LMFDB - Embedded newform 136.2.h.a.101.7

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			101.7
Root			$-0.289081 + 0.578468i$ of defining polynomial
Character	$\chi$	$=$	136.101
Dual form			136.2.h.a.101.5

$q$-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} +(5.66438 - 1.38375i) 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} +(-1.83046 + 8.04049i) 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	$-0.812629\pi$
$3$	−2.88107			−1.66339			−0.831695	+	0.555233i	$0.812629\pi$
$4$	−1.20068	−	1.59949i	−0.600338	−	0.799746i
$5$	0.914541			0.408995			0.204498	−	0.978867i	$-0.434444\pi$
$5$	0.914541			0.408995			0.204498	+	0.978867i	$0.434444\pi$
$6$	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	$-0.481051\pi$
$11$	0.394636			0.118987			0.0594936	+	0.998229i	$0.481051\pi$
$12$	3.45924	+	4.60826i	0.998596	+	1.33029i
$13$		−	3.33322i		−	0.924468i	−0.886758	−	0.462234i	$-0.847048\pi$
$13$		−	3.33322i		−	0.924468i	0.886758	−	0.462234i	$-0.152952\pi$
$14$	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	$-0.710574\pi$
$19$		−	6.87876i		−	1.57810i	0.614331	−	0.789048i	$-0.289426\pi$
$20$	−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	$-0.224533\pi$
$29$	8.20007			1.52271			0.761357	+	0.648333i	$0.224533\pi$
$30$	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
$34$	5.66438	−	1.38375i	0.971434	−	0.237310i
$35$		−	2.39586i		−	0.404974i
$36$	−6.36429	−	8.47826i	−1.06072	−	1.41304i
$37$	−8.98934			−1.47784			−0.738919	−	0.673794i	$-0.764663\pi$
$37$	−8.98934			−1.47784			−0.738919	+	0.673794i	$0.764663\pi$
$38$	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	$-0.946756\pi$
$43$		−	2.18353i		−	0.332985i	0.986043	−	0.166493i	$-0.0532442\pi$
$44$	−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	$0.165749\pi$
$53$			7.24371i			0.995000i	−0.867464	+	0.497500i	$0.834251\pi$
$54$	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	$0.0175327\pi$
$59$			0.845737i			0.110106i	−0.998483	+	0.0550528i	$0.982467\pi$
$60$	3.16361	+	4.21444i	0.408421	+	0.544082i
$61$	3.22719			0.413199			0.206600	−	0.978426i	$-0.433760\pi$
$61$	3.22719			0.413199			0.206600	+	0.978426i	$0.433760\pi$
$62$	−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	$0.167368\pi$
$67$			8.21656i			1.00381i	−0.864922	+	0.501906i	$0.832632\pi$
$68$	−1.83046	+	8.04049i	−0.221976	+	0.975052i
$69$			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	$-0.896501\pi$
$83$		−	5.82070i		−	0.638905i	0.947602	−	0.319452i	$-0.103499\pi$
$84$	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	$0.132461\pi$
$101$			8.12493i			0.808461i	−0.914657	+	0.404231i	$0.867539\pi$
$102$	−16.3195	+	3.98667i	−1.61587	+	0.394739i
$103$	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	$-0.460272\pi$
$107$	2.57537			0.248970			0.124485	+	0.992221i	$0.460272\pi$
$108$	7.95828	+	10.6017i	0.765786	+	1.02015i
$109$	−0.125269			−0.0119986			−0.00599932	−	0.999982i	$-0.501910\pi$
$109$	−0.125269			−0.0119986			−0.00599932	+	0.999982i	$0.501910\pi$
$110$	−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	$-0.670606\pi$
$131$	−11.6900			−1.02136			−0.510679	+	0.859771i	$0.670606\pi$
$132$	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
$136$	−9.01438	−	7.39871i	−0.772977	−	0.634434i
$137$	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	$-0.367869\pi$
$139$	9.50924			0.806564			0.403282	+	0.915076i	$0.367869\pi$
$140$	−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	$0.190557\pi$
