LMFDB - Embedded newform 275.2.h.e.201.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(26,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 13 x^{13} + 53 x^{12} - 12 x^{11} + 136 x^{10} + 8 x^{9} + 300 x^{8} + \cdots + 16 $ x^16 - 4x^15 + 10x^14 - 13x^13 + 53x^12 - 12x^11 + 136x^10 + 8x^9 + 300x^8 - 256x^7 + 472x^6 - 48x^5 + 432x^4 + 88x^3 + 128x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.3
Root			$0.977523 + 0.710212i$ of defining polynomial
Character	$\chi$	$=$	275.201
Dual form			275.2.h.e.26.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.168506 - 0.122427i) q^{2} +(0.585361 + 1.80155i) q^{3} +(-0.604628 + 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-0.398265 + 1.22573i) q^{7} +(0.254662 + 0.783769i) q^{8} +(-0.475901 + 0.345762i) q^{9} +(0.898964 - 3.19247i) q^{11} -3.70635 q^{12} +(-4.40926 + 3.20351i) q^{13} +(0.0829527 + 0.255302i) q^{14} +(-3.02701 - 2.19925i) q^{16} +(3.18058 + 2.31083i) q^{17} +(-0.0378616 + 0.116526i) q^{18} +(0.693894 + 2.13559i) q^{19} -2.44136 q^{21} +(-0.239363 - 0.648008i) q^{22} -0.711128 q^{23} +(-1.26293 + 0.917575i) q^{24} +(-0.350791 + 1.07962i) q^{26} +(3.69600 + 2.68530i) q^{27} +(-2.04011 - 1.48223i) q^{28} +(1.13043 - 3.47910i) q^{29} +(5.22959 - 3.79952i) q^{31} -2.42752 q^{32} +(6.27763 - 0.249213i) q^{33} +0.818854 q^{34} +(-0.355670 - 1.09464i) q^{36} +(2.55355 - 7.85902i) q^{37} +(0.378379 + 0.274908i) q^{38} +(-8.35231 - 6.06831i) q^{39} +(3.90378 + 12.0146i) q^{41} +(-0.411383 + 0.298888i) q^{42} -1.31169 q^{43} +(5.39718 + 3.60310i) q^{44} +(-0.119829 + 0.0870611i) q^{46} +(1.39523 + 4.29408i) q^{47} +(2.19018 - 6.74067i) q^{48} +(4.31931 + 3.13816i) q^{49} +(-2.30129 + 7.08265i) q^{51} +(-3.29531 - 10.1419i) q^{52} +(7.86297 - 5.71278i) q^{53} +0.951551 q^{54} -1.06212 q^{56} +(-3.44120 + 2.50018i) q^{57} +(-0.235451 - 0.724644i) q^{58} +(2.75455 - 8.47763i) q^{59} +(1.48965 + 1.08229i) q^{61} +(0.416055 - 1.28048i) q^{62} +(-0.234278 - 0.721033i) q^{63} +(5.64496 - 4.10130i) q^{64} +(1.02731 - 0.810544i) q^{66} -4.30232 q^{67} +(-6.22318 + 4.52140i) q^{68} +(-0.416266 - 1.28114i) q^{69} +(-8.21746 - 5.97033i) q^{71} +(-0.392192 - 0.284944i) q^{72} +(3.70969 - 11.4173i) q^{73} +(-0.531866 - 1.63692i) q^{74} -4.39356 q^{76} +(3.55509 + 2.37334i) q^{77} -2.15034 q^{78} +(-10.3649 + 7.53052i) q^{79} +(-3.21956 + 9.90878i) q^{81} +(2.12872 + 1.54661i) q^{82} +(-10.1477 - 7.37274i) q^{83} +(1.47611 - 4.54301i) q^{84} +(-0.221028 + 0.160586i) q^{86} +6.92949 q^{87} +(2.73109 - 0.108421i) q^{88} -6.28392 q^{89} +(-2.17060 - 6.68043i) q^{91} +(0.429968 - 1.32330i) q^{92} +(9.90624 + 7.19730i) q^{93} +(0.760816 + 0.552765i) q^{94} +(-1.42098 - 4.37332i) q^{96} +(0.245459 - 0.178336i) q^{97} +1.11202 q^{98} +(0.676018 + 1.83013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 5 q^{11} + 6 q^{12} - 7 q^{13} + 3 q^{14} - 4 q^{16} - 12 q^{17} - 16 q^{18} - 13 q^{19} + 10 q^{21} - 28 q^{22} + 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 5 * q^11 + 6 * q^12 - 7 * q^13 + 3 * q^14 - 4 * q^16 - 12 * q^17 - 16 * q^18 - 13 * q^19 + 10 * q^21 - 28 * q^22 + 4 * q^23 - 43 * q^24 - 34 * q^26 + 11 * q^27 - 47 * q^28 - 11 * q^29 - 10 * q^31 + 58 * q^32 + 34 * q^33 + 20 * q^34 + 3 * q^36 + 4 * q^37 + 36 * q^38 + 3 * q^39 + 25 * q^41 - 13 * q^42 + 28 * q^43 - q^44 + 40 * q^46 - 8 * q^47 + 106 * q^48 + 16 * q^49 + 35 * q^51 - 39 * q^52 + 22 * q^53 + 60 * q^54 - 20 * q^56 - 29 * q^57 - 6 * q^58 + 14 * q^59 + 16 * q^61 + 10 * q^62 - 73 * q^63 + 40 * q^64 - 55 * q^66 + 14 * q^67 - 83 * q^68 + 35 * q^69 - 46 * q^71 - 28 * q^72 - 7 * q^73 - 7 * q^74 - 62 * q^76 + 51 * q^77 - 34 * q^78 - 39 * q^79 - 43 * q^81 + 51 * q^82 - 28 * q^83 - 54 * q^84 + 2 * q^86 + 50 * q^87 + 76 * q^88 - 22 * q^89 - 34 * q^91 - 4 * q^92 - 3 * q^93 - 40 * q^94 + 108 * q^96 + 39 * q^97 + 52 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.168506	−	0.122427i	0.119152	−	0.0865688i	−0.526613	−	0.850105i	$-0.676538\pi$
$2$	0.168506	−	0.122427i	0.119152	−	0.0865688i	0.645765	+	0.763536i	$0.276538\pi$
$3$	0.585361	+	1.80155i	0.337958	+	1.04013i	0.965247	+	0.261341i	$0.0841647\pi$
$3$	0.585361	+	1.80155i	0.337958	+	1.04013i	−0.627288	+	0.778787i	$0.715835\pi$
$4$	−0.604628	+	1.86085i	−0.302314	+	0.930427i
$5$		0			0
$5$		0			0
$6$	0.319195	+	0.231909i	0.130311	+	0.0946765i
$7$	−0.398265	+	1.22573i	−0.150530	+	0.463284i	−0.997681	−	0.0680689i	$-0.978316\pi$
$7$	−0.398265	+	1.22573i	−0.150530	+	0.463284i	0.847150	+	0.531353i	$0.178316\pi$
$8$	0.254662	+	0.783769i	0.0900367	+	0.277104i
$9$	−0.475901	+	0.345762i	−0.158634	+	0.115254i
$10$		0			0
$11$	0.898964	−	3.19247i	0.271048	−	0.962566i
$11$	0.898964	−	3.19247i	0.271048	−	0.962566i
$12$	−3.70635			−1.06993
$13$	−4.40926	+	3.20351i	−1.22291	+	0.888494i	−0.996338	−	0.0855007i	$-0.972751\pi$
$13$	−4.40926	+	3.20351i	−1.22291	+	0.888494i	−0.226569	+	0.973995i	$0.572751\pi$
$14$	0.0829527	+	0.255302i	0.0221700	+	0.0682324i
$15$		0			0
$16$	−3.02701	−	2.19925i	−0.756752	−	0.549812i
$17$	3.18058	+	2.31083i	0.771404	+	0.560458i	0.902387	−	0.430927i	$-0.141813\pi$
$17$	3.18058	+	2.31083i	0.771404	+	0.560458i	−0.130983	+	0.991385i	$0.541813\pi$
$18$	−0.0378616	+	0.116526i	−0.00892407	+	0.0274655i
$19$	0.693894	+	2.13559i	0.159190	+	0.489937i	0.998561	−	0.0536215i	$-0.0170764\pi$
$19$	0.693894	+	2.13559i	0.159190	+	0.489937i	−0.839371	+	0.543559i	$0.817076\pi$
$20$		0			0
$21$	−2.44136			−0.532748
$22$	−0.239363	−	0.648008i	−0.0510324	−	0.138156i
$23$	−0.711128			−0.148280			−0.0741402	−	0.997248i	$-0.523621\pi$
$23$	−0.711128			−0.148280			−0.0741402	+	0.997248i	$0.523621\pi$
$24$	−1.26293	+	0.917575i	−0.257795	+	0.187299i
$25$		0			0
$26$	−0.350791	+	1.07962i	−0.0687957	+	0.211731i
$27$	3.69600	+	2.68530i	0.711295	+	0.516786i
$28$	−2.04011	−	1.48223i	−0.385545	−	0.280115i
$29$	1.13043	−	3.47910i	0.209915	−	0.646052i	−0.789561	−	0.613673i	$-0.789691\pi$
$29$	1.13043	−	3.47910i	0.209915	−	0.646052i	0.999476	−	0.0323796i	$-0.0103085\pi$
$30$		0			0
$31$	5.22959	−	3.79952i	0.939262	−	0.682414i	−0.00898085	−	0.999960i	$-0.502859\pi$
$31$	5.22959	−	3.79952i	0.939262	−	0.682414i	0.948243	+	0.317546i	$0.102859\pi$
$32$	−2.42752			−0.429130
$33$	6.27763	−	0.249213i	1.09279	−	0.0433824i
$34$	0.818854			0.140432
$35$		0			0
$36$	−0.355670	−	1.09464i	−0.0592783	−	0.182440i
$37$	2.55355	−	7.85902i	0.419801	−	1.29201i	−0.488085	−	0.872796i	$-0.662304\pi$
$37$	2.55355	−	7.85902i	0.419801	−	1.29201i	0.907886	−	0.419218i	$-0.137696\pi$
$38$	0.378379	+	0.274908i	0.0613811	+	0.0445960i
$39$	−8.35231	−	6.06831i	−1.33744	−	0.971707i
$40$		0			0
$41$	3.90378	+	12.0146i	0.609668	+	1.87637i	0.460789	+	0.887510i	$0.347566\pi$
$41$	3.90378	+	12.0146i	0.609668	+	1.87637i	0.148879	+	0.988855i	$0.452434\pi$
$42$	−0.411383	+	0.298888i	−0.0634779	+	0.0461194i
$43$	−1.31169			−0.200031			−0.100015	−	0.994986i	$-0.531889\pi$
$43$	−1.31169			−0.200031			−0.100015	+	0.994986i	$0.531889\pi$
$44$	5.39718	+	3.60310i	0.813656	+	0.543187i
$45$		0			0
$46$	−0.119829	+	0.0870611i	−0.0176679	+	0.0128365i
$47$	1.39523	+	4.29408i	0.203515	+	0.626356i	0.999771	+	0.0213959i	$0.00681104\pi$
$47$	1.39523	+	4.29408i	0.203515	+	0.626356i	−0.796256	+	0.604960i	$0.793189\pi$
$48$	2.19018	−	6.74067i	0.316125	−	0.972932i
$49$	4.31931	+	3.13816i	0.617044	+	0.448309i
$50$		0			0
$51$	−2.30129	+	7.08265i	−0.322246	+	0.991770i
$52$	−3.29531	−	10.1419i	−0.456977	−	1.40643i
$53$	7.86297	−	5.71278i	1.08006	−	0.784711i	0.102369	−	0.994747i	$-0.467358\pi$
$53$	7.86297	−	5.71278i	1.08006	−	0.784711i	0.977694	+	0.210035i	$0.0673579\pi$
$54$	0.951551			0.129490
$55$		0			0
$56$	−1.06212			−0.141931
$57$	−3.44120	+	2.50018i	−0.455798	+	0.331157i
$58$	−0.235451	−	0.724644i	−0.0309162	−	0.0951504i
$59$	2.75455	−	8.47763i	0.358612	−	1.10369i	−0.595274	−	0.803523i	$-0.702956\pi$
$59$	2.75455	−	8.47763i	0.358612	−	1.10369i	0.953886	−	0.300171i	$-0.0970436\pi$
$60$		0			0
$61$	1.48965	+	1.08229i	0.190730	+	0.138574i	0.679052	−	0.734090i	$-0.262391\pi$
$61$	1.48965	+	1.08229i	0.190730	+	0.138574i	−0.488322	+	0.872663i	$0.662391\pi$
$62$	0.416055	−	1.28048i	0.0528390	−	0.162622i
$63$	−0.234278	−	0.721033i	−0.0295162	−	0.0908417i
$64$	5.64496	−	4.10130i	0.705620	−	0.512663i
$65$		0			0
