	11.4332	1.07554	0.537770	−	0.843091i	$-0.319267\pi$
$113$	11.4332	1.07554	0.537770	+	0.843091i	$0.319267\pi$
$114$	−1.39575	−0.130724
$115$	−27.0609	−2.52344
$116$	4.66037	0.432705
$117$	1.00000	0.0924500
$118$	10.7201	0.986865
$119$	1.39136	0.127546
$120$	−3.11723	−0.284563
$121$	8.84740	0.804309
$122$	−5.89487	−0.533697
$123$	−9.79488	−0.883174
$124$	1.39575	0.125342
$125$	0.881715	0.0788630
$126$	−0.395748	−0.0352560
$127$	13.2490	1.17566	0.587831	−	0.808984i	$-0.299982\pi$
$127$	13.2490	1.17566	0.587831	+	0.808984i	$0.299982\pi$
$128$	1.00000	0.0883883
$129$	2.61985	0.230665
$130$	−3.11723	−0.273400
$131$	6.27830	0.548538	0.274269	−	0.961653i	$-0.411564\pi$
$131$	6.27830	0.548538	0.274269	+	0.961653i	$0.411564\pi$
$132$	−4.45504	−0.387762
$133$	0.552364	0.0478961
$134$	6.69566	0.578417
$135$	−3.11723	−0.268289
$136$	−3.51577	−0.301475
$137$	15.3825	1.31422	0.657109	−	0.753796i	$-0.271779\pi$
$137$	15.3825	1.31422	0.657109	+	0.753796i	$0.271779\pi$
$138$	8.68105	0.738980
$139$	13.3140	1.12928	0.564638	−	0.825339i	$-0.309016\pi$
$139$	13.3140	1.12928	0.564638	+	0.825339i	$0.309016\pi$
$140$	1.23364	0.104262
$141$	7.31044	0.615650
$142$	9.60739	0.806234
$143$	−4.45504	−0.372549
$144$	1.00000	0.0833333
$145$	−14.5275	−1.20644
$146$	−4.96846	−0.411193
$147$	−6.84338	−0.564433
$148$	−7.36973	−0.605788
$149$	18.5004	1.51562	0.757808	−	0.652478i	$-0.226270\pi$
$149$	18.5004	1.51562	0.757808	+	0.652478i	$0.226270\pi$
$150$	4.71715	0.385154
$151$	−12.5281	−1.01952	−0.509761	−	0.860316i	$-0.670266\pi$
$151$	−12.5281	−1.01952	−0.509761	+	0.860316i	$0.670266\pi$
$152$	−1.39575	−0.113210
$153$	−3.51577	−0.284233
$154$	1.76307	0.142073
$155$	−4.35087	−0.349471
$156$	1.00000	0.0800641
$157$	−15.5588	−1.24173	−0.620864	−	0.783918i	$-0.713218\pi$
$157$	−15.5588	−1.24173	−0.620864	+	0.783918i	$0.713218\pi$
$158$	5.73789	0.456482
$159$	8.42466	0.668119
$160$	−3.11723	−0.246439
$161$	−3.43551	−0.270756
$162$	1.00000	0.0785674
$163$	12.1473	0.951448	0.475724	−	0.879595i	$-0.342186\pi$
$163$	12.1473	0.951448	0.475724	+	0.879595i	$0.342186\pi$
$164$	−9.79488	−0.764851
$165$	13.8874	1.08113
$166$	6.11228	0.474405
$167$	25.2285	1.95224	0.976120	−	0.217234i	$-0.0697035\pi$
$167$	25.2285	1.95224	0.976120	+	0.217234i	$0.0697035\pi$
$168$	−0.395748	−0.0305326
$169$	1.00000	0.0769231
$170$	10.9595	0.840553
$171$	−1.39575	−0.106736
$172$	2.61985	0.199761
$173$	−10.5109	−0.799130	−0.399565	−	0.916705i	$-0.630839\pi$
$173$	−10.5109	−0.799130	−0.399565	+	0.916705i	$0.630839\pi$
$174$	4.66037	0.353302
$175$	−1.86680	−0.141117
$176$	−4.45504	−0.335811
$177$	10.7201	0.805772
$178$	−16.4938	−1.23626
$179$	18.7115	1.39856	0.699282	−	0.714846i	$-0.253503\pi$
$179$	18.7115	1.39856	0.699282	+	0.714846i	$0.253503\pi$
$180$	−3.11723	−0.232345
$181$	−23.4971	−1.74653	−0.873263	−	0.487250i	$-0.838000\pi$
$181$	−23.4971	−1.74653	−0.873263	+	0.487250i	$0.838000\pi$
$182$	−0.395748	−0.0293348
$183$	−5.89487	−0.435762
$184$	8.68105	0.639976
$185$	22.9732	1.68902
$186$	1.39575	0.102341
$187$	15.6629	1.14538
$188$	7.31044	0.533169
$189$	−0.395748	−0.0287864
$190$	4.35087	0.315645
$191$	16.0310	1.15996	0.579981	−	0.814630i	$-0.303060\pi$
$191$	16.0310	1.15996	0.579981	+	0.814630i	$0.303060\pi$
$192$	1.00000	0.0721688
$193$	9.29200	0.668853	0.334426	−	0.942422i	$-0.391457\pi$
$193$	9.29200	0.668853	0.334426	+	0.942422i	$0.391457\pi$
$194$	−9.52005	−0.683500
$195$	−3.11723	−0.223230
$196$	−6.84338	−0.488813
$197$	19.7417	1.40654	0.703268	−	0.710925i	$-0.251723\pi$
$197$	19.7417	1.40654	0.703268	+	0.710925i	$0.251723\pi$
$198$	−4.45504	−0.316606
$199$	21.8668	1.55010	0.775048	−	0.631902i	$-0.217726\pi$
$199$	21.8668	1.55010	0.775048	+	0.631902i	$0.217726\pi$
$200$	4.71715	0.333553
$201$	6.69566	0.472275
$202$	10.9949	0.773602
$203$	−1.84433	−0.129447
$204$	−3.51577	−0.246153
$205$	30.5329	2.13251
$206$	−1.00000	−0.0696733
$207$	8.68105	0.603375
$208$	1.00000	0.0693375
$209$	6.21812	0.430116
$210$	1.23364	0.0851292
$211$	−2.80006	−0.192764	−0.0963820	−	0.995344i	$-0.530727\pi$
$211$	−2.80006	−0.192764	−0.0963820	+	0.995344i	$0.530727\pi$
$212$	8.42466	0.578608
$213$	9.60739	0.658287
$214$	0.878878	0.0600788
$215$	−8.16667	−0.556963
$216$	1.00000	0.0680414
$217$	−0.552364	−0.0374969
$218$	7.53530	0.510355
$219$	−4.96846	−0.335737
$220$	13.8874	0.936289
$221$	−3.51577	−0.236496
$222$	−7.36973	−0.494624
$223$	−9.79868	−0.656168	−0.328084	−	0.944649i	$-0.606403\pi$
$223$	−9.79868	−0.656168	−0.328084	+	0.944649i	$0.606403\pi$
$224$	−0.395748	−0.0264420
$225$	4.71715	0.314477
$226$	11.4332	0.760522
$227$	−16.9937	−1.12791	−0.563957	−	0.825804i	$-0.690722\pi$
$227$	−16.9937	−1.12791	−0.563957	+	0.825804i	$0.690722\pi$
$228$	−1.39575	−0.0924357
