LMFDB - Embedded newform 122.2.i.a.83.2

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			83.2
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	122.83
Dual form			122.2.i.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 - 0.743145i) q^{2} +(0.852091 - 2.62247i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(0.708788 - 0.315573i) q^{5} +(-2.51903 + 1.12155i) q^{6} +(1.40187 + 0.297977i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-3.72422 - 2.70581i) q^{9} +O(q^{10})$	\(q+(-0.669131 - 0.743145i) q^{2} +(0.852091 - 2.62247i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(0.708788 - 0.315573i) q^{5} +(-2.51903 + 1.12155i) q^{6} +(1.40187 + 0.297977i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-3.72422 - 2.70581i) q^{9} +(-0.708788 - 0.315573i) q^{10} -2.82868 q^{11} +(2.51903 + 1.12155i) q^{12} +(-2.60712 + 4.51566i) q^{13} +(-0.716596 - 1.24118i) q^{14} +(-0.223627 - 2.12767i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(0.258271 - 2.45728i) q^{17} +(0.481186 + 4.57818i) q^{18} +(6.95903 - 1.47919i) q^{19} +(0.239756 + 0.737892i) q^{20} +(1.97596 - 3.42246i) q^{21} +(1.89276 + 2.10212i) q^{22} +(4.93925 + 3.58857i) q^{23} +(-0.852091 - 2.62247i) q^{24} +(-2.94286 + 3.26838i) q^{25} +(5.10030 - 1.08410i) q^{26} +(-3.57686 + 2.59874i) q^{27} +(-0.442880 + 1.36305i) q^{28} +(-0.287655 - 0.498233i) q^{29} +(-1.43153 + 1.58988i) q^{30} +(0.252656 - 0.280603i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.41029 + 7.41812i) q^{33} +(-1.99894 + 1.45231i) q^{34} +(1.08766 - 0.231190i) q^{35} +(3.08027 - 3.42099i) q^{36} +(2.49835 + 7.68913i) q^{37} +(-5.75575 - 4.18180i) q^{38} +(9.62068 + 10.6848i) q^{39} +(0.387933 - 0.671919i) q^{40} +(-3.03062 - 9.32728i) q^{41} +(-3.86556 + 0.821650i) q^{42} +(0.460214 + 4.37865i) q^{43} +(0.295677 - 2.81318i) q^{44} +(-3.49357 - 0.742581i) q^{45} +(-0.638172 - 6.07180i) q^{46} +(-4.19497 - 7.26591i) q^{47} +(-1.37871 + 2.38800i) q^{48} +(-4.51836 - 2.01170i) q^{49} +4.39803 q^{50} +(-6.22408 - 2.77114i) q^{51} +(-4.21841 - 3.06485i) q^{52} +(-2.36878 + 1.72102i) q^{53} +(4.32463 + 0.919228i) q^{54} +(-2.00493 + 0.892654i) q^{55} +(1.30929 - 0.582931i) q^{56} +(2.05061 - 19.5102i) q^{57} +(-0.177781 + 0.547153i) q^{58} +(9.07635 + 10.0803i) q^{59} +2.13939 q^{60} +(7.68733 - 1.38022i) q^{61} -0.377589 q^{62} +(-4.41462 - 4.90293i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.422875 + 4.02339i) q^{65} +(7.12554 - 3.17249i) q^{66} +(-11.0005 + 4.89775i) q^{67} +(2.41683 + 0.513712i) q^{68} +(13.6196 - 9.89523i) q^{69} +(-0.899598 - 0.653596i) q^{70} +(-11.3658 - 5.06037i) q^{71} -4.60340 q^{72} +(-7.61739 - 3.39148i) q^{73} +(4.04241 - 7.00166i) q^{74} +(6.06362 + 10.5025i) q^{75} +(0.743668 + 7.07553i) q^{76} +(-3.96545 - 0.842882i) q^{77} +(1.50290 - 14.2991i) q^{78} +(-0.259169 - 2.46583i) q^{79} +(-0.758911 + 0.161312i) q^{80} +(-0.500280 - 1.53970i) q^{81} +(-4.90364 + 8.49335i) q^{82} +(0.405775 + 0.450659i) q^{83} +(3.19717 + 2.32288i) q^{84} +(-0.592393 - 1.82320i) q^{85} +(2.94602 - 3.27189i) q^{86} +(-1.55171 + 0.329826i) q^{87} +(-2.28845 + 1.66266i) q^{88} +(-2.77648 + 8.54513i) q^{89} +(1.78581 + 3.09311i) q^{90} +(-5.00042 + 5.55352i) q^{91} +(-4.08521 + 4.53708i) q^{92} +(-0.520587 - 0.901683i) q^{93} +(-2.59264 + 7.97931i) q^{94} +(4.46569 - 3.24451i) q^{95} +(2.69717 - 0.573301i) q^{96} +(-8.00452 + 8.88992i) q^{97} +(1.52839 + 4.70389i) q^{98} +(10.5346 + 7.65386i) 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 $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$2$	−0.669131	−	0.743145i	−0.473147	−	0.525483i
$3$	0.852091	−	2.62247i	0.491955	−	1.51408i	−0.329694	−	0.944088i	$-0.606945\pi$
$3$	0.852091	−	2.62247i	0.491955	−	1.51408i	0.821649	−	0.569994i	$-0.193055\pi$
$4$	−0.104528	+	0.994522i	−0.0522642	+	0.497261i
$5$	0.708788	−	0.315573i	0.316980	−	0.141129i	−0.242079	−	0.970257i	$-0.577829\pi$
$5$	0.708788	−	0.315573i	0.316980	−	0.141129i	0.559059	+	0.829128i	$0.311163\pi$
$6$	−2.51903	+	1.12155i	−1.02839	+	0.457869i
$7$	1.40187	+	0.297977i	0.529858	+	0.112625i	0.465069	−	0.885274i	$-0.346029\pi$
$7$	1.40187	+	0.297977i	0.529858	+	0.112625i	0.0647886	+	0.997899i	$0.479363\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−3.72422	−	2.70581i	−1.24141	−	0.901936i
$10$	−0.708788	−	0.315573i	−0.224139	−	0.0997929i
$11$	−2.82868			−0.852879			−0.426439	−	0.904516i	$-0.640232\pi$
$11$	−2.82868			−0.852879			−0.426439	+	0.904516i	$0.640232\pi$
$12$	2.51903	+	1.12155i	0.727182	+	0.323762i
$13$	−2.60712	+	4.51566i	−0.723085	+	1.25242i	0.236672	+	0.971590i	$0.423943\pi$
$13$	−2.60712	+	4.51566i	−0.723085	+	1.25242i	−0.959757	+	0.280831i	$0.909390\pi$
$14$	−0.716596	−	1.24118i	−0.191518	−	0.331719i
$15$	−0.223627	−	2.12767i	−0.0577403	−	0.549362i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	0.258271	−	2.45728i	0.0626399	−	0.595979i	−0.917509	−	0.397715i	$-0.869803\pi$
$17$	0.258271	−	2.45728i	0.0626399	−	0.595979i	0.980149	−	0.198264i	$-0.0635302\pi$
$18$	0.481186	+	4.57818i	0.113417	+	1.07909i
$19$	6.95903	−	1.47919i	1.59651	−	0.339349i	0.678098	−	0.734971i	$-0.262804\pi$
$19$	6.95903	−	1.47919i	1.59651	−	0.339349i	0.918413	+	0.395622i	$0.129471\pi$
$20$	0.239756	+	0.737892i	0.0536110	+	0.164998i
$21$	1.97596	−	3.42246i	0.431190	−	0.746842i
$22$	1.89276	+	2.10212i	0.403537	+	0.448173i
$23$	4.93925	+	3.58857i	1.02990	+	0.748269i	0.968290	−	0.249831i	$-0.0803749\pi$
$23$	4.93925	+	3.58857i	1.02990	+	0.748269i	0.0616150	+	0.998100i	$0.480375\pi$
$24$	−0.852091	−	2.62247i	−0.173932	−	0.535309i
$25$	−2.94286	+	3.26838i	−0.588572	+	0.653675i
$26$	5.10030	−	1.08410i	1.00025	−	0.212610i
$27$	−3.57686	+	2.59874i	−0.688367	+	0.500128i
$28$	−0.442880	+	1.36305i	−0.0836965	+	0.257591i
$29$	−0.287655	−	0.498233i	−0.0534162	−	0.0925196i	0.838081	−	0.545546i	$-0.183678\pi$
$29$	−0.287655	−	0.498233i	−0.0534162	−	0.0925196i	−0.891497	+	0.453026i	$0.850344\pi$
$30$	−1.43153	+	1.58988i	−0.261361	+	0.290271i
$31$	0.252656	−	0.280603i	0.0453784	−	0.0503979i	−0.720028	−	0.693945i	$-0.755871\pi$
$31$	0.252656	−	0.280603i	0.0453784	−	0.0503979i	0.765407	+	0.643547i	$0.222538\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.41029	+	7.41812i	−0.419578	+	1.29133i
$34$	−1.99894	+	1.45231i	−0.342815	+	0.249069i
$35$	1.08766	−	0.231190i	0.183849	−	0.0390783i
$36$	3.08027	−	3.42099i	0.513379	−	0.570165i
$37$	2.49835	+	7.68913i	0.410726	+	1.26408i	0.916018	+	0.401136i	$0.131385\pi$
$37$	2.49835	+	7.68913i	0.410726	+	1.26408i	−0.505292	+	0.862948i	$0.668615\pi$
$38$	−5.75575	−	4.18180i	−0.933707	−	0.678378i
$39$	9.62068	+	10.6848i	1.54054	+	1.71094i
$40$	0.387933	−	0.671919i	0.0613376	−	0.106240i
$41$	−3.03062	−	9.32728i	−0.473303	−	1.45668i	−0.848233	−	0.529623i	$-0.822333\pi$
$41$	−3.03062	−	9.32728i	−0.473303	−	1.45668i	0.374931	−	0.927053i	$-0.377667\pi$
$42$	−3.86556	+	0.821650i	−0.596469	+	0.126783i
$43$	0.460214	+	4.37865i	0.0701820	+	0.667737i	0.971897	+	0.235406i	$0.0756421\pi$
$43$	0.460214	+	4.37865i	0.0701820	+	0.667737i	−0.901715	+	0.432331i	$0.857691\pi$
$44$	0.295677	−	2.81318i	0.0445750	−	0.424103i
$45$	−3.49357	−	0.742581i	−0.520790	−	0.110697i
$46$	−0.638172	−	6.07180i	−0.0940933	−	0.895238i
$47$	−4.19497	−	7.26591i	−0.611900	−	1.05984i	−0.990920	−	0.134453i	$-0.957072\pi$
$47$	−4.19497	−	7.26591i	−0.611900	−	1.05984i	0.379020	−	0.925388i	$-0.376261\pi$
$48$	−1.37871	+	2.38800i	−0.199000	+	0.344678i
$49$	−4.51836	−	2.01170i	−0.645480	−	0.287386i
$50$	4.39803			0.621976
$51$	−6.22408	−	2.77114i	−0.871545	−	0.388037i
$52$	−4.21841	−	3.06485i	−0.584988	−	0.425019i
$53$	−2.36878	+	1.72102i	−0.325377	+	0.236400i	−0.738466	−	0.674290i	$-0.764450\pi$
$53$	−2.36878	+	1.72102i	−0.325377	+	0.236400i	0.413090	+	0.910690i	$0.364450\pi$
$54$	4.32463	+	0.919228i	0.588507	+	0.125091i
$55$	−2.00493	+	0.892654i	−0.270345	+	0.120365i
$56$	1.30929	−	0.582931i	0.174961	−	0.0778975i
$57$	2.05061	−	19.5102i	0.271610	−	2.58419i
$58$	−0.177781	+	0.547153i	−0.0233437	+	0.0718446i
$59$	9.07635	+	10.0803i	1.18164	+	1.31234i	0.939678	+	0.342059i	$0.111124\pi$
$59$	9.07635	+	10.0803i	1.18164	+	1.31234i	0.241962	+	0.970286i	$0.422209\pi$
$60$	2.13939			0.276194
$61$	7.68733	−	1.38022i	0.984261	−	0.176720i
$61$	7.68733	−	1.38022i	0.984261	−	0.176720i
$62$	−0.377589			−0.0479539
$63$	−4.41462	−	4.90293i	−0.556190	−	0.617711i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.422875	+	4.02339i	−0.0524512	+	0.499040i
$66$	7.12554	−	3.17249i	0.877093	−	0.390507i
$67$	−11.0005	+	4.89775i	−1.34393	+	0.598356i	−0.947514	−	0.319715i	$-0.896413\pi$
$67$	−11.0005	+	4.89775i	−1.34393	+	0.598356i	−0.396416	+	0.918071i	$0.629746\pi$
$68$	2.41683	+	0.513712i	0.293083	+	0.0622968i
$69$	13.6196	−	9.89523i	1.63961	−	1.19125i
$70$	−0.899598	−	0.653596i	−0.107522	−	0.0781197i
$71$	−11.3658	−	5.06037i	−1.34887	−	0.600556i	−0.400086	−	0.916478i	$-0.631020\pi$
$71$	−11.3658	−	5.06037i	−1.34887	−	0.600556i	−0.948785	+	0.315922i	$0.897686\pi$
$72$	−4.60340			−0.542515
$73$	−7.61739	−	3.39148i	−0.891548	−	0.396943i	−0.0907478	−	0.995874i	$-0.528926\pi$
$73$	−7.61739	−	3.39148i	−0.891548	−	0.396943i	−0.800801	+	0.598931i	$0.795592\pi$
$74$	4.04241	−	7.00166i	0.469921	−	0.813927i
$75$	6.06362	+	10.5025i	0.700167	+	1.21272i
