LMFDB - Embedded newform 8034.2.a.bb.1.14

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-3.69005$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.69005 q^{5} -1.00000 q^{6} -0.801879 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.69005 q^{5} -1.00000 q^{6} -0.801879 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.69005 q^{10} -2.09517 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.801879 q^{14} +3.69005 q^{15} +1.00000 q^{16} -7.28473 q^{17} -1.00000 q^{18} +6.41973 q^{19} +3.69005 q^{20} -0.801879 q^{21} +2.09517 q^{22} -6.18478 q^{23} -1.00000 q^{24} +8.61644 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.801879 q^{28} -8.16717 q^{29} -3.69005 q^{30} -4.92193 q^{31} -1.00000 q^{32} -2.09517 q^{33} +7.28473 q^{34} -2.95897 q^{35} +1.00000 q^{36} +7.56623 q^{37} -6.41973 q^{38} -1.00000 q^{39} -3.69005 q^{40} -12.6172 q^{41} +0.801879 q^{42} -1.69130 q^{43} -2.09517 q^{44} +3.69005 q^{45} +6.18478 q^{46} -1.40161 q^{47} +1.00000 q^{48} -6.35699 q^{49} -8.61644 q^{50} -7.28473 q^{51} -1.00000 q^{52} +10.3169 q^{53} -1.00000 q^{54} -7.73128 q^{55} +0.801879 q^{56} +6.41973 q^{57} +8.16717 q^{58} +11.6675 q^{59} +3.69005 q^{60} +3.80363 q^{61} +4.92193 q^{62} -0.801879 q^{63} +1.00000 q^{64} -3.69005 q^{65} +2.09517 q^{66} -1.82701 q^{67} -7.28473 q^{68} -6.18478 q^{69} +2.95897 q^{70} -12.5083 q^{71} -1.00000 q^{72} -9.57442 q^{73} -7.56623 q^{74} +8.61644 q^{75} +6.41973 q^{76} +1.68007 q^{77} +1.00000 q^{78} -16.2346 q^{79} +3.69005 q^{80} +1.00000 q^{81} +12.6172 q^{82} -9.35341 q^{83} -0.801879 q^{84} -26.8810 q^{85} +1.69130 q^{86} -8.16717 q^{87} +2.09517 q^{88} +3.88578 q^{89} -3.69005 q^{90} +0.801879 q^{91} -6.18478 q^{92} -4.92193 q^{93} +1.40161 q^{94} +23.6891 q^{95} -1.00000 q^{96} +10.4617 q^{97} +6.35699 q^{98} -2.09517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * 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
$5$	3.69005	1.65024	0.825119	−	0.564958i	$-0.191108\pi$
$5$	3.69005	1.65024	0.825119	+	0.564958i	$0.191108\pi$
$6$	−1.00000	−0.408248
$7$	−0.801879	−0.303082	−0.151541	−	0.988451i	$-0.548424\pi$
$7$	−0.801879	−0.303082	−0.151541	+	0.988451i	$0.548424\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.69005	−1.16690
$11$	−2.09517	−0.631718	−0.315859	−	0.948806i	$-0.602293\pi$
$11$	−2.09517	−0.631718	−0.315859	+	0.948806i	$0.602293\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.801879	0.214311
$15$	3.69005	0.952766
$16$	1.00000	0.250000
$17$	−7.28473	−1.76681	−0.883403	−	0.468613i	$-0.844754\pi$
$17$	−7.28473	−1.76681	−0.883403	+	0.468613i	$0.844754\pi$
$18$	−1.00000	−0.235702
$19$	6.41973	1.47279	0.736393	−	0.676554i	$-0.236527\pi$
$19$	6.41973	1.47279	0.736393	+	0.676554i	$0.236527\pi$
$20$	3.69005	0.825119
$21$	−0.801879	−0.174984
$22$	2.09517	0.446692
$23$	−6.18478	−1.28962	−0.644808	−	0.764345i	$-0.723062\pi$
$23$	−6.18478	−1.28962	−0.644808	+	0.764345i	$0.723062\pi$
$24$	−1.00000	−0.204124
$25$	8.61644	1.72329
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−0.801879	−0.151541
$29$	−8.16717	−1.51660	−0.758302	−	0.651903i	$-0.773971\pi$
$29$	−8.16717	−1.51660	−0.758302	+	0.651903i	$0.773971\pi$
$30$	−3.69005	−0.673707
$31$	−4.92193	−0.884004	−0.442002	−	0.897014i	$-0.645732\pi$
$31$	−4.92193	−0.884004	−0.442002	+	0.897014i	$0.645732\pi$
$32$	−1.00000	−0.176777
$33$	−2.09517	−0.364723
$34$	7.28473	1.24932
$35$	−2.95897	−0.500157
$36$	1.00000	0.166667
$37$	7.56623	1.24388	0.621940	−	0.783065i	$-0.286345\pi$
$37$	7.56623	1.24388	0.621940	+	0.783065i	$0.286345\pi$
$38$	−6.41973	−1.04142
$39$	−1.00000	−0.160128
$40$	−3.69005	−0.583448
$41$	−12.6172	−1.97047	−0.985234	−	0.171213i	$-0.945231\pi$
$41$	−12.6172	−1.97047	−0.985234	+	0.171213i	$0.945231\pi$
$42$	0.801879	0.123733
$43$	−1.69130	−0.257921	−0.128960	−	0.991650i	$-0.541164\pi$
$43$	−1.69130	−0.257921	−0.128960	+	0.991650i	$0.541164\pi$
$44$	−2.09517	−0.315859
$45$	3.69005	0.550080
$46$	6.18478	0.911896
$47$	−1.40161	−0.204446	−0.102223	−	0.994762i	$-0.532595\pi$
$47$	−1.40161	−0.204446	−0.102223	+	0.994762i	$0.532595\pi$
$48$	1.00000	0.144338
$49$	−6.35699	−0.908141
$50$	−8.61644	−1.21855
$51$	−7.28473	−1.02007
$52$	−1.00000	−0.138675
$53$	10.3169	1.41714	0.708568	−	0.705642i	$-0.249341\pi$
$53$	10.3169	1.41714	0.708568	+	0.705642i	$0.249341\pi$
$54$	−1.00000	−0.136083
$55$	−7.73128	−1.04249
$56$	0.801879	0.107156
$57$	6.41973	0.850313
$58$	8.16717	1.07240
$59$	11.6675	1.51898	0.759491	−	0.650518i	$-0.225448\pi$
$59$	11.6675	1.51898	0.759491	+	0.650518i	$0.225448\pi$
$60$	3.69005	0.476383
$61$	3.80363	0.487005	0.243503	−	0.969900i	$-0.421704\pi$
$61$	3.80363	0.487005	0.243503	+	0.969900i	$0.421704\pi$
$62$	4.92193	0.625085
$63$	−0.801879	−0.101027
$64$	1.00000	0.125000
$65$	−3.69005	−0.457694
$66$	2.09517	0.257898
$67$	−1.82701	−0.223205	−0.111603	−	0.993753i	$-0.535598\pi$
$67$	−1.82701	−0.223205	−0.111603	+	0.993753i	$0.535598\pi$
$68$	−7.28473	−0.883403
$69$	−6.18478	−0.744560
$70$	2.95897	0.353665
$71$	−12.5083	−1.48446	−0.742230	−	0.670145i	$-0.766232\pi$
$71$	−12.5083	−1.48446	−0.742230	+	0.670145i	$0.766232\pi$
$72$	−1.00000	−0.117851
$73$	−9.57442	−1.12060	−0.560301	−	0.828289i	$-0.689314\pi$
$73$	−9.57442	−1.12060	−0.560301	+	0.828289i	$0.689314\pi$
$74$	−7.56623	−0.879556
$75$	8.61644	0.994941
$76$	6.41973	0.736393
$77$	1.68007	0.191462
$78$	1.00000	0.113228
$79$	−16.2346	−1.82654	−0.913268	−	0.407359i	$-0.866450\pi$
$79$	−16.2346	−1.82654	−0.913268	+	0.407359i	$0.866450\pi$