$66$	1.02731	−	0.810544i	0.126453	−	0.0997711i
$67$	−4.30232			−0.525612			−0.262806	−	0.964849i	$-0.584648\pi$
$67$	−4.30232			−0.525612			−0.262806	+	0.964849i	$0.584648\pi$
$68$	−6.22318	+	4.52140i	−0.754671	+	0.548301i
$69$	−0.416266	−	1.28114i	−0.0501126	−	0.154231i
$70$		0			0
$71$	−8.21746	−	5.97033i	−0.975233	−	0.708548i	−0.0185947	−	0.999827i	$-0.505919\pi$
$71$	−8.21746	−	5.97033i	−0.975233	−	0.708548i	−0.956638	+	0.291279i	$0.905919\pi$
$72$	−0.392192	−	0.284944i	−0.0462202	−	0.0335810i
$73$	3.70969	−	11.4173i	0.434187	−	1.33629i	−0.459731	−	0.888058i	$-0.652054\pi$
$73$	3.70969	−	11.4173i	0.434187	−	1.33629i	0.893917	−	0.448232i	$-0.147946\pi$
$74$	−0.531866	−	1.63692i	−0.0618282	−	0.190288i
$75$		0			0
$76$	−4.39356			−0.503976
$77$	3.55509	+	2.37334i	0.405141	+	0.270467i
$78$	−2.15034			−0.243478
$79$	−10.3649	+	7.53052i	−1.16614	+	0.847249i	−0.990542	−	0.137213i	$-0.956186\pi$
$79$	−10.3649	+	7.53052i	−1.16614	+	0.847249i	−0.175597	+	0.984462i	$0.556186\pi$
$80$		0			0
$81$	−3.21956	+	9.90878i	−0.357729	+	1.10098i
$82$	2.12872	+	1.54661i	0.235078	+	0.170794i
$83$	−10.1477	−	7.37274i	−1.11386	−	0.809263i	−0.130589	−	0.991437i	$-0.541687\pi$
$83$	−10.1477	−	7.37274i	−1.11386	−	0.809263i	−0.983266	+	0.182174i	$0.941687\pi$
$84$	1.47611	−	4.54301i	0.161057	−	0.495683i
$85$		0			0
$86$	−0.221028	+	0.160586i	−0.0238340	+	0.0173164i
$87$	6.92949			0.742920
$88$	2.73109	−	0.108421i	0.291135	−	0.0115577i
$89$	−6.28392			−0.666095			−0.333047	−	0.942910i	$-0.608077\pi$
$89$	−6.28392			−0.666095			−0.333047	+	0.942910i	$0.608077\pi$
$90$		0			0
$91$	−2.17060	−	6.68043i	−0.227541	−	0.700299i
$92$	0.429968	−	1.32330i	0.0448272	−	0.137964i
$93$	9.90624	+	7.19730i	1.02723	+	0.746326i
$94$	0.760816	+	0.552765i	0.0784722	+	0.0570134i
$95$		0			0
$96$	−1.42098	−	4.37332i	−0.145028	−	0.446350i
$97$	0.245459	−	0.178336i	0.0249226	−	0.0181073i	−0.575254	−	0.817975i	$-0.695097\pi$
$97$	0.245459	−	0.178336i	0.0249226	−	0.0181073i	0.600177	+	0.799867i	$0.295097\pi$
$98$	1.11202			0.112331
$99$	0.676018	+	1.83013i	0.0679423	+	0.183935i
$100$		0			0
$101$	4.99821	−	3.63141i	0.497340	−	0.361339i	−0.310660	−	0.950521i	$-0.600550\pi$
$101$	4.99821	−	3.63141i	0.497340	−	0.361339i	0.808000	+	0.589182i	$0.200550\pi$
$102$	0.479325	+	1.47521i	0.0474602	+	0.146068i
$103$	2.46558	−	7.58828i	0.242941	−	0.747695i	−0.753027	−	0.657989i	$-0.771407\pi$
$103$	2.46558	−	7.58828i	0.242941	−	0.747695i	0.995968	−	0.0897061i	$-0.0285928\pi$
$104$	−3.63369	−	2.64003i	−0.356312	−	0.258876i
$105$		0			0
$106$	0.625561	−	1.92528i	0.0607598	−	0.187000i
$107$	3.10415	+	9.55358i	0.300089	+	0.923580i	0.981464	+	0.191645i	$0.0613823\pi$
$107$	3.10415	+	9.55358i	0.300089	+	0.923580i	−0.681375	+	0.731934i	$0.738618\pi$
$108$	−7.23165	+	5.25410i	−0.695866	+	0.505576i
$109$	7.63832			0.731619			0.365809	−	0.930690i	$-0.380792\pi$
$109$	7.63832			0.731619			0.365809	+	0.930690i	$0.380792\pi$
$110$		0			0
$111$	15.6532			1.48574
$112$	3.90125	−	2.83442i	0.368633	−	0.267828i
$113$	6.05767	+	18.6436i	0.569858	+	1.75384i	0.653057	+	0.757309i	$0.273486\pi$
$113$	6.05767	+	18.6436i	0.569858	+	1.75384i	−0.0831991	+	0.996533i	$0.526514\pi$
$114$	−0.273774	+	0.842590i	−0.0256413	+	0.0789158i
$115$		0			0
$116$	5.79060	+	4.20712i	0.537644	+	0.390621i
$117$	0.990715	−	3.04911i	0.0915916	−	0.281890i
$118$	−0.573731	−	1.76576i	−0.0528162	−	0.162552i
$119$	−4.09918	+	2.97823i	−0.375771	+	0.273013i
$120$		0			0
$121$	−9.38373	−	5.73983i	−0.853066	−	0.521803i
$122$	0.383517			0.0347220
$123$	−19.3598	+	14.0657i	−1.74562	+	1.26827i
$124$	3.90839	+	12.0288i	0.350984	+	1.08022i
$125$		0			0
$126$	−0.127751	−	0.0928166i	−0.0113810	−	0.00826876i
$127$	−13.8869	−	10.0894i	−1.23226	−	0.895293i	−0.235207	−	0.971945i	$-0.575577\pi$
$127$	−13.8869	−	10.0894i	−1.23226	−	0.895293i	−0.997058	+	0.0766526i	$0.975577\pi$
$128$	1.94939	−	5.99961i	0.172304	−	0.530296i
$129$	−0.767812	−	2.36308i	−0.0676020	−	0.208058i
$130$		0			0
$131$	10.0223			0.875655			0.437828	−	0.899059i	$-0.355748\pi$
$131$	10.0223			0.875655			0.437828	+	0.899059i	$0.355748\pi$
$132$	−3.33188	+	11.8324i	−0.290003	+	1.02988i
$133$	−2.89402			−0.250943
$134$	−0.724967	+	0.526720i	−0.0626276	+	0.0455016i
$135$		0			0
$136$	−1.00118	+	3.08132i	−0.0858506	+	0.264221i
$137$	−2.85366	−	2.07331i	−0.243805	−	0.177134i	0.459172	−	0.888347i	$-0.348146\pi$
$137$	−2.85366	−	2.07331i	−0.243805	−	0.177134i	−0.702977	+	0.711213i	$0.748146\pi$
$138$	−0.226989	−	0.164917i	−0.0193226	−	0.0140387i
$139$	−2.71237	+	8.34781i	−0.230060	+	0.708052i	0.767679	+	0.640835i	$0.221412\pi$
$139$	−2.71237	+	8.34781i	−0.230060	+	0.708052i	−0.997738	+	0.0672164i	$0.978588\pi$
$140$		0			0
$141$	−6.91931	+	5.02717i	−0.582711	+	0.423364i
$142$	−2.11562			−0.177539
$143$	6.26335	+	16.9563i	0.523768	+	1.41795i
$144$	2.20097			0.183414
$145$		0			0
$146$	−0.772674	−	2.37805i	−0.0639469	−	0.196808i
$147$	−3.12522	+	9.61843i	−0.257763	+	0.793314i
$148$	13.0805	+	9.50356i	1.07521	+	0.781188i
$149$	6.79312	+	4.93549i	0.556514	+	0.404331i	0.830181	−	0.557493i	$-0.188237\pi$
$149$	6.79312	+	4.93549i	0.556514	+	0.404331i	−0.273667	+	0.961824i	$0.588237\pi$
$150$		0			0
$151$	−2.63804	−	8.11906i	−0.214681	−	0.660720i	−0.999176	−	0.0405849i	$-0.987078\pi$
$151$	−2.63804	−	8.11906i	−0.214681	−	0.660720i	0.784495	−	0.620135i	$-0.212922\pi$
$152$	−1.49710	+	1.08771i	−0.121431	+	0.0882247i
$153$	−2.31264			−0.186966
$154$	0.889616	−	0.0353165i	0.0716873	−	0.00284588i
$155$		0			0
$156$	16.3423	−	11.8734i	1.30843	−	0.950629i
$157$	−3.90892	−	12.0304i	−0.311966	−	0.960131i	−0.976986	−	0.213306i	$-0.931577\pi$
$157$	−3.90892	−	12.0304i	−0.311966	−	0.960131i	0.665020	−	0.746826i	$-0.268423\pi$
$158$	−0.824606	+	2.53788i	−0.0656021	+	0.201903i
$159$	14.8946	+	10.8215i	1.18122	+	0.858204i
$160$		0			0
$161$	0.283218	−	0.871654i	0.0223207	−	0.0686960i
$162$	0.670585	+	2.06385i	0.0526862	+	0.162151i
$163$	−6.80311	+	4.94275i	−0.532860	+	0.387146i	−0.821427	−	0.570314i	$-0.806821\pi$
$163$	−6.80311	+	4.94275i	−0.532860	+	0.387146i	0.288566	+	0.957460i	$0.406821\pi$
$164$	−24.7177			−1.93013
$165$		0			0
$166$	−2.61257			−0.202775
$167$	−15.4725	+	11.2414i	−1.19730	+	0.869888i	−0.994016	−	0.109233i	$-0.965161\pi$
$167$	−15.4725	+	11.2414i	−1.19730	+	0.869888i	−0.203281	+	0.979120i	$0.565161\pi$
$168$	−0.621721	−	1.91346i	−0.0479668	−	0.147627i
$169$	5.16183	−	15.8865i	0.397064	−	1.22204i
$170$		0			0
$171$	−1.06863	−	0.776405i	−0.0817202	−	0.0593732i
$172$	0.793085	−	2.44086i	0.0604721	−	0.186114i
$173$	−3.78197	−	11.6397i	−0.287538	−	0.884950i	−0.985626	−	0.168939i	$-0.945966\pi$
$173$	−3.78197	−	11.6397i	−0.287538	−	0.884950i	0.698089	−	0.716011i	$-0.254034\pi$
$174$	1.16766	−	0.848356i	0.0885202	−	0.0643137i
$175$		0			0
$176$	−9.74221	+	7.68658i	−0.734347	+	0.579398i
$177$	16.8853			1.26918
$178$	−1.05888	+	0.769321i	−0.0793664	+	0.0576630i
$179$	0.988945	+	3.04366i	0.0739172	+	0.227494i	0.981189	−	0.193052i	$-0.0618386\pi$
$179$	0.988945	+	3.04366i	0.0739172	+	0.227494i	−0.907271	+	0.420546i	$0.861839\pi$
$180$		0			0
$181$	−1.75310	−	1.27370i	−0.130307	−	0.0946734i	0.520723	−	0.853726i	$-0.325663\pi$
$181$	−1.75310	−	1.27370i	−0.130307	−	0.0946734i	−0.651029	+	0.759053i	$0.725663\pi$
$182$	−1.18362	−	0.859952i	−0.0877360	−	0.0637439i
$183$	−1.07783	+	3.31722i	−0.0796754	+	0.245216i
$184$	−0.181097	−	0.557360i	−0.0133507	−	0.0410891i
$185$		0			0
$186$	2.55040			0.187005
$187$	10.2365	−	8.07655i	0.748565	−	0.590616i
$188$	−8.83425			−0.644304
$189$	−4.76345	+	3.46085i	−0.346490	+	0.251740i
$190$		0			0
$191$	0.544810	−	1.67675i	0.0394211	−	0.121326i	−0.929409	−	0.369051i	$-0.879683\pi$
$191$	0.544810	−	1.67675i	0.0394211	−	0.121326i	0.968830	+	0.247725i	$0.0796829\pi$
$192$	10.6931	+	7.76896i	0.771705	+	0.560677i
$193$	−12.4647	−	9.05616i	−0.897231	−	0.651877i	0.0405221	−	0.999179i	$-0.487098\pi$
$193$	−12.4647	−	9.05616i	−0.897231	−	0.651877i	−0.937753	+	0.347302i	$0.887098\pi$
$194$	0.0195282	−	0.0601015i	0.00140204	−	0.00431503i
$195$		0			0
$196$	−8.45123	+	6.14018i	−0.603660	+	0.438584i
$197$	1.78727			0.127338			0.0636689	−	0.997971i	$-0.479720\pi$
$197$	1.78727			0.127338			0.0636689	+	0.997971i	$0.479720\pi$
$198$	0.337970	+	0.225625i	0.0240185	+	0.0160345i
