LMFDB - Embedded newform 4334.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.167063$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.167063 q^{3} +1.00000 q^{4} -1.86132 q^{5} +0.167063 q^{6} -4.61549 q^{7} -1.00000 q^{8} -2.97209 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.167063 q^{3} +1.00000 q^{4} -1.86132 q^{5} +0.167063 q^{6} -4.61549 q^{7} -1.00000 q^{8} -2.97209 q^{9} +1.86132 q^{10} +1.00000 q^{11} -0.167063 q^{12} +0.766750 q^{13} +4.61549 q^{14} +0.310957 q^{15} +1.00000 q^{16} +3.09252 q^{17} +2.97209 q^{18} +2.62682 q^{19} -1.86132 q^{20} +0.771075 q^{21} -1.00000 q^{22} +7.16942 q^{23} +0.167063 q^{24} -1.53548 q^{25} -0.766750 q^{26} +0.997713 q^{27} -4.61549 q^{28} -2.94527 q^{29} -0.310957 q^{30} -0.0691519 q^{31} -1.00000 q^{32} -0.167063 q^{33} -3.09252 q^{34} +8.59091 q^{35} -2.97209 q^{36} +6.85349 q^{37} -2.62682 q^{38} -0.128095 q^{39} +1.86132 q^{40} +0.348403 q^{41} -0.771075 q^{42} -2.62794 q^{43} +1.00000 q^{44} +5.53202 q^{45} -7.16942 q^{46} +0.00342972 q^{47} -0.167063 q^{48} +14.3027 q^{49} +1.53548 q^{50} -0.516644 q^{51} +0.766750 q^{52} -8.61819 q^{53} -0.997713 q^{54} -1.86132 q^{55} +4.61549 q^{56} -0.438843 q^{57} +2.94527 q^{58} +4.25981 q^{59} +0.310957 q^{60} +14.7030 q^{61} +0.0691519 q^{62} +13.7176 q^{63} +1.00000 q^{64} -1.42717 q^{65} +0.167063 q^{66} -5.35030 q^{67} +3.09252 q^{68} -1.19774 q^{69} -8.59091 q^{70} -4.54261 q^{71} +2.97209 q^{72} +12.4711 q^{73} -6.85349 q^{74} +0.256521 q^{75} +2.62682 q^{76} -4.61549 q^{77} +0.128095 q^{78} -2.65657 q^{79} -1.86132 q^{80} +8.74959 q^{81} -0.348403 q^{82} +0.0519205 q^{83} +0.771075 q^{84} -5.75617 q^{85} +2.62794 q^{86} +0.492044 q^{87} -1.00000 q^{88} -16.0406 q^{89} -5.53202 q^{90} -3.53892 q^{91} +7.16942 q^{92} +0.0115527 q^{93} -0.00342972 q^{94} -4.88935 q^{95} +0.167063 q^{96} -1.12190 q^{97} -14.3027 q^{98} -2.97209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.167063	−0.0964536	−0.0482268	−	0.998836i	$-0.515357\pi$
$3$	−0.167063	−0.0964536	−0.0482268	+	0.998836i	$0.515357\pi$
$4$	1.00000	0.500000
$5$	−1.86132	−0.832408	−0.416204	−	0.909271i	$-0.636640\pi$
$5$	−1.86132	−0.832408	−0.416204	+	0.909271i	$0.636640\pi$
$6$	0.167063	0.0682030
$7$	−4.61549	−1.74449	−0.872245	−	0.489069i	$-0.837337\pi$
$7$	−4.61549	−1.74449	−0.872245	+	0.489069i	$0.837337\pi$
$8$	−1.00000	−0.353553
$9$	−2.97209	−0.990697
$10$	1.86132	0.588602
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.167063	−0.0482268
$13$	0.766750	0.212658	0.106329	−	0.994331i	$-0.466090\pi$
$13$	0.766750	0.212658	0.106329	+	0.994331i	$0.466090\pi$
$14$	4.61549	1.23354
$15$	0.310957	0.0802888
$16$	1.00000	0.250000
$17$	3.09252	0.750046	0.375023	−	0.927016i	$-0.377635\pi$
$17$	3.09252	0.750046	0.375023	+	0.927016i	$0.377635\pi$
$18$	2.97209	0.700528
$19$	2.62682	0.602633	0.301317	−	0.953524i	$-0.402574\pi$
$19$	2.62682	0.602633	0.301317	+	0.953524i	$0.402574\pi$
$20$	−1.86132	−0.416204
$21$	0.771075	0.168262
$22$	−1.00000	−0.213201
$23$	7.16942	1.49493	0.747463	−	0.664303i	$-0.231272\pi$
$23$	7.16942	1.49493	0.747463	+	0.664303i	$0.231272\pi$
$24$	0.167063	0.0341015
$25$	−1.53548	−0.307096
$26$	−0.766750	−0.150372
$27$	0.997713	0.192010
$28$	−4.61549	−0.872245
$29$	−2.94527	−0.546923	−0.273461	−	0.961883i	$-0.588169\pi$
$29$	−2.94527	−0.546923	−0.273461	+	0.961883i	$0.588169\pi$
$30$	−0.310957	−0.0567728
$31$	−0.0691519	−0.0124200	−0.00621002	−	0.999981i	$-0.501977\pi$
$31$	−0.0691519	−0.0124200	−0.00621002	+	0.999981i	$0.501977\pi$
$32$	−1.00000	−0.176777
$33$	−0.167063	−0.0290819
$34$	−3.09252	−0.530362
$35$	8.59091	1.45213
$36$	−2.97209	−0.495348
$37$	6.85349	1.12671	0.563353	−	0.826216i	$-0.309511\pi$
$37$	6.85349	1.12671	0.563353	+	0.826216i	$0.309511\pi$
$38$	−2.62682	−0.426126
$39$	−0.128095	−0.0205117
$40$	1.86132	0.294301
$41$	0.348403	0.0544115	0.0272057	−	0.999630i	$-0.491339\pi$
$41$	0.348403	0.0544115	0.0272057	+	0.999630i	$0.491339\pi$
$42$	−0.771075	−0.118979
$43$	−2.62794	−0.400757	−0.200379	−	0.979719i	$-0.564217\pi$
$43$	−2.62794	−0.400757	−0.200379	+	0.979719i	$0.564217\pi$
$44$	1.00000	0.150756
$45$	5.53202	0.824664
$46$	−7.16942	−1.05707
$47$	0.00342972	0.000500277 0	0.000250138	−	1.00000i	$-0.499920\pi$
$47$	0.00342972	0.000500277 0	0.000250138		1.00000i	$0.499920\pi$
$48$	−0.167063	−0.0241134
$49$	14.3027	2.04325
$50$	1.53548	0.217150
$51$	−0.516644	−0.0723446
$52$	0.766750	0.106329
$53$	−8.61819	−1.18380	−0.591900	−	0.806011i	$-0.701622\pi$
$53$	−8.61819	−1.18380	−0.591900	+	0.806011i	$0.701622\pi$
$54$	−0.997713	−0.135772
$55$	−1.86132	−0.250981
$56$	4.61549	0.616770
$57$	−0.438843	−0.0581262
$58$	2.94527	0.386733
$59$	4.25981	0.554580	0.277290	−	0.960786i	$-0.410564\pi$
$59$	4.25981	0.554580	0.277290	+	0.960786i	$0.410564\pi$
$60$	0.310957	0.0401444
$61$	14.7030	1.88252	0.941261	−	0.337679i	$-0.109642\pi$
$61$	14.7030	1.88252	0.941261	+	0.337679i	$0.109642\pi$
$62$	0.0691519	0.00878230
$63$	13.7176	1.72826
$64$	1.00000	0.125000
$65$	−1.42717	−0.177018
$66$	0.167063	0.0205640
$67$	−5.35030	−0.653643	−0.326822	−	0.945086i	$-0.605978\pi$
$67$	−5.35030	−0.653643	−0.326822	+	0.945086i	$0.605978\pi$
$68$	3.09252	0.375023
$69$	−1.19774	−0.144191
$70$	−8.59091	−1.02681
$71$	−4.54261	−0.539109	−0.269554	−	0.962985i	$-0.586876\pi$
$71$	−4.54261	−0.539109	−0.269554	+	0.962985i	$0.586876\pi$
$72$	2.97209	0.350264
$73$	12.4711	1.45963	0.729815	−	0.683645i	$-0.239606\pi$
$73$	12.4711	1.45963	0.729815	+	0.683645i	$0.239606\pi$
$74$	−6.85349	−0.796702
$75$	0.256521	0.0296205
$76$	2.62682	0.301317
$77$	−4.61549	−0.525984
$78$	0.128095	0.0145039
