LMFDB - Embedded newform 136.2.h.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(101,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.h (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 $ x^16 + 8x^14 + 20x^12 + 36x^10 + 240x^8 - 156x^6 + 268x^4 + 136*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$-0.970055 + 0.510012i$ of defining polynomial
Character	$\chi$	$=$	136.101
Dual form			136.2.h.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25175 + 0.658116i) q^{2} +0.909242 q^{3} +(1.13377 - 1.64760i) q^{4} +1.54992 q^{5} +(-1.13815 + 0.598386i) q^{6} -3.57366i q^{7} +(-0.334887 + 2.80853i) q^{8} -2.17328 q^{9} +O(q^{10})$	\(q+(-1.25175 + 0.658116i) q^{2} +0.909242 q^{3} +(1.13377 - 1.64760i) q^{4} +1.54992 q^{5} +(-1.13815 + 0.598386i) q^{6} -3.57366i q^{7} +(-0.334887 + 2.80853i) q^{8} -2.17328 q^{9} +(-1.94011 + 1.02002i) q^{10} +5.24727 q^{11} +(1.03087 - 1.49806i) q^{12} +0.927449i q^{13} +(2.35188 + 4.47334i) q^{14} +1.40925 q^{15} +(-1.42914 - 3.73598i) q^{16} +(0.764030 + 4.05170i) q^{17} +(2.72041 - 1.43027i) q^{18} +5.22828i q^{19} +(1.75724 - 2.55363i) q^{20} -3.24932i q^{21} +(-6.56828 + 3.45331i) q^{22} -5.37301i q^{23} +(-0.304494 + 2.55363i) q^{24} -2.59776 q^{25} +(-0.610369 - 1.16094i) q^{26} -4.70376 q^{27} +(-5.88795 - 4.05170i) q^{28} -3.00267 q^{29} +(-1.76403 + 0.927449i) q^{30} +0.336838i q^{31} +(4.24764 + 3.73598i) q^{32} +4.77104 q^{33} +(-3.62286 - 4.56890i) q^{34} -5.53887i q^{35} +(-2.46399 + 3.58069i) q^{36} -7.49188 q^{37} +(-3.44081 - 6.54451i) q^{38} +0.843275i q^{39} +(-0.519047 + 4.35299i) q^{40} +5.03617i q^{41} +(2.13843 + 4.06734i) q^{42} -8.91225i q^{43} +(5.94918 - 8.64538i) q^{44} -3.36840 q^{45} +(3.53606 + 6.72568i) q^{46} -4.93731 q^{47} +(-1.29944 - 3.39691i) q^{48} -5.77104 q^{49} +(3.25175 - 1.70963i) q^{50} +(0.694688 + 3.68397i) q^{51} +(1.52806 + 1.05151i) q^{52} +11.5447i q^{53} +(5.88795 - 3.09562i) q^{54} +8.13283 q^{55} +(10.0367 + 1.19677i) q^{56} +4.75377i q^{57} +(3.75859 - 1.97610i) q^{58} +4.95434i q^{59} +(1.59776 - 2.32187i) q^{60} +9.31036 q^{61} +(-0.221678 - 0.421638i) q^{62} +7.76656i q^{63} +(-7.77570 - 1.88108i) q^{64} +1.43747i q^{65} +(-5.97216 + 3.13990i) q^{66} -1.27036i q^{67} +(7.54179 + 3.33487i) q^{68} -4.88537i q^{69} +(3.64522 + 6.93329i) q^{70} -4.52974i q^{71} +(0.727803 - 6.10372i) q^{72} -9.78995i q^{73} +(9.37797 - 4.93052i) q^{74} -2.36199 q^{75} +(8.61409 + 5.92765i) q^{76} -18.7520i q^{77} +(-0.554973 - 1.05557i) q^{78} +7.76656i q^{79} +(-2.21505 - 5.79046i) q^{80} +2.24298 q^{81} +(-3.31439 - 6.30404i) q^{82} +6.80923i q^{83} +(-5.35357 - 3.68397i) q^{84} +(1.18418 + 6.27979i) q^{85} +(5.86530 + 11.1559i) q^{86} -2.73015 q^{87} +(-1.75724 + 14.7371i) q^{88} -0.0474582 q^{89} +(4.21640 - 2.21680i) q^{90} +3.31439 q^{91} +(-8.85255 - 6.09175i) q^{92} +0.306267i q^{93} +(6.18029 - 3.24932i) q^{94} +8.10340i q^{95} +(3.86213 + 3.39691i) q^{96} -9.54086i q^{97} +(7.22391 - 3.79801i) q^{98} -11.4038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.25175	+	0.658116i	−0.885123	+	0.465358i
$2$	−1.25175	+	0.658116i	−0.885123	+	0.465358i
$3$	0.909242			0.524951			0.262476	−	0.964939i	$-0.415461\pi$
$3$	0.909242			0.524951			0.262476	+	0.964939i	$0.415461\pi$
$4$	1.13377	−	1.64760i	0.566884	−	0.823798i
$5$	1.54992			0.693144			0.346572	−	0.938023i	$-0.387346\pi$
$5$	1.54992			0.693144			0.346572	+	0.938023i	$0.387346\pi$
$6$	−1.13815	+	0.598386i	−0.464646	+	0.244290i
$7$		−	3.57366i		−	1.35072i	−0.737490	−	0.675358i	$-0.763989\pi$
$7$		−	3.57366i		−	1.35072i	0.737490	−	0.675358i	$-0.236011\pi$
$8$	−0.334887	+	2.80853i	−0.118401	+	0.992966i
$9$	−2.17328			−0.724426
$10$	−1.94011	+	1.02002i	−0.613517	+	0.322560i
$11$	5.24727			1.58211			0.791056	−	0.611744i	$-0.209532\pi$
$11$	5.24727			1.58211			0.791056	+	0.611744i	$0.209532\pi$
$12$	1.03087	−	1.49806i	0.297586	−	0.432454i
$13$			0.927449i			0.257228i	0.991695	+	0.128614i	$0.0410528\pi$
$13$			0.927449i			0.257228i	−0.991695	+	0.128614i	$0.958947\pi$
$14$	2.35188	+	4.47334i	0.628567	+	1.19555i
$15$	1.40925			0.363866
$16$	−1.42914	−	3.73598i	−0.357286	−	0.933995i
$17$	0.764030	+	4.05170i	0.185305	+	0.982681i
$17$	0.764030	+	4.05170i	0.185305	+	0.982681i
$18$	2.72041	−	1.43027i	0.641206	−	0.337118i
$19$			5.22828i			1.19945i	0.800206	+	0.599725i	$0.204723\pi$
$19$			5.22828i			1.19945i	−0.800206	+	0.599725i	$0.795277\pi$
$20$	1.75724	−	2.55363i	0.392932	−	0.571010i
$21$		−	3.24932i		−	0.709060i
$22$	−6.56828	+	3.45331i	−1.40036	+	0.736249i
$23$		−	5.37301i		−	1.12035i	−0.828374	−	0.560175i	$-0.810734\pi$
$23$		−	5.37301i		−	1.12035i	0.828374	−	0.560175i	$-0.189266\pi$
$24$	−0.304494	+	2.55363i	−0.0621545	+	0.521259i
$25$	−2.59776			−0.519552
$26$	−0.610369	−	1.16094i	−0.119703	−	0.227678i
$27$	−4.70376			−0.905240
$28$	−5.88795	−	4.05170i	−1.11272	−	0.765699i
$29$	−3.00267			−0.557581			−0.278791	−	0.960352i	$-0.589934\pi$
$29$	−3.00267			−0.557581			−0.278791	+	0.960352i	$0.589934\pi$
$30$	−1.76403	+	0.927449i	−0.322066	+	0.169328i
$31$			0.336838i			0.0604979i	0.999542	+	0.0302489i	$0.00963001\pi$
$31$			0.336838i			0.0604979i	−0.999542	+	0.0302489i	$0.990370\pi$
$32$	4.24764	+	3.73598i	0.750884	+	0.660434i
$33$	4.77104			0.830531
$34$	−3.62286	−	4.56890i	−0.621316	−	0.783560i
$35$		−	5.53887i		−	0.936240i
$36$	−2.46399	+	3.58069i	−0.410665	+	0.596781i
$37$	−7.49188			−1.23166			−0.615828	−	0.787880i	$-0.711179\pi$
$37$	−7.49188			−1.23166			−0.615828	+	0.787880i	$0.711179\pi$
$38$	−3.44081	−	6.54451i	−0.558174	−	1.06166i
$39$			0.843275i			0.135032i
$40$	−0.519047	+	4.35299i	−0.0820686	+	0.688268i
$41$			5.03617i			0.786518i	0.919428	+	0.393259i	$0.128652\pi$
$41$			5.03617i			0.786518i	−0.919428	+	0.393259i	$0.871348\pi$
$42$	2.13843	+	4.06734i	0.329967	+	0.627605i
$43$		−	8.91225i		−	1.35911i	−0.733626	−	0.679553i	$-0.762174\pi$
$43$		−	8.91225i		−	1.35911i	0.733626	−	0.679553i	$-0.237826\pi$
$44$	5.94918	−	8.64538i	0.896873	−	1.30334i
$45$	−3.36840			−0.502131
$46$	3.53606	+	6.72568i	0.521364	+	0.991647i
$47$	−4.93731			−0.720181			−0.360090	−	0.932917i	$-0.617254\pi$
$47$	−4.93731			−0.720181			−0.360090	+	0.932917i	$0.617254\pi$
$48$	−1.29944	−	3.39691i	−0.187558	−	0.490302i
$49$	−5.77104			−0.824434
$50$	3.25175	−	1.70963i	0.459867	−	0.241778i
$51$	0.694688	+	3.68397i	0.0972758	+	0.515860i
$52$	1.52806	+	1.05151i	0.211904	+	0.145818i
$53$			11.5447i			1.58579i	0.609359	+	0.792894i	$0.291427\pi$
$53$			11.5447i			1.58579i	−0.609359	+	0.792894i	$0.708573\pi$
$54$	5.88795	−	3.09562i	0.801248	−	0.421261i
$55$	8.13283			1.09663
$56$	10.0367	+	1.19677i	1.34122	+	0.159926i
$57$			4.75377i			0.629653i
$58$	3.75859	−	1.97610i	0.493528	−	0.259475i
$59$			4.95434i			0.644999i	0.946570	+	0.322500i	$0.104523\pi$
$59$			4.95434i			0.644999i	−0.946570	+	0.322500i	$0.895477\pi$
$60$	1.59776	−	2.32187i	0.206270	−	0.299752i
$61$	9.31036			1.19207			0.596035	−	0.802959i	$-0.296742\pi$
$61$	9.31036			1.19207			0.596035	+	0.802959i	$0.296742\pi$
$62$	−0.221678	−	0.421638i	−0.0281532	−	0.0535480i
$63$			7.76656i			0.978494i
$64$	−7.77570	−	1.88108i	−0.971963	−	0.235135i
$65$			1.43747i			0.178296i
$66$	−5.97216	+	3.13990i	−0.735122	+	0.386494i
$67$		−	1.27036i		−	0.155199i	−0.996985	−	0.0775996i	$-0.975274\pi$
$67$		−	1.27036i		−	0.155199i	0.996985	−	0.0775996i	$-0.0247256\pi$
$68$	7.54179	+	3.33487i	0.914577	+	0.404412i
$69$		−	4.88537i		−	0.588129i
$70$	3.64522	+	6.93329i	0.435687	+	0.828687i
$71$		−	4.52974i		−	0.537581i	−0.963199	−	0.268790i	$-0.913376\pi$
$71$		−	4.52974i		−	0.537581i	0.963199	−	0.268790i	$-0.0866239\pi$
$72$	0.727803	−	6.10372i	0.0857725	−	0.719331i
$73$		−	9.78995i		−	1.14583i	−0.819616	−	0.572913i	$-0.805813\pi$
$73$		−	9.78995i		−	1.14583i	0.819616	−	0.572913i	$-0.194187\pi$
$74$	9.37797	−	4.93052i	1.09017	−	0.573161i
