LMFDB - Embedded newform 90.3.k.a.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,3,Mod(7,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("90.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	90.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	90.67
Dual form			90.3.k.a.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(2.78364 - 1.11865i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.80008 - 1.39971i) q^{5} +(-0.509217 - 4.21197i) q^{6} +(2.39851 - 8.95134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.49726 - 6.22781i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(2.78364 - 1.11865i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.80008 - 1.39971i) q^{5} +(-0.509217 - 4.21197i) q^{6} +(2.39851 - 8.95134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.49726 - 6.22781i) q^{9} +(-3.66899 + 6.04471i) q^{10} +(10.5150 + 18.2126i) q^{11} +(-5.94005 - 0.846085i) q^{12} +(-1.42873 - 5.33210i) q^{13} +(-11.3498 - 6.55284i) q^{14} +(-14.9275 + 1.47332i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.93855 + 2.93855i) q^{17} +(-6.12918 - 11.1550i) q^{18} +9.36376i q^{19} +(6.91428 + 7.22445i) q^{20} +(-3.33682 - 27.6004i) q^{21} +(28.7276 - 7.69753i) q^{22} +(3.43617 + 12.8240i) q^{23} +(-3.32998 + 7.80456i) q^{24} +(21.0816 + 13.4374i) q^{25} -7.80674 q^{26} +(11.1193 - 24.6041i) q^{27} +(-13.1057 + 13.1057i) q^{28} +(-42.4981 + 24.5363i) q^{29} +(-3.45125 + 20.9306i) q^{30} +(9.65636 - 16.7253i) q^{31} +(5.46410 - 1.46410i) q^{32} +(49.6434 + 38.9345i) q^{33} +(5.08973 - 2.93855i) q^{34} +(-24.0423 + 39.6100i) q^{35} +(-17.4814 + 4.28961i) q^{36} +(36.5256 + 36.5256i) q^{37} +(12.7911 + 3.42738i) q^{38} +(-9.94181 - 13.2444i) q^{39} +(12.3996 - 6.80075i) q^{40} +(12.1362 - 21.0205i) q^{41} +(-38.9242 - 5.54426i) q^{42} +(-23.1645 - 6.20691i) q^{43} -42.0601i q^{44} +(-39.9045 + 20.7997i) q^{45} +18.7756 q^{46} +(6.12087 - 22.8434i) q^{47} +(9.44238 + 7.40551i) q^{48} +(-31.9385 - 18.4397i) q^{49} +(26.0723 - 23.8796i) q^{50} +(11.4671 + 4.89267i) q^{51} +(-2.85746 + 10.6642i) q^{52} +(26.0581 - 26.0581i) q^{53} +(-29.5399 - 24.1950i) q^{54} +(-24.9807 - 102.140i) q^{55} +(13.1057 + 22.6997i) q^{56} +(10.4747 + 26.0653i) q^{57} +(17.9618 + 67.0344i) q^{58} +(-51.9031 - 29.9663i) q^{59} +(27.3285 + 12.3756i) q^{60} +(-10.7005 - 18.5338i) q^{61} +(-19.3127 - 19.3127i) q^{62} +(-40.1635 - 73.0967i) q^{63} -8.00000i q^{64} +(-0.605352 + 27.5944i) q^{65} +(71.3563 - 53.5631i) q^{66} +(-81.3506 + 21.7978i) q^{67} +(-2.15117 - 8.02828i) q^{68} +(23.9105 + 31.8534i) q^{69} +(45.3082 + 47.3407i) q^{70} -130.133 q^{71} +(-0.538913 + 25.4501i) q^{72} +(-34.8091 + 34.8091i) q^{73} +(63.2642 - 36.5256i) q^{74} +(73.7153 + 13.8221i) q^{75} +(9.36376 - 16.2185i) q^{76} +(188.247 - 50.4407i) q^{77} +(-21.7311 + 8.73298i) q^{78} +(20.3592 - 11.7544i) q^{79} +(-4.75144 - 19.4274i) q^{80} +(3.42885 - 80.9274i) q^{81} +(-24.2724 - 24.2724i) q^{82} +(56.9883 + 15.2700i) q^{83} +(-21.8208 + 51.1421i) q^{84} +(-9.99219 - 18.2184i) q^{85} +(-16.9576 + 29.3714i) q^{86} +(-90.8519 + 115.841i) q^{87} +(-57.4552 - 15.3951i) q^{88} +75.6878i q^{89} +(13.8069 + 62.1238i) q^{90} -51.1563 q^{91} +(6.87234 - 25.6479i) q^{92} +(8.17010 - 57.3592i) q^{93} +(-28.9642 - 16.7225i) q^{94} +(13.1065 - 44.9469i) q^{95} +(13.5723 - 10.1879i) q^{96} +(-9.61362 + 35.8785i) q^{97} +(-36.8794 + 36.8794i) q^{98} +(181.743 + 52.8462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 6 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 6 * q^7 - 48 * q^8	$ 24 q - 12 q^{2} - 6 q^{7} - 48 q^{8} - 12 q^{10} - 12 q^{11} + 42 q^{15} + 48 q^{16} - 36 q^{17} - 12 q^{18} + 12 q^{20} + 96 q^{21} - 12 q^{22} - 54 q^{23} + 54 q^{25} + 162 q^{27} - 24 q^{28} - 48 q^{30} - 72 q^{31} + 48 q^{32} + 6 q^{33} - 336 q^{35} - 72 q^{36} + 132 q^{37} - 36 q^{38} + 12 q^{40} + 24 q^{41} - 144 q^{42} + 108 q^{43} - 186 q^{45} + 216 q^{46} + 48 q^{47} + 54 q^{50} + 108 q^{51} + 384 q^{53} - 552 q^{55} + 24 q^{56} + 186 q^{57} + 60 q^{58} + 144 q^{60} - 456 q^{61} + 144 q^{62} + 72 q^{63} + 264 q^{65} + 240 q^{66} + 12 q^{67} - 36 q^{68} + 174 q^{70} - 168 q^{71} + 96 q^{72} - 432 q^{73} - 468 q^{75} - 72 q^{76} - 48 q^{77} - 264 q^{78} - 480 q^{81} - 48 q^{82} - 246 q^{83} + 324 q^{85} + 216 q^{86} - 636 q^{87} + 24 q^{88} - 12 q^{90} + 1224 q^{91} - 108 q^{92} + 180 q^{93} + 432 q^{95} - 102 q^{97} + 24 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 6 * q^7 - 48 * q^8 - 12 * q^10 - 12 * q^11 + 42 * q^15 + 48 * q^16 - 36 * q^17 - 12 * q^18 + 12 * q^20 + 96 * q^21 - 12 * q^22 - 54 * q^23 + 54 * q^25 + 162 * q^27 - 24 * q^28 - 48 * q^30 - 72 * q^31 + 48 * q^32 + 6 * q^33 - 336 * q^35 - 72 * q^36 + 132 * q^37 - 36 * q^38 + 12 * q^40 + 24 * q^41 - 144 * q^42 + 108 * q^43 - 186 * q^45 + 216 * q^46 + 48 * q^47 + 54 * q^50 + 108 * q^51 + 384 * q^53 - 552 * q^55 + 24 * q^56 + 186 * q^57 + 60 * q^58 + 144 * q^60 - 456 * q^61 + 144 * q^62 + 72 * q^63 + 264 * q^65 + 240 * q^66 + 12 * q^67 - 36 * q^68 + 174 * q^70 - 168 * q^71 + 96 * q^72 - 432 * q^73 - 468 * q^75 - 72 * q^76 - 48 * q^77 - 264 * q^78 - 480 * q^81 - 48 * q^82 - 246 * q^83 + 324 * q^85 + 216 * q^86 - 636 * q^87 + 24 * q^88 - 12 * q^90 + 1224 * q^91 - 108 * q^92 + 180 * q^93 + 432 * q^95 - 102 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	2.78364	−	1.11865i	0.927879	−	0.372882i
$3$	2.78364	−	1.11865i	0.927879	−	0.372882i
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	−4.80008	−	1.39971i	−0.960017	−	0.279942i
$5$	−4.80008	−	1.39971i	−0.960017	−	0.279942i
$6$	−0.509217	−	4.21197i	−0.0848695	−	0.701995i
$7$	2.39851	−	8.95134i	0.342644	−	1.27876i	−0.552697	−	0.833382i	$-0.686401\pi$
$7$	2.39851	−	8.95134i	0.342644	−	1.27876i	0.895341	−	0.445381i	$-0.146932\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	6.49726	−	6.22781i	0.721918	−	0.691978i
$10$	−3.66899	+	6.04471i	−0.366899	+	0.604471i
$11$	10.5150	+	18.2126i	0.955911	+	1.65569i	0.732269	+	0.681016i	$0.238461\pi$
$11$	10.5150	+	18.2126i	0.955911	+	1.65569i	0.223642	+	0.974671i	$0.428205\pi$
$12$	−5.94005	−	0.846085i	−0.495004	−	0.0705071i
$13$	−1.42873	−	5.33210i	−0.109902	−	0.410162i	0.888953	−	0.457999i	$-0.151434\pi$
$13$	−1.42873	−	5.33210i	−0.109902	−	0.410162i	−0.998855	+	0.0478374i	$0.984767\pi$
$14$	−11.3498	−	6.55284i	−0.810704	−	0.468060i
$15$	−14.9275	+	1.47332i	−0.995165	+	0.0982210i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	2.93855	+	2.93855i	0.172856	+	0.172856i	0.788233	−	0.615377i	$-0.210996\pi$
$17$	2.93855	+	2.93855i	0.172856	+	0.172856i	−0.615377	+	0.788233i	$0.710996\pi$
$18$	−6.12918	−	11.1550i	−0.340510	−	0.619720i
$19$			9.36376i			0.492830i	0.969164	+	0.246415i	$0.0792526\pi$
$19$			9.36376i			0.492830i	−0.969164	+	0.246415i	$0.920747\pi$
$20$	6.91428	+	7.22445i	0.345714	+	0.361223i
$21$	−3.33682	−	27.6004i	−0.158896	−	1.31430i
$22$	28.7276	−	7.69753i	1.30580	−	0.349888i
$23$	3.43617	+	12.8240i	0.149399	+	0.557564i	0.999520	+	0.0309768i	$0.00986180\pi$
$23$	3.43617	+	12.8240i	0.149399	+	0.557564i	−0.850121	+	0.526587i	$0.823472\pi$
$24$	−3.32998	+	7.80456i	−0.138749	+	0.325190i
$25$	21.0816	+	13.4374i	0.843265	+	0.537498i
$26$	−7.80674			−0.300259
$27$	11.1193	−	24.6041i	0.411826	−	0.911262i
$28$	−13.1057	+	13.1057i	−0.468060	+	0.468060i
$29$	−42.4981	+	24.5363i	−1.46545	+	0.846080i	−0.999255	−	0.0386006i	$-0.987710\pi$
$29$	−42.4981	+	24.5363i	−1.46545	+	0.846080i	−0.466198	+	0.884680i	$0.654377\pi$
$30$	−3.45125	+	20.9306i	−0.115042	+	0.697686i
$31$	9.65636	−	16.7253i	0.311496	−	0.539526i	−0.667191	−	0.744887i	$-0.732503\pi$
$31$	9.65636	−	16.7253i	0.311496	−	0.539526i	0.978686	+	0.205361i	$0.0658367\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	49.6434	+	38.9345i	1.50435	+	1.17983i
$34$	5.08973	−	2.93855i	0.149698	−	0.0864281i
$35$	−24.0423	+	39.6100i	−0.686923	+	1.13171i
$36$	−17.4814	+	4.28961i	−0.485594	+	0.119156i
$37$	36.5256	+	36.5256i	0.987179	+	0.987179i	0.999919	−	0.0127397i	$-0.00405528\pi$
$37$	36.5256	+	36.5256i	0.987179	+	0.987179i	−0.0127397	+	0.999919i	$0.504055\pi$
$38$	12.7911	+	3.42738i	0.336609	+	0.0901941i
$39$	−9.94181	−	13.2444i	−0.254918	−	0.339600i
$40$	12.3996	−	6.80075i	0.309990	−	0.170019i
$41$	12.1362	−	21.0205i	0.296005	−	0.512696i	−0.679213	−	0.733941i	$-0.737679\pi$
$41$	12.1362	−	21.0205i	0.296005	−	0.512696i	0.975218	+	0.221245i	$0.0710120\pi$
$42$	−38.9242	−	5.54426i	−0.926766	−	0.132006i
$43$	−23.1645	−	6.20691i	−0.538710	−	0.144347i	−0.0208024	−	0.999784i	$-0.506622\pi$
$43$	−23.1645	−	6.20691i	−0.538710	−	0.144347i	−0.517907	+	0.855437i	$0.673289\pi$
$44$		−	42.0601i		−	0.955911i
$45$	−39.9045	+	20.7997i	−0.886767	+	0.462216i
$46$	18.7756			0.408165
$47$	6.12087	−	22.8434i	0.130231	−	0.486029i	−0.869741	−	0.493509i	$-0.835714\pi$
$47$	6.12087	−	22.8434i	0.130231	−	0.486029i	0.999972	+	0.00747935i	$0.00238077\pi$
$48$	9.44238	+	7.40551i	0.196716	+	0.154281i
$49$	−31.9385	−	18.4397i	−0.651806	−	0.376320i
$50$	26.0723	−	23.8796i	0.521446	−	0.477592i
$51$	11.4671	+	4.89267i	0.224845	+	0.0959346i
$52$	−2.85746	+	10.6642i	−0.0549512	+	0.205081i
$53$	26.0581	−	26.0581i	0.491663	−	0.491663i	−0.417167	−	0.908830i	$-0.636977\pi$
$53$	26.0581	−	26.0581i	0.491663	−	0.491663i	0.908830	+	0.417167i	$0.136977\pi$
$54$	−29.5399	−	24.1950i	−0.547034	−	0.448055i
$55$	−24.9807	−	102.140i	−0.454195	−	1.85709i
$56$	13.1057	+	22.6997i	0.234030	+	0.405352i
$57$	10.4747	+	26.0653i	0.183767	+	0.457286i
$58$	17.9618	+	67.0344i	0.309687	+	1.15577i
$59$	−51.9031	−	29.9663i	−0.879714	−	0.507903i	−0.00914957	−	0.999958i	$-0.502912\pi$