$76$	0.743668	+	7.07553i	0.0853046	+	0.811619i
$77$	−3.96545	−	0.842882i	−0.451905	−	0.0960553i
$78$	1.50290	−	14.2991i	0.170170	−	1.61906i
$79$	−0.259169	−	2.46583i	−0.0291588	−	0.277427i	−0.999380	−	0.0352070i	$-0.988791\pi$
$79$	−0.259169	−	2.46583i	−0.0291588	−	0.277427i	0.970221	−	0.242220i	$-0.0778757\pi$
$80$	−0.758911	+	0.161312i	−0.0848488	+	0.0180352i
$81$	−0.500280	−	1.53970i	−0.0555866	−	0.171078i
$82$	−4.90364	+	8.49335i	−0.541516	+	0.937934i
$83$	0.405775	+	0.450659i	0.0445396	+	0.0494663i	0.765003	−	0.644027i	$-0.222737\pi$
$83$	0.405775	+	0.450659i	0.0445396	+	0.0494663i	−0.720463	+	0.693493i	$0.756071\pi$
$84$	3.19717	+	2.32288i	0.348840	+	0.253447i
$85$	−0.592393	−	1.82320i	−0.0642540	−	0.197754i
$86$	2.94602	−	3.27189i	0.317678	−	0.352817i
$87$	−1.55171	+	0.329826i	−0.166361	+	0.0353610i
$88$	−2.28845	+	1.66266i	−0.243949	+	0.177240i
$89$	−2.77648	+	8.54513i	−0.294306	+	0.905782i	0.689147	+	0.724622i	$0.257985\pi$
$89$	−2.77648	+	8.54513i	−0.294306	+	0.905782i	−0.983454	+	0.181161i	$0.942015\pi$
$90$	1.78581	+	3.09311i	0.188241	+	0.326042i
$91$	−5.00042	+	5.55352i	−0.524186	+	0.582168i
$92$	−4.08521	+	4.53708i	−0.425912	+	0.473024i
$93$	−0.520587	−	0.901683i	−0.0539824	−	0.0935002i
$94$	−2.59264	+	7.97931i	−0.267410	+	0.823003i
$95$	4.46569	−	3.24451i	0.458170	−	0.332880i
$96$	2.69717	−	0.573301i	0.275279	−	0.0585123i
$97$	−8.00452	+	8.88992i	−0.812736	+	0.902635i	−0.996772	−	0.0802848i	$-0.974417\pi$
$97$	−8.00452	+	8.88992i	−0.812736	+	0.902635i	0.184036	+	0.982920i	$0.441084\pi$
$98$	1.52839	+	4.70389i	0.154390	+	0.475165i
$99$	10.5346	+	7.65386i	1.05877	+	0.769242i
$100$	−2.94286	−	3.26838i	−0.294286	−	0.326838i
$101$	−7.49884	+	12.9884i	−0.746163	+	1.29239i	0.203487	+	0.979078i	$0.434773\pi$
$101$	−7.49884	+	12.9884i	−0.746163	+	1.29239i	−0.949650	+	0.313314i	$0.898561\pi$
$102$	2.10536	+	6.47964i	0.208462	+	0.641580i
$103$	8.57731	−	1.82316i	0.845147	−	0.179642i	0.235065	−	0.971980i	$-0.424470\pi$
$103$	8.57731	−	1.82316i	0.845147	−	0.179642i	0.610082	+	0.792338i	$0.291136\pi$
$104$	0.545037	+	5.18568i	0.0534452	+	0.508497i
$105$	0.320501	−	3.04936i	0.0312777	−	0.297587i
$106$	2.86399	+	0.608760i	0.278175	+	0.0591280i
$107$	−0.208563	−	1.98434i	−0.0201625	−	0.191834i	0.979804	−	0.199958i	$-0.0640806\pi$
$107$	−0.208563	−	1.98434i	−0.0201625	−	0.191834i	−0.999967	+	0.00812434i	$0.997414\pi$
$108$	−2.21062	−	3.82891i	−0.212717	−	0.368437i
$109$	6.46127	−	11.1912i	0.618878	−	1.07193i	−0.370813	−	0.928707i	$-0.620921\pi$
$109$	6.46127	−	11.1912i	0.618878	−	1.07193i	0.989691	−	0.143220i	$-0.0457456\pi$
$110$	2.00493	+	0.892654i	0.191163	+	0.0851113i
$111$	22.2933			2.11599
$112$	−1.30929	−	0.582931i	−0.123716	−	0.0550818i
$113$	−0.580453	−	0.421724i	−0.0546044	−	0.0396724i	0.560148	−	0.828392i	$-0.310744\pi$
$113$	−0.580453	−	0.421724i	−0.0546044	−	0.0396724i	−0.614753	+	0.788720i	$0.710744\pi$
$114$	−15.8711	+	11.5310i	−1.48646	+	1.07998i
$115$	4.63334	+	0.984847i	0.432061	+	0.0918374i
$116$	0.525572	−	0.234000i	0.0487981	−	0.0217263i
$117$	21.9280	−	9.76298i	2.02725	−	0.902588i
$118$	1.41787	−	13.4901i	0.130525	−	1.24186i
$119$	1.09428	−	3.36784i	0.100312	−	0.308729i
$120$	−1.43153	−	1.58988i	−0.130680	−	0.145135i
$121$	−2.99858			−0.272598
$122$	−6.16953	−	4.78925i	−0.558563	−	0.433598i
$123$	−27.0428			−2.43837
$124$	0.252656	+	0.280603i	0.0226892	+	0.0251989i
$125$	−2.25323	+	6.93473i	−0.201535	+	0.620261i
$126$	−0.689631	+	6.56140i	−0.0614372	+	0.584536i
$127$	16.0431	−	7.14284i	1.42359	−	0.633825i	0.456843	−	0.889547i	$-0.348980\pi$
$127$	16.0431	−	7.14284i	1.42359	−	0.633825i	0.966750	+	0.255723i	$0.0823134\pi$
$128$	−0.913545	+	0.406737i	−0.0807468	+	0.0359508i
$129$	11.8750	+	2.52411i	1.04554	+	0.222235i
$130$	3.27292	−	2.37791i	0.287054	−	0.208557i
$131$	−4.98044	−	3.61850i	−0.435143	−	0.316150i	0.348559	−	0.937287i	$-0.386671\pi$
$131$	−4.98044	−	3.61850i	−0.435143	−	0.316150i	−0.783702	+	0.621137i	$0.786671\pi$
$132$	−7.12554	−	3.17249i	−0.620198	−	0.276130i
$133$	10.1964			0.884144
$134$	11.0005	+	4.89775i	0.950301	+	0.423101i
$135$	−1.71514	+	2.97072i	−0.147616	+	0.255679i
$136$	−1.23541	−	2.13979i	−0.105936	−	0.183486i
$137$	0.734575	+	6.98901i	0.0627590	+	0.597112i	0.980030	+	0.198849i	$0.0637202\pi$
$137$	0.734575	+	6.98901i	0.0627590	+	0.597112i	−0.917271	+	0.398263i	$0.869613\pi$
$138$	−16.4669	−	3.50014i	−1.40175	−	0.297952i
$139$	0.710175	−	6.75687i	0.0602363	−	0.573110i	−0.922226	−	0.386650i	$-0.873632\pi$
$139$	0.710175	−	6.75687i	0.0602363	−	0.573110i	0.982463	−	0.186460i	$-0.0597013\pi$
$140$	0.116232	+	1.10587i	0.00982339	+	0.0934633i
$141$	−22.6291	+	4.80997i	−1.90571	+	0.405072i
$142$	3.84461	+	11.8325i	0.322632	+	0.992960i
$143$	7.37470	−	12.7734i	0.616704	−	1.06816i
$144$	3.08027	+	3.42099i	0.256689	+	0.285082i
$145$	−0.361116	−	0.262366i	−0.0299890	−	0.0217883i
$146$	2.57667	+	7.93017i	0.213247	+	0.656306i
$147$	−9.12569	+	10.1351i	−0.752674	+	0.835929i
$148$	−7.90815	+	1.68093i	−0.650046	+	0.138172i
$149$	−5.37090	+	3.90219i	−0.440001	+	0.319680i	−0.785635	−	0.618690i	$-0.787664\pi$
$149$	−5.37090	+	3.90219i	−0.440001	+	0.319680i	0.345634	+	0.938369i	$0.387664\pi$
$150$	3.74753	−	11.5337i	0.305984	−	0.941722i
$151$	−4.09266	−	7.08869i	−0.333056	−	0.576870i	0.650054	−	0.759888i	$-0.274746\pi$
$151$	−4.09266	−	7.08869i	−0.333056	−	0.576870i	−0.983109	+	0.183019i	$0.941413\pi$
$152$	4.76053	−	5.28711i	0.386130	−	0.428841i
$153$	−7.61080	+	8.45265i	−0.615297	+	0.683356i
$154$	2.02702	+	3.51090i	0.163342	+	0.282916i
$155$	0.0905291	−	0.278620i	0.00727147	−	0.0223793i
$156$	−11.6319	+	8.45111i	−0.931301	+	0.676630i
$157$	5.05067	−	1.07355i	0.403087	−	0.0856788i	−0.00190679	−	0.999998i	$-0.500607\pi$
$157$	5.05067	−	1.07355i	0.403087	−	0.0856788i	0.404994	+	0.914319i	$0.367274\pi$
$158$	−1.65905	+	1.84256i	−0.131987	+	0.146586i
$159$	2.49490	+	7.67851i	0.197858	+	0.608946i
$160$	0.627688	+	0.456042i	0.0496231	+	0.0360533i
$161$	5.85488	+	6.50251i	0.461430	+	0.512469i
$162$	−0.809469	+	1.40204i	−0.0635979	+	0.110155i
$163$	−2.06673	−	6.36075i	−0.161879	−	0.498212i	0.836914	−	0.547335i	$-0.184358\pi$
$163$	−2.06673	−	6.36075i	−0.161879	−	0.498212i	−0.998793	+	0.0491226i	$0.984358\pi$
$164$	9.59297	−	2.03905i	0.749085	−	0.159223i
$165$	0.632570	+	6.01850i	0.0492455	+	0.468539i
$166$	0.0633883	−	0.603100i	0.00491989	−	0.0468096i
$167$	−14.4348	−	3.06821i	−1.11700	−	0.237425i	−0.387809	−	0.921740i	$-0.626768\pi$
$167$	−14.4348	−	3.06821i	−1.11700	−	0.237425i	−0.729187	+	0.684315i	$0.760101\pi$
$168$	−0.413088	−	3.93027i	−0.0318704	−	0.303227i
$169$	−7.09415	−	12.2874i	−0.545704	−	0.945187i
$170$	−0.958512	+	1.66019i	−0.0735145	+	0.127331i
$171$	−29.9194	−	13.3210i	−2.28799	−	1.01868i
$172$	−4.40276			−0.335708
$173$	5.49021	+	2.44440i	0.417413	+	0.185844i	0.604687	−	0.796464i	$-0.293298\pi$
$173$	5.49021	+	2.44440i	0.417413	+	0.185844i	−0.187273	+	0.982308i	$0.559965\pi$
$174$	1.28340	+	0.932448i	0.0972946	+	0.0706887i
$175$	−5.09941	+	3.70494i	−0.385479	+	0.280067i
$176$	2.76686	+	0.588115i	0.208560	+	0.0443309i
$177$	34.1692	−	15.2131i	2.56831	−	1.14349i
$178$	8.20810	−	3.65448i	0.615223	−	0.273915i
$179$	2.12648	−	20.2321i	0.158941	−	1.51222i	−0.566572	−	0.824012i	$-0.691731\pi$
$179$	2.12648	−	20.2321i	0.158941	−	1.51222i	0.725513	−	0.688209i	$-0.241603\pi$
$180$	1.10369	−	3.39681i	0.0822642	−	0.253183i
$181$	−9.13204	−	10.1422i	−0.678779	−	0.753861i	0.301069	−	0.953602i	$-0.402656\pi$
$181$	−9.13204	−	10.1422i	−0.678779	−	0.753861i	−0.979849	+	0.199742i	$0.935990\pi$
$182$	7.47300			0.553936
$183$	2.93071	−	21.3358i	0.216644	−	1.57719i
$184$	6.10525			0.450085
$185$	4.19728	+	4.66155i	0.308590	+	0.342724i
$186$	−0.321740	+	0.990215i	−0.0235912	+	0.0726061i
$187$	−0.730566	+	6.95087i	−0.0534242	+	0.508298i
$188$	7.66460	−	3.41250i	0.558998	−	0.248882i
$189$	−5.78867	+	2.57728i	−0.421064	+	0.187470i
$190$	−5.39928	−	1.14765i	−0.391705	−	0.0832594i
$191$	−4.77227	+	3.46726i	−0.345309	+	0.250882i	−0.746899	−	0.664938i	$-0.768458\pi$
$191$	−4.77227	+	3.46726i	−0.345309	+	0.250882i	0.401589	+	0.915820i	$0.368458\pi$
$192$	−2.23080	−	1.62077i	−0.160994	−	0.116969i
$193$	11.2471	+	5.00751i	0.809581	+	0.360449i	0.769419	−	0.638744i	$-0.220546\pi$
$193$	11.2471	+	5.00751i	0.809581	+	0.360449i	0.0401621	+	0.999193i	$0.487213\pi$
$194$	11.9626			0.858862
$195$	10.1909	+	4.53727i	0.729784	+	0.324921i
$196$	2.47298	−	4.28333i	0.176642	−	0.305952i
$197$	0.673828	+	1.16710i	0.0480083	+	0.0831527i	0.889031	−	0.457847i	$-0.151379\pi$
$197$	0.673828	+	1.16710i	0.0480083	+	0.0831527i	−0.841023	+	0.541000i	$0.818046\pi$
$198$	−1.36112	−	12.9502i	−0.0967306	−	0.920330i
$199$	19.7317	+	4.19410i	1.39874	+	0.297312i	0.844728	−	0.535196i	$-0.179762\pi$
$199$	19.7317	+	4.19410i	1.39874	+	0.297312i	0.554014	+	0.832507i	$0.313095\pi$
$200$	−0.459720	+	4.37394i	−0.0325071	+	0.309284i
$201$	3.47074	+	33.0219i	0.244807	+	2.32918i
$202$	14.6700	−	3.11819i	1.03217	−	0.219395i
$203$	−0.254794	−	0.784174i	−0.0178830	−	0.0550382i
$204$	3.40655	−	5.90032i	0.238506	−	0.413105i
$205$	−5.09150	−	5.65468i	−0.355606	−	0.394940i
$206$	−7.09421	−	5.15425i	−0.494277	−	0.359114i
$207$	−8.68488	−	26.7293i	−0.603641	−	1.85782i