$75$	−2.36199			−0.272739
$76$	8.61409	+	5.92765i	0.988104	+	0.679949i
$77$		−	18.7520i		−	2.13698i
$78$	−0.554973	−	1.05557i	−0.0628383	−	0.119520i
$79$			7.76656i			0.873806i	0.899509	+	0.436903i	$0.143925\pi$
$79$			7.76656i			0.873806i	−0.899509	+	0.436903i	$0.856075\pi$
$80$	−2.21505	−	5.79046i	−0.247650	−	0.647393i
$81$	2.24298			0.249220
$82$	−3.31439	−	6.30404i	−0.366013	−	0.696165i
$83$			6.80923i			0.747410i	0.927548	+	0.373705i	$0.121913\pi$
$83$			6.80923i			0.747410i	−0.927548	+	0.373705i	$0.878087\pi$
$84$	−5.35357	−	3.68397i	−0.584122	−	0.401955i
$85$	1.18418	+	6.27979i	0.128443	+	0.681139i
$86$	5.86530	+	11.1559i	0.632471	+	1.20298i
$87$	−2.73015			−0.292703
$88$	−1.75724	+	14.7371i	−0.187323	+	1.57098i
$89$	−0.0474582			−0.00503056			−0.00251528	−	0.999997i	$-0.500801\pi$
$89$	−0.0474582			−0.00503056			−0.00251528	+	0.999997i	$0.500801\pi$
$90$	4.21640	−	2.21680i	0.444448	−	0.233671i
$91$	3.31439			0.347442
$92$	−8.85255	−	6.09175i	−0.922942	−	0.635108i
$93$			0.306267i			0.0317584i
$94$	6.18029	−	3.24932i	0.637448	−	0.335142i
$95$			8.10340i			0.831391i
$96$	3.86213	+	3.39691i	0.394177	+	0.346696i
$97$		−	9.54086i		−	0.968728i	−0.874867	−	0.484364i	$-0.839051\pi$
$97$		−	9.54086i		−	0.968728i	0.874867	−	0.484364i	$-0.160949\pi$
$98$	7.22391	−	3.79801i	0.729725	−	0.383657i
$99$	−11.4038			−1.14612
$100$	−2.94526	+	4.28006i	−0.294526	+	0.428006i
$101$			10.1503i			1.00999i	0.863122	+	0.504996i	$0.168506\pi$
$101$			10.1503i			1.00999i	−0.863122	+	0.504996i	$0.831494\pi$
$102$	−3.29406	−	4.15424i	−0.326160	−	0.411331i
$103$	−15.5561			−1.53279			−0.766394	−	0.642371i	$-0.777951\pi$
$103$	−15.5561			−1.53279			−0.766394	+	0.642371i	$0.777951\pi$
$104$	−2.60477	−	0.310591i	−0.255419	−	0.0304559i
$105$		−	5.03617i		−	0.491480i
$106$	−7.59776	−	14.4511i	−0.737960	−	1.40362i
$107$	−6.74317			−0.651887			−0.325944	−	0.945389i	$-0.605682\pi$
$107$	−6.74317			−0.651887			−0.325944	+	0.945389i	$0.605682\pi$
$108$	−5.33297	+	7.74990i	−0.513166	+	0.745734i
$109$	8.94463			0.856740			0.428370	−	0.903603i	$-0.359088\pi$
$109$	8.94463			0.856740			0.428370	+	0.903603i	$0.359088\pi$
$110$	−10.1803	+	5.35234i	−0.970652	+	0.510326i
$111$	−6.81193			−0.646560
$112$	−13.3511	+	5.10727i	−1.26156	+	0.482592i
$113$		−	1.43747i		−	0.135226i	−0.997712	−	0.0676128i	$-0.978462\pi$
$113$		−	1.43747i		−	0.135226i	0.997712	−	0.0676128i	$-0.0215383\pi$
$114$	−3.12853	−	5.95055i	−0.293014	−	0.557320i
$115$		−	8.32772i		−	0.776564i
$116$	−3.40433	+	4.94718i	−0.316084	+	0.459334i
$117$		−	2.01560i		−	0.186343i
$118$	−3.26053	−	6.20160i	−0.300156	−	0.570904i
$119$	14.4794	−	2.73038i	1.32732	−	0.250294i
$120$	−0.471939	+	3.95792i	−0.0430820	+	0.361307i
$121$	16.5339			1.50308
$122$	−11.6543	+	6.12729i	−1.05513	+	0.554739i
$123$			4.57910i			0.412884i
$124$	0.554973	+	0.381896i	0.0498380	+	0.0342953i
$125$	−11.7759			−1.05327
$126$	−5.11129	−	9.72181i	−0.455350	−	0.866087i
$127$	7.29044			0.646922			0.323461	−	0.946242i	$-0.395154\pi$
$127$	7.29044			0.646922			0.323461	+	0.946242i	$0.395154\pi$
$128$	10.9712	−	2.76266i	0.969728	−	0.244187i
$129$		−	8.10340i		−	0.713464i
$130$	−0.946020	−	1.79935i	−0.0829715	−	0.157814i
$131$	8.19592			0.716081			0.358041	−	0.933706i	$-0.383445\pi$
$131$	8.19592			0.716081			0.358041	+	0.933706i	$0.383445\pi$
$132$	5.40925	−	7.86074i	0.470815	−	0.684190i
$133$	18.6841			1.62012
$134$	0.836045	+	1.59018i	0.0722232	+	0.137370i
$135$	−7.29044			−0.627461
$136$	−11.6352	+	0.788941i	−0.997709	+	0.0676512i
$137$	2.11716			0.180881			0.0904405	−	0.995902i	$-0.471173\pi$
$137$	2.11716			0.180881			0.0904405	+	0.995902i	$0.471173\pi$
$138$	3.21514	+	6.11527i	0.273691	+	0.520566i
$139$	3.79452			0.321847			0.160924	−	0.986967i	$-0.448553\pi$
$139$	3.79452			0.321847			0.160924	+	0.986967i	$0.448553\pi$
$140$	−9.12582	−	6.27979i	−0.771273	−	0.530739i
$141$	−4.48921			−0.378060
$142$	2.98109	+	5.67011i	0.250168	+	0.475825i
$143$			4.86658i			0.406963i
$144$	3.10593	+	8.11933i	0.258827	+	0.676611i
$145$	−4.65388			−0.386484
$146$	6.44292	+	12.2546i	0.533220	+	1.01420i
$147$	−5.24727			−0.432788
$148$	−8.49404	+	12.3436i	−0.698206	+	1.01464i
$149$		−	10.4566i		−	0.856635i	−0.903628	−	0.428317i	$-0.859107\pi$
$149$		−	10.4566i		−	0.856635i	0.903628	−	0.428317i	$-0.140893\pi$
$150$	2.95663	−	1.55446i	0.241408	−	0.126921i
$151$	4.84896			0.394603			0.197301	−	0.980343i	$-0.436782\pi$
$151$	4.84896			0.394603			0.197301	+	0.980343i	$0.436782\pi$
$152$	−14.6838	−	1.75088i	−1.19101	−	0.142015i
$153$	−1.66045	−	8.80547i	−0.134240	−	0.711880i
$154$	12.3410	+	23.4728i	0.994463	+	1.89149i
$155$			0.522071i			0.0419337i
$156$	1.38938	+	0.956078i	0.111239	+	0.0765475i
$157$			12.0926i			0.965095i	0.875870	+	0.482548i	$0.160288\pi$
$157$			12.0926i			0.965095i	−0.875870	+	0.482548i	$0.839712\pi$
$158$	−5.11129	−	9.72181i	−0.406633	−	0.773425i
$159$			10.4969i			0.832462i
$160$	6.58349	+	5.79046i	0.520470	+	0.457776i
$161$	−19.2013			−1.51328
$162$	−2.80765	+	1.47614i	−0.220590	+	0.115976i
$163$	9.99418			0.782805			0.391402	−	0.920220i	$-0.371990\pi$
$163$	9.99418			0.782805			0.391402	+	0.920220i	$0.371990\pi$
$164$	8.29758	+	5.70985i	0.647932	+	0.445864i
$165$	7.39471			0.575677
$166$	−4.48126	−	8.52347i	−0.347813	−	0.661550i
$167$		−	14.0706i		−	1.08882i	−0.838821	−	0.544408i	$-0.816754\pi$
$167$		−	14.0706i		−	1.08882i	0.838821	−	0.544408i	$-0.183246\pi$
$168$	9.12582	+	1.08816i	0.704072	+	0.0839531i
$169$	12.1398			0.933834
$170$	−5.61513	−	7.08141i	−0.430661	−	0.543120i
$171$		−	11.3625i		−	0.868913i
$172$	−14.6838	−	10.1044i	−1.11963	−	0.770455i
$173$	19.2678			1.46490			0.732451	−	0.680820i	$-0.238377\pi$
$173$	19.2678			1.46490			0.732451	+	0.680820i	$0.238377\pi$
$174$	3.41747	−	1.79676i	0.259078	−	0.136212i
$175$			9.28351i			0.701767i
$176$	−7.49910	−	19.6037i	−0.565266	−	1.47768i
$177$			4.50469i			0.338593i
$178$	0.0594059	−	0.0312330i	0.00445266	−	0.00234101i
$179$		−	18.4090i		−	1.37596i	−0.725731	−	0.687978i	$-0.758498\pi$
$179$		−	18.4090i		−	1.37596i	0.725731	−	0.687978i	$-0.241502\pi$
$180$	−3.81898	+	5.54976i	−0.284650	+	0.413655i
$181$	1.00003			0.0743320			0.0371660	−	0.999309i	$-0.488167\pi$
$181$	1.00003			0.0743320			0.0371660	+	0.999309i	$0.488167\pi$
$182$	−4.14879	+	2.18125i	−0.307529	+	0.161685i
$183$	8.46537			0.625778
$184$	15.0903	+	1.79935i	1.11247	+	0.132650i
$185$	−11.6118			−0.853715
$186$	−0.201559	−	0.383371i	−0.0147790	−	0.0281101i
$187$	4.00907	+	21.2604i	0.293173	+	1.55471i
$188$	−5.59776	+	8.13469i	−0.408259	+	0.593283i
$189$			16.8096i			1.22272i
$190$	−5.33297	−	10.1434i	−0.386894	−	0.735883i
$191$	7.42327			0.537129			0.268564	−	0.963262i	$-0.413451\pi$
$191$	7.42327			0.537129			0.268564	+	0.963262i	$0.413451\pi$
$192$	−7.06999	−	1.71036i	−0.510233	−	0.123435i
$193$		−	22.3980i		−	1.61225i	−0.591748	−	0.806123i	$-0.701562\pi$
$193$		−	22.3980i		−	1.61225i	0.591748	−	0.806123i	$-0.298438\pi$
$194$	6.27899	+	11.9428i	0.450805	+	0.857443i
$195$			1.30701i			0.0935966i
$196$	−6.54302	+	9.50834i	−0.467358	+	0.679167i
$197$	−27.9945			−1.99452			−0.997261	−	0.0739616i	$-0.976436\pi$
$197$	−27.9945			−1.99452			−0.997261	+	0.0739616i	$0.976436\pi$
$198$	14.2747	−	7.50501i	1.01446	−	0.533358i
$199$		−	11.0829i		−	0.785643i	−0.919615	−	0.392822i	$-0.871499\pi$
$199$		−	11.0829i		−	0.785643i	0.919615	−	0.392822i	$-0.128501\pi$
$200$	0.869957	−	7.29589i	0.0615152	−	0.515897i
$201$		−	1.15507i		−	0.0814720i
$202$	−6.68007	−	12.7057i	−0.470008	−	0.893967i
$203$			10.7305i			0.753134i
$204$	6.85731	+	3.03220i	0.480108	+	0.212297i
$205$			7.80565i			0.545170i
$206$	19.4724	−	10.2377i	1.35670	−	0.713295i
$207$			11.6771i			0.811611i
$208$	3.46493	−	1.32546i	0.240250	−	0.0919039i
$209$			27.4342i			1.89766i
$210$	3.31439	+	6.30404i	0.228714	+	0.435020i
$211$	−5.65616			−0.389386			−0.194693	−	0.980864i	$-0.562371\pi$
