LMFDB - Embedded newform 231.2.j.g.148.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.5
Root			$-0.864833 + 2.66168i$ of defining polynomial
Character	$\chi$	$=$	231.148
Dual form			231.2.j.g.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.864833 + 2.66168i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.71859 + 3.42825i) q^{4} +(-0.518429 + 1.59556i) q^{5} +(0.864833 - 2.66168i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-8.67739 - 6.30449i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.864833 + 2.66168i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.71859 + 3.42825i) q^{4} +(-0.518429 + 1.59556i) q^{5} +(0.864833 - 2.66168i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-8.67739 - 6.30449i) q^{8} +(0.309017 + 0.951057i) q^{9} -4.69523 q^{10} +(-3.13215 - 1.09071i) q^{11} +5.83249 q^{12} +(1.81428 + 5.58378i) q^{13} +(2.26416 + 1.64501i) q^{14} +(1.35727 - 0.986111i) q^{15} +(5.67139 - 17.4547i) q^{16} +(-0.0939932 + 0.289281i) q^{17} +(-2.26416 + 1.64501i) q^{18} +(3.74462 + 2.72062i) q^{19} +(-3.02374 - 9.30610i) q^{20} -1.00000 q^{21} +(0.194331 - 9.28007i) q^{22} -1.38164 q^{23} +(3.31447 + 10.2009i) q^{24} +(1.76804 + 1.28455i) q^{25} +(-13.2932 + 9.65808i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.80234 + 5.54703i) q^{28} +(-3.21073 + 2.33273i) q^{29} +(3.79852 + 2.75979i) q^{30} +(0.236120 + 0.726701i) q^{31} +29.9121 q^{32} +(1.89286 + 2.72343i) q^{33} -0.851264 q^{34} +(0.518429 + 1.59556i) q^{35} +(-4.71859 - 3.42825i) q^{36} +(-2.59713 + 1.88693i) q^{37} +(-4.00297 + 12.3199i) q^{38} +(1.81428 - 5.58378i) q^{39} +(14.5578 - 10.5769i) q^{40} +(6.72515 + 4.88611i) q^{41} +(-0.864833 - 2.66168i) q^{42} -1.01069 q^{43} +(18.5185 - 5.59120i) q^{44} -1.67767 q^{45} +(-1.19489 - 3.67749i) q^{46} +(2.09283 + 1.52053i) q^{47} +(-14.8479 + 10.7876i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-1.89002 + 5.81688i) q^{50} +(0.246078 - 0.178786i) q^{51} +(-27.7035 - 20.1277i) q^{52} +(-0.449229 - 1.38259i) q^{53} +2.79866 q^{54} +(3.36409 - 4.43208i) q^{55} -10.7258 q^{56} +(-1.43032 - 4.40206i) q^{57} +(-8.98574 - 6.52852i) q^{58} +(2.01805 - 1.46620i) q^{59} +(-3.02374 + 9.30610i) q^{60} +(1.04848 - 3.22689i) q^{61} +(-1.73004 + 1.25695i) q^{62} +(0.809017 + 0.587785i) q^{63} +(14.5262 + 44.7071i) q^{64} -9.84984 q^{65} +(-5.61190 + 7.39351i) q^{66} +6.16878 q^{67} +(-0.548215 - 1.68723i) q^{68} +(1.11777 + 0.812107i) q^{69} +(-3.79852 + 2.75979i) q^{70} +(2.34835 - 7.22749i) q^{71} +(3.31447 - 10.2009i) q^{72} +(10.3114 - 7.49164i) q^{73} +(-7.26848 - 5.28086i) q^{74} +(-0.675330 - 2.07845i) q^{75} -26.9963 q^{76} +(-3.17506 + 0.958630i) q^{77} +16.4313 q^{78} +(-1.90206 - 5.85393i) q^{79} +(24.9099 + 18.0981i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-7.18913 + 22.1259i) q^{82} +(-0.621946 + 1.91415i) q^{83} +(4.71859 - 3.42825i) q^{84} +(-0.412837 - 0.299944i) q^{85} +(-0.874082 - 2.69015i) q^{86} +3.96868 q^{87} +(20.3025 + 29.2111i) q^{88} +0.0843908 q^{89} +(-1.45091 - 4.46543i) q^{90} +(4.74985 + 3.45097i) q^{91} +(6.51938 - 4.73661i) q^{92} +(0.236120 - 0.726701i) q^{93} +(-2.23722 + 6.88545i) q^{94} +(-6.28224 + 4.56431i) q^{95} +(-24.1994 - 17.5819i) q^{96} +(0.320682 + 0.986957i) q^{97} +2.79866 q^{98} +(0.0694373 - 3.31590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.864833	+	2.66168i	0.611530	+	1.88209i	0.443383	+	0.896332i	$0.353778\pi$
$2$	0.864833	+	2.66168i	0.611530	+	1.88209i	0.168147	+	0.985762i	$0.446222\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−4.71859	+	3.42825i	−2.35929	+	1.71413i
$5$	−0.518429	+	1.59556i	−0.231849	+	0.713557i	0.765675	+	0.643227i	$0.222405\pi$
$5$	−0.518429	+	1.59556i	−0.231849	+	0.713557i	−0.997524	+	0.0703294i	$0.977595\pi$
$6$	0.864833	−	2.66168i	0.353067	−	1.08663i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−8.67739	−	6.30449i	−3.06792	−	2.22898i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−4.69523			−1.48476
$11$	−3.13215	−	1.09071i	−0.944378	−	0.328861i
$11$	−3.13215	−	1.09071i	−0.944378	−	0.328861i
$12$	5.83249			1.68370
$13$	1.81428	+	5.58378i	0.503191	+	1.54866i	0.803791	+	0.594912i	$0.202813\pi$
$13$	1.81428	+	5.58378i	0.503191	+	1.54866i	−0.300600	+	0.953750i	$0.597187\pi$
$14$	2.26416	+	1.64501i	0.605123	+	0.439648i
$15$	1.35727	−	0.986111i	0.350444	−	0.254613i
$16$	5.67139	−	17.4547i	1.41785	−	4.36369i
$17$	−0.0939932	+	0.289281i	−0.0227967	+	0.0701611i	−0.961808	−	0.273726i	$-0.911744\pi$
$17$	−0.0939932	+	0.289281i	−0.0227967	+	0.0701611i	0.939011	+	0.343887i	$0.111744\pi$
$18$	−2.26416	+	1.64501i	−0.533668	+	0.387733i
$19$	3.74462	+	2.72062i	0.859074	+	0.624154i	0.927633	−	0.373494i	$-0.121840\pi$
$19$	3.74462	+	2.72062i	0.859074	+	0.624154i	−0.0685591	+	0.997647i	$0.521840\pi$
$20$	−3.02374	−	9.30610i	−0.676128	−	2.08091i
$21$	−1.00000			−0.218218
$22$	0.194331	−	9.28007i	0.0414316	−	1.97852i
$23$	−1.38164			−0.288092			−0.144046	−	0.989571i	$-0.546011\pi$
$23$	−1.38164			−0.288092			−0.144046	+	0.989571i	$0.546011\pi$
$24$	3.31447	+	10.2009i	0.676563	+	2.08225i
$25$	1.76804	+	1.28455i	0.353607	+	0.256911i
$26$	−13.2932	+	9.65808i	−2.60701	+	1.89411i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−1.80234	+	5.54703i	−0.340610	+	1.04829i
$29$	−3.21073	+	2.33273i	−0.596217	+	0.433177i	−0.844534	−	0.535502i	$-0.820123\pi$
$29$	−3.21073	+	2.33273i	−0.596217	+	0.433177i	0.248317	+	0.968679i	$0.420123\pi$
$30$	3.79852	+	2.75979i	0.693512	+	0.503866i
$31$	0.236120	+	0.726701i	0.0424083	+	0.130519i	0.970019	−	0.243029i	$-0.0781410\pi$
$31$	0.236120	+	0.726701i	0.0424083	+	0.130519i	−0.927611	+	0.373548i	$0.878141\pi$
$32$	29.9121			5.28776
$33$	1.89286	+	2.72343i	0.329505	+	0.474089i
$34$	−0.851264			−0.145991
$35$	0.518429	+	1.59556i	0.0876306	+	0.269699i
$36$	−4.71859	−	3.42825i	−0.786431	−	0.571376i
$37$	−2.59713	+	1.88693i	−0.426966	+	0.310209i	−0.780434	−	0.625238i	$-0.785002\pi$
$37$	−2.59713	+	1.88693i	−0.426966	+	0.310209i	0.353469	+	0.935446i	$0.385002\pi$
$38$	−4.00297	+	12.3199i	−0.649367	+	1.99855i
$39$	1.81428	−	5.58378i	0.290517	−	0.894121i
$40$	14.5578	−	10.5769i	2.30179	−	1.67235i
$41$	6.72515	+	4.88611i	1.05029	+	0.763081i	0.972268	−	0.233870i	$-0.0751390\pi$
$41$	6.72515	+	4.88611i	1.05029	+	0.763081i	0.0780237	+	0.996952i	$0.475139\pi$
$42$	−0.864833	−	2.66168i	−0.133447	−	0.410707i
$43$	−1.01069			−0.154129			−0.0770647	−	0.997026i	$-0.524555\pi$
$43$	−1.01069			−0.154129			−0.0770647	+	0.997026i	$0.524555\pi$
$44$	18.5185	−	5.59120i	2.79178	−	0.842906i
$45$	−1.67767			−0.250093
$46$	−1.19489	−	3.67749i	−0.176177	−	0.542216i
$47$	2.09283	+	1.52053i	0.305271	+	0.221792i	0.729865	−	0.683592i	$-0.239583\pi$
$47$	2.09283	+	1.52053i	0.305271	+	0.221792i	−0.424594	+	0.905384i	$0.639583\pi$
$48$	−14.8479	+	10.7876i	−2.14311	+	1.55706i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−1.89002	+	5.81688i	−0.267289	+	0.822631i
$51$	0.246078	−	0.178786i	0.0344577	−	0.0250350i
$52$	−27.7035	−	20.1277i	−3.84178	−	2.79122i
$53$	−0.449229	−	1.38259i	−0.0617064	−	0.189913i	0.915451	−	0.402429i	$-0.131834\pi$
$53$	−0.449229	−	1.38259i	−0.0617064	−	0.189913i	−0.977157	+	0.212517i	$0.931834\pi$
$54$	2.79866			0.380849
$55$	3.36409	−	4.43208i	0.453614	−	0.597622i
$56$	−10.7258			−1.43330
$57$	−1.43032	−	4.40206i	−0.189450	−	0.583067i
$58$	−8.98574	−	6.52852i	−1.17988	−	0.857237i
$59$	2.01805	−	1.46620i	0.262727	−	0.190883i	−0.448621	−	0.893722i	$-0.648085\pi$
$59$	2.01805	−	1.46620i	0.262727	−	0.190883i	0.711349	+	0.702839i	$0.248085\pi$
$60$	−3.02374	+	9.30610i	−0.390363	+	1.20141i
$61$	1.04848	−	3.22689i	0.134244	−	0.413161i	−0.861228	−	0.508219i	$-0.830304\pi$
$61$	1.04848	−	3.22689i	0.134244	−	0.413161i	0.995472	+	0.0950587i	$0.0303039\pi$
$62$	−1.73004	+	1.25695i	−0.219716	+	0.159633i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	14.5262	+	44.7071i	1.81578	+	5.58839i
$65$	−9.84984			−1.22172
$66$	−5.61190	+	7.39351i	−0.690778	+	0.910078i
$67$	6.16878			0.753636			0.376818	−	0.926287i	$-0.377018\pi$
$67$	6.16878			0.753636			0.376818	+	0.926287i	$0.377018\pi$
$68$	−0.548215	−	1.68723i	−0.0664808	−	0.204607i
$69$	1.11777	+	0.812107i	0.134564	+	0.0977662i
$70$	−3.79852	+	2.75979i	−0.454011	+	0.329858i
$71$	2.34835	−	7.22749i	0.278698	−	0.857745i	−0.709519	−	0.704686i	$-0.751088\pi$
$71$	2.34835	−	7.22749i	0.278698	−	0.857745i	0.988217	−	0.153058i	$-0.0489123\pi$
$72$	3.31447	−	10.2009i	0.390614	−	1.20219i
$73$	10.3114	−	7.49164i	1.20685	−	0.876831i	0.211913	−	0.977289i	$-0.432031\pi$
$73$	10.3114	−	7.49164i	1.20685	−	0.876831i	0.994941	+	0.100458i	$0.0320308\pi$
$74$	−7.26848	−	5.28086i	−0.844944	−	0.613888i
$75$	−0.675330	−	2.07845i	−0.0779804	−	0.239999i
$76$	−26.9963			−3.09669
$77$	−3.17506	+	0.958630i	−0.361832	+	0.109246i
$78$	16.4313			1.86048
