LMFDB - Embedded newform 475.2.e.d.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$-1.25351 - 2.17114i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.d.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25351 - 2.17114i) q^{2} +(0.610938 + 1.05818i) q^{3} +(-2.14257 + 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876 q^{7} +5.72889 q^{8} +(0.753509 - 1.30512i) q^{9} +O(q^{10})$	\(q+(-1.25351 - 2.17114i) q^{2} +(0.610938 + 1.05818i) q^{3} +(-2.14257 + 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876 q^{7} +5.72889 q^{8} +(0.753509 - 1.30512i) q^{9} -0.778124 q^{11} -5.23591 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.278124 - 0.481725i) q^{14} +(-2.89608 - 5.01616i) q^{16} +(3.53865 + 6.12912i) q^{17} -3.77812 q^{18} +(1.33281 + 4.15013i) q^{19} +(0.135553 + 0.234784i) q^{21} +(0.975385 + 1.68942i) q^{22} +(4.03865 - 6.99515i) q^{23} +(3.50000 + 6.06218i) q^{24} +12.5351 q^{26} +5.50702 q^{27} +(-0.475385 + 0.823392i) q^{28} +(-0.110938 + 0.192150i) q^{29} +2.50702 q^{31} +(-1.53163 + 2.65287i) q^{32} +(-0.475385 - 0.823392i) q^{33} +(8.87147 - 15.3658i) q^{34} +(3.22889 + 5.59261i) q^{36} +1.90466 q^{37} +(7.33983 - 8.09596i) q^{38} -6.10938 q^{39} +(3.61796 + 6.26648i) q^{41} +(0.339833 - 0.588608i) q^{42} +(3.64959 + 6.32128i) q^{43} +(1.66719 - 2.88765i) q^{44} -20.2500 q^{46} +(-1.39608 + 2.41808i) q^{47} +(3.53865 - 6.12912i) q^{48} -6.95077 q^{49} +(-4.32379 + 7.48903i) q^{51} +(-10.7129 - 18.5552i) q^{52} +(2.19024 - 3.79361i) q^{53} +(-6.90310 - 11.9565i) q^{54} +1.27111 q^{56} +(-3.57730 + 3.94583i) q^{57} +0.556248 q^{58} +(1.39608 + 2.41808i) q^{59} +(6.29216 - 10.8983i) q^{61} +(-3.14257 - 5.44309i) q^{62} +(0.167186 - 0.289574i) q^{63} -3.90466 q^{64} +(-1.19180 + 2.06426i) q^{66} +(-5.28514 + 9.15414i) q^{67} -30.3273 q^{68} +9.86946 q^{69} +(4.92070 + 8.52289i) q^{71} +(4.31678 - 7.47687i) q^{72} +(-7.03865 - 12.1913i) q^{73} +(-2.38750 - 4.13528i) q^{74} +(-18.2570 - 3.94583i) q^{76} -0.172647 q^{77} +(7.65817 + 13.2643i) q^{78} +(-0.792161 - 1.37206i) q^{79} +(1.10392 + 1.91204i) q^{81} +(9.07028 - 15.7102i) q^{82} +9.52106 q^{83} -1.16172 q^{84} +(9.14959 - 15.8476i) q^{86} -0.271105 q^{87} -4.45779 q^{88} +(-1.57028 + 2.71981i) q^{89} +(-0.554690 + 0.960752i) q^{91} +(17.3062 + 29.9752i) q^{92} +(1.53163 + 2.65287i) q^{93} +7.00000 q^{94} -3.74293 q^{96} +(-3.18122 - 5.51004i) q^{97} +(8.71286 + 15.0911i) q^{98} +(-0.586324 + 1.01554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9	$ 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26} + 16 q^{27} + 11 q^{28} + 2 q^{29} - 2 q^{31} - 6 q^{32} + 11 q^{33} + 25 q^{34} - 3 q^{36} + 4 q^{37} + 19 q^{38} - 10 q^{39} + 2 q^{41} - 23 q^{42} - q^{43} + 18 q^{44} - 48 q^{46} + 6 q^{47} + q^{48} - 14 q^{49} + 6 q^{51} - 35 q^{52} + 11 q^{53} - 10 q^{54} + 30 q^{56} + 19 q^{57} + 14 q^{58} - 6 q^{59} + 9 q^{61} - 13 q^{62} + 9 q^{63} - 16 q^{64} - 29 q^{66} - 20 q^{67} - 68 q^{68} - 10 q^{69} + 29 q^{71} + 11 q^{72} - 22 q^{73} + 7 q^{74} - 19 q^{76} + 32 q^{77} + 30 q^{78} + 24 q^{79} + 21 q^{81} + 31 q^{82} + 6 q^{83} - 56 q^{84} + 32 q^{86} - 24 q^{87} + 18 q^{88} + 14 q^{89} + 10 q^{91} + 41 q^{92} + 6 q^{93} + 42 q^{94} + 34 q^{96} + 7 q^{97} + 23 q^{98} + 13 q^{99}+O(q^{100}) $ 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9 - 10 * q^11 + 8 * q^12 - 15 * q^13 - 7 * q^14 - 3 * q^16 + q^17 - 28 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^23 + 21 * q^24 - 10 * q^26 + 16 * q^27 + 11 * q^28 + 2 * q^29 - 2 * q^31 - 6 * q^32 + 11 * q^33 + 25 * q^34 - 3 * q^36 + 4 * q^37 + 19 * q^38 - 10 * q^39 + 2 * q^41 - 23 * q^42 - q^43 + 18 * q^44 - 48 * q^46 + 6 * q^47 + q^48 - 14 * q^49 + 6 * q^51 - 35 * q^52 + 11 * q^53 - 10 * q^54 + 30 * q^56 + 19 * q^57 + 14 * q^58 - 6 * q^59 + 9 * q^61 - 13 * q^62 + 9 * q^63 - 16 * q^64 - 29 * q^66 - 20 * q^67 - 68 * q^68 - 10 * q^69 + 29 * q^71 + 11 * q^72 - 22 * q^73 + 7 * q^74 - 19 * q^76 + 32 * q^77 + 30 * q^78 + 24 * q^79 + 21 * q^81 + 31 * q^82 + 6 * q^83 - 56 * q^84 + 32 * q^86 - 24 * q^87 + 18 * q^88 + 14 * q^89 + 10 * q^91 + 41 * q^92 + 6 * q^93 + 42 * q^94 + 34 * q^96 + 7 * q^97 + 23 * q^98 + 13 * 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 $

$2$	−1.25351	−	2.17114i	−0.886365	−	1.53523i	−0.844141	−	0.536121i	$-0.819889\pi$
$2$	−1.25351	−	2.17114i	−0.886365	−	1.53523i	−0.0422238	−	0.999108i	$-0.513444\pi$
$3$	0.610938	+	1.05818i	0.352725	+	0.610938i	0.986726	−	0.162394i	$-0.0519217\pi$
$3$	0.610938	+	1.05818i	0.352725	+	0.610938i	−0.634001	+	0.773333i	$0.718588\pi$
$4$	−2.14257	+	3.71104i	−1.07129	+	1.85552i
$5$		0			0
$5$		0			0
$6$	1.53163	−	2.65287i	0.625287	−	1.08303i
$7$	0.221876			0.0838613			0.0419307	−	0.999121i	$-0.486649\pi$
$7$	0.221876			0.0838613			0.0419307	+	0.999121i	$0.486649\pi$
$8$	5.72889			2.02547
$9$	0.753509	−	1.30512i	0.251170	−	0.435039i
$10$		0			0
$11$	−0.778124			−0.234613			−0.117307	−	0.993096i	$-0.537426\pi$
$11$	−0.778124			−0.234613			−0.117307	+	0.993096i	$0.537426\pi$
$12$	−5.23591			−1.51148
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.278124	−	0.481725i	−0.0743317	−	0.128746i
$15$		0			0
$16$	−2.89608	−	5.01616i	−0.724020	−	1.25404i
$17$	3.53865	+	6.12912i	0.858249	+	1.48653i	0.873598	+	0.486649i	$0.161781\pi$
$17$	3.53865	+	6.12912i	0.858249	+	1.48653i	−0.0153485	+	0.999882i	$0.504886\pi$
$18$	−3.77812			−0.890512
$19$	1.33281	+	4.15013i	0.305769	+	0.952106i
$19$	1.33281	+	4.15013i	0.305769	+	0.952106i
$20$		0			0
$21$	0.135553	+	0.234784i	0.0295800	+	0.0512341i
$22$	0.975385	+	1.68942i	0.207953	+	0.360185i
$23$	4.03865	−	6.99515i	0.842117	−	1.45859i	−0.0459843	−	0.998942i	$-0.514642\pi$
$23$	4.03865	−	6.99515i	0.842117	−	1.45859i	0.888101	−	0.459647i	$-0.152024\pi$
$24$	3.50000	+	6.06218i	0.714435	+	1.23744i
$25$		0			0
$26$	12.5351			2.45833
$27$	5.50702			1.05983
$28$	−0.475385	+	0.823392i	−0.0898394	+	0.155606i
$29$	−0.110938	+	0.192150i	−0.0206007	+	0.0356814i	−0.876142	−	0.482053i	$-0.839891\pi$
$29$	−0.110938	+	0.192150i	−0.0206007	+	0.0356814i	0.855541	+	0.517735i	$0.173225\pi$
$30$		0			0
$31$	2.50702			0.450274			0.225137	−	0.974327i	$-0.427717\pi$
$31$	2.50702			0.450274			0.225137	+	0.974327i	$0.427717\pi$
$32$	−1.53163	+	2.65287i	−0.270757	+	0.468965i
$33$	−0.475385	−	0.823392i	−0.0827540	−	0.143334i
$34$	8.87147	−	15.3658i	1.52144	−	2.63522i
$35$		0			0
$36$	3.22889	+	5.59261i	0.538149	+	0.932102i
$37$	1.90466			0.313124			0.156562	−	0.987668i	$-0.449959\pi$
$37$	1.90466			0.313124			0.156562	+	0.987668i	$0.449959\pi$
$38$	7.33983	−	8.09596i	1.19068	−	1.31334i
$39$	−6.10938			−0.978284
$40$		0			0
$41$	3.61796	+	6.26648i	0.565030	+	0.978661i	0.997047	+	0.0767950i	$0.0244687\pi$
$41$	3.61796	+	6.26648i	0.565030	+	0.978661i	−0.432017	+	0.901865i	$0.642198\pi$
$42$	0.339833	−	0.588608i	0.0524374	−	0.0908242i
$43$	3.64959	+	6.32128i	0.556557	+	0.963985i	0.997781	+	0.0665881i	$0.0212113\pi$
$43$	3.64959	+	6.32128i	0.556557	+	0.963985i	−0.441223	+	0.897397i	$0.645455\pi$
$44$	1.66719	−	2.88765i	0.251338	−	0.435330i
$45$		0			0
$46$	−20.2500			−2.98569
$47$	−1.39608	+	2.41808i	−0.203639	+	0.352714i	−0.949698	−	0.313166i	$-0.898610\pi$
$47$	−1.39608	+	2.41808i	−0.203639	+	0.352714i	0.746059	+	0.665880i	$0.231944\pi$
$48$	3.53865	−	6.12912i	0.510760	−	0.884663i
$49$	−6.95077			−0.992967
$50$		0			0
$51$	−4.32379	+	7.48903i	−0.605452	+	1.04867i
$52$	−10.7129	−	18.5552i	−1.48561	−	2.57314i
$53$	2.19024	−	3.79361i	0.300853	−	0.521093i	−0.675476	−	0.737382i	$-0.736062\pi$
$53$	2.19024	−	3.79361i	0.300853	−	0.521093i	0.976329	+	0.216289i	$0.0693953\pi$
$54$	−6.90310	−	11.9565i	−0.939393	−	1.62708i
$55$		0			0
$56$	1.27111			0.169859
$57$	−3.57730	+	3.94583i	−0.473825	+	0.522637i
$58$	0.556248			0.0730389
$59$	1.39608	+	2.41808i	0.181754	+	0.314808i	0.942478	−	0.334268i	$-0.108489\pi$
$59$	1.39608	+	2.41808i	0.181754	+	0.314808i	−0.760724	+	0.649076i	$0.775156\pi$
$60$		0			0