$211$	−5.65616			−0.389386			−0.194693	+	0.980864i	$0.562371\pi$
$212$	19.0210	+	13.0890i	1.30637	+	0.898958i
$213$		−	4.11863i		−	0.282204i
$214$	8.44078	−	4.43779i	0.577000	−	0.303361i
$215$		−	13.8132i		−	0.942056i
$216$	1.57523	−	13.2107i	0.107181	−	0.898872i
$217$	1.20374			0.0817155
$218$	−11.1965	+	5.88660i	−0.758320	+	0.398691i
$219$		−	8.90143i		−	0.601503i
$220$	9.22074	−	13.3996i	0.621662	−	0.903402i
$221$	−3.75774	+	0.708599i	−0.252773	+	0.0476655i
$222$	8.52685	−	4.48304i	0.572284	−	0.300882i
$223$	−20.1164			−1.34709			−0.673546	−	0.739145i	$-0.735230\pi$
$223$	−20.1164			−1.34709			−0.673546	+	0.739145i	$0.735230\pi$
$224$	13.3511	−	15.1796i	0.892059	−	1.01423i
$225$	5.64566			0.376377
$226$	0.946020	+	1.79935i	0.0629283	+	0.119691i
$227$	0.500358			0.0332099			0.0166050	−	0.999862i	$-0.494714\pi$
$227$	0.500358			0.0332099			0.0166050	+	0.999862i	$0.494714\pi$
$228$	7.83229	+	5.38967i	0.518706	+	0.356940i
$229$		−	25.8718i		−	1.70966i	−0.518912	−	0.854828i	$-0.673663\pi$
$229$		−	25.8718i		−	1.70966i	0.518912	−	0.854828i	$-0.326337\pi$
$230$	5.48060	+	10.4242i	0.361380	+	0.687354i
$231$		−	17.0501i		−	1.12181i
$232$	1.00555	−	8.43308i	0.0660179	−	0.553659i
$233$			19.0484i			1.24790i	0.781463	+	0.623951i	$0.214474\pi$
$233$			19.0484i			1.24790i	−0.781463	+	0.623951i	$0.785526\pi$
$234$	1.32650	+	2.52304i	0.0867161	+	0.164936i
$235$	−7.65241			−0.499189
$236$	8.16274	+	5.61706i	0.531349	+	0.365640i
$237$			7.06168i			0.458705i
$238$	−16.3277	+	12.9469i	−1.05837	+	0.839221i
$239$	−22.8564			−1.47846			−0.739229	−	0.673454i	$-0.764810\pi$
$239$	−22.8564			−1.47846			−0.739229	+	0.673454i	$0.764810\pi$
$240$	−2.01402	−	5.26493i	−0.130004	−	0.339849i
$241$			13.1396i			0.846394i	0.906038	+	0.423197i	$0.139092\pi$
$241$			13.1396i			0.846394i	−0.906038	+	0.423197i	$0.860908\pi$
$242$	−20.6963	+	10.8812i	−1.33041	+	0.699469i
$243$	16.1507			1.03607
$244$	10.5558	−	15.3397i	0.675765	−	0.982024i
$245$	−8.94463			−0.571451
$246$	−3.01358	−	5.73190i	−0.192139	−	0.365453i
$247$	−4.84896			−0.308532
$248$	−0.946020	−	0.112803i	−0.0600723	−	0.00716298i
$249$			6.19124i			0.392354i
$250$	14.7405	−	7.74990i	0.932271	−	0.490147i
$251$		−	7.70436i		−	0.486295i	−0.969989	−	0.243147i	$-0.921820\pi$
$251$		−	7.70436i		−	0.486295i	0.969989	−	0.243147i	$-0.0781799\pi$
$252$	12.7961	+	8.80547i	0.806082	+	0.554693i
$253$		−	28.1937i		−	1.77252i
$254$	−9.12582	+	4.79795i	−0.572605	+	0.301050i
$255$	1.07671	+	5.70985i	0.0674261	+	0.357565i
$256$	−11.9151	+	10.6785i	−0.744694	+	0.667406i
$257$	28.6345			1.78617			0.893084	−	0.449889i	$-0.148537\pi$
$257$	28.6345			1.78617			0.893084	+	0.449889i	$0.148537\pi$
$258$	5.33297	+	10.1434i	0.332016	+	0.631503i
$259$			26.7734i			1.66362i
$260$	2.36837	+	1.62975i	0.146880	+	0.101073i
$261$	6.52563			0.403927
$262$	−10.2593	+	5.39387i	−0.633820	+	0.333234i
$263$	15.5561			0.959230			0.479615	−	0.877479i	$-0.340776\pi$
$263$	15.5561			0.959230			0.479615	+	0.877479i	$0.340776\pi$
$264$	−1.59776	+	13.3996i	−0.0983353	+	0.824689i
$265$			17.8933i			1.09918i
$266$	−23.3879	+	12.2963i	−1.43400	+	0.753934i
$267$	−0.0431510			−0.00264080
$268$	−2.09304	−	1.44029i	−0.127853	−	0.0879799i
$269$	−22.1605			−1.35115			−0.675575	−	0.737291i	$-0.736105\pi$
$269$	−22.1605			−1.35115			−0.675575	+	0.737291i	$0.736105\pi$
$270$	9.12582	−	4.79795i	0.555380	−	0.291994i
$271$	17.6304			1.07097			0.535486	−	0.844544i	$-0.320128\pi$
$271$	17.6304			1.07097			0.535486	+	0.844544i	$0.320128\pi$
$272$	14.0452	−	8.64486i	0.851613	−	0.524172i
$273$	3.01358			0.182390
$274$	−2.65016	+	1.39333i	−0.160102	+	0.0841744i
$275$	−13.6312			−0.821989
$276$	−8.04911	−	5.53887i	−0.484500	−	0.333401i
$277$	5.30766			0.318906			0.159453	−	0.987205i	$-0.449027\pi$
$277$	5.30766			0.318906			0.159453	+	0.987205i	$0.449027\pi$
$278$	−4.74980	+	2.49723i	−0.284874	+	0.149774i
$279$		−	0.732043i		−	0.0438263i
$280$	15.5561	+	1.85490i	0.929655	+	0.110851i
$281$	−18.3049			−1.09198			−0.545989	−	0.837792i	$-0.683846\pi$
$281$	−18.3049			−1.09198			−0.545989	+	0.837792i	$0.683846\pi$
$282$	5.61938	−	2.95442i	0.334629	−	0.175933i
$283$	−6.63665			−0.394508			−0.197254	−	0.980352i	$-0.563202\pi$
$283$	−6.63665			−0.394508			−0.197254	+	0.980352i	$0.563202\pi$
$284$	−7.46318	−	5.13567i	−0.442858	−	0.304746i
$285$			7.36795i			0.436440i
$286$	−3.20277	−	6.09175i	−0.189384	−	0.360213i
$287$	17.9976			1.06236
$288$	−9.23131	−	8.11933i	−0.543960	−	0.478436i
$289$	−15.8325	+	6.19124i	−0.931324	+	0.364191i
$290$	5.82551	−	3.06279i	0.342086	−	0.179853i
$291$		−	8.67495i		−	0.508535i
$292$	−16.1299	−	11.0995i	−0.943929	−	0.649550i
$293$			5.81282i			0.339588i	0.985480	+	0.169794i	$0.0543103\pi$
$293$			5.81282i			0.339588i	−0.985480	+	0.169794i	$0.945690\pi$
$294$	6.56828	−	3.45331i	0.383070	−	0.201401i
$295$			7.67880i			0.447077i
$296$	2.50893	−	21.0412i	0.145829	−	1.22299i
$297$	−24.6819			−1.43219
$298$	6.88163	+	13.0890i	0.398642	+	0.758227i
$299$	4.98319			0.288186
$300$	−2.67795	+	3.89161i	−0.154612	+	0.224682i
$301$	−31.8494			−1.83577
$302$	−6.06970	+	3.19118i	−0.349272	+	0.183632i
$303$			9.22907i			0.530196i
$304$	19.5328	−	7.47196i	1.12028	−	0.428546i
$305$	14.4303			0.826275
$306$	7.87349	+	9.92950i	0.450098	+	0.567632i
$307$		−	16.6533i		−	0.950452i	−0.879864	−	0.475226i	$-0.842366\pi$
$307$		−	16.6533i		−	0.950452i	0.879864	−	0.475226i	$-0.157634\pi$
$308$	−30.8956	−	21.2604i	−1.76044	−	1.21142i
$309$	−14.1443			−0.804639
$310$	−0.343583	−	0.653503i	−0.0195142	−	0.0371165i
$311$		−	33.6505i		−	1.90814i	−0.299577	−	0.954072i	$-0.596845\pi$
$311$		−	33.6505i		−	1.90814i	0.299577	−	0.954072i	$-0.403155\pi$
$312$	−2.36837	−	0.282402i	−0.134082	−	0.0159879i
$313$		−	24.3670i		−	1.37730i	−0.725092	−	0.688652i	$-0.758203\pi$
$313$		−	24.3670i		−	1.37730i	0.725092	−	0.688652i	$-0.241797\pi$
$314$	−7.95834	−	15.1370i	−0.449115	−	0.854228i
$315$			12.0375i			0.678237i
$316$	12.7961	+	8.80547i	0.719840	+	0.495346i
$317$	−1.17144			−0.0657945			−0.0328972	−	0.999459i	$-0.510473\pi$
$317$	−1.17144			−0.0657945			−0.0328972	+	0.999459i	$0.510473\pi$
$318$	−6.90820	−	13.1396i	−0.387393	−	0.736831i
$319$	−15.7558			−0.882156
$320$	−12.0517	−	2.91552i	−0.673710	−	0.162983i
$321$	−6.13118			−0.342209
$322$	24.0353	−	12.6367i	1.33943	−	0.704215i
$323$	−21.1834	+	3.99456i	−1.17868	+	0.222264i
$324$	2.54302	−	3.69552i	0.141279	−	0.205307i
$325$		−	2.40929i		−	0.133643i
$326$	−12.5102	+	6.57733i	−0.692878	+	0.364285i
$327$	8.13283			0.449747
$328$	−14.1443	−	1.68655i	−0.780986	−	0.0931242i
$329$			17.6443i			0.972760i
$330$	−9.25635	+	4.86658i	−0.509545	+	0.267896i
$331$		−	7.60525i		−	0.418022i	−0.977913	−	0.209011i	$-0.932976\pi$
$331$		−	7.60525i		−	0.418022i	0.977913	−	0.209011i	$-0.0670245\pi$
$332$	11.2189	+	7.72009i	0.615715	+	0.423695i
$333$	16.2819			0.892245
$334$	9.26008	+	17.6129i	0.506689	+	0.963735i
$335$		−	1.96895i		−	0.107575i
$336$	−12.1394	+	4.64374i	−0.662259	+	0.253337i
$337$			25.4653i			1.38718i	0.720370	+	0.693590i	$0.243972\pi$
$337$			25.4653i			1.38718i	−0.720370	+	0.693590i	$0.756028\pi$
$338$	−15.1961	+	7.98942i	−0.826557	+	0.434567i
$339$		−	1.30701i		−	0.0709868i
$340$	11.6891	+	5.16877i	0.633933	+	0.280316i
$341$			1.76748i			0.0957144i
$342$	7.47785	+	14.2231i	0.404356	+	0.769095i
$343$		−	4.39189i		−	0.237140i
$344$	25.0304	+	2.98460i	1.34955	+	0.160919i
$345$		−	7.57191i		−	0.407658i
$346$	−24.1185	+	12.6804i	−1.29662	+	0.681704i
$347$	13.6945			0.735161			0.367580	−	0.929992i	$-0.380186\pi$
$347$	13.6945			0.735161			0.367580	+	0.929992i	$0.380186\pi$
$348$	−3.09536	+	4.49818i	−0.165928	+	0.241128i
$349$			16.1885i			0.866549i	0.901262	+	0.433274i	$0.142642\pi$
$349$			16.1885i			0.866549i	−0.901262	+	0.433274i	$0.857358\pi$
$350$	−6.10962	−	11.6207i	−0.326573	−	0.621150i