$229$	−10.5732	−0.698696	−0.349348	−	0.936993i	$-0.613597\pi$
$229$	−10.5732	−0.698696	−0.349348	+	0.936993i	$0.613597\pi$
$230$	−27.0609	−1.78434
$231$	1.76307	0.116002
$232$	4.66037	0.305968
$233$	14.6303	0.958464	0.479232	−	0.877688i	$-0.340915\pi$
$233$	14.6303	0.958464	0.479232	+	0.877688i	$0.340915\pi$
$234$	1.00000	0.0653720
$235$	−22.7883	−1.48655
$236$	10.7201	0.697819
$237$	5.73789	0.372716
$238$	1.39136	0.0901883
$239$	−11.6152	−0.751326	−0.375663	−	0.926756i	$-0.622585\pi$
$239$	−11.6152	−0.751326	−0.375663	+	0.926756i	$0.622585\pi$
$240$	−3.11723	−0.201217
$241$	7.91036	0.509551	0.254776	−	0.967000i	$-0.417998\pi$
$241$	7.91036	0.509551	0.254776	+	0.967000i	$0.417998\pi$
$242$	8.84740	0.568733
$243$	1.00000	0.0641500
$244$	−5.89487	−0.377381
$245$	21.3324	1.36288
$246$	−9.79488	−0.624499
$247$	−1.39575	−0.0888093
$248$	1.39575	0.0886301
$249$	6.11228	0.387350
$250$	0.881715	0.0557646
$251$	−16.5536	−1.04485	−0.522426	−	0.852685i	$-0.674973\pi$
$251$	−16.5536	−1.04485	−0.522426	+	0.852685i	$0.674973\pi$
$252$	−0.395748	−0.0249298
$253$	−38.6745	−2.43144
$254$	13.2490	0.831319
$255$	10.9595	0.686308
$256$	1.00000	0.0625000
$257$	5.06257	0.315794	0.157897	−	0.987456i	$-0.449529\pi$
$257$	5.06257	0.315794	0.157897	+	0.987456i	$0.449529\pi$
$258$	2.61985	0.163105
$259$	2.91656	0.181226
$260$	−3.11723	−0.193323
$261$	4.66037	0.288470
$262$	6.27830	0.387875
$263$	−14.7597	−0.910120	−0.455060	−	0.890461i	$-0.650382\pi$
$263$	−14.7597	−0.910120	−0.455060	+	0.890461i	$0.650382\pi$
$264$	−4.45504	−0.274189
$265$	−26.2617	−1.61324
$266$	0.552364	0.0338676
$267$	−16.4938	−1.00940
$268$	6.69566	0.409002
$269$	19.1024	1.16470	0.582348	−	0.812939i	$-0.302134\pi$
$269$	19.1024	1.16470	0.582348	+	0.812939i	$0.302134\pi$
$270$	−3.11723	−0.189709
$271$	11.1338	0.676332	0.338166	−	0.941087i	$-0.390193\pi$
$271$	11.1338	0.676332	0.338166	+	0.941087i	$0.390193\pi$
$272$	−3.51577	−0.213175
$273$	−0.395748	−0.0239518
$274$	15.3825	0.929292
$275$	−21.0151	−1.26726
$276$	8.68105	0.522538
$277$	5.74958	0.345459	0.172730	−	0.984969i	$-0.444741\pi$
$277$	5.74958	0.345459	0.172730	+	0.984969i	$0.444741\pi$
$278$	13.3140	0.798518
$279$	1.39575	0.0835612
$280$	1.23364	0.0737240
$281$	−26.2332	−1.56494	−0.782472	−	0.622686i	$-0.786041\pi$
$281$	−26.2332	−1.56494	−0.782472	+	0.622686i	$0.786041\pi$
$282$	7.31044	0.435330
$283$	7.49114	0.445302	0.222651	−	0.974898i	$-0.428529\pi$
$283$	7.49114	0.445302	0.222651	+	0.974898i	$0.428529\pi$
$284$	9.60739	0.570093
$285$	4.35087	0.257723
$286$	−4.45504	−0.263432
$287$	3.87630	0.228811
$288$	1.00000	0.0589256
$289$	−4.63938	−0.272905
$290$	−14.5275	−0.853082
$291$	−9.52005	−0.558075
$292$	−4.96846	−0.290757
$293$	−3.16441	−0.184867	−0.0924334	−	0.995719i	$-0.529465\pi$
$293$	−3.16441	−0.184867	−0.0924334	+	0.995719i	$0.529465\pi$
$294$	−6.84338	−0.399114
$295$	−33.4170	−1.94562
$296$	−7.36973	−0.428357
$297$	−4.45504	−0.258508
$298$	18.5004	1.07170
$299$	8.68105	0.502038
$300$	4.71715	0.272345
$301$	−1.03680	−0.0597601
$302$	−12.5281	−0.720911
$303$	10.9949	0.631643
$304$	−1.39575	−0.0800516
$305$	18.3757	1.05219
$306$	−3.51577	−0.200983
$307$	−32.7128	−1.86702	−0.933510	−	0.358552i	$-0.883271\pi$
$307$	−32.7128	−1.86702	−0.933510	+	0.358552i	$0.883271\pi$
$308$	1.76307	0.100460
$309$	−1.00000	−0.0568880
$310$	−4.35087	−0.247113
$311$	−27.4036	−1.55391	−0.776957	−	0.629553i	$-0.783238\pi$
$311$	−27.4036	−1.55391	−0.776957	+	0.629553i	$0.783238\pi$
$312$	1.00000	0.0566139
$313$	13.5077	0.763500	0.381750	−	0.924266i	$-0.375321\pi$
$313$	13.5077	0.763500	0.381750	+	0.924266i	$0.375321\pi$
$314$	−15.5588	−0.878034
$315$	1.23364	0.0695077
$316$	5.73789	0.322782
$317$	26.0026	1.46045	0.730226	−	0.683205i	$-0.239415\pi$
$317$	26.0026	1.46045	0.730226	+	0.683205i	$0.239415\pi$
$318$	8.42466	0.472432
$319$	−20.7621	−1.16246
$320$	−3.11723	−0.174259
$321$	0.878878	0.0490542
$322$	−3.43551	−0.191453
$323$	4.90712	0.273040
$324$	1.00000	0.0555556
$325$	4.71715	0.261660
$326$	12.1473	0.672776
$327$	7.53530	0.416703
$328$	−9.79488	−0.540832
$329$	−2.89309	−0.159501
$330$	13.8874	0.764477
$331$	−12.2672	−0.674266	−0.337133	−	0.941457i	$-0.609457\pi$
$331$	−12.2672	−0.674266	−0.337133	+	0.941457i	$0.609457\pi$
$332$	6.11228	0.335455
$333$	−7.36973	−0.403859
$334$	25.2285	1.38044
$335$	−20.8719	−1.14036
$336$	−0.395748	−0.0215898
$337$	22.6809	1.23551	0.617753	−	0.786373i	$-0.288043\pi$
$337$	22.6809	1.23551	0.617753	+	0.786373i	$0.288043\pi$
$338$	1.00000	0.0543928
$339$	11.4332	0.620964
$340$	10.9595	0.594361
$341$	−6.21812	−0.336730
$342$	−1.39575	−0.0754734
$343$	5.47849	0.295811
$344$	2.61985	0.141253
$345$	−27.0609	−1.45691
$346$	−10.5109	−0.565070
$347$	−2.33972	−0.125603	−0.0628014	−	0.998026i	$-0.520003\pi$