$79$	−2.65657	−0.298888	−0.149444	−	0.988770i	$-0.547748\pi$
$79$	−2.65657	−0.298888	−0.149444	+	0.988770i	$0.547748\pi$
$80$	−1.86132	−0.208102
$81$	8.74959	0.972177
$82$	−0.348403	−0.0384747
$83$	0.0519205	0.00569902	0.00284951	−	0.999996i	$-0.499093\pi$
$83$	0.0519205	0.00569902	0.00284951	+	0.999996i	$0.499093\pi$
$84$	0.771075	0.0841312
$85$	−5.75617	−0.624344
$86$	2.62794	0.283378
$87$	0.492044	0.0527527
$88$	−1.00000	−0.106600
$89$	−16.0406	−1.70031	−0.850153	−	0.526536i	$-0.823490\pi$
$89$	−16.0406	−1.70031	−0.850153	+	0.526536i	$0.823490\pi$
$90$	−5.53202	−0.583126
$91$	−3.53892	−0.370980
$92$	7.16942	0.747463
$93$	0.0115527	0.00119796
$94$	−0.00342972	−0.000353749 0
$95$	−4.88935	−0.501637
$96$	0.167063	0.0170508
$97$	−1.12190	−0.113912	−0.0569560	−	0.998377i	$-0.518139\pi$
$97$	−1.12190	−0.113912	−0.0569560	+	0.998377i	$0.518139\pi$
$98$	−14.3027	−1.44479
$99$	−2.97209	−0.298706
$100$	−1.53548	−0.153548
$101$	4.94451	0.491997	0.245999	−	0.969270i	$-0.420884\pi$
$101$	4.94451	0.491997	0.245999	+	0.969270i	$0.420884\pi$
$102$	0.516644	0.0511554
$103$	1.86370	0.183635	0.0918177	−	0.995776i	$-0.470732\pi$
$103$	1.86370	0.183635	0.0918177	+	0.995776i	$0.470732\pi$
$104$	−0.766750	−0.0751860
$105$	−1.43522	−0.140063
$106$	8.61819	0.837073
$107$	−0.00496111	−0.000479609 0	−0.000239805	−	1.00000i	$-0.500076\pi$
$107$	−0.00496111	−0.000479609 0	−0.000239805		1.00000i	$0.500076\pi$
$108$	0.997713	0.0960050
$109$	−12.9210	−1.23761	−0.618805	−	0.785544i	$-0.712383\pi$
$109$	−12.9210	−1.23761	−0.618805	+	0.785544i	$0.712383\pi$
$110$	1.86132	0.177470
$111$	−1.14496	−0.108675
$112$	−4.61549	−0.436122
$113$	−9.44185	−0.888214	−0.444107	−	0.895974i	$-0.646479\pi$
$113$	−9.44185	−0.888214	−0.444107	+	0.895974i	$0.646479\pi$
$114$	0.438843	0.0411014
$115$	−13.3446	−1.24439
$116$	−2.94527	−0.273461
$117$	−2.27885	−0.210680
$118$	−4.25981	−0.392148
$119$	−14.2735	−1.30845
$120$	−0.310957	−0.0283864
$121$	1.00000	0.0909091
$122$	−14.7030	−1.33114
$123$	−0.0582052	−0.00524819
$124$	−0.0691519	−0.00621002
$125$	12.1646	1.08804
$126$	−13.7176	−1.22206
$127$	6.88360	0.610821	0.305410	−	0.952221i	$-0.401206\pi$
$127$	6.88360	0.610821	0.305410	+	0.952221i	$0.401206\pi$
$128$	−1.00000	−0.0883883
$129$	0.439031	0.0386545
$130$	1.42717	0.125171
$131$	−14.9540	−1.30654	−0.653270	−	0.757125i	$-0.726604\pi$
$131$	−14.9540	−1.30654	−0.653270	+	0.757125i	$0.726604\pi$
$132$	−0.167063	−0.0145409
$133$	−12.1240	−1.05129
$134$	5.35030	0.462195
$135$	−1.85706	−0.159831
$136$	−3.09252	−0.265181
$137$	−4.15741	−0.355191	−0.177596	−	0.984104i	$-0.556832\pi$
$137$	−4.15741	−0.355191	−0.177596	+	0.984104i	$0.556832\pi$
$138$	1.19774	0.101959
$139$	−9.49264	−0.805155	−0.402578	−	0.915386i	$-0.631886\pi$
$139$	−9.49264	−0.805155	−0.402578	+	0.915386i	$0.631886\pi$
$140$	8.59091	0.726064
$141$	−0.000572979 0	−4.82535e−5 0
$142$	4.54261	0.381207
$143$	0.766750	0.0641188
$144$	−2.97209	−0.247674
$145$	5.48209	0.455263
$146$	−12.4711	−1.03211
$147$	−2.38945	−0.197078
$148$	6.85349	0.563353
$149$	9.12216	0.747316	0.373658	−	0.927567i	$-0.378103\pi$
$149$	9.12216	0.747316	0.373658	+	0.927567i	$0.378103\pi$
$150$	−0.256521	−0.0209449
$151$	−17.1985	−1.39959	−0.699796	−	0.714343i	$-0.746726\pi$
$151$	−17.1985	−1.39959	−0.699796	+	0.714343i	$0.746726\pi$
$152$	−2.62682	−0.213063
$153$	−9.19124	−0.743068
$154$	4.61549	0.371927
$155$	0.128714	0.0103386
$156$	−0.128095	−0.0102558
$157$	3.61251	0.288310	0.144155	−	0.989555i	$-0.453954\pi$
$157$	3.61251	0.288310	0.144155	+	0.989555i	$0.453954\pi$
$158$	2.65657	0.211345
$159$	1.43978	0.114182
$160$	1.86132	0.147150
$161$	−33.0903	−2.60788
$162$	−8.74959	−0.687433
$163$	−8.16062	−0.639189	−0.319594	−	0.947554i	$-0.603547\pi$
$163$	−8.16062	−0.639189	−0.319594	+	0.947554i	$0.603547\pi$
$164$	0.348403	0.0272057
$165$	0.310957	0.0242080
$166$	−0.0519205	−0.00402981
$167$	6.65523	0.514998	0.257499	−	0.966279i	$-0.417102\pi$
$167$	6.65523	0.514998	0.257499	+	0.966279i	$0.417102\pi$
$168$	−0.771075	−0.0594897
$169$	−12.4121	−0.954777
$170$	5.75617	0.441478
$171$	−7.80714	−0.597027
$172$	−2.62794	−0.200379
$173$	3.45011	0.262307	0.131153	−	0.991362i	$-0.458132\pi$
$173$	3.45011	0.262307	0.131153	+	0.991362i	$0.458132\pi$
$174$	−0.492044	−0.0373018
$175$	7.08699	0.535726
$176$	1.00000	0.0753778
$177$	−0.711656	−0.0534913
$178$	16.0406	1.20230
$179$	10.6133	0.793278	0.396639	−	0.917975i	$-0.370177\pi$
$179$	10.6133	0.793278	0.396639	+	0.917975i	$0.370177\pi$
$180$	5.53202	0.412332
$181$	−7.53078	−0.559759	−0.279879	−	0.960035i	$-0.590294\pi$
$181$	−7.53078	−0.559759	−0.279879	+	0.960035i	$0.590294\pi$
$182$	3.53892	0.262322
$183$	−2.45632	−0.181576
$184$	−7.16942	−0.528536
$185$	−12.7565	−0.937880
$186$	−0.0115527	−0.000847085 0
$187$	3.09252	0.226147
$188$	0.00342972	0.000250138 0
$189$	−4.60493	−0.334959
$190$	4.88935	0.354711
$191$	11.2004	0.810433	0.405216	−	0.914221i	$-0.367196\pi$
$191$	11.2004	0.810433	0.405216	+	0.914221i	$0.367196\pi$
$192$	−0.167063	−0.0120567
$193$	−16.3513	−1.17699	−0.588497	−	0.808499i	$-0.700280\pi$
$193$	−16.3513	−1.17699	−0.588497	+	0.808499i	$0.700280\pi$
$194$	1.12190	0.0805480
$195$	0.238426	0.0170741
$196$	14.3027	1.02162
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.97209	0.211217
$199$	−23.9557	−1.69817	−0.849086	−	0.528255i	$-0.822846\pi$
$199$	−23.9557	−1.69817	−0.849086	+	0.528255i	$0.822846\pi$
$200$	1.53548	0.108575
$201$	0.893835	0.0630463
$202$	−4.94451	−0.347894
$203$	13.5939	0.954101
$204$	−0.516644	−0.0361723
$205$	−0.648491	−0.0452926
$206$	−1.86370	−0.129850
$207$	−21.3082	−1.48102
$208$	0.766750	0.0531645
