LMFDB - Embedded newform 370.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(1,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, 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("370.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.95446487479$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	370.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} -1.26795 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} -1.26795 q^{7} -1.00000 q^{8} +4.46410 q^{9} -1.00000 q^{10} +1.46410 q^{11} -2.73205 q^{12} +1.46410 q^{13} +1.26795 q^{14} -2.73205 q^{15} +1.00000 q^{16} -1.46410 q^{17} -4.46410 q^{18} -4.19615 q^{19} +1.00000 q^{20} +3.46410 q^{21} -1.46410 q^{22} -8.00000 q^{23} +2.73205 q^{24} +1.00000 q^{25} -1.46410 q^{26} -4.00000 q^{27} -1.26795 q^{28} -8.92820 q^{29} +2.73205 q^{30} -2.73205 q^{31} -1.00000 q^{32} -4.00000 q^{33} +1.46410 q^{34} -1.26795 q^{35} +4.46410 q^{36} +1.00000 q^{37} +4.19615 q^{38} -4.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -3.46410 q^{42} -6.92820 q^{43} +1.46410 q^{44} +4.46410 q^{45} +8.00000 q^{46} -1.26795 q^{47} -2.73205 q^{48} -5.39230 q^{49} -1.00000 q^{50} +4.00000 q^{51} +1.46410 q^{52} -6.00000 q^{53} +4.00000 q^{54} +1.46410 q^{55} +1.26795 q^{56} +11.4641 q^{57} +8.92820 q^{58} +0.196152 q^{59} -2.73205 q^{60} +8.92820 q^{61} +2.73205 q^{62} -5.66025 q^{63} +1.00000 q^{64} +1.46410 q^{65} +4.00000 q^{66} +13.6603 q^{67} -1.46410 q^{68} +21.8564 q^{69} +1.26795 q^{70} -10.9282 q^{71} -4.46410 q^{72} +12.9282 q^{73} -1.00000 q^{74} -2.73205 q^{75} -4.19615 q^{76} -1.85641 q^{77} +4.00000 q^{78} +5.26795 q^{79} +1.00000 q^{80} -2.46410 q^{81} +2.00000 q^{82} -5.26795 q^{83} +3.46410 q^{84} -1.46410 q^{85} +6.92820 q^{86} +24.3923 q^{87} -1.46410 q^{88} -2.00000 q^{89} -4.46410 q^{90} -1.85641 q^{91} -8.00000 q^{92} +7.46410 q^{93} +1.26795 q^{94} -4.19615 q^{95} +2.73205 q^{96} -2.00000 q^{97} +5.39230 q^{98} +6.53590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} - 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} - 4 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} - 8 q^{33} - 4 q^{34} - 6 q^{35} + 2 q^{36} + 2 q^{37} - 2 q^{38} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{45} + 16 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{51} - 4 q^{52} - 12 q^{53} + 8 q^{54} - 4 q^{55} + 6 q^{56} + 16 q^{57} + 4 q^{58} - 10 q^{59} - 2 q^{60} + 4 q^{61} + 2 q^{62} + 6 q^{63} + 2 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} + 4 q^{68} + 16 q^{69} + 6 q^{70} - 8 q^{71} - 2 q^{72} + 12 q^{73} - 2 q^{74} - 2 q^{75} + 2 q^{76} + 24 q^{77} + 8 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{83} + 4 q^{85} + 28 q^{87} + 4 q^{88} - 4 q^{89} - 2 q^{90} + 24 q^{91} - 16 q^{92} + 8 q^{93} + 6 q^{94} + 2 q^{95} + 2 q^{96} - 4 q^{97} - 10 q^{98} + 20 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^22 - 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 - 4 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 - 8 * q^33 - 4 * q^34 - 6 * q^35 + 2 * q^36 + 2 * q^37 - 2 * q^38 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^45 + 16 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^51 - 4 * q^52 - 12 * q^53 + 8 * q^54 - 4 * q^55 + 6 * q^56 + 16 * q^57 + 4 * q^58 - 10 * q^59 - 2 * q^60 + 4 * q^61 + 2 * q^62 + 6 * q^63 + 2 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 + 4 * q^68 + 16 * q^69 + 6 * q^70 - 8 * q^71 - 2 * q^72 + 12 * q^73 - 2 * q^74 - 2 * q^75 + 2 * q^76 + 24 * q^77 + 8 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^83 + 4 * q^85 + 28 * q^87 + 4 * q^88 - 4 * q^89 - 2 * q^90 + 24 * q^91 - 16 * q^92 + 8 * q^93 + 6 * q^94 + 2 * q^95 + 2 * q^96 - 4 * q^97 - 10 * q^98 + 20 * 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
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.73205	1.11536
$7$	−1.26795	−0.479240	−0.239620	−	0.970867i	$-0.577023\pi$
$7$	−1.26795	−0.479240	−0.239620	+	0.970867i	$0.577023\pi$
$8$	−1.00000	−0.353553
$9$	4.46410	1.48803
$10$	−1.00000	−0.316228
$11$	1.46410	0.441443	0.220722	−	0.975337i	$-0.429159\pi$
$11$	1.46410	0.441443	0.220722	+	0.975337i	$0.429159\pi$
$12$	−2.73205	−0.788675
$13$	1.46410	0.406069	0.203034	−	0.979172i	$-0.434920\pi$
$13$	1.46410	0.406069	0.203034	+	0.979172i	$0.434920\pi$
$14$	1.26795	0.338874
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	−1.46410	−0.355097	−0.177548	−	0.984112i	$-0.556817\pi$
$17$	−1.46410	−0.355097	−0.177548	+	0.984112i	$0.556817\pi$
$18$	−4.46410	−1.05220
$19$	−4.19615	−0.962663	−0.481332	−	0.876539i	$-0.659847\pi$
$19$	−4.19615	−0.962663	−0.481332	+	0.876539i	$0.659847\pi$
$20$	1.00000	0.223607
$21$	3.46410	0.755929
$22$	−1.46410	−0.312148
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	2.73205	0.557678
$25$	1.00000	0.200000
$26$	−1.46410	−0.287134
$27$	−4.00000	−0.769800
$28$	−1.26795	−0.239620
$29$	−8.92820	−1.65793	−0.828963	−	0.559304i	$-0.811069\pi$
$29$	−8.92820	−1.65793	−0.828963	+	0.559304i	$0.811069\pi$
$30$	2.73205	0.498802
$31$	−2.73205	−0.490691	−0.245345	−	0.969436i	$-0.578901\pi$
$31$	−2.73205	−0.490691	−0.245345	+	0.969436i	$0.578901\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	1.46410	0.251091
$35$	−1.26795	−0.214323
$36$	4.46410	0.744017
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	4.19615	0.680706
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−3.46410	−0.534522
$43$	−6.92820	−1.05654	−0.528271	−	0.849076i	$-0.677159\pi$
$43$	−6.92820	−1.05654	−0.528271	+	0.849076i	$0.677159\pi$
$44$	1.46410	0.220722
$45$	4.46410	0.665469
$46$	8.00000	1.17954
$47$	−1.26795	−0.184949	−0.0924747	−	0.995715i	$-0.529478\pi$
$47$	−1.26795	−0.184949	−0.0924747	+	0.995715i	$0.529478\pi$
$48$	−2.73205	−0.394338
$49$	−5.39230	−0.770329
$50$	−1.00000	−0.141421
