LMFDB - Embedded newform 930.2.o.e.161.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.20
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.68621 + 0.395836i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.395836 + 1.68621i) q^{6} +(-1.28701 - 2.22916i) q^{7} -1.00000i q^{8} +(2.68663 + 1.33493i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.68621 + 0.395836i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.395836 + 1.68621i) q^{6} +(-1.28701 - 2.22916i) q^{7} -1.00000i q^{8} +(2.68663 + 1.33493i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.56707 + 4.44629i) q^{11} +(-1.68621 - 0.395836i) q^{12} +(4.59412 + 2.65242i) q^{13} +(2.22916 - 1.28701i) q^{14} +(-1.26238 - 1.18591i) q^{15} +1.00000 q^{16} +(2.59376 + 4.49252i) q^{17} +(-1.33493 + 2.68663i) q^{18} +(-0.264764 - 0.458584i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.28778 - 4.26828i) q^{21} +(-4.44629 - 2.56707i) q^{22} -3.03318 q^{23} +(0.395836 - 1.68621i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.65242 + 4.59412i) q^{26} +(4.00181 + 3.31444i) q^{27} +(1.28701 + 2.22916i) q^{28} +8.44680 q^{29} +(1.18591 - 1.26238i) q^{30} +(0.790363 + 5.51138i) q^{31} +1.00000i q^{32} +(-6.08863 + 6.48126i) q^{33} +(-4.49252 + 2.59376i) q^{34} +2.57401i q^{35} +(-2.68663 - 1.33493i) q^{36} +(0.580888 - 0.335376i) q^{37} +(0.458584 - 0.264764i) q^{38} +(6.69674 + 6.29106i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(9.85425 + 5.68936i) q^{41} +(4.26828 - 1.28778i) q^{42} +(-6.69156 + 3.86337i) q^{43} +(2.56707 - 4.44629i) q^{44} +(-1.65922 - 2.49940i) q^{45} -3.03318i q^{46} -6.75256i q^{47} +(1.68621 + 0.395836i) q^{48} +(0.187231 - 0.324294i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.59533 + 8.60205i) q^{51} +(-4.59412 - 2.65242i) q^{52} +(-0.822328 + 1.42431i) q^{53} +(-3.31444 + 4.00181i) q^{54} +(4.44629 - 2.56707i) q^{55} +(-2.22916 + 1.28701i) q^{56} +(-0.264924 - 0.878074i) q^{57} +8.44680i q^{58} +(-10.4486 + 6.03251i) q^{59} +(1.26238 + 1.18591i) q^{60} -7.06279i q^{61} +(-5.51138 + 0.790363i) q^{62} +(-0.481936 - 7.70698i) q^{63} -1.00000 q^{64} +(-2.65242 - 4.59412i) q^{65} +(-6.48126 - 6.08863i) q^{66} +(3.98360 - 6.89980i) q^{67} +(-2.59376 - 4.49252i) q^{68} +(-5.11459 - 1.20064i) q^{69} -2.57401 q^{70} +(-8.45327 - 4.88050i) q^{71} +(1.33493 - 2.68663i) q^{72} +(-3.21521 - 1.85630i) q^{73} +(0.335376 + 0.580888i) q^{74} +(0.500302 + 1.65822i) q^{75} +(0.264764 + 0.458584i) q^{76} +13.2153 q^{77} +(-6.29106 + 6.69674i) q^{78} +(8.75345 - 5.05381i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.43593 + 7.17291i) q^{81} +(-5.68936 + 9.85425i) q^{82} +(3.97145 - 6.87875i) q^{83} +(1.28778 + 4.26828i) q^{84} -5.18752i q^{85} +(-3.86337 - 6.69156i) q^{86} +(14.2431 + 3.34355i) q^{87} +(4.44629 + 2.56707i) q^{88} -14.8905 q^{89} +(2.49940 - 1.65922i) q^{90} -13.6547i q^{91} +3.03318 q^{92} +(-0.848884 + 9.60622i) q^{93} +6.75256 q^{94} +0.529528i q^{95} +(-0.395836 + 1.68621i) q^{96} -6.46323 q^{97} +(0.324294 + 0.187231i) q^{98} +(-12.8322 + 8.51868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.68621	+	0.395836i	0.973535	+	0.228536i
$3$	1.68621	+	0.395836i	0.973535	+	0.228536i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.395836	+	1.68621i	−0.161600	+	0.688393i
$7$	−1.28701	−	2.22916i	−0.486443	−	0.842543i	0.513436	−	0.858128i	$-0.328372\pi$
$7$	−1.28701	−	2.22916i	−0.486443	−	0.842543i	−0.999879	+	0.0155847i	$0.995039\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.68663	+	1.33493i	0.895542	+	0.444976i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.56707	+	4.44629i	−0.774000	+	1.34061i	0.161355	+	0.986897i	$0.448414\pi$
$11$	−2.56707	+	4.44629i	−0.774000	+	1.34061i	−0.935355	+	0.353711i	$0.884920\pi$
$12$	−1.68621	−	0.395836i	−0.486768	−	0.114268i
$13$	4.59412	+	2.65242i	1.27418	+	0.735648i	0.975772	−	0.218790i	$-0.0702109\pi$
$13$	4.59412	+	2.65242i	1.27418	+	0.735648i	0.298408	+	0.954438i	$0.403544\pi$
$14$	2.22916	−	1.28701i	0.595768	−	0.343967i
$15$	−1.26238	−	1.18591i	−0.325946	−	0.306201i
$16$	1.00000			0.250000
$17$	2.59376	+	4.49252i	0.629079	+	1.08960i	0.987737	+	0.156127i	$0.0499011\pi$
$17$	2.59376	+	4.49252i	0.629079	+	1.08960i	−0.358658	+	0.933469i	$0.616766\pi$
$18$	−1.33493	+	2.68663i	−0.314646	+	0.633244i
$19$	−0.264764	−	0.458584i	−0.0607410	−	0.105206i	0.834056	−	0.551680i	$-0.186013\pi$
$19$	−0.264764	−	0.458584i	−0.0607410	−	0.105206i	−0.894797	+	0.446474i	$0.852680\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.28778	−	4.26828i	−0.281017	−	0.931415i
$22$	−4.44629	−	2.56707i	−0.947953	−	0.547301i
$23$	−3.03318			−0.632462			−0.316231	−	0.948682i	$-0.602417\pi$
$23$	−3.03318			−0.632462			−0.316231	+	0.948682i	$0.602417\pi$
$24$	0.395836	−	1.68621i	0.0807998	−	0.344197i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.65242	+	4.59412i	−0.520182	+	0.900982i
$27$	4.00181	+	3.31444i	0.770149	+	0.637864i
$28$	1.28701	+	2.22916i	0.243221	+	0.421272i
$29$	8.44680			1.56853			0.784265	−	0.620426i	$-0.213040\pi$
$29$	8.44680			1.56853			0.784265	+	0.620426i	$0.213040\pi$
$30$	1.18591	−	1.26238i	0.216517	−	0.230479i
$31$	0.790363	+	5.51138i	0.141953	+	0.989873i
$31$	0.790363	+	5.51138i	0.141953	+	0.989873i
$32$			1.00000i			0.176777i
$33$	−6.08863	+	6.48126i	−1.05989	+	1.12824i
$34$	−4.49252	+	2.59376i	−0.770461	+	0.444826i
$35$			2.57401i			0.435087i
$36$	−2.68663	−	1.33493i	−0.447771	−	0.222488i
$37$	0.580888	−	0.335376i	0.0954974	−	0.0551355i	−0.451491	−	0.892276i	$-0.649108\pi$
$37$	0.580888	−	0.335376i	0.0954974	−	0.0551355i	0.546988	+	0.837140i	$0.315774\pi$
$38$	0.458584	−	0.264764i	0.0743922	−	0.0429504i
$39$	6.69674	+	6.29106i	1.07234	+	1.00738i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	9.85425	+	5.68936i	1.53898	+	0.888528i	0.998899	+	0.0469123i	$0.0149381\pi$
$41$	9.85425	+	5.68936i	1.53898	+	0.888528i	0.540077	+	0.841616i	$0.318395\pi$
$42$	4.26828	−	1.28778i	0.658610	−	0.198709i
$43$	−6.69156	+	3.86337i	−1.02045	+	0.589159i	−0.914235	−	0.405184i	$-0.867207\pi$
$43$	−6.69156	+	3.86337i	−1.02045	+	0.589159i	−0.106218	+	0.994343i	$0.533874\pi$
$44$	2.56707	−	4.44629i	0.387000	−	0.670304i
$45$	−1.65922	−	2.49940i	−0.247342	−	0.372588i
$46$		−	3.03318i		−	0.447218i
$47$		−	6.75256i		−	0.984961i	−0.870323	−	0.492481i	$-0.836090\pi$
$47$		−	6.75256i		−	0.984961i	0.870323	−	0.492481i	$-0.163910\pi$
$48$	1.68621	+	0.395836i	0.243384	+	0.0571341i
$49$	0.187231	−	0.324294i	0.0267473	−	0.0463278i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	2.59533	+	8.60205i	0.363418	+	1.20453i
$52$	−4.59412	−	2.65242i	−0.637090	−	0.367824i
$53$	−0.822328	+	1.42431i	−0.112955	+	0.195644i	−0.916961	−	0.398978i	$-0.869365\pi$
$53$	−0.822328	+	1.42431i	−0.112955	+	0.195644i	0.804005	+	0.594622i	$0.202698\pi$
$54$	−3.31444	+	4.00181i	−0.451038	+	0.544578i
$55$	4.44629	−	2.56707i	0.599538	−	0.346143i
$56$	−2.22916	+	1.28701i	−0.297884	+	0.171983i
$57$	−0.264924	−	0.878074i	−0.0350900	−	0.116304i
$58$			8.44680i			1.10912i
$59$	−10.4486	+	6.03251i	−1.36029	+	0.785366i	−0.989663	−	0.143414i	$-0.954192\pi$
$59$	−10.4486	+	6.03251i	−1.36029	+	0.785366i	−0.370632	+	0.928780i	$0.620859\pi$
$60$	1.26238	+	1.18591i	0.162973	+	0.153100i
$61$		−	7.06279i		−	0.904297i	−0.891943	−	0.452149i	$-0.850658\pi$
$61$		−	7.06279i		−	0.904297i	0.891943	−	0.452149i	$-0.149342\pi$
$62$	−5.51138	+	0.790363i	−0.699946	+	0.100376i
$63$	−0.481936	−	7.70698i	−0.0607182	−	0.970988i
$64$	−1.00000			−0.125000
$65$	−2.65242	−	4.59412i	−0.328992	−	0.569831i
$66$	−6.48126	−	6.08863i	−0.797787	−	0.749458i
$67$	3.98360	−	6.89980i	0.486675	−	0.842945i	−0.513208	−	0.858264i	$-0.671543\pi$
$67$	3.98360	−	6.89980i	0.486675	−	0.842945i	0.999883	+	0.0153191i	$0.00487642\pi$
$68$	−2.59376	−	4.49252i	−0.314539	−	0.544798i
$69$	−5.11459	−	1.20064i	−0.615724	−	0.144540i
$70$	−2.57401			−0.307653
$71$	−8.45327	−	4.88050i	−1.00322	−	0.579208i	−0.0940192	−	0.995570i	$-0.529972\pi$
$71$	−8.45327	−	4.88050i	−1.00322	−	0.579208i	−0.909199	+	0.416362i	$0.863305\pi$
$72$	1.33493	−	2.68663i	0.157323	−	0.316622i
$73$	−3.21521	−	1.85630i	−0.376312	−	0.217264i	0.299901	−	0.953970i	$-0.403047\pi$
$73$	−3.21521	−	1.85630i	−0.376312	−	0.217264i	−0.676212	+	0.736707i	$0.736380\pi$
$74$	0.335376	+	0.580888i	0.0389867	+	0.0675269i
$75$	0.500302	+	1.65822i	0.0577699	+	0.191475i
$76$	0.264764	+	0.458584i	0.0303705	+	0.0526032i
$77$	13.2153			1.50603
$78$	−6.29106	+	6.69674i	−0.712322	+	0.758257i
$79$	8.75345	−	5.05381i	0.984841	−	0.568598i	0.0811125	−	0.996705i	$-0.474153\pi$
$79$	8.75345	−	5.05381i	0.984841	−	0.568598i	0.903728	+	0.428107i	$0.140819\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	5.43593	+	7.17291i	0.603992	+	0.796990i