$351$		−	4.36250i		−	0.232853i
$352$	22.2885	+	19.6037i	1.18798	+	1.04488i
$353$	13.0954			0.696995			0.348498	−	0.937310i	$-0.386692\pi$
$353$	13.0954			0.696995			0.348498	+	0.937310i	$0.386692\pi$
$354$	−2.96461	−	5.63876i	−0.157567	−	0.299696i
$355$		−	7.02071i		−	0.372621i
$356$	−0.0538066	+	0.0781919i	−0.00285174	+	0.00414416i
$357$	13.1653	−	2.48258i	0.696780	−	0.131392i
$358$	12.1153	+	23.0436i	0.640313	+	1.21789i
$359$	−10.0206			−0.528866			−0.264433	−	0.964404i	$-0.585185\pi$
$359$	−10.0206			−0.528866			−0.264433	+	0.964404i	$0.585185\pi$
$360$	1.12803	−	9.46026i	0.0594526	−	0.498599i
$361$	−8.33492			−0.438680
$362$	−1.25180	+	0.658138i	−0.0657929	+	0.0345910i
$363$	15.0333			0.789042
$364$	3.75774	−	5.46077i	0.196959	−	0.286222i
$365$		−	15.1736i		−	0.794222i
$366$	−10.5965	+	5.57119i	−0.553890	+	0.291211i
$367$		−	9.28351i		−	0.484595i	−0.970202	−	0.242298i	$-0.922099\pi$
$367$		−	9.28351i		−	0.484595i	0.970202	−	0.242298i	$-0.0779010\pi$
$368$	−20.0735	+	7.67880i	−1.04640	+	0.400285i
$369$		−	10.9450i		−	0.569775i
$370$	14.5351	−	7.64189i	0.755642	−	0.397283i
$371$	41.2569			2.14195
$372$	0.504605	+	0.347236i	0.0261625	+	0.0180033i
$373$			12.9391i			0.669963i	0.942225	+	0.334982i	$0.108730\pi$
$373$			12.9391i			0.669963i	−0.942225	+	0.334982i	$0.891270\pi$
$374$	−19.0101	−	23.9743i	−0.982991	−	1.23968i
$375$	−10.7071			−0.552914
$376$	1.65344	−	13.8666i	0.0852698	−	0.715115i
$377$		−	2.78482i		−	0.143426i
$378$	−11.0627	−	21.0415i	−0.569003	−	1.08226i
$379$	−9.29312			−0.477356			−0.238678	−	0.971099i	$-0.576714\pi$
$379$	−9.29312			−0.477356			−0.238678	+	0.971099i	$0.576714\pi$
$380$	13.3511	+	9.18737i	0.684898	+	0.471302i
$381$	6.62877			0.339602
$382$	−9.29209	+	4.88537i	−0.475425	+	0.249957i
$383$	−3.41670			−0.174585			−0.0872925	−	0.996183i	$-0.527821\pi$
$383$	−3.41670			−0.174585			−0.0872925	+	0.996183i	$0.527821\pi$
$384$	9.97550	−	2.51193i	0.509060	−	0.128186i
$385$		−	29.0640i		−	1.48124i
$386$	14.7405	+	28.0368i	0.750272	+	1.42703i
$387$			19.3688i			0.984572i
$388$	−15.7195	−	10.8171i	−0.798036	−	0.549156i
$389$			4.26419i			0.216203i	0.994140	+	0.108101i	$0.0344771\pi$
$389$			4.26419i			0.216203i	−0.994140	+	0.108101i	$0.965523\pi$
$390$	−0.860161	−	1.63605i	−0.0435560	−	0.0828445i
$391$	21.7698	−	4.10514i	1.10095	−	0.207606i
$392$	1.93265	−	16.2081i	0.0976134	−	0.818635i
$393$	7.45208			0.375908
$394$	35.0421	−	18.4236i	1.76540	−	0.928167i
$395$			12.0375i			0.605673i
$396$	−12.9292	+	18.7888i	−0.649719	+	0.944174i
$397$	24.0653			1.20780			0.603902	−	0.797059i	$-0.293612\pi$
$397$	24.0653			1.20780			0.603902	+	0.797059i	$0.293612\pi$
$398$	7.29381	+	13.8730i	0.365605	+	0.695391i
$399$	16.9884			0.850482
$400$	3.71257	+	9.70518i	0.185629	+	0.485259i
$401$			4.97938i			0.248658i	0.992241	+	0.124329i	$0.0396779\pi$
$401$			4.97938i			0.248658i	−0.992241	+	0.124329i	$0.960322\pi$
$402$	0.760167	+	1.44586i	0.0379137	+	0.0721127i
$403$	−0.312400			−0.0155617
$404$	16.7236	+	11.5081i	0.832029	+	0.572548i
$405$	3.47643			0.172745
$406$	−7.06192	−	13.4319i	−0.350477	−	0.666616i
$407$	−39.3119			−1.94862
$408$	−10.5792	+	0.717338i	−0.523748	+	0.0355135i
$409$	24.3746			1.20525			0.602623	−	0.798026i	$-0.294122\pi$
$409$	24.3746			1.20525			0.602623	+	0.798026i	$0.294122\pi$
$410$	−5.13702	−	9.77074i	−0.253699	−	0.482542i
$411$	1.92501			0.0949537
$412$	−17.6370	+	25.6302i	−0.868912	+	1.26271i
$413$	17.7051			0.871211
$414$	−7.68485	−	14.6168i	−0.377690	−	0.718376i
$415$			10.5537i			0.518063i
$416$	−3.46493	+	3.93947i	−0.169882	+	0.193148i
$417$	3.45014			0.168954
$418$	−18.0549	−	34.3408i	−0.883093	−	1.67966i
$419$	21.8983			1.06980			0.534902	−	0.844914i	$-0.320349\pi$
$419$	21.8983			1.06980			0.534902	+	0.844914i	$0.320349\pi$
$420$	−8.29758	−	5.70985i	−0.404880	−	0.278612i
$421$			16.6489i			0.811419i	0.914002	+	0.405710i	$0.132976\pi$
$421$			16.6489i			0.811419i	−0.914002	+	0.405710i	$0.867024\pi$
$422$	7.08011	−	3.72240i	0.344654	−	0.181204i
$423$	10.7302			0.521718
$424$	−32.4237	−	3.86618i	−1.57463	−	0.187758i
$425$	−1.98477	−	10.5253i	−0.0962754	−	0.510554i
$426$	2.71053	+	5.15550i	0.131326	+	0.249785i
$427$		−	33.2721i		−	1.61015i
$428$	−7.64519	+	11.1100i	−0.369544	+	0.537023i
$429$			4.42489i			0.213636i
$430$	9.09071	+	17.2908i	0.438393	+	0.833835i
$431$			2.97947i			0.143516i	0.997422	+	0.0717579i	$0.0228609\pi$
$431$			2.97947i			0.143516i	−0.997422	+	0.0717579i	$0.977139\pi$
$432$	6.72235	+	17.5732i	0.323429	+	0.845489i
$433$	−13.1176			−0.630391			−0.315196	−	0.949027i	$-0.602070\pi$
$433$	−13.1176			−0.630391			−0.315196	+	0.949027i	$0.602070\pi$
$434$	−1.50679	+	0.792203i	−0.0723282	+	0.0380270i
$435$	−4.23150			−0.202885
$436$	10.1411	−	14.7371i	0.485672	−	0.705780i
$437$	28.0916			1.34380
$438$	5.85817	+	11.1424i	0.279914	+	0.532404i
$439$			20.2618i			0.967045i	0.875332	+	0.483522i	$0.160643\pi$
$439$			20.2618i			0.967045i	−0.875332	+	0.483522i	$0.839357\pi$
$440$	−2.72358	+	22.8413i	−0.129842	+	1.08892i
$441$	12.5421			0.597242
$442$	4.23742	−	3.36002i	0.201554	−	0.159820i
$443$		−	13.2821i		−	0.631049i	−0.948917	−	0.315525i	$-0.897819\pi$
$443$		−	13.2821i		−	0.631049i	0.948917	−	0.315525i	$-0.102181\pi$
$444$	−7.72314	+	11.2233i	−0.366524	+	0.532634i
$445$	−0.0735562			−0.00348690
$446$	25.1807	−	13.2389i	1.19234	−	0.626880i
$447$		−	9.50754i		−	0.449691i
$448$	−6.72235	+	27.7877i	−0.317601	+	1.31285i
$449$		−	6.41685i		−	0.302830i	−0.988470	−	0.151415i	$-0.951617\pi$
$449$		−	6.41685i		−	0.302830i	0.988470	−	0.151415i	$-0.0483829\pi$
$450$	−7.06696	+	3.71550i	−0.333140	+	0.175150i
$451$			26.4262i			1.24436i
$452$	−2.36837	−	1.62975i	−0.111399	−	0.0766572i
$453$	4.40888			0.207147
$454$	−0.626324	+	0.329293i	−0.0293948	+	0.0154545i
$455$	5.13702			0.240827
$456$	−13.3511	−	1.59198i	−0.625224	−	0.0745512i
$457$	−19.4642			−0.910495			−0.455247	−	0.890365i	$-0.650449\pi$
$457$	−19.4642			−0.910495			−0.455247	+	0.890365i	$0.650449\pi$
$458$	17.0266	+	32.3851i	0.795602	+	1.51325i
$459$	−3.59382	−	19.0582i	−0.167745	−	0.889562i
$460$	−13.7207	−	9.44170i	−0.639732	−	0.440221i
$461$			1.70934i			0.0796118i	0.999207	+	0.0398059i	$0.0126740\pi$
$461$			1.70934i			0.0796118i	−0.999207	+	0.0398059i	$0.987326\pi$
$462$	11.2209	+	21.3425i	0.522044	+	0.992941i
$463$	28.9588			1.34583			0.672914	−	0.739721i	$-0.265042\pi$
$463$	28.9588			1.34583			0.672914	+	0.739721i	$0.265042\pi$
$464$	4.29124	+	11.2179i	0.199216	+	0.520778i
$465$			0.474688i			0.0220132i
$466$	−12.5361	−	23.8439i	−0.580722	−	1.10455i
$467$			11.1144i			0.514313i	0.966370	+	0.257156i	$0.0827855\pi$
$467$			11.1144i			0.514313i	−0.966370	+	0.257156i	$0.917214\pi$
$468$	−3.32090	−	2.28523i	−0.153509	−	0.105635i
$469$	−4.53984			−0.209630
$470$	9.57893	−	5.03617i	0.441843	−	0.232301i
$471$			10.9951i			0.506628i
$472$	−13.9144	−	1.65914i	−0.640463	−	0.0763683i
$473$		−	46.7650i		−	2.15026i
$474$	−4.64740	−	8.83947i	−0.213462	−	0.406011i
$475$		−	13.5818i		−	0.623177i
$476$	11.9177	−	26.9518i	0.546246	−	1.23533i
$477$		−	25.0899i		−	1.14879i
$478$	28.6106	−	15.0422i	1.30862	−	0.688013i
$479$		−	0.818228i		−	0.0373858i	−0.999825	−	0.0186929i	$-0.994050\pi$
$479$		−	0.818228i		−	0.0373858i	0.999825	−	0.0186929i	$-0.00595048\pi$
$480$	5.98598	+	5.26493i	0.273221	+	0.240310i
$481$		−	6.94833i		−	0.316817i
$482$	−8.64736	−	16.4475i	−0.393876	−	0.749163i
$483$	−17.4586			−0.794396
$484$	18.7455	−	27.2411i	0.852070	−	1.23823i
$485$		−	14.7875i		−	0.671468i
$486$	−20.2167	+	10.6290i	−0.917047	+	0.482143i
$487$			23.0968i			1.04661i	0.852144	+	0.523307i	$0.175302\pi$
$487$			23.0968i			1.04661i	−0.852144	+	0.523307i	$0.824698\pi$
$488$	−3.11792	+	26.1484i	−0.141142	+	1.18368i
$489$	9.08713			0.410934
$490$	11.1965	−	5.88660i	0.505804	−	0.265929i
$491$			38.5262i			1.73866i	0.494231	+	0.869330i	$0.335450\pi$
