LMFDB - Embedded newform 152.2.c.b.77.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(77,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, 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("152.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.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:	$1.21372611072$
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} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 4x^12 + 4x^11 - 10x^10 + 24x^9 - 40x^8 + 48x^7 - 40x^6 + 32x^5 + 64x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.9
Root			$1.33852 - 0.456455i$ of defining polynomial
Character	$\chi$	$=$	152.77
Dual form			152.2.c.b.77.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456455 - 1.33852i) q^{2} +2.09554i q^{3} +(-1.58330 - 1.22195i) q^{4} -3.36827i q^{5} +(2.80493 + 0.956520i) q^{6} +4.47116 q^{7} +(-2.35832 + 1.56152i) q^{8} -1.39129 q^{9} +O(q^{10})$	\(q+(0.456455 - 1.33852i) q^{2} +2.09554i q^{3} +(-1.58330 - 1.22195i) q^{4} -3.36827i q^{5} +(2.80493 + 0.956520i) q^{6} +4.47116 q^{7} +(-2.35832 + 1.56152i) q^{8} -1.39129 q^{9} +(-4.50852 - 1.53746i) q^{10} -0.608709i q^{11} +(2.56065 - 3.31787i) q^{12} +1.03922i q^{13} +(2.04088 - 5.98476i) q^{14} +7.05835 q^{15} +(1.01366 + 3.86943i) q^{16} -3.06367 q^{17} +(-0.635061 + 1.86228i) q^{18} +1.00000i q^{19} +(-4.11587 + 5.33298i) q^{20} +9.36950i q^{21} +(-0.814773 - 0.277848i) q^{22} -8.50224 q^{23} +(-3.27222 - 4.94195i) q^{24} -6.34525 q^{25} +(1.39102 + 0.474357i) q^{26} +3.37112i q^{27} +(-7.07918 - 5.46355i) q^{28} +7.27343i q^{29} +(3.22182 - 9.44778i) q^{30} +4.02054 q^{31} +(5.64202 + 0.409404i) q^{32} +1.27558 q^{33} +(-1.39843 + 4.10080i) q^{34} -15.0601i q^{35} +(2.20283 + 1.70009i) q^{36} -4.31265i q^{37} +(1.33852 + 0.456455i) q^{38} -2.17773 q^{39} +(5.25962 + 7.94345i) q^{40} -4.15770 q^{41} +(12.5413 + 4.27676i) q^{42} +6.27910i q^{43} +(-0.743814 + 0.963768i) q^{44} +4.68624i q^{45} +(-3.88089 + 11.3805i) q^{46} +4.73522 q^{47} +(-8.10855 + 2.12418i) q^{48} +12.9913 q^{49} +(-2.89632 + 8.49328i) q^{50} -6.42005i q^{51} +(1.26988 - 1.64539i) q^{52} -6.98132i q^{53} +(4.51232 + 1.53876i) q^{54} -2.05030 q^{55} +(-10.5444 + 6.98180i) q^{56} -2.09554 q^{57} +(9.73567 + 3.31999i) q^{58} +2.64652i q^{59} +(-11.1755 - 8.62497i) q^{60} -5.11145i q^{61} +(1.83520 - 5.38159i) q^{62} -6.22069 q^{63} +(3.12332 - 7.36511i) q^{64} +3.50037 q^{65} +(0.582242 - 1.70739i) q^{66} +2.62178i q^{67} +(4.85071 + 3.74366i) q^{68} -17.8168i q^{69} +(-20.1583 - 6.87425i) q^{70} +12.0085 q^{71} +(3.28111 - 2.17253i) q^{72} -12.5175 q^{73} +(-5.77259 - 1.96853i) q^{74} -13.2967i q^{75} +(1.22195 - 1.58330i) q^{76} -2.72164i q^{77} +(-0.994034 + 2.91494i) q^{78} -0.913307 q^{79} +(13.0333 - 3.41430i) q^{80} -11.2382 q^{81} +(-1.89780 + 5.56518i) q^{82} -0.887809i q^{83} +(11.4491 - 14.8347i) q^{84} +10.3193i q^{85} +(8.40473 + 2.86613i) q^{86} -15.2418 q^{87} +(0.950510 + 1.43553i) q^{88} -7.61792 q^{89} +(6.27266 + 2.13906i) q^{90} +4.64652i q^{91} +(13.4616 + 10.3893i) q^{92} +8.42521i q^{93} +(2.16141 - 6.33820i) q^{94} +3.36827 q^{95} +(-0.857923 + 11.8231i) q^{96} -5.93426 q^{97} +(5.92994 - 17.3892i) q^{98} +0.846892i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	$ 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.456455	−	1.33852i	0.322762	−	0.946480i
$2$	0.456455	−	1.33852i	0.322762	−	0.946480i
$3$			2.09554i			1.20986i	0.796278	+	0.604930i	$0.206799\pi$
$3$			2.09554i			1.20986i	−0.796278	+	0.604930i	$0.793201\pi$
$4$	−1.58330	−	1.22195i	−0.791649	−	0.610976i
$5$		−	3.36827i		−	1.50634i	−0.657828	−	0.753168i	$-0.728525\pi$
$5$		−	3.36827i		−	1.50634i	0.657828	−	0.753168i	$-0.271475\pi$
$6$	2.80493	+	0.956520i	1.14511	+	0.390498i
$7$	4.47116			1.68994			0.844970	−	0.534813i	$-0.179618\pi$
$7$	4.47116			1.68994			0.844970	+	0.534813i	$0.179618\pi$
$8$	−2.35832	+	1.56152i	−0.833791	+	0.552080i
$9$	−1.39129			−0.463764
$10$	−4.50852	−	1.53746i	−1.42572	−	0.486189i
$11$		−	0.608709i		−	0.183533i	−0.995781	−	0.0917664i	$-0.970749\pi$
$11$		−	0.608709i		−	0.183533i	0.995781	−	0.0917664i	$-0.0292513\pi$
$12$	2.56065	−	3.31787i	0.739196	−	0.957785i
$13$			1.03922i			0.288228i	0.989561	+	0.144114i	$0.0460331\pi$
$13$			1.03922i			0.288228i	−0.989561	+	0.144114i	$0.953967\pi$
$14$	2.04088	−	5.98476i	0.545449	−	1.59950i
$15$	7.05835			1.82246
$16$	1.01366	+	3.86943i	0.253416	+	0.967357i
$17$	−3.06367			−0.743050			−0.371525	−	0.928423i	$-0.621165\pi$
$17$	−3.06367			−0.743050			−0.371525	+	0.928423i	$0.621165\pi$
$18$	−0.635061	+	1.86228i	−0.149685	+	0.438943i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−4.11587	+	5.33298i	−0.920336	+	1.19249i
$21$			9.36950i			2.04459i
$22$	−0.814773	−	0.277848i	−0.173710	−	0.0592375i
$23$	−8.50224			−1.77284			−0.886419	−	0.462883i	$-0.846815\pi$
$23$	−8.50224			−1.77284			−0.886419	+	0.462883i	$0.846815\pi$
$24$	−3.27222	−	4.94195i	−0.667940	−	1.00877i
$25$	−6.34525			−1.26905
$26$	1.39102	+	0.474357i	0.272802	+	0.0930290i
$27$			3.37112i			0.648772i
$28$	−7.07918	−	5.46355i	−1.33784	−	1.03251i
$29$			7.27343i			1.35064i	0.737524	+	0.675321i	$0.235995\pi$
$29$			7.27343i			1.35064i	−0.737524	+	0.675321i	$0.764005\pi$
$30$	3.22182	−	9.44778i	0.588221	−	1.72492i
$31$	4.02054			0.722111			0.361055	−	0.932544i	$-0.382417\pi$
$31$	4.02054			0.722111			0.361055	+	0.932544i	$0.382417\pi$
$32$	5.64202	+	0.409404i	0.997378	+	0.0723731i
$33$	1.27558			0.222049
$34$	−1.39843	+	4.10080i	−0.239828	+	0.703282i
$35$		−	15.0601i		−	2.54562i
$36$	2.20283	+	1.70009i	0.367138	+	0.283348i
$37$		−	4.31265i		−	0.708995i	−0.935057	−	0.354498i	$-0.884652\pi$
$37$		−	4.31265i		−	0.708995i	0.935057	−	0.354498i	$-0.115348\pi$
$38$	1.33852	+	0.456455i	0.217137	+	0.0740468i
$39$	−2.17773			−0.348715
$40$	5.25962	+	7.94345i	0.831618	+	1.25597i
$41$	−4.15770			−0.649323			−0.324661	−	0.945830i	$-0.605250\pi$
$41$	−4.15770			−0.649323			−0.324661	+	0.945830i	$0.605250\pi$
$42$	12.5413	+	4.27676i	1.93517	+	0.659918i
$43$			6.27910i			0.957554i	0.877937	+	0.478777i	$0.158920\pi$
$43$			6.27910i			0.957554i	−0.877937	+	0.478777i	$0.841080\pi$
$44$	−0.743814	+	0.963768i	−0.112134	+	0.145294i
$45$			4.68624i			0.698584i
$46$	−3.88089	+	11.3805i	−0.572205	+	1.67796i
$47$	4.73522			0.690702			0.345351	−	0.938474i	$-0.387760\pi$
$47$	4.73522			0.690702			0.345351	+	0.938474i	$0.387760\pi$
$48$	−8.10855	+	2.12418i	−1.17037	+	0.306598i
$49$	12.9913			1.85590
$50$	−2.89632	+	8.49328i	−0.409602	+	1.20113i
$51$		−	6.42005i		−	0.898987i
$52$	1.26988	−	1.64539i	0.176100	−	0.228175i
$53$		−	6.98132i		−	0.958958i	−0.877553	−	0.479479i	$-0.840826\pi$
$53$		−	6.98132i		−	0.958958i	0.877553	−	0.479479i	$-0.159174\pi$
$54$	4.51232	+	1.53876i	0.614049	+	0.209399i
$55$	−2.05030			−0.276462
$56$	−10.5444	+	6.98180i	−1.40906	+	0.932982i
$57$	−2.09554			−0.277561
$58$	9.73567	+	3.31999i	1.27836	+	0.435936i
$59$			2.64652i			0.344547i	0.985049	+	0.172274i	$0.0551113\pi$
$59$			2.64652i			0.344547i	−0.985049	+	0.172274i	$0.944889\pi$
$60$	−11.1755	−	8.62497i	−1.44275	−	1.11348i
$61$		−	5.11145i		−	0.654454i	−0.944946	−	0.327227i	$-0.893886\pi$
$61$		−	5.11145i		−	0.654454i	0.944946	−	0.327227i	$-0.106114\pi$
$62$	1.83520	−	5.38159i	0.233070	−	0.683463i
$63$	−6.22069			−0.783733
$64$	3.12332	−	7.36511i	0.390416	−	0.920639i
$65$	3.50037			0.434168
$66$	0.582242	−	1.70739i	0.0716691	−	0.210165i
$67$			2.62178i			0.320301i	0.987093	+	0.160150i	$0.0511979\pi$
$67$			2.62178i			0.320301i	−0.987093	+	0.160150i	$0.948802\pi$
$68$	4.85071	+	3.74366i	0.588235	+	0.453986i
$69$		−	17.8168i		−	2.14489i
$70$	−20.1583	−	6.87425i	−2.40938	−	0.821630i
$71$	12.0085			1.42514			0.712572	−	0.701599i	$-0.247530\pi$
$71$	12.0085			1.42514			0.712572	+	0.701599i	$0.247530\pi$
$72$	3.28111	−	2.17253i	0.386682	−	0.256035i
$73$	−12.5175			−1.46507			−0.732533	−	0.680731i	$-0.761662\pi$