$79$	−1.90206	−	5.85393i	−0.213998	−	0.658618i	−0.999223	−	0.0394080i	$-0.987453\pi$
$79$	−1.90206	−	5.85393i	−0.213998	−	0.658618i	0.785225	−	0.619210i	$-0.212547\pi$
$80$	24.9099	+	18.0981i	2.78501	+	2.02343i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−7.18913	+	22.1259i	−0.793907	+	2.44339i
$83$	−0.621946	+	1.91415i	−0.0682675	+	0.210106i	−0.979370	−	0.202073i	$-0.935232\pi$
$83$	−0.621946	+	1.91415i	−0.0682675	+	0.210106i	0.911103	+	0.412179i	$0.135232\pi$
$84$	4.71859	−	3.42825i	0.514840	−	0.374053i
$85$	−0.412837	−	0.299944i	−0.0447785	−	0.0325335i
$86$	−0.874082	−	2.69015i	−0.0942546	−	0.290086i
$87$	3.96868			0.425487
$88$	20.3025	+	29.2111i	2.16426	+	3.11392i
$89$	0.0843908			0.00894541			0.00447270	−	0.999990i	$-0.498576\pi$
$89$	0.0843908			0.00894541			0.00447270	+	0.999990i	$0.498576\pi$
$90$	−1.45091	−	4.46543i	−0.152939	−	0.470698i
$91$	4.74985	+	3.45097i	0.497919	+	0.361760i
$92$	6.51938	−	4.73661i	0.679693	−	0.493826i
$93$	0.236120	−	0.726701i	0.0244845	−	0.0753554i
$94$	−2.23722	+	6.88545i	−0.230752	+	0.710180i
$95$	−6.28224	+	4.56431i	−0.644544	+	0.468289i
$96$	−24.1994	−	17.5819i	−2.46984	−	1.79445i
$97$	0.320682	+	0.986957i	0.0325603	+	0.100210i	0.966016	−	0.258483i	$-0.0832225\pi$
$97$	0.320682	+	0.986957i	0.0325603	+	0.100210i	−0.933456	+	0.358693i	$0.883223\pi$
$98$	2.79866			0.282707
$99$	0.0694373	−	3.31590i	0.00697871	−	0.333260i
$100$	−12.7464			−1.27464
$101$	−6.08676	−	18.7331i	−0.605656	−	1.86402i	−0.492220	−	0.870471i	$-0.663815\pi$
$101$	−6.08676	−	18.7331i	−0.605656	−	1.86402i	−0.113435	−	0.993545i	$-0.536185\pi$
$102$	0.688687	+	0.500360i	0.0681902	+	0.0495431i
$103$	1.95189	−	1.41813i	0.192325	−	0.139733i	−0.487455	−	0.873148i	$-0.662075\pi$
$103$	1.95189	−	1.41813i	0.192325	−	0.139733i	0.679781	+	0.733415i	$0.262075\pi$
$104$	19.4597	−	59.8908i	1.90818	−	5.87277i
$105$	0.518429	−	1.59556i	0.0505935	−	0.155711i
$106$	3.29150	−	2.39141i	0.319698	−	0.232275i
$107$	7.49357	+	5.44439i	0.724430	+	0.526330i	0.887797	−	0.460236i	$-0.152235\pi$
$107$	7.49357	+	5.44439i	0.724430	+	0.526330i	−0.163366	+	0.986566i	$0.552235\pi$
$108$	1.80234	+	5.54703i	0.173430	+	0.533763i
$109$	−8.30530			−0.795503			−0.397752	−	0.917493i	$-0.630209\pi$
$109$	−8.30530			−0.795503			−0.397752	+	0.917493i	$0.630209\pi$
$110$	14.7062	+	5.12113i	1.40218	+	0.488280i
$111$	3.21023			0.304702
$112$	−5.67139	−	17.4547i	−0.535896	−	1.64932i
$113$	−4.43310	−	3.22084i	−0.417031	−	0.302991i	0.359411	−	0.933179i	$-0.382978\pi$
$113$	−4.43310	−	3.22084i	−0.417031	−	0.302991i	−0.776442	+	0.630188i	$0.782978\pi$
$114$	10.4799	−	7.61410i	0.981533	−	0.713125i
$115$	0.716282	−	2.20449i	0.0667937	−	0.205570i
$116$	7.15291	−	22.0144i	0.664131	−	2.04398i
$117$	−4.74985	+	3.45097i	−0.439124	+	0.319042i
$118$	5.64783	+	4.10339i	0.519925	+	0.377747i
$119$	0.0939932	+	0.289281i	0.00861635	+	0.0265184i
$120$	−17.9945			−1.64266
$121$	8.62071	+	6.83252i	0.783701	+	0.621138i
$122$	9.49572			0.859702
$123$	−2.56878	−	7.90588i	−0.231619	−	0.712850i
$124$	−3.60547	−	2.61953i	−0.323781	−	0.235240i
$125$	−9.75252	+	7.08562i	−0.872292	+	0.633757i
$126$	−0.864833	+	2.66168i	−0.0770455	+	0.237122i
$127$	6.19815	−	19.0759i	0.549997	−	1.69272i	−0.158807	−	0.987310i	$-0.550765\pi$
$127$	6.19815	−	19.0759i	0.549997	−	1.69272i	0.708803	−	0.705406i	$-0.249235\pi$
$128$	−58.0345	+	42.1646i	−5.12958	+	3.72686i
$129$	0.817668	+	0.594071i	0.0719917	+	0.0523050i
$130$	−8.51847	−	26.2172i	−0.747119	−	2.29940i
$131$	4.22096			0.368787			0.184394	−	0.982852i	$-0.440968\pi$
$131$	4.22096			0.368787			0.184394	+	0.982852i	$0.440968\pi$
$132$	−18.2682	−	6.36155i	−1.59005	−	0.553701i
$133$	4.62860			0.401350
$134$	5.33496	+	16.4193i	0.460871	+	1.41841i
$135$	1.35727	+	0.986111i	0.116815	+	0.0848709i
$136$	2.63939	−	1.91763i	0.226326	−	0.164435i
$137$	−4.49191	+	13.8247i	−0.383770	+	1.18112i	0.553598	+	0.832784i	$0.313254\pi$
$137$	−4.49191	+	13.8247i	−0.383770	+	1.18112i	−0.937369	+	0.348339i	$0.886746\pi$
$138$	−1.19489	+	3.67749i	−0.101716	+	0.313048i
$139$	−5.61956	+	4.08285i	−0.476645	+	0.346303i	−0.800025	−	0.599966i	$-0.795181\pi$
$139$	−5.61956	+	4.08285i	−0.476645	+	0.346303i	0.323381	+	0.946269i	$0.395181\pi$
$140$	−7.91624	−	5.75149i	−0.669045	−	0.486089i
$141$	−0.799390	−	2.46027i	−0.0673208	−	0.207192i
$142$	21.2682			1.78479
$143$	0.407675	−	19.4681i	0.0340915	−	1.62800i
$144$	18.3530			1.52942
$145$	−2.05748	−	6.33227i	−0.170864	−	0.525866i
$146$	28.8580	+	20.9666i	2.38830	+	1.73521i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	5.78593	−	17.8072i	0.475600	−	1.46375i
$149$	−4.31512	+	13.2806i	−0.353508	+	1.08799i	0.603361	+	0.797468i	$0.293828\pi$
$149$	−4.31512	+	13.2806i	−0.353508	+	1.08799i	−0.956869	+	0.290519i	$0.906172\pi$
$150$	4.94813	−	3.59503i	0.404014	−	0.293533i
$151$	1.10900	+	0.805737i	0.0902492	+	0.0655699i	0.631995	−	0.774973i	$-0.282236\pi$
$151$	1.10900	+	0.805737i	0.0902492	+	0.0655699i	−0.541746	+	0.840543i	$0.682236\pi$
$152$	−15.3413	−	47.2158i	−1.24435	−	3.82971i
$153$	−0.304169			−0.0245906
$154$	−5.29747	−	7.62196i	−0.426882	−	0.614195i
$155$	−1.28191			−0.102965
$156$	10.5818	+	32.5674i	0.847220	+	2.60748i
$157$	12.8632	+	9.34563i	1.02659	+	0.745863i	0.967624	−	0.252397i	$-0.0812190\pi$
$157$	12.8632	+	9.34563i	1.02659	+	0.745863i	0.0589681	+	0.998260i	$0.481219\pi$
$158$	13.9363	−	10.1253i	1.10872	−	0.805529i
$159$	−0.449229	+	1.38259i	−0.0356262	+	0.109646i
$160$	−15.5073	+	47.7266i	−1.22596	+	3.77312i
$161$	−1.11777	+	0.812107i	−0.0880926	+	0.0640030i
$162$	−2.26416	−	1.64501i	−0.177889	−	0.129244i
$163$	3.23495	+	9.95614i	0.253381	+	0.779825i	0.994144	+	0.108060i	$0.0344637\pi$
$163$	3.23495	+	9.95614i	0.253381	+	0.779825i	−0.740764	+	0.671766i	$0.765536\pi$
$164$	−48.4840			−3.78596
$165$	−5.32672	+	1.60827i	−0.414684	+	0.125203i
$166$	−5.63275			−0.437186
$167$	2.64937	+	8.15393i	0.205015	+	0.630970i	0.999713	+	0.0239655i	$0.00762918\pi$
$167$	2.64937	+	8.15393i	0.205015	+	0.630970i	−0.794698	+	0.607005i	$0.792371\pi$
$168$	8.67739	+	6.30449i	0.669475	+	0.486402i
$169$	−17.3698	+	12.6199i	−1.33614	+	0.970760i
$170$	0.441320	−	1.35824i	0.0338477	−	0.104173i
$171$	−1.43032	+	4.40206i	−0.109379	+	0.336634i
$172$	4.76905	−	3.46491i	0.363636	−	0.264197i
$173$	11.1216	+	8.08034i	0.845562	+	0.614337i	0.923919	−	0.382589i	$-0.124967\pi$
$173$	11.1216	+	8.08034i	0.845562	+	0.614337i	−0.0783569	+	0.996925i	$0.524967\pi$
$174$	3.43225	+	10.5634i	0.260198	+	0.800807i
$175$	2.18541			0.165202
$176$	−36.8017	+	48.4850i	−2.77403	+	3.65470i
$177$	−2.49444			−0.187494
$178$	0.0729840	+	0.224622i	0.00547038	+	0.0168361i
$179$	3.11483	+	2.26306i	0.232813	+	0.169149i	0.698076	−	0.716024i	$-0.254040\pi$
$179$	3.11483	+	2.26306i	0.232813	+	0.169149i	−0.465262	+	0.885173i	$0.654040\pi$
$180$	7.91624	−	5.75149i	0.590042	−	0.428691i
$181$	−6.04339	+	18.5996i	−0.449201	+	1.38250i	0.428608	+	0.903490i	$0.359004\pi$
$181$	−6.04339	+	18.5996i	−0.449201	+	1.38250i	−0.877810	+	0.479009i	$0.840996\pi$
$182$	−5.07755	+	15.6271i	−0.376373	+	1.15836i
$183$	−2.74496	+	1.99433i	−0.202913	+	0.147425i
$184$	11.9890	+	8.71054i	0.883843	+	0.642149i
$185$	−1.66428	−	5.12212i	−0.122360	−	0.376586i
$186$	2.13845			0.156799
$187$	0.609922	−	0.803553i	0.0446019	−	0.0587616i
$188$	−15.0880			−1.10040
$189$	−0.309017	−	0.951057i	−0.0224777	−	0.0691792i
$190$	−17.5818	−	12.7740i	−1.27552	−	0.926720i
$191$	2.05896	−	1.49592i	0.148981	−	0.108241i	−0.510798	−	0.859701i	$-0.670650\pi$
$191$	2.05896	−	1.49592i	0.148981	−	0.108241i	0.659779	+	0.751460i	$0.270650\pi$
$192$	14.5262	−	44.7071i	1.04834	−	3.22646i
$193$	6.68348	−	20.5696i	0.481087	−	1.48063i	−0.356482	−	0.934302i	$-0.616024\pi$
$193$	6.68348	−	20.5696i	0.481087	−	1.48063i	0.837569	−	0.546332i	$-0.183976\pi$
$194$	−2.34963	+	1.70711i	−0.168694	+	0.122563i
$195$	7.96869	+	5.78959i	0.570650	+	0.414601i
$196$	1.80234	+	5.54703i	0.128739	+	0.396217i
$197$	−22.0693			−1.57237			−0.786187	−	0.617989i	$-0.787948\pi$
$197$	−22.0693			−1.57237			−0.786187	+	0.617989i	$0.787948\pi$
$198$	8.88592	−	2.68288i	0.631495	−	0.190664i
$199$	−12.8315			−0.909598			−0.454799	−	0.890594i	$-0.650289\pi$
$199$	−12.8315			−0.909598			−0.454799	+	0.890594i	$0.650289\pi$
$200$	−7.24349	−	22.2932i	−0.512192	−	1.57636i
$201$	−4.99065	−	3.62592i	−0.352013	−	0.255752i
$202$	44.5976	−	32.4021i	3.13788	−	2.27980i
$203$	−1.22639	+	3.77444i	−0.0860756	+	0.264914i
$204$	−0.548215	+	1.68723i	−0.0383827	+	0.118130i
$205$	−11.2826	+	8.19729i	−0.788011	+	0.572523i
$206$	5.46268	+	3.96887i	0.380603	+	0.276524i
$207$	−0.426950	−	1.31402i	−0.0296751	−	0.0913305i
$208$	107.753			7.47132
$209$	−8.76129	−	12.6057i	−0.606031	−	0.871953i
$210$	4.69523			0.324002
$211$	−5.48213	−	16.8723i	−0.377406	−	1.16154i	−0.941841	−	0.336058i	$-0.890906\pi$
