LMFDB - Embedded newform 375.2.o.a.229.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(4,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.o (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	375.229
Dual form			375.2.o.a.244.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.556779 - 2.16851i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-2.63982 + 1.45126i) q^{4} +(-0.155729 + 2.23064i) q^{5} +(-0.953255 - 2.02577i) q^{6} +(-2.80366 + 3.85891i) q^{7} +(1.55167 + 1.65236i) q^{8} +(0.929776 - 0.368125i) q^{9} +(4.92387 - 0.904273i) q^{10} +(-4.98086 + 1.27887i) q^{11} +(-2.32113 + 1.92020i) q^{12} +(0.886998 + 2.24030i) q^{13} +(9.92911 + 3.93121i) q^{14} +(0.265010 + 2.22031i) q^{15} +(-0.509076 + 0.802175i) q^{16} +(1.31571 - 2.39328i) q^{17} +(-1.31596 - 1.81127i) q^{18} +(-0.532240 + 2.79010i) q^{19} +(-2.82613 - 6.11449i) q^{20} +(-2.03091 + 4.31591i) q^{21} +(5.54648 + 10.0890i) q^{22} +(2.14566 + 0.134994i) q^{23} +(1.83380 + 1.33234i) q^{24} +(-4.95150 - 0.694749i) q^{25} +(4.36426 - 3.17082i) q^{26} +(0.844328 - 0.535827i) q^{27} +(1.80091 - 14.2557i) q^{28} +(3.05236 + 0.385603i) q^{29} +(4.66721 - 1.81090i) q^{30} +(-8.04194 - 4.42109i) q^{31} +(6.33450 + 2.05820i) q^{32} +(-4.65300 + 2.18954i) q^{33} +(-5.92241 - 1.52062i) q^{34} +(-8.17122 - 6.85490i) q^{35} +(-1.92020 + 2.32113i) q^{36} +(8.18512 + 5.19444i) q^{37} +(6.34670 - 0.399300i) q^{38} +(1.29108 + 2.03441i) q^{39} +(-3.92745 + 3.20389i) q^{40} +(-0.687393 - 10.9258i) q^{41} +(10.4899 + 2.00105i) q^{42} +(-2.63721 + 0.856881i) q^{43} +(11.2926 - 10.6045i) q^{44} +(0.676360 + 2.13132i) q^{45} +(-0.901924 - 4.72805i) q^{46} +(-0.926878 + 0.987024i) q^{47} +(-0.349746 + 0.883357i) q^{48} +(-4.86754 - 14.9807i) q^{49} +(1.25032 + 11.1242i) q^{50} +(0.843955 - 2.59743i) q^{51} +(-5.59277 - 4.62674i) q^{52} +(3.51967 + 1.65623i) q^{53} +(-1.63205 - 1.53260i) q^{54} +(-2.07703 - 11.3097i) q^{55} +(-10.7266 + 1.35509i) q^{56} +2.84041i q^{57} +(-0.863306 - 6.83377i) q^{58} +(4.98395 + 6.02456i) q^{59} +(-3.92181 - 5.47663i) q^{60} +(-0.387695 + 6.16224i) q^{61} +(-5.10960 + 19.9006i) q^{62} +(-1.18622 + 4.62002i) q^{63} +(0.817009 - 12.9860i) q^{64} +(-5.13544 + 1.62969i) q^{65} +(7.33873 + 8.87100i) q^{66} +(0.302168 + 2.39191i) q^{67} +8.22727i q^{68} +(2.13295 - 0.269454i) q^{69} +(-10.3154 + 21.5360i) q^{70} +(1.82683 + 1.71551i) q^{71} +(2.05098 + 0.965116i) q^{72} +(6.57662 + 5.44065i) q^{73} +(6.70689 - 20.6417i) q^{74} +(-4.99398 + 0.245375i) q^{75} +(-2.64413 - 8.13778i) q^{76} +(9.02962 - 22.8062i) q^{77} +(3.69280 - 3.93244i) q^{78} +(1.51075 + 7.91964i) q^{79} +(-1.71008 - 1.26049i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-23.3100 + 7.57388i) q^{82} +(7.78667 + 1.48539i) q^{83} +(-0.902235 - 14.3406i) q^{84} +(5.13364 + 3.30759i) q^{85} +(3.32650 + 5.24172i) q^{86} +(3.07055 - 0.193183i) q^{87} +(-9.84179 - 6.24579i) q^{88} +(-10.0819 + 12.1869i) q^{89} +(4.24521 - 2.65337i) q^{90} +(-11.1320 - 2.85820i) q^{91} +(-5.86008 + 2.75754i) q^{92} +(-8.72792 - 2.83587i) q^{93} +(2.65644 + 1.46039i) q^{94} +(-6.14082 - 1.62173i) q^{95} +(6.60796 + 0.834780i) q^{96} +(-0.691753 + 5.47579i) q^{97} +(-29.7758 + 18.8963i) q^{98} +(-4.16031 + 3.02264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 30 q^{8} + 10 q^{11} + 20 q^{16} - 10 q^{17} - 10 q^{19} - 20 q^{20} + 30 q^{22} - 180 q^{23} - 30 q^{24} - 40 q^{25} - 30 q^{28} - 20 q^{29} + 20 q^{30} + 10 q^{31} - 10 q^{33} + 20 q^{34} - 10 q^{35}+ \cdots - 60 q^{98}+O(q^{100}) $ 480 * q + 30 * q^8 + 10 * q^11 + 20 * q^16 - 10 * q^17 - 10 * q^19 - 20 * q^20 + 30 * q^22 - 180 * q^23 - 30 * q^24 - 40 * q^25 - 30 * q^28 - 20 * q^29 + 20 * q^30 + 10 * q^31 - 10 * q^33 + 20 * q^34 - 10 * q^35 + 10 * q^37 - 30 * q^38 - 10 * q^40 + 30 * q^41 + 10 * q^42 - 70 * q^44 + 20 * q^46 - 40 * q^47 + 80 * q^49 - 20 * q^50 + 40 * q^51 - 40 * q^52 - 10 * q^53 - 10 * q^55 - 240 * q^56 - 310 * q^58 - 40 * q^59 - 120 * q^60 + 20 * q^61 + 10 * q^62 + 10 * q^63 - 70 * q^64 + 70 * q^65 - 260 * q^67 - 30 * q^70 - 160 * q^71 + 30 * q^72 + 20 * q^73 + 100 * q^76 + 40 * q^77 - 20 * q^79 - 200 * q^82 - 10 * q^83 - 40 * q^84 + 20 * q^85 + 100 * q^86 - 40 * q^87 + 40 * q^88 - 50 * q^89 - 30 * q^90 - 120 * q^91 - 10 * q^92 - 300 * q^93 - 20 * q^94 - 60 * q^95 + 50 * q^96 - 40 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	−0.556779	−	2.16851i	−0.393702	−	1.53337i	−0.788753	−	0.614710i	$-0.789273\pi$
$2$	−0.556779	−	2.16851i	−0.393702	−	1.53337i	0.395051	−	0.918659i	$-0.370727\pi$
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$4$	−2.63982	+	1.45126i	−1.31991	+	0.725628i
$5$	−0.155729	+	2.23064i	−0.0696440	+	0.997572i
$5$	−0.155729	+	2.23064i	−0.0696440	+	0.997572i
$6$	−0.953255	−	2.02577i	−0.389165	−	0.827017i
$7$	−2.80366	+	3.85891i	−1.05968	+	1.45853i	−0.179584	+	0.983743i	$0.557475\pi$
$7$	−2.80366	+	3.85891i	−1.05968	+	1.45853i	−0.880100	+	0.474788i	$0.842525\pi$
$8$	1.55167	+	1.65236i	0.548597	+	0.584197i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	4.92387	−	0.904273i	1.55706	−	0.285956i
$11$	−4.98086	+	1.27887i	−1.50179	+	0.385593i	−0.907980	−	0.419014i	$-0.862376\pi$
$11$	−4.98086	+	1.27887i	−1.50179	+	0.385593i	−0.593807	+	0.804607i	$0.702376\pi$
$12$	−2.32113	+	1.92020i	−0.670052	+	0.554315i
$13$	0.886998	+	2.24030i	0.246009	+	0.621348i	0.999341	−	0.0362922i	$-0.0115547\pi$
$13$	0.886998	+	2.24030i	0.246009	+	0.621348i	−0.753332	+	0.657640i	$0.771555\pi$
$14$	9.92911	+	3.93121i	2.65367	+	1.05066i
$15$	0.265010	+	2.22031i	0.0684252	+	0.573281i
$16$	−0.509076	+	0.802175i	−0.127269	+	0.200544i
$17$	1.31571	−	2.39328i	0.319108	−	0.580455i	−0.667296	−	0.744792i	$-0.732549\pi$
$17$	1.31571	−	2.39328i	0.319108	−	0.580455i	0.986404	+	0.164337i	$0.0525486\pi$
$18$	−1.31596	−	1.81127i	−0.310175	−	0.426920i
$19$	−0.532240	+	2.79010i	−0.122104	+	0.640093i	0.867634	+	0.497203i	$0.165639\pi$
$19$	−0.532240	+	2.79010i	−0.122104	+	0.640093i	−0.989739	+	0.142890i	$0.954361\pi$
$20$	−2.82613	−	6.11449i	−0.631942	−	1.36724i
$21$	−2.03091	+	4.31591i	−0.443182	+	0.941809i
$22$	5.54648	+	10.0890i	1.18251	+	2.15098i
$23$	2.14566	+	0.134994i	0.447401	+	0.0281481i	0.284894	−	0.958559i	$-0.408042\pi$
$23$	2.14566	+	0.134994i	0.447401	+	0.0281481i	0.162508	+	0.986707i	$0.448042\pi$
$24$	1.83380	+	1.33234i	0.374324	+	0.271962i
$25$	−4.95150	−	0.694749i	−0.990299	−	0.138950i
$26$	4.36426	−	3.17082i	0.855901	−	0.621849i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	1.80091	−	14.2557i	0.340340	−	2.69407i
$29$	3.05236	+	0.385603i	0.566809	+	0.0716046i	0.403515	−	0.914973i	$-0.367788\pi$
$29$	3.05236	+	0.385603i	0.566809	+	0.0716046i	0.163294	+	0.986578i	$0.447788\pi$
$30$	4.66721	−	1.81090i	0.852112	−	0.330623i
$31$	−8.04194	−	4.42109i	−1.44437	−	0.794051i	−0.449319	−	0.893372i	$-0.648333\pi$
$31$	−8.04194	−	4.42109i	−1.44437	−	0.794051i	−0.995056	+	0.0993201i	$0.968333\pi$
$32$	6.33450	+	2.05820i	1.11979	+	0.363842i
$33$	−4.65300	+	2.18954i	−0.809984	+	0.381149i
$34$	−5.92241	−	1.52062i	−1.01568	−	0.260784i
$35$	−8.17122	−	6.85490i	−1.38119	−	1.15869i
$36$	−1.92020	+	2.32113i	−0.320034	+	0.386854i
$37$	8.18512	+	5.19444i	1.34563	+	0.853960i	0.996539	−	0.0831304i	$-0.0264918\pi$
$37$	8.18512	+	5.19444i	1.34563	+	0.853960i	0.349087	+	0.937090i	$0.386492\pi$
$38$	6.34670	−	0.399300i	1.02957	−	0.0647751i
$39$	1.29108	+	2.03441i	0.206738	+	0.325767i
$40$	−3.92745	+	3.20389i	−0.620985	+	0.506579i
$41$	−0.687393	−	10.9258i	−0.107353	−	1.70632i	−0.571530	−	0.820581i	$-0.693650\pi$
$41$	−0.687393	−	10.9258i	−0.107353	−	1.70632i	0.464177	−	0.885742i	$-0.346350\pi$
$42$	10.4899	+	2.00105i	1.61862	+	0.308769i
$43$	−2.63721	+	0.856881i	−0.402171	+	0.130673i	−0.503116	−	0.864219i	$-0.667813\pi$
$43$	−2.63721	+	0.856881i	−0.402171	+	0.130673i	0.100946	+	0.994892i	$0.467813\pi$
$44$	11.2926	−	10.6045i	1.70243	−	1.59869i
$45$	0.676360	+	2.13132i	0.100826	+	0.317719i
$46$	−0.901924	−	4.72805i	−0.132981	−	0.697113i
$47$	−0.926878	+	0.987024i	−0.135199	+	0.143972i	−0.793005	−	0.609215i	$-0.791485\pi$
$47$	−0.926878	+	0.987024i	−0.135199	+	0.143972i	0.657806	+	0.753187i	$0.271485\pi$
$48$	−0.349746	+	0.883357i	−0.0504815	+	0.127502i
$49$	−4.86754	−	14.9807i	−0.695363	−	2.14011i
$50$	1.25032	+	11.1242i	0.176822	+	1.57320i
$51$	0.843955	−	2.59743i	0.118177	−	0.363712i
$52$	−5.59277	−	4.62674i	−0.775578	−	0.641614i
$53$	3.51967	+	1.65623i	0.483463	+	0.227501i	0.652035	−	0.758189i	$-0.273916\pi$
$53$	3.51967	+	1.65623i	0.483463	+	0.227501i	−0.168572	+	0.985689i	$0.553916\pi$
$54$	−1.63205	−	1.53260i	−0.222094	−	0.208560i
$55$	−2.07703	−	11.3097i	−0.280067	−	1.52499i
$56$	−10.7266	+	1.35509i	−1.43341	+	0.181082i
$57$			2.84041i			0.376222i
$58$	−0.863306	−	6.83377i	−0.113358	−	0.897318i
$59$	4.98395	+	6.02456i	0.648855	+	0.784332i	0.987675	−	0.156520i	$-0.0500275\pi$
$59$	4.98395	+	6.02456i	0.648855	+	0.784332i	−0.338819	+	0.940851i	$0.610028\pi$
$60$	−3.92181	−	5.47663i	−0.506304	−	0.707029i
$61$	−0.387695	+	6.16224i	−0.0496393	+	0.788994i	0.891930	+	0.452174i	$0.149351\pi$
$61$	−0.387695	+	6.16224i	−0.0496393	+	0.788994i	−0.941569	+	0.336820i	$0.890649\pi$
$62$	−5.10960	+	19.9006i	−0.648920	+	2.52738i
$63$	−1.18622	+	4.62002i	−0.149450	+	0.582068i
$64$	0.817009	−	12.9860i	0.102126	−	1.62325i
$65$	−5.13544	+	1.62969i	−0.636972	+	0.202139i
$66$	7.33873	+	8.87100i	0.903335	+	1.09194i
$67$	0.302168	+	2.39191i	0.0369157	+	0.292218i	0.999755	+	0.0221424i	$0.00704871\pi$
