LMFDB - Embedded newform 122.2.e.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(9,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("122.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} + 10 x^{9} + 34 x^{8} - 107 x^{7} + 287 x^{6} - 358 x^{5} + 1201 x^{4} + \cdots + 81 $ x^12 - x^11 + 11x^10 + 10x^9 + 34x^8 - 107x^7 + 287x^6 - 358x^5 + 1201x^4 - 1164x^3 + 981x^2 - 405x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$1.12096 + 3.44996i$ of defining polynomial
Character	$\chi$	$=$	122.81
Dual form			122.2.e.a.119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.811944 - 2.49891i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-3.26564 + 2.37263i) q^{5} +(-2.12570 + 1.54441i) q^{6} +(1.31194 - 4.03775i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-3.15823 + 2.29459i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.811944 - 2.49891i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-3.26564 + 2.37263i) q^{5} +(-2.12570 + 1.54441i) q^{6} +(1.31194 - 4.03775i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-3.15823 + 2.29459i) q^{9} +(3.26564 + 2.37263i) q^{10} -1.83287 q^{11} +(2.12570 + 1.54441i) q^{12} -1.17660 q^{13} -4.24554 q^{14} +(8.58050 + 6.23410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.80110 - 2.76166i) q^{17} +(3.15823 + 2.29459i) q^{18} +(-1.82549 - 5.61827i) q^{19} +(1.24737 - 3.83900i) q^{20} -11.1552 q^{21} +(0.566387 + 1.74316i) q^{22} +(0.944229 - 0.686023i) q^{23} +(0.811944 - 2.49891i) q^{24} +(3.48998 - 10.7410i) q^{25} +(0.363590 + 1.11902i) q^{26} +(1.92117 + 1.39581i) q^{27} +(1.31194 + 4.03775i) q^{28} +5.84819 q^{29} +(3.27746 - 10.0870i) q^{30} +(-0.794355 + 2.44477i) q^{31} -1.00000 q^{32} +(1.48819 + 4.58017i) q^{33} +(-3.80110 - 2.76166i) q^{34} +(5.29574 + 16.2986i) q^{35} +(1.20634 - 3.71272i) q^{36} +(-0.227968 + 0.701613i) q^{37} +(-4.77919 + 3.47228i) q^{38} +(0.955335 + 2.94022i) q^{39} -4.03656 q^{40} +(-0.634067 + 1.95146i) q^{41} +(3.44714 + 10.6092i) q^{42} +(6.70983 + 4.87498i) q^{43} +(1.48282 - 1.07733i) q^{44} +(4.86944 - 14.9866i) q^{45} +(-0.944229 - 0.686023i) q^{46} -2.80666 q^{47} -2.62751 q^{48} +(-8.91909 - 6.48010i) q^{49} -11.2938 q^{50} +(-9.98742 - 7.25628i) q^{51} +(0.951892 - 0.691590i) q^{52} +(0.358726 + 0.260630i) q^{53} +(0.733822 - 2.25847i) q^{54} +(5.98550 - 4.34872i) q^{55} +(3.43471 - 2.49547i) q^{56} +(-12.5573 + 9.12344i) q^{57} +(-1.80719 - 5.56196i) q^{58} +(-0.301764 - 0.928736i) q^{59} -10.6061 q^{60} +(4.26102 + 6.54551i) q^{61} +2.57059 q^{62} +(5.12154 + 15.7625i) q^{63} +(0.309017 + 0.951057i) q^{64} +(3.84237 - 2.79164i) q^{65} +(3.89612 - 2.83070i) q^{66} +(2.21013 - 1.60575i) q^{67} +(-1.45189 + 4.46846i) q^{68} +(-2.48097 - 1.80253i) q^{69} +(13.8644 - 10.0731i) q^{70} +(-2.12392 - 1.54311i) q^{71} -3.90378 q^{72} +(2.08706 + 1.51634i) q^{73} +0.737720 q^{74} -29.6745 q^{75} +(4.77919 + 3.47228i) q^{76} +(-2.40462 + 7.40066i) q^{77} +(2.50110 - 1.81716i) q^{78} +(7.31501 + 5.31467i) q^{79} +(1.24737 + 3.83900i) q^{80} +(-1.69089 + 5.20401i) q^{81} +2.05188 q^{82} +(-4.50645 - 13.8694i) q^{83} +(9.02473 - 6.55685i) q^{84} +(-5.86065 + 18.0372i) q^{85} +(2.56293 - 7.88788i) q^{86} +(-4.74840 - 14.6141i) q^{87} +(-1.48282 - 1.07733i) q^{88} +(-4.95317 - 15.2443i) q^{89} -15.7579 q^{90} +(-1.54364 + 4.75083i) q^{91} +(-0.360664 + 1.11001i) q^{92} +6.75423 q^{93} +(0.867304 + 2.66929i) q^{94} +(19.2915 + 14.0161i) q^{95} +(0.811944 + 2.49891i) q^{96} +(3.08929 - 9.50787i) q^{97} +(-3.40679 + 10.4850i) q^{98} +(5.78861 - 4.20567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9} + 6 q^{10} - 4 q^{11} + q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 7 q^{17} + 7 q^{18} - 6 q^{19} + 4 q^{20} - 56 q^{21} - q^{22} + 8 q^{23} + 4 q^{24} - 21 q^{25} - 7 q^{26} + 2 q^{27} + 10 q^{28} + 30 q^{29} + 3 q^{30} + q^{31} - 12 q^{32} + 21 q^{33} - 7 q^{34} + 5 q^{35} - 2 q^{36} - 14 q^{38} - 21 q^{39} - 4 q^{40} + 2 q^{41} - 14 q^{42} - 8 q^{43} + q^{44} + 49 q^{45} - 8 q^{46} - 10 q^{47} + 6 q^{48} - 3 q^{49} - 44 q^{50} + 8 q^{51} - 3 q^{52} + 8 q^{53} + 8 q^{54} + 13 q^{55} + 10 q^{56} + 5 q^{57} + 25 q^{58} + 4 q^{59} - 18 q^{60} - 26 q^{61} + 34 q^{62} + 29 q^{63} - 3 q^{64} + 3 q^{65} + 29 q^{66} + 33 q^{67} - 3 q^{68} + 26 q^{69} + 20 q^{70} - 13 q^{71} - 18 q^{72} - 38 q^{73} + 30 q^{74} - 8 q^{75} + 14 q^{76} - 23 q^{77} - 9 q^{78} + 26 q^{79} + 4 q^{80} + 20 q^{81} - 42 q^{82} + 18 q^{83} + 14 q^{84} - 5 q^{85} - 12 q^{86} - 66 q^{87} - q^{88} + 2 q^{89} - 14 q^{90} + 17 q^{91} + 8 q^{92} - 68 q^{93} + 20 q^{94} + 65 q^{95} + 4 q^{96} - 4 q^{97} - 7 q^{98} - 50 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9 + 6 * q^10 - 4 * q^11 + q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 7 * q^17 + 7 * q^18 - 6 * q^19 + 4 * q^20 - 56 * q^21 - q^22 + 8 * q^23 + 4 * q^24 - 21 * q^25 - 7 * q^26 + 2 * q^27 + 10 * q^28 + 30 * q^29 + 3 * q^30 + q^31 - 12 * q^32 + 21 * q^33 - 7 * q^34 + 5 * q^35 - 2 * q^36 - 14 * q^38 - 21 * q^39 - 4 * q^40 + 2 * q^41 - 14 * q^42 - 8 * q^43 + q^44 + 49 * q^45 - 8 * q^46 - 10 * q^47 + 6 * q^48 - 3 * q^49 - 44 * q^50 + 8 * q^51 - 3 * q^52 + 8 * q^53 + 8 * q^54 + 13 * q^55 + 10 * q^56 + 5 * q^57 + 25 * q^58 + 4 * q^59 - 18 * q^60 - 26 * q^61 + 34 * q^62 + 29 * q^63 - 3 * q^64 + 3 * q^65 + 29 * q^66 + 33 * q^67 - 3 * q^68 + 26 * q^69 + 20 * q^70 - 13 * q^71 - 18 * q^72 - 38 * q^73 + 30 * q^74 - 8 * q^75 + 14 * q^76 - 23 * q^77 - 9 * q^78 + 26 * q^79 + 4 * q^80 + 20 * q^81 - 42 * q^82 + 18 * q^83 + 14 * q^84 - 5 * q^85 - 12 * q^86 - 66 * q^87 - q^88 + 2 * q^89 - 14 * q^90 + 17 * q^91 + 8 * q^92 - 68 * q^93 + 20 * q^94 + 65 * q^95 + 4 * q^96 - 4 * q^97 - 7 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.811944	−	2.49891i	−0.468776	−	1.44274i	−0.854171	−	0.519992i	$-0.825935\pi$
$3$	−0.811944	−	2.49891i	−0.468776	−	1.44274i	0.385395	−	0.922752i	$-0.374065\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−3.26564	+	2.37263i	−1.46044	+	1.06107i	−0.477193	+	0.878799i	$0.658346\pi$
$5$	−3.26564	+	2.37263i	−1.46044	+	1.06107i	−0.983248	+	0.182274i	$0.941654\pi$
$6$	−2.12570	+	1.54441i	−0.867812	+	0.630502i
$7$	1.31194	−	4.03775i	0.495868	−	1.52613i	−0.319731	−	0.947508i	$-0.603593\pi$
$7$	1.31194	−	4.03775i	0.495868	−	1.52613i	0.815599	−	0.578617i	$-0.196407\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−3.15823	+	2.29459i	−1.05274	+	0.764862i
$10$	3.26564	+	2.37263i	1.03269	+	0.750291i
$11$	−1.83287			−0.552631			−0.276315	−	0.961067i	$-0.589113\pi$
$11$	−1.83287			−0.552631			−0.276315	+	0.961067i	$0.589113\pi$
$12$	2.12570	+	1.54441i	0.613636	+	0.445832i
$13$	−1.17660			−0.326331			−0.163165	−	0.986599i	$-0.552170\pi$
$13$	−1.17660			−0.326331			−0.163165	+	0.986599i	$0.552170\pi$
$14$	−4.24554			−1.13467
$15$	8.58050	+	6.23410i	2.21548	+	1.60964i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.80110	−	2.76166i	0.921903	−	0.669802i	−0.0220942	−	0.999756i	$-0.507033\pi$
$17$	3.80110	−	2.76166i	0.921903	−	0.669802i	0.943997	+	0.329954i	$0.107033\pi$
$18$	3.15823	+	2.29459i	0.744401	+	0.540839i
$19$	−1.82549	−	5.61827i	−0.418796	−	1.28892i	−0.908812	−	0.417207i	$-0.863009\pi$
$19$	−1.82549	−	5.61827i	−0.418796	−	1.28892i	0.490016	−	0.871713i	$-0.336991\pi$
$20$	1.24737	−	3.83900i	0.278919	−	0.858425i
$21$	−11.1552			−2.43426
$22$	0.566387	+	1.74316i	0.120754	+	0.371643i
$23$	0.944229	−	0.686023i	0.196885	−	0.143046i	−0.484975	−	0.874528i	$-0.661171\pi$
$23$	0.944229	−	0.686023i	0.196885	−	0.143046i	0.681860	+	0.731482i	$0.261171\pi$
$24$	0.811944	−	2.49891i	0.165737	−	0.510087i
$25$	3.48998	−	10.7410i	0.697996	−	2.14821i
$26$	0.363590	+	1.11902i	0.0713059	+	0.219457i
$27$	1.92117	+	1.39581i	0.369729	+	0.268624i
$28$	1.31194	+	4.03775i	0.247934	+	0.763063i
$29$	5.84819			1.08598			0.542991	−	0.839738i	$-0.317292\pi$
$29$	5.84819			1.08598			0.542991	+	0.839738i	$0.317292\pi$
$30$	3.27746	−	10.0870i	0.598379	−	1.84162i
$31$	−0.794355	+	2.44477i	−0.142670	+	0.439094i	−0.996704	−	0.0811233i	$-0.974149\pi$
$31$	−0.794355	+	2.44477i	−0.142670	+	0.439094i	0.854034	+	0.520218i	$0.174149\pi$
$32$	−1.00000			−0.176777
$33$	1.48819	+	4.58017i	0.259060	+	0.797304i
$34$	−3.80110	−	2.76166i	−0.651884	−	0.473621i
$35$	5.29574	+	16.2986i	0.895143	+	2.75497i
$36$	1.20634	−	3.71272i	0.201056	−	0.618786i
$37$	−0.227968	+	0.701613i	−0.0374777	+	0.115345i	−0.968045	−	0.250776i	$-0.919314\pi$
$37$	−0.227968	+	0.701613i	−0.0374777	+	0.115345i	0.930567	+	0.366121i	$0.119314\pi$
$38$	−4.77919	+	3.47228i	−0.775287	+	0.563279i
$39$	0.955335	+	2.94022i	0.152976	+	0.470812i
$40$	−4.03656			−0.638236
$41$	−0.634067	+	1.95146i	−0.0990246	+	0.304766i	−0.988282	−	0.152641i	$-0.951222\pi$
$41$	−0.634067	+	1.95146i	−0.0990246	+	0.304766i	0.889257	+	0.457408i	$0.151222\pi$
$42$	3.44714	+	10.6092i	0.531905	+	1.63704i
$43$	6.70983	+	4.87498i	1.02324	+	0.743427i	0.966944	−	0.254987i	$-0.0820713\pi$
$43$	6.70983	+	4.87498i	1.02324	+	0.743427i	0.0562949	+	0.998414i	$0.482071\pi$
$44$	1.48282	−	1.07733i	0.223544	−	0.162414i
$45$	4.86944	−	14.9866i	0.725894	−	2.23407i
$46$	−0.944229	−	0.686023i	−0.139219	−	0.101149i
$47$	−2.80666			−0.409393			−0.204696	−	0.978826i	$-0.565621\pi$
$47$	−2.80666			−0.409393			−0.204696	+	0.978826i	$0.565621\pi$
$48$	−2.62751			−0.379248
$49$	−8.91909	−	6.48010i	−1.27416	−	0.925728i