$51$	4.00000	0.560112
$52$	1.46410	0.203034
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	4.00000	0.544331
$55$	1.46410	0.197419
$56$	1.26795	0.169437
$57$	11.4641	1.51846
$58$	8.92820	1.17233
$59$	0.196152	0.0255369	0.0127684	−	0.999918i	$-0.495936\pi$
$59$	0.196152	0.0255369	0.0127684	+	0.999918i	$0.495936\pi$
$60$	−2.73205	−0.352706
$61$	8.92820	1.14314	0.571570	−	0.820554i	$-0.306335\pi$
$61$	8.92820	1.14314	0.571570	+	0.820554i	$0.306335\pi$
$62$	2.73205	0.346971
$63$	−5.66025	−0.713125
$64$	1.00000	0.125000
$65$	1.46410	0.181599
$66$	4.00000	0.492366
$67$	13.6603	1.66887	0.834433	−	0.551110i	$-0.185795\pi$
$67$	13.6603	1.66887	0.834433	+	0.551110i	$0.185795\pi$
$68$	−1.46410	−0.177548
$69$	21.8564	2.63120
$70$	1.26795	0.151549
$71$	−10.9282	−1.29694	−0.648470	−	0.761241i	$-0.724591\pi$
$71$	−10.9282	−1.29694	−0.648470	+	0.761241i	$0.724591\pi$
$72$	−4.46410	−0.526099
$73$	12.9282	1.51313	0.756566	−	0.653917i	$-0.226876\pi$
$73$	12.9282	1.51313	0.756566	+	0.653917i	$0.226876\pi$
$74$	−1.00000	−0.116248
$75$	−2.73205	−0.315470
$76$	−4.19615	−0.481332
$77$	−1.85641	−0.211557
$78$	4.00000	0.452911
$79$	5.26795	0.592691	0.296345	−	0.955081i	$-0.404232\pi$
$79$	5.26795	0.592691	0.296345	+	0.955081i	$0.404232\pi$
$80$	1.00000	0.111803
$81$	−2.46410	−0.273789
$82$	2.00000	0.220863
$83$	−5.26795	−0.578233	−0.289116	−	0.957294i	$-0.593361\pi$
$83$	−5.26795	−0.578233	−0.289116	+	0.957294i	$0.593361\pi$
$84$	3.46410	0.377964
$85$	−1.46410	−0.158804
$86$	6.92820	0.747087
$87$	24.3923	2.61513
$88$	−1.46410	−0.156074
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	−4.46410	−0.470558
$91$	−1.85641	−0.194604
$92$	−8.00000	−0.834058
$93$	7.46410	0.773991
$94$	1.26795	0.130779
$95$	−4.19615	−0.430516
$96$	2.73205	0.278839
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	5.39230	0.544705
$99$	6.53590	0.656883
$100$	1.00000	0.100000
$101$	−2.53590	−0.252331	−0.126166	−	0.992009i	$-0.540267\pi$
$101$	−2.53590	−0.252331	−0.126166	+	0.992009i	$0.540267\pi$
$102$	−4.00000	−0.396059
$103$	−13.4641	−1.32666	−0.663329	−	0.748328i	$-0.730857\pi$
$103$	−13.4641	−1.32666	−0.663329	+	0.748328i	$0.730857\pi$
$104$	−1.46410	−0.143567
$105$	3.46410	0.338062
$106$	6.00000	0.582772
$107$	6.73205	0.650812	0.325406	−	0.945574i	$-0.394499\pi$
$107$	6.73205	0.650812	0.325406	+	0.945574i	$0.394499\pi$
$108$	−4.00000	−0.384900
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.46410	−0.139597
$111$	−2.73205	−0.259315
$112$	−1.26795	−0.119810
$113$	−17.4641	−1.64288	−0.821442	−	0.570292i	$-0.806830\pi$
$113$	−17.4641	−1.64288	−0.821442	+	0.570292i	$0.806830\pi$
$114$	−11.4641	−1.07371
$115$	−8.00000	−0.746004
$116$	−8.92820	−0.828963
$117$	6.53590	0.604244
$118$	−0.196152	−0.0180573
$119$	1.85641	0.170177
$120$	2.73205	0.249401
$121$	−8.85641	−0.805128
$122$	−8.92820	−0.808322
$123$	5.46410	0.492681
$124$	−2.73205	−0.245345
$125$	1.00000	0.0894427
$126$	5.66025	0.504256
$127$	−13.6603	−1.21215	−0.606076	−	0.795407i	$-0.707257\pi$
$127$	−13.6603	−1.21215	−0.606076	+	0.795407i	$0.707257\pi$
$128$	−1.00000	−0.0883883
$129$	18.9282	1.66654
$130$	−1.46410	−0.128410
$131$	12.5885	1.09986	0.549929	−	0.835211i	$-0.314655\pi$
$131$	12.5885	1.09986	0.549929	+	0.835211i	$0.314655\pi$
$132$	−4.00000	−0.348155
$133$	5.32051	0.461347
$134$	−13.6603	−1.18007
$135$	−4.00000	−0.344265
$136$	1.46410	0.125546
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−21.8564	−1.86054
$139$	−6.92820	−0.587643	−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820	−0.587643	−0.293821	+	0.955860i	$0.594927\pi$
$140$	−1.26795	−0.107161
$141$	3.46410	0.291730
$142$	10.9282	0.917074
$143$	2.14359	0.179256
$144$	4.46410	0.372008
$145$	−8.92820	−0.741447
$146$	−12.9282	−1.06995
$147$	14.7321	1.21508
$148$	1.00000	0.0821995
$149$	−16.3923	−1.34291	−0.671455	−	0.741045i	$-0.734330\pi$
$149$	−16.3923	−1.34291	−0.671455	+	0.741045i	$0.734330\pi$
$150$	2.73205	0.223071
$151$	8.39230	0.682956	0.341478	−	0.939890i	$-0.389073\pi$
$151$	8.39230	0.682956	0.341478	+	0.939890i	$0.389073\pi$
$152$	4.19615	0.340353
$153$	−6.53590	−0.528396
$154$	1.85641	0.149593
$155$	−2.73205	−0.219444
$156$	−4.00000	−0.320256
$157$	16.9282	1.35102	0.675509	−	0.737352i	$-0.263924\pi$
$157$	16.9282	1.35102	0.675509	+	0.737352i	$0.263924\pi$
$158$	−5.26795	−0.419096
$159$	16.3923	1.29999
$160$	−1.00000	−0.0790569
$161$	10.1436	0.799427
$162$	2.46410	0.193598
$163$	23.3205	1.82660	0.913302	−	0.407284i	$-0.133524\pi$
$163$	23.3205	1.82660	0.913302	+	0.407284i	$0.133524\pi$
$164$	−2.00000	−0.156174
$165$	−4.00000	−0.311400
$166$	5.26795	0.408872
$167$	5.46410	0.422825	0.211412	−	0.977397i	$-0.432194\pi$
$167$	5.46410	0.422825	0.211412	+	0.977397i	$0.432194\pi$
$168$	−3.46410	−0.267261
$169$	−10.8564	−0.835108
$170$	1.46410	0.112291
$171$	−18.7321	−1.43248
$172$	−6.92820	−0.528271
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	−24.3923	−1.84918
$175$	−1.26795	−0.0958479
$176$	1.46410	0.110361
$177$	−0.535898	−0.0402806
$178$	2.00000	0.149906
$179$	−17.6603	−1.31999	−0.659995	−	0.751270i	$-0.729441\pi$
$179$	−17.6603	−1.31999	−0.659995	+	0.751270i	$0.729441\pi$
$180$	4.46410	0.332734
$181$	−1.46410	−0.108826	−0.0544129	−	0.998519i	$-0.517329\pi$
$181$	−1.46410	−0.108826	−0.0544129	+	0.998519i	$0.517329\pi$
$182$	1.85641	0.137606
$183$	−24.3923	−1.80313
$184$	8.00000	0.589768
$185$	1.00000	0.0735215
$186$	−7.46410	−0.547294
$187$	−2.14359	−0.156755
$188$	−1.26795	−0.0924747
$189$	5.07180	0.368919
$190$	4.19615	0.304421
$191$	−5.26795	−0.381175	−0.190588	−	0.981670i	$-0.561039\pi$
$191$	−5.26795	−0.381175	−0.190588	+	0.981670i	$0.561039\pi$
$192$	−2.73205	−0.197169
$193$	−11.8564	−0.853443	−0.426721	−	0.904383i	$-0.640332\pi$
$193$	−11.8564	−0.853443	−0.426721	+	0.904383i	$0.640332\pi$