$73$	−12.5175			−1.46507			−0.732533	+	0.680731i	$0.761662\pi$
$74$	−5.77259	−	1.96853i	−0.671050	−	0.228837i
$75$		−	13.2967i		−	1.53537i
$76$	1.22195	−	1.58330i	0.140168	−	0.181617i
$77$		−	2.72164i		−	0.310159i
$78$	−0.994034	+	2.91494i	−0.112552	+	0.330052i
$79$	−0.913307			−0.102755			−0.0513775	−	0.998679i	$-0.516361\pi$
$79$	−0.913307			−0.102755			−0.0513775	+	0.998679i	$0.516361\pi$
$80$	13.0333	−	3.41430i	1.45717	−	0.381730i
$81$	−11.2382			−1.24869
$82$	−1.89780	+	5.56518i	−0.209577	+	0.614571i
$83$		−	0.887809i		−	0.0974497i	−0.998812	−	0.0487249i	$-0.984484\pi$
$83$		−	0.887809i		−	0.0974497i	0.998812	−	0.0487249i	$-0.0155158\pi$
$84$	11.4491	−	14.8347i	1.24920	−	1.61860i
$85$			10.3193i			1.11928i
$86$	8.40473	+	2.86613i	0.906306	+	0.309062i
$87$	−15.2418			−1.63409
$88$	0.950510	+	1.43553i	0.101325	+	0.153028i
$89$	−7.61792			−0.807498			−0.403749	−	0.914870i	$-0.632293\pi$
$89$	−7.61792			−0.807498			−0.403749	+	0.914870i	$0.632293\pi$
$90$	6.27266	+	2.13906i	0.661196	+	0.225477i
$91$			4.64652i			0.487087i
$92$	13.4616	+	10.3893i	1.40347	+	1.08316i
$93$			8.42521i			0.873653i
$94$	2.16141	−	6.33820i	0.222933	−	0.653736i
$95$	3.36827			0.345577
$96$	−0.857923	+	11.8231i	−0.0875614	+	1.20669i
$97$	−5.93426			−0.602533			−0.301267	−	0.953540i	$-0.597409\pi$
$97$	−5.93426			−0.602533			−0.301267	+	0.953540i	$0.597409\pi$
$98$	5.92994	−	17.3892i	0.599014	−	1.75657i
$99$			0.846892i			0.0851158i
$100$	10.0464	+	7.75360i	1.00464	+	0.775360i
$101$		−	16.5793i		−	1.64970i	−0.565353	−	0.824849i	$-0.691260\pi$
$101$		−	16.5793i		−	1.64970i	0.565353	−	0.824849i	$-0.308740\pi$
$102$	−8.59340	−	2.93046i	−0.850873	−	0.290159i
$103$	−11.6631			−1.14920			−0.574600	−	0.818434i	$-0.694842\pi$
$103$	−11.6631			−1.14920			−0.574600	+	0.818434i	$0.694842\pi$
$104$	−1.62276	−	2.45081i	−0.159125	−	0.240322i
$105$	31.5590			3.07985
$106$	−9.34467	−	3.18666i	−0.907635	−	0.309516i
$107$			10.3213i			0.997801i	0.866659	+	0.498900i	$0.166263\pi$
$107$			10.3213i			0.997801i	−0.866659	+	0.498900i	$0.833737\pi$
$108$	4.11934	−	5.33748i	0.396384	−	0.513599i
$109$			1.85592i			0.177765i	0.996042	+	0.0888824i	$0.0283295\pi$
$109$			1.85592i			0.177765i	−0.996042	+	0.0888824i	$0.971670\pi$
$110$	−0.935868	+	2.74438i	−0.0892316	+	0.261666i
$111$	9.03734			0.857786
$112$	4.53226	+	17.3008i	0.428258	+	1.63478i
$113$	18.4343			1.73415			0.867077	−	0.498174i	$-0.165996\pi$
$113$	18.4343			1.73415			0.867077	+	0.498174i	$0.165996\pi$
$114$	−0.956520	+	2.80493i	−0.0895863	+	0.262706i
$115$			28.6378i			2.67049i
$116$	8.88779	−	11.5160i	0.825210	−	1.06923i
$117$		−	1.44586i		−	0.133669i
$118$	3.54243	+	1.20802i	0.326107	+	0.111207i
$119$	−13.6982			−1.25571
$120$	−16.6458	+	11.0217i	−1.51955	+	1.00614i
$121$	10.6295			0.966316
$122$	−6.84181	−	2.33315i	−0.619428	−	0.211233i
$123$		−	8.71262i		−	0.785591i
$124$	−6.36571	−	4.91291i	−0.571658	−	0.441192i
$125$			4.53117i			0.405281i
$126$	−2.83946	+	8.32654i	−0.252959	+	0.741788i
$127$	−9.29686			−0.824963			−0.412481	−	0.910966i	$-0.635338\pi$
$127$	−9.29686			−0.824963			−0.412481	+	0.910966i	$0.635338\pi$
$128$	−8.43273	−	7.54249i	−0.745355	−	0.666668i
$129$	−13.1581			−1.15851
$130$	1.59776	−	4.68534i	0.140133	−	0.410931i
$131$		−	8.15016i		−	0.712083i	−0.934470	−	0.356042i	$-0.884126\pi$
$131$		−	8.15016i		−	0.712083i	0.934470	−	0.356042i	$-0.115874\pi$
$132$	−2.01962	−	1.55869i	−0.175785	−	0.135667i
$133$			4.47116i			0.387699i
$134$	3.50931	+	1.19672i	0.303158	+	0.103381i
$135$	11.3548			0.977268
$136$	7.22511	−	4.78398i	0.619548	−	0.410223i
$137$	11.0756			0.946254			0.473127	−	0.880994i	$-0.343125\pi$
$137$	11.0756			0.946254			0.473127	+	0.880994i	$0.343125\pi$
$138$	−23.8482	−	8.13256i	−2.03009	−	0.692289i
$139$		−	12.2091i		−	1.03557i	−0.855512	−	0.517783i	$-0.826758\pi$
$139$		−	12.2091i		−	1.03557i	0.855512	−	0.517783i	$-0.173242\pi$
$140$	−18.4027	+	23.8446i	−1.55531	+	2.01524i
$141$			9.92284i			0.835654i
$142$	5.48133	−	16.0736i	0.459983	−	1.34887i
$143$	0.632582			0.0528992
$144$	−1.41030	−	5.38350i	−0.117525	−	0.448625i
$145$	24.4989			2.03452
$146$	−5.71369	+	16.7550i	−0.472868	+	1.38666i
$147$			27.2238i			2.24538i
$148$	−5.26985	+	6.82821i	−0.433179	+	0.561275i
$149$			4.31060i			0.353138i	0.984288	+	0.176569i	$0.0564998\pi$
$149$			4.31060i			0.353138i	−0.984288	+	0.176569i	$0.943500\pi$
$150$	−17.7980	−	6.06936i	−1.45320	−	0.495561i
$151$	−9.89022			−0.804855			−0.402428	−	0.915452i	$-0.631833\pi$
$151$	−9.89022			−0.804855			−0.402428	+	0.915452i	$0.631833\pi$
$152$	−1.56152	−	2.35832i	−0.126656	−	0.191285i
$153$	4.26246			0.344599
$154$	−3.64298	−	1.24230i	−0.293560	−	0.100108i
$155$		−	13.5423i		−	1.08774i
$156$	3.44799	+	2.66108i	0.276060	+	0.213057i
$157$		−	7.39359i		−	0.590073i	−0.955486	−	0.295036i	$-0.904668\pi$
$157$		−	7.39359i		−	0.590073i	0.955486	−	0.295036i	$-0.0953318\pi$
$158$	−0.416883	+	1.22248i	−0.0331655	+	0.0972556i
$159$	14.6296			1.16021
$160$	1.37898	−	19.0039i	0.109018	−	1.50239i
$161$	−38.0149			−2.99599
$162$	−5.12972	+	15.0426i	−0.403029	+	1.18186i
$163$			12.5566i			0.983509i	0.870734	+	0.491755i	$0.163644\pi$
$163$			12.5566i			0.983509i	−0.870734	+	0.491755i	$0.836356\pi$
$164$	6.58287	+	5.08051i	0.514036	+	0.396721i
$165$		−	4.29648i		−	0.334481i
$166$	−1.18836	−	0.405245i	−0.0922342	−	0.0314531i
$167$	−0.00624861			−0.000483532			−0.000241766	−	1.00000i	$-0.500077\pi$
$167$	−0.00624861			−0.000483532			−0.000241766		1.00000i	$0.500077\pi$
$168$	−14.6306	−	22.0963i	−1.12878	−	1.70476i
$169$	11.9200			0.916925
$170$	13.8126	+	4.71029i	1.05938	+	0.361262i
$171$		−	1.39129i		−	0.106395i
$172$	7.67276	−	9.94169i	0.585043	−	0.758046i
$173$			4.45345i			0.338589i	0.985565	+	0.169295i	$0.0541489\pi$
$173$			4.45345i			0.338589i	−0.985565	+	0.169295i	$0.945851\pi$
$174$	−6.95718	+	20.4015i	−0.527422	+	1.54663i
$175$	−28.3707			−2.14462
$176$	2.35536	−	0.617027i	0.177542	−	0.0465102i
$177$	−5.54589			−0.416854
$178$	−3.47724	+	10.1968i	−0.260630	+	0.764281i
$179$		−	9.80470i		−	0.732838i	−0.930450	−	0.366419i	$-0.880584\pi$
$179$		−	9.80470i		−	0.732838i	0.930450	−	0.366419i	$-0.119416\pi$
$180$	5.72637	−	7.41972i	0.426818	−	0.553033i
$181$		−	17.9475i		−	1.33403i	−0.745046	−	0.667013i	$-0.767573\pi$
$181$		−	17.9475i		−	1.33403i	0.745046	−	0.667013i	$-0.232427\pi$
$182$	6.21948	+	2.12093i	0.461019	+	0.157213i
$183$	10.7113			0.791799
$184$	20.0510	−	13.2764i	1.47818	−	0.978749i
$185$	−14.5262			−1.06799
$186$	11.2774	+	3.84573i	0.826895	+	0.281982i
$187$			1.86489i			0.136374i
$188$	−7.49726	−	5.78621i	−0.546794	−	0.422003i
$189$			15.0728i			1.09639i
$190$	1.53746	−	4.50852i	0.111539	−	0.327082i
$191$	3.85328			0.278814			0.139407	−	0.990235i	$-0.455480\pi$
$191$	3.85328			0.278814			0.139407	+	0.990235i	$0.455480\pi$
$192$	15.4339	+	6.54505i	1.11384	+	0.472349i
$193$	19.5610			1.40803			0.704017	−	0.710183i	$-0.251388\pi$
$193$	19.5610			1.40803			0.704017	+	0.710183i	$0.251388\pi$
$194$	−2.70872	+	7.94316i	−0.194475	+	0.570285i
$195$			7.33517i			0.525283i
$196$	−20.5691	−	15.8747i	−1.46922	−	1.13391i
$197$			3.44831i			0.245682i	0.992426	+	0.122841i	$0.0392006\pi$
$197$			3.44831i			0.245682i	−0.992426	+	0.122841i	$0.960799\pi$
$198$	1.13359	+	0.386568i	0.0805604	+	0.0274722i
$199$	−7.64829			−0.542173			−0.271087	−	0.962555i	$-0.587383\pi$
$199$	−7.64829			−0.542173			−0.271087	+	0.962555i	$0.587383\pi$
$200$	14.9641	−	9.90822i	1.05812	−	0.700617i
$201$	−5.49404			−0.387520
$202$	−22.1918	−	7.56768i	−1.56141	−	0.532460i
$203$			32.5207i			2.28251i
$204$	−7.84500	+	10.1649i	−0.549260	+	0.711682i
$205$			14.0042i			0.978099i
$206$	−5.32368	+	15.6114i	−0.370919	+	1.08770i
$207$	11.8291			0.822178
$208$	−4.02118	+	1.05342i	−0.278819	+	0.0730415i
$209$	0.608709			0.0421053
$210$	14.4053	−	42.2425i	0.994058	−	2.91501i
$211$		−	14.4648i		−	0.995801i	−0.867234	−	0.497900i	$-0.834105\pi$
$211$		−	14.4648i		−	0.995801i	0.867234	−	0.497900i	$-0.165895\pi$