$211$	−5.48213	−	16.8723i	−0.377406	−	1.16154i	0.564436	−	0.825477i	$-0.309094\pi$
$212$	6.85958	+	4.98378i	0.471118	+	0.342287i
$213$	−6.14807	+	4.46683i	−0.421259	+	0.306062i
$214$	−8.01057	+	24.6540i	−0.547591	+	1.68531i
$215$	0.523973	−	1.61262i	0.0357347	−	0.109980i
$216$	−8.67739	+	6.30449i	−0.590422	+	0.428967i
$217$	0.618169	+	0.449126i	0.0419640	+	0.0304887i
$218$	−7.18270	−	22.1061i	−0.486474	−	1.49721i
$219$	−12.7455			−0.861264
$220$	−0.679445	+	32.4461i	−0.0458082	+	2.18752i
$221$	−1.78581			−0.120127
$222$	2.77631	+	8.54462i	0.186334	+	0.573477i
$223$	−13.8483	−	10.0614i	−0.927349	−	0.673759i	0.0179932	−	0.999838i	$-0.494272\pi$
$223$	−13.8483	−	10.0614i	−0.927349	−	0.673759i	−0.945342	+	0.326080i	$0.894272\pi$
$224$	24.1994	−	17.5819i	1.61689	−	1.17474i
$225$	−0.675330	+	2.07845i	−0.0450220	+	0.138564i
$226$	4.73896	−	14.5850i	0.315231	−	0.970180i
$227$	16.5744	−	12.0420i	1.10008	−	0.799256i	0.119008	−	0.992893i	$-0.462029\pi$
$227$	16.5744	−	12.0420i	1.10008	−	0.799256i	0.981073	+	0.193637i	$0.0620285\pi$
$228$	21.8404	+	15.8680i	1.44642	+	1.05088i
$229$	7.55058	+	23.2383i	0.498956	+	1.53563i	0.810699	+	0.585463i	$0.199087\pi$
$229$	7.55058	+	23.2383i	0.498956	+	1.53563i	−0.311743	+	0.950167i	$0.600913\pi$
$230$	6.48712			0.427748
$231$	3.13215	+	1.09071i	0.206080	+	0.0717633i
$232$	42.5674			2.79469
$233$	−7.32533	−	22.5450i	−0.479898	−	1.47697i	−0.839236	−	0.543767i	$-0.816998\pi$
$233$	−7.32533	−	22.5450i	−0.479898	−	1.47697i	0.359338	−	0.933207i	$-0.383002\pi$
$234$	−13.2932	−	9.65808i	−0.869004	−	0.631368i
$235$	−3.51108	+	2.55095i	−0.229038	+	0.166406i
$236$	−4.49584	+	13.8368i	−0.292654	+	0.900696i
$237$	−1.90206	+	5.85393i	−0.123552	+	0.380254i
$238$	−0.688687	+	0.500360i	−0.0446410	+	0.0324336i
$239$	1.27822	+	0.928682i	0.0826813	+	0.0600714i	0.628358	−	0.777924i	$-0.283727\pi$
$239$	1.27822	+	0.928682i	0.0826813	+	0.0600714i	−0.545677	+	0.837996i	$0.683727\pi$
$240$	−9.51474	−	29.2833i	−0.614174	−	1.89023i
$241$	−12.2382			−0.788333			−0.394167	−	0.919039i	$-0.628967\pi$
$241$	−12.2382			−0.788333			−0.394167	+	0.919039i	$0.628967\pi$
$242$	−10.7305	+	28.8546i	−0.689784	+	1.85484i
$243$	1.00000			0.0641500
$244$	6.11525	+	18.8208i	0.391489	+	1.20488i
$245$	1.35727	+	0.986111i	0.0867125	+	0.0630003i
$246$	18.8214	−	13.6745i	1.20001	−	0.871857i
$247$	−8.39758	+	25.8451i	−0.534325	+	1.64448i
$248$	2.53258	−	7.79449i	0.160819	−	0.494950i
$249$	1.62828	−	1.18301i	0.103188	−	0.0749704i
$250$	−27.2940	−	19.8302i	−1.72622	−	1.25417i
$251$	5.99825	+	18.4607i	0.378606	+	1.16523i	0.941013	+	0.338370i	$0.109875\pi$
$251$	5.99825	+	18.4607i	0.378606	+	1.16523i	−0.562407	+	0.826861i	$0.690125\pi$
$252$	−5.83249			−0.367413
$253$	4.32750	+	1.50696i	0.272068	+	0.0947420i
$254$	56.1345			3.52219
$255$	0.157690	+	0.485320i	0.00987492	+	0.0303919i
$256$	−86.3587	−	62.7432i	−5.39742	−	3.92145i
$257$	0.218519	−	0.158763i	0.0136308	−	0.00990337i	−0.580949	−	0.813940i	$-0.697318\pi$
$257$	0.218519	−	0.158763i	0.0136308	−	0.00990337i	0.594580	+	0.804037i	$0.297318\pi$
$258$	−0.874082	+	2.69015i	−0.0544179	+	0.167481i
$259$	−0.992016	+	3.05311i	−0.0616408	+	0.189711i
$260$	46.4773	−	33.7678i	2.88240	−	2.09419i
$261$	−3.21073	−	2.33273i	−0.198739	−	0.144392i
$262$	3.65043	+	11.2349i	0.225524	+	0.694092i
$263$	27.9927			1.72611			0.863053	−	0.505113i	$-0.168549\pi$
$263$	27.9927			1.72611			0.863053	+	0.505113i	$0.168549\pi$
$264$	0.744773	−	35.5658i	0.0458376	−	2.18892i
$265$	2.43889			0.149820
$266$	4.00297	+	12.3199i	0.245438	+	0.755379i
$267$	−0.0682736	−	0.0496037i	−0.00417828	−	0.00303570i
$268$	−29.1079	+	21.1481i	−1.77805	+	1.29183i
$269$	0.345128	−	1.06220i	0.0210428	−	0.0647632i	−0.939984	−	0.341219i	$-0.889160\pi$
$269$	0.345128	−	1.06220i	0.0210428	−	0.0647632i	0.961027	+	0.276456i	$0.0891601\pi$
$270$	−1.45091	+	4.46543i	−0.0882994	+	0.271758i
$271$	−20.0887	+	14.5953i	−1.22030	+	0.886600i	−0.996125	−	0.0879490i	$-0.971969\pi$
$271$	−20.0887	+	14.5953i	−1.22030	+	0.886600i	−0.224175	+	0.974549i	$0.571969\pi$
$272$	4.51626	+	3.28126i	0.273839	+	0.198955i
$273$	−1.81428	−	5.58378i	−0.109805	−	0.337946i
$274$	−40.6817			−2.45767
$275$	−4.13668	−	5.95183i	−0.249451	−	0.358909i
$276$	−8.05840			−0.485059
$277$	−3.84216	−	11.8250i	−0.230853	−	0.710493i	−0.997644	−	0.0685967i	$-0.978148\pi$
$277$	−3.84216	−	11.8250i	−0.230853	−	0.710493i	0.766791	−	0.641897i	$-0.221852\pi$
$278$	−15.7272	−	11.4265i	−0.943256	−	0.685316i
$279$	−0.618169	+	0.449126i	−0.0370088	+	0.0268885i
$280$	5.56059	−	17.1137i	0.332309	−	1.02274i
$281$	−2.08141	+	6.40594i	−0.124167	+	0.382146i	−0.993748	−	0.111643i	$-0.964389\pi$
$281$	−2.08141	+	6.40594i	−0.124167	+	0.382146i	0.869582	+	0.493789i	$0.164389\pi$
$282$	5.85712	−	4.25544i	0.348786	−	0.253408i
$283$	9.02913	+	6.56005i	0.536726	+	0.389954i	0.822868	−	0.568233i	$-0.192373\pi$
$283$	9.02913	+	6.56005i	0.536726	+	0.389954i	−0.286142	+	0.958187i	$0.592373\pi$
$284$	13.6968	+	42.1543i	0.812753	+	2.50140i
$285$	7.76527			0.459975
$286$	52.1704	−	15.7515i	3.08490	−	0.931408i
$287$	8.31274			0.490685
$288$	9.24335	+	28.4481i	0.544670	+	1.67632i
$289$	13.6784	+	9.93797i	0.804614	+	0.584586i
$290$	15.0751	−	10.9527i	0.885242	−	0.643166i
$291$	0.320682	−	0.986957i	0.0187987	−	0.0578564i
$292$	−22.9718	+	70.7000i	−1.34432	+	4.13740i
$293$	13.6731	−	9.93412i	0.798794	−	0.580358i	−0.111766	−	0.993735i	$-0.535651\pi$
$293$	13.6731	−	9.93412i	0.798794	−	0.580358i	0.910560	+	0.413377i	$0.135651\pi$
$294$	−2.26416	−	1.64501i	−0.132049	−	0.0959390i
$295$	1.29319	+	3.98004i	0.0752926	+	0.231727i
$296$	34.4324			2.00134
$297$	−2.00521	+	2.64180i	−0.116354	+	0.153293i
$298$	−39.0805			−2.26388
$299$	−2.50668	−	7.71477i	−0.144965	−	0.446157i
$300$	10.3121	+	7.49216i	0.595368	+	0.432560i
$301$	−0.817668	+	0.594071i	−0.0471296	+	0.0342417i
$302$	−1.18551	+	3.64864i	−0.0682187	+	0.209956i
$303$	−6.08676	+	18.7331i	−0.349675	+	1.07619i
$304$	68.7249	−	49.9316i	3.94165	−	2.86377i
$305$	4.60514	+	3.34583i	0.263689	+	0.191582i
$306$	−0.263055	−	0.809600i	−0.0150379	−	0.0462818i
$307$	−11.3453			−0.647511			−0.323755	−	0.946141i	$-0.604946\pi$
$307$	−11.3453			−0.647511			−0.323755	+	0.946141i	$0.604946\pi$
$308$	11.6954	−	15.4083i	0.666407	−	0.877970i
$309$	−2.41267			−0.137252
$310$	−1.10864	−	3.41203i	−0.0629663	−	0.193790i
$311$	−19.2940	−	14.0179i	−1.09406	−	0.794884i	−0.113983	−	0.993483i	$-0.536361\pi$
$311$	−19.2940	−	14.0179i	−1.09406	−	0.794884i	−0.980081	+	0.198599i	$0.936361\pi$
$312$	−50.9461	+	37.0145i	−2.88426	+	2.09554i
$313$	9.56921	−	29.4510i	0.540884	−	1.66467i	−0.189696	−	0.981843i	$-0.560750\pi$
$313$	9.56921	−	29.4510i	0.540884	−	1.66467i	0.730580	−	0.682827i	$-0.239250\pi$
$314$	−13.7506	+	42.3201i	−0.775993	+	2.38826i
$315$	−1.35727	+	0.986111i	−0.0764733	+	0.0555611i
$316$	29.0438	+	21.1015i	1.63384	+	1.18705i
$317$	0.991557	+	3.05170i	0.0556914	+	0.171401i	0.975033	−	0.222060i	$-0.0712779\pi$
$317$	0.991557	+	3.05170i	0.0556914	+	0.171401i	−0.919342	+	0.393460i	$0.871278\pi$
$318$	−4.06851			−0.228151
$319$	12.6008	−	3.80449i	0.705510	−	0.213011i
$320$	−78.8637			−4.40862
$321$	−2.86229	−	8.80922i	−0.159757	−	0.491682i
$322$	−3.12826	−	2.27281i	−0.174331	−	0.126659i
$323$	−1.13899	+	0.827528i	−0.0633753	+	0.0460449i
$324$	1.80234	−	5.54703i	0.100130	−	0.308168i
$325$	−3.96495	+	12.2029i	−0.219936	+	0.676894i
$326$	−23.7024	+	17.2208i	−1.31275	+	0.953772i
$327$	6.71913	+	4.88173i	0.371569	+	0.269960i
$328$	−27.5523	−	84.7973i	−1.52132	−	4.68215i
$329$	2.58688			0.142619
$330$	−8.88742	−	12.7872i	−0.489236	−	0.703909i
$331$	−3.98424			−0.218994			−0.109497	−	0.993987i	$-0.534924\pi$
$331$	−3.98424			−0.218994			−0.109497	+	0.993987i	$0.534924\pi$
$332$	−3.62750	−	11.1643i	−0.199085	−	0.612720i
$333$	−2.59713	−	1.88693i	−0.142322	−	0.103403i
$334$	−19.4119	+	14.1036i	−1.06217	+	0.771714i
$335$	−3.19808	+	9.84266i	−0.174730	+	0.537762i
$336$	−5.67139	+	17.4547i	−0.309400	+	0.952234i
$337$	9.14237	−	6.64232i	0.498017	−	0.361830i	−0.310242	−	0.950658i	$-0.600410\pi$
$337$	9.14237	−	6.64232i	0.498017	−	0.361830i	0.808259	+	0.588827i	$0.200410\pi$
$338$	−48.6121	−	35.3187i	−2.64415	−	1.92109i
$339$	1.69330	+	5.21143i	0.0919672	+	0.283046i
$340$	2.97629			0.161412
$341$	0.0530569	−	2.53367i	0.00287319	−	0.137206i
$342$	−12.9539			−0.700465
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	8.77019	+	6.37191i	0.472857	+	0.343550i
$345$	−1.87525	+	1.36245i	−0.100960	+	0.0733518i
$346$	−11.8889	+	36.5904i	−0.639154	+	1.96711i
$347$	2.03593	−	6.26594i	0.109294	−	0.336373i	−0.881420	−	0.472333i	$-0.843412\pi$
$347$	2.03593	−	6.26594i	0.109294	−	0.336373i	0.990714	+	0.135960i	$0.0434119\pi$
$348$	−18.7266	+	13.6056i	−1.00385	+	0.729339i
$349$	−16.5317	−	12.0110i	−0.884923	−	0.642934i	0.0496266	−	0.998768i	$-0.484197\pi$