$59$	−51.9031	−	29.9663i	−0.879714	−	0.507903i	−0.870564	+	0.492055i	$0.836246\pi$
$60$	27.3285	+	12.3756i	0.455474	+	0.206260i
$61$	−10.7005	−	18.5338i	−0.175418	−	0.303833i	0.764888	−	0.644163i	$-0.222794\pi$
$61$	−10.7005	−	18.5338i	−0.175418	−	0.303833i	−0.940306	+	0.340331i	$0.889461\pi$
$62$	−19.3127	−	19.3127i	−0.311496	−	0.311496i
$63$	−40.1635	−	73.0967i	−0.637516	−	1.16026i
$64$		−	8.00000i		−	0.125000i
$65$	−0.605352	+	27.5944i	−0.00931310	+	0.424528i
$66$	71.3563	−	53.5631i	1.08116	−	0.811562i
$67$	−81.3506	+	21.7978i	−1.21419	+	0.325341i	−0.808404	−	0.588628i	$-0.799668\pi$
$67$	−81.3506	+	21.7978i	−1.21419	+	0.325341i	−0.405784	+	0.913969i	$0.633002\pi$
$68$	−2.15117	−	8.02828i	−0.0316349	−	0.118063i
$69$	23.9105	+	31.8534i	0.346529	+	0.461643i
$70$	45.3082	+	47.3407i	0.647260	+	0.676295i
$71$	−130.133			−1.83286			−0.916430	−	0.400195i	$-0.868942\pi$
$71$	−130.133			−1.83286			−0.916430	+	0.400195i	$0.868942\pi$
$72$	−0.538913	+	25.4501i	−0.00748490	+	0.353474i
$73$	−34.8091	+	34.8091i	−0.476838	+	0.476838i	−0.904119	−	0.427281i	$-0.859471\pi$
$73$	−34.8091	+	34.8091i	−0.476838	+	0.476838i	0.427281	+	0.904119i	$0.359471\pi$
$74$	63.2642	−	36.5256i	0.854922	−	0.493590i
$75$	73.7153	+	13.8221i	0.982871	+	0.184294i
$76$	9.36376	−	16.2185i	0.123207	−	0.213402i
$77$	188.247	−	50.4407i	2.44477	−	0.655074i
$78$	−21.7311	+	8.73298i	−0.278604	+	0.111961i
$79$	20.3592	−	11.7544i	0.257712	−	0.148790i	−0.365579	−	0.930781i	$-0.619129\pi$
$79$	20.3592	−	11.7544i	0.257712	−	0.148790i	0.623290	+	0.781991i	$0.285795\pi$
$80$	−4.75144	−	19.4274i	−0.0593930	−	0.242842i
$81$	3.42885	−	80.9274i	0.0423315	−	0.999104i
$82$	−24.2724	−	24.2724i	−0.296005	−	0.296005i
$83$	56.9883	+	15.2700i	0.686606	+	0.183975i	0.585223	−	0.810872i	$-0.301007\pi$
$83$	56.9883	+	15.2700i	0.686606	+	0.183975i	0.101382	+	0.994848i	$0.467673\pi$
$84$	−21.8208	+	51.1421i	−0.259772	+	0.608834i
$85$	−9.99219	−	18.2184i	−0.117555	−	0.214335i
$86$	−16.9576	+	29.3714i	−0.197181	+	0.341528i
$87$	−90.8519	+	115.841i	−1.04427	+	1.33150i
$88$	−57.4552	−	15.3951i	−0.652900	−	0.174944i
$89$			75.6878i			0.850425i	0.905094	+	0.425212i	$0.139801\pi$
$89$			75.6878i			0.850425i	−0.905094	+	0.425212i	$0.860199\pi$
$90$	13.8069	+	62.1238i	0.153410	+	0.690265i
$91$	−51.1563			−0.562157
$92$	6.87234	−	25.6479i	0.0746994	−	0.278782i
$93$	8.17010	−	57.3592i	0.0878506	−	0.616766i
$94$	−28.9642	−	16.7225i	−0.308130	−	0.177899i
$95$	13.1065	−	44.9469i	0.137964	−	0.473125i
$96$	13.5723	−	10.1879i	0.141378	−	0.106124i
$97$	−9.61362	+	35.8785i	−0.0991095	+	0.369882i	−0.997610	−	0.0690899i	$-0.977990\pi$
$97$	−9.61362	+	35.8785i	−0.0991095	+	0.369882i	0.898501	+	0.438972i	$0.144657\pi$
$98$	−36.8794	+	36.8794i	−0.376320	+	0.376320i
$99$	181.743	+	52.8462i	1.83579	+	0.533800i
$100$	−23.0770	−	44.3560i	−0.230770	−	0.443560i
$101$	57.6090	+	99.7817i	0.570386	+	0.987937i	0.996526	+	0.0832802i	$0.0265397\pi$
$101$	57.6090	+	99.7817i	0.570386	+	0.987937i	−0.426140	+	0.904657i	$0.640127\pi$
$102$	10.8807	−	13.8735i	0.106674	−	0.136014i
$103$	−22.9957	−	85.8210i	−0.223259	−	0.833213i	−0.983095	−	0.183098i	$-0.941387\pi$
$103$	−22.9957	−	85.8210i	−0.223259	−	0.833213i	0.759836	−	0.650115i	$-0.225279\pi$
$104$	13.5217	+	7.80674i	0.130016	+	0.0750648i
$105$	−22.6155	+	137.155i	−0.215385	+	1.30623i
$106$	−26.0581	−	45.1340i	−0.245832	−	0.425793i
$107$	−23.1784	−	23.1784i	−0.216620	−	0.216620i	0.590452	−	0.807072i	$-0.298949\pi$
$107$	−23.1784	−	23.1784i	−0.216620	−	0.216620i	−0.807072	+	0.590452i	$0.798949\pi$
$108$	−43.8633	+	31.4962i	−0.406142	+	0.291632i
$109$			9.44541i			0.0866551i	0.999061	+	0.0433275i	$0.0137959\pi$
$109$			9.44541i			0.0866551i	−0.999061	+	0.0433275i	$0.986204\pi$
$110$	−148.669	−	3.26143i	−1.35154	−	0.0296494i
$111$	142.533	+	60.8148i	1.28408	+	0.547881i
$112$	35.8054	−	9.59402i	0.319691	−	0.0856609i
$113$	−2.23310	−	8.33405i	−0.0197620	−	0.0737527i	0.955341	−	0.295507i	$-0.0954885\pi$
$113$	−2.23310	−	8.33405i	−0.0197620	−	0.0737527i	−0.975103	+	0.221754i	$0.928822\pi$
$114$	39.4399	−	4.76819i	0.345964	−	0.0418262i
$115$	1.45590	−	66.3657i	0.0126600	−	0.577093i
$116$	98.1452			0.846080
$117$	−42.4902	−	25.7462i	−0.363164	−	0.220053i
$118$	−59.9325	+	59.9325i	−0.507903	+	0.507903i
$119$	33.3522	−	19.2559i	0.280270	−	0.161814i
$120$	26.9083	−	32.8016i	0.224236	−	0.273346i
$121$	−160.631	+	278.222i	−1.32753	+	2.29935i
$122$	−29.2343	+	7.83330i	−0.239625	+	0.0642074i
$123$	10.2683	−	72.0897i	0.0834819	−	0.586095i
$124$	−33.4506	+	19.3127i	−0.269763	+	0.155748i
$125$	−82.3851	−	94.0090i	−0.659081	−	0.752072i
$126$	−114.553	+	28.1092i	−0.909149	+	0.223088i
$127$	109.071	+	109.071i	0.858830	+	0.858830i	0.991200	−	0.132370i	$-0.0422588\pi$
$127$	109.071	+	109.071i	0.858830	+	0.858830i	−0.132370	+	0.991200i	$0.542259\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$	−71.4249	+	8.63510i	−0.553682	+	0.0669388i
$130$	37.4730	+	10.9272i	0.288254	+	0.0840551i
$131$	−26.4539	+	45.8195i	−0.201938	+	0.349767i	−0.949153	−	0.314816i	$-0.898057\pi$
$131$	−26.4539	+	45.8195i	−0.201938	+	0.349767i	0.747215	+	0.664583i	$0.231391\pi$
$132$	−47.0504	−	117.080i	−0.356442	−	0.886970i
$133$	83.8183	+	22.4590i	0.630213	+	0.168865i
$134$			119.106i			0.888848i
$135$	−87.8122	+	102.538i	−0.650461	+	0.759540i
$136$	−11.7542			−0.0864281
$137$	50.8157	−	189.647i	0.370917	−	1.38428i	−0.488302	−	0.872675i	$-0.662384\pi$
$137$	50.8157	−	189.647i	0.370917	−	1.38428i	0.859219	−	0.511608i	$-0.170950\pi$
$138$	52.2644	−	21.0032i	0.378728	−	0.152197i
$139$	132.443	+	76.4658i	0.952825	+	0.550114i	0.893957	−	0.448152i	$-0.147918\pi$
$139$	132.443	+	76.4658i	0.952825	+	0.550114i	0.0588679	+	0.998266i	$0.481251\pi$
$140$	81.2525	−	44.5642i	0.580375	−	0.318316i
$141$	−8.51539	−	70.4347i	−0.0603928	−	0.499537i
$142$	−47.6320	+	177.765i	−0.335437	+	1.25187i
$143$	82.0881	−	82.0881i	0.574042	−	0.574042i
$144$	34.5683	+	10.0516i	0.240058	+	0.0698025i
$145$	238.338	−	58.2914i	1.64371	−	0.402009i
$146$	34.8091	+	60.2912i	0.238419	+	0.412953i
$147$	−109.533	−	15.6015i	−0.745120	−	0.106133i
$148$	−26.7386	−	99.7899i	−0.180666	−	0.674256i
$149$	−35.3844	−	20.4292i	−0.237479	−	0.137109i	0.376538	−	0.926401i	$-0.377114\pi$
$149$	−35.3844	−	20.4292i	−0.237479	−	0.137109i	−0.614018	+	0.789292i	$0.710448\pi$
$150$	45.8630	−	95.6378i	0.305753	−	0.637585i
$151$	−123.463	−	213.845i	−0.817639	−	1.41619i	−0.907418	−	0.420230i	$-0.861949\pi$
$151$	−123.463	−	213.845i	−0.817639	−	1.41619i	0.0897788	−	0.995962i	$-0.471384\pi$
$152$	−18.7275	−	18.7275i	−0.123207	−	0.123207i
$153$	37.3933	+	0.791813i	0.244401	+	0.00517525i
$154$		−	275.613i		−	1.78970i
$155$	−69.7619	+	66.7668i	−0.450077	+	0.430754i
$156$	3.97532	+	32.8818i	0.0254828	+	0.210780i
$157$	78.3798	−	21.0018i	0.499234	−	0.133769i	−0.000410342	−	1.00000i	$-0.500131\pi$
$157$	78.3798	−	21.0018i	0.499234	−	0.133769i	0.499645	+	0.866231i	$0.333464\pi$
$158$	−8.60482	−	32.1136i	−0.0544609	−	0.203251i
$159$	43.3866	−	101.686i	0.272872	−	0.639536i
$160$	−28.2775	−	0.620338i	−0.176734	−	0.00387711i
$161$	123.033			0.764182
$162$	−109.294	−	34.3054i	−0.674653	−	0.211762i
$163$	−23.5722	+	23.5722i	−0.144615	+	0.144615i	−0.775707	−	0.631093i	$-0.782607\pi$
$163$	−23.5722	+	23.5722i	−0.144615	+	0.144615i	0.631093	+	0.775707i	$0.282607\pi$
$164$	−42.0411	+	24.2724i	−0.256348	+	0.148003i
$165$	−183.796	−	256.375i	−1.11391	−	1.55379i
$166$	41.7183	−	72.2583i	0.251315	−	0.435291i
$167$	−228.230	+	61.1542i	−1.36665	+	0.366193i	−0.866254	−	0.499604i	$-0.833479\pi$
$167$	−228.230	+	61.1542i	−1.36665	+	0.366193i	−0.500396	+	0.865797i	$0.666812\pi$
$168$	61.8744	+	48.5271i	0.368300	+	0.288852i
$169$	119.968	−	69.2637i	0.709871	−	0.409844i
$170$	−28.5442	+	6.98118i	−0.167907	+	0.0410658i
$171$	58.3157	+	60.8388i	0.341028	+	0.355783i
$172$	33.9152	+	33.9152i	0.197181	+	0.197181i
$173$	13.1371	+	3.52008i	0.0759371	+	0.0203473i	0.296588	−	0.955006i	$-0.404151\pi$
$173$	13.1371	+	3.52008i	0.0759371	+	0.0203473i	−0.220650	+	0.975353i	$0.570818\pi$
$174$	124.987	+	166.507i	0.718316	+	0.956935i
$175$	170.848	−	156.479i	0.976272	−	0.894167i
$176$	−42.0601	+	72.8502i	−0.238978	+	0.413922i
$177$	−178.001	−	25.3540i	−1.00566	−	0.143243i
$178$	103.391	+	27.7037i	0.580851	+	0.155639i
$179$			40.1086i			0.224070i	0.993704	+	0.112035i	$0.0357369\pi$
$179$			40.1086i			0.224070i	−0.993704	+	0.112035i	$0.964263\pi$
$180$	89.9164	+	3.87835i	0.499536	+	0.0215464i
$181$	153.466			0.847878			0.423939	−	0.905691i	$-0.360647\pi$
$181$	153.466			0.847878			0.423939	+	0.905691i	$0.360647\pi$
$182$	−18.7245	+	69.8808i	−0.102882	+	0.383960i
$183$	−50.5190	−	39.6213i	−0.276060	−	0.216510i
$184$	−32.5203	−	18.7756i	−0.176741	−	0.102041i
$185$	−124.201	−	226.451i	−0.671356	−	1.22406i
$186$	−75.3637	−	32.1555i	−0.405181	−	0.172879i
$187$	−22.6196	+	84.4176i	−0.120961	+	0.451431i
$188$	−33.4450	+	33.4450i	−0.177899	+	0.177899i
$189$	−193.570	−	158.546i	−1.02418	−	0.838867i
$190$	−56.6012	−	34.3556i	−0.297901	−	0.180819i
$191$	−10.0403	−	17.3902i	−0.0525668	−	0.0910483i	0.838545	−	0.544833i	$-0.183407\pi$
$191$	−10.0403	−	17.3902i	−0.0525668	−	0.0910483i	−0.891111	+	0.453785i	$0.850074\pi$
$192$	−8.94917	−	22.2691i	−0.0466102	−	0.115985i
$193$	13.7648	+	51.3711i	0.0713204	+	0.266171i	0.992374	−	0.123265i	$-0.0393365\pi$
$193$	13.7648	+	51.3711i	0.0713204	+	0.266171i	−0.921053	+	0.389436i	$0.872670\pi$
$194$	45.4922	+	26.2649i	0.234496	+	0.135386i
$195$	29.1832	+	77.4898i	0.149658	+	0.397384i
$196$	36.8794	+	63.8770i	0.188160	+	0.325903i
$197$	21.2077	+	21.2077i	0.107653	+	0.107653i	0.758882	−	0.651229i	$-0.225746\pi$