$209$	2.62682	0.181701
$210$	1.43522	0.0990395
$211$	5.05236	0.347819	0.173910	−	0.984762i	$-0.444360\pi$
$211$	5.05236	0.347819	0.173910	+	0.984762i	$0.444360\pi$
$212$	−8.61819	−0.591900
$213$	0.758900	0.0519990
$214$	0.00496111	0.000339135 0
$215$	4.89144	0.333594
$216$	−0.997713	−0.0678858
$217$	0.319170	0.0216666
$218$	12.9210	0.875123
$219$	−2.08345	−0.140787
$220$	−1.86132	−0.125490
$221$	2.37119	0.159503
$222$	1.14496	0.0768448
$223$	6.94619	0.465151	0.232576	−	0.972578i	$-0.425285\pi$
$223$	6.94619	0.465151	0.232576	+	0.972578i	$0.425285\pi$
$224$	4.61549	0.308385
$225$	4.56359	0.304239
$226$	9.44185	0.628062
$227$	1.74932	0.116106	0.0580532	−	0.998313i	$-0.481511\pi$
$227$	1.74932	0.116106	0.0580532	+	0.998313i	$0.481511\pi$
$228$	−0.438843	−0.0290631
$229$	−23.1180	−1.52768	−0.763839	−	0.645407i	$-0.776688\pi$
$229$	−23.1180	−1.52768	−0.763839	+	0.645407i	$0.776688\pi$
$230$	13.3446	0.879916
$231$	0.771075	0.0507330
$232$	2.94527	0.193366
$233$	−12.5675	−0.823327	−0.411663	−	0.911336i	$-0.635052\pi$
$233$	−12.5675	−0.823327	−0.411663	+	0.911336i	$0.635052\pi$
$234$	2.27885	0.148973
$235$	−0.00638382	−0.000416434 0
$236$	4.25981	0.277290
$237$	0.443814	0.0288288
$238$	14.2735	0.925212
$239$	8.35587	0.540497	0.270248	−	0.962791i	$-0.412894\pi$
$239$	8.35587	0.540497	0.270248	+	0.962791i	$0.412894\pi$
$240$	0.310957	0.0200722
$241$	−3.63304	−0.234025	−0.117012	−	0.993130i	$-0.537332\pi$
$241$	−3.63304	−0.234025	−0.117012	+	0.993130i	$0.537332\pi$
$242$	−1.00000	−0.0642824
$243$	−4.45487	−0.285780
$244$	14.7030	0.941261
$245$	−26.6220	−1.70081
$246$	0.0582052	0.00371103
$247$	2.01411	0.128155
$248$	0.0691519	0.00439115
$249$	−0.00867398	−0.000549691 0
$250$	−12.1646	−0.769359
$251$	5.04598	0.318499	0.159250	−	0.987238i	$-0.449093\pi$
$251$	5.04598	0.318499	0.159250	+	0.987238i	$0.449093\pi$
$252$	13.7176	0.864130
$253$	7.16942	0.450737
$254$	−6.88360	−0.431915
$255$	0.961641	0.0602203
$256$	1.00000	0.0625000
$257$	13.5262	0.843744	0.421872	−	0.906655i	$-0.361373\pi$
$257$	13.5262	0.843744	0.421872	+	0.906655i	$0.361373\pi$
$258$	−0.439031	−0.0273329
$259$	−31.6322	−1.96553
$260$	−1.42717	−0.0885092
$261$	8.75361	0.541835
$262$	14.9540	0.923864
$263$	18.1268	1.11775	0.558873	−	0.829253i	$-0.311234\pi$
$263$	18.1268	1.11775	0.558873	+	0.829253i	$0.311234\pi$
$264$	0.167063	0.0102820
$265$	16.0412	0.985405
$266$	12.1240	0.743373
$267$	2.67979	0.164001
$268$	−5.35030	−0.326822
$269$	27.1232	1.65373	0.826866	−	0.562399i	$-0.190122\pi$
$269$	27.1232	1.65373	0.826866	+	0.562399i	$0.190122\pi$
$270$	1.85706	0.113017
$271$	11.8860	0.722024	0.361012	−	0.932561i	$-0.382431\pi$
$271$	11.8860	0.722024	0.361012	+	0.932561i	$0.382431\pi$
$272$	3.09252	0.187511
$273$	0.591222	0.0357824
$274$	4.15741	0.251158
$275$	−1.53548	−0.0925930
$276$	−1.19774	−0.0720956
$277$	−13.9047	−0.835450	−0.417725	−	0.908574i	$-0.637172\pi$
$277$	−13.9047	−0.835450	−0.417725	+	0.908574i	$0.637172\pi$
$278$	9.49264	0.569331
$279$	0.205526	0.0123045
$280$	−8.59091	−0.513405
$281$	12.2407	0.730218	0.365109	−	0.930965i	$-0.381032\pi$
$281$	12.2407	0.730218	0.365109	+	0.930965i	$0.381032\pi$
$282$	0.000572979 0	3.41204e−5 0
$283$	−13.3753	−0.795079	−0.397540	−	0.917585i	$-0.630136\pi$
$283$	−13.3753	−0.795079	−0.397540	+	0.917585i	$0.630136\pi$
$284$	−4.54261	−0.269554
$285$	0.816828	0.0483847
$286$	−0.766750	−0.0453389
$287$	−1.60805	−0.0949203
$288$	2.97209	0.175132
$289$	−7.43633	−0.437431
$290$	−5.48209	−0.321920
$291$	0.187428	0.0109872
$292$	12.4711	0.729815
$293$	12.5642	0.734010	0.367005	−	0.930219i	$-0.380383\pi$
$293$	12.5642	0.734010	0.367005	+	0.930219i	$0.380383\pi$
$294$	2.38945	0.139355
$295$	−7.92888	−0.461638
$296$	−6.85349	−0.398351
$297$	0.997713	0.0578932
$298$	−9.12216	−0.528432
$299$	5.49715	0.317908
$300$	0.256521	0.0148103
$301$	12.1292	0.699117
$302$	17.1985	0.989661
$303$	−0.826043	−0.0474549
$304$	2.62682	0.150658
$305$	−27.3670	−1.56703
$306$	9.19124	0.525428
$307$	−3.67654	−0.209831	−0.104916	−	0.994481i	$-0.533457\pi$
$307$	−3.67654	−0.209831	−0.104916	+	0.994481i	$0.533457\pi$
$308$	−4.61549	−0.262992
$309$	−0.311354	−0.0177123
$310$	−0.128714	−0.00731046
$311$	10.2199	0.579517	0.289758	−	0.957100i	$-0.406425\pi$
$311$	10.2199	0.579517	0.289758	+	0.957100i	$0.406425\pi$
$312$	0.128095	0.00725196
$313$	−12.1734	−0.688080	−0.344040	−	0.938955i	$-0.611796\pi$
$313$	−12.1734	−0.688080	−0.344040	+	0.938955i	$0.611796\pi$
$314$	−3.61251	−0.203866
$315$	−25.5329	−1.43862
$316$	−2.65657	−0.149444
$317$	−29.9220	−1.68059	−0.840294	−	0.542131i	$-0.817618\pi$
$317$	−29.9220	−1.68059	−0.840294	+	0.542131i	$0.817618\pi$
$318$	−1.43978	−0.0807387
$319$	−2.94527	−0.164903
$320$	−1.86132	−0.104051
$321$	0.000828817 0	4.62600e−5 0
$322$	33.0903	1.84405
$323$	8.12348	0.452002
$324$	8.74959	0.486088
$325$	−1.17733	−0.0653065
$326$	8.16062	0.451975
$327$	2.15862	0.119372
$328$	−0.348403	−0.0192374
$329$	−0.0158298	−0.000872727 0
$330$	−0.310957	−0.0171176
$331$	−2.82999	−0.155550	−0.0777752	−	0.996971i	$-0.524782\pi$
$331$	−2.82999	−0.155550	−0.0777752	+	0.996971i	$0.524782\pi$
$332$	0.0519205	0.00284951
$333$	−20.3692	−1.11622
$334$	−6.65523	−0.364158
$335$	9.95863	0.544098
$336$	0.771075	0.0420656
$337$	−5.85900	−0.319160	−0.159580	−	0.987185i	$-0.551014\pi$
$337$	−5.85900	−0.319160	−0.159580	+	0.987185i	$0.551014\pi$
$338$	12.4121	0.675129
$339$	1.57738	0.0856715
$340$	−5.75617	−0.312172
$341$	−0.0691519	−0.00374478
$342$	7.80714	0.422162
$343$	−33.7056	−1.81993
$344$	2.62794	0.141689
$345$	2.22938	0.120026
$346$	−3.45011	−0.185479
