LMFDB - Embedded newform 475.2.j.c.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(49,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("475.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 $ x^16 - 11x^14 + 82x^12 - 337x^10 + 1006x^8 - 1596x^6 + 1765x^4 - 414*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$-0.426014 - 0.245959i$ of defining polynomial
Character	$\chi$	$=$	475.349
Dual form			475.2.j.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} +O(q^{10})$	\(q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} -0.864801 q^{11} -8.36467i q^{12} +(-0.557098 - 0.321640i) q^{13} +(-3.92829 - 6.80401i) q^{14} +(-8.11063 - 14.0480i) q^{16} +(-3.24054 + 1.87093i) q^{17} -2.13520i q^{18} +(3.36069 + 2.77592i) q^{19} +(2.12497 + 3.68055i) q^{21} +(2.06559 - 1.19257i) q^{22} +(-0.361531 - 0.208730i) q^{23} +(7.42021 + 12.8522i) q^{24} +1.77418 q^{26} +5.63077i q^{27} +(13.8316 + 7.98566i) q^{28} +(-4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(21.5156 + 12.4220i) q^{32} +(-1.11736 + 0.645106i) q^{33} +(5.16005 - 8.93746i) q^{34} +(2.17028 + 3.75903i) q^{36} -6.36467i q^{37} +(-11.8551 - 1.99589i) q^{38} -0.959723 q^{39} +(2.00686 + 3.47598i) q^{41} +(-10.1510 - 5.86069i) q^{42} +(-1.78254 + 1.02915i) q^{43} +(-2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-3.42423 - 1.97698i) q^{47} +(-20.9585 - 12.1004i) q^{48} -1.11474 q^{49} +(-2.79127 + 4.83462i) q^{51} +(-3.12345 + 1.80333i) q^{52} +(9.51544 + 5.49374i) q^{53} +(-7.76487 - 13.4492i) q^{54} -28.3360 q^{56} +(6.41287 + 1.07966i) q^{57} -26.7672i q^{58} +(1.22980 + 2.13007i) q^{59} +(-3.16740 + 5.48609i) q^{61} +(-11.7837 + 6.80333i) q^{62} +(-1.90989 - 1.10268i) q^{63} -36.0778 q^{64} +(1.77921 - 3.08169i) q^{66} +(-2.19295 - 1.26610i) q^{67} +20.9793i q^{68} -0.622817 q^{69} +(0.891065 + 1.54337i) q^{71} +(-6.66920 - 3.85046i) q^{72} +(-6.17554 + 3.56545i) q^{73} +(8.77693 + 15.2021i) q^{74} +(22.8996 - 8.53606i) q^{76} -2.46350i q^{77} +(2.29231 - 1.32347i) q^{78} +(0.912262 + 1.58008i) q^{79} +(3.03905 + 5.26380i) q^{81} +(-9.58681 - 5.53495i) q^{82} -7.43913i q^{83} +23.8279 q^{84} +(2.83841 - 4.91626i) q^{86} +14.4794i q^{87} -8.60235i q^{88} +(2.22294 - 3.85024i) q^{89} +(0.916237 - 1.58697i) q^{91} +(-2.02698 + 1.17028i) q^{92} +(6.37427 - 3.68018i) q^{93} +10.9051 q^{94} +37.0653 q^{96} +(9.39996 - 5.42707i) q^{97} +(2.66256 - 1.53723i) q^{98} +(0.334755 - 0.579813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9	$ 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49} - 44 q^{51} - 68 q^{54} - 164 q^{56} - 10 q^{59} - 224 q^{64} + 62 q^{66} + 36 q^{69} - 40 q^{71} + 50 q^{74} + 126 q^{76} + 34 q^{79} - 24 q^{81} + 80 q^{84} - 16 q^{86} + 22 q^{89} - 12 q^{91} + 124 q^{94} + 84 q^{96} + 76 q^{99}+O(q^{100}) $ 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.38851	+	1.37901i	−1.68893	+	0.975106i	−0.733597	+	0.679585i	$0.762160\pi$
$2$	−2.38851	+	1.37901i	−1.68893	+	0.975106i	−0.955336	+	0.295521i	$0.904507\pi$
$3$	1.29204	−	0.745959i	0.745959	−	0.430680i	−0.0782728	−	0.996932i	$-0.524941\pi$
$3$	1.29204	−	0.745959i	0.745959	−	0.430680i	0.824232	+	0.566252i	$0.191607\pi$
$4$	2.80333	−	4.85550i	1.40166	−	2.42775i
$5$		0			0
$5$		0			0
$6$	−2.05737	+	3.56347i	−0.839917	+	1.45478i
$7$			2.84864i			1.07668i	0.842727	+	0.538342i	$0.180949\pi$
$7$			2.84864i			1.07668i	−0.842727	+	0.538342i	$0.819051\pi$
$8$			9.94721i			3.51687i
$9$	−0.387090	+	0.670459i	−0.129030	+	0.223486i
$10$		0			0
$11$	−0.864801			−0.260747			−0.130374	−	0.991465i	$-0.541618\pi$
$11$	−0.864801			−0.260747			−0.130374	+	0.991465i	$0.541618\pi$
$12$		−	8.36467i		−	2.41467i
$13$	−0.557098	−	0.321640i	−0.154511	−	0.0892070i	0.420751	−	0.907176i	$-0.361767\pi$
$13$	−0.557098	−	0.321640i	−0.154511	−	0.0892070i	−0.575262	+	0.817969i	$0.695100\pi$
$14$	−3.92829	−	6.80401i	−1.04988	−	1.81845i
$15$		0			0
$16$	−8.11063	−	14.0480i	−2.02766	−	3.51201i
$17$	−3.24054	+	1.87093i	−0.785946	+	0.453766i	−0.838534	−	0.544850i	$-0.816587\pi$
$17$	−3.24054	+	1.87093i	−0.785946	+	0.453766i	0.0525872	+	0.998616i	$0.483253\pi$
$18$		−	2.13520i		−	0.503271i
$19$	3.36069	+	2.77592i	0.770996	+	0.636840i
$19$	3.36069	+	2.77592i	0.770996	+	0.636840i
$20$		0			0
$21$	2.12497	+	3.68055i	0.463706	+	0.803162i
$22$	2.06559	−	1.19257i	0.440385	−	0.254256i
$23$	−0.361531	−	0.208730i	−0.0753845	−	0.0435233i	0.461834	−	0.886966i	$-0.347192\pi$
$23$	−0.361531	−	0.208730i	−0.0753845	−	0.0435233i	−0.537218	+	0.843443i	$0.680525\pi$
$24$	7.42021	+	12.8522i	1.51464	+	2.62344i
$25$		0			0
$26$	1.77418			0.347945
$27$			5.63077i			1.08364i
$28$	13.8316	+	7.98566i	2.61392	+	1.50915i
$29$	−4.85261	+	8.40497i	−0.901108	+	1.56076i	−0.0750490	+	0.997180i	$0.523911\pi$
$29$	−4.85261	+	8.40497i	−0.901108	+	1.56076i	−0.826059	+	0.563584i	$0.809422\pi$
$30$		0			0
$31$	4.93349			0.886081			0.443041	−	0.896501i	$-0.353900\pi$
$31$	4.93349			0.886081			0.443041	+	0.896501i	$0.353900\pi$
$32$	21.5156	+	12.4220i	3.80346	+	2.19593i
$33$	−1.11736	+	0.645106i	−0.194507	+	0.112299i
$34$	5.16005	−	8.93746i	0.884941	−	1.53276i
$35$		0			0
$36$	2.17028	+	3.75903i	0.361713	+	0.626505i
$37$		−	6.36467i		−	1.04635i	−0.852227	−	0.523173i	$-0.824748\pi$
$37$		−	6.36467i		−	1.04635i	0.852227	−	0.523173i	$-0.175252\pi$
$38$	−11.8551	−	1.99589i	−1.92315	−	0.323777i
$39$	−0.959723			−0.153679
$40$		0			0
$41$	2.00686	+	3.47598i	0.313419	+	0.542857i	0.979100	−	0.203379i	$-0.0651924\pi$
$41$	2.00686	+	3.47598i	0.313419	+	0.542857i	−0.665681	+	0.746236i	$0.731859\pi$
$42$	−10.1510	−	5.86069i	−1.56634	−	0.904325i
$43$	−1.78254	+	1.02915i	−0.271834	+	0.156944i	−0.629721	−	0.776821i	$-0.716831\pi$
$43$	−1.78254	+	1.02915i	−0.271834	+	0.156944i	0.357887	+	0.933765i	$0.383497\pi$
$44$	−2.42432	+	4.19904i	−0.365480	+	0.633030i
$45$		0			0
$46$	1.15136			0.169759
$47$	−3.42423	−	1.97698i	−0.499475	−	0.288372i	0.229022	−	0.973421i	$-0.426447\pi$
$47$	−3.42423	−	1.97698i	−0.499475	−	0.288372i	−0.728497	+	0.685049i	$0.759781\pi$
$48$	−20.9585	−	12.1004i	−3.02510	−	1.74654i
$49$	−1.11474			−0.159248
$50$		0			0
$51$	−2.79127	+	4.83462i	−0.390856	+	0.676982i
$52$	−3.12345	+	1.80333i	−0.433145	+	0.250076i
$53$	9.51544	+	5.49374i	1.30705	+	0.754624i	0.981602	−	0.190937i	$-0.0611528\pi$
$53$	9.51544	+	5.49374i	1.30705	+	0.754624i	0.325444	+	0.945561i	$0.394486\pi$
$54$	−7.76487	−	13.4492i	−1.05667	−	1.83020i
$55$		0			0
$56$	−28.3360			−3.78656
$57$	6.41287	+	1.07966i	0.849406	+	0.143004i
$58$		−	26.7672i		−	3.51470i
$59$	1.22980	+	2.13007i	0.160106	+	0.277311i	0.934906	−	0.354894i	$-0.115483\pi$
$59$	1.22980	+	2.13007i	0.160106	+	0.277311i	−0.774801	+	0.632206i	$0.782150\pi$
$60$		0			0
$61$	−3.16740	+	5.48609i	−0.405543	+	0.702422i	−0.994385	−	0.105827i	$-0.966251\pi$
$61$	−3.16740	+	5.48609i	−0.405543	+	0.702422i	0.588841	+	0.808249i	$0.299584\pi$
$62$	−11.7837	+	6.80333i	−1.49653	+	0.864023i
$63$	−1.90989	−	1.10268i	−0.240624	−	0.138924i
$64$	−36.0778			−4.50973
$65$		0			0
$66$	1.77921	−	3.08169i	0.219006	−	0.379329i
$67$	−2.19295	−	1.26610i	−0.267911	−	0.154678i	0.360027	−	0.932942i	$-0.382767\pi$
$67$	−2.19295	−	1.26610i	−0.267911	−	0.154678i	−0.627938	+	0.778263i	$0.716101\pi$
$68$			20.9793i			2.54411i
$69$	−0.622817			−0.0749783
$70$		0			0
$71$	0.891065	+	1.54337i	0.105750	+	0.183164i	0.914044	−	0.405614i	$-0.132942\pi$
$71$	0.891065	+	1.54337i	0.105750	+	0.183164i	−0.808294	+	0.588779i	$0.799609\pi$
$72$	−6.66920	−	3.85046i	−0.785972	−	0.453781i
$73$	−6.17554	+	3.56545i	−0.722792	+	0.417304i	−0.815780	−	0.578363i	$-0.803692\pi$
$73$	−6.17554	+	3.56545i	−0.722792	+	0.417304i	0.0929873	+	0.995667i	$0.470358\pi$