$61$	6.29216	−	10.8983i	0.805629	−	1.39539i	−0.110237	−	0.993905i	$-0.535161\pi$
$61$	6.29216	−	10.8983i	0.805629	−	1.39539i	0.915866	−	0.401484i	$-0.131506\pi$
$62$	−3.14257	−	5.44309i	−0.399107	−	0.691274i
$63$	0.167186	−	0.289574i	0.0210634	−	0.0364829i
$64$	−3.90466			−0.488082
$65$		0			0
$66$	−1.19180	+	2.06426i	−0.146700	+	0.254093i
$67$	−5.28514	+	9.15414i	−0.645683	+	1.11836i	0.338460	+	0.940981i	$0.390094\pi$
$67$	−5.28514	+	9.15414i	−0.645683	+	1.11836i	−0.984143	+	0.177375i	$0.943239\pi$
$68$	−30.3273			−3.67772
$69$	9.86946			1.18814
$70$		0			0
$71$	4.92070	+	8.52289i	0.583979	+	1.01148i	0.995002	+	0.0998563i	$0.0318383\pi$
$71$	4.92070	+	8.52289i	0.583979	+	1.01148i	−0.411023	+	0.911625i	$0.634828\pi$
$72$	4.31678	−	7.47687i	0.508737	−	0.881158i
$73$	−7.03865	−	12.1913i	−0.823812	−	1.42688i	−0.902824	−	0.430010i	$-0.858510\pi$
$73$	−7.03865	−	12.1913i	−0.823812	−	1.42688i	0.0790121	−	0.996874i	$-0.474823\pi$
$74$	−2.38750	−	4.13528i	−0.277542	−	0.480716i
$75$		0			0
$76$	−18.2570	−	3.94583i	−2.09422	−	0.452617i
$77$	−0.172647			−0.0196750
$78$	7.65817	+	13.2643i	0.867117	+	1.50189i
$79$	−0.792161	−	1.37206i	−0.0891251	−	0.154369i	0.818016	−	0.575195i	$-0.195074\pi$
$79$	−0.792161	−	1.37206i	−0.0891251	−	0.154369i	−0.907142	+	0.420826i	$0.861740\pi$
$80$		0			0
$81$	1.10392	+	1.91204i	0.122658	+	0.212449i
$82$	9.07028	−	15.7102i	1.00165	−	1.73490i
$83$	9.52106			1.04507			0.522536	−	0.852617i	$-0.324986\pi$
$83$	9.52106			1.04507			0.522536	+	0.852617i	$0.324986\pi$
$84$	−1.16172			−0.126755
$85$		0			0
$86$	9.14959	−	15.8476i	0.986626	−	1.70889i
$87$	−0.271105			−0.0290655
$88$	−4.45779			−0.475202
$89$	−1.57028	+	2.71981i	−0.166450	+	0.288300i	−0.937169	−	0.348875i	$-0.886564\pi$
$89$	−1.57028	+	2.71981i	−0.166450	+	0.288300i	0.770719	+	0.637175i	$0.219897\pi$
$90$		0			0
$91$	−0.554690	+	0.960752i	−0.0581474	+	0.100714i
$92$	17.3062	+	29.9752i	1.80430	+	3.12513i
$93$	1.53163	+	2.65287i	0.158823	+	0.275089i
$94$	7.00000			0.721995
$95$		0			0
$96$	−3.74293			−0.382011
$97$	−3.18122	−	5.51004i	−0.323004	−	0.559460i	0.658102	−	0.752929i	$-0.271359\pi$
$97$	−3.18122	−	5.51004i	−0.323004	−	0.559460i	−0.981106	+	0.193469i	$0.938026\pi$
$98$	8.71286	+	15.0911i	0.880131	+	1.52443i
$99$	−0.586324	+	1.01554i	−0.0589277	+	0.102066i
$100$		0			0
$101$	3.69726	−	6.40385i	0.367891	−	0.637206i	−0.621344	−	0.783538i	$-0.713413\pi$
$101$	3.69726	−	6.40385i	0.367891	−	0.637206i	0.989236	+	0.146331i	$0.0467465\pi$
$102$	21.6797			2.14661
$103$	−12.2038			−1.20248			−0.601240	−	0.799069i	$-0.705326\pi$
$103$	−12.2038			−1.20248			−0.601240	+	0.799069i	$0.705326\pi$
$104$	−14.3222	+	24.8068i	−1.40441	+	2.43251i
$105$		0			0
$106$	−10.9820			−1.06666
$107$	1.63355			0.157921			0.0789607	−	0.996878i	$-0.474840\pi$
$107$	1.63355			0.157921			0.0789607	+	0.996878i	$0.474840\pi$
$108$	−11.7992	+	20.4368i	−1.13538	+	1.96653i
$109$	3.80820	+	6.59600i	0.364759	+	0.631782i	0.988738	−	0.149660i	$-0.0478179\pi$
$109$	3.80820	+	6.59600i	0.364759	+	0.631782i	−0.623978	+	0.781442i	$0.714485\pi$
$110$		0			0
$111$	1.16363	+	2.01546i	0.110447	+	0.191299i
$112$	−0.642571	−	1.11297i	−0.0607173	−	0.105165i
$113$	−12.4890			−1.17486			−0.587432	−	0.809273i	$-0.699861\pi$
$113$	−12.4890			−1.17486			−0.587432	+	0.809273i	$0.699861\pi$
$114$	13.0511	+	2.82070i	1.22235	+	0.264183i
$115$		0			0
$116$	−0.475385	−	0.823392i	−0.0441384	−	0.0764500i
$117$	3.76755	+	6.52558i	0.348310	+	0.603290i
$118$	3.50000	−	6.06218i	0.322201	−	0.558069i
$119$	0.785142	+	1.35991i	0.0719739	+	0.124662i
$120$		0			0
$121$	−10.3945			−0.944957
$122$	−31.5491			−2.85632
$123$	−4.42070	+	7.65687i	−0.398601	+	0.690397i
$124$	−5.37147	+	9.30365i	−0.482372	+	0.835493i
$125$		0			0
$126$	−0.838276			−0.0746795
$127$	−6.52106	+	11.2948i	−0.578650	+	1.00225i	0.416984	+	0.908914i	$0.363087\pi$
$127$	−6.52106	+	11.2948i	−0.578650	+	1.00225i	−0.995635	+	0.0933378i	$0.970246\pi$
$128$	7.95779	+	13.7833i	0.703376	+	1.21828i
$129$	−4.45935	+	7.72382i	−0.392624	+	0.680044i
$130$		0			0
$131$	−3.55469	−	6.15690i	−0.310575	−	0.537931i	0.667912	−	0.744240i	$-0.267188\pi$
$131$	−3.55469	−	6.15690i	−0.310575	−	0.537931i	−0.978487	+	0.206309i	$0.933855\pi$
$132$	4.07419			0.354613
$133$	0.295720	+	0.920816i	0.0256422	+	0.0798448i
$134$	26.4999			2.28924
$135$		0			0
$136$	20.2726	+	35.1131i	1.73836	+	3.01092i
$137$	2.71286	−	4.69880i	0.231775	−	0.401446i	−0.726556	−	0.687108i	$-0.758880\pi$
$137$	2.71286	−	4.69880i	0.231775	−	0.401446i	0.958331	+	0.285662i	$0.0922134\pi$
$138$	−12.3715	−	21.4280i	−1.05313	−	1.82407i
$139$	−1.78514	+	3.09196i	−0.151414	+	0.262256i	−0.931747	−	0.363107i	$-0.881716\pi$
$139$	−1.78514	+	3.09196i	−0.151414	+	0.262256i	0.780334	+	0.625363i	$0.215049\pi$
$140$		0			0
$141$	−3.41168			−0.287315
$142$	12.3363	−	21.3671i	1.03524	−	1.79308i
$143$	1.94531	−	3.36938i	0.162675	−	0.281761i
$144$	−8.72889			−0.727408
$145$		0			0
$146$	−17.6460	+	30.5638i	−1.46040	+	2.52948i
$147$	−4.24649	−	7.35514i	−0.350245	−	0.606642i
$148$	−4.08086	+	7.06826i	−0.335445	+	0.581007i
$149$	0.468367	+	0.811235i	0.0383701	+	0.0664590i	0.884573	−	0.466402i	$-0.154450\pi$
$149$	0.468367	+	0.811235i	0.0383701	+	0.0664590i	−0.846203	+	0.532861i	$0.821117\pi$
$150$		0			0
$151$	−0.971925			−0.0790942			−0.0395471	−	0.999218i	$-0.512592\pi$
$151$	−0.971925			−0.0790942			−0.0395471	+	0.999218i	$0.512592\pi$
$152$	7.63555	+	23.7757i	0.619325	+	1.92846i
$153$	10.6656			0.862265
$154$	0.216415	+	0.374841i	0.0174392	+	0.0302056i
$155$		0			0
$156$	13.0898	−	22.6722i	1.04802	−	1.81523i
$157$	1.35743	+	2.35114i	0.108335	+	0.187641i	0.915096	−	0.403237i	$-0.132115\pi$
$157$	1.35743	+	2.35114i	0.108335	+	0.187641i	−0.806761	+	0.590878i	$0.798782\pi$
$158$	−1.98596	+	3.43979i	−0.157995	+	0.273655i
$159$	5.35241			0.424474
$160$		0			0
$161$	0.896081	−	1.55206i	0.0706210	−	0.122319i
$162$	2.76755	−	4.79353i	0.217439	−	0.376615i
$163$	3.20384			0.250944			0.125472	−	0.992097i	$-0.459956\pi$
$163$	3.20384			0.250944			0.125472	+	0.992097i	$0.459956\pi$
$164$	−31.0069			−2.42123
$165$		0			0
$166$	−11.9347	−	20.6716i	−0.926315	−	1.60442i
$167$	5.11094	−	8.85240i	0.395496	−	0.685020i	−0.597668	−	0.801744i	$-0.703906\pi$
$167$	5.11094	−	8.85240i	0.395496	−	0.685020i	0.993164	+	0.116724i	$0.0372393\pi$
$168$	0.776567	+	1.34505i	0.0599134	+	0.103773i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	6.42070	+	1.38769i	0.491003	+	0.106119i
$172$	−31.2780			−2.38493
$173$	−1.33281	−	2.30850i	−0.101332	−	0.175512i	0.810902	−	0.585182i	$-0.198977\pi$
$173$	−1.33281	−	2.30850i	−0.101332	−	0.175512i	−0.912234	+	0.409670i	$0.865644\pi$
$174$	0.339833	+	0.588608i	0.0257627	+	0.0446222i
$175$		0			0
$176$	2.25351	+	3.90319i	0.169865	+	0.294214i
$177$	−1.70584	+	2.95460i	−0.128219	+	0.222081i
$178$	7.87347			0.590141
$179$	−12.9367			−0.966937			−0.483468	−	0.875362i	$-0.660623\pi$
$179$	−12.9367			−0.966937			−0.483468	+	0.875362i	$0.660623\pi$
$180$		0			0
$181$	9.30620	−	16.1188i	0.691724	−	1.19810i	−0.279548	−	0.960132i	$-0.590185\pi$
$181$	9.30620	−	16.1188i	0.691724	−	1.19810i	0.971273	−	0.237970i	$-0.0764820\pi$
$182$	2.78124			0.206159
$183$	15.3765			1.13666
$184$	23.1370	−	40.0745i	1.70568	−	2.95433i
$185$		0			0
$186$	3.83983	−	6.65079i	0.281550	−	0.487659i
$187$	−2.75351	−	4.76922i	−0.201357	−	0.348760i
$188$	−5.98240	−	10.3618i	−0.436312	−	0.755714i
$189$	1.22188			0.0888784
$190$		0			0
$191$	−23.0421			−1.66727			−0.833634	−	0.552317i	$-0.813744\pi$
$191$	−23.0421			−1.66727			−0.833634	+	0.552317i	$0.813744\pi$
$192$	−2.38550	−	4.13181i	−0.172159	−	0.298188i
$193$	−8.53865	−	14.7894i	−0.614626	−	1.06456i	−0.990450	−	0.137872i	$-0.955974\pi$
$193$	−8.53865	−	14.7894i	−0.614626	−	1.06456i	0.375824	−	0.926691i	$-0.377360\pi$
$194$	−7.97539	+	13.8138i	−0.572599	+	0.991771i
$195$		0			0
$196$	14.8925	−	25.7946i	1.06375	−	1.84247i
$197$	8.82024			0.628416			0.314208	−	0.949354i	$-0.398261\pi$
