LMFDB - Embedded newform 350.2.q.a.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			331.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	350.331
Dual form			350.2.q.a.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(-1.47815 - 0.658114i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.255585 - 0.283856i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(-1.47815 - 0.658114i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.255585 - 0.283856i) q^{9} +(-1.49622 + 1.66172i) q^{10} +(-1.90977 + 2.12101i) q^{11} +(-1.08268 - 1.20243i) q^{12} +(0.263932 - 0.812299i) q^{13} +(-1.02924 + 2.43735i) q^{14} +(2.92705 - 2.12663i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.596670 + 5.67693i) q^{17} +(-0.190983 - 0.330792i) q^{18} +(-5.48127 + 2.44042i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(2.44890 - 3.51128i) q^{21} +(-2.30902 + 1.67760i) q^{22} +(7.30885 + 1.55354i) q^{23} +(-0.809017 - 1.40126i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(0.427051 - 0.739674i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-1.51351 + 2.17009i) q^{28} +(4.42705 - 3.21644i) q^{29} +(3.30524 - 1.47159i) q^{30} +(-0.193806 + 1.84395i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.21878 - 1.87832i) q^{33} +(-1.76393 + 5.42882i) q^{34} +(-4.47214 - 3.87298i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(1.75181 + 1.94558i) q^{37} +(-5.86889 + 1.24747i) q^{38} +(-0.924716 + 1.02700i) q^{39} +(-2.04275 + 0.909491i) q^{40} +(3.59017 - 11.0494i) q^{41} +(3.12543 - 2.92540i) q^{42} -2.23607 q^{43} +(-2.60735 + 1.16087i) q^{44} +(0.835438 - 0.177578i) q^{45} +(6.82614 + 3.03919i) q^{46} +(-0.497966 - 4.73783i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.54508 - 4.75528i) q^{50} +(4.61803 - 7.99867i) q^{51} +(0.571506 - 0.634721i) q^{52} +(3.86984 + 1.72296i) q^{53} +(0.571994 + 5.44216i) q^{54} +(-1.97214 - 6.06961i) q^{55} +(-1.93162 + 1.80800i) q^{56} +9.70820 q^{57} +(4.99904 - 2.22572i) q^{58} +(-10.1006 + 2.14695i) q^{59} +(3.53897 - 0.752232i) q^{60} +(-3.68168 - 0.782565i) q^{61} +(-0.572949 + 1.76336i) q^{62} +(0.865272 - 0.522102i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.27793 + 1.41928i) q^{65} +(4.51712 - 0.960143i) q^{66} +(0.104528 - 0.994522i) q^{67} +(-2.85410 + 4.94345i) q^{68} +(-9.78115 - 7.10642i) q^{69} +(-3.56917 - 4.71816i) q^{70} +(1.57295 - 1.14281i) q^{71} +(-0.0399263 - 0.379874i) q^{72} +(5.09746 - 5.66130i) q^{73} +(1.30902 + 2.26728i) q^{74} +(0.845653 + 8.04585i) q^{75} -6.00000 q^{76} +(-4.55567 - 6.02223i) q^{77} +(-1.11803 + 0.812299i) q^{78} +(0.934931 + 8.89527i) q^{79} +(-2.18720 + 0.464905i) q^{80} +(0.805727 - 7.66598i) q^{81} +(5.80902 - 10.0615i) q^{82} +(8.28115 + 6.01661i) q^{83} +(3.66535 - 2.21166i) q^{84} +(-10.3262 - 7.50245i) q^{85} +(-2.18720 - 0.464905i) q^{86} +(-8.66062 + 1.84087i) q^{87} +(-2.79173 + 0.593401i) q^{88} +(16.7167 + 3.55325i) q^{89} +0.854102 q^{90} +(1.97845 + 1.09187i) q^{91} +(6.04508 + 4.39201i) q^{92} +(1.50000 - 2.59808i) q^{93} +(0.497966 - 4.73783i) q^{94} +(1.40240 - 13.3429i) q^{95} +(-0.169131 - 1.60917i) q^{96} +(5.47214 - 3.97574i) q^{97} +(-5.81779 - 3.89273i) q^{98} +1.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	−1.47815	−	0.658114i	−0.853409	−	0.379962i	−0.0670631	−	0.997749i	$-0.521363\pi$
$3$	−1.47815	−	0.658114i	−0.853409	−	0.379962i	−0.786346	+	0.617787i	$0.788030\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i
$6$	−1.30902	−	0.951057i	−0.534404	−	0.388267i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.255585	−	0.283856i	−0.0851950	−	0.0946187i
$10$	−1.49622	+	1.66172i	−0.473147	+	0.525483i
$11$	−1.90977	+	2.12101i	−0.575816	+	0.639509i	−0.958744	−	0.284269i	$-0.908249\pi$
$11$	−1.90977	+	2.12101i	−0.575816	+	0.639509i	0.382928	+	0.923778i	$0.374916\pi$
$12$	−1.08268	−	1.20243i	−0.312542	−	0.347113i
$13$	0.263932	−	0.812299i	0.0732016	−	0.225291i	−0.907761	−	0.419487i	$-0.862210\pi$
$13$	0.263932	−	0.812299i	0.0732016	−	0.225291i	0.980963	+	0.194196i	$0.0622098\pi$
$14$	−1.02924	+	2.43735i	−0.275077	+	0.651408i
$15$	2.92705	−	2.12663i	0.755761	−	0.549093i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.596670	+	5.67693i	−0.144714	+	1.37686i	0.645375	+	0.763866i	$0.276701\pi$
$17$	−0.596670	+	5.67693i	−0.144714	+	1.37686i	−0.790089	+	0.612993i	$0.789965\pi$
$18$	−0.190983	−	0.330792i	−0.0450151	−	0.0779685i
$19$	−5.48127	+	2.44042i	−1.25749	+	0.559871i	−0.923823	−	0.382820i	$-0.874953\pi$
$19$	−5.48127	+	2.44042i	−1.25749	+	0.559871i	−0.333667	+	0.942691i	$0.608286\pi$
$20$	−1.80902	+	1.31433i	−0.404508	+	0.293893i
$21$	2.44890	−	3.51128i	0.534395	−	0.766225i
$22$	−2.30902	+	1.67760i	−0.492284	+	0.357665i
$23$	7.30885	+	1.55354i	1.52400	+	0.323936i	0.892360	−	0.451325i	$-0.149048\pi$
$23$	7.30885	+	1.55354i	1.52400	+	0.323936i	0.631641	+	0.775261i	$0.282382\pi$
$24$	−0.809017	−	1.40126i	−0.165140	−	0.286031i
$25$	−2.50000	−	4.33013i	−0.500000	−	0.866025i
$26$	0.427051	−	0.739674i	0.0837516	−	0.145062i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−1.51351	+	2.17009i	−0.286026	+	0.410109i
$29$	4.42705	−	3.21644i	0.822083	−	0.597278i	−0.0952256	−	0.995456i	$-0.530357\pi$
$29$	4.42705	−	3.21644i	0.822083	−	0.597278i	0.917308	+	0.398178i	$0.130357\pi$
$30$	3.30524	−	1.47159i	0.603451	−	0.268674i
$31$	−0.193806	+	1.84395i	−0.0348087	+	0.331182i	0.963235	+	0.268660i	$0.0865810\pi$
$31$	−0.193806	+	1.84395i	−0.0348087	+	0.331182i	−0.998044	+	0.0625218i	$0.980086\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.21878	−	1.87832i	0.734396	−	0.326974i
$34$	−1.76393	+	5.42882i	−0.302512	+	0.931036i
$35$	−4.47214	−	3.87298i	−0.755929	−	0.654654i
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	1.75181	+	1.94558i	0.287995	+	0.319851i	0.869730	−	0.493527i	$-0.164293\pi$
$37$	1.75181	+	1.94558i	0.287995	+	0.319851i	−0.581735	+	0.813378i	$0.697626\pi$
$38$	−5.86889	+	1.24747i	−0.952059	+	0.202366i
$39$	−0.924716	+	1.02700i	−0.148073	+	0.164452i
$40$	−2.04275	+	0.909491i	−0.322987	+	0.143803i
$41$	3.59017	−	11.0494i	0.560690	−	1.72563i	−0.119731	−	0.992806i	$-0.538203\pi$
$41$	3.59017	−	11.0494i	0.560690	−	1.72563i	0.680421	−	0.732821i	$-0.261797\pi$
$42$	3.12543	−	2.92540i	0.482264	−	0.451399i
$43$	−2.23607			−0.340997			−0.170499	−	0.985358i	$-0.554538\pi$
$43$	−2.23607			−0.340997			−0.170499	+	0.985358i	$0.554538\pi$
$44$	−2.60735	+	1.16087i	−0.393073	+	0.175007i
$45$	0.835438	−	0.177578i	0.124540	−	0.0264717i
$46$	6.82614	+	3.03919i	1.00646	+	0.448104i
$47$	−0.497966	−	4.73783i	−0.0726359	−	0.691084i	−0.968881	−	0.247526i	$-0.920383\pi$
$47$	−0.497966	−	4.73783i	−0.0726359	−	0.691084i	0.896245	−	0.443558i	$-0.146284\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−1.54508	−	4.75528i	−0.218508	−	0.672499i
$51$	4.61803	−	7.99867i	0.646654	−	1.12004i
$52$	0.571506	−	0.634721i	0.0792536	−	0.0880200i
$53$	3.86984	+	1.72296i	0.531563	+	0.236667i	0.654924	−	0.755695i	$-0.272701\pi$
$53$	3.86984	+	1.72296i	0.531563	+	0.236667i	−0.123361	+	0.992362i	$0.539367\pi$
$54$	0.571994	+	5.44216i	0.0778385	+	0.740584i
$55$	−1.97214	−	6.06961i	−0.265923	−	0.818426i
$56$	−1.93162	+	1.80800i	−0.258123	+	0.241604i
$57$	9.70820			1.28588
$58$	4.99904	−	2.22572i	0.656407	−	0.292251i
$59$	−10.1006	+	2.14695i	−1.31498	+	0.279509i	−0.811427	−	0.584454i	$-0.801309\pi$
$59$	−10.1006	+	2.14695i	−1.31498	+	0.279509i	−0.503557	+	0.863962i	$0.667976\pi$
$60$	3.53897	−	0.752232i	0.456879	−	0.0971127i
$61$	−3.68168	−	0.782565i	−0.471391	−	0.100197i	−0.0339100	−	0.999425i	$-0.510796\pi$
$61$	−3.68168	−	0.782565i	−0.471391	−	0.100197i	−0.437481	+	0.899228i	$0.644129\pi$
$62$	−0.572949	+	1.76336i	−0.0727646	+	0.223946i
$63$	0.865272	−	0.522102i	0.109014	−	0.0657786i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.27793	+	1.41928i	0.158507	+	0.176040i
$66$	4.51712	−	0.960143i	0.556019	−	0.118185i
$67$	0.104528	−	0.994522i	0.0127702	−	0.121500i	−0.986280	−	0.165083i	$-0.947211\pi$
$67$	0.104528	−	0.994522i	0.0127702	−	0.121500i	0.999050	+	0.0435832i	$0.0138774\pi$
$68$	−2.85410	+	4.94345i	−0.346111	+	0.599481i
$69$	−9.78115	−	7.10642i	−1.17751	−	0.855513i
$70$	−3.56917	−	4.71816i	−0.426597	−	0.563928i
$71$	1.57295	−	1.14281i	0.186675	−	0.135627i	−0.490523	−	0.871428i	$-0.663194\pi$
$71$	1.57295	−	1.14281i	0.186675	−	0.135627i	0.677198	+	0.735801i	$0.263194\pi$
$72$	−0.0399263	−	0.379874i	−0.00470536	−	0.0447685i
$73$	5.09746	−	5.66130i	0.596613	−	0.662605i	−0.366903	−	0.930259i	$-0.619582\pi$
$73$	5.09746	−	5.66130i	0.596613	−	0.662605i	0.963515	+	0.267654i	$0.0862484\pi$
$74$	1.30902	+	2.26728i	0.152170	+	0.263566i
$75$	0.845653	+	8.04585i	0.0976476	+	0.929055i
$76$	−6.00000			−0.688247
$77$	−4.55567	−	6.02223i	−0.519166	−	0.686296i
$78$	−1.11803	+	0.812299i	−0.126592	+	0.0919748i
$79$	0.934931	+	8.89527i	0.105188	+	1.00080i	0.912056	+	0.410065i	$0.134494\pi$
$79$	0.934931	+	8.89527i	0.105188	+	1.00080i	−0.806868	+	0.590731i	$0.798839\pi$
$80$	−2.18720	+	0.464905i	−0.244537	+	0.0519779i
$81$	0.805727	−	7.66598i	0.0895252	−	0.851775i
$82$	5.80902	−	10.0615i	0.641499	−	1.11111i