$50$	−11.2938			−1.59719
$51$	−9.98742	−	7.25628i	−1.39852	−	1.01608i
$52$	0.951892	−	0.691590i	0.132004	−	0.0959063i
$53$	0.358726	+	0.260630i	0.0492749	+	0.0358003i	0.612150	−	0.790742i	$-0.290305\pi$
$53$	0.358726	+	0.260630i	0.0492749	+	0.0358003i	−0.562875	+	0.826542i	$0.690305\pi$
$54$	0.733822	−	2.25847i	0.0998605	−	0.307339i
$55$	5.98550	−	4.34872i	0.807084	−	0.586381i
$56$	3.43471	−	2.49547i	0.458983	−	0.333471i
$57$	−12.5573	+	9.12344i	−1.66326	+	1.20843i
$58$	−1.80719	−	5.56196i	−0.237296	−	0.730321i
$59$	−0.301764	−	0.928736i	−0.0392864	−	0.120911i	0.929490	−	0.368848i	$-0.120248\pi$
$59$	−0.301764	−	0.928736i	−0.0392864	−	0.120911i	−0.968776	+	0.247936i	$0.920248\pi$
$60$	−10.6061			−1.36924
$61$	4.26102	+	6.54551i	0.545568	+	0.838067i
$61$	4.26102	+	6.54551i	0.545568	+	0.838067i
$62$	2.57059			0.326465
$63$	5.12154	+	15.7625i	0.645254	+	1.98589i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	3.84237	−	2.79164i	0.476587	−	0.346261i
$66$	3.89612	−	2.83070i	0.479579	−	0.348435i
$67$	2.21013	−	1.60575i	0.270010	−	0.196174i	−0.444538	−	0.895760i	$-0.646632\pi$
$67$	2.21013	−	1.60575i	0.270010	−	0.196174i	0.714548	+	0.699586i	$0.246632\pi$
$68$	−1.45189	+	4.46846i	−0.176068	+	0.541881i
$69$	−2.48097	−	1.80253i	−0.298673	−	0.216999i
$70$	13.8644	−	10.0731i	1.65712	−	1.20396i
$71$	−2.12392	−	1.54311i	−0.252062	−	0.183134i	0.454578	−	0.890707i	$-0.349790\pi$
$71$	−2.12392	−	1.54311i	−0.252062	−	0.183134i	−0.706640	+	0.707573i	$0.749790\pi$
$72$	−3.90378			−0.460065
$73$	2.08706	+	1.51634i	0.244272	+	0.177474i	0.703184	−	0.711008i	$-0.251761\pi$
$73$	2.08706	+	1.51634i	0.244272	+	0.177474i	−0.458912	+	0.888481i	$0.651761\pi$
$74$	0.737720			0.0857582
$75$	−29.6745			−3.42652
$76$	4.77919	+	3.47228i	0.548210	+	0.398298i
$77$	−2.40462	+	7.40066i	−0.274032	+	0.843383i
$78$	2.50110	−	1.81716i	0.283194	−	0.205752i
$79$	7.31501	+	5.31467i	0.823003	+	0.597947i	0.917571	−	0.397572i	$-0.130147\pi$
$79$	7.31501	+	5.31467i	0.823003	+	0.597947i	−0.0945682	+	0.995518i	$0.530147\pi$
$80$	1.24737	+	3.83900i	0.139460	+	0.429213i
$81$	−1.69089	+	5.20401i	−0.187876	+	0.578224i
$82$	2.05188			0.226593
$83$	−4.50645	−	13.8694i	−0.494647	−	1.52237i	−0.817506	−	0.575920i	$-0.804644\pi$
$83$	−4.50645	−	13.8694i	−0.494647	−	1.52237i	0.322859	−	0.946447i	$-0.395356\pi$
$84$	9.02473	−	6.55685i	0.984678	−	0.715411i
$85$	−5.86065	+	18.0372i	−0.635676	+	1.95641i
$86$	2.56293	−	7.88788i	0.276367	−	0.850572i
$87$	−4.74840	−	14.6141i	−0.509082	−	1.56679i
$88$	−1.48282	−	1.07733i	−0.158069	−	0.114844i
$89$	−4.95317	−	15.2443i	−0.525035	−	1.61589i	−0.764247	−	0.644923i	$-0.776889\pi$
$89$	−4.95317	−	15.2443i	−0.525035	−	1.61589i	0.239213	−	0.970967i	$-0.423111\pi$
$90$	−15.7579			−1.66102
$91$	−1.54364	+	4.75083i	−0.161817	+	0.498022i
$92$	−0.360664	+	1.11001i	−0.0376018	+	0.115726i
$93$	6.75423			0.700381
$94$	0.867304	+	2.66929i	0.0894556	+	0.275316i
$95$	19.2915	+	14.0161i	1.97926	+	1.43802i
$96$	0.811944	+	2.49891i	0.0828687	+	0.255044i
$97$	3.08929	−	9.50787i	0.313670	−	0.965378i	−0.662628	−	0.748949i	$-0.730559\pi$
$97$	3.08929	−	9.50787i	0.313670	−	0.965378i	0.976298	−	0.216429i	$-0.0694411\pi$
$98$	−3.40679	+	10.4850i	−0.344138	+	1.05915i
$99$	5.78861	−	4.20567i	0.581778	−	0.422686i
$100$	3.48998	+	10.7410i	0.348998	+	1.07410i
$101$	−1.76657			−0.175780			−0.0878902	−	0.996130i	$-0.528012\pi$
$101$	−1.76657			−0.175780			−0.0878902	+	0.996130i	$0.528012\pi$
$102$	−3.81485	+	11.7409i	−0.377727	+	1.16252i
$103$	2.10332	+	6.47337i	0.207247	+	0.637840i	0.999614	+	0.0277951i	$0.00884860\pi$
$103$	2.10332	+	6.47337i	0.207247	+	0.637840i	−0.792367	+	0.610045i	$0.791151\pi$
$104$	−0.951892	−	0.691590i	−0.0933407	−	0.0678160i
$105$	36.4288	−	26.4671i	3.55509	−	2.58292i
$106$	0.137021	−	0.421708i	0.0133087	−	0.0409599i
$107$	−8.90229	−	6.46789i	−0.860617	−	0.625275i	0.0674356	−	0.997724i	$-0.478518\pi$
$107$	−8.90229	−	6.46789i	−0.860617	−	0.625275i	−0.928053	+	0.372449i	$0.878518\pi$
$108$	−2.37470			−0.228505
$109$	7.08055			0.678193			0.339097	−	0.940752i	$-0.389879\pi$
$109$	7.08055			0.678193			0.339097	+	0.940752i	$0.389879\pi$
$110$	−5.98550	−	4.34872i	−0.570695	−	0.414634i
$111$	1.93836			0.183981
$112$	−3.43471	−	2.49547i	−0.324550	−	0.235799i
$113$	−6.61033	+	4.80268i	−0.621847	+	0.451798i	−0.853566	−	0.520984i	$-0.825565\pi$
$113$	−6.61033	+	4.80268i	−0.621847	+	0.451798i	0.231719	+	0.972783i	$0.425565\pi$
$114$	12.5573	+	9.12344i	1.17610	+	0.854489i
$115$	−1.45584	+	4.48061i	−0.135758	+	0.417819i
$116$	−4.73129	+	3.43748i	−0.439289	+	0.319162i
$117$	3.71598	−	2.69982i	0.343542	−	0.249598i
$118$	−0.790030	+	0.573990i	−0.0727281	+	0.0528401i
$119$	−6.16406	−	18.9710i	−0.565059	−	1.73907i
$120$	3.27746	+	10.0870i	0.299190	+	0.920811i
$121$	−7.64059			−0.694599
$122$	4.90842	−	6.07514i	0.444388	−	0.550018i
$123$	5.39133			0.486120
$124$	−0.794355	−	2.44477i	−0.0713352	−	0.219547i
$125$	7.85067	+	24.1619i	0.702186	+	2.16110i
$126$	13.4084	−	9.74176i	1.19451	−	0.867865i
$127$	15.0678	−	10.9474i	1.33705	−	0.971421i	0.337500	−	0.941326i	$-0.390419\pi$
$127$	15.0678	−	10.9474i	1.33705	−	0.971421i	0.999547	−	0.0300956i	$-0.00958119\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	6.73410	−	20.7254i	0.592905	−	1.82477i
$130$	−3.84237	−	2.79164i	−0.336998	−	0.244843i
$131$	−10.3739	+	7.53711i	−0.906375	+	0.658520i	−0.940095	−	0.340911i	$-0.889264\pi$
$131$	−10.3739	+	7.53711i	−0.906375	+	0.658520i	0.0337204	+	0.999431i	$0.489264\pi$
$132$	−3.89612	−	2.83070i	−0.339114	−	0.246381i
$133$	−25.0801			−2.17472
$134$	−2.21013	−	1.60575i	−0.190926	−	0.138716i
$135$	−9.58560			−0.824997
$136$	4.69842			0.402886
$137$	15.1512	+	11.0080i	1.29446	+	0.940477i	0.999885	−	0.0151527i	$-0.00482343\pi$
$137$	15.1512	+	11.0080i	1.29446	+	0.940477i	0.294570	+	0.955630i	$0.404823\pi$
$138$	−0.947645	+	2.91655i	−0.0806689	+	0.248273i
$139$	16.8216	−	12.2216i	1.42679	−	1.03663i	0.436190	−	0.899855i	$-0.356328\pi$
$139$	16.8216	−	12.2216i	1.42679	−	1.03663i	0.990603	−	0.136771i	$-0.0436724\pi$
$140$	−13.8644	−	10.0731i	−1.17176	−	0.851332i
$141$	2.27885	+	7.01357i	0.191914	+	0.590649i
$142$	−0.811263	+	2.49681i	−0.0680797	+	0.209528i
$143$	2.15656			0.180340
$144$	1.20634	+	3.71272i	0.100528	+	0.309393i
$145$	−19.0981	+	13.8756i	−1.58601	+	1.15231i
$146$	0.797186	−	2.45349i	0.0659756	−	0.203052i
$147$	−8.95136	+	27.5494i	−0.738296	+	2.27224i
$148$	−0.227968	−	0.701613i	−0.0187389	−	0.0576723i
$149$	−2.15975	−	1.56915i	−0.176934	−	0.128550i	0.495793	−	0.868440i	$-0.334877\pi$
$149$	−2.15975	−	1.56915i	−0.176934	−	0.128550i	−0.672727	+	0.739890i	$0.734877\pi$
$150$	9.16993	+	28.2222i	0.748722	+	2.30433i
$151$	5.53103			0.450109			0.225055	−	0.974346i	$-0.427744\pi$
$151$	5.53103			0.450109			0.225055	+	0.974346i	$0.427744\pi$
$152$	1.82549	−	5.61827i	0.148067	−	0.455702i
$153$	−5.66787	+	17.4439i	−0.458220	+	1.41026i
$154$	7.78151			0.627052
$155$	−3.20646	−	9.86848i	−0.257549	−	0.792655i
$156$	−2.50110	−	1.81716i	−0.200248	−	0.145489i
$157$	−2.04364	−	6.28967i	−0.163100	−	0.501970i	0.835791	−	0.549047i	$-0.185009\pi$
$157$	−2.04364	−	6.28967i	−0.163100	−	0.501970i	−0.998891	+	0.0470772i	$0.985009\pi$
$158$	2.79408	−	8.59931i	0.222285	−	0.684124i
$159$	0.360024	−	1.10804i	0.0285518	−	0.0878733i
$160$	3.26564	−	2.37263i	0.258172	−	0.187573i
$161$	−1.53121	−	4.71258i	−0.120676	−	0.371404i
$162$	5.47182			0.429907
$163$	0.246090	−	0.757388i	0.0192753	−	0.0593232i	−0.940956	−	0.338528i	$-0.890071\pi$
$163$	0.246090	−	0.757388i	0.0192753	−	0.0593232i	0.960232	+	0.279205i	$0.0900709\pi$
$164$	−0.634067	−	1.95146i	−0.0495123	−	0.152383i
$165$	−15.7269	−	11.4263i	−1.22434	−	0.889534i
$166$	−11.7980	+	8.57177i	−0.915705	+	0.665299i
$167$	−0.203566	+	0.626511i	−0.0157524	+	0.0484808i	−0.958624	−	0.284676i	$-0.908114\pi$
$167$	−0.203566	+	0.626511i	−0.0157524	+	0.0484808i	0.942871	+	0.333157i	$0.108114\pi$
$168$	−9.02473	−	6.55685i	−0.696273	−	0.505872i
$169$	−11.6156			−0.893508
$170$	18.9655			1.45458
$171$	18.6569	+	13.5550i	1.42673	+	1.03658i
$172$	−8.29380			−0.632397
$173$	6.34929	+	4.61303i	0.482728	+	0.350722i	0.802381	−	0.596812i	$-0.203566\pi$
$173$	6.34929	+	4.61303i	0.482728	+	0.350722i	−0.319653	+	0.947535i	$0.603566\pi$
$174$	−12.4315	+	9.03200i	−0.942428	+	0.684714i
$175$	−38.7910	−	28.1833i	−2.93232	−	2.13046i
$176$	−0.566387	+	1.74316i	−0.0426931	+	0.131396i
$177$	−2.07581	+	1.50816i	−0.156027	+	0.113360i
$178$	−12.9676	+	9.42148i	−0.971960	+	0.706170i
$179$	−0.266382	+	0.193538i	−0.0199103	+	0.0144657i	−0.597696	−	0.801723i	$-0.703917\pi$
$179$	−0.266382	+	0.193538i	−0.0199103	+	0.0144657i	0.577786	+	0.816189i	$0.303917\pi$
$180$	4.86944	+	14.9866i	0.362947	+	1.11704i
$181$	−3.09197	−	9.51610i	−0.229824	−	0.707326i	−0.997766	−	0.0668064i	$-0.978719\pi$
$181$	−3.09197	−	9.51610i	−0.229824	−	0.707326i	0.767942	−	0.640520i	$-0.221281\pi$
$182$	4.99531			0.370277
$183$	12.8969	−	15.9625i	0.953367	−	1.17998i
$184$	1.16713			0.0860421
$185$	−0.920206	−	2.83210i	−0.0676549	−	0.208220i
$186$	−2.08717	−	6.42366i	−0.153039	−	0.471005i
$187$	−6.96692	+	5.06176i	−0.509472	+	0.370153i
$188$	2.27063	−	1.64971i	0.165603	−	0.120318i
$189$	8.15640	−	5.92597i	0.593291	−	0.431051i
$190$	7.36869	−	22.6785i	0.534581	−	1.64527i
$191$	2.11256	+	1.53487i	0.152860	+	0.111059i	0.661586	−	0.749869i	$-0.269884\pi$