$212$	−8.53084	+	11.0535i	−0.585901	+	0.759158i
$213$			25.1643i			1.72423i
$214$	13.8154	+	4.71122i	0.944398	+	0.322052i
$215$	21.1497			1.44240
$216$	−5.26406	−	7.95016i	−0.358174	−	0.540940i
$217$	17.9765			1.22032
$218$	2.48419	+	0.847143i	0.168251	+	0.0573758i
$219$		−	26.2310i		−	1.77253i
$220$	3.24623	+	2.50537i	0.218861	+	0.168912i
$221$		−	3.18383i		−	0.214167i
$222$	4.12514	−	12.0967i	0.276861	−	0.811877i
$223$	4.74734			0.317906			0.158953	−	0.987286i	$-0.449188\pi$
$223$	4.74734			0.317906			0.158953	+	0.987286i	$0.449188\pi$
$224$	25.2264	+	1.83051i	1.68551	+	0.122306i
$225$	8.82809			0.588539
$226$	8.41443	−	24.6748i	0.559719	−	1.64134i
$227$		−	2.67149i		−	0.177313i	−0.996062	−	0.0886566i	$-0.971743\pi$
$227$		−	2.67149i		−	0.177313i	0.996062	−	0.0886566i	$-0.0282574\pi$
$228$	3.31787	+	2.56065i	0.219731	+	0.169583i
$229$		−	7.87392i		−	0.520323i	−0.965565	−	0.260162i	$-0.916224\pi$
$229$		−	7.87392i		−	0.520323i	0.965565	−	0.260162i	$-0.0837758\pi$
$230$	38.3325	+	13.0719i	2.52757	+	0.861934i
$231$	5.70330			0.375250
$232$	−11.3576	−	17.1531i	−0.745662	−	1.12615i
$233$	−10.2320			−0.670321			−0.335160	−	0.942161i	$-0.608791\pi$
$233$	−10.2320			−0.670321			−0.335160	+	0.942161i	$0.608791\pi$
$234$	−1.93531	−	0.659968i	−0.126515	−	0.0431435i
$235$		−	15.9495i		−	1.04043i
$236$	3.23392	−	4.19023i	0.210510	−	0.272760i
$237$		−	1.91387i		−	0.124319i
$238$	−6.25260	+	18.3354i	−0.405296	+	1.18850i
$239$	−15.1051			−0.977067			−0.488533	−	0.872545i	$-0.662468\pi$
$239$	−15.1051			−0.977067			−0.488533	+	0.872545i	$0.662468\pi$
$240$	7.15480	+	27.3118i	0.461840	+	1.76297i
$241$	6.17274			0.397621			0.198811	−	0.980038i	$-0.436292\pi$
$241$	6.17274			0.397621			0.198811	+	0.980038i	$0.436292\pi$
$242$	4.85187	−	14.2278i	0.311890	−	0.914599i
$243$		−	13.4367i		−	0.861966i
$244$	−6.24595	+	8.09295i	−0.399856	+	0.518098i
$245$		−	43.7582i		−	2.79561i
$246$	−11.6621	−	3.97692i	−0.743546	−	0.253559i
$247$	−1.03922			−0.0661239
$248$	−9.48171	+	6.27815i	−0.602089	+	0.398663i
$249$	1.86044			0.117901
$250$	6.06509	+	2.06828i	0.383590	+	0.130809i
$251$			6.78315i			0.428149i	0.976817	+	0.214074i	$0.0686735\pi$
$251$			6.78315i			0.428149i	−0.976817	+	0.214074i	$0.931327\pi$
$252$	9.84920	+	7.60138i	0.620441	+	0.478842i
$253$			5.17539i			0.325374i
$254$	−4.24360	+	12.4441i	−0.266267	+	0.780811i
$255$	−21.6245			−1.35418
$256$	−13.9450	+	7.84461i	−0.871560	+	0.490288i
$257$	−26.6333			−1.66134			−0.830669	−	0.556766i	$-0.812042\pi$
$257$	−26.6333			−1.66134			−0.830669	+	0.556766i	$0.812042\pi$
$258$	−6.00608	+	17.6125i	−0.373922	+	1.09650i
$259$		−	19.2826i		−	1.19816i
$260$	−5.54213	−	4.27729i	−0.343708	−	0.265266i
$261$		−	10.1195i		−	0.626379i
$262$	−10.9092	−	3.72018i	−0.673972	−	0.229834i
$263$	14.6785			0.905117			0.452559	−	0.891735i	$-0.350511\pi$
$263$	14.6785			0.905117			0.452559	+	0.891735i	$0.350511\pi$
$264$	−3.00821	+	1.99183i	−0.185143	+	0.122589i
$265$	−23.5150			−1.44451
$266$	5.98476	+	2.04088i	0.366949	+	0.125135i
$267$		−	15.9637i		−	0.976961i
$268$	3.20369	−	4.15105i	0.195696	−	0.253566i
$269$			11.6590i			0.710862i	0.934702	+	0.355431i	$0.115666\pi$
$269$			11.6590i			0.710862i	−0.934702	+	0.355431i	$0.884334\pi$
$270$	5.18297	−	15.1987i	0.315425	−	0.924965i
$271$	0.125029			0.00759496			0.00379748	−	0.999993i	$-0.498791\pi$
$271$	0.125029			0.00759496			0.00379748	+	0.999993i	$0.498791\pi$
$272$	−3.10554	−	11.8547i	−0.188301	−	0.718795i
$273$	−9.73697			−0.589308
$274$	5.05552	−	14.8250i	0.305415	−	0.895610i
$275$			3.86241i			0.232912i
$276$	−21.7713	+	28.2093i	−1.31048	+	1.69800i
$277$		−	19.8203i		−	1.19088i	−0.803398	−	0.595442i	$-0.796977\pi$
$277$		−	19.8203i		−	1.19088i	0.803398	−	0.595442i	$-0.203023\pi$
$278$	−16.3422	−	5.57292i	−0.980142	−	0.334242i
$279$	−5.59374			−0.334889
$280$	23.5166	+	35.5165i	1.40539	+	2.12252i
$281$	9.24019			0.551223			0.275612	−	0.961269i	$-0.411120\pi$
$281$	9.24019			0.551223			0.275612	+	0.961269i	$0.411120\pi$
$282$	13.2820	+	4.52933i	0.790929	+	0.269717i
$283$			30.3491i			1.80407i	0.431664	+	0.902035i	$0.357927\pi$
$283$			30.3491i			1.80407i	−0.431664	+	0.902035i	$0.642073\pi$
$284$	−19.0130	−	14.6738i	−1.12821	−	0.870729i
$285$			7.05835i			0.418101i
$286$	0.288745	−	0.846727i	0.0170739	−	0.0500680i
$287$	−18.5897			−1.09732
$288$	−7.84969	−	0.569600i	−0.462547	−	0.0335640i
$289$	−7.61391			−0.447877
$290$	11.1826	−	32.7924i	0.656667	−	1.92563i
$291$		−	12.4355i		−	0.728981i
$292$	19.8190	+	15.2958i	1.15982	+	0.895121i
$293$			19.5780i			1.14376i	0.820337	+	0.571880i	$0.193786\pi$
$293$			19.5780i			1.14376i	−0.820337	+	0.571880i	$0.806214\pi$
$294$	36.4397	+	12.4264i	2.12521	+	0.724724i
$295$	8.91419			0.519004
$296$	6.73428	+	10.1706i	0.391422	+	0.591154i
$297$	2.05203			0.119071
$298$	5.76984	+	1.96759i	0.334238	+	0.113980i
$299$		−	8.83569i		−	0.510981i
$300$	−16.2480	+	21.0527i	−0.938077	+	1.21548i
$301$			28.0749i			1.61821i
$302$	−4.51444	+	13.2383i	−0.259777	+	0.761779i
$303$	34.7425			1.99591
$304$	−3.86943	+	1.01366i	−0.221927	+	0.0581377i
$305$	−17.2168			−0.985829
$306$	1.94562	−	5.70541i	0.111224	−	0.326156i
$307$		−	1.54809i		−	0.0883541i	−0.999024	−	0.0441770i	$-0.985933\pi$
$307$		−	1.54809i		−	0.0883541i	0.999024	−	0.0441770i	$-0.0140666\pi$
$308$	−3.32571	+	4.30916i	−0.189500	+	0.245537i
$309$		−	24.4405i		−	1.39037i
$310$	−18.1267	−	6.18144i	−1.02953	−	0.351082i
$311$	−3.34671			−0.189774			−0.0948872	−	0.995488i	$-0.530249\pi$
$311$	−3.34671			−0.189774			−0.0948872	+	0.995488i	$0.530249\pi$
$312$	5.13577	−	3.40056i	0.290756	−	0.192519i
$313$	6.40232			0.361881			0.180940	−	0.983494i	$-0.442086\pi$
$313$	6.40232			0.361881			0.180940	+	0.983494i	$0.442086\pi$
$314$	−9.89651	−	3.37484i	−0.558492	−	0.190453i
$315$			20.9530i			1.18057i
$316$	1.44604	+	1.11602i	0.0813459	+	0.0627809i
$317$		−	9.23830i		−	0.518875i	−0.965760	−	0.259437i	$-0.916463\pi$
$317$		−	9.23830i		−	0.518875i	0.965760	−	0.259437i	$-0.0835371\pi$
$318$	6.67777	−	19.5821i	0.374471	−	1.09811i
$319$	4.42741			0.247887
$320$	−24.8077	−	10.5202i	−1.38679	−	0.588097i
$321$	−21.6288			−1.20720
$322$	−17.3521	+	50.8839i	−0.966993	+	2.83565i
$323$		−	3.06367i		−	0.170467i
$324$	17.7934	+	13.7325i	0.988522	+	0.762918i
$325$		−	6.59411i		−	0.365775i
$326$	16.8073	+	5.73152i	0.930872	+	0.317440i
$327$	−3.88915			−0.215071
$328$	9.80517	−	6.49232i	0.541400	−	0.358478i
$329$	21.1719			1.16725
$330$	−5.75095	−	1.96115i	−0.316579	−	0.107958i
$331$		−	4.65778i		−	0.256015i	−0.991773	−	0.128007i	$-0.959142\pi$
$331$		−	4.65778i		−	0.256015i	0.991773	−	0.128007i	$-0.0408582\pi$
$332$	−1.08486	+	1.40567i	−0.0595395	+	0.0771460i
$333$			6.00015i			0.328806i
$334$	−0.00285221	+	0.00836392i	−0.000156066	+	0.000457654i
$335$	8.83085			0.482481
$336$	−36.2546	+	9.49754i	−1.97785	+	0.518133i
$337$	−9.34371			−0.508984			−0.254492	−	0.967075i	$-0.581908\pi$
$337$	−9.34371			−0.508984			−0.254492	+	0.967075i	$0.581908\pi$
$338$	5.44095	−	15.9552i	0.295949	−	0.867851i
$339$			38.6298i			2.09808i
$340$	12.6097	−	16.3385i	0.683855	−	0.886079i
$341$		−	2.44734i		−	0.132531i
$342$	−1.86228	−	0.635061i	−0.100700	−	0.0343402i
$343$	26.7881			1.44642
$344$	−9.80493	−	14.8081i	−0.528646	−	0.798400i
$345$	−60.0117			−3.23092
$346$	5.96105	+	2.03280i	0.320468	+	0.109284i
$347$			30.9185i			1.65979i	0.557917	+	0.829897i	$0.311601\pi$
$347$			30.9185i			1.65979i	−0.557917	+	0.829897i	$0.688399\pi$
$348$	24.1323	+	18.6247i	1.29363	+	0.998390i
$349$		−	25.2445i		−	1.35131i	−0.737220	−	0.675653i	$-0.763862\pi$
$349$		−	25.2445i		−	1.35131i	0.737220	−	0.675653i	$-0.236138\pi$
$350$	−12.9499	+	37.9748i	−0.692202	+	2.02984i
$351$	−3.50333			−0.186994
$352$	0.249208	−	3.43435i	0.0132828	−	0.183051i
$353$	−2.15727			−0.114820			−0.0574099	−	0.998351i	$-0.518284\pi$
$353$	−2.15727			−0.114820			−0.0574099	+	0.998351i	$0.518284\pi$
