LMFDB - Embedded newform 475.2.n.a.39.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.5
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02546 - 1.41142i) q^{2} +(-2.62954 - 0.854391i) q^{3} +(-0.322513 + 0.992591i) q^{4} +(1.35649 + 1.77762i) q^{5} +(1.49058 + 4.58753i) q^{6} +0.182993i q^{7} +(-1.58676 + 0.515570i) q^{8} +(3.75747 + 2.72996i) q^{9} +O(q^{10})$	\(q+(-1.02546 - 1.41142i) q^{2} +(-2.62954 - 0.854391i) q^{3} +(-0.322513 + 0.992591i) q^{4} +(1.35649 + 1.77762i) q^{5} +(1.49058 + 4.58753i) q^{6} +0.182993i q^{7} +(-1.58676 + 0.515570i) q^{8} +(3.75747 + 2.72996i) q^{9} +(1.11795 - 3.73745i) q^{10} +(1.75447 - 1.27469i) q^{11} +(1.69612 - 2.33451i) q^{12} +(0.787300 - 1.08363i) q^{13} +(0.258279 - 0.187651i) q^{14} +(-2.04817 - 5.83330i) q^{15} +(4.04354 + 2.93781i) q^{16} +(5.42356 - 1.76222i) q^{17} -8.10282i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.20194 + 0.773135i) q^{20} +(0.156347 - 0.481187i) q^{21} +(-3.59826 - 1.16915i) q^{22} +(-3.84307 - 5.28953i) q^{23} +4.61296 q^{24} +(-1.31987 + 4.82265i) q^{25} -2.33680 q^{26} +(-2.67253 - 3.67842i) q^{27} +(-0.181637 - 0.0590174i) q^{28} +(0.536374 - 1.65079i) q^{29} +(-6.13294 + 8.87263i) q^{30} +(0.376695 + 1.15935i) q^{31} -5.38289i q^{32} +(-5.70253 + 1.85286i) q^{33} +(-8.04887 - 5.84785i) q^{34} +(-0.325291 + 0.248227i) q^{35} +(-3.92156 + 2.84918i) q^{36} +(-0.0702389 + 0.0966756i) q^{37} +(-1.02546 + 1.41142i) q^{38} +(-2.99608 + 2.17678i) q^{39} +(-3.06892 - 2.12130i) q^{40} +(-2.97651 - 2.16256i) q^{41} +(-0.839484 + 0.272765i) q^{42} -4.44899i q^{43} +(0.699413 + 2.15257i) q^{44} +(0.244133 + 10.3825i) q^{45} +(-3.52485 + 10.8484i) q^{46} +(-5.12038 - 1.66371i) q^{47} +(-8.12264 - 11.1799i) q^{48} +6.96651 q^{49} +(8.16026 - 3.08253i) q^{50} -15.7671 q^{51} +(0.821684 + 1.13095i) q^{52} +(-5.56509 - 1.80821i) q^{53} +(-2.45124 + 7.54413i) q^{54} +(4.64584 + 1.38966i) q^{55} +(-0.0943455 - 0.290366i) q^{56} +2.76487i q^{57} +(-2.87999 + 0.935765i) q^{58} +(-3.45806 - 2.51243i) q^{59} +(6.45065 - 0.151680i) q^{60} +(6.88904 - 5.00518i) q^{61} +(1.25004 - 1.72054i) q^{62} +(-0.499562 + 0.687588i) q^{63} +(0.489556 - 0.355683i) q^{64} +(2.99424 - 0.0704061i) q^{65} +(8.46287 + 6.14864i) q^{66} +(10.4246 - 3.38717i) q^{67} +5.95172i q^{68} +(5.58619 + 17.1925i) q^{69} +(0.683926 + 0.204576i) q^{70} +(3.29737 - 10.1483i) q^{71} +(-7.36969 - 2.39456i) q^{72} +(-0.671208 - 0.923839i) q^{73} +0.208477 q^{74} +(7.59108 - 11.5537i) q^{75} +1.04367 q^{76} +(0.233259 + 0.321054i) q^{77} +(6.14471 + 1.99654i) q^{78} +(2.06863 - 6.36659i) q^{79} +(0.262720 + 11.1730i) q^{80} +(-0.420949 - 1.29555i) q^{81} +6.41871i q^{82} +(-0.177587 + 0.0577014i) q^{83} +(0.427198 + 0.310378i) q^{84} +(10.4896 + 7.25060i) q^{85} +(-6.27940 + 4.56225i) q^{86} +(-2.82084 + 3.88255i) q^{87} +(-2.12673 + 2.92719i) q^{88} +(7.27274 - 5.28396i) q^{89} +(14.4037 - 10.9914i) q^{90} +(0.198295 + 0.144070i) q^{91} +(6.48978 - 2.10866i) q^{92} -3.37040i q^{93} +(2.90253 + 8.93308i) q^{94} +(1.27144 - 1.83941i) q^{95} +(-4.59909 + 14.1546i) q^{96} +(14.9162 + 4.84658i) q^{97} +(-7.14386 - 9.83268i) q^{98} +10.0722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.02546	−	1.41142i	−0.725108	−	0.998025i	−0.999339	−	0.0363615i	$-0.988423\pi$
$2$	−1.02546	−	1.41142i	−0.725108	−	0.998025i	0.274231	−	0.961664i	$-0.411577\pi$
$3$	−2.62954	−	0.854391i	−1.51817	−	0.493283i	−0.572913	−	0.819616i	$-0.694187\pi$
$3$	−2.62954	−	0.854391i	−1.51817	−	0.493283i	−0.945255	+	0.326333i	$0.894187\pi$
$4$	−0.322513	+	0.992591i	−0.161256	+	0.496296i
$5$	1.35649	+	1.77762i	0.606641	+	0.794976i
$5$	1.35649	+	1.77762i	0.606641	+	0.794976i
$6$	1.49058	+	4.58753i	0.608527	+	1.87285i
$7$			0.182993i			0.0691647i	0.999402	+	0.0345823i	$0.0110101\pi$
$7$			0.182993i			0.0691647i	−0.999402	+	0.0345823i	$0.988990\pi$
$8$	−1.58676	+	0.515570i	−0.561005	+	0.182282i
$9$	3.75747	+	2.72996i	1.25249	+	0.909986i
$10$	1.11795	−	3.73745i	0.353526	−	1.18189i
$11$	1.75447	−	1.27469i	0.528991	−	0.384335i	−0.290989	−	0.956726i	$-0.593984\pi$
$11$	1.75447	−	1.27469i	0.528991	−	0.384335i	0.819980	+	0.572392i	$0.193984\pi$
$12$	1.69612	−	2.33451i	0.489628	−	0.673915i
$13$	0.787300	−	1.08363i	0.218358	−	0.300544i	−0.685759	−	0.727828i	$-0.740530\pi$
$13$	0.787300	−	1.08363i	0.218358	−	0.300544i	0.904117	+	0.427285i	$0.140530\pi$
$14$	0.258279	−	0.187651i	0.0690281	−	0.0501518i
$15$	−2.04817	−	5.83330i	−0.528834	−	1.50615i
$16$	4.04354	+	2.93781i	1.01089	+	0.734451i
$17$	5.42356	−	1.76222i	1.31541	−	0.427402i	0.434492	−	0.900676i	$-0.356928\pi$
$17$	5.42356	−	1.76222i	1.31541	−	0.427402i	0.880915	+	0.473274i	$0.156928\pi$
$18$		−	8.10282i		−	1.90985i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−2.20194	+	0.773135i	−0.492368	+	0.172878i
$21$	0.156347	−	0.481187i	0.0341177	−	0.105004i
$22$	−3.59826	−	1.16915i	−0.767151	−	0.249263i
$23$	−3.84307	−	5.28953i	−0.801335	−	1.10294i	−0.992603	−	0.121406i	$-0.961260\pi$
$23$	−3.84307	−	5.28953i	−0.801335	−	1.10294i	0.191268	−	0.981538i	$-0.438740\pi$
$24$	4.61296			0.941617
$25$	−1.31987	+	4.82265i	−0.263974	+	0.964530i
$26$	−2.33680			−0.458283
$27$	−2.67253	−	3.67842i	−0.514329	−	0.707912i
$28$	−0.181637	−	0.0590174i	−0.0343261	−	0.0111532i
$29$	0.536374	−	1.65079i	0.0996022	−	0.306544i	−0.888824	−	0.458250i	$-0.848477\pi$
$29$	0.536374	−	1.65079i	0.0996022	−	0.306544i	0.988426	+	0.151706i	$0.0484766\pi$
$30$	−6.13294	+	8.87263i	−1.11972	+	1.61991i
$31$	0.376695	+	1.15935i	0.0676564	+	0.208225i	0.979169	−	0.203047i	$-0.0650845\pi$
$31$	0.376695	+	1.15935i	0.0676564	+	0.208225i	−0.911513	+	0.411272i	$0.865085\pi$
$32$		−	5.38289i		−	0.951570i
$33$	−5.70253	+	1.85286i	−0.992683	+	0.322542i
$34$	−8.04887	−	5.84785i	−1.38037	−	1.00290i
$35$	−0.325291	+	0.248227i	−0.0549843	+	0.0419581i
$36$	−3.92156	+	2.84918i	−0.653594	+	0.474864i
$37$	−0.0702389	+	0.0966756i	−0.0115472	+	0.0158934i	−0.814752	−	0.579810i	$-0.803127\pi$
$37$	−0.0702389	+	0.0966756i	−0.0115472	+	0.0158934i	0.803204	+	0.595704i	$0.203127\pi$
$38$	−1.02546	+	1.41142i	−0.166351	+	0.228963i
$39$	−2.99608	+	2.17678i	−0.479757	+	0.348564i
$40$	−3.06892	−	2.12130i	−0.485238	−	0.335406i
$41$	−2.97651	−	2.16256i	−0.464852	−	0.337735i	0.330580	−	0.943778i	$-0.392756\pi$
$41$	−2.97651	−	2.16256i	−0.464852	−	0.337735i	−0.795432	+	0.606043i	$0.792756\pi$
$42$	−0.839484	+	0.272765i	−0.129535	+	0.0420886i
$43$		−	4.44899i		−	0.678465i	−0.940703	−	0.339233i	$-0.889833\pi$
$43$		−	4.44899i		−	0.678465i	0.940703	−	0.339233i	$-0.110167\pi$
$44$	0.699413	+	2.15257i	0.105440	+	0.324512i
$45$	0.244133	+	10.3825i	0.0363932	+	1.54773i
$46$	−3.52485	+	10.8484i	−0.519711	+	1.59951i
$47$	−5.12038	−	1.66371i	−0.746885	−	0.242678i	−0.0892445	−	0.996010i	$-0.528445\pi$
$47$	−5.12038	−	1.66371i	−0.746885	−	0.242678i	−0.657640	+	0.753332i	$0.728445\pi$
$48$	−8.12264	−	11.1799i	−1.17240	−	1.61367i
$49$	6.96651			0.995216
$50$	8.16026	−	3.08253i	1.15403	−	0.435935i
$51$	−15.7671			−2.20784
$52$	0.821684	+	1.13095i	0.113947	+	0.156835i
$53$	−5.56509	−	1.80821i	−0.764423	−	0.248376i	−0.0992473	−	0.995063i	$-0.531643\pi$
$53$	−5.56509	−	1.80821i	−0.764423	−	0.248376i	−0.665176	+	0.746687i	$0.731643\pi$
$54$	−2.45124	+	7.54413i	−0.333571	+	1.02663i
$55$	4.64584	+	1.38966i	0.626444	+	0.187382i
$56$	−0.0943455	−	0.290366i	−0.0126075	−	0.0388017i
$57$			2.76487i			0.366215i
$58$	−2.87999	+	0.935765i	−0.378161	+	0.122872i
$59$	−3.45806	−	2.51243i	−0.450201	−	0.327091i	0.339474	−	0.940615i	$-0.389751\pi$
$59$	−3.45806	−	2.51243i	−0.450201	−	0.327091i	−0.789675	+	0.613525i	$0.789751\pi$
$60$	6.45065	−	0.151680i	0.832775	−	0.0195817i
$61$	6.88904	−	5.00518i	0.882051	−	0.640848i	−0.0517420	−	0.998660i	$-0.516477\pi$
$61$	6.88904	−	5.00518i	0.882051	−	0.640848i	0.933793	+	0.357813i	$0.116477\pi$
$62$	1.25004	−	1.72054i	0.158756	−	0.218508i
$63$	−0.499562	+	0.687588i	−0.0629389	+	0.0866280i
$64$	0.489556	−	0.355683i	0.0611945	−	0.0444604i
$65$	2.99424	−	0.0704061i	0.371390	−	0.00873280i
$66$	8.46287	+	6.14864i	1.04171	+	0.756845i
$67$	10.4246	−	3.38717i	1.27357	−	0.413809i	0.407260	−	0.913312i	$-0.366484\pi$
$67$	10.4246	−	3.38717i	1.27357	−	0.413809i	0.866312	+	0.499503i	$0.166484\pi$
$68$			5.95172i			0.721752i
$69$	5.58619	+	17.1925i	0.672499	+	2.06974i
$70$	0.683926	+	0.204576i	0.0817448	+	0.0244515i
$71$	3.29737	−	10.1483i	0.391326	−	1.20438i	−0.540460	−	0.841370i	$-0.681750\pi$
$71$	3.29737	−	10.1483i	0.391326	−	1.20438i	0.931786	−	0.363008i	$-0.118250\pi$
$72$	−7.36969	−	2.39456i	−0.868527	−	0.282201i
$73$	−0.671208	−	0.923839i	−0.0785590	−	0.108127i	0.767929	−	0.640535i	$-0.221287\pi$
$73$	−0.671208	−	0.923839i	−0.0785590	−	0.108127i	−0.846488	+	0.532408i	$0.821287\pi$
$74$	0.208477			0.0242350
$75$	7.59108	−	11.5537i	0.876543	−	1.33410i
$76$	1.04367			0.119717
$77$	0.233259	+	0.321054i	0.0265824	+	0.0365875i