$347$	−2.33972	−0.125603	−0.0628014	+	0.998026i	$0.520003\pi$
$348$	4.66037	0.249822
$349$	−18.4422	−0.987190	−0.493595	−	0.869692i	$-0.664318\pi$
$349$	−18.4422	−0.987190	−0.493595	+	0.869692i	$0.664318\pi$
$350$	−1.86680	−0.0997847
$351$	1.00000	0.0533761
$352$	−4.45504	−0.237455
$353$	12.6037	0.670826	0.335413	−	0.942071i	$-0.391124\pi$
$353$	12.6037	0.670826	0.335413	+	0.942071i	$0.391124\pi$
$354$	10.7201	0.569767
$355$	−29.9485	−1.58950
$356$	−16.4938	−0.874170
$357$	1.39136	0.0736384
$358$	18.7115	0.988934
$359$	−11.1564	−0.588814	−0.294407	−	0.955680i	$-0.595122\pi$
$359$	−11.1564	−0.588814	−0.294407	+	0.955680i	$0.595122\pi$
$360$	−3.11723	−0.164293
$361$	−17.0519	−0.897468
$362$	−23.4971	−1.23498
$363$	8.84740	0.464368
$364$	−0.395748	−0.0207428
$365$	15.4879	0.810671
$366$	−5.89487	−0.308130
$367$	14.2040	0.741443	0.370721	−	0.928744i	$-0.379110\pi$
$367$	14.2040	0.741443	0.370721	+	0.928744i	$0.379110\pi$
$368$	8.68105	0.452531
$369$	−9.79488	−0.509901
$370$	22.9732	1.19432
$371$	−3.33404	−0.173095
$372$	1.39575	0.0723662
$373$	−24.9327	−1.29097	−0.645483	−	0.763775i	$-0.723344\pi$
$373$	−24.9327	−1.29097	−0.645483	+	0.763775i	$0.723344\pi$
$374$	15.6629	0.809909
$375$	0.881715	0.0455316
$376$	7.31044	0.377007
$377$	4.66037	0.240021
$378$	−0.395748	−0.0203551
$379$	−25.7734	−1.32389	−0.661946	−	0.749552i	$-0.730269\pi$
$379$	−25.7734	−1.32389	−0.661946	+	0.749552i	$0.730269\pi$
$380$	4.35087	0.223195
$381$	13.2490	0.678769
$382$	16.0310	0.820217
$383$	−15.9430	−0.814650	−0.407325	−	0.913283i	$-0.633538\pi$
$383$	−15.9430	−0.814650	−0.407325	+	0.913283i	$0.633538\pi$
$384$	1.00000	0.0510310
$385$	−5.49591	−0.280098
$386$	9.29200	0.472950
$387$	2.61985	0.133174
$388$	−9.52005	−0.483307
$389$	−22.4711	−1.13933	−0.569665	−	0.821877i	$-0.692927\pi$
$389$	−22.4711	−1.13933	−0.569665	+	0.821877i	$0.692927\pi$
$390$	−3.11723	−0.157847
$391$	−30.5206	−1.54349
$392$	−6.84338	−0.345643
$393$	6.27830	0.316698
$394$	19.7417	0.994571
$395$	−17.8864	−0.899960
$396$	−4.45504	−0.223874
$397$	30.7847	1.54504	0.772521	−	0.634989i	$-0.218995\pi$
$397$	30.7847	1.54504	0.772521	+	0.634989i	$0.218995\pi$
$398$	21.8668	1.09608
$399$	0.552364	0.0276528
$400$	4.71715	0.235857
$401$	−9.16950	−0.457903	−0.228951	−	0.973438i	$-0.573530\pi$
$401$	−9.16950	−0.457903	−0.228951	+	0.973438i	$0.573530\pi$
$402$	6.69566	0.333949
$403$	1.39575	0.0695272
$404$	10.9949	0.547019
$405$	−3.11723	−0.154897
$406$	−1.84433	−0.0915327
$407$	32.8325	1.62745
$408$	−3.51577	−0.174056
$409$	16.3009	0.806029	0.403015	−	0.915193i	$-0.367962\pi$
$409$	16.3009	0.806029	0.403015	+	0.915193i	$0.367962\pi$
$410$	30.5329	1.50791
$411$	15.3825	0.758764
$412$	−1.00000	−0.0492665
$413$	−4.24245	−0.208758
$414$	8.68105	0.426650
$415$	−19.0534	−0.935295
$416$	1.00000	0.0490290
$417$	13.3140	0.651987
$418$	6.21812	0.304138
$419$	18.8851	0.922597	0.461299	−	0.887245i	$-0.347384\pi$
$419$	18.8851	0.922597	0.461299	+	0.887245i	$0.347384\pi$
$420$	1.23364	0.0601954
$421$	28.8633	1.40671	0.703355	−	0.710839i	$-0.251684\pi$
$421$	28.8633	1.40671	0.703355	+	0.710839i	$0.251684\pi$
$422$	−2.80006	−0.136305
$423$	7.31044	0.355446
$424$	8.42466	0.409138
$425$	−16.5844	−0.804461
$426$	9.60739	0.465479
$427$	2.33288	0.112896
$428$	0.878878	0.0424822
$429$	−4.45504	−0.215091
$430$	−8.16667	−0.393832
$431$	13.0378	0.628007	0.314004	−	0.949422i	$-0.398330\pi$
$431$	13.0378	0.628007	0.314004	+	0.949422i	$0.398330\pi$
$432$	1.00000	0.0481125
$433$	19.7537	0.949301	0.474650	−	0.880174i	$-0.342575\pi$
$433$	19.7537	0.949301	0.474650	+	0.880174i	$0.342575\pi$
$434$	−0.552364	−0.0265143
$435$	−14.5275	−0.696539
$436$	7.53530	0.360875
$437$	−12.1166	−0.579614
$438$	−4.96846	−0.237402
$439$	37.3104	1.78073	0.890364	−	0.455249i	$-0.150450\pi$
$439$	37.3104	1.78073	0.890364	+	0.455249i	$0.150450\pi$
$440$	13.8874	0.662056
$441$	−6.84338	−0.325875
$442$	−3.51577	−0.167228
$443$	25.1459	1.19472	0.597359	−	0.801974i	$-0.296217\pi$
$443$	25.1459	1.19472	0.597359	+	0.801974i	$0.296217\pi$
$444$	−7.36973	−0.349752
$445$	51.4150	2.43731
$446$	−9.79868	−0.463981
$447$	18.5004	0.875041
$448$	−0.395748	−0.0186973
$449$	−29.6979	−1.40153	−0.700765	−	0.713393i	$-0.747158\pi$
$449$	−29.6979	−1.40153	−0.700765	+	0.713393i	$0.747158\pi$
$450$	4.71715	0.222368
$451$	43.6366	2.05477
$452$	11.4332	0.537770
$453$	−12.5281	−0.588622
$454$	−16.9937	−0.797556
$455$	1.23364	0.0578339
$456$	−1.39575	−0.0653619
$457$	−34.5255	−1.61504	−0.807518	−	0.589844i	$-0.799189\pi$
$457$	−34.5255	−1.61504	−0.807518	+	0.589844i	$0.799189\pi$
$458$	−10.5732	−0.494052
$459$	−3.51577	−0.164102
$460$	−27.0609	−1.26172
$461$	−15.5890	−0.726053	−0.363027	−	0.931779i	$-0.618257\pi$
$461$	−15.5890	−0.726053	−0.363027	+	0.931779i	$0.618257\pi$
$462$	1.76307	0.0820256