$491$			38.5262i			1.73866i	−0.494231	+	0.869330i	$0.664550\pi$
$492$	7.54451	+	5.19164i	0.340133	+	0.234057i
$493$	−2.29413	−	12.1659i	−0.103322	−	0.547925i
$494$	6.06970	−	3.19118i	0.273089	−	0.143578i
$495$	−17.6749			−0.794428
$496$	1.25842	−	0.481390i	0.0565047	−	0.0216150i
$497$	−16.1877			−0.726119
$498$	−4.07455	−	7.74990i	−0.182585	−	0.347281i
$499$	−43.4028			−1.94298			−0.971489	−	0.237086i	$-0.923808\pi$
$499$	−43.4028			−1.94298			−0.971489	+	0.237086i	$0.923808\pi$
$500$	−13.3511	+	19.4019i	−0.597080	+	0.867680i
$501$		−	12.7936i		−	0.571575i
$502$	5.07036	+	9.64395i	0.226301	+	0.430431i
$503$			25.5471i			1.13909i	0.821961	+	0.569544i	$0.192880\pi$
$503$			25.5471i			1.13909i	−0.821961	+	0.569544i	$0.807120\pi$
$504$	−21.8126	−	2.60092i	−0.971612	−	0.115854i
$505$			15.7321i			0.700069i
$506$	18.5547	+	35.2915i	0.824856	+	1.56890i
$507$	11.0381			0.490217
$508$	8.26566	−	12.0117i	0.366729	−	0.532933i
$509$			21.9720i			0.973892i	0.873432	+	0.486946i	$0.161889\pi$
$509$			21.9720i			0.973892i	−0.873432	+	0.486946i	$0.838111\pi$
$510$	−5.10551	−	6.43872i	−0.226076	−	0.285111i
$511$	−34.9859			−1.54769
$512$	7.88706	−	21.2084i	0.348562	−	0.937286i
$513$		−	24.5926i		−	1.08579i
$514$	−35.8432	+	18.8448i	−1.58098	+	0.831208i
$515$	−24.1106			−1.06244
$516$	−13.3511	−	9.18737i	−0.587750	−	0.404451i
$517$	−25.9074			−1.13941
$518$	−17.6200	−	33.5137i	−0.774178	−	1.47251i
$519$	17.5191			0.769001
$520$	−4.03717	−	0.481390i	−0.177042	−	0.0211103i
$521$			25.4653i			1.11565i	0.829958	+	0.557827i	$0.188365\pi$
$521$			25.4653i			1.11565i	−0.829958	+	0.557827i	$0.811635\pi$
$522$	−8.16848	+	4.29462i	−0.357524	+	0.187970i
$523$			7.95248i			0.347738i	0.984769	+	0.173869i	$0.0556269\pi$
$523$			7.95248i			0.347738i	−0.984769	+	0.173869i	$0.944373\pi$
$524$	9.29227	−	13.5036i	0.405935	−	0.589906i
$525$			8.44096i			0.368394i
$526$	−19.4724	+	10.2377i	−0.849036	+	0.446385i
$527$	−1.36477	+	0.257354i	−0.0594501	+	0.0112105i
$528$	−6.81850	−	17.8245i	−0.296737	−	0.775712i
$529$	−5.86926			−0.255185
$530$	−11.7759	−	22.3980i	−0.511512	−	0.972908i
$531$		−	10.7672i		−	0.467255i
$532$	21.1834	−	30.7838i	0.918418	−	1.33465i
$533$	−4.67079			−0.202315
$534$	0.0540143	−	0.0283983i	0.00233743	−	0.00122892i
$535$	−10.4514			−0.451851
$536$	3.56785	+	0.425428i	0.154108	+	0.0183757i
$537$		−	16.7383i		−	0.722310i
$538$	27.7395	−	14.5842i	1.19593	−	0.628769i
$539$	−30.2822			−1.30435
$540$	−8.26566	+	12.0117i	−0.355697	+	0.516901i
$541$	−29.1550			−1.25347			−0.626736	−	0.779231i	$-0.715610\pi$
$541$	−29.1550			−1.25347			−0.626736	+	0.779231i	$0.715610\pi$
$542$	−22.0689	+	11.6029i	−0.947941	+	0.498386i
$543$	0.909273			0.0390207
$544$	−11.8917	+	20.0646i	−0.509854	+	0.860261i
$545$	13.8634			0.593844
$546$	−3.77225	+	1.98328i	−0.161438	+	0.0848767i
$547$	11.7061			0.500519			0.250259	−	0.968179i	$-0.419484\pi$
$547$	11.7061			0.500519			0.250259	+	0.968179i	$0.419484\pi$
$548$	2.40036	−	3.48822i	0.102538	−	0.149009i
$549$	−20.2340			−0.863566
$550$	17.0628	−	8.97088i	0.727561	−	0.382519i
$551$		−	15.6988i		−	0.668791i
$552$	13.7207	+	1.63605i	0.583992	+	0.0696348i
$553$	27.7550			1.18026
$554$	−6.64387	+	3.49305i	−0.282271	+	0.148406i
$555$	−10.5579			−0.448159
$556$	4.30210	−	6.25184i	0.182450	−	0.265137i
$557$			16.7136i			0.708177i	0.935212	+	0.354089i	$0.115209\pi$
$557$			16.7136i			0.708177i	−0.935212	+	0.354089i	$0.884791\pi$
$558$	0.481769	+	0.916336i	0.0203949	+	0.0387916i
$559$	8.26566			0.349600
$560$	−20.6931	+	7.91584i	−0.874444	+	0.334505i
$561$	3.64522	+	19.3308i	0.153901	+	0.816147i
$562$	22.9132	−	12.0467i	0.966535	−	0.508161i
$563$		−	14.8630i		−	0.626401i	−0.949687	−	0.313200i	$-0.898599\pi$
$563$		−	14.8630i		−	0.626401i	0.949687	−	0.313200i	$-0.101401\pi$
$564$	−5.08972	+	7.39640i	−0.214316	+	0.311445i
$565$		−	2.22795i		−	0.0937307i
$566$	8.30744	−	4.36768i	0.349188	−	0.183587i
$567$		−	8.01564i		−	0.336625i
$568$	12.7219	+	1.51695i	0.533800	+	0.0636499i
$569$	2.18194			0.0914718			0.0457359	−	0.998954i	$-0.485437\pi$
$569$	2.18194			0.0914718			0.0457359	+	0.998954i	$0.485437\pi$
$570$	−4.84896	−	9.22285i	−0.203101	−	0.386302i
$571$	−28.2349			−1.18159			−0.590797	−	0.806820i	$-0.701187\pi$
$571$	−28.2349			−1.18159			−0.590797	+	0.806820i	$0.701187\pi$
$572$	8.01815	+	5.51756i	0.335256	+	0.230701i
$573$	6.74955			0.281966
$574$	−22.5285	+	11.8445i	−0.940321	+	0.494379i
$575$			13.9578i			0.582080i
$576$	16.8988	+	4.08812i	0.704115	+	0.170338i
$577$	8.22940			0.342594			0.171297	−	0.985219i	$-0.445204\pi$
$577$	8.22940			0.342594			0.171297	+	0.985219i	$0.445204\pi$
$578$	15.7438	−	18.1695i	0.654857	−	0.755753i
$579$		−	20.3652i		−	0.846350i
$580$	−5.27642	+	7.66771i	−0.219091	+	0.318385i
$581$	24.3339			1.00954
$582$	5.70912	+	10.8589i	0.236651	+	0.450116i
$583$			60.5783i			2.50890i
$584$	27.4954	+	3.27853i	1.13777	+	0.135666i
$585$		−	3.12402i		−	0.129162i
$586$	−3.82551	−	7.27621i	−0.158030	−	0.300577i
$587$		−	12.8960i		−	0.532275i	−0.963935	−	0.266137i	$-0.914253\pi$
$587$		−	12.8960i		−	0.532275i	0.963935	−	0.266137i	$-0.0857475\pi$
$588$	−5.94918	+	8.64538i	−0.245340	+	0.356530i
$589$	−1.76108			−0.0725642
$590$	−5.05354	−	9.61196i	−0.208051	−	0.395718i
$591$	−25.4537			−1.04703
$592$	10.7070	+	27.9895i	0.440053	+	1.15036i
$593$	−31.3915			−1.28909			−0.644547	−	0.764565i	$-0.722954\pi$
$593$	−31.3915			−1.28909			−0.644547	+	0.764565i	$0.722954\pi$
$594$	30.8956	−	16.2436i	1.26766	−	0.666481i
$595$	22.4418	−	4.23187i	0.920026	−	0.173490i
$596$	−17.2282	−	11.8553i	−0.705694	−	0.485612i
$597$		−	10.0770i		−	0.412424i
$598$	−6.23772	+	3.27952i	−0.255080	+	0.134109i
$599$	−8.26566			−0.337726			−0.168863	−	0.985640i	$-0.554009\pi$
$599$	−8.26566			−0.337726			−0.168863	+	0.985640i	$0.554009\pi$
$600$	0.791001	−	6.63373i	0.0322925	−	0.270821i
$601$			12.4158i			0.506451i	0.967407	+	0.253226i	$0.0814915\pi$
$601$			12.4158i			0.506451i	−0.967407	+	0.253226i	$0.918509\pi$
$602$	39.8675	−	20.9606i	1.62488	−	0.854289i
$603$			2.76085i			0.112430i
$604$	5.49760	−	7.98913i	0.223694	−	0.325073i
$605$	25.6261			1.04185
$606$	−6.07380	−	11.5525i	−0.246731	−	0.469289i
$607$		−	16.2945i		−	0.661375i	−0.943740	−	0.330688i	$-0.892719\pi$
$607$		−	16.2945i		−	0.661375i	0.943740	−	0.330688i	$-0.107281\pi$
$608$	−19.5328	+	22.2079i	−0.792158	+	0.900648i
$609$			9.75663i			0.395359i
$610$	−18.0631	+	9.49679i	−0.731355	+	0.384514i
$611$		−	4.57910i		−	0.185251i
$612$	−16.3904	−	7.24760i	−0.662543	−	0.292967i
$613$			24.6446i			0.995385i	0.867354	+	0.497692i	$0.165819\pi$
$613$			24.6446i			0.995385i	−0.867354	+	0.497692i	$0.834181\pi$
$614$	10.9598	+	20.8458i	0.442300	+	0.841266i
$615$			7.09722i			0.286188i
$616$	52.6655	+	6.27979i	2.12195	+	0.253020i
$617$		−	5.94216i		−	0.239222i	−0.992821	−	0.119611i	$-0.961835\pi$
$617$		−	5.94216i		−	0.239222i	0.992821	−	0.119611i	$-0.0381648\pi$
$618$	17.7051	−	9.30856i	0.712204	−	0.374445i
$619$	24.5042			0.984906			0.492453	−	0.870339i	$-0.336100\pi$
$619$	24.5042			0.984906			0.492453	+	0.870339i	$0.336100\pi$
$620$	0.860161	+	0.591907i	0.0345449	+	0.0237715i
$621$			25.2734i			1.01419i
$622$	22.1459	+	42.1221i	0.887970	+	1.68894i
$623$			0.169599i			0.00679486i
$624$	3.15046	−	1.20516i	0.126119	−	0.0482451i
$625$	−5.26284			−0.210514
$626$	16.0363	+	30.5014i	0.640939	+	1.21908i
$627$			24.9443i			0.996181i
$628$	19.9237	+	13.7102i	0.795043	+	0.547097i
$629$	−5.72402	−	30.3548i	−0.228232	−	1.21033i
$630$	−7.92208	−	15.0680i	−0.315623	−	0.600323i
$631$	−15.5215			−0.617901			−0.308950	−	0.951078i	$-0.599978\pi$
$631$	−15.5215			−0.617901			−0.308950	+	0.951078i	$0.599978\pi$
$632$	−21.8126	−	2.60092i	−0.867660	−	0.103459i
$633$	−5.14281			−0.204409
$634$	1.46635	−	0.770941i	0.0582362	−	0.0306180i
$635$	11.2996			0.448410
