LMFDB - Embedded newform 122.2.i.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			73.2
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	122.73
Dual form			122.2.i.a.117.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(0.578959 - 0.420639i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.23343 - 0.262173i) q^{5} +(-0.699995 + 0.148788i) q^{6} +(0.200979 - 1.91219i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.768794 + 2.36610i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(0.578959 - 0.420639i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.23343 - 0.262173i) q^{5} +(-0.699995 + 0.148788i) q^{6} +(0.200979 - 1.91219i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.768794 + 2.36610i) q^{9} +(-1.23343 - 0.262173i) q^{10} +5.96587 q^{11} +(0.699995 + 0.148788i) q^{12} +(-3.04224 - 5.26931i) q^{13} +(-0.961361 + 1.66513i) q^{14} +(0.603824 - 0.670615i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-0.396997 - 0.440910i) q^{17} +(1.66471 - 1.84885i) q^{18} +(0.0598412 + 0.569351i) q^{19} +(1.02016 + 0.741187i) q^{20} +(-0.687982 - 1.19162i) q^{21} +(-5.45010 - 2.42654i) q^{22} +(-2.81799 + 8.67289i) q^{23} +(-0.578959 - 0.420639i) q^{24} +(-3.11512 + 1.38694i) q^{25} +(0.636001 + 6.05115i) q^{26} +(1.21360 + 3.73509i) q^{27} +(1.55551 - 1.13015i) q^{28} +(-2.34835 + 4.06745i) q^{29} +(-0.824384 + 0.367040i) q^{30} +(-0.883386 + 0.393309i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.45400 - 2.50948i) q^{33} +(0.183341 + 0.564264i) q^{34} +(-0.253431 - 2.41124i) q^{35} +(-2.27278 + 1.01191i) q^{36} +(-3.43589 - 2.49632i) q^{37} +(0.176908 - 0.544468i) q^{38} +(-3.97781 - 1.77103i) q^{39} +(-0.630491 - 1.09204i) q^{40} +(-2.23434 - 1.62334i) q^{41} +(0.143827 + 1.36843i) q^{42} +(-5.68536 + 6.31423i) q^{43} +(3.99195 + 4.43351i) q^{44} +(-0.327923 + 3.11997i) q^{45} +(6.10195 - 6.77690i) q^{46} +(4.57617 - 7.92615i) q^{47} +(0.357817 + 0.619756i) q^{48} +(3.23096 + 0.686762i) q^{49} +3.40992 q^{50} +(-0.415309 - 0.0882766i) q^{51} +(1.88021 - 5.78668i) q^{52} +(0.833469 + 2.56515i) q^{53} +(0.410515 - 3.90579i) q^{54} +(7.35847 - 1.56409i) q^{55} +(-1.88071 + 0.399756i) q^{56} +(0.274137 + 0.304460i) q^{57} +(3.79970 - 2.76065i) q^{58} +(-1.97074 - 0.877428i) q^{59} +0.902401 q^{60} +(-1.54265 - 7.65639i) q^{61} +0.966986 q^{62} +(4.36993 + 1.94562i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-5.13385 - 5.70172i) q^{65} +(-4.17608 + 0.887653i) q^{66} +(7.73845 - 1.64486i) q^{67} +(0.0620170 - 0.590052i) q^{68} +(2.01665 + 6.20661i) q^{69} +(-0.749217 + 2.30585i) q^{70} +(2.11029 + 0.448556i) q^{71} +2.48787 q^{72} +(-5.07396 - 1.07850i) q^{73} +(2.12349 + 3.67800i) q^{74} +(-1.22013 + 2.11332i) q^{75} +(-0.383069 + 0.425441i) q^{76} +(1.19902 - 11.4079i) q^{77} +(2.91356 + 3.23584i) q^{78} +(4.24314 - 4.71248i) q^{79} +(0.131809 + 1.25407i) q^{80} +(-3.76444 - 2.73502i) q^{81} +(1.38090 + 2.39179i) q^{82} +(7.99970 + 3.56170i) q^{83} +(0.425196 - 1.30862i) q^{84} +(-0.605261 - 0.439748i) q^{85} +(7.76207 - 3.45589i) q^{86} +(0.351331 + 3.34269i) q^{87} +(-1.84356 - 5.67388i) q^{88} +(-13.2298 + 9.61203i) q^{89} +(1.56858 - 2.71686i) q^{90} +(-10.6873 + 4.75831i) q^{91} +(-8.33082 + 3.70912i) q^{92} +(-0.346004 + 0.599296i) q^{93} +(-7.40439 + 5.37961i) q^{94} +(0.223078 + 0.686564i) q^{95} +(-0.0748040 - 0.711713i) q^{96} +(-4.39997 + 1.95899i) q^{97} +(-2.67230 - 1.94154i) q^{98} +(-4.58653 + 14.1159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	0.578959	−	0.420639i	0.334262	−	0.242856i	−0.407975	−	0.912993i	$-0.633765\pi$
$3$	0.578959	−	0.420639i	0.334262	−	0.242856i	0.742237	+	0.670137i	$0.233765\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	1.23343	−	0.262173i	0.551605	−	0.117247i	0.0763270	−	0.997083i	$-0.475681\pi$
$5$	1.23343	−	0.262173i	0.551605	−	0.117247i	0.475278	+	0.879835i	$0.342347\pi$
$6$	−0.699995	+	0.148788i	−0.285772	+	0.0607426i
$7$	0.200979	−	1.91219i	0.0759630	−	0.722739i	−0.888564	−	0.458753i	$-0.848296\pi$
$7$	0.200979	−	1.91219i	0.0759630	−	0.722739i	0.964527	−	0.263986i	$-0.0850372\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.768794	+	2.36610i	−0.256265	+	0.788701i
$10$	−1.23343	−	0.262173i	−0.390044	−	0.0829064i
$11$	5.96587			1.79878			0.899389	−	0.437149i	$-0.144012\pi$
$11$	5.96587			1.79878			0.899389	+	0.437149i	$0.144012\pi$
$12$	0.699995	+	0.148788i	0.202071	+	0.0429515i
$13$	−3.04224	−	5.26931i	−0.843765	−	1.46144i	−0.886689	−	0.462366i	$-0.847001\pi$
$13$	−3.04224	−	5.26931i	−0.843765	−	1.46144i	0.0429242	−	0.999078i	$-0.486333\pi$
$14$	−0.961361	+	1.66513i	−0.256934	+	0.445024i
$15$	0.603824	−	0.670615i	0.155907	−	0.173152i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	−0.396997	−	0.440910i	−0.0962859	−	0.106936i	0.693076	−	0.720865i	$-0.256255\pi$
$17$	−0.396997	−	0.440910i	−0.0962859	−	0.106936i	−0.789362	+	0.613928i	$0.789588\pi$
$18$	1.66471	−	1.84885i	0.392376	−	0.435777i
$19$	0.0598412	+	0.569351i	0.0137285	+	0.130618i	0.999239	−	0.0389938i	$-0.0124153\pi$
$19$	0.0598412	+	0.569351i	0.0137285	+	0.130618i	−0.985511	+	0.169612i	$0.945749\pi$
$20$	1.02016	+	0.741187i	0.228114	+	0.165734i
$21$	−0.687982	−	1.19162i	−0.150130	−	0.260033i
$22$	−5.45010	−	2.42654i	−1.16196	−	0.517340i
$23$	−2.81799	+	8.67289i	−0.587592	+	1.80842i	0.00100989	+	0.999999i	$0.499679\pi$
$23$	−2.81799	+	8.67289i	−0.587592	+	1.80842i	−0.588602	+	0.808423i	$0.700321\pi$
$24$	−0.578959	−	0.420639i	−0.118180	−	0.0858625i
$25$	−3.11512	+	1.38694i	−0.623024	+	0.277388i
$26$	0.636001	+	6.05115i	0.124730	+	1.18673i
$27$	1.21360	+	3.73509i	0.233558	+	0.718817i
$28$	1.55551	−	1.13015i	0.293965	−	0.213578i
$29$	−2.34835	+	4.06745i	−0.436077	+	0.755307i	−0.997383	−	0.0723011i	$-0.976966\pi$
$29$	−2.34835	+	4.06745i	−0.436077	+	0.755307i	0.561306	+	0.827608i	$0.310299\pi$
$30$	−0.824384	+	0.367040i	−0.150511	+	0.0670119i
$31$	−0.883386	+	0.393309i	−0.158661	+	0.0706403i	−0.484531	−	0.874774i	$-0.661010\pi$
$31$	−0.883386	+	0.393309i	−0.158661	+	0.0706403i	0.325870	+	0.945415i	$0.394343\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.45400	−	2.50948i	0.601264	−	0.436844i
$34$	0.183341	+	0.564264i	0.0314426	+	0.0967705i
$35$	−0.253431	−	2.41124i	−0.0428377	−	0.407573i
$36$	−2.27278	+	1.01191i	−0.378797	+	0.168651i
$37$	−3.43589	−	2.49632i	−0.564856	−	0.410392i	0.268377	−	0.963314i	$-0.413513\pi$
$37$	−3.43589	−	2.49632i	−0.564856	−	0.410392i	−0.833233	+	0.552922i	$0.813513\pi$
$38$	0.176908	−	0.544468i	0.0286983	−	0.0883243i
$39$	−3.97781	−	1.77103i	−0.636959	−	0.283592i
$40$	−0.630491	−	1.09204i	−0.0996894	−	0.172667i
$41$	−2.23434	−	1.62334i	−0.348946	−	0.253524i	0.399481	−	0.916742i	$-0.369190\pi$
$41$	−2.23434	−	1.62334i	−0.348946	−	0.253524i	−0.748427	+	0.663218i	$0.769190\pi$
$42$	0.143827	+	1.36843i	0.0221930	+	0.211153i
$43$	−5.68536	+	6.31423i	−0.867009	+	0.962912i	−0.999601	−	0.0282593i	$-0.991004\pi$
$43$	−5.68536	+	6.31423i	−0.867009	+	0.962912i	0.132591	+	0.991171i	$0.457670\pi$
$44$	3.99195	+	4.43351i	0.601809	+	0.668376i
$45$	−0.327923	+	3.11997i	−0.0488838	+	0.465098i
$46$	6.10195	−	6.77690i	0.899683	−	0.999199i
$47$	4.57617	−	7.92615i	0.667503	−	1.15615i	−0.311098	−	0.950378i	$-0.600697\pi$
$47$	4.57617	−	7.92615i	0.667503	−	1.15615i	0.978600	−	0.205770i	$-0.0659700\pi$
$48$	0.357817	+	0.619756i	0.0516464	+	0.0894541i
$49$	3.23096	+	0.686762i	0.461566	+	0.0981088i
$50$	3.40992			0.482236
$51$	−0.415309	−	0.0882766i	−0.0581548	−	0.0123612i
$52$	1.88021	−	5.78668i	0.260738	−	0.802468i
$53$	0.833469	+	2.56515i	0.114486	+	0.352351i	0.991839	−	0.127493i	$-0.0406931\pi$
$53$	0.833469	+	2.56515i	0.114486	+	0.352351i	−0.877354	+	0.479844i	$0.840693\pi$
$54$	0.410515	−	3.90579i	0.0558640	−	0.531510i
$55$	7.35847	−	1.56409i	0.992216	−	0.210902i
$56$	−1.88071	+	0.399756i	−0.251320	+	0.0534197i
$57$	0.274137	+	0.304460i	0.0363103	+	0.0403267i
$58$	3.79970	−	2.76065i	0.498925	−	0.362491i
$59$	−1.97074	−	0.877428i	−0.256568	−	0.114231i	0.274423	−	0.961609i	$-0.411513\pi$
$59$	−1.97074	−	0.877428i	−0.256568	−	0.114231i	−0.530990	+	0.847378i	$0.678180\pi$
$60$	0.902401			0.116499
$61$	−1.54265	−	7.65639i	−0.197516	−	0.980300i
$61$	−1.54265	−	7.65639i	−0.197516	−	0.980300i
$62$	0.966986			0.122807
$63$	4.36993	+	1.94562i	0.550559	+	0.245125i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.13385	−	5.70172i	−0.636776	−	0.707211i
$66$	−4.17608	+	0.887653i	−0.514040	+	0.109263i
$67$	7.73845	−	1.64486i	0.945402	−	0.200951i	0.290679	−	0.956821i	$-0.406119\pi$
$67$	7.73845	−	1.64486i	0.945402	−	0.200951i	0.654723	+	0.755869i	$0.272785\pi$
$68$	0.0620170	−	0.590052i	0.00752067	−	0.0715543i
$69$	2.01665	+	6.20661i	0.242776	+	0.747188i
$70$	−0.749217	+	2.30585i	−0.0895486	+	0.275602i
$71$	2.11029	+	0.448556i	0.250446	+	0.0532338i	0.331424	−	0.943482i	$-0.392471\pi$
$71$	2.11029	+	0.448556i	0.250446	+	0.0532338i	−0.0809781	+	0.996716i	$0.525804\pi$
$72$	2.48787			0.293198
$73$	−5.07396	−	1.07850i	−0.593862	−	0.126229i	−0.0988304	−	0.995104i	$-0.531510\pi$
$73$	−5.07396	−	1.07850i	−0.593862	−	0.126229i	−0.495031	+	0.868875i	$0.664843\pi$
$74$	2.12349	+	3.67800i	0.246851	+	0.427559i
$75$	−1.22013	+	2.11332i	−0.140888	+	0.244025i
$76$	−0.383069	+	0.425441i	−0.0439410	+	0.0488014i
$77$	1.19902	−	11.4079i	0.136641	−	1.30005i
$78$	2.91356	+	3.23584i	0.329896	+	0.366387i
$79$	4.24314	−	4.71248i	0.477390	−	0.530196i	−0.455558	−	0.890206i	$-0.650560\pi$
$79$	4.24314	−	4.71248i	0.477390	−	0.530196i	0.932948	+	0.360010i	$0.117227\pi$
$80$	0.131809	+	1.25407i	0.0147366	+	0.140210i