$82$	−5.68936	+	9.85425i	−0.628284	+	1.08822i
$83$	3.97145	−	6.87875i	0.435923	−	0.755041i	−0.561447	−	0.827513i	$-0.689755\pi$
$83$	3.97145	−	6.87875i	0.435923	−	0.755041i	0.997371	+	0.0724712i	$0.0230886\pi$
$84$	1.28778	+	4.26828i	0.140509	+	0.465708i
$85$		−	5.18752i		−	0.562665i
$86$	−3.86337	−	6.69156i	−0.416598	−	0.721569i
$87$	14.2431	+	3.34355i	1.52702	+	0.358466i
$88$	4.44629	+	2.56707i	0.473976	+	0.273650i
$89$	−14.8905			−1.57839			−0.789195	−	0.614143i	$-0.789502\pi$
$89$	−14.8905			−1.57839			−0.789195	+	0.614143i	$0.789502\pi$
$90$	2.49940	−	1.65922i	0.263459	−	0.174897i
$91$		−	13.6547i		−	1.43140i
$92$	3.03318			0.316231
$93$	−0.848884	+	9.60622i	−0.0880252	+	0.996118i
$94$	6.75256			0.696473
$95$			0.529528i			0.0543284i
$96$	−0.395836	+	1.68621i	−0.0403999	+	0.172098i
$97$	−6.46323			−0.656242			−0.328121	−	0.944636i	$-0.606415\pi$
$97$	−6.46323			−0.656242			−0.328121	+	0.944636i	$0.606415\pi$
$98$	0.324294	+	0.187231i	0.0327587	+	0.0189132i
$99$	−12.8322	+	8.51868i	−1.28969	+	0.856159i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	8.88476i		−	0.884067i	−0.896999	−	0.442034i	$-0.854257\pi$
$101$		−	8.88476i		−	0.884067i	0.896999	−	0.442034i	$-0.145743\pi$
$102$	−8.60205	+	2.59533i	−0.851730	+	0.256975i
$103$	−5.26044	+	9.11135i	−0.518327	+	0.897768i	0.481447	+	0.876475i	$0.340111\pi$
$103$	−5.26044	+	9.11135i	−0.518327	+	0.897768i	−0.999773	+	0.0212926i	$0.993222\pi$
$104$	2.65242	−	4.59412i	0.260091	−	0.450491i
$105$	−1.01889	+	4.34033i	−0.0994332	+	0.423573i
$106$	−1.42431	−	0.822328i	−0.138342	−	0.0798715i
$107$	11.2096	−	6.47185i	1.08367	−	0.625657i	0.151786	−	0.988413i	$-0.451497\pi$
$107$	11.2096	−	6.47185i	1.08367	−	0.625657i	0.931884	+	0.362756i	$0.118164\pi$
$108$	−4.00181	−	3.31444i	−0.385075	−	0.318932i
$109$	−1.35138			−0.129439			−0.0647193	−	0.997904i	$-0.520615\pi$
$109$	−1.35138			−0.129439			−0.0647193	+	0.997904i	$0.520615\pi$
$110$	2.56707	+	4.44629i	0.244760	+	0.423937i
$111$	1.11225	−	0.335578i	0.105571	−	0.0318517i
$112$	−1.28701	−	2.22916i	−0.121611	−	0.210636i
$113$	−4.08230	−	2.35692i	−0.384030	−	0.221720i	0.295540	−	0.955330i	$-0.404500\pi$
$113$	−4.08230	−	2.35692i	−0.384030	−	0.221720i	−0.679570	+	0.733610i	$0.737834\pi$
$114$	0.878074	−	0.264924i	0.0822392	−	0.0248124i
$115$	2.62681	+	1.51659i	0.244951	+	0.141423i
$116$	−8.44680			−0.784265
$117$	8.80191	+	13.2589i	0.813736	+	1.22578i
$118$	−6.03251	−	10.4486i	−0.555338	−	0.961873i
$119$	6.67636	−	11.5638i	0.612021	−	1.06005i
$120$	−1.18591	+	1.26238i	−0.108258	+	0.115239i
$121$	−7.67968	−	13.3016i	−0.698152	−	1.20924i
$122$	7.06279			0.639435
$123$	14.3643	+	13.4941i	1.29519	+	1.21673i
$124$	−0.790363	−	5.51138i	−0.0709767	−	0.494937i
$125$		−	1.00000i		−	0.0894427i
$126$	7.70698	−	0.481936i	0.686593	−	0.0429343i
$127$	13.5026	−	7.79574i	1.19816	−	0.691760i	0.238018	−	0.971261i	$-0.423502\pi$
$127$	13.5026	−	7.79574i	1.19816	−	0.691760i	0.960146	+	0.279500i	$0.0901688\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.8127	+	3.86571i	−1.12809	+	0.340356i
$130$	4.59412	−	2.65242i	0.402931	−	0.232632i
$131$	−16.4069	+	9.47252i	−1.43348	+	0.827618i	−0.997384	−	0.0722837i	$-0.976971\pi$
$131$	−16.4069	+	9.47252i	−1.43348	+	0.827618i	−0.436093	+	0.899902i	$0.643638\pi$
$132$	6.08863	−	6.48126i	0.529947	−	0.564121i
$133$	−0.681505	+	1.18040i	−0.0590940	+	0.102354i
$134$	6.89980	+	3.98360i	0.596052	+	0.344131i
$135$	−1.80845	−	4.87129i	−0.155647	−	0.419254i
$136$	4.49252	−	2.59376i	0.385231	−	0.222413i
$137$	2.98906	−	5.17720i	0.255373	−	0.442318i	−0.709624	−	0.704580i	$-0.751135\pi$
$137$	2.98906	−	5.17720i	0.255373	−	0.442318i	0.964997	+	0.262262i	$0.0844686\pi$
$138$	1.20064	−	5.11459i	0.102206	−	0.435383i
$139$		−	20.6001i		−	1.74728i	−0.486573	−	0.873640i	$-0.661753\pi$
$139$		−	20.6001i		−	1.74728i	0.486573	−	0.873640i	$-0.338247\pi$
$140$		−	2.57401i		−	0.217544i
$141$	2.67291	−	11.3862i	0.225099	−	0.958895i
$142$	4.88050	−	8.45327i	0.409562	−	0.709382i
$143$	−23.5869	+	13.6179i	−1.97243	+	1.13878i
$144$	2.68663	+	1.33493i	0.223886	+	0.111244i
$145$	−7.31514	−	4.22340i	−0.607489	−	0.350734i
$146$	1.85630	−	3.21521i	0.153629	−	0.266093i
$147$	0.444079	−	0.472716i	0.0366271	−	0.0389890i
$148$	−0.580888	+	0.335376i	−0.0477487	+	0.0275677i
$149$	−20.8920	+	12.0620i	−1.71154	+	0.988160i	−0.779057	+	0.626953i	$0.784302\pi$
$149$	−20.8920	+	12.0620i	−1.71154	+	0.988160i	−0.932486	+	0.361206i	$0.882365\pi$
$150$	−1.65822	+	0.500302i	−0.135393	+	0.0408495i
$151$			16.5788i			1.34916i	0.738201	+	0.674581i	$0.235676\pi$
$151$			16.5788i			1.34916i	−0.738201	+	0.674581i	$0.764324\pi$
$152$	−0.458584	+	0.264764i	−0.0371961	+	0.0214752i
$153$	0.971266	+	15.5322i	0.0785222	+	1.25570i
$154$			13.2153i			1.06492i
$155$	2.07122	−	5.16818i	0.166364	−	0.415118i
$156$	−6.69674	−	6.29106i	−0.536169	−	0.503688i
$157$	14.6508			1.16926			0.584631	−	0.811300i	$-0.301239\pi$
$157$	14.6508			1.16926			0.584631	+	0.811300i	$0.301239\pi$
$158$	5.05381	+	8.75345i	0.402059	+	0.696387i
$159$	−1.95041	+	2.07619i	−0.154678	+	0.164652i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	3.90372	+	6.76144i	0.307656	+	0.532876i
$162$	−7.17291	+	5.43593i	−0.563557	+	0.427087i
$163$	22.4774			1.76056			0.880281	−	0.474452i	$-0.157354\pi$
$163$	22.4774			1.76056			0.880281	+	0.474452i	$0.157354\pi$
$164$	−9.85425	−	5.68936i	−0.769488	−	0.444264i
$165$	8.51353	−	2.56862i	0.662778	−	0.199967i
$166$	6.87875	+	3.97145i	0.533895	+	0.308244i
$167$	8.21327	+	14.2258i	0.635562	+	1.10083i	0.986396	+	0.164388i	$0.0525650\pi$
$167$	8.21327	+	14.2258i	0.635562	+	1.10083i	−0.350833	+	0.936438i	$0.614102\pi$
$168$	−4.26828	+	1.28778i	−0.329305	+	0.0993546i
$169$	7.57064	+	13.1127i	0.582357	+	1.00867i
$170$	5.18752			0.397864
$171$	−0.0991442	−	1.58549i	−0.00758174	−	0.121245i
$172$	6.69156	−	3.86337i	0.510226	−	0.294579i
$173$	2.51861	+	1.45412i	0.191486	+	0.110554i	0.592678	−	0.805439i	$-0.298071\pi$
$173$	2.51861	+	1.45412i	0.191486	+	0.110554i	−0.401192	+	0.915994i	$0.631404\pi$
$174$	−3.34355	+	14.2431i	−0.253474	+	1.07977i
$175$	1.28701	−	2.22916i	0.0972885	−	0.168509i
$176$	−2.56707	+	4.44629i	−0.193500	+	0.335152i
$177$	−20.0065	+	6.03616i	−1.50378	+	0.453705i
$178$		−	14.8905i		−	1.11609i
$179$	2.85826	+	4.95065i	0.213637	+	0.370029i	0.952850	−	0.303442i	$-0.0981358\pi$
$179$	2.85826	+	4.95065i	0.213637	+	0.370029i	−0.739213	+	0.673471i	$0.764803\pi$
$180$	1.65922	+	2.49940i	0.123671	+	0.186294i
$181$	−13.2525	−	7.65134i	−0.985051	−	0.568719i	−0.0812595	−	0.996693i	$-0.525894\pi$
$181$	−13.2525	−	7.65134i	−0.985051	−	0.568719i	−0.903791	+	0.427974i	$0.859228\pi$
$182$	13.6547			1.01215
$183$	2.79571	−	11.9094i	0.206665	−	0.880365i
$184$			3.03318i			0.223609i
$185$	−0.670752			−0.0493146
$186$	−9.60622	−	0.848884i	−0.704362	−	0.0622432i
$187$	−26.6334			−1.94763
$188$			6.75256i			0.492481i
$189$	2.23806	−	13.1864i	0.162795	−	0.959168i
$190$	−0.529528			−0.0384160
$191$	−4.31841	−	2.49324i	−0.312470	−	0.180404i	0.335562	−	0.942018i	$-0.391074\pi$
$191$	−4.31841	−	2.49324i	−0.312470	−	0.180404i	−0.648031	+	0.761614i	$0.724407\pi$
$192$	−1.68621	−	0.395836i	−0.121692	−	0.0285670i
$193$	8.08463	+	14.0030i	0.581945	+	1.00796i	0.995249	+	0.0973645i	$0.0310413\pi$
$193$	8.08463	+	14.0030i	0.581945	+	1.00796i	−0.413304	+	0.910593i	$0.635625\pi$
$194$		−	6.46323i		−	0.464033i
$195$	−2.65402	−	8.79659i	−0.190058	−	0.629937i
$196$	−0.187231	+	0.324294i	−0.0133737	+	0.0231639i
$197$	4.30925	−	7.46384i	0.307021	−	0.531777i	−0.670688	−	0.741740i	$-0.734001\pi$
$197$	4.30925	−	7.46384i	0.307021	−	0.531777i	0.977709	+	0.209963i	$0.0673343\pi$
$198$	−8.51868	−	12.8322i	−0.605396	−	0.911947i
$199$	4.91862	+	2.83976i	0.348671	+	0.201306i	0.664100	−	0.747644i	$-0.268815\pi$
$199$	4.91862	+	2.83976i	0.348671	+	0.201306i	−0.315429	+	0.948949i	$0.602148\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	9.44840	−	10.0577i	0.666438	−	0.709414i
$202$	8.88476			0.625130
$203$	−10.8711	−	18.8293i	−0.763000	−	1.32155i
$204$	−2.59533	−	8.60205i	−0.181709	−	0.602264i
$205$	−5.68936	−	9.85425i	−0.397362	−	0.688251i
$206$	−9.11135	−	5.26044i	−0.634818	−	0.366512i
$207$	−8.14902	−	4.04908i	−0.566396	−	0.281430i
$208$	4.59412	+	2.65242i	0.318545	+	0.183912i
$209$	2.71867			0.188054
$210$	−4.34033	−	1.01889i	−0.299511	−	0.0703099i
$211$	0.695561	+	1.20475i	0.0478844	+	0.0829382i	0.888974	−	0.457957i	$-0.151419\pi$
$211$	0.695561	+	1.20475i	0.0478844	+	0.0829382i	−0.841090	+	0.540896i	$0.818085\pi$
$212$	0.822328	−	1.42431i	0.0564777	−	0.0978222i