$199$	−19.6066			−1.38988			−0.694938	−	0.719070i	$-0.744568\pi$
$199$	−19.6066			−1.38988			−0.694938	+	0.719070i	$0.744568\pi$
$200$		0			0
$201$	−2.51841	−	7.75087i	−0.177635	−	0.546704i
$202$	0.397646	−	1.22383i	0.0279783	−	0.0861083i
$203$	3.81424	+	2.77121i	0.267707	+	0.194501i
$204$	−11.7884	−	8.56474i	−0.825350	−	0.599652i
$205$		0			0
$206$	−0.513544	−	1.58052i	−0.0357803	−	0.110120i
$207$	0.338426	−	0.245881i	0.0235223	−	0.0170899i
$208$	20.3922			1.41394
$209$	7.44159	−	0.295420i	0.514745	−	0.0204347i
$210$		0			0
$211$	13.5246	−	9.82620i	0.931072	−	0.676464i	−0.0151828	−	0.999885i	$-0.504833\pi$
$211$	13.5246	−	9.82620i	0.931072	−	0.676464i	0.946255	+	0.323421i	$0.104833\pi$
$212$	5.87648	+	18.0860i	0.403598	+	1.24215i
$213$	5.94570	−	18.2990i	0.407393	−	1.25383i
$214$	1.69268	+	1.22981i	0.115709	+	0.0840678i
$215$		0			0
$216$	−1.16343	+	3.58065i	−0.0791611	+	0.243633i
$217$	2.57444	+	7.92331i	0.174764	+	0.537869i
$218$	1.28710	−	0.935136i	0.0871737	−	0.0633354i
$219$	22.7403			1.53665
$220$		0			0
$221$	−21.4267			−1.44132
$222$	2.63766	−	1.91637i	0.177028	−	0.128618i
$223$	−1.84839	−	5.68876i	−0.123777	−	0.380947i	0.869899	−	0.493230i	$-0.164184\pi$
$223$	−1.84839	−	5.68876i	−0.123777	−	0.380947i	−0.993676	+	0.112283i	$0.964184\pi$
$224$	0.966799	−	2.97550i	0.0645970	−	0.198809i
$225$		0			0
$226$	3.30323	+	2.39994i	0.219728	+	0.159641i
$227$	6.87537	−	21.1602i	0.456334	−	1.40445i	−0.413227	−	0.910628i	$-0.635599\pi$
$227$	6.87537	−	21.1602i	0.456334	−	1.40445i	0.869562	−	0.493825i	$-0.164401\pi$
$228$	−2.57182	−	7.91525i	−0.170323	−	0.524200i
$229$	−4.83195	+	3.51062i	−0.319305	+	0.231988i	−0.735879	−	0.677113i	$-0.763231\pi$
$229$	−4.83195	+	3.51062i	−0.319305	+	0.231988i	0.416574	+	0.909102i	$0.363231\pi$
$230$		0			0
$231$	−2.19469	+	7.79396i	−0.144400	+	0.512805i
$232$	3.01469			0.197924
$233$	14.3479	−	10.4243i	0.939960	−	0.682921i	−0.00845137	−	0.999964i	$-0.502690\pi$
$233$	14.3479	−	10.4243i	0.939960	−	0.682921i	0.948411	+	0.317044i	$0.102690\pi$
$234$	−0.206351	−	0.635083i	−0.0134896	−	0.0415167i
$235$		0			0
$236$	14.1102	+	10.2516i	0.918493	+	0.667324i
$237$	−19.6338	−	14.2648i	−1.27535	−	0.926599i
$238$	−0.326121	+	1.00370i	−0.0211393	+	0.0650601i
$239$	−5.90708	−	18.1801i	−0.382097	−	1.17597i	−0.938564	−	0.345104i	$-0.887844\pi$
$239$	−5.90708	−	18.1801i	−0.382097	−	1.17597i	0.556467	−	0.830870i	$-0.312156\pi$
$240$		0			0
$241$	−1.79437			−0.115586			−0.0577929	−	0.998329i	$-0.518406\pi$
$241$	−1.79437			−0.115586			−0.0577929	+	0.998329i	$0.518406\pi$
$242$	−2.28392	+	0.181623i	−0.146816	+	0.0116752i
$243$	−6.03029			−0.386843
$244$	−2.91468	+	2.11764i	−0.186593	+	0.135568i
$245$		0			0
$246$	−1.54023	+	4.74033i	−0.0982012	+	0.302232i
$247$	−9.90094	−	7.19345i	−0.629982	−	0.457708i
$248$	4.30973	+	3.13120i	0.273668	+	0.198831i
$249$	7.34232	−	22.5973i	0.465301	−	1.43205i
$250$		0			0
$251$	−8.55143	+	6.21298i	−0.539761	+	0.392160i	−0.823996	−	0.566595i	$-0.808260\pi$
$251$	−8.55143	+	6.21298i	−0.539761	+	0.392160i	0.284235	+	0.958755i	$0.408260\pi$
$252$	1.48339			0.0934447
$253$	−0.639278	+	2.27025i	−0.0401911	+	0.142730i
$254$	−3.57525			−0.224331
$255$		0			0
$256$	3.90634	+	12.0225i	0.244146	+	0.751404i
$257$	−1.39033	+	4.27900i	−0.0867265	+	0.266917i	−0.985009	−	0.172501i	$-0.944815\pi$
$257$	−1.39033	+	4.27900i	−0.0867265	+	0.266917i	0.898283	+	0.439418i	$0.144815\pi$
$258$	−0.418686	−	0.304193i	−0.0260662	−	0.0189382i
$259$	8.61608	+	6.25995i	0.535377	+	0.388974i
$260$		0			0
$261$	0.664969	+	2.04656i	0.0411606	+	0.126679i
$262$	1.68882	−	1.22700i	0.104336	−	0.0758045i
$263$	−8.87966			−0.547543			−0.273772	−	0.961795i	$-0.588271\pi$
$263$	−8.87966			−0.547543			−0.273772	+	0.961795i	$0.588271\pi$
$264$	1.79400	+	4.85675i	0.110413	+	0.298912i
$265$		0			0
$266$	−0.487660	+	0.354305i	−0.0299003	+	0.0217239i
$267$	−3.67836	−	11.3208i	−0.225112	−	0.692824i
$268$	2.60130	−	8.00599i	0.158900	−	0.489044i
$269$	13.5968	+	9.87862i	0.829009	+	0.602310i	0.919279	−	0.393607i	$-0.128773\pi$
$269$	13.5968	+	9.87862i	0.829009	+	0.602310i	−0.0902701	+	0.995917i	$0.528773\pi$
$270$		0			0
$271$	−4.18182	+	12.8703i	−0.254028	+	0.781817i	0.739992	+	0.672616i	$0.234829\pi$
$271$	−4.18182	+	12.8703i	−0.254028	+	0.781817i	−0.994020	+	0.109201i	$0.965171\pi$
$272$	−4.54555	−	13.9898i	−0.275615	−	0.848255i
$273$	10.7646	−	7.82092i	0.651501	−	0.473343i
$274$	−0.734688			−0.0443841
$275$		0			0
$276$	2.63569			0.158650
$277$	−16.5592	+	12.0310i	−0.994946	+	0.722870i	−0.960999	−	0.276553i	$-0.910808\pi$
$277$	−16.5592	+	12.0310i	−0.994946	+	0.722870i	−0.0339471	+	0.999424i	$0.510808\pi$
$278$	0.564945	+	1.73872i	0.0338832	+	0.104282i
$279$	−1.17504	+	3.61639i	−0.0703476	+	0.216508i
$280$		0			0
$281$	8.09848	+	5.88389i	0.483115	+	0.351004i	0.802530	−	0.596611i	$-0.203487\pi$
$281$	8.09848	+	5.88389i	0.483115	+	0.351004i	−0.319415	+	0.947615i	$0.603487\pi$
$282$	−0.550485	+	1.69422i	−0.0327809	+	0.100889i
$283$	−0.827516	−	2.54683i	−0.0491907	−	0.151394i	0.923444	−	0.383733i	$-0.125362\pi$
$283$	−0.827516	−	2.54683i	−0.0491907	−	0.151394i	−0.972635	+	0.232340i	$0.925362\pi$
$284$	16.0784	−	11.6817i	0.954079	−	0.693179i
$285$		0			0
$286$	3.13131	+	2.09043i	0.185158	+	0.123610i
$287$	−16.2815			−0.961064
$288$	1.15526	−	0.839346i	0.0680744	−	0.0494589i
$289$	−0.477120	−	1.46843i	−0.0280659	−	0.0863780i
$290$		0			0
$291$	0.464964	+	0.337816i	0.0272567	+	0.0198031i
$292$	19.0029	+	13.8064i	1.11206	+	0.807958i
$293$	7.81514	−	24.0525i	0.456565	−	1.40516i	−0.412723	−	0.910857i	$-0.635422\pi$
$293$	7.81514	−	24.0525i	0.456565	−	1.40516i	0.869288	−	0.494306i	$-0.164578\pi$
$294$	0.650936	+	2.00337i	0.0379633	+	0.116839i
$295$		0			0
$296$	6.80995			0.395820
$297$	11.8953	−	9.38538i	0.690236	−	0.544595i
$298$	1.74892			0.101312
$299$	3.13554	−	2.27811i	0.181333	−	0.131746i
$300$		0			0
$301$	0.522401	−	1.60778i	0.0301107	−	0.0926711i
$302$	−1.43852	−	1.04514i	−0.0827774	−	0.0601413i
$303$	9.46794	+	6.87886i	0.543919	+	0.395180i
$304$	2.59627	−	7.99049i	0.148906	−	0.458286i
$305$		0			0
$306$	−0.389693	+	0.283129i	−0.0222773	+	0.0161854i
$307$	−8.53224			−0.486960			−0.243480	−	0.969906i	$-0.578289\pi$
$307$	−8.53224			−0.486960			−0.243480	+	0.969906i	$0.578289\pi$
$308$	−6.56595	+	5.18052i	−0.374130	+	0.295188i
$309$	15.1140			0.859803
$310$		0			0
$311$	−0.341159	−	1.04998i	−0.0193454	−	0.0595389i	0.940918	−	0.338635i	$-0.109965\pi$
$311$	−0.341159	−	1.04998i	−0.0193454	−	0.0595389i	−0.960263	+	0.279096i	$0.909965\pi$
$312$	2.62914	−	8.09165i	0.148846	−	0.458099i
$313$	−4.52358	−	3.28657i	−0.255688	−	0.185768i	0.452556	−	0.891736i	$-0.350512\pi$
$313$	−4.52358	−	3.28657i	−0.255688	−	0.185768i	−0.708244	+	0.705968i	$0.750512\pi$
$314$	−2.13152	−	1.54864i	−0.120289	−	0.0873949i
$315$		0			0
$316$	−7.74630	−	23.8407i	−0.435764	−	1.34114i
$317$	22.9349	−	16.6632i	1.28815	−	0.935897i	0.288385	−	0.957514i	$-0.406882\pi$
$317$	22.9349	−	16.6632i	1.28815	−	0.935897i	0.999766	+	0.0216175i	$0.00688161\pi$
$318$	3.83467			0.215038
$319$	−10.0907	−	6.73644i	−0.564971	−	0.377168i
$320$		0			0
$321$	−15.3943	+	11.1846i	−0.859223	+	0.624262i
$322$	−0.0589900	−	0.181552i	−0.00328738	−	0.0101175i
$323$	−2.72799	+	8.39588i	−0.151789	+	0.467159i
$324$	−16.4921	−	11.9822i	−0.916231	−	0.665680i
$325$		0			0
$326$	−0.541240	+	1.66577i	−0.0299765	+	0.0922582i
$327$	4.47117	+	13.7609i	0.247256	+	0.760977i
$328$	−8.42253	+	6.11933i	−0.465056	+	0.337883i
$329$	−5.81908			−0.320816
$330$		0			0
$331$	18.6052			1.02263			0.511317	−	0.859392i	$-0.329158\pi$
$331$	18.6052			1.02263			0.511317	+	0.859392i	$0.329158\pi$
$332$	19.8552	−	14.4256i	1.08969	−	0.791709i
$333$	1.50211	+	4.62303i	0.0823154	+	0.253341i
$334$	−1.23096	+	3.78850i	−0.0673550	+	0.207297i
$335$		0			0
$336$	7.39000	+	5.36915i	0.403158	+	0.292911i
$337$	−9.10777	+	28.0308i	−0.496132	+	1.52694i	0.319054	+	0.947737i	$0.396635\pi$
$337$	−9.10777	+	28.0308i	−0.496132	+	1.52694i	−0.815186	+	0.579200i	$0.803365\pi$
$338$	−1.07513	−	3.30891i	−0.0584794	−	0.179981i
$339$	−30.0415	+	21.8264i	−1.63163	+	1.18545i
$340$		0			0
$341$	−7.42864	−	20.1109i	−0.402283	−	1.08907i
$342$	−0.275124			−0.0148770
$343$	−12.8655	+	9.34733i	−0.694671	+	0.504708i