$81$	−3.76444	−	2.73502i	−0.418271	−	0.303892i
$82$	1.38090	+	2.39179i	0.152495	+	0.264129i
$83$	7.99970	+	3.56170i	0.878082	+	0.390947i	0.795727	−	0.605656i	$-0.207089\pi$
$83$	7.99970	+	3.56170i	0.878082	+	0.390947i	0.0823550	+	0.996603i	$0.473756\pi$
$84$	0.425196	−	1.30862i	0.0463927	−	0.142782i
$85$	−0.605261	−	0.439748i	−0.0656498	−	0.0476974i
$86$	7.76207	−	3.45589i	0.837005	−	0.372659i
$87$	0.351331	+	3.34269i	0.0376667	+	0.358375i
$88$	−1.84356	−	5.67388i	−0.196524	−	0.604838i
$89$	−13.2298	+	9.61203i	−1.40236	+	1.01887i	−0.407980	+	0.912991i	$0.633767\pi$
$89$	−13.2298	+	9.61203i	−1.40236	+	1.01887i	−0.994379	+	0.105883i	$0.966233\pi$
$90$	1.56858	−	2.71686i	0.165343	−	0.286382i
$91$	−10.6873	+	4.75831i	−1.12034	+	0.498807i
$92$	−8.33082	+	3.70912i	−0.868548	+	0.386702i
$93$	−0.346004	+	0.599296i	−0.0358789	+	0.0621441i
$94$	−7.40439	+	5.37961i	−0.763705	+	0.554864i
$95$	0.223078	+	0.686564i	0.0228873	+	0.0704400i
$96$	−0.0748040	−	0.711713i	−0.00763465	−	0.0726389i
$97$	−4.39997	+	1.95899i	−0.446750	+	0.198906i	−0.617765	−	0.786363i	$-0.711962\pi$
$97$	−4.39997	+	1.95899i	−0.446750	+	0.198906i	0.171016	+	0.985268i	$0.445295\pi$
$98$	−2.67230	−	1.94154i	−0.269943	−	0.196125i
$99$	−4.58653	+	14.1159i	−0.460963	+	1.41870i
$100$	−3.11512	−	1.38694i	−0.311512	−	0.138694i
$101$	5.51780	+	9.55712i	0.549042	+	0.950969i	0.998341	+	0.0575868i	$0.0183406\pi$
$101$	5.51780	+	9.55712i	0.549042	+	0.950969i	−0.449299	+	0.893382i	$0.648326\pi$
$102$	0.343498	+	0.249566i	0.0340114	+	0.0247107i
$103$	−0.968329	−	9.21304i	−0.0954123	−	0.907787i	−0.932610	−	0.360887i	$-0.882474\pi$
$103$	−0.968329	−	9.21304i	−0.0954123	−	0.907787i	0.837197	−	0.546901i	$-0.184193\pi$
$104$	−4.07131	+	4.52165i	−0.399225	+	0.443384i
$105$	−1.16099	−	1.28940i	−0.113301	−	0.125833i
$106$	0.281930	−	2.68239i	0.0273835	−	0.260537i
$107$	3.75096	−	4.16586i	0.362619	−	0.402729i	−0.534034	−	0.845463i	$-0.679325\pi$
$107$	3.75096	−	4.16586i	0.362619	−	0.402729i	0.896653	+	0.442734i	$0.145991\pi$
$108$	−1.96365	+	3.40114i	−0.188952	+	0.327275i
$109$	0.378576	+	0.655712i	0.0362610	+	0.0628059i	0.883586	−	0.468268i	$-0.155122\pi$
$109$	0.378576	+	0.655712i	0.0362610	+	0.0628059i	−0.847325	+	0.531074i	$0.821789\pi$
$110$	−7.35847	−	1.56409i	−0.701603	−	0.149130i
$111$	−3.03929			−0.288476
$112$	1.88071	+	0.399756i	0.177710	+	0.0377734i
$113$	5.85337	−	18.0148i	0.550639	−	1.69469i	−0.156551	−	0.987670i	$-0.550038\pi$
$113$	5.85337	−	18.0148i	0.550639	−	1.69469i	0.707190	−	0.707023i	$-0.249962\pi$
$114$	−0.126601	−	0.389639i	−0.0118573	−	0.0364930i
$115$	−1.20199	+	11.4362i	−0.112086	+	1.06643i
$116$	−4.59406	+	0.976497i	−0.426547	+	0.0906655i
$117$	14.8066	−	3.14724i	1.36887	−	0.290962i
$118$	1.44347	+	1.60314i	0.132883	+	0.147581i
$119$	−0.922890	+	0.670519i	−0.0846012	+	0.0614664i
$120$	−0.824384	−	0.367040i	−0.0752556	−	0.0335060i
$121$	24.5916			2.23560
$122$	−1.70486	+	7.62191i	−0.154350	+	0.690055i
$123$	−1.97644			−0.178209
$124$	−0.883386	−	0.393309i	−0.0793304	−	0.0353202i
$125$	−8.57944	+	6.23333i	−0.767368	+	0.557526i
$126$	−3.20077	−	3.55482i	−0.285147	−	0.316688i
$127$	−12.4363	+	2.64342i	−1.10354	+	0.234565i	−0.723446	−	0.690381i	$-0.757443\pi$
$127$	−12.4363	+	2.64342i	−1.10354	+	0.234565i	−0.380097	+	0.924947i	$0.624109\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	−0.635583	+	6.04717i	−0.0559599	+	0.532423i
$130$	2.37091	+	7.29690i	0.207942	+	0.639981i
$131$	1.58716	−	4.88476i	0.138670	−	0.426784i	−0.857472	−	0.514530i	$-0.827966\pi$
$131$	1.58716	−	4.88476i	0.138670	−	0.426784i	0.996143	+	0.0877463i	$0.0279665\pi$
$132$	4.17608	+	0.887653i	0.363481	+	0.0772603i
$133$	1.10073			0.0954457
$134$	−7.73845	−	1.64486i	−0.668500	−	0.142094i
$135$	2.47613	+	4.28878i	0.213111	+	0.369120i
$136$	−0.296651	+	0.513815i	−0.0254376	+	0.0440593i
$137$	−1.48234	+	1.64631i	−0.126645	+	0.140654i	−0.803132	−	0.595801i	$-0.796835\pi$
$137$	−1.48234	+	1.64631i	−0.126645	+	0.140654i	0.676487	+	0.736454i	$0.263501\pi$
$138$	0.682154	−	6.49026i	0.0580688	−	0.552488i
$139$	8.11863	+	9.01666i	0.688613	+	0.764783i	0.981520	−	0.191358i	$-0.0612892\pi$
$139$	8.11863	+	9.01666i	0.688613	+	0.764783i	−0.292907	+	0.956141i	$0.594623\pi$
$140$	1.62232	−	1.80177i	0.137111	−	0.152277i
$141$	−0.684631	−	6.51383i	−0.0576564	−	0.548564i
$142$	−1.74540	−	1.26811i	−0.146471	−	0.106417i
$143$	−18.1496	−	31.4360i	−1.51775	−	2.62881i
$144$	−2.27278	−	1.01191i	−0.189398	−	0.0843256i
$145$	−1.83014	+	5.63258i	−0.151985	+	0.467760i
$146$	4.19662	+	3.04903i	0.347315	+	0.252339i
$147$	2.15947	−	0.961460i	0.178110	−	0.0792998i
$148$	−0.443931	−	4.22372i	−0.0364909	−	0.347188i
$149$	−2.33767	−	7.19460i	−0.191509	−	0.589404i	−1.00000		0.000895197i	$-0.999715\pi$
$149$	−2.33767	−	7.19460i	−0.191509	−	0.589404i	0.808490	−	0.588509i	$-0.200285\pi$
$150$	1.97421	−	1.43435i	0.161193	−	0.117114i
$151$	8.62315	−	14.9357i	0.701742	−	1.21545i	−0.266112	−	0.963942i	$-0.585739\pi$
$151$	8.62315	−	14.9357i	0.701742	−	1.21545i	0.967854	−	0.251511i	$-0.0809274\pi$
$152$	0.522993	−	0.232851i	0.0424203	−	0.0188867i
$153$	1.34845	−	0.600367i	0.109015	−	0.0485368i
$154$	−5.73536	+	9.93393i	−0.462168	+	0.800499i
$155$	−0.986477	+	0.716717i	−0.0792357	+	0.0575681i
$156$	−1.34554	−	4.14114i	−0.107729	−	0.331557i
$157$	1.33025	+	12.6565i	0.106166	+	1.01010i	0.909820	+	0.415002i	$0.136219\pi$
$157$	1.33025	+	12.6565i	0.106166	+	1.01010i	−0.803655	+	0.595096i	$0.797114\pi$
$158$	−5.79304	+	2.57923i	−0.460870	+	0.205192i
$159$	1.56155	+	1.13453i	0.123839	+	0.0899742i
$160$	0.389665	−	1.19927i	0.0308057	−	0.0948103i
$161$	16.0178	+	7.13160i	1.26238	+	0.562049i
$162$	2.32655	+	4.02970i	0.182791	+	0.316603i
$163$	4.65709	+	3.38358i	0.364772	+	0.265022i	0.755040	−	0.655679i	$-0.227618\pi$
$163$	4.65709	+	3.38358i	0.364772	+	0.265022i	−0.390268	+	0.920701i	$0.627618\pi$
$164$	−0.288687	−	2.74667i	−0.0225426	−	0.214479i
$165$	3.60234	−	4.00080i	0.280442	−	0.311462i
$166$	−5.85942	−	6.50755i	−0.454779	−	0.505084i
$167$	1.73571	−	16.5142i	0.134313	−	1.27791i	−0.694954	−	0.719054i	$-0.744575\pi$
$167$	1.73571	−	16.5142i	0.134313	−	1.27791i	0.829267	−	0.558852i	$-0.188758\pi$
$168$	−0.920699	+	1.02254i	−0.0710335	+	0.0788907i
$169$	−12.0104	+	20.8027i	−0.923879	+	1.60021i
$170$	0.374072	+	0.647912i	0.0286900	+	0.0496926i
$171$	−1.39315	−	0.296123i	−0.106537	−	0.0226451i
$172$	−8.49664			−0.647863
$173$	19.8412	+	4.21739i	1.50850	+	0.320642i	0.886631	−	0.462478i	$-0.153040\pi$
$173$	19.8412	+	4.21739i	1.50850	+	0.320642i	0.621871	+	0.783120i	$0.286373\pi$
$174$	1.03864	−	3.19660i	0.0787390	−	0.242334i
$175$	2.02602	+	6.23544i	0.153153	+	0.471355i
$176$	−0.623604	+	5.93319i	−0.0470059	+	0.447231i
$177$	−1.51006	+	0.320972i	−0.113503	+	0.0241257i
$178$	15.9956	−	3.39997i	1.19892	−	0.254839i
$179$	2.76620	+	3.07218i	0.206755	+	0.229625i	0.837600	−	0.546284i	$-0.183958\pi$
$179$	2.76620	+	3.07218i	0.206755	+	0.229625i	−0.630845	+	0.775909i	$0.717291\pi$
$180$	−2.53802	+	1.84398i	−0.189173	+	0.137442i
$181$	−20.3938	−	9.07989i	−1.51586	−	0.674903i	−0.530857	−	0.847461i	$-0.678130\pi$
$181$	−20.3938	−	9.07989i	−1.51586	−	0.674903i	−0.984999	+	0.172558i	$0.944797\pi$
$182$	11.6988			0.867169
$183$	−4.11370	−	3.78384i	−0.304093	−	0.279709i
$184$	9.11922			0.672277
$185$	−4.89238	−	2.17823i	−0.359695	−	0.160147i
$186$	0.559846	−	0.406752i	0.0410499	−	0.0298245i
$187$	−2.36843	−	2.63041i	−0.173197	−	0.192355i
$188$	8.95233	−	1.90288i	0.652916	−	0.138782i
$189$	7.38610	−	1.56996i	0.537259	−	0.114198i
$190$	0.0754587	−	0.717942i	0.00547435	−	0.0520850i
$191$	−3.43644	−	10.5763i	−0.248652	−	0.765273i	−0.995014	−	0.0997330i	$-0.968201\pi$
$191$	−3.43644	−	10.5763i	−0.248652	−	0.765273i	0.746362	−	0.665540i	$-0.231799\pi$
$192$	−0.221143	+	0.680608i	−0.0159596	+	0.0491186i
$193$	16.1678	+	3.43657i	1.16378	+	0.247370i	0.749012	−	0.662556i	$-0.230529\pi$
$193$	16.1678	+	3.43657i	1.16378	+	0.247370i	0.414770	+	0.909926i	$0.363862\pi$
$194$	4.81637			0.345795
$195$	−5.37065	−	1.14157i	−0.384600	−	0.0817494i
$196$	1.65157	+	2.86061i	0.117969	+	0.204329i
$197$	−6.13855	+	10.6323i	−0.437354	+	0.757519i	−0.997484	−	0.0708852i	$-0.977418\pi$
$197$	−6.13855	+	10.6323i	−0.437354	+	0.757519i	0.560131	+	0.828404i	$0.310751\pi$
$198$	9.93145	−	11.0300i	0.705797	−	0.783867i
$199$	0.152012	−	1.44630i	0.0107758	−	0.102525i	−0.987812	−	0.155652i	$-0.950252\pi$
$199$	0.152012	−	1.44630i	0.0107758	−	0.102525i	0.998588	+	0.0531269i	$0.0169188\pi$
$200$	2.28168	+	2.53407i	0.161339	+	0.179186i
$201$	3.78836	−	4.20740i	0.267210	−	0.296767i
$202$	−1.15353	−	10.9752i	−0.0811624	−	0.772209i
$203$	7.30577	+	5.30795i	0.512765	+	0.372545i
$204$	−0.212293	−	0.367703i	−0.0148635	−	0.0257444i
$205$	−3.18150	−	1.41649i	−0.222205	−	0.0989322i
$206$	−2.86267	+	8.81038i	−0.199451	+	0.613848i
$207$	−18.3545	−	13.3353i	−1.27573	−	0.926869i
$208$	5.55845	−	2.47478i	0.385409	−	0.171595i
$209$	0.357005	+	3.39668i	0.0246946	+	0.234953i
$210$	0.536165	+	1.65015i	0.0369989	+	0.113871i
$211$	−7.99679	+	5.81001i	−0.550521	+	0.399977i	−0.827978	−	0.560761i	$-0.810509\pi$
$211$	−7.99679	+	5.81001i	−0.550521	+	0.399977i	0.277456	+	0.960738i	$0.410509\pi$
$212$	−1.34858	+	2.33581i	−0.0926210	+	0.160424i
$213$	1.41045	−	0.627974i	0.0966427	−	0.0430281i
$214$	−5.12108	+	2.28005i	−0.350070	+	0.155861i
$215$	−5.35706	+	9.27869i	−0.365348	+	0.632802i
$216$	3.17725	−	2.30841i	0.216185	−	0.157067i
$217$	0.574538	+	1.76825i	0.0390022	+	0.120036i
$218$	−0.0791439	−	0.753004i	−0.00536030	−	0.0509999i
$219$	−3.39128	+	1.50989i	−0.229161	+	0.102029i