$194$	2.00000	0.143592
$195$	−4.00000	−0.286446
$196$	−5.39230	−0.385165
$197$	18.7846	1.33835	0.669174	−	0.743106i	$-0.266648\pi$
$197$	18.7846	1.33835	0.669174	+	0.743106i	$0.266648\pi$
$198$	−6.53590	−0.464486
$199$	26.0526	1.84682	0.923408	−	0.383819i	$-0.125391\pi$
$199$	26.0526	1.84682	0.923408	+	0.383819i	$0.125391\pi$
$200$	−1.00000	−0.0707107
$201$	−37.3205	−2.63239
$202$	2.53590	0.178425
$203$	11.3205	0.794544
$204$	4.00000	0.280056
$205$	−2.00000	−0.139686
$206$	13.4641	0.938088
$207$	−35.7128	−2.48221
$208$	1.46410	0.101517
$209$	−6.14359	−0.424961
$210$	−3.46410	−0.239046
$211$	9.85641	0.678543	0.339272	−	0.940688i	$-0.389819\pi$
$211$	9.85641	0.678543	0.339272	+	0.940688i	$0.389819\pi$
$212$	−6.00000	−0.412082
$213$	29.8564	2.04573
$214$	−6.73205	−0.460194
$215$	−6.92820	−0.472500
$216$	4.00000	0.272166
$217$	3.46410	0.235159
$218$	−2.00000	−0.135457
$219$	−35.3205	−2.38674
$220$	1.46410	0.0987097
$221$	−2.14359	−0.144194
$222$	2.73205	0.183363
$223$	−22.0526	−1.47675	−0.738374	−	0.674391i	$-0.764406\pi$
$223$	−22.0526	−1.47675	−0.738374	+	0.674391i	$0.764406\pi$
$224$	1.26795	0.0847184
$225$	4.46410	0.297607
$226$	17.4641	1.16169
$227$	3.60770	0.239451	0.119726	−	0.992807i	$-0.461799\pi$
$227$	3.60770	0.239451	0.119726	+	0.992807i	$0.461799\pi$
$228$	11.4641	0.759229
$229$	15.8564	1.04782	0.523910	−	0.851773i	$-0.324473\pi$
$229$	15.8564	1.04782	0.523910	+	0.851773i	$0.324473\pi$
$230$	8.00000	0.527504
$231$	5.07180	0.333700
$232$	8.92820	0.586165
$233$	15.0718	0.987386	0.493693	−	0.869636i	$-0.335647\pi$
$233$	15.0718	0.987386	0.493693	+	0.869636i	$0.335647\pi$
$234$	−6.53590	−0.427265
$235$	−1.26795	−0.0827119
$236$	0.196152	0.0127684
$237$	−14.3923	−0.934881
$238$	−1.85641	−0.120333
$239$	−17.2679	−1.11697	−0.558485	−	0.829514i	$-0.688617\pi$
$239$	−17.2679	−1.11697	−0.558485	+	0.829514i	$0.688617\pi$
$240$	−2.73205	−0.176353
$241$	−8.92820	−0.575116	−0.287558	−	0.957763i	$-0.592843\pi$
$241$	−8.92820	−0.575116	−0.287558	+	0.957763i	$0.592843\pi$
$242$	8.85641	0.569311
$243$	18.7321	1.20166
$244$	8.92820	0.571570
$245$	−5.39230	−0.344502
$246$	−5.46410	−0.348378
$247$	−6.14359	−0.390907
$248$	2.73205	0.173485
$249$	14.3923	0.912075
$250$	−1.00000	−0.0632456
$251$	22.7321	1.43483	0.717417	−	0.696644i	$-0.245324\pi$
$251$	22.7321	1.43483	0.717417	+	0.696644i	$0.245324\pi$
$252$	−5.66025	−0.356562
$253$	−11.7128	−0.736378
$254$	13.6603	0.857121
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	−25.4641	−1.58841	−0.794204	−	0.607652i	$-0.792112\pi$
$257$	−25.4641	−1.58841	−0.794204	+	0.607652i	$0.792112\pi$
$258$	−18.9282	−1.17842
$259$	−1.26795	−0.0787865
$260$	1.46410	0.0907997
$261$	−39.8564	−2.46705
$262$	−12.5885	−0.777717
$263$	30.0526	1.85312	0.926560	−	0.376147i	$-0.122751\pi$
$263$	30.0526	1.85312	0.926560	+	0.376147i	$0.122751\pi$
$264$	4.00000	0.246183
$265$	−6.00000	−0.368577
$266$	−5.32051	−0.326221
$267$	5.46410	0.334398
$268$	13.6603	0.834433
$269$	−0.392305	−0.0239192	−0.0119596	−	0.999928i	$-0.503807\pi$
$269$	−0.392305	−0.0239192	−0.0119596	+	0.999928i	$0.503807\pi$
$270$	4.00000	0.243432
$271$	16.7846	1.01959	0.509796	−	0.860295i	$-0.329721\pi$
$271$	16.7846	1.01959	0.509796	+	0.860295i	$0.329721\pi$
$272$	−1.46410	−0.0887742
$273$	5.07180	0.306959
$274$	−2.00000	−0.120824
$275$	1.46410	0.0882886
$276$	21.8564	1.31560
$277$	−26.2487	−1.57713	−0.788566	−	0.614950i	$-0.789176\pi$
$277$	−26.2487	−1.57713	−0.788566	+	0.614950i	$0.789176\pi$
$278$	6.92820	0.415526
$279$	−12.1962	−0.730165
$280$	1.26795	0.0757745
$281$	4.92820	0.293992	0.146996	−	0.989137i	$-0.453040\pi$
$281$	4.92820	0.293992	0.146996	+	0.989137i	$0.453040\pi$
$282$	−3.46410	−0.206284
$283$	−4.39230	−0.261095	−0.130548	−	0.991442i	$-0.541674\pi$
$283$	−4.39230	−0.261095	−0.130548	+	0.991442i	$0.541674\pi$
$284$	−10.9282	−0.648470
$285$	11.4641	0.679075
$286$	−2.14359	−0.126753
$287$	2.53590	0.149689
$288$	−4.46410	−0.263050
$289$	−14.8564	−0.873906
$290$	8.92820	0.524282
$291$	5.46410	0.320311
$292$	12.9282	0.756566
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−14.7321	−0.859191
$295$	0.196152	0.0114204
$296$	−1.00000	−0.0581238
$297$	−5.85641	−0.339823
$298$	16.3923	0.949581
$299$	−11.7128	−0.677369
$300$	−2.73205	−0.157735
$301$	8.78461	0.506336
$302$	−8.39230	−0.482923
$303$	6.92820	0.398015
$304$	−4.19615	−0.240666
$305$	8.92820	0.511227
$306$	6.53590	0.373632
$307$	−12.5885	−0.718461	−0.359231	−	0.933249i	$-0.616961\pi$
$307$	−12.5885	−0.718461	−0.359231	+	0.933249i	$0.616961\pi$
$308$	−1.85641	−0.105779
$309$	36.7846	2.09260
$310$	2.73205	0.155170
$311$	27.1244	1.53808	0.769041	−	0.639200i	$-0.220734\pi$
$311$	27.1244	1.53808	0.769041	+	0.639200i	$0.220734\pi$
$312$	4.00000	0.226455
$313$	3.85641	0.217977	0.108988	−	0.994043i	$-0.465239\pi$
$313$	3.85641	0.217977	0.108988	+	0.994043i	$0.465239\pi$
$314$	−16.9282	−0.955314
$315$	−5.66025	−0.318919
$316$	5.26795	0.296345
$317$	−31.8564	−1.78923	−0.894617	−	0.446834i	$-0.852552\pi$
$317$	−31.8564	−1.78923	−0.894617	+	0.446834i	$0.852552\pi$
$318$	−16.3923	−0.919235
$319$	−13.0718	−0.731880
$320$	1.00000	0.0559017
$321$	−18.3923	−1.02656
$322$	−10.1436	−0.565280
$323$	6.14359	0.341839
$324$	−2.46410	−0.136895
$325$	1.46410	0.0812137
$326$	−23.3205	−1.29160
$327$	−5.46410	−0.302166
$328$	2.00000	0.110432
$329$	1.60770	0.0886351
$330$	4.00000	0.220193
$331$	−8.87564	−0.487850	−0.243925	−	0.969794i	$-0.578435\pi$
$331$	−8.87564	−0.487850	−0.243925	+	0.969794i	$0.578435\pi$
$332$	−5.26795	−0.289116
$333$	4.46410	0.244631
$334$	−5.46410	−0.298982
$335$	13.6603	0.746339
$336$	3.46410	0.188982
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	10.8564	0.590511
$339$	47.7128	2.59140
$340$	−1.46410	−0.0794021
$341$	−4.00000	−0.216612