$197$	21.2077	+	21.2077i	0.107653	+	0.107653i	−0.651229	+	0.758882i	$0.725746\pi$
$198$	138.712	−	228.923i	0.700565	−	1.15618i
$199$			371.939i			1.86904i	0.355910	+	0.934520i	$0.384171\pi$
$199$			371.939i			1.86904i	−0.355910	+	0.934520i	$0.615829\pi$
$200$	−69.0381	+	15.2884i	−0.345191	+	0.0764419i
$201$	−202.067	+	151.680i	−1.00531	+	0.754626i
$202$	157.391	−	42.1727i	0.779162	−	0.208776i
$203$	117.701	+	439.266i	0.579808	+	2.16387i
$204$	−14.9689	−	19.9414i	−0.0733769	−	0.0977520i
$205$	−87.6775	+	83.9132i	−0.427695	+	0.409333i
$206$	−125.651			−0.609954
$207$	102.191	+	61.9208i	0.493676	+	0.299135i
$208$	15.6135	−	15.6135i	0.0750648	−	0.0750648i
$209$	−170.538	+	98.4602i	−0.815972	+	0.471101i
$210$	179.079	+	81.0954i	0.852757	+	0.386169i
$211$	−22.0749	+	38.2349i	−0.104621	+	0.181208i	−0.913583	−	0.406652i	$-0.866696\pi$
$211$	−22.0749	+	38.2349i	−0.104621	+	0.181208i	0.808963	+	0.587860i	$0.200029\pi$
$212$	−71.1922	+	19.0759i	−0.335812	+	0.0899806i
$213$	−362.243	+	145.573i	−1.70067	+	0.683440i
$214$	−40.1461	+	23.1784i	−0.187599	+	0.108310i
$215$	102.504	+	62.2173i	0.476762	+	0.289383i
$216$	26.9696	+	71.4468i	0.124859	+	0.330772i
$217$	−126.553	−	126.553i	−0.583194	−	0.583194i
$218$	12.9027	+	3.45726i	0.0591865	+	0.0158590i
$219$	−57.9569	+	135.835i	−0.264643	+	0.620252i
$220$	−58.8719	+	201.892i	−0.267599	+	0.917691i
$221$	11.4703	−	19.8671i	0.0519017	−	0.0898963i
$222$	135.245	−	172.444i	0.609214	−	0.776776i
$223$	−94.5496	−	25.3345i	−0.423989	−	0.113608i	0.0405139	−	0.999179i	$-0.487100\pi$
$223$	−94.5496	−	25.3345i	−0.423989	−	0.113608i	−0.464503	+	0.885571i	$0.653767\pi$
$224$		−	52.4227i		−	0.234030i
$225$	220.659	−	43.9857i	0.980705	−	0.195492i
$226$	−12.2019			−0.0539907
$227$	24.8277	−	92.6582i	0.109373	−	0.408186i	−0.889431	−	0.457069i	$-0.848899\pi$
$227$	24.8277	−	92.6582i	0.109373	−	0.408186i	0.998805	+	0.0488827i	$0.0155660\pi$
$228$	7.92254	−	55.6212i	0.0347480	−	0.243953i
$229$	104.939	+	60.5868i	0.458250	+	0.264571i	0.711308	−	0.702880i	$-0.248103\pi$
$229$	104.939	+	60.5868i	0.458250	+	0.264571i	−0.253058	+	0.967451i	$0.581436\pi$
$230$	−90.1244	−	26.2803i	−0.391845	−	0.114262i
$231$	467.587	−	350.990i	2.02418	−	1.51944i
$232$	35.9237	−	134.069i	0.154843	−	0.577883i
$233$	100.933	−	100.933i	0.433190	−	0.433190i	−0.456522	−	0.889712i	$-0.650905\pi$
$233$	100.933	−	100.933i	0.433190	−	0.433190i	0.889712	+	0.456522i	$0.150905\pi$
$234$	−50.7224	+	48.6189i	−0.216763	+	0.207773i
$235$	−61.3547	+	101.083i	−0.261084	+	0.430139i
$236$	59.9325	+	103.806i	0.253951	+	0.439857i
$237$	43.5237	−	55.4948i	0.183644	−	0.234155i
$238$	−14.0963	−	52.6080i	−0.0592281	−	0.221042i
$239$	−131.016	−	75.6423i	−0.548185	−	0.316495i	0.200205	−	0.979754i	$-0.435839\pi$
$239$	−131.016	−	75.6423i	−0.548185	−	0.316495i	−0.748390	+	0.663259i	$0.769173\pi$
$240$	−34.9587	−	48.7636i	−0.145661	−	0.203182i
$241$	−146.347	−	253.480i	−0.607249	−	1.05179i	−0.991692	−	0.128637i	$-0.958940\pi$
$241$	−146.347	−	253.480i	−0.607249	−	1.05179i	0.384443	−	0.923149i	$-0.374393\pi$
$242$	321.263	+	321.263i	1.32753	+	1.32753i
$243$	−80.9844	−	229.108i	−0.333269	−	0.942832i
$244$			42.8019i			0.175418i
$245$	127.497	+	133.217i	0.520397	+	0.543742i
$246$	−94.7179	−	40.4134i	−0.385032	−	0.164282i
$247$	49.9285	−	13.3783i	0.202140	−	0.0541632i
$248$	14.1379	+	52.7634i	0.0570077	+	0.212755i
$249$	175.716	−	21.2437i	0.705688	−	0.0853160i
$250$	−158.574	+	78.1305i	−0.634295	+	0.312522i
$251$	166.350			0.662751			0.331375	−	0.943499i	$-0.392487\pi$
$251$	166.350			0.662751			0.331375	+	0.943499i	$0.392487\pi$
$252$	−3.53141	+	166.771i	−0.0140135	+	0.661788i
$253$	−197.426	+	197.426i	−0.780339	+	0.780339i
$254$	188.917	−	109.071i	0.743769	−	0.429415i
$255$	−48.1946	−	39.5358i	−0.188998	−	0.155042i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	64.7288	−	17.3440i	0.251863	−	0.0674865i	−0.130678	−	0.991425i	$-0.541716\pi$
$257$	64.7288	−	17.3440i	0.251863	−	0.0674865i	0.382542	+	0.923938i	$0.375049\pi$
$258$	−14.3476	+	100.729i	−0.0556107	+	0.390422i
$259$	414.560	−	239.347i	1.60062	−	0.924118i
$260$	28.6429	−	47.1895i	0.110165	−	0.181498i
$261$	−123.314	+	424.089i	−0.472468	+	1.62486i
$262$	52.9078	+	52.9078i	0.201938	+	0.201938i
$263$	−282.927	−	75.8101i	−1.07577	−	0.288251i	−0.322908	−	0.946430i	$-0.604660\pi$
$263$	−282.927	−	75.8101i	−1.07577	−	0.288251i	−0.752861	+	0.658179i	$0.771327\pi$
$264$	−177.156	+	21.4177i	−0.671045	+	0.0811277i
$265$	−161.555	+	88.6075i	−0.609642	+	0.334368i
$266$	61.3592	−	106.277i	0.230674	−	0.399539i
$267$	84.6679	+	210.687i	0.317108	+	0.789091i
$268$	162.701	+	43.5957i	0.607094	+	0.162670i
$269$		−	174.314i		−	0.648006i	−0.946056	−	0.324003i	$-0.894971\pi$
$269$		−	174.314i		−	0.648006i	0.946056	−	0.324003i	$-0.105029\pi$
$270$	107.928	+	157.485i	0.399733	+	0.583278i
$271$	−18.2298			−0.0672685			−0.0336343	−	0.999434i	$-0.510708\pi$
$271$	−18.2298			−0.0672685			−0.0336343	+	0.999434i	$0.510708\pi$
$272$	−4.30234	+	16.0566i	−0.0158174	+	0.0590315i
$273$	−142.401	+	57.2258i	−0.521614	+	0.209618i
$274$	−240.462	−	138.831i	−0.877600	−	0.506682i
$275$	−23.0563	+	525.245i	−0.0838410	+	1.90998i
$276$	−9.56085	−	79.0822i	−0.0346407	−	0.286530i
$277$	−102.033	+	380.792i	−0.368350	+	1.37470i	0.494473	+	0.869193i	$0.335361\pi$
$277$	−102.033	+	380.792i	−0.368350	+	1.37470i	−0.862823	+	0.505506i	$0.831306\pi$
$278$	152.932	−	152.932i	0.550114	−	0.550114i
$279$	−41.4221	−	168.807i	−0.148466	−	0.605042i
$280$	−31.1354	−	127.305i	−0.111198	−	0.454659i
$281$	−265.887	−	460.530i	−0.946217	−	1.63890i	−0.753297	−	0.657681i	$-0.771538\pi$
$281$	−265.887	−	460.530i	−0.946217	−	1.63890i	−0.192920	−	0.981215i	$-0.561796\pi$
$282$	−99.3325	−	14.1487i	−0.352243	−	0.0501726i
$283$	−126.666	−	472.724i	−0.447583	−	1.67040i	−0.709024	−	0.705184i	$-0.750864\pi$
$283$	−126.666	−	472.724i	−0.447583	−	1.67040i	0.261441	−	0.965220i	$-0.415802\pi$
$284$	225.397	+	130.133i	0.793652	+	0.458215i
$285$	−13.7958	−	139.777i	−0.0484062	−	0.490447i
$286$	−82.0881	−	142.181i	−0.287021	−	0.497135i
$287$	−159.053	−	159.053i	−0.554193	−	0.554193i
$288$	26.3836	−	43.5420i	0.0916096	−	0.151188i
$289$		−	271.730i		−	0.940241i
$290$	7.61040	−	346.912i	0.0262428	−	1.19625i
$291$	13.3745	+	110.627i	0.0459606	+	0.380162i
$292$	95.1003	−	25.4821i	0.325686	−	0.0872673i
$293$	65.2245	+	243.421i	0.222609	+	0.830789i	0.983348	+	0.181731i	$0.0581700\pi$
$293$	65.2245	+	243.421i	0.222609	+	0.830789i	−0.760739	+	0.649058i	$0.775163\pi$
$294$	−61.4038	+	143.914i	−0.208857	+	0.489503i
$295$	207.195	+	216.490i	0.702357	+	0.733864i
$296$	−146.103			−0.493590
$297$	565.023	−	56.2015i	1.90243	−	0.189231i
$298$	−40.8584	+	40.8584i	−0.137109	+	0.137109i
$299$	63.4693	−	36.6440i	0.212272	−	0.122555i
$300$	−113.857	−	97.6559i	−0.379522	−	0.325520i
$301$	−111.120	+	192.466i	−0.369171	+	0.639423i
$302$	−337.308	+	90.3815i	−1.11692	+	0.299277i
$303$	271.983	+	213.312i	0.897633	+	0.704000i
$304$	−32.4370	+	18.7275i	−0.106701	+	0.0616037i
$305$	25.4213	+	103.941i	0.0833487	+	0.340791i
$306$	14.7685	−	50.7904i	0.0482632	−	0.165982i
$307$	−286.502	−	286.502i	−0.933233	−	0.933233i	0.0646738	−	0.997906i	$-0.479399\pi$
$307$	−286.502	−	286.502i	−0.933233	−	0.933233i	−0.997906	+	0.0646738i	$0.979399\pi$
$308$	−376.494	−	100.881i	−1.22238	−	0.327537i
$309$	−160.015	−	213.170i	−0.517847	−	0.689872i
$310$	65.6705	+	119.735i	0.211840	+	0.386242i
$311$	190.772	−	330.426i	0.613414	−	1.06246i	−0.377247	−	0.926113i	$-0.623129\pi$
$311$	190.772	−	330.426i	0.613414	−	1.06246i	0.990661	−	0.136351i	$-0.0435375\pi$
$312$	46.3724	+	6.60516i	0.148629	+	0.0211704i
$313$	431.390	+	115.590i	1.37824	+	0.369299i	0.870482	−	0.492200i	$-0.163807\pi$
$313$	431.390	+	115.590i	1.37824	+	0.369299i	0.507759	+	0.861499i	$0.330474\pi$
$314$		−	114.756i		−	0.365465i
$315$	90.4743	+	407.087i	0.287220	+	1.29234i
$316$	−47.0176			−0.148790
$317$	81.9656	−	305.900i	0.258567	−	0.964984i	−0.707505	−	0.706708i	$-0.750179\pi$
$317$	81.9656	−	305.900i	0.258567	−	0.964984i	0.966071	−	0.258275i	$-0.0831541\pi$
$318$	−123.025	−	96.4869i	−0.386872	−	0.303418i
$319$	−893.738	−	516.000i	−2.80169	−	1.61755i
$320$	−11.1977	+	38.4007i	−0.0349927	+	0.120002i
$321$	−90.4485	−	38.5917i	−0.281771	−	0.120223i
$322$	45.0333	−	168.067i	0.139855	−	0.521946i
$323$	−27.5159	+	27.5159i	−0.0851886	+	0.0851886i
$324$	−86.8663	+	136.742i	−0.268106	+	0.422042i
$325$	41.5298	−	131.608i	0.127784	−	0.404947i
$326$	23.5722	+	40.8283i	0.0723074	+	0.125240i
$327$	10.5661	+	26.2926i	0.0323121	+	0.0804054i
$328$	17.7687	+	66.3135i	0.0541727	+	0.202175i
$329$	−189.798	−	109.580i	−0.576894	−	0.333070i
$330$	−417.489	+	157.229i	−1.26512	+	0.476453i
$331$	146.508	+	253.759i	0.442621	+	0.766642i	0.997883	−	0.0650332i	$-0.0207153\pi$
$331$	146.508	+	253.759i	0.442621	+	0.766642i	−0.555262	+	0.831675i	$0.687382\pi$
$332$	−83.4366	−	83.4366i	−0.251315	−	0.251315i
$333$	464.791	+	9.84207i	1.39577	+	0.0295558i
$334$			334.153i			1.00046i
$335$	421.001	+	9.23571i	1.25672	+	0.0275693i
$336$	88.9368	−	66.7598i	0.264693	−	0.198690i
$337$	−139.258	+	37.3140i	−0.413228	+	0.110724i	−0.459443	−	0.888207i	$-0.651951\pi$
$337$	−139.258	+	37.3140i	−0.413228	+	0.110724i	0.0462148	+	0.998932i	$0.485284\pi$
$338$	−50.7046	−	189.232i	−0.150013	−	0.559858i
$339$	−15.5390	−	20.7009i	−0.0458377	−	0.0610646i
$340$	−0.911448	+	41.5474i	−0.00268073	+	0.122198i
$341$	406.148			1.19105
$342$	104.452	−	57.3922i	0.305416	−	0.167813i
$343$	79.4244	−	79.4244i	0.231558	−	0.231558i
$344$	58.7429	−	33.9152i	0.170764	−	0.0985907i