$636$	17.2947	+	11.9011i	0.685780	+	0.471909i
$637$		−	5.35234i		−	0.212068i
$638$	19.7224	−	10.3691i	0.780816	−	0.410518i
$639$			9.84438i			0.389438i
$640$	17.0045	−	4.28189i	0.672161	−	0.169257i
$641$		−	46.6749i		−	1.84355i	−0.387728	−	0.921774i	$-0.626740\pi$
$641$		−	46.6749i		−	1.84355i	0.387728	−	0.921774i	$-0.373260\pi$
$642$	7.67471	−	4.03502i	0.302897	−	0.159250i
$643$	−23.5901			−0.930301			−0.465151	−	0.885232i	$-0.654000\pi$
$643$	−23.5901			−0.930301			−0.465151	+	0.885232i	$0.654000\pi$
$644$	−21.7698	+	31.6360i	−0.857851	+	1.24663i
$645$		−	12.5596i		−	0.494533i
$646$	23.8875	−	18.9413i	0.939841	−	0.745237i
$647$	27.7054			1.08921			0.544605	−	0.838692i	$-0.316679\pi$
$647$	27.7054			1.08921			0.544605	+	0.838692i	$0.316679\pi$
$648$	−0.751145	+	6.29948i	−0.0295078	+	0.247467i
$649$			25.9967i			1.02046i
$650$	1.58559	+	3.01583i	0.0621920	+	0.118291i
$651$	1.09449			0.0428966
$652$	11.3311	−	16.4664i	0.443759	−	0.644873i
$653$	−8.07066			−0.315829			−0.157915	−	0.987453i	$-0.550477\pi$
$653$	−8.07066			−0.315829			−0.157915	+	0.987453i	$0.550477\pi$
$654$	−10.1803	+	5.35234i	−0.398081	+	0.209293i
$655$	12.7030			0.496347
$656$	18.8150	−	7.19741i	0.734604	−	0.281012i
$657$			21.2763i			0.830067i
$658$	−11.6120	−	22.0862i	−0.452682	−	0.861011i
$659$			2.23013i			0.0868736i	0.999056	+	0.0434368i	$0.0138307\pi$
$659$			2.23013i			0.0868736i	−0.999056	+	0.0434368i	$0.986169\pi$
$660$	8.38388	−	12.1835i	0.326342	−	0.474242i
$661$		−	19.7441i		−	0.767955i	−0.923343	−	0.383977i	$-0.874554\pi$
$661$		−	19.7441i		−	0.767955i	0.923343	−	0.383977i	$-0.125446\pi$
$662$	5.00513	+	9.51989i	0.194530	+	0.370001i
$663$	−3.41670	+	0.644288i	−0.132694	+	0.0250221i
$664$	−19.1239	−	2.28033i	−0.742153	−	0.0884938i
$665$	28.9588			1.12297
$666$	−20.3810	+	10.7154i	−0.789746	+	0.415213i
$667$			16.1334i			0.624686i
$668$	−23.1827	−	15.9528i	−0.896964	−	0.617232i
$669$	−18.2907			−0.707158
$670$	1.29580	+	2.46464i	0.0500611	+	0.0952174i
$671$	48.8540			1.88599
$672$	12.1394	−	13.8019i	0.468287	−	0.532422i
$673$		−	15.9244i		−	0.613840i	−0.951735	−	0.306920i	$-0.900702\pi$
$673$		−	15.9244i		−	0.613840i	0.951735	−	0.306920i	$-0.0992984\pi$
$674$	−16.7591	−	31.8762i	−0.645536	−	1.22782i
$675$	12.2192			0.470319
$676$	13.7638	−	20.0015i	0.529375	−	0.769290i
$677$	13.2557			0.509456			0.254728	−	0.967013i	$-0.418014\pi$
$677$	13.2557			0.509456			0.254728	+	0.967013i	$0.418014\pi$
$678$	0.860161	+	1.63605i	0.0330343	+	0.0628320i
$679$	−34.0958			−1.30848
$680$	−18.0336	+	1.22279i	−0.691556	+	0.0468920i
$681$	0.454946			0.0174336
$682$	−1.16321	−	2.21245i	−0.0445415	−	0.0847190i
$683$	0.200704			0.00767971			0.00383985	−	0.999993i	$-0.498778\pi$
$683$	0.200704			0.00767971			0.00383985	+	0.999993i	$0.498778\pi$
$684$	−18.7208	−	12.8824i	−0.715809	−	0.492573i
$685$	3.28142			0.125376
$686$	2.89037	+	5.49755i	0.110355	+	0.209898i
$687$		−	23.5237i		−	0.897486i
$688$	−33.2960	+	12.7369i	−1.26940	+	0.485589i
$689$	−10.7071			−0.407909
$690$	4.98319	+	9.47816i	0.189707	+	0.360827i
$691$	−34.6202			−1.31702			−0.658508	−	0.752574i	$-0.728812\pi$
$691$	−34.6202			−1.31702			−0.658508	+	0.752574i	$0.728812\pi$
$692$	21.8452	−	31.7455i	0.830429	−	1.20678i
$693$			40.7532i			1.54809i
$694$	−17.1422	+	9.01258i	−0.650707	+	0.342113i
$695$	5.88119			0.223086
$696$	0.914293	−	7.66771i	0.0346562	−	0.290644i
$697$	−20.4051	+	3.84779i	−0.772897	+	0.145745i
$698$	−10.6539	−	20.2639i	−0.403255	−	0.767002i
$699$			17.3196i			0.655088i
$700$	15.2955	+	10.5253i	0.578114	+	0.397820i
$701$		−	46.3472i		−	1.75051i	−0.483662	−	0.875255i	$-0.660694\pi$
$701$		−	46.3472i		−	1.75051i	0.483662	−	0.875255i	$-0.339306\pi$
$702$	2.87103	+	5.46077i	0.108360	+	0.206103i
$703$		−	39.1696i		−	1.47731i
$704$	−40.8012	−	9.87055i	−1.53775	−	0.372010i
$705$	−6.95790			−0.262050
$706$	−16.3921	+	8.61826i	−0.616926	+	0.324352i
$707$	36.2737			1.36421
$708$	7.42191	+	5.10727i	0.278932	+	0.191943i
$709$	14.2920			0.536749			0.268375	−	0.963315i	$-0.413514\pi$
$709$	14.2920			0.536749			0.268375	+	0.963315i	$0.413514\pi$
$710$	4.62044	+	8.78819i	0.173402	+	0.329815i
$711$		−	16.8789i		−	0.633008i
$712$	0.0158931	−	0.133288i	0.000595621	−	0.00499517i
$713$	1.80983			0.0677788
$714$	−14.8458	+	11.7718i	−0.555591	+	0.440550i
$715$			7.54278i			0.282084i
$716$	−30.3307	−	20.8716i	−1.13351	−	0.780007i
$717$	−20.7820			−0.776118
$718$	12.5433	−	6.59471i	0.468112	−	0.246112i
$719$			10.7210i			0.399825i	0.979814	+	0.199912i	$0.0640658\pi$
$719$			10.7210i			0.399825i	−0.979814	+	0.199912i	$0.935934\pi$
$720$	4.81393	+	12.5843i	0.179404	+	0.468988i
$721$			55.5922i			2.07036i
$722$	10.4333	−	5.48534i	0.388286	−	0.204143i
$723$			11.9470i			0.444316i
$724$	1.13381	−	1.64765i	0.0421376	−	0.0612345i
$725$	7.80021			0.289692
$726$	−18.8179	+	9.89363i	−0.698399	+	0.367187i
$727$	24.3671			0.903727			0.451864	−	0.892087i	$-0.350759\pi$
$727$	24.3671			0.903727			0.451864	+	0.892087i	$0.350759\pi$
$728$	−1.10995	+	9.30856i	−0.0411373	+	0.344998i
$729$	7.95596			0.294665
$730$	9.98598	+	18.9936i	0.369598	+	0.702984i
$731$	36.1098	−	6.80923i	1.33557	−	0.251849i
$732$	9.59776	−	13.9475i	0.354743	−	0.515515i
$733$		−	16.8389i		−	0.621960i	−0.950417	−	0.310980i	$-0.899343\pi$
$733$		−	16.8389i		−	0.621960i	0.950417	−	0.310980i	$-0.100657\pi$
$734$	6.10962	+	11.6207i	0.225510	+	0.428926i
$735$	−8.13283			−0.299984
$736$	20.0735	−	22.8226i	0.739918	−	0.841253i
$737$		−	6.66593i		−	0.245543i
$738$	7.20308	+	13.7004i	0.265149	+	0.504320i
$739$		−	8.63831i		−	0.317765i	−0.987297	−	0.158883i	$-0.949211\pi$
$739$		−	8.63831i		−	0.317765i	0.987297	−	0.158883i	$-0.0507892\pi$
$740$	−13.1651	+	19.1315i	−0.483957	+	0.703289i
$741$	−4.40888			−0.161964
$742$	−51.6434	+	27.1518i	−1.89589	+	0.996774i
$743$			3.40406i			0.124883i	0.998049	+	0.0624414i	$0.0198887\pi$
$743$			3.40406i			0.124883i	−0.998049	+	0.0624414i	$0.980111\pi$
$744$	−0.860161	−	0.102565i	−0.0315350	−	0.00376021i
$745$		−	16.2068i		−	0.593771i
$746$	−8.51545	−	16.1966i	−0.311773	−	0.593000i
$747$		−	14.7984i		−	0.541444i
$748$	39.5738	+	17.4990i	1.44696	+	0.639826i
$749$			24.0978i			0.880514i
$750$	13.4027	−	7.04653i	0.489397	−	0.257303i
$751$		−	37.4748i		−	1.36748i	−0.729728	−	0.683738i	$-0.760353\pi$
$751$		−	37.4748i		−	1.36748i	0.729728	−	0.683738i	$-0.239647\pi$
$752$	7.05612	+	18.4457i	0.257310	+	0.672645i
$753$		−	7.00513i		−	0.255281i
$754$	1.83273	+	3.48590i	0.0667442	+	0.126949i
$755$	7.51548			0.273516
$756$	27.6955	+	19.0582i	1.00728	+	0.693141i
$757$			39.6737i			1.44197i	0.692953	+	0.720983i	$0.256309\pi$
$757$			39.6737i			1.44197i	−0.692953	+	0.720983i	$0.743691\pi$
$758$	11.6327	−	6.11595i	0.422518	−	0.222141i
$759$		−	25.6349i		−	0.930486i
$760$	−22.7586	−	2.71372i	−0.825543	−	0.0984371i
$761$	−8.58998			−0.311386			−0.155693	−	0.987805i	$-0.549761\pi$
$761$	−8.58998			−0.311386			−0.155693	+	0.987805i	$0.549761\pi$
$762$	−8.29758	+	4.36250i	−0.300590	+	0.158037i
$763$		−	31.9650i		−	1.15721i
$764$	8.41626	−	12.2305i	0.304490	−	0.442485i
$765$	−2.57356	−	13.6477i	−0.0930472	−	0.493435i
$766$	4.27686	−	2.24858i	0.154529	−	0.0812446i
$767$	−4.59489			−0.165912
$768$	−10.8337	+	9.70934i	−0.390928	+	0.350356i
$769$	−19.4661			−0.701965			−0.350983	−	0.936382i	$-0.614152\pi$
$769$	−19.4661			−0.701965			−0.350983	+	0.936382i	$0.614152\pi$
$770$	19.1274	+	36.3809i	0.689305	+	1.31108i
$771$	26.0357			0.937651
$772$	−36.9029	−	25.3942i	−1.32816	−	0.913956i
$773$			36.1388i			1.29982i	0.760011	+	0.649911i	$0.225194\pi$
$773$			36.1388i			1.29982i	−0.760011	+	0.649911i	$0.774806\pi$
$774$	−12.7469	−	24.2450i	−0.458179	−	0.871467i
$775$		−	0.875024i		−	0.0314318i
$776$	26.7958	+	3.19511i	0.961914	+	0.114698i
$777$			24.3435i			0.873318i
$778$	−2.80633	−	5.33771i	−0.100612	−	0.191366i
$779$	−26.3305			−0.943389