$74$	8.77693	+	15.2021i	1.02030	+	1.76721i
$75$		0			0
$76$	22.8996	−	8.53606i	2.62677	−	0.979153i
$77$		−	2.46350i		−	0.280742i
$78$	2.29231	−	1.32347i	0.259553	−	0.149853i
$79$	0.912262	+	1.58008i	0.102637	+	0.177773i	0.912771	−	0.408473i	$-0.133939\pi$
$79$	0.912262	+	1.58008i	0.102637	+	0.177773i	−0.810133	+	0.586246i	$0.800605\pi$
$80$		0			0
$81$	3.03905	+	5.26380i	0.337673	+	0.584866i
$82$	−9.58681	−	5.53495i	−1.05869	−	0.611233i
$83$		−	7.43913i		−	0.816550i	−0.912859	−	0.408275i	$-0.866130\pi$
$83$		−	7.43913i		−	0.816550i	0.912859	−	0.408275i	$-0.133870\pi$
$84$	23.8279			2.59984
$85$		0			0
$86$	2.83841	−	4.91626i	0.306073	−	0.530134i
$87$			14.4794i			1.55236i
$88$		−	8.60235i		−	0.917014i
$89$	2.22294	−	3.85024i	0.235631	−	0.408125i	−0.723825	−	0.689984i	$-0.757618\pi$
$89$	2.22294	−	3.85024i	0.235631	−	0.408125i	0.959456	+	0.281859i	$0.0909510\pi$
$90$		0			0
$91$	0.916237	−	1.58697i	0.0960478	−	0.166360i
$92$	−2.02698	+	1.17028i	−0.211327	+	0.122010i
$93$	6.37427	−	3.68018i	0.660981	−	0.381617i
$94$	10.9051			1.12477
$95$		0			0
$96$	37.0653			3.78296
$97$	9.39996	−	5.42707i	0.954422	−	0.551036i	0.0599699	−	0.998200i	$-0.480900\pi$
$97$	9.39996	−	5.42707i	0.954422	−	0.551036i	0.894452	+	0.447165i	$0.147566\pi$
$98$	2.66256	−	1.53723i	0.268959	−	0.155284i
$99$	0.334755	−	0.579813i	0.0336442	−	0.0582734i
$100$		0			0
$101$	2.64799	−	4.58645i	0.263485	−	0.456369i	−0.703681	−	0.710516i	$-0.748461\pi$
$101$	2.64799	−	4.58645i	0.263485	−	0.456369i	0.967166	+	0.254147i	$0.0817948\pi$
$102$		−	15.3967i		−	1.52450i
$103$		−	0.385134i		−	0.0379484i	−0.999820	−	0.0189742i	$-0.993960\pi$
$103$		−	0.385134i		−	0.0379484i	0.999820	−	0.0189742i	$-0.00604004\pi$
$104$	3.19943	−	5.54157i	0.313729	−	0.543395i
$105$		0			0
$106$	−30.3037			−2.94335
$107$			6.43336i			0.621937i	0.950420	+	0.310968i	$0.100653\pi$
$107$			6.43336i			0.621937i	−0.950420	+	0.310968i	$0.899347\pi$
$108$	27.3402	+	15.7849i	2.63081	+	1.51890i
$109$	3.28441	+	5.68877i	0.314590	+	0.544885i	0.979350	−	0.202171i	$-0.0647998\pi$
$109$	3.28441	+	5.68877i	0.314590	+	0.544885i	−0.664761	+	0.747056i	$0.731466\pi$
$110$		0			0
$111$	−4.74778	−	8.22340i	−0.450640	−	0.780531i
$112$	40.0177	−	23.1042i	3.78132	−	2.18315i
$113$			0.294513i			0.0277054i	0.999904	+	0.0138527i	$0.00440960\pi$
$113$			0.294513i			0.0277054i	−0.999904	+	0.0138527i	$0.995590\pi$
$114$	−16.8061	+	6.26463i	−1.57403	+	0.586736i
$115$		0			0
$116$	27.2069	+	47.1238i	2.52610	+	4.37533i
$117$	0.431294	−	0.249007i	0.0398731	−	0.0230207i
$118$	−5.87477	−	3.39180i	−0.540816	−	0.312240i
$119$	−5.32959	−	9.23112i	−0.488563	−	0.846216i
$120$		0			0
$121$	−10.2521			−0.932011
$122$		−	17.4715i		−	1.58179i
$123$	5.18588	+	2.99407i	0.467595	+	0.269966i
$124$	13.8302	−	23.9546i	1.24199	−	2.15119i
$125$		0			0
$126$	6.08241			0.541864
$127$	7.65127	+	4.41746i	0.678940	+	0.391986i	0.799456	−	0.600725i	$-0.205121\pi$
$127$	7.65127	+	4.41746i	0.678940	+	0.391986i	−0.120516	+	0.992711i	$0.538455\pi$
$128$	43.1412	−	24.9076i	3.81318	−	2.20154i
$129$	−1.53540	+	2.65940i	−0.135185	+	0.234147i
$130$		0			0
$131$	−10.4564	−	18.1110i	−0.913578	−	1.58236i	−0.808969	−	0.587851i	$-0.799974\pi$
$131$	−10.4564	−	18.1110i	−0.913578	−	1.58236i	−0.104609	−	0.994513i	$-0.533359\pi$
$132$			7.23377i			0.629619i
$133$	−7.90759	+	9.57340i	−0.685675	+	0.830119i
$134$	6.98384			0.603312
$135$		0			0
$136$	−18.6105	−	32.2343i	−1.59584	−	2.76407i
$137$	4.51613	+	2.60739i	0.385839	+	0.222764i	0.680356	−	0.732882i	$-0.261825\pi$
$137$	4.51613	+	2.60739i	0.385839	+	0.222764i	−0.294517	+	0.955646i	$0.595159\pi$
$138$	1.48761	−	0.858870i	0.126633	−	0.0731118i
$139$	−5.36192	+	9.28711i	−0.454792	+	0.787723i	−0.998676	−	0.0514375i	$-0.983620\pi$
$139$	−5.36192	+	9.28711i	−0.454792	+	0.787723i	0.543884	+	0.839160i	$0.316953\pi$
$140$		0			0
$141$	−5.89898			−0.496784
$142$	−4.25664	−	2.45757i	−0.357209	−	0.206235i
$143$	0.481778	+	0.278155i	0.0402883	+	0.0232605i
$144$	12.5582			1.04651
$145$		0			0
$146$	9.83357	−	17.0322i	0.813832	−	1.40960i
$147$	−1.44028	+	0.831547i	−0.118792	+	0.0685848i
$148$	−30.9037	−	17.8423i	−2.54027	−	1.46662i
$149$	−7.45578	−	12.9138i	−0.610801	−	1.05794i	−0.991106	−	0.133078i	$-0.957514\pi$
$149$	−7.45578	−	12.9138i	−0.610801	−	1.05794i	0.380304	−	0.924861i	$-0.375819\pi$
$150$		0			0
$151$	21.4589			1.74630			0.873152	−	0.487448i	$-0.162072\pi$
$151$	21.4589			1.74630			0.873152	+	0.487448i	$0.162072\pi$
$152$	−27.6127	+	33.4295i	−2.23968	+	2.71149i
$153$		−	2.89687i		−	0.234198i
$154$	3.39719	+	5.88411i	0.273753	+	0.474155i
$155$		0			0
$156$	−2.69042	+	4.65994i	−0.215406	+	0.373094i
$157$	2.10546	−	1.21559i	0.168034	−	0.0970145i	−0.413624	−	0.910448i	$-0.635737\pi$
$157$	2.10546	−	1.21559i	0.168034	−	0.0970145i	0.581659	+	0.813433i	$0.302404\pi$
$158$	−4.35790	−	2.51603i	−0.346696	−	0.200165i
$159$	16.3924			1.30000
$160$		0			0
$161$	0.594597	−	1.02987i	0.0468608	−	0.0811653i
$162$	−14.5176	−	8.38176i	−1.14061	−	0.658533i
$163$			17.8175i			1.39558i	0.716305	+	0.697788i	$0.245832\pi$
$163$			17.8175i			1.39558i	−0.716305	+	0.697788i	$0.754168\pi$
$164$	22.5035			1.75723
$165$		0			0
$166$	10.2586	+	17.7684i	0.796223	+	1.37910i
$167$	−0.351258	−	0.202799i	−0.0271812	−	0.0156931i	0.486348	−	0.873765i	$-0.338329\pi$
$167$	−0.351258	−	0.202799i	−0.0271812	−	0.0156931i	−0.513529	+	0.858072i	$0.671662\pi$
$168$	−36.6112	+	21.1375i	−2.82462	+	1.63079i
$169$	−6.29309	−	10.9000i	−0.484084	−	0.838458i
$170$		0			0
$171$	−3.16203	+	1.17868i	−0.241807	+	0.0901358i
$172$			11.5401i			0.879928i
$173$	15.6067	−	9.01051i	1.18655	−	0.685056i	0.229031	−	0.973419i	$-0.426444\pi$
$173$	15.6067	−	9.01051i	1.18655	−	0.685056i	0.957521	+	0.288363i	$0.0931109\pi$
$174$	−19.9672	−	34.5842i	−1.51371	−	2.62182i
$175$		0			0
$176$	7.01408	+	12.1487i	0.528706	+	0.915746i
$177$	3.17789	+	1.83476i	0.238865	+	0.137909i
$178$			12.2618i			0.919061i
$179$	−20.1523			−1.50625			−0.753127	−	0.657875i	$-0.771455\pi$
$179$	−20.1523			−1.50625			−0.753127	+	0.657875i	$0.771455\pi$
$180$		0			0
$181$	8.55541	−	14.8184i	0.635919	−	1.10144i	−0.350401	−	0.936600i	$-0.613955\pi$
$181$	8.55541	−	14.8184i	0.635919	−	1.10144i	0.986320	−	0.164844i	$-0.0527120\pi$
$182$			5.05399i			0.374627i
$183$			9.45099i			0.698637i
$184$	2.07628	−	3.59623i	0.153066	−	0.265117i
$185$		0			0
$186$	−10.1500	+	17.5803i	−0.744235	+	1.28905i
$187$	2.80242	−	1.61798i	0.204933	−	0.118318i
$188$	−19.1985	+	11.0842i	−1.40019	+	0.808401i
$189$	−16.0400			−1.16674
$190$		0			0
$191$	5.28080			0.382105			0.191053	−	0.981580i	$-0.438810\pi$
$191$	5.28080			0.382105			0.191053	+	0.981580i	$0.438810\pi$
$192$	−46.6140	+	26.9126i	−3.36408	+	1.94225i
$193$	15.5916	−	9.00182i	1.12231	−	0.647966i	0.180320	−	0.983608i	$-0.442287\pi$
$193$	15.5916	−	9.00182i	1.12231	−	0.647966i	0.941989	+	0.335642i	$0.108953\pi$
$194$	−14.9679	+	25.9252i	−1.07464	+	1.86132i
$195$		0			0
$196$	−3.12497	+	5.41260i	−0.223212	+	0.386614i
$197$		−	8.07785i		−	0.575523i	−0.957702	−	0.287761i	$-0.907089\pi$
$197$		−	8.07785i		−	0.575523i	0.957702	−	0.287761i	$-0.0929110\pi$
$198$			1.84652i			0.131227i
$199$	0.701872	−	1.21568i	0.0497544	−	0.0861771i	−0.840076	−	0.542469i	$-0.817489\pi$
$199$	0.701872	−	1.21568i	0.0497544	−	0.0861771i	0.889830	+	0.456292i	$0.150823\pi$
$200$		0			0
$201$	−3.77783			−0.266468
$202$			14.6064i			1.02770i
$203$	−23.9427	−	13.8233i	−1.68045	−	0.970208i
$204$	15.6497	+	27.1060i	1.09570	+	1.89780i
$205$		0			0
$206$	0.531103	+	0.919897i	0.0370037	+	0.0640923i
$207$	0.279890	−	0.161595i	0.0194537	−	0.0112316i
$208$			10.4348i			0.723525i
$209$	−2.90633	−	2.40062i	−0.201035	−	0.166054i
