LMFDB - Embedded newform 136.2.h.a.101.6

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			101.6
Root			$0.289081 + 0.578468i$ of defining polynomial
Character	$\chi$	$=$	136.101
Dual form			136.2.h.a.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.632188 - 1.26504i) q^{2} +2.88107 q^{3} +(-1.20068 + 1.59949i) q^{4} -0.914541 q^{5} +(-1.82138 - 3.64469i) q^{6} -2.61974i q^{7} +(2.78248 + 0.507728i) q^{8} +5.30059 q^{9} +O(q^{10})$	\(q+(-0.632188 - 1.26504i) q^{2} +2.88107 q^{3} +(-1.20068 + 1.59949i) q^{4} -0.914541 q^{5} +(-1.82138 - 3.64469i) q^{6} -2.61974i q^{7} +(2.78248 + 0.507728i) q^{8} +5.30059 q^{9} +(0.578162 + 1.15694i) q^{10} -0.394636 q^{11} +(-3.45924 + 4.60826i) q^{12} +3.33322i q^{13} +(-3.31408 + 1.65617i) q^{14} -2.63486 q^{15} +(-1.11675 - 3.84095i) q^{16} +(-2.66573 - 3.14546i) q^{17} +(-3.35097 - 6.70548i) q^{18} +6.87876i q^{19} +(1.09807 - 1.46280i) q^{20} -7.54766i q^{21} +(0.249484 + 0.499232i) q^{22} -0.692597i q^{23} +(8.01654 + 1.46280i) q^{24} -4.16361 q^{25} +(4.21667 - 2.10722i) q^{26} +6.62817 q^{27} +(4.19025 + 3.14546i) q^{28} -8.20007 q^{29} +(1.66573 + 3.33322i) q^{30} +7.59524i q^{31} +(-4.15297 + 3.84095i) q^{32} -1.13698 q^{33} +(-2.29390 + 5.36079i) q^{34} +2.39586i q^{35} +(-6.36429 + 8.47826i) q^{36} +8.98934 q^{37} +(8.70194 - 4.34867i) q^{38} +9.60325i q^{39} +(-2.54470 - 0.464338i) q^{40} -6.90264i q^{41} +(-9.54813 + 4.77154i) q^{42} +2.18353i q^{43} +(0.473830 - 0.631217i) q^{44} -4.84761 q^{45} +(-0.876166 + 0.437852i) q^{46} +5.96632 q^{47} +(-3.21745 - 11.0660i) q^{48} +0.136975 q^{49} +(2.63219 + 5.26716i) q^{50} +(-7.68016 - 9.06229i) q^{51} +(-5.33146 - 4.00211i) q^{52} -7.24371i q^{53} +(-4.19025 - 8.38493i) q^{54} +0.360911 q^{55} +(1.33011 - 7.28938i) q^{56} +19.8182i q^{57} +(5.18399 + 10.3735i) q^{58} -0.845737i q^{59} +(3.16361 - 4.21444i) q^{60} -3.22719 q^{61} +(9.60832 - 4.80162i) q^{62} -13.8862i q^{63} +(7.48442 + 2.82549i) q^{64} -3.04836i q^{65} +(0.718782 + 1.43832i) q^{66} -8.21656i q^{67} +(8.23181 - 0.487141i) q^{68} -1.99542i q^{69} +(3.03087 - 1.51463i) q^{70} +8.91065i q^{71} +(14.7488 + 2.69126i) q^{72} -12.9156i q^{73} +(-5.68295 - 11.3719i) q^{74} -11.9957 q^{75} +(-11.0025 - 8.25916i) q^{76} +1.03384i q^{77} +(12.1485 - 6.07106i) q^{78} -13.8862i q^{79} +(1.02132 + 3.51270i) q^{80} +3.19448 q^{81} +(-8.73215 + 4.36377i) q^{82} +5.82070i q^{83} +(12.0724 + 9.06229i) q^{84} +(2.43792 + 2.87665i) q^{85} +(2.76226 - 1.38040i) q^{86} -23.6250 q^{87} +(-1.09807 - 0.200368i) q^{88} +2.13275 q^{89} +(3.06460 + 6.13244i) q^{90} +8.73215 q^{91} +(1.10780 + 0.831585i) q^{92} +21.8825i q^{93} +(-3.77184 - 7.54766i) q^{94} -6.29091i q^{95} +(-11.9650 + 11.0660i) q^{96} +9.33928i q^{97} +(-0.0865941 - 0.173280i) q^{98} -2.09180 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 $

$2$	−0.632188	−	1.26504i	−0.447025	−	0.894522i
$2$	−0.632188	−	1.26504i	−0.447025	−	0.894522i
$3$	2.88107			1.66339			0.831695	−	0.555233i	$-0.187371\pi$
$3$	2.88107			1.66339			0.831695	+	0.555233i	$0.187371\pi$
$4$	−1.20068	+	1.59949i	−0.600338	+	0.799746i
$5$	−0.914541			−0.408995			−0.204498	−	0.978867i	$-0.565556\pi$
$5$	−0.914541			−0.408995			−0.204498	+	0.978867i	$0.565556\pi$
$6$	−1.82138	−	3.64469i	−0.743576	−	1.48794i
$7$		−	2.61974i		−	0.990168i	−0.868845	−	0.495084i	$-0.835137\pi$
$7$		−	2.61974i		−	0.990168i	0.868845	−	0.495084i	$-0.164863\pi$
$8$	2.78248	+	0.507728i	0.983756	+	0.179509i
$9$	5.30059			1.76686
$10$	0.578162	+	1.15694i	0.182831	+	0.365855i
$11$	−0.394636			−0.118987			−0.0594936	−	0.998229i	$-0.518949\pi$
$11$	−0.394636			−0.118987			−0.0594936	+	0.998229i	$0.518949\pi$
$12$	−3.45924	+	4.60826i	−0.998596	+	1.33029i
$13$			3.33322i			0.924468i	0.886758	+	0.462234i	$0.152952\pi$
$13$			3.33322i			0.924468i	−0.886758	+	0.462234i	$0.847048\pi$
$14$	−3.31408	+	1.65617i	−0.885726	+	0.442629i
$15$	−2.63486			−0.680318
$16$	−1.11675	−	3.84095i	−0.279189	−	0.960236i
$17$	−2.66573	−	3.14546i	−0.646534	−	0.762885i
$17$	−2.66573	−	3.14546i	−0.646534	−	0.762885i
$18$	−3.35097	−	6.70548i	−0.789831	−	1.58050i
$19$			6.87876i			1.57810i	0.614331	+	0.789048i	$0.289426\pi$
$19$			6.87876i			1.57810i	−0.614331	+	0.789048i	$0.710574\pi$
$20$	1.09807	−	1.46280i	0.245535	−	0.327092i
$21$		−	7.54766i		−	1.64703i
$22$	0.249484	+	0.499232i	0.0531902	+	0.106437i
$23$		−	0.692597i		−	0.144417i	−0.997390	−	0.0722083i	$-0.976995\pi$
$23$		−	0.692597i		−	0.144417i	0.997390	−	0.0722083i	$-0.0230046\pi$
$24$	8.01654	+	1.46280i	1.63637	+	0.298593i
$25$	−4.16361			−0.832723
$26$	4.21667	−	2.10722i	0.826957	−	0.413260i
$27$	6.62817			1.27559
$28$	4.19025	+	3.14546i	0.791883	+	0.594435i
$29$	−8.20007			−1.52271			−0.761357	−	0.648333i	$-0.775467\pi$
$29$	−8.20007			−1.52271			−0.761357	+	0.648333i	$0.775467\pi$
$30$	1.66573	+	3.33322i	0.304119	+	0.608559i
$31$			7.59524i			1.36415i	0.731284	+	0.682073i	$0.238921\pi$
$31$			7.59524i			1.36415i	−0.731284	+	0.682073i	$0.761079\pi$
$32$	−4.15297	+	3.84095i	−0.734148	+	0.678990i
$33$	−1.13698			−0.197922
$34$	−2.29390	+	5.36079i	−0.393401	+	0.919367i
$35$			2.39586i			0.404974i
$36$	−6.36429	+	8.47826i	−1.06072	+	1.41304i
$37$	8.98934			1.47784			0.738919	−	0.673794i	$-0.235337\pi$
$37$	8.98934			1.47784			0.738919	+	0.673794i	$0.235337\pi$
$38$	8.70194	−	4.34867i	1.41164	−	0.705448i
$39$			9.60325i			1.53775i
$40$	−2.54470	−	0.464338i	−0.402352	−	0.0734183i
$41$		−	6.90264i		−	1.07801i	−0.842302	−	0.539006i	$-0.818800\pi$
$41$		−	6.90264i		−	1.07801i	0.842302	−	0.539006i	$-0.181200\pi$
$42$	−9.54813	+	4.77154i	−1.47331	+	0.736265i
$43$			2.18353i			0.332985i	0.986043	+	0.166493i	$0.0532442\pi$
$43$			2.18353i			0.332985i	−0.986043	+	0.166493i	$0.946756\pi$
$44$	0.473830	−	0.631217i	0.0714325	−	0.0951596i
$45$	−4.84761			−0.722639
$46$	−0.876166	+	0.437852i	−0.129184	+	0.0645577i
$47$	5.96632			0.870277			0.435138	−	0.900364i	$-0.356699\pi$
$47$	5.96632			0.870277			0.435138	+	0.900364i	$0.356699\pi$
$48$	−3.21745	−	11.0660i	−0.464399	−	1.59725i
$49$	0.136975			0.0195679
$50$	2.63219	+	5.26716i	0.372248	+	0.744889i
$51$	−7.68016	−	9.06229i	−1.07544	−	1.26897i
$52$	−5.33146	−	4.00211i	−0.739340	−	0.554993i
$53$		−	7.24371i		−	0.995000i	−0.867464	−	0.497500i	$-0.834251\pi$
$53$		−	7.24371i		−	0.995000i	0.867464	−	0.497500i	$-0.165749\pi$
$54$	−4.19025	−	8.38493i	−0.570221	−	1.14104i
$55$	0.360911			0.0486652
$56$	1.33011	−	7.28938i	0.177744	−	0.974084i
$57$			19.8182i			2.62499i
$58$	5.18399	+	10.3735i	0.680691	+	1.36210i
$59$		−	0.845737i		−	0.110106i	−0.998483	−	0.0550528i	$-0.982467\pi$
$59$		−	0.845737i		−	0.110106i	0.998483	−	0.0550528i	$-0.0175327\pi$
$60$	3.16361	−	4.21444i	0.408421	−	0.544082i
$61$	−3.22719			−0.413199			−0.206600	−	0.978426i	$-0.566240\pi$
$61$	−3.22719			−0.413199			−0.206600	+	0.978426i	$0.566240\pi$
$62$	9.60832	−	4.80162i	1.22026	−	0.609807i
$63$		−	13.8862i		−	1.74949i
$64$	7.48442	+	2.82549i	0.935553	+	0.353186i
$65$		−	3.04836i		−	0.378103i
$66$	0.718782	+	1.43832i	0.0884760	+	0.177045i
$67$		−	8.21656i		−	1.00381i	−0.864922	−	0.501906i	$-0.832632\pi$
$67$		−	8.21656i		−	1.00381i	0.864922	−	0.501906i	$-0.167368\pi$
$68$	8.23181	−	0.487141i	0.998254	−	0.0590745i
$69$		−	1.99542i		−	0.240221i
$70$	3.03087	−	1.51463i	0.362258	−	0.181033i
$71$			8.91065i			1.05750i	0.848778	+	0.528750i	$0.177339\pi$
$71$			8.91065i			1.05750i	−0.848778	+	0.528750i	$0.822661\pi$
$72$	14.7488	+	2.69126i	1.73816	+	0.317168i
$73$		−	12.9156i		−	1.51165i	−0.654771	−	0.755827i	$-0.727235\pi$
$73$		−	12.9156i		−	1.51165i	0.654771	−	0.755827i	$-0.272765\pi$
$74$	−5.68295	−	11.3719i	−0.660630	−	1.32196i
$75$	−11.9957			−1.38514
$76$	−11.0025	−	8.25916i	−1.26208	−	0.947391i
$77$			1.03384i			0.117817i
$78$	12.1485	−	6.07106i	1.37555	−	0.687412i