$208$	3.48901	−	3.87494i	0.241919	−	0.268678i
$209$	−19.6849	+	4.18415i	−1.36163	+	0.289424i
$210$	−2.48057	+	1.80224i	−0.171176	+	0.124367i
$211$	4.64891	−	14.3079i	0.320044	−	0.984996i	−0.653584	−	0.756854i	$-0.726735\pi$
$211$	4.64891	−	14.3079i	0.320044	−	0.984996i	0.973628	−	0.228141i	$-0.0732648\pi$
$212$	−1.46399	−	2.53570i	−0.100547	−	0.174152i
$213$	−22.9554	+	25.4945i	−1.57288	+	1.74685i
$214$	−1.33510	+	1.48278i	−0.0912655	+	0.101361i
$215$	1.70798	+	2.95830i	0.116483	+	0.201755i
$216$	−1.36624	+	4.20485i	−0.0929608	+	0.286104i
$217$	0.437806	−	0.318084i	0.0297202	−	0.0215930i
$218$	−12.6402	+	2.68675i	−0.856099	+	0.181970i
$219$	−15.3848	+	17.0865i	−1.03961	+	1.15460i
$220$	−0.678192	−	2.08726i	−0.0457237	−	0.140723i
$221$	10.4229	+	7.57270i	0.701122	+	0.509395i
$222$	−14.9171	−	16.5672i	−1.00117	−	1.11191i
$223$	8.58137	−	14.8634i	0.574651	−	0.995325i	−0.421429	−	0.906862i	$-0.638471\pi$
$223$	8.58137	−	14.8634i	0.574651	−	0.995325i	0.996079	−	0.0884629i	$-0.0281955\pi$
$224$	0.442880	+	1.36305i	0.0295912	+	0.0910723i
$225$	19.8035	−	4.20936i	1.32023	−	0.280624i
$226$	0.0749970	+	0.713549i	0.00498873	+	0.0474646i
$227$	−0.594247	+	5.65388i	−0.0394415	+	0.375261i	0.956941	+	0.290282i	$0.0937491\pi$
$227$	−0.594247	+	5.65388i	−0.0394415	+	0.375261i	−0.996383	+	0.0849793i	$0.972918\pi$
$228$	19.1890	+	4.07875i	1.27082	+	0.270122i
$229$	1.09867	+	10.4532i	0.0726024	+	0.690766i	0.968924	+	0.247360i	$0.0795632\pi$
$229$	1.09867	+	10.4532i	0.0726024	+	0.690766i	−0.896321	+	0.443406i	$0.853770\pi$
$230$	−2.36843	−	4.10223i	−0.156169	−	0.270493i
$231$	−5.58935	+	9.68104i	−0.367752	+	0.636966i
$232$	−0.525572	−	0.234000i	−0.0345055	−	0.0153628i
$233$	13.0660			0.855980			0.427990	−	0.903784i	$-0.359222\pi$
$233$	13.0660			0.855980			0.427990	+	0.903784i	$0.359222\pi$
$234$	−21.9280	−	9.76298i	−1.43348	−	0.638226i
$235$	−5.26627	−	3.82617i	−0.343534	−	0.249592i
$236$	−10.9738	+	7.97295i	−0.714335	+	0.518995i
$237$	−6.68739	−	1.42145i	−0.434393	−	0.0923330i
$238$	−3.23501	+	1.44032i	−0.209694	+	0.0933620i
$239$	−3.79493	+	1.68961i	−0.245473	+	0.109292i	−0.525786	−	0.850617i	$-0.676229\pi$
$239$	−3.79493	+	1.68961i	−0.245473	+	0.109292i	0.280312	+	0.959909i	$0.409562\pi$
$240$	−0.223627	+	2.12767i	−0.0144351	+	0.137341i
$241$	8.09497	−	24.9138i	0.521443	−	1.60484i	−0.249801	−	0.968297i	$-0.580365\pi$
$241$	8.09497	−	24.9138i	0.521443	−	1.60484i	0.771244	−	0.636540i	$-0.219635\pi$
$242$	2.00644	+	2.22838i	0.128979	+	0.143246i
$243$	−17.7278			−1.13724
$244$	0.569118	+	7.78949i	0.0364341	+	0.498671i
$245$	−3.83740			−0.245163
$246$	18.0952	+	20.0967i	1.15371	+	1.28132i
$247$	−11.4635	+	35.2811i	−0.729406	+	2.24488i
$248$	0.0394688	−	0.375521i	0.00250627	−	0.0238456i
$249$	1.52760	−	0.680130i	0.0968075	−	0.0431015i
$250$	6.66122	−	2.96576i	0.421292	−	0.187571i
$251$	24.8310	+	5.27800i	1.56732	+	0.333144i	0.908083	−	0.418790i	$-0.137546\pi$
$251$	24.8310	+	5.27800i	1.56732	+	0.333144i	0.659238	+	0.751934i	$0.270879\pi$
$252$	5.33753	−	3.87794i	0.336233	−	0.244287i
$253$	−13.9715	−	10.1509i	−0.878383	−	0.638183i
$254$	−16.0431	−	7.14284i	−1.00663	−	0.448182i
$255$	−5.28605			−0.331025
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−12.4140	+	21.5017i	−0.774366	+	1.34124i	0.160784	+	0.986990i	$0.448598\pi$
$257$	−12.4140	+	21.5017i	−0.774366	+	1.34124i	−0.935150	+	0.354252i	$0.884735\pi$
$258$	−6.07015	−	10.5138i	−0.377911	−	0.654561i
$259$	1.21118	+	11.5236i	0.0752592	+	0.716043i
$260$	−3.95714	−	0.841117i	−0.245412	−	0.0521639i
$261$	−0.276831	+	2.63387i	−0.0171354	+	0.163033i
$262$	0.643494	+	6.12244i	0.0397552	+	0.378246i
$263$	−8.94226	+	1.90074i	−0.551403	+	0.117204i	−0.475184	−	0.879887i	$-0.657618\pi$
$263$	−8.94226	+	1.90074i	−0.551403	+	0.117204i	−0.0762197	+	0.997091i	$0.524285\pi$
$264$	2.41029	+	7.41812i	0.148343	+	0.456554i
$265$	−1.13586	+	1.96736i	−0.0697751	+	0.120854i
$266$	−6.82275	−	7.57743i	−0.418330	−	0.464602i
$267$	20.0435	+	14.5625i	1.22664	+	0.891208i
$268$	−3.72105	−	11.4522i	−0.227300	−	0.699556i
$269$	15.2447	−	16.9309i	0.929484	−	1.03230i	−0.0699121	−	0.997553i	$-0.522272\pi$
$269$	15.2447	−	16.9309i	0.929484	−	1.03230i	0.999396	−	0.0347435i	$-0.0110614\pi$
$270$	3.35533	−	0.713197i	0.204199	−	0.0434038i
$271$	−2.53555	+	1.84218i	−0.154023	+	0.111905i	−0.662128	−	0.749391i	$-0.730346\pi$
$271$	−2.53555	+	1.84218i	−0.154023	+	0.111905i	0.508104	+	0.861296i	$0.330346\pi$
$272$	−0.763525	+	2.34989i	−0.0462955	+	0.142483i
$273$	10.3031	+	17.8455i	0.623574	+	1.08006i
$274$	4.70232	−	5.22246i	0.284078	−	0.315500i
$275$	8.32440	−	9.24518i	0.501980	−	0.557505i
$276$	8.41738	+	14.5793i	0.506667	+	0.877573i
$277$	−5.07143	+	15.6083i	−0.304713	+	0.937810i	0.675071	+	0.737753i	$0.264113\pi$
$277$	−5.07143	+	15.6083i	−0.304713	+	0.937810i	−0.979784	+	0.200057i	$0.935887\pi$
$278$	−5.49653	+	3.99346i	−0.329660	+	0.239512i
$279$	−1.70021	+	0.361390i	−0.101789	+	0.0216359i
$280$	0.744049	−	0.826350i	0.0444654	−	0.0493839i
$281$	−5.75453	−	17.7106i	−0.343287	−	1.05653i	−0.962495	−	0.271301i	$-0.912546\pi$
$281$	−5.75453	−	17.7106i	−0.343287	−	1.05653i	0.619208	−	0.785227i	$-0.287454\pi$
$282$	18.7163	+	13.5982i	1.11454	+	0.809762i
$283$	−6.73228	−	7.47696i	−0.400193	−	0.444459i	0.509043	−	0.860741i	$-0.329999\pi$
$283$	−6.73228	−	7.47696i	−0.400193	−	0.444459i	−0.909235	+	0.416282i	$0.863333\pi$
$284$	6.22070	−	10.7746i	0.369131	−	0.639353i
$285$	−4.70346	−	14.4758i	−0.278609	−	0.857470i
$286$	−14.4271	+	3.06657i	−0.853092	+	0.181330i
$287$	−1.46922	−	13.9787i	−0.0867254	−	0.825137i
$288$	0.481186	−	4.57818i	0.0283541	−	0.269772i
$289$	10.6570	+	2.26521i	0.626880	+	0.133248i
$290$	0.0466577	+	0.443918i	0.00273983	+	0.0260678i
$291$	16.4929	+	28.5666i	0.966834	+	1.67460i
$292$	4.16914	−	7.22116i	0.243980	−	0.422586i
$293$	16.4157	+	7.30876i	0.959017	+	0.426982i	0.825711	−	0.564093i	$-0.190774\pi$
$293$	16.4157	+	7.30876i	0.959017	+	0.426982i	0.133306	+	0.991075i	$0.457441\pi$
$294$	13.6381			0.795391
$295$	9.61429	+	4.28056i	0.559766	+	0.249224i
$296$	6.54076	+	4.75214i	0.380174	+	0.276213i
$297$	10.1178	−	7.35100i	0.587094	−	0.426548i
$298$	6.49372	+	1.38028i	0.376171	+	0.0799577i
$299$	−29.0820	+	12.9481i	−1.68186	+	0.748811i
$300$	−11.0788	+	4.93260i	−0.639634	+	0.284784i
$301$	−0.659575	+	6.27544i	−0.0380173	+	0.361710i
$302$	−2.52940	+	7.78470i	−0.145551	+	0.447959i
$303$	27.6719	+	30.7328i	1.58971	+	1.76555i
$304$	−7.11450			−0.408045
$305$	5.01313	−	3.40420i	0.287051	−	0.194924i
$306$	11.3742			0.650217
$307$	−10.4390	−	11.5936i	−0.595783	−	0.661684i	0.367547	−	0.930005i	$-0.380198\pi$
$307$	−10.4390	−	11.5936i	−0.595783	−	0.661684i	−0.963330	+	0.268321i	$0.913531\pi$
$308$	1.25277	−	3.85562i	0.0713830	−	0.219694i
$309$	2.52746	−	24.0472i	0.143782	−	1.36800i
$310$	−0.267631	+	0.119157i	−0.0152004	+	0.00676766i
$311$	−11.3947	+	5.07325i	−0.646134	+	0.287678i	−0.703521	−	0.710674i	$-0.748390\pi$
$311$	−11.3947	+	5.07325i	−0.646134	+	0.287678i	0.0573866	+	0.998352i	$0.481723\pi$
$312$	14.0637	+	2.98933i	0.796200	+	0.169237i
$313$	−1.61393	+	1.17259i	−0.0912247	+	0.0662787i	−0.632463	−	0.774591i	$-0.717956\pi$
$313$	−1.61393	+	1.17259i	−0.0912247	+	0.0662787i	0.541238	+	0.840869i	$0.317956\pi$
$314$	−4.17736	−	3.03503i	−0.235742	−	0.171277i
$315$	−4.67626	−	2.08201i	−0.263478	−	0.117308i
$316$	2.47941			0.139478
$317$	5.98544	+	2.66489i	0.336176	+	0.149675i	0.567880	−	0.823111i	$-0.307764\pi$
$317$	5.98544	+	2.66489i	0.336176	+	0.149675i	−0.231705	+	0.972786i	$0.574430\pi$
$318$	4.03683	−	6.99200i	0.226374	−	0.392092i
$319$	0.813684	+	1.40934i	0.0455575	+	0.0789080i
$320$	−0.0811000	−	0.771615i	−0.00453363	−	0.0431346i
$321$	−5.38159	−	1.14389i	−0.300371	−	0.0638458i
$322$	0.914623	−	8.70205i	0.0509699	−	0.484947i
$323$	−1.83747	−	17.4824i	−0.102240	−	0.972744i
$324$	1.58356	−	0.336596i	0.0879756	−	0.0186998i
$325$	−7.08650	−	21.8100i	−0.393088	−	1.20980i
$326$	−3.34404	+	5.79205i	−0.185209	+	0.320792i
$327$	−23.8431	−	26.4804i	−1.31853	−	1.46437i
$328$	−7.93425	−	5.76457i	−0.438096	−	0.318295i
$329$	−3.71574	−	11.4359i	−0.204856	−	0.630481i
$330$	4.04934	−	4.49725i	0.222909	−	0.247566i
$331$	9.12546	−	1.93968i	0.501580	−	0.106614i	0.0498285	−	0.998758i	$-0.484133\pi$
$331$	9.12546	−	1.93968i	0.501580	−	0.106614i	0.451752	+	0.892144i	$0.350799\pi$
$332$	−0.490605	+	0.356446i	−0.0269255	+	0.0195625i
$333$	11.5009	−	35.3961i	0.630245	−	1.93969i
$334$	7.37863	+	12.7802i	0.403741	+	0.699299i
$335$	−6.25145	+	6.94294i	−0.341553	+	0.379333i
$336$	−2.64435	+	2.93685i	−0.144261	+	0.160218i
$337$	−9.76624	−	16.9156i	−0.532001	−	0.921453i	−0.999302	−	0.0373548i	$-0.988107\pi$
$337$	−9.76624	−	16.9156i	−0.532001	−	0.921453i	0.467301	−	0.884098i	$-0.345227\pi$
$338$	−4.38443	+	13.4939i	−0.238481	+	0.733970i
$339$	−1.60056	+	1.16287i	−0.0869303	+	0.0631585i
$340$	1.87513	−	0.398572i	0.101693	−	0.0216156i
$341$	−0.714684	+	0.793737i	−0.0387023	+	0.0429833i
$342$	10.1206	+	31.1479i	0.547258	+	1.68429i
$343$	−13.8511	−	10.0634i	−0.747887	−	0.543372i
$344$	2.94602	+	3.27189i	0.158839	+	0.176409i
$345$	6.53076	−	11.3116i	0.351604	−	0.608996i
$346$	−1.85713	−	5.71565i	−0.0998397	−	0.307275i
$347$	−4.85858	+	1.03272i	−0.260822	+	0.0554395i	−0.336467	−	0.941695i	$-0.609232\pi$