$345$	−70.1871	−	186.367i	−0.203441	−	0.540193i
$346$	9.61703	−	16.6572i	0.0277949	−	0.0481422i
$347$	343.455	−	92.0284i	0.989783	−	0.265212i	0.272624	−	0.962121i	$-0.412109\pi$
$347$	343.455	−	92.0284i	0.989783	−	0.265212i	0.717159	+	0.696909i	$0.245442\pi$
$348$	273.201	−	109.790i	0.785059	−	0.315488i
$349$	−291.991	+	168.581i	−0.836652	+	0.483041i	−0.856125	−	0.516769i	$-0.827135\pi$
$349$	−291.991	+	168.581i	−0.836652	+	0.483041i	0.0194730	+	0.999810i	$0.493801\pi$
$350$	−151.220	−	290.657i	−0.432057	−	0.830450i
$351$	−147.078	−	24.1366i	−0.419026	−	0.0687653i
$352$	84.1202	+	84.1202i	0.238978	+	0.238978i
$353$	−4.08000	−	1.09323i	−0.0115581	−	0.00309697i	0.253035	−	0.967457i	$-0.418571\pi$
$353$	−4.08000	−	1.09323i	−0.0115581	−	0.00309697i	−0.264593	+	0.964360i	$0.585238\pi$
$354$	−99.7871	+	233.874i	−0.281884	+	0.660660i
$355$	624.650	+	182.148i	1.75958	+	0.513094i
$356$	75.6878	−	131.095i	0.212606	−	0.368245i
$357$	71.2998	−	90.9106i	0.199719	−	0.254652i
$358$	54.7894	+	14.6808i	0.153043	+	0.0410077i
$359$			544.965i			1.51801i	0.651085	+	0.759005i	$0.274314\pi$
$359$			544.965i			1.51801i	−0.651085	+	0.759005i	$0.725686\pi$
$360$	38.2096	−	121.409i	0.106138	−	0.337246i
$361$	273.320			0.757119
$362$	56.1725	−	209.638i	0.155173	−	0.579112i
$363$	−135.908	+	954.158i	−0.374402	+	2.62854i
$364$	88.6053	+	51.1563i	0.243421	+	0.140539i
$365$	215.809	−	118.364i	0.591259	−	0.324285i
$366$	−72.6149	+	54.5079i	−0.198401	+	0.148929i
$367$	127.547	−	476.012i	0.347540	−	1.29704i	−0.542078	−	0.840328i	$-0.682362\pi$
$367$	127.547	−	476.012i	0.347540	−	1.29704i	0.889617	−	0.456707i	$-0.150971\pi$
$368$	−37.5512	+	37.5512i	−0.102041	+	0.102041i
$369$	−52.0597	−	212.158i	−0.141083	−	0.574954i
$370$	−354.799	+	86.7746i	−0.958916	+	0.234526i
$371$	−170.755	−	295.756i	−0.460256	−	0.797186i
$372$	−71.5103	+	91.1790i	−0.192232	+	0.245105i
$373$	66.7224	+	249.011i	0.178880	+	0.667591i	0.995858	+	0.0909215i	$0.0289812\pi$
$373$	66.7224	+	249.011i	0.178880	+	0.667591i	−0.816978	+	0.576669i	$0.804352\pi$
$374$	107.037	+	61.7979i	0.286196	+	0.165235i
$375$	−334.493	−	169.527i	−0.891981	−	0.452072i
$376$	33.4450	+	57.9285i	0.0889495	+	0.154065i
$377$	191.549	+	191.549i	0.508086	+	0.508086i
$378$	−287.429	+	206.390i	−0.760394	+	0.546004i
$379$			342.477i			0.903633i	0.892111	+	0.451816i	$0.149224\pi$
$379$			342.477i			0.903633i	−0.892111	+	0.451816i	$0.850776\pi$
$380$	−67.6481	+	64.7437i	−0.178021	+	0.170378i
$381$	425.627	+	181.603i	1.11713	+	0.476648i
$382$	−27.4305	+	7.34998i	−0.0718075	+	0.0192408i
$383$	−124.482	−	464.574i	−0.325019	−	1.21299i	−0.914293	−	0.405053i	$-0.867253\pi$
$383$	−124.482	−	464.574i	−0.325019	−	1.21299i	0.589275	−	0.807933i	$-0.299414\pi$
$384$	−33.6958	+	4.07374i	−0.0877494	+	0.0106087i
$385$	−974.205	−	21.3716i	−2.53040	−	0.0555108i
$386$	75.2125			0.194851
$387$	−189.161	+	103.936i	−0.488789	+	0.268569i
$388$	52.5298	−	52.5298i	0.135386	−	0.135386i
$389$	104.339	−	60.2399i	0.268223	−	0.154858i	−0.359857	−	0.933007i	$-0.617175\pi$
$389$	104.339	−	60.2399i	0.268223	−	0.154858i	0.628080	+	0.778149i	$0.283841\pi$
$390$	116.535	−	11.5018i	0.298807	−	0.0294918i
$391$	−27.5865	+	47.7813i	−0.0705538	+	0.122203i
$392$	100.756	−	26.9976i	0.257032	−	0.0688714i
$393$	−22.3822	+	157.137i	−0.0569523	+	0.399840i
$394$	36.7328	−	21.2077i	0.0932304	−	0.0538266i
$395$	−114.179	+	27.9252i	−0.289060	+	0.0706966i
$396$	−261.942	−	273.276i	−0.661470	−	0.690090i
$397$	−340.634	−	340.634i	−0.858019	−	0.858019i	0.133086	−	0.991105i	$-0.457512\pi$
$397$	−340.634	−	340.634i	−0.858019	−	0.858019i	−0.991105	+	0.133086i	$0.957512\pi$
$398$	508.078	+	136.139i	1.27658	+	0.342058i
$399$	258.443	−	31.2452i	0.647728	−	0.0783087i
$400$	−4.38539	+	99.9038i	−0.0109635	+	0.249759i
$401$	−331.703	+	574.527i	−0.827190	+	1.43274i	0.0730440	+	0.997329i	$0.476729\pi$
$401$	−331.703	+	574.527i	−0.827190	+	1.43274i	−0.900234	+	0.435406i	$0.856605\pi$
$402$	133.237	+	331.547i	0.331435	+	0.824743i
$403$	−102.977	−	27.5927i	−0.255527	−	0.0684683i
$404$		−	230.436i		−	0.570386i
$405$	−129.734	+	383.659i	−0.320330	+	0.947306i
$406$	643.130			1.58406
$407$	−281.157	+	1049.29i	−0.690804	+	2.57812i
$408$	−32.7195	+	13.1488i	−0.0801948	+	0.0322275i
$409$	480.208	+	277.248i	1.17410	+	0.677869i	0.954643	−	0.297753i	$-0.0962371\pi$
$409$	480.208	+	277.248i	1.17410	+	0.677869i	0.219460	+	0.975621i	$0.429570\pi$
$410$	82.5354	+	150.484i	0.201306	+	0.367034i
$411$	−70.6951	−	584.752i	−0.172008	−	1.42275i
$412$	−45.9913	+	171.642i	−0.111629	+	0.416607i
$413$	−392.728	+	392.728i	−0.950916	+	0.950916i
$414$	121.990	−	116.931i	0.294662	−	0.282441i
$415$	−252.175	−	153.064i	−0.607651	−	0.368829i
$416$	−15.6135	−	27.0433i	−0.0375324	−	0.0650080i
$417$	454.211	+	64.6966i	1.08923	+	0.155148i
$418$	72.0779	+	268.998i	0.172435	+	0.643537i
$419$	−307.090	−	177.298i	−0.732911	−	0.423146i	0.0865750	−	0.996245i	$-0.472408\pi$
$419$	−307.090	−	177.298i	−0.732911	−	0.423146i	−0.819486	+	0.573099i	$0.805741\pi$
$420$	176.326	−	214.943i	0.419823	−	0.511770i
$421$	37.7780	+	65.4335i	0.0897340	+	0.155424i	0.907399	−	0.420271i	$-0.138065\pi$
$421$	37.7780	+	65.4335i	0.0897340	+	0.155424i	−0.817665	+	0.575695i	$0.804732\pi$
$422$	44.1499	+	44.1499i	0.104621	+	0.104621i
$423$	−102.495	−	186.539i	−0.242306	−	0.440991i
$424$			104.233i			0.245832i
$425$	22.4629	+	101.436i	0.0528538	+	0.238673i
$426$	66.2660	+	548.117i	0.155554	+	1.28666i
$427$	−191.567	+	51.3303i	−0.448636	+	0.120212i
$428$	16.9677	+	63.3244i	0.0396442	+	0.147954i
$429$	136.676	−	320.331i	0.318592	−	0.746692i
$430$	122.509	−	117.250i	0.284906	−	0.272674i
$431$	−645.212			−1.49701			−0.748506	−	0.663128i	$-0.769228\pi$
$431$	−645.212			−1.49701			−0.748506	+	0.663128i	$0.769228\pi$
$432$	107.470	−	10.6898i	0.248772	−	0.0247448i
$433$	547.156	−	547.156i	1.26364	−	1.26364i	0.314324	−	0.949316i	$-0.398222\pi$
$433$	547.156	−	547.156i	1.26364	−	1.26364i	0.949316	−	0.314324i	$-0.101778\pi$
$434$	−219.197	+	126.553i	−0.505061	+	0.291597i
$435$	598.240	−	428.878i	1.37526	−	0.985927i
$436$	9.44541	−	16.3599i	0.0216638	−	0.0375228i
$437$	−120.081	+	32.1755i	−0.274784	+	0.0736281i
$438$	164.340	+	128.890i	0.375207	+	0.294269i
$439$	−237.814	+	137.302i	−0.541718	+	0.312761i	−0.745775	−	0.666198i	$-0.767921\pi$
$439$	−237.814	+	137.302i	−0.541718	+	0.312761i	0.204057	+	0.978959i	$0.434587\pi$
$440$	254.241	+	154.318i	0.577821	+	0.350723i
$441$	−322.352	+	79.0992i	−0.730956	+	0.179363i
$442$	−22.9405	−	22.9405i	−0.0519017	−	0.0519017i
$443$	−161.066	−	43.1575i	−0.363580	−	0.0974210i	0.0724038	−	0.997375i	$-0.476933\pi$
$443$	−161.066	−	43.1575i	−0.363580	−	0.0974210i	−0.435984	+	0.899954i	$0.643600\pi$
$444$	−186.060	−	247.868i	−0.419054	−	0.558261i
$445$	105.941	−	363.308i	0.238069	−	0.816422i
$446$	−69.2151	+	119.884i	−0.155191	+	0.268799i
$447$	−121.350	−	17.2848i	−0.271477	−	0.0386685i
$448$	−71.6108	−	19.1880i	−0.159845	−	0.0428305i
$449$			115.374i			0.256958i	0.991712	+	0.128479i	$0.0410095\pi$
$449$			115.374i			0.256958i	−0.991712	+	0.128479i	$0.958991\pi$
$450$	20.6810	−	317.525i	0.0459579	−	0.705612i
$451$	510.451			1.13182
$452$	−4.46620	+	16.6681i	−0.00988098	+	0.0368763i
$453$	−582.894	−	457.155i	−1.28674	−	1.00917i
$454$	−117.486	−	67.8305i	−0.258780	−	0.149406i
$455$	245.555	+	71.6039i	0.539680	+	0.157371i
$456$	−73.0801	−	31.1812i	−0.160263	−	0.0683797i
$457$	109.958	−	410.369i	0.240609	−	0.897964i	−0.734931	−	0.678142i	$-0.762786\pi$
$457$	109.958	−	410.369i	0.240609	−	0.897964i	0.975540	−	0.219822i	$-0.0705477\pi$
$458$	121.174	−	121.174i	0.264571	−	0.264571i
$459$	104.975	−	39.6258i	0.228704	−	0.0863306i
$460$	−68.8874	+	113.493i	−0.149755	+	0.246724i
$461$	69.1739	+	119.813i	0.150052	+	0.259897i	0.931246	−	0.364390i	$-0.118723\pi$
$461$	69.1739	+	119.813i	0.150052	+	0.259897i	−0.781194	+	0.624288i	$0.785389\pi$
$462$	−308.313	−	767.206i	−0.667345	−	1.66062i
$463$	−2.43537	−	9.08893i	−0.00525998	−	0.0196305i	0.963246	−	0.268621i	$-0.0865679\pi$
$463$	−2.43537	−	9.08893i	−0.00525998	−	0.0196305i	−0.968506	+	0.248990i	$0.919901\pi$
$464$	−169.993	−	98.1452i	−0.366363	−	0.211520i
$465$	−119.503	+	263.893i	−0.256997	+	0.567513i
$466$	−100.933	−	174.821i	−0.216595	−	0.375153i
$467$	−204.967	−	204.967i	−0.438901	−	0.438901i	0.452741	−	0.891642i	$-0.350446\pi$
$467$	−204.967	−	204.967i	−0.438901	−	0.438901i	−0.891642	+	0.452741i	$0.850446\pi$
$468$	47.8489	+	87.0839i	0.102241	+	0.186077i
$469$			780.480i			1.66414i
$470$	115.624	+	120.811i	0.246009	+	0.257045i
$471$	194.687	−	146.141i	0.413349	−	0.310277i
$472$	163.739	−	43.8737i	0.346904	−	0.0929527i
$473$	−130.532	−	487.151i	−0.275966	−	1.02992i
$474$	−59.8765	−	79.7669i	−0.126322	−	0.168285i
$475$	−125.825	+	197.403i	−0.264895	+	0.415586i
$476$	−77.0235			−0.161814
$477$	7.02154	−	331.592i	0.0147202	−	0.695161i
$478$	−151.285	+	151.285i	−0.316495	+	0.316495i
$479$	409.873	−	236.640i	0.855685	−	0.494030i	−0.00687978	−	0.999976i	$-0.502190\pi$
$479$	409.873	−	236.640i	0.855685	−	0.494030i	0.862565	+	0.505946i	$0.168857\pi$
$480$	−79.4081	+	29.9057i	−0.165434	+	0.0623035i
$481$	142.573	−	246.944i	0.296410	−	0.513397i
$482$	−399.827	+	107.133i	−0.829517	+	0.222268i
$483$	342.480	−	137.631i	0.709069	−	0.284950i
$484$	556.444	−	321.263i	1.14968	−	0.663766i
$485$	96.3657	−	158.764i	0.198692	−	0.327348i
$486$	−342.610	+	26.7674i	−0.704959	+	0.0550769i
$487$	−418.149	−	418.149i	−0.858623	−	0.858623i	0.132553	−	0.991176i	$-0.457683\pi$
$487$	−418.149	−	418.149i	−0.858623	−	0.858623i	−0.991176	+	0.132553i	$0.957683\pi$
$488$	58.4685	+	15.6666i	0.119813	+	0.0321037i