$342$	18.7321	1.01291
$343$	15.7128	0.848412
$344$	6.92820	0.373544
$345$	21.8564	1.17671
$346$	−10.0000	−0.537603
$347$	17.0718	0.916462	0.458231	−	0.888833i	$-0.348483\pi$
$347$	17.0718	0.916462	0.458231	+	0.888833i	$0.348483\pi$
$348$	24.3923	1.30756
$349$	19.3205	1.03420	0.517102	−	0.855924i	$-0.327011\pi$
$349$	19.3205	1.03420	0.517102	+	0.855924i	$0.327011\pi$
$350$	1.26795	0.0677747
$351$	−5.85641	−0.312592
$352$	−1.46410	−0.0780369
$353$	15.8564	0.843951	0.421976	−	0.906607i	$-0.361337\pi$
$353$	15.8564	0.843951	0.421976	+	0.906607i	$0.361337\pi$
$354$	0.535898	0.0284827
$355$	−10.9282	−0.580009
$356$	−2.00000	−0.106000
$357$	−5.07180	−0.268428
$358$	17.6603	0.933373
$359$	8.39230	0.442929	0.221464	−	0.975168i	$-0.428916\pi$
$359$	8.39230	0.442929	0.221464	+	0.975168i	$0.428916\pi$
$360$	−4.46410	−0.235279
$361$	−1.39230	−0.0732792
$362$	1.46410	0.0769515
$363$	24.1962	1.26997
$364$	−1.85641	−0.0973021
$365$	12.9282	0.676693
$366$	24.3923	1.27501
$367$	−21.6603	−1.13066	−0.565328	−	0.824866i	$-0.691250\pi$
$367$	−21.6603	−1.13066	−0.565328	+	0.824866i	$0.691250\pi$
$368$	−8.00000	−0.417029
$369$	−8.92820	−0.464784
$370$	−1.00000	−0.0519875
$371$	7.60770	0.394972
$372$	7.46410	0.386996
$373$	30.7846	1.59397	0.796983	−	0.604001i	$-0.206428\pi$
$373$	30.7846	1.59397	0.796983	+	0.604001i	$0.206428\pi$
$374$	2.14359	0.110843
$375$	−2.73205	−0.141082
$376$	1.26795	0.0653895
$377$	−13.0718	−0.673232
$378$	−5.07180	−0.260865
$379$	11.6077	0.596247	0.298124	−	0.954527i	$-0.403639\pi$
$379$	11.6077	0.596247	0.298124	+	0.954527i	$0.403639\pi$
$380$	−4.19615	−0.215258
$381$	37.3205	1.91199
$382$	5.26795	0.269532
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	2.73205	0.139419
$385$	−1.85641	−0.0946112
$386$	11.8564	0.603475
$387$	−30.9282	−1.57217
$388$	−2.00000	−0.101535
$389$	15.8564	0.803952	0.401976	−	0.915650i	$-0.368324\pi$
$389$	15.8564	0.803952	0.401976	+	0.915650i	$0.368324\pi$
$390$	4.00000	0.202548
$391$	11.7128	0.592342
$392$	5.39230	0.272353
$393$	−34.3923	−1.73486
$394$	−18.7846	−0.946355
$395$	5.26795	0.265059
$396$	6.53590	0.328441
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−26.0526	−1.30590
$399$	−14.5359	−0.727705
$400$	1.00000	0.0500000
$401$	−19.0718	−0.952400	−0.476200	−	0.879337i	$-0.657986\pi$
$401$	−19.0718	−0.952400	−0.476200	+	0.879337i	$0.657986\pi$
$402$	37.3205	1.86138
$403$	−4.00000	−0.199254
$404$	−2.53590	−0.126166
$405$	−2.46410	−0.122442
$406$	−11.3205	−0.561827
$407$	1.46410	0.0725728
$408$	−4.00000	−0.198030
$409$	16.9282	0.837046	0.418523	−	0.908206i	$-0.362548\pi$
$409$	16.9282	0.837046	0.418523	+	0.908206i	$0.362548\pi$
$410$	2.00000	0.0987730
$411$	−5.46410	−0.269524
$412$	−13.4641	−0.663329
$413$	−0.248711	−0.0122383
$414$	35.7128	1.75519
$415$	−5.26795	−0.258593
$416$	−1.46410	−0.0717835
$417$	18.9282	0.926918
$418$	6.14359	0.300493
$419$	−34.2487	−1.67316	−0.836580	−	0.547846i	$-0.815448\pi$
$419$	−34.2487	−1.67316	−0.836580	+	0.547846i	$0.815448\pi$
$420$	3.46410	0.169031
$421$	−27.8564	−1.35764	−0.678819	−	0.734306i	$-0.737508\pi$
$421$	−27.8564	−1.35764	−0.678819	+	0.734306i	$0.737508\pi$
$422$	−9.85641	−0.479802
$423$	−5.66025	−0.275211
$424$	6.00000	0.291386
$425$	−1.46410	−0.0710194
$426$	−29.8564	−1.44655
$427$	−11.3205	−0.547838
$428$	6.73205	0.325406
$429$	−5.85641	−0.282750
$430$	6.92820	0.334108
$431$	8.19615	0.394795	0.197397	−	0.980324i	$-0.436751\pi$
$431$	8.19615	0.394795	0.197397	+	0.980324i	$0.436751\pi$
$432$	−4.00000	−0.192450
$433$	−34.0000	−1.63394	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000	−1.63394	−0.816968	+	0.576683i	$0.804347\pi$
$434$	−3.46410	−0.166282
$435$	24.3923	1.16952
$436$	2.00000	0.0957826
$437$	33.5692	1.60583
$438$	35.3205	1.68768
$439$	−31.5167	−1.50421	−0.752104	−	0.659044i	$-0.770961\pi$
$439$	−31.5167	−1.50421	−0.752104	+	0.659044i	$0.770961\pi$
$440$	−1.46410	−0.0697983
$441$	−24.0718	−1.14628
$442$	2.14359	0.101960
$443$	−39.1244	−1.85885	−0.929427	−	0.369006i	$-0.879698\pi$
$443$	−39.1244	−1.85885	−0.929427	+	0.369006i	$0.879698\pi$
$444$	−2.73205	−0.129657
$445$	−2.00000	−0.0948091
$446$	22.0526	1.04422
$447$	44.7846	2.11824
$448$	−1.26795	−0.0599050
$449$	33.7128	1.59101	0.795503	−	0.605950i	$-0.207207\pi$
$449$	33.7128	1.59101	0.795503	+	0.605950i	$0.207207\pi$
$450$	−4.46410	−0.210440
$451$	−2.92820	−0.137884
$452$	−17.4641	−0.821442
$453$	−22.9282	−1.07726
$454$	−3.60770	−0.169318
$455$	−1.85641	−0.0870297
$456$	−11.4641	−0.536856
$457$	−4.14359	−0.193829	−0.0969146	−	0.995293i	$-0.530897\pi$
$457$	−4.14359	−0.193829	−0.0969146	+	0.995293i	$0.530897\pi$
$458$	−15.8564	−0.740921
$459$	5.85641	0.273354
$460$	−8.00000	−0.373002
$461$	−26.7846	−1.24748	−0.623742	−	0.781630i	$-0.714388\pi$
$461$	−26.7846	−1.24748	−0.623742	+	0.781630i	$0.714388\pi$
$462$	−5.07180	−0.235961
$463$	5.07180	0.235706	0.117853	−	0.993031i	$-0.462399\pi$
$463$	5.07180	0.235706	0.117853	+	0.993031i	$0.462399\pi$
$464$	−8.92820	−0.414481
$465$	7.46410	0.346139
$466$	−15.0718	−0.698188
$467$	37.1769	1.72034	0.860171	−	0.510005i	$-0.170357\pi$
$467$	37.1769	1.72034	0.860171	+	0.510005i	$0.170357\pi$
$468$	6.53590	0.302122
$469$	−17.3205	−0.799787
$470$	1.26795	0.0584861
$471$	−46.2487	−2.13103
$472$	−0.196152	−0.00902865
$473$	−10.1436	−0.466403
$474$	14.3923	0.661060
$475$	−4.19615	−0.192533
$476$	1.85641	0.0850883
$477$	−26.7846	−1.22638
$478$	17.2679	0.789818
$479$	−34.0526	−1.55590	−0.777951	−	0.628325i	$-0.783741\pi$
$479$	−34.0526	−1.55590	−0.777951	+	0.628325i	$0.783741\pi$
$480$	2.73205	0.124700
$481$	1.46410	0.0667573
$482$	8.92820	0.406669
$483$	−27.7128	−1.26098
$484$	−8.85641	−0.402564
$485$	−2.00000	−0.0908153
$486$	−18.7321	−0.849703
$487$	−16.3923	−0.742806	−0.371403	−	0.928472i	$-0.621123\pi$