$210$		0			0
$211$	−9.45817	−	16.3820i	−0.651128	−	1.12779i	−0.982850	−	0.184409i	$-0.940963\pi$
$211$	−9.45817	−	16.3820i	−0.651128	−	1.12779i	0.331722	−	0.943377i	$-0.392370\pi$
$212$	53.3498	−	30.8015i	3.66408	−	2.11546i
$213$	2.30258	+	1.32940i	0.157770	+	0.0910888i
$214$	−8.87166	−	15.3662i	−0.606454	−	1.05041i
$215$		0			0
$216$	−56.0104			−3.81103
$217$			14.0537i			0.954030i
$218$	−15.6897	−	9.05846i	−1.06264	−	0.613516i
$219$	−5.31936	+	9.21340i	−0.359449	+	0.622584i
$220$		0			0
$221$	2.40706			0.161917
$222$	22.6803	+	13.0945i	1.52220	+	0.878843i
$223$	−13.9846	+	8.07400i	−0.936477	+	0.540675i	−0.888854	−	0.458190i	$-0.848498\pi$
$223$	−13.9846	+	8.07400i	−0.936477	+	0.540675i	−0.0476227	+	0.998865i	$0.515165\pi$
$224$	−35.3859	+	61.2901i	−2.36432	+	4.09512i
$225$		0			0
$226$	−0.406136	−	0.703448i	−0.0270157	−	0.0467926i
$227$		−	26.3186i		−	1.74683i	−0.486978	−	0.873414i	$-0.661901\pi$
$227$		−	26.3186i		−	1.74683i	0.486978	−	0.873414i	$-0.338099\pi$
$228$	23.2197	−	28.1111i	1.53776	−	1.86170i
$229$	13.3323			0.881026			0.440513	−	0.897746i	$-0.354797\pi$
$229$	13.3323			0.881026			0.440513	+	0.897746i	$0.354797\pi$
$230$		0			0
$231$	−1.83767	−	3.18294i	−0.120910	−	0.209422i
$232$	−83.6060	−	48.2700i	−5.48900	−	3.16908i
$233$	21.9186	−	12.6547i	1.43594	−	0.829038i	0.438372	−	0.898794i	$-0.355555\pi$
$233$	21.9186	−	12.6547i	1.43594	−	0.829038i	0.997564	+	0.0697556i	$0.0222220\pi$
$234$	−0.686767	+	1.18951i	−0.0448953	+	0.0777610i
$235$		0			0
$236$	13.7901			0.897658
$237$	2.35736	+	1.36102i	0.153127	+	0.0884077i
$238$	25.4596	+	14.6991i	1.65030	+	0.952801i
$239$	23.5500			1.52332			0.761660	−	0.647977i	$-0.224385\pi$
$239$	23.5500			1.52332			0.761660	+	0.647977i	$0.224385\pi$
$240$		0			0
$241$	−4.19208	+	7.26089i	−0.270035	+	0.467715i	−0.968871	−	0.247568i	$-0.920369\pi$
$241$	−4.19208	+	7.26089i	−0.270035	+	0.467715i	0.698835	+	0.715283i	$0.253702\pi$
$242$	24.4873	−	14.1378i	1.57410	−	0.908809i
$243$	−6.77601	−	3.91213i	−0.434681	−	0.250963i
$244$	17.7585	+	30.7586i	1.13687	+	1.96912i
$245$		0			0
$246$	−16.5154			−1.05298
$247$	−0.979387	−	2.62739i	−0.0623169	−	0.167177i
$248$			49.0745i			3.11623i
$249$	−5.54929	−	9.61165i	−0.351672	−	0.609113i
$250$		0			0
$251$	−9.12391	+	15.8031i	−0.575896	+	0.997481i	0.420048	+	0.907502i	$0.362013\pi$
$251$	−9.12391	+	15.8031i	−0.575896	+	0.997481i	−0.995944	+	0.0899792i	$0.971320\pi$
$252$	−10.7081	+	6.18233i	−0.674548	+	0.389450i
$253$	0.312652	+	0.180510i	0.0196563	+	0.0113486i
$254$	−24.3669			−1.52891
$255$		0			0
$256$	−32.6176	+	56.4954i	−2.03860	+	3.53096i
$257$	12.2108	+	7.04989i	0.761687	+	0.439760i	0.829901	−	0.557911i	$-0.188397\pi$
$257$	12.2108	+	7.04989i	0.761687	+	0.439760i	−0.0682144	+	0.997671i	$0.521730\pi$
$258$		−	8.46934i		−	0.527278i
$259$	18.1306			1.12658
$260$		0			0
$261$	−3.75679	−	6.50696i	−0.232540	−	0.402770i
$262$	49.9504	+	28.8389i	3.08595	+	1.78167i
$263$	−5.55184	+	3.20536i	−0.342341	+	0.197651i	−0.661307	−	0.750116i	$-0.729998\pi$
$263$	−5.55184	+	3.20536i	−0.342341	+	0.197651i	0.318966	+	0.947766i	$0.396665\pi$
$264$	−6.41700	−	11.1146i	−0.394939	−	0.684055i
$265$		0			0
$266$	5.68558	−	33.7708i	0.348605	−	2.07062i
$267$		−	6.63288i		−	0.405926i
$268$	−12.2951	+	7.09857i	−0.751042	+	0.433614i
$269$	8.99557	+	15.5808i	0.548469	+	0.949977i	0.998380	+	0.0569032i	$0.0181226\pi$
$269$	8.99557	+	15.5808i	0.548469	+	0.949977i	−0.449910	+	0.893074i	$0.648544\pi$
$270$		0			0
$271$	−5.94095	−	10.2900i	−0.360887	−	0.625075i	0.627220	−	0.778842i	$-0.284193\pi$
$271$	−5.94095	−	10.2900i	−0.360887	−	0.625075i	−0.988107	+	0.153767i	$0.950859\pi$
$272$	52.5656	+	30.3488i	3.18726	+	1.84017i
$273$		−	2.73390i		−	0.165463i
$274$	−14.3824			−0.868874
$275$		0			0
$276$	−1.74596	+	3.02409i	−0.105094	+	0.182029i
$277$		−	23.6240i		−	1.41943i	−0.704489	−	0.709715i	$-0.748824\pi$
$277$		−	23.6240i		−	1.41943i	0.704489	−	0.709715i	$-0.251176\pi$
$278$		−	29.5765i		−	1.77388i
$279$	−1.90970	+	3.30770i	−0.114331	+	0.198027i
$280$		0			0
$281$	−6.90465	+	11.9592i	−0.411897	+	0.713426i	−0.995097	−	0.0989020i	$-0.968467\pi$
$281$	−6.90465	+	11.9592i	−0.411897	+	0.713426i	0.583200	+	0.812328i	$0.301800\pi$
$282$	14.0898	−	8.13474i	0.839035	−	0.484417i
$283$	−10.1822	+	5.87868i	−0.605268	+	0.349451i	−0.771111	−	0.636701i	$-0.780299\pi$
$283$	−10.1822	+	5.87868i	−0.605268	+	0.349451i	0.165843	+	0.986152i	$0.446965\pi$
$284$	9.99179			0.592904
$285$		0			0
$286$	−1.53431			−0.0907257
$287$	−9.90181	+	5.71681i	−0.584485	+	0.337453i
$288$	−16.6569	+	9.61689i	−0.981519	+	0.566680i
$289$	−1.49927	+	2.59681i	−0.0881922	+	0.152753i
$290$		0			0
$291$	8.09675	−	14.0240i	0.474640	−	0.822100i
$292$			39.9805i			2.33968i
$293$		−	27.0576i		−	1.58072i	−0.612640	−	0.790362i	$-0.709892\pi$
$293$		−	27.0576i		−	1.58072i	0.612640	−	0.790362i	$-0.290108\pi$
$294$	2.29342	−	3.97232i	0.133755	−	0.231670i
$295$		0			0
$296$	63.3107			3.67986
$297$		−	4.86949i		−	0.282557i
$298$	35.6165	+	20.5632i	2.06321	+	1.19119i
$299$	0.134272	+	0.232566i	0.00776516	+	0.0134497i
$300$		0			0
$301$	−2.93167	−	5.07780i	−0.168979	−	0.292679i
$302$	−51.2549	+	29.5921i	−2.94939	+	1.70283i
$303$		−	7.90117i		−	0.453910i
$304$	11.7388	−	69.7256i	0.673269	−	3.99904i
$305$		0			0
$306$	3.99480	+	6.91920i	0.228368	+	0.395544i
$307$	−7.65414	+	4.41912i	−0.436845	+	0.252212i	−0.702258	−	0.711922i	$-0.747825\pi$
$307$	−7.65414	+	4.41912i	−0.436845	+	0.252212i	0.265414	+	0.964135i	$0.414492\pi$
$308$	−11.9616	−	6.90601i	−0.681573	−	0.393506i
$309$	−0.287294	−	0.497608i	−0.0163436	−	0.0283080i
$310$		0			0
$311$	−0.651493			−0.0369428			−0.0184714	−	0.999829i	$-0.505880\pi$
$311$	−0.651493			−0.0369428			−0.0184714	+	0.999829i	$0.505880\pi$
$312$		−	9.54656i		−	0.540468i
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	0.570824	−	0.821073i	$-0.306624\pi$
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	−0.425658	+	0.904884i	$0.639957\pi$
$314$	−3.35261	+	5.80690i	−0.189199	+	0.327702i
$315$		0			0
$316$	10.2295			0.575453
$317$	−8.98921	−	5.18993i	−0.504885	−	0.291495i	0.225844	−	0.974164i	$-0.427486\pi$
$317$	−8.98921	−	5.18993i	−0.504885	−	0.291495i	−0.730728	+	0.682668i	$0.760819\pi$
$318$	−39.1535	+	22.6053i	−2.19562	+	1.26764i
$319$	4.19654	−	7.26862i	0.234961	−	0.406965i
$320$		0			0
$321$	4.79903	+	8.31216i	0.267856	+	0.463939i
$322$			3.27981i			0.182777i
$323$	−16.0840	−	2.70787i	−0.894938	−	0.150670i
$324$	34.0778			1.89321
$325$		0			0
$326$	−24.5705	−	42.5574i	−1.36083	−	2.35703i
$327$	8.48718	+	4.90007i	0.469342	+	0.270975i
$328$	−34.5763	+	19.9626i	−1.90916	+	1.10225i
$329$	5.63170	−	9.75438i	0.310485	−	0.537776i
$330$		0			0
$331$	15.0922			0.829543			0.414772	−	0.909926i	$-0.363861\pi$
$331$	15.0922			0.829543			0.414772	+	0.909926i	$0.363861\pi$
$332$	−36.1207	−	20.8543i	−1.98238	−	1.14453i
$333$	4.26725	+	2.46370i	0.233844	+	0.135010i
$334$	1.11865			0.0612096
$335$		0			0
$336$	34.4696	−	59.7032i	1.88047	−	3.25708i
$337$	−13.6810	+	7.89872i	−0.745251	+	0.430271i	−0.823975	−	0.566626i	$-0.808249\pi$
$337$	−13.6810	+	7.89872i	−0.745251	+	0.430271i	0.0787246	+	0.996896i	$0.474915\pi$
$338$	30.0623	+	17.3565i	1.63517	+	0.944067i
$339$	0.219695	+	0.380522i	0.0119322	+	0.0206671i
$340$		0			0
$341$	−4.26649			−0.231043
$342$	5.92714	−	7.17575i	0.320503	−	0.388020i
$343$			16.7650i			0.905224i
$344$	−10.2371	−	17.7313i	−0.551950	−	0.956005i
$345$		0			0
$346$	−24.8511	+	43.0434i	−1.33600	+	2.31403i
$347$	18.4915	−	10.6761i	0.992676	−	0.573122i	0.0866031	−	0.996243i	$-0.472399\pi$
$347$	18.4915	−	10.6761i	0.992676	−	0.573122i	0.906073	+	0.423121i	$0.139065\pi$