$149$			13.7575i			1.12706i	−0.826095	+	0.563530i	$0.809443\pi$
$150$	−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	$-0.893819\pi$
$157$		−	8.20529i		−	0.654853i	0.944877	−	0.327427i	$-0.106181\pi$
$158$	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	$-0.327541\pi$
$163$	13.1674			1.03135			0.515676	+	0.856784i	$0.327541\pi$
$164$	−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
$170$	5.18031	−	1.26549i	0.397312	−	0.0970588i
$171$		−	36.4615i		−	2.78828i
$172$	−3.49254	+	2.62171i	−0.266304	+	0.199904i
$173$	17.3698			1.32060			0.660302	−	0.751000i	$-0.270428\pi$
$173$	17.3698			1.32060			0.660302	+	0.751000i	$0.270428\pi$
$174$	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	$-0.929024\pi$
$179$		−	5.91718i		−	0.442271i	0.975243	−	0.221135i	$-0.0709763\pi$
$180$	−5.82041	−	7.75371i	−0.433827	−	0.577928i
$181$	0.0282293			0.00209827			0.00104913	−	0.999999i	$-0.499666\pi$
$181$	0.0282293			0.00209827			0.00104913	+	0.999999i	$0.499666\pi$
$182$	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	$-0.323320\pi$
$197$	14.7934			1.05398			0.526992	+	0.849870i	$0.323320\pi$
$198$	−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
$204$	5.27369	−	23.1652i	0.369232	−	1.62189i
$205$		−	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	$-0.610592\pi$
$211$	−9.89170			−0.680973			−0.340486	+	0.940249i	$0.610592\pi$
$212$	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	$-0.634745\pi$
$227$	−12.3781			−0.821566			−0.410783	+	0.911733i	$0.634745\pi$
$228$	31.6991	−	23.7953i	2.09932	−	1.57588i
$229$		−	4.48777i		−	0.296560i	−0.988945	−	0.148280i	$-0.952626\pi$
$229$		−	4.48777i		−	0.296560i	0.988945	−	0.148280i	$-0.0473737\pi$
$230$	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
$238$	−3.62505	−	14.8392i	−0.234977	−	0.961882i
$239$	−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	$-0.949519\pi$
$251$		−	5.00404i		−	0.315852i	0.987451	−	0.157926i	$-0.0504808\pi$
$252$	−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	$-0.347741\pi$
$269$	15.0991			0.920606			0.460303	+	0.887762i	$0.347741\pi$
$270$	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	$0.748469\pi$
$272$	15.0585	−	6.72621i	0.913055	−	0.407837i
$273$	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	$-0.388743\pi$
$277$	11.3990			0.684901			0.342451	+	0.939536i	$0.388743\pi$
$278$	−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	$-0.655122\pi$
$283$	−15.7550			−0.936535			−0.468268	+	0.883587i	$0.655122\pi$
$284$	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	$-0.950252\pi$
$293$		−	5.32864i		−	0.311303i	0.987812	−	0.155651i	$-0.0497476\pi$
$294$	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
$306$	30.0246	−	7.33467i	1.71639	−	0.419295i
$307$		−	24.1867i		−	1.38041i	−0.723615	−	0.690204i	$-0.757521\pi$
$307$		−	24.1867i		−	1.38041i	0.723615	−	0.690204i	$-0.242479\pi$
$308$	−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	$-0.344847\pi$
$317$	16.6776			0.936708			0.468354	+	0.883541i	$0.344847\pi$
$318$	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	$0.0580492\pi$
$331$			6.59903i			0.362716i	−0.983417	+	0.181358i	$0.941951\pi$
$332$	−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
$340$	−1.67403	+	7.35336i	−0.0907870	+	0.398792i
$341$			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	$-0.709972\pi$
$347$	−22.8318			−1.22568			−0.612838	+	0.790208i	$0.709972\pi$
$348$	28.3660	+	37.7880i	1.52058	+	2.02565i