$344$	−0.334038	−	1.02806i	−0.0180101	−	0.0554294i
$345$		0			0
$346$	−2.06230	−	1.49835i	−0.110870	−	0.0805516i
$347$	14.3171	+	10.4020i	0.768583	+	0.558408i	0.901531	−	0.432715i	$-0.142444\pi$
$347$	14.3171	+	10.4020i	0.768583	+	0.558408i	−0.132948	+	0.991123i	$0.542444\pi$
$348$	−4.18977	+	12.8948i	−0.224595	+	0.691232i
$349$	0.483116	+	1.48688i	0.0258606	+	0.0795908i	0.963154	−	0.268951i	$-0.0866770\pi$
$349$	0.483116	+	1.48688i	0.0258606	+	0.0795908i	−0.937293	+	0.348542i	$0.886677\pi$
$350$		0			0
$351$	−24.8990			−1.32901
$352$	−2.18226	+	7.74980i	−0.116315	+	0.413066i
$353$	1.66213			0.0884663			0.0442331	−	0.999021i	$-0.485916\pi$
$353$	1.66213			0.0884663			0.0442331	+	0.999021i	$0.485916\pi$
$354$	2.84528	−	2.06722i	0.151225	−	0.109871i
$355$		0			0
$356$	3.79944	−	11.6935i	0.201370	−	0.619752i
$357$	−7.76493	−	5.64155i	−0.410964	−	0.298583i
$358$	0.539269	+	0.391802i	0.0285012	+	0.0207074i
$359$	−9.64641	+	29.6886i	−0.509118	+	1.56690i	0.284617	+	0.958641i	$0.408134\pi$
$359$	−9.64641	+	29.6886i	−0.509118	+	1.56690i	−0.793735	+	0.608263i	$0.791866\pi$
$360$		0			0
$361$	11.2921	−	8.20418i	0.594320	−	0.431799i
$362$	−0.451343			−0.0237220
$363$	4.84776	−	20.2652i	0.254441	−	1.06365i
$364$	13.7437			0.720366
$365$		0			0
$366$	0.224496	+	0.690927i	0.0117346	+	0.0361153i
$367$	2.88261	−	8.87177i	0.150471	−	0.463103i	−0.847203	−	0.531270i	$-0.821715\pi$
$367$	2.88261	−	8.87177i	0.150471	−	0.463103i	0.997674	+	0.0681670i	$0.0217151\pi$
$368$	2.15259	+	1.56395i	0.112211	+	0.0815264i
$369$	−6.01201	−	4.36798i	−0.312973	−	0.227388i
$370$		0			0
$371$	3.87081	+	11.9131i	0.200962	+	0.618499i
$372$	−19.3827	+	14.0824i	−1.00495	+	0.730137i
$373$	−9.77497			−0.506129			−0.253064	−	0.967449i	$-0.581438\pi$
$373$	−9.77497			−0.506129			−0.253064	+	0.967449i	$0.581438\pi$
$374$	0.736121	−	2.61417i	0.0380639	−	0.135175i
$375$		0			0
$376$	−3.01026	+	2.18708i	−0.155242	+	0.112790i
$377$	6.16099	+	18.9616i	0.317307	+	0.976571i
$378$	−0.378970	+	1.16635i	−0.0194921	+	0.0599905i
$379$	−10.8852	−	7.90855i	−0.559135	−	0.406235i	0.272007	−	0.962295i	$-0.412312\pi$
$379$	−10.8852	−	7.90855i	−0.559135	−	0.406235i	−0.831142	+	0.556060i	$0.812312\pi$
$380$		0			0
$381$	10.0478	−	30.9240i	0.514765	−	1.58428i
$382$	−0.113476	−	0.349242i	−0.00580592	−	0.0178688i
$383$	−3.16673	+	2.30076i	−0.161812	+	0.117563i	−0.665745	−	0.746180i	$-0.731886\pi$
$383$	−3.16673	+	2.30076i	−0.161812	+	0.117563i	0.503933	+	0.863743i	$0.331886\pi$
$384$	11.9497			0.609807
$385$		0			0
$386$	−3.20910			−0.163339
$387$	0.624234	−	0.453533i	0.0317316	−	0.0230544i
$388$	0.183446	+	0.564590i	0.00931308	+	0.0286627i
$389$	−4.11854	+	12.6755i	−0.208818	+	0.642676i	0.790717	+	0.612182i	$0.209708\pi$
$389$	−4.11854	+	12.6755i	−0.208818	+	0.642676i	−0.999535	+	0.0304938i	$0.990292\pi$
$390$		0			0
$391$	−2.26180	−	1.64329i	−0.114384	−	0.0831049i
$392$	−1.35963	+	4.18451i	−0.0686717	+	0.211350i
$393$	5.86668	+	18.0558i	0.295935	+	0.910794i
$394$	0.301166	−	0.218810i	0.0151725	−	0.0110235i
$395$		0			0
$396$	−3.81434	+	0.151424i	−0.191678	+	0.00760933i
$397$	8.80209			0.441764			0.220882	−	0.975300i	$-0.429106\pi$
$397$	8.80209			0.441764			0.220882	+	0.975300i	$0.429106\pi$
$398$	−3.30383	+	2.40038i	−0.165606	+	0.120320i
$399$	−1.69404	−	5.21373i	−0.0848083	−	0.261013i
$400$		0			0
$401$	−13.2728	−	9.64323i	−0.662810	−	0.481560i	0.204801	−	0.978804i	$-0.434345\pi$
$401$	−13.2728	−	9.64323i	−0.662810	−	0.481560i	−0.867611	+	0.497244i	$0.834345\pi$
$402$	−1.37328	−	0.997747i	−0.0684931	−	0.0497631i
$403$	−10.8868	+	33.5061i	−0.542310	+	1.66906i
$404$	3.73547	+	11.4966i	0.185846	+	0.571976i
$405$		0			0
$406$	0.981993			0.0487355
$407$	−22.7941	−	15.2171i	−1.12986	−	0.754284i
$408$	−6.13722			−0.303838
$409$	9.55575	−	6.94266i	0.472501	−	0.343292i	−0.325914	−	0.945399i	$-0.605672\pi$
$409$	9.55575	−	6.94266i	0.472501	−	0.343292i	0.798415	+	0.602107i	$0.205672\pi$
$410$		0			0
$411$	2.06475	−	6.35466i	0.101847	−	0.313452i
$412$	12.6299	+	9.17617i	0.622231	+	0.452078i
$413$	9.29429	+	6.75269i	0.457342	+	0.332278i
$414$	0.0269244	−	0.0828649i	0.00132326	−	0.00407259i
$415$		0			0
$416$	10.7036	−	7.77660i	0.524786	−	0.381279i
$417$	−16.6267			−0.814215
$418$	1.21778	−	0.960830i	0.0595638	−	0.0469957i
$419$	26.3901			1.28924			0.644620	−	0.764503i	$-0.277015\pi$
$419$	26.3901			1.28924			0.644620	+	0.764503i	$0.277015\pi$
$420$		0			0
$421$	3.51334	+	10.8130i	0.171230	+	0.526991i	0.999441	−	0.0334246i	$-0.0106414\pi$
$421$	3.51334	+	10.8130i	0.171230	+	0.526991i	−0.828211	+	0.560416i	$0.810641\pi$
$422$	1.07599	−	3.31155i	0.0523783	−	0.161204i
$423$	−2.14872	−	1.56114i	−0.104474	−	0.0759052i
$424$	6.47991	+	4.70793i	0.314692	+	0.228637i
$425$		0			0
$426$	−1.23840	−	3.81141i	−0.0600007	−	0.184663i
$427$	−1.91988	+	1.39488i	−0.0929096	+	0.0675028i
$428$	−19.6547			−0.950044
$429$	−26.8813	+	21.2093i	−1.29784	+	1.02399i
$430$		0			0
$431$	−14.5688	+	10.5849i	−0.701756	+	0.509856i	−0.880504	−	0.474039i	$-0.842795\pi$
$431$	−14.5688	+	10.5849i	−0.701756	+	0.509856i	0.178747	+	0.983895i	$0.442795\pi$
$432$	−5.28217	−	16.2568i	−0.254138	−	0.782158i
$433$	−11.8233	+	36.3883i	−0.568191	+	1.74871i	0.0900851	+	0.995934i	$0.471286\pi$
$433$	−11.8233	+	36.3883i	−0.568191	+	1.74871i	−0.658276	+	0.752777i	$0.728714\pi$
$434$	1.40383	+	1.01995i	0.0673862	+	0.0489589i
$435$		0			0
$436$	−4.61834	+	14.2138i	−0.221179	+	0.680718i
$437$	−0.493448	−	1.51868i	−0.0236048	−	0.0726481i
$438$	3.83189	−	2.78403i	0.183095	−	0.133026i
$439$	−8.67958			−0.414254			−0.207127	−	0.978314i	$-0.566411\pi$
$439$	−8.67958			−0.414254			−0.207127	+	0.978314i	$0.566411\pi$
$440$		0			0
$441$	−3.14062			−0.149553
$442$	−3.61054	+	2.62321i	−0.171736	+	0.124773i
$443$	−4.13947	−	12.7400i	−0.196672	−	0.605295i	−0.999953	−	0.00969443i	$-0.996914\pi$
$443$	−4.13947	−	12.7400i	−0.196672	−	0.605295i	0.803281	−	0.595601i	$-0.203086\pi$
$444$	−9.46436	+	29.1283i	−0.449159	+	1.38237i
$445$		0			0
$446$	−1.00792	−	0.732298i	−0.0477264	−	0.0346753i
$447$	−4.91513	+	15.1272i	−0.232478	+	0.715493i
$448$	2.77892	+	8.55263i	0.131292	+	0.404074i
$449$	15.8011	−	11.4802i	0.745700	−	0.541783i	−0.148791	−	0.988869i	$-0.547538\pi$
$449$	15.8011	−	11.4802i	0.745700	−	0.541783i	0.894491	+	0.447086i	$0.147538\pi$
$450$		0			0
$451$	41.8656	−	1.66201i	1.97137	−	0.0782608i
$452$	−38.3556			−1.80410
$453$	13.0827	−	9.50515i	0.614680	−	0.446591i
$454$	−1.43204	−	4.40735i	−0.0672088	−	0.206847i
$455$		0			0
$456$	−2.83591	−	2.06041i	−0.132803	−	0.0964874i
$457$	20.8569	+	15.1535i	0.975647	+	0.708849i	0.956731	−	0.290972i	$-0.0939788\pi$
$457$	20.8569	+	15.1535i	0.975647	+	0.708849i	0.0189151	+	0.999821i	$0.493979\pi$
$458$	−0.384420	+	1.18312i	−0.0179627	+	0.0552836i
$459$	5.55016	+	17.0816i	0.259059	+	0.797302i
$460$		0			0
$461$	19.0542			0.887441			0.443720	−	0.896165i	$-0.353658\pi$
$461$	19.0542			0.887441			0.443720	+	0.896165i	$0.353658\pi$
$462$	0.584371	+	1.58202i	0.0271874	+	0.0736022i
$463$	20.0792			0.933161			0.466580	−	0.884479i	$-0.345486\pi$
$463$	20.0792			0.933161			0.466580	+	0.884479i	$0.345486\pi$
$464$	−11.0732	+	8.04516i	−0.514061	+	0.373487i
$465$		0			0
$466$	1.14148	−	3.51313i	0.0528782	−	0.162742i
$467$	−13.3534	−	9.70181i	−0.617921	−	0.448946i	0.234273	−	0.972171i	$-0.424729\pi$
$467$	−13.3534	−	9.70181i	−0.617921	−	0.448946i	−0.852195	+	0.523225i	$0.824729\pi$
$468$	5.07493	+	3.68715i	0.234589	+	0.170439i
$469$	1.71347	−	5.27350i	0.0791205	−	0.243508i
$470$		0			0
$471$	19.3853	−	14.0843i	0.893228	−	0.648968i
$472$	7.34599			0.338127
$473$	−1.17916	+	4.18753i	−0.0542179	+	0.192543i
$474$	−5.05481			−0.232175
$475$		0			0
$476$	−3.06356	−	9.42868i	−0.140418	−	0.432163i
$477$	−1.76673	+	5.43744i	−0.0808930	+	0.248963i
$478$	−3.22111	−	2.34028i	−0.147330	−	0.107042i
$479$	−4.15087	−	3.01578i	−0.189658	−	0.137795i	0.488904	−	0.872337i	$-0.337397\pi$
$479$	−4.15087	−	3.01578i	−0.189658	−	0.137795i	−0.678562	+	0.734543i	$0.737397\pi$
$480$		0			0
$481$	13.9172	+	42.8327i	0.634570	+	1.95300i
$482$	−0.302363	+	0.219680i	−0.0137723	+	0.0100061i
$483$	1.73612			0.0789960
$484$	16.3547	−	13.9913i	0.743393	−	0.635967i
$485$		0			0
$486$	−1.01614	+	0.738269i	−0.0460930	+	0.0334886i