$197$	8.82024			0.628416			0.314208	+	0.949354i	$0.398261\pi$
$198$	2.93985			0.208926
$199$	1.42771	−	2.47287i	0.101208	−	0.175297i	−0.810975	−	0.585081i	$-0.801063\pi$
$199$	1.42771	−	2.47287i	0.101208	−	0.175297i	0.912183	+	0.409784i	$0.134396\pi$
$200$		0			0
$201$	−12.9156			−0.910995
$202$	−18.5382			−1.30434
$203$	−0.0246145	+	0.0426336i	−0.00172760	+	0.00299229i
$204$	−18.5281	−	32.0916i	−1.29722	−	2.24686i
$205$		0			0
$206$	15.2976	+	26.4963i	1.06584	+	1.84608i
$207$	−6.08632	−	10.5418i	−0.423029	−	0.732707i
$208$	28.9608			2.00807
$209$	−1.03709	−	3.22932i	−0.0717373	−	0.223377i
$210$		0			0
$211$	6.44375	+	11.1609i	0.443606	+	0.768348i	0.997954	−	0.0639367i	$-0.0203656\pi$
$211$	6.44375	+	11.1609i	0.443606	+	0.768348i	−0.554348	+	0.832285i	$0.687032\pi$
$212$	9.38550	+	16.2562i	0.644599	+	1.11648i
$213$	−6.01248	+	10.4139i	−0.411968	+	0.713550i
$214$	−2.04767	−	3.54667i	−0.139976	−	0.242445i
$215$		0			0
$216$	31.5491			2.14665
$217$	0.556248			0.0377606
$218$	9.54723	−	16.5363i	0.646620	−	1.11998i
$219$	8.60036	−	14.8963i	0.581159	−	1.00660i
$220$		0			0
$221$	−35.3865			−2.38035
$222$	2.91724	−	5.05280i	0.195792	−	0.339122i
$223$	10.3539	+	17.9334i	0.693346	+	1.20091i	0.970735	+	0.240153i	$0.0771978\pi$
$223$	10.3539	+	17.9334i	0.693346	+	1.20091i	−0.277389	+	0.960758i	$0.589469\pi$
$224$	−0.339833	+	0.588608i	−0.0227060	+	0.0393280i
$225$		0			0
$226$	15.6551	+	27.1153i	1.04136	+	1.80369i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$	−6.97850	−	21.7297i	−0.462162	−	1.43909i
$229$	3.53910			0.233870			0.116935	−	0.993140i	$-0.462693\pi$
$229$	3.53910			0.233870			0.116935	+	0.993140i	$0.462693\pi$
$230$		0			0
$231$	−0.105477	−	0.182691i	−0.00693986	−	0.0120202i
$232$	−0.635553	+	1.10081i	−0.0417261	+	0.0722717i
$233$	−9.89252	−	17.1344i	−0.648081	−	1.12251i	−0.983581	−	0.180468i	$-0.942239\pi$
$233$	−9.89252	−	17.1344i	−0.648081	−	1.12251i	0.335500	−	0.942040i	$-0.391095\pi$
$234$	9.44531	−	16.3598i	0.617459	−	1.06947i
$235$		0			0
$236$	−11.9648			−0.778843
$237$	0.967923	−	1.67649i	0.0628733	−	0.108900i
$238$	1.96837	−	3.40931i	0.127590	−	0.220993i
$239$	23.7741			1.53782			0.768910	−	0.639357i	$-0.220799\pi$
$239$	23.7741			1.53782			0.768910	+	0.639357i	$0.220799\pi$
$240$		0			0
$241$	2.27111	−	3.93367i	0.146295	−	0.253390i	−0.783561	−	0.621315i	$-0.786599\pi$
$241$	2.27111	−	3.93367i	0.146295	−	0.253390i	0.929855	+	0.367926i	$0.119932\pi$
$242$	13.0296	+	22.5680i	0.837576	+	1.45072i
$243$	6.91168	−	11.9714i	0.443384	−	0.767964i
$244$	26.9628	+	46.7010i	1.72612	+	2.98972i
$245$		0			0
$246$	22.1655			1.41322
$247$	−21.3026	−	4.60408i	−1.35545	−	0.292950i
$248$	14.3624			0.912016
$249$	5.81678	+	10.0750i	0.368623	+	0.638474i
$250$		0			0
$251$	9.75151	−	16.8901i	0.615510	−	1.06609i	−0.374785	−	0.927112i	$-0.622284\pi$
$251$	9.75151	−	16.8901i	0.615510	−	1.06609i	0.990295	−	0.138982i	$-0.0443832\pi$
$252$	0.716415	+	1.24087i	0.0451299	+	0.0781673i
$253$	−3.14257	+	5.44309i	−0.197572	+	0.342204i
$254$	32.6968			2.05158
$255$		0			0
$256$	16.0457	−	27.7919i	1.00285	−	1.73699i
$257$	0.882043	−	1.52774i	0.0550203	−	0.0952980i	−0.837203	−	0.546892i	$-0.815811\pi$
$257$	0.882043	−	1.52774i	0.0550203	−	0.0952980i	0.892224	+	0.451594i	$0.149144\pi$
$258$	22.3593			1.39203
$259$	0.422598			0.0262590
$260$		0			0
$261$	0.167186	+	0.289574i	0.0103485	+	0.0179242i
$262$	−8.91168	+	15.4355i	−0.550565	+	0.953607i
$263$	−3.23591	−	5.60477i	−0.199535	−	0.345605i	0.748843	−	0.662748i	$-0.230610\pi$
$263$	−3.23591	−	5.60477i	−0.199535	−	0.345605i	−0.948378	+	0.317143i	$0.897276\pi$
$264$	−2.72343	−	4.71713i	−0.167616	−	0.290319i
$265$		0			0
$266$	1.62853	−	1.79630i	0.0998518	−	0.110138i
$267$	−3.83739			−0.234844
$268$	−22.6476	−	39.2268i	−1.38342	−	2.39616i
$269$	−14.2429	−	24.6695i	−0.868407	−	1.50412i	−0.863624	−	0.504136i	$-0.831811\pi$
$269$	−14.2429	−	24.6695i	−0.868407	−	1.50412i	−0.00478280	−	0.999989i	$-0.501522\pi$
$270$		0			0
$271$	0.246491	+	0.426934i	0.0149732	+	0.0259344i	0.873415	−	0.486977i	$-0.161900\pi$
$271$	0.246491	+	0.426934i	0.0149732	+	0.0259344i	−0.858442	+	0.512911i	$0.828567\pi$
$272$	20.4964	−	35.5009i	1.24278	−	2.15256i
$273$	−1.35553			−0.0820402
$274$	−13.6024			−0.821749
$275$		0			0
$276$	−21.1460	+	36.6260i	−1.27284	+	2.20463i
$277$	8.78905			0.528083			0.264041	−	0.964511i	$-0.414944\pi$
$277$	8.78905			0.528083			0.264041	+	0.964511i	$0.414944\pi$
$278$	8.95077			0.536832
$279$	1.88906	−	3.27195i	0.113095	−	0.195887i
$280$		0			0
$281$	2.37147	−	4.10750i	0.141470	−	0.245033i	−0.786581	−	0.617488i	$-0.788151\pi$
$281$	2.37147	−	4.10750i	0.141470	−	0.245033i	0.928050	+	0.372455i	$0.121484\pi$
$282$	4.27657	+	7.40723i	0.254666	+	0.441094i
$283$	8.43473	+	14.6094i	0.501393	+	0.868438i	0.999999	+	0.00160901i	$0.000512164\pi$
$283$	8.43473	+	14.6094i	0.501393	+	0.868438i	−0.498606	+	0.866829i	$0.666155\pi$
$284$	−42.1718			−2.50243
$285$		0			0
$286$	−9.75385			−0.576758
$287$	0.802738	+	1.39038i	0.0473841	+	0.0820717i
$288$	2.30820	+	3.99792i	0.136012	+	0.235580i
$289$	−16.5441	+	28.6552i	−0.973183	+	1.68560i
$290$		0			0
$291$	3.88706	−	6.73259i	0.227864	−	0.394671i
$292$	60.3233			3.53015
$293$	−11.6336			−0.679639			−0.339820	−	0.940491i	$-0.610366\pi$
$293$	−11.6336			−0.679639			−0.339820	+	0.940491i	$0.610366\pi$
$294$	−10.6460	+	18.4395i	−0.620889	+	1.07541i
$295$		0			0
$296$	10.9116			0.634223
$297$	−4.28514			−0.248649
$298$	1.17420	−	2.03378i	0.0680198	−	0.117814i
$299$	20.1933	+	34.9758i	1.16781	+	2.02270i
$300$		0			0
$301$	0.809757	+	1.40254i	0.0466736	+	0.0808411i
$302$	1.21832	+	2.11019i	0.0701063	+	0.121428i
$303$	9.03519			0.519058
$304$	16.9578	−	18.7047i	0.972596	−	1.07279i
$305$		0			0
$306$	−13.3695	−	23.1566i	−0.764281	−	1.32377i
$307$	2.94531	+	5.10143i	0.168098	+	0.291154i	0.937751	−	0.347308i	$-0.112904\pi$
$307$	2.94531	+	5.10143i	0.168098	+	0.291154i	−0.769653	+	0.638462i	$0.779571\pi$
$308$	0.369909	−	0.640701i	0.0210775	−	0.0365073i
$309$	−7.45579	−	12.9138i	−0.424145	−	0.734641i
$310$		0			0
$311$	14.8202			0.840378			0.420189	−	0.907437i	$-0.361964\pi$
$311$	14.8202			0.840378			0.420189	+	0.907437i	$0.361964\pi$
$312$	−35.0000			−1.98148
$313$	−2.94731	+	5.10489i	−0.166592	+	0.288546i	−0.937219	−	0.348740i	$-0.886610\pi$
$313$	−2.94731	+	5.10489i	−0.166592	+	0.288546i	0.770628	+	0.637286i	$0.219943\pi$
$314$	3.40310	−	5.89434i	0.192048	−	0.332637i
$315$		0			0
$316$	6.78905			0.381914
$317$	−2.07930	+	3.60146i	−0.116785	+	0.202278i	−0.918492	−	0.395439i	$-0.870592\pi$
$317$	−2.07930	+	3.60146i	−0.116785	+	0.202278i	0.801707	+	0.597718i	$0.203926\pi$
$318$	−6.70930	−	11.6208i	−0.376239	−	0.651665i
$319$	0.0863236	−	0.149517i	0.00483319	−	0.00837133i
$320$		0			0
$321$	0.997999	+	1.72858i	0.0557029	+	0.0964802i
$322$	−4.49298			−0.250384
$323$	−20.7203	+	22.8549i	−1.15291	+	1.27168i
$324$	−9.46090			−0.525606
$325$		0			0
$326$	−4.01604	−	6.95598i	−0.222428	−	0.385256i
$327$	−4.65315	+	8.05949i	−0.257320	+	0.445691i
$328$	20.7269	+	35.9000i	1.14445	+	1.98225i
$329$	−0.309757	+	0.536515i	−0.0170775	+	0.0295790i
$330$		0			0
$331$	10.6797			0.587008			0.293504	−	0.955958i	$-0.405179\pi$
$331$	10.6797			0.587008			0.293504	+	0.955958i	$0.405179\pi$
$332$	−20.3995	+	35.3330i	−1.11957	+	1.93915i
$333$	1.43518	−	2.48580i	0.0786472	−	0.136221i
$334$	−25.6264			−1.40222
$335$		0			0
$336$	0.785142	−	1.35991i	0.0428330	−	0.0741890i
$337$	−13.1726	−	22.8157i	−0.717560	−	1.24285i	−0.961964	−	0.273177i	$-0.911926\pi$
$337$	−13.1726	−	22.8157i	−0.717560	−	1.24285i	0.244404	−	0.969673i	$-0.421408\pi$
$338$	−15.0421	+	26.0537i	−0.818183	+	1.41713i
$339$	−7.62999	−	13.2155i	−0.414404	−	0.717769i
$340$		0			0
$341$	−1.95077			−0.105640
$342$	−5.03554	−	15.6797i	−0.272291	−	0.847862i
$343$	−3.09534			−0.167133
$344$	20.9081	+	36.2139i	1.12729	+	1.95252i
$345$		0			0
$346$	−3.34139	+	5.78746i	−0.179634	+	0.311136i
$347$	−8.44175	−	14.6215i	−0.453177	−	0.784925i	0.545404	−	0.838173i	$-0.316376\pi$
