LMFDB - Embedded newform 136.2.c.a.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(69,136)]

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, 0]))

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

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

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.c (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:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.1
Root			$1.40014 + 0.199044i$ of defining polynomial
Character	$\chi$	$=$	136.69
Dual form			136.2.c.a.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40014 - 0.199044i) q^{2} -1.72010i q^{3} +(1.92076 + 0.557378i) q^{4} +3.30391i q^{5} +(-0.342376 + 2.40838i) q^{6} +3.45790 q^{7} +(-2.57839 - 1.16272i) q^{8} +0.0412530 q^{9} +O(q^{10})$	\(q+(-1.40014 - 0.199044i) q^{2} -1.72010i q^{3} +(1.92076 + 0.557378i) q^{4} +3.30391i q^{5} +(-0.342376 + 2.40838i) q^{6} +3.45790 q^{7} +(-2.57839 - 1.16272i) q^{8} +0.0412530 q^{9} +(0.657624 - 4.62592i) q^{10} -3.09665i q^{11} +(0.958747 - 3.30391i) q^{12} -2.50773i q^{13} +(-4.84153 - 0.688275i) q^{14} +5.68305 q^{15} +(3.37866 + 2.14118i) q^{16} -1.00000 q^{17} +(-0.0577599 - 0.00821118i) q^{18} +4.43508i q^{19} +(-1.84153 + 6.34602i) q^{20} -5.94793i q^{21} +(-0.616371 + 4.33573i) q^{22} +4.14265 q^{23} +(-2.00000 + 4.43508i) q^{24} -5.91579 q^{25} +(-0.499149 + 3.51116i) q^{26} -5.23126i q^{27} +(6.64180 + 1.92736i) q^{28} +7.15862i q^{29} +(-7.95705 - 1.13118i) q^{30} -6.22515 q^{31} +(-4.30439 - 3.67045i) q^{32} -5.32655 q^{33} +(1.40014 + 0.199044i) q^{34} +11.4246i q^{35} +(0.0792373 + 0.0229935i) q^{36} -6.74411i q^{37} +(0.882778 - 6.20972i) q^{38} -4.31355 q^{39} +(3.84153 - 8.51875i) q^{40} -6.99830 q^{41} +(-1.18390 + 8.32791i) q^{42} +2.22951i q^{43} +(1.72601 - 5.94793i) q^{44} +0.136296i q^{45} +(-5.80027 - 0.824571i) q^{46} -3.31525 q^{47} +(3.68305 - 5.81163i) q^{48} +4.95705 q^{49} +(8.28291 + 1.17750i) q^{50} +1.72010i q^{51} +(1.39775 - 4.81675i) q^{52} +6.19330i q^{53} +(-1.04125 + 7.32448i) q^{54} +10.2310 q^{55} +(-8.91579 - 4.02057i) q^{56} +7.62879 q^{57} +(1.42488 - 10.0230i) q^{58} -8.83732i q^{59} +(10.9158 + 3.16761i) q^{60} +14.3707i q^{61} +(8.71606 + 1.23908i) q^{62} +0.142649 q^{63} +(5.29615 + 5.99590i) q^{64} +8.28530 q^{65} +(7.45790 + 1.06022i) q^{66} -6.44195i q^{67} +(-1.92076 - 0.557378i) q^{68} -7.12577i q^{69} +(2.27399 - 15.9959i) q^{70} -5.66069 q^{71} +(-0.106366 - 0.0479658i) q^{72} -15.4486 q^{73} +(-1.34238 + 9.44267i) q^{74} +10.1758i q^{75} +(-2.47202 + 8.51875i) q^{76} -10.7079i q^{77} +(6.03955 + 0.858587i) q^{78} -8.14265 q^{79} +(-7.07427 + 11.1628i) q^{80} -8.87454 q^{81} +(9.79857 + 1.39297i) q^{82} -13.8528i q^{83} +(3.31525 - 11.4246i) q^{84} -3.30391i q^{85} +(0.443772 - 3.12162i) q^{86} +12.3135 q^{87} +(-3.60054 + 7.98436i) q^{88} +7.32655 q^{89} +(0.0271290 - 0.190833i) q^{90} -8.67146i q^{91} +(7.95705 + 2.30902i) q^{92} +10.7079i q^{93} +(4.64180 + 0.659881i) q^{94} -14.6531 q^{95} +(-6.31355 + 7.40399i) q^{96} +8.36780 q^{97} +(-6.94054 - 0.986672i) q^{98} -0.127746i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9	$ 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9} + 6 q^{10} + 16 q^{12} - 10 q^{14} - 12 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} + 14 q^{20} - 14 q^{22} + 12 q^{23} - 16 q^{24} - 8 q^{25} + 24 q^{26} + 4 q^{28} - 16 q^{30} - 12 q^{31} - 11 q^{32} + 8 q^{33} + q^{34} + 15 q^{36} - 30 q^{38} + 20 q^{39} + 2 q^{40} + 20 q^{42} + 4 q^{44} - 26 q^{46} - 28 q^{47} - 28 q^{48} - 8 q^{49} + 19 q^{50} - 4 q^{52} + 44 q^{55} - 32 q^{56} + 8 q^{57} - 6 q^{58} + 48 q^{60} + 10 q^{62} - 20 q^{63} + 25 q^{64} + 24 q^{65} + 40 q^{66} - q^{68} + 28 q^{70} - 13 q^{72} + 8 q^{73} - 10 q^{74} + 6 q^{76} - 16 q^{78} - 44 q^{79} - 46 q^{80} - 40 q^{81} + 2 q^{82} + 28 q^{84} - 10 q^{86} + 44 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} + 16 q^{92} - 12 q^{94} - 16 q^{95} + 4 q^{96} + 8 q^{97} - 9 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9 + 6 * q^10 + 16 * q^12 - 10 * q^14 - 12 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 + 14 * q^20 - 14 * q^22 + 12 * q^23 - 16 * q^24 - 8 * q^25 + 24 * q^26 + 4 * q^28 - 16 * q^30 - 12 * q^31 - 11 * q^32 + 8 * q^33 + q^34 + 15 * q^36 - 30 * q^38 + 20 * q^39 + 2 * q^40 + 20 * q^42 + 4 * q^44 - 26 * q^46 - 28 * q^47 - 28 * q^48 - 8 * q^49 + 19 * q^50 - 4 * q^52 + 44 * q^55 - 32 * q^56 + 8 * q^57 - 6 * q^58 + 48 * q^60 + 10 * q^62 - 20 * q^63 + 25 * q^64 + 24 * q^65 + 40 * q^66 - q^68 + 28 * q^70 - 13 * q^72 + 8 * q^73 - 10 * q^74 + 6 * q^76 - 16 * q^78 - 44 * q^79 - 46 * q^80 - 40 * q^81 + 2 * q^82 + 28 * q^84 - 10 * q^86 + 44 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 + 16 * q^92 - 12 * q^94 - 16 * q^95 + 4 * q^96 + 8 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.40014	−	0.199044i	−0.990046	−	0.140746i
$2$	−1.40014	−	0.199044i	−0.990046	−	0.140746i
$3$		−	1.72010i		−	0.993101i	−0.868008	−	0.496550i	$-0.834600\pi$
$3$		−	1.72010i		−	0.993101i	0.868008	−	0.496550i	$-0.165400\pi$
$4$	1.92076	+	0.557378i	0.960381	+	0.278689i
$5$			3.30391i			1.47755i	0.673951	+	0.738776i	$0.264596\pi$
$5$			3.30391i			1.47755i	−0.673951	+	0.738776i	$0.735404\pi$
$6$	−0.342376	+	2.40838i	−0.139775	+	0.983215i
$7$	3.45790			1.30696			0.653481	−	0.756943i	$-0.273308\pi$
$7$	3.45790			1.30696			0.653481	+	0.756943i	$0.273308\pi$
$8$	−2.57839	−	1.16272i	−0.911597	−	0.411084i
$9$	0.0412530			0.0137510
$10$	0.657624	−	4.62592i	0.207959	−	1.46284i
$11$		−	3.09665i		−	0.933675i	−0.884343	−	0.466838i	$-0.845393\pi$
$11$		−	3.09665i		−	0.933675i	0.884343	−	0.466838i	$-0.154607\pi$
$12$	0.958747	−	3.30391i	0.276766	−	0.953755i
$13$		−	2.50773i		−	0.695519i	−0.937584	−	0.347759i	$-0.886943\pi$
$13$		−	2.50773i		−	0.695519i	0.937584	−	0.347759i	$-0.113057\pi$
$14$	−4.84153	−	0.688275i	−1.29395	−	0.183949i
$15$	5.68305			1.46736
$16$	3.37866	+	2.14118i	0.844665	+	0.535296i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−0.0577599	−	0.00821118i	−0.0136141	−	0.00193539i
$19$			4.43508i			1.01748i	0.860921	+	0.508739i	$0.169888\pi$
$19$			4.43508i			1.01748i	−0.860921	+	0.508739i	$0.830112\pi$
$20$	−1.84153	+	6.34602i	−0.411778	+	1.41901i
$21$		−	5.94793i		−	1.29794i
$22$	−0.616371	+	4.33573i	−0.131411	+	0.924381i
$23$	4.14265			0.863802			0.431901	−	0.901921i	$-0.357843\pi$
$23$	4.14265			0.863802			0.431901	+	0.901921i	$0.357843\pi$
$24$	−2.00000	+	4.43508i	−0.408248	+	0.905308i
$25$	−5.91579			−1.18316
$26$	−0.499149	+	3.51116i	−0.0978912	+	0.688595i
$27$		−	5.23126i		−	1.00676i
$28$	6.64180	+	1.92736i	1.25518	+	0.364236i
$29$			7.15862i			1.32932i	0.747145	+	0.664661i	$0.231424\pi$
$29$			7.15862i			1.32932i	−0.747145	+	0.664661i	$0.768576\pi$
$30$	−7.95705	−	1.13118i	−1.45275	−	0.206524i
$31$	−6.22515			−1.11807			−0.559035	−	0.829144i	$-0.688828\pi$
$31$	−6.22515			−1.11807			−0.559035	+	0.829144i	$0.688828\pi$
$32$	−4.30439	−	3.67045i	−0.760916	−	0.648850i
$33$	−5.32655			−0.927233
$34$	1.40014	+	0.199044i	0.240121	+	0.0341358i
$35$			11.4246i			1.93110i
$36$	0.0792373	+	0.0229935i	0.0132062	+	0.00383226i
$37$		−	6.74411i		−	1.10872i	−0.832276	−	0.554362i	$-0.812962\pi$
$37$		−	6.74411i		−	1.10872i	0.832276	−	0.554362i	$-0.187038\pi$
$38$	0.882778	−	6.20972i	0.143206	−	1.00735i
$39$	−4.31355			−0.690720
$40$	3.84153	−	8.51875i	0.607399	−	1.34693i
$41$	−6.99830			−1.09295			−0.546475	−	0.837475i	$-0.684031\pi$
$41$	−6.99830			−1.09295			−0.546475	+	0.837475i	$0.684031\pi$
$42$	−1.18390	+	8.32791i	−0.182680	+	1.28502i
$43$			2.22951i			0.339998i	0.985444	+	0.169999i	$0.0543764\pi$
$43$			2.22951i			0.339998i	−0.985444	+	0.169999i	$0.945624\pi$
$44$	1.72601	−	5.94793i	0.260205	−	0.896684i
$45$			0.136296i			0.0203178i
$46$	−5.80027	−	0.824571i	−0.855204	−	0.121576i
$47$	−3.31525			−0.483579			−0.241789	−	0.970329i	$-0.577734\pi$
$47$	−3.31525			−0.483579			−0.241789	+	0.970329i	$0.577734\pi$
$48$	3.68305	−	5.81163i	0.531603	−	0.838837i
$49$	4.95705			0.708149
$50$	8.28291	+	1.17750i	1.17138	+	0.166524i
$51$			1.72010i			0.240862i
$52$	1.39775	−	4.81675i	0.193834	−	0.667963i