$487$	5.17276	+	15.9201i	0.234400	+	0.721409i	0.997200	+	0.0747753i	$0.0238239\pi$
$487$	5.17276	+	15.9201i	0.234400	+	0.721409i	−0.762800	+	0.646634i	$0.776176\pi$
$488$	−0.468912	+	1.44316i	−0.0212266	+	0.0653289i
$489$	−12.8869	−	9.36288i	−0.582766	−	0.423404i
$490$		0			0
$491$	−0.238396	+	0.733708i	−0.0107587	+	0.0331118i	−0.956292	−	0.292414i	$-0.905541\pi$
$491$	−0.238396	+	0.733708i	−0.0107587	+	0.0331118i	0.945533	+	0.325526i	$0.105541\pi$
$492$	−14.4688	−	44.5304i	−0.652304	−	2.00758i
$493$	11.6350	−	8.45333i	0.524014	−	0.380719i
$494$	−2.54904			−0.114687
$495$		0			0
$496$	−24.1861			−1.08599
$497$	10.5908	−	7.69465i	0.475061	−	0.345152i
$498$	−1.52930	−	4.70669i	−0.0685294	−	0.210912i
$499$	5.40385	−	16.6313i	0.241909	−	0.744521i	−0.754220	−	0.656622i	$-0.771985\pi$
$499$	5.40385	−	16.6313i	0.241909	−	0.744521i	0.996129	−	0.0878988i	$-0.0280152\pi$
$500$		0			0
$501$	−29.3090	−	21.2943i	−1.30943	−	0.951357i
$502$	−0.680333	+	2.09385i	−0.0303647	+	0.0934530i
$503$	12.1050	+	37.2553i	0.539734	+	1.66113i	0.733193	+	0.680021i	$0.238029\pi$
$503$	12.1050	+	37.2553i	0.539734	+	1.66113i	−0.193459	+	0.981108i	$0.561971\pi$
$504$	0.505462	−	0.367240i	0.0225151	−	0.0163582i
$505$		0			0
$506$	0.170218	+	0.460816i	0.00756710	+	0.0204858i
$507$	31.6419			1.40526
$508$	27.1714	−	19.7412i	1.20554	−	0.875873i
$509$	1.00212	+	3.08420i	0.0444181	+	0.136705i	0.970806	−	0.239865i	$-0.0771033\pi$
$509$	1.00212	+	3.08420i	0.0444181	+	0.136705i	−0.926388	+	0.376570i	$0.877103\pi$
$510$		0			0
$511$	12.5171	+	9.09420i	0.553724	+	0.402304i
$512$	12.3373	+	8.96355i	0.545235	+	0.396137i
$513$	−3.17006	+	9.75644i	−0.139962	+	0.430757i
$514$	0.289585	+	0.891252i	0.0127731	+	0.0393114i
$515$		0			0
$516$	4.86159			0.214020
$517$	14.9630	−	0.594010i	0.658072	−	0.0261245i
$518$	2.21825			0.0974642
$519$	18.7557	−	13.6268i	0.823286	−	0.598152i
$520$		0			0
$521$	3.60355	−	11.0906i	0.157874	−	0.485887i	−0.840567	−	0.541708i	$-0.817778\pi$
$521$	3.60355	−	11.0906i	0.157874	−	0.485887i	0.998441	+	0.0558215i	$0.0177778\pi$
$522$	0.362606	+	0.263449i	0.0158708	+	0.0115308i
$523$	−4.13469	−	3.00403i	−0.180797	−	0.131357i	0.493706	−	0.869629i	$-0.335642\pi$
$523$	−4.13469	−	3.00403i	−0.180797	−	0.131357i	−0.674503	+	0.738272i	$0.735642\pi$
$524$	−6.05978	+	18.6501i	−0.264723	+	0.814733i
$525$		0			0
$526$	−1.49628	+	1.08711i	−0.0652407	+	0.0474002i
$527$	25.4132			1.10701
$528$	−19.5505	−	13.0517i	−0.850826	−	0.568002i
$529$	−22.4943			−0.978013
$530$		0			0
$531$	1.62035	+	4.98693i	0.0703173	+	0.216414i
$532$	1.74980	−	5.38534i	0.0758636	−	0.233484i
$533$	−55.7017	−	40.4696i	−2.41271	−	1.75293i
$534$	−2.00580	−	1.45730i	−0.0867994	−	0.0630635i
$535$		0			0
$536$	−1.09564	−	3.37203i	−0.0473244	−	0.145649i
$537$	−4.90443	+	3.56328i	−0.211642	+	0.153767i
$538$	3.50054			0.150919
$539$	13.9014	−	10.9682i	0.598775	−	0.472432i
$540$		0			0
$541$	−29.3114	+	21.2960i	−1.26019	+	0.915585i	−0.998767	−	0.0496388i	$-0.984193\pi$
$541$	−29.3114	+	21.2960i	−1.26019	+	0.915585i	−0.261427	+	0.965223i	$0.584193\pi$
$542$	0.871011	+	2.68070i	0.0374131	+	0.115146i
$543$	1.26845	−	3.90388i	0.0544342	−	0.167531i
$544$	−7.72093	−	5.60959i	−0.331032	−	0.240509i
$545$		0			0
$546$	0.856405	−	2.63574i	0.0366508	−	0.112799i
$547$	5.91930	+	18.2177i	0.253091	+	0.778934i	0.994200	+	0.107549i	$0.0343002\pi$
$547$	5.91930	+	18.2177i	0.253091	+	0.778934i	−0.741109	+	0.671385i	$0.765700\pi$
$548$	5.58352	−	4.05667i	0.238516	−	0.173292i
$549$	−1.08314			−0.0462274
$550$		0			0
$551$	8.21432			0.349942
$552$	0.898108	−	0.652513i	0.0382260	−	0.0277728i
$553$	−5.10245	−	15.7037i	−0.216978	−	0.667790i
$554$	−1.31741	+	4.05458i	−0.0559715	+	0.172263i
$555$		0			0
$556$	−13.8941	−	10.0946i	−0.589240	−	0.428108i
$557$	8.24779	−	25.3841i	0.349470	−	1.07556i	−0.609677	−	0.792650i	$-0.708701\pi$
$557$	8.24779	−	25.3841i	0.349470	−	1.07556i	0.959147	−	0.282908i	$-0.0912991\pi$
$558$	0.244742	+	0.753239i	0.0103608	+	0.0318872i
$559$	5.78358	−	4.20201i	0.244619	−	0.177726i
$560$		0			0
$561$	20.5424	+	13.7139i	0.867300	+	0.579000i
$562$	2.08499			0.0879500
$563$	27.5770	−	20.0359i	1.16223	−	0.844412i	0.172174	−	0.985066i	$-0.444921\pi$
$563$	27.5770	−	20.0359i	1.16223	−	0.844412i	0.990059	+	0.140655i	$0.0449207\pi$
$564$	−5.17122	−	15.9154i	−0.217748	−	0.670159i
$565$		0			0
$566$	−0.451242	−	0.327847i	−0.0189671	−	0.0137804i
$567$	−10.8633	−	7.89265i	−0.456215	−	0.331460i
$568$	2.58669	−	7.96101i	0.108535	−	0.334037i
$569$	−7.05363	−	21.7088i	−0.295703	−	0.910082i	−0.982984	−	0.183690i	$-0.941196\pi$
$569$	−7.05363	−	21.7088i	−0.295703	−	0.910082i	0.687281	−	0.726392i	$-0.258804\pi$
$570$		0			0
$571$	−36.9818			−1.54764			−0.773820	−	0.633406i	$-0.781656\pi$
$571$	−36.9818			−1.54764			−0.773820	+	0.633406i	$0.781656\pi$
$572$	−35.3401	+	1.40295i	−1.47764	+	0.0586604i
$573$	3.33967			0.139517
$574$	−2.74352	+	1.99329i	−0.114512	+	0.0831982i
$575$		0			0
$576$	−1.26837	+	3.90363i	−0.0528486	+	0.162651i
$577$	23.3962	+	16.9984i	0.973999	+	0.707651i	0.956359	−	0.292193i	$-0.0943850\pi$
$577$	23.3962	+	16.9984i	0.973999	+	0.707651i	0.0176392	+	0.999844i	$0.494385\pi$
$578$	−0.260172	−	0.189026i	−0.0108217	−	0.00786246i
$579$	9.01880	−	27.7570i	0.374809	−	1.15354i
$580$		0			0
$581$	13.0785	−	9.50209i	0.542588	−	0.394213i
$582$	0.119707			0.00496202
$583$	−11.1694	−	30.2379i	−0.462588	−	1.25233i
$584$	9.89322			0.409385
$585$		0			0
$586$	−1.62778	−	5.00978i	−0.0672428	−	0.206952i
$587$	−2.23223	+	6.87011i	−0.0921341	+	0.283560i	−0.986496	−	0.163784i	$-0.947630\pi$
$587$	−2.23223	+	6.87011i	−0.0921341	+	0.283560i	0.894362	+	0.447344i	$0.147630\pi$
$588$	−16.0089	−	11.6311i	−0.660195	−	0.479660i
$589$	11.7430	+	8.53178i	0.483861	+	0.351546i
$590$		0			0
$591$	1.04620	+	3.21986i	0.0430348	+	0.132448i
$592$	−25.0135	+	18.1734i	−1.02805	+	0.746922i
$593$	10.9657			0.450308			0.225154	−	0.974323i	$-0.427711\pi$
$593$	10.9657			0.450308			0.225154	+	0.974323i	$0.427711\pi$
$594$	0.855410	−	3.03780i	0.0350979	−	0.124642i
$595$		0			0
$596$	−13.2915	+	9.65687i	−0.544442	+	0.395561i
$597$	−11.4769	−	35.3224i	−0.469720	−	1.44565i
$598$	0.249457	−	0.767749i	0.0102011	−	0.0313956i
$599$	−4.69066	−	3.40797i	−0.191655	−	0.139246i	0.487820	−	0.872944i	$-0.337792\pi$
$599$	−4.69066	−	3.40797i	−0.191655	−	0.139246i	−0.679475	+	0.733699i	$0.737792\pi$
$600$		0			0
$601$	−2.51599	+	7.74343i	−0.102629	+	0.315861i	−0.989167	−	0.146796i	$-0.953104\pi$
$601$	−2.51599	+	7.74343i	−0.102629	+	0.315861i	0.886537	+	0.462657i	$0.153104\pi$
$602$	−0.108808	−	0.334877i	−0.00443469	−	0.0136486i
$603$	2.04748	−	1.48758i	0.0833798	−	0.0605789i
$604$	16.7034			0.679652
$605$		0			0
$606$	2.43756			0.0990192
$607$	21.5706	−	15.6720i	0.875525	−	0.636106i	−0.0565387	−	0.998400i	$-0.518006\pi$
$607$	21.5706	−	15.6720i	0.875525	−	0.636106i	0.932064	+	0.362294i	$0.118006\pi$
$608$	−1.68445	−	5.18419i	−0.0683133	−	0.210247i
$609$	−2.75978	+	8.49372i	−0.111832	+	0.344183i
$610$		0			0
$611$	−19.9081	−	14.4641i	−0.805395	−	0.585153i
$612$	1.39829	−	4.30348i	0.0565223	−	0.173958i
$613$	3.19030	+	9.81873i	0.128855	+	0.396575i	0.994584	−	0.103939i	$-0.0331446\pi$
$613$	3.19030	+	9.81873i	0.128855	+	0.396575i	−0.865729	+	0.500513i	$0.833145\pi$
$614$	−1.43773	+	1.04457i	−0.0580222	+	0.0421556i
$615$		0			0
$616$	−0.954805	+	3.39078i	−0.0384702	+	0.136618i
$617$	−8.79766			−0.354180			−0.177090	−	0.984195i	$-0.556668\pi$
$617$	−8.79766			−0.354180			−0.177090	+	0.984195i	$0.556668\pi$
$618$	2.54679	−	1.85035i	0.102447	−	0.0744321i
$619$	−4.20736	−	12.9489i	−0.169108	−	0.520461i	0.830208	−	0.557454i	$-0.188222\pi$
$619$	−4.20736	−	12.9489i	−0.169108	−	0.520461i	−0.999315	+	0.0369937i	$0.988222\pi$
$620$		0			0
$621$	−2.62833	−	1.90959i	−0.105471	−	0.0766293i
$622$	−0.186033	−	0.135161i	−0.00745925	−	0.00541946i
$623$	2.50267	−	7.70242i	0.100267	−	0.308591i
$624$	11.9368	+	36.7376i	0.477853	+	1.47068i
$625$		0			0
$626$	−1.16462			−0.0465474
$627$	4.88823	+	13.2335i	0.195217	+	0.528495i
$628$	24.7503			0.987643
$629$	26.2826	−	19.0954i	1.04796	−	0.761384i
$630$		0			0
$631$	−8.10923	+	24.9576i	−0.322823	+	0.993548i	0.649590	+	0.760285i	$0.274941\pi$
$631$	−8.10923	+	24.9576i	−0.322823	+	0.993548i	−0.972414	+	0.233264i	$0.925059\pi$