$78$	6.14471	+	1.99654i	0.695751	+	0.226063i
$79$	2.06863	−	6.36659i	0.232739	−	0.716298i	−0.764674	−	0.644417i	$-0.777100\pi$
$79$	2.06863	−	6.36659i	0.232739	−	0.716298i	0.997413	−	0.0718804i	$-0.0229000\pi$
$80$	0.262720	+	11.1730i	0.0293730	+	1.24918i
$81$	−0.420949	−	1.29555i	−0.0467721	−	0.143950i
$82$			6.41871i			0.708828i
$83$	−0.177587	+	0.0577014i	−0.0194927	+	0.00633356i	−0.318747	−	0.947840i	$-0.603262\pi$
$83$	−0.177587	+	0.0577014i	−0.0194927	+	0.00633356i	0.299254	+	0.954173i	$0.403262\pi$
$84$	0.427198	+	0.310378i	0.0466111	+	0.0338650i
$85$	10.4896	+	7.25060i	1.13775	+	0.786438i
$86$	−6.27940	+	4.56225i	−0.677126	+	0.491961i
$87$	−2.82084	+	3.88255i	−0.302426	+	0.416253i
$88$	−2.12673	+	2.92719i	−0.226710	+	0.312039i
$89$	7.27274	−	5.28396i	0.770909	−	0.560098i	−0.131328	−	0.991339i	$-0.541924\pi$
$89$	7.27274	−	5.28396i	0.770909	−	0.560098i	0.902237	+	0.431241i	$0.141924\pi$
$90$	14.4037	−	10.9914i	1.51829	−	1.15860i
$91$	0.198295	+	0.144070i	0.0207870	+	0.0151026i
$92$	6.48978	−	2.10866i	0.676606	−	0.219843i
$93$		−	3.37040i		−	0.349494i
$94$	2.90253	+	8.93308i	0.299374	+	0.921377i
$95$	1.27144	−	1.83941i	0.130447	−	0.188720i
$96$	−4.59909	+	14.1546i	−0.469393	+	1.44464i
$97$	14.9162	+	4.84658i	1.51451	+	0.492096i	0.944212	−	0.329339i	$-0.106826\pi$
$97$	14.9162	+	4.84658i	1.51451	+	0.492096i	0.570303	+	0.821434i	$0.306826\pi$
$98$	−7.14386	−	9.83268i	−0.721639	−	0.993251i
$99$	10.0722			1.01229
$100$	−4.36124	−	2.86546i	−0.436124	−	0.286546i
$101$	−15.8213			−1.57428			−0.787138	−	0.616777i	$-0.788438\pi$
$101$	−15.8213			−1.57428			−0.787138	+	0.616777i	$0.788438\pi$
$102$	16.1685	+	22.2540i	1.60092	+	2.20348i
$103$	12.2562	+	3.98229i	1.20764	+	0.392387i	0.842568	−	0.538591i	$-0.181043\pi$
$103$	12.2562	+	3.98229i	1.20764	+	0.392387i	0.365076	+	0.930978i	$0.381043\pi$
$104$	−0.690573	+	2.12537i	−0.0677163	+	0.208409i
$105$	1.06745	−	0.374799i	0.104173	−	0.0365767i
$106$	3.15462	+	9.70892i	0.306404	+	0.943013i
$107$			13.7243i			1.32678i	0.748273	+	0.663391i	$0.230883\pi$
$107$			13.7243i			1.32678i	−0.748273	+	0.663391i	$0.769117\pi$
$108$	4.51309	−	1.46639i	0.434273	−	0.141104i
$109$	−6.46772	−	4.69907i	−0.619495	−	0.450090i	0.233250	−	0.972417i	$-0.425064\pi$
$109$	−6.46772	−	4.69907i	−0.619495	−	0.450090i	−0.852745	+	0.522327i	$0.825064\pi$
$110$	−2.80270	−	7.98227i	−0.267227	−	0.761080i
$111$	0.267295	−	0.194201i	0.0253705	−	0.0184328i
$112$	−0.537596	+	0.739938i	−0.0507981	+	0.0699176i
$113$	7.06861	−	9.72911i	0.664959	−	0.915238i	−0.334674	−	0.942334i	$-0.608626\pi$
$113$	7.06861	−	9.72911i	0.664959	−	0.915238i	0.999633	+	0.0270962i	$0.00862605\pi$
$114$	3.90239	−	2.83525i	0.365492	−	0.265546i
$115$	4.18970	−	14.0067i	0.390691	−	1.30613i
$116$	1.46557	+	1.06480i	0.136075	+	0.0988643i
$117$	5.91651	−	1.92239i	0.546982	−	0.177725i
$118$			7.45717i			0.686488i
$119$	0.322473	+	0.992471i	0.0295611	+	0.0909797i
$120$	6.25743	+	8.20009i	0.571223	+	0.748563i
$121$	−1.94588	+	5.98881i	−0.176898	+	0.544437i
$122$	−14.1288	−	4.59074i	−1.27916	−	0.415626i
$123$	5.97918	+	8.22964i	0.539125	+	0.742042i
$124$	−1.27225			−0.114251
$125$	−10.3632	+	4.19564i	−0.926916	+	0.375270i
$126$	1.48276			0.132094
$127$	−2.44230	−	3.36153i	−0.216719	−	0.298288i	0.686791	−	0.726855i	$-0.259019\pi$
$127$	−2.44230	−	3.36153i	−0.216719	−	0.298288i	−0.903510	+	0.428567i	$0.859019\pi$
$128$	−11.2429	−	3.65304i	−0.993742	−	0.322886i
$129$	−3.80118	+	11.6988i	−0.334675	+	1.03002i
$130$	−3.16984	−	4.15394i	−0.278013	−	0.364324i
$131$	−4.77274	−	14.6890i	−0.416996	−	1.28338i	−0.910453	−	0.413612i	$-0.864267\pi$
$131$	−4.77274	−	14.6890i	−0.416996	−	1.28338i	0.493457	−	0.869770i	$-0.335733\pi$
$132$		−	6.25785i		−	0.544676i
$133$	0.174036	−	0.0565478i	0.0150909	−	0.00490332i
$134$	−15.4707	−	11.2402i	−1.33647	−	0.971002i
$135$	2.91358	−	9.74048i	0.250761	−	0.838327i
$136$	−7.69736	+	5.59246i	−0.660043	+	0.479549i
$137$	8.62684	−	11.8738i	0.737040	−	1.01445i	−0.261743	−	0.965138i	$-0.584297\pi$
$137$	8.62684	−	11.8738i	0.737040	−	1.01445i	0.998783	−	0.0493115i	$-0.0157027\pi$
$138$	18.5375	−	25.5147i	1.57802	−	2.17195i
$139$	12.6598	−	9.19788i	1.07379	−	0.780154i	0.0972005	−	0.995265i	$-0.469011\pi$
$139$	12.6598	−	9.19788i	1.07379	−	0.780154i	0.976590	+	0.215111i	$0.0690112\pi$
$140$	−0.141478	−	0.402938i	−0.0119571	−	0.0340545i
$141$	12.0428	+	8.74961i	1.01419	+	0.736850i
$142$	−17.7048	+	5.75264i	−1.48575	+	0.482751i
$143$		−	2.90475i		−	0.242907i
$144$	7.17339	+	22.0774i	0.597782	+	1.83978i
$145$	3.66207	−	1.28581i	0.304118	−	0.106781i
$146$	−0.615630	+	1.89472i	−0.0509499	+	0.156808i
$147$	−18.3188	−	5.95212i	−1.51091	−	0.490923i
$148$	−0.0733064	−	0.100898i	−0.00602575	−	0.00829373i
$149$	−16.2615			−1.33219			−0.666096	−	0.745866i	$-0.732036\pi$
$149$	−16.2615			−1.33219			−0.666096	+	0.745866i	$0.732036\pi$
$150$	−24.0914	+	1.13359i	−1.96706	+	0.0925574i
$151$	−17.5248			−1.42614			−0.713072	−	0.701091i	$-0.752697\pi$
$151$	−17.5248			−1.42614			−0.713072	+	0.701091i	$0.752697\pi$
$152$	0.980673	+	1.34978i	0.0795431	+	0.109482i
$153$	25.1896	+	8.18461i	2.03646	+	0.661687i
$154$	0.213945	−	0.658454i	0.0172402	−	0.0530598i
$155$	−1.54990	+	2.24226i	−0.124491	+	0.180103i
$156$	−1.19438	−	3.67592i	−0.0956269	−	0.294309i
$157$		−	8.35830i		−	0.667065i	−0.942739	−	0.333533i	$-0.891759\pi$
$157$		−	8.35830i		−	0.667065i	0.942739	−	0.333533i	$-0.108241\pi$
$158$	−11.1072	+	3.60896i	−0.883644	+	0.287113i
$159$	13.0887	+	9.50951i	1.03800	+	0.754154i
$160$	9.56874	−	7.30184i	0.756475	−	0.577261i
$161$	0.967945	−	0.703253i	0.0762847	−	0.0554241i
$162$	−1.39690	+	1.92266i	−0.109751	+	0.151059i
$163$	−10.3885	+	14.2985i	−0.813689	+	1.11995i	0.177054	+	0.984201i	$0.443343\pi$
$163$	−10.3885	+	14.2985i	−0.813689	+	1.11995i	−0.990744	+	0.135746i	$0.956657\pi$
$164$	3.10650	−	2.25700i	0.242577	−	0.176242i
$165$	−11.0291	−	7.62354i	−0.858615	−	0.593492i
$166$	0.263549	+	0.191479i	0.0204553	+	0.0148617i
$167$	7.07530	−	2.29890i	0.547503	−	0.177895i	−0.0221875	−	0.999754i	$-0.507063\pi$
$167$	7.07530	−	2.29890i	0.547503	−	0.177895i	0.569691	+	0.821859i	$0.307063\pi$
$168$			0.844137i			0.0651266i
$169$	3.46282	+	10.6575i	0.266371	+	0.819804i
$170$	−0.522957	−	22.2404i	−0.0401090	−	1.70576i
$171$	1.43522	−	4.41717i	0.109754	−	0.337789i
$172$	4.41603	+	1.43486i	0.336719	+	0.109407i
$173$	13.5722	+	18.6805i	1.03187	+	1.42025i	0.903533	+	0.428519i	$0.140964\pi$
$173$	13.5722	+	18.6805i	1.03187	+	1.42025i	0.128339	+	0.991730i	$0.459036\pi$
$174$	8.37257			0.634723
$175$	−0.882509	−	0.241527i	−0.0667114	−	0.0182577i
$176$	10.8391			0.817024
$177$	6.94653	+	9.56108i	0.522133	+	0.718655i
$178$	−14.9158	−	4.84643i	−1.11798	−	0.363255i
$179$	−2.76194	+	8.50038i	−0.206437	+	0.635348i	0.793214	+	0.608943i	$0.208406\pi$
$179$	−2.76194	+	8.50038i	−0.206437	+	0.635348i	−0.999651	+	0.0264053i	$0.991594\pi$
$180$	−10.3843	−	3.10617i	−0.774002	−	0.231520i
$181$	−4.07516	−	12.5421i	−0.302905	−	0.932244i	−0.980451	−	0.196764i	$-0.936957\pi$
$181$	−4.07516	−	12.5421i	−0.302905	−	0.932244i	0.677546	−	0.735480i	$-0.263043\pi$
$182$		−	0.427616i		−	0.0316970i
$183$	−22.3914	+	7.27541i	−1.65522	+	0.537814i
$184$	8.82517	+	6.41186i	0.650600	+	0.472688i
$185$	−0.267131	+	0.00628127i	−0.0196399	+	0.000461808i
$186$	−4.75705	+	3.45620i	−0.348804	+	0.253421i
$187$	7.26916	−	10.0051i	0.531573	−	0.731648i
$188$	3.30277	−	4.54588i	0.240880	−	0.331542i
$189$	0.673123	−	0.489053i	0.0489625	−	0.0355734i
$190$	−3.89999	+	0.0917039i	−0.282935	+	0.00665290i
$191$	22.2662	+	16.1774i	1.61113	+	1.17055i	0.859813	+	0.510609i	$0.170580\pi$
$191$	22.2662	+	16.1774i	1.61113	+	1.17055i	0.751315	+	0.659944i	$0.229420\pi$
$192$	−1.59120	+	0.517013i	−0.114835	+	0.0373122i
$193$			25.7948i			1.85675i	0.371648	+	0.928374i	$0.378793\pi$
$193$			25.7948i			1.85675i	−0.371648	+	0.928374i	$0.621207\pi$
$194$	−8.45541	−	26.0231i	−0.607063	−	1.86835i
$195$	−7.93364	−	2.37312i	−0.568140	−	0.169942i
$196$	−2.24679	+	6.91490i	−0.160485	+	0.493922i
$197$	21.5842	+	7.01312i	1.53781	+	0.499664i	0.950771	−	0.309895i	$-0.100294\pi$
$197$	21.5842	+	7.01312i	1.53781	+	0.499664i	0.587038	+	0.809559i	$0.300294\pi$
$198$	−10.3286	−	14.2161i	−0.734023	−	1.01030i
$199$	−7.89131			−0.559400			−0.279700	−	0.960087i	$-0.590235\pi$
$199$	−7.89131			−0.559400			−0.279700	+	0.960087i	$0.590235\pi$
$200$	−0.392093	−	8.33289i	−0.0277252	−	0.589224i
$201$	−30.3060			−2.13762
$202$	16.2240	+	22.3305i	1.14152	+	1.57117i
$203$	0.302082	+	0.0981525i	0.0212020	+	0.00688895i
$204$	5.08509	−	15.6503i	0.356028	−	1.09574i
$205$	−0.193392	−	8.22459i	−0.0135071	−	0.574430i
$206$	−6.94756	−	21.3824i	−0.484059	−	1.48978i
$207$		−	30.3667i		−	2.11063i
$208$	6.36696	−	2.06875i	0.441470	−	0.143442i
$209$	−1.75447	−	1.27469i	−0.121359	−	0.0881724i
$210$	−1.62362	−	1.12228i	−0.112041	−	0.0774448i
$211$	4.27277	−	3.10435i	0.294149	−	0.213712i	−0.430916	−	0.902392i	$-0.641810\pi$