$67$	0.302168	+	2.39191i	0.0369157	+	0.292218i	−0.962839	+	0.270076i	$0.912951\pi$
$68$			8.22727i			0.997703i
$69$	2.13295	−	0.269454i	0.256777	−	0.0324385i
$70$	−10.3154	+	21.5360i	−1.23292	+	2.57405i
$71$	1.82683	+	1.71551i	0.216805	+	0.203594i	0.785338	−	0.619067i	$-0.212489\pi$
$71$	1.82683	+	1.71551i	0.216805	+	0.203594i	−0.568533	+	0.822660i	$0.692489\pi$
$72$	2.05098	+	0.965116i	0.241710	+	0.113740i
$73$	6.57662	+	5.44065i	0.769735	+	0.636780i	0.937079	−	0.349119i	$-0.113519\pi$
$73$	6.57662	+	5.44065i	0.769735	+	0.636780i	−0.167344	+	0.985899i	$0.553519\pi$
$74$	6.70689	−	20.6417i	0.779660	−	2.39955i
$75$	−4.99398	+	0.245375i	−0.576655	+	0.0283335i
$76$	−2.64413	−	8.13778i	−0.303302	−	0.933468i
$77$	9.02962	−	22.8062i	1.02902	−	2.59901i
$78$	3.69280	−	3.93244i	0.418128	−	0.445261i
$79$	1.51075	+	7.91964i	0.169973	+	0.891029i	0.960432	+	0.278514i	$0.0898420\pi$
$79$	1.51075	+	7.91964i	0.169973	+	0.891029i	−0.790459	+	0.612515i	$0.790158\pi$
$80$	−1.71008	−	1.26049i	−0.191193	−	0.140927i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	−23.3100	+	7.57388i	−2.57416	+	0.836395i
$83$	7.78667	+	1.48539i	0.854698	+	0.163042i	0.596068	−	0.802934i	$-0.296729\pi$
$83$	7.78667	+	1.48539i	0.854698	+	0.163042i	0.258630	+	0.965976i	$0.416729\pi$
$84$	−0.902235	−	14.3406i	−0.0984419	−	1.56469i
$85$	5.13364	+	3.30759i	0.556822	+	0.358758i
$86$	3.32650	+	5.24172i	0.358706	+	0.565230i
$87$	3.07055	−	0.193183i	0.329197	−	0.0207113i
$88$	−9.84179	−	6.24579i	−1.04914	−	0.665803i
$89$	−10.0819	+	12.1869i	−1.06868	+	1.29181i	−0.114225	+	0.993455i	$0.536438\pi$
$89$	−10.0819	+	12.1869i	−1.06868	+	1.29181i	−0.954455	+	0.298356i	$0.903562\pi$
$90$	4.24521	−	2.65337i	0.447485	−	0.279690i
$91$	−11.1320	−	2.85820i	−1.16695	−	0.299621i
$92$	−5.86008	+	2.75754i	−0.610955	+	0.287494i
$93$	−8.72792	−	2.83587i	−0.905043	−	0.294066i
$94$	2.65644	+	1.46039i	0.273991	+	0.150628i
$95$	−6.14082	−	1.62173i	−0.630034	−	0.166386i
$96$	6.60796	+	0.834780i	0.674423	+	0.0851994i
$97$	−0.691753	+	5.47579i	−0.0702369	+	0.555982i	0.917254	+	0.398304i	$0.130401\pi$
$97$	−0.691753	+	5.47579i	−0.0702369	+	0.555982i	−0.987490	+	0.157679i	$0.949599\pi$
$98$	−29.7758	+	18.8963i	−3.00781	+	1.90881i
$99$	−4.16031	+	3.02264i	−0.418127	+	0.303787i
$100$	14.0793	−	5.35187i	1.40793	−	0.535187i
$101$	−9.22338	−	6.70117i	−0.917760	−	0.666792i	0.0252053	−	0.999682i	$-0.491976\pi$
$101$	−9.22338	−	6.70117i	−0.917760	−	0.666792i	−0.942965	+	0.332891i	$0.891976\pi$
$102$	−6.10244	−	0.383933i	−0.604232	−	0.0380150i
$103$	8.75240	+	15.9206i	0.862400	+	1.56870i	0.821980	+	0.569517i	$0.192870\pi$
$103$	8.75240	+	15.9206i	0.862400	+	1.56870i	0.0404202	+	0.999183i	$0.487130\pi$
$104$	−2.32545	+	4.94184i	−0.228029	+	0.484587i
$105$	−9.31097	−	5.20234i	−0.908657	−	0.507697i
$106$	1.63187	−	8.55459i	0.158502	−	0.830895i
$107$	−6.01566	−	8.27984i	−0.581555	−	0.800442i	0.412309	−	0.911044i	$-0.364722\pi$
$107$	−6.01566	−	8.27984i	−0.581555	−	0.800442i	−0.993865	+	0.110602i	$0.964722\pi$
$108$	−1.45126	+	2.63982i	−0.139647	+	0.254017i
$109$	−1.80192	+	2.83938i	−0.172593	+	0.271963i	−0.919602	−	0.392851i	$-0.871489\pi$
$109$	−1.80192	+	2.83938i	−0.172593	+	0.271963i	0.747009	+	0.664813i	$0.231489\pi$
$110$	−23.3687	+	10.8010i	−2.22812	+	1.02984i
$111$	9.01348	+	3.56869i	0.855522	+	0.338725i
$112$	−1.66824	−	4.21350i	−0.157634	−	0.398139i
$113$	−5.13942	+	4.25170i	−0.483476	+	0.399966i	−0.846979	−	0.531627i	$-0.821581\pi$
$113$	−5.13942	+	4.25170i	−0.483476	+	0.399966i	0.363503	+	0.931593i	$0.381581\pi$
$114$	6.15946	−	1.58148i	0.576886	−	0.148119i
$115$	−0.635263	+	4.76517i	−0.0592386	+	0.444355i
$116$	−8.61730	+	3.41183i	−0.800096	+	0.316780i
$117$	1.64942	+	1.75645i	0.152489	+	0.162384i
$118$	10.2894	−	14.1621i	0.947214	−	1.30373i
$119$	5.54662	+	11.7872i	0.508458	+	1.08053i
$120$	−3.25754	+	3.88307i	−0.297371	+	0.354474i
$121$	13.5341	−	7.44045i	1.23038	−	0.676404i
$122$	13.5787	−	2.59028i	1.22936	−	0.234513i
$123$	−2.72251	−	10.6035i	−0.245480	−	0.956083i
$124$	27.6454			2.48263
$125$	2.32082	−	10.9368i	0.207581	−	0.978218i
$126$	10.6790			0.951363
$127$	−1.03708	−	4.03917i	−0.0920263	−	0.358419i	0.905847	−	0.423605i	$-0.139236\pi$
$127$	−1.03708	−	4.03917i	−0.0920263	−	0.358419i	−0.997873	+	0.0651868i	$0.979236\pi$
$128$	−15.5301	+	2.96253i	−1.37268	+	0.261853i
$129$	−2.42993	+	1.33587i	−0.213944	+	0.117617i
$130$	6.39331	+	10.2289i	0.560730	+	0.897131i
$131$	5.44668	+	11.5748i	0.475879	+	1.01129i	0.988295	+	0.152556i	$0.0487506\pi$
$131$	5.44668	+	11.5748i	0.475879	+	1.01129i	−0.512416	+	0.858737i	$0.671249\pi$
$132$	9.10553	−	12.5327i	0.792535	−	1.09083i
$133$	−9.27452	−	9.87636i	−0.804203	−	0.856389i
$134$	5.01864	−	1.98702i	0.433544	−	0.171652i
$135$	1.06375	+	1.96683i	0.0915530	+	0.169278i
$136$	5.99610	−	1.53954i	0.514161	−	0.132014i
$137$	−9.34351	+	7.72962i	−0.798270	+	0.660386i	−0.944371	−	0.328883i	$-0.893328\pi$
$137$	−9.34351	+	7.72962i	−0.798270	+	0.660386i	0.146101	+	0.989270i	$0.453328\pi$
$138$	−1.77190	−	4.47530i	−0.150834	−	0.380963i
$139$	4.59400	+	1.81889i	0.389658	+	0.154277i	0.554781	−	0.831996i	$-0.312802\pi$
$139$	4.59400	+	1.81889i	0.389658	+	0.154277i	−0.165123	+	0.986273i	$0.552802\pi$
$140$	31.5188	+	6.23719i	2.66382	+	0.527139i
$141$	−0.725510	+	1.14322i	−0.0610990	+	0.0962766i
$142$	2.70296	−	4.91667i	0.226828	−	0.412598i
$143$	−7.28307	−	10.0243i	−0.609041	−	0.838273i
$144$	−0.178026	+	0.933246i	−0.0148355	+	0.0777705i
$145$	−1.33548	+	6.74866i	−0.110906	+	0.560446i
$146$	8.13639	−	17.2907i	0.673372	−	1.43099i
$147$	−7.58844	−	13.8033i	−0.625884	−	1.13848i
$148$	−29.1457	−	1.83369i	−2.39576	−	0.150729i
$149$	−8.64667	−	6.28217i	−0.708363	−	0.514656i	0.174282	−	0.984696i	$-0.444239\pi$
$149$	−8.64667	−	6.28217i	−0.708363	−	0.514656i	−0.882645	+	0.470040i	$0.844239\pi$
$150$	3.31264	+	10.6929i	0.270476	+	0.873069i
$151$	12.6614	−	9.19902i	1.03037	−	0.748606i	0.0619853	−	0.998077i	$-0.480257\pi$
$151$	12.6614	−	9.19902i	1.03037	−	0.748606i	0.968382	+	0.249471i	$0.0802568\pi$
$152$	−5.43610	+	3.44985i	−0.440926	+	0.279820i
$153$	0.342297	−	2.70956i	0.0276731	−	0.219055i
$154$	−54.4830	−	6.88281i	−4.39037	−	0.554632i
$155$	11.1142	−	17.2502i	0.892715	−	1.38557i
$156$	−6.36067	−	3.49681i	−0.509261	−	0.279969i
$157$	16.7698	+	5.44882i	1.33837	+	0.434863i	0.888765	−	0.458363i	$-0.151564\pi$
$157$	16.7698	+	5.44882i	1.33837	+	0.434863i	0.449607	+	0.893227i	$0.351564\pi$
$158$	16.3327	−	7.68557i	1.29936	−	0.611431i
$159$	3.76767	+	0.967373i	0.298796	+	0.0767177i
$160$	−5.57757	+	13.8095i	−0.440946	+	1.09173i
$161$	−6.53664	+	7.90144i	−0.515159	+	0.622720i
$162$	−1.89032	−	1.19964i	−0.148518	−	0.0942522i
$163$	2.21670	−	0.139463i	0.173626	−	0.0109236i	0.0242602	−	0.999706i	$-0.492277\pi$
$163$	2.21670	−	0.139463i	0.173626	−	0.0109236i	0.149365	+	0.988782i	$0.452277\pi$
$164$	17.6707	+	27.8446i	1.37985	+	2.17430i
$165$	−4.15946	−	10.7201i	−0.323814	−	0.834562i
$166$	−1.11438	−	17.7125i	−0.0864924	−	1.37476i
$167$	−3.24604	−	0.619215i	−0.251186	−	0.0479163i	0.0602503	−	0.998183i	$-0.480810\pi$
$167$	−3.24604	−	0.619215i	−0.251186	−	0.0479163i	−0.311436	+	0.950267i	$0.600810\pi$
$168$	−10.2827	+	3.34106i	−0.793330	+	0.257768i
$169$	5.24440	−	4.92482i	0.403416	−	0.378833i
$170$	4.31423	−	12.9740i	0.330887	−	0.995057i
$171$	0.532240	+	2.79010i	0.0407014	+	0.213364i
$172$	5.71821	−	6.08928i	0.436010	−	0.464303i
$173$	2.49690	−	6.30644i	0.189835	−	0.479470i	−0.803420	−	0.595412i	$-0.796989\pi$
$173$	2.49690	−	6.30644i	0.189835	−	0.479470i	0.993256	+	0.115942i	$0.0369888\pi$
$174$	−2.12854	−	6.55096i	−0.161364	−	0.496627i
$175$	16.5633	−	17.1595i	1.25207	−	1.29714i
$176$	1.50976	−	4.64656i	0.113802	−	0.350248i
$177$	6.02456	+	4.98395i	0.452834	+	0.374617i
$178$	32.0409	+	15.0773i	2.40156	+	1.13009i
$179$	12.7145	+	11.9397i	0.950324	+	0.892414i	0.994300	−	0.106619i	$-0.0340025\pi$
$179$	12.7145	+	11.9397i	0.950324	+	0.892414i	−0.0439760	+	0.999033i	$0.514003\pi$
$180$	−4.87856	−	4.64475i	−0.363627	−	0.346199i
$181$	8.33394	−	1.05282i	0.619457	−	0.0782556i	0.190659	−	0.981656i	$-0.438937\pi$
$181$	8.33394	−	1.05282i	0.619457	−	0.0782556i	0.428797	+	0.903401i	$0.358937\pi$
$182$			25.7312i			1.90732i
$183$	0.773860	+	6.12573i	0.0572054	+	0.452827i
$184$	3.10629	+	3.75486i	0.228999	+	0.276812i
$185$	−12.8616	+	17.4491i	−0.945601	+	1.28289i
$186$	−1.29010	+	20.5055i	−0.0945947	+	1.50354i
$187$	−3.49271	+	13.6032i	−0.255412	+	0.994765i
$188$	1.01437	−	3.95071i	0.0739805	−	0.288135i
$189$	−0.299503	+	4.76046i	−0.0217856	+	0.346273i
$190$	−0.0976678	+	14.2194i	−0.00708557	+	1.03158i
$191$	−0.205094	−	0.247916i	−0.0148401	−	0.0179385i	0.763041	−	0.646350i	$-0.223705\pi$
$191$	−0.205094	−	0.247916i	−0.0148401	−	0.0179385i	−0.777881	+	0.628412i	$0.783705\pi$
$192$	−1.63079	−	12.9091i	−0.117692	−	0.931632i
$193$		−	6.89686i		−	0.496447i	−0.968703	−	0.248224i	$-0.920153\pi$
$193$		−	6.89686i		−	0.496447i	0.968703	−	0.248224i	$-0.0798467\pi$
$194$	12.2595	−	1.54873i	0.880178	−	0.111192i
$195$	−4.73910	+	2.56311i	−0.339374	+	0.183548i
$196$	34.5903	+	32.4825i	2.47074	+	2.32018i
$197$	2.43677	+	1.14666i	0.173613	+	0.0816960i	0.510622	−	0.859805i	$-0.329415\pi$
$197$	2.43677	+	1.14666i	0.173613	+	0.0816960i	−0.337009	+	0.941501i	$0.609415\pi$
$198$	8.87100	+	7.33873i	0.630435	+	0.521541i
$199$	2.78454	−	8.56994i	0.197391	−	0.607507i	−0.802549	−	0.596586i	$-0.796524\pi$
$199$	2.78454	−	8.56994i	0.197391	−	0.607507i	0.999940	−	0.0109213i	$-0.00347642\pi$
