LMFDB - Embedded newform 4030.2.a.q.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 48x^{6} + 66x^{5} - 202x^{4} - 75x^{3} + 210x^{2} + 68x - 16 $ x^9 - 3x^8 - 16x^7 + 48x^6 + 66x^5 - 202x^4 - 75x^3 + 210x^2 + 68x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.63839$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.63839 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63839 q^{6} +2.17174 q^{7} +1.00000 q^{8} +3.96109 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.63839 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63839 q^{6} +2.17174 q^{7} +1.00000 q^{8} +3.96109 q^{9} -1.00000 q^{10} -3.04430 q^{11} +2.63839 q^{12} +1.00000 q^{13} +2.17174 q^{14} -2.63839 q^{15} +1.00000 q^{16} +8.01343 q^{17} +3.96109 q^{18} +2.33430 q^{19} -1.00000 q^{20} +5.72988 q^{21} -3.04430 q^{22} -4.65210 q^{23} +2.63839 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.53574 q^{27} +2.17174 q^{28} +5.50426 q^{29} -2.63839 q^{30} +1.00000 q^{31} +1.00000 q^{32} -8.03204 q^{33} +8.01343 q^{34} -2.17174 q^{35} +3.96109 q^{36} +3.09686 q^{37} +2.33430 q^{38} +2.63839 q^{39} -1.00000 q^{40} -3.63489 q^{41} +5.72988 q^{42} -4.32649 q^{43} -3.04430 q^{44} -3.96109 q^{45} -4.65210 q^{46} -1.12007 q^{47} +2.63839 q^{48} -2.28357 q^{49} +1.00000 q^{50} +21.1425 q^{51} +1.00000 q^{52} -0.606019 q^{53} +2.53574 q^{54} +3.04430 q^{55} +2.17174 q^{56} +6.15879 q^{57} +5.50426 q^{58} +2.30213 q^{59} -2.63839 q^{60} +0.292016 q^{61} +1.00000 q^{62} +8.60244 q^{63} +1.00000 q^{64} -1.00000 q^{65} -8.03204 q^{66} -0.869662 q^{67} +8.01343 q^{68} -12.2740 q^{69} -2.17174 q^{70} -0.662572 q^{71} +3.96109 q^{72} -15.9341 q^{73} +3.09686 q^{74} +2.63839 q^{75} +2.33430 q^{76} -6.61141 q^{77} +2.63839 q^{78} +4.06263 q^{79} -1.00000 q^{80} -5.19302 q^{81} -3.63489 q^{82} +14.9547 q^{83} +5.72988 q^{84} -8.01343 q^{85} -4.32649 q^{86} +14.5224 q^{87} -3.04430 q^{88} +9.85856 q^{89} -3.96109 q^{90} +2.17174 q^{91} -4.65210 q^{92} +2.63839 q^{93} -1.12007 q^{94} -2.33430 q^{95} +2.63839 q^{96} -2.38196 q^{97} -2.28357 q^{98} -12.0588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * 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
$3$	2.63839	1.52327	0.761637	−	0.648004i	$-0.224396\pi$
$3$	2.63839	1.52327	0.761637	+	0.648004i	$0.224396\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.63839	1.07712
$7$	2.17174	0.820839	0.410419	−	0.911897i	$-0.365382\pi$
$7$	2.17174	0.820839	0.410419	+	0.911897i	$0.365382\pi$
$8$	1.00000	0.353553
$9$	3.96109	1.32036
$10$	−1.00000	−0.316228
$11$	−3.04430	−0.917891	−0.458945	−	0.888464i	$-0.651773\pi$
$11$	−3.04430	−0.917891	−0.458945	+	0.888464i	$0.651773\pi$
$12$	2.63839	0.761637
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.17174	0.580421
$15$	−2.63839	−0.681229
$16$	1.00000	0.250000
$17$	8.01343	1.94354	0.971771	−	0.235928i	$-0.0758129\pi$
$17$	8.01343	1.94354	0.971771	+	0.235928i	$0.0758129\pi$
$18$	3.96109	0.933639
$19$	2.33430	0.535526	0.267763	−	0.963485i	$-0.413716\pi$
$19$	2.33430	0.535526	0.267763	+	0.963485i	$0.413716\pi$
$20$	−1.00000	−0.223607
$21$	5.72988	1.25036
$22$	−3.04430	−0.649047
$23$	−4.65210	−0.970030	−0.485015	−	0.874506i	$-0.661186\pi$
$23$	−4.65210	−0.970030	−0.485015	+	0.874506i	$0.661186\pi$
$24$	2.63839	0.538559
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	2.53574	0.488003
$28$	2.17174	0.410419
$29$	5.50426	1.02211	0.511057	−	0.859547i	$-0.329254\pi$
$29$	5.50426	1.02211	0.511057	+	0.859547i	$0.329254\pi$
$30$	−2.63839	−0.481702
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−8.03204	−1.39820
$34$	8.01343	1.37429
$35$	−2.17174	−0.367090
$36$	3.96109	0.660182
$37$	3.09686	0.509120	0.254560	−	0.967057i	$-0.418069\pi$
$37$	3.09686	0.509120	0.254560	+	0.967057i	$0.418069\pi$
$38$	2.33430	0.378674
$39$	2.63839	0.422480
$40$	−1.00000	−0.158114
$41$	−3.63489	−0.567674	−0.283837	−	0.958873i	$-0.591607\pi$
$41$	−3.63489	−0.567674	−0.283837	+	0.958873i	$0.591607\pi$
$42$	5.72988	0.884140
$43$	−4.32649	−0.659784	−0.329892	−	0.944019i	$-0.607012\pi$
$43$	−4.32649	−0.659784	−0.329892	+	0.944019i	$0.607012\pi$
$44$	−3.04430	−0.458945
$45$	−3.96109	−0.590485
$46$	−4.65210	−0.685915
$47$	−1.12007	−0.163379	−0.0816893	−	0.996658i	$-0.526032\pi$
$47$	−1.12007	−0.163379	−0.0816893	+	0.996658i	$0.526032\pi$
$48$	2.63839	0.380819
$49$	−2.28357	−0.326224
$50$	1.00000	0.141421
$51$	21.1425	2.96055
$52$	1.00000	0.138675
$53$	−0.606019	−0.0832431	−0.0416216	−	0.999133i	$-0.513252\pi$
$53$	−0.606019	−0.0832431	−0.0416216	+	0.999133i	$0.513252\pi$
$54$	2.53574	0.345070
$55$	3.04430	0.410493
$56$	2.17174	0.290210
$57$	6.15879	0.815752
$58$	5.50426	0.722744
$59$	2.30213	0.299712	0.149856	−	0.988708i	$-0.452119\pi$
$59$	2.30213	0.299712	0.149856	+	0.988708i	$0.452119\pi$
$60$	−2.63839	−0.340614
$61$	0.292016	0.0373888	0.0186944	−	0.999825i	$-0.494049\pi$
$61$	0.292016	0.0373888	0.0186944	+	0.999825i	$0.494049\pi$
$62$	1.00000	0.127000
$63$	8.60244	1.08381
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−8.03204	−0.988676
$67$	−0.869662	−0.106246	−0.0531231	−	0.998588i	$-0.516918\pi$
$67$	−0.869662	−0.106246	−0.0531231	+	0.998588i	$0.516918\pi$
$68$	8.01343	0.971771
$69$	−12.2740	−1.47762
$70$	−2.17174	−0.259572
$71$	−0.662572	−0.0786328	−0.0393164	−	0.999227i	$-0.512518\pi$
$71$	−0.662572	−0.0786328	−0.0393164	+	0.999227i	$0.512518\pi$
$72$	3.96109	0.466819
$73$	−15.9341	−1.86494	−0.932472	−	0.361242i	$-0.882353\pi$
$73$	−15.9341	−1.86494	−0.932472	+	0.361242i	$0.882353\pi$
$74$	3.09686	0.360002