$347$	−8.44175	−	14.6215i	−0.453177	−	0.784925i	−0.998581	+	0.0532476i	$0.983043\pi$
$348$	0.580862	−	1.00608i	0.0311375	−	0.0539317i
$349$	4.61640			0.247110			0.123555	−	0.992338i	$-0.460570\pi$
$349$	4.61640			0.247110			0.123555	+	0.992338i	$0.460570\pi$
$350$		0			0
$351$	−13.7675	+	23.8461i	−0.734857	+	1.27281i
$352$	1.19180	−	2.06426i	0.0635232	−	0.110025i
$353$	24.9508			1.32800			0.663998	−	0.747735i	$-0.268858\pi$
$353$	24.9508			1.32800			0.663998	+	0.747735i	$0.268858\pi$
$354$	8.55313			0.454594
$355$		0			0
$356$	−6.72889	−	11.6548i	−0.356631	−	0.617703i
$357$	−0.959347	+	1.66164i	−0.0507740	+	0.0879432i
$358$	16.2163	+	28.0875i	0.857059	+	1.48447i
$359$	−5.90110	−	10.2210i	−0.311448	−	0.539444i	0.667228	−	0.744854i	$-0.267481\pi$
$359$	−5.90110	−	10.2210i	−0.311448	−	0.539444i	−0.978676	+	0.205410i	$0.934147\pi$
$360$		0			0
$361$	−15.4472	+	11.0627i	−0.813011	+	0.582248i
$362$	−46.6616			−2.45248
$363$	−6.35041	−	10.9992i	−0.333310	−	0.577310i
$364$	−2.37693	−	4.11696i	−0.124585	−	0.215787i
$365$		0			0
$366$	−19.2746	−	33.3845i	−1.00750	−	1.74504i
$367$	13.1164	−	22.7183i	0.684670	−	1.18588i	−0.288870	−	0.957368i	$-0.593279\pi$
$367$	13.1164	−	22.7183i	0.684670	−	1.18588i	0.973540	−	0.228516i	$-0.0733872\pi$
$368$	−46.7850			−2.43884
$369$	10.9047			0.567674
$370$		0			0
$371$	0.485963	−	0.841712i	0.0252299	−	0.0436995i
$372$	−13.1265			−0.680579
$373$	−11.9960			−0.621129			−0.310565	−	0.950552i	$-0.600518\pi$
$373$	−11.9960			−0.621129			−0.310565	+	0.950552i	$0.600518\pi$
$374$	−6.90310	+	11.9565i	−0.356951	+	0.618257i
$375$		0			0
$376$	−7.99800	+	13.8529i	−0.412465	+	0.714411i
$377$	−0.554690	−	0.960752i	−0.0285680	−	0.0494812i
$378$	−1.53163	−	2.65287i	−0.0787787	−	0.136449i
$379$	0.313217			0.0160889			0.00804444	−	0.999968i	$-0.497439\pi$
$379$	0.313217			0.0160889			0.00804444	+	0.999968i	$0.497439\pi$
$380$		0			0
$381$	−15.9358			−0.816418
$382$	28.8835	+	50.0277i	1.47781	+	2.55964i
$383$	15.0441	+	26.0572i	0.768718	+	1.33146i	0.938258	+	0.345936i	$0.112439\pi$
$383$	15.0441	+	26.0572i	0.768718	+	1.33146i	−0.169540	+	0.985523i	$0.554228\pi$
$384$	−9.72343	+	16.8415i	−0.496197	+	0.859438i
$385$		0			0
$386$	−21.4066	+	37.0772i	−1.08957	+	1.88718i
$387$	11.0000			0.559161
$388$	27.2640			1.38412
$389$	17.8609	−	30.9360i	0.905583	−	1.56852i	0.0854503	−	0.996342i	$-0.472767\pi$
$389$	17.8609	−	30.9360i	0.905583	−	1.56852i	0.820133	−	0.572173i	$-0.193900\pi$
$390$		0			0
$391$	57.1655			2.89099
$392$	−39.8202			−2.01123
$393$	4.34339	−	7.52297i	0.219095	−	0.379484i
$394$	−11.0562	−	19.1500i	−0.557006	−	0.964762i
$395$		0			0
$396$	−2.51248	−	4.35174i	−0.126257	−	0.218683i
$397$	4.77657	+	8.27326i	0.239729	+	0.415223i	0.960636	−	0.277809i	$-0.0896081\pi$
$397$	4.77657	+	8.27326i	0.239729	+	0.415223i	−0.720907	+	0.693031i	$0.756275\pi$
$398$	−7.15861			−0.358829
$399$	−0.793718	+	0.875485i	−0.0397356	+	0.0438291i
$400$		0			0
$401$	−15.4418	−	26.7459i	−0.771124	−	1.33563i	−0.936947	−	0.349471i	$-0.886361\pi$
$401$	−15.4418	−	26.7459i	−0.771124	−	1.33563i	0.165823	−	0.986156i	$-0.446972\pi$
$402$	16.1898	+	28.0416i	0.807474	+	1.39859i
$403$	−6.26755	+	10.8557i	−0.312209	+	0.540761i
$404$	15.8433	+	27.4414i	0.788233	+	1.36526i
$405$		0			0
$406$	0.123418			0.00612514
$407$	−1.48206			−0.0734629
$408$	−24.7706	+	42.9039i	−1.22633	+	2.12406i
$409$	−15.7816	+	27.3345i	−0.780349	+	1.35160i	0.151389	+	0.988474i	$0.451625\pi$
$409$	−15.7816	+	27.3345i	−0.780349	+	1.35160i	−0.931738	+	0.363130i	$0.881708\pi$
$410$		0			0
$411$	6.62955			0.327012
$412$	26.1476	−	45.2890i	1.28820	−	2.23123i
$413$	0.309757	+	0.536515i	0.0152421	+	0.0264002i
$414$	−15.2585	+	26.4285i	−0.749916	+	1.29889i
$415$		0			0
$416$	−7.65817	−	13.2643i	−0.375472	−	0.650337i
$417$	−4.36245			−0.213630
$418$	−5.71130	+	6.29966i	−0.279349	+	0.308126i
$419$	−26.5070			−1.29495			−0.647476	−	0.762086i	$-0.724176\pi$
$419$	−26.5070			−1.29495			−0.647476	+	0.762086i	$0.724176\pi$
$420$		0			0
$421$	10.1180	+	17.5248i	0.493119	+	0.854107i	0.999969	−	0.00792731i	$-0.00252337\pi$
$421$	10.1180	+	17.5248i	0.493119	+	0.854107i	−0.506850	+	0.862035i	$0.669190\pi$
$422$	16.1546	−	27.9806i	0.786394	−	1.36207i
$423$	2.10392	+	3.64410i	0.102296	+	0.177182i
$424$	12.5477	−	21.7332i	0.609369	−	1.05546i
$425$		0			0
$426$	30.1468			1.46062
$427$	1.39608	−	2.41808i	0.0675611	−	0.117019i
$428$	−3.50000	+	6.06218i	−0.169179	+	0.293026i
$429$	4.75385			0.229518
$430$		0			0
$431$	5.73045	−	9.92543i	0.276026	−	0.478091i	−0.694367	−	0.719621i	$-0.744316\pi$
$431$	5.73045	−	9.92543i	0.276026	−	0.478091i	0.970394	+	0.241529i	$0.0776490\pi$
$432$	−15.9488	−	27.6241i	−0.767336	−	1.32906i
$433$	12.9734	−	22.4706i	0.623461	−	1.07987i	−0.365375	−	0.930860i	$-0.619059\pi$
$433$	12.9734	−	22.4706i	0.623461	−	1.07987i	0.988836	−	0.149006i	$-0.0476073\pi$
$434$	−0.697262	−	1.20769i	−0.0334696	−	0.0579711i
$435$		0			0
$436$	−32.6374			−1.56305
$437$	34.4136	+	7.43771i	1.64622	+	0.355794i
$438$	−43.1225			−2.06047
$439$	−12.6562	−	21.9211i	−0.604046	−	1.04624i	−0.992202	−	0.124644i	$-0.960221\pi$
$439$	−12.6562	−	21.9211i	−0.604046	−	1.04624i	0.388156	−	0.921594i	$-0.373112\pi$
$440$		0			0
$441$	−5.23747	+	9.07157i	−0.249403	+	0.431979i
$442$	44.3573	+	76.8291i	2.10986	+	3.65439i
$443$	10.0125	−	17.3421i	0.475707	−	0.823949i	−0.523905	−	0.851776i	$-0.675525\pi$
$443$	10.0125	−	17.3421i	0.475707	−	0.823949i	0.999613	+	0.0278272i	$0.00885883\pi$
$444$	−9.97262			−0.473279
$445$		0			0
$446$	25.9573	−	44.9594i	1.22912	−	2.12889i
$447$	−0.572286	+	0.991229i	−0.0270682	+	0.0468835i
$448$	−0.866350			−0.0409312
$449$	19.7601			0.932536			0.466268	−	0.884644i	$-0.345598\pi$
$449$	19.7601			0.932536			0.466268	+	0.884644i	$0.345598\pi$
$450$		0			0
$451$	−2.81522	−	4.87610i	−0.132563	−	0.229607i
$452$	26.7585	−	46.3471i	1.25862	−	2.17999i
$453$	−0.593786	−	1.02847i	−0.0278985	−	0.0483216i
$454$	5.01404	+	8.68457i	0.235320	+	0.407587i
$455$		0			0
$456$	−20.4940	+	22.6052i	−0.959719	+	1.05859i
$457$	34.4647			1.61219			0.806096	−	0.591785i	$-0.201577\pi$
$457$	34.4647			1.61219			0.806096	+	0.591785i	$0.201577\pi$
$458$	−4.43629	−	7.68388i	−0.207294	−	0.359044i
$459$	19.4874	+	33.7532i	0.909595	+	1.57546i
$460$		0			0
$461$	3.96637	+	6.86995i	0.184732	+	0.319965i	0.943486	−	0.331412i	$-0.107525\pi$
$461$	3.96637	+	6.86995i	0.184732	+	0.319965i	−0.758754	+	0.651377i	$0.774192\pi$
$462$	−0.264432	+	0.458010i	−0.0123025	+	0.0213085i
$463$	−9.25395			−0.430068			−0.215034	−	0.976607i	$-0.568986\pi$
$463$	−9.25395			−0.430068			−0.215034	+	0.976607i	$0.568986\pi$
$464$	1.28514			0.0596612
$465$		0			0
$466$	−24.8007	+	42.9561i	−1.14887	+	1.98990i
$467$	−9.47183			−0.438304			−0.219152	−	0.975691i	$-0.570329\pi$
$467$	−9.47183			−0.438304			−0.219152	+	0.975691i	$0.570329\pi$
$468$	−32.2889			−1.49256
$469$	−1.17265	+	2.03108i	−0.0541478	+	0.0937868i
$470$		0			0
$471$	−1.65861	+	2.87280i	−0.0764247	+	0.132371i
$472$	7.99800	+	13.8529i	0.368138	+	0.637633i
$473$	−2.83983	−	4.91873i	−0.130576	−	0.226164i
$474$	−4.85320			−0.222915
$475$		0			0
$476$	−6.72889			−0.308418
$477$	−3.30074	−	5.71704i	−0.151130	−	0.261765i
$478$	−29.8011	−	51.6170i	−1.36307	−	2.36091i
$479$	17.3574	−	30.0639i	0.793081	−	1.37366i	−0.130969	−	0.991386i	$-0.541809\pi$
$479$	17.3574	−	30.0639i	0.793081	−	1.37366i	0.924050	−	0.382270i	$-0.124858\pi$
$480$		0			0
$481$	−4.76164	+	8.24740i	−0.217112	+	0.376049i
$482$	−11.3874			−0.518682
$483$	2.18980			0.0996393
$484$	22.2710	−	38.5745i	1.01232	−	1.75339i
$485$		0			0
$486$	−34.6554			−1.57200
$487$	28.5070			1.29178			0.645888	−	0.763432i	$-0.276487\pi$
$487$	28.5070			1.29178			0.645888	+	0.763432i	$0.276487\pi$
$488$	36.0471	−	62.4355i	1.63178	−	2.82632i
$489$	1.95735	+	3.39022i	0.0885142	+	0.153311i
$490$		0			0
$491$	15.5949	+	27.0112i	0.703788	+	1.21900i	0.967127	+	0.254293i	$0.0818428\pi$