$489$	−39.2475	+	91.9855i	−0.0802608	+	0.188109i
$490$	228.645	−	125.404i	0.466622	−	0.255926i
$491$	−146.593	+	253.907i	−0.298560	+	0.517122i	−0.975807	−	0.218635i	$-0.929840\pi$
$491$	−146.593	+	253.907i	−0.298560	+	0.517122i	0.677246	+	0.735756i	$0.263173\pi$
$492$	−89.8749	+	114.595i	−0.182672	+	0.232916i
$493$	−196.984	−	52.7818i	−0.399563	−	0.107062i
$494$		−	73.1005i		−	0.147977i
$495$	−798.413	−	508.054i	−1.61296	−	1.02637i
$496$	77.2509			0.155748
$497$	−312.125	+	1164.87i	−0.628018	+	2.34379i
$498$	35.2972	−	247.809i	0.0708780	−	0.497608i
$499$	425.524	+	245.676i	0.852753	+	0.492337i	0.861579	−	0.507624i	$-0.169476\pi$
$499$	425.524	+	245.676i	0.852753	+	0.492337i	−0.00882571	+	0.999961i	$0.502809\pi$
$500$	48.6862	+	245.213i	0.0973725	+	0.490427i
$501$	−566.901	+	425.540i	−1.13154	+	0.849381i
$502$	60.8885	−	227.239i	0.121292	−	0.452667i
$503$	530.029	−	530.029i	1.05373	−	1.05373i	0.0552630	−	0.998472i	$-0.482400\pi$
$503$	530.029	−	530.029i	1.05373	−	1.05373i	0.998472	−	0.0552630i	$-0.0175997\pi$
$504$	226.520	+	65.8663i	0.449445	+	0.130687i
$505$	−136.863	−	559.596i	−0.271015	−	1.10811i
$506$	197.426	+	341.951i	0.390169	+	0.675793i
$507$	256.466	−	327.007i	0.505851	−	0.644984i
$508$	−79.8458	−	297.989i	−0.157177	−	0.586592i
$509$	568.855	+	328.428i	1.11759	+	0.645242i	0.940785	−	0.339003i	$-0.110090\pi$
$509$	568.855	+	328.428i	1.11759	+	0.645242i	0.176807	+	0.984245i	$0.443423\pi$
$510$	−71.6473	+	51.3640i	−0.140485	+	0.100714i
$511$	228.099	+	395.078i	0.446377	+	0.773148i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	230.387	+	104.119i	0.449097	+	0.202960i
$514$		−	94.7695i		−	0.184377i
$515$	−9.74323	+	444.135i	−0.0189189	+	0.862398i
$516$	132.347	+	56.4685i	0.256486	+	0.109435i
$517$	480.397	−	128.722i	0.929202	−	0.248979i
$518$	−175.214	−	653.907i	−0.338251	−	1.26237i
$519$	40.5067	−	4.89716i	0.0780475	−	0.00943576i
$520$	−53.9780	−	56.3994i	−0.103804	−	0.108460i
$521$	138.712			0.266242			0.133121	−	0.991100i	$-0.457500\pi$
$521$	138.712			0.266242			0.133121	+	0.991100i	$0.457500\pi$
$522$	534.180	+	323.678i	1.02333	+	0.620072i
$523$	−605.607	+	605.607i	−1.15795	+	1.15795i	−0.173033	+	0.984916i	$0.555357\pi$
$523$	−605.607	+	605.607i	−1.15795	+	1.15795i	−0.984916	+	0.173033i	$0.944643\pi$
$524$	91.6389	−	52.9078i	0.174883	−	0.100969i
$525$	300.533	−	626.699i	0.572443	−	1.19371i
$526$	−207.117	+	358.737i	−0.393759	+	0.682010i
$527$	77.5240	−	20.7725i	0.147104	−	0.0394165i
$528$	−35.5864	+	249.839i	−0.0673985	+	0.473180i
$529$	305.481	−	176.369i	0.577468	−	0.333401i
$530$	61.9068	+	253.121i	0.116805	+	0.477587i
$531$	−523.852	+	128.544i	−0.986539	+	0.242079i
$532$	−122.718	−	122.718i	−0.230674	−	0.230674i
$533$	−129.423	−	34.6788i	−0.242820	−	0.0650634i
$534$	318.795	−	38.5415i	0.596994	−	0.0721751i
$535$	78.8151	+	143.701i	0.147318	+	0.268600i
$536$	119.106	−	206.297i	0.222212	−	0.384882i
$537$	44.8673	+	111.648i	0.0835518	+	0.207910i
$538$	−238.117	−	63.8032i	−0.442596	−	0.118593i
$539$		−	775.575i		−	1.43892i
$540$	254.633	−	89.7887i	0.471543	−	0.166275i
$541$	243.344			0.449803			0.224902	−	0.974381i	$-0.427794\pi$
$541$	243.344			0.449803			0.224902	+	0.974381i	$0.427794\pi$
$542$	−6.67256	+	24.9023i	−0.0123110	+	0.0459453i
$543$	427.194	−	171.674i	0.786728	−	0.316159i
$544$	20.3589	+	11.7542i	0.0374245	+	0.0216070i
$545$	13.2208	−	45.3387i	0.0242584	−	0.0831904i
$546$	26.0497	+	215.469i	0.0477100	+	0.394632i
$547$	−142.537	+	531.954i	−0.260579	+	0.972494i	0.704322	+	0.709880i	$0.251251\pi$
$547$	−142.537	+	531.954i	−0.260579	+	0.972494i	−0.964901	+	0.262613i	$0.915416\pi$
$548$	−277.662	+	277.662i	−0.506682	+	0.506682i
$549$	−184.949	−	53.7783i	−0.336883	−	0.0979569i
$550$	709.059	+	223.749i	1.28920	+	0.406816i
$551$	−229.752	−	397.943i	−0.416973	−	0.722219i
$552$	−111.528	−	15.8857i	−0.202043	−	0.0287785i
$553$	−56.3860	−	210.436i	−0.101964	−	0.380534i
$554$	482.825	+	278.759i	0.871524	+	0.503175i
$555$	−599.049	−	491.421i	−1.07937	−	0.885444i
$556$	−152.932	−	264.885i	−0.275057	−	0.476413i
$557$	−384.029	−	384.029i	−0.689459	−	0.689459i	0.272653	−	0.962112i	$-0.412099\pi$
$557$	−384.029	−	384.029i	−0.689459	−	0.689459i	−0.962112	+	0.272653i	$0.912099\pi$
$558$	−245.756	−	5.20394i	−0.440423	−	0.00932606i
$559$			132.384i			0.236822i
$560$	−185.298	−	4.06497i	−0.330889	−	0.00725888i
$561$	31.4686	+	260.291i	0.0560937	+	0.463977i
$562$	−726.416	+	194.643i	−1.29256	+	0.346339i
$563$	−150.746	−	562.590i	−0.267754	−	0.999272i	−0.960543	−	0.278131i	$-0.910285\pi$
$563$	−150.746	−	562.590i	−0.267754	−	0.999272i	0.692789	−	0.721140i	$-0.256382\pi$
$564$	−55.6857	+	130.512i	−0.0987334	+	0.231404i
$565$	−0.946162	+	43.1298i	−0.00167462	+	0.0763360i
$566$	−692.116			−1.22282
$567$	−716.185	−	224.798i	−1.26311	−	0.396469i
$568$	260.266	−	260.266i	0.458215	−	0.458215i
$569$	−411.667	+	237.676i	−0.723492	+	0.417708i	−0.816037	−	0.578000i	$-0.803833\pi$
$569$	−411.667	+	237.676i	−0.723492	+	0.417708i	0.0925446	+	0.995709i	$0.470500\pi$
$570$	−195.989	−	32.3167i	−0.343840	−	0.0566959i
$571$	−24.1780	+	41.8774i	−0.0423432	+	0.0733405i	−0.886420	−	0.462881i	$-0.846816\pi$
$571$	−24.1780	+	41.8774i	−0.0423432	+	0.0733405i	0.844077	+	0.536222i	$0.180149\pi$
$572$	−224.269	+	60.0926i	−0.392078	+	0.105057i
$573$	−47.4019	−	37.1766i	−0.0827259	−	0.0648806i
$574$	−275.489	+	159.053i	−0.479945	+	0.277096i
$575$	−99.8811	+	316.523i	−0.173706	+	0.550475i
$576$	−49.8225	−	51.9781i	−0.0864973	−	0.0902398i
$577$	670.891	+	670.891i	1.16272	+	1.16272i	0.983877	+	0.178845i	$0.0572362\pi$
$577$	670.891	+	670.891i	1.16272	+	1.16272i	0.178845	+	0.983877i	$0.442764\pi$
$578$	−371.190	−	99.4600i	−0.642197	−	0.172076i
$579$	95.7823	+	127.600i	0.165427	+	0.220381i
$580$	−471.106	−	137.375i	−0.812251	−	0.236853i
$581$	273.373	−	473.497i	0.470522	−	0.814968i
$582$	156.015	+	22.2223i	0.268067	+	0.0381827i
$583$	748.588	+	200.583i	1.28403	+	0.344054i
$584$		−	139.237i		−	0.238419i
$585$	167.919	+	183.058i	0.287041	+	0.312919i
$586$	356.393			0.608180
$587$	21.7513	−	81.1770i	0.0370551	−	0.138291i	−0.944920	−	0.327301i	$-0.893861\pi$
$587$	21.7513	−	81.1770i	0.0370551	−	0.138291i	0.981975	+	0.189009i	$0.0605277\pi$
$588$	174.115	+	136.555i	0.296113	+	0.232237i
$589$	156.612	+	90.4199i	0.265895	+	0.153514i
$590$	371.569	−	203.793i	0.629779	−	0.345412i
$591$	82.7583	+	35.3106i	0.140031	+	0.0597472i
$592$	−53.4772	+	199.580i	−0.0903332	+	0.337128i
$593$	−706.704	+	706.704i	−1.19174	+	1.19174i	−0.215165	+	0.976578i	$0.569029\pi$
$593$	−706.704	+	706.704i	−1.19174	+	1.19174i	−0.976578	+	0.215165i	$0.930971\pi$
$594$	130.040	−	792.407i	0.218923	−	1.33402i
$595$	−187.046	+	45.7465i	−0.314363	+	0.0768849i
$596$	40.8584	+	70.7688i	0.0685543	+	0.118740i
$597$	416.068	+	1035.34i	0.696932	+	1.73424i
$598$	−26.8253	−	100.113i	−0.0448583	−	0.167414i
$599$	481.659	+	278.086i	0.804106	+	0.464251i	0.844905	−	0.534917i	$-0.179657\pi$
$599$	481.659	+	278.086i	0.804106	+	0.464251i	−0.0407989	+	0.999167i	$0.512990\pi$
$600$	−175.075	+	119.787i	−0.291791	+	0.199644i
$601$	−311.839	−	540.121i	−0.518867	−	0.898704i	−0.999760	−	0.0219247i	$-0.993021\pi$
$601$	−311.839	−	540.121i	−0.518867	−	0.898704i	0.480892	−	0.876780i	$-0.340313\pi$
$602$	222.241	+	222.241i	0.369171	+	0.369171i
$603$	−392.804	+	648.262i	−0.651416	+	1.07506i
$604$			493.854i			0.817639i
$605$	1160.47	−	1110.65i	1.91814	−	1.83579i
$606$	390.942	−	293.458i	0.645119	−	0.484254i
$607$	205.980	−	55.1922i	0.339341	−	0.0909262i	−0.0851242	−	0.996370i	$-0.527129\pi$
$607$	205.980	−	55.1922i	0.339341	−	0.0909262i	0.424465	+	0.905444i	$0.360462\pi$
$608$	13.7095	+	51.1646i	0.0225485	+	0.0841522i
$609$	819.020	+	1091.09i	1.34486	+	1.79161i
$610$	151.291	+	3.31896i	0.248019	+	0.00544091i
$611$	−130.548			−0.213663
$612$	−63.9753	−	38.7648i	−0.104535	−	0.0633411i
$613$	−2.34342	+	2.34342i	−0.00382288	+	0.00382288i	−0.709016	−	0.705193i	$-0.750860\pi$
$613$	−2.34342	+	2.34342i	−0.00382288	+	0.00382288i	0.705193	+	0.709016i	$0.250860\pi$
$614$	−496.237	+	286.502i	−0.808203	+	0.466616i
$615$	−150.193	+	331.664i	−0.244216	+	0.539291i
$616$	−275.613	+	477.376i	−0.447424	+	0.774961i
$617$	−216.951	+	58.1318i	−0.351622	+	0.0942168i	−0.430307	−	0.902683i	$-0.641595\pi$
$617$	−216.951	+	58.1318i	−0.351622	+	0.0942168i	0.0786849	+	0.996900i	$0.474928\pi$
$618$	−349.766	+	140.559i	−0.565964	+	0.227441i
$619$	−49.2096	+	28.4112i	−0.0794985	+	0.0458985i	−0.539222	−	0.842163i	$-0.681282\pi$
$619$	−49.2096	+	28.4112i	−0.0794985	+	0.0458985i	0.459724	+	0.888062i	$0.347948\pi$
$620$	187.598	−	45.8816i	0.302577	−	0.0740026i
$621$	353.730	+	58.0498i	0.569613	+	0.0934779i
$622$	−381.543	−	381.543i	−0.613414	−	0.613414i
$623$	677.508	+	181.538i	1.08749	+	0.291393i
$624$	25.9963	−	60.9282i	0.0416607	−	0.0976413i
$625$	263.870	+	566.566i	0.422193	+	0.906506i
$626$	315.799	−	546.980i	0.504471	−	0.873770i
$627$	−364.574	+	464.849i	−0.581458	+	0.741386i
$628$	−156.760	−	42.0036i	−0.249617	−	0.0668847i
$629$			214.665i			0.341280i
$630$	589.208	+	25.4142i	0.935250	+	0.0403400i
$631$	−77.7427			−0.123206			−0.0616028	−	0.998101i	$-0.519621\pi$
$631$	−77.7427			−0.123206			−0.0616028	+	0.998101i	$0.519621\pi$
$632$	−17.2096	+	64.2273i	−0.0272305	+	0.101625i
$633$	−18.6773	+	131.126i	−0.0295060	+	0.207150i
$634$	−387.865	−	223.934i	−0.611775	−	0.353208i
$635$	−370.884	−	676.220i	−0.584069	−	1.06491i
$636$	−176.834	+	132.739i	−0.278041	+	0.208709i
$637$	−52.6908	+	196.645i	−0.0827171	+	0.308704i
$638$	−1032.00	+	1032.00i	−1.61755	+	1.61755i
$639$	−845.509	+	810.443i	−1.32317	+	1.26830i