$200$	−6.53510	−	9.25966i	−0.462101	−	0.654757i
$201$	0.745015	+	2.29292i	0.0525493	+	0.161730i
$202$	−9.39619	+	23.7321i	−0.661114	+	1.66978i
$203$	−10.0458	+	10.6977i	−0.705076	+	0.750830i
$204$	1.54164	+	8.08154i	0.107936	+	0.565821i
$205$	24.4786	+	0.168134i	1.70966	+	0.0117430i
$206$	29.6508	−	27.8439i	2.06587	−	1.93998i
$207$	2.04468	−	0.664357i	0.142115	−	0.0461760i
$208$	−2.24866	−	0.428955i	−0.155917	−	0.0297427i
$209$	−0.917155	−	14.5778i	−0.0634410	−	1.00837i
$210$	−6.09719	+	23.0875i	−0.420746	+	1.59319i
$211$	−11.0240	−	17.3710i	−0.758922	−	1.19587i	−0.975585	−	0.219623i	$-0.929517\pi$
$211$	−11.0240	−	17.3710i	−0.758922	−	1.19587i	0.216663	−	0.976246i	$-0.430483\pi$
$212$	−11.6949	+	0.735781i	−0.803209	+	0.0505337i
$213$	2.11593	+	1.34281i	0.144981	+	0.0920078i
$214$	−14.6055	+	17.6551i	−0.998414	+	1.20687i
$215$	−1.50070	−	6.01610i	−0.102347	−	0.410295i
$216$	2.19549	+	0.563707i	0.149384	+	0.0383554i
$217$	39.6075	−	18.6379i	2.68873	−	1.26522i
$218$	7.16049	+	2.32659i	0.484970	+	0.157576i
$219$	7.47960	+	4.11195i	0.505425	+	0.277860i
$220$	21.8962	+	26.8412i	1.47624	+	1.80963i
$221$	6.52870	+	0.824767i	0.439168	+	0.0554798i
$222$	2.72023	−	21.5328i	0.182570	−	1.44519i
$223$	−13.3078	+	8.44539i	−0.891156	+	0.565545i	−0.900716	−	0.434409i	$-0.856957\pi$
$223$	−13.3078	+	8.44539i	−0.891156	+	0.565545i	0.00955934	+	0.999954i	$0.496957\pi$
$224$	−25.7022	+	18.6737i	−1.71730	+	1.24769i
$225$	−4.85954	+	1.17681i	−0.323969	+	0.0784538i
$226$	12.0814	+	8.77763i	0.803641	+	0.583879i
$227$	−7.33480	−	0.461467i	−0.486828	−	0.0306286i	−0.182520	−	0.983202i	$-0.558425\pi$
$227$	−7.33480	−	0.461467i	−0.486828	−	0.0306286i	−0.304308	+	0.952574i	$0.598425\pi$
$228$	−4.12216	−	7.49818i	−0.272997	−	0.496579i
$229$	−4.98344	+	10.5903i	−0.329315	+	0.699830i	−0.999086	−	0.0427374i	$-0.986392\pi$
$229$	−4.98344	+	10.5903i	−0.329315	+	0.699830i	0.669771	+	0.742567i	$0.266392\pi$
$230$	10.6870	−	1.27557i	0.704682	−	0.0841088i
$231$	4.59622	−	24.0942i	0.302409	−	1.58528i
$232$	4.09909	+	5.64192i	0.269119	+	0.370410i
$233$	3.76194	−	6.84294i	0.246453	−	0.448296i	−0.723928	−	0.689875i	$-0.757665\pi$
$233$	3.76194	−	6.84294i	0.246453	−	0.448296i	0.970381	+	0.241579i	$0.0776653\pi$
$234$	2.89053	−	4.55474i	0.188960	−	0.297753i
$235$	−2.05735	−	2.22124i	−0.134207	−	0.144898i
$236$	−21.8999	−	8.67080i	−1.42556	−	0.564421i
$237$	2.96799	+	7.49627i	0.192791	+	0.486935i
$238$	22.4723	−	18.5907i	1.45667	−	1.20506i
$239$	−8.80896	+	2.26176i	−0.569804	+	0.146301i	−0.522590	−	0.852584i	$-0.675034\pi$
$239$	−8.80896	+	2.26176i	−0.569804	+	0.146301i	−0.0472139	+	0.998885i	$0.515034\pi$
$240$	−1.91599	−	0.917721i	−0.123676	−	0.0592386i
$241$	−9.83243	+	3.89293i	−0.633363	+	0.250766i	−0.662795	−	0.748801i	$-0.730630\pi$
$241$	−9.83243	+	3.89293i	−0.633363	+	0.250766i	0.0294326	+	0.999567i	$0.490630\pi$
$242$	−23.6702	−	25.2062i	−1.52158	−	1.62032i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	−7.91953	−	16.8299i	−0.506996	−	1.07742i
$245$	34.1747	−	8.52479i	2.18334	−	0.544629i
$246$	−21.4779	+	11.8076i	−1.36938	+	0.752824i
$247$	−6.72276	+	1.28243i	−0.427759	+	0.0815994i
$248$	−5.17318	−	20.1482i	−0.328497	−	1.27941i
$249$	7.92708			0.502358
$250$	−25.0088	+	1.05665i	−1.58169	+	0.0668287i
$251$	−23.3818			−1.47584			−0.737922	−	0.674886i	$-0.764193\pi$
$251$	−23.3818			−1.47584			−0.737922	+	0.674886i	$0.764193\pi$
$252$	−3.57342	−	13.9175i	−0.225104	−	0.876723i
$253$	−10.8599	+	2.07163i	−0.682755	+	0.130243i
$254$	−8.18156	+	4.49785i	−0.513357	+	0.282220i
$255$	5.66249	+	2.28705i	0.354599	+	0.143221i
$256$	3.99094	+	8.48119i	0.249434	+	0.530074i
$257$	6.13160	−	8.43942i	0.382479	−	0.526437i	−0.573760	−	0.819023i	$-0.694516\pi$
$257$	6.13160	−	8.43942i	0.382479	−	0.526437i	0.956239	+	0.292586i	$0.0945159\pi$
$258$	4.24978	+	4.52556i	0.264580	+	0.281749i
$259$	−42.9932	+	17.0222i	−2.67146	+	1.05771i
$260$	11.1915	−	11.7549i	0.694070	−	0.729010i
$261$	2.97996	−	0.765124i	0.184455	−	0.0473600i
$262$	22.0675	−	18.2558i	1.36333	−	1.12785i
$263$	−6.40490	−	16.1769i	−0.394943	−	0.997512i	−0.982154	−	0.188078i	$-0.939774\pi$
$263$	−6.40490	−	16.1769i	−0.394943	−	0.997512i	0.587211	−	0.809434i	$-0.300226\pi$
$264$	−10.8378	−	4.29099i	−0.667021	−	0.264092i
$265$	−4.24256	+	7.59318i	−0.260618	+	0.466445i
$266$	−16.2531	+	25.6108i	−0.996543	+	1.57030i
$267$	−7.61972	+	13.8602i	−0.466319	+	0.848232i
$268$	−4.26894	−	5.87569i	−0.260767	−	0.358915i
$269$	4.09758	−	21.4803i	0.249834	−	1.30968i	−0.607255	−	0.794507i	$-0.707729\pi$
$269$	4.09758	−	21.4803i	0.249834	−	1.30968i	0.857089	−	0.515169i	$-0.172271\pi$
$270$	3.67283	−	3.40185i	0.223521	−	0.207030i
$271$	−8.23096	+	17.4917i	−0.499995	+	1.06254i	0.482438	+	0.875930i	$0.339751\pi$
$271$	−8.23096	+	17.4917i	−0.499995	+	1.06254i	−0.982433	+	0.186614i	$0.940249\pi$
$272$	1.25003	+	2.27379i	0.0757941	+	0.137869i
$273$	−11.4704	−	0.721654i	−0.694218	−	0.0436765i
$274$	21.9640	+	15.9578i	1.32690	+	0.964047i
$275$	25.5512	−	2.87187i	1.54080	−	0.173180i
$276$	−5.23957	+	3.80677i	−0.315385	+	0.229141i
$277$	19.0078	−	12.0627i	1.14207	−	0.724779i	0.176340	−	0.984329i	$-0.443574\pi$
$277$	19.0078	−	12.0627i	1.14207	−	0.724779i	0.965730	+	0.259550i	$0.0835742\pi$
$278$	1.38645	−	10.9749i	0.0831536	−	0.658229i
$279$	−9.10471	−	1.15019i	−0.545085	−	0.0688602i
$280$	−1.35227	−	24.1383i	−0.0808136	−	1.44254i
$281$	−9.64783	−	5.30394i	−0.575541	−	0.316407i	0.167266	−	0.985912i	$-0.446506\pi$
$281$	−9.64783	−	5.30394i	−0.575541	−	0.316407i	−0.742807	+	0.669505i	$0.766506\pi$
$282$	2.88304	+	0.936755i	0.171682	+	0.0557830i
$283$	−10.6223	+	4.99849i	−0.631432	+	0.297129i	−0.714736	−	0.699395i	$-0.753453\pi$
$283$	−10.6223	+	4.99849i	−0.631432	+	0.297129i	0.0833034	+	0.996524i	$0.473453\pi$
$284$	−7.31216	−	1.87744i	−0.433897	−	0.111406i
$285$	−6.33593	−	0.442333i	−0.375308	−	0.0262016i
$286$	−17.6827	+	21.3747i	−1.04560	+	1.26391i
$287$	44.0889	+	27.9797i	2.60248	+	1.65159i
$288$	6.64734	−	0.418215i	0.391698	−	0.0246436i
$289$	5.11239	+	8.05583i	0.300729	+	0.473873i
$290$	15.3781	−	0.861510i	0.903034	−	0.0505896i
$291$	0.346561	+	5.50842i	0.0203157	+	0.322909i
$292$	−25.2569	−	4.81801i	−1.47805	−	0.281953i
$293$	−12.0657	+	3.92037i	−0.704883	+	0.229030i	−0.639457	−	0.768827i	$-0.720841\pi$
$293$	−12.0657	+	3.92037i	−0.704883	+	0.229030i	−0.0654263	+	0.997857i	$0.520841\pi$
$294$	−25.7076	+	24.1410i	−1.49930	+	1.40793i
$295$	−14.2148	+	10.1792i	−0.827616	+	0.592656i
$296$	4.11752	+	21.5848i	0.239326	+	1.25459i
$297$	−3.52023	+	3.74866i	−0.204264	+	0.217520i
$298$	−8.80868	+	22.2482i	−0.510273	+	1.28880i
$299$	1.60077	+	4.92667i	0.0925750	+	0.284917i
$300$	12.8271	−	7.89528i	0.740574	−	0.455834i
$301$	4.08722	−	12.5792i	0.235583	−	0.725050i
$302$	−26.9978	−	22.3345i	−1.55355	−	1.28521i
$303$	−10.3157	−	4.85419i	−0.592620	−	0.278866i
$304$	−1.96720	−	1.84732i	−0.112826	−	0.105951i
$305$	−13.6853	−	1.82444i	−0.783621	−	0.104467i
$306$	−6.06629	+	0.766351i	−0.346787	+	0.0438094i
$307$		−	22.0014i		−	1.25569i	−0.778340	−	0.627843i	$-0.783938\pi$
$307$		−	22.0014i		−	1.25569i	0.778340	−	0.627843i	$-0.216062\pi$
$308$	9.26104	+	73.3087i	0.527697	+	4.17715i
$309$	11.5806	+	13.9985i	0.658797	+	0.796348i
$310$	−43.5953	−	14.4968i	−2.47605	−	0.823361i
$311$	0.0830776	−	1.32048i	0.00471090	−	0.0748776i	−0.994969	−	0.100185i	$-0.968057\pi$
$311$	0.0830776	−	1.32048i	0.00471090	−	0.0748776i	0.999680	+	0.0253075i	$0.00805650\pi$
$312$	−1.35825	+	5.29005i	−0.0768960	+	0.299490i
$313$	8.40470	−	32.7341i	0.475062	−	1.85024i	−0.0493549	−	0.998781i	$-0.515717\pi$
$313$	8.40470	−	32.7341i	0.475062	−	1.85024i	0.524417	−	0.851462i	$-0.324283\pi$
$314$	2.47879	−	39.3992i	0.139886	−	2.22342i
$315$	−10.1209	−	3.36550i	−0.570246	−	0.189624i
$316$	−15.4815	−	18.7140i	−0.870905	−	1.05274i
$317$	2.48850	+	19.6985i	0.139768	+	1.10638i	0.893457	+	0.449149i	$0.148273\pi$
$317$	2.48850	+	19.6985i	0.139768	+	1.10638i	−0.753689	+	0.657232i	$0.771727\pi$
$318$		−	8.70884i		−	0.488368i
$319$	−15.6965	+	1.98293i	−0.878837	+	0.111023i
$320$	28.8398	+	3.84474i	1.61220	+	0.214928i
$321$	−7.46059	−	7.00596i	−0.416409	−	0.391035i
$322$	20.7738	+	9.77541i	1.15768	+	0.544763i
$323$	5.97720	+	4.94477i	0.332580	+	0.275134i
$324$	−0.930896	+	2.86500i	−0.0517164	+	0.159167i
$325$	−2.83552	−	11.7091i	−0.157287	−	0.649503i
$326$	−1.53664	−	4.72929i	−0.0851067	−	0.261931i
$327$	−1.23796	+	3.12673i	−0.0684593	+	0.172909i
$328$	16.9867	−	18.0890i	0.937935	−	0.998799i
$329$	−1.21019	−	6.34402i	−0.0667197	−	0.349757i
$330$	−20.9308	+	14.9886i	−1.15221	+	0.825094i
$331$	−14.1947	+	13.3298i	−0.780214	+	0.732670i	−0.968383	−	0.249467i	$-0.919745\pi$
$331$	−14.1947	+	13.3298i	−0.780214	+	0.732670i	0.188169	+	0.982137i	$0.439745\pi$
$332$	−22.7111	+	7.37929i	−1.24643	+	0.404991i
$333$	9.52253	+	1.81652i	0.521832	+	0.0995447i
$334$	0.464552	+	7.38384i	0.0254191	+	0.404026i
$335$	−5.38254	+	0.301540i	−0.294079	+	0.0164749i
$336$	−2.42823	−	3.82627i	−0.132471	−	0.208740i
$337$	−9.81398	+	0.617443i	−0.534601	+	0.0336343i	−0.327797	−	0.944748i	$-0.606306\pi$
$337$	−9.81398	+	0.617443i	−0.534601	+	0.0336343i	−0.206804	+	0.978382i	$0.566306\pi$
$338$	−13.5995	−	8.63051i	−0.739716	−	0.469438i
$339$	−4.25170	+	5.13942i	−0.230921	+	0.279135i
$340$	−18.3521	−	1.28122i	−0.995280	−	0.0694840i
$341$	45.7098	+	11.7363i	2.47532	+	0.635555i
$342$	5.75402	−	2.70764i	0.311142	−	0.146412i
$343$	39.7013	+	12.8997i	2.14367	+	0.696521i