$220$	6.08612	+	4.42183i	0.410326	+	0.298120i
$221$	−1.11553	+	3.43325i	−0.0750388	+	0.230946i
$222$	2.77653	+	1.23619i	0.186348	+	0.0829676i
$223$	5.10242	+	8.83765i	0.341683	+	0.591813i	0.984745	−	0.174001i	$-0.0556696\pi$
$223$	5.10242	+	8.83765i	0.341683	+	0.591813i	−0.643062	+	0.765814i	$0.722336\pi$
$224$	−1.55551	−	1.13015i	−0.103932	−	0.0755111i
$225$	−0.886761	−	8.43697i	−0.0591174	−	0.562465i
$226$	−12.6746	+	14.0766i	−0.843103	+	0.936361i
$227$	4.95641	+	5.50465i	0.328969	+	0.365357i	0.884826	−	0.465921i	$-0.154277\pi$
$227$	4.95641	+	5.50465i	0.328969	+	0.365357i	−0.555858	+	0.831277i	$0.687610\pi$
$228$	−0.0428243	+	0.407446i	−0.00283611	+	0.0269838i
$229$	19.1831	−	21.3050i	1.26765	−	1.40787i	0.395627	−	0.918411i	$-0.370527\pi$
$229$	19.1831	−	21.3050i	1.26765	−	1.40787i	0.872026	−	0.489459i	$-0.162806\pi$
$230$	5.74959	−	9.95858i	0.379116	−	0.656649i
$231$	−4.10441	−	7.10905i	−0.270050	−	0.467741i
$232$	4.59406	+	0.976497i	0.301615	+	0.0641102i
$233$	−14.6786			−0.961630			−0.480815	−	0.876822i	$-0.659659\pi$
$233$	−14.6786			−0.961630			−0.480815	+	0.876822i	$0.659659\pi$
$234$	−14.8066	−	3.14724i	−0.967937	−	0.205741i
$235$	3.56634	−	10.9761i	0.232643	−	0.716001i
$236$	−0.666623	−	2.05166i	−0.0433935	−	0.133551i
$237$	0.474353	−	4.51316i	0.0308125	−	0.293162i
$238$	1.11583	−	0.237176i	0.0723283	−	0.0153739i
$239$	−13.4957	+	2.86860i	−0.872965	+	0.185554i	−0.622546	−	0.782583i	$-0.713902\pi$
$239$	−13.4957	+	2.86860i	−0.872965	+	0.185554i	−0.250419	+	0.968138i	$0.580568\pi$
$240$	0.603824	+	0.670615i	0.0389767	+	0.0432880i
$241$	12.1891	−	8.85593i	0.785171	−	0.570460i	−0.121355	−	0.992609i	$-0.538724\pi$
$241$	12.1891	−	8.85593i	0.785171	−	0.570460i	0.906527	+	0.422149i	$0.138724\pi$
$242$	−22.4656	−	10.0023i	−1.44414	−	0.642974i
$243$	−15.1118			−0.969423
$244$	4.65757	−	6.26953i	0.298171	−	0.401366i
$245$	4.16521			0.266105
$246$	1.80556	+	0.803889i	0.115119	+	0.0512541i
$247$	2.81804	−	2.04742i	0.179307	−	0.130274i
$248$	0.647040	+	0.718611i	0.0410871	+	0.0456318i
$249$	6.12969	−	1.30291i	0.388453	−	0.0825683i
$250$	10.3730	−	2.20485i	0.656048	−	0.139447i
$251$	0.673956	−	6.41226i	0.0425397	−	0.404738i	−0.952445	−	0.304711i	$-0.901440\pi$
$251$	0.673956	−	6.41226i	0.0425397	−	0.404738i	0.994985	−	0.100028i	$-0.0318931\pi$
$252$	1.47818	+	4.54936i	0.0931164	+	0.286583i
$253$	−16.8118	+	51.7414i	−1.05695	+	3.25295i
$254$	12.4363	+	2.64342i	0.780322	+	0.165863i
$255$	−0.535397			−0.0335278
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	11.8032	+	20.4438i	0.736266	+	1.27525i	0.954166	+	0.299279i	$0.0967462\pi$
$257$	11.8032	+	20.4438i	0.736266	+	1.27525i	−0.217899	+	0.975971i	$0.569920\pi$
$258$	3.04024	−	5.26585i	0.189277	−	0.327837i
$259$	−5.46397	+	6.06836i	−0.339515	+	0.377069i
$260$	0.801986	−	7.63039i	0.0497371	−	0.473217i
$261$	−7.81863	−	8.68346i	−0.483961	−	0.537493i
$262$	−3.43675	+	3.81690i	−0.212323	+	0.235809i
$263$	0.401330	+	3.81840i	0.0247471	+	0.235453i	0.999903	+	0.0139329i	$0.00443513\pi$
$263$	0.401330	+	3.81840i	0.0247471	+	0.235453i	−0.975156	+	0.221520i	$0.928898\pi$
$264$	−3.45400	−	2.50948i	−0.212579	−	0.154448i
$265$	1.70054	+	2.94542i	0.104463	+	0.180936i
$266$	−1.00557	−	0.447709i	−0.0616554	−	0.0274508i
$267$	−3.61634	+	11.1300i	−0.221316	+	0.681142i
$268$	6.40040	+	4.65016i	0.390967	+	0.284054i
$269$	−12.4306	+	5.53444i	−0.757904	+	0.337441i	−0.749044	−	0.662520i	$-0.769487\pi$
$269$	−12.4306	+	5.53444i	−0.757904	+	0.337441i	−0.00885999	+	0.999961i	$0.502820\pi$
$270$	−0.517652	−	4.92513i	−0.0315033	−	0.299734i
$271$	2.03092	+	6.25054i	0.123370	+	0.379693i	0.993601	−	0.112951i	$-0.0360303\pi$
$271$	2.03092	+	6.25054i	0.123370	+	0.379693i	−0.870231	+	0.492644i	$0.836030\pi$
$272$	0.479992	−	0.348734i	0.0291038	−	0.0211451i
$273$	−4.18601	+	7.25038i	−0.253349	+	0.438813i
$274$	2.02380	−	0.901055i	0.122262	−	0.0544347i
$275$	−18.5844	+	8.27431i	−1.12068	+	0.498960i
$276$	−3.26301	+	5.65169i	−0.196410	+	0.340192i
$277$	9.03788	−	6.56640i	0.543034	−	0.394537i	−0.282177	−	0.959362i	$-0.591057\pi$
$277$	9.03788	−	6.56640i	0.543034	−	0.394537i	0.825210	+	0.564825i	$0.191057\pi$
$278$	−3.74934	−	11.5393i	−0.224870	−	0.692079i
$279$	−0.251468	−	2.39256i	−0.0150550	−	0.143239i
$280$	−2.21491	+	0.986140i	−0.132366	+	0.0589332i
$281$	−17.1432	−	12.4553i	−1.02268	−	0.743020i	−0.0558490	−	0.998439i	$-0.517787\pi$
$281$	−17.1432	−	12.4553i	−1.02268	−	0.743020i	−0.966830	+	0.255419i	$0.917787\pi$
$282$	−2.02397	+	6.22915i	−0.120526	+	0.370940i
$283$	−29.0811	−	12.9477i	−1.72869	−	0.769663i	−0.996025	−	0.0890746i	$-0.971609\pi$
$283$	−29.0811	−	12.9477i	−1.72869	−	0.769663i	−0.732666	−	0.680588i	$-0.761724\pi$
$284$	1.07872	+	1.86840i	0.0640102	+	0.110869i
$285$	0.417949	+	0.303657i	0.0247571	+	0.0179871i
$286$	3.79430	+	36.1004i	0.224362	+	2.13466i
$287$	−3.55320	+	3.94623i	−0.209739	+	0.232938i
$288$	1.66471	+	1.84885i	0.0980939	+	0.108944i
$289$	1.74019	−	16.5568i	0.102364	−	0.973929i
$290$	3.96289	−	4.40123i	0.232709	−	0.258449i
$291$	−1.72338	+	2.98498i	−0.101026	+	0.174982i
$292$	−2.59366	−	4.49234i	−0.151782	−	0.262895i
$293$	−17.2435	−	3.66521i	−1.00737	−	0.214124i	−0.325459	−	0.945556i	$-0.605519\pi$
$293$	−17.2435	−	3.66521i	−1.00737	−	0.214124i	−0.681914	+	0.731432i	$0.738852\pi$
$294$	−2.36384			−0.137862
$295$	−2.66080	−	0.565570i	−0.154918	−	0.0329287i
$296$	−1.31239	+	4.03913i	−0.0762812	+	0.234769i
$297$	7.24020	+	22.2830i	0.420119	+	1.29299i
$298$	−0.790742	+	7.52341i	−0.0458065	+	0.435819i
$299$	54.2732	−	11.5361i	3.13870	−	0.667151i
$300$	−2.38693	+	0.507357i	−0.137809	+	0.0292923i
$301$	10.9314	+	12.1405i	0.630073	+	0.699767i
$302$	−13.9526	+	10.1371i	−0.802879	+	0.583326i
$303$	7.21467	+	3.21218i	0.414472	+	0.184535i
$304$	−0.572487			−0.0328344
$305$	−3.91004	−	9.03915i	−0.223888	−	0.517580i
$306$	−1.47606			−0.0843807
$307$	−5.64869	−	2.51496i	−0.322388	−	0.143536i	0.239161	−	0.970980i	$-0.423128\pi$
$307$	−5.64869	−	2.51496i	−0.322388	−	0.143536i	−0.561549	+	0.827444i	$0.689794\pi$
$308$	9.28000	−	6.74232i	0.528777	−	0.384179i
$309$	−4.43598	−	4.92666i	−0.252354	−	0.280268i
$310$	1.19271	−	0.253518i	0.0677412	−	0.0143988i
$311$	20.2043	−	4.29455i	1.14568	−	0.243522i	0.404312	−	0.914621i	$-0.367511\pi$
$311$	20.2043	−	4.29455i	1.14568	−	0.243522i	0.741367	+	0.671100i	$0.234178\pi$
$312$	−0.455143	+	4.33040i	−0.0257674	+	0.245161i
$313$	−7.09412	−	21.8335i	−0.400984	−	1.23410i	−0.924203	−	0.381902i	$-0.875269\pi$
$313$	−7.09412	−	21.8335i	−0.400984	−	1.23410i	0.523219	−	0.852198i	$-0.324731\pi$
$314$	3.93261	−	12.1033i	0.221930	−	0.683031i
$315$	5.90007	+	1.25410i	0.332431	+	0.0706605i
$316$	6.34127			0.356724
$317$	1.98485	+	0.421892i	0.111480	+	0.0236958i	0.263314	−	0.964710i	$-0.415185\pi$
$317$	1.98485	+	0.421892i	0.111480	+	0.0236958i	−0.151834	+	0.988406i	$0.548518\pi$
$318$	−0.965090	−	1.67158i	−0.0541195	−	0.0937378i
$319$	−14.0099	+	24.2659i	−0.784406	+	1.35863i
$320$	−0.843762	+	0.937093i	−0.0471677	+	0.0523851i
$321$	0.419330	−	3.98966i	0.0234047	−	0.222681i
$322$	−11.7323	−	13.0301i	−0.653818	−	0.726138i
$323$	0.227276	−	0.252415i	0.0126460	−	0.0140448i
$324$	−0.486382	−	4.62761i	−0.0270212	−	0.257090i
$325$	16.7852	+	12.1951i	0.931073	+	0.676464i
$326$	−2.87824	−	4.98526i	−0.159411	−	0.276108i
$327$	0.494998	+	0.220387i	0.0273734	+	0.0121874i
$328$	−0.853443	+	2.62663i	−0.0471235	+	0.145031i
$329$	−14.2366	−	10.3435i	−0.784888	−	0.570255i
$330$	−4.91817	+	2.18971i	−0.270736	+	0.120540i
$331$	2.63541	+	25.0742i	0.144855	+	1.37820i	0.789513	+	0.613733i	$0.210333\pi$
$331$	2.63541	+	25.0742i	0.144855	+	1.37820i	−0.644658	+	0.764471i	$0.723000\pi$
$332$	2.70599	+	8.32818i	0.148510	+	0.457068i
$333$	8.54804	−	6.21051i	0.468430	−	0.340334i
$334$	−8.30257	+	14.3805i	−0.454297	+	0.786865i
$335$	9.11358	−	4.05763i	0.497928	−	0.221692i
$336$	1.25700	−	0.559655i	0.0685752	−	0.0305317i
$337$	11.4039	−	19.7521i	0.621209	−	1.07597i	−0.368052	−	0.929805i	$-0.619975\pi$
$337$	11.4039	−	19.7521i	0.621209	−	1.07597i	0.989261	−	0.146161i	$-0.0466916\pi$
$338$	19.4333	−	14.1191i	1.05703	−	0.767978i
$339$	−4.18887	−	12.8920i	−0.227508	−	0.700198i
$340$	−0.0782024	−	0.744046i	−0.00424112	−	0.0403515i
$341$	−5.27017	+	2.34643i	−0.285396	+	0.127066i
$342$	1.15226	+	0.837167i	0.0623071	+	0.0452688i
$343$	6.12165	−	18.8405i	0.330538	−	1.01729i
$344$	7.76207	+	3.45589i	0.418503	+	0.186329i
$345$	4.11459	+	7.12669i	0.221522	+	0.383688i
$346$	−16.4105	−	11.9229i	−0.882235	−	0.640981i
$347$	2.98695	+	28.4189i	0.160348	+	1.52561i	0.718300	+	0.695733i	$0.244920\pi$
$347$	2.98695	+	28.4189i	0.160348	+	1.52561i	−0.557953	+	0.829873i	$0.688413\pi$
$348$	−2.24902	+	2.49779i	−0.120560	+	0.133896i
$349$	−5.40789	−	6.00607i	−0.289478	−	0.321498i	0.580812	−	0.814038i	$-0.302735\pi$
$349$	−5.40789	−	6.00607i	−0.289478	−	0.321498i	−0.870290	+	0.492540i	$0.836068\pi$
$350$	0.685323	−	6.52042i	0.0366321	−	0.348531i
$351$	15.9893	−	17.7579i	0.853443	−	0.947845i
$352$	2.98294	−	5.16660i	0.158991	−	0.275381i
$353$	−5.32264	−	9.21909i	−0.283296	−	0.490683i	0.688899	−	0.724858i	$-0.258094\pi$
$353$	−5.32264	−	9.21909i	−0.283296	−	0.490683i	−0.972194	+	0.234175i	$0.924761\pi$
$354$	1.51006	+	0.320972i	0.0802585	+	0.0170595i
$355$	2.72049			0.144389
$356$	−15.9956	−	3.39997i	−0.847766	−	0.180198i
$357$	−0.252270	+	0.776407i	−0.0133515	+	0.0410918i
$358$	−1.27748	−	3.93169i	−0.0675170	−	0.207796i
$359$	1.87147	−	17.8059i	0.0987724	−	0.939757i	−0.827134	−	0.562004i	$-0.810030\pi$
$359$	1.87147	−	17.8059i	0.0987724	−	0.939757i	0.925907	−	0.377752i	$-0.123303\pi$