$75$	2.63839	0.304655
$76$	2.33430	0.267763
$77$	−6.61141	−0.753440
$78$	2.63839	0.298739
$79$	4.06263	0.457081	0.228541	−	0.973534i	$-0.426605\pi$
$79$	4.06263	0.457081	0.228541	+	0.973534i	$0.426605\pi$
$80$	−1.00000	−0.111803
$81$	−5.19302	−0.577002
$82$	−3.63489	−0.401406
$83$	14.9547	1.64149	0.820745	−	0.571294i	$-0.193559\pi$
$83$	14.9547	1.64149	0.820745	+	0.571294i	$0.193559\pi$
$84$	5.72988	0.625181
$85$	−8.01343	−0.869178
$86$	−4.32649	−0.466538
$87$	14.5224	1.55696
$88$	−3.04430	−0.324523
$89$	9.85856	1.04501	0.522503	−	0.852638i	$-0.324998\pi$
$89$	9.85856	1.04501	0.522503	+	0.852638i	$0.324998\pi$
$90$	−3.96109	−0.417536
$91$	2.17174	0.227660
$92$	−4.65210	−0.485015
$93$	2.63839	0.273588
$94$	−1.12007	−0.115526
$95$	−2.33430	−0.239494
$96$	2.63839	0.269279
$97$	−2.38196	−0.241851	−0.120926	−	0.992662i	$-0.538586\pi$
$97$	−2.38196	−0.241851	−0.120926	+	0.992662i	$0.538586\pi$
$98$	−2.28357	−0.230675
$99$	−12.0588	−1.21195
$100$	1.00000	0.100000
$101$	6.08621	0.605601	0.302800	−	0.953054i	$-0.402078\pi$
$101$	6.08621	0.605601	0.302800	+	0.953054i	$0.402078\pi$
$102$	21.1425	2.09342
$103$	2.86726	0.282520	0.141260	−	0.989973i	$-0.454885\pi$
$103$	2.86726	0.282520	0.141260	+	0.989973i	$0.454885\pi$
$104$	1.00000	0.0980581
$105$	−5.72988	−0.559179
$106$	−0.606019	−0.0588618
$107$	14.3975	1.39186	0.695928	−	0.718112i	$-0.254993\pi$
$107$	14.3975	1.39186	0.695928	+	0.718112i	$0.254993\pi$
$108$	2.53574	0.244001
$109$	−3.70705	−0.355071	−0.177535	−	0.984114i	$-0.556812\pi$
$109$	−3.70705	−0.355071	−0.177535	+	0.984114i	$0.556812\pi$
$110$	3.04430	0.290263
$111$	8.17071	0.775529
$112$	2.17174	0.205210
$113$	10.9553	1.03058	0.515292	−	0.857015i	$-0.327684\pi$
$113$	10.9553	1.03058	0.515292	+	0.857015i	$0.327684\pi$
$114$	6.15879	0.576824
$115$	4.65210	0.433810
$116$	5.50426	0.511057
$117$	3.96109	0.366203
$118$	2.30213	0.211929
$119$	17.4030	1.59533
$120$	−2.63839	−0.240851
$121$	−1.73224	−0.157477
$122$	0.292016	0.0264379
$123$	−9.59024	−0.864723
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	8.60244	0.766367
$127$	12.0934	1.07311	0.536557	−	0.843864i	$-0.319725\pi$
$127$	12.0934	1.07311	0.536557	+	0.843864i	$0.319725\pi$
$128$	1.00000	0.0883883
$129$	−11.4150	−1.00503
$130$	−1.00000	−0.0877058
$131$	−3.15171	−0.275366	−0.137683	−	0.990476i	$-0.543966\pi$
$131$	−3.15171	−0.275366	−0.137683	+	0.990476i	$0.543966\pi$
$132$	−8.03204	−0.699100
$133$	5.06948	0.439580
$134$	−0.869662	−0.0751274
$135$	−2.53574	−0.218241
$136$	8.01343	0.687146
$137$	−14.1157	−1.20599	−0.602994	−	0.797745i	$-0.706026\pi$
$137$	−14.1157	−1.20599	−0.602994	+	0.797745i	$0.706026\pi$
$138$	−12.2740	−1.04484
$139$	−11.6844	−0.991060	−0.495530	−	0.868591i	$-0.665026\pi$
$139$	−11.6844	−0.991060	−0.495530	+	0.868591i	$0.665026\pi$
$140$	−2.17174	−0.183545
$141$	−2.95517	−0.248870
$142$	−0.662572	−0.0556018
$143$	−3.04430	−0.254577
$144$	3.96109	0.330091
$145$	−5.50426	−0.457104
$146$	−15.9341	−1.31871
$147$	−6.02494	−0.496928
$148$	3.09686	0.254560
$149$	−22.4748	−1.84121	−0.920605	−	0.390495i	$-0.872304\pi$
$149$	−22.4748	−1.84121	−0.920605	+	0.390495i	$0.872304\pi$
$150$	2.63839	0.215424
$151$	−16.5172	−1.34415	−0.672074	−	0.740484i	$-0.734597\pi$
$151$	−16.5172	−1.34415	−0.672074	+	0.740484i	$0.734597\pi$
$152$	2.33430	0.189337
$153$	31.7419	2.56618
$154$	−6.61141	−0.532763
$155$	−1.00000	−0.0803219
$156$	2.63839	0.211240
$157$	−5.59031	−0.446156	−0.223078	−	0.974801i	$-0.571610\pi$
$157$	−5.59031	−0.446156	−0.223078	+	0.974801i	$0.571610\pi$
$158$	4.06263	0.323205
$159$	−1.59891	−0.126802
$160$	−1.00000	−0.0790569
$161$	−10.1031	−0.796238
$162$	−5.19302	−0.408002
$163$	0.289194	0.0226514	0.0113257	−	0.999936i	$-0.496395\pi$
$163$	0.289194	0.0226514	0.0113257	+	0.999936i	$0.496395\pi$
$164$	−3.63489	−0.283837
$165$	8.03204	0.625294
$166$	14.9547	1.16071
$167$	14.3122	1.10751	0.553755	−	0.832680i	$-0.313195\pi$
$167$	14.3122	1.10751	0.553755	+	0.832680i	$0.313195\pi$
$168$	5.72988	0.442070
$169$	1.00000	0.0769231
$170$	−8.01343	−0.614602
$171$	9.24639	0.707089
$172$	−4.32649	−0.329892
$173$	17.1853	1.30657	0.653286	−	0.757111i	$-0.273390\pi$
$173$	17.1853	1.30657	0.653286	+	0.757111i	$0.273390\pi$
$174$	14.5224	1.10094
$175$	2.17174	0.164168
$176$	−3.04430	−0.229473
$177$	6.07392	0.456544
$178$	9.85856	0.738930
$179$	−15.3537	−1.14759	−0.573796	−	0.818999i	$-0.694530\pi$
$179$	−15.3537	−1.14759	−0.573796	+	0.818999i	$0.694530\pi$
$180$	−3.96109	−0.295242
$181$	3.22958	0.240053	0.120027	−	0.992771i	$-0.461702\pi$
$181$	3.22958	0.240053	0.120027	+	0.992771i	$0.461702\pi$
$182$	2.17174	0.160980
$183$	0.770452	0.0569535
$184$	−4.65210	−0.342957
$185$	−3.09686	−0.227685
$186$	2.63839	0.193456
$187$	−24.3953	−1.78396
$188$	−1.12007	−0.0816893
$189$	5.50695	0.400572
$190$	−2.33430	−0.169348
$191$	15.4010	1.11438	0.557188	−	0.830387i	$-0.311880\pi$
$191$	15.4010	1.11438	0.557188	+	0.830387i	$0.311880\pi$
$192$	2.63839	0.190409
$193$	2.38620	0.171762	0.0858811	−	0.996305i	$-0.472629\pi$
$193$	2.38620	0.171762	0.0858811	+	0.996305i	$0.472629\pi$
$194$	−2.38196	−0.171015
$195$	−2.63839	−0.188939
$196$	−2.28357	−0.163112
$197$	−22.5615	−1.60744	−0.803722	−	0.595005i	$-0.797150\pi$
$197$	−22.5615	−1.60744	−0.803722	+	0.595005i	$0.797150\pi$
$198$	−12.0588	−0.856978
$199$	−4.85256	−0.343989	−0.171994	−	0.985098i	$-0.555021\pi$
$199$	−4.85256	−0.343989	−0.171994	+	0.985098i	$0.555021\pi$
$200$	1.00000	0.0707107
$201$	−2.29451	−0.161842
$202$	6.08621	0.428224
$203$	11.9538	0.838991
$204$	21.1425	1.48027