$79$		−	13.8862i		−	1.56231i	−0.624334	−	0.781157i	$-0.714630\pi$
$79$		−	13.8862i		−	1.56231i	0.624334	−	0.781157i	$-0.285370\pi$
$80$	1.02132	+	3.51270i	0.114187	+	0.392732i
$81$	3.19448			0.354942
$82$	−8.73215	+	4.36377i	−0.964305	+	0.481898i
$83$			5.82070i			0.638905i	0.947602	+	0.319452i	$0.103499\pi$
$83$			5.82070i			0.638905i	−0.947602	+	0.319452i	$0.896501\pi$
$84$	12.0724	+	9.06229i	1.31721	+	0.988777i
$85$	2.43792	+	2.87665i	0.264429	+	0.312016i
$86$	2.76226	−	1.38040i	0.297862	−	0.148853i
$87$	−23.6250			−2.53287
$88$	−1.09807	−	0.200368i	−0.117054	−	0.0213593i
$89$	2.13275			0.226071			0.113035	−	0.993591i	$-0.463943\pi$
$89$	2.13275			0.226071			0.113035	+	0.993591i	$0.463943\pi$
$90$	3.06460	+	6.13244i	0.323037	+	0.646416i
$91$	8.73215			0.915378
$92$	1.10780	+	0.831585i	0.115497	+	0.0866987i
$93$			21.8825i			2.26911i
$94$	−3.77184	−	7.54766i	−0.389035	−	0.778482i
$95$		−	6.29091i		−	0.645434i
$96$	−11.9650	+	11.0660i	−1.22117	+	1.12942i
$97$			9.33928i			0.948260i	0.880455	+	0.474130i	$0.157237\pi$
$97$			9.33928i			0.948260i	−0.880455	+	0.474130i	$0.842763\pi$
$98$	−0.0865941	−	0.173280i	−0.00874733	−	0.0175039i
$99$	−2.09180			−0.210234
$100$	4.99915	−	6.65967i	0.499915	−	0.665967i
$101$		−	8.12493i		−	0.808461i	−0.914657	−	0.404231i	$-0.867539\pi$
$101$		−	8.12493i		−	0.808461i	0.914657	−	0.404231i	$-0.132461\pi$
$102$	−6.60890	+	15.4448i	−0.654378	+	1.52927i
$103$	1.21644			0.119860			0.0599299	−	0.998203i	$-0.480912\pi$
$103$	1.21644			0.119860			0.0599299	+	0.998203i	$0.480912\pi$
$104$	−1.69237	+	9.27462i	−0.165950	+	0.909451i
$105$			6.90264i			0.673629i
$106$	−9.16361	+	4.57939i	−0.890049	+	0.444789i
$107$	−2.57537			−0.248970			−0.124485	−	0.992221i	$-0.539728\pi$
$107$	−2.57537			−0.248970			−0.124485	+	0.992221i	$0.539728\pi$
$108$	−7.95828	+	10.6017i	−0.765786	+	1.02015i
$109$	0.125269			0.0119986			0.00599932	−	0.999982i	$-0.498090\pi$
$109$	0.125269			0.0119986			0.00599932	+	0.999982i	$0.498090\pi$
$110$	−0.228164	−	0.456568i	−0.0217545	−	0.0435321i
$111$	25.8990			2.45822
$112$	−10.0623	+	2.92560i	−0.950795	+	0.276444i
$113$			3.04836i			0.286766i	0.989667	+	0.143383i	$0.0457981\pi$
$113$			3.04836i			0.286766i	−0.989667	+	0.143383i	$0.954202\pi$
$114$	25.0709	−	12.5289i	2.34811	−	1.17343i
$115$			0.633409i			0.0590657i
$116$	9.84562	−	13.1159i	0.914143	−	1.21779i
$117$			17.6680i			1.63341i
$118$	−1.06989	+	0.534665i	−0.0984918	+	0.0492199i
$119$	−8.24027	+	6.98351i	−0.755384	+	0.640177i
$120$	−7.33146	−	1.33779i	−0.669267	−	0.122123i
$121$	−10.8443			−0.985842
$122$	2.04019	+	4.08254i	0.184710	+	0.369616i
$123$		−	19.8870i		−	1.79315i
$124$	−12.1485	−	9.11942i	−1.09097	−	0.818948i
$125$	8.38050			0.749575
$126$	−17.5666	+	8.77866i	−1.56496	+	0.782066i
$127$	6.06173			0.537892			0.268946	−	0.963155i	$-0.413325\pi$
$127$	6.06173			0.537892			0.268946	+	0.963155i	$0.413325\pi$
$128$	−1.15720	−	11.2544i	−0.102283	−	0.994755i
$129$			6.29091i			0.553884i
$130$	−3.85632	+	1.92714i	−0.338221	+	0.169021i
$131$	11.6900			1.02136			0.510679	−	0.859771i	$-0.329394\pi$
$131$	11.6900			1.02136			0.510679	+	0.859771i	$0.329394\pi$
$132$	1.36514	−	1.81858i	0.118820	−	0.158287i
$133$	18.0206			1.56258
$134$	−10.3943	+	5.19441i	−0.897932	+	0.448729i
$135$	−6.06173			−0.521711
$136$	−5.82031	−	10.1056i	−0.499087	−	0.866552i
$137$	8.36232			0.714442			0.357221	−	0.934020i	$-0.383724\pi$
$137$	8.36232			0.714442			0.357221	+	0.934020i	$0.383724\pi$
$138$	−2.52430	+	1.26148i	−0.214883	+	0.107385i
$139$	−9.50924			−0.806564			−0.403282	−	0.915076i	$-0.632131\pi$
$139$	−9.50924			−0.806564			−0.403282	+	0.915076i	$0.632131\pi$
$140$	−3.83216	−	2.87665i	−0.323876	−	0.243121i
$141$	17.1894			1.44761
$142$	11.2724	−	5.63321i	0.945956	−	0.472728i
$143$		−	1.31541i		−	0.110000i
$144$	−5.91946	−	20.3593i	−0.493288	−	1.69661i
$145$	7.49930			0.622783
$146$	−16.3388	+	8.16508i	−1.35221	+	0.675747i
$147$	0.394636			0.0325490
$148$	−10.7933	+	14.3784i	−0.887202	+	1.18190i
$149$		−	13.7575i		−	1.12706i	−0.826095	−	0.563530i	$-0.809443\pi$
$149$		−	13.7575i		−	1.12706i	0.826095	−	0.563530i	$-0.190557\pi$
$150$	7.58353	+	15.1751i	0.619193	+	1.23904i
$151$	22.9284			1.86589			0.932944	−	0.360022i	$-0.117231\pi$
$151$	22.9284			1.86589			0.932944	+	0.360022i	$0.117231\pi$
$152$	−3.49254	+	19.1400i	−0.283282	+	1.55246i
$153$	−14.1299	−	16.6728i	−1.14234	−	1.34791i
$154$	1.30786	−	0.653583i	0.105390	−	0.0526672i
$155$		−	6.94616i		−	0.557929i
$156$	−15.3603	−	11.5304i	−1.22981	−	0.923170i
$157$			8.20529i			0.654853i	0.944877	+	0.327427i	$0.106181\pi$
$157$			8.20529i			0.654853i	−0.944877	+	0.327427i	$0.893819\pi$
$158$	−17.5666	+	8.77866i	−1.39752	+	0.698393i
$159$		−	20.8697i		−	1.65507i
$160$	3.79806	−	3.51270i	0.300263	−	0.277704i
$161$	−1.81442			−0.142997
$162$	−2.01951	−	4.04116i	−0.158668	−	0.317504i
$163$	−13.1674			−1.03135			−0.515676	−	0.856784i	$-0.672459\pi$
$163$	−13.1674			−1.03135			−0.515676	+	0.856784i	$0.672459\pi$
$164$	11.0407	+	8.28784i	0.862136	+	0.647172i
$165$	1.03981			0.0809492
$166$	7.36344	−	3.67978i	0.571514	−	0.285606i
$167$			18.2499i			1.41222i	0.708101	+	0.706111i	$0.249552\pi$
$167$			18.2499i			1.41222i	−0.708101	+	0.706111i	$0.750448\pi$
$168$	3.83216	−	21.0012i	0.295657	−	1.62028i
$169$	1.88966			0.145359
$170$	2.09787	−	4.90266i	0.160899	−	0.376017i
$171$			36.4615i			2.78828i
$172$	−3.49254	−	2.62171i	−0.266304	−	0.199904i
$173$	−17.3698			−1.32060			−0.660302	−	0.751000i	$-0.729572\pi$
$173$	−17.3698			−1.32060			−0.660302	+	0.751000i	$0.729572\pi$
$174$	14.9355	+	29.8867i	1.13225	+	2.26570i
$175$			10.9076i			0.824535i
$176$	0.440711	+	1.51577i	0.0332199	+	0.114256i
$177$		−	2.43663i		−	0.183148i
$178$	−1.34830	−	2.69802i	−0.101059	−	0.202225i
$179$			5.91718i			0.442271i	0.975243	+	0.221135i	$0.0709763\pi$
$179$			5.91718i			0.442271i	−0.975243	+	0.221135i	$0.929024\pi$
$180$	5.82041	−	7.75371i	0.433827	−	0.577928i
$181$	−0.0282293			−0.00209827			−0.00104913	−	0.999999i	$-0.500334\pi$
$181$	−0.0282293			−0.00209827			−0.00104913	+	0.999999i	$0.500334\pi$
$182$	−5.52037	−	11.0466i	−0.409197	−	0.818826i
$183$	−9.29777			−0.687311
$184$	0.351651	−	1.92714i	0.0259241	−	0.142071i
$185$	−8.22112			−0.604429
$186$	27.6823	−	13.8338i	2.02976	−	1.01435i
$187$	1.05199	+	1.24131i	0.0769293	+	0.0907735i
$188$	−7.16361	+	9.54308i	−0.522460	+	0.696001i
$189$		−	17.3641i		−	1.26305i
$190$	−7.95828	+	3.97704i	−0.577355	+	0.288525i
$191$	−1.57735			−0.114133			−0.0570667	−	0.998370i	$-0.518175\pi$
$191$	−1.57735			−0.114133			−0.0570667	+	0.998370i	$0.518175\pi$
$192$	21.5632	+	8.14044i	1.55619	+	0.587486i
$193$		−	4.18804i		−	0.301462i	−0.988575	−	0.150731i	$-0.951837\pi$
$193$		−	4.18804i		−	0.301462i	0.988575	−	0.150731i	$-0.0481627\pi$
$194$	11.8146	−	5.90418i	0.848239	−	0.423895i
$195$		−	8.78256i		−	0.628932i
$196$	−0.164463	+	0.219091i	−0.0117473	+	0.0156494i
$197$	−14.7934			−1.05398			−0.526992	−	0.849870i	$-0.676680\pi$
$197$	−14.7934			−1.05398			−0.526992	+	0.849870i	$0.676680\pi$
$198$	1.32241	+	2.64622i	0.0939798	+	0.188059i
$199$		−	8.98044i		−	0.636606i	−0.947989	−	0.318303i	$-0.896887\pi$
$199$		−	8.98044i		−	0.636606i	0.947989	−	0.318303i	$-0.103113\pi$
$200$	−11.5852	−	2.11398i	−0.819196	−	0.149481i
$201$		−	23.6725i		−	1.66973i
$202$	−10.2784	+	5.13649i	−0.723186	+	0.361402i
$203$			21.4820i			1.50774i
$204$	23.7165	−	1.40349i	1.66048	−	0.0982638i
$205$			6.31275i			0.440902i
$206$	−0.769022	−	1.53886i	−0.0535803	−	0.107217i
$207$		−	3.67117i		−	0.255164i
$208$	12.8027	−	3.72239i	0.887708	−	0.258101i
$209$		−	2.71461i		−	0.187773i
$210$	8.73215	−	4.36377i	0.602576	−	0.301129i
$211$	9.89170			0.680973			0.340486	−	0.940249i	$-0.389408\pi$
$211$	9.89170			0.680973			0.340486	+	0.940249i	$0.389408\pi$
