LMFDB - Embedded newform 525.2.i.i.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 3x^{5} + 50x^{4} - 27x^{3} + 53x^{2} + 20x + 16 $ x^8 - x^7 + 8x^6 - 3x^5 + 50x^4 - 27x^3 + 53x^2 + 20x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$1.35143 - 2.34074i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.i.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35143 + 2.34074i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(-1.65271 + 2.06605i) q^{7} +8.93406 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.35143 + 2.34074i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(-1.65271 + 2.06605i) q^{7} +8.93406 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.41275 - 2.44696i) q^{11} +(2.65271 - 4.59463i) q^{12} -4.47992 q^{13} +(-2.60256 - 6.66067i) q^{14} +(-6.76831 + 11.7231i) q^{16} +(-2.11560 - 3.66433i) q^{17} +(-1.35143 - 2.34074i) q^{18} +(-1.05014 + 1.81890i) q^{19} +(-2.61560 - 0.398264i) q^{21} +7.63692 q^{22} +(3.30542 - 5.72515i) q^{23} +(4.46703 + 7.73712i) q^{24} +(6.05428 - 10.4863i) q^{26} -1.00000 q^{27} +(13.8769 + 2.11296i) q^{28} +4.00000 q^{29} +(-4.66575 - 8.08131i) q^{31} +(-9.35970 - 16.2115i) q^{32} +(1.41275 - 2.44696i) q^{33} +11.4363 q^{34} +5.30542 q^{36} +(-2.10256 + 3.64175i) q^{37} +(-2.83839 - 4.91623i) q^{38} +(-2.23996 - 3.87972i) q^{39} +2.37963 q^{41} +(4.46703 - 5.58422i) q^{42} -3.13092 q^{43} +(-7.49523 + 12.9821i) q^{44} +(8.93406 + 15.4742i) q^{46} +(-3.89267 + 6.74230i) q^{47} -13.5366 q^{48} +(-1.53710 - 6.82915i) q^{49} +(2.11560 - 3.66433i) q^{51} +(11.8839 + 20.5835i) q^{52} +(-1.29010 - 2.23452i) q^{53} +(1.35143 - 2.34074i) q^{54} +(-14.7654 + 18.4582i) q^{56} -2.10029 q^{57} +(-5.40571 + 9.36296i) q^{58} +(1.89267 + 3.27820i) q^{59} +(2.50000 - 4.33013i) q^{61} +25.2217 q^{62} +(-0.962895 - 2.46431i) q^{63} +23.5225 q^{64} +(3.81846 + 6.61376i) q^{66} +(1.65271 + 2.86258i) q^{67} +(-11.2242 + 19.4408i) q^{68} +6.61084 q^{69} -11.4223 q^{71} +(-4.46703 + 7.73712i) q^{72} +(-1.32550 - 2.29584i) q^{73} +(-5.68292 - 9.84311i) q^{74} +11.1429 q^{76} +(7.39039 + 1.12530i) q^{77} +12.1086 q^{78} +(-6.31846 + 10.9439i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.21589 + 5.57009i) q^{82} -3.02608 q^{83} +(5.10856 + 13.0742i) q^{84} +(4.23121 - 7.32867i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-12.6216 - 21.8613i) q^{88} +(4.11560 - 7.12844i) q^{89} +(7.40400 - 9.25572i) q^{91} -35.0733 q^{92} +(4.66575 - 8.08131i) q^{93} +(-10.5213 - 18.2234i) q^{94} +(9.35970 - 16.2115i) q^{96} -15.0165 q^{97} +(18.0626 + 5.63114i) q^{98} +2.82550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.35143	+	2.34074i	−0.955603	+	1.65515i	−0.222621	+	0.974905i	$0.571461\pi$
$2$	−1.35143	+	2.34074i	−0.955603	+	1.65515i	−0.732982	+	0.680248i	$0.761872\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.65271	−	4.59463i	−1.32635	−	2.29731i
$5$		0			0
$5$		0			0
$6$	−2.70285			−1.10344
$7$	−1.65271	+	2.06605i	−0.624665	+	0.780893i
$7$	−1.65271	+	2.06605i	−0.624665	+	0.780893i
$8$	8.93406			3.15867
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.41275	−	2.44696i	−0.425960	−	0.737785i	0.570549	−	0.821263i	$-0.306730\pi$
$11$	−1.41275	−	2.44696i	−0.425960	−	0.737785i	−0.996510	+	0.0834785i	$0.973397\pi$
$12$	2.65271	−	4.59463i	0.765771	−	1.32635i
$13$	−4.47992			−1.24251			−0.621253	−	0.783610i	$-0.713376\pi$
$13$	−4.47992			−1.24251			−0.621253	+	0.783610i	$0.713376\pi$
$14$	−2.60256	−	6.66067i	−0.695565	−	1.78014i
$15$		0			0
$16$	−6.76831	+	11.7231i	−1.69208	+	2.93077i
$17$	−2.11560	−	3.66433i	−0.513109	−	0.888732i	−0.999884	−	0.0152042i	$-0.995160\pi$
$17$	−2.11560	−	3.66433i	−0.513109	−	0.888732i	0.486775	−	0.873527i	$-0.338173\pi$
$18$	−1.35143	−	2.34074i	−0.318534	−	0.551718i
$19$	−1.05014	+	1.81890i	−0.240920	+	0.417285i	−0.960977	−	0.276630i	$-0.910782\pi$
$19$	−1.05014	+	1.81890i	−0.240920	+	0.417285i	0.720057	+	0.693915i	$0.244116\pi$
$20$		0			0
$21$	−2.61560	−	0.398264i	−0.570772	−	0.0869084i
$22$	7.63692			1.62820
$23$	3.30542	−	5.72515i	0.689227	−	1.19378i	−0.282861	−	0.959161i	$-0.591283\pi$
$23$	3.30542	−	5.72515i	0.689227	−	1.19378i	0.972088	−	0.234616i	$-0.0753832\pi$
$24$	4.46703	+	7.73712i	0.911829	+	1.57933i
$25$		0			0
$26$	6.05428	−	10.4863i	1.18734	−	2.05654i
$27$	−1.00000			−0.192450
$28$	13.8769	+	2.11296i	2.62248	+	0.399312i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−4.66575	−	8.08131i	−0.837993	−	1.45145i	−0.891570	−	0.452883i	$-0.850395\pi$
$31$	−4.66575	−	8.08131i	−0.837993	−	1.45145i	0.0535767	−	0.998564i	$-0.482938\pi$
$32$	−9.35970	−	16.2115i	−1.65458	−	2.86581i
$33$	1.41275	−	2.44696i	0.245928	−	0.425960i
$34$	11.4363			1.96132
$35$		0			0
$36$	5.30542			0.884236
$37$	−2.10256	+	3.64175i	−0.345659	+	0.598700i	−0.985473	−	0.169830i	$-0.945678\pi$
$37$	−2.10256	+	3.64175i	−0.345659	+	0.598700i	0.639814	+	0.768530i	$0.279011\pi$
$38$	−2.83839	−	4.91623i	−0.460447	−	0.797518i
$39$	−2.23996	−	3.87972i	−0.358680	−	0.621253i
$40$		0			0
$41$	2.37963			0.371635			0.185818	−	0.982584i	$-0.440507\pi$
$41$	2.37963			0.371635			0.185818	+	0.982584i	$0.440507\pi$
$42$	4.46703	−	5.58422i	0.689278	−	0.861665i
$43$	−3.13092			−0.477461			−0.238730	−	0.971086i	$-0.576731\pi$
$43$	−3.13092			−0.477461			−0.238730	+	0.971086i	$0.576731\pi$
$44$	−7.49523	+	12.9821i	−1.12995	+	1.95713i
$45$		0			0
$46$	8.93406	+	15.4742i	1.31726	+	2.28155i
$47$	−3.89267	+	6.74230i	−0.567804	+	0.983465i	0.428979	+	0.903315i	$0.358874\pi$
$47$	−3.89267	+	6.74230i	−0.567804	+	0.983465i	−0.996783	+	0.0801507i	$0.974460\pi$
$48$	−13.5366			−1.95384
$49$	−1.53710	−	6.82915i	−0.219586	−	0.975593i
$50$		0			0
$51$	2.11560	−	3.66433i	0.296244	−	0.513109i
$52$	11.8839	+	20.5835i	1.64800	+	2.85442i
$53$	−1.29010	−	2.23452i	−0.177209	−	0.306936i	0.763714	−	0.645554i	$-0.223374\pi$
$53$	−1.29010	−	2.23452i	−0.177209	−	0.306936i	−0.940924	+	0.338619i	$0.890040\pi$
$54$	1.35143	−	2.34074i	0.183906	−	0.318534i
$55$		0			0
$56$	−14.7654	+	18.4582i	−1.97311	+	2.46658i
$57$	−2.10029			−0.278190
$58$	−5.40571	+	9.36296i	−0.709804	+	1.22942i
$59$	1.89267	+	3.27820i	0.246404	+	0.426785i	0.962526	−	0.271191i	$-0.0874175\pi$
$59$	1.89267	+	3.27820i	0.246404	+	0.426785i	−0.716121	+	0.697976i	$0.754084\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	25.2217			3.20316
$63$	−0.962895	−	2.46431i	−0.121313	−	0.310474i
$64$	23.5225			2.94032
$65$		0			0
$66$	3.81846	+	6.61376i	0.470020	+	0.814098i
$67$	1.65271	+	2.86258i	0.201911	+	0.349719i	0.949144	−	0.314842i	$-0.101952\pi$
$67$	1.65271	+	2.86258i	0.201911	+	0.349719i	−0.747233	+	0.664562i	$0.768618\pi$
$68$	−11.2242	+	19.4408i	−1.36113	+	2.35755i
$69$	6.61084			0.795851
$70$		0			0
$71$	−11.4223			−1.35557			−0.677786	−	0.735259i	$-0.737060\pi$
$71$	−11.4223			−1.35557			−0.677786	+	0.735259i	$0.737060\pi$
$72$	−4.46703	+	7.73712i	−0.526445	+	0.911829i
$73$	−1.32550	−	2.29584i	−0.155138	−	0.268707i	0.777971	−	0.628300i	$-0.216249\pi$
$73$	−1.32550	−	2.29584i	−0.155138	−	0.268707i	−0.933109	+	0.359593i	$0.882916\pi$
$74$	−5.68292	−	9.84311i	−0.660627	−	1.14424i
$75$		0			0
$76$	11.1429			1.27818
$77$	7.39039	+	1.12530i	0.842213	+	0.128239i
$78$	12.1086			1.37102
$79$	−6.31846	+	10.9439i	−0.710882	+	1.23128i	0.253644	+	0.967298i	$0.418371\pi$
$79$	−6.31846	+	10.9439i	−0.710882	+	1.23128i	−0.964526	+	0.263986i	$0.914963\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.21589	+	5.57009i	−0.355136	+	0.615114i
$83$	−3.02608			−0.332155			−0.166078	−	0.986113i	$-0.553110\pi$