$463$	16.7817	0.779910	0.389955	−	0.920834i	$-0.372491\pi$
$463$	16.7817	0.779910	0.389955	+	0.920834i	$0.372491\pi$
$464$	4.66037	0.216352
$465$	−4.35087	−0.201767
$466$	14.6303	0.677736
$467$	39.2242	1.81508	0.907540	−	0.419966i	$-0.137958\pi$
$467$	39.2242	1.81508	0.907540	+	0.419966i	$0.137958\pi$
$468$	1.00000	0.0462250
$469$	−2.64979	−0.122356
$470$	−22.7883	−1.05115
$471$	−15.5588	−0.716912
$472$	10.7201	0.493432
$473$	−11.6715	−0.536657
$474$	5.73789	0.263550
$475$	−6.58395	−0.302092
$476$	1.39136	0.0637728
$477$	8.42466	0.385739
$478$	−11.6152	−0.531268
$479$	25.0626	1.14514	0.572570	−	0.819856i	$-0.305946\pi$
$479$	25.0626	1.14514	0.572570	+	0.819856i	$0.305946\pi$
$480$	−3.11723	−0.142282
$481$	−7.36973	−0.336031
$482$	7.91036	0.360307
$483$	−3.43551	−0.156321
$484$	8.84740	0.402155
$485$	29.6762	1.34753
$486$	1.00000	0.0453609
$487$	−29.9148	−1.35557	−0.677783	−	0.735262i	$-0.737059\pi$
$487$	−29.9148	−1.35557	−0.677783	+	0.735262i	$0.737059\pi$
$488$	−5.89487	−0.266848
$489$	12.1473	0.549319
$490$	21.3324	0.963701
$491$	−25.2832	−1.14101	−0.570507	−	0.821293i	$-0.693253\pi$
$491$	−25.2832	−1.14101	−0.570507	+	0.821293i	$0.693253\pi$
$492$	−9.79488	−0.441587
$493$	−16.3848	−0.737933
$494$	−1.39575	−0.0627977
$495$	13.8874	0.624193
$496$	1.39575	0.0626709
$497$	−3.80210	−0.170548
$498$	6.11228	0.273898
$499$	35.1947	1.57553	0.787766	−	0.615974i	$-0.211238\pi$
$499$	35.1947	1.57553	0.787766	+	0.615974i	$0.211238\pi$
$500$	0.881715	0.0394315
$501$	25.2285	1.12713
$502$	−16.5536	−0.738822
$503$	−19.6224	−0.874918	−0.437459	−	0.899238i	$-0.644122\pi$
$503$	−19.6224	−0.874918	−0.437459	+	0.899238i	$0.644122\pi$
$504$	−0.395748	−0.0176280
$505$	−34.2738	−1.52517
$506$	−38.6745	−1.71929
$507$	1.00000	0.0444116
$508$	13.2490	0.587831
$509$	11.0810	0.491156	0.245578	−	0.969377i	$-0.421022\pi$
$509$	11.0810	0.491156	0.245578	+	0.969377i	$0.421022\pi$
$510$	10.9595	0.485293
$511$	1.96626	0.0869821
$512$	1.00000	0.0441942
$513$	−1.39575	−0.0616238
$514$	5.06257	0.223300
$515$	3.11723	0.137362
$516$	2.61985	0.115332
$517$	−32.5683	−1.43235
$518$	2.91656	0.128146
$519$	−10.5109	−0.461378
$520$	−3.11723	−0.136700
$521$	39.4891	1.73005	0.865024	−	0.501731i	$-0.167303\pi$
$521$	39.4891	1.73005	0.865024	+	0.501731i	$0.167303\pi$
$522$	4.66037	0.203979
$523$	28.8190	1.26017	0.630084	−	0.776527i	$-0.283021\pi$
$523$	28.8190	1.26017	0.630084	+	0.776527i	$0.283021\pi$
$524$	6.27830	0.274269
$525$	−1.86680	−0.0814739
$526$	−14.7597	−0.643552
$527$	−4.90712	−0.213758
$528$	−4.45504	−0.193881
$529$	52.3607	2.27655
$530$	−26.2617	−1.14073
$531$	10.7201	0.465212
$532$	0.552364	0.0239480
$533$	−9.79488	−0.424263
$534$	−16.4938	−0.713757
$535$	−2.73967	−0.118446
$536$	6.69566	0.289208
$537$	18.7115	0.807461
$538$	19.1024	0.823565
$539$	30.4876	1.31319
$540$	−3.11723	−0.134144
$541$	−42.3868	−1.82235	−0.911175	−	0.412020i	$-0.864823\pi$
$541$	−42.3868	−1.82235	−0.911175	+	0.412020i	$0.864823\pi$
$542$	11.1338	0.478239
$543$	−23.4971	−1.00836
$544$	−3.51577	−0.150737
$545$	−23.4893	−1.00617
$546$	−0.395748	−0.0169364
$547$	17.0905	0.730736	0.365368	−	0.930863i	$-0.380943\pi$
$547$	17.0905	0.730736	0.365368	+	0.930863i	$0.380943\pi$
$548$	15.3825	0.657109
$549$	−5.89487	−0.251587
$550$	−21.0151	−0.896087
$551$	−6.50470	−0.277110
$552$	8.68105	0.369490
$553$	−2.27076	−0.0965625
$554$	5.74958	0.244276
$555$	22.9732	0.975157
$556$	13.3140	0.564638
$557$	−8.26420	−0.350165	−0.175083	−	0.984554i	$-0.556019\pi$
$557$	−8.26420	−0.350165	−0.175083	+	0.984554i	$0.556019\pi$
$558$	1.39575	0.0590867
$559$	2.61985	0.110808
$560$	1.23364	0.0521308
$561$	15.6629	0.661288
$562$	−26.2332	−1.10658
$563$	12.1470	0.511935	0.255967	−	0.966685i	$-0.417606\pi$
$563$	12.1470	0.511935	0.255967	+	0.966685i	$0.417606\pi$
$564$	7.31044	0.307825
$565$	−35.6398	−1.49938
$566$	7.49114	0.314876
$567$	−0.395748	−0.0166199
$568$	9.60739	0.403117
$569$	−41.1320	−1.72434	−0.862172	−	0.506616i	$-0.830896\pi$
$569$	−41.1320	−1.72434	−0.862172	+	0.506616i	$0.830896\pi$
$570$	4.35087	0.182238
$571$	−18.0960	−0.757296	−0.378648	−	0.925541i	$-0.623611\pi$
$571$	−18.0960	−0.757296	−0.378648	+	0.925541i	$0.623611\pi$
$572$	−4.45504	−0.186275
$573$	16.0310	0.669705
$574$	3.87630	0.161794
$575$	40.9498	1.70773
$576$	1.00000	0.0416667
$577$	−20.3020	−0.845182	−0.422591	−	0.906320i	$-0.638879\pi$
$577$	−20.3020	−0.845182	−0.422591	+	0.906320i	$0.638879\pi$
$578$	−4.63938	−0.192973
$579$	9.29200	0.386162
$580$	−14.5275	−0.603220
$581$	−2.41892	−0.100354
$582$	−9.52005	−0.394619
$583$	−37.5322	−1.55443
$584$	−4.96846	−0.205596
$585$	−3.11723	−0.128882
$586$	−3.16441	−0.130721
$587$	−28.0330	−1.15704	−0.578522	−	0.815666i	$-0.696370\pi$
$587$	−28.0330	−1.15704	−0.578522	+	0.815666i	$0.696370\pi$