$354$	−2.53145	+	7.42331i	−0.134545	+	0.394544i
$355$		−	40.4478i		−	2.14675i
$356$	12.0614	+	9.30874i	0.639255	+	0.493362i
$357$		−	28.7051i		−	1.51923i
$358$	−13.1238	−	4.47540i	−0.693616	−	0.236532i
$359$	32.0925			1.69378			0.846889	−	0.531770i	$-0.178473\pi$
$359$	32.0925			1.69378			0.846889	+	0.531770i	$0.178473\pi$
$360$	−7.31765	−	11.0517i	−0.385674	−	0.582473i
$361$	−1.00000			−0.0526316
$362$	−24.0231	−	8.19221i	−1.26263	−	0.430573i
$363$			22.2745i			1.16911i
$364$	5.67782	−	7.35682i	0.297599	−	0.385602i
$365$			42.1624i			2.20688i
$366$	4.88920	−	14.3373i	0.255563	−	0.749422i
$367$	10.3206			0.538729			0.269365	−	0.963038i	$-0.413186\pi$
$367$	10.3206			0.538729			0.269365	+	0.963038i	$0.413186\pi$
$368$	−8.61842	−	32.8988i	−0.449266	−	1.71497i
$369$	5.78456			0.301132
$370$	−6.63054	+	19.4437i	−0.344706	+	1.01083i
$371$		−	31.2146i		−	1.62058i
$372$	10.2952	−	13.3396i	0.533781	−	0.691627i
$373$			20.3031i			1.05125i	0.850715	+	0.525627i	$0.176169\pi$
$373$			20.3031i			1.05125i	−0.850715	+	0.525627i	$0.823831\pi$
$374$	2.49620	+	0.851236i	0.129075	+	0.0440164i
$375$	−9.49526			−0.490333
$376$	−11.1671	+	7.39412i	−0.575901	+	0.381323i
$377$	−7.55869			−0.389292
$378$	20.1753	+	6.88006i	1.03771	+	0.353872i
$379$		−	15.4355i		−	0.792867i	−0.918063	−	0.396433i	$-0.870248\pi$
$379$		−	15.4355i		−	0.792867i	0.918063	−	0.396433i	$-0.129752\pi$
$380$	−5.33298	−	4.11587i	−0.273576	−	0.211140i
$381$		−	19.4819i		−	0.998090i
$382$	1.75885	−	5.15771i	0.0899906	−	0.263892i
$383$	−37.7837			−1.93066			−0.965328	−	0.261041i	$-0.915934\pi$
$383$	−37.7837			−1.93066			−0.965328	+	0.261041i	$0.915934\pi$
$384$	15.8056	−	17.6711i	0.806576	−	0.901776i
$385$	−9.16722			−0.467205
$386$	8.92873	−	26.1829i	0.454460	−	1.33268i
$387$		−	8.73605i		−	0.444079i
$388$	9.39571	+	7.25139i	0.476995	+	0.368133i
$389$			13.7943i			0.699399i	0.936862	+	0.349700i	$0.113716\pi$
$389$			13.7943i			0.699399i	−0.936862	+	0.349700i	$0.886284\pi$
$390$	9.81831	+	3.34817i	0.497169	+	0.169541i
$391$	26.0481			1.31731
$392$	−30.6376	+	20.2861i	−1.54743	+	1.02460i
$393$	17.0790			0.861522
$394$	4.61566	+	1.57400i	0.232533	+	0.0792970i
$395$			3.07627i			0.154784i
$396$	1.03486	−	1.34088i	0.0520037	−	0.0673818i
$397$		−	33.1665i		−	1.66458i	−0.554343	−	0.832288i	$-0.687030\pi$
$397$		−	33.1665i		−	1.66458i	0.554343	−	0.832288i	$-0.312970\pi$
$398$	−3.49110	+	10.2374i	−0.174993	+	0.513156i
$399$	−9.36950			−0.469062
$400$	−6.43196	−	24.5525i	−0.321598	−	1.22763i
$401$	−8.24620			−0.411796			−0.205898	−	0.978573i	$-0.566011\pi$
$401$	−8.24620			−0.411796			−0.205898	+	0.978573i	$0.566011\pi$
$402$	−2.50778	+	7.35391i	−0.125077	+	0.366780i
$403$			4.17822i			0.208132i
$404$	−20.2591	+	26.2499i	−1.00793	+	1.30598i
$405$			37.8532i			1.88094i
$406$	43.5298	+	14.8442i	2.16035	+	0.736707i
$407$	−2.62515			−0.130124
$408$	10.0250	+	15.1405i	0.496313	+	0.749567i
$409$	30.4291			1.50462			0.752312	−	0.658807i	$-0.228939\pi$
$409$	30.4291			1.50462			0.752312	+	0.658807i	$0.228939\pi$
$410$	18.7450	+	6.39231i	0.925751	+	0.315694i
$411$			23.2094i			1.14484i
$412$	18.4662	+	14.2518i	0.909763	+	0.702134i
$413$			11.8330i			0.582264i
$414$	5.39944	−	15.8335i	0.265368	−	0.778175i
$415$	−2.99038			−0.146792
$416$	−0.425460	+	5.86329i	−0.0208599	+	0.287472i
$417$	25.5847			1.25289
$418$	0.277848	−	0.814773i	0.0135900	−	0.0398518i
$419$			5.11734i			0.249999i	0.992157	+	0.124999i	$0.0398929\pi$
$419$			5.11734i			0.249999i	−0.992157	+	0.124999i	$0.960107\pi$
$420$	−49.9673	−	38.5636i	−2.43816	−	1.88171i
$421$			28.8854i			1.40779i	0.710305	+	0.703894i	$0.248557\pi$
$421$			28.8854i			1.40779i	−0.710305	+	0.703894i	$0.751443\pi$
$422$	−19.3616	−	6.60255i	−0.942506	−	0.321407i
$423$	−6.58806			−0.320323
$424$	10.9015	+	16.4642i	0.529422	+	0.799571i
$425$	19.4398			0.942967
$426$	33.6830	+	11.4863i	1.63195	+	0.556515i
$427$		−	22.8541i		−	1.10599i
$428$	12.6122	−	16.3417i	0.609632	−	0.789908i
$429$			1.32560i			0.0640007i
$430$	9.65389	−	28.3094i	0.465552	−	1.36520i
$431$	−19.3963			−0.934288			−0.467144	−	0.884181i	$-0.654717\pi$
$431$	−19.3963			−0.934288			−0.467144	+	0.884181i	$0.654717\pi$
$432$	−13.0443	+	3.41718i	−0.627594	+	0.164409i
$433$	30.5791			1.46954			0.734770	−	0.678317i	$-0.237290\pi$
$433$	30.5791			1.46954			0.734770	+	0.678317i	$0.237290\pi$
$434$	8.20546	−	24.0620i	0.393875	−	1.15501i
$435$			51.3384i			2.46149i
$436$	2.26784	−	2.93847i	0.108610	−	0.140727i
$437$		−	8.50224i		−	0.406717i
$438$	−35.1108	−	11.9733i	−1.67766	−	0.572105i
$439$	−21.4056			−1.02163			−0.510817	−	0.859690i	$-0.670657\pi$
$439$	−21.4056			−1.02163			−0.510817	+	0.859690i	$0.670657\pi$
$440$	4.83525	−	3.20158i	0.230512	−	0.152629i
$441$	−18.0747			−0.860699
$442$	−4.26163	−	1.45327i	−0.202705	−	0.0691252i
$443$		−	8.83665i		−	0.419842i	−0.977718	−	0.209921i	$-0.932679\pi$
$443$		−	8.83665i		−	0.419842i	0.977718	−	0.209921i	$-0.0673207\pi$
$444$	−14.3088	−	11.0432i	−0.679065	−	0.524087i
$445$			25.6592i			1.21636i
$446$	2.16695	−	6.35444i	0.102608	−	0.300891i
$447$	−9.03303			−0.427248
$448$	13.9649	−	32.9306i	0.659779	−	1.55582i
$449$	17.9257			0.845968			0.422984	−	0.906137i	$-0.360983\pi$
$449$	17.9257			0.845968			0.422984	+	0.906137i	$0.360983\pi$
$450$	4.02962	−	11.8166i	0.189958	−	0.557041i
$451$			2.53083i			0.119172i
$452$	−29.1870	−	22.5258i	−1.37284	−	1.05953i
$453$		−	20.7254i		−	0.973763i
$454$	−3.57586	−	1.21942i	−0.167823	−	0.0572300i
$455$	15.6507			0.733718
$456$	4.94195	−	3.27222i	0.231428	−	0.153236i
$457$	−11.8630			−0.554930			−0.277465	−	0.960736i	$-0.589494\pi$
$457$	−11.8630			−0.554930			−0.277465	+	0.960736i	$0.589494\pi$
$458$	−10.5394	−	3.59409i	−0.492475	−	0.167941i
$459$		−	10.3280i		−	0.482069i
$460$	34.9941	−	45.3422i	1.63161	−	2.11409i
$461$			7.03036i			0.327436i	0.986507	+	0.163718i	$0.0523488\pi$
$461$			7.03036i			0.327436i	−0.986507	+	0.163718i	$0.947651\pi$
$462$	2.60330	−	7.63401i	0.121117	−	0.355166i
$463$	−0.523381			−0.0243236			−0.0121618	−	0.999926i	$-0.503871\pi$
$463$	−0.523381			−0.0243236			−0.0121618	+	0.999926i	$0.503871\pi$
$464$	−28.1440	+	7.37282i	−1.30655	+	0.342275i
$465$	28.3784			1.31602
$466$	−4.67045	+	13.6958i	−0.216354	+	0.634445i
$467$		−	15.1010i		−	0.698789i	−0.936976	−	0.349395i	$-0.886387\pi$
$467$		−	15.1010i		−	0.698789i	0.936976	−	0.349395i	$-0.113613\pi$
$468$	−1.76677	+	2.28922i	−0.0816688	+	0.105819i
$469$			11.7224i			0.541290i
$470$	−21.3488	−	7.28022i	−0.984746	−	0.335812i
$471$	15.4936			0.713906
$472$	−4.13258	−	6.24133i	−0.190218	−	0.287280i
$473$	3.82215			0.175742
$474$	−2.56177	−	0.873596i	−0.117666	−	0.0401256i
$475$		−	6.34525i		−	0.291140i
$476$	21.6883	+	16.7385i	0.994081	+	0.767209i
$477$			9.71305i			0.444730i
$478$	−6.89479	+	20.2185i	−0.315360	+	0.924774i
$479$	42.8653			1.95857			0.979284	−	0.202493i	$-0.0649043\pi$
$479$	42.8653			1.95857			0.979284	+	0.202493i	$0.0649043\pi$
$480$	39.8233	+	2.88972i	1.81768	+	0.131897i
$481$	4.48179			0.204352
$482$	2.81758	−	8.26237i	0.128337	−	0.376340i
$483$		−	79.6617i		−	3.62473i
$484$	−16.8296	−	12.9887i	−0.764983	−	0.590396i
$485$			19.9882i			0.907618i
$486$	−17.9854	−	6.13326i	−0.815834	−	0.278210i
$487$	−26.1098			−1.18315			−0.591573	−	0.806251i	$-0.701493\pi$
$487$	−26.1098			−1.18315			−0.591573	+	0.806251i	$0.701493\pi$
$488$	7.98162	+	12.0544i	0.361311	+	0.545678i
$489$	−26.3129			−1.18991
$490$	−58.5715	−	19.9736i	−2.64599	−	0.902317i
$491$		−	31.5875i		−	1.42552i	−0.701407	−	0.712761i	$-0.747444\pi$
$491$		−	31.5875i		−	1.42552i	0.701407	−	0.712761i	$-0.252556\pi$
$492$	−10.6464	+	13.7947i	−0.479977	+	0.621912i
$493$		−	22.2834i		−	1.00359i
$494$	−0.474357	+	1.39102i	−0.0213423	+	0.0625850i
$495$	2.85256			0.128213
$496$	4.07548	+	15.5572i	0.182995	+	0.698539i
$497$	53.6919			2.40841
$498$	0.849207	−	2.49025i	0.0380539	−	0.111591i
$499$			16.1119i			0.721268i	0.932707	+	0.360634i	$0.117440\pi$