$487$	−16.3923	−0.742806	−0.371403	+	0.928472i	$0.621123\pi$
$488$	−8.92820	−0.404161
$489$	−63.7128	−2.88119
$490$	5.39230	0.243600
$491$	−1.07180	−0.0483695	−0.0241848	−	0.999708i	$-0.507699\pi$
$491$	−1.07180	−0.0483695	−0.0241848	+	0.999708i	$0.507699\pi$
$492$	5.46410	0.246341
$493$	13.0718	0.588724
$494$	6.14359	0.276413
$495$	6.53590	0.293767
$496$	−2.73205	−0.122673
$497$	13.8564	0.621545
$498$	−14.3923	−0.644935
$499$	40.5885	1.81699	0.908494	−	0.417897i	$-0.137233\pi$
$499$	40.5885	1.81699	0.908494	+	0.417897i	$0.137233\pi$
$500$	1.00000	0.0447214
$501$	−14.9282	−0.666943
$502$	−22.7321	−1.01458
$503$	−5.07180	−0.226140	−0.113070	−	0.993587i	$-0.536068\pi$
$503$	−5.07180	−0.226140	−0.113070	+	0.993587i	$0.536068\pi$
$504$	5.66025	0.252128
$505$	−2.53590	−0.112846
$506$	11.7128	0.520698
$507$	29.6603	1.31726
$508$	−13.6603	−0.606076
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	−4.00000	−0.177123
$511$	−16.3923	−0.725153
$512$	−1.00000	−0.0441942
$513$	16.7846	0.741059
$514$	25.4641	1.12317
$515$	−13.4641	−0.593299
$516$	18.9282	0.833268
$517$	−1.85641	−0.0816447
$518$	1.26795	0.0557105
$519$	−27.3205	−1.19924
$520$	−1.46410	−0.0642051
$521$	33.4641	1.46609	0.733044	−	0.680181i	$-0.238099\pi$
$521$	33.4641	1.46609	0.733044	+	0.680181i	$0.238099\pi$
$522$	39.8564	1.74447
$523$	−4.78461	−0.209216	−0.104608	−	0.994514i	$-0.533359\pi$
$523$	−4.78461	−0.209216	−0.104608	+	0.994514i	$0.533359\pi$
$524$	12.5885	0.549929
$525$	3.46410	0.151186
$526$	−30.0526	−1.31035
$527$	4.00000	0.174243
$528$	−4.00000	−0.174078
$529$	41.0000	1.78261
$530$	6.00000	0.260623
$531$	0.875644	0.0379997
$532$	5.32051	0.230673
$533$	−2.92820	−0.126835
$534$	−5.46410	−0.236455
$535$	6.73205	0.291052
$536$	−13.6603	−0.590033
$537$	48.2487	2.08209
$538$	0.392305	0.0169135
$539$	−7.89488	−0.340057
$540$	−4.00000	−0.172133
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−16.7846	−0.720961
$543$	4.00000	0.171656
$544$	1.46410	0.0627728
$545$	2.00000	0.0856706
$546$	−5.07180	−0.217053
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	2.00000	0.0854358
$549$	39.8564	1.70103
$550$	−1.46410	−0.0624295
$551$	37.4641	1.59602
$552$	−21.8564	−0.930270
$553$	−6.67949	−0.284041
$554$	26.2487	1.11520
$555$	−2.73205	−0.115969
$556$	−6.92820	−0.293821
$557$	−32.1051	−1.36034	−0.680169	−	0.733056i	$-0.738094\pi$
$557$	−32.1051	−1.36034	−0.680169	+	0.733056i	$0.738094\pi$
$558$	12.1962	0.516304
$559$	−10.1436	−0.429028
$560$	−1.26795	−0.0535806
$561$	5.85641	0.247258
$562$	−4.92820	−0.207884
$563$	17.0718	0.719490	0.359745	−	0.933051i	$-0.382864\pi$
$563$	17.0718	0.719490	0.359745	+	0.933051i	$0.382864\pi$
$564$	3.46410	0.145865
$565$	−17.4641	−0.734720
$566$	4.39230	0.184622
$567$	3.12436	0.131211
$568$	10.9282	0.458537
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	−11.4641	−0.480178
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	2.14359	0.0896281
$573$	14.3923	0.601247
$574$	−2.53590	−0.105846
$575$	−8.00000	−0.333623
$576$	4.46410	0.186004
$577$	−3.60770	−0.150190	−0.0750952	−	0.997176i	$-0.523926\pi$
$577$	−3.60770	−0.150190	−0.0750952	+	0.997176i	$0.523926\pi$
$578$	14.8564	0.617945
$579$	32.3923	1.34618
$580$	−8.92820	−0.370723
$581$	6.67949	0.277112
$582$	−5.46410	−0.226494
$583$	−8.78461	−0.363821
$584$	−12.9282	−0.534973
$585$	6.53590	0.270226
$586$	−6.00000	−0.247858
$587$	3.21539	0.132713	0.0663567	−	0.997796i	$-0.478862\pi$
$587$	3.21539	0.132713	0.0663567	+	0.997796i	$0.478862\pi$
$588$	14.7321	0.607540
$589$	11.4641	0.472370
$590$	−0.196152	−0.00807547
$591$	−51.3205	−2.11104
$592$	1.00000	0.0410997
$593$	6.78461	0.278611	0.139305	−	0.990249i	$-0.455513\pi$
$593$	6.78461	0.278611	0.139305	+	0.990249i	$0.455513\pi$
$594$	5.85641	0.240291
$595$	1.85641	0.0761052
$596$	−16.3923	−0.671455
$597$	−71.1769	−2.91308
$598$	11.7128	0.478973
$599$	2.53590	0.103614	0.0518070	−	0.998657i	$-0.483502\pi$
$599$	2.53590	0.103614	0.0518070	+	0.998657i	$0.483502\pi$
$600$	2.73205	0.111536
$601$	48.3923	1.97396	0.986982	−	0.160833i	$-0.0514180\pi$
$601$	48.3923	1.97396	0.986982	+	0.160833i	$0.0514180\pi$
$602$	−8.78461	−0.358034
$603$	60.9808	2.48333
$604$	8.39230	0.341478
$605$	−8.85641	−0.360064
$606$	−6.92820	−0.281439
$607$	−40.7846	−1.65540	−0.827698	−	0.561174i	$-0.810350\pi$
$607$	−40.7846	−1.65540	−0.827698	+	0.561174i	$0.810350\pi$
$608$	4.19615	0.170176
$609$	−30.9282	−1.25327
$610$	−8.92820	−0.361492
$611$	−1.85641	−0.0751022
$612$	−6.53590	−0.264198
$613$	3.07180	0.124069	0.0620344	−	0.998074i	$-0.480241\pi$
$613$	3.07180	0.124069	0.0620344	+	0.998074i	$0.480241\pi$
$614$	12.5885	0.508029
$615$	5.46410	0.220334
$616$	1.85641	0.0747967
$617$	12.9282	0.520470	0.260235	−	0.965545i	$-0.416200\pi$
$617$	12.9282	0.520470	0.260235	+	0.965545i	$0.416200\pi$
$618$	−36.7846	−1.47969
$619$	9.85641	0.396162	0.198081	−	0.980186i	$-0.436529\pi$
$619$	9.85641	0.396162	0.198081	+	0.980186i	$0.436529\pi$
$620$	−2.73205	−0.109722
$621$	32.0000	1.28412
$622$	−27.1244	−1.08759
$623$	2.53590	0.101599
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−3.85641	−0.154133
$627$	16.7846	0.670313
$628$	16.9282	0.675509
$629$	−1.46410	−0.0583776
$630$	5.66025	0.225510
$631$	−20.9808	−0.835231	−0.417615	−	0.908624i	$-0.637134\pi$
$631$	−20.9808	−0.835231	−0.417615	+	0.908624i	$0.637134\pi$
$632$	−5.26795	−0.209548
$633$	−26.9282	−1.07030
$634$	31.8564	1.26518
$635$	−13.6603	−0.542091
$636$	16.3923	0.649997
$637$	−7.89488	−0.312807
$638$	13.0718	0.517517
$639$	−48.7846	−1.92989
$640$	−1.00000	−0.0395285
$641$	−13.4641	−0.531800	−0.265900	−	0.964001i	$-0.585669\pi$
$641$	−13.4641	−0.531800	−0.265900	+	0.964001i	$0.585669\pi$
$642$	18.3923	0.725886
$643$	41.4641	1.63518	0.817592	−	0.575798i	$-0.195308\pi$
$643$	41.4641	1.63518	0.817592	+	0.575798i	$0.195308\pi$