$349$	−16.5317	−	12.0110i	−0.884923	−	0.642934i	−0.934549	+	0.355834i	$0.884197\pi$
$350$	1.89002	+	5.81688i	0.101026	+	0.310925i
$351$	5.87113			0.313378
$352$	−93.6892	−	32.6254i	−4.99365	−	1.73894i
$353$	36.5457			1.94513			0.972565	−	0.232630i	$-0.0747330\pi$
$353$	36.5457			1.94513			0.972565	+	0.232630i	$0.0747330\pi$
$354$	−2.15728	−	6.63942i	−0.114658	−	0.352881i
$355$	10.3144	+	7.49388i	0.547434	+	0.397734i
$356$	−0.398205	+	0.289313i	−0.0211048	+	0.0153336i
$357$	0.0939932	−	0.289281i	0.00497465	−	0.0153104i
$358$	−3.32973	+	10.2479i	−0.175982	+	0.541616i
$359$	−0.254415	+	0.184843i	−0.0134275	+	0.00975564i	−0.594479	−	0.804111i	$-0.702642\pi$
$359$	−0.254415	+	0.184843i	−0.0134275	+	0.00975564i	0.581051	+	0.813867i	$0.302642\pi$
$360$	14.5578	+	10.5769i	0.767265	+	0.557450i
$361$	0.749035	+	2.30529i	0.0394229	+	0.121331i
$362$	−54.7328			−2.87669
$363$	−2.95825	−	10.5948i	−0.155268	−	0.556080i
$364$	−34.2434			−1.79484
$365$	6.60767	+	20.3363i	0.345861	+	1.06445i
$366$	−7.68220	−	5.58144i	−0.401555	−	0.291747i
$367$	−18.3608	+	13.3399i	−0.958426	+	0.696337i	−0.952785	−	0.303647i	$-0.901796\pi$
$367$	−18.3608	+	13.3399i	−0.958426	+	0.696337i	−0.00564133	+	0.999984i	$0.501796\pi$
$368$	−7.83581	+	24.1162i	−0.408470	+	1.25714i
$369$	−2.56878	+	7.90588i	−0.133725	+	0.411564i
$370$	12.1941	−	8.85956i	0.633943	−	0.460587i
$371$	−1.17610	−	0.854485i	−0.0610599	−	0.0443626i
$372$	1.37717	+	4.23848i	0.0714027	+	0.219755i
$373$	32.8020			1.69843			0.849213	−	0.528051i	$-0.177077\pi$
$373$	32.8020			1.69843			0.849213	+	0.528051i	$0.177077\pi$
$374$	2.66629	+	0.928480i	0.137870	+	0.0480106i
$375$	12.0548			0.622506
$376$	−8.57413	−	26.3885i	−0.442177	−	1.36088i
$377$	−18.8506	−	13.6958i	−0.970856	−	0.705368i
$378$	2.26416	−	1.64501i	0.116456	−	0.0846102i
$379$	7.86491	−	24.2057i	0.403993	−	1.24336i	−0.517740	−	0.855538i	$-0.673227\pi$
$379$	7.86491	−	24.2057i	0.403993	−	1.24336i	0.921733	−	0.387825i	$-0.126773\pi$
$380$	13.9957	−	43.0742i	0.717962	−	2.20966i
$381$	−16.2270	+	11.7896i	−0.831332	+	0.603998i
$382$	5.76234	+	4.18658i	0.294827	+	0.214204i
$383$	−4.31159	−	13.2697i	−0.220312	−	0.678050i	−0.998734	−	0.0503087i	$-0.983979\pi$
$383$	−4.31159	−	13.2697i	−0.220312	−	0.678050i	0.778422	−	0.627742i	$-0.216021\pi$
$384$	71.7346			3.66069
$385$	0.116493	−	5.56299i	0.00593703	−	0.283516i
$386$	60.5299			3.08089
$387$	−0.312321	−	0.961227i	−0.0158762	−	0.0488619i
$388$	−4.89670	−	3.55766i	−0.248592	−	0.180613i
$389$	7.33758	−	5.33107i	0.372030	−	0.270296i	−0.386022	−	0.922490i	$-0.626151\pi$
$389$	7.33758	−	5.33107i	0.372030	−	0.270296i	0.758052	+	0.652194i	$0.226151\pi$
$390$	−8.51847	+	26.2172i	−0.431350	+	1.32756i
$391$	0.129865	−	0.399683i	0.00656754	−	0.0202128i
$392$	−8.67739	+	6.30449i	−0.438275	+	0.318425i
$393$	−3.41483	−	2.48102i	−0.172255	−	0.125151i
$394$	−19.0863	−	58.7415i	−0.961553	−	2.95936i
$395$	10.3264			0.519577
$396$	11.0401	+	15.8844i	0.554786	+	0.798221i
$397$	24.1849			1.21381			0.606904	−	0.794775i	$-0.292411\pi$
$397$	24.1849			1.21381			0.606904	+	0.794775i	$0.292411\pi$
$398$	−11.0971	−	34.1533i	−0.556246	−	1.71195i
$399$	−3.74462	−	2.72062i	−0.187465	−	0.136201i
$400$	32.4488	−	23.5754i	1.62244	−	1.17877i
$401$	1.19394	−	3.67458i	0.0596226	−	0.183500i	−0.916809	−	0.399325i	$-0.869244\pi$
$401$	1.19394	−	3.67458i	0.0596226	−	0.183500i	0.976432	+	0.215826i	$0.0692444\pi$
$402$	5.33496	−	16.4193i	0.266084	−	0.818922i
$403$	−3.62935	+	2.63688i	−0.180791	+	0.131352i
$404$	92.9429	+	67.5269i	4.62408	+	3.35959i
$405$	−0.518429	−	1.59556i	−0.0257610	−	0.0792841i
$406$	−11.1070			−0.551230
$407$	10.1927	−	3.07742i	0.505233	−	0.152542i
$408$	−3.26247			−0.161516
$409$	6.21077	+	19.1148i	0.307103	+	0.945166i	0.978884	+	0.204416i	$0.0655296\pi$
$409$	6.21077	+	19.1148i	0.307103	+	0.945166i	−0.671781	+	0.740750i	$0.734470\pi$
$410$	−31.5761	−	22.9414i	−1.55943	−	1.13300i
$411$	11.7600	−	8.54413i	0.580077	−	0.421451i
$412$	−4.34845	+	13.3832i	−0.214233	+	0.659341i
$413$	0.770825	−	2.37236i	0.0379298	−	0.116736i
$414$	3.12826	−	2.27281i	0.153745	−	0.111703i
$415$	−2.73172	−	1.98471i	−0.134095	−	0.0974255i
$416$	54.2690	+	167.023i	2.66075	+	8.18896i
$417$	6.94615			0.340155
$418$	25.9753	−	34.2216i	1.27049	−	1.67383i
$419$	−2.12825			−0.103972			−0.0519859	−	0.998648i	$-0.516555\pi$
$419$	−2.12825			−0.103972			−0.0519859	+	0.998648i	$0.516555\pi$
$420$	3.02374	+	9.30610i	0.147543	+	0.454091i
$421$	3.11470	+	2.26296i	0.151801	+	0.110290i	0.661093	−	0.750304i	$-0.270093\pi$
$421$	3.11470	+	2.26296i	0.151801	+	0.110290i	−0.509292	+	0.860594i	$0.670093\pi$
$422$	40.1675	−	29.1834i	1.95532	−	1.42063i
$423$	−0.799390	+	2.46027i	−0.0388677	+	0.119622i
$424$	−4.81837	+	14.8294i	−0.234000	+	0.720179i
$425$	−0.537781	+	0.390721i	−0.0260862	+	0.0189528i
$426$	−17.2063	−	12.5011i	−0.833650	−	0.605682i
$427$	−1.04848	−	3.22689i	−0.0507395	−	0.156160i
$428$	−54.0238			−2.61134
$429$	−11.7729	+	15.5104i	−0.568399	+	0.748848i
$430$	4.74544			0.228846
$431$	−5.16151	−	15.8855i	−0.248621	−	0.765177i	−0.995020	−	0.0996781i	$-0.968219\pi$
$431$	−5.16151	−	15.8855i	−0.248621	−	0.765177i	0.746399	−	0.665499i	$-0.231781\pi$
$432$	−14.8479	−	10.7876i	−0.714370	−	0.519020i
$433$	−13.6898	+	9.94621i	−0.657889	+	0.477984i	−0.865949	−	0.500132i	$-0.833285\pi$
$433$	−13.6898	+	9.94621i	−0.657889	+	0.477984i	0.208060	+	0.978116i	$0.433285\pi$
$434$	−0.660818	+	2.03379i	−0.0317203	+	0.0976250i
$435$	−2.05748	+	6.33227i	−0.0986486	+	0.303609i
$436$	39.1893	−	28.4727i	1.87683	−	1.36359i
$437$	−5.17371	−	3.75892i	−0.247492	−	0.179813i
$438$	−11.0228	−	33.9246i	−0.526689	−	1.62098i
$439$	−26.7946			−1.27883			−0.639417	−	0.768860i	$-0.720824\pi$
$439$	−26.7946			−1.27883			−0.639417	+	0.768860i	$0.720824\pi$
$440$	−57.1336	+	17.2500i	−2.72374	+	0.822363i
$441$	1.00000			0.0476190
$442$	−1.54443	−	4.75327i	−0.0734611	−	0.226090i
$443$	3.17465	+	2.30652i	0.150832	+	0.109586i	0.660642	−	0.750701i	$-0.270284\pi$
$443$	3.17465	+	2.30652i	0.150832	+	0.109586i	−0.509810	+	0.860287i	$0.670284\pi$
$444$	−15.1477	+	11.0055i	−0.718880	+	0.522297i
$445$	−0.0437507	+	0.134651i	−0.00207398	+	0.00638306i
$446$	14.8037	−	45.5611i	0.700976	−	2.15738i
$447$	11.2971	−	8.20785i	0.534336	−	0.388218i
$448$	38.0301	+	27.6305i	1.79675	+	1.30542i
$449$	6.08099	+	18.7154i	0.286980	+	0.883233i	0.985798	+	0.167934i	$0.0537095\pi$
$449$	6.08099	+	18.7154i	0.286980	+	0.883233i	−0.698819	+	0.715299i	$0.746291\pi$
$450$	−6.11623			−0.288322
$451$	−15.7349	−	22.6392i	−0.740925	−	1.06604i
$452$	31.9598			1.50326
$453$	−0.423601	−	1.30371i	−0.0199025	−	0.0612536i
$454$	46.3861	+	33.7015i	2.17701	+	1.58169i
$455$	−7.96869	+	5.78959i	−0.373578	+	0.271420i
$456$	−15.3413	+	47.2158i	−0.718424	+	2.21108i
$457$	6.11005	−	18.8048i	0.285816	−	0.879652i	−0.700337	−	0.713813i	$-0.746967\pi$
$457$	6.11005	−	18.8048i	0.285816	−	0.879652i	0.986153	−	0.165839i	$-0.0530332\pi$
$458$	−55.3230	+	40.1945i	−2.58507	+	1.87817i
$459$	0.246078	+	0.178786i	0.0114859	+	0.00834501i
$460$	4.17771	+	12.8577i	0.194787	+	0.599492i
$461$	9.69184			0.451394			0.225697	−	0.974198i	$-0.427534\pi$
$461$	9.69184			0.451394			0.225697	+	0.974198i	$0.427534\pi$
$462$	−0.194331	+	9.28007i	−0.00904111	+	0.431748i
$463$	7.21162			0.335152			0.167576	−	0.985859i	$-0.446406\pi$
$463$	7.21162			0.335152			0.167576	+	0.985859i	$0.446406\pi$
$464$	22.5079	+	69.2723i	1.04490	+	3.21588i
$465$	1.03709	+	0.753487i	0.0480937	+	0.0349421i
$466$	53.6726	−	38.9954i	2.48633	−	1.80643i
$467$	11.3013	−	34.7818i	0.522962	−	1.60951i	−0.245349	−	0.969435i	$-0.578902\pi$
$467$	11.3013	−	34.7818i	0.522962	−	1.60951i	0.768311	−	0.640077i	$-0.221098\pi$
$468$	10.5818	−	32.5674i	0.489143	−	1.50543i
$469$	4.99065	−	3.62592i	0.230447	−	0.167429i
$470$	−9.82633	−	7.13924i	−0.453255	−	0.329309i
$471$	−4.91329	−	15.1215i	−0.226392	−	0.696764i
$472$	−26.7550			−1.23150
$473$	3.16564	+	1.10237i	0.145556	+	0.0506871i
$474$	−17.2263			−0.791229
$475$	3.12583	+	9.62032i	0.143423	+	0.441411i
$476$	−1.43525	−	1.04277i	−0.0657844	−	0.0477951i
$477$	1.17610	−	0.854485i	0.0538498	−	0.0391242i
$478$	−1.36641	+	4.20538i	−0.0624981	+	0.192349i
$479$	12.0424	−	37.0626i	0.550229	−	1.69343i	−0.157991	−	0.987441i	$-0.550502\pi$
$479$	12.0424	−	37.0626i	0.550229	−	1.69343i	0.708220	−	0.705992i	$-0.249498\pi$
$480$	40.5987	−	29.4967i	1.85307	−	1.34633i
$481$	−15.2481	−	11.0784i	−0.695254	−	0.505131i
$482$	−10.5840	−	32.5743i	−0.482089	−	1.48372i
$483$	1.38164			0.0628667
$484$	−64.1012	−	2.68583i	−2.91369	−	0.122083i
$485$	−1.74100			−0.0790548
$486$	0.864833	+	2.66168i	0.0392296	+	0.120736i
$487$	19.4030	+	14.0971i	0.879235	+	0.638802i	0.933049	−	0.359749i	$-0.117138\pi$
$487$	19.4030	+	14.0971i	0.879235	+	0.638802i	−0.0538139	+	0.998551i	$0.517138\pi$