$212$	11.5863	+	8.69735i	0.795748	+	0.597336i
$213$			25.6722i			1.75903i
$214$	1.62812	+	3.25796i	0.111296	+	0.222709i
$215$		−	1.99693i		−	0.136189i
$216$	18.4428	+	3.36531i	1.25487	+	0.228980i
$217$	19.8975			1.35073
$218$	−0.0791939	−	0.158472i	−0.00536369	−	0.0107330i
$219$		−	37.2108i		−	2.51447i
$220$	−0.433337	+	0.577274i	−0.0292156	+	0.0389198i
$221$	10.4845	−	8.88545i	0.705263	−	0.597700i
$222$	−16.3730	−	32.7633i	−1.09888	−	2.19893i
$223$	18.7797			1.25758			0.628791	−	0.777574i	$-0.283550\pi$
$223$	18.7797			1.25758			0.628791	+	0.777574i	$0.283550\pi$
$224$	10.0623	+	10.8797i	0.672314	+	0.726930i
$225$	−22.0696			−1.47131
$226$	3.85632	−	1.92714i	0.256518	−	0.128191i
$227$	12.3781			0.821566			0.410783	−	0.911733i	$-0.365255\pi$
$227$	12.3781			0.821566			0.410783	+	0.911733i	$0.365255\pi$
$228$	−31.6991	−	23.7953i	−2.09932	−	1.57588i
$229$			4.48777i			0.296560i	0.988945	+	0.148280i	$0.0473737\pi$
$229$			4.48777i			0.296560i	−0.988945	+	0.148280i	$0.952626\pi$
$230$	0.801290	−	0.400434i	0.0528355	−	0.0264038i
$231$			2.97858i			0.195976i
$232$	−22.8165	−	4.16340i	−1.49798	−	0.273341i
$233$			30.2972i			1.98483i	0.122917	+	0.992417i	$0.460775\pi$
$233$			30.2972i			1.98483i	−0.122917	+	0.992417i	$0.539225\pi$
$234$	22.3508	−	11.1695i	1.46112	−	0.730174i
$235$	−5.45644			−0.355939
$236$	1.35275	+	1.01546i	0.0880565	+	0.0661006i
$237$		−	40.0070i		−	2.59874i
$238$	14.0439	+	6.00942i	0.910328	+	0.389533i
$239$	−11.3567			−0.734603			−0.367301	−	0.930102i	$-0.619718\pi$
$239$	−11.3567			−0.734603			−0.367301	+	0.930102i	$0.619718\pi$
$240$	2.94249	+	10.1204i	0.189937	+	0.653266i
$241$		−	13.1936i		−	0.849872i	−0.905223	−	0.424936i	$-0.860297\pi$
$241$		−	13.1936i		−	0.849872i	0.905223	−	0.424936i	$-0.139703\pi$
$242$	6.85562	+	13.7185i	0.440696	+	0.881857i
$243$	−10.6810			−0.685185
$244$	3.87481	−	5.16187i	0.248059	−	0.330455i
$245$	−0.125269			−0.00800317
$246$	−25.1580	+	12.5723i	−1.60401	+	0.801584i
$247$	−22.9284			−1.45890
$248$	−3.85632	+	21.1336i	−0.244876	+	1.34199i
$249$			16.7699i			1.06275i
$250$	−5.29806	−	10.6017i	−0.335078	−	0.670511i
$251$			5.00404i			0.315852i	0.987451	+	0.157926i	$0.0504808\pi$
$251$			5.00404i			0.315852i	−0.987451	+	0.157926i	$0.949519\pi$
$252$	22.2108	+	16.6728i	1.39915	+	1.05029i
$253$			0.273324i			0.0171837i
$254$	−3.83216	−	7.66836i	−0.240451	−	0.481156i
$255$	7.02382	+	8.28784i	0.439849	+	0.519005i
$256$	−13.5057	+	8.57879i	−0.844107	+	0.536174i
$257$	8.74846			0.545714			0.272857	−	0.962055i	$-0.412031\pi$
$257$	8.74846			0.545714			0.272857	+	0.962055i	$0.412031\pi$
$258$	7.95828	−	3.97704i	0.495461	−	0.247600i
$259$		−	23.5497i		−	1.46331i
$260$	4.87584	+	3.66010i	0.302387	+	0.226990i
$261$	−43.4652			−2.69043
$262$	−7.39027	−	14.7883i	−0.456572	−	0.913627i
$263$	−1.21644			−0.0750092			−0.0375046	−	0.999296i	$-0.511941\pi$
$263$	−1.21644			−0.0750092			−0.0375046	+	0.999296i	$0.511941\pi$
$264$	−3.16361	−	0.577274i	−0.194707	−	0.0355288i
$265$			6.62467i			0.406950i
$266$	−11.3924	−	22.7968i	−0.698512	−	1.39776i
$267$	6.14460			0.376044
$268$	13.1423	+	9.86542i	0.802795	+	0.602626i
$269$	−15.0991			−0.920606			−0.460303	−	0.887762i	$-0.652259\pi$
$269$	−15.0991			−0.920606			−0.460303	+	0.887762i	$0.652259\pi$
$270$	3.83216	+	7.66836i	0.233218	+	0.466682i
$271$	−23.1687			−1.40740			−0.703698	−	0.710499i	$-0.748469\pi$
$271$	−23.1687			−1.40740			−0.703698	+	0.710499i	$0.748469\pi$
$272$	−9.10456	+	13.7516i	−0.552045	+	0.833814i
$273$	25.1580			1.52263
$274$	−5.28656	−	10.5787i	−0.319373	−	0.639083i
$275$	1.64311			0.0990834
$276$	3.19167	+	2.39586i	0.192116	+	0.144214i
$277$	−11.3990			−0.684901			−0.342451	−	0.939536i	$-0.611257\pi$
$277$	−11.3990			−0.684901			−0.342451	+	0.939536i	$0.611257\pi$
$278$	6.01163	+	12.0296i	0.360554	+	0.721489i
$279$			40.2593i			2.41026i
$280$	−1.21644	+	6.66643i	−0.0726964	+	0.398396i
$281$	14.9812			0.893706			0.446853	−	0.894607i	$-0.352545\pi$
$281$	14.9812			0.893706			0.446853	+	0.894607i	$0.352545\pi$
$282$	−10.8669	−	21.7454i	−0.647117	−	1.29492i
$283$	15.7550			0.936535			0.468268	−	0.883587i	$-0.344878\pi$
$283$	15.7550			0.936535			0.468268	+	0.883587i	$0.344878\pi$
$284$	−14.2525	−	10.6988i	−0.845731	−	0.634857i
$285$		−	18.1246i		−	1.07361i
$286$	−1.66405	+	0.831585i	−0.0983973	+	0.0491726i
$287$	−18.0831			−1.06741
$288$	−22.0132	+	20.3593i	−1.29714	+	1.19968i
$289$	−2.78778	+	16.7699i	−0.163987	+	0.986462i
$290$	−4.74097	−	9.48695i	−0.278399	−	0.557093i
$291$			26.9071i			1.57732i
$292$	20.6584	+	15.5074i	1.20894	+	0.907504i
$293$			5.32864i			0.311303i	0.987812	+	0.155651i	$0.0497476\pi$
$293$			5.32864i			0.311303i	−0.987812	+	0.155651i	$0.950252\pi$
$294$	−0.249484	−	0.499232i	−0.0145502	−	0.0291158i
$295$			0.773461i			0.0450327i
$296$	25.0127	+	4.56414i	1.45383	+	0.265285i
$297$	−2.61571			−0.151779
$298$	−17.4039	+	8.69735i	−1.00818	+	0.503824i
$299$	2.30858			0.133508
$300$	14.4029	−	19.1870i	0.831553	−	1.10776i
$301$	5.72027			0.329711
$302$	−14.4951	−	29.0055i	−0.834098	−	1.66908i
$303$		−	23.4085i		−	1.34479i
$304$	26.4209	−	7.68189i	1.51535	−	0.440587i
$305$	2.95140			0.168997
$306$	−12.1590	+	28.4153i	−0.695085	+	1.62440i
$307$			24.1867i			1.38041i	0.723615	+	0.690204i	$0.242479\pi$
$307$			24.1867i			1.38041i	−0.723615	+	0.690204i	$0.757521\pi$
$308$	−1.65362	−	1.24131i	−0.0942239	−	0.0707302i
$309$	3.50467			0.199373
$310$	−8.78720	+	4.39128i	−0.499080	+	0.249408i
$311$		−	7.58124i		−	0.429893i	−0.976626	−	0.214946i	$-0.931042\pi$
$311$		−	7.58124i		−	0.429893i	0.976626	−	0.214946i	$-0.0689576\pi$
$312$	−4.87584	+	26.7209i	−0.276040	+	1.51277i
$313$			3.32634i			0.188016i	0.995571	+	0.0940079i	$0.0299679\pi$
$313$			3.32634i			0.188016i	−0.995571	+	0.0940079i	$0.970032\pi$
$314$	10.3801	−	5.18729i	0.585781	−	0.292736i
$315$			12.6995i			0.715533i
$316$	22.2108	+	16.6728i	1.24946	+	0.937917i
$317$	−16.6776			−0.936708			−0.468354	−	0.883541i	$-0.655153\pi$
$317$	−16.6776			−0.936708			−0.468354	+	0.883541i	$0.655153\pi$
$318$	−26.4011	+	13.1936i	−1.48050	+	0.739858i
$319$	3.23604			0.181183
$320$	−6.84481	−	2.58403i	−0.382637	−	0.144451i
$321$	−7.41983			−0.414135
$322$	1.14706	+	2.29533i	0.0639230	+	0.127914i
$323$	21.6368	−	18.3369i	1.20391	−	1.02029i
$324$	−3.83554	+	5.10955i	−0.213085	+	0.283864i
$325$		−	13.8782i		−	0.769826i
$326$	8.32428	+	16.6574i	0.461039	+	0.922566i
$327$	0.360911			0.0199584
$328$	3.50467	−	19.2065i	0.193513	−	1.06050i
$329$		−	15.6302i		−	0.861720i
$330$	−0.657356	−	1.31541i	−0.0361863	−	0.0724108i
$331$		−	6.59903i		−	0.362716i	−0.983417	−	0.181358i	$-0.941951\pi$
$331$		−	6.59903i		−	0.362716i	0.983417	−	0.181358i	$-0.0580492\pi$
$332$	−9.31016	−	6.98877i	−0.510962	−	0.383559i
$333$	47.6488			2.61114
$334$	23.0870	−	11.5374i	1.26326	−	0.631298i
$335$			7.51438i			0.410554i
$336$	−28.9901	+	8.42888i	−1.58154	+	0.459833i
$337$			4.79977i			0.261460i	0.991418	+	0.130730i	$0.0417321\pi$
$337$			4.79977i			0.261460i	−0.991418	+	0.130730i	$0.958268\pi$
$338$	−1.19462	−	2.39051i	−0.0649789	−	0.130027i
$339$			8.78256i			0.477003i
$340$	−7.52833	+	0.445510i	−0.408281	+	0.0241612i
$341$		−	2.99735i		−	0.162316i
$342$	46.1254	−	23.0505i	2.49418	−	1.24643i
$343$		−	18.6970i		−	1.00954i
$344$	−1.10864	+	6.07563i	−0.0597738	+	0.327576i
$345$			1.82490i			0.0982492i
$346$	10.9810	+	21.9736i	0.590343	+	1.18131i
$347$	22.8318			1.22568			0.612838	−	0.790208i	$-0.290028\pi$
$347$	22.8318			1.22568			0.612838	+	0.790208i	$0.290028\pi$
$348$	28.3660	−	37.7880i	1.52058	−	2.02565i
$349$			1.18518i			0.0634410i	0.999497	+	0.0317205i	$0.0100986\pi$
$349$			1.18518i			0.0634410i	−0.999497	+	0.0317205i	$0.989901\pi$
$350$	13.7986	−	6.89564i	0.737565	−	0.368588i
$351$			22.0931i			1.17924i
$352$	1.63891	−	1.51577i	0.0873542	−	0.0807911i