$360$	3.06861	−	0.652252i	0.161730	−	0.0343767i
$361$	18.2642	−	3.88218i	0.961275	−	0.204325i
$362$	14.9375	+	16.5898i	0.785098	+	0.871940i
$363$	14.2376	−	10.3442i	0.747278	−	0.542929i
$364$	−10.6873	−	4.75831i	−0.560169	−	0.249403i
$365$	−6.54111			−0.342377
$366$	2.21903	+	5.12990i	0.115990	+	0.268144i
$367$	1.40018			0.0730890			0.0365445	−	0.999332i	$-0.488365\pi$
$367$	1.40018			0.0730890			0.0365445	+	0.999332i	$0.488365\pi$
$368$	−8.33082	−	3.70912i	−0.434274	−	0.193351i
$369$	5.55875	−	4.03867i	0.289377	−	0.210245i
$370$	3.58345	+	3.97982i	0.186295	+	0.206901i
$371$	5.07257	−	1.07821i	0.263355	−	0.0559778i
$372$	−0.676885	+	0.143876i	−0.0350949	+	0.00745964i
$373$	−0.524345	+	4.98881i	−0.0271495	+	0.258311i	0.972525	+	0.232799i	$0.0747883\pi$
$373$	−0.524345	+	4.98881i	−0.0271495	+	0.258311i	−0.999675	+	0.0255120i	$0.991878\pi$
$374$	1.09379	+	3.36633i	0.0565584	+	0.174069i
$375$	−2.34517	+	7.21768i	−0.121104	+	0.372720i
$376$	−8.95233	−	1.90288i	−0.461681	−	0.0981334i
$377$	28.5769			1.47179
$378$	−7.38610	−	1.56996i	−0.379900	−	0.0807502i
$379$	−7.26457	−	12.5826i	−0.373156	−	0.646325i	0.616893	−	0.787047i	$-0.288391\pi$
$379$	−7.26457	−	12.5826i	−0.373156	−	0.646325i	−0.990049	+	0.140722i	$0.955058\pi$
$380$	−0.360948	+	0.625181i	−0.0185162	+	0.0320711i
$381$	−6.08818	+	6.76161i	−0.311907	+	0.346408i
$382$	−1.16242	+	11.0596i	−0.0594744	+	0.565861i
$383$	19.6246	+	21.7953i	1.00277	+	1.11369i	0.993512	+	0.113730i	$0.0362799\pi$
$383$	19.6246	+	21.7953i	1.00277	+	1.11369i	0.00925669	+	0.999957i	$0.497053\pi$
$384$	0.478852	−	0.531819i	0.0244363	−	0.0271393i
$385$	−1.51194	−	14.3851i	−0.0770555	−	0.733134i
$386$	−13.3722	−	9.71549i	−0.680628	−	0.494505i
$387$	−10.5693	−	18.3065i	−0.537266	−	0.930572i
$388$	−4.39997	−	1.95899i	−0.223375	−	0.0994529i
$389$	−2.17488	+	6.69359i	−0.110271	+	0.339378i	−0.990931	−	0.134369i	$-0.957099\pi$
$389$	−2.17488	+	6.69359i	−0.110271	+	0.339378i	0.880661	+	0.473748i	$0.157099\pi$
$390$	4.44202	+	3.22732i	0.224930	+	0.163421i
$391$	4.94269	−	2.20063i	0.249963	−	0.111291i
$392$	−0.345272	−	3.28505i	−0.0174389	−	0.165920i
$393$	−1.13582	−	3.49570i	−0.0572946	−	0.176335i
$394$	9.93239	−	7.21630i	0.500386	−	0.363552i
$395$	3.99812	−	6.92494i	0.201167	−	0.348432i
$396$	−13.5591	+	6.03691i	−0.681372	+	0.303366i
$397$	17.1491	−	7.63529i	0.860690	−	0.383204i	0.0715649	−	0.997436i	$-0.477201\pi$
$397$	17.1491	−	7.63529i	0.860690	−	0.383204i	0.789126	+	0.614232i	$0.210534\pi$
$398$	−0.727132	+	1.25943i	−0.0364478	+	0.0631295i
$399$	0.637280	−	0.463011i	0.0319039	−	0.0231795i
$400$	−1.05372	−	3.24303i	−0.0526862	−	0.162151i
$401$	0.645483	+	6.14136i	0.0322339	+	0.306685i	0.998746	+	0.0500639i	$0.0159425\pi$
$401$	0.645483	+	6.14136i	0.0322339	+	0.306685i	−0.966512	+	0.256621i	$0.917391\pi$
$402$	−5.17214	+	2.30278i	−0.257963	+	0.114852i
$403$	4.75994	+	3.45830i	0.237109	+	0.172270i
$404$	−3.41019	+	10.4955i	−0.169663	+	0.522170i
$405$	−5.36021	−	2.38652i	−0.266351	−	0.118587i
$406$	−4.51521	−	7.82058i	−0.224086	−	0.388129i
$407$	−20.4981	−	14.8927i	−1.01605	−	0.738205i
$408$	0.0443814	+	0.422261i	0.00219721	+	0.0209050i
$409$	1.98198	−	2.20121i	0.0980024	−	0.108843i	−0.692148	−	0.721755i	$-0.743336\pi$
$409$	1.98198	−	2.20121i	0.0980024	−	0.108843i	0.790151	+	0.612913i	$0.210002\pi$
$410$	2.33030	+	2.58806i	0.115085	+	0.127815i
$411$	−0.165715	+	1.57668i	−0.00817414	+	0.0777717i
$412$	6.19868	−	6.88433i	0.305387	−	0.339167i
$413$	−2.07388	+	3.59207i	−0.102049	+	0.176754i
$414$	11.3437	+	19.6479i	0.557513	+	0.965641i
$415$	10.8008	+	2.29579i	0.530192	+	0.112696i
$416$	−6.08448			−0.298316
$417$	8.49311	+	1.80527i	0.415909	+	0.0884043i
$418$	1.05541	−	3.24822i	0.0516219	−	0.158876i
$419$	9.30725	+	28.6448i	0.454689	+	1.39939i	0.871500	+	0.490395i	$0.163148\pi$
$419$	9.30725	+	28.6448i	0.454689	+	1.39939i	−0.416811	+	0.908993i	$0.636852\pi$
$420$	0.181364	−	1.72556i	0.00884964	−	0.0841987i
$421$	16.5014	−	3.50748i	0.804230	−	0.170944i	0.212584	−	0.977143i	$-0.431812\pi$
$421$	16.5014	−	3.50748i	0.804230	−	0.170944i	0.591645	+	0.806198i	$0.298479\pi$
$422$	9.66857	−	2.05512i	0.470659	−	0.100042i
$423$	15.2360	+	16.9213i	0.740799	+	0.822740i
$424$	2.18205	−	1.58535i	0.105970	−	0.0769915i
$425$	1.84821	+	0.822875i	0.0896513	+	0.0399153i
$426$	−1.54393			−0.0748038
$427$	−14.9505	+	1.41106i	−0.723505	+	0.0682858i
$428$	5.60572			0.270962
$429$	−23.7311	−	10.5658i	−1.14575	−	0.510120i
$430$	8.66790	−	6.29760i	0.418003	−	0.303697i
$431$	4.00835	+	4.45173i	0.193076	+	0.214432i	0.831908	−	0.554914i	$-0.187249\pi$
$431$	4.00835	+	4.45173i	0.193076	+	0.214432i	−0.638832	+	0.769346i	$0.720582\pi$
$432$	−3.84148	+	0.816532i	−0.184823	+	0.0392854i
$433$	−11.7702	+	2.50183i	−0.565639	+	0.120230i	−0.481851	−	0.876253i	$-0.660035\pi$
$433$	−11.7702	+	2.50183i	−0.565639	+	0.120230i	−0.0837883	+	0.996484i	$0.526702\pi$
$434$	0.194344	−	1.84906i	0.00932881	−	0.0887577i
$435$	1.30971	+	4.03086i	0.0627956	+	0.193265i
$436$	−0.233973	+	0.720094i	−0.0112053	+	0.0344862i
$437$	−5.10655	−	1.08543i	−0.244279	−	0.0519232i
$438$	3.71221			0.177376
$439$	−11.4845	−	2.44111i	−0.548126	−	0.116508i	−0.0744792	−	0.997223i	$-0.523729\pi$
$439$	−11.4845	−	2.44111i	−0.548126	−	0.116508i	−0.473647	+	0.880715i	$0.657063\pi$
$440$	−3.76143	−	6.51499i	−0.179319	−	0.310590i
$441$	−4.10889	+	7.11681i	−0.195662	+	0.338896i
$442$	2.41552	−	2.68270i	0.114894	−	0.127603i
$443$	1.71394	−	16.3070i	0.0814316	−	0.774770i	−0.875257	−	0.483658i	$-0.839308\pi$
$443$	1.71394	−	16.3070i	0.0814316	−	0.774770i	0.956689	−	0.291112i	$-0.0940253\pi$
$444$	−2.03368	−	2.25863i	−0.0965142	−	0.107190i
$445$	−13.7980	+	15.3242i	−0.654089	+	0.726439i
$446$	−1.06670	−	10.1489i	−0.0505095	−	0.480566i
$447$	−4.37974	−	3.18207i	−0.207155	−	0.150507i
$448$	0.961361	+	1.66513i	0.0454200	+	0.0786698i
$449$	−10.7457	−	4.78430i	−0.507121	−	0.225785i	0.137195	−	0.990544i	$-0.456191\pi$
$449$	−10.7457	−	4.78430i	−0.507121	−	0.225785i	−0.644316	+	0.764759i	$0.722858\pi$
$450$	−2.62153	+	8.06823i	−0.123580	+	0.380340i
$451$	−13.3298	−	9.68467i	−0.627676	−	0.456033i
$452$	17.3043	−	7.70437i	0.813926	−	0.362383i
$453$	−1.29009	−	12.2744i	−0.0606139	−	0.576702i
$454$	−2.28896	−	7.04471i	−0.107426	−	0.330624i
$455$	−11.9346	+	8.67096i	−0.559501	+	0.406501i
$456$	0.204845	−	0.354803i	0.00959276	−	0.0166152i
$457$	−24.2540	+	10.7986i	−1.13455	+	0.505135i	−0.886093	−	0.463507i	$-0.846591\pi$
$457$	−24.2540	+	10.7986i	−1.13455	+	0.505135i	−0.248459	+	0.968642i	$0.579924\pi$
$458$	−26.1901	+	11.6606i	−1.22378	+	0.544863i
$459$	1.16504	−	2.01791i	0.0543793	−	0.0941878i
$460$	−9.30303	+	6.75904i	−0.433756	+	0.315142i
$461$	10.1360	+	31.1953i	0.472079	+	1.45291i	0.849857	+	0.527014i	$0.176688\pi$
$461$	10.1360	+	31.1953i	0.472079	+	1.45291i	−0.377778	+	0.925896i	$0.623312\pi$
$462$	0.858055	+	8.16385i	0.0399204	+	0.379817i
$463$	−16.6295	+	7.40391i	−0.772837	+	0.344089i	−0.754977	−	0.655751i	$-0.772352\pi$
$463$	−16.6295	+	7.40391i	−0.772837	+	0.344089i	−0.0178599	+	0.999840i	$0.505685\pi$
$464$	−3.79970	−	2.76065i	−0.176397	−	0.128160i
$465$	−0.269651	+	0.829901i	−0.0125048	+	0.0384857i
$466$	13.4096	+	5.97034i	0.621188	+	0.276571i
$467$	3.88709	+	6.73264i	0.179873	+	0.311550i	0.941837	−	0.336070i	$-0.109098\pi$
$467$	3.88709	+	6.73264i	0.179873	+	0.311550i	−0.761964	+	0.647620i	$0.775765\pi$
$468$	12.2464	+	8.89753i	0.566090	+	0.411288i
$469$	−1.59001	−	15.1280i	−0.0734199	−	0.698544i
$470$	−7.72239	+	8.57658i	−0.356207	+	0.395608i
$471$	6.09397	+	6.76804i	0.280795	+	0.311855i
$472$	−0.225493	+	2.14542i	−0.0103791	+	0.0987510i
$473$	−33.9181	+	37.6699i	−1.55956	+	1.73206i
$474$	−2.26901	+	3.93004i	−0.104219	+	0.180513i
$475$	−0.976068	−	1.69060i	−0.0447851	−	0.0775701i
$476$	−1.11583	−	0.237176i	−0.0511439	−	0.0108710i
$477$	−6.71019			−0.307238
$478$	13.4957	+	2.86860i	0.617279	+	0.131207i
$479$	0.697047	−	2.14529i	0.0318489	−	0.0980208i	−0.933868	−	0.357617i	$-0.883589\pi$
$479$	0.697047	−	2.14529i	0.0318489	−	0.0980208i	0.965717	+	0.259596i	$0.0835894\pi$
$480$	−0.278857	−	0.858234i	−0.0127280	−	0.0391729i
$481$	−2.70109	+	25.6992i	−0.123159	+	1.17178i
$482$	−14.7374	+	3.13252i	−0.671268	+	0.142682i
$483$	12.2735	−	2.60881i	0.558464	−	0.118705i
$484$	16.4550	+	18.2752i	0.747956	+	0.830689i
$485$	−4.91345	+	3.56983i	−0.223108	+	0.162098i
$486$	13.8053	+	6.14653i	0.626223	+	0.278812i
$487$	−16.9497			−0.768066			−0.384033	−	0.923319i	$-0.625465\pi$
$487$	−16.9497			−0.768066			−0.384033	+	0.923319i	$0.625465\pi$
$488$	−6.80495	+	3.83310i	−0.308046	+	0.173516i
$489$	4.11953			0.186292
$490$	−3.80510	−	1.69414i	−0.171897	−	0.0765335i
$491$	21.3420	−	15.5059i	0.963152	−	0.699771i	0.00927136	−	0.999957i	$-0.497049\pi$
$491$	21.3420	−	15.5059i	0.963152	−	0.699771i	0.953881	+	0.300186i	$0.0970488\pi$
$492$	−1.32249	−	1.46878i	−0.0596226	−	0.0662176i
$493$	2.72567	−	0.579358i	0.122758	−	0.0260930i
$494$	−3.40717	+	0.724216i	−0.153296	+	0.0325840i
$495$	−1.95634	+	18.6134i	−0.0879311	+	0.836609i
$496$	−0.298815	−	0.919658i	−0.0134172	−	0.0412939i
$497$	1.28185	−	3.94513i	0.0574988	−	0.176963i
$498$	−6.12969	−	1.30291i	−0.274678	−	0.0583846i
$499$	−1.60972			−0.0720611			−0.0360306	−	0.999351i	$-0.511471\pi$
$499$	−1.60972			−0.0720611			−0.0360306	+	0.999351i	$0.511471\pi$
$500$	−10.3730	−	2.20485i	−0.463896	−	0.0986041i
$501$	−5.94160	−	10.2911i	−0.265451	−	0.459775i
$502$	−3.22379	+	5.58377i	−0.143885	+	0.249216i
$503$	−14.5325	+	16.1400i	−0.647972	+	0.719646i	−0.974210	−	0.225641i	$-0.927552\pi$