$640$	48.3577	+	29.3519i	0.0755589	+	0.0458624i
$641$	418.814	+	725.407i	0.653376	+	1.13168i	0.982298	+	0.187324i	$0.0599814\pi$
$641$	418.814	+	725.407i	0.653376	+	1.13168i	−0.328922	+	0.944357i	$0.606685\pi$
$642$	−85.8237	+	109.429i	−0.133682	+	0.170451i
$643$	−274.595	−	1024.80i	−0.427053	−	1.59378i	−0.759399	−	0.650626i	$-0.774507\pi$
$643$	−274.595	−	1024.80i	−0.427053	−	1.59378i	0.332346	−	0.943158i	$-0.392160\pi$
$644$	−213.100	−	123.033i	−0.330901	−	0.191046i
$645$	354.932	+	58.5249i	0.550283	+	0.0907362i
$646$	27.5159	+	47.6590i	0.0425943	+	0.0737755i
$647$	248.658	+	248.658i	0.384325	+	0.384325i	0.872657	−	0.488333i	$-0.162395\pi$
$647$	248.658	+	248.658i	0.384325	+	0.384325i	−0.488333	+	0.872657i	$0.662395\pi$
$648$	154.997	+	168.712i	0.239193	+	0.260359i
$649$		−	1260.38i		−	1.94204i
$650$	−164.579	−	104.903i	−0.253198	−	0.161389i
$651$	−493.846	−	210.710i	−0.758596	−	0.323671i
$652$	64.4005	−	17.2561i	0.0987738	−	0.0264664i
$653$	170.003	+	634.459i	0.260341	+	0.971607i	0.965041	+	0.262101i	$0.0844152\pi$
$653$	170.003	+	634.459i	0.260341	+	0.971607i	−0.704699	+	0.709506i	$0.748918\pi$
$654$	39.7838	−	4.80976i	0.0608315	−	0.00735437i
$655$	191.115	−	182.910i	0.291778	−	0.279251i
$656$	97.0897			0.148003
$657$	−9.37955	+	442.949i	−0.0142763	+	0.674199i
$658$	−219.160	+	219.160i	−0.333070	+	0.333070i
$659$	422.865	−	244.141i	0.641676	−	0.370472i	−0.143584	−	0.989638i	$-0.545863\pi$
$659$	422.865	−	244.141i	0.641676	−	0.370472i	0.785260	+	0.619166i	$0.212529\pi$
$660$	61.9678	+	627.851i	0.0938906	+	0.951289i
$661$	−237.485	+	411.337i	−0.359282	+	0.622294i	−0.987841	−	0.155467i	$-0.950312\pi$
$661$	−237.485	+	411.337i	−0.359282	+	0.622294i	0.628559	+	0.777762i	$0.283645\pi$
$662$	400.266	−	107.251i	0.604632	−	0.162011i
$663$	9.70482	−	68.1339i	0.0146377	−	0.102766i
$664$	−144.517	+	83.4366i	−0.217645	+	0.125658i
$665$	−370.899	−	225.126i	−0.557742	−	0.338536i
$666$	183.570	−	631.314i	0.275630	−	0.947919i
$667$	−460.684	−	460.684i	−0.690680	−	0.690680i
$668$	456.461	+	122.308i	0.683325	+	0.183096i
$669$	−291.532	+	35.2455i	−0.435773	+	0.0526839i
$670$	166.713	−	571.717i	0.248826	−	0.853309i
$671$	225.032	−	389.766i	0.335368	−	0.580874i
$672$	−58.6424	−	145.926i	−0.0872655	−	0.217151i
$673$	469.529	+	125.810i	0.697666	+	0.186939i	0.590185	−	0.807268i	$-0.299055\pi$
$673$	469.529	+	125.810i	0.697666	+	0.186939i	0.107481	+	0.994207i	$0.465721\pi$
$674$			203.887i			0.302504i
$675$	565.029	−	369.279i	0.837080	−	0.547080i
$676$	−277.055			−0.409844
$677$	271.727	−	1014.10i	0.401370	−	1.49793i	−0.409284	−	0.912407i	$-0.634221\pi$
$677$	271.727	−	1014.10i	0.401370	−	1.49793i	0.810654	−	0.585526i	$-0.199112\pi$
$678$	−33.9656	+	13.6496i	−0.0500968	+	0.0201322i
$679$	298.103	+	172.110i	0.439032	+	0.253475i
$680$	56.4213	+	16.4525i	0.0829724	+	0.0241948i
$681$	−34.5405	−	285.700i	−0.0507202	−	0.419530i
$682$	148.660	−	554.808i	0.217977	−	0.813501i
$683$	889.225	−	889.225i	1.30194	−	1.30194i	0.374858	−	0.927082i	$-0.377692\pi$
$683$	889.225	−	889.225i	1.30194	−	1.30194i	0.927082	−	0.374858i	$-0.122308\pi$
$684$	−40.1669	−	163.692i	−0.0587236	−	0.239315i
$685$	−509.370	+	839.193i	−0.743605	+	1.22510i
$686$	−79.4244	−	137.567i	−0.115779	−	0.200535i
$687$	359.888	+	51.2615i	0.523855	+	0.0746165i
$688$	−24.8277	−	92.6581i	−0.0360867	−	0.134677i
$689$	−176.175	−	101.715i	−0.255696	−	0.147626i
$690$	−280.272	+	27.6624i	−0.406191	+	0.0400904i
$691$	450.332	+	779.998i	0.651711	+	1.12880i	0.982708	+	0.185165i	$0.0592818\pi$
$691$	450.332	+	779.998i	0.651711	+	1.12880i	−0.330996	+	0.943632i	$0.607385\pi$
$692$	−19.2341	−	19.2341i	−0.0277949	−	0.0277949i
$693$	908.957	−	1500.09i	1.31163	−	2.16464i
$694$		−	502.852i		−	0.724571i
$695$	−528.706	−	552.424i	−0.760729	−	0.794854i
$696$	−49.9772	−	413.385i	−0.0718064	−	0.593944i
$697$	97.4330	−	26.1071i	0.139789	−	0.0374564i
$698$	123.410	+	460.573i	0.176805	+	0.659846i
$699$	168.053	−	393.870i	0.240419	−	0.563476i
$700$	−452.396	+	100.182i	−0.646280	+	0.143118i
$701$	197.341			0.281514			0.140757	−	0.990044i	$-0.455046\pi$
$701$	197.341			0.281514			0.140757	+	0.990044i	$0.455046\pi$
$702$	−86.8055	+	192.078i	−0.123655	+	0.273615i
$703$	−342.017	+	342.017i	−0.486511	+	0.486511i
$704$	145.700	−	84.1202i	0.206961	−	0.119489i
$705$	−57.7135	+	350.012i	−0.0818632	+	0.496471i
$706$	−2.98676	+	5.17323i	−0.00423054	+	0.00732752i
$707$	1031.36	−	276.351i	1.45878	−	0.390878i
$708$	282.953	+	221.915i	0.399651	+	0.313440i
$709$	−796.364	+	459.781i	−1.12322	+	0.648492i	−0.942221	−	0.334991i	$-0.891267\pi$
$709$	−796.364	+	459.781i	−1.12322	+	0.648492i	−0.181000	+	0.983483i	$0.557933\pi$
$710$	477.457	−	786.616i	0.672475	−	1.10791i
$711$	59.0751	−	203.165i	0.0830874	−	0.285745i
$712$	−151.376	−	151.376i	−0.212606	−	0.212606i
$713$	247.666	+	66.3618i	0.347357	+	0.0930741i
$714$	−98.0887	−	130.673i	−0.137379	−	0.183015i
$715$	−508.929	+	279.130i	−0.711789	+	0.390392i
$716$	40.1086	−	69.4701i	0.0560176	−	0.0970253i
$717$	−449.318	−	63.9998i	−0.626665	−	0.0892605i
$718$	744.437	+	199.471i	1.03682	+	0.277815i
$719$		−	101.167i		−	0.140705i	−0.997522	−	0.0703527i	$-0.977588\pi$
$719$		−	101.167i		−	0.140705i	0.997522	−	0.0703527i	$-0.0224125\pi$
$720$	−151.861	−	96.6339i	−0.210919	−	0.134214i
$721$	−823.368			−1.14198
$722$	100.042	−	373.362i	0.138562	−	0.517122i
$723$	−690.931	−	541.887i	−0.955645	−	0.749497i
$724$	−265.811	−	153.466i	−0.367142	−	0.211970i
$725$	−1225.64	−	53.8007i	−1.69053	−	0.0742079i
$726$	1253.66	+	534.900i	1.72680	+	0.736777i
$727$	−154.448	+	576.407i	−0.212445	+	0.792857i	0.774605	+	0.632446i	$0.217949\pi$
$727$	−154.448	+	576.407i	−0.212445	+	0.792857i	−0.987050	+	0.160412i	$0.948718\pi$
$728$	102.313	−	102.313i	0.140539	−	0.140539i
$729$	−481.722	−	547.161i	−0.660798	−	0.750564i
$730$	−82.6967	−	338.126i	−0.113283	−	0.463186i
$731$	−49.8308	−	86.3096i	−0.0681681	−	0.118071i
$732$	47.8802	+	119.145i	0.0654101	+	0.162766i
$733$	80.6115	+	300.846i	0.109975	+	0.410431i	0.998862	−	0.0476948i	$-0.0151875\pi$
$733$	80.6115	+	300.846i	0.109975	+	0.410431i	−0.888887	+	0.458126i	$0.848521\pi$
$734$	−603.559	−	348.465i	−0.822287	−	0.474748i
$735$	503.928	+	228.203i	0.685617	+	0.310480i
$736$	37.5512	+	65.0405i	0.0510206	+	0.0883703i
$737$	−1252.40	−	1252.40i	−1.69932	−	1.69932i
$738$	−308.868	−	6.54037i	−0.418521	−	0.00886229i
$739$		−	806.022i		−	1.09069i	−0.838211	−	0.545347i	$-0.816398\pi$
$739$		−	806.022i		−	1.09069i	0.838211	−	0.545347i	$-0.183602\pi$
$740$	−11.3291	+	516.426i	−0.0153096	+	0.697873i
$741$	124.017	−	93.0927i	0.167365	−	0.125631i
$742$	−466.511	+	125.001i	−0.628721	+	0.168465i
$743$	92.4739	+	345.117i	0.124460	+	0.464492i	0.999820	−	0.0189806i	$-0.00604206\pi$
$743$	92.4739	+	345.117i	0.124460	+	0.464492i	−0.875360	+	0.483472i	$0.839375\pi$
$744$	98.3783	+	131.059i	0.132229	+	0.176154i
$745$	141.253	+	147.590i	0.189602	+	0.198107i
$746$	364.578			0.488710
$747$	465.366	−	255.699i	0.622980	−	0.342301i
$748$	123.596	−	123.596i	0.165235	−	0.165235i
$749$	−263.071	+	151.884i	−0.351229	+	0.202782i
$750$	−354.011	+	394.875i	−0.472015	+	0.526500i
$751$	−233.466	+	404.374i	−0.310873	+	0.538448i	−0.978552	−	0.206002i	$-0.933955\pi$
$751$	−233.466	+	404.374i	−0.310873	+	0.538448i	0.667679	+	0.744450i	$0.267288\pi$
$752$	91.3735	−	24.4835i	0.121507	−	0.0325578i
$753$	463.059	−	186.087i	0.614952	−	0.247128i
$754$	331.772	−	191.549i	0.440016	−	0.254043i
$755$	293.314	+	1199.29i	0.388496	+	1.58846i
$756$	176.727	+	468.179i	0.233766	+	0.619285i
$757$	6.70238	+	6.70238i	0.00885387	+	0.00885387i	0.711520	−	0.702666i	$-0.248007\pi$
$757$	6.70238	+	6.70238i	0.00885387	+	0.00885387i	−0.702666	+	0.711520i	$0.748007\pi$
$758$	467.832	+	125.355i	0.617193	+	0.165376i
$759$	−328.712	+	770.411i	−0.433086	+	1.01503i
$760$	63.6806	+	116.107i	0.0837903	+	0.152772i
$761$	−213.864	+	370.424i	−0.281031	+	0.486759i	−0.971639	−	0.236470i	$-0.924010\pi$
$761$	−213.864	+	370.424i	−0.281031	+	0.486759i	0.690608	+	0.723229i	$0.257343\pi$
$762$	403.865	−	514.947i	0.530006	−	0.675783i
$763$	84.5491	+	22.6549i	0.110811	+	0.0296918i
$764$			40.1610i			0.0525668i
$765$	−178.383	−	56.1405i	−0.233180	−	0.0733863i
$766$	−680.183			−0.887967
$767$	−85.6276	+	319.566i	−0.111640	+	0.416645i
$768$	−6.76868	+	47.5204i	−0.00881339	+	0.0618755i
$769$	−941.226	−	543.417i	−1.22396	−	0.706654i	−0.258201	−	0.966091i	$-0.583130\pi$
$769$	−941.226	−	543.417i	−1.22396	−	0.706654i	−0.965760	+	0.259437i	$0.916463\pi$
$770$	−385.778	+	1322.97i	−0.501010	+	1.71814i
$771$	160.780	−	120.688i	0.208534	−	0.156534i
$772$	27.5297	−	102.742i	0.0356602	−	0.133086i
$773$	99.8089	−	99.8089i	0.129119	−	0.129119i	−0.639594	−	0.768713i	$-0.720898\pi$
$773$	99.8089	−	99.8089i	0.129119	−	0.129119i	0.768713	+	0.639594i	$0.220898\pi$
$774$	72.7416	+	296.443i	0.0939814	+	0.383001i
$775$	428.317	−	222.840i	0.552667	−	0.287536i
$776$	−52.5298	−	90.9843i	−0.0676931	−	0.117248i
$777$	886.241	−	1130.00i	1.14059	−	1.45431i
$778$	−44.0987	−	164.579i	−0.0566821	−	0.211541i
$779$	196.831	+	113.641i	0.252672	+	0.145880i
$780$	26.9430	−	163.400i	0.0345423	−	0.209487i
$781$	−1368.35	−	2370.06i	−1.75205	−	3.03464i
$782$	55.1731	+	55.1731i	0.0705538	+	0.0705538i
$783$	131.144	+	1318.45i	0.167489	+	1.68385i
$784$		−	147.518i		−	0.188160i
$785$	−405.626	−	8.89843i	−0.516721	−	0.0113356i
$786$	206.461	+	88.0909i	0.262673	+	0.112075i
$787$	543.274	−	145.570i	0.690311	−	0.184968i	0.103424	−	0.994637i	$-0.467020\pi$
$787$	543.274	−	145.570i	0.690311	−	0.184968i	0.586887	+	0.809669i	$0.300353\pi$
$788$	−15.5251	−	57.9404i	−0.0197019	−	0.0735285i