$488$	−29.4420	+	21.3908i	−1.33278	+	0.968318i
$489$	3.23495	−	9.95614i	0.146289	−	0.450232i
$490$	−1.45091	+	4.46543i	−0.0655453	+	0.201728i
$491$	−2.58327	+	1.87686i	−0.116581	+	0.0847014i	−0.644548	−	0.764564i	$-0.722955\pi$
$491$	−2.58327	+	1.87686i	−0.116581	+	0.0847014i	0.527967	+	0.849265i	$0.322955\pi$
$492$	39.2244	+	28.4982i	1.76837	+	1.28480i
$493$	−0.373029	−	1.14807i	−0.0168004	−	0.0517063i
$494$	−76.0539			−3.42183
$495$	5.25472	+	1.82985i	0.236182	+	0.0822457i
$496$	14.0235			0.629674
$497$	−2.34835	−	7.22749i	−0.105338	−	0.324197i
$498$	4.55699	+	3.31085i	0.204204	+	0.148363i
$499$	−22.2747	+	16.1835i	−0.997154	+	0.724475i	−0.961476	−	0.274889i	$-0.911359\pi$
$499$	−22.2747	+	16.1835i	−0.997154	+	0.724475i	−0.0356777	+	0.999363i	$0.511359\pi$
$500$	21.7268	−	66.8682i	0.971652	−	2.99044i
$501$	2.64937	−	8.15393i	0.118365	−	0.364291i
$502$	−43.9491	+	31.9309i	−1.96154	+	1.42515i
$503$	26.8244	+	19.4891i	1.19604	+	0.868976i	0.993890	−	0.110378i	$-0.0352062\pi$
$503$	26.8244	+	19.4891i	1.19604	+	0.868976i	0.202153	+	0.979354i	$0.435206\pi$
$504$	−3.31447	−	10.2009i	−0.147638	−	0.454384i
$505$	33.0454			1.47050
$506$	−0.268496	+	12.8217i	−0.0119361	+	0.569994i
$507$	21.4702			0.953526
$508$	36.1507	+	111.260i	1.60393	+	4.93638i
$509$	6.22522	+	4.52288i	0.275928	+	0.200473i	0.717139	−	0.696930i	$-0.245451\pi$
$509$	6.22522	+	4.52288i	0.275928	+	0.200473i	−0.441211	+	0.897403i	$0.645451\pi$
$510$	−1.15539	+	0.839441i	−0.0511616	+	0.0371711i
$511$	3.93859	−	12.1217i	0.174233	−	0.536234i
$512$	47.9823	−	147.674i	2.12054	−	6.52635i
$513$	3.74462	−	2.72062i	0.165329	−	0.120118i
$514$	0.611559	+	0.444324i	0.0269747	+	0.0195983i
$515$	1.25080	+	3.84956i	0.0551168	+	0.169632i
$516$	−5.89486			−0.259507
$517$	−4.89660	−	7.04519i	−0.215352	−	0.309847i
$518$	−8.98434			−0.394749
$519$	−4.24808	−	13.0743i	−0.186470	−	0.573896i
$520$	85.4709	+	62.0983i	3.74815	+	2.72319i
$521$	6.55164	−	4.76004i	0.287032	−	0.208541i	−0.434946	−	0.900456i	$-0.643233\pi$
$521$	6.55164	−	4.76004i	0.287032	−	0.208541i	0.721979	+	0.691915i	$0.243233\pi$
$522$	3.43225	−	10.5634i	0.150225	−	0.462346i
$523$	5.98036	−	18.4056i	0.261503	−	0.804823i	−0.730976	−	0.682404i	$-0.760935\pi$
$523$	5.98036	−	18.4056i	0.261503	−	0.804823i	0.992478	−	0.122419i	$-0.0390653\pi$
$524$	−19.9170	+	14.4705i	−0.870077	+	0.632148i
$525$	−1.76804	−	1.28455i	−0.0771635	−	0.0560626i
$526$	24.2091	+	74.5078i	1.05557	+	3.24870i
$527$	−0.232415			−0.0101241
$528$	58.2720	−	17.5937i	2.53596	−	0.765669i
$529$	−21.0911			−0.917003
$530$	2.10924	+	6.49156i	0.0916194	+	0.281976i
$531$	2.01805	+	1.46620i	0.0875758	+	0.0636275i
$532$	−21.8404	+	15.8680i	−0.946904	+	0.687966i
$533$	−15.0816	+	46.4165i	−0.653258	+	2.01052i
$534$	0.0729840	−	0.224622i	0.00315833	−	0.00972033i
$535$	−12.5718	+	9.13391i	−0.543524	+	0.394893i
$536$	−53.5289	−	38.8910i	−2.31210	−	1.67984i
$537$	−1.18976	−	3.66170i	−0.0513419	−	0.158014i
$538$	3.12571			0.134759
$539$	−2.00521	+	2.64180i	−0.0863706	+	0.113791i
$540$	−9.78502			−0.421080
$541$	−8.83427	−	27.1891i	−0.379815	−	1.16895i	−0.940172	−	0.340700i	$-0.889336\pi$
$541$	−8.83427	−	27.1891i	−0.379815	−	1.16895i	0.560357	−	0.828251i	$-0.310664\pi$
$542$	−56.2214	−	40.8472i	−2.41491	−	1.75454i
$543$	15.8218	−	11.4952i	0.678978	−	0.493306i
$544$	−2.81154	+	8.65302i	−0.120544	+	0.370995i
$545$	4.30571	−	13.2516i	0.184436	−	0.567637i
$546$	13.2932	−	9.65808i	0.568897	−	0.413328i
$547$	−18.9243	−	13.7493i	−0.809143	−	0.587877i	0.104439	−	0.994531i	$-0.466695\pi$
$547$	−18.9243	−	13.7493i	−0.809143	−	0.587877i	−0.913582	+	0.406654i	$0.866695\pi$
$548$	−26.1991	−	80.6324i	−1.11917	−	3.44445i
$549$	3.39295			0.144808
$550$	12.2643	−	16.1579i	0.522953	−	0.688974i
$551$	−18.3694			−0.782564
$552$	−4.57940	−	14.0939i	−0.194912	−	0.599878i
$553$	−4.97965	−	3.61793i	−0.211756	−	0.153850i
$554$	28.1515	−	20.4532i	1.19604	−	0.868975i
$555$	−1.66428	+	5.12212i	−0.0706446	+	0.217422i
$556$	12.5193	−	38.5305i	0.530938	−	1.63406i
$557$	−20.5782	+	14.9510i	−0.871927	+	0.633492i	−0.931103	−	0.364755i	$-0.881153\pi$
$557$	−20.5782	+	14.9510i	−0.871927	+	0.633492i	0.0591762	+	0.998248i	$0.481153\pi$
$558$	−1.73004	−	1.25695i	−0.0732386	−	0.0532110i
$559$	−1.83368	−	5.64349i	−0.0775565	−	0.238694i
$560$	30.7903			1.30113
$561$	−0.965754	+	0.291585i	−0.0407742	+	0.0123107i
$562$	−18.8506			−0.795167
$563$	12.3233	+	37.9273i	0.519366	+	1.59844i	0.775195	+	0.631722i	$0.217652\pi$
$563$	12.3233	+	37.9273i	0.519366	+	1.59844i	−0.255829	+	0.966722i	$0.582348\pi$
$564$	12.2064	+	8.86848i	0.513983	+	0.373430i
$565$	7.43730	−	5.40351i	0.312890	−	0.227328i
$566$	−9.65207	+	29.7060i	−0.405707	+	1.24864i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	−65.9432	+	47.9106i	−2.76692	+	2.01028i
$569$	−26.0897	−	18.9553i	−1.09374	−	0.794648i	−0.113712	−	0.993514i	$-0.536274\pi$
$569$	−26.0897	−	18.9553i	−1.09374	−	0.794648i	−0.980027	+	0.198866i	$0.936274\pi$
$570$	6.71567	+	20.6687i	0.281288	+	0.865717i
$571$	−20.6844			−0.865615			−0.432807	−	0.901486i	$-0.642477\pi$
$571$	−20.6844			−0.865615			−0.432807	+	0.901486i	$0.642477\pi$
$572$	64.8179	+	93.2595i	2.71017	+	3.89937i
$573$	−2.54502			−0.106320
$574$	7.18913	+	22.1259i	0.300069	+	0.923516i
$575$	−2.44279	−	1.77479i	−0.101871	−	0.0740139i
$576$	−38.0301	+	27.6305i	−1.58459	+	1.15127i
$577$	4.85769	−	14.9504i	0.202228	−	0.622394i	−0.797588	−	0.603203i	$-0.793891\pi$
$577$	4.85769	−	14.9504i	0.202228	−	0.622394i	0.999816	−	0.0191913i	$-0.00610914\pi$
$578$	−14.6222	+	45.0024i	−0.608201	+	1.87185i
$579$	−17.4976	+	12.7127i	−0.727174	+	0.528323i
$580$	31.4170	+	22.8258i	1.30452	+	0.947790i
$581$	0.621946	+	1.91415i	0.0258027	+	0.0794125i
$582$	2.90430			0.120387
$583$	−0.100943	+	4.82044i	−0.00418065	+	0.199642i
$584$	−136.707			−5.65697
$585$	−3.04377	−	9.36776i	−0.125844	−	0.387309i
$586$	38.2665	+	27.8022i	1.58077	+	1.14850i
$587$	−16.6401	+	12.0898i	−0.686812	+	0.498998i	−0.875611	−	0.483018i	$-0.839541\pi$
$587$	−16.6401	+	12.0898i	−0.686812	+	0.498998i	0.188799	+	0.982016i	$0.439541\pi$
$588$	1.80234	−	5.54703i	0.0743272	−	0.228756i
$589$	−1.09290	+	3.36361i	−0.0450323	+	0.138595i
$590$	−9.47521	+	6.88414i	−0.390088	+	0.283416i
$591$	17.8545	+	12.9720i	0.734434	+	0.533598i
$592$	18.2065	+	56.0337i	0.748281	+	2.30297i
$593$	21.1496			0.868511			0.434255	−	0.900790i	$-0.357012\pi$
$593$	21.1496			0.868511			0.434255	+	0.900790i	$0.357012\pi$
$594$	−8.76582	−	3.05252i	−0.359666	−	0.125246i
$595$	−0.510295			−0.0209201
$596$	−25.1679	−	77.4589i	−1.03092	−	3.17284i
$597$	10.3809	+	7.54214i	0.424860	+	0.308679i
$598$	18.3664	−	13.3440i	0.751058	−	0.545676i
$599$	−10.4136	+	32.0499i	−0.425490	+	1.30952i	0.477034	+	0.878885i	$0.341712\pi$
$599$	−10.4136	+	32.0499i	−0.425490	+	1.30952i	−0.902524	+	0.430639i	$0.858288\pi$
$600$	−7.24349	+	22.2932i	−0.295714	+	0.910115i
$601$	29.7628	−	21.6239i	1.21405	−	0.882059i	0.218458	−	0.975846i	$-0.429897\pi$
$601$	29.7628	−	21.6239i	1.21405	−	0.882059i	0.995592	+	0.0937876i	$0.0298974\pi$
$602$	−2.28838	−	1.66260i	−0.0932672	−	0.0677626i
$603$	1.90626	+	5.86686i	0.0776288	+	0.238917i
$604$	−7.99519			−0.325320
$605$	−15.3709	+	10.2127i	−0.624917	+	0.415205i
$606$	−55.1257			−2.23933
$607$	3.72718	+	11.4711i	0.151282	+	0.465597i	0.997765	−	0.0668177i	$-0.0212846\pi$
$607$	3.72718	+	11.4711i	0.151282	+	0.465597i	−0.846483	+	0.532415i	$0.821285\pi$
$608$	112.009	+	81.3796i	4.54258	+	3.30038i
$609$	3.21073	−	2.33273i	0.130105	−	0.0945270i
$610$	−4.92286	+	15.1510i	−0.199321	+	0.613446i
$611$	−4.69332	+	14.4446i	−0.189872	+	0.584365i
$612$	1.43525	−	1.04277i	0.0580164	−	0.0421514i
$613$	−6.93847	−	5.04109i	−0.280242	−	0.203608i	0.438781	−	0.898594i	$-0.355410\pi$
$613$	−6.93847	−	5.04109i	−0.280242	−	0.203608i	−0.719023	+	0.694986i	$0.755410\pi$
$614$	−9.81180	−	30.1976i	−0.395972	−	1.21868i
$615$	13.9461			0.562359
$616$	33.5950	+	11.6988i	1.35358	+	0.471357i
$617$	−0.0309560			−0.00124624			−0.000623121	−	1.00000i	$-0.500198\pi$
$617$	−0.0309560			−0.00124624			−0.000623121		1.00000i	$0.500198\pi$
$618$	−2.08656	−	6.42176i	−0.0839336	−	0.258321i
$619$	17.2270	+	12.5162i	0.692412	+	0.503067i	0.877452	−	0.479664i	$-0.159241\pi$
$619$	17.2270	+	12.5162i	0.692412	+	0.503067i	−0.185040	+	0.982731i	$0.559241\pi$
$620$	6.04879	−	4.39471i	0.242925	−	0.176496i
$621$	−0.426950	+	1.31402i	−0.0171329	+	0.0527297i
$622$	20.6252	−	63.4778i	0.826994	−	2.54523i
$623$	0.0682736	−	0.0496037i	0.00273532	−	0.00198733i
$624$	−87.1740	−	63.3356i	−3.48975	−	2.53545i
$625$	−2.87290	−	8.84187i	−0.114916	−	0.353675i
$626$	86.6650			3.46383
$627$	−0.321397	+	15.3480i	−0.0128354	+	0.612939i
$628$	−92.7351			−3.70053
$629$	−0.301740	−	0.928660i	−0.0120312	−	0.0370281i
$630$	−3.79852	−	2.75979i	−0.151337	−	0.109953i