$205$	3.63489	0.253871
$206$	2.86726	0.199772
$207$	−18.4274	−1.28079
$208$	1.00000	0.0693375
$209$	−7.10631	−0.491554
$210$	−5.72988	−0.395399
$211$	−4.53112	−0.311935	−0.155968	−	0.987762i	$-0.549850\pi$
$211$	−4.53112	−0.311935	−0.155968	+	0.987762i	$0.549850\pi$
$212$	−0.606019	−0.0416216
$213$	−1.74812	−0.119779
$214$	14.3975	0.984191
$215$	4.32649	0.295064
$216$	2.53574	0.172535
$217$	2.17174	0.147427
$218$	−3.70705	−0.251073
$219$	−42.0403	−2.84082
$220$	3.04430	0.205247
$221$	8.01343	0.539041
$222$	8.17071	0.548382
$223$	−0.737351	−0.0493767	−0.0246883	−	0.999695i	$-0.507859\pi$
$223$	−0.737351	−0.0493767	−0.0246883	+	0.999695i	$0.507859\pi$
$224$	2.17174	0.145105
$225$	3.96109	0.264073
$226$	10.9553	0.728733
$227$	2.41766	0.160466	0.0802328	−	0.996776i	$-0.474434\pi$
$227$	2.41766	0.160466	0.0802328	+	0.996776i	$0.474434\pi$
$228$	6.15879	0.407876
$229$	−6.16652	−0.407495	−0.203748	−	0.979023i	$-0.565312\pi$
$229$	−6.16652	−0.407495	−0.203748	+	0.979023i	$0.565312\pi$
$230$	4.65210	0.306750
$231$	−17.4435	−1.14770
$232$	5.50426	0.361372
$233$	−7.36936	−0.482783	−0.241392	−	0.970428i	$-0.577604\pi$
$233$	−7.36936	−0.482783	−0.241392	+	0.970428i	$0.577604\pi$
$234$	3.96109	0.258945
$235$	1.12007	0.0730651
$236$	2.30213	0.149856
$237$	10.7188	0.696260
$238$	17.4030	1.12807
$239$	6.69241	0.432896	0.216448	−	0.976294i	$-0.430553\pi$
$239$	6.69241	0.432896	0.216448	+	0.976294i	$0.430553\pi$
$240$	−2.63839	−0.170307
$241$	−19.3584	−1.24698	−0.623492	−	0.781830i	$-0.714287\pi$
$241$	−19.3584	−1.24698	−0.623492	+	0.781830i	$0.714287\pi$
$242$	−1.73224	−0.111353
$243$	−21.3084	−1.36694
$244$	0.292016	0.0186944
$245$	2.28357	0.145892
$246$	−9.59024	−0.611451
$247$	2.33430	0.148528
$248$	1.00000	0.0635001
$249$	39.4563	2.50044
$250$	−1.00000	−0.0632456
$251$	−8.90358	−0.561989	−0.280994	−	0.959709i	$-0.590664\pi$
$251$	−8.90358	−0.561989	−0.280994	+	0.959709i	$0.590664\pi$
$252$	8.60244	0.541903
$253$	14.1624	0.890381
$254$	12.0934	0.758806
$255$	−21.1425	−1.32400
$256$	1.00000	0.0625000
$257$	−20.3663	−1.27042	−0.635208	−	0.772341i	$-0.719086\pi$
$257$	−20.3663	−1.27042	−0.635208	+	0.772341i	$0.719086\pi$
$258$	−11.4150	−0.710665
$259$	6.72555	0.417905
$260$	−1.00000	−0.0620174
$261$	21.8029	1.34956
$262$	−3.15171	−0.194713
$263$	8.59817	0.530186	0.265093	−	0.964223i	$-0.414597\pi$
$263$	8.59817	0.530186	0.265093	+	0.964223i	$0.414597\pi$
$264$	−8.03204	−0.494338
$265$	0.606019	0.0372275
$266$	5.06948	0.310830
$267$	26.0107	1.59183
$268$	−0.869662	−0.0531231
$269$	−2.38498	−0.145415	−0.0727073	−	0.997353i	$-0.523164\pi$
$269$	−2.38498	−0.145415	−0.0727073	+	0.997353i	$0.523164\pi$
$270$	−2.53574	−0.154320
$271$	−18.1069	−1.09992	−0.549959	−	0.835192i	$-0.685357\pi$
$271$	−18.1069	−1.09992	−0.549959	+	0.835192i	$0.685357\pi$
$272$	8.01343	0.485885
$273$	5.72988	0.346788
$274$	−14.1157	−0.852763
$275$	−3.04430	−0.183578
$276$	−12.2740	−0.738811
$277$	−11.7377	−0.705253	−0.352626	−	0.935764i	$-0.614711\pi$
$277$	−11.7377	−0.705253	−0.352626	+	0.935764i	$0.614711\pi$
$278$	−11.6844	−0.700785
$279$	3.96109	0.237144
$280$	−2.17174	−0.129786
$281$	−25.3867	−1.51445	−0.757223	−	0.653157i	$-0.773444\pi$
$281$	−25.3867	−1.51445	−0.757223	+	0.653157i	$0.773444\pi$
$282$	−2.95517	−0.175978
$283$	−15.3911	−0.914905	−0.457452	−	0.889234i	$-0.651238\pi$
$283$	−15.3911	−0.914905	−0.457452	+	0.889234i	$0.651238\pi$
$284$	−0.662572	−0.0393164
$285$	−6.15879	−0.364816
$286$	−3.04430	−0.180013
$287$	−7.89401	−0.465969
$288$	3.96109	0.233410
$289$	47.2150	2.77735
$290$	−5.50426	−0.323221
$291$	−6.28453	−0.368406
$292$	−15.9341	−0.932472
$293$	0.579105	0.0338317	0.0169158	−	0.999857i	$-0.494615\pi$
$293$	0.579105	0.0338317	0.0169158	+	0.999857i	$0.494615\pi$
$294$	−6.02494	−0.351381
$295$	−2.30213	−0.134035
$296$	3.09686	0.180001
$297$	−7.71954	−0.447933
$298$	−22.4748	−1.30193
$299$	−4.65210	−0.269038
$300$	2.63839	0.152327
$301$	−9.39600	−0.541576
$302$	−16.5172	−0.950457
$303$	16.0578	0.922496
$304$	2.33430	0.133881
$305$	−0.292016	−0.0167208
$306$	31.7419	1.81457
$307$	−29.9049	−1.70676	−0.853380	−	0.521289i	$-0.825451\pi$
$307$	−29.9049	−1.70676	−0.853380	+	0.521289i	$0.825451\pi$
$308$	−6.61141	−0.376720
$309$	7.56495	0.430355
$310$	−1.00000	−0.0567962
$311$	10.7630	0.610311	0.305155	−	0.952303i	$-0.401292\pi$
$311$	10.7630	0.610311	0.305155	+	0.952303i	$0.401292\pi$
$312$	2.63839	0.149369
$313$	14.2028	0.802789	0.401394	−	0.915905i	$-0.368526\pi$
$313$	14.2028	0.802789	0.401394	+	0.915905i	$0.368526\pi$
$314$	−5.59031	−0.315480
$315$	−8.60244	−0.484693
$316$	4.06263	0.228541
$317$	−2.29858	−0.129101	−0.0645504	−	0.997914i	$-0.520561\pi$
$317$	−2.29858	−0.129101	−0.0645504	+	0.997914i	$0.520561\pi$
$318$	−1.59891	−0.0896626
$319$	−16.7566	−0.938190
$320$	−1.00000	−0.0559017
$321$	37.9861	2.12018
$322$	−10.1031	−0.563025
$323$	18.7058	1.04082
$324$	−5.19302	−0.288501
$325$	1.00000	0.0554700
$326$	0.289194	0.0160170
$327$	−9.78063	−0.540870
$328$	−3.63489	−0.200703
$329$	−2.43249	−0.134107
$330$	8.03204	0.442149
$331$	19.1992	1.05528	0.527642	−	0.849467i	$-0.323076\pi$
$331$	19.1992	1.05528	0.527642	+	0.849467i	$0.323076\pi$
$332$	14.9547	0.820745
$333$	12.2669	0.672224
$334$	14.3122	0.783127
$335$	0.869662	0.0475147
$336$	5.72988	0.312591
$337$	−31.5190	−1.71695	−0.858476	−	0.512854i	$-0.828588\pi$
$337$	−31.5190	−1.71695	−0.858476	+	0.512854i	$0.828588\pi$
$338$	1.00000	0.0543928
$339$	28.9042	1.56986
$340$	−8.01343	−0.434589
$341$	−3.04430	−0.164858
$342$	9.24639	0.499987
$343$	−20.1614	−1.08862