$53$			6.19330i			0.850715i	0.905025	+	0.425358i	$0.139852\pi$
$53$			6.19330i			0.850715i	−0.905025	+	0.425358i	$0.860148\pi$
$54$	−1.04125	+	7.32448i	−0.141697	+	0.996735i
$55$	10.2310			1.37955
$56$	−8.91579	−	4.02057i	−1.19142	−	0.537272i
$57$	7.62879			1.01046
$58$	1.42488	−	10.0230i	0.187096	−	1.31609i
$59$		−	8.83732i		−	1.15052i	−0.817970	−	0.575261i	$-0.804901\pi$
$59$		−	8.83732i		−	1.15052i	0.817970	−	0.575261i	$-0.195099\pi$
$60$	10.9158	+	3.16761i	1.40922	+	0.408937i
$61$			14.3707i			1.83999i	0.391936	+	0.919993i	$0.371806\pi$
$61$			14.3707i			1.83999i	−0.391936	+	0.919993i	$0.628194\pi$
$62$	8.71606	+	1.23908i	1.10694	+	0.157364i
$63$	0.142649			0.0179720
$64$	5.29615	+	5.99590i	0.662019	+	0.749487i
$65$	8.28530			1.02766
$66$	7.45790	+	1.06022i	0.918004	+	0.130504i
$67$		−	6.44195i		−	0.787009i	−0.919323	−	0.393505i	$-0.871262\pi$
$67$		−	6.44195i		−	0.787009i	0.919323	−	0.393505i	$-0.128738\pi$
$68$	−1.92076	−	0.557378i	−0.232927	−	0.0675921i
$69$		−	7.12577i		−	0.857842i
$70$	2.27399	−	15.9959i	0.271794	−	1.91188i
$71$	−5.66069			−0.671800			−0.335900	−	0.941898i	$-0.609040\pi$
$71$	−5.66069			−0.671800			−0.335900	+	0.941898i	$0.609040\pi$
$72$	−0.106366	−	0.0479658i	−0.0125354	−	0.00565283i
$73$	−15.4486			−1.80812			−0.904061	−	0.427403i	$-0.859429\pi$
$73$	−15.4486			−1.80812			−0.904061	+	0.427403i	$0.859429\pi$
$74$	−1.34238	+	9.44267i	−0.156048	+	1.09769i
$75$			10.1758i			1.17500i
$76$	−2.47202	+	8.51875i	−0.283560	+	0.977167i
$77$		−	10.7079i		−	1.22028i
$78$	6.03955	+	0.858587i	0.683845	+	0.0972158i
$79$	−8.14265			−0.916120			−0.458060	−	0.888921i	$-0.651455\pi$
$79$	−8.14265			−0.916120			−0.458060	+	0.888921i	$0.651455\pi$
$80$	−7.07427	+	11.1628i	−0.790927	+	1.24804i
$81$	−8.87454			−0.986060
$82$	9.79857	+	1.39297i	1.08207	+	0.153828i
$83$		−	13.8528i		−	1.52054i	−0.649607	−	0.760270i	$-0.725067\pi$
$83$		−	13.8528i		−	1.52054i	0.649607	−	0.760270i	$-0.274933\pi$
$84$	3.31525	−	11.4246i	0.361723	−	1.24652i
$85$		−	3.30391i		−	0.358359i
$86$	0.443772	−	3.12162i	0.0478532	−	0.336613i
$87$	12.3135			1.32015
$88$	−3.60054	+	7.98436i	−0.383819	+	0.851136i
$89$	7.32655			0.776613			0.388306	−	0.921530i	$-0.373060\pi$
$89$	7.32655			0.776613			0.388306	+	0.921530i	$0.373060\pi$
$90$	0.0271290	−	0.190833i	0.00285964	−	0.0201156i
$91$		−	8.67146i		−	0.909016i
$92$	7.95705	+	2.30902i	0.829579	+	0.240732i
$93$			10.7079i			1.11036i
$94$	4.64180	+	0.659881i	0.478765	+	0.0680615i
$95$	−14.6531			−1.50338
$96$	−6.31355	+	7.40399i	−0.644374	+	0.755666i
$97$	8.36780			0.849622			0.424811	−	0.905282i	$-0.360341\pi$
$97$	8.36780			0.849622			0.424811	+	0.905282i	$0.360341\pi$
$98$	−6.94054	−	0.986672i	−0.701100	−	0.0996689i
$99$		−	0.127746i		−	0.0128390i
$100$	−11.3628	−	3.29733i	−1.13628	−	0.329733i
$101$		−	7.95480i		−	0.791532i	−0.918351	−	0.395766i	$-0.870479\pi$
$101$		−	7.95480i		−	0.791532i	0.918351	−	0.395766i	$-0.129521\pi$
$102$	0.342376	−	2.40838i	0.0339003	−	0.238465i
$103$	−7.91409			−0.779798			−0.389899	−	0.920858i	$-0.627490\pi$
$103$	−7.91409			−0.779798			−0.389899	+	0.920858i	$0.627490\pi$
$104$	−2.91579	+	6.46589i	−0.285917	+	0.634033i
$105$	19.6514			1.91778
$106$	1.23274	−	8.67146i	0.119734	−	0.842247i
$107$			13.3605i			1.29161i	0.763504	+	0.645803i	$0.223477\pi$
$107$			13.3605i			1.29161i	−0.763504	+	0.645803i	$0.776523\pi$
$108$	2.91579	−	10.0480i	0.280572	−	0.966870i
$109$		−	2.12606i		−	0.203640i	−0.994803	−	0.101820i	$-0.967533\pi$
$109$		−	2.12606i		−	0.203640i	0.994803	−	0.101820i	$-0.0324665\pi$
$110$	−14.3248	−	2.03643i	−1.36582	−	0.194166i
$111$	−11.6005			−1.10107
$112$	11.6831	+	7.40399i	1.10394	+	0.699611i
$113$	2.28530			0.214983			0.107491	−	0.994206i	$-0.465718\pi$
$113$	2.28530			0.214983			0.107491	+	0.994206i	$0.465718\pi$
$114$	−10.6813	−	1.51847i	−1.00040	−	0.142218i
$115$			13.6869i			1.27631i
$116$	−3.99006	+	13.7500i	−0.370468	+	1.27666i
$117$		−	0.103451i		−	0.00956409i
$118$	−1.75902	+	12.3735i	−0.161931	+	1.13907i
$119$	−3.45790			−0.316985
$120$	−14.6531	−	6.60781i	−1.33764	−	0.603208i
$121$	1.41076			0.128251
$122$	2.86042	−	20.1210i	0.258970	−	1.82167i
$123$			12.0378i			1.08541i
$124$	−11.9570	−	3.46977i	−1.07377	−	0.311594i
$125$		−	3.02569i		−	0.270626i
$126$	−0.199728	−	0.0283934i	−0.0177932	−	0.00252949i
$127$	2.36780			0.210109			0.105054	−	0.994466i	$-0.466498\pi$
$127$	2.36780			0.210109			0.105054	+	0.994466i	$0.466498\pi$
$128$	−6.22189	−	9.44924i	−0.549942	−	0.835203i
$129$	3.83499			0.337652
$130$	−11.6005	−	1.64914i	−1.01744	−	0.144639i
$131$		−	2.73893i		−	0.239301i	−0.992816	−	0.119651i	$-0.961823\pi$
$131$		−	2.73893i		−	0.239301i	0.992816	−	0.119651i	$-0.0381774\pi$
$132$	−10.2310	−	2.96890i	−0.890498	−	0.258410i
$133$			15.3361i			1.32981i
$134$	−1.28223	+	9.01961i	−0.110768	+	0.779175i
$135$	17.2836			1.48754
$136$	2.57839	+	1.16272i	0.221095	+	0.0997026i
$137$	22.7044			1.93977			0.969885	−	0.243564i	$-0.0783166\pi$
$137$	22.7044			1.93977			0.969885	+	0.243564i	$0.0783166\pi$
$138$	−1.41834	+	9.97705i	−0.120738	+	0.849303i
$139$			0.502570i			0.0426275i	0.999773	+	0.0213137i	$0.00678488\pi$
$139$			0.502570i			0.0426275i	−0.999773	+	0.0213137i	$0.993215\pi$
$140$	−6.36780	+	21.9439i	−0.538178	+	1.85460i
$141$			5.70256i			0.480242i
$142$	7.92573	+	1.12673i	0.665113	+	0.0945529i
$143$	−7.76556			−0.649388
$144$	0.139380	+	0.0883303i	0.0116150	+	0.00736086i
$145$	−23.6514			−1.96414
$146$	21.6302	+	3.07496i	1.79012	+	0.254485i
$147$		−	8.52662i		−	0.703264i
$148$	3.75902	−	12.9538i	0.308989	−	1.06480i
$149$		−	7.21213i		−	0.590840i	−0.955367	−	0.295420i	$-0.904540\pi$
$149$		−	7.21213i		−	0.590840i	0.955367	−	0.295420i	$-0.0954596\pi$
$150$	2.02543	−	14.2474i	0.165375	−	1.16330i
$151$	3.16671			0.257704			0.128852	−	0.991664i	$-0.458871\pi$
$151$	3.16671			0.257704			0.128852	+	0.991664i	$0.458871\pi$
$152$	5.15677	−	11.4354i	0.418270	−	0.927530i
$153$	−0.0412530			−0.00333511
$154$	−2.13135	+	14.9925i	−0.171749	+	1.20813i
$155$		−	20.5673i		−	1.65201i
$156$	−8.28530	−	2.40428i	−0.663355	−	0.192496i
$157$			3.16761i			0.252803i	0.991979	+	0.126401i	$0.0403427\pi$
$157$			3.16761i			0.252803i	−0.991979	+	0.126401i	$0.959657\pi$
$158$	11.4008	+	1.62075i	0.907000	+	0.128940i
$159$	10.6531			0.844846
$160$	12.1268	−	14.2213i	0.958710	−	1.12429i
$161$	14.3248			1.12896
$162$	12.4256	+	1.76643i	0.976244	+	0.138784i
$163$		−	1.66331i		−	0.130281i	−0.997876	−	0.0651404i	$-0.979250\pi$
$163$		−	1.66331i		−	0.130281i	0.997876	−	0.0651404i	$-0.0207495\pi$
$164$	−13.4421	−	3.90070i	−1.04965	−	0.304593i
$165$		−	17.5984i		−	1.37004i
$166$	−2.75732	+	19.3958i	−0.214009	+	1.50540i
$167$	−8.57648			−0.663668			−0.331834	−	0.943338i	$-0.607667\pi$
$167$	−8.57648			−0.663668			−0.331834	+	0.943338i	$0.607667\pi$
$168$	−6.91579	+	15.3361i	−0.533565	+	1.18320i
$169$	6.71130			0.516254
$170$	−0.657624	+	4.62592i	−0.0504374	+	0.354792i
$171$			0.182961i			0.0139914i
$172$	−1.24268	+	4.28237i	−0.0947536	+	0.326527i
$173$		−	4.48175i		−	0.340741i	−0.985380	−	0.170371i	$-0.945504\pi$
$173$		−	4.48175i		−	0.340741i	0.985380	−	0.170371i	$-0.0544965\pi$
$174$	−17.2406	−	2.45094i	−1.30701	−	0.185805i
$175$	−20.4562			−1.54634
$176$	6.63049	−	10.4625i	0.499792	−	0.788642i
$177$	−15.2011			−1.14258
$178$	−10.2582	−	1.45831i	−0.768882	−	0.109305i
$179$			3.60606i			0.269530i	0.990878	+	0.134765i	$0.0430279\pi$
$179$			3.60606i			0.269530i	−0.990878	+	0.134765i	$0.956972\pi$
$180$	−0.0759685	+	0.261793i	−0.00566236	+	0.0195129i
$181$			17.5384i			1.30362i	0.758384	+	0.651808i	$0.225989\pi$
$181$			17.5384i			1.30362i	−0.758384	+	0.651808i	$0.774011\pi$
$182$	−1.72601	+	12.1412i	−0.127940	+	0.899968i
$183$	24.7191			1.82729
$184$	−10.6813	−	4.81675i	−0.787439	−	0.355096i
$185$	22.2819			1.63820
$186$	2.13135	−	14.9925i	0.156278	−	1.09930i
$187$			3.09665i			0.226449i
$188$	−6.36780	−	1.84785i	−0.464420	−	0.134768i
$189$		−	18.0892i		−	1.31579i
$190$	20.5163	+	2.91662i	1.48841	+	0.211594i
$191$	8.76386			0.634130			0.317065	−	0.948404i	$-0.397303\pi$
$191$	8.76386			0.634130			0.317065	+	0.948404i	$0.397303\pi$
$192$	10.3135	−	9.10992i	0.744316	−	0.657452i