$211$	4.27277	−	3.10435i	0.294149	−	0.213712i	0.725065	+	0.688680i	$0.241810\pi$
$212$	3.58962	−	4.94069i	0.246536	−	0.339328i
$213$	−17.3412	+	23.8681i	−1.18820	+	1.63541i
$214$	19.3708	−	14.0737i	1.32416	−	0.962061i
$215$	7.90863	−	6.03502i	0.539364	−	0.411585i
$216$	6.13715	+	4.45890i	0.417581	+	0.303390i
$217$	−0.212152	+	0.0689323i	−0.0144018	+	0.00467943i
$218$			13.9474i			0.944636i
$219$	0.975652	+	3.00275i	0.0659285	+	0.202907i
$220$	−2.87771	+	4.16323i	−0.194015	+	0.280685i
$221$	2.36038	−	7.26451i	0.158777	−	0.488664i
$222$	−0.548199	−	0.178121i	−0.0367927	−	0.0119547i
$223$	9.75180	+	13.4222i	0.653029	+	0.898817i	0.999226	−	0.0393450i	$-0.0125271\pi$
$223$	9.75180	+	13.4222i	0.653029	+	0.898817i	−0.346197	+	0.938162i	$0.612527\pi$
$224$	0.985029			0.0658150
$225$	−18.1250	+	14.5177i	−1.20833	+	0.967850i
$226$	−20.9804			−1.39560
$227$	−8.26050	−	11.3696i	−0.548269	−	0.754627i	0.441507	−	0.897258i	$-0.354444\pi$
$227$	−8.26050	−	11.3696i	−0.548269	−	0.754627i	−0.989776	+	0.142630i	$0.954444\pi$
$228$	−2.74438	−	0.891704i	−0.181751	−	0.0590545i
$229$	−2.02349	+	6.22768i	−0.133716	+	0.411536i	−0.995388	−	0.0959295i	$-0.969418\pi$
$229$	−2.02349	+	6.22768i	−0.133716	+	0.411536i	0.861672	+	0.507466i	$0.169418\pi$
$230$	−24.0657	+	8.44986i	−1.58685	+	0.557168i
$231$	−0.339060	−	1.04352i	−0.0223085	−	0.0686586i
$232$			2.89595i			0.190129i
$233$	−24.1345	+	7.84177i	−1.58110	+	0.513732i	−0.962341	−	0.271847i	$-0.912366\pi$
$233$	−24.1345	+	7.84177i	−1.58110	+	0.513732i	−0.618762	+	0.785578i	$0.712366\pi$
$234$	−8.78043	−	6.37936i	−0.573995	−	0.417032i
$235$	−3.98830	−	11.3589i	−0.260168	−	0.740974i
$236$	3.60909	−	2.62215i	0.234931	−	0.170688i
$237$	−10.8791	+	14.9738i	−0.706674	+	0.972654i
$238$	1.07011	−	1.47288i	0.0693650	−	0.0954728i
$239$	−2.88318	+	2.09475i	−0.186497	+	0.135498i	−0.677116	−	0.735876i	$-0.736771\pi$
$239$	−2.88318	+	2.09475i	−0.186497	+	0.135498i	0.490619	+	0.871374i	$0.336771\pi$
$240$	8.85526	−	29.6043i	0.571605	−	1.91095i
$241$	13.8342	+	10.0511i	0.891140	+	0.647451i	0.936175	−	0.351534i	$-0.114340\pi$
$241$	13.8342	+	10.0511i	0.891140	+	0.647451i	−0.0450349	+	0.998985i	$0.514340\pi$
$242$	10.4482	−	3.39481i	0.671633	−	0.218227i
$243$			17.4067i			1.11664i
$244$	2.74630	+	8.45224i	0.175814	+	0.541099i
$245$	9.45000	+	12.3838i	0.603739	+	0.791173i
$246$	5.48409	−	16.8783i	0.349653	−	1.07612i
$247$	−1.27388	−	0.413908i	−0.0810550	−	0.0263364i
$248$	−1.19545	−	1.64540i	−0.0759112	−	0.104483i
$249$	0.516272			0.0327174
$250$	16.5489	+	10.3244i	1.04664	+	0.652974i
$251$	−2.12838			−0.134342			−0.0671710	−	0.997741i	$-0.521397\pi$
$251$	−2.12838			−0.134342			−0.0671710	+	0.997741i	$0.521397\pi$
$252$	−0.521379	−	0.717617i	−0.0328438	−	0.0452056i
$253$	−13.4851	−	4.38156i	−0.847799	−	0.275466i
$254$	−2.24007	+	6.89422i	−0.140554	+	0.432582i
$255$	−21.3879	−	28.0280i	−1.33936	−	1.75518i
$256$	5.99916	+	18.4635i	0.374947	+	1.15397i
$257$		−	13.2602i		−	0.827151i	−0.910470	−	0.413575i	$-0.864280\pi$
$257$		−	13.2602i		−	0.827151i	0.910470	−	0.413575i	$-0.135720\pi$
$258$	20.4099	−	6.63158i	1.27067	−	0.412864i
$259$	−0.0176909	−	0.0128532i	−0.00109926	−	0.000798659i
$260$	−0.895796	+	2.99476i	−0.0555549	+	0.185727i
$261$	6.52200	−	4.73851i	0.403702	−	0.293306i
$262$	−15.8381	+	21.7993i	−0.978481	+	1.34676i
$263$	8.28311	−	11.4007i	0.510759	−	0.702999i	−0.473288	−	0.880908i	$-0.656933\pi$
$263$	8.28311	−	11.4007i	0.510759	−	0.702999i	0.984047	+	0.177909i	$0.0569331\pi$
$264$	8.09328	−	5.88011i	0.498107	−	0.361896i
$265$	−4.33468	−	12.3454i	−0.266277	−	0.758373i
$266$	−0.258279	−	0.187651i	−0.0158361	−	0.0115056i
$267$	−23.6386	+	7.68063i	−1.44666	+	0.470047i
$268$			11.4398i			0.698798i
$269$	−6.80780	−	20.9522i	−0.415079	−	1.27748i	−0.912181	−	0.409788i	$-0.865603\pi$
$269$	−6.80780	−	20.9522i	−0.415079	−	1.27748i	0.497102	−	0.867692i	$-0.334397\pi$
$270$	−16.7357	+	5.87617i	−1.01850	+	0.357612i
$271$	5.92868	−	18.2466i	0.360142	−	1.10840i	−0.592826	−	0.805331i	$-0.701988\pi$
$271$	5.92868	−	18.2466i	0.360142	−	1.10840i	0.952968	−	0.303072i	$-0.0980123\pi$
$272$	27.1075	+	8.80775i	1.64363	+	0.534048i
$273$	−0.398334	−	0.548260i	−0.0241083	−	0.0331822i
$274$	−25.6054			−1.54688
$275$	3.83173	+	10.1436i	0.231062	+	0.611682i
$276$	−18.8668			−1.13565
$277$	−0.220167	−	0.303034i	−0.0132285	−	0.0182075i	0.802351	−	0.596852i	$-0.203582\pi$
$277$	−0.220167	−	0.303034i	−0.0132285	−	0.0182075i	−0.815580	+	0.578644i	$0.803582\pi$
$278$	−25.9642	−	8.43627i	−1.55723	−	0.505974i
$279$	−1.74955	+	5.38457i	−0.104743	+	0.322366i
$280$	0.388181	−	0.561589i	0.0231983	−	0.0335613i
$281$	8.18546	+	25.1922i	0.488303	+	1.50284i	0.827139	+	0.561998i	$0.189967\pi$
$281$	8.18546	+	25.1922i	0.488303	+	1.50284i	−0.338835	+	0.940846i	$0.610033\pi$
$282$		−	25.9698i		−	1.54648i
$283$	−13.9485	+	4.53215i	−0.829153	+	0.269408i	−0.692689	−	0.721237i	$-0.743574\pi$
$283$	−13.9485	+	4.53215i	−0.829153	+	0.269408i	−0.136464	+	0.990645i	$0.543574\pi$
$284$	9.00964	+	6.54589i	0.534624	+	0.388427i
$285$	−4.91488	+	3.75051i	−0.291133	+	0.222161i
$286$	−4.09983	+	2.97870i	−0.242428	+	0.176134i
$287$	0.395732	−	0.544678i	0.0233593	−	0.0321513i
$288$	14.6951	−	20.2260i	0.865916	−	1.19183i
$289$	12.5563	−	9.12269i	0.738606	−	0.536629i
$290$	−5.57011	−	3.85017i	−0.327088	−	0.226090i
$291$	−35.0820	−	25.4886i	−2.05655	−	1.49417i
$292$	1.13347	−	0.368286i	0.0663312	−	0.0215523i
$293$		−	21.3554i		−	1.24760i	−0.781585	−	0.623799i	$-0.785588\pi$
$293$		−	21.3554i		−	1.24760i	0.781585	−	0.623799i	$-0.214412\pi$
$294$	10.3841	+	31.9591i	0.605616	+	1.86389i
$295$	−0.224680	−	9.55521i	−0.0130814	−	0.556326i
$296$	0.0616094	−	0.189614i	0.00358098	−	0.0110211i
$297$	−9.37772	−	3.04701i	−0.544150	−	0.176805i
$298$	16.6755	+	22.9518i	0.965983	+	1.32956i
$299$	−8.75752			−0.506461
$300$	9.01986	+	11.2611i	0.520762	+	0.650157i
$301$	0.814133			0.0469258
$302$	17.9709	+	24.7348i	1.03411	+	1.42333i
$303$	41.6027	+	13.5176i	2.39002	+	0.776563i
$304$	1.54450	−	4.75347i	0.0885829	−	0.272630i
$305$	18.2422	+	5.45663i	1.04455	+	0.312445i
$306$	−14.2790	−	43.9462i	−0.816275	−	2.51224i
$307$			3.75799i			0.214480i	0.994233	+	0.107240i	$0.0342013\pi$
$307$			3.75799i			0.214480i	−0.994233	+	0.107240i	$0.965799\pi$
$308$	−0.393904	+	0.127987i	−0.0224448	+	0.00729275i
$309$	−28.8259	−	20.9432i	−1.63985	−	1.19142i
$310$	4.75413	−	0.111788i	0.270016	−	0.00634913i
$311$	14.8835	−	10.8135i	0.843968	−	0.613178i	−0.0795086	−	0.996834i	$-0.525335\pi$
$311$	14.8835	−	10.8135i	0.843968	−	0.613178i	0.923476	+	0.383656i	$0.125335\pi$
$312$	3.63179	−	4.99872i	0.205609	−	0.282997i
$313$	−4.10153	+	5.64527i	−0.231832	+	0.319090i	−0.909045	−	0.416697i	$-0.863188\pi$
$313$	−4.10153	+	5.64527i	−0.231832	+	0.319090i	0.677213	+	0.735787i	$0.263188\pi$
$314$	−11.7971	+	8.57108i	−0.665748	+	0.483694i
$315$	−1.89992	+	0.0446745i	−0.107048	+	0.00251712i
$316$	5.65227	+	4.10661i	0.317965	+	0.231015i
$317$	9.11673	−	2.96221i	0.512047	−	0.166374i	−0.0415861	−	0.999135i	$-0.513241\pi$
$317$	9.11673	−	2.96221i	0.512047	−	0.166374i	0.553633	+	0.832761i	$0.313241\pi$
$318$		−	28.2253i		−	1.58280i
$319$	−1.16320	−	3.57997i	−0.0651268	−	0.200440i
$320$	1.29635	+	0.387764i	0.0724681	+	0.0216767i
$321$	11.7260	−	36.0888i	0.654479	−	2.01428i
$322$	−1.98517	−	0.645021i	−0.110629	−	0.0359456i
$323$	−3.35195	−	4.61356i	−0.186507	−	0.256705i
$324$	1.42171			0.0789839
$325$	4.18681	+	5.22712i	0.232243	+	0.289948i
$326$	30.8342			1.70775
$327$	12.9923	+	17.8824i	0.718476	+	0.988898i
$328$	5.83796	+	1.89687i	0.322347	+	0.104737i
$329$	0.304447	−	0.936992i	0.0167847	−	0.0516580i
$330$	0.549856	+	23.3843i	0.0302686	+	1.28727i
$331$	9.49891	+	29.2346i	0.522107	+	1.60688i	0.769966	+	0.638085i	$0.220273\pi$
$331$	9.49891	+	29.2346i	0.522107	+	1.60688i	−0.247859	+	0.968796i	$0.579727\pi$
$332$		−	0.194881i		−	0.0106955i
$333$	−0.527841	+	0.171506i	−0.0289255	+	0.00939846i
$334$	−10.5001	−	7.62880i	−0.574542	−	0.417429i
$335$	20.1620	+	13.9364i	1.10157	+	0.761426i
$336$	2.04583	−	1.48638i	0.111609	−	0.0810888i
$337$	−0.123662	+	0.170206i	−0.00673630	+	0.00927173i	−0.812372	−	0.583140i	$-0.801824\pi$
$337$	−0.123662	+	0.170206i	−0.00673630	+	0.00927173i	0.805636	+	0.592411i	$0.201824\pi$
$338$	11.4912	−	15.8163i	0.625038	−	0.860291i
$339$	−26.8997	+	19.5438i	−1.46099	+	1.06147i
$340$	−10.5799	+	8.07345i	−0.573776	+	0.437844i
$341$	2.13871	+	1.55386i	0.115818	+	0.0841464i
$342$	−7.70624	+	2.50391i	−0.416706	+	0.135396i
$343$			2.55577i			0.137998i
$344$	2.29377	+	7.05950i	0.123672	+	0.380623i
$345$	−22.9842	+	33.2516i	−1.23743	+	1.79021i
$346$	12.4483	−	38.3120i	0.669227	−	2.05967i
$347$	−7.28979	−	2.36860i	−0.391337	−	0.127153i	0.106738	−	0.994287i	$-0.465959\pi$
$347$	−7.28979	−	2.36860i	−0.391337	−	0.127153i	−0.498075	+	0.867134i	$0.665959\pi$
$348$	−2.94403	−	4.05211i	−0.157817	−	0.217216i