$80$	3.69005	0.412560
$81$	1.00000	0.111111
$82$	12.6172	1.39333
$83$	−9.35341	−1.02667	−0.513335	−	0.858188i	$-0.671590\pi$
$83$	−9.35341	−1.02667	−0.513335	+	0.858188i	$0.671590\pi$
$84$	−0.801879	−0.0874922
$85$	−26.8810	−2.91565
$86$	1.69130	0.182378
$87$	−8.16717	−0.875612
$88$	2.09517	0.223346
$89$	3.88578	0.411892	0.205946	−	0.978563i	$-0.433973\pi$
$89$	3.88578	0.411892	0.205946	+	0.978563i	$0.433973\pi$
$90$	−3.69005	−0.388965
$91$	0.801879	0.0840598
$92$	−6.18478	−0.644808
$93$	−4.92193	−0.510380
$94$	1.40161	0.144565
$95$	23.6891	2.43045
$96$	−1.00000	−0.102062
$97$	10.4617	1.06222	0.531111	−	0.847302i	$-0.321775\pi$
$97$	10.4617	1.06222	0.531111	+	0.847302i	$0.321775\pi$
$98$	6.35699	0.642153
$99$	−2.09517	−0.210573
$100$	8.61644	0.861644
$101$	5.37036	0.534371	0.267185	−	0.963645i	$-0.413906\pi$
$101$	5.37036	0.534371	0.267185	+	0.963645i	$0.413906\pi$
$102$	7.28473	0.721296
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−2.95897	−0.288766
$106$	−10.3169	−1.00207
$107$	−5.84497	−0.565054	−0.282527	−	0.959259i	$-0.591173\pi$
$107$	−5.84497	−0.565054	−0.282527	+	0.959259i	$0.591173\pi$
$108$	1.00000	0.0962250
$109$	18.8090	1.80158	0.900789	−	0.434257i	$-0.142989\pi$
$109$	18.8090	1.80158	0.900789	+	0.434257i	$0.142989\pi$
$110$	7.73128	0.737149
$111$	7.56623	0.718155
$112$	−0.801879	−0.0757704
$113$	−8.04354	−0.756673	−0.378336	−	0.925668i	$-0.623504\pi$
$113$	−8.04354	−0.756673	−0.378336	+	0.925668i	$0.623504\pi$
$114$	−6.41973	−0.601262
$115$	−22.8221	−2.12817
$116$	−8.16717	−0.758302
$117$	−1.00000	−0.0924500
$118$	−11.6675	−1.07408
$119$	5.84147	0.535487
$120$	−3.69005	−0.336854
$121$	−6.61026	−0.600932
$122$	−3.80363	−0.344365
$123$	−12.6172	−1.13765
$124$	−4.92193	−0.442002
$125$	13.3448	1.19360
$126$	0.801879	0.0714371
$127$	6.32994	0.561692	0.280846	−	0.959753i	$-0.409385\pi$
$127$	6.32994	0.561692	0.280846	+	0.959753i	$0.409385\pi$
$128$	−1.00000	−0.0883883
$129$	−1.69130	−0.148911
$130$	3.69005	0.323638
$131$	−11.7846	−1.02963	−0.514813	−	0.857303i	$-0.672139\pi$
$131$	−11.7846	−1.02963	−0.514813	+	0.857303i	$0.672139\pi$
$132$	−2.09517	−0.182361
$133$	−5.14784	−0.446375
$134$	1.82701	0.157830
$135$	3.69005	0.317589
$136$	7.28473	0.624660
$137$	12.9694	1.10805	0.554027	−	0.832499i	$-0.313090\pi$
$137$	12.9694	1.10805	0.554027	+	0.832499i	$0.313090\pi$
$138$	6.18478	0.526483
$139$	17.3953	1.47545	0.737724	−	0.675103i	$-0.235901\pi$
$139$	17.3953	1.47545	0.737724	+	0.675103i	$0.235901\pi$
$140$	−2.95897	−0.250079
$141$	−1.40161	−0.118037
$142$	12.5083	1.04967
$143$	2.09517	0.175207
$144$	1.00000	0.0833333
$145$	−30.1372	−2.50276
$146$	9.57442	0.792385
$147$	−6.35699	−0.524316
$148$	7.56623	0.621940
$149$	13.0943	1.07273	0.536363	−	0.843988i	$-0.319798\pi$
$149$	13.0943	1.07273	0.536363	+	0.843988i	$0.319798\pi$
$150$	−8.61644	−0.703530
$151$	−20.0305	−1.63006	−0.815031	−	0.579417i	$-0.803280\pi$
$151$	−20.0305	−1.63006	−0.815031	+	0.579417i	$0.803280\pi$
$152$	−6.41973	−0.520709
$153$	−7.28473	−0.588936
$154$	−1.68007	−0.135384
$155$	−18.1621	−1.45882
$156$	−1.00000	−0.0800641
$157$	−18.5752	−1.48246	−0.741230	−	0.671251i	$-0.765757\pi$
$157$	−18.5752	−1.48246	−0.741230	+	0.671251i	$0.765757\pi$
$158$	16.2346	1.29156
$159$	10.3169	0.818184
$160$	−3.69005	−0.291724
$161$	4.95944	0.390859
$162$	−1.00000	−0.0785674
$163$	3.81533	0.298840	0.149420	−	0.988774i	$-0.452259\pi$
$163$	3.81533	0.298840	0.149420	+	0.988774i	$0.452259\pi$
$164$	−12.6172	−0.985234
$165$	−7.73128	−0.601879
$166$	9.35341	0.725965
$167$	−11.8008	−0.913177	−0.456588	−	0.889678i	$-0.650929\pi$
$167$	−11.8008	−0.913177	−0.456588	+	0.889678i	$0.650929\pi$
$168$	0.801879	0.0618663
$169$	1.00000	0.0769231
$170$	26.8810	2.06168
$171$	6.41973	0.490929
$172$	−1.69130	−0.128960
$173$	−24.7683	−1.88310	−0.941549	−	0.336877i	$-0.890629\pi$
$173$	−24.7683	−1.88310	−0.941549	+	0.336877i	$0.890629\pi$
$174$	8.16717	0.619151
$175$	−6.90934	−0.522297
$176$	−2.09517	−0.157930
$177$	11.6675	0.876985
$178$	−3.88578	−0.291252
$179$	−13.6899	−1.02323	−0.511616	−	0.859214i	$-0.670953\pi$
$179$	−13.6899	−1.02323	−0.511616	+	0.859214i	$0.670953\pi$
$180$	3.69005	0.275040
$181$	−26.3059	−1.95530	−0.977652	−	0.210229i	$-0.932579\pi$
$181$	−26.3059	−1.95530	−0.977652	+	0.210229i	$0.932579\pi$
$182$	−0.801879	−0.0594392
$183$	3.80363	0.281173
$184$	6.18478	0.455948
$185$	27.9197	2.05270
$186$	4.92193	0.360893
$187$	15.2628	1.11612
$188$	−1.40161	−0.102223
$189$	−0.801879	−0.0583281
$190$	−23.6891	−1.71859
$191$	27.0533	1.95751	0.978753	−	0.205044i	$-0.0657337\pi$
$191$	27.0533	1.95751	0.978753	+	0.205044i	$0.0657337\pi$
$192$	1.00000	0.0721688
$193$	−6.88418	−0.495534	−0.247767	−	0.968820i	$-0.579697\pi$
$193$	−6.88418	−0.495534	−0.247767	+	0.968820i	$0.579697\pi$
$194$	−10.4617	−0.751105
$195$	−3.69005	−0.264250
$196$	−6.35699	−0.454071
$197$	−12.1767	−0.867558	−0.433779	−	0.901019i	$-0.642820\pi$
$197$	−12.1767	−0.867558	−0.433779	+	0.901019i	$0.642820\pi$
$198$	2.09517	0.148897
$199$	6.86514	0.486657	0.243328	−	0.969944i	$-0.421761\pi$
$199$	6.86514	0.486657	0.243328	+	0.969944i	$0.421761\pi$
$200$	−8.61644	−0.609274
$201$	−1.82701	−0.128868
$202$	−5.37036	−0.377857
$203$	6.54908	0.459655
$204$	−7.28473	−0.510033
$205$	−46.5579	−3.25174
$206$	−1.00000	−0.0696733
$207$	−6.18478	−0.429872
$208$	−1.00000	−0.0693375
$209$	−13.4504	−0.930386
$210$	2.95897	0.204188
$211$	−25.0346	−1.72345	−0.861727	−	0.507371i	$-0.830617\pi$