$344$	−4.32649	−0.233269
$345$	12.2740	0.660812
$346$	17.1853	0.923886
$347$	15.0204	0.806338	0.403169	−	0.915125i	$-0.367909\pi$
$347$	15.0204	0.806338	0.403169	+	0.915125i	$0.367909\pi$
$348$	14.5224	0.778480
$349$	28.0264	1.50022	0.750108	−	0.661315i	$-0.230001\pi$
$349$	28.0264	1.50022	0.750108	+	0.661315i	$0.230001\pi$
$350$	2.17174	0.116084
$351$	2.53574	0.135348
$352$	−3.04430	−0.162262
$353$	18.1756	0.967392	0.483696	−	0.875236i	$-0.339294\pi$
$353$	18.1756	0.967392	0.483696	+	0.875236i	$0.339294\pi$
$354$	6.07392	0.322825
$355$	0.662572	0.0351657
$356$	9.85856	0.522503
$357$	45.9160	2.43013
$358$	−15.3537	−0.811469
$359$	−20.9880	−1.10770	−0.553852	−	0.832615i	$-0.686843\pi$
$359$	−20.9880	−1.10770	−0.553852	+	0.832615i	$0.686843\pi$
$360$	−3.96109	−0.208768
$361$	−13.5510	−0.713212
$362$	3.22958	0.169743
$363$	−4.57033	−0.239880
$364$	2.17174	0.113830
$365$	15.9341	0.834029
$366$	0.770452	0.0402722
$367$	23.2613	1.21423	0.607115	−	0.794614i	$-0.292327\pi$
$367$	23.2613	1.21423	0.607115	+	0.794614i	$0.292327\pi$
$368$	−4.65210	−0.242507
$369$	−14.3981	−0.749536
$370$	−3.09686	−0.160998
$371$	−1.31611	−0.0683292
$372$	2.63839	0.136794
$373$	−20.9744	−1.08601	−0.543006	−	0.839729i	$-0.682714\pi$
$373$	−20.9744	−1.08601	−0.543006	+	0.839729i	$0.682714\pi$
$374$	−24.3953	−1.26145
$375$	−2.63839	−0.136246
$376$	−1.12007	−0.0577630
$377$	5.50426	0.283484
$378$	5.50695	0.283247
$379$	−27.3166	−1.40316	−0.701579	−	0.712592i	$-0.747521\pi$
$379$	−27.3166	−1.40316	−0.701579	+	0.712592i	$0.747521\pi$
$380$	−2.33430	−0.119747
$381$	31.9070	1.63465
$382$	15.4010	0.787982
$383$	33.6680	1.72035	0.860176	−	0.509997i	$-0.170353\pi$
$383$	33.6680	1.72035	0.860176	+	0.509997i	$0.170353\pi$
$384$	2.63839	0.134640
$385$	6.61141	0.336949
$386$	2.38620	0.121454
$387$	−17.1376	−0.871155
$388$	−2.38196	−0.120926
$389$	6.32373	0.320626	0.160313	−	0.987066i	$-0.448750\pi$
$389$	6.32373	0.320626	0.160313	+	0.987066i	$0.448750\pi$
$390$	−2.63839	−0.133600
$391$	−37.2793	−1.88529
$392$	−2.28357	−0.115338
$393$	−8.31544	−0.419458
$394$	−22.5615	−1.13663
$395$	−4.06263	−0.204413
$396$	−12.0588	−0.605975
$397$	−2.79938	−0.140497	−0.0702485	−	0.997530i	$-0.522379\pi$
$397$	−2.79938	−0.140497	−0.0702485	+	0.997530i	$0.522379\pi$
$398$	−4.85256	−0.243237
$399$	13.3753	0.669601
$400$	1.00000	0.0500000
$401$	−5.48303	−0.273810	−0.136905	−	0.990584i	$-0.543715\pi$
$401$	−5.48303	−0.273810	−0.136905	+	0.990584i	$0.543715\pi$
$402$	−2.29451	−0.114440
$403$	1.00000	0.0498135
$404$	6.08621	0.302800
$405$	5.19302	0.258043
$406$	11.9538	0.593256
$407$	−9.42776	−0.467317
$408$	21.1425	1.04671
$409$	3.26729	0.161557	0.0807785	−	0.996732i	$-0.474259\pi$
$409$	3.26729	0.161557	0.0807785	+	0.996732i	$0.474259\pi$
$410$	3.63489	0.179514
$411$	−37.2428	−1.83705
$412$	2.86726	0.141260
$413$	4.99963	0.246015
$414$	−18.4274	−0.905657
$415$	−14.9547	−0.734097
$416$	1.00000	0.0490290
$417$	−30.8281	−1.50966
$418$	−7.10631	−0.347581
$419$	1.23504	0.0603357	0.0301679	−	0.999545i	$-0.490396\pi$
$419$	1.23504	0.0603357	0.0301679	+	0.999545i	$0.490396\pi$
$420$	−5.72988	−0.279590
$421$	−26.4397	−1.28859	−0.644296	−	0.764776i	$-0.722850\pi$
$421$	−26.4397	−1.28859	−0.644296	+	0.764776i	$0.722850\pi$
$422$	−4.53112	−0.220572
$423$	−4.43669	−0.215719
$424$	−0.606019	−0.0294309
$425$	8.01343	0.388708
$426$	−1.74812	−0.0846968
$427$	0.634182	0.0306902
$428$	14.3975	0.695928
$429$	−8.03204	−0.387791
$430$	4.32649	0.208642
$431$	27.6299	1.33088	0.665442	−	0.746450i	$-0.268243\pi$
$431$	27.6299	1.33088	0.665442	+	0.746450i	$0.268243\pi$
$432$	2.53574	0.122001
$433$	11.7571	0.565012	0.282506	−	0.959266i	$-0.408834\pi$
$433$	11.7571	0.565012	0.282506	+	0.959266i	$0.408834\pi$
$434$	2.17174	0.104247
$435$	−14.5224	−0.696294
$436$	−3.70705	−0.177535
$437$	−10.8594	−0.519476
$438$	−42.0403	−2.00876
$439$	6.81192	0.325115	0.162558	−	0.986699i	$-0.448026\pi$
$439$	6.81192	0.325115	0.162558	+	0.986699i	$0.448026\pi$
$440$	3.04430	0.145131
$441$	−9.04542	−0.430734
$442$	8.01343	0.381160
$443$	29.7087	1.41150	0.705752	−	0.708459i	$-0.250609\pi$
$443$	29.7087	1.41150	0.705752	+	0.708459i	$0.250609\pi$
$444$	8.17071	0.387765
$445$	−9.85856	−0.467341
$446$	−0.737351	−0.0349146
$447$	−59.2973	−2.80467
$448$	2.17174	0.102605
$449$	−34.1207	−1.61025	−0.805127	−	0.593103i	$-0.797903\pi$
$449$	−34.1207	−1.61025	−0.805127	+	0.593103i	$0.797903\pi$
$450$	3.96109	0.186728
$451$	11.0657	0.521063
$452$	10.9553	0.515292
$453$	−43.5787	−2.04751
$454$	2.41766	0.113466
$455$	−2.17174	−0.101813
$456$	6.15879	0.288412
$457$	−18.6174	−0.870885	−0.435442	−	0.900217i	$-0.643408\pi$
$457$	−18.6174	−0.870885	−0.435442	+	0.900217i	$0.643408\pi$
$458$	−6.16652	−0.288143
$459$	20.3199	0.948453
$460$	4.65210	0.216905
$461$	10.1431	0.472413	0.236207	−	0.971703i	$-0.424096\pi$
$461$	10.1431	0.472413	0.236207	+	0.971703i	$0.424096\pi$
$462$	−17.4435	−0.811544
$463$	−9.93757	−0.461838	−0.230919	−	0.972973i	$-0.574173\pi$
$463$	−9.93757	−0.461838	−0.230919	+	0.972973i	$0.574173\pi$
$464$	5.50426	0.255529
$465$	−2.63839	−0.122352
$466$	−7.36936	−0.341379
$467$	−38.4926	−1.78123	−0.890614	−	0.454761i	$-0.849725\pi$
$467$	−38.4926	−1.78123	−0.890614	+	0.454761i	$0.849725\pi$
$468$	3.96109	0.183102
$469$	−1.88868	−0.0872109
$470$	1.12007	0.0516648
$471$	−14.7494	−0.679617
$472$	2.30213	0.105964
$473$	13.1711	0.605610
$474$	10.7188	0.492330
$475$	2.33430	0.107105
$476$	17.4030	0.797667
$477$	−2.40050	−0.109911
$478$	6.69241	0.306104
$479$	−5.40623	−0.247017	−0.123508	−	0.992344i	$-0.539415\pi$