$353$	−18.3660			−0.977522			−0.488761	−	0.872418i	$-0.662551\pi$
$353$	−18.3660			−0.977522			−0.488761	+	0.872418i	$0.662551\pi$
$354$	−3.08245	+	1.54041i	−0.163830	+	0.0818718i
$355$		−	8.14916i		−	0.432512i
$356$	−2.56074	+	3.41131i	−0.135719	+	0.180799i
$357$	−23.7408	+	20.1200i	−1.25650	+	1.06486i
$358$	7.48550	−	3.74077i	0.395621	−	0.197706i
$359$	−29.6867			−1.56681			−0.783403	−	0.621514i	$-0.786518\pi$
$359$	−29.6867			−1.56681			−0.783403	+	0.621514i	$0.786518\pi$
$360$	−13.4884	−	2.46127i	−0.710900	−	0.129720i
$361$	−28.3174			−1.49039
$362$	0.0178463	+	0.0357114i	0.000937978	+	0.00187695i
$363$	−31.2431			−1.63984
$364$	−10.4845	+	13.9670i	−0.549536	+	0.732071i
$365$			11.8118i			0.618259i
$366$	5.87794	+	11.7621i	0.307245	+	0.614815i
$367$		−	10.9076i		−	0.569371i	−0.958621	−	0.284685i	$-0.908111\pi$
$367$		−	10.9076i		−	0.569371i	0.958621	−	0.284685i	$-0.0918891\pi$
$368$	−2.66023	+	0.773461i	−0.138674	+	0.0403195i
$369$		−	36.5881i		−	1.90470i
$370$	5.19730	+	10.4001i	0.270195	+	0.540675i
$371$	−18.9766			−0.985217
$372$	−35.0008	−	26.2737i	−1.81471	−	1.36223i
$373$		−	6.36248i		−	0.329437i	−0.986341	−	0.164718i	$-0.947328\pi$
$373$		−	6.36248i		−	0.329437i	0.986341	−	0.164718i	$-0.0526716\pi$
$374$	0.905255	−	2.11556i	0.0468096	−	0.109393i
$375$	24.1449			1.24683
$376$	16.6012	+	3.02927i	0.856140	+	0.156222i
$377$		−	27.3326i		−	1.40770i
$378$	−21.9663	+	10.9774i	−1.12983	+	0.564614i
$379$	−1.63260			−0.0838610			−0.0419305	−	0.999121i	$-0.513351\pi$
$379$	−1.63260			−0.0838610			−0.0419305	+	0.999121i	$0.513351\pi$
$380$	10.0623	+	7.55335i	0.516183	+	0.387478i
$381$	17.4643			0.894724
$382$	0.997185	+	1.99542i	0.0510204	+	0.102095i
$383$	30.2066			1.54348			0.771742	−	0.635935i	$-0.219386\pi$
$383$	30.2066			1.54348			0.771742	+	0.635935i	$0.219386\pi$
$384$	−3.33397	−	32.4247i	−0.170136	−	1.65467i
$385$		−	0.945491i		−	0.0481867i
$386$	−5.29806	+	2.64763i	−0.269664	+	0.134761i
$387$			11.5740i			0.588339i
$388$	−14.9381	−	11.2134i	−0.758367	−	0.569276i
$389$			20.5447i			1.04166i	0.853662	+	0.520828i	$0.174377\pi$
$389$			20.5447i			1.04166i	−0.853662	+	0.520828i	$0.825623\pi$
$390$	−11.1103	+	5.55223i	−0.562594	+	0.281148i
$391$	−2.17853	+	1.84628i	−0.110173	+	0.0933702i
$392$	0.381131	+	0.0695462i	0.0192500	+	0.00351261i
$393$	33.6797			1.69892
$394$	9.35219	+	18.7143i	0.471157	+	0.942811i
$395$			12.6995i			0.638979i
$396$	2.51158	−	3.34582i	0.126211	−	0.168134i
$397$	8.57201			0.430217			0.215108	−	0.976590i	$-0.430990\pi$
$397$	8.57201			0.430217			0.215108	+	0.976590i	$0.430990\pi$
$398$	−11.3607	+	5.67733i	−0.569458	+	0.284579i
$399$	51.9186			2.59918
$400$	4.64974	+	15.9922i	0.232487	+	0.799611i
$401$		−	22.4490i		−	1.12105i	−0.828137	−	0.560526i	$-0.810599\pi$
$401$		−	22.4490i		−	1.12105i	0.828137	−	0.560526i	$-0.189401\pi$
$402$	−29.9468	+	14.9655i	−1.49361	+	0.746410i
$403$	−25.3166			−1.26111
$404$	12.9958	+	9.75541i	0.646564	+	0.485350i
$405$	−2.92149			−0.145170
$406$	27.1757	−	13.5807i	1.34871	−	0.673998i
$407$	−3.54752			−0.175844
$408$	−16.7687	−	29.1151i	−0.830176	−	1.44141i
$409$	−0.486167			−0.0240394			−0.0120197	−	0.999928i	$-0.503826\pi$
$409$	−0.486167			−0.0240394			−0.0120197	+	0.999928i	$0.503826\pi$
$410$	7.98591	−	3.99085i	0.394396	−	0.197094i
$411$	24.0925			1.18839
$412$	−1.46056	+	1.94569i	−0.0719564	+	0.0958574i
$413$	−2.21561			−0.109023
$414$	−4.64420	+	2.32087i	−0.228250	+	0.114065i
$415$		−	5.32327i		−	0.261309i
$416$	−12.8027	−	13.8427i	−0.627704	−	0.678696i
$417$	−27.3968			−1.34163
$418$	−3.43410	+	1.71614i	−0.167967	+	0.0839393i
$419$	1.30253			0.0636328			0.0318164	−	0.999494i	$-0.489871\pi$
$419$	1.30253			0.0636328			0.0318164	+	0.999494i	$0.489871\pi$
$420$	−11.0407	−	8.28784i	−0.538733	−	0.404405i
$421$			6.97038i			0.339716i	0.985469	+	0.169858i	$0.0543309\pi$
$421$			6.97038i			0.339716i	−0.985469	+	0.169858i	$0.945669\pi$
$422$	−6.25342	−	12.5134i	−0.304412	−	0.609145i
$423$	31.6250			1.53766
$424$	3.67783	−	20.1555i	0.178611	−	0.978837i
$425$	11.0991	+	13.0965i	0.538384	+	0.635272i
$426$	32.4765	−	16.2297i	1.57349	−	0.786331i
$427$			8.45439i			0.409137i
$428$	3.09218	−	4.11928i	0.149466	−	0.199113i
$429$		−	3.78979i		−	0.182973i
$430$	−2.52620	+	1.26243i	−0.121824	+	0.0608800i
$431$			15.2713i			0.735595i	0.929906	+	0.367797i	$0.119888\pi$
$431$			15.2713i			0.735595i	−0.929906	+	0.367797i	$0.880112\pi$
$432$	−7.40204	−	25.4584i	−0.356131	−	1.22487i
$433$	7.73815			0.371872			0.185936	−	0.982562i	$-0.440468\pi$
$433$	7.73815			0.371872			0.185936	+	0.982562i	$0.440468\pi$
$434$	−12.5790	−	25.1713i	−0.603811	−	1.20826i
$435$	21.6060			1.03593
$436$	−0.150408	+	0.200368i	−0.00720324	+	0.00959587i
$437$	4.76421			0.227903
$438$	−47.0733	+	23.5242i	−2.24925	+	1.12403i
$439$		−	1.48006i		−	0.0706396i	−0.999376	−	0.0353198i	$-0.988755\pi$
$439$		−	1.48006i		−	0.0706396i	0.999376	−	0.0353198i	$-0.0112450\pi$
$440$	1.00423	+	0.183244i	0.0478747	+	0.00873584i
$441$	0.726050			0.0345738
$442$	−17.8687	−	7.64607i	−0.849926	−	0.363686i
$443$			1.47915i			0.0702763i	0.999382	+	0.0351382i	$0.0111871\pi$
$443$			1.47915i			0.0702763i	−0.999382	+	0.0351382i	$0.988813\pi$
$444$	−31.0963	+	41.4252i	−1.47576	+	1.96595i
$445$	−1.95049			−0.0924619
$446$	−11.8723	−	23.7572i	−0.562170	−	1.12493i
$447$		−	39.6365i		−	1.87474i
$448$	7.40204	−	19.6072i	0.349714	−	0.926354i
$449$			25.4974i			1.20330i	0.798761	+	0.601648i	$0.205489\pi$
$449$			25.4974i			1.20330i	−0.798761	+	0.601648i	$0.794511\pi$
$450$	13.9522	+	27.9190i	0.657711	+	1.31612i
$451$			2.72403i			0.128270i
$452$	−4.87584	−	3.66010i	−0.229340	−	0.172157i
$453$	66.0584			3.10370
$454$	−7.82531	−	15.6589i	−0.367260	−	0.734908i
$455$	−7.98591			−0.374385
$456$	−10.0623	+	55.1439i	−0.471209	+	2.58235i
$457$	16.3393			0.764322			0.382161	−	0.924096i	$-0.375180\pi$
$457$	16.3393			0.764322			0.382161	+	0.924096i	$0.375180\pi$
$458$	5.67722	−	2.83711i	0.265279	−	0.132570i
$459$	−17.6689	−	20.8486i	−0.824714	−	0.973130i
$460$	−1.01313	−	0.760519i	−0.0472376	−	0.0354594i
$461$		−	39.5505i		−	1.84205i	−0.389504	−	0.921025i	$-0.627354\pi$
$461$		−	39.5505i		−	1.84205i	0.389504	−	0.921025i	$-0.372646\pi$
$462$	3.76803	−	1.88302i	0.175305	−	0.0876061i
$463$	−16.4805			−0.765916			−0.382958	−	0.923766i	$-0.625095\pi$
$463$	−16.4805			−0.765916			−0.382958	+	0.923766i	$0.625095\pi$
$464$	9.15746	+	31.4960i	0.425125	+	1.46217i
$465$		−	20.0124i		−	0.928053i
$466$	38.3273	−	19.1535i	1.77548	−	0.887270i
$467$		−	21.7908i		−	1.00836i	−0.863599	−	0.504180i	$-0.831795\pi$
$467$		−	21.7908i		−	1.00836i	0.863599	−	0.504180i	$-0.168205\pi$
$468$	−28.2599	−	21.2136i	−1.30631	−	0.980597i
$469$	−21.5252			−0.993942
$470$	3.44950	+	6.90264i	0.159114	+	0.318395i
$471$			23.6401i			1.08928i
$472$	0.429404	−	2.35325i	0.0197649	−	0.108317i
$473$		−	0.861699i		−	0.0396210i
$474$	−50.6107	+	25.2920i	−2.32463	+	1.16170i
$475$		−	28.6405i		−	1.31412i
$476$	−1.27618	−	21.5652i	−0.0584936	−	0.988438i
$477$		−	38.3959i		−	1.75803i
$478$	7.17956	+	14.3667i	0.328386	+	0.657118i
$479$		−	16.0773i		−	0.734589i	−0.930105	−	0.367294i	$-0.880284\pi$
$479$		−	16.0773i		−	0.734589i	0.930105	−	0.367294i	$-0.119716\pi$
$480$	10.9425	−	10.1204i	0.499454	−	0.461929i
$481$			29.9634i			1.36621i
$482$	−16.6904	+	8.34081i	−0.760229	+	0.379914i
$483$	−5.22749			−0.237859
$484$	13.0204	−	17.3453i	0.591838	−	0.788424i
$485$		−	8.54115i		−	0.387834i
$486$	6.75238	+	13.5119i	0.306294	+	0.612912i
$487$			12.9045i			0.584759i	0.956302	+	0.292379i	$0.0944470\pi$
$487$			12.9045i			0.584759i	−0.956302	+	0.292379i	$0.905553\pi$
$488$	−8.97960	−	1.63853i	−0.406487	−	0.0741730i
$489$	−37.9363			−1.71554
$490$	0.0791939	+	0.158472i	0.00357762	+	0.00715901i
$491$			20.8195i			0.939572i	0.882780	+	0.469786i	$0.155669\pi$