$193$	−18.4847			−1.33056			−0.665278	−	0.746595i	$-0.731687\pi$
$193$	−18.4847			−1.33056			−0.665278	+	0.746595i	$0.731687\pi$
$194$	−11.7161	−	1.66556i	−0.841164	−	0.119581i
$195$		−	14.2515i		−	1.02057i
$196$	9.52131	+	2.76295i	0.680093	+	0.197354i
$197$		−	3.87744i		−	0.276256i	−0.990414	−	0.138128i	$-0.955891\pi$
$197$		−	3.87744i		−	0.276256i	0.990414	−	0.138128i	$-0.0441085\pi$
$198$	−0.0254272	+	0.178862i	−0.00180703	+	0.0127112i
$199$	13.1409			0.931537			0.465769	−	0.884907i	$-0.345778\pi$
$199$	13.1409			0.931537			0.465769	+	0.884907i	$0.345778\pi$
$200$	15.2532	+	6.87842i	1.07856	+	0.486378i
$201$	−11.0808			−0.781580
$202$	−1.58336	+	11.1378i	−0.111405	+	0.783653i
$203$			24.7538i			1.73737i
$204$	−0.958747	+	3.30391i	−0.0671257	+	0.231320i
$205$		−	23.1217i		−	1.61489i
$206$	11.0808	+	1.57525i	0.772036	+	0.109753i
$207$	0.170897			0.0118782
$208$	5.36951	−	8.47276i	0.372308	−	0.587480i
$209$	13.7339			0.949994
$210$	−27.5146	−	3.91150i	−1.89869	−	0.269919i
$211$		−	13.5024i		−	0.929543i	−0.885431	−	0.464771i	$-0.846137\pi$
$211$		−	13.5024i		−	0.929543i	0.885431	−	0.464771i	$-0.153863\pi$
$212$	−3.45201	+	11.8959i	−0.237085	+	0.817011i
$213$			9.73695i			0.667165i
$214$	2.65933	−	18.7065i	0.181788	−	1.27875i
$215$	−7.36610			−0.502364
$216$	−6.08251	+	13.4882i	−0.413862	+	0.917757i
$217$	−21.5259			−1.46128
$218$	−0.423181	+	2.97678i	−0.0286614	+	0.201613i
$219$			26.5732i			1.79565i
$220$	19.6514	+	5.70256i	1.32490	+	0.384467i
$221$			2.50773i			0.168688i
$222$	16.2423	+	2.30902i	1.09011	+	0.154971i
$223$	−7.85147			−0.525773			−0.262887	−	0.964827i	$-0.584674\pi$
$223$	−7.85147			−0.525773			−0.262887	+	0.964827i	$0.584674\pi$
$224$	−14.8841	−	12.6920i	−0.994488	−	0.848022i
$225$	−0.244044			−0.0162696
$226$	−3.19973	−	0.454875i	−0.212843	−	0.0302579i
$227$			21.1858i			1.40615i	0.711115	+	0.703076i	$0.248191\pi$
$227$			21.1858i			1.40615i	−0.711115	+	0.703076i	$0.751809\pi$
$228$	14.6531	+	4.25212i	0.970425	+	0.281604i
$229$			13.6745i			0.903633i	0.892111	+	0.451817i	$0.149224\pi$
$229$			13.6745i			0.903633i	−0.892111	+	0.451817i	$0.850776\pi$
$230$	2.72430	−	19.1636i	0.179635	−	1.26361i
$231$	−18.4187			−1.21186
$232$	8.32349	−	18.4577i	0.546464	−	1.21181i
$233$	−18.1994			−1.19228			−0.596141	−	0.802880i	$-0.703300\pi$
$233$	−18.1994			−1.19228			−0.596141	+	0.802880i	$0.703300\pi$
$234$	−0.0205914	+	0.144846i	−0.00134610	+	0.00946888i
$235$		−	10.9533i		−	0.714512i
$236$	4.92573	−	16.9744i	0.320638	−	1.10494i
$237$			14.0062i			0.909799i
$238$	4.84153	+	0.688275i	0.313829	+	0.0446142i
$239$	2.93227			0.189673			0.0948364	−	0.995493i	$-0.469767\pi$
$239$	2.93227			0.189673			0.0948364	+	0.995493i	$0.469767\pi$
$240$	19.2011	+	12.1685i	1.23942	+	0.785470i
$241$	27.3180			1.75971			0.879853	−	0.475247i	$-0.157641\pi$
$241$	27.3180			1.75971			0.879853	+	0.475247i	$0.157641\pi$
$242$	−1.97525	−	0.280803i	−0.126974	−	0.0180507i
$243$		−	0.428684i		−	0.0275001i
$244$	−8.00994	+	27.6028i	−0.512784	+	1.76709i
$245$			16.3776i			1.04633i
$246$	2.39605	−	16.8545i	0.152767	−	1.07461i
$247$	11.1220			0.707675
$248$	16.0509	+	7.23813i	1.01923	+	0.459622i
$249$	−23.8282			−1.51005
$250$	−0.602247	+	4.23638i	−0.0380894	+	0.267932i
$251$		−	18.8286i		−	1.18845i	−0.804300	−	0.594224i	$-0.797459\pi$
$251$		−	18.8286i		−	1.18845i	0.804300	−	0.594224i	$-0.202541\pi$
$252$	0.273994	+	0.0795093i	0.0172600	+	0.00500862i
$253$		−	12.8283i		−	0.806510i
$254$	−3.31525	−	0.471298i	−0.208017	−	0.0295719i
$255$	−5.68305			−0.355886
$256$	6.83067	+	14.4687i	0.426917	+	0.904291i
$257$	7.58924			0.473404			0.236702	−	0.971582i	$-0.423934\pi$
$257$	7.58924			0.473404			0.236702	+	0.971582i	$0.423934\pi$
$258$	−5.36951	−	0.763333i	−0.334291	−	0.0475230i
$259$		−	23.3204i		−	1.44906i
$260$	15.9141	+	4.61805i	0.986950	+	0.286399i
$261$			0.295315i			0.0182795i
$262$	−0.545168	+	3.83487i	−0.0336806	+	0.236919i
$263$	30.0310			1.85179			0.925895	−	0.377782i	$-0.123313\pi$
$263$	30.0310			1.85179			0.925895	+	0.377782i	$0.123313\pi$
$264$	13.7339	+	6.19330i	0.845263	+	0.381171i
$265$	−20.4621			−1.25698
$266$	3.05256	−	21.4726i	0.187164	−	1.31657i
$267$		−	12.6024i		−	0.771255i
$268$	3.59060	−	12.3735i	0.219331	−	0.755829i
$269$		−	3.24478i		−	0.197837i	−0.995096	−	0.0989187i	$-0.968462\pi$
$269$		−	3.24478i		−	0.197837i	0.995096	−	0.0989187i	$-0.0315384\pi$
$270$	−24.1994	−	3.44020i	−1.47273	−	0.209364i
$271$	−11.6453			−0.707400			−0.353700	−	0.935359i	$-0.615077\pi$
$271$	−11.6453			−0.707400			−0.353700	+	0.935359i	$0.615077\pi$
$272$	−3.37866	−	2.14118i	−0.204861	−	0.129828i
$273$	−14.9158			−0.902745
$274$	−31.7893	−	4.51919i	−1.92046	−	0.273014i
$275$			18.3191i			1.10469i
$276$	3.97175	−	13.6869i	0.239071	−	0.823856i
$277$		−	16.9340i		−	1.01747i	−0.860924	−	0.508734i	$-0.830114\pi$
$277$		−	16.9340i		−	1.01747i	0.860924	−	0.508734i	$-0.169886\pi$
$278$	0.100034	−	0.703667i	0.00599963	−	0.0422031i
$279$	−0.256807			−0.0153746
$280$	13.2836	−	29.4569i	0.793847	−	1.76039i
$281$	7.38127			0.440330			0.220165	−	0.975463i	$-0.429340\pi$
$281$	7.38127			0.440330			0.220165	+	0.975463i	$0.429340\pi$
$282$	1.13506	−	7.98436i	0.0675920	−	0.475462i
$283$			19.3209i			1.14851i	0.818678	+	0.574253i	$0.194707\pi$
$283$			19.3209i			1.14851i	−0.818678	+	0.574253i	$0.805293\pi$
$284$	−10.8728	−	3.15514i	−0.645184	−	0.187223i
$285$			25.2048i			1.49300i
$286$	10.8728	+	1.54569i	0.642924	+	0.0913986i
$287$	−24.1994			−1.42844
$288$	−0.177569	−	0.151417i	−0.0104634	−	0.00892235i
$289$	1.00000			0.0588235
$290$	33.1152	+	4.70768i	1.94459	+	0.276444i
$291$		−	14.3935i		−	0.843760i
$292$	−29.6731	−	8.61072i	−1.73649	−	0.503904i
$293$			5.71966i			0.334146i	0.985945	+	0.167073i	$0.0534316\pi$
$293$			5.71966i			0.334146i	−0.985945	+	0.167073i	$0.946568\pi$
$294$	−1.69717	+	11.9384i	−0.0989813	+	0.696263i
$295$	29.1977			1.69995
$296$	−7.84153	+	17.3889i	−0.455779	+	1.01071i
$297$	−16.1994			−0.939984
$298$	−1.43553	+	10.0980i	−0.0831582	+	0.584959i
$299$		−	10.3886i		−	0.600790i
$300$	−5.67175	+	19.5452i	−0.327459	+	1.12844i
$301$			7.70943i			0.444364i
$302$	−4.43383	−	0.630316i	−0.255138	−	0.0362706i
$303$	−13.6831			−0.786071
$304$	−9.49633	+	14.9846i	−0.544652	+	0.859428i
$305$	−47.4796			−2.71867
$306$	0.0577599	+	0.00821118i	0.00330191	+	0.000469402i
$307$		−	0.222648i		−	0.0127072i	−0.999980	−	0.00635359i	$-0.997978\pi$
$307$		−	0.222648i		−	0.0127072i	0.999980	−	0.00635359i	$-0.00202242\pi$
$308$	5.96835	−	20.5673i	0.340078	−	1.17193i
$309$			13.6130i			0.774418i
$310$	−4.09381	+	28.7971i	−0.232513	+	1.63556i
$311$	3.88560			0.220332			0.110166	−	0.993913i	$-0.464862\pi$
$311$	3.88560			0.220332			0.110166	+	0.993913i	$0.464862\pi$
$312$	11.1220	+	5.01546i	0.629659	+	0.283944i
$313$	−20.4022			−1.15320			−0.576600	−	0.817027i	$-0.695621\pi$
$313$	−20.4022			−1.15320			−0.576600	+	0.817027i	$0.695621\pi$
$314$	0.630495	−	4.43508i	0.0355809	−	0.250286i
$315$			0.471298i			0.0265546i
$316$	−15.6401	−	4.53854i	−0.879824	−	0.255313i
$317$		−	6.32960i		−	0.355506i	−0.984075	−	0.177753i	$-0.943117\pi$
$317$		−	6.32960i		−	0.355506i	0.984075	−	0.177753i	$-0.0568827\pi$
$318$	−14.9158	−	2.12044i	−0.836436	−	0.118908i
$319$	22.1677			1.24115
$320$	−19.8099	+	17.4980i	−1.10741	+	0.978167i
$321$	22.9814			1.28269
$322$	−20.0567	−	2.85128i	−1.11772	−	0.158896i
$323$		−	4.43508i		−	0.246775i
$324$	−17.0459	−	4.94648i	−0.946994	−	0.274804i
$325$			14.8352i			0.822909i
$326$	−0.331073	+	2.32887i	−0.0183365	+	0.128984i
$327$	−3.65704			−0.202235
$328$	18.0443	+	8.13708i	0.996331	+	0.449295i
$329$	−11.4638			−0.632019
$330$	−3.50287	+	24.6402i	−0.192826	+	1.35640i
$331$			20.8922i			1.14834i	0.818736	+	0.574170i	$0.194675\pi$
$331$			20.8922i			1.14834i	−0.818736	+	0.574170i	$0.805325\pi$
$332$	7.72124	−	26.6079i	0.423758	−	1.46030i
$333$		−	0.278215i		−	0.0152461i
$334$	12.0082	+	1.70710i	0.657062	+	0.0934083i
$335$	21.2836			1.16285
$336$	12.7356	−	20.0960i	0.694784	−	1.09633i
$337$	8.82988			0.480994			0.240497	−	0.970650i	$-0.422690\pi$
$337$	8.82988			0.480994			0.240497	+	0.970650i	$0.422690\pi$
$338$	−9.39673	−	1.33585i	−0.511115	−	0.0726604i