$479$	−5.40623	−0.247017	−0.123508	+	0.992344i	$0.539415\pi$
$480$	−2.63839	−0.120425
$481$	3.09686	0.141204
$482$	−19.3584	−0.881751
$483$	−26.6560	−1.21289
$484$	−1.73224	−0.0787383
$485$	2.38196	0.108159
$486$	−21.3084	−0.966569
$487$	−19.1324	−0.866971	−0.433485	−	0.901161i	$-0.642716\pi$
$487$	−19.1324	−0.866971	−0.433485	+	0.901161i	$0.642716\pi$
$488$	0.292016	0.0132190
$489$	0.763007	0.0345044
$490$	2.28357	0.103161
$491$	−24.7794	−1.11828	−0.559140	−	0.829073i	$-0.688869\pi$
$491$	−24.7794	−1.11828	−0.559140	+	0.829073i	$0.688869\pi$
$492$	−9.59024	−0.432361
$493$	44.1079	1.98652
$494$	2.33430	0.105025
$495$	12.0588	0.542001
$496$	1.00000	0.0449013
$497$	−1.43893	−0.0645449
$498$	39.4563	1.76808
$499$	−20.8152	−0.931814	−0.465907	−	0.884834i	$-0.654272\pi$
$499$	−20.8152	−0.931814	−0.465907	+	0.884834i	$0.654272\pi$
$500$	−1.00000	−0.0447214
$501$	37.7611	1.68704
$502$	−8.90358	−0.397386
$503$	−30.2473	−1.34866	−0.674330	−	0.738430i	$-0.735567\pi$
$503$	−30.2473	−1.34866	−0.674330	+	0.738430i	$0.735567\pi$
$504$	8.60244	0.383183
$505$	−6.08621	−0.270833
$506$	14.1624	0.629595
$507$	2.63839	0.117175
$508$	12.0934	0.536557
$509$	−25.6550	−1.13714	−0.568570	−	0.822635i	$-0.692503\pi$
$509$	−25.6550	−1.13714	−0.568570	+	0.822635i	$0.692503\pi$
$510$	−21.1425	−0.936207
$511$	−34.6046	−1.53082
$512$	1.00000	0.0441942
$513$	5.91917	0.261338
$514$	−20.3663	−0.898320
$515$	−2.86726	−0.126347
$516$	−11.4150	−0.502516
$517$	3.40982	0.149964
$518$	6.72555	0.295504
$519$	45.3414	1.99027
$520$	−1.00000	−0.0438529
$521$	20.2542	0.887352	0.443676	−	0.896187i	$-0.353674\pi$
$521$	20.2542	0.887352	0.443676	+	0.896187i	$0.353674\pi$
$522$	21.8029	0.954286
$523$	15.8162	0.691593	0.345797	−	0.938309i	$-0.387609\pi$
$523$	15.8162	0.691593	0.345797	+	0.938309i	$0.387609\pi$
$524$	−3.15171	−0.137683
$525$	5.72988	0.250072
$526$	8.59817	0.374898
$527$	8.01343	0.349070
$528$	−8.03204	−0.349550
$529$	−1.35797	−0.0590423
$530$	0.606019	0.0263238
$531$	9.11897	0.395729
$532$	5.06948	0.219790
$533$	−3.63489	−0.157444
$534$	26.0107	1.12559
$535$	−14.3975	−0.622457
$536$	−0.869662	−0.0375637
$537$	−40.5091	−1.74810
$538$	−2.38498	−0.102824
$539$	6.95186	0.299438
$540$	−2.53574	−0.109121
$541$	−36.2543	−1.55869	−0.779347	−	0.626592i	$-0.784449\pi$
$541$	−36.2543	−1.55869	−0.779347	+	0.626592i	$0.784449\pi$
$542$	−18.1069	−0.777759
$543$	8.52090	0.365667
$544$	8.01343	0.343573
$545$	3.70705	0.158792
$546$	5.72988	0.245216
$547$	42.0994	1.80004	0.900021	−	0.435847i	$-0.143551\pi$
$547$	42.0994	1.80004	0.900021	+	0.435847i	$0.143551\pi$
$548$	−14.1157	−0.602994
$549$	1.15670	0.0493669
$550$	−3.04430	−0.129809
$551$	12.8486	0.547369
$552$	−12.2740	−0.522418
$553$	8.82295	0.375190
$554$	−11.7377	−0.498689
$555$	−8.17071	−0.346827
$556$	−11.6844	−0.495530
$557$	16.0851	0.681547	0.340774	−	0.940145i	$-0.389311\pi$
$557$	16.0851	0.681547	0.340774	+	0.940145i	$0.389311\pi$
$558$	3.96109	0.167686
$559$	−4.32649	−0.182991
$560$	−2.17174	−0.0917726
$561$	−64.3642	−2.71746
$562$	−25.3867	−1.07087
$563$	10.6756	0.449924	0.224962	−	0.974368i	$-0.427774\pi$
$563$	10.6756	0.449924	0.224962	+	0.974368i	$0.427774\pi$
$564$	−2.95517	−0.124435
$565$	−10.9553	−0.460891
$566$	−15.3911	−0.646935
$567$	−11.2779	−0.473626
$568$	−0.662572	−0.0278009
$569$	12.0952	0.507057	0.253528	−	0.967328i	$-0.418409\pi$
$569$	12.0952	0.507057	0.253528	+	0.967328i	$0.418409\pi$
$570$	−6.15879	−0.257964
$571$	−0.104732	−0.00438291	−0.00219145	−	0.999998i	$-0.500698\pi$
$571$	−0.104732	−0.00438291	−0.00219145	+	0.999998i	$0.500698\pi$
$572$	−3.04430	−0.127289
$573$	40.6337	1.69750
$574$	−7.89401	−0.329490
$575$	−4.65210	−0.194006
$576$	3.96109	0.165046
$577$	35.5624	1.48048	0.740242	−	0.672341i	$-0.234711\pi$
$577$	35.5624	1.48048	0.740242	+	0.672341i	$0.234711\pi$
$578$	47.2150	1.96388
$579$	6.29571	0.261641
$580$	−5.50426	−0.228552
$581$	32.4776	1.34740
$582$	−6.28453	−0.260502
$583$	1.84490	0.0764081
$584$	−15.9341	−0.659357
$585$	−3.96109	−0.163771
$586$	0.579105	0.0239226
$587$	−16.7599	−0.691754	−0.345877	−	0.938280i	$-0.612419\pi$
$587$	−16.7599	−0.691754	−0.345877	+	0.938280i	$0.612419\pi$
$588$	−6.02494	−0.248464
$589$	2.33430	0.0961832
$590$	−2.30213	−0.0947774
$591$	−59.5261	−2.44858
$592$	3.09686	0.127280
$593$	−12.0013	−0.492835	−0.246417	−	0.969164i	$-0.579253\pi$
$593$	−12.0013	−0.492835	−0.246417	+	0.969164i	$0.579253\pi$
$594$	−7.71954	−0.316737
$595$	−17.4030	−0.713455
$596$	−22.4748	−0.920605
$597$	−12.8029	−0.523990
$598$	−4.65210	−0.190238
$599$	7.73214	0.315926	0.157963	−	0.987445i	$-0.449507\pi$
$599$	7.73214	0.315926	0.157963	+	0.987445i	$0.449507\pi$
$600$	2.63839	0.107712
$601$	19.0805	0.778309	0.389154	−	0.921173i	$-0.372767\pi$
$601$	19.0805	0.778309	0.389154	+	0.921173i	$0.372767\pi$
$602$	−9.39600	−0.382952
$603$	−3.44481	−0.140284
$604$	−16.5172	−0.672074
$605$	1.73224	0.0704257
$606$	16.0578	0.652303
$607$	15.4612	0.627549	0.313775	−	0.949497i	$-0.398406\pi$
$607$	15.4612	0.627549	0.313775	+	0.949497i	$0.398406\pi$
$608$	2.33430	0.0946684
$609$	31.5387	1.27801
$610$	−0.292016	−0.0118234
$611$	−1.12007	−0.0453130
$612$	31.7419	1.28309
$613$	−17.2716	−0.697592	−0.348796	−	0.937199i	$-0.613409\pi$
$613$	−17.2716	−0.697592	−0.348796	+	0.937199i	$0.613409\pi$
$614$	−29.9049	−1.20686
$615$	9.59024	0.386716
$616$	−6.61141	−0.266381
$617$	10.9371	0.440313	0.220156	−	0.975465i	$-0.429343\pi$
$617$	10.9371	0.440313	0.220156	+	0.975465i	$0.429343\pi$
$618$	7.56495	0.304307