$211$	−25.0346	−1.72345	−0.861727	+	0.507371i	$0.830617\pi$
$212$	10.3169	0.708568
$213$	−12.5083	−0.857054
$214$	5.84497	0.399554
$215$	−6.24097	−0.425631
$216$	−1.00000	−0.0680414
$217$	3.94679	0.267926
$218$	−18.8090	−1.27391
$219$	−9.57442	−0.646979
$220$	−7.73128	−0.521243
$221$	7.28473	0.490024
$222$	−7.56623	−0.507812
$223$	11.4805	0.768788	0.384394	−	0.923169i	$-0.374410\pi$
$223$	11.4805	0.768788	0.384394	+	0.923169i	$0.374410\pi$
$224$	0.801879	0.0535778
$225$	8.61644	0.574429
$226$	8.04354	0.535048
$227$	−6.32844	−0.420033	−0.210017	−	0.977698i	$-0.567352\pi$
$227$	−6.32844	−0.420033	−0.210017	+	0.977698i	$0.567352\pi$
$228$	6.41973	0.425157
$229$	−1.09206	−0.0721656	−0.0360828	−	0.999349i	$-0.511488\pi$
$229$	−1.09206	−0.0721656	−0.0360828	+	0.999349i	$0.511488\pi$
$230$	22.8221	1.50485
$231$	1.68007	0.110541
$232$	8.16717	0.536201
$233$	−6.15204	−0.403033	−0.201517	−	0.979485i	$-0.564587\pi$
$233$	−6.15204	−0.403033	−0.201517	+	0.979485i	$0.564587\pi$
$234$	1.00000	0.0653720
$235$	−5.17200	−0.337384
$236$	11.6675	0.759491
$237$	−16.2346	−1.05455
$238$	−5.84147	−0.378646
$239$	−3.86903	−0.250267	−0.125133	−	0.992140i	$-0.539936\pi$
$239$	−3.86903	−0.250267	−0.125133	+	0.992140i	$0.539936\pi$
$240$	3.69005	0.238191
$241$	8.24640	0.531197	0.265599	−	0.964084i	$-0.414430\pi$
$241$	8.24640	0.531197	0.265599	+	0.964084i	$0.414430\pi$
$242$	6.61026	0.424923
$243$	1.00000	0.0641500
$244$	3.80363	0.243503
$245$	−23.4576	−1.49865
$246$	12.6172	0.804440
$247$	−6.41973	−0.408477
$248$	4.92193	0.312543
$249$	−9.35341	−0.592748
$250$	−13.3448	−0.844002
$251$	−20.8393	−1.31537	−0.657683	−	0.753294i	$-0.728464\pi$
$251$	−20.8393	−1.31537	−0.657683	+	0.753294i	$0.728464\pi$
$252$	−0.801879	−0.0505136
$253$	12.9582	0.814673
$254$	−6.32994	−0.397176
$255$	−26.8810	−1.68335
$256$	1.00000	0.0625000
$257$	16.9120	1.05494	0.527472	−	0.849573i	$-0.323140\pi$
$257$	16.9120	1.05494	0.527472	+	0.849573i	$0.323140\pi$
$258$	1.69130	0.105296
$259$	−6.06720	−0.376997
$260$	−3.69005	−0.228847
$261$	−8.16717	−0.505535
$262$	11.7846	0.728055
$263$	18.1348	1.11824	0.559120	−	0.829086i	$-0.311139\pi$
$263$	18.1348	1.11824	0.559120	+	0.829086i	$0.311139\pi$
$264$	2.09517	0.128949
$265$	38.0699	2.33861
$266$	5.14784	0.315635
$267$	3.88578	0.237806
$268$	−1.82701	−0.111603
$269$	0.636581	0.0388130	0.0194065	−	0.999812i	$-0.493822\pi$
$269$	0.636581	0.0388130	0.0194065	+	0.999812i	$0.493822\pi$
$270$	−3.69005	−0.224569
$271$	−6.65381	−0.404190	−0.202095	−	0.979366i	$-0.564775\pi$
$271$	−6.65381	−0.404190	−0.202095	+	0.979366i	$0.564775\pi$
$272$	−7.28473	−0.441702
$273$	0.801879	0.0485319
$274$	−12.9694	−0.783513
$275$	−18.0529	−1.08863
$276$	−6.18478	−0.372280
$277$	−18.6247	−1.11905	−0.559526	−	0.828813i	$-0.689017\pi$
$277$	−18.6247	−1.11905	−0.559526	+	0.828813i	$0.689017\pi$
$278$	−17.3953	−1.04330
$279$	−4.92193	−0.294668
$280$	2.95897	0.176832
$281$	−15.8147	−0.943427	−0.471713	−	0.881752i	$-0.656364\pi$
$281$	−15.8147	−0.943427	−0.471713	+	0.881752i	$0.656364\pi$
$282$	1.40161	0.0834646
$283$	1.14296	0.0679421	0.0339710	−	0.999423i	$-0.489185\pi$
$283$	1.14296	0.0679421	0.0339710	+	0.999423i	$0.489185\pi$
$284$	−12.5083	−0.742230
$285$	23.6891	1.40322
$286$	−2.09517	−0.123890
$287$	10.1174	0.597213
$288$	−1.00000	−0.0589256
$289$	36.0673	2.12161
$290$	30.1372	1.76972
$291$	10.4617	0.613274
$292$	−9.57442	−0.560301
$293$	19.8586	1.16015	0.580077	−	0.814561i	$-0.303022\pi$
$293$	19.8586	1.16015	0.580077	+	0.814561i	$0.303022\pi$
$294$	6.35699	0.370747
$295$	43.0537	2.50668
$296$	−7.56623	−0.439778
$297$	−2.09517	−0.121574
$298$	−13.0943	−0.758532
$299$	6.18478	0.357675
$300$	8.61644	0.497470
$301$	1.35622	0.0781711
$302$	20.0305	1.15263
$303$	5.37036	0.308519
$304$	6.41973	0.368197
$305$	14.0356	0.803675
$306$	7.28473	0.416440
$307$	14.4202	0.823004	0.411502	−	0.911409i	$-0.365004\pi$
$307$	14.4202	0.823004	0.411502	+	0.911409i	$0.365004\pi$
$308$	1.68007	0.0957311
$309$	1.00000	0.0568880
$310$	18.1621	1.03154
$311$	−16.9322	−0.960138	−0.480069	−	0.877231i	$-0.659388\pi$
$311$	−16.9322	−0.960138	−0.480069	+	0.877231i	$0.659388\pi$
$312$	1.00000	0.0566139
$313$	8.02812	0.453776	0.226888	−	0.973921i	$-0.427145\pi$
$313$	8.02812	0.453776	0.226888	+	0.973921i	$0.427145\pi$
$314$	18.5752	1.04826
$315$	−2.95897	−0.166719
$316$	−16.2346	−0.913268
$317$	26.3844	1.48189	0.740947	−	0.671563i	$-0.234377\pi$
$317$	26.3844	1.48189	0.740947	+	0.671563i	$0.234377\pi$
$318$	−10.3169	−0.578543
$319$	17.1116	0.958066
$320$	3.69005	0.206280
$321$	−5.84497	−0.326234
$322$	−4.95944	−0.276379
$323$	−46.7660	−2.60213
$324$	1.00000	0.0555556
$325$	−8.61644	−0.477954
$326$	−3.81533	−0.211312
$327$	18.8090	1.04014
$328$	12.6172	0.696666
$329$	1.12392	0.0619638
$330$	7.73128	0.425593
$331$	19.3054	1.06112	0.530560	−	0.847648i	$-0.321982\pi$
$331$	19.3054	1.06112	0.530560	+	0.847648i	$0.321982\pi$
$332$	−9.35341	−0.513335
$333$	7.56623	0.414627
$334$	11.8008	0.645714
$335$	−6.74176	−0.368342
$336$	−0.801879	−0.0437461
$337$	7.12603	0.388179	0.194090	−	0.980984i	$-0.437825\pi$
$337$	7.12603	0.388179	0.194090	+	0.980984i	$0.437825\pi$
$338$	−1.00000	−0.0543928
$339$	−8.04354	−0.436865
$340$	−26.8810	−1.45783
$341$	10.3123	0.558441
$342$	−6.41973	−0.347139
$343$	10.7107	0.578323
$344$	1.69130	0.0911888
$345$	−22.8221	−1.22870
$346$	24.7683	1.33155
$347$	33.6190	1.80476	0.902381	−	0.430939i	$-0.141818\pi$
$347$	33.6190	1.80476	0.902381	+	0.430939i	$0.141818\pi$