$191$	2.11256	+	1.53487i	0.152860	+	0.111059i	−0.508727	+	0.860928i	$0.669884\pi$
$192$	2.12570	−	1.54441i	0.153409	−	0.111458i
$193$	7.36818	+	5.35330i	0.530373	+	0.385339i	0.820497	−	0.571650i	$-0.193697\pi$
$193$	7.36818	+	5.35330i	0.530373	+	0.385339i	−0.290124	+	0.956989i	$0.593697\pi$
$194$	−9.99717			−0.717755
$195$	−10.0958	−	7.33506i	−0.722978	−	0.525274i
$196$	11.0246			0.787472
$197$	22.7254			1.61911			0.809557	−	0.587041i	$-0.199707\pi$
$197$	22.7254			1.61911			0.809557	+	0.587041i	$0.199707\pi$
$198$	−5.78861	−	4.20567i	−0.411379	−	0.298884i
$199$	−5.53127	+	17.0235i	−0.392101	+	1.20676i	0.539095	+	0.842245i	$0.318767\pi$
$199$	−5.53127	+	17.0235i	−0.392101	+	1.20676i	−0.931196	+	0.364519i	$0.881233\pi$
$200$	9.13688	−	6.63833i	0.646075	−	0.469401i
$201$	−5.80712	−	4.21912i	−0.409603	−	0.297594i
$202$	0.545901	+	1.68011i	0.0384094	+	0.118212i
$203$	7.67250	−	23.6135i	0.538504	−	1.65734i
$204$	12.3451			0.864332
$205$	−2.55945	−	7.87717i	−0.178760	−	0.550165i
$206$	5.50658	−	4.00076i	0.383661	−	0.278746i
$207$	−1.40795	+	4.33323i	−0.0978595	+	0.301180i
$208$	−0.363590	+	1.11902i	−0.0252105	+	0.0775898i
$209$	3.34588	+	10.2976i	0.231439	+	0.712297i
$210$	−36.4288	−	26.4671i	−2.51383	−	1.82640i
$211$	6.99226	+	21.5200i	0.481367	+	1.48150i	0.837174	+	0.546936i	$0.184206\pi$
$211$	6.99226	+	21.5200i	0.481367	+	1.48150i	−0.355807	+	0.934559i	$0.615794\pi$
$212$	−0.443410			−0.0304535
$213$	−2.13160	+	6.56039i	−0.146055	+	0.449510i
$214$	−3.40037	+	10.4653i	−0.232445	+	0.715391i
$215$	−33.4784			−2.28321
$216$	0.733822	+	2.25847i	0.0499302	+	0.153669i
$217$	8.82923	+	6.41481i	0.599367	+	0.435466i
$218$	−2.18801	−	6.73400i	−0.148191	−	0.456084i
$219$	2.09461	−	6.44655i	0.141541	−	0.435617i
$220$	−2.28626	+	7.03637i	−0.154139	+	0.474392i
$221$	−4.47239	+	3.24938i	−0.300845	+	0.218577i
$222$	−0.598987	−	1.84349i	−0.0402014	−	0.123727i
$223$	−20.6667			−1.38395			−0.691973	−	0.721924i	$-0.743258\pi$
$223$	−20.6667			−1.38395			−0.691973	+	0.721924i	$0.743258\pi$
$224$	−1.31194	+	4.03775i	−0.0876579	+	0.269783i
$225$	13.6241	+	41.9307i	0.908275	+	2.79538i
$226$	6.61033	+	4.80268i	0.439712	+	0.319470i
$227$	−8.44273	+	6.13401i	−0.560364	+	0.407128i	−0.831592	−	0.555387i	$-0.812570\pi$
$227$	−8.44273	+	6.13401i	−0.560364	+	0.407128i	0.271228	+	0.962515i	$0.412570\pi$
$228$	4.79648	−	14.7620i	0.317654	−	0.977640i
$229$	−5.20418	−	3.78106i	−0.343902	−	0.249859i	0.402404	−	0.915462i	$-0.368175\pi$
$229$	−5.20418	−	3.78106i	−0.343902	−	0.249859i	−0.746306	+	0.665603i	$0.768175\pi$
$230$	4.71120			0.310647
$231$	20.4460			1.34525
$232$	4.73129	+	3.43748i	0.310624	+	0.225682i
$233$	−20.6613			−1.35356			−0.676782	−	0.736183i	$-0.736626\pi$
$233$	−20.6613			−1.35356			−0.676782	+	0.736183i	$0.736626\pi$
$234$	−3.71598	−	2.69982i	−0.242921	−	0.176493i
$235$	9.16554	−	6.65916i	0.597894	−	0.434395i
$236$	0.790030	+	0.573990i	0.0514266	+	0.0373636i
$237$	7.34147	−	22.5947i	0.476880	−	1.46769i
$238$	−16.1377	+	11.7247i	−1.04605	+	0.760002i
$239$	11.1011	−	8.06541i	0.718070	−	0.521708i	−0.167697	−	0.985839i	$-0.553633\pi$
$239$	11.1011	−	8.06541i	0.718070	−	0.521708i	0.885767	+	0.464130i	$0.153633\pi$
$240$	8.58050	−	6.23410i	0.553869	−	0.402409i
$241$	7.95560	+	24.4848i	0.512465	+	1.57721i	0.787847	+	0.615871i	$0.211196\pi$
$241$	7.95560	+	24.4848i	0.512465	+	1.57721i	−0.275382	+	0.961335i	$0.588804\pi$
$242$	2.36107	+	7.26664i	0.151776	+	0.467117i
$243$	21.5013			1.37931
$244$	−7.29459	−	2.79086i	−0.466988	−	0.178667i
$245$	44.5015			2.84309
$246$	−1.66601	−	5.12746i	−0.106221	−	0.326915i
$247$	2.14787	+	6.61048i	0.136666	+	0.420615i
$248$	−2.07965	+	1.51095i	−0.132058	+	0.0959457i
$249$	−30.9994	+	22.5224i	−1.96451	+	1.42730i
$250$	20.5533	−	14.9329i	1.29991	−	0.944437i
$251$	1.46160	−	4.49833i	0.0922551	−	0.283932i	−0.894274	−	0.447521i	$-0.852307\pi$
$251$	1.46160	−	4.49833i	0.0922551	−	0.283932i	0.986529	+	0.163589i	$0.0523070\pi$
$252$	−13.4084	−	9.74176i	−0.844648	−	0.613673i
$253$	−1.73065	+	1.25739i	−0.108805	+	0.0790514i
$254$	−15.0678	−	10.9474i	−0.945435	−	0.686899i
$255$	49.8318			3.12059
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	25.9850			1.62090			0.810449	−	0.585809i	$-0.199223\pi$
$257$	25.9850			1.62090			0.810449	+	0.585809i	$0.199223\pi$
$258$	−21.7920			−1.35671
$259$	2.53386	+	1.84095i	0.157446	+	0.114391i
$260$	−1.46765	+	4.51697i	−0.0910200	+	0.280131i
$261$	−18.4699	+	13.4192i	−1.14326	+	0.830627i
$262$	10.3739	+	7.53711i	0.640904	+	0.465644i
$263$	3.38165	+	10.4077i	0.208522	+	0.641764i	0.999550	+	0.0299846i	$0.00954584\pi$
$263$	3.38165	+	10.4077i	0.208522	+	0.641764i	−0.791029	+	0.611779i	$0.790454\pi$
$264$	−1.48819	+	4.58017i	−0.0915915	+	0.281890i
$265$	−1.78985			−0.109950
$266$	7.75018	+	23.8526i	0.475194	+	1.46250i
$267$	−34.0723	+	24.7550i	−2.08519	+	1.51498i
$268$	−0.844193	+	2.59816i	−0.0515673	+	0.158708i
$269$	−4.22917	+	13.0160i	−0.257857	+	0.793601i	0.735397	+	0.677637i	$0.236996\pi$
$269$	−4.22917	+	13.0160i	−0.257857	+	0.793601i	−0.993253	+	0.115965i	$0.963004\pi$
$270$	2.96211	+	9.11645i	0.180268	+	0.554809i
$271$	−8.63104	−	6.27082i	−0.524299	−	0.380925i	0.293922	−	0.955829i	$-0.405039\pi$
$271$	−8.63104	−	6.27082i	−0.524299	−	0.380925i	−0.818221	+	0.574904i	$0.805039\pi$
$272$	−1.45189	−	4.46846i	−0.0880339	−	0.270940i
$273$	13.1252			0.794374
$274$	5.78725	−	17.8113i	0.349621	−	1.07602i
$275$	−6.39667	+	19.6869i	−0.385734	+	1.18717i
$276$	3.06664			0.184590
$277$	−3.32700	−	10.2394i	−0.199900	−	0.615229i	−0.999884	−	0.0152079i	$-0.995159\pi$
$277$	−3.32700	−	10.2394i	−0.199900	−	0.615229i	0.799984	−	0.600021i	$-0.204841\pi$
$278$	−16.8216	−	12.2216i	−1.00889	−	0.733005i
$279$	−3.10099	−	9.54387i	−0.185652	−	0.571377i
$280$	−5.29574	+	16.2986i	−0.316481	+	0.974028i
$281$	9.21326	−	28.3555i	0.549617	−	1.69155i	−0.160135	−	0.987095i	$-0.551193\pi$
$281$	9.21326	−	28.3555i	0.549617	−	1.69155i	0.709752	−	0.704452i	$-0.248807\pi$
$282$	5.96610	−	4.33462i	0.355276	−	0.258123i
$283$	−4.58745	−	14.1187i	−0.272696	−	0.839272i	−0.989820	−	0.142326i	$-0.954542\pi$
$283$	−4.58745	−	14.1187i	−0.272696	−	0.839272i	0.717124	−	0.696946i	$-0.245458\pi$
$284$	2.62530			0.155783
$285$	19.3613	−	59.5878i	1.14686	−	3.52968i
$286$	−0.666413	−	2.05101i	−0.0394058	−	0.121279i
$287$	7.04763	+	5.12040i	0.416009	+	0.302248i
$288$	3.15823	−	2.29459i	0.186100	−	0.135210i
$289$	1.56831	−	4.82676i	0.0922535	−	0.283927i
$290$	19.0981	+	13.8756i	1.12148	+	0.814803i
$291$	−26.2676			−1.53983
$292$	−2.57975			−0.150968
$293$	9.83250	+	7.14373i	0.574421	+	0.417341i	0.836708	−	0.547649i	$-0.184477\pi$
$293$	9.83250	+	7.14373i	0.574421	+	0.417341i	−0.262288	+	0.964990i	$0.584477\pi$
$294$	28.9672			1.68940
$295$	3.18900	+	2.31694i	0.185671	+	0.134898i
$296$	−0.596828	+	0.433621i	−0.0346899	+	0.0252037i
$297$	−3.52125	−	2.55834i	−0.204324	−	0.148450i
$298$	−0.824952	+	2.53894i	−0.0477882	+	0.147077i
$299$	−1.11098	+	0.807177i	−0.0642498	+	0.0466802i
$300$	24.0072	−	17.4423i	1.38606	−	1.00703i
$301$	28.4868	−	20.6969i	1.64195	−	1.19295i
$302$	−1.70918	−	5.26032i	−0.0983524	−	0.302698i
$303$	1.43436	+	4.41450i	0.0824016	+	0.253606i
$304$	−5.90740			−0.338813
$305$	−29.4450	−	11.2655i	−1.68602	−	0.645060i
$306$	18.3416			1.04852
$307$	−3.89089	−	11.9749i	−0.222065	−	0.683444i	−0.998576	−	0.0533417i	$-0.983013\pi$
$307$	−3.89089	−	11.9749i	−0.222065	−	0.683444i	0.776512	−	0.630103i	$-0.216987\pi$
$308$	−2.40462	−	7.40066i	−0.137016	−	0.421692i
$309$	14.4686	−	10.5120i	0.823088	−	0.598008i
$310$	−8.39463	+	6.09905i	−0.476783	+	0.346403i
$311$	7.54440	−	5.48133i	0.427804	−	0.310818i	−0.352966	−	0.935636i	$-0.614827\pi$
$311$	7.54440	−	5.48133i	0.427804	−	0.310818i	0.780770	+	0.624818i	$0.214827\pi$
$312$	−0.955335	+	2.94022i	−0.0540852	+	0.166457i
$313$	26.7447	+	19.4312i	1.51170	+	1.09832i	0.965415	+	0.260719i	$0.0839595\pi$
$313$	26.7447	+	19.4312i	1.51170	+	1.09832i	0.546288	+	0.837598i	$0.316040\pi$
$314$	−5.35031	+	3.88723i	−0.301936	+	0.219369i
$315$	−54.1237	−	39.3232i	−3.04953	−	2.21561i
$316$	−9.04185			−0.508644
$317$	−5.87792	−	4.27056i	−0.330137	−	0.239859i	0.410352	−	0.911927i	$-0.365406\pi$
$317$	−5.87792	−	4.27056i	−0.330137	−	0.239859i	−0.740489	+	0.672069i	$0.765406\pi$
$318$	−1.16506			−0.0653335
$319$	−10.7190			−0.600147
$320$	−3.26564	−	2.37263i	−0.182555	−	0.132634i
$321$	−8.93450	+	27.4976i	−0.498675	+	1.53476i
$322$	−4.00876	+	2.91254i	−0.223400	+	0.162309i
$323$	−22.4546	−	16.3142i	−1.24941	−	0.907749i
$324$	−1.69089	−	5.20401i	−0.0939381	−	0.289112i
$325$	−4.10632	+	12.6379i	−0.227778	+	0.701027i
$326$	−0.796365			−0.0441066
$327$	−5.74900	−	17.6936i	−0.317921	−	0.978459i
$328$	−1.66001	+	1.20607i	−0.0916586	+	0.0665939i
$329$	−3.68217	+	11.3326i	−0.203005	+	0.624785i
$330$	−6.00715	+	18.4881i	−0.330683	+	1.01774i
$331$	2.84390	+	8.75262i	0.156315	+	0.481087i	0.998292	−	0.0584261i	$-0.0186082\pi$
$331$	2.84390	+	8.75262i	0.156315	+	0.481087i	−0.841977	+	0.539513i	$0.818608\pi$
$332$	11.7980	+	8.57177i	0.647501	+	0.470437i
$333$	−0.889938	−	2.73895i	−0.0487683	−	0.150093i
$334$	0.658752			0.0360453
$335$	−3.40764	+	10.4876i	−0.186179	+	0.573000i
$336$	−3.44714	+	10.6092i	−0.188057	+	0.578779i
$337$	19.2807			1.05029			0.525144	−	0.851013i	$-0.324011\pi$
$337$	19.2807			1.05029			0.525144	+	0.851013i	$0.324011\pi$