$83$	8.28115	+	6.01661i	0.908975	+	0.660409i	0.940755	−	0.339086i	$-0.110118\pi$
$83$	8.28115	+	6.01661i	0.908975	+	0.660409i	−0.0317807	+	0.999495i	$0.510118\pi$
$84$	3.66535	−	2.21166i	0.399923	−	0.241312i
$85$	−10.3262	−	7.50245i	−1.12004	−	0.813755i
$86$	−2.18720	−	0.464905i	−0.235852	−	0.0501320i
$87$	−8.66062	+	1.84087i	−0.928516	+	0.197362i
$88$	−2.79173	+	0.593401i	−0.297600	+	0.0632568i
$89$	16.7167	+	3.55325i	1.77197	+	0.376643i	0.974087	−	0.226173i	$-0.0726213\pi$
$89$	16.7167	+	3.55325i	1.77197	+	0.376643i	0.797880	+	0.602816i	$0.205955\pi$
$90$	0.854102			0.0900303
$91$	1.97845	+	1.09187i	0.207398	+	0.114459i
$92$	6.04508	+	4.39201i	0.630244	+	0.457899i
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$	0.497966	−	4.73783i	0.0513613	−	0.488670i
$95$	1.40240	−	13.3429i	0.143883	−	1.36895i
$96$	−0.169131	−	1.60917i	−0.0172618	−	0.164235i
$97$	5.47214	−	3.97574i	0.555611	−	0.403675i	−0.274239	−	0.961662i	$-0.588426\pi$
$97$	5.47214	−	3.97574i	0.555611	−	0.403675i	0.829850	+	0.557986i	$0.188426\pi$
$98$	−5.81779	−	3.89273i	−0.587685	−	0.393225i
$99$	1.09017			0.109566
$100$	−0.522642	−	4.97261i	−0.0522642	−	0.497261i
$101$	4.35410	+	7.54153i	0.433249	+	0.750410i	0.997151	−	0.0754321i	$-0.0240336\pi$
$101$	4.35410	+	7.54153i	0.433249	+	0.750410i	−0.563902	+	0.825842i	$0.690700\pi$
$102$	6.18014	−	6.86374i	0.611925	−	0.679611i
$103$	1.56210	+	14.8624i	0.153918	+	1.46444i	0.749960	+	0.661483i	$0.230073\pi$
$103$	1.56210	+	14.8624i	0.153918	+	1.46444i	−0.596042	+	0.802953i	$0.703261\pi$
$104$	0.690983	−	0.502029i	0.0677565	−	0.0492279i
$105$	4.06161	+	8.66802i	0.396373	+	0.845912i
$106$	3.42705	+	2.48990i	0.332865	+	0.241840i
$107$	−2.28115	+	3.95107i	−0.220527	+	0.381965i	−0.954968	−	0.296708i	$-0.904111\pi$
$107$	−2.28115	+	3.95107i	−0.220527	+	0.381965i	0.734441	+	0.678673i	$0.237445\pi$
$108$	−0.571994	+	5.44216i	−0.0550401	+	0.523672i
$109$	−3.16535	+	0.672816i	−0.303186	+	0.0644441i	−0.356993	−	0.934107i	$-0.616198\pi$
$109$	−3.16535	+	0.672816i	−0.303186	+	0.0644441i	0.0538068	+	0.998551i	$0.482865\pi$
$110$	−0.667097	−	6.34700i	−0.0636052	−	0.605163i
$111$	−1.30902	−	4.02874i	−0.124246	−	0.382391i
$112$	−2.26531	+	1.36688i	−0.214052	+	0.129158i
$113$	−6.30902	+	19.4172i	−0.593502	+	1.82661i	−0.0314586	+	0.999505i	$0.510015\pi$
$113$	−6.30902	+	19.4172i	−0.593502	+	1.82661i	−0.562044	+	0.827107i	$0.689985\pi$
$114$	9.49606	+	2.01845i	0.889387	+	0.189045i
$115$	−11.1800	+	12.4166i	−1.04254	+	1.15786i
$116$	5.35256	−	1.13772i	0.496972	−	0.105635i
$117$	−0.298033	+	0.132693i	−0.0275532	+	0.0122675i
$118$	−10.3262			−0.950607
$119$	−14.4508	−	4.38866i	−1.32470	−	0.402308i
$120$	3.61803			0.330280
$121$	0.298335	+	2.83847i	0.0271214	+	0.258042i
$122$	−3.43852	−	1.53093i	−0.311309	−	0.138604i
$123$	−12.5786	+	13.9699i	−1.13417	+	1.25962i
$124$	−0.927051	+	1.60570i	−0.0832516	+	0.144196i
$125$	11.1803			1.00000
$126$	0.954915	−	0.330792i	0.0850706	−	0.0294693i
$127$	2.78115	+	8.55951i	0.246787	+	0.759534i	0.995337	+	0.0964551i	$0.0307504\pi$
$127$	2.78115	+	8.55951i	0.246787	+	0.759534i	−0.748550	+	0.663078i	$0.769250\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	3.30524	+	1.47159i	0.291010	+	0.129566i
$130$	0.954915	+	1.65396i	0.0837516	+	0.145062i
$131$	16.2596	−	7.23925i	1.42061	−	0.632496i	0.454528	−	0.890732i	$-0.349808\pi$
$131$	16.2596	−	7.23925i	1.42061	−	0.632496i	0.966082	+	0.258236i	$0.0831413\pi$
$132$	4.61803			0.401948
$133$	−3.59976	−	15.4610i	−0.312139	−	1.34064i
$134$	0.309017	−	0.951057i	0.0266950	−	0.0821588i
$135$	−11.9687	−	2.54402i	−1.03010	−	0.218955i
$136$	−3.81953	+	4.24202i	−0.327522	+	0.363750i
$137$	6.33070	−	1.34563i	0.540869	−	0.114965i	0.0706268	−	0.997503i	$-0.477500\pi$
$137$	6.33070	−	1.34563i	0.540869	−	0.114965i	0.470242	+	0.882538i	$0.344167\pi$
$138$	−8.08990	−	8.98475i	−0.688658	−	0.764832i
$139$	1.85410	+	5.70634i	0.157263	+	0.484005i	0.998383	−	0.0568428i	$-0.0181034\pi$
$139$	1.85410	+	5.70634i	0.157263	+	0.484005i	−0.841120	+	0.540848i	$0.818103\pi$
$140$	−2.51022	−	5.35713i	−0.212152	−	0.452760i
$141$	−2.38197	+	7.33094i	−0.200598	+	0.617376i
$142$	1.77618	−	0.790807i	0.149054	−	0.0663630i
$143$	1.21885	+	2.11111i	0.101925	+	0.176539i
$144$	0.0399263	−	0.379874i	0.00332719	−	0.0316561i
$145$	1.27902	+	12.1690i	0.106217	+	1.01058i
$146$	6.16312	−	4.47777i	0.510063	−	0.370583i
$147$	7.89813	+	8.11808i	0.651427	+	0.669568i
$148$	0.809017	+	2.48990i	0.0665008	+	0.204668i
$149$	4.61803	−	7.99867i	0.378324	−	0.655277i	−0.612494	−	0.790475i	$-0.709834\pi$
$149$	4.61803	−	7.99867i	0.378324	−	0.655277i	0.990819	+	0.135198i	$0.0431672\pi$
$150$	−0.845653	+	8.04585i	−0.0690473	+	0.656941i
$151$	−7.69098	−	13.3212i	−0.625883	−	1.08406i	−0.988369	−	0.152073i	$-0.951405\pi$
$151$	−7.69098	−	13.3212i	−0.625883	−	1.08406i	0.362486	−	0.931989i	$-0.381928\pi$
$152$	−5.86889	−	1.24747i	−0.476029	−	0.101183i
$153$	1.76393	−	1.28157i	0.142605	−	0.103609i
$154$	−3.20402	−	6.83780i	−0.258187	−	0.551006i
$155$	−3.35410	−	2.43690i	−0.269408	−	0.195736i
$156$	−1.26249	+	0.562096i	−0.101080	+	0.0450037i
$157$	1.80902	+	3.13331i	0.144375	+	0.250065i	0.929140	−	0.369729i	$-0.120549\pi$
$157$	1.80902	+	3.13331i	0.144375	+	0.250065i	−0.784764	+	0.619794i	$0.787216\pi$
$158$	−0.934931	+	8.89527i	−0.0743791	+	0.707670i
$159$	−4.58629	−	5.09359i	−0.363716	−	0.403948i
$160$	−2.23607			−0.176777
$161$	−7.69065	+	18.2122i	−0.606108	+	1.43532i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	−13.3453	−	14.8215i	−1.04529	−	1.16091i	−0.986688	−	0.162626i	$-0.948003\pi$
$163$	−13.3453	−	14.8215i	−1.04529	−	1.16091i	−0.0585986	−	0.998282i	$-0.518663\pi$
$164$	7.77398	−	8.63388i	0.607046	−	0.674193i
$165$	−1.07939	+	10.2697i	−0.0840301	+	0.799493i
$166$	6.84927	+	7.60688i	0.531606	+	0.590408i
$167$	−5.54508	−	4.02874i	−0.429092	−	0.311753i	0.352194	−	0.935927i	$-0.385436\pi$
$167$	−5.54508	−	4.02874i	−0.429092	−	0.311753i	−0.781286	+	0.624174i	$0.785436\pi$
$168$	4.04508	−	1.40126i	0.312085	−	0.108109i
$169$	9.92705	+	7.21242i	0.763619	+	0.554802i
$170$	−8.54074	−	9.48545i	−0.655045	−	0.727501i
$171$	2.09366	+	0.932157i	0.160106	+	0.0712839i
$172$	−2.04275	−	0.909491i	−0.155758	−	0.0693480i
$173$	−3.62717	−	0.770979i	−0.275769	−	0.0586164i	0.0679513	−	0.997689i	$-0.478354\pi$
$173$	−3.62717	−	0.770979i	−0.275769	−	0.0586164i	−0.343720	+	0.939072i	$0.611687\pi$
$174$	−8.85410			−0.671228
$175$	12.5000	−	4.33013i	0.944911	−	0.327327i
$176$	−2.85410			−0.215136
$177$	16.3431	+	3.47383i	1.22842	+	0.261109i
$178$	15.6126	+	6.95120i	1.17022	+	0.521014i
$179$	−9.35111	−	4.16338i	−0.698935	−	0.311186i	0.0263323	−	0.999653i	$-0.491617\pi$
$179$	−9.35111	−	4.16338i	−0.698935	−	0.311186i	−0.725267	+	0.688467i	$0.758284\pi$
$180$	0.835438	+	0.177578i	0.0622699	+	0.0132359i
$181$	−20.5623	−	14.9394i	−1.52838	−	1.11044i	−0.957128	−	0.289664i	$-0.906456\pi$
$181$	−20.5623	−	14.9394i	−1.52838	−	1.11044i	−0.571256	−	0.820772i	$-0.693544\pi$
$182$	1.70820	+	1.47935i	0.126620	+	0.109657i
$183$	4.92705	+	3.57971i	0.364218	+	0.264620i
$184$	4.99983	+	5.55288i	0.368593	+	0.409364i
$185$	−5.72618	+	1.21714i	−0.420997	+	0.0894856i
$186$	2.00739	−	2.22943i	0.147189	−	0.163470i
$187$	−10.9013	−	12.1072i	−0.797185	−	0.885364i
$188$	1.47214	−	4.53077i	0.107367	−	0.330440i
$189$	−14.3667	+	1.79115i	−1.04502	+	0.130287i
$190$	4.14590	−	12.7598i	0.300775	−	0.925690i
$191$	−13.5406	−	15.0383i	−0.979761	−	1.08814i	−0.996097	−	0.0882687i	$-0.971867\pi$
$191$	−13.5406	−	15.0383i	−0.979761	−	1.08814i	0.0163353	−	0.999867i	$-0.494800\pi$
$192$	0.169131	−	1.60917i	0.0122060	−	0.116132i
$193$	0.399187	+	0.691412i	0.0287341	+	0.0497689i	0.880035	−	0.474909i	$-0.157519\pi$
$193$	0.399187	+	0.691412i	0.0287341	+	0.0497689i	−0.851301	+	0.524678i	$0.824186\pi$
$194$	6.17916	−	2.75114i	0.443638	−	0.197520i
$195$	−0.954915	−	2.93893i	−0.0683829	−	0.210461i
$196$	−4.88131	−	5.01725i	−0.348665	−	0.358375i
$197$	−13.8713	+	10.0781i	−0.988291	+	0.718035i	−0.959546	−	0.281551i	$-0.909151\pi$
$197$	−13.8713	+	10.0781i	−0.988291	+	0.718035i	−0.0287447	+	0.999587i	$0.509151\pi$
$198$	1.06635	+	0.226659i	0.0757820	+	0.0161080i
$199$	−2.20820	−	3.82472i	−0.156535	−	0.271127i	0.777082	−	0.629400i	$-0.216699\pi$
$199$	−2.20820	−	3.82472i	−0.156535	−	0.271127i	−0.933617	+	0.358273i	$0.883366\pi$
$200$	0.522642	−	4.97261i	0.0369564	−	0.351617i
$201$	−0.809017	+	1.40126i	−0.0570637	+	0.0988372i
$202$	2.69098	+	8.28199i	0.189337	+	0.582719i
$203$	6.14303	+	13.1100i	0.431156	+	0.920144i
$204$	7.47214	−	5.42882i	0.523154	−	0.380094i
$205$	17.3832	+	19.3059i	1.21409	+	1.34839i
$206$	−1.56210	+	14.8624i	−0.108837	+	1.03551i
$207$	−1.42705	−	2.47172i	−0.0991869	−	0.171797i
$208$	0.780261	−	0.347395i	0.0541014	−	0.0240875i
$209$	5.29180	−	16.2865i	0.366041	−	1.12656i
$210$	2.17068	+	9.32306i	0.149791	+	0.643352i
$211$	7.19098	+	22.1316i	0.495048	+	1.52360i	0.816882	+	0.576804i	$0.195700\pi$
$211$	7.19098	+	22.1316i	0.495048	+	1.52360i	−0.321835	+	0.946796i	$0.604300\pi$
$212$	2.83448	+	3.14801i	0.194673	+	0.216206i
$213$	−3.07715	+	0.654069i	−0.210843	+	0.0448161i
$214$	−3.05278	+	3.39045i	−0.208684	+	0.231767i
