LMFDB - Embedded newform 475.2.e.d.201.1

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			201.1
Root			$-1.25351 + 2.17114i$ of defining polynomial
Character	$\chi$	$=$	475.201
Dual form			475.2.e.d.26.1

$q$-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} -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} - 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}+ \cdots + 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

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.0422238	+	0.999108i	$0.513444\pi$
$2$	−1.25351	+	2.17114i	−0.886365	+	1.53523i	−0.844141	+	0.536121i	$0.819889\pi$
$3$	0.610938	−	1.05818i	0.352725	−	0.610938i	−0.634001	−	0.773333i	$-0.718588\pi$
$3$	0.610938	−	1.05818i	0.352725	−	0.610938i	0.986726	+	0.162394i	$0.0519217\pi$
$4$	−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	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−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	−0.0153485	−	0.999882i	$-0.504886\pi$
$17$	3.53865	−	6.12912i	0.858249	−	1.48653i	0.873598	−	0.486649i	$-0.161781\pi$
$18$	−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	0.888101	+	0.459647i	$0.152024\pi$
$23$	4.03865	+	6.99515i	0.842117	+	1.45859i	−0.0459843	+	0.998942i	$0.514642\pi$
$24$	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	0.855541	−	0.517735i	$-0.173225\pi$
$29$	−0.110938	−	0.192150i	−0.0206007	−	0.0356814i	−0.876142	+	0.482053i	$0.839891\pi$
$30$		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	−0.432017	−	0.901865i	$-0.642198\pi$
$41$	3.61796	−	6.26648i	0.565030	−	0.978661i	0.997047	−	0.0767950i	$-0.0244687\pi$
$42$	0.339833	+	0.588608i	0.0524374	+	0.0908242i
$43$	3.64959	−	6.32128i	0.556557	−	0.963985i	−0.441223	−	0.897397i	$-0.645455\pi$
$43$	3.64959	−	6.32128i	0.556557	−	0.963985i	0.997781	−	0.0665881i	$-0.0212113\pi$
$44$	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	0.746059	−	0.665880i	$-0.231944\pi$
$47$	−1.39608	−	2.41808i	−0.203639	−	0.352714i	−0.949698	+	0.313166i	$0.898610\pi$
$48$	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	0.976329	−	0.216289i	$-0.0693953\pi$
$53$	2.19024	+	3.79361i	0.300853	+	0.521093i	−0.675476	+	0.737382i	$0.736062\pi$
$54$	−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	−0.760724	−	0.649076i	$-0.775156\pi$
$59$	1.39608	−	2.41808i	0.181754	−	0.314808i	0.942478	+	0.334268i	$0.108489\pi$
$60$		0			0
$61$	6.29216	+	10.8983i	0.805629	+	1.39539i	0.915866	+	0.401484i	$0.131506\pi$
$61$	6.29216	+	10.8983i	0.805629	+	1.39539i	−0.110237	+	0.993905i	$0.535161\pi$
$62$	−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	−0.984143	−	0.177375i	$-0.943239\pi$
$67$	−5.28514	−	9.15414i	−0.645683	−	1.11836i	0.338460	−	0.940981i	$-0.390094\pi$
$68$	−30.3273			−3.67772
$69$	9.86946			1.18814
$70$		0			0
$71$	4.92070	−	8.52289i	0.583979	−	1.01148i	−0.411023	−	0.911625i	$-0.634828\pi$
$71$	4.92070	−	8.52289i	0.583979	−	1.01148i	0.995002	−	0.0998563i	$-0.0318383\pi$
$72$	4.31678	+	7.47687i	0.508737	+	0.881158i
$73$	−7.03865	+	12.1913i	−0.823812	+	1.42688i	0.0790121	+	0.996874i	$0.474823\pi$
$73$	−7.03865	+	12.1913i	−0.823812	+	1.42688i	−0.902824	+	0.430010i	$0.858510\pi$
$74$	−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	−0.907142	−	0.420826i	$-0.861740\pi$
$79$	−0.792161	+	1.37206i	−0.0891251	+	0.154369i	0.818016	+	0.575195i	$0.195074\pi$
$80$		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	0.770719	−	0.637175i	$-0.219897\pi$