$213$	−12.3221	−	11.5757i	−0.844298	−	0.793151i
$214$	6.47185	+	11.2096i	0.442407	+	0.766271i
$215$	7.72674			0.526960
$216$	3.31444	−	4.00181i	0.225519	−	0.272289i
$217$	11.2685	−	8.85503i	0.764959	−	0.601118i
$218$		−	1.35138i		−	0.0915269i
$219$	−4.68674	−	4.40282i	−0.316700	−	0.297515i
$220$	−4.44629	+	2.56707i	−0.299769	+	0.173072i
$221$			27.5189i			1.85112i
$222$	0.335578	+	1.11225i	0.0225226	+	0.0746497i
$223$	11.5712	−	6.68062i	0.774863	−	0.447368i	−0.0597434	−	0.998214i	$-0.519028\pi$
$223$	11.5712	−	6.68062i	0.774863	−	0.447368i	0.834607	+	0.550846i	$0.185695\pi$
$224$	2.22916	−	1.28701i	0.148942	−	0.0859917i
$225$	0.187231	+	2.99415i	0.0124821	+	0.199610i
$226$	2.35692	−	4.08230i	0.156780	−	0.271550i
$227$	−13.4583	−	7.77017i	−0.893261	−	0.515724i	−0.0182532	−	0.999833i	$-0.505810\pi$
$227$	−13.4583	−	7.77017i	−0.893261	−	0.515724i	−0.875008	+	0.484109i	$0.839144\pi$
$228$	0.264924	+	0.878074i	0.0175450	+	0.0581519i
$229$	12.6066	−	7.27845i	0.833071	−	0.480974i	−0.0218323	−	0.999762i	$-0.506950\pi$
$229$	12.6066	−	7.27845i	0.833071	−	0.480974i	0.854903	+	0.518788i	$0.173617\pi$
$230$	−1.51659	+	2.62681i	−0.100001	+	0.173207i
$231$	22.2839	+	5.23111i	1.46617	+	0.344182i
$232$		−	8.44680i		−	0.554559i
$233$		−	2.89624i		−	0.189739i	−0.995490	−	0.0948694i	$-0.969757\pi$
$233$		−	2.89624i		−	0.189739i	0.995490	−	0.0948694i	$-0.0302434\pi$
$234$	−13.2589	+	8.80191i	−0.866760	+	0.575399i
$235$	−3.37628	+	5.84788i	−0.220244	+	0.381474i
$236$	10.4486	−	6.03251i	0.680147	−	0.392683i
$237$	16.7607	−	5.05686i	1.08872	−	0.328479i
$238$	11.5638	+	6.67636i	0.749570	+	0.432764i
$239$	2.74446	−	4.75354i	0.177524	−	0.307481i	−0.763508	−	0.645799i	$-0.776524\pi$
$239$	2.74446	−	4.75354i	0.177524	−	0.307481i	0.941032	+	0.338318i	$0.109858\pi$
$240$	−1.26238	−	1.18591i	−0.0814866	−	0.0765502i
$241$	−4.61436	+	2.66410i	−0.297237	+	0.171610i	−0.641201	−	0.767373i	$-0.721564\pi$
$241$	−4.61436	+	2.66410i	−0.297237	+	0.171610i	0.343964	+	0.938983i	$0.388230\pi$
$242$	13.3016	−	7.67968i	0.855059	−	0.493668i
$243$	6.32684	+	14.2468i	0.405867	+	0.913932i
$244$			7.06279i			0.452149i
$245$	−0.324294	+	0.187231i	−0.0207184	+	0.0119618i
$246$	−13.4941	+	14.3643i	−0.860355	+	0.915835i
$247$		−	2.80906i		−	0.178736i
$248$	5.51138	−	0.790363i	0.349973	−	0.0501881i
$249$	9.41957	−	10.0270i	0.596941	−	0.635435i
$250$	1.00000			0.0632456
$251$	−0.392937	−	0.680586i	−0.0248019	−	0.0429582i	0.853358	−	0.521325i	$-0.174562\pi$
$251$	−0.392937	−	0.680586i	−0.0248019	−	0.0429582i	−0.878160	+	0.478367i	$0.841229\pi$
$252$	0.481936	+	7.70698i	0.0303591	+	0.485494i
$253$	7.78638	−	13.4864i	0.489526	−	0.847883i
$254$	7.79574	+	13.5026i	0.489148	+	0.847230i
$255$	2.05341	−	8.74726i	0.128589	−	0.547774i
$256$	1.00000			0.0625000
$257$	10.4435	+	6.02954i	0.651446	+	0.376113i	0.789010	−	0.614380i	$-0.210594\pi$
$257$	10.4435	+	6.02954i	0.651446	+	0.376113i	−0.137564	+	0.990493i	$0.543927\pi$
$258$	−3.86571	−	12.8127i	−0.240668	−	0.797681i
$259$	−1.49521	−	0.863261i	−0.0929080	−	0.0536405i
$260$	2.65242	+	4.59412i	0.164496	+	0.284915i
$261$	22.6934	+	11.2759i	1.40469	+	0.697959i
$262$	−9.47252	−	16.4069i	−0.585214	−	1.01362i
$263$	2.04756			0.126258			0.0631291	−	0.998005i	$-0.479892\pi$
$263$	2.04756			0.126258			0.0631291	+	0.998005i	$0.479892\pi$
$264$	6.48126	+	6.08863i	0.398894	+	0.374729i
$265$	1.42431	−	0.822328i	0.0874949	−	0.0505152i
$266$	−1.18040	−	0.681505i	−0.0723751	−	0.0417858i
$267$	−25.1085	−	5.89420i	−1.53662	−	0.360719i
$268$	−3.98360	+	6.89980i	−0.243337	+	0.421473i
$269$	13.5077	−	23.3961i	0.823581	−	1.42648i	−0.0794184	−	0.996841i	$-0.525306\pi$
$269$	13.5077	−	23.3961i	0.823581	−	1.42648i	0.902999	−	0.429642i	$-0.141360\pi$
$270$	4.87129	−	1.80845i	0.296458	−	0.110059i
$271$		−	3.17938i		−	0.193134i	−0.995327	−	0.0965668i	$-0.969214\pi$
$271$		−	3.17938i		−	0.193134i	0.995327	−	0.0965668i	$-0.0307861\pi$
$272$	2.59376	+	4.49252i	0.157270	+	0.272399i
$273$	5.40503	−	23.0247i	0.327127	−	1.39352i
$274$	5.17720	+	2.98906i	0.312766	+	0.180576i
$275$	−5.13414			−0.309600
$276$	5.11459	+	1.20064i	0.307862	+	0.0722702i
$277$		−	16.5427i		−	0.993955i	−0.867763	−	0.496978i	$-0.834443\pi$
$277$		−	16.5427i		−	0.993955i	0.867763	−	0.496978i	$-0.165557\pi$
$278$	20.6001			1.23551
$279$	−5.23389	+	15.8621i	−0.313345	+	0.949639i
$280$	2.57401			0.153827
$281$		−	1.55339i		−	0.0926672i	−0.998926	−	0.0463336i	$-0.985246\pi$
$281$		−	1.55339i		−	0.0926672i	0.998926	−	0.0463336i	$-0.0147537\pi$
$282$	11.3862	+	2.67291i	0.678041	+	0.159169i
$283$	−3.03122			−0.180187			−0.0900936	−	0.995933i	$-0.528717\pi$
$283$	−3.03122			−0.180187			−0.0900936	+	0.995933i	$0.528717\pi$
$284$	8.45327	+	4.88050i	0.501609	+	0.289604i
$285$	−0.209606	+	0.892896i	−0.0124160	+	0.0528906i
$286$	−13.6179	−	23.5869i	−0.805242	−	1.39472i
$287$		−	29.2889i		−	1.72887i
$288$	−1.33493	+	2.68663i	−0.0786614	+	0.158311i
$289$	−4.95516	+	8.58260i	−0.291480	+	0.504859i
$290$	4.22340	−	7.31514i	0.248006	−	0.429560i
$291$	−10.8984	−	2.55838i	−0.638875	−	0.149975i
$292$	3.21521	+	1.85630i	0.188156	+	0.108632i
$293$	6.74006	−	3.89138i	0.393759	−	0.227337i	−0.290029	−	0.957018i	$-0.593665\pi$
$293$	6.74006	−	3.89138i	0.393759	−	0.227337i	0.683787	+	0.729681i	$0.260332\pi$
$294$	0.472716	+	0.444079i	0.0275694	+	0.0258992i
$295$	12.0650			0.702453
$296$	−0.335376	−	0.580888i	−0.0194933	−	0.0337634i
$297$	−25.0099	+	9.28484i	−1.45122	+	0.538761i
$298$	−12.0620	−	20.8920i	−0.698734	−	1.21024i
$299$	−13.9348	−	8.04526i	−0.805870	−	0.465270i
$300$	−0.500302	−	1.65822i	−0.0288850	−	0.0957375i
$301$	17.2241	+	9.94437i	0.992783	+	0.573184i
$302$	−16.5788			−0.954002
$303$	3.51691	−	14.9816i	0.202041	−	0.860671i
$304$	−0.264764	−	0.458584i	−0.0151852	−	0.0263016i
$305$	−3.53139	+	6.11655i	−0.202207	+	0.350233i
$306$	−15.5322	+	0.971266i	−0.887917	+	0.0555236i
$307$	−5.71957	−	9.90659i	−0.326433	−	0.565399i	0.655368	−	0.755310i	$-0.272513\pi$
$307$	−5.71957	−	9.90659i	−0.326433	−	0.565399i	−0.981801	+	0.189911i	$0.939180\pi$
$308$	−13.2153			−0.753013
$309$	−12.4768	+	13.2814i	−0.709782	+	0.755552i
$310$	5.16818	+	2.07122i	0.293533	+	0.117637i
$311$			7.22744i			0.409831i	0.978780	+	0.204915i	$0.0656919\pi$
$311$			7.22744i			0.409831i	−0.978780	+	0.204915i	$0.934308\pi$
$312$	6.29106	−	6.69674i	0.356161	−	0.379129i
$313$	11.2641	−	6.50334i	0.636686	−	0.367591i	−0.146651	−	0.989188i	$-0.546849\pi$
$313$	11.2641	−	6.50334i	0.636686	−	0.367591i	0.783337	+	0.621598i	$0.213516\pi$
$314$			14.6508i			0.826793i
$315$	−3.43612	+	6.91541i	−0.193604	+	0.389639i
$316$	−8.75345	+	5.05381i	−0.492420	+	0.284299i
$317$	19.7129	−	11.3812i	1.10718	−	0.639233i	0.169086	−	0.985601i	$-0.445918\pi$
$317$	19.7129	−	11.3812i	1.10718	−	0.639233i	0.938099	+	0.346368i	$0.112585\pi$
$318$	−2.07619	−	1.95041i	−0.116427	−	0.109374i
$319$	−21.6835	+	37.5569i	−1.21404	+	2.10278i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	21.4635	−	6.47576i	1.19798	−	0.361442i
$322$	−6.76144	+	3.90372i	−0.376801	+	0.217546i
$323$	1.37347	−	2.37891i	0.0764217	−	0.132366i
$324$	−5.43593	−	7.17291i	−0.301996	−	0.398495i
$325$			5.30484i			0.294259i
$326$			22.4774i			1.24491i
$327$	−2.27871	−	0.534925i	−0.126013	−	0.0295814i
$328$	5.68936	−	9.85425i	0.314142	−	0.544110i
$329$	−15.0525	+	8.69058i	−0.829873	+	0.479127i
$330$	2.56862	+	8.51353i	0.141398	+	0.468655i
$331$	4.25023	+	2.45387i	0.233614	+	0.134877i	0.612238	−	0.790673i	$-0.290269\pi$
$331$	4.25023	+	2.45387i	0.233614	+	0.134877i	−0.378624	+	0.925550i	$0.623603\pi$
$332$	−3.97145	+	6.87875i	−0.217962	+	0.377521i
$333$	2.00833	−	0.125586i	0.110056	−	0.00688206i
$334$	−14.2258	+	8.21327i	−0.778402	+	0.449410i
$335$	−6.89980	+	3.98360i	−0.376977	+	0.217647i
$336$	−1.28778	−	4.26828i	−0.0702543	−	0.232854i
$337$			27.0752i			1.47488i	0.675414	+	0.737439i	$0.263965\pi$
$337$			27.0752i			1.47488i	−0.675414	+	0.737439i	$0.736035\pi$
$338$	−13.1127	+	7.57064i	−0.713239	+	0.411789i
$339$	−5.95067	−	5.59018i	−0.323196	−	0.303617i
$340$			5.18752i			0.281333i
$341$	−26.5341	−	10.6339i	−1.43690	−	0.575858i
$342$	1.58549	−	0.0991442i	0.0857333	−	0.00536110i
$343$	−18.9820			−1.02493
$344$	3.86337	+	6.69156i	0.208299	+	0.360785i
$345$	3.82904	+	3.59708i	0.206149	+	0.193660i
$346$	−1.45412	+	2.51861i	−0.0781738	+	0.135401i
$347$	−10.2487	−	17.7512i	−0.550178	−	0.952936i	−0.998261	−	0.0589439i	$-0.981227\pi$
$347$	−10.2487	−	17.7512i	−0.550178	−	0.952936i	0.448084	−	0.893992i	$-0.352107\pi$
$348$	−14.2431	−	3.34355i	−0.763510	−	0.179233i
$349$	−20.0539			−1.07346			−0.536732	−	0.843753i	$-0.680341\pi$
$349$	−20.0539			−1.07346			−0.536732	+	0.843753i	$0.680341\pi$