$349$	−15.9786			−0.855316			−0.427658	−	0.903941i	$-0.640661\pi$
$349$	−15.9786			−0.855316			−0.427658	+	0.903941i	$0.640661\pi$
$350$	0.564079	+	1.49327i	0.0301513	+	0.0798184i
$351$	−6.09012			−0.325066
$352$	−6.86154	−	9.44410i	−0.365721	−	0.503372i
$353$	−7.27556	−	2.36397i	−0.387239	−	0.125821i	0.108926	−	0.994050i	$-0.465259\pi$
$353$	−7.27556	−	2.36397i	−0.387239	−	0.125821i	−0.496165	+	0.868228i	$0.665259\pi$
$354$	6.37134	−	19.6090i	0.338633	−	1.04220i
$355$	22.5126	−	7.90454i	1.19485	−	0.419530i
$356$	2.89926	+	8.92301i	0.153660	+	0.472918i
$357$		−	2.88526i		−	0.152704i
$358$	14.8299	−	4.81851i	0.783783	−	0.254666i
$359$	18.7439	+	13.6182i	0.989265	+	0.718743i	0.959760	−	0.280822i	$-0.0906070\pi$
$359$	18.7439	+	13.6182i	0.989265	+	0.718743i	0.0295047	+	0.999565i	$0.490607\pi$
$360$	−5.74030	−	16.3487i	−0.302540	−	0.861653i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−13.5232	+	18.6131i	−0.710765	+	0.978284i
$363$	10.2336	−	14.0853i	0.537123	−	0.739286i
$364$	−0.206955	+	0.150362i	−0.0108474	+	0.00788111i
$365$	0.731748	−	2.44633i	0.0383015	−	0.128047i
$366$	33.2301	+	24.1431i	1.73697	+	1.26198i
$367$	−15.3799	+	4.99722i	−0.802822	+	0.260853i	−0.681555	−	0.731767i	$-0.738696\pi$
$367$	−15.3799	+	4.99722i	−0.802822	+	0.260853i	−0.121267	+	0.992620i	$0.538696\pi$
$368$		−	32.6786i		−	1.70349i
$369$	−5.28043	−	16.2515i	−0.274888	−	0.846018i
$370$	0.282797	+	0.370593i	0.0147019	+	0.0192662i
$371$	0.330888	−	1.01837i	0.0171789	−	0.0528711i
$372$	3.34543	+	1.08700i	0.173452	+	0.0563581i
$373$	−8.49486	−	11.6922i	−0.439847	−	0.605398i	0.530331	−	0.847791i	$-0.322068\pi$
$373$	−8.49486	−	11.6922i	−0.439847	−	0.605398i	−0.970178	+	0.242393i	$0.922068\pi$
$374$	−21.5757			−1.11565
$375$	30.8353	−	2.17838i	1.59233	−	0.112491i
$376$	8.98259			0.463242
$377$	−1.36655	−	1.88090i	−0.0703810	−	0.0968711i
$378$	−1.38052	−	0.448558i	−0.0710062	−	0.0230713i
$379$	−12.0138	+	36.9745i	−0.617105	+	1.89925i	−0.256434	+	0.966562i	$0.582548\pi$
$379$	−12.0138	+	36.9745i	−0.617105	+	1.89925i	−0.360671	+	0.932693i	$0.617452\pi$
$380$	1.41573	+	1.85525i	0.0726255	+	0.0951725i
$381$	3.55006	+	10.9260i	0.181875	+	0.559755i
$382$		−	48.0162i		−	2.45672i
$383$	−28.2117	+	9.16653i	−1.44155	+	0.468388i	−0.922380	−	0.386284i	$-0.873758\pi$
$383$	−28.2117	+	9.16653i	−1.44155	+	0.468388i	−0.519169	+	0.854672i	$0.673758\pi$
$384$	26.4426	+	19.2117i	1.34939	+	0.980391i
$385$	−0.254298	+	0.850153i	−0.0129602	+	0.0433278i
$386$	36.4073	−	26.4514i	1.85308	−	1.34634i
$387$	12.1456	−	16.7169i	0.617394	−	0.849770i
$388$	−9.62135	+	13.2427i	−0.488450	+	0.672294i
$389$	−17.6688	+	12.8371i	−0.895844	+	0.650869i	−0.937395	−	0.348268i	$-0.886770\pi$
$389$	−17.6688	+	12.8371i	−0.895844	+	0.650869i	0.0415512	+	0.999136i	$0.486770\pi$
$390$	4.78615	+	13.6312i	0.242356	+	0.690245i
$391$	−30.1645	−	21.9158i	−1.52548	−	1.10833i
$392$	−11.0542	+	3.59173i	−0.558322	+	0.181410i
$393$			42.7031i			2.15409i
$394$	−12.2352	−	37.6560i	−0.616400	−	1.89708i
$395$	14.1235	−	4.95898i	0.710629	−	0.249513i
$396$	−3.24841	+	9.99758i	−0.163239	+	0.502398i
$397$	12.5309	+	4.07153i	0.628907	+	0.204344i	0.606091	−	0.795395i	$-0.292737\pi$
$397$	12.5309	+	4.07153i	0.628907	+	0.204344i	0.0228163	+	0.999740i	$0.492737\pi$
$398$	8.09220	+	11.1380i	0.405625	+	0.558295i
$399$	−0.505950			−0.0253292
$400$	−19.5050	+	15.6231i	−0.975248	+	0.781153i
$401$	0.716498			0.0357802			0.0178901	−	0.999840i	$-0.494305\pi$
$401$	0.716498			0.0357802			0.0178901	+	0.999840i	$0.494305\pi$
$402$	31.0775	+	42.7745i	1.55001	+	2.13340i
$403$	1.55287	+	0.504558i	0.0773540	+	0.0251338i
$404$	5.10256	−	15.7041i	0.253862	−	0.781306i
$405$	1.73198	−	2.50568i	0.0860627	−	0.124508i
$406$	−0.171238	−	0.527016i	−0.00849840	−	0.0261554i
$407$			0.259147i			0.0128454i
$408$	25.0187	−	8.12906i	1.23861	−	0.402448i
$409$	−19.7486	−	14.3482i	−0.976503	−	0.709471i	−0.0195788	−	0.999808i	$-0.506233\pi$
$409$	−19.7486	−	14.3482i	−0.976503	−	0.709471i	−0.956924	+	0.290337i	$0.906233\pi$
$410$	−11.4100	+	8.70692i	−0.563502	+	0.430004i
$411$	−32.8295	+	23.8520i	−1.61936	+	1.17653i
$412$	−7.90558	+	10.8811i	−0.389480	+	0.536073i
$413$	0.459756	−	0.632800i	0.0226231	−	0.0311380i
$414$	−42.8601	+	31.1397i	−2.10646	+	1.53043i
$415$	−0.343466	−	0.237411i	−0.0168601	−	0.0116540i
$416$	−5.83304	−	4.23795i	−0.285988	−	0.207783i
$417$	−41.1481	+	13.3698i	−2.01503	+	0.654723i
$418$			3.78343i			0.185054i
$419$	10.5519	+	32.4755i	0.515495	+	1.58653i	0.782379	+	0.622802i	$0.214006\pi$
$419$	10.5519	+	32.4755i	0.515495	+	1.58653i	−0.266884	+	0.963729i	$0.585994\pi$
$420$	0.0277562	+	1.18042i	0.00135436	+	0.0575986i
$421$	−2.14782	+	6.61032i	−0.104679	+	0.322167i	−0.989655	−	0.143469i	$-0.954174\pi$
$421$	−2.14782	+	6.61032i	−0.104679	+	0.322167i	0.884976	+	0.465636i	$0.154174\pi$
$422$	−8.76308	−	2.84730i	−0.426580	−	0.138604i
$423$	−14.6978	−	20.2298i	−0.714631	−	0.983606i
$424$	9.76273			0.474120
$425$	1.34018	+	28.4818i	0.0650081	+	1.38157i
$426$	51.4705			2.49376
$427$	0.915911	+	1.26064i	0.0443240	+	0.0610068i
$428$	−13.6227	−	4.42627i	−0.658477	−	0.213952i
$429$	−2.48179	+	7.63817i	−0.119822	+	0.368774i
$430$	−16.6279	−	4.97375i	−0.801869	−	0.239855i
$431$	1.58661	+	4.88309i	0.0764244	+	0.235210i	0.981969	−	0.189040i	$-0.0605377\pi$
$431$	1.58661	+	4.88309i	0.0764244	+	0.235210i	−0.905545	+	0.424250i	$0.860538\pi$
$432$		−	22.7252i		−	1.09337i
$433$	25.1959	−	8.18664i	1.21084	−	0.393425i	0.367100	−	0.930181i	$-0.380351\pi$
$433$	25.1959	−	8.18664i	1.21084	−	0.393425i	0.843737	+	0.536757i	$0.180351\pi$
$434$	0.314845	+	0.228748i	0.0151131	+	0.0109803i
$435$	−10.7281	+	0.252260i	−0.514375	+	0.0120949i
$436$	6.75018	−	4.90429i	0.323275	−	0.234873i
$437$	−3.84307	+	5.28953i	−0.183839	+	0.253033i
$438$	3.23765	−	4.45625i	0.154701	−	0.212928i
$439$	32.5741	−	23.6664i	1.55468	−	1.12954i	0.614465	−	0.788944i	$-0.289372\pi$
$439$	32.5741	−	23.6664i	1.55468	−	1.12954i	0.940211	−	0.340593i	$-0.110628\pi$
$440$	−8.08831	+	0.190187i	−0.385595	+	0.00906682i
$441$	26.1764	+	19.0183i	1.24650	+	0.905633i
$442$	−12.6738	+	4.11795i	−0.602829	+	0.195871i
$443$			2.38411i			0.113272i	0.998395	+	0.0566362i	$0.0180375\pi$
$443$			2.38411i			0.113272i	−0.998395	+	0.0566362i	$0.981962\pi$
$444$	0.106556	+	0.327947i	0.00505695	+	0.0155637i
$445$	19.2583	+	5.76055i	0.912930	+	0.273076i
$446$	8.94432	−	27.5278i	0.423526	−	1.30348i
$447$	42.7603	+	13.8937i	2.02249	+	0.657147i
$448$	0.0650874	+	0.0895851i	0.00307509	+	0.00423250i
$449$	1.16937			0.0551858			0.0275929	−	0.999619i	$-0.491216\pi$
$449$	1.16937			0.0551858			0.0275929	+	0.999619i	$0.491216\pi$
$450$	39.0771	+	10.6947i	1.84211	+	0.504152i
$451$	−7.97877			−0.375706
$452$	7.37732	+	10.1540i	0.347000	+	0.477604i
$453$	46.0821	+	14.9730i	2.16513	+	0.703492i
$454$	−7.57651	+	23.3181i	−0.355583	+	1.09437i
$455$	0.0128838	+	0.547924i	0.000604002	+	0.0256871i
$456$	−1.42548	−	4.38719i	−0.0667544	−	0.205449i
$457$		−	14.1371i		−	0.661308i	−0.943752	−	0.330654i	$-0.892731\pi$
$457$		−	14.1371i		−	0.661308i	0.943752	−	0.330654i	$-0.107269\pi$
$458$	10.8649	−	3.53021i	0.507683	−	0.164956i
$459$	−20.9768	−	15.2406i	−0.979114	−	0.711368i
$460$	12.5517	+	8.67600i	0.585227	+	0.404520i
$461$	18.5154	−	13.4522i	0.862346	−	0.626531i	−0.0661763	−	0.997808i	$-0.521080\pi$
$461$	18.5154	−	13.4522i	0.862346	−	0.626531i	0.928522	+	0.371277i	$0.121080\pi$
$462$	−1.12515	+	1.54864i	−0.0523469	+	0.0720494i
$463$	14.2258	−	19.5801i	0.661127	−	0.909963i	−0.338391	−	0.941006i	$-0.609883\pi$
$463$	14.2258	−	19.5801i	0.661127	−	0.909963i	0.999518	+	0.0310422i	$0.00988262\pi$
$464$	7.01855	−	5.09928i	0.325828	−	0.236728i
$465$	5.99129	−	4.57191i	0.277839	−	0.212017i
$466$	35.8169	+	26.0225i	1.65919	+	1.20547i
$467$	−11.5009	+	3.73686i	−0.532197	+	0.172921i	−0.562773	−	0.826611i	$-0.690266\pi$
$467$	−11.5009	+	3.73686i	−0.532197	+	0.172921i	0.0305767	+	0.999532i	$0.490266\pi$
$468$			6.49267i			0.300124i
$469$	0.619827	+	1.90763i	0.0286209	+	0.0880862i
$470$	−11.9424	+	17.2772i	−0.550861	+	0.796940i
$471$	−7.14125	+	21.9785i	−0.329052	+	1.01272i
$472$	6.78246	+	2.20375i	0.312188	+	0.101436i
$473$	−5.67110	−	7.80561i	−0.260758	−	0.358902i
$474$	32.2904			1.48315
$475$	4.99447	−	0.235009i	0.229162	−	0.0107829i
$476$	−1.08912			−0.0499197
$477$	−15.9743	−	21.9867i	−0.731413	−	1.00670i
$478$	5.91316	+	1.92130i	0.270462	+	0.0878783i
$479$	2.10159	−	6.46803i	0.0960241	−	0.295532i	−0.891495	−	0.453030i	$-0.850343\pi$
$479$	2.10159	−	6.46803i	0.0960241	−	0.295532i	0.987519	+	0.157499i	$0.0503430\pi$
$480$	−31.4000	+	11.0251i	−1.43321	+	0.503223i
$481$	0.0494610	+	0.152225i	0.00225523	+	0.00694088i
$482$		−	29.8329i		−	1.35885i
$483$	−3.14611	+	1.02223i	−0.143153	+	0.0465131i
$484$	−5.31687	−	3.86293i	−0.241676	−	0.175588i
$485$	11.6183	+	33.0898i	0.527562	+	1.50253i
$486$	24.5682	−	17.8498i	1.11443	−	0.809684i