$347$	16.3450	0.877446	0.438723	−	0.898622i	$-0.355431\pi$
$347$	16.3450	0.877446	0.438723	+	0.898622i	$0.355431\pi$
$348$	0.492044	0.0263763
$349$	−18.0019	−0.963619	−0.481810	−	0.876276i	$-0.660020\pi$
$349$	−18.0019	−0.963619	−0.481810	+	0.876276i	$0.660020\pi$
$350$	−7.08699	−0.378816
$351$	0.764996	0.0408325
$352$	−1.00000	−0.0533002
$353$	−24.6429	−1.31161	−0.655804	−	0.754931i	$-0.727670\pi$
$353$	−24.6429	−1.31161	−0.655804	+	0.754931i	$0.727670\pi$
$354$	0.711656	0.0378241
$355$	8.45526	0.448759
$356$	−16.0406	−0.850153
$357$	2.38456	0.126205
$358$	−10.6133	−0.560932
$359$	3.81069	0.201121	0.100560	−	0.994931i	$-0.467936\pi$
$359$	3.81069	0.201121	0.100560	+	0.994931i	$0.467936\pi$
$360$	−5.53202	−0.291563
$361$	−12.0998	−0.636833
$362$	7.53078	0.395809
$363$	−0.167063	−0.00876851
$364$	−3.53892	−0.185490
$365$	−23.2127	−1.21501
$366$	2.45632	0.128394
$367$	31.2838	1.63300	0.816501	−	0.577344i	$-0.195911\pi$
$367$	31.2838	1.63300	0.816501	+	0.577344i	$0.195911\pi$
$368$	7.16942	0.373732
$369$	−1.03549	−0.0539053
$370$	12.7565	0.663181
$371$	39.7772	2.06513
$372$	0.0115527	0.000598979 0
$373$	−13.1366	−0.680188	−0.340094	−	0.940391i	$-0.610459\pi$
$373$	−13.1366	−0.680188	−0.340094	+	0.940391i	$0.610459\pi$
$374$	−3.09252	−0.159910
$375$	−2.03226	−0.104945
$376$	−0.00342972	−0.000176874 0
$377$	−2.25828	−0.116308
$378$	4.60493	0.236852
$379$	−35.7510	−1.83641	−0.918203	−	0.396110i	$-0.870360\pi$
$379$	−35.7510	−1.83641	−0.918203	+	0.396110i	$0.870360\pi$
$380$	−4.88935	−0.250818
$381$	−1.14999	−0.0589159
$382$	−11.2004	−0.573062
$383$	36.8510	1.88300	0.941500	−	0.337012i	$-0.109416\pi$
$383$	36.8510	1.88300	0.941500	+	0.337012i	$0.109416\pi$
$384$	0.167063	0.00852538
$385$	8.59091	0.437833
$386$	16.3513	0.832261
$387$	7.81048	0.397029
$388$	−1.12190	−0.0569560
$389$	−19.6441	−0.995994	−0.497997	−	0.867179i	$-0.665931\pi$
$389$	−19.6441	−0.995994	−0.497997	+	0.867179i	$0.665931\pi$
$390$	−0.238426	−0.0120732
$391$	22.1715	1.12126
$392$	−14.3027	−0.722396
$393$	2.49826	0.126021
$394$	−1.00000	−0.0503793
$395$	4.94473	0.248797
$396$	−2.97209	−0.149353
$397$	−23.2280	−1.16578	−0.582890	−	0.812551i	$-0.698078\pi$
$397$	−23.2280	−1.16578	−0.582890	+	0.812551i	$0.698078\pi$
$398$	23.9557	1.20079
$399$	2.02547	0.101401
$400$	−1.53548	−0.0767740
$401$	18.6094	0.929308	0.464654	−	0.885492i	$-0.346179\pi$
$401$	18.6094	0.929308	0.464654	+	0.885492i	$0.346179\pi$
$402$	−0.893835	−0.0445804
$403$	−0.0530222	−0.00264122
$404$	4.94451	0.245999
$405$	−16.2858	−0.809248
$406$	−13.5939	−0.674652
$407$	6.85349	0.339715
$408$	0.516644	0.0255777
$409$	20.3250	1.00501	0.502503	−	0.864575i	$-0.332412\pi$
$409$	20.3250	1.00501	0.502503	+	0.864575i	$0.332412\pi$
$410$	0.648491	0.0320267
$411$	0.694547	0.0342595
$412$	1.86370	0.0918177
$413$	−19.6611	−0.967460
$414$	21.3082	1.04724
$415$	−0.0966408	−0.00474391
$416$	−0.766750	−0.0375930
$417$	1.58586	0.0776601
$418$	−2.62682	−0.128482
$419$	−23.4401	−1.14512	−0.572562	−	0.819861i	$-0.694051\pi$
$419$	−23.4401	−1.14512	−0.572562	+	0.819861i	$0.694051\pi$
$420$	−1.43522	−0.0700315
$421$	−13.7791	−0.671554	−0.335777	−	0.941942i	$-0.608999\pi$
$421$	−13.7791	−0.671554	−0.335777	+	0.941942i	$0.608999\pi$
$422$	−5.05236	−0.245945
$423$	−0.0101934	−0.000495622 0
$424$	8.61819	0.418536
$425$	−4.74850	−0.230336
$426$	−0.758900	−0.0367688
$427$	−67.8614	−3.28404
$428$	−0.00496111	−0.000239805 0
$429$	−0.128095	−0.00618450
$430$	−4.89144	−0.235886
$431$	13.0165	0.626985	0.313492	−	0.949591i	$-0.398501\pi$
$431$	13.0165	0.626985	0.313492	+	0.949591i	$0.398501\pi$
$432$	0.997713	0.0480025
$433$	11.8471	0.569336	0.284668	−	0.958626i	$-0.408117\pi$
$433$	11.8471	0.569336	0.284668	+	0.958626i	$0.408117\pi$
$434$	−0.319170	−0.0153206
$435$	−0.915853	−0.0439118
$436$	−12.9210	−0.618805
$437$	18.8327	0.900892
$438$	2.08345	0.0995511
$439$	−11.7832	−0.562384	−0.281192	−	0.959652i	$-0.590730\pi$
$439$	−11.7832	−0.562384	−0.281192	+	0.959652i	$0.590730\pi$
$440$	1.86132	0.0887350
$441$	−42.5090	−2.02424
$442$	−2.37119	−0.112786
$443$	22.9335	1.08960	0.544801	−	0.838565i	$-0.316605\pi$
$443$	22.9335	1.08960	0.544801	+	0.838565i	$0.316605\pi$
$444$	−1.14496	−0.0543375
$445$	29.8568	1.41535
$446$	−6.94619	−0.328911
$447$	−1.52397	−0.0720814
$448$	−4.61549	−0.218061
$449$	−6.27328	−0.296054	−0.148027	−	0.988983i	$-0.547292\pi$
$449$	−6.27328	−0.296054	−0.148027	+	0.988983i	$0.547292\pi$
$450$	−4.56359	−0.215130
$451$	0.348403	0.0164057
$452$	−9.44185	−0.444107
$453$	2.87322	0.134996
$454$	−1.74932	−0.0820997
$455$	6.58708	0.308807
$456$	0.438843	0.0205507
$457$	2.92970	0.137046	0.0685228	−	0.997650i	$-0.478171\pi$
$457$	2.92970	0.137046	0.0685228	+	0.997650i	$0.478171\pi$
$458$	23.1180	1.08023
$459$	3.08545	0.144016
$460$	−13.3446	−0.622195
$461$	1.87748	0.0874428	0.0437214	−	0.999044i	$-0.486079\pi$
$461$	1.87748	0.0874428	0.0437214	+	0.999044i	$0.486079\pi$
$462$	−0.771075	−0.0358737
$463$	4.41179	0.205033	0.102517	−	0.994731i	$-0.467311\pi$
$463$	4.41179	0.205033	0.102517	+	0.994731i	$0.467311\pi$
$464$	−2.94527	−0.136731
$465$	−0.0215033	−0.000997191 0
$466$	12.5675	0.582180
$467$	−4.98030	−0.230461	−0.115230	−	0.993339i	$-0.536761\pi$
$467$	−4.98030	−0.230461	−0.115230	+	0.993339i	$0.536761\pi$
$468$	−2.27885	−0.105340
$469$	24.6942	1.14027
$470$	0.00638382	0.000294464 0
$471$	−0.603516	−0.0278086
$472$	−4.25981	−0.196074
$473$	−2.62794	−0.120833
$474$	−0.443814	−0.0203850
$475$	−4.03343	−0.185066
$476$	−14.2735	−0.654224
$477$	25.6140	1.17279
$478$	−8.35587	−0.382189
$479$	−13.0140	−0.594625	−0.297313	−	0.954780i	$-0.596090\pi$
$479$	−13.0140	−0.594625	−0.297313	+	0.954780i	$0.596090\pi$