$338$	3.58942	+	11.0471i	0.195239	+	0.600883i
$339$	17.3687	+	12.6191i	0.943337	+	0.685374i
$340$	−5.86065	−	18.0372i	−0.317838	−	0.978205i
$341$	1.45595	−	4.48095i	0.0788440	−	0.242657i
$342$	7.12631	−	21.9325i	0.385347	−	1.18597i
$343$	−13.8234	+	10.0433i	−0.746391	+	0.542285i
$344$	2.56293	+	7.88788i	0.138184	+	0.425286i
$345$	12.3787			0.666446
$346$	2.42521	−	7.46404i	0.130380	−	0.401269i
$347$	−1.94067	−	5.97278i	−0.104181	−	0.320636i	0.885356	−	0.464913i	$-0.153914\pi$
$347$	−1.94067	−	5.97278i	−0.104181	−	0.320636i	−0.989537	+	0.144277i	$0.953914\pi$
$348$	12.4315	+	9.03200i	0.666397	+	0.484166i
$349$	−1.77010	+	1.28605i	−0.0947513	+	0.0688408i	−0.634152	−	0.773208i	$-0.718651\pi$
$349$	−1.77010	+	1.28605i	−0.0947513	+	0.0688408i	0.539401	+	0.842049i	$0.318651\pi$
$350$	−14.8168	+	45.6015i	−0.791993	+	2.43750i
$351$	−2.26045	−	1.64232i	−0.120654	−	0.0876603i
$352$	1.83287			0.0976922
$353$	7.80685			0.415517			0.207758	−	0.978180i	$-0.433383\pi$
$353$	7.80685			0.415517			0.207758	+	0.978180i	$0.433383\pi$
$354$	2.07581	+	1.50816i	0.110328	+	0.0801579i
$355$	10.5972			0.562441
$356$	12.9676	+	9.42148i	0.687279	+	0.499338i
$357$	−42.4020	+	30.8068i	−2.24415	+	1.63047i
$358$	0.266382	+	0.193538i	0.0140787	+	0.0102288i
$359$	−10.9811	+	33.7962i	−0.579558	+	1.78370i	0.0405459	+	0.999178i	$0.487090\pi$
$359$	−10.9811	+	33.7962i	−0.579558	+	1.78370i	−0.620104	+	0.784519i	$0.712910\pi$
$360$	12.7484	−	9.26223i	0.671898	−	0.488163i
$361$	−12.8613	+	9.34425i	−0.676908	+	0.491803i
$362$	−8.09488	+	5.88127i	−0.425457	+	0.309113i
$363$	6.20373	+	19.0931i	0.325612	+	1.00213i
$364$	−1.54364	−	4.75083i	−0.0809086	−	0.249011i
$365$	−10.4133			−0.545057
$366$	−19.1666	−	7.33301i	−1.00185	−	0.383303i
$367$	−36.7374			−1.91768			−0.958838	−	0.283953i	$-0.908354\pi$
$367$	−36.7374			−1.91768			−0.958838	+	0.283953i	$0.908354\pi$
$368$	−0.360664	−	1.11001i	−0.0188009	−	0.0578632i
$369$	−2.47526	−	7.61807i	−0.128857	−	0.396581i
$370$	−2.40913	+	1.75034i	−0.125245	+	0.0909956i
$371$	1.52299	−	1.10651i	0.0790696	−	0.0574474i
$372$	−5.46429	+	3.97004i	−0.283310	+	0.205837i
$373$	−7.07175	+	21.7646i	−0.366161	+	1.12693i	0.583090	+	0.812408i	$0.301844\pi$
$373$	−7.07175	+	21.7646i	−0.366161	+	1.12693i	−0.949251	+	0.314520i	$0.898156\pi$
$374$	6.96692	+	5.06176i	0.360251	+	0.261738i
$375$	54.0040	−	39.2362i	2.78875	−	2.02615i
$376$	−2.27063	−	1.64971i	−0.117099	−	0.0850774i
$377$	−6.88100			−0.354390
$378$	−8.15640	−	5.92597i	−0.419520	−	0.304799i
$379$	12.2381			0.628628			0.314314	−	0.949319i	$-0.398226\pi$
$379$	12.2381			0.628628			0.314314	+	0.949319i	$0.398226\pi$
$380$	−23.8456			−1.22325
$381$	−39.5906	−	28.7643i	−2.02829	−	1.47364i
$382$	0.806927	−	2.48346i	0.0412860	−	0.127065i
$383$	13.5114	−	9.81662i	0.690401	−	0.501606i	−0.186391	−	0.982476i	$-0.559679\pi$
$383$	13.5114	−	9.81662i	0.690401	−	0.501606i	0.876792	+	0.480870i	$0.159679\pi$
$384$	−2.12570	−	1.54441i	−0.108476	−	0.0788128i
$385$	−9.70639	−	29.8732i	−0.494683	−	1.52248i
$386$	2.81440	−	8.66182i	0.143249	−	0.440875i
$387$	−32.3772			−1.64583
$388$	3.08929	+	9.50787i	0.156835	+	0.482689i
$389$	21.2195	−	15.4169i	1.07587	−	0.781667i	0.0989137	−	0.995096i	$-0.468463\pi$
$389$	21.2195	−	15.4169i	1.07587	−	0.781667i	0.976959	+	0.213429i	$0.0684632\pi$
$390$	−3.85627	+	11.8684i	−0.195270	+	0.600978i
$391$	1.69455	−	5.21529i	0.0856970	−	0.263748i
$392$	−3.40679	−	10.4850i	−0.172069	−	0.529574i
$393$	27.2576	+	19.8038i	1.37496	+	0.998969i
$394$	−7.02252	−	21.6131i	−0.353789	−	1.08885i
$395$	−36.4980			−1.83641
$396$	−2.21105	+	6.80492i	−0.111110	+	0.341960i
$397$	−0.874495	+	2.69142i	−0.0438896	+	0.135078i	−0.970600	−	0.240698i	$-0.922624\pi$
$397$	−0.874495	+	2.69142i	−0.0438896	+	0.135078i	0.926711	+	0.375776i	$0.122624\pi$
$398$	17.8996			0.897224
$399$	20.3636	+	62.6728i	1.01946	+	3.13757i
$400$	−9.13688	−	6.63833i	−0.456844	−	0.331917i
$401$	−1.40988	−	4.33917i	−0.0704061	−	0.216688i	0.909662	−	0.415349i	$-0.136341\pi$
$401$	−1.40988	−	4.33917i	−0.0704061	−	0.216688i	−0.980068	+	0.198661i	$0.936341\pi$
$402$	−2.21812	+	6.82668i	−0.110630	+	0.340484i
$403$	0.934641	−	2.87653i	0.0465578	−	0.143290i
$404$	1.42919	−	1.03836i	0.0711047	−	0.0516606i
$405$	−6.82536	−	21.0063i	−0.339155	−	1.04381i
$406$	−24.8287			−1.23223
$407$	0.417835	−	1.28596i	0.0207113	−	0.0637429i
$408$	−3.81485	−	11.7409i	−0.188863	−	0.581262i
$409$	−23.7835	−	17.2797i	−1.17602	−	0.854428i	−0.184302	−	0.982870i	$-0.559002\pi$
$409$	−23.7835	−	17.2797i	−1.17602	−	0.854428i	−0.991717	+	0.128442i	$0.959002\pi$
$410$	−6.70072	+	4.86836i	−0.330925	+	0.240431i
$411$	15.2060	−	46.7993i	0.750058	−	2.30844i
$412$	−5.50658	−	4.00076i	−0.271290	−	0.197103i
$413$	−4.14590			−0.204006
$414$	4.55623			0.223926
$415$	47.6235	+	34.6005i	2.33774	+	1.69847i
$416$	1.17660			0.0576877
$417$	−44.1989	−	32.1124i	−2.16443	−	1.57255i
$418$	8.75962	−	6.36424i	0.428447	−	0.311285i
$419$	26.2589	+	19.0782i	1.28283	+	0.932030i	0.999635	−	0.0270326i	$-0.00860578\pi$
$419$	26.2589	+	19.0782i	1.28283	+	0.932030i	0.283195	+	0.959062i	$0.408606\pi$
$420$	−13.9146	+	42.8247i	−0.678962	+	2.08963i
$421$	−20.1651	+	14.6508i	−0.982785	+	0.714035i	−0.958329	−	0.285665i	$-0.907785\pi$
$421$	−20.1651	+	14.6508i	−0.982785	+	0.714035i	−0.0244561	+	0.999701i	$0.507785\pi$
$422$	18.3060	−	13.3001i	0.891121	−	0.647437i
$423$	8.86406	−	6.44012i	0.430985	−	0.313129i
$424$	0.137021	+	0.421708i	0.00665434	+	0.0204800i
$425$	−16.3974	−	50.4660i	−0.795390	−	2.44796i
$426$	6.89800			0.334209
$427$	32.0193	−	8.61758i	1.54952	−	0.417034i
$428$	11.0038			0.531891
$429$	−1.75100	−	5.38904i	−0.0845393	−	0.260185i
$430$	10.3454	+	31.8399i	0.498900	+	1.53546i
$431$	0.703990	−	0.511479i	0.0339100	−	0.0246371i	−0.570701	−	0.821158i	$-0.693329\pi$
$431$	0.703990	−	0.511479i	0.0339100	−	0.0246371i	0.604611	+	0.796521i	$0.293329\pi$
$432$	1.92117	−	1.39581i	0.0924323	−	0.0671560i
$433$	2.06132	−	1.49764i	0.0990607	−	0.0719718i	−0.537152	−	0.843485i	$-0.680500\pi$
$433$	2.06132	−	1.49764i	0.0990607	−	0.0719718i	0.636213	+	0.771513i	$0.280500\pi$
$434$	3.37247	−	10.3794i	0.161884	−	0.498226i
$435$	50.1804	+	36.4582i	2.40597	+	1.74804i
$436$	−5.72828	+	4.16184i	−0.274335	+	0.199316i
$437$	−5.57794	−	4.05261i	−0.266829	−	0.193863i
$438$	−6.77830			−0.323880
$439$	13.2691	+	9.64058i	0.633301	+	0.460120i	0.857542	−	0.514414i	$-0.171990\pi$
$439$	13.2691	+	9.64058i	0.633301	+	0.460120i	−0.224242	+	0.974534i	$0.571990\pi$
$440$	7.39848			0.352709
$441$	43.0377			2.04941
$442$	4.47239	+	3.24938i	0.212730	+	0.154557i
$443$	12.1018	−	37.2455i	0.574974	−	1.76959i	−0.0612941	−	0.998120i	$-0.519523\pi$
$443$	12.1018	−	37.2455i	0.574974	−	1.76959i	0.636268	−	0.771468i	$-0.280477\pi$
$444$	−1.56817	+	1.13934i	−0.0744220	+	0.0540707i
$445$	52.3443	+	38.0304i	2.48136	+	1.80281i
$446$	6.38637	+	19.6552i	0.302403	+	0.930701i
$447$	−2.16757	+	6.67109i	−0.102522	+	0.315532i
$448$	4.24554			0.200583
$449$	6.44893	+	19.8478i	0.304344	+	0.936674i	0.979921	+	0.199385i	$0.0638944\pi$
$449$	6.44893	+	19.8478i	0.304344	+	0.936674i	−0.675577	+	0.737289i	$0.736106\pi$
$450$	35.6684	−	25.9146i	1.68142	−	1.22163i
$451$	1.16216	−	3.57676i	0.0547240	−	0.168423i
$452$	2.52492	−	7.77091i	0.118762	−	0.365513i
$453$	−4.49089	−	13.8215i	−0.211000	−	0.649392i
$454$	8.44273	+	6.13401i	0.396237	+	0.287883i
$455$	−6.23098	−	19.1770i	−0.292113	−	0.899031i
$456$	−15.5217			−0.726872
$457$	−3.03227	+	9.33236i	−0.141844	+	0.436550i	−0.996592	−	0.0824936i	$-0.973712\pi$
$457$	−3.03227	+	9.33236i	−0.141844	+	0.436550i	0.854748	+	0.519043i	$0.173712\pi$
$458$	−1.98782	+	6.11788i	−0.0928847	+	0.285870i
$459$	11.1573			0.520779
$460$	−1.45584	−	4.48061i	−0.0678789	−	0.208910i
$461$	−19.4555	−	14.1353i	−0.906135	−	0.658346i	0.0338993	−	0.999425i	$-0.489207\pi$
$461$	−19.4555	−	14.1353i	−0.906135	−	0.658346i	−0.940034	+	0.341080i	$0.889207\pi$
$462$	−6.31815	−	19.4453i	−0.293947	−	0.904676i
$463$	7.81792	−	24.0611i	0.363330	−	1.11821i	−0.587691	−	0.809086i	$-0.699963\pi$
$463$	7.81792	−	24.0611i	0.363330	−	1.11821i	0.951020	−	0.309128i	$-0.100037\pi$
$464$	1.80719	−	5.56196i	0.0838967	−	0.258208i
$465$	−22.0569	+	16.0253i	−1.02287	+	0.743155i
$466$	6.38468	+	19.6500i	0.295765	+	0.910270i
$467$	11.6845			0.540696			0.270348	−	0.962763i	$-0.412861\pi$
$467$	11.6845			0.540696			0.270348	+	0.962763i	$0.412861\pi$
$468$	−1.41938	+	4.36840i	−0.0656108	+	0.201929i
$469$	−3.58406	−	11.0306i	−0.165496	−	0.509345i
$470$	−9.16554	−	6.65916i	−0.422775	−	0.307164i
$471$	−14.0580	+	10.2137i	−0.647757	+	0.470623i
$472$	0.301764	−	0.928736i	0.0138898	−	0.0427485i
$473$	−12.2982	−	8.93519i	−0.565473	−	0.410840i
$474$	−23.7575			−1.09122
$475$	−66.7170			−3.06119
$476$	16.1377	+	11.7247i	0.739672	+	0.537403i
$477$	−1.73098			−0.0792560
$478$	−11.1011	−	8.06541i	−0.507752	−	0.368903i
$479$	−25.8383	+	18.7726i	−1.18058	+	0.857743i	−0.992237	−	0.124360i	$-0.960312\pi$
$479$	−25.8383	+	18.7726i	−1.18058	+	0.857743i	−0.188344	+	0.982103i	$0.560312\pi$
$480$	−8.58050	−	6.23410i	−0.391644	−	0.284546i
$481$	0.268228	−	0.825520i	0.0122301	−	0.0376405i
$482$	20.8280	−	15.1325i	0.948691	−	0.689264i
$483$	−10.5330	+	7.65271i	−0.479270	+	0.348210i
$484$	6.18137	−	4.49103i	0.280971	−	0.204138i
$485$	12.4701	+	38.3791i	0.566239	+	1.74270i