$215$	2.50000	−	4.33013i	0.170499	−	0.295312i
$216$	−1.69098	+	5.20431i	−0.115057	+	0.354108i
$217$	−4.69381	−	1.42550i	−0.318636	−	0.0967690i
$218$	−3.23607			−0.219174
$219$	−11.2606	+	5.01353i	−0.760919	+	0.338783i
$220$	0.667097	−	6.34700i	0.0449757	−	0.427915i
$221$	4.45389	+	1.98300i	0.299601	+	0.133391i
$222$	−0.442790	−	4.21286i	−0.0297181	−	0.282749i
$223$	2.59017	+	7.97172i	0.173451	+	0.533826i	0.999559	−	0.0296847i	$-0.00945032\pi$
$223$	2.59017	+	7.97172i	0.173451	+	0.533826i	−0.826109	+	0.563511i	$0.809450\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	−0.590170	+	1.81636i	−0.0393447	+	0.121090i
$226$	−10.2082	+	17.6811i	−0.679040	+	1.17613i
$227$	−1.37555	+	1.52770i	−0.0912985	+	0.101397i	−0.787063	−	0.616873i	$-0.788399\pi$
$227$	−1.37555	+	1.52770i	−0.0912985	+	0.101397i	0.695764	+	0.718270i	$0.255066\pi$
$228$	8.86889	+	3.94868i	0.587356	+	0.261508i
$229$	0.347687	+	3.30802i	0.0229758	+	0.218600i	0.999985	+	0.00540467i	$0.00172037\pi$
$229$	0.347687	+	3.30802i	0.0229758	+	0.218600i	−0.977010	+	0.213195i	$0.931613\pi$
$230$	−13.5172	+	9.82084i	−0.891299	+	0.647567i
$231$	2.77064	+	11.8999i	0.182294	+	0.782955i
$232$	5.47214			0.359263
$233$	25.4265	−	11.3206i	1.66575	−	0.741639i	0.665758	−	0.746167i	$-0.268108\pi$
$233$	25.4265	−	11.3206i	1.66575	−	0.741639i	0.999990	+	0.00452848i	$0.00144146\pi$
$234$	−0.319109	+	0.0678287i	−0.0208608	+	0.00443410i
$235$	9.73152	+	4.33275i	0.634814	+	0.282638i
$236$	−10.1006	−	2.14695i	−0.657492	−	0.139754i
$237$	4.47214	−	13.7638i	0.290496	−	0.894056i
$238$	−13.2225	−	7.29724i	−0.857090	−	0.473010i
$239$	6.59017	+	20.2825i	0.426283	+	1.31196i	0.901761	+	0.432236i	$0.142275\pi$
$239$	6.59017	+	20.2825i	0.426283	+	1.31196i	−0.475478	+	0.879728i	$0.657725\pi$
$240$	3.53897	+	0.752232i	0.228440	+	0.0485563i
$241$	4.05530	−	0.861981i	0.261225	−	0.0555251i	−0.0754374	−	0.997151i	$-0.524035\pi$
$241$	4.05530	−	0.861981i	0.261225	−	0.0555251i	0.336662	+	0.941625i	$0.390702\pi$
$242$	−0.298335	+	2.83847i	−0.0191777	+	0.182464i
$243$	1.97214	−	3.41584i	0.126513	−	0.219126i
$244$	−3.04508	−	2.21238i	−0.194942	−	0.141633i
$245$	12.2984	−	9.68246i	0.785714	−	0.618590i
$246$	−15.2082	+	11.0494i	−0.969640	+	0.704484i
$247$	0.535668	+	5.09654i	0.0340837	+	0.324285i
$248$	−1.24064	+	1.37787i	−0.0787805	+	0.0874946i
$249$	−8.28115	−	14.3434i	−0.524797	−	0.908975i
$250$	10.9360	+	2.32452i	0.691655	+	0.147016i
$251$	8.81966			0.556692			0.278346	−	0.960481i	$-0.410214\pi$
$251$	8.81966			0.556692			0.278346	+	0.960481i	$0.410214\pi$
$252$	1.00282	−	0.125026i	0.0631719	−	0.00787588i
$253$	−17.2533	+	12.5352i	−1.08470	+	0.788084i
$254$	0.940756	+	8.95070i	0.0590283	+	0.561617i
$255$	10.3262	+	17.8856i	0.646654	+	1.12004i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	0.482779	−	0.836198i	0.0301149	−	0.0521606i	−0.850575	−	0.525854i	$-0.823746\pi$
$257$	0.482779	−	0.836198i	0.0301149	−	0.0521606i	0.880690	+	0.473693i	$0.157079\pi$
$258$	2.92705	+	2.12663i	0.182230	+	0.132398i
$259$	−5.93066	+	3.57854i	−0.368514	+	0.222360i
$260$	0.590170	+	1.81636i	0.0366008	+	0.112646i
$261$	−2.04449	−	0.434571i	−0.126551	−	0.0268993i
$262$	17.4094	−	3.70049i	1.07556	−	0.228617i
$263$	16.3431	−	3.47383i	1.00776	−	0.214206i	0.325676	−	0.945481i	$-0.394408\pi$
$263$	16.3431	−	3.47383i	1.00776	−	0.214206i	0.682082	+	0.731276i	$0.261075\pi$
$264$	4.51712	+	0.960143i	0.278009	+	0.0590927i
$265$	−7.66312	+	5.56758i	−0.470742	+	0.342014i
$266$	−0.306580	−	15.8715i	−0.0187976	−	0.973147i
$267$	−22.3713	−	16.2537i	−1.36910	−	0.994711i
$268$	0.500000	−	0.866025i	0.0305424	−	0.0529009i
$269$	−0.279484	+	2.65911i	−0.0170405	+	0.162129i	−0.999733	−	0.0231161i	$-0.992641\pi$
$269$	−0.279484	+	2.65911i	−0.0170405	+	0.162129i	0.982692	+	0.185245i	$0.0593079\pi$
$270$	−11.1782	−	4.97686i	−0.680284	−	0.302882i
$271$	−0.0951031	−	0.904846i	−0.00577710	−	0.0549655i	0.991254	−	0.131971i	$-0.0421307\pi$
$271$	−0.0951031	−	0.904846i	−0.00577710	−	0.0549655i	−0.997031	+	0.0770058i	$0.975464\pi$
$272$	−4.61803	+	3.35520i	−0.280009	+	0.203439i
$273$	−2.20587	−	2.91598i	−0.133505	−	0.176483i
$274$	6.47214			0.390996
$275$	13.9587	+	2.96701i	0.841739	+	0.178917i
$276$	−6.04508	−	10.4704i	−0.363871	−	0.630244i
$277$	−13.6612	+	15.1723i	−0.820825	+	0.911618i	−0.997356	−	0.0726771i	$-0.976846\pi$
$277$	−13.6612	+	15.1723i	−0.820825	+	0.911618i	0.176531	+	0.984295i	$0.443512\pi$
$278$	0.627171	+	5.96713i	0.0376152	+	0.357885i
$279$	0.572949	−	0.416272i	0.0343016	−	0.0249215i
$280$	−1.34155	−	5.76196i	−0.0801730	−	0.344343i
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	−3.85410	+	6.67550i	−0.229508	+	0.397520i
$283$	0.895005	−	8.51540i	0.0532025	−	0.506188i	−0.935177	−	0.354181i	$-0.884760\pi$
$283$	0.895005	−	8.51540i	0.0532025	−	0.506188i	0.988379	−	0.152007i	$-0.0485736\pi$
$284$	1.90178	−	0.404237i	0.112850	−	0.0239870i
$285$	−10.8541	+	18.7999i	−0.642942	+	1.11361i
$286$	0.753289	+	2.31838i	0.0445429	+	0.137089i
$287$	26.9121	+	14.8522i	1.58857	+	0.876700i
$288$	0.118034	−	0.363271i	0.00695522	−	0.0214060i
$289$	−15.2431	−	3.24001i	−0.896650	−	0.190589i
$290$	−1.27902	+	12.1690i	−0.0751065	+	0.714590i
$291$	−10.7051	+	2.27544i	−0.627545	+	0.133389i
$292$	6.95942	−	3.09853i	0.407269	−	0.181328i
$293$	10.0902			0.589474			0.294737	−	0.955578i	$-0.404768\pi$
$293$	10.0902			0.589474			0.294737	+	0.955578i	$0.404768\pi$
$294$	6.03769	+	9.58279i	0.352125	+	0.558880i
$295$	7.13525	−	21.9601i	0.415431	−	1.27856i
$296$	0.273659	+	2.60369i	0.0159061	+	0.151337i
$297$	−14.2678	−	6.35243i	−0.827901	−	0.368605i
$298$	6.18014	−	6.86374i	0.358006	−	0.397606i
$299$	3.19098	−	5.52694i	0.184539	−	0.319631i
$300$	−2.50000	+	7.69421i	−0.144338	+	0.444225i
$301$	1.11803	−	5.80948i	0.0644424	−	0.334853i
$302$	−4.75329	−	14.6291i	−0.273521	−	0.841811i
$303$	−1.47282	−	14.0130i	−0.0846115	−	0.805025i
$304$	−5.48127	−	2.44042i	−0.314373	−	0.139968i
$305$	5.63168	−	6.25461i	0.322469	−	0.358138i
$306$	1.99184	−	0.886824i	0.113866	−	0.0506964i
$307$	−27.1246			−1.54808			−0.774042	−	0.633135i	$-0.781768\pi$
$307$	−27.1246			−1.54808			−0.774042	+	0.633135i	$0.781768\pi$
$308$	−1.71235	−	7.35453i	−0.0975700	−	0.419063i
$309$	7.47214	−	22.9969i	0.425075	−	1.30825i
$310$	−2.77415	−	3.08100i	−0.157561	−	0.174989i
$311$	20.3525	−	22.6038i	1.15409	−	1.28174i	0.200816	−	0.979629i	$-0.435641\pi$
$311$	20.3525	−	22.6038i	1.15409	−	1.28174i	0.953272	−	0.302115i	$-0.0976925\pi$
$312$	−1.35177	+	0.287327i	−0.0765287	+	0.0162667i
$313$	−9.05191	−	10.0532i	−0.511644	−	0.568238i	0.430866	−	0.902416i	$-0.358208\pi$
$313$	−9.05191	−	10.0532i	−0.511644	−	0.568238i	−0.942510	+	0.334178i	$0.891541\pi$
$314$	1.11803	+	3.44095i	0.0630943	+	0.194184i
$315$	0.0436417	+	2.25932i	0.00245893	+	0.127298i
$316$	−2.76393	+	8.50651i	−0.155483	+	0.478528i
$317$	−15.2952	+	6.80985i	−0.859062	+	0.382479i	−0.788505	−	0.615029i	$-0.789144\pi$
$317$	−15.2952	+	6.80985i	−0.859062	+	0.382479i	−0.0705574	+	0.997508i	$0.522478\pi$
$318$	−3.42705	−	5.93583i	−0.192179	−	0.332865i
$319$	−1.63253	+	15.5325i	−0.0914041	+	0.869652i
$320$	−2.18720	−	0.464905i	−0.122268	−	0.0259890i
$321$	5.97214	−	4.33901i	0.333332	−	0.242180i
$322$	−11.3091	+	16.2152i	−0.630233	+	0.903639i
$323$	−10.5836	−	32.5729i	−0.588887	−	1.81241i
$324$	3.85410	−	6.67550i	0.214117	−	0.370861i
$325$	−4.17719	+	0.887889i	−0.231709	+	0.0492512i
$326$	−9.97214	−	17.2722i	−0.552306	−	0.956621i
$327$	5.12165	+	1.08864i	0.283228	+	0.0602019i
$328$	9.39919	−	6.82891i	0.518983	−	0.377063i
$329$	12.5582	+	1.07516i	0.692358	+	0.0592756i
$330$	−3.19098	+	9.82084i	−0.175658	+	0.540619i
$331$	8.68469	−	3.86667i	0.477354	−	0.212532i	−0.153933	−	0.988081i	$-0.549194\pi$
$331$	8.68469	−	3.86667i	0.477354	−	0.212532i	0.631286	+	0.775550i	$0.282527\pi$
$332$	5.11803	+	8.86469i	0.280889	+	0.486513i
$333$	0.104528	−	0.994522i	0.00572812	−	0.0544995i
$334$	−4.58629	−	5.09359i	−0.250951	−	0.278709i
$335$	1.80902	+	1.31433i	0.0988372	+	0.0718094i
$336$	4.24803	−	0.529617i	0.231749	−	0.0288930i
$337$	2.87132	−	8.83702i	0.156411	−	0.481383i	−0.841890	−	0.539649i	$-0.818557\pi$
$337$	2.87132	−	8.83702i	0.156411	−	0.481383i	0.998301	+	0.0582655i	$0.0185570\pi$
$338$	8.21057	+	9.11877i	0.446596	+	0.495995i
$339$	22.1044	−	24.5494i	1.20054	−	1.33334i
$340$	−6.38197	−	11.0539i	−0.346111	−	0.599481i
$341$	−3.54090	−	3.93257i	−0.191751	−	0.212961i
$342$	1.85410	+	1.34708i	0.100258	+	0.0728420i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−1.80902	−	1.31433i	−0.0975357	−	0.0708638i
$345$	24.6972	−	10.9959i	1.32965	−	0.591999i
$346$	−3.38761	−	1.50826i	−0.182119	−	0.0810847i
$347$	17.7378	+	7.89736i	0.952213	+	0.423953i	0.823239	−	0.567695i	$-0.192165\pi$
$347$	17.7378	+	7.89736i	0.952213	+	0.423953i	0.128975	+	0.991648i	$0.458831\pi$
$348$	−8.66062	−	1.84087i	−0.464258	−	0.0986811i
$349$	21.3820			1.14455			0.572275	−	0.820062i	$-0.306061\pi$
$349$	21.3820			1.14455			0.572275	+	0.820062i	$0.306061\pi$
$350$	13.1271	−	1.63661i	0.701675	−	0.0874803i
$351$	4.67376			0.249467
$352$	−2.79173	−	0.593401i	−0.148800	−	0.0316284i
$353$	13.7346	+	6.11506i	0.731021	+	0.325472i	0.738273	−	0.674502i	$-0.235642\pi$