$588$	−6.84338	−0.282216
$589$	−1.94811	−0.0802706
$590$	−33.4170	−1.37576
$591$	19.7417	0.812064
$592$	−7.36973	−0.302894
$593$	1.52306	0.0625445	0.0312722	−	0.999511i	$-0.490044\pi$
$593$	1.52306	0.0625445	0.0312722	+	0.999511i	$0.490044\pi$
$594$	−4.45504	−0.182793
$595$	−4.33719	−0.177807
$596$	18.5004	0.757808
$597$	21.8668	0.894948
$598$	8.68105	0.354995
$599$	−36.9700	−1.51055	−0.755277	−	0.655406i	$-0.772497\pi$
$599$	−36.9700	−1.51055	−0.755277	+	0.655406i	$0.772497\pi$
$600$	4.71715	0.192577
$601$	−11.6678	−0.475940	−0.237970	−	0.971273i	$-0.576482\pi$
$601$	−11.6678	−0.475940	−0.237970	+	0.971273i	$0.576482\pi$
$602$	−1.03680	−0.0422568
$603$	6.69566	0.272668
$604$	−12.5281	−0.509761
$605$	−27.5794	−1.12126
$606$	10.9949	0.446639
$607$	3.87060	0.157103	0.0785513	−	0.996910i	$-0.474971\pi$
$607$	3.87060	0.157103	0.0785513	+	0.996910i	$0.474971\pi$
$608$	−1.39575	−0.0566051
$609$	−1.84433	−0.0747361
$610$	18.3757	0.744010
$611$	7.31044	0.295749
$612$	−3.51577	−0.142116
$613$	−6.62033	−0.267393	−0.133696	−	0.991022i	$-0.542685\pi$
$613$	−6.62033	−0.267393	−0.133696	+	0.991022i	$0.542685\pi$
$614$	−32.7128	−1.32018
$615$	30.5329	1.23121
$616$	1.76307	0.0710363
$617$	−16.2714	−0.655060	−0.327530	−	0.944841i	$-0.606216\pi$
$617$	−16.2714	−0.655060	−0.327530	+	0.944841i	$0.606216\pi$
$618$	−1.00000	−0.0402259
$619$	12.7570	0.512749	0.256375	−	0.966578i	$-0.417472\pi$
$619$	12.7570	0.512749	0.256375	+	0.966578i	$0.417472\pi$
$620$	−4.35087	−0.174735
$621$	8.68105	0.348359
$622$	−27.4036	−1.09878
$623$	6.52739	0.261514
$624$	1.00000	0.0400320
$625$	−26.3343	−1.05337
$626$	13.5077	0.539876
$627$	6.21812	0.248328
$628$	−15.5588	−0.620864
$629$	25.9103	1.03311
$630$	1.23364	0.0491493
$631$	−19.1841	−0.763707	−0.381853	−	0.924223i	$-0.624714\pi$
$631$	−19.1841	−0.763707	−0.381853	+	0.924223i	$0.624714\pi$
$632$	5.73789	0.228241
$633$	−2.80006	−0.111292
$634$	26.0026	1.03270
$635$	−41.3004	−1.63896
$636$	8.42466	0.334060
$637$	−6.84338	−0.271145
$638$	−20.7621	−0.821981
$639$	9.60739	0.380062
$640$	−3.11723	−0.123219
$641$	−2.07919	−0.0821231	−0.0410616	−	0.999157i	$-0.513074\pi$
$641$	−2.07919	−0.0821231	−0.0410616	+	0.999157i	$0.513074\pi$
$642$	0.878878	0.0346865
$643$	8.26675	0.326009	0.163004	−	0.986625i	$-0.447882\pi$
$643$	8.26675	0.326009	0.163004	+	0.986625i	$0.447882\pi$
$644$	−3.43551	−0.135378
$645$	−8.16667	−0.321563
$646$	4.90712	0.193068
$647$	−30.8770	−1.21390	−0.606949	−	0.794740i	$-0.707607\pi$
$647$	−30.8770	−1.21390	−0.606949	+	0.794740i	$0.707607\pi$
$648$	1.00000	0.0392837
$649$	−47.7585	−1.87468
$650$	4.71715	0.185022
$651$	−0.552364	−0.0216489
$652$	12.1473	0.475724
$653$	15.7945	0.618088	0.309044	−	0.951048i	$-0.399991\pi$
$653$	15.7945	0.618088	0.309044	+	0.951048i	$0.399991\pi$
$654$	7.53530	0.294653
$655$	−19.5709	−0.764700
$656$	−9.79488	−0.382426
$657$	−4.96846	−0.193838
$658$	−2.89309	−0.112784
$659$	−40.0903	−1.56170	−0.780848	−	0.624721i	$-0.785213\pi$
$659$	−40.0903	−1.56170	−0.780848	+	0.624721i	$0.785213\pi$
$660$	13.8874	0.540567
$661$	−42.3860	−1.64862	−0.824311	−	0.566137i	$-0.808437\pi$
$661$	−42.3860	−1.64862	−0.824311	+	0.566137i	$0.808437\pi$
$662$	−12.2672	−0.476778
$663$	−3.51577	−0.136541
$664$	6.11228	0.237203
$665$	−1.72185	−0.0667704
$666$	−7.36973	−0.285571
$667$	40.4569	1.56650
$668$	25.2285	0.976120
$669$	−9.79868	−0.378839
$670$	−20.8719	−0.806353
$671$	26.2619	1.01383
$672$	−0.395748	−0.0152663
$673$	30.8628	1.18967	0.594837	−	0.803846i	$-0.297217\pi$
$673$	30.8628	1.18967	0.594837	+	0.803846i	$0.297217\pi$
$674$	22.6809	0.873634
$675$	4.71715	0.181563
$676$	1.00000	0.0384615
$677$	6.50370	0.249958	0.124979	−	0.992159i	$-0.460114\pi$
$677$	6.50370	0.249958	0.124979	+	0.992159i	$0.460114\pi$
$678$	11.4332	0.439088
$679$	3.76754	0.144585
$680$	10.9595	0.420276
$681$	−16.9937	−0.651202
$682$	−6.21812	−0.238104
$683$	9.97403	0.381645	0.190823	−	0.981625i	$-0.438884\pi$
$683$	9.97403	0.381645	0.190823	+	0.981625i	$0.438884\pi$
$684$	−1.39575	−0.0533678
$685$	−47.9509	−1.83211
$686$	5.47849	0.209170
$687$	−10.5732	−0.403392
$688$	2.61985	0.0998807
$689$	8.42466	0.320954
$690$	−27.0609	−1.03019
$691$	39.0651	1.48611	0.743053	−	0.669233i	$-0.233377\pi$
$691$	39.0651	1.48611	0.743053	+	0.669233i	$0.233377\pi$
$692$	−10.5109	−0.399565
$693$	1.76307	0.0669736
$694$	−2.33972	−0.0888147
$695$	−41.5027	−1.57429
$696$	4.66037	0.176651
$697$	34.4365	1.30438
$698$	−18.4422	−0.698049
$699$	14.6303	0.553369
$700$	−1.86680	−0.0705585
$701$	−15.7253	−0.593937	−0.296969	−	0.954887i	$-0.595976\pi$
$701$	−15.7253	−0.593937	−0.296969	+	0.954887i	$0.595976\pi$
$702$	1.00000	0.0377426
$703$	10.2863	0.387955
$704$	−4.45504	−0.167906
$705$	−22.7883	−0.858259