$503$	−14.5325	+	16.1400i	−0.647972	+	0.719646i	0.326238	+	0.945288i	$0.394219\pi$
$504$	0.500010	−	4.75728i	0.0222722	−	0.211906i
$505$	9.31143	+	10.3414i	0.414353	+	0.460186i
$506$	36.4034	−	40.4301i	1.61833	−	1.79734i
$507$	1.79686	+	17.0960i	0.0798012	+	0.759258i
$508$	−10.2859	−	7.47318i	−0.456365	−	0.331569i
$509$	−16.6582	−	28.8528i	−0.738361	−	1.27888i	−0.953233	−	0.302236i	$-0.902267\pi$
$509$	−16.6582	−	28.8528i	−0.738361	−	1.27888i	0.214872	−	0.976642i	$-0.431066\pi$
$510$	0.489109	+	0.217765i	0.0216581	+	0.00964282i
$511$	−3.08206	+	9.48561i	−0.136342	+	0.419619i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−2.05395	+	0.914478i	−0.0906841	+	0.0403752i
$514$	−2.46755	−	23.4772i	−0.108839	−	1.03553i
$515$	−3.60977	−	11.1097i	−0.159066	−	0.489554i
$516$	−4.91921	+	3.57401i	−0.216556	+	0.157337i
$517$	27.3008	−	47.2864i	1.20069	−	2.07965i
$518$	7.45981	−	3.32132i	0.327765	−	0.145930i
$519$	13.2613	−	5.90430i	0.582105	−	0.259170i
$520$	−3.83621	+	6.64451i	−0.168229	+	0.291381i
$521$	−27.7798	+	20.1832i	−1.21705	+	0.884241i	−0.995852	−	0.0909874i	$-0.970998\pi$
$521$	−27.7798	+	20.1832i	−1.21705	+	0.884241i	−0.221201	+	0.975228i	$0.570998\pi$
$522$	3.61079	+	11.1129i	0.158040	+	0.486397i
$523$	0.941984	+	8.96238i	0.0411901	+	0.391898i	0.995622	+	0.0934693i	$0.0297957\pi$
$523$	0.941984	+	8.96238i	0.0411901	+	0.391898i	−0.954432	+	0.298428i	$0.903538\pi$
$524$	4.69210	−	2.08906i	0.204975	−	0.0912609i
$525$	3.79585	+	2.75785i	0.165664	+	0.120362i
$526$	1.18645	−	3.65152i	0.0517317	−	0.159214i
$527$	0.524115	+	0.233351i	0.0228308	+	0.0101649i
$528$	2.13469	+	3.69739i	0.0929004	+	0.160908i
$529$	−48.6705	−	35.3612i	−2.11611	−	1.53744i
$530$	−0.355509	−	3.38244i	−0.0154423	−	0.146924i
$531$	3.59117	−	3.98840i	0.155844	−	0.173082i
$532$	0.736534	+	0.818004i	0.0319328	+	0.0354650i
$533$	−1.75651	+	16.7120i	−0.0760828	+	0.723879i
$534$	7.83065	−	8.69682i	0.338865	−	0.376348i
$535$	3.53435	−	6.12168i	0.152803	−	0.264663i
$536$	−3.95567	−	6.85141i	−0.170859	−	0.295936i
$537$	2.89379	+	0.615095i	0.124876	+	0.0265433i
$538$	13.6069			0.586637
$539$	19.2755	+	4.09713i	0.830255	+	0.176476i
$540$	−1.53033	+	4.70988i	−0.0658550	+	0.202681i
$541$	−8.40431	−	25.8658i	−0.361330	−	1.11206i	−0.952248	−	0.305327i	$-0.901234\pi$
$541$	−8.40431	−	25.8658i	−0.361330	−	1.11206i	0.590918	−	0.806732i	$-0.298766\pi$
$542$	0.686983	−	6.53621i	0.0295084	−	0.280754i
$543$	−15.6265	+	3.32152i	−0.670598	+	0.142540i
$544$	−0.580337	+	0.123355i	−0.0248818	+	0.00528878i
$545$	0.638856	+	0.709521i	0.0273656	+	0.0303925i
$546$	6.77310	−	4.92095i	0.289862	−	0.210597i
$547$	−9.22590	−	4.10764i	−0.394471	−	0.175630i	0.199908	−	0.979815i	$-0.435936\pi$
$547$	−9.22590	−	4.10764i	−0.394471	−	0.175630i	−0.594379	+	0.804185i	$0.702602\pi$
$548$	−2.21533			−0.0946341
$549$	19.3018	+	2.23612i	0.823780	+	0.0954354i
$550$	20.3432			0.867436
$551$	−2.45634	−	1.09363i	−0.104643	−	0.0465903i
$552$	5.27966	−	3.83589i	0.224717	−	0.163266i
$553$	−8.15837	−	9.06079i	−0.346929	−	0.385304i
$554$	−10.9273	+	2.32267i	−0.464257	+	0.0986809i
$555$	−3.74874	+	0.796819i	−0.159125	+	0.0338231i
$556$	−1.26825	+	12.0666i	−0.0537860	+	0.511740i
$557$	4.09502	+	12.6032i	0.173512	+	0.534014i	0.999562	−	0.0295817i	$-0.00941751\pi$
$557$	4.09502	+	12.6032i	0.173512	+	0.534014i	−0.826051	+	0.563596i	$0.809418\pi$
$558$	−0.743413	+	2.28799i	−0.0314712	+	0.0968583i
$559$	50.5679	+	10.7485i	2.13879	+	0.454615i
$560$	2.42452			0.102455
$561$	−2.47768	−	0.526647i	−0.104608	−	0.0222350i
$562$	10.5951	+	18.3513i	0.446927	+	0.774101i
$563$	5.38543	−	9.32783i	0.226969	−	0.393121i	−0.729940	−	0.683512i	$-0.760452\pi$
$563$	5.38543	−	9.32783i	0.226969	−	0.393121i	0.956908	+	0.290390i	$0.0937851\pi$
$564$	4.38261	−	4.86739i	0.184541	−	0.204954i
$565$	2.49671	−	23.7546i	0.105037	−	0.999363i
$566$	21.3006	+	23.6567i	0.895330	+	0.994365i
$567$	−5.98646	+	6.64863i	−0.251408	+	0.279216i
$568$	−0.225514	−	2.14562i	−0.00946234	−	0.0900281i
$569$	15.7803	+	11.4650i	0.661543	+	0.480639i	0.867184	−	0.497988i	$-0.165928\pi$
$569$	15.7803	+	11.4650i	0.661543	+	0.480639i	−0.205640	+	0.978628i	$0.565928\pi$
$570$	−0.258306	−	0.447400i	−0.0108193	−	0.0187395i
$571$	9.28858	+	4.13554i	0.388715	+	0.173067i	0.591783	−	0.806098i	$-0.298424\pi$
$571$	9.28858	+	4.13554i	0.388715	+	0.173067i	−0.203067	+	0.979165i	$0.565091\pi$
$572$	11.2171	−	34.5226i	0.469009	−	1.44346i
$573$	−6.43836	−	4.67774i	−0.268966	−	0.195415i
$574$	4.85108	−	2.15984i	0.202480	−	0.0901500i
$575$	−3.25040	−	30.9255i	−0.135551	−	1.28968i
$576$	−0.768794	−	2.36610i	−0.0320331	−	0.0985877i
$577$	−6.94338	+	5.04466i	−0.289057	+	0.210012i	−0.722858	−	0.690997i	$-0.757172\pi$
$577$	−6.94338	+	5.04466i	−0.289057	+	0.210012i	0.433801	+	0.901009i	$0.357172\pi$
$578$	−8.32400	+	14.4176i	−0.346233	+	0.599692i
$579$	10.8060	−	4.81116i	0.449084	−	0.199945i
$580$	−5.41042	+	2.40888i	−0.224656	+	0.100023i
$581$	8.41841	−	14.5811i	0.349255	−	0.604927i
$582$	2.78848	−	2.02595i	0.115586	−	0.0839784i
$583$	4.97237	+	15.3034i	0.205935	+	0.633802i
$584$	0.542222	+	5.15890i	0.0224373	+	0.213477i
$585$	17.4377	−	7.76378i	0.720962	−	0.320993i
$586$	14.2619	+	10.3619i	0.589154	+	0.428045i
$587$	−4.07594	+	12.5445i	−0.168232	+	0.517765i	−0.999260	−	0.0384658i	$-0.987753\pi$
$587$	−4.07594	+	12.5445i	−0.168232	+	0.517765i	0.831028	+	0.556231i	$0.187753\pi$
$588$	2.15947	+	0.961460i	0.0890552	+	0.0396499i
$589$	−0.276794	−	0.479420i	−0.0114051	−	0.0197542i
$590$	2.20072	+	1.59892i	0.0906022	+	0.0658264i
$591$	0.918377	+	8.73777i	0.0377770	+	0.359424i
$592$	2.84179	−	3.15613i	0.116797	−	0.129716i
$593$	−7.07739	−	7.86024i	−0.290634	−	0.322781i	0.580091	−	0.814551i	$-0.303017\pi$
$593$	−7.07739	−	7.86024i	−0.290634	−	0.322781i	−0.870725	+	0.491770i	$0.836350\pi$
$594$	2.44908	−	23.3014i	0.100487	−	0.956069i
$595$	−0.962526	+	1.06899i	−0.0394597	+	0.0438245i
$596$	3.78242	−	6.55135i	0.154934	−	0.268354i
$597$	−0.520360	−	0.901289i	−0.0212969	−	0.0368873i
$598$	−54.2732	−	11.5361i	−2.21939	−	0.471747i
$599$	12.3223			0.503474			0.251737	−	0.967796i	$-0.418998\pi$
$599$	12.3223			0.503474			0.251737	+	0.967796i	$0.418998\pi$
$600$	2.38693	+	0.507357i	0.0974459	+	0.0207128i
$601$	7.32392	−	22.5407i	0.298749	−	0.919455i	−0.683187	−	0.730243i	$-0.739407\pi$
$601$	7.32392	−	22.5407i	0.298749	−	0.919455i	0.981936	−	0.189212i	$-0.0605932\pi$
$602$	−5.04831	−	15.5371i	−0.205754	−	0.633245i
$603$	−2.05737	+	19.5745i	−0.0837824	+	0.797137i
$604$	16.8694	−	3.58571i	0.686407	−	0.145900i
$605$	30.3320	−	6.44727i	1.23317	−	0.262119i
$606$	−5.28442	−	5.86895i	−0.214665	−	0.238410i
$607$	1.10684	−	0.804165i	0.0449252	−	0.0326400i	−0.565096	−	0.825025i	$-0.691161\pi$
$607$	1.10684	−	0.804165i	0.0449252	−	0.0326400i	0.610021	+	0.792385i	$0.291161\pi$
$608$	0.522993	+	0.232851i	0.0212102	+	0.00944337i
$609$	6.46247			0.261873
$610$	−0.104557	+	9.84803i	−0.00423339	+	0.398735i
$611$	−55.6872			−2.25286
$612$	1.34845	+	0.600367i	0.0545077	+	0.0242684i
$613$	−8.15528	+	5.92516i	−0.329389	+	0.239315i	−0.740171	−	0.672418i	$-0.765256\pi$
$613$	−8.15528	+	5.92516i	−0.329389	+	0.239315i	0.410782	+	0.911733i	$0.365256\pi$
$614$	4.13741	+	4.59506i	0.166972	+	0.185441i
$615$	−2.43779	+	0.518168i	−0.0983011	+	0.0208945i
$616$	−11.2200	+	2.38490i	−0.452069	+	0.0960902i
$617$	−3.77470	+	35.9139i	−0.151964	+	1.44584i	0.606999	+	0.794703i	$0.292373\pi$
$617$	−3.77470	+	35.9139i	−0.151964	+	1.44584i	−0.758962	+	0.651135i	$0.774293\pi$
$618$	2.04862	+	6.30500i	0.0824075	+	0.253624i
$619$	12.7282	−	39.1733i	0.511588	−	1.57451i	−0.277816	−	0.960634i	$-0.589611\pi$
$619$	12.7282	−	39.1733i	0.511588	−	1.57451i	0.789405	−	0.613873i	$-0.210389\pi$
$620$	−1.19271	−	0.253518i	−0.0479003	−	0.0101815i
$621$	−35.8139			−1.43716
$622$	−20.2043	−	4.29455i	−0.810117	−	0.172196i
$623$	15.7211	+	27.2297i	0.629853	+	1.09094i
$624$	2.17713	−	3.77089i	0.0871548	−	0.150957i
$625$	2.46052	−	2.73268i	0.0984208	−	0.109307i
$626$	−2.39967	+	22.8313i	−0.0959100	+	0.912523i
$627$	1.63546	+	1.81637i	0.0653142	+	0.0725387i
$628$	−8.51549	+	9.45741i	−0.339805	+	0.377392i
$629$	0.263386	+	2.50595i	0.0105019	+	0.0999186i
$630$	−4.87990	−	3.54545i	−0.194420	−	0.141254i
$631$	16.4450	+	28.4836i	0.654667	+	1.13392i	0.981977	+	0.188999i	$0.0605243\pi$
$631$	16.4450	+	28.4836i	0.654667	+	1.13392i	−0.327311	+	0.944917i	$0.606142\pi$
$632$	−5.79304	−	2.57923i	−0.230435	−	0.102596i
$633$	−2.18590	+	6.72751i	−0.0868818	+	0.267395i
$634$	−1.64165	−	1.19273i	−0.0651982	−	0.0473692i
$635$	−14.6462	+	6.52092i	−0.581218	+	0.258775i
$636$	0.201759	+	1.91961i	0.00800025	+	0.0761173i
$637$	−6.21059	−	19.1142i	−0.246073	−	0.757333i
$638$	22.6685	−	16.4697i	0.897456	−	0.652040i
$639$	−2.68371	+	4.64832i	−0.106166	+	0.183885i
$640$	1.15196	−	0.512888i	0.0455354	−	0.0202737i
$641$	15.8851	−	7.07248i	0.627422	−	0.279346i	−0.0682918	−	0.997665i	$-0.521755\pi$
$641$	15.8851	−	7.07248i	0.627422	−	0.279346i	0.695714	+	0.718319i	$0.255088\pi$
$642$	−2.00582	+	3.47418i	−0.0791633	+	0.137115i
$643$	30.3916	−	22.0808i	1.19853	−	0.870782i	0.204390	−	0.978890i	$-0.434479\pi$
$643$	30.3916	−	22.0808i	1.19853	−	0.870782i	0.994139	+	0.108107i	$0.0344789\pi$
$644$	5.41821	+	16.6756i	0.213508	+	0.657109i
$645$	0.801459	+	7.62537i	0.0315574	+	0.300249i
$646$	−0.310293	+	0.138151i	−0.0122083	+	0.00543549i
$647$	14.9781	+	10.8822i	0.588851	+	0.427825i	0.841904	−	0.539627i	$-0.181435\pi$
$647$	14.9781	+	10.8822i	0.588851	+	0.427825i	−0.253053	+	0.967452i	$0.581435\pi$
$648$	−1.43789	+	4.42536i	−0.0564856	+	0.173845i