$348$	−8.16717	−0.437806
$349$	0.865602	0.0463346	0.0231673	−	0.999732i	$-0.492625\pi$
$349$	0.865602	0.0463346	0.0231673	+	0.999732i	$0.492625\pi$
$350$	6.90934	0.369320
$351$	−1.00000	−0.0533761
$352$	2.09517	0.111673
$353$	32.6448	1.73751	0.868754	−	0.495243i	$-0.164921\pi$
$353$	32.6448	1.73751	0.868754	+	0.495243i	$0.164921\pi$
$354$	−11.6675	−0.620122
$355$	−46.1562	−2.44972
$356$	3.88578	0.205946
$357$	5.84147	0.309163
$358$	13.6899	0.723534
$359$	−13.5526	−0.715277	−0.357639	−	0.933860i	$-0.616418\pi$
$359$	−13.5526	−0.715277	−0.357639	+	0.933860i	$0.616418\pi$
$360$	−3.69005	−0.194483
$361$	22.2129	1.16910
$362$	26.3059	1.38261
$363$	−6.61026	−0.346948
$364$	0.801879	0.0420299
$365$	−35.3301	−1.84926
$366$	−3.80363	−0.198819
$367$	−3.18662	−0.166340	−0.0831702	−	0.996535i	$-0.526505\pi$
$367$	−3.18662	−0.166340	−0.0831702	+	0.996535i	$0.526505\pi$
$368$	−6.18478	−0.322404
$369$	−12.6172	−0.656823
$370$	−27.9197	−1.45148
$371$	−8.27291	−0.429508
$372$	−4.92193	−0.255190
$373$	12.2027	0.631834	0.315917	−	0.948787i	$-0.397688\pi$
$373$	12.2027	0.631834	0.315917	+	0.948787i	$0.397688\pi$
$374$	−15.2628	−0.789219
$375$	13.3448	0.689124
$376$	1.40161	0.0722825
$377$	8.16717	0.420630
$378$	0.801879	0.0412442
$379$	−4.04966	−0.208017	−0.104008	−	0.994576i	$-0.533167\pi$
$379$	−4.04966	−0.208017	−0.104008	+	0.994576i	$0.533167\pi$
$380$	23.6891	1.21522
$381$	6.32994	0.324293
$382$	−27.0533	−1.38417
$383$	−8.52524	−0.435620	−0.217810	−	0.975991i	$-0.569891\pi$
$383$	−8.52524	−0.435620	−0.217810	+	0.975991i	$0.569891\pi$
$384$	−1.00000	−0.0510310
$385$	6.19955	0.315958
$386$	6.88418	0.350396
$387$	−1.69130	−0.0859736
$388$	10.4617	0.531111
$389$	−2.55183	−0.129383	−0.0646914	−	0.997905i	$-0.520606\pi$
$389$	−2.55183	−0.129383	−0.0646914	+	0.997905i	$0.520606\pi$
$390$	3.69005	0.186853
$391$	45.0544	2.27850
$392$	6.35699	0.321076
$393$	−11.7846	−0.594455
$394$	12.1767	0.613456
$395$	−59.9065	−3.01422
$396$	−2.09517	−0.105286
$397$	−15.6618	−0.786042	−0.393021	−	0.919530i	$-0.628570\pi$
$397$	−15.6618	−0.786042	−0.393021	+	0.919530i	$0.628570\pi$
$398$	−6.86514	−0.344118
$399$	−5.14784	−0.257715
$400$	8.61644	0.430822
$401$	−10.6910	−0.533883	−0.266942	−	0.963713i	$-0.586013\pi$
$401$	−10.6910	−0.533883	−0.266942	+	0.963713i	$0.586013\pi$
$402$	1.82701	0.0911231
$403$	4.92193	0.245179
$404$	5.37036	0.267185
$405$	3.69005	0.183360
$406$	−6.54908	−0.325025
$407$	−15.8525	−0.785782
$408$	7.28473	0.360648
$409$	14.4409	0.714055	0.357028	−	0.934094i	$-0.383790\pi$
$409$	14.4409	0.714055	0.357028	+	0.934094i	$0.383790\pi$
$410$	46.5579	2.29933
$411$	12.9694	0.639736
$412$	1.00000	0.0492665
$413$	−9.35594	−0.460376
$414$	6.18478	0.303965
$415$	−34.5145	−1.69425
$416$	1.00000	0.0490290
$417$	17.3953	0.851850
$418$	13.4504	0.657882
$419$	−14.0266	−0.685244	−0.342622	−	0.939473i	$-0.611315\pi$
$419$	−14.0266	−0.685244	−0.342622	+	0.939473i	$0.611315\pi$
$420$	−2.95897	−0.144383
$421$	21.9429	1.06943	0.534715	−	0.845032i	$-0.320419\pi$
$421$	21.9429	1.06943	0.534715	+	0.845032i	$0.320419\pi$
$422$	25.0346	1.21867
$423$	−1.40161	−0.0681486
$424$	−10.3169	−0.501033
$425$	−62.7685	−3.04472
$426$	12.5083	0.606029
$427$	−3.05005	−0.147602
$428$	−5.84497	−0.282527
$429$	2.09517	0.101156
$430$	6.24097	0.300966
$431$	1.88113	0.0906108	0.0453054	−	0.998973i	$-0.485574\pi$
$431$	1.88113	0.0906108	0.0453054	+	0.998973i	$0.485574\pi$
$432$	1.00000	0.0481125
$433$	15.2492	0.732831	0.366415	−	0.930451i	$-0.380585\pi$
$433$	15.2492	0.732831	0.366415	+	0.930451i	$0.380585\pi$
$434$	−3.94679	−0.189452
$435$	−30.1372	−1.44497
$436$	18.8090	0.900789
$437$	−39.7046	−1.89933
$438$	9.57442	0.457484
$439$	38.1006	1.81844	0.909220	−	0.416315i	$-0.136679\pi$
$439$	38.1006	1.81844	0.909220	+	0.416315i	$0.136679\pi$
$440$	7.73128	0.368574
$441$	−6.35699	−0.302714
$442$	−7.28473	−0.346499
$443$	−2.12579	−0.100999	−0.0504996	−	0.998724i	$-0.516081\pi$
$443$	−2.12579	−0.100999	−0.0504996	+	0.998724i	$0.516081\pi$
$444$	7.56623	0.359077
$445$	14.3387	0.679720
$446$	−11.4805	−0.543615
$447$	13.0943	0.619338
$448$	−0.801879	−0.0378852
$449$	−22.5617	−1.06475	−0.532377	−	0.846507i	$-0.678701\pi$
$449$	−22.5617	−1.06475	−0.532377	+	0.846507i	$0.678701\pi$
$450$	−8.61644	−0.406183
$451$	26.4351	1.24478
$452$	−8.04354	−0.378336
$453$	−20.0305	−0.941117
$454$	6.32844	0.297008
$455$	2.95897	0.138719
$456$	−6.41973	−0.300631
$457$	−28.9729	−1.35529	−0.677647	−	0.735387i	$-0.737000\pi$
$457$	−28.9729	−1.35529	−0.677647	+	0.735387i	$0.737000\pi$
$458$	1.09206	0.0510288
$459$	−7.28473	−0.340022
$460$	−22.8221	−1.06409
$461$	−26.4125	−1.23015	−0.615077	−	0.788467i	$-0.710875\pi$
$461$	−26.4125	−1.23015	−0.615077	+	0.788467i	$0.710875\pi$
$462$	−1.68007	−0.0781641
$463$	−32.9808	−1.53275	−0.766374	−	0.642394i	$-0.777941\pi$
$463$	−32.9808	−1.53275	−0.766374	+	0.642394i	$0.777941\pi$
$464$	−8.16717	−0.379151
$465$	−18.1621	−0.842249
$466$	6.15204	0.284988
$467$	22.2234	1.02838	0.514188	−	0.857678i	$-0.328093\pi$
$467$	22.2234	1.02838	0.514188	+	0.857678i	$0.328093\pi$
$468$	−1.00000	−0.0462250
$469$	1.46504	0.0676494
$470$	5.17200	0.238567
$471$	−18.5752	−0.855898
$472$	−11.6675	−0.537041
$473$	3.54356	0.162933
$474$	16.2346	0.745680
$475$	55.3152	2.53804
$476$	5.84147	0.267743
$477$	10.3169	0.472379
$478$	3.86903	0.176965
$479$	12.2928	0.561673	0.280837	−	0.959756i	$-0.409388\pi$
$479$	12.2928	0.561673	0.280837	+	0.959756i	$0.409388\pi$
$480$	−3.69005	−0.168427
$481$	−7.56623	−0.344990