$706$	12.6037	0.474346
$707$	−4.35123	−0.163645
$708$	10.7201	0.402886
$709$	11.8136	0.443671	0.221835	−	0.975084i	$-0.428795\pi$
$709$	11.8136	0.443671	0.221835	+	0.975084i	$0.428795\pi$
$710$	−29.9485	−1.12395
$711$	5.73789	0.215188
$712$	−16.4938	−0.618131
$713$	12.1166	0.453769
$714$	1.39136	0.0520702
$715$	13.8874	0.519360
$716$	18.7115	0.699282
$717$	−11.6152	−0.433778
$718$	−11.1564	−0.416355
$719$	−26.8546	−1.00151	−0.500754	−	0.865589i	$-0.666944\pi$
$719$	−26.8546	−1.00151	−0.500754	+	0.865589i	$0.666944\pi$
$720$	−3.11723	−0.116172
$721$	0.395748	0.0147384
$722$	−17.0519	−0.634606
$723$	7.91036	0.294190
$724$	−23.4971	−0.873263
$725$	21.9837	0.816453
$726$	8.84740	0.328358
$727$	−30.5445	−1.13283	−0.566417	−	0.824119i	$-0.691671\pi$
$727$	−30.5445	−1.13283	−0.566417	+	0.824119i	$0.691671\pi$
$728$	−0.395748	−0.0146674
$729$	1.00000	0.0370370
$730$	15.4879	0.573231
$731$	−9.21077	−0.340673
$732$	−5.89487	−0.217881
$733$	−6.26703	−0.231478	−0.115739	−	0.993280i	$-0.536924\pi$
$733$	−6.26703	−0.231478	−0.115739	+	0.993280i	$0.536924\pi$
$734$	14.2040	0.524279
$735$	21.3324	0.786858
$736$	8.68105	0.319988
$737$	−29.8294	−1.09878
$738$	−9.79488	−0.360554
$739$	22.6799	0.834292	0.417146	−	0.908839i	$-0.363030\pi$
$739$	22.6799	0.834292	0.417146	+	0.908839i	$0.363030\pi$
$740$	22.9732	0.844511
$741$	−1.39575	−0.0512741
$742$	−3.33404	−0.122397
$743$	12.6634	0.464574	0.232287	−	0.972647i	$-0.425379\pi$
$743$	12.6634	0.464574	0.232287	+	0.972647i	$0.425379\pi$
$744$	1.39575	0.0511706
$745$	−57.6702	−2.11287
$746$	−24.9327	−0.912850
$747$	6.11228	0.223637
$748$	15.6629	0.572692
$749$	−0.347814	−0.0127088
$750$	0.881715	0.0321957
$751$	−45.7681	−1.67010	−0.835051	−	0.550172i	$-0.814562\pi$
$751$	−45.7681	−1.67010	−0.835051	+	0.550172i	$0.814562\pi$
$752$	7.31044	0.266584
$753$	−16.5536	−0.603245
$754$	4.66037	0.169721
$755$	39.0530	1.42129
$756$	−0.395748	−0.0143932
$757$	40.3337	1.46595	0.732977	−	0.680254i	$-0.238130\pi$
$757$	40.3337	1.46595	0.732977	+	0.680254i	$0.238130\pi$
$758$	−25.7734	−0.936133
$759$	−38.6745	−1.40379
$760$	4.35087	0.157823
$761$	32.1180	1.16428	0.582139	−	0.813090i	$-0.302216\pi$
$761$	32.1180	1.16428	0.582139	+	0.813090i	$0.302216\pi$
$762$	13.2490	0.479962
$763$	−2.98208	−0.107958
$764$	16.0310	0.579981
$765$	10.9595	0.396240
$766$	−15.9430	−0.576044
$767$	10.7201	0.387080
$768$	1.00000	0.0360844
$769$	48.9844	1.76642	0.883211	−	0.468975i	$-0.155377\pi$
$769$	48.9844	1.76642	0.883211	+	0.468975i	$0.155377\pi$
$770$	−5.49591	−0.198059
$771$	5.06257	0.182324
$772$	9.29200	0.334426
$773$	−8.90054	−0.320130	−0.160065	−	0.987106i	$-0.551170\pi$
$773$	−8.90054	−0.320130	−0.160065	+	0.987106i	$0.551170\pi$
$774$	2.61985	0.0941684
$775$	6.58395	0.236502
$776$	−9.52005	−0.341750
$777$	2.91656	0.104631
$778$	−22.4711	−0.805628
$779$	13.6712	0.489821
$780$	−3.11723	−0.111615
$781$	−42.8013	−1.53155
$782$	−30.5206	−1.09141
$783$	4.66037	0.166548
$784$	−6.84338	−0.244407
$785$	48.5004	1.73105
$786$	6.27830	0.223940
$787$	−12.3823	−0.441380	−0.220690	−	0.975344i	$-0.570831\pi$
$787$	−12.3823	−0.441380	−0.220690	+	0.975344i	$0.570831\pi$
$788$	19.7417	0.703268
$789$	−14.7597	−0.525458
$790$	−17.8864	−0.636368
$791$	−4.52465	−0.160878
$792$	−4.45504	−0.158303
$793$	−5.89487	−0.209333
$794$	30.7847	1.09251
$795$	−26.2617	−0.931405
$796$	21.8668	0.775048
$797$	34.0504	1.20613	0.603064	−	0.797693i	$-0.293946\pi$
$797$	34.0504	1.20613	0.603064	+	0.797693i	$0.293946\pi$
$798$	0.552364	0.0195535
$799$	−25.7018	−0.909264
$800$	4.71715	0.166776
$801$	−16.4938	−0.582780
$802$	−9.16950	−0.323786
$803$	22.1347	0.781117
$804$	6.69566	0.236138
$805$	10.7093	0.377453
$806$	1.39575	0.0491631
$807$	19.1024	0.672438
$808$	10.9949	0.386801
$809$	−32.0829	−1.12797	−0.563987	−	0.825784i	$-0.690733\pi$
$809$	−32.0829	−1.12797	−0.563987	+	0.825784i	$0.690733\pi$
$810$	−3.11723	−0.109528
$811$	25.8463	0.907588	0.453794	−	0.891107i	$-0.350070\pi$
$811$	25.8463	0.907588	0.453794	+	0.891107i	$0.350070\pi$
$812$	−1.84433	−0.0647234
$813$	11.1338	0.390480
$814$	32.8325	1.15078
$815$	−37.8659	−1.32639
$816$	−3.51577	−0.123076
$817$	−3.65665	−0.127930
$818$	16.3009	0.569949
$819$	−0.395748	−0.0138286
$820$	30.5329	1.06626
$821$	42.2801	1.47558	0.737792	−	0.675028i	$-0.235868\pi$
$821$	42.2801	1.47558	0.737792	+	0.675028i	$0.235868\pi$
$822$	15.3825	0.536527
$823$	−16.3769	−0.570861	−0.285431	−	0.958399i	$-0.592137\pi$
$823$	−16.3769	−0.570861	−0.285431	+	0.958399i	$0.592137\pi$
$824$	−1.00000	−0.0348367
$825$	−21.0151	−0.731652
$826$	−4.24245	−0.147614
$827$	5.75073	0.199973	0.0999863	−	0.994989i	$-0.468120\pi$
$827$	5.75073	0.199973	0.0999863	+	0.994989i	$0.468120\pi$
$828$	8.68105	0.301687
$829$	−22.6240	−0.785763	−0.392881	−	0.919589i	$-0.628522\pi$