$347$	−4.85858	+	1.03272i	−0.260822	+	0.0554395i	0.0756443	+	0.997135i	$0.475899\pi$
$348$	−0.165821	−	1.57768i	−0.00888896	−	0.0845728i
$349$	−2.44628	+	23.2748i	−0.130946	+	1.24587i	0.709784	+	0.704419i	$0.248792\pi$
$349$	−2.44628	+	23.2748i	−0.130946	+	1.24587i	−0.840731	+	0.541453i	$0.817874\pi$
$350$	6.16548	+	1.31051i	0.329559	+	0.0700499i
$351$	−2.40974	−	22.9271i	−0.128622	−	1.22376i
$352$	−1.41434	−	2.44971i	−0.0753845	−	0.130570i
$353$	−14.9914	+	25.9660i	−0.797914	+	1.38203i	0.123058	+	0.992400i	$0.460730\pi$
$353$	−14.9914	+	25.9660i	−0.797914	+	1.38203i	−0.920972	+	0.389629i	$0.872603\pi$
$354$	−34.1692	−	15.2131i	−1.81607	−	0.808567i
$355$	−9.65286			−0.512320
$356$	−8.20810	−	3.65448i	−0.435028	−	0.193687i
$357$	−7.89963	−	5.73942i	−0.418093	−	0.303762i
$358$	−16.4583	+	11.9577i	−0.869849	+	0.631982i
$359$	9.93876	+	2.11255i	0.524548	+	0.111496i	0.462572	−	0.886582i	$-0.346927\pi$
$359$	9.93876	+	2.11255i	0.524548	+	0.111496i	0.0619755	+	0.998078i	$0.480260\pi$
$360$	−3.26283	+	1.45271i	−0.171966	+	0.0765644i
$361$	28.8828	−	12.8594i	1.52015	−	0.676813i
$362$	−1.42656	+	13.5729i	−0.0749786	+	0.713373i
$363$	−2.55506	+	7.86368i	−0.134106	+	0.412736i
$364$	−5.00042	−	5.55352i	−0.262093	−	0.291084i
$365$	−6.46938			−0.338623
$366$	−17.8166	+	12.0985i	−0.931291	+	0.632400i
$367$	21.4827			1.12139			0.560693	−	0.828024i	$-0.310535\pi$
$367$	21.4827			1.12139			0.560693	+	0.828024i	$0.310535\pi$
$368$	−4.08521	−	4.53708i	−0.212956	−	0.236512i
$369$	−13.9511	+	42.9371i	−0.726266	+	2.23522i
$370$	0.655680	−	6.23838i	0.0340872	−	0.324318i
$371$	−3.83355	+	1.70681i	−0.199028	+	0.0886130i
$372$	0.951160	−	0.423484i	0.0493153	−	0.0219566i
$373$	9.99057	+	2.12356i	0.517292	+	0.109954i	0.459158	−	0.888355i	$-0.348151\pi$
$373$	9.99057	+	2.12356i	0.517292	+	0.109954i	0.0581348	+	0.998309i	$0.481485\pi$
$374$	5.65434	−	4.10812i	0.292379	−	0.212426i
$375$	16.2662	+	11.8181i	0.839981	+	0.610282i
$376$	−7.66460	−	3.41250i	−0.395271	−	0.175986i
$377$	2.99981			0.154498
$378$	5.78867	+	2.57728i	0.297737	+	0.132561i
$379$	−8.51102	+	14.7415i	−0.437182	+	0.757221i	−0.997471	−	0.0710760i	$-0.977357\pi$
$379$	−8.51102	+	14.7415i	−0.437182	+	0.757221i	0.560289	+	0.828297i	$0.310690\pi$
$380$	2.75995	+	4.78037i	0.141582	+	0.245228i
$381$	−5.06169	−	48.1588i	−0.259318	−	2.46725i
$382$	5.76995	+	1.22644i	0.295216	+	0.0627502i
$383$	1.54117	−	14.6633i	0.0787501	−	0.749257i	−0.881889	−	0.471457i	$-0.843728\pi$
$383$	1.54117	−	14.6633i	0.0787501	−	0.749257i	0.960639	−	0.277800i	$-0.0896052\pi$
$384$	0.288229	+	2.74232i	0.0147086	+	0.139943i
$385$	−3.07665	+	0.653963i	−0.156801	+	0.0333290i
$386$	−3.80444	−	11.7089i	−0.193641	−	0.595966i
$387$	10.1338	−	17.5523i	0.515132	−	0.892234i
$388$	−8.00452	−	8.88992i	−0.406368	−	0.451317i
$389$	−11.5610	−	8.39953i	−0.586164	−	0.425873i	0.254777	−	0.967000i	$-0.417998\pi$
$389$	−11.5610	−	8.39953i	−0.586164	−	0.425873i	−0.840941	+	0.541127i	$0.817998\pi$
$390$	−3.44718	−	10.6093i	−0.174555	−	0.537224i
$391$	10.0938	−	11.2103i	0.510466	−	0.566930i
$392$	−4.83788	+	1.02832i	−0.244350	+	0.0519382i
$393$	−13.7332	+	9.97775i	−0.692748	+	0.503311i
$394$	0.416449	−	1.28170i	0.0209804	−	0.0645710i
$395$	−0.961845	−	1.66596i	−0.0483957	−	0.0838237i
$396$	−8.71310	+	9.67688i	−0.437850	+	0.486281i
$397$	−14.7668	+	16.4002i	−0.741126	+	0.823104i	−0.989343	−	0.145601i	$-0.953489\pi$
$397$	−14.7668	+	16.4002i	−0.741126	+	0.823104i	0.248218	+	0.968704i	$0.420155\pi$
$398$	−10.0863	−	17.4699i	−0.505578	−	0.875687i
$399$	8.68830	−	26.7398i	0.434959	−	1.33867i
$400$	3.55808	−	2.58510i	0.177904	−	0.129255i
$401$	30.6309	−	6.51079i	1.52963	−	0.325133i	0.635204	−	0.772344i	$-0.280916\pi$
$401$	30.6309	−	6.51079i	1.52963	−	0.325133i	0.894429	+	0.447211i	$0.147583\pi$
$402$	22.2177	−	24.6752i	1.10812	−	1.23069i
$403$	0.608405	+	1.87248i	0.0303068	+	0.0932748i
$404$	−12.1334	−	8.81542i	−0.603658	−	0.438583i
$405$	−0.840481	−	0.933449i	−0.0417638	−	0.0463834i
$406$	−0.412265	+	0.714064i	−0.0204604	+	0.0354384i
$407$	−7.06702	−	21.7501i	−0.350299	−	1.07811i
$408$	−6.66422	+	1.41652i	−0.329928	+	0.0701284i
$409$	−0.842839	−	8.01908i	−0.0416757	−	0.396518i	−0.995398	−	0.0958285i	$-0.969450\pi$
$409$	−0.842839	−	8.01908i	−0.0416757	−	0.396518i	0.953722	−	0.300689i	$-0.0972167\pi$
$410$	−0.795371	+	7.56745i	−0.0392806	+	0.373729i
$411$	18.9544	+	4.02888i	0.934951	+	0.198730i
$412$	0.916603	+	8.72089i	0.0451578	+	0.429648i
$413$	9.72019	+	16.8359i	0.478299	+	0.828439i
$414$	−14.0524	+	24.3395i	−0.690639	+	1.19622i
$415$	0.429825	+	0.191370i	0.0210993	+	0.00939400i
$416$	−5.21424			−0.255649
$417$	−17.1145	−	7.61988i	−0.838102	−	0.373147i
$418$	16.2812	+	11.8290i	0.796338	+	0.578574i
$419$	12.3746	−	8.99070i	0.604541	−	0.439225i	−0.242947	−	0.970040i	$-0.578114\pi$
$419$	12.3746	−	8.99070i	0.604541	−	0.439225i	0.847488	+	0.530815i	$0.178114\pi$
$420$	2.99915	+	0.637490i	0.146344	+	0.0311063i
$421$	−15.9754	+	7.11269i	−0.778592	+	0.346651i	−0.757254	−	0.653121i	$-0.773459\pi$
$421$	−15.9754	+	7.11269i	−0.778592	+	0.346651i	−0.0213383	+	0.999772i	$0.506793\pi$
$422$	−13.7436	+	6.11903i	−0.669026	+	0.297870i
$423$	−4.03712	+	38.4107i	−0.196292	+	1.86759i
$424$	−0.904793	+	2.78467i	−0.0439406	+	0.135235i
$425$	7.27127	+	8.07557i	0.352709	+	0.391722i
$426$	34.3062			1.66214
$427$	11.1879	+	0.355750i	0.541422	+	0.0172160i
$428$	1.99527			0.0964452
$429$	−27.2138	−	30.2240i	−1.31389	−	1.45923i
$430$	1.05559	−	3.24876i	0.0509049	−	0.156669i
$431$	2.34196	−	22.2823i	0.112808	−	1.07330i	−0.780902	−	0.624654i	$-0.785240\pi$
$431$	2.34196	−	22.2823i	0.112808	−	1.07330i	0.893710	−	0.448645i	$-0.148093\pi$
$432$	4.03901	−	1.79828i	0.194327	−	0.0865198i
$433$	25.4975	−	11.3522i	1.22533	−	0.545553i	0.310958	−	0.950424i	$-0.399350\pi$
$433$	25.4975	−	11.3522i	1.22533	−	0.545553i	0.914374	+	0.404871i	$0.132684\pi$
$434$	−0.529332	−	0.112513i	−0.0254087	−	0.00540080i
$435$	−0.995749	+	0.723454i	−0.0477425	+	0.0346870i
$436$	10.4546	+	7.59568i	0.500682	+	0.363767i
$437$	39.6806	+	17.6669i	1.89818	+	0.845124i
$438$	22.9922			1.09861
$439$	15.9930	+	7.12053i	0.763303	+	0.339845i	0.751193	−	0.660082i	$-0.229479\pi$
$439$	15.9930	+	7.12053i	0.763303	+	0.339845i	0.0121099	+	0.999927i	$0.496145\pi$
$440$	−1.09734	+	1.90064i	−0.0523135	+	0.0906096i
$441$	11.3841	+	19.7179i	0.542100	+	0.938946i
$442$	−1.34669	−	12.8129i	−0.0640554	−	0.609446i
$443$	15.4544	+	3.28493i	0.734260	+	0.156072i	0.559842	−	0.828600i	$-0.310862\pi$
$443$	15.4544	+	3.28493i	0.734260	+	0.156072i	0.174419	+	0.984672i	$0.444195\pi$
$444$	−2.33028	+	22.1712i	−0.110590	+	1.05220i
$445$	0.728674	+	6.93287i	0.0345425	+	0.328650i
$446$	−16.7877	+	3.56833i	−0.794920	+	0.168965i
$447$	5.65686	+	17.4100i	0.267560	+	0.823466i
$448$	0.716596	−	1.24118i	0.0338560	−	0.0586402i
$449$	−2.80168	−	3.11158i	−0.132219	−	0.146845i	0.673399	−	0.739279i	$-0.264834\pi$
$449$	−2.80168	−	3.11158i	−0.132219	−	0.146845i	−0.805619	+	0.592435i	$0.798167\pi$
$450$	−16.3793	−	11.9002i	−0.772126	−	0.560982i
$451$	8.57264	+	26.3839i	0.403670	+	1.24237i
$452$	0.480088	−	0.533191i	0.0225814	−	0.0250792i
$453$	−22.0772	+	4.69265i	−1.03728	+	0.220480i
$454$	4.59928	−	3.34157i	0.215855	−	0.156828i
$455$	−1.79169	+	5.51427i	−0.0839960	+	0.258513i
$456$	−9.80886	−	16.9894i	−0.459342	−	0.795603i
$457$	3.28754	−	3.65118i	0.153785	−	0.170795i	−0.661329	−	0.750096i	$-0.730007\pi$
$457$	3.28754	−	3.65118i	0.153785	−	0.170795i	0.815114	+	0.579300i	$0.196674\pi$
$458$	7.03308	−	7.81102i	0.328634	−	0.364985i
$459$	5.46205	+	9.46054i	0.254946	+	0.441580i
$460$	−1.46377	+	4.50501i	−0.0682485	+	0.210047i
$461$	−21.6072	+	15.6986i	−1.00635	+	0.731156i	−0.963440	−	0.267923i	$-0.913663\pi$
$461$	−21.6072	+	15.6986i	−1.00635	+	0.731156i	−0.0429093	+	0.999079i	$0.513663\pi$
$462$	10.9344	−	2.32418i	0.508715	−	0.108131i
$463$	−23.6864	+	26.3064i	−1.10080	+	1.22256i	−0.127791	+	0.991801i	$0.540789\pi$
$463$	−23.6864	+	26.3064i	−1.10080	+	1.22256i	−0.973010	+	0.230762i	$0.925878\pi$
$464$	0.177781	+	0.547153i	0.00825326	+	0.0254009i
$465$	−0.653533	−	0.474819i	−0.0303069	−	0.0220192i
$466$	−8.74284	−	9.70990i	−0.405004	−	0.449803i
$467$	−3.30238	+	5.71989i	−0.152816	+	0.264685i	−0.932262	−	0.361785i	$-0.882168\pi$
$467$	−3.30238	+	5.71989i	−0.152816	+	0.264685i	0.779446	+	0.626470i	$0.215501\pi$
$468$	7.41740	+	22.8284i	0.342869	+	1.05524i
$469$	−16.8808	+	3.58812i	−0.779481	+	0.165684i
$470$	0.680425	+	6.47381i	0.0313857	+	0.298615i
$471$	1.48827	−	14.1600i	0.0685760	−	0.652457i
$472$	13.2680	+	2.82020i	0.610708	+	0.129810i
$473$	−1.30180	−	12.3858i	−0.0598567	−	0.569499i
$474$	3.41840	+	5.92083i	0.157012	+	0.271953i
$475$	−15.6449	+	27.0978i	−0.717838	+	1.24333i
$476$	3.23501	+	1.44032i	0.148276	+	0.0660169i
$477$	13.4786			0.617143
$478$	3.79493	+	1.68961i	0.173576	+	0.0772810i
$479$	28.1101	+	20.4232i	1.28438	+	0.933160i	0.999676	−	0.0254543i	$-0.00810322\pi$
$479$	28.1101	+	20.4232i	1.28438	+	0.933160i	0.284708	+	0.958614i	$0.408103\pi$
$480$	1.73080	−	1.25750i	0.0790000	−	0.0573969i
$481$	−41.2350	−	8.76477i	−1.88015	−	0.399639i
$482$	−23.9311	+	10.6548i	−1.09003	+	0.485314i
$483$	22.0415	−	9.81351i	1.00292	−	0.446530i
$484$	0.313437	−	2.98215i	0.0142471	−	0.135552i