$631$	−17.6281	+	12.8075i	−0.701762	+	0.509860i	−0.880506	−	0.474036i	$-0.842797\pi$
$631$	−17.6281	+	12.8075i	−0.701762	+	0.509860i	0.178744	+	0.983896i	$0.442797\pi$
$632$	−20.4012	+	62.7883i	−0.811515	+	2.49759i
$633$	−5.48213	+	16.8723i	−0.217895	+	0.670613i
$634$	−7.26513	+	5.27842i	−0.288535	+	0.209633i
$635$	27.2235	+	19.7791i	1.08033	+	0.784908i
$636$	−2.62013	−	8.06392i	−0.103895	−	0.319755i
$637$	5.87113			0.232623
$638$	21.0240	+	30.2491i	0.832346	+	1.19757i
$639$	7.59943			0.300629
$640$	−37.1893	−	114.457i	−1.47004	−	4.52431i
$641$	32.2773	+	23.4508i	1.27487	+	0.926251i	0.999385	−	0.0350534i	$-0.0111601\pi$
$641$	32.2773	+	23.4508i	1.27487	+	0.926251i	0.275489	+	0.961304i	$0.411160\pi$
$642$	20.9719	−	15.2370i	0.827696	−	0.601357i
$643$	2.21134	−	6.80580i	0.0872067	−	0.268395i	−0.897938	−	0.440123i	$-0.854935\pi$
$643$	2.21134	−	6.80580i	0.0872067	−	0.268395i	0.985144	+	0.171728i	$0.0549350\pi$
$644$	2.49018	−	7.66400i	0.0981270	−	0.302004i
$645$	−1.37178	+	0.996656i	−0.0540138	+	0.0392433i
$646$	−3.18766	−	2.31597i	−0.125417	−	0.0911205i
$647$	−1.46751	−	4.51654i	−0.0576938	−	0.177563i	0.918057	−	0.396449i	$-0.129758\pi$
$647$	−1.46751	−	4.51654i	−0.0576938	−	0.177563i	−0.975750	+	0.218886i	$0.929758\pi$
$648$	10.7258			0.421351
$649$	−7.92002	+	2.39125i	−0.310888	+	0.0938647i
$650$	−35.9092			−1.40848
$651$	−0.236120	−	0.726701i	−0.00925425	−	0.0284817i
$652$	−49.3966	−	35.8887i	−1.93452	−	1.40551i
$653$	4.07243	−	2.95879i	0.159366	−	0.115786i	−0.505244	−	0.862976i	$-0.668598\pi$
$653$	4.07243	−	2.95879i	0.159366	−	0.115786i	0.664610	+	0.747190i	$0.268598\pi$
$654$	−7.18270	+	22.1061i	−0.280866	+	0.864416i
$655$	−2.18827	+	6.73480i	−0.0855028	+	0.263151i
$656$	123.427	−	89.6747i	4.81900	−	3.50121i
$657$	10.3114	+	7.49164i	0.402285	+	0.292277i
$658$	2.23722	+	6.88545i	0.0872159	+	0.268423i
$659$	6.55136			0.255205			0.127602	−	0.991825i	$-0.459272\pi$
$659$	6.55136			0.255205			0.127602	+	0.991825i	$0.459272\pi$
$660$	19.6210	−	25.8501i	0.763748	−	1.00621i
$661$	36.4255			1.41679			0.708394	−	0.705818i	$-0.249420\pi$
$661$	36.4255			1.41679			0.708394	+	0.705818i	$0.249420\pi$
$662$	−3.44570	−	10.6048i	−0.133921	−	0.412167i
$663$	1.44475	+	1.04968i	0.0561096	+	0.0407660i
$664$	17.4647	−	12.6888i	0.677760	−	0.492421i
$665$	−2.39960	+	7.38521i	−0.0930526	+	0.286386i
$666$	2.77631	−	8.54462i	0.107580	−	0.331097i
$667$	4.43607	−	3.22299i	0.171765	−	0.124795i
$668$	−40.4551	−	29.3923i	−1.56525	−	1.13722i
$669$	5.28957	+	16.2796i	0.204507	+	0.629407i
$670$	−28.9639			−1.11897
$671$	−6.80359	+	8.96351i	−0.262650	+	0.346033i
$672$	−29.9121			−1.15388
$673$	9.88569	+	30.4250i	0.381065	+	1.17280i	0.939295	+	0.343112i	$0.111481\pi$
$673$	9.88569	+	30.4250i	0.381065	+	1.17280i	−0.558229	+	0.829687i	$0.688519\pi$
$674$	25.5864	+	18.5896i	0.985551	+	0.716044i
$675$	1.76804	−	1.28455i	0.0680518	−	0.0494425i
$676$	38.6966	−	119.096i	1.48833	−	4.58062i
$677$	−6.68766	+	20.5825i	−0.257028	+	0.791050i	0.736396	+	0.676551i	$0.236526\pi$
$677$	−6.68766	+	20.5825i	−0.257028	+	0.791050i	−0.993423	+	0.114499i	$0.963474\pi$
$678$	−12.4068	+	9.01403i	−0.476478	+	0.346182i
$679$	0.839556	+	0.609973i	0.0322192	+	0.0234086i
$680$	1.69136	+	5.20546i	0.0648606	+	0.199620i
$681$	−20.4871			−0.785067
$682$	6.78972	−	2.04998i	0.259992	−	0.0784980i
$683$	−23.1587			−0.886144			−0.443072	−	0.896486i	$-0.646111\pi$
$683$	−23.1587			−0.886144			−0.443072	+	0.896486i	$0.646111\pi$
$684$	−8.34231	−	25.6750i	−0.318976	−	0.981708i
$685$	−19.7294	−	14.3343i	−0.753822	−	0.547684i
$686$	2.26416	−	1.64501i	0.0864461	−	0.0628068i
$687$	7.55058	−	23.2383i	0.288073	−	0.886596i
$688$	−5.73204	+	17.6414i	−0.218532	+	0.672572i
$689$	6.90503	−	5.01680i	0.263061	−	0.191125i
$690$	−5.24819	−	3.81303i	−0.199795	−	0.145160i
$691$	0.833105	+	2.56403i	0.0316928	+	0.0975404i	0.965652	−	0.259840i	$-0.0836699\pi$
$691$	0.833105	+	2.56403i	0.0316928	+	0.0975404i	−0.933959	+	0.357381i	$0.883670\pi$
$692$	−80.1798			−3.04798
$693$	−1.89286	−	2.72343i	−0.0719038	−	0.103455i
$694$	18.4387			0.699923
$695$	−3.60109	−	11.0830i	−0.136597	−	0.420403i
$696$	−34.4378	−	25.0205i	−1.30536	−	0.948400i
$697$	−2.04558	+	1.48620i	−0.0774818	+	0.0562938i
$698$	17.6723	−	54.3897i	0.668906	−	2.05868i
$699$	−7.32533	+	22.5450i	−0.277069	+	0.852732i
$700$	−10.3121	+	7.49216i	−0.389760	+	0.283177i
$701$	−0.361861	−	0.262907i	−0.0136673	−	0.00992987i	0.580931	−	0.813953i	$-0.302689\pi$
$701$	−0.361861	−	0.262907i	−0.0136673	−	0.00992987i	−0.594598	+	0.804023i	$0.702689\pi$
$702$	5.07755	+	15.6271i	0.191640	+	0.589807i
$703$	−14.8589			−0.560413
$704$	3.26409	−	155.873i	0.123020	−	5.87469i
$705$	4.33994			0.163451
$706$	31.6059	+	97.2731i	1.18950	+	3.66092i
$707$	−15.9354	−	11.5777i	−0.599311	−	0.435425i
$708$	11.7703	−	8.55159i	0.442353	−	0.321388i
$709$	3.46998	−	10.6795i	0.130318	−	0.401077i	−0.864515	−	0.502608i	$-0.832374\pi$
$709$	3.46998	−	10.6795i	0.130318	−	0.401077i	0.994832	+	0.101531i	$0.0323740\pi$
$710$	−11.0261	+	33.9347i	−0.413801	+	1.27355i
$711$	4.97965	−	3.61793i	0.186751	−	0.135683i
$712$	−0.732292	−	0.532041i	−0.0274438	−	0.0199391i
$713$	−0.326232	−	1.00404i	−0.0122175	−	0.0376015i
$714$	0.851264			0.0318578
$715$	30.8512	+	10.7433i	1.15377	+	0.401777i
$716$	−22.4559			−0.839218
$717$	−0.488237	−	1.50264i	−0.0182335	−	0.0561171i
$718$	−0.712020	−	0.517313i	−0.0265723	−	0.0193059i
$719$	−7.31641	+	5.31568i	−0.272856	+	0.198241i	−0.715795	−	0.698310i	$-0.753936\pi$
$719$	−7.31641	+	5.31568i	−0.272856	+	0.198241i	0.442939	+	0.896552i	$0.353936\pi$
$720$	−9.51474	+	29.2833i	−0.354593	+	1.09133i
$721$	0.745556	−	2.29458i	0.0277659	−	0.0854548i
$722$	−5.48817	+	3.98739i	−0.204249	+	0.148395i
$723$	9.90093	+	7.19345i	0.368220	+	0.267527i
$724$	−35.2480	−	108.482i	−1.30998	−	4.03171i
$725$	−8.67321			−0.322115
$726$	25.6415	−	17.0366i	0.951644	−	0.632288i
$727$	−44.1368			−1.63694			−0.818471	−	0.574548i	$-0.805178\pi$
$727$	−44.1368			−1.63694			−0.818471	+	0.574548i	$0.805178\pi$
$728$	−19.4597	−	59.8908i	−0.721224	−	2.21970i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−48.4143	+	35.1750i	−1.79189	+	1.30189i
$731$	0.0949984	−	0.292375i	0.00351364	−	0.0108139i
$732$	6.11525	−	18.8208i	0.226026	−	0.695637i
$733$	22.6879	−	16.4837i	0.837997	−	0.608840i	−0.0838136	−	0.996481i	$-0.526710\pi$
$733$	22.6879	−	16.4837i	0.837997	−	0.608840i	0.921810	+	0.387641i	$0.126710\pi$
$734$	−51.3856	−	37.3338i	−1.89668	−	1.37802i
$735$	−0.518429	−	1.59556i	−0.0191226	−	0.0588532i
$736$	−41.3277			−1.52336
$737$	−19.3215	−	6.72833i	−0.711718	−	0.247841i
$738$	−23.2645			−0.856379
$739$	−13.5061	−	41.5674i	−0.496829	−	1.52908i	−0.814088	−	0.580742i	$-0.802762\pi$
$739$	−13.5061	−	41.5674i	−0.496829	−	1.52908i	0.317259	−	0.948339i	$-0.397238\pi$
$740$	25.4130	+	18.4636i	0.934199	+	0.678735i
$741$	21.9851	−	15.9731i	0.807644	−	0.586788i
$742$	1.25724	−	3.86939i	0.0461547	−	0.142050i
$743$	−6.60295	+	20.3218i	−0.242239	+	0.745534i	0.753840	+	0.657058i	$0.228199\pi$
$743$	−6.60295	+	20.3218i	−0.242239	+	0.745534i	−0.996078	+	0.0884755i	$0.971801\pi$
$744$	−6.63039	+	4.81726i	−0.243082	+	0.176609i
$745$	−18.9529	−	13.7701i	−0.694380	−	0.504497i
$746$	28.3683	+	87.3086i	1.03864	+	3.19660i
$747$	−2.01266			−0.0736394
$748$	−0.123186	+	5.88261i	−0.00450412	+	0.215089i
$749$	9.26256			0.338446
$750$	10.4254	+	32.0860i	0.380681	+	1.17161i
$751$	−1.81171	−	1.31629i	−0.0661104	−	0.0480320i	0.554239	−	0.832357i	$-0.313009\pi$
$751$	−1.81171	−	1.31629i	−0.0661104	−	0.0480320i	−0.620350	+	0.784325i	$0.713009\pi$
$752$	38.4097	−	27.9063i	1.40066	−	1.01764i
$753$	5.99825	−	18.4607i	0.218588	−	0.672746i
$754$	20.1512	−	62.0189i	0.733863	−	2.25860i
$755$	−1.86054	+	1.35176i	−0.0677120	+	0.0491957i
$756$	4.71859	+	3.42825i	0.171613	+	0.124684i
$757$	14.7429	+	45.3740i	0.535840	+	1.64915i	0.741828	+	0.670591i	$0.233959\pi$
$757$	14.7429	+	45.3740i	0.535840	+	1.64915i	−0.205988	+	0.978555i	$0.566041\pi$
$758$	71.2297			2.58718
$759$	−2.61525	−	3.76280i	−0.0949275	−	0.136581i
$760$	83.2891			3.02121
$761$	−11.0143	−	33.8985i	−0.399268	−	1.22882i	−0.925588	−	0.378534i	$-0.876428\pi$
$761$	−11.0143	−	33.8985i	−0.399268	−	1.22882i	0.526320	−	0.850287i	$-0.323572\pi$
$762$	−45.4137	−	32.9950i	−1.64517	−	1.19528i
$763$	−6.71913	+	4.88173i	−0.243249	+	0.176731i
$764$	−4.58699	+	14.1173i	−0.165951	+	0.510746i
$765$	0.157690	−	0.485320i	0.00570129	−	0.0175468i
$766$	31.5909	−	22.9522i	1.14143	−	0.829296i
$767$	11.8482	+	8.60824i	0.427815	+	0.310826i
$768$	32.9861	+	101.521i	1.19028	+	3.66331i
$769$	22.0645			0.795665			0.397832	−	0.917458i	$-0.369763\pi$
$769$	22.0645			0.795665			0.397832	+	0.917458i	$0.369763\pi$
$770$	14.9077	−	4.50099i	0.537235	−	0.162205i
$771$	−0.270104			−0.00972755
$772$	38.9813	+	119.972i	1.40297	+	4.31789i