$349$		−	1.18518i		−	0.0634410i	−0.999497	−	0.0317205i	$-0.989901\pi$
$349$		−	1.18518i		−	0.0634410i	0.999497	−	0.0317205i	$-0.0100986\pi$
$350$	−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	$0.0526716\pi$
$373$			6.36248i			0.329437i	−0.986341	+	0.164718i	$0.947328\pi$
$374$	2.23537	−	0.546075i	0.115588	−	0.0282369i
$375$	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	$-0.486649\pi$
$379$	1.63260			0.0838610			0.0419305	+	0.999121i	$0.486649\pi$
$380$	−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	$-0.825623\pi$
$389$		−	20.5447i		−	1.04166i	0.853662	−	0.520828i	$-0.174377\pi$
$390$	−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	$-0.569010\pi$
$397$	−8.57201			−0.430217			−0.215108	+	0.976590i	$0.569010\pi$
$398$	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
$408$	25.9711	+	21.3162i	1.28576	+	1.05531i
$409$	−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	$-0.510129\pi$
$419$	−1.30253			−0.0636328			−0.0318164	+	0.999494i	$0.510129\pi$
$420$	11.0407	−	8.28784i	0.538733	−	0.404405i
$421$		−	6.97038i		−	0.339716i	−0.985469	−	0.169858i	$-0.945669\pi$
$421$		−	6.97038i		−	0.339716i	0.985469	−	0.169858i	$-0.0543309\pi$
$422$	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
$442$	−4.61232	−	18.8806i	−0.219386	−	0.898060i
$443$		−	1.47915i		−	0.0702763i	−0.999382	−	0.0351382i	$-0.988813\pi$
$443$		−	1.47915i		−	0.0702763i	0.999382	−	0.0351382i	$-0.0111871\pi$
$444$	−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	$0.372646\pi$
$461$			39.5505i			1.84205i	−0.389504	+	0.921025i	$0.627354\pi$
$462$	−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	$0.168205\pi$
$467$			21.7908i			1.00836i	−0.863599	+	0.504180i	$0.831795\pi$
$468$	−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
$476$	21.0640	+	4.79532i	0.965465	+	0.219793i
$477$			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	$-0.844331\pi$
$491$		−	20.8195i		−	0.939572i	0.882780	−	0.469786i	$-0.155669\pi$
$492$	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	$-0.438653\pi$
$499$	8.55725			0.383075			0.191538	+	0.981485i	$0.438653\pi$
$500$	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	$-0.734691\pi$
$509$		−	33.4031i		−	1.48057i	0.672294	−	0.740284i	$-0.265309\pi$
$510$	−14.9249	+	3.64598i	−0.660884	+	0.161447i
$511$	−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	$0.141542\pi$
$523$			19.6747i			0.860315i	−0.902754	+	0.430157i	$0.858458\pi$
$524$	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	$-0.283899\pi$
$541$	29.2109			1.25588			0.627938	+	0.778264i	$0.283899\pi$
$542$	14.6470	−	29.3094i	0.629141	−	1.25895i
$543$	−0.0813308			−0.00349024
$544$	−1.01084	+	23.3019i	−0.0433393	+	0.999060i
$545$	−0.114564			−0.00490739
$546$	−15.9046	+	31.8260i	−0.680653	+	1.36203i
$547$	25.7356			1.10037			0.550187	−	0.835041i	$-0.314556\pi$
$547$	25.7356			1.10037			0.550187	+	0.835041i	$0.314556\pi$
$548$	−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	$-0.731223\pi$
$557$		−	35.2863i		−	1.49513i	0.664189	−	0.747564i	$-0.268777\pi$
$558$	−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	$-0.982973\pi$
$563$		−	2.53721i		−	0.106931i	0.998570	−	0.0534653i	$-0.0170267\pi$
$564$	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	$-0.331992\pi$
$571$	24.0698			1.00729			0.503645	+	0.863911i	$0.331992\pi$
$572$	−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	$0.586970\pi$
$578$	−19.4522	−	14.1284i	−0.809106	−	0.587663i
$579$			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	$0.127353\pi$