$485$	−2.86809	+	8.82708i	−0.130233	+	0.400817i
$486$	11.8622	+	13.1743i	0.538082	+	0.597600i
$487$	8.14081			0.368895			0.184448	−	0.982842i	$-0.440950\pi$
$487$	8.14081			0.368895			0.184448	+	0.982842i	$0.440950\pi$
$488$	5.40790	−	5.63512i	0.244804	−	0.255090i
$489$	−18.4419			−0.833971
$490$	2.56772	+	2.85175i	0.115998	+	0.128829i
$491$	13.5210	−	41.6134i	0.610195	−	1.87799i	0.154102	−	0.988055i	$-0.450752\pi$
$491$	13.5210	−	41.6134i	0.610195	−	1.87799i	0.456093	−	0.889932i	$-0.349248\pi$
$492$	2.82675	−	26.8947i	0.127440	−	1.21251i
$493$	−1.29859	+	0.578171i	−0.0584857	+	0.0260395i
$494$	33.8895	−	15.0886i	1.52476	−	0.678868i
$495$	9.88218	+	2.10052i	0.444171	+	0.0944114i
$496$	−0.305476	+	0.221941i	−0.0137163	+	0.00996546i
$497$	−14.4255	−	10.4807i	−0.647073	−	0.470126i
$498$	−1.52760	−	0.680130i	−0.0684532	−	0.0304773i
$499$	−32.8738			−1.47163			−0.735816	−	0.677181i	$-0.763201\pi$
$499$	−32.8738			−1.47163			−0.735816	+	0.677181i	$0.763201\pi$
$500$	−6.66122	−	2.96576i	−0.297899	−	0.132633i
$501$	−20.3460	+	35.2403i	−0.908993	+	1.57442i
$502$	−12.6929	−	21.9847i	−0.566511	−	0.981226i
$503$	2.93802	+	27.9534i	0.131000	+	1.24638i	0.840554	+	0.541728i	$0.182230\pi$
$503$	2.93802	+	27.9534i	0.131000	+	1.24638i	−0.709554	+	0.704651i	$0.751104\pi$
$504$	−6.45337	−	1.37171i	−0.287456	−	0.0611007i
$505$	−1.21631	+	11.5724i	−0.0541252	+	0.514967i
$506$	1.80518	+	17.1752i	0.0802502	+	0.763530i
$507$	−38.2683	+	8.13417i	−1.69955	+	0.361251i
$508$	5.42675	+	16.7018i	0.240773	+	0.741024i
$509$	−6.65610	+	11.5287i	−0.295026	+	0.511001i	−0.974991	−	0.222244i	$-0.928662\pi$
$509$	−6.65610	+	11.5287i	−0.295026	+	0.511001i	0.679965	+	0.733245i	$0.261995\pi$
$510$	3.53706	+	3.92830i	0.156624	+	0.173948i
$511$	−9.66803	−	7.02424i	−0.427688	−	0.310734i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−21.0475	+	23.3756i	−0.929268	+	1.03206i
$514$	24.2855	−	5.16205i	1.07119	−	0.227688i
$515$	5.50416	−	3.99900i	0.242542	−	0.176217i
$516$	−3.75156	+	11.5461i	−0.165153	+	0.508289i
$517$	11.8662	+	20.5529i	0.521876	+	0.903916i
$518$	7.75328	−	8.61089i	0.340660	−	0.378341i
$519$	11.0885	−	12.3151i	0.486732	−	0.540571i
$520$	2.02277	+	3.50355i	0.0887045	+	0.153641i
$521$	7.48342	−	23.0316i	0.327854	−	1.00903i	−0.642281	−	0.766469i	$-0.722012\pi$
$521$	7.48342	−	23.0316i	0.327854	−	1.00903i	0.970136	−	0.242563i	$-0.0779881\pi$
$522$	2.14258	−	1.55668i	0.0937784	−	0.0681340i
$523$	−4.25644	+	0.904735i	−0.186121	+	0.0395613i	−0.300029	−	0.953930i	$-0.596996\pi$
$523$	−4.25644	+	0.904735i	−0.186121	+	0.0395613i	0.113908	+	0.993491i	$0.463663\pi$
$524$	4.11928	−	4.57492i	0.179951	−	0.199856i
$525$	5.37092	+	16.5300i	0.234406	+	0.721428i
$526$	7.39606	+	5.37355i	0.322484	+	0.234298i
$527$	−0.624269	−	0.693320i	−0.0271936	−	0.0302015i
$528$	3.89993	−	6.75488i	0.169723	−	0.293969i
$529$	4.41092	+	13.5754i	0.191779	+	0.590236i
$530$	2.22207	−	0.472316i	0.0965206	−	0.0205161i
$531$	−6.52700	−	62.1002i	−0.283248	−	2.69492i
$532$	−1.06582	+	10.1406i	−0.0462091	+	0.439650i
$533$	50.0200	+	10.6321i	2.16661	+	0.460527i
$534$	−2.58971	−	24.6394i	−0.112068	−	1.06625i
$535$	−0.774032	−	1.34066i	−0.0334643	−	0.0579619i
$536$	−6.02079	+	10.4283i	−0.260059	+	0.450435i
$537$	−51.2462	−	22.8163i	−2.21144	−	0.984595i
$538$	−22.7828			−0.982237
$539$	12.7810	+	5.69046i	0.550516	+	0.245106i
$540$	−2.77516	−	2.01627i	−0.119424	−	0.0867666i
$541$	32.0212	−	23.2647i	1.37670	−	1.00023i	0.379518	−	0.925184i	$-0.376090\pi$
$541$	32.0212	−	23.2647i	1.37670	−	1.00023i	0.997180	−	0.0750452i	$-0.0239101\pi$
$542$	3.06562	+	0.651617i	0.131680	+	0.0279894i
$543$	−34.3788	+	15.3064i	−1.47534	+	0.656862i
$544$	2.25721	−	1.00497i	0.0967769	−	0.0430879i
$545$	1.04802	−	9.97123i	0.0448922	−	0.427121i
$546$	6.36768	−	19.5977i	0.272512	−	0.838705i
$547$	17.6318	+	19.5821i	0.753880	+	0.837268i	0.990951	−	0.134224i	$-0.0428542\pi$
$547$	17.6318	+	19.5821i	0.753880	+	0.837268i	−0.237071	+	0.971492i	$0.576188\pi$
$548$	−7.02751			−0.300200
$549$	−32.3640	−	15.6602i	−1.38126	−	0.668359i
$550$	−12.4406			−0.530470
$551$	−2.73878	−	3.04173i	−0.116676	−	0.129582i
$552$	5.20223	−	16.0108i	0.221422	−	0.681465i
$553$	0.371439	−	3.53400i	0.0157952	−	0.150281i
$554$	14.9927	−	6.67516i	0.636977	−	0.283600i
$555$	15.8012	−	7.03516i	0.670725	−	0.298626i
$556$	6.64562	+	1.41257i	0.281837	+	0.0599063i
$557$	6.35735	−	4.61889i	0.269370	−	0.195708i	−0.444898	−	0.895581i	$-0.646760\pi$
$557$	6.35735	−	4.61889i	0.269370	−	0.195708i	0.714267	+	0.699873i	$0.246760\pi$
$558$	1.40623	+	1.02168i	0.0595303	+	0.0432513i
$559$	−20.9723	−	9.33748i	−0.887035	−	0.394933i
$560$	−1.11196			−0.0469890
$561$	17.6059	+	7.83866i	0.743322	+	0.330948i
$562$	−9.31103	+	16.1272i	−0.392762	+	0.680284i
$563$	5.90994	+	10.2363i	0.249074	+	0.431410i	0.963269	−	0.268537i	$-0.0865403\pi$
$563$	5.90994	+	10.2363i	0.249074	+	0.431410i	−0.714195	+	0.699947i	$0.753207\pi$
$564$	−2.41823	−	23.0079i	−0.101826	−	0.968808i
$565$	−0.544503	−	0.115738i	−0.0229074	−	0.00486912i
$566$	−1.05169	+	10.0061i	−0.0442056	+	0.420589i
$567$	−0.242532	−	2.30754i	−0.0101854	−	0.0969075i
$568$	−12.1695	+	2.58671i	−0.510622	+	0.108536i
$569$	−1.41099	−	4.34259i	−0.0591519	−	0.182051i	0.917115	−	0.398624i	$-0.130512\pi$
$569$	−1.41099	−	4.34259i	−0.0591519	−	0.182051i	−0.976266	+	0.216573i	$0.930512\pi$
$570$	−7.61035	+	13.1815i	−0.318763	+	0.552113i
$571$	−8.07964	−	8.97334i	−0.338122	−	0.375523i	0.549973	−	0.835183i	$-0.314638\pi$
$571$	−8.07964	−	8.97334i	−0.338122	−	0.375523i	−0.888095	+	0.459660i	$0.847971\pi$
$572$	11.9325	+	8.66948i	0.498924	+	0.362489i
$573$	5.02636	+	15.4695i	0.209979	+	0.646250i
$574$	−9.40510	+	10.4454i	−0.392561	+	0.435984i
$575$	−26.2643	+	5.58265i	−1.09530	+	0.232813i
$576$	−3.72422	+	2.70581i	−0.155176	+	0.112742i
$577$	−5.40782	+	16.6436i	−0.225130	+	0.692880i	0.773148	+	0.634226i	$0.218681\pi$
$577$	−5.40782	+	16.6436i	−0.225130	+	0.692880i	−0.998278	+	0.0586545i	$0.981319\pi$
$578$	−5.44752	−	9.43539i	−0.226587	−	0.392460i
$579$	22.7156	−	25.2282i	0.944027	−	1.04845i
$580$	0.298675	−	0.331713i	0.0124018	−	0.0137736i
$581$	0.434559	+	0.752678i	0.0180285	+	0.0312264i
$582$	10.1932	−	31.3714i	0.422522	−	1.30039i
$583$	6.70051	−	4.86821i	0.277507	−	0.201621i
$584$	−8.15606	+	1.73362i	−0.337500	+	0.0717379i
$585$	12.4614	−	13.8398i	0.515215	−	0.572205i
$586$	−5.55281	−	17.0898i	−0.229384	−	0.705972i
$587$	−2.20233	−	1.60008i	−0.0908997	−	0.0660425i	0.541407	−	0.840761i	$-0.317892\pi$
$587$	−2.20233	−	1.60008i	−0.0908997	−	0.0660425i	−0.632307	+	0.774718i	$0.717892\pi$
$588$	−9.12569	−	10.1351i	−0.376337	−	0.417964i
$589$	1.34318	−	2.32646i	0.0553447	−	0.0958599i
$590$	−3.25214	−	10.0091i	−0.133889	−	0.412067i
$591$	3.63486	−	0.772612i	0.149518	−	0.0317810i
$592$	−0.845094	−	8.04054i	−0.0347332	−	0.330464i
$593$	−1.14868	+	10.9290i	−0.0471707	+	0.448799i	0.945290	+	0.326232i	$0.105779\pi$
$593$	−1.14868	+	10.9290i	−0.0471707	+	0.448799i	−0.992460	+	0.122567i	$0.960888\pi$
$594$	−12.2330	−	2.60020i	−0.501925	−	0.106688i
$595$	−0.287188	−	2.73241i	−0.0117736	−	0.112018i
$596$	−3.31940	−	5.74937i	−0.135968	−	0.235503i
$597$	27.8121	−	48.1719i	1.13827	−	1.97155i
$598$	29.0820	+	12.9481i	1.18925	+	0.529489i
$599$	−8.23852			−0.336617			−0.168308	−	0.985734i	$-0.553830\pi$
$599$	−8.23852			−0.336617			−0.168308	+	0.985734i	$0.553830\pi$
$600$	11.0788	+	4.93260i	0.452290	+	0.201372i
$601$	−5.27562	−	3.83296i	−0.215197	−	0.156350i	0.474965	−	0.880005i	$-0.342461\pi$
$601$	−5.27562	−	3.83296i	−0.215197	−	0.156350i	−0.690162	+	0.723655i	$0.742461\pi$
$602$	5.10490	−	3.70893i	0.208060	−	0.151165i
$603$	54.2208	+	11.5250i	2.20804	+	0.469334i
$604$	7.47766	−	3.32927i	0.304262	−	0.135466i
$605$	−2.12536	+	0.946271i	−0.0864081	+	0.0384714i
$606$	4.32277	−	41.1285i	0.175601	−	1.67073i
$607$	3.93826	−	12.1207i	0.159849	−	0.491964i	−0.838771	−	0.544484i	$-0.816725\pi$
$607$	3.93826	−	12.1207i	0.159849	−	0.491964i	0.998620	+	0.0525201i	$0.0167254\pi$
$608$	4.76053	+	5.28711i	0.193065	+	0.214420i
$609$	−2.27358			−0.0921301
$610$	−5.88425	−	1.44763i	−0.238246	−	0.0586126i
$611$	43.7472			1.76982
$612$	−7.61080	−	8.45265i	−0.307648	−	0.341678i
$613$	3.28232	−	10.1019i	0.132571	−	0.408013i	−0.862633	−	0.505830i	$-0.831186\pi$
$613$	3.28232	−	10.1019i	0.132571	−	0.408013i	0.995204	+	0.0978174i	$0.0311861\pi$
$614$	−1.63073	+	15.5153i	−0.0658107	+	0.626147i
$615$	−19.1677	+	8.53399i	−0.772914	+	0.344124i
$616$	−3.70355	+	1.64893i	−0.149220	+	0.0664371i
$617$	−37.6691	−	8.00681i	−1.51650	−	0.322342i	−0.626906	−	0.779095i	$-0.715679\pi$
$617$	−37.6691	−	8.00681i	−1.51650	−	0.322342i	−0.889594	+	0.456753i	$0.849012\pi$
$618$	−19.5618	+	14.2125i	−0.786890	+	0.571709i
$619$	9.28819	+	6.74827i	0.373324	+	0.271236i	0.758588	−	0.651571i	$-0.225890\pi$
$619$	9.28819	+	6.74827i	0.373324	+	0.271236i	−0.385264	+	0.922806i	$0.625890\pi$
$620$	0.267631	+	0.119157i	0.0107483	+	0.00478546i
$621$	−26.9928			−1.08318
$622$	11.3947	+	5.07325i	0.456886	+	0.203419i
$623$	−6.43853	+	11.1519i	−0.257954	+	0.446790i
$624$	−7.18894	−	12.4516i	−0.287788	−	0.498463i
$625$	−1.70725	−	16.2434i	−0.0682899	−	0.649735i
$626$	1.95133	+	0.414769i	0.0779910	+	0.0165775i
$627$	−5.80051	+	55.1882i	−0.231650	+	2.20400i