$491$			20.8195i			0.939572i	−0.882780	+	0.469786i	$0.844331\pi$
$492$	31.8092	+	23.8779i	1.43407	+	1.07650i
$493$	21.8592	+	25.7929i	0.984487	+	1.16166i
$494$	14.4951	+	29.0055i	0.652164	+	1.30502i
$495$	1.91304			0.0859847
$496$	29.1729	−	8.48202i	1.30990	−	0.380854i
$497$	23.3436			1.04710
$498$	21.2146	−	10.6017i	0.950650	−	0.475074i
$499$	−8.55725			−0.383075			−0.191538	−	0.981485i	$-0.561347\pi$
$499$	−8.55725			−0.383075			−0.191538	+	0.981485i	$0.561347\pi$
$500$	−10.0623	+	13.4046i	−0.449998	+	0.599470i
$501$			52.5794i			2.34907i
$502$	6.33034	−	3.16350i	0.282537	−	0.141194i
$503$			13.8721i			0.618529i	0.950976	+	0.309264i	$0.100083\pi$
$503$			13.8721i			0.618529i	−0.950976	+	0.309264i	$0.899917\pi$
$504$	7.05039	−	38.6380i	0.314049	−	1.72107i
$505$			7.43059i			0.330657i
$506$	0.345767	−	0.172792i	0.0153712	−	0.00768154i
$507$	5.44426			0.241788
$508$	−7.27818	+	9.69570i	−0.322917	+	0.430177i
$509$			33.4031i			1.48057i	0.672294	+	0.740284i	$0.265309\pi$
$509$			33.4031i			1.48057i	−0.672294	+	0.740284i	$0.734691\pi$
$510$	6.04411	−	14.1249i	0.267638	−	0.625462i
$511$	−33.8354			−1.49679
$512$	19.3907	+	11.6619i	0.856956	+	0.515389i
$513$			45.5936i			2.01301i
$514$	−5.53067	−	11.0672i	−0.243948	−	0.488153i
$515$	−1.11249			−0.0490221
$516$	−10.0623	−	7.55335i	−0.442967	−	0.332518i
$517$	−2.35452			−0.103552
$518$	−29.7914	+	14.8879i	−1.30896	+	0.654135i
$519$	−50.0438			−2.19668
$520$	1.54774	−	8.48202i	0.0678729	−	0.371961i
$521$			4.79977i			0.210282i	0.994457	+	0.105141i	$0.0335294\pi$
$521$			4.79977i			0.210282i	−0.994457	+	0.105141i	$0.966471\pi$
$522$	27.4782	+	54.9854i	1.20269	+	2.40665i
$523$		−	19.6747i		−	0.860315i	−0.902754	−	0.430157i	$-0.858458\pi$
$523$		−	19.6747i		−	0.860315i	0.902754	−	0.430157i	$-0.141542\pi$
$524$	−14.0359	+	18.6980i	−0.613160	+	0.816827i
$525$			31.4255i			1.37152i
$526$	0.769022	+	1.53886i	0.0335309	+	0.0670973i
$527$	23.8905	−	20.2469i	1.04069	−	0.881967i
$528$	1.26972	+	4.36706i	0.0552576	+	0.190052i
$529$	22.5203			0.979144
$530$	8.38050	−	4.18804i	0.364026	−	0.181917i
$531$		−	4.48290i		−	0.194541i
$532$	−21.6368	+	28.8237i	−0.938076	+	1.24967i
$533$	23.0080			0.996588
$534$	−3.88455	−	7.77320i	−0.168101	−	0.336379i
$535$	2.35528			0.101828
$536$	4.17177	−	22.8624i	0.180193	−	0.987506i
$537$			17.0478i			0.735668i
$538$	9.54545	+	19.1010i	0.411534	+	0.823502i
$539$	−0.0540553			−0.00232833
$540$	7.27818	−	9.69570i	0.313203	−	0.417237i
$541$	−29.2109			−1.25588			−0.627938	−	0.778264i	$-0.716101\pi$
$541$	−29.2109			−1.25588			−0.627938	+	0.778264i	$0.716101\pi$
$542$	14.6470	+	29.3094i	0.629141	+	1.25895i
$543$	−0.0813308			−0.00349024
$544$	23.1522	+	2.82406i	0.992643	+	0.121081i
$545$	−0.114564			−0.00490739
$546$	−15.9046	−	31.8260i	−0.680653	−	1.36203i
$547$	−25.7356			−1.10037			−0.550187	−	0.835041i	$-0.685444\pi$
$547$	−25.7356			−1.10037			−0.550187	+	0.835041i	$0.685444\pi$
$548$	−10.0404	+	13.3755i	−0.428906	+	0.571372i
$549$	−17.1060			−0.730067
$550$	−1.03876	−	2.07861i	−0.0442927	−	0.0886322i
$551$		−	56.4063i		−	2.40299i
$552$	1.01313	−	5.55223i	0.0431218	−	0.236319i
$553$	−36.3781			−1.54695
$554$	7.20633	+	14.4203i	0.306168	+	0.612659i
$555$	−23.6857			−1.00540
$556$	11.4175	−	15.2100i	0.484211	−	0.645046i
$557$			35.2863i			1.49513i	0.664189	+	0.747564i	$0.268777\pi$
$557$			35.2863i			1.49513i	−0.664189	+	0.747564i	$0.731223\pi$
$558$	50.9298	−	25.4514i	2.15603	−	1.07745i
$559$	−7.27818			−0.307834
$560$	9.20236	−	2.67559i	0.388871	−	0.113064i
$561$	3.03087	+	3.57631i	0.127963	+	0.150992i
$562$	−9.47096	−	18.9519i	−0.399508	−	0.799439i
$563$			2.53721i			0.106931i	0.998570	+	0.0534653i	$0.0170267\pi$
$563$			2.53721i			0.106931i	−0.998570	+	0.0534653i	$0.982973\pi$
$564$	−20.6389	+	27.4943i	−0.869055	+	1.15772i
$565$		−	2.78785i		−	0.117286i
$566$	−9.96010	−	19.9307i	−0.418654	−	0.837751i
$567$		−	8.36870i		−	0.351453i
$568$	−4.52419	+	24.7937i	−0.189831	+	1.04032i
$569$	−16.8308			−0.705582			−0.352791	−	0.935702i	$-0.614767\pi$
$569$	−16.8308			−0.705582			−0.352791	+	0.935702i	$0.614767\pi$
$570$	−22.9284	+	11.4581i	−0.960365	+	0.479929i
$571$	−24.0698			−1.00729			−0.503645	−	0.863911i	$-0.668008\pi$
$571$	−24.0698			−1.00729			−0.503645	+	0.863911i	$0.668008\pi$
$572$	2.10398	+	1.57938i	0.0879720	+	0.0660371i
$573$	−4.54448			−0.189848
$574$	11.4319	+	22.8760i	0.477160	+	0.954824i
$575$			2.88371i			0.120259i
$576$	39.6719	+	14.9768i	1.65299	+	0.624032i
$577$	−12.9635			−0.539678			−0.269839	−	0.962905i	$-0.586970\pi$
$577$	−12.9635			−0.539678			−0.269839	+	0.962905i	$0.586970\pi$
$578$	22.9770	−	7.07504i	0.955718	−	0.294283i
$579$		−	12.0661i		−	0.501448i
$580$	−9.00423	+	11.9951i	−0.373880	+	0.498068i
$581$	15.2487			0.632623
$582$	34.0387	−	17.0104i	1.41095	−	0.705103i
$583$			2.85863i			0.118392i
$584$	6.55760	−	35.9374i	0.271356	−	1.48710i
$585$		−	16.1581i		−	0.668056i
$586$	6.74097	−	3.36870i	0.278467	−	0.139160i
$587$		−	18.8738i		−	0.779007i	−0.921025	−	0.389503i	$-0.872647\pi$
$587$		−	18.8738i		−	0.779007i	0.921025	−	0.389503i	$-0.127353\pi$
$588$	−0.473830	+	0.631217i	−0.0195404	+	0.0260310i
$589$	−52.2459			−2.15275
$590$	0.978463	−	0.488973i	0.0402827	−	0.0201307i
$591$	−42.6208			−1.75318
$592$	−10.0389	−	34.5276i	−0.412596	−	1.41907i
$593$	−10.5540			−0.433400			−0.216700	−	0.976238i	$-0.569529\pi$
$593$	−10.5540			−0.433400			−0.216700	+	0.976238i	$0.569529\pi$
$594$	1.65362	+	3.30899i	0.0678490	+	0.135770i
$595$	7.53607	−	6.38671i	0.308949	−	0.261829i
$596$	22.0051	+	16.5183i	0.901362	+	0.676617i
$597$		−	25.8733i		−	1.05892i
$598$	−1.45946	−	2.92045i	−0.0596816	−	0.119426i
$599$	7.27818			0.297378			0.148689	−	0.988884i	$-0.452495\pi$
$599$	7.27818			0.297378			0.148689	+	0.988884i	$0.452495\pi$
$600$	−33.3778	−	6.09054i	−1.36264	−	0.248645i
$601$		−	15.4360i		−	0.629648i	−0.949150	−	0.314824i	$-0.898055\pi$
$601$		−	15.4360i		−	0.629648i	0.949150	−	0.314824i	$-0.101945\pi$
$602$	−3.61629	−	7.23640i	−0.147389	−	0.294934i
$603$		−	43.5526i		−	1.77360i
$604$	−27.5296	+	36.6738i	−1.12016	+	1.49224i
$605$	9.91752			0.403205
$606$	−29.6128	+	14.7986i	−1.20294	+	0.601152i
$607$			27.2414i			1.10570i	0.833282	+	0.552848i	$0.186459\pi$
$607$			27.2414i			1.10570i	−0.833282	+	0.552848i	$0.813541\pi$
$608$	−26.4209	−	28.5673i	−1.07151	−	1.15856i
$609$			61.8913i			2.50796i
$610$	−1.86584	−	3.73365i	−0.0755456	−	0.151171i
$611$			19.8870i			0.804543i
$612$	43.6334	−	2.58213i	1.76378	−	0.104377i
$613$		−	37.9406i		−	1.53241i	−0.642597	−	0.766204i	$-0.722143\pi$
$613$		−	37.9406i		−	1.53241i	0.642597	−	0.766204i	$-0.277857\pi$
$614$	30.5972	−	15.2905i	1.23480	−	0.617076i
$615$			18.1875i			0.733391i
$616$	−0.524911	+	2.87665i	−0.0211493	+	0.115903i
$617$			5.48500i			0.220818i	0.993886	+	0.110409i	$0.0352160\pi$
$617$			5.48500i			0.220818i	−0.993886	+	0.110409i	$0.964784\pi$
$618$	−2.21561	−	4.43356i	−0.0891249	−	0.178344i
$619$	−20.0245			−0.804854			−0.402427	−	0.915452i	$-0.631833\pi$
$619$	−20.0245			−0.804854			−0.402427	+	0.915452i	$0.631833\pi$
$620$	11.1103	+	8.34009i	0.446202	+	0.334946i
$621$		−	4.59065i		−	0.184217i
$622$	−9.59060	+	4.79277i	−0.384548	+	0.192173i
$623$		−	5.58724i		−	0.223848i
$624$	36.8855	−	10.7245i	1.47660	−	0.429322i
$625$	13.1538			0.526150
$626$	4.20797	−	2.10287i	0.168184	−	0.0840477i
$627$		−	7.82098i		−	0.312340i
$628$	−13.1243	−	9.85189i	−0.523717	−	0.393133i
$629$	−23.9631	−	28.2756i	−0.955473	−	1.12742i
$630$	16.0654	−	8.02845i	0.640060	−	0.319861i
$631$	15.9607			0.635385			0.317692	−	0.948194i	$-0.397092\pi$
$631$	15.9607			0.635385			0.317692	+	0.948194i	$0.397092\pi$
$632$	7.05039	−	38.6380i	0.280449	−	1.53694i
$633$	28.4987			1.13272
$634$	10.5434	+	21.0979i	0.418732	+	0.837906i
$635$	−5.54371			−0.219995