$486$	−6.64428	−	20.4490i	−0.301391	−	0.927585i
$487$	16.3072			0.738952			0.369476	−	0.929240i	$-0.379537\pi$
$487$	16.3072			0.738952			0.369476	+	0.929240i	$0.379537\pi$
$488$	−0.400117	+	7.79999i	−0.0181124	+	0.353089i
$489$	−2.09245			−0.0946240
$490$	−13.7517	−	42.3234i	−0.621239	−	1.91198i
$491$	−4.93638	−	15.1926i	−0.222776	−	0.685634i	−0.998510	−	0.0545734i	$-0.982620\pi$
$491$	−4.93638	−	15.1926i	−0.222776	−	0.685634i	0.775734	−	0.631060i	$-0.217380\pi$
$492$	−4.36168	+	3.16895i	−0.196640	+	0.142867i
$493$	22.2296	−	16.1507i	1.00117	−	0.727393i
$494$	5.62321	−	4.08550i	0.253000	−	0.183815i
$495$	−8.92505	+	27.4685i	−0.401151	+	1.23462i
$496$	2.07965	+	1.51095i	0.0933790	+	0.0678438i
$497$	−9.01717	+	6.55135i	−0.404475	+	0.293868i
$498$	30.9994	+	22.5224i	1.38912	+	1.00925i
$499$	4.06988			0.182193			0.0910964	−	0.995842i	$-0.470963\pi$
$499$	4.06988			0.182193			0.0910964	+	0.995842i	$0.470963\pi$
$500$	−20.5533	−	14.9329i	−0.919173	−	0.667818i
$501$	1.73087			0.0773298
$502$	−4.72982			−0.211102
$503$	20.4987	+	14.8932i	0.913990	+	0.664053i	0.942021	−	0.335554i	$-0.108924\pi$
$503$	20.4987	+	14.8932i	0.913990	+	0.664053i	−0.0280305	+	0.999607i	$0.508924\pi$
$504$	−5.12154	+	15.7625i	−0.228132	+	0.702117i
$505$	5.76899	−	4.19142i	0.256717	−	0.186516i
$506$	1.73065	+	1.25739i	0.0769367	+	0.0558978i
$507$	9.43122	+	29.0263i	0.418855	+	1.28910i
$508$	−5.75537	+	17.7132i	−0.255353	+	0.785896i
$509$	15.3068			0.678461			0.339231	−	0.940703i	$-0.389833\pi$
$509$	15.3068			0.678461			0.339231	+	0.940703i	$0.389833\pi$
$510$	−15.3989	−	47.3929i	−0.681874	−	2.09859i
$511$	8.86069	−	6.43767i	0.391974	−	0.284786i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.33498	−	13.3417i	0.191394	−	0.589050i
$514$	−8.02980	−	24.7132i	−0.354179	−	1.09005i
$515$	−22.2276	−	16.1493i	−0.979466	−	0.711624i
$516$	6.73410	+	20.7254i	0.296452	+	0.912387i
$517$	5.14423			0.226243
$518$	0.967847	−	2.97873i	0.0425248	−	0.130878i
$519$	6.37226	−	19.6118i	0.279711	−	0.860863i
$520$	4.74943			0.208276
$521$	4.23886	+	13.0459i	0.185708	+	0.571550i	0.999960	−	0.00896166i	$-0.00285262\pi$
$521$	4.23886	+	13.0459i	0.185708	+	0.571550i	−0.814252	+	0.580512i	$0.802853\pi$
$522$	18.4699	+	13.4192i	0.808407	+	0.587342i
$523$	3.36954	+	10.3704i	0.147340	+	0.453465i	0.997304	−	0.0733744i	$-0.0233768\pi$
$523$	3.36954	+	10.3704i	0.147340	+	0.453465i	−0.849965	+	0.526840i	$0.823377\pi$
$524$	3.96249	−	12.1953i	0.173102	−	0.532754i
$525$	−38.9313	+	119.818i	−1.69910	+	5.22930i
$526$	8.85328	−	6.43229i	0.386021	−	0.280461i
$527$	3.73222	+	11.4866i	0.162578	+	0.500363i
$528$	4.81587			0.209584
$529$	−6.68645	+	20.5788i	−0.290715	+	0.894729i
$530$	0.553095	+	1.70225i	0.0240249	+	0.0739410i
$531$	3.08410	+	2.24073i	0.133839	+	0.0972395i
$532$	20.2902	−	14.7417i	0.879693	−	0.639134i
$533$	0.746045	−	2.29609i	0.0323148	−	0.0994547i
$534$	34.0723	+	24.7550i	1.47445	+	1.07125i
$535$	44.4176			1.92034
$536$	2.73187			0.117999
$537$	0.699919	+	0.508521i	0.0302037	+	0.0219443i
$538$	13.6859			0.590040
$539$	16.3475	+	11.8772i	0.704137	+	0.511586i
$540$	7.75491	−	5.63427i	0.333718	−	0.242461i
$541$	−35.4375	−	25.7468i	−1.52358	−	1.10694i	−0.959679	−	0.281097i	$-0.909302\pi$
$541$	−35.4375	−	25.7468i	−1.52358	−	1.10694i	−0.563896	−	0.825846i	$-0.690698\pi$
$542$	−3.29677	+	10.1464i	−0.141608	+	0.435825i
$543$	−21.2693	+	15.4531i	−0.912754	+	0.663155i
$544$	−3.80110	+	2.76166i	−0.162971	+	0.118405i
$545$	−23.1225	+	16.7995i	−0.990461	+	0.719612i
$546$	−4.05591	−	12.4828i	−0.173577	−	0.534215i
$547$	−6.52445	−	20.0802i	−0.278965	−	0.858567i	−0.988143	−	0.153537i	$-0.950933\pi$
$547$	−6.52445	−	20.0802i	−0.278965	−	0.858567i	0.709177	−	0.705030i	$-0.249067\pi$
$548$	−18.7279			−0.800018
$549$	−28.4765	−	10.8949i	−1.21535	−	0.464984i
$550$	20.7001			0.882653
$551$	−10.6758	−	32.8567i	−0.454804	−	1.39974i
$552$	−0.947645	−	2.91655i	−0.0403345	−	0.124137i
$553$	31.0562	−	22.5636i	1.32064	−	0.959503i
$554$	−8.71019	+	6.32833i	−0.370061	+	0.268865i
$555$	−6.33000	+	4.59902i	−0.268694	+	0.195217i
$556$	−6.42529	+	19.7750i	−0.272493	+	0.838648i
$557$	14.3723	+	10.4421i	0.608973	+	0.442445i	0.849053	−	0.528308i	$-0.177173\pi$
$557$	14.3723	+	10.4421i	0.608973	+	0.442445i	−0.240079	+	0.970753i	$0.577173\pi$
$558$	−8.11850	+	5.89844i	−0.343684	+	0.249701i
$559$	−7.89481	−	5.73591i	−0.333915	−	0.242603i
$560$	17.1374			0.724186
$561$	18.3056	+	13.2998i	0.772864	+	0.561518i
$562$	−29.8147			−1.25766
$563$	28.9165			1.21869			0.609343	−	0.792907i	$-0.291433\pi$
$563$	28.9165			1.21869			0.609343	+	0.792907i	$0.291433\pi$
$564$	−5.96610	−	4.33462i	−0.251218	−	0.182521i
$565$	10.1920	−	31.3677i	0.428780	−	1.31965i
$566$	−12.0101	+	8.72586i	−0.504823	+	0.366775i
$567$	18.7941	+	13.6547i	0.789280	+	0.573445i
$568$	−0.811263	−	2.49681i	−0.0340399	−	0.104764i
$569$	11.9215	−	36.6907i	0.499777	−	1.53816i	−0.309600	−	0.950867i	$-0.600195\pi$
$569$	11.9215	−	36.6907i	0.499777	−	1.53816i	0.809377	−	0.587289i	$-0.199805\pi$
$570$	−62.6544			−2.62430
$571$	6.80897	+	20.9559i	0.284947	+	0.876976i	0.986415	+	0.164275i	$0.0525283\pi$
$571$	6.80897	+	20.9559i	0.284947	+	0.876976i	−0.701468	+	0.712701i	$0.747472\pi$
$572$	−1.74469	+	1.26759i	−0.0729492	+	0.0530007i
$573$	2.12020	−	6.52532i	0.0885728	−	0.272599i
$574$	2.69196	−	8.28499i	0.112360	−	0.345809i
$575$	−4.07326	−	12.5362i	−0.169867	−	0.522796i
$576$	−3.15823	−	2.29459i	−0.131593	−	0.0956078i
$577$	−13.1472	−	40.4631i	−0.547327	−	1.68450i	−0.715392	−	0.698724i	$-0.753752\pi$
$577$	−13.1472	−	40.4631i	−0.547327	−	1.68450i	0.168065	−	0.985776i	$-0.446248\pi$
$578$	−5.07516			−0.211099
$579$	7.39484	−	22.7590i	0.307319	−	0.945831i
$580$	7.29483	−	22.4512i	0.302901	−	0.932235i
$581$	−61.9134			−2.56860
$582$	8.11714	+	24.9820i	0.336466	+	1.03554i
$583$	−0.657498	−	0.477700i	−0.0272308	−	0.0197843i
$584$	0.797186	+	2.45349i	0.0329878	+	0.101526i
$585$	−5.72940	+	17.6333i	−0.236882	+	0.729047i
$586$	3.75568	−	11.5588i	0.155146	−	0.477489i
$587$	3.14193	−	2.28275i	0.129681	−	0.0942191i	−0.521054	−	0.853524i	$-0.674461\pi$
$587$	3.14193	−	2.28275i	0.129681	−	0.0942191i	0.650735	+	0.759305i	$0.274461\pi$
$588$	−8.95136	−	27.5494i	−0.369148	−	1.13612i
$589$	15.1855			0.625707
$590$	1.21809	−	3.74890i	0.0501480	−	0.154340i
$591$	−18.4517	−	56.7885i	−0.759002	−	2.33597i
$592$	0.596828	+	0.433621i	0.0245295	+	0.0178217i
$593$	−26.4212	+	19.1961i	−1.08499	+	0.788289i	−0.978546	−	0.206030i	$-0.933946\pi$
$593$	−26.4212	+	19.1961i	−1.08499	+	0.788289i	−0.106441	+	0.994319i	$0.533946\pi$
$594$	−1.34500	+	4.13948i	−0.0551859	+	0.169845i
$595$	65.1409	+	47.3276i	2.67052	+	1.94024i
$596$	2.66960			0.109351
$597$	47.0312			1.92486
$598$	1.11098	+	0.807177i	0.0454315	+	0.0330079i
$599$	−30.8074			−1.25875			−0.629377	−	0.777100i	$-0.716690\pi$
$599$	−30.8074			−1.25875			−0.629377	+	0.777100i	$0.716690\pi$
$600$	−24.0072	−	17.4423i	−0.980090	−	0.712077i
$601$	1.23810	−	0.899530i	0.0505030	−	0.0366926i	−0.562247	−	0.826969i	$-0.690063\pi$
$601$	1.23810	−	0.899530i	0.0505030	−	0.0366926i	0.612750	+	0.790277i	$0.290063\pi$
$602$	−28.4868	−	20.6969i	−1.16104	−	0.843543i
$603$	−3.29555	+	10.1427i	−0.134205	+	0.413041i
$604$	−4.47470	+	3.25106i	−0.182073	+	0.132284i
$605$	24.9515	−	18.1283i	1.01442	−	0.737020i
$606$	3.75519	−	2.72831i	0.152544	−	0.110830i
$607$	−2.71082	−	8.34303i	−0.110029	−	0.338633i	0.880849	−	0.473397i	$-0.156972\pi$
$607$	−2.71082	−	8.34303i	−0.110029	−	0.338633i	−0.990878	+	0.134764i	$0.956972\pi$
$608$	1.82549	+	5.61827i	0.0740333	+	0.227851i
$609$	−65.2376			−2.64356
$610$	−1.61510	+	31.4851i	−0.0653933	+	1.27480i
$611$	3.30232			0.133598
$612$	−5.66787	−	17.4439i	−0.229110	−	0.705128i
$613$	5.80451	+	17.8644i	0.234442	+	0.721538i	0.997195	+	0.0748480i	$0.0238472\pi$
$613$	5.80451	+	17.8644i	0.234442	+	0.721538i	−0.762753	+	0.646690i	$0.776153\pi$
$614$	−10.1865	+	7.40090i	−0.411093	+	0.298676i
$615$	−17.6062	+	12.7916i	−0.709950	+	0.515809i
$616$	−6.29538	+	4.57386i	−0.253648	+	0.184286i
$617$	−0.937598	+	2.88563i	−0.0377463	+	0.116171i	−0.968154	−	0.250355i	$-0.919453\pi$
$617$	−0.937598	+	2.88563i	−0.0377463	+	0.116171i	0.930408	+	0.366526i	$0.119453\pi$
$618$	−14.4686	−	10.5120i	−0.582011	−	0.422856i
$619$	−12.7208	+	9.24224i	−0.511294	+	0.371477i	−0.813314	−	0.581825i	$-0.802339\pi$
$619$	−12.7208	+	9.24224i	−0.511294	+	0.371477i	0.302020	+	0.953302i	$0.402339\pi$
$620$	8.39463	+	6.09905i	0.337136	+	0.244944i
$621$	2.77158			0.111220
$622$	−7.54440	−	5.48133i	−0.302503	−	0.219781i
$623$	−68.0508			−2.72640
$624$	3.09153			0.123760
$625$	−37.2803	−	27.0857i	−1.49121	−	1.08343i
$626$	10.2156	−	31.4403i	0.408297	−	1.25661i
$627$	23.0160	−	16.7221i	0.919169	−	0.667815i
$628$	5.35031	+	3.88723i	0.213501	+	0.155117i
$629$	1.07109	+	3.29647i	0.0427071	+	0.131439i
$630$	−20.6734	+	63.6262i	−0.823649	+	2.53493i
$631$	−30.5625			−1.21668			−0.608338	−	0.793678i	$-0.708163\pi$
$631$	−30.5625			−1.21668			−0.608338	+	0.793678i	$0.708163\pi$
$632$	2.79408	+	8.59931i	0.111143	+	0.342062i
$633$	48.0990	−	34.9460i	1.91177	−	1.38898i
$634$	−2.24517	+	6.90991i	−0.0891670	+	0.274428i
$635$	−23.2319	+	71.5004i	−0.921929	+	2.83741i
$636$	0.360024	+	1.10804i	0.0142759	+	0.0439367i
$637$	10.4942	+	7.62450i	0.415797	+	0.302094i
$638$	3.31234	+	10.1943i	0.131137	+	0.403598i
$639$	10.2486			0.405429