$628$	0.539733	+	5.13522i	0.0215377	+	0.204917i
$629$	19.5396	−	4.15327i	0.779096	−	0.165602i
$630$	1.58180	+	4.86828i	0.0630204	+	0.193957i
$631$	−22.7358	+	39.3796i	−0.905099	+	1.56768i	−0.0843155	+	0.996439i	$0.526870\pi$
$631$	−22.7358	+	39.3796i	−0.905099	+	1.56768i	−0.820784	+	0.571239i	$0.806463\pi$
$632$	−1.65905	−	1.84256i	−0.0659934	−	0.0732931i
$633$	−33.5607	−	24.3833i	−1.33392	−	0.969147i
$634$	−2.02464	−	6.23121i	−0.0804088	−	0.247473i
$635$	9.11706	−	10.1255i	0.361800	−	0.401819i
$636$	−7.89724	+	1.67861i	−0.313146	+	0.0665612i
$637$	20.8641	−	15.1587i	0.826665	−	0.600608i
$638$	0.502884	−	1.54772i	0.0199094	−	0.0612748i
$639$	28.6363	+	49.5996i	1.13284	+	1.96213i
$640$	−0.519155	+	0.576580i	−0.0205214	+	0.0227913i
$641$	−2.20640	+	2.45046i	−0.0871476	+	0.0967872i	−0.785141	−	0.619317i	$-0.787410\pi$
$641$	−2.20640	+	2.45046i	−0.0871476	+	0.0967872i	0.697994	+	0.716104i	$0.254076\pi$
$642$	2.75091	+	4.76471i	0.108570	+	0.188048i
$643$	−4.90318	+	15.0904i	−0.193362	+	0.595109i	0.806629	+	0.591058i	$0.201289\pi$
$643$	−4.90318	+	15.0904i	−0.193362	+	0.595109i	−0.999992	+	0.00405087i	$0.998711\pi$
$644$	−7.07889	+	5.14311i	−0.278947	+	0.202667i
$645$	9.21340	−	1.95837i	0.362777	−	0.0771107i
$646$	−11.7624	+	13.0635i	−0.462786	+	0.513976i
$647$	−4.59623	−	14.1457i	−0.180696	−	0.556126i	0.819151	−	0.573577i	$-0.194445\pi$
$647$	−4.59623	−	14.1457i	−0.180696	−	0.556126i	−0.999848	+	0.0174513i	$0.994445\pi$
$648$	−1.30975	−	0.951588i	−0.0514518	−	0.0373819i
$649$	−25.6741	−	28.5140i	−1.00780	−	1.11927i
$650$	−11.4662	+	19.8600i	−0.449741	+	0.778975i
$651$	−0.461116	−	1.41917i	−0.0180725	−	0.0556216i
$652$	6.54193	−	1.39053i	0.256202	−	0.0544574i
$653$	−1.71948	−	16.3597i	−0.0672883	−	0.640205i	−0.975243	−	0.221137i	$-0.929023\pi$
$653$	−1.71948	−	16.3597i	−0.0672883	−	0.640205i	0.907955	−	0.419069i	$-0.137643\pi$
$654$	−3.72466	+	35.4377i	−0.145646	+	1.38573i
$655$	−4.67198	−	0.993060i	−0.182549	−	0.0388021i
$656$	1.02514	+	9.75355i	0.0400250	+	0.380812i
$657$	19.1922	+	33.2418i	0.748758	+	1.29689i
$658$	−6.01220	+	10.4134i	−0.234380	+	0.405958i
$659$	−36.0931	−	16.0697i	−1.40599	−	0.625985i	−0.443242	−	0.896402i	$-0.646172\pi$
$659$	−36.0931	−	16.0697i	−1.40599	−	0.625985i	−0.962743	+	0.270417i	$0.912839\pi$
$660$	−6.05165			−0.235560
$661$	12.3153	+	5.48313i	0.479010	+	0.213269i	0.632015	−	0.774956i	$-0.282228\pi$
$661$	12.3153	+	5.48313i	0.479010	+	0.213269i	−0.153005	+	0.988225i	$0.548895\pi$
$662$	−7.54758	−	5.48364i	−0.293345	−	0.213128i
$663$	28.7404	−	20.8812i	1.11619	−	0.810957i
$664$	0.593170	+	0.126082i	0.0230195	+	0.00489294i
$665$	7.22712	−	3.21772i	0.280256	−	0.124778i
$666$	−34.0000	+	15.1378i	−1.31747	+	0.586577i
$667$	0.367147	−	3.49317i	0.0142160	−	0.135256i
$668$	4.56024	−	14.0350i	0.176441	−	0.543030i
$669$	−31.6666	−	35.1693i	−1.22430	−	1.35972i
$670$	9.34265			0.360938
$671$	−21.7450	+	3.90421i	−0.839455	+	0.150720i
$672$	3.95192			0.152449
$673$	7.59345	+	8.43338i	0.292706	+	0.325083i	0.871504	−	0.490388i	$-0.163145\pi$
$673$	7.59345	+	8.43338i	0.292706	+	0.325083i	−0.578798	+	0.815471i	$0.696478\pi$
$674$	−6.03587	+	18.5765i	−0.232493	+	0.715540i
$675$	2.03253	−	19.3382i	0.0782322	−	0.744330i
$676$	12.9617	−	5.77090i	0.498525	−	0.221958i
$677$	26.1150	−	11.6272i	1.00368	−	0.446868i	0.161970	−	0.986796i	$-0.448215\pi$
$677$	26.1150	−	11.6272i	1.00368	−	0.446868i	0.841711	+	0.539928i	$0.181548\pi$
$678$	1.93516	+	0.411332i	0.0743195	+	0.0157971i
$679$	−13.8703	+	10.0774i	−0.532294	+	0.386734i
$680$	−1.55090	−	1.12680i	−0.0594745	−	0.0432107i
$681$	14.3208	+	6.37601i	0.548773	+	0.244329i
$682$	1.06808			0.0408988
$683$	−1.48282	−	0.660195i	−0.0567386	−	0.0252617i	0.378171	−	0.925736i	$-0.376553\pi$
$683$	−1.48282	−	0.660195i	−0.0567386	−	0.0252617i	−0.434910	+	0.900474i	$0.643220\pi$
$684$	16.3754	−	28.3631i	0.626130	−	1.08449i
$685$	2.72620	+	4.72192i	0.104163	+	0.180415i
$686$	1.78962	+	17.0271i	0.0683279	+	0.650096i
$687$	28.3493	+	6.02583i	1.08159	+	0.229900i
$688$	0.460214	−	4.37865i	0.0175455	−	0.166934i
$689$	−1.59585	−	15.1835i	−0.0607971	−	0.578446i
$690$	−12.7761	+	2.71564i	−0.486377	+	0.103383i
$691$	−9.34638	−	28.7652i	−0.355553	−	1.09428i	−0.955688	−	0.294381i	$-0.904886\pi$
$691$	−9.34638	−	28.7652i	−0.355553	−	1.09428i	0.600135	−	0.799899i	$-0.295114\pi$
$692$	−3.00489	+	5.20463i	−0.114229	+	0.197850i
$693$	12.4875	+	13.8688i	0.474362	+	0.526833i
$694$	4.01849	+	2.91960i	0.152540	+	0.110827i
$695$	−1.62892	−	5.01330i	−0.0617885	−	0.190165i
$696$	−1.06149	+	1.17891i	−0.0402358	+	0.0446863i
$697$	−23.7025	+	5.03812i	−0.897796	+	0.190832i
$698$	18.9334	−	13.7560i	0.716641	−	0.520670i
$699$	11.1334	−	34.2651i	0.421104	−	1.29602i
$700$	−3.15161	−	5.45875i	−0.119120	−	0.206321i
$701$	−6.42189	+	7.13223i	−0.242551	+	0.269380i	−0.852113	−	0.523358i	$-0.824679\pi$
$701$	−6.42189	+	7.13223i	−0.242551	+	0.269380i	0.609561	+	0.792739i	$0.291346\pi$
$702$	−15.4257	+	17.1320i	−0.582207	+	0.646607i
$703$	28.7598	+	49.8134i	1.08469	+	1.87875i
$704$	−0.874110	+	2.69023i	−0.0329442	+	0.101392i
$705$	−14.5214	+	10.5504i	−0.546906	+	0.397350i
$706$	29.3277	−	6.23379i	1.10376	−	0.234612i
$707$	−14.3827	+	15.9736i	−0.540916	+	0.600748i
$708$	11.5581	+	35.5722i	0.434380	+	1.33688i
$709$	−18.5632	−	13.4870i	−0.697157	−	0.506514i	0.181848	−	0.983327i	$-0.441792\pi$
$709$	−18.5632	−	13.4870i	−0.697157	−	0.506514i	−0.879005	+	0.476813i	$0.841792\pi$
$710$	6.45902	+	7.17347i	0.242403	+	0.269216i
$711$	−5.70685	+	9.88456i	−0.214024	+	0.370700i
$712$	2.77648	+	8.54513i	0.104053	+	0.320242i
$713$	2.25490	−	0.479294i	0.0844466	−	0.0179497i
$714$	1.02067	+	9.71099i	0.0381975	+	0.363425i
$715$	1.19618	−	11.3809i	0.0447345	−	0.425620i
$716$	19.8990	+	4.22967i	0.743662	+	0.158070i
$717$	1.19732	+	11.3918i	0.0447149	+	0.425434i
$718$	−5.08040	−	8.79951i	−0.189599	−	0.328395i
$719$	12.9046	−	22.3515i	0.481261	−	0.833569i	−0.518507	−	0.855073i	$-0.673512\pi$
$719$	12.9046	−	22.3515i	0.481261	−	0.833569i	0.999769	+	0.0215039i	$0.00684542\pi$
$720$	3.26283	+	1.45271i	0.121599	+	0.0541392i
$721$	12.5676			0.468040
$722$	−28.8828	−	12.8594i	−1.07491	−	0.478579i
$723$	−58.4379	−	42.4576i	−2.17333	−	1.57902i
$724$	11.0412	−	8.02187i	0.410341	−	0.298130i
$725$	2.47494	+	0.526065i	0.0919170	+	0.0195376i
$726$	7.55352	−	3.36304i	0.280338	−	0.124814i
$727$	0.492939	−	0.219471i	0.0182821	−	0.00813971i	−0.397575	−	0.917570i	$-0.630148\pi$
$727$	0.492939	−	0.219471i	0.0182821	−	0.00813971i	0.415857	+	0.909430i	$0.363482\pi$
$728$	−0.781142	+	7.43207i	−0.0289510	+	0.275451i
$729$	−13.6049	+	41.8716i	−0.503885	+	1.55080i
$730$	4.32886	+	4.80769i	0.160218	+	0.177940i
$731$	10.8784			0.402353
$732$	20.9126	+	5.14486i	0.772953	+	0.190159i
$733$	−16.5097			−0.609799			−0.304900	−	0.952385i	$-0.598623\pi$
$733$	−16.5097			−0.609799			−0.304900	+	0.952385i	$0.598623\pi$
$734$	−14.3747	−	15.9647i	−0.530580	−	0.589269i
$735$	−3.26982	+	10.0635i	−0.120609	+	0.371196i
$736$	−0.638172	+	6.07180i	−0.0235233	+	0.223810i
$737$	31.1170	−	13.8542i	1.14621	−	0.510325i
$738$	41.2436	−	18.3628i	1.51820	−	0.675946i
$739$	3.74778	+	0.796615i	0.137864	+	0.0293040i	0.276327	−	0.961064i	$-0.410883\pi$
$739$	3.74778	+	0.796615i	0.137864	+	0.0293040i	−0.138463	+	0.990368i	$0.544216\pi$
$740$	−5.07475	+	3.68702i	−0.186552	+	0.135538i
$741$	82.7555	+	60.1254i	3.04010	+	2.20876i
$742$	3.83355	+	1.70681i	0.140734	+	0.0626589i
$743$	31.7650			1.16535			0.582673	−	0.812707i	$-0.302007\pi$
$743$	31.7650			1.16535			0.582673	+	0.812707i	$0.302007\pi$
$744$	−0.951160	−	0.423484i	−0.0348712	−	0.0155257i
$745$	−2.57541	+	4.46073i	−0.0943556	+	0.163429i
$746$	−5.10688	−	8.84538i	−0.186976	−	0.323853i
$747$	−0.291801	−	2.77631i	−0.0106765	−	0.101580i
$748$	−6.83642	−	1.45313i	−0.249964	−	0.0531316i
$749$	0.298910	−	2.84394i	0.0109220	−	0.103915i
$750$	−2.10166	−	19.9959i	−0.0767417	−	0.730148i
$751$	−26.7953	+	5.69551i	−0.977773	+	0.207832i	−0.668966	−	0.743293i	$-0.733263\pi$
$751$	−26.7953	+	5.69551i	−0.977773	+	0.207832i	−0.308807	+	0.951125i	$0.599930\pi$
$752$	2.59264	+	7.97931i	0.0945437	+	0.290976i
$753$	34.9997	−	60.6212i	1.27546	−	2.20916i
$754$	−2.00726	−	2.22929i	−0.0731002	−	0.0811860i
$755$	−5.13783	−	3.73285i	−0.186985	−	0.135852i
$756$	−1.95808	−	6.02636i	−0.0712148	−	0.219176i
$757$	−1.46765	+	1.62999i	−0.0533427	+	0.0592431i	−0.769226	−	0.638977i	$-0.779358\pi$
$757$	−1.46765	+	1.62999i	−0.0533427	+	0.0592431i	0.715883	+	0.698220i	$0.246024\pi$
$758$	16.6501	−	3.53908i	0.604758	−	0.128545i
$759$	−38.5255	+	27.9904i	−1.39839	+	1.01599i
$760$	1.70574	−	5.24974i	0.0618738	−	0.190428i
$761$	−8.36352	−	14.4860i	−0.303177	−	0.525119i	0.673676	−	0.739026i	$-0.264714\pi$
$761$	−8.36352	−	14.4860i	−0.303177	−	0.525119i	−0.976854	+	0.213908i	$0.931381\pi$
$762$	−32.4020	+	35.9861i	−1.17380	+	1.30364i
$763$	12.3926	−	13.7634i	0.448643	−	0.498268i
$764$	−2.94943	−	5.10856i	−0.106707	−	0.184821i
$765$	−2.72702	+	8.39290i	−0.0985956	+	0.303446i
$766$	−11.9282	+	8.66632i	−0.430982	+	0.313127i
$767$	−69.1825	+	14.7052i	−2.49803	+	0.530973i
$768$	1.84508	−	2.04917i	0.0665785	−	0.0739429i
$769$	−15.3900	−	47.3656i	−0.554978	−	1.70805i	−0.696002	−	0.718040i	$-0.745039\pi$
$769$	−15.3900	−	47.3656i	−0.554978	−	1.70805i	0.141024	−	0.990006i	$-0.454961\pi$