$587$			18.8738i			0.779007i	−0.921025	+	0.389503i	$0.872647\pi$
$588$	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
$612$	−9.70251	+	42.6193i	−0.392201	+	1.72278i
$613$			37.9406i			1.53241i	0.642597	+	0.766204i	$0.277857\pi$
$613$			37.9406i			1.53241i	−0.642597	+	0.766204i	$0.722143\pi$
$614$	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	$-0.368167\pi$
$619$	20.0245			0.804854			0.402427	+	0.915452i	$0.368167\pi$
$620$	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	$-0.809330\pi$
$643$	−41.8852			−1.65179			−0.825895	+	0.563824i	$0.809330\pi$
$644$	2.17853	+	2.90216i	0.0858463	+	0.114361i
$645$			5.75330i			0.226536i
$646$	−9.51845	−	38.9640i	−0.374499	−	1.53302i
$647$	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	$-0.342146\pi$
$653$	24.3189			0.951671			0.475835	+	0.879534i	$0.342146\pi$
$654$	−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	$-0.833070\pi$
$659$		−	25.7077i		−	1.00143i	0.865612	−	0.500715i	$-0.166930\pi$
$660$	1.24848	+	1.66317i	0.0485968	+	0.0647388i
$661$			30.6153i			1.19080i	0.803431	+	0.595398i	$0.203006\pi$
$661$			30.6153i			1.19080i	−0.803431	+	0.595398i	$0.796994\pi$
$662$	−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	$-0.951211\pi$
$677$	−51.4284			−1.97655			−0.988276	+	0.152676i	$0.951211\pi$
$678$	11.1103	+	5.55223i	0.426690	+	0.213232i
$679$	24.4665			0.938936
$680$	−8.24402	−	6.76643i	−0.316144	−	0.259481i
$681$	35.6623			1.36658
$682$	−3.79179	−	1.89489i	−0.145195	−	0.0725592i
$683$	27.1781			1.03994			0.519971	−	0.854184i	$-0.325943\pi$
$683$	27.1781			1.03994			0.519971	+	0.854184i	$0.325943\pi$
$684$	−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	$-0.519518\pi$
$691$	−3.22165			−0.122558			−0.0612788	+	0.998121i	$0.519518\pi$
$692$	−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	$-0.991523\pi$
$701$		−	1.41005i		−	0.0532570i	0.999645	−	0.0266285i	$-0.00847711\pi$
$702$	−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	$-0.656772\pi$
$709$	−25.1808			−0.945685			−0.472843	+	0.881147i	$0.656772\pi$
$710$	−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
$714$	10.4440	+	42.7528i	0.390858	+	1.59998i
$715$		−	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	$-0.695487\pi$
$733$		−	44.2534i		−	1.63454i	0.576257	−	0.817268i	$-0.304513\pi$
$734$	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	$-0.941666\pi$
$739$		−	9.90803i		−	0.364473i	0.983255	−	0.182236i	$-0.0583336\pi$
$740$	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
$748$	−0.722364	+	3.17306i	−0.0264123	+	0.116019i
$749$		−	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	$0.225728\pi$
$757$			35.8329i			1.30237i	−0.758919	+	0.651185i	$0.774272\pi$
$758$	−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	$0.180293\pi$
$773$			29.8382i			1.07321i	−0.843835	+	0.536603i	$0.819707\pi$
$774$	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
$782$	−0.958378	−	3.92314i	−0.0342715	−	0.140291i
$783$	−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	$-0.636521\pi$
$787$	−23.3329			−0.831728			−0.415864	+	0.909427i	$0.636521\pi$
$788$	−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	$-0.916050\pi$
$797$		−	14.7191i		−	0.521378i	0.965423	−	0.260689i	$-0.0839496\pi$
$798$	−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	$-0.734724\pi$
$811$	−38.2956			−1.34474			−0.672371	+	0.740215i	$0.734724\pi$
$812$	−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