$83$	−3.02608			−0.332155			−0.166078	+	0.986113i	$0.553110\pi$
$84$	5.10856	+	13.0742i	0.557390	+	1.42651i
$85$		0			0
$86$	4.23121	−	7.32867i	0.456263	−	0.790271i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	−12.6216	−	21.8613i	−1.34547	−	2.33042i
$89$	4.11560	−	7.12844i	0.436253	−	0.755613i	−0.561144	−	0.827718i	$-0.689639\pi$
$89$	4.11560	−	7.12844i	0.436253	−	0.755613i	0.997397	+	0.0721056i	$0.0229719\pi$
$90$		0			0
$91$	7.40400	−	9.25572i	0.776150	−	0.970263i
$92$	−35.0733			−3.65664
$93$	4.66575	−	8.08131i	0.483816	−	0.837993i
$94$	−10.5213	−	18.2234i	−1.08519	−	1.87960i
$95$		0			0
$96$	9.35970	−	16.2115i	0.955270	−	1.65458i
$97$	−15.0165			−1.52470			−0.762350	−	0.647166i	$-0.775954\pi$
$97$	−15.0165			−1.52470			−0.762350	+	0.647166i	$0.775954\pi$
$98$	18.0626	+	5.63114i	1.82459	+	0.568831i
$99$	2.82550			0.283974
$100$		0			0
$101$	1.11560	+	1.93228i	0.111007	+	0.192269i	0.916176	−	0.400775i	$-0.131259\pi$
$101$	1.11560	+	1.93228i	0.111007	+	0.192269i	−0.805170	+	0.593045i	$0.797926\pi$
$102$	5.71817	+	9.90416i	0.566183	+	0.980658i
$103$	−3.92102	+	6.79141i	−0.386350	+	0.669178i	−0.991955	−	0.126587i	$-0.959598\pi$
$103$	−3.92102	+	6.79141i	−0.386350	+	0.669178i	0.605606	+	0.795765i	$0.292931\pi$
$104$	−40.0239			−3.92466
$105$		0			0
$106$	6.97392			0.677367
$107$	7.81846	−	13.5420i	0.755839	−	1.30915i	−0.189117	−	0.981954i	$-0.560563\pi$
$107$	7.81846	−	13.5420i	0.755839	−	1.30915i	0.944956	−	0.327197i	$-0.106104\pi$
$108$	2.65271	+	4.59463i	0.255257	+	0.442118i
$109$	−1.53710	−	2.66234i	−0.147228	−	0.255006i	0.782974	−	0.622054i	$-0.213702\pi$
$109$	−1.53710	−	2.66234i	−0.147228	−	0.255006i	−0.930202	+	0.367048i	$0.880368\pi$
$110$		0			0
$111$	−4.20513			−0.399133
$112$	−13.0344	−	33.3585i	−1.23163	−	3.15208i
$113$	0.348998			0.0328310			0.0164155	−	0.999865i	$-0.494775\pi$
$113$	0.348998			0.0328310			0.0164155	+	0.999865i	$0.494775\pi$
$114$	2.83839	−	4.91623i	0.265839	−	0.460447i
$115$		0			0
$116$	−10.6108	−	18.3785i	−0.985191	−	1.70640i
$117$	2.23996	−	3.87972i	0.207084	−	0.358680i
$118$	−10.2312			−0.941859
$119$	11.0672	+	1.68514i	1.01453	+	0.154476i
$120$		0			0
$121$	1.50827	−	2.61240i	0.137116	−	0.237491i
$122$	6.75713	+	11.7037i	0.611762	+	1.05960i
$123$	1.18981	+	2.06082i	0.107282	+	0.185818i
$124$	−24.7537	+	42.8748i	−2.22295	+	3.85027i
$125$		0			0
$126$	7.06960	+	1.07645i	0.629810	+	0.0958978i
$127$	−2.27137			−0.201552			−0.100776	−	0.994909i	$-0.532133\pi$
$127$	−2.27137			−0.201552			−0.100776	+	0.994909i	$0.532133\pi$
$128$	−13.0696	+	22.6372i	−1.15520	+	2.00087i
$129$	−1.56546	−	2.71146i	−0.137831	−	0.238730i
$130$		0			0
$131$	−9.61084	+	16.6465i	−0.839703	+	1.45441i	0.0504406	+	0.998727i	$0.483937\pi$
$131$	−9.61084	+	16.6465i	−0.839703	+	1.45441i	−0.890143	+	0.455681i	$0.849396\pi$
$132$	−14.9905			−1.30475
$133$	−2.02236	−	5.17577i	−0.175361	−	0.448796i
$134$	−8.93406			−0.771785
$135$		0			0
$136$	−18.9009	−	32.7374i	−1.62074	−	2.80721i
$137$	−4.13092	−	7.15496i	−0.352928	−	0.611290i	0.633833	−	0.773470i	$-0.281481\pi$
$137$	−4.13092	−	7.15496i	−0.352928	−	0.611290i	−0.986761	+	0.162180i	$0.948147\pi$
$138$	−8.93406	+	15.4742i	−0.760518	+	1.31726i
$139$	0.985914			0.0836241			0.0418121	−	0.999125i	$-0.486687\pi$
$139$	0.985914			0.0836241			0.0418121	+	0.999125i	$0.486687\pi$
$140$		0			0
$141$	−7.78534			−0.655644
$142$	15.4363	−	26.7365i	1.29539	−	2.24368i
$143$	6.32901	+	10.9622i	0.529258	+	0.916702i
$144$	−6.76831	−	11.7231i	−0.564026	−	0.976922i
$145$		0			0
$146$	7.16527			0.593002
$147$	5.14567	−	4.74575i	0.424407	−	0.391423i
$148$	22.3100			1.83387
$149$	−3.91048	+	6.77314i	−0.320359	+	0.554877i	−0.980562	−	0.196209i	$-0.937137\pi$
$149$	−3.91048	+	6.77314i	−0.320359	+	0.554877i	0.660203	+	0.751087i	$0.270470\pi$
$150$		0			0
$151$	1.56717	+	2.71441i	0.127534	+	0.220896i	0.922721	−	0.385469i	$-0.125960\pi$
$151$	1.56717	+	2.71441i	0.127534	+	0.220896i	−0.795186	+	0.606365i	$0.792627\pi$
$152$	−9.38206	+	16.2502i	−0.760985	+	1.31807i
$153$	4.23121			0.342073
$154$	−12.6216	+	15.7782i	−1.01708	+	1.27145i
$155$		0			0
$156$	−11.8839	+	20.5835i	−0.951475	+	1.64800i
$157$	−11.7395	−	20.3334i	−0.936913	−	1.62278i	−0.771187	−	0.636608i	$-0.780337\pi$
$157$	−11.7395	−	20.3334i	−0.936913	−	1.62278i	−0.165725	−	0.986172i	$-0.552996\pi$
$158$	−17.0779	−	29.5797i	−1.35864	−	2.35324i
$159$	1.29010	−	2.23452i	0.102312	−	0.177209i
$160$		0			0
$161$	6.36554	+	16.2912i	0.501675	+	1.28392i
$162$	2.70285			0.212356
$163$	−6.21817	+	10.7702i	−0.487045	+	0.843586i	−0.999889	−	0.0148956i	$-0.995258\pi$
$163$	−6.21817	+	10.7702i	−0.487045	+	0.843586i	0.512844	+	0.858482i	$0.328592\pi$
$164$	−6.31246	−	10.9335i	−0.492920	−	0.853763i
$165$		0			0
$166$	4.08952	−	7.08326i	0.317409	−	0.549768i
$167$	−18.4483			−1.42757			−0.713787	−	0.700362i	$-0.753022\pi$
$167$	−18.4483			−1.42757			−0.713787	+	0.700362i	$0.753022\pi$
$168$	−23.3680	−	3.55812i	−1.80288	−	0.274515i
$169$	7.06966			0.543820
$170$		0			0
$171$	−1.05014	−	1.81890i	−0.0803066	−	0.139095i
$172$	8.30542	+	14.3854i	0.633282	+	1.09688i
$173$	3.82550	−	6.62596i	0.290847	−	0.503763i	−0.683163	−	0.730266i	$-0.739396\pi$
$173$	3.82550	−	6.62596i	0.290847	−	0.503763i	0.974010	+	0.226503i	$0.0727295\pi$
$174$	−10.8114			−0.819611
$175$		0			0
$176$	38.2478			2.88303
$177$	−1.89267	+	3.27820i	−0.142262	+	0.246404i
$178$	11.1239	+	19.2671i	0.833770	+	1.44413i
$179$	1.20513	+	2.08734i	0.0900756	+	0.156015i	0.907543	−	0.419960i	$-0.137956\pi$
$179$	1.20513	+	2.08734i	0.0900756	+	0.156015i	−0.817467	+	0.575975i	$0.804622\pi$
$180$		0			0
$181$	−13.6970			−1.01809			−0.509046	−	0.860739i	$-0.670002\pi$
$181$	−13.6970			−1.01809			−0.509046	+	0.860739i	$0.670002\pi$
$182$	11.6593	+	29.8393i	0.864243	+	2.21183i
$183$	5.00000			0.369611
$184$	29.5308	−	51.1489i	2.17704	−	3.77074i
$185$		0			0
$186$	12.6108	+	21.8426i	0.924671	+	1.60158i
$187$	−5.97764	+	10.3536i	−0.437128	+	0.757129i
$188$	41.3045			3.01244
$189$	1.65271	−	2.06605i	0.120217	−	0.150283i
$190$		0			0
$191$	6.06717	−	10.5086i	0.439005	−	0.760379i	−0.558608	−	0.829432i	$-0.688664\pi$
$191$	6.06717	−	10.5086i	0.439005	−	0.760379i	0.997613	+	0.0690531i	$0.0219978\pi$
$192$	11.7613	+	20.3711i	0.848797	+	1.47016i
$193$	5.96290	+	10.3280i	0.429219	+	0.743428i	0.996804	−	0.0798861i	$-0.0254557\pi$
$193$	5.96290	+	10.3280i	0.429219	+	0.743428i	−0.567585	+	0.823315i	$0.692122\pi$
$194$	20.2938	−	35.1498i	1.45701	−	2.52361i
$195$		0			0
$196$	−27.2999	+	25.1782i	−1.94999	+	1.79844i
$197$	5.50258			0.392043			0.196021	−	0.980600i	$-0.437198\pi$
$197$	5.50258			0.392043			0.196021	+	0.980600i	$0.437198\pi$
$198$	−3.81846	+	6.61376i	−0.271366	+	0.470020i
$199$	5.66404	+	9.81041i	0.401513	+	0.695441i	0.993909	−	0.110206i	$-0.0351510\pi$
$199$	5.66404	+	9.81041i	0.401513	+	0.695441i	−0.592396	+	0.805647i	$0.701818\pi$
$200$		0			0
$201$	−1.65271	+	2.86258i	−0.116573	+	0.201911i
$202$	−6.03063			−0.424314
$203$	−6.61084	+	8.26419i	−0.463990	+	0.580032i
$204$	−22.4483			−1.57170
$205$		0			0
$206$	−10.5980	−	18.3562i	−0.738394	−	1.27894i
$207$	3.30542	+	5.72515i	0.229742	+	0.397926i
$208$	30.3215	−	52.5184i	2.10242	−	3.64149i
$209$	5.93437			0.410489
$210$		0			0
$211$	8.82095			0.607259			0.303630	−	0.952790i	$-0.401801\pi$
$211$	8.82095			0.607259			0.303630	+	0.952790i	$0.401801\pi$
$212$	−6.84454	+	11.8551i	−0.470085	+	0.814211i
$213$	−5.71113	−	9.89196i	−0.391320	−	0.677786i
$214$	21.1321	+	36.6020i	1.44456	+	2.50206i
$215$		0			0
$216$	−8.93406			−0.607886