$487$	−1.67309	+	2.30282i	−0.0758152	+	0.104351i	−0.845240	−	0.534386i	$-0.820543\pi$
$487$	−1.67309	+	2.30282i	−0.0758152	+	0.104351i	0.769425	+	0.638737i	$0.220543\pi$
$488$	−8.35075	+	11.4938i	−0.378021	+	0.520301i
$489$	39.5335	−	28.7228i	1.78777	−	1.29889i
$490$	7.78821	−	26.0370i	0.351835	−	1.17623i
$491$	12.8344	+	9.32474i	0.579208	+	0.420819i	0.838439	−	0.544996i	$-0.183469\pi$
$491$	12.8344	+	9.32474i	0.579208	+	0.420819i	−0.259230	+	0.965816i	$0.583469\pi$
$492$	−10.0970	+	3.28072i	−0.455209	+	0.147906i
$493$		−	9.89837i		−	0.445800i
$494$	0.722110	+	2.22242i	0.0324892	+	0.0999916i
$495$	13.6628	+	17.9046i	0.614099	+	0.804750i
$496$	−1.88276	+	5.79452i	−0.0845382	+	0.260182i
$497$	1.85706	+	0.603394i	0.0833004	+	0.0270659i
$498$	−0.529415	−	0.728677i	−0.0237236	−	0.0326528i
$499$	−42.4528			−1.90045			−0.950224	−	0.311568i	$-0.899146\pi$
$499$	−42.4528			−1.90045			−0.950224	+	0.311568i	$0.899146\pi$
$500$	−0.822288	−	11.6396i	−0.0367738	−	0.520539i
$501$	−20.5690			−0.918954
$502$	2.18256	+	3.00404i	0.0974125	+	0.134077i
$503$	12.0860	+	3.92696i	0.538886	+	0.175095i	0.565799	−	0.824543i	$-0.308568\pi$
$503$	12.0860	+	3.92696i	0.538886	+	0.175095i	−0.0269132	+	0.999638i	$0.508568\pi$
$504$	0.438186	−	1.34860i	0.0195184	−	0.0600714i
$505$	−21.4614	−	28.1242i	−0.955020	−	1.25151i
$506$	7.64413	+	23.5262i	0.339823	+	1.04587i
$507$		−	30.9828i		−	1.37600i
$508$	4.12430	−	1.34007i	0.182986	−	0.0594558i
$509$	−20.8730	−	15.1651i	−0.925179	−	0.672182i	0.0196288	−	0.999807i	$-0.493752\pi$
$509$	−20.8730	−	15.1651i	−0.925179	−	0.672182i	−0.944808	+	0.327626i	$0.893752\pi$
$510$	−17.6268	+	58.9289i	−0.780529	+	2.60941i
$511$	0.169056	−	0.122826i	0.00747858	−	0.00543351i
$512$	6.01090	−	8.27329i	0.265647	−	0.365631i
$513$	−2.67253	+	3.67842i	−0.117995	+	0.162406i
$514$	−18.7158	+	13.5978i	−0.825517	+	0.599773i
$515$	9.54646	+	27.1889i	0.420667	+	1.19809i
$516$	−10.3862	−	7.54604i	−0.457228	−	0.332196i
$517$	−11.1043	+	3.60799i	−0.488365	+	0.158679i
$518$			0.0381497i			0.00167620i
$519$	−19.7282	−	60.7170i	−0.865970	−	2.66518i
$520$	−4.71485	+	1.65546i	−0.206760	+	0.0725967i
$521$	−9.16309	+	28.2011i	−0.401442	+	1.23551i	0.522388	+	0.852708i	$0.325041\pi$
$521$	−9.16309	+	28.2011i	−0.401442	+	1.23551i	−0.923830	+	0.382804i	$0.874959\pi$
$522$	−13.3761	−	4.34615i	−0.585454	−	0.190226i
$523$	2.96660	+	4.08317i	0.129720	+	0.178545i	0.868937	−	0.494923i	$-0.164804\pi$
$523$	2.96660	+	4.08317i	0.129720	+	0.178545i	−0.739216	+	0.673468i	$0.764804\pi$
$524$	16.1194			0.704181
$525$	2.11424	+	1.38911i	0.0922729	+	0.0606258i
$526$	−24.5852			−1.07197
$527$	4.08605	+	5.62397i	0.177991	+	0.244984i
$528$	−28.5018	−	9.26079i	−1.24038	−	0.403024i
$529$	−6.10257	+	18.7818i	−0.265329	+	0.816599i
$530$	−12.9796	+	18.7778i	−0.563796	+	0.815654i
$531$	−6.13473	−	18.8807i	−0.266224	−	0.819354i
$532$			0.190984i			0.00828022i
$533$	−4.68681	+	1.52284i	−0.203008	+	0.0659614i
$534$	35.0809	+	25.4878i	1.51810	+	1.10297i
$535$	−24.3967	+	18.6169i	−1.05476	+	0.804880i
$536$	−14.7951	+	10.7493i	−0.639051	+	0.464298i
$537$	14.5253	−	19.9923i	0.626812	−	0.862733i
$538$	−22.5913	+	31.0943i	−0.973981	+	1.34057i
$539$	12.2225	−	8.88017i	0.526461	−	0.382496i
$540$	8.72866	+	6.03342i	0.375622	+	0.259637i
$541$	−11.1729	−	8.11759i	−0.480360	−	0.349002i	0.321105	−	0.947044i	$-0.395946\pi$
$541$	−11.1729	−	8.11759i	−0.480360	−	0.349002i	−0.801465	+	0.598041i	$0.795946\pi$
$542$	−31.8333	+	10.3433i	−1.36736	+	0.444281i
$543$			36.4617i			1.56472i
$544$	−9.48585	−	29.1944i	−0.406703	−	1.25170i
$545$	−0.420225	−	17.8714i	−0.0180005	−	0.765527i
$546$	−0.365351	+	1.12444i	−0.0156356	+	0.0481214i
$547$	−30.1095	−	9.78318i	−1.28739	−	0.418299i	−0.416213	−	0.909267i	$-0.636643\pi$
$547$	−30.1095	−	9.78318i	−1.28739	−	0.418299i	−0.871177	+	0.490968i	$0.836643\pi$
$548$	9.00359	+	12.3924i	0.384614	+	0.529376i
$549$	39.5493			1.68792
$550$	10.3876	−	15.8100i	0.442929	−	0.674141i
$551$	−1.73574			−0.0739452
$552$	−17.7279	−	24.4004i	−0.754551	−	1.03855i
$553$	1.16504	+	0.378544i	0.0495425	+	0.0160973i
$554$	−0.201936	+	0.621496i	−0.00857946	+	0.0264049i
$555$	0.707799	+	0.211717i	0.0300444	+	0.00898690i
$556$	5.04680	+	15.5324i	0.214032	+	0.658722i
$557$		−	2.02274i		−	0.0857065i	−0.999081	−	0.0428532i	$-0.986355\pi$
$557$		−	2.02274i		−	0.0857065i	0.999081	−	0.0428532i	$-0.0136448\pi$
$558$	9.39399	−	3.05229i	0.397679	−	0.129214i
$559$	−4.82105	−	3.50270i	−0.203909	−	0.148148i
$560$	−2.04457	+	0.0480758i	−0.0863990	+	0.00203157i
$561$	−27.6629	+	20.0982i	−1.16793	+	0.848548i
$562$	27.1630	−	37.3867i	1.14580	−	1.57706i
$563$	0.0798271	−	0.109873i	0.00336431	−	0.00463058i	−0.807332	−	0.590098i	$-0.799089\pi$
$563$	0.0798271	−	0.109873i	0.00336431	−	0.00463058i	0.810696	+	0.585468i	$0.199089\pi$
$564$	−12.5687	+	9.13173i	−0.529240	+	0.384515i
$565$	26.8832	−	0.632127i	1.13098	−	0.0265938i
$566$	20.7004	+	15.0397i	0.870102	+	0.632166i
$567$	0.237075	−	0.0770305i	0.00995623	−	0.00323498i
$568$			17.8029i			0.746994i
$569$	−1.32757	−	4.08583i	−0.0556545	−	0.171287i	0.919365	−	0.393405i	$-0.128703\pi$
$569$	−1.32757	−	4.08583i	−0.0556545	−	0.171287i	−0.975020	+	0.222118i	$0.928703\pi$
$570$	10.3336	+	3.09098i	0.432825	+	0.129467i
$571$	−5.19251	+	15.9809i	−0.217300	+	0.668780i	0.781683	+	0.623676i	$0.214362\pi$
$571$	−5.19251	+	15.9809i	−0.217300	+	0.668780i	−0.998982	+	0.0451034i	$0.985638\pi$
$572$	2.88323	+	0.936818i	0.120554	+	0.0391703i
$573$	−44.7282	−	61.5631i	−1.86855	−	2.57184i
$574$	−1.17458			−0.0490259
$575$	30.5819	−	11.5523i	1.27535	−	0.481763i
$576$	2.81049			0.117104
$577$	−19.8647	−	27.3414i	−0.826977	−	1.13824i	−0.988478	−	0.151363i	$-0.951634\pi$
$577$	−19.8647	−	27.3414i	−0.826977	−	1.13824i	0.161501	−	0.986872i	$-0.448366\pi$
$578$	−25.7519	−	8.36730i	−1.07114	−	0.348034i
$579$	22.0388	−	67.8285i	0.915901	−	2.81885i
$580$	0.0952222	+	4.04962i	0.00395389	+	0.168151i
$581$	−0.0105589	−	0.0324971i	−0.000438058	−	0.00134820i
$582$			75.6530i			3.13592i
$583$	−12.0687	+	3.92134i	−0.499833	+	0.162405i
$584$	1.54135	+	1.11986i	0.0637816	+	0.0463401i
$585$	11.4430	+	7.90961i	0.473108	+	0.327022i
$586$	−30.1415	+	21.8991i	−1.24513	+	0.904644i
$587$	−16.1323	+	22.2042i	−0.665851	+	0.916465i	−0.999657	−	0.0261765i	$-0.991667\pi$
$587$	−16.1323	+	22.2042i	−0.665851	+	0.916465i	0.333806	+	0.942642i	$0.391667\pi$
$588$	11.8161	−	16.2634i	0.487286	−	0.670691i
$589$	0.986200	−	0.716516i	0.0406356	−	0.0295235i
$590$	−13.2560	+	10.1156i	−0.545742	+	0.416452i
$591$	−50.7646	−	36.8826i	−2.08818	−	1.51715i
$592$	−0.568028	+	0.184564i	−0.0233458	+	0.00758551i
$593$		−	24.4473i		−	1.00393i	−0.864887	−	0.501966i	$-0.832610\pi$
$593$		−	24.4473i		−	1.00393i	0.864887	−	0.501966i	$-0.167390\pi$
$594$	5.31584	+	16.3605i	0.218112	+	0.671279i
$595$	−1.32681	+	1.91951i	−0.0543937	+	0.0786923i
$596$	5.24453	−	16.1410i	0.214824	−	0.661161i
$597$	20.7505	+	6.74226i	0.849263	+	0.275942i
$598$	8.98047	+	12.3606i	0.367239	+	0.505461i
$599$	16.9862			0.694038			0.347019	−	0.937858i	$-0.387194\pi$
$599$	16.9862			0.694038			0.347019	+	0.937858i	$0.387194\pi$
$600$	−6.08851	+	22.2467i	−0.248562	+	0.908217i
$601$	28.4769			1.16160			0.580798	−	0.814048i	$-0.302741\pi$
$601$	28.4769			1.16160			0.580798	+	0.814048i	$0.302741\pi$
$602$	−0.834858	−	1.14908i	−0.0340263	−	0.0468332i
$603$	48.4171	+	15.7317i	1.97170	+	0.640643i
$604$	5.65195	−	17.3949i	0.229975	−	0.707789i
$605$	−13.2854	+	4.66472i	−0.540129	+	0.189648i
$606$	−23.5829	−	72.5807i	−0.957989	−	2.94839i
$607$		−	0.425849i		−	0.0172847i	−0.999963	−	0.00864235i	$-0.997249\pi$
$607$		−	0.425849i		−	0.0172847i	0.999963	−	0.00864235i	$-0.00275098\pi$
$608$	−5.11943	+	1.66341i	−0.207621	+	0.0674600i
$609$	−0.710478	−	0.516192i	−0.0287900	−	0.0209172i
$610$	−11.0050	−	31.3430i	−0.445581	−	1.26904i
$611$	−5.83412	+	4.23874i	−0.236023	+	0.171481i
$612$	−16.2480	+	22.3634i	−0.656784	+	0.903986i
$613$	−4.19735	+	5.77716i	−0.169529	+	0.233337i	−0.885325	−	0.464973i	$-0.846064\pi$
$613$	−4.19735	+	5.77716i	−0.169529	+	0.233337i	0.715796	+	0.698310i	$0.246064\pi$
$614$	5.30410	−	3.85365i	0.214056	−	0.155521i
$615$	−6.51848	+	21.7921i	−0.262850	+	0.878744i
$616$	−0.535653	−	0.389175i	−0.0215821	−	0.0156803i
$617$	−26.0209	+	8.45470i	−1.04756	+	0.340374i	−0.781711	−	0.623641i	$-0.785653\pi$
$617$	−26.0209	+	8.45470i	−1.04756	+	0.340374i	−0.265851	+	0.964014i	$0.585653\pi$
$618$			62.1619i			2.50052i
$619$	7.59551	+	23.3766i	0.305290	+	0.939584i	0.979569	+	0.201108i	$0.0644543\pi$
$619$	7.59551	+	23.3766i	0.305290	+	0.939584i	−0.674280	+	0.738476i	$0.735546\pi$
$620$	−1.72579	−	2.26157i	−0.0693094	−	0.0908269i
$621$	−9.18641	+	28.2729i	−0.368638	+	1.13455i
$622$	−30.5249	−	9.91813i	−1.22394	−	0.397681i
$623$	0.966925	+	1.33086i	0.0387390	+	0.0533197i
$624$	−18.5097			−0.740982
$625$	−21.5159	−	12.7305i	−0.860635	−	0.509222i