$344$	−5.50794	−	3.02802i	−0.296968	−	0.163260i
$345$	0.268894	+	4.79981i	0.0144768	+	0.258413i
$346$	−15.0658	−	1.90325i	−0.809942	−	0.102320i
$347$	0.284883	−	2.25508i	0.0152933	−	0.121059i	−0.982620	−	0.185629i	$-0.940568\pi$
$347$	0.284883	−	2.25508i	0.0152933	−	0.121059i	0.997913	+	0.0645703i	$0.0205677\pi$
$348$	−7.82535	+	4.96612i	−0.419483	+	0.266212i
$349$	−12.8210	+	9.31498i	−0.686291	+	0.498619i	−0.875439	−	0.483329i	$-0.839427\pi$
$349$	−12.8210	+	9.31498i	−0.686291	+	0.498619i	0.189148	+	0.981949i	$0.439427\pi$
$350$	−46.4327	−	26.3636i	−2.48193	−	1.40919i
$351$	1.94933	+	1.41627i	0.104048	+	0.0755950i
$352$	−34.1834	−	2.15064i	−1.82198	−	0.114629i
$353$	14.7060	+	26.7501i	0.782721	+	1.42376i	0.902376	+	0.430949i	$0.141821\pi$
$353$	14.7060	+	26.7501i	0.782721	+	1.42376i	−0.119655	+	0.992816i	$0.538179\pi$
$354$	7.45341	−	15.8393i	0.396144	−	0.841849i
$355$	−4.11118	+	3.80785i	−0.218199	+	0.202100i
$356$	8.92810	−	46.8027i	0.473188	−	2.48054i
$357$	7.65706	+	10.5390i	0.405255	+	0.557785i
$358$	18.8122	−	34.2192i	0.994255	−	1.80854i
$359$	3.94212	−	6.21179i	0.208057	−	0.327846i	−0.724234	−	0.689554i	$-0.757806\pi$
$359$	3.94212	−	6.21179i	0.208057	−	0.327846i	0.932291	+	0.361708i	$0.117806\pi$
$360$	−2.47222	+	4.42469i	−0.130298	+	0.233202i
$361$	10.1644	+	4.02436i	0.534967	+	0.211809i
$362$	−6.92322	−	17.4860i	−0.363876	−	0.919046i
$363$	11.9002	−	9.84470i	0.624598	−	0.516713i
$364$	33.5344	−	8.61017i	1.75768	−	0.451296i
$365$	−13.1603	+	13.8228i	−0.688841	+	0.723518i
$366$	12.8529	−	5.08880i	0.671829	−	0.265996i
$367$	1.32650	+	1.41258i	0.0692427	+	0.0737360i	0.762657	−	0.646803i	$-0.223894\pi$
$367$	1.32650	+	1.41258i	0.0692427	+	0.0737360i	−0.693414	+	0.720539i	$0.743894\pi$
$368$	−1.20059	+	1.65247i	−0.0625852	+	0.0861411i
$369$	−4.66118	−	9.90551i	−0.242651	−	0.515660i
$370$	44.9997	+	18.1751i	2.33942	+	0.944881i
$371$	−16.2592	+	8.93856i	−0.844135	+	0.464067i
$372$	27.1557	−	5.18024i	1.40796	−	0.268583i
$373$	6.86673	+	26.7441i	0.355546	+	1.38476i	0.855094	+	0.518473i	$0.173499\pi$
$373$	6.86673	+	26.7441i	0.355546	+	1.38476i	−0.499549	+	0.866286i	$0.666501\pi$
$374$	31.4434			1.62590
$375$	0.230361	−	11.1780i	0.0118958	−	0.577228i
$376$	−3.06912			−0.158278
$377$	1.84357	+	7.18024i	0.0949488	+	0.369801i
$378$	10.4899	−	2.00105i	0.539541	−	0.102923i
$379$	23.6060	−	12.9775i	1.21256	−	0.666610i	0.258437	−	0.966028i	$-0.416792\pi$
$379$	23.6060	−	12.9775i	1.21256	−	0.666610i	0.954122	+	0.299418i	$0.0967924\pi$
$380$	18.5642	−	4.63080i	0.952324	−	0.237555i
$381$	−1.77558	−	3.77330i	−0.0909657	−	0.193312i
$382$	−0.423416	+	0.582782i	−0.0216638	+	0.0298177i
$383$	9.65705	+	10.2837i	0.493452	+	0.525473i	0.926700	−	0.375802i	$-0.122633\pi$
$383$	9.65705	+	10.2837i	0.493452	+	0.525473i	−0.433248	+	0.901275i	$0.642633\pi$
$384$	−14.6999	+	5.82012i	−0.750153	+	0.297007i
$385$	49.4662	+	23.6934i	2.52103	+	1.20753i
$386$	−14.9559	+	3.84003i	−0.761236	+	0.195452i
$387$	−2.13658	+	1.76753i	−0.108608	+	0.0898486i
$388$	−6.12066	−	15.4590i	−0.310730	−	0.784814i
$389$	24.9753	+	9.88841i	1.26630	+	0.501362i	0.902731	−	0.430206i	$-0.141559\pi$
$389$	24.9753	+	9.88841i	1.26630	+	0.501362i	0.363566	+	0.931568i	$0.381559\pi$
$390$	8.19677	+	8.84970i	0.415059	+	0.448122i
$391$	3.14616	−	4.95755i	0.159108	−	0.250714i
$392$	17.2007	−	31.2880i	0.868769	−	1.58029i
$393$	7.51910	+	10.3492i	0.379289	+	0.522046i
$394$	1.12980	−	5.92260i	0.0569183	−	0.298376i
$395$	−17.9011	+	2.13663i	−0.900703	+	0.107505i
$396$	6.59585	−	14.0169i	0.331454	−	0.704376i
$397$	−12.6501	−	23.0104i	−0.634889	−	1.15486i	−0.976602	−	0.215054i	$-0.931007\pi$
$397$	−12.6501	−	23.0104i	−0.634889	−	1.15486i	0.341714	−	0.939804i	$-0.388993\pi$
$398$	−20.1344	−	1.26675i	−1.00925	−	0.0634963i
$399$	−10.9609	−	7.96355i	−0.548730	−	0.398676i
$400$	3.07800	−	3.61829i	0.153900	−	0.180914i
$401$	−4.64673	+	3.37605i	−0.232047	+	0.168592i	−0.697733	−	0.716358i	$-0.745808\pi$
$401$	−4.64673	+	3.37605i	−0.232047	+	0.168592i	0.465686	+	0.884950i	$0.345808\pi$
$402$	4.55741	−	2.89222i	0.227303	−	0.144251i
$403$	2.77140	−	21.9379i	0.138053	−	1.09280i
$404$	34.0732	+	4.30445i	1.69520	+	0.214154i
$405$	1.41346	+	1.73267i	0.0702352	+	0.0860970i
$406$	28.7913	+	15.8282i	1.42889	+	0.785538i
$407$	−47.4120	−	15.4051i	−2.35012	−	0.763602i
$408$	5.60141	−	2.63582i	0.277311	−	0.130493i
$409$	23.6594	+	6.07469i	1.16988	+	0.300374i	0.783158	−	0.621822i	$-0.213607\pi$
$409$	23.6594	+	6.07469i	1.16988	+	0.300374i	0.386722	+	0.922196i	$0.373607\pi$
$410$	−13.2645	−	53.1756i	−0.655089	−	2.62616i
$411$	−7.72962	+	9.34351i	−0.381274	+	0.460881i
$412$	−46.2096	−	29.3255i	−2.27658	−	1.44476i
$413$	−37.2216	+	2.34178i	−1.83155	+	0.115232i
$414$	−2.57910	−	4.06401i	−0.126756	−	0.199735i
$415$	−4.52597	+	17.1379i	−0.222171	+	0.841268i
$416$	1.00769	+	16.0168i	0.0494062	+	0.785289i
$417$	4.85346	+	0.925846i	0.237675	+	0.0453389i
$418$	−31.1014	+	10.1055i	−1.52122	+	0.494274i
$419$	−6.06075	+	5.69143i	−0.296087	+	0.278044i	−0.818325	−	0.574755i	$-0.805097\pi$
$419$	−6.06075	+	5.69143i	−0.296087	+	0.278044i	0.522238	+	0.852800i	$0.325097\pi$
$420$	32.1292	+	0.220684i	1.56775	+	0.0107683i
$421$	−1.81632	−	9.52148i	−0.0885220	−	0.464048i	−0.998752	−	0.0499453i	$-0.984095\pi$
$421$	−1.81632	−	9.52148i	−0.0885220	−	0.464048i	0.910230	−	0.414103i	$-0.135905\pi$
$422$	−31.5313	+	33.5774i	−1.53492	+	1.63452i
$423$	−0.498441	+	1.25892i	−0.0242350	+	0.0612107i
$424$	2.72467	+	8.38566i	0.132321	+	0.407244i
$425$	−8.17748	+	10.9362i	−0.396666	+	0.530484i
$426$	1.73379	−	5.33607i	0.0840026	−	0.258533i
$427$	−22.6925	−	18.7729i	−1.09817	−	0.908485i
$428$	27.8964	+	13.1271i	1.34842	+	0.634521i
$429$	−9.03243	−	8.48202i	−0.436090	−	0.409516i
$430$	−12.2104	+	6.60393i	−0.588839	+	0.318470i
$431$	28.8207	−	3.64091i	1.38825	−	0.175376i	0.604573	−	0.796550i	$-0.293344\pi$
$431$	28.8207	−	3.64091i	1.38825	−	0.175376i	0.783673	+	0.621173i	$0.213344\pi$
$432$			0.950075i			0.0457105i
$433$	4.08296	+	32.3199i	0.196214	+	1.55320i	0.715510	+	0.698603i	$0.246194\pi$
$433$	4.08296	+	32.3199i	0.196214	+	1.55320i	−0.519295	+	0.854595i	$0.673806\pi$
$434$	−62.4690	−	75.5120i	−2.99861	−	3.62469i
$435$	−0.0472519	+	6.87937i	−0.00226556	+	0.329841i
$436$	0.636099	−	10.1105i	0.0304636	−	0.484205i
$437$	−1.51865	+	5.91476i	−0.0726470	+	0.282941i
$438$	4.75232	−	18.5091i	0.227074	−	0.884397i
$439$	0.577439	−	9.17813i	0.0275597	−	0.438048i	−0.959917	−	0.280284i	$-0.909571\pi$
$439$	0.577439	−	9.17813i	0.0275597	−	0.438048i	0.987477	−	0.157764i	$-0.0504286\pi$
$440$	15.4647	−	20.9808i	0.737253	−	1.00022i
$441$	−10.0405	−	12.1369i	−0.478119	−	0.577947i
$442$	−1.84653	−	14.6168i	−0.0878304	−	0.695249i
$443$		−	8.97150i		−	0.426249i	−0.977025	−	0.213124i	$-0.931636\pi$
$443$		−	8.97150i		−	0.426249i	0.977025	−	0.213124i	$-0.0683640\pi$
$444$	−28.9731	+	3.66015i	−1.37500	+	0.173703i
$445$	−25.6146	−	24.3869i	−1.21425	−	1.15605i
$446$	25.7234	+	24.1559i	1.21804	+	1.14381i
$447$	−9.67068	−	4.55068i	−0.457407	−	0.215240i
$448$	47.8211	+	39.5611i	2.25934	+	1.86909i
$449$	−11.0003	+	33.8555i	−0.519137	+	1.59774i	0.256490	+	0.966547i	$0.417434\pi$
$449$	−11.0003	+	33.8555i	−0.519137	+	1.59774i	−0.775627	+	0.631192i	$0.782566\pi$
$450$	5.25761	+	9.88274i	0.247846	+	0.465877i
$451$	17.3965	+	53.5408i	0.819168	+	2.52114i
$452$	7.39686	−	18.6823i	0.347919	−	0.878744i
$453$	10.7134	−	11.4086i	0.503358	−	0.536022i
$454$	3.08317	+	16.1625i	0.144700	+	0.758546i
$455$	8.10918	−	24.3863i	0.380164	−	1.14325i
$456$	−4.69337	+	4.40737i	−0.219787	+	0.206394i
$457$	37.7828	−	12.2764i	1.76740	−	0.574265i	0.769481	−	0.638670i	$-0.220515\pi$
$457$	37.7828	−	12.2764i	1.76740	−	0.574265i	0.997924	+	0.0644053i	$0.0205151\pi$
$458$	25.7400	+	4.91016i	1.20275	+	0.229437i
$459$	−0.171487	−	2.72571i	−0.00800432	−	0.127225i
$460$	−5.23850	−	13.5011i	−0.244246	−	0.629494i
$461$	−1.27517	−	2.00935i	−0.0593908	−	0.0935849i	0.813335	−	0.581796i	$-0.197650\pi$
$461$	−1.27517	−	2.00935i	−0.0593908	−	0.0935849i	−0.872726	+	0.488211i	$0.837650\pi$
$462$	−54.8077	+	3.44821i	−2.54988	+	0.160425i
$463$	2.33459	+	1.48158i	0.108498	+	0.0688546i	0.588968	−	0.808156i	$-0.299534\pi$
$463$	2.33459	+	1.48158i	0.108498	+	0.0688546i	−0.480471	+	0.877011i	$0.659534\pi$
$464$	−1.86320	+	2.25222i	−0.0864970	+	0.104557i
$465$	7.68500	−	19.0272i	0.356383	−	0.882366i
$466$	−16.9336	−	4.34780i	−0.784432	−	0.201408i
$467$	3.37498	−	1.58815i	0.156176	−	0.0734906i	−0.346103	−	0.938197i	$-0.612495\pi$
$467$	3.37498	−	1.58815i	0.156176	−	0.0734906i	0.502279	+	0.864706i	$0.332495\pi$
$468$	−6.90324	−	2.24300i	−0.319102	−	0.103683i
$469$	−10.0773	−	5.54006i	−0.465328	−	0.255816i
$470$	−3.67129	+	5.69813i	−0.169344	+	0.262835i
$471$	17.4937	+	2.20997i	0.806068	+	0.101830i
$472$	−2.22130	+	17.5834i	−0.102244	+	0.809341i
$473$	12.0397	−	7.64065i	0.553588	−	0.351318i
$474$	14.6032	−	10.6099i	0.670749	−	0.487328i
$475$	4.57380	−	13.4454i	0.209860	−	0.616917i
$476$	−31.7483	−	23.0665i	−1.45518	−	1.05725i
$477$	3.88220	+	0.244247i	0.177754	+	0.0111833i
$478$	9.80929	+	17.8430i	0.448666	+	0.816121i
$479$	5.61901	−	11.9410i	0.256739	−	0.545599i	−0.734354	−	0.678766i	$-0.762515\pi$
$479$	5.61901	−	11.9410i	0.256739	−	0.545599i	0.991094	+	0.133168i	$0.0425149\pi$
$480$	−2.89114	+	14.6100i	−0.131962	+	0.666851i
$481$	−4.37692	+	22.9446i	−0.199570	+	1.04618i
$482$	13.9164	+	19.1542i	0.633873	+	0.872451i
$483$	−4.94027	+	8.98632i	−0.224790	+	0.408892i