$773$	15.2956	+	11.1129i	0.550145	+	0.399703i	0.827839	−	0.560966i	$-0.189570\pi$
$773$	15.2956	+	11.1129i	0.550145	+	0.399703i	−0.277694	+	0.960670i	$0.589570\pi$
$774$	2.28838	−	1.66260i	0.0822539	−	0.0597610i
$775$	−0.516019	+	1.58814i	−0.0185360	+	0.0570478i
$776$	3.43958	−	10.5859i	0.123474	−	0.380013i
$777$	2.59713	−	1.88693i	0.0931715	−	0.0676931i
$778$	20.5354	+	14.9198i	0.736230	+	0.534902i
$779$	11.8898	+	36.5932i	0.425998	+	1.31109i
$780$	−57.4491			−2.05701
$781$	−15.2385	+	20.0762i	−0.545275	+	0.718383i
$782$	1.17614			0.0420587
$783$	1.22639	+	3.77444i	0.0438276	+	0.134887i
$784$	−14.8479	−	10.7876i	−0.530282	−	0.385272i
$785$	−21.5802	+	15.6789i	−0.770229	+	0.559604i
$786$	3.65043	−	11.2349i	0.130206	−	0.400734i
$787$	2.05310	−	6.31878i	0.0731850	−	0.225240i	−0.907772	−	0.419463i	$-0.862218\pi$
$787$	2.05310	−	6.31878i	0.0731850	−	0.225240i	0.980957	+	0.194223i	$0.0622184\pi$
$788$	104.136	−	75.6592i	3.70969	−	2.69525i
$789$	−22.6466	−	16.4537i	−0.806241	−	0.585768i
$790$	8.93060	+	27.4856i	0.317737	+	0.977893i
$791$	−5.47962			−0.194833
$792$	−21.5076	+	28.3356i	−0.764239	+	1.00686i
$793$	19.9205			0.707397
$794$	20.9159	+	64.3727i	0.742279	+	2.28450i
$795$	−1.97311	−	1.43355i	−0.0699789	−	0.0508426i
$796$	60.5463	−	43.9895i	2.14601	−	1.55917i
$797$	−4.72849	+	14.5528i	−0.167492	+	0.515486i	−0.999211	−	0.0397097i	$-0.987357\pi$
$797$	−4.72849	+	14.5528i	−0.167492	+	0.515486i	0.831720	+	0.555196i	$0.187357\pi$
$798$	4.00297	−	12.3199i	0.141703	−	0.436118i
$799$	−0.636573	+	0.462497i	−0.0225203	+	0.0163620i
$800$	52.8857	+	38.4237i	1.86979	+	1.35848i
$801$	0.0260782	+	0.0802604i	0.000921428	+	0.00283586i
$802$	10.8131			0.381825
$803$	−40.4679	+	12.2183i	−1.42808	+	0.431173i
$804$	35.9794			1.26889
$805$	−0.716282	−	2.20449i	−0.0252456	−	0.0776981i
$806$	−10.1573	−	7.37973i	−0.357776	−	0.259940i
$807$	−0.903557	+	0.656473i	−0.0318067	+	0.0231089i
$808$	−65.2857	+	200.929i	−2.29674	+	7.06865i
$809$	7.63556	−	23.4998i	0.268452	−	0.826210i	−0.722426	−	0.691448i	$-0.756973\pi$
$809$	7.63556	−	23.4998i	0.268452	−	0.826210i	0.990878	−	0.134762i	$-0.0430269\pi$
$810$	3.79852	−	2.75979i	0.133467	−	0.0969691i
$811$	−20.8629	−	15.1578i	−0.732597	−	0.532263i	0.157787	−	0.987473i	$-0.449564\pi$
$811$	−20.8629	−	15.1578i	−0.732597	−	0.532263i	−0.890384	+	0.455211i	$0.849564\pi$
$812$	−7.15291	−	22.0144i	−0.251018	−	0.772554i
$813$	24.8310			0.870860
$814$	17.0061	+	24.4682i	0.596063	+	0.857611i
$815$	−17.5627			−0.615195
$816$	−1.72506	−	5.30918i	−0.0603891	−	0.185859i
$817$	−3.78466	−	2.74972i	−0.132408	−	0.0962004i
$818$	−45.5063	+	33.0622i	−1.59109	+	1.15599i
$819$	−1.81428	+	5.58378i	−0.0633961	+	0.195113i
$820$	25.1355	−	77.3592i	0.877771	−	2.70150i
$821$	14.8104	−	10.7604i	0.516885	−	0.375539i	−0.298544	−	0.954396i	$-0.596501\pi$
$821$	14.8104	−	10.7604i	0.516885	−	0.375539i	0.815429	+	0.578857i	$0.196501\pi$
$822$	32.9122	+	23.9121i	1.14794	+	0.834030i
$823$	−1.49684	−	4.60680i	−0.0521766	−	0.160583i	0.921573	−	0.388205i	$-0.126905\pi$
$823$	−1.49684	−	4.60680i	−0.0521766	−	0.160583i	−0.973750	+	0.227622i	$0.926905\pi$
$824$	−25.8779			−0.901500
$825$	−0.151749	+	7.24661i	−0.00528323	+	0.252295i
$826$	6.98110			0.242903
$827$	7.99793	+	24.6151i	0.278115	+	0.855951i	0.988378	+	0.152014i	$0.0485760\pi$
$827$	7.99793	+	24.6151i	0.278115	+	0.855951i	−0.710263	+	0.703936i	$0.751424\pi$
$828$	6.51938	+	4.73661i	0.226564	+	0.164609i
$829$	−43.8054	+	31.8265i	−1.52142	+	1.10538i	−0.560649	+	0.828054i	$0.689448\pi$
$829$	−43.8054	+	31.8265i	−1.52142	+	1.10538i	−0.960776	+	0.277326i	$0.910552\pi$
$830$	2.92018	−	8.98740i	0.101361	−	0.311957i
$831$	−3.84216	+	11.8250i	−0.133283	+	0.410204i
$832$	−223.280	+	162.222i	−7.74084	+	5.62405i
$833$	0.246078	+	0.178786i	0.00852608	+	0.00619456i
$834$	6.00727	+	18.4885i	0.208015	+	0.640203i
$835$	−14.3836			−0.497766
$836$	84.5564	+	29.4450i	2.92444	+	1.01838i
$837$	0.764099			0.0264111
$838$	−1.84058	−	5.66473i	−0.0635819	−	0.195685i
$839$	−26.1821	−	19.0224i	−0.903907	−	0.656727i	0.0355593	−	0.999368i	$-0.488679\pi$
$839$	−26.1821	−	19.0224i	−0.903907	−	0.656727i	−0.939467	+	0.342640i	$0.888679\pi$
$840$	−14.5578	+	10.5769i	−0.502293	+	0.364937i
$841$	−4.09435	+	12.6011i	−0.141184	+	0.434521i
$842$	−3.32959	+	10.2474i	−0.114745	+	0.353149i
$843$	5.44921	−	3.95909i	0.187681	−	0.136358i
$844$	83.7104	+	60.8191i	2.88143	+	2.09348i
$845$	−11.1308	−	34.2571i	−0.382911	−	1.17848i
$846$	−7.23980			−0.248909
$847$	10.9904	+	0.460494i	0.377633	+	0.0158228i
$848$	−26.6804			−0.916210
$849$	−3.44882	−	10.6144i	−0.118363	−	0.364285i
$850$	−1.50507	−	1.09350i	−0.0516234	−	0.0375066i
$851$	3.58830	−	2.60705i	0.123005	−	0.0893685i
$852$	13.6968	−	42.1543i	0.469243	−	1.44418i
$853$	1.89308	−	5.82631i	0.0648180	−	0.199489i	−0.913403	−	0.407057i	$-0.866555\pi$
$853$	1.89308	−	5.82631i	0.0648180	−	0.199489i	0.978221	+	0.207568i	$0.0665549\pi$
$854$	7.68220	−	5.58144i	0.262879	−	0.190993i
$855$	−6.28224	−	4.56431i	−0.214848	−	0.156096i
$856$	−30.7005	−	94.4863i	−1.04932	−	3.22948i
$857$	−22.6396			−0.773354			−0.386677	−	0.922215i	$-0.626377\pi$
$857$	−22.6396			−0.773354			−0.386677	+	0.922215i	$0.626377\pi$
$858$	−51.4653	−	17.9217i	−1.75700	−	0.611838i
$859$	−13.7204			−0.468134			−0.234067	−	0.972220i	$-0.575204\pi$
$859$	−13.7204			−0.468134			−0.234067	+	0.972220i	$0.575204\pi$
$860$	3.05607	+	9.40562i	0.104211	+	0.320729i
$861$	−6.72515	−	4.88611i	−0.229192	−	0.166518i
$862$	37.8183	−	27.4766i	1.28810	−	0.935857i
$863$	13.4826	−	41.4951i	0.458953	−	1.41251i	−0.407479	−	0.913215i	$-0.633592\pi$
$863$	13.4826	−	41.4951i	0.458953	−	1.41251i	0.866431	−	0.499296i	$-0.166408\pi$
$864$	9.24335	−	28.4481i	0.314465	−	0.967824i
$865$	−18.6585	+	13.5562i	−0.634407	+	0.460923i
$866$	−38.3131	−	27.8361i	−1.30193	−	0.945908i
$867$	−5.22470	−	16.0800i	−0.177440	−	0.546104i
$868$	−4.45660			−0.151267
$869$	−0.427399	+	20.4100i	−0.0144985	+	0.692361i
$870$	−18.6339			−0.631748
$871$	11.1919	+	34.4451i	0.379223	+	1.16713i
$872$	72.0683	+	52.3607i	2.44054	+	1.77316i
$873$	−0.839556	+	0.609973i	−0.0284146	+	0.0206445i
$874$	5.53065	−	17.0216i	0.187077	−	0.575764i
$875$	−3.72513	+	11.4648i	−0.125932	+	0.387580i
$876$	60.1410	−	43.6950i	2.03198	−	1.47632i
$877$	−27.4356	−	19.9331i	−0.926433	−	0.673093i	0.0186840	−	0.999825i	$-0.494052\pi$
$877$	−27.4356	−	19.9331i	−0.926433	−	0.673093i	−0.945117	+	0.326733i	$0.894052\pi$
$878$	−23.1728	−	71.3186i	−0.782045	−	2.40689i
$879$	−16.9009			−0.570055
$880$	−58.2818	−	83.8554i	−1.96468	−	2.82676i
$881$	12.7514			0.429605			0.214803	−	0.976657i	$-0.431089\pi$
$881$	12.7514			0.429605			0.214803	+	0.976657i	$0.431089\pi$
$882$	0.864833	+	2.66168i	0.0291205	+	0.0896235i
$883$	−0.713738	−	0.518561i	−0.0240192	−	0.0174510i	0.575711	−	0.817653i	$-0.304725\pi$
$883$	−0.713738	−	0.518561i	−0.0240192	−	0.0174510i	−0.599730	+	0.800202i	$0.704725\pi$
$884$	8.42652	−	6.12223i	0.283415	−	0.205913i
$885$	1.29319	−	3.98004i	0.0434702	−	0.133788i
$886$	−3.39368	+	10.4447i	−0.114013	+	0.350895i
$887$	−27.8500	+	20.2342i	−0.935112	+	0.679399i	−0.947239	−	0.320528i	$-0.896140\pi$
$887$	−27.8500	+	20.2342i	−0.935112	+	0.679399i	0.0121270	+	0.999926i	$0.496140\pi$
$888$	−27.8564	−	20.2389i	−0.934800	−	0.679172i
$889$	−6.19815	−	19.0759i	−0.207879	−	0.639786i
$890$	−0.396235			−0.0132818
$891$	3.17506	−	0.958630i	0.106369	−	0.0321153i
$892$	99.8372			3.34280
$893$	3.70005	+	11.3876i	0.123818	+	0.381071i
$894$	31.6168	+	22.9710i	1.05742	+	0.768264i
$895$	−5.22567	+	3.79667i	−0.174675	+	0.126909i
$896$	−22.1672	+	68.2237i	−0.740555	+	2.27919i
$897$	−2.50668	+	7.71477i	−0.0836956	+	0.257589i
$898$	−44.5553	+	32.3713i	−1.48683	+	1.08025i
$899$	−2.45331	−	1.78244i	−0.0818226	−	0.0594476i
$900$	−3.93886	−	12.1226i	−0.131295	−	0.404085i
$901$	0.442181			0.0147312
$902$	46.6503	−	61.4603i	1.55329	−	2.04640i
$903$	1.01069			0.0336338
$904$	18.1620	+	55.8970i	0.604060	+	1.85911i
$905$	−26.5438	−	19.2852i	−0.882345	−	0.641061i
$906$	3.10372	−	2.25498i	0.103114	−	0.0749168i
$907$	11.4750	−	35.3164i	0.381021	−	1.17266i	−0.558304	−	0.829636i	$-0.688548\pi$
$907$	11.4750	−	35.3164i	0.381021	−	1.17266i	0.939326	−	0.343027i	$-0.111452\pi$
$908$	−36.9247	+	113.642i	−1.22539	+	3.77136i
$909$	15.9354	−	11.5777i	0.528542	−	0.384008i
$910$	−22.3016	−	16.2031i	−0.739292	−	0.537127i
$911$	−12.0293	−	37.0223i	−0.398548	−	1.22660i	−0.926164	−	0.377121i	$-0.876914\pi$
$911$	−12.0293	−	37.0223i	−0.398548	−	1.22660i	0.527617	−	0.849483i	$-0.323086\pi$
$912$	−84.9487			−2.81293
$913$	4.03581	−	5.31706i	0.133566	−	0.175969i
$914$	55.3366			1.83037
$915$	−1.75901	−	5.41366i	−0.0581509	−	0.178970i
$916$	−115.295	−	83.7666i	−3.80945	−	2.76773i
$917$	3.41483	−	2.48102i	0.112768	−	0.0819305i
$918$	−0.263055	+	0.809600i	−0.00868211	+	0.0267208i