$350$	2.22916	+	1.28701i	0.119154	+	0.0687934i
$351$	9.59354	+	25.8414i	0.512065	+	1.37931i
$352$	−4.44629	−	2.56707i	−0.236988	−	0.136825i
$353$	4.20458	+	7.28255i	0.223787	+	0.387611i	0.955955	−	0.293513i	$-0.0948246\pi$
$353$	4.20458	+	7.28255i	0.223787	+	0.387611i	−0.732168	+	0.681125i	$0.761491\pi$
$354$	−6.03616	−	20.0065i	−0.320818	−	1.06333i
$355$	4.88050	+	8.45327i	0.259030	+	0.448653i
$356$	14.8905			0.789195
$357$	15.8351	−	16.8563i	0.838085	−	0.892129i
$358$	−4.95065	+	2.85826i	−0.261650	+	0.151064i
$359$	−22.0093	−	12.7070i	−1.16160	−	0.670652i	−0.209916	−	0.977719i	$-0.567319\pi$
$359$	−22.0093	−	12.7070i	−1.16160	−	0.670652i	−0.951688	+	0.307067i	$0.900652\pi$
$360$	−2.49940	+	1.65922i	−0.131730	+	0.0874487i
$361$	9.35980	−	16.2116i	0.492621	−	0.853245i
$362$	7.65134	−	13.2525i	0.402145	−	0.696536i
$363$	−7.68432	−	25.4692i	−0.403322	−	1.33679i
$364$			13.6547i			0.715701i
$365$	1.85630	+	3.21521i	0.0971633	+	0.168292i
$366$	11.9094	+	2.79571i	0.622512	+	0.146134i
$367$	14.9832	+	8.65053i	0.782114	+	0.451554i	0.837179	−	0.546929i	$-0.184203\pi$
$367$	14.9832	+	8.65053i	0.782114	+	0.451554i	−0.0550648	+	0.998483i	$0.517537\pi$
$368$	−3.03318			−0.158115
$369$	18.8798	+	28.4399i	0.982844	+	1.48052i
$370$		−	0.670752i		−	0.0348707i
$371$	4.23336			0.219785
$372$	0.848884	−	9.60622i	0.0440126	−	0.498059i
$373$	−14.4940			−0.750471			−0.375236	−	0.926929i	$-0.622438\pi$
$373$	−14.4940			−0.750471			−0.375236	+	0.926929i	$0.622438\pi$
$374$		−	26.6334i		−	1.37718i
$375$	0.395836	−	1.68621i	0.0204409	−	0.0870757i
$376$	−6.75256			−0.348236
$377$	38.8056	+	22.4044i	1.99859	+	1.15389i
$378$	13.1864	+	2.23806i	0.678234	+	0.115113i
$379$	−9.90778	−	17.1608i	−0.508929	−	0.881490i	−0.999947	−	0.0103407i	$-0.996708\pi$
$379$	−9.90778	−	17.1608i	−0.508929	−	0.881490i	0.491018	−	0.871149i	$-0.336625\pi$
$380$		−	0.529528i		−	0.0271642i
$381$	25.8541	−	7.80045i	1.32455	−	0.399629i
$382$	2.49324	−	4.31841i	0.127565	−	0.220949i
$383$	1.97590	−	3.42236i	0.100964	−	0.174874i	−0.811118	−	0.584882i	$-0.801141\pi$
$383$	1.97590	−	3.42236i	0.100964	−	0.174874i	0.912082	+	0.410008i	$0.134474\pi$
$384$	0.395836	−	1.68621i	0.0201999	−	0.0860492i
$385$	−11.4448	−	6.60766i	−0.583282	−	0.336758i
$386$	−14.0030	+	8.08463i	−0.712734	+	0.411497i
$387$	−23.1350	+	1.44669i	−1.17602	+	0.0735393i
$388$	6.46323			0.328121
$389$	9.71945	+	16.8346i	0.492796	+	0.853547i	0.999966	−	0.00829898i	$-0.00264168\pi$
$389$	9.71945	+	16.8346i	0.492796	+	0.853547i	−0.507170	+	0.861846i	$0.669308\pi$
$390$	8.79659	−	2.65402i	0.445433	−	0.134392i
$391$	−7.86734	−	13.6266i	−0.397868	−	0.689128i
$392$	−0.324294	−	0.187231i	−0.0163793	−	0.00945661i
$393$	−31.4151	+	9.47824i	−1.58468	+	0.478114i
$394$	7.46384	+	4.30925i	0.376023	+	0.217097i
$395$	−10.1076			−0.508569
$396$	12.8322	−	8.51868i	0.644844	−	0.428080i
$397$	11.9703	+	20.7332i	0.600772	+	1.04057i	0.992704	+	0.120574i	$0.0384735\pi$
$397$	11.9703	+	20.7332i	0.600772	+	1.04057i	−0.391932	+	0.919994i	$0.628193\pi$
$398$	−2.83976	+	4.91862i	−0.142344	+	0.246548i
$399$	−1.61641	+	1.72064i	−0.0809216	+	0.0861399i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−20.4973			−1.02359			−0.511793	−	0.859109i	$-0.671019\pi$
$401$	−20.4973			−1.02359			−0.511793	+	0.859109i	$0.671019\pi$
$402$	10.0577	+	9.44840i	0.501632	+	0.471243i
$403$	−10.9875	+	27.4163i	−0.547324	+	1.36571i
$404$			8.88476i			0.442034i
$405$	−1.12120	−	8.92989i	−0.0557128	−	0.443730i
$406$	18.8293	−	10.8711i	0.934480	−	0.539522i
$407$			3.44373i			0.170699i
$408$	8.60205	−	2.59533i	0.425865	−	0.128488i
$409$	7.58719	−	4.38047i	0.375163	−	0.216600i	−0.300549	−	0.953766i	$-0.597170\pi$
$409$	7.58719	−	4.38047i	0.375163	−	0.216600i	0.675712	+	0.737166i	$0.263837\pi$
$410$	9.85425	−	5.68936i	0.486667	−	0.280977i
$411$	7.08951	−	7.54669i	0.349700	−	0.372251i
$412$	5.26044	−	9.11135i	0.259163	−	0.448884i
$413$	26.8949	+	15.5278i	1.32341	+	0.764071i
$414$	4.04908	−	8.14902i	0.199001	−	0.400503i
$415$	−6.87875	+	3.97145i	−0.337665	+	0.194951i
$416$	−2.65242	+	4.59412i	−0.130045	+	0.225245i
$417$	8.15428	−	34.7362i	0.399317	−	1.70104i
$418$			2.71867i			0.132974i
$419$			17.8444i			0.871754i	0.900006	+	0.435877i	$0.143562\pi$
$419$			17.8444i			0.871754i	−0.900006	+	0.435877i	$0.856438\pi$
$420$	1.01889	−	4.34033i	0.0497166	−	0.211787i
$421$	−8.25775	+	14.3028i	−0.402458	+	0.697078i	−0.994022	−	0.109180i	$-0.965177\pi$
$421$	−8.25775	+	14.3028i	−0.402458	+	0.697078i	0.591564	+	0.806258i	$0.298511\pi$
$422$	−1.20475	+	0.695561i	−0.0586462	+	0.0338594i
$423$	9.01418	−	18.1416i	0.438284	−	0.882075i
$424$	1.42431	+	0.822328i	0.0691708	+	0.0399358i
$425$	−2.59376	+	4.49252i	−0.125816	+	0.217919i
$426$	11.5757	−	12.3221i	0.560843	−	0.597009i
$427$	−15.7441	+	9.08985i	−0.761909	+	0.439889i
$428$	−11.2096	+	6.47185i	−0.541835	+	0.312829i
$429$	−45.1629	+	13.6261i	−2.18049	+	0.657874i
$430$			7.72674i			0.372617i
$431$	10.7198	−	6.18908i	0.516354	−	0.298117i	−0.219087	−	0.975705i	$-0.570308\pi$
$431$	10.7198	−	6.18908i	0.516354	−	0.298117i	0.735442	+	0.677588i	$0.236975\pi$
$432$	4.00181	+	3.31444i	0.192537	+	0.159466i
$433$			1.18613i			0.0570017i	0.999594	+	0.0285008i	$0.00907333\pi$
$433$			1.18613i			0.0570017i	−0.999594	+	0.0285008i	$0.990927\pi$
$434$	8.85503	+	11.2685i	0.425055	+	0.540908i
$435$	−10.6631	−	10.0171i	−0.511257	−	0.480285i
$436$	1.35138			0.0647193
$437$	0.803076	+	1.39097i	0.0384163	+	0.0665391i
$438$	4.40282	−	4.68674i	0.210375	−	0.223941i
$439$	8.22962	−	14.2541i	0.392778	−	0.680312i	−0.600036	−	0.799973i	$-0.704847\pi$
$439$	8.22962	−	14.2541i	0.392778	−	0.680312i	0.992815	+	0.119660i	$0.0381806\pi$
$440$	−2.56707	−	4.44629i	−0.122380	−	0.211969i
$441$	0.935931	−	0.621317i	0.0445681	−	0.0295865i
$442$	−27.5189			−1.30894
$443$	20.9565	+	12.0992i	0.995671	+	0.574851i	0.906965	−	0.421207i	$-0.138393\pi$
$443$	20.9565	+	12.0992i	0.995671	+	0.574851i	0.0887065	+	0.996058i	$0.471727\pi$
$444$	−1.11225	+	0.335578i	−0.0527853	+	0.0159258i
$445$	12.8955	+	7.44525i	0.611308	+	0.352939i
$446$	6.68062	+	11.5712i	0.316337	+	0.547911i
$447$	−40.0030	+	12.0693i	−1.89208	+	0.570859i
$448$	1.28701	+	2.22916i	0.0608053	+	0.105318i
$449$	−32.2944			−1.52406			−0.762032	−	0.647539i	$-0.775798\pi$
$449$	−32.2944			−1.52406			−0.762032	+	0.647539i	$0.775798\pi$
$450$	−2.99415	+	0.187231i	−0.141146	+	0.00882617i
$451$	−50.5931	+	29.2099i	−2.38233	+	1.37544i
$452$	4.08230	+	2.35692i	0.192015	+	0.110860i
$453$	−6.56248	+	27.9553i	−0.308332	+	1.31346i
$454$	7.77017	−	13.4583i	0.364672	−	0.631631i
$455$	−6.82736	+	11.8253i	−0.320071	+	0.554380i
$456$	−0.878074	+	0.264924i	−0.0411196	+	0.0124062i
$457$		−	19.0886i		−	0.892929i	−0.894801	−	0.446464i	$-0.852683\pi$
$457$		−	19.0886i		−	0.892929i	0.894801	−	0.446464i	$-0.147317\pi$
$458$	7.27845	+	12.6066i	0.340100	+	0.589070i
$459$	−4.51045	+	26.5751i	−0.210530	+	1.24042i
$460$	−2.62681	−	1.51659i	−0.122476	−	0.0707114i
$461$	−12.8115			−0.596691			−0.298345	−	0.954458i	$-0.596435\pi$
$461$	−12.8115			−0.596691			−0.298345	+	0.954458i	$0.596435\pi$
$462$	−5.23111	+	22.2839i	−0.243373	+	1.03674i
$463$			20.6891i			0.961503i	0.876857	+	0.480751i	$0.159636\pi$
$463$			20.6891i			0.961503i	−0.876857	+	0.480751i	$0.840364\pi$
$464$	8.44680			0.392133
$465$	5.53826	−	7.89479i	0.256831	−	0.366112i
$466$	2.89624			0.134166
$467$		−	23.8528i		−	1.10378i	−0.833918	−	0.551889i	$-0.813907\pi$
$467$		−	23.8528i		−	1.10378i	0.833918	−	0.551889i	$-0.186093\pi$
$468$	−8.80191	−	13.2589i	−0.406868	−	0.612892i
$469$	−20.5077			−0.946957
$470$	−5.84788	−	3.37628i	−0.269743	−	0.155736i
$471$	24.7044	+	5.79932i	1.13832	+	0.267219i
$472$	6.03251	+	10.4486i	0.277669	+	0.480937i
$473$		−	39.6702i		−	1.82404i
$474$	5.05686	+	16.7607i	0.232269	+	0.769843i
$475$	0.264764	−	0.458584i	0.0121482	−	0.0210413i
$476$	−6.67636	+	11.5638i	−0.306011	+	0.530026i
$477$	−4.11064	+	2.72885i	−0.188213	+	0.124945i
$478$	4.75354	+	2.74446i	0.217422	+	0.125529i
$479$	2.62035	−	1.51286i	0.119727	−	0.0691243i	−0.438941	−	0.898516i	$-0.644646\pi$
$479$	2.62035	−	1.51286i	0.119727	−	0.0691243i	0.558667	+	0.829392i	$0.311313\pi$
$480$	1.18591	−	1.26238i	0.0541292	−	0.0576197i
$481$	3.55823			0.162241
$482$	−2.66410	−	4.61436i	−0.121347	−	0.210178i
$483$	3.90608	+	12.9465i	0.177733	+	0.589085i
$484$	7.67968	+	13.3016i	0.349076	+	0.604618i
$485$	5.59732	+	3.23162i	0.254161	+	0.146740i
$486$	−14.2468	+	6.32684i	−0.646248	+	0.286991i
$487$	−33.0749	−	19.0958i	−1.49877	−	0.865314i	−0.498768	−	0.866735i	$-0.666214\pi$
$487$	−33.0749	−	19.0958i	−1.49877	−	0.865314i	−0.999999	+	0.00142186i	$0.999547\pi$
$488$	−7.06279			−0.319717