$640$	−1.24737	+	3.83900i	−0.0493064	+	0.151750i
$641$	4.37860	−	13.4760i	0.172944	−	0.532268i	−0.826589	−	0.562806i	$-0.809722\pi$
$641$	4.37860	−	13.4760i	0.172944	−	0.532268i	0.999534	+	0.0305376i	$0.00972193\pi$
$642$	28.9126			1.14109
$643$	−7.72794	−	23.7841i	−0.304760	−	0.937955i	−0.979767	−	0.200143i	$-0.935859\pi$
$643$	−7.72794	−	23.7841i	−0.304760	−	0.937955i	0.675007	−	0.737812i	$-0.264141\pi$
$644$	4.00876	+	2.91254i	0.157967	+	0.114770i
$645$	27.1826	+	83.6594i	1.07031	+	3.29409i
$646$	−8.57691	+	26.3970i	−0.337454	+	1.03858i
$647$	−2.23793	+	6.88765i	−0.0879823	+	0.270782i	−0.985361	−	0.170479i	$-0.945469\pi$
$647$	−2.23793	+	6.88765i	−0.0879823	+	0.270782i	0.897379	+	0.441261i	$0.145469\pi$
$648$	−4.42680	+	3.21626i	−0.173901	+	0.126347i
$649$	0.553095	+	1.70225i	0.0217109	+	0.0668192i
$650$	13.2883			0.521211
$651$	8.86117	−	27.2719i	0.347297	−	1.06887i
$652$	0.246090	+	0.757388i	0.00963764	+	0.0296616i
$653$	−27.7999	−	20.1978i	−1.08790	−	0.790402i	−0.108853	−	0.994058i	$-0.534718\pi$
$653$	−27.7999	−	20.1978i	−1.08790	−	0.790402i	−0.979043	+	0.203656i	$0.934718\pi$
$654$	−15.0511	+	10.9353i	−0.588544	+	0.427602i
$655$	15.9948	−	49.2270i	0.624970	−	1.92346i
$656$	1.66001	+	1.20607i	0.0648124	+	0.0470890i
$657$	−10.0708			−0.392898
$658$	11.9158			0.464525
$659$	−15.2913	−	11.1098i	−0.595665	−	0.432776i	0.248673	−	0.968588i	$-0.420006\pi$
$659$	−15.2913	−	11.1098i	−0.595665	−	0.432776i	−0.844337	+	0.535812i	$0.820006\pi$
$660$	19.4395			0.756683
$661$	31.7231	+	23.0482i	1.23389	+	0.896470i	0.997175	−	0.0751104i	$-0.0239309\pi$
$661$	31.7231	+	23.0482i	1.23389	+	0.896470i	0.236710	+	0.971580i	$0.423931\pi$
$662$	7.44542	−	5.40942i	0.289375	−	0.210243i
$663$	11.7512	+	8.53776i	0.456380	+	0.331579i
$664$	4.50645	−	13.8694i	0.174884	−	0.538238i
$665$	81.9027	−	59.5058i	3.17605	−	2.30754i
$666$	−2.32989	+	1.69276i	−0.0902813	+	0.0655932i
$667$	5.52204	−	4.01199i	0.213814	−	0.155345i
$668$	−0.203566	−	0.626511i	−0.00787619	−	0.0242404i
$669$	16.7802	+	51.6442i	0.648760	+	1.99668i
$670$	11.0273			0.426023
$671$	−7.80989	−	11.9971i	−0.301497	−	0.463141i
$672$	11.1552			0.430320
$673$	−0.467956	−	1.44022i	−0.0180384	−	0.0555164i	0.941632	−	0.336644i	$-0.109292\pi$
$673$	−0.467956	−	1.44022i	−0.0180384	−	0.0555164i	−0.959671	+	0.281127i	$0.909292\pi$
$674$	−5.95808	−	18.3371i	−0.229496	−	0.706318i
$675$	21.6973	−	15.7640i	0.835130	−	0.606758i
$676$	9.39722	−	6.82748i	0.361432	−	0.262595i
$677$	0.696948	−	0.506362i	0.0267859	−	0.0194611i	−0.574312	−	0.818637i	$-0.694730\pi$
$677$	0.696948	−	0.506362i	0.0267859	−	0.0194611i	0.601098	+	0.799176i	$0.294730\pi$
$678$	6.63424	−	20.4181i	0.254786	−	0.784152i
$679$	−34.3374	−	24.9476i	−1.31775	−	0.957400i
$680$	−15.3434	+	11.1476i	−0.588391	+	0.427491i
$681$	22.1833	+	16.1171i	0.850067	+	0.617610i
$682$	−4.71155			−0.180415
$683$	31.4314	+	22.8363i	1.20269	+	0.873806i	0.994547	−	0.104292i	$-0.0332578\pi$
$683$	31.4314	+	22.8363i	1.20269	+	0.873806i	0.208144	+	0.978098i	$0.433258\pi$
$684$	−23.0612			−0.881768
$685$	−75.5964			−2.88839
$686$	13.8234	+	10.0433i	0.527778	+	0.383453i
$687$	−5.22300	+	16.0748i	−0.199270	+	0.613290i
$688$	6.70983	−	4.87498i	0.255810	−	0.185857i
$689$	−0.422079	−	0.306658i	−0.0160799	−	0.0116827i
$690$	−3.82523	−	11.7728i	−0.145624	−	0.448184i
$691$	−3.66001	+	11.2644i	−0.139233	+	0.428516i	−0.996224	−	0.0868149i	$-0.972331\pi$
$691$	−3.66001	+	11.2644i	−0.139233	+	0.428516i	0.856991	+	0.515331i	$0.172331\pi$
$692$	−7.84816			−0.298342
$693$	−9.38712	−	28.8906i	−0.356587	−	1.09746i
$694$	−5.08075	+	3.69138i	−0.192863	+	0.140123i
$695$	−25.9361	+	79.8230i	−0.983811	+	3.02786i
$696$	4.74840	−	14.6141i	0.179988	−	0.553945i
$697$	2.97911	+	9.16877i	0.112842	+	0.347292i
$698$	1.77010	+	1.28605i	0.0669993	+	0.0486778i
$699$	16.7758	+	51.6306i	0.634518	+	1.95285i
$700$	47.9483			1.81228
$701$	8.91302	−	27.4314i	0.336640	−	1.03607i	−0.629269	−	0.777188i	$-0.716645\pi$
$701$	8.91302	−	27.4314i	0.336640	−	1.03607i	0.965909	−	0.258883i	$-0.0833545\pi$
$702$	−0.863417	+	2.65732i	−0.0325876	+	0.100294i
$703$	4.35801			0.164365
$704$	−0.566387	−	1.74316i	−0.0213465	−	0.0656979i
$705$	−24.0825	−	17.4970i	−0.907000	−	0.658974i
$706$	−2.41245	−	7.42475i	−0.0907937	−	0.279434i
$707$	−2.31764	+	7.13297i	−0.0871639	+	0.268263i
$708$	0.792888	−	2.44026i	0.0297985	−	0.0917105i
$709$	−34.4262	+	25.0121i	−1.29290	+	0.939348i	−0.999860	−	0.0167517i	$-0.994668\pi$
$709$	−34.4262	+	25.0121i	−1.29290	+	0.939348i	−0.293042	+	0.956100i	$0.594668\pi$
$710$	−3.27471	−	10.0785i	−0.122898	−	0.378240i
$711$	−35.2974			−1.32376
$712$	4.95317	−	15.2443i	0.185628	−	0.571304i
$713$	0.927117	+	2.85337i	0.0347208	+	0.106860i
$714$	42.4020	+	30.8068i	1.58685	+	1.15292i
$715$	−7.04255	+	5.11671i	−0.263377	+	0.191354i
$716$	0.101749	−	0.313150i	0.00380253	−	0.0117030i
$717$	−29.1682	−	21.1919i	−1.08930	−	0.791426i
$718$	35.5355			1.32617
$719$	−44.8832			−1.67386			−0.836931	−	0.547309i	$-0.815652\pi$
$719$	−44.8832			−1.67386			−0.836931	+	0.547309i	$0.815652\pi$
$720$	−12.7484	−	9.26223i	−0.475104	−	0.345183i
$721$	28.8973			1.07619
$722$	12.8613	+	9.34425i	0.478647	+	0.347757i
$723$	54.7258	−	39.7606i	2.03527	−	1.47871i
$724$	8.09488	+	5.88127i	0.300844	+	0.218576i
$725$	20.4101	−	62.8157i	0.758011	−	2.33292i
$726$	16.2416	−	11.8002i	0.602782	−	0.437947i
$727$	−10.5926	+	7.69594i	−0.392856	+	0.285427i	−0.766625	−	0.642095i	$-0.778065\pi$
$727$	−10.5926	+	7.69594i	−0.392856	+	0.285427i	0.373769	+	0.927522i	$0.378065\pi$
$728$	−4.04129	+	2.93617i	−0.149780	+	0.108822i
$729$	−12.3852	−	38.1178i	−0.458712	−	1.41177i
$730$	3.21789	+	9.90364i	0.119099	+	0.366550i
$731$	38.9678			1.44128
$732$	−1.05131	+	20.4945i	−0.0388575	+	0.757499i
$733$	39.9304			1.47486			0.737431	−	0.675423i	$-0.236039\pi$
$733$	39.9304			1.47486			0.737431	+	0.675423i	$0.236039\pi$
$734$	11.3525	+	34.9393i	0.419028	+	1.28963i
$735$	−36.1327	−	111.205i	−1.33277	−	4.10186i
$736$	−0.944229	+	0.686023i	−0.0348048	+	0.0252871i
$737$	−4.05087	+	2.94313i	−0.149216	+	0.108412i
$738$	−6.48031	+	4.70822i	−0.238544	+	0.173312i
$739$	0.523388	−	1.61082i	0.0192531	−	0.0592551i	−0.940968	−	0.338495i	$-0.890082\pi$
$739$	0.523388	−	1.61082i	0.0192531	−	0.0592551i	0.960221	+	0.279239i	$0.0900823\pi$
$740$	2.40913	+	1.75034i	0.0885614	+	0.0643436i
$741$	14.7750	−	10.7347i	0.542773	−	0.394348i
$742$	−1.52299	−	1.10651i	−0.0559106	−	0.0406214i
$743$	−24.3738			−0.894186			−0.447093	−	0.894487i	$-0.647541\pi$
$743$	−24.3738			−0.894186			−0.447093	+	0.894487i	$0.647541\pi$
$744$	5.46429	+	3.97004i	0.200331	+	0.145549i
$745$	10.7760			0.394802
$746$	22.8847			0.837867
$747$	46.0570	+	33.4623i	1.68514	+	1.22432i
$748$	2.66113	−	8.19010i	0.0973004	−	0.299460i
$749$	−37.7950	+	27.4597i	−1.38100	+	1.00336i
$750$	−54.0040	−	39.2362i	−1.97195	−	1.43270i
$751$	8.13897	+	25.0492i	0.296995	+	0.914057i	0.982544	+	0.186030i	$0.0595623\pi$
$751$	8.13897	+	25.0492i	0.296995	+	0.914057i	−0.685549	+	0.728027i	$0.740438\pi$
$752$	−0.867304	+	2.66929i	−0.0316273	+	0.0973389i
$753$	−12.4276			−0.452888
$754$	2.12635	+	6.54422i	0.0774370	+	0.238326i
$755$	−18.0624	+	13.1231i	−0.657358	+	0.477598i
$756$	−3.11547	+	9.58842i	−0.113308	+	0.348728i
$757$	−5.92195	+	18.2259i	−0.215237	+	0.662431i	0.783900	+	0.620887i	$0.213228\pi$
$757$	−5.92195	+	18.2259i	−0.215237	+	0.662431i	−0.999137	+	0.0415436i	$0.986772\pi$
$758$	−3.78177	−	11.6391i	−0.137360	−	0.422751i
$759$	4.54729	+	3.30380i	0.165056	+	0.119920i
$760$	7.36869	+	22.6785i	0.267290	+	0.822635i
$761$	43.5210			1.57764			0.788818	−	0.614627i	$-0.210693\pi$
$761$	43.5210			1.57764			0.788818	+	0.614627i	$0.210693\pi$
$762$	−15.1223	+	46.5415i	−0.547822	+	1.68602i
$763$	9.28928	−	28.5895i	0.336294	−	1.03501i
$764$	−2.61127			−0.0944724
$765$	−22.8787	−	70.4134i	−0.827181	−	2.54580i
$766$	−13.5114	−	9.81662i	−0.488187	−	0.354689i
$767$	0.355057	+	1.09275i	0.0128204	+	0.0394570i
$768$	−0.811944	+	2.49891i	−0.0292985	+	0.0901715i
$769$	−7.91807	+	24.3693i	−0.285533	+	0.878779i	0.700706	+	0.713450i	$0.252869\pi$
$769$	−7.91807	+	24.3693i	−0.285533	+	0.878779i	−0.986238	+	0.165329i	$0.947131\pi$
$770$	−25.4117	+	18.4626i	−0.915773	+	0.665348i
$771$	−21.0983	−	64.9340i	−0.759838	−	2.33854i
$772$	−9.10757			−0.327789
$773$	−11.5724	+	35.6162i	−0.416231	+	1.28103i	0.494915	+	0.868941i	$0.335199\pi$
$773$	−11.5724	+	35.6162i	−0.416231	+	1.28103i	−0.911146	+	0.412085i	$0.864801\pi$
$774$	10.0051	+	30.7926i	0.359626	+	1.10682i
$775$	23.4872	+	17.0644i	0.843684	+	0.612972i
$776$	8.08788	−	5.87619i	0.290338	−	0.210943i
$777$	2.54302	−	7.82662i	0.0912304	−	0.280778i
$778$	−21.2195	−	15.4169i	−0.760757	−	0.552722i
$779$	12.1213			0.434291
$780$	12.4791			0.446825
$781$	3.89286	+	2.82833i	0.139297	+	0.101205i
$782$	−5.48368			−0.196096
$783$	11.2354	+	8.16298i	0.401519	+	0.291721i
$784$	−8.91909	+	6.48010i	−0.318539	+	0.231432i
$785$	21.5968	+	15.6910i	0.770824	+	0.560037i
$786$	10.4115	−	32.0432i	0.371365	−	1.14294i
$787$	−11.4407	+	8.31217i	−0.407818	+	0.296297i	−0.772718	−	0.634750i	$-0.781103\pi$
$787$	−11.4407	+	8.31217i	−0.407818	+	0.296297i	0.364900	+	0.931047i	$0.381103\pi$
$788$	−18.3852	+	13.3576i	−0.654945	+	0.475846i
$789$	23.2620	−	16.9009i	0.828151	−	0.601687i
$790$	11.2785	+	34.7116i	0.401271	+	1.23498i