$339$		−	3.93094i		−	0.213499i
$340$	1.84153	−	6.34602i	0.0998707	−	0.344161i
$341$			19.2771i			1.04391i
$342$	0.0364173	−	0.256170i	0.00196922	−	0.0138521i
$343$	−7.06433			−0.381438
$344$	2.59231	−	5.74855i	0.139768	−	0.309941i
$345$	23.5429			1.26751
$346$	−0.892067	+	6.27506i	−0.0479578	+	0.337349i
$347$		−	2.62301i		−	0.140811i	−0.997518	−	0.0704053i	$-0.977571\pi$
$347$		−	2.62301i		−	0.140811i	0.997518	−	0.0704053i	$-0.0224292\pi$
$348$	23.6514	+	6.86330i	1.26785	+	0.367912i
$349$			13.3575i			0.715013i	0.933911	+	0.357506i	$0.116373\pi$
$349$			13.3575i			0.715013i	−0.933911	+	0.357506i	$0.883627\pi$
$350$	28.6415	+	4.07169i	1.53095	+	0.217641i
$351$	−13.1186			−0.700218
$352$	−11.3661	+	13.3292i	−0.605815	+	0.710449i
$353$	0.510209			0.0271557			0.0135779	−	0.999908i	$-0.495678\pi$
$353$	0.510209			0.0271557			0.0135779	+	0.999908i	$0.495678\pi$
$354$	21.2836	+	3.02569i	1.13121	+	0.160814i
$355$		−	18.7024i		−	0.992619i
$356$	14.0726	+	4.08366i	0.745844	+	0.216434i
$357$			5.94793i			0.314798i
$358$	0.717766	−	5.04898i	0.0379351	−	0.266847i
$359$	−0.861534			−0.0454700			−0.0227350	−	0.999742i	$-0.507237\pi$
$359$	−0.861534			−0.0454700			−0.0227350	+	0.999742i	$0.507237\pi$
$360$	0.158475	−	0.351424i	0.00835234	−	0.0185217i
$361$	−0.669976			−0.0352619
$362$	3.49091	−	24.5561i	0.183478	−	1.29064i
$363$		−	2.42665i		−	0.127366i
$364$	4.83329	−	16.6558i	0.253333	−	0.873002i
$365$		−	51.0407i		−	2.67159i
$366$	−34.6101	−	4.92020i	−1.80910	−	0.257183i
$367$	3.07492			0.160509			0.0802547	−	0.996774i	$-0.474427\pi$
$367$	3.07492			0.160509			0.0802547	+	0.996774i	$0.474427\pi$
$368$	13.9966	+	8.87017i	0.729623	+	0.462390i
$369$	−0.288701			−0.0150292
$370$	−31.1977	−	4.43508i	−1.62189	−	0.230569i
$371$			21.4158i			1.11185i
$372$	−5.96835	+	20.5673i	−0.309444	+	1.06637i
$373$		−	8.12750i		−	0.420826i	−0.977613	−	0.210413i	$-0.932519\pi$
$373$		−	8.12750i		−	0.420826i	0.977613	−	0.210413i	$-0.0674809\pi$
$374$	0.616371	−	4.33573i	0.0318718	−	0.224195i
$375$	−5.20449			−0.268759
$376$	8.54799	+	3.85471i	0.440829	+	0.198792i
$377$	17.9519			0.924568
$378$	−3.60054	+	25.3273i	−0.185192	+	1.30270i
$379$		−	9.01502i		−	0.463070i	−0.972827	−	0.231535i	$-0.925625\pi$
$379$		−	9.01502i		−	0.463070i	0.972827	−	0.231535i	$-0.0743748\pi$
$380$	−28.1451	−	8.16732i	−1.44381	−	0.418975i
$381$		−	4.07286i		−	0.208659i
$382$	−12.2706	−	1.74440i	−0.627818	−	0.0892510i
$383$	−1.79721			−0.0918331			−0.0459165	−	0.998945i	$-0.514621\pi$
$383$	−1.79721			−0.0918331			−0.0459165	+	0.998945i	$0.514621\pi$
$384$	−16.2536	+	10.7023i	−0.829440	+	0.546148i
$385$	35.3779			1.80302
$386$	25.8811	+	3.67927i	1.31731	+	0.187270i
$387$			0.0919742i			0.00467531i
$388$	16.0726	+	4.66403i	0.815961	+	0.236780i
$389$		−	18.7490i		−	0.950614i	−0.879820	−	0.475307i	$-0.842337\pi$
$389$		−	18.7490i		−	0.950614i	0.879820	−	0.475307i	$-0.157663\pi$
$390$	−2.83669	+	19.9541i	−0.143641	+	1.01042i
$391$	−4.14265			−0.209503
$392$	−12.7812	−	5.76367i	−0.645547	−	0.291109i
$393$	−4.71123			−0.237650
$394$	−0.771781	+	5.42894i	−0.0388818	+	0.273506i
$395$		−	26.9025i		−	1.35361i
$396$	0.0712030	−	0.245370i	0.00357808	−	0.0123303i
$397$		−	23.9280i		−	1.20091i	−0.799658	−	0.600456i	$-0.794986\pi$
$397$		−	23.9280i		−	1.20091i	0.799658	−	0.600456i	$-0.205014\pi$
$398$	−18.3991	−	2.61563i	−0.922264	−	0.131110i
$399$	26.3796			1.32063
$400$	−19.9874	−	12.6668i	−0.999372	−	0.633340i
$401$	6.58236			0.328708			0.164354	−	0.986401i	$-0.447446\pi$
$401$	6.58236			0.328708			0.164354	+	0.986401i	$0.447446\pi$
$402$	15.5146	+	2.20557i	0.773800	+	0.110004i
$403$			15.6110i			0.777639i
$404$	4.43383	−	15.2793i	0.220591	−	0.760172i
$405$		−	29.3206i		−	1.45695i
$406$	4.92710	−	34.6586i	0.244528	−	1.72008i
$407$	−20.8841			−1.03519
$408$	2.00000	−	4.43508i	0.0990148	−	0.219569i
$409$	29.7717			1.47212			0.736058	−	0.676919i	$-0.236685\pi$
$409$	29.7717			1.47212			0.736058	+	0.676919i	$0.236685\pi$
$410$	−4.60225	+	32.3736i	−0.227289	+	1.59882i
$411$		−	39.0539i		−	1.92639i
$412$	−15.2011	−	4.41114i	−0.748904	−	0.217321i
$413$		−	30.5585i		−	1.50369i
$414$	−0.239279	−	0.0340160i	−0.0117599	−	0.00167180i
$415$	45.7683			2.24668
$416$	−9.20449	+	10.7942i	−0.451287	+	0.529231i
$417$	0.864472			0.0423334
$418$	−19.2293	−	2.73366i	−0.940538	−	0.133707i
$419$			24.2375i			1.18408i	0.805909	+	0.592040i	$0.201677\pi$
$419$			24.2375i			1.18408i	−0.805909	+	0.592040i	$0.798323\pi$
$420$	37.7457	+	10.9533i	1.84180	+	0.534465i
$421$		−	19.8507i		−	0.967462i	−0.875217	−	0.483731i	$-0.839281\pi$
$421$		−	19.8507i		−	0.967462i	0.875217	−	0.483731i	$-0.160719\pi$
$422$	−2.68757	+	18.9052i	−0.130829	+	0.920290i
$423$	−0.136764			−0.00664969
$424$	7.20109	−	15.9687i	0.349716	−	0.775510i
$425$	5.91579			0.286958
$426$	1.93809	−	13.6331i	0.0939005	−	0.660524i
$427$			49.6925i			2.40479i
$428$	−7.44684	+	25.6623i	−0.359956	+	1.24043i
$429$			13.3575i			0.644908i
$430$	10.3135	+	1.46618i	0.497363	+	0.0707055i
$431$	−1.84218			−0.0887346			−0.0443673	−	0.999015i	$-0.514127\pi$
$431$	−1.84218			−0.0887346			−0.0443673	+	0.999015i	$0.514127\pi$
$432$	11.2011	−	17.6746i	0.538913	−	0.850372i
$433$	8.03955			0.386356			0.193178	−	0.981164i	$-0.438120\pi$
$433$	8.03955			0.386356			0.193178	+	0.981164i	$0.438120\pi$
$434$	30.1392	+	4.28462i	1.44673	+	0.205668i
$435$			40.6828i			1.95059i
$436$	1.18502	−	4.08366i	0.0567522	−	0.195572i
$437$			18.3730i			0.878900i
$438$	5.28924	−	37.2060i	0.252730	−	1.77777i
$439$	14.4184			0.688153			0.344077	−	0.938942i	$-0.388192\pi$
$439$	14.4184			0.688153			0.344077	+	0.938942i	$0.388192\pi$
$440$	−26.3796	−	11.8959i	−1.25760	−	0.567113i
$441$	0.204493			0.00973777
$442$	0.499149	−	3.51116i	0.0237421	−	0.167009i
$443$		−	30.7835i		−	1.46257i	−0.682072	−	0.731285i	$-0.738921\pi$
$443$		−	30.7835i		−	1.46257i	0.682072	−	0.731285i	$-0.261079\pi$
$444$	−22.2819	−	6.46589i	−1.05745	−	0.306858i
$445$			24.2062i			1.14749i
$446$	10.9931	+	1.56279i	0.520539	+	0.0740002i
$447$	−12.4056			−0.586764
$448$	18.3135	+	20.7332i	0.865234	+	0.979551i
$449$	12.6305			0.596070			0.298035	−	0.954555i	$-0.403669\pi$
$449$	12.6305			0.596070			0.298035	+	0.954555i	$0.403669\pi$
$450$	0.341695	+	0.0485757i	0.0161077	+	0.00228988i
$451$			21.6713i			1.02046i
$452$	4.38951	+	1.27378i	0.206465	+	0.0599133i
$453$		−	5.44707i		−	0.255926i
$454$	4.21692	−	29.6630i	0.197910	−	1.39215i
$455$	28.6497			1.34312
$456$	−19.6700	−	8.87017i	−0.921131	−	0.415384i
$457$	20.3592			0.952364			0.476182	−	0.879347i	$-0.342020\pi$
$457$	20.3592			0.952364			0.476182	+	0.879347i	$0.342020\pi$
$458$	2.72182	−	19.1461i	0.127182	−	0.894638i
$459$			5.23126i			0.244174i
$460$	−7.62879	+	26.2893i	−0.355694	+	1.22575i
$461$			33.5671i			1.56338i	0.623669	+	0.781689i	$0.285641\pi$
$461$			33.5671i			1.56338i	−0.623669	+	0.781689i	$0.714359\pi$
$462$	25.7886	+	3.66613i	1.19980	+	0.170564i
$463$	−21.8316			−1.01460			−0.507300	−	0.861770i	$-0.669356\pi$
$463$	−21.8316			−1.01460			−0.507300	+	0.861770i	$0.669356\pi$
$464$	−15.3279	+	24.1865i	−0.711580	+	1.12283i
$465$	−35.3779			−1.64061
$466$	25.4816	+	3.62248i	1.18041	+	0.167808i
$467$			23.2705i			1.07683i	0.842680	+	0.538415i	$0.180977\pi$
$467$			23.2705i			1.07683i	−0.842680	+	0.538415i	$0.819023\pi$
$468$	0.0576616	−	0.198706i	0.00266541	−	0.00918517i
$469$		−	22.2756i		−	1.02859i
$470$	−2.18019	+	15.3361i	−0.100564	+	0.707400i
$471$	5.44861			0.251059
$472$	−10.2754	+	22.7860i	−0.472962	+	1.04881i
$473$	6.90402			0.317447
$474$	2.78785	−	19.6106i	0.128050	−	0.900743i
$475$		−	26.2370i		−	1.20384i
$476$	−6.64180	−	1.92736i	−0.304426	−	0.0883402i
$477$			0.255492i			0.0116982i
$478$	−4.10558	−	0.583652i	−0.187785	−	0.0266956i
$479$	−43.5363			−1.98923			−0.994613	−	0.103662i	$-0.966944\pi$
$479$	−43.5363			−1.98923			−0.994613	+	0.103662i	$0.966944\pi$
$480$	−24.4621	−	20.8594i	−1.11654	−	0.952095i
$481$	−16.9124			−0.771139
$482$	−38.2489	−	5.43749i	−1.74219	−	0.247671i
$483$		−	24.6402i		−	1.12117i
$484$	2.70973	+	0.786326i	0.123170	+	0.0357421i
$485$			27.6464i			1.25536i
$486$	−0.0853270	+	0.600215i	−0.00387051	+	0.0272263i