$353$	13.7346	+	6.11506i	0.731021	+	0.325472i	−0.00725158	+	0.999974i	$0.502308\pi$
$354$	15.2637	+	6.79584i	0.811257	+	0.361195i
$355$	0.454440	+	4.32371i	0.0241192	+	0.229479i
$356$	13.8262	+	10.0453i	0.732789	+	0.532402i
$357$	18.4721	+	15.9973i	0.977649	+	0.846669i
$358$	−8.28115	−	6.01661i	−0.437673	−	0.317988i
$359$	−4.17274	−	4.63430i	−0.220229	−	0.244589i	0.622899	−	0.782303i	$-0.285955\pi$
$359$	−4.17274	−	4.63430i	−0.220229	−	0.244589i	−0.843128	+	0.537713i	$0.819288\pi$
$360$	0.780261	+	0.347395i	0.0411234	+	0.0183093i
$361$	11.3752	−	12.6335i	0.598696	−	0.664919i
$362$	−17.0069	−	18.8881i	−0.893863	−	0.992735i
$363$	1.42705	−	4.39201i	0.0749008	−	0.230521i
$364$	1.36330	+	1.80218i	0.0714564	+	0.0944597i
$365$	5.26393	+	16.2007i	0.275527	+	0.847984i
$366$	4.07512	+	4.52588i	0.213010	+	0.236571i
$367$	1.57375	−	14.9733i	0.0821492	−	0.781597i	−0.873447	−	0.486919i	$-0.838121\pi$
$367$	1.57375	−	14.9733i	0.0821492	−	0.781597i	0.955596	−	0.294679i	$-0.0952126\pi$
$368$	3.73607	+	6.47106i	0.194756	+	0.337327i
$369$	−4.05404	+	1.80497i	−0.211045	+	0.0939631i
$370$	−5.85410			−0.304340
$371$	−6.41131	+	9.19266i	−0.332859	+	0.477259i
$372$	2.42705	−	1.76336i	0.125837	−	0.0914257i
$373$	−29.0045	−	6.16510i	−1.50180	−	0.319217i	−0.617660	−	0.786446i	$-0.711919\pi$
$373$	−29.0045	−	6.16510i	−1.50180	−	0.319217i	−0.884136	+	0.467229i	$0.845252\pi$
$374$	−8.14590	−	14.1091i	−0.421214	−	0.729565i
$375$	−16.5262	−	7.35793i	−0.853409	−	0.379962i
$376$	2.38197	−	4.12569i	0.122841	−	0.212766i
$377$	−1.44427	−	4.44501i	−0.0743838	−	0.228930i
$378$	−14.4251	−	1.23500i	−0.741949	−	0.0635213i
$379$	19.3713	−	14.0741i	0.995038	−	0.722937i	0.0340194	−	0.999421i	$-0.489169\pi$
$379$	19.3713	−	14.0741i	0.995038	−	0.722937i	0.961019	+	0.276484i	$0.0891692\pi$
$380$	6.70820	−	11.6190i	0.344124	−	0.596040i
$381$	1.52218	−	14.4825i	0.0779834	−	0.741963i
$382$	−10.1180	−	17.5249i	−0.517684	−	0.896654i
$383$	18.2709	−	8.13473i	0.933600	−	0.415665i	0.117171	−	0.993112i	$-0.462617\pi$
$383$	18.2709	−	8.13473i	0.933600	−	0.415665i	0.816429	+	0.577446i	$0.195951\pi$
$384$	0.500000	−	1.53884i	0.0255155	−	0.0785287i
$385$	16.7554	−	2.08895i	0.853933	−	0.106463i
$386$	0.246711	+	0.759299i	0.0125573	+	0.0386473i
$387$	0.571506	+	0.634721i	0.0290513	+	0.0322647i
$388$	6.61612	−	1.40630i	0.335883	−	0.0713941i
$389$	2.73686	−	3.03959i	0.138764	−	0.154113i	−0.669757	−	0.742580i	$-0.733602\pi$
$389$	2.73686	−	3.03959i	0.138764	−	0.154113i	0.808521	+	0.588467i	$0.200268\pi$
$390$	−0.323011	−	3.07324i	−0.0163563	−	0.155620i
$391$	−13.1803	+	40.5649i	−0.666558	+	2.05146i
$392$	−3.73150	−	5.92249i	−0.188469	−	0.299131i
$393$	−28.7984			−1.45269
$394$	−15.6636	+	6.97387i	−0.789119	+	0.351338i
$395$	−18.2709	−	8.13473i	−0.919309	−	0.409303i
$396$	0.995920	+	0.443412i	0.0500469	+	0.0222823i
$397$	−2.88465	−	27.4456i	−0.144776	−	1.37745i	−0.789834	−	0.613320i	$-0.789834\pi$
$397$	−2.88465	−	27.4456i	−0.144776	−	1.37745i	0.645058	−	0.764133i	$-0.276833\pi$
$398$	−1.36475	−	4.20025i	−0.0684085	−	0.210540i
$399$	−4.85410	+	25.2227i	−0.243009	+	1.26271i
$400$	1.54508	−	4.75528i	0.0772542	−	0.237764i
$401$	−5.76393	+	9.98342i	−0.287837	+	0.498548i	−0.973293	−	0.229566i	$-0.926269\pi$
$401$	−5.76393	+	9.98342i	−0.287837	+	0.498548i	0.685456	+	0.728114i	$0.259603\pi$
$402$	−1.08268	+	1.20243i	−0.0539990	+	0.0599719i
$403$	1.44668	+	0.644105i	0.0720644	+	0.0320852i
$404$	0.910255	+	8.66050i	0.0452869	+	0.430876i
$405$	13.9443	+	10.1311i	0.692896	+	0.503419i
$406$	3.28306	+	14.1008i	0.162936	+	0.699809i
$407$	−7.47214			−0.370380
$408$	8.43757	−	3.75665i	0.417722	−	0.185982i
$409$	−7.30885	+	1.55354i	−0.361399	+	0.0768178i	−0.385033	−	0.922903i	$-0.625810\pi$
$409$	−7.30885	+	1.55354i	−0.361399	+	0.0768178i	0.0236334	+	0.999721i	$0.492477\pi$
$410$	12.9894	+	22.4982i	0.641499	+	1.11111i
$411$	−10.2433	−	2.17728i	−0.505264	−	0.107397i
$412$	−4.61803	+	14.2128i	−0.227514	+	0.700217i
$413$	−0.527636	−	27.3156i	−0.0259633	−	1.34411i
$414$	−0.881966	−	2.71441i	−0.0433463	−	0.133406i
$415$	−20.9097	+	9.30961i	−1.02642	+	0.456991i
$416$	0.835438	−	0.177578i	0.0409607	−	0.00870647i
$417$	1.01478	−	9.65502i	0.0496942	−	0.472808i
$418$	8.56231	−	14.8303i	0.418796	−	0.725376i
$419$	6.28115	+	4.56352i	0.306854	+	0.222943i	0.730546	−	0.682864i	$-0.239266\pi$
$419$	6.28115	+	4.56352i	0.306854	+	0.222943i	−0.423691	+	0.905807i	$0.639266\pi$
$420$	0.184869	+	9.57063i	0.00902070	+	0.466999i
$421$	−10.4443	+	7.58821i	−0.509023	+	0.369827i	−0.812453	−	0.583027i	$-0.801868\pi$
$421$	−10.4443	+	7.58821i	−0.509023	+	0.369827i	0.303430	+	0.952854i	$0.401868\pi$
$422$	2.43243	+	23.1430i	0.118409	+	1.12659i
$423$	−1.21759	+	1.35227i	−0.0592013	+	0.0657497i
$424$	2.11803	+	3.66854i	0.102861	+	0.178160i
$425$	26.0735	−	11.6087i	1.26475	−	0.563104i
$426$	−3.14590			−0.152419
$427$	3.87401	−	9.17401i	0.187476	−	0.443961i
$428$	−3.69098	+	2.68166i	−0.178410	+	0.129623i
$429$	−0.412289	−	3.92266i	−0.0199055	−	0.189388i
$430$	3.34565	−	3.71572i	0.161342	−	0.179188i
$431$	−0.212657	+	2.02330i	−0.0102433	+	0.0974588i	−0.998449	−	0.0556735i	$-0.982269\pi$
$431$	−0.212657	+	2.02330i	−0.0102433	+	0.0974588i	0.988206	+	0.153132i	$0.0489361\pi$
$432$	−2.73607	+	4.73901i	−0.131639	+	0.228006i
$433$	−7.51722	−	5.46158i	−0.361255	−	0.262467i	0.392321	−	0.919829i	$-0.371672\pi$
$433$	−7.51722	−	5.46158i	−0.361255	−	0.262467i	−0.753575	+	0.657362i	$0.771672\pi$
$434$	−4.29486	−	2.37024i	−0.206160	−	0.113775i
$435$	6.11803	−	18.8294i	0.293337	−	0.902799i
$436$	−3.16535	−	0.672816i	−0.151593	−	0.0322221i
$437$	−43.8531	+	9.32127i	−2.09778	+	0.445897i
$438$	−12.0569	+	2.56277i	−0.576100	+	0.122454i
$439$	13.6396	+	2.89918i	0.650980	+	0.138370i	0.521553	−	0.853219i	$-0.325353\pi$
$439$	13.6396	+	2.89918i	0.650980	+	0.138370i	0.129427	+	0.991589i	$0.458686\pi$
$440$	1.97214	−	6.06961i	0.0940179	−	0.289357i
$441$	0.923824	+	2.50909i	0.0439916	+	0.119481i
$442$	3.94427	+	2.86568i	0.187610	+	0.136307i
$443$	−4.92705	+	8.53390i	−0.234091	+	0.405458i	−0.959008	−	0.283378i	$-0.908545\pi$
$443$	−4.92705	+	8.53390i	−0.234091	+	0.405458i	0.724917	+	0.688836i	$0.241878\pi$
$444$	0.442790	−	4.21286i	0.0210139	−	0.199934i
$445$	−25.5707	+	28.3991i	−1.21217	+	1.34625i
$446$	0.876154	+	8.33605i	0.0414871	+	0.394723i
$447$	−12.0902	+	8.78402i	−0.571845	+	0.415470i
$448$	−2.62543	+	0.327321i	−0.124040	+	0.0154645i
$449$	34.0344			1.60618			0.803092	−	0.595855i	$-0.203187\pi$
$449$	34.0344			1.60618			0.803092	+	0.595855i	$0.203187\pi$
$450$	−0.954915	+	1.65396i	−0.0450151	+	0.0779685i
$451$	16.5795	+	28.7166i	0.780699	+	1.35221i
$452$	−13.6612	+	15.1723i	−0.642571	+	0.713647i
$453$	2.60156	+	24.7522i	0.122232	+	1.16296i
$454$	−1.66312	+	1.20833i	−0.0780540	+	0.0567096i
$455$	−4.32636	+	2.61051i	−0.202823	+	0.122383i
$456$	7.85410	+	5.70634i	0.367802	+	0.267224i
$457$	7.61803	−	13.1948i	0.356357	−	0.617228i	−0.630993	−	0.775789i	$-0.717352\pi$
$457$	7.61803	−	13.1948i	0.356357	−	0.617228i	0.987349	+	0.158561i	$0.0506855\pi$
$458$	−0.347687	+	3.30802i	−0.0162463	+	0.154573i
$459$	−30.5535	+	6.49434i	−1.42611	+	0.303130i
$460$	−15.2637	+	6.79584i	−0.711674	+	0.316858i
$461$	−7.12868	−	21.9398i	−0.332016	−	1.02184i	−0.968173	−	0.250280i	$-0.919477\pi$
$461$	−7.12868	−	21.9398i	−0.332016	−	1.02184i	0.636158	−	0.771559i	$-0.280523\pi$
$462$	0.235966	+	12.2159i	0.0109781	+	0.568335i
$463$	5.01722	−	15.4414i	0.233170	−	0.717624i	−0.764189	−	0.644993i	$-0.776860\pi$
$463$	5.01722	−	15.4414i	0.233170	−	0.717624i	0.997359	−	0.0726310i	$-0.0231395\pi$
$464$	5.35256	+	1.13772i	0.248486	+	0.0528174i
$465$	3.35410	+	5.80948i	0.155543	+	0.269408i
$466$	27.2246	−	5.78677i	1.26116	−	0.268067i
$467$	−31.0920	+	13.8431i	−1.43877	+	0.640580i	−0.970080	−	0.242784i	$-0.921939\pi$
$467$	−31.0920	+	13.8431i	−1.43877	+	0.640580i	−0.468686	+	0.883365i	$0.655273\pi$
$468$	−0.326238			−0.0150804
$469$	2.53158	+	0.768834i	0.116897	+	0.0355014i
$470$	8.61803	+	6.26137i	0.397520	+	0.288815i
$471$	−0.611920	−	5.82203i	−0.0281958	−	0.268265i
$472$	−9.43349	−	4.20006i	−0.434211	−	0.193323i
$473$	4.27037	−	4.74273i	0.196352	−	0.218071i
$474$	7.23607	−	12.5332i	0.332364	−	0.575671i
$475$	24.2705	+	17.6336i	1.11361	+	0.809083i
$476$	−11.4164	−	9.88690i	−0.523270	−	0.453165i
$477$	−0.500000	−	1.53884i	−0.0228934	−	0.0704587i
$478$	2.22920	+	21.2094i	0.101961	+	0.970096i
$479$	−7.04179	−	3.13521i	−0.321748	−	0.143251i	0.239506	−	0.970895i	$-0.423014\pi$
$479$	−7.04179	−	3.13521i	−0.321748	−	0.143251i	−0.561254	+	0.827643i	$0.689681\pi$
$480$	3.30524	+	1.47159i	0.150863	+	0.0671684i
$481$	2.04275	−	0.909491i	0.0931414	−	0.0414692i
$482$	4.14590			0.188840
$483$	23.3536	−	21.8590i	1.06263	−	0.994618i
$484$	−0.881966	+	2.71441i	−0.0400894	+	0.123382i
$485$	1.58095	+	15.0418i	0.0717874	+	0.683011i
$486$	2.63923	−	2.93117i	0.119718	−	0.132960i
$487$	8.40889	−	1.78736i	0.381043	−	0.0809932i	−0.0134081	−	0.999910i	$-0.504268\pi$
$487$	8.40889	−	1.78736i	0.381043	−	0.0809932i	0.394451	+	0.918917i	$0.370935\pi$
$488$	−2.51856	−	2.79715i	−0.114010	−	0.126621i