$491$	15.5949	+	27.0112i	0.703788	+	1.21900i	−0.263339	+	0.964703i	$0.584824\pi$
$492$	−18.9433	−	32.8108i	−0.854030	−	1.47922i
$493$	−1.57028			−0.0707221
$494$	16.7070	+	52.0223i	0.751681	+	2.34059i
$495$		0			0
$496$	−7.26053	−	12.5756i	−0.326007	−	0.564661i
$497$	1.09178	+	1.89103i	0.0489732	+	0.0848242i
$498$	14.5828	−	25.2581i	0.653469	−	1.13184i
$499$	−8.09334	−	14.0181i	−0.362308	−	0.627535i	0.626032	−	0.779797i	$-0.284678\pi$
$499$	−8.09334	−	14.0181i	−0.362308	−	0.627535i	−0.988340	+	0.152262i	$0.951344\pi$
$500$		0			0
$501$	12.4899			0.558006
$502$	−48.8944			−2.18226
$503$	8.61094	−	14.9146i	0.383943	−	0.665008i	−0.607679	−	0.794183i	$-0.707899\pi$
$503$	8.61094	−	14.9146i	0.383943	−	0.665008i	0.991622	+	0.129174i	$0.0412327\pi$
$504$	0.957790	−	1.65894i	0.0426633	−	0.0738951i
$505$		0			0
$506$	15.7570			0.700483
$507$	7.33126	−	12.6981i	0.325593	−	0.563943i
$508$	−27.9437	−	48.3998i	−1.23980	−	2.14740i
$509$	18.2956	−	31.6889i	0.810939	−	1.40459i	−0.101268	−	0.994859i	$-0.532290\pi$
$509$	18.2956	−	31.6889i	0.810939	−	1.40459i	0.912207	−	0.409729i	$-0.134377\pi$
$510$		0			0
$511$	−1.56171	−	2.70496i	−0.0690859	−	0.119660i
$512$	−48.6224			−2.14883
$513$	7.33983	+	22.8549i	0.324062	+	1.00907i
$514$	−4.42260			−0.195072
$515$		0			0
$516$	−19.1089	−	33.0976i	−0.841224	−	1.45704i
$517$	1.08632	−	1.88157i	0.0477765	−	0.0827512i
$518$	−0.529730	−	0.917520i	−0.0232750	−	0.0403135i
$519$	1.62853	−	2.82070i	0.0714847	−	0.123815i
$520$		0			0
$521$	−3.63667			−0.159325			−0.0796626	−	0.996822i	$-0.525384\pi$
$521$	−3.63667			−0.159325			−0.0796626	+	0.996822i	$0.525384\pi$
$522$	0.419138	−	0.725968i	0.0183452	−	0.0317748i
$523$	−17.8117	+	30.8507i	−0.778850	+	1.34901i	0.153756	+	0.988109i	$0.450863\pi$
$523$	−17.8117	+	30.8507i	−0.778850	+	1.34901i	−0.932605	+	0.360898i	$0.882470\pi$
$524$	30.4647			1.33086
$525$		0			0
$526$	−8.11250	+	14.0513i	−0.353722	+	0.612664i
$527$	8.87147	+	15.3658i	0.386447	+	0.669346i
$528$	−2.75351	+	4.76922i	−0.119831	+	0.207554i
$529$	−21.1214	−	36.5834i	−0.918322	−	1.59058i
$530$		0			0
$531$	4.20784			0.182605
$532$	−4.05079	−	0.875485i	−0.175624	−	0.0379571i
$533$	−36.1796			−1.56711
$534$	4.81020	+	8.33151i	0.208158	+	0.360540i
$535$		0			0
$536$	−30.2780	+	52.4431i	−1.30781	+	2.26520i
$537$	−7.90354	−	13.6893i	−0.341063	−	0.590739i
$538$	−35.7073	+	61.8469i	−1.53945	+	2.66641i
$539$	5.40856			0.232963
$540$		0			0
$541$	−1.58632	+	2.74759i	−0.0682014	+	0.118128i	−0.898110	−	0.439772i	$-0.855059\pi$
$541$	−1.58632	+	2.74759i	−0.0682014	+	0.118128i	0.829908	+	0.557900i	$0.188393\pi$
$542$	0.617957	−	1.07033i	0.0265435	−	0.0459747i
$543$	22.7420			0.975955
$544$	−21.6797			−0.929508
$545$		0			0
$546$	1.69916	+	2.94304i	0.0727175	+	0.125950i
$547$	−14.1902	+	24.5782i	−0.606731	+	1.05089i	0.385044	+	0.922898i	$0.374186\pi$
$547$	−14.1902	+	24.5782i	−0.606731	+	1.05089i	−0.991775	+	0.127991i	$0.959147\pi$
$548$	11.6250	+	20.1350i	0.496594	+	0.860127i
$549$	−9.48240	−	16.4240i	−0.404699	−	0.700959i
$550$		0			0
$551$	−0.945310	−	0.204307i	−0.0402715	−	0.00870377i
$552$	56.5411			2.40655
$553$	−0.175762	−	0.304428i	−0.00747415	−	0.0129456i
$554$	−11.0172	−	19.0823i	−0.468074	−	0.810728i
$555$		0			0
$556$	−7.64959	−	13.2495i	−0.324415	−	0.561903i
$557$	1.06527	−	1.84510i	0.0451368	−	0.0781793i	−0.842574	−	0.538580i	$-0.818961\pi$
$557$	1.06527	−	1.84510i	0.0451368	−	0.0781793i	0.887711	+	0.460401i	$0.152294\pi$
$558$	−9.47183			−0.400974
$559$	−36.4959			−1.54361
$560$		0			0
$561$	3.36445	−	5.82739i	0.142047	−	0.246033i
$562$	−11.8906			−0.501575
$563$	20.2609			0.853894			0.426947	−	0.904277i	$-0.359589\pi$
$563$	20.2609			0.853894			0.426947	+	0.904277i	$0.359589\pi$
$564$	7.30976	−	12.6609i	0.307796	−	0.533119i
$565$		0			0
$566$	21.1460	−	36.6260i	0.888834	−	1.53951i
$567$	0.244933	+	0.424237i	0.0102862	+	0.0178163i
$568$	28.1901	+	48.8268i	1.18283	+	2.04873i
$569$	−34.7530			−1.45692			−0.728460	−	0.685088i	$-0.759764\pi$
$569$	−34.7530			−1.45692			−0.728460	+	0.685088i	$0.759764\pi$
$570$		0			0
$571$	32.0702			1.34210			0.671048	−	0.741414i	$-0.265845\pi$
$571$	32.0702			1.34210			0.671048	+	0.741414i	$0.265845\pi$
$572$	8.33593	+	14.4383i	0.348543	+	0.603694i
$573$	−14.0773	−	24.3826i	−0.588088	−	1.01860i
$574$	2.01248	−	3.48572i	0.0839993	−	0.145491i
$575$		0			0
$576$	−2.94220	+	5.09603i	−0.122591	+	0.212335i
$577$	−30.2740			−1.26032			−0.630162	−	0.776464i	$-0.717012\pi$
$577$	−30.2740			−1.26032			−0.630162	+	0.776464i	$0.717012\pi$
$578$	82.9528			3.45038
$579$	10.4332	−	18.0708i	0.433588	−	0.750996i
$580$		0			0
$581$	2.11250			0.0876411
$582$	−19.4899			−0.807881
$583$	−1.70428	+	2.95190i	−0.0705841	+	0.122255i
$584$	−40.3237	−	69.8427i	−1.66861	−	2.89011i
$585$		0			0
$586$	14.5828	+	25.2581i	0.602408	+	1.04340i
$587$	1.24805	+	2.16168i	0.0515125	+	0.0892222i	0.890632	−	0.454725i	$-0.150262\pi$
$587$	1.24805	+	2.16168i	0.0515125	+	0.0892222i	−0.839119	+	0.543947i	$0.816929\pi$
$588$	36.3936			1.50085
$589$	3.34139	+	10.4045i	0.137680	+	0.428708i
$590$		0			0
$591$	5.38862	+	9.33336i	0.221658	+	0.383923i
$592$	−5.51604	−	9.55406i	−0.226708	−	0.392669i
$593$	−4.98196	+	8.62901i	−0.204585	+	0.354351i	−0.950000	−	0.312249i	$-0.898918\pi$
$593$	−4.98196	+	8.62901i	−0.204585	+	0.354351i	0.745416	+	0.666600i	$0.232251\pi$
$594$	5.37147	+	9.30365i	0.220394	+	0.381733i
$595$		0			0
$596$	−4.01404			−0.164421
$597$	3.48898			0.142794
$598$	50.6249	−	87.6849i	2.07021	−	3.58570i
$599$	−16.0351	+	27.7736i	−0.655176	+	1.13480i	0.326673	+	0.945137i	$0.394072\pi$
$599$	−16.0351	+	27.7736i	−0.655176	+	1.13480i	−0.981850	+	0.189661i	$0.939261\pi$
$600$		0			0
$601$	3.68278			0.150224			0.0751119	−	0.997175i	$-0.476069\pi$
$601$	3.68278			0.150224			0.0751119	+	0.997175i	$0.476069\pi$
$602$	2.03008	−	3.51619i	0.0827397	−	0.143309i
$603$	7.96481	+	13.7955i	0.324352	+	0.561794i
$604$	2.08242	−	3.60686i	0.0847324	−	0.146761i
$605$		0			0
$606$	−11.3257	−	19.6167i	−0.460075	−	0.796873i
$607$	20.4850			0.831460			0.415730	−	0.909488i	$-0.363526\pi$
$607$	20.4850			0.831460			0.415730	+	0.909488i	$0.363526\pi$
$608$	−13.0511	−	2.82070i	−0.529293	−	0.114395i
$609$	−0.0601518			−0.00243747
$610$		0			0
$611$	−6.98040	−	12.0904i	−0.282397	−	0.489126i
$612$	−22.8519	+	39.5806i	−0.923732	+	1.59995i
$613$	5.35587	+	9.27664i	0.216322	+	0.374680i	0.953681	−	0.300821i	$-0.0972607\pi$
$613$	5.35587	+	9.27664i	0.216322	+	0.374680i	−0.737359	+	0.675501i	$0.763927\pi$
$614$	7.38395	−	12.7894i	0.297992	−	0.516137i
$615$		0			0
$616$	−0.989077			−0.0398511
$617$	−8.86600	+	15.3564i	−0.356932	+	0.618224i	−0.987447	−	0.157953i	$-0.949511\pi$
$617$	−8.86600	+	15.3564i	−0.356932	+	0.618224i	0.630515	+	0.776177i	$0.282844\pi$
$618$	−18.6918	+	32.3751i	−0.751894	+	1.30232i
$619$	−13.2780			−0.533689			−0.266844	−	0.963740i	$-0.585981\pi$
$619$	−13.2780			−0.533689			−0.266844	+	0.963740i	$0.585981\pi$
$620$		0			0
$621$	22.2409	−	38.5224i	0.892498	−	1.54585i
$622$	−18.5773	−	32.1768i	−0.744882	−	1.29017i
$623$	−0.348409	+	0.603462i	−0.0139587	+	0.0241772i
$624$	17.6933	+	30.6456i	0.708297	+	1.22681i
$625$		0			0
$626$	14.7779			0.590645
$627$	2.78359	−	3.07034i	0.111166	−	0.122618i
$628$	−11.6336			−0.464229
$629$	6.73992	+	11.6739i	0.268738	+	0.465468i
$630$		0			0
$631$	−2.03208	+	3.51966i	−0.0808957	+	0.140115i	−0.903635	−	0.428304i	$-0.859111\pi$
$631$	−2.03208	+	3.51966i	−0.0808957	+	0.140115i	0.822739	+	0.568419i	$0.192445\pi$
$632$	−4.53821	−	7.86041i	−0.180520	−	0.312670i
$633$	−7.87347	+	13.6372i	−0.312942	+	0.542032i
$634$	10.4257			0.414058
$635$		0			0
$636$	−11.4679	+	19.8630i	−0.454733	+	0.787620i
$637$	17.3769	−	30.0977i	0.688499	−	1.19252i
$638$	−0.432830			−0.0171359
$639$	14.8312			0.586712
$640$		0			0
$641$	−2.49254	−	4.31720i	−0.0984493	−	0.170519i	0.812594	−	0.582831i	$-0.198055\pi$
$641$	−2.49254	−	4.31720i	−0.0984493	−	0.170519i	−0.911043	+	0.412311i	$0.864722\pi$
$642$	2.50200	−	4.33359i	0.0987461	−	0.171033i