$348$	70.3048	+	40.5905i	3.76873	+	2.17588i
$349$	32.3897			1.73378			0.866891	−	0.498497i	$-0.166115\pi$
$349$	32.3897			1.73378			0.866891	+	0.498497i	$0.166115\pi$
$350$		0			0
$351$	1.81108	−	3.13689i	0.0966685	−	0.167435i
$352$	−18.6067	−	10.7426i	−0.991741	−	0.572582i
$353$			0.730583i			0.0388850i	0.999811	+	0.0194425i	$0.00618913\pi$
$353$			0.730583i			0.0388850i	−0.999811	+	0.0194425i	$0.993811\pi$
$354$	−10.1206			−0.537902
$355$		0			0
$356$	−12.4632	−	21.5870i	−0.660551	−	1.14411i
$357$	−13.7721	−	7.95132i	−0.728896	−	0.420828i
$358$	48.1340	−	27.7902i	2.54396	−	1.46876i
$359$	−13.4248	−	23.2524i	−0.708533	−	1.22722i	−0.965401	−	0.260769i	$-0.916024\pi$
$359$	−13.4248	−	23.2524i	−0.708533	−	1.22722i	0.256868	−	0.966447i	$-0.417309\pi$
$360$		0			0
$361$	3.58853	+	18.6580i	0.188870	+	0.982002i
$362$			47.1919i			2.48035i
$363$	−13.2461	+	7.64766i	−0.695242	+	0.401398i
$364$	−5.13702	−	8.89759i	−0.269253	−	0.466360i
$365$		0			0
$366$	−13.0330	−	22.5738i	−0.681245	−	1.17995i
$367$	−19.8877	−	11.4822i	−1.03813	−	0.599364i	−0.118826	−	0.992915i	$-0.537913\pi$
$367$	−19.8877	−	11.4822i	−1.03813	−	0.599364i	−0.919303	+	0.393551i	$0.871246\pi$
$368$			6.77173i			0.353001i
$369$	−3.10734			−0.161761
$370$		0			0
$371$	−15.6497	+	27.1060i	−0.812491	+	1.40728i
$372$		−	41.2670i		−	2.13960i
$373$			29.5305i			1.52903i	0.644606	+	0.764515i	$0.277021\pi$
$373$			29.5305i			1.52903i	−0.644606	+	0.764515i	$0.722979\pi$
$374$	−4.46241	+	7.72912i	−0.230746	+	0.399663i
$375$		0			0
$376$	19.6654	−	34.0615i	1.01417	−	1.75659i
$377$	5.40676	−	3.12159i	0.278462	−	0.160770i
$378$	38.3118	−	22.1193i	1.97054	−	1.13769i
$379$	−17.5117			−0.899517			−0.449759	−	0.893150i	$-0.648490\pi$
$379$	−17.5117			−0.899517			−0.449759	+	0.893150i	$0.648490\pi$
$380$		0			0
$381$	13.1810			0.675282
$382$	−12.6132	+	7.28226i	−0.645350	+	0.372593i
$383$	7.02045	−	4.05326i	0.358728	−	0.207112i	−0.309794	−	0.950804i	$-0.600260\pi$
$383$	7.02045	−	4.05326i	0.358728	−	0.207112i	0.668523	+	0.743692i	$0.266927\pi$
$384$	37.1601	−	64.3631i	1.89632	−	3.28452i
$385$		0			0
$386$	−24.8272	+	43.0019i	−1.26367	+	2.18874i
$387$		−	1.59349i		−	0.0810016i
$388$		−	60.8554i		−	3.08947i
$389$	8.65392	−	14.9890i	0.438771	−	0.759974i	−0.558824	−	0.829286i	$-0.688747\pi$
$389$	8.65392	−	14.9890i	0.438771	−	0.759974i	0.997595	+	0.0693125i	$0.0220805\pi$
$390$		0			0
$391$	1.56208			0.0789976
$392$		−	11.0885i		−	0.560054i
$393$	−27.0201	−	15.6001i	−1.36298	−	0.786920i
$394$	11.1394	+	19.2940i	0.561196	+	0.972019i
$395$		0			0
$396$	−1.87686	−	3.25081i	−0.0943156	−	0.163359i
$397$	9.86354	−	5.69472i	0.495037	−	0.285810i	−0.231625	−	0.972805i	$-0.574404\pi$
$397$	9.86354	−	5.69472i	0.495037	−	0.285810i	0.726662	+	0.686996i	$0.241071\pi$
$398$			3.87155i			0.194063i
$399$	−3.07555	+	18.2679i	−0.153970	+	0.914541i
$400$		0			0
$401$	4.46930	+	7.74106i	0.223186	+	0.386570i	0.955774	−	0.294103i	$-0.0950208\pi$
$401$	4.46930	+	7.74106i	0.223186	+	0.386570i	−0.732587	+	0.680673i	$0.761687\pi$
$402$	9.02339	−	5.20966i	0.450046	−	0.259834i
$403$	−2.74844	−	1.58681i	−0.136909	−	0.0790447i
$404$	−14.8464	−	25.7146i	−0.738634	−	1.27935i
$405$		0			0
$406$	76.2500			3.78422
$407$			5.50417i			0.272832i
$408$	−48.0910	−	27.7653i	−2.38086	−	1.37459i
$409$	−3.27235	+	5.66788i	−0.161808	+	0.280259i	−0.935517	−	0.353282i	$-0.885066\pi$
$409$	−3.27235	+	5.66788i	−0.161808	+	0.280259i	0.773709	+	0.633541i	$0.218399\pi$
$410$		0			0
$411$	7.78001			0.383760
$412$	−1.87002	−	1.07966i	−0.0921293	−	0.0531909i
$413$	−6.06780	+	3.50324i	−0.298577	+	0.172383i
$414$	−0.445681	+	0.771941i	−0.0219040	+	0.0379389i
$415$		0			0
$416$	−7.99086	−	13.8406i	−0.391784	−	0.678590i
$417$			15.9991i			0.783479i
$418$	10.2523	+	1.72605i	0.501455	+	0.0844239i
$419$	−21.8441			−1.06715			−0.533576	−	0.845752i	$-0.679152\pi$
$419$	−21.8441			−1.06715			−0.533576	+	0.845752i	$0.679152\pi$
$420$		0			0
$421$	14.6717	+	25.4121i	0.715054	+	1.23851i	0.962939	+	0.269720i	$0.0869311\pi$
$421$	14.6717	+	25.4121i	0.715054	+	1.23851i	−0.247885	+	0.968789i	$0.579736\pi$
$422$	45.1819	+	26.0858i	2.19942	+	1.26984i
$423$	2.65097	−	1.53054i	0.128894	−	0.0744172i
$424$	−54.6474	+	94.6521i	−2.65391	+	4.59671i
$425$		0			0
$426$	−7.33299			−0.355285
$427$	−15.6279	−	9.02276i	−0.756286	−	0.436642i
$428$	31.2372	+	18.0348i	1.50991	+	0.871746i
$429$	0.829969			0.0400713
$430$		0			0
$431$	6.44336	−	11.1602i	0.310366	−	0.537570i	−0.668076	−	0.744093i	$-0.732882\pi$
$431$	6.44336	−	11.1602i	0.310366	−	0.537570i	0.978442	+	0.206524i	$0.0662151\pi$
$432$	79.1011	−	45.6691i	3.80576	−	2.19725i
$433$	11.9883	+	6.92144i	0.576120	+	0.332623i	0.759590	−	0.650402i	$-0.225400\pi$
$433$	11.9883	+	6.92144i	0.576120	+	0.332623i	−0.183470	+	0.983025i	$0.558733\pi$
$434$	−19.3802	−	33.5675i	−0.930280	−	1.61129i
$435$		0			0
$436$	36.8291			1.76379
$437$	−0.635578	−	1.70506i	−0.0304038	−	0.0815641i
$438$		−	29.3418i		−	1.40200i
$439$	−0.0354040	−	0.0613216i	−0.00168974	−	0.00292672i	0.865179	−	0.501463i	$-0.167205\pi$
$439$	−0.0354040	−	0.0613216i	−0.00168974	−	0.00292672i	−0.866869	+	0.498536i	$0.833871\pi$
$440$		0			0
$441$	0.431503	−	0.747384i	0.0205477	−	0.0355897i
$442$	−5.74930	+	3.31936i	−0.273466	+	0.157886i
$443$	3.28149	+	1.89457i	0.155908	+	0.0900137i	0.575924	−	0.817503i	$-0.304642\pi$
$443$	3.28149	+	1.89457i	0.155908	+	0.0900137i	−0.420016	+	0.907517i	$0.637976\pi$
$444$	−53.2384			−2.52658
$445$		0			0
$446$	22.2682	−	38.5697i	1.05443	−	1.82633i
$447$	−19.2663	−	11.1234i	−0.911266	−	0.526120i
$448$		−	102.773i		−	4.85555i
$449$	26.5765			1.25422			0.627112	−	0.778929i	$-0.284237\pi$
$449$	26.5765			1.25422			0.627112	+	0.778929i	$0.284237\pi$
$450$		0			0
$451$	−1.73553	−	3.00603i	−0.0817230	−	0.141548i
$452$	1.43001	+	0.825616i	0.0672620	+	0.0388337i
$453$	27.7258	−	16.0075i	1.30267	−	0.752098i
$454$	36.2936	+	62.8624i	1.70334	+	2.95028i
$455$		0			0
$456$	−10.7396	+	63.7902i	−0.502927	+	2.98725i
$457$			33.1523i			1.55080i	0.631471	+	0.775400i	$0.282452\pi$
$457$			33.1523i			1.55080i	−0.631471	+	0.775400i	$0.717548\pi$
$458$	−31.8445	+	18.3854i	−1.48799	+	0.859094i
$459$	−10.5348	−	18.2467i	−0.491720	−	0.851684i
$460$		0			0
$461$	9.62679	+	16.6741i	0.448364	+	0.776590i	0.998280	−	0.0586304i	$-0.0186734\pi$
$461$	9.62679	+	16.6741i	0.448364	+	0.776590i	−0.549915	+	0.835220i	$0.685340\pi$
$462$	8.77861	+	5.06833i	0.408418	+	0.235800i
$463$			39.1713i			1.82044i	0.414120	+	0.910222i	$0.364089\pi$
$463$			39.1713i			1.82044i	−0.414120	+	0.910222i	$0.635911\pi$
$464$	157.431			7.30855
$465$		0			0
$466$	−34.9019	+	60.4519i	−1.61680	+	2.80038i
$467$			39.0650i			1.80771i	0.427836	+	0.903856i	$0.359276\pi$
$467$			39.0650i			1.80771i	−0.427836	+	0.903856i	$0.640724\pi$
$468$		−	2.79220i		−	0.129069i
$469$	3.60665	−	6.24691i	0.166540	−	0.288455i
$470$		0			0
$471$	1.81356	−	3.14118i	0.0835644	−	0.144738i
$472$	−21.1882	+	12.2330i	−0.975268	+	0.563071i
$473$	1.54154	−	0.890007i	0.0708800	−	0.0409226i
$474$	−7.50743			−0.344828
$475$		0			0
$476$	−59.7623			−2.73920
$477$	−7.36666	+	4.25314i	−0.337296	+	0.194738i
$478$	−56.2493	+	32.4756i	−2.57279	+	1.48540i
$479$	−12.3775	+	21.4385i	−0.565543	+	0.979550i	0.431455	+	0.902134i	$0.358000\pi$
$479$	−12.3775	+	21.4385i	−0.565543	+	0.979550i	−0.996999	+	0.0774158i	$0.975333\pi$
$480$		0			0
$481$	−2.04714	+	3.54574i	−0.0933413	+	0.161672i
$482$		−	23.1236i		−	1.05325i
$483$		−	1.77418i		−	0.0807280i
$484$	−28.7400	+	49.7792i	−1.30637	+	2.26269i
$485$		0			0
$486$	21.5794			0.978863
$487$		−	21.8871i		−	0.991797i	−0.868380	−	0.495899i	$-0.834839\pi$
$487$		−	21.8871i		−	0.991797i	0.868380	−	0.495899i	$-0.165161\pi$