$626$	12.1738			0.486563
$627$	3.52436	+	4.85086i	0.140749	+	0.193725i
$628$	8.29638	+	2.69566i	0.331062	+	0.107568i
$629$	−0.210581	+	0.648103i	−0.00839643	+	0.0258415i
$630$	2.01134	+	2.63578i	0.0801338	+	0.105012i
$631$	2.87382	+	8.84470i	0.114405	+	0.352102i	0.991822	−	0.127625i	$-0.0407356\pi$
$631$	2.87382	+	8.84470i	0.114405	+	0.352102i	−0.877418	+	0.479727i	$0.840736\pi$
$632$			11.1688i			0.444271i
$633$	−13.8877	+	4.51240i	−0.551988	+	0.179352i
$634$	−13.5297	−	9.82993i	−0.537335	−	0.390397i
$635$	2.66258	−	8.90136i	0.105661	−	0.353240i
$636$	−13.6603	+	9.92482i	−0.541668	+	0.393545i
$637$	5.48474	−	7.54910i	0.217313	−	0.299106i
$638$	−3.86003	+	5.31287i	−0.152820	+	0.210339i
$639$	40.0941	−	29.1301i	1.58610	−	1.15237i
$640$	−8.75717	−	24.9409i	−0.346157	−	0.985877i
$641$	13.6328	+	9.90482i	0.538464	+	0.391217i	0.823514	−	0.567296i	$-0.192010\pi$
$641$	13.6328	+	9.90482i	0.538464	+	0.391217i	−0.285050	+	0.958513i	$0.592010\pi$
$642$	−62.9609	+	20.4572i	−2.48487	+	0.807383i
$643$		−	48.2349i		−	1.90220i	−0.308886	−	0.951099i	$-0.599956\pi$
$643$		−	48.2349i		−	1.90220i	0.308886	−	0.951099i	$-0.400044\pi$
$644$	0.385869	+	1.18758i	0.0152054	+	0.0467973i
$645$	−25.9523	+	9.11228i	−1.02187	+	0.358796i
$646$	−3.07439	+	9.46201i	−0.120960	+	0.372278i
$647$	16.3946	+	5.32694i	0.644540	+	0.209424i	0.613005	−	0.790079i	$-0.289961\pi$
$647$	16.3946	+	5.32694i	0.644540	+	0.209424i	0.0315346	+	0.999503i	$0.489961\pi$
$648$	1.33589	+	1.83870i	0.0524788	+	0.0722309i
$649$	−9.26963			−0.363865
$650$	3.08427	−	11.2695i	0.120975	−	0.442028i
$651$	0.616758			0.0241726
$652$	−10.8422	−	14.9230i	−0.424613	−	0.584429i
$653$	−14.0574	−	4.56754i	−0.550110	−	0.178742i	0.0207563	−	0.999785i	$-0.493393\pi$
$653$	−14.0574	−	4.56754i	−0.550110	−	0.178742i	−0.570866	+	0.821043i	$0.693393\pi$
$654$	11.9165	−	36.6752i	0.465972	−	1.43412i
$655$	19.6373	−	28.4096i	0.767292	−	1.11005i
$656$	−5.68245	−	17.4888i	−0.221862	−	0.682822i
$657$		−	5.30367i		−	0.206916i
$658$	−1.63469	+	0.531142i	−0.0637267	+	0.0207061i
$659$	10.2480	+	7.44564i	0.399207	+	0.290041i	0.769218	−	0.638987i	$-0.220646\pi$
$659$	10.2480	+	7.44564i	0.399207	+	0.290041i	−0.370011	+	0.929027i	$0.620646\pi$
$660$	11.1241	−	8.48871i	0.433005	−	0.330423i
$661$	27.0529	−	19.6551i	1.05224	−	0.764495i	0.0796003	−	0.996827i	$-0.474636\pi$
$661$	27.0529	−	19.6551i	1.05224	−	0.764495i	0.972637	+	0.232332i	$0.0746356\pi$
$662$	31.5217	−	43.3858i	1.22512	−	1.68624i
$663$	−12.4135	+	17.0857i	−0.482099	+	0.663552i
$664$	0.252039	−	0.183117i	0.00978101	−	0.00710632i
$665$	0.336599	+	0.232664i	0.0130527	+	0.00902232i
$666$	0.783345	+	0.569134i	0.0303540	+	0.0220535i
$667$	−10.7932	+	3.50693i	−0.417916	+	0.135789i
$668$			7.76431i			0.300410i
$669$	−14.1750	−	43.6261i	−0.548036	−	1.68668i
$670$	−1.00518	−	42.7483i	−0.0388334	−	1.65151i
$671$	5.70651	−	17.5628i	0.220297	−	0.678006i
$672$	−2.59018	−	0.841600i	−0.0999182	−	0.0324654i
$673$	3.27693	+	4.51031i	0.126316	+	0.173859i	0.867491	−	0.497452i	$-0.165731\pi$
$673$	3.27693	+	4.51031i	0.126316	+	0.173859i	−0.741175	+	0.671312i	$0.765731\pi$
$674$	0.367043			0.0141380
$675$	21.2671	−	8.03363i	0.818572	−	0.309215i
$676$	−11.6953			−0.449819
$677$	−5.42431	−	7.46592i	−0.208473	−	0.286939i	0.691958	−	0.721938i	$-0.256748\pi$
$677$	−5.42431	−	7.46592i	−0.208473	−	0.286939i	−0.900431	+	0.435000i	$0.856748\pi$
$678$	55.1690	+	17.9255i	2.11875	+	0.688424i
$679$	−0.886888	+	2.72956i	−0.0340356	+	0.104751i
$680$	−20.3826	−	6.09687i	−0.781639	−	0.233804i
$681$	12.0073	+	36.9546i	0.460120	+	1.41610i
$682$		−	4.61204i		−	0.176604i
$683$	−39.9942	+	12.9949i	−1.53034	+	0.497236i	−0.948691	−	0.316206i	$-0.897591\pi$
$683$	−39.9942	+	12.9949i	−1.53034	+	0.497236i	−0.581646	+	0.813442i	$0.697591\pi$
$684$	3.92156	+	2.84918i	0.149945	+	0.108941i
$685$	32.8094	−	0.771474i	1.25358	−	0.0294765i
$686$	3.60726	−	2.62083i	0.137726	−	0.100064i
$687$	10.6417	−	14.6471i	0.406008	−	0.558821i
$688$	13.0703	−	17.9897i	0.498300	−	0.685851i
$689$	−6.34081	+	4.60687i	−0.241566	+	0.175508i
$690$	70.5014	−	1.65776i	2.68394	−	0.0631098i
$691$	−7.37993	−	5.36183i	−0.280746	−	0.203974i	0.438497	−	0.898733i	$-0.355511\pi$
$691$	−7.37993	−	5.36183i	−0.280746	−	0.203974i	−0.719243	+	0.694759i	$0.755511\pi$
$692$	−22.9193	+	7.44692i	−0.871259	+	0.283089i
$693$			1.84314i			0.0700150i
$694$	4.13228	+	12.7179i	0.156859	+	0.482763i
$695$	33.5232	+	10.0275i	1.27161	+	0.380364i
$696$	2.47427	−	7.61503i	0.0937871	−	0.288647i
$697$	−19.9542	−	6.48350i	−0.755818	−	0.245580i
$698$	16.3854	+	22.5526i	0.620197	+	0.853627i
$699$	70.1626			2.65379
$700$	0.524357	−	0.798075i	0.0198188	−	0.0301644i
$701$	−1.37067			−0.0517694			−0.0258847	−	0.999665i	$-0.508240\pi$
$701$	−1.37067			−0.0517694			−0.0258847	+	0.999665i	$0.508240\pi$
$702$	6.24515	+	8.59572i	0.235708	+	0.324424i
$703$	0.113649	+	0.0369268i	0.00428635	+	0.00139272i
$704$	0.405522	−	1.24807i	0.0152837	−	0.0470383i
$705$	0.782454	+	33.2763i	0.0294689	+	1.25326i
$706$	4.12421	+	12.6930i	0.155217	+	0.477708i
$707$		−	2.89518i		−	0.108884i
$708$	−11.7306	+	3.81150i	−0.440863	+	0.143245i
$709$	−14.4547	−	10.5019i	−0.542856	−	0.394408i	0.282289	−	0.959329i	$-0.408906\pi$
$709$	−14.4547	−	10.5019i	−0.542856	−	0.394408i	−0.825145	+	0.564922i	$0.808906\pi$
$710$	−34.2424	−	23.6690i	−1.28509	−	0.888282i
$711$	25.1534	−	18.2750i	0.943324	−	0.685365i
$712$	−8.81587	+	12.1340i	−0.330389	+	0.454741i
$713$	4.68474	−	6.44799i	0.175445	−	0.241479i
$714$	−4.07232	+	2.95872i	−0.152403	+	0.110727i
$715$	5.16355	−	3.94026i	0.193106	−	0.147358i
$716$	−7.54664	−	5.48295i	−0.282031	−	0.204908i
$717$	9.37119	−	3.04488i	0.349973	−	0.113713i
$718$		−	40.4204i		−	1.50848i
$719$	0.738903	+	2.27411i	0.0275564	+	0.0848100i	0.963889	−	0.266305i	$-0.0858027\pi$
$719$	0.738903	+	2.27411i	0.0275564	+	0.0848100i	−0.936332	+	0.351115i	$0.885803\pi$
$720$	−29.5146	+	42.6993i	−1.09995	+	1.59131i
$721$	−0.728730	+	2.24280i	−0.0271393	+	0.0835262i
$722$	1.65922	+	0.539115i	0.0617500	+	0.0200638i
$723$	−27.7901	−	38.2498i	−1.03352	−	1.42252i
$724$	13.7634			0.511514
$725$	7.25324	+	4.76557i	0.269378	+	0.176989i
$726$	−30.3744			−1.12730
$727$	29.0969	+	40.0484i	1.07914	+	1.48531i	0.860461	+	0.509517i	$0.170176\pi$
$727$	29.0969	+	40.0484i	1.07914	+	1.48531i	0.218682	+	0.975796i	$0.429824\pi$
$728$	−0.388926	−	0.126370i	−0.0144146	−	0.00468357i
$729$	13.6093	−	41.8850i	0.504047	−	1.55130i
$730$	−4.20318	+	1.47580i	−0.155567	+	0.0546220i
$731$	−7.84012	−	24.1294i	−0.289977	−	0.892458i
$732$		−	24.5719i		−	0.908205i
$733$	47.3827	−	15.3956i	1.75012	−	0.568649i	0.754018	−	0.656854i	$-0.228113\pi$
$733$	47.3827	−	15.3956i	1.75012	−	0.568649i	0.996102	+	0.0882051i	$0.0281131\pi$
$734$	22.8246	+	16.5830i	0.842470	+	0.612090i
$735$	−14.2686	−	40.6378i	−0.526305	−	1.49895i
$736$	−28.4730	+	20.6868i	−1.04953	+	0.762527i
$737$	13.9721	−	19.2309i	0.514667	−	0.708379i
$738$	−17.5228	+	24.1181i	−0.645024	+	0.887800i
$739$	−6.88215	+	5.00018i	−0.253164	+	0.183934i	−0.707128	−	0.707086i	$-0.750010\pi$
$739$	−6.88215	+	5.00018i	−0.253164	+	0.183934i	0.453964	+	0.891020i	$0.350010\pi$
$740$	0.0799183	−	0.267178i	0.00293786	−	0.00982164i
$741$	2.99608	+	2.17678i	0.110064	+	0.0799660i
$742$	−1.77666	+	0.577272i	−0.0652232	+	0.0211923i
$743$			5.05504i			0.185451i	0.995692	+	0.0927257i	$0.0295580\pi$
$743$			5.05504i			0.185451i	−0.995692	+	0.0927257i	$0.970442\pi$
$744$	1.73768	+	5.34802i	0.0637064	+	0.196068i
$745$	−22.0585	−	28.9067i	−0.808162	−	1.05906i
$746$	−7.79146	+	23.9797i	−0.285266	+	0.877958i
$747$	−0.824799	−	0.267993i	−0.0301778	−	0.00980537i
$748$	7.58662	+	10.4421i	0.277394	+	0.381800i
$749$	−2.51145			−0.0917665
$750$	−34.6949	−	41.2877i	−1.26688	−	1.50762i
$751$	−31.3324			−1.14334			−0.571668	−	0.820485i	$-0.693704\pi$
$751$	−31.3324			−1.14334			−0.571668	+	0.820485i	$0.693704\pi$
$752$	−15.8168	−	21.7700i	−0.576780	−	0.793870i
$753$	5.59667	+	1.81847i	0.203954	+	0.0662686i
$754$	−1.25340	+	3.85756i	−0.0456460	+	0.140484i
$755$	−23.7721	−	31.1524i	−0.865157	−	1.13375i
$756$	0.268339	+	0.825862i	0.00975939	+	0.0300363i
$757$			33.9610i			1.23433i	0.786832	+	0.617167i	$0.211720\pi$
$757$			33.9610i			1.23433i	−0.786832	+	0.617167i	$0.788280\pi$
$758$	64.5062	−	20.9594i	2.34297	−	0.761278i
$759$	31.7160	+	23.0430i	1.15122	+	0.836409i
$760$	−1.06913	+	3.57423i	−0.0387813	+	0.129651i
$761$	21.5702	−	15.6717i	0.781920	−	0.568098i	−0.123635	−	0.992328i	$-0.539455\pi$
$761$	21.5702	−	15.6717i	0.781920	−	0.568098i	0.905555	+	0.424230i	$0.139455\pi$
$762$	11.7807	−	16.2148i	0.426770	−	0.587399i
$763$	0.859895	−	1.18354i	0.0311303	−	0.0428472i
$764$	−23.2386	+	16.8839i	−0.840745	+	0.610837i
$765$	19.6204	+	55.8800i	0.709376	+	2.02034i
$766$	41.8677	+	30.4187i	1.51274	+	1.09907i
$767$	−5.44507	+	1.76921i	−0.196610	+	0.0638825i
$768$		−	53.6762i		−	1.93687i