$644$	10.1436	0.399714
$645$	18.9282	0.745297
$646$	−6.14359	−0.241716
$647$	19.7128	0.774991	0.387495	−	0.921872i	$-0.373340\pi$
$647$	19.7128	0.774991	0.387495	+	0.921872i	$0.373340\pi$
$648$	2.46410	0.0967991
$649$	0.287187	0.0112731
$650$	−1.46410	−0.0574268
$651$	−9.46410	−0.370927
$652$	23.3205	0.913302
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	5.46410	0.213663
$655$	12.5885	0.491872
$656$	−2.00000	−0.0780869
$657$	57.7128	2.25159
$658$	−1.60770	−0.0626745
$659$	6.92820	0.269884	0.134942	−	0.990853i	$-0.456915\pi$
$659$	6.92820	0.269884	0.134942	+	0.990853i	$0.456915\pi$
$660$	−4.00000	−0.155700
$661$	−44.9282	−1.74750	−0.873752	−	0.486371i	$-0.838320\pi$
$661$	−44.9282	−1.74750	−0.873752	+	0.486371i	$0.838320\pi$
$662$	8.87564	0.344962
$663$	5.85641	0.227444
$664$	5.26795	0.204436
$665$	5.32051	0.206320
$666$	−4.46410	−0.172980
$667$	71.4256	2.76561
$668$	5.46410	0.211412
$669$	60.2487	2.32935
$670$	−13.6603	−0.527742
$671$	13.0718	0.504631
$672$	−3.46410	−0.133631
$673$	−19.0718	−0.735164	−0.367582	−	0.929991i	$-0.619814\pi$
$673$	−19.0718	−0.735164	−0.367582	+	0.929991i	$0.619814\pi$
$674$	−26.0000	−1.00148
$675$	−4.00000	−0.153960
$676$	−10.8564	−0.417554
$677$	−31.8564	−1.22434	−0.612171	−	0.790726i	$-0.709703\pi$
$677$	−31.8564	−1.22434	−0.612171	+	0.790726i	$0.709703\pi$
$678$	−47.7128	−1.83240
$679$	2.53590	0.0973188
$680$	1.46410	0.0561457
$681$	−9.85641	−0.377698
$682$	4.00000	0.153168
$683$	36.7846	1.40752	0.703762	−	0.710436i	$-0.251502\pi$
$683$	36.7846	1.40752	0.703762	+	0.710436i	$0.251502\pi$
$684$	−18.7321	−0.716238
$685$	2.00000	0.0764161
$686$	−15.7128	−0.599918
$687$	−43.3205	−1.65278
$688$	−6.92820	−0.264135
$689$	−8.78461	−0.334667
$690$	−21.8564	−0.832059
$691$	20.3923	0.775760	0.387880	−	0.921710i	$-0.373208\pi$
$691$	20.3923	0.775760	0.387880	+	0.921710i	$0.373208\pi$
$692$	10.0000	0.380143
$693$	−8.28719	−0.314804
$694$	−17.0718	−0.648037
$695$	−6.92820	−0.262802
$696$	−24.3923	−0.924588
$697$	2.92820	0.110914
$698$	−19.3205	−0.731292
$699$	−41.1769	−1.55745
$700$	−1.26795	−0.0479240
$701$	15.8564	0.598888	0.299444	−	0.954114i	$-0.403199\pi$
$701$	15.8564	0.598888	0.299444	+	0.954114i	$0.403199\pi$
$702$	5.85641	0.221036
$703$	−4.19615	−0.158261
$704$	1.46410	0.0551804
$705$	3.46410	0.130466
$706$	−15.8564	−0.596764
$707$	3.21539	0.120927
$708$	−0.535898	−0.0201403
$709$	16.1436	0.606285	0.303143	−	0.952945i	$-0.401964\pi$
$709$	16.1436	0.606285	0.303143	+	0.952945i	$0.401964\pi$
$710$	10.9282	0.410128
$711$	23.5167	0.881944
$712$	2.00000	0.0749532
$713$	21.8564	0.818529
$714$	5.07180	0.189807
$715$	2.14359	0.0801659
$716$	−17.6603	−0.659995
$717$	47.1769	1.76185
$718$	−8.39230	−0.313198
$719$	8.39230	0.312980	0.156490	−	0.987680i	$-0.449982\pi$
$719$	8.39230	0.312980	0.156490	+	0.987680i	$0.449982\pi$
$720$	4.46410	0.166367
$721$	17.0718	0.635787
$722$	1.39230	0.0518162
$723$	24.3923	0.907160
$724$	−1.46410	−0.0544129
$725$	−8.92820	−0.331585
$726$	−24.1962	−0.898003
$727$	−32.7846	−1.21591	−0.607957	−	0.793970i	$-0.708011\pi$
$727$	−32.7846	−1.21591	−0.607957	+	0.793970i	$0.708011\pi$
$728$	1.85641	0.0688030
$729$	−43.7846	−1.62165
$730$	−12.9282	−0.478494
$731$	10.1436	0.375174
$732$	−24.3923	−0.901566
$733$	0.143594	0.00530375	0.00265187	−	0.999996i	$-0.499156\pi$
$733$	0.143594	0.00530375	0.00265187	+	0.999996i	$0.499156\pi$
$734$	21.6603	0.799495
$735$	14.7321	0.543400
$736$	8.00000	0.294884
$737$	20.0000	0.736709
$738$	8.92820	0.328652
$739$	−6.92820	−0.254858	−0.127429	−	0.991848i	$-0.540673\pi$
$739$	−6.92820	−0.254858	−0.127429	+	0.991848i	$0.540673\pi$
$740$	1.00000	0.0367607
$741$	16.7846	0.616598
$742$	−7.60770	−0.279287
$743$	−7.12436	−0.261367	−0.130684	−	0.991424i	$-0.541717\pi$
$743$	−7.12436	−0.261367	−0.130684	+	0.991424i	$0.541717\pi$
$744$	−7.46410	−0.273647
$745$	−16.3923	−0.600568
$746$	−30.7846	−1.12710
$747$	−23.5167	−0.860430
$748$	−2.14359	−0.0783775
$749$	−8.53590	−0.311895
$750$	2.73205	0.0997604
$751$	0.392305	0.0143154	0.00715770	−	0.999974i	$-0.497722\pi$
$751$	0.392305	0.0143154	0.00715770	+	0.999974i	$0.497722\pi$
$752$	−1.26795	−0.0462373
$753$	−62.1051	−2.26324
$754$	13.0718	0.476047
$755$	8.39230	0.305427
$756$	5.07180	0.184459
$757$	−53.7128	−1.95223	−0.976113	−	0.217265i	$-0.930286\pi$
$757$	−53.7128	−1.95223	−0.976113	+	0.217265i	$0.930286\pi$
$758$	−11.6077	−0.421610
$759$	32.0000	1.16153
$760$	4.19615	0.152210
$761$	10.0000	0.362500	0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000	0.362500	0.181250	+	0.983437i	$0.441986\pi$
$762$	−37.3205	−1.35198
$763$	−2.53590	−0.0918057
$764$	−5.26795	−0.190588
$765$	−6.53590	−0.236306
$766$	8.00000	0.289052
$767$	0.287187	0.0103697
$768$	−2.73205	−0.0985844
$769$	20.9282	0.754690	0.377345	−	0.926073i	$-0.376837\pi$
$769$	20.9282	0.754690	0.377345	+	0.926073i	$0.376837\pi$
$770$	1.85641	0.0669002
$771$	69.5692	2.50547
$772$	−11.8564	−0.426721
$773$	−38.7846	−1.39499	−0.697493	−	0.716592i	$-0.745701\pi$
$773$	−38.7846	−1.39499	−0.697493	+	0.716592i	$0.745701\pi$
$774$	30.9282	1.11169
$775$	−2.73205	−0.0981382
$776$	2.00000	0.0717958
$777$	3.46410	0.124274
$778$	−15.8564	−0.568480
$779$	8.39230	0.300686
$780$	−4.00000	−0.143223
$781$	−16.0000	−0.572525
$782$	−11.7128	−0.418849
$783$	35.7128	1.27627
$784$	−5.39230	−0.192582
$785$	16.9282	0.604193
$786$	34.3923	1.22673
$787$	11.8038	0.420762	0.210381	−	0.977620i	$-0.432530\pi$
$787$	11.8038	0.420762	0.210381	+	0.977620i	$0.432530\pi$
$788$	18.7846	0.669174
$789$	−82.1051	−2.92302
$790$	−5.26795	−0.187425
$791$	22.1436	0.787336
$792$	−6.53590	−0.232243
$793$	13.0718	0.464193
$794$	22.0000	0.780751
$795$	16.3923	0.581375
$796$	26.0526	0.923408
$797$	17.4641	0.618610	0.309305	−	0.950963i	$-0.399904\pi$