$770$	2.54467	+	1.84881i	0.0917036	+	0.0666266i
$771$	45.8097	+	50.8769i	1.64980	+	1.83229i
$772$	−6.15572	+	10.6620i	−0.221549	+	0.383734i
$773$	−1.90575	−	5.86531i	−0.0685452	−	0.210960i	0.910917	−	0.412591i	$-0.135376\pi$
$773$	−1.90575	−	5.86531i	−0.0685452	−	0.210960i	−0.979462	+	0.201630i	$0.935376\pi$
$774$	−19.8248	+	4.21388i	−0.712586	+	0.151465i
$775$	0.173585	+	1.65155i	0.00623536	+	0.0593255i
$776$	−1.25043	+	11.8970i	−0.0448878	+	0.427079i
$777$	31.2524	+	6.64290i	1.12117	+	0.238313i
$778$	1.49373	+	14.2119i	0.0535527	+	0.509520i
$779$	−34.8870	−	60.4260i	−1.24995	−	2.16499i
$780$	−5.57765	+	9.66077i	−0.199712	+	0.345911i
$781$	32.1502	+	14.3142i	1.15042	+	0.512201i
$782$	−15.0850			−0.539437
$783$	2.32368	+	1.03457i	0.0830416	+	0.0369725i
$784$	4.00137	+	2.90716i	0.142906	+	0.103827i
$785$	3.24107	−	2.35478i	0.115679	−	0.0840456i
$786$	16.6042	+	3.52933i	0.592253	+	0.125887i
$787$	−31.3209	+	13.9450i	−1.11647	+	0.497085i	−0.880200	−	0.474602i	$-0.842592\pi$
$787$	−31.3209	+	13.9450i	−1.11647	+	0.497085i	−0.236271	+	0.971687i	$0.575925\pi$
$788$	−1.23114	+	0.548141i	−0.0438577	+	0.0195267i
$789$	−2.63500	+	25.0704i	−0.0938086	+	0.892529i
$790$	−0.594453	+	1.82954i	−0.0211497	+	0.0650920i
$791$	−0.688057	−	0.764165i	−0.0244645	−	0.0271706i
$792$	13.0215			0.462700
$793$	−13.8092	+	38.3118i	−0.490377	+	1.36049i
$794$	22.0687			0.783188
$795$	4.19149	+	4.65512i	0.148657	+	0.165100i
$796$	−6.23365	+	19.1852i	−0.220946	+	0.680001i
$797$	0.643252	−	6.12014i	0.0227852	−	0.216786i	−0.977205	−	0.212299i	$-0.931905\pi$
$797$	0.643252	−	6.12014i	0.0227852	−	0.216786i	0.999990	−	0.00448738i	$-0.00142838\pi$
$798$	−25.6852	+	11.4358i	−0.909246	+	0.404822i
$799$	−18.9378	+	8.43167i	−0.669973	+	0.298291i
$800$	−4.30193	−	0.914402i	−0.152096	−	0.0323290i
$801$	33.4617	−	24.3114i	1.18231	−	0.859000i
$802$	−25.3345	−	18.4066i	−0.894593	−	0.649960i
$803$	21.5472	+	9.59341i	0.760383	+	0.338544i
$804$	−33.2038			−1.17101
$805$	6.20189	+	2.76126i	0.218588	+	0.0973216i
$806$	0.984420	−	1.70507i	0.0346747	−	0.0600584i
$807$	−31.4109	−	54.4054i	−1.10572	−	1.91516i
$808$	1.56769	+	14.9155i	0.0551510	+	0.524726i
$809$	−5.75969	−	1.22426i	−0.202500	−	0.0430427i	0.105545	−	0.994415i	$-0.466341\pi$
$809$	−5.75969	−	1.22426i	−0.202500	−	0.0430427i	−0.308045	+	0.951372i	$0.599675\pi$
$810$	−0.131296	+	1.24920i	−0.00461327	+	0.0438923i
$811$	3.44957	+	32.8204i	0.121131	+	1.15248i	0.871133	+	0.491046i	$0.163385\pi$
$811$	3.44957	+	32.8204i	0.121131	+	1.15248i	−0.750003	+	0.661435i	$0.769948\pi$
$812$	0.806512	−	0.171429i	0.0283030	−	0.00601599i
$813$	2.67055	+	8.21909i	0.0936601	+	0.288256i
$814$	−11.4347	+	19.8055i	−0.400786	+	0.694181i
$815$	−3.47216	−	3.85622i	−0.121624	−	0.135077i
$816$	5.51191	+	4.00464i	0.192956	+	0.140190i
$817$	9.67949	+	29.7904i	0.338642	+	1.04223i
$818$	−5.39537	+	5.99216i	−0.188645	+	0.209511i
$819$	33.6494	−	7.15241i	1.17581	−	0.249925i
$820$	6.15591	−	4.47253i	0.214974	−	0.156188i
$821$	−13.2683	+	40.8356i	−0.463066	+	1.42517i	0.398332	+	0.917241i	$0.369589\pi$
$821$	−13.2683	+	40.8356i	−0.463066	+	1.42517i	−0.861398	+	0.507930i	$0.830411\pi$
$822$	−9.68892	−	16.7817i	−0.337940	−	0.585329i
$823$	23.0317	−	25.5793i	0.802836	−	0.891640i	−0.193148	−	0.981170i	$-0.561870\pi$
$823$	23.0317	−	25.5793i	0.802836	−	0.891640i	0.995984	+	0.0895300i	$0.0285365\pi$
$824$	5.86756	−	6.51659i	0.204406	−	0.227016i
$825$	−17.1520	−	29.7082i	−0.597157	−	1.03431i
$826$	6.00741	−	18.4889i	0.209024	−	0.643311i
$827$	25.4977	−	18.5252i	0.886642	−	0.644183i	−0.0483583	−	0.998830i	$-0.515399\pi$
$827$	25.4977	−	18.5252i	0.886642	−	0.644183i	0.935000	+	0.354647i	$0.115399\pi$
$828$	27.4907	−	5.84333i	0.955368	−	0.203070i
$829$	−9.15846	+	10.1715i	−0.318086	+	0.353271i	−0.880891	−	0.473319i	$-0.843056\pi$
$829$	−9.15846	+	10.1715i	−0.318086	+	0.353271i	0.562805	+	0.826590i	$0.309722\pi$
$830$	−0.145393	−	0.447474i	−0.00504666	−	0.0155320i
$831$	36.6109	+	26.5993i	1.27002	+	0.922721i
$832$	3.48901	+	3.87494i	0.120960	+	0.134339i
$833$	−6.11029	+	10.5833i	−0.211709	+	0.366691i
$834$	5.78918	+	17.8173i	0.200463	+	0.616962i
$835$	−11.1994	+	2.38052i	−0.387573	+	0.0823811i
$836$	−2.10360	−	20.0144i	−0.0727544	−	0.692212i
$837$	−0.174501	+	1.66027i	−0.00603164	+	0.0573873i
$838$	−14.9616	−	3.18020i	−0.516842	−	0.109858i
$839$	3.57108	+	33.9766i	0.123287	+	1.17300i	0.864819	+	0.502083i	$0.167433\pi$
$839$	3.57108	+	33.9766i	0.123287	+	1.17300i	−0.741532	+	0.670918i	$0.765900\pi$
$840$	−1.53308	−	2.65537i	−0.0528962	−	0.0916190i
$841$	14.3345	−	24.8281i	0.494293	−	0.856141i
$842$	15.9754	+	7.11269i	0.550548	+	0.245120i
$843$	−51.3489			−1.76855
$844$	13.7436	+	6.11903i	0.473073	+	0.210626i
$845$	−8.90583	−	6.47047i	−0.306370	−	0.222591i
$846$	31.2461	−	22.7016i	1.07426	−	0.780497i
$847$	−4.20363	−	0.893508i	−0.144438	−	0.0307013i
$848$	2.67484	−	1.19091i	0.0918542	−	0.0408961i
$849$	−25.3446	+	11.2841i	−0.869824	+	0.387271i
$850$	1.13588	−	10.8072i	0.0389605	−	0.370684i
$851$	−15.2530	+	46.9440i	−0.522867	+	1.60922i
$852$	−22.9554	−	25.4945i	−0.786438	−	0.873427i
$853$	19.7840			0.677390			0.338695	−	0.940896i	$-0.390015\pi$
$853$	19.7840			0.677390			0.338695	+	0.940896i	$0.390015\pi$
$854$	−7.22181	−	8.55229i	−0.247125	−	0.292653i
$855$	−25.4103			−0.869013
$856$	−1.33510	−	1.48278i	−0.0456327	−	0.0506803i
$857$	−4.66894	+	14.3695i	−0.159488	+	0.490853i	−0.998588	−	0.0531239i	$-0.983082\pi$
$857$	−4.66894	+	14.3695i	−0.159488	+	0.490853i	0.839100	+	0.543977i	$0.183082\pi$
$858$	−4.25121	+	40.4476i	−0.145134	+	1.38086i
$859$	41.1904	−	18.3391i	1.40540	−	0.625723i	0.442790	−	0.896625i	$-0.353989\pi$
$859$	41.1904	−	18.3391i	1.40540	−	0.625723i	0.962607	+	0.270902i	$0.0873219\pi$
$860$	−3.12063	+	1.38939i	−0.106413	+	0.0473779i
$861$	−37.9106	−	8.05815i	−1.29199	−	0.274621i
$862$	−18.1260	+	13.1693i	−0.617375	+	0.448549i
$863$	−19.6126	−	14.2494i	−0.667620	−	0.485054i	0.201608	−	0.979466i	$-0.435383\pi$
$863$	−19.6126	−	14.2494i	−0.667620	−	0.485054i	−0.869228	+	0.494412i	$0.835383\pi$
$864$	−4.03901	−	1.79828i	−0.137410	−	0.0611788i
$865$	4.66279			0.158539
$866$	−25.4975	−	11.3522i	−0.866440	−	0.385764i
$867$	15.0211	−	26.0174i	0.510145	−	0.883597i
$868$	0.270579	+	0.468656i	0.00918404	+	0.0159072i
$869$	0.733106	+	6.97503i	0.0248689	+	0.236612i
$870$	1.20392	+	0.255901i	0.0408166	+	0.00867584i
$871$	6.56310	−	62.4438i	0.222382	−	2.11583i
$872$	−1.35077	−	12.8518i	−0.0457430	−	0.435215i
$873$	53.8651	−	11.4494i	1.82306	−	0.387502i
$874$	−13.4224	−	41.3099i	−0.454019	−	1.39733i
$875$	−5.22514	+	9.05020i	−0.176642	+	0.305953i
$876$	−15.3848	−	17.0865i	−0.519803	−	0.577300i
$877$	17.8493	+	12.9683i	0.602728	+	0.437907i	0.846846	−	0.531838i	$-0.178499\pi$
$877$	17.8493	+	12.9683i	0.602728	+	0.437907i	−0.244118	+	0.969745i	$0.578499\pi$
$878$	−5.40981	−	16.6497i	−0.182572	−	0.561899i
$879$	33.1547	−	36.8220i	1.11828	−	1.24198i
$880$	2.14672	−	0.456298i	0.0723658	−	0.0153818i
$881$	−17.6035	+	12.7897i	−0.593076	+	0.430895i	−0.843415	−	0.537263i	$-0.819458\pi$
$881$	−17.6035	+	12.7897i	−0.593076	+	0.430895i	0.250338	+	0.968158i	$0.419458\pi$
$882$	7.03577	−	21.6539i	0.236907	−	0.729124i
$883$	−0.907455	−	1.57176i	−0.0305383	−	0.0528939i	0.850352	−	0.526214i	$-0.176389\pi$
$883$	−0.907455	−	1.57176i	−0.0305383	−	0.0528939i	−0.880891	+	0.473320i	$0.843055\pi$
$884$	−8.62071	+	9.57427i	−0.289946	+	0.322017i
$885$	19.4179	−	21.5657i	0.652725	−	0.724924i
$886$	−7.89983	−	13.6829i	−0.265400	−	0.459686i
$887$	−8.01701	+	24.6738i	−0.269185	+	0.828466i	0.721515	+	0.692399i	$0.243446\pi$
$887$	−8.01701	+	24.6738i	−0.269185	+	0.828466i	−0.990700	+	0.136067i	$0.956554\pi$
$888$	18.0357	−	13.1037i	0.605237	−	0.439731i
$889$	24.6188	−	5.23288i	0.825687	−	0.175505i
$890$	4.66455	−	5.18051i	0.156356	−	0.173651i
$891$	1.41513	+	4.35532i	0.0474086	+	0.145909i
$892$	13.8849	+	10.0880i	0.464902	+	0.337771i
$893$	−39.9406	−	44.3585i	−1.33656	−	1.48440i
$894$	9.15299	−	15.8534i	0.306122	−	0.530219i
$895$	−4.87749	−	15.0114i	−0.163037	−	0.501775i
$896$	−1.40187	+	0.297977i	−0.0468333	+	0.00995472i
$897$	9.17556	+	87.2996i	0.306363	+	2.91485i
$898$	−0.437665	+	4.16411i	−0.0146051	+	0.138958i
$899$	−0.212484	−	0.0451648i	−0.00708673	−	0.00150633i
$900$	2.11627	+	20.1350i	0.0705424	+	0.671166i
$901$	3.61725	+	6.26525i	0.120508	+	0.208726i
$902$	13.8708	−	24.0250i	0.461848	−	0.799944i
$903$	15.8951	+	7.07696i	0.528956	+	0.235506i
$904$	−0.717480			−0.0238630
$905$	−9.67327	−	4.30682i	−0.321551	−	0.143164i
$906$	18.2598	+	13.2666i	0.606643	+	0.440752i
$907$	5.85066	−	4.25076i	0.194268	−	0.141144i	−0.486399	−	0.873737i	$-0.661690\pi$
$907$	5.85066	−	4.25076i	0.194268	−	0.141144i	0.680667	+	0.732593i	$0.261690\pi$
$908$	−5.56079	−	1.18198i	−0.184541	−	0.0392255i
$909$	63.0714	−	28.0812i	2.09195	−	0.931395i
$910$	5.29678	−	2.35828i	0.175587	−	0.0781762i
$911$	−1.68894	+	16.0692i	−0.0559572	+	0.532397i	0.930255	+	0.366913i	$0.119585\pi$
$911$	−1.68894	+	16.0692i	−0.0559572	+	0.532397i	−0.986212	+	0.165484i	$0.947081\pi$
$912$	−6.06221	+	18.6576i	−0.200740	+	0.617813i
$913$	−1.14781	−	1.27477i	−0.0379869	−	0.0421887i
$914$	−4.91315			−0.162513
$915$	−4.65576	−	16.0475i	−0.153915	−	0.530512i