$649$	−11.7572	−	5.23462i	−0.461509	−	0.205477i
$650$	−10.3738	−	17.9679i	−0.406894	−	0.704761i
$651$	1.07643	+	0.782070i	0.0421885	+	0.0306517i
$652$	0.601716	+	5.72495i	0.0235650	+	0.224206i
$653$	−22.4702	+	24.9557i	−0.879326	+	0.976590i	−0.999870	−	0.0161178i	$-0.994869\pi$
$653$	−22.4702	+	24.9557i	−0.879326	+	0.976590i	0.120544	+	0.992708i	$0.461536\pi$
$654$	−0.362564	−	0.402668i	−0.0141774	−	0.0157455i
$655$	0.676988	−	6.44111i	0.0264521	−	0.251675i
$656$	1.84800	−	2.05242i	0.0721525	−	0.0801334i
$657$	6.45268	−	11.1764i	0.251743	−	0.436032i
$658$	8.79869	+	15.2398i	0.343009	+	0.594109i
$659$	24.2646	+	5.15759i	0.945213	+	0.200911i	0.654639	−	0.755941i	$-0.272821\pi$
$659$	24.2646	+	5.15759i	0.945213	+	0.200911i	0.290574	+	0.956853i	$0.406154\pi$
$660$	5.38361			0.209557
$661$	15.6760	+	3.33204i	0.609726	+	0.129601i	0.502418	−	0.864625i	$-0.332444\pi$
$661$	15.6760	+	3.33204i	0.609726	+	0.129601i	0.107307	+	0.994226i	$0.465777\pi$
$662$	7.79104	−	23.9784i	0.302807	−	0.931946i
$663$	0.798311	+	2.45695i	0.0310038	+	0.0954200i
$664$	0.915331	−	8.70880i	0.0355217	−	0.337967i
$665$	1.35767	−	0.288583i	0.0526483	−	0.0111908i
$666$	−10.3351	+	2.19679i	−0.400476	+	0.0851237i
$667$	−28.6590	−	31.8290i	−1.10968	−	1.23242i
$668$	13.4338	−	9.76026i	0.519771	−	0.377636i
$669$	6.67155	+	2.97037i	0.257937	+	0.114841i
$670$	−9.97605			−0.385408
$671$	−9.20323	−	45.6770i	−0.355287	−	1.76334i
$672$	−1.37596			−0.0530789
$673$	25.4735	+	11.3415i	0.981930	+	0.437183i	0.833970	−	0.551810i	$-0.186063\pi$
$673$	25.4735	+	11.3415i	0.981930	+	0.437183i	0.147960	+	0.988993i	$0.452729\pi$
$674$	−18.4519	+	13.4061i	−0.710740	+	0.516383i
$675$	−8.96086	−	9.95204i	−0.344904	−	0.383054i
$676$	−23.4959	+	4.99422i	−0.903690	+	0.192085i
$677$	−0.110646	+	0.0235185i	−0.00425247	+	0.000903891i	−0.210037	−	0.977693i	$-0.567359\pi$
$677$	−0.110646	+	0.0235185i	−0.00425247	+	0.000903891i	0.205785	+	0.978597i	$0.434025\pi$
$678$	−1.41693	+	13.4812i	−0.0544169	+	0.517743i
$679$	2.86166	+	8.80730i	0.109821	+	0.337993i
$680$	−0.231189	+	0.711527i	−0.00886570	+	0.0272858i
$681$	5.18503	+	1.10211i	0.198691	+	0.0422330i
$682$	5.76892			0.220903
$683$	−31.9076	−	6.78218i	−1.22091	−	0.259513i	−0.448004	−	0.894031i	$-0.647865\pi$
$683$	−31.9076	−	6.78218i	−1.22091	−	0.259513i	−0.772908	+	0.634518i	$0.781198\pi$
$684$	−0.712137	−	1.23346i	−0.0272292	−	0.0471624i
$685$	−1.39674	+	2.41923i	−0.0533669	+	0.0924341i
$686$	−13.2555	+	14.7218i	−0.506098	+	0.562079i
$687$	2.14453	−	20.4038i	0.0818189	−	0.778455i
$688$	−5.68536	−	6.31423i	−0.216752	−	0.240728i
$689$	10.9810	−	12.1956i	0.418342	−	0.464616i
$690$	−0.860184	−	8.18411i	−0.0327467	−	0.311564i
$691$	36.7196	+	26.6784i	1.39688	+	1.01489i	0.995070	+	0.0991710i	$0.0316191\pi$
$691$	36.7196	+	26.6784i	1.39688	+	1.01489i	0.401811	+	0.915723i	$0.368381\pi$
$692$	10.1423	+	17.5669i	0.385551	+	0.667793i
$693$	26.0704	+	11.6073i	0.990334	+	0.440925i
$694$	8.83029	−	27.1768i	0.335193	−	1.03162i
$695$	12.3777	+	8.99290i	0.469512	+	0.341120i
$696$	3.07052	−	1.36709i	0.116388	−	0.0518192i
$697$	0.171278	+	1.62961i	0.00648764	+	0.0617257i
$698$	2.49747	+	7.68641i	0.0945304	+	0.290935i
$699$	−8.49834	+	6.17440i	−0.321437	+	0.233537i
$700$	−3.27817	+	5.67795i	−0.123903	+	0.214606i
$701$	−26.9672	+	12.0066i	−1.01854	+	0.453482i	−0.846941	−	0.531686i	$-0.821559\pi$
$701$	−26.9672	+	12.0066i	−1.01854	+	0.453482i	−0.171595	+	0.985168i	$0.554892\pi$
$702$	−21.8297	+	9.71920i	−0.823909	+	0.366828i
$703$	1.21567	−	2.10561i	0.0458500	−	0.0794145i
$704$	−4.82649	+	3.50665i	−0.181905	+	0.132162i
$705$	−2.55219	−	7.85485i	−0.0961212	−	0.295831i
$706$	1.11274	+	10.5870i	0.0418784	+	0.398446i
$707$	19.3840	−	8.63030i	0.729009	−	0.324576i
$708$	−1.24895	−	0.907418i	−0.0469385	−	0.0341028i
$709$	−12.9105	+	39.7344i	−0.484863	+	1.49226i	0.347315	+	0.937748i	$0.387093\pi$
$709$	−12.9105	+	39.7344i	−0.484863	+	1.49226i	−0.832179	+	0.554508i	$0.812907\pi$
$710$	−2.48529	−	1.10652i	−0.0932713	−	0.0415271i
$711$	7.88813	+	13.6626i	0.295828	+	0.512389i
$712$	13.2298	+	9.61203i	0.495809	+	0.360226i
$713$	−0.921748	−	8.76985i	−0.0345197	−	0.328433i
$714$	0.546253	−	0.606675i	0.0204430	−	0.0227043i
$715$	−30.6279	−	34.0157i	−1.14542	−	1.27212i
$716$	−0.432123	+	4.11137i	−0.0161492	+	0.153649i
$717$	−6.60682	+	7.33762i	−0.246736	+	0.274028i
$718$	−8.95197	+	15.5053i	−0.334084	+	0.578651i
$719$	4.92321	+	8.52726i	0.183605	+	0.318013i	0.943106	−	0.332494i	$-0.107890\pi$
$719$	4.92321	+	8.52726i	0.183605	+	0.318013i	−0.759501	+	0.650507i	$0.774557\pi$
$720$	−3.06861	−	0.652252i	−0.114360	−	0.0243080i
$721$	−17.8117			−0.663341
$722$	−18.2642	−	3.88218i	−0.679724	−	0.144480i
$723$	3.33187	−	10.2544i	0.123914	−	0.381367i
$724$	−6.89842	−	21.2312i	−0.256378	−	0.789050i
$725$	1.67406	−	15.9276i	0.0621730	−	0.591537i
$726$	−17.2140	+	3.65895i	−0.638872	+	0.135797i
$727$	−44.9422	+	9.55276i	−1.66681	+	0.354292i	−0.942249	−	0.334914i	$-0.891293\pi$
$727$	−44.9422	+	9.55276i	−1.66681	+	0.354292i	−0.724565	+	0.689206i	$0.757959\pi$
$728$	7.82799	+	8.69387i	0.290125	+	0.322216i
$729$	2.54419	−	1.84846i	0.0942292	−	0.0684615i
$730$	5.97560	+	2.66051i	0.221167	+	0.0984699i
$731$	5.04108			0.186451
$732$	0.0593382	−	5.58896i	0.00219320	−	0.206574i
$733$	−11.5039			−0.424907			−0.212454	−	0.977171i	$-0.568145\pi$
$733$	−11.5039			−0.424907			−0.212454	+	0.977171i	$0.568145\pi$
$734$	−1.27913	−	0.569506i	−0.0472136	−	0.0210209i
$735$	2.41148	−	1.75205i	0.0889489	−	0.0646252i
$736$	6.10195	+	6.77690i	0.224921	+	0.249800i
$737$	46.1666	−	9.81302i	1.70057	−	0.361467i
$738$	−6.72085	+	1.42856i	−0.247398	+	0.0525860i
$739$	1.83851	−	17.4923i	0.0676308	−	0.643464i	−0.907228	−	0.420640i	$-0.861806\pi$
$739$	1.83851	−	17.4923i	0.0676308	−	0.643464i	0.974859	−	0.222824i	$-0.0715277\pi$
$740$	−1.65490	−	5.09327i	−0.0608355	−	0.187232i
$741$	0.770303	−	2.37075i	0.0282978	−	0.0870917i
$742$	−5.07257	−	1.07821i	−0.186220	−	0.0395823i
$743$	−5.64499			−0.207094			−0.103547	−	0.994625i	$-0.533019\pi$
$743$	−5.64499			−0.207094			−0.103547	+	0.994625i	$0.533019\pi$
$744$	0.676885	+	0.143876i	0.0248158	+	0.00527476i
$745$	−4.76957	−	8.26114i	−0.174744	−	0.302665i
$746$	2.50814	−	4.34423i	0.0918296	−	0.159054i
$747$	−14.5775	+	16.1899i	−0.533362	+	0.592358i
$748$	0.369986	−	3.52018i	0.0135280	−	0.128710i
$749$	−7.21204	−	8.00978i	−0.263522	−	0.292671i
$750$	5.07811	−	5.63982i	0.185426	−	0.205937i
$751$	3.26969	+	31.1090i	0.119313	+	1.13518i	0.876304	+	0.481759i	$0.160002\pi$
$751$	3.26969	+	31.1090i	0.119313	+	1.13518i	−0.756991	+	0.653425i	$0.773331\pi$
$752$	7.40439	+	5.37961i	0.270010	+	0.196174i
$753$	−2.30705	−	3.99593i	−0.0840736	−	0.145620i
$754$	−26.1063	−	11.6233i	−0.950735	−	0.423295i
$755$	6.72028	−	20.6829i	0.244576	−	0.752728i
$756$	6.10897	+	4.43843i	0.222181	+	0.161424i
$757$	14.1300	−	6.29106i	0.513562	−	0.228653i	−0.133557	−	0.991041i	$-0.542640\pi$
$757$	14.1300	−	6.29106i	0.513562	−	0.228653i	0.647120	+	0.762388i	$0.275973\pi$
$758$	1.51871	+	14.4496i	0.0551620	+	0.524831i
$759$	12.0311	+	37.0278i	0.436700	+	1.34403i
$760$	0.584026	−	0.424320i	0.0211849	−	0.0153917i
$761$	4.61545	−	7.99420i	0.167310	−	0.289789i	−0.770163	−	0.637847i	$-0.779825\pi$
$761$	4.61545	−	7.99420i	0.167310	−	0.289789i	0.937473	+	0.348057i	$0.113159\pi$
$762$	8.31203	−	3.70075i	0.301113	−	0.134064i
$763$	1.32993	−	0.592124i	0.0481468	−	0.0214363i
$764$	5.56028	−	9.63069i	0.201164	−	0.348426i
$765$	1.50581	−	1.09404i	0.0544427	−	0.0395549i
$766$	−9.06299	−	27.8930i	−0.327459	−	1.00782i
$767$	1.37201	+	13.0538i	0.0495403	+	0.471344i
$768$	−0.653763	+	0.291074i	−0.0235907	+	0.0105032i
$769$	−3.57182	−	2.59508i	−0.128803	−	0.0935809i	0.521518	−	0.853240i	$-0.325366\pi$
$769$	−3.57182	−	2.59508i	−0.128803	−	0.0935809i	−0.650321	+	0.759659i	$0.725366\pi$
$770$	−4.46974	+	13.7564i	−0.161078	+	0.495747i
$771$	15.4331	+	6.87124i	0.555808	+	0.247462i
$772$	8.26449	+	14.3145i	0.297446	+	0.515191i
$773$	12.4487	+	9.04451i	0.447749	+	0.325308i	0.788706	−	0.614770i	$-0.210751\pi$
$773$	12.4487	+	9.04451i	0.447749	+	0.325308i	−0.340958	+	0.940079i	$0.610751\pi$
$774$	2.20958	+	21.0227i	0.0794216	+	0.755646i
$775$	2.20636	−	2.45041i	0.0792547	−	0.0880212i
$776$	3.22278	+	3.57926i	0.115691	+	0.128488i
$777$	−0.610833	+	5.81169i	−0.0219135	+	0.208493i
$778$	4.70938	−	5.23030i	0.168839	−	0.187515i
$779$	0.790547	−	1.36927i	0.0283243	−	0.0490591i
$780$	−2.74532	−	4.75503i	−0.0982982	−	0.170257i
$781$	12.5897	+	2.67603i	0.450496	+	0.0957559i
$782$	−5.41045			−0.193477
$783$	−18.0422	−	3.83500i	−0.644777	−	0.137052i
$784$	−1.02073	+	3.14148i	−0.0364545	+	0.112196i
$785$	4.95896	+	15.2621i	0.176993	+	0.544728i
$786$	−0.384204	+	3.65546i	−0.0137041	+	0.130386i
$787$	−3.60791	+	0.766885i	−0.128608	+	0.0273365i	−0.271766	−	0.962363i	$-0.587608\pi$
$787$	−3.60791	+	0.766885i	−0.128608	+	0.0273365i	0.143158	+	0.989700i	$0.454274\pi$
$788$	−12.0088	+	2.55255i	−0.427797	+	0.0909310i
$789$	1.83852	+	2.04189i	0.0654531	+	0.0726930i
$790$	−6.46909	+	4.70007i	−0.230160	+	0.167221i
$791$	−33.2714	−	14.8134i	−1.18299	−	0.526702i
$792$	14.8423			0.527399
$793$	−35.6508	+	31.4212i	−1.26600	+	1.11580i
$794$	−18.7721			−0.666196
$795$	2.22350	+	0.989965i	0.0788594	+	0.0351105i
$796$	1.17652	−	0.854795i	0.0417008	−	0.0302974i
$797$	1.31601	+	1.46158i	0.0466155	+	0.0517718i	0.766002	−	0.642839i	$-0.222243\pi$
$797$	1.31601	+	1.46158i	0.0466155	+	0.0517718i	−0.719386	+	0.694610i	$0.755577\pi$
$798$	−0.770508	+	0.163776i	−0.0272757	+	0.00579762i