$797$	17.4641	0.618610	0.309305	+	0.950963i	$0.399904\pi$
$798$	14.5359	0.514565
$799$	1.85641	0.0656749
$800$	−1.00000	−0.0353553
$801$	−8.92820	−0.315463
$802$	19.0718	0.673449
$803$	18.9282	0.667962
$804$	−37.3205	−1.31619
$805$	10.1436	0.357515
$806$	4.00000	0.140894
$807$	1.07180	0.0377290
$808$	2.53590	0.0892126
$809$	−39.5692	−1.39118	−0.695590	−	0.718439i	$-0.744857\pi$
$809$	−39.5692	−1.39118	−0.695590	+	0.718439i	$0.744857\pi$
$810$	2.46410	0.0865797
$811$	−14.1436	−0.496649	−0.248324	−	0.968677i	$-0.579880\pi$
$811$	−14.1436	−0.496649	−0.248324	+	0.968677i	$0.579880\pi$
$812$	11.3205	0.397272
$813$	−45.8564	−1.60825
$814$	−1.46410	−0.0513167
$815$	23.3205	0.816882
$816$	4.00000	0.140028
$817$	29.0718	1.01709
$818$	−16.9282	−0.591881
$819$	−8.28719	−0.289578
$820$	−2.00000	−0.0698430
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	5.46410	0.190582
$823$	−10.4449	−0.364085	−0.182043	−	0.983291i	$-0.558271\pi$
$823$	−10.4449	−0.364085	−0.182043	+	0.983291i	$0.558271\pi$
$824$	13.4641	0.469044
$825$	−4.00000	−0.139262
$826$	0.248711	0.00865377
$827$	4.39230	0.152735	0.0763677	−	0.997080i	$-0.475668\pi$
$827$	4.39230	0.152735	0.0763677	+	0.997080i	$0.475668\pi$
$828$	−35.7128	−1.24111
$829$	31.5692	1.09644	0.548222	−	0.836333i	$-0.315305\pi$
$829$	31.5692	1.09644	0.548222	+	0.836333i	$0.315305\pi$
$830$	5.26795	0.182853
$831$	71.7128	2.48769
$832$	1.46410	0.0507586
$833$	7.89488	0.273541
$834$	−18.9282	−0.655430
$835$	5.46410	0.189093
$836$	−6.14359	−0.212481
$837$	10.9282	0.377734
$838$	34.2487	1.18310
$839$	32.7846	1.13185	0.565925	−	0.824457i	$-0.308519\pi$
$839$	32.7846	1.13185	0.565925	+	0.824457i	$0.308519\pi$
$840$	−3.46410	−0.119523
$841$	50.7128	1.74872
$842$	27.8564	0.959995
$843$	−13.4641	−0.463728
$844$	9.85641	0.339272
$845$	−10.8564	−0.373472
$846$	5.66025	0.194604
$847$	11.2295	0.385849
$848$	−6.00000	−0.206041
$849$	12.0000	0.411839
$850$	1.46410	0.0502183
$851$	−8.00000	−0.274236
$852$	29.8564	1.02286
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	11.3205	0.387380
$855$	−18.7321	−0.640623
$856$	−6.73205	−0.230097
$857$	−4.14359	−0.141542	−0.0707712	−	0.997493i	$-0.522546\pi$
$857$	−4.14359	−0.141542	−0.0707712	+	0.997493i	$0.522546\pi$
$858$	5.85641	0.199934
$859$	−14.4449	−0.492852	−0.246426	−	0.969162i	$-0.579256\pi$
$859$	−14.4449	−0.492852	−0.246426	+	0.969162i	$0.579256\pi$
$860$	−6.92820	−0.236250
$861$	−6.92820	−0.236113
$862$	−8.19615	−0.279162
$863$	38.4449	1.30868	0.654339	−	0.756201i	$-0.272947\pi$
$863$	38.4449	1.30868	0.654339	+	0.756201i	$0.272947\pi$
$864$	4.00000	0.136083
$865$	10.0000	0.340010
$866$	34.0000	1.15537
$867$	40.5885	1.37846
$868$	3.46410	0.117579
$869$	7.71281	0.261639
$870$	−24.3923	−0.826977
$871$	20.0000	0.677674
$872$	−2.00000	−0.0677285
$873$	−8.92820	−0.302174
$874$	−33.5692	−1.13550
$875$	−1.26795	−0.0428645
$876$	−35.3205	−1.19337
$877$	−50.7846	−1.71487	−0.857437	−	0.514589i	$-0.827945\pi$
$877$	−50.7846	−1.71487	−0.857437	+	0.514589i	$0.827945\pi$
$878$	31.5167	1.06364
$879$	−16.3923	−0.552899
$880$	1.46410	0.0493549
$881$	47.3205	1.59427	0.797134	−	0.603802i	$-0.206348\pi$
$881$	47.3205	1.59427	0.797134	+	0.603802i	$0.206348\pi$
$882$	24.0718	0.810540
$883$	−34.2487	−1.15256	−0.576280	−	0.817252i	$-0.695496\pi$
$883$	−34.2487	−1.15256	−0.576280	+	0.817252i	$0.695496\pi$
$884$	−2.14359	−0.0720969
$885$	−0.535898	−0.0180140
$886$	39.1244	1.31441
$887$	20.1962	0.678120	0.339060	−	0.940765i	$-0.389891\pi$
$887$	20.1962	0.678120	0.339060	+	0.940765i	$0.389891\pi$
$888$	2.73205	0.0916816
$889$	17.3205	0.580911
$890$	2.00000	0.0670402
$891$	−3.60770	−0.120862
$892$	−22.0526	−0.738374
$893$	5.32051	0.178044
$894$	−44.7846	−1.49782
$895$	−17.6603	−0.590317
$896$	1.26795	0.0423592
$897$	32.0000	1.06845
$898$	−33.7128	−1.12501
$899$	24.3923	0.813529
$900$	4.46410	0.148803
$901$	8.78461	0.292658
$902$	2.92820	0.0974985
$903$	−24.0000	−0.798670
$904$	17.4641	0.580847
$905$	−1.46410	−0.0486684
$906$	22.9282	0.761739
$907$	5.75129	0.190968	0.0954842	−	0.995431i	$-0.469560\pi$
$907$	5.75129	0.190968	0.0954842	+	0.995431i	$0.469560\pi$
$908$	3.60770	0.119726
$909$	−11.3205	−0.375478
$910$	1.85641	0.0615393
$911$	−27.9090	−0.924665	−0.462333	−	0.886707i	$-0.652987\pi$
$911$	−27.9090	−0.924665	−0.462333	+	0.886707i	$0.652987\pi$
$912$	11.4641	0.379614
$913$	−7.71281	−0.255257
$914$	4.14359	0.137058
$915$	−24.3923	−0.806385
$916$	15.8564	0.523910
$917$	−15.9615	−0.527096
$918$	−5.85641	−0.193290
$919$	−13.2679	−0.437669	−0.218835	−	0.975762i	$-0.570226\pi$
$919$	−13.2679	−0.437669	−0.218835	+	0.975762i	$0.570226\pi$
$920$	8.00000	0.263752
$921$	34.3923	1.13326
$922$	26.7846	0.882104
$923$	−16.0000	−0.526646
$924$	5.07180	0.166850
$925$	1.00000	0.0328798
$926$	−5.07180	−0.166670
$927$	−60.1051	−1.97411
$928$	8.92820	0.293083
$929$	−15.8564	−0.520232	−0.260116	−	0.965577i	$-0.583761\pi$
$929$	−15.8564	−0.520232	−0.260116	+	0.965577i	$0.583761\pi$
$930$	−7.46410	−0.244758
$931$	22.6269	0.741568
$932$	15.0718	0.493693
$933$	−74.1051	−2.42609
$934$	−37.1769	−1.21647
$935$	−2.14359	−0.0701030
$936$	−6.53590	−0.213633
$937$	3.85641	0.125983	0.0629917	−	0.998014i	$-0.479936\pi$
$937$	3.85641	0.125983	0.0629917	+	0.998014i	$0.479936\pi$
$938$	17.3205	0.565535
$939$	−10.5359	−0.343826
$940$	−1.26795	−0.0413559
$941$	28.3923	0.925563	0.462781	−	0.886472i	$-0.346852\pi$
$941$	28.3923	0.925563	0.462781	+	0.886472i	$0.346852\pi$
$942$	46.2487	1.50686
$943$	16.0000	0.521032
$944$	0.196152	0.00638422
$945$	5.07180	0.164986
$946$	10.1436	0.329797
$947$	−45.1769	−1.46805	−0.734026	−	0.679121i	$-0.762361\pi$
$947$	−45.1769	−1.46805	−0.734026	+	0.679121i	$0.762361\pi$
$948$	−14.3923	−0.467440
$949$	18.9282	0.614435
$950$	4.19615	0.136141
$951$	87.0333	2.82225