$489$	37.9016	+	8.89736i	1.71397	+	0.402352i
$490$	−0.187231	−	0.324294i	−0.00845825	−	0.0146501i
$491$	12.7244	−	22.0394i	0.574245	−	0.994622i	−0.421878	−	0.906653i	$-0.638629\pi$
$491$	12.7244	−	22.0394i	0.574245	−	0.994622i	0.996123	−	0.0879695i	$-0.0280378\pi$
$492$	−14.3643	−	13.4941i	−0.647593	−	0.608363i
$493$	21.9089	+	37.9474i	0.986729	+	1.70907i
$494$	2.80906			0.126385
$495$	15.3724	−	0.961271i	0.690937	−	0.0432059i
$496$	0.790363	+	5.51138i	0.0354884	+	0.247468i
$497$			25.1249i			1.12701i
$498$	10.0270	+	9.41957i	0.449321	+	0.422101i
$499$	−7.16472	+	4.13656i	−0.320737	+	0.185178i	−0.651721	−	0.758459i	$-0.725953\pi$
$499$	−7.16472	+	4.13656i	−0.320737	+	0.185178i	0.330984	+	0.943636i	$0.392619\pi$
$500$			1.00000i			0.0447214i
$501$	8.21824	+	27.2389i	0.367164	+	1.21694i
$502$	0.680586	−	0.392937i	0.0303760	−	0.0175376i
$503$	−12.4153	+	7.16797i	−0.553570	+	0.319604i	−0.750561	−	0.660802i	$-0.770216\pi$
$503$	−12.4153	+	7.16797i	−0.553570	+	0.319604i	0.196991	+	0.980405i	$0.436883\pi$
$504$	−7.70698	+	0.481936i	−0.343296	+	0.0214671i
$505$	−4.44238	+	7.69443i	−0.197683	+	0.342398i
$506$	13.4864	+	7.78638i	0.599544	+	0.346147i
$507$	7.57522	+	25.1076i	0.336427	+	1.11507i
$508$	−13.5026	+	7.79574i	−0.599082	+	0.345880i
$509$	17.7292	−	30.7078i	0.785832	−	1.36110i	−0.142668	−	0.989771i	$-0.545568\pi$
$509$	17.7292	−	30.7078i	0.785832	−	1.36110i	0.928501	−	0.371331i	$-0.121098\pi$
$510$	8.74726	+	2.05341i	0.387335	+	0.0909264i
$511$			9.55629i			0.422745i
$512$			1.00000i			0.0441942i
$513$	0.460415	−	2.71271i	0.0203278	−	0.119769i
$514$	−6.02954	+	10.4435i	−0.265952	+	0.460642i
$515$	9.11135	−	5.26044i	0.401494	−	0.231803i
$516$	12.8127	−	3.86571i	0.564046	−	0.170178i
$517$	30.0238	+	17.3343i	1.32045	+	0.762360i
$518$	0.863261	−	1.49521i	0.0379295	−	0.0656959i
$519$	3.67131	+	3.44891i	0.161153	+	0.151390i
$520$	−4.59412	+	2.65242i	−0.201466	+	0.116316i
$521$	13.5448	−	7.82011i	0.593410	−	0.342605i	−0.173035	−	0.984916i	$-0.555357\pi$
$521$	13.5448	−	7.82011i	0.593410	−	0.342605i	0.766445	+	0.642310i	$0.222024\pi$
$522$	−11.2759	+	22.6934i	−0.493531	+	0.993263i
$523$			26.2117i			1.14616i	0.819500	+	0.573078i	$0.194251\pi$
$523$			26.2117i			1.14616i	−0.819500	+	0.573078i	$0.805749\pi$
$524$	16.4069	−	9.47252i	0.716738	−	0.413809i
$525$	3.05255	−	3.24939i	0.133224	−	0.141815i
$526$			2.04756i			0.0892780i
$527$	−22.7100	+	17.8459i	−0.989263	+	0.777380i
$528$	−6.08863	+	6.48126i	−0.264973	+	0.282060i
$529$	−13.7998			−0.599992
$530$	0.822328	+	1.42431i	0.0357196	+	0.0618682i
$531$	−36.1245	+	2.25895i	−1.56767	+	0.0980302i
$532$	0.681505	−	1.18040i	0.0295470	−	0.0511769i
$533$	30.1811	+	52.2752i	1.30729	+	2.26429i
$534$	5.89420	−	25.1085i	0.255067	−	1.08655i
$535$	−12.9437			−0.559605
$536$	−6.89980	−	3.98360i	−0.298026	−	0.172065i
$537$	2.85999	+	9.47926i	0.123418	+	0.409060i
$538$	23.3961	+	13.5077i	1.00868	+	0.582360i
$539$	0.961271	+	1.66497i	0.0414049	+	0.0717154i
$540$	1.80845	+	4.87129i	0.0778234	+	0.209627i
$541$	−2.17123	−	3.76069i	−0.0933487	−	0.161685i	0.815570	−	0.578659i	$-0.196424\pi$
$541$	−2.17123	−	3.76069i	−0.0933487	−	0.161685i	−0.908918	+	0.416974i	$0.863090\pi$
$542$	3.17938			0.136566
$543$	−19.3179	−	18.1476i	−0.829009	−	0.778788i
$544$	−4.49252	+	2.59376i	−0.192615	+	0.111206i
$545$	1.17033	+	0.675690i	0.0501314	+	0.0289434i
$546$	23.0247	+	5.40503i	0.985368	+	0.231314i
$547$	−3.95664	+	6.85310i	−0.169174	+	0.293017i	−0.938130	−	0.346285i	$-0.887443\pi$
$547$	−3.95664	+	6.85310i	−0.169174	+	0.293017i	0.768956	+	0.639302i	$0.220777\pi$
$548$	−2.98906	+	5.17720i	−0.127686	+	0.221159i
$549$	9.42832	−	18.9751i	0.402391	−	0.809836i
$550$		−	5.13414i		−	0.218920i
$551$	−2.23641	−	3.87357i	−0.0952741	−	0.165020i
$552$	−1.20064	+	5.11459i	−0.0511028	+	0.217691i
$553$	−22.5315	−	13.0086i	−0.958137	−	0.553180i
$554$	16.5427			0.702833
$555$	−1.13103	−	0.265508i	−0.0480096	−	0.0112702i
$556$			20.6001i			0.873640i
$557$	−23.6372			−1.00154			−0.500770	−	0.865580i	$-0.666950\pi$
$557$	−23.6372			−1.00154			−0.500770	+	0.865580i	$0.666950\pi$
$558$	−15.8621	−	5.23389i	−0.671496	−	0.221568i
$559$	−40.9891			−1.73365
$560$			2.57401i			0.108772i
$561$	−44.9096	−	10.5425i	−1.89609	−	0.445104i
$562$	1.55339			0.0655256
$563$	−9.05588	−	5.22841i	−0.381660	−	0.220351i	0.296880	−	0.954915i	$-0.404054\pi$
$563$	−9.05588	−	5.22841i	−0.381660	−	0.220351i	−0.678540	+	0.734563i	$0.737387\pi$
$564$	−2.67291	+	11.3862i	−0.112550	+	0.479447i
$565$	2.35692	+	4.08230i	0.0991562	+	0.171744i
$566$		−	3.03122i		−	0.127412i
$567$	8.99349	−	21.3491i	0.377691	−	0.896579i
$568$	−4.88050	+	8.45327i	−0.204781	+	0.354691i
$569$	5.12252	−	8.87246i	0.214747	−	0.371953i	−0.738447	−	0.674311i	$-0.764441\pi$
$569$	5.12252	−	8.87246i	0.214747	−	0.371953i	0.953194	+	0.302358i	$0.0977739\pi$
$570$	−0.892896	−	0.209606i	−0.0373993	−	0.00877944i
$571$	27.0944	+	15.6430i	1.13387	+	0.654638i	0.944904	−	0.327346i	$-0.106154\pi$
$571$	27.0944	+	15.6430i	1.13387	+	0.654638i	0.188962	+	0.981984i	$0.439488\pi$
$572$	23.5869	−	13.6179i	0.986216	−	0.569392i
$573$	−6.29485	−	5.91352i	−0.262971	−	0.247041i
$574$	29.2889			1.22250
$575$	−1.51659	−	2.62681i	−0.0632462	−	0.109546i
$576$	−2.68663	−	1.33493i	−0.111943	−	0.0556220i
$577$	−12.2866	−	21.2810i	−0.511498	−	0.885941i	−0.999911	−	0.0133282i	$-0.995757\pi$
$577$	−12.2866	−	21.2810i	−0.511498	−	0.885941i	0.488413	−	0.872613i	$-0.337576\pi$
$578$	−8.58260	−	4.95516i	−0.356989	−	0.206108i
$579$	8.08952	+	26.8122i	0.336189	+	1.11428i
$580$	7.31514	+	4.22340i	0.303745	+	0.175367i
$581$	−20.4451			−0.848207
$582$	2.55838	−	10.8984i	0.106048	−	0.451753i
$583$	−4.22194	−	7.31262i	−0.174855	−	0.302858i
$584$	−1.85630	+	3.21521i	−0.0768143	+	0.133046i
$585$	−0.993232	−	15.8835i	−0.0410651	−	0.656701i
$586$	3.89138	+	6.74006i	0.160751	+	0.278429i
$587$	−28.3116			−1.16855			−0.584273	−	0.811557i	$-0.698620\pi$
$587$	−28.3116			−1.16855			−0.584273	+	0.811557i	$0.698620\pi$
$588$	−0.444079	+	0.472716i	−0.0183135	+	0.0194945i
$589$	2.31817	−	1.82166i	0.0955187	−	0.0750603i
$590$			12.0650i			0.496709i
$591$	10.2208	−	10.8799i	0.420426	−	0.447538i
$592$	0.580888	−	0.335376i	0.0238744	−	0.0137839i
$593$		−	26.2219i		−	1.07680i	−0.842689	−	0.538401i	$-0.819028\pi$
$593$		−	26.2219i		−	1.07680i	0.842689	−	0.538401i	$-0.180972\pi$
$594$	−9.28484	−	25.0099i	−0.380961	−	1.02617i
$595$	−11.5638	+	6.67636i	−0.474070	+	0.273704i
$596$	20.8920	−	12.0620i	0.855771	−	0.494080i
$597$	7.16975	+	6.73541i	0.293438	+	0.275662i
$598$	8.04526	−	13.9348i	0.328995	−	0.569836i
$599$	29.8917	+	17.2580i	1.22134	+	0.705141i	0.965204	−	0.261500i	$-0.0842171\pi$
$599$	29.8917	+	17.2580i	1.22134	+	0.705141i	0.256136	+	0.966641i	$0.417550\pi$
$600$	1.65822	−	0.500302i	0.0676966	−	0.0204247i
$601$	−23.6671	+	13.6642i	−0.965403	+	0.557375i	−0.897832	−	0.440339i	$-0.854858\pi$
$601$	−23.6671	+	13.6642i	−0.965403	+	0.557375i	−0.0675710	+	0.997714i	$0.521525\pi$
$602$	−9.94437	+	17.2241i	−0.405302	+	0.702004i
$603$	19.9132	−	13.2194i	0.810928	−	0.538334i
$604$		−	16.5788i		−	0.674581i
$605$			15.3594i			0.624447i
$606$	14.9816	+	3.51691i	0.608586	+	0.142865i
$607$	11.0332	−	19.1100i	0.447822	−	0.775651i	−0.550422	−	0.834887i	$-0.685533\pi$
$607$	11.0332	−	19.1100i	0.447822	−	0.775651i	0.998244	+	0.0592358i	$0.0188664\pi$
$608$	0.458584	−	0.264764i	0.0185980	−	0.0107376i
$609$	−10.8776	−	36.0533i	−0.440784	−	1.46095i
$610$	−6.11655	−	3.53139i	−0.247652	−	0.142982i
$611$	17.9106	−	31.0221i	0.724585	−	1.25502i
$612$	−0.971266	−	15.5322i	−0.0392611	−	0.627852i
$613$	24.3755	−	14.0732i	0.984517	−	0.568411i	0.0808859	−	0.996723i	$-0.474225\pi$
$613$	24.3755	−	14.0732i	0.984517	−	0.568411i	0.903631	+	0.428312i	$0.140892\pi$
$614$	9.90659	−	5.71957i	0.399797	−	0.230823i
$615$	−5.69279	−	18.8684i	−0.229556	−	0.760848i
$616$		−	13.2153i		−	0.532461i
$617$	24.9200	−	14.3875i	1.00324	−	0.579221i	0.0940345	−	0.995569i	$-0.470024\pi$
$617$	24.9200	−	14.3875i	1.00324	−	0.579221i	0.909205	+	0.416348i	$0.136690\pi$
$618$	−13.2814	−	12.4768i	−0.534256	−	0.501891i
$619$		−	14.4354i		−	0.580208i	−0.956995	−	0.290104i	$-0.906310\pi$
$619$		−	14.4354i		−	0.580208i	0.956995	−	0.290104i	$-0.0936899\pi$
$620$	−2.07122	+	5.16818i	−0.0831820	+	0.207559i
$621$	−12.1382	−	10.0533i	−0.487090	−	0.403425i
$622$	−7.22744			−0.289794
$623$	19.1642	+	33.1933i	0.767796	+	1.32986i
$624$	6.69674	+	6.29106i	0.268084	+	0.251844i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.50334	+	11.2641i	0.259926	+	0.450205i
$627$	4.58425	+	1.07615i	0.183077	+	0.0429772i
$628$	−14.6508			−0.584631
$629$	3.01337	+	1.73977i	0.120151	+	0.0693691i