$488$	−54.5713	−	31.5067i	−2.47033	−	1.42624i
$489$	13.2911	+	23.0209i	0.601046	+	1.04104i
$490$		0			0
$491$	−4.69777	−	8.13677i	−0.212007	−	0.367207i	0.740335	−	0.672238i	$-0.234667\pi$
$491$	−4.69777	−	8.13677i	−0.212007	−	0.367207i	−0.952343	+	0.305030i	$0.901333\pi$
$492$	29.0754	−	16.7867i	1.31082	−	0.756803i
$493$		−	36.3155i		−	1.63557i
$494$	5.96247	+	4.92498i	0.268264	+	0.221585i
$495$		0			0
$496$	−40.0137	−	69.3058i	−1.79667	−	3.11192i
$497$	−4.39650	+	2.53832i	−0.197210	+	0.113859i
$498$	26.5091	+	15.3050i	1.18790	+	0.685834i
$499$	12.4558	+	21.5740i	0.557596	+	0.965785i	0.997696	+	0.0678367i	$0.0216097\pi$
$499$	12.4558	+	21.5740i	0.557596	+	0.965785i	−0.440100	+	0.897949i	$0.645057\pi$
$500$		0			0
$501$	−0.605119			−0.0270347
$502$		−	50.3278i		−	2.24624i
$503$	27.1222	+	15.6590i	1.20932	+	0.698200i	0.962610	−	0.270890i	$-0.0873181\pi$
$503$	27.1222	+	15.6590i	1.20932	+	0.698200i	0.246707	+	0.969090i	$0.420651\pi$
$504$	10.9686	−	18.9981i	0.488579	−	0.846244i
$505$		0			0
$506$	−0.995699			−0.0442642
$507$	−16.2619	−	9.38878i	−0.722214	−	0.416971i
$508$	42.8980	−	24.7672i	1.90329	−	1.09887i
$509$	−4.83310	+	8.37117i	−0.214223	+	0.371045i	−0.953032	−	0.302870i	$-0.902055\pi$
$509$	−4.83310	+	8.37117i	−0.214223	+	0.371045i	0.738809	+	0.673915i	$0.235389\pi$
$510$		0			0
$511$	−10.1567	−	17.5919i	−0.449305	−	0.778219i
$512$		−	80.2896i		−	3.54833i
$513$	−15.6306	+	18.9233i	−0.690106	+	0.835484i
$514$	−38.8874			−1.71525
$515$		0			0
$516$	8.60848	+	14.9103i	0.378967	+	0.656390i
$517$	2.96127	+	1.70969i	0.130237	+	0.0751922i
$518$	−43.3052	+	25.0023i	−1.90272	+	1.09854i
$519$	13.4429	−	23.2839i	0.590080	−	1.02205i
$520$		0			0
$521$	−0.982633			−0.0430499			−0.0215250	−	0.999768i	$-0.506852\pi$
$521$	−0.982633			−0.0430499			−0.0215250	+	0.999768i	$0.506852\pi$
$522$	17.9463	+	10.3613i	0.785488	+	0.453502i
$523$	−34.3993	−	19.8604i	−1.50418	−	0.868436i	−0.999988	−	0.00484172i	$-0.998459\pi$
$523$	−34.3993	−	19.8604i	−1.50418	−	0.868436i	−0.504187	−	0.863594i	$-0.668208\pi$
$524$	−117.251			−5.12212
$525$		0			0
$526$	8.84043	−	15.3121i	0.385461	−	0.667638i
$527$	−15.9872	+	9.23020i	−0.696413	+	0.402074i
$528$	18.1249	+	10.4644i	0.788786	+	0.455406i
$529$	−11.4129	−	19.7677i	−0.496211	−	0.859463i
$530$		0			0
$531$	−1.90417			−0.0826337
$532$	24.3161	+	65.2327i	1.05424	+	2.82820i
$533$		−	2.58195i		−	0.111837i
$534$	9.14680	+	15.8427i	0.395821	+	0.685582i
$535$		0			0
$536$	12.5941	−	21.8137i	0.543984	−	0.942208i
$537$	−26.0376	+	15.0328i	−1.12360	+	0.648713i
$538$	−42.9720	−	24.8099i	−1.85266	−	1.06963i
$539$	0.964024			0.0415234
$540$		0			0
$541$	−15.3887	+	26.6541i	−0.661614	+	1.14595i	0.318577	+	0.947897i	$0.396795\pi$
$541$	−15.3887	+	26.6541i	−0.661614	+	1.14595i	−0.980191	+	0.198052i	$0.936538\pi$
$542$	28.3801	+	16.3852i	1.21903	+	0.703807i
$543$		−	25.5280i		−	1.09551i
$544$	−92.9629			−3.98575
$545$		0			0
$546$	3.77007	+	6.52996i	0.161344	+	0.279456i
$547$	−15.4722	−	8.93287i	−0.661543	−	0.381942i	0.131322	−	0.991340i	$-0.458078\pi$
$547$	−15.4722	−	8.93287i	−0.661543	−	0.381942i	−0.792865	+	0.609398i	$0.791411\pi$
$548$	25.3203	−	14.6187i	1.08163	−	0.624480i
$549$	−2.45213	−	4.24722i	−0.104654	−	0.181267i
$550$		0			0
$551$	−39.6397	+	14.7761i	−1.68871	+	0.629482i
$552$		−	6.19529i		−	0.263689i
$553$	−4.50109	+	2.59870i	−0.191406	+	0.110508i
$554$	32.5777	+	56.4263i	1.38409	+	2.39732i
$555$		0			0
$556$	30.0624	+	52.0696i	1.27493	+	2.20824i
$557$	−9.22971	−	5.32878i	−0.391075	−	0.225787i	0.291551	−	0.956555i	$-0.405829\pi$
$557$	−9.22971	−	5.32878i	−0.391075	−	0.225787i	−0.682626	+	0.730768i	$0.739162\pi$
$558$		−	10.5340i		−	0.445939i
$559$	1.32406			0.0560019
$560$		0			0
$561$	2.41389	−	4.18098i	0.101915	−	0.176521i
$562$		−	38.0863i		−	1.60657i
$563$			7.75961i			0.327029i	0.986541	+	0.163514i	$0.0522830\pi$
$563$			7.75961i			0.327029i	−0.986541	+	0.163514i	$0.947717\pi$
$564$	−16.5368	+	28.6425i	−0.696324	+	1.20607i
$565$		0			0
$566$	16.2135	−	28.0826i	0.681504	−	1.18040i
$567$	−14.9946	+	8.65716i	−0.629716	+	0.363567i
$568$	−15.3522	+	8.86361i	−0.644165	+	0.371909i
$569$	−5.72754			−0.240111			−0.120056	−	0.992767i	$-0.538307\pi$
$569$	−5.72754			−0.240111			−0.120056	+	0.992767i	$0.538307\pi$
$570$		0			0
$571$	−20.8347			−0.871903			−0.435952	−	0.899970i	$-0.643588\pi$
$571$	−20.8347			−0.871903			−0.435952	+	0.899970i	$0.643588\pi$
$572$	2.70116	−	1.55952i	0.112941	−	0.0652067i
$573$	6.82300	−	3.93926i	0.285035	−	0.164565i
$574$	15.7671	−	27.3093i	0.658104	−	1.13987i
$575$		0			0
$576$	13.9654	−	24.1887i	0.581890	−	1.00786i
$577$			5.11190i			0.212811i	0.994323	+	0.106406i	$0.0339342\pi$
$577$			5.11190i			0.212811i	−0.994323	+	0.106406i	$0.966066\pi$
$578$		−	8.27001i		−	0.343987i
$579$	13.4300	−	23.2614i	0.558131	−	0.966712i
$580$		0			0
$581$	21.1914			0.879167
$582$			44.6619i			1.85130i
$583$	−8.22896	−	4.75099i	−0.340809	−	0.196766i
$584$	−35.4663	−	61.4294i	−1.46760	−	2.54197i
$585$		0			0
$586$	37.3127	+	64.6275i	1.54137	+	2.66974i
$587$	9.23984	−	5.33462i	0.381369	−	0.220184i	−0.297045	−	0.954864i	$-0.596001\pi$
$587$	9.23984	−	5.33462i	0.381369	−	0.220184i	0.678414	+	0.734680i	$0.262668\pi$
$588$			9.32439i			0.384531i
$589$	16.5800	+	13.6950i	0.683165	+	0.564292i
$590$		0			0
$591$	−6.02574	−	10.4369i	−0.247866	−	0.429316i
$592$	−89.4110	+	51.6215i	−3.67477	+	2.12163i
$593$	14.7247	+	8.50133i	0.604673	+	0.349108i	0.770878	−	0.636983i	$-0.219818\pi$
$593$	14.7247	+	8.50133i	0.604673	+	0.349108i	−0.166205	+	0.986091i	$0.553151\pi$
$594$	6.71507	+	11.6308i	0.275523	+	0.477219i
$595$		0			0
$596$	−83.6040			−3.42455
$597$		−	2.09427i		−	0.0857128i
$598$	−0.641421	−	0.370325i	−0.0262297	−	0.0151437i
$599$	14.3375	−	24.8334i	0.585816	−	1.01466i	−0.408957	−	0.912554i	$-0.634107\pi$
$599$	14.3375	−	24.8334i	0.585816	−	1.01466i	0.994773	−	0.102110i	$-0.0325592\pi$
$600$		0			0
$601$	27.4370			1.11918			0.559590	−	0.828770i	$-0.310959\pi$
$601$	27.4370			1.11918			0.559590	+	0.828770i	$0.310959\pi$
$602$	14.0046	+	8.08559i	0.570787	+	0.329544i
$603$	1.69773	−	0.980187i	0.0691371	−	0.0399163i
$604$	60.1564	−	104.194i	2.44773	−	4.23959i
$605$		0			0
$606$	10.8958	+	18.8720i	0.442611	+	0.766624i
$607$			17.7547i			0.720639i	0.932829	+	0.360320i	$0.117332\pi$
$607$			17.7547i			0.720639i	−0.932829	+	0.360320i	$0.882668\pi$
$608$	37.8248	+	101.472i	1.53400	+	4.11524i
$609$	−41.2466			−1.67140
$610$		0			0
$611$	1.27175	+	2.20274i	0.0514496	+	0.0891133i
$612$	−14.0657	−	8.12086i	−0.568574	−	0.328266i
$613$	29.9983	−	17.3196i	1.21162	−	0.699530i	0.248509	−	0.968629i	$-0.420059\pi$
$613$	29.9983	−	17.3196i	1.21162	−	0.699530i	0.963112	+	0.269099i	$0.0867260\pi$
$614$	12.1880	−	21.1102i	0.491868	−	0.851940i
$615$		0			0
$616$	24.5050			0.987334
$617$	3.86740	+	2.23284i	0.155696	+	0.0898909i	0.575824	−	0.817574i	$-0.304681\pi$
$617$	3.86740	+	2.23284i	0.155696	+	0.0898909i	−0.420128	+	0.907465i	$0.638015\pi$
$618$	1.37241	+	0.792362i	0.0552065	+	0.0318735i
$619$	17.9112			0.719913			0.359957	−	0.932969i	$-0.382791\pi$
$619$	17.9112			0.719913			0.359957	+	0.932969i	$0.382791\pi$
$620$		0			0
$621$	1.17531	−	2.03570i	0.0471636	−	0.0816898i
$622$	1.55610	−	0.898414i	0.0623939	−	0.0360231i
$623$	10.9679	+	6.33234i	0.439421	+	0.253700i
$624$	7.78396	+	13.4822i	0.311608	+	0.539720i
$625$		0			0
$626$	−8.17906			−0.326901
$627$	−5.54586	−	0.933688i	−0.221480	−	0.0372879i
$628$		−	13.6308i		−	0.543927i
$629$	11.9078	+	20.6250i	0.474796	+	0.822371i
$630$		0			0
$631$	−2.48440	+	4.30311i	−0.0989026	+	0.171304i	−0.911231	−	0.411896i	$-0.864867\pi$