$632$	−8.54173	−	6.20593i	−0.339772	−	0.246859i
$633$	25.6192	+	18.6134i	1.01827	+	0.739818i
$634$	1.82465	−	5.61569i	0.0724661	−	0.223028i
$635$		0			0
$636$	−29.1430	+	21.1736i	−1.15559	+	0.839588i
$637$	−29.0981			−1.15291
$638$	−2.52507	+	0.100242i	−0.0999683	+	0.00396860i
$639$	5.97501			0.236368
$640$		0			0
$641$	12.3908	+	38.1350i	0.489407	+	1.50624i	0.825495	+	0.564410i	$0.190896\pi$
$641$	12.3908	+	38.1350i	0.489407	+	1.50624i	−0.336087	+	0.941831i	$0.609104\pi$
$642$	−1.22473	+	3.76934i	−0.0483363	+	0.148764i
$643$	2.12044	+	1.54059i	0.0836218	+	0.0607548i	0.628811	−	0.777558i	$-0.283542\pi$
$643$	2.12044	+	1.54059i	0.0836218	+	0.0607548i	−0.545189	+	0.838313i	$0.683542\pi$
$644$	1.45078	+	1.05405i	0.0571687	+	0.0415355i
$645$		0			0
$646$	0.568198	+	1.74873i	0.0223555	+	0.0688031i
$647$	24.4251	−	17.7459i	0.960250	−	0.697662i	0.00704095	−	0.999975i	$-0.497759\pi$
$647$	24.4251	−	17.7459i	0.960250	−	0.697662i	0.953209	+	0.302313i	$0.0977588\pi$
$648$	−8.58610			−0.337294
$649$	−24.5883	−	16.4149i	−0.965177	−	0.644341i
$650$		0			0
$651$	−12.7673	+	9.27598i	−0.500390	+	0.363554i
$652$	−5.08438	−	15.6481i	−0.199120	−	0.612827i
$653$	−11.2515	+	34.6286i	−0.440305	+	1.35512i	0.447246	+	0.894411i	$0.352405\pi$
$653$	−11.2515	+	34.6286i	−0.440305	+	1.35512i	−0.887551	+	0.460709i	$0.847595\pi$
$654$	2.43812	+	1.77140i	0.0953380	+	0.0692671i
$655$		0			0
$656$	14.6063	−	44.9537i	0.570281	−	1.75515i
$657$	2.18221	+	6.71616i	0.0851362	+	0.262022i
$658$	−0.980550	+	0.712411i	−0.0382258	+	0.0277727i
$659$	−32.9001			−1.28161			−0.640803	−	0.767706i	$-0.721398\pi$
$659$	−32.9001			−1.28161			−0.640803	+	0.767706i	$0.721398\pi$
$660$		0			0
$661$	31.0455			1.20753			0.603766	−	0.797162i	$-0.293666\pi$
$661$	31.0455			1.20753			0.603766	+	0.797162i	$0.293666\pi$
$662$	3.13509	−	2.27778i	0.121849	−	0.0885283i
$663$	−12.5424	−	38.6015i	−0.487105	−	1.49916i
$664$	3.19429	−	9.83102i	0.123963	−	0.381517i
$665$		0			0
$666$	0.819099	+	0.595110i	0.0317394	+	0.0230601i
$667$	−0.803878	+	2.47408i	−0.0311263	+	0.0957969i
$668$	−11.5635	−	35.5889i	−0.447407	−	1.37698i
$669$	9.16663	−	6.65995i	0.354402	−	0.257488i
$670$		0			0
$671$	4.79433	−	3.78272i	0.185083	−	0.146030i
$672$	5.92645			0.228618
$673$	3.74637	−	2.72189i	0.144412	−	0.104921i	−0.513234	−	0.858249i	$-0.671553\pi$
$673$	3.74637	−	2.72189i	0.144412	−	0.104921i	0.657645	+	0.753328i	$0.271553\pi$
$674$	1.89701	+	5.83840i	0.0730701	+	0.224887i
$675$		0			0
$676$	26.4414	+	19.2108i	1.01698	+	0.738877i
$677$	−17.9475	−	13.0396i	−0.689780	−	0.501154i	0.186808	−	0.982396i	$-0.440186\pi$
$677$	−17.9475	−	13.0396i	−0.689780	−	0.501154i	−0.876588	+	0.481242i	$0.840186\pi$
$678$	−2.39004	+	7.35578i	−0.0917888	+	0.282497i
$679$	0.120835	+	0.371892i	0.00463723	+	0.0142719i
$680$		0			0
$681$	42.1458			1.61503
$682$	−3.71389	−	2.47935i	−0.142212	−	0.0949393i
$683$	42.5540			1.62828			0.814142	−	0.580665i	$-0.197207\pi$
$683$	42.5540			1.62828			0.814142	+	0.580665i	$0.197207\pi$
$684$	2.09090	−	1.51913i	0.0799476	−	0.0580853i
$685$		0			0
$686$	−1.02355	+	3.15016i	−0.0390793	+	0.120274i
$687$	−9.15301	−	6.65005i	−0.349209	−	0.253715i
$688$	3.97050	+	2.88473i	0.151374	+	0.109979i
$689$	−16.3689	+	50.3783i	−0.623605	+	1.91926i
$690$		0			0
$691$	3.05397	−	2.21884i	0.116178	−	0.0844086i	−0.528179	−	0.849133i	$-0.677125\pi$
$691$	3.05397	−	2.21884i	0.116178	−	0.0844086i	0.644357	+	0.764725i	$0.277125\pi$
$692$	23.9465			0.910308
$693$	−2.51248	+	0.0997421i	−0.0954414	+	0.00378889i
$694$	3.68600			0.139919
$695$		0			0
$696$	1.76468	+	5.43112i	0.0668900	+	0.205866i
$697$	−15.3474	+	47.2343i	−0.581323	+	1.78913i
$698$	0.263442	+	0.191402i	0.00997143	+	0.00724466i
$699$	27.1787	+	19.7465i	1.02799	+	0.746880i
$700$		0			0
$701$	−0.265067	−	0.815792i	−0.0100114	−	0.0308120i	0.945926	−	0.324382i	$-0.105156\pi$
$701$	−0.265067	−	0.815792i	−0.0100114	−	0.0308120i	−0.955937	+	0.293570i	$0.905156\pi$
$702$	−4.19563	+	3.04830i	−0.158354	+	0.115051i
$703$	18.5555			0.699834
$704$	−8.01867	−	21.7083i	−0.302215	−	0.818162i
$705$		0			0
$706$	0.280079	−	0.203489i	0.0105409	−	0.00765842i
$707$	2.46053	+	7.57274i	0.0925378	+	0.284802i
$708$	−10.2093	+	31.4211i	−0.383690	+	1.18088i
$709$	−20.0202	−	14.5455i	−0.751874	−	0.546269i	0.144533	−	0.989500i	$-0.453832\pi$
$709$	−20.0202	−	14.5455i	−0.751874	−	0.546269i	−0.896407	+	0.443231i	$0.853832\pi$
$710$		0			0
$711$	2.32888	−	7.16756i	0.0873399	−	0.268804i
$712$	−1.60028	−	4.92515i	−0.0599729	−	0.184578i
$713$	−3.71891	+	2.70194i	−0.139274	+	0.101189i
$714$	−1.99912			−0.0748150
$715$		0			0
$716$	−6.26175			−0.234012
$717$	29.2947	−	21.2838i	1.09403	−	0.794860i
$718$	2.00920	+	6.18369i	0.0749828	+	0.230773i
$719$	−5.40434	+	16.6329i	−0.201548	+	0.620301i	0.798289	+	0.602274i	$0.205739\pi$
$719$	−5.40434	+	16.6329i	−0.201548	+	0.620301i	−0.999837	+	0.0180271i	$0.994261\pi$
$720$		0			0
$721$	8.31926	+	6.04430i	0.309826	+	0.225101i
$722$	0.898373	−	2.76491i	0.0334340	−	0.102899i
$723$	−1.05036	−	3.23266i	−0.0390632	−	0.120224i
$724$	3.43014	−	2.49214i	0.127480	−	0.0926198i
$725$		0			0
$726$	−1.66412	−	4.00830i	−0.0617614	−	0.148762i
$727$	13.8835			0.514909			0.257455	−	0.966290i	$-0.417116\pi$
$727$	13.8835			0.514909			0.257455	+	0.966290i	$0.417116\pi$
$728$	4.68314	−	3.40250i	0.173569	−	0.126105i
$729$	6.12878	+	18.8624i	0.226992	+	0.698609i
$730$		0			0
$731$	−4.17194	−	3.03109i	−0.154305	−	0.112109i
$732$	−5.52117	−	4.01137i	−0.204068	−	0.148264i
$733$	−9.34742	+	28.7684i	−0.345255	+	1.06259i	0.616192	+	0.787596i	$0.288674\pi$
$733$	−9.34742	+	28.7684i	−0.345255	+	1.06259i	−0.961447	+	0.274990i	$0.911326\pi$
$734$	−0.600405	−	1.84786i	−0.0221614	−	0.0682056i
$735$		0			0
$736$	1.72628			0.0636315
$737$	−3.86763	+	13.7350i	−0.142466	+	0.505936i
$738$	−1.54782			−0.0569759
$739$	19.8185	−	14.3990i	0.729037	−	0.529676i	−0.160222	−	0.987081i	$-0.551221\pi$
$739$	19.8185	−	14.3990i	0.729037	−	0.529676i	0.889259	+	0.457405i	$0.151221\pi$
$740$		0			0
$741$	7.16378	−	22.0478i	0.263168	−	0.809948i
$742$	2.11074	+	1.53354i	0.0774877	+	0.0562981i
$743$	−5.37625	−	3.90607i	−0.197235	−	0.143300i	0.484784	−	0.874634i	$-0.338898\pi$
$743$	−5.37625	−	3.90607i	−0.197235	−	0.143300i	−0.682020	+	0.731334i	$0.738898\pi$
$744$	−3.11828	+	9.59709i	−0.114322	+	0.351846i
$745$		0			0
$746$	−1.64714	+	1.19672i	−0.0603061	+	0.0438150i
$747$	7.37851			0.269966
$748$	8.84003	+	23.9319i	0.323223	+	0.875036i
$749$	−12.9464			−0.473052
$750$		0			0
$751$	−5.58167	−	17.1786i	−0.203678	−	0.626857i	−0.999765	−	0.0216746i	$-0.993100\pi$
$751$	−5.58167	−	17.1786i	−0.203678	−	0.626857i	0.796087	−	0.605182i	$-0.206900\pi$
$752$	5.22038	−	16.0667i	0.190368	−	0.585891i
$753$	−16.1987	−	11.7690i	−0.590313	−	0.428887i
$754$	3.35957	+	2.44087i	0.122348	+	0.0888912i
$755$		0			0
$756$	−3.56002	−	10.9566i	−0.129477	−	0.398488i
$757$	−8.56321	+	6.22154i	−0.311235	+	0.226126i	−0.732426	−	0.680846i	$-0.761612\pi$
$757$	−8.56321	+	6.22154i	−0.311235	+	0.226126i	0.421191	+	0.906972i	$0.361612\pi$
$758$	−2.80244			−0.101789
$759$	−4.46419	+	0.177222i	−0.162040	+	0.00643276i
$760$		0			0
$761$	−6.26922	+	4.55485i	−0.227259	+	0.165113i	−0.695588	−	0.718441i	$-0.744856\pi$
$761$	−6.26922	+	4.55485i	−0.227259	+	0.165113i	0.468329	+	0.883554i	$0.344856\pi$
$762$	−2.09281	−	6.44100i	−0.0758145	−	0.233333i
$763$	−3.04208	+	9.36256i	−0.110131	+	0.338947i
$764$	2.79078	+	2.02762i	0.100967	+	0.0733569i
$765$		0			0
$766$	−0.251938	+	0.775384i	−0.00910288	+	0.0280158i
$767$	15.0127	+	46.2043i	0.542076	+	1.66834i
$768$	−19.3725	+	14.0750i	−0.699046	+	0.507886i
$769$	−23.9339			−0.863078			−0.431539	−	0.902094i	$-0.642029\pi$
$769$	−23.9339			−0.863078			−0.431539	+	0.902094i	$0.642029\pi$
$770$		0			0
$771$	−8.52270			−0.306938
$772$	24.3887	−	17.7194i	0.877769	−	0.637737i
$773$	10.7378	+	33.0476i	0.386212	+	1.18864i	0.935597	+	0.353069i	$0.114862\pi$
$773$	10.7378	+	33.0476i	0.386212	+	1.18864i	−0.549385	+	0.835569i	$0.685138\pi$
$774$	0.0496627	−	0.152846i	0.00178509	−	0.00549394i
$775$		0			0
$776$	0.202284	+	0.146968i	0.00726156	+	0.00527583i
$777$	−6.23413	+	19.1867i	−0.223648	+	0.688318i
$778$	0.857829	+	2.64013i	0.0307547	+	0.0946531i