$619$	29.3213	1.17852	0.589262	−	0.807942i	$-0.299419\pi$
$619$	29.3213	1.17852	0.589262	+	0.807942i	$0.299419\pi$
$620$	−1.00000	−0.0401610
$621$	−11.7965	−0.473377
$622$	10.7630	0.431555
$623$	21.4102	0.857781
$624$	2.63839	0.105620
$625$	1.00000	0.0400000
$626$	14.2028	0.567657
$627$	−18.7492	−0.748771
$628$	−5.59031	−0.223078
$629$	24.8164	0.989496
$630$	−8.60244	−0.342730
$631$	−34.1983	−1.36141	−0.680706	−	0.732557i	$-0.738327\pi$
$631$	−34.1983	−1.36141	−0.680706	+	0.732557i	$0.738327\pi$
$632$	4.06263	0.161603
$633$	−11.9549	−0.475163
$634$	−2.29858	−0.0912881
$635$	−12.0934	−0.479911
$636$	−1.59891	−0.0634010
$637$	−2.28357	−0.0904782
$638$	−16.7566	−0.663400
$639$	−2.62451	−0.103824
$640$	−1.00000	−0.0395285
$641$	−37.8361	−1.49444	−0.747219	−	0.664578i	$-0.768611\pi$
$641$	−37.8361	−1.49444	−0.747219	+	0.664578i	$0.768611\pi$
$642$	37.9861	1.49919
$643$	22.3535	0.881537	0.440769	−	0.897621i	$-0.354706\pi$
$643$	22.3535	0.881537	0.440769	+	0.897621i	$0.354706\pi$
$644$	−10.1031	−0.398119
$645$	11.4150	0.449464
$646$	18.7058	0.735968
$647$	19.8499	0.780382	0.390191	−	0.920734i	$-0.372409\pi$
$647$	19.8499	0.780382	0.390191	+	0.920734i	$0.372409\pi$
$648$	−5.19302	−0.204001
$649$	−7.00838	−0.275103
$650$	1.00000	0.0392232
$651$	5.72988	0.224572
$652$	0.289194	0.0113257
$653$	23.9774	0.938308	0.469154	−	0.883116i	$-0.344559\pi$
$653$	23.9774	0.938308	0.469154	+	0.883116i	$0.344559\pi$
$654$	−9.78063	−0.382453
$655$	3.15171	0.123148
$656$	−3.63489	−0.141918
$657$	−63.1164	−2.46241
$658$	−2.43249	−0.0948283
$659$	−14.3153	−0.557646	−0.278823	−	0.960343i	$-0.589944\pi$
$659$	−14.3153	−0.557646	−0.278823	+	0.960343i	$0.589944\pi$
$660$	8.03204	0.312647
$661$	50.2365	1.95397	0.976986	−	0.213301i	$-0.0684216\pi$
$661$	50.2365	1.95397	0.976986	+	0.213301i	$0.0684216\pi$
$662$	19.1992	0.746198
$663$	21.1425	0.821108
$664$	14.9547	0.580355
$665$	−5.06948	−0.196586
$666$	12.2669	0.475334
$667$	−25.6063	−0.991482
$668$	14.3122	0.553755
$669$	−1.94542	−0.0752142
$670$	0.869662	0.0335980
$671$	−0.888985	−0.0343189
$672$	5.72988	0.221035
$673$	−4.31641	−0.166385	−0.0831927	−	0.996533i	$-0.526512\pi$
$673$	−4.31641	−0.166385	−0.0831927	+	0.996533i	$0.526512\pi$
$674$	−31.5190	−1.21407
$675$	2.53574	0.0976006
$676$	1.00000	0.0384615
$677$	−1.84832	−0.0710367	−0.0355183	−	0.999369i	$-0.511308\pi$
$677$	−1.84832	−0.0710367	−0.0355183	+	0.999369i	$0.511308\pi$
$678$	28.9042	1.11006
$679$	−5.17298	−0.198521
$680$	−8.01343	−0.307301
$681$	6.37872	0.244433
$682$	−3.04430	−0.116572
$683$	47.8213	1.82983	0.914916	−	0.403644i	$-0.132257\pi$
$683$	47.8213	1.82983	0.914916	+	0.403644i	$0.132257\pi$
$684$	9.24639	0.353544
$685$	14.1157	0.539335
$686$	−20.1614	−0.769768
$687$	−16.2697	−0.620727
$688$	−4.32649	−0.164946
$689$	−0.606019	−0.0230875
$690$	12.2740	0.467265
$691$	−12.7707	−0.485822	−0.242911	−	0.970049i	$-0.578102\pi$
$691$	−12.7707	−0.485822	−0.242911	+	0.970049i	$0.578102\pi$
$692$	17.1853	0.653286
$693$	−26.1884	−0.994816
$694$	15.0204	0.570167
$695$	11.6844	0.443216
$696$	14.5224	0.550469
$697$	−29.1279	−1.10330
$698$	28.0264	1.06081
$699$	−19.4432	−0.735411
$700$	2.17174	0.0820839
$701$	8.31904	0.314206	0.157103	−	0.987582i	$-0.449785\pi$
$701$	8.31904	0.314206	0.157103	+	0.987582i	$0.449785\pi$
$702$	2.53574	0.0957052
$703$	7.22900	0.272647
$704$	−3.04430	−0.114736
$705$	2.95517	0.111298
$706$	18.1756	0.684049
$707$	13.2176	0.497101
$708$	6.07392	0.228272
$709$	−13.5812	−0.510053	−0.255027	−	0.966934i	$-0.582084\pi$
$709$	−13.5812	−0.510053	−0.255027	+	0.966934i	$0.582084\pi$
$710$	0.662572	0.0248659
$711$	16.0924	0.603514
$712$	9.85856	0.369465
$713$	−4.65210	−0.174222
$714$	45.9160	1.71836
$715$	3.04430	0.113850
$716$	−15.3537	−0.573796
$717$	17.6572	0.659419
$718$	−20.9880	−0.783265
$719$	−0.395574	−0.0147524	−0.00737622	−	0.999973i	$-0.502348\pi$
$719$	−0.395574	−0.0147524	−0.00737622	+	0.999973i	$0.502348\pi$
$720$	−3.96109	−0.147621
$721$	6.22694	0.231903
$722$	−13.5510	−0.504317
$723$	−51.0750	−1.89950
$724$	3.22958	0.120027
$725$	5.50426	0.204423
$726$	−4.57033	−0.169621
$727$	43.2648	1.60460	0.802301	−	0.596919i	$-0.203609\pi$
$727$	43.2648	1.60460	0.802301	+	0.596919i	$0.203609\pi$
$728$	2.17174	0.0804899
$729$	−40.6408	−1.50522
$730$	15.9341	0.589747
$731$	−34.6700	−1.28232
$732$	0.770452	0.0284767
$733$	−15.3357	−0.566438	−0.283219	−	0.959055i	$-0.591402\pi$
$733$	−15.3357	−0.566438	−0.283219	+	0.959055i	$0.591402\pi$
$734$	23.2613	0.858590
$735$	6.02494	0.222233
$736$	−4.65210	−0.171479
$737$	2.64751	0.0975224
$738$	−14.3981	−0.530002
$739$	−0.624796	−0.0229835	−0.0114917	−	0.999934i	$-0.503658\pi$
$739$	−0.624796	−0.0229835	−0.0114917	+	0.999934i	$0.503658\pi$
$740$	−3.09686	−0.113843
$741$	6.15879	0.226249
$742$	−1.31611	−0.0483160
$743$	31.4127	1.15242	0.576210	−	0.817302i	$-0.304531\pi$
$743$	31.4127	1.15242	0.576210	+	0.817302i	$0.304531\pi$
$744$	2.63839	0.0967280
$745$	22.4748	0.823414
$746$	−20.9744	−0.767926
$747$	59.2369	2.16737
$748$	−24.3953	−0.891979
$749$	31.2675	1.14249
$750$	−2.63839	−0.0963403
$751$	−19.8891	−0.725762	−0.362881	−	0.931835i	$-0.618207\pi$
$751$	−19.8891	−0.725762	−0.362881	+	0.931835i	$0.618207\pi$
$752$	−1.12007	−0.0408446
$753$	−23.4911	−0.856063
$754$	5.50426	0.200453
$755$	16.5172	0.601122
$756$	5.50695	0.200286
$757$	1.79507	0.0652429	0.0326215	−	0.999468i	$-0.489614\pi$
$757$	1.79507	0.0652429	0.0326215	+	0.999468i	$0.489614\pi$
$758$	−27.3166	−0.992182
$759$	37.3659	1.35629
$760$	−2.33430	−0.0846740
$761$	40.5342	1.46936	0.734682	−	0.678412i	$-0.237331\pi$