$631$	−2.48440	+	4.30311i	−0.0989026	+	0.171304i	0.812328	+	0.583201i	$0.198200\pi$
$632$	−15.7174	+	9.07446i	−0.625205	+	0.360963i
$633$	−24.4407	−	14.1108i	−0.971429	−	0.560855i
$634$	28.6278			1.13696
$635$		0			0
$636$	45.9534	−	79.5935i	1.82217	−	3.15609i
$637$	0.621016	+	0.358544i	0.0246056	+	0.0142060i
$638$			23.1483i			0.916449i
$639$	−1.37969			−0.0545796
$640$		0			0
$641$	18.9760	+	32.8675i	0.749508	+	1.29819i	0.948059	+	0.318096i	$0.103043\pi$
$641$	18.9760	+	32.8675i	0.749508	+	1.29819i	−0.198550	+	0.980091i	$0.563623\pi$
$642$	−22.9251	−	13.2358i	−0.904780	−	0.522375i
$643$	30.5276	−	17.6251i	1.20389	−	0.695067i	0.242473	−	0.970158i	$-0.422042\pi$
$643$	30.5276	−	17.6251i	1.20389	−	0.695067i	0.961418	+	0.275092i	$0.0887082\pi$
$644$	−3.33370	−	5.77413i	−0.131366	−	0.227533i
$645$		0			0
$646$	42.1510	−	15.7122i	1.65841	−	0.618188i
$647$		−	35.5219i		−	1.39651i	−0.715850	−	0.698254i	$-0.753960\pi$
$647$		−	35.5219i		−	1.39651i	0.715850	−	0.698254i	$-0.246040\pi$
$648$	−52.3601	+	30.2301i	−2.05690	+	1.18755i
$649$	−1.06353	−	1.84209i	−0.0417471	−	0.0723082i
$650$		0			0
$651$	10.4835	+	18.1580i	0.410881	+	0.711667i
$652$	86.5130	+	49.9483i	3.38811	+	1.95613i
$653$			8.02411i			0.314008i	0.987598	+	0.157004i	$0.0501835\pi$
$653$			8.02411i			0.314008i	−0.987598	+	0.157004i	$0.949816\pi$
$654$	−27.0290			−1.05692
$655$		0			0
$656$	32.5538	−	56.3848i	1.27101	−	2.20146i
$657$		−	5.52059i		−	0.215379i
$658$			31.0646i			1.21102i
$659$	−23.6098	+	40.8933i	−0.919706	+	1.59298i	−0.119844	+	0.992793i	$0.538240\pi$
$659$	−23.6098	+	40.8933i	−0.919706	+	1.59298i	−0.799861	+	0.600185i	$0.795094\pi$
$660$		0			0
$661$	13.0580	−	22.6171i	0.507896	−	0.879702i	−0.492062	−	0.870560i	$-0.663757\pi$
$661$	13.0580	−	22.6171i	0.507896	−	0.879702i	0.999958	−	0.00914181i	$-0.00290997\pi$
$662$	−36.0479	+	20.8123i	−1.40104	+	0.808892i
$663$	3.11002	−	1.79557i	0.120783	−	0.0697342i
$664$	73.9986			2.87170
$665$		0			0
$666$	−13.5898			−0.526596
$667$	3.50874	−	2.02577i	0.135859	−	0.0784383i
$668$	−1.96938	+	1.13702i	−0.0761978	+	0.0439928i
$669$	−12.0458	+	20.8639i	−0.465716	+	0.806643i
$670$		0			0
$671$	2.73917	−	4.74437i	0.105744	−	0.183154i
$672$			105.586i			4.07306i
$673$			15.3820i			0.592931i	0.955044	+	0.296466i	$0.0958080\pi$
$673$			15.3820i			0.592931i	−0.955044	+	0.296466i	$0.904192\pi$
$674$	21.7848	−	37.7324i	0.839119	−	1.45340i
$675$		0			0
$676$	−70.5664			−2.71409
$677$		−	24.4763i		−	0.940701i	−0.882480	−	0.470350i	$-0.844128\pi$
$677$		−	24.4763i		−	0.940701i	0.882480	−	0.470350i	$-0.155872\pi$
$678$	−1.04949	−	0.605921i	−0.0403053	−	0.0232703i
$679$	15.4598	+	26.7771i	0.593291	+	1.02761i
$680$		0			0
$681$	−19.6326	−	34.0047i	−0.752324	−	1.30306i
$682$	10.1906	−	5.88352i	0.390217	−	0.225292i
$683$		−	17.8502i		−	0.683018i	−0.939879	−	0.341509i	$-0.889062\pi$
$683$		−	17.8502i		−	0.683018i	0.939879	−	0.341509i	$-0.110938\pi$
$684$	−3.14113	+	18.6575i	−0.120104	+	0.713386i
$685$		0			0
$686$	−23.1191	−	40.0434i	−0.882689	−	1.52886i
$687$	17.2259	−	9.94538i	0.657210	−	0.379440i
$688$	28.9150	+	16.6941i	1.10237	+	0.636455i
$689$	−3.53402	−	6.12110i	−0.134635	−	0.233195i
$690$		0			0
$691$	−9.27242			−0.352739			−0.176370	−	0.984324i	$-0.556435\pi$
$691$	−9.27242			−0.352739			−0.176370	+	0.984324i	$0.556435\pi$
$692$		−	101.038i		−	3.84087i
$693$	1.65168	+	0.953597i	0.0627421	+	0.0362241i
$694$	−29.4448	+	50.9999i	−1.11771	+	1.93593i
$695$		0			0
$696$	−144.030			−5.45943
$697$	−13.0066	−	7.50937i	−0.492660	−	0.284438i
$698$	−77.3633	+	44.6657i	−2.92824	+	1.69062i
$699$	18.8798	−	32.7008i	0.714100	−	1.23686i
$700$		0			0
$701$	3.84453	+	6.65892i	0.145206	+	0.251504i	0.929450	−	0.368949i	$-0.120282\pi$
$701$	3.84453	+	6.65892i	0.145206	+	0.251504i	−0.784244	+	0.620453i	$0.786949\pi$
$702$			9.98999i			0.377048i
$703$	17.6678	−	21.3897i	0.666354	−	0.806728i
$704$	31.2001			1.17590
$705$		0			0
$706$	−1.00748	−	1.74501i	−0.0379170	−	0.0656742i
$707$	13.0651	+	7.54316i	0.491365	+	0.283690i
$708$	17.8173	−	10.2868i	0.669616	−	0.386603i
$709$	12.2187	−	21.1635i	0.458885	−	0.794812i	−0.540018	−	0.841654i	$-0.681582\pi$
$709$	12.2187	−	21.1635i	0.458885	−	0.794812i	0.998902	+	0.0468421i	$0.0149158\pi$
$710$		0			0
$711$	−1.41251			−0.0529732
$712$	38.2992	+	22.1120i	1.43532	+	0.828683i
$713$	−1.78361	−	1.02977i	−0.0667968	−	0.0385652i
$714$	43.8597			1.64141
$715$		0			0
$716$	−56.4935	+	97.8496i	−2.11126	+	3.65681i
$717$	30.4275	−	17.5673i	1.13633	−	0.656063i
$718$	64.1305	+	37.0258i	2.39333	+	1.38179i
$719$	−11.0563	−	19.1501i	−0.412331	−	0.714178i	0.582813	−	0.812606i	$-0.301952\pi$
$719$	−11.0563	−	19.1501i	−0.412331	−	0.714178i	−0.995144	+	0.0984282i	$0.968619\pi$
$720$		0			0
$721$	1.09711			0.0408584
$722$	−34.3008	−	39.6163i	−1.27655	−	1.47437i
$723$			12.5085i			0.465195i
$724$	−47.9672	−	83.0817i	−1.78269	−	3.08771i
$725$		0			0
$726$	21.0924	−	36.5331i	0.782812	−	1.35587i
$727$	25.1575	−	14.5247i	0.933042	−	0.538692i	0.0452694	−	0.998975i	$-0.485585\pi$
$727$	25.1575	−	14.5247i	0.933042	−	0.538692i	0.887772	+	0.460283i	$0.152252\pi$
$728$	15.7859	+	9.11400i	0.585065	+	0.337787i
$729$	−29.9075			−1.10768
$730$		0			0
$731$	3.85092	−	6.66999i	0.142431	−	0.246698i
$732$	45.8893	+	26.4942i	1.69612	+	0.979254i
$733$			14.5428i			0.537151i	0.963259	+	0.268576i	$0.0865529\pi$
$733$			14.5428i			0.537151i	−0.963259	+	0.268576i	$0.913447\pi$
$734$	63.3360			2.33777
$735$		0			0
$736$	−5.18571	−	8.98191i	−0.191148	−	0.331078i
$737$	1.89646	+	1.09492i	0.0698570	+	0.0403320i
$738$	7.42191	−	4.28504i	0.273204	−	0.157735i
$739$	−2.37798	−	4.11878i	−0.0874754	−	0.151512i	0.818968	−	0.573839i	$-0.194547\pi$
$739$	−2.37798	−	4.11878i	−0.0874754	−	0.151512i	−0.906443	+	0.422327i	$0.861213\pi$
$740$		0			0
$741$	−3.22533	−	2.66411i	−0.118486	−	0.0978687i
$742$		−	86.3242i		−	3.16906i
$743$	5.08968	−	2.93853i	0.186722	−	0.107804i	−0.403725	−	0.914880i	$-0.632285\pi$
$743$	5.08968	−	2.93853i	0.186722	−	0.107804i	0.590447	+	0.807076i	$0.298951\pi$
$744$	36.6076	+	63.4062i	1.34210	+	2.32458i
$745$		0			0
$746$	−40.7228	−	70.5339i	−1.49097	−	2.58243i
$747$	4.98763	+	2.87961i	0.182488	+	0.105359i
$748$		−	18.1429i		−	0.663370i
$749$	−18.3263			−0.669629
$750$		0			0
$751$	−0.810481	+	1.40379i	−0.0295749	+	0.0512252i	−0.880434	−	0.474169i	$-0.842749\pi$
$751$	−0.810481	+	1.40379i	−0.0295749	+	0.0512252i	0.850859	+	0.525394i	$0.176082\pi$
$752$			64.1382i			2.33888i
$753$			27.2243i			0.992107i
$754$	−8.60941	+	14.9119i	−0.313536	+	0.543060i
$755$		0			0
$756$	−44.9654	+	77.8824i	−1.63538	+	2.83255i
$757$	24.3470	−	14.0567i	0.884907	−	0.510901i	0.0126336	−	0.999920i	$-0.495978\pi$
$757$	24.3470	−	14.0567i	0.884907	−	0.510901i	0.872273	+	0.489019i	$0.162645\pi$
$758$	41.8270	−	24.1488i	1.51922	−	0.877125i
$759$	0.538612			0.0195504
$760$		0			0
$761$	20.1663			0.731027			0.365514	−	0.930806i	$-0.380893\pi$
$761$	20.1663			0.731027			0.365514	+	0.930806i	$0.380893\pi$
$762$	−31.4829	+	18.1767i	−1.14051	+	0.658472i
$763$	−16.2052	+	9.35610i	−0.586669	+	0.338713i
$764$	14.8038	−	25.6409i	0.535583	−	0.927656i
$765$		0			0
$766$	−11.1790	+	19.3625i	−0.403912	+	0.699597i
$767$		−	1.58221i		−	0.0571303i
$768$			97.3257i			3.51194i
$769$	22.6524	−	39.2350i	0.816865	−	1.41485i	−0.0911160	−	0.995840i	$-0.529043\pi$
$769$	22.6524	−	39.2350i	0.816865	−	1.41485i	0.907981	−	0.419011i	$-0.137623\pi$
$770$		0			0
$771$	21.0357			0.757583
$772$		−	100.940i		−	3.63292i
$773$	17.4731	+	10.0881i	0.628462	+	0.362843i	0.780156	−	0.625585i	$-0.215139\pi$
$773$	17.4731	+	10.0881i	0.628462	+	0.362843i	−0.151694	+	0.988428i	$0.548473\pi$
$774$	2.19744	+	3.80607i	0.0789852	+	0.136806i