$489$	9.97214	+	30.6911i	0.450956	+	1.38790i
$490$	14.0427	−	6.91390i	0.634385	−	0.312338i
$491$	−8.60739	+	26.4908i	−0.388446	+	1.19551i	0.545503	+	0.838109i	$0.316339\pi$
$491$	−8.60739	+	26.4908i	−0.388446	+	1.19551i	−0.933949	+	0.357405i	$0.883661\pi$
$492$	−17.1732	+	7.64599i	−0.774226	+	0.344708i
$493$	15.6180	+	27.0512i	0.703401	+	1.21833i
$494$	−0.535668	+	5.09654i	−0.0241008	+	0.229304i
$495$	−1.21885	+	2.11111i	−0.0547831	+	0.0948871i
$496$	−1.50000	+	1.08981i	−0.0673520	+	0.0489341i
$497$	2.18264	+	4.65805i	0.0979050	+	0.208942i
$498$	−5.11803	−	15.7517i	−0.229345	−	0.705850i
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	−0.968500	−	0.249015i	$-0.919893\pi$
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	0.699903	+	0.714238i	$0.253227\pi$
$500$	10.2137	+	4.54745i	0.456773	+	0.203368i
$501$	5.54508	+	9.60437i	0.247736	+	0.429092i
$502$	8.62693	+	1.83371i	0.385039	+	0.0818425i
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	−0.402526	−	0.915409i	$-0.631868\pi$
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	0.746218	+	0.665702i	$0.231868\pi$
$504$	1.00690	+	0.0862052i	0.0448511	+	0.00383988i
$505$	−19.4721			−0.866499
$506$	−19.4825	+	8.67416i	−0.866102	+	0.385614i
$507$	−9.92705	−	17.1942i	−0.440876	−	0.763619i
$508$	−0.940756	+	8.95070i	−0.0417393	+	0.397123i
$509$	21.7511	+	24.1571i	0.964103	+	1.07074i	0.997455	+	0.0713008i	$0.0227150\pi$
$509$	21.7511	+	24.1571i	0.964103	+	1.07074i	−0.0333523	+	0.999444i	$0.510618\pi$
$510$	6.38197	+	19.6417i	0.282598	+	0.869748i
$511$	12.1598	+	16.0742i	0.537916	+	0.711083i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−21.9694	−	24.3995i	−0.969975	−	1.07727i
$514$	0.646085	−	0.717550i	0.0284976	−	0.0316498i
$515$	−30.5274	−	13.5917i	−1.34520	−	0.598921i
$516$	2.42094	+	2.68872i	0.106576	+	0.118364i
$517$	11.0000	+	7.99197i	0.483779	+	0.351486i
$518$	−6.54508	+	2.26728i	−0.287575	+	0.0996187i
$519$	4.85410	+	3.52671i	0.213071	+	0.154805i
$520$	0.199632	+	1.89937i	0.00875442	+	0.0832928i
$521$	−16.7928	−	7.47662i	−0.735704	−	0.327557i	0.00445335	−	0.999990i	$-0.498582\pi$
$521$	−16.7928	−	7.47662i	−0.735704	−	0.327557i	−0.740158	+	0.672433i	$0.765249\pi$
$522$	−1.90947	−	0.850149i	−0.0835750	−	0.0372100i
$523$	−19.0466	−	4.04848i	−0.832851	−	0.177028i	−0.228296	−	0.973592i	$-0.573315\pi$
$523$	−19.0466	−	4.04848i	−0.832851	−	0.177028i	−0.604554	+	0.796564i	$0.706649\pi$
$524$	17.7984			0.777526
$525$	−21.3266	−	1.82585i	−0.930767	−	0.0796868i
$526$	16.7082			0.728512
$527$	−10.3523	−	2.20045i	−0.450954	−	0.0958532i
$528$	4.21878	+	1.87832i	0.183599	+	0.0817435i
$529$	29.9943	+	13.3543i	1.30410	+	0.580622i
$530$	−8.65323	+	3.85266i	−0.375872	+	0.167349i
$531$	3.19098	+	2.31838i	0.138477	+	0.100609i
$532$	3.00000	−	15.5885i	0.130066	−	0.675845i
$533$	−8.02786	−	5.83258i	−0.347725	−	0.252637i
$534$	−18.5031	−	20.5498i	−0.800708	−	0.889277i
$535$	−5.10081	−	8.83487i	−0.220527	−	0.381965i
$536$	0.669131	−	0.743145i	0.0289020	−	0.0320990i
$537$	11.0823	+	12.3082i	0.478239	+	0.531138i
$538$	−0.826238	+	2.54290i	−0.0356216	+	0.109632i
$539$	17.9240	−	8.82485i	0.772043	−	0.380113i
$540$	−9.89919	−	7.19218i	−0.425993	−	0.309502i
$541$	−13.2247	−	14.6875i	−0.568572	−	0.631463i	0.388453	−	0.921469i	$-0.373010\pi$
$541$	−13.2247	−	14.6875i	−0.568572	−	0.631463i	−0.957025	+	0.290005i	$0.906343\pi$
$542$	0.0951031	−	0.904846i	0.00408503	−	0.0388665i
$543$	20.5623	+	35.6150i	0.882413	+	1.52838i
$544$	−5.21470	+	2.32174i	−0.223579	+	0.0995436i
$545$	2.23607	−	6.88191i	0.0957826	−	0.294789i
$546$	−1.55140	−	3.31089i	−0.0663937	−	0.141693i
$547$	34.5066	−	25.0705i	1.47539	−	1.07194i	0.496390	−	0.868100i	$-0.334659\pi$
$547$	34.5066	−	25.0705i	1.47539	−	1.07194i	0.979005	−	0.203837i	$-0.0653414\pi$
$548$	6.33070	+	1.34563i	0.270434	+	0.0574826i
$549$	0.718847	+	1.24508i	0.0306796	+	0.0531387i
$550$	13.0368	+	5.80434i	0.555889	+	0.247498i
$551$	−16.4164	+	28.4341i	−0.699362	+	1.21133i
$552$	−3.73607	−	11.4984i	−0.159018	−	0.489406i
$553$	−23.5781	−	2.01862i	−1.00264	−	0.0858402i
$554$	−16.5172	+	12.0005i	−0.701749	+	0.509851i
$555$	9.26515	+	1.96937i	0.393284	+	0.0835950i
$556$	−0.627171	+	5.96713i	−0.0265980	+	0.253063i
$557$	−14.0902	−	24.4049i	−0.597020	−	1.03407i	−0.993258	−	0.115921i	$-0.963018\pi$
$557$	−14.0902	−	24.4049i	−0.597020	−	1.03407i	0.396239	−	0.918147i	$-0.370315\pi$
$558$	0.646976	−	0.288052i	0.0273887	−	0.0121942i
$559$	−0.590170	+	1.81636i	−0.0249615	+	0.0768237i
$560$	−0.114256	−	5.91498i	−0.00482818	−	0.249953i
$561$	8.14590	+	25.0705i	0.343920	+	1.05848i
$562$	−11.3752	−	12.6335i	−0.479835	−	0.532910i
$563$	39.0169	−	8.29329i	1.64437	−	0.349521i	0.709550	−	0.704655i	$-0.248898\pi$
$563$	39.0169	−	8.29329i	1.64437	−	0.349521i	0.934815	+	0.355134i	$0.115565\pi$
$564$	−5.15780	+	5.72831i	−0.217182	+	0.241205i
$565$	−30.5475	−	33.9264i	−1.28514	−	1.42729i
$566$	2.64590	−	8.14324i	0.111215	−	0.342286i
$567$	19.5139	+	5.92633i	0.819508	+	0.248882i
$568$	1.94427			0.0815798
$569$	−6.64194	+	2.95718i	−0.278445	+	0.123972i	−0.541208	−	0.840889i	$-0.682033\pi$
$569$	−6.64194	+	2.95718i	−0.278445	+	0.123972i	0.262763	+	0.964860i	$0.415366\pi$
$570$	−14.5256	+	16.1323i	−0.608411	+	0.675709i
$571$	27.5202	+	12.2528i	1.15168	+	0.512763i	0.891600	−	0.452823i	$-0.149583\pi$
$571$	27.5202	+	12.2528i	1.15168	+	0.512763i	0.260084	+	0.965586i	$0.416250\pi$
$572$	0.254808	+	2.42434i	0.0106541	+	0.101367i
$573$	10.1180	+	31.1401i	0.422687	+	1.30090i
$574$	23.2361	+	20.1230i	0.969855	+	0.839919i
$575$	−11.5451	−	35.5321i	−0.481463	−	1.48179i
$576$	0.190983	−	0.330792i	0.00795763	−	0.0137830i
$577$	−8.18753	+	9.09317i	−0.340851	+	0.378554i	−0.889062	−	0.457786i	$-0.848642\pi$
$577$	−8.18753	+	9.09317i	−0.340851	+	0.378554i	0.548211	+	0.836340i	$0.315309\pi$
$578$	−14.2363	−	6.33842i	−0.592153	−	0.263643i
$579$	−0.135029	−	1.28472i	−0.00561163	−	0.0533911i
$580$	−3.78115	+	11.6372i	−0.157004	+	0.483208i
$581$	−19.7722	+	18.5068i	−0.820289	+	0.767790i
$582$	−10.9443			−0.453655
$583$	−11.0449	+	4.91752i	−0.457434	+	0.203663i
$584$	7.45156	−	1.58388i	0.308348	−	0.0655414i
$585$	0.0762525	−	0.725494i	0.00315265	−	0.0299955i
$586$	9.86968	+	2.09786i	0.407713	+	0.0866620i
$587$	−1.20820	+	3.71847i	−0.0498679	+	0.153478i	−0.972889	−	0.231271i	$-0.925712\pi$
$587$	−1.20820	+	3.71847i	−0.0498679	+	0.153478i	0.923022	+	0.384748i	$0.125712\pi$
$588$	3.91338	+	10.6287i	0.161385	+	0.438320i
$589$	−3.43769	−	10.5801i	−0.141648	−	0.435947i
$590$	11.5451	−	19.9967i	0.475304	−	0.823250i
$591$	27.1364	−	5.76802i	1.11624	−	0.237265i
$592$	−0.273659	+	2.60369i	−0.0112473	+	0.107011i
$593$	−19.4443	+	33.6785i	−0.798481	+	1.38301i	0.122125	+	0.992515i	$0.461029\pi$
$593$	−19.4443	+	33.6785i	−0.798481	+	1.38301i	−0.920605	+	0.390494i	$0.872304\pi$
$594$	−12.6353	−	9.18005i	−0.518431	−	0.376662i
$595$	24.6551	−	23.0771i	1.01076	−	0.946070i
$596$	7.47214	−	5.42882i	0.306071	−	0.222373i
$597$	0.746950	+	7.10675i	0.0305706	+	0.290860i
$598$	4.27037	−	4.74273i	0.174628	−	0.193944i
$599$	−19.9443	−	34.5445i	−0.814901	−	1.41145i	−0.909399	−	0.415925i	$-0.863458\pi$
$599$	−19.9443	−	34.5445i	−0.814901	−	1.41145i	0.0944982	−	0.995525i	$-0.469875\pi$
$600$	−4.04508	+	7.00629i	−0.165140	+	0.286031i
$601$	−3.85410			−0.157212			−0.0786060	−	0.996906i	$-0.525047\pi$
$601$	−3.85410			−0.157212			−0.0786060	+	0.996906i	$0.525047\pi$
$602$	2.30146	−	5.45007i	0.0938005	−	0.222128i
$603$	−0.309017	+	0.224514i	−0.0125841	+	0.00914292i
$604$	−1.60785	−	15.2977i	−0.0654226	−	0.622455i
$605$	−5.83022	−	2.59578i	−0.237032	−	0.105533i
$606$	1.47282	−	14.0130i	0.0598294	−	0.569239i
$607$	−6.89919	+	11.9497i	−0.280029	+	0.485025i	−0.971392	−	0.237483i	$-0.923678\pi$
$607$	−6.89919	+	11.9497i	−0.280029	+	0.485025i	0.691362	+	0.722508i	$0.257011\pi$
$608$	−4.85410	−	3.52671i	−0.196860	−	0.143027i
$609$	−0.452415	−	23.4214i	−0.0183328	−	0.949082i
$610$	6.80902	−	4.94704i	0.275689	−	0.200300i
$611$	−3.97997	−	0.845968i	−0.161012	−	0.0342242i
$612$	2.13269	−	0.453318i	0.0862091	−	0.0183243i
$613$	−12.7159	+	2.70285i	−0.513591	+	0.109167i	−0.457414	−	0.889254i	$-0.651224\pi$
$613$	−12.7159	+	2.70285i	−0.513591	+	0.109167i	−0.0561768	+	0.998421i	$0.517891\pi$
$614$	−26.5319	−	5.63952i	−1.07074	−	0.227593i
$615$	−12.9894	−	39.9771i	−0.523781	−	1.61203i
$616$	−0.145835	−	7.54984i	−0.00587586	−	0.304192i
$617$	31.1246	+	22.6134i	1.25303	+	0.910379i	0.998394	−	0.0566576i	$-0.0180443\pi$
$617$	31.1246	+	22.6134i	1.25303	+	0.910379i	0.254636	+	0.967037i	$0.418044\pi$
$618$	12.0902	−	20.9408i	0.486338	−	0.842362i
$619$	1.01838	−	9.68927i	0.0409323	−	0.389445i	−0.954807	−	0.297228i	$-0.903938\pi$
$619$	1.01838	−	9.68927i	0.0409323	−	0.389445i	0.995739	−	0.0922171i	$-0.0293954\pi$
$620$	−2.07295	−	3.59045i	−0.0832516	−	0.144196i
$621$	4.27402	+	40.6646i	0.171510	+	1.63181i
$622$	24.6074	−	17.8783i	0.986666	−	0.716855i
$623$	−17.5900	+	41.6547i	−0.704727	+	1.66886i
$624$	−1.38197			−0.0553229
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−6.76393	−	11.7155i	−0.270341	−	0.468245i
$627$	−18.5404	+	20.5912i	−0.740433	+	0.822334i
$628$	0.378188	+	3.59821i	0.0150913	+	0.143584i