$789$	−872.371	+	105.468i	−1.10567	+	0.133672i
$790$	−3.64585	+	166.192i	−0.00461500	+	0.210370i
$791$	−79.9571			−0.101084
$792$	−469.179	+	257.794i	−0.592397	+	0.325497i
$793$	−83.5359	+	83.5359i	−0.105342	+	0.105342i
$794$	−589.995	+	340.634i	−0.743066	+	0.429010i
$795$	−350.590	+	427.374i	−0.440994	+	0.537577i
$796$	371.939	−	644.217i	0.467260	−	0.809318i
$797$	451.428	−	120.960i	0.566409	−	0.151769i	0.0357598	−	0.999360i	$-0.488615\pi$
$797$	451.428	−	120.960i	0.566409	−	0.151769i	0.530649	+	0.847592i	$0.321948\pi$
$798$	51.9151	−	364.477i	0.0650566	−	0.456738i
$799$	85.1130	−	49.1400i	0.106524	−	0.0615019i
$800$	134.866	+	42.5579i	0.168582	+	0.0531974i
$801$	471.369	+	491.764i	0.588476	+	0.613937i
$802$	663.406	+	663.406i	0.827190	+	0.827190i
$803$	−999.982	−	267.944i	−1.24531	−	0.333679i
$804$	501.669	−	60.6506i	0.623967	−	0.0754361i
$805$	−590.571	−	172.211i	−0.733628	−	0.213927i
$806$	−75.3847	+	130.570i	−0.0935294	+	0.161998i
$807$	−194.995	−	485.225i	−0.241630	−	0.601271i
$808$	−314.781	−	84.3454i	−0.389581	−	0.104388i
$809$		−	349.626i		−	0.432170i	−0.976375	−	0.216085i	$-0.930671\pi$
$809$		−	349.626i		−	0.432170i	0.976375	−	0.216085i	$-0.0693289\pi$
$810$	476.602	+	317.648i	0.588398	+	0.392158i
$811$	−30.8407			−0.0380279			−0.0190140	−	0.999819i	$-0.506053\pi$
$811$	−30.8407			−0.0380279			−0.0190140	+	0.999819i	$0.506053\pi$
$812$	235.402	−	878.532i	0.289904	−	1.08194i
$813$	−50.7451	+	20.3927i	−0.0624170	+	0.0250832i
$814$	1330.45	+	768.136i	1.63446	+	0.943656i
$815$	146.143	−	80.1544i	0.179316	−	0.0983490i
$816$	5.98545	+	49.5084i	0.00733511	+	0.0606721i
$817$	58.1201	−	216.907i	0.0711384	−	0.265492i
$818$	554.497	−	554.497i	0.677869	−	0.677869i
$819$	−332.376	+	318.592i	−0.405831	+	0.389001i
$820$	235.775	−	57.6645i	0.287531	−	0.0703225i
$821$	233.988	+	405.278i	0.285003	+	0.493640i	0.972610	−	0.232443i	$-0.0746720\pi$
$821$	233.988	+	405.278i	0.285003	+	0.493640i	−0.687607	+	0.726083i	$0.741339\pi$
$822$	−824.662	−	117.463i	−1.00324	−	0.142899i
$823$	226.159	+	844.037i	0.274798	+	1.02556i	0.955976	+	0.293444i	$0.0948013\pi$
$823$	226.159	+	844.037i	0.274798	+	1.02556i	−0.681178	+	0.732118i	$0.738532\pi$
$824$	217.633	+	125.651i	0.264118	+	0.152489i
$825$	523.383	+	1487.88i	0.634404	+	1.80350i
$826$	392.728	+	680.225i	0.475458	+	0.823517i
$827$	752.181	+	752.181i	0.909530	+	0.909530i	0.996234	−	0.0867044i	$-0.0276336\pi$
$827$	752.181	+	752.181i	0.909530	+	0.909530i	−0.0867044	+	0.996234i	$0.527634\pi$
$828$	−115.079	−	209.441i	−0.138984	−	0.252948i
$829$			400.247i			0.482807i	0.970425	+	0.241403i	$0.0776077\pi$
$829$			400.247i			0.482807i	−0.970425	+	0.241403i	$0.922392\pi$
$830$	−301.392	+	288.452i	−0.363123	+	0.347533i
$831$	141.949	+	1174.12i	0.170817	+	1.41291i
$832$	−42.6568	+	11.4299i	−0.0512702	+	0.0137378i
$833$	−39.6669	−	148.039i	−0.0476194	−	0.177718i
$834$	254.630	−	596.783i	0.305312	−	0.715567i
$835$	1181.12	+	25.9109i	1.41452	+	0.0310310i
$836$	393.841			0.471101
$837$	−304.139	−	423.560i	−0.363368	−	0.506045i
$838$	−354.597	+	354.597i	−0.423146	+	0.423146i
$839$	452.007	−	260.966i	0.538745	−	0.311044i	−0.205825	−	0.978589i	$-0.565988\pi$
$839$	452.007	−	260.966i	0.538745	−	0.311044i	0.744570	+	0.667544i	$0.232655\pi$
$840$	−229.078	−	319.540i	−0.272712	−	0.380405i
$841$	783.561	−	1357.17i	0.931702	−	1.61375i
$842$	103.211	−	27.6554i	0.122579	−	0.0328449i
$843$	−1255.30	−	984.514i	−1.48909	−	1.16787i
$844$	76.4698	−	44.1499i	0.0906041	−	0.0523103i
$845$	−672.807	+	164.551i	−0.796221	+	0.194735i
$846$	−292.333	+	71.7331i	−0.345547	+	0.0847909i
$847$	2105.18	+	2105.18i	2.48546	+	2.48546i
$848$	142.384	+	38.1518i	0.167906	+	0.0449903i
$849$	−881.403	−	1174.20i	−1.03817	−	1.38304i
$850$	146.786	+	6.44336i	0.172690	+	0.00758042i
$851$	−342.895	+	593.912i	−0.402932	+	0.697898i
$852$	772.996	+	110.104i	0.907273	+	0.129230i
$853$	−1107.85	−	296.846i	−1.29876	−	0.348003i	−0.457781	−	0.889065i	$-0.651356\pi$
$853$	−1107.85	−	296.846i	−1.29876	−	0.348003i	−0.840983	+	0.541062i	$0.818022\pi$
$854$			280.474i			0.328424i
$855$	−194.764	−	373.657i	−0.227794	−	0.437025i
$856$	92.7134			0.108310
$857$	−247.113	+	922.239i	−0.288347	+	1.07613i	0.658012	+	0.753008i	$0.271398\pi$
$857$	−247.113	+	922.239i	−0.288347	+	1.07613i	−0.946359	+	0.323118i	$0.895269\pi$
$858$	−387.553	−	303.952i	−0.451694	−	0.354256i
$859$	−1057.96	−	610.813i	−1.23162	−	0.711075i	−0.264250	−	0.964454i	$-0.585125\pi$
$859$	−1057.96	−	610.813i	−1.23162	−	0.711075i	−0.967367	+	0.253380i	$0.918458\pi$
$860$	−115.324	−	210.267i	−0.134098	−	0.244497i
$861$	−620.671	−	264.822i	−0.720872	−	0.307575i
$862$	−236.164	+	881.376i	−0.273972	+	1.02248i
$863$	−216.363	+	216.363i	−0.250711	+	0.250711i	−0.821262	−	0.570551i	$-0.806730\pi$
$863$	−216.363	+	216.363i	−0.250711	+	0.250711i	0.570551	+	0.821262i	$0.306730\pi$
$864$	24.7341	−	150.719i	0.0286275	−	0.174443i
$865$	−58.1322	−	35.2848i	−0.0672048	−	0.0407917i
$866$	−547.156	−	947.702i	−0.631820	−	1.09434i
$867$	−303.969	−	756.397i	−0.350599	−	0.872430i
$868$	92.6434	+	345.750i	0.106732	+	0.398329i
$869$	428.156	+	247.196i	0.492699	+	0.284460i
$870$	−366.887	−	974.191i	−0.421710	−	1.11976i
$871$	232.457	+	402.627i	0.266885	+	0.462258i
$872$	−18.8908	−	18.8908i	−0.0216638	−	0.0216638i
$873$	160.982	+	292.984i	0.184401	+	0.335606i
$874$			175.810i			0.201156i
$875$	−1039.11	+	511.977i	−1.18755	+	0.585116i
$876$	236.219	−	177.316i	0.269657	−	0.202416i
$877$	541.093	−	144.985i	0.616982	−	0.165320i	0.0632263	−	0.997999i	$-0.479861\pi$
$877$	541.093	−	144.985i	0.616982	−	0.165320i	0.553755	+	0.832679i	$0.313194\pi$
$878$	100.512	+	375.116i	0.114478	+	0.427239i
$879$	453.863	+	604.633i	0.516341	+	0.687865i
$880$	303.861	−	290.815i	0.345297	−	0.330472i
$881$	1463.42			1.66109			0.830544	−	0.556952i	$-0.188029\pi$
$881$	1463.42			1.66109			0.830544	+	0.556952i	$0.188029\pi$
$882$	−9.93739	+	469.293i	−0.0112669	+	0.532078i
$883$	114.539	−	114.539i	0.129716	−	0.129716i	−0.639268	−	0.768984i	$-0.720763\pi$
$883$	114.539	−	114.539i	0.129716	−	0.129716i	0.768984	+	0.639268i	$0.220763\pi$
$884$	−39.7342	+	22.9405i	−0.0449481	+	0.0259508i
$885$	818.932	+	370.851i	0.925347	+	0.419041i
$886$	−117.909	+	204.224i	−0.133080	+	0.230501i
$887$	−326.737	+	87.5489i	−0.368362	+	0.0987023i	−0.438251	−	0.898852i	$-0.644402\pi$
$887$	−326.737	+	87.5489i	−0.368362	+	0.0987023i	0.0698894	+	0.997555i	$0.477735\pi$
$888$	−406.696	+	163.437i	−0.457991	+	0.184051i
$889$	1237.94	−	714.727i	1.39251	−	0.803968i
$890$	−457.511	−	277.698i	−0.514057	−	0.312020i
$891$	1509.95	−	788.505i	1.69467	−	0.884967i
$892$	138.430	+	138.430i	0.155191	+	0.155191i
$893$	213.900	+	57.3143i	0.239530	+	0.0641818i
$894$	−68.0288	+	159.441i	−0.0760949	+	0.178346i
$895$	56.1404	−	192.525i	0.0627267	−	0.215111i
$896$	−52.4227	+	90.7988i	−0.0585075	+	0.101338i
$897$	135.684	−	173.003i	0.151264	−	0.192869i
$898$	157.604	+	42.2298i	0.175505	+	0.0470265i
$899$			947.726i			1.05420i
$900$	−426.178	−	144.473i	−0.473531	−	0.160526i
$901$	153.147			0.169974
$902$	186.838	−	697.288i	0.207137	−	0.773047i
$903$	−94.0173	+	660.060i	−0.104117	+	0.730964i
$904$	21.1343	+	12.2019i	0.0233787	+	0.0134977i
$905$	−736.650	−	214.808i	−0.813978	−	0.237357i
$906$	−837.839	+	628.918i	−0.924767	+	0.694170i
$907$	162.780	−	607.502i	0.179471	−	0.669793i	−0.816276	−	0.577662i	$-0.803965\pi$
$907$	162.780	−	607.502i	0.179471	−	0.669793i	0.995747	−	0.0921315i	$-0.0293680\pi$
$908$	−135.661	+	135.661i	−0.149406	+	0.149406i
$909$	995.722	+	289.530i	1.09540	+	0.318515i
$910$	187.692	−	309.225i	0.206255	−	0.339808i
$911$	−201.739	−	349.422i	−0.221448	−	0.383559i	0.733800	−	0.679366i	$-0.237745\pi$
$911$	−201.739	−	349.422i	−0.221448	−	0.383559i	−0.955248	+	0.295807i	$0.904412\pi$
$912$	−69.3434	+	88.4162i	−0.0760345	+	0.0969476i
$913$	321.128	+	1198.47i	0.351728	+	1.31267i
$914$	−520.328	−	300.411i	−0.569286	−	0.328678i
$915$	187.037	+	260.897i	0.204412	+	0.285134i
$916$	−121.174	−	209.879i	−0.132285	−	0.229125i
$917$	346.696	+	346.696i	0.378076	+	0.378076i
$918$	−15.7062	−	157.903i	−0.0171092	−	0.172007i
$919$			299.486i			0.325883i	0.986636	+	0.162941i	$0.0520981\pi$
$919$			299.486i			0.325883i	−0.986636	+	0.162941i	$0.947902\pi$
$920$	129.820	+	135.643i	0.141108	+	0.147438i
$921$	−1118.01	−	477.024i	−1.21391	−	0.517941i
$922$	188.987	−	50.6388i	0.204975	−	0.0549228i
$923$	185.925	+	693.883i	0.201436	+	0.751769i
$924$	−1160.87	+	140.347i	−1.25636	+	0.151891i
$925$	279.209	+	1260.83i	0.301847	+	1.36306i
$926$	−13.3071			−0.0143705
$927$	−683.885	−	414.389i	−0.737740	−	0.447021i
$928$	−196.290	+	196.290i	−0.211520	+	0.211520i
$929$	−878.836	+	507.396i	−0.946002	+	0.546174i	−0.891837	−	0.452358i	$-0.850583\pi$
$929$	−878.836	+	507.396i	−0.946002	+	0.546174i	−0.0541651	+	0.998532i	$0.517250\pi$
$930$	316.744	+	259.836i	0.340585	+	0.279394i
$931$	172.665	−	299.064i	0.185462	−	0.321229i
$932$	−275.755	+	73.8883i	−0.295874	+	0.0792792i
$933$	161.409	−	1133.19i	0.173000	−	1.21457i
$934$	−355.013	+	204.967i	−0.380099	+	0.219450i
$935$	226.736	−	373.551i	0.242498	−	0.399519i
$936$	136.473	−	33.4879i	0.145804	−	0.0357777i
$937$	−379.548	−	379.548i	−0.405067	−	0.405067i	0.474947	−	0.880014i	$-0.342467\pi$
$937$	−379.548	−	379.548i	−0.405067	−	0.405067i	−0.880014	+	0.474947i	$0.842467\pi$
$938$	1066.16	+	285.675i	1.13663	+	0.304558i
$939$	1330.14	−	160.810i	1.41655	−	0.171257i
$940$	207.352	−	113.726i	0.220588	−	0.120985i
$941$	−751.860	+	1302.26i	−0.799001	+	1.38391i	0.121266	+	0.992620i	$0.461305\pi$
$941$	−751.860	+	1302.26i	−0.799001	+	1.38391i	−0.920267	+	0.391291i	$0.872029\pi$