$484$	−24.9297	+	39.2829i	−1.13317	+	1.78559i
$485$	−12.1068	−	2.39579i	−0.549741	−	0.108787i
$486$	−2.08163	−	0.824175i	−0.0944246	−	0.0373853i
$487$	0.677884	+	1.71214i	0.0307179	+	0.0775844i	0.944326	−	0.329012i	$-0.106716\pi$
$487$	0.677884	+	1.71214i	0.0307179	+	0.0775844i	−0.913608	+	0.406596i	$0.866716\pi$
$488$	−10.7838	+	8.92113i	−0.488159	+	0.403840i
$489$	2.15131	−	0.552361i	0.0972854	−	0.0249786i
$490$	−37.5138	−	69.3617i	−1.69470	−	3.13344i
$491$	−23.5772	+	9.33486i	−1.06402	+	0.421276i	−0.833917	−	0.551890i	$-0.813907\pi$
$491$	−23.5772	+	9.33486i	−1.06402	+	0.421276i	−0.230105	+	0.973166i	$0.573907\pi$
$492$	22.5753	+	24.0402i	1.01777	+	1.08382i
$493$	4.93889	−	6.79780i	0.222436	−	0.306157i
$494$	6.52407	+	13.8643i	0.293532	+	0.623786i
$495$	−6.09454	−	9.75085i	−0.273929	−	0.438268i
$496$	7.64044	−	4.20037i	0.343066	−	0.188602i
$497$	−11.7418	+	2.23987i	−0.526693	+	0.100472i
$498$	−4.41363	−	17.1900i	−0.197780	−	0.770300i
$499$	30.3517			1.35873			0.679365	−	0.733801i	$-0.262255\pi$
$499$	30.3517			1.35873			0.679365	+	0.733801i	$0.262255\pi$
$500$	9.74554	+	32.2394i	0.435834	+	1.44179i
$501$	−3.30457			−0.147637
$502$	13.0185	+	50.7036i	0.581043	+	2.26301i
$503$	4.44196	−	0.847349i	0.198057	−	0.0377814i	−0.0873981	−	0.996173i	$-0.527855\pi$
$503$	4.44196	−	0.847349i	0.198057	−	0.0377814i	0.285455	+	0.958392i	$0.407855\pi$
$504$	−9.47454	+	5.20867i	−0.422030	+	0.232013i
$505$	16.3842	−	19.5305i	0.729089	−	0.869094i
$506$	10.5389	+	22.3963i	0.468512	+	0.995639i
$507$	4.22869	−	5.82030i	0.187803	−	0.258488i
$508$	8.59959	+	9.15763i	0.381545	+	0.406304i
$509$	32.3148	−	12.7943i	1.43233	−	0.567099i	0.481397	−	0.876503i	$-0.340130\pi$
$509$	32.3148	−	12.7943i	1.43233	−	0.567099i	0.950931	+	0.309404i	$0.100130\pi$
$510$	1.80674	−	13.5526i	0.0800038	−	0.600117i
$511$	−39.4336	+	10.1248i	−1.74444	+	0.447896i
$512$	−8.19444	+	6.77903i	−0.362146	+	0.299594i
$513$	1.04562	+	2.64095i	0.0461655	+	0.116601i
$514$	−21.7149	−	8.59755i	−0.957804	−	0.379222i
$515$	−36.8760	+	17.0442i	−1.62495	+	0.751055i
$516$	4.47591	−	7.05291i	0.197041	−	0.310487i
$517$	3.35438	−	6.10159i	0.147525	−	0.268348i
$518$	60.8505	+	83.7535i	2.67362	+	3.67992i
$519$	1.27096	−	6.66261i	0.0557890	−	0.292456i
$520$	−10.6613	−	5.95683i	−0.467530	−	0.261224i
$521$	9.17957	−	19.5076i	0.402164	−	0.854643i	−0.596482	−	0.802626i	$-0.703435\pi$
$521$	9.17957	−	19.5076i	0.402164	−	0.854643i	0.998646	−	0.0520161i	$-0.0165647\pi$
$522$	−3.31836	−	6.03608i	−0.145241	−	0.264192i
$523$	−19.5873	−	1.23233i	−0.856491	−	0.0538859i	−0.371529	−	0.928421i	$-0.621167\pi$
$523$	−19.5873	−	1.23233i	−0.856491	−	0.0538859i	−0.484962	+	0.874535i	$0.661167\pi$
$524$	−31.1762	−	22.6509i	−1.36194	−	0.989508i
$525$	13.0545	−	19.9592i	0.569747	−	0.871093i
$526$	−31.5137	+	22.8961i	−1.37406	+	0.998315i
$527$	−21.1618	+	13.4297i	−0.921822	+	0.585006i
$528$	0.612339	−	4.84716i	0.0266486	−	0.210946i
$529$	−18.2330	−	2.30336i	−0.792739	−	0.100146i
$530$	18.8281	+	4.97232i	0.817839	+	0.215984i
$531$	6.85175	+	3.76678i	0.297341	+	0.163464i
$532$	38.8162	+	12.6121i	1.68290	+	0.546806i
$533$	23.8674	−	11.2311i	1.03381	−	0.486475i
$534$	34.2985	+	8.80637i	1.48424	+	0.381089i
$535$	19.4061	−	12.1293i	0.839001	−	0.524397i
$536$	−3.48342	+	4.21073i	−0.150461	+	0.181876i
$537$	14.7265	+	9.34574i	0.635497	+	0.403299i
$538$	−48.8617	+	3.07412i	−2.10658	+	0.132535i
$539$	43.4030	+	68.3921i	1.86950	+	2.94586i
$540$	−5.66249	−	3.64832i	−0.243675	−	0.156999i
$541$	−0.559530	−	8.89347i	−0.0240561	−	0.382360i	−0.991573	−	0.129552i	$-0.958646\pi$
$541$	−0.559530	−	8.89347i	−0.0240561	−	0.382360i	0.967517	−	0.252808i	$-0.0813540\pi$
$542$	42.5137	+	8.10993i	1.82612	+	0.348351i
$543$	7.98904	−	2.59580i	0.342843	−	0.111396i
$544$	13.2602	−	12.4522i	0.568528	−	0.533884i
$545$	−6.05301	−	4.46161i	−0.259283	−	0.191114i
$546$	4.82154	+	25.2754i	0.206343	+	1.08169i
$547$	15.6719	−	16.6889i	0.670082	−	0.713565i	−0.300649	−	0.953735i	$-0.597203\pi$
$547$	15.6719	−	16.6889i	0.670082	−	0.713565i	0.970731	+	0.240170i	$0.0772032\pi$
$548$	13.4476	−	33.9647i	0.574451	−	1.45090i
$549$	1.90800	+	5.87222i	0.0814315	+	0.250620i
$550$	−20.4541	−	53.8091i	−0.872164	−	2.29443i
$551$	−2.70046	+	8.31115i	−0.115043	+	0.354067i
$552$	3.75486	+	3.10629i	0.159818	+	0.132213i
$553$	−34.7968	−	16.3741i	−1.47971	−	0.696299i
$554$	−36.7413	−	34.5024i	−1.56099	−	1.46587i
$555$	−9.36411	+	19.5501i	−0.397484	+	0.829854i
$556$	−14.7670	+	1.86551i	−0.626262	+	0.0791153i
$557$			4.26448i			0.180692i	0.995910	+	0.0903459i	$0.0287972\pi$
$557$			4.26448i			0.180692i	−0.995910	+	0.0903459i	$0.971203\pi$
$558$	2.57511	+	20.3841i	0.109013	+	0.862927i
$559$	−4.25887	−	5.14809i	−0.180131	−	0.217741i
$560$	9.65859	−	3.06509i	0.408150	−	0.129523i
$561$	−0.881858	+	14.0167i	−0.0372321	+	0.591787i
$562$	−6.12994	+	23.8745i	−0.258576	+	1.00709i
$563$	5.52223	−	21.5077i	0.232734	−	0.906440i	−0.739638	−	0.673005i	$-0.765003\pi$
$563$	5.52223	−	21.5077i	0.232734	−	0.906440i	0.972372	−	0.233435i	$-0.0749967\pi$
$564$	0.256113	−	4.07080i	0.0107843	−	0.171412i
$565$	−8.68365	−	12.1263i	−0.365324	−	0.510157i
$566$	16.7536	+	20.2516i	0.704205	+	0.851238i
$567$	0.597824	+	4.73226i	0.0251062	+	0.198736i
$568$			5.68048i			0.238348i
$569$	−43.6268	+	5.51135i	−1.82893	+	0.231048i	−0.963073	−	0.269240i	$-0.913228\pi$
$569$	−43.6268	+	5.51135i	−1.82893	+	0.231048i	−0.865859	+	0.500288i	$0.833228\pi$
$570$	2.56851	+	13.9858i	0.107583	+	0.585801i
$571$	8.39397	+	7.88246i	0.351277	+	0.329871i	0.840018	−	0.542558i	$-0.182544\pi$
$571$	8.39397	+	7.88246i	0.351277	+	0.329871i	−0.488742	+	0.872428i	$0.662544\pi$
$572$	33.7738	+	15.8928i	1.41215	+	0.664509i
$573$	−0.247916	−	0.205094i	−0.0103568	−	0.00856791i
$574$	36.1264	−	111.186i	1.50789	−	4.64080i
$575$	−10.5305	−	2.15912i	−0.439150	−	0.0900414i
$576$	−4.02083	−	12.3748i	−0.167534	−	0.515618i
$577$	−11.7489	+	29.6744i	−0.489114	+	1.23536i	0.450392	+	0.892831i	$0.351284\pi$
$577$	−11.7489	+	29.6744i	−0.489114	+	1.23536i	−0.939506	+	0.342531i	$0.888716\pi$
$578$	14.6227	−	15.5716i	0.608224	−	0.647693i
$579$	−1.29234	−	6.77470i	−0.0537079	−	0.281547i
$580$	−6.26860	−	19.7534i	−0.260289	−	0.820215i
$581$	−27.5632	+	25.8835i	−1.14351	+	1.07383i
$582$	11.7521	−	3.81849i	0.487141	−	0.158282i
$583$	−19.6491	−	3.74826i	−0.813781	−	0.155237i
$584$	1.21482	+	19.3090i	0.0502696	+	0.799012i
$585$	−4.17488	+	3.40573i	−0.172610	+	0.140810i
$586$	15.2193	+	23.9817i	0.628702	+	0.990676i
$587$	−19.4791	+	1.22552i	−0.803989	+	0.0505827i	−0.459466	−	0.888195i	$-0.651959\pi$
$587$	−19.4791	+	1.22552i	−0.803989	+	0.0505827i	−0.344523	+	0.938778i	$0.611959\pi$
$588$	40.0643	+	25.4256i	1.65222	+	1.04853i
$589$	16.6155	−	20.0847i	0.684631	−	0.827576i
$590$	29.9882	+	25.1573i	1.23459	+	1.03571i
$591$	2.60847	+	0.669742i	0.107298	+	0.0275495i
$592$	−8.33369	+	3.92154i	−0.342513	+	0.161174i
$593$	28.5646	+	9.28120i	1.17301	+	0.381133i	0.829765	−	0.558113i	$-0.188475\pi$
$593$	28.5646	+	9.28120i	1.17301	+	0.381133i	0.343243	+	0.939247i	$0.388475\pi$
$594$	10.0890	+	5.54648i	0.413957	+	0.227575i
$595$	−27.1567	+	10.5369i	−1.11331	+	0.431971i
$596$	31.9427	+	4.03530i	1.30842	+	0.165293i
$597$	1.12937	−	8.93991i	0.0462222	−	0.365886i
$598$	9.79226	−	6.21436i	0.400435	−	0.254124i
$599$	−10.5723	+	7.68119i	−0.431971	+	0.313845i	−0.782436	−	0.622730i	$-0.786023\pi$
$599$	−10.5723	+	7.68119i	−0.431971	+	0.313845i	0.350466	+	0.936576i	$0.386023\pi$
$600$	−8.15443	−	7.87109i	−0.332903	−	0.321336i
$601$	6.95605	+	5.05386i	0.283743	+	0.206151i	0.720548	−	0.693405i	$-0.243890\pi$
$601$	6.95605	+	5.05386i	0.283743	+	0.206151i	−0.436805	+	0.899556i	$0.643890\pi$
$602$	−29.5537	−	1.85936i	−1.20452	−	0.0757819i
$603$	1.16147	+	2.11270i	0.0472987	+	0.0860360i
$604$	−20.0736	+	42.6587i	−0.816785	+	1.73576i
$605$	14.4893	+	31.3484i	0.589074	+	1.27450i
$606$	−4.78281	+	25.0724i	−0.194288	+	1.01850i
$607$	6.95193	+	9.56851i	0.282170	+	0.388374i	0.926451	−	0.376415i	$-0.122843\pi$
$607$	6.95193	+	9.56851i	0.282170	+	0.388374i	−0.644281	+	0.764789i	$0.722843\pi$
$608$	−9.11406	+	16.5784i	−0.369624	+	0.672344i
$609$	−7.86331	+	12.3906i	−0.318637	+	0.502092i
$610$	3.66339	+	30.6926i	0.148326	+	1.24271i
$611$	−3.03337	−	1.20100i	−0.122717	−	0.0485871i
$612$	3.02866	+	7.64952i	0.122426	+	0.309213i
$613$	−15.0420	+	12.4438i	−0.607541	+	0.502601i	−0.889567	−	0.456805i	$-0.848994\pi$
$613$	−15.0420	+	12.4438i	−0.607541	+	0.502601i	0.282026	+	0.959407i	$0.408994\pi$
$614$	−47.7103	+	12.2499i	−1.92543	+	0.494367i
$615$	24.0765	−	4.42167i	0.970858	−	0.178299i
$616$	51.6950	−	20.4675i	2.08285	−	0.824659i
$617$	−12.1815	−	12.9720i	−0.490410	−	0.522234i	0.435392	−	0.900241i	$-0.356610\pi$
$617$	−12.1815	−	12.9720i	−0.490410	−	0.522234i	−0.925803	+	0.378007i	$0.876610\pi$
$618$	23.9081	−	32.9067i	0.961726	−	1.32370i
$619$	3.77588	+	8.02416i	0.151766	+	0.322518i	0.966224	−	0.257704i	$-0.0829658\pi$
$619$	3.77588	+	8.02416i	0.151766	+	0.322518i	−0.814458	+	0.580222i	$0.802966\pi$
$620$	−4.30518	+	61.6669i	−0.172900	+	2.47660i
$621$	1.88398	−	1.03572i	0.0756013	−	0.0415622i
$622$	−2.90973	+	0.555061i	−0.116670	+	0.0222559i
$623$	−18.7620	−	73.0731i	−0.751683	−	2.92761i
$624$	−2.28921			−0.0916418
$625$	24.0346	+	6.88009i	0.961386	+	0.275204i
$626$	−75.6639			−3.02414
$627$	−3.63251	−	14.1477i	−0.145069	−	0.565005i
$628$	−52.1768	+	9.95326i	−2.08208	+	0.397178i
$629$	23.2010	−	12.7549i	0.925085	−	0.508570i
$630$	−1.66303	+	23.8210i	−0.0662567	+	0.949053i