$630$	−6.91541	−	3.43612i	−0.275517	−	0.136898i
$631$	18.2779	+	10.5528i	0.727633	+	0.420099i	0.817556	−	0.575850i	$-0.195329\pi$
$631$	18.2779	+	10.5528i	0.727633	+	0.420099i	−0.0899227	+	0.995949i	$0.528662\pi$
$632$	−5.05381	−	8.75345i	−0.201030	−	0.348194i
$633$	0.695981	+	2.30679i	0.0276628	+	0.0916866i
$634$	11.3812	+	19.7129i	0.452006	+	0.782898i
$635$	−15.5915			−0.618729
$636$	1.95041	−	2.07619i	0.0773390	−	0.0823262i
$637$	1.72033	−	0.993232i	0.0681619	−	0.0393533i
$638$	−37.5569	−	21.6835i	−1.48689	−	0.858458i
$639$	−16.1957	−	24.3966i	−0.640690	−	0.965114i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−13.7198	+	23.7633i	−0.541898	+	0.938594i	0.456898	+	0.889519i	$0.348961\pi$
$641$	−13.7198	+	23.7633i	−0.541898	+	0.938594i	−0.998795	+	0.0490748i	$0.984373\pi$
$642$	6.47576	+	21.4635i	0.255578	+	0.847098i
$643$			34.0135i			1.34136i	0.741747	+	0.670680i	$0.233998\pi$
$643$			34.0135i			1.34136i	−0.741747	+	0.670680i	$0.766002\pi$
$644$	−3.90372	−	6.76144i	−0.153828	−	0.266438i
$645$	13.0289	+	3.05853i	0.513014	+	0.120429i
$646$	2.37891	+	1.37347i	0.0935971	+	0.0540383i
$647$	−12.8461			−0.505031			−0.252516	−	0.967593i	$-0.581258\pi$
$647$	−12.8461			−0.505031			−0.252516	+	0.967593i	$0.581258\pi$
$648$	7.17291	−	5.43593i	0.281779	−	0.213544i
$649$		−	61.9435i		−	2.43149i
$650$	−5.30484			−0.208073
$651$	22.5063	−	10.4710i	0.882092	−	0.410389i
$652$	−22.4774			−0.880281
$653$		−	0.0217666i		−	0.000851794i	−1.00000		0.000425897i	$-0.999864\pi$
$653$		−	0.0217666i		−	0.000851794i	1.00000		0.000425897i	$-0.000135567\pi$
$654$	0.534925	−	2.27871i	0.0209172	−	0.0891047i
$655$	18.9450			0.740244
$656$	9.85425	+	5.68936i	0.384744	+	0.222132i
$657$	−6.16004	−	9.27927i	−0.240326	−	0.362019i
$658$	−8.69058	−	15.0525i	−0.338794	−	0.586808i
$659$		−	42.3998i		−	1.65166i	−0.563917	−	0.825832i	$-0.690706\pi$
$659$		−	42.3998i		−	1.65166i	0.563917	−	0.825832i	$-0.309294\pi$
$660$	−8.51353	+	2.56862i	−0.331389	+	0.0999834i
$661$	3.57820	−	6.19762i	0.139176	−	0.241059i	−0.788009	−	0.615664i	$-0.788888\pi$
$661$	3.57820	−	6.19762i	0.139176	−	0.241059i	0.927185	+	0.374604i	$0.122221\pi$
$662$	−2.45387	+	4.25023i	−0.0953724	+	0.165190i
$663$	−10.8930	+	46.4028i	−0.423049	+	1.80213i
$664$	−6.87875	−	3.97145i	−0.266947	−	0.154122i
$665$	1.18040	−	0.681505i	0.0457740	−	0.0264276i
$666$	0.125586	+	2.00833i	0.00486635	+	0.0778213i
$667$	−25.6207			−0.992036
$668$	−8.21327	−	14.2258i	−0.317781	−	0.550413i
$669$	22.1559	−	6.68466i	0.856597	−	0.258444i
$670$	−3.98360	−	6.89980i	−0.153900	−	0.266563i
$671$	31.4032	+	18.1307i	1.21231	+	0.699926i
$672$	4.26828	−	1.28778i	0.164653	−	0.0496773i
$673$	−15.4883	−	8.94220i	−0.597032	−	0.344696i	0.170841	−	0.985299i	$-0.445351\pi$
$673$	−15.4883	−	8.94220i	−0.597032	−	0.344696i	−0.767873	+	0.640602i	$0.778685\pi$
$674$	−27.0752			−1.04290
$675$	−0.869482	+	5.12289i	−0.0334664	+	0.197180i
$676$	−7.57064	−	13.1127i	−0.291179	−	0.504336i
$677$	16.7056	−	28.9349i	0.642048	−	1.11206i	−0.342927	−	0.939362i	$-0.611418\pi$
$677$	16.7056	−	28.9349i	0.642048	−	1.11206i	0.984975	−	0.172698i	$-0.0552483\pi$
$678$	5.59018	−	5.95067i	0.214690	−	0.228534i
$679$	8.31822	+	14.4076i	0.319224	+	0.552912i
$680$	−5.18752			−0.198932
$681$	−19.6179	−	18.4295i	−0.751759	−	0.706218i
$682$	10.6339	−	26.5341i	0.407193	−	1.01604i
$683$		−	19.4433i		−	0.743979i	−0.928237	−	0.371990i	$-0.878676\pi$
$683$		−	19.4433i		−	0.743979i	0.928237	−	0.371990i	$-0.121324\pi$
$684$	0.0991442	+	1.58549i	0.00379087	+	0.0606226i
$685$	−5.17720	+	2.98906i	−0.197811	+	0.114206i
$686$		−	18.9820i		−	0.724734i
$687$	24.1386	−	7.28285i	0.920944	−	0.277858i
$688$	−6.69156	+	3.86337i	−0.255113	+	0.147290i
$689$	−7.55575	+	4.36231i	−0.287851	+	0.166191i
$690$	−3.59708	+	3.82904i	−0.136939	+	0.145769i
$691$	−10.6087	+	18.3747i	−0.403572	+	0.699007i	−0.994154	−	0.107970i	$-0.965565\pi$
$691$	−10.6087	+	18.3747i	−0.403572	+	0.699007i	0.590582	+	0.806978i	$0.298898\pi$
$692$	−2.51861	−	1.45412i	−0.0957430	−	0.0552772i
$693$	35.5047	+	17.6415i	1.34871	+	0.670146i
$694$	17.7512	−	10.2487i	0.673827	−	0.389034i
$695$	−10.3001	+	17.8402i	−0.390704	+	0.676718i
$696$	3.34355	−	14.2431i	0.126737	−	0.539883i
$697$			59.0273i			2.23582i
$698$		−	20.0539i		−	0.759053i
$699$	1.14644	−	4.88367i	0.0433622	−	0.184718i
$700$	−1.28701	+	2.22916i	−0.0486443	+	0.0842543i
$701$	−28.4019	+	16.3979i	−1.07273	+	0.619338i	−0.928925	−	0.370268i	$-0.879266\pi$
$701$	−28.4019	+	16.3979i	−1.07273	+	0.619338i	−0.143801	+	0.989607i	$0.545932\pi$
$702$	−25.8414	+	9.59354i	−0.975321	+	0.362085i
$703$	−0.307596	−	0.177591i	−0.0116012	−	0.00669796i
$704$	2.56707	−	4.44629i	0.0967500	−	0.167576i
$705$	−8.00793	+	8.52432i	−0.301596	+	0.321045i
$706$	−7.28255	+	4.20458i	−0.274082	+	0.158242i
$707$	−19.8056	+	11.4347i	−0.744865	+	0.430048i
$708$	20.0065	−	6.03616i	0.751890	−	0.226853i
$709$		−	49.3472i		−	1.85327i	−0.375960	−	0.926636i	$-0.622687\pi$
$709$		−	49.3472i		−	1.85327i	0.375960	−	0.926636i	$-0.377313\pi$
$710$	−8.45327	+	4.88050i	−0.317245	+	0.183162i
$711$	30.2637	−	1.89246i	1.13498	−	0.0709729i
$712$			14.8905i			0.558045i
$713$	−2.39732	−	16.7170i	−0.0897802	−	0.626057i
$714$	16.8563	+	15.8351i	0.630831	+	0.592615i
$715$	27.2358			1.01856
$716$	−2.85826	−	4.95065i	−0.106818	−	0.185015i
$717$	6.50937	−	6.92913i	0.243097	−	0.258773i
$718$	12.7070	−	22.0093i	0.474223	−	0.821378i
$719$	−3.77117	−	6.53187i	−0.140641	−	0.243598i	0.787097	−	0.616829i	$-0.211583\pi$
$719$	−3.77117	−	6.53187i	−0.140641	−	0.243598i	−0.927738	+	0.373232i	$0.878250\pi$
$720$	−1.65922	−	2.49940i	−0.0618356	−	0.0931470i
$721$	27.0809			1.00854
$722$	16.2116	+	9.35980i	0.603335	+	0.348336i
$723$	−8.83535	+	2.66571i	−0.328590	+	0.0991389i
$724$	13.2525	+	7.65134i	0.492525	+	0.284360i
$725$	4.22340	+	7.31514i	0.156853	+	0.271677i
$726$	25.4692	−	7.68432i	0.945251	−	0.285192i
$727$	20.0826	+	34.7841i	0.744822	+	1.29007i	0.950278	+	0.311403i	$0.100799\pi$
$727$	20.0826	+	34.7841i	0.744822	+	1.29007i	−0.205456	+	0.978666i	$0.565868\pi$
$728$	−13.6547			−0.506077
$729$	5.02899	+	26.5275i	0.186259	+	0.982501i
$730$	−3.21521	+	1.85630i	−0.119000	+	0.0687048i
$731$	−34.7126	−	20.0413i	−1.28389	−	0.741255i
$732$	−2.79571	+	11.9094i	−0.103332	+	0.440183i
$733$	7.73727	−	13.4013i	0.285783	−	0.494990i	−0.687016	−	0.726642i	$-0.741080\pi$
$733$	7.73727	−	13.4013i	0.285783	−	0.494990i	0.972799	+	0.231652i	$0.0744132\pi$
$734$	−8.65053	+	14.9832i	−0.319297	+	0.553038i
$735$	−0.620942	+	0.187344i	−0.0229038	+	0.00691031i
$736$		−	3.03318i		−	0.111805i
$737$	20.4524	+	35.4245i	0.753372	+	1.30488i
$738$	−28.4399	+	18.8798i	−1.04689	+	0.694976i
$739$	20.8170	+	12.0187i	0.765767	+	0.442116i	0.831362	−	0.555731i	$-0.187561\pi$
$739$	20.8170	+	12.0187i	0.765767	+	0.442116i	−0.0655955	+	0.997846i	$0.520895\pi$
$740$	0.670752			0.0246573
$741$	1.11193	−	4.73667i	0.0408477	−	0.174006i
$742$			4.23336i			0.155412i
$743$	−16.5869			−0.608516			−0.304258	−	0.952590i	$-0.598409\pi$
$743$	−16.5869			−0.608516			−0.304258	+	0.952590i	$0.598409\pi$
$744$	9.60622	+	0.848884i	0.352181	+	0.0311216i
$745$	24.1241			0.883837
$746$		−	14.4940i		−	0.530663i
$747$	19.8525	−	13.1790i	0.726363	−	0.482196i
$748$	26.6334			0.973814
$749$	−28.8536	−	16.6586i	−1.05429	−	0.608693i
$750$	1.68621	+	0.395836i	0.0615718	+	0.0144539i
$751$	−15.3278	−	26.5485i	−0.559318	−	0.968768i	−0.997553	−	0.0699074i	$-0.977730\pi$
$751$	−15.3278	−	26.5485i	−0.559318	−	0.968768i	0.438235	−	0.898860i	$-0.355604\pi$
$752$		−	6.75256i		−	0.246240i
$753$	−0.393174	−	1.30315i	−0.0143281	−	0.0474895i
$754$	−22.4044	+	38.8056i	−0.815921	+	1.41322i
$755$	8.28939	−	14.3576i	0.301682	−	0.522528i
$756$	−2.23806	+	13.1864i	−0.0813974	+	0.479584i
$757$	15.7629	+	9.10072i	0.572913	+	0.330771i	0.758312	−	0.651892i	$-0.226024\pi$
$757$	15.7629	+	9.10072i	0.572913	+	0.330771i	−0.185399	+	0.982663i	$0.559358\pi$
$758$	17.1608	−	9.90778i	0.623308	−	0.359867i
$759$	18.4679	−	19.6588i	0.670343	−	0.713570i
$760$	0.529528			0.0192080
$761$	18.2034	+	31.5292i	0.659873	+	1.14293i	0.980648	+	0.195778i	$0.0627232\pi$
$761$	18.2034	+	31.5292i	0.659873	+	1.14293i	−0.320775	+	0.947155i	$0.603943\pi$
$762$	7.80045	+	25.8541i	0.282581	+	0.936596i
$763$	1.73923	+	3.01244i	0.0629645	+	0.109058i
$764$	4.31841	+	2.49324i	0.156235	+	0.0902022i
$765$	6.92496	−	13.9369i	0.250373	−	0.503891i
$766$	3.42236	+	1.97590i	0.123655	+	0.0713922i
$767$	−64.0030			−2.31101
$768$	1.68621	+	0.395836i	0.0608460	+	0.0142835i
$769$	15.0861	+	26.1298i	0.544017	+	0.942265i	0.998668	+	0.0515956i	$0.0164307\pi$
$769$	15.0861	+	26.1298i	0.544017	+	0.942265i	−0.454651	+	0.890670i	$0.650236\pi$