$779$	−22.9494	+	16.6737i	−0.822248	+	0.597398i
$780$		0			0
$781$	−26.4473	+	20.8669i	−0.946359	+	0.746675i
$782$	−0.582310			−0.0208234
$783$	13.5205	−	9.82320i	0.483183	−	0.351053i
$784$	−6.17298	−	18.9985i	−0.220463	−	0.678517i
$785$		0			0
$786$	3.19908	+	2.32427i	0.114108	+	0.0829040i
$787$	−7.10333	−	5.16087i	−0.253206	−	0.183965i	0.453940	−	0.891032i	$-0.350018\pi$
$787$	−7.10333	−	5.16087i	−0.253206	−	0.183965i	−0.707147	+	0.707067i	$0.750018\pi$
$788$	−1.08063	+	3.32585i	−0.0384960	+	0.118478i
$789$	−5.19780	−	15.9972i	−0.185047	−	0.569515i
$790$		0			0
$791$	−25.2647			−0.898308
$792$	−1.26224	+	0.995906i	−0.0448518	+	0.0353880i
$793$	−10.0354			−0.356367
$794$	1.48321	−	1.07761i	0.0526370	−	0.0382430i
$795$		0			0
$796$	11.8547	−	36.4850i	0.420179	−	1.29318i
$797$	−40.0732	−	29.1149i	−1.41946	−	1.03130i	−0.991860	−	0.127336i	$-0.959357\pi$
$797$	−40.0732	−	29.1149i	−1.41946	−	1.03130i	−0.427605	−	0.903966i	$-0.640643\pi$
$798$	−0.923757	−	0.671149i	−0.0327007	−	0.0237584i
$799$	−5.48523	+	16.8818i	−0.194054	+	0.597235i
$800$		0			0
$801$	2.99052	−	2.17274i	0.105665	−	0.0767701i
$802$	−3.41713			−0.120663
$803$	−33.1144	−	22.1068i	−1.16858	−	0.780132i
$804$	15.9459			0.562370
$805$		0			0
$806$	2.26756	+	6.97882i	0.0798712	+	0.245818i
$807$	−9.83787	+	30.2778i	−0.346309	+	1.06583i
$808$	4.11904	+	2.99266i	0.144907	+	0.105281i
$809$	32.0568	+	23.2906i	1.12706	+	0.818854i	0.985264	−	0.171042i	$-0.0547135\pi$
$809$	32.0568	+	23.2906i	1.12706	+	0.818854i	0.141792	+	0.989896i	$0.454714\pi$
$810$		0			0
$811$	−15.4557	−	47.5676i	−0.542722	−	1.67033i	−0.726346	−	0.687329i	$-0.758783\pi$
$811$	−15.4557	−	47.5676i	−0.542722	−	1.67033i	0.183624	−	0.982997i	$-0.441217\pi$
$812$	−7.46301	+	5.42219i	−0.261900	+	0.190282i
$813$	−25.6345			−0.899040
$814$	−5.70393	+	0.226438i	−0.199923	+	0.00793665i
$815$		0			0
$816$	22.5426	−	16.3781i	0.789147	−	0.573349i
$817$	−0.910175	−	2.80123i	−0.0318430	−	0.0980026i
$818$	0.760234	−	2.33976i	0.0265810	−	0.0818078i
$819$	3.34283	+	2.42871i	0.116808	+	0.0848659i
$820$		0			0
$821$	12.5676	−	38.6792i	0.438613	−	1.34991i	−0.450725	−	0.892663i	$-0.648834\pi$
$821$	12.5676	−	38.6792i	0.438613	−	1.34991i	0.889338	−	0.457250i	$-0.151166\pi$
$822$	−0.430057	−	1.32358i	−0.0150000	−	0.0461651i
$823$	−24.0661	+	17.4851i	−0.838892	+	0.609491i	−0.922061	−	0.387045i	$-0.873496\pi$
$823$	−24.0661	+	17.4851i	−0.838892	+	0.609491i	0.0831687	+	0.996535i	$0.473496\pi$
$824$	6.57535			0.229063
$825$		0			0
$826$	2.39285			0.0832581
$827$	−37.3653	+	27.1475i	−1.29932	+	0.944011i	−0.999949	−	0.0101260i	$-0.996777\pi$
$827$	−37.3653	+	27.1475i	−1.29932	+	0.944011i	−0.299371	+	0.954137i	$0.596777\pi$
$828$	0.252927	+	0.778428i	0.00878981	+	0.0270523i
$829$	−15.1310	+	46.5683i	−0.525520	+	1.61738i	0.237766	+	0.971323i	$0.423585\pi$
$829$	−15.1310	+	46.5683i	−0.525520	+	1.61738i	−0.763285	+	0.646061i	$0.776415\pi$
$830$		0			0
$831$	−31.3675	−	22.7898i	−1.08813	−	0.790571i
$832$	−11.7515	+	36.1674i	−0.407410	+	1.25388i
$833$	6.48616	+	19.9623i	0.224732	+	0.691654i
$834$	−2.80171	+	2.03556i	−0.0970152	+	0.0704856i
$835$		0			0
$836$	−3.94966	+	14.0263i	−0.136602	+	0.485110i
$837$	29.5314			1.02075
$838$	4.44689	−	3.23086i	0.153615	−	0.111608i
$839$	−14.2351	−	43.8112i	−0.491451	−	1.51253i	−0.822415	−	0.568889i	$-0.807374\pi$
$839$	−14.2351	−	43.8112i	−0.491451	−	1.51253i	0.330963	−	0.943644i	$-0.392626\pi$
$840$		0			0
$841$	12.6352	+	9.18004i	0.435698	+	0.316553i
$842$	1.91582	+	1.39192i	0.0660233	+	0.0479688i
$843$	−5.85962	+	18.0341i	−0.201816	+	0.621126i
$844$	10.1078	+	31.1085i	0.347924	+	1.07080i
$845$		0			0
$846$	−0.553198			−0.0190193
$847$	10.7727	−	9.21598i	0.370155	−	0.316665i
$848$	−36.3651			−1.24878
$849$	4.10386	−	2.98163i	0.140844	−	0.102329i
$850$		0			0
$851$	−1.81590	+	5.58877i	−0.0622482	+	0.191580i
$852$	30.4568	+	22.1282i	1.04343	+	0.758099i
$853$	17.3122	+	12.5780i	0.592757	+	0.430663i	0.843301	−	0.537442i	$-0.180609\pi$
$853$	17.3122	+	12.5780i	0.592757	+	0.430663i	−0.250543	+	0.968105i	$0.580609\pi$
$854$	−0.152742	+	0.470090i	−0.00522671	+	0.0160862i
$855$		0			0
$856$	−6.69730	+	4.86587i	−0.228909	+	0.166312i
$857$	−10.0178			−0.342201			−0.171100	−	0.985254i	$-0.554732\pi$
$857$	−10.0178			−0.342201			−0.171100	+	0.985254i	$0.554732\pi$
$858$	−1.93308	+	6.86489i	−0.0659941	+	0.234363i
$859$	−31.7860			−1.08452			−0.542261	−	0.840210i	$-0.682432\pi$
$859$	−31.7860			−1.08452			−0.542261	+	0.840210i	$0.682432\pi$
$860$		0			0
$861$	−9.53052	−	29.3319i	−0.324799	−	0.999629i
$862$	−1.15906	+	3.56723i	−0.0394779	+	0.121500i
$863$	22.2577	+	16.1711i	0.757660	+	0.550472i	0.898192	−	0.439604i	$-0.144881\pi$
$863$	22.2577	+	16.1711i	0.757660	+	0.550472i	−0.140532	+	0.990076i	$0.544881\pi$
$864$	−8.97213	−	6.51863i	−0.305238	−	0.221768i
$865$		0			0
$866$	2.46261	+	7.57914i	0.0836830	+	0.257550i
$867$	2.36616	−	1.71912i	0.0803590	−	0.0583843i
$868$	−16.3007			−0.553282
$869$	14.7233	+	39.8592i	0.499454	+	1.35213i
$870$		0			0
$871$	18.9700	−	13.7825i	0.642775	−	0.467003i
$872$	1.94519	+	5.98668i	0.0658725	+	0.202735i
$873$	−0.0551521	+	0.169741i	−0.00186662	+	0.00574485i
$874$	−0.269076	−	0.195495i	−0.00910162	−	0.00661271i
$875$		0			0
$876$	−13.7494	+	42.3164i	−0.464551	+	1.42974i
$877$	−8.44797	−	26.0002i	−0.285268	−	0.877964i	−0.986318	−	0.164852i	$-0.947285\pi$
$877$	−8.44797	−	26.0002i	−0.285268	−	0.877964i	0.701050	−	0.713112i	$-0.252715\pi$
$878$	−1.46256	+	1.06261i	−0.0493591	+	0.0358615i
$879$	47.9066			1.61585
$880$		0			0
$881$	−48.8428			−1.64555			−0.822777	−	0.568364i	$-0.807576\pi$
$881$	−48.8428			−1.64555			−0.822777	+	0.568364i	$0.807576\pi$
$882$	−0.529214	+	0.384496i	−0.0178195	+	0.0129467i
$883$	−14.8801	−	45.7961i	−0.500754	−	1.54116i	−0.807793	−	0.589466i	$-0.799338\pi$
$883$	−14.8801	−	45.7961i	−0.500754	−	1.54116i	0.307039	−	0.951697i	$-0.400662\pi$
$884$	12.9552	−	39.8720i	0.435731	−	1.34104i
$885$		0			0
$886$	−2.25724	−	1.63998i	−0.0758335	−	0.0550963i
$887$	18.0406	−	55.5232i	0.605744	−	1.86429i	0.114148	−	0.993464i	$-0.463586\pi$
$887$	18.0406	−	55.5232i	0.605744	−	1.86429i	0.491596	−	0.870824i	$-0.336414\pi$
$888$	3.98628	+	12.2685i	0.133771	+	0.411704i
$889$	17.8977	−	13.0034i	0.600268	−	0.436120i
$890$		0			0
$891$	28.7392	+	19.1860i	0.962800	+	0.642754i
$892$	11.7035			0.391863
$893$	−8.20224	+	5.95928i	−0.274478	+	0.199420i
$894$	1.02375	+	3.15077i	0.0342392	+	0.105378i
$895$		0			0
$896$	6.57756	+	4.77888i	0.219741	+	0.159651i
$897$	5.93956	+	4.31534i	0.198316	+	0.144085i
$898$	1.25710	−	3.86896i	0.0419500	−	0.129109i
$899$	−7.30723	−	22.4893i	−0.243710	−	0.750061i
$900$		0			0
$901$	38.2101			1.27296
$902$	6.85113	−	5.40553i	0.228118	−	0.179985i
$903$	3.20230			0.106566
$904$	−13.0696	+	9.49563i	−0.434689	+	0.315820i
$905$		0			0
$906$	1.04083	−	3.20335i	0.0345793	−	0.106424i
$907$	−36.4485	−	26.4814i	−1.21025	−	0.879299i	−0.214998	−	0.976614i	$-0.568975\pi$
$907$	−36.4485	−	26.4814i	−1.21025	−	0.879299i	−0.995254	+	0.0973150i	$0.968975\pi$
$908$	35.2190	+	25.5881i	1.16878	+	0.849171i
$909$	−1.12305	+	3.45638i	−0.0372491	+	0.114641i
$910$		0			0
$911$	−5.00639	+	3.63735i	−0.165869	+	0.120511i	−0.667623	−	0.744499i	$-0.732688\pi$
$911$	−5.00639	+	3.63735i	−0.165869	+	0.120511i	0.501754	+	0.865010i	$0.332688\pi$
$912$	15.9150			0.527000
$913$	−32.6597	+	25.7684i	−1.08088	+	0.852810i
$914$	5.36971			0.177614
$915$		0			0
$916$	−3.61122	−	11.1142i	−0.119318	−	0.367223i
$917$	−3.99155	+	12.2847i	−0.131813	+	0.405677i
$918$	3.02648	+	2.19887i	0.0998889	+	0.0725735i
$919$	−6.73240	−	4.89138i	−0.222081	−	0.161352i	0.471182	−	0.882036i	$-0.343828\pi$
$919$	−6.73240	−	4.89138i	−0.222081	−	0.161352i	−0.693263	+	0.720685i	$0.743828\pi$
$920$		0			0
$921$	−4.99444	−	15.3713i	−0.164572	−	0.506501i
$922$	3.21074	−	2.33274i	0.105740	−	0.0768247i
$923$	55.3589			1.82216
$924$	−13.1764	−	8.79645i	−0.433473	−	0.289382i
$925$		0			0
$926$	3.38347	−	2.45824i	0.111188	−	0.0807826i
$927$	1.45037	+	4.46377i	0.0476363	+	0.146610i
$928$	−2.74414	+	8.44559i	−0.0900808	+	0.277240i
$929$	−8.60810	−	6.25415i	−0.282423	−	0.205192i	0.437551	−	0.899194i	$-0.355846\pi$
$929$	−8.60810	−	6.25415i	−0.282423	−	0.205192i	−0.719973	+	0.694002i	$0.755846\pi$
$930$		0			0