$799$	−5.31144	+	1.12898i	−0.187905	+	0.0399405i
$800$	−0.356434	+	3.39124i	−0.0126018	+	0.119899i
$801$	−12.5721	−	38.6928i	−0.444212	−	1.36714i
$802$	1.90824	−	5.87295i	0.0673822	−	0.207381i
$803$	−30.2706	−	6.43421i	−1.06823	−	0.227058i
$804$	5.66161			0.199670
$805$	21.6266	+	4.59687i	0.762236	+	0.162018i
$806$	−2.94180	−	5.09535i	−0.103621	−	0.179476i
$807$	−4.86879	+	8.43298i	−0.171389	+	0.296855i
$808$	7.38426	−	8.20105i	0.259777	−	0.288512i
$809$	−3.15774	+	30.0439i	−0.111020	+	1.05629i	0.787187	+	0.616714i	$0.211537\pi$
$809$	−3.15774	+	30.0439i	−0.111020	+	1.05629i	−0.898207	+	0.439572i	$0.855130\pi$
$810$	3.92611	+	4.36039i	0.137949	+	0.153208i
$811$	−36.5056	+	40.5436i	−1.28189	+	1.42368i	−0.427521	+	0.904005i	$0.640613\pi$
$811$	−36.5056	+	40.5436i	−1.28189	+	1.42368i	−0.854365	+	0.519673i	$0.826054\pi$
$812$	0.943937	+	8.98096i	0.0331257	+	0.315170i
$813$	3.80504	+	2.76452i	0.133449	+	0.0969561i
$814$	12.6685	+	21.9425i	0.444031	+	0.769084i
$815$	6.63127	+	2.95243i	0.232283	+	0.103419i
$816$	0.131205	−	0.403806i	0.00459308	−	0.0141360i
$817$	−3.93523	−	2.85911i	−0.137676	−	0.100028i
$818$	−2.70594	+	1.20476i	−0.0946109	+	0.0421235i
$819$	−3.04230	−	28.9455i	−0.106306	−	1.01144i
$820$	−1.07618	−	3.31213i	−0.0375817	−	0.115665i
$821$	18.2023	−	13.2248i	0.635265	−	0.461547i	−0.222955	−	0.974829i	$-0.571570\pi$
$821$	18.2023	−	13.2248i	0.635265	−	0.461547i	0.858220	+	0.513282i	$0.171570\pi$
$822$	0.792681	−	1.37296i	0.0276479	−	0.0478876i
$823$	31.2974	−	13.9345i	1.09096	−	0.485726i	0.219209	−	0.975678i	$-0.429652\pi$
$823$	31.2974	−	13.9345i	1.09096	−	0.485726i	0.871749	+	0.489952i	$0.162986\pi$
$824$	−8.46289	+	3.76792i	−0.294819	+	0.131262i
$825$	−7.27912	+	12.6078i	−0.253427	+	0.438948i
$826$	3.35561	−	2.43800i	0.116757	−	0.0848288i
$827$	7.87250	+	24.2291i	0.273754	+	0.842527i	0.989546	+	0.144214i	$0.0460655\pi$
$827$	7.87250	+	24.2291i	0.273754	+	0.842527i	−0.715793	+	0.698313i	$0.753935\pi$
$828$	−2.37148	−	22.5631i	−0.0824147	−	0.784123i
$829$	26.2354	−	11.6808i	0.911193	−	0.405689i	0.103051	−	0.994676i	$-0.467140\pi$
$829$	26.2354	−	11.6808i	0.911193	−	0.405689i	0.808143	+	0.588987i	$0.200473\pi$
$830$	−8.93327	−	6.49040i	−0.310078	−	0.225285i
$831$	2.47048	−	7.60336i	0.0857001	−	0.263758i
$832$	5.55845	+	2.47478i	0.192704	+	0.0857975i
$833$	−0.979881	−	1.69720i	−0.0339509	−	0.0588046i
$834$	−7.02458	−	5.10365i	−0.243241	−	0.176725i
$835$	−2.18870	−	20.8241i	−0.0757431	−	0.720648i
$836$	−2.28534	+	2.53813i	−0.0790401	+	0.0877829i
$837$	−2.54112	−	2.82220i	−0.0878340	−	0.0975495i
$838$	3.14828	−	29.9539i	0.108756	−	1.03474i
$839$	−11.7512	+	13.0510i	−0.405696	+	0.450571i	−0.911022	−	0.412357i	$-0.864706\pi$
$839$	−11.7512	+	13.0510i	−0.405696	+	0.450571i	0.505326	+	0.862928i	$0.331372\pi$
$840$	−0.867533	+	1.50261i	−0.0299327	+	0.0518450i
$841$	3.47055	+	6.01117i	0.119674	+	0.207282i
$842$	−16.5014	−	3.50748i	−0.568676	−	0.120876i
$843$	−15.1644			−0.522290
$844$	−9.66857	−	2.05512i	−0.332806	−	0.0707401i
$845$	−9.36009	+	28.8074i	−0.321997	+	0.991004i
$846$	−7.03626	−	21.6554i	−0.241912	−	0.744527i
$847$	4.94241	−	47.0239i	0.169823	−	1.61576i
$848$	−2.63822	+	0.560772i	−0.0905970	+	0.0192570i
$849$	−22.2831	+	4.73642i	−0.764753	+	0.162553i
$850$	−1.35373	−	1.50347i	−0.0464325	−	0.0515685i
$851$	31.3326	−	22.7645i	1.07407	−	0.780356i
$852$	1.41045	+	0.627974i	0.0483213	+	0.0215140i
$853$	−7.45705			−0.255324			−0.127662	−	0.991818i	$-0.540747\pi$
$853$	−7.45705			−0.255324			−0.127662	+	0.991818i	$0.540747\pi$
$854$	14.2319	+	4.79185i	0.487005	+	0.163974i
$855$	−1.79598			−0.0614213
$856$	−5.12108	−	2.28005i	−0.175035	−	0.0779305i
$857$	37.5322	−	27.2687i	1.28207	−	0.931482i	0.282461	−	0.959279i	$-0.408849\pi$
$857$	37.5322	−	27.2687i	1.28207	−	0.931482i	0.999614	+	0.0277971i	$0.00884922\pi$
$858$	17.3820	+	19.3046i	0.593410	+	0.659049i
$859$	56.3856	−	11.9851i	1.92385	−	0.408927i	0.924218	−	0.381865i	$-0.124718\pi$
$859$	56.3856	−	11.9851i	1.92385	−	0.408927i	0.999634	−	0.0270624i	$-0.00861527\pi$
$860$	−10.4800	+	2.22759i	−0.357365	+	0.0759602i
$861$	−0.397222	+	3.77932i	−0.0135373	+	0.128799i
$862$	−1.85113	−	5.69720i	−0.0630498	−	0.194047i
$863$	−10.7997	+	33.2379i	−0.367625	+	1.13143i	0.580696	+	0.814120i	$0.302780\pi$
$863$	−10.7997	+	33.2379i	−0.367625	+	1.13143i	−0.948321	+	0.317312i	$0.897220\pi$
$864$	3.84148	+	0.816532i	0.130690	+	0.0277790i
$865$	25.5784			0.869692
$866$	11.7702	+	2.50183i	0.399967	+	0.0850157i
$867$	−5.95693	−	10.3177i	−0.202308	−	0.350407i
$868$	−0.929622	+	1.61015i	−0.0315534	+	0.0546522i
$869$	25.3140	−	28.1141i	0.858720	−	0.953705i
$870$	0.443023	−	4.21508i	0.0150199	−	0.142905i
$871$	−32.2095	−	35.7722i	−1.09138	−	1.21210i
$872$	0.506633	−	0.562673i	0.0171568	−	0.0190545i
$873$	−1.25251	−	11.9169i	−0.0423911	−	0.403325i
$874$	4.22358	+	3.06861i	0.142865	+	0.103797i
$875$	10.1950	+	17.6583i	0.344654	+	0.596958i
$876$	−3.39128	−	1.50989i	−0.114581	−	0.0510146i
$877$	−14.8925	+	45.8345i	−0.502885	+	1.54772i	0.301412	+	0.953494i	$0.402542\pi$
$877$	−14.8925	+	45.8345i	−0.502885	+	1.54772i	−0.804297	+	0.594227i	$0.797458\pi$
$878$	9.49874	+	6.90124i	0.320567	+	0.232906i
$879$	−11.5250	+	5.13126i	−0.388728	+	0.173073i
$880$	0.786353	+	7.48165i	0.0265080	+	0.252206i
$881$	10.6696	+	32.8378i	0.359469	+	1.10633i	0.953372	+	0.301796i	$0.0975862\pi$
$881$	10.6696	+	32.8378i	0.359469	+	1.10633i	−0.593903	+	0.804537i	$0.702414\pi$
$882$	6.64833	−	4.83029i	0.223861	−	0.162644i
$883$	−8.94965	+	15.5012i	−0.301180	+	0.521659i	−0.976403	−	0.215954i	$-0.930714\pi$
$883$	−8.94965	+	15.5012i	−0.301180	+	0.521659i	0.675224	+	0.737613i	$0.264047\pi$
$884$	−3.29784	+	1.46829i	−0.110918	+	0.0493840i
$885$	−1.77839	+	0.791792i	−0.0597800	+	0.0266158i
$886$	−8.19842	+	14.2001i	−0.275431	+	0.477061i
$887$	−10.4224	+	7.57231i	−0.349949	+	0.254253i	−0.748848	−	0.662742i	$-0.769393\pi$
$887$	−10.4224	+	7.57231i	−0.349949	+	0.254253i	0.398898	+	0.916995i	$0.369393\pi$
$888$	0.939191	+	2.89053i	0.0315172	+	0.0969999i
$889$	2.55527	+	24.3118i	0.0857011	+	0.815392i
$890$	18.8380	−	8.38724i	0.631453	−	0.281141i
$891$	−22.4582	−	16.3168i	−0.752377	−	0.546634i
$892$	−3.15347	+	9.70538i	−0.105586	+	0.324960i
$893$	4.78661	+	2.13113i	0.160178	+	0.0713157i
$894$	2.70683	+	4.68836i	0.0905299	+	0.156802i
$895$	4.21735	+	3.06408i	0.140970	+	0.102421i
$896$	−0.200979	−	1.91219i	−0.00671424	−	0.0638817i
$897$	26.5694	−	29.5083i	0.887127	−	0.985254i
$898$	7.87074	+	8.74135i	0.262650	+	0.291702i
$899$	0.474730	−	4.51675i	0.0158331	−	0.150642i
$900$	5.67653	−	6.30443i	0.189218	−	0.210148i
$901$	0.800117	−	1.38584i	0.0266558	−	0.0461691i
$902$	8.23827	+	14.2691i	0.274304	+	0.475109i
$903$	11.4356	+	2.43071i	0.380552	+	0.0808889i
$904$	−18.9419			−0.629999
$905$	−27.5347	−	5.85269i	−0.915285	−	0.194550i
$906$	−3.81390	+	11.7380i	−0.126708	+	0.389968i
$907$	−1.89131	−	5.82084i	−0.0627998	−	0.193278i	0.914734	−	0.404056i	$-0.132400\pi$
$907$	−1.89131	−	5.82084i	−0.0627998	−	0.193278i	−0.977534	+	0.210779i	$0.932400\pi$
$908$	−0.774268	+	7.36666i	−0.0256950	+	0.244471i
$909$	−26.8552	+	5.70825i	−0.890730	+	0.189331i
$910$	14.4296	−	3.06710i	0.478335	−	0.101673i
$911$	−20.6558	−	22.9406i	−0.684359	−	0.760057i	0.296446	−	0.955050i	$-0.404199\pi$
$911$	−20.6558	−	22.9406i	−0.684359	−	0.760057i	−0.980805	+	0.194992i	$0.937532\pi$
$912$	−0.331447	+	0.240810i	−0.0109753	+	0.00797402i
$913$	47.7252	+	21.2486i	1.57947	+	0.703227i
$914$	26.5493			0.878171
$915$	−6.06597	−	3.58859i	−0.200535	−	0.118635i
$916$	28.6686			0.947239
$917$	−9.02160	−	4.01667i	−0.297919	−	0.132642i
$918$	−1.88507	+	1.36959i	−0.0622166	+	0.0452030i
$919$	−16.9599	−	18.8359i	−0.559457	−	0.621340i	0.395363	−	0.918525i	$-0.370619\pi$
$919$	−16.9599	−	18.8359i	−0.559457	−	0.621340i	−0.954820	+	0.297185i	$0.903952\pi$
$920$	11.2479	−	2.39081i	0.370832	−	0.0788227i
$921$	−4.32825	+	0.919997i	−0.142621	+	0.0303149i
$922$	3.42860	−	32.6210i	0.112915	−	1.07432i
$923$	−4.05643	−	12.4844i	−0.133519	−	0.410929i
$924$	2.53667	−	7.80705i	0.0834502	−	0.256833i
$925$	14.1654	+	3.01096i	0.465757	+	0.0989997i
$926$	18.2032			0.598195
$927$	22.5434	+	4.79176i	0.740424	+	0.157382i
$928$	2.34835	+	4.06745i	0.0770882	+	0.133521i
$929$	3.49497	−	6.05346i	0.114666	−	0.198608i	−0.802980	−	0.596006i	$-0.796753\pi$
$929$	3.49497	−	6.05346i	0.114666	−	0.198608i	0.917646	+	0.397398i	$0.130087\pi$
$930$	0.583889	−	0.648475i	0.0191465	−	0.0212643i
$931$	−0.197664	+	1.88065i	−0.00647818	+	0.0616357i
$932$	−9.82193	−	10.9084i	−0.321728	−	0.357315i
$933$	9.89100	−	10.9851i	0.323817	−	0.359635i
$934$	−0.812624	−	7.73160i	−0.0265899	−	0.252986i
$935$	−3.61091	−	2.62348i	−0.118089	−	0.0857970i
$936$	−7.56869	−	13.1094i	−0.247390	−	0.428493i
$937$	−29.5636	−	13.1626i	−0.965802	−	0.430003i	−0.137634	−	0.990483i	$-0.543950\pi$
$937$	−29.5636	−	13.1626i	−0.965802	−	0.430003i	−0.828168	+	0.560480i	$0.810617\pi$
$938$	−4.70055	+	14.4668i	−0.153478	+	0.472358i
$939$	−13.2912	−	9.65663i	−0.433742	−	0.315132i
$940$	10.5432	−	4.69412i	0.343880	−	0.153105i
$941$	1.93289	+	18.3902i	0.0630103	+	0.599503i	0.979779	+	0.200084i	$0.0641215\pi$
$941$	1.93289	+	18.3902i	0.0630103	+	0.599503i	−0.916768	+	0.399419i	$0.869212\pi$
$942$	−2.81431	−	8.66155i	−0.0916951	−	0.282209i
$943$	20.3755	−	14.8036i	0.663516	−	0.482073i
$944$	1.07862	−	1.86822i	0.0351061	−	0.0608055i
$945$	8.69861	−	3.87287i	0.282966	−	0.125984i
$946$	46.3075	−	20.6174i	1.50559	−	0.670330i
$947$	25.3758	−	43.9521i	0.824601	−	1.42825i	−0.0776225	−	0.996983i	$-0.524733\pi$