$499$			16.1119i			0.721268i	−0.932707	+	0.360634i	$0.882560\pi$
$500$	5.53688	−	7.17420i	0.247617	−	0.320840i
$501$		−	0.0130942i		−	0.000585007i
$502$	9.07941	+	3.09620i	0.405234	+	0.138190i
$503$	6.81093			0.303684			0.151842	−	0.988405i	$-0.451479\pi$
$503$	6.81093			0.303684			0.151842	+	0.988405i	$0.451479\pi$
$504$	14.6704	−	9.71371i	0.653470	−	0.432683i
$505$	−55.8435			−2.48500
$506$	6.92739	+	2.36233i	0.307960	+	0.105018i
$507$			24.9789i			1.10935i
$508$	14.7197	+	11.3603i	0.653081	+	0.504033i
$509$			15.5299i			0.688350i	0.938905	+	0.344175i	$0.111841\pi$
$509$			15.5299i			0.688350i	−0.938905	+	0.344175i	$0.888159\pi$
$510$	−9.87059	+	28.9449i	−0.437077	+	1.28170i
$511$	−55.9679			−2.47588
$512$	4.13496	+	22.2464i	0.182741	+	0.983161i
$513$	−3.37112			−0.148838
$514$	−12.1569	+	35.6493i	−0.536217	+	1.57242i
$515$			39.2845i			1.73108i
$516$	20.8332	+	16.0786i	0.917131	+	0.707820i
$517$		−	2.88237i		−	0.126766i
$518$	−25.8102	−	8.80162i	−1.13403	−	0.386721i
$519$	−9.33238			−0.409646
$520$	−8.25499	+	5.46589i	−0.362005	+	0.239695i
$521$	−4.33054			−0.189724			−0.0948622	−	0.995490i	$-0.530241\pi$
$521$	−4.33054			−0.189724			−0.0948622	+	0.995490i	$0.530241\pi$
$522$	−13.5451	−	4.61908i	−0.592855	−	0.202171i
$523$			5.17275i			0.226189i	0.993584	+	0.113094i	$0.0360762\pi$
$523$			5.17275i			0.226189i	−0.993584	+	0.113094i	$0.963924\pi$
$524$	−9.95911	+	12.9041i	−0.435066	+	0.563720i
$525$		−	59.4519i		−	2.59469i
$526$	6.70009	−	19.6476i	0.292138	−	0.856675i
$527$	−12.3176			−0.536564
$528$	1.29301	+	4.93575i	0.0562708	+	0.214801i
$529$	49.2880			2.14296
$530$	−10.7335	+	31.4754i	−0.466235	+	1.36720i
$531$		−	3.68208i		−	0.159788i
$532$	5.46355	−	7.07918i	0.236875	−	0.306922i
$533$		−	4.32076i		−	0.187153i
$534$	−21.3678	−	7.28669i	−0.924674	−	0.315326i
$535$	34.7650			1.50302
$536$	−4.09395	−	6.18298i	−0.176832	−	0.267064i
$537$	20.5462			0.886632
$538$	15.6059	+	5.32181i	0.672817	+	0.229440i
$539$		−	7.90792i		−	0.340618i
$540$	−17.9781	−	13.8751i	−0.773654	−	0.597088i
$541$			18.2195i			0.783316i	0.920111	+	0.391658i	$0.128098\pi$
$541$			18.2195i			0.783316i	−0.920111	+	0.391658i	$0.871902\pi$
$542$	0.0570700	−	0.167354i	0.00245137	−	0.00718848i
$543$	37.6097			1.61399
$544$	−17.2853	−	1.25428i	−0.741101	−	0.0537768i
$545$	6.25124			0.267774
$546$	−4.44449	+	13.0332i	−0.190206	+	0.557768i
$547$			39.0195i			1.66835i	0.551499	+	0.834176i	$0.314056\pi$
$547$			39.0195i			1.66835i	−0.551499	+	0.834176i	$0.685944\pi$
$548$	−17.5360	−	13.5339i	−0.749101	−	0.578139i
$549$			7.11152i			0.303512i
$550$	5.16994	+	1.76302i	0.220447	+	0.0751753i
$551$	−7.27343			−0.309859
$552$	27.8212	+	42.0176i	1.18415	+	1.78839i
$553$	−4.08354			−0.173650
$554$	−26.5299	−	9.04706i	−1.12715	−	0.384373i
$555$		−	30.4402i		−	1.29211i
$556$	−14.9190	+	19.3307i	−0.632706	+	0.819805i
$557$			17.3116i			0.733516i	0.930316	+	0.366758i	$0.119532\pi$
$557$			17.3116i			0.733516i	−0.930316	+	0.366758i	$0.880468\pi$
$558$	−2.55329	+	7.48736i	−0.108089	+	0.316965i
$559$	−6.52536			−0.275993
$560$	58.2740	−	15.2659i	2.46252	−	0.645101i
$561$	−3.90794			−0.164994
$562$	4.21773	−	12.3682i	0.177914	−	0.521722i
$563$			1.53556i			0.0647162i	0.999476	+	0.0323581i	$0.0103017\pi$
$563$			1.53556i			0.0647162i	−0.999476	+	0.0323581i	$0.989698\pi$
$564$	12.1252	−	15.7108i	0.510564	−	0.661544i
$565$		−	62.0917i		−	2.61222i
$566$	40.6231	+	13.8530i	1.70752	+	0.582286i
$567$	−50.2477			−2.11021
$568$	−28.3198	+	18.7515i	−1.18827	+	0.786793i
$569$	25.4671			1.06764			0.533818	−	0.845600i	$-0.320757\pi$
$569$	25.4671			1.06764			0.533818	+	0.845600i	$0.320757\pi$
$570$	9.44778	+	3.22182i	0.395724	+	0.134947i
$571$			31.1021i			1.30158i	0.759256	+	0.650792i	$0.225563\pi$
$571$			31.1021i			1.30158i	−0.759256	+	0.650792i	$0.774437\pi$
$572$	−1.00157	−	0.772985i	−0.0418776	−	0.0323201i
$573$			8.07471i			0.337326i
$574$	−8.48537	+	24.8828i	−0.354173	+	1.03859i
$575$	53.9488			2.24982
$576$	−4.34545	+	10.2470i	−0.181061	+	0.426959i
$577$	6.93064			0.288526			0.144263	−	0.989539i	$-0.453919\pi$
$577$	6.93064			0.288526			0.144263	+	0.989539i	$0.453919\pi$
$578$	−3.47541	+	10.1914i	−0.144558	+	0.423907i
$579$			40.9909i			1.70353i
$580$	−38.7890	−	29.9365i	−1.61063	−	1.24304i
$581$		−	3.96954i		−	0.164684i
$582$	−16.6452	−	5.67624i	−0.689966	−	0.235288i
$583$	−4.24960			−0.176000
$584$	29.5203	−	19.5463i	1.22156	−	0.808834i
$585$	−4.87004			−0.201351
$586$	26.2057	+	8.93649i	1.08255	+	0.369163i
$587$		−	14.2948i		−	0.590009i	−0.955496	−	0.295005i	$-0.904679\pi$
$587$		−	14.2948i		−	0.590009i	0.955496	−	0.295005i	$-0.0953212\pi$
$588$	33.2662	−	43.1034i	1.37187	−	1.77755i
$589$			4.02054i			0.165664i
$590$	4.06893	−	11.9319i	0.167515	−	0.491227i
$591$	−7.22608			−0.297241
$592$	16.6875	−	4.37158i	0.685852	−	0.179671i
$593$	−21.2046			−0.870770			−0.435385	−	0.900244i	$-0.643388\pi$
$593$	−21.2046			−0.870770			−0.435385	+	0.900244i	$0.643388\pi$
$594$	0.936659	−	2.74669i	0.0384316	−	0.112698i
$595$			46.1392i			1.89152i
$596$	5.26734	−	6.82496i	0.215759	−	0.279561i
$597$		−	16.0273i		−	0.655954i
$598$	−11.8268	−	4.03309i	−0.483633	−	0.164925i
$599$	6.52684			0.266679			0.133340	−	0.991070i	$-0.457430\pi$
$599$	6.52684			0.266679			0.133340	+	0.991070i	$0.457430\pi$
$600$	20.7631	+	31.3579i	0.847649	+	1.28018i
$601$	−37.6306			−1.53498			−0.767492	−	0.641059i	$-0.778495\pi$
$601$	−37.6306			−1.53498			−0.767492	+	0.641059i	$0.778495\pi$
$602$	37.5789	+	12.8149i	1.53160	+	0.522297i
$603$		−	3.64765i		−	0.148544i
$604$	15.6592	+	12.0854i	0.637163	+	0.491747i
$605$		−	35.8029i		−	1.45560i
$606$	15.8584	−	46.5037i	0.644203	−	1.88908i
$607$	−24.8911			−1.01030			−0.505150	−	0.863032i	$-0.668563\pi$
$607$	−24.8911			−1.01030			−0.505150	+	0.863032i	$0.668563\pi$
$608$	−0.409404	+	5.64202i	−0.0166035	+	0.228814i
$609$	−68.1484			−2.76151
$610$	−7.85867	+	23.0451i	−0.318188	+	0.933067i
$611$			4.92093i			0.199079i
$612$	−6.74874	−	5.20852i	−0.272802	−	0.210542i
$613$		−	0.491774i		−	0.0198626i	−0.999951	−	0.00993128i	$-0.996839\pi$
$613$		−	0.491774i		−	0.0198626i	0.999951	−	0.00993128i	$-0.00316128\pi$
$614$	−2.07216	−	0.706633i	−0.0836254	−	0.0285174i
$615$	−29.3465			−1.18336
$616$	4.24989	+	6.41849i	0.171233	+	0.258608i
$617$	14.2755			0.574711			0.287356	−	0.957824i	$-0.407224\pi$
$617$	14.2755			0.574711			0.287356	+	0.957824i	$0.407224\pi$
$618$	−32.7142	−	11.1560i	−1.31596	−	0.448760i
$619$			17.6251i			0.708411i	0.935168	+	0.354206i	$0.115249\pi$
$619$			17.6251i			0.708411i	−0.935168	+	0.354206i	$0.884751\pi$
$620$	−16.5480	+	21.4415i	−0.664584	+	0.861110i
$621$		−	28.6620i		−	1.15017i
$622$	−1.52762	+	4.47965i	−0.0612520	+	0.179618i
$623$	−34.0610			−1.36462
$624$	−2.20748	−	8.42656i	−0.0883701	−	0.337332i
$625$	−16.4640			−0.658561
$626$	2.92237	−	8.56967i	0.116801	−	0.342513i
$627$			1.27558i			0.0509416i
$628$	−9.03462	+	11.7063i	−0.360520	+	0.467130i
$629$			13.2125i			0.526819i
$630$	28.0461	+	9.56408i	1.11738	+	0.381042i
$631$	−0.532668			−0.0212052			−0.0106026	−	0.999944i	$-0.503375\pi$
$631$	−0.532668			−0.0212052			−0.0106026	+	0.999944i	$0.503375\pi$
$632$	2.15387	−	1.42615i	0.0856763	−	0.0567290i
$633$	30.3117			1.20478
$634$	−12.3657	−	4.21687i	−0.491105	−	0.167473i
$635$			31.3143i			1.24267i
$636$	−23.1631	−	17.8767i	−0.918476	−	0.708858i
$637$			13.5008i			0.534921i
$638$	2.02091	−	5.92619i	0.0800086	−	0.234620i
$639$	−16.7073			−0.660930
$640$	−25.4051	+	28.4037i	−1.00423	+	1.12276i
$641$	16.5745			0.654654			0.327327	−	0.944911i	$-0.393852\pi$
$641$	16.5745			0.654654			0.327327	+	0.944911i	$0.393852\pi$
$642$	−9.87256	+	28.9506i	−0.389639	+	1.14259i
$643$		−	9.17617i		−	0.361873i	−0.983495	−	0.180936i	$-0.942087\pi$
$643$		−	9.17617i		−	0.361873i	0.983495	−	0.180936i	$-0.0579128\pi$
$644$	60.1889	+	46.4524i	2.37177	+	1.83048i
$645$			44.3201i			1.74510i
$646$	−4.10080	−	1.39843i	−0.161344	−	0.0550204i