$952$	−1.85641	−0.0601665
$953$	−11.8564	−0.384067	−0.192033	−	0.981388i	$-0.561508\pi$
$953$	−11.8564	−0.384067	−0.192033	+	0.981388i	$0.561508\pi$
$954$	26.7846	0.867184
$955$	−5.26795	−0.170467
$956$	−17.2679	−0.558485
$957$	35.7128	1.15443
$958$	34.0526	1.10019
$959$	−2.53590	−0.0818884
$960$	−2.73205	−0.0881766
$961$	−23.5359	−0.759223
$962$	−1.46410	−0.0472045
$963$	30.0526	0.968430
$964$	−8.92820	−0.287558
$965$	−11.8564	−0.381671
$966$	27.7128	0.891645
$967$	−23.6077	−0.759172	−0.379586	−	0.925156i	$-0.623934\pi$
$967$	−23.6077	−0.759172	−0.379586	+	0.925156i	$0.623934\pi$
$968$	8.85641	0.284656
$969$	−16.7846	−0.539199
$970$	2.00000	0.0642161
$971$	14.9282	0.479069	0.239534	−	0.970888i	$-0.423005\pi$
$971$	14.9282	0.479069	0.239534	+	0.970888i	$0.423005\pi$
$972$	18.7321	0.600831
$973$	8.78461	0.281622
$974$	16.3923	0.525243
$975$	−4.00000	−0.128103
$976$	8.92820	0.285785
$977$	−34.0000	−1.08776	−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000	−1.08776	−0.543878	+	0.839164i	$0.683045\pi$
$978$	63.7128	2.03731
$979$	−2.92820	−0.0935858
$980$	−5.39230	−0.172251
$981$	8.92820	0.285056
$982$	1.07180	0.0342024
$983$	−38.4449	−1.22620	−0.613100	−	0.790005i	$-0.710078\pi$
$983$	−38.4449	−1.22620	−0.613100	+	0.790005i	$0.710078\pi$
$984$	−5.46410	−0.174189
$985$	18.7846	0.598527
$986$	−13.0718	−0.416291
$987$	−4.39230	−0.139809
$988$	−6.14359	−0.195454
$989$	55.4256	1.76243
$990$	−6.53590	−0.207724
$991$	5.94744	0.188927	0.0944633	−	0.995528i	$-0.469886\pi$
$991$	5.94744	0.188927	0.0944633	+	0.995528i	$0.469886\pi$
$992$	2.73205	0.0867427
$993$	24.2487	0.769510
$994$	−13.8564	−0.439499
$995$	26.0526	0.825922
$996$	14.3923	0.456038
$997$	−4.14359	−0.131229	−0.0656145	−	0.997845i	$-0.520901\pi$
$997$	−4.14359	−0.131229	−0.0656145	+	0.997845i	$0.520901\pi$
$998$	−40.5885	−1.28481
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.a.e.1.1	✓	2
3.2	odd	2		3330.2.a.bd.1.2		2
4.3	odd	2		2960.2.a.q.1.2		2
5.2	odd	4		1850.2.b.l.149.2		4
5.3	odd	4		1850.2.b.l.149.3		4
5.4	even	2		1850.2.a.x.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.e.1.1	✓	2	1.1	even	1	trivial
1850.2.a.x.1.2		2	5.4	even	2
1850.2.b.l.149.2		4	5.2	odd	4
1850.2.b.l.149.3		4	5.3	odd	4
2960.2.a.q.1.2		2	4.3	odd	2
3330.2.a.bd.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} -1.26795 q^{7} -1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.73205 q^{6} -1.26795 q^{7} -1.00000 q^{8} +4.46410 q^{9} -1.00000 q^{10} +1.46410 q^{11} -2.73205 q^{12} +1.46410 q^{13} +1.26795 q^{14} -2.73205 q^{15} +1.00000 q^{16} -1.46410 q^{17} -4.46410 q^{18} -4.19615 q^{19} +1.00000 q^{20} +3.46410 q^{21} -1.46410 q^{22} -8.00000 q^{23} +2.73205 q^{24} +1.00000 q^{25} -1.46410 q^{26} -4.00000 q^{27} -1.26795 q^{28} -8.92820 q^{29} +2.73205 q^{30} -2.73205 q^{31} -1.00000 q^{32} -4.00000 q^{33} +1.46410 q^{34} -1.26795 q^{35} +4.46410 q^{36} +1.00000 q^{37} +4.19615 q^{38} -4.00000 q^{39} -1.00000 q^{40} -2.00000 q^{41} -3.46410 q^{42} -6.92820 q^{43} +1.46410 q^{44} +4.46410 q^{45} +8.00000 q^{46} -1.26795 q^{47} -2.73205 q^{48} -5.39230 q^{49} -1.00000 q^{50} +4.00000 q^{51} +1.46410 q^{52} -6.00000 q^{53} +4.00000 q^{54} +1.46410 q^{55} +1.26795 q^{56} +11.4641 q^{57} +8.92820 q^{58} +0.196152 q^{59} -2.73205 q^{60} +8.92820 q^{61} +2.73205 q^{62} -5.66025 q^{63} +1.00000 q^{64} +1.46410 q^{65} +4.00000 q^{66} +13.6603 q^{67} -1.46410 q^{68} +21.8564 q^{69} +1.26795 q^{70} -10.9282 q^{71} -4.46410 q^{72} +12.9282 q^{73} -1.00000 q^{74} -2.73205 q^{75} -4.19615 q^{76} -1.85641 q^{77} +4.00000 q^{78} +5.26795 q^{79} +1.00000 q^{80} -2.46410 q^{81} +2.00000 q^{82} -5.26795 q^{83} +3.46410 q^{84} -1.46410 q^{85} +6.92820 q^{86} +24.3923 q^{87} -1.46410 q^{88} -2.00000 q^{89} -4.46410 q^{90} -1.85641 q^{91} -8.00000 q^{92} +7.46410 q^{93} +1.26795 q^{94} -4.19615 q^{95} +2.73205 q^{96} -2.00000 q^{97} +5.39230 q^{98} +6.53590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} - 16 q^{23} + 2 q^{24} + 2 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} - 4 q^{29} + 2 q^{30} - 2 q^{31} - 2 q^{32} - 8 q^{33} - 4 q^{34} - 6 q^{35} + 2 q^{36} + 2 q^{37} - 2 q^{38} - 8 q^{39} - 2 q^{40} - 4 q^{41} - 4 q^{44} + 2 q^{45} + 16 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{49} - 2 q^{50} + 8 q^{51} - 4 q^{52} - 12 q^{53} + 8 q^{54} - 4 q^{55} + 6 q^{56} + 16 q^{57} + 4 q^{58} - 10 q^{59} - 2 q^{60} + 4 q^{61} + 2 q^{62} + 6 q^{63} + 2 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} + 4 q^{68} + 16 q^{69} + 6 q^{70} - 8 q^{71} - 2 q^{72} + 12 q^{73} - 2 q^{74} - 2 q^{75} + 2 q^{76} + 24 q^{77} + 8 q^{78} + 14 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{83} + 4 q^{85} + 28 q^{87} + 4 q^{88} - 4 q^{89} - 2 q^{90} + 24 q^{91} - 16 q^{92} + 8 q^{93} + 6 q^{94} + 2 q^{95} + 2 q^{96} - 4 q^{97} - 10 q^{98} + 20 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^22 - 16 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 - 4 * q^29 + 2 * q^30 - 2 * q^31 - 2 * q^32 - 8 * q^33 - 4 * q^34 - 6 * q^35 + 2 * q^36 + 2 * q^37 - 2 * q^38 - 8 * q^39 - 2 * q^40 - 4 * q^41 - 4 * q^44 + 2 * q^45 + 16 * q^46 - 6 * q^47 - 2 * q^48 + 10 * q^49 - 2 * q^50 + 8 * q^51 - 4 * q^52 - 12 * q^53 + 8 * q^54 - 4 * q^55 + 6 * q^56 + 16 * q^57 + 4 * q^58 - 10 * q^59 - 2 * q^60 + 4 * q^61 + 2 * q^62 + 6 * q^63 + 2 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 + 4 * q^68 + 16 * q^69 + 6 * q^70 - 8 * q^71 - 2 * q^72 + 12 * q^73 - 2 * q^74 - 2 * q^75 + 2 * q^76 + 24 * q^77 + 8 * q^78 + 14 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^83 + 4 * q^85 + 28 * q^87 + 4 * q^88 - 4 * q^89 - 2 * q^90 + 24 * q^91 - 16 * q^92 + 8 * q^93 + 6 * q^94 + 2 * q^95 + 2 * q^96 - 4 * q^97 - 10 * q^98 + 20 * q^99

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