$931$	−3.70467	+	11.4018i	−0.121416	+	0.373679i
$932$	10.7230	+	33.0021i	0.351245	+	1.08102i
$933$	1.69190	−	1.22923i	0.0553902	−	0.0402433i
$934$	−3.43789			−0.112491
$935$		0			0
$936$	2.64210			0.0863596
$937$	−30.8835	+	22.4382i	−1.00892	+	0.733023i	−0.963982	−	0.265967i	$-0.914309\pi$
$937$	−30.8835	+	22.4382i	−1.00892	+	0.733023i	−0.0449375	+	0.998990i	$0.514309\pi$
$938$	−0.356889	−	1.09839i	−0.0116528	−	0.0358638i
$939$	3.27302	−	10.0733i	0.106811	−	0.328730i
$940$		0			0
$941$	32.7729	+	23.8109i	1.06837	+	0.776213i	0.975618	−	0.219476i	$-0.0704349\pi$
$941$	32.7729	+	23.8109i	1.06837	+	0.776213i	0.0927480	+	0.995690i	$0.470435\pi$
$942$	1.54225	−	4.74656i	0.0502493	−	0.154651i
$943$	−2.77609	−	8.54391i	−0.0904018	−	0.278228i
$944$	−26.9825	+	19.6039i	−0.878204	+	0.638053i
$945$		0			0
$946$	0.313970	+	0.849986i	0.0102081	+	0.0276354i
$947$	−25.2006			−0.818909			−0.409455	−	0.912330i	$-0.634281\pi$
$947$	−25.2006			−0.818909			−0.409455	+	0.912330i	$0.634281\pi$
$948$	38.4159	−	27.9108i	1.24769	−	0.906500i
$949$	20.2184	+	62.2257i	0.656316	+	2.01993i
$950$		0			0
$951$	43.4448	+	31.5645i	1.40879	+	1.02355i
$952$	−3.37815	−	2.45437i	−0.109486	−	0.0795465i
$953$	6.29862	−	19.3852i	0.204032	−	0.627947i	−0.795720	−	0.605665i	$-0.792907\pi$
$953$	6.29862	−	19.3852i	0.204032	−	0.627947i	0.999752	−	0.0222813i	$-0.00709296\pi$
$954$	0.367983	+	1.13254i	0.0119139	+	0.0366672i
$955$		0			0
$956$	37.4021			1.20967
$957$	6.22937	−	22.1222i	0.201367	−	0.715109i
$958$	−1.06866			−0.0345268
$959$	3.67784	−	2.67211i	0.118764	−	0.0862868i
$960$		0			0
$961$	3.33274	−	10.2571i	0.107508	−	0.330874i
$962$	7.58901	+	5.51374i	0.244680	+	0.177770i
$963$	−4.78053	−	3.47326i	−0.154051	−	0.111924i
$964$	1.08493	−	3.33907i	0.0349432	−	0.107544i
$965$		0			0
$966$	0.292546	−	0.212547i	0.00941252	−	0.00683860i
$967$	−4.49928			−0.144687			−0.0723436	−	0.997380i	$-0.523048\pi$
$967$	−4.49928			−0.144687			−0.0723436	+	0.997380i	$0.523048\pi$
$968$	2.10902	−	8.81640i	0.0677866	−	0.283370i
$969$	−16.7225			−0.537204
$970$		0			0
$971$	10.5776	+	32.5546i	0.339452	+	1.04473i	0.964487	+	0.264129i	$0.0850845\pi$
$971$	10.5776	+	32.5546i	0.339452	+	1.04473i	−0.625035	+	0.780596i	$0.714915\pi$
$972$	3.64608	−	11.2215i	0.116948	−	0.359929i
$973$	−9.15195	−	6.64928i	−0.293398	−	0.213166i
$974$	2.82069	+	2.04935i	0.0903808	+	0.0656655i
$975$		0			0
$976$	−2.12895	−	6.55222i	−0.0681459	−	0.209732i
$977$	35.4877	−	25.7833i	1.13535	−	0.824881i	0.148887	−	0.988854i	$-0.452431\pi$
$977$	35.4877	−	25.7833i	1.13535	−	0.824881i	0.986465	+	0.163973i	$0.0524310\pi$
$978$	−3.31779			−0.106091
$979$	−5.64902	+	20.0612i	−0.180544	+	0.641160i
$980$		0			0
$981$	−3.63508	+	2.64104i	−0.116059	+	0.0843220i
$982$	0.0496543	+	0.152820i	0.00158453	+	0.00487669i
$983$	5.54416	−	17.0632i	0.176831	−	0.544231i	−0.822881	−	0.568214i	$-0.807635\pi$
$983$	5.54416	−	17.0632i	0.176831	−	0.544231i	0.999712	+	0.0239829i	$0.00763472\pi$
$984$	−15.9545	−	11.5916i	−0.508611	−	0.369528i
$985$		0			0
$986$	0.925655	−	2.84887i	0.0294789	−	0.0907266i
$987$	−3.40626	−	10.4834i	−0.108422	−	0.333690i
$988$	19.3723	−	14.0748i	0.616316	−	0.447780i
$989$	0.932779			0.0296607
$990$		0			0
$991$	−33.5351			−1.06528			−0.532638	−	0.846343i	$-0.678799\pi$
$991$	−33.5351			−1.06528			−0.532638	+	0.846343i	$0.678799\pi$
$992$	−12.6950	+	9.22343i	−0.403065	+	0.292844i
$993$	10.8908	+	33.5183i	0.345608	+	1.06367i
$994$	0.842578	−	2.59319i	0.0267250	−	0.0822510i
$995$		0			0
$996$	37.6110	+	27.3260i	1.19175	+	0.865857i
$997$	−6.85905	+	21.1100i	−0.217228	+	0.668560i	0.781759	+	0.623580i	$0.214322\pi$
$997$	−6.85905	+	21.1100i	−0.217228	+	0.668560i	−0.998988	+	0.0449802i	$0.985678\pi$
$998$	−1.12554	−	3.46406i	−0.0356283	−	0.109653i
$999$	30.5417	−	22.1899i	0.966298	−	0.702056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.h.e.201.3	yes	16
5.2	odd	4		275.2.z.c.124.5		32
5.3	odd	4		275.2.z.c.124.4		32
5.4	even	2		275.2.h.c.201.2	yes	16
11.2	odd	10		3025.2.a.bj.1.6		8
11.4	even	5	inner	275.2.h.e.26.3	yes	16
11.9	even	5		3025.2.a.bn.1.3		8
55.4	even	10		275.2.h.c.26.2	✓	16
55.9	even	10		3025.2.a.bi.1.6		8
55.24	odd	10		3025.2.a.bm.1.3		8
55.37	odd	20		275.2.z.c.224.4		32
55.48	odd	20		275.2.z.c.224.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.h.c.26.2	✓	16	55.4	even	10
275.2.h.c.201.2	yes	16	5.4	even	2
275.2.h.e.26.3	yes	16	11.4	even	5	inner
275.2.h.e.201.3	yes	16	1.1	even	1	trivial
275.2.z.c.124.4		32	5.3	odd	4
275.2.z.c.124.5		32	5.2	odd	4
275.2.z.c.224.4		32	55.37	odd	20
275.2.z.c.224.5		32	55.48	odd	20
3025.2.a.bi.1.6		8	55.9	even	10
3025.2.a.bj.1.6		8	11.2	odd	10
3025.2.a.bm.1.3		8	55.24	odd	10
3025.2.a.bn.1.3		8	11.9	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.168506 - 0.122427i) q^{2} +(0.585361 + 1.80155i) q^{3} +(-0.604628 + 1.86085i) q^{4} +(0.319195 + 0.231909i) q^{6} +(-0.398265 + 1.22573i) q^{7} +(0.254662 + 0.783769i) q^{8} +(-0.475901 + 0.345762i) q^{9} +(0.898964 - 3.19247i) q^{11} -3.70635 q^{12} +(-4.40926 + 3.20351i) q^{13} +(0.0829527 + 0.255302i) q^{14} +(-3.02701 - 2.19925i) q^{16} +(3.18058 + 2.31083i) q^{17} +(-0.0378616 + 0.116526i) q^{18} +(0.693894 + 2.13559i) q^{19} -2.44136 q^{21} +(-0.239363 - 0.648008i) q^{22} -0.711128 q^{23} +(-1.26293 + 0.917575i) q^{24} +(-0.350791 + 1.07962i) q^{26} +(3.69600 + 2.68530i) q^{27} +(-2.04011 - 1.48223i) q^{28} +(1.13043 - 3.47910i) q^{29} +(5.22959 - 3.79952i) q^{31} -2.42752 q^{32} +(6.27763 - 0.249213i) q^{33} +0.818854 q^{34} +(-0.355670 - 1.09464i) q^{36} +(2.55355 - 7.85902i) q^{37} +(0.378379 + 0.274908i) q^{38} +(-8.35231 - 6.06831i) q^{39} +(3.90378 + 12.0146i) q^{41} +(-0.411383 + 0.298888i) q^{42} -1.31169 q^{43} +(5.39718 + 3.60310i) q^{44} +(-0.119829 + 0.0870611i) q^{46} +(1.39523 + 4.29408i) q^{47} +(2.19018 - 6.74067i) q^{48} +(4.31931 + 3.13816i) q^{49} +(-2.30129 + 7.08265i) q^{51} +(-3.29531 - 10.1419i) q^{52} +(7.86297 - 5.71278i) q^{53} +0.951551 q^{54} -1.06212 q^{56} +(-3.44120 + 2.50018i) q^{57} +(-0.235451 - 0.724644i) q^{58} +(2.75455 - 8.47763i) q^{59} +(1.48965 + 1.08229i) q^{61} +(0.416055 - 1.28048i) q^{62} +(-0.234278 - 0.721033i) q^{63} +(5.64496 - 4.10130i) q^{64} +(1.02731 - 0.810544i) q^{66} -4.30232 q^{67} +(-6.22318 + 4.52140i) q^{68} +(-0.416266 - 1.28114i) q^{69} +(-8.21746 - 5.97033i) q^{71} +(-0.392192 - 0.284944i) q^{72} +(3.70969 - 11.4173i) q^{73} +(-0.531866 - 1.63692i) q^{74} -4.39356 q^{76} +(3.55509 + 2.37334i) q^{77} -2.15034 q^{78} +(-10.3649 + 7.53052i) q^{79} +(-3.21956 + 9.90878i) q^{81} +(2.12872 + 1.54661i) q^{82} +(-10.1477 - 7.37274i) q^{83} +(1.47611 - 4.54301i) q^{84} +(-0.221028 + 0.160586i) q^{86} +6.92949 q^{87} +(2.73109 - 0.108421i) q^{88} -6.28392 q^{89} +(-2.17060 - 6.68043i) q^{91} +(0.429968 - 1.32330i) q^{92} +(9.90624 + 7.19730i) q^{93} +(0.760816 + 0.552765i) q^{94} +(-1.42098 - 4.37332i) q^{96} +(0.245459 - 0.178336i) q^{97} +1.11202 q^{98} +(0.676018 + 1.83013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} - 16 q^{8} + 8 q^{9} - 5 q^{11} + 6 q^{12} - 7 q^{13} + 3 q^{14} - 4 q^{16} - 12 q^{17} - 16 q^{18} - 13 q^{19} + 10 q^{21} - 28 q^{22} + 4 q^{23} - 43 q^{24}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 - 16 * q^8 + 8 * q^9 - 5 * q^11 + 6 * q^12 - 7 * q^13 + 3 * q^14 - 4 * q^16 - 12 * q^17 - 16 * q^18 - 13 * q^19 + 10 * q^21 - 28 * q^22 + 4 * q^23 - 43 * q^24 - 34 * q^26 + 11 * q^27 - 47 * q^28 - 11 * q^29 - 10 * q^31 + 58 * q^32 + 34 * q^33 + 20 * q^34 + 3 * q^36 + 4 * q^37 + 36 * q^38 + 3 * q^39 + 25 * q^41 - 13 * q^42 + 28 * q^43 - q^44 + 40 * q^46 - 8 * q^47 + 106 * q^48 + 16 * q^49 + 35 * q^51 - 39 * q^52 + 22 * q^53 + 60 * q^54 - 20 * q^56 - 29 * q^57 - 6 * q^58 + 14 * q^59 + 16 * q^61 + 10 * q^62 - 73 * q^63 + 40 * q^64 - 55 * q^66 + 14 * q^67 - 83 * q^68 + 35 * q^69 - 46 * q^71 - 28 * q^72 - 7 * q^73 - 7 * q^74 - 62 * q^76 + 51 * q^77 - 34 * q^78 - 39 * q^79 - 43 * q^81 + 51 * q^82 - 28 * q^83 - 54 * q^84 + 2 * q^86 + 50 * q^87 + 76 * q^88 - 22 * q^89 - 34 * q^91 - 4 * q^92 - 3 * q^93 - 40 * q^94 + 108 * q^96 + 39 * q^97 + 52 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

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Database

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