$636$	33.3809	+	25.0577i	1.32364	+	0.993602i
$637$			0.456568i			0.0180899i
$638$	−2.04579	−	4.09374i	−0.0809935	−	0.162073i
$639$			47.2317i			1.86846i
$640$	1.05830	+	10.2926i	0.0418331	+	0.406850i
$641$		−	34.2910i		−	1.35441i	−0.735792	−	0.677207i	$-0.763190\pi$
$641$		−	34.2910i		−	1.35441i	0.735792	−	0.677207i	$-0.236810\pi$
$642$	4.69073	+	9.38642i	0.185128	+	0.370452i
$643$	41.8852			1.65179			0.825895	−	0.563824i	$-0.190670\pi$
$643$	41.8852			1.65179			0.825895	+	0.563824i	$0.190670\pi$
$644$	2.17853	−	2.90216i	0.0858463	−	0.114361i
$645$		−	5.75330i		−	0.226536i
$646$	−36.8756	−	15.7792i	−1.45085	−	0.620824i
$647$	34.2851			1.34789			0.673943	−	0.738783i	$-0.264599\pi$
$647$	34.2851			1.34789			0.673943	+	0.738783i	$0.264599\pi$
$648$	8.88859	+	1.62193i	0.349177	+	0.0637153i
$649$			0.333758i			0.0131012i
$650$	−17.5566	+	8.77365i	−0.688626	+	0.344131i
$651$	57.3263			2.24679
$652$	15.8098	−	21.0612i	0.619159	−	0.824819i
$653$	−24.3189			−0.951671			−0.475835	−	0.879534i	$-0.657854\pi$
$653$	−24.3189			−0.951671			−0.475835	+	0.879534i	$0.657854\pi$
$654$	−0.228164	−	0.456568i	−0.00892190	−	0.0178532i
$655$	−10.6910			−0.417731
$656$	−26.5127	+	7.70856i	−1.03515	+	0.300969i
$657$		−	68.4602i		−	2.67089i
$658$	−19.7729	+	9.88122i	−0.770827	+	0.385210i
$659$			25.7077i			1.00143i	0.865612	+	0.500715i	$0.166930\pi$
$659$			25.7077i			1.00143i	−0.865612	+	0.500715i	$0.833070\pi$
$660$	−1.24848	+	1.66317i	−0.0485968	+	0.0647388i
$661$		−	30.6153i		−	1.19080i	−0.803431	−	0.595398i	$-0.796994\pi$
$661$		−	30.6153i		−	1.19080i	0.803431	−	0.595398i	$-0.203006\pi$
$662$	−8.34807	+	4.17183i	−0.324457	+	0.162143i
$663$	30.2066	−	25.5996i	1.17313	−	0.994208i
$664$	−2.95533	+	16.1960i	−0.114689	+	0.628526i
$665$	−16.4805			−0.639088
$666$	−30.1230	−	60.2779i	−1.16724	−	2.33572i
$667$			5.67934i			0.219905i
$668$	−29.1906	−	21.9122i	−1.12942	−	0.847810i
$669$	54.1058			2.09185
$670$	9.50602	−	4.75050i	0.367250	−	0.183528i
$671$	1.27356			0.0491654
$672$	28.9901	+	31.3452i	1.11832	+	1.20917i
$673$		−	14.1390i		−	0.545020i	−0.962153	−	0.272510i	$-0.912146\pi$
$673$		−	14.1390i		−	0.545020i	0.962153	−	0.272510i	$-0.0878538\pi$
$674$	6.07193	−	3.03436i	0.233882	−	0.116879i
$675$	−27.5971			−1.06221
$676$	−2.26887	+	3.02250i	−0.0872644	+	0.116250i
$677$	51.4284			1.97655			0.988276	−	0.152676i	$-0.0487891\pi$
$677$	51.4284			1.97655			0.988276	+	0.152676i	$0.0487891\pi$
$678$	11.1103	−	5.55223i	0.426690	−	0.213232i
$679$	24.4665			0.938936
$680$	5.32291	+	9.24203i	0.204124	+	0.354416i
$681$	35.6623			1.36658
$682$	−3.79179	+	1.89489i	−0.145195	+	0.0725592i
$683$	−27.1781			−1.03994			−0.519971	−	0.854184i	$-0.674057\pi$
$683$	−27.1781			−1.03994			−0.519971	+	0.854184i	$0.674057\pi$
$684$	−58.3199	−	43.7784i	−2.22992	−	1.67391i
$685$	−7.64769			−0.292203
$686$	−23.6525	+	11.8200i	−0.903058	+	0.451291i
$687$			12.9296i			0.493294i
$688$	8.38682	−	2.43847i	0.319744	−	0.0929657i
$689$	24.1449			0.919846
$690$	2.30858	−	1.15368i	0.0878860	−	0.0439198i
$691$	3.22165			0.122558			0.0612788	−	0.998121i	$-0.480482\pi$
$691$	3.22165			0.122558			0.0612788	+	0.998121i	$0.480482\pi$
$692$	20.8556	−	27.7829i	0.792809	−	1.05615i
$693$			5.47997i			0.208167i
$694$	−14.4340	−	28.8833i	−0.547908	−	1.09639i
$695$	8.69660			0.329881
$696$	−65.7362	−	11.9951i	−2.49172	−	0.454672i
$697$	−21.7120	+	18.4006i	−0.822399	+	0.696972i
$698$	1.49930	−	0.749254i	0.0567493	−	0.0283597i
$699$			87.2884i			3.30155i
$700$	−17.4466	−	13.0965i	−0.659419	−	0.495000i
$701$			1.41005i			0.0532570i	0.999645	+	0.0266285i	$0.00847711\pi$
$701$			1.41005i			0.0532570i	−0.999645	+	0.0266285i	$0.991523\pi$
$702$	27.9488	−	13.9670i	1.05486	−	0.527151i
$703$			61.8355i			2.33217i
$704$	−2.95362	−	1.11504i	−0.111319	−	0.0420246i
$705$	−15.7204			−0.592065
$706$	11.6108	+	23.2338i	0.436976	+	0.874415i
$707$	−21.2852			−0.800512
$708$	3.89737	+	2.92560i	0.146472	+	0.109951i
$709$	25.1808			0.945685			0.472843	−	0.881147i	$-0.343228\pi$
$709$	25.1808			0.945685			0.472843	+	0.881147i	$0.343228\pi$
$710$	−10.3090	+	5.15180i	−0.386892	+	0.193344i
$711$		−	73.6048i		−	2.76040i
$712$	5.93433	+	1.08286i	0.222399	+	0.0405817i
$713$	5.26044			0.197005
$714$	40.4614	+	17.3136i	1.51423	+	0.647944i
$715$			1.20299i			0.0449894i
$716$	−9.46449	−	7.10462i	−0.353705	−	0.265512i
$717$	−32.7194			−1.22193
$718$	18.7676	+	37.5550i	0.700401	+	1.40154i
$719$			7.85921i			0.293099i	0.989203	+	0.146550i	$0.0468168\pi$
$719$			7.85921i			0.293099i	−0.989203	+	0.146550i	$0.953183\pi$
$720$	5.41359	+	18.6194i	0.201753	+	0.693904i
$721$		−	3.18676i		−	0.118681i
$722$	17.9019	+	35.8227i	0.666240	+	1.33318i
$723$		−	38.0116i		−	1.41367i
$724$	0.0338943	−	0.0451526i	0.00125967	−	0.00167808i
$725$	34.1419			1.26800
$726$	19.7515	+	39.5240i	0.733048	+	1.46687i
$727$	29.0856			1.07872			0.539362	−	0.842074i	$-0.318666\pi$
$727$	29.0856			1.07872			0.539362	+	0.842074i	$0.318666\pi$
$728$	24.2971	+	4.43356i	0.900509	+	0.164319i
$729$	−40.3561			−1.49467
$730$	14.9425	−	7.46730i	0.553047	−	0.276377i
$731$	6.86820	−	5.82070i	0.254029	−	0.215286i
$732$	11.1636	−	14.8717i	0.412619	−	0.549675i
$733$			44.2534i			1.63454i	0.576257	+	0.817268i	$0.304513\pi$
$733$			44.2534i			1.63454i	−0.576257	+	0.817268i	$0.695487\pi$
$734$	−13.7986	+	6.89564i	−0.509315	+	0.254523i
$735$	−0.360911			−0.0133124
$736$	2.66023	+	2.87633i	0.0980573	+	0.106023i
$737$			3.24255i			0.119441i
$738$	−46.2856	+	23.1306i	−1.70380	+	0.851448i
$739$			9.90803i			0.364473i	0.983255	+	0.182236i	$0.0583336\pi$
$739$			9.90803i			0.364473i	−0.983255	+	0.182236i	$0.941666\pi$
$740$	9.87090	−	13.1496i	0.362862	−	0.483390i
$741$	−66.0584			−2.42672
$742$	11.9968	+	24.0063i	0.440416	+	0.881298i
$743$			8.20698i			0.301085i	0.988604	+	0.150542i	$0.0481020\pi$
$743$			8.20698i			0.301085i	−0.988604	+	0.150542i	$0.951898\pi$
$744$	−11.1103	+	60.8876i	−0.407325	+	2.23225i
$745$			12.5818i			0.460962i
$746$	−8.04883	+	4.02229i	−0.294688	+	0.147266i
$747$			30.8531i			1.12886i
$748$	−3.24857	+	0.192243i	−0.118779	+	0.00702910i
$749$			6.74679i			0.246522i
$750$	−15.2641	−	30.5443i	−0.557366	−	1.11532i
$751$			38.5403i			1.40636i	0.711014	+	0.703178i	$0.248236\pi$
$751$			38.5403i			1.40636i	−0.711014	+	0.703178i	$0.751764\pi$
$752$	−6.66291	−	22.9163i	−0.242971	−	0.835671i
$753$			14.4170i			0.525386i
$754$	−34.5770	+	17.2794i	−1.25922	+	0.629277i
$755$	−20.9690			−0.763139
$756$	27.7737	+	20.8486i	1.01012	+	0.758257i
$757$		−	35.8329i		−	1.30237i	−0.758919	−	0.651185i	$-0.774272\pi$
$757$		−	35.8329i		−	1.30237i	0.758919	−	0.651185i	$-0.225728\pi$
$758$	1.03211	+	2.06531i	0.0374879	+	0.0750154i
$759$			0.787466i			0.0285832i
$760$	3.19407	−	17.5044i	0.115861	−	0.634950i
$761$	32.5072			1.17838			0.589192	−	0.807993i	$-0.299446\pi$
$761$	32.5072			1.17838			0.589192	+	0.807993i	$0.299446\pi$
$762$	−11.0407	−	22.0931i	−0.399963	−	0.800350i
$763$		−	0.328173i		−	0.0118807i
$764$	1.89389	−	2.52297i	0.0685186	−	0.0912778i
$765$	12.9224	+	15.2479i	0.467211	+	0.551290i
$766$	−19.0963	−	38.2127i	−0.689976	−	1.38068i
$767$	2.81902			0.101789
$768$	−38.9110	+	24.7161i	−1.40408	+	0.891866i
$769$	−40.7372			−1.46902			−0.734511	−	0.678597i	$-0.762588\pi$
$769$	−40.7372			−1.46902			−0.734511	+	0.678597i	$0.762588\pi$
$770$	−1.19609	+	0.597729i	−0.0431041	+	0.0215406i
$771$	25.2050			0.907735
$772$	6.69874	+	5.02848i	0.241093	+	0.180979i
$773$		−	29.8382i		−	1.07321i	−0.843835	−	0.536603i	$-0.819707\pi$
$773$		−	29.8382i		−	1.07321i	0.843835	−	0.536603i	$-0.180293\pi$
$774$	14.6416	−	7.31694i	0.526282	−	0.263002i
$775$		−	31.6237i		−	1.13596i
$776$	−4.74181	+	25.9864i	−0.170221	+	0.932857i
$777$		−	67.8485i		−	2.43405i
$778$	25.9899	−	12.9881i	0.931784	−	0.465646i
$779$	47.4817			1.70121
$780$	14.0476	+	10.5450i	0.502987	+	0.377572i