$217$	24.4075	+	3.71640i	1.65689	+	0.252286i
$218$	8.30914			0.562766
$219$	1.32550	−	2.29584i	0.0895691	−	0.155138i
$220$		0			0
$221$	9.47773	+	16.4159i	0.637541	+	1.10425i
$222$	5.68292	−	9.84311i	0.381413	−	0.660627i
$223$	−26.4885			−1.77380			−0.886900	−	0.461961i	$-0.847146\pi$
$223$	−26.4885			−1.77380			−0.886900	+	0.461961i	$0.847146\pi$
$224$	48.9625	+	7.45527i	3.27145	+	0.498126i
$225$		0			0
$226$	−0.471645	+	0.816914i	−0.0313734	+	0.0543403i
$227$	−8.88562	−	15.3904i	−0.589760	−	1.02149i	−0.994264	−	0.106957i	$-0.965889\pi$
$227$	−8.88562	−	15.3904i	−0.589760	−	1.02149i	0.404504	−	0.914536i	$-0.367444\pi$
$228$	5.57146	+	9.65005i	0.368979	+	0.639090i
$229$	−9.32244	+	16.1469i	−0.616044	+	1.06702i	0.374156	+	0.927366i	$0.377932\pi$
$229$	−9.32244	+	16.1469i	−0.616044	+	1.06702i	−0.990200	+	0.139654i	$0.955401\pi$
$230$		0			0
$231$	2.72066	+	6.96292i	0.179006	+	0.458126i
$232$	35.7362			2.34620
$233$	−4.88440	+	8.46002i	−0.319987	+	0.554234i	−0.980485	−	0.196594i	$-0.937012\pi$
$233$	−4.88440	+	8.46002i	−0.319987	+	0.554234i	0.660498	+	0.750828i	$0.270345\pi$
$234$	6.05428	+	10.4863i	0.395781	+	0.685512i
$235$		0			0
$236$	10.0414	−	17.3922i	0.653639	−	1.13214i
$237$	−12.6369			−0.820856
$238$	−18.9009	+	23.6280i	−1.22517	+	1.53158i
$239$	−6.20058			−0.401082			−0.200541	−	0.979685i	$-0.564270\pi$
$239$	−6.20058			−0.401082			−0.200541	+	0.979685i	$0.564270\pi$
$240$		0			0
$241$	10.1191	+	17.5268i	0.651829	+	1.12900i	0.982679	+	0.185318i	$0.0593314\pi$
$241$	10.1191	+	17.5268i	0.651829	+	1.12900i	−0.330850	+	0.943684i	$0.607335\pi$
$242$	4.07664	+	7.06095i	0.262056	+	0.453895i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−26.5271			−1.69822
$245$		0			0
$246$	−6.43179			−0.410076
$247$	4.70456	−	8.14854i	0.299344	−	0.518479i
$248$	−41.6841	−	72.1990i	−2.64694	−	4.58464i
$249$	−1.51304	−	2.62066i	−0.0958850	−	0.166078i
$250$		0			0
$251$	−6.21466			−0.392266			−0.196133	−	0.980577i	$-0.562838\pi$
$251$	−6.21466			−0.392266			−0.196133	+	0.980577i	$0.562838\pi$
$252$	−8.76831	+	10.9612i	−0.552352	+	0.690494i
$253$	−18.6789			−1.17433
$254$	3.06960	−	5.31670i	0.192604	−	0.333599i
$255$		0			0
$256$	−11.8027	−	20.4428i	−0.737667	−	1.27768i
$257$	2.82673	−	4.89604i	0.176327	−	0.305407i	−0.764293	−	0.644869i	$-0.776912\pi$
$257$	2.82673	−	4.89604i	0.176327	−	0.305407i	0.940620	+	0.339463i	$0.110245\pi$
$258$	8.46242			0.526847
$259$	−4.04910	−	10.3627i	−0.251599	−	0.643910i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−25.9767	−	44.9929i	−1.60484	−	2.77967i
$263$	12.5060	+	21.6610i	0.771153	+	1.33568i	0.936932	+	0.349513i	$0.113653\pi$
$263$	12.5060	+	21.6610i	0.771153	+	1.33568i	−0.165779	+	0.986163i	$0.553014\pi$
$264$	12.6216	−	21.8613i	0.776806	−	1.34547i
$265$		0			0
$266$	14.8482	+	2.26086i	0.910401	+	0.138622i
$267$	8.23121			0.503742
$268$	8.76831	−	15.1872i	0.535610	−	0.927704i
$269$	3.94111	+	6.82619i	0.240293	+	0.416200i	0.960798	−	0.277250i	$-0.0894230\pi$
$269$	3.94111	+	6.82619i	0.240293	+	0.416200i	−0.720504	+	0.693450i	$0.756090\pi$
$270$		0			0
$271$	−2.37136	+	4.10731i	−0.144050	+	0.249501i	−0.929018	−	0.370035i	$-0.879346\pi$
$271$	−2.37136	+	4.10731i	−0.144050	+	0.249501i	0.784968	+	0.619536i	$0.212679\pi$
$272$	57.2763			3.47289
$273$	11.7177	+	1.78419i	0.709187	+	0.107984i
$274$	22.3305			1.34904
$275$		0			0
$276$	−17.5366	−	30.3743i	−1.05558	−	1.82832i
$277$	3.86860	+	6.70062i	0.232442	+	0.402601i	0.958526	−	0.285005i	$-0.0919951\pi$
$277$	3.86860	+	6.70062i	0.232442	+	0.402601i	−0.726084	+	0.687606i	$0.758662\pi$
$278$	−1.33239	+	2.30777i	−0.0799115	+	0.138411i
$279$	9.33150			0.558662
$280$		0			0
$281$	2.11779			0.126337			0.0631684	−	0.998003i	$-0.479879\pi$
$281$	2.11779			0.126337			0.0631684	+	0.998003i	$0.479879\pi$
$282$	10.5213	−	18.2234i	0.626535	−	1.08519i
$283$	2.19887	+	3.80856i	0.130709	+	0.226395i	0.923950	−	0.382513i	$-0.124941\pi$
$283$	2.19887	+	3.80856i	0.130709	+	0.226395i	−0.793241	+	0.608908i	$0.791608\pi$
$284$	30.2999	+	52.4810i	1.79797	+	3.11417i
$285$		0			0
$286$	−34.2128			−2.02304
$287$	−3.93283	+	4.91642i	−0.232148	+	0.290207i
$288$	18.7194			1.10305
$289$	−0.451563	+	0.782129i	−0.0265625	+	0.0460076i
$290$		0			0
$291$	−7.50827	−	13.0047i	−0.440143	−	0.762350i
$292$	−7.03234	+	12.1804i	−0.411536	+	0.712802i
$293$	14.2006			0.829607			0.414803	−	0.909911i	$-0.363850\pi$
$293$	14.2006			0.829607			0.414803	+	0.909911i	$0.363850\pi$
$294$	4.15457	+	18.4582i	0.242299	+	1.07650i
$295$		0			0
$296$	−18.7844	+	32.5356i	−1.09182	+	1.89109i
$297$	1.41275	+	2.44696i	0.0819761	+	0.141987i
$298$	−10.5694	−	18.3068i	−0.612271	−	1.06049i
$299$	−14.8080	+	25.6482i	−0.856369	+	1.48327i
$300$		0			0
$301$	5.17450	−	6.46863i	0.298253	−	0.372846i
$302$	−8.47165			−0.487488
$303$	−1.11560	+	1.93228i	−0.0640898	+	0.111007i
$304$	−14.2154	−	24.6218i	−0.815310	−	1.41216i
$305$		0			0
$306$	−5.71817	+	9.90416i	−0.326886	+	0.566183i
$307$	13.9423			0.795731			0.397866	−	0.917444i	$-0.369751\pi$
$307$	13.9423			0.795731			0.397866	+	0.917444i	$0.369751\pi$
$308$	−14.4342	−	36.9412i	−0.822467	−	2.10492i
$309$	−7.84205			−0.446118
$310$		0			0
$311$	1.89971	+	3.29040i	0.107723	+	0.186581i	0.914847	−	0.403800i	$-0.132311\pi$
$311$	1.89971	+	3.29040i	0.107723	+	0.186581i	−0.807125	+	0.590381i	$0.798977\pi$
$312$	−20.0119	−	34.6617i	−1.13295	−	1.96233i
$313$	13.9488	−	24.1600i	0.788433	−	1.36561i	−0.138493	−	0.990363i	$-0.544226\pi$
$313$	13.9488	−	24.1600i	0.788433	−	1.36561i	0.926926	−	0.375243i	$-0.122441\pi$
$314$	63.4602			3.58127
$315$		0			0
$316$	67.0441			3.77153
$317$	17.2478	−	29.8740i	0.968730	−	1.67789i	0.269490	−	0.963003i	$-0.413145\pi$
$317$	17.2478	−	29.8740i	0.968730	−	1.67789i	0.699240	−	0.714887i	$-0.253522\pi$
$318$	3.48696	+	6.03959i	0.195539	+	0.338684i
$319$	−5.65100	−	9.78782i	−0.316395	−	0.548013i
$320$		0			0
$321$	15.6369			0.872768
$322$	−46.7359	−	7.11624i	−2.60449	−	0.396572i
$323$	8.88676			0.494473
$324$	−2.65271	+	4.59463i	−0.147373	+	0.255257i
$325$		0			0
$326$	−16.8068	−	29.1102i	−0.930843	−	1.61227i
$327$	1.53710	−	2.66234i	0.0850021	−	0.147228i
$328$	21.2597			1.17387
$329$	−7.49646	−	19.1855i	−0.413293	−	1.05773i
$330$		0			0
$331$	14.9471	−	25.8891i	0.821567	−	1.42300i	−0.0829479	−	0.996554i	$-0.526434\pi$
$331$	14.9471	−	25.8891i	0.821567	−	1.42300i	0.904515	−	0.426442i	$-0.140233\pi$
$332$	8.02731	+	13.9037i	0.440556	+	0.763065i
$333$	−2.10256	−	3.64175i	−0.115220	−	0.199567i
$334$	24.9316	−	43.1827i	1.36419	−	2.36285i
$335$		0			0
$336$	22.3721	−	27.9673i	1.22050	−	1.52574i
$337$	−19.3480			−1.05395			−0.526977	−	0.849879i	$-0.676675\pi$
$337$	−19.3480			−1.05395			−0.526977	+	0.849879i	$0.676675\pi$
$338$	−9.55413	+	16.5482i	−0.519676	+	0.900105i
$339$	0.174499	+	0.302241i	0.00947748	+	0.0164155i
$340$		0			0
$341$	−13.1831	+	22.8338i	−0.713904	+	1.23652i
$342$	5.67677			0.306965
$343$	16.6497	+	8.11087i	0.899001	+	0.437946i
$344$	−27.9718			−1.50814
$345$		0			0
$346$	10.3398	+	17.9090i	0.555869	+	0.962794i
$347$	13.1500	+	22.7764i	0.705927	+	1.22270i	0.966356	+	0.257208i	$0.0828025\pi$
$347$	13.1500	+	22.7764i	0.705927	+	1.22270i	−0.260429	+	0.965493i	$0.583864\pi$
$348$	10.6108	−	18.3785i	0.568801	−	0.985191i
$349$	−14.9083			−0.798022			−0.399011	−	0.916946i	$-0.630647\pi$
$349$	−14.9083			−0.798022			−0.399011	+	0.916946i	$0.630647\pi$
$350$		0			0
$351$	4.47992			0.239120
$352$	−26.4458	+	45.8055i	−1.40957	+	2.44144i
$353$	−7.91048	−	13.7013i	−0.421032	−	0.729249i	0.575009	−	0.818147i	$-0.304999\pi$