$816$	−43.3846	+	19.3787i	−1.51877	+	0.678391i
$817$	−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	$-0.495540\pi$
$821$	0.802916			0.0280220			0.0140110	+	0.999902i	$0.495540\pi$
$822$	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	$-0.277893\pi$
$827$	36.9542			1.28502			0.642511	+	0.766276i	$0.277893\pi$
$828$	−5.87202	+	4.40789i	−0.204067	+	0.153185i
$829$			45.5580i			1.58229i	0.611626	+	0.791147i	$0.290516\pi$
$829$			45.5580i			1.58229i	−0.611626	+	0.791147i	$0.709484\pi$
$830$	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
$850$	−23.5843	+	5.76138i	−0.808935	+	0.197614i
$851$			6.22599i			0.213424i
$852$	−41.0626	+	30.8240i	−1.40678	+	1.05601i
$853$	−35.3904			−1.21174			−0.605872	−	0.795562i	$-0.707176\pi$
$853$	−35.3904			−1.21174			−0.605872	+	0.795562i	$0.707176\pi$
$854$	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	$-0.841575\pi$
$859$		−	27.9846i		−	0.954821i	0.878680	−	0.477411i	$-0.158425\pi$
$860$	−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	$-0.658307\pi$
$877$	−28.2571			−0.954174			−0.477087	+	0.878856i	$0.658307\pi$
$878$	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	$-0.714743\pi$
$883$		−	46.4114i		−	1.56187i	0.624613	−	0.780934i	$-0.285257\pi$
$884$	26.8007	+	6.10131i	0.901405	+	0.205209i
$885$		−	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	$-0.470919\pi$
$907$	5.49536			0.182470			0.0912352	+	0.995829i	$0.470919\pi$
$908$	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
$918$	−37.5445	+	9.17170i	−1.23915	+	0.302711i
$919$	−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	$-0.668668\pi$
$941$	−31.0092			−1.01087			−0.505435	+	0.862864i	$0.668668\pi$
$942$	−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	$-0.595138\pi$
$947$	−18.1228			−0.588911			−0.294456	+	0.955665i	$0.595138\pi$
$948$	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
$952$	−19.3827	+	23.6153i	−0.628196	+	0.765377i
$953$	−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	$0.315944\pi$
$971$			52.1902i			1.67486i	−0.546542	+	0.837432i	$0.684056\pi$
$972$	−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
$986$	46.4483	−	11.3468i	1.47922	−	0.361356i
$987$			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	$-0.610270\pi$
$997$	−21.4418			−0.679069			−0.339535	+	0.940594i	$0.610270\pi$
$998$	−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.101.7	yes	16
3.2	odd	2		1224.2.l.b.1189.9		16
4.3	odd	2		544.2.h.a.305.16		16
8.3	odd	2		544.2.h.a.305.2		16
8.5	even	2	inner	136.2.h.a.101.6	yes	16
12.11	even	2		4896.2.l.b.3025.8		16
17.16	even	2	inner	136.2.h.a.101.8	yes	16
24.5	odd	2		1224.2.l.b.1189.12		16
24.11	even	2		4896.2.l.b.3025.10		16
51.50	odd	2		1224.2.l.b.1189.10		16
68.67	odd	2		544.2.h.a.305.1		16
136.67	odd	2		544.2.h.a.305.15		16
136.101	even	2	inner	136.2.h.a.101.5	✓	16
204.203	even	2		4896.2.l.b.3025.9		16
408.101	odd	2		1224.2.l.b.1189.11		16
408.203	even	2		4896.2.l.b.3025.7		16

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

\(f(q)\)	\(=\)	\(q+(-0.632188 + 1.26504i) q^{2} -2.88107 q^{3} +(-1.20068 - 1.59949i) q^{4} +0.914541 q^{5} +(1.82138 - 3.64469i) q^{6} -2.61974i q^{7} +(2.78248 - 0.507728i) q^{8} +5.30059 q^{9} +O(q^{10})\)	\(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} +(5.66438 - 1.38375i) 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} +(-1.83046 + 8.04049i) 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

Introduction

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