$781$		−	3.51646i		−	0.125829i
$782$	3.71287	+	1.58875i	0.132772	+	0.0568135i
$783$	−54.3514			−1.94236
$784$	−0.152968	−	0.526114i	−0.00546313	−	0.0187898i
$785$		−	7.50408i		−	0.267832i
$786$	−21.2919	−	42.6063i	−0.759457	−	1.51972i
$787$	23.3329			0.831728			0.415864	−	0.909427i	$-0.363479\pi$
$787$	23.3329			0.831728			0.415864	+	0.909427i	$0.363479\pi$
$788$	17.7620	−	23.6619i	0.632746	−	0.842919i
$789$	−3.50467			−0.124769
$790$	16.0654	−	8.02845i	0.571581	−	0.285639i
$791$	7.98591			0.283946
$792$	−5.82041	−	1.06207i	−0.206819	−	0.0377389i
$793$		−	10.7569i		−	0.381990i
$794$	−5.41912	−	10.8440i	−0.192318	−	0.384838i
$795$			19.0862i			0.676917i
$796$	14.3641	+	10.7826i	0.509124	+	0.382179i
$797$			14.7191i			0.521378i	0.965423	+	0.260689i	$0.0839496\pi$
$797$			14.7191i			0.521378i	−0.965423	+	0.260689i	$0.916050\pi$
$798$	−32.8223	−	65.6793i	−1.16190	−	2.32502i
$799$	−15.9046	−	18.7668i	−0.562664	−	0.663921i
$800$	17.2914	−	15.9922i	0.611342	−	0.565410i
$801$	11.3048			0.399436
$802$	−28.3990	+	14.1920i	−1.00280	+	0.501138i
$803$			5.09695i			0.179868i
$804$	37.8640	+	28.4230i	1.33536	+	1.00240i
$805$	1.65936			0.0584849
$806$	16.0049	+	32.0266i	0.563747	+	1.12809i
$807$	−43.5015			−1.53133
$808$	4.12526	−	22.6075i	0.145126	−	0.795329i
$809$		−	35.7822i		−	1.25803i	−0.777391	−	0.629017i	$-0.783458\pi$
$809$		−	35.7822i		−	1.25803i	0.777391	−	0.629017i	$-0.216542\pi$
$810$	1.84693	+	3.69581i	0.0648945	+	0.129857i
$811$	38.2956			1.34474			0.672371	−	0.740215i	$-0.265276\pi$
$811$	38.2956			1.34474			0.672371	+	0.740215i	$0.265276\pi$
$812$	−34.3603	−	25.7929i	−1.20581	−	0.905155i
$813$	−66.7507			−2.34105
$814$	2.24270	+	4.48777i	0.0786065	+	0.157296i
$815$	12.0421			0.421818
$816$	−26.2309	+	39.6194i	−0.918265	+	1.38696i
$817$	−15.0200			−0.525483
$818$	0.307349	+	0.615022i	0.0107462	+	0.0215038i
$819$	46.2856			1.61735
$820$	−10.0972	−	7.57957i	−0.352610	−	0.264690i
$821$	−0.802916			−0.0280220			−0.0140110	−	0.999902i	$-0.504460\pi$
$821$	−0.802916			−0.0280220			−0.0140110	+	0.999902i	$0.504460\pi$
$822$	−15.2310	−	30.4781i	−0.531242	−	1.06304i
$823$		−	36.2470i		−	1.26349i	−0.775176	−	0.631745i	$-0.782339\pi$
$823$		−	36.2470i		−	1.26349i	0.775176	−	0.631745i	$-0.217661\pi$
$824$	3.38474	+	0.617623i	0.117913	+	0.0215159i
$825$	4.73393			0.164814
$826$	1.40068	+	2.80284i	0.0487360	+	0.0975234i
$827$	−36.9542			−1.28502			−0.642511	−	0.766276i	$-0.722107\pi$
$827$	−36.9542			−1.28502			−0.642511	+	0.766276i	$0.722107\pi$
$828$	5.87202	+	4.40789i	0.204067	+	0.153185i
$829$		−	45.5580i		−	1.58229i	−0.611626	−	0.791147i	$-0.709484\pi$
$829$		−	45.5580i		−	1.58229i	0.611626	−	0.791147i	$-0.290516\pi$
$830$	−6.73417	+	3.36531i	−0.233746	+	0.116812i
$831$	−32.8414			−1.13926
$832$	−9.41797	+	24.9472i	−0.326509	+	0.864889i
$833$	−0.365139	−	0.430850i	−0.0126513	−	0.0149281i
$834$	17.3200	+	34.6582i	0.599741	+	1.20012i
$835$		−	16.6903i		−	0.577592i
$836$	4.34199	+	3.25936i	0.150171	+	0.112727i
$837$			50.3426i			1.74009i
$838$	−0.823445	−	1.64776i	−0.0284454	−	0.0569209i
$839$			48.6309i			1.67892i	0.543418	+	0.839462i	$0.317130\pi$
$839$			48.6309i			1.67892i	−0.543418	+	0.839462i	$0.682870\pi$
$840$	−3.50467	+	19.2065i	−0.120922	+	0.662687i
$841$	38.2411			1.31866
$842$	8.81785	−	4.40660i	0.303883	−	0.151861i
$843$	43.1621			1.48658
$844$	−11.8767	+	15.8217i	−0.408814	+	0.544605i
$845$	−1.72818			−0.0594510
$846$	−19.9930	−	40.0070i	−0.687372	−	1.37547i
$847$			28.4091i			0.976149i
$848$	−27.8227	+	8.08945i	−0.955435	+	0.277793i
$849$	45.3912			1.55782
$850$	9.55091	−	22.3202i	0.327594	−	0.765578i
$851$		−	6.22599i		−	0.213424i
$852$	−41.0626	−	30.8240i	−1.40678	−	1.05601i
$853$	35.3904			1.21174			0.605872	−	0.795562i	$-0.292824\pi$
$853$	35.3904			1.21174			0.605872	+	0.795562i	$0.292824\pi$
$854$	10.6952	−	5.34477i	0.365982	−	0.182894i
$855$		−	33.3455i		−	1.14039i
$856$	−7.16592	−	1.30759i	−0.244926	−	0.0446924i
$857$			28.4620i			0.972243i	0.873891	+	0.486121i	$0.161589\pi$
$857$			28.4620i			0.972243i	−0.873891	+	0.486121i	$0.838411\pi$
$858$	−4.79425	+	2.39586i	−0.163673	+	0.0817932i
$859$			27.9846i			0.954821i	0.878680	+	0.477411i	$0.158425\pi$
$859$			27.9846i			0.954821i	−0.878680	+	0.477411i	$0.841575\pi$
$860$	3.19407	+	2.39766i	0.108917	+	0.0817596i
$861$	−52.0988			−1.77552
$862$	19.3189	−	9.65437i	0.658006	−	0.328829i
$863$	−19.7878			−0.673584			−0.336792	−	0.941579i	$-0.609342\pi$
$863$	−19.7878			−0.673584			−0.336792	+	0.941579i	$0.609342\pi$
$864$	−27.5266	+	25.4584i	−0.936473	+	0.866114i
$865$	15.8854			0.540121
$866$	−4.89197	−	9.78911i	−0.166236	−	0.332648i
$867$	−8.03181	+	48.3152i	−0.272775	+	1.64087i
$868$	−23.8905	+	31.8260i	−0.810896	+	1.08024i
$869$			5.47997i			0.185895i
$870$	−13.6591	−	27.3326i	−0.463086	−	0.926662i
$871$	27.3876			0.927992
$872$	0.348560	+	0.0636028i	0.0118037	+	0.00215386i
$873$			49.5037i			1.67545i
$874$	−3.01188	−	6.02694i	−0.101878	−	0.203864i
$875$		−	21.9547i		−	0.742205i
$876$	59.5183	+	44.6781i	2.01094	+	1.50953i
$877$	28.2571			0.954174			0.477087	−	0.878856i	$-0.341693\pi$
$877$	28.2571			0.954174			0.477087	+	0.878856i	$0.341693\pi$
$878$	−1.87235	+	0.935679i	−0.0631886	+	0.0315776i
$879$			15.3522i			0.517817i
$880$	−0.403049	−	1.38624i	−0.0135868	−	0.0467301i
$881$			10.2010i			0.343680i	0.985125	+	0.171840i	$0.0549711\pi$
$881$			10.2010i			0.343680i	−0.985125	+	0.171840i	$0.945029\pi$
$882$	−0.459000	−	0.918485i	−0.0154553	−	0.0309270i
$883$			46.4114i			1.56187i	0.624613	+	0.780934i	$0.285257\pi$
$883$			46.4114i			1.56187i	−0.624613	+	0.780934i	$0.714743\pi$
$884$	1.62375	+	27.4384i	0.0546125	+	0.922854i
$885$			2.22840i			0.0749068i
$886$	1.87119	−	0.935099i	0.0628637	−	0.0314153i
$887$		−	0.113319i		−	0.00380488i	−0.999998	−	0.00190244i	$-0.999394\pi$
$887$		−	0.113319i		−	0.00380488i	0.999998	−	0.00190244i	$-0.000605565\pi$
$888$	72.0634	+	13.1496i	2.41829	+	0.441272i
$889$		−	15.8802i		−	0.532603i
$890$	1.23307	+	2.46745i	0.0413327	+	0.0827091i
$891$	−1.26066			−0.0422336
$892$	−22.5483	+	30.0380i	−0.754975	+	1.00575i
$893$			41.0409i			1.37338i
$894$	−50.1419	+	25.0577i	−1.67700	+	0.838055i
$895$		−	5.41151i		−	0.180887i
$896$	−29.4835	+	3.03155i	−0.984975	+	0.101277i
$897$	6.65118			0.222077
$898$	32.2554	−	16.1192i	1.07638	−	0.537903i
$899$		−	62.2815i		−	2.07720i
$900$	26.4985	−	35.3002i	0.883282	−	1.17667i
$901$	−22.7848	+	19.3098i	−0.759071	+	0.643301i
$902$	3.44602	−	1.72210i	0.114740	−	0.0573397i
$903$	16.4805			0.548438
$904$	−1.54774	+	8.48202i	−0.0514771	+	0.282108i
$905$	0.0258169			0.000858182
$906$	−41.7614	−	83.5669i	−1.38743	−	2.77632i
$907$	−5.49536			−0.182470			−0.0912352	−	0.995829i	$-0.529081\pi$
$907$	−5.49536			−0.182470			−0.0912352	+	0.995829i	$0.529081\pi$
$908$	−14.8621	+	19.7987i	−0.493217	+	0.657044i
$909$		−	43.0669i		−	1.42844i
$910$	5.04860	+	10.1025i	0.167360	+	0.334896i
$911$		−	15.3736i		−	0.509350i	−0.967027	−	0.254675i	$-0.918032\pi$
$911$		−	15.3736i		−	0.509350i	0.967027	−	0.254675i	$-0.0819685\pi$
$912$	76.1207	−	22.1321i	2.52061	−	0.732867i
$913$		−	2.29706i		−	0.0760215i
$914$	−10.3295	−	20.6700i	−0.341671	−	0.683702i
$915$	8.50320			0.281107
$916$	−7.17815	−	5.38835i	−0.237173	−	0.178036i
$917$		−	30.6247i		−	1.01132i
$918$	−15.2044	+	35.5322i	−0.501819	+	1.17274i
$919$	−21.1602			−0.698011			−0.349006	−	0.937121i	$-0.613481\pi$
$919$	−21.1602			−0.698011			−0.349006	+	0.937121i	$0.613481\pi$
$920$	−0.321599	+	1.76245i	−0.0106028	+	0.0581062i
$921$			69.6837i			2.29615i
$922$	−50.0331	+	25.0033i	−1.64775	+	0.823441i
$923$	−29.7011			−0.977625
$924$	−4.76421	−	3.57631i	−0.156731	−	0.117652i
$925$	−37.4281			−1.23063
$926$	10.4188	+	20.8486i	0.342383	+	0.685128i
$927$	6.44787			0.211776
$928$	34.0546	−	31.4960i	1.11790	−	1.03391i