$482$	−8.24640	−0.375613
$483$	4.95944	0.225662
$484$	−6.61026	−0.300466
$485$	38.6041	1.75292
$486$	−1.00000	−0.0453609
$487$	11.6049	0.525867	0.262934	−	0.964814i	$-0.415310\pi$
$487$	11.6049	0.525867	0.262934	+	0.964814i	$0.415310\pi$
$488$	−3.80363	−0.172182
$489$	3.81533	0.172535
$490$	23.4576	1.05971
$491$	11.2148	0.506115	0.253057	−	0.967451i	$-0.418564\pi$
$491$	11.2148	0.506115	0.253057	+	0.967451i	$0.418564\pi$
$492$	−12.6172	−0.568825
$493$	59.4956	2.67955
$494$	6.41973	0.288837
$495$	−7.73128	−0.347495
$496$	−4.92193	−0.221001
$497$	10.0301	0.449913
$498$	9.35341	0.419136
$499$	−8.47929	−0.379585	−0.189793	−	0.981824i	$-0.560782\pi$
$499$	−8.47929	−0.379585	−0.189793	+	0.981824i	$0.560782\pi$
$500$	13.3448	0.596799
$501$	−11.8008	−0.527223
$502$	20.8393	0.930105
$503$	18.4500	0.822644	0.411322	−	0.911490i	$-0.365067\pi$
$503$	18.4500	0.822644	0.411322	+	0.911490i	$0.365067\pi$
$504$	0.801879	0.0357185
$505$	19.8169	0.881839
$506$	−12.9582	−0.576061
$507$	1.00000	0.0444116
$508$	6.32994	0.280846
$509$	2.89416	0.128281	0.0641406	−	0.997941i	$-0.479569\pi$
$509$	2.89416	0.128281	0.0641406	+	0.997941i	$0.479569\pi$
$510$	26.8810	1.19031
$511$	7.67753	0.339634
$512$	−1.00000	−0.0441942
$513$	6.41973	0.283438
$514$	−16.9120	−0.745958
$515$	3.69005	0.162603
$516$	−1.69130	−0.0744553
$517$	2.93661	0.129152
$518$	6.06720	0.266577
$519$	−24.7683	−1.08721
$520$	3.69005	0.161819
$521$	−17.4473	−0.764379	−0.382190	−	0.924084i	$-0.624830\pi$
$521$	−17.4473	−0.764379	−0.382190	+	0.924084i	$0.624830\pi$
$522$	8.16717	0.357467
$523$	26.5858	1.16252	0.581259	−	0.813719i	$-0.302560\pi$
$523$	26.5858	1.16252	0.581259	+	0.813719i	$0.302560\pi$
$524$	−11.7846	−0.514813
$525$	−6.90934	−0.301548
$526$	−18.1348	−0.790716
$527$	35.8549	1.56186
$528$	−2.09517	−0.0911806
$529$	15.2515	0.663107
$530$	−38.0699	−1.65365
$531$	11.6675	0.506327
$532$	−5.14784	−0.223187
$533$	12.6172	0.546510
$534$	−3.88578	−0.168154
$535$	−21.5682	−0.932475
$536$	1.82701	0.0789150
$537$	−13.6899	−0.590763
$538$	−0.636581	−0.0274450
$539$	13.3190	0.573689
$540$	3.69005	0.158794
$541$	23.5105	1.01079	0.505397	−	0.862887i	$-0.331346\pi$
$541$	23.5105	1.01079	0.505397	+	0.862887i	$0.331346\pi$
$542$	6.65381	0.285806
$543$	−26.3059	−1.12890
$544$	7.28473	0.312330
$545$	69.4062	2.97303
$546$	−0.801879	−0.0343173
$547$	28.0184	1.19798	0.598990	−	0.800756i	$-0.295569\pi$
$547$	28.0184	1.19798	0.598990	+	0.800756i	$0.295569\pi$
$548$	12.9694	0.554027
$549$	3.80363	0.162335
$550$	18.0529	0.769779
$551$	−52.4310	−2.23363
$552$	6.18478	0.263242
$553$	13.0182	0.553590
$554$	18.6247	0.791289
$555$	27.9197	1.18513
$556$	17.3953	0.737724
$557$	−9.47001	−0.401257	−0.200629	−	0.979667i	$-0.564298\pi$
$557$	−9.47001	−0.401257	−0.200629	+	0.979667i	$0.564298\pi$
$558$	4.92193	0.208362
$559$	1.69130	0.0715344
$560$	−2.95897	−0.125039
$561$	15.2628	0.644394
$562$	15.8147	0.667104
$563$	−38.8473	−1.63722	−0.818608	−	0.574352i	$-0.805254\pi$
$563$	−38.8473	−1.63722	−0.818608	+	0.574352i	$0.805254\pi$
$564$	−1.40161	−0.0590184
$565$	−29.6810	−1.24869
$566$	−1.14296	−0.0480423
$567$	−0.801879	−0.0336758
$568$	12.5083	0.524836
$569$	2.91023	0.122003	0.0610017	−	0.998138i	$-0.480570\pi$
$569$	2.91023	0.122003	0.0610017	+	0.998138i	$0.480570\pi$
$570$	−23.6891	−0.992227
$571$	−6.33484	−0.265105	−0.132552	−	0.991176i	$-0.542317\pi$
$571$	−6.33484	−0.265105	−0.132552	+	0.991176i	$0.542317\pi$
$572$	2.09517	0.0876035
$573$	27.0533	1.13017
$574$	−10.1174	−0.422293
$575$	−53.2908	−2.22238
$576$	1.00000	0.0416667
$577$	34.2196	1.42458	0.712290	−	0.701886i	$-0.247658\pi$
$577$	34.2196	1.42458	0.712290	+	0.701886i	$0.247658\pi$
$578$	−36.0673	−1.50020
$579$	−6.88418	−0.286097
$580$	−30.1372	−1.25138
$581$	7.50030	0.311165
$582$	−10.4617	−0.433651
$583$	−21.6157	−0.895230
$584$	9.57442	0.396192
$585$	−3.69005	−0.152565
$586$	−19.8586	−0.820353
$587$	−3.59839	−0.148522	−0.0742608	−	0.997239i	$-0.523660\pi$
$587$	−3.59839	−0.148522	−0.0742608	+	0.997239i	$0.523660\pi$
$588$	−6.35699	−0.262158
$589$	−31.5974	−1.30195
$590$	−43.0537	−1.77249
$591$	−12.1767	−0.500885
$592$	7.56623	0.310970
$593$	−11.5291	−0.473443	−0.236722	−	0.971578i	$-0.576073\pi$
$593$	−11.5291	−0.473443	−0.236722	+	0.971578i	$0.576073\pi$
$594$	2.09517	0.0859659
$595$	21.5553	0.883681
$596$	13.0943	0.536363
$597$	6.86514	0.280971
$598$	−6.18478	−0.252914
$599$	−10.3969	−0.424807	−0.212403	−	0.977182i	$-0.568129\pi$
$599$	−10.3969	−0.424807	−0.212403	+	0.977182i	$0.568129\pi$
$600$	−8.61644	−0.351765
$601$	13.9017	0.567060	0.283530	−	0.958963i	$-0.408494\pi$
$601$	13.9017	0.567060	0.283530	+	0.958963i	$0.408494\pi$
$602$	−1.35622	−0.0552753
$603$	−1.82701	−0.0744017
$604$	−20.0305	−0.815031
$605$	−24.3921	−0.991682
$606$	−5.37036	−0.218156
$607$	−23.6585	−0.960267	−0.480134	−	0.877195i	$-0.659412\pi$
$607$	−23.6585	−0.960267	−0.480134	+	0.877195i	$0.659412\pi$
$608$	−6.41973	−0.260354
$609$	6.54908	0.265382
$610$	−14.0356	−0.568284
$611$	1.40161	0.0567031
$612$	−7.28473	−0.294468
$613$	11.6937	0.472303	0.236152	−	0.971716i	$-0.424114\pi$
$613$	11.6937	0.472303	0.236152	+	0.971716i	$0.424114\pi$
$614$	−14.4202	−0.581952
$615$	−46.5579	−1.87739
$616$	−1.68007	−0.0676921
$617$	−26.1720	−1.05365	−0.526823	−	0.849975i	$-0.676617\pi$
$617$	−26.1720	−1.05365	−0.526823	+	0.849975i	$0.676617\pi$
$618$	−1.00000	−0.0402259
$619$	−23.6493	−0.950545	−0.475273	−	0.879839i	$-0.657651\pi$
$619$	−23.6493	−0.950545	−0.475273	+	0.879839i	$0.657651\pi$