$631$	3.24813	+	6.90262i	0.129306	+	0.274789i	0.958988	−	0.283448i	$-0.0914782\pi$
$631$	3.24813	+	6.90262i	0.129306	+	0.274789i	−0.829682	+	0.558236i	$0.811478\pi$
$632$	−10.7419	+	14.7849i	−0.427289	+	0.588114i
$633$	−14.0837	−	14.9976i	−0.559777	−	0.596102i
$634$	41.3310	−	16.3641i	1.64146	−	0.649901i
$635$	9.17144	−	1.68434i	0.363957	−	0.0668411i
$636$	−11.3499	+	2.91416i	−0.450052	+	0.115554i
$637$	29.2439	−	24.1927i	1.15869	−	0.958548i
$638$	13.0395	+	32.9340i	0.516239	+	1.30387i
$639$	2.33007	+	0.922540i	0.0921761	+	0.0364951i
$640$	−4.18985	−	35.1035i	−0.165618	−	1.38759i
$641$	−26.1821	+	41.2563i	−1.03413	+	1.62953i	−0.295592	+	0.955314i	$0.595517\pi$
$641$	−26.1821	+	41.2563i	−1.03413	+	1.62953i	−0.738537	+	0.674213i	$0.764483\pi$
$642$	−11.0386	+	20.0791i	−0.435659	+	0.792460i
$643$	16.8435	+	23.1831i	0.664244	+	0.914254i	0.999613	−	0.0278334i	$-0.00886080\pi$
$643$	16.8435	+	23.1831i	0.664244	+	0.914254i	−0.335368	+	0.942087i	$0.608861\pi$
$644$	5.78857	−	30.3447i	0.228101	−	1.19575i
$645$	−2.60143	−	5.62834i	−0.102431	−	0.221616i
$646$	7.39481	−	15.7148i	0.290945	−	0.618289i
$647$	12.6660	+	23.0394i	0.497953	+	0.905772i	0.999181	+	0.0404575i	$0.0128816\pi$
$647$	12.6660	+	23.0394i	0.497953	+	0.905772i	−0.501229	+	0.865315i	$0.667118\pi$
$648$	2.26223	+	0.142328i	0.0888689	+	0.00559116i
$649$	−32.5290	−	23.6337i	−1.27688	−	0.927704i
$650$	−23.8125	+	12.6682i	−0.934004	+	0.496889i
$651$	35.4135	−	25.7294i	1.38796	−	1.00842i
$652$	−5.64931	+	3.58516i	−0.221244	+	0.140406i
$653$	−0.698353	+	5.52803i	−0.0273287	+	0.216329i	−0.999865	−	0.0164218i	$-0.994773\pi$
$653$	−0.698353	+	5.52803i	−0.0273287	+	0.216329i	0.972536	+	0.232750i	$0.0747725\pi$
$654$	7.46962	+	0.943632i	0.292085	+	0.0368989i
$655$	−26.6674	+	10.3471i	−1.04198	+	0.404293i
$656$	9.11434	+	5.01065i	0.355855	+	0.195633i
$657$	8.11762	+	2.63758i	0.316699	+	0.102902i
$658$	−13.0833	+	6.15652i	−0.510039	+	0.240006i
$659$	13.6060	+	3.49343i	0.530016	+	0.136085i	0.504208	−	0.863582i	$-0.331784\pi$
$659$	13.6060	+	3.49343i	0.530016	+	0.136085i	0.0258073	+	0.999667i	$0.491784\pi$
$660$	26.5379	+	22.2628i	1.03299	+	0.866580i
$661$	11.3971	−	13.7767i	0.443295	−	0.535852i	−0.500783	−	0.865573i	$-0.666955\pi$
$661$	11.3971	−	13.7767i	0.443295	−	0.535852i	0.944078	+	0.329721i	$0.106955\pi$
$662$	36.8091	+	23.3597i	1.43062	+	0.907902i
$663$	6.56760	−	0.413199i	0.255065	−	0.0160473i
$664$	9.62793	+	15.1712i	0.373636	+	0.588756i
$665$	23.4749	−	19.1501i	0.910317	−	0.742608i
$666$	−1.36280	−	21.6611i	−0.0528075	−	0.839351i
$667$	6.49728	+	1.23942i	0.251576	+	0.0479906i
$668$	9.46761	−	3.07621i	0.366313	−	0.119022i
$669$	−11.4896	+	10.7894i	−0.444213	+	0.417143i
$670$	3.65078	+	11.5042i	0.141042	+	0.444446i
$671$	−5.94963	−	31.1891i	−0.229683	−	1.20404i
$672$	−21.7478	+	23.1591i	−0.838941	+	0.893381i
$673$	1.60052	−	4.04246i	0.0616957	−	0.155825i	−0.895658	−	0.444743i	$-0.853295\pi$
$673$	1.60052	−	4.04246i	0.0616957	−	0.155825i	0.957354	+	0.288917i	$0.0932952\pi$
$674$	6.80315	+	20.9379i	0.262047	+	0.806499i
$675$	−4.55295	+	2.06655i	−0.175243	+	0.0795415i
$676$	−6.69713	+	20.6116i	−0.257582	+	0.792755i
$677$	4.42878	+	3.66381i	0.170212	+	0.140812i	0.718630	−	0.695393i	$-0.244770\pi$
$677$	4.42878	+	3.66381i	0.170212	+	0.140812i	−0.548418	+	0.836204i	$0.684770\pi$
$678$	13.5121	+	6.35833i	0.518931	+	0.244190i
$679$	−19.1911	−	18.0217i	−0.736488	−	0.691608i
$680$	2.50039	+	13.6149i	0.0958854	+	0.522107i
$681$	−7.29136	+	0.921112i	−0.279405	+	0.0352971i
$682$		−	105.657i		−	4.04580i
$683$	−5.87258	−	46.4863i	−0.224708	−	1.77875i	−0.552019	−	0.833831i	$-0.686143\pi$
$683$	−5.87258	−	46.4863i	−0.224708	−	1.77875i	0.327311	−	0.944917i	$-0.393857\pi$
$684$	−5.45416	−	6.59295i	−0.208545	−	0.252088i
$685$	−15.7869	−	22.0457i	−0.603188	−	0.842324i
$686$	5.86837	−	93.2751i	0.224056	−	3.56126i
$687$	−2.91074	+	11.3366i	−0.111052	+	0.432517i
$688$	0.655170	−	2.55172i	0.0249781	−	0.0972834i
$689$	−0.588515	+	9.35419i	−0.0224207	+	0.356366i
$690$	10.2587	−	3.25553i	0.390543	−	0.123936i
$691$	11.2745	+	13.6286i	0.428903	+	0.518455i	0.940049	−	0.341039i	$-0.110779\pi$
$691$	11.2745	+	13.6286i	0.428903	+	0.518455i	−0.511146	+	0.859494i	$0.670779\pi$
$692$	2.56089	+	20.2715i	0.0973504	+	0.770607i
$693$		−	24.5287i		−	0.931768i
$694$	−5.04878	+	0.637809i	−0.191649	+	0.0242109i
$695$	−4.77271	+	9.96431i	−0.181039	+	0.377968i
$696$	5.08368	+	4.77389i	0.192696	+	0.180954i
$697$	−27.0529	−	12.7301i	−1.02470	−	0.482188i
$698$	27.3381	+	22.6160i	1.03476	+	0.856029i
$699$	2.41307	−	7.42665i	0.0912705	−	0.280902i
$700$	−18.8213	+	69.3357i	−0.711378	+	2.62064i
$701$	−9.91228	−	30.5069i	−0.374382	−	1.15223i	−0.943895	−	0.330246i	$-0.892868\pi$
$701$	−9.91228	−	30.5069i	−0.374382	−	1.15223i	0.569513	−	0.821982i	$-0.307132\pi$
$702$	1.98585	−	5.01570i	0.0749513	−	0.189305i
$703$	−18.8494	+	20.0726i	−0.710920	+	0.757053i
$704$	12.5380	+	65.7263i	0.472542	+	2.47715i
$705$	−2.43713	−	1.79638i	−0.0917876	−	0.0676557i
$706$	49.8199	−	46.7840i	1.87500	−	1.76074i
$707$	51.7184	−	16.8043i	1.94507	−	0.631992i
$708$	−23.1368	−	4.41358i	−0.869533	−	0.165872i
$709$	−0.149759	−	2.38035i	−0.00562432	−	0.0893960i	0.994213	−	0.107426i	$-0.0342607\pi$
$709$	−0.149759	−	2.38035i	−0.00562432	−	0.0893960i	−0.999837	+	0.0180295i	$0.994261\pi$
$710$	10.5464	+	6.79500i	0.395799	+	0.255012i
$711$	4.32008	+	6.80735i	0.162016	+	0.255296i
$712$	−35.7809	+	2.25114i	−1.34095	+	0.0843652i
$713$	−16.6585	−	10.5718i	−0.623864	−	0.395916i
$714$	18.5907	−	22.4723i	0.695741	−	0.841006i
$715$	23.4947	−	14.6848i	0.878653	−	0.549181i
$716$	−50.8915	−	13.0667i	−1.90190	−	0.488326i
$717$	−8.22912	+	3.87233i	−0.307322	+	0.144615i
$718$	−15.6652	−	5.08994i	−0.584621	−	0.189955i
$719$	−6.20991	−	3.41393i	−0.231591	−	0.127318i	0.361734	−	0.932281i	$-0.382185\pi$
$719$	−6.20991	−	3.41393i	−0.231591	−	0.127318i	−0.593325	+	0.804963i	$0.702185\pi$
$720$	−2.05401	−	0.542445i	−0.0765485	−	0.0202157i
$721$	−85.9748	−	10.8611i	−3.20187	−	0.404490i
$722$	3.06756	−	24.2823i	0.114163	−	0.903692i
$723$	−8.92881	+	5.66639i	−0.332066	+	0.210735i
$724$	−20.4722	+	14.8739i	−0.760844	+	0.552785i
$725$	−14.8459	−	4.02993i	−0.551361	−	0.149668i
$726$	−27.9741	−	20.3244i	−1.03822	−	0.754309i
$727$	28.6909	+	1.80508i	1.06409	+	0.0669467i	0.585168	−	0.810912i	$-0.301029\pi$
$727$	28.6909	+	1.80508i	1.06409	+	0.0669467i	0.478919	+	0.877859i	$0.341029\pi$
$728$	−12.5503	−	22.8290i	−0.465146	−	0.846098i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	37.3023	+	20.8420i	1.38062	+	0.771397i
$731$	−1.41906	+	7.43898i	−0.0524859	+	0.275141i
$732$	−10.9329	−	15.0478i	−0.404090	−	0.556182i
$733$	−14.0079	+	25.4804i	−0.517395	+	0.941139i	0.480544	+	0.876971i	$0.340439\pi$
$733$	−14.0079	+	25.4804i	−0.517395	+	0.941139i	−0.997939	+	0.0641680i	$0.979561\pi$
$734$	2.32462	−	3.66302i	0.0858034	−	0.135205i
$735$	31.9719	−	14.7775i	1.17930	−	0.545076i
$736$	13.3138	+	5.27132i	0.490755	+	0.194304i
$737$	−4.56399	−	11.5273i	−0.168117	−	0.424615i
$738$	−18.8850	+	15.6230i	−0.695165	+	0.575090i
$739$	9.33435	−	2.39665i	0.343370	−	0.0881623i	−0.0730671	−	0.997327i	$-0.523279\pi$
$739$	9.33435	−	2.39665i	0.343370	−	0.0881623i	0.416437	+	0.909165i	$0.363279\pi$
$740$	8.62913	−	64.7280i	0.317213	−	2.37945i
$741$	−6.36338	+	2.51944i	−0.233764	+	0.0925539i
$742$	28.4361	+	30.2814i	1.04392	+	1.11167i
$743$	0.910729	−	1.25351i	0.0334114	−	0.0459868i	−0.791984	−	0.610541i	$-0.790952\pi$
$743$	0.910729	−	1.25351i	0.0334114	−	0.0459868i	0.825396	+	0.564554i	$0.190952\pi$
$744$	−8.85695	−	18.8220i	−0.324711	−	0.690047i
$745$	15.3598	−	18.3093i	0.562739	−	0.670800i
$746$	54.1717	−	29.7811i	1.98337	−	1.09037i
$747$	7.78667	−	1.48539i	0.284899	−	0.0543474i
$748$	−10.5216	−	40.9789i	−0.384707	−	1.49834i
$749$	48.8170			1.78373
$750$	−24.3678	+	5.72412i	−0.889786	+	0.209015i
$751$	−27.7336			−1.01202			−0.506008	−	0.862529i	$-0.668879\pi$
$751$	−27.7336			−1.01202			−0.506008	+	0.862529i	$0.668879\pi$
$752$	−0.319915	−	1.24599i	−0.0116661	−	0.0454365i
$753$	−22.9676	+	4.38131i	−0.836986	+	0.159664i
$754$	14.5440	−	7.99561i	0.529660	−	0.291183i
$755$	18.5480	+	29.6755i	0.675029	+	1.08000i
$756$	−6.11801	−	13.0014i	−0.222510	−	0.472858i
$757$	6.14991	−	8.46462i	0.223522	−	0.307652i	−0.682497	−	0.730888i	$-0.739106\pi$
$757$	6.14991	−	8.46462i	0.223522	−	0.307652i	0.906019	+	0.423236i	$0.139106\pi$
$758$	−41.2852	−	43.9643i	−1.49955	−	1.59686i
$759$	−10.2793	+	4.06988i	−0.373117	+	0.147727i
$760$	−6.84882	−	12.6632i	−0.248433	−	0.459343i
$761$	48.3986	−	12.4267i	1.75445	−	0.450466i	0.771788	−	0.635880i	$-0.219363\pi$
$761$	48.3986	−	12.4267i	1.75445	−	0.450466i	0.982660	+	0.185414i	$0.0593628\pi$
$762$	−7.19383	+	5.95126i	−0.260605	+	0.215591i
$763$	−5.90491	−	14.9141i	−0.213772	−	0.539927i
$764$	0.901200	+	0.356810i	0.0326043	+	0.0129089i
$765$	5.99074	+	1.18550i	0.216596	+	0.0428617i
$766$	16.9235	−	26.6672i	0.611471	−	0.963524i
$767$	−9.07609	+	16.5093i	−0.327718	+	0.596118i
$768$	5.50947	+	7.58313i	0.198806	+	0.273633i
$769$	8.27412	−	43.3745i	0.298372	−	1.56412i	−0.445177	−	0.895442i	$-0.646859\pi$
$769$	8.27412	−	43.3745i	0.298372	−	1.56412i	0.743550	−	0.668681i	$-0.233141\pi$
$770$	23.8376	−	120.460i	0.859048	−	4.34108i
$771$	4.44160	−	9.43889i	0.159960	−	0.339933i
$772$	10.0091	+	18.2065i	0.360236	+	0.655266i
$773$	29.7636	+	1.87257i	1.07052	+	0.0673515i	0.588257	−	0.808674i	$-0.299814\pi$