$919$	−9.02013	+	27.7611i	−0.297547	+	0.915754i	0.684808	+	0.728724i	$0.259886\pi$
$919$	−9.02013	+	27.7611i	−0.297547	+	0.915754i	−0.982354	+	0.187030i	$0.940114\pi$
$920$	−20.1137	+	14.6134i	−0.663128	+	0.481790i
$921$	9.17855	+	6.66861i	0.302443	+	0.219738i
$922$	8.38183	+	25.7966i	0.276041	+	0.849566i
$923$	44.6173			1.46860
$924$	−18.5185	+	5.59120i	−0.609215	+	0.183937i
$925$	−7.01568			−0.230674
$926$	6.23685	+	19.1951i	0.204956	+	0.630789i
$927$	1.95189	+	1.41813i	0.0641085	+	0.0465775i
$928$	−96.0397	+	69.7769i	−3.15266	+	2.29054i
$929$	5.86670	−	18.0559i	0.192480	−	0.592393i	−0.807517	−	0.589845i	$-0.799189\pi$
$929$	5.86670	−	18.0559i	0.192480	−	0.592393i	0.999997	−	0.00254832i	$-0.000811155\pi$
$930$	−1.10864	+	3.41203i	−0.0363536	+	0.111885i
$931$	3.74462	−	2.72062i	0.122725	−	0.0891648i
$932$	111.855	+	81.2676i	3.66394	+	2.66201i
$933$	7.36966	+	22.6815i	0.241272	+	0.742559i
$934$	102.352			3.34906
$935$	0.965917	+	1.38975i	0.0315889	+	0.0454498i
$936$	62.9729			2.05833
$937$	−6.14700	−	18.9185i	−0.200814	−	0.618041i	−0.999859	−	0.0167709i	$-0.994661\pi$
$937$	−6.14700	−	18.9185i	−0.200814	−	0.618041i	0.799046	−	0.601271i	$-0.205339\pi$
$938$	13.9671	+	10.1477i	0.456043	+	0.331334i
$939$	−25.0525	+	18.2017i	−0.817558	+	0.593991i
$940$	7.82204	−	24.0738i	0.255127	−	0.785200i
$941$	−3.38976	+	10.4326i	−0.110503	+	0.340093i	−0.990983	−	0.133991i	$-0.957221\pi$
$941$	−3.38976	+	10.4326i	−0.110503	+	0.340093i	0.880480	+	0.474084i	$0.157221\pi$
$942$	35.9996	−	26.1552i	1.17293	−	0.852184i
$943$	−9.29173	−	6.75083i	−0.302580	−	0.219837i
$944$	−14.1470	−	43.5399i	−0.460444	−	1.41710i
$945$	1.67767			0.0545747
$946$	−0.196409	+	9.37931i	−0.00638582	+	0.304948i
$947$	−40.5321			−1.31712			−0.658558	−	0.752530i	$-0.728833\pi$
$947$	−40.5321			−1.31712			−0.658558	+	0.752530i	$0.728833\pi$
$948$	−11.0937	−	34.1430i	−0.360308	−	1.10891i
$949$	60.5394	+	43.9845i	1.96519	+	1.42780i
$950$	−22.9029	+	16.6400i	−0.743069	+	0.539871i
$951$	0.991557	−	3.05170i	0.0321535	−	0.0989582i
$952$	1.00816	−	3.10279i	0.0326746	−	0.100562i
$953$	37.7198	−	27.4051i	1.22187	−	0.887737i	0.225612	−	0.974217i	$-0.427562\pi$
$953$	37.7198	−	27.4051i	1.22187	−	0.887737i	0.996254	+	0.0864799i	$0.0275618\pi$
$954$	3.29150	+	2.39141i	0.106566	+	0.0774248i
$955$	1.31941	+	4.06073i	0.0426952	+	0.131402i
$956$	−9.21516			−0.298039
$957$	−12.4305	−	4.32867i	−0.401821	−	0.139926i
$958$	109.063			3.52368
$959$	4.49191	+	13.8247i	0.145051	+	0.446423i
$960$	63.8021	+	46.3549i	2.05920	+	1.49610i
$961$	24.6072	−	17.8782i	0.793780	−	0.576715i
$962$	16.3001	−	50.1666i	0.525537	−	1.61744i
$963$	−2.86229	+	8.80922i	−0.0922359	+	0.283873i
$964$	57.7471	−	41.9557i	1.85991	−	1.35130i
$965$	29.3552	+	21.3278i	0.944977	+	0.686566i
$966$	1.19489	+	3.67749i	0.0384449	+	0.118321i
$967$	27.2512			0.876338			0.438169	−	0.898893i	$-0.355627\pi$
$967$	27.2512			0.876338			0.438169	+	0.898893i	$0.355627\pi$
$968$	−31.7298	−	113.638i	−1.01983	−	3.65245i
$969$	1.40787			0.0452274
$970$	−1.50568	−	4.63399i	−0.0483443	−	0.148789i
$971$	−18.7984	−	13.6579i	−0.603271	−	0.438302i	0.243768	−	0.969834i	$-0.421617\pi$
$971$	−18.7984	−	13.6579i	−0.603271	−	0.438302i	−0.847038	+	0.531532i	$0.821617\pi$
$972$	−4.71859	+	3.42825i	−0.151349	+	0.109961i
$973$	−2.14648	+	6.60619i	−0.0688130	+	0.211785i
$974$	−20.7417	+	63.8364i	−0.664607	+	2.04545i
$975$	10.3804	−	7.54179i	0.332438	−	0.241531i
$976$	−50.3782	−	36.6019i	−1.61257	−	1.17160i
$977$	−8.89186	−	27.3663i	−0.284476	−	0.875527i	−0.986555	−	0.163428i	$-0.947745\pi$
$977$	−8.89186	−	27.3663i	−0.284476	−	0.875527i	0.702079	−	0.712099i	$-0.252255\pi$
$978$	29.2978			0.936840
$979$	−0.264325	−	0.0920457i	−0.00844785	−	0.00294179i
$980$	−9.78502			−0.312571
$981$	−2.56648	−	7.89881i	−0.0819413	−	0.252189i
$982$	−7.22970	−	5.25268i	−0.230709	−	0.167620i
$983$	22.8080	−	16.5710i	0.727462	−	0.528532i	−0.161298	−	0.986906i	$-0.551568\pi$
$983$	22.8080	−	16.5710i	0.727462	−	0.528532i	0.888759	+	0.458374i	$0.151568\pi$
$984$	−27.5523	+	84.7973i	−0.878336	+	2.70324i
$985$	11.4414	−	35.2130i	0.364553	−	1.12198i
$986$	2.73318	−	1.98577i	0.0870421	−	0.0632398i
$987$	−2.09283	−	1.52053i	−0.0666155	−	0.0483990i
$988$	−48.9788	−	150.741i	−1.55822	−	4.79572i
$989$	1.39641			0.0444034
$990$	−0.326024	+	15.5689i	−0.0103617	+	0.494813i
$991$	−47.6676			−1.51421			−0.757106	−	0.653293i	$-0.773387\pi$
$991$	−47.6676			−1.51421			−0.757106	+	0.653293i	$0.773387\pi$
$992$	7.06283	+	21.7372i	0.224245	+	0.690156i
$993$	3.22332	+	2.34188i	0.102289	+	0.0743173i
$994$	17.2063	−	12.5011i	0.545752	−	0.396512i
$995$	6.65220	−	20.4734i	0.210889	−	0.649050i
$996$	−3.62750	+	11.1643i	−0.114942	+	0.353754i
$997$	15.0982	−	10.9695i	0.478166	−	0.347408i	−0.322449	−	0.946587i	$-0.604506\pi$
$997$	15.0982	−	10.9695i	0.478166	−	0.347408i	0.800615	+	0.599179i	$0.204506\pi$
$998$	−62.3394	−	45.2922i	−1.97332	−	1.43370i
$999$	0.992016	+	3.05311i	0.0313860	+	0.0965961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.148.5	yes	20
3.2	odd	2		693.2.m.j.379.1		20
11.3	even	5		2541.2.a.bq.1.10		10
11.8	odd	10		2541.2.a.br.1.1		10
11.9	even	5	inner	231.2.j.g.64.5	✓	20
33.8	even	10		7623.2.a.cy.1.10		10
33.14	odd	10		7623.2.a.cx.1.1		10
33.20	odd	10		693.2.m.j.64.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.5	✓	20	11.9	even	5	inner
231.2.j.g.148.5	yes	20	1.1	even	1	trivial
693.2.m.j.64.1		20	33.20	odd	10
693.2.m.j.379.1		20	3.2	odd	2
2541.2.a.bq.1.10		10	11.3	even	5
2541.2.a.br.1.1		10	11.8	odd	10
7623.2.a.cx.1.1		10	33.14	odd	10
7623.2.a.cy.1.10		10	33.8	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.864833 + 2.66168i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.71859 + 3.42825i) q^{4} +(-0.518429 + 1.59556i) q^{5} +(0.864833 - 2.66168i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-8.67739 - 6.30449i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.864833 + 2.66168i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-4.71859 + 3.42825i) q^{4} +(-0.518429 + 1.59556i) q^{5} +(0.864833 - 2.66168i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-8.67739 - 6.30449i) q^{8} +(0.309017 + 0.951057i) q^{9} -4.69523 q^{10} +(-3.13215 - 1.09071i) q^{11} +5.83249 q^{12} +(1.81428 + 5.58378i) q^{13} +(2.26416 + 1.64501i) q^{14} +(1.35727 - 0.986111i) q^{15} +(5.67139 - 17.4547i) q^{16} +(-0.0939932 + 0.289281i) q^{17} +(-2.26416 + 1.64501i) q^{18} +(3.74462 + 2.72062i) q^{19} +(-3.02374 - 9.30610i) q^{20} -1.00000 q^{21} +(0.194331 - 9.28007i) q^{22} -1.38164 q^{23} +(3.31447 + 10.2009i) q^{24} +(1.76804 + 1.28455i) q^{25} +(-13.2932 + 9.65808i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.80234 + 5.54703i) q^{28} +(-3.21073 + 2.33273i) q^{29} +(3.79852 + 2.75979i) q^{30} +(0.236120 + 0.726701i) q^{31} +29.9121 q^{32} +(1.89286 + 2.72343i) q^{33} -0.851264 q^{34} +(0.518429 + 1.59556i) q^{35} +(-4.71859 - 3.42825i) q^{36} +(-2.59713 + 1.88693i) q^{37} +(-4.00297 + 12.3199i) q^{38} +(1.81428 - 5.58378i) q^{39} +(14.5578 - 10.5769i) q^{40} +(6.72515 + 4.88611i) q^{41} +(-0.864833 - 2.66168i) q^{42} -1.01069 q^{43} +(18.5185 - 5.59120i) q^{44} -1.67767 q^{45} +(-1.19489 - 3.67749i) q^{46} +(2.09283 + 1.52053i) q^{47} +(-14.8479 + 10.7876i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-1.89002 + 5.81688i) q^{50} +(0.246078 - 0.178786i) q^{51} +(-27.7035 - 20.1277i) q^{52} +(-0.449229 - 1.38259i) q^{53} +2.79866 q^{54} +(3.36409 - 4.43208i) q^{55} -10.7258 q^{56} +(-1.43032 - 4.40206i) q^{57} +(-8.98574 - 6.52852i) q^{58} +(2.01805 - 1.46620i) q^{59} +(-3.02374 + 9.30610i) q^{60} +(1.04848 - 3.22689i) q^{61} +(-1.73004 + 1.25695i) q^{62} +(0.809017 + 0.587785i) q^{63} +(14.5262 + 44.7071i) q^{64} -9.84984 q^{65} +(-5.61190 + 7.39351i) q^{66} +6.16878 q^{67} +(-0.548215 - 1.68723i) q^{68} +(1.11777 + 0.812107i) q^{69} +(-3.79852 + 2.75979i) q^{70} +(2.34835 - 7.22749i) q^{71} +(3.31447 - 10.2009i) q^{72} +(10.3114 - 7.49164i) q^{73} +(-7.26848 - 5.28086i) q^{74} +(-0.675330 - 2.07845i) q^{75} -26.9963 q^{76} +(-3.17506 + 0.958630i) q^{77} +16.4313 q^{78} +(-1.90206 - 5.85393i) q^{79} +(24.9099 + 18.0981i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-7.18913 + 22.1259i) q^{82} +(-0.621946 + 1.91415i) q^{83} +(4.71859 - 3.42825i) q^{84} +(-0.412837 - 0.299944i) q^{85} +(-0.874082 - 2.69015i) q^{86} +3.96868 q^{87} +(20.3025 + 29.2111i) q^{88} +0.0843908 q^{89} +(-1.45091 - 4.46543i) q^{90} +(4.74985 + 3.45097i) q^{91} +(6.51938 - 4.73661i) q^{92} +(0.236120 - 0.726701i) q^{93} +(-2.23722 + 6.88545i) q^{94} +(-6.28224 + 4.56431i) q^{95} +(-24.1994 - 17.5819i) q^{96} +(0.320682 + 0.986957i) q^{97} +2.79866 q^{98} +(0.0694373 - 3.31590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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