$620$	−18.1621	−0.729409
$621$	−6.18478	−0.248187
$622$	16.9322	0.678920
$623$	−3.11593	−0.124837
$624$	−1.00000	−0.0400320
$625$	6.16086	0.246434
$626$	−8.02812	−0.320868
$627$	−13.4504	−0.537158
$628$	−18.5752	−0.741230
$629$	−55.1179	−2.19770
$630$	2.95897	0.117888
$631$	−11.2193	−0.446632	−0.223316	−	0.974746i	$-0.571688\pi$
$631$	−11.2193	−0.446632	−0.223316	+	0.974746i	$0.571688\pi$
$632$	16.2346	0.645778
$633$	−25.0346	−0.995037
$634$	−26.3844	−1.04786
$635$	23.3578	0.926925
$636$	10.3169	0.409092
$637$	6.35699	0.251873
$638$	−17.1116	−0.677455
$639$	−12.5083	−0.494820
$640$	−3.69005	−0.145862
$641$	39.6666	1.56674	0.783368	−	0.621558i	$-0.213500\pi$
$641$	39.6666	1.56674	0.783368	+	0.621558i	$0.213500\pi$
$642$	5.84497	0.230683
$643$	−43.2448	−1.70541	−0.852705	−	0.522393i	$-0.825039\pi$
$643$	−43.2448	−1.70541	−0.852705	+	0.522393i	$0.825039\pi$
$644$	4.95944	0.195429
$645$	−6.24097	−0.245738
$646$	46.7660	1.83998
$647$	30.1059	1.18359	0.591793	−	0.806090i	$-0.298420\pi$
$647$	30.1059	1.18359	0.591793	+	0.806090i	$0.298420\pi$
$648$	−1.00000	−0.0392837
$649$	−24.4455	−0.959568
$650$	8.61644	0.337965
$651$	3.94679	0.154687
$652$	3.81533	0.149420
$653$	−16.3241	−0.638813	−0.319406	−	0.947618i	$-0.603483\pi$
$653$	−16.3241	−0.638813	−0.319406	+	0.947618i	$0.603483\pi$
$654$	−18.8090	−0.735491
$655$	−43.4857	−1.69913
$656$	−12.6172	−0.492617
$657$	−9.57442	−0.373534
$658$	−1.12392	−0.0438150
$659$	7.27050	0.283219	0.141609	−	0.989923i	$-0.454772\pi$
$659$	7.27050	0.283219	0.141609	+	0.989923i	$0.454772\pi$
$660$	−7.73128	−0.300940
$661$	−14.1712	−0.551195	−0.275597	−	0.961273i	$-0.588876\pi$
$661$	−14.1712	−0.551195	−0.275597	+	0.961273i	$0.588876\pi$
$662$	−19.3054	−0.750325
$663$	7.28473	0.282915
$664$	9.35341	0.362983
$665$	−18.9958	−0.736625
$666$	−7.56623	−0.293185
$667$	50.5121	1.95584
$668$	−11.8008	−0.456588
$669$	11.4805	0.443860
$670$	6.74176	0.260457
$671$	−7.96926	−0.307650
$672$	0.801879	0.0309332
$673$	40.3104	1.55385	0.776925	−	0.629593i	$-0.216778\pi$
$673$	40.3104	1.55385	0.776925	+	0.629593i	$0.216778\pi$
$674$	−7.12603	−0.274484
$675$	8.61644	0.331647
$676$	1.00000	0.0384615
$677$	28.8923	1.11042	0.555210	−	0.831710i	$-0.312638\pi$
$677$	28.8923	1.11042	0.555210	+	0.831710i	$0.312638\pi$
$678$	8.04354	0.308910
$679$	−8.38900	−0.321940
$680$	26.8810	1.03084
$681$	−6.32844	−0.242506
$682$	−10.3123	−0.394878
$683$	−11.9995	−0.459148	−0.229574	−	0.973291i	$-0.573733\pi$
$683$	−11.9995	−0.459148	−0.229574	+	0.973291i	$0.573733\pi$
$684$	6.41973	0.245464
$685$	47.8579	1.82855
$686$	−10.7107	−0.408936
$687$	−1.09206	−0.0416648
$688$	−1.69130	−0.0644802
$689$	−10.3169	−0.393043
$690$	22.8221	0.868823
$691$	−16.3492	−0.621954	−0.310977	−	0.950417i	$-0.600656\pi$
$691$	−16.3492	−0.621954	−0.310977	+	0.950417i	$0.600656\pi$
$692$	−24.7683	−0.941549
$693$	1.68007	0.0638207
$694$	−33.6190	−1.27616
$695$	64.1894	2.43484
$696$	8.16717	0.309576
$697$	91.9126	3.48144
$698$	−0.865602	−0.0327635
$699$	−6.15204	−0.232691
$700$	−6.90934	−0.261149
$701$	33.1110	1.25059	0.625293	−	0.780390i	$-0.284980\pi$
$701$	33.1110	1.25059	0.625293	+	0.780390i	$0.284980\pi$
$702$	1.00000	0.0377426
$703$	48.5731	1.83197
$704$	−2.09517	−0.0789648
$705$	−5.17200	−0.194789
$706$	−32.6448	−1.22860
$707$	−4.30638	−0.161958
$708$	11.6675	0.438492
$709$	−44.6576	−1.67715	−0.838576	−	0.544784i	$-0.816612\pi$
$709$	−44.6576	−1.67715	−0.838576	+	0.544784i	$0.816612\pi$
$710$	46.1562	1.73221
$711$	−16.2346	−0.608845
$712$	−3.88578	−0.145626
$713$	30.4410	1.14003
$714$	−5.84147	−0.218612
$715$	7.73128	0.289133
$716$	−13.6899	−0.511616
$717$	−3.86903	−0.144491
$718$	13.5526	0.505777
$719$	−33.5215	−1.25014	−0.625070	−	0.780568i	$-0.714930\pi$
$719$	−33.5215	−1.25014	−0.625070	+	0.780568i	$0.714930\pi$
$720$	3.69005	0.137520
$721$	−0.801879	−0.0298635
$722$	−22.2129	−0.826678
$723$	8.24640	0.306687
$724$	−26.3059	−0.977652
$725$	−70.3719	−2.61355
$726$	6.61026	0.245330
$727$	2.63467	0.0977143	0.0488572	−	0.998806i	$-0.484442\pi$
$727$	2.63467	0.0977143	0.0488572	+	0.998806i	$0.484442\pi$
$728$	−0.801879	−0.0297196
$729$	1.00000	0.0370370
$730$	35.3301	1.30762
$731$	12.3207	0.455696
$732$	3.80363	0.140586
$733$	3.95177	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$733$	3.95177	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$734$	3.18662	0.117620
$735$	−23.4576	−0.865246
$736$	6.18478	0.227974
$737$	3.82791	0.141003
$738$	12.6172	0.464444
$739$	−45.8517	−1.68668	−0.843342	−	0.537377i	$-0.819415\pi$
$739$	−45.8517	−1.68668	−0.843342	+	0.537377i	$0.819415\pi$
$740$	27.9197	1.02635
$741$	−6.41973	−0.235835
$742$	8.27291	0.303708
$743$	25.6074	0.939444	0.469722	−	0.882814i	$-0.344354\pi$
$743$	25.6074	0.939444	0.469722	+	0.882814i	$0.344354\pi$
$744$	4.92193	0.180447
$745$	48.3185	1.77025
$746$	−12.2027	−0.446774
$747$	−9.35341	−0.342223
$748$	15.2628	0.558062
$749$	4.68696	0.171258
$750$	−13.3448	−0.487285
$751$	−38.7288	−1.41323	−0.706617	−	0.707597i	$-0.749779\pi$
$751$	−38.7288	−1.41323	−0.706617	+	0.707597i	$0.749779\pi$
$752$	−1.40161	−0.0511114
$753$	−20.8393	−0.759427
$754$	−8.16717	−0.297431
$755$	−73.9137	−2.68999
$756$	−0.801879	−0.0291641
$757$	−10.4638	−0.380313	−0.190156	−	0.981754i	$-0.560899\pi$
$757$	−10.4638	−0.380313	−0.190156	+	0.981754i	$0.560899\pi$
$758$	4.04966	0.147090
$759$	12.9582	0.470352
$760$	−23.6891	−0.859293
$761$	−21.4493	−0.777536	−0.388768	−	0.921336i	$-0.627099\pi$