$770$	6.60766	−	11.4448i	0.238124	−	0.412442i
$771$	15.2232	+	14.3010i	0.548251	+	0.515038i
$772$	−8.08463	−	14.0030i	−0.290972	−	0.503979i
$773$	14.9673			0.538336			0.269168	−	0.963093i	$-0.413251\pi$
$773$	14.9673			0.538336			0.269168	+	0.963093i	$0.413251\pi$
$774$	−1.44669	−	23.1350i	−0.0520002	−	0.831572i
$775$	−4.37781	+	3.44017i	−0.157256	+	0.123574i
$776$			6.46323i			0.232016i
$777$	−2.17954	−	2.04750i	−0.0781904	−	0.0734537i
$778$	−16.8346	+	9.71945i	−0.603549	+	0.348459i
$779$		−	6.02534i		−	0.215880i
$780$	2.65402	+	8.79659i	0.0950292	+	0.314969i
$781$	43.4002	−	25.0571i	1.55298	−	0.896615i
$782$	13.6266	−	7.86734i	0.487287	−	0.281335i
$783$	33.8025	+	27.9964i	1.20800	+	1.00051i
$784$	0.187231	−	0.324294i	0.00668684	−	0.0115819i
$785$	−12.6880	−	7.32540i	−0.452853	−	0.261455i
$786$	−9.47824	−	31.4151i	−0.338078	−	1.12054i
$787$	−0.227315	+	0.131240i	−0.00810290	+	0.00467821i	−0.504046	−	0.863677i	$-0.668156\pi$
$787$	−0.227315	+	0.131240i	−0.00810290	+	0.00467821i	0.495943	+	0.868355i	$0.334822\pi$
$788$	−4.30925	+	7.46384i	−0.153511	+	0.265888i
$789$	3.45263	+	0.810500i	0.122917	+	0.0288546i
$790$		−	10.1076i		−	0.359613i
$791$			12.1335i			0.431416i
$792$	8.51868	+	12.8322i	0.302698	+	0.455974i
$793$	18.7335	−	32.4473i	0.665245	−	1.15224i
$794$	−20.7332	+	11.9703i	−0.735793	+	0.424810i
$795$	2.72720	−	0.822824i	0.0967239	−	0.0291826i
$796$	−4.91862	−	2.83976i	−0.174336	−	0.100653i
$797$	4.06441	−	7.03976i	0.143969	−	0.249361i	−0.785019	−	0.619472i	$-0.787347\pi$
$797$	4.06441	−	7.03976i	0.143969	−	0.249361i	0.928988	+	0.370111i	$0.120680\pi$
$798$	−1.72064	−	1.61641i	−0.0609101	−	0.0572202i
$799$	30.3360	−	17.5145i	1.07321	−	0.619618i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−40.0052	−	19.8778i	−1.41351	−	0.702346i
$802$		−	20.4973i		−	0.723785i
$803$	16.5073	−	9.53051i	0.582531	−	0.336324i
$804$	−9.44840	+	10.0577i	−0.333219	+	0.354707i
$805$		−	7.80744i		−	0.275176i
$806$	−27.4163	−	10.9875i	−0.965699	−	0.387017i
$807$	32.0379	−	34.1039i	1.12779	−	1.20051i
$808$	−8.88476			−0.312565
$809$	1.67849	+	2.90724i	0.0590127	+	0.102213i	0.894022	−	0.448022i	$-0.147871\pi$
$809$	1.67849	+	2.90724i	0.0590127	+	0.102213i	−0.835010	+	0.550235i	$0.814538\pi$
$810$	8.92989	−	1.12120i	0.313764	−	0.0393949i
$811$	−17.9731	+	31.1303i	−0.631120	+	1.09313i	0.356203	+	0.934409i	$0.384071\pi$
$811$	−17.9731	+	31.1303i	−0.631120	+	1.09313i	−0.987323	+	0.158724i	$0.949262\pi$
$812$	10.8711	+	18.8293i	0.381500	+	0.660777i
$813$	1.25851	−	5.36111i	0.0441380	−	0.188022i
$814$	−3.44373			−0.120703
$815$	−19.4660	−	11.2387i	−0.681863	−	0.393674i
$816$	2.59533	+	8.60205i	0.0908546	+	0.301132i
$817$	3.54336	+	2.04576i	0.123967	+	0.0715722i
$818$	4.38047	+	7.58719i	0.153160	+	0.265280i
$819$	18.2281	−	36.6851i	0.636940	−	1.28188i
$820$	5.68936	+	9.85425i	0.198681	+	0.344125i
$821$	−21.8066			−0.761056			−0.380528	−	0.924769i	$-0.624258\pi$
$821$	−21.8066			−0.761056			−0.380528	+	0.924769i	$0.624258\pi$
$822$	7.54669	+	7.08951i	0.263221	+	0.247275i
$823$	18.4662	−	10.6615i	0.643692	−	0.371636i	−0.142343	−	0.989817i	$-0.545464\pi$
$823$	18.4662	−	10.6615i	0.643692	−	0.371636i	0.786035	+	0.618181i	$0.212130\pi$
$824$	9.11135	+	5.26044i	0.317409	+	0.183256i
$825$	−8.65725	−	2.03228i	−0.301407	−	0.0707548i
$826$	−15.5278	+	26.8949i	−0.540280	+	0.935792i
$827$	−12.4338	+	21.5359i	−0.432364	+	0.748877i	−0.997076	−	0.0764112i	$-0.975654\pi$
$827$	−12.4338	+	21.5359i	−0.432364	+	0.748877i	0.564712	+	0.825288i	$0.308987\pi$
$828$	8.14902	+	4.04908i	0.283198	+	0.140715i
$829$			1.77571i			0.0616728i	0.999524	+	0.0308364i	$0.00981709\pi$
$829$			1.77571i			0.0616728i	−0.999524	+	0.0308364i	$0.990183\pi$
$830$	−3.97145	−	6.87875i	−0.137851	−	0.238765i
$831$	6.54821	−	27.8945i	0.227155	−	0.967651i
$832$	−4.59412	−	2.65242i	−0.159273	−	0.0919560i
$833$	1.94253			0.0673047
$834$	34.7362	+	8.15428i	1.20282	+	0.282360i
$835$		−	16.4265i		−	0.568464i
$836$	−2.71867			−0.0940270
$837$	−15.1042	+	24.6751i	−0.522079	+	0.852897i
$838$	−17.8444			−0.616423
$839$			2.30549i			0.0795945i	0.999208	+	0.0397973i	$0.0126712\pi$
$839$			2.30549i			0.0795945i	−0.999208	+	0.0397973i	$0.987329\pi$
$840$	4.34033	+	1.01889i	0.149756	+	0.0351550i
$841$	42.3483			1.46029
$842$	−14.3028	−	8.25775i	−0.492909	−	0.284581i
$843$	0.614886	−	2.61934i	0.0211778	−	0.0902148i
$844$	−0.695561	−	1.20475i	−0.0239422	−	0.0414691i
$845$		−	15.1413i		−	0.520876i
$846$	18.1416	+	9.01418i	0.623721	+	0.309914i
$847$	−19.7676	+	34.2385i	−0.679222	+	1.17645i
$848$	−0.822328	+	1.42431i	−0.0282388	+	0.0489111i
$849$	−5.11128	−	1.19987i	−0.175419	−	0.0411793i
$850$	−4.49252	−	2.59376i	−0.154092	−	0.0889652i
$851$	−1.76194	+	1.01726i	−0.0603985	+	0.0348711i
$852$	12.3221	+	11.5757i	0.422149	+	0.396576i
$853$	−28.9723			−0.991991			−0.495996	−	0.868325i	$-0.665197\pi$
$853$	−28.9723			−0.991991			−0.495996	+	0.868325i	$0.665197\pi$
$854$	−9.08985	−	15.7441i	−0.311048	−	0.538751i
$855$	−0.706882	+	1.42264i	−0.0241748	+	0.0486534i
$856$	−6.47185	−	11.2096i	−0.221203	−	0.383135i
$857$	−3.20393	−	1.84979i	−0.109444	−	0.0631877i	0.444279	−	0.895889i	$-0.353460\pi$
$857$	−3.20393	−	1.84979i	−0.109444	−	0.0631877i	−0.553723	+	0.832701i	$0.686793\pi$
$858$	−13.6261	−	45.1629i	−0.465187	−	1.54184i
$859$	−37.3943	−	21.5896i	−1.27588	−	0.736629i	−0.299791	−	0.954005i	$-0.596917\pi$
$859$	−37.3943	−	21.5896i	−1.27588	−	0.736629i	−0.976088	+	0.217376i	$0.930250\pi$
$860$	−7.72674			−0.263480
$861$	11.5936	−	49.3874i	0.395110	−	1.68312i
$862$	6.18908	+	10.7198i	0.210801	+	0.365118i
$863$	7.65540	−	13.2595i	0.260593	−	0.451360i	−0.705807	−	0.708405i	$-0.749415\pi$
$863$	7.65540	−	13.2595i	0.260593	−	0.451360i	0.966400	+	0.257044i	$0.0827486\pi$
$864$	−3.31444	+	4.00181i	−0.112759	+	0.136144i
$865$	−1.45412	−	2.51861i	−0.0494415	−	0.0856351i
$866$	−1.18613			−0.0403063
$867$	−11.7528	+	12.5107i	−0.399145	+	0.424884i
$868$	−11.2685	+	8.85503i	−0.382479	+	0.300559i
$869$			51.8939i			1.76038i
$870$	10.0171	−	10.6631i	0.339613	−	0.361513i
$871$	36.6023	−	21.1324i	1.24022	−	0.716043i
$872$			1.35138i			0.0457635i
$873$	−17.3643	−	8.62795i	−0.587692	−	0.292012i
$874$	−1.39097	+	0.803076i	−0.0470502	+	0.0271645i
$875$	−2.22916	+	1.28701i	−0.0753594	+	0.0435087i
$876$	4.68674	+	4.40282i	0.158350	+	0.148757i
$877$	−19.7173	+	34.1513i	−0.665805	+	1.15321i	0.313262	+	0.949667i	$0.398578\pi$
$877$	−19.7173	+	34.1513i	−0.665805	+	1.15321i	−0.979066	+	0.203541i	$0.934755\pi$
$878$	14.2541	+	8.22962i	0.481053	+	0.277736i
$879$	12.9055	−	3.89373i	0.435293	−	0.131332i
$880$	4.44629	−	2.56707i	0.149884	−	0.0865358i
$881$	−9.28944	+	16.0898i	−0.312969	+	0.542079i	−0.979004	−	0.203842i	$-0.934657\pi$
$881$	−9.28944	+	16.0898i	−0.312969	+	0.542079i	0.666035	+	0.745921i	$0.267990\pi$
$882$	0.621317	+	0.935931i	0.0209208	+	0.0315144i
$883$		−	17.4530i		−	0.587339i	−0.955907	−	0.293669i	$-0.905123\pi$
$883$		−	17.4530i		−	0.587339i	0.955907	−	0.293669i	$-0.0948765\pi$
$884$		−	27.5189i		−	0.925562i
$885$	20.3442	+	4.77578i	0.683863	+	0.160536i
$886$	−12.0992	+	20.9565i	−0.406481	+	0.704046i
$887$	43.3396	−	25.0221i	1.45520	−	0.840161i	0.456433	−	0.889758i	$-0.349127\pi$
$887$	43.3396	−	25.0221i	1.45520	−	0.840161i	0.998769	+	0.0495968i	$0.0157936\pi$
$888$	−0.335578	−	1.11225i	−0.0112613	−	0.0373248i
$889$	−34.7559	−	20.0663i	−1.16568	−	0.673003i
$890$	−7.44525	+	12.8955i	−0.249565	+	0.432260i
$891$	−45.8473	+	5.75638i	−1.53594	+	0.192846i
$892$	−11.5712	+	6.68062i	−0.387432	+	0.223684i
$893$	−3.09662	+	1.78783i	−0.103624	+	0.0598275i
$894$	−12.0693	−	40.0030i	−0.403658	−	1.33790i
$895$		−	5.71652i		−	0.191082i
$896$	−2.22916	+	1.28701i	−0.0744710	+	0.0429959i
$897$	−20.3124	−	19.0819i	−0.678212	−	0.637127i
$898$		−	32.2944i		−	1.07768i
$899$	6.67604	+	46.5535i	0.222658	+	1.55265i
$900$	−0.187231	−	2.99415i	−0.00624105	−	0.0998051i
$901$	−8.53168			−0.284231
$902$	−29.2099	−	50.5931i	−0.972584	−	1.68457i
$903$	25.1072	+	23.5863i	0.835516	+	0.784902i
$904$	−2.35692	+	4.08230i	−0.0783899	+	0.135775i
$905$	7.65134	+	13.2525i	0.254339	+	0.440528i
$906$	−27.9553	−	6.56248i	−0.928754	−	0.218024i
$907$	10.6428			0.353387			0.176693	−	0.984266i	$-0.443460\pi$
$907$	10.6428			0.353387			0.176693	+	0.984266i	$0.443460\pi$
$908$	13.4583	+	7.77017i	0.446630	+	0.257862i
$909$	11.8605	−	23.8700i	0.393389	−	0.791720i
$910$	−11.8253	−	6.82736i	−0.392006	−	0.226325i
$911$	−0.881044	−	1.52601i	−0.0291903	−	0.0505591i	0.851061	−	0.525066i	$-0.175960\pi$
$911$	−0.881044	−	1.52601i	−0.0291903	−	0.0505591i	−0.880252	+	0.474507i	$0.842626\pi$
$912$	−0.264924	−	0.878074i	−0.00877250	−	0.0290759i