$647$	−20.1025			−0.790311			−0.395155	−	0.918614i	$-0.629309\pi$
$647$	−20.1025			−0.790311			−0.395155	+	0.918614i	$0.629309\pi$
$648$	26.5032	−	17.5486i	1.04114	−	0.689375i
$649$	1.61096			0.0632357
$650$	−8.82638	−	3.00991i	−0.346199	−	0.118058i
$651$			37.6705i			1.47642i
$652$	15.3436	−	19.8809i	0.600901	−	0.778594i
$653$		−	42.6830i		−	1.67031i	−0.550012	−	0.835157i	$-0.685377\pi$
$653$		−	42.6830i		−	1.67031i	0.550012	−	0.835157i	$-0.314623\pi$
$654$	−1.77522	+	5.20573i	−0.0694167	+	0.203560i
$655$	−27.4520			−1.07264
$656$	−4.21451	−	16.0879i	−0.164549	−	0.628127i
$657$	17.4155			0.679444
$658$	9.66403	−	28.3391i	0.376743	−	1.10477i
$659$			34.7270i			1.35277i	0.736548	+	0.676385i	$0.236454\pi$
$659$			34.7270i			1.35277i	−0.736548	+	0.676385i	$0.763546\pi$
$660$	−5.25010	+	6.80261i	−0.204360	+	0.264791i
$661$			0.0670508i			0.00260797i	0.999999	+	0.00130399i	$0.000415072\pi$
$661$			0.0670508i			0.00260797i	−0.999999	+	0.00130399i	$0.999585\pi$
$662$	−6.23456	−	2.12607i	−0.242313	−	0.0826320i
$663$	6.67184			0.259113
$664$	1.38633	+	2.09374i	0.0538000	+	0.0812527i
$665$	15.0601			0.584005
$666$	8.03135	+	2.73880i	0.311209	+	0.106126i
$667$		−	61.8404i		−	2.39447i
$668$	0.00989342	+	0.00763551i	0.000382788	+	0.000295427i
$669$			9.94825i			0.384622i
$670$	4.03089	−	11.8203i	0.155727	−	0.456659i
$671$	−3.11139			−0.120114
$672$	−3.83591	+	52.8629i	−0.147974	+	2.03923i
$673$	−26.4049			−1.01783			−0.508917	−	0.860816i	$-0.669954\pi$
$673$	−26.4049			−1.01783			−0.508917	+	0.860816i	$0.669954\pi$
$674$	−4.26498	+	12.5068i	−0.164281	+	0.481743i
$675$		−	21.3906i		−	0.823324i
$676$	−18.8729	−	14.5657i	−0.725883	−	0.560219i
$677$			17.9627i			0.690361i	0.938536	+	0.345181i	$0.112182\pi$
$677$			17.9627i			0.690361i	−0.938536	+	0.345181i	$0.887818\pi$
$678$	51.7070	+	17.6328i	1.98580	+	0.677183i
$679$	−26.5331			−1.01825
$680$	−16.1137	−	24.3361i	−0.617934	−	0.933248i
$681$	5.59822			0.214524
$682$	−3.27583	−	1.11710i	−0.125438	−	0.0427760i
$683$		−	32.3268i		−	1.23695i	−0.785805	−	0.618475i	$-0.787751\pi$
$683$		−	32.3268i		−	1.23695i	0.785805	−	0.618475i	$-0.212249\pi$
$684$	−1.70009	+	2.20283i	−0.0650046	+	0.0842272i
$685$		−	37.3057i		−	1.42538i
$686$	12.2275	−	35.8565i	0.466850	−	1.36901i
$687$	16.5001			0.629519
$688$	−24.2965	+	6.36490i	−0.926297	+	0.242660i
$689$	7.25512			0.276398
$690$	−27.3927	+	80.3272i	−1.04282	+	3.05801i
$691$		−	1.75007i		−	0.0665757i	−0.999446	−	0.0332878i	$-0.989402\pi$
$691$		−	1.75007i		−	0.0665757i	0.999446	−	0.0332878i	$-0.0105978\pi$
$692$	5.44190	−	7.05113i	0.206870	−	0.268044i
$693$			3.78659i			0.143841i
$694$	41.3852	+	14.1129i	1.57096	+	0.535719i
$695$	−41.1237			−1.55991
$696$	35.9449	−	23.8003i	1.36249	−	0.902148i
$697$	12.7378			0.482479
$698$	−33.7903	−	11.5230i	−1.27898	−	0.436150i
$699$		−	21.4416i		−	0.810995i
$700$	44.9192	+	34.6676i	1.69779	+	1.31031i
$701$			27.7248i			1.04715i	0.851979	+	0.523576i	$0.175403\pi$
$701$			27.7248i			1.04715i	−0.851979	+	0.523576i	$0.824597\pi$
$702$	−1.59911	+	4.68929i	−0.0603546	+	0.176986i
$703$	4.31265			0.162655
$704$	−4.48321	−	1.90120i	−0.168967	−	0.0716540i
$705$	33.4228			1.25878
$706$	−0.984696	+	2.88756i	−0.0370595	+	0.108675i
$707$		−	74.1286i		−	2.78789i
$708$	8.78079	+	6.77681i	0.330002	+	0.254688i
$709$		−	50.2818i		−	1.88837i	−0.329412	−	0.944186i	$-0.606850\pi$
$709$		−	50.2818i		−	1.88837i	0.329412	−	0.944186i	$-0.393150\pi$
$710$	−54.1404	−	18.4626i	−2.03185	−	0.692889i
$711$	1.27068			0.0476541
$712$	17.9655	−	11.8955i	0.673285	−	0.445804i
$713$	−34.1836			−1.28019
$714$	−38.4225	−	13.1026i	−1.43793	−	0.490352i
$715$		−	2.13071i		−	0.0796840i
$716$	−11.9809	+	15.5238i	−0.447746	+	0.580150i
$717$		−	31.6533i		−	1.18211i
$718$	14.6488	−	42.9566i	0.546687	−	1.60313i
$719$	−13.1202			−0.489300			−0.244650	−	0.969611i	$-0.578673\pi$
$719$	−13.1202			−0.489300			−0.244650	+	0.969611i	$0.578673\pi$
$720$	−18.1331	+	4.75028i	−0.675780	+	0.177033i
$721$	−52.1477			−1.94208
$722$	−0.456455	+	1.33852i	−0.0169875	+	0.0498147i
$723$			12.9352i			0.481066i
$724$	−21.9310	+	28.4162i	−0.815058	+	1.05608i
$725$		−	46.1518i		−	1.71403i
$726$	29.8150	+	10.1673i	1.10654	+	0.377344i
$727$	32.5922			1.20878			0.604389	−	0.796690i	$-0.293417\pi$
$727$	32.5922			1.20878			0.604389	+	0.796690i	$0.293417\pi$
$728$	−7.25562	−	10.9580i	−0.268911	−	0.406129i
$729$	−5.55735			−0.205828
$730$	56.4355	+	19.2453i	2.08877	+	0.712299i
$731$		−	19.2371i		−	0.711510i
$732$	−16.9591	−	13.0886i	−0.626827	−	0.483770i
$733$			8.28509i			0.306017i	0.988225	+	0.153008i	$0.0488961\pi$
$733$			8.28509i			0.306017i	−0.988225	+	0.153008i	$0.951104\pi$
$734$	4.71087	−	13.8143i	0.173882	−	0.509897i
$735$	91.6971			3.38230
$736$	−47.9698	−	3.48085i	−1.76819	−	0.128306i
$737$	1.59590			0.0587857
$738$	2.64039	−	7.74278i	0.0971942	−	0.285016i
$739$		−	48.5291i		−	1.78517i	−0.450876	−	0.892587i	$-0.648888\pi$
$739$		−	48.5291i		−	1.78517i	0.450876	−	0.892587i	$-0.351112\pi$
$740$	22.9993	+	17.7503i	0.845470	+	0.652514i
$741$		−	2.17773i		−	0.0800008i
$742$	−41.7816	−	14.2481i	−1.53385	−	0.523063i
$743$	3.81374			0.139913			0.0699563	−	0.997550i	$-0.477714\pi$
$743$	3.81374			0.139913			0.0699563	+	0.997550i	$0.477714\pi$
$744$	−13.1561	−	19.8693i	−0.482326	−	0.728444i
$745$	14.5193			0.531945
$746$	27.1762	+	9.26743i	0.994990	+	0.339305i
$747$			1.23520i			0.0451936i
$748$	2.27880	−	2.95267i	0.0833212	−	0.107960i
$749$			46.1483i			1.68622i
$750$	−4.33416	+	12.7096i	−0.158261	+	0.464090i
$751$	46.7083			1.70441			0.852205	−	0.523208i	$-0.175265\pi$
$751$	46.7083			1.70441			0.852205	+	0.523208i	$0.175265\pi$
$752$	4.79992	+	18.3226i	0.175035	+	0.668156i
$753$	−14.2144			−0.518000
$754$	−3.45020	+	10.1175i	−0.125649	+	0.368457i
$755$			33.3130i			1.21238i
$756$	18.4183	−	23.8647i	0.669865	−	0.867952i
$757$			38.8886i			1.41343i	0.707498	+	0.706716i	$0.249824\pi$
$757$			38.8886i			1.41343i	−0.707498	+	0.706716i	$0.750176\pi$
$758$	−20.6608	−	7.04560i	−0.750433	−	0.255908i
$759$	−10.8452			−0.393657
$760$	−7.94345	+	5.25962i	−0.288139	+	0.190786i
$761$	36.7676			1.33283			0.666413	−	0.745583i	$-0.267829\pi$
$761$	36.7676			1.33283			0.666413	+	0.745583i	$0.267829\pi$
$762$	−26.0771	−	8.89263i	−0.944672	−	0.322146i
$763$			8.29812i			0.300412i
$764$	−6.10089	−	4.70853i	−0.220723	−	0.170349i
$765$		−	14.3571i		−	0.519083i
$766$	−17.2465	+	50.5744i	−0.623143	+	1.82733i
$767$	−2.75031			−0.0993080
$768$	−16.4387	−	29.2222i	−0.593180	−	1.05447i
$769$	52.3408			1.88746			0.943730	−	0.330718i	$-0.107291\pi$
$769$	52.3408			1.88746			0.943730	+	0.330718i	$0.107291\pi$
$770$	−4.18442	+	12.2705i	−0.150796	+	0.442200i
$771$		−	55.8111i		−	2.00999i
$772$	−30.9709	−	23.9026i	−1.11467	−	0.860275i
$773$			13.8632i			0.498626i	0.968423	+	0.249313i	$0.0802048\pi$
$773$			13.8632i			0.498626i	−0.968423	+	0.249313i	$0.919795\pi$
$774$	−11.6934	−	3.98761i	−0.420312	−	0.143332i
$775$	−25.5113			−0.916395
$776$	13.9949	−	9.26646i	0.502387	−	0.332646i
$777$	40.4074			1.44961
$778$	18.4640	+	6.29648i	0.661967	+	0.225740i
$779$		−	4.15770i		−	0.148965i
$780$	8.96323	−	11.6138i	0.320935	−	0.415839i
$781$		−	7.30967i		−	0.261561i
$782$	11.8898	−	34.8660i	0.425177	−	1.24680i
$783$	−24.5196			−0.876258
$784$	13.1688	+	50.2689i	0.470315	+	1.79532i
$785$	−24.9036			−0.888848
$786$	7.79579	−	22.8607i	0.278067	−	0.815413i
$787$		−	7.53623i		−	0.268638i	−0.990938	−	0.134319i	$-0.957115\pi$
$787$		−	7.53623i		−	0.268638i	0.990938	−	0.134319i	$-0.0428846\pi$
$788$	4.21368	−	5.45971i	0.150106	−	0.194494i
$789$			30.7595i			1.09507i
$790$	4.11766	+	1.40418i	0.146500	+	0.0499584i
$791$	82.4228			2.93062
$792$	−1.32244	−	1.99724i	−0.0469907	−	0.0709688i
$793$	5.31192			0.188632
$794$	−44.3941	−	15.1390i	−1.57549	−	0.537263i
$795$		−	49.2766i		−	1.74766i
$796$	12.1095	+	9.34585i	0.429211	+	0.331255i
$797$			44.5030i			1.57638i	0.615433	+	0.788189i	$0.288981\pi$