$353$	−7.91048	−	13.7013i	−0.421032	−	0.729249i	−0.996041	+	0.0888984i	$0.971665\pi$
$354$	−5.11560	−	8.86049i	−0.271891	−	0.470930i
$355$		0			0
$356$	−43.6700			−2.31451
$357$	4.07421	+	10.4270i	0.215630	+	0.551856i
$358$	−6.51458			−0.344306
$359$	−8.33854	+	14.4428i	−0.440091	+	0.762261i	−0.997696	−	0.0678462i	$-0.978387\pi$
$359$	−8.33854	+	14.4428i	−0.440091	+	0.762261i	0.557604	+	0.830107i	$0.311721\pi$
$360$		0			0
$361$	7.29439	+	12.6343i	0.383915	+	0.664961i
$362$	18.5105	−	32.0612i	0.972893	−	1.68510i
$363$	3.01654			0.158328
$364$	−62.1673	−	9.46588i	−3.25845	−	0.496147i
$365$		0			0
$366$	−6.75713	+	11.7037i	−0.353201	+	0.611762i
$367$	14.0938	+	24.4112i	0.735691	+	1.27425i	0.954419	+	0.298469i	$0.0964758\pi$
$367$	14.0938	+	24.4112i	0.735691	+	1.27425i	−0.218728	+	0.975786i	$0.570191\pi$
$368$	44.7442	+	77.4993i	2.33245	+	4.03993i
$369$	−1.18981	+	2.06082i	−0.0619392	+	0.107282i
$370$		0			0
$371$	6.74880	+	1.02760i	0.350380	+	0.0533506i
$372$	−49.5075			−2.56684
$373$	11.9995	−	20.7838i	0.621312	−	1.07614i	−0.367930	−	0.929853i	$-0.619933\pi$
$373$	11.9995	−	20.7838i	0.621312	−	1.07614i	0.989242	−	0.146290i	$-0.0467332\pi$
$374$	−16.1567	−	27.9842i	−0.835443	−	1.44703i
$375$		0			0
$376$	−34.7773	+	60.2361i	−1.79350	+	3.10644i
$377$	−17.9197			−0.922910
$378$	2.60256	+	6.66067i	0.133861	+	0.342588i
$379$	13.8550			0.711683			0.355842	−	0.934546i	$-0.384194\pi$
$379$	13.8550			0.711683			0.355842	+	0.934546i	$0.384194\pi$
$380$		0			0
$381$	−1.13569	−	1.96707i	−0.0581830	−	0.100776i
$382$	16.3987	+	28.4033i	0.839029	+	1.45324i
$383$	−15.3882	+	26.6532i	−0.786301	+	1.36191i	0.141918	+	0.989878i	$0.454673\pi$
$383$	−15.3882	+	26.6532i	−0.786301	+	1.36191i	−0.928219	+	0.372034i	$0.878660\pi$
$384$	−26.1392			−1.33391
$385$		0			0
$386$	−32.2337			−1.64065
$387$	1.56546	−	2.71146i	0.0795768	−	0.137831i
$388$	39.8345	+	68.9954i	2.02229	+	3.50271i
$389$	−19.2064	−	33.2664i	−0.973801	−	1.68667i	−0.683836	−	0.729636i	$-0.739690\pi$
$389$	−19.2064	−	33.2664i	−0.973801	−	1.68667i	−0.289965	−	0.957037i	$-0.593644\pi$
$390$		0			0
$391$	−27.9718			−1.41460
$392$	−13.7326	−	61.0121i	−0.693601	−	3.08157i
$393$	−19.2217			−0.969605
$394$	−7.43634	+	12.8801i	−0.374637	+	0.648891i
$395$		0			0
$396$	−7.49523	−	12.9821i	−0.376650	−	0.652376i
$397$	−16.7307	+	28.9785i	−0.839691	+	1.45439i	0.0504616	+	0.998726i	$0.483931\pi$
$397$	−16.7307	+	28.9785i	−0.839691	+	1.45439i	−0.890153	+	0.455662i	$0.849403\pi$
$398$	−30.6182			−1.53475
$399$	3.47117	−	4.33930i	0.173776	−	0.217237i
$400$		0			0
$401$	−7.42102	+	12.8536i	−0.370588	+	0.641878i	−0.989656	−	0.143460i	$-0.954177\pi$
$401$	−7.42102	+	12.8536i	−0.370588	+	0.641878i	0.619068	+	0.785337i	$0.287511\pi$
$402$	−4.46703	−	7.73712i	−0.222795	−	0.385893i
$403$	20.9022	+	36.2036i	1.04121	+	1.80343i
$404$	5.91875	−	10.2516i	0.294469	−	0.510035i
$405$		0			0
$406$	−10.4103	−	26.6427i	−0.516652	−	1.32225i
$407$	11.8816			0.588949
$408$	18.9009	−	32.7374i	0.935736	−	1.62074i
$409$	−4.22246	−	7.31351i	−0.208787	−	0.361630i	0.742546	−	0.669796i	$-0.233618\pi$
$409$	−4.22246	−	7.31351i	−0.208787	−	0.361630i	−0.951333	+	0.308166i	$0.900285\pi$
$410$		0			0
$411$	4.13092	−	7.15496i	0.203763	−	0.352928i
$412$	41.6053			2.04975
$413$	−9.90094	−	1.50756i	−0.487193	−	0.0741824i
$414$	−17.8681			−0.878170
$415$		0			0
$416$	41.9307	+	72.6261i	2.05582	+	3.56079i
$417$	0.492957	+	0.853827i	0.0241402	+	0.0418121i
$418$	−8.01987	+	13.8908i	−0.392264	+	0.679422i
$419$	−18.8427			−0.920524			−0.460262	−	0.887783i	$-0.652245\pi$
$419$	−18.8427			−0.920524			−0.460262	+	0.887783i	$0.652245\pi$
$420$		0			0
$421$	−9.09687			−0.443355			−0.221677	−	0.975120i	$-0.571153\pi$
$421$	−9.09687			−0.443355			−0.221677	+	0.975120i	$0.571153\pi$
$422$	−11.9209	+	20.6476i	−0.580299	+	1.00511i
$423$	−3.89267	−	6.74230i	−0.189268	−	0.327822i
$424$	−11.5259	−	19.9634i	−0.559745	−	0.969507i
$425$		0			0
$426$	30.8727			1.49579
$427$	4.81448	+	12.3216i	0.232989	+	0.596282i
$428$	−82.9604			−4.01004
$429$	−6.32901	+	10.9622i	−0.305567	+	0.529258i
$430$		0			0
$431$	2.47992	+	4.29534i	0.119453	+	0.206899i	0.919551	−	0.392970i	$-0.128552\pi$
$431$	2.47992	+	4.29534i	0.119453	+	0.206899i	−0.800098	+	0.599870i	$0.795219\pi$
$432$	6.76831	−	11.7231i	0.325641	−	0.564026i
$433$	2.61696			0.125763			0.0628815	−	0.998021i	$-0.479971\pi$
$433$	2.61696			0.125763			0.0628815	+	0.998021i	$0.479971\pi$
$434$	−41.6841	+	52.1092i	−2.00090	+	2.50132i
$435$		0			0
$436$	−8.15498	+	14.1248i	−0.390553	+	0.676458i
$437$	6.94233	+	12.0245i	0.332097	+	0.575209i
$438$	3.58264	+	6.20531i	0.171185	+	0.296501i
$439$	13.2525	−	22.9540i	0.632508	−	1.09554i	−0.354529	−	0.935045i	$-0.615359\pi$
$439$	13.2525	−	22.9540i	0.632508	−	1.09554i	0.987037	−	0.160491i	$-0.0513079\pi$
$440$		0			0
$441$	6.68277	+	2.08340i	0.318227	+	0.0992097i
$442$	−51.2338			−2.43695
$443$	19.7452	−	34.1996i	0.938121	−	1.62487i	0.169150	−	0.985590i	$-0.445898\pi$
$443$	19.7452	−	34.1996i	0.938121	−	1.62487i	0.768971	−	0.639284i	$-0.220769\pi$
$444$	11.1550	+	19.3210i	0.529392	+	0.916934i
$445$		0			0
$446$	35.7973	−	62.0027i	1.69505	−	2.93591i
$447$	−7.82095			−0.369918
$448$	−38.8759	+	48.5987i	−1.83671	+	2.29607i
$449$	21.3045			1.00542			0.502710	−	0.864455i	$-0.332336\pi$
$449$	21.3045			1.00542			0.502710	+	0.864455i	$0.332336\pi$
$450$		0			0
$451$	−3.36182	−	5.82284i	−0.158302	−	0.274187i
$452$	−0.925790	−	1.60352i	−0.0435455	−	0.0754230i
$453$	−1.56717	+	2.71441i	−0.0736319	+	0.127534i
$454$	48.0331			2.25430
$455$		0			0
$456$	−18.7641			−0.878710
$457$	13.9401	−	24.1449i	0.652088	−	1.12945i	−0.330527	−	0.943797i	$-0.607226\pi$
$457$	13.9401	−	24.1449i	0.652088	−	1.12945i	0.982615	−	0.185654i	$-0.0594403\pi$
$458$	−25.1972	−	43.6428i	−1.17739	−	2.03929i
$459$	2.11560	+	3.66433i	0.0987479	+	0.171036i
$460$		0			0
$461$	22.5237			1.04903			0.524516	−	0.851401i	$-0.324246\pi$
$461$	22.5237			1.04903			0.524516	+	0.851401i	$0.324246\pi$
$462$	−19.9751	−	3.04151i	−0.929328	−	0.141504i
$463$	1.69301			0.0786809			0.0393405	−	0.999226i	$-0.487474\pi$
$463$	1.69301			0.0786809			0.0393405	+	0.999226i	$0.487474\pi$
$464$	−27.0733	+	46.8923i	−1.25684	+	2.17692i
$465$		0			0
$466$	−13.2018	−	22.8662i	−0.611562	−	1.05926i
$467$	−0.0401654	+	0.0695685i	−0.00185863	+	0.00321925i	−0.866953	−	0.498390i	$-0.833925\pi$
$467$	−0.0401654	+	0.0695685i	−0.00185863	+	0.00321925i	0.865095	+	0.501609i	$0.167258\pi$
$468$	−23.7678			−1.09867
$469$	−8.64567	−	1.31643i	−0.399220	−	0.0607871i
$470$		0			0
$471$	11.7395	−	20.3334i	0.540927	−	0.936913i
$472$	16.9092	+	29.2876i	0.778310	+	1.34807i
$473$	4.42321	+	7.66122i	0.203379	+	0.352263i
$474$	17.0779	−	29.5797i	0.784412	−	1.35864i
$475$		0			0
$476$	−21.6154	−	55.3197i	−0.990740	−	2.53557i
$477$	2.58021			0.118140
$478$	8.37963	−	14.5139i	0.383275	−	0.663852i
$479$	19.3891	+	33.5830i	0.885912	+	1.53444i	0.844665	+	0.535295i	$0.179800\pi$
$479$	19.3891	+	33.5830i	0.885912	+	1.53444i	0.0412471	+	0.999149i	$0.486867\pi$
$480$		0			0
$481$	9.41932	−	16.3147i	0.429484	−	0.743888i
$482$	−54.7009			−2.49156
$483$	−10.9258	+	13.6583i	−0.497141	+	0.621474i
$484$	−16.0040			−0.727456
$485$		0			0
$486$	1.35143	+	2.34074i	0.0613020	+	0.106178i
$487$	−13.5655	−	23.4961i	−0.614710	−	1.06471i	−0.990435	−	0.137977i	$-0.955940\pi$
$487$	−13.5655	−	23.4961i	−0.614710	−	1.06471i	0.375726	−	0.926731i	$-0.377393\pi$
$488$	22.3352	−	38.6856i	1.01106	−	1.75122i
$489$	−12.4363			−0.562391
$490$		0			0