$89$	−1.57028	−	2.71981i	−0.166450	−	0.288300i	−0.937169	+	0.348875i	$0.886564\pi$
$90$		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	−0.981106	−	0.193469i	$-0.938026\pi$
$97$	−3.18122	+	5.51004i	−0.323004	+	0.559460i	0.658102	+	0.752929i	$0.271359\pi$
$98$	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	0.989236	−	0.146331i	$-0.0467465\pi$
$101$	3.69726	+	6.40385i	0.367891	+	0.637206i	−0.621344	+	0.783538i	$0.713413\pi$
$102$	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	−0.623978	−	0.781442i	$-0.714485\pi$
$109$	3.80820	−	6.59600i	0.364759	−	0.631782i	0.988738	+	0.149660i	$0.0478179\pi$
$110$		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	−0.995635	−	0.0933378i	$-0.970246\pi$
$127$	−6.52106	−	11.2948i	−0.578650	−	1.00225i	0.416984	−	0.908914i	$-0.363087\pi$
$128$	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	−0.978487	−	0.206309i	$-0.933855\pi$
$131$	−3.55469	+	6.15690i	−0.310575	+	0.537931i	0.667912	+	0.744240i	$0.267188\pi$
$132$	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	0.958331	−	0.285662i	$-0.0922134\pi$
$137$	2.71286	+	4.69880i	0.231775	+	0.401446i	−0.726556	+	0.687108i	$0.758880\pi$
$138$	−12.3715	+	21.4280i	−1.05313	+	1.82407i
$139$	−1.78514	−	3.09196i	−0.151414	−	0.262256i	0.780334	−	0.625363i	$-0.215049\pi$
$139$	−1.78514	−	3.09196i	−0.151414	−	0.262256i	−0.931747	+	0.363107i	$0.881716\pi$
$140$		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	−0.846203	−	0.532861i	$-0.821117\pi$
$149$	0.468367	−	0.811235i	0.0383701	−	0.0664590i	0.884573	+	0.466402i	$0.154450\pi$
$150$		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	−0.806761	−	0.590878i	$-0.798782\pi$
$157$	1.35743	−	2.35114i	0.108335	−	0.187641i	0.915096	+	0.403237i	$0.132115\pi$
$158$	−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	0.993164	−	0.116724i	$-0.0372393\pi$
$167$	5.11094	+	8.85240i	0.395496	+	0.685020i	−0.597668	+	0.801744i	$0.703906\pi$
$168$	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	−0.912234	−	0.409670i	$-0.865644\pi$
$173$	−1.33281	+	2.30850i	−0.101332	+	0.175512i	0.810902	+	0.585182i	$0.198977\pi$
$174$	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	0.971273	+	0.237970i	$0.0764820\pi$
$181$	9.30620	+	16.1188i	0.691724	+	1.19810i	−0.279548	+	0.960132i	$0.590185\pi$
$182$	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	0.375824	+	0.926691i	$0.377360\pi$
$193$	−8.53865	+	14.7894i	−0.614626	+	1.06456i	−0.990450	+	0.137872i	$0.955974\pi$
$194$	−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	0.912183	−	0.409784i	$-0.134396\pi$
$199$	1.42771	+	2.47287i	0.101208	+	0.175297i	−0.810975	+	0.585081i	$0.801063\pi$
$200$		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	−0.554348	−	0.832285i	$-0.687032\pi$
$211$	6.44375	−	11.1609i	0.443606	−	0.768348i	0.997954	+	0.0639367i	$0.0203656\pi$
$212$	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	−0.277389	−	0.960758i	$-0.589469\pi$
$223$	10.3539	−	17.9334i	0.693346	−	1.20091i	0.970735	−	0.240153i	$-0.0771978\pi$
$224$	−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	0.335500	+	0.942040i	$0.391095\pi$
$233$	−9.89252	+	17.1344i	−0.648081	+	1.12251i	−0.983581	+	0.180468i	$0.942239\pi$
$234$	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	0.929855	−	0.367926i	$-0.119932\pi$
$241$	2.27111	+	3.93367i	0.146295	+	0.253390i	−0.783561	+	0.621315i	$0.786599\pi$
$242$	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	0.990295	+	0.138982i	$0.0443832\pi$
$251$	9.75151	+	16.8901i	0.615510	+	1.06609i	−0.374785	+	0.927112i	$0.622284\pi$