$791$	10.7196	+	32.9917i	0.381147	+	1.17305i
$792$	7.15512			0.254246
$793$	−5.01353	−	7.70147i	−0.178036	−	0.273487i
$794$	2.82992			0.100430
$795$	1.45326	+	4.47267i	0.0515418	+	0.158629i
$796$	−5.53127	−	17.0235i	−0.196051	−	0.603382i
$797$	31.4593	−	22.8565i	1.11435	−	0.809620i	0.131003	−	0.991382i	$-0.458180\pi$
$797$	31.4593	−	22.8565i	1.11435	−	0.809620i	0.983342	+	0.181762i	$0.0581802\pi$
$798$	53.3127	−	38.7339i	1.88725	−	1.37117i
$799$	−10.6684	+	7.75104i	−0.377420	+	0.274212i
$800$	−3.48998	+	10.7410i	−0.123389	+	0.379753i
$801$	50.6225	+	36.7794i	1.78866	+	1.29954i
$802$	−3.69112	+	2.68175i	−0.130338	+	0.0946960i
$803$	−3.82530	−	2.77925i	−0.134992	−	0.0980775i
$804$	7.17799			0.253148
$805$	16.1816	+	11.7566i	0.570327	+	0.414367i
$806$	−3.02456			−0.106536
$807$	35.9597			1.26584
$808$	−1.42919	−	1.03836i	−0.0502786	−	0.0365295i
$809$	−8.26459	+	25.4358i	−0.290567	+	0.894275i	0.694107	+	0.719872i	$0.255799\pi$
$809$	−8.26459	+	25.4358i	−0.290567	+	0.894275i	−0.984674	+	0.174403i	$0.944201\pi$
$810$	−17.8690	+	12.9826i	−0.627854	+	0.456162i
$811$	21.1246	+	15.3479i	0.741785	+	0.538938i	0.893270	−	0.449521i	$-0.148405\pi$
$811$	21.1246	+	15.3479i	0.741785	+	0.538938i	−0.151485	+	0.988460i	$0.548405\pi$
$812$	7.67250	+	23.6135i	0.269252	+	0.828672i
$813$	−8.66227	+	26.6597i	−0.303799	+	0.934997i
$814$	−1.35214			−0.0473926
$815$	0.993358	+	3.05724i	0.0347958	+	0.107091i
$816$	−9.98742	+	7.25628i	−0.349629	+	0.254021i
$817$	15.1402	−	46.5969i	0.529690	−	1.63022i
$818$	−9.08449	+	27.9592i	−0.317632	+	0.977570i
$819$	−6.02602	−	18.5462i	−0.210566	−	0.648057i
$820$	6.70072	+	4.86836i	0.233999	+	0.170010i
$821$	1.05225	+	3.23850i	0.0367239	+	0.113025i	0.967738	−	0.251959i	$-0.0810747\pi$
$821$	1.05225	+	3.23850i	0.0367239	+	0.113025i	−0.931014	+	0.364983i	$0.881075\pi$
$822$	−49.2077			−1.71632
$823$	10.1556	−	31.2558i	0.354003	−	1.08951i	−0.602583	−	0.798056i	$-0.705862\pi$
$823$	10.1556	−	31.2558i	0.354003	−	1.08951i	0.956586	−	0.291452i	$-0.0941382\pi$
$824$	−2.10332	+	6.47337i	−0.0732728	+	0.225510i
$825$	54.3895			1.89360
$826$	1.28115	+	3.94298i	0.0445770	+	0.137194i
$827$	−20.5375	−	14.9214i	−0.714160	−	0.518867i	0.170353	−	0.985383i	$-0.445509\pi$
$827$	−20.5375	−	14.9214i	−0.714160	−	0.518867i	−0.884513	+	0.466516i	$0.845509\pi$
$828$	−1.40795	−	4.33323i	−0.0489297	−	0.150590i
$829$	−5.52129	+	16.9928i	−0.191762	+	0.590184i	0.808237	+	0.588858i	$0.200422\pi$
$829$	−5.52129	+	16.9928i	−0.191762	+	0.590184i	−0.999999	+	0.00132633i	$0.999578\pi$
$830$	18.1905	−	55.9847i	0.631403	−	1.94326i
$831$	−22.8861	+	16.6277i	−0.793909	+	0.576809i
$832$	−0.363590	−	1.11902i	−0.0126052	−	0.0387949i
$833$	−51.7982			−1.79470
$834$	−16.8825	+	51.9590i	−0.584593	+	1.79919i
$835$	−0.821705	−	2.52895i	−0.0284363	−	0.0875178i
$836$	−8.75962	−	6.36424i	−0.302958	−	0.220112i
$837$	−4.93854	+	3.58806i	−0.170701	+	0.124021i
$838$	10.0300	−	30.8691i	0.346480	−	1.06636i
$839$	26.3838	+	19.1689i	0.910869	+	0.661785i	0.941234	−	0.337754i	$-0.109667\pi$
$839$	26.3838	+	19.1689i	0.910869	+	0.661785i	−0.0303655	+	0.999539i	$0.509667\pi$
$840$	45.0285			1.55363
$841$	5.20136			0.179357
$842$	20.1651	+	14.6508i	0.694934	+	0.504899i
$843$	−78.3384			−2.69812
$844$	−18.3060	−	13.3001i	−0.630118	−	0.457807i
$845$	37.9324	−	27.5595i	1.30492	−	0.948077i
$846$	−8.86406	−	6.44012i	−0.304753	−	0.221416i
$847$	−10.0240	+	30.8508i	−0.344430	+	1.06005i
$848$	0.358726	−	0.260630i	0.0123187	−	0.00895007i
$849$	−31.5566	+	22.9272i	−1.08302	+	0.786861i
$850$	−42.9289	+	31.1897i	−1.47245	+	1.06980i
$851$	0.266069	+	0.818875i	0.00912072	+	0.0280707i
$852$	−2.13160	−	6.56039i	−0.0730274	−	0.224755i
$853$	−33.6008			−1.15047			−0.575235	−	0.817988i	$-0.695090\pi$
$853$	−33.6008			−1.15047			−0.575235	+	0.817988i	$0.695090\pi$
$854$	−18.0903	−	27.7892i	−0.619038	−	0.950928i
$855$	−93.0880			−3.18354
$856$	−3.40037	−	10.4653i	−0.116222	−	0.357696i
$857$	8.53172	+	26.2579i	0.291438	+	0.896954i	0.984395	+	0.175975i	$0.0563077\pi$
$857$	8.53172	+	26.2579i	0.291438	+	0.896954i	−0.692957	+	0.720979i	$0.743692\pi$
$858$	−4.58419	+	3.33061i	−0.156502	+	0.113705i
$859$	−17.5017	+	12.7158i	−0.597151	+	0.433856i	−0.844867	−	0.534977i	$-0.820320\pi$
$859$	−17.5017	+	12.7158i	−0.597151	+	0.433856i	0.247715	+	0.968833i	$0.420320\pi$
$860$	27.0846	−	19.6781i	0.923578	−	0.671019i
$861$	7.07313	−	21.7688i	0.241052	−	0.741880i
$862$	−0.703990	−	0.511479i	−0.0239780	−	0.0174210i
$863$	8.30055	−	6.03070i	0.282554	−	0.205287i	−0.437477	−	0.899230i	$-0.644128\pi$
$863$	8.30055	−	6.03070i	0.282554	−	0.205287i	0.720031	+	0.693942i	$0.244128\pi$
$864$	−1.92117	−	1.39581i	−0.0653595	−	0.0474865i
$865$	−31.6796			−1.07714
$866$	−2.06132	−	1.49764i	−0.0700465	−	0.0508918i
$867$	−13.3350			−0.452880
$868$	−10.9135			−0.370429
$869$	−13.4074	−	9.74108i	−0.454817	−	0.330444i
$870$	19.1672	−	58.9906i	0.649829	−	1.99997i
$871$	−2.60044	+	1.88933i	−0.0881126	+	0.0640175i
$872$	5.72828	+	4.16184i	0.193984	+	0.140938i
$873$	12.0599	+	37.1167i	0.408167	+	1.25621i
$874$	−2.13058	+	6.55726i	−0.0720681	+	0.221803i
$875$	107.859			3.64631
$876$	2.09461	+	6.44655i	0.0707703	+	0.217809i
$877$	−0.624578	+	0.453783i	−0.0210905	+	0.0153232i	−0.598281	−	0.801287i	$-0.704149\pi$
$877$	−0.624578	+	0.453783i	−0.0210905	+	0.0153232i	0.577190	+	0.816610i	$0.304149\pi$
$878$	5.06835	−	15.5988i	0.171049	−	0.526434i
$879$	9.86807	−	30.3708i	0.332842	−	1.02438i
$880$	−2.28626	−	7.03637i	−0.0770697	−	0.237196i
$881$	14.3859	+	10.4520i	0.484673	+	0.352136i	0.803132	−	0.595801i	$-0.203165\pi$
$881$	14.3859	+	10.4520i	0.484673	+	0.352136i	−0.318459	+	0.947937i	$0.603165\pi$
$882$	−13.2994	−	40.9313i	−0.447813	−	1.37823i
$883$	−26.3823			−0.887833			−0.443917	−	0.896068i	$-0.646411\pi$
$883$	−26.3823			−0.887833			−0.443917	+	0.896068i	$0.646411\pi$
$884$	1.70830	−	5.25761i	0.0574564	−	0.176832i
$885$	3.20054	−	9.85024i	0.107585	−	0.331112i
$886$	−39.1623			−1.31568
$887$	−3.35904	−	10.3381i	−0.112786	−	0.347119i	0.878693	−	0.477387i	$-0.158416\pi$
$887$	−3.35904	−	10.3381i	−0.112786	−	0.347119i	−0.991479	+	0.130269i	$0.958416\pi$
$888$	1.56817	+	1.13934i	0.0526243	+	0.0382338i
$889$	−24.4346	−	75.2021i	−0.819512	−	2.52220i
$890$	19.9937	−	61.5344i	0.670192	−	2.06264i
$891$	3.09917	−	9.53827i	0.103826	−	0.319544i
$892$	16.7197	−	12.1476i	0.559818	−	0.406731i
$893$	5.12352	+	15.7686i	0.171452	+	0.527675i
$894$	7.01439			0.234596
$895$	0.410715	−	1.26405i	0.0137287	−	0.0422525i
$896$	−1.31194	−	4.03775i	−0.0438290	−	0.134892i
$897$	2.91911	+	2.12086i	0.0974664	+	0.0708135i
$898$	16.8835	−	12.2666i	0.563410	−	0.409342i
$899$	−4.64554	+	14.2975i	−0.154938	+	0.476849i
$900$	−35.6684	−	25.9146i	−1.18895	−	0.863820i
$901$	2.08333			0.0694057
$902$	−3.76083			−0.125222
$903$	−74.8493	−	54.3812i	−2.49083	−	1.80969i
$904$	−8.17081			−0.271757
$905$	32.6754	+	23.7401i	1.08617	+	0.789148i
$906$	−11.7573	+	8.54218i	−0.390610	+	0.283795i
$907$	−13.7466	−	9.98749i	−0.456449	−	0.331629i	0.335688	−	0.941973i	$-0.391031\pi$
$907$	−13.7466	−	9.98749i	−0.456449	−	0.331629i	−0.792137	+	0.610344i	$0.791031\pi$
$908$	3.22484	−	9.92503i	0.107020	−	0.329374i
$909$	5.57923	−	4.05355i	0.185052	−	0.134448i
$910$	−16.3129	+	11.8520i	−0.540768	+	0.392891i
$911$	6.86138	−	4.98508i	0.227328	−	0.165163i	−0.468291	−	0.883574i	$-0.655130\pi$
$911$	6.86138	−	4.98508i	0.227328	−	0.165163i	0.695619	+	0.718411i	$0.255130\pi$
$912$	4.79648	+	14.7620i	0.158827	+	0.488820i
$913$	8.25973	+	25.4208i	0.273357	+	0.841306i
$914$	9.81263			0.324573
$915$	−4.24367	+	82.7273i	−0.140291	+	2.73488i
$916$	6.43272			0.212543
$917$	16.8229	+	51.7756i	0.555542	+	1.70978i
$918$	−3.44780	−	10.6112i	−0.113794	−	0.350223i
$919$	39.5080	−	28.7042i	1.30325	−	0.946865i	0.303266	−	0.952906i	$-0.401923\pi$
$919$	39.5080	−	28.7042i	1.30325	−	0.946865i	0.999982	+	0.00604082i	$0.00192286\pi$
$920$	−3.81144	+	2.76917i	−0.125659	+	0.0912969i
$921$	−26.7650	+	19.4459i	−0.881937	+	0.640765i
$922$	−7.43136	+	22.8714i	−0.244739	+	0.753228i
$923$	2.49901	+	1.81563i	0.0822558	+	0.0597623i
$924$	−16.5411	+	12.0178i	−0.544163	+	0.395358i
$925$	6.74046	+	4.89723i	0.221625	+	0.161020i
$926$	−25.2993			−0.831388
$927$	−21.4965	−	15.6181i	−0.706037	−	0.512966i
$928$	−5.84819			−0.191976
$929$	22.9996			0.754594			0.377297	−	0.926092i	$-0.376854\pi$
$929$	22.9996			0.754594			0.377297	+	0.926092i	$0.376854\pi$
$930$	22.0569	+	16.0253i	0.723275	+	0.525490i
$931$	−20.1253	+	61.9392i	−0.659579	+	2.02998i
$932$	16.7153	−	12.1444i	0.547528	−	0.397803i
$933$	−19.8230	−	14.4022i	−0.648975	−	0.471508i
$934$	−3.61072	−	11.1127i	−0.118146	−	0.363617i
$935$	10.7418	−	33.0598i	0.351294	−	1.08117i
$936$	4.59320			0.150134
$937$	−10.4842	−	32.2672i	−0.342505	−	1.05412i	−0.962906	−	0.269838i	$-0.913030\pi$
$937$	−10.4842	−	32.2672i	−0.342505	−	1.05412i	0.620400	−	0.784285i	$-0.286970\pi$
$938$	−9.38318	+	6.81728i	−0.306372	+	0.222592i
$939$	26.8415	−	82.6097i	0.875939	−	2.69586i
$940$	−3.50093	+	10.7747i	−0.114188	+	0.351433i
$941$	6.26364	+	19.2775i	0.204189	+	0.628429i	0.999746	+	0.0225498i	$0.00717844\pi$
$941$	6.26364	+	19.2775i	0.204189	+	0.628429i	−0.795557	+	0.605879i	$0.792822\pi$
$942$	14.0580	+	10.2137i	0.458033	+	0.332781i
$943$	0.740040	+	2.27761i	0.0240990	+	0.0741691i
$944$	−0.976530			−0.0317834
$945$	−12.5758	+	38.7042i	−0.409090	+	1.25905i