$491$	16.7243			0.754755			0.377378	−	0.926059i	$-0.376826\pi$
$491$	16.7243			0.754755			0.377378	+	0.926059i	$0.376826\pi$
$492$	6.31246	−	10.9335i	0.284588	−	0.492920i
$493$	−8.46242	−	14.6573i	−0.381128	−	0.660133i
$494$	12.7157	+	22.0243i	0.572108	+	0.990920i
$495$		0			0
$496$	126.317			5.67180
$497$	18.8777	−	23.5989i	0.846779	−	1.05856i
$498$	8.17905			0.366512
$499$	−9.89219	+	17.1338i	−0.442835	+	0.767013i	−0.997899	−	0.0647949i	$-0.979361\pi$
$499$	−9.89219	+	17.1338i	−0.442835	+	0.767013i	0.555063	+	0.831808i	$0.312694\pi$
$500$		0			0
$501$	−9.22417	−	15.9767i	−0.412105	−	0.713787i
$502$	8.39866	−	14.5469i	0.374851	−	0.649261i
$503$	6.75015			0.300975			0.150487	−	0.988612i	$-0.451916\pi$
$503$	6.75015			0.300975			0.150487	+	0.988612i	$0.451916\pi$
$504$	−8.60256	−	22.0163i	−0.383189	−	0.980685i
$505$		0			0
$506$	25.2432	−	43.7225i	1.12220	−	1.94370i
$507$	3.53483	+	6.12250i	0.156987	+	0.271910i
$508$	6.02529	+	10.4361i	0.267329	+	0.463028i
$509$	20.1735	−	34.9416i	0.894177	−	1.54876i	0.0593561	−	0.998237i	$-0.481095\pi$
$509$	20.1735	−	34.9416i	0.894177	−	1.54876i	0.834820	−	0.550522i	$-0.185571\pi$
$510$		0			0
$511$	6.93397	+	1.05580i	0.306741	+	0.0467058i
$512$	11.5234			0.509266
$513$	1.05014	−	1.81890i	0.0463650	−	0.0803066i
$514$	7.64024	+	13.2333i	0.336996	+	0.583695i
$515$		0			0
$516$	−8.30542	+	14.3854i	−0.365626	+	0.633282i
$517$	21.9975			0.967448
$518$	29.7286	+	4.52661i	1.30620	+	0.198888i
$519$	7.65100			0.335842
$520$		0			0
$521$	−18.8019	−	32.5658i	−0.823725	−	1.42673i	−0.902890	−	0.429872i	$-0.858559\pi$
$521$	−18.8019	−	32.5658i	−0.823725	−	1.42673i	0.0791643	−	0.996862i	$-0.474775\pi$
$522$	−5.40571	−	9.36296i	−0.236601	−	0.409806i
$523$	19.6562	−	34.0456i	0.859506	−	1.48871i	−0.0128944	−	0.999917i	$-0.504105\pi$
$523$	19.6562	−	34.0456i	0.859506	−	1.48871i	0.872401	−	0.488792i	$-0.162562\pi$
$524$	101.979			4.45497
$525$		0			0
$526$	−67.6038			−2.94766
$527$	−19.7418	+	34.1937i	−0.859964	+	1.48950i
$528$	19.1239	+	33.1235i	0.832260	+	1.44152i
$529$	−10.3516	−	17.9295i	−0.450069	−	0.779542i
$530$		0			0
$531$	−3.78534			−0.164270
$532$	−18.4160	+	23.0218i	−0.798435	+	0.998121i
$533$	−10.6605			−0.461759
$534$	−11.1239	+	19.2671i	−0.481377	+	0.833770i
$535$		0			0
$536$	14.7654	+	25.5744i	0.637768	+	1.10465i
$537$	−1.20513	+	2.08734i	−0.0520052	+	0.0900756i
$538$	−21.3045			−0.918501
$539$	−14.5391	+	13.4091i	−0.626243	+	0.577571i
$540$		0			0
$541$	−10.7861	+	18.6821i	−0.463732	+	0.803207i	−0.999143	−	0.0413846i	$-0.986823\pi$
$541$	−10.7861	+	18.6821i	−0.463732	+	0.803207i	0.535412	+	0.844591i	$0.320156\pi$
$542$	−6.40943	−	11.1015i	−0.275309	−	0.476848i
$543$	−6.84852	−	11.8620i	−0.293898	−	0.509046i
$544$	−39.6028	+	68.5941i	−1.69796	+	2.94095i
$545$		0			0
$546$	−20.0119	+	25.0169i	−0.856432	+	1.07062i
$547$	21.3707			0.913745			0.456873	−	0.889532i	$-0.348969\pi$
$547$	21.3707			0.913745			0.456873	+	0.889532i	$0.348969\pi$
$548$	−21.9163	+	37.9601i	−0.936216	+	1.62157i
$549$	2.50000	+	4.33013i	0.106697	+	0.184805i
$550$		0			0
$551$	−4.20058	+	7.27562i	−0.178951	+	0.309952i
$552$	59.0616			2.51383
$553$	−12.1680	−	31.1413i	−0.517437	−	1.32426i
$554$	−20.9125			−0.888488
$555$		0			0
$556$	−2.61534	−	4.52991i	−0.110915	−	0.192111i
$557$	7.13092	+	12.3511i	0.302147	+	0.523334i	0.976622	−	0.214964i	$-0.0689634\pi$
$557$	7.13092	+	12.3511i	0.302147	+	0.523334i	−0.674475	+	0.738297i	$0.735630\pi$
$558$	−12.6108	+	21.8426i	−0.533859	+	0.924671i
$559$	14.0263			0.593248
$560$		0			0
$561$	−11.9553			−0.504752
$562$	−2.86204	+	4.95719i	−0.120728	+	0.209107i
$563$	−1.18154	−	2.04649i	−0.0497961	−	0.0862493i	0.840053	−	0.542504i	$-0.182524\pi$
$563$	−1.18154	−	2.04649i	−0.0497961	−	0.0862493i	−0.889849	+	0.456255i	$0.849190\pi$
$564$	20.6522	+	35.7707i	0.869616	+	1.50622i
$565$		0			0
$566$	−11.8865			−0.499625
$567$	2.61560	+	0.398264i	0.109845	+	0.0167255i
$568$	−102.047			−4.28180
$569$	6.37289	−	11.0382i	0.267166	−	0.462744i	−0.700963	−	0.713197i	$-0.747246\pi$
$569$	6.37289	−	11.0382i	0.267166	−	0.462744i	0.968129	+	0.250453i	$0.0805796\pi$
$570$		0			0
$571$	−0.180757	−	0.313080i	−0.00756444	−	0.0131020i	0.862218	−	0.506537i	$-0.169075\pi$
$571$	−0.180757	−	0.313080i	−0.00756444	−	0.0131020i	−0.869783	+	0.493435i	$0.835741\pi$
$572$	33.5780	−	58.1588i	1.40397	−	2.43174i
$573$	12.1343			0.506919
$574$	−6.19314	−	15.8499i	−0.258496	−	0.661563i
$575$		0			0
$576$	−11.7613	+	20.3711i	−0.490053	+	0.848797i
$577$	4.79667	+	8.30807i	0.199688	+	0.345870i	0.948427	−	0.316995i	$-0.102674\pi$
$577$	4.79667	+	8.30807i	0.199688	+	0.345870i	−0.748739	+	0.662865i	$0.769341\pi$
$578$	−1.22051	−	2.11398i	−0.0507664	−	0.0879300i
$579$	−5.96290	+	10.3280i	−0.247809	+	0.429219i
$580$		0			0
$581$	5.00123	−	6.25202i	0.207486	−	0.259378i
$582$	40.5875			1.68241
$583$	−3.64519	+	6.31365i	−0.150968	+	0.261485i
$584$	−11.8421	−	20.5111i	−0.490030	−	0.848757i
$585$		0			0
$586$	−19.1910	+	33.2399i	−0.792775	+	1.37313i
$587$	−19.2217			−0.793363			−0.396682	−	0.917956i	$-0.629838\pi$
$587$	−19.2217			−0.793363			−0.396682	+	0.917956i	$0.629838\pi$
$588$	−35.4549	−	11.0533i	−1.46214	−	0.455832i
$589$	19.5988			0.807556
$590$		0			0
$591$	2.75129	+	4.76538i	0.113173	+	0.196021i
$592$	−28.4616	−	49.2970i	−1.16977	−	2.02609i
$593$	5.89971	−	10.2186i	0.242272	−	0.419628i	−0.719089	−	0.694918i	$-0.755441\pi$
$593$	5.89971	−	10.2186i	0.242272	−	0.419628i	0.961361	+	0.275290i	$0.0887740\pi$
$594$	−7.63692			−0.313346
$595$		0			0
$596$	41.4934			1.69964
$597$	−5.66404	+	9.81041i	−0.231814	+	0.401513i
$598$	−40.0239	−	69.3234i	−1.63670	−	2.83484i
$599$	−20.1981	−	34.9841i	−0.825271	−	1.42941i	−0.901712	−	0.432338i	$-0.857689\pi$
$599$	−20.1981	−	34.9841i	−0.825271	−	1.42941i	0.0764403	−	0.997074i	$-0.475645\pi$
$600$		0			0
$601$	−20.9073			−0.852828			−0.426414	−	0.904528i	$-0.640223\pi$
$601$	−20.9073			−0.852828			−0.426414	+	0.904528i	$0.640223\pi$
$602$	8.14842	+	20.8540i	0.332105	+	0.849947i
$603$	−3.30542			−0.134607
$604$	8.31448	−	14.4011i	0.338311	−	0.585972i
$605$		0			0
$606$	−3.01532	−	5.22268i	−0.122489	−	0.212157i
$607$	−2.10379	+	3.64388i	−0.0853903	+	0.147900i	−0.905557	−	0.424224i	$-0.860547\pi$
$607$	−2.10379	+	3.64388i	−0.0853903	+	0.147900i	0.820167	+	0.572124i	$0.193880\pi$
$608$	39.3161			1.59448
$609$	−10.4624	−	1.59306i	−0.423959	−	0.0645539i
$610$		0			0
$611$	17.4388	−	30.2049i	0.705500	−	1.22196i
$612$	−11.2242	−	19.4408i	−0.453710	−	0.785849i
$613$	−8.21340	−	14.2260i	−0.331736	−	0.574584i	0.651116	−	0.758978i	$-0.274301\pi$
$613$	−8.21340	−	14.2260i	−0.331736	−	0.574584i	−0.982852	+	0.184394i	$0.940968\pi$
$614$	−18.8420	+	32.6354i	−0.760403	+	1.31706i
$615$		0			0
$616$	66.0262	+	10.0535i	2.66027	+	0.405066i
$617$	21.9037			0.881811			0.440906	−	0.897553i	$-0.354657\pi$
$617$	21.9037			0.881811			0.440906	+	0.897553i	$0.354657\pi$
$618$	10.5980	−	18.3562i	0.426312	−	0.738394i
$619$	−0.159752	−	0.276699i	−0.00642098	−	0.0111215i	0.862797	−	0.505550i	$-0.168711\pi$
$619$	−0.159752	−	0.276699i	−0.00642098	−	0.0111215i	−0.869218	+	0.494429i	$0.835377\pi$
$620$		0			0
$621$	−3.30542	+	5.72515i	−0.132642	+	0.229742i
$622$	−10.2693			−0.411761
$623$	7.92579	+	20.2843i	0.317540	+	0.812672i
$624$	60.6430			2.42766
$625$		0			0
$626$	37.7016	+	65.3011i	1.50686	+	2.60996i
$627$	2.96718	+	5.13931i	0.118498	+	0.205244i
$628$	−62.2829	+	107.877i	−2.48536	+	4.30476i
$629$	17.7928			0.709445
$630$		0			0
$631$	17.3090			0.689061			0.344530	−	0.938775i	$-0.388038\pi$