$487$	20.2912			0.919481			0.459741	−	0.888053i	$-0.347942\pi$
$487$	20.2912			0.919481			0.459741	+	0.888053i	$0.347942\pi$
$488$	16.7092	−	37.0533i	0.756389	−	1.67733i
$489$	−2.86107			−0.129382
$490$	3.25987	−	22.9309i	0.147266	−	1.03591i
$491$			39.6117i			1.78765i	0.448416	+	0.893825i	$0.351988\pi$
$491$			39.6117i			1.78765i	−0.448416	+	0.893825i	$0.648012\pi$
$492$	−6.70960	+	23.1217i	−0.302492	+	1.04241i
$493$		−	7.15862i		−	0.322408i
$494$	−15.5723	−	2.21377i	−0.700631	−	0.0996022i
$495$	0.422061			0.0189703
$496$	−21.0327	−	13.3292i	−0.944395	−	0.598499i
$497$	−19.5741			−0.878017
$498$	33.3627	+	4.74286i	1.49502	+	0.212533i
$499$		−	9.69556i		−	0.434033i	−0.976168	−	0.217016i	$-0.930367\pi$
$499$		−	9.69556i		−	0.434033i	0.976168	−	0.217016i	$-0.0696325\pi$
$500$	1.68645	−	5.81163i	0.0754205	−	0.259904i
$501$			14.7524i			0.659089i
$502$	−3.74772	+	26.3625i	−0.167269	+	1.17662i
$503$	−39.2861			−1.75168			−0.875840	−	0.482602i	$-0.839692\pi$
$503$	−39.2861			−1.75168			−0.875840	+	0.482602i	$0.839692\pi$
$504$	−0.367803	−	0.165861i	−0.0163833	−	0.00738803i
$505$	26.2819			1.16953
$506$	−2.55341	+	17.9614i	−0.113513	+	0.798482i
$507$		−	11.5441i		−	0.512692i
$508$	4.54799	+	1.31976i	0.201784	+	0.0585550i
$509$			7.64374i			0.338803i	0.985547	+	0.169401i	$0.0541834\pi$
$509$			7.64374i			0.338803i	−0.985547	+	0.169401i	$0.945817\pi$
$510$	7.95705	+	1.13118i	0.352344	+	0.0500895i
$511$	−53.4197			−2.36315
$512$	−6.68396	−	21.6177i	−0.295392	−	0.955376i
$513$	23.2011			1.02435
$514$	−10.6260	−	1.51060i	−0.468692	−	0.0666295i
$515$		−	26.1474i		−	1.15219i
$516$	7.36610	+	2.13754i	0.324275	+	0.0940999i
$517$			10.2662i			0.451505i
$518$	−4.64180	+	32.6518i	−0.203949	+	1.43464i
$519$	−7.70906			−0.338390
$520$	−21.3627	−	9.63350i	−0.936816	−	0.422457i
$521$	4.66487			0.204372			0.102186	−	0.994765i	$-0.467416\pi$
$521$	4.66487			0.204372			0.102186	+	0.994765i	$0.467416\pi$
$522$	0.0587807	−	0.413481i	0.00257276	−	0.0180976i
$523$		−	34.7381i		−	1.51899i	−0.650511	−	0.759496i	$-0.725445\pi$
$523$		−	34.7381i		−	1.51899i	0.650511	−	0.759496i	$-0.274555\pi$
$524$	1.52662	−	5.26083i	0.0666906	−	0.229820i
$525$			35.1867i			1.53567i
$526$	−42.0475	−	5.97749i	−1.83336	−	0.260631i
$527$	6.22515			0.271172
$528$	−17.9966	−	11.4051i	−0.783201	−	0.496344i
$529$	−5.83846			−0.253846
$530$	28.6497	+	4.07286i	1.24446	+	0.176914i
$531$		−	0.364566i		−	0.0158208i
$532$	−8.54799	+	29.4569i	−0.370602	+	1.27712i
$533$			17.5498i			0.760168i
$534$	−2.50844	+	17.6451i	−0.108551	+	0.763577i
$535$	−44.1417			−1.90841
$536$	−7.49020	+	16.6098i	−0.323527	+	0.717436i
$537$	6.20279			0.267670
$538$	−0.645854	+	4.54313i	−0.0278448	+	0.195868i
$539$		−	15.3502i		−	0.661181i
$540$	33.1977	+	9.63350i	1.42860	+	0.414560i
$541$		−	24.8504i		−	1.06840i	−0.845358	−	0.534200i	$-0.820613\pi$
$541$		−	24.8504i		−	1.06840i	0.845358	−	0.534200i	$-0.179387\pi$
$542$	16.3050	+	2.31793i	0.700358	+	0.0995634i
$543$	30.1677			1.29462
$544$	4.30439	+	3.67045i	0.184549	+	0.157369i
$545$	7.02431			0.300888
$546$	20.8841	+	2.96890i	0.893759	+	0.127057i
$547$			7.32619i			0.313245i	0.987659	+	0.156623i	$0.0500606\pi$
$547$			7.32619i			0.313245i	−0.987659	+	0.156623i	$0.949939\pi$
$548$	43.6098	+	12.6550i	1.86292	+	0.540593i
$549$			0.592837i			0.0253017i
$550$	3.64632	−	25.6493i	0.155480	−	1.09369i
$551$	−31.7491			−1.35256
$552$	−8.28530	+	18.3730i	−0.352646	+	0.782007i
$553$	−28.1564			−1.19733
$554$	−3.37062	+	23.7100i	−0.143204	+	1.00734i
$555$		−	38.3271i		−	1.62689i
$556$	−0.280122	+	0.965318i	−0.0118798	+	0.0409386i
$557$			36.3646i			1.54082i	0.637551	+	0.770408i	$0.279947\pi$
$557$			36.3646i			1.54082i	−0.637551	+	0.770408i	$0.720053\pi$
$558$	0.359564	+	0.0511159i	0.0152216	+	0.00216391i
$559$	5.59101			0.236475
$560$	−24.4621	+	38.5997i	−1.03371	+	1.63113i
$561$	5.32655			0.224887
$562$	−10.3348	−	1.46920i	−0.435947	−	0.0619745i
$563$		−	20.9579i		−	0.883270i	−0.897195	−	0.441635i	$-0.854399\pi$
$563$		−	20.9579i		−	0.883270i	0.897195	−	0.441635i	$-0.145601\pi$
$564$	−3.17848	+	10.9533i	−0.133838	+	0.461216i
$565$			7.55041i			0.317648i
$566$	3.84571	−	27.0518i	0.161647	−	1.13707i
$567$	−30.6872			−1.28874
$568$	14.5954	+	6.58181i	0.612411	+	0.276167i
$569$	−17.3214			−0.726150			−0.363075	−	0.931760i	$-0.618273\pi$
$569$	−17.3214			−0.726150			−0.363075	+	0.931760i	$0.618273\pi$
$570$	5.01687	−	35.2902i	0.210134	−	1.47814i
$571$			41.5633i			1.73937i	0.493606	+	0.869686i	$0.335678\pi$
$571$			41.5633i			1.73937i	−0.493606	+	0.869686i	$0.664322\pi$
$572$	−14.9158	−	4.32835i	−0.623661	−	0.180978i
$573$		−	15.0747i		−	0.629755i
$574$	33.8824	+	4.81675i	1.41423	+	0.201047i
$575$	−24.5070			−1.02201
$576$	0.218482	+	0.247349i	0.00910343	+	0.0103062i
$577$	−3.88631			−0.161789			−0.0808946	−	0.996723i	$-0.525778\pi$
$577$	−3.88631			−0.161789			−0.0808946	+	0.996723i	$0.525778\pi$
$578$	−1.40014	−	0.199044i	−0.0582380	−	0.00827915i
$579$			31.7955i			1.32138i
$580$	−45.4287	−	13.1828i	−1.88633	−	0.547385i
$581$		−	47.9015i		−	1.98729i
$582$	−2.86494	+	20.1528i	−0.118755	+	0.835361i
$583$	19.1785			0.794292
$584$	39.8325	+	17.9624i	1.64828	+	0.743291i
$585$	0.341794			0.0141314
$586$	1.13847	−	8.00830i	0.0470296	−	0.330820i
$587$		−	14.7386i		−	0.608327i	−0.952620	−	0.304163i	$-0.901623\pi$
$587$		−	14.7386i		−	0.608327i	0.952620	−	0.304163i	$-0.0983769\pi$
$588$	4.75255	−	16.3776i	0.195992	−	0.675401i
$589$		−	27.6091i		−	1.13761i
$590$	−40.8807	−	5.81163i	−1.68303	−	0.239261i
$591$	−6.66958			−0.274350
$592$	14.4404	−	22.7860i	0.593495	−	0.936500i
$593$	−40.2819			−1.65418			−0.827090	−	0.562070i	$-0.810005\pi$
$593$	−40.2819			−1.65418			−0.827090	+	0.562070i	$0.810005\pi$
$594$	22.6813	+	3.22440i	0.930627	+	0.132299i
$595$		−	11.4246i		−	0.468361i
$596$	4.01988	−	13.8528i	0.164661	−	0.567432i
$597$		−	22.6038i		−	0.925110i
$598$	−2.06780	+	14.5455i	−0.0845586	+	0.594810i
$599$	15.4982			0.633238			0.316619	−	0.948553i	$-0.397452\pi$
$599$	15.4982			0.633238			0.316619	+	0.948553i	$0.397452\pi$
$600$	11.8316	−	26.2370i	0.483022	−	1.07112i
$601$	31.9519			1.30334			0.651672	−	0.758501i	$-0.274068\pi$
$601$	31.9519			1.30334			0.651672	+	0.758501i	$0.274068\pi$
$602$	1.53452	−	10.7942i	0.0625423	−	0.439941i
$603$		−	0.265750i		−	0.0108222i
$604$	6.08251	+	1.76506i	0.247494	+	0.0718192i
$605$			4.66101i			0.189497i
$606$	19.1581	+	2.72353i	0.778246	+	0.110636i
$607$	−3.04667			−0.123661			−0.0618303	−	0.998087i	$-0.519694\pi$
$607$	−3.04667			−0.123661			−0.0618303	+	0.998087i	$0.519694\pi$
$608$	16.2788	−	19.0903i	0.660191	−	0.774216i
$609$	42.5790			1.72539
$610$	66.4779	+	9.45054i	2.69161	+	0.382641i
$611$			8.31374i			0.336338i
$612$	−0.0792373	−	0.0229935i	−0.00320298	−	0.000929459i
$613$			34.0750i			1.37628i	0.725580	+	0.688138i	$0.241572\pi$
$613$			34.0750i			1.37628i	−0.725580	+	0.688138i	$0.758428\pi$
$614$	−0.0443168	+	0.311737i	−0.00178848	+	0.0125807i
$615$	−39.7717			−1.60375
$616$	−12.4503	+	27.6091i	−0.501637	+	1.11240i
$617$	40.1395			1.61595			0.807977	−	0.589213i	$-0.200562\pi$
$617$	40.1395			1.61595			0.807977	+	0.589213i	$0.200562\pi$
$618$	2.70960	−	19.0601i	0.108996	−	0.766710i
$619$			9.21372i			0.370331i	0.982707	+	0.185165i	$0.0592821\pi$
$619$			9.21372i			0.370331i	−0.982707	+	0.185165i	$0.940718\pi$
$620$	11.4638	−	39.5049i	0.460397	−	1.58656i
$621$		−	21.6713i		−	0.869639i
$622$	−5.44037	−	0.773407i	−0.218139	−	0.0310108i
$623$	25.3344			1.01500
$624$	−14.5740	−	9.23609i	−0.583427	−	0.369740i
$625$	−19.5824			−0.783295
$626$	28.5658	+	4.06094i	1.14172	+	0.162308i
$627$		−	23.6237i		−	0.943440i
$628$	−1.76556	+	6.08423i	−0.0704534	+	0.242787i
$629$			6.74411i			0.268905i
$630$	0.0938092	−	0.659881i	0.00373745	−	0.0262903i
$631$	23.0526			0.917708			0.458854	−	0.888512i	$-0.348260\pi$
$631$	23.0526			0.917708			0.458854	+	0.888512i	$0.348260\pi$
$632$	20.9949	+	9.46764i	0.835132	+	0.376603i
$633$	−23.2255			−0.923129
$634$	−1.25987	+	8.86230i	−0.0500358	+	0.351967i
$635$			7.82300i			0.310446i
$636$	20.4621	+	5.93781i	0.811374	+	0.235449i
$637$		−	12.4309i		−	0.492531i
$638$	−31.0378	−	4.41236i	−1.22880	−	0.174687i