$773$	29.7636	+	1.87257i	1.07052	+	0.0673515i	0.482264	+	0.876026i	$0.339814\pi$
$774$	5.02251	+	3.64907i	0.180530	+	0.131163i
$775$	36.7481	+	27.4781i	1.32003	+	0.987044i
$776$	−10.1213	+	7.35358i	−0.363335	+	0.263978i
$777$	−39.0420	+	24.7768i	−1.40062	+	0.888863i
$778$	7.53742	−	59.6648i	0.270230	−	2.13909i
$779$	30.8499	+	3.89725i	1.10531	+	0.139634i
$780$	8.79065	−	13.6438i	0.314756	−	0.488527i
$781$	−11.2931	−	6.20845i	−0.404100	−	0.222156i
$782$	−12.5022	−	4.06222i	−0.447078	−	0.145265i
$783$	2.78381	−	1.30996i	0.0994852	−	0.0468142i
$784$	14.4951	+	3.72172i	0.517683	+	0.132918i
$785$	−14.7659	+	36.5587i	−0.527017	+	1.30484i
$786$	18.2558	−	22.0675i	0.651162	−	0.787120i
$787$	−24.3642	−	15.4620i	−0.868490	−	0.551160i	0.0252830	−	0.999680i	$-0.491951\pi$
$787$	−24.3642	−	15.4620i	−0.868490	−	0.551160i	−0.893773	+	0.448520i	$0.851951\pi$
$788$	−8.09674	+	0.509404i	−0.288434	+	0.0181468i
$789$	−9.32270	−	14.6902i	−0.331897	−	0.522986i
$790$	14.6003	+	37.6292i	0.519454	+	1.33879i
$791$	−1.99772	−	31.7529i	−0.0710308	−	1.12900i
$792$	−11.4499	−	2.18418i	−0.406854	−	0.0776116i
$793$	−14.1492	+	4.59734i	−0.502451	+	0.163256i
$794$	−42.8550	+	40.2435i	−1.52087	+	1.42819i
$795$	−2.74459	+	8.25366i	−0.0973407	+	0.292727i
$796$	5.08647	+	26.6642i	0.180285	+	0.945088i
$797$	13.4708	−	14.3450i	0.477161	−	0.508124i	−0.444682	−	0.895688i	$-0.646683\pi$
$797$	13.4708	−	14.3450i	0.477161	−	0.508124i	0.921843	+	0.387564i	$0.126683\pi$
$798$	−11.1663	+	28.2027i	−0.395281	+	0.998366i
$799$	1.14272	+	3.51692i	0.0404264	+	0.124420i
$800$	−29.9353	−	14.5921i	−1.05837	−	0.515908i
$801$	−4.88761	+	15.0425i	−0.172695	+	0.531501i
$802$	9.90820	+	8.19677i	0.349871	+	0.289438i
$803$	−39.7151	−	18.6885i	−1.40152	−	0.659503i
$804$	−5.29432	−	4.97170i	−0.186716	−	0.175338i
$805$	−16.6073	−	15.8114i	−0.585331	−	0.557277i
$806$	−49.1156	+	6.20474i	−1.73002	+	0.218553i
$807$		−	21.8676i		−	0.769777i
$808$	−3.23887	−	25.6383i	−0.113943	−	0.901952i
$809$	8.47743	+	10.2475i	0.298051	+	0.360281i	0.898185	−	0.439618i	$-0.144886\pi$
$809$	8.47743	+	10.2475i	0.298051	+	0.360281i	−0.600134	+	0.799899i	$0.704886\pi$
$810$	2.97033	−	4.02981i	0.104367	−	0.141593i
$811$	−2.33576	+	37.1259i	−0.0820197	+	1.30367i	0.714749	+	0.699381i	$0.246541\pi$
$811$	−2.33576	+	37.1259i	−0.0820197	+	1.30367i	−0.796769	+	0.604284i	$0.793459\pi$
$812$	10.9940	−	42.8190i	0.385815	−	1.50265i
$813$	−4.80756	+	18.7242i	−0.168608	+	0.656686i
$814$	−7.00810	+	111.391i	−0.245634	+	3.90424i
$815$	−0.0341123	+	4.96638i	−0.00119490	+	0.173965i
$816$	1.65395	+	1.99928i	0.0578999	+	0.0699890i
$817$	−0.987156	−	7.81414i	−0.0345362	−	0.273382i
$818$		−	54.6878i		−	1.91212i
$819$	−11.4024	+	1.44046i	−0.398433	+	0.0503337i
$820$	−64.8631	+	35.0808i	−2.26512	+	1.22507i
$821$	−30.7371	−	28.8640i	−1.07273	−	1.00736i	−0.999950	−	0.0100140i	$-0.996812\pi$
$821$	−30.7371	−	28.8640i	−1.07273	−	1.00736i	−0.0727816	−	0.997348i	$-0.523188\pi$
$822$	24.5652	+	11.5595i	0.856810	+	0.403184i
$823$	4.86810	+	4.02724i	0.169691	+	0.140381i	0.718393	−	0.695637i	$-0.244878\pi$
$823$	4.86810	+	4.02724i	0.169691	+	0.140381i	−0.548702	+	0.836018i	$0.684878\pi$
$824$	−12.7256	+	39.1655i	−0.443319	+	1.36439i
$825$	24.5605	−	7.60882i	0.855087	−	0.264905i
$826$	25.8024	+	79.4115i	0.897779	+	2.76308i
$827$	14.7717	−	37.3090i	0.513661	−	1.29736i	−0.409276	−	0.912411i	$-0.634219\pi$
$827$	14.7717	−	37.3090i	0.513661	−	1.29736i	0.922938	−	0.384950i	$-0.125781\pi$
$828$	−4.43344	+	4.72114i	−0.154073	+	0.164071i
$829$	1.23075	+	6.45181i	0.0427457	+	0.224081i	0.997249	−	0.0741181i	$-0.0236142\pi$
$829$	1.23075	+	6.45181i	0.0427457	+	0.224081i	−0.954504	+	0.298199i	$0.903614\pi$
$830$	39.6837	+	0.272573i	1.37744	+	0.00946116i
$831$	16.4108	−	15.4108i	0.569285	−	0.534594i
$832$	29.8172	−	9.68820i	1.03373	−	0.335878i
$833$	−42.2574	−	8.06103i	−1.46413	−	0.279298i
$834$	−0.694595	−	11.0403i	−0.0240518	−	0.382293i
$835$	1.88675	−	7.14431i	0.0652936	−	0.247239i
$836$	23.5772	+	37.1517i	0.815434	+	1.28492i
$837$	−9.15897	+	0.576234i	−0.316580	+	0.0199175i
$838$	15.7164	+	9.97394i	0.542915	+	0.344544i
$839$	−14.1196	+	17.0676i	−0.487461	+	0.589239i	−0.955693	−	0.294367i	$-0.904891\pi$
$839$	−14.1196	+	17.0676i	−0.487461	+	0.589239i	0.468231	+	0.883606i	$0.344891\pi$
$840$	−5.85138	−	23.4573i	−0.201892	−	0.809355i
$841$	−18.9207	−	4.85801i	−0.652438	−	0.167518i
$842$	−19.6361	+	9.24007i	−0.676706	+	0.318434i
$843$	−10.4708	−	3.40217i	−0.360634	−	0.117177i
$844$	54.3111	+	29.8578i	1.86947	+	1.02775i
$845$	10.1688	+	12.4653i	0.349817	+	0.428820i
$846$	3.00750	+	0.379936i	0.103400	+	0.0130625i
$847$	−9.23309	+	73.0875i	−0.317253	+	2.51131i
$848$	−3.12036	+	1.98024i	−0.107154	+	0.0680017i
$849$	−9.49756	+	6.90038i	−0.325955	+	0.236820i
$850$	28.2683	+	11.6439i	0.969596	+	0.399383i
$851$	16.8613	+	12.2504i	0.577997	+	0.419940i
$852$	−7.53444	−	0.474027i	−0.258126	−	0.0162399i
$853$	3.24143	+	5.89613i	0.110984	+	0.201880i	0.925966	−	0.377607i	$-0.123253\pi$
$853$	3.24143	+	5.89613i	0.110984	+	0.201880i	−0.814982	+	0.579487i	$0.803253\pi$
$854$	−28.0745	+	59.6614i	−0.960690	+	2.04157i
$855$	−6.30659	+	0.752736i	−0.215681	+	0.0257430i
$856$	4.34696	−	22.7876i	0.148576	−	0.778863i
$857$	−3.52095	−	4.84617i	−0.120273	−	0.165542i	0.744635	−	0.667472i	$-0.232624\pi$
$857$	−3.52095	−	4.84617i	−0.120273	−	0.165542i	−0.864908	+	0.501930i	$0.832624\pi$
$858$	−13.3643	+	24.3095i	−0.456249	+	0.829914i
$859$	−6.91994	+	10.9041i	−0.236105	+	0.372042i	−0.941634	−	0.336639i	$-0.890710\pi$
$859$	−6.91994	+	10.9041i	−0.236105	+	0.372042i	0.705528	+	0.708682i	$0.250710\pi$
$860$	12.6925	+	13.7035i	0.432810	+	0.467287i
$861$	48.5508	+	19.2226i	1.65461	+	0.655105i
$862$	−23.9421	−	60.4709i	−0.815472	−	2.05965i
$863$	11.4611	−	9.48148i	0.390142	−	0.322753i	−0.421587	−	0.906788i	$-0.638527\pi$
$863$	11.4611	−	9.48148i	0.390142	−	0.322753i	0.811729	+	0.584035i	$0.198527\pi$
$864$	6.45123	−	1.65640i	0.219475	−	0.0563517i
$865$	13.6785	+	6.55176i	0.465085	+	0.222767i
$866$	67.8128	−	26.8490i	2.30437	−	0.912366i
$867$	6.53135	+	6.95518i	0.221816	+	0.236210i
$868$	−77.5084	+	106.681i	−2.63081	+	3.62099i
$869$	−17.6530	−	37.5146i	−0.598838	−	1.27260i
$870$	14.9443	−	3.72782i	0.506659	−	0.126385i
$871$	−5.09057	+	2.79857i	−0.172487	+	0.0948258i
$872$	−7.48765	+	1.42835i	−0.253564	+	0.0483699i
$873$	1.37260	+	5.34591i	0.0464554	+	0.180932i
$874$	13.6718			0.462455
$875$	35.6973	+	39.6190i	1.20679	+	1.33936i
$876$	−25.7123			−0.868739
$877$	−6.82937	−	26.5986i	−0.230611	−	0.898172i	−0.973487	−	0.228742i	$-0.926539\pi$
$877$	−6.82937	−	26.5986i	−0.230611	−	0.898172i	0.742876	−	0.669429i	$-0.233461\pi$
$878$	−20.2244	+	3.85801i	−0.682540	+	0.130201i
$879$	−11.1173	+	6.11181i	−0.374978	+	0.206146i
$880$	10.1297	+	4.09133i	0.341472	+	0.137919i
$881$	−1.96134	−	4.16805i	−0.0660791	−	0.140425i	0.869059	−	0.494708i	$-0.164725\pi$
$881$	−1.96134	−	4.16805i	−0.0660791	−	0.140425i	−0.935138	+	0.354283i	$0.884725\pi$
$882$	−20.7286	+	28.5305i	−0.697969	+	0.960672i
$883$	−6.59369	−	7.02157i	−0.221895	−	0.236295i	0.608383	−	0.793644i	$-0.291819\pi$
$883$	−6.59369	−	7.02157i	−0.221895	−	0.236295i	−0.830278	+	0.557349i	$0.811819\pi$
$884$	−18.4316	+	7.29757i	−0.619921	+	0.245444i
$885$	−12.0556	+	12.6625i	−0.405244	+	0.425645i
$886$	−19.4548	+	4.99514i	−0.653597	+	0.167815i
$887$	0.625850	−	0.517748i	0.0210140	−	0.0173843i	−0.626858	−	0.779134i	$-0.715659\pi$
$887$	0.625850	−	0.517748i	0.0210140	−	0.0173843i	0.647872	+	0.761749i	$0.275659\pi$
$888$	8.08917	+	20.4309i	0.271455	+	0.685616i
$889$	18.4944	+	7.32246i	0.620283	+	0.245588i
$890$	−38.6217	+	69.1236i	−1.29460	+	2.31703i
$891$	−2.75545	+	4.34189i	−0.0923110	+	0.145459i
$892$	22.8738	−	41.6073i	0.765873	−	1.39312i
$893$	−2.26057	−	3.11141i	−0.0756472	−	0.104119i
$894$	−4.48376	+	23.5047i	−0.149959	+	0.786114i
$895$	−28.6131	+	26.5020i	−0.956431	+	0.885865i
$896$	32.1091	−	68.2353i	1.07269	−	2.27958i
$897$	2.49558	+	4.53945i	0.0833251	+	0.151568i
$898$	79.5407	+	5.00428i	2.65431	+	0.166995i
$899$	−22.8421	−	16.5958i	−0.761827	−	0.553499i
$900$	11.1205	−	10.1590i	0.370683	−	0.338633i
$901$	8.59469	−	6.24441i	0.286331	−	0.208031i
$902$	106.418	−	67.5349i	3.54333	−	2.24867i
$903$	1.65772	−	13.1222i	0.0551655	−	0.436680i
$904$	−15.0000	−	1.89494i	−0.498892	−	0.0630248i
$905$	1.05063	+	18.7540i	0.0349242	+	0.623403i
$906$	−30.7046	−	16.8800i	−1.02009	−	0.560801i
$907$	−31.2601	−	10.1570i	−1.03798	−	0.337259i	−0.260037	−	0.965599i	$-0.583735\pi$
$907$	−31.2601	−	10.1570i	−1.03798	−	0.337259i	−0.777939	+	0.628340i	$0.783735\pi$
$908$	20.0323	−	9.42648i	0.664795	−	0.312829i
$909$	−11.0425	−	2.83524i	−0.366258	−	0.0940391i
$910$	−57.3969	−	4.00708i	−1.90269	−	0.132833i
$911$	−31.0269	+	37.5051i	−1.02797	+	1.24260i	−0.0582664	+	0.998301i	$0.518557\pi$
$911$	−31.0269	+	37.5051i	−1.02797	+	1.24260i	−0.969700	+	0.244297i	$0.921443\pi$
$912$	−2.27851	−	1.44598i	−0.0754488	−	0.0478813i
$913$	−40.6839	+	2.55962i	−1.34644	+	0.0847110i
$914$	−47.6581	−	75.0972i	−1.57639	−	2.48399i
$915$	−13.7848	+	0.772250i	−0.455712	+	0.0255298i
$916$	−2.21390	−	35.1889i	−0.0731492	−	1.16267i
$917$	−59.9367	−	11.4335i	−1.97928	−	0.377569i
$918$	−5.81524	+	1.88949i	−0.191932	+	0.0623624i
$919$	−33.2215	+	31.1971i	−1.09588	+	1.02910i	−0.0964468	+	0.995338i	$0.530748\pi$
$919$	−33.2215	+	31.1971i	−1.09588	+	1.02910i	−0.999430	+	0.0337587i	$0.989252\pi$
$920$	−8.85948	+	6.34428i	−0.292089	+	0.209165i
$921$	−4.12265	−	21.6117i	−0.135846	−	0.712130i