$480$	−0.310957	−0.0141932
$481$	5.25491	0.239603
$482$	3.63304	0.165480
$483$	5.52816	0.251540
$484$	1.00000	0.0454545
$485$	2.08822	0.0948214
$486$	4.45487	0.202077
$487$	20.3762	0.923333	0.461666	−	0.887054i	$-0.347252\pi$
$487$	20.3762	0.923333	0.461666	+	0.887054i	$0.347252\pi$
$488$	−14.7030	−0.665572
$489$	1.36333	0.0616521
$490$	26.6220	1.20266
$491$	−16.2963	−0.735443	−0.367721	−	0.929936i	$-0.619862\pi$
$491$	−16.2963	−0.735443	−0.367721	+	0.929936i	$0.619862\pi$
$492$	−0.0582052	−0.00262409
$493$	−9.10830	−0.410217
$494$	−2.01411	−0.0906192
$495$	5.53202	0.248646
$496$	−0.0691519	−0.00310501
$497$	20.9664	0.940470
$498$	0.00867398	0.000388690 0
$499$	9.49845	0.425209	0.212604	−	0.977138i	$-0.431805\pi$
$499$	9.49845	0.425209	0.212604	+	0.977138i	$0.431805\pi$
$500$	12.1646	0.544019
$501$	−1.11184	−0.0496734
$502$	−5.04598	−0.225213
$503$	3.89797	0.173802	0.0869010	−	0.996217i	$-0.472304\pi$
$503$	3.89797	0.173802	0.0869010	+	0.996217i	$0.472304\pi$
$504$	−13.7176	−0.611032
$505$	−9.20332	−0.409542
$506$	−7.16942	−0.318719
$507$	2.07360	0.0920917
$508$	6.88360	0.305410
$509$	−5.49663	−0.243634	−0.121817	−	0.992553i	$-0.538872\pi$
$509$	−5.49663	−0.243634	−0.121817	+	0.992553i	$0.538872\pi$
$510$	−0.961641	−0.0425822
$511$	−57.5601	−2.54631
$512$	−1.00000	−0.0441942
$513$	2.62081	0.115712
$514$	−13.5262	−0.596617
$515$	−3.46894	−0.152860
$516$	0.439031	0.0193272
$517$	0.00342972	0.000150839 0
$518$	31.6322	1.38984
$519$	−0.576384	−0.0253004
$520$	1.42717	0.0625855
$521$	−23.3541	−1.02316	−0.511581	−	0.859235i	$-0.670940\pi$
$521$	−23.3541	−1.02316	−0.511581	+	0.859235i	$0.670940\pi$
$522$	−8.75361	−0.383135
$523$	−8.62311	−0.377062	−0.188531	−	0.982067i	$-0.560373\pi$
$523$	−8.62311	−0.377062	−0.188531	+	0.982067i	$0.560373\pi$
$524$	−14.9540	−0.653270
$525$	−1.18397	−0.0516727
$526$	−18.1268	−0.790366
$527$	−0.213853	−0.00931560
$528$	−0.167063	−0.00727047
$529$	28.4005	1.23481
$530$	−16.0412	−0.696787
$531$	−12.6605	−0.549421
$532$	−12.1240	−0.525644
$533$	0.267138	0.0115710
$534$	−2.67979	−0.115966
$535$	0.00923423	0.000399231 0
$536$	5.35030	0.231098
$537$	−1.77309	−0.0765145
$538$	−27.1232	−1.16936
$539$	14.3027	0.616062
$540$	−1.85706	−0.0799154
$541$	−34.6401	−1.48929	−0.744646	−	0.667459i	$-0.767382\pi$
$541$	−34.6401	−1.48929	−0.744646	+	0.667459i	$0.767382\pi$
$542$	−11.8860	−0.510548
$543$	1.25811	0.0539908
$544$	−3.09252	−0.132591
$545$	24.0502	1.03020
$546$	−0.591222	−0.0253020
$547$	−25.1481	−1.07525	−0.537627	−	0.843183i	$-0.680679\pi$
$547$	−25.1481	−1.07525	−0.537627	+	0.843183i	$0.680679\pi$
$548$	−4.15741	−0.177596
$549$	−43.6986	−1.86501
$550$	1.53548	0.0654731
$551$	−7.73668	−0.329594
$552$	1.19774	0.0509793
$553$	12.2614	0.521406
$554$	13.9047	0.590752
$555$	2.13114	0.0904619
$556$	−9.49264	−0.402578
$557$	−7.69238	−0.325936	−0.162968	−	0.986631i	$-0.552107\pi$
$557$	−7.69238	−0.325936	−0.162968	+	0.986631i	$0.552107\pi$
$558$	−0.205526	−0.00870059
$559$	−2.01497	−0.0852243
$560$	8.59091	0.363032
$561$	−0.516644	−0.0218127
$562$	−12.2407	−0.516342
$563$	30.9146	1.30289	0.651447	−	0.758694i	$-0.274162\pi$
$563$	30.9146	1.30289	0.651447	+	0.758694i	$0.274162\pi$
$564$	−0.000572979 0	−2.41267e−5 0
$565$	17.5743	0.739357
$566$	13.3753	0.562206
$567$	−40.3836	−1.69595
$568$	4.54261	0.190604
$569$	−21.2904	−0.892541	−0.446271	−	0.894898i	$-0.647248\pi$
$569$	−21.2904	−0.892541	−0.446271	+	0.894898i	$0.647248\pi$
$570$	−0.816828	−0.0342132
$571$	47.0197	1.96771	0.983857	−	0.178959i	$-0.0572729\pi$
$571$	47.0197	1.96771	0.983857	+	0.178959i	$0.0572729\pi$
$572$	0.766750	0.0320594
$573$	−1.87117	−0.0781692
$574$	1.60805	0.0671188
$575$	−11.0085	−0.459086
$576$	−2.97209	−0.123837
$577$	−10.4734	−0.436013	−0.218007	−	0.975947i	$-0.569955\pi$
$577$	−10.4734	−0.436013	−0.218007	+	0.975947i	$0.569955\pi$
$578$	7.43633	0.309311
$579$	2.73170	0.113525
$580$	5.48209	0.227632
$581$	−0.239639	−0.00994188
$582$	−0.187428	−0.00776915
$583$	−8.61819	−0.356929
$584$	−12.4711	−0.516057
$585$	4.24167	0.175372
$586$	−12.5642	−0.519024
$587$	−30.0873	−1.24184	−0.620918	−	0.783876i	$-0.713240\pi$
$587$	−30.0873	−1.24184	−0.620918	+	0.783876i	$0.713240\pi$
$588$	−2.38945	−0.0985392
$589$	−0.181649	−0.00748473
$590$	7.92888	0.326427
$591$	−0.167063	−0.00687204
$592$	6.85349	0.281677
$593$	−15.8157	−0.649475	−0.324737	−	0.945804i	$-0.605276\pi$
$593$	−15.8157	−0.649475	−0.324737	+	0.945804i	$0.605276\pi$
$594$	−0.997713	−0.0409367
$595$	26.5675	1.08916
$596$	9.12216	0.373658
$597$	4.00209	0.163795
$598$	−5.49715	−0.224795
$599$	−33.7367	−1.37844	−0.689222	−	0.724550i	$-0.742048\pi$
$599$	−33.7367	−1.37844	−0.689222	+	0.724550i	$0.742048\pi$
$600$	−0.256521	−0.0104724
$601$	−1.20994	−0.0493543	−0.0246772	−	0.999695i	$-0.507856\pi$
$601$	−1.20994	−0.0493543	−0.0246772	+	0.999695i	$0.507856\pi$
$602$	−12.1292	−0.494350
$603$	15.9016	0.647562
$604$	−17.1985	−0.699796
$605$	−1.86132	−0.0756735
$606$	0.826043	0.0335557
$607$	4.92241	0.199794	0.0998971	−	0.994998i	$-0.468149\pi$
$607$	4.92241	0.199794	0.0998971	+	0.994998i	$0.468149\pi$
$608$	−2.62682	−0.106532
$609$	−2.27102	−0.0920265
$610$	27.3670	1.10806
$611$	0.00262974	0.000106388 0
$612$	−9.19124	−0.371534
$613$	3.23770	0.130769	0.0653846	−	0.997860i	$-0.479173\pi$
$613$	3.23770	0.130769	0.0653846	+	0.997860i	$0.479173\pi$
$614$	3.67654	0.148373
$615$	0.108339	0.00436863
$616$	4.61549	0.185963
$617$	31.8788	1.28339	0.641696	−	0.766959i	$-0.278231\pi$
$617$	31.8788	1.28339	0.641696	+	0.766959i	$0.278231\pi$
$618$	0.311354	0.0125245
$619$	−37.4208	−1.50407	−0.752034	−	0.659124i	$-0.770927\pi$