$639$	−0.233521			−0.00923793
$640$	31.2194	−	20.5565i	1.23406	−	0.812568i
$641$	11.6322			0.459444			0.229722	−	0.973256i	$-0.426218\pi$
$641$	11.6322			0.459444			0.229722	+	0.973256i	$0.426218\pi$
$642$	−32.1770	−	4.57431i	−1.26993	−	0.180534i
$643$			21.1290i			0.833247i	0.909079	+	0.416624i	$0.136787\pi$
$643$			21.1290i			0.833247i	−0.909079	+	0.416624i	$0.863213\pi$
$644$	27.5146	+	7.98436i	1.08423	+	0.314628i
$645$			12.6704i			0.498898i
$646$	−0.882778	+	6.20972i	−0.0347325	+	0.244318i
$647$	−29.5854			−1.16312			−0.581560	−	0.813503i	$-0.697558\pi$
$647$	−29.5854			−1.16312			−0.581560	+	0.813503i	$0.697558\pi$
$648$	22.8820	+	10.3186i	0.898889	+	0.405354i
$649$	−27.3661			−1.07421
$650$	2.95286	−	20.7713i	0.115821	−	0.814717i
$651$			37.0268i			1.45119i
$652$	0.927095	−	3.19483i	0.0363079	−	0.125119i
$653$			2.85861i			0.111866i	0.998435	+	0.0559330i	$0.0178133\pi$
$653$			2.85861i			0.111866i	−0.998435	+	0.0559330i	$0.982187\pi$
$654$	5.12036	+	0.727913i	0.200222	+	0.0284637i
$655$	9.04915			0.353580
$656$	−23.6449	−	14.9846i	−0.923177	−	0.585052i
$657$	−0.637302			−0.0248635
$658$	16.0509	+	2.28180i	0.625727	+	0.0889538i
$659$		−	0.654259i		−	0.0254863i	−0.999919	−	0.0127431i	$-0.995944\pi$
$659$		−	0.654259i		−	0.0254863i	0.999919	−	0.0127431i	$-0.00405638\pi$
$660$	9.80898	−	33.8024i	0.381814	−	1.31576i
$661$		−	16.3412i		−	0.635599i	−0.948158	−	0.317800i	$-0.897056\pi$
$661$		−	16.3412i		−	0.635599i	0.948158	−	0.317800i	$-0.102944\pi$
$662$	4.15847	−	29.2519i	0.161624	−	1.13691i
$663$	4.31355			0.167524
$664$	−16.1069	+	35.7178i	−0.625071	+	1.38612i
$665$	−50.6689			−1.96486
$666$	−0.0553771	+	0.389539i	−0.00214582	+	0.0150943i
$667$			29.6556i			1.14827i
$668$	−16.4734	−	4.78034i	−0.637374	−	0.184957i
$669$			13.5053i			0.522146i
$670$	−29.7999	−	4.23638i	−1.15127	−	0.163666i
$671$	44.5012			1.71795
$672$	−21.8316	+	25.6022i	−0.842172	+	0.987627i
$673$	18.7921			0.724382			0.362191	−	0.932104i	$-0.382029\pi$
$673$	18.7921			0.724382			0.362191	+	0.932104i	$0.382029\pi$
$674$	−12.3630	−	1.75754i	−0.476206	−	0.0676978i
$675$			30.9471i			1.19115i
$676$	12.8908	+	3.74073i	0.495800	+	0.143874i
$677$			20.5706i			0.790593i	0.918554	+	0.395296i	$0.129358\pi$
$677$			20.5706i			0.790593i	−0.918554	+	0.395296i	$0.870642\pi$
$678$	−0.782432	+	5.50385i	−0.0300491	+	0.211374i
$679$	28.9350			1.11042
$680$	−3.84153	+	8.51875i	−0.147316	+	0.326679i
$681$	36.4417			1.39645
$682$	3.83700	−	26.9906i	0.146926	−	1.03352i
$683$			40.4925i			1.54940i	0.632327	+	0.774701i	$0.282100\pi$
$683$			40.4925i			1.54940i	−0.632327	+	0.774701i	$0.717900\pi$
$684$	−0.101978	+	0.351424i	−0.00389924	+	0.0134370i
$685$			75.0133i			2.86611i
$686$	9.89102	+	1.40611i	0.377641	+	0.0536857i
$687$	23.5214			0.897399
$688$	−4.77380	+	7.53276i	−0.181999	+	0.287184i
$689$	15.5311			0.591688
$690$	−32.9632	−	4.68608i	−1.25489	−	0.178396i
$691$		−	9.29651i		−	0.353656i	−0.984242	−	0.176828i	$-0.943416\pi$
$691$		−	9.29651i		−	0.353656i	0.984242	−	0.176828i	$-0.0565836\pi$
$692$	2.49803	−	8.60838i	0.0949608	−	0.327241i
$693$		−	0.441733i		−	0.0167801i
$694$	−0.522095	+	3.67257i	−0.0198185	+	0.139409i
$695$	−1.66044			−0.0629843
$696$	−31.7491	−	14.3172i	−1.20345	−	0.542693i
$697$	6.99830			0.265079
$698$	2.65874	−	18.7024i	0.100635	−	0.707895i
$699$			31.3048i			1.18406i
$700$	−39.2915	−	11.4018i	−1.48508	−	0.430949i
$701$		−	46.6793i		−	1.76305i	−0.472134	−	0.881527i	$-0.656516\pi$
$701$		−	46.6793i		−	1.76305i	0.472134	−	0.881527i	$-0.343484\pi$
$702$	18.3678	+	2.61118i	0.693248	+	0.0985526i
$703$	29.9107			1.12810
$704$	18.5672	−	16.4003i	0.699777	−	0.618111i
$705$	−18.8407			−0.709583
$706$	−0.714363	−	0.101554i	−0.0268854	−	0.00382205i
$707$		−	27.5069i		−	1.03450i
$708$	−29.1977	−	8.47276i	−1.09732	−	0.318426i
$709$		−	39.5821i		−	1.48654i	−0.668993	−	0.743269i	$-0.733274\pi$
$709$		−	39.5821i		−	1.48654i	0.668993	−	0.743269i	$-0.266726\pi$
$710$	−3.72260	+	26.1859i	−0.139707	+	0.982738i
$711$	−0.335909			−0.0125976
$712$	−18.8907	−	8.51875i	−0.707958	−	0.319253i
$713$	−25.7886			−0.965792
$714$	1.18390	−	8.32791i	0.0443064	−	0.311664i
$715$		−	25.6567i		−	0.959505i
$716$	−2.00994	+	6.92639i	−0.0751150	+	0.258851i
$717$		−	5.04380i		−	0.188364i
$718$	1.20627	+	0.171483i	0.0450174	+	0.00639971i
$719$	38.3669			1.43084			0.715422	−	0.698693i	$-0.246235\pi$
$719$	38.3669			1.43084			0.715422	+	0.698693i	$0.246235\pi$
$720$	−0.291835	+	0.460498i	−0.0108760	+	0.0171618i
$721$	−27.3661			−1.01917
$722$	0.938057	+	0.133355i	0.0349109	+	0.00496295i
$723$		−	46.9897i		−	1.74756i
$724$	−9.77550	+	33.6870i	−0.363304	+	1.25197i
$725$		−	42.3489i		−	1.57280i
$726$	−0.483010	+	3.39764i	−0.0179262	+	0.126098i
$727$	−17.3344			−0.642899			−0.321450	−	0.946927i	$-0.604170\pi$
$727$	−17.3344			−0.642899			−0.321450	+	0.946927i	$0.604170\pi$
$728$	−10.0825	+	22.3584i	−0.373683	+	0.828657i
$729$	−27.3610			−1.01337
$730$	−10.1594	+	71.4640i	−0.376015	+	2.64500i
$731$		−	2.22951i		−	0.0824615i
$732$	47.4796	+	13.7779i	1.75490	+	0.509246i
$733$		−	45.3211i		−	1.67397i	−0.547224	−	0.836986i	$-0.684315\pi$
$733$		−	45.3211i		−	1.67397i	0.547224	−	0.836986i	$-0.315685\pi$
$734$	−4.30531	−	0.612045i	−0.158912	−	0.0225910i
$735$	28.1711			1.03911
$736$	−17.8316	−	15.2054i	−0.657281	−	0.560478i
$737$	−19.9485			−0.734811
$738$	0.404221	+	0.0574643i	0.0148796	+	0.00211529i
$739$		−	20.9602i		−	0.771035i	−0.922701	−	0.385517i	$-0.874023\pi$
$739$		−	20.9602i		−	0.771035i	0.922701	−	0.385517i	$-0.125977\pi$
$740$	42.7982	+	12.4194i	1.57329	+	0.456548i
$741$		−	19.1309i		−	0.702793i
$742$	4.26269	−	29.9850i	0.156488	−	1.10078i
$743$	−20.7354			−0.760707			−0.380353	−	0.924841i	$-0.624198\pi$
$743$	−20.7354			−0.760707			−0.380353	+	0.924841i	$0.624198\pi$
$744$	12.4503	−	27.6091i	0.456450	−	1.01220i
$745$	23.8282			0.872997
$746$	−1.61773	+	11.3796i	−0.0592294	+	0.416637i
$747$		−	0.571469i		−	0.0209090i
$748$	−1.72601	+	5.94793i	−0.0631090	+	0.217478i
$749$			46.1991i			1.68808i
$750$	7.28700	+	1.03592i	0.266084	+	0.0378266i
$751$	−17.6725			−0.644877			−0.322439	−	0.946590i	$-0.604503\pi$
$751$	−17.6725			−0.644877			−0.322439	+	0.946590i	$0.604503\pi$
$752$	−11.2011	−	7.09855i	−0.408462	−	0.258858i
$753$	−32.3870			−1.18025
$754$	−25.1351	−	3.57322i	−0.915365	−	0.130129i
$755$			10.4625i			0.380770i
$756$	10.0825	−	34.7450i	0.366697	−	1.26366i
$757$		−	22.0131i		−	0.800081i	−0.916498	−	0.400040i	$-0.868996\pi$
$757$		−	22.0131i		−	0.800081i	0.916498	−	0.400040i	$-0.131004\pi$
$758$	−1.79439	+	12.6222i	−0.0651751	+	0.458461i
$759$	−22.0660			−0.800946
$760$	37.7814	+	17.0375i	1.37047	+	0.618015i
$761$	18.9024			0.685211			0.342606	−	0.939479i	$-0.388691\pi$
$761$	18.9024			0.685211			0.342606	+	0.939479i	$0.388691\pi$
$762$	−0.810680	+	5.70256i	−0.0293678	+	0.206582i
$763$		−	7.35170i		−	0.266149i
$764$	16.8333	+	4.88478i	0.609007	+	0.176725i
$765$		−	0.136296i		−	0.00492780i
$766$	2.51634	+	0.357724i	0.0909189	+	0.0129251i
$767$	−22.1616			−0.800209
$768$	24.8875	−	11.7494i	0.898052	−	0.423971i
$769$	44.8954			1.61897			0.809486	−	0.587140i	$-0.199746\pi$
$769$	44.8954			1.61897			0.809486	+	0.587140i	$0.199746\pi$
$770$	−49.5338	−	7.04176i	−1.78508	−	0.253768i
$771$		−	13.0543i		−	0.470138i
$772$	−35.5047	−	10.3030i	−1.27784	−	0.370812i
$773$			14.2196i			0.511445i	0.966750	+	0.255722i	$0.0823133\pi$
$773$			14.2196i			0.511445i	−0.966750	+	0.255722i	$0.917687\pi$
$774$	0.0183069	−	0.128776i	0.000658029	−	0.00462877i
$775$	36.8267			1.32285
$776$	−21.5754	−	9.72943i	−0.774513	−	0.349266i
$777$	−40.1135			−1.43906
$778$	−3.73189	+	26.2512i	−0.133795	+	0.941152i
$779$		−	31.0380i		−	1.11205i
$780$	7.94350	−	27.3738i	0.284423	−	0.980141i
$781$			17.5292i			0.627243i
$782$	5.80027	+	0.824571i	0.207417	+	0.0294866i
$783$	37.4486			1.33830
$784$	16.7482	+	10.6139i	0.598149	+	0.379069i
$785$	−10.4655			−0.373529
$786$	6.59636	+	0.937743i	0.235284	+	0.0334482i
$787$		−	37.9008i		−	1.35102i	−0.737353	−	0.675508i	$-0.763924\pi$
$787$		−	37.9008i		−	1.35102i	0.737353	−	0.675508i	$-0.236076\pi$
$788$	2.16120	−	7.44763i	0.0769895	−	0.265311i
$789$		−	51.6563i		−	1.83901i