$252$	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	0.892224	−	0.451594i	$-0.149144\pi$
$257$	0.882043	+	1.52774i	0.0550203	+	0.0952980i	−0.837203	+	0.546892i	$0.815811\pi$
$258$	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	−0.948378	−	0.317143i	$-0.897276\pi$
$263$	−3.23591	+	5.60477i	−0.199535	+	0.345605i	0.748843	+	0.662748i	$0.230610\pi$
$264$	−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	−0.00478280	+	0.999989i	$0.501522\pi$
$269$	−14.2429	+	24.6695i	−0.868407	+	1.50412i	−0.863624	+	0.504136i	$0.831811\pi$
$270$		0			0
$271$	0.246491	−	0.426934i	0.0149732	−	0.0259344i	−0.858442	−	0.512911i	$-0.828567\pi$
$271$	0.246491	−	0.426934i	0.0149732	−	0.0259344i	0.873415	+	0.486977i	$0.161900\pi$
$272$	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	0.928050	−	0.372455i	$-0.121484\pi$
$281$	2.37147	+	4.10750i	0.141470	+	0.245033i	−0.786581	+	0.617488i	$0.788151\pi$
$282$	4.27657	−	7.40723i	0.254666	−	0.441094i
$283$	8.43473	−	14.6094i	0.501393	−	0.868438i	−0.498606	−	0.866829i	$-0.666155\pi$
$283$	8.43473	−	14.6094i	0.501393	−	0.868438i	0.999999	−	0.00160901i	$-0.000512164\pi$
$284$	−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	−0.769653	−	0.638462i	$-0.779571\pi$
$307$	2.94531	−	5.10143i	0.168098	−	0.291154i	0.937751	+	0.347308i	$0.112904\pi$
$308$	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	0.770628	−	0.637286i	$-0.219943\pi$
$313$	−2.94731	−	5.10489i	−0.166592	−	0.288546i	−0.937219	+	0.348740i	$0.886610\pi$
$314$	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	0.801707	−	0.597718i	$-0.203926\pi$
$317$	−2.07930	−	3.60146i	−0.116785	−	0.202278i	−0.918492	+	0.395439i	$0.870592\pi$
$318$	−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	0.244404	+	0.969673i	$0.421408\pi$
$337$	−13.1726	+	22.8157i	−0.717560	+	1.24285i	−0.961964	+	0.273177i	$0.911926\pi$
$338$	−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	−0.998581	−	0.0532476i	$-0.983043\pi$
$347$	−8.44175	+	14.6215i	−0.453177	+	0.784925i	0.545404	+	0.838173i	$0.316376\pi$
$348$	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	−0.978676	−	0.205410i	$-0.934147\pi$
$359$	−5.90110	+	10.2210i	−0.311448	+	0.539444i	0.667228	+	0.744854i	$0.267481\pi$
$360$		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	0.973540	+	0.228516i	$0.0733872\pi$
$367$	13.1164	+	22.7183i	0.684670	+	1.18588i	−0.288870	+	0.957368i	$0.593279\pi$
$368$	−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	−0.169540	−	0.985523i	$-0.554228\pi$
$383$	15.0441	−	26.0572i	0.768718	−	1.33146i	0.938258	−	0.345936i	$-0.112439\pi$
$384$	−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	0.820133	+	0.572173i	$0.193900\pi$
$389$	17.8609	+	30.9360i	0.905583	+	1.56852i	0.0854503	+	0.996342i	$0.472767\pi$
$390$		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	−0.720907	−	0.693031i	$-0.756275\pi$
$397$	4.77657	−	8.27326i	0.239729	−	0.415223i	0.960636	+	0.277809i	$0.0896081\pi$
$398$	−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	0.165823	+	0.986156i	$0.446972\pi$
$401$	−15.4418	+	26.7459i	−0.771124	+	1.33563i	−0.936947	+	0.349471i	$0.886361\pi$
$402$	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	−0.931738	−	0.363130i	$-0.881708\pi$
$409$	−15.7816	−	27.3345i	−0.780349	−	1.35160i	0.151389	−	0.988474i	$-0.451625\pi$
$410$		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	−0.506850	−	0.862035i	$-0.669190\pi$