$929$			8.81133i			0.289091i	0.989498	+	0.144545i	$0.0461719\pi$
$929$			8.81133i			0.289091i	−0.989498	+	0.144545i	$0.953828\pi$
$930$	−25.3166	+	12.6516i	−0.830164	+	0.414863i
$931$			0.942220i			0.0308800i
$932$	−48.4601	−	36.3771i	−1.58736	−	1.19157i
$933$		−	21.8421i		−	0.715079i
$934$	−27.5664	+	13.7759i	−0.901999	+	0.450762i
$935$	−0.962090	−	1.13523i	−0.0314637	−	0.0371260i
$936$	−8.97055	+	49.1610i	−0.293211	+	1.60688i
$937$	52.1606			1.70401			0.852006	−	0.523531i	$-0.175386\pi$
$937$	52.1606			1.70401			0.852006	+	0.523531i	$0.175386\pi$
$938$	13.6080	+	27.2304i	0.444317	+	0.889103i
$939$			9.58343i			0.312743i
$940$	6.55142	−	8.72754i	0.213684	−	0.284661i
$941$	31.0092			1.01087			0.505435	−	0.862864i	$-0.331332\pi$
$941$	31.0092			1.01087			0.505435	+	0.862864i	$0.331332\pi$
$942$	29.9057	−	14.9450i	0.974381	−	0.486933i
$943$	−4.78075			−0.155683
$944$	−3.24843	+	0.944481i	−0.105727	+	0.0307402i
$945$			15.8802i			0.516581i
$946$	−1.09009	+	0.544756i	−0.0354418	+	0.0177115i
$947$	18.1228			0.588911			0.294456	−	0.955665i	$-0.404862\pi$
$947$	18.1228			0.588911			0.294456	+	0.955665i	$0.404862\pi$
$948$	63.9910	+	48.0355i	2.07833	+	1.56012i
$949$	43.0504			1.39748
$950$	−36.2315	+	18.1062i	−1.17551	+	0.587443i
$951$	−48.0494			−1.55811
$952$	−26.4741	+	15.2477i	−0.858032	+	0.494180i
$953$	−54.3337			−1.76004			−0.880021	−	0.474935i	$-0.842471\pi$
$953$	−54.3337			−1.76004			−0.880021	+	0.474935i	$0.842471\pi$
$954$	−48.5726	+	24.2735i	−1.57259	+	0.785882i
$955$	1.44256			0.0466800
$956$	13.6357	−	18.1649i	0.441010	−	0.587496i
$957$	9.32327			0.301379
$958$	−20.3385	+	10.1639i	−0.657106	+	0.328379i
$959$		−	21.9071i		−	0.707417i
$960$	−19.7204	−	7.44477i	−0.636474	−	0.240279i
$961$	−26.6877			−0.860894
$962$	37.9051	−	18.9425i	1.22211	−	0.610731i
$963$	−13.6510			−0.439897
$964$	21.1030	+	15.8412i	0.679682	+	0.510210i
$965$			3.83013i			0.123296i
$966$	3.30476	+	6.61301i	0.106329	+	0.212770i
$967$	14.7583			0.474596			0.237298	−	0.971437i	$-0.423738\pi$
$967$	14.7583			0.474596			0.237298	+	0.971437i	$0.423738\pi$
$968$	−30.1740	−	5.50594i	−0.969828	−	0.176967i
$969$	62.3374	−	52.8300i	2.00256	−	1.69714i
$970$	−10.8049	+	5.39962i	−0.346926	+	0.173371i
$971$		−	52.1902i		−	1.67486i	−0.546542	−	0.837432i	$-0.684056\pi$
$971$		−	52.1902i		−	1.67486i	0.546542	−	0.837432i	$-0.315944\pi$
$972$	12.8244	−	17.0841i	0.411342	−	0.547974i
$973$			24.9117i			0.798633i
$974$	16.3248	−	8.15808i	0.523080	−	0.261402i
$975$		−	39.9842i		−	1.28052i
$976$	3.60398	+	12.3955i	0.115361	+	0.396769i
$977$	−42.1219			−1.34760			−0.673799	−	0.738915i	$-0.735339\pi$
$977$	−42.1219			−1.34760			−0.673799	+	0.738915i	$0.735339\pi$
$978$	23.9829	+	47.9911i	0.766888	+	1.53459i
$979$	−0.841658			−0.0268995
$980$	0.150408	−	0.200368i	0.00480461	−	0.00640051i
$981$	0.664002			0.0212000
$982$	26.3376	−	13.1619i	0.840468	−	0.420012i
$983$			25.5746i			0.815702i	0.913049	+	0.407851i	$0.133722\pi$
$983$			25.5746i			0.815702i	−0.913049	+	0.407851i	$0.866278\pi$
$984$	10.0972	−	55.3353i	0.321887	−	1.76403i
$985$	13.5291			0.431074
$986$	18.8101	−	43.9588i	0.599037	−	1.39993i
$987$		−	45.0317i		−	1.43338i
$988$	27.5296	−	36.6738i	0.875833	−	1.16675i
$989$	1.51231			0.0480886
$990$	−1.20940	−	2.42008i	−0.0384373	−	0.0769152i
$991$			45.6047i			1.44868i	0.689443	+	0.724340i	$0.257856\pi$
$991$			45.6047i			1.44868i	−0.689443	+	0.724340i	$0.742144\pi$
$992$	−29.1729	−	31.5428i	−0.926241	−	1.00148i
$993$		−	19.0123i		−	0.603337i
$994$	−14.7575	−	29.5306i	−0.468080	−	0.936655i
$995$			8.21298i			0.260369i
$996$	−26.8233	−	20.1352i	−0.849928	−	0.638007i
$997$	21.4418			0.679069			0.339535	−	0.940594i	$-0.389730\pi$
$997$	21.4418			0.679069			0.339535	+	0.940594i	$0.389730\pi$
$998$	5.40980	+	10.8253i	0.171244	+	0.342669i
$999$	59.5829			1.88512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.h.a.101.6	yes	16
3.2	odd	2		1224.2.l.b.1189.12		16
4.3	odd	2		544.2.h.a.305.2		16
8.3	odd	2		544.2.h.a.305.16		16
8.5	even	2	inner	136.2.h.a.101.7	yes	16
12.11	even	2		4896.2.l.b.3025.10		16
17.16	even	2	inner	136.2.h.a.101.5	✓	16
24.5	odd	2		1224.2.l.b.1189.9		16
24.11	even	2		4896.2.l.b.3025.8		16
51.50	odd	2		1224.2.l.b.1189.11		16
68.67	odd	2		544.2.h.a.305.15		16
136.67	odd	2		544.2.h.a.305.1		16
136.101	even	2	inner	136.2.h.a.101.8	yes	16
204.203	even	2		4896.2.l.b.3025.7		16
408.101	odd	2		1224.2.l.b.1189.10		16
408.203	even	2		4896.2.l.b.3025.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.h.a.101.5	✓	16	17.16	even	2	inner
136.2.h.a.101.6	yes	16	1.1	even	1	trivial
136.2.h.a.101.7	yes	16	8.5	even	2	inner
136.2.h.a.101.8	yes	16	136.101	even	2	inner
544.2.h.a.305.1		16	136.67	odd	2
544.2.h.a.305.2		16	4.3	odd	2
544.2.h.a.305.15		16	68.67	odd	2
544.2.h.a.305.16		16	8.3	odd	2
1224.2.l.b.1189.9		16	24.5	odd	2
1224.2.l.b.1189.10		16	408.101	odd	2
1224.2.l.b.1189.11		16	51.50	odd	2
1224.2.l.b.1189.12		16	3.2	odd	2
4896.2.l.b.3025.7		16	204.203	even	2
4896.2.l.b.3025.8		16	24.11	even	2
4896.2.l.b.3025.9		16	408.203	even	2
4896.2.l.b.3025.10		16	12.11	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)

\(f(q)\)	\(=\)	\(q+(-0.632188 - 1.26504i) q^{2} +2.88107 q^{3} +(-1.20068 + 1.59949i) q^{4} -0.914541 q^{5} +(-1.82138 - 3.64469i) q^{6} -2.61974i q^{7} +(2.78248 + 0.507728i) q^{8} +5.30059 q^{9} +O(q^{10})\)	\(q+(-0.632188 - 1.26504i) q^{2} +2.88107 q^{3} +(-1.20068 + 1.59949i) q^{4} -0.914541 q^{5} +(-1.82138 - 3.64469i) q^{6} -2.61974i q^{7} +(2.78248 + 0.507728i) q^{8} +5.30059 q^{9} +(0.578162 + 1.15694i) q^{10} -0.394636 q^{11} +(-3.45924 + 4.60826i) q^{12} +3.33322i q^{13} +(-3.31408 + 1.65617i) q^{14} -2.63486 q^{15} +(-1.11675 - 3.84095i) q^{16} +(-2.66573 - 3.14546i) q^{17} +(-3.35097 - 6.70548i) q^{18} +6.87876i q^{19} +(1.09807 - 1.46280i) q^{20} -7.54766i q^{21} +(0.249484 + 0.499232i) q^{22} -0.692597i q^{23} +(8.01654 + 1.46280i) q^{24} -4.16361 q^{25} +(4.21667 - 2.10722i) q^{26} +6.62817 q^{27} +(4.19025 + 3.14546i) q^{28} -8.20007 q^{29} +(1.66573 + 3.33322i) q^{30} +7.59524i q^{31} +(-4.15297 + 3.84095i) q^{32} -1.13698 q^{33} +(-2.29390 + 5.36079i) q^{34} +2.39586i q^{35} +(-6.36429 + 8.47826i) q^{36} +8.98934 q^{37} +(8.70194 - 4.34867i) q^{38} +9.60325i q^{39} +(-2.54470 - 0.464338i) q^{40} -6.90264i q^{41} +(-9.54813 + 4.77154i) q^{42} +2.18353i q^{43} +(0.473830 - 0.631217i) q^{44} -4.84761 q^{45} +(-0.876166 + 0.437852i) q^{46} +5.96632 q^{47} +(-3.21745 - 11.0660i) q^{48} +0.136975 q^{49} +(2.63219 + 5.26716i) q^{50} +(-7.68016 - 9.06229i) q^{51} +(-5.33146 - 4.00211i) q^{52} -7.24371i q^{53} +(-4.19025 - 8.38493i) q^{54} +0.360911 q^{55} +(1.33011 - 7.28938i) q^{56} +19.8182i q^{57} +(5.18399 + 10.3735i) q^{58} -0.845737i q^{59} +(3.16361 - 4.21444i) q^{60} -3.22719 q^{61} +(9.60832 - 4.80162i) q^{62} -13.8862i q^{63} +(7.48442 + 2.82549i) q^{64} -3.04836i q^{65} +(0.718782 + 1.43832i) q^{66} -8.21656i q^{67} +(8.23181 - 0.487141i) q^{68} -1.99542i q^{69} +(3.03087 - 1.51463i) q^{70} +8.91065i q^{71} +(14.7488 + 2.69126i) q^{72} -12.9156i q^{73} +(-5.68295 - 11.3719i) q^{74} -11.9957 q^{75} +(-11.0025 - 8.25916i) q^{76} +1.03384i q^{77} +(12.1485 - 6.07106i) q^{78} -13.8862i q^{79} +(1.02132 + 3.51270i) q^{80} +3.19448 q^{81} +(-8.73215 + 4.36377i) q^{82} +5.82070i q^{83} +(12.0724 + 9.06229i) q^{84} +(2.43792 + 2.87665i) q^{85} +(2.76226 - 1.38040i) q^{86} -23.6250 q^{87} +(-1.09807 - 0.200368i) q^{88} +2.13275 q^{89} +(3.06460 + 6.13244i) q^{90} +8.73215 q^{91} +(1.10780 + 0.831585i) q^{92} +21.8825i q^{93} +(-3.77184 - 7.54766i) q^{94} -6.29091i q^{95} +(-11.9650 + 11.0660i) q^{96} +9.33928i q^{97} +(-0.0865941 - 0.173280i) q^{98} -2.09180 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

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