$797$			44.5030i			1.57638i	−0.615433	+	0.788189i	$0.711019\pi$
$798$	−4.27676	+	12.5413i	−0.151395	+	0.443958i
$799$	−14.5071			−0.513226
$800$	−35.8000	−	2.59777i	−1.26572	−	0.0918451i
$801$	10.5987			0.374488
$802$	−3.76402	+	11.0377i	−0.132912	+	0.389756i
$803$			7.61954i			0.268888i
$804$	8.69870	+	6.71345i	0.306780	+	0.236765i
$805$			128.044i			4.51297i
$806$	5.59266	+	1.90717i	0.196993	+	0.0671772i
$807$	−24.4319			−0.860044
$808$	25.8888	+	39.0992i	0.910765	+	1.37550i
$809$	−3.45607			−0.121509			−0.0607544	−	0.998153i	$-0.519351\pi$
$809$	−3.45607			−0.121509			−0.0607544	+	0.998153i	$0.519351\pi$
$810$	50.6675	+	17.2783i	1.78028	+	0.607098i
$811$		−	14.9470i		−	0.524860i	−0.964951	−	0.262430i	$-0.915476\pi$
$811$		−	14.9470i		−	0.524860i	0.964951	−	0.262430i	$-0.0845239\pi$
$812$	39.7387	−	51.4900i	1.39456	−	1.80694i
$813$			0.262003i			0.00918885i
$814$	−1.19826	+	3.51383i	−0.0419991	+	0.123160i
$815$	42.2941			1.48150
$816$	24.8419	−	6.50778i	0.869641	−	0.227818i
$817$	−6.27910			−0.219678
$818$	13.8895	−	40.7302i	0.485636	−	1.42410i
$819$		−	6.46466i		−	0.225893i
$820$	17.1125	−	22.1729i	0.597595	−	0.774311i
$821$			3.72440i			0.129982i	0.997886	+	0.0649912i	$0.0207019\pi$
$821$			3.72440i			0.129982i	−0.997886	+	0.0649912i	$0.979298\pi$
$822$	31.0664	+	10.5940i	1.08356	+	0.369510i
$823$	15.0687			0.525262			0.262631	−	0.964896i	$-0.415410\pi$
$823$	15.0687			0.525262			0.262631	+	0.964896i	$0.415410\pi$
$824$	27.5053	−	18.2122i	0.958193	−	0.634450i
$825$	−8.09385			−0.281792
$826$	15.8388	+	5.40124i	0.551102	+	0.187933i
$827$			37.8202i			1.31514i	0.753395	+	0.657568i	$0.228415\pi$
$827$			37.8202i			1.31514i	−0.753395	+	0.657568i	$0.771585\pi$
$828$	−18.7290	−	14.4546i	−0.650876	−	0.502331i
$829$		−	38.8523i		−	1.34940i	−0.738094	−	0.674698i	$-0.764274\pi$
$829$		−	38.8523i		−	1.34940i	0.738094	−	0.674698i	$-0.235726\pi$
$830$	−1.36497	+	4.00270i	−0.0473790	+	0.138936i
$831$	41.5342			1.44080
$832$	7.65396	+	3.24582i	0.265353	+	0.112529i
$833$	−39.8011			−1.37903
$834$	11.6783	−	34.2458i	0.404386	−	1.18584i
$835$			0.0210470i			0.000728362i
$836$	−0.963768	−	0.743814i	−0.0333326	−	0.0257253i
$837$			13.5537i			0.468485i
$838$	6.84969	+	2.33584i	0.236619	+	0.0806901i
$839$	−15.8272			−0.546417			−0.273209	−	0.961955i	$-0.588085\pi$
$839$	−15.8272			−0.546417			−0.273209	+	0.961955i	$0.588085\pi$
$840$	−74.4262	+	49.2800i	−2.56795	+	1.70032i
$841$	−23.9028			−0.824235
$842$	38.6638	+	13.1849i	1.33244	+	0.454381i
$843$			19.3632i			0.666904i
$844$	−17.6753	+	22.9022i	−0.608411	+	0.788325i
$845$		−	40.1499i		−	1.38120i
$846$	−3.00715	+	8.81828i	−0.103388	+	0.303179i
$847$	47.5261			1.63302
$848$	27.0137	−	7.07672i	0.927655	−	0.243016i
$849$	−63.5979			−2.18267
$850$	8.87338	−	26.0206i	0.304354	−	0.892500i
$851$			36.6672i			1.25693i
$852$	30.7495	−	39.8425i	1.05346	−	1.36498i
$853$		−	6.18601i		−	0.211805i	−0.994377	−	0.105902i	$-0.966227\pi$
$853$		−	6.18601i		−	0.211805i	0.994377	−	0.105902i	$-0.0337731\pi$
$854$	−30.5908	−	10.4319i	−1.04680	−	0.356972i
$855$	−4.68624			−0.160266
$856$	−16.1169	−	24.3410i	−0.550866	−	0.831957i
$857$	12.2246			0.417583			0.208792	−	0.977960i	$-0.433047\pi$
$857$	12.2246			0.417583			0.208792	+	0.977960i	$0.433047\pi$
$858$	1.77435	+	0.605077i	0.0605754	+	0.0206570i
$859$			44.9215i			1.53270i	0.642423	+	0.766350i	$0.277929\pi$
$859$			44.9215i			1.53270i	−0.642423	+	0.766350i	$0.722071\pi$
$860$	−33.4863	−	25.8439i	−1.14187	−	0.881271i
$861$		−	38.9555i		−	1.32760i
$862$	−8.85355	+	25.9625i	−0.301553	+	0.884285i
$863$	21.2268			0.722568			0.361284	−	0.932456i	$-0.382339\pi$
$863$	21.2268			0.722568			0.361284	+	0.932456i	$0.382339\pi$
$864$	−1.38015	+	19.0199i	−0.0469536	+	0.647070i
$865$	15.0004			0.510029
$866$	13.9580	−	40.9309i	0.474312	−	1.39089i
$867$		−	15.9553i		−	0.541869i
$868$	−28.4621	−	21.9664i	−0.966068	−	0.745589i
$869$			0.555938i			0.0188589i
$870$	68.7178	+	23.4337i	2.32975	+	0.794476i
$871$	−2.72460			−0.0923196
$872$	−2.89805	−	4.37685i	−0.0981404	−	0.148219i
$873$	8.25628			0.279433
$874$	−11.3805	−	3.88089i	−0.384950	−	0.131273i
$875$			20.2596i			0.684900i
$876$	−32.0530	+	41.5315i	−1.08297	+	1.40322i
$877$		−	15.4462i		−	0.521582i	−0.965395	−	0.260791i	$-0.916017\pi$
$877$		−	15.4462i		−	0.521582i	0.965395	−	0.260791i	$-0.0839834\pi$
$878$	−9.77069	+	28.6519i	−0.329745	+	0.966956i
$879$	−41.0266			−1.38379
$880$	−2.07832	−	7.93348i	−0.0700600	−	0.267438i
$881$	−25.4049			−0.855912			−0.427956	−	0.903800i	$-0.640766\pi$
$881$	−25.4049			−0.855912			−0.427956	+	0.903800i	$0.640766\pi$
$882$	−8.25027	+	24.1934i	−0.277801	+	0.814634i
$883$			29.9928i			1.00934i	0.863313	+	0.504669i	$0.168385\pi$
$883$			29.9928i			1.00934i	−0.863313	+	0.504669i	$0.831615\pi$
$884$	−3.89048	+	5.04095i	−0.130851	+	0.169545i
$885$			18.6800i			0.627923i
$886$	−11.8281	−	4.03353i	−0.397372	−	0.135509i
$887$	−27.5162			−0.923903			−0.461952	−	0.886905i	$-0.652851\pi$
$887$	−27.5162			−0.923903			−0.461952	+	0.886905i	$0.652851\pi$
$888$	−21.3129	+	14.1120i	−0.715214	+	0.473566i
$889$	−41.5678			−1.39414
$890$	34.3455	+	11.7123i	1.15126	+	0.392597i
$891$			6.84079i			0.229175i
$892$	−7.51646	−	5.80103i	−0.251670	−	0.194233i
$893$			4.73522i			0.158458i
$894$	−4.12317	+	12.0909i	−0.137899	+	0.404381i
$895$	−33.0249			−1.10390
$896$	−37.7041	−	33.7237i	−1.25961	−	1.12663i
$897$	18.5155			0.618216
$898$	8.18229	−	23.9940i	0.273046	−	0.800692i
$899$			29.2431i			0.975313i
$900$	−13.9775	−	10.7875i	−0.465917	−	0.359584i
$901$			21.3885i			0.712554i
$902$	3.38758	+	1.15521i	0.112794	+	0.0384642i
$903$	−58.8321			−1.95781
$904$	−43.4739	+	28.7855i	−1.44592	+	0.957391i
$905$	−60.4520			−2.00949
$906$	−27.7414	−	9.46019i	−0.921647	−	0.314294i
$907$			26.8589i			0.891837i	0.895074	+	0.445918i	$0.147123\pi$
$907$			26.8589i			0.891837i	−0.895074	+	0.445918i	$0.852877\pi$
$908$	−3.26444	+	4.22977i	−0.108334	+	0.140370i
$909$			23.0666i			0.765070i
$910$	7.14385	−	20.9489i	0.236816	−	0.694449i
$911$	−34.5330			−1.14413			−0.572065	−	0.820208i	$-0.693858\pi$
$911$	−34.5330			−1.14413			−0.572065	+	0.820208i	$0.693858\pi$
$912$	−2.12418	−	8.10855i	−0.0703385	−	0.268501i
$913$	−0.540418			−0.0178852
$914$	−5.41494	+	15.8790i	−0.179110	+	0.525230i
$915$		−	36.0784i		−	1.19272i
$916$	−9.62155	+	12.4668i	−0.317905	+	0.411913i
$917$		−	36.4407i		−	1.20338i
$918$	−13.8243	−	4.71426i	−0.456269	−	0.155594i
$919$	−20.0300			−0.660729			−0.330365	−	0.943853i	$-0.607172\pi$
$919$	−20.0300			−0.660729			−0.330365	+	0.943853i	$0.607172\pi$
$920$	−44.7185	−	67.5371i	−1.47432	−	2.22663i
$921$	3.24408			0.106896
$922$	9.41031	+	3.20904i	0.309912	+	0.105684i
$923$			12.4794i			0.410766i
$924$	−9.03003	−	6.96917i	−0.297066	−	0.229269i
$925$			27.3649i			0.899751i
$926$	−0.238900	+	0.700559i	−0.00785073	+	0.0230218i
$927$	16.2268			0.532957
$928$	−2.97777	+	41.0368i	−0.0977502	+	1.34710i
$929$	2.91198			0.0955389			0.0477695	−	0.998858i	$-0.484789\pi$
$929$	2.91198			0.0955389			0.0477695	+	0.998858i	$0.484789\pi$
$930$	12.9535	−	37.9852i	0.424760	−	1.24558i
$931$			12.9913i			0.425773i
$932$	16.2003	+	12.5030i	0.530659	+	0.409550i
$933$		−	7.01316i		−	0.229601i
$934$	−20.2130	−	6.89291i	−0.661390	−	0.225543i
$935$	6.28144			0.205425
$936$	2.25773	+	3.40979i	0.0737962	+	0.111452i
$937$	4.03574			0.131842			0.0659210	−	0.997825i	$-0.479001\pi$
$937$	4.03574			0.131842			0.0659210	+	0.997825i	$0.479001\pi$
$938$	15.6907	+	5.35074i	0.512320	+	0.174708i
$939$			13.4163i			0.437825i
$940$	−19.4895	+	25.2528i	−0.635678	+	0.823655i
$941$			51.2751i			1.67152i	0.549096	+	0.835760i	$0.314972\pi$
$941$			51.2751i			1.67152i	−0.549096	+	0.835760i	$0.685028\pi$
$942$	7.07211	−	20.7385i	0.230422	−	0.675698i
$943$	35.3497			1.15114
$944$	−10.2405	+	2.68268i	−0.333300	+	0.0873139i
$945$	50.7693			1.65153
$946$	1.74464	−	5.11604i	0.0567230	−	0.166337i