$829$	−22.6240	−0.785763	−0.392881	+	0.919589i	$0.628522\pi$
$830$	−19.0534	−0.661354
$831$	5.74958	0.199451
$832$	1.00000	0.0346688
$833$	24.0597	0.833621
$834$	13.3140	0.461025
$835$	−78.6431	−2.72156
$836$	6.21812	0.215058
$837$	1.39575	0.0482441
$838$	18.8851	0.652375
$839$	−32.2843	−1.11458	−0.557290	−	0.830318i	$-0.688159\pi$
$839$	−32.2843	−1.11458	−0.557290	+	0.830318i	$0.688159\pi$
$840$	1.23364	0.0425646
$841$	−7.28095	−0.251067
$842$	28.8633	0.994694
$843$	−26.2332	−0.903520
$844$	−2.80006	−0.0963820
$845$	−3.11723	−0.107236
$846$	7.31044	0.251338
$847$	−3.50134	−0.120308
$848$	8.42466	0.289304
$849$	7.49114	0.257095
$850$	−16.5844	−0.568840
$851$	−63.9770	−2.19310
$852$	9.60739	0.329144
$853$	−16.0041	−0.547970	−0.273985	−	0.961734i	$-0.588342\pi$
$853$	−16.0041	−0.547970	−0.273985	+	0.961734i	$0.588342\pi$
$854$	2.33288	0.0798296
$855$	4.35087	0.148797
$856$	0.878878	0.0300394
$857$	40.6506	1.38860	0.694298	−	0.719687i	$-0.255715\pi$
$857$	40.6506	1.38860	0.694298	+	0.719687i	$0.255715\pi$
$858$	−4.45504	−0.152093
$859$	44.7629	1.52729	0.763644	−	0.645637i	$-0.223408\pi$
$859$	44.7629	1.52729	0.763644	+	0.645637i	$0.223408\pi$
$860$	−8.16667	−0.278481
$861$	3.87630	0.132104
$862$	13.0378	0.444068
$863$	29.2927	0.997136	0.498568	−	0.866851i	$-0.333859\pi$
$863$	29.2927	0.997136	0.498568	+	0.866851i	$0.333859\pi$
$864$	1.00000	0.0340207
$865$	32.7650	1.11404
$866$	19.7537	0.671257
$867$	−4.63938	−0.157562
$868$	−0.552364	−0.0187485
$869$	−25.5626	−0.867151
$870$	−14.5275	−0.492527
$871$	6.69566	0.226874
$872$	7.53530	0.255177
$873$	−9.52005	−0.322205
$874$	−12.1166	−0.409849
$875$	−0.348937	−0.0117962
$876$	−4.96846	−0.167869
$877$	40.7874	1.37729	0.688647	−	0.725097i	$-0.258205\pi$
$877$	40.7874	1.37729	0.688647	+	0.725097i	$0.258205\pi$
$878$	37.3104	1.25916
$879$	−3.16441	−0.106733
$880$	13.8874	0.468145
$881$	−26.2459	−0.884248	−0.442124	−	0.896954i	$-0.645775\pi$
$881$	−26.2459	−0.884248	−0.442124	+	0.896954i	$0.645775\pi$
$882$	−6.84338	−0.230429
$883$	−33.7696	−1.13644	−0.568219	−	0.822878i	$-0.692367\pi$
$883$	−33.7696	−1.13644	−0.568219	+	0.822878i	$0.692367\pi$
$884$	−3.51577	−0.118248
$885$	−33.4170	−1.12330
$886$	25.1459	0.844794
$887$	−13.2622	−0.445302	−0.222651	−	0.974898i	$-0.571471\pi$
$887$	−13.2622	−0.445302	−0.222651	+	0.974898i	$0.571471\pi$
$888$	−7.36973	−0.247312
$889$	−5.24328	−0.175854
$890$	51.4150	1.72344
$891$	−4.45504	−0.149250
$892$	−9.79868	−0.328084
$893$	−10.2035	−0.341448
$894$	18.5004	0.618748
$895$	−58.3282	−1.94970
$896$	−0.395748	−0.0132210
$897$	8.68105	0.289852
$898$	−29.6979	−0.991031
$899$	6.50470	0.216944
$900$	4.71715	0.157238
$901$	−29.6192	−0.986757
$902$	43.6366	1.45294
$903$	−1.03680	−0.0345025
$904$	11.4332	0.380261
$905$	73.2460	2.43478
$906$	−12.5281	−0.416218
$907$	−1.05565	−0.0350523	−0.0175262	−	0.999846i	$-0.505579\pi$
$907$	−1.05565	−0.0350523	−0.0175262	+	0.999846i	$0.505579\pi$
$908$	−16.9937	−0.563957
$909$	10.9949	0.364679
$910$	1.23364	0.0408947
$911$	−35.4697	−1.17516	−0.587582	−	0.809165i	$-0.699920\pi$
$911$	−35.4697	−1.17516	−0.587582	+	0.809165i	$0.699920\pi$
$912$	−1.39575	−0.0462178
$913$	−27.2305	−0.901197
$914$	−34.5255	−1.14200
$915$	18.3757	0.607482
$916$	−10.5732	−0.349348
$917$	−2.48462	−0.0820495
$918$	−3.51577	−0.116038
$919$	57.0756	1.88275	0.941376	−	0.337360i	$-0.109534\pi$
$919$	57.0756	1.88275	0.941376	+	0.337360i	$0.109534\pi$
$920$	−27.0609	−0.892170
$921$	−32.7128	−1.07792
$922$	−15.5890	−0.513397
$923$	9.60739	0.316231
$924$	1.76307	0.0580009
$925$	−34.7641	−1.14304
$926$	16.7817	0.551479
$927$	−1.00000	−0.0328443
$928$	4.66037	0.152984
$929$	−20.8809	−0.685079	−0.342539	−	0.939503i	$-0.611287\pi$
$929$	−20.8809	−0.685079	−0.342539	+	0.939503i	$0.611287\pi$
$930$	−4.35087	−0.142671
$931$	9.55164	0.313042
$932$	14.6303	0.479232
$933$	−27.4036	−0.897153
$934$	39.2242	1.28346
$935$	−48.8249	−1.59674
$936$	1.00000	0.0326860
$937$	−17.8720	−0.583853	−0.291926	−	0.956441i	$-0.594296\pi$
$937$	−17.8720	−0.583853	−0.291926	+	0.956441i	$0.594296\pi$
$938$	−2.64979	−0.0865188
$939$	13.5077	0.440807
$940$	−22.7883	−0.743274
$941$	53.5467	1.74557	0.872786	−	0.488102i	$-0.162311\pi$
$941$	53.5467	1.74557	0.872786	+	0.488102i	$0.162311\pi$
$942$	−15.5588	−0.506933
$943$	−85.0298	−2.76895
$944$	10.7201	0.348909
$945$	1.23364	0.0401303
$946$	−11.6715	−0.379474
$947$	20.6071	0.669640	0.334820	−	0.942282i	$-0.391324\pi$
$947$	20.6071	0.669640	0.334820	+	0.942282i	$0.391324\pi$
$948$	5.73789	0.186358
$949$	−4.96846	−0.161283
$950$	−6.58395	−0.213612
$951$	26.0026	0.843193
$952$	1.39136	0.0450941
$953$	−8.47819	−0.274636	−0.137318	−	0.990527i	$-0.543848\pi$
$953$	−8.47819	−0.274636	−0.137318	+	0.990527i	$0.543848\pi$