$643$	−2.93829	−	5.08927i	−0.115875	−	0.200701i	0.802254	−	0.596983i	$-0.203634\pi$
$643$	−2.93829	−	5.08927i	−0.115875	−	0.200701i	−0.918129	+	0.396281i	$0.870300\pi$
$644$	3.83983	+	6.65079i	0.151311	+	0.262078i
$645$		0			0
$646$	75.5943	+	16.3380i	2.97422	+	0.642809i
$647$	−16.9757			−0.667385			−0.333692	−	0.942682i	$-0.608295\pi$
$647$	−16.9757			−0.667385			−0.333692	+	0.942682i	$0.608295\pi$
$648$	6.32424	+	10.9539i	0.248440	+	0.430310i
$649$	−1.08632	−	1.88157i	−0.0426419	−	0.0738580i
$650$		0			0
$651$	0.339833	+	0.588608i	0.0133191	+	0.0230694i
$652$	−6.86445	+	11.8896i	−0.268833	+	0.465632i
$653$	−24.6797			−0.965790			−0.482895	−	0.875678i	$-0.660415\pi$
$653$	−24.6797			−0.965790			−0.482895	+	0.875678i	$0.660415\pi$
$654$	23.3311			0.912317
$655$		0			0
$656$	20.9558	−	36.2965i	0.818186	−	1.41714i
$657$	−21.2148			−0.827667
$658$	1.55313			0.0605474
$659$	−0.943308	+	1.63386i	−0.0367461	+	0.0636461i	−0.883814	−	0.467839i	$-0.845033\pi$
$659$	−0.943308	+	1.63386i	−0.0367461	+	0.0636461i	0.847067	+	0.531485i	$0.178366\pi$
$660$		0			0
$661$	−22.3749	+	38.7545i	−0.870284	+	1.50738i	−0.00858048	+	0.999963i	$0.502731\pi$
$661$	−22.3749	+	38.7545i	−0.870284	+	1.50738i	−0.861703	+	0.507413i	$0.830602\pi$
$662$	−13.3871	−	23.1871i	−0.520303	−	0.901191i
$663$	−21.6190	−	37.4452i	−0.839611	−	1.45425i
$664$	54.5451			2.11676
$665$		0			0
$666$	−7.19603			−0.278840
$667$	0.896081	+	1.55206i	0.0346964	+	0.0600959i
$668$	21.9011	+	37.9338i	0.847379	+	1.46770i
$669$	−12.6511	+	21.9124i	−0.489122	+	0.847183i
$670$		0			0
$671$	−4.89608	+	8.48026i	−0.189011	+	0.327377i
$672$	−0.830467			−0.0320360
$673$	−25.4046			−0.979274			−0.489637	−	0.871926i	$-0.662871\pi$
$673$	−25.4046			−0.979274			−0.489637	+	0.871926i	$0.662871\pi$
$674$	−33.0241	+	57.1994i	−1.27204	+	2.20324i
$675$		0			0
$676$	51.4217			1.97776
$677$	3.86946			0.148716			0.0743578	−	0.997232i	$-0.476309\pi$
$677$	3.86946			0.148716			0.0743578	+	0.997232i	$0.476309\pi$
$678$	−19.1285	+	33.1316i	−0.734627	+	1.27241i
$679$	−0.705838	−	1.22255i	−0.0270876	−	0.0469170i
$680$		0			0
$681$	−2.44375	−	4.23270i	−0.0936448	−	0.162198i
$682$	2.44531	+	4.23540i	0.0936357	+	0.162182i
$683$	48.5171			1.85645			0.928227	−	0.372015i	$-0.121333\pi$
$683$	48.5171			1.85645			0.928227	+	0.372015i	$0.121333\pi$
$684$	−18.9066	+	20.8543i	−0.722910	+	0.797382i
$685$		0			0
$686$	3.88004	+	6.72043i	0.148141	+	0.256587i
$687$	2.16217	+	3.74499i	0.0824919	+	0.142880i
$688$	21.1390	−	36.6138i	0.805917	−	1.39589i
$689$	10.9512	+	18.9681i	0.417208	+	0.722626i
$690$		0			0
$691$	−47.6374			−1.81221			−0.906105	−	0.423052i	$-0.860959\pi$
$691$	−47.6374			−1.81221			−0.906105	+	0.423052i	$0.860959\pi$
$692$	11.4226			0.434222
$693$	−0.130091	+	0.225325i	−0.00494176	+	0.00855937i
$694$	−21.1636	+	36.6565i	−0.803360	+	1.39146i
$695$		0			0
$696$	−1.55313			−0.0588714
$697$	−25.6054	+	44.3498i	−0.969873	+	1.67987i
$698$	−5.78670	−	10.0229i	−0.219030	−	0.379371i
$699$	12.0874	−	20.9361i	0.457189	−	0.791874i
$700$		0			0
$701$	−14.2766	−	24.7277i	−0.539218	−	0.933954i	−0.998946	−	0.0458939i	$-0.985386\pi$
$701$	−14.2766	−	24.7277i	−0.539218	−	0.933954i	0.459728	−	0.888060i	$-0.347947\pi$
$702$	69.0310			2.60541
$703$	2.53855	+	7.90458i	0.0957434	+	0.298127i
$704$	3.03831			0.114510
$705$		0			0
$706$	−31.2760	−	54.1717i	−1.17709	−	2.03878i
$707$	0.820334	−	1.42086i	0.0308518	−	0.0534370i
$708$	−7.30976	−	12.6609i	−0.274717	−	0.475825i
$709$	−9.74137	+	16.8726i	−0.365845	+	0.633662i	−0.988911	−	0.148507i	$-0.952553\pi$
$709$	−9.74137	+	16.8726i	−0.365845	+	0.633662i	0.623066	+	0.782169i	$0.285887\pi$
$710$		0			0
$711$	−2.38760			−0.0895421
$712$	−8.99600	+	15.5815i	−0.337139	+	0.583942i
$713$	10.1250	−	17.5370i	0.379183	−	0.656765i
$714$	4.81020			0.180017
$715$		0			0
$716$	27.7179	−	48.0088i	1.03587	−	1.79417i
$717$	14.5245	+	25.1572i	0.542428	+	0.939513i
$718$	−14.7942	+	25.6242i	−0.552113	+	0.956288i
$719$	−2.05313	−	3.55613i	−0.0765689	−	0.132621i	0.825199	−	0.564843i	$-0.191063\pi$
$719$	−2.05313	−	3.55613i	−0.0765689	−	0.132621i	−0.901767	+	0.432221i	$0.857730\pi$
$720$		0			0
$721$	−2.70774			−0.100842
$722$	43.3819	+	19.6709i	1.61451	+	0.732074i
$723$	5.55002			0.206407
$724$	39.8784	+	69.0714i	1.48207	+	2.56702i
$725$		0			0
$726$	−15.9206	+	27.5753i	−0.590869	+	1.02341i
$727$	−6.20584	−	10.7488i	−0.230162	−	0.398652i	0.727694	−	0.685902i	$-0.240592\pi$
$727$	−6.20584	−	10.7488i	−0.230162	−	0.398652i	−0.957856	+	0.287250i	$0.907259\pi$
$728$	−3.17776	+	5.50405i	−0.117776	+	0.203994i
$729$	23.5139			0.870887
$730$		0			0
$731$	−25.8293	+	44.7376i	−0.955330	+	1.65468i
$732$	−32.9452	+	57.0628i	−1.21769	+	2.10910i
$733$	16.3985			0.605693			0.302847	−	0.953039i	$-0.402063\pi$
$733$	16.3985			0.605693			0.302847	+	0.953039i	$0.402063\pi$
$734$	−65.7661			−2.42747
$735$		0			0
$736$	12.3715	+	21.4280i	0.456018	+	0.789847i
$737$	4.11250	−	7.12305i	0.151486	−	0.262381i
$738$	−13.6691	−	23.6756i	−0.503166	−	0.871509i
$739$	23.1018	+	40.0135i	0.849814	+	1.47192i	0.881374	+	0.472419i	$0.156619\pi$
$739$	23.1018	+	40.0135i	0.849814	+	1.47192i	−0.0315597	+	0.999502i	$0.510047\pi$
$740$		0			0
$741$	−8.14267	−	25.3547i	−0.299128	−	0.931430i
$742$	−2.43664			−0.0894517
$743$	−12.4066	−	21.4888i	−0.455153	−	0.788347i	0.543544	−	0.839380i	$-0.317082\pi$
$743$	−12.4066	−	21.4888i	−0.455153	−	0.788347i	−0.998697	+	0.0510331i	$0.983749\pi$
$744$	8.77457	+	15.1980i	0.321691	+	0.557185i
$745$		0			0
$746$	15.0371	+	26.0450i	0.550547	+	0.953576i
$747$	7.17420	−	12.4261i	0.262490	−	0.454647i
$748$	23.5984			0.862841
$749$	0.362446			0.0132435
$750$		0			0
$751$	5.26955	−	9.12712i	0.192289	−	0.333054i	−0.753720	−	0.657196i	$-0.771742\pi$
$751$	5.26955	−	9.12712i	0.192289	−	0.333054i	0.946008	+	0.324142i	$0.105076\pi$
$752$	16.1726			0.589756
$753$	23.8303			0.868423
$754$	−1.39062	+	2.40862i	−0.0506434	+	0.0877169i
$755$		0			0
$756$	−2.61796	+	4.53443i	−0.0952142	+	0.164916i
$757$	−3.09836	−	5.36652i	−0.112612	−	0.195049i	0.804211	−	0.594344i	$-0.202588\pi$
$757$	−3.09836	−	5.36652i	−0.112612	−	0.195049i	−0.916823	+	0.399295i	$0.869255\pi$
$758$	−0.392621	−	0.680039i	−0.0142606	−	0.0247001i
$759$	−7.67967			−0.278754
$760$		0			0
$761$	35.6084			1.29080			0.645402	−	0.763843i	$-0.276690\pi$
$761$	35.6084			1.29080			0.645402	+	0.763843i	$0.276690\pi$
$762$	19.9757	+	34.5990i	0.723644	+	1.25339i
$763$	0.844949	+	1.46349i	0.0305892	+	0.0529820i
$764$	49.3694	−	85.5103i	1.78612	−	3.09365i
$765$		0			0
$766$	37.7159	−	65.3258i	1.36273	−	2.36032i
$767$	−13.9608			−0.504095
$768$	39.2116			1.41493
$769$	0.0777477	−	0.134663i	0.00280365	−	0.00485607i	−0.864620	−	0.502426i	$-0.832441\pi$
$769$	0.0777477	−	0.134663i	0.00280365	−	0.00485607i	0.867424	+	0.497570i	$0.165774\pi$
$770$		0			0
$771$	2.15550			0.0776283
$772$	73.1787			2.63376
$773$	−2.54411	+	4.40653i	−0.0915054	+	0.158492i	−0.908145	−	0.418656i	$-0.862501\pi$
$773$	−2.54411	+	4.40653i	−0.0915054	+	0.158492i	0.816639	+	0.577148i	$0.195835\pi$
$774$	−13.7886	−	23.8826i	−0.495621	−	0.858441i
$775$		0			0
$776$	−18.2249	−	31.5664i	−0.654236	−	1.13317i
$777$	0.258181	+	0.447183i	0.00926220	+	0.0160426i
$778$	−89.5552			−3.21071
$779$	−21.1847	+	23.3671i	−0.759020	+	0.837212i
$780$		0			0
$781$	−3.82891	−	6.63187i	−0.137009	−	0.237307i
$782$	−71.6575	−	124.114i	−2.56247	−	4.43832i
$783$	−0.610938	+	1.05818i	−0.0218331	+	0.0378161i
$784$	20.1300	+	34.8662i	0.718928	+	1.24522i
$785$		0			0
$786$	−21.7779			−0.776793
$787$	22.5070			0.802289			0.401144	−	0.916015i	$-0.368613\pi$
$787$	22.5070			0.802289			0.401144	+	0.916015i	$0.368613\pi$
$788$	−18.8980	+	32.7323i	−0.673213	+	1.16604i
$789$	3.95389	−	6.84833i	0.140762	−	0.243807i
$790$		0			0
$791$	−2.77101			−0.0985257
$792$	−3.35899	+	5.81793i	−0.119356	+	0.206731i
$793$	31.4608	+	54.4917i	1.11721	+	1.93506i
$794$	11.9749	−	20.7412i	0.424975	−	0.736078i
$795$		0			0