$942$	−128.371	−	319.439i	−0.136275	−	0.339107i
$943$	311.269	+	83.4042i	0.330084	+	0.0884456i
$944$		−	239.730i		−	0.253951i
$945$	707.234	+	1031.97i	0.748396	+	1.09204i
$946$	−713.238			−0.753952
$947$	134.901	−	503.457i	0.142451	−	0.531633i	−0.857405	−	0.514642i	$-0.827925\pi$
$947$	134.901	−	503.457i	0.142451	−	0.531633i	0.999856	−	0.0169909i	$-0.00540865\pi$
$948$	−130.880	+	52.5961i	−0.138059	+	0.0554811i
$949$	235.339	+	135.873i	0.247986	+	0.143175i
$950$	223.603	+	244.135i	0.235372	+	0.256984i
$951$	−114.031	−	943.204i	−0.119907	−	0.991803i
$952$	−28.1926	+	105.216i	−0.0296140	+	0.110521i
$953$	−590.201	+	590.201i	−0.619308	+	0.619308i	−0.945354	−	0.326046i	$-0.894284\pi$
$953$	−590.201	+	590.201i	−0.619308	+	0.619308i	0.326046	+	0.945354i	$0.394284\pi$
$954$	−450.393	−	130.963i	−0.472110	−	0.137277i
$955$	23.8528	+	97.5280i	0.0249768	+	0.102124i
$956$	151.285	+	262.032i	0.158247	+	0.274093i
$957$	−3065.06	−	436.580i	−3.20278	−	0.456196i
$958$	−173.233	−	646.514i	−0.180828	−	0.674858i
$959$	−1575.71	−	909.737i	−1.64308	−	0.948631i
$960$	11.7865	+	119.420i	0.0122776	+	0.124396i
$961$	294.009	+	509.239i	0.305941	+	0.529905i
$962$	−285.146	−	285.146i	−0.296410	−	0.296410i
$963$	−294.946	−	6.24556i	−0.306278	−	0.00648552i
$964$			585.388i			0.607249i
$965$	5.83214	−	265.852i	0.00604367	−	0.275495i
$966$	−62.6507	−	518.213i	−0.0648558	−	0.536452i
$967$	183.924	−	49.2822i	0.190200	−	0.0509640i	−0.162461	−	0.986715i	$-0.551943\pi$
$967$	183.924	−	49.2822i	0.190200	−	0.0509640i	0.352662	+	0.935751i	$0.385277\pi$
$968$	−235.181	−	877.707i	−0.242955	−	0.906722i
$969$	−45.8138	+	107.375i	−0.0472794	+	0.110810i
$970$	−181.603	−	189.750i	−0.187220	−	0.195618i
$971$	1340.57			1.38061			0.690306	−	0.723518i	$-0.257476\pi$
$971$	1340.57			1.38061			0.690306	+	0.723518i	$0.257476\pi$
$972$	−88.8390	+	477.811i	−0.0913981	+	0.491575i
$973$	1002.14	−	1002.14i	1.02995	−	1.02995i
$974$	−724.256	+	418.149i	−0.743589	+	0.429311i
$975$	−31.6188	−	412.806i	−0.0324296	−	0.423390i
$976$	42.8019	−	74.1351i	0.0438545	−	0.0759581i
$977$	18.4987	−	4.95670i	0.0189341	−	0.00507339i	−0.249340	−	0.968416i	$-0.580214\pi$
$977$	18.4987	−	4.95670i	0.0189341	−	0.00507339i	0.268274	+	0.963343i	$0.413547\pi$
$978$	111.289	+	87.2821i	0.113792	+	0.0892455i
$979$	−1378.47	+	795.859i	−1.40804	+	0.812931i
$980$	−87.6151	−	358.235i	−0.0894031	−	0.365546i
$981$	58.8242	+	61.3693i	0.0599635	+	0.0625579i
$982$	293.186	+	293.186i	0.298560	+	0.298560i
$983$	885.201	+	237.189i	0.900510	+	0.241291i	0.679235	−	0.733921i	$-0.262312\pi$
$983$	885.201	+	237.189i	0.900510	+	0.241291i	0.221275	+	0.975211i	$0.428978\pi$
$984$	123.643	+	164.716i	0.125653	+	0.167394i
$985$	−72.1141	−	131.483i	−0.0732122	−	0.133485i
$986$	−144.203	+	249.766i	−0.146250	+	0.253313i
$987$	−650.910	−	92.7139i	−0.659483	−	0.0939351i
$988$	−99.8571	−	26.7566i	−0.101070	−	0.0270816i
$989$		−	318.389i		−	0.321930i
$990$	−986.254	+	904.692i	−0.996216	+	0.913830i
$991$	−459.297			−0.463468			−0.231734	−	0.972779i	$-0.574440\pi$
$991$	−459.297			−0.463468			−0.231734	+	0.972779i	$0.574440\pi$
$992$	28.2758	−	105.527i	0.0285038	−	0.106378i
$993$	691.690	+	542.482i	0.696566	+	0.546306i
$994$	1476.99	+	852.741i	1.48591	+	0.857888i
$995$	520.606	−	1785.34i	0.523222	−	1.79431i
$996$	−325.593	−	138.921i	−0.326901	−	0.139479i
$997$	−260.356	+	971.661i	−0.261139	+	0.974585i	0.703432	+	0.710762i	$0.251650\pi$
$997$	−260.356	+	971.661i	−0.261139	+	0.974585i	−0.964571	+	0.263822i	$0.915017\pi$
$998$	491.353	−	491.353i	0.492337	−	0.492337i
$999$	1304.82	−	492.540i	1.30613	−	0.493033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.k.a.67.5	yes	24
3.2	odd	2		270.3.l.b.37.5		24
5.3	odd	4	inner	90.3.k.a.13.4	yes	24
9.2	odd	6		270.3.l.b.127.2		24
9.4	even	3		810.3.g.k.487.4		12
9.5	odd	6		810.3.g.i.487.3		12
9.7	even	3	inner	90.3.k.a.7.4	✓	24
15.8	even	4		270.3.l.b.253.2		24
45.13	odd	12		810.3.g.k.163.4		12
45.23	even	12		810.3.g.i.163.3		12
45.38	even	12		270.3.l.b.73.5		24
45.43	odd	12	inner	90.3.k.a.43.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.4	✓	24	9.7	even	3	inner
90.3.k.a.13.4	yes	24	5.3	odd	4	inner
90.3.k.a.43.5	yes	24	45.43	odd	12	inner
90.3.k.a.67.5	yes	24	1.1	even	1	trivial
270.3.l.b.37.5		24	3.2	odd	2
270.3.l.b.73.5		24	45.38	even	12
270.3.l.b.127.2		24	9.2	odd	6
270.3.l.b.253.2		24	15.8	even	4
810.3.g.i.163.3		12	45.23	even	12
810.3.g.i.487.3		12	9.5	odd	6
810.3.g.k.163.4		12	45.13	odd	12
810.3.g.k.487.4		12	9.4	even	3

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(2.78364 - 1.11865i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.80008 - 1.39971i) q^{5} +(-0.509217 - 4.21197i) q^{6} +(2.39851 - 8.95134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.49726 - 6.22781i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(2.78364 - 1.11865i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-4.80008 - 1.39971i) q^{5} +(-0.509217 - 4.21197i) q^{6} +(2.39851 - 8.95134i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(6.49726 - 6.22781i) q^{9} +(-3.66899 + 6.04471i) q^{10} +(10.5150 + 18.2126i) q^{11} +(-5.94005 - 0.846085i) q^{12} +(-1.42873 - 5.33210i) q^{13} +(-11.3498 - 6.55284i) q^{14} +(-14.9275 + 1.47332i) q^{15} +(2.00000 + 3.46410i) q^{16} +(2.93855 + 2.93855i) q^{17} +(-6.12918 - 11.1550i) q^{18} +9.36376i q^{19} +(6.91428 + 7.22445i) q^{20} +(-3.33682 - 27.6004i) q^{21} +(28.7276 - 7.69753i) q^{22} +(3.43617 + 12.8240i) q^{23} +(-3.32998 + 7.80456i) q^{24} +(21.0816 + 13.4374i) q^{25} -7.80674 q^{26} +(11.1193 - 24.6041i) q^{27} +(-13.1057 + 13.1057i) q^{28} +(-42.4981 + 24.5363i) q^{29} +(-3.45125 + 20.9306i) q^{30} +(9.65636 - 16.7253i) q^{31} +(5.46410 - 1.46410i) q^{32} +(49.6434 + 38.9345i) q^{33} +(5.08973 - 2.93855i) q^{34} +(-24.0423 + 39.6100i) q^{35} +(-17.4814 + 4.28961i) q^{36} +(36.5256 + 36.5256i) q^{37} +(12.7911 + 3.42738i) q^{38} +(-9.94181 - 13.2444i) q^{39} +(12.3996 - 6.80075i) q^{40} +(12.1362 - 21.0205i) q^{41} +(-38.9242 - 5.54426i) q^{42} +(-23.1645 - 6.20691i) q^{43} -42.0601i q^{44} +(-39.9045 + 20.7997i) q^{45} +18.7756 q^{46} +(6.12087 - 22.8434i) q^{47} +(9.44238 + 7.40551i) q^{48} +(-31.9385 - 18.4397i) q^{49} +(26.0723 - 23.8796i) q^{50} +(11.4671 + 4.89267i) q^{51} +(-2.85746 + 10.6642i) q^{52} +(26.0581 - 26.0581i) q^{53} +(-29.5399 - 24.1950i) q^{54} +(-24.9807 - 102.140i) q^{55} +(13.1057 + 22.6997i) q^{56} +(10.4747 + 26.0653i) q^{57} +(17.9618 + 67.0344i) q^{58} +(-51.9031 - 29.9663i) q^{59} +(27.3285 + 12.3756i) q^{60} +(-10.7005 - 18.5338i) q^{61} +(-19.3127 - 19.3127i) q^{62} +(-40.1635 - 73.0967i) q^{63} -8.00000i q^{64} +(-0.605352 + 27.5944i) q^{65} +(71.3563 - 53.5631i) q^{66} +(-81.3506 + 21.7978i) q^{67} +(-2.15117 - 8.02828i) q^{68} +(23.9105 + 31.8534i) q^{69} +(45.3082 + 47.3407i) q^{70} -130.133 q^{71} +(-0.538913 + 25.4501i) q^{72} +(-34.8091 + 34.8091i) q^{73} +(63.2642 - 36.5256i) q^{74} +(73.7153 + 13.8221i) q^{75} +(9.36376 - 16.2185i) q^{76} +(188.247 - 50.4407i) q^{77} +(-21.7311 + 8.73298i) q^{78} +(20.3592 - 11.7544i) q^{79} +(-4.75144 - 19.4274i) q^{80} +(3.42885 - 80.9274i) q^{81} +(-24.2724 - 24.2724i) q^{82} +(56.9883 + 15.2700i) q^{83} +(-21.8208 + 51.1421i) q^{84} +(-9.99219 - 18.2184i) q^{85} +(-16.9576 + 29.3714i) q^{86} +(-90.8519 + 115.841i) q^{87} +(-57.4552 - 15.3951i) q^{88} +75.6878i q^{89} +(13.8069 + 62.1238i) q^{90} -51.1563 q^{91} +(6.87234 - 25.6479i) q^{92} +(8.17010 - 57.3592i) q^{93} +(-28.9642 - 16.7225i) q^{94} +(13.1065 - 44.9469i) q^{95} +(13.5723 - 10.1879i) q^{96} +(-9.61362 + 35.8785i) q^{97} +(-36.8794 + 36.8794i) q^{98} +(181.743 + 52.8462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 6 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q - 12 * q^2 - 6 * q^7 - 48 * q^8	\( 24 q - 12 q^{2} - 6 q^{7} - 48 q^{8} - 12 q^{10} - 12 q^{11} + 42 q^{15} + 48 q^{16} - 36 q^{17} - 12 q^{18} + 12 q^{20} + 96 q^{21} - 12 q^{22} - 54 q^{23} + 54 q^{25} + 162 q^{27} - 24 q^{28} - 48 q^{30} - 72 q^{31} + 48 q^{32} + 6 q^{33} - 336 q^{35} - 72 q^{36} + 132 q^{37} - 36 q^{38} + 12 q^{40} + 24 q^{41} - 144 q^{42} + 108 q^{43} - 186 q^{45} + 216 q^{46} + 48 q^{47} + 54 q^{50} + 108 q^{51} + 384 q^{53} - 552 q^{55} + 24 q^{56} + 186 q^{57} + 60 q^{58} + 144 q^{60} - 456 q^{61} + 144 q^{62} + 72 q^{63} + 264 q^{65} + 240 q^{66} + 12 q^{67} - 36 q^{68} + 174 q^{70} - 168 q^{71} + 96 q^{72} - 432 q^{73} - 468 q^{75} - 72 q^{76} - 48 q^{77} - 264 q^{78} - 480 q^{81} - 48 q^{82} - 246 q^{83} + 324 q^{85} + 216 q^{86} - 636 q^{87} + 24 q^{88} - 12 q^{90} + 1224 q^{91} - 108 q^{92} + 180 q^{93} + 432 q^{95} - 102 q^{97} + 24 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 - 6 * q^7 - 48 * q^8 - 12 * q^10 - 12 * q^11 + 42 * q^15 + 48 * q^16 - 36 * q^17 - 12 * q^18 + 12 * q^20 + 96 * q^21 - 12 * q^22 - 54 * q^23 + 54 * q^25 + 162 * q^27 - 24 * q^28 - 48 * q^30 - 72 * q^31 + 48 * q^32 + 6 * q^33 - 336 * q^35 - 72 * q^36 + 132 * q^37 - 36 * q^38 + 12 * q^40 + 24 * q^41 - 144 * q^42 + 108 * q^43 - 186 * q^45 + 216 * q^46 + 48 * q^47 + 54 * q^50 + 108 * q^51 + 384 * q^53 - 552 * q^55 + 24 * q^56 + 186 * q^57 + 60 * q^58 + 144 * q^60 - 456 * q^61 + 144 * q^62 + 72 * q^63 + 264 * q^65 + 240 * q^66 + 12 * q^67 - 36 * q^68 + 174 * q^70 - 168 * q^71 + 96 * q^72 - 432 * q^73 - 468 * q^75 - 72 * q^76 - 48 * q^77 - 264 * q^78 - 480 * q^81 - 48 * q^82 - 246 * q^83 + 324 * q^85 + 216 * q^86 - 636 * q^87 + 24 * q^88 - 12 * q^90 + 1224 * q^91 - 108 * q^92 + 180 * q^93 + 432 * q^95 - 102 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more