$631$	17.3090			0.689061			0.344530	+	0.938775i	$0.388038\pi$
$632$	−56.4495	+	97.7734i	−2.24544	+	3.88922i
$633$	4.41048	+	7.63917i	0.175301	+	0.303630i
$634$	46.6182	+	80.7450i	1.85144	+	3.20679i
$635$		0			0
$636$	−13.6891			−0.542807
$637$	6.88610	+	30.5940i	0.272837	+	1.21218i
$638$	30.5477			1.20939
$639$	5.71113	−	9.89196i	0.225929	−	0.391320i
$640$		0			0
$641$	−24.1429	−	41.8168i	−0.953588	−	1.65166i	−0.737567	−	0.675273i	$-0.764026\pi$
$641$	−24.1429	−	41.8168i	−0.953588	−	1.65166i	−0.216020	−	0.976389i	$-0.569308\pi$
$642$	−21.1321	+	36.6020i	−0.834019	+	1.44456i
$643$	12.6460			0.498710			0.249355	−	0.968412i	$-0.419781\pi$
$643$	12.6460			0.498710			0.249355	+	0.968412i	$0.419781\pi$
$644$	57.9659	−	72.4630i	2.28418	−	2.85544i
$645$		0			0
$646$	−12.0098	+	20.8016i	−0.472520	+	0.818428i
$647$	7.92671	+	13.7295i	0.311631	+	0.539761i	0.978716	−	0.205221i	$-0.0657913\pi$
$647$	7.92671	+	13.7295i	0.311631	+	0.539761i	−0.667084	+	0.744982i	$0.732458\pi$
$648$	−4.46703	−	7.73712i	−0.175482	−	0.303943i
$649$	5.34773	−	9.26255i	0.209917	−	0.363587i
$650$		0			0
$651$	8.98525	+	22.9957i	0.352160	+	0.901273i
$652$	65.9800			2.58398
$653$	−0.578977	+	1.00282i	−0.0226571	+	0.0392433i	−0.877132	−	0.480250i	$-0.840546\pi$
$653$	−0.578977	+	1.00282i	−0.0226571	+	0.0392433i	0.854475	+	0.519493i	$0.173879\pi$
$654$	4.15457	+	7.19593i	0.162457	+	0.281383i
$655$		0			0
$656$	−16.1061	+	27.8965i	−0.628836	+	1.08918i
$657$	2.65100			0.103425
$658$	55.0392	+	8.38053i	2.14565	+	0.326707i
$659$	−34.5617			−1.34633			−0.673167	−	0.739490i	$-0.735067\pi$
$659$	−34.5617			−1.34633			−0.673167	+	0.739490i	$0.735067\pi$
$660$		0			0
$661$	0.640148	+	1.10877i	0.0248989	+	0.0431261i	0.878206	−	0.478282i	$-0.158740\pi$
$661$	0.640148	+	1.10877i	0.0248989	+	0.0431261i	−0.853307	+	0.521408i	$0.825407\pi$
$662$	40.3998	+	69.9746i	1.57018	+	2.71964i
$663$	−9.47773	+	16.4159i	−0.368085	+	0.637541i
$664$	−27.0352			−1.04917
$665$		0			0
$666$	11.3658			0.440418
$667$	13.2217	−	22.9006i	0.511945	−	0.886715i
$668$	48.9381	+	84.7632i	1.89347	+	3.27959i
$669$	−13.2442	−	22.9397i	−0.512052	−	0.886900i
$670$		0			0
$671$	−14.1275			−0.545386
$672$	18.0248	+	46.1304i	0.695322	+	1.77952i
$673$	45.9058			1.76954			0.884769	−	0.466031i	$-0.154316\pi$
$673$	45.9058			1.76954			0.884769	+	0.466031i	$0.154316\pi$
$674$	26.1475	−	45.2887i	1.00716	−	1.74446i
$675$		0			0
$676$	−18.7537	−	32.4824i	−0.721298	−	1.24932i
$677$	−9.85499	+	17.0694i	−0.378758	+	0.656028i	−0.990882	−	0.134734i	$-0.956982\pi$
$677$	−9.85499	+	17.0694i	−0.378758	+	0.656028i	0.612124	+	0.790762i	$0.290315\pi$
$678$	−0.943291			−0.0362269
$679$	24.8180	−	31.0249i	0.952427	−	1.19063i
$680$		0			0
$681$	8.88562	−	15.3904i	0.340498	−	0.589760i
$682$	−35.6319	−	61.7163i	−1.36442	−	2.36324i
$683$	−0.721583	−	1.24982i	−0.0276106	−	0.0478230i	0.851890	−	0.523721i	$-0.175457\pi$
$683$	−0.721583	−	1.24982i	−0.0276106	−	0.0478230i	−0.879501	+	0.475898i	$0.842123\pi$
$684$	−5.57146	+	9.65005i	−0.213030	+	0.368979i
$685$		0			0
$686$	−41.4863	+	28.0115i	−1.58396	+	1.06948i
$687$	−18.6449			−0.711347
$688$	21.1910	−	36.7040i	0.807901	−	1.39933i
$689$	5.77956	+	10.0105i	0.220184	+	0.381369i
$690$		0			0
$691$	15.4611	−	26.7793i	0.588167	−	1.01873i	−0.406306	−	0.913737i	$-0.633183\pi$
$691$	15.4611	−	26.7793i	0.588167	−	1.01873i	0.994473	−	0.104997i	$-0.0334834\pi$
$692$	−40.5918			−1.54307
$693$	−4.66973	+	5.83762i	−0.177388	+	0.221753i
$694$	−71.0848			−2.69834
$695$		0			0
$696$	17.8681	+	30.9485i	0.677290	+	1.17310i
$697$	−5.03435	−	8.71975i	−0.190690	−	0.330284i
$698$	20.1475	−	34.8964i	0.762593	−	1.32085i
$699$	−9.76879			−0.369490
$700$		0			0
$701$	50.6746			1.91395			0.956976	−	0.290168i	$-0.0937111\pi$
$701$	50.6746			1.91395			0.956976	+	0.290168i	$0.0937111\pi$
$702$	−6.05428	+	10.4863i	−0.228504	+	0.395781i
$703$	−4.41599	−	7.64873i	−0.166552	−	0.288477i
$704$	−33.2315	−	57.5586i	−1.25246	−	2.16932i
$705$		0			0
$706$	42.7617			1.60936
$707$	−5.83596	−	0.888611i	−0.219484	−	0.0334196i
$708$	20.0828			0.754757
$709$	10.0885	−	17.4738i	0.378881	−	0.656241i	−0.612019	−	0.790843i	$-0.709642\pi$
$709$	10.0885	−	17.4738i	0.378881	−	0.656241i	0.990900	+	0.134602i	$0.0429757\pi$
$710$		0			0
$711$	−6.31846	−	10.9439i	−0.236961	−	0.410428i
$712$	36.7691	−	63.6859i	1.37798	−	2.38673i
$713$	−61.6890			−2.31027
$714$	−29.9129	−	4.55469i	−1.11946	−	0.170455i
$715$		0			0
$716$	6.39371	−	11.0742i	0.238944	−	0.413864i
$717$	−3.10029	−	5.36986i	−0.115782	−	0.200541i
$718$	−22.5379	−	39.0367i	−0.841105	−	1.45684i
$719$	−22.6639	+	39.2551i	−0.845221	+	1.46397i	0.0402072	+	0.999191i	$0.487198\pi$
$719$	−22.6639	+	39.2551i	−0.845221	+	1.46397i	−0.885429	+	0.464775i	$0.846135\pi$
$720$		0			0
$721$	−7.55107	−	19.3252i	−0.281216	−	0.719710i
$722$	−39.4314			−1.46748
$723$	−10.1191	+	17.5268i	−0.376334	+	0.651829i
$724$	36.3343	+	62.9328i	1.35035	+	2.33888i
$725$		0			0
$726$	−4.07664	+	7.06095i	−0.151298	+	0.262056i
$727$	−16.9117			−0.627220			−0.313610	−	0.949552i	$-0.601539\pi$
$727$	−16.9117			−0.627220			−0.313610	+	0.949552i	$0.601539\pi$
$728$	66.1478	−	82.6912i	2.45160	−	3.06474i
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.62379	+	11.4727i	0.244990	+	0.424334i
$732$	−13.2635	−	22.9731i	−0.490235	−	0.849112i
$733$	3.58279	−	6.20557i	0.132333	−	0.229208i	−0.792242	−	0.610207i	$-0.791086\pi$
$733$	3.58279	−	6.20557i	0.132333	−	0.229208i	0.924576	+	0.380999i	$0.124420\pi$
$734$	−76.1870			−2.81211
$735$		0			0
$736$	−123.751			−4.56152
$737$	4.66973	−	8.08821i	0.172012	−	0.297933i
$738$	−3.21589	−	5.57009i	−0.118379	−	0.205038i
$739$	10.1924	+	17.6537i	0.374933	+	0.649404i	0.990317	−	0.138824i	$-0.0443323\pi$
$739$	10.1924	+	17.6537i	0.374933	+	0.649404i	−0.615384	+	0.788228i	$0.710999\pi$
$740$		0			0
$741$	9.40912			0.345653
$742$	−11.5259	+	14.4085i	−0.423128	+	0.528951i
$743$	−16.9267			−0.620982			−0.310491	−	0.950576i	$-0.600493\pi$
$743$	−16.9267			−0.620982			−0.310491	+	0.950576i	$0.600493\pi$
$744$	41.6841	−	72.1990i	1.52821	−	2.64694i
$745$		0			0
$746$	32.4330	+	56.1755i	1.18745	+	2.05673i
$747$	1.51304	−	2.62066i	0.0553592	−	0.0958850i
$748$	63.4278			2.31915
$749$	15.0567	+	38.5342i	0.550160	+	1.40801i
$750$		0			0
$751$	−19.5439	+	33.8509i	−0.713165	+	1.23524i	0.250498	+	0.968117i	$0.419406\pi$
$751$	−19.5439	+	33.8509i	−0.713165	+	1.23524i	−0.963663	+	0.267121i	$0.913928\pi$
$752$	−52.6936	−	91.2680i	−1.92154	−	3.32820i
$753$	−3.10733	−	5.38206i	−0.113237	−	0.196133i
$754$	24.2171	−	41.9453i	0.881936	−	1.52756i
$755$		0			0
$756$	−13.8769	−	2.11296i	−0.504697	−	0.0768476i
$757$	22.6675			0.823866			0.411933	−	0.911214i	$-0.364854\pi$
$757$	22.6675			0.823866			0.411933	+	0.911214i	$0.364854\pi$
$758$	−18.7240	+	32.4309i	−0.680087	+	1.17794i
$759$	−9.33946	−	16.1764i	−0.339001	−	0.587167i
$760$		0			0
$761$	−5.16373	+	8.94385i	−0.187185	+	0.324214i	−0.944311	−	0.329055i	$-0.893270\pi$
$761$	−5.16373	+	8.94385i	−0.187185	+	0.324214i	0.757125	+	0.653269i	$0.226603\pi$
$762$	6.13919			0.222399
$763$	8.04092	+	1.22435i	0.291101	+	0.0443244i
$764$	−64.3777			−2.32910
$765$		0			0
$766$	−41.5921	−	72.0396i	−1.50278	−	2.60290i
$767$	−8.47900	−	14.6861i	−0.306159	−	0.530283i
$768$	11.8027	−	20.4428i	0.425892	−	0.737667i
$769$	−25.8785			−0.933204			−0.466602	−	0.884467i	$-0.654522\pi$
$769$	−25.8785			−0.933204			−0.466602	+	0.884467i	$0.654522\pi$
$770$		0			0
$771$	5.65346			0.203604
$772$	31.6357	−	54.7946i	1.13859	−	1.97210i