$922$	−3.64731	+	3.88399i	−0.120118	+	0.127913i
$923$	−2.22286	+	5.61432i	−0.0731665	+	0.184797i
$924$	22.8337	+	70.2748i	0.751173	+	2.31187i
$925$	−36.9198	−	31.4068i	−1.21391	−	1.03265i
$926$	1.91296	−	5.88749i	0.0628638	−	0.193475i
$927$	13.9985	+	11.5806i	0.459772	+	0.380356i
$928$	18.5415	+	8.72498i	0.608655	+	0.286411i
$929$	−10.7432	−	10.0885i	−0.352471	−	0.330993i	0.488005	−	0.872841i	$-0.337725\pi$
$929$	−10.7432	−	10.0885i	−0.352471	−	0.330993i	−0.840476	+	0.541848i	$0.817725\pi$
$930$	−45.5396	−	6.07105i	−1.49330	−	0.199077i
$931$	44.3885	−	5.60757i	1.45477	−	0.183781i
$932$			23.5237i			0.770544i
$933$	−0.165827	−	1.31266i	−0.00542894	−	0.0429745i
$934$	−5.32303	−	6.43444i	−0.174175	−	0.210541i
$935$	−29.7999	−	9.90939i	−0.974562	−	0.324072i
$936$	−0.342939	+	5.45086i	−0.0112093	+	0.178167i
$937$	−2.90560	+	11.3166i	−0.0949217	+	0.369696i	−0.998242	−	0.0592712i	$-0.981122\pi$
$937$	−2.90560	+	11.3166i	−0.0949217	+	0.369696i	0.903320	+	0.428967i	$0.141122\pi$
$938$	−6.40283	+	24.9374i	−0.209060	+	0.814235i
$939$	2.12206	−	33.7292i	0.0692509	−	1.10071i
$940$	8.65463	+	2.87793i	0.282283	+	0.0938677i
$941$	−18.2297	−	22.0359i	−0.594270	−	0.718349i	0.384543	−	0.923107i	$-0.374359\pi$
$941$	−18.2297	−	22.0359i	−0.594270	−	0.718349i	−0.978813	+	0.204759i	$0.934359\pi$
$942$	−4.94779	−	39.1658i	−0.161208	−	1.27609i
$943$		−	23.5359i		−	0.766433i
$944$	−7.36996	+	0.931043i	−0.239872	+	0.0303029i
$945$	−10.5722	−	1.40942i	−0.343915	−	0.0458485i
$946$	−23.2723	−	21.8542i	−0.756648	−	0.710540i
$947$	−3.57347	−	1.68155i	−0.116122	−	0.0546429i	0.366841	−	0.930284i	$-0.380439\pi$
$947$	−3.57347	−	1.68155i	−0.116122	−	0.0546429i	−0.482963	+	0.875641i	$0.660439\pi$
$948$	−18.7140	−	15.4815i	−0.607801	−	0.502817i
$949$	−6.35525	+	19.5595i	−0.206300	+	0.634927i
$950$	−31.7031	−	2.43223i	−1.02858	−	0.0789118i
$951$	6.13557	+	18.8833i	0.198959	+	0.612334i
$952$	−10.8701	+	27.4547i	−0.352302	+	0.889813i
$953$	−15.1636	+	16.1476i	−0.491197	+	0.523071i	−0.926035	−	0.377437i	$-0.876805\pi$
$953$	−15.1636	+	16.1476i	−0.491197	+	0.523071i	0.434839	+	0.900508i	$0.356805\pi$
$954$	−1.63187	−	8.55459i	−0.0528339	−	0.276965i
$955$	0.584949	−	0.418882i	0.0189285	−	0.0135547i
$956$	19.9717	−	18.7547i	0.645931	−	0.606570i
$957$	−15.0469	+	4.88904i	−0.486398	+	0.158040i
$958$	−29.0228	−	5.53639i	−0.937683	−	0.178873i
$959$	−3.63188	−	57.7270i	−0.117279	−	1.86410i
$960$	29.0494	−	1.62740i	0.937566	−	0.0525242i
$961$	28.5160	+	44.9341i	0.919872	+	1.44949i
$962$	52.1926	−	3.28368i	1.68276	−	0.105870i
$963$	−8.64123	−	5.48389i	−0.278460	−	0.176716i
$964$	20.3062	−	24.5460i	0.654020	−	0.790574i
$965$	15.3844	+	1.07404i	0.495242	+	0.0345745i
$966$	22.2376	+	5.70964i	0.715482	+	0.183705i
$967$	−20.6617	+	9.72267i	−0.664436	+	0.312660i	−0.728260	−	0.685301i	$-0.759671\pi$
$967$	−20.6617	+	9.72267i	−0.664436	+	0.312660i	0.0638235	+	0.997961i	$0.479671\pi$
$968$	33.2947	+	10.8181i	1.07013	+	0.347707i
$969$	6.79789	+	3.73717i	0.218380	+	0.120055i
$970$	1.54551	+	27.5876i	0.0496233	+	0.885785i
$971$	30.4489	+	3.84659i	0.977151	+	0.123443i	0.597658	−	0.801751i	$-0.296098\pi$
$971$	30.4489	+	3.84659i	0.977151	+	0.123443i	0.379494	+	0.925194i	$0.376098\pi$
$972$	−0.377559	+	2.98869i	−0.0121102	+	0.0958622i
$973$	−19.8990	+	12.6283i	−0.637932	+	0.404844i
$974$	3.33536	−	2.42328i	0.106872	−	0.0776470i
$975$	−4.97936	−	10.9704i	−0.159467	−	0.351333i
$976$	−4.74582	−	3.44804i	−0.151910	−	0.110369i
$977$	−3.71923	−	0.233994i	−0.118989	−	0.00748614i	0.00318443	−	0.999995i	$-0.498986\pi$
$977$	−3.71923	−	0.233994i	−0.118989	−	0.00748614i	−0.122173	+	0.992509i	$0.538986\pi$
$978$	−2.39560	−	4.35759i	−0.0766030	−	0.139340i
$979$	34.6311	−	73.5948i	1.10681	−	2.35210i
$980$	−77.8434	+	72.1001i	−2.48662	+	2.30315i
$981$	−0.630142	+	3.30332i	−0.0201189	+	0.105467i
$982$	33.3700	+	45.9299i	1.06488	+	1.46568i
$983$	−13.0188	+	23.6812i	−0.415237	+	0.755313i	−0.998371	−	0.0570633i	$-0.981826\pi$
$983$	−13.0188	+	23.6812i	−0.415237	+	0.755313i	0.583134	+	0.812376i	$0.301826\pi$
$984$	13.2963	−	20.9516i	0.423870	−	0.667913i
$985$	−2.93725	+	5.25699i	−0.0935887	+	0.167502i
$986$	−17.4910	−	6.92517i	−0.557026	−	0.220542i
$987$	−2.37750	−	6.00488i	−0.0756767	−	0.191138i
$988$	15.8858	−	13.1418i	0.505393	−	0.418098i
$989$	−5.77423	+	1.48257i	−0.183610	+	0.0471430i
$990$	−17.7515	+	18.6451i	−0.564180	+	0.592582i
$991$	43.9598	−	17.4049i	1.39643	−	0.552885i	0.455120	−	0.890430i	$-0.349597\pi$
$991$	43.9598	−	17.4049i	1.39643	−	0.552885i	0.941309	+	0.337545i	$0.109597\pi$
$992$	−41.8421	−	44.5573i	−1.32849	−	1.41470i
$993$	−11.4456	+	15.7535i	−0.363214	+	0.499922i
$994$	11.3948	+	24.2152i	0.361421	+	0.768058i
$995$	18.6828	+	7.54589i	0.592285	+	0.239221i
$996$	−20.9261	+	11.5042i	−0.663068	+	0.364525i
$997$	−23.5806	+	4.49823i	−0.746804	+	0.142460i	−0.546717	−	0.837318i	$-0.684123\pi$
$997$	−23.5806	+	4.49823i	−0.746804	+	0.142460i	−0.200087	+	0.979778i	$0.564123\pi$
$998$	−16.8992	−	65.8180i	−0.534935	−	2.08343i
$999$	9.69424			0.306712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.o.a.229.4	✓	480
125.119	even	50	inner	375.2.o.a.244.4	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.2.o.a.229.4	✓	480	1.1	even	1	trivial
375.2.o.a.244.4	yes	480	125.119	even	50	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.556779 - 2.16851i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-2.63982 + 1.45126i) q^{4} +(-0.155729 + 2.23064i) q^{5} +(-0.953255 - 2.02577i) q^{6} +(-2.80366 + 3.85891i) q^{7} +(1.55167 + 1.65236i) q^{8} +(0.929776 - 0.368125i) q^{9} +(4.92387 - 0.904273i) q^{10} +(-4.98086 + 1.27887i) q^{11} +(-2.32113 + 1.92020i) q^{12} +(0.886998 + 2.24030i) q^{13} +(9.92911 + 3.93121i) q^{14} +(0.265010 + 2.22031i) q^{15} +(-0.509076 + 0.802175i) q^{16} +(1.31571 - 2.39328i) q^{17} +(-1.31596 - 1.81127i) q^{18} +(-0.532240 + 2.79010i) q^{19} +(-2.82613 - 6.11449i) q^{20} +(-2.03091 + 4.31591i) q^{21} +(5.54648 + 10.0890i) q^{22} +(2.14566 + 0.134994i) q^{23} +(1.83380 + 1.33234i) q^{24} +(-4.95150 - 0.694749i) q^{25} +(4.36426 - 3.17082i) q^{26} +(0.844328 - 0.535827i) q^{27} +(1.80091 - 14.2557i) q^{28} +(3.05236 + 0.385603i) q^{29} +(4.66721 - 1.81090i) q^{30} +(-8.04194 - 4.42109i) q^{31} +(6.33450 + 2.05820i) q^{32} +(-4.65300 + 2.18954i) q^{33} +(-5.92241 - 1.52062i) q^{34} +(-8.17122 - 6.85490i) q^{35} +(-1.92020 + 2.32113i) q^{36} +(8.18512 + 5.19444i) q^{37} +(6.34670 - 0.399300i) q^{38} +(1.29108 + 2.03441i) q^{39} +(-3.92745 + 3.20389i) q^{40} +(-0.687393 - 10.9258i) q^{41} +(10.4899 + 2.00105i) q^{42} +(-2.63721 + 0.856881i) q^{43} +(11.2926 - 10.6045i) q^{44} +(0.676360 + 2.13132i) q^{45} +(-0.901924 - 4.72805i) q^{46} +(-0.926878 + 0.987024i) q^{47} +(-0.349746 + 0.883357i) q^{48} +(-4.86754 - 14.9807i) q^{49} +(1.25032 + 11.1242i) q^{50} +(0.843955 - 2.59743i) q^{51} +(-5.59277 - 4.62674i) q^{52} +(3.51967 + 1.65623i) q^{53} +(-1.63205 - 1.53260i) q^{54} +(-2.07703 - 11.3097i) q^{55} +(-10.7266 + 1.35509i) q^{56} +2.84041i q^{57} +(-0.863306 - 6.83377i) q^{58} +(4.98395 + 6.02456i) q^{59} +(-3.92181 - 5.47663i) q^{60} +(-0.387695 + 6.16224i) q^{61} +(-5.10960 + 19.9006i) q^{62} +(-1.18622 + 4.62002i) q^{63} +(0.817009 - 12.9860i) q^{64} +(-5.13544 + 1.62969i) q^{65} +(7.33873 + 8.87100i) q^{66} +(0.302168 + 2.39191i) q^{67} +8.22727i q^{68} +(2.13295 - 0.269454i) q^{69} +(-10.3154 + 21.5360i) q^{70} +(1.82683 + 1.71551i) q^{71} +(2.05098 + 0.965116i) q^{72} +(6.57662 + 5.44065i) q^{73} +(6.70689 - 20.6417i) q^{74} +(-4.99398 + 0.245375i) q^{75} +(-2.64413 - 8.13778i) q^{76} +(9.02962 - 22.8062i) q^{77} +(3.69280 - 3.93244i) q^{78} +(1.51075 + 7.91964i) q^{79} +(-1.71008 - 1.26049i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-23.3100 + 7.57388i) q^{82} +(7.78667 + 1.48539i) q^{83} +(-0.902235 - 14.3406i) q^{84} +(5.13364 + 3.30759i) q^{85} +(3.32650 + 5.24172i) q^{86} +(3.07055 - 0.193183i) q^{87} +(-9.84179 - 6.24579i) q^{88} +(-10.0819 + 12.1869i) q^{89} +(4.24521 - 2.65337i) q^{90} +(-11.1320 - 2.85820i) q^{91} +(-5.86008 + 2.75754i) q^{92} +(-8.72792 - 2.83587i) q^{93} +(2.65644 + 1.46039i) q^{94} +(-6.14082 - 1.62173i) q^{95} +(6.60796 + 0.834780i) q^{96} +(-0.691753 + 5.47579i) q^{97} +(-29.7758 + 18.8963i) q^{98} +(-4.16031 + 3.02264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 30 q^{8} + 10 q^{11} + 20 q^{16} - 10 q^{17} - 10 q^{19} - 20 q^{20} + 30 q^{22} - 180 q^{23} - 30 q^{24} - 40 q^{25} - 30 q^{28} - 20 q^{29} + 20 q^{30} + 10 q^{31} - 10 q^{33} + 20 q^{34} - 10 q^{35}+ \cdots - 60 q^{98}+O(q^{100}) \) 480 * q + 30 * q^8 + 10 * q^11 + 20 * q^16 - 10 * q^17 - 10 * q^19 - 20 * q^20 + 30 * q^22 - 180 * q^23 - 30 * q^24 - 40 * q^25 - 30 * q^28 - 20 * q^29 + 20 * q^30 + 10 * q^31 - 10 * q^33 + 20 * q^34 - 10 * q^35 + 10 * q^37 - 30 * q^38 - 10 * q^40 + 30 * q^41 + 10 * q^42 - 70 * q^44 + 20 * q^46 - 40 * q^47 + 80 * q^49 - 20 * q^50 + 40 * q^51 - 40 * q^52 - 10 * q^53 - 10 * q^55 - 240 * q^56 - 310 * q^58 - 40 * q^59 - 120 * q^60 + 20 * q^61 + 10 * q^62 + 10 * q^63 - 70 * q^64 + 70 * q^65 - 260 * q^67 - 30 * q^70 - 160 * q^71 + 30 * q^72 + 20 * q^73 + 100 * q^76 + 40 * q^77 - 20 * q^79 - 200 * q^82 - 10 * q^83 - 40 * q^84 + 20 * q^85 + 100 * q^86 - 40 * q^87 + 40 * q^88 - 50 * q^89 - 30 * q^90 - 120 * q^91 - 10 * q^92 - 300 * q^93 - 20 * q^94 - 60 * q^95 + 50 * q^96 - 40 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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