$947$			37.7009i			1.22511i	0.790426	+	0.612557i	$0.209859\pi$
$947$			37.7009i			1.22511i	−0.790426	+	0.612557i	$0.790141\pi$
$948$	−2.33866	+	3.03023i	−0.0759562	+	0.0984173i
$949$		−	13.0085i		−	0.422272i
$950$	−8.49328	−	2.89632i	−0.275558	−	0.0939691i
$951$	19.3592			0.627766
$952$	32.3047	−	21.3899i	1.04700	−	0.693252i
$953$	41.4066			1.34129			0.670645	−	0.741779i	$-0.266017\pi$
$953$	41.4066			1.34129			0.670645	+	0.741779i	$0.266017\pi$
$954$	13.0012	+	4.43357i	0.420928	+	0.143542i
$955$		−	12.9789i		−	0.419987i
$956$	23.9159	+	18.4577i	0.773494	+	0.596964i
$957$			9.27781i			0.299909i
$958$	19.5661	−	57.3763i	0.632152	−	1.85375i
$959$	49.5209			1.59911
$960$	22.0455	−	51.9855i	0.711516	−	1.67783i
$961$	−14.8352			−0.478556
$962$	2.04573	−	5.99899i	0.0659571	−	0.193415i
$963$		−	14.3600i		−	0.462744i
$964$	−9.77329	−	7.54279i	−0.314776	−	0.242937i
$965$		−	65.8869i		−	2.12097i
$966$	−106.629	−	36.3620i	−3.43074	−	1.16993i
$967$	29.9529			0.963220			0.481610	−	0.876386i	$-0.340052\pi$
$967$	29.9529			0.963220			0.481610	+	0.876386i	$0.340052\pi$
$968$	−25.0677	+	16.5981i	−0.805706	+	0.533483i
$969$	6.42005			0.206242
$970$	26.7547	+	9.12371i	0.859042	+	0.292945i
$971$		−	53.5633i		−	1.71893i	−0.511195	−	0.859465i	$-0.670797\pi$
$971$		−	53.5633i		−	1.71893i	0.511195	−	0.859465i	$-0.329203\pi$
$972$	−16.4190	+	21.2743i	−0.526641	+	0.682375i
$973$		−	54.5890i		−	1.75004i
$974$	−11.9179	+	34.9486i	−0.381875	+	1.11982i
$975$	13.8182			0.442537
$976$	19.7784	−	5.18130i	0.633091	−	0.165849i
$977$	−26.2092			−0.838506			−0.419253	−	0.907869i	$-0.637708\pi$
$977$	−26.2092			−0.838506			−0.419253	+	0.907869i	$0.637708\pi$
$978$	−12.0106	+	35.2205i	−0.384058	+	1.12623i
$979$			4.63710i			0.148202i
$980$	−53.4704	+	69.2823i	−1.70805	+	2.21314i
$981$		−	2.58212i		−	0.0824408i
$982$	−42.2806	−	14.4182i	−1.34923	−	0.460105i
$983$	6.77344			0.216039			0.108020	−	0.994149i	$-0.465549\pi$
$983$	6.77344			0.216039			0.108020	+	0.994149i	$0.465549\pi$
$984$	13.6049	+	20.5471i	0.433709	+	0.655018i
$985$	11.6149			0.370080
$986$	−29.8269	−	10.1714i	−0.949882	−	0.323922i
$987$			44.3666i			1.41221i
$988$	1.64539	+	1.26988i	0.0523469	+	0.0404001i
$989$		−	53.3864i		−	1.69759i
$990$	1.30207	−	3.81822i	0.0413823	−	0.121351i
$991$	−8.71348			−0.276793			−0.138396	−	0.990377i	$-0.544195\pi$
$991$	−8.71348			−0.276793			−0.138396	+	0.990377i	$0.544195\pi$
$992$	22.6840	+	1.64603i	0.720217	+	0.0522614i
$993$	9.76058			0.309743
$994$	24.5079	−	71.8679i	0.777344	−	2.27951i
$995$			25.7615i			0.816695i
$996$	−2.94563	−	2.27337i	−0.0933359	−	0.0720345i
$997$			58.7540i			1.86076i	0.366599	+	0.930379i	$0.380522\pi$
$997$			58.7540i			1.86076i	−0.366599	+	0.930379i	$0.619478\pi$
$998$	21.5662	+	7.35436i	0.682666	+	0.232798i
$999$	14.5384			0.459976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.c.b.77.9	✓	16
3.2	odd	2		1368.2.g.b.685.8		16
4.3	odd	2		608.2.c.b.305.4		16
8.3	odd	2		608.2.c.b.305.13		16
8.5	even	2	inner	152.2.c.b.77.10	yes	16
12.11	even	2		5472.2.g.b.2737.15		16
16.3	odd	4		4864.2.a.bn.1.7		8
16.5	even	4		4864.2.a.bq.1.7		8
16.11	odd	4		4864.2.a.bp.1.2		8
16.13	even	4		4864.2.a.bo.1.2		8
24.5	odd	2		1368.2.g.b.685.7		16
24.11	even	2		5472.2.g.b.2737.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.c.b.77.9	✓	16	1.1	even	1	trivial
152.2.c.b.77.10	yes	16	8.5	even	2	inner
608.2.c.b.305.4		16	4.3	odd	2
608.2.c.b.305.13		16	8.3	odd	2
1368.2.g.b.685.7		16	24.5	odd	2
1368.2.g.b.685.8		16	3.2	odd	2
4864.2.a.bn.1.7		8	16.3	odd	4
4864.2.a.bo.1.2		8	16.13	even	4
4864.2.a.bp.1.2		8	16.11	odd	4
4864.2.a.bq.1.7		8	16.5	even	4
5472.2.g.b.2737.2		16	24.11	even	2
5472.2.g.b.2737.15		16	12.11	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456455 - 1.33852i) q^{2} +2.09554i q^{3} +(-1.58330 - 1.22195i) q^{4} -3.36827i q^{5} +(2.80493 + 0.956520i) q^{6} +4.47116 q^{7} +(-2.35832 + 1.56152i) q^{8} -1.39129 q^{9} +O(q^{10})\)	\(q+(0.456455 - 1.33852i) q^{2} +2.09554i q^{3} +(-1.58330 - 1.22195i) q^{4} -3.36827i q^{5} +(2.80493 + 0.956520i) q^{6} +4.47116 q^{7} +(-2.35832 + 1.56152i) q^{8} -1.39129 q^{9} +(-4.50852 - 1.53746i) q^{10} -0.608709i q^{11} +(2.56065 - 3.31787i) q^{12} +1.03922i q^{13} +(2.04088 - 5.98476i) q^{14} +7.05835 q^{15} +(1.01366 + 3.86943i) q^{16} -3.06367 q^{17} +(-0.635061 + 1.86228i) q^{18} +1.00000i q^{19} +(-4.11587 + 5.33298i) q^{20} +9.36950i q^{21} +(-0.814773 - 0.277848i) q^{22} -8.50224 q^{23} +(-3.27222 - 4.94195i) q^{24} -6.34525 q^{25} +(1.39102 + 0.474357i) q^{26} +3.37112i q^{27} +(-7.07918 - 5.46355i) q^{28} +7.27343i q^{29} +(3.22182 - 9.44778i) q^{30} +4.02054 q^{31} +(5.64202 + 0.409404i) q^{32} +1.27558 q^{33} +(-1.39843 + 4.10080i) q^{34} -15.0601i q^{35} +(2.20283 + 1.70009i) q^{36} -4.31265i q^{37} +(1.33852 + 0.456455i) q^{38} -2.17773 q^{39} +(5.25962 + 7.94345i) q^{40} -4.15770 q^{41} +(12.5413 + 4.27676i) q^{42} +6.27910i q^{43} +(-0.743814 + 0.963768i) q^{44} +4.68624i q^{45} +(-3.88089 + 11.3805i) q^{46} +4.73522 q^{47} +(-8.10855 + 2.12418i) q^{48} +12.9913 q^{49} +(-2.89632 + 8.49328i) q^{50} -6.42005i q^{51} +(1.26988 - 1.64539i) q^{52} -6.98132i q^{53} +(4.51232 + 1.53876i) q^{54} -2.05030 q^{55} +(-10.5444 + 6.98180i) q^{56} -2.09554 q^{57} +(9.73567 + 3.31999i) q^{58} +2.64652i q^{59} +(-11.1755 - 8.62497i) q^{60} -5.11145i q^{61} +(1.83520 - 5.38159i) q^{62} -6.22069 q^{63} +(3.12332 - 7.36511i) q^{64} +3.50037 q^{65} +(0.582242 - 1.70739i) q^{66} +2.62178i q^{67} +(4.85071 + 3.74366i) q^{68} -17.8168i q^{69} +(-20.1583 - 6.87425i) q^{70} +12.0085 q^{71} +(3.28111 - 2.17253i) q^{72} -12.5175 q^{73} +(-5.77259 - 1.96853i) q^{74} -13.2967i q^{75} +(1.22195 - 1.58330i) q^{76} -2.72164i q^{77} +(-0.994034 + 2.91494i) q^{78} -0.913307 q^{79} +(13.0333 - 3.41430i) q^{80} -11.2382 q^{81} +(-1.89780 + 5.56518i) q^{82} -0.887809i q^{83} +(11.4491 - 14.8347i) q^{84} +10.3193i q^{85} +(8.40473 + 2.86613i) q^{86} -15.2418 q^{87} +(0.950510 + 1.43553i) q^{88} -7.61792 q^{89} +(6.27266 + 2.13906i) q^{90} +4.64652i q^{91} +(13.4616 + 10.3893i) q^{92} +8.42521i q^{93} +(2.16141 - 6.33820i) q^{94} +3.36827 q^{95} +(-0.857923 + 11.8231i) q^{96} -5.93426 q^{97} +(5.92994 - 17.3892i) q^{98} +0.846892i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9	\( 16 q + 2 q^{4} + 6 q^{6} - 8 q^{7} - 12 q^{8} - 24 q^{9} - 8 q^{10} + 4 q^{12} + 4 q^{14} + 2 q^{16} - 8 q^{17} + 20 q^{18} + 8 q^{20} + 20 q^{22} + 6 q^{24} - 24 q^{25} - 10 q^{26} - 14 q^{28} + 4 q^{30} + 16 q^{31} - 20 q^{32} + 8 q^{36} + 2 q^{38} + 8 q^{39} + 28 q^{40} + 16 q^{41} - 2 q^{42} - 28 q^{44} - 48 q^{46} + 24 q^{47} + 36 q^{48} + 24 q^{49} + 12 q^{50} + 8 q^{52} - 34 q^{54} + 16 q^{55} - 48 q^{56} + 38 q^{58} - 28 q^{60} - 16 q^{62} - 32 q^{63} + 14 q^{64} + 16 q^{65} - 24 q^{66} - 26 q^{68} - 32 q^{70} + 48 q^{71} - 20 q^{74} - 4 q^{76} + 56 q^{78} - 48 q^{79} + 4 q^{80} - 16 q^{81} - 12 q^{82} + 64 q^{84} + 48 q^{86} - 48 q^{87} + 40 q^{88} - 16 q^{89} + 12 q^{90} + 62 q^{92} - 36 q^{94} + 16 q^{95} - 70 q^{96} + 32 q^{97} - 48 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 6 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 8 * q^10 + 4 * q^12 + 4 * q^14 + 2 * q^16 - 8 * q^17 + 20 * q^18 + 8 * q^20 + 20 * q^22 + 6 * q^24 - 24 * q^25 - 10 * q^26 - 14 * q^28 + 4 * q^30 + 16 * q^31 - 20 * q^32 + 8 * q^36 + 2 * q^38 + 8 * q^39 + 28 * q^40 + 16 * q^41 - 2 * q^42 - 28 * q^44 - 48 * q^46 + 24 * q^47 + 36 * q^48 + 24 * q^49 + 12 * q^50 + 8 * q^52 - 34 * q^54 + 16 * q^55 - 48 * q^56 + 38 * q^58 - 28 * q^60 - 16 * q^62 - 32 * q^63 + 14 * q^64 + 16 * q^65 - 24 * q^66 - 26 * q^68 - 32 * q^70 + 48 * q^71 - 20 * q^74 - 4 * q^76 + 56 * q^78 - 48 * q^79 + 4 * q^80 - 16 * q^81 - 12 * q^82 + 64 * q^84 + 48 * q^86 - 48 * q^87 + 40 * q^88 - 16 * q^89 + 12 * q^90 + 62 * q^92 - 36 * q^94 + 16 * q^95 - 70 * q^96 + 32 * q^97 - 48 * q^98

Introduction

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