$773$	4.67708	+	8.10094i	0.168223	+	0.291371i	0.937795	−	0.347189i	$-0.112864\pi$
$773$	4.67708	+	8.10094i	0.168223	+	0.291371i	−0.769572	+	0.638560i	$0.779530\pi$
$774$	4.23121	+	7.32867i	0.152088	+	0.263424i
$775$		0			0
$776$	−134.159			−4.81602
$777$	6.94986	−	8.68800i	0.249325	−	0.311680i
$778$	103.824			3.72227
$779$	−2.49895	+	4.32831i	−0.0895343	+	0.155078i
$780$		0			0
$781$	16.1368	+	27.9497i	0.577420	+	1.00012i
$782$	37.8019	−	65.4748i	1.35179	−	2.34137i
$783$	−4.00000			−0.142948
$784$	90.4622	+	28.2023i	3.23079	+	1.00722i
$785$		0			0
$786$	25.9767	−	44.9929i	0.926558	−	1.60484i
$787$	−1.40094	−	2.42650i	−0.0499381	−	0.0864953i	0.839976	−	0.542624i	$-0.182569\pi$
$787$	−1.40094	−	2.42650i	−0.0499381	−	0.0864953i	−0.889914	+	0.456128i	$0.849236\pi$
$788$	−14.5968	−	25.2823i	−0.519988	−	0.900645i
$789$	−12.5060	+	21.6610i	−0.445225	+	0.771153i
$790$		0			0
$791$	−0.576792	+	0.721046i	−0.0205084	+	0.0256375i
$792$	25.2432			0.896978
$793$	−11.1998	+	19.3986i	−0.397716	+	0.688865i
$794$	−45.2207	−	78.3246i	−1.60482	−	2.77964i
$795$		0			0
$796$	30.0501	−	52.0483i	1.06510	−	1.84480i
$797$	−13.0211			−0.461231			−0.230615	−	0.973045i	$-0.574074\pi$
$797$	−13.0211			−0.461231			−0.230615	+	0.973045i	$0.574074\pi$
$798$	5.46614	+	13.9893i	0.193499	+	0.495217i
$799$	32.9414			1.16538
$800$		0			0
$801$	4.11560	+	7.12844i	0.145418	+	0.251871i
$802$	−20.0579	−	34.7414i	−0.708270	−	1.22676i
$803$	−3.74520	+	6.48688i	−0.132165	+	0.228917i
$804$	17.5366			0.618469
$805$		0			0
$806$	−112.991			−3.97994
$807$	−3.94111	+	6.82619i	−0.138733	+	0.240293i
$808$	9.96688	+	17.2631i	0.350634	+	0.607315i
$809$	−10.5105	−	18.2048i	−0.369531	−	0.640047i	0.619961	−	0.784633i	$-0.287148\pi$
$809$	−10.5105	−	18.2048i	−0.369531	−	0.640047i	−0.989492	+	0.144586i	$0.953815\pi$
$810$		0			0
$811$	−46.2591			−1.62438			−0.812189	−	0.583395i	$-0.801724\pi$
$811$	−46.2591			−1.62438			−0.812189	+	0.583395i	$0.801724\pi$
$812$	55.5075	+	8.45184i	1.94793	+	0.296601i
$813$	−4.74271			−0.166334
$814$	−16.0571	+	27.8117i	−0.562801	+	0.974801i
$815$		0			0
$816$	28.6381	+	49.6027i	1.00254	+	1.73644i
$817$	3.28792	−	5.69484i	0.115030	−	0.199237i
$818$	22.8254			0.798070
$819$	4.31369	+	11.0399i	0.150733	+	0.385766i
$820$		0			0
$821$	−8.46915	+	14.6690i	−0.295575	+	0.511952i	−0.975119	−	0.221684i	$-0.928845\pi$
$821$	−8.46915	+	14.6690i	−0.295575	+	0.511952i	0.679543	+	0.733636i	$0.262178\pi$
$822$	11.1653	+	19.3388i	0.389434	+	0.674519i
$823$	9.26661	+	16.0502i	0.323014	+	0.559476i	0.981108	−	0.193459i	$-0.0619707\pi$
$823$	9.26661	+	16.0502i	0.323014	+	0.559476i	−0.658095	+	0.752935i	$0.728637\pi$
$824$	−35.0307	+	60.6749i	−1.22035	+	2.11371i
$825$		0			0
$826$	16.9092	−	21.1382i	0.588347	−	0.735491i
$827$	32.5496			1.13186			0.565930	−	0.824453i	$-0.308517\pi$
$827$	32.5496			1.13186			0.565930	+	0.824453i	$0.308517\pi$
$828$	17.5366	−	30.3743i	0.609440	−	1.05558i
$829$	5.47764	+	9.48755i	0.190246	+	0.329516i	0.945332	−	0.326110i	$-0.105738\pi$
$829$	5.47764	+	9.48755i	0.190246	+	0.329516i	−0.755085	+	0.655626i	$0.772405\pi$
$830$		0			0
$831$	−3.86860	+	6.70062i	−0.134200	+	0.232442i
$832$	−105.379			−3.65336
$833$	−21.7724	+	20.0802i	−0.754368	+	0.695739i
$834$	−2.66478			−0.0922738
$835$		0			0
$836$	−15.7422	−	27.2662i	−0.544454	−	0.943022i
$837$	4.66575	+	8.08131i	0.161272	+	0.279331i
$838$	25.4645	−	44.1058i	0.879656	−	1.52361i
$839$	1.24074			0.0428352			0.0214176	−	0.999771i	$-0.493182\pi$
$839$	1.24074			0.0428352			0.0214176	+	0.999771i	$0.493182\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	12.2938	−	21.2934i	0.423671	−	0.733820i
$843$	1.05889	+	1.83406i	0.0364703	+	0.0631684i
$844$	−23.3994	−	40.5290i	−0.805441	−	1.39506i
$845$		0			0
$846$	21.0426			0.723460
$847$	2.90462	+	7.43371i	0.0998038	+	0.255425i
$848$	34.9273			1.19941
$849$	−2.19887	+	3.80856i	−0.0754651	+	0.130709i
$850$		0			0
$851$	13.8997	+	24.0750i	0.476476	+	0.825281i
$852$	−30.2999	+	52.4810i	−1.03806	+	1.79797i
$853$	44.8500			1.53564			0.767818	−	0.640669i	$-0.221343\pi$
$853$	44.8500			1.53564			0.767818	+	0.640669i	$0.221343\pi$
$854$	−35.3480	−	5.38225i	−1.20958	−	0.184177i
$855$		0			0
$856$	69.8506	−	120.985i	2.38744	−	4.13517i
$857$	−19.3054	−	33.4380i	−0.659461	−	1.14222i	−0.980756	−	0.195240i	$-0.937451\pi$
$857$	−19.3054	−	33.4380i	−0.659461	−	1.14222i	0.321295	−	0.946979i	$-0.395882\pi$
$858$	−17.1064	−	29.6291i	−0.584002	−	1.01152i
$859$	−17.5541	+	30.4046i	−0.598939	+	1.03739i	0.394039	+	0.919094i	$0.371078\pi$
$859$	−17.5541	+	30.4046i	−0.598939	+	1.03739i	−0.992978	+	0.118299i	$0.962256\pi$
$860$		0			0
$861$	−6.22417	−	0.947721i	−0.212119	−	0.0322982i
$862$	−13.4057			−0.456600
$863$	−2.47287	+	4.28314i	−0.0841776	+	0.145800i	−0.905040	−	0.425325i	$-0.860160\pi$
$863$	−2.47287	+	4.28314i	−0.0841776	+	0.145800i	0.820863	+	0.571125i	$0.193493\pi$
$864$	9.35970	+	16.2115i	0.318423	+	0.551526i
$865$		0			0
$866$	−3.53663	+	6.12562i	−0.120179	+	0.208157i
$867$	−0.903125			−0.0306717
$868$	−47.6705	−	122.002i	−1.61804	−	4.14101i
$869$	35.7056			1.21123
$870$		0			0
$871$	−7.40400	−	12.8241i	−0.250875	−	0.434528i
$872$	−13.7326	−	23.7855i	−0.465044	−	0.805480i
$873$	7.50827	−	13.0047i	0.254117	−	0.440143i
$874$	−37.5282			−1.26941
$875$		0			0
$876$	−14.0647			−0.475201
$877$	5.35613	−	9.27709i	0.180864	−	0.313265i	−0.761311	−	0.648387i	$-0.775444\pi$
$877$	5.35613	−	9.27709i	0.180864	−	0.313265i	0.942175	+	0.335122i	$0.108777\pi$
$878$	35.8196	+	62.0414i	1.20885	+	2.09380i
$879$	7.10029	+	12.2981i	0.239487	+	0.414803i
$880$		0			0
$881$	40.2527			1.35615			0.678075	−	0.734993i	$-0.262815\pi$
$881$	40.2527			1.35615			0.678075	+	0.734993i	$0.262815\pi$
$882$	−13.9080	+	12.8271i	−0.468306	+	0.431910i
$883$	−26.2228			−0.882468			−0.441234	−	0.897392i	$-0.645459\pi$
$883$	−26.2228			−0.882468			−0.441234	+	0.897392i	$0.645459\pi$
$884$	50.2833	−	87.0933i	1.69121	−	2.92926i
$885$		0			0
$886$	53.3683	+	92.4366i	1.79294	+	3.10547i
$887$	−24.6982	+	42.7785i	−0.829284	+	1.43636i	0.0693174	+	0.997595i	$0.477918\pi$
$887$	−24.6982	+	42.7785i	−0.829284	+	1.43636i	−0.898601	+	0.438767i	$0.855415\pi$
$888$	−37.5689			−1.26073
$889$	3.75392	−	4.69277i	0.125902	−	0.157390i
$890$		0			0
$891$	−1.41275	+	2.44696i	−0.0473289	+	0.0819761i
$892$	70.2663	+	121.705i	2.35269	+	4.07498i
$893$	−8.17573	−	14.1608i	−0.273590	−	0.473872i
$894$	10.5694	−	18.3068i	0.353495	−	0.612271i
$895$		0			0
$896$	−25.1693	−	64.4151i	−0.840847	−	2.15196i
$897$	−29.6160			−0.988850
$898$	−28.7914	+	49.8682i	−0.960782	+	1.66412i
$899$	−18.6630	−	32.3253i	−0.622446	−	1.07811i
$900$		0			0
$901$	−5.45870	+	9.45474i	−0.181856	+	0.314983i
$902$	18.1730			0.605095
$903$	8.18925	+	1.24693i	0.272521	+	0.0414953i
$904$	3.11797			0.103702
$905$		0			0
$906$	−4.23582	−	7.33666i	−0.140726	−	0.243744i
$907$	−28.0814	−	48.6385i	−0.932429	−	1.61501i	−0.779156	−	0.626830i	$-0.784352\pi$
$907$	−28.0814	−	48.6385i	−0.932429	−	1.61501i	−0.153273	−	0.988184i	$-0.548981\pi$
$908$	−47.1420	+	81.6523i	−1.56446	+	2.70973i
$909$	−2.23121			−0.0740045
$910$		0			0
$911$	−35.9981			−1.19267			−0.596335	−	0.802736i	$-0.703377\pi$
$911$	−35.9981			−1.19267			−0.596335	+	0.802736i	$0.703377\pi$
$912$	14.2154	−	24.6218i	0.470719	−	0.815310i
$913$	4.27510	+	7.40468i	0.141485	+	0.245059i
$914$	37.6779	+	65.2601i	1.24628	+	2.15861i
$915$		0			0
$916$	98.9189			3.26837
$917$	−18.5085	−	47.3682i	−0.611203	−	1.56424i
$918$	−11.4363			−0.377455
$919$	3.77400	−	6.53677i	0.124493	−	0.215628i	−0.797042	−	0.603924i	$-0.793603\pi$