$916$	−10.5108			−0.347286
$917$	−5.90371	−	6.55674i	−0.194958	−	0.216523i
$918$	3.37573	−	10.3894i	0.111416	−	0.342902i
$919$	0.0395704	−	0.376487i	0.00130531	−	0.0124192i	−0.993850	−	0.110736i	$-0.964679\pi$
$919$	0.0395704	−	0.376487i	0.00130531	−	0.0124192i	0.995155	+	0.0983168i	$0.0313459\pi$
$920$	4.32733	−	1.92665i	0.142668	−	0.0635198i
$921$	−39.2989	+	17.4970i	−1.29494	+	0.576545i
$922$	26.1244	+	5.55291i	0.860361	+	0.182875i
$923$	52.4829	−	38.1311i	1.72750	−	1.25510i
$924$	−9.04376	−	6.57068i	−0.297518	−	0.216159i
$925$	−32.4832	−	14.4625i	−1.06804	−	0.475523i
$926$	35.3988			1.16328
$927$	−36.8770	−	16.4187i	−1.21120	−	0.539260i
$928$	0.287655	−	0.498233i	0.00944274	−	0.0163553i
$929$	15.6675	+	27.1369i	0.514034	+	0.890333i	0.999867	+	0.0162817i	$0.00518285\pi$
$929$	15.6675	+	27.1369i	0.514034	+	0.890333i	−0.485833	+	0.874051i	$0.661484\pi$
$930$	0.0844392	+	0.803386i	0.00276887	+	0.0263441i
$931$	−34.4191	−	7.31601i	−1.12804	−	0.239773i
$932$	−1.36577	+	12.9944i	−0.0447371	+	0.425645i
$933$	3.59510	+	34.2051i	0.117698	+	1.11983i
$934$	6.46043	−	1.37321i	0.211392	−	0.0449327i
$935$	1.67569	+	5.15724i	0.0548009	+	0.168660i
$936$	12.0016	−	20.7874i	0.392285	−	0.679457i
$937$	−12.9966	−	14.4341i	−0.424579	−	0.471543i	0.492463	−	0.870333i	$-0.336097\pi$
$937$	−12.9966	−	14.4341i	−0.424579	−	0.471543i	−0.917042	+	0.398791i	$0.869430\pi$
$938$	13.9619	+	10.1439i	0.455873	+	0.331211i
$939$	1.69986	+	5.23163i	0.0554729	+	0.170728i
$940$	4.35569	−	4.83748i	0.142067	−	0.157781i
$941$	−46.0583	+	9.78999i	−1.50146	+	0.319145i	−0.884010	−	0.467468i	$-0.845166\pi$
$941$	−46.0583	+	9.78999i	−1.50146	+	0.319145i	−0.617447	+	0.786612i	$0.711833\pi$
$942$	−11.5188	+	8.36887i	−0.375302	+	0.272673i
$943$	18.5027	−	56.9453i	0.602529	−	1.85439i
$944$	−6.78220	−	11.7471i	−0.220742	−	0.382336i
$945$	−3.28962	+	3.65349i	−0.107011	+	0.118848i
$946$	−8.33335	+	9.25513i	−0.270941	+	0.300910i
$947$	−10.1395	−	17.5621i	−0.329490	−	0.570693i	0.652921	−	0.757426i	$-0.273543\pi$
$947$	−10.1395	−	17.5621i	−0.329490	−	0.570693i	−0.982411	+	0.186733i	$0.940210\pi$
$948$	2.11268	−	6.50217i	0.0686168	−	0.211181i
$949$	35.1743	−	25.5556i	1.14180	−	0.829570i
$950$	30.6061	−	6.50552i	0.992992	−	0.211067i
$951$	12.0887	−	13.4259i	0.392004	−	0.435364i
$952$	−1.09428	−	3.36784i	−0.0354657	−	0.109152i
$953$	−23.3270	−	16.9480i	−0.755635	−	0.549001i	0.141933	−	0.989876i	$-0.454668\pi$
$953$	−23.3270	−	16.9480i	−0.755635	−	0.549001i	−0.897568	+	0.440875i	$0.854668\pi$
$954$	−9.01895	−	10.0166i	−0.291999	−	0.324298i
$955$	−2.28836	+	3.96355i	−0.0740495	+	0.128258i
$956$	−1.28368	−	3.95075i	−0.0415171	−	0.127776i
$957$	4.38929	−	0.932971i	0.141885	−	0.0301587i
$958$	−3.63195	−	34.5557i	−0.117343	−	1.11644i
$959$	−1.05279	+	10.0166i	−0.0339962	+	0.323453i
$960$	−2.09264	−	0.444804i	−0.0675397	−	0.0143560i
$961$	3.22548	+	30.6884i	0.104048	+	0.989948i
$962$	21.0781	+	36.5084i	0.679586	+	1.17708i
$963$	−4.59252	+	7.95447i	−0.147992	+	0.256329i
$964$	23.9311	+	10.6548i	0.770770	+	0.343169i
$965$	9.55202			0.307490
$966$	−22.0415	−	9.81351i	−0.709174	−	0.315745i
$967$	4.60415	+	3.34511i	0.148060	+	0.107572i	0.659349	−	0.751837i	$-0.270832\pi$
$967$	4.60415	+	3.34511i	0.148060	+	0.107572i	−0.511289	+	0.859409i	$0.670832\pi$
$968$	−2.42590	+	1.76252i	−0.0779714	+	0.0566496i
$969$	−47.4126	−	10.0779i	−1.52311	−	0.323748i
$970$	8.47893	−	3.77506i	0.272242	−	0.121210i
$971$	−41.1855	+	18.3370i	−1.32170	+	0.588461i	−0.941678	−	0.336515i	$-0.890752\pi$
$971$	−41.1855	+	18.3370i	−1.32170	+	0.588461i	−0.380027	+	0.924976i	$0.624085\pi$
$972$	1.85306	−	17.6307i	0.0594370	−	0.565505i
$973$	3.00897	−	9.26065i	0.0964631	−	0.296883i
$974$	−5.44726	−	6.04980i	−0.174542	−	0.193848i
$975$	−63.2344			−2.02512
$976$	−7.80630	−	0.248222i	−0.249874	−	0.00794541i
$977$	−10.9912			−0.351640			−0.175820	−	0.984422i	$-0.556258\pi$
$977$	−10.9912			−0.351640			−0.175820	+	0.984422i	$0.556258\pi$
$978$	12.3400	+	13.7050i	0.394591	+	0.438238i
$979$	7.85377	−	24.1714i	0.251008	−	0.772522i
$980$	0.401118	−	3.81638i	0.0128132	−	0.121910i
$981$	−54.3446	+	24.1958i	−1.73509	+	0.772512i
$982$	−39.9721	+	17.7967i	−1.27556	+	0.567917i
$983$	2.94913	+	0.626857i	0.0940627	+	0.0199936i	0.254703	−	0.967019i	$-0.418022\pi$
$983$	2.94913	+	0.626857i	0.0940627	+	0.0199936i	−0.160640	+	0.987013i	$0.551356\pi$
$984$	−21.8781	+	15.8954i	−0.697449	+	0.506726i
$985$	0.845908	+	0.614588i	0.0269529	+	0.0195824i
$986$	1.29859	+	0.578171i	0.0413556	+	0.0184127i
$987$	−33.1564			−1.05538
$988$	−33.8895	−	15.0886i	−1.07817	−	0.480032i
$989$	−13.4400	+	23.2787i	−0.427367	+	0.740221i
$990$	−5.05148	−	8.74941i	−0.160546	−	0.278075i
$991$	3.51906	+	33.4816i	0.111787	+	1.06358i	0.896294	+	0.443460i	$0.146249\pi$
$991$	3.51906	+	33.4816i	0.111787	+	1.06358i	−0.784507	+	0.620119i	$0.787084\pi$
$992$	0.369338	+	0.0785052i	0.0117265	+	0.00249254i
$993$	2.68899	−	25.5840i	0.0853324	−	0.811884i
$994$	1.86384	+	17.7332i	0.0591173	+	0.562464i
$995$	15.3091	−	3.25406i	0.485332	−	0.103161i
$996$	0.516727	+	1.59032i	0.0163731	+	0.0503912i
$997$	−3.29042	+	5.69918i	−0.104209	+	0.180495i	−0.913415	−	0.407030i	$-0.866564\pi$
$997$	−3.29042	+	5.69918i	−0.104209	+	0.180495i	0.809206	+	0.587525i	$0.199898\pi$
$998$	21.9969	+	24.4300i	0.696298	+	0.773318i
$999$	−28.9183	−	21.0104i	−0.914934	−	0.664739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.a.83.2	yes	16
4.3	odd	2		976.2.bw.a.449.1		16
61.5	even	30		7442.2.a.r.1.8		8
61.25	even	15	inner	122.2.i.a.25.2	✓	16
61.56	even	15		7442.2.a.p.1.8		8
244.147	odd	30		976.2.bw.a.513.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.a.25.2	✓	16	61.25	even	15	inner
122.2.i.a.83.2	yes	16	1.1	even	1	trivial
976.2.bw.a.449.1		16	4.3	odd	2
976.2.bw.a.513.1		16	244.147	odd	30
7442.2.a.p.1.8		8	61.56	even	15
7442.2.a.r.1.8		8	61.5	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)

\(f(q)\)	\(=\)	\(q+(-0.669131 - 0.743145i) q^{2} +(0.852091 - 2.62247i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(0.708788 - 0.315573i) q^{5} +(-2.51903 + 1.12155i) q^{6} +(1.40187 + 0.297977i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-3.72422 - 2.70581i) q^{9} +O(q^{10})\)	\(q+(-0.669131 - 0.743145i) q^{2} +(0.852091 - 2.62247i) q^{3} +(-0.104528 + 0.994522i) q^{4} +(0.708788 - 0.315573i) q^{5} +(-2.51903 + 1.12155i) q^{6} +(1.40187 + 0.297977i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-3.72422 - 2.70581i) q^{9} +(-0.708788 - 0.315573i) q^{10} -2.82868 q^{11} +(2.51903 + 1.12155i) q^{12} +(-2.60712 + 4.51566i) q^{13} +(-0.716596 - 1.24118i) q^{14} +(-0.223627 - 2.12767i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(0.258271 - 2.45728i) q^{17} +(0.481186 + 4.57818i) q^{18} +(6.95903 - 1.47919i) q^{19} +(0.239756 + 0.737892i) q^{20} +(1.97596 - 3.42246i) q^{21} +(1.89276 + 2.10212i) q^{22} +(4.93925 + 3.58857i) q^{23} +(-0.852091 - 2.62247i) q^{24} +(-2.94286 + 3.26838i) q^{25} +(5.10030 - 1.08410i) q^{26} +(-3.57686 + 2.59874i) q^{27} +(-0.442880 + 1.36305i) q^{28} +(-0.287655 - 0.498233i) q^{29} +(-1.43153 + 1.58988i) q^{30} +(0.252656 - 0.280603i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.41029 + 7.41812i) q^{33} +(-1.99894 + 1.45231i) q^{34} +(1.08766 - 0.231190i) q^{35} +(3.08027 - 3.42099i) q^{36} +(2.49835 + 7.68913i) q^{37} +(-5.75575 - 4.18180i) q^{38} +(9.62068 + 10.6848i) q^{39} +(0.387933 - 0.671919i) q^{40} +(-3.03062 - 9.32728i) q^{41} +(-3.86556 + 0.821650i) q^{42} +(0.460214 + 4.37865i) q^{43} +(0.295677 - 2.81318i) q^{44} +(-3.49357 - 0.742581i) q^{45} +(-0.638172 - 6.07180i) q^{46} +(-4.19497 - 7.26591i) q^{47} +(-1.37871 + 2.38800i) q^{48} +(-4.51836 - 2.01170i) q^{49} +4.39803 q^{50} +(-6.22408 - 2.77114i) q^{51} +(-4.21841 - 3.06485i) q^{52} +(-2.36878 + 1.72102i) q^{53} +(4.32463 + 0.919228i) q^{54} +(-2.00493 + 0.892654i) q^{55} +(1.30929 - 0.582931i) q^{56} +(2.05061 - 19.5102i) q^{57} +(-0.177781 + 0.547153i) q^{58} +(9.07635 + 10.0803i) q^{59} +2.13939 q^{60} +(7.68733 - 1.38022i) q^{61} -0.377589 q^{62} +(-4.41462 - 4.90293i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.422875 + 4.02339i) q^{65} +(7.12554 - 3.17249i) q^{66} +(-11.0005 + 4.89775i) q^{67} +(2.41683 + 0.513712i) q^{68} +(13.6196 - 9.89523i) q^{69} +(-0.899598 - 0.653596i) q^{70} +(-11.3658 - 5.06037i) q^{71} -4.60340 q^{72} +(-7.61739 - 3.39148i) q^{73} +(4.04241 - 7.00166i) q^{74} +(6.06362 + 10.5025i) q^{75} +(0.743668 + 7.07553i) q^{76} +(-3.96545 - 0.842882i) q^{77} +(1.50290 - 14.2991i) q^{78} +(-0.259169 - 2.46583i) q^{79} +(-0.758911 + 0.161312i) q^{80} +(-0.500280 - 1.53970i) q^{81} +(-4.90364 + 8.49335i) q^{82} +(0.405775 + 0.450659i) q^{83} +(3.19717 + 2.32288i) q^{84} +(-0.592393 - 1.82320i) q^{85} +(2.94602 - 3.27189i) q^{86} +(-1.55171 + 0.329826i) q^{87} +(-2.28845 + 1.66266i) q^{88} +(-2.77648 + 8.54513i) q^{89} +(1.78581 + 3.09311i) q^{90} +(-5.00042 + 5.55352i) q^{91} +(-4.08521 + 4.53708i) q^{92} +(-0.520587 - 0.901683i) q^{93} +(-2.59264 + 7.97931i) q^{94} +(4.46569 - 3.24451i) q^{95} +(2.69717 - 0.573301i) q^{96} +(-8.00452 + 8.88992i) q^{97} +(1.52839 + 4.70389i) q^{98} +(10.5346 + 7.65386i) 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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