$421$	10.1180	−	17.5248i	0.493119	−	0.854107i	0.999969	+	0.00792731i	$0.00252337\pi$
$422$	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	0.970394	−	0.241529i	$-0.0776490\pi$
$431$	5.73045	+	9.92543i	0.276026	+	0.478091i	−0.694367	+	0.719621i	$0.744316\pi$
$432$	−15.9488	+	27.6241i	−0.767336	+	1.32906i
$433$	12.9734	+	22.4706i	0.623461	+	1.07987i	0.988836	+	0.149006i	$0.0476073\pi$
$433$	12.9734	+	22.4706i	0.623461	+	1.07987i	−0.365375	+	0.930860i	$0.619059\pi$
$434$	−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	0.388156	+	0.921594i	$0.373112\pi$
$439$	−12.6562	+	21.9211i	−0.604046	+	1.04624i	−0.992202	+	0.124644i	$0.960221\pi$
$440$		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	0.999613	−	0.0278272i	$-0.00885883\pi$
$443$	10.0125	+	17.3421i	0.475707	+	0.823949i	−0.523905	+	0.851776i	$0.675525\pi$
$444$	−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	−0.758754	−	0.651377i	$-0.774192\pi$
$461$	3.96637	−	6.86995i	0.184732	−	0.319965i	0.943486	+	0.331412i	$0.107525\pi$
$462$	−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	0.924050	+	0.382270i	$0.124858\pi$
$479$	17.3574	+	30.0639i	0.793081	+	1.37366i	−0.130969	+	0.991386i	$0.541809\pi$
$480$		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	−0.263339	−	0.964703i	$-0.584824\pi$
$491$	15.5949	−	27.0112i	0.703788	−	1.21900i	0.967127	−	0.254293i	$-0.0818428\pi$
$492$	−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	−0.988340	−	0.152262i	$-0.951344\pi$
$499$	−8.09334	+	14.0181i	−0.362308	+	0.627535i	0.626032	+	0.779797i	$0.284678\pi$
$500$		0			0
$501$	12.4899			0.558006
$502$	−48.8944			−2.18226
$503$	8.61094	+	14.9146i	0.383943	+	0.665008i	0.991622	−	0.129174i	$-0.0412327\pi$
$503$	8.61094	+	14.9146i	0.383943	+	0.665008i	−0.607679	+	0.794183i	$0.707899\pi$
$504$	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	0.912207	+	0.409729i	$0.134377\pi$
$509$	18.2956	+	31.6889i	0.810939	+	1.40459i	−0.101268	+	0.994859i	$0.532290\pi$
$510$		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	−0.932605	−	0.360898i	$-0.882470\pi$
$523$	−17.8117	−	30.8507i	−0.778850	−	1.34901i	0.153756	−	0.988109i	$-0.450863\pi$
$524$	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	0.829908	−	0.557900i	$-0.188393\pi$
$541$	−1.58632	−	2.74759i	−0.0682014	−	0.118128i	−0.898110	+	0.439772i	$0.855059\pi$
$542$	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	−0.991775	−	0.127991i	$-0.959147\pi$
$547$	−14.1902	−	24.5782i	−0.606731	−	1.05089i	0.385044	−	0.922898i	$-0.374186\pi$
$548$	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	0.887711	−	0.460401i	$-0.152294\pi$
$557$	1.06527	+	1.84510i	0.0451368	+	0.0781793i	−0.842574	+	0.538580i	$0.818961\pi$
$558$	−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	−0.839119	−	0.543947i	$-0.816929\pi$
$587$	1.24805	−	2.16168i	0.0515125	−	0.0892222i	0.890632	+	0.454725i	$0.150262\pi$
$588$	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	0.745416	−	0.666600i	$-0.232251\pi$
$593$	−4.98196	−	8.62901i	−0.204585	−	0.354351i	−0.950000	+	0.312249i	$0.898918\pi$
$594$	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	−0.981850	−	0.189661i	$-0.939261\pi$
$599$	−16.0351	−	27.7736i	−0.655176	−	1.13480i	0.326673	−	0.945137i	$-0.394072\pi$
$600$		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	−0.737359	−	0.675501i	$-0.763927\pi$
$613$	5.35587	−	9.27664i	0.216322	−	0.374680i	0.953681	+	0.300821i	$0.0972607\pi$
$614$	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	0.630515	−	0.776177i	$-0.282844\pi$