$769$	3.17992	+	9.78678i	0.114671	+	0.352920i	0.991878	−	0.127191i	$-0.0405962\pi$
$769$	3.17992	+	9.78678i	0.114671	+	0.352920i	−0.877207	+	0.480111i	$0.840596\pi$
$770$	1.46070	−	0.512874i	0.0526398	−	0.0184827i
$771$	−11.3294	+	34.8684i	−0.408019	+	1.25575i
$772$	−25.6037	−	8.31913i	−0.921496	−	0.299412i
$773$	−22.6595	−	31.1881i	−0.815004	−	1.12176i	−0.990532	−	0.137282i	$-0.956163\pi$
$773$	−22.6595	−	31.1881i	−0.815004	−	1.12176i	0.175528	−	0.984474i	$-0.443837\pi$
$774$	−36.0494			−1.29577
$775$	−6.08831	+	0.286478i	−0.218699	+	0.0102906i
$776$	−26.1673			−0.939351
$777$	0.0355374	+	0.0489130i	0.00127490	+	0.00175474i
$778$	36.2372	+	11.7742i	1.29917	+	0.422125i
$779$	−1.13692	+	3.49909i	−0.0407345	+	0.125368i
$780$	4.91423	−	7.10951i	0.175958	−	0.254561i
$781$	−7.15081	−	22.0079i	−0.255876	−	0.787505i
$782$			65.0484i			2.32613i
$783$	−7.50578	+	2.43877i	−0.268235	+	0.0871547i
$784$	28.1694	+	20.4663i	1.00605	+	0.730938i
$785$	14.8579	−	11.3380i	0.530301	−	0.404669i
$786$	60.2721	−	43.7902i	2.14983	−	1.56195i
$787$	−18.8193	+	25.9025i	−0.670835	+	0.923326i	−0.999779	−	0.0210238i	$-0.993307\pi$
$787$	−18.8193	+	25.9025i	−0.670835	+	0.923326i	0.328944	+	0.944350i	$0.393307\pi$
$788$	−13.9223	+	19.1624i	−0.495963	+	0.682634i
$789$	−31.5215	+	22.9017i	−1.12219	+	0.815322i
$790$	−21.4822	−	14.8489i	−0.764303	−	0.528302i
$791$	1.78035	+	1.29350i	0.0633021	+	0.0459917i
$792$	−15.9822	+	5.19293i	−0.567903	+	0.184523i
$793$		−	11.4057i		−	0.405029i
$794$	−7.10325	−	21.8615i	−0.252085	−	0.775837i
$795$	0.850410	+	36.1663i	0.0301609	+	1.28269i
$796$	2.54504	−	7.83284i	0.0902067	−	0.277628i
$797$	−25.1255	−	8.16377i	−0.889991	−	0.289176i	−0.171891	−	0.985116i	$-0.554988\pi$
$797$	−25.1255	−	8.16377i	−0.889991	−	0.289176i	−0.718100	+	0.695940i	$0.754988\pi$
$798$	0.518830	+	0.714108i	0.0183664	+	0.0252792i
$799$	−30.7025			−1.08618
$800$	25.9598	+	7.10472i	0.917818	+	0.251190i
$801$	41.7521			1.47524
$802$	−0.734739	−	1.01128i	−0.0259445	−	0.0357096i
$803$	−2.35522	−	0.765258i	−0.0831140	−	0.0270054i
$804$	9.77407	−	30.0815i	0.344705	−	1.06089i
$805$	2.56312	+	0.766683i	0.0903382	+	0.0270220i
$806$	−0.880259	−	2.70916i	−0.0310058	−	0.0954260i
$807$			60.9113i			2.14418i
$808$	25.1046	−	8.15698i	0.883177	−	0.286962i
$809$	1.90214	+	1.38198i	0.0668756	+	0.0485880i	0.620721	−	0.784032i	$-0.286840\pi$
$809$	1.90214	+	1.38198i	0.0668756	+	0.0485880i	−0.553845	+	0.832620i	$0.686840\pi$
$810$	−5.31265	+	0.124921i	−0.186667	+	0.00438927i
$811$	−26.5665	+	19.3017i	−0.932876	+	0.677774i	−0.946695	−	0.322131i	$-0.895601\pi$
$811$	−26.5665	+	19.3017i	−0.932876	+	0.677774i	0.0138194	+	0.999905i	$0.495601\pi$
$812$	−0.194851	+	0.268189i	−0.00683792	+	0.00941158i
$813$	−31.1795	+	42.9149i	−1.09351	+	1.50509i
$814$	0.365766	−	0.265744i	0.0128201	−	0.00931433i
$815$	−39.5092	+	0.929014i	−1.38395	+	0.0325419i
$816$	−63.7550	−	46.3207i	−2.23187	−	1.62155i
$817$	−4.23125	+	1.37481i	−0.148033	+	0.0480987i
$818$			42.5870i			1.48902i
$819$	0.351783	+	1.08268i	0.0122923	+	0.0378318i
$820$	8.22603	+	2.46057i	0.287265	+	0.0859269i
$821$	−6.55344	+	20.1694i	−0.228716	+	0.703917i	0.769177	+	0.639036i	$0.220667\pi$
$821$	−6.55344	+	20.1694i	−0.228716	+	0.703917i	−0.997893	+	0.0648806i	$0.979333\pi$
$822$	67.3306	+	21.8770i	2.34842	+	0.763049i
$823$	17.5280	+	24.1252i	0.610988	+	0.840953i	0.996658	−	0.0816836i	$-0.0260297\pi$
$823$	17.5280	+	24.1252i	0.610988	+	0.840953i	−0.385670	+	0.922637i	$0.626030\pi$
$824$	−21.5009			−0.749019
$825$	−1.40911	−	29.9468i	−0.0490589	−	1.04261i
$826$	−1.36461			−0.0474807
$827$	10.4495	+	14.3825i	0.363364	+	0.500127i	0.951082	−	0.308938i	$-0.0999737\pi$
$827$	10.4495	+	14.3825i	0.363364	+	0.500127i	−0.587718	+	0.809066i	$0.699974\pi$
$828$	30.1417	+	9.79363i	1.04750	+	0.340352i
$829$	8.30371	−	25.5562i	0.288400	−	0.887603i	−0.696959	−	0.717111i	$-0.745464\pi$
$829$	8.30371	−	25.5562i	0.288400	−	0.887603i	0.985359	−	0.170492i	$-0.0545358\pi$
$830$	0.0171235	+	0.728229i	0.000594365	+	0.0252772i
$831$	0.320029	+	0.984949i	0.0111017	+	0.0341675i
$832$		−	0.810525i		−	0.0280999i
$833$	37.7833	−	12.2765i	1.30911	−	0.425357i
$834$	61.0661	+	44.3671i	2.11454	+	1.53631i
$835$	13.6841	+	9.45876i	0.473559	+	0.327334i
$836$	1.83109	−	1.33036i	0.0633295	−	0.0460115i
$837$	3.25784	−	4.48403i	0.112607	−	0.154991i
$838$	35.0160	−	48.1954i	1.20961	−	1.66488i
$839$	−29.0854	+	21.1318i	−1.00414	+	0.729551i	−0.962972	−	0.269601i	$-0.913108\pi$
$839$	−29.0854	+	21.1318i	−1.00414	+	0.729551i	−0.0411690	+	0.999152i	$0.513108\pi$
$840$	−1.50056	+	1.14506i	−0.0517741	+	0.0395084i
$841$	21.0241	+	15.2749i	0.724968	+	0.526720i
$842$	11.5324	−	3.74712i	0.397434	−	0.129134i
$843$		−	73.2377i		−	2.52244i
$844$	1.70333	+	5.24230i	0.0586309	+	0.180447i
$845$	−14.2476	+	20.6123i	−0.490134	+	0.709085i
$846$	−13.4808	+	41.4896i	−0.463479	+	1.42644i
$847$	−1.09591	−	0.356082i	−0.0376558	−	0.0122351i
$848$	−17.1905	−	23.6607i	−0.590324	−	0.812512i
$849$	40.5504			1.39169
$850$	38.8256	−	31.0985i	1.33171	−	1.06667i
$851$	0.781302			0.0267827
$852$	−18.0985	−	24.9104i	−0.620044	−	0.853418i
$853$	19.1883	+	6.23466i	0.656995	+	0.213471i	0.618496	−	0.785788i	$-0.287742\pi$
$853$	19.1883	+	6.23466i	0.656995	+	0.213471i	0.0384991	+	0.999259i	$0.487742\pi$
$854$	0.840071	−	2.58547i	0.0287466	−	0.0884730i
$855$	9.79891	−	3.44056i	0.335116	−	0.117665i
$856$	−7.07587	−	21.7773i	−0.241848	−	0.744332i
$857$			40.5678i			1.38577i	0.721049	+	0.692885i	$0.243660\pi$
$857$			40.5678i			1.38577i	−0.721049	+	0.692885i	$0.756340\pi$
$858$	13.3256	−	4.32976i	0.454930	−	0.147816i
$859$	4.29197	+	3.11830i	0.146440	+	0.106395i	0.658593	−	0.752499i	$-0.271152\pi$
$859$	4.29197	+	3.11830i	0.146440	+	0.106395i	−0.512153	+	0.858894i	$0.671152\pi$
$860$	3.43967	+	9.79640i	0.117292	+	0.334055i
$861$	−1.50596	+	1.09415i	−0.0513231	+	0.0372884i
$862$	5.26509	−	7.24678i	0.179330	−	0.246826i
$863$	3.72425	−	5.12599i	0.126775	−	0.174491i	−0.740911	−	0.671603i	$-0.765606\pi$
$863$	3.72425	−	5.12599i	0.126775	−	0.174491i	0.867686	+	0.497112i	$0.165606\pi$
$864$	−19.8005	+	14.3859i	−0.673628	+	0.489420i
$865$	−14.7963	+	49.4660i	−0.503089	+	1.68189i
$866$	−37.3921	−	27.1670i	−1.27064	−	0.923171i
$867$	−40.8117	+	13.2605i	−1.38604	+	0.450351i
$868$		−	0.232812i		−	0.00790214i
$869$	−4.48611	−	13.8068i	−0.152181	−	0.468365i
$870$	11.3573	+	14.8832i	0.385049	+	0.504589i
$871$	4.53690	−	13.9631i	0.153727	−	0.473123i
$872$	12.6854	+	4.12175i	0.429583	+	0.139580i
$873$	42.8163	+	58.9316i	1.44911	+	1.99453i
$874$	11.4067			0.385836
$875$	−0.767771	−	1.89639i	−0.0259554	−	0.0641098i
$876$	−3.29516			−0.111333
$877$	−17.5185	−	24.1121i	−0.591557	−	0.814209i	0.403345	−	0.915048i	$-0.367847\pi$
$877$	−17.5185	−	24.1121i	−0.591557	−	0.814209i	−0.994903	+	0.100839i	$0.967847\pi$
$878$	−66.8066	−	21.7068i	−2.25461	−	0.732569i
$879$	−18.2459	+	56.1551i	−0.615419	+	1.89406i
$880$	14.7031	+	19.2677i	0.495640	+	0.649515i
$881$	7.66453	+	23.5890i	0.258225	+	0.794733i	0.993177	+	0.116615i	$0.0372044\pi$
$881$	7.66453	+	23.5890i	0.258225	+	0.794733i	−0.734953	+	0.678118i	$0.762796\pi$
$882$		−	56.4484i		−	1.90072i
$883$	24.3027	−	7.89643i	0.817851	−	0.265736i	0.129932	−	0.991523i	$-0.458524\pi$
$883$	24.3027	−	7.89643i	0.817851	−	0.265736i	0.687920	+	0.725787i	$0.258524\pi$
$884$	6.44944	+	4.68579i	0.216918	+	0.157600i
$885$	−7.57308	+	25.3178i	−0.254566	+	0.851049i
$886$	3.36498	−	2.44480i	0.113049	−	0.0821347i
$887$	2.86154	−	3.93857i	0.0960811	−	0.132244i	−0.758270	−	0.651941i	$-0.773955\pi$
$887$	2.86154	−	3.93857i	0.0960811	−	0.132244i	0.854351	+	0.519697i	$0.173955\pi$
$888$	−0.324009	+	0.445961i	−0.0108730	+	0.0149655i
$889$	0.615135	−	0.446922i	0.0206310	−	0.0149893i
$890$	−11.6180	−	33.0887i	−0.389436	−	1.10914i
$891$	−2.38997	−	1.73641i	−0.0800669	−	0.0581720i
$892$	−16.4678	+	5.35072i	−0.551384	+	0.179155i
$893$			5.38389i			0.180165i
$894$	−24.2390	−	74.6001i	−0.810675	−	2.49500i
$895$	−18.8570	+	6.62099i	−0.630320	+	0.221315i
$896$	0.668479	−	2.05737i	0.0223323	−	0.0687318i
$897$	23.0283	+	7.48235i	0.768892	+	0.249828i
$898$	−1.19913	−	1.65047i	−0.0400156	−	0.0550768i
$899$	2.11589			0.0705688
$900$	−8.56465	−	22.6729i	−0.285488	−	0.755763i
$901$	−33.3690			−1.11168
$902$	8.18189	+	11.2614i	0.272427	+	0.374964i
$903$	−2.14080	−	0.695587i	−0.0712413	−	0.0231477i
$904$	−6.20017	+	19.0822i	−0.206215	+	0.634663i
$905$	16.7671	−	24.2573i	0.557358	−	0.806339i
$906$	−26.1221	−	80.3954i	−0.867847	−	2.67096i
$907$			21.6232i			0.717987i	0.933340	+	0.358994i	$0.116880\pi$
$907$			21.6232i			0.717987i	−0.933340	+	0.358994i	$0.883120\pi$
$908$	13.9495	−	4.53246i	0.462930	−	0.150415i
$909$	−59.4479	−	43.1914i	−1.97176	−	1.43257i
$910$	0.760139	−	0.580057i	0.0251984	−	0.0192287i
$911$	38.5574	−	28.0136i	1.27746	−	0.928132i	0.277991	−	0.960584i	$-0.410331\pi$
$911$	38.5574	−	28.0136i	1.27746	−	0.928132i	0.999473	+	0.0324515i	$0.0103314\pi$