$775$		0			0
$776$	53.9842	+	93.5034i	1.93792	+	3.35658i
$777$	23.4255	−	13.5247i	0.840385	−	0.485196i
$778$			47.7353i			1.71139i
$779$	−2.90461	+	17.2526i	−0.104068	+	0.618138i
$780$		0			0
$781$	−0.770594	−	1.33471i	−0.0275740	−	0.0477596i
$782$	−3.73104	+	2.15411i	−0.133422	+	0.0770310i
$783$	−47.3264	−	27.3239i	−1.69131	−	0.976478i
$784$	9.04120	+	15.6598i	0.322900	+	0.559279i
$785$		0			0
$786$	86.0505			3.06932
$787$			46.1385i			1.64466i	0.569010	+	0.822331i	$0.307327\pi$
$787$			46.1385i			1.64466i	−0.569010	+	0.822331i	$0.692673\pi$
$788$	−39.2220	−	22.6448i	−1.39723	−	0.806689i
$789$	−4.78213	+	8.28289i	−0.170248	+	0.294879i
$790$		0			0
$791$	−0.838961			−0.0298300
$792$	5.76753	+	3.32988i	0.204940	+	0.118322i
$793$	3.52910	−	2.03753i	0.125322	−	0.0723546i
$794$	−15.7061	+	27.2038i	−0.557389	+	0.965427i
$795$		0			0
$796$	−3.93515	−	6.81588i	−0.139478	−	0.241583i
$797$			1.86497i			0.0660606i	0.999454	+	0.0330303i	$0.0105158\pi$
$797$			1.86497i			0.0660606i	−0.999454	+	0.0330303i	$0.989484\pi$
$798$	−17.8457	−	47.8744i	−0.631729	−	1.69474i
$799$	14.7951			0.523414
$800$		0			0
$801$	1.72095	+	2.98078i	0.0608069	+	0.105321i
$802$	−21.3500	−	12.3264i	−0.753894	−	0.435261i
$803$	5.34061	−	3.08340i	0.188466	−	0.108811i
$804$	−10.5905	+	18.3433i	−0.373498	+	0.646917i
$805$		0			0
$806$	8.75290			0.308308
$807$	23.2453	+	13.4207i	0.818272	+	0.472429i
$808$	45.6224	+	26.3401i	1.60499	+	0.926641i
$809$	−18.2267			−0.640816			−0.320408	−	0.947280i	$-0.603820\pi$
$809$	−18.2267			−0.640816			−0.320408	+	0.947280i	$0.603820\pi$
$810$		0			0
$811$	10.4890	−	18.1674i	0.368317	−	0.637944i	−0.620986	−	0.783822i	$-0.713267\pi$
$811$	10.4890	−	18.1674i	0.368317	−	0.637944i	0.989303	+	0.145878i	$0.0466008\pi$
$812$	−134.239	+	77.5027i	−4.71085	+	2.71981i
$813$	−15.3519	−	8.86342i	−0.538414	−	0.310854i
$814$	−7.59030	−	13.1468i	−0.266040	−	0.460794i
$815$		0			0
$816$	90.5558			3.17009
$817$	−8.84739	−	1.48953i	−0.309531	−	0.0521119i
$818$		−	18.0504i		−	0.631118i
$819$	0.709332	+	1.22860i	0.0247861	+	0.0429307i
$820$		0			0
$821$	11.0433	−	19.1276i	0.385415	−	0.667558i	−0.606412	−	0.795151i	$-0.707392\pi$
$821$	11.0433	−	19.1276i	0.385415	−	0.667558i	0.991827	+	0.127593i	$0.0407251\pi$
$822$	−18.5827	+	10.7287i	−0.648145	+	0.374207i
$823$	−13.8364	−	7.98847i	−0.482308	−	0.278461i	0.239070	−	0.971002i	$-0.423157\pi$
$823$	−13.8364	−	7.98847i	−0.482308	−	0.278461i	−0.721378	+	0.692542i	$0.756491\pi$
$824$	3.83101			0.133460
$825$		0			0
$826$	9.66200	−	16.7351i	0.336184	−	0.582288i
$827$	42.6092	+	24.6004i	1.48167	+	0.855441i	0.999784	−	0.0207946i	$-0.00661961\pi$
$827$	42.6092	+	24.6004i	1.48167	+	0.855441i	0.481883	+	0.876235i	$0.339953\pi$
$828$		−	1.81201i		−	0.0629717i
$829$	35.8564			1.24534			0.622672	−	0.782483i	$-0.286047\pi$
$829$	35.8564			1.24534			0.622672	+	0.782483i	$0.286047\pi$
$830$		0			0
$831$	−17.6226	−	30.5232i	−0.611320	−	1.05884i
$832$	20.0989	+	11.6041i	0.696803	+	0.402300i
$833$	3.61234	−	2.08559i	0.125160	−	0.0722613i
$834$	−22.0629	−	38.2140i	−0.763975	−	1.32324i
$835$		0			0
$836$	−19.8036	+	7.38199i	−0.684922	+	0.255311i
$837$			27.7794i			0.960195i
$838$	52.1748	−	30.1232i	1.80235	−	1.04059i
$839$	−12.7415	−	22.0689i	−0.439885	−	0.761903i	0.557795	−	0.829979i	$-0.311648\pi$
$839$	−12.7415	−	22.0689i	−0.439885	−	0.761903i	−0.997680	+	0.0680753i	$0.978314\pi$
$840$		0			0
$841$	−32.5957	−	56.4574i	−1.12399	−	1.94681i
$842$	−70.0870	−	40.4647i	−2.41536	−	1.39451i
$843$			20.6024i			0.709583i
$844$	−106.057			−3.65065
$845$		0			0
$846$	−4.22124	+	7.31141i	−0.145129	+	0.251371i
$847$		−	29.2046i		−	1.00348i
$848$		−	178.231i		−	6.12047i
$849$	−8.77051	+	15.1910i	−0.301003	+	0.521353i
$850$		0			0
$851$	−1.32850	+	2.30103i	−0.0455404	+	0.0788782i
$852$	12.9098	−	7.45347i	0.442282	−	0.255352i
$853$	−49.5039	+	28.5811i	−1.69498	+	0.978598i	−0.744600	+	0.667511i	$0.767360\pi$
$853$	−49.5039	+	28.5811i	−1.69498	+	0.978598i	−0.950382	+	0.311087i	$0.899307\pi$
$854$	49.7698			1.70309
$855$		0			0
$856$	−63.9940			−2.18727
$857$	−22.6876	+	13.0987i	−0.774993	+	0.447442i	−0.834653	−	0.550776i	$-0.814332\pi$
$857$	−22.6876	+	13.0987i	−0.774993	+	0.447442i	0.0596598	+	0.998219i	$0.480998\pi$
$858$	−1.98239	+	1.14453i	−0.0676777	+	0.0390737i
$859$	−8.87246	+	15.3675i	−0.302724	+	0.524334i	−0.976752	−	0.214372i	$-0.931229\pi$
$859$	−8.87246	+	15.3675i	−0.302724	+	0.524334i	0.674028	+	0.738706i	$0.264563\pi$
$860$		0			0
$861$	−8.52902	+	14.7727i	−0.290668	+	0.503452i
$862$			35.5418i			1.21056i
$863$			25.0867i			0.853960i	0.904261	+	0.426980i	$0.140422\pi$
$863$			25.0867i			0.853960i	−0.904261	+	0.426980i	$0.859578\pi$
$864$	−69.9456	+	121.149i	−2.37960	+	4.12158i
$865$		0			0
$866$	−38.1789			−1.29737
$867$			4.47357i			0.151930i
$868$	68.2380	+	39.3972i	2.31615	+	1.33723i
$869$	−0.788924	−	1.36646i	−0.0267624	−	0.0463539i
$870$		0			0
$871$	0.814457	+	1.41068i	0.0275968	+	0.0477991i
$872$	−56.5874	+	32.6707i	−1.91629	+	1.10637i
$873$			8.40305i			0.284400i
$874$	3.86938	+	3.19609i	0.130884	+	0.108109i
$875$		0			0
$876$	29.8238	+	51.6563i	1.00765	+	1.74531i
$877$	−8.67383	+	5.00784i	−0.292895	+	0.169103i	−0.639246	−	0.769002i	$-0.720754\pi$
$877$	−8.67383	+	5.00784i	−0.292895	+	0.169103i	0.346352	+	0.938105i	$0.387420\pi$
$878$	0.169126	+	0.0976449i	0.00570772	+	0.00329536i
$879$	−20.1839	−	34.9595i	−0.680786	−	1.17916i
$880$		0			0
$881$	33.3473			1.12350			0.561750	−	0.827307i	$-0.310128\pi$
$881$	33.3473			1.12350			0.561750	+	0.827307i	$0.310128\pi$
$882$			2.38018i			0.0801449i
$883$	23.6919	+	13.6785i	0.797296	+	0.460319i	0.842525	−	0.538658i	$-0.181068\pi$
$883$	23.6919	+	13.6785i	0.797296	+	0.460319i	−0.0452288	+	0.998977i	$0.514402\pi$
$884$	6.74778	−	11.6875i	0.226953	−	0.393093i
$885$		0			0
$886$	−10.4505			−0.351092
$887$	14.8640	+	8.58172i	0.499084	+	0.288146i	0.728335	−	0.685221i	$-0.240294\pi$
$887$	14.8640	+	8.58172i	0.499084	+	0.288146i	−0.229251	+	0.973367i	$0.573628\pi$
$888$	81.7999	−	47.2272i	2.74503	−	1.58484i
$889$	−12.5837	+	21.7957i	−0.422045	+	0.731004i
$890$		0			0
$891$	−2.62818	−	4.55213i	−0.0880472	−	0.152502i
$892$			90.5363i			3.03138i
$893$	−6.01985	−	16.1494i	−0.201447	−	0.540419i
$894$	61.3571			2.05209
$895$		0			0
$896$	70.9526	+	122.894i	2.37036	+	4.10559i
$897$	0.346970	+	0.200323i	0.0115850	+	0.00668859i
$898$	−63.4783	+	36.6492i	−2.11830	+	1.22300i
$899$	−23.9403	+	41.4659i	−0.798455	+	1.38296i
$900$		0			0
$901$	−41.1136			−1.36969
$902$	8.29068	+	4.78663i	0.276049	+	0.159377i
$903$	−7.57566	−	4.37381i	−0.252102	−	0.145551i
$904$	−2.92958			−0.0974364
$905$		0			0
$906$	−44.1489	+	76.4682i	−1.46675	+	2.54049i
$907$	−2.61631	+	1.51053i	−0.0868732	+	0.0501563i	−0.542807	−	0.839857i	$-0.682639\pi$
$907$	−2.61631	+	1.51053i	−0.0868732	+	0.0501563i	0.455934	+	0.890014i	$0.349305\pi$
$908$	−127.790	−	73.7797i	−4.24087	−	2.44847i
$909$	2.05002	+	3.55074i	0.0679948	+	0.117770i
$910$		0			0
$911$	−19.5682			−0.648324			−0.324162	−	0.946002i	$-0.605082\pi$
$911$	−19.5682			−0.648324			−0.324162	+	0.946002i	$0.605082\pi$
$912$	−36.8454	−	98.8449i	−1.22007	−	3.27308i
$913$			6.43336i			0.212913i
$914$	−45.7173	−	79.1847i	−1.51219	−	2.61920i
$915$		0			0
$916$	37.3749	−	64.7353i	1.23490	−	2.13891i
$917$	51.5916	−	29.7864i	1.70371	−	0.983635i
$918$	50.3248	+	29.0550i	1.66096	+	0.958959i
$919$	1.81420			0.0598448			0.0299224	−	0.999552i	$-0.490474\pi$
$919$	1.81420			0.0598448			0.0299224	+	0.999552i	$0.490474\pi$
$920$		0			0
$921$	−6.59297	+	11.4194i	−0.217246	+	0.376280i
$922$	−45.9874	−	26.5508i	−1.51452	−	0.874406i
$923$		−	1.14641i		−	0.0377346i
$924$	−20.6064			−0.677901