$919$	3.77400	−	6.53677i	0.124493	−	0.215628i	0.921535	+	0.388296i	$0.126936\pi$
$920$		0			0
$921$	6.97117	+	12.0744i	0.229708	+	0.397866i
$922$	−30.4391	+	52.7221i	−1.00246	+	1.73631i
$923$	51.1707			1.68431
$924$	24.7749	−	30.9710i	0.815034	−	1.01887i
$925$		0			0
$926$	−2.28798	+	3.96290i	−0.0751877	+	0.130229i
$927$	−3.92102	−	6.79141i	−0.128783	−	0.223059i
$928$	−37.4388	−	64.8459i	−1.22899	−	2.12867i
$929$	−2.59552	+	4.49558i	−0.0851563	+	0.147495i	−0.905458	−	0.424436i	$-0.860472\pi$
$929$	−2.59552	+	4.49558i	−0.0851563	+	0.147495i	0.820302	+	0.571931i	$0.193806\pi$
$930$		0			0
$931$	14.0358	+	4.37575i	0.460003	+	0.143409i
$932$	51.8275			1.69767
$933$	−1.89971	+	3.29040i	−0.0621937	+	0.107723i
$934$	−0.108561	−	0.188034i	−0.00355223	−	0.00615264i
$935$		0			0
$936$	20.0119	−	34.6617i	0.654110	−	1.13295i
$937$	−5.23690			−0.171082			−0.0855410	−	0.996335i	$-0.527262\pi$
$937$	−5.23690			−0.171082			−0.0855410	+	0.996335i	$0.527262\pi$
$938$	14.7654	−	18.4582i	0.482108	−	0.602682i
$939$	27.8976			0.910404
$940$		0			0
$941$	6.47195	+	11.2098i	0.210980	+	0.365427i	0.952021	−	0.306032i	$-0.0990013\pi$
$941$	6.47195	+	11.2098i	0.210980	+	0.365427i	−0.741042	+	0.671459i	$0.765668\pi$
$942$	31.7301	+	54.9581i	1.03382	+	1.79063i
$943$	7.86567	−	13.6237i	0.256141	−	0.443650i
$944$	−51.2407			−1.66774
$945$		0			0
$946$	−23.9106			−0.777400
$947$	11.5071	−	19.9309i	0.373932	−	0.647669i	−0.616235	−	0.787562i	$-0.711343\pi$
$947$	11.5071	−	19.9309i	0.373932	−	0.647669i	0.990167	+	0.139894i	$0.0446761\pi$
$948$	33.5221	+	58.0619i	1.08875	+	1.88576i
$949$	5.93813	+	10.2852i	0.192760	+	0.333870i
$950$		0			0
$951$	34.4955			1.11859
$952$	98.8748	+	15.0551i	3.20455	+	0.487940i
$953$	−15.1560			−0.490952			−0.245476	−	0.969403i	$-0.578944\pi$
$953$	−15.1560			−0.490952			−0.245476	+	0.969403i	$0.578944\pi$
$954$	−3.48696	+	6.03959i	−0.112895	+	0.195539i
$955$		0			0
$956$	16.4483	+	28.4893i	0.531977	+	0.921411i
$957$	5.65100	−	9.78782i	0.182671	−	0.316395i
$958$	−104.812			−3.38632
$959$	21.6097	+	3.29040i	0.697814	+	0.106252i
$960$		0			0
$961$	−28.0384	+	48.5640i	−0.904465	+	1.56658i
$962$	25.4590	+	44.0963i	0.820832	+	1.42172i
$963$	7.81846	+	13.5420i	0.251946	+	0.436384i
$964$	53.6861	−	92.9871i	1.72911	−	2.99491i
$965$		0			0
$966$	−17.2051	−	44.0326i	−0.553566	−	1.41673i
$967$	−45.5145			−1.46365			−0.731824	−	0.681494i	$-0.761331\pi$
$967$	−45.5145			−1.46365			−0.731824	+	0.681494i	$0.761331\pi$
$968$	13.4750	−	23.3394i	0.433103	−	0.750156i
$969$	4.44338	+	7.69616i	0.142742	+	0.247236i
$970$		0			0
$971$	3.80096	−	6.58345i	0.121979	−	0.211273i	−0.798569	−	0.601903i	$-0.794409\pi$
$971$	3.80096	−	6.58345i	0.121979	−	0.211273i	0.920548	+	0.390630i	$0.127743\pi$
$972$	−5.30542			−0.170171
$973$	−1.62943	+	2.03695i	−0.0522371	+	0.0653015i
$974$	73.3309			2.34967
$975$		0			0
$976$	33.8416	+	58.6153i	1.08324	+	1.87623i
$977$	17.3468	+	30.0456i	0.554974	+	0.961243i	0.997906	+	0.0646874i	$0.0206050\pi$
$977$	17.3468	+	30.0456i	0.554974	+	0.961243i	−0.442932	+	0.896555i	$0.646062\pi$
$978$	16.8068	−	29.1102i	0.537422	−	0.930843i
$979$	−23.2573			−0.743306
$980$		0			0
$981$	3.07421			0.0981520
$982$	−22.6016	+	39.1471i	−0.721246	+	1.24924i
$983$	−7.78896	−	13.4909i	−0.248429	−	0.430292i	0.714661	−	0.699471i	$-0.246581\pi$
$983$	−7.78896	−	13.4909i	−0.248429	−	0.430292i	−0.963090	+	0.269179i	$0.913248\pi$
$984$	10.6299	+	18.4115i	0.338868	+	0.586937i
$985$		0			0
$986$	45.7454			1.45683
$987$	12.8669	−	16.0849i	0.409558	−	0.511987i
$988$	−49.9193			−1.58815
$989$	−10.3490	+	17.9250i	−0.329079	+	0.569982i
$990$		0			0
$991$	22.9794	+	39.8016i	0.729966	+	1.26434i	0.956897	+	0.290427i	$0.0937974\pi$
$991$	22.9794	+	39.8016i	0.729966	+	1.26434i	−0.226931	+	0.973911i	$0.572869\pi$
$992$	−87.3400	+	151.277i	−2.77305	+	4.80306i
$993$	29.8942			0.948664
$994$	29.7271	+	76.0799i	0.942888	+	2.41311i
$995$		0			0
$996$	−8.02731	+	13.9037i	−0.254355	+	0.440556i
$997$	−20.5344	−	35.5665i	−0.650329	−	1.12640i	−0.983043	−	0.183376i	$-0.941298\pi$
$997$	−20.5344	−	35.5665i	−0.650329	−	1.12640i	0.332713	−	0.943028i	$-0.392036\pi$
$998$	−26.7371	−	46.3101i	−0.846349	−	1.46592i
$999$	2.10256	−	3.64175i	0.0665222	−	0.115220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.i.226.1	yes	8
5.2	odd	4		525.2.r.h.499.1		16
5.3	odd	4		525.2.r.h.499.8		16
5.4	even	2		525.2.i.j.226.4	yes	8
7.2	even	3		3675.2.a.bw.1.4		4
7.4	even	3	inner	525.2.i.i.151.1	✓	8
7.5	odd	6		3675.2.a.bx.1.4		4
35.4	even	6		525.2.i.j.151.4	yes	8
35.9	even	6		3675.2.a.br.1.1		4
35.18	odd	12		525.2.r.h.424.1		16
35.19	odd	6		3675.2.a.bq.1.1		4
35.32	odd	12		525.2.r.h.424.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.1	✓	8	7.4	even	3	inner
525.2.i.i.226.1	yes	8	1.1	even	1	trivial
525.2.i.j.151.4	yes	8	35.4	even	6
525.2.i.j.226.4	yes	8	5.4	even	2
525.2.r.h.424.1		16	35.18	odd	12
525.2.r.h.424.8		16	35.32	odd	12
525.2.r.h.499.1		16	5.2	odd	4
525.2.r.h.499.8		16	5.3	odd	4
3675.2.a.bq.1.1		4	35.19	odd	6
3675.2.a.br.1.1		4	35.9	even	6
3675.2.a.bw.1.4		4	7.2	even	3
3675.2.a.bx.1.4		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35143 + 2.34074i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(-1.65271 + 2.06605i) q^{7} +8.93406 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.35143 + 2.34074i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.65271 - 4.59463i) q^{4} -2.70285 q^{6} +(-1.65271 + 2.06605i) q^{7} +8.93406 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.41275 - 2.44696i) q^{11} +(2.65271 - 4.59463i) q^{12} -4.47992 q^{13} +(-2.60256 - 6.66067i) q^{14} +(-6.76831 + 11.7231i) q^{16} +(-2.11560 - 3.66433i) q^{17} +(-1.35143 - 2.34074i) q^{18} +(-1.05014 + 1.81890i) q^{19} +(-2.61560 - 0.398264i) q^{21} +7.63692 q^{22} +(3.30542 - 5.72515i) q^{23} +(4.46703 + 7.73712i) q^{24} +(6.05428 - 10.4863i) q^{26} -1.00000 q^{27} +(13.8769 + 2.11296i) q^{28} +4.00000 q^{29} +(-4.66575 - 8.08131i) q^{31} +(-9.35970 - 16.2115i) q^{32} +(1.41275 - 2.44696i) q^{33} +11.4363 q^{34} +5.30542 q^{36} +(-2.10256 + 3.64175i) q^{37} +(-2.83839 - 4.91623i) q^{38} +(-2.23996 - 3.87972i) q^{39} +2.37963 q^{41} +(4.46703 - 5.58422i) q^{42} -3.13092 q^{43} +(-7.49523 + 12.9821i) q^{44} +(8.93406 + 15.4742i) q^{46} +(-3.89267 + 6.74230i) q^{47} -13.5366 q^{48} +(-1.53710 - 6.82915i) q^{49} +(2.11560 - 3.66433i) q^{51} +(11.8839 + 20.5835i) q^{52} +(-1.29010 - 2.23452i) q^{53} +(1.35143 - 2.34074i) q^{54} +(-14.7654 + 18.4582i) q^{56} -2.10029 q^{57} +(-5.40571 + 9.36296i) q^{58} +(1.89267 + 3.27820i) q^{59} +(2.50000 - 4.33013i) q^{61} +25.2217 q^{62} +(-0.962895 - 2.46431i) q^{63} +23.5225 q^{64} +(3.81846 + 6.61376i) q^{66} +(1.65271 + 2.86258i) q^{67} +(-11.2242 + 19.4408i) q^{68} +6.61084 q^{69} -11.4223 q^{71} +(-4.46703 + 7.73712i) q^{72} +(-1.32550 - 2.29584i) q^{73} +(-5.68292 - 9.84311i) q^{74} +11.1429 q^{76} +(7.39039 + 1.12530i) q^{77} +12.1086 q^{78} +(-6.31846 + 10.9439i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.21589 + 5.57009i) q^{82} -3.02608 q^{83} +(5.10856 + 13.0742i) q^{84} +(4.23121 - 7.32867i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-12.6216 - 21.8613i) q^{88} +(4.11560 - 7.12844i) q^{89} +(7.40400 - 9.25572i) q^{91} -35.0733 q^{92} +(4.66575 - 8.08131i) q^{93} +(-10.5213 - 18.2234i) q^{94} +(9.35970 - 16.2115i) q^{96} -15.0165 q^{97} +(18.0626 + 5.63114i) q^{98} +2.82550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * q^99

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