$761$	−21.4493	−0.777536	−0.388768	+	0.921336i	$0.627099\pi$
$762$	−6.32994	−0.229310
$763$	−15.0826	−0.546025
$764$	27.0533	0.978753
$765$	−26.8810	−0.971884
$766$	8.52524	0.308030
$767$	−11.6675	−0.421290
$768$	1.00000	0.0360844
$769$	26.1613	0.943401	0.471701	−	0.881759i	$-0.343640\pi$
$769$	26.1613	0.943401	0.471701	+	0.881759i	$0.343640\pi$
$770$	−6.19955	−0.223416
$771$	16.9120	0.609072
$772$	−6.88418	−0.247767
$773$	27.5564	0.991134	0.495567	−	0.868570i	$-0.334960\pi$
$773$	27.5564	0.991134	0.495567	+	0.868570i	$0.334960\pi$
$774$	1.69130	0.0607925
$775$	−42.4095	−1.52339
$776$	−10.4617	−0.375552
$777$	−6.06720	−0.217660
$778$	2.55183	0.0914875
$779$	−80.9987	−2.90208
$780$	−3.69005	−0.132125
$781$	26.2070	0.937761
$782$	−45.0544	−1.61114
$783$	−8.16717	−0.291871
$784$	−6.35699	−0.227035
$785$	−68.5432	−2.44641
$786$	11.7846	0.420343
$787$	23.2778	0.829763	0.414882	−	0.909875i	$-0.363823\pi$
$787$	23.2778	0.829763	0.414882	+	0.909875i	$0.363823\pi$
$788$	−12.1767	−0.433779
$789$	18.1348	0.645617
$790$	59.9065	2.13138
$791$	6.44995	0.229334
$792$	2.09517	0.0744487
$793$	−3.80363	−0.135071
$794$	15.6618	0.555815
$795$	38.0699	1.35020
$796$	6.86514	0.243328
$797$	11.9373	0.422839	0.211420	−	0.977395i	$-0.432191\pi$
$797$	11.9373	0.422839	0.211420	+	0.977395i	$0.432191\pi$
$798$	5.14784	0.182232
$799$	10.2103	0.361216
$800$	−8.61644	−0.304637
$801$	3.88578	0.137297
$802$	10.6910	0.377512
$803$	20.0601	0.707904
$804$	−1.82701	−0.0644338
$805$	18.3006	0.645010
$806$	−4.92193	−0.173368
$807$	0.636581	0.0224087
$808$	−5.37036	−0.188929
$809$	46.2084	1.62460	0.812300	−	0.583239i	$-0.198215\pi$
$809$	46.2084	1.62460	0.812300	+	0.583239i	$0.198215\pi$
$810$	−3.69005	−0.129655
$811$	−23.2023	−0.814741	−0.407371	−	0.913263i	$-0.633554\pi$
$811$	−23.2023	−0.814741	−0.407371	+	0.913263i	$0.633554\pi$
$812$	6.54908	0.229828
$813$	−6.65381	−0.233359
$814$	15.8525	0.555631
$815$	14.0787	0.493157
$816$	−7.28473	−0.255017
$817$	−10.8577	−0.379862
$818$	−14.4409	−0.504913
$819$	0.801879	0.0280199
$820$	−46.5579	−1.62587
$821$	14.9328	0.521157	0.260579	−	0.965453i	$-0.416087\pi$
$821$	14.9328	0.521157	0.260579	+	0.965453i	$0.416087\pi$
$822$	−12.9694	−0.452361
$823$	−17.3180	−0.603667	−0.301833	−	0.953361i	$-0.597599\pi$
$823$	−17.3180	−0.603667	−0.301833	+	0.953361i	$0.597599\pi$
$824$	−1.00000	−0.0348367
$825$	−18.0529	−0.628522
$826$	9.35594	0.325535
$827$	−19.6705	−0.684010	−0.342005	−	0.939698i	$-0.611106\pi$
$827$	−19.6705	−0.684010	−0.342005	+	0.939698i	$0.611106\pi$
$828$	−6.18478	−0.214936
$829$	−21.9011	−0.760658	−0.380329	−	0.924851i	$-0.624189\pi$
$829$	−21.9011	−0.760658	−0.380329	+	0.924851i	$0.624189\pi$
$830$	34.5145	1.19802
$831$	−18.6247	−0.646085
$832$	−1.00000	−0.0346688
$833$	46.3090	1.60451
$834$	−17.3953	−0.602349
$835$	−43.5457	−1.50696
$836$	−13.4504	−0.465193
$837$	−4.92193	−0.170127
$838$	14.0266	0.484540
$839$	−57.0194	−1.96853	−0.984264	−	0.176705i	$-0.943456\pi$
$839$	−57.0194	−1.96853	−0.984264	+	0.176705i	$0.943456\pi$
$840$	2.95897	0.102094
$841$	37.7026	1.30009
$842$	−21.9429	−0.756201
$843$	−15.8147	−0.544688
$844$	−25.0346	−0.861727
$845$	3.69005	0.126941
$846$	1.40161	0.0481883
$847$	5.30063	0.182132
$848$	10.3169	0.354284
$849$	1.14296	0.0392264
$850$	62.7685	2.15294
$851$	−46.7954	−1.60413
$852$	−12.5083	−0.428527
$853$	29.7693	1.01928	0.509641	−	0.860387i	$-0.329778\pi$
$853$	29.7693	1.01928	0.509641	+	0.860387i	$0.329778\pi$
$854$	3.05005	0.104371
$855$	23.6891	0.810150
$856$	5.84497	0.199777
$857$	14.0815	0.481014	0.240507	−	0.970647i	$-0.422686\pi$
$857$	14.0815	0.481014	0.240507	+	0.970647i	$0.422686\pi$
$858$	−2.09517	−0.0715280
$859$	−36.9848	−1.26190	−0.630952	−	0.775822i	$-0.717335\pi$
$859$	−36.9848	−1.26190	−0.630952	+	0.775822i	$0.717335\pi$
$860$	−6.24097	−0.212815
$861$	10.1174	0.344801
$862$	−1.88113	−0.0640715
$863$	−39.8626	−1.35694	−0.678470	−	0.734628i	$-0.737357\pi$
$863$	−39.8626	−1.35694	−0.678470	+	0.734628i	$0.737357\pi$
$864$	−1.00000	−0.0340207
$865$	−91.3961	−3.10756
$866$	−15.2492	−0.518190
$867$	36.0673	1.22491
$868$	3.94679	0.133963
$869$	34.0143	1.15386
$870$	30.1372	1.02175
$871$	1.82701	0.0619060
$872$	−18.8090	−0.636954
$873$	10.4617	0.354074
$874$	39.7046	1.34303
$875$	−10.7009	−0.361758
$876$	−9.57442	−0.323490
$877$	56.4669	1.90675	0.953375	−	0.301787i	$-0.0975831\pi$
$877$	56.4669	1.90675	0.953375	+	0.301787i	$0.0975831\pi$
$878$	−38.1006	−1.28583
$879$	19.8586	0.669815
$880$	−7.73128	−0.260621
$881$	13.1832	0.444153	0.222077	−	0.975029i	$-0.428716\pi$
$881$	13.1832	0.444153	0.222077	+	0.975029i	$0.428716\pi$
$882$	6.35699	0.214051
$883$	−36.4169	−1.22553	−0.612764	−	0.790266i	$-0.709942\pi$
$883$	−36.4169	−1.22553	−0.612764	+	0.790266i	$0.709942\pi$
$884$	7.28473	0.245012
$885$	43.0537	1.44723
$886$	2.12579	0.0714173
$887$	1.43736	0.0482619	0.0241310	−	0.999709i	$-0.492318\pi$
$887$	1.43736	0.0482619	0.0241310	+	0.999709i	$0.492318\pi$
$888$	−7.56623	−0.253906
$889$	−5.07585	−0.170238
$890$	−14.3387	−0.480635
$891$	−2.09517	−0.0701909
$892$	11.4805	0.384394
$893$	−8.99795	−0.301105
$894$	−13.0943	−0.437938
$895$	−50.5164	−1.68858
$896$	0.801879	0.0267889
$897$	6.18478	0.206504
$898$	22.5617	0.752895
$899$	40.1982	1.34069
$900$	8.61644	0.287215
$901$	−75.1559	−2.50381
$902$	−26.4351	−0.880193
$903$	1.35622	0.0451321
$904$	8.04354	0.267524
$905$	−97.0701	−3.22672
$906$	20.0305	0.665470
$907$	−32.2421	−1.07058	−0.535290	−	0.844668i	$-0.679798\pi$