$629$	−12.0902	+	8.78402i	−0.482067	+	0.350242i
$630$	−0.427051	+	2.21902i	−0.0170141	+	0.0884080i
$631$	−20.3992	−	14.8209i	−0.812079	−	0.590010i	0.102354	−	0.994748i	$-0.467363\pi$
$631$	−20.3992	−	14.8209i	−0.812079	−	0.590010i	−0.914433	+	0.404738i	$0.867363\pi$
$632$	−4.47214	+	7.74597i	−0.177892	+	0.308118i
$633$	3.93576	−	37.4462i	0.156432	−	1.48835i
$634$	−16.3768	+	3.48099i	−0.650405	+	0.138248i
$635$	−19.6848	−	4.18414i	−0.781169	−	0.166043i
$636$	−2.11803	−	6.51864i	−0.0839855	−	0.258481i
$637$	−3.82597	+	4.59423i	−0.151591	+	0.182030i
$638$	−4.82624	+	14.8536i	−0.191073	+	0.588061i
$639$	−0.726417	−	0.154405i	−0.0287366	−	0.00610816i
$640$	−2.04275	−	0.909491i	−0.0807468	−	0.0359508i
$641$	−43.1059	+	9.16244i	−1.70258	+	0.361894i	−0.953688	−	0.300798i	$-0.902747\pi$
$641$	−43.1059	+	9.16244i	−1.70258	+	0.361894i	−0.748892	+	0.662692i	$0.769414\pi$
$642$	6.74376	−	3.00252i	0.266155	−	0.118500i
$643$	5.94427			0.234419			0.117210	−	0.993107i	$-0.462605\pi$
$643$	5.94427			0.234419			0.117210	+	0.993107i	$0.462605\pi$
$644$	−14.4333	+	13.5096i	−0.568753	+	0.532352i
$645$	−6.54508	+	4.75528i	−0.257712	+	0.187239i
$646$	−3.58002	−	34.0616i	−0.140854	−	1.34014i
$647$	−31.9546	−	14.2271i	−1.25627	−	0.559326i	−0.332797	−	0.942998i	$-0.607993\pi$
$647$	−31.9546	−	14.2271i	−1.25627	−	0.559326i	−0.923469	+	0.383672i	$0.874659\pi$
$648$	5.15780	−	5.72831i	0.202617	−	0.225029i
$649$	14.7361	−	25.5236i	0.578441	−	1.00189i
$650$	−4.27051			−0.167503
$651$	6.00000	+	5.19615i	0.235159	+	0.203653i
$652$	−6.16312	−	18.9681i	−0.241366	−	0.742849i
$653$	2.21617	+	21.0855i	0.0867256	+	0.825139i	0.948272	+	0.317460i	$0.102830\pi$
$653$	2.21617	+	21.0855i	0.0867256	+	0.825139i	−0.861546	+	0.507679i	$0.830504\pi$
$654$	4.78339	+	2.12970i	0.187045	+	0.0832779i
$655$	−4.16006	+	39.5804i	−0.162547	+	1.54653i
$656$	10.6136	−	4.72548i	0.414392	−	0.184499i
$657$	−2.90983			−0.113523
$658$	12.0603	+	3.66267i	0.470158	+	0.142786i
$659$	−12.6074	+	38.8016i	−0.491114	+	1.51149i	0.331812	+	0.943346i	$0.392340\pi$
$659$	−12.6074	+	38.8016i	−0.491114	+	1.51149i	−0.822926	+	0.568149i	$0.807660\pi$
$660$	−5.16312	+	8.94278i	−0.200974	+	0.348097i
$661$	27.1042	−	30.1023i	1.05423	−	1.17084i	0.0693529	−	0.997592i	$-0.477907\pi$
$661$	27.1042	−	30.1023i	1.05423	−	1.17084i	0.984878	−	0.173250i	$-0.0554268\pi$
$662$	9.29884	−	1.97653i	0.361410	−	0.0768200i
$663$	−5.27847	−	5.86233i	−0.204999	−	0.227674i
$664$	3.16312	+	9.73508i	0.122753	+	0.377794i
$665$	33.9647	+	10.3150i	1.31709	+	0.399998i
$666$	0.309017	−	0.951057i	0.0119742	−	0.0368527i
$667$	37.3535	−	16.6309i	1.44633	−	0.643950i
$668$	−3.42705	−	5.93583i	−0.132597	−	0.229664i
$669$	1.41765	−	13.4880i	0.0548094	−	0.521477i
$670$	1.49622	+	1.66172i	0.0578041	+	0.0641979i
$671$	8.69098	−	6.31437i	0.335512	−	0.243764i
$672$	4.26531	+	0.365171i	0.164538	+	0.0140868i
$673$	4.89261	+	15.0579i	0.188596	+	0.580439i	0.999992	−	0.00405796i	$-0.00129169\pi$
$673$	4.89261	+	15.0579i	0.188596	+	0.580439i	−0.811396	+	0.584497i	$0.801292\pi$
$674$	4.64590	−	8.04693i	0.178953	−	0.309956i
$675$	18.3079	−	20.3329i	0.704670	−	0.782616i
$676$	6.13525	+	10.6266i	0.235971	+	0.408714i
$677$	23.1901	+	4.92921i	0.891269	+	0.189445i	0.630715	−	0.776014i	$-0.282762\pi$
$677$	23.1901	+	4.92921i	0.891269	+	0.189445i	0.260554	+	0.965459i	$0.416095\pi$
$678$	26.7254	−	19.4172i	1.02638	−	0.745711i
$679$	7.59321	+	16.2049i	0.291401	+	0.621887i
$680$	−3.94427	−	12.1392i	−0.151256	−	0.465518i
$681$	3.03867	−	1.35290i	0.116442	−	0.0518433i
$682$	−2.64590	−	4.58283i	−0.101317	−	0.175486i
$683$	2.00489	−	19.0753i	0.0767150	−	0.729895i	−0.886784	−	0.462184i	$-0.847066\pi$
$683$	2.00489	−	19.0753i	0.0767150	−	0.729895i	0.963499	−	0.267711i	$-0.0862673\pi$
$684$	1.53351	+	1.70314i	0.0586353	+	0.0651210i
$685$	−4.47214	+	13.7638i	−0.170872	+	0.525888i
$686$	13.0225	−	13.1687i	0.497201	−	0.502783i
$687$	1.66312	−	5.11855i	0.0634519	−	0.195285i
$688$	−1.49622	−	1.66172i	−0.0570429	−	0.0633526i
$689$	2.42094	−	2.68872i	0.0922304	−	0.102432i
$690$	26.4437	−	5.62078i	1.00669	−	0.213979i
$691$	4.11241	+	4.56729i	0.156443	+	0.173748i	0.816271	−	0.577669i	$-0.196037\pi$
$691$	4.11241	+	4.56729i	0.156443	+	0.173748i	−0.659828	+	0.751417i	$0.729371\pi$
$692$	−3.00000	−	2.17963i	−0.114043	−	0.0828570i
$693$	−0.545085	+	2.83234i	−0.0207061	+	0.107592i
$694$	15.7082	+	11.4127i	0.596275	+	0.433219i
$695$	−13.1232	−	2.78943i	−0.497792	−	0.105809i
$696$	−8.08862	−	3.60129i	−0.306599	−	0.136506i
$697$	60.5846	+	26.9740i	2.29481	+	1.02171i
$698$	20.9147	+	4.44556i	0.791634	+	0.168267i
$699$	−45.0344			−1.70336
$700$	13.1805	+	1.12844i	0.498178	+	0.0426510i
$701$	41.0132			1.54905			0.774523	−	0.632546i	$-0.217990\pi$
$701$	41.0132			1.54905			0.774523	+	0.632546i	$0.217990\pi$
$702$	4.57163	+	0.971730i	0.172545	+	0.0366756i
$703$	−14.3502	−	6.38910i	−0.541226	−	0.240970i
$704$	−2.60735	−	1.16087i	−0.0982683	−	0.0437519i
$705$	−11.5332	−	12.8089i	−0.434365	−	0.482411i
$706$	12.1631	+	8.83702i	0.457765	+	0.332586i
$707$	−21.7705	+	7.54153i	−0.818764	+	0.283628i
$708$	13.5172	+	9.82084i	0.508008	+	0.369090i
$709$	−5.07441	−	5.63571i	−0.190574	−	0.211653i	0.640284	−	0.768138i	$-0.278817\pi$
$709$	−5.07441	−	5.63571i	−0.190574	−	0.211653i	−0.830858	+	0.556485i	$0.812150\pi$
$710$	−0.454440	+	4.32371i	−0.0170548	+	0.162266i
$711$	2.28602	−	2.53889i	0.0857326	−	0.0952157i
$712$	11.4356	+	12.7005i	0.428566	+	0.475970i
$713$	−4.28115	+	13.1760i	−0.160330	+	0.493446i
$714$	14.7424	+	19.4883i	0.551722	+	0.729332i
$715$	−5.45085			−0.203850
$716$	−6.84927	−	7.60688i	−0.255969	−	0.284282i
$717$	3.60692	−	34.3175i	0.134703	−	1.28161i
$718$	−3.11803	−	5.40059i	−0.116364	−	0.201548i
$719$	33.8836	−	15.0859i	1.26364	−	0.562610i	0.338050	−	0.941128i	$-0.390233\pi$
$719$	33.8836	−	15.0859i	1.26364	−	0.562610i	0.925594	+	0.378518i	$0.123566\pi$
$720$	0.690983	+	0.502029i	0.0257514	+	0.0187095i
$721$	−39.3947	−	3.37274i	−1.46714	−	0.125608i
$722$	13.7533	−	9.99235i	0.511844	−	0.371877i
$723$	−6.56161	−	1.39471i	−0.244029	−	0.0518700i
$724$	−12.7082	−	22.0113i	−0.472297	−	0.818042i
$725$	−24.9952	−	11.1286i	−0.928299	−	0.413305i
$726$	2.30902	−	3.99933i	0.0856957	−	0.148429i
$727$	−0.583592	−	1.79611i	−0.0216442	−	0.0666141i	0.939651	−	0.342134i	$-0.111150\pi$
$727$	−0.583592	−	1.79611i	−0.0216442	−	0.0666141i	−0.961295	+	0.275520i	$0.911150\pi$
$728$	0.958817	+	2.04624i	0.0355361	+	0.0758387i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	1.78058	+	16.9411i	0.0659024	+	0.627019i
$731$	1.33419	−	12.6940i	0.0493470	−	0.469505i
$732$	3.04508	+	5.27424i	0.112550	+	0.194942i
$733$	13.4366	−	5.98237i	0.496293	−	0.220964i	−0.143298	−	0.989680i	$-0.545771\pi$
$733$	13.4366	−	5.98237i	0.496293	−	0.220964i	0.639590	+	0.768716i	$0.279104\pi$
$734$	4.65248	−	14.3188i	0.171726	−	0.528518i
$735$	−24.5510	+	6.21837i	−0.905576	+	0.229368i
$736$	2.30902	+	7.10642i	0.0851115	+	0.261946i
$737$	1.90977	+	2.12101i	0.0703472	+	0.0781284i
$738$	−4.34072	+	0.922648i	−0.159784	+	0.0339632i
$739$	25.9469	−	28.8170i	0.954473	−	1.06005i	−0.0436641	−	0.999046i	$-0.513903\pi$
$739$	25.9469	−	28.8170i	0.954473	−	1.06005i	0.998138	−	0.0610039i	$-0.0194302\pi$
$740$	−5.72618	−	1.21714i	−0.210498	−	0.0447428i
$741$	2.56231	−	7.88597i	0.0941287	−	0.289698i
$742$	−8.18247	+	7.65879i	−0.300388	+	0.281163i
$743$	−31.7639			−1.16531			−0.582653	−	0.812721i	$-0.697985\pi$
$743$	−31.7639			−1.16531			−0.582653	+	0.812721i	$0.697985\pi$
$744$	2.74064	−	1.22021i	0.100477	−	0.0447351i
$745$	10.3262	+	17.8856i	0.378324	+	0.655277i
$746$	−27.0889	−	12.0607i	−0.991795	−	0.441575i
$747$	−0.408689	−	3.88841i	−0.0149531	−	0.142270i
$748$	−5.03444	−	15.4944i	−0.184077	−	0.566532i
$749$	−9.12461	−	7.90215i	−0.333406	−	0.288738i
$750$	−14.6353	−	10.6331i	−0.534404	−	0.388267i
$751$	2.75329	−	4.76884i	0.100469	−	0.174017i	−0.811409	−	0.584479i	$-0.801299\pi$
$751$	2.75329	−	4.76884i	0.100469	−	0.174017i	0.911878	+	0.410461i	$0.134632\pi$
$752$	3.18769	−	3.54029i	0.116243	−	0.129101i
$753$	−13.0368	−	5.80434i	−0.475086	−	0.211522i
$754$	−0.488541	−	4.64816i	−0.0177916	−	0.169276i
$755$	34.3951			1.25177
$756$	−13.8531	−	4.20716i	−0.503834	−	0.153013i
$757$	38.7984			1.41015			0.705075	−	0.709132i	$-0.250913\pi$
$757$	38.7984			1.41015			0.705075	+	0.709132i	$0.250913\pi$
$758$	21.8742	−	9.73901i	0.794506	−	0.353737i
$759$	33.7525	−	7.17432i	1.22514	−	0.260411i
$760$	8.97733	−	9.97033i	0.325642	−	0.361662i
$761$	−15.8813	−	3.37567i	−0.575696	−	0.122368i	−0.0891425	−	0.996019i	$-0.528413\pi$
$761$	−15.8813	−	3.37567i	−0.575696	−	0.122368i	−0.486553	+	0.873651i	$0.661746\pi$
$762$	4.50000	−	13.8496i	0.163018	−	0.501717i
$763$	−0.165352	−	8.56023i	−0.00598615	−	0.309901i
$764$	−6.25329	−	19.2456i	−0.226236	−	0.696283i
$765$	0.509617	+	4.84868i	0.0184252	+	0.175304i
$766$	19.5630	−	4.15823i	0.706838	−	0.150243i
$767$	−0.921906	+	8.77135i	−0.0332881	+	0.316715i
$768$	0.809017	−	1.40126i	0.0291929	−	0.0505636i
$769$	−23.3713	−	16.9803i	−0.842791	−	0.612324i	0.0803576	−	0.996766i	$-0.474394\pi$