$619$	−37.4208	−1.50407	−0.752034	+	0.659124i	$0.770927\pi$
$620$	0.128714	0.00516928
$621$	7.15302	0.287041
$622$	−10.2199	−0.409780
$623$	74.0354	2.96617
$624$	−0.128095	−0.00512791
$625$	−14.9649	−0.598596
$626$	12.1734	0.486546
$627$	−0.438843	−0.0175257
$628$	3.61251	0.144155
$629$	21.1945	0.845081
$630$	25.5329	1.01726
$631$	−39.6769	−1.57951	−0.789757	−	0.613420i	$-0.789793\pi$
$631$	−39.6769	−1.57951	−0.789757	+	0.613420i	$0.789793\pi$
$632$	2.65657	0.105673
$633$	−0.844061	−0.0335484
$634$	29.9220	1.18836
$635$	−12.8126	−0.508452
$636$	1.43978	0.0570909
$637$	10.9666	0.434513
$638$	2.94527	0.116604
$639$	13.5010	0.534093
$640$	1.86132	0.0735752
$641$	−26.0901	−1.03050	−0.515249	−	0.857041i	$-0.672300\pi$
$641$	−26.0901	−1.03050	−0.515249	+	0.857041i	$0.672300\pi$
$642$	−0.000828817 0	−3.27108e−5 0
$643$	5.40090	0.212991	0.106495	−	0.994313i	$-0.466037\pi$
$643$	5.40090	0.212991	0.106495	+	0.994313i	$0.466037\pi$
$644$	−33.0903	−1.30394
$645$	−0.817177	−0.0321763
$646$	−8.12348	−0.319614
$647$	−34.6039	−1.36042	−0.680210	−	0.733017i	$-0.738111\pi$
$647$	−34.6039	−1.36042	−0.680210	+	0.733017i	$0.738111\pi$
$648$	−8.74959	−0.343716
$649$	4.25981	0.167212
$650$	1.17733	0.0461787
$651$	−0.0533213	−0.00208983
$652$	−8.16062	−0.319594
$653$	−5.28364	−0.206765	−0.103382	−	0.994642i	$-0.532967\pi$
$653$	−5.28364	−0.206765	−0.103382	+	0.994642i	$0.532967\pi$
$654$	−2.15862	−0.0844088
$655$	27.8343	1.08758
$656$	0.348403	0.0136029
$657$	−37.0652	−1.44605
$658$	0.0158298	0.000617112 0
$659$	24.6718	0.961077	0.480538	−	0.876974i	$-0.340441\pi$
$659$	24.6718	0.961077	0.480538	+	0.876974i	$0.340441\pi$
$660$	0.310957	0.0121040
$661$	4.10641	0.159721	0.0798605	−	0.996806i	$-0.474553\pi$
$661$	4.10641	0.159721	0.0798605	+	0.996806i	$0.474553\pi$
$662$	2.82999	0.109991
$663$	−0.396137	−0.0153847
$664$	−0.0519205	−0.00201491
$665$	22.5667	0.875101
$666$	20.3692	0.789290
$667$	−21.1159	−0.817609
$668$	6.65523	0.257499
$669$	−1.16045	−0.0448655
$670$	−9.95863	−0.384735
$671$	14.7030	0.567602
$672$	−0.771075	−0.0297449
$673$	46.0123	1.77365	0.886823	−	0.462110i	$-0.152908\pi$
$673$	46.0123	1.77365	0.886823	+	0.462110i	$0.152908\pi$
$674$	5.85900	0.225680
$675$	−1.53197	−0.0589655
$676$	−12.4121	−0.477388
$677$	18.4541	0.709247	0.354624	−	0.935009i	$-0.384609\pi$
$677$	18.4541	0.709247	0.354624	+	0.935009i	$0.384609\pi$
$678$	−1.57738	−0.0605789
$679$	5.17813	0.198718
$680$	5.75617	0.220739
$681$	−0.292246	−0.0111989
$682$	0.0691519	0.00264796
$683$	−21.1476	−0.809190	−0.404595	−	0.914496i	$-0.632588\pi$
$683$	−21.1476	−0.809190	−0.404595	+	0.914496i	$0.632588\pi$
$684$	−7.80714	−0.298513
$685$	7.73827	0.295664
$686$	33.7056	1.28689
$687$	3.86215	0.147350
$688$	−2.62794	−0.100189
$689$	−6.60800	−0.251745
$690$	−2.22938	−0.0848711
$691$	−39.5602	−1.50494	−0.752471	−	0.658625i	$-0.771138\pi$
$691$	−39.5602	−1.50494	−0.752471	+	0.658625i	$0.771138\pi$
$692$	3.45011	0.131153
$693$	13.7176	0.521090
$694$	−16.3450	−0.620448
$695$	17.6689	0.670218
$696$	−0.492044	−0.0186509
$697$	1.07744	0.0408111
$698$	18.0019	0.681382
$699$	2.09957	0.0794129
$700$	7.08699	0.267863
$701$	30.6129	1.15623	0.578117	−	0.815954i	$-0.303788\pi$
$701$	30.6129	1.15623	0.578117	+	0.815954i	$0.303788\pi$
$702$	−0.764996	−0.0288729
$703$	18.0029	0.678991
$704$	1.00000	0.0376889
$705$	0.00106650	4.01666e−5 0
$706$	24.6429	0.927447
$707$	−22.8213	−0.858284
$708$	−0.711656	−0.0267457
$709$	−18.1229	−0.680619	−0.340310	−	0.940313i	$-0.610532\pi$
$709$	−18.1229	−0.680619	−0.340310	+	0.940313i	$0.610532\pi$
$710$	−8.45526	−0.317320
$711$	7.89557	0.296107
$712$	16.0406	0.601149
$713$	−0.495779	−0.0185671
$714$	−2.38456	−0.0892401
$715$	−1.42717	−0.0533731
$716$	10.6133	0.396639
$717$	−1.39595	−0.0521329
$718$	−3.81069	−0.142214
$719$	−41.4671	−1.54646	−0.773230	−	0.634126i	$-0.781360\pi$
$719$	−41.4671	−1.54646	−0.773230	+	0.634126i	$0.781360\pi$
$720$	5.53202	0.206166
$721$	−8.60187	−0.320350
$722$	12.0998	0.450309
$723$	0.606945	0.0225725
$724$	−7.53078	−0.279879
$725$	4.52240	0.167958
$726$	0.167063	0.00620027
$727$	33.4093	1.23908	0.619542	−	0.784964i	$-0.287318\pi$
$727$	33.4093	1.23908	0.619542	+	0.784964i	$0.287318\pi$
$728$	3.53892	0.131161
$729$	−25.5045	−0.944612
$730$	23.2127	0.859140
$731$	−8.12695	−0.300586
$732$	−2.45632	−0.0907881
$733$	14.6362	0.540599	0.270300	−	0.962776i	$-0.412877\pi$
$733$	14.6362	0.540599	0.270300	+	0.962776i	$0.412877\pi$
$734$	−31.2838	−1.15471
$735$	4.44753	0.164050
$736$	−7.16942	−0.264268
$737$	−5.35030	−0.197081
$738$	1.03549	0.0381168
$739$	−15.8005	−0.581231	−0.290615	−	0.956840i	$-0.593860\pi$
$739$	−15.8005	−0.581231	−0.290615	+	0.956840i	$0.593860\pi$
$740$	−12.7565	−0.468940
$741$	−0.336483	−0.0123610
$742$	−39.7772	−1.46027
$743$	32.7347	1.20092	0.600461	−	0.799654i	$-0.294984\pi$
$743$	32.7347	1.20092	0.600461	+	0.799654i	$0.294984\pi$
$744$	−0.0115527	−0.000423542 0
$745$	−16.9793	−0.622072
$746$	13.1366	0.480966
$747$	−0.154312	−0.00564600
$748$	3.09252	0.113074
$749$	0.0228980	0.000836673 0
$750$	2.03226	0.0742075
$751$	−3.90980	−0.142671	−0.0713353	−	0.997452i	$-0.522726\pi$
$751$	−3.90980	−0.142671	−0.0713353	+	0.997452i	$0.522726\pi$
$752$	0.00342972	0.000125069 0
$753$	−0.842994	−0.0307204
$754$	2.25828	0.0822419
$755$	32.0119	1.16503
$756$	−4.60493	−0.167480
$757$	5.53866	0.201306	0.100653	−	0.994922i	$-0.467907\pi$
$757$	5.53866	0.201306	0.100653	+	0.994922i	$0.467907\pi$
$758$	35.7510	1.29854
$759$	−1.19774	−0.0434753
$760$	4.88935	0.177355
$761$	−17.4750	−0.633467	−0.316733	−	0.948515i	$-0.602586\pi$