$907$	−32.2421	−1.07058	−0.535290	+	0.844668i	$0.679798\pi$
$908$	−6.32844	−0.210017
$909$	5.37036	0.178124
$910$	−2.95897	−0.0980889
$911$	9.72458	0.322190	0.161095	−	0.986939i	$-0.448497\pi$
$911$	9.72458	0.322190	0.161095	+	0.986939i	$0.448497\pi$
$912$	6.41973	0.212578
$913$	19.5970	0.648566
$914$	28.9729	0.958338
$915$	14.0356	0.464002
$916$	−1.09206	−0.0360828
$917$	9.44983	0.312061
$918$	7.28473	0.240432
$919$	12.4522	0.410760	0.205380	−	0.978682i	$-0.434157\pi$
$919$	12.4522	0.410760	0.205380	+	0.978682i	$0.434157\pi$
$920$	22.8221	0.752423
$921$	14.4202	0.475161
$922$	26.4125	0.869851
$923$	12.5083	0.411715
$924$	1.68007	0.0552704
$925$	65.1940	2.14356
$926$	32.9808	1.08382
$927$	1.00000	0.0328443
$928$	8.16717	0.268100
$929$	4.97961	0.163376	0.0816878	−	0.996658i	$-0.473969\pi$
$929$	4.97961	0.163376	0.0816878	+	0.996658i	$0.473969\pi$
$930$	18.1621	0.595560
$931$	−40.8101	−1.33750
$932$	−6.15204	−0.201517
$933$	−16.9322	−0.554336
$934$	−22.2234	−0.727172
$935$	56.3203	1.84187
$936$	1.00000	0.0326860
$937$	−3.07753	−0.100539	−0.0502693	−	0.998736i	$-0.516008\pi$
$937$	−3.07753	−0.100539	−0.0502693	+	0.998736i	$0.516008\pi$
$938$	−1.46504	−0.0478354
$939$	8.02812	0.261988
$940$	−5.17200	−0.168692
$941$	−40.1334	−1.30831	−0.654156	−	0.756360i	$-0.726976\pi$
$941$	−40.1334	−1.30831	−0.654156	+	0.756360i	$0.726976\pi$
$942$	18.5752	0.605212
$943$	78.0343	2.54115
$944$	11.6675	0.379746
$945$	−2.95897	−0.0962553
$946$	−3.54356	−0.115211
$947$	0.788239	0.0256143	0.0128072	−	0.999918i	$-0.495923\pi$
$947$	0.788239	0.0256143	0.0128072	+	0.999918i	$0.495923\pi$
$948$	−16.2346	−0.527276
$949$	9.57442	0.310799
$950$	−55.3152	−1.79466
$951$	26.3844	0.855572
$952$	−5.84147	−0.189323
$953$	−50.7289	−1.64327	−0.821636	−	0.570013i	$-0.806938\pi$
$953$	−50.7289	−1.64327	−0.821636	+	0.570013i	$0.806938\pi$
$954$	−10.3169	−0.334022
$955$	99.8278	3.23035
$956$	−3.86903	−0.125133
$957$	17.1116	0.553140
$958$	−12.2928	−0.397163
$959$	−10.3999	−0.335831
$960$	3.69005	0.119096
$961$	−6.77463	−0.218536
$962$	7.56623	0.243945
$963$	−5.84497	−0.188351
$964$	8.24640	0.265599
$965$	−25.4030	−0.817750
$966$	−4.95944	−0.159567
$967$	−30.7771	−0.989724	−0.494862	−	0.868972i	$-0.664781\pi$
$967$	−30.7771	−0.989724	−0.494862	+	0.868972i	$0.664781\pi$
$968$	6.61026	0.212462
$969$	−46.7660	−1.50234
$970$	−38.6041	−1.23950
$971$	−34.1303	−1.09529	−0.547647	−	0.836709i	$-0.684476\pi$
$971$	−34.1303	−1.09529	−0.547647	+	0.836709i	$0.684476\pi$
$972$	1.00000	0.0320750
$973$	−13.9489	−0.447181
$974$	−11.6049	−0.371844
$975$	−8.61644	−0.275947
$976$	3.80363	0.121751
$977$	−7.28451	−0.233052	−0.116526	−	0.993188i	$-0.537176\pi$
$977$	−7.28451	−0.233052	−0.116526	+	0.993188i	$0.537176\pi$
$978$	−3.81533	−0.122001
$979$	−8.14138	−0.260200
$980$	−23.4576	−0.749325
$981$	18.8090	0.600526
$982$	−11.2148	−0.357877
$983$	−45.7382	−1.45882	−0.729411	−	0.684076i	$-0.760206\pi$
$983$	−45.7382	−1.45882	−0.729411	+	0.684076i	$0.760206\pi$
$984$	12.6172	0.402220
$985$	−44.9328	−1.43168
$986$	−59.4956	−1.89473
$987$	1.12392	0.0357748
$988$	−6.41973	−0.204239
$989$	10.4603	0.332619
$990$	7.73128	0.245716
$991$	19.9232	0.632882	0.316441	−	0.948612i	$-0.397512\pi$
$991$	19.9232	0.632882	0.316441	+	0.948612i	$0.397512\pi$
$992$	4.92193	0.156271
$993$	19.3054	0.612637
$994$	−10.0301	−0.318137
$995$	25.3327	0.803100
$996$	−9.35341	−0.296374
$997$	47.5548	1.50608	0.753038	−	0.657977i	$-0.228588\pi$
$997$	47.5548	1.50608	0.753038	+	0.657977i	$0.228588\pi$
$998$	8.47929	0.268407
$999$	7.56623	0.239385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.14	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.14	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.69005 q^{5} -1.00000 q^{6} -0.801879 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.69005 q^{5} -1.00000 q^{6} -0.801879 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.69005 q^{10} -2.09517 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.801879 q^{14} +3.69005 q^{15} +1.00000 q^{16} -7.28473 q^{17} -1.00000 q^{18} +6.41973 q^{19} +3.69005 q^{20} -0.801879 q^{21} +2.09517 q^{22} -6.18478 q^{23} -1.00000 q^{24} +8.61644 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.801879 q^{28} -8.16717 q^{29} -3.69005 q^{30} -4.92193 q^{31} -1.00000 q^{32} -2.09517 q^{33} +7.28473 q^{34} -2.95897 q^{35} +1.00000 q^{36} +7.56623 q^{37} -6.41973 q^{38} -1.00000 q^{39} -3.69005 q^{40} -12.6172 q^{41} +0.801879 q^{42} -1.69130 q^{43} -2.09517 q^{44} +3.69005 q^{45} +6.18478 q^{46} -1.40161 q^{47} +1.00000 q^{48} -6.35699 q^{49} -8.61644 q^{50} -7.28473 q^{51} -1.00000 q^{52} +10.3169 q^{53} -1.00000 q^{54} -7.73128 q^{55} +0.801879 q^{56} +6.41973 q^{57} +8.16717 q^{58} +11.6675 q^{59} +3.69005 q^{60} +3.80363 q^{61} +4.92193 q^{62} -0.801879 q^{63} +1.00000 q^{64} -3.69005 q^{65} +2.09517 q^{66} -1.82701 q^{67} -7.28473 q^{68} -6.18478 q^{69} +2.95897 q^{70} -12.5083 q^{71} -1.00000 q^{72} -9.57442 q^{73} -7.56623 q^{74} +8.61644 q^{75} +6.41973 q^{76} +1.68007 q^{77} +1.00000 q^{78} -16.2346 q^{79} +3.69005 q^{80} +1.00000 q^{81} +12.6172 q^{82} -9.35341 q^{83} -0.801879 q^{84} -26.8810 q^{85} +1.69130 q^{86} -8.16717 q^{87} +2.09517 q^{88} +3.88578 q^{89} -3.69005 q^{90} +0.801879 q^{91} -6.18478 q^{92} -4.92193 q^{93} +1.40161 q^{94} +23.6891 q^{95} -1.00000 q^{96} +10.4617 q^{97} +6.35699 q^{98} -2.09517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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