$780$	2.15342	+	1.48184i	0.0771047	+	0.0530584i
$781$		−	23.7688i		−	0.850513i
$782$	−24.5488	+	19.4657i	−0.877862	+	0.696092i
$783$	14.1238			0.504745
$784$	8.24764	+	21.5605i	0.294559	+	0.770018i
$785$			18.7425i			0.668950i
$786$	−9.32816	+	4.90433i	−0.332724	+	0.174932i
$787$	49.4730			1.76352			0.881762	−	0.471695i	$-0.156358\pi$
$787$	49.4730			1.76352			0.881762	+	0.471695i	$0.156358\pi$
$788$	−31.7392	+	46.1235i	−1.13066	+	1.64308i
$789$	14.1443			0.503549
$790$	−7.92208	−	15.0680i	−0.281855	−	0.536095i
$791$	−5.13702			−0.182651
$792$	3.81898	−	32.0279i	0.135702	−	1.13806i
$793$			8.63488i			0.306634i
$794$	−30.1238	+	15.8378i	−1.06905	+	0.562061i
$795$			16.2694i			0.577015i
$796$	−18.2601	−	12.5654i	−0.647211	−	0.445368i
$797$			34.0939i			1.20767i	0.797110	+	0.603834i	$0.206361\pi$
$797$			34.0939i			1.20767i	−0.797110	+	0.603834i	$0.793639\pi$
$798$	−21.2652	+	11.1803i	−0.752781	+	0.395779i
$799$	−3.77225	−	20.0045i	−0.133453	−	0.707708i
$800$	−11.0344	−	9.70518i	−0.390123	−	0.343130i
$801$	0.103140			0.00364427
$802$	−3.27701	−	6.23295i	−0.115715	−	0.220093i
$803$		−	51.3705i		−	1.81283i
$804$	−1.90308	−	1.30958i	−0.0671165	−	0.0461852i
$805$	−29.7604			−1.04892
$806$	0.391047	−	0.205595i	0.0137741	−	0.00724179i
$807$	−20.1493			−0.709288
$808$	−28.5074	−	3.39920i	−1.00289	−	0.119584i
$809$		−	13.1063i		−	0.460791i	−0.973097	−	0.230396i	$-0.925998\pi$
$809$		−	13.1063i		−	0.460791i	0.973097	−	0.230396i	$-0.0740020\pi$
$810$	−4.35163	+	2.28789i	−0.152901	+	0.0803883i
$811$	12.0692			0.423806			0.211903	−	0.977291i	$-0.432034\pi$
$811$	12.0692			0.423806			0.211903	+	0.977291i	$0.432034\pi$
$812$	17.6795	+	12.1659i	0.620430	+	0.426939i
$813$	16.0303			0.562208
$814$	49.2088	−	25.8718i	1.72477	−	0.906805i
$815$	15.4901			0.542596
$816$	12.7704	−	7.86027i	0.447055	−	0.275164i
$817$	46.5958			1.63018
$818$	−30.5110	+	16.0413i	−1.06679	+	0.560871i
$819$	−7.20308			−0.251696
$820$	12.8606	+	8.84979i	0.449110	+	0.309048i
$821$	−24.1733			−0.843655			−0.421828	−	0.906676i	$-0.638611\pi$
$821$	−24.1733			−0.843655			−0.421828	+	0.906676i	$0.638611\pi$
$822$	−2.40963	+	1.26688i	−0.0840456	+	0.0441875i
$823$			51.8322i			1.80676i	0.428846	+	0.903378i	$0.358920\pi$
$823$			51.8322i			1.80676i	−0.428846	+	0.903378i	$0.641080\pi$
$824$	5.20954	−	43.6898i	0.181483	−	1.52201i
$825$	−12.3940			−0.431504
$826$	−22.1624	+	11.6520i	−0.771129	+	0.405425i
$827$	2.23524			0.0777271			0.0388635	−	0.999245i	$-0.487626\pi$
$827$	2.23524			0.0777271			0.0388635	+	0.999245i	$0.487626\pi$
$828$	19.2391	+	13.2391i	0.668604	+	0.460089i
$829$		−	46.3891i		−	1.61116i	−0.592488	−	0.805580i	$-0.701854\pi$
$829$		−	46.3891i		−	1.61116i	0.592488	−	0.805580i	$-0.298146\pi$
$830$	−6.94558	−	13.2107i	−0.241085	−	0.458549i
$831$	4.82595			0.167410
$832$	1.74461	−	7.21156i	0.0604834	−	0.250016i
$833$	−4.40925	−	23.3825i	−0.152771	−	0.810156i
$834$	−4.31872	+	2.27059i	−0.149545	+	0.0786241i
$835$		−	21.8083i		−	0.754706i
$836$	45.2005	+	31.1040i	1.56329	+	1.07575i
$837$		−	1.58441i		−	0.0547651i
$838$	−27.4113	+	14.4116i	−0.946907	+	0.497842i
$839$		−	12.7232i		−	0.439255i	−0.975584	−	0.219628i	$-0.929516\pi$
$839$		−	12.7232i		−	0.439255i	0.975584	−	0.219628i	$-0.0704843\pi$
$840$	14.1443	+	1.68655i	0.488023	+	0.0581915i
$841$	−19.9840			−0.689103
$842$	−10.9569	−	20.8403i	−0.377601	−	0.718206i
$843$	−16.6436			−0.573235
$844$	−6.41276	+	9.31906i	−0.220736	+	0.320775i
$845$	18.8157			0.647281
$846$	−13.4315	+	7.06168i	−0.461784	+	0.242786i
$847$		−	59.0864i		−	2.03023i
$848$	43.1308	−	16.4991i	1.48112	−	0.566580i
$849$	−6.03432			−0.207097
$850$	9.41133	+	11.8689i	0.322806	+	0.407100i
$851$			40.2539i			1.37989i
$852$	−6.78583	−	4.66957i	−0.232479	−	0.159977i
$853$	−0.583673			−0.0199846			−0.00999229	−	0.999950i	$-0.503181\pi$
$853$	−0.583673			−0.0199846			−0.00999229	+	0.999950i	$0.503181\pi$
$854$	21.8969	+	41.6484i	0.749295	+	1.42518i
$855$		−	17.6109i		−	0.602281i
$856$	2.25820	−	18.9384i	0.0771838	−	0.647302i
$857$			9.84674i			0.336358i	0.985756	+	0.168179i	$0.0537887\pi$
$857$			9.84674i			0.336358i	−0.985756	+	0.168179i	$0.946211\pi$
$858$	−2.91209	−	5.53887i	−0.0994172	−	0.189094i
$859$			43.5540i			1.48604i	0.669267	+	0.743022i	$0.266608\pi$
$859$			43.5540i			1.48604i	−0.669267	+	0.743022i	$0.733392\pi$
$860$	−22.7586	−	15.6610i	−0.776063	−	0.534036i
$861$	16.3641			0.557689
$862$	−1.96083	−	3.72955i	−0.0667863	−	0.127029i
$863$	−32.8325			−1.11763			−0.558816	−	0.829292i	$-0.688744\pi$
$863$	−32.8325			−1.11763			−0.558816	+	0.829292i	$0.688744\pi$
$864$	−19.9799	−	17.5732i	−0.679730	−	0.597851i
$865$	29.8634			1.01539
$866$	16.4200	−	8.63290i	0.557974	−	0.293358i
$867$	−14.3956	+	5.62934i	−0.488900	+	0.191182i
$868$	1.36477	−	1.98328i	0.0463232	−	0.0673170i
$869$			40.7532i			1.38246i
$870$	5.29680	−	2.78482i	0.179578	−	0.0944142i
$871$	1.17819			0.0399216
$872$	−2.99544	+	25.1213i	−0.101438	+	0.850713i
$873$			20.7350i			0.701772i
$874$	−35.1637	+	18.4875i	−1.18943	+	0.625350i
$875$			42.0830i			1.42267i
$876$	−14.6660	−	10.0922i	−0.495517	−	0.340982i
$877$	−18.9148			−0.638707			−0.319353	−	0.947636i	$-0.603466\pi$
$877$	−18.9148			−0.638707			−0.319353	+	0.947636i	$0.603466\pi$
$878$	−13.3346	−	25.3628i	−0.450022	−	0.855953i
$879$			5.28526i			0.178267i
$880$	−11.6230	−	30.3841i	−0.391810	−	1.02425i
$881$			37.2242i			1.25411i	0.778974	+	0.627057i	$0.215741\pi$
$881$			37.2242i			1.25411i	−0.778974	+	0.627057i	$0.784259\pi$
$882$	−15.6996	+	8.25414i	−0.528632	+	0.277931i
$883$			12.1646i			0.409372i	0.978828	+	0.204686i	$0.0656173\pi$
$883$			12.1646i			0.409372i	−0.978828	+	0.204686i	$0.934383\pi$
$884$	−3.09292	+	6.99463i	−0.104026	+	0.235255i
$885$			6.98189i			0.234694i
$886$	8.74113	+	16.6258i	0.293664	+	0.558556i
$887$			7.53425i			0.252975i	0.991968	+	0.126488i	$0.0403704\pi$
$887$			7.53425i			0.252975i	−0.991968	+	0.126488i	$0.959630\pi$
$888$	2.28123	−	19.1315i	0.0765530	−	0.642012i
$889$		−	26.0535i		−	0.873808i
$890$	0.0920742	−	0.0484085i	0.00308633	−	0.00162266i
$891$	11.7695			0.394294
$892$	−22.8073	+	33.1437i	−0.763645	+	1.10973i
$893$		−	25.8136i		−	0.863821i
$894$	6.25706	+	11.9011i	0.209268	+	0.398032i
$895$		−	28.5325i		−	0.953735i
$896$	−9.87281	−	39.2074i	−0.329827	−	1.30983i
$897$	4.53093			0.151283
$898$	4.22303	+	8.03230i	0.140924	+	0.268041i
$899$		−	1.01141i		−	0.0337325i
$900$	6.40086	−	9.30176i	0.213362	−	0.310059i
$901$	−46.7757	+	8.82051i	−1.55832	+	0.293854i
$902$	−17.3915	−	33.0790i	−0.579073	−	1.10141i
$903$	−28.9588			−0.963688
$904$	4.03717	+	0.481390i	0.134274	+	0.0160108i
$905$	1.54997			0.0515227
$906$	−5.51883	+	2.90155i	−0.183351	+	0.0963977i
$907$	−0.0585048			−0.00194262			−0.000971310	−	1.00000i	$-0.500309\pi$
$907$	−0.0585048			−0.00194262			−0.000971310		1.00000i	$0.500309\pi$
$908$	0.567289	−	0.824387i	0.0188262	−	0.0273583i
$909$		−	22.0594i		−	0.731665i
$910$	−6.43028	+	3.38075i	−0.213162	+	0.112071i
$911$		−	8.75202i		−	0.289968i	−0.989434	−	0.144984i	$-0.953687\pi$
$911$		−	8.75202i		−	0.289968i	0.989434	−	0.144984i	$-0.0463130\pi$
$912$	17.7600	−	6.79382i	0.588092	−	0.224966i
$913$			35.7299i			1.18249i
$914$	24.3643	−	12.8097i	0.805899	−	0.423706i
$915$	13.1206			0.433754
$916$	−42.6262	−	29.3326i	−1.40841	−	0.969176i
$917$		−	29.2894i		−	0.967222i
$918$	17.0411	+	21.4910i	0.562440	+	0.709310i
$919$	12.1833			0.401889			0.200944	−	0.979603i	$-0.435599\pi$
$919$	12.1833			0.401889			0.200944	+	0.979603i	$0.435599\pi$
$920$	23.3887	+	2.78885i	0.771101	+	0.0919456i
$921$		−	15.1418i		−	0.498941i
$922$	−1.12494	−	2.13967i	−0.0370480	−	0.0704662i
$923$	4.20110			0.138281
$924$	−28.0916	−	19.3308i	−0.924146	−	0.635937i
$925$	19.4621			0.639910
$926$	−36.2492	+	19.0582i	−1.19122	+	0.626292i
$927$	33.8077			1.11039
$928$	−12.7542	−	11.2179i	−0.418679	−	0.368246i