$769$	−23.3713	−	16.9803i	−0.842791	−	0.612324i	−0.923149	+	0.384442i	$0.874394\pi$
$770$	16.8236	+	1.44033i	0.606279	+	0.0519060i
$771$	−1.26393	+	0.918300i	−0.0455194	+	0.0330718i
$772$	0.0834528	+	0.794000i	0.00300353	+	0.0285767i
$773$	−33.8789	+	37.6263i	−1.21854	+	1.35332i	−0.302035	+	0.953297i	$0.597666\pi$
$773$	−33.8789	+	37.6263i	−1.21854	+	1.35332i	−0.916503	+	0.400027i	$0.869001\pi$
$774$	0.427051	+	0.739674i	0.0153500	+	0.0265870i
$775$	8.46903	−	3.77066i	0.304217	−	0.135446i
$776$	6.76393			0.242811
$777$	11.1215	−	1.38656i	0.398981	−	0.0497424i
$778$	3.30902	−	2.40414i	0.118634	−	0.0861927i
$779$	7.28649	+	69.3263i	0.261066	+	2.48387i
$780$	0.323011	−	3.07324i	0.0115656	−	0.110040i
$781$	−0.580044	+	5.51875i	−0.0207556	+	0.197476i
$782$	−21.3262	+	36.9381i	−0.762625	+	1.32090i
$783$	24.2254	+	17.6008i	0.865746	+	0.629001i
$784$	−2.41860	−	6.56889i	−0.0863786	−	0.234603i
$785$	−8.09017			−0.288751
$786$	−28.1691	−	5.98752i	−1.00476	−	0.213568i
$787$	22.5311	−	4.78913i	0.803146	−	0.170714i	0.211991	−	0.977272i	$-0.432005\pi$
$787$	22.5311	−	4.78913i	0.803146	−	0.170714i	0.591156	+	0.806558i	$0.298672\pi$
$788$	−16.7712	+	3.56483i	−0.597450	+	0.126992i
$789$	−26.4437	−	5.62078i	−0.941420	−	0.200105i
$790$	−16.1803	−	11.7557i	−0.575671	−	0.418249i
$791$	−47.2927	−	26.0999i	−1.68154	−	0.928005i
$792$	0.881966	+	0.640786i	0.0313393	+	0.0227693i
$793$	−1.60739	+	2.78408i	−0.0570801	+	0.0988657i
$794$	2.88465	−	27.4456i	0.102372	−	0.974007i
$795$	14.9913	−	3.18650i	0.531687	−	0.113014i
$796$	−0.461640	−	4.39221i	−0.0163624	−	0.155678i
$797$	−13.1910	+	9.58381i	−0.467249	+	0.339476i	−0.796368	−	0.604812i	$-0.793248\pi$
$797$	−13.1910	+	9.58381i	−0.467249	+	0.339476i	0.329119	+	0.944288i	$0.393248\pi$
$798$	−9.99211	+	23.6623i	−0.353717	+	0.837635i
$799$	27.1935			0.962037
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−3.26393	−	5.65330i	−0.115325	−	0.199749i
$802$	−7.71365	+	8.56687i	−0.272378	+	0.302507i
$803$	2.27273	+	21.6235i	0.0802027	+	0.763078i
$804$	−1.30902	+	0.951057i	−0.0461655	+	0.0335412i
$805$	−26.6693	−	35.2547i	−0.939970	−	1.24257i
$806$	1.28115	+	0.930812i	0.0451267	+	0.0327865i
$807$	2.16312	−	3.74663i	0.0761454	−	0.131888i
$808$	−0.910255	+	8.66050i	−0.0320227	+	0.304675i
$809$	29.8062	−	6.33551i	1.04793	−	0.222745i	0.348400	−	0.937346i	$-0.386725\pi$
$809$	29.8062	−	6.33551i	1.04793	−	0.222745i	0.699532	+	0.714601i	$0.253392\pi$
$810$	11.5332	+	12.8089i	0.405235	+	0.450059i
$811$	−6.51722	−	20.0579i	−0.228851	−	0.704330i	−0.997878	−	0.0651137i	$-0.979259\pi$
$811$	−6.51722	−	20.0579i	−0.228851	−	0.704330i	0.769027	−	0.639216i	$-0.220741\pi$
$812$	0.279608	+	14.4752i	0.00981230	+	0.507980i
$813$	−0.454915	+	1.40008i	−0.0159546	+	0.0491031i
$814$	−7.30885	−	1.55354i	−0.256175	−	0.0544517i
$815$	43.6222	−	9.27219i	1.52802	−	0.324790i
$816$	9.03424	−	1.92029i	0.316262	−	0.0672235i
$817$	12.2565	−	5.45694i	0.428801	−	0.190914i
$818$	−7.47214			−0.261257
$819$	−0.195730	−	0.840659i	−0.00683935	−	0.0293750i
$820$	8.02786	+	24.7072i	0.280345	+	0.862814i
$821$	−2.51228	−	23.9028i	−0.0876793	−	0.834213i	−0.946666	−	0.322215i	$-0.895572\pi$
$821$	−2.51228	−	23.9028i	−0.0876793	−	0.834213i	0.858987	−	0.511997i	$-0.171094\pi$
$822$	−9.56677	−	4.25940i	−0.333679	−	0.148564i
$823$	23.0291	−	25.5764i	0.802743	−	0.891536i	−0.193233	−	0.981153i	$-0.561897\pi$
$823$	23.0291	−	25.5764i	0.802743	−	0.891536i	0.995976	+	0.0896164i	$0.0285641\pi$
$824$	−7.47214	+	12.9421i	−0.260304	+	0.450860i
$825$	−18.6803	−	13.5721i	−0.650366	−	0.472519i
$826$	5.16312	−	26.8284i	0.179648	−	0.933478i
$827$	−16.1631	−	49.7450i	−0.562047	−	1.72980i	−0.676567	−	0.736381i	$-0.736533\pi$
$827$	−16.1631	−	49.7450i	−0.562047	−	1.72980i	0.114520	−	0.993421i	$-0.463467\pi$
$828$	−0.298335	−	2.83847i	−0.0103679	−	0.0986435i
$829$	−29.1002	−	12.9562i	−1.01069	−	0.449988i	−0.166506	−	0.986040i	$-0.553248\pi$
$829$	−29.1002	−	12.9562i	−1.01069	−	0.449988i	−0.844185	+	0.536052i	$0.819915\pi$
$830$	−22.3884	+	4.75880i	−0.777112	+	0.165180i
$831$	30.1785	−	13.4363i	1.04688	−	0.466101i
$832$	0.854102			0.0296107
$833$	18.6275	−	35.3499i	0.645403	−	1.22480i
$834$	3.00000	−	9.23305i	0.103882	−	0.319714i
$835$	14.0012	−	6.23374i	0.484532	−	0.215728i
$836$	11.4586	−	12.7261i	0.396304	−	0.440140i
$837$	−9.92419	+	2.10945i	−0.343030	+	0.0729133i
$838$	5.19508	+	5.76973i	0.179461	+	0.199312i
$839$	0.0557281	+	0.171513i	0.00192395	+	0.00592130i	0.952014	−	0.306055i	$-0.0990091\pi$
$839$	0.0557281	+	0.171513i	0.00192395	+	0.00592130i	−0.950090	+	0.311976i	$0.899009\pi$
$840$	−1.80902	+	9.39993i	−0.0624170	+	0.324328i
$841$	0.291796	−	0.898056i	0.0100619	−	0.0309674i
$842$	−11.7937	+	5.25090i	−0.406438	+	0.180958i
$843$	13.7533	+	23.8214i	0.473688	+	0.820452i
$844$	−2.43243	+	23.1430i	−0.0837277	+	0.796616i
$845$	−25.0656	+	11.1599i	−0.862282	+	0.383913i
$846$	−1.47214	+	1.06957i	−0.0506131	+	0.0367726i
$847$	−7.52372	−	0.644137i	−0.258518	−	0.0221328i
$848$	1.30902	+	4.02874i	0.0449518	+	0.138348i
$849$	−6.92705	+	11.9980i	−0.237736	+	0.411770i
$850$	27.9173	−	5.93401i	0.957557	−	0.203535i
$851$	9.78115	+	16.9415i	0.335294	+	0.580746i
$852$	−3.07715	−	0.654069i	−0.105422	−	0.0224080i
$853$	−0.972136	+	0.706298i	−0.0332853	+	0.0241832i	−0.604304	−	0.796754i	$-0.706549\pi$
$853$	−0.972136	+	0.706298i	−0.0332853	+	0.0241832i	0.571018	+	0.820937i	$0.306549\pi$
$854$	5.69673	−	8.16808i	0.194938	−	0.279506i
$855$	−4.14590	+	3.01217i	−0.141787	+	0.103014i
$856$	−4.16787	+	1.85566i	−0.142455	+	0.0634251i
$857$	10.2082	+	17.6811i	0.348706	+	0.603976i	0.986020	−	0.166628i	$-0.0532880\pi$
$857$	10.2082	+	17.6811i	0.348706	+	0.603976i	−0.637314	+	0.770604i	$0.719955\pi$
$858$	0.412289	−	3.92266i	0.0140753	−	0.133918i
$859$	−13.1040	−	14.5534i	−0.447102	−	0.496557i	0.476893	−	0.878961i	$-0.341763\pi$
$859$	−13.1040	−	14.5534i	−0.447102	−	0.496557i	−0.923995	+	0.382404i	$0.875096\pi$
$860$	4.04508	−	2.93893i	0.137936	−	0.100217i
$861$	−30.0056	−	39.6650i	−1.02259	−	1.35178i
$862$	−0.628677	+	1.93487i	−0.0214128	+	0.0659019i
$863$	−4.03783	−	4.48446i	−0.137449	−	0.152653i	0.670490	−	0.741918i	$-0.266084\pi$
$863$	−4.03783	−	4.48446i	−0.137449	−	0.152653i	−0.807939	+	0.589266i	$0.799417\pi$
$864$	−3.66157	+	4.06659i	−0.124569	+	0.138348i
$865$	5.54829	−	6.16201i	0.188648	−	0.209514i
$866$	−6.21743	−	6.90515i	−0.211277	−	0.234647i
$867$	20.3992	+	14.8209i	0.692793	+	0.503343i
$868$	−3.70820	−	3.21140i	−0.125865	−	0.109002i
$869$	−20.6525	−	15.0049i	−0.700587	−	0.509006i
$870$	9.89919	−	17.1459i	0.335614	−	0.581300i
$871$	−0.780261	−	0.347395i	−0.0264381	−	0.0117710i
$872$	−2.95630	−	1.31623i	−0.100113	−	0.0445731i
$873$	−2.52713	−	0.537159i	−0.0855305	−	0.0181801i
$874$	−44.8328			−1.51649
$875$	−5.59017	+	29.0474i	−0.188982	+	0.981981i
$876$	−12.3262			−0.416465
$877$	24.4874	+	5.20495i	0.826880	+	0.175759i	0.601866	−	0.798597i	$-0.294424\pi$
$877$	24.4874	+	5.20495i	0.826880	+	0.175759i	0.225014	+	0.974356i	$0.427757\pi$
$878$	12.7387	+	5.67165i	0.429911	+	0.191409i
$879$	−14.9148	−	6.64048i	−0.503062	−	0.223978i
$880$	3.19098	−	5.52694i	0.107568	−	0.186313i
$881$	0.236068	+	0.171513i	0.00795333	+	0.00577843i	0.591755	−	0.806118i	$-0.298435\pi$
$881$	0.236068	+	0.171513i	0.00795333	+	0.00577843i	−0.583801	+	0.811896i	$0.698435\pi$
$882$	0.381966	+	2.64634i	0.0128615	+	0.0891068i
$883$	13.9721	+	10.1514i	0.470200	+	0.341620i	0.797519	−	0.603294i	$-0.206145\pi$
$883$	13.9721	+	10.1514i	0.470200	+	0.341620i	−0.327319	+	0.944914i	$0.606145\pi$
$884$	3.26227	+	3.62312i	0.109722	+	0.121859i
$885$	−24.9992	+	27.7644i	−0.840338	+	0.933290i
$886$	−6.59368	+	7.32302i	−0.221519	+	0.246022i
$887$	7.27706	+	8.08199i	0.244340	+	0.271367i	0.852823	−	0.522200i	$-0.174889\pi$
$887$	7.27706	+	8.08199i	0.244340	+	0.271367i	−0.608484	+	0.793567i	$0.708222\pi$
$888$	1.30902	−	4.02874i	0.0439277	−	0.135196i
$889$	−23.6288	+	2.94589i	−0.792486	+	0.0988021i
$890$	−30.9164	+	22.4621i	−1.03632	+	0.752931i
$891$	14.7209	+	16.3492i	0.493168	+	0.547718i
$892$	−0.876154	+	8.33605i	−0.0293358	+	0.279112i
$893$	14.2918	+	24.7541i	0.478257	+	0.828365i
$894$	−13.6523	+	6.07838i	−0.456600	+	0.203292i
$895$	18.5172	−	13.4535i	0.618962	−	0.449703i
$896$	−2.63611	−	0.225688i	−0.0880662	−	0.00753971i
$897$	−8.35410	+	6.06961i	−0.278935	+	0.202658i
$898$	33.2907	+	7.07616i	1.11093	+	0.236134i
$899$	5.07295	+	8.78661i	0.169192	+	0.293050i
$900$	−1.27793	+	1.41928i	−0.0425975	+	0.0473093i
$901$	−12.0902	+	20.9408i	−0.402782	+	0.697639i
$902$	10.2467	+	31.5361i	0.341178	+	1.05004i
$903$	−5.47591	+	7.85147i	−0.182227	+	0.261280i
$904$	−16.5172	+	12.0005i	−0.549355	+	0.399129i
$905$	51.9194	−	23.1160i	1.72586	−	0.768401i
$906$	−2.60156	+	24.7522i	−0.0864311	+	0.822337i
$907$	−0.364745	−	0.631757i	−0.0121112	−	0.0209771i	0.859906	−	0.510452i	$-0.170522\pi$
$907$	−0.364745	−	0.631757i	−0.0121112	−	0.0209771i	−0.872017	+	0.489475i	$0.837189\pi$
$908$	−1.87800	+	0.836140i	−0.0623237	+	0.0277483i
$909$	1.02786	−	3.16344i	0.0340921	−	0.104925i
$910$	−4.77458	+	1.65396i	−0.158276	+	0.0548283i
$911$	2.17376	+	6.69015i	0.0720200	+	0.221655i	0.980587	−	0.196084i	$-0.0628227\pi$