$947$	25.3758	−	43.9521i	0.824601	−	1.42825i	0.902224	−	0.431268i	$-0.141934\pi$
$948$	3.67134	−	2.66738i	0.119240	−	0.0866326i
$949$	9.75322	+	30.0173i	0.316603	+	0.974404i
$950$	0.204054	+	1.94144i	0.00662038	+	0.0629887i
$951$	1.32661	−	0.590645i	0.0430183	−	0.0191530i
$952$	0.922890	+	0.670519i	0.0299111	+	0.0217317i
$953$	18.4687	−	56.8408i	0.598260	−	1.84126i	0.0604810	−	0.998169i	$-0.480737\pi$
$953$	18.4687	−	56.8408i	0.598260	−	1.84126i	0.537779	−	0.843086i	$-0.319263\pi$
$954$	6.13006	+	2.72928i	0.198468	+	0.0883637i
$955$	−7.01142	−	12.1441i	−0.226884	−	0.392975i
$956$	−11.1622	−	8.10980i	−0.361011	−	0.262290i
$957$	2.09600	+	19.9421i	0.0677540	+	0.644636i
$958$	−1.50935	+	1.67631i	−0.0487650	+	0.0541590i
$959$	2.85013	+	3.16539i	0.0920356	+	0.102216i
$960$	−0.0943266	+	0.897457i	−0.00304438	+	0.0289653i
$961$	−20.1174	+	22.3426i	−0.648947	+	0.720729i
$962$	12.9204	−	22.3787i	0.416569	−	0.721519i
$963$	6.97314	+	12.0778i	0.224706	+	0.389203i
$964$	14.7374	+	3.13252i	0.474658	+	0.100892i
$965$	20.8428			0.670952
$966$	−12.2735	−	2.60881i	−0.394894	−	0.0839372i
$967$	−12.0813	+	37.1824i	−0.388509	+	1.19571i	0.545394	+	0.838180i	$0.316380\pi$
$967$	−12.0813	+	37.1824i	−0.388509	+	1.19571i	−0.933903	+	0.357527i	$0.883620\pi$
$968$	−7.59924	−	23.3880i	−0.244249	−	0.751720i
$969$	0.0254078	−	0.241739i	0.000816216	−	0.00776577i
$970$	5.94064	−	1.26272i	0.190743	−	0.0405436i
$971$	6.23014	−	1.32426i	0.199935	−	0.0424974i	−0.106856	−	0.994275i	$-0.534078\pi$
$971$	6.23014	−	1.32426i	0.199935	−	0.0424974i	0.306790	+	0.951777i	$0.400745\pi$
$972$	−10.1118	−	11.2303i	−0.324335	−	0.360211i
$973$	18.8732	−	13.7122i	0.605048	−	0.439593i
$974$	15.4843	+	6.89408i	0.496151	+	0.220900i
$975$	14.8477			0.475506
$976$	7.77569	−	0.733884i	0.248894	−	0.0234911i
$977$	20.6754			0.661466			0.330733	−	0.943724i	$-0.392704\pi$
$977$	20.6754			0.661466			0.330733	+	0.943724i	$0.392704\pi$
$978$	−3.76338	−	1.67556i	−0.120340	−	0.0535786i
$979$	−78.9275	+	57.3442i	−2.52253	+	1.83273i
$980$	2.78707	+	3.09535i	0.0890296	+	0.0988773i
$981$	−1.84253	+	0.391642i	−0.0588275	+	0.0125042i
$982$	−25.8037	+	5.48475i	−0.823430	+	0.175025i
$983$	−0.600080	+	5.70938i	−0.0191396	+	0.182101i	−0.999915	−	0.0130389i	$-0.995849\pi$
$983$	−0.600080	+	5.70938i	−0.0191396	+	0.182101i	0.980775	+	0.195140i	$0.0625161\pi$
$984$	0.610752	+	1.87970i	0.0194701	+	0.0599227i
$985$	−4.78396	+	14.7235i	−0.152430	+	0.469130i
$986$	−2.72567	−	0.579358i	−0.0868029	−	0.0184505i
$987$	−12.5933			−0.400848
$988$	3.40717	+	0.724216i	0.108396	+	0.0230404i
$989$	−38.7413	−	67.1020i	−1.23190	−	2.13372i
$990$	9.35795	−	16.2084i	0.297415	−	0.515138i
$991$	−26.0258	+	28.9045i	−0.826736	+	0.918183i	−0.997747	−	0.0670861i	$-0.978630\pi$
$991$	−26.0258	+	28.9045i	−0.826736	+	0.918183i	0.171012	+	0.985269i	$0.445296\pi$
$992$	−0.101078	+	0.961689i	−0.00320922	+	0.0305336i
$993$	12.0730	+	13.4084i	0.383125	+	0.425503i
$994$	−2.77565	+	3.08268i	−0.0880384	+	0.0977766i
$995$	−0.191684	−	1.82376i	−0.00607680	−	0.0578169i
$996$	5.06981	+	3.68343i	0.160643	+	0.116714i
$997$	−19.6821	−	34.0905i	−0.623340	−	1.07966i	−0.988859	−	0.148853i	$-0.952442\pi$
$997$	−19.6821	−	34.0905i	−0.623340	−	1.07966i	0.365520	−	0.930804i	$-0.380891\pi$
$998$	1.47056	+	0.654734i	0.0465496	+	0.0207252i
$999$	5.15416	−	15.8629i	0.163070	−	0.501879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.73.2	✓	16
4.3	odd	2		976.2.bw.a.561.1		16
61.19	even	30		7442.2.a.r.1.4		8
61.42	even	15		7442.2.a.p.1.4		8
61.56	even	15	inner	122.2.i.a.117.2	yes	16
244.239	odd	30		976.2.bw.a.849.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.73.2	✓	16	1.1	even	1	trivial
122.2.i.a.117.2	yes	16	61.56	even	15	inner
976.2.bw.a.561.1		16	4.3	odd	2
976.2.bw.a.849.1		16	244.239	odd	30
7442.2.a.p.1.4		8	61.42	even	15
7442.2.a.r.1.4		8	61.19	even	30

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(0.578959 - 0.420639i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.23343 - 0.262173i) q^{5} +(-0.699995 + 0.148788i) q^{6} +(0.200979 - 1.91219i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.768794 + 2.36610i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(0.578959 - 0.420639i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.23343 - 0.262173i) q^{5} +(-0.699995 + 0.148788i) q^{6} +(0.200979 - 1.91219i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.768794 + 2.36610i) q^{9} +(-1.23343 - 0.262173i) q^{10} +5.96587 q^{11} +(0.699995 + 0.148788i) q^{12} +(-3.04224 - 5.26931i) q^{13} +(-0.961361 + 1.66513i) q^{14} +(0.603824 - 0.670615i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-0.396997 - 0.440910i) q^{17} +(1.66471 - 1.84885i) q^{18} +(0.0598412 + 0.569351i) q^{19} +(1.02016 + 0.741187i) q^{20} +(-0.687982 - 1.19162i) q^{21} +(-5.45010 - 2.42654i) q^{22} +(-2.81799 + 8.67289i) q^{23} +(-0.578959 - 0.420639i) q^{24} +(-3.11512 + 1.38694i) q^{25} +(0.636001 + 6.05115i) q^{26} +(1.21360 + 3.73509i) q^{27} +(1.55551 - 1.13015i) q^{28} +(-2.34835 + 4.06745i) q^{29} +(-0.824384 + 0.367040i) q^{30} +(-0.883386 + 0.393309i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.45400 - 2.50948i) q^{33} +(0.183341 + 0.564264i) q^{34} +(-0.253431 - 2.41124i) q^{35} +(-2.27278 + 1.01191i) q^{36} +(-3.43589 - 2.49632i) q^{37} +(0.176908 - 0.544468i) q^{38} +(-3.97781 - 1.77103i) q^{39} +(-0.630491 - 1.09204i) q^{40} +(-2.23434 - 1.62334i) q^{41} +(0.143827 + 1.36843i) q^{42} +(-5.68536 + 6.31423i) q^{43} +(3.99195 + 4.43351i) q^{44} +(-0.327923 + 3.11997i) q^{45} +(6.10195 - 6.77690i) q^{46} +(4.57617 - 7.92615i) q^{47} +(0.357817 + 0.619756i) q^{48} +(3.23096 + 0.686762i) q^{49} +3.40992 q^{50} +(-0.415309 - 0.0882766i) q^{51} +(1.88021 - 5.78668i) q^{52} +(0.833469 + 2.56515i) q^{53} +(0.410515 - 3.90579i) q^{54} +(7.35847 - 1.56409i) q^{55} +(-1.88071 + 0.399756i) q^{56} +(0.274137 + 0.304460i) q^{57} +(3.79970 - 2.76065i) q^{58} +(-1.97074 - 0.877428i) q^{59} +0.902401 q^{60} +(-1.54265 - 7.65639i) q^{61} +0.966986 q^{62} +(4.36993 + 1.94562i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-5.13385 - 5.70172i) q^{65} +(-4.17608 + 0.887653i) q^{66} +(7.73845 - 1.64486i) q^{67} +(0.0620170 - 0.590052i) q^{68} +(2.01665 + 6.20661i) q^{69} +(-0.749217 + 2.30585i) q^{70} +(2.11029 + 0.448556i) q^{71} +2.48787 q^{72} +(-5.07396 - 1.07850i) q^{73} +(2.12349 + 3.67800i) q^{74} +(-1.22013 + 2.11332i) q^{75} +(-0.383069 + 0.425441i) q^{76} +(1.19902 - 11.4079i) q^{77} +(2.91356 + 3.23584i) q^{78} +(4.24314 - 4.71248i) q^{79} +(0.131809 + 1.25407i) q^{80} +(-3.76444 - 2.73502i) q^{81} +(1.38090 + 2.39179i) q^{82} +(7.99970 + 3.56170i) q^{83} +(0.425196 - 1.30862i) q^{84} +(-0.605261 - 0.439748i) q^{85} +(7.76207 - 3.45589i) q^{86} +(0.351331 + 3.34269i) q^{87} +(-1.84356 - 5.67388i) q^{88} +(-13.2298 + 9.61203i) q^{89} +(1.56858 - 2.71686i) q^{90} +(-10.6873 + 4.75831i) q^{91} +(-8.33082 + 3.70912i) q^{92} +(-0.346004 + 0.599296i) q^{93} +(-7.40439 + 5.37961i) q^{94} +(0.223078 + 0.686564i) q^{95} +(-0.0748040 - 0.711713i) q^{96} +(-4.39997 + 1.95899i) q^{97} +(-2.67230 - 1.94154i) q^{98} +(-4.58653 + 14.1159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9	\( 16 q - 2 q^{2} + 3 q^{3} + 2 q^{4} + 6 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} + 3 q^{9} - 6 q^{10} - 2 q^{11} + q^{12} - 9 q^{13} - 10 q^{14} - 3 q^{15} + 2 q^{16} + 2 q^{17} + 24 q^{18} + 10 q^{19} - 7 q^{20} - 6 q^{21} - 11 q^{22} - 11 q^{23} - 3 q^{24} - 28 q^{25} + 4 q^{26} - 33 q^{27} + 5 q^{28} + 15 q^{29} - 12 q^{30} - 12 q^{31} + 8 q^{32} + 15 q^{33} - 11 q^{34} + 19 q^{35} + q^{36} + 16 q^{37} - 10 q^{38} + 24 q^{39} + 4 q^{40} - 20 q^{41} - 19 q^{42} - 21 q^{43} - 4 q^{44} + 17 q^{45} + 2 q^{46} - 11 q^{47} + q^{48} - 10 q^{49} + 4 q^{50} - 56 q^{51} - 2 q^{52} - 8 q^{53} + 41 q^{54} + 35 q^{55} + 10 q^{56} + 49 q^{57} - 10 q^{58} + 35 q^{59} + 6 q^{60} + 15 q^{61} + 16 q^{62} - 26 q^{63} - 4 q^{64} + 24 q^{65} + 10 q^{66} + 22 q^{67} + 12 q^{68} + 46 q^{69} + 28 q^{70} + 10 q^{71} + 2 q^{72} + 9 q^{73} - 7 q^{74} - 15 q^{75} - 20 q^{76} + 2 q^{77} + 11 q^{78} + 10 q^{79} - 4 q^{80} - 27 q^{81} + 15 q^{82} - 45 q^{83} + 17 q^{84} + 2 q^{85} + 11 q^{86} - 9 q^{87} - 8 q^{88} - 26 q^{89} + 8 q^{90} - 84 q^{91} - 47 q^{92} - 33 q^{93} - 2 q^{94} + 37 q^{95} + 9 q^{96} - 41 q^{97} - 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 + 6 * q^5 - q^6 - 10 * q^7 + 4 * q^8 + 3 * q^9 - 6 * q^10 - 2 * q^11 + q^12 - 9 * q^13 - 10 * q^14 - 3 * q^15 + 2 * q^16 + 2 * q^17 + 24 * q^18 + 10 * q^19 - 7 * q^20 - 6 * q^21 - 11 * q^22 - 11 * q^23 - 3 * q^24 - 28 * q^25 + 4 * q^26 - 33 * q^27 + 5 * q^28 + 15 * q^29 - 12 * q^30 - 12 * q^31 + 8 * q^32 + 15 * q^33 - 11 * q^34 + 19 * q^35 + q^36 + 16 * q^37 - 10 * q^38 + 24 * q^39 + 4 * q^40 - 20 * q^41 - 19 * q^42 - 21 * q^43 - 4 * q^44 + 17 * q^45 + 2 * q^46 - 11 * q^47 + q^48 - 10 * q^49 + 4 * q^50 - 56 * q^51 - 2 * q^52 - 8 * q^53 + 41 * q^54 + 35 * q^55 + 10 * q^56 + 49 * q^57 - 10 * q^58 + 35 * q^59 + 6 * q^60 + 15 * q^61 + 16 * q^62 - 26 * q^63 - 4 * q^64 + 24 * q^65 + 10 * q^66 + 22 * q^67 + 12 * q^68 + 46 * q^69 + 28 * q^70 + 10 * q^71 + 2 * q^72 + 9 * q^73 - 7 * q^74 - 15 * q^75 - 20 * q^76 + 2 * q^77 + 11 * q^78 + 10 * q^79 - 4 * q^80 - 27 * q^81 + 15 * q^82 - 45 * q^83 + 17 * q^84 + 2 * q^85 + 11 * q^86 - 9 * q^87 - 8 * q^88 - 26 * q^89 + 8 * q^90 - 84 * q^91 - 47 * q^92 - 33 * q^93 - 2 * q^94 + 37 * q^95 + 9 * q^96 - 41 * q^97 - 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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