$929$		−	30.3091i		−	0.994411i	−0.867633	−	0.497205i	$-0.834360\pi$
$929$		−	30.3091i		−	0.994411i	0.867633	−	0.497205i	$-0.165640\pi$
$930$	−0.312400	−	0.594192i	−0.0102440	−	0.0194843i
$931$		−	30.1726i		−	0.988867i
$932$	31.3841	+	21.5965i	1.02802	+	0.707416i
$933$		−	30.5964i		−	1.00168i
$934$	−7.31455	−	13.9125i	−0.239340	−	0.455230i
$935$	6.21373	+	32.9518i	0.203211	+	1.07764i
$936$	5.66089	+	0.675000i	0.185032	+	0.0220631i
$937$	−40.5793			−1.32567			−0.662834	−	0.748766i	$-0.730647\pi$
$937$	−40.5793			−1.32567			−0.662834	+	0.748766i	$0.730647\pi$
$938$	5.68275	−	2.98774i	0.185548	−	0.0975531i
$939$		−	22.1555i		−	0.723017i
$940$	−8.67606	+	12.6081i	−0.282982	+	0.411230i
$941$	43.0071			1.40199			0.700996	−	0.713165i	$-0.252739\pi$
$941$	43.0071			1.40199			0.700996	+	0.713165i	$0.252739\pi$
$942$	−7.23605	−	13.7632i	−0.235763	−	0.448428i
$943$	27.0594			0.881176
$944$	18.5093	−	7.08045i	0.602426	−	0.230449i
$945$			26.0535i			0.847522i
$946$	30.7768	+	58.5382i	1.00064	+	1.90324i
$947$	−38.1203			−1.23874			−0.619371	−	0.785098i	$-0.712612\pi$
$947$	−38.1203			−1.23874			−0.619371	+	0.785098i	$0.712612\pi$
$948$	11.6348	+	8.00630i	0.377881	+	0.260033i
$949$	9.07967			0.294739
$950$	8.93841	+	17.0011i	0.290000	+	0.551588i
$951$	−1.06512			−0.0345389
$952$	2.81941	+	41.5802i	0.0913775	+	1.34762i
$953$	2.04834			0.0663521			0.0331761	−	0.999450i	$-0.489438\pi$
$953$	2.04834			0.0663521			0.0331761	+	0.999450i	$0.489438\pi$
$954$	16.5121	+	31.4063i	0.534597	+	1.01682i
$955$	11.5054			0.372307
$956$	−25.9139	+	37.6581i	−0.838114	+	1.21795i
$957$	−14.3258			−0.463089
$958$	0.538488	+	1.02422i	0.0173978	+	0.0330910i
$959$		−	7.56600i		−	0.244319i
$960$	−10.9579	−	2.65091i	−0.353665	−	0.0855579i
$961$	30.8865			0.996340
$962$	4.57281	+	8.69759i	0.147433	+	0.280422i
$963$	14.6548			0.472244
$964$	21.6487	+	14.8972i	0.697258	+	0.479807i
$965$		−	34.7151i		−	1.11752i
$966$	21.8539	−	11.4898i	0.703138	−	0.369678i
$967$	13.1716			0.423571			0.211785	−	0.977316i	$-0.432072\pi$
$967$	13.1716			0.423571			0.211785	+	0.977316i	$0.432072\pi$
$968$	−5.53698	+	46.4359i	−0.177965	+	1.49250i
$969$	−19.2609	+	3.63203i	−0.618748	+	0.116677i
$970$	9.73191	+	18.5103i	0.312473	+	0.594331i
$971$			13.1916i			0.423338i	0.977341	+	0.211669i	$0.0678899\pi$
$971$			13.1916i			0.423338i	−0.977341	+	0.211669i	$0.932110\pi$
$972$	18.3111	−	26.6098i	0.587330	−	0.853510i
$973$		−	13.5603i		−	0.434724i
$974$	−15.2003	−	28.9114i	−0.487050	−	0.926382i
$975$		−	2.19063i		−	0.0701562i
$976$	−13.3058	−	34.7833i	−0.425909	−	1.11339i
$977$	22.2884			0.713071			0.356535	−	0.934282i	$-0.383958\pi$
$977$	22.2884			0.713071			0.356535	+	0.934282i	$0.383958\pi$
$978$	−11.3748	+	5.98038i	−0.363727	+	0.191232i
$979$	−0.249026			−0.00795891
$980$	−10.1411	+	14.7371i	−0.323946	+	0.470760i
$981$	−19.4392			−0.620645
$982$	−25.3547	−	48.2252i	−0.809100	−	1.53893i
$983$			45.9762i			1.46641i	0.680006	+	0.733206i	$0.261977\pi$
$983$			45.9762i			1.46641i	−0.680006	+	0.733206i	$0.738023\pi$
$984$	−12.8606	−	1.53348i	−0.409979	−	0.0488856i
$985$	−43.3891			−1.38249
$986$	10.8782	+	13.7189i	0.346434	+	0.436898i
$987$			16.0429i			0.510651i
$988$	−5.49760	+	7.98913i	−0.174902	+	0.254168i
$989$	−47.8857			−1.52268
$990$	22.1246	−	11.6321i	0.703166	−	0.369694i
$991$		−	37.8994i		−	1.20391i	−0.798528	−	0.601957i	$-0.794388\pi$
$991$		−	37.8994i		−	1.20391i	0.798528	−	0.601957i	$-0.205612\pi$
$992$	−1.25842	+	1.43077i	−0.0399549	+	0.0454269i
$993$		−	6.91501i		−	0.219441i
$994$	20.2630	−	10.6534i	0.642704	−	0.337905i
$995$		−	17.1775i		−	0.544564i
$996$	10.2007	+	7.01943i	0.323220	+	0.222419i
$997$	29.2631			0.926770			0.463385	−	0.886157i	$-0.346635\pi$
$997$	29.2631			0.926770			0.463385	+	0.886157i	$0.346635\pi$
$998$	54.3296	−	28.5641i	1.71977	−	0.904180i
$999$	35.2400			1.11494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.h.a.101.4	yes	16
3.2	odd	2		1224.2.l.b.1189.13		16
4.3	odd	2		544.2.h.a.305.8		16
8.3	odd	2		544.2.h.a.305.10		16
8.5	even	2	inner	136.2.h.a.101.1	✓	16
12.11	even	2		4896.2.l.b.3025.6		16
17.16	even	2	inner	136.2.h.a.101.3	yes	16
24.5	odd	2		1224.2.l.b.1189.16		16
24.11	even	2		4896.2.l.b.3025.12		16
51.50	odd	2		1224.2.l.b.1189.14		16
68.67	odd	2		544.2.h.a.305.9		16
136.67	odd	2		544.2.h.a.305.7		16
136.101	even	2	inner	136.2.h.a.101.2	yes	16
204.203	even	2		4896.2.l.b.3025.11		16
408.101	odd	2		1224.2.l.b.1189.15		16
408.203	even	2		4896.2.l.b.3025.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.h.a.101.1	✓	16	8.5	even	2	inner
136.2.h.a.101.2	yes	16	136.101	even	2	inner
136.2.h.a.101.3	yes	16	17.16	even	2	inner
136.2.h.a.101.4	yes	16	1.1	even	1	trivial
544.2.h.a.305.7		16	136.67	odd	2
544.2.h.a.305.8		16	4.3	odd	2
544.2.h.a.305.9		16	68.67	odd	2
544.2.h.a.305.10		16	8.3	odd	2
1224.2.l.b.1189.13		16	3.2	odd	2
1224.2.l.b.1189.14		16	51.50	odd	2
1224.2.l.b.1189.15		16	408.101	odd	2
1224.2.l.b.1189.16		16	24.5	odd	2
4896.2.l.b.3025.5		16	408.203	even	2
4896.2.l.b.3025.6		16	12.11	even	2
4896.2.l.b.3025.11		16	204.203	even	2
4896.2.l.b.3025.12		16	24.11	even	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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25175 + 0.658116i) q^{2} +0.909242 q^{3} +(1.13377 - 1.64760i) q^{4} +1.54992 q^{5} +(-1.13815 + 0.598386i) q^{6} -3.57366i q^{7} +(-0.334887 + 2.80853i) q^{8} -2.17328 q^{9} +O(q^{10})\)	\(q+(-1.25175 + 0.658116i) q^{2} +0.909242 q^{3} +(1.13377 - 1.64760i) q^{4} +1.54992 q^{5} +(-1.13815 + 0.598386i) q^{6} -3.57366i q^{7} +(-0.334887 + 2.80853i) q^{8} -2.17328 q^{9} +(-1.94011 + 1.02002i) q^{10} +5.24727 q^{11} +(1.03087 - 1.49806i) q^{12} +0.927449i q^{13} +(2.35188 + 4.47334i) q^{14} +1.40925 q^{15} +(-1.42914 - 3.73598i) q^{16} +(0.764030 + 4.05170i) q^{17} +(2.72041 - 1.43027i) q^{18} +5.22828i q^{19} +(1.75724 - 2.55363i) q^{20} -3.24932i q^{21} +(-6.56828 + 3.45331i) q^{22} -5.37301i q^{23} +(-0.304494 + 2.55363i) q^{24} -2.59776 q^{25} +(-0.610369 - 1.16094i) q^{26} -4.70376 q^{27} +(-5.88795 - 4.05170i) q^{28} -3.00267 q^{29} +(-1.76403 + 0.927449i) q^{30} +0.336838i q^{31} +(4.24764 + 3.73598i) q^{32} +4.77104 q^{33} +(-3.62286 - 4.56890i) q^{34} -5.53887i q^{35} +(-2.46399 + 3.58069i) q^{36} -7.49188 q^{37} +(-3.44081 - 6.54451i) q^{38} +0.843275i q^{39} +(-0.519047 + 4.35299i) q^{40} +5.03617i q^{41} +(2.13843 + 4.06734i) q^{42} -8.91225i q^{43} +(5.94918 - 8.64538i) q^{44} -3.36840 q^{45} +(3.53606 + 6.72568i) q^{46} -4.93731 q^{47} +(-1.29944 - 3.39691i) q^{48} -5.77104 q^{49} +(3.25175 - 1.70963i) q^{50} +(0.694688 + 3.68397i) q^{51} +(1.52806 + 1.05151i) q^{52} +11.5447i q^{53} +(5.88795 - 3.09562i) q^{54} +8.13283 q^{55} +(10.0367 + 1.19677i) q^{56} +4.75377i q^{57} +(3.75859 - 1.97610i) q^{58} +4.95434i q^{59} +(1.59776 - 2.32187i) q^{60} +9.31036 q^{61} +(-0.221678 - 0.421638i) q^{62} +7.76656i q^{63} +(-7.77570 - 1.88108i) q^{64} +1.43747i q^{65} +(-5.97216 + 3.13990i) q^{66} -1.27036i q^{67} +(7.54179 + 3.33487i) q^{68} -4.88537i q^{69} +(3.64522 + 6.93329i) q^{70} -4.52974i q^{71} +(0.727803 - 6.10372i) q^{72} -9.78995i q^{73} +(9.37797 - 4.93052i) q^{74} -2.36199 q^{75} +(8.61409 + 5.92765i) q^{76} -18.7520i q^{77} +(-0.554973 - 1.05557i) q^{78} +7.76656i q^{79} +(-2.21505 - 5.79046i) q^{80} +2.24298 q^{81} +(-3.31439 - 6.30404i) q^{82} +6.80923i q^{83} +(-5.35357 - 3.68397i) q^{84} +(1.18418 + 6.27979i) q^{85} +(5.86530 + 11.1559i) q^{86} -2.73015 q^{87} +(-1.75724 + 14.7371i) q^{88} -0.0474582 q^{89} +(4.21640 - 2.21680i) q^{90} +3.31439 q^{91} +(-8.85255 - 6.09175i) q^{92} +0.306267i q^{93} +(6.18029 - 3.24932i) q^{94} +8.10340i q^{95} +(3.86213 + 3.39691i) q^{96} -9.54086i q^{97} +(7.22391 - 3.79801i) q^{98} -11.4038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * q^98

Introduction

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