$913$	20.3900	+	35.3165i	0.674809	+	1.16880i
$914$	19.0886			0.631396
$915$	−8.37583	+	8.91595i	−0.276897	+	0.294752i
$916$	−12.6066	+	7.27845i	−0.416535	+	0.240487i
$917$	42.2315	+	24.3824i	1.39461	+	0.805177i
$918$	−26.5751	−	4.51045i	−0.877108	−	0.148867i
$919$	3.39521	−	5.88068i	0.111998	−	0.193986i	−0.804578	−	0.593847i	$-0.797608\pi$
$919$	3.39521	−	5.88068i	0.111998	−	0.193986i	0.916576	+	0.399861i	$0.130942\pi$
$920$	1.51659	−	2.62681i	0.0500005	−	0.0866034i
$921$	−5.72303	−	18.9686i	−0.188580	−	0.625038i
$922$		−	12.8115i		−	0.421924i
$923$	−25.8902	−	44.8432i	−0.852187	−	1.47603i
$924$	−22.2839	−	5.23111i	−0.733085	−	0.172091i
$925$	0.580888	+	0.335376i	0.0190995	+	0.0110271i
$926$	−20.6891			−0.679885
$927$	−26.2958	+	17.4565i	−0.863669	+	0.573346i
$928$			8.44680i			0.277280i
$929$	59.0112			1.93610			0.968048	−	0.250766i	$-0.0806824\pi$
$929$	59.0112			1.93610			0.968048	+	0.250766i	$0.0806824\pi$
$930$	7.89479	+	5.53826i	0.258880	+	0.181607i
$931$	−0.198288			−0.00649864
$932$			2.89624i			0.0948694i
$933$	−2.86089	+	12.1870i	−0.0936612	+	0.398985i
$934$	23.8528			0.780489
$935$	23.0652	+	13.3167i	0.754313	+	0.435503i
$936$	13.2589	−	8.80191i	0.433380	−	0.287699i
$937$	1.34945	+	2.33732i	0.0440847	+	0.0763569i	0.887226	−	0.461335i	$-0.152630\pi$
$937$	1.34945	+	2.33732i	0.0440847	+	0.0763569i	−0.843141	+	0.537692i	$0.819296\pi$
$938$		−	20.5077i		−	0.669600i
$939$	21.5680	−	6.50727i	0.703844	−	0.212357i
$940$	3.37628	−	5.84788i	0.110122	−	0.190737i
$941$	−4.89303	+	8.47498i	−0.159508	+	0.276276i	−0.934691	−	0.355460i	$-0.884324\pi$
$941$	−4.89303	+	8.47498i	−0.159508	+	0.276276i	0.775183	+	0.631737i	$0.217658\pi$
$942$	−5.79932	+	24.7044i	−0.188952	+	0.804912i
$943$	−29.8897	−	17.2568i	−0.973343	−	0.561960i
$944$	−10.4486	+	6.03251i	−0.340074	+	0.196342i
$945$	−8.53140	+	10.3007i	−0.277527	+	0.335082i
$946$	39.6702			1.28979
$947$	−16.6868	−	28.9023i	−0.542247	−	0.939199i	−0.998775	−	0.0494896i	$-0.984241\pi$
$947$	−16.6868	−	28.9023i	−0.542247	−	0.939199i	0.456528	−	0.889709i	$-0.349093\pi$
$948$	−16.7607	+	5.05686i	−0.544361	+	0.164239i
$949$	−9.84738	−	17.0562i	−0.319659	−	0.553666i
$950$	0.458584	+	0.264764i	0.0148784	+	0.00859007i
$951$	37.7452	−	11.3881i	1.22397	−	0.369284i
$952$	−11.5638	−	6.67636i	−0.374785	−	0.216382i
$953$	12.6811			0.410781			0.205391	−	0.978680i	$-0.434153\pi$
$953$	12.6811			0.410781			0.205391	+	0.978680i	$0.434153\pi$
$954$	−2.72885	−	4.11064i	−0.0883498	−	0.133087i
$955$	2.49324	+	4.31841i	0.0806793	+	0.139741i
$956$	−2.74446	+	4.75354i	−0.0887622	+	0.153741i
$957$	−51.4294	+	54.7458i	−1.66248	+	1.76968i
$958$	1.51286	+	2.62035i	0.0488783	+	0.0846596i
$959$	−15.3877			−0.496896
$960$	1.26238	+	1.18591i	0.0407433	+	0.0382751i
$961$	−29.7507	+	8.71199i	−0.959698	+	0.281032i
$962$			3.55823i			0.114722i
$963$	38.7554	−	2.42347i	1.24888	−	0.0780951i
$964$	4.61436	−	2.66410i	0.148619	−	0.0858050i
$965$		−	16.1693i		−	0.520507i
$966$	−12.9465	+	3.90608i	−0.416546	+	0.125676i
$967$	33.0932	−	19.1063i	1.06420	−	0.614419i	0.137612	−	0.990486i	$-0.456057\pi$
$967$	33.0932	−	19.1063i	1.06420	−	0.614419i	0.926592	+	0.376068i	$0.122724\pi$
$968$	−13.3016	+	7.67968i	−0.427529	+	0.246834i
$969$	3.25762	−	3.46769i	0.104650	−	0.111398i
$970$	−3.23162	+	5.59732i	−0.103761	+	0.179719i
$971$	6.71435	+	3.87653i	0.215474	+	0.124404i	0.603853	−	0.797096i	$-0.293632\pi$
$971$	6.71435	+	3.87653i	0.215474	+	0.124404i	−0.388379	+	0.921500i	$0.626965\pi$
$972$	−6.32684	−	14.2468i	−0.202933	−	0.456966i
$973$	−45.9210	+	26.5125i	−1.47216	+	0.849951i
$974$	19.0958	−	33.0749i	0.611869	−	1.05979i
$975$	−2.09985	+	8.94508i	−0.0672489	+	0.286472i
$976$		−	7.06279i		−	0.226074i
$977$		−	45.6238i		−	1.45963i	−0.683643	−	0.729817i	$-0.739605\pi$
$977$		−	45.6238i		−	1.45963i	0.683643	−	0.729817i	$-0.260395\pi$
$978$	−8.89736	+	37.9016i	−0.284506	+	1.21196i
$979$	38.2249	−	66.2075i	1.22167	−	2.11600i
$980$	0.324294	−	0.187231i	0.0103592	−	0.00598089i
$981$	−3.63065	−	1.80399i	−0.115918	−	0.0575971i
$982$	22.0394	+	12.7244i	0.703304	+	0.406053i
$983$	1.48950	−	2.57989i	0.0475077	−	0.0822858i	−0.841294	−	0.540578i	$-0.818205\pi$
$983$	1.48950	−	2.57989i	0.0475077	−	0.0822858i	0.888801	+	0.458293i	$0.151539\pi$
$984$	13.4941	−	14.3643i	0.430177	−	0.457918i
$985$	−7.46384	+	4.30925i	−0.237818	+	0.137304i
$986$	−37.9474	+	21.9089i	−1.20849	+	0.697723i
$987$	−28.8218	+	8.69583i	−0.917408	+	0.276791i
$988$			2.80906i			0.0893680i
$989$	20.2967	−	11.7183i	0.645398	−	0.372620i
$990$	0.961271	+	15.3724i	0.0305512	+	0.488566i
$991$			3.63959i			0.115615i	0.998328	+	0.0578077i	$0.0184110\pi$
$991$			3.63959i			0.115615i	−0.998328	+	0.0578077i	$0.981589\pi$
$992$	−5.51138	+	0.790363i	−0.174987	+	0.0250941i
$993$	6.19546	+	5.82014i	0.196607	+	0.184697i
$994$	−25.1249			−0.796914
$995$	−2.83976	−	4.91862i	−0.0900266	−	0.155931i
$996$	−9.41957	+	10.0270i	−0.298471	+	0.317718i
$997$	−23.0520	+	39.9272i	−0.730064	+	1.26451i	0.226792	+	0.973943i	$0.427176\pi$
$997$	−23.0520	+	39.9272i	−0.730064	+	1.26451i	−0.956855	+	0.290564i	$0.906157\pi$
$998$	−4.13656	−	7.16472i	−0.130940	−	0.226795i
$999$	3.43619	+	0.583207i	0.108716	+	0.0184518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.20	yes	40
3.2	odd	2	inner	930.2.o.e.161.7	✓	40
31.26	odd	6	inner	930.2.o.e.491.17	yes	40
93.26	even	6	inner	930.2.o.e.491.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.7	✓	40	3.2	odd	2	inner
930.2.o.e.161.20	yes	40	1.1	even	1	trivial
930.2.o.e.491.10	yes	40	93.26	even	6	inner
930.2.o.e.491.17	yes	40	31.26	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.68621 + 0.395836i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.395836 + 1.68621i) q^{6} +(-1.28701 - 2.22916i) q^{7} -1.00000i q^{8} +(2.68663 + 1.33493i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.68621 + 0.395836i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.395836 + 1.68621i) q^{6} +(-1.28701 - 2.22916i) q^{7} -1.00000i q^{8} +(2.68663 + 1.33493i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.56707 + 4.44629i) q^{11} +(-1.68621 - 0.395836i) q^{12} +(4.59412 + 2.65242i) q^{13} +(2.22916 - 1.28701i) q^{14} +(-1.26238 - 1.18591i) q^{15} +1.00000 q^{16} +(2.59376 + 4.49252i) q^{17} +(-1.33493 + 2.68663i) q^{18} +(-0.264764 - 0.458584i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.28778 - 4.26828i) q^{21} +(-4.44629 - 2.56707i) q^{22} -3.03318 q^{23} +(0.395836 - 1.68621i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.65242 + 4.59412i) q^{26} +(4.00181 + 3.31444i) q^{27} +(1.28701 + 2.22916i) q^{28} +8.44680 q^{29} +(1.18591 - 1.26238i) q^{30} +(0.790363 + 5.51138i) q^{31} +1.00000i q^{32} +(-6.08863 + 6.48126i) q^{33} +(-4.49252 + 2.59376i) q^{34} +2.57401i q^{35} +(-2.68663 - 1.33493i) q^{36} +(0.580888 - 0.335376i) q^{37} +(0.458584 - 0.264764i) q^{38} +(6.69674 + 6.29106i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(9.85425 + 5.68936i) q^{41} +(4.26828 - 1.28778i) q^{42} +(-6.69156 + 3.86337i) q^{43} +(2.56707 - 4.44629i) q^{44} +(-1.65922 - 2.49940i) q^{45} -3.03318i q^{46} -6.75256i q^{47} +(1.68621 + 0.395836i) q^{48} +(0.187231 - 0.324294i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(2.59533 + 8.60205i) q^{51} +(-4.59412 - 2.65242i) q^{52} +(-0.822328 + 1.42431i) q^{53} +(-3.31444 + 4.00181i) q^{54} +(4.44629 - 2.56707i) q^{55} +(-2.22916 + 1.28701i) q^{56} +(-0.264924 - 0.878074i) q^{57} +8.44680i q^{58} +(-10.4486 + 6.03251i) q^{59} +(1.26238 + 1.18591i) q^{60} -7.06279i q^{61} +(-5.51138 + 0.790363i) q^{62} +(-0.481936 - 7.70698i) q^{63} -1.00000 q^{64} +(-2.65242 - 4.59412i) q^{65} +(-6.48126 - 6.08863i) q^{66} +(3.98360 - 6.89980i) q^{67} +(-2.59376 - 4.49252i) q^{68} +(-5.11459 - 1.20064i) q^{69} -2.57401 q^{70} +(-8.45327 - 4.88050i) q^{71} +(1.33493 - 2.68663i) q^{72} +(-3.21521 - 1.85630i) q^{73} +(0.335376 + 0.580888i) q^{74} +(0.500302 + 1.65822i) q^{75} +(0.264764 + 0.458584i) q^{76} +13.2153 q^{77} +(-6.29106 + 6.69674i) q^{78} +(8.75345 - 5.05381i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.43593 + 7.17291i) q^{81} +(-5.68936 + 9.85425i) q^{82} +(3.97145 - 6.87875i) q^{83} +(1.28778 + 4.26828i) q^{84} -5.18752i q^{85} +(-3.86337 - 6.69156i) q^{86} +(14.2431 + 3.34355i) q^{87} +(4.44629 + 2.56707i) q^{88} -14.8905 q^{89} +(2.49940 - 1.65922i) q^{90} -13.6547i q^{91} +3.03318 q^{92} +(-0.848884 + 9.60622i) q^{93} +6.75256 q^{94} +0.529528i q^{95} +(-0.395836 + 1.68621i) q^{96} -6.46323 q^{97} +(0.324294 + 0.187231i) q^{98} +(-12.8322 + 8.51868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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