$617$	−8.86600	−	15.3564i	−0.356932	−	0.618224i	−0.987447	+	0.157953i	$0.949511\pi$
$618$	−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	0.822739	−	0.568419i	$-0.192445\pi$
$631$	−2.03208	−	3.51966i	−0.0808957	−	0.140115i	−0.903635	+	0.428304i	$0.859111\pi$
$632$	−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	−0.911043	−	0.412311i	$-0.864722\pi$
$641$	−2.49254	+	4.31720i	−0.0984493	+	0.170519i	0.812594	+	0.582831i	$0.198055\pi$
$642$	2.50200	+	4.33359i	0.0987461	+	0.171033i
$643$	−2.93829	+	5.08927i	−0.115875	+	0.200701i	−0.918129	−	0.396281i	$-0.870300\pi$
$643$	−2.93829	+	5.08927i	−0.115875	+	0.200701i	0.802254	+	0.596983i	$0.203634\pi$
$644$	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	0.847067	−	0.531485i	$-0.178366\pi$
$659$	−0.943308	−	1.63386i	−0.0367461	−	0.0636461i	−0.883814	+	0.467839i	$0.845033\pi$
$660$		0			0
$661$	−22.3749	−	38.7545i	−0.870284	−	1.50738i	−0.861703	−	0.507413i	$-0.830602\pi$
$661$	−22.3749	−	38.7545i	−0.870284	−	1.50738i	−0.00858048	−	0.999963i	$-0.502731\pi$
$662$	−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	0.459728	+	0.888060i	$0.347947\pi$
$701$	−14.2766	+	24.7277i	−0.539218	+	0.933954i	−0.998946	+	0.0458939i	$0.985386\pi$
$702$	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	0.623066	−	0.782169i	$-0.285887\pi$
$709$	−9.74137	−	16.8726i	−0.365845	−	0.633662i	−0.988911	+	0.148507i	$0.952553\pi$
$710$		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	−0.901767	−	0.432221i	$-0.857730\pi$
$719$	−2.05313	+	3.55613i	−0.0765689	+	0.132621i	0.825199	+	0.564843i	$0.191063\pi$
$720$		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	−0.957856	−	0.287250i	$-0.907259\pi$
$727$	−6.20584	+	10.7488i	−0.230162	+	0.398652i	0.727694	+	0.685902i	$0.240592\pi$
$728$	−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	−0.0315597	−	0.999502i	$-0.510047\pi$
$739$	23.1018	−	40.0135i	0.849814	−	1.47192i	0.881374	−	0.472419i	$-0.156619\pi$
$740$		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	−0.998697	−	0.0510331i	$-0.983749\pi$
$743$	−12.4066	+	21.4888i	−0.455153	+	0.788347i	0.543544	+	0.839380i	$0.317082\pi$
$744$	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	0.946008	−	0.324142i	$-0.105076\pi$
$751$	5.26955	+	9.12712i	0.192289	+	0.333054i	−0.753720	+	0.657196i	$0.771742\pi$
$752$	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	−0.916823	−	0.399295i	$-0.869255\pi$
$757$	−3.09836	+	5.36652i	−0.112612	+	0.195049i	0.804211	+	0.594344i	$0.202588\pi$
$758$	−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	0.867424	−	0.497570i	$-0.165774\pi$
$769$	0.0777477	+	0.134663i	0.00280365	+	0.00485607i	−0.864620	+	0.502426i	$0.832441\pi$
$770$		0			0
$771$	2.15550			0.0776283
$772$	73.1787			2.63376
$773$	−2.54411	−	4.40653i	−0.0915054	−	0.158492i	0.816639	−	0.577148i	$-0.195835\pi$
$773$	−2.54411	−	4.40653i	−0.0915054	−	0.158492i	−0.908145	+	0.418656i	$0.862501\pi$
$774$	−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

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} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{3} - 7 q^{4} + 6 q^{6} - 4 q^{7} + 12 q^{8} - 4 q^{9} - 10 q^{11} + 8 q^{12} - 15 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} - 28 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{23} + 21 q^{24} - 10 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) \) 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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