$925$		0			0
$926$	−54.0175	−	93.5611i	−1.77513	−	3.07461i
$927$	0.258217	+	0.149081i	0.00848095	+	0.00489648i
$928$	−208.814	+	120.559i	−6.85465	+	3.95753i
$929$	−11.2377	−	19.4643i	−0.368698	−	0.638603i	0.620665	−	0.784076i	$-0.286863\pi$
$929$	−11.2377	−	19.4643i	−0.368698	−	0.638603i	−0.989362	+	0.145473i	$0.953530\pi$
$930$		0			0
$931$	−3.74628	−	3.09442i	−0.122780	−	0.101415i
$932$		−	141.901i		−	4.64813i
$933$	−0.841755	+	0.485987i	−0.0275578	+	0.0159105i
$934$	−53.8710	−	93.3072i	−1.76271	−	3.05311i
$935$		0			0
$936$	2.47693	+	4.29017i	0.0809610	+	0.140229i
$937$	47.6647	+	27.5193i	1.55714	+	0.899015i	0.997529	+	0.0702593i	$0.0223827\pi$
$937$	47.6647	+	27.5193i	1.55714	+	0.899015i	0.559611	+	0.828756i	$0.310951\pi$
$938$			19.8944i			0.649576i
$939$	4.42437			0.144384
$940$		0			0
$941$	6.09781	−	10.5617i	0.198783	−	0.344302i	−0.749351	−	0.662173i	$-0.769635\pi$
$941$	6.09781	−	10.5617i	0.198783	−	0.344302i	0.948134	+	0.317871i	$0.102968\pi$
$942$			10.0036i			0.325937i
$943$		−	1.67557i		−	0.0545640i
$944$	19.9488	−	34.5524i	0.649279	−	1.12458i
$945$		0			0
$946$	−2.45465	+	4.25159i	−0.0798077	+	0.138231i
$947$	−26.3537	+	15.2153i	−0.856381	+	0.494432i	−0.862799	−	0.505548i	$-0.831290\pi$
$947$	−26.3537	+	15.2153i	−0.856381	+	0.494432i	0.00641783	+	0.999979i	$0.497957\pi$
$948$	13.2169	−	7.63077i	0.429264	−	0.247836i
$949$	4.58717			0.148906
$950$		0			0
$951$	−15.4859			−0.502164
$952$	91.8239	−	53.0146i	2.97603	−	1.71821i
$953$	13.6293	−	7.86891i	0.441498	−	0.254899i	−0.262735	−	0.964868i	$-0.584624\pi$
$953$	13.6293	−	7.86891i	0.441498	−	0.254899i	0.704233	+	0.709969i	$0.251291\pi$
$954$	11.7302	−	20.3174i	0.379780	−	0.657799i
$955$		0			0
$956$	66.0182	−	114.347i	2.13518	−	3.69824i
$957$		−	12.5218i		−	0.404772i
$958$		−	68.2748i		−	2.20586i
$959$	−7.42750	+	12.8648i	−0.239846	+	0.415426i
$960$		0			0
$961$	−6.66065			−0.214860
$962$		−	11.2921i		−	0.364071i
$963$	−4.31331	−	2.49029i	−0.138994	−	0.0802484i
$964$	23.5035	+	40.7093i	0.756997	+	1.31116i
$965$		0			0
$966$	2.44661	+	4.23765i	0.0787183	+	0.136344i
$967$	−26.5326	+	15.3186i	−0.853232	+	0.492614i	−0.861740	−	0.507350i	$-0.830625\pi$
$967$	−26.5326	+	15.3186i	−0.853232	+	0.492614i	0.00850791	+	0.999964i	$0.497292\pi$
$968$		−	101.980i		−	3.27776i
$969$	−22.8011	+	8.49934i	−0.732478	+	0.273038i
$970$		0			0
$971$	−8.23824	−	14.2690i	−0.264378	−	0.457915i	0.703023	−	0.711167i	$-0.251833\pi$
$971$	−8.23824	−	14.2690i	−0.264378	−	0.457915i	−0.967400	+	0.253252i	$0.918500\pi$
$972$	−37.9907	+	21.9340i	−1.21855	+	0.703532i
$973$	−26.4556	−	15.2742i	−0.848128	−	0.489667i
$974$	30.1824	+	52.2775i	0.967108	+	1.67508i
$975$		0			0
$976$	102.758			3.28921
$977$			2.77995i			0.0889383i	0.999011	+	0.0444692i	$0.0141596\pi$
$977$			2.77995i			0.0889383i	−0.999011	+	0.0444692i	$0.985840\pi$
$978$	−63.4921	−	36.6572i	−2.03025	−	1.17217i
$979$	−1.92240	+	3.32969i	−0.0614401	+	0.106417i
$980$		0			0
$981$	−5.08545			−0.162366
$982$	22.4413	+	12.9565i	0.716132	+	0.413459i
$983$	−1.48239	+	0.855856i	−0.0472808	+	0.0272976i	−0.523454	−	0.852054i	$-0.675357\pi$
$983$	−1.48239	+	0.855856i	−0.0472808	+	0.0272976i	0.476173	+	0.879351i	$0.342023\pi$
$984$	−29.7826	+	51.5850i	−0.949436	+	1.64447i
$985$		0			0
$986$	50.0794	+	86.7401i	1.59485	+	2.76237i
$987$		−	16.8041i		−	0.534879i
$988$	−15.5029	−	2.61003i	−0.493212	−	0.0830360i
$989$	0.859257			0.0273228
$990$		0			0
$991$	4.83711	+	8.37811i	0.153656	+	0.266140i	0.932569	−	0.360992i	$-0.117562\pi$
$991$	4.83711	+	8.37811i	0.153656	+	0.266140i	−0.778913	+	0.627132i	$0.784229\pi$
$992$	106.147	+	61.2840i	3.37017	+	1.94577i
$993$	19.4997	−	11.2582i	0.618805	−	0.357267i
$994$	7.00073	−	12.1256i	0.222050	−	0.384601i
$995$		0			0
$996$	−62.2259			−1.97170
$997$	19.6857	+	11.3656i	0.623454	+	0.359951i	0.778212	−	0.628001i	$-0.216127\pi$
$997$	19.6857	+	11.3656i	0.623454	+	0.359951i	−0.154759	+	0.987952i	$0.549460\pi$
$998$	−59.5015	−	34.3532i	−1.88349	−	1.08743i
$999$	35.8380			1.13386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.c.349.1		16
5.2	odd	4		95.2.e.c.26.1	yes	8
5.3	odd	4		475.2.e.e.26.4		8
5.4	even	2	inner	475.2.j.c.349.8		16
15.2	even	4		855.2.k.h.406.4		8
19.11	even	3	inner	475.2.j.c.49.8		16
20.7	even	4		1520.2.q.o.881.3		8
95.7	odd	12		1805.2.a.o.1.4		4
95.12	even	12		1805.2.a.i.1.1		4
95.49	even	6	inner	475.2.j.c.49.1		16
95.68	odd	12		475.2.e.e.201.4		8
95.83	odd	12		9025.2.a.bg.1.1		4
95.87	odd	12		95.2.e.c.11.1	✓	8
95.88	even	12		9025.2.a.bp.1.4		4
285.182	even	12		855.2.k.h.676.4		8
380.87	even	12		1520.2.q.o.961.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.1	✓	8	95.87	odd	12
95.2.e.c.26.1	yes	8	5.2	odd	4
475.2.e.e.26.4		8	5.3	odd	4
475.2.e.e.201.4		8	95.68	odd	12
475.2.j.c.49.1		16	95.49	even	6	inner
475.2.j.c.49.8		16	19.11	even	3	inner
475.2.j.c.349.1		16	1.1	even	1	trivial
475.2.j.c.349.8		16	5.4	even	2	inner
855.2.k.h.406.4		8	15.2	even	4
855.2.k.h.676.4		8	285.182	even	12
1520.2.q.o.881.3		8	20.7	even	4
1520.2.q.o.961.3		8	380.87	even	12
1805.2.a.i.1.1		4	95.12	even	12
1805.2.a.o.1.4		4	95.7	odd	12
9025.2.a.bg.1.1		4	95.83	odd	12
9025.2.a.bp.1.4		4	95.88	even	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} +O(q^{10})\)	\(q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} -0.864801 q^{11} -8.36467i q^{12} +(-0.557098 - 0.321640i) q^{13} +(-3.92829 - 6.80401i) q^{14} +(-8.11063 - 14.0480i) q^{16} +(-3.24054 + 1.87093i) q^{17} -2.13520i q^{18} +(3.36069 + 2.77592i) q^{19} +(2.12497 + 3.68055i) q^{21} +(2.06559 - 1.19257i) q^{22} +(-0.361531 - 0.208730i) q^{23} +(7.42021 + 12.8522i) q^{24} +1.77418 q^{26} +5.63077i q^{27} +(13.8316 + 7.98566i) q^{28} +(-4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(21.5156 + 12.4220i) q^{32} +(-1.11736 + 0.645106i) q^{33} +(5.16005 - 8.93746i) q^{34} +(2.17028 + 3.75903i) q^{36} -6.36467i q^{37} +(-11.8551 - 1.99589i) q^{38} -0.959723 q^{39} +(2.00686 + 3.47598i) q^{41} +(-10.1510 - 5.86069i) q^{42} +(-1.78254 + 1.02915i) q^{43} +(-2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-3.42423 - 1.97698i) q^{47} +(-20.9585 - 12.1004i) q^{48} -1.11474 q^{49} +(-2.79127 + 4.83462i) q^{51} +(-3.12345 + 1.80333i) q^{52} +(9.51544 + 5.49374i) q^{53} +(-7.76487 - 13.4492i) q^{54} -28.3360 q^{56} +(6.41287 + 1.07966i) q^{57} -26.7672i q^{58} +(1.22980 + 2.13007i) q^{59} +(-3.16740 + 5.48609i) q^{61} +(-11.7837 + 6.80333i) q^{62} +(-1.90989 - 1.10268i) q^{63} -36.0778 q^{64} +(1.77921 - 3.08169i) q^{66} +(-2.19295 - 1.26610i) q^{67} +20.9793i q^{68} -0.622817 q^{69} +(0.891065 + 1.54337i) q^{71} +(-6.66920 - 3.85046i) q^{72} +(-6.17554 + 3.56545i) q^{73} +(8.77693 + 15.2021i) q^{74} +(22.8996 - 8.53606i) q^{76} -2.46350i q^{77} +(2.29231 - 1.32347i) q^{78} +(0.912262 + 1.58008i) q^{79} +(3.03905 + 5.26380i) q^{81} +(-9.58681 - 5.53495i) q^{82} -7.43913i q^{83} +23.8279 q^{84} +(2.83841 - 4.91626i) q^{86} +14.4794i q^{87} -8.60235i q^{88} +(2.22294 - 3.85024i) q^{89} +(0.916237 - 1.58697i) q^{91} +(-2.02698 + 1.17028i) q^{92} +(6.37427 - 3.68018i) q^{93} +10.9051 q^{94} +37.0653 q^{96} +(9.39996 - 5.42707i) q^{97} +(2.66256 - 1.53723i) q^{98} +(0.334755 - 0.579813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9	\( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49} - 44 q^{51} - 68 q^{54} - 164 q^{56} - 10 q^{59} - 224 q^{64} + 62 q^{66} + 36 q^{69} - 40 q^{71} + 50 q^{74} + 126 q^{76} + 34 q^{79} - 24 q^{81} + 80 q^{84} - 16 q^{86} + 22 q^{89} - 12 q^{91} + 124 q^{94} + 84 q^{96} + 76 q^{99}+O(q^{100}) \) 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * q^99

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