$796$	6.11796	+	10.5966i	0.216845	+	0.375587i
$797$	−29.2219			−1.03509			−0.517546	−	0.855655i	$-0.673154\pi$
$797$	−29.2219			−1.03509			−0.517546	+	0.855655i	$0.673154\pi$
$798$	2.89574	+	0.625847i	0.102508	+	0.0221547i
$799$	−19.7610			−0.699093
$800$		0			0
$801$	2.36645	+	4.09881i	0.0836144	+	0.144824i
$802$	−38.7128	+	67.0525i	−1.36699	+	2.36770i
$803$	5.47694	+	9.48634i	0.193277	+	0.334766i
$804$	27.6725	−	47.9303i	0.975936	−	1.69037i
$805$		0			0
$806$	31.4257			1.10692
$807$	17.4031	−	30.1431i	0.612618	−	1.06109i
$808$	21.1812	−	36.6870i	0.745153	−	1.29064i
$809$	25.8664			0.909412			0.454706	−	0.890641i	$-0.349744\pi$
$809$	25.8664			0.909412			0.454706	+	0.890641i	$0.349744\pi$
$810$		0			0
$811$	9.84841	−	17.0579i	0.345824	−	0.598985i	−0.639679	−	0.768642i	$-0.720933\pi$
$811$	9.84841	−	17.0579i	0.345824	−	0.598985i	0.985503	+	0.169657i	$0.0542660\pi$
$812$	−0.105477	−	0.182691i	−0.00370151	−	0.00641120i
$813$	−0.301181	+	0.521661i	−0.0105629	+	0.0182954i
$814$	1.85777	+	3.21776i	0.0651150	+	0.112782i
$815$		0			0
$816$	50.0882			1.75344
$817$	−21.3699	+	23.5714i	−0.747638	+	0.824658i
$818$	79.1295			2.76670
$819$	0.835929	+	1.44787i	0.0292097	+	0.0505927i
$820$		0			0
$821$	−2.04021	+	3.53375i	−0.0712038	+	0.123329i	−0.899429	−	0.437067i	$-0.856017\pi$
$821$	−2.04021	+	3.53375i	−0.0712038	+	0.123329i	0.828225	+	0.560395i	$0.189351\pi$
$822$	−8.31020	−	14.3937i	−0.289852	−	0.502038i
$823$	5.30318	−	9.18538i	0.184857	−	0.320182i	−0.758671	−	0.651474i	$-0.774151\pi$
$823$	5.30318	−	9.18538i	0.184857	−	0.320182i	0.943528	+	0.331292i	$0.107484\pi$
$824$	−69.9145			−2.43559
$825$		0			0
$826$	0.776567	−	1.34505i	0.0270202	−	0.0468004i
$827$	7.70228	−	13.3407i	0.267834	−	0.463903i	−0.700468	−	0.713684i	$-0.747025\pi$
$827$	7.70228	−	13.3407i	0.267834	−	0.463903i	0.968302	+	0.249781i	$0.0803586\pi$
$828$	52.1615			1.81274
$829$	21.2350			0.737523			0.368761	−	0.929524i	$-0.379782\pi$
$829$	21.2350			0.737523			0.368761	+	0.929524i	$0.379782\pi$
$830$		0			0
$831$	5.36956	+	9.30036i	0.186268	+	0.322626i
$832$	9.76164	−	16.9077i	0.338424	−	0.586168i
$833$	−24.5964	−	42.6021i	−0.852213	−	1.47608i
$834$	5.46837	+	9.47149i	0.189354	+	0.327971i
$835$		0			0
$836$	14.2062	+	3.07034i	0.491331	+	0.106190i
$837$	13.8062			0.477212
$838$	33.2268	+	57.5505i	1.14780	+	1.98805i
$839$	3.04567	+	5.27526i	0.105148	+	0.182122i	0.913799	−	0.406167i	$-0.133135\pi$
$839$	3.04567	+	5.27526i	0.105148	+	0.182122i	−0.808651	+	0.588289i	$0.799802\pi$
$840$		0			0
$841$	14.4754	+	25.0721i	0.499151	+	0.864555i
$842$	25.3659	−	43.9350i	0.874167	−	1.51410i
$843$	5.79528			0.199600
$844$	−55.2248			−1.90092
$845$		0			0
$846$	5.27457	−	9.13582i	0.181343	−	0.314096i
$847$	−2.30630			−0.0792453
$848$	−25.3725			−0.871295
$849$	−10.3062	+	17.8509i	−0.353708	+	0.612640i
$850$		0			0
$851$	7.69224	−	13.3234i	0.263687	−	0.456719i
$852$	−25.7643	−	44.6251i	−0.882672	−	1.52883i
$853$	−17.4824	−	30.2804i	−0.598586	−	1.03678i	−0.993030	−	0.117862i	$-0.962396\pi$
$853$	−17.4824	−	30.2804i	−0.598586	−	1.03678i	0.394444	−	0.918920i	$-0.370937\pi$
$854$	−7.00000			−0.239535
$855$		0			0
$856$	9.35844			0.319865
$857$	2.07575	+	3.59530i	0.0709061	+	0.122813i	0.899299	−	0.437335i	$-0.144078\pi$
$857$	2.07575	+	3.59530i	0.0709061	+	0.122813i	−0.828393	+	0.560148i	$0.810744\pi$
$858$	−5.95900	−	10.3213i	−0.203437	−	0.352363i
$859$	−14.1245	+	24.4644i	−0.481923	+	0.834715i	−0.999785	−	0.0207495i	$-0.993395\pi$
$859$	−14.1245	+	24.4644i	−0.481923	+	0.834715i	0.517862	+	0.855464i	$0.326728\pi$
$860$		0			0
$861$	−0.980847	+	1.69888i	−0.0334272	+	0.0578976i
$862$	−28.7327			−0.978640
$863$	−51.8272			−1.76422			−0.882108	−	0.471046i	$-0.843876\pi$
$863$	−51.8272			−1.76422			−0.882108	+	0.471046i	$0.843876\pi$
$864$	−8.43473	+	14.6094i	−0.286955	+	0.497021i
$865$		0			0
$866$	−65.0490			−2.21046
$867$	−40.4297			−1.37307
$868$	−1.19180	+	2.06426i	−0.0404523	+	0.0700655i
$869$	0.616399	+	1.06764i	0.0209099	+	0.0362170i
$870$		0			0
$871$	−26.4257	−	45.7707i	−0.895401	−	1.55088i
$872$	21.8168	+	37.7878i	0.738809	+	1.27966i
$873$	−9.58832			−0.324516
$874$	−26.9894	−	84.0400i	−0.912931	−	2.84270i
$875$		0			0
$876$	36.8538	+	63.8326i	1.24517	+	2.15670i
$877$	−23.5999	−	40.8763i	−0.796913	−	1.38029i	−0.921618	−	0.388099i	$-0.873132\pi$
$877$	−23.5999	−	40.8763i	−0.796913	−	1.38029i	0.124705	−	0.992194i	$-0.460202\pi$
$878$	−31.7292	+	54.9567i	−1.07081	+	1.85470i
$879$	−7.10738	−	12.3103i	−0.239726	−	0.415218i
$880$		0			0
$881$	−33.8935			−1.14190			−0.570951	−	0.820984i	$-0.693425\pi$
$881$	−33.8935			−1.14190			−0.570951	+	0.820984i	$0.693425\pi$
$882$	26.2609			0.884250
$883$	10.5331	−	18.2439i	0.354467	−	0.613954i	−0.632560	−	0.774512i	$-0.717996\pi$
$883$	10.5331	−	18.2439i	0.354467	−	0.613954i	0.987027	+	0.160557i	$0.0513291\pi$
$884$	75.8181	−	131.321i	2.55004	−	4.41680i
$885$		0			0
$886$	−50.2029			−1.68660
$887$	3.60738	−	6.24816i	0.121124	−	0.209793i	−0.799087	−	0.601215i	$-0.794683\pi$
$887$	3.60738	−	6.24816i	0.121124	−	0.209793i	0.920211	+	0.391422i	$0.128017\pi$
$888$	6.66630	+	11.5464i	0.223706	+	0.387471i
$889$	−1.44687	+	2.50605i	−0.0485264	+	0.0840501i
$890$		0			0
$891$	−0.858986	−	1.48781i	−0.0287771	−	0.0498434i
$892$	−88.7356			−2.97109
$893$	−11.8961	−	2.57107i	−0.398087	−	0.0860374i
$894$	2.86946			0.0959693
$895$		0			0
$896$	1.76564	+	3.05818i	0.0589860	+	0.102167i
$897$	−24.6737	+	42.7360i	−0.823830	+	1.42691i
$898$	−24.7694	−	42.9019i	−0.826567	−	1.43166i
$899$	−0.278124	+	0.481725i	−0.00927595	+	0.0160664i
$900$		0			0
$901$	31.0020			1.03283
$902$	−7.05780	+	12.2245i	−0.234999	+	0.407031i
$903$	−0.989423	+	1.71373i	−0.0329259	+	0.0570294i
$904$	−71.5480			−2.37965
$905$		0			0
$906$	−1.48863	+	2.57839i	−0.0494565	+	0.0856612i
$907$	0.584322	+	1.01208i	0.0194021	+	0.0336054i	0.875563	−	0.483103i	$-0.160490\pi$
$907$	0.584322	+	1.01208i	0.0194021	+	0.0336054i	−0.856161	+	0.516709i	$0.827157\pi$
$908$	8.57028	−	14.8442i	0.284415	−	0.492621i
$909$	−5.57184	−	9.65071i	−0.184806	−	0.320094i
$910$		0			0
$911$	−12.3313			−0.408553			−0.204276	−	0.978913i	$-0.565484\pi$
$911$	−12.3313			−0.408553			−0.204276	+	0.978913i	$0.565484\pi$
$912$	30.1530	+	6.51689i	0.998467	+	0.215796i
$913$	−7.40856			−0.245188
$914$	−43.2018	−	74.8278i	−1.42899	−	2.47508i
$915$		0			0
$916$	−7.58276	+	13.1337i	−0.250542	+	0.433951i
$917$	−0.788701	−	1.36607i	−0.0260452	−	0.0451116i
$918$	48.8553	−	84.6199i	1.61247	−	2.79287i
$919$	52.8895			1.74466			0.872332	−	0.488913i	$-0.162607\pi$
$919$	52.8895			1.74466			0.872332	+	0.488913i	$0.162607\pi$
$920$		0			0
$921$	−3.59880	+	6.23331i	−0.118585	+	0.205395i
$922$	9.94375	−	17.2231i	0.327480	−	0.567212i
$923$	−49.2070			−1.61967
$924$	0.903965			0.0297383
$925$		0			0
$926$	11.5999	+	20.0916i	0.381197	+	0.660252i
$927$	−9.19570	+	15.9274i	−0.302027	+	0.523125i
$928$	−0.339833	−	0.588608i	−0.0111556	−	0.0193220i
$929$	−0.695704	−	1.20500i	−0.0228253	−	0.0395346i	0.854387	−	0.519637i	$-0.173933\pi$
$929$	−0.695704	−	1.20500i	−0.0228253	−	0.0395346i	−0.877212	+	0.480102i	$0.840599\pi$
$930$		0			0
$931$	−9.26409	−	28.8466i	−0.303618	−	0.945410i
$932$	84.7817			2.77712
$933$	9.05425	+	15.6824i	0.296423	+	0.513419i
$934$	11.8730	+	20.5647i	0.388497	+	0.672897i
$935$		0			0
$936$	21.5839	+	37.3844i	0.705491	+	1.22195i
$937$	−16.6847	+	28.8987i	−0.545065	+	0.944080i	0.453538	+	0.891237i	$0.350162\pi$
$937$	−16.6847	+	28.8987i	−0.545065	+	0.944080i	−0.998603	+	0.0528430i	$0.983172\pi$
$938$	5.87970			0.191979
$939$	−7.20250			−0.235045
$940$		0			0
$941$	−17.6616	+	30.5908i	−0.575753	+	0.997233i	0.420207	+	0.907428i	$0.361958\pi$
$941$	−17.6616	+	30.5908i	−0.575753	+	0.997233i	−0.995959	+	0.0898043i	$0.971376\pi$
$942$	8.31633			0.270961
$943$	58.4467			1.90329
$944$	8.08632	−	14.0059i	0.263187	−	0.455854i
$945$		0			0
$946$	−7.11951	+	12.3314i	−0.231475	+	0.400927i
$947$	6.62853	+	11.4810i	0.215398	+	0.373081i	0.953396	−	0.301723i	$-0.0975617\pi$