$954$	8.42466	0.272759
$955$	−49.9724	−1.61707
$956$	−11.6152	−0.375663
$957$	−20.7621	−0.671145
$958$	25.0626	0.809736
$959$	−6.08760	−0.196579
$960$	−3.11723	−0.100608
$961$	−29.0519	−0.937158
$962$	−7.36973	−0.237610
$963$	0.878878	0.0283214
$964$	7.91036	0.254776
$965$	−28.9653	−0.932427
$966$	−3.43551	−0.110536
$967$	48.5209	1.56033	0.780163	−	0.625576i	$-0.215136\pi$
$967$	48.5209	1.56033	0.780163	+	0.625576i	$0.215136\pi$
$968$	8.84740	0.284366
$969$	4.90712	0.157640
$970$	29.6762	0.952846
$971$	8.78901	0.282053	0.141026	−	0.990006i	$-0.454960\pi$
$971$	8.78901	0.282053	0.141026	+	0.990006i	$0.454960\pi$
$972$	1.00000	0.0320750
$973$	−5.26897	−0.168915
$974$	−29.9148	−0.958531
$975$	4.71715	0.151070
$976$	−5.89487	−0.188690
$977$	−37.8470	−1.21083	−0.605416	−	0.795909i	$-0.706993\pi$
$977$	−37.8470	−1.21083	−0.605416	+	0.795909i	$0.706993\pi$
$978$	12.1473	0.388427
$979$	73.4806	2.34845
$980$	21.3324	0.681439
$981$	7.53530	0.240583
$982$	−25.2832	−0.806819
$983$	0.258183	0.00823477	0.00411738	−	0.999992i	$-0.498689\pi$
$983$	0.258183	0.00823477	0.00411738	+	0.999992i	$0.498689\pi$
$984$	−9.79488	−0.312249
$985$	−61.5394	−1.96081
$986$	−16.3848	−0.521798
$987$	−2.89309	−0.0920881
$988$	−1.39575	−0.0444047
$989$	22.7430	0.723186
$990$	13.8874	0.441371
$991$	11.6089	0.368770	0.184385	−	0.982854i	$-0.440971\pi$
$991$	11.6089	0.368770	0.184385	+	0.982854i	$0.440971\pi$
$992$	1.39575	0.0443150
$993$	−12.2672	−0.389288
$994$	−3.80210	−0.120595
$995$	−68.1639	−2.16094
$996$	6.11228	0.193675
$997$	38.8121	1.22919	0.614596	−	0.788842i	$-0.289319\pi$
$997$	38.8121	1.22919	0.614596	+	0.788842i	$0.289319\pi$
$998$	35.1947	1.11407
$999$	−7.36973	−0.233168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.v.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.v.1.2	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.11723 q^{5} +1.00000 q^{6} -0.395748 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.11723 q^{5} +1.00000 q^{6} -0.395748 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.11723 q^{10} -4.45504 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.395748 q^{14} -3.11723 q^{15} +1.00000 q^{16} -3.51577 q^{17} +1.00000 q^{18} -1.39575 q^{19} -3.11723 q^{20} -0.395748 q^{21} -4.45504 q^{22} +8.68105 q^{23} +1.00000 q^{24} +4.71715 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.395748 q^{28} +4.66037 q^{29} -3.11723 q^{30} +1.39575 q^{31} +1.00000 q^{32} -4.45504 q^{33} -3.51577 q^{34} +1.23364 q^{35} +1.00000 q^{36} -7.36973 q^{37} -1.39575 q^{38} +1.00000 q^{39} -3.11723 q^{40} -9.79488 q^{41} -0.395748 q^{42} +2.61985 q^{43} -4.45504 q^{44} -3.11723 q^{45} +8.68105 q^{46} +7.31044 q^{47} +1.00000 q^{48} -6.84338 q^{49} +4.71715 q^{50} -3.51577 q^{51} +1.00000 q^{52} +8.42466 q^{53} +1.00000 q^{54} +13.8874 q^{55} -0.395748 q^{56} -1.39575 q^{57} +4.66037 q^{58} +10.7201 q^{59} -3.11723 q^{60} -5.89487 q^{61} +1.39575 q^{62} -0.395748 q^{63} +1.00000 q^{64} -3.11723 q^{65} -4.45504 q^{66} +6.69566 q^{67} -3.51577 q^{68} +8.68105 q^{69} +1.23364 q^{70} +9.60739 q^{71} +1.00000 q^{72} -4.96846 q^{73} -7.36973 q^{74} +4.71715 q^{75} -1.39575 q^{76} +1.76307 q^{77} +1.00000 q^{78} +5.73789 q^{79} -3.11723 q^{80} +1.00000 q^{81} -9.79488 q^{82} +6.11228 q^{83} -0.395748 q^{84} +10.9595 q^{85} +2.61985 q^{86} +4.66037 q^{87} -4.45504 q^{88} -16.4938 q^{89} -3.11723 q^{90} -0.395748 q^{91} +8.68105 q^{92} +1.39575 q^{93} +7.31044 q^{94} +4.35087 q^{95} +1.00000 q^{96} -9.52005 q^{97} -6.84338 q^{98} -4.45504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 11 * q^3 + 11 * q^4 + 5 * q^5 + 11 * q^6 + 4 * q^7 + 11 * q^8 + 11 * q^9 + 5 * q^10 - 7 * q^11 + 11 * q^12 + 11 * q^13 + 4 * q^14 + 5 * q^15 + 11 * q^16 + 10 * q^17 + 11 * q^18 - 7 * q^19 + 5 * q^20 + 4 * q^21 - 7 * q^22 + 18 * q^23 + 11 * q^24 + 32 * q^25 + 11 * q^26 + 11 * q^27 + 4 * q^28 + 29 * q^29 + 5 * q^30 + 7 * q^31 + 11 * q^32 - 7 * q^33 + 10 * q^34 + 31 * q^35 + 11 * q^36 + 21 * q^37 - 7 * q^38 + 11 * q^39 + 5 * q^40 - 3 * q^41 + 4 * q^42 - 17 * q^43 - 7 * q^44 + 5 * q^45 + 18 * q^46 + 12 * q^47 + 11 * q^48 + 21 * q^49 + 32 * q^50 + 10 * q^51 + 11 * q^52 + 11 * q^53 + 11 * q^54 + 4 * q^55 + 4 * q^56 - 7 * q^57 + 29 * q^58 - 48 * q^59 + 5 * q^60 - q^61 + 7 * q^62 + 4 * q^63 + 11 * q^64 + 5 * q^65 - 7 * q^66 - 9 * q^67 + 10 * q^68 + 18 * q^69 + 31 * q^70 + 17 * q^71 + 11 * q^72 - 23 * q^73 + 21 * q^74 + 32 * q^75 - 7 * q^76 + 26 * q^77 + 11 * q^78 + 41 * q^79 + 5 * q^80 + 11 * q^81 - 3 * q^82 + 19 * q^83 + 4 * q^84 + 17 * q^85 - 17 * q^86 + 29 * q^87 - 7 * q^88 + 32 * q^89 + 5 * q^90 + 4 * q^91 + 18 * q^92 + 7 * q^93 + 12 * q^94 + 26 * q^95 + 11 * q^96 - 16 * q^97 + 21 * q^98 - 7 * q^99

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