$761$	40.5342	1.46936	0.734682	+	0.678412i	$0.237331\pi$
$762$	31.9070	1.15587
$763$	−8.05072	−0.291456
$764$	15.4010	0.557188
$765$	−31.7419	−1.14763
$766$	33.6680	1.21647
$767$	2.30213	0.0831252
$768$	2.63839	0.0952046
$769$	−4.92492	−0.177597	−0.0887986	−	0.996050i	$-0.528303\pi$
$769$	−4.92492	−0.177597	−0.0887986	+	0.996050i	$0.528303\pi$
$770$	6.61141	0.238259
$771$	−53.7342	−1.93519
$772$	2.38620	0.0858811
$773$	11.2684	0.405298	0.202649	−	0.979251i	$-0.435045\pi$
$773$	11.2684	0.405298	0.202649	+	0.979251i	$0.435045\pi$
$774$	−17.1376	−0.616000
$775$	1.00000	0.0359211
$776$	−2.38196	−0.0855073
$777$	17.7446	0.636584
$778$	6.32373	0.226717
$779$	−8.48492	−0.304004
$780$	−2.63839	−0.0944695
$781$	2.01707	0.0721763
$782$	−37.2793	−1.33310
$783$	13.9573	0.498795
$784$	−2.28357	−0.0815560
$785$	5.59031	0.199527
$786$	−8.31544	−0.296602
$787$	−9.15926	−0.326492	−0.163246	−	0.986585i	$-0.552196\pi$
$787$	−9.15926	−0.326492	−0.163246	+	0.986585i	$0.552196\pi$
$788$	−22.5615	−0.803722
$789$	22.6853	0.807619
$790$	−4.06263	−0.144542
$791$	23.7919	0.845943
$792$	−12.0588	−0.428489
$793$	0.292016	0.0103698
$794$	−2.79938	−0.0993463
$795$	1.59891	0.0567076
$796$	−4.85256	−0.171994
$797$	55.0042	1.94835	0.974175	−	0.225796i	$-0.0724984\pi$
$797$	55.0042	1.94835	0.974175	+	0.225796i	$0.0724984\pi$
$798$	13.3753	0.473479
$799$	−8.97557	−0.317533
$800$	1.00000	0.0353553
$801$	39.0507	1.37979
$802$	−5.48303	−0.193613
$803$	48.5081	1.71182
$804$	−2.29451	−0.0809210
$805$	10.1031	0.356088
$806$	1.00000	0.0352235
$807$	−6.29249	−0.221506
$808$	6.08621	0.214112
$809$	46.0801	1.62009	0.810045	−	0.586368i	$-0.199443\pi$
$809$	46.0801	1.62009	0.810045	+	0.586368i	$0.199443\pi$
$810$	5.19302	0.182464
$811$	37.6626	1.32251	0.661257	−	0.750159i	$-0.270023\pi$
$811$	37.6626	1.32251	0.661257	+	0.750159i	$0.270023\pi$
$812$	11.9538	0.419496
$813$	−47.7731	−1.67548
$814$	−9.42776	−0.330443
$815$	−0.289194	−0.0101300
$816$	21.1425	0.740137
$817$	−10.0993	−0.353331
$818$	3.26729	0.114238
$819$	8.60244	0.300594
$820$	3.63489	0.126936
$821$	22.0944	0.771101	0.385551	−	0.922687i	$-0.374012\pi$
$821$	22.0944	0.771101	0.385551	+	0.922687i	$0.374012\pi$
$822$	−37.2428	−1.29899
$823$	−9.63666	−0.335913	−0.167956	−	0.985794i	$-0.553717\pi$
$823$	−9.63666	−0.335913	−0.167956	+	0.985794i	$0.553717\pi$
$824$	2.86726	0.0998858
$825$	−8.03204	−0.279640
$826$	4.99963	0.173959
$827$	20.7053	0.719994	0.359997	−	0.932954i	$-0.382778\pi$
$827$	20.7053	0.719994	0.359997	+	0.932954i	$0.382778\pi$
$828$	−18.4274	−0.640396
$829$	48.9679	1.70073	0.850363	−	0.526196i	$-0.176382\pi$
$829$	48.9679	1.70073	0.850363	+	0.526196i	$0.176382\pi$
$830$	−14.9547	−0.519085
$831$	−30.9687	−1.07429
$832$	1.00000	0.0346688
$833$	−18.2992	−0.634029
$834$	−30.8281	−1.06749
$835$	−14.3122	−0.495293
$836$	−7.10631	−0.245777
$837$	2.53574	0.0876479
$838$	1.23504	0.0426638
$839$	−24.9636	−0.861839	−0.430920	−	0.902390i	$-0.641811\pi$
$839$	−24.9636	−0.861839	−0.430920	+	0.902390i	$0.641811\pi$
$840$	−5.72988	−0.197700
$841$	1.29683	0.0447183
$842$	−26.4397	−0.911173
$843$	−66.9800	−2.30692
$844$	−4.53112	−0.155968
$845$	−1.00000	−0.0344010
$846$	−4.43669	−0.152536
$847$	−3.76197	−0.129263
$848$	−0.606019	−0.0208108
$849$	−40.6076	−1.39365
$850$	8.01343	0.274858
$851$	−14.4069	−0.493862
$852$	−1.74812	−0.0598897
$853$	7.83465	0.268253	0.134127	−	0.990964i	$-0.457177\pi$
$853$	7.83465	0.268253	0.134127	+	0.990964i	$0.457177\pi$
$854$	0.634182	0.0217013
$855$	−9.24639	−0.316220
$856$	14.3975	0.492095
$857$	−16.1323	−0.551068	−0.275534	−	0.961291i	$-0.588855\pi$
$857$	−16.1323	−0.551068	−0.275534	+	0.961291i	$0.588855\pi$
$858$	−8.03204	−0.274209
$859$	50.5685	1.72537	0.862687	−	0.505738i	$-0.168780\pi$
$859$	50.5685	1.72537	0.862687	+	0.505738i	$0.168780\pi$
$860$	4.32649	0.147532
$861$	−20.8275	−0.709798
$862$	27.6299	0.941077
$863$	43.7893	1.49061	0.745303	−	0.666726i	$-0.232305\pi$
$863$	43.7893	1.49061	0.745303	+	0.666726i	$0.232305\pi$
$864$	2.53574	0.0862675
$865$	−17.1853	−0.584317
$866$	11.7571	0.399523
$867$	124.571	4.23067
$868$	2.17174	0.0737135
$869$	−12.3678	−0.419550
$870$	−14.5224	−0.492354
$871$	−0.869662	−0.0294674
$872$	−3.70705	−0.125536
$873$	−9.43516	−0.319332
$874$	−10.8594	−0.367325
$875$	−2.17174	−0.0734180
$876$	−42.0403	−1.42041
$877$	21.3131	0.719693	0.359847	−	0.933012i	$-0.382829\pi$
$877$	21.3131	0.719693	0.359847	+	0.933012i	$0.382829\pi$
$878$	6.81192	0.229891
$879$	1.52790	0.0515349
$880$	3.04430	0.102623
$881$	−56.2747	−1.89594	−0.947971	−	0.318355i	$-0.896870\pi$
$881$	−56.2747	−1.89594	−0.947971	+	0.318355i	$0.896870\pi$
$882$	−9.04542	−0.304575
$883$	18.8279	0.633609	0.316805	−	0.948491i	$-0.397390\pi$
$883$	18.8279	0.633609	0.316805	+	0.948491i	$0.397390\pi$
$884$	8.01343	0.269521
$885$	−6.07392	−0.204173
$886$	29.7087	0.998083
$887$	−30.2007	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$887$	−30.2007	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$888$	8.17071	0.274191
$889$	26.2636	0.880854
$890$	−9.85856	−0.330460
$891$	15.8091	0.529625
$892$	−0.737351	−0.0246883
$893$	−2.61457	−0.0874934
$894$	−59.2973	−1.98320
$895$	15.3537	0.513218
$896$	2.17174	0.0725526
$897$	−12.2740	−0.409818
$898$	−34.1207	−1.13862
$899$	5.50426	0.183577
$900$	3.96109	0.132036
$901$	−4.85629	−0.161786
$902$	11.0657	0.368447
$903$	−24.7903	−0.824969
$904$	10.9553	0.364366
$905$	−3.22958	−0.107355
$906$	−43.5787	−1.44781
$907$	−25.0254	−0.830953	−0.415477	−	0.909604i	$-0.636385\pi$