$947$	6.62853	+	11.4810i	0.215398	+	0.373081i	−0.737997	+	0.674804i	$0.764228\pi$
$948$	4.14769	+	7.18400i	0.134711	+	0.233326i
$949$	70.3865			2.28484
$950$		0			0
$951$	−5.08131			−0.164773
$952$	4.49800	+	7.79076i	0.145781	+	0.252500i
$953$	9.13511	+	15.8225i	0.295915	+	0.512540i	0.975197	−	0.221337i	$-0.0710421\pi$
$953$	9.13511	+	15.8225i	0.295915	+	0.512540i	−0.679282	+	0.733877i	$0.737709\pi$
$954$	−8.27501	+	14.3327i	−0.267913	+	0.464039i
$955$		0			0
$956$	−50.9377	+	88.2268i	−1.64744	+	2.85346i
$957$	0.210953			0.00681916
$958$	−87.0308			−2.81184
$959$	0.601918	−	1.04255i	0.0194369	−	0.0336658i
$960$		0			0
$961$	−24.7149			−0.797253
$962$	23.8750			0.769762
$963$	1.23090	−	2.13197i	0.0396651	−	0.0687019i
$964$	9.73201	+	16.8563i	0.313447	+	0.542906i
$965$		0			0
$966$	−2.74493	−	4.75436i	−0.0883168	−	0.152969i
$967$	−22.5562	−	39.0686i	−0.725360	−	1.25636i	−0.958826	−	0.283995i	$-0.908340\pi$
$967$	−22.5562	−	39.0686i	−0.725360	−	1.25636i	0.233466	−	0.972365i	$-0.424993\pi$
$968$	−59.5491			−1.91398
$969$	−36.8433	−	7.96283i	−1.18358	−	0.255803i
$970$		0			0
$971$	−7.80118	−	13.5120i	−0.250352	−	0.433622i	0.713271	−	0.700888i	$-0.247213\pi$
$971$	−7.80118	−	13.5120i	−0.250352	−	0.433622i	−0.963623	+	0.267266i	$0.913880\pi$
$972$	29.6175	+	51.2990i	0.949982	+	1.64542i
$973$	−0.396081	+	0.686032i	−0.0126978	+	0.0219932i
$974$	−35.7338	−	61.8928i	−1.14499	−	1.98317i
$975$		0			0
$976$	−72.8904			−2.33317
$977$	−26.2319			−0.839233			−0.419617	−	0.907701i	$-0.637835\pi$
$977$	−26.2319			−0.839233			−0.419617	+	0.907701i	$0.637835\pi$
$978$	4.90710	−	8.49935i	0.156912	−	0.271779i
$979$	1.22188	−	2.11635i	0.0390513	−	0.0676389i
$980$		0			0
$981$	11.4781			0.366466
$982$	39.0967	−	67.7175i	1.24763	−	2.16095i
$983$	−17.1706	−	29.7404i	−0.547659	−	0.948572i	−0.998434	−	0.0559353i	$-0.982186\pi$
$983$	−17.1706	−	29.7404i	−0.547659	−	0.948572i	0.450776	−	0.892637i	$-0.351147\pi$
$984$	−25.3257	+	43.8654i	−0.807354	+	1.39838i
$985$		0			0
$986$	1.96837	+	3.40931i	0.0626856	+	0.108575i
$987$	−0.756969			−0.0240946
$988$	62.7284	−	69.1904i	1.99565	−	2.20124i
$989$	58.9577			1.87475
$990$		0			0
$991$	−1.65159	−	2.86064i	−0.0524645	−	0.0908712i	0.838600	−	0.544747i	$-0.183374\pi$
$991$	−1.65159	−	2.86064i	−0.0524645	−	0.0908712i	−0.891065	+	0.453876i	$0.850041\pi$
$992$	−3.83983	+	6.65079i	−0.121915	+	0.211163i
$993$	6.52461	+	11.3010i	0.207052	+	0.358625i
$994$	2.73713	−	4.74084i	0.0868163	−	0.150370i
$995$		0			0
$996$	−49.8514			−1.57960
$997$	4.91168	−	8.50727i	0.155554	−	0.269428i	−0.777706	−	0.628628i	$-0.783617\pi$
$997$	4.91168	−	8.50727i	0.155554	−	0.269428i	0.933261	+	0.359200i	$0.116950\pi$
$998$	−20.2902	+	35.1436i	−0.642274	+	1.11245i
$999$	10.4890			0.331857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.d.26.1		6
5.2	odd	4		475.2.j.b.349.6		12
5.3	odd	4		475.2.j.b.349.1		12
5.4	even	2		95.2.e.b.26.3	yes	6
15.14	odd	2		855.2.k.g.406.1		6
19.7	even	3		9025.2.a.z.1.3		3
19.11	even	3	inner	475.2.e.d.201.1		6
19.12	odd	6		9025.2.a.ba.1.1		3
20.19	odd	2		1520.2.q.j.881.2		6
95.49	even	6		95.2.e.b.11.3	✓	6
95.64	even	6		1805.2.a.h.1.1		3
95.68	odd	12		475.2.j.b.49.6		12
95.69	odd	6		1805.2.a.g.1.3		3
95.87	odd	12		475.2.j.b.49.1		12
285.239	odd	6		855.2.k.g.676.1		6
380.239	odd	6		1520.2.q.j.961.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.b.11.3	✓	6	95.49	even	6
95.2.e.b.26.3	yes	6	5.4	even	2
475.2.e.d.26.1		6	1.1	even	1	trivial
475.2.e.d.201.1		6	19.11	even	3	inner
475.2.j.b.49.1		12	95.87	odd	12
475.2.j.b.49.6		12	95.68	odd	12
475.2.j.b.349.1		12	5.3	odd	4
475.2.j.b.349.6		12	5.2	odd	4
855.2.k.g.406.1		6	15.14	odd	2
855.2.k.g.676.1		6	285.239	odd	6
1520.2.q.j.881.2		6	20.19	odd	2
1520.2.q.j.961.2		6	380.239	odd	6
1805.2.a.g.1.3		3	95.69	odd	6
1805.2.a.h.1.1		3	95.64	even	6
9025.2.a.z.1.3		3	19.7	even	3
9025.2.a.ba.1.1		3	19.12	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25351 - 2.17114i) q^{2} +(0.610938 + 1.05818i) q^{3} +(-2.14257 + 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876 q^{7} +5.72889 q^{8} +(0.753509 - 1.30512i) q^{9} +O(q^{10})\)	\(q+(-1.25351 - 2.17114i) q^{2} +(0.610938 + 1.05818i) q^{3} +(-2.14257 + 3.71104i) q^{4} +(1.53163 - 2.65287i) q^{6} +0.221876 q^{7} +5.72889 q^{8} +(0.753509 - 1.30512i) q^{9} -0.778124 q^{11} -5.23591 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.278124 - 0.481725i) q^{14} +(-2.89608 - 5.01616i) q^{16} +(3.53865 + 6.12912i) q^{17} -3.77812 q^{18} +(1.33281 + 4.15013i) q^{19} +(0.135553 + 0.234784i) q^{21} +(0.975385 + 1.68942i) q^{22} +(4.03865 - 6.99515i) q^{23} +(3.50000 + 6.06218i) q^{24} +12.5351 q^{26} +5.50702 q^{27} +(-0.475385 + 0.823392i) q^{28} +(-0.110938 + 0.192150i) q^{29} +2.50702 q^{31} +(-1.53163 + 2.65287i) q^{32} +(-0.475385 - 0.823392i) q^{33} +(8.87147 - 15.3658i) q^{34} +(3.22889 + 5.59261i) q^{36} +1.90466 q^{37} +(7.33983 - 8.09596i) q^{38} -6.10938 q^{39} +(3.61796 + 6.26648i) q^{41} +(0.339833 - 0.588608i) q^{42} +(3.64959 + 6.32128i) q^{43} +(1.66719 - 2.88765i) q^{44} -20.2500 q^{46} +(-1.39608 + 2.41808i) q^{47} +(3.53865 - 6.12912i) q^{48} -6.95077 q^{49} +(-4.32379 + 7.48903i) q^{51} +(-10.7129 - 18.5552i) q^{52} +(2.19024 - 3.79361i) q^{53} +(-6.90310 - 11.9565i) q^{54} +1.27111 q^{56} +(-3.57730 + 3.94583i) q^{57} +0.556248 q^{58} +(1.39608 + 2.41808i) q^{59} +(6.29216 - 10.8983i) q^{61} +(-3.14257 - 5.44309i) q^{62} +(0.167186 - 0.289574i) q^{63} -3.90466 q^{64} +(-1.19180 + 2.06426i) q^{66} +(-5.28514 + 9.15414i) q^{67} -30.3273 q^{68} +9.86946 q^{69} +(4.92070 + 8.52289i) q^{71} +(4.31678 - 7.47687i) q^{72} +(-7.03865 - 12.1913i) q^{73} +(-2.38750 - 4.13528i) q^{74} +(-18.2570 - 3.94583i) q^{76} -0.172647 q^{77} +(7.65817 + 13.2643i) q^{78} +(-0.792161 - 1.37206i) q^{79} +(1.10392 + 1.91204i) q^{81} +(9.07028 - 15.7102i) q^{82} +9.52106 q^{83} -1.16172 q^{84} +(9.14959 - 15.8476i) q^{86} -0.271105 q^{87} -4.45779 q^{88} +(-1.57028 + 2.71981i) q^{89} +(-0.554690 + 0.960752i) q^{91} +(17.3062 + 29.9752i) q^{92} +(1.53163 + 2.65287i) q^{93} +7.00000 q^{94} -3.74293 q^{96} +(-3.18122 - 5.51004i) q^{97} +(8.71286 + 15.0911i) q^{98} +(-0.586324 + 1.01554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9	\( 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26} + 16 q^{27} + 11 q^{28} + 2 q^{29} - 2 q^{31} - 6 q^{32} + 11 q^{33} + 25 q^{34} - 3 q^{36} + 4 q^{37} + 19 q^{38} - 10 q^{39} + 2 q^{41} - 23 q^{42} - q^{43} + 18 q^{44} - 48 q^{46} + 6 q^{47} + q^{48} - 14 q^{49} + 6 q^{51} - 35 q^{52} + 11 q^{53} - 10 q^{54} + 30 q^{56} + 19 q^{57} + 14 q^{58} - 6 q^{59} + 9 q^{61} - 13 q^{62} + 9 q^{63} - 16 q^{64} - 29 q^{66} - 20 q^{67} - 68 q^{68} - 10 q^{69} + 29 q^{71} + 11 q^{72} - 22 q^{73} + 7 q^{74} - 19 q^{76} + 32 q^{77} + 30 q^{78} + 24 q^{79} + 21 q^{81} + 31 q^{82} + 6 q^{83} - 56 q^{84} + 32 q^{86} - 24 q^{87} + 18 q^{88} + 14 q^{89} + 10 q^{91} + 41 q^{92} + 6 q^{93} + 42 q^{94} + 34 q^{96} + 7 q^{97} + 23 q^{98} + 13 q^{99}+O(q^{100}) \) 6 * q + q^2 + q^3 - 7 * q^4 + 6 * q^6 - 4 * q^7 + 12 * q^8 - 4 * q^9 - 10 * q^11 + 8 * q^12 - 15 * q^13 - 7 * q^14 - 3 * q^16 + q^17 - 28 * q^18 + 12 * q^21 - 8 * q^22 + 4 * q^23 + 21 * q^24 - 10 * q^26 + 16 * q^27 + 11 * q^28 + 2 * q^29 - 2 * q^31 - 6 * q^32 + 11 * q^33 + 25 * q^34 - 3 * q^36 + 4 * q^37 + 19 * q^38 - 10 * q^39 + 2 * q^41 - 23 * q^42 - q^43 + 18 * q^44 - 48 * q^46 + 6 * q^47 + q^48 - 14 * q^49 + 6 * q^51 - 35 * q^52 + 11 * q^53 - 10 * q^54 + 30 * q^56 + 19 * q^57 + 14 * q^58 - 6 * q^59 + 9 * q^61 - 13 * q^62 + 9 * q^63 - 16 * q^64 - 29 * q^66 - 20 * q^67 - 68 * q^68 - 10 * q^69 + 29 * q^71 + 11 * q^72 - 22 * q^73 + 7 * q^74 - 19 * q^76 + 32 * q^77 + 30 * q^78 + 24 * q^79 + 21 * q^81 + 31 * q^82 + 6 * q^83 - 56 * q^84 + 32 * q^86 - 24 * q^87 + 18 * q^88 + 14 * q^89 + 10 * q^91 + 41 * q^92 + 6 * q^93 + 42 * q^94 + 34 * q^96 + 7 * q^97 + 23 * q^98 + 13 * q^99

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