$912$	−8.12264	+	11.1799i	−0.268967	+	0.370202i
$913$	−0.238018	+	0.327604i	−0.00787725	+	0.0108421i
$914$	−19.9535	+	14.4970i	−0.660002	+	0.479519i
$915$	−43.3067	−	29.9344i	−1.43167	−	0.989602i
$916$	−5.52894	−	4.01701i	−0.182681	−	0.132726i
$917$	2.68797	−	0.873376i	0.0887647	−	0.0288414i
$918$			45.2357i			1.49300i
$919$	−2.15949	−	6.64624i	−0.0712351	−	0.219239i	0.909100	−	0.416577i	$-0.136770\pi$
$919$	−2.15949	−	6.64624i	−0.0712351	−	0.219239i	−0.980336	+	0.197338i	$0.936770\pi$
$920$	0.573395	+	24.3854i	0.0189043	+	0.803963i
$921$	3.21079	−	9.88179i	0.105799	−	0.325616i
$922$	−37.9734	−	12.3383i	−1.25059	−	0.406341i
$923$	−8.40091	−	11.5629i	−0.276519	−	0.380596i
$924$	1.14514			0.0376723
$925$	−0.373526	−	0.466337i	−0.0122815	−	0.0153331i
$926$	−42.2236			−1.38756
$927$	35.1809	+	48.4224i	1.15549	+	1.59040i
$928$	−8.88603	−	2.88725i	−0.291698	−	0.0947785i
$929$	−5.93302	+	18.2600i	−0.194656	+	0.599090i	0.805324	+	0.592835i	$0.201991\pi$
$929$	−5.93302	+	18.2600i	−0.194656	+	0.599090i	−0.999980	+	0.00625543i	$0.998009\pi$
$930$	−12.5967	−	3.76793i	−0.413062	−	0.123555i
$931$	−2.15277	−	6.62555i	−0.0705542	−	0.217144i
$932$		−	26.4848i		−	0.867537i
$933$	−48.3759	+	15.7183i	−1.58375	+	0.514593i
$934$	17.0679	+	12.4006i	0.558480	+	0.405759i
$935$	27.6459	−	0.650061i	0.904117	−	0.0212593i
$936$	−8.39697	+	6.10076i	−0.274464	+	0.199409i
$937$	−27.2232	+	37.4696i	−0.889344	+	1.22408i	0.0844002	+	0.996432i	$0.473103\pi$
$937$	−27.2232	+	37.4696i	−0.889344	+	1.22408i	−0.973744	+	0.227645i	$0.926897\pi$
$938$	2.05686	−	2.83103i	0.0671590	−	0.0924364i
$939$	15.6084	−	11.3402i	0.509362	−	0.370073i
$940$	12.5610	−	0.295358i	0.409696	−	0.00963352i
$941$	48.9754	+	35.5827i	1.59655	+	1.15996i	0.893736	+	0.448593i	$0.148075\pi$
$941$	48.9754	+	35.5827i	1.59655	+	1.15996i	0.702817	+	0.711371i	$0.251925\pi$
$942$	38.3440	−	12.4587i	1.24931	−	0.405927i
$943$			24.0552i			0.783344i
$944$	−6.60179	−	20.3182i	−0.214870	−	0.661302i
$945$	1.78244	+	0.533163i	0.0579826	+	0.0173438i
$946$	−5.20152	+	16.0086i	−0.169116	+	0.520486i
$947$	22.6972	+	7.37478i	0.737561	+	0.239648i	0.653620	−	0.756823i	$-0.273249\pi$
$947$	22.6972	+	7.37478i	0.737561	+	0.239648i	0.0839407	+	0.996471i	$0.473249\pi$
$948$	−11.3542	−	15.6278i	−0.368768	−	0.507566i
$949$	−1.52954			−0.0496509
$950$	−5.45332	−	6.80831i	−0.176929	−	0.220891i
$951$	−26.5037			−0.859442
$952$	−1.02338	−	1.40856i	−0.0331679	−	0.0456516i
$953$	−30.1199	−	9.78654i	−0.975678	−	0.317017i	−0.222572	−	0.974916i	$-0.571445\pi$
$953$	−30.1199	−	9.78654i	−0.975678	−	0.317017i	−0.753106	+	0.657899i	$0.771445\pi$
$954$	−14.6516	+	45.0929i	−0.474362	+	1.45994i
$955$	1.44670	+	61.5253i	0.0468140	+	1.99091i
$956$	−1.14937	−	3.53740i	−0.0371734	−	0.114408i
$957$			10.4075i			0.336427i
$958$	−11.2842	+	3.66646i	−0.364576	+	0.118458i
$959$	2.17282	+	1.57865i	0.0701640	+	0.0509772i
$960$	−3.07750	−	2.12723i	−0.0993259	−	0.0686561i
$961$	23.8773	−	17.3479i	0.770237	−	0.559610i
$962$	0.164134	−	0.225911i	0.00529189	−	0.00728367i
$963$	−37.4669	+	51.5688i	−1.20735	+	1.66178i
$964$	−14.4384	+	10.4901i	−0.465029	+	0.337863i
$965$	−45.8533	+	34.9903i	−1.47607	+	1.12638i
$966$	4.66900	+	3.39222i	0.150222	+	0.109143i
$967$	10.7050	−	3.47827i	0.344250	−	0.111854i	−0.131789	−	0.991278i	$-0.542072\pi$
$967$	10.7050	−	3.47827i	0.344250	−	0.111854i	0.476039	+	0.879424i	$0.342072\pi$
$968$		−	10.5061i		−	0.337678i
$969$	4.87231	+	14.9954i	0.156521	+	0.481722i
$970$	34.7895	−	50.3305i	1.11702	−	1.61602i
$971$	−5.43016	+	16.7123i	−0.174262	+	0.536324i	−0.999599	−	0.0283168i	$-0.990985\pi$
$971$	−5.43016	+	16.7123i	−0.174262	+	0.536324i	0.825337	+	0.564641i	$0.190985\pi$
$972$	−17.2777	−	5.61387i	−0.554183	−	0.180065i
$973$	1.68314	+	2.31665i	0.0539591	+	0.0742683i
$974$	4.96593			0.159119
$975$	−6.54341	−	17.3221i	−0.209557	−	0.554752i
$976$	42.5604			1.36232
$977$	14.7557	+	20.3095i	0.472077	+	0.649758i	0.976958	−	0.213431i	$-0.0684638\pi$
$977$	14.7557	+	20.3095i	0.472077	+	0.649758i	−0.504882	+	0.863189i	$0.668464\pi$
$978$	−81.0799	−	26.3445i	−2.59265	−	0.842403i
$979$	6.02435	−	18.5410i	0.192539	−	0.592574i
$980$	−15.3398	+	5.38606i	−0.490012	+	0.172051i
$981$	−11.4740	−	35.3132i	−0.366335	−	1.12746i
$982$		−	27.6769i		−	0.883204i
$983$	−54.6106	+	17.7440i	−1.74181	+	0.565947i	−0.995070	−	0.0991735i	$-0.968380\pi$
$983$	−54.6106	+	17.7440i	−1.74181	+	0.565947i	−0.746736	+	0.665121i	$0.768380\pi$
$984$	−13.7305	−	9.97580i	−0.437712	−	0.318017i
$985$	16.8120	+	47.8817i	0.535676	+	1.52564i
$986$	−13.9708	+	10.1504i	−0.444920	+	0.323253i
$987$	−1.60111	+	2.20374i	−0.0509640	+	0.0701459i
$988$	0.821684	−	1.13095i	0.0261412	−	0.0359803i
$989$	−23.5331	+	17.0978i	−0.748309	+	0.543678i
$990$	11.2602	−	37.6444i	0.357873	−	1.19642i
$991$	17.7197	+	12.8741i	0.562884	+	0.408959i	0.832513	−	0.554005i	$-0.186901\pi$
$991$	17.7197	+	12.8741i	0.562884	+	0.408959i	−0.269629	+	0.962964i	$0.586901\pi$
$992$	6.24064	−	2.02771i	0.198141	−	0.0643798i
$993$		−	84.9895i		−	2.69706i
$994$	−1.05269	−	3.23984i	−0.0333893	−	0.102762i
$995$	−10.7045	−	14.0277i	−0.339355	−	0.444709i
$996$	−0.166504	+	0.512447i	−0.00527588	+	0.0162375i
$997$	−5.54312	−	1.80107i	−0.175552	−	0.0570404i	0.219922	−	0.975517i	$-0.429420\pi$
$997$	−5.54312	−	1.80107i	−0.175552	−	0.0570404i	−0.395474	+	0.918477i	$0.629420\pi$
$998$	43.5335	+	59.9187i	1.37803	+	1.89669i
$999$	0.543329			0.0171902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.5	✓	80
25.9	even	10	inner	475.2.n.a.134.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.5	✓	80	1.1	even	1	trivial
475.2.n.a.134.5	yes	80	25.9	even	10	inner

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.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02546 - 1.41142i) q^{2} +(-2.62954 - 0.854391i) q^{3} +(-0.322513 + 0.992591i) q^{4} +(1.35649 + 1.77762i) q^{5} +(1.49058 + 4.58753i) q^{6} +0.182993i q^{7} +(-1.58676 + 0.515570i) q^{8} +(3.75747 + 2.72996i) q^{9} +O(q^{10})\)	\(q+(-1.02546 - 1.41142i) q^{2} +(-2.62954 - 0.854391i) q^{3} +(-0.322513 + 0.992591i) q^{4} +(1.35649 + 1.77762i) q^{5} +(1.49058 + 4.58753i) q^{6} +0.182993i q^{7} +(-1.58676 + 0.515570i) q^{8} +(3.75747 + 2.72996i) q^{9} +(1.11795 - 3.73745i) q^{10} +(1.75447 - 1.27469i) q^{11} +(1.69612 - 2.33451i) q^{12} +(0.787300 - 1.08363i) q^{13} +(0.258279 - 0.187651i) q^{14} +(-2.04817 - 5.83330i) q^{15} +(4.04354 + 2.93781i) q^{16} +(5.42356 - 1.76222i) q^{17} -8.10282i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.20194 + 0.773135i) q^{20} +(0.156347 - 0.481187i) q^{21} +(-3.59826 - 1.16915i) q^{22} +(-3.84307 - 5.28953i) q^{23} +4.61296 q^{24} +(-1.31987 + 4.82265i) q^{25} -2.33680 q^{26} +(-2.67253 - 3.67842i) q^{27} +(-0.181637 - 0.0590174i) q^{28} +(0.536374 - 1.65079i) q^{29} +(-6.13294 + 8.87263i) q^{30} +(0.376695 + 1.15935i) q^{31} -5.38289i q^{32} +(-5.70253 + 1.85286i) q^{33} +(-8.04887 - 5.84785i) q^{34} +(-0.325291 + 0.248227i) q^{35} +(-3.92156 + 2.84918i) q^{36} +(-0.0702389 + 0.0966756i) q^{37} +(-1.02546 + 1.41142i) q^{38} +(-2.99608 + 2.17678i) q^{39} +(-3.06892 - 2.12130i) q^{40} +(-2.97651 - 2.16256i) q^{41} +(-0.839484 + 0.272765i) q^{42} -4.44899i q^{43} +(0.699413 + 2.15257i) q^{44} +(0.244133 + 10.3825i) q^{45} +(-3.52485 + 10.8484i) q^{46} +(-5.12038 - 1.66371i) q^{47} +(-8.12264 - 11.1799i) q^{48} +6.96651 q^{49} +(8.16026 - 3.08253i) q^{50} -15.7671 q^{51} +(0.821684 + 1.13095i) q^{52} +(-5.56509 - 1.80821i) q^{53} +(-2.45124 + 7.54413i) q^{54} +(4.64584 + 1.38966i) q^{55} +(-0.0943455 - 0.290366i) q^{56} +2.76487i q^{57} +(-2.87999 + 0.935765i) q^{58} +(-3.45806 - 2.51243i) q^{59} +(6.45065 - 0.151680i) q^{60} +(6.88904 - 5.00518i) q^{61} +(1.25004 - 1.72054i) q^{62} +(-0.499562 + 0.687588i) q^{63} +(0.489556 - 0.355683i) q^{64} +(2.99424 - 0.0704061i) q^{65} +(8.46287 + 6.14864i) q^{66} +(10.4246 - 3.38717i) q^{67} +5.95172i q^{68} +(5.58619 + 17.1925i) q^{69} +(0.683926 + 0.204576i) q^{70} +(3.29737 - 10.1483i) q^{71} +(-7.36969 - 2.39456i) q^{72} +(-0.671208 - 0.923839i) q^{73} +0.208477 q^{74} +(7.59108 - 11.5537i) q^{75} +1.04367 q^{76} +(0.233259 + 0.321054i) q^{77} +(6.14471 + 1.99654i) q^{78} +(2.06863 - 6.36659i) q^{79} +(0.262720 + 11.1730i) q^{80} +(-0.420949 - 1.29555i) q^{81} +6.41871i q^{82} +(-0.177587 + 0.0577014i) q^{83} +(0.427198 + 0.310378i) q^{84} +(10.4896 + 7.25060i) q^{85} +(-6.27940 + 4.56225i) q^{86} +(-2.82084 + 3.88255i) q^{87} +(-2.12673 + 2.92719i) q^{88} +(7.27274 - 5.28396i) q^{89} +(14.4037 - 10.9914i) q^{90} +(0.198295 + 0.144070i) q^{91} +(6.48978 - 2.10866i) q^{92} -3.37040i q^{93} +(2.90253 + 8.93308i) q^{94} +(1.27144 - 1.83941i) q^{95} +(-4.59909 + 14.1546i) q^{96} +(14.9162 + 4.84658i) q^{97} +(-7.14386 - 9.83268i) q^{98} +10.0722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

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