$907$	−25.0254	−0.830953	−0.415477	+	0.909604i	$0.636385\pi$
$908$	2.41766	0.0802328
$909$	24.1081	0.799614
$910$	−2.17174	−0.0719923
$911$	42.7512	1.41641	0.708205	−	0.706007i	$-0.249505\pi$
$911$	42.7512	1.41641	0.708205	+	0.706007i	$0.249505\pi$
$912$	6.15879	0.203938
$913$	−45.5266	−1.50671
$914$	−18.6174	−0.615808
$915$	−0.770452	−0.0254704
$916$	−6.16652	−0.203748
$917$	−6.84468	−0.226031
$918$	20.3199	0.670658
$919$	−7.89459	−0.260419	−0.130209	−	0.991487i	$-0.541565\pi$
$919$	−7.89459	−0.260419	−0.130209	+	0.991487i	$0.541565\pi$
$920$	4.65210	0.153375
$921$	−78.9006	−2.59986
$922$	10.1431	0.334046
$923$	−0.662572	−0.0218088
$924$	−17.4435	−0.573848
$925$	3.09686	0.101824
$926$	−9.93757	−0.326569
$927$	11.3575	0.373029
$928$	5.50426	0.180686
$929$	−29.2540	−0.959792	−0.479896	−	0.877325i	$-0.659326\pi$
$929$	−29.2540	−0.959792	−0.479896	+	0.877325i	$0.659326\pi$
$930$	−2.63839	−0.0865162
$931$	−5.33053	−0.174701
$932$	−7.36936	−0.241392
$933$	28.3968	0.929671
$934$	−38.4926	−1.25952
$935$	24.3953	0.797810
$936$	3.96109	0.129472
$937$	−17.5449	−0.573166	−0.286583	−	0.958055i	$-0.592519\pi$
$937$	−17.5449	−0.573166	−0.286583	+	0.958055i	$0.592519\pi$
$938$	−1.88868	−0.0616674
$939$	37.4725	1.22287
$940$	1.12007	0.0365325
$941$	1.91926	0.0625660	0.0312830	−	0.999511i	$-0.490041\pi$
$941$	1.91926	0.0625660	0.0312830	+	0.999511i	$0.490041\pi$
$942$	−14.7494	−0.480562
$943$	16.9098	0.550660
$944$	2.30213	0.0749281
$945$	−5.50695	−0.179141
$946$	13.1711	0.428231
$947$	18.5632	0.603222	0.301611	−	0.953431i	$-0.402476\pi$
$947$	18.5632	0.603222	0.301611	+	0.953431i	$0.402476\pi$
$948$	10.7188	0.348130
$949$	−15.9341	−0.517243
$950$	2.33430	0.0757347
$951$	−6.06453	−0.196656
$952$	17.4030	0.564036
$953$	−61.5535	−1.99391	−0.996956	−	0.0779625i	$-0.975159\pi$
$953$	−61.5535	−1.99391	−0.996956	+	0.0779625i	$0.975159\pi$
$954$	−2.40050	−0.0777190
$955$	−15.4010	−0.498364
$956$	6.69241	0.216448
$957$	−44.2104	−1.42912
$958$	−5.40623	−0.174667
$959$	−30.6556	−0.989922
$960$	−2.63839	−0.0851536
$961$	1.00000	0.0322581
$962$	3.09686	0.0998466
$963$	57.0297	1.83776
$964$	−19.3584	−0.623492
$965$	−2.38620	−0.0768144
$966$	−26.6560	−0.857642
$967$	1.45125	0.0466690	0.0233345	−	0.999728i	$-0.492572\pi$
$967$	1.45125	0.0466690	0.0233345	+	0.999728i	$0.492572\pi$
$968$	−1.73224	−0.0556764
$969$	49.3530	1.58545
$970$	2.38196	0.0764801
$971$	−45.0408	−1.44543	−0.722715	−	0.691146i	$-0.757106\pi$
$971$	−45.0408	−1.44543	−0.722715	+	0.691146i	$0.757106\pi$
$972$	−21.3084	−0.683468
$973$	−25.3755	−0.813501
$974$	−19.1324	−0.613041
$975$	2.63839	0.0844961
$976$	0.292016	0.00934721
$977$	−37.3239	−1.19410	−0.597049	−	0.802205i	$-0.703660\pi$
$977$	−37.3239	−1.19410	−0.597049	+	0.802205i	$0.703660\pi$
$978$	0.763007	0.0243983
$979$	−30.0124	−0.959201
$980$	2.28357	0.0729459
$981$	−14.6840	−0.468823
$982$	−24.7794	−0.790743
$983$	−26.7707	−0.853853	−0.426927	−	0.904286i	$-0.640404\pi$
$983$	−26.7707	−0.853853	−0.426927	+	0.904286i	$0.640404\pi$
$984$	−9.59024	−0.305726
$985$	22.5615	0.718871
$986$	44.1079	1.40468
$987$	−6.41785	−0.204282
$988$	2.33430	0.0742640
$989$	20.1273	0.640010
$990$	12.0588	0.383252
$991$	24.5703	0.780502	0.390251	−	0.920708i	$-0.372388\pi$
$991$	24.5703	0.780502	0.390251	+	0.920708i	$0.372388\pi$
$992$	1.00000	0.0317500
$993$	50.6550	1.60749
$994$	−1.43893	−0.0456401
$995$	4.85256	0.153837
$996$	39.4563	1.25022
$997$	−10.4860	−0.332095	−0.166047	−	0.986118i	$-0.553100\pi$
$997$	−10.4860	−0.332095	−0.166047	+	0.986118i	$0.553100\pi$
$998$	−20.8152	−0.658892
$999$	7.85281	0.248452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.8	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.63839 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63839 q^{6} +2.17174 q^{7} +1.00000 q^{8} +3.96109 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.63839 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.63839 q^{6} +2.17174 q^{7} +1.00000 q^{8} +3.96109 q^{9} -1.00000 q^{10} -3.04430 q^{11} +2.63839 q^{12} +1.00000 q^{13} +2.17174 q^{14} -2.63839 q^{15} +1.00000 q^{16} +8.01343 q^{17} +3.96109 q^{18} +2.33430 q^{19} -1.00000 q^{20} +5.72988 q^{21} -3.04430 q^{22} -4.65210 q^{23} +2.63839 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.53574 q^{27} +2.17174 q^{28} +5.50426 q^{29} -2.63839 q^{30} +1.00000 q^{31} +1.00000 q^{32} -8.03204 q^{33} +8.01343 q^{34} -2.17174 q^{35} +3.96109 q^{36} +3.09686 q^{37} +2.33430 q^{38} +2.63839 q^{39} -1.00000 q^{40} -3.63489 q^{41} +5.72988 q^{42} -4.32649 q^{43} -3.04430 q^{44} -3.96109 q^{45} -4.65210 q^{46} -1.12007 q^{47} +2.63839 q^{48} -2.28357 q^{49} +1.00000 q^{50} +21.1425 q^{51} +1.00000 q^{52} -0.606019 q^{53} +2.53574 q^{54} +3.04430 q^{55} +2.17174 q^{56} +6.15879 q^{57} +5.50426 q^{58} +2.30213 q^{59} -2.63839 q^{60} +0.292016 q^{61} +1.00000 q^{62} +8.60244 q^{63} +1.00000 q^{64} -1.00000 q^{65} -8.03204 q^{66} -0.869662 q^{67} +8.01343 q^{68} -12.2740 q^{69} -2.17174 q^{70} -0.662572 q^{71} +3.96109 q^{72} -15.9341 q^{73} +3.09686 q^{74} +2.63839 q^{75} +2.33430 q^{76} -6.61141 q^{77} +2.63839 q^{78} +4.06263 q^{79} -1.00000 q^{80} -5.19302 q^{81} -3.63489 q^{82} +14.9547 q^{83} +5.72988 q^{84} -8.01343 q^{85} -4.32649 q^{86} +14.5224 q^{87} -3.04430 q^{88} +9.85856 q^{89} -3.96109 q^{90} +2.17174 q^{91} -4.65210 q^{92} +2.63839 q^{93} -1.12007 q^{94} -2.33430 q^{95} +2.63839 q^{96} -2.38196 q^{97} -2.28357 q^{98} -12.0588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

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