$790$	−5.35480	+	37.6672i	−0.190515	+	1.34014i
$791$	7.90232			0.280974
$792$	−0.148533	+	0.329379i	−0.00527790	+	0.0117040i
$793$	36.0379			1.27974
$794$	−4.76274	+	33.5025i	−0.169023	+	1.18896i
$795$			35.1968i			1.24830i
$796$	25.2406	+	7.32448i	0.894631	+	0.259609i
$797$			24.8276i			0.879440i	0.898135	+	0.439720i	$0.144922\pi$
$797$			24.8276i			0.879440i	−0.898135	+	0.439720i	$0.855078\pi$
$798$	−36.9350	−	5.25070i	−1.30748	−	0.185873i
$799$	3.31525			0.117285
$800$	25.4639	+	21.7136i	0.900284	+	0.767693i
$801$	0.302242			0.0106792
$802$	−9.21621	−	1.31018i	−0.325436	−	0.0462641i
$803$			47.8389i			1.68820i
$804$	−21.2836	−	6.17620i	−0.750615	−	0.217818i
$805$			47.3279i			1.66809i
$806$	3.10728	−	21.8575i	0.109449	−	0.769898i
$807$	−5.58134			−0.196473
$808$	−9.24922	+	20.5105i	−0.325386	+	0.721558i
$809$	6.87801			0.241818			0.120909	−	0.992664i	$-0.461419\pi$
$809$	6.87801			0.241818			0.120909	+	0.992664i	$0.461419\pi$
$810$	−5.83611	+	41.0529i	−0.205060	+	1.44245i
$811$		−	5.35901i		−	0.188180i	−0.995564	−	0.0940901i	$-0.970006\pi$
$811$		−	5.35901i		−	0.188180i	0.995564	−	0.0940901i	$-0.0299942\pi$
$812$	−13.7972	+	47.5461i	−0.484187	+	1.66854i
$813$			20.0310i			0.702519i
$814$	29.2406	+	4.15687i	1.02488	+	0.145698i
$815$	5.49543			0.192497
$816$	−3.68305	+	5.81163i	−0.128933	+	0.203448i
$817$	−9.88808			−0.345940
$818$	−41.6844	−	5.92588i	−1.45746	−	0.207194i
$819$		−	0.357724i		−	0.0124999i
$820$	12.8875	−	44.4113i	0.450053	−	1.55091i
$821$			2.17151i			0.0757861i	0.999282	+	0.0378931i	$0.0120646\pi$
$821$			2.17151i			0.0757861i	−0.999282	+	0.0378931i	$0.987935\pi$
$822$	−7.77346	+	54.6808i	−0.271130	+	1.90721i
$823$	38.9210			1.35670			0.678350	−	0.734739i	$-0.262695\pi$
$823$	38.9210			1.35670			0.678350	+	0.734739i	$0.262695\pi$
$824$	20.4056	+	9.20189i	0.710862	+	0.320563i
$825$	31.5108			1.09706
$826$	−6.08251	+	42.7861i	−0.211637	+	1.48872i
$827$			22.5203i			0.783109i	0.920155	+	0.391554i	$0.128062\pi$
$827$			22.5203i			0.783109i	−0.920155	+	0.391554i	$0.871938\pi$
$828$	0.328252	+	0.0952542i	0.0114076	+	0.00331031i
$829$		−	11.4269i		−	0.396873i	−0.980114	−	0.198436i	$-0.936414\pi$
$829$		−	11.4269i		−	0.396873i	0.980114	−	0.198436i	$-0.0635863\pi$
$830$	−64.0818	−	9.10992i	−2.22431	−	0.316210i
$831$	−29.1283			−1.01045
$832$	15.0361	−	13.2813i	0.521282	−	0.460447i
$833$	−4.95705			−0.171751
$834$	−1.21038	−	0.172068i	−0.0419120	−	0.00595823i
$835$		−	28.3359i		−	0.980604i
$836$	26.3796	+	7.65498i	0.912357	+	0.264753i
$837$			32.5654i			1.12563i
$838$	4.82434	−	33.9358i	0.166654	−	1.17229i
$839$	−28.1591			−0.972161			−0.486081	−	0.873914i	$-0.661574\pi$
$839$	−28.1591			−0.972161			−0.486081	+	0.873914i	$0.661574\pi$
$840$	−50.6689	−	22.8491i	−1.74824	−	0.788370i
$841$	−22.2458			−0.767097
$842$	−3.95116	+	27.7936i	−0.136166	+	0.957831i
$843$		−	12.6965i		−	0.437292i
$844$	7.52594	−	25.9349i	0.259053	−	0.892715i
$845$			22.1735i			0.762792i
$846$	0.191488	+	0.0272221i	0.00658350	+	0.000935915i
$847$	4.87826			0.167619
$848$	−13.2610	+	20.9250i	−0.455384	+	0.718569i
$849$	33.2338			1.14058
$850$	−8.28291	−	1.17750i	−0.284102	−	0.0403881i
$851$		−	27.9385i		−	0.957718i
$852$	−5.42717	+	18.7024i	−0.185932	+	0.640733i
$853$			0.516607i			0.0176883i	0.999961	+	0.00884415i	$0.00281522\pi$
$853$			0.516607i			0.0176883i	−0.999961	+	0.00884415i	$0.997185\pi$
$854$	9.89102	−	69.5763i	0.338464	−	2.38085i
$855$	−0.604485			−0.0206729
$856$	15.5345	−	34.4484i	0.530959	−	1.17742i
$857$	−7.72307			−0.263815			−0.131907	−	0.991262i	$-0.542110\pi$
$857$	−7.72307			−0.263815			−0.131907	+	0.991262i	$0.542110\pi$
$858$	2.65874	−	18.7024i	0.0907680	−	0.638489i
$859$		−	36.3045i		−	1.23869i	−0.785118	−	0.619347i	$-0.787398\pi$
$859$		−	36.3045i		−	1.23869i	0.785118	−	0.619347i	$-0.212602\pi$
$860$	−14.1485	−	4.10571i	−0.482461	−	0.140003i
$861$			41.6254i			1.41859i
$862$	2.57930	+	0.366675i	0.0878513	+	0.0124890i
$863$	39.9299			1.35923			0.679615	−	0.733569i	$-0.262147\pi$
$863$	39.9299			1.35923			0.679615	+	0.733569i	$0.262147\pi$
$864$	−19.2011	+	22.5174i	−0.653234	+	0.766058i
$865$	14.8073			0.503462
$866$	−11.2565	−	1.60023i	−0.382510	−	0.0543779i
$867$		−	1.72010i		−	0.0584177i
$868$	−41.3462	−	11.9981i	−1.40338	−	0.407242i
$869$			25.2149i			0.855358i
$870$	8.09768	−	56.9614i	0.274537	−	1.93117i
$871$	−16.1547			−0.547380
$872$	−2.47202	+	5.48181i	−0.0837132	+	0.185637i
$873$	0.345197			0.0116832
$874$	3.65704	−	25.7247i	0.123701	−	0.870151i
$875$		−	10.4625i		−	0.353698i
$876$	−14.8113	+	51.0407i	−0.500428	+	1.72451i
$877$		−	3.73210i		−	0.126024i	−0.998013	−	0.0630121i	$-0.979929\pi$
$877$		−	3.73210i		−	0.126024i	0.998013	−	0.0630121i	$-0.0200707\pi$
$878$	−20.1877	−	2.86990i	−0.681303	−	0.0968546i
$879$	9.83839			0.331841
$880$	34.5672	+	21.9065i	1.16526	+	0.738469i
$881$	−26.3644			−0.888239			−0.444120	−	0.895968i	$-0.646483\pi$
$881$	−26.3644			−0.888239			−0.444120	+	0.895968i	$0.646483\pi$
$882$	−0.286318	−	0.0407032i	−0.00964084	−	0.00137055i
$883$		−	19.9236i		−	0.670483i	−0.942132	−	0.335241i	$-0.891182\pi$
$883$		−	19.9236i		−	0.670483i	0.942132	−	0.335241i	$-0.108818\pi$
$884$	−1.39775	+	4.81675i	−0.0470115	+	0.162005i
$885$		−	50.2230i		−	1.68823i
$886$	−6.12729	+	43.1011i	−0.205850	+	1.44801i
$887$	29.2662			0.982663			0.491331	−	0.870973i	$-0.336510\pi$
$887$	29.2662			0.982663			0.491331	+	0.870973i	$0.336510\pi$
$888$	29.9107	+	13.4882i	1.00374	+	0.452635i
$889$	8.18762			0.274604
$890$	4.81811	−	33.8920i	0.161504	−	1.13606i
$891$			27.4813i			0.920660i
$892$	−15.0808	−	4.37624i	−0.504943	−	0.146527i
$893$		−	14.7034i		−	0.492031i
$894$	17.3695	+	2.46926i	0.580923	+	0.0825844i
$895$	−11.9141			−0.398244
$896$	−21.5146	−	32.6745i	−0.718754	−	1.09158i
$897$	−17.8695			−0.596645
$898$	−17.6844	−	2.51403i	−0.590136	−	0.0838942i
$899$		−	44.5635i		−	1.48628i
$900$	−0.468751	−	0.136025i	−0.0156250	−	0.00453417i
$901$		−	6.19330i		−	0.206329i
$902$	4.31355	−	30.3427i	0.143625	−	1.01030i
$903$	13.2610			0.441298
$904$	−5.89238	−	2.65717i	−0.195978	−	0.0883761i
$905$	−57.9451			−1.92616
$906$	−1.08421	+	7.62664i	−0.0360204	+	0.253378i
$907$		−	54.0895i		−	1.79601i	−0.439983	−	0.898006i	$-0.645015\pi$
$907$		−	54.0895i		−	1.79601i	0.439983	−	0.898006i	$-0.354985\pi$
$908$	−11.8085	+	40.6929i	−0.391879	+	1.35044i
$909$		−	0.328159i		−	0.0108844i
$910$	−40.1135	−	5.70256i	−1.32975	−	0.189038i
$911$	51.8223			1.71695			0.858475	−	0.512856i	$-0.171413\pi$
$911$	51.8223			1.71695			0.858475	+	0.512856i	$0.171413\pi$
$912$	25.7751	+	16.3346i	0.853498	+	0.540894i
$913$	−42.8972			−1.41969
$914$	−28.5057	−	4.05239i	−0.942884	−	0.134041i
$915$			81.6697i			2.69992i
$916$	−7.62185	+	26.2654i	−0.251833	+	0.867833i
$917$		−	9.47092i		−	0.312757i
$918$	1.04125	−	7.32448i	0.0343665	−	0.241744i
$919$	−19.5888			−0.646174			−0.323087	−	0.946369i	$-0.604721\pi$
$919$	−19.5888			−0.646174			−0.323087	+	0.946369i	$0.604721\pi$
$920$	15.9141	−	35.2902i	0.524672	−	1.16348i
$921$	−0.382976			−0.0126195
$922$	6.68135	−	46.9986i	0.220039	−	1.54782i
$923$			14.1955i			0.467249i
$924$	−35.3779	−	10.2662i	−1.16385	−	0.337732i
$925$			39.8967i			1.31180i
$926$	30.5672	+	4.34545i	1.00450	+	0.142800i
$927$	−0.326480			−0.0107230
$928$	26.2754	−	30.8135i	0.862531	−	1.01150i
$929$	−12.9090			−0.423530			−0.211765	−	0.977321i	$-0.567921\pi$
$929$	−12.9090			−0.423530			−0.211765	+	0.977321i	$0.567921\pi$
$930$	49.5338	+	7.04176i	1.62428	+	0.230909i
$931$			21.9849i			0.720526i
$932$	−34.9567	−	10.1439i	−1.14504	−	0.332276i
$933$		−	6.68362i		−	0.218812i
$934$	4.63186	−	32.5818i	0.151559	−	1.06611i
$935$	−10.2310			−0.334591
$936$	−0.120285	+	0.266738i	−0.00393165	+	0.00871859i
$937$	4.57400			0.149426			0.0747130	−	0.997205i	$-0.476196\pi$
$937$	4.57400			0.149426			0.0747130	+	0.997205i	$0.476196\pi$
$938$	−4.43383	+	31.1889i	−0.144770	+	1.01835i
$939$			35.0938i			1.14524i
$940$	6.10511	−	21.0386i	0.199127	−	0.686204i
$941$			27.2967i			0.889846i	0.895569	+	0.444923i	$0.146769\pi$
$941$			27.2967i			0.889846i	−0.895569	+	0.444923i	$0.853231\pi$
$942$	−7.62879	−	1.08451i	−0.248560	−	0.0353354i
$943$	−28.9915			−0.944093