$911$	2.17376	+	6.69015i	0.0720200	+	0.221655i	−0.908567	+	0.417739i	$0.862823\pi$
$912$	6.49606	+	7.21460i	0.215106	+	0.238899i
$913$	−28.5764	+	6.07409i	−0.945740	+	0.201023i
$914$	10.1949	−	11.3226i	0.337218	−	0.374518i
$915$	−12.4407	+	5.53895i	−0.411277	+	0.183112i
$916$	−1.02786	+	3.16344i	−0.0339616	+	0.104523i
$917$	10.6783	+	45.8634i	0.352629	+	1.51454i
$918$	−31.2361			−1.03094
$919$	−34.8795	+	15.5293i	−1.15057	+	0.512266i	−0.891244	−	0.453525i	$-0.850166\pi$
$919$	−34.8795	+	15.5293i	−1.15057	+	0.512266i	−0.259324	+	0.965790i	$0.583500\pi$
$920$	−16.3431	+	3.47383i	−0.538816	+	0.114529i
$921$	40.0942	+	17.8511i	1.32115	+	0.588213i
$922$	−2.41135	−	22.9425i	−0.0794137	−	0.755571i
$923$	−0.513156	−	1.57933i	−0.0168907	−	0.0519843i
$924$	−2.30902	+	11.9980i	−0.0759611	+	0.394705i
$925$	4.04508	−	12.4495i	0.133002	−	0.409337i
$926$	8.11803	−	14.0608i	0.266775	−	0.462068i
$927$	3.81953	−	4.24202i	0.125450	−	0.139326i
$928$	4.99904	+	2.22572i	0.164102	+	0.0730628i
$929$	−3.48354	−	33.1437i	−0.114291	−	1.08741i	−0.889888	−	0.456180i	$-0.849217\pi$
$929$	−3.48354	−	33.1437i	−0.114291	−	1.08741i	0.775596	−	0.631229i	$-0.217449\pi$
$930$	2.07295	+	6.37988i	0.0679747	+	0.209205i
$931$	41.9687	−	1.62196i	1.37547	−	0.0531577i
$932$	27.8328			0.911694
$933$	−44.9599	+	20.0175i	−1.47192	+	0.655342i
$934$	−33.2907	+	7.07616i	−1.08931	+	0.231539i
$935$	35.6335	−	7.57413i	1.16534	−	0.247701i
$936$	−0.319109	−	0.0678287i	−0.0104304	−	0.00221705i
$937$	−8.31966	+	25.6053i	−0.271791	+	0.836488i	0.718259	+	0.695776i	$0.244939\pi$
$937$	−8.31966	+	25.6053i	−0.271791	+	0.836488i	−0.990051	+	0.140712i	$0.955061\pi$
$938$	2.31641	+	1.27838i	0.0756334	+	0.0417405i
$939$	6.76393	+	20.8172i	0.220733	+	0.679345i
$940$	7.12790	+	7.91633i	0.232486	+	0.258202i
$941$	−3.79070	+	0.805739i	−0.123573	+	0.0262663i	−0.269283	−	0.963061i	$-0.586787\pi$
$941$	−3.79070	+	0.805739i	−0.123573	+	0.0262663i	0.145710	+	0.989327i	$0.453453\pi$
$942$	0.611920	−	5.82203i	0.0199374	−	0.189692i
$943$	43.4058	−	75.1810i	1.41349	−	2.44823i
$944$	−8.35410	−	6.06961i	−0.271903	−	0.197549i
$945$	12.5939	−	29.8235i	0.409680	−	0.970160i
$946$	5.16312	−	3.75123i	0.167867	−	0.121963i
$947$	−5.11607	−	48.6762i	−0.166250	−	1.58176i	−0.686102	−	0.727506i	$-0.740679\pi$
$947$	−5.11607	−	48.6762i	−0.166250	−	1.58176i	0.519852	−	0.854257i	$-0.325987\pi$
$948$	9.68375	−	10.7549i	0.314514	−	0.349303i
$949$	−3.25329	−	5.63486i	−0.105606	−	0.182915i
$950$	20.0739	+	22.2943i	0.651284	+	0.723324i
$951$	27.0902			0.878459
$952$	−9.11133	−	12.0445i	−0.295300	−	0.390363i
$953$	−32.1074	+	23.3274i	−1.04006	+	0.755648i	−0.970297	−	0.241915i	$-0.922224\pi$
$953$	−32.1074	+	23.3274i	−1.04006	+	0.755648i	−0.0697631	+	0.997564i	$0.522224\pi$
$954$	−0.169131	−	1.60917i	−0.00547581	−	0.0520988i
$955$	44.2604	−	9.40784i	1.43223	−	0.304431i
$956$	−2.22920	+	21.2094i	−0.0720974	+	0.685961i
$957$	12.6353	−	21.8849i	0.408440	−	0.707438i
$958$	−6.23607	−	4.53077i	−0.201478	−	0.146382i
$959$	0.330704	+	17.1205i	0.0106790	+	0.552849i
$960$	2.92705	+	2.12663i	0.0944702	+	0.0686366i
$961$	26.9600	+	5.73053i	0.869678	+	0.184856i
$962$	2.18720	−	0.464905i	0.0705183	−	0.0149891i
$963$	1.70456	−	0.362316i	0.0549288	−	0.0116755i
$964$	4.05530	+	0.861981i	0.130612	+	0.0277625i
$965$	−1.78522			−0.0574682
$966$	27.3880	−	16.5258i	0.881195	−	0.531709i
$967$	−10.1910	−	7.40418i	−0.327720	−	0.238102i	0.411743	−	0.911300i	$-0.364920\pi$
$967$	−10.1910	−	7.40418i	−0.327720	−	0.238102i	−0.739463	+	0.673198i	$0.764920\pi$
$968$	−1.42705	+	2.47172i	−0.0458672	+	0.0794442i
$969$	−5.79259	+	55.1128i	−0.186085	+	1.77048i
$970$	−1.58095	+	15.0418i	−0.0507613	+	0.482962i
$971$	−2.43603	−	23.1773i	−0.0781759	−	0.743794i	−0.961458	−	0.274952i	$-0.911338\pi$
$971$	−2.43603	−	23.1773i	−0.0781759	−	0.743794i	0.883282	−	0.468842i	$-0.155329\pi$
$972$	3.19098	−	2.31838i	0.102351	−	0.0743622i
$973$	−15.7526	+	1.96393i	−0.505004	+	0.0629607i
$974$	8.59675			0.275458
$975$	6.75883	+	1.43663i	0.216456	+	0.0460091i
$976$	−1.88197	−	3.25966i	−0.0602403	−	0.104339i
$977$	28.4282	−	31.5727i	0.909499	−	1.01010i	−0.0904003	−	0.995906i	$-0.528815\pi$
$977$	28.4282	−	31.5727i	0.909499	−	1.01010i	0.999899	−	0.0141954i	$-0.00451870\pi$
$978$	3.37319	+	32.0937i	0.107863	+	1.02624i
$979$	−39.4615	+	28.6705i	−1.26119	+	0.916312i
$980$	15.1733	−	3.84317i	0.484694	−	0.122765i
$981$	1.00000	+	0.726543i	0.0319275	+	0.0231967i
$982$	−13.9271	+	24.1224i	−0.444430	+	0.769775i
$983$	−5.24305	+	49.8843i	−0.167227	+	1.59106i	0.513215	+	0.858260i	$0.328454\pi$
$983$	−5.24305	+	49.8843i	−0.167227	+	1.59106i	−0.680443	+	0.732801i	$0.738212\pi$
$984$	−18.3876	+	3.90840i	−0.586175	+	0.124595i
$985$	−4.00756	−	38.1294i	−0.127691	−	1.21490i
$986$	9.65248	+	29.7073i	0.307397	+	0.946072i
$987$	−17.8554	−	9.85400i	−0.568342	−	0.313656i
$988$	−1.58359	+	4.87380i	−0.0503808	+	0.155056i
$989$	−16.3431	−	3.47383i	−0.519680	−	0.110461i
$990$	−1.63114	+	1.81156i	−0.0518409	+	0.0575751i
$991$	−21.7502	+	4.62314i	−0.690916	+	0.146859i	−0.539971	−	0.841683i	$-0.681565\pi$
$991$	−21.7502	+	4.62314i	−0.690916	+	0.146859i	−0.150945	+	0.988542i	$0.548232\pi$
$992$	−1.69381	+	0.754131i	−0.0537784	+	0.0239437i
$993$	−15.3820			−0.488132
$994$	1.16649	+	5.01006i	0.0369987	+	0.158909i
$995$	9.87539			0.313071
$996$	−1.73123	−	16.4716i	−0.0548562	−	0.521922i
$997$	19.9647	+	8.88886i	0.632289	+	0.281513i	0.697749	−	0.716342i	$-0.254185\pi$
$997$	19.9647	+	8.88886i	0.632289	+	0.281513i	−0.0654604	+	0.997855i	$0.520852\pi$
$998$	−8.02957	+	8.91774i	−0.254172	+	0.282286i
$999$	−7.16312	+	12.4069i	−0.226631	+	0.392537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.a.331.1	yes	8
7.4	even	3	inner	350.2.q.a.81.1	✓	8
25.21	even	5	inner	350.2.q.a.121.1	yes	8
175.46	even	15	inner	350.2.q.a.221.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.a.81.1	✓	8	7.4	even	3	inner
350.2.q.a.121.1	yes	8	25.21	even	5	inner
350.2.q.a.221.1	yes	8	175.46	even	15	inner
350.2.q.a.331.1	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(-1.47815 - 0.658114i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.255585 - 0.283856i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(-1.47815 - 0.658114i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.255585 - 0.283856i) q^{9} +(-1.49622 + 1.66172i) q^{10} +(-1.90977 + 2.12101i) q^{11} +(-1.08268 - 1.20243i) q^{12} +(0.263932 - 0.812299i) q^{13} +(-1.02924 + 2.43735i) q^{14} +(2.92705 - 2.12663i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.596670 + 5.67693i) q^{17} +(-0.190983 - 0.330792i) q^{18} +(-5.48127 + 2.44042i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(2.44890 - 3.51128i) q^{21} +(-2.30902 + 1.67760i) q^{22} +(7.30885 + 1.55354i) q^{23} +(-0.809017 - 1.40126i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(0.427051 - 0.739674i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-1.51351 + 2.17009i) q^{28} +(4.42705 - 3.21644i) q^{29} +(3.30524 - 1.47159i) q^{30} +(-0.193806 + 1.84395i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.21878 - 1.87832i) q^{33} +(-1.76393 + 5.42882i) q^{34} +(-4.47214 - 3.87298i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(1.75181 + 1.94558i) q^{37} +(-5.86889 + 1.24747i) q^{38} +(-0.924716 + 1.02700i) q^{39} +(-2.04275 + 0.909491i) q^{40} +(3.59017 - 11.0494i) q^{41} +(3.12543 - 2.92540i) q^{42} -2.23607 q^{43} +(-2.60735 + 1.16087i) q^{44} +(0.835438 - 0.177578i) q^{45} +(6.82614 + 3.03919i) q^{46} +(-0.497966 - 4.73783i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.54508 - 4.75528i) q^{50} +(4.61803 - 7.99867i) q^{51} +(0.571506 - 0.634721i) q^{52} +(3.86984 + 1.72296i) q^{53} +(0.571994 + 5.44216i) q^{54} +(-1.97214 - 6.06961i) q^{55} +(-1.93162 + 1.80800i) q^{56} +9.70820 q^{57} +(4.99904 - 2.22572i) q^{58} +(-10.1006 + 2.14695i) q^{59} +(3.53897 - 0.752232i) q^{60} +(-3.68168 - 0.782565i) q^{61} +(-0.572949 + 1.76336i) q^{62} +(0.865272 - 0.522102i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.27793 + 1.41928i) q^{65} +(4.51712 - 0.960143i) q^{66} +(0.104528 - 0.994522i) q^{67} +(-2.85410 + 4.94345i) q^{68} +(-9.78115 - 7.10642i) q^{69} +(-3.56917 - 4.71816i) q^{70} +(1.57295 - 1.14281i) q^{71} +(-0.0399263 - 0.379874i) q^{72} +(5.09746 - 5.66130i) q^{73} +(1.30902 + 2.26728i) q^{74} +(0.845653 + 8.04585i) q^{75} -6.00000 q^{76} +(-4.55567 - 6.02223i) q^{77} +(-1.11803 + 0.812299i) q^{78} +(0.934931 + 8.89527i) q^{79} +(-2.18720 + 0.464905i) q^{80} +(0.805727 - 7.66598i) q^{81} +(5.80902 - 10.0615i) q^{82} +(8.28115 + 6.01661i) q^{83} +(3.66535 - 2.21166i) q^{84} +(-10.3262 - 7.50245i) q^{85} +(-2.18720 - 0.464905i) q^{86} +(-8.66062 + 1.84087i) q^{87} +(-2.79173 + 0.593401i) q^{88} +(16.7167 + 3.55325i) q^{89} +0.854102 q^{90} +(1.97845 + 1.09187i) q^{91} +(6.04508 + 4.39201i) q^{92} +(1.50000 - 2.59808i) q^{93} +(0.497966 - 4.73783i) q^{94} +(1.40240 - 13.3429i) q^{95} +(-0.169131 - 1.60917i) q^{96} +(5.47214 - 3.97574i) q^{97} +(-5.81779 - 3.89273i) q^{98} +1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Introduction

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