$946$	−4.69751	+	14.4574i	−0.152729	+	0.470052i
$947$	−29.1771			−0.948128			−0.474064	−	0.880490i	$-0.657214\pi$
$947$	−29.1771			−0.948128			−0.474064	+	0.880490i	$0.657214\pi$
$948$	7.34147	+	22.5947i	0.238440	+	0.733843i
$949$	−2.45564	−	1.78413i	−0.0797135	−	0.0579152i
$950$	20.6167	+	63.4517i	0.668894	+	2.05864i
$951$	−5.89919	+	18.1558i	−0.191294	+	0.588743i
$952$	6.16406	−	18.9710i	0.199778	−	0.614855i
$953$	1.33239	−	0.968036i	0.0431603	−	0.0313578i	−0.565996	−	0.824408i	$-0.691508\pi$
$953$	1.33239	−	0.968036i	0.0431603	−	0.0313578i	0.609156	+	0.793050i	$0.291508\pi$
$954$	0.534902	+	1.64626i	0.0173181	+	0.0532996i
$955$	−10.5405			−0.341084
$956$	−4.24024	+	13.0501i	−0.137139	+	0.422071i
$957$	8.70320	+	26.7857i	0.281334	+	0.865858i
$958$	25.8383	+	18.7726i	0.834797	+	0.606516i
$959$	64.3251	−	46.7349i	2.07717	−	1.50915i
$960$	−3.27746	+	10.0870i	−0.105780	+	0.325556i
$961$	19.7336	+	14.3373i	0.636568	+	0.462494i
$962$	−0.868003			−0.0279856
$963$	42.9566			1.38426
$964$	−20.8280	−	15.1325i	−0.670826	−	0.487383i
$965$	−36.7633			−1.18345
$966$	10.5330	+	7.65271i	0.338895	+	0.246222i
$967$	−29.1102	+	21.1498i	−0.936121	+	0.680132i	−0.947484	−	0.319804i	$-0.896383\pi$
$967$	−29.1102	+	21.1498i	−0.936121	+	0.680132i	0.0113627	+	0.999935i	$0.496383\pi$
$968$	−6.18137	−	4.49103i	−0.198677	−	0.144347i
$969$	−22.5359	+	69.3583i	−0.723956	+	2.22811i
$970$	32.6472	−	23.7196i	1.04824	−	0.761590i
$971$	8.76645	−	6.36920i	0.281329	−	0.204397i	−0.438168	−	0.898893i	$-0.644372\pi$
$971$	8.76645	−	6.36920i	0.281329	−	0.204397i	0.719497	+	0.694496i	$0.244372\pi$
$972$	−17.3949	+	12.6382i	−0.557943	+	0.405369i
$973$	−27.2788	−	83.9556i	−0.874519	−	2.69149i
$974$	−5.03922	−	15.5091i	−0.161467	−	0.496944i
$975$	34.9151			1.11818
$976$	7.54188	−	2.02980i	0.241410	−	0.0649722i
$977$	−44.3704			−1.41953			−0.709767	−	0.704437i	$-0.751200\pi$
$977$	−44.3704			−1.41953			−0.709767	+	0.704437i	$0.751200\pi$
$978$	0.646604	+	1.99004i	0.0206761	+	0.0636345i
$979$	9.07850	+	27.9408i	0.290150	+	0.892990i
$980$	−36.0024	+	26.1573i	−1.15006	+	0.835564i
$981$	−22.3620	+	16.2469i	−0.713963	+	0.518724i
$982$	−12.9236	+	9.38956i	−0.412409	+	0.299633i
$983$	4.05116	−	12.4682i	0.129212	−	0.397674i	−0.865433	−	0.501025i	$-0.832957\pi$
$983$	4.05116	−	12.4682i	0.129212	−	0.397674i	0.994645	+	0.103351i	$0.0329565\pi$
$984$	4.36168	+	3.16895i	0.139045	+	0.101022i
$985$	−74.2129	+	53.9188i	−2.36462	+	1.71800i
$986$	−22.2296	−	16.1507i	−0.707934	−	0.514344i
$987$	31.3087			0.996568
$988$	−5.62321	−	4.08550i	−0.178898	−	0.129977i
$989$	9.67996			0.307805
$990$	28.8821			0.917932
$991$	−5.57156	−	4.04797i	−0.176986	−	0.128588i	0.495765	−	0.868457i	$-0.334888\pi$
$991$	−5.57156	−	4.04797i	−0.176986	−	0.128588i	−0.672752	+	0.739869i	$0.734888\pi$
$992$	0.794355	−	2.44477i	0.0252208	−	0.0776217i
$993$	19.5629	−	14.2133i	0.620809	−	0.451044i
$994$	9.01717	+	6.55135i	0.286007	+	0.207796i
$995$	−22.3273	−	68.7164i	−0.707823	−	2.17846i
$996$	11.8407	−	36.4420i	0.375187	−	1.15471i
$997$	33.5759			1.06336			0.531680	−	0.846945i	$-0.321561\pi$
$997$	33.5759			1.06336			0.531680	+	0.846945i	$0.321561\pi$
$998$	−1.25766	−	3.87068i	−0.0398106	−	0.122524i
$999$	−1.41729	+	1.02972i	−0.0448409	+	0.0325788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.e.a.81.1	✓	12
3.2	odd	2		1098.2.k.j.325.3		12
4.3	odd	2		976.2.v.b.81.3		12
61.27	even	10		7442.2.a.o.1.1		6
61.34	even	5		7442.2.a.n.1.1		6
61.58	even	5	inner	122.2.e.a.119.1	yes	12
183.119	odd	10		1098.2.k.j.973.3		12
244.119	odd	10		976.2.v.b.241.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.e.a.81.1	✓	12	1.1	even	1	trivial
122.2.e.a.119.1	yes	12	61.58	even	5	inner
976.2.v.b.81.3		12	4.3	odd	2
976.2.v.b.241.3		12	244.119	odd	10
1098.2.k.j.325.3		12	3.2	odd	2
1098.2.k.j.973.3		12	183.119	odd	10
7442.2.a.n.1.1		6	61.34	even	5
7442.2.a.o.1.1		6	61.27	even	10

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.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.811944 - 2.49891i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-3.26564 + 2.37263i) q^{5} +(-2.12570 + 1.54441i) q^{6} +(1.31194 - 4.03775i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-3.15823 + 2.29459i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.811944 - 2.49891i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-3.26564 + 2.37263i) q^{5} +(-2.12570 + 1.54441i) q^{6} +(1.31194 - 4.03775i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-3.15823 + 2.29459i) q^{9} +(3.26564 + 2.37263i) q^{10} -1.83287 q^{11} +(2.12570 + 1.54441i) q^{12} -1.17660 q^{13} -4.24554 q^{14} +(8.58050 + 6.23410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.80110 - 2.76166i) q^{17} +(3.15823 + 2.29459i) q^{18} +(-1.82549 - 5.61827i) q^{19} +(1.24737 - 3.83900i) q^{20} -11.1552 q^{21} +(0.566387 + 1.74316i) q^{22} +(0.944229 - 0.686023i) q^{23} +(0.811944 - 2.49891i) q^{24} +(3.48998 - 10.7410i) q^{25} +(0.363590 + 1.11902i) q^{26} +(1.92117 + 1.39581i) q^{27} +(1.31194 + 4.03775i) q^{28} +5.84819 q^{29} +(3.27746 - 10.0870i) q^{30} +(-0.794355 + 2.44477i) q^{31} -1.00000 q^{32} +(1.48819 + 4.58017i) q^{33} +(-3.80110 - 2.76166i) q^{34} +(5.29574 + 16.2986i) q^{35} +(1.20634 - 3.71272i) q^{36} +(-0.227968 + 0.701613i) q^{37} +(-4.77919 + 3.47228i) q^{38} +(0.955335 + 2.94022i) q^{39} -4.03656 q^{40} +(-0.634067 + 1.95146i) q^{41} +(3.44714 + 10.6092i) q^{42} +(6.70983 + 4.87498i) q^{43} +(1.48282 - 1.07733i) q^{44} +(4.86944 - 14.9866i) q^{45} +(-0.944229 - 0.686023i) q^{46} -2.80666 q^{47} -2.62751 q^{48} +(-8.91909 - 6.48010i) q^{49} -11.2938 q^{50} +(-9.98742 - 7.25628i) q^{51} +(0.951892 - 0.691590i) q^{52} +(0.358726 + 0.260630i) q^{53} +(0.733822 - 2.25847i) q^{54} +(5.98550 - 4.34872i) q^{55} +(3.43471 - 2.49547i) q^{56} +(-12.5573 + 9.12344i) q^{57} +(-1.80719 - 5.56196i) q^{58} +(-0.301764 - 0.928736i) q^{59} -10.6061 q^{60} +(4.26102 + 6.54551i) q^{61} +2.57059 q^{62} +(5.12154 + 15.7625i) q^{63} +(0.309017 + 0.951057i) q^{64} +(3.84237 - 2.79164i) q^{65} +(3.89612 - 2.83070i) q^{66} +(2.21013 - 1.60575i) q^{67} +(-1.45189 + 4.46846i) q^{68} +(-2.48097 - 1.80253i) q^{69} +(13.8644 - 10.0731i) q^{70} +(-2.12392 - 1.54311i) q^{71} -3.90378 q^{72} +(2.08706 + 1.51634i) q^{73} +0.737720 q^{74} -29.6745 q^{75} +(4.77919 + 3.47228i) q^{76} +(-2.40462 + 7.40066i) q^{77} +(2.50110 - 1.81716i) q^{78} +(7.31501 + 5.31467i) q^{79} +(1.24737 + 3.83900i) q^{80} +(-1.69089 + 5.20401i) q^{81} +2.05188 q^{82} +(-4.50645 - 13.8694i) q^{83} +(9.02473 - 6.55685i) q^{84} +(-5.86065 + 18.0372i) q^{85} +(2.56293 - 7.88788i) q^{86} +(-4.74840 - 14.6141i) q^{87} +(-1.48282 - 1.07733i) q^{88} +(-4.95317 - 15.2443i) q^{89} -15.7579 q^{90} +(-1.54364 + 4.75083i) q^{91} +(-0.360664 + 1.11001i) q^{92} +6.75423 q^{93} +(0.867304 + 2.66929i) q^{94} +(19.2915 + 14.0161i) q^{95} +(0.811944 + 2.49891i) q^{96} +(3.08929 - 9.50787i) q^{97} +(-3.40679 + 10.4850i) q^{98} +(5.78861 - 4.20567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9	\( 12 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - 6 q^{5} - q^{6} + 10 q^{7} + 3 q^{8} - 7 q^{9} + 6 q^{10} - 4 q^{11} + q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 7 q^{17} + 7 q^{18} - 6 q^{19} + 4 q^{20} - 56 q^{21} - q^{22} + 8 q^{23} + 4 q^{24} - 21 q^{25} - 7 q^{26} + 2 q^{27} + 10 q^{28} + 30 q^{29} + 3 q^{30} + q^{31} - 12 q^{32} + 21 q^{33} - 7 q^{34} + 5 q^{35} - 2 q^{36} - 14 q^{38} - 21 q^{39} - 4 q^{40} + 2 q^{41} - 14 q^{42} - 8 q^{43} + q^{44} + 49 q^{45} - 8 q^{46} - 10 q^{47} + 6 q^{48} - 3 q^{49} - 44 q^{50} + 8 q^{51} - 3 q^{52} + 8 q^{53} + 8 q^{54} + 13 q^{55} + 10 q^{56} + 5 q^{57} + 25 q^{58} + 4 q^{59} - 18 q^{60} - 26 q^{61} + 34 q^{62} + 29 q^{63} - 3 q^{64} + 3 q^{65} + 29 q^{66} + 33 q^{67} - 3 q^{68} + 26 q^{69} + 20 q^{70} - 13 q^{71} - 18 q^{72} - 38 q^{73} + 30 q^{74} - 8 q^{75} + 14 q^{76} - 23 q^{77} - 9 q^{78} + 26 q^{79} + 4 q^{80} + 20 q^{81} - 42 q^{82} + 18 q^{83} + 14 q^{84} - 5 q^{85} - 12 q^{86} - 66 q^{87} - q^{88} + 2 q^{89} - 14 q^{90} + 17 q^{91} + 8 q^{92} - 68 q^{93} + 20 q^{94} + 65 q^{95} + 4 q^{96} - 4 q^{97} - 7 q^{98} - 50 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - 6 * q^5 - q^6 + 10 * q^7 + 3 * q^8 - 7 * q^9 + 6 * q^10 - 4 * q^11 + q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 7 * q^17 + 7 * q^18 - 6 * q^19 + 4 * q^20 - 56 * q^21 - q^22 + 8 * q^23 + 4 * q^24 - 21 * q^25 - 7 * q^26 + 2 * q^27 + 10 * q^28 + 30 * q^29 + 3 * q^30 + q^31 - 12 * q^32 + 21 * q^33 - 7 * q^34 + 5 * q^35 - 2 * q^36 - 14 * q^38 - 21 * q^39 - 4 * q^40 + 2 * q^41 - 14 * q^42 - 8 * q^43 + q^44 + 49 * q^45 - 8 * q^46 - 10 * q^47 + 6 * q^48 - 3 * q^49 - 44 * q^50 + 8 * q^51 - 3 * q^52 + 8 * q^53 + 8 * q^54 + 13 * q^55 + 10 * q^56 + 5 * q^57 + 25 * q^58 + 4 * q^59 - 18 * q^60 - 26 * q^61 + 34 * q^62 + 29 * q^63 - 3 * q^64 + 3 * q^65 + 29 * q^66 + 33 * q^67 - 3 * q^68 + 26 * q^69 + 20 * q^70 - 13 * q^71 - 18 * q^72 - 38 * q^73 + 30 * q^74 - 8 * q^75 + 14 * q^76 - 23 * q^77 - 9 * q^78 + 26 * q^79 + 4 * q^80 + 20 * q^81 - 42 * q^82 + 18 * q^83 + 14 * q^84 - 5 * q^85 - 12 * q^86 - 66 * q^87 - q^88 + 2 * q^89 - 14 * q^90 + 17 * q^91 + 8 * q^92 - 68 * q^93 + 20 * q^94 + 65 * q^95 + 4 * q^96 - 4 * q^97 - 7 * q^98 - 50 * q^99

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