$944$	18.9223	−	29.8583i	0.615869	−	0.971805i
$945$	59.7649			1.94415
$946$	−9.66657	−	1.37421i	−0.314287	−	0.0446793i
$947$		−	16.0284i		−	0.520854i	−0.965494	−	0.260427i	$-0.916137\pi$
$947$		−	16.0284i		−	0.520854i	0.965494	−	0.260427i	$-0.0838634\pi$
$948$	−7.80674	+	26.9025i	−0.253551	+	0.873754i
$949$			38.7409i			1.25758i
$950$	−5.22233	+	36.7354i	−0.169435	+	1.19185i
$951$	−10.8875			−0.353053
$952$	8.91579	+	4.02057i	0.288962	+	0.130308i
$953$	−34.0588			−1.10327			−0.551636	−	0.834085i	$-0.685996\pi$
$953$	−34.0588			−1.10327			−0.551636	+	0.834085i	$0.685996\pi$
$954$	0.0508543	−	0.357724i	0.00164647	−	0.0115817i
$955$			28.9549i			0.936960i
$956$	5.63220	+	1.63438i	0.182158	+	0.0528598i
$957$		−	38.1307i		−	1.23259i
$958$	60.9568	+	8.66566i	1.96942	+	0.279975i
$959$	78.5095			2.53520
$960$	30.0983	+	34.0750i	0.971419	+	1.09977i
$961$	7.75255			0.250082
$962$	23.6796	+	3.36632i	0.763462	+	0.108534i
$963$			0.551160i			0.0177609i
$964$	52.4713	+	15.2264i	1.68999	+	0.490411i
$965$		−	61.0717i		−	1.96597i
$966$	−4.90449	+	34.4996i	−0.157799	+	1.11001i
$967$	−22.8242			−0.733978			−0.366989	−	0.930225i	$-0.619611\pi$
$967$	−22.8242			−0.733978			−0.366989	+	0.930225i	$0.619611\pi$
$968$	−3.63748	−	1.64032i	−0.116913	−	0.0527219i
$969$	−7.62879			−0.245072
$970$	5.50287	−	38.7088i	0.176686	−	1.24286i
$971$			5.49360i			0.176298i	0.996107	+	0.0881490i	$0.0280951\pi$
$971$			5.49360i			0.176298i	−0.996107	+	0.0881490i	$0.971905\pi$
$972$	0.238939	−	0.823399i	0.00766397	−	0.0264105i
$973$			1.73784i			0.0557125i
$974$	−28.4104	−	4.03884i	−0.910329	−	0.129413i
$975$	25.5180			0.817231
$976$	−30.7704	+	48.5538i	−0.984936	+	1.55417i
$977$	−24.2254			−0.775039			−0.387520	−	0.921861i	$-0.626668\pi$
$977$	−24.2254			−0.775039			−0.387520	+	0.921861i	$0.626668\pi$
$978$	4.00588	+	0.569479i	0.128094	+	0.0182099i
$979$		−	22.6878i		−	0.725104i
$980$	−9.12852	+	31.4575i	−0.291600	+	1.00487i
$981$		−	0.0877065i		−	0.00280025i
$982$	7.88448	−	55.4617i	0.251604	−	1.76986i
$983$	−5.00418			−0.159609			−0.0798043	−	0.996811i	$-0.525430\pi$
$983$	−5.00418			−0.159609			−0.0798043	+	0.996811i	$0.525430\pi$
$984$	13.9966	−	31.0380i	0.446195	−	0.989457i
$985$	12.8107			0.408182
$986$	−1.42488	+	10.0230i	−0.0453775	+	0.319199i
$987$			19.7189i			0.627658i
$988$	21.3627	+	6.19915i	0.679638	+	0.197221i
$989$			9.23609i			0.293691i
$990$	−0.590943	−	0.0840089i	−0.0187814	−	0.00266998i
$991$	−43.0455			−1.36739			−0.683693	−	0.729770i	$-0.739627\pi$
$991$	−43.0455			−1.36739			−0.683693	+	0.729770i	$0.739627\pi$
$992$	26.7955	+	22.8491i	0.850758	+	0.725460i
$993$	35.9367			1.14042
$994$	27.4064	+	3.89611i	0.869277	+	0.123577i
$995$			43.4164i			1.37639i
$996$	−45.7683	−	13.2813i	−1.45022	−	0.420834i
$997$			3.28681i			0.104094i	0.998645	+	0.0520471i	$0.0165746\pi$
$997$			3.28681i			0.104094i	−0.998645	+	0.0520471i	$0.983425\pi$
$998$	−1.92985	+	13.5751i	−0.0610882	+	0.429712i
$999$	−35.2802			−1.11622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.c.a.69.1	✓	8
3.2	odd	2		1224.2.f.d.613.8		8
4.3	odd	2		544.2.c.a.273.6		8
8.3	odd	2		544.2.c.a.273.3		8
8.5	even	2	inner	136.2.c.a.69.2	yes	8
12.11	even	2		4896.2.f.c.2449.1		8
16.3	odd	4		4352.2.a.be.1.3		8
16.5	even	4		4352.2.a.bc.1.3		8
16.11	odd	4		4352.2.a.be.1.6		8
16.13	even	4		4352.2.a.bc.1.6		8
24.5	odd	2		1224.2.f.d.613.7		8
24.11	even	2		4896.2.f.c.2449.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.c.a.69.1	✓	8	1.1	even	1	trivial
136.2.c.a.69.2	yes	8	8.5	even	2	inner
544.2.c.a.273.3		8	8.3	odd	2
544.2.c.a.273.6		8	4.3	odd	2
1224.2.f.d.613.7		8	24.5	odd	2
1224.2.f.d.613.8		8	3.2	odd	2
4352.2.a.bc.1.3		8	16.5	even	4
4352.2.a.bc.1.6		8	16.13	even	4
4352.2.a.be.1.3		8	16.3	odd	4
4352.2.a.be.1.6		8	16.11	odd	4
4896.2.f.c.2449.1		8	12.11	even	2
4896.2.f.c.2449.8		8	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40014 - 0.199044i) q^{2} -1.72010i q^{3} +(1.92076 + 0.557378i) q^{4} +3.30391i q^{5} +(-0.342376 + 2.40838i) q^{6} +3.45790 q^{7} +(-2.57839 - 1.16272i) q^{8} +0.0412530 q^{9} +O(q^{10})\)	\(q+(-1.40014 - 0.199044i) q^{2} -1.72010i q^{3} +(1.92076 + 0.557378i) q^{4} +3.30391i q^{5} +(-0.342376 + 2.40838i) q^{6} +3.45790 q^{7} +(-2.57839 - 1.16272i) q^{8} +0.0412530 q^{9} +(0.657624 - 4.62592i) q^{10} -3.09665i q^{11} +(0.958747 - 3.30391i) q^{12} -2.50773i q^{13} +(-4.84153 - 0.688275i) q^{14} +5.68305 q^{15} +(3.37866 + 2.14118i) q^{16} -1.00000 q^{17} +(-0.0577599 - 0.00821118i) q^{18} +4.43508i q^{19} +(-1.84153 + 6.34602i) q^{20} -5.94793i q^{21} +(-0.616371 + 4.33573i) q^{22} +4.14265 q^{23} +(-2.00000 + 4.43508i) q^{24} -5.91579 q^{25} +(-0.499149 + 3.51116i) q^{26} -5.23126i q^{27} +(6.64180 + 1.92736i) q^{28} +7.15862i q^{29} +(-7.95705 - 1.13118i) q^{30} -6.22515 q^{31} +(-4.30439 - 3.67045i) q^{32} -5.32655 q^{33} +(1.40014 + 0.199044i) q^{34} +11.4246i q^{35} +(0.0792373 + 0.0229935i) q^{36} -6.74411i q^{37} +(0.882778 - 6.20972i) q^{38} -4.31355 q^{39} +(3.84153 - 8.51875i) q^{40} -6.99830 q^{41} +(-1.18390 + 8.32791i) q^{42} +2.22951i q^{43} +(1.72601 - 5.94793i) q^{44} +0.136296i q^{45} +(-5.80027 - 0.824571i) q^{46} -3.31525 q^{47} +(3.68305 - 5.81163i) q^{48} +4.95705 q^{49} +(8.28291 + 1.17750i) q^{50} +1.72010i q^{51} +(1.39775 - 4.81675i) q^{52} +6.19330i q^{53} +(-1.04125 + 7.32448i) q^{54} +10.2310 q^{55} +(-8.91579 - 4.02057i) q^{56} +7.62879 q^{57} +(1.42488 - 10.0230i) q^{58} -8.83732i q^{59} +(10.9158 + 3.16761i) q^{60} +14.3707i q^{61} +(8.71606 + 1.23908i) q^{62} +0.142649 q^{63} +(5.29615 + 5.99590i) q^{64} +8.28530 q^{65} +(7.45790 + 1.06022i) q^{66} -6.44195i q^{67} +(-1.92076 - 0.557378i) q^{68} -7.12577i q^{69} +(2.27399 - 15.9959i) q^{70} -5.66069 q^{71} +(-0.106366 - 0.0479658i) q^{72} -15.4486 q^{73} +(-1.34238 + 9.44267i) q^{74} +10.1758i q^{75} +(-2.47202 + 8.51875i) q^{76} -10.7079i q^{77} +(6.03955 + 0.858587i) q^{78} -8.14265 q^{79} +(-7.07427 + 11.1628i) q^{80} -8.87454 q^{81} +(9.79857 + 1.39297i) q^{82} -13.8528i q^{83} +(3.31525 - 11.4246i) q^{84} -3.30391i q^{85} +(0.443772 - 3.12162i) q^{86} +12.3135 q^{87} +(-3.60054 + 7.98436i) q^{88} +7.32655 q^{89} +(0.0271290 - 0.190833i) q^{90} -8.67146i q^{91} +(7.95705 + 2.30902i) q^{92} +10.7079i q^{93} +(4.64180 + 0.659881i) q^{94} -14.6531 q^{95} +(-6.31355 + 7.40399i) q^{96} +8.36780 q^{97} +(-6.94054 - 0.986672i) q^{98} -0.127746i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9	\( 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9} + 6 q^{10} + 16 q^{12} - 10 q^{14} - 12 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} + 14 q^{20} - 14 q^{22} + 12 q^{23} - 16 q^{24} - 8 q^{25} + 24 q^{26} + 4 q^{28} - 16 q^{30} - 12 q^{31} - 11 q^{32} + 8 q^{33} + q^{34} + 15 q^{36} - 30 q^{38} + 20 q^{39} + 2 q^{40} + 20 q^{42} + 4 q^{44} - 26 q^{46} - 28 q^{47} - 28 q^{48} - 8 q^{49} + 19 q^{50} - 4 q^{52} + 44 q^{55} - 32 q^{56} + 8 q^{57} - 6 q^{58} + 48 q^{60} + 10 q^{62} - 20 q^{63} + 25 q^{64} + 24 q^{65} + 40 q^{66} - q^{68} + 28 q^{70} - 13 q^{72} + 8 q^{73} - 10 q^{74} + 6 q^{76} - 16 q^{78} - 44 q^{79} - 46 q^{80} - 40 q^{81} + 2 q^{82} + 28 q^{84} - 10 q^{86} + 44 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} + 16 q^{92} - 12 q^{94} - 16 q^{95} + 4 q^{96} + 8 q^{97} - 9 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9 + 6 * q^10 + 16 * q^12 - 10 * q^14 - 12 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 + 14 * q^20 - 14 * q^22 + 12 * q^23 - 16 * q^24 - 8 * q^25 + 24 * q^26 + 4 * q^28 - 16 * q^30 - 12 * q^31 - 11 * q^32 + 8 * q^33 + q^34 + 15 * q^36 - 30 * q^38 + 20 * q^39 + 2 * q^40 + 20 * q^42 + 4 * q^44 - 26 * q^46 - 28 * q^47 - 28 * q^48 - 8 * q^49 + 19 * q^50 - 4 * q^52 + 44 * q^55 - 32 * q^56 + 8 * q^57 - 6 * q^58 + 48 * q^60 + 10 * q^62 - 20 * q^63 + 25 * q^64 + 24 * q^65 + 40 * q^66 - q^68 + 28 * q^70 - 13 * q^72 + 8 * q^73 - 10 * q^74 + 6 * q^76 - 16 * q^78 - 44 * q^79 - 46 * q^80 - 40 * q^81 + 2 * q^82 + 28 * q^84 - 10 * q^86 + 44 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 + 16 * q^92 - 12 * q^94 - 16 * q^95 + 4 * q^96 + 8 * q^97 - 9 * q^98

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