$761$	−17.4750	−0.633467	−0.316733	+	0.948515i	$0.602586\pi$
$762$	1.14999	0.0416598
$763$	59.6369	2.15900
$764$	11.2004	0.405216
$765$	17.1079	0.618536
$766$	−36.8510	−1.33148
$767$	3.26621	0.117936
$768$	−0.167063	−0.00602835
$769$	6.50575	0.234604	0.117302	−	0.993096i	$-0.462576\pi$
$769$	6.50575	0.234604	0.117302	+	0.993096i	$0.462576\pi$
$770$	−8.59091	−0.309595
$771$	−2.25973	−0.0813822
$772$	−16.3513	−0.588497
$773$	−11.7085	−0.421125	−0.210563	−	0.977580i	$-0.567530\pi$
$773$	−11.7085	−0.421125	−0.210563	+	0.977580i	$0.567530\pi$
$774$	−7.81048	−0.280742
$775$	0.106181	0.00381415
$776$	1.12190	0.0402740
$777$	5.28455	0.189582
$778$	19.6441	0.704274
$779$	0.915192	0.0327902
$780$	0.238426	0.00853704
$781$	−4.54261	−0.162547
$782$	−22.1715	−0.792853
$783$	−2.93853	−0.105015
$784$	14.3027	0.510811
$785$	−6.72405	−0.239992
$786$	−2.49826	−0.0891100
$787$	−0.146261	−0.00521363	−0.00260682	−	0.999997i	$-0.500830\pi$
$787$	−0.146261	−0.00521363	−0.00260682	+	0.999997i	$0.500830\pi$
$788$	1.00000	0.0356235
$789$	−3.02831	−0.107811
$790$	−4.94473	−0.175926
$791$	43.5787	1.54948
$792$	2.97209	0.105609
$793$	11.2735	0.400334
$794$	23.2280	0.824331
$795$	−2.67989	−0.0950459
$796$	−23.9557	−0.849086
$797$	−16.5521	−0.586305	−0.293153	−	0.956066i	$-0.594704\pi$
$797$	−16.5521	−0.586305	−0.293153	+	0.956066i	$0.594704\pi$
$798$	−2.02547	−0.0717010
$799$	0.0106065	0.000375230 0
$800$	1.53548	0.0542874
$801$	47.6742	1.68449
$802$	−18.6094	−0.657120
$803$	12.4711	0.440095
$804$	0.893835	0.0315231
$805$	61.5918	2.17083
$806$	0.0530222	0.00186763
$807$	−4.53128	−0.159508
$808$	−4.94451	−0.173947
$809$	−19.6051	−0.689278	−0.344639	−	0.938735i	$-0.611999\pi$
$809$	−19.6051	−0.689278	−0.344639	+	0.938735i	$0.611999\pi$
$810$	16.2858	0.572225
$811$	9.47790	0.332814	0.166407	−	0.986057i	$-0.446783\pi$
$811$	9.47790	0.332814	0.166407	+	0.986057i	$0.446783\pi$
$812$	13.5939	0.477051
$813$	−1.98571	−0.0696419
$814$	−6.85349	−0.240215
$815$	15.1895	0.532066
$816$	−0.516644	−0.0180862
$817$	−6.90312	−0.241510
$818$	−20.3250	−0.710647
$819$	10.5180	0.367529
$820$	−0.648491	−0.0226463
$821$	21.6703	0.756297	0.378149	−	0.925745i	$-0.376561\pi$
$821$	21.6703	0.756297	0.378149	+	0.925745i	$0.376561\pi$
$822$	−0.694547	−0.0242251
$823$	38.9377	1.35728	0.678642	−	0.734469i	$-0.262569\pi$
$823$	38.9377	1.35728	0.678642	+	0.734469i	$0.262569\pi$
$824$	−1.86370	−0.0649249
$825$	0.256521	0.00893093
$826$	19.6611	0.684098
$827$	−17.4816	−0.607894	−0.303947	−	0.952689i	$-0.598305\pi$
$827$	−17.4816	−0.607894	−0.303947	+	0.952689i	$0.598305\pi$
$828$	−21.3082	−0.740509
$829$	−6.77218	−0.235208	−0.117604	−	0.993061i	$-0.537521\pi$
$829$	−6.77218	−0.235208	−0.117604	+	0.993061i	$0.537521\pi$
$830$	0.0966408	0.00335445
$831$	2.32295	0.0805822
$832$	0.766750	0.0265823
$833$	44.2314	1.53253
$834$	−1.58586	−0.0549140
$835$	−12.3875	−0.428688
$836$	2.62682	0.0908504
$837$	−0.0689937	−0.00238477
$838$	23.4401	0.809725
$839$	−7.06823	−0.244022	−0.122011	−	0.992529i	$-0.538934\pi$
$839$	−7.06823	−0.244022	−0.122011	+	0.992529i	$0.538934\pi$
$840$	1.43522	0.0495198
$841$	−20.3254	−0.700875
$842$	13.7791	0.474860
$843$	−2.04496	−0.0704321
$844$	5.05236	0.173910
$845$	23.1029	0.794764
$846$	0.0101934	0.000350458 0
$847$	−4.61549	−0.158590
$848$	−8.61819	−0.295950
$849$	2.23451	0.0766883
$850$	4.74850	0.162872
$851$	49.1355	1.68434
$852$	0.758900	0.0259995
$853$	38.1760	1.30712	0.653561	−	0.756874i	$-0.273274\pi$
$853$	38.1760	1.30712	0.653561	+	0.756874i	$0.273274\pi$
$854$	67.8614	2.32217
$855$	14.5316	0.496970
$856$	0.00496111	0.000169567 0
$857$	26.0906	0.891237	0.445618	−	0.895223i	$-0.352984\pi$
$857$	26.0906	0.891237	0.445618	+	0.895223i	$0.352984\pi$
$858$	0.128095	0.00437310
$859$	−5.14443	−0.175526	−0.0877629	−	0.996141i	$-0.527972\pi$
$859$	−5.14443	−0.175526	−0.0877629	+	0.996141i	$0.527972\pi$
$860$	4.89144	0.166797
$861$	0.268645	0.00915541
$862$	−13.0165	−0.443345
$863$	2.54618	0.0866729	0.0433365	−	0.999061i	$-0.486201\pi$
$863$	2.54618	0.0866729	0.0433365	+	0.999061i	$0.486201\pi$
$864$	−0.997713	−0.0339429
$865$	−6.42176	−0.218346
$866$	−11.8471	−0.402582
$867$	1.24233	0.0421918
$868$	0.319170	0.0108333
$869$	−2.65657	−0.0901180
$870$	0.915853	0.0310503
$871$	−4.10234	−0.139003
$872$	12.9210	0.437561
$873$	3.33440	0.112852
$874$	−18.8327	−0.637027
$875$	−56.1457	−1.89807
$876$	−2.08345	−0.0703933
$877$	−48.5236	−1.63853	−0.819264	−	0.573417i	$-0.805617\pi$
$877$	−48.5236	−1.63853	−0.819264	+	0.573417i	$0.805617\pi$
$878$	11.7832	0.397665
$879$	−2.09901	−0.0707980
$880$	−1.86132	−0.0627451
$881$	−5.59529	−0.188510	−0.0942551	−	0.995548i	$-0.530047\pi$
$881$	−5.59529	−0.188510	−0.0942551	+	0.995548i	$0.530047\pi$
$882$	42.5090	1.43135
$883$	33.8580	1.13941	0.569706	−	0.821848i	$-0.307057\pi$
$883$	33.8580	1.13941	0.569706	+	0.821848i	$0.307057\pi$
$884$	2.37119	0.0797517
$885$	1.32462	0.0445266
$886$	−22.9335	−0.770466
$887$	53.5777	1.79896	0.899481	−	0.436960i	$-0.143945\pi$
$887$	53.5777	1.79896	0.899481	+	0.436960i	$0.143945\pi$
$888$	1.14496	0.0384224
$889$	−31.7712	−1.06557
$890$	−29.8568	−1.00080
$891$	8.74959	0.293122
$892$	6.94619	0.232576
$893$	0.00900926	0.000301483 0
$894$	1.52397	0.0509692
$895$	−19.7548	−0.660331
$896$	4.61549	0.154193
$897$	−0.918368	−0.0306634
$898$	6.27328	0.209342
$899$	0.203671	0.00679281
$900$	4.56359	0.152120
$901$	−26.6519	−0.887904
$902$	−0.348403	−0.0116006
$903$	−2.02634	−0.0674324
$904$	9.44185	0.314031
$905$	14.0172	0.465948
$906$	−2.87322	−0.0954564
$907$	51.9707	1.72566	0.862830	−	0.505495i	$-0.168690\pi$
$907$	51.9707	1.72566	0.862830	+	0.505495i	$0.168690\pi$
$908$	1.74932	0.0580532
$909$	−14.6955	−0.487420
$910$	−6.58708	−0.218359
$911$	30.5503	1.01218	0.506089	−	0.862481i	$-0.331091\pi$
$911$	30.5503	1.01218	0.506089	+	0.862481i	$0.331091\pi$
$912$	−0.438843	−0.0145315
$913$	0.0519205	0.00171832
$914$	−2.92970	−0.0969058
$915$	4.57200	0.151146
$916$	−23.1180	−0.763839
$917$	69.0202	2.27925
$918$	−3.08545	−0.101835
$919$	−42.3257	−1.39620	−0.698098	−	0.716002i	$-0.745970\pi$
$919$	−42.3257	−1.39620	−0.698098	+	0.716002i	$0.745970\pi$
$920$	13.3446	0.439958
$921$	0.614212	0.0202390
$922$	−1.87748	−0.0618314
$923$	−3.48305	−0.114646
$924$	0.771075	0.0253665
$925$	−10.5234	−0.346007
$926$	−4.41179	−0.144980
$927$	−5.53907	−0.181927
$928$	2.94527	0.0966832
$929$	−28.2748	−0.927667	−0.463833	−	0.885922i	$-0.653526\pi$
$929$	−28.2748	−0.927667	−0.463833	+	0.885922i	$0.653526\pi$
$930$	0.0215033	0.000705120 0
$931$	37.5706	1.23133
$932$	−12.5675	−0.411663
$933$	−1.70736	−0.0558965
$934$	4.98030	0.162960
$935$	−5.75617	−0.188247
$936$	2.27885	0.0744865
$937$	−24.2506	−0.792232	−0.396116	−	0.918200i	$-0.629642\pi$
$937$	−24.2506	−0.792232	−0.396116	+	0.918200i	$0.629642\pi$
$938$	−24.6942	−0.806295
$939$	2.03372	0.0663678
$940$	−0.00638382	−0.000208217 0
$941$	−13.2950	−0.433403	−0.216702	−	0.976238i	$-0.569530\pi$
$941$	−13.2950	−0.433403	−0.216702	+	0.976238i	$0.569530\pi$
$942$	0.603516	0.0196636
$943$	2.49785	0.0813412
$944$	4.25981	0.138645
$945$	8.57126	0.278823
$946$	2.62794	0.0854417
$947$	9.21087	0.299313	0.149657	−	0.988738i	$-0.452183\pi$
$947$	9.21087	0.299313	0.149657	+	0.988738i	$0.452183\pi$
$948$	0.443814	0.0144144
$949$	9.56220	0.310402
$950$	4.03343	0.130862
$951$	4.99885	0.162099
$952$	14.2735	0.462606
$953$	−26.7384	−0.866140	−0.433070	−	0.901360i	$-0.642570\pi$
$953$	−26.7384	−0.866140	−0.433070	+	0.901360i	$0.642570\pi$
$954$	−25.6140	−0.829285
$955$	−20.8476	−0.674611
$956$	8.35587	0.270248
$957$	0.492044	0.0159055
$958$	13.0140	0.420464
$959$	19.1885	0.619628
$960$	0.310957	0.0100361
$961$	−30.9952	−0.999846
$962$	−5.25491	−0.169425
$963$	0.0147449	0.000475147 0
$964$	−3.63304	−0.117012
$965$	30.4351	0.979740
$966$	−5.52816	−0.177866
$967$	−36.9443	−1.18805	−0.594024	−	0.804447i	$-0.702462\pi$
$967$	−36.9443	−1.18805	−0.594024	+	0.804447i	$0.702462\pi$
$968$	−1.00000	−0.0321412
$969$	−1.35713	−0.0435973
$970$	−2.08822	−0.0670488
$971$	−59.7843	−1.91857	−0.959284	−	0.282443i	$-0.908855\pi$
$971$	−59.7843	−1.91857	−0.959284	+	0.282443i	$0.908855\pi$
$972$	−4.45487	−0.142890
$973$	43.8131	1.40459
$974$	−20.3762	−0.652895
$975$	0.196688	0.00629905
$976$	14.7030	0.470631
$977$	−18.8416	−0.602797	−0.301398	−	0.953498i	$-0.597453\pi$
$977$	−18.8416	−0.602797	−0.301398	+	0.953498i	$0.597453\pi$
$978$	−1.36333	−0.0435946
$979$	−16.0406	−0.512661
$980$	−26.6220	−0.850407
$981$	38.4025	1.22610
$982$	16.2963	0.520036
$983$	−17.5099	−0.558481	−0.279240	−	0.960221i	$-0.590083\pi$
$983$	−17.5099	−0.558481	−0.279240	+	0.960221i	$0.590083\pi$
$984$	0.0582052	0.00185551
$985$	−1.86132	−0.0593066
$986$	9.10830	0.290067
$987$	0.00264457	8.41777e−5 0
$988$	2.01411	0.0640774
$989$	−18.8408	−0.599103
$990$	−5.53202	−0.175819
$991$	33.2265	1.05547	0.527737	−	0.849408i	$-0.323041\pi$
$991$	33.2265	1.05547	0.527737	+	0.849408i	$0.323041\pi$
$992$	0.0691519	0.00219557
$993$	0.472786	0.0150034
$994$	−20.9664	−0.665012
$995$	44.5892	1.41357
$996$	−0.00867398	−0.000274846 0
$997$	25.4433	0.805796	0.402898	−	0.915245i	$-0.368003\pi$
$997$	25.4433	0.805796	0.402898	+	0.915245i	$0.368003\pi$
$998$	−9.49845	−0.300668
$999$	6.83781	0.216339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.8	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.8	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.167063 q^{3} +1.00000 q^{4} -1.86132 q^{5} +0.167063 q^{6} -4.61549 q^{7} -1.00000 q^{8} -2.97209 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.167063 q^{3} +1.00000 q^{4} -1.86132 q^{5} +0.167063 q^{6} -4.61549 q^{7} -1.00000 q^{8} -2.97209 q^{9} +1.86132 q^{10} +1.00000 q^{11} -0.167063 q^{12} +0.766750 q^{13} +4.61549 q^{14} +0.310957 q^{15} +1.00000 q^{16} +3.09252 q^{17} +2.97209 q^{18} +2.62682 q^{19} -1.86132 q^{20} +0.771075 q^{21} -1.00000 q^{22} +7.16942 q^{23} +0.167063 q^{24} -1.53548 q^{25} -0.766750 q^{26} +0.997713 q^{27} -4.61549 q^{28} -2.94527 q^{29} -0.310957 q^{30} -0.0691519 q^{31} -1.00000 q^{32} -0.167063 q^{33} -3.09252 q^{34} +8.59091 q^{35} -2.97209 q^{36} +6.85349 q^{37} -2.62682 q^{38} -0.128095 q^{39} +1.86132 q^{40} +0.348403 q^{41} -0.771075 q^{42} -2.62794 q^{43} +1.00000 q^{44} +5.53202 q^{45} -7.16942 q^{46} +0.00342972 q^{47} -0.167063 q^{48} +14.3027 q^{49} +1.53548 q^{50} -0.516644 q^{51} +0.766750 q^{52} -8.61819 q^{53} -0.997713 q^{54} -1.86132 q^{55} +4.61549 q^{56} -0.438843 q^{57} +2.94527 q^{58} +4.25981 q^{59} +0.310957 q^{60} +14.7030 q^{61} +0.0691519 q^{62} +13.7176 q^{63} +1.00000 q^{64} -1.42717 q^{65} +0.167063 q^{66} -5.35030 q^{67} +3.09252 q^{68} -1.19774 q^{69} -8.59091 q^{70} -4.54261 q^{71} +2.97209 q^{72} +12.4711 q^{73} -6.85349 q^{74} +0.256521 q^{75} +2.62682 q^{76} -4.61549 q^{77} +0.128095 q^{78} -2.65657 q^{79} -1.86132 q^{80} +8.74959 q^{81} -0.348403 q^{82} +0.0519205 q^{83} +0.771075 q^{84} -5.75617 q^{85} +2.62794 q^{86} +0.492044 q^{87} -1.00000 q^{88} -16.0406 q^{89} -5.53202 q^{90} -3.53892 q^{91} +7.16942 q^{92} +0.0115527 q^{93} -0.00342972 q^{94} -4.88935 q^{95} +0.167063 q^{96} -1.12190 